LMFDB - Embedded newform 504.2.br.a.155.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(155,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1, 0]))

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

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

chi := DirichletCharacter("504.155");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.br (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$72$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			155.4
Character	$\chi$	$=$	504.155
Dual form			504.2.br.a.491.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40981 + 0.111460i) q^{2} +(-1.64186 + 0.551643i) q^{3} +(1.97515 - 0.314275i) q^{4} +(-1.45065 - 2.51260i) q^{5} +(2.25323 - 0.960715i) q^{6} +(-0.866025 - 0.500000i) q^{7} +(-2.74957 + 0.663220i) q^{8} +(2.39138 - 1.81144i) q^{9} +O(q^{10})$	\(q+(-1.40981 + 0.111460i) q^{2} +(-1.64186 + 0.551643i) q^{3} +(1.97515 - 0.314275i) q^{4} +(-1.45065 - 2.51260i) q^{5} +(2.25323 - 0.960715i) q^{6} +(-0.866025 - 0.500000i) q^{7} +(-2.74957 + 0.663220i) q^{8} +(2.39138 - 1.81144i) q^{9} +(2.32520 + 3.38061i) q^{10} +(-3.17215 - 1.83144i) q^{11} +(-3.06955 + 1.60557i) q^{12} +(2.39274 - 1.38145i) q^{13} +(1.27667 + 0.608380i) q^{14} +(3.76782 + 3.32509i) q^{15} +(3.80246 - 1.24148i) q^{16} +5.78249i q^{17} +(-3.16950 + 2.82033i) q^{18} -2.12986 q^{19} +(-3.65491 - 4.50687i) q^{20} +(1.69771 + 0.343191i) q^{21} +(4.67628 + 2.22843i) q^{22} +(0.628156 + 1.08800i) q^{23} +(4.14854 - 2.60569i) q^{24} +(-1.70877 + 2.95968i) q^{25} +(-3.21934 + 2.21428i) q^{26} +(-2.92704 + 4.29330i) q^{27} +(-1.86767 - 0.715406i) q^{28} +(3.77071 - 6.53107i) q^{29} +(-5.68253 - 4.26779i) q^{30} +(-4.40355 + 2.54239i) q^{31} +(-5.22239 + 2.17408i) q^{32} +(6.21852 + 1.25707i) q^{33} +(-0.644515 - 8.15224i) q^{34} +2.90130i q^{35} +(4.15405 - 4.32941i) q^{36} +7.96354i q^{37} +(3.00271 - 0.237394i) q^{38} +(-3.16646 + 3.58807i) q^{39} +(5.65507 + 5.94647i) q^{40} +(-8.61268 + 4.97253i) q^{41} +(-2.43171 - 0.294610i) q^{42} +(-4.03285 + 6.98510i) q^{43} +(-6.84107 - 2.62045i) q^{44} +(-8.02047 - 3.38082i) q^{45} +(-1.00685 - 1.46386i) q^{46} +(0.483756 - 0.837890i) q^{47} +(-5.55824 + 4.13594i) q^{48} +(0.500000 + 0.866025i) q^{49} +(2.07917 - 4.36306i) q^{50} +(-3.18987 - 9.49401i) q^{51} +(4.29187 - 3.48055i) q^{52} -4.62509 q^{53} +(3.64805 - 6.37901i) q^{54} +10.6271i q^{55} +(2.71281 + 0.800420i) q^{56} +(3.49693 - 1.17492i) q^{57} +(-4.58806 + 9.62788i) q^{58} +(-10.0677 + 5.81260i) q^{59} +(8.48701 + 5.38342i) q^{60} +(-2.64949 - 1.52968i) q^{61} +(5.92482 - 4.07512i) q^{62} +(-2.97671 + 0.373059i) q^{63} +(7.12028 - 3.64714i) q^{64} +(-6.94205 - 4.00800i) q^{65} +(-8.90707 - 1.07912i) q^{66} +(1.20248 + 2.08275i) q^{67} +(1.81729 + 11.4213i) q^{68} +(-1.63153 - 1.43982i) q^{69} +(-0.323379 - 4.09030i) q^{70} +15.4812 q^{71} +(-5.37389 + 6.56668i) q^{72} -3.53416 q^{73} +(-0.887615 - 11.2271i) q^{74} +(1.17287 - 5.80200i) q^{75} +(-4.20681 + 0.669363i) q^{76} +(1.83144 + 3.17215i) q^{77} +(4.06420 - 5.41145i) q^{78} +(-0.208098 - 0.120145i) q^{79} +(-8.63540 - 7.75311i) q^{80} +(2.43740 - 8.66366i) q^{81} +(11.5880 - 7.97032i) q^{82} +(6.05703 + 3.49703i) q^{83} +(3.46109 + 0.144307i) q^{84} +(14.5291 - 8.38837i) q^{85} +(4.90701 - 10.2972i) q^{86} +(-2.58815 + 12.8032i) q^{87} +(9.93671 + 2.93185i) q^{88} +13.9231i q^{89} +(11.6842 + 3.87237i) q^{90} -2.76290 q^{91} +(1.58263 + 1.95155i) q^{92} +(5.82751 - 6.60343i) q^{93} +(-0.588615 + 1.23519i) q^{94} +(3.08969 + 5.35149i) q^{95} +(7.37509 - 6.45043i) q^{96} +(4.72943 - 8.19162i) q^{97} +(-0.801434 - 1.16521i) q^{98} +(-10.9034 + 1.36647i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 6 q^{6}+O(q^{10}) $ 144 * q + 6 * q^6	$ 144 q + 6 q^{6} - 12 q^{12} + 34 q^{18} - 42 q^{20} - 30 q^{24} - 72 q^{25} + 24 q^{27} - 36 q^{30} - 30 q^{32} - 16 q^{33} + 12 q^{34} - 12 q^{36} + 12 q^{40} + 24 q^{41} - 20 q^{42} - 24 q^{46} - 24 q^{48} + 72 q^{49} - 78 q^{50} + 18 q^{52} + 10 q^{54} + 8 q^{57} - 18 q^{58} - 72 q^{59} + 88 q^{60} - 12 q^{64} + 2 q^{66} + 78 q^{68} + 42 q^{72} + 84 q^{74} - 112 q^{75} + 12 q^{76} + 112 q^{78} - 8 q^{81} - 36 q^{82} - 14 q^{84} + 30 q^{86} + 24 q^{88} + 104 q^{90} - 114 q^{92} - 42 q^{94} - 80 q^{96} - 64 q^{99}+O(q^{100}) $ 144 * q + 6 * q^6 - 12 * q^12 + 34 * q^18 - 42 * q^20 - 30 * q^24 - 72 * q^25 + 24 * q^27 - 36 * q^30 - 30 * q^32 - 16 * q^33 + 12 * q^34 - 12 * q^36 + 12 * q^40 + 24 * q^41 - 20 * q^42 - 24 * q^46 - 24 * q^48 + 72 * q^49 - 78 * q^50 + 18 * q^52 + 10 * q^54 + 8 * q^57 - 18 * q^58 - 72 * q^59 + 88 * q^60 - 12 * q^64 + 2 * q^66 + 78 * q^68 + 42 * q^72 + 84 * q^74 - 112 * q^75 + 12 * q^76 + 112 * q^78 - 8 * q^81 - 36 * q^82 - 14 * q^84 + 30 * q^86 + 24 * q^88 + 104 * q^90 - 114 * q^92 - 42 * q^94 - 80 * q^96 - 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−1.40981	+	0.111460i	−0.996889	+	0.0788140i
$2$	−1.40981	+	0.111460i	−0.996889	+	0.0788140i
$3$	−1.64186	+	0.551643i	−0.947926	+	0.318491i
$3$	−1.64186	+	0.551643i	−0.947926	+	0.318491i
$4$	1.97515	−	0.314275i	0.987577	−	0.157138i
$5$	−1.45065	−	2.51260i	−0.648751	−	1.12367i	−0.983422	−	0.181334i	$-0.941959\pi$
$5$	−1.45065	−	2.51260i	−0.648751	−	1.12367i	0.334671	−	0.942335i	$-0.391375\pi$
$6$	2.25323	−	0.960715i	0.919876	−	0.392210i
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i
$8$	−2.74957	+	0.663220i	−0.972120	+	0.234484i
$9$	2.39138	−	1.81144i	0.797127	−	0.603812i
$10$	2.32520	+	3.38061i	0.735293	+	1.06904i
$11$	−3.17215	−	1.83144i	−0.956440	−	0.552201i	−0.0613647	−	0.998115i	$-0.519545\pi$
$11$	−3.17215	−	1.83144i	−0.956440	−	0.552201i	−0.895076	+	0.445914i	$0.852879\pi$
$12$	−3.06955	+	1.60557i	−0.886103	+	0.463489i
$13$	2.39274	−	1.38145i	0.663626	−	0.383145i	−0.130031	−	0.991510i	$-0.541508\pi$
$13$	2.39274	−	1.38145i	0.663626	−	0.383145i	0.793657	+	0.608365i	$0.208174\pi$
$14$	1.27667	+	0.608380i	0.341203	+	0.162596i
$15$	3.76782	+	3.32509i	0.972846	+	0.858534i
$16$	3.80246	−	1.24148i	0.950615	−	0.310371i
$17$			5.78249i			1.40246i	0.712935	+	0.701230i	$0.247365\pi$
$17$			5.78249i			1.40246i	−0.712935	+	0.701230i	$0.752635\pi$
$18$	−3.16950	+	2.82033i	−0.747059	+	0.664758i
$19$	−2.12986			−0.488624			−0.244312	−	0.969697i	$-0.578562\pi$
$19$	−2.12986			−0.488624			−0.244312	+	0.969697i	$0.578562\pi$
$20$	−3.65491	−	4.50687i	−0.817262	−	1.00777i
$21$	1.69771	+	0.343191i	0.370471	+	0.0748905i
$22$	4.67628	+	2.22843i	0.996986	+	0.475102i
$23$	0.628156	+	1.08800i	0.130979	+	0.226863i	0.924054	−	0.382261i	$-0.124854\pi$
$23$	0.628156	+	1.08800i	0.130979	+	0.226863i	−0.793075	+	0.609124i	$0.791521\pi$
$24$	4.14854	−	2.60569i	0.846817	−	0.531885i
$25$	−1.70877	+	2.95968i	−0.341755	+	0.591936i
$26$	−3.21934	+	2.21428i	−0.631365	+	0.434256i
$27$	−2.92704	+	4.29330i	−0.563309	+	0.826247i
$28$	−1.86767	−	0.715406i	−0.352957	−	0.135199i
$29$	3.77071	−	6.53107i	0.700204	−	1.21279i	−0.268191	−	0.963366i	$-0.586426\pi$
$29$	3.77071	−	6.53107i	0.700204	−	1.21279i	0.968395	−	0.249423i	$-0.0802410\pi$
$30$	−5.68253	−	4.26779i	−1.03748	−	0.779189i
$31$	−4.40355	+	2.54239i	−0.790902	+	0.456627i	−0.840280	−	0.542153i	$-0.817609\pi$
$31$	−4.40355	+	2.54239i	−0.790902	+	0.456627i	0.0493782	+	0.998780i	$0.484276\pi$
$32$	−5.22239	+	2.17408i	−0.923197	+	0.384327i
$33$	6.21852	+	1.25707i	1.08251	+	0.218828i
$34$	−0.644515	−	8.15224i	−0.110533	−	1.39810i
$35$			2.90130i			0.490409i
$36$	4.15405	−	4.32941i	0.692342	−	0.721569i
$37$			7.96354i			1.30920i	0.755976	+	0.654599i	$0.227163\pi$
$37$			7.96354i			1.30920i	−0.755976	+	0.654599i	$0.772837\pi$
$38$	3.00271	−	0.237394i	0.487104	−	0.0385104i
$39$	−3.16646	+	3.58807i	−0.507040	+	0.574552i
$40$	5.65507	+	5.94647i	0.894146	+	0.940220i
$41$	−8.61268	+	4.97253i	−1.34508	+	0.776579i	−0.987547	−	0.157323i	$-0.949714\pi$
$41$	−8.61268	+	4.97253i	−1.34508	+	0.776579i	−0.357528	+	0.933902i	$0.616380\pi$
$42$	−2.43171	−	0.294610i	−0.375221	−	0.0454592i
$43$	−4.03285	+	6.98510i	−0.615004	+	1.06522i	0.375380	+	0.926871i	$0.377512\pi$
$43$	−4.03285	+	6.98510i	−0.615004	+	1.06522i	−0.990384	+	0.138347i	$0.955821\pi$
$44$	−6.84107	−	2.62045i	−1.03133	−	0.395048i
$45$	−8.02047	−	3.38082i	−1.19562	−	0.503984i
$46$	−1.00685	−	1.46386i	−0.148452	−	0.215834i
$47$	0.483756	−	0.837890i	0.0705631	−	0.122219i	−0.828585	−	0.559863i	$-0.810854\pi$
$47$	0.483756	−	0.837890i	0.0705631	−	0.122219i	0.899148	+	0.437644i	$0.144187\pi$
$48$	−5.55824	+	4.13594i	−0.802263	+	0.596971i
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$	2.07917	−	4.36306i	0.294039	−	0.617030i
$51$	−3.18987	−	9.49401i	−0.446671	−	1.32943i
$52$	4.29187	−	3.48055i	0.595175	−	0.482665i
$53$	−4.62509			−0.635305			−0.317652	−	0.948207i	$-0.602895\pi$
$53$	−4.62509			−0.635305			−0.317652	+	0.948207i	$0.602895\pi$
$54$	3.64805	−	6.37901i	0.496437	−	0.868073i
$55$			10.6271i			1.43296i
$56$	2.71281	+	0.800420i	0.362514	+	0.106961i
$57$	3.49693	−	1.17492i	0.463179	−	0.155622i
$58$	−4.58806	+	9.62788i	−0.602441	+	1.26420i
$59$	−10.0677	+	5.81260i	−1.31071	+	0.756737i	−0.982213	−	0.187770i	$-0.939874\pi$
$59$	−10.0677	+	5.81260i	−1.31071	+	0.756737i	−0.328493	+	0.944506i	$0.606541\pi$
$60$	8.48701	+	5.38342i	1.09567	+	0.694997i
