LMFDB - Embedded newform 804.2.l.a.431.132

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(431,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 4]))

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

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

chi := DirichletCharacter("804.431");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.l (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:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$264$
Relative dimension:	$132$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			431.132
Character	$\chi$	$=$	804.431
Dual form			804.2.l.a.707.132

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.41407 + 0.0202093i) q^{2} +(1.20523 - 1.24395i) q^{3} +(1.99918 + 0.0571548i) q^{4} +3.26426i q^{5} +(1.72942 - 1.73468i) q^{6} +(-0.138760 + 0.0801133i) q^{7} +(2.82583 + 0.121223i) q^{8} +(-0.0948278 - 2.99850i) q^{9} +O(q^{10})$	\(q+(1.41407 + 0.0202093i) q^{2} +(1.20523 - 1.24395i) q^{3} +(1.99918 + 0.0571548i) q^{4} +3.26426i q^{5} +(1.72942 - 1.73468i) q^{6} +(-0.138760 + 0.0801133i) q^{7} +(2.82583 + 0.121223i) q^{8} +(-0.0948278 - 2.99850i) q^{9} +(-0.0659686 + 4.61589i) q^{10} +(2.28979 + 3.96603i) q^{11} +(2.48058 - 2.41800i) q^{12} +(-1.92708 + 3.33780i) q^{13} +(-0.197836 + 0.110482i) q^{14} +(4.06058 + 3.93420i) q^{15} +(3.99347 + 0.228526i) q^{16} +(-1.69868 - 0.980734i) q^{17} +(-0.0734954 - 4.24200i) q^{18} +(-5.13295 - 2.96351i) q^{19} +(-0.186568 + 6.52586i) q^{20} +(-0.0675815 + 0.269166i) q^{21} +(3.15777 + 5.65451i) q^{22} +(3.13953 - 5.43782i) q^{23} +(3.55658 - 3.36909i) q^{24} -5.65541 q^{25} +(-2.79248 + 4.68093i) q^{26} +(-3.84428 - 3.49593i) q^{27} +(-0.281986 + 0.152230i) q^{28} +(3.51351 - 2.02853i) q^{29} +(5.66244 + 5.64529i) q^{30} +(-0.634737 + 0.366466i) q^{31} +(5.64242 + 0.403856i) q^{32} +(7.69327 + 1.93160i) q^{33} +(-2.38223 - 1.42115i) q^{34} +(-0.261511 - 0.452950i) q^{35} +(-0.0181995 - 5.99997i) q^{36} +(5.86348 - 10.1559i) q^{37} +(-7.19846 - 4.29435i) q^{38} +(1.82948 + 6.42002i) q^{39} +(-0.395704 + 9.22424i) q^{40} +(-9.85112 + 5.68755i) q^{41} +(-0.101005 + 0.379254i) q^{42} -4.58428i q^{43} +(4.35103 + 8.05969i) q^{44} +(9.78789 - 0.309543i) q^{45} +(4.54941 - 7.62601i) q^{46} +(-4.06328 - 7.03780i) q^{47} +(5.09733 - 4.69225i) q^{48} +(-3.48716 + 6.03994i) q^{49} +(-7.99714 - 0.114292i) q^{50} +(-3.26729 + 0.931063i) q^{51} +(-4.04336 + 6.56273i) q^{52} -11.1601i q^{53} +(-5.36542 - 5.02118i) q^{54} +(-12.9462 + 7.47446i) q^{55} +(-0.401825 + 0.209566i) q^{56} +(-9.87287 + 2.81342i) q^{57} +(5.00935 - 2.79747i) q^{58} +13.8883 q^{59} +(7.89299 + 8.09726i) q^{60} +(-2.34882 + 4.06828i) q^{61} +(-0.904968 + 0.505380i) q^{62} +(0.253378 + 0.408476i) q^{63} +(7.97061 + 0.685111i) q^{64} +(-10.8955 - 6.29049i) q^{65} +(10.8398 + 2.88690i) q^{66} +(-3.19984 + 7.53399i) q^{67} +(-3.33992 - 2.05775i) q^{68} +(-2.98052 - 10.4593i) q^{69} +(-0.360641 - 0.645788i) q^{70} +(2.11856 + 3.66945i) q^{71} +(0.0955200 - 8.48474i) q^{72} +(-1.25134 + 2.16739i) q^{73} +(8.49662 - 14.2426i) q^{74} +(-6.81608 + 7.03505i) q^{75} +(-10.0923 - 6.21798i) q^{76} +(-0.635463 - 0.366885i) q^{77} +(2.45727 + 9.11532i) q^{78} +(5.47250 - 3.15955i) q^{79} +(-0.745968 + 13.0357i) q^{80} +(-8.98202 + 0.568683i) q^{81} +(-14.0451 + 7.84350i) q^{82} +(4.53373 - 7.85265i) q^{83} +(-0.150492 + 0.534250i) q^{84} +(3.20137 - 5.54494i) q^{85} +(0.0926453 - 6.48250i) q^{86} +(1.71121 - 6.81549i) q^{87} +(5.98977 + 11.4849i) q^{88} +1.13753i q^{89} +(13.8470 - 0.239908i) q^{90} -0.617539i q^{91} +(6.58729 - 10.6918i) q^{92} +(-0.309141 + 1.23126i) q^{93} +(-5.60352 - 10.0341i) q^{94} +(9.67368 - 16.7553i) q^{95} +(7.30281 - 6.53215i) q^{96} +(-4.43186 + 7.67620i) q^{97} +(-5.05315 + 8.47043i) q^{98} +(11.6750 - 7.24202i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 264 q - 2 q^{4} - 3 q^{6} - 12 q^{9}+O(q^{10}) $ 264 * q - 2 * q^4 - 3 * q^6 - 12 * q^9	$ 264 q - 2 q^{4} - 3 q^{6} - 12 q^{9} + 2 q^{10} + 2 q^{12} - 18 q^{16} + q^{18} - 4 q^{22} - 248 q^{25} + 7 q^{30} - 38 q^{34} + 13 q^{36} + 4 q^{37} + 48 q^{40} - 12 q^{42} + 48 q^{45} - 2 q^{46} - 11 q^{48} + 128 q^{49} + 32 q^{52} - 8 q^{54} - 2 q^{57} - 32 q^{58} + 68 q^{60} - 8 q^{61} + 4 q^{64} + 30 q^{66} - 40 q^{69} - 140 q^{70} + 108 q^{72} - 4 q^{73} - 120 q^{76} + 44 q^{78} - 28 q^{81} - 64 q^{82} + 33 q^{84} + 16 q^{85} - 14 q^{88} + 42 q^{90} + 16 q^{93} - 12 q^{94} - 4 q^{96} + 20 q^{97}+O(q^{100}) $ 264 * q - 2 * q^4 - 3 * q^6 - 12 * q^9 + 2 * q^10 + 2 * q^12 - 18 * q^16 + q^18 - 4 * q^22 - 248 * q^25 + 7 * q^30 - 38 * q^34 + 13 * q^36 + 4 * q^37 + 48 * q^40 - 12 * q^42 + 48 * q^45 - 2 * q^46 - 11 * q^48 + 128 * q^49 + 32 * q^52 - 8 * q^54 - 2 * q^57 - 32 * q^58 + 68 * q^60 - 8 * q^61 + 4 * q^64 + 30 * q^66 - 40 * q^69 - 140 * q^70 + 108 * q^72 - 4 * q^73 - 120 * q^76 + 44 * q^78 - 28 * q^81 - 64 * q^82 + 33 * q^84 + 16 * q^85 - 14 * q^88 + 42 * q^90 + 16 * q^93 - 12 * q^94 - 4 * q^96 + 20 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$	1.41407	+	0.0202093i	0.999898	+	0.0142902i
$2$	1.41407	+	0.0202093i	0.999898	+	0.0142902i
$3$	1.20523	−	1.24395i	0.695841	−	0.718195i
$3$	1.20523	−	1.24395i	0.695841	−	0.718195i
$4$	1.99918	+	0.0571548i	0.999592	+	0.0285774i
$5$			3.26426i			1.45982i	0.683542	+	0.729911i	$0.260439\pi$
$5$			3.26426i			1.45982i	−0.683542	+	0.729911i	$0.739561\pi$
$6$	1.72942	−	1.73468i	0.706034	−	0.708178i
$7$	−0.138760	+	0.0801133i	−0.0524465	+	0.0302800i	−0.525994	−	0.850488i	$-0.676307\pi$
$7$	−0.138760	+	0.0801133i	−0.0524465	+	0.0302800i	0.473547	+	0.880768i	$0.342973\pi$
$8$	2.82583	+	0.121223i	0.999081	+	0.0428588i
$9$	−0.0948278	−	2.99850i	−0.0316093	−	0.999500i
$10$	−0.0659686	+	4.61589i	−0.0208611	+	1.45967i
$11$	2.28979	+	3.96603i	0.690397	+	1.19580i	0.971708	+	0.236185i	$0.0758973\pi$
$11$	2.28979	+	3.96603i	0.690397	+	1.19580i	−0.281311	+	0.959617i	$0.590769\pi$
$12$	2.48058	−	2.41800i	0.716081	−	0.698017i
$13$	−1.92708	+	3.33780i	−0.534476	+	0.925739i	0.464713	+	0.885461i	$0.346158\pi$
$13$	−1.92708	+	3.33780i	−0.534476	+	0.925739i	−0.999189	+	0.0402777i	$0.987176\pi$
$14$	−0.197836	+	0.110482i	−0.0528738	+	0.0295274i
$15$	4.06058	+	3.93420i	1.04844	+	1.01581i
$16$	3.99347	+	0.228526i	0.998367	+	0.0571314i
$17$	−1.69868	−	0.980734i	−0.411991	−	0.237863i	0.279654	−	0.960101i	$-0.409780\pi$
$17$	−1.69868	−	0.980734i	−0.411991	−	0.237863i	−0.691645	+	0.722238i	$0.743114\pi$
$18$	−0.0734954	−	4.24200i	−0.0173230	−	0.999850i
$19$	−5.13295	−	2.96351i	−1.17758	−	0.679876i	−0.222127	−	0.975018i	$-0.571300\pi$
$19$	−5.13295	−	2.96351i	−1.17758	−	0.679876i	−0.955454	+	0.295141i	$0.904633\pi$
$20$	−0.186568	+	6.52586i	−0.0417179	+	1.45923i
$21$	−0.0675815	+	0.269166i	−0.0147475	+	0.0587369i
$22$	3.15777	+	5.65451i	0.673238	+	1.20555i
$23$	3.13953	−	5.43782i	0.654637	−	1.13386i	−0.327347	−	0.944904i	$-0.606155\pi$
$23$	3.13953	−	5.43782i	0.654637	−	1.13386i	0.981985	−	0.188961i	$-0.0605119\pi$
$24$	3.55658	−	3.36909i	0.725983	−	0.687713i
$25$	−5.65541			−1.13108
$26$	−2.79248	+	4.68093i	−0.547650	+	0.918007i
$27$	−3.84428	−	3.49593i	−0.739832	−	0.672792i
$28$	−0.281986	+	0.152230i	−0.0532904	+	0.0287688i
$29$	3.51351	−	2.02853i	0.652443	−	0.376688i	−0.136948	−	0.990578i	$-0.543729\pi$
$29$	3.51351	−	2.02853i	0.652443	−	0.376688i	0.789392	+	0.613890i	$0.210396\pi$
$30$	5.66244	+	5.64529i	1.03381	+	1.03068i
$31$	−0.634737	+	0.366466i	−0.114002	+	0.0658192i	−0.555917	−	0.831238i	$-0.687633\pi$
$31$	−0.634737	+	0.366466i	−0.114002	+	0.0658192i	0.441915	+	0.897057i	$0.354299\pi$
$32$	5.64242	+	0.403856i	0.997448	+	0.0713924i
$33$	7.69327	+	1.93160i	1.33923	+	0.336249i
$34$	−2.38223	−	1.42115i	−0.408549	−	0.243726i
$35$	−0.261511	−	0.452950i	−0.0442034	−	0.0765626i
$36$	−0.0181995	−	5.99997i	−0.00303325	−	0.999995i
$37$	5.86348	−	10.1559i	0.963951	−	1.66961i	0.251543	−	0.967846i	$-0.419062\pi$
$37$	5.86348	−	10.1559i	0.963951	−	1.66961i	0.712408	−	0.701766i	$-0.247605\pi$
$38$	−7.19846	−	4.29435i	−1.16774	−	0.696635i
$39$	1.82948	+	6.42002i	0.292951	+	1.02803i
$40$	−0.395704	+	9.22424i	−0.0625662	+	1.45848i
$41$	−9.85112	+	5.68755i	−1.53849	+	0.888246i	−0.539559	+	0.841948i	$0.681409\pi$
$41$	−9.85112	+	5.68755i	−1.53849	+	0.888246i	−0.998928	+	0.0462983i	$0.985258\pi$
$42$	−0.101005	+	0.379254i	−0.0155853	+	0.0585202i
$43$		−	4.58428i		−	0.699097i	−0.936918	−	0.349548i	$-0.886335\pi$
$43$		−	4.58428i		−	0.699097i	0.936918	−	0.349548i	$-0.113665\pi$
$44$	4.35103	+	8.05969i	0.655942	+	1.21504i
$45$	9.78789	−	0.309543i	1.45909	−	0.0461439i
$46$	4.54941	−	7.62601i	0.670773	−	1.12439i
$47$	−4.06328	−	7.03780i	−0.592690	−	1.02657i	−0.993868	−	0.110569i	$-0.964733\pi$
$47$	−4.06328	−	7.03780i	−0.592690	−	1.02657i	0.401179	−	0.916000i	$-0.368601\pi$
$48$	5.09733	−	4.69225i	0.735736	−	0.677268i
$49$	−3.48716	+	6.03994i	−0.498166	+	0.862849i
$50$	−7.99714	−	0.114292i	−1.13097	−	0.0161633i
$51$	−3.26729	+	0.931063i	−0.457512	+	0.130375i
$52$	−4.04336	+	6.56273i	−0.560713	+	0.910087i
$53$		−	11.1601i		−	1.53295i	−0.642273	−	0.766476i	$-0.722009\pi$
$53$		−	11.1601i		−	1.53295i	0.642273	−	0.766476i	$-0.277991\pi$
$54$	−5.36542	−	5.02118i	−0.730142	−	0.683296i
$55$	−12.9462	+	7.47446i	−1.74566	+	1.00786i
$56$	−0.401825	+	0.209566i	−0.0536961	+	0.0280044i
$57$	−9.87287	+	2.81342i	−1.30769	+	0.372647i
$58$	5.00935	−	2.79747i	0.657760	−	0.367326i
