LMFDB - Embedded newform 804.2.l.a.431.1

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			431.1
Character	$\chi$	$=$	804.431
Dual form			804.2.l.a.707.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41407 - 0.0202093i) q^{2} +(-1.20523 - 1.24395i) q^{3} +(1.99918 + 0.0571548i) q^{4} -3.26426i q^{5} +(1.67914 + 1.78339i) q^{6} +(-0.138760 + 0.0801133i) q^{7} +(-2.82583 - 0.121223i) q^{8} +(-0.0948278 + 2.99850i) q^{9} +O(q^{10})$	\(q+(-1.41407 - 0.0202093i) q^{2} +(-1.20523 - 1.24395i) q^{3} +(1.99918 + 0.0571548i) q^{4} -3.26426i q^{5} +(1.67914 + 1.78339i) 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} +(-2.33838 - 2.55577i) 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} +(0.194691 - 4.23817i) q^{18} +(-5.13295 - 2.96351i) q^{19} +(0.186568 - 6.52586i) q^{20} +(0.266896 + 0.0760559i) q^{21} +(3.15777 + 5.65451i) q^{22} +(-3.13953 + 5.43782i) q^{23} +(3.25499 + 3.66129i) 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} +(5.82145 - 5.48116i) q^{30} +(-0.634737 + 0.366466i) q^{31} +(-5.64242 - 0.403856i) q^{32} +(-2.17382 + 7.62837i) q^{33} +(-2.38223 - 1.42115i) q^{34} +(0.261511 + 0.452950i) q^{35} +(-0.360957 + 5.98913i) q^{36} +(5.86348 - 10.1559i) q^{37} +(7.19846 + 4.29435i) q^{38} +(6.47464 - 1.62563i) q^{39} +(-0.395704 + 9.22424i) q^{40} +(9.85112 - 5.68755i) q^{41} +(-0.375872 - 0.112942i) 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} +(-4.52878 - 5.24310i) q^{48} +(-3.48716 + 6.03994i) q^{49} +(7.99714 + 0.114292i) q^{50} +(-0.827321 - 3.29509i) q^{51} +(-4.04336 + 6.56273i) q^{52} +11.1601i q^{53} +(-5.50672 + 4.86580i) q^{54} +(-12.9462 + 7.47446i) q^{55} +(0.401825 - 0.209566i) q^{56} +(2.49994 + 9.95687i) q^{57} +(5.00935 - 2.79747i) q^{58} -13.8883 q^{59} +(-8.34271 + 7.63310i) q^{60} +(-2.34882 + 4.06828i) q^{61} +(0.904968 - 0.505380i) q^{62} +(-0.227062 - 0.423670i) q^{63} +(7.97061 + 0.685111i) q^{64} +(10.8955 + 6.29049i) q^{65} +(3.22809 - 10.7431i) q^{66} +(-3.19984 + 7.53399i) q^{67} +(3.33992 + 2.05775i) q^{68} +(10.5483 - 2.64842i) q^{69} +(-0.360641 - 0.645788i) q^{70} +(-2.11856 - 3.66945i) q^{71} +(0.631454 - 8.46175i) 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} +(-9.18844 + 2.16791i) 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} +(0.529226 + 0.167304i) q^{84} +(3.20137 - 5.54494i) q^{85} +(-0.0926453 + 6.48250i) q^{86} +(6.75799 + 1.92579i) q^{87} +(5.98977 + 11.4849i) q^{88} -1.13753i q^{89} +(-13.8345 - 0.635522i) q^{90} -0.617539i q^{91} +(-6.58729 + 10.6918i) q^{92} +(1.22087 + 0.347905i) q^{93} +(-5.60352 - 10.0341i) q^{94} +(-9.67368 + 16.7553i) q^{95} +(6.29805 + 7.50563i) q^{96} +(-4.43186 + 7.67620i) q^{97} +(5.05315 - 8.47043i) q^{98} +(12.1093 - 6.48984i) 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	$-0.739561\pi$
$5$		−	3.26426i		−	1.45982i	0.683542	−	0.729911i	$-0.260439\pi$
$6$	1.67914	+	1.78339i	0.685507	+	0.728066i
$7$	−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	$-0.924103\pi$
$11$	−2.28979	−	3.96603i	−0.690397	−	1.19580i	0.281311	−	0.959617i	$-0.409231\pi$
$12$	−2.33838	−	2.55577i	−0.675033	−	0.737787i
$13$	−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	0.691645	−	0.722238i	$-0.256886\pi$
$17$	1.69868	+	0.980734i	0.411991	+	0.237863i	−0.279654	+	0.960101i	$0.590220\pi$
$18$	0.194691	−	4.23817i	0.0458891	−	0.998947i
$19$	−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
$21$	0.266896	+	0.0760559i	0.0582414	+	0.0165968i
$22$	3.15777	+	5.65451i	0.673238	+	1.20555i
$23$	−3.13953	+	5.43782i	−0.654637	+	1.13386i	0.327347	+	0.944904i	$0.393845\pi$
$23$	−3.13953	+	5.43782i	−0.654637	+	1.13386i	−0.981985	+	0.188961i	$0.939488\pi$
$24$	3.25499	+	3.66129i	0.664421	+	0.747358i
$25$	−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	−0.789392	−	0.613890i	$-0.789604\pi$
$29$	−3.51351	+	2.02853i	−0.652443	+	0.376688i	0.136948	+	0.990578i	$0.456271\pi$
$30$	5.82145	−	5.48116i	1.06285	−	1.00072i
$31$	−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
$33$	−2.17382	+	7.62837i	−0.378413	+	1.32793i
$34$	−2.38223	−	1.42115i	−0.408549	−	0.243726i
$35$	0.261511	+	0.452950i	0.0442034	+	0.0765626i
$36$	−0.360957	+	5.98913i	−0.0601595	+	0.998189i
$37$	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
$39$	6.47464	−	1.62563i	1.03677	−	0.260310i
$40$	−0.395704	+	9.22424i	−0.0625662	+	1.45848i
$41$	9.85112	−	5.68755i	1.53849	−	0.888246i	0.539559	−	0.841948i	$-0.318591\pi$
$41$	9.85112	−	5.68755i	1.53849	−	0.888246i	0.998928	−	0.0462983i	$-0.0147425\pi$
$42$	−0.375872	−	0.112942i	−0.0579983	−	0.0174273i
$43$		−	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	$0.0352673\pi$
$47$	4.06328	+	7.03780i	0.592690	+	1.02657i	−0.401179	+	0.916000i	$0.631399\pi$
$48$	−4.52878	−	5.24310i	−0.653673	−	0.756777i
$49$	−3.48716	+	6.03994i	−0.498166	+	0.862849i
$50$	7.99714	+	0.114292i	1.13097	+	0.0161633i
$51$	−0.827321	−	3.29509i	−0.115848	−	0.461405i
$52$	−4.04336	+	6.56273i	−0.560713	+	0.910087i
$53$			11.1601i			1.53295i	0.642273	+	0.766476i	$0.277991\pi$
$53$			11.1601i			1.53295i	−0.642273	+	0.766476i	$0.722009\pi$
$54$	−5.50672	+	4.86580i	−0.749370	+	0.662151i
$55$	−12.9462	+	7.47446i	−1.74566	+	1.00786i
$56$	0.401825	−	0.209566i	0.0536961	−	0.0280044i
$57$	2.49994	+	9.95687i	0.331125	+	1.31882i
$58$	5.00935	−	2.79747i	0.657760	−	0.367326i
$59$	−13.8883			−1.80810			−0.904052	−	0.427422i	$-0.859422\pi$
$59$	−13.8883			−1.80810			−0.904052	+	0.427422i	$0.859422\pi$
$60$	−8.34271	+	7.63310i	−1.07704	+	0.985429i
$61$	−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
$63$	−0.227062	−	0.423670i	−0.0286071	−	0.0533774i
$64$	7.97061	+	0.685111i	0.996326	+	0.0856388i
$65$	10.8955	+	6.29049i	1.35141	+	0.780240i
$66$	3.22809	−	10.7431i	0.397351	−	1.32239i
$67$	−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
$69$	10.5483	−	2.64842i	1.26986	−	0.318833i
$70$	−0.360641	−	0.645788i	−0.0431048	−	0.0771864i
$71$	−2.11856	−	3.66945i	−0.251427	−	0.435484i	0.712492	−	0.701680i	$-0.247566\pi$
$71$	−2.11856	−	3.66945i	−0.251427	−	0.435484i	−0.963919	+	0.266196i	$0.914233\pi$
$72$	0.631454	−	8.46175i	0.0744176	−	0.997227i
$73$	−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
$78$	−9.18844	+	2.16791i	−1.04039	+	0.245467i