$61$	−2.64949	−	1.52968i	−0.339232	−	0.195856i	0.320700	−	0.947181i	$-0.396082\pi$
$61$	−2.64949	−	1.52968i	−0.339232	−	0.195856i	−0.659932	+	0.751325i	$0.729415\pi$
$62$	5.92482	−	4.07512i	0.752453	−	0.517541i
$63$	−2.97671	+	0.373059i	−0.375031	+	0.0470010i
$64$	7.12028	−	3.64714i	0.890035	−	0.455893i
$65$	−6.94205	−	4.00800i	−0.861056	−	0.497131i
$66$	−8.90707	−	1.07912i	−1.09639	−	0.132831i
$67$	1.20248	+	2.08275i	0.146906	+	0.254448i	0.930082	−	0.367351i	$-0.119735\pi$
$67$	1.20248	+	2.08275i	0.146906	+	0.254448i	−0.783177	+	0.621799i	$0.786402\pi$
$68$	1.81729	+	11.4213i	0.220379	+	1.38504i
$69$	−1.63153	−	1.43982i	−0.196413	−	0.173334i
$70$	−0.323379	−	4.09030i	−0.0386511	−	0.488884i
$71$	15.4812			1.83728			0.918638	−	0.395101i	$-0.129290\pi$
$71$	15.4812			1.83728			0.918638	+	0.395101i	$0.129290\pi$
$72$	−5.37389	+	6.56668i	−0.633319	+	0.773891i
$73$	−3.53416			−0.413642			−0.206821	−	0.978379i	$-0.566312\pi$
$73$	−3.53416			−0.413642			−0.206821	+	0.978379i	$0.566312\pi$
$74$	−0.887615	−	11.2271i	−0.103183	−	1.30513i
$75$	1.17287	−	5.80200i	0.135432	−	0.669957i
$76$	−4.20681	+	0.669363i	−0.482554	+	0.0767813i
$77$	1.83144	+	3.17215i	0.208712	+	0.361500i
$78$	4.06420	−	5.41145i	0.460180	−	0.612726i
$79$	−0.208098	−	0.120145i	−0.0234128	−	0.0135174i	0.488248	−	0.872705i	$-0.337636\pi$
$79$	−0.208098	−	0.120145i	−0.0234128	−	0.0135174i	−0.511661	+	0.859188i	$0.670970\pi$
$80$	−8.63540	−	7.75311i	−0.965467	−	0.866824i
$81$	2.43740	−	8.66366i	0.270823	−	0.962629i
$82$	11.5880	−	7.97032i	1.27969	−	0.880175i
$83$	6.05703	+	3.49703i	0.664845	+	0.383849i	0.794121	−	0.607760i	$-0.207932\pi$
$83$	6.05703	+	3.49703i	0.664845	+	0.383849i	−0.129275	+	0.991609i	$0.541265\pi$
$84$	3.46109	+	0.144307i	0.377636	+	0.0157452i
$85$	14.5291	−	8.38837i	1.57590	−	0.909846i
$86$	4.90701	−	10.2972i	0.529137	−	1.11038i
$87$	−2.58815	+	12.8032i	−0.277479	+	1.37264i
$88$	9.93671	+	2.93185i	1.05926	+	0.312536i
$89$			13.9231i			1.47585i	0.674885	+	0.737923i	$0.264193\pi$
$89$			13.9231i			1.47585i	−0.674885	+	0.737923i	$0.735807\pi$
$90$	11.6842	+	3.87237i	1.23162	+	0.408184i
$91$	−2.76290			−0.289630
$92$	1.58263	+	1.95155i	0.165001	+	0.203463i
$93$	5.82751	−	6.60343i	0.604284	−	0.684744i
$94$	−0.588615	+	1.23519i	−0.0607110	+	0.127400i
$95$	3.08969	+	5.35149i	0.316995	+	0.549052i
$96$	7.37509	−	6.45043i	0.752717	−	0.658344i
$97$	4.72943	−	8.19162i	0.480201	−	0.831733i	−0.519541	−	0.854446i	$-0.673897\pi$
$97$	4.72943	−	8.19162i	0.480201	−	0.831733i	0.999742	+	0.0227127i	$0.00723029\pi$
$98$	−0.801434	−	1.16521i	−0.0809571	−	0.117703i
$99$	−10.9034	+	1.36647i	−1.09583	+	0.137336i
$100$	−2.44493	+	6.38285i	−0.244493	+	0.638285i
$101$	−2.06865	+	3.58301i	−0.205839	+	0.356523i	−0.950400	−	0.311032i	$-0.899326\pi$
$101$	−2.06865	+	3.58301i	−0.205839	+	0.356523i	0.744561	+	0.667554i	$0.232659\pi$
$102$	5.55532	+	13.0293i	0.550059	+	1.29009i
$103$	−9.10517	+	5.25687i	−0.897159	+	0.517975i	−0.876277	−	0.481807i	$-0.839981\pi$
$103$	−9.10517	+	5.25687i	−0.897159	+	0.517975i	−0.0208814	+	0.999782i	$0.506647\pi$
$104$	−5.66280	+	5.38530i	−0.555283	+	0.528072i
$105$	−1.60048	−	4.76352i	−0.156191	−	0.464872i
$106$	6.52052	−	0.515512i	0.633329	−	0.0500709i
$107$			7.10059i			0.686440i	0.939255	+	0.343220i	$0.111518\pi$
$107$			7.10059i			0.686440i	−0.939255	+	0.343220i	$0.888482\pi$
$108$	−4.43207	+	9.39983i	−0.426476	+	0.904499i
$109$		−	13.0792i		−	1.25276i	−0.779518	−	0.626380i	$-0.784536\pi$
$109$		−	13.0792i		−	1.25276i	0.779518	−	0.626380i	$-0.215464\pi$
$110$	−1.18450	−	14.9823i	−0.112938	−	1.42851i
$111$	−4.39303	−	13.0750i	−0.416968	−	1.24102i
$112$	−3.91377	−	0.826074i	−0.369817	−	0.0780567i
$113$	15.4322	−	8.90976i	1.45174	−	0.838160i	0.453156	−	0.891431i	$-0.350298\pi$
$113$	15.4322	−	8.90976i	1.45174	−	0.838160i	0.998580	+	0.0532712i	$0.0169648\pi$
$114$	−4.79906	+	2.04619i	−0.449473	+	0.191643i
$115$	1.82247	−	3.15661i	0.169946	−	0.294355i
$116$	5.39518	−	14.0849i	0.500930	−	1.30775i
$117$	3.21954	−	7.63786i	0.297647	−	0.706120i
$118$	13.5458	−	9.31684i	1.24699	−	0.857685i
$119$	2.89124	−	5.00778i	0.265040	−	0.459063i
$120$	−12.5651	−	6.64367i	−1.14704	−	0.606481i
$121$	1.20837	+	2.09296i	0.109852	+	0.190269i
$122$	3.90578	+	1.86126i	0.353613	+	0.168510i
$123$	11.3977	−	12.9153i	1.02770	−	1.16453i
$124$	−7.89868	+	6.40554i	−0.709323	+	0.575235i
$125$	−4.59118			−0.410647
$126$	4.15503	−	0.857727i	0.370160	−	0.0764124i
$127$			4.38653i			0.389242i	0.980879	+	0.194621i	$0.0623477\pi$
$127$			4.38653i			0.389242i	−0.980879	+	0.194621i	$0.937652\pi$
$128$	−9.63176	+	5.93542i	−0.851335	+	0.524622i
$129$	2.76808	−	13.6932i	0.243716	−	1.20562i
$130$	10.2337	+	4.87677i	0.897558	+	0.427721i
$131$	18.0559	−	10.4246i	1.57755	−	0.910800i	0.582352	−	0.812937i	$-0.302133\pi$
$131$	18.0559	−	10.4246i	1.57755	−	0.910800i	0.995200	−	0.0978634i	$-0.0312008\pi$
$132$	12.6776	+	0.528580i	1.10344	+	0.0460070i
$133$	1.84452	+	1.06493i	0.159940	+	0.0923413i
$134$	−1.92741	−	2.80226i	−0.166503	−	0.242079i
$135$	15.0335	+	1.12639i	1.29387	+	0.0969445i
$136$	−3.83506	−	15.8994i	−0.328854	−	1.36336i
$137$	−7.46985	−	4.31272i	−0.638193	−	0.368461i	0.145725	−	0.989325i	$-0.453448\pi$
$137$	−7.46985	−	4.31272i	−0.638193	−	0.368461i	−0.783918	+	0.620864i	$0.786782\pi$
$138$	2.46063	+	1.84803i	0.209463	+	0.157314i
$139$	−5.36402	−	9.29075i	−0.454970	−	0.788032i	0.543716	−	0.839269i	$-0.317017\pi$
$139$	−5.36402	−	9.29075i	−0.454970	−	0.788032i	−0.998686	+	0.0512376i	$0.983683\pi$
$140$	0.911807	+	5.73051i	0.0770618	+	0.484317i
$141$	−0.332042	+	1.64256i	−0.0279630	+	0.138328i
$142$	−21.8256	+	1.72553i	−1.83156	+	0.144803i
$143$	−10.1202			−0.846292
$144$	6.84427	−	9.85678i	0.570356	−	0.821398i
$145$	−21.8799			−1.81703
$146$	4.98251	−	0.393917i	0.412355	−	0.0326008i
$147$	−1.29866	−	1.14607i	−0.107112	−	0.0945261i
$148$	2.50275	+	15.7292i	0.205724	+	1.29293i
$149$	3.60567	+	6.24520i	0.295388	+	0.511626i	0.975075	−	0.221876i	$-0.0712179\pi$
$149$	3.60567	+	6.24520i	0.295388	+	0.511626i	−0.679687	+	0.733502i	$0.737885\pi$
$150$	−1.00684	+	8.31047i	−0.0822083	+	0.678547i
$151$	−2.96846	−	1.71384i	−0.241570	−	0.139470i	0.374328	−	0.927296i	$-0.377873\pi$
$151$	−2.96846	−	1.71384i	−0.241570	−	0.139470i	−0.615898	+	0.787826i	$0.711207\pi$
$152$	5.85621	−	1.41257i	0.475001	−	0.114574i
$153$	10.4746	+	13.8281i	0.846822	+	1.11794i
$154$	−2.93556	−	4.26802i	−0.236554	−	0.343926i
$155$	12.7760	+	7.37625i	1.02620	+	0.592474i
$156$	−5.12661	+	8.08214i	−0.410457	+	0.647089i
$157$	−4.43077	+	2.55810i	−0.353614	+	0.204159i	−0.666276	−	0.745705i	$-0.732113\pi$
$157$	−4.43077	+	2.55810i	−0.353614	+	0.204159i	0.312662	+	0.949864i	$0.398779\pi$
$158$	0.306770	+	0.146188i	0.0244053	+	0.0116301i
$159$	7.59373	−	2.55140i	0.602222	−	0.202339i
$160$	13.0385	+	9.96794i	1.03078	+	0.788035i
$161$		−	1.25631i		−	0.0990112i
$162$	−2.47064	+	12.4858i	−0.194112	+	0.980979i
$163$	−7.70243			−0.603301			−0.301651	−	0.953419i	$-0.597538\pi$
$163$	−7.70243			−0.603301			−0.301651	+	0.953419i	$0.597538\pi$
$164$	−15.4486	+	12.5283i	−1.20633	+	0.978294i
$165$	−5.86238	−	17.4482i	−0.456386	−	1.35834i
$166$	−8.92906	−	4.25504i	−0.693030	−	0.330255i
$167$	−6.37034	−	11.0338i	−0.492952	−	0.853818i	0.507015	−	0.861937i	$-0.330749\pi$
$167$	−6.37034	−	11.0338i	−0.492952	−	0.853818i	−0.999967	+	0.00811941i	$0.997415\pi$
$168$	−4.89559	+	0.182327i	−0.377703	+	0.0140668i
$169$	−2.68320	+	4.64745i	−0.206400	+	0.357496i
$170$	−19.5483	+	13.4455i	−1.49929	+	1.03122i
$171$	−5.09331	+	3.85811i	−0.389495	+	0.295037i
$172$	−5.77025	+	15.0641i	−0.439978	+	1.14862i
$173$	−5.78675	+	10.0229i	−0.439958	+	0.762030i	−0.997686	−	0.0679942i	$-0.978340\pi$
$173$	−5.78675	+	10.0229i	−0.439958	+	0.762030i	0.557728	+	0.830024i	$0.311673\pi$
$174$	2.22178	−	18.3386i	0.168432	−	1.39024i
$175$	2.95968	−	1.70877i	0.223731	−	0.129171i
$176$	−14.3357	−	3.02582i	−1.08059	−	0.228079i
$177$	13.3233	−	15.0972i	1.00144	−	1.13478i
$178$	−1.55187	−	19.6290i	−0.116317	−	1.47126i
$179$			19.2163i			1.43630i	0.695890	+	0.718148i	$0.255010\pi$
$179$			19.2163i			1.43630i	−0.695890	+	0.718148i	$0.744990\pi$
$180$	−16.9042	−	4.15701i	−1.25996	−	0.309845i
$181$			16.9296i			1.25837i	0.777256	+	0.629184i	$0.216611\pi$
$181$			16.9296i			1.25837i	−0.777256	+	0.629184i	$0.783389\pi$
$182$	3.89517	−	0.307952i	0.288729	−	0.0228269i
$183$	5.19391	+	1.04995i	0.383945	+	0.0776143i
$184$	−2.44874	−	2.57492i	−0.180524	−	0.189826i
$185$	20.0092	−	11.5523i	1.47111	−	0.849343i
$186$	−7.47969	+	9.95914i	−0.548437	+	0.730240i
$187$	10.5903	−	18.3429i	0.774440	−	1.34137i
$188$	0.692164	−	1.80699i	0.0504813	−	0.131789i
$189$	4.68154	−	2.25459i	0.340532	−	0.163997i
$190$	−4.95236	−	7.20024i	−0.359282	−	0.522360i
$191$	−5.48409	+	9.49873i	−0.396815	+	0.687304i	−0.993331	−	0.115297i	$-0.963218\pi$
$191$	−5.48409	+	9.49873i	−0.396815	+	0.687304i	0.596516	+	0.802601i	$0.296551\pi$
$192$	−9.67855	+	9.91593i	−0.698489	+	0.715621i
$193$	12.4131	+	21.5001i	0.893513	+	1.54761i	0.835634	+	0.549286i	$0.185100\pi$
$193$	12.4131	+	21.5001i	0.893513	+	1.54761i	0.0578785	+	0.998324i	$0.481566\pi$
$194$	−5.75459	+	12.0758i	−0.413155	+	0.866992i
$195$	13.6088	+	2.75102i	0.974548	+	0.197005i
$196$	1.25975	+	1.55340i	0.0899819	+	0.110957i
$197$	−25.7759			−1.83646			−0.918228	−	0.396051i	$-0.870380\pi$