$59$	13.8883			1.80810			0.904052	−	0.427422i	$-0.140578\pi$
$59$	13.8883			1.80810			0.904052	+	0.427422i	$0.140578\pi$
$60$	7.89299	+	8.09726i	1.01898	+	1.04535i
$61$	−2.34882	+	4.06828i	−0.300736	+	0.520890i	−0.976303	−	0.216409i	$-0.930566\pi$
$61$	−2.34882	+	4.06828i	−0.300736	+	0.520890i	0.675567	+	0.737299i	$0.263899\pi$
$62$	−0.904968	+	0.505380i	−0.114931	+	0.0641834i
$63$	0.253378	+	0.408476i	0.0319227	+	0.0514632i
$64$	7.97061	+	0.685111i	0.996326	+	0.0856388i
$65$	−10.8955	−	6.29049i	−1.35141	−	0.780240i
$66$	10.8398	+	2.88690i	1.33428	+	0.355352i
$67$	−3.19984	+	7.53399i	−0.390922	+	0.920424i
$67$	−3.19984	+	7.53399i	−0.390922	+	0.920424i
$68$	−3.33992	−	2.05775i	−0.405025	−	0.249539i
$69$	−2.98052	−	10.4593i	−0.358813	−	1.25915i
$70$	−0.360641	−	0.645788i	−0.0431048	−	0.0771864i
$71$	2.11856	+	3.66945i	0.251427	+	0.435484i	0.963919	−	0.266196i	$-0.0857669\pi$
$71$	2.11856	+	3.66945i	0.251427	+	0.435484i	−0.712492	+	0.701680i	$0.752434\pi$
$72$	0.0955200	−	8.48474i	0.0112571	−	0.999937i
$73$	−1.25134	+	2.16739i	−0.146458	+	0.253674i	−0.929916	−	0.367772i	$-0.880121\pi$
$73$	−1.25134	+	2.16739i	−0.146458	+	0.253674i	0.783458	+	0.621445i	$0.213454\pi$
$74$	8.49662	−	14.2426i	0.987711	−	1.65567i
$75$	−6.81608	+	7.03505i	−0.787053	+	0.812338i
$76$	−10.0923	−	6.21798i	−1.15767	−	0.713251i
$77$	−0.635463	−	0.366885i	−0.0724178	−	0.0418104i
$78$	2.45727	+	9.11532i	0.278231	+	1.03211i
$79$	5.47250	−	3.15955i	0.615705	−	0.355477i	−0.159490	−	0.987200i	$-0.550985\pi$
$79$	5.47250	−	3.15955i	0.615705	−	0.355477i	0.775195	+	0.631722i	$0.217652\pi$
$80$	−0.745968	+	13.0357i	−0.0834018	+	1.45744i
$81$	−8.98202	+	0.568683i	−0.998002	+	0.0631870i
$82$	−14.0451	+	7.84350i	−1.55102	+	0.866170i
$83$	4.53373	−	7.85265i	0.497641	−	0.861940i	−0.502355	−	0.864662i	$-0.667533\pi$
$83$	4.53373	−	7.85265i	0.497641	−	0.861940i	0.999996	+	0.00272128i	$0.000866210\pi$
$84$	−0.150492	+	0.534250i	−0.0164200	+	0.0582915i
$85$	3.20137	−	5.54494i	0.347238	−	0.601433i
$86$	0.0926453	−	6.48250i	0.00999020	−	0.699025i
$87$	1.71121	−	6.81549i	0.183461	−	0.730697i
$88$	5.98977	+	11.4849i	0.638512	+	1.22429i
$89$			1.13753i			0.120578i	0.998181	+	0.0602891i	$0.0192023\pi$
$89$			1.13753i			0.120578i	−0.998181	+	0.0602891i	$0.980798\pi$
$90$	13.8470	−	0.239908i	1.45960	−	0.0252885i
$91$		−	0.617539i		−	0.0647357i
$92$	6.58729	−	10.6918i	0.686773	−	1.11469i
$93$	−0.309141	+	1.23126i	−0.0320564	+	0.127676i
$94$	−5.60352	−	10.0341i	−0.577959	−	1.03493i
$95$	9.67368	−	16.7553i	0.992499	−	1.71906i
$96$	7.30281	−	6.53215i	0.745340	−	0.666685i
$97$	−4.43186	+	7.67620i	−0.449987	+	0.779400i	−0.998385	−	0.0568176i	$-0.981905\pi$
$97$	−4.43186	+	7.67620i	−0.449987	+	0.779400i	0.548398	+	0.836218i	$0.315238\pi$
$98$	−5.05315	+	8.47043i	−0.510446	+	0.855642i
$99$	11.6750	−	7.24202i	1.17338	−	0.727850i
$100$	−11.3062	−	0.323234i	−1.13062	−	0.0323234i
$101$	1.30801	−	0.755181i	0.130152	−	0.0751433i	−0.433510	−	0.901149i	$-0.642725\pi$
$101$	1.30801	−	0.755181i	0.130152	−	0.0751433i	0.563662	+	0.826005i	$0.309392\pi$
$102$	−4.63899	+	1.25056i	−0.459328	+	0.123824i
$103$	−1.63137	+	0.941874i	−0.160744	+	0.0928056i	−0.578214	−	0.815885i	$-0.696250\pi$
$103$	−1.63137	+	0.941874i	−0.160744	+	0.0928056i	0.417470	+	0.908691i	$0.362917\pi$
$104$	−5.85021	+	9.19844i	−0.573661	+	0.901982i
$105$	−0.878629	−	0.220604i	−0.0857455	−	0.0215287i
$106$	0.225537	−	15.7811i	0.0219061	−	1.53279i
$107$	−14.1483			−1.36777			−0.683883	−	0.729592i	$-0.739710\pi$
$107$	−14.1483			−1.36777			−0.683883	+	0.729592i	$0.739710\pi$
$108$	−7.48561	−	7.20872i	−0.720303	−	0.693660i
$109$	−7.21391			−0.690968			−0.345484	−	0.938425i	$-0.612285\pi$
$109$	−7.21391			−0.690968			−0.345484	+	0.938425i	$0.612285\pi$
$110$	−18.4578	+	10.3078i	−1.75988	+	0.982808i
$111$	−5.56652	−	19.5341i	−0.528351	−	1.85409i
$112$	−0.572443	+	0.288220i	−0.0540908	+	0.0272342i
$113$	3.24018	−	1.87072i	0.304811	−	0.175983i	−0.339791	−	0.940501i	$-0.610356\pi$
$113$	3.24018	−	1.87072i	0.304811	−	0.175983i	0.644602	+	0.764518i	$0.277023\pi$
$114$	−14.0178	+	3.77885i	−1.31289	+	0.353922i
$115$	17.7505	+	10.2482i	1.65524	+	0.955654i
$116$	7.14010	−	3.85459i	0.662942	−	0.357889i
$117$	10.1911	+	5.46183i	0.942171	+	0.504947i
$118$	19.6390	+	0.280674i	1.80792	+	0.0258381i
$119$	0.314279			0.0288099
$120$	10.9976	+	11.6096i	1.00394	+	1.05981i
$121$	−4.98624	+	8.63643i	−0.453295	+	0.785130i
$122$	−3.40361	+	5.70536i	−0.308149	+	0.516539i
$123$	−4.79787	+	19.1091i	−0.432609	+	1.72301i
$124$	−1.28990	+	0.696354i	−0.115837	+	0.0625344i
$125$		−	2.13942i		−	0.191356i
$126$	0.350039	+	0.582734i	0.0311840	+	0.0519141i
$127$	1.59521	−	0.920997i	0.141552	−	0.0817253i	−0.427551	−	0.903991i	$-0.640624\pi$
$127$	1.59521	−	0.920997i	0.141552	−	0.0817253i	0.569104	+	0.822266i	$0.307290\pi$
$128$	11.2571	+	1.12987i	0.995001	+	0.0998677i
$129$	−5.70263	−	5.52513i	−0.502088	−	0.486461i
$130$	−15.2798	−	9.11538i	−1.34013	−	0.799472i
$131$	−7.05785			−0.616648			−0.308324	−	0.951281i	$-0.599768\pi$
$131$	−7.05785			−0.616648			−0.308324	+	0.951281i	$0.599768\pi$
$132$	15.2699	+	4.30134i	1.32907	+	0.374383i
$133$	0.949668			0.0823466
$134$	−4.67705	+	10.5889i	−0.404035	+	0.914743i
$135$	11.4116	−	12.5487i	0.982157	−	1.08002i
$136$	−4.68129	−	2.97730i	−0.401417	−	0.255302i
$137$			13.9091i			1.18833i	0.804343	+	0.594165i	$0.202518\pi$
$137$			13.9091i			1.18833i	−0.804343	+	0.594165i	$0.797482\pi$
$138$	−4.00329	−	14.8504i	−0.340783	−	1.26415i
$139$		−	3.77237i		−	0.319968i	−0.987120	−	0.159984i	$-0.948856\pi$
$139$		−	3.77237i		−	0.319968i	0.987120	−	0.159984i	$-0.0511443\pi$
$140$	−0.496920	−	0.920477i	−0.0419974	−	0.0777945i
$141$	−13.6519	−	3.42767i	−1.14970	−	0.288662i
$142$	2.92163	+	5.23168i	0.245178	+	0.439032i
$143$	−17.6504			−1.47600
$144$	0.306543	−	11.9961i	0.0255452	−	0.999674i
$145$	6.62165	+	11.4690i	0.549898	+	0.952451i
$146$	−1.81329	+	3.03955i	−0.150069	+	0.251555i
$147$	3.31055	+	11.6174i	0.273050	+	0.958187i
$148$	12.3026	−	19.9683i	1.01127	−	1.64138i
$149$			16.1239i			1.32092i	0.750860	+	0.660462i	$0.229639\pi$
$149$			16.1239i			1.32092i	−0.750860	+	0.660462i	$0.770361\pi$
$150$	−9.78059	+	9.81030i	−0.798582	+	0.801008i
$151$	5.71430	+	3.29916i	0.465023	+	0.268481i	0.714154	−	0.699988i	$-0.246812\pi$
$151$	5.71430	+	3.29916i	0.465023	+	0.268481i	−0.249131	+	0.968470i	$0.580145\pi$
$152$	−14.1456	−	8.99661i	−1.14736	−	0.729721i
$153$	−2.77965	+	5.18650i	−0.224721	+	0.419303i
$154$	−0.891175	−	0.531643i	−0.0718129	−	0.0428410i
$155$	−1.19624	−	2.07195i	−0.0960843	−	0.166423i
$156$	3.29053	+	12.9394i	0.263453	+	1.03598i
$157$	−7.63357	+	13.2217i	−0.609225	+	1.05521i	0.382143	+	0.924103i	$0.375186\pi$
$157$	−7.63357	+	13.2217i	−0.609225	+	1.05521i	−0.991368	+	0.131106i	$0.958147\pi$
$158$	7.80235	−	4.35723i	0.620722	−	0.346642i
$159$	−13.8826	−	13.4505i	−1.10096	−	1.06669i
$160$	−1.31829	+	18.4183i	−0.104220	+	1.45610i
$161$			1.00607i			0.0792896i
$162$	−12.7127	+	0.622636i	−0.998803	+	0.0489189i
$163$	−7.08423	+	4.09008i	−0.554880	+	0.320360i	−0.751088	−	0.660202i	$-0.770471\pi$
$163$	−7.08423	+	4.09008i	−0.554880	+	0.320360i	0.196208	+	0.980562i	$0.437137\pi$
$164$	−20.0193	+	10.8074i	−1.56324	+	0.843917i
$165$	−6.30526	+	25.1128i	−0.490864	+	1.95503i
$166$	6.56970	−	11.0126i	0.509908	−	0.854741i
$167$	2.79975	+	4.84931i	0.216651	+	0.375251i	0.953782	−	0.300499i	$-0.0971532\pi$
$167$	2.79975	+	4.84931i	0.216651	+	0.375251i	−0.737131	+	0.675750i	$0.763820\pi$
$168$	−0.223603	+	0.752425i	−0.0172513	+	0.0580509i
$169$	−0.927272	−	1.60608i	−0.0713286	−	0.123545i
$170$	4.63902	−	7.77623i	0.355797	−	0.596410i
$171$	−8.39935	+	15.6722i	−0.642314	+	1.19848i
$172$	0.262014	−	9.16482i	0.0199784	−	0.698811i
$173$	10.1245	+	5.84541i	0.769755	+	0.444418i	0.832787	−	0.553593i	$-0.186744\pi$
$173$	10.1245	+	5.84541i	0.769755	+	0.444418i	−0.0630324	+	0.998011i	$0.520077\pi$
$174$	2.55751	−	9.60299i	0.193884	−	0.728001i
$175$	0.784747	−	0.453074i	0.0593213	−	0.0342491i
$176$	8.23785	+	16.3615i	0.620951	+	1.23329i
$177$	16.7387	−	17.2764i	1.25815	−	1.29857i
$178$	−0.0229888	+	1.60855i	−0.00172308	+	0.120566i
$179$	5.40113			0.403699			0.201850	−	0.979417i	$-0.435305\pi$
$179$	5.40113			0.403699			0.201850	+	0.979417i	$0.435305\pi$
$180$	19.5855	−	0.0594080i	1.45982	−	0.00442801i
$181$	−6.68719	−	11.5825i	−0.497055	−	0.860924i	0.502940	−	0.864322i	$-0.332252\pi$
$181$	−6.68719	−	11.5825i	−0.497055	−	0.860924i	−0.999994	+	0.00339770i	$0.998918\pi$
$182$	0.0124801	−	0.873243i	0.000925083	−	0.0647291i
$183$	2.22986	+	7.82504i	0.164836	+	0.578444i
$184$	9.53096	−	14.9858i	0.702632	−	1.10477i
$185$	33.1514	+	19.1400i	2.43734	+	1.40720i
$186$	−0.462029	+	1.73484i	−0.0338776	+	0.127204i
$187$		−	8.98268i		−	0.656879i
$188$	−7.72099	−	14.3021i	−0.563111	−	1.04309i
$189$	0.813504	+	0.177119i	0.0591737	+	0.0128835i
$190$	14.0179	−	23.4977i	1.01696	−	1.70470i
$191$	−4.04451	+	7.00529i	−0.292650	+	0.506885i	−0.974436	−	0.224667i	$-0.927870\pi$
$191$	−4.04451	+	7.00529i	−0.292650	+	0.506885i	0.681785	+	0.731552i	$0.261204\pi$
$192$	10.4587	−	9.08933i	0.754791	−	0.655966i
$193$	−15.7773			−1.13568			−0.567838	−	0.823140i	$-0.692220\pi$
$193$	−15.7773			−1.13568			−0.567838	+	0.823140i	$0.692220\pi$
$194$	−6.42208	+	10.7651i	−0.461079	+	0.772890i
$195$	−20.9566	+	5.97190i	−1.50073	+	0.427657i
$196$	−7.31669	+	11.8756i	−0.522621	+	0.848261i
$197$	4.23128	−	2.44293i	0.301466	−	0.174051i	−0.341635	−	0.939833i	$-0.610981\pi$