$79$	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	−0.999996	−	0.00272128i	$-0.999134\pi$
$83$	−4.53373	+	7.85265i	−0.497641	+	0.861940i	0.502355	+	0.864662i	$0.332467\pi$
$84$	0.529226	+	0.167304i	0.0577433	+	0.0182544i
$85$	3.20137	−	5.54494i	0.347238	−	0.601433i
$86$	−0.0926453	+	6.48250i	−0.00999020	+	0.699025i
$87$	6.75799	+	1.92579i	0.724533	+	0.206466i
$88$	5.98977	+	11.4849i	0.638512	+	1.22429i
$89$		−	1.13753i		−	0.120578i	−0.998181	−	0.0602891i	$-0.980798\pi$
$89$		−	1.13753i		−	0.120578i	0.998181	−	0.0602891i	$-0.0192023\pi$
$90$	−13.8345	−	0.635522i	−1.45828	−	0.0669899i
$91$		−	0.617539i		−	0.0647357i
$92$	−6.58729	+	10.6918i	−0.686773	+	1.11469i
$93$	1.22087	+	0.347905i	0.126598	+	0.0360761i
$94$	−5.60352	−	10.0341i	−0.577959	−	1.03493i
$95$	−9.67368	+	16.7553i	−0.992499	+	1.71906i
$96$	6.29805	+	7.50563i	0.642792	+	0.766041i
$97$	−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
$99$	12.1093	−	6.48984i	1.21703	−	0.652253i
$100$	−11.3062	−	0.323234i	−1.13062	−	0.0323234i
$101$	−1.30801	+	0.755181i	−0.130152	+	0.0751433i	−0.563662	−	0.826005i	$-0.690608\pi$
$101$	−1.30801	+	0.755181i	−0.130152	+	0.0751433i	0.433510	+	0.901149i	$0.357275\pi$
$102$	1.10330	+	4.67620i	0.109243	+	0.463013i
$103$	−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
$105$	0.248266	−	0.871217i	0.0242283	−	0.0850221i
$106$	0.225537	−	15.7811i	0.0219061	−	1.53279i
$107$	14.1483			1.36777			0.683883	−	0.729592i	$-0.260290\pi$
$107$	14.1483			1.36777			0.683883	+	0.729592i	$0.260290\pi$
$108$	7.88522	−	6.76929i	0.758756	−	0.651375i
$109$	−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
$111$	−19.7002	+	4.94628i	−1.86986	+	0.469480i
$112$	−0.572443	+	0.288220i	−0.0540908	+	0.0272342i
$113$	−3.24018	+	1.87072i	−0.304811	+	0.175983i	−0.644602	−	0.764518i	$-0.722977\pi$
$113$	−3.24018	+	1.87072i	−0.304811	+	0.175983i	0.339791	+	0.940501i	$0.389644\pi$
$114$	−3.33387	−	14.1302i	−0.312245	−	1.32342i
$115$	17.7505	+	10.2482i	1.65524	+	0.955654i
$116$	−7.14010	+	3.85459i	−0.662942	+	0.357889i
$117$	−9.82566	−	6.09487i	−0.908382	−	0.563471i
$118$	19.6390	+	0.280674i	1.80792	+	0.0258381i
$119$	−0.314279			−0.0288099
$120$	11.9514	−	10.6251i	1.09101	−	0.969937i
$121$	−4.98624	+	8.63643i	−0.453295	+	0.785130i
$122$	3.40361	−	5.70536i	0.308149	−	0.516539i
$123$	−18.9479	−	5.39949i	−1.70848	−	0.486856i
$124$	−1.28990	+	0.696354i	−0.115837	+	0.0625344i
$125$			2.13942i			0.191356i
$126$	0.312519	+	0.603688i	0.0278414	+	0.0537808i
$127$	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	$-0.400232\pi$
$131$	7.05785			0.616648			0.308324	+	0.951281i	$0.400232\pi$
$132$	−4.78186	+	15.1263i	−0.416207	+	1.31657i
$133$	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	$-0.797482\pi$
$137$		−	13.9091i		−	1.18833i	0.804343	−	0.594165i	$-0.202518\pi$
$138$	−14.9695	+	3.53188i	−1.27429	+	0.300654i
$139$		−	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
$141$	3.85749	−	13.5367i	0.324859	−	1.14000i
$142$	2.92163	+	5.23168i	0.245178	+	0.439032i
$143$	17.6504			1.47600
$144$	−1.06393	+	11.9527i	−0.0886605	+	0.996062i
$145$	6.62165	+	11.4690i	0.549898	+	0.952451i
$146$	1.81329	−	3.03955i	0.150069	−	0.251555i
$147$	11.7162	−	2.94168i	0.966339	−	0.242626i
$148$	12.3026	−	19.9683i	1.01127	−	1.64138i
$149$		−	16.1239i		−	1.32092i	−0.750860	−	0.660462i	$-0.770361\pi$
$149$		−	16.1239i		−	1.32092i	0.750860	−	0.660462i	$-0.229639\pi$
$150$	−9.49624	−	10.0858i	−0.775365	−	0.823502i
$151$	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
$153$	−3.10181	+	5.00049i	−0.250767	+	0.404266i
$154$	−0.891175	−	0.531643i	−0.0718129	−	0.0428410i
$155$	1.19624	+	2.07195i	0.0960843	+	0.166423i
$156$	13.0369	−	2.87988i	1.04379	−	0.230575i
$157$	−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
$162$	12.6897	+	0.985677i	0.996997	+	0.0774421i
$163$	−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
$165$	24.9010	+	7.09591i	1.93854	+	0.552416i
$166$	6.56970	−	11.0126i	0.509908	−	0.854741i
$167$	−2.79975	−	4.84931i	−0.216651	−	0.375251i	0.737131	−	0.675750i	$-0.236180\pi$
$167$	−2.79975	−	4.84931i	−0.216651	−	0.375251i	−0.953782	+	0.300499i	$0.902847\pi$
$168$	−0.744981	−	0.247275i	−0.0574766	−	0.0190777i
$169$	−0.927272	−	1.60608i	−0.0713286	−	0.123545i
$170$	−4.63902	+	7.77623i	−0.355797	+	0.596410i
$171$	9.37284	−	15.1101i	0.716759	−	1.15550i
$172$	0.262014	−	9.16482i	0.0199784	−	0.698811i
$173$	−10.1245	−	5.84541i	−0.769755	−	0.444418i	0.0630324	−	0.998011i	$-0.479923\pi$
$173$	−10.1245	−	5.84541i	−0.769755	−	0.444418i	−0.832787	+	0.553593i	$0.813256\pi$
$174$	−9.51735	−	2.85978i	−0.721509	−	0.216799i
$175$	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	$-0.564695\pi$
$179$	−5.40113			−0.403699			−0.201850	+	0.979417i	$0.564695\pi$
$180$	19.5501	+	1.17826i	1.45718	+	0.0878221i
$181$	−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
$183$	7.89161	−	1.98140i	0.583365	−	0.146470i
$184$	9.53096	−	14.9858i	0.702632	−	1.10477i
$185$	−33.1514	−	19.1400i	−2.43734	−	1.40720i
$186$	−1.71937	−	0.516635i	−0.126070	−	0.0378815i
$187$		−	8.98268i		−	0.656879i
$188$	7.72099	+	14.3021i	0.563111	+	1.04309i
$189$	−0.253363	+	0.793075i	−0.0184294	+	0.0576877i
$190$	14.0179	−	23.4977i	1.01696	−	1.70470i
$191$	4.04451	−	7.00529i	0.292650	−	0.506885i	−0.681785	−	0.731552i	$-0.738796\pi$
$191$	4.04451	−	7.00529i	0.292650	−	0.506885i	0.974436	+	0.224667i	$0.0721295\pi$
$192$	−8.75420	−	10.7408i	−0.631780	−	0.775148i
$193$	−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
$195$	−5.30649	−	21.1349i	−0.380006	−	1.51350i
$196$	−7.31669	+	11.8756i	−0.522621	+	0.848261i
$197$	−4.23128	+	2.44293i	−0.301466	+	0.174051i	−0.643101	−	0.765781i	$-0.722353\pi$
$197$	−4.23128	+	2.44293i	−0.301466	+	0.174051i	0.341635	+	0.939833i	$0.389019\pi$
$198$	−17.2545	+	8.93236i	−1.22622	+	0.634795i
$199$	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
$201$	13.2285	−	5.09978i	0.933064	−	0.359710i
$202$	1.86488	−	1.04144i	0.131212	−	0.0732757i
$203$	0.325024	−	0.562959i	0.0228122	−	0.0395120i
$204$	−1.46564	−	6.63477i	−0.102615	−	0.464527i
$205$	−18.5657	−	32.1566i	−1.29668	−	2.24592i
$206$	2.32591	−	1.29891i	0.162054	−	0.0904991i
$207$	−16.0076	−	9.92954i	−1.11261	−	0.690151i
$208$	−8.45850	+	12.8890i	−0.586492	+	0.893692i
