LMFDB - Embedded newform 770.2.bv.a.3.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(3,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([45, 10, 48]))

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

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

chi := DirichletCharacter("770.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.bv (of order $60$, degree $16$, 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:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$768$
Relative dimension:	$48$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			3.1
Character	$\chi$	$=$	770.3
Dual form			770.2.bv.a.257.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.933580 + 0.358368i) q^{2} +(-2.69941 + 1.75302i) q^{3} +(0.743145 - 0.669131i) q^{4} +(2.18170 - 0.490086i) q^{5} +(1.89189 - 2.60396i) q^{6} +(0.165124 - 2.64059i) q^{7} +(-0.453990 + 0.891007i) q^{8} +(2.99352 - 6.72356i) q^{9} +O(q^{10})$	\(q+(-0.933580 + 0.358368i) q^{2} +(-2.69941 + 1.75302i) q^{3} +(0.743145 - 0.669131i) q^{4} +(2.18170 - 0.490086i) q^{5} +(1.89189 - 2.60396i) q^{6} +(0.165124 - 2.64059i) q^{7} +(-0.453990 + 0.891007i) q^{8} +(2.99352 - 6.72356i) q^{9} +(-1.86116 + 1.23939i) q^{10} +(-1.08813 - 3.13305i) q^{11} +(-0.833054 + 3.10900i) q^{12} +(-0.449779 + 2.83979i) q^{13} +(0.792148 + 2.52438i) q^{14} +(-5.03017 + 5.14749i) q^{15} +(0.104528 - 0.994522i) q^{16} +(-4.74388 - 1.82100i) q^{17} +(-0.385185 + 7.34977i) q^{18} +(-2.30935 + 2.56479i) q^{19} +(1.29339 - 1.82405i) q^{20} +(4.18326 + 7.41750i) q^{21} +(2.13864 + 2.53500i) q^{22} +(-1.42738 + 5.32705i) q^{23} +(-0.336443 - 3.20104i) q^{24} +(4.51963 - 2.13844i) q^{25} +(-0.597786 - 2.81236i) q^{26} +(2.19524 + 13.8602i) q^{27} +(-1.64419 - 2.07283i) q^{28} +(6.19603 + 2.01321i) q^{29} +(2.85137 - 6.60825i) q^{30} +(-10.5203 + 1.10573i) q^{31} +(0.258819 + 0.965926i) q^{32} +(8.42957 + 6.54987i) q^{33} +5.08138 q^{34} +(-0.933867 - 5.84191i) q^{35} +(-2.27432 - 6.99964i) q^{36} +(-4.96589 + 7.64681i) q^{37} +(1.23682 - 3.22203i) q^{38} +(-3.76406 - 8.45422i) q^{39} +(-0.553801 + 2.16640i) q^{40} +(-6.13033 + 1.99187i) q^{41} +(-6.56361 - 5.42569i) q^{42} +(-5.89521 - 5.89521i) q^{43} +(-2.90505 - 1.60021i) q^{44} +(3.23585 - 16.1359i) q^{45} +(-0.576471 - 5.48476i) q^{46} +(-3.62357 + 0.189903i) q^{47} +(1.46125 + 2.86786i) q^{48} +(-6.94547 - 0.872051i) q^{49} +(-3.45309 + 3.61610i) q^{50} +(15.9979 - 3.40046i) q^{51} +(1.56594 + 2.41134i) q^{52} +(1.61958 - 2.00001i) q^{53} +(-7.01648 - 12.1529i) q^{54} +(-3.90943 - 6.30209i) q^{55} +(2.27782 + 1.34593i) q^{56} +(1.73775 - 10.9717i) q^{57} +(-6.50596 + 0.340963i) q^{58} +(4.09261 + 4.54530i) q^{59} +(-0.293796 + 7.19117i) q^{60} +(-0.185139 - 0.0194589i) q^{61} +(9.42530 - 4.80243i) q^{62} +(-17.2599 - 9.01490i) q^{63} +(-0.587785 - 0.809017i) q^{64} +(0.410460 + 6.41601i) q^{65} +(-10.2169 - 3.09394i) q^{66} +(-0.415709 - 1.55145i) q^{67} +(-4.74388 + 1.82100i) q^{68} +(-5.48532 - 16.8821i) q^{69} +(2.96539 + 5.11922i) q^{70} +(2.66137 + 1.93360i) q^{71} +(4.63171 + 5.71968i) q^{72} +(2.12024 + 0.111117i) q^{73} +(1.89569 - 8.91853i) q^{74} +(-8.45160 + 13.6955i) q^{75} +3.45127i q^{76} +(-8.45278 + 2.35596i) q^{77} +(6.54378 + 6.54378i) q^{78} +(-0.0795894 + 0.178761i) q^{79} +(-0.259352 - 2.22098i) q^{80} +(-15.4488 - 17.1577i) q^{81} +(5.00934 - 4.05648i) q^{82} +(-0.269022 + 0.0426090i) q^{83} +(8.07205 + 2.71313i) q^{84} +(-11.2422 - 1.64798i) q^{85} +(7.61631 + 3.39100i) q^{86} +(-20.2548 + 5.42726i) q^{87} +(3.28556 + 0.452846i) q^{88} +(0.977585 + 1.69323i) q^{89} +(2.76166 + 16.2238i) q^{90} +(7.42447 + 1.65660i) q^{91} +(2.50374 + 4.91387i) q^{92} +(26.4602 - 21.4271i) q^{93} +(3.31484 - 1.47586i) q^{94} +(-3.78134 + 6.72738i) q^{95} +(-2.39194 - 2.15371i) q^{96} +(10.4436 + 1.65410i) q^{97} +(6.79667 - 1.67490i) q^{98} +(-24.3226 - 2.06277i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 768 q + 24 q^{5} + 4 q^{7}+O(q^{10}) $ 768 * q + 24 * q^5 + 4 * q^7	$ 768 q + 24 q^{5} + 4 q^{7} + 24 q^{10} + 12 q^{11} - 24 q^{15} - 96 q^{16} + 8 q^{22} + 8 q^{23} + 16 q^{25} - 24 q^{26} - 28 q^{28} - 16 q^{30} + 252 q^{33} - 40 q^{35} + 160 q^{36} - 8 q^{37} - 44 q^{42} + 80 q^{43} + 96 q^{45} - 8 q^{46} - 24 q^{47} + 64 q^{50} - 8 q^{51} + 40 q^{53} + 16 q^{56} + 64 q^{57} - 48 q^{58} - 164 q^{63} - 88 q^{65} + 32 q^{67} - 100 q^{70} + 32 q^{71} + 120 q^{73} - 336 q^{75} - 96 q^{77} - 36 q^{80} - 24 q^{81} + 48 q^{82} - 112 q^{85} - 24 q^{87} + 4 q^{88} - 12 q^{91} - 16 q^{92} - 88 q^{93} - 44 q^{95} + 32 q^{98}+O(q^{100}) $ 768 * q + 24 * q^5 + 4 * q^7 + 24 * q^10 + 12 * q^11 - 24 * q^15 - 96 * q^16 + 8 * q^22 + 8 * q^23 + 16 * q^25 - 24 * q^26 - 28 * q^28 - 16 * q^30 + 252 * q^33 - 40 * q^35 + 160 * q^36 - 8 * q^37 - 44 * q^42 + 80 * q^43 + 96 * q^45 - 8 * q^46 - 24 * q^47 + 64 * q^50 - 8 * q^51 + 40 * q^53 + 16 * q^56 + 64 * q^57 - 48 * q^58 - 164 * q^63 - 88 * q^65 + 32 * q^67 - 100 * q^70 + 32 * q^71 + 120 * q^73 - 336 * q^75 - 96 * q^77 - 36 * q^80 - 24 * q^81 + 48 * q^82 - 112 * q^85 - 24 * q^87 + 4 * q^88 - 12 * q^91 - 16 * q^92 - 88 * q^93 - 44 * q^95 + 32 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−0.933580	+	0.358368i	−0.660141	+	0.253404i
$2$	−0.933580	+	0.358368i	−0.660141	+	0.253404i
$3$	−2.69941	+	1.75302i	−1.55850	+	1.01210i	−0.577898	+	0.816109i	$0.696127\pi$
$3$	−2.69941	+	1.75302i	−1.55850	+	1.01210i	−0.980605	+	0.195995i	$0.937206\pi$
$4$	0.743145	−	0.669131i	0.371572	−	0.334565i
$5$	2.18170	−	0.490086i	0.975686	−	0.219173i
$5$	2.18170	−	0.490086i	0.975686	−	0.219173i
$6$	1.89189	−	2.60396i	0.772360	−	1.06306i
$7$	0.165124	−	2.64059i	0.0624110	−	0.998051i
$7$	0.165124	−	2.64059i	0.0624110	−	0.998051i
$8$	−0.453990	+	0.891007i	−0.160510	+	0.315018i
$9$	2.99352	−	6.72356i	0.997841	−	2.24119i