$197$	4.23128	−	2.44293i	0.301466	−	0.174051i	0.643101	+	0.765781i	$0.277647\pi$
$198$	16.6556	−	10.0048i	1.18366	−	0.711008i
$199$	6.00532	+	3.46717i	0.425706	+	0.245781i	0.697516	−	0.716570i	$-0.254289\pi$
$199$	6.00532	+	3.46717i	0.425706	+	0.245781i	−0.271810	+	0.962351i	$0.587622\pi$
$200$	−15.9812	−	0.685565i	−1.13004	−	0.0484768i
$201$	5.51537	+	13.0607i	0.389024	+	0.921228i
$202$	1.86488	−	1.04144i	0.131212	−	0.0732757i
$203$	−0.325024	+	0.562959i	−0.0228122	+	0.0395120i
$204$	−6.58513	+	1.67462i	−0.461051	+	0.117247i
$205$	−18.5657	−	32.1566i	−1.29668	−	2.24592i
$206$	−2.32591	+	1.29891i	−0.162054	+	0.0904991i
$207$	−16.6030	−	8.89823i	−1.15399	−	0.618469i
$208$	−8.45850	+	12.8890i	−0.586492	+	0.893692i
$209$		−	27.1432i		−	1.87754i
$210$	−1.23798	−	0.329705i	−0.0854291	−	0.0227518i
$211$	−17.2693	−	9.97046i	−1.18887	−	0.686395i	−0.230821	−	0.972996i	$-0.574141\pi$
$211$	−17.2693	−	9.97046i	−1.18887	−	0.686395i	−0.958050	+	0.286602i	$0.907474\pi$
$212$	0.637850	−	22.3110i	0.0438078	−	1.53233i
$213$	7.11798	+	1.78716i	0.487716	+	0.122454i
$214$	−20.0067	−	0.285927i	−1.36763	−	0.0195456i
$215$	14.9643			1.02056
$216$	−10.4395	−	10.3449i	−0.710317	−	0.703882i
$217$	0.0587176	−	0.101702i	0.00398601	−	0.00690397i
$218$	−10.2010	−	0.145788i	−0.690897	−	0.00987403i
$219$	1.18797	+	4.16881i	0.0802753	+	0.281702i
$220$	−26.3089	+	14.2029i	−1.77375	+	0.957558i
$221$	6.54698	−	3.77990i	0.440398	−	0.254264i
$222$	−7.47667	−	27.7350i	−0.501801	−	1.86145i
$223$			4.34790i			0.291157i	0.989347	+	0.145579i	$0.0465044\pi$
$223$			4.34790i			0.291157i	−0.989347	+	0.145579i	$0.953496\pi$
$224$	−0.815299	+	0.395994i	−0.0544744	+	0.0264584i
$225$	0.536290	+	16.9577i	0.0357527	+	1.13052i
$226$	4.61965	−	2.57985i	0.307295	−	0.171609i
$227$	−5.48882	−	9.50692i	−0.364306	−	0.630997i	0.624359	−	0.781138i	$-0.285360\pi$
$227$	−5.48882	−	9.50692i	−0.364306	−	0.630997i	−0.988665	+	0.150141i	$0.952027\pi$
$228$	−19.8985	+	5.06026i	−1.31781	+	0.335124i
$229$	−0.968580	+	1.67763i	−0.0640055	+	0.110861i	−0.896252	−	0.443544i	$-0.853721\pi$
$229$	−0.968580	+	1.67763i	−0.0640055	+	0.110861i	0.832247	+	0.554405i	$0.187054\pi$
$230$	24.8933	+	14.8505i	1.64142	+	0.979210i
$231$	−1.22227	+	0.348303i	−0.0804193	+	0.0229167i
$232$	10.1745	−	5.30635i	0.667988	−	0.348379i
$233$	−21.9685	+	12.6835i	−1.43921	+	0.830927i	−0.997795	−	0.0663775i	$-0.978856\pi$
$233$	−21.9685	+	12.6835i	−1.43921	+	0.830927i	−0.441413	+	0.897304i	$0.645523\pi$
$234$	14.3006	+	7.92937i	0.934859	+	0.518359i
$235$	22.9732	−	13.2636i	1.49861	−	0.865222i
$236$	27.7653	+	0.793784i	1.80737	+	0.0516709i
$237$	2.66531	−	10.6155i	0.173131	−	0.689552i
$238$	0.444413	+	0.00635138i	0.0288070	+	0.000411699i
$239$	10.8169	+	18.7354i	0.699687	+	1.21189i	0.968575	+	0.248722i	$0.0800104\pi$
$239$	10.8169	+	18.7354i	0.699687	+	1.21189i	−0.268888	+	0.963171i	$0.586656\pi$
$240$	15.3167	+	16.6390i	0.988691	+	1.07404i
$241$	−15.1570			−0.976349			−0.488174	−	0.872746i	$-0.662337\pi$
$241$	−15.1570			−0.976349			−0.488174	+	0.872746i	$0.662337\pi$
$242$	−7.22543	+	12.1117i	−0.464468	+	0.778572i
$243$	−10.1180	+	11.8586i	−0.649070	+	0.760728i
$244$	−4.92825	+	7.99899i	−0.315499	+	0.512083i
$245$	−19.7160	−	11.3830i	−1.25961	−	0.727234i
$246$	−7.17070	+	26.9247i	−0.457187	+	1.71665i
$247$	19.7832	−	11.4219i	1.25878	−	0.726755i
$248$	−1.83808	+	0.958624i	−0.116718	+	0.0608727i
$249$	−4.30411	−	15.1040i	−0.272762	−	0.957178i
$250$	0.0432363	−	3.02529i	0.00273450	−	0.191336i
$251$	15.2605	−	26.4319i	0.963233	−	1.66837i	0.248944	−	0.968518i	$-0.419917\pi$
$251$	15.2605	−	26.4319i	0.963233	−	1.66837i	0.714289	−	0.699851i	$-0.246750\pi$
$252$	0.483203	+	0.831100i	0.0304389	+	0.0523544i
$253$	28.7554			1.80784
$254$	2.27436	−	1.27012i	0.142706	−	0.0796942i
$255$	−3.03923	−	10.6653i	−0.190324	−	0.667886i
$256$	15.8956	+	1.82522i	0.993472	+	0.114076i
$257$	24.1344	−	13.9340i	1.50546	−	0.869180i	0.505483	−	0.862836i	$-0.331314\pi$
$257$	24.1344	−	13.9340i	1.50546	−	0.869180i	0.999980	−	0.00634335i	$-0.00201916\pi$
$258$	−7.95225	−	7.92816i	−0.495085	−	0.493586i
$259$			1.87897i			0.116754i
$260$	−21.4225	−	13.1986i	−1.32857	−	0.818541i
$261$	−6.41572	−	10.3429i	−0.397123	−	0.640210i
$262$	−9.98029	−	0.142635i	−0.616585	−	0.00881199i
$263$	4.04383			0.249353			0.124677	−	0.992197i	$-0.460211\pi$
$263$	4.04383			0.249353			0.124677	+	0.992197i	$0.460211\pi$
$264$	21.5057	+	6.39098i	1.32358	+	0.393338i
$265$	36.4293			2.23784
$266$	1.34290	+	0.0191921i	0.0823382	+	0.00117675i
$267$	1.41504	+	1.37099i	0.0865988	+	0.0839034i
$268$	−6.82766	+	14.8789i	−0.417066	+	0.908876i
$269$		−	3.69339i		−	0.225190i	−0.993641	−	0.112595i	$-0.964084\pi$
$269$		−	3.69339i		−	0.225190i	0.993641	−	0.112595i	$-0.0359162\pi$
$270$	16.3904	−	17.5142i	0.997490	−	1.06588i
$271$		−	20.5361i		−	1.24748i	−0.781632	−	0.623740i	$-0.785613\pi$
$271$		−	20.5361i		−	1.24748i	0.781632	−	0.623740i	$-0.214387\pi$
$272$	−6.55950	−	4.30472i	−0.397728	−	0.261012i
$273$	−0.768188	−	0.744278i	−0.0464929	−	0.0450458i
$274$	−0.281093	+	19.6684i	−0.0169814	+	1.18821i
$275$	−12.9497	−	22.4295i	−0.780895	−	1.35255i
$276$	−5.36081	−	21.0803i	−0.322683	−	1.26889i
$277$	−0.00610007			−0.000366518			−0.000183259	−	1.00000i	$-0.500058\pi$
$277$	−0.00610007			−0.000366518			−0.000183259		1.00000i	$0.500058\pi$
$278$	0.0762370	−	5.33439i	0.00457239	−	0.319935i
$279$	1.15904	+	1.86851i	0.0693898	+	0.111865i
$280$	−0.684077	−	1.31166i	−0.0408814	−	0.0783867i
$281$	16.3857	+	9.46026i	0.977486	+	0.564352i	0.901510	−	0.432758i	$-0.142459\pi$
$281$	16.3857	+	9.46026i	0.977486	+	0.564352i	0.0759760	+	0.997110i	$0.475793\pi$
$282$	−19.2354	−	5.12286i	−1.14545	−	0.305062i
$283$			0.447790i			0.0266183i	0.999911	+	0.0133092i	$0.00423656\pi$
$283$			0.447790i			0.0266183i	−0.999911	+	0.0133092i	$0.995763\pi$
$284$	4.02566	+	7.45699i	0.238879	+	0.442491i
$285$	−9.18374	−	32.2276i	−0.543998	−	1.90900i
$286$	−24.9589	−	0.356703i	−1.47585	−	0.0210923i
$287$	0.911297	−	1.57841i	0.0537922	−	0.0931708i
$288$	0.675906	−	16.9571i	0.0398281	−	0.999207i
$289$	−6.57632	−	11.3905i	−0.386843	−	0.670031i
$290$	9.13169	+	16.3518i	0.536231	+	0.960212i
$291$	4.20740	+	14.7646i	0.246642	+	0.865517i
$292$	−2.62554	+	4.26148i	−0.153648	+	0.249385i
$293$		−	0.0667158i		−	0.00389758i	−0.999998	−	0.00194879i	$-0.999380\pi$
$293$		−	0.0667158i		−	0.00389758i	0.999998	−	0.00194879i	$-0.000620319\pi$
$294$	4.44657	+	16.4947i	0.259329	+	0.961991i
$295$			45.3351i			2.63951i
$296$	17.8003	−	27.9879i	1.03462	−	1.62676i
$297$	5.06238	−	23.2514i	0.293749	−	1.34919i
$298$	−0.325854	+	22.8003i	−0.0188762	+	1.32079i
$299$	12.1002	+	20.9582i	0.699775	+	1.21205i
$300$	−14.0287	+	13.6748i	−0.809947	+	0.789514i
$301$	0.367262	+	0.636117i	0.0211687	+	0.0366652i
$302$	8.01375	+	4.78072i	0.461139	+	0.275099i
$303$	0.637050	−	2.53727i	0.0365976	−	0.145762i
$304$	−19.8210	−	13.0077i	−1.13681	−	0.746043i
$305$	−13.2799	−	7.66717i	−0.760406	−	0.439021i
$306$	−4.03543	+	7.27789i	−0.230690	+	0.416049i
$307$	−8.16753	−	4.71553i	−0.466146	−	0.269129i	0.248479	−	0.968637i	$-0.420069\pi$
$307$	−8.16753	−	4.71553i	−0.466146	−	0.269129i	−0.714625	+	0.699508i	$0.753403\pi$
$308$	−1.24944	−	0.769790i	−0.0711934	−	0.0438628i
$309$	−0.794540	+	3.16453i	−0.0451998	+	0.180024i
$310$	−1.64969	−	2.95405i	−0.0936963	−	0.167779i
$311$	11.3942			0.646108			0.323054	−	0.946381i	$-0.395290\pi$
$311$	11.3942			0.646108			0.323054	+	0.946381i	$0.395290\pi$
$312$	4.39154	+	18.3636i	0.248622	+	1.03964i
$313$	−3.47090			−0.196187			−0.0980934	−	0.995177i	$-0.531274\pi$
$313$	−3.47090			−0.196187			−0.0980934	+	0.995177i	$0.531274\pi$
$314$	−11.0616	+	18.5422i	−0.624242	+	1.04640i
$315$	−1.33337	+	0.827093i	−0.0751271	+	0.0466014i
$316$	11.1211	−	6.00374i	0.625612	−	0.337737i
$317$	30.2129	+	17.4434i	1.69693	+	0.979722i	0.948646	+	0.316341i	$0.102454\pi$
$317$	30.2129	+	17.4434i	1.69693	+	0.979722i	0.748282	+	0.663381i	$0.230879\pi$
$318$	−19.3591	−	19.3004i	−1.08560	−	1.08232i
$319$	16.0904	+	9.28980i	0.900889	+	0.520129i
$320$	−2.23638	+	26.0182i	−0.125017	+	1.45446i
$321$	−17.0520	+	17.5998i	−0.951749	+	0.982324i
$322$	−0.0203321	+	1.42266i	−0.00113306	+	0.0792816i
$323$	5.81283	+	10.0681i	0.323435	+	0.560205i
$324$	−17.9892	+	0.623536i	−0.999400	+	0.0346409i
$325$	10.8984	−	18.8766i	0.604536	−	1.04709i
$326$	−10.1003	+	5.64050i	−0.559401	+	0.312398i
$327$	−8.69445	+	8.97375i	−0.480804	+	0.496250i
$328$	−28.5270	+	14.8779i	−1.57514	+	0.821492i
$329$	1.12764	+	0.651045i	0.0621690	+	0.0358933i
$330$	−9.42359	+	35.3839i	−0.518751	+	1.94782i
$331$	−13.0783	+	7.55079i	−0.718851	+	0.415029i	−0.814330	−	0.580403i	$-0.802895\pi$
$331$	−13.0783	+	7.55079i	−0.718851	+	0.415029i	0.0954786	+	0.995431i	$0.469562\pi$
$332$	9.51257	−	15.4398i	0.522070	−	0.847367i
$333$	−31.0084	−	16.6186i	−1.69925	−	0.910694i
$334$	3.86104	+	6.91384i	0.211267	+	0.378309i
$335$	−24.5929	−	10.4451i	−1.34366	−	0.570677i
$336$	−0.331396	+	1.05946i	−0.0180791	+	0.0577984i
$337$	5.86113	−	10.1518i	0.319276	−	0.553002i	−0.661061	−	0.750332i	$-0.729894\pi$
$337$	5.86113	−	10.1518i	0.319276	−	0.553002i	0.980337	+	0.197330i	$0.0632270\pi$
$338$	−1.27877	−	2.28985i	−0.0695559	−	0.124551i
$339$	1.57809	−	6.28528i	0.0857101	−	0.341370i
$340$	6.71705	−	10.9024i	0.364283	−	0.591264i
$341$	−2.90683	−	1.67826i	−0.157413	−	0.0908827i
$342$	−12.1940	+	21.9918i	−0.659375	+	1.18918i