$209$			27.1432i			1.87754i
$210$	−0.368672	+	1.22694i	−0.0254408	+	0.0846672i
$211$	−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
$213$	−2.01126	+	7.05793i	−0.137809	+	0.483601i
$214$	−20.0067	−	0.285927i	−1.36763	−	0.0195456i
$215$	−14.9643			−1.02056
$216$	−11.2871	+	9.41288i	−0.767987	+	0.640466i
$217$	0.0587176	−	0.101702i	0.00398601	−	0.00690397i
$218$	10.2010	+	0.145788i	0.690897	+	0.00987403i
$219$	4.20428	−	1.05560i	0.284099	−	0.0713308i
$220$	−26.3089	+	14.2029i	−1.77375	+	0.957558i
$221$	−6.54698	+	3.77990i	−0.440398	+	0.254264i
$222$	27.9575	−	6.59625i	1.87638	−	0.442712i
$223$			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	0.988665	−	0.150141i	$-0.0479729\pi$
$227$	5.48882	+	9.50692i	0.364306	+	0.630997i	−0.624359	+	0.781138i	$0.714640\pi$
$228$	4.42876	+	20.0485i	0.293302	+	1.32774i
$229$	−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
$231$	−0.309494	−	1.23267i	−0.0203632	−	0.0811035i
$232$	10.1745	−	5.30635i	0.667988	−	0.348379i
$233$	21.9685	−	12.6835i	1.43921	−	0.830927i	0.441413	−	0.897304i	$-0.354477\pi$
$233$	21.9685	−	12.6835i	1.43921	−	0.830927i	0.997795	+	0.0663775i	$0.0211442\pi$
$234$	13.7710	+	8.81713i	0.900237	+	0.576394i
$235$	22.9732	−	13.2636i	1.49861	−	0.865222i
$236$	−27.7653	−	0.793784i	−1.80737	−	0.0516709i
$237$	−10.5260	−	2.99953i	−0.683735	−	0.194840i
$238$	0.444413	+	0.00635138i	0.0288070	+	0.000411699i
$239$	−10.8169	−	18.7354i	−0.699687	−	1.21189i	−0.968575	−	0.248722i	$-0.919990\pi$
$239$	−10.8169	−	18.7354i	−0.699687	−	1.21189i	0.268888	−	0.963171i	$-0.413344\pi$
$240$	−17.1149	+	14.7831i	−1.10476	+	0.954247i
$241$	−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
$246$	26.6846	+	8.01818i	1.70135	+	0.511221i
$247$	19.7832	−	11.4219i	1.25878	−	0.726755i
$248$	1.83808	−	0.958624i	0.116718	−	0.0608727i
$249$	15.2325	−	3.82453i	0.965321	−	0.242370i
$250$	0.0432363	−	3.02529i	0.00273450	−	0.191336i
$251$	−15.2605	+	26.4319i	−0.963233	+	1.66837i	−0.248944	+	0.968518i	$0.580083\pi$
$251$	−15.2605	+	26.4319i	−0.963233	+	1.66837i	−0.714289	+	0.699851i	$0.753250\pi$
$252$	−0.429723	−	0.859972i	−0.0270700	−	0.0541731i
$253$	28.7554			1.80784
$254$	−2.27436	+	1.27012i	−0.142706	+	0.0796942i
$255$	−10.7560	+	2.70059i	−0.673569	+	0.169118i
$256$	15.8956	+	1.82522i	0.993472	+	0.114076i
$257$	−24.1344	+	13.9340i	−1.50546	+	0.869180i	−0.505483	+	0.862836i	$0.668686\pi$
$257$	−24.1344	+	13.9340i	−1.50546	+	0.869180i	−0.999980	+	0.00634335i	$0.997981\pi$
$258$	8.17557	−	7.69767i	0.508988	−	0.479236i
$259$			1.87897i			0.116754i
$260$	21.4225	+	13.1986i	1.32857	+	0.818541i
$261$	−5.74937	−	10.7276i	−0.355877	−	0.664024i
$262$	−9.98029	−	0.142635i	−0.616585	−	0.00881199i
$263$	−4.04383			−0.249353			−0.124677	−	0.992197i	$-0.539789\pi$
$263$	−4.04383			−0.249353			−0.124677	+	0.992197i	$0.539789\pi$
$264$	7.06757	−	21.2929i	0.434979	−	1.31049i
$265$	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	$0.0359162\pi$
$269$			3.69339i			0.225190i	−0.993641	+	0.112595i	$0.964084\pi$
$270$	15.8832	+	17.9754i	0.966623	+	1.09395i
$271$		−	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
$276$	21.2393	−	4.69180i	1.27845	−	0.282413i
$277$	−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
$279$	−1.03866	−	1.93801i	−0.0621828	−	0.116026i
$280$	−0.684077	−	1.31166i	−0.0408814	−	0.0783867i
$281$	−16.3857	−	9.46026i	−0.977486	−	0.564352i	−0.0759760	−	0.997110i	$-0.524207\pi$
$281$	−16.3857	−	9.46026i	−0.977486	−	0.564352i	−0.901510	+	0.432758i	$0.857541\pi$
$282$	−5.72832	+	19.0639i	−0.341116	+	1.13524i
$283$			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
$285$	32.5018	−	8.16046i	1.92524	−	0.483384i
$286$	−24.9589	−	0.356703i	−1.47585	−	0.0210923i
$287$	−0.911297	+	1.57841i	−0.0537922	+	0.0931708i
$288$	1.74602	−	16.8805i	0.102885	−	0.994693i
$289$	−6.57632	−	11.3905i	−0.386843	−	0.670031i
$290$	−9.13169	−	16.3518i	−0.536231	−	0.960212i
$291$	14.8902	−	3.73860i	0.872881	−	0.219160i
$292$	−2.62554	+	4.26148i	−0.153648	+	0.249385i
$293$			0.0667158i			0.00389758i	0.999998	+	0.00194879i	$0.000620319\pi$
$293$			0.0667158i			0.00389758i	−0.999998	+	0.00194879i	$0.999380\pi$
$294$	−16.6270	+	3.92296i	−0.969708	+	0.228792i
$295$			45.3351i			2.63951i
$296$	−17.8003	+	27.9879i	−1.03462	+	1.62676i
$297$	−22.6675	−	7.24157i	−1.31530	−	0.420199i
$298$	−0.325854	+	22.8003i	−0.0188762	+	1.32079i
$299$	−12.1002	−	20.9582i	−0.699775	−	1.21205i
$300$	13.2245	+	14.4539i	0.763518	+	0.834498i
$301$	0.367262	+	0.636117i	0.0211687	+	0.0366652i
$302$	−8.01375	−	4.78072i	−0.461139	−	0.275099i
$303$	2.51587	+	0.716933i	0.144533	+	0.0411867i
$304$	−19.8210	−	13.0077i	−1.13681	−	0.746043i
$305$	13.2799	+	7.66717i	0.760406	+	0.439021i
$306$	4.48723	−	7.00836i	0.256518	−	0.400641i
$307$	−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
$309$	3.13783	+	0.894171i	0.178505	+	0.0508676i
$310$	−1.64969	−	2.95405i	−0.0936963	−	0.167779i
$311$	−11.3942			−0.646108			−0.323054	−	0.946381i	$-0.604710\pi$
$311$	−11.3942			−0.646108			−0.323054	+	0.946381i	$0.604710\pi$
$312$	−18.4933	+	3.80889i	−1.04698	+	0.215636i
$313$	−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
$315$	−1.38297	+	0.741189i	−0.0779215	+	0.0417612i
$316$	11.1211	−	6.00374i	0.625612	−	0.337737i
$317$	−30.2129	−	17.4434i	−1.69693	−	0.979722i	−0.948646	−	0.316341i	$-0.897546\pi$
$317$	−30.2129	−	17.4434i	−1.69693	−	0.979722i	−0.748282	−	0.663381i	$-0.769121\pi$
$318$	−19.9027	+	18.7393i	−1.11609	+	1.05085i
$319$	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
$324$	−17.9242	−	1.65027i	−0.995788	−	0.0916814i
$325$	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
$330$	−35.0683	−	10.5373i	−1.93045	−	0.580061i
$331$	−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
$333$	29.8963	+	18.5447i	1.63831	+	1.01624i
$334$	3.86104	+	6.91384i	0.211267	+	0.378309i
$335$	24.5929	+	10.4451i	1.34366	+	0.570677i
$336$	1.04846	+	0.364719i	0.0571981	+	0.0198971i
$337$	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
$339$	6.23226	+	1.77598i	0.338490	+	0.0964577i
$340$	6.71705	−	10.9024i	0.364283	−	0.591264i
$341$	2.90683	+	1.67826i	0.157413	+	0.0908827i
$342$	−13.5592	+	21.1774i	−0.733198	+	1.14514i
$343$		−	2.23906i		−	0.120898i
$344$	−0.555721	+	12.9544i	−0.0299624	+	0.698454i