$10$	−1.86116	+	1.23939i	−0.588551	+	0.391928i
$11$	−1.08813	−	3.13305i	−0.328082	−	0.944649i
$11$	−1.08813	−	3.13305i	−0.328082	−	0.944649i
$12$	−0.833054	+	3.10900i	−0.240482	+	0.897491i
$13$	−0.449779	+	2.83979i	−0.124746	+	0.787617i	0.843410	+	0.537270i	$0.180545\pi$
$13$	−0.449779	+	2.83979i	−0.124746	+	0.787617i	−0.968156	+	0.250346i	$0.919455\pi$
$14$	0.792148	+	2.52438i	0.211710	+	0.674669i
$15$	−5.03017	+	5.14749i	−1.29878	+	1.32908i
$16$	0.104528	−	0.994522i	0.0261321	−	0.248630i
$17$	−4.74388	−	1.82100i	−1.15056	−	0.441658i	−0.293035	−	0.956102i	$-0.594665\pi$
$17$	−4.74388	−	1.82100i	−1.15056	−	0.441658i	−0.857524	+	0.514443i	$0.827999\pi$
$18$	−0.385185	+	7.34977i	−0.0907890	+	1.73236i
$19$	−2.30935	+	2.56479i	−0.529801	+	0.588403i	−0.947330	−	0.320260i	$-0.896230\pi$
$19$	−2.30935	+	2.56479i	−0.529801	+	0.588403i	0.417529	+	0.908664i	$0.362896\pi$
$20$	1.29339	−	1.82405i	0.289210	−	0.407869i
$21$	4.18326	+	7.41750i	0.912863	+	1.61863i
$22$	2.13864	+	2.53500i	0.455959	+	0.540464i
$23$	−1.42738	+	5.32705i	−0.297629	+	1.11077i	0.641478	+	0.767142i	$0.278322\pi$
$23$	−1.42738	+	5.32705i	−0.297629	+	1.11077i	−0.939107	+	0.343625i	$0.888345\pi$
$24$	−0.336443	−	3.20104i	−0.0686761	−	0.653410i
$25$	4.51963	−	2.13844i	0.903926	−	0.427688i
$26$	−0.597786	−	2.81236i	−0.117235	−	0.551549i
$27$	2.19524	+	13.8602i	0.422474	+	2.66739i
$28$	−1.64419	−	2.07283i	−0.310723	−	0.391729i
$29$	6.19603	+	2.01321i	1.15057	+	0.373844i	0.821359	−	0.570411i	$-0.193216\pi$
$29$	6.19603	+	2.01321i	1.15057	+	0.373844i	0.329215	+	0.944255i	$0.393216\pi$
$30$	2.85137	−	6.60825i	0.520586	−	1.20650i
$31$	−10.5203	+	1.10573i	−1.88950	+	0.198595i	−0.977405	−	0.211375i	$-0.932206\pi$
$31$	−10.5203	+	1.10573i	−1.88950	+	0.198595i	−0.912099	+	0.409970i	$0.865539\pi$
$32$	0.258819	+	0.965926i	0.0457532	+	0.170753i
$33$	8.42957	+	6.54987i	1.46740	+	1.14019i
$34$	5.08138			0.871449
$35$	−0.933867	−	5.84191i	−0.157852	−	0.987463i
$36$	−2.27432	−	6.99964i	−0.379053	−	1.16661i
$37$	−4.96589	+	7.64681i	−0.816388	+	1.25713i	0.147032	+	0.989132i	$0.453028\pi$
$37$	−4.96589	+	7.64681i	−0.816388	+	1.25713i	−0.963420	+	0.267996i	$0.913639\pi$
$38$	1.23682	−	3.22203i	0.200639	−	0.522683i
$39$	−3.76406	−	8.45422i	−0.602732	−	1.35376i
$40$	−0.553801	+	2.16640i	−0.0875637	+	0.342538i
$41$	−6.13033	+	1.99187i	−0.957397	+	0.311077i	−0.745718	−	0.666262i	$-0.767893\pi$
$41$	−6.13033	+	1.99187i	−0.957397	+	0.311077i	−0.211679	+	0.977339i	$0.567893\pi$
$42$	−6.56361	−	5.42569i	−1.01279	−	0.837201i
$43$	−5.89521	−	5.89521i	−0.899012	−	0.899012i	0.0963372	−	0.995349i	$-0.469287\pi$
$43$	−5.89521	−	5.89521i	−0.899012	−	0.899012i	−0.995349	+	0.0963372i	$0.969287\pi$
$44$	−2.90505	−	1.60021i	−0.437953	−	0.241241i
$45$	3.23585	−	16.1359i	0.482371	−	2.40540i
$46$	−0.576471	−	5.48476i	−0.0849961	−	0.808683i
$47$	−3.62357	+	0.189903i	−0.528552	+	0.0277002i	−0.314746	−	0.949176i	$-0.601919\pi$
$47$	−3.62357	+	0.189903i	−0.528552	+	0.0277002i	−0.213806	+	0.976876i	$0.568586\pi$
$48$	1.46125	+	2.86786i	0.210913	+	0.413940i
$49$	−6.94547	−	0.872051i	−0.992210	−	0.124579i
$50$	−3.45309	+	3.61610i	−0.488341	+	0.511394i
$51$	15.9979	−	3.40046i	2.24015	−	0.476159i
$52$	1.56594	+	2.41134i	0.217157	+	0.334392i
$53$	1.61958	−	2.00001i	0.222466	−	0.274723i	−0.653677	−	0.756774i	$-0.726775\pi$
$53$	1.61958	−	2.00001i	0.222466	−	0.274723i	0.876143	+	0.482051i	$0.160108\pi$
$54$	−7.01648	−	12.1529i	−0.954822	−	1.65380i
$55$	−3.90943	−	6.30209i	−0.527147	−	0.849774i
$56$	2.27782	+	1.34593i	0.304387	+	0.179858i
$57$	1.73775	−	10.9717i	0.230171	−	1.45324i
$58$	−6.50596	+	0.340963i	−0.854275	+	0.0447707i
$59$	4.09261	+	4.54530i	0.532812	+	0.591748i	0.948112	−	0.317937i	$-0.102990\pi$
$59$	4.09261	+	4.54530i	0.532812	+	0.591748i	−0.415300	+	0.909685i	$0.636323\pi$
$60$	−0.293796	+	7.19117i	−0.0379290	+	0.928376i
$61$	−0.185139	−	0.0194589i	−0.0237046	−	0.00249146i	0.0926687	−	0.995697i	$-0.470460\pi$
$61$	−0.185139	−	0.0194589i	−0.0237046	−	0.00249146i	−0.116373	+	0.993206i	$0.537127\pi$
$62$	9.42530	−	4.80243i	1.19701	−	0.609909i
$63$	−17.2599	−	9.01490i	−2.17454	−	1.13577i
$64$	−0.587785	−	0.809017i	−0.0734732	−	0.101127i
$65$	0.410460	+	6.41601i	0.0509113	+	0.795808i
$66$	−10.2169	−	3.09394i	−1.25762	−	0.380837i
$67$	−0.415709	−	1.55145i	−0.0507869	−	0.189539i	0.935872	−	0.352340i	$-0.114614\pi$
$67$	−0.415709	−	1.55145i	−0.0507869	−	0.189539i	−0.986659	+	0.162801i	$0.947947\pi$
$68$	−4.74388	+	1.82100i	−0.575280	+	0.220829i
$69$	−5.48532	−	16.8821i	−0.660356	−	2.03237i
$70$	2.96539	+	5.11922i	0.354432	+	0.611864i
$71$	2.66137	+	1.93360i	0.315847	+	0.229476i	0.734401	−	0.678716i	$-0.237463\pi$
$71$	2.66137	+	1.93360i	0.315847	+	0.229476i	−0.418554	+	0.908192i	$0.637463\pi$
$72$	4.63171	+	5.71968i	0.545852	+	0.674071i
$73$	2.12024	+	0.111117i	0.248155	+	0.0130053i	0.176008	−	0.984389i	$-0.443682\pi$
$73$	2.12024	+	0.111117i	0.248155	+	0.0130053i	0.0721471	+	0.997394i	$0.477015\pi$
$74$	1.89569	−	8.91853i	0.220370	−	1.03676i
$75$	−8.45160	+	13.6955i	−0.975907	+	1.58142i
$76$			3.45127i			0.395887i
$77$	−8.45278	+	2.35596i	−0.963284	+	0.268486i
$78$	6.54378	+	6.54378i	0.740937	+	0.740937i
$79$	−0.0795894	+	0.178761i	−0.00895451	+	0.0201122i	−0.917967	−	0.396656i	$-0.870171\pi$
$79$	−0.0795894	+	0.178761i	−0.00895451	+	0.0201122i	0.909013	+	0.416768i	$0.136837\pi$
$80$	−0.259352	−	2.22098i	−0.0289964	−	0.248313i
$81$	−15.4488	−	17.1577i	−1.71654	−	1.90641i
$82$	5.00934	−	4.05648i	0.553189	−	0.447963i
$83$	−0.269022	+	0.0426090i	−0.0295290	+	0.00467694i	−0.171182	−	0.985240i	$-0.554758\pi$
$83$	−0.269022	+	0.0426090i	−0.0295290	+	0.00467694i	0.141652	+	0.989916i	$0.454758\pi$
$84$	8.07205	+	2.71313i	0.880733	+	0.296026i
$85$	−11.2422	−	1.64798i	−1.21938	−	0.178748i
$86$	7.61631	+	3.39100i	0.821288	+	0.365661i