$343$		−	2.23906i		−	0.120898i
$344$	0.555721	−	12.9544i	0.0299624	−	0.698454i
$345$	34.1418	−	9.72921i	1.83813	−	0.523803i
$346$	14.1987	+	8.47042i	0.763325	+	0.455373i
$347$	−3.49659	−	6.05627i	−0.187707	−	0.325118i	0.756779	−	0.653671i	$-0.226772\pi$
$347$	−3.49659	−	6.05627i	−0.187707	−	0.325118i	−0.944485	+	0.328554i	$0.893439\pi$
$348$	3.81057	−	13.5276i	0.204268	−	0.725156i
$349$	17.3716			0.929878			0.464939	−	0.885343i	$-0.346076\pi$
$349$	17.3716			0.929878			0.464939	+	0.885343i	$0.346076\pi$
$350$	1.11884	−	0.624818i	0.0598046	−	0.0333979i
$351$	19.0769	−	6.09449i	1.01825	−	0.325300i
$352$	11.3182	+	23.3027i	0.603264	+	1.24204i
$353$	24.6286	+	14.2193i	1.31085	+	0.756819i	0.982237	−	0.187646i	$-0.0600858\pi$
$353$	24.6286	+	14.2193i	1.31085	+	0.756819i	0.328612	+	0.944465i	$0.393419\pi$
$354$	24.0188	−	24.0917i	1.27658	−	1.28046i
$355$	−11.9781	+	6.91553i	−0.635729	+	0.367038i
$356$	−0.0650155	+	2.27414i	−0.00344581	+	0.120529i
$357$	0.378780	−	0.390948i	0.0200472	−	0.0206912i
$358$	7.63757	+	0.109153i	0.403658	+	0.00576893i
$359$	−31.6370			−1.66974			−0.834870	−	0.550448i	$-0.814457\pi$
$359$	−31.6370			−1.66974			−0.834870	+	0.550448i	$0.814457\pi$
$360$	27.6964	+	0.311802i	1.45973	+	0.0164334i
$361$	8.06481	+	13.9687i	0.424464	+	0.735193i
$362$	−9.22207	−	16.5137i	−0.484701	−	0.867939i
$363$	4.73371	+	16.6116i	0.248455	+	0.871880i
$364$	0.0352953	−	1.23457i	0.00184998	−	0.0647093i
$365$	−7.07492	−	4.08471i	−0.370318	−	0.213803i
$366$	2.99504	+	11.1102i	0.156553	+	0.580740i
$367$	−9.46160	+	5.46266i	−0.493891	+	0.285148i	−0.726187	−	0.687497i	$-0.758710\pi$
$367$	−9.46160	+	5.46266i	−0.493891	+	0.285148i	0.232296	+	0.972645i	$0.425376\pi$
$368$	13.7803	−	20.9983i	0.718347	−	1.09461i
$369$	17.9883	+	28.9993i	0.936432	+	1.50964i
$370$	46.4915	+	27.7352i	2.41698	+	1.44188i
$371$	0.894069	+	1.54857i	0.0464178	+	0.0803979i
$372$	−0.688401	+	2.44384i	−0.0356919	+	0.126707i
$373$	17.2935	+	29.9533i	0.895425	+	1.55092i	0.833277	+	0.552855i	$0.186462\pi$
$373$	17.2935	+	29.9533i	0.895425	+	1.55092i	0.0621481	+	0.998067i	$0.480205\pi$
$374$	0.181534	−	12.7021i	0.00938690	−	0.656812i
$375$	−2.66134	−	2.57850i	−0.137431	−	0.133153i
$376$	−10.6290	−	20.3802i	−0.548148	−	1.05103i
$377$			15.6365i			0.805323i
$378$	1.14677	+	0.266898i	0.0589836	+	0.0137278i
$379$	−17.7755	−	10.2627i	−0.913068	−	0.527160i	−0.0316509	−	0.999499i	$-0.510076\pi$
$379$	−17.7755	−	10.2627i	−0.913068	−	0.527160i	−0.881417	+	0.472339i	$0.843410\pi$
$380$	20.2971	−	32.9440i	1.04122	−	1.68999i
$381$	0.776929	−	3.09438i	0.0398033	−	0.158530i
$382$	−5.86078	+	9.82423i	−0.299864	+	0.502651i
$383$	7.33196	−	12.6993i	0.374646	−	0.648906i	−0.615628	−	0.788037i	$-0.711098\pi$
$383$	7.33196	−	12.6993i	0.374646	−	0.648906i	0.990274	+	0.139131i	$0.0444310\pi$
$384$	14.9730	−	12.6416i	0.764087	−	0.645113i
$385$	1.19761	−	2.07432i	0.0610358	−	0.105717i
$386$	−22.3102	−	0.318849i	−1.13556	−	0.0162290i
$387$	−13.7460	+	0.434718i	−0.698748	+	0.0220979i
$388$	−9.29882	+	15.0928i	−0.472076	+	0.766222i
$389$	13.5678	+	7.83337i	0.687915	+	0.397168i	0.802830	−	0.596208i	$-0.203326\pi$
$389$	13.5678	+	7.83337i	0.687915	+	0.397168i	−0.114916	+	0.993375i	$0.536660\pi$
$390$	−29.7548	+	8.02116i	−1.50669	+	0.406167i
$391$	−10.6661	+	6.15808i	−0.539409	+	0.311428i
$392$	−10.5863	+	16.6451i	−0.534689	+	0.840706i
$393$	−8.50636	+	8.77962i	−0.429089	+	0.442873i
$394$	6.03269	−	3.36896i	0.303922	−	0.169726i
$395$	10.3136	+	17.8637i	0.518934	+	0.898819i
$396$	23.7544	−	13.8108i	1.19370	−	0.694021i
$397$	26.3161			1.32077			0.660385	−	0.750928i	$-0.270393\pi$
$397$	26.3161			1.32077			0.660385	+	0.750928i	$0.270393\pi$
$398$	8.42187	+	5.02419i	0.422150	+	0.251840i
$399$	1.14457	−	1.18134i	0.0573002	−	0.0591410i
$400$	−22.5847	−	1.29241i	−1.12923	−	0.0646203i
$401$			12.8334i			0.640872i	0.947270	+	0.320436i	$0.103829\pi$
$401$			12.8334i			0.640872i	−0.947270	+	0.320436i	$0.896171\pi$
$402$	7.53517	+	18.5801i	0.375820	+	0.926693i
$403$		−	2.82483i		−	0.140715i
$404$	2.65812	−	1.43499i	0.132246	−	0.0713932i
$405$	−1.85633	−	29.3197i	−0.0922417	−	1.45691i
$406$	−0.470984	+	0.789494i	−0.0233745	+	0.0391819i
$407$	53.7045			2.66203
$408$	−9.34567	+	2.23495i	−0.462679	+	0.110647i
$409$	−9.83122	−	17.0282i	−0.486123	−	0.841989i	0.513750	−	0.857940i	$-0.328256\pi$
$409$	−9.83122	−	17.0282i	−0.486123	−	0.841989i	−0.999873	+	0.0159507i	$0.994923\pi$
$410$	−25.6032	−	45.8469i	−1.26445	−	2.26422i
$411$	17.3022	+	16.7637i	0.853454	+	0.826890i
$412$	−3.31525	+	1.78974i	−0.163330	+	0.0881740i
$413$	−1.92715	+	1.11264i	−0.0948288	+	0.0547494i
$414$	−23.2980	−	12.9182i	−1.14504	−	0.634897i
$415$	25.6331	+	14.7993i	1.25828	+	0.726468i
$416$	−12.2214	+	18.0550i	−0.599203	+	0.885219i
$417$	−4.69264	−	4.54658i	−0.229800	−	0.222647i
$418$	0.548547	−	38.3824i	0.0268303	−	1.87735i
$419$	1.12710	−	1.95219i	0.0550623	−	0.0953707i	−0.837180	−	0.546927i	$-0.815798\pi$
$419$	1.12710	−	1.95219i	0.0550623	−	0.0953707i	0.892243	+	0.451556i	$0.149131\pi$
$420$	−1.74393	−	0.491245i	−0.0850952	−	0.0239703i
$421$	−8.88685	+	15.3925i	−0.433118	+	0.750183i	−0.997140	−	0.0755770i	$-0.975920\pi$
$421$	−8.88685	+	15.3925i	−0.433118	+	0.750183i	0.564022	+	0.825760i	$0.309253\pi$
$422$	−24.2185	−	14.4479i	−1.17894	−	0.703314i
$423$	−20.7175	+	12.8511i	−1.00732	+	0.624843i
$424$	1.35285	−	31.5364i	0.0657004	−	1.53154i
$425$	9.60673	+	5.54645i	0.465995	+	0.269042i
$426$	10.0292	+	2.67102i	0.485916	+	0.129411i
$427$		−	0.752688i		−	0.0364251i
$428$	−28.2850	−	0.808642i	−1.36721	−	0.0390872i
$429$	−21.2728	+	21.9562i	−1.02706	+	1.06006i
$430$	21.1606	+	0.302419i	1.02045	+	0.0145839i
$431$	−5.05091	−	8.74842i	−0.243294	−	0.421397i	0.718357	−	0.695675i	$-0.244894\pi$
$431$	−5.05091	−	8.74842i	−0.243294	−	0.421397i	−0.961650	+	0.274278i	$0.911561\pi$
$432$	−14.5531	−	14.8394i	−0.700186	−	0.713961i
$433$	−12.8545	−	22.2646i	−0.617747	−	1.06997i	−0.989896	−	0.141796i	$-0.954712\pi$
$433$	−12.8545	−	22.2646i	−0.617747	−	1.06997i	0.372149	−	0.928173i	$-0.378621\pi$
$434$	0.0850861	−	0.142627i	0.00408426	−	0.00684631i
$435$	22.2475	+	5.58585i	1.06669	+	0.267821i
$436$	−14.4219	−	0.412310i	−0.690685	−	0.0197461i
$437$	−32.2301	+	18.6081i	−1.54178	+	0.890145i
$438$	1.59562	+	5.91900i	0.0762415	+	0.282821i
$439$	2.10256	+	1.21391i	0.100350	+	0.0579368i	0.549335	−	0.835602i	$-0.314881\pi$
$439$	2.10256	+	1.21391i	0.100350	+	0.0579368i	−0.448985	+	0.893539i	$0.648214\pi$
$440$	−37.4897	+	19.5522i	−1.78725	+	0.932114i
$441$	18.4415	+	9.88351i	0.878165	+	0.470643i
$442$	9.33428	−	5.21273i	0.443986	−	0.247945i
$443$	−8.35524	−	14.4717i	−0.396969	−	0.687571i	0.596381	−	0.802701i	$-0.296605\pi$
$443$	−8.35524	−	14.4717i	−0.396969	−	0.687571i	−0.993350	+	0.115130i	$0.963271\pi$
$444$	−10.0120	−	39.3703i	−0.475150	−	1.86843i
$445$	−3.71321			−0.176023
$446$	−0.0878682	+	6.14824i	−0.00416068	+	0.291128i
$447$	20.0574	+	19.4331i	0.948681	+	0.919153i
$448$	−1.16089	+	0.543486i	−0.0548470	+	0.0256773i
$449$	22.9180	−	13.2317i	1.08157	−	0.624444i	0.150250	−	0.988648i	$-0.451992\pi$
$449$	22.9180	−	13.2317i	1.08157	−	0.624444i	0.931319	+	0.364204i	$0.118659\pi$
$450$	0.415646	+	23.9903i	0.0195938	+	1.13091i
$451$	−45.1139	−	26.0465i	−2.12433	−	1.22648i
$452$	6.58464	−	3.55472i	0.309715	−	0.167200i
$453$	10.9911	−	3.13206i	0.516405	−	0.147157i
$454$	−7.56945	−	13.5544i	−0.355252	−	0.636138i
$455$	2.01581			0.0945026
$456$	−28.2401	+	6.75343i	−1.32246	+	0.316258i
$457$	−1.76926	−	3.06445i	−0.0827625	−	0.143349i	0.821673	−	0.569959i	$-0.193041\pi$
$457$	−1.76926	−	3.06445i	−0.0827625	−	0.143349i	−0.904436	+	0.426610i	$0.859708\pi$
$458$	−1.40354	+	2.35271i	−0.0655832	+	0.109935i
$459$	3.10162	+	9.70868i	0.144771	+	0.453162i
$460$	34.9007	+	21.5027i	1.62726	+	1.00257i
$461$		−	17.3200i		−	0.806672i	−0.915052	−	0.403336i	$-0.867851\pi$
$461$		−	17.3200i		−	0.806672i	0.915052	−	0.403336i	$-0.132149\pi$
$462$	−1.73541	+	0.467824i	−0.0807386	+	0.0217651i
$463$	−0.157777	−	0.0910929i	−0.00733254	−	0.00423344i	0.496329	−	0.868134i	$-0.334681\pi$
$463$	−0.157777	−	0.0910929i	−0.00733254	−	0.00423344i	−0.503662	+	0.863901i	$0.668014\pi$
$464$	14.4947	−	7.29793i	0.672898	−	0.338798i
$465$	−4.01915	−	1.00912i	−0.186384	−	0.0467967i
$466$	−31.3214	+	17.4914i	−1.45093	+	0.810275i
$467$	−4.65066	+	8.05518i	−0.215207	+	0.372749i	−0.953337	−	0.301910i	$-0.902376\pi$
$467$	−4.65066	+	8.05518i	−0.215207	+	0.372749i	0.738130	+	0.674659i	$0.235709\pi$
$468$	20.0618	+	11.5017i	0.927356	+	0.531665i
$469$	−0.159563	−	1.30177i	−0.00736792	−	0.0601101i
$470$	32.7538	−	18.2914i	1.51082	−	0.843718i
$471$	7.24696	+	25.4310i	0.333922	+	1.17180i
$472$	39.2460	+	1.68358i	1.80644	+	0.0774932i
$473$	18.1814	−	10.4970i	0.835981	−	0.482654i
$474$	3.98347	−	14.9572i	0.182967	−	0.687008i
$475$	29.0290	+	16.7599i	1.33194	+	0.768996i
$476$	0.628302	+	0.0179626i	0.0287982	+	0.000823313i
$477$	−33.4634	+	1.05828i	−1.53219	+	0.0484555i
$478$	14.9172	+	26.7118i	0.682297	+	1.22177i
$479$	−9.81494	+	17.0000i	−0.448456	+	0.776749i	−0.998286	−	0.0585279i	$-0.981359\pi$
$479$	−9.81494	+	17.0000i	−0.448456	+	0.776749i	0.549830	+	0.835277i	$0.314693\pi$
$480$	21.3227	+	23.8383i	0.973242	+	1.08806i
$481$	22.5988	+	39.1423i	1.03042	+	1.78473i
$482$	−21.4331	−	0.306313i	−0.976249	−	0.0139522i
$483$	1.25151	+	1.21255i	0.0569455	+	0.0551730i
$484$	−10.4620	+	16.9808i	−0.475547	+	0.771855i