$345$	−8.64515	−	34.4323i	−0.465439	−	1.85377i
$346$	14.1987	+	8.47042i	0.763325	+	0.455373i
$347$	3.49659	+	6.05627i	0.187707	+	0.325118i	0.944485	−	0.328554i	$-0.106561\pi$
$347$	3.49659	+	6.05627i	0.187707	+	0.325118i	−0.756779	+	0.653671i	$0.773228\pi$
$348$	13.4004	+	4.23626i	0.718337	+	0.227087i
$349$	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
$351$	4.26049	+	19.5684i	0.227408	+	1.04448i
$352$	11.3182	+	23.3027i	0.603264	+	1.24204i
$353$	−24.6286	−	14.2193i	−1.31085	−	0.756819i	−0.328612	−	0.944465i	$-0.606581\pi$
$353$	−24.6286	−	14.2193i	−1.31085	−	0.756819i	−0.982237	+	0.187646i	$0.939914\pi$
$354$	−23.3205	−	24.7683i	−1.23947	−	1.31642i
$355$	−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	$-0.185543\pi$
$359$	31.6370			1.66974			0.834870	+	0.550448i	$0.185543\pi$
$360$	−27.6214	−	2.06123i	−1.45577	−	0.108636i
$361$	8.06481	+	13.9687i	0.424464	+	0.735193i
$362$	9.22207	+	16.5137i	0.484701	+	0.867939i
$363$	16.7529	−	4.20626i	0.879298	−	0.220772i
$364$	0.0352953	−	1.23457i	0.00184998	−	0.0647093i
$365$	7.07492	+	4.08471i	0.370318	+	0.213803i
$366$	−11.1993	+	2.64236i	−0.585398	+	0.138118i
$367$	−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
$369$	16.1200	+	30.0779i	0.839172	+	1.56579i
$370$	46.4915	+	27.7352i	2.41698	+	1.44188i
$371$	−0.894069	−	1.54857i	−0.0464178	−	0.0803979i
$372$	2.42086	+	0.765305i	0.125516	+	0.0396792i
$373$	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
$378$	0.374300	−	1.11634i	0.0192519	−	0.0574184i
$379$	−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
$381$	−3.06828	−	0.874352i	−0.157193	−	0.0447944i
$382$	−5.86078	+	9.82423i	−0.299864	+	0.502651i
$383$	−7.33196	+	12.6993i	−0.374646	+	0.648906i	−0.990274	−	0.139131i	$-0.955569\pi$
$383$	−7.33196	+	12.6993i	−0.374646	+	0.648906i	0.615628	+	0.788037i	$0.288902\pi$
$384$	12.1620	+	15.3651i	0.620638	+	0.784097i
$385$	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	0.114916	−	0.993375i	$-0.463340\pi$
$389$	−13.5678	−	7.83337i	−0.687915	−	0.397168i	−0.802830	+	0.596208i	$0.796674\pi$
$390$	7.07663	+	29.9935i	0.358339	+	1.51878i
$391$	−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
$396$	24.5796	−	12.2823i	1.23517	−	0.617207i
$397$	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	$-0.896171\pi$
$401$		−	12.8334i		−	0.640872i	0.947270	−	0.320436i	$-0.103829\pi$
$402$	−18.8090	+	6.94410i	−0.938109	+	0.346340i
$403$		−	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
$408$	1.93843	+	9.41164i	0.0959664	+	0.465946i
$409$	−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
$414$	22.4352	+	14.3646i	1.10263	+	0.705980i
$415$	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	−0.892243	−	0.451556i	$-0.850869\pi$
$419$	−1.12710	+	1.95219i	−0.0550623	+	0.0953707i	0.837180	+	0.546927i	$0.184202\pi$
$420$	0.546124	−	1.72753i	0.0266481	−	0.0842950i
$421$	−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
$423$	−21.4882	+	11.5164i	−1.04479	+	0.559945i
$424$	1.35285	−	31.5364i	0.0657004	−	1.53154i
$425$	−9.60673	−	5.54645i	−0.465995	−	0.269042i
$426$	2.98670	−	9.93975i	0.144706	−	0.481583i
$427$		−	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	0.961650	−	0.274278i	$-0.0884388\pi$
$431$	5.05091	+	8.74842i	0.243294	+	0.421397i	−0.718357	+	0.695675i	$0.755106\pi$
$432$	16.1509	−	13.0824i	0.777061	−	0.629426i
$433$	−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
$435$	6.28629	−	22.0599i	0.301404	−	1.05769i
$436$	−14.4219	−	0.412310i	−0.690685	−	0.0197461i
$437$	32.2301	−	18.6081i	1.54178	−	0.890145i
$438$	−5.96648	+	1.40772i	−0.285089	+	0.0672637i
$439$	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
$441$	−17.7801	−	11.0290i	−0.846671	−	0.525191i
$442$	9.33428	−	5.21273i	0.443986	−	0.247945i
$443$	8.35524	+	14.4717i	0.396969	+	0.687571i	0.993350	−	0.115130i	$-0.0367286\pi$
$443$	8.35524	+	14.4717i	0.396969	+	0.687571i	−0.596381	+	0.802701i	$0.703395\pi$
$444$	−39.6671	+	8.76256i	−1.88252	+	0.415853i
$445$	−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	−0.931319	−	0.364204i	$-0.881341\pi$
$449$	−22.9180	+	13.2317i	−1.08157	+	0.624444i	−0.150250	+	0.988648i	$0.548008\pi$
$450$	−1.10106	+	23.9686i	−0.0519043	+	1.12989i
$451$	−45.1139	−	26.0465i	−2.12433	−	1.22648i
$452$	−6.58464	+	3.55472i	−0.309715	+	0.167200i
$453$	−2.78308	−	11.0846i	−0.130760	−	0.520798i
$454$	−7.56945	−	13.5544i	−0.355252	−	0.636138i
$455$	−2.01581			−0.0945026
$456$	−5.85740	−	28.4394i	−0.274298	−	1.33180i
$457$	−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
$459$	9.95878	−	2.16826i	0.464836	−	0.101206i
$460$	34.9007	+	21.5027i	1.62726	+	1.00257i
$461$			17.3200i			0.806672i	0.915052	+	0.403336i	$0.132149\pi$
$461$			17.3200i			0.806672i	−0.915052	+	0.403336i	$0.867851\pi$
$462$	0.412735	+	1.74933i	0.0192022	+	0.0813862i
$463$	−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
$465$	1.13565	−	3.98524i	0.0526647	−	0.184811i
$466$	−31.3214	+	17.4914i	−1.45093	+	0.810275i
$467$	4.65066	−	8.05518i	0.215207	−	0.372749i	−0.738130	−	0.674659i	$-0.764291\pi$
$467$	4.65066	−	8.05518i	0.215207	−	0.372749i	0.953337	+	0.301910i	$0.0976241\pi$
$468$	−19.2949	−	12.7463i	−0.891909	−	0.589200i
$469$	−0.159563	−	1.30177i	−0.00736792	−	0.0601101i
$470$	−32.7538	+	18.2914i	−1.51082	+	0.843718i
$471$	25.6474	−	6.43948i	1.18177	−	0.296715i
$472$	39.2460	+	1.68358i	1.80644	+	0.0774932i
$473$	−18.1814	+	10.4970i	−0.835981	+	0.482654i
$474$	14.8238	+	4.45427i	0.680881	+	0.204591i
$475$	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	−0.549830	−	0.835277i	$-0.685307\pi$
$479$	9.81494	−	17.0000i	0.448456	−	0.776749i	0.998286	+	0.0585279i	$0.0186407\pi$
$480$	24.5004	−	20.5585i	1.11828	−	0.938362i
$481$	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
$486$	−14.0679	−	16.9733i	−0.638133	−	0.769926i
$487$	−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
$489$	13.6260	+	3.88294i	0.616190	+	0.175592i
$490$	−27.6497	−	16.4948i	−1.24909	−	0.745160i
$491$	12.0872			0.545488			0.272744	−	0.962087i	$-0.412069\pi$
$491$	12.0872			0.545488			0.272744	+	0.962087i	$0.412069\pi$
$492$	−37.5718	−	11.8775i	−1.69387	−	0.535481i
$493$	−7.95779			−0.358401
$494$	−28.2057	+	15.7515i	−1.26903	+	0.708693i
$495$	−21.1845	−	39.5278i	−0.952174	−	1.77664i