$87$	−20.2548	+	5.42726i	−2.17154	+	0.581863i
$88$	3.28556	+	0.452846i	0.350242	+	0.0482736i
$89$	0.977585	+	1.69323i	0.103624	+	0.179482i	0.913175	−	0.407567i	$-0.133623\pi$
$89$	0.977585	+	1.69323i	0.103624	+	0.179482i	−0.809551	+	0.587049i	$0.800290\pi$
$90$	2.76166	+	16.2238i	0.291105	+	1.71014i
$91$	7.42447	+	1.65660i	0.778296	+	0.173659i
$92$	2.50374	+	4.91387i	0.261033	+	0.512307i
$93$	26.4602	−	21.4271i	2.74380	−	2.22188i
$94$	3.31484	−	1.47586i	0.341900	−	0.152223i
$95$	−3.78134	+	6.72738i	−0.387957	+	0.690215i
$96$	−2.39194	−	2.15371i	−0.244126	−	0.219812i
$97$	10.4436	+	1.65410i	1.06038	+	0.167948i	0.662177	−	0.749347i	$-0.269633\pi$
$97$	10.4436	+	1.65410i	1.06038	+	0.167948i	0.398207	+	0.917296i	$0.369633\pi$
$98$	6.79667	−	1.67490i	0.686567	−	0.169191i
$99$	−24.3226	−	2.06277i	−2.44451	−	0.207316i
$100$	1.92784	−	4.61340i	0.192784	−	0.461340i
$101$	−8.06073	+	0.847217i	−0.802072	+	0.0843012i	−0.496689	−	0.867928i	$-0.665451\pi$
$101$	−8.06073	+	0.847217i	−0.802072	+	0.0843012i	−0.305383	+	0.952230i	$0.598785\pi$
$102$	−13.7167	+	8.90774i	−1.35816	+	0.881997i
$103$	−5.57167	+	8.57961i	−0.548993	+	0.845374i	−0.998861	−	0.0477206i	$-0.984804\pi$
$103$	−5.57167	+	8.57961i	−0.548993	+	0.845374i	0.449868	+	0.893095i	$0.351471\pi$
$104$	−2.32608	−	1.68999i	−0.228091	−	0.165718i
$105$	12.7618	+	14.1326i	1.24543	+	1.37920i
$106$	−0.795267	+	2.44758i	−0.0772431	+	0.237730i
$107$	−0.193477	−	3.69177i	−0.0187042	−	0.356897i	−0.991909	−	0.126955i	$-0.959480\pi$
$107$	−0.193477	−	3.69177i	−0.0187042	−	0.356897i	0.973204	−	0.229942i	$-0.0738536\pi$
$108$	10.9057	+	8.83122i	1.04940	+	0.849785i
$109$	−12.7909	−	7.38481i	−1.22514	−	0.707337i	−0.259133	−	0.965842i	$-0.583437\pi$
$109$	−12.7909	−	7.38481i	−1.22514	−	0.707337i	−0.966010	+	0.258505i	$0.916770\pi$
$110$	5.90823	+	4.48250i	0.563328	+	0.427389i
$111$		−	29.3471i		−	2.78551i
$112$	−2.60887	−	0.440237i	−0.246515	−	0.0415985i
$113$	1.23793	−	2.42958i	0.116455	−	0.228555i	−0.825420	−	0.564519i	$-0.809062\pi$
$113$	1.23793	−	2.42958i	0.116455	−	0.228555i	0.941875	+	0.335963i	$0.109062\pi$
$114$	2.30959	+	10.8657i	0.216313	+	1.01767i
$115$	−0.503399	+	12.3216i	−0.0469422	+	1.14899i
$116$	5.95165	−	2.64985i	0.552597	−	0.246032i
$117$	17.7471	+	11.5251i	1.64072	+	1.06550i
$118$	−5.44967	−	2.77675i	−0.501683	−	0.255620i
$119$	−5.59186	+	12.2260i	−0.512605	+	1.12075i
$120$	−2.30280	−	6.81883i	−0.210216	−	0.622471i
$121$	−8.63196	+	6.81830i	−0.784724	+	0.619845i
$122$	0.179816	−	0.0481815i	0.0162797	−	0.00436214i
$123$	13.0565	−	16.1234i	1.17726	−	1.45380i
$124$	−7.07824	+	7.86118i	−0.635645	+	0.705955i
$125$	8.81246	−	6.88045i	0.788210	−	0.615406i
$126$	19.3442	+	2.23074i	1.72331	+	0.198730i
$127$	−20.4095	+	3.23254i	−1.81105	+	0.286842i	−0.967992	−	0.250982i	$-0.919246\pi$
$127$	−20.4095	+	3.23254i	−1.81105	+	0.286842i	−0.843057	+	0.537824i	$0.819246\pi$
$128$	0.838671	+	0.544639i	0.0741287	+	0.0481397i
$129$	26.2480	+	5.57918i	2.31101	+	0.491219i
$130$	−2.68249	−	5.84276i	−0.235270	−	0.512444i
$131$	17.0698	−	9.85527i	1.49140	−	0.861059i	0.491446	−	0.870908i	$-0.336469\pi$
$131$	17.0698	−	9.85527i	1.49140	−	0.861059i	0.999951	+	0.00984937i	$0.00313520\pi$
$132$	10.6471	−	0.772986i	0.926712	−	0.0672798i
$133$	6.39124	+	6.52156i	0.554191	+	0.565491i
$134$	0.944087	+	1.29942i	0.0815567	+	0.112253i
$135$	11.5820	+	29.1629i	0.996823	+	2.50994i
$136$	3.77620	−	3.40011i	0.323807	−	0.291557i
$137$	0.295857	−	0.770734i	0.0252768	−	0.0658482i	−0.920361	−	0.391069i	$-0.872105\pi$
$137$	0.295857	−	0.770734i	0.0252768	−	0.0658482i	0.945638	+	0.325221i	$0.105439\pi$
$138$	11.1710	+	13.7950i	0.950938	+	1.17431i
$139$	−3.05268	+	9.39518i	−0.258925	+	0.796888i	0.734106	+	0.679035i	$0.237601\pi$
$139$	−3.05268	+	9.39518i	−0.258925	+	0.796888i	−0.993031	+	0.117854i	$0.962399\pi$
$140$	−4.60300	−	3.71650i	−0.389024	−	0.314102i
$141$	9.44859	−	6.86480i	0.795715	−	0.578120i
$142$	−3.17754	−	0.851421i	−0.266654	−	0.0714496i
$143$	9.38662	−	1.68087i	0.784949	−	0.140562i
$144$	−6.37382	−	3.67993i	−0.531152	−	0.306661i
$145$	14.5045	+	1.35564i	1.20454	+	0.112580i
$146$	−2.01923	+	0.656089i	−0.167113	+	0.0542983i
$147$	20.2774	−	9.82149i	1.67245	−	0.810063i
$148$	1.42633	+	9.00552i	0.117244	+	0.740249i
$149$	−6.99600	−	0.735310i	−0.573135	−	0.0602389i	−0.186472	−	0.982460i	$-0.559705\pi$
$149$	−6.99600	−	0.735310i	−0.573135	−	0.0602389i	−0.386662	+	0.922221i	$0.626372\pi$
$150$	2.98222	−	15.8146i	0.243497	−	1.29126i
$151$	−4.94331	−	1.05073i	−0.402281	−	0.0855075i	0.00232781	−	0.999997i	$-0.499259\pi$
$151$	−4.94331	−	1.05073i	−0.402281	−	0.0855075i	−0.404609	+	0.914490i	$0.632592\pi$
$152$	−1.23682	−	3.22203i	−0.100320	−	0.261341i
$153$	−26.4445	+	26.4445i	−2.13791	+	2.13791i
$154$	7.04705	−	5.22868i	0.567867	−	0.421339i
$155$	−22.4103	+	7.56823i	−1.80004	+	0.607895i
$156$	−8.45422	−	3.76406i	−0.676880	−	0.301366i
$157$	4.66574	+	7.18460i	0.372366	+	0.573394i	0.974329	−	0.225131i	$-0.0722809\pi$
$157$	4.66574	+	7.18460i	0.372366	+	0.573394i	−0.601962	+	0.798524i	$0.705614\pi$
$158$	0.0102410	−	0.195410i	0.000814730	−	0.0155460i
$159$	−0.865848	+	8.23800i	−0.0686662	+	0.653316i
$160$	1.03805	+	1.98052i	0.0820652	+	0.156574i
$161$	13.8309	+	4.64875i	1.09003	+	0.366373i
$162$	20.5715	+	10.4817i	1.61625	+	0.823520i
$163$	−1.70243	−	4.43498i	−0.133345	−	0.347374i	0.850609	−	0.525799i	$-0.176233\pi$
$163$	−1.70243	−	4.43498i	−0.133345	−	0.347374i	−0.983954	+	0.178424i	$0.942900\pi$
$164$	−3.22291	+	5.58224i	−0.251667	+	0.435900i
$165$	21.6008	+	10.1586i	1.68162	+	0.790848i
$166$	0.235884	−	0.136188i	0.0183082	−	0.0105702i
$167$	−0.579927	−	0.0918514i	−0.0448761	−	0.00710767i	0.133956	−	0.990987i	$-0.457232\pi$
$167$	−0.579927	−	0.0918514i	−0.0448761	−	0.00710767i	−0.178832	+	0.983880i	$0.557232\pi$