$485$	−25.0571	−	14.4667i	−1.13779	−	0.656901i
$486$	−14.5472	+	16.5644i	−0.659875	+	0.751375i
$487$	−32.7729	−	18.9214i	−1.48508	−	0.857411i	−0.485224	−	0.874390i	$-0.661262\pi$
$487$	−32.7729	−	18.9214i	−1.48508	−	0.857411i	−0.999856	+	0.0169786i	$0.994595\pi$
$488$	−7.13053	+	11.2115i	−0.322784	+	0.507522i
$489$	−3.45029	+	13.7419i	−0.156027	+	0.621432i
$490$	−27.6497	−	16.4948i	−1.24909	−	0.745160i
$491$	−12.0872			−0.545488			−0.272744	−	0.962087i	$-0.587931\pi$
$491$	−12.0872			−0.545488			−0.272744	+	0.962087i	$0.587931\pi$
$492$	−10.6840	+	37.9284i	−0.481671	+	1.70995i
$493$	−7.95779			−0.358401
$494$	28.2057	−	15.7515i	1.26903	−	0.708693i
$495$	23.6398	+	38.1103i	1.06253	+	1.71293i
$496$	−2.61855	+	1.31841i	−0.117576	+	0.0591986i
$497$	−0.587944	−	0.339450i	−0.0263729	−	0.0152264i
$498$	−5.78107	−	21.4451i	−0.259056	−	0.960978i
$499$	33.0366	+	19.0737i	1.47892	+	0.853854i	0.999716	−	0.0238493i	$-0.00759218\pi$
$499$	33.0366	+	19.0737i	1.47892	+	0.853854i	0.479204	+	0.877704i	$0.340926\pi$
$500$	0.122278	−	4.27710i	0.00546845	−	0.191278i
$501$	9.40666	+	2.36180i	0.420259	+	0.105517i
$502$	22.1135	−	37.0682i	0.986976	−	1.65443i
$503$	9.03287	+	15.6454i	0.402756	+	0.697593i	0.994057	−	0.108857i	$-0.0347191\pi$
$503$	9.03287	+	15.6454i	0.402756	+	0.697593i	−0.591302	+	0.806450i	$0.701386\pi$
$504$	0.666487	+	1.18500i	0.0296877	+	0.0527840i
$505$	2.46511	+	4.26969i	0.109696	+	0.189999i
$506$	40.6621	+	0.581128i	1.80765	+	0.0258343i
$507$	−3.11547	−	0.782222i	−0.138363	−	0.0347397i
$508$	3.24177	−	1.75007i	0.143830	−	0.0776467i
$509$		−	23.8953i		−	1.05914i	−0.848266	−	0.529570i	$-0.822353\pi$
$509$		−	23.8953i		−	1.05914i	0.848266	−	0.529570i	$-0.177647\pi$
$510$	−4.08215	−	15.1429i	−0.180761	−	0.670538i
$511$		−	0.400997i		−	0.0177391i
$512$	22.4405	+	2.90223i	0.991740	+	0.128261i
$513$	9.37227	+	29.3370i	0.413796	+	1.29526i
$514$	34.4093	−	19.2159i	1.51773	−	0.847578i
$515$	−3.07452	−	5.32523i	−0.135480	−	0.234658i
$516$	−11.0848	−	11.3717i	−0.487981	−	0.500610i
$517$	18.6081	−	32.2301i	0.818382	−	1.41748i
$518$	−0.0379728	+	2.65700i	−0.00166843	+	0.116742i
$519$	19.4738	−	5.54936i	0.854806	−	0.243590i
$520$	−30.0261	−	19.0966i	−1.31673	−	0.837443i
$521$			18.0615i			0.791288i	0.918404	+	0.395644i	$0.129478\pi$
$521$			18.0615i			0.791288i	−0.918404	+	0.395644i	$0.870522\pi$
$522$	−8.86325	−	14.7553i	−0.387934	−	0.645820i
$523$	0.698376	+	0.403208i	0.0305379	+	0.0176310i	0.515191	−	0.857075i	$-0.327721\pi$
$523$	0.698376	+	0.403208i	0.0305379	+	0.0176310i	−0.484653	+	0.874706i	$0.661054\pi$
$524$	−14.1099	−	0.403390i	−0.616396	−	0.0176222i
$525$	0.382201	−	1.52225i	0.0166806	−	0.0664362i
$526$	5.71826	+	0.0817232i	0.249328	+	0.00356330i
$527$	1.43762			0.0626238
$528$	30.2814	+	9.47190i	1.31783	+	0.412212i
$529$	−8.21329	−	14.2258i	−0.357100	−	0.618515i
$530$	51.5136	+	0.736213i	2.23761	+	0.0319790i
$531$	−1.31700	−	41.6441i	−0.0571529	−	1.80720i
$532$	1.89856	+	0.0542780i	0.0823130	+	0.00235325i
$533$		−	43.8414i		−	1.89898i
$534$	1.97325	+	1.96728i	0.0853909	+	0.0851323i
$535$		−	46.1837i		−	1.99670i
$536$	−9.95548	+	20.9019i	−0.430011	+	0.902824i
$537$	6.50962	−	6.71874i	0.280911	−	0.289935i
$538$	0.0746409	−	5.22271i	0.00321800	−	0.225167i
$539$	−31.9394			−1.37573
$540$	23.5312	−	24.4350i	1.01262	−	1.05151i
$541$	18.9264			0.813710			0.406855	−	0.913493i	$-0.366625\pi$
$541$	18.9264			0.813710			0.406855	+	0.913493i	$0.366625\pi$
$542$	0.415021	−	29.0395i	0.0178267	−	1.24735i
$543$	−22.4677	−	5.64113i	−0.964183	−	0.242084i
$544$	−9.18859	−	6.21973i	−0.393958	−	0.266669i
$545$		−	23.5481i		−	1.00869i
$546$	−1.07123	−	1.06799i	−0.0458444	−	0.0457056i
$547$	−4.83634	+	2.79226i	−0.206787	+	0.119389i	−0.599817	−	0.800137i	$-0.704760\pi$
$547$	−4.83634	+	2.79226i	−0.206787	+	0.119389i	0.393030	+	0.919526i	$0.371427\pi$
$548$	−0.794969	+	27.8068i	−0.0339594	+	1.18785i
$549$	12.4215	+	6.65716i	0.530135	+	0.284121i
$550$	−17.8585	−	31.9786i	−0.761487	−	1.36357i
$551$	−24.0463			−1.02441
$552$	−7.15454	−	29.9174i	−0.304518	−	1.27337i
$553$	−0.506244	+	0.876841i	−0.0215277	+	0.0372871i
$554$	−0.00862592		0.000123278i	−0.000366480		5.23759e-6i
$555$	63.7643	−	18.1706i	2.70664	−	0.771298i
$556$	0.215609	−	7.54166i	0.00914385	−	0.319837i
$557$	−28.3558	+	16.3712i	−1.20147	+	0.693670i	−0.960882	−	0.276957i	$-0.910674\pi$
$557$	−28.3558	+	16.3712i	−1.20147	+	0.693670i	−0.240589	+	0.970627i	$0.577341\pi$
$558$	1.60120	+	2.66562i	0.0677842	+	0.112845i
$559$	15.3014	+	8.83428i	0.647181	+	0.373650i
$560$	−0.940824	−	1.86860i	−0.0397571	−	0.0789629i
$561$	−11.1740	−	10.8262i	−0.471767	−	0.457084i
$562$	22.9793	+	13.7086i	0.969322	+	0.578263i
$563$	39.2486			1.65413			0.827066	−	0.562105i	$-0.190008\pi$
$563$	39.2486			1.65413			0.827066	+	0.562105i	$0.190008\pi$
$564$	−27.0967	−	7.63281i	−1.14098	−	0.321399i
$565$	6.10652	+	10.5768i	0.256903	+	0.444970i
$566$	−0.00904953	+	0.633206i	−0.000380380	+	0.0266156i
$567$	1.20079	−	0.798490i	0.0504284	−	0.0335334i
$568$	5.54186	+	10.6261i	0.232531	+	0.445860i
$569$	−6.00999	+	3.46987i	−0.251952	+	0.145464i	−0.620658	−	0.784082i	$-0.713134\pi$
$569$	−6.00999	+	3.46987i	−0.251952	+	0.145464i	0.368706	+	0.929546i	$0.379801\pi$
$570$	−12.3351	−	45.7577i	−0.516663	−	1.91658i
$571$	−20.2754	+	11.7060i	−0.848499	+	0.489881i	−0.860144	−	0.510051i	$-0.829627\pi$
$571$	−20.2754	+	11.7060i	−0.848499	+	0.489881i	0.0116448	+	0.999932i	$0.496293\pi$
$572$	−35.2864	−	1.00880i	−1.47540	−	0.0421803i
$573$	3.83966	+	13.4742i	0.160404	+	0.562892i
$574$	1.32054	−	2.21357i	0.0551181	−	0.0923925i
$575$	−17.7553	+	30.7531i	−0.740448	+	1.28249i
$576$	1.29847	−	23.9648i	0.0541029	−	0.998535i
$577$	−15.2351	−	26.3880i	−0.634246	−	1.09855i	−0.986674	−	0.162708i	$-0.947977\pi$
$577$	−15.2351	−	26.3880i	−0.634246	−	1.09855i	0.352428	−	0.935839i	$-0.385356\pi$
$578$	−9.06918	−	16.2399i	−0.377228	−	0.675491i
$579$	−19.0154	+	19.6262i	−0.790251	+	0.815638i
$580$	12.5824	+	23.3072i	0.522455	+	0.967777i
$581$			1.45285i			0.0602743i
$582$	5.65117	+	20.9632i	0.234248	+	0.868954i
$583$	44.2611	−	25.5541i	1.83311	−	1.05834i
$584$	−3.79881	+	5.97297i	−0.157196	+	0.247163i
$585$	−17.8289	+	33.2665i	−0.737133	+	1.37540i
$586$	0.00134828	−	0.0943407i	5.56970e−5	−	0.00389718i
$587$	−2.74961	+	4.76246i	−0.113488	+	0.196568i	−0.917174	−	0.398486i	$-0.869536\pi$
$587$	−2.74961	+	4.76246i	−0.113488	+	0.196568i	0.803686	+	0.595053i	$0.202869\pi$
$588$	5.95441	+	23.4145i	0.245556	+	0.965599i
$589$	4.34410			0.178996
$590$	−0.916192	+	64.1070i	−0.0377190	+	2.63924i
$591$	2.06079	−	8.20780i	0.0847696	−	0.337624i
$592$	25.7365	−	39.2171i	1.05776	−	1.61181i
$593$	34.7977	+	20.0904i	1.42897	+	0.825016i	0.997039	−	0.0768917i	$-0.0244996\pi$
$593$	34.7977	+	20.0904i	1.42897	+	0.825016i	0.431930	+	0.901907i	$0.357833\pi$
$594$	7.62845	−	32.7768i	0.312999	−	1.34485i
$595$			1.02589i			0.0420574i
$596$	−0.921559	+	32.2347i	−0.0377485	+	1.32038i
$597$	11.5508	−	3.29157i	0.472743	−	0.134715i
$598$	16.6870	+	29.8809i	0.682384	+	1.22192i
$599$	−11.7651	−	20.3777i	−0.480709	−	0.832612i	0.519046	−	0.854746i	$-0.326287\pi$
$599$	−11.7651	−	20.3777i	−0.480709	−	0.832612i	−0.999755	+	0.0221343i	$0.992954\pi$
$600$	−20.1139	+	19.0536i	−0.821146	+	0.777859i
$601$	−8.80919	+	15.2580i	−0.359334	+	0.622386i	−0.987850	−	0.155412i	$-0.950330\pi$
$601$	−8.80919	+	15.2580i	−0.359334	+	0.622386i	0.628515	+	0.777797i	$0.283663\pi$
$602$	0.506479	+	0.906936i	0.0206425	+	0.0369639i
$603$	22.8941	+	8.88028i	0.932321	+	0.361633i
$604$	11.2354	+	6.92222i	0.457161	+	0.281661i
$605$	−28.1916	−	16.2764i	−1.14615	−	0.661730i
$606$	0.952110	−	3.57500i	0.0386768	−	0.145224i
$607$	13.4389	−	7.75898i	0.545470	−	0.314927i	−0.201823	−	0.979422i	$-0.564687\pi$
$607$	13.4389	−	7.75898i	0.545470	−	0.314927i	0.747293	+	0.664495i	$0.231353\pi$
$608$	−27.7654	−	18.7944i	−1.12604	−	0.762212i
$609$	0.308563	+	1.08281i	0.0125036	+	0.0438777i
$610$	−18.6238	−	11.1103i	−0.754055	−	0.449842i
$611$	31.3210			1.26711
$612$	−5.85346	+	10.2099i	−0.236612	+	0.412710i
$613$	20.1524	−	34.9051i	0.813949	−	1.40980i	−0.0961303	−	0.995369i	$-0.530647\pi$
$613$	20.1524	−	34.9051i	0.813949	−	1.40980i	0.910080	−	0.414433i	$-0.136020\pi$
$614$	−11.4542	−	6.83314i	−0.462252	−	0.275763i
$615$	−62.3772	−	15.6615i	−2.51529	−	0.631532i
$616$	−1.75124	−	1.11379i	−0.0705593	−	0.0448757i
$617$			16.2201i			0.652997i	0.945198	+	0.326498i	$0.105869\pi$
$617$			16.2201i			0.652997i	−0.945198	+	0.326498i	$0.894131\pi$
$618$	−1.18749	+	4.45880i	−0.0477677	+	0.179359i
$619$	30.1252	+	17.3928i	1.21083	+	0.699075i	0.962941	−	0.269712i	$-0.0869287\pi$
$619$	30.1252	+	17.3928i	1.21083	+	0.699075i	0.247893	+	0.968788i	$0.420262\pi$
$620$	−2.27308	−	4.21058i	−0.0912892	−	0.169101i
$621$	−31.0795	+	9.92893i	−1.24718	+	0.398434i
$622$	16.1122	+	0.230270i	0.646042	+	0.00923298i
$623$	−0.0911316	−	0.157845i	−0.00365111	−	0.00632391i
$624$	5.83883	+	26.0562i	0.233740	+	1.04308i
$625$	−21.2934			−0.851736
$626$	−4.90809	−	0.0701445i	−0.196167	−	0.00280354i
$627$	−33.7649	−	32.7139i	−1.34844	−	1.30647i
$628$	−16.0166	+	25.9964i	−0.639131	+	1.03737i
$629$	−19.9204	+	11.5010i	−0.794277	+	0.458576i
$630$	−1.90220	+	1.14262i	−0.0757853	+	0.0455231i
$631$	14.3462	+	8.28280i	0.571114	+	0.329733i	0.757594	−	0.652726i	$-0.226375\pi$
$631$	14.3462	+	8.28280i	0.571114	+	0.329733i	−0.186480	+	0.982459i	$0.559708\pi$
$632$	15.8474	−	8.26495i	0.630374	−	0.328762i