$496$	−2.61855	+	1.31841i	−0.117576	+	0.0591986i
$497$	0.587944	+	0.339450i	0.0263729	+	0.0152264i
$498$	−21.6171	+	5.10032i	−0.968686	+	0.228551i
$499$	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
$501$	−2.65795	+	9.32731i	−0.118749	+	0.416713i
$502$	22.1135	−	37.0682i	0.986976	−	1.65443i
$503$	−9.03287	−	15.6454i	−0.402756	−	0.697593i	0.591302	−	0.806450i	$-0.298614\pi$
$503$	−9.03287	−	15.6454i	−0.402756	−	0.697593i	−0.994057	+	0.108857i	$0.965281\pi$
$504$	0.590278	+	1.22474i	0.0262931	+	0.0545544i
$505$	2.46511	+	4.26969i	0.109696	+	0.189999i
$506$	−40.6621	−	0.581128i	−1.80765	−	0.0258343i
$507$	−0.880309	+	3.08918i	−0.0390959	+	0.137195i
$508$	3.24177	−	1.75007i	0.143830	−	0.0776467i
$509$			23.8953i			1.05914i	0.848266	+	0.529570i	$0.177647\pi$
$509$			23.8953i			1.05914i	−0.848266	+	0.529570i	$0.822353\pi$
$510$	15.2643	−	3.60145i	0.675917	−	0.159475i
$511$		−	0.400997i		−	0.0177391i
$512$	−22.4405	−	2.90223i	−0.991740	−	0.128261i
$513$	−30.0927	+	6.55189i	−1.32863	+	0.289273i
$514$	34.4093	−	19.2159i	1.51773	−	0.847578i
$515$	3.07452	+	5.32523i	0.135480	+	0.234658i
$516$	−11.7164	+	10.7198i	−0.515785	+	0.471914i
$517$	18.6081	−	32.2301i	0.818382	−	1.41748i
$518$	0.0379728	−	2.65700i	0.00166843	−	0.116742i
$519$	4.93103	+	19.6395i	0.216448	+	0.862079i
$520$	−30.0261	−	19.0966i	−1.31673	−	0.837443i
$521$		−	18.0615i		−	0.791288i	−0.918404	−	0.395644i	$-0.870522\pi$
$521$		−	18.0615i		−	0.791288i	0.918404	−	0.395644i	$-0.129478\pi$
$522$	7.91320	+	15.2858i	0.346351	+	0.669042i
$523$	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
$525$	−1.50940	−	0.430127i	−0.0658758	−	0.0187723i
$526$	5.71826	+	0.0817232i	0.249328	+	0.00356330i
$527$	−1.43762			−0.0626238
$528$	−10.4243	+	29.9669i	−0.453661	+	1.30414i
$529$	−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
$534$	2.02866	−	1.91008i	0.0877889	−	0.0826573i
$535$		−	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
$540$	−22.0967	−	25.7394i	−0.950892	−	1.10765i
$541$	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
$543$	−6.34850	+	22.2782i	−0.272440	+	0.956049i
$544$	−9.18859	−	6.21973i	−0.393958	−	0.266669i
$545$			23.5481i			1.00869i
$546$	1.10131	−	1.03694i	0.0471318	−	0.0443768i
$547$	−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
$549$	−11.9760	−	7.42873i	−0.511123	−	0.317050i
$550$	−17.8585	−	31.9786i	−0.761487	−	1.36357i
$551$	24.0463			1.02441
$552$	−30.1286	+	6.20530i	−1.28236	+	0.264115i
$553$	−0.506244	+	0.876841i	−0.0215277	+	0.0372871i
$554$	0.00862592		0.000123278i	0.000366480		5.23759e-6i
$555$	16.1460	+	64.3068i	0.685358	+	2.72967i
$556$	0.215609	−	7.54166i	0.00914385	−	0.319837i
$557$	28.3558	−	16.3712i	1.20147	−	0.693670i	0.240589	−	0.970627i	$-0.422659\pi$
$557$	28.3558	−	16.3712i	1.20147	−	0.693670i	0.960882	+	0.276957i	$0.0893259\pi$
$558$	1.42957	+	2.76147i	0.0605184	+	0.116902i
$559$	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	$-0.809992\pi$
$563$	−39.2486			−1.65413			−0.827066	+	0.562105i	$0.809992\pi$
$564$	8.48551	−	26.8419i	0.357304	−	1.13025i
$565$	6.10652	+	10.5768i	0.256903	+	0.444970i
$566$	0.00904953	−	0.633206i	0.000380380	−	0.0266156i
$567$	1.29191	−	0.640669i	0.0542550	−	0.0269056i
$568$	5.54186	+	10.6261i	0.232531	+	0.445860i
$569$	6.00999	−	3.46987i	0.251952	−	0.145464i	−0.368706	−	0.929546i	$-0.620199\pi$
$569$	6.00999	−	3.46987i	0.251952	−	0.145464i	0.620658	+	0.784082i	$0.286866\pi$
$570$	−46.1247	+	10.8826i	−1.93195	+	0.455823i
$571$	−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
$573$	−13.5888	+	3.41184i	−0.567681	+	0.142532i
$574$	1.32054	−	2.21357i	0.0551181	−	0.0923925i
$575$	17.7553	−	30.7531i	0.740448	−	1.28249i
$576$	−2.81014	+	23.8349i	−0.117089	+	0.993121i
$577$	−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
$582$	−21.1314	+	4.98571i	−0.875924	+	0.206664i
$583$	44.2611	−	25.5541i	1.83311	−	1.05834i
$584$	3.79881	−	5.97297i	0.157196	−	0.247163i
$585$	−19.8952	+	32.0735i	−0.822567	+	1.32608i
$586$	0.00134828	−	0.0943407i	5.56970e−5	−	0.00389718i
$587$	2.74961	−	4.76246i	0.113488	−	0.196568i	−0.803686	−	0.595053i	$-0.797131\pi$
$587$	2.74961	−	4.76246i	0.113488	−	0.196568i	0.917174	+	0.398486i	$0.130464\pi$
$588$	23.5910	−	5.21132i	0.972878	−	0.214911i
$589$	4.34410			0.178996
$590$	0.916192	−	64.1070i	0.0377190	−	2.63924i
$591$	8.13856	+	2.31920i	0.334775	+	0.0953993i
$592$	25.7365	−	39.2171i	1.05776	−	1.61181i
$593$	−34.7977	−	20.0904i	−1.42897	−	0.825016i	−0.431930	−	0.901907i	$-0.642167\pi$
$593$	−34.7977	−	20.0904i	−1.42897	−	0.825016i	−0.997039	+	0.0768917i	$0.975500\pi$
$594$	31.9071	+	10.6982i	1.30916	+	0.438952i
$595$			1.02589i			0.0420574i
$596$	0.921559	−	32.2347i	0.0377485	−	1.32038i
$597$	−2.92482	−	11.6491i	−0.119705	−	0.476765i
$598$	16.6870	+	29.8809i	0.682384	+	1.22192i
$599$	11.7651	+	20.3777i	0.480709	+	0.832612i	0.999755	−	0.0221343i	$-0.00704613\pi$
$599$	11.7651	+	20.3777i	0.480709	+	0.832612i	−0.519046	+	0.854746i	$0.673713\pi$
$600$	−18.4083	−	20.7061i	−0.751514	−	0.845323i
$601$	−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
$603$	−22.2873	−	10.3091i	−0.907607	−	0.419821i
$604$	11.2354	+	6.92222i	0.457161	+	0.281661i
$605$	28.1916	+	16.2764i	1.14615	+	0.661730i
$606$	−3.54312	−	1.06464i	−0.143929	−	0.0432479i
$607$	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
$609$	−1.09202	+	0.274182i	−0.0442510	+	0.0111104i
$610$	−18.6238	−	11.1103i	−0.754055	−	0.449842i
$611$	−31.3210			−1.26711
$612$	−6.48689	+	9.81962i	−0.262217	+	0.396935i
$613$	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
$615$	−17.6254	+	61.8510i	−0.710723	+	2.49407i
$616$	−1.75124	−	1.11379i	−0.0705593	−	0.0448757i
$617$		−	16.2201i		−	0.652997i	−0.945198	−	0.326498i	$-0.894131\pi$
$617$		−	16.2201i		−	0.652997i	0.945198	−	0.326498i	$-0.105869\pi$
$618$	−4.41904	−	1.32783i	−0.177760	−	0.0534133i
$619$	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
$621$	6.94103	+	31.8801i	0.278534	+	1.27930i
$622$	16.1122	+	0.230270i	0.646042	+	0.00923298i
$623$	0.0911316	+	0.157845i	0.00365111	+	0.00632391i
$624$	26.2278	−	5.01229i	1.04995	−	0.200652i
$625$	−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
$630$	1.97059	−	1.02014i	0.0785104	−	0.0406435i