$197$	−25.7759			−1.83646			−0.918228	+	0.396051i	$0.870380\pi$
$198$	15.2194	−	3.14176i	1.08160	−	0.223275i
$199$		−	15.8428i		−	1.12306i	−0.827455	−	0.561532i	$-0.810212\pi$
$199$		−	15.8428i		−	1.12306i	0.827455	−	0.561532i	$-0.189788\pi$
$200$	2.73547	−	9.27114i	0.193427	−	0.655569i
$201$	−3.12323	−	2.75624i	−0.220295	−	0.194410i
$202$	2.51705	−	5.28195i	0.177099	−	0.371637i
$203$	−6.53107	+	3.77071i	−0.458391	+	0.264652i
$204$	−9.28421	−	17.7496i	−0.650025	−	1.24272i
$205$	24.9880	+	14.4268i	1.74524	+	1.00761i
$206$	12.2507	−	8.42607i	0.853544	−	0.587072i
$207$	3.47300	+	1.46395i	0.241390	+	0.101752i
$208$	7.38325	−	8.22345i	0.511936	−	0.570194i
$209$	6.75625	+	3.90072i	0.467340	+	0.269819i
$210$	2.78732	+	6.53729i	0.192344	+	0.451116i
$211$	−7.69139	−	13.3219i	−0.529497	−	0.917116i	−0.999408	−	0.0344018i	$-0.989047\pi$
$211$	−7.69139	−	13.3219i	−0.529497	−	0.917116i	0.469911	−	0.882714i	$-0.344286\pi$
$212$	−9.13526	+	1.45355i	−0.627412	+	0.0998304i
$213$	−25.4178	+	8.54007i	−1.74160	+	0.585156i
$214$	−0.791431	−	10.0105i	−0.0541011	−	0.684305i
$215$	23.4010			1.59594
$216$	5.20069	−	13.7460i	0.353862	−	0.935298i
$217$	5.08479			0.345178
$218$	1.45780	+	18.4392i	0.0987350	+	1.24886i
$219$	5.80258	−	1.94959i	0.392102	−	0.131741i
$220$	3.33985	+	20.9902i	0.225173	+	1.41516i
$221$	7.98821	+	13.8360i	0.537345	+	0.930709i
$222$	7.65069	+	17.9437i	0.513481	+	1.20430i
$223$	−15.3256	−	8.84821i	−1.02628	−	0.592520i	−0.110360	−	0.993892i	$-0.535200\pi$
$223$	−15.3256	−	8.84821i	−1.02628	−	0.592520i	−0.915915	+	0.401372i	$0.868534\pi$
$224$	5.60976	+	0.728383i	0.374818	+	0.0486671i
$225$	1.27494	+	10.1731i	0.0849963	+	0.678204i
$226$	−20.7634	+	14.2812i	−1.38116	+	0.949970i
$227$	−4.18974	−	2.41895i	−0.278083	−	0.160551i	0.354472	−	0.935067i	$-0.384661\pi$
$227$	−4.18974	−	2.41895i	−0.278083	−	0.160551i	−0.632555	+	0.774515i	$0.717994\pi$
$228$	6.53772	−	3.41965i	0.432971	−	0.226472i
$229$	−8.27205	+	4.77587i	−0.546632	+	0.315598i	−0.747763	−	0.663966i	$-0.768872\pi$
$229$	−8.27205	+	4.77587i	−0.546632	+	0.315598i	0.201130	+	0.979565i	$0.435539\pi$
$230$	−2.21751	+	4.65336i	−0.146218	+	0.306834i
$231$	−4.75686	−	4.19792i	−0.312979	−	0.276203i
$232$	−6.03631	+	20.4584i	−0.396303	+	1.34316i
$233$			2.16385i			0.141759i	0.997485	+	0.0708794i	$0.0225806\pi$
$233$			2.16385i			0.141759i	−0.997485	+	0.0708794i	$0.977419\pi$
$234$	−3.68765	+	11.1268i	−0.241069	+	0.727382i
$235$	−2.80704			−0.183111
$236$	−18.0585	+	14.6448i	−1.17551	+	0.953297i
$237$	0.407943	+	0.0824656i	0.0264988	+	0.00535672i
$238$	−3.51795	+	7.38230i	−0.228035	+	0.478524i
$239$	−10.8361	−	18.7687i	−0.700928	−	1.21404i	−0.968141	−	0.250406i	$-0.919436\pi$
$239$	−10.8361	−	18.7687i	−0.700928	−	1.21404i	0.267213	−	0.963638i	$-0.413897\pi$
$240$	18.4550	+	7.96583i	1.19127	+	0.514192i
$241$	2.40984	−	4.17396i	0.155231	−	0.268868i	−0.777912	−	0.628373i	$-0.783721\pi$
$241$	2.40984	−	4.17396i	0.155231	−	0.268868i	0.933143	+	0.359505i	$0.117054\pi$
$242$	−1.93686	−	2.81600i	−0.124506	−	0.181020i
$243$	0.777380	+	15.5691i	0.0498689	+	0.998756i
$244$	−5.71388	−	2.18869i	−0.365794	−	0.140116i
$245$	1.45065	−	2.51260i	0.0926786	−	0.160524i
$246$	−14.6291	+	19.4786i	−0.932719	+	1.24191i
$247$	−5.09620	+	2.94229i	−0.324264	+	0.187214i
$248$	10.4217	−	9.91102i	0.661780	−	0.629350i
$249$	−11.8739	−	2.40030i	−0.752476	−	0.152113i
$250$	6.47271	−	0.511732i	0.409370	−	0.0323648i
$251$			13.0394i			0.823039i	0.911401	+	0.411520i	$0.135002\pi$
$251$			13.0394i			0.823039i	−0.911401	+	0.411520i	$0.864998\pi$
$252$	−5.76222	+	1.67236i	−0.362986	+	0.105349i
$253$		−	4.60173i		−	0.289308i
$254$	−0.488922	−	6.18420i	−0.0306777	−	0.388031i
$255$	−19.2273	+	21.7874i	−1.20406	+	1.36438i
$256$	12.9174	−	9.44139i	0.807340	−	0.590087i
$257$	−1.56344	+	0.902650i	−0.0975245	+	0.0563058i	−0.547969	−	0.836499i	$-0.684599\pi$
$257$	−1.56344	+	0.902650i	−0.0975245	+	0.0563058i	0.450445	+	0.892804i	$0.351266\pi$
$258$	−2.37623	+	19.6134i	−0.147938	+	1.22108i
$259$	3.98177	−	6.89663i	0.247415	−	0.428536i
$260$	−14.9712	−	5.73469i	−0.928476	−	0.355650i
$261$	−2.81339	−	22.4487i	−0.174145	−	1.38954i
$262$	−24.2936	+	16.7092i	−1.50086	+	1.03230i
$263$	5.64050	−	9.76963i	0.347808	−	0.602421i	−0.638052	−	0.769993i	$-0.720259\pi$
$263$	5.64050	−	9.76963i	0.347808	−	0.602421i	0.985860	+	0.167572i	$0.0535928\pi$
$264$	−17.9320	+	0.667843i	−1.10364	+	0.0411029i
$265$	6.70939	+	11.6210i	0.412154	+	0.713872i
$266$	−2.71912	−	1.29577i	−0.166720	−	0.0794485i
$267$	−7.68058	−	22.8597i	−0.470044	−	1.39899i
$268$	3.02963	+	3.73584i	0.185064	+	0.228203i
$269$	28.0152			1.70812			0.854058	−	0.520179i	$-0.174135\pi$
$269$	28.0152			1.70812			0.854058	+	0.520179i	$0.174135\pi$
$270$	−21.3199	+	0.0876224i	−1.29749	+	0.00533253i
$271$		−	23.2915i		−	1.41486i	−0.706785	−	0.707429i	$-0.749855\pi$
$271$		−	23.2915i		−	1.41486i	0.706785	−	0.707429i	$-0.250145\pi$
$272$	7.17887	+	21.9877i	0.435283	+	1.33320i
$273$	4.53628	−	1.52413i	0.274548	−	0.0922446i
$274$	11.0118	+	5.24755i	0.665247	+	0.317016i
$275$	10.8410	−	6.25904i	0.653736	−	0.377434i
$276$	−3.67501	−	2.33111i	−0.221210	−	0.140316i
$277$	−23.7207	−	13.6952i	−1.42524	−	0.822863i	−0.428500	−	0.903542i	$-0.640958\pi$
$277$	−23.7207	−	13.6952i	−1.42524	−	0.822863i	−0.996740	+	0.0806788i	$0.974291\pi$
$278$	8.59782	+	12.5004i	0.515663	+	0.749722i
$279$	−5.92519	+	14.0566i	−0.354732	+	0.841546i
$280$	−1.92420	−	7.97733i	−0.114993	−	0.476737i
$281$	−9.23996	−	5.33469i	−0.551210	−	0.318241i	0.198400	−	0.980121i	$-0.436425\pi$
$281$	−9.23996	−	5.33469i	−0.551210	−	0.318241i	−0.749610	+	0.661880i	$0.769759\pi$
$282$	0.285038	−	2.35271i	0.0169738	−	0.140102i
$283$	7.69690	+	13.3314i	0.457533	+	0.792471i	0.998830	−	0.0483606i	$-0.0153997\pi$
$283$	7.69690	+	13.3314i	0.457533	+	0.792471i	−0.541296	+	0.840832i	$0.682066\pi$
$284$	30.5777	−	4.86535i	1.81445	−	0.288705i
$285$	−8.02493	−	7.08198i	−0.475356	−	0.419500i
$286$	14.2676	−	1.12799i	0.843659	−	0.0666996i
$287$	9.94507			0.587039
$288$	−8.55051	+	14.6591i	−0.503844	+	0.863795i
$289$	−16.4372			−0.966893
$290$	30.8467	−	2.43874i	1.81138	−	0.143207i
$291$	−3.24620	+	16.0584i	−0.190296	+	0.941361i
$292$	−6.98051	+	1.11070i	−0.408503	+	0.0649988i
$293$	−8.98797	−	15.5676i	−0.525083	−	0.909470i	−0.999573	−	0.0292093i	$-0.990701\pi$
$293$	−8.98797	−	15.5676i	−0.525083	−	0.909470i	0.474491	−	0.880261i	$-0.342632\pi$
$294$	1.95862	+	1.47099i	0.114229	+	0.0857901i
$295$	29.2095	+	16.8641i	1.70064	+	0.981866i
$296$	−5.28158	−	21.8963i	−0.306986	−	1.27270i
$297$	17.1480	−	8.25831i	0.995025	−	0.479196i
$298$	−5.77941	−	8.40268i	−0.334792	−	0.486754i
$299$	3.00602	+	1.73553i	0.173843	+	0.100368i
$300$	0.493176	−	11.8284i	0.0284735	−	0.682916i
$301$	6.98510	−	4.03285i	0.402615	−	0.232450i
$302$	4.37600	+	2.08534i	0.251811	+	0.119998i
$303$	1.41989	−	7.02394i	0.0815704	−	0.403515i
$304$	−8.09872	+	2.64419i	−0.464494	+	0.151655i
$305$			8.87613i			0.508246i
$306$	−16.3085	−	18.3276i	−0.932297	−	1.04772i
$307$	−22.4176			−1.27944			−0.639721	−	0.768607i	$-0.720950\pi$
$307$	−22.4176			−1.27944			−0.639721	+	0.768607i	$0.720950\pi$
$308$	4.61431	+	5.68991i	0.262925	+	0.324213i
$309$	12.0495	−	13.6538i	0.685470	−	0.776739i
$310$	−18.8340	−	8.97512i	−1.06970	−	0.509753i
$311$	−12.1544	−	21.0520i	−0.689211	−	1.19375i	−0.972094	−	0.234594i	$-0.924624\pi$
$311$	−12.1544	−	21.0520i	−0.689211	−	1.19375i	0.282883	−	0.959154i	$-0.408709\pi$
$312$	6.32674	−	11.9657i	0.358181	−	0.677426i
$313$	−10.6852	+	18.5073i	−0.603962	+	1.04609i	0.388253	+	0.921553i	$0.373079\pi$
$313$	−10.6852	+	18.5073i	−0.603962	+	1.04609i	−0.992215	+	0.124539i	$0.960255\pi$
$314$	5.96143	−	4.10030i	0.336423	−	0.231394i
$315$	5.25552	+	6.93811i	0.296115	+	0.390918i
$316$	−0.448783	−	0.171905i	−0.0252460	−	0.00967043i
$317$	2.73827	−	4.74282i	0.153796	−	0.266383i	−0.778824	−	0.627243i	$-0.784183\pi$
$317$	2.73827	−	4.74282i	0.153796	−	0.266383i	0.932620	+	0.360860i	$0.117517\pi$
$318$	−10.4214	+	4.44339i	−0.584402	+	0.249173i
$319$	−23.9226	+	13.8117i	−1.33941	+	0.773307i
$320$	−19.4928	−	12.5997i	−1.08968	−	0.704344i
$321$	−3.91699	−	11.6581i	−0.218625	−	0.650694i
$322$	0.140028	+	1.77117i	0.00780347	+	0.0987032i
$323$		−	12.3159i		−	0.685275i
$324$	2.09147	−	17.8781i	0.116193	−	0.993227i
$325$			9.44232i			0.523766i
$326$	10.8590	−	0.858512i	0.601424	−	0.0475486i
$327$	7.21504	+	21.4741i	0.398993	+	1.18752i
$328$	20.3833	−	19.3844i	1.12548	−	1.07033i
$329$	−0.837890	+	0.483756i	−0.0461944	+	0.0266703i
$330$	10.2096	+	23.9453i	0.562023	+	1.31815i
$331$	0.812343	−	1.40702i	0.0446504	−	0.0773368i	−0.842836	−	0.538170i	$-0.819116\pi$
$331$	0.812343	−	1.40702i	0.0446504	−	0.0773368i	0.887487	+	0.460833i	$0.152449\pi$
$332$	13.0626	+	5.00359i	0.716903	+	0.274608i
$333$	14.4254	+	19.0439i	0.790509	+	1.04360i
$334$	10.2108	+	14.8455i	0.558711	+	0.812310i
$335$	3.48874	−	6.04268i	0.190610	−	0.330147i
$336$	6.88154	−	0.802708i	0.375419	−	0.0437913i
$337$	−8.42556	−	14.5935i	−0.458970	−	0.794959i	0.539937	−	0.841705i	$-0.318448\pi$
$337$	−8.42556	−	14.5935i	−0.458970	−	0.794959i	−0.998907	+	0.0467466i	$0.985115\pi$
$338$	3.26482	−	6.85110i	0.177583	−	0.372651i
$339$	−20.4224	+	23.1416i	−1.10919	+	1.25688i