$168$	−8.50820	+	0.359840i	−0.656422	+	0.0277623i
$169$	4.50161	+	1.46266i	0.346278	+	0.112513i
$170$	11.0860	−	2.49031i	0.850261	−	0.190998i
$171$	10.3314	+	23.2048i	0.790065	+	1.77452i
$172$	−8.32566	−	0.436330i	−0.634826	−	0.0332698i
$173$	−0.722994	−	13.7956i	−0.0549683	−	1.04886i	−0.877329	−	0.479890i	$-0.840677\pi$
$173$	−0.722994	−	13.7956i	−0.0549683	−	1.04886i	0.822360	−	0.568967i	$-0.192657\pi$
$174$	16.9645	−	12.3255i	1.28608	−	0.934390i
$175$	−4.90046	−	12.2876i	−0.370440	−	0.928857i
$176$	−3.22962	+	0.754672i	−0.243442	+	0.0568856i
$177$	−19.0156	−	5.09521i	−1.42930	−	0.382980i
$178$	−1.51945	−	1.23043i	−0.113888	−	0.0922245i
$179$	−1.38426	+	6.51242i	−0.103464	+	0.486761i	0.895653	+	0.444754i	$0.146709\pi$
$179$	−1.38426	+	6.51242i	−0.103464	+	0.486761i	−0.999117	+	0.0420077i	$0.986625\pi$
$180$	−8.39231	−	14.1565i	−0.625526	−	1.05516i
$181$	−6.15692	+	8.47427i	−0.457640	+	0.629888i	−0.974017	−	0.226474i	$-0.927280\pi$
$181$	−6.15692	+	8.47427i	−0.457640	+	0.629888i	0.516377	+	0.856361i	$0.327280\pi$
$182$	−7.52501	+	1.11412i	−0.557791	+	0.0825841i
$183$	0.533877	−	0.272024i	0.0394654	−	0.0201086i
$184$	−4.09842	−	3.69023i	−0.302140	−	0.272048i
$185$	−7.08650	+	19.1168i	−0.521010	+	1.40549i
$186$	−17.0240	+	29.4864i	−1.24826	+	2.16205i
$187$	−0.543355	+	16.8443i	−0.0397341	+	1.23177i
$188$	−2.56577	+	2.56577i	−0.187128	+	0.187128i
$189$	36.9616	−	3.50808i	2.68856	−	0.255175i
$190$	1.11930	−	7.63566i	0.0812028	−	0.553949i
$191$	25.6333	−	5.44853i	1.85476	−	0.394242i	0.861271	−	0.508147i	$-0.169669\pi$
$191$	25.6333	−	5.44853i	1.85476	−	0.394242i	0.993492	+	0.113905i	$0.0363358\pi$
$192$	3.00489	+	1.15347i	0.216859	+	0.0832445i
$193$	−25.3335	−	9.72461i	−1.82354	−	0.699992i	−0.988779	−	0.149384i	$-0.952271\pi$
$193$	−25.3335	−	9.72461i	−1.82354	−	0.699992i	−0.834763	−	0.550609i	$-0.814396\pi$
$194$	−10.3427	+	2.19841i	−0.742562	+	0.157836i
$195$	−12.3554	−	16.5999i	−0.884785	−	1.18874i
$196$	−5.74500	+	3.99937i	−0.410357	+	0.285669i
$197$	9.63369	−	9.63369i	0.686372	−	0.686372i	−0.275056	−	0.961428i	$-0.588697\pi$
$197$	9.63369	−	9.63369i	0.686372	−	0.686372i	0.961428	+	0.275056i	$0.0886965\pi$
$198$	23.4463	−	6.79067i	1.66626	−	0.482592i
$199$	−2.48167	+	4.29837i	−0.175921	+	0.304703i	−0.940479	−	0.339850i	$-0.889624\pi$
$199$	−2.48167	+	4.29837i	−0.175921	+	0.304703i	0.764559	+	0.644554i	$0.222957\pi$
$200$	−0.146504	+	4.99785i	−0.0103594	+	0.353402i
$201$	3.84188	+	3.45924i	0.270985	+	0.243996i
$202$	7.22172	−	3.67965i	0.508119	−	0.258899i
$203$	6.33919	−	16.0288i	0.444924	−	1.12500i
$204$	9.61341	−	13.2317i	0.673073	−	0.926405i
$205$	−12.3984	+	7.35005i	−0.865939	+	0.513349i
$206$	2.12694	−	10.0065i	0.148191	−	0.697183i
$207$	31.5439	+	25.5437i	2.19245	+	1.77541i
$208$	2.77722	+	0.744154i	0.192566	+	0.0515978i
$209$	10.5485	+	4.44448i	0.729653	+	0.307431i
$210$	−16.9789	−	8.62049i	−1.17165	−	0.594870i
$211$	1.19873	−	0.870925i	0.0825237	−	0.0599569i	−0.545758	−	0.837943i	$-0.683758\pi$
$211$	1.19873	−	0.870925i	0.0825237	−	0.0599569i	0.628282	+	0.777986i	$0.283758\pi$
$212$	−0.134689	−	2.57001i	−0.00925045	−	0.176509i
$213$	−10.5738	−	0.554147i	−0.724502	−	0.0379695i
$214$	1.50364	+	3.37723i	0.102787	+	0.230862i
$215$	−15.7507	−	9.97243i	−1.07419	−	0.680114i
$216$	−13.3461	−	4.33642i	−0.908089	−	0.295056i
$217$	1.18263	+	27.9625i	0.0802819	+	1.89821i
$218$	14.5878	+	2.31048i	0.988009	+	0.156485i
$219$	−5.91817	+	3.41686i	−0.399913	+	0.230890i
$220$	−7.12219	−	2.06745i	−0.480178	−	0.139388i
$221$	7.30497	−	12.6526i	0.491385	−	0.851105i
$222$	10.5171	+	27.3979i	0.705860	+	1.83883i
$223$	−15.1092	−	7.69850i	−1.01178	−	0.515530i	−0.132174	−	0.991226i	$-0.542196\pi$
$223$	−15.1092	−	7.69850i	−1.01178	−	0.515530i	−0.879609	+	0.475697i	$0.842196\pi$
$224$	2.59335	−	0.523938i	0.173276	−	0.0350071i
$225$	−0.848328	−	36.7895i	−0.0565552	−	2.45263i
$226$	−0.285026	+	2.71184i	−0.0189596	+	0.180389i
$227$	0.775420	−	14.7959i	0.0514665	−	0.982038i	−0.843842	−	0.536592i	$-0.819712\pi$
$227$	0.775420	−	14.7959i	0.0514665	−	0.982038i	0.895308	−	0.445447i	$-0.146955\pi$
$228$	−6.05012	−	9.31637i	−0.400679	−	0.616992i
$229$	−6.87579	−	3.06130i	−0.454365	−	0.202296i	0.166777	−	0.985995i	$-0.446664\pi$
$229$	−6.87579	−	3.06130i	−0.454365	−	0.202296i	−0.621141	+	0.783698i	$0.713331\pi$
$230$	−3.94569	−	11.6836i	−0.260171	−	0.770392i
$231$	18.6875	−	21.1775i	1.22954	−	1.39338i
$232$	−4.60672	+	4.60672i	−0.302446	+	0.302446i
$233$	−2.86245	−	7.45693i	−0.187525	−	0.488520i	0.807298	−	0.590145i	$-0.200929\pi$
$233$	−2.86245	−	7.45693i	−0.187525	−	0.488520i	−0.994823	+	0.101625i	$0.967596\pi$
$234$	−20.6986	−	4.39962i	−1.35311	−	0.287612i
$235$	−7.81248	+	2.19017i	−0.509630	+	0.142871i
$236$	6.08280	+	0.639328i	0.395957	+	0.0416167i
$237$	−0.0985261	−	0.622069i	−0.00639996	−	0.0404077i
$238$	0.839058	−	13.4179i	0.0543880	−	0.869751i
$239$	−6.49504	+	2.11037i	−0.420129	+	0.136508i	−0.511449	−	0.859313i	$-0.670891\pi$
$239$	−6.49504	+	2.11037i	−0.420129	+	0.136508i	0.0913204	+	0.995822i	$0.470891\pi$
$240$	4.59350	+	5.54067i	0.296509	+	0.357649i
$241$	−1.13878	−	0.657476i	−0.0733553	−	0.0423517i	0.462874	−	0.886424i	$-0.346818\pi$
$241$	−1.13878	−	0.657476i	−0.0733553	−	0.0423517i	−0.536229	+	0.844073i	$0.680152\pi$
$242$	5.61517	−	9.45885i	0.360957	−	0.608038i
$243$	31.1160	+	8.33750i	1.99609	+	0.534851i
$244$	−0.150606	+	0.109421i	−0.00964154	+	0.00700499i
$245$	−15.5803	+	1.50132i	−0.995389	+	0.0959161i
$246$	−6.41117	+	19.7315i	−0.408761	+	1.25804i
$247$	−6.24478	−	7.71166i	−0.397346	−	0.490681i
$248$	3.79091	−	9.87566i	0.240723	−	0.627105i
$249$	0.651507	−	0.586619i	0.0412876	−	0.0371755i
$250$	−5.76141	+	9.58155i	−0.364383	+	0.605991i
$251$	−3.52460	−	4.85119i	−0.222471	−	0.306205i	0.683163	−	0.730266i	$-0.260604\pi$