$631$	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
$633$	8.41081	+	33.4989i	0.334300	+	1.33146i
$634$	42.3707	+	25.2768i	1.68275	+	1.00387i
$635$	−3.00638	−	5.20720i	−0.119304	−	0.206641i
$636$	28.5225	−	26.0965i	1.13099	−	1.03479i
$637$	−13.4401	−	23.2789i	−0.532516	−	0.922344i
$638$	−22.5652	−	13.4616i	−0.893365	−	0.532949i
$639$	11.2038	−	6.00454i	0.443214	−	0.237536i
$640$	−3.68821	+	36.7463i	−0.145789	+	1.45252i
$641$	19.3962	−	11.1984i	0.766103	−	0.442310i	−0.0653794	−	0.997860i	$-0.520826\pi$
$641$	19.3962	−	11.1984i	0.766103	−	0.442310i	0.831483	+	0.555550i	$0.187492\pi$
$642$	23.7570	+	25.2319i	0.937614	+	0.995824i
$643$			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	−0.911603	−	0.411071i	$-0.865155\pi$
$647$	−2.53863	+	4.39704i	−0.0998038	+	0.172865i	0.811800	+	0.583936i	$0.198488\pi$
$648$	25.3127	+	2.69583i	0.994377	+	0.105902i
$649$	31.8013	+	55.0814i	1.24831	+	2.16214i
$650$	−15.7926	+	26.4726i	−0.619437	+	1.03834i
$651$	−0.197280	+	0.0495326i	−0.00773203	+	0.00194134i
$652$	−14.3965	+	7.77193i	−0.563809	+	0.304372i
$653$	8.45915	+	4.88389i	0.331032	+	0.191121i	0.656299	−	0.754501i	$-0.272121\pi$
$653$	8.45915	+	4.88389i	0.331032	+	0.191121i	−0.325267	+	0.945622i	$0.605454\pi$
$654$	−12.1132	−	12.8652i	−0.473663	−	0.503070i
$655$		−	23.0387i		−	0.900196i
$656$	40.6399	−	20.4618i	1.58672	−	0.798899i
$657$	−6.38025	−	3.95768i	−0.248917	−	0.154404i
$658$	1.58141	+	0.943412i	0.0616497	+	0.0367780i
$659$	−1.71880	−	2.97705i	−0.0669549	−	0.115969i	0.830605	−	0.556863i	$-0.187995\pi$
$659$	−1.71880	−	2.97705i	−0.0669549	−	0.115969i	−0.897559	+	0.440893i	$0.854662\pi$
$660$	49.3761	+	15.6092i	1.92196	+	0.607588i
$661$	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
$663$	12.5927	+	3.58846i	0.489058	+	0.139364i
$664$	13.7635	−	21.6406i	0.534126	−	0.839820i
$665$		−	3.09996i		−	0.120211i
$666$	−41.9007	−	26.8277i	−1.62362	−	1.03955i
$667$		−	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
$672$	−1.47522	−	0.536927i	−0.0569079	−	0.0207124i
$673$	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	−0.698285	−	0.715820i	$-0.746053\pi$
$677$	−11.1234	+	6.42212i	−0.427508	+	0.246822i	0.270776	+	0.962642i	$0.412720\pi$
$678$	−8.77696	−	2.63730i	−0.337077	−	0.101285i
$679$		−	1.42020i		−	0.0545024i
$680$	−9.71870	+	15.2810i	−0.372695	+	0.585998i
$681$	5.21083	−	18.2859i	0.199680	−	0.700716i
$682$	−4.07654	−	2.43192i	−0.156099	−	0.0931229i
$683$	−8.07672	+	13.9893i	−0.309047	+	0.535285i	−0.978154	−	0.207881i	$-0.933343\pi$
$683$	−8.07672	+	13.9893i	−0.309047	+	0.535285i	0.669107	+	0.743166i	$0.266677\pi$
$684$	19.6016	−	29.6722i	0.749488	−	1.13455i
$685$	−45.4028			−1.73475
$686$	−0.0452499	+	3.16619i	−0.00172765	+	0.120886i
$687$	3.25425	−	0.817068i	0.124157	−	0.0311731i
$688$	1.04763	−	18.3072i	0.0399404	−	0.697955i
$689$	−37.2500	−	21.5063i	−1.41911	−	0.819325i
$690$	11.5290	+	48.8643i	0.438901	+	1.86023i
$691$	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
$693$	−1.16036	+	1.87065i	−0.0440786	+	0.0710600i
$694$	−4.82203	−	8.63465i	−0.183042	−	0.327767i
$695$	−12.3140			−0.467097
$696$	−18.8635	−	6.26118i	−0.715018	−	0.237329i
$697$	22.3119			0.845123
$698$	−24.5646	−	0.351068i	−0.929783	−	0.0132881i
$699$	−42.2549	−	12.0412i	−1.59823	−	0.455439i
$700$	1.59475	−	0.860925i	0.0602758	−	0.0325399i
$701$	31.0034	−	17.8998i	1.17098	−	0.676066i	0.217070	−	0.976156i	$-0.430350\pi$
$701$	31.0034	−	17.8998i	1.17098	−	0.676066i	0.953911	+	0.300090i	$0.0970166\pi$
$702$	−5.62916	−	27.7571i	−0.212459	−	1.04763i
$703$	−60.1940	+	34.7530i	−2.27026	+	1.31073i
$704$	−15.5338	−	33.1804i	−0.585453	−	1.25053i
$705$	−44.1874	−	12.5918i	−1.66419	−	0.474236i
$706$	34.5392	+	20.6049i	1.29990	+	0.775474i
$707$	0.121000	−	0.209578i	0.00455068	−	0.00788200i
$708$	32.4762	+	35.4954i	1.22053	+	1.33400i
$709$	−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
$711$	8.95497	+	16.7089i	0.335838	+	0.626633i
$712$	−0.137895	+	3.21447i	−0.00516784	+	0.120467i
$713$		−	4.60212i		−	0.172351i
$714$	−0.527720	−	0.560483i	−0.0197494	−	0.0209755i
$715$		−	57.6155i		−	2.15470i
$716$	−10.7978	−	0.308700i	−0.403534	−	0.0115367i
$717$	−10.2691	+	36.0362i	−0.383505	+	1.34580i
$718$	−44.7370	−	0.639363i	−1.66957	−	0.0238608i
$719$	6.65515	−	11.5271i	0.248195	−	0.429886i	−0.714830	−	0.699298i	$-0.753496\pi$
$719$	6.65515	−	11.5271i	0.248195	−	0.429886i	0.963025	+	0.269412i	$0.0868293\pi$
$720$	39.0169	+	3.47293i	1.45407	+	0.129429i
$721$	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
$726$	−23.7747	+	5.60938i	−0.882363	+	0.208184i
$727$	−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
$732$	15.8900	−	3.51014i	0.587312	−	0.129739i
$733$	−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
$735$	−9.60241	−	38.2449i	−0.354190	−	1.41068i
$736$	19.9106	−	29.4146i	0.733916	−	1.08424i
$737$	37.2070	−	4.56060i	1.37054	−	0.167992i
$738$	−22.1869	−	42.8581i	−0.816710	−	1.57763i
$739$	−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
$741$	−38.0516	−	10.8434i	−1.39786	−	0.398341i
$742$	1.23298	+	2.20786i	0.0452641	+	0.0810530i
$743$	−10.3678	+	17.9576i	−0.380359	+	0.658802i	−0.991114	−	0.133019i	$-0.957533\pi$
$743$	−10.3678	+	17.9576i	−0.380359	+	0.658802i	0.610754	+	0.791820i	$0.290866\pi$
$744$	−3.40780	−	1.13112i	−0.124936	−	0.0414688i
$745$	−52.6327			−1.92831
$746$	−23.8489	−	42.7055i	−0.873171	−	1.56356i
$747$	−23.1163	−	14.3390i	−0.845779	−	0.524638i
$748$	0.513403	−	17.9580i	0.0187719	−	0.656611i
$749$	−1.96322	+	1.13347i	−0.0717346	+	0.0414160i
$750$	−3.81543	+	3.59240i	−0.139320	+	0.131176i
$751$		−	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
$753$	51.2725	−	12.8733i	1.86847	−	0.469130i
$754$	−0.316004	+	22.1112i	−0.0115082	+	0.805241i
$755$	10.7693	−	18.6530i	0.391935	−	0.678852i
$756$	−0.551847	+	1.57102i	−0.0200705	+	0.0571375i
$757$	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	$0.280467\pi$
$761$			42.5627i			1.54290i	−0.636293	+	0.771448i	$0.719533\pi$
$762$	4.32109	+	1.29840i	0.156537	+	0.0470361i
$763$	1.00101	−	0.577931i	0.0362388	−	0.0209225i
$764$	8.48609	−	13.7737i	0.307016	−	0.498315i
$765$	16.3229	+	10.1251i	0.590157	+	0.366075i
$766$	10.6245	−	17.8096i	0.383881	−	0.643486i
$767$	26.7639	−	46.3564i	0.966388	−	1.67383i