$340$	26.0609	−	21.1345i	1.41335	−	1.14618i
$341$	18.6250			1.00860
$342$	6.75060	−	6.00692i	0.365031	−	0.324817i
$343$		−	1.00000i		−	0.0539949i
$344$	6.45595	−	21.8807i	0.348081	−	1.17973i
$345$	−1.25091	+	6.18805i	−0.0673468	+	0.333153i
$346$	7.04108	−	14.7755i	0.378531	−	0.794334i
$347$	6.19879	−	3.57887i	0.332768	−	0.192124i	−0.324301	−	0.945954i	$-0.605129\pi$
$347$	6.19879	−	3.57887i	0.332768	−	0.192124i	0.657070	+	0.753830i	$0.271796\pi$
$348$	−1.08828	+	26.1016i	−0.0583380	+	1.39919i
$349$	−4.32743	−	2.49844i	−0.231642	−	0.133739i	0.379687	−	0.925115i	$-0.376032\pi$
$349$	−4.32743	−	2.49844i	−0.231642	−	0.133739i	−0.611329	+	0.791376i	$0.709365\pi$
$350$	−3.98214	+	2.73894i	−0.212854	+	0.146402i
$351$	−1.07266	+	14.3163i	−0.0572543	+	0.764147i
$352$	20.5479	+	2.66798i	1.09521	+	0.142204i
$353$	−13.2844	−	7.66973i	−0.707055	−	0.408219i	0.102914	−	0.994690i	$-0.467183\pi$
$353$	−13.2844	−	7.66973i	−0.707055	−	0.408219i	−0.809970	+	0.586472i	$0.800517\pi$
$354$	−17.1006	+	22.7693i	−0.908887	+	1.21018i
$355$	−22.4577	−	38.8980i	−1.19193	−	2.06449i
$356$	4.37569	+	27.5003i	0.231911	+	1.45751i
$357$	−1.98450	+	9.81699i	−0.105031	+	0.519570i
$358$	−2.14185	−	27.0915i	−0.113200	−	1.43183i
$359$	−8.20721			−0.433160			−0.216580	−	0.976265i	$-0.569490\pi$
$359$	−8.20721			−0.433160			−0.216580	+	0.976265i	$0.569490\pi$
$360$	24.2951	+	3.97648i	1.28046	+	0.209579i
$361$	−14.4637			−0.761247
$362$	−1.88697	−	23.8676i	−0.0991770	−	1.25445i
$363$	−3.13854	−	2.76975i	−0.164731	−	0.145374i
$364$	−5.45714	+	0.868310i	−0.286032	+	0.0455118i
$365$	5.12683	+	8.87993i	0.268350	+	0.464797i
$366$	−7.43948	−	0.901318i	−0.388868	−	0.0471126i
$367$	−13.4190	−	7.74745i	−0.700465	−	0.404413i	0.107056	−	0.994253i	$-0.465858\pi$
$367$	−13.4190	−	7.74745i	−0.700465	−	0.404413i	−0.807520	+	0.589840i	$0.799191\pi$
$368$	3.73927	+	3.35722i	0.194923	+	0.175007i
$369$	−11.5888	+	27.4925i	−0.603288	+	1.43120i
$370$	−26.9216	+	18.5168i	−1.39959	+	0.962645i
$371$	4.00545	+	2.31254i	0.207952	+	0.120061i
$372$	9.43493	−	14.8742i	0.489178	−	0.771193i
$373$	−2.14252	+	1.23698i	−0.110935	+	0.0640486i	−0.554441	−	0.832223i	$-0.687068\pi$
$373$	−2.14252	+	1.23698i	−0.110935	+	0.0640486i	0.443506	+	0.896272i	$0.353735\pi$
$374$	−12.8859	+	27.0405i	−0.666312	+	1.39823i
$375$	7.53805	−	2.53269i	0.389263	−	0.130788i
$376$	−0.774416	+	2.62468i	−0.0399375	+	0.135357i
$377$		−	20.8362i		−	1.07312i
$378$	−6.34881	+	3.70036i	−0.326547	+	0.190326i
$379$	26.6736			1.37013			0.685066	−	0.728481i	$-0.259774\pi$
$379$	26.6736			1.37013			0.685066	+	0.728481i	$0.259774\pi$
$380$	7.78445	+	9.59901i	0.399334	+	0.492419i
$381$	−2.41980	−	7.20206i	−0.123970	−	0.368973i
$382$	6.67283	−	14.0027i	0.341412	−	0.716441i
$383$	15.1577	+	26.2539i	0.774522	+	1.34151i	0.935063	+	0.354482i	$0.115343\pi$
$383$	15.1577	+	26.2539i	0.774522	+	1.34151i	−0.160541	+	0.987029i	$0.551324\pi$
$384$	12.5397	−	15.0584i	0.639915	−	0.768445i
$385$	5.31357	−	9.20337i	0.270805	−	0.469047i
$386$	−19.8965	−	28.9276i	−1.01271	−	1.47237i
$387$	3.00898	+	24.0093i	0.152955	+	1.22046i
$388$	6.76693	−	17.6661i	0.343539	−	0.896858i
$389$	−19.1181	+	33.1136i	−0.969327	+	1.67892i	−0.271818	+	0.962349i	$0.587625\pi$
$389$	−19.1181	+	33.1136i	−0.969327	+	1.67892i	−0.697509	+	0.716576i	$0.745708\pi$
$390$	−19.4926	−	2.36159i	−0.987044	−	0.119584i
$391$	−6.29133	+	3.63230i	−0.318166	+	0.183693i
$392$	−1.94915	−	2.04959i	−0.0984470	−	0.103520i
$393$	−23.8946	+	27.0761i	−1.20532	+	1.36581i
$394$	36.3392	−	2.87298i	1.83074	−	0.144739i
$395$			0.697155i			0.0350777i
$396$	−21.1064	+	6.12565i	−1.06064	+	0.307826i
$397$		−	0.203380i		−	0.0102074i	−0.999987	−	0.00510368i	$-0.998375\pi$
$397$		−	0.203380i		−	0.0102074i	0.999987	−	0.00510368i	$-0.00162456\pi$
$398$	1.76583	+	22.3354i	0.0885132	+	1.11957i
$399$	−3.61589	−	0.730950i	−0.181021	−	0.0365933i
$400$	−2.82315	+	13.3755i	−0.141157	+	0.668774i
$401$	−2.51948	+	1.45462i	−0.125817	+	0.0726404i	−0.561588	−	0.827417i	$-0.689809\pi$
$401$	−2.51948	+	1.45462i	−0.125817	+	0.0726404i	0.435771	+	0.900058i	$0.356476\pi$
$402$	4.71038	+	3.53767i	0.234932	+	0.176443i
$403$	−7.02437	+	12.1666i	−0.349909	+	0.606060i
$404$	−2.95985	+	7.72712i	−0.147258	+	0.384439i
$405$	−25.3041	+	6.44372i	−1.25737	+	0.320191i
$406$	8.78731	−	6.04396i	0.436107	−	0.299957i
$407$	14.5848	−	25.2616i	0.722941	−	1.25217i
$408$	15.0674	+	23.9889i	0.745947	+	1.18763i
$409$	0.380507	+	0.659057i	0.0188149	+	0.0325883i	0.875280	−	0.483617i	$-0.160677\pi$
$409$	0.380507	+	0.659057i	0.0188149	+	0.0325883i	−0.856465	+	0.516206i	$0.827344\pi$
$410$	−36.8364	−	17.5540i	−1.81922	−	0.866929i
$411$	14.6435	+	2.96018i	0.722311	+	0.146015i
$412$	−16.3320	+	13.2447i	−0.804620	+	0.652517i
$413$	11.6252			0.572039
$414$	−5.05945	−	1.67680i	−0.248659	−	0.0824103i
$415$		−	20.2918i		−	0.996088i
$416$	−9.49243	+	12.4165i	−0.465404	+	0.608768i
$417$	13.9321	+	12.2951i	0.682259	+	0.602092i
$418$	−9.95984	−	4.74625i	−0.487151	−	0.232146i
$419$	14.6564	−	8.46186i	0.716010	−	0.413389i	−0.0972722	−	0.995258i	$-0.531012\pi$
$419$	14.6564	−	8.46186i	0.716010	−	0.413389i	0.813282	+	0.581869i	$0.197678\pi$
$420$	−4.65825	−	8.90569i	−0.227299	−	0.434553i
$421$	27.2143	+	15.7122i	1.32634	+	0.765765i	0.984732	−	0.174077i	$-0.0556941\pi$
$421$	27.2143	+	15.7122i	1.32634	+	0.765765i	0.341611	+	0.939841i	$0.389027\pi$
$422$	12.3283	+	17.9241i	0.600131	+	0.872531i
$423$	−0.360939	−	2.88001i	−0.0175494	−	0.140031i
$424$	12.7170	−	3.06745i	0.617593	−	0.148969i
$425$	−17.1143	−	9.88096i	−0.830167	−	0.479297i
$426$	34.8825	−	14.8730i	1.69006	−	0.720598i
$427$	1.52968	+	2.64949i	0.0740265	+	0.128218i
$428$	2.23154	+	14.0248i	0.107866	+	0.677912i
$429$	16.6159	−	5.58272i	0.802222	−	0.269536i
$430$	−32.9911	+	2.60827i	−1.59097	+	0.125782i
$431$	−0.899079			−0.0433071			−0.0216536	−	0.999766i	$-0.506893\pi$
$431$	−0.899079			−0.0433071			−0.0216536	+	0.999766i	$0.506893\pi$
$432$	−5.79988	+	19.9590i	−0.279047	+	0.960277i
$433$	−7.04400			−0.338513			−0.169257	−	0.985572i	$-0.554137\pi$
$433$	−7.04400			−0.338513			−0.169257	+	0.985572i	$0.554137\pi$
$434$	−7.16860	+	0.566749i	−0.344104	+	0.0272048i
$435$	35.9237	−	12.0699i	1.72241	−	0.578708i
$436$	−4.11047	−	25.8334i	−0.196856	−	1.23720i
$437$	−1.33789	−	2.31729i	−0.0639997	−	0.110851i
$438$	−7.96326	+	3.39532i	−0.380499	+	0.162235i
$439$	10.2730	+	5.93113i	0.490304	+	0.283077i	0.724701	−	0.689064i	$-0.241978\pi$
$439$	10.2730	+	5.93113i	0.490304	+	0.283077i	−0.234396	+	0.972141i	$0.575311\pi$
$440$	−7.04813	−	29.2201i	−0.336007	−	1.39301i
$441$	2.76444	+	1.16528i	0.131640	+	0.0554895i
$442$	−12.8040	−	18.6158i	−0.609026	−	0.885463i
$443$	−6.92330	−	3.99717i	−0.328936	−	0.189911i	0.326433	−	0.945220i	$-0.394153\pi$
$443$	−6.92330	−	3.99717i	−0.328936	−	0.189911i	−0.655369	+	0.755309i	$0.727487\pi$
$444$	−12.7861	−	24.4445i	−0.606799	−	1.16008i
$445$	34.9832	−	20.1976i	1.65836	−	0.957456i
$446$	22.5924	+	10.7662i	1.06978	+	0.509792i
$447$	−9.36510	−	8.26467i	−0.442954	−	0.390906i
$448$	−7.98991	−	0.401621i	−0.377488	−	0.0189748i
$449$		−	20.8358i		−	0.983301i	−0.870793	−	0.491650i	$-0.836394\pi$
$449$		−	20.8358i		−	0.983301i	0.870793	−	0.491650i	$-0.163606\pi$
$450$	−2.93132	−	14.2000i	−0.138184	−	0.669395i
$451$	36.4277			1.71531
$452$	27.6808	−	22.4481i	1.30199	−	1.05587i
$453$	5.81921	+	1.17635i	0.273411	+	0.0552698i
$454$	6.17637	+	2.94328i	0.289872	+	0.138135i
$455$	4.00800	+	6.94205i	0.187898	+	0.325448i
$456$	−8.83582	+	5.54977i	−0.413775	+	0.259892i
$457$	15.7400	−	27.2625i	0.736286	−	1.27528i	−0.217872	−	0.975977i	$-0.569911\pi$
$457$	15.7400	−	27.2625i	0.736286	−	1.27528i	0.954157	−	0.299306i	$-0.0967553\pi$
$458$	11.1297	−	7.65509i	0.520058	−	0.357699i
$459$	−24.8260	−	16.9256i	−1.15878	−	0.790018i
$460$	2.60761	−	6.80754i	0.121580	−	0.317403i
$461$	−12.5645	+	21.7624i	−0.585188	+	1.01357i	0.409664	+	0.912236i	$0.365646\pi$
$461$	−12.5645	+	21.7624i	−0.585188	+	1.01357i	−0.994852	+	0.101338i	$0.967688\pi$
$462$	7.17419	+	5.38808i	0.333774	+	0.250676i
$463$	−27.0262	+	15.6036i	−1.25601	+	0.725159i	−0.972297	−	0.233750i	$-0.924900\pi$
$463$	−27.0262	+	15.6036i	−1.25601	+	0.725159i	−0.283715	+	0.958909i	$0.591567\pi$
$464$	6.22978	−	29.5154i	0.289210	−	1.37022i
$465$	−25.0455	−	5.06293i	−1.16146	−	0.234788i
$466$	−0.241183	−	3.05063i	−0.0111726	−	0.141318i
$467$		−	15.8405i		−	0.733012i	−0.930416	−	0.366506i	$-0.880554\pi$
$467$		−	15.8405i		−	0.733012i	0.930416	−	0.366506i	$-0.119446\pi$
$468$	3.95870	−	16.0978i	0.182991	−	0.744119i
$469$		−	2.40495i		−	0.111050i
$470$	3.95741	−	0.312873i	0.182542	−	0.0144317i
$471$	5.86352	−	6.64424i	0.270177	−	0.306150i
$472$	23.8269	−	22.6593i	1.09672	−	1.04298i
$473$	25.5856	−	14.7719i	1.17643	−	0.679212i
$474$	−0.584316	−	0.0707919i	−0.0268385	−	0.00325158i
$475$	3.63945	−	6.30371i	0.166989	−	0.289234i
$476$	4.13683	−	10.7998i	0.189611	−	0.495007i
$477$	−11.0604	+	8.37805i	−0.506419	+	0.383605i
$478$	17.3688	+	25.2525i	0.794431	+	1.15502i
$479$	3.52934	−	6.11300i	0.161260	−	0.279310i	−0.774061	−	0.633111i	$-0.781778\pi$
$479$	3.52934	−	6.11300i	0.161260	−	0.279310i	0.935321	+	0.353801i	$0.115111\pi$
$480$	−26.9060	−	9.17335i	−1.22809	−	0.418704i
$481$	11.0012	+	19.0547i	0.501612	+	0.868818i