$251$	−3.52460	−	4.85119i	−0.222471	−	0.306205i	−0.905633	+	0.424062i	$0.860604\pi$
$252$	−18.8587	+	4.84975i	−1.18799	+	0.305505i
$253$	18.2431	−	1.32446i	1.14693	−	0.0832679i
$254$	17.8955	−	10.3319i	1.12286	−	0.648284i
$255$	33.2361	−	15.2591i	2.08133	−	0.955564i
$256$	−0.978148	−	0.207912i	−0.0611342	−	0.0129945i
$257$	−17.8343	−	11.5817i	−1.11247	−	0.722449i	−0.148624	−	0.988894i	$-0.547484\pi$
$257$	−17.8343	−	11.5817i	−1.11247	−	0.722449i	−0.963850	+	0.266444i	$0.914151\pi$
$258$	−26.5040	+	4.19782i	−1.65007	+	0.261345i
$259$	19.3721	+	14.3756i	1.20373	+	0.893255i
$260$	4.59818	+	4.49337i	0.285167	+	0.278667i
$261$	32.0839	−	35.6328i	1.98595	−	2.20562i
$262$	−12.4042	+	15.3180i	−0.766337	+	0.946347i
$263$	1.84652	−	0.494774i	0.113861	−	0.0305091i	−0.201438	−	0.979501i	$-0.564562\pi$
$263$	1.84652	−	0.494774i	0.113861	−	0.0305091i	0.315300	+	0.948992i	$0.397895\pi$
$264$	−9.66292	+	4.53723i	−0.594712	+	0.279247i
$265$	2.55326	−	5.15716i	0.156845	−	0.316802i
$266$	−8.30385	−	3.79798i	−0.509142	−	0.232869i
$267$	−5.60715	−	2.85699i	−0.343152	−	0.174845i
$268$	−1.34705	−	0.874786i	−0.0822844	−	0.0534361i
$269$	−17.2477	+	7.67916i	−1.05161	+	0.468207i	−0.858416	−	0.512954i	$-0.828551\pi$
$269$	−17.2477	+	7.67916i	−1.05161	+	0.468207i	−0.193194	+	0.981161i	$0.561885\pi$
$270$	−21.2638	−	23.0753i	−1.29407	−	1.40432i
$271$	2.89195	+	13.6056i	0.175674	+	0.826480i	0.974406	+	0.224794i	$0.0721708\pi$
$271$	2.89195	+	13.6056i	0.175674	+	0.826480i	−0.798733	+	0.601686i	$0.794496\pi$
$272$	−2.30690	+	4.52754i	−0.139876	+	0.274523i
$273$	−22.9457	+	8.54337i	−1.38874	+	0.517068i
$274$			0.825568i			0.0498744i
$275$	−11.6178	−	11.8333i	−0.700578	−	0.713576i
$276$	−15.3727	−	8.87544i	−0.925329	−	0.534239i
$277$	−2.58212	−	2.09096i	−0.155145	−	0.125634i	0.548605	−	0.836082i	$-0.315159\pi$
$277$	−2.58212	−	2.09096i	−0.155145	−	0.125634i	−0.703750	+	0.710448i	$0.748492\pi$
$278$	−0.517010	−	9.86513i	−0.0310082	−	0.591671i
$279$	−24.0584	+	74.0440i	−1.44034	+	4.43290i
$280$	5.62915	+	1.82009i	0.336406	+	0.108771i
$281$	−0.446613	−	0.324483i	−0.0266427	−	0.0193570i	0.574384	−	0.818586i	$-0.305242\pi$
$281$	−0.446613	−	0.324483i	−0.0266427	−	0.0193570i	−0.601027	+	0.799229i	$0.705242\pi$
$282$	−6.36089	+	9.79491i	−0.378786	+	0.583279i
$283$	1.03660	−	0.673179i	0.0616198	−	0.0400163i	−0.513462	−	0.858113i	$-0.671637\pi$
$283$	1.03660	−	0.673179i	0.0616198	−	0.0400163i	0.575081	+	0.818096i	$0.304970\pi$
$284$	3.27162	−	0.343861i	0.194135	−	0.0204044i
$285$	−1.58584	−	24.7887i	−0.0939371	−	1.46835i
$286$	−8.16079	+	4.93309i	−0.482558	+	0.291700i
$287$	4.24744	+	16.5166i	0.250719	+	0.974945i
$288$	7.26924	+	1.15134i	0.428344	+	0.0678431i
$289$	6.55485	+	5.90202i	0.385580	+	0.347177i
$290$	−14.0270	+	3.93236i	−0.823692	+	0.230916i
$291$	−31.0911	+	13.8427i	−1.82259	+	0.811471i
$292$	1.65000	−	1.33614i	0.0965587	−	0.0781917i
$293$	6.09864	+	11.9693i	0.356286	+	0.699251i	0.997688	−	0.0679535i	$-0.0216470\pi$
$293$	6.09864	+	11.9693i	0.356286	+	0.699251i	−0.641402	+	0.767205i	$0.721647\pi$
$294$	−15.4108	+	16.4359i	−0.898778	+	0.958562i
$295$	11.1564	+	7.91076i	0.649553	+	0.460582i
$296$	−4.55889	−	7.89622i	−0.264980	−	0.458959i
$297$	41.0359	−	21.9594i	2.38115	−	1.27421i
$298$	6.79484	−	1.82067i	0.393615	−	0.105469i
$299$	−14.4857	−	6.44946i	−0.837731	−	0.372982i
$300$	2.88332	+	15.8330i	0.166468	+	0.914117i
$301$	−16.5403	+	14.5934i	−0.953367	+	0.841151i
$302$	4.99153	−	0.790581i	0.287230	−	0.0454928i
$303$	20.2740	−	16.4176i	1.16471	−	0.943164i
$304$	2.30935	+	2.56479i	0.132450	+	0.147101i
$305$	−0.413455	+	0.0482806i	−0.0236743	+	0.00276454i
$306$	15.2112	−	34.1650i	0.869568	−	1.95308i
$307$	−4.08952	−	4.08952i	−0.233401	−	0.233401i	0.580709	−	0.814111i	$-0.302775\pi$
$307$	−4.08952	−	4.08952i	−0.233401	−	0.233401i	−0.814111	+	0.580709i	$0.802775\pi$
$308$	−4.70520	+	7.40683i	−0.268103	+	0.422043i
$309$		−	32.9271i		−	1.87316i
$310$	18.2096	−	15.0967i	1.03423	−	0.857433i
$311$	−1.76777	+	8.31672i	−0.100241	+	0.471598i	0.899180	+	0.437579i	$0.144164\pi$
$311$	−1.76777	+	8.31672i	−0.100241	+	0.471598i	−0.999421	+	0.0340190i	$0.989169\pi$
$312$	9.24162	+	0.484333i	0.523204	+	0.0274199i
$313$	−3.61895	−	4.46903i	−0.204555	−	0.252605i	0.664536	−	0.747256i	$-0.268629\pi$
$313$	−3.61895	−	4.46903i	−0.204555	−	0.252605i	−0.869091	+	0.494651i	$0.835296\pi$
$314$	−6.93057	−	5.03535i	−0.391115	−	0.284161i
$315$	−42.0740	−	11.2090i	−2.37060	−	0.631554i
$316$	0.0604678	+	0.186101i	0.00340158	+	0.0104690i
$317$	11.8204	−	4.53743i	0.663900	−	0.254847i	−0.00299874	−	0.999996i	$-0.500955\pi$
$317$	11.8204	−	4.53743i	0.663900	−	0.254847i	0.666899	+	0.745148i	$0.267621\pi$
$318$	−2.14390	−	8.00113i	−0.120224	−	0.448681i
$319$	−0.434572	−	21.6031i	−0.0243314	−	1.20954i
$320$	−1.67886	−	1.47697i	−0.0938511	−	0.0825650i
$321$	6.99400	+	9.62642i	0.390367	+	0.537294i
$322$	−14.5782	+	0.616561i	−0.812412	+	0.0343596i
$323$	15.6258	−	7.96172i	0.869440	−	0.443002i
$324$	−22.9614	−	2.41334i	−1.27564	−	0.134075i
$325$	4.03990	+	13.7966i	0.224093	+	0.765300i
$326$	3.17871	+	3.53031i	0.176052	+	0.195526i
$327$	47.4734	−	2.48798i	2.62529	−	0.137585i
$328$	1.00835	−	6.36645i	0.0556767	−	0.351529i
$329$	−0.0968811	+	9.59973i	−0.00534123	+	0.529251i
$330$	−23.8066	−	1.74286i	−1.31051	−	0.0959414i
$331$	10.5716	+	18.3105i	0.581066	+	1.00644i	0.995353	+	0.0962893i	$0.0306974\pi$
$331$	10.5716	+	18.3105i	0.581066	+	1.00644i	−0.414288	+	0.910146i	$0.635969\pi$
$332$	−0.171412	+	0.211676i	−0.00940744	+	0.0116172i
$333$	36.5483	+	56.2794i	2.00283	+	3.08409i
$334$	0.574325	−	0.122077i	0.0314257	−	0.00667973i
$335$	−1.66730	−	3.18106i	−0.0910941	−	0.173800i
$336$	7.81414	−	3.38501i	0.426296	−	0.184667i
$337$	6.45714	+	12.6729i	0.351743	+	0.690335i	0.997305	−	0.0733737i	$-0.0233766\pi$
$337$	6.45714	+	12.6729i	0.351743	+	0.690335i	−0.645561	+	0.763708i	$0.723377\pi$