$768$	−16.8874	−	21.9731i	−0.609370	−	0.792886i
$769$	−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
$771$	46.4208	+	13.2283i	1.67180	+	0.476406i
$772$	−31.5418	−	0.901750i	−1.13521	−	0.0324547i
$773$	33.0068	−	19.0565i	1.18717	−	0.685415i	0.229511	−	0.973306i	$-0.426287\pi$
$773$	33.0068	−	19.0565i	1.18717	−	0.685415i	0.957663	+	0.287891i	$0.0929541\pi$
$774$	−19.4290	−	0.892518i	−0.698360	−	0.0320809i
$775$	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
$780$	−9.40069	−	42.5559i	−0.336599	−	1.52374i
$781$	−9.70210	+	16.8045i	−0.347168	+	0.601313i
$782$	15.2071	−	8.49240i	0.543804	−	0.303688i
$783$	−6.41533	+	20.0812i	−0.229265	+	0.717645i
$784$	−15.3062	+	23.3234i	−0.546648	+	0.832979i
$785$	43.1592	+	24.9180i	1.54042	+	0.889361i
$786$	11.8511	+	12.5869i	0.422716	+	0.448960i
$787$	−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
$792$	−35.0054	+	16.8712i	−1.24386	+	0.599494i
$793$	−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	−0.666169	−	0.745800i	$-0.732067\pi$
$797$	−9.97611	+	5.75971i	−0.353372	+	0.204019i	0.312797	+	0.949820i	$0.398734\pi$
$798$	1.59463	+	1.69363i	0.0564492	+	0.0599538i
$799$			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
$804$	26.7376	−	9.43931i	0.942962	−	0.332899i
$805$	−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	$-0.772212\pi$
$809$		−	37.3218i		−	1.31216i	0.754689	−	0.656082i	$-0.227788\pi$
$810$	3.21751	−	41.4225i	0.113052	−	1.45544i
$811$	−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
$816$	−2.55087	−	13.3479i	−0.0892982	−	0.467269i
$817$	−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	0.857373	−	0.514695i	$-0.172095\pi$
$821$	24.0778	+	13.9013i	0.840320	+	0.485159i	−0.0170527	+	0.999855i	$0.505428\pi$
$822$	24.8053	−	23.3553i	0.865183	−	0.814609i
$823$	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
$825$	12.2938	−	43.1415i	0.428016	−	1.50200i
$826$	−2.74761	+	1.53440i	−0.0956014	+	0.0533887i
$827$	−18.8868	+	32.7128i	−0.656757	+	1.13754i	0.324693	+	0.945819i	$0.394739\pi$
$827$	−18.8868	+	32.7128i	−0.656757	+	1.13754i	−0.981450	+	0.191717i	$0.938594\pi$
$828$	−31.4346	−	20.7659i	−1.09243	−	0.721664i
$829$	−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
$834$	6.72760	−	6.33435i	0.232958	−	0.219340i
$835$	−15.8294	+	9.13912i	−0.547800	+	0.316272i
$836$	−1.55137	+	54.2643i	−0.0536551	+	1.87677i
$837$	−1.15897	+	3.62779i	−0.0400598	+	0.125395i
$838$	1.63325	−	2.73775i	0.0564196	−	0.0945742i
$839$	1.36027	+	2.35605i	0.0469617	+	0.0813400i	0.888551	−	0.458778i	$-0.151713\pi$
$839$	1.36027	+	2.35605i	0.0469617	+	0.0813400i	−0.841589	+	0.540118i	$0.818379\pi$
$840$	−0.807169	+	2.43181i	−0.0278500	+	0.0839056i
$841$	−6.27014	+	10.8602i	−0.216212	+	0.374490i
$842$	12.8777	−	21.5864i	0.443794	−	0.743917i
$843$	7.98043	+	31.7848i	0.274861	+	1.09473i
$844$	−33.9547	−	20.9198i	−1.16877	−	0.720089i
$845$	−5.24267	+	3.02686i	−0.180353	+	0.104127i
$846$	30.6185	−	15.8507i	1.05269	−	0.544957i
$847$		−	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
$852$	−4.42428	+	13.9951i	−0.151573	+	0.479466i
$853$	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
$855$	−49.3235	−	30.5954i	−1.68683	−	1.04634i
$856$	−39.9806	−	1.71510i	−1.36651	−	0.0586208i
$857$		−	7.20462i		−	0.246105i	−0.992400	−	0.123053i	$-0.960732\pi$
$857$		−	7.20462i		−	0.246105i	0.992400	−	0.123053i	$-0.0392684\pi$
$858$	29.6376	+	31.4775i	1.01181	+	1.07463i
$859$	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
$861$	3.06179	−	0.768746i	0.104346	−	0.0261988i
$862$	−6.96553	−	12.4730i	−0.237247	−	0.424830i
$863$	−3.28834			−0.111936			−0.0559682	−	0.998433i	$-0.517825\pi$
$863$	−3.28834			−0.111936			−0.0559682	+	0.998433i	$0.517825\pi$
$864$	−23.1029	+	18.1730i	−0.785976	+	0.618257i
$865$	−19.0809	+	33.0492i	−0.648772	+	1.12371i
$866$	17.7272	+	31.7435i	0.602394	+	1.07869i
$867$	−6.24325	+	21.9089i	−0.212032	+	0.744064i
$868$	0.123200	−	0.199965i	0.00418168	−	0.00678724i
$869$	−25.0617	−	14.4694i	−0.850161	−	0.490841i
$870$	−9.33506	+	31.0671i	−0.316488	+	1.05327i
$871$	−18.9806	−	25.1990i	−0.643134	−	0.853836i
$872$	20.3853	+	0.874492i	0.690333	+	0.0296140i
$873$	−22.5968	−	14.0168i	−0.764787	−	0.474398i
$874$	−45.9517	+	25.6618i	−1.55434	+	0.868022i
$875$	−0.171396	−	0.296867i	−0.00579425	−	0.0100359i
$876$	8.46546	−	1.87004i	0.286021	−	0.0631828i
$877$	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	0.927690	−	0.373352i	$-0.121792\pi$
$881$	31.7060	+	18.3055i	1.06820	+	0.616727i	0.140513	+	0.990079i	$0.455125\pi$
$882$	24.9194	+	15.9551i	0.839080	+	0.537237i
$883$	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	$-0.445103\pi$
$887$	27.9653	−	48.4373i	0.938983	−	1.62637i	0.767372	−	0.641202i	$-0.221564\pi$
$888$	56.2691	−	11.5892i	1.88827	−	0.388909i
$889$	−0.147568	+	0.255596i	−0.00494928	+	0.00857241i
$890$	5.25073	+	0.0750414i	0.176005	+	0.00251539i
$891$	18.3115	+	36.9251i	0.613458	+	1.23704i
$892$	−0.248504	+	8.69226i	−0.00832051	+	0.291038i
$893$		−	48.1663i		−	1.61182i
$894$	28.7552	−	27.0744i	0.961719	−	0.905503i
$895$			17.6307i			0.589329i
$896$	1.65256	−	0.745066i	0.0552083	−	0.0248909i
$897$	−11.4874	+	40.3117i	−0.383553	+	1.34597i
$898$	32.6751	−	18.2474i	1.09038	−	0.608925i
$899$	1.48677	−	2.57517i	0.0495866	−	0.0858866i
$900$	2.04136	−	33.8710i	0.0680453	−	1.12903i
$901$	−10.9450	+	18.9574i	−0.364632	+	0.631561i
$902$	63.2678	+	37.7433i	2.10659	+	1.25672i
$903$	0.348662	−	1.22353i	0.0116027	−	0.0407164i
$904$	9.38298	−	4.89355i	0.312073	−	0.162757i
$905$	−37.8085	+	21.8287i	−1.25680	+	0.725611i
$906$	3.71146	+	15.7306i	0.123305	+	0.522614i
$907$	−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
$909$	−2.14037	−	3.99368i	−0.0709917	−	0.132462i
$910$	2.85049	+	0.0407382i	0.0944930	+	0.00135046i
$911$	54.0430			1.79053			0.895263	−	0.445539i	$-0.146988\pi$
$911$	54.0430			1.79053			0.895263	+	0.445539i	$0.146988\pi$
$912$	7.70803	+	40.3337i	0.255238	+	1.33558i
$913$	41.5251			1.37428
$914$	2.43992	+	4.36910i	0.0807055	+	0.144517i
$915$	−6.46782	−	25.7603i	−0.213820	−	0.851609i
$916$	−2.03225	+	3.29853i	−0.0671475	+	0.108986i
$917$	−0.979351	+	0.565428i	−0.0323410	+	0.0186721i
$918$	−14.1262	+	2.86480i	−0.466235	+	0.0945526i
$919$	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