$482$	−2.93219	+	6.15310i	−0.133558	+	0.280266i
$483$	0.693035	+	2.06268i	0.0315342	+	0.0938553i
$484$	3.04449	+	3.75416i	0.138386	+	0.170644i
$485$	−27.4430			−1.24612
$486$	−2.83129	−	21.8628i	−0.128430	−	0.991719i
$487$		−	34.3450i		−	1.55632i	−0.628065	−	0.778161i	$-0.716153\pi$
$487$		−	34.3450i		−	1.55632i	0.628065	−	0.778161i	$-0.283847\pi$
$488$	8.29947	+	2.44878i	0.375699	+	0.110851i
$489$	12.6463	−	4.24899i	0.571885	−	0.192146i
$490$	−1.76509	+	3.70399i	−0.0797388	+	0.167329i
$491$	−20.4085	+	11.7828i	−0.921022	+	0.531753i	−0.883961	−	0.467560i	$-0.845133\pi$
$491$	−20.4085	+	11.7828i	−0.921022	+	0.531753i	−0.0370613	+	0.999313i	$0.511800\pi$
$492$	18.4533	−	29.0917i	0.831938	−	1.31156i
$493$	37.7658	+	21.8041i	1.70089	+	0.982008i
$494$	6.85675	−	4.71611i	0.308500	−	0.212188i
$495$	19.2504	+	25.4135i	0.865240	+	1.14225i
$496$	−13.5880	+	15.1343i	−0.610119	+	0.679550i
$497$	−13.4071	−	7.74058i	−0.601389	−	0.347212i
$498$	17.0075	+	2.06052i	0.762124	+	0.0923339i
$499$	4.17024	+	7.22307i	0.186686	+	0.323349i	0.944143	−	0.329535i	$-0.106892\pi$
$499$	4.17024	+	7.22307i	0.186686	+	0.323349i	−0.757458	+	0.652884i	$0.773559\pi$
$500$	−9.06828	+	1.44289i	−0.405546	+	0.0645282i
$501$	16.5459	+	14.6017i	0.739215	+	0.652355i
$502$	−1.45337	−	18.3831i	−0.0648670	−	0.820479i
$503$	−6.02715			−0.268738			−0.134369	−	0.990931i	$-0.542901\pi$
$503$	−6.02715			−0.268738			−0.134369	+	0.990931i	$0.542901\pi$
$504$	7.93727	−	2.99997i	0.353554	−	0.133629i
$505$	12.0036			0.534151
$506$	0.512908	+	6.48758i	0.0228015	+	0.288408i
$507$	1.84170	−	9.11060i	0.0817930	−	0.404616i
$508$	1.37858	+	8.66408i	0.0611646	+	0.384406i
$509$	−7.07966	−	12.2623i	−0.313800	−	0.543518i	0.665381	−	0.746504i	$-0.268269\pi$
$509$	−7.07966	−	12.2623i	−0.313800	−	0.543518i	−0.979182	+	0.202985i	$0.934936\pi$
$510$	24.6785	−	32.8592i	1.09278	−	1.45503i
$511$	3.06067	+	1.76708i	0.135396	+	0.0781710i
$512$	−17.1588	+	14.7504i	−0.758321	+	0.651881i
$513$	6.23419	−	9.14415i	0.275246	−	0.403724i
$514$	2.10355	−	1.44683i	0.0927834	−	0.0638169i
$515$	26.4168	+	15.2518i	1.16406	+	0.672073i
$516$	1.16394	−	27.9162i	0.0512395	−	1.22894i
$517$	−3.06910	+	1.77194i	−0.134979	+	0.0779300i
$518$	−4.84486	+	10.1668i	−0.212871	+	0.446703i
$519$	3.97192	−	19.6484i	0.174348	−	0.862471i
$520$	21.7458	+	6.41616i	0.953618	+	0.281367i
$521$			23.3238i			1.02183i	0.859630	+	0.510917i	$0.170694\pi$
$521$			23.3238i			1.02183i	−0.859630	+	0.510917i	$0.829306\pi$
$522$	6.46849	+	31.3349i	0.283118	+	1.37149i
$523$	16.3272			0.713940			0.356970	−	0.934116i	$-0.383810\pi$
$523$	16.3272			0.713940			0.356970	+	0.934116i	$0.383810\pi$
$524$	32.3870	−	26.2647i	1.41483	−	1.14738i
$525$	−3.91674	+	4.43824i	−0.170940	+	0.193701i
$526$	−6.86313	+	14.4021i	−0.299247	+	0.627959i
$527$	−14.7014	−	25.4635i	−0.640401	−	1.10921i
$528$	25.2063	−	2.94023i	1.09696	−	0.127957i
$529$	10.7108	−	18.5517i	0.465689	−	0.806597i
$530$	−10.7543	−	15.6356i	−0.467136	−	0.679168i
$531$	−13.5466	+	32.1372i	−0.587873	+	1.39463i
$532$	3.97788	+	1.52372i	0.172463	+	0.0660615i
$533$	−13.7386	+	23.7959i	−0.595085	+	1.03072i
$534$	13.3761	+	31.3719i	0.578842	+	1.35759i
$535$	17.8409	−	10.3005i	0.771331	−	0.445328i
$536$	−4.68762	−	4.92916i	−0.202474	−	0.212907i
$537$	−10.6006	−	31.5505i	−0.457448	−	1.36150i
$538$	−39.4962	+	3.12257i	−1.70280	+	0.134623i
$539$		−	3.66289i		−	0.157772i
$540$	30.0474	−	2.49985i	1.29303	−	0.107576i
$541$			25.2084i			1.08380i	0.840445	+	0.541898i	$0.182294\pi$
$541$			25.2084i			1.08380i	−0.840445	+	0.541898i	$0.817706\pi$
$542$	2.59607	+	32.8367i	0.111511	+	1.41046i
$543$	−9.33909	−	27.7960i	−0.400779	−	1.19284i
$544$	−12.5716	−	30.1984i	−0.539004	−	1.29475i
$545$	−32.8628	+	18.9733i	−1.40769	+	0.812728i
$546$	−6.22543	+	2.65435i	−0.266424	+	0.113596i
$547$	3.24712	−	5.62418i	0.138837	−	0.240472i	−0.788220	−	0.615394i	$-0.788997\pi$
$547$	3.24712	−	5.62418i	0.138837	−	0.240472i	0.927057	+	0.374921i	$0.122330\pi$
$548$	−16.1095	−	6.17070i	−0.688163	−	0.263599i
$549$	−9.10685	+	1.14132i	−0.388671	+	0.0487104i
$550$	−14.5861	+	10.0324i	−0.621955	+	0.427784i
$551$	−8.03110	+	13.9103i	−0.342136	+	0.592598i
$552$	5.44091	+	2.87682i	0.231581	+	0.122446i
$553$	0.120145	+	0.208098i	0.00510909	+	0.00884921i
$554$	34.9683	+	16.6637i	1.48566	+	0.707974i
$555$	−26.4795	+	30.0052i	−1.12399	+	1.27365i
$556$	−13.5146	−	16.6649i	−0.573147	−	0.706749i
$557$	−8.30328			−0.351821			−0.175911	−	0.984406i	$-0.556287\pi$
$557$	−8.30328			−0.351821			−0.175911	+	0.984406i	$0.556287\pi$
$558$	6.78668	−	20.4776i	0.287303	−	0.866886i
$559$			22.2847i			0.942542i
$560$	3.60192	+	11.0321i	0.152209	+	0.466191i
$561$	−7.26900	+	35.9585i	−0.306897	+	1.51817i
$562$	13.6212	+	6.49104i	0.574577	+	0.273808i
$563$	17.2669	−	9.96903i	0.727712	−	0.420145i	−0.0898727	−	0.995953i	$-0.528646\pi$
$563$	17.2669	−	9.96903i	0.727712	−	0.420145i	0.817584	+	0.575809i	$0.195313\pi$
$564$	−0.139619	+	3.34865i	−0.00587901	+	0.141004i
$565$	−44.7733	−	25.8499i	−1.88363	−	1.08751i
$566$	−12.3371	−	17.9369i	−0.518568	−	0.753946i
$567$	−6.44269	+	6.28425i	−0.270567	+	0.263914i
$568$	−42.5665	+	10.2674i	−1.78605	+	0.430811i
$569$	−11.5852	−	6.68874i	−0.485678	−	0.280407i	0.237101	−	0.971485i	$-0.423803\pi$
$569$	−11.5852	−	6.68874i	−0.485678	−	0.280407i	−0.722780	+	0.691078i	$0.757136\pi$
$570$	12.1030	+	9.08982i	0.506940	+	0.380730i
$571$	7.85236	+	13.6007i	0.328611	+	0.569171i	0.982237	−	0.187647i	$-0.0600861\pi$
$571$	7.85236	+	13.6007i	0.328611	+	0.569171i	−0.653625	+	0.756818i	$0.726753\pi$
$572$	−19.9889	+	3.18052i	−0.835778	+	0.132984i
$573$	3.76419	−	18.6208i	0.157251	−	0.777895i
$574$	−14.0207	+	1.10848i	−0.585213	+	0.0462669i
$575$	−4.29350			−0.179051
$576$	10.4207	−	21.6196i	0.434197	−	0.900818i
$577$	−20.7956			−0.865732			−0.432866	−	0.901458i	$-0.642498\pi$
$577$	−20.7956			−0.865732			−0.432866	+	0.901458i	$0.642498\pi$
$578$	23.1734	−	1.83209i	0.963885	−	0.0762047i
$579$	−32.2408	−	28.4524i	−1.33988	−	1.18244i
$580$	−43.2163	+	6.87633i	−1.79446	+	0.285524i
$581$	−3.49703	−	6.05703i	−0.145081	−	0.251288i
$582$	2.78667	−	23.0012i	0.115511	−	0.953431i
$583$	14.6715	+	8.47059i	0.607631	+	0.350816i
$584$	9.71742	−	2.34393i	0.402110	−	0.0969923i
$585$	−23.8613	+	2.99043i	−0.986544	+	0.123639i
$586$	14.4065	+	20.9457i	0.595128	+	0.865257i
$587$	−22.2467	−	12.8441i	−0.918218	−	0.530133i	−0.0351515	−	0.999382i	$-0.511191\pi$
$587$	−22.2467	−	12.8441i	−0.918218	−	0.530133i	−0.883066	+	0.469249i	$0.844525\pi$
$588$	−2.92524	−	1.85552i	−0.120635	−	0.0765204i
$589$	9.37896	−	5.41495i	0.386454	−	0.223119i
$590$	−43.0596	−	20.5196i	−1.77274	−	0.844778i
$591$	42.3203	−	14.2191i	1.74082	−	0.584895i
$592$	9.88661	+	30.2811i	0.406337	+	1.24454i
$593$			23.4450i			0.962771i	0.876509	+	0.481386i	$0.159866\pi$
$593$			23.4450i			0.962771i	−0.876509	+	0.481386i	$0.840134\pi$
$594$	−23.2550	+	13.5540i	−0.954163	+	0.556127i
$595$	−16.7767			−0.687779
$596$	9.08445	+	11.2020i	0.372114	+	0.458854i
$597$	8.73955	+	26.0116i	0.357686	+	1.06458i
$598$	−4.43138	−	2.11172i	−0.181212	−	0.0863547i
$599$	13.7470	+	23.8104i	0.561685	+	0.972868i	0.997350	+	0.0727585i	$0.0231802\pi$
$599$	13.7470	+	23.8104i	0.561685	+	0.972868i	−0.435664	+	0.900109i	$0.643486\pi$
$600$	0.623111	+	16.7309i	0.0254384	+	0.683035i
$601$	−13.8813	+	24.0430i	−0.566228	+	0.980736i	0.430706	+	0.902492i	$0.358265\pi$
$601$	−13.8813	+	24.0430i	−0.566228	+	0.980736i	−0.996934	+	0.0782440i	$0.975069\pi$
$602$	−9.39820	+	6.46413i	−0.383042	+	0.263458i
$603$	6.64835	+	2.80244i	0.270742	+	0.114124i
$604$	−6.40179	−	2.45219i	−0.260485	−	0.0997781i
$605$	3.50585	−	6.07231i	0.142533	−	0.246875i
$606$	−1.21889	+	10.0607i	−0.0495140	+	0.408689i
$607$	25.6765	−	14.8244i	1.04218	−	0.601702i	0.121729	−	0.992563i	$-0.461156\pi$
$607$	25.6765	−	14.8244i	1.04218	−	0.601702i	0.920449	+	0.390862i	$0.127823\pi$
$608$	11.1230	−	4.63050i	0.451096	−	0.187792i
$609$	8.64299	−	9.79378i	0.350231	−	0.396864i
$610$	−0.989333	−	12.5137i	−0.0400569	−	0.506665i
$611$		−	2.67314i		−	0.108144i
$612$	25.0348	+	24.0208i	1.01197	+	0.970982i
$613$			24.4473i			0.987417i	0.869628	+	0.493708i	$0.164359\pi$
$613$			24.4473i			0.987417i	−0.869628	+	0.493708i	$0.835641\pi$
$614$	31.6047	−	2.49867i	1.27546	−	0.100838i
$615$	−48.9851	−	9.90232i	−1.97527	−	0.399300i
$616$	−7.13952	−	7.50741i	−0.287659	−	0.302482i
$617$	−13.5853	+	7.84350i	−0.546925	+	0.315767i	−0.747881	−	0.663833i	$-0.768929\pi$
$617$	−13.5853	+	7.84350i	−0.546925	+	0.315767i	0.200956	+	0.979600i	$0.435595\pi$
$618$	−15.4656	+	20.5924i	−0.622119	+	0.828347i
$619$	−9.41555	+	16.3082i	−0.378443	+	0.655482i	−0.990836	−	0.135071i	$-0.956874\pi$
$619$	−9.41555	+	16.3082i	−0.378443	+	0.655482i	0.612393	+	0.790554i	$0.290207\pi$
$620$	27.5528	+	10.5540i	1.10655	+	0.423860i
$621$	−6.50974	−	0.487747i	−0.261227	−	0.0195726i
$622$	19.4818	+	28.3247i	0.781151	+	1.13572i
$623$	6.96155	−	12.0578i	0.278909	−	0.483084i
$624$	−7.58582	+	17.5746i	−0.303676	+	0.703548i
$625$	15.2041	+	26.3342i	0.608162	+	1.05337i
$626$	13.0013	−	27.2828i	0.519636	−	1.09044i
$627$	−13.2446	−	2.67739i	−0.528938	−	0.106925i
$628$	−7.94749	+	6.44513i	−0.317140	+	0.257189i
$629$	−46.0491			−1.83610
$630$	−8.18263	−	9.19567i	−0.326004	−	0.366364i