$633$	−33.2163	+	9.46549i	−1.32023	+	0.376219i
$634$	42.3707	+	25.2768i	1.68275	+	1.00387i
$635$	3.00638	+	5.20720i	0.119304	+	0.206641i
$636$	−26.9850	−	27.6834i	−1.07003	−	1.09772i
$637$	−13.4401	−	23.2789i	−0.532516	−	0.922344i
$638$	22.5652	+	13.4616i	0.893365	+	0.532949i
$639$	10.8020	−	6.70047i	0.427319	−	0.265066i
$640$	−3.68821	+	36.7463i	−0.145789	+	1.45252i
$641$	−19.3962	+	11.1984i	−0.766103	+	0.442310i	−0.831483	−	0.555550i	$-0.812508\pi$
$641$	−19.3962	+	11.1984i	−0.766103	+	0.442310i	0.0653794	+	0.997860i	$0.479174\pi$
$642$	−24.4684	+	24.5427i	−0.965689	+	0.968623i
$643$			23.0365i			0.908471i	0.890882	+	0.454236i	$0.150088\pi$
$643$			23.0365i			0.908471i	−0.890882	+	0.454236i	$0.849912\pi$
$644$	−0.0575019	+	2.01132i	−0.00226589	+	0.0792573i
$645$	18.0355	−	18.6149i	0.710146	−	0.732960i
$646$	8.01628	+	14.3545i	0.315396	+	0.564770i
$647$	2.53863	−	4.39704i	0.0998038	−	0.172865i	−0.811800	−	0.583936i	$-0.801512\pi$
$647$	2.53863	−	4.39704i	0.0998038	−	0.172865i	0.911603	+	0.411071i	$0.134845\pi$
$648$	−25.4506	+	0.518173i	−0.999793	+	0.0203557i
$649$	31.8013	+	55.0814i	1.24831	+	2.16214i
$650$	15.7926	−	26.4726i	0.619437	−	1.03834i
$651$	−0.0557437	−	0.195616i	−0.00218477	−	0.00766680i
$652$	−14.3965	+	7.77193i	−0.563809	+	0.304372i
$653$	−8.45915	−	4.88389i	−0.331032	−	0.191121i	0.325267	−	0.945622i	$-0.394546\pi$
$653$	−8.45915	−	4.88389i	−0.331032	−	0.191121i	−0.656299	+	0.754501i	$0.727879\pi$
$654$	−12.4759	+	12.5138i	−0.487846	+	0.489328i
$655$		−	23.0387i		−	0.900196i
$656$	−40.6399	+	20.4618i	−1.58672	+	0.798899i
$657$	6.61758	+	3.54662i	0.258176	+	0.138367i
$658$	1.58141	+	0.943412i	0.0616497	+	0.0367780i
$659$	1.71880	+	2.97705i	0.0669549	+	0.115969i	0.897559	−	0.440893i	$-0.145338\pi$
$659$	1.71880	+	2.97705i	0.0669549	+	0.115969i	−0.830605	+	0.556863i	$0.812005\pi$
$660$	−14.0407	+	49.8448i	−0.546533	+	1.94021i
$661$	14.5587			0.566267			0.283133	−	0.959081i	$-0.408626\pi$
$661$	14.5587			0.566267			0.283133	+	0.959081i	$0.408626\pi$
$662$	−18.6463	+	10.4130i	−0.724708	+	0.404714i
$663$	3.18863	−	12.6998i	0.123836	−	0.493219i
$664$	13.7635	−	21.6406i	0.534126	−	0.839820i
$665$			3.09996i			0.120211i
$666$	−43.5121	−	24.1265i	−1.68606	−	0.934883i
$667$		−	25.4745i		−	0.986377i
$668$	5.32006	+	9.85468i	0.205839	+	0.381289i
$669$	5.40858	+	5.24024i	0.209108	+	0.202599i
$670$	−34.5650	−	15.2671i	−1.33536	−	0.589820i
$671$	−21.5132			−0.830508
$672$	−0.490028	+	1.49146i	−0.0189032	+	0.0575342i
$673$	41.5741			1.60256			0.801282	−	0.598287i	$-0.204152\pi$
$673$	41.5741			1.60256			0.801282	+	0.598287i	$0.204152\pi$
$674$	8.49320	−	14.2369i	0.327146	−	0.548383i
$675$	21.7410	+	19.7709i	0.836810	+	0.760983i
$676$	−1.76199	−	3.26385i	−0.0677689	−	0.125533i
$677$	11.1234	−	6.42212i	0.427508	−	0.246822i	−0.270776	−	0.962642i	$-0.587280\pi$
$677$	11.1234	−	6.42212i	0.427508	−	0.246822i	0.698285	+	0.715820i	$0.253947\pi$
$678$	2.35855	−	8.85593i	0.0905796	−	0.340110i
$679$		−	1.42020i		−	0.0545024i
$680$	9.71870	−	15.2810i	0.372695	−	0.585998i
$681$	−18.4415	−	4.63023i	−0.706678	−	0.177431i
$682$	−4.07654	−	2.43192i	−0.156099	−	0.0931229i
$683$	8.07672	−	13.9893i	0.309047	−	0.535285i	−0.669107	−	0.743166i	$-0.733323\pi$
$683$	8.07672	−	13.9893i	0.309047	−	0.535285i	0.978154	+	0.207881i	$0.0666566\pi$
$684$	−17.6876	+	30.8515i	−0.676301	+	1.17964i
$685$	−45.4028			−1.73475
$686$	0.0452499	−	3.16619i	0.00172765	−	0.120886i
$687$	0.919524	+	3.22680i	0.0350820	+	0.123110i
$688$	1.04763	−	18.3072i	0.0399404	−	0.697955i
$689$	37.2500	+	21.5063i	1.41911	+	0.819325i
$690$	48.4755	−	13.0678i	1.84543	−	0.497482i
$691$	1.55133	−	0.895660i	0.0590153	−	0.0340725i	−0.470202	−	0.882559i	$-0.655819\pi$
$691$	1.55133	−	0.895660i	0.0590153	−	0.0340725i	0.529217	+	0.848486i	$0.322486\pi$
$692$	19.9067	+	12.2647i	0.756740	+	0.466234i
$693$	−1.03985	+	1.94023i	−0.0395004	+	0.0737032i
$694$	−4.82203	−	8.63465i	−0.183042	−	0.327767i
$695$	12.3140			0.467097
$696$	5.66179	−	19.0520i	0.214610	−	0.722163i
$697$	22.3119			0.845123
$698$	24.5646	+	0.351068i	0.929783	+	0.0132881i
$699$	−10.6995	+	42.6144i	−0.404692	+	1.61183i
$700$	1.59475	−	0.860925i	0.0602758	−	0.0325399i
$701$	−31.0034	+	17.8998i	−1.17098	+	0.676066i	−0.953911	−	0.300090i	$-0.902983\pi$
$701$	−31.0034	+	17.8998i	−1.17098	+	0.676066i	−0.217070	+	0.976156i	$0.569650\pi$
$702$	27.0993	−	8.23250i	1.02280	−	0.310716i
$703$	−60.1940	+	34.7530i	−2.27026	+	1.31073i
$704$	15.5338	+	33.1804i	0.585453	+	1.25053i
$705$	11.1888	−	44.5633i	0.421395	−	1.67835i
$706$	34.5392	+	20.6049i	1.29990	+	0.775474i
$707$	−0.121000	+	0.209578i	−0.00455068	+	0.00788200i
$708$	34.4511	−	33.5820i	1.29475	−	1.26209i
$709$	−3.97319	+	6.88177i	−0.149216	+	0.258450i	−0.930938	−	0.365177i	$-0.881008\pi$
$709$	−3.97319	+	6.88177i	−0.149216	+	0.258450i	0.781722	+	0.623627i	$0.214342\pi$
$710$	−17.0776	+	9.53698i	−0.640909	+	0.357916i
$711$	−9.99286	−	16.1097i	−0.374762	−	0.604161i
$712$	−0.137895	+	3.21447i	−0.00516784	+	0.120467i
$713$			4.60212i			0.172351i
$714$	0.543522	−	0.545173i	0.0203408	−	0.0204026i
$715$		−	57.6155i		−	2.15470i
$716$	10.7978	+	0.308700i	0.403534	+	0.0115367i
$717$	36.3428	+	9.12485i	1.35725	+	0.340774i
$718$	−44.7370	−	0.639363i	−1.66957	−	0.0238608i
$719$	−6.65515	+	11.5271i	−0.248195	+	0.429886i	−0.963025	−	0.269412i	$-0.913171\pi$
$719$	−6.65515	+	11.5271i	−0.248195	+	0.429886i	0.714830	+	0.699298i	$0.246504\pi$
$720$	39.1584	+	1.00064i	1.45935	+	0.0372915i
$721$	0.150913	−	0.261390i	0.00562031	−	0.00973465i
$722$	11.1219	+	19.9156i	0.413915	+	0.741184i
$723$	−18.2677	+	18.8546i	−0.679384	+	0.701209i
$724$	−12.7069	−	23.5378i	−0.472249	−	0.874777i
$725$	−19.8704	+	11.4722i	−0.737967	+	0.426065i
$726$	6.35808	+	23.5855i	0.235971	+	0.875342i
$727$	−33.8881	−	19.5653i	−1.25684	−	0.725638i	−0.284382	−	0.958711i	$-0.591788\pi$
$727$	−33.8881	−	19.5653i	−1.25684	−	0.725638i	−0.972459	+	0.233073i	$0.925122\pi$
$728$	0.0748599	−	1.74506i	0.00277449	−	0.0646762i
$729$	2.55694	+	26.8787i	0.0947015	+	0.995506i
$730$	−9.92188	−	5.91904i	−0.367225	−	0.219073i
$731$	−4.49596	+	7.78723i	−0.166289	+	0.288021i
$732$	4.01066	+	15.7711i	0.148238	+	0.582918i
$733$	−2.66365	−	4.61357i	−0.0983841	−	0.170406i	0.812632	−	0.582777i	$-0.198034\pi$
$733$	−2.66365	−	4.61357i	−0.0983841	−	0.170406i	−0.911016	+	0.412371i	$0.864701\pi$
$734$	−13.4897	+	7.53336i	−0.497916	+	0.278061i
$735$	−37.9222	+	10.8065i	−1.39878	+	0.398604i
$736$	19.9106	−	29.4146i	0.733916	−	1.08424i
$737$	−37.2070	+	4.56060i	−1.37054	+	0.167992i
$738$	24.8506	+	41.3705i	0.914764	+	1.52287i
$739$	−26.2355	−	15.1470i	−0.965087	−	0.557193i	−0.0673518	−	0.997729i	$-0.521455\pi$
$739$	−26.2355	−	15.1470i	−0.965087	−	0.557193i	−0.897735	+	0.440536i	$0.854788\pi$
$740$	65.1817	+	40.1590i	2.39613	+	1.47628i
$741$	9.63517	−	38.3753i	0.353957	−	1.40975i
$742$	1.23298	+	2.20786i	0.0452641	+	0.0810530i
$743$	10.3678	−	17.9576i	0.380359	−	0.658802i	−0.610754	−	0.791820i	$-0.709134\pi$
$743$	10.3678	−	17.9576i	0.380359	−	0.658802i	0.991114	+	0.133019i	$0.0424670\pi$
$744$	−1.02284	+	3.44185i	−0.0374990	+	0.126184i
$745$	−52.6327			−1.92831
$746$	23.8489	+	42.7055i	0.873171	+	1.56356i
$747$	−23.9761	−	12.8497i	−0.877240	−	0.470147i
$748$	0.513403	−	17.9580i	0.0187719	−	0.656611i
$749$	1.96322	−	1.13347i	0.0717346	−	0.0414160i
$750$	−3.71121	−	3.69997i	−0.135514	−	0.135104i
$751$		−	15.5049i		−	0.565783i	−0.959152	−	0.282891i	$-0.908706\pi$
$751$		−	15.5049i		−	0.565783i	0.959152	−	0.282891i	$-0.0912936\pi$
$752$	−14.6182	−	29.0338i	−0.533072	−	1.05875i
$753$	−14.4876	−	50.8399i	−0.527957	−	1.85271i
$754$	−0.316004	+	22.1112i	−0.0115082	+	0.805241i
$755$	−10.7693	+	18.6530i	−0.391935	+	0.678852i
$756$	1.61622	+	0.400588i	0.0587814	+	0.0145693i
$757$	7.96746	+	13.8000i	0.289582	+	0.501571i	0.973710	−	0.227791i	$-0.0731503\pi$
$757$	7.96746	+	13.8000i	0.289582	+	0.501571i	−0.684128	+	0.729362i	$0.739817\pi$
$758$	−24.9284	−	14.8714i	−0.905441	−	0.540154i
$759$	34.6570	−	35.7703i	1.25797	−	1.29838i
$760$	29.3673	−	46.1750i	1.06526	−	1.67494i
$761$		−	42.5627i		−	1.54290i	−0.636293	−	0.771448i	$-0.719533\pi$
$761$		−	42.5627i		−	1.54290i	0.636293	−	0.771448i	$-0.280467\pi$
$762$	1.16117	−	4.35997i	0.0420646	−	0.157945i
$763$	1.00101	−	0.577931i	0.0362388	−	0.0209225i
$764$	−8.48609	+	13.7737i	−0.307016	+	0.498315i
$765$	−16.9301	−	9.07350i	−0.612108	−	0.328053i
$766$	10.6245	−	17.8096i	0.383881	−	0.643486i
$767$	−26.7639	+	46.3564i	−0.966388	+	1.67383i
$768$	21.4283	−	17.5735i	0.773228	−	0.634128i
$769$	−7.23249	−	12.5270i	−0.260810	−	0.451737i	0.705647	−	0.708563i	$-0.250656\pi$
$769$	−7.23249	−	12.5270i	−0.260810	−	0.451737i	−0.966457	+	0.256827i	$0.917323\pi$
$770$	1.73542	−	2.90903i	0.0625403	−	0.104834i
$771$	11.7544	−	46.8158i	0.423323	−	1.68603i
$772$	−31.5418	−	0.901750i	−1.13521	−	0.0324547i
$773$	−33.0068	+	19.0565i	−1.18717	+	0.685415i	−0.957663	−	0.287891i	$-0.907046\pi$
$773$	−33.0068	+	19.0565i	−1.18717	+	0.685415i	−0.229511	+	0.973306i	$0.573713\pi$
$774$	−19.4466	+	0.336924i	−0.698992	+	0.0121105i
$775$	3.58970	−	2.07251i	0.128946	−	0.0744469i
$776$	−13.4542	+	21.1544i	−0.482977	+	0.759398i
$777$	2.33735	+	2.26460i	0.0838520	+	0.0812421i
$778$	19.0275	+	11.3511i	0.682169	+	0.406958i
$779$	67.4205			2.41559
$780$	−42.2375	+	10.7412i	−1.51234	+	0.384595i
$781$	−9.70210	+	16.8045i	−0.347168	+	0.601313i