$921$	3.97789	+	15.8433i	0.131076	+	0.522055i
$922$	0.350025	−	24.4916i	0.0115275	−	0.806589i
$923$	16.3305			0.537526
$924$	−0.548283	−	2.48202i	−0.0180372	−	0.0816523i
$925$	−33.1604	+	57.4355i	−1.09031	+	1.88847i
$926$	0.221267	+	0.132000i	0.00727129	+	0.00433779i
$927$	−2.66951	−	4.98099i	−0.0876782	−	0.163597i
$928$	20.6440	−	10.0269i	0.677671	−	0.329148i
$929$		−	13.8378i		−	0.454003i	−0.973894	−	0.227002i	$-0.927108\pi$
$929$		−	13.8378i		−	0.454003i	0.973894	−	0.227002i	$-0.0728923\pi$
$930$	−1.68643	+	5.61246i	−0.0553003	+	0.184040i
$931$	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
$936$	27.0268	+	18.4141i	0.883398	+	0.601885i
$937$	−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	$0.00539254\pi$
$941$			1.03931i			0.0338807i	−0.999857	+	0.0169403i	$0.994607\pi$
$942$	−36.3974	+	8.58755i	−1.18589	+	0.279797i
$943$			71.4249i			2.32592i
$944$	−55.4625	−	3.17384i	−1.80515	−	0.103300i
$945$	2.58880	+	0.827042i	0.0842138	+	0.0269037i
$946$	25.9219	−	14.4761i	0.842793	−	0.470659i
$947$	−4.15691			−0.135081			−0.0675407	−	0.997717i	$-0.521515\pi$
$947$	−4.15691			−0.135081			−0.0675407	+	0.997717i	$0.521515\pi$
$948$	−20.8719	−	6.59822i	−0.677888	−	0.214300i
$949$	−4.82287	−	8.35346i	−0.156557	−	0.271165i
$950$	−40.7102	−	24.2863i	−1.32081	−	0.787951i
$951$	14.7148	+	58.6068i	0.477161	+	1.90046i
$952$	0.888100	+	0.0380979i	0.0287835	+	0.00123476i
$953$		−	0.653441i		−	0.0211670i	−0.999944	−	0.0105835i	$-0.996631\pi$
$953$		−	0.653441i		−	0.0211670i	0.999944	−	0.0105835i	$-0.00336890\pi$
$954$	47.2982	+	2.17276i	1.53134	+	0.0703457i
$955$	−22.8671	−	13.2023i	−0.739962	−	0.427217i
$956$	−20.5541	−	38.0738i	−0.664768	−	1.23139i
$957$	−7.83663	−	31.2120i	−0.253322	−	1.00894i
$958$	−14.2226	+	23.8408i	−0.459510	+	0.770261i
$959$	1.11430	+	1.93003i	0.0359827	+	0.0623238i
$960$	−35.0607	+	28.5760i	−1.13158	+	0.922286i
$961$	−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
$966$	1.79422	−	1.68934i	0.0577281	−	0.0543536i
$967$	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
$969$	−5.51843	+	19.3653i	−0.177278	+	0.622103i
$970$	−35.1402	−	20.9634i	−1.12828	−	0.673093i
$971$	1.87747	+	3.25187i	0.0602509	+	0.104358i	0.894578	−	0.446913i	$-0.147477\pi$
$971$	1.87747	+	3.25187i	0.0602509	+	0.104358i	−0.834327	+	0.551270i	$0.814143\pi$
$972$	19.5500	+	24.2858i	0.627066	+	0.778966i
$973$	0.302217	+	0.523455i	0.00968863	+	0.0167812i
$974$	45.9607	+	27.4185i	1.47268	+	0.878546i
$975$	−36.6167	+	9.19362i	−1.17267	+	0.294431i
$976$	−10.3096	+	15.7098i	−0.330004	+	0.502857i
$977$	21.5798	+	12.4591i	0.690398	+	0.398601i	0.803761	−	0.594952i	$-0.202829\pi$
$977$	21.5798	+	12.4591i	0.690398	+	0.398601i	−0.113363	+	0.993554i	$0.536162\pi$
$978$	−19.1897	−	5.76611i	−0.613618	−	0.184380i
$979$	−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	$-0.911538\pi$
$983$	−60.2997			−1.92326			−0.961630	+	0.274349i	$0.911538\pi$
$984$	52.8890	+	17.5550i	1.68604	+	0.559632i
$985$	7.97436	+	13.8120i	0.254084	+	0.440087i
$986$	11.2529	+	0.160821i	0.358364	+	0.00512160i
$987$	0.549205	+	2.18739i	0.0174814	+	0.0696255i
$988$	40.2031	−	21.7037i	1.27903	−	0.690486i
$989$	24.9285	+	14.3925i	0.792681	+	0.457655i
$990$	29.1576	+	56.3232i	0.926688	+	1.79007i
$991$		−	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
$993$	25.1553	+	7.16837i	0.798278	+	0.227481i
$994$	−0.824534	−	0.491887i	−0.0261526	−	0.0156017i
$995$	11.3178	−	19.6029i	0.358797	−	0.621455i
$996$	30.6712	−	6.77533i	0.971853	−	0.214685i
$997$	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
$999$	−12.9633	−	59.5402i	−0.410140	−	1.88377i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-1.41407 - 0.0202093i) q^{2} +(-1.20523 - 1.24395i) q^{3} +(1.99918 + 0.0571548i) q^{4} -3.26426i q^{5} +(1.67914 + 1.78339i) q^{6} +(-0.138760 + 0.0801133i) q^{7} +(-2.82583 - 0.121223i) q^{8} +(-0.0948278 + 2.99850i) q^{9} +O(q^{10})\)	\(q+(-1.41407 - 0.0202093i) q^{2} +(-1.20523 - 1.24395i) q^{3} +(1.99918 + 0.0571548i) q^{4} -3.26426i q^{5} +(1.67914 + 1.78339i) 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} +(-2.33838 - 2.55577i) 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} +(0.194691 - 4.23817i) q^{18} +(-5.13295 - 2.96351i) q^{19} +(0.186568 - 6.52586i) q^{20} +(0.266896 + 0.0760559i) q^{21} +(3.15777 + 5.65451i) q^{22} +(-3.13953 + 5.43782i) q^{23} +(3.25499 + 3.66129i) 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} +(5.82145 - 5.48116i) q^{30} +(-0.634737 + 0.366466i) q^{31} +(-5.64242 - 0.403856i) q^{32} +(-2.17382 + 7.62837i) q^{33} +(-2.38223 - 1.42115i) q^{34} +(0.261511 + 0.452950i) q^{35} +(-0.360957 + 5.98913i) q^{36} +(5.86348 - 10.1559i) q^{37} +(7.19846 + 4.29435i) q^{38} +(6.47464 - 1.62563i) q^{39} +(-0.395704 + 9.22424i) q^{40} +(9.85112 - 5.68755i) q^{41} +(-0.375872 - 0.112942i) 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} +(-4.52878 - 5.24310i) q^{48} +(-3.48716 + 6.03994i) q^{49} +(7.99714 + 0.114292i) q^{50} +(-0.827321 - 3.29509i) q^{51} +(-4.04336 + 6.56273i) q^{52} +11.1601i q^{53} +(-5.50672 + 4.86580i) q^{54} +(-12.9462 + 7.47446i) q^{55} +(0.401825 - 0.209566i) q^{56} +(2.49994 + 9.95687i) q^{57} +(5.00935 - 2.79747i) q^{58} -13.8883 q^{59} +(-8.34271 + 7.63310i) q^{60} +(-2.34882 + 4.06828i) q^{61} +(0.904968 - 0.505380i) q^{62} +(-0.227062 - 0.423670i) q^{63} +(7.97061 + 0.685111i) q^{64} +(10.8955 + 6.29049i) q^{65} +(3.22809 - 10.7431i) q^{66} +(-3.19984 + 7.53399i) q^{67} +(3.33992 + 2.05775i) q^{68} +(10.5483 - 2.64842i) q^{69} +(-0.360641 - 0.645788i) q^{70} +(-2.11856 - 3.66945i) q^{71} +(0.631454 - 8.46175i) 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} +(-9.18844 + 2.16791i) 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} +(0.529226 + 0.167304i) q^{84} +(3.20137 - 5.54494i) q^{85} +(-0.0926453 + 6.48250i) q^{86} +(6.75799 + 1.92579i) q^{87} +(5.98977 + 11.4849i) q^{88} -1.13753i q^{89} +(-13.8345 - 0.635522i) q^{90} -0.617539i q^{91} +(-6.58729 + 10.6918i) q^{92} +(1.22087 + 0.347905i) q^{93} +(-5.60352 - 10.0341i) q^{94} +(-9.67368 + 16.7553i) q^{95} +(6.29805 + 7.50563i) q^{96} +(-4.43186 + 7.67620i) q^{97} +(5.05315 - 8.47043i) q^{98} +(12.1093 - 6.48984i) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more