$631$			6.86500i			0.273291i	0.990620	+	0.136646i	$0.0436322\pi$
$631$			6.86500i			0.273291i	−0.990620	+	0.136646i	$0.956368\pi$
$632$	0.651862	+	0.192333i	0.0259297	+	0.00765060i
$633$	19.9771	+	17.6297i	0.794017	+	0.700718i
$634$	−3.33182	+	6.99170i	−0.132323	+	0.277676i
$635$	11.0216	−	6.36333i	0.437379	−	0.252521i
$636$	14.1969	−	7.42592i	0.562945	−	0.294457i
$637$	2.39274	+	1.38145i	0.0948037	+	0.0547350i
$638$	32.1869	−	22.1383i	1.27429	−	0.876465i
$639$	37.0213	−	28.0431i	1.46454	−	1.10937i
$640$	28.8856	+	15.5905i	1.14181	+	0.616270i
$641$	7.99458	+	4.61568i	0.315767	+	0.182308i	0.649504	−	0.760358i	$-0.274976\pi$
$641$	7.99458	+	4.61568i	0.315767	+	0.182308i	−0.333737	+	0.942666i	$0.608310\pi$
$642$	6.82164	+	15.9992i	0.269229	+	0.631439i
$643$	9.12120	+	15.7984i	0.359705	+	0.623027i	0.987911	−	0.155020i	$-0.0495440\pi$
$643$	9.12120	+	15.7984i	0.359705	+	0.623027i	−0.628207	+	0.778047i	$0.716211\pi$
$644$	−0.394828	−	2.48141i	−0.0155584	−	0.0977811i
$645$	−38.4211	+	12.9090i	−1.51283	+	0.508291i
$646$	1.37273	+	17.3631i	0.0540093	+	0.683144i
$647$	9.09602			0.357601			0.178801	−	0.983885i	$-0.442778\pi$
$647$	9.09602			0.357601			0.178801	+	0.983885i	$0.442778\pi$
$648$	−0.955898	+	25.4379i	−0.0375512	+	0.999295i
$649$	42.5818			1.67148
$650$	−1.05244	−	13.3119i	−0.0412801	−	0.522136i
$651$	−8.34849	+	2.80498i	−0.327203	+	0.109936i
$652$	−15.2135	+	2.42069i	−0.595806	+	0.0948013i
$653$	2.37644	+	4.11611i	0.0929973	+	0.161076i	0.908771	−	0.417295i	$-0.137022\pi$
$653$	2.37644	+	4.11611i	0.0929973	+	0.161076i	−0.815774	+	0.578371i	$0.803689\pi$
$654$	−12.5654	−	29.4704i	−0.491345	−	1.15238i
$655$	−52.3856	−	30.2448i	−2.04688	−	1.18176i
$656$	−26.5761	+	29.6004i	−1.03762	+	1.15570i
$657$	−8.45152	+	6.40190i	−0.329725	+	0.249762i
$658$	1.12735	−	0.775398i	0.0439487	−	0.0302281i
$659$	−29.6263	−	17.1048i	−1.15408	−	0.666307i	−0.204200	−	0.978929i	$-0.565459\pi$
$659$	−29.6263	−	17.1048i	−1.15408	−	0.666307i	−0.949878	+	0.312622i	$0.898793\pi$
$660$	−17.0627	−	32.6205i	−0.664163	−	1.26975i
$661$	24.5237	−	14.1588i	0.953861	−	0.550712i	0.0595826	−	0.998223i	$-0.481023\pi$
$661$	24.5237	−	14.1588i	0.953861	−	0.550712i	0.894278	+	0.447512i	$0.147690\pi$
$662$	−0.988427	+	2.07418i	−0.0384163	+	0.0806153i
$663$	−20.7480	−	18.3101i	−0.805786	−	0.711103i
$664$	−18.9735	−	5.59818i	−0.736316	−	0.217251i
$665$		−	6.17937i		−	0.239626i
$666$	−22.4598	−	25.2405i	−0.870301	−	0.978048i
$667$	9.47438			0.366849
$668$	−16.0500	−	19.7913i	−0.620995	−	0.765749i
$669$	30.0434	+	6.07326i	1.16155	+	0.234806i
$670$	−4.24497	+	8.90792i	−0.163997	+	0.344143i
$671$	5.60305	+	9.70477i	0.216303	+	0.374649i
$672$	−9.61223	+	1.89869i	−0.370800	+	0.0732434i
$673$	−20.9750	+	36.3297i	−0.808526	+	1.40041i	0.105359	+	0.994434i	$0.466401\pi$
$673$	−20.9750	+	36.3297i	−0.808526	+	1.40041i	−0.913885	+	0.405974i	$0.866932\pi$
$674$	13.5051	+	19.6350i	0.520196	+	0.756313i
$675$	−7.70517	−	15.9994i	−0.296572	−	0.615816i
$676$	−3.83916	+	10.0227i	−0.147660	+	0.385488i
$677$	−6.21450	+	10.7638i	−0.238843	+	0.413688i	−0.960382	−	0.278685i	$-0.910101\pi$
$677$	−6.21450	+	10.7638i	−0.238843	+	0.413688i	0.721540	+	0.692373i	$0.243435\pi$
$678$	26.2124	−	34.9016i	1.00668	−	1.34039i
$679$	−8.19162	+	4.72943i	−0.314366	+	0.181499i
$680$	−34.3854	+	32.7004i	−1.31862	+	1.25400i
$681$	8.21335	+	1.66032i	0.314736	+	0.0636238i
$682$	−26.2578	+	2.07594i	−1.00546	+	0.0794918i
$683$			10.7413i			0.411005i	0.978657	+	0.205502i	$0.0658828\pi$
$683$			10.7413i			0.411005i	−0.978657	+	0.205502i	$0.934117\pi$
$684$	−8.84757	+	9.22106i	−0.338295	+	0.352576i
$685$			25.0250i			0.956156i
$686$	0.111460	+	1.40981i	0.00425556	+	0.0538270i
$687$	10.9469	−	12.4045i	0.417652	−	0.473261i
$688$	−6.66287	+	31.5673i	−0.254019	+	1.20349i
$689$	−11.0666	+	6.38932i	−0.421605	+	0.243414i
$690$	1.07383	−	8.86342i	0.0408801	−	0.337425i
$691$	−1.11440	+	1.93020i	−0.0423937	+	0.0734281i	−0.886444	−	0.462836i	$-0.846832\pi$
$691$	−1.11440	+	1.93020i	−0.0423937	+	0.0734281i	0.844050	+	0.536265i	$0.180165\pi$
$692$	−8.27975	+	21.6155i	−0.314749	+	0.821697i
$693$	10.1258	+	4.26829i	0.384648	+	0.162139i
$694$	−8.34024	+	5.73646i	−0.316591	+	0.217753i
$695$	−15.5626	+	26.9553i	−0.590324	+	1.02247i
$696$	−1.37501	−	36.9197i	−0.0521194	−	1.39944i
$697$	−28.7536	−	49.8027i	−1.08912	−	1.88641i
$698$	6.37935	+	3.04001i	0.241462	+	0.115066i
$699$	−1.19367	−	3.55274i	−0.0451489	−	0.134377i
$700$	5.30880	−	4.30524i	0.200654	−	0.162723i
$701$	29.7564			1.12388			0.561942	−	0.827177i	$-0.310054\pi$
$701$	29.7564			1.12388			0.561942	+	0.827177i	$0.310054\pi$
$702$	−0.0834425	−	20.3029i	−0.00314933	−	0.766283i
$703$		−	16.9613i		−	0.639706i
$704$	−29.2662	−	1.47109i	−1.10301	−	0.0554439i
$705$	4.60876	−	1.54849i	0.173576	−	0.0583193i
$706$	19.5834	+	9.33222i	0.737029	+	0.351223i
$707$	3.58301	−	2.06865i	0.134753	−	0.0777997i
$708$	21.5708	−	34.0065i	0.810681	−	1.27804i
$709$	−20.6605	−	11.9283i	−0.775920	−	0.447977i	0.0590627	−	0.998254i	$-0.481189\pi$
$709$	−20.6605	−	11.9283i	−0.775920	−	0.447977i	−0.834982	+	0.550277i	$0.814522\pi$
$710$	35.9968	+	52.3358i	1.35094	+	1.96413i
$711$	−0.715276	+	0.0896424i	−0.0268249	+	0.00336185i
$712$	−9.23409	−	38.2826i	−0.346062	−	1.43470i
$713$	−5.53223	−	3.19404i	−0.207184	−	0.119618i
$714$	1.70358	−	14.0613i	0.0637548	−	0.526232i
$715$	14.6808	+	25.4280i	0.549032	+	0.950952i
$716$	6.03922	+	37.9552i	0.225696	+	1.41845i
$717$	28.1449	+	24.8378i	1.05109	+	0.927584i
$718$	11.5706	−	0.914774i	0.431813	−	0.0341391i
$719$	15.2687			0.569427			0.284713	−	0.958613i	$-0.408102\pi$
$719$	15.2687			0.569427			0.284713	+	0.958613i	$0.408102\pi$
$720$	−34.6948	−	2.89817i	−1.29300	−	0.108008i
$721$	10.5137			0.391552
$722$	20.3911	−	1.61212i	0.758879	−	0.0599969i
$723$	−1.65407	+	8.18240i	−0.0615155	+	0.304307i
$724$	5.32056	+	33.4386i	0.197737	+	1.24273i
$725$	12.8866	+	22.3202i	0.478596	+	0.828952i
$726$	4.73348	+	3.55502i	0.175676	+	0.131939i
$727$	42.1184	+	24.3171i	1.56209	+	0.901870i	0.997046	+	0.0768061i	$0.0244722\pi$
$727$	42.1184	+	24.3171i	1.56209	+	0.901870i	0.565039	+	0.825064i	$0.308861\pi$
$728$	7.59678	−	1.83241i	0.281555	−	0.0679136i
$729$	−9.86490	−	25.1333i	−0.365367	−	0.930864i
$730$	−8.21763	−	11.9476i	−0.304148	−	0.442201i
$731$	−40.3913	−	23.3199i	−1.49393	−	0.862518i
$732$	10.5887	+	0.441488i	0.391371	+	0.0163179i
$733$	3.29924	−	1.90482i	0.121860	−	0.0703561i	−0.437831	−	0.899057i	$-0.644253\pi$
$733$	3.29924	−	1.90482i	0.121860	−	0.0703561i	0.559691	+	0.828701i	$0.310920\pi$
$734$	19.7818	+	9.42679i	0.730159	+	0.347949i
$735$	−0.995701	+	4.92557i	−0.0367270	+	0.181682i
$736$	−5.64587	−	4.31628i	−0.208110	−	0.159100i
$737$		−	8.80907i		−	0.324486i
$738$	13.2737	−	40.0511i	0.488612	−	1.47430i
$739$	9.24202			0.339973			0.169987	−	0.985446i	$-0.445628\pi$
$739$	9.24202			0.339973			0.169987	+	0.985446i	$0.445628\pi$
$740$	35.8906	−	29.1060i	1.31937	−	1.06996i
$741$	6.74414	−	7.64211i	0.247752	−	0.280740i
$742$	−5.90469	−	2.81381i	−0.216768	−	0.103298i
$743$	−22.1465	−	38.3588i	−0.812476	−	1.40725i	−0.911126	−	0.412127i	$-0.864786\pi$
$743$	−22.1465	−	38.3588i	−0.812476	−	1.40725i	0.0986504	−	0.995122i	$-0.468547\pi$
$744$	−11.6436	+	22.0215i	−0.426876	+	0.807348i
$745$	10.4611	−	18.1192i	0.383266	−	0.663836i
$746$	2.88268	−	1.98272i	0.105542	−	0.0725926i
$747$	20.8193	−	2.60919i	0.761738	−	0.0954653i
$748$	15.1527	−	39.5584i	0.554039	−	1.44640i
$749$	3.55030	−	6.14929i	0.129725	−	0.224690i
$750$	−10.3450	+	4.41081i	−0.377745	+	0.161060i
$751$	−16.7922	+	9.69500i	−0.612757	+	0.353775i	−0.774044	−	0.633132i	$-0.781769\pi$
$751$	−16.7922	+	9.69500i	−0.612757	+	0.353775i	0.161287	+	0.986908i	$0.448436\pi$
$752$	0.799237	−	3.78662i	0.0291452	−	0.138084i
$753$	−7.19308	−	21.4088i	−0.262131	−	0.780180i
$754$	2.32240	+	29.3751i	0.0845767	+	1.06978i
$755$			9.94474i			0.361926i
$756$	8.53820	−	5.92446i	0.310531	−	0.215470i
$757$		−	23.4834i		−	0.853519i	−0.904365	−	0.426759i	$-0.859655\pi$
$757$		−	23.4834i		−	0.853519i	0.904365	−	0.426759i	$-0.140345\pi$
$758$	−37.6048	+	2.97304i	−1.36587	+	0.107986i
$759$	2.53851	+	7.55537i	0.0921420	+	0.274243i
$760$	−12.0445	−	12.6652i	−0.436901	−	0.459414i
$761$	−35.6785	+	20.5990i	−1.29335	+	0.746714i	−0.979246	−	0.202676i	$-0.935036\pi$
$761$	−35.6785	+	20.5990i	−1.29335	+	0.746714i	−0.314100	+	0.949390i	$0.601703\pi$
$762$	4.21421	+	9.88385i	0.152665	+	0.358054i
$763$	−6.53960	+	11.3269i	−0.236749	+	0.410062i
$764$	−7.84671	+	20.4850i	−0.283884	+	0.741120i
$765$	19.5496	−	46.3783i	0.706817	−	1.67681i
$766$	−24.2958	−	35.3236i	−0.877842	−	1.27629i
$767$	−16.0596	+	27.8161i	−0.579879	+	1.00438i
$768$	−16.0003	+	22.6272i	−0.577361	+	0.816489i
$769$	18.7354	+	32.4507i	0.675616	+	1.17020i	0.976289	+	0.216473i	$0.0694554\pi$
$769$	18.7354	+	32.4507i	0.675616	+	1.17020i	−0.300673	+	0.953727i	$0.597211\pi$
$770$	−6.46534	+	13.5673i	−0.232995	+	0.488931i
$771$	2.06900	−	2.34448i	0.0745131	−	0.0844344i
$772$	31.2747	+	38.5648i	1.12560	+	1.38798i
$773$	53.5196			1.92497			0.962484	−	0.271340i	$-0.0874666\pi$
$773$	53.5196			1.92497			0.962484	+	0.271340i	$0.0874666\pi$
$774$	−6.91817	−	33.5133i	−0.248669	−	1.20461i
$775$		−	17.3775i		−	0.624218i
$776$	−7.57106	+	25.6601i	−0.271785	+	0.921144i