$338$	−4.72679	+	0.247721i	−0.257103	+	0.0134742i
$339$	0.917405	+	8.72852i	0.0498266	+	0.474068i
$340$	−9.45727	+	6.29779i	−0.512892	+	0.341546i
$341$	14.9117	+	31.7575i	0.807515	+	1.71976i
$342$	−17.9611	−	17.9611i	−0.971225	−	0.971225i
$343$	−3.44960	+	18.1962i	−0.186261	+	0.982500i
$344$	7.92904	−	2.57630i	0.427505	−	0.138905i
$345$	−20.2410	−	34.1434i	−1.08974	−	1.83822i
$346$	5.61886	+	12.6202i	0.302072	+	0.678464i
$347$	2.18370	−	5.68874i	0.117227	−	0.305388i	−0.862395	−	0.506236i	$-0.831036\pi$
$347$	2.18370	−	5.68874i	0.117227	−	0.305388i	0.979622	+	0.200848i	$0.0643698\pi$
$348$	−11.4207	+	17.5863i	−0.612214	+	0.942727i
$349$	2.59476	+	7.98585i	0.138894	+	0.427473i	0.996175	−	0.0873758i	$-0.0278481\pi$
$349$	2.59476	+	7.98585i	0.138894	+	0.427473i	−0.857281	+	0.514849i	$0.827848\pi$
$350$	8.97846	+	9.71531i	0.479919	+	0.519305i
$351$	−40.3474			−2.15359
$352$	2.74466	−	1.86194i	0.146291	−	0.0992418i
$353$	0.968568	+	3.61474i	0.0515517	+	0.192393i	0.986900	−	0.161336i	$-0.0515802\pi$
$353$	0.968568	+	3.61474i	0.0515517	+	0.192393i	−0.935348	+	0.353729i	$0.884913\pi$
$354$	19.5786	−	2.05779i	1.04059	−	0.109370i
$355$	6.75395	+	2.91423i	0.358462	+	0.154671i
$356$	1.85948	+	0.604181i	0.0985521	+	0.0320215i
$357$	−6.33759	−	42.8054i	−0.335421	−	2.26550i
$358$	−1.04153	−	6.57594i	−0.0550464	−	0.347549i
$359$	−3.71125	−	17.4601i	−0.195873	−	0.921508i	−0.960768	−	0.277353i	$-0.910543\pi$
$359$	−3.71125	−	17.4601i	−0.195873	−	0.921508i	0.764895	−	0.644154i	$-0.222791\pi$
$360$	12.9081	+	10.2087i	0.680318	+	0.538046i
$361$	0.740978	+	7.04993i	0.0389988	+	0.371049i
$362$	2.71107	−	10.1179i	0.142491	−	0.531783i
$363$	11.3486	−	33.5373i	0.595647	−	1.76025i
$364$	6.62594	−	3.73684i	0.347294	−	0.195864i
$365$	4.68018	−	0.796675i	0.244972	−	0.0416999i
$366$	−0.400933	+	0.445281i	−0.0209571	+	0.0232752i
$367$	0.790502	−	15.0837i	0.0412639	−	0.787362i	−0.897124	−	0.441778i	$-0.854348\pi$
$367$	0.790502	−	15.0837i	0.0412639	−	0.787362i	0.938388	−	0.345583i	$-0.112319\pi$
$368$	5.14867	+	1.97639i	0.268393	+	0.103026i
$369$	−4.95886	+	47.1804i	−0.258148	+	2.45611i
$370$	−0.235016	−	20.3866i	−0.0122179	−	1.05985i
$371$	−5.01379	−	4.60690i	−0.260303	−	0.239178i
$372$	5.32628	−	33.6288i	0.276155	−	1.74357i
$373$	3.93204	−	14.6746i	0.203593	−	0.759820i	−0.786280	−	0.617870i	$-0.787996\pi$
$373$	3.93204	−	14.6746i	0.203593	−	0.759820i	0.989874	−	0.141951i	$-0.0453374\pi$
$374$	−5.52918	−	15.9202i	−0.285907	−	0.823214i
$375$	−11.7269	+	34.0215i	−0.605574	+	1.75686i
$376$	1.47586	−	3.31484i	0.0761117	−	0.170950i
$377$	−8.50395	+	16.6899i	−0.437976	+	0.859576i
$378$	−33.2494	+	16.5209i	−1.71017	+	0.849745i
$379$	19.7770	−	27.2208i	1.01588	−	1.39824i	0.100825	−	0.994904i	$-0.467852\pi$
$379$	19.7770	−	27.2208i	1.01588	−	1.39824i	0.915053	−	0.403333i	$-0.132148\pi$
$380$	1.69142	+	7.52963i	0.0867679	+	0.386262i
$381$	49.4268	−	44.5041i	2.53221	−	2.28001i
$382$	−21.9782	+	14.2728i	−1.12450	+	0.730260i
$383$	27.7849	−	10.6656i	1.41974	−	0.544989i	0.477118	−	0.878839i	$-0.341681\pi$
$383$	27.7849	−	10.6656i	1.41974	−	0.544989i	0.942626	+	0.333851i	$0.108348\pi$
$384$	−3.21867			−0.164252
$385$	−17.2868	+	9.28258i	−0.881017	+	0.473084i
$386$	27.1358			1.38118
$387$	−57.2843	+	21.9894i	−2.91192	+	1.11778i
$388$	8.86790	−	5.75888i	0.450199	−	0.292363i
$389$	−21.6050	+	19.4532i	−1.09542	+	0.986318i	−0.999958	−	0.00911575i	$-0.997098\pi$
$389$	−21.6050	+	19.4532i	−1.09542	+	0.986318i	−0.0954583	+	0.995433i	$0.530432\pi$
$390$	17.4836	+	11.0695i	0.885315	+	0.560528i
$391$	16.4719	−	22.6716i	0.833019	−	1.14655i
$392$	3.93018	−	5.79255i	0.198504	−	0.292568i
$393$	−28.8020	+	56.5270i	−1.45287	+	2.85141i
$394$	−5.54142	+	12.4462i	−0.279173	+	0.627032i
$395$	−0.0860321	+	0.429008i	−0.00432874	+	0.0215857i
$396$	−19.4555	+	14.7420i	−0.977673	+	0.740815i
$397$	3.86826	−	14.4365i	0.194142	−	0.724549i	−0.798345	−	0.602201i	$-0.794291\pi$
$397$	3.86826	−	14.4365i	0.194142	−	0.724549i	0.992487	−	0.122349i	$-0.0390426\pi$
$398$	0.776436	−	4.90222i	0.0389192	−	0.245726i
$399$	−28.6849	−	6.40039i	−1.43604	−	0.320420i
$400$	−1.65430	−	4.71840i	−0.0827149	−	0.235920i
$401$	−3.31049	+	31.4972i	−0.165318	+	1.57289i	0.526089	+	0.850429i	$0.323658\pi$
$401$	−3.31049	+	31.4972i	−0.165318	+	1.57289i	−0.691407	+	0.722465i	$0.743009\pi$
$402$	−4.82638	−	1.85268i	−0.240718	−	0.0924030i
$403$	1.59177	−	30.3728i	0.0792919	−	1.51298i
$404$	−5.42339	+	6.02328i	−0.269824	+	0.299670i
$405$	−42.1135	−	29.8616i	−2.09263	−	1.48384i
$406$	−0.173946	+	17.2359i	−0.00863279	+	0.855404i
$407$	29.3613	+	7.23769i	1.45539	+	0.358759i
$408$	−4.23306	+	15.7980i	−0.209568	+	0.782118i
$409$	−3.60204	−	34.2712i	−0.178110	−	1.69460i	−0.609782	−	0.792569i	$-0.708743\pi$
$409$	−3.60204	−	34.2712i	−0.178110	−	1.69460i	0.431673	−	0.902030i	$-0.357924\pi$
$410$	8.94085	−	11.3050i	0.441557	−	0.558316i
$411$	0.552470	+	2.59917i	0.0272513	+	0.128207i
$412$	1.60033	+	10.1041i	0.0788425	+	0.497792i
$413$	12.6781	−	10.0564i	0.623848	−	0.494842i
$414$	−38.6028	−	12.5428i	−1.89722	−	0.616445i
$415$	−0.566044	+	0.224804i	−0.0277860	+	0.0110352i
$416$	−2.85944	+	0.300539i	−0.140196	+	0.0147352i
$417$	−8.22947	−	30.7128i	−0.402999	−	1.50401i
$418$	−11.4406	−	0.369046i	−0.559578	−	0.0180506i
$419$	21.0651			1.02910			0.514549	−	0.857461i	$-0.327959\pi$
$419$	21.0651			1.02910			0.514549	+	0.857461i	$0.327959\pi$
$420$	18.9405	+	1.96323i	0.924199	+	0.0957959i
$421$	6.53984	+	20.1275i	0.318732	+	0.980957i	0.974191	+	0.225726i	$0.0724753\pi$
$421$	6.53984	+	20.1275i	0.318732	+	0.980957i	−0.655459	+	0.755231i	$0.727525\pi$
$422$	−0.806995	+	1.24266i	−0.0392839	+	0.0604919i
$423$	−9.57042	+	24.9318i	−0.465330	+	1.21223i
$424$	1.04675	+	2.35104i	0.0508348	+	0.114177i
$425$	−25.3347	+	1.91424i	−1.22891	+	0.0928543i