$782$	−15.2071	+	8.49240i	−0.543804	+	0.303688i
$783$	−20.5985	−	4.48478i	−0.736131	−	0.160273i
$784$	−15.3062	+	23.3234i	−0.546648	+	0.832979i
$785$	−43.1592	−	24.9180i	−1.54042	−	0.889361i
$786$	−12.2060	+	12.2431i	−0.435374	+	0.436697i
$787$	−12.7171	−	7.34224i	−0.453317	−	0.261723i	0.255913	−	0.966700i	$-0.417624\pi$
$787$	−12.7171	−	7.34224i	−0.453317	−	0.261723i	−0.709230	+	0.704977i	$0.750957\pi$
$788$	8.59872	−	4.64202i	0.306317	−	0.165365i
$789$	4.87376	−	5.03033i	0.173510	−	0.179085i
$790$	14.2231	+	25.4689i	0.506036	+	0.906143i
$791$	−0.299739	+	0.519164i	−0.0106575	+	0.0184593i
$792$	33.8694	−	19.0494i	1.20350	−	0.676892i
$793$	−9.05273	−	15.6798i	−0.321472	−	0.556806i
$794$	37.2128	+	0.531831i	1.32063	+	0.0188740i
$795$	43.9058	−	45.3163i	1.55718	−	1.60720i
$796$	11.8076	+	7.27475i	0.418508	+	0.257847i
$797$	9.97611	−	5.75971i	0.353372	−	0.204019i	−0.312797	−	0.949820i	$-0.601266\pi$
$797$	9.97611	−	5.75971i	0.353372	−	0.204019i	0.666169	+	0.745800i	$0.267933\pi$
$798$	1.64238	−	1.64737i	0.0581395	−	0.0583161i
$799$			15.9400i			0.563915i
$800$	−31.9102	−	2.28397i	−1.12820	−	0.0807506i
$801$	3.41089	−	0.107870i	0.120518	−	0.00381139i
$802$	−0.259355	+	18.1474i	−0.00915816	+	0.640806i
$803$	−11.4612			−0.404458
$804$	10.2798	+	26.4259i	0.362539	+	0.931969i
$805$	−3.28409			−0.115749
$806$	0.0570880	−	3.99451i	0.00201084	−	0.140701i
$807$	−4.59439	−	4.45139i	−0.161730	−	0.156696i
$808$	3.78776	−	1.97545i	0.133253	−	0.0694961i
$809$			37.3218i			1.31216i	0.754689	+	0.656082i	$0.227788\pi$
$809$			37.3218i			1.31216i	−0.754689	+	0.656082i	$0.772212\pi$
$810$	−2.03245	−	41.4975i	−0.0714129	−	1.45807i
$811$	−0.911767	+	0.526409i	−0.0320165	+	0.0184847i	−0.515923	−	0.856635i	$-0.672551\pi$
$811$	−0.911767	+	0.526409i	−0.0320165	+	0.0184847i	0.483906	+	0.875120i	$0.339218\pi$
$812$	−0.681959	+	1.10688i	−0.0239321	+	0.0388439i
$813$	−25.5459	−	24.7508i	−0.895934	−	0.868048i
$814$	75.9419	+	1.08533i	2.66176	+	0.0380409i
$815$	−13.3511	−	23.1248i	−0.467669	−	0.810026i
$816$	−13.2606	+	2.97151i	−0.464213	+	0.104024i
$817$	−13.5856	+	23.5309i	−0.475299	+	0.823243i
$818$	−13.5579	−	24.2777i	−0.474041	−	0.848850i
$819$	−1.85169	+	0.0585599i	−0.0647033	+	0.00204625i
$820$	−35.2782	−	65.3481i	−1.23197	−	2.28206i
$821$	−24.0778	−	13.9013i	−0.840320	−	0.485159i	0.0170527	−	0.999855i	$-0.494572\pi$
$821$	−24.0778	−	13.9013i	−0.840320	−	0.485159i	−0.857373	+	0.514695i	$0.827905\pi$
$822$	24.1277	+	24.0546i	0.841550	+	0.839001i
$823$	0.288116	+	0.166344i	0.0100431	+	0.00579837i	0.505013	−	0.863112i	$-0.331488\pi$
$823$	0.288116	+	0.166344i	0.0100431	+	0.00579837i	−0.494970	+	0.868910i	$0.664821\pi$
$824$	−4.72416	+	2.46381i	−0.164574	+	0.0858310i
$825$	−43.5086	−	10.9240i	−1.51477	−	0.380325i
$826$	−2.74761	+	1.53440i	−0.0956014	+	0.0533887i
$827$	18.8868	−	32.7128i	0.656757	−	1.13754i	−0.324693	−	0.945819i	$-0.605261\pi$
$827$	18.8868	−	32.7128i	0.656757	−	1.13754i	0.981450	−	0.191717i	$-0.0614056\pi$
$828$	−32.6839	−	18.7381i	−1.13585	−	0.651195i
$829$	−38.9002			−1.35106			−0.675530	−	0.737333i	$-0.736085\pi$
$829$	−38.9002			−1.35106			−0.675530	+	0.737333i	$0.736085\pi$
$830$	35.9479	+	21.4452i	1.24777	+	0.744375i
$831$	−0.00735200	+	0.00758819i	−0.000255038	+	0.000263231i
$832$	−17.6468	+	25.2840i	−0.611791	+	0.876566i
$833$	11.8472	−	6.83996i	0.410480	−	0.236990i
$834$	−6.54384	−	6.52402i	−0.226595	−	0.225908i
$835$	−15.8294	+	9.13912i	−0.547800	+	0.316272i
$836$	1.55137	−	54.2643i	0.0536551	−	1.87677i
$837$	3.72124	+	0.810201i	0.128625	+	0.0280047i
$838$	1.63325	−	2.73775i	0.0564196	−	0.0945742i
$839$	−1.36027	−	2.35605i	−0.0469617	−	0.0813400i	0.841589	−	0.540118i	$-0.181621\pi$
$839$	−1.36027	−	2.35605i	−0.0469617	−	0.0813400i	−0.888551	+	0.458778i	$0.848287\pi$
$840$	−2.45611	−	0.729898i	−0.0847440	−	0.0251839i
$841$	−6.27014	+	10.8602i	−0.216212	+	0.374490i
$842$	−12.8777	+	21.5864i	−0.443794	+	0.743917i
$843$	31.5166	−	8.98113i	1.08549	−	0.309327i
$844$	−33.9547	−	20.9198i	−1.16877	−	0.720089i
$845$	5.24267	−	3.02686i	0.180353	−	0.104127i
$846$	−29.5557	+	17.7537i	−1.01615	+	0.610384i
$847$		−	1.59786i		−	0.0549031i
$848$	2.55036	−	44.5673i	0.0875797	−	1.53045i
$849$	0.557028	+	0.539691i	0.0191172	+	0.0185221i
$850$	13.4725	+	8.03721i	0.462103	+	0.275674i
$851$	−36.8172	−	63.7692i	−1.26208	−	2.18598i
$852$	14.1280	+	3.97969i	0.484017	+	0.136342i
$853$	5.11696	−	8.86284i	0.175202	−	0.303458i	−0.765029	−	0.643995i	$-0.777276\pi$
$853$	5.11696	−	8.86284i	0.175202	−	0.303458i	0.940231	+	0.340537i	$0.110609\pi$
$854$	0.0152113	−	1.06435i	0.000520520	−	0.0364214i
$855$	−51.1581	−	27.4177i	−1.74957	−	0.937665i
$856$	−39.9806	−	1.71510i	−1.36651	−	0.0586208i
$857$			7.20462i			0.246105i	0.992400	+	0.123053i	$0.0392684\pi$
$857$			7.20462i			0.246105i	−0.992400	+	0.123053i	$0.960732\pi$
$858$	−30.5250	+	30.6177i	−1.04211	+	1.04527i
$859$	0.524773	−	0.302978i	0.0179050	−	0.0103375i	−0.491021	−	0.871148i	$-0.663376\pi$
$859$	0.524773	−	0.302978i	0.0179050	−	0.0103375i	0.508926	+	0.860810i	$0.330043\pi$
$860$	29.9164	+	0.855282i	1.02014	+	0.0291649i
$861$	−0.865143	−	3.03596i	−0.0294840	−	0.103465i
$862$	−6.96553	−	12.4730i	−0.237247	−	0.424830i
$863$	3.28834			0.111936			0.0559682	−	0.998433i	$-0.482175\pi$
$863$	3.28834			0.111936			0.0559682	+	0.998433i	$0.482175\pi$
$864$	−20.2792	−	21.2780i	−0.689911	−	0.723894i
$865$	−19.0809	+	33.0492i	−0.648772	+	1.12371i
$866$	−17.7272	−	31.7435i	−0.602394	−	1.07869i
$867$	−22.0953	−	5.54761i	−0.750394	−	0.188407i
$868$	0.123200	−	0.199965i	0.00418168	−	0.00678724i
$869$	25.0617	+	14.4694i	0.850161	+	0.490841i
$870$	31.3467	+	8.34838i	1.06275	+	0.283037i
$871$	−18.9806	−	25.1990i	−0.643134	−	0.853836i
$872$	−20.3853	−	0.874492i	−0.690333	−	0.0296140i
$873$	23.4374	+	12.5610i	0.793234	+	0.425126i
$874$	−45.9517	+	25.6618i	−1.55434	+	0.868022i
$875$	0.171396	+	0.296867i	0.00579425	+	0.0100359i
$876$	2.13669	+	8.40212i	0.0721922	+	0.283881i
$877$	15.3748	−	26.6299i	0.519169	−	0.899226i	−0.480583	−	0.876949i	$-0.659575\pi$
$877$	15.3748	−	26.6299i	0.519169	−	0.899226i	0.999752	−	0.0222773i	$-0.00709166\pi$
$878$	2.94863	+	1.75905i	0.0995114	+	0.0593649i
$879$	−0.0829911	−	0.0804080i	−0.00279922	−	0.00271210i
$880$	−53.4081	+	26.8905i	−1.80039	+	0.906478i
$881$	−31.7060	−	18.3055i	−1.06820	−	0.616727i	−0.140513	−	0.990079i	$-0.544875\pi$
$881$	−31.7060	−	18.3055i	−1.06820	−	0.616727i	−0.927690	+	0.373352i	$0.878208\pi$
$882$	25.8778	+	14.3487i	0.871350	+	0.483144i
$883$	36.7436	−	21.2139i	1.23652	−	0.713906i	0.268140	−	0.963380i	$-0.413591\pi$
$883$	36.7436	−	21.2139i	1.23652	−	0.713906i	0.968382	+	0.249474i	$0.0802577\pi$
$884$	13.3047	−	7.18253i	0.447484	−	0.241575i
$885$	56.3946	+	54.6394i	1.89569	+	1.83668i
$886$	−11.5224	−	20.6328i	−0.387103	−	0.693174i
$887$	−27.9653	+	48.4373i	−0.938983	+	1.62637i	−0.171612	+	0.985165i	$0.554897\pi$
$887$	−27.9653	+	48.4373i	−0.938983	+	1.62637i	−0.767372	+	0.641202i	$0.778436\pi$
$888$	−13.3620	−	55.8747i	−0.448401	−	1.87503i
$889$	−0.147568	+	0.255596i	−0.00494928	+	0.00857241i
$890$	−5.25073	−	0.0750414i	−0.176005	−	0.00251539i
$891$	−22.8223	−	34.3208i	−0.764576	−	1.14979i
$892$	−0.248504	+	8.69226i	−0.00832051	+	0.291038i
$893$			48.1663i			1.61182i
$894$	27.9698	+	27.8851i	0.935449	+	0.932616i
$895$			17.6307i			0.589329i
$896$	−1.65256	+	0.745066i	−0.0552083	+	0.0248909i
$897$	40.6546	+	10.2074i	1.35742	+	0.340817i
$898$	32.6751	−	18.2474i	1.09038	−	0.608925i
$899$	−1.48677	+	2.57517i	−0.0495866	+	0.0858866i
$900$	0.102926	+	33.9323i	0.00343086	+	1.13108i
$901$	−10.9450	+	18.9574i	−0.364632	+	0.631561i
$902$	−63.2678	−	37.7433i	−2.10659	−	1.25672i
$903$	1.23394	+	0.309813i	0.0410628	+	0.0103099i
$904$	9.38298	−	4.89355i	0.312073	−	0.162757i
$905$	37.8085	−	21.8287i	1.25680	−	0.725611i
$906$	15.6054	−	4.20683i	0.518455	−	0.139763i
$907$	−42.6410	+	24.6188i	−1.41587	+	0.817453i	−0.995933	−	0.0900998i	$-0.971281\pi$
$907$	−42.6410	+	24.6188i	−1.41587	+	0.817453i	−0.419938	+	0.907553i	$0.637948\pi$
$908$	−10.4298	−	19.3198i	−0.346125	−	0.641150i
$909$	−2.38845	−	3.85046i	−0.0792197	−	0.127712i
$910$	2.85049	+	0.0407382i	0.0944930	+	0.00135046i
$911$	−54.0430			−1.79053			−0.895263	−	0.445539i	$-0.853012\pi$
$911$	−54.0430			−1.79053			−0.895263	+	0.445539i	$0.853012\pi$
$912$	−40.0699	+	8.97910i	−1.32685	+	0.297328i
$913$	41.5251			1.37428
$914$	−2.43992	−	4.36910i	−0.0807055	−	0.144517i
$915$	−25.5430	+	7.27885i	−0.844425	+	0.240631i
$916$	−2.03225	+	3.29853i	−0.0671475	+	0.108986i
$917$	0.979351	−	0.565428i	0.0323410	−	0.0186721i
$918$	4.18970	+	13.7914i	0.138281	+	0.455185i
$919$	28.9581	+	16.7190i	0.955239	+	0.551508i	0.894705	−	0.446658i	$-0.147386\pi$
$919$	28.9581	+	16.7190i	0.955239	+	0.551508i	0.0605348	+	0.998166i	$0.480719\pi$
$920$	48.9175	+	31.1116i	1.61276	+	1.02572i
$921$	−15.7097	+	4.47670i	−0.517651	+	0.147512i
$922$	0.350025	−	24.4916i	0.0115275	−	0.806589i
$923$	−16.3305			−0.537526
$924$	−2.46344	+	0.626464i	−0.0810414	+	0.0206091i
$925$	−33.1604	+	57.4355i	−1.09031	+	1.88847i
$926$	−0.221267	−	0.132000i	−0.00727129	−	0.00433779i
$927$	2.97891	+	4.80236i	0.0978402	+	0.157730i
$928$	20.6440	−	10.0269i	0.677671	−	0.329148i
$929$			13.8378i			0.454003i	0.973894	+	0.227002i	$0.0728923\pi$
$929$			13.8378i			0.454003i	−0.973894	+	0.227002i	$0.927108\pi$
$930$	−5.66296	−	1.50818i	−0.185696	−	0.0494553i
$931$	35.7989	−	20.6685i	1.17326	−	0.677383i