$777$	−2.73302	+	13.5198i	−0.0980465	+	0.485020i
$778$	23.2622	−	48.8149i	0.833989	−	1.75010i
$779$	18.3438	−	10.5908i	0.657236	−	0.379455i
$780$	27.7441	+	1.15676i	0.993398	+	0.0414188i
$781$	−49.1086	−	28.3529i	−1.75724	−	1.01455i
$782$	8.46476	−	5.82210i	0.302699	−	0.208198i
$783$	17.0028	+	35.3055i	0.607632	+	1.26172i
$784$	2.97639	+	2.67229i	0.106300	+	0.0954388i
$785$	12.8550	+	7.42183i	0.458814	+	0.264896i
$786$	30.6690	−	40.8355i	1.09393	−	1.45655i
$787$	−6.56797	−	11.3761i	−0.234123	−	0.405513i	0.724894	−	0.688860i	$-0.241889\pi$
$787$	−6.56797	−	11.3761i	−0.234123	−	0.405513i	−0.959017	+	0.283347i	$0.908555\pi$
$788$	−50.9114	+	8.10073i	−1.81364	+	0.288577i
$789$	−3.87154	+	19.1519i	−0.137830	+	0.681824i
$790$	−0.0777048	−	0.982859i	−0.00276461	−	0.0349685i
$791$	−17.8195			−0.633589
$792$	29.0733	−	10.9885i	1.03308	−	0.390461i
$793$	−8.45270			−0.300164
$794$	0.0226687	+	0.286728i	0.000804483	+	0.0101756i
$795$	−17.4265	−	15.3788i	−0.618054	−	0.545431i
$796$	−4.97899	−	31.2919i	−0.176476	−	1.10911i
$797$	−24.7132	−	42.8046i	−0.875388	−	1.51622i	−0.856349	−	0.516397i	$-0.827273\pi$
$797$	−24.7132	−	42.8046i	−0.875388	−	1.51622i	−0.0190383	−	0.999819i	$-0.506060\pi$
$798$	5.17920	+	0.627478i	0.183342	+	0.0222125i
$799$	4.84509	+	2.79732i	0.171407	+	0.0989619i
$800$	2.48928	−	19.1716i	0.0880094	−	0.677819i
$801$	25.2208	+	33.2954i	0.891133	+	1.17644i
$802$	3.38987	−	2.33157i	0.119700	−	0.0823306i
$803$	11.2109	+	6.47261i	0.395624	+	0.228414i
$804$	−7.03507	−	4.46244i	−0.248108	−	0.157378i
$805$	−3.15661	+	1.82247i	−0.111256	+	0.0642336i
$806$	8.54697	−	17.9355i	0.301054	−	0.631752i
$807$	−45.9969	+	15.4544i	−1.61917	+	0.544019i
$808$	3.31158	−	11.2237i	0.116501	−	0.394849i
$809$		−	43.3173i		−	1.52295i	−0.648192	−	0.761477i	$-0.724475\pi$
$809$		−	43.3173i		−	1.52295i	0.648192	−	0.761477i	$-0.275525\pi$
$810$	34.9559	−	11.9049i	1.22823	−	0.418294i
$811$	24.2897			0.852927			0.426464	−	0.904505i	$-0.359759\pi$
$811$	24.2897			0.852927			0.426464	+	0.904505i	$0.359759\pi$
$812$	−11.7148	+	9.50029i	−0.411110	+	0.333395i
$813$	12.8486	+	38.2413i	0.450619	+	1.34118i
$814$	−17.7462	+	37.2398i	−0.622003	+	1.30525i
$815$	11.1735	+	19.3531i	0.391392	+	0.677911i
$816$	−23.9160	−	32.1405i	−0.837228	−	1.12514i
$817$	8.58942	−	14.8773i	0.300506	−	0.520491i
$818$	−0.609903	−	0.886737i	−0.0213247	−	0.0310040i
$819$	−6.60714	+	5.00481i	−0.230872	+	0.174882i
$820$	53.8891	+	20.6421i	1.88189	+	0.720852i
$821$	10.7413	−	18.6045i	0.374874	−	0.649300i	−0.615434	−	0.788188i	$-0.711019\pi$
$821$	10.7413	−	18.6045i	0.374874	−	0.649300i	0.990308	+	0.138888i	$0.0443527\pi$
$822$	−20.9746	−	2.54114i	−0.731572	−	0.0886324i
$823$	−35.7383	+	20.6335i	−1.24576	+	0.719239i	−0.970261	−	0.242062i	$-0.922176\pi$
$823$	−35.7383	+	20.6335i	−1.24576	+	0.719239i	−0.275498	+	0.961302i	$0.588843\pi$
$824$	21.5488	−	20.4929i	0.750689	−	0.713903i
$825$	−14.3466	+	16.2568i	−0.499483	+	0.565989i
$826$	−16.3894	+	1.29574i	−0.570260	+	0.0450847i
$827$		−	5.76065i		−	0.200318i	−0.994971	−	0.100159i	$-0.968065\pi$
$827$		−	5.76065i		−	0.200318i	0.994971	−	0.100159i	$-0.0319351\pi$
$828$	7.31978	+	1.80005i	0.254380	+	0.0625562i
$829$			4.96253i			0.172356i	0.996280	+	0.0861779i	$0.0274653\pi$
$829$			4.96253i			0.172356i	−0.996280	+	0.0861779i	$0.972535\pi$
$830$	2.26173	+	28.6077i	0.0785057	+	0.992989i
$831$	46.5009	+	9.40013i	1.61310	+	0.326087i
$832$	11.9986	−	18.5629i	0.415977	−	0.643554i
$833$	−5.00778	+	2.89124i	−0.173509	+	0.100176i
$834$	−21.0121	−	15.7809i	−0.727590	−	0.546447i
$835$	−18.4823	+	32.0122i	−0.639606	+	1.10783i
$836$	14.5705	+	5.58120i	0.503932	+	0.193030i
$837$	1.97410	−	26.3475i	0.0682350	−	0.910702i
$838$	−19.7196	+	13.5632i	−0.681202	+	0.468534i
$839$	2.62641	−	4.54907i	0.0906736	−	0.157051i	−0.817121	−	0.576466i	$-0.804431\pi$
$839$	2.62641	−	4.54907i	0.0906736	−	0.157051i	0.907795	+	0.419415i	$0.137765\pi$
$840$	7.55990	+	12.0362i	0.260841	+	0.415287i
$841$	−13.9366	−	24.1388i	−0.480571	−	0.832374i
$842$	−40.1184	−	19.1179i	−1.38257	−	0.658848i
$843$	18.1135	+	3.66164i	0.623863	+	0.126114i
$844$	−19.3784	−	23.8955i	−0.667032	−	0.822518i
$845$	15.5696			0.535609
$846$	0.829862	+	4.02005i	0.0285312	+	0.138212i
$847$		−	2.41675i		−	0.0830403i
$848$	−17.5867	+	5.74198i	−0.603931	+	0.197180i
$849$	−19.9914	−	17.6423i	−0.686103	−	0.605484i
$850$	25.2294	+	12.0228i	0.865360	+	0.412377i
$851$	−8.66431	+	5.00234i	−0.297009	+	0.171478i
$852$	−47.5202	+	24.8561i	−1.62801	+	0.851557i
$853$	−17.8937	−	10.3309i	−0.612667	−	0.353724i	0.161341	−	0.986899i	$-0.448418\pi$
$853$	−17.8937	−	10.3309i	−0.612667	−	0.353724i	−0.774009	+	0.633175i	$0.781751\pi$
$854$	−2.45188	−	3.56479i	−0.0839016	−	0.121984i
$855$	17.0825	+	7.20069i	0.584209	+	0.246258i
$856$	−4.70926	−	19.5236i	−0.160959	−	0.667302i
$857$	4.09249	+	2.36280i	0.139797	+	0.0807117i	0.568267	−	0.822844i	$-0.307614\pi$
$857$	4.09249	+	2.36280i	0.139797	+	0.0807117i	−0.428470	+	0.903556i	$0.640947\pi$
$858$	−22.8030	+	9.72260i	−0.778483	+	0.331924i
$859$	15.9791	+	27.6766i	0.545200	+	0.944314i	0.998594	+	0.0530038i	$0.0168795\pi$
$859$	15.9791	+	27.6766i	0.545200	+	0.944314i	−0.453395	+	0.891310i	$0.649787\pi$
$860$	46.2206	−	7.35437i	1.57611	−	0.250782i
$861$	−16.3284	+	5.48612i	−0.556469	+	0.186967i
$862$	1.26753	−	0.100211i	0.0431724	−	0.00341321i
$863$	9.75500			0.332064			0.166032	−	0.986120i	$-0.446905\pi$
$863$	9.75500			0.332064			0.166032	+	0.986120i	$0.446905\pi$
$864$	5.95213	−	28.7849i	0.202496	−	0.979283i
$865$	33.5782			1.14169
$866$	9.93073	−	0.785123i	0.337460	−	0.0266796i
$867$	26.9875	−	9.06745i	0.916543	−	0.307947i
$868$	10.0432	−	1.59802i	0.340890	−	0.0542404i
$869$	0.440078	+	0.762238i	0.0149286	+	0.0258572i
$870$	−49.3005	+	21.0204i	−1.67144	+	0.712658i
$871$	5.75442	+	3.32232i	0.194981	+	0.112572i
$872$	8.67439	+	35.9622i	0.293752	+	1.21783i
$873$	−3.52871	−	28.1563i	−0.119429	−	0.952948i
$874$	2.14445	+	3.11782i	0.0725372	+	0.105462i
$875$	3.97608	+	2.29559i	0.134416	+	0.0776051i
$876$	10.8483	−	5.67435i	0.366529	−	0.191719i
$877$	−6.13588	+	3.54255i	−0.207194	+	0.119624i	−0.600007	−	0.799995i	$-0.704835\pi$
$877$	−6.13588	+	3.54255i	−0.207194	+	0.119624i	0.392813	+	0.919619i	$0.371502\pi$
$878$	−15.1441	−	7.21676i	−0.511090	−	0.243554i
$879$	23.3447	+	20.6016i	0.787397	+	0.694876i
$880$	13.1934	+	40.4093i	0.444750	+	1.36220i
$881$		−	14.0425i		−	0.473102i	−0.971619	−	0.236551i	$-0.923983\pi$
$881$		−	14.0425i		−	0.473102i	0.971619	−	0.236551i	$-0.0760171\pi$
$882$	−4.02723	−	1.33470i	−0.135604	−	0.0449418i
$883$	39.5019			1.32934			0.664672	−	0.747135i	$-0.268571\pi$
$883$	39.5019			1.32934			0.664672	+	0.747135i	$0.268571\pi$
$884$	20.1262	+	24.8177i	0.676919	+	0.834709i
$885$	−57.2607	−	11.5752i	−1.92480	−	0.389097i
$886$	10.2061	+	4.86359i	0.342880	+	0.163396i
$887$	5.35649	+	9.27771i	0.179853	+	0.311515i	0.941830	−	0.336089i	$-0.109104\pi$
$887$	5.35649	+	9.27771i	0.179853	+	0.311515i	−0.761977	+	0.647604i	$0.775771\pi$
$888$	20.7505	+	33.0371i	0.696343	+	1.10865i
$889$	2.19327	−	3.79885i	0.0735598	−	0.127409i
$890$	−47.0686	+	32.3740i	−1.57774	+	1.08518i
$891$	−23.5988	+	23.0185i	−0.790591	+	0.771149i
$892$	−33.0511	−	12.6601i	−1.10663	−	0.423893i
$893$	−1.03033	+	1.78459i	−0.0344788	+	0.0597191i
$894$	14.1242	+	10.6078i	0.472385	+	0.354779i
$895$	48.2830	−	27.8762i	1.61392	−	0.931798i
$896$	11.3091	−	0.324343i	0.377809	−	0.0108355i
$897$	−5.89285	−	1.19124i	−0.196756	−	0.0397742i
$898$	2.32235	+	29.3746i	0.0774979	+	0.980242i
$899$			38.3465i			1.27893i
$900$	5.71535	+	19.6927i	0.190512	+	0.656422i
$901$		−	26.7445i		−	0.890990i
$902$	−51.3563	+	4.06022i	−1.70998	+	0.135191i
$903$	−9.24384	+	10.4746i	−0.307616	+	0.348574i
$904$	−36.5227	+	34.7330i	−1.21473	+	1.15520i
$905$	42.5373	−	24.5589i	1.41399	−	0.816367i
$906$	−8.33513	−	1.00983i	−0.276916	−	0.0335493i
$907$	−17.8179	+	30.8615i	−0.591633	+	1.02474i	0.402380	+	0.915473i	$0.368183\pi$
$907$	−17.8179	+	30.8615i	−0.591633	+	1.02474i	−0.994013	+	0.109265i	$0.965150\pi$
$908$	−9.03560	−	3.46106i	−0.299857	−	0.114859i
$909$	1.54346	+	12.3156i	0.0511932	+	0.408482i
$910$	−6.42429	−	9.34027i	−0.212963	−	0.309627i
$911$	−20.2077	+	35.0008i	−0.669512	+	1.15963i	0.308529	+	0.951215i	$0.400163\pi$
$911$	−20.2077	+	35.0008i	−0.669512	+	1.15963i	−0.978041	+	0.208414i	$0.933170\pi$
$912$	11.8383	−	8.80898i	0.392005	−	0.291694i
$913$	−12.8092	−	22.1862i	−0.423923	−	0.734256i
$914$	−19.1518	+	40.1894i	−0.633485	+	1.32935i
$915$	−4.89645	−	14.5733i	−0.161872	−	0.481779i
$916$	−14.8376	+	12.0328i	−0.490249	+	0.397574i
$917$	−20.8492			−0.688500
$918$	36.8865	+	21.0948i	1.21744	+	0.696232i
$919$			18.3111i			0.604029i	0.953303	+	0.302014i	$0.0976590\pi$
$919$			18.3111i			0.604029i	−0.953303	+	0.302014i	$0.902341\pi$
$920$	−2.91748	+	9.88801i	−0.0961864	+	0.325998i
$921$	36.8065	−	12.3665i	1.21282	−	0.407491i
$922$	15.2880	−	32.0813i	0.503483	−	1.05654i
$923$	37.0423	−	21.3864i	1.21926	−	0.703942i
$924$	−10.7148	−	6.79656i	−0.352492	−	0.223591i
$925$	−23.5695	−	13.6079i	−0.774962	−	0.447424i
$926$	36.3627	−	25.0104i	1.19495	−	0.821894i
$927$	−12.2514	+	29.0646i	−0.402390	+	0.954607i
$928$	−5.49305	+	42.3056i	−0.180318	+	1.38875i