$426$	10.0700	−	3.27195i	0.487895	−	0.158527i
$427$	−0.0819540	+	0.485664i	−0.00396603	+	0.0235029i
$428$	−2.61406	−	2.61406i	−0.126355	−	0.126355i
$429$	−22.3917	+	20.9922i	−1.08108	+	1.01352i
$430$	18.2784	+	3.66550i	0.881462	+	0.176766i
$431$	0.920396	+	8.75699i	0.0443339	+	0.421809i	0.994069	+	0.108754i	$0.0346859\pi$
$431$	0.920396	+	8.75699i	0.0443339	+	0.421809i	−0.949735	+	0.313056i	$0.898647\pi$
$432$	14.0137	−	0.734428i	0.674236	−	0.0353352i
$433$	−14.0647	−	27.6036i	−0.675907	−	1.32654i	−0.932902	−	0.360130i	$-0.882732\pi$
$433$	−14.0647	−	27.6036i	−0.675907	−	1.32654i	0.256995	−	0.966413i	$-0.417268\pi$
$434$	−11.1249	−	25.6814i	−0.534013	−	1.23275i
$435$	−41.5301	+	21.7672i	−1.99121	+	1.04366i
$436$	−14.4469	+	3.07078i	−0.691880	+	0.147064i
$437$	−10.3665	−	15.9629i	−0.495895	−	0.763611i
$438$	4.30060	−	5.31080i	0.205490	−	0.253760i
$439$	−0.438843	−	0.760098i	−0.0209448	−	0.0362775i	0.855363	−	0.518029i	$-0.173334\pi$
$439$	−0.438843	−	0.760098i	−0.0209448	−	0.0362775i	−0.876308	+	0.481752i	$0.840001\pi$
$440$	7.39005	−	0.622234i	0.352307	−	0.0296639i
$441$	−26.6547	+	44.0878i	−1.26927	+	2.09942i
$442$	−2.28550	+	14.4301i	−0.108710	+	0.686368i
$443$	21.4225	−	1.12270i	1.01781	−	0.0533413i	0.463876	−	0.885900i	$-0.346458\pi$
$443$	21.4225	−	1.12270i	1.01781	−	0.0533413i	0.553937	+	0.832559i	$0.313125\pi$
$444$	−19.6371	−	21.8092i	−0.931934	−	1.03502i
$445$	2.96263	+	3.21501i	0.140442	+	0.152406i
$446$	16.8645	+	1.77253i	0.798557	+	0.0839318i
$447$	20.1741	−	10.2792i	0.954200	−	0.486189i
$448$	−2.23334	+	1.41851i	−0.105516	+	0.0670185i
$449$	−5.04105	−	6.93841i	−0.237902	−	0.327444i	0.673327	−	0.739345i	$-0.264865\pi$
$449$	−5.04105	−	6.93841i	−0.237902	−	0.327444i	−0.911228	+	0.411901i	$0.864865\pi$
$450$	13.9762	+	34.0419i	0.658843	+	1.60475i
$451$	12.9112	+	17.0392i	0.607964	+	0.802345i
$452$	−0.705742	−	2.63386i	−0.0331953	−	0.123887i
$453$	15.1860	−	5.82935i	0.713499	−	0.273887i
$454$	4.57846	+	14.0911i	0.214878	+	0.661326i
$455$	17.0098	−	0.0244214i	0.797434	−	0.00114489i
$456$	8.98696	+	6.52941i	0.420853	+	0.305768i
$457$	−12.4445	−	15.3677i	−0.582130	−	0.718870i	0.397965	−	0.917401i	$-0.369717\pi$
$457$	−12.4445	−	15.3677i	−0.582130	−	0.718870i	−0.980095	+	0.198530i	$0.936383\pi$
$458$	7.51617	+	0.393906i	0.351208	+	0.0184060i
$459$	14.8255	−	69.7485i	0.691996	−	3.25558i
$460$	7.87064	+	9.49355i	0.366970	+	0.442639i
$461$		−	17.0570i		−	0.794422i	−0.917727	−	0.397211i	$-0.869978\pi$
$461$		−	17.0570i		−	0.794422i	0.917727	−	0.397211i	$-0.130022\pi$
$462$	−9.85690	+	26.4679i	−0.458584	+	1.23140i
$463$	6.29539	+	6.29539i	0.292571	+	0.292571i	0.838095	−	0.545524i	$-0.183669\pi$
$463$	6.29539	+	6.29539i	0.292571	+	0.292571i	−0.545524	+	0.838095i	$0.683669\pi$
$464$	2.64985	−	5.95165i	0.123016	−	0.276298i
$465$	47.2272	−	59.7153i	2.19011	−	2.76923i
$466$	5.34465	+	5.93584i	0.247586	+	0.274972i
$467$	−17.7172	+	14.3471i	−0.819855	+	0.663905i	−0.944578	−	0.328286i	$-0.893529\pi$
$467$	−17.7172	+	14.3471i	−0.819855	+	0.663905i	0.124723	+	0.992192i	$0.460196\pi$
$468$	20.9005	−	3.31031i	0.966124	−	0.153019i
$469$	−4.16539	+	0.841537i	−0.192340	+	0.0388586i
$470$	6.50869	−	4.84444i	0.300223	−	0.223458i
$471$	−25.1894	−	11.2151i	−1.16067	−	0.516763i
$472$	−5.90790	+	1.58302i	−0.271933	+	0.0728643i
$473$	−12.0552	+	24.8847i	−0.554301	+	1.14420i
$474$	0.314912	+	0.545443i	0.0144644	+	0.0250530i
$475$	−4.95274	+	16.5303i	−0.227248	+	0.758463i
$476$	4.02520	+	12.8273i	0.184495	+	0.587940i
$477$	−8.59897	−	16.8764i	−0.393720	−	0.772719i
$478$	5.30735	−	4.29781i	0.242753	−	0.196577i
$479$	15.5948	−	6.94324i	0.712543	−	0.317245i	−0.0182595	−	0.999833i	$-0.505813\pi$
$479$	15.5948	−	6.94324i	0.712543	−	0.317245i	0.730803	+	0.682589i	$0.239146\pi$
$480$	−6.27400	−	3.52650i	−0.286368	−	0.160962i
$481$	−19.4818	−	17.5415i	−0.888293	−	0.799823i
$482$	1.29876	+	0.205704i	0.0591570	+	0.00936955i
$483$	−45.4845	+	11.6969i	−2.06962	+	0.532226i
$484$	−1.85247	+	10.8429i	−0.0842031	+	0.492859i
$485$	23.5954	−	1.50950i	1.07141	−	0.0685429i
$486$	−32.0371	+	3.36724i	−1.45323	+	0.152741i
$487$	−24.3227	+	15.7954i	−1.10217	+	0.715756i	−0.961638	−	0.274320i	$-0.911547\pi$
$487$	−24.3227	+	15.7954i	−1.10217	+	0.715756i	−0.140529	+	0.990077i	$0.544880\pi$
$488$	0.101389	−	0.156126i	0.00458968	−	0.00706749i
$489$	12.3701	+	8.98743i	0.559397	+	0.406426i
$490$	14.0074	−	6.98509i	0.632792	−	0.315554i
$491$	7.27128	−	22.3787i	0.328148	−	1.00994i	−0.641851	−	0.766829i	$-0.721833\pi$
$491$	7.27128	−	22.3787i	0.328148	−	1.00994i	0.969999	−	0.243107i	$-0.0781667\pi$
$492$	−1.08581	−	20.7185i	−0.0489522	−	0.934064i
$493$	−25.7271	−	20.8334i	−1.15869	−	0.938290i
$494$	8.59361	+	4.96152i	0.386645	+	0.223230i
$495$	−54.0755	+	7.41982i	−2.43051	+	0.333496i
$496$			10.5783i			0.474978i
$497$	5.54531	−	6.70832i	0.248741	−	0.300909i
$498$	−0.398008	+	0.781135i	−0.0178352	+	0.0350035i
$499$	4.90141	+	23.0593i	0.219417	+	1.03228i	0.940596	+	0.339528i	$0.110267\pi$
$499$	4.90141	+	23.0593i	0.219417	+	1.03228i	−0.721178	+	0.692749i	$0.756399\pi$
$500$	1.94502	−	11.0099i	0.0869838	−	0.492376i
$501$	1.72648	−	0.768676i	0.0771332	−	0.0343419i
$502$	5.02901	+	3.26588i	0.224456	+	0.145763i
$503$	12.5444	+	6.39170i	0.559328	+	0.284992i	0.710712	−	0.703483i	$-0.248373\pi$
$503$	12.5444	+	6.39170i	0.559328	+	0.284992i	−0.151384	+	0.988475i	$0.548373\pi$
$504$	15.8682	−	11.2860i	0.706824	−	0.502718i
$505$	−17.1709	+	5.79882i	−0.764094	+	0.258044i
$506$	−16.5567	+	7.77422i	−0.736036	+	0.345606i
$507$	−14.7158	+	3.94307i	−0.653550	+	0.175118i
$508$	−13.0042	+	16.0589i	−0.576968	+	0.712497i
$509$	2.17307	−	2.41344i	0.0963196	−	0.106974i	−0.693058	−	0.720882i	$-0.743737\pi$
$509$	2.17307	−	2.41344i	0.0963196	−	0.106974i	0.789377	+	0.613908i	$0.210404\pi$