$932$	−44.6441	+	24.1011i	−1.46237	+	0.789459i
$933$	13.7327	−	14.1739i	0.449589	−	0.464032i
$934$	−6.73914	+	11.2966i	−0.220512	+	0.369636i
$935$	29.3218			0.958926
$936$	28.1363	+	16.6696i	0.919664	+	0.544863i
$937$	−0.232362			−0.00759095			−0.00379547	−	0.999993i	$-0.501208\pi$
$937$	−0.232362			−0.00759095			−0.00379547	+	0.999993i	$0.501208\pi$
$938$	−0.199325	−	1.84402i	−0.00650819	−	0.0602093i
$939$	−4.18324	+	4.31763i	−0.136515	+	0.140900i
$940$	46.6858	−	25.2033i	1.52272	−	0.822042i
$941$		−	1.03931i		−	0.0338807i	−0.999857	−	0.0169403i	$-0.994607\pi$
$941$		−	1.03931i		−	0.0338807i	0.999857	−	0.0169403i	$-0.00539254\pi$
$942$	9.73375	+	36.1077i	0.317143	+	1.17645i
$943$			71.4249i			2.32592i
$944$	55.4625	+	3.17384i	1.80515	+	0.103300i
$945$	−0.578162	+	2.65549i	−0.0188076	+	0.0863831i
$946$	25.9219	−	14.4761i	0.842793	−	0.470659i
$947$	4.15691			0.135081			0.0675407	−	0.997717i	$-0.478485\pi$
$947$	4.15691			0.135081			0.0675407	+	0.997717i	$0.478485\pi$
$948$	5.93518	−	21.0700i	0.192766	−	0.684323i
$949$	−4.82287	−	8.35346i	−0.156557	−	0.271165i
$950$	40.7102	+	24.2863i	1.32081	+	0.787951i
$951$	58.1124	−	16.5600i	1.88442	−	0.536995i
$952$	0.888100	+	0.0380979i	0.0287835	+	0.00123476i
$953$			0.653441i			0.0211670i	0.999944	+	0.0105835i	$0.00336890\pi$
$953$			0.653441i			0.0211670i	−0.999944	+	0.0105835i	$0.996631\pi$
$954$	−47.3410	+	0.820213i	−1.53272	+	0.0265554i
$955$	−22.8671	−	13.2023i	−0.739962	−	0.427217i
$956$	20.5541	+	38.0738i	0.664768	+	1.23139i
$957$	30.9487	−	8.81930i	1.00043	−	0.285087i
$958$	−14.2226	+	23.8408i	−0.459510	+	0.770261i
$959$	−1.11430	−	1.93003i	−0.0359827	−	0.0623238i
$960$	29.6700	+	34.1399i	0.957594	+	1.10186i
$961$	−15.2314	+	26.3816i	−0.491336	+	0.851018i
$962$	31.1652	+	55.8066i	1.00481	+	1.79928i
$963$	1.34165	+	42.4236i	0.0432341	+	1.36708i
$964$	−30.3016	−	0.866295i	−0.975950	−	0.0279015i
$965$		−	51.5013i		−	1.65789i
$966$	1.74521	+	1.73992i	0.0561512	+	0.0559812i
$967$	19.4276	−	11.2165i	0.624749	−	0.360699i	−0.153967	−	0.988076i	$-0.549205\pi$
$967$	19.4276	−	11.2165i	0.624749	−	0.360699i	0.778716	+	0.627377i	$0.215871\pi$
$968$	−15.1372	+	23.8006i	−0.486528	+	0.764981i
$969$	19.5301	+	4.90355i	0.627396	+	0.157525i
$970$	−35.1402	−	20.9634i	−1.12828	−	0.673093i
$971$	−1.87747	−	3.25187i	−0.0602509	−	0.104358i	0.834327	−	0.551270i	$-0.185857\pi$
$971$	−1.87747	−	3.25187i	−0.0602509	−	0.104358i	−0.894578	+	0.446913i	$0.852523\pi$
$972$	−20.9055	+	23.1292i	−0.670545	+	0.741869i
$973$	0.302217	+	0.523455i	0.00968863	+	0.0167812i
$974$	−45.9607	−	27.4185i	−1.47268	−	0.878546i
$975$	−10.3465	−	36.3078i	−0.331352	−	1.16278i
$976$	−10.3096	+	15.7098i	−0.330004	+	0.502857i
$977$	−21.5798	−	12.4591i	−0.690398	−	0.398601i	0.113363	−	0.993554i	$-0.463838\pi$
$977$	−21.5798	−	12.4591i	−0.690398	−	0.398601i	−0.803761	+	0.594952i	$0.797171\pi$
$978$	−5.15666	+	19.3623i	−0.164892	+	0.619139i
$979$	−4.51149	+	2.60471i	−0.144188	+	0.0832468i
$980$	−38.7652	−	23.8836i	−1.23831	−	0.762934i
$981$	0.684080	+	21.6309i	0.0218410	+	0.690622i
$982$	−17.0921	−	0.244274i	−0.545432	−	0.00779511i
$983$	60.2997			1.92326			0.961630	−	0.274349i	$-0.0884622\pi$
$983$	60.2997			1.92326			0.961630	+	0.274349i	$0.0884622\pi$
$984$	−15.8744	+	53.4175i	−0.506058	+	1.70289i
$985$	7.97436	+	13.8120i	0.254084	+	0.440087i
$986$	−11.2529	−	0.160821i	−0.358364	−	0.00512160i
$987$	2.16894	−	0.618072i	0.0690382	−	0.0196735i
$988$	40.2031	−	21.7037i	1.27903	−	0.690486i
$989$	−24.9285	−	14.3925i	−0.792681	−	0.457655i
$990$	32.6582	+	54.3683i	1.03795	+	1.72794i
$991$		−	10.6919i		−	0.339639i	−0.985475	−	0.169819i	$-0.945682\pi$
$991$		−	10.6919i		−	0.339639i	0.985475	−	0.169819i	$-0.0543184\pi$
$992$	−3.72945	+	1.81141i	−0.118410	+	0.0575123i
$993$	−6.36964	+	25.3693i	−0.202135	+	0.805070i
$994$	−0.824534	−	0.491887i	−0.0261526	−	0.0156017i
$995$	−11.3178	+	19.6029i	−0.358797	+	0.621455i
$996$	−7.74144	−	30.4417i	−0.245297	−	0.964582i
$997$	7.49263			0.237294			0.118647	−	0.992937i	$-0.462144\pi$
$997$	7.49263			0.237294			0.118647	+	0.992937i	$0.462144\pi$
$998$	46.3305	+	27.6391i	1.46657	+	0.874901i
$999$	−58.0450	+	18.5436i	−1.83646	+	0.586693i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.l.a.431.132	yes	264
3.2	odd	2	inner	804.2.l.a.431.1	✓	264
4.3	odd	2	inner	804.2.l.a.431.89	yes	264
12.11	even	2	inner	804.2.l.a.431.44	yes	264
67.37	even	3	inner	804.2.l.a.707.44	yes	264
201.104	odd	6	inner	804.2.l.a.707.89	yes	264
268.171	odd	6	inner	804.2.l.a.707.1	yes	264
804.707	even	6	inner	804.2.l.a.707.132	yes	264

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.l.a.431.1	✓	264	3.2	odd	2	inner
804.2.l.a.431.44	yes	264	12.11	even	2	inner
804.2.l.a.431.89	yes	264	4.3	odd	2	inner
804.2.l.a.431.132	yes	264	1.1	even	1	trivial
804.2.l.a.707.1	yes	264	268.171	odd	6	inner
804.2.l.a.707.44	yes	264	67.37	even	3	inner
804.2.l.a.707.89	yes	264	201.104	odd	6	inner
804.2.l.a.707.132	yes	264	804.707	even	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:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.41407 + 0.0202093i) q^{2} +(1.20523 - 1.24395i) q^{3} +(1.99918 + 0.0571548i) q^{4} +3.26426i q^{5} +(1.72942 - 1.73468i) q^{6} +(-0.138760 + 0.0801133i) q^{7} +(2.82583 + 0.121223i) q^{8} +(-0.0948278 - 2.99850i) q^{9} +O(q^{10})\)	\(q+(1.41407 + 0.0202093i) q^{2} +(1.20523 - 1.24395i) q^{3} +(1.99918 + 0.0571548i) q^{4} +3.26426i q^{5} +(1.72942 - 1.73468i) q^{6} +(-0.138760 + 0.0801133i) q^{7} +(2.82583 + 0.121223i) q^{8} +(-0.0948278 - 2.99850i) q^{9} +(-0.0659686 + 4.61589i) q^{10} +(2.28979 + 3.96603i) q^{11} +(2.48058 - 2.41800i) q^{12} +(-1.92708 + 3.33780i) q^{13} +(-0.197836 + 0.110482i) q^{14} +(4.06058 + 3.93420i) q^{15} +(3.99347 + 0.228526i) q^{16} +(-1.69868 - 0.980734i) q^{17} +(-0.0734954 - 4.24200i) q^{18} +(-5.13295 - 2.96351i) q^{19} +(-0.186568 + 6.52586i) q^{20} +(-0.0675815 + 0.269166i) q^{21} +(3.15777 + 5.65451i) q^{22} +(3.13953 - 5.43782i) q^{23} +(3.55658 - 3.36909i) q^{24} -5.65541 q^{25} +(-2.79248 + 4.68093i) q^{26} +(-3.84428 - 3.49593i) q^{27} +(-0.281986 + 0.152230i) q^{28} +(3.51351 - 2.02853i) q^{29} +(5.66244 + 5.64529i) q^{30} +(-0.634737 + 0.366466i) q^{31} +(5.64242 + 0.403856i) q^{32} +(7.69327 + 1.93160i) q^{33} +(-2.38223 - 1.42115i) q^{34} +(-0.261511 - 0.452950i) q^{35} +(-0.0181995 - 5.99997i) q^{36} +(5.86348 - 10.1559i) q^{37} +(-7.19846 - 4.29435i) q^{38} +(1.82948 + 6.42002i) q^{39} +(-0.395704 + 9.22424i) q^{40} +(-9.85112 + 5.68755i) q^{41} +(-0.101005 + 0.379254i) q^{42} -4.58428i q^{43} +(4.35103 + 8.05969i) q^{44} +(9.78789 - 0.309543i) q^{45} +(4.54941 - 7.62601i) q^{46} +(-4.06328 - 7.03780i) q^{47} +(5.09733 - 4.69225i) q^{48} +(-3.48716 + 6.03994i) q^{49} +(-7.99714 - 0.114292i) q^{50} +(-3.26729 + 0.931063i) q^{51} +(-4.04336 + 6.56273i) q^{52} -11.1601i q^{53} +(-5.36542 - 5.02118i) q^{54} +(-12.9462 + 7.47446i) q^{55} +(-0.401825 + 0.209566i) q^{56} +(-9.87287 + 2.81342i) q^{57} +(5.00935 - 2.79747i) q^{58} +13.8883 q^{59} +(7.89299 + 8.09726i) q^{60} +(-2.34882 + 4.06828i) q^{61} +(-0.904968 + 0.505380i) q^{62} +(0.253378 + 0.408476i) q^{63} +(7.97061 + 0.685111i) q^{64} +(-10.8955 - 6.29049i) q^{65} +(10.8398 + 2.88690i) q^{66} +(-3.19984 + 7.53399i) q^{67} +(-3.33992 - 2.05775i) q^{68} +(-2.98052 - 10.4593i) q^{69} +(-0.360641 - 0.645788i) q^{70} +(2.11856 + 3.66945i) q^{71} +(0.0955200 - 8.48474i) q^{72} +(-1.25134 + 2.16739i) q^{73} +(8.49662 - 14.2426i) q^{74} +(-6.81608 + 7.03505i) q^{75} +(-10.0923 - 6.21798i) q^{76} +(-0.635463 - 0.366885i) q^{77} +(2.45727 + 9.11532i) q^{78} +(5.47250 - 3.15955i) q^{79} +(-0.745968 + 13.0357i) q^{80} +(-8.98202 + 0.568683i) q^{81} +(-14.0451 + 7.84350i) q^{82} +(4.53373 - 7.85265i) q^{83} +(-0.150492 + 0.534250i) q^{84} +(3.20137 - 5.54494i) q^{85} +(0.0926453 - 6.48250i) q^{86} +(1.71121 - 6.81549i) q^{87} +(5.98977 + 11.4849i) q^{88} +1.13753i q^{89} +(13.8470 - 0.239908i) q^{90} -0.617539i q^{91} +(6.58729 - 10.6918i) q^{92} +(-0.309141 + 1.23126i) q^{93} +(-5.60352 - 10.0341i) q^{94} +(9.67368 - 16.7553i) q^{95} +(7.30281 - 6.53215i) q^{96} +(-4.43186 + 7.67620i) q^{97} +(-5.05315 + 8.47043i) q^{98} +(11.6750 - 7.24202i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 264 q - 2 q^{4} - 3 q^{6} - 12 q^{9}+O(q^{10}) \) 264 * q - 2 * q^4 - 3 * q^6 - 12 * q^9	\( 264 q - 2 q^{4} - 3 q^{6} - 12 q^{9} + 2 q^{10} + 2 q^{12} - 18 q^{16} + q^{18} - 4 q^{22} - 248 q^{25} + 7 q^{30} - 38 q^{34} + 13 q^{36} + 4 q^{37} + 48 q^{40} - 12 q^{42} + 48 q^{45} - 2 q^{46} - 11 q^{48} + 128 q^{49} + 32 q^{52} - 8 q^{54} - 2 q^{57} - 32 q^{58} + 68 q^{60} - 8 q^{61} + 4 q^{64} + 30 q^{66} - 40 q^{69} - 140 q^{70} + 108 q^{72} - 4 q^{73} - 120 q^{76} + 44 q^{78} - 28 q^{81} - 64 q^{82} + 33 q^{84} + 16 q^{85} - 14 q^{88} + 42 q^{90} + 16 q^{93} - 12 q^{94} - 4 q^{96} + 20 q^{97}+O(q^{100}) \) 264 * q - 2 * q^4 - 3 * q^6 - 12 * q^9 + 2 * q^10 + 2 * q^12 - 18 * q^16 + q^18 - 4 * q^22 - 248 * q^25 + 7 * q^30 - 38 * q^34 + 13 * q^36 + 4 * q^37 + 48 * q^40 - 12 * q^42 + 48 * q^45 - 2 * q^46 - 11 * q^48 + 128 * q^49 + 32 * q^52 - 8 * q^54 - 2 * q^57 - 32 * q^58 + 68 * q^60 - 8 * q^61 + 4 * q^64 + 30 * q^66 - 40 * q^69 - 140 * q^70 + 108 * q^72 - 4 * q^73 - 120 * q^76 + 44 * q^78 - 28 * q^81 - 64 * q^82 + 33 * q^84 + 16 * q^85 - 14 * q^88 + 42 * q^90 + 16 * q^93 - 12 * q^94 - 4 * q^96 + 20 * q^97

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