$929$	11.4630	+	6.61819i	0.376090	+	0.217136i	0.676116	−	0.736795i	$-0.263662\pi$
$929$	11.4630	+	6.61819i	0.376090	+	0.217136i	−0.300026	+	0.953931i	$0.596995\pi$
$930$	35.8738	+	4.34623i	1.17635	+	0.142518i
$931$	−1.06493	−	1.84452i	−0.0349017	−	0.0604515i
$932$	0.680046	+	4.27395i	0.0222757	+	0.139998i
$933$	31.5689	+	27.8594i	1.03352	+	0.912077i
$934$	1.76558	+	22.3322i	0.0577716	+	0.730731i
$935$	−61.4513			−2.00967
$936$	−3.78678	+	23.1361i	−0.123775	+	0.756227i
$937$	47.0514			1.53710			0.768552	−	0.639788i	$-0.220978\pi$
$937$	47.0514			1.53710			0.768552	+	0.639788i	$0.220978\pi$
$938$	0.268056	+	3.39054i	0.00875233	+	0.110705i
$939$	7.33412	−	36.2807i	0.239340	−	1.18397i
$940$	−5.54434	+	0.882185i	−0.180837	+	0.0287737i
$941$	−15.1746	−	26.2832i	−0.494678	−	0.856808i	0.505303	−	0.862942i	$-0.331381\pi$
$941$	−15.1746	−	26.2832i	−0.494678	−	0.856808i	−0.999981	+	0.00613411i	$0.998047\pi$
$942$	−7.52591	+	10.0207i	−0.245207	+	0.326492i
$943$	−10.8202	−	6.24705i	−0.352355	−	0.203432i
$944$	−31.0659	+	34.6011i	−1.01111	+	1.12617i
$945$	−12.4562	−	8.49222i	−0.405199	−	0.276252i
$946$	−34.4245	+	23.6774i	−1.11924	+	0.769818i
$947$	−45.5485	−	26.2975i	−1.48013	−	0.854553i	−0.480382	−	0.877060i	$-0.659502\pi$
$947$	−45.5485	−	26.2975i	−1.48013	−	0.854553i	−0.999747	+	0.0225070i	$0.992835\pi$
$948$	0.831668	+	0.0346756i	0.0270113	+	0.00112621i
$949$	−8.45632	+	4.88226i	−0.274504	+	0.158485i
$950$	−4.42834	+	9.29272i	−0.143674	+	0.301496i
$951$	−1.87950	+	9.29757i	−0.0609470	+	0.301494i
$952$	−4.62842	+	15.6868i	−0.150008	+	0.508412i
$953$			18.5827i			0.601953i	0.953632	+	0.300976i	$0.0973126\pi$
$953$			18.5827i			0.601953i	−0.953632	+	0.300976i	$0.902687\pi$
$954$	14.6592	−	13.0443i	0.474610	−	0.422324i
$955$	31.8220			1.02974
$956$	−27.3015	−	33.6655i	−0.882992	−	1.08882i
$957$	31.6583	−	35.8735i	1.02337	−	1.15963i
$958$	−4.29436	+	9.01157i	−0.138744	+	0.291151i
$959$	4.31272	+	7.46985i	0.139265	+	0.241214i
$960$	38.9550	+	9.93378i	1.25727	+	0.320611i
$961$	−2.57248	+	4.45566i	−0.0829831	+	0.143731i
$962$	−17.6335	−	25.6374i	−0.568527	−	0.826582i
$963$	12.8623	+	16.9802i	0.414481	+	0.547180i
$964$	3.44802	−	9.00156i	0.111053	−	0.289921i
$965$	36.0141	−	62.3782i	1.15933	−	2.00803i
$966$	−1.20696	−	2.83075i	−0.0388332	−	0.0910780i
$967$	−20.6404	+	11.9167i	−0.663750	+	0.383216i	−0.793704	−	0.608304i	$-0.791850\pi$
$967$	−20.6404	+	11.9167i	−0.663750	+	0.383216i	0.129954	+	0.991520i	$0.458517\pi$
$968$	−4.71060	−	4.95333i	−0.151404	−	0.159206i
$969$	6.79398	+	20.2209i	0.218254	+	0.649590i
$970$	38.6896	−	3.05879i	1.24225	−	0.0982120i
$971$		−	33.7376i		−	1.08269i	−0.840800	−	0.541345i	$-0.817915\pi$
$971$		−	33.7376i		−	1.08269i	0.840800	−	0.541345i	$-0.182085\pi$
$972$	6.42842	+	30.5070i	0.206192	+	0.978512i
$973$			10.7280i			0.343925i
$974$	3.82809	+	48.4201i	0.122660	+	1.55148i
$975$	−5.20879	−	15.5029i	−0.166815	−	0.496491i
$976$	−11.9736	−	2.52726i	−0.383267	−	0.0808957i
$977$	33.6017	−	19.4000i	1.07501	−	0.620660i	0.145467	−	0.989363i	$-0.453532\pi$
$977$	33.6017	−	19.4000i	1.07501	−	0.620660i	0.929547	+	0.368703i	$0.120198\pi$
$978$	−17.3553	+	7.39984i	−0.554962	+	0.236621i
$979$	25.4994	−	44.1662i	0.814964	−	1.41156i
$980$	2.07561	−	5.41867i	0.0663029	−	0.173093i
$981$	−23.6921	−	31.2773i	−0.756431	−	0.998608i
$982$	27.4589	−	18.8864i	0.876248	−	0.602688i
$983$	23.4560	−	40.6270i	0.748131	−	1.29580i	−0.200587	−	0.979676i	$-0.564285\pi$
$983$	23.4560	−	40.6270i	0.748131	−	1.29580i	0.948718	−	0.316125i	$-0.102382\pi$
$984$	−22.7731	+	43.0708i	−0.725981	+	1.37305i
$985$	37.3918	+	64.7645i	1.19140	+	2.06357i
$986$	−55.6731	−	26.5304i	−1.77299	−	0.844899i
$987$	1.10883	−	1.25647i	0.0352946	−	0.0399940i
$988$	−9.14109	+	7.41309i	−0.290817	+	0.235842i
$989$	−10.1330			−0.322212
$990$	−29.9720	−	33.6827i	−0.952574	−	1.07051i
$991$		−	0.969562i		−	0.0307992i	−0.999881	−	0.0153996i	$-0.995098\pi$
$991$		−	0.969562i		−	0.0307992i	0.999881	−	0.0153996i	$-0.00490203\pi$
$992$	17.4697	−	22.8511i	0.554663	−	0.725522i
$993$	−0.557578	+	2.75825i	−0.0176942	+	0.0875303i
$994$	19.7643	+	9.41843i	0.626884	+	0.298734i
$995$	−39.8066	+	22.9823i	−1.26195	+	0.728589i
$996$	−24.2071	−	1.00929i	−0.767031	−	0.0319806i
$997$	−35.6790	−	20.5993i	−1.12997	−	0.652386i	−0.186040	−	0.982542i	$-0.559565\pi$
$997$	−35.6790	−	20.5993i	−1.12997	−	0.652386i	−0.943926	+	0.330156i	$0.892899\pi$
$998$	−6.68435	−	9.71838i	−0.211589	−	0.307630i
$999$	−34.1899	−	23.3096i	−1.08172	−	0.737483i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.br.a.155.4	✓	144
8.3	odd	2	inner	504.2.br.a.155.28	yes	144
9.5	odd	6	inner	504.2.br.a.491.28	yes	144
72.59	even	6	inner	504.2.br.a.491.4	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.br.a.155.4	✓	144	1.1	even	1	trivial
504.2.br.a.155.28	yes	144	8.3	odd	2	inner
504.2.br.a.491.4	yes	144	72.59	even	6	inner
504.2.br.a.491.28	yes	144	9.5	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.br (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40981 + 0.111460i) q^{2} +(-1.64186 + 0.551643i) q^{3} +(1.97515 - 0.314275i) q^{4} +(-1.45065 - 2.51260i) q^{5} +(2.25323 - 0.960715i) q^{6} +(-0.866025 - 0.500000i) q^{7} +(-2.74957 + 0.663220i) q^{8} +(2.39138 - 1.81144i) q^{9} +O(q^{10})\)	\(q+(-1.40981 + 0.111460i) q^{2} +(-1.64186 + 0.551643i) q^{3} +(1.97515 - 0.314275i) q^{4} +(-1.45065 - 2.51260i) q^{5} +(2.25323 - 0.960715i) q^{6} +(-0.866025 - 0.500000i) q^{7} +(-2.74957 + 0.663220i) q^{8} +(2.39138 - 1.81144i) q^{9} +(2.32520 + 3.38061i) q^{10} +(-3.17215 - 1.83144i) q^{11} +(-3.06955 + 1.60557i) q^{12} +(2.39274 - 1.38145i) q^{13} +(1.27667 + 0.608380i) q^{14} +(3.76782 + 3.32509i) q^{15} +(3.80246 - 1.24148i) q^{16} +5.78249i q^{17} +(-3.16950 + 2.82033i) q^{18} -2.12986 q^{19} +(-3.65491 - 4.50687i) q^{20} +(1.69771 + 0.343191i) q^{21} +(4.67628 + 2.22843i) q^{22} +(0.628156 + 1.08800i) q^{23} +(4.14854 - 2.60569i) q^{24} +(-1.70877 + 2.95968i) q^{25} +(-3.21934 + 2.21428i) q^{26} +(-2.92704 + 4.29330i) q^{27} +(-1.86767 - 0.715406i) q^{28} +(3.77071 - 6.53107i) q^{29} +(-5.68253 - 4.26779i) q^{30} +(-4.40355 + 2.54239i) q^{31} +(-5.22239 + 2.17408i) q^{32} +(6.21852 + 1.25707i) q^{33} +(-0.644515 - 8.15224i) q^{34} +2.90130i q^{35} +(4.15405 - 4.32941i) q^{36} +7.96354i q^{37} +(3.00271 - 0.237394i) q^{38} +(-3.16646 + 3.58807i) q^{39} +(5.65507 + 5.94647i) q^{40} +(-8.61268 + 4.97253i) q^{41} +(-2.43171 - 0.294610i) q^{42} +(-4.03285 + 6.98510i) q^{43} +(-6.84107 - 2.62045i) q^{44} +(-8.02047 - 3.38082i) q^{45} +(-1.00685 - 1.46386i) q^{46} +(0.483756 - 0.837890i) q^{47} +(-5.55824 + 4.13594i) q^{48} +(0.500000 + 0.866025i) q^{49} +(2.07917 - 4.36306i) q^{50} +(-3.18987 - 9.49401i) q^{51} +(4.29187 - 3.48055i) q^{52} -4.62509 q^{53} +(3.64805 - 6.37901i) q^{54} +10.6271i q^{55} +(2.71281 + 0.800420i) q^{56} +(3.49693 - 1.17492i) q^{57} +(-4.58806 + 9.62788i) q^{58} +(-10.0677 + 5.81260i) q^{59} +(8.48701 + 5.38342i) q^{60} +(-2.64949 - 1.52968i) q^{61} +(5.92482 - 4.07512i) q^{62} +(-2.97671 + 0.373059i) q^{63} +(7.12028 - 3.64714i) q^{64} +(-6.94205 - 4.00800i) q^{65} +(-8.90707 - 1.07912i) q^{66} +(1.20248 + 2.08275i) q^{67} +(1.81729 + 11.4213i) q^{68} +(-1.63153 - 1.43982i) q^{69} +(-0.323379 - 4.09030i) q^{70} +15.4812 q^{71} +(-5.37389 + 6.56668i) q^{72} -3.53416 q^{73} +(-0.887615 - 11.2271i) q^{74} +(1.17287 - 5.80200i) q^{75} +(-4.20681 + 0.669363i) q^{76} +(1.83144 + 3.17215i) q^{77} +(4.06420 - 5.41145i) q^{78} +(-0.208098 - 0.120145i) q^{79} +(-8.63540 - 7.75311i) q^{80} +(2.43740 - 8.66366i) q^{81} +(11.5880 - 7.97032i) q^{82} +(6.05703 + 3.49703i) q^{83} +(3.46109 + 0.144307i) q^{84} +(14.5291 - 8.38837i) q^{85} +(4.90701 - 10.2972i) q^{86} +(-2.58815 + 12.8032i) q^{87} +(9.93671 + 2.93185i) q^{88} +13.9231i q^{89} +(11.6842 + 3.87237i) q^{90} -2.76290 q^{91} +(1.58263 + 1.95155i) q^{92} +(5.82751 - 6.60343i) q^{93} +(-0.588615 + 1.23519i) q^{94} +(3.08969 + 5.35149i) q^{95} +(7.37509 - 6.45043i) q^{96} +(4.72943 - 8.19162i) q^{97} +(-0.801434 - 1.16521i) q^{98} +(-10.9034 + 1.36647i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 6 q^{6}+O(q^{10}) \) 144 * q + 6 * q^6	\( 144 q + 6 q^{6} - 12 q^{12} + 34 q^{18} - 42 q^{20} - 30 q^{24} - 72 q^{25} + 24 q^{27} - 36 q^{30} - 30 q^{32} - 16 q^{33} + 12 q^{34} - 12 q^{36} + 12 q^{40} + 24 q^{41} - 20 q^{42} - 24 q^{46} - 24 q^{48} + 72 q^{49} - 78 q^{50} + 18 q^{52} + 10 q^{54} + 8 q^{57} - 18 q^{58} - 72 q^{59} + 88 q^{60} - 12 q^{64} + 2 q^{66} + 78 q^{68} + 42 q^{72} + 84 q^{74} - 112 q^{75} + 12 q^{76} + 112 q^{78} - 8 q^{81} - 36 q^{82} - 14 q^{84} + 30 q^{86} + 24 q^{88} + 104 q^{90} - 114 q^{92} - 42 q^{94} - 80 q^{96} - 64 q^{99}+O(q^{100}) \) 144 * q + 6 * q^6 - 12 * q^12 + 34 * q^18 - 42 * q^20 - 30 * q^24 - 72 * q^25 + 24 * q^27 - 36 * q^30 - 30 * q^32 - 16 * q^33 + 12 * q^34 - 12 * q^36 + 12 * q^40 + 24 * q^41 - 20 * q^42 - 24 * q^46 - 24 * q^48 + 72 * q^49 - 78 * q^50 + 18 * q^52 + 10 * q^54 + 8 * q^57 - 18 * q^58 - 72 * q^59 + 88 * q^60 - 12 * q^64 + 2 * q^66 + 78 * q^68 + 42 * q^72 + 84 * q^74 - 112 * q^75 + 12 * q^76 + 112 * q^78 - 8 * q^81 - 36 * q^82 - 14 * q^84 + 30 * q^86 + 24 * q^88 + 104 * q^90 - 114 * q^92 - 42 * q^94 - 80 * q^96 - 64 * q^99

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