$510$	−25.5602	+	26.1564i	−1.13182	+	1.15822i
$511$	0.643517	−	5.58034i	0.0284675	−	0.246860i
$512$	0.987688	−	0.156434i	0.0436501	−	0.00691349i
$513$	−40.6180	−	26.3777i	−1.79333	−	1.16460i
$514$	20.8003	+	4.42124i	0.917462	+	0.195013i
$515$	−7.95096	+	21.4487i	−0.350361	+	0.945144i
$516$	23.2392	−	13.4172i	1.02305	−	0.590659i
$517$	4.53788	+	11.1462i	0.199576	+	0.490208i
$518$	−23.2372	−	6.47841i	−1.02098	−	0.284645i
$519$	26.1355	+	35.9724i	1.14722	+	1.57901i
$520$	−5.90305	−	2.54708i	−0.258866	−	0.111697i
$521$	−16.8623	+	15.1829i	−0.738751	+	0.665174i	−0.949997	−	0.312259i	$-0.898914\pi$
$521$	−16.8623	+	15.1829i	−0.738751	+	0.665174i	0.211246	+	0.977433i	$0.432248\pi$
$522$	−17.1833	+	44.7639i	−0.752091	+	1.95926i
$523$	23.6402	+	29.1932i	1.03371	+	1.27653i	0.960223	+	0.279236i	$0.0900811\pi$
$523$	23.6402	+	29.1932i	1.03371	+	1.27653i	0.0734923	+	0.997296i	$0.476586\pi$
$524$	6.09089	−	18.7458i	0.266082	−	0.818915i
$525$	34.7687	+	24.5787i	1.51743	+	1.07270i
$526$	−1.54657	+	1.12365i	−0.0674335	+	0.0489933i
$527$	51.9206	+	13.9121i	2.26170	+	0.606020i
$528$	7.39512	−	7.69875i	0.321831	−	0.335045i
$529$	−6.42148	−	3.70744i	−0.279195	−	0.161193i
$530$	−0.535509	+	5.72963i	−0.0232610	+	0.248879i
$531$	42.8120	−	13.9104i	1.85788	−	0.603662i
$532$	9.11339	+	0.569887i	0.395116	+	0.0247077i
$533$	−2.89919	−	18.3048i	−0.125578	−	0.792868i
$534$	6.25858	+	0.657803i	0.270835	+	0.0284659i
$535$	−2.23139	−	7.95951i	−0.0964716	−	0.344120i
$536$	1.57108	+	0.333943i	0.0678602	+	0.0144241i
$537$	−7.67970	−	20.0063i	−0.331403	−	0.863335i
$538$	13.3501	−	13.3501i	0.575565	−	0.575565i
$539$	4.82537	+	22.7094i	0.207843	+	0.978162i
$540$	28.1209	+	13.9224i	1.21013	+	0.599124i
$541$	−9.39411	−	4.18253i	−0.403885	−	0.179821i	0.194732	−	0.980856i	$-0.437616\pi$
$541$	−9.39411	−	4.18253i	−0.403885	−	0.179821i	−0.598617	+	0.801035i	$0.704283\pi$
$542$	−7.57567	−	11.6655i	−0.325403	−	0.501077i
$543$	1.76450	−	33.6687i	0.0757220	−	1.44486i
$544$	0.531149	−	5.05354i	0.0227728	−	0.216669i
$545$	−31.5250	−	9.84282i	−1.35038	−	0.421620i
$546$	18.3600	−	16.1989i	0.785735	−	0.693250i
$547$	−11.9114	−	6.06915i	−0.509293	−	0.259498i	0.180408	−	0.983592i	$-0.442258\pi$
$547$	−11.9114	−	6.06915i	−0.509293	−	0.259498i	−0.689701	+	0.724094i	$0.742258\pi$
$548$	−0.295857	−	0.770734i	−0.0126384	−	0.0329241i
$549$	−0.685051	+	1.18654i	−0.0292373	+	0.0506405i
$550$	15.0868	+	6.88392i	0.643303	+	0.293531i
$551$	−19.4723	+	11.2423i	−0.829546	+	0.478939i
$552$	17.5323	+	2.77685i	0.746226	+	0.118191i
$553$	0.458892	+	0.239681i	0.0195141	+	0.0101923i
$554$	3.15996	+	1.02673i	0.134254	+	0.0436216i
$555$	−14.3826	−	64.0266i	−0.610508	−	2.71778i
$556$	4.01802	+	9.02462i	0.170402	+	0.382729i
$557$	−3.81828	−	0.200108i	−0.161786	−	0.00847883i	−0.0287289	−	0.999587i	$-0.509146\pi$
$557$	−3.81828	−	0.200108i	−0.161786	−	0.00847883i	−0.133057	+	0.991108i	$0.542479\pi$
$558$	−4.07459	−	77.7478i	−0.172491	−	3.29133i
$559$	19.3927	−	14.0896i	0.820225	−	0.595928i
$560$	−5.90752	+	0.318106i	−0.249638	+	0.0134424i
$561$	−28.0615	−	46.4220i	−1.18476	−	1.95994i
$562$	0.533233	+	0.142879i	0.0224931	+	0.00602700i
$563$	−0.476040	−	0.385490i	−0.0200627	−	0.0162464i	0.619237	−	0.785204i	$-0.287442\pi$
$563$	−0.476040	−	0.385490i	−0.0200627	−	0.0162464i	−0.639299	+	0.768958i	$0.720776\pi$
$564$	2.42822	−	11.4239i	0.102247	−	0.481032i
$565$	1.51009	−	5.90730i	0.0635300	−	0.248522i
$566$	−0.726508	+	0.999953i	−0.0305374	+	0.0420311i
$567$	−47.8574	+	37.9609i	−2.00982	+	1.59421i
$568$	−2.93109	+	1.49346i	−0.122986	+	0.0626643i
$569$	25.1220	+	22.6200i	1.05317	+	0.948278i	0.998737	−	0.0502398i	$-0.0159986\pi$
$569$	25.1220	+	22.6200i	1.05317	+	0.948278i	0.0544319	+	0.998517i	$0.482665\pi$
$570$	10.3640	+	22.5739i	0.434099	+	0.945517i
$571$	16.2487	−	28.1435i	0.679986	−	1.17777i	−0.294999	−	0.955498i	$-0.595319\pi$
$571$	16.2487	−	28.1435i	0.679986	−	1.17777i	0.974985	−	0.222272i	$-0.0713473\pi$
$572$	5.85089	−	7.53001i	0.244638	−	0.314845i
$573$	−59.6434	+	59.6434i	−2.49164	+	2.49164i
$574$	−9.88436	−	13.8974i	−0.412565	−	0.580068i
$575$	4.94036	+	27.1287i	0.206027	+	1.13134i
$576$	−7.19903	+	1.53020i	−0.299959	+	0.0637583i
$577$	43.9326	+	16.8641i	1.82894	+	0.702064i	0.986610	+	0.163099i	$0.0521491\pi$
$577$	43.9326	+	16.8641i	1.82894	+	0.702064i	0.842329	+	0.538964i	$0.181184\pi$
$578$	−8.23457	−	3.16096i	−0.342513	−	0.131478i
$579$	85.4327	−	18.1593i	3.55046	−	0.754674i
$580$	11.6861	−	8.69799i	0.485237	−	0.361164i
$581$	0.0680909	+	0.717415i	0.00282489	+	0.0297634i
$582$	24.0653	−	24.0653i	0.997538	−	0.997538i
$583$	−8.02844	−	2.89795i	−0.332504	−	0.120021i
$584$	−1.06157	+	1.83870i	−0.0439282	+	0.0760859i
$585$	44.3672	+	16.4467i	1.83436	+	0.679988i
$586$	−9.98297	−	8.98870i	−0.412393	−	0.371320i
$587$	31.1447	−	15.8690i	1.28548	−	0.654984i	0.328325	−	0.944565i	$-0.393516\pi$
$587$	31.1447	−	15.8690i	1.28548	−	0.654984i	0.957154	+	0.289581i	$0.0935159\pi$
$588$	8.49715	−	20.8670i	0.350417	−	0.860540i
$589$	21.4591	−	29.5359i	0.884207	−	1.21701i
$590$	−13.2504	−	3.38722i	−0.545510	−	0.139450i
$591$	−9.11724	+	42.8932i	−0.375033	+	1.76439i
$592$	7.08584	+	5.73800i	0.291226	+	0.235830i
$593$	−21.8180	−	5.84611i	−0.895957	−	0.240071i	−0.218678	−	0.975797i	$-0.570174\pi$
$593$	−21.8180	−	5.84611i	−0.895957	−	0.240071i	−0.677279	+	0.735726i	$0.736841\pi$
$594$	−30.4408	+	35.2068i	−1.24900	+	1.44455i
$595$	−6.20799	+	29.4139i	−0.254503	+	1.20585i
$596$	−5.69106	+	4.13480i	−0.233115	+	0.169368i
$597$	−0.836085	−	15.9534i	−0.0342187	−	0.652931i
$598$	15.8349	+	0.829870i	0.647536	+	0.0339359i
$599$	−13.8238	−	31.0488i	−0.564826	−	1.26862i	−0.939844	−	0.341603i	$-0.889030\pi$
$599$	−13.8238	−	31.0488i	−0.564826	−	1.26862i	0.375018	−	0.927017i	$-0.377636\pi$
$600$	−8.36584	−	13.7481i	−0.341534	−	0.561262i
$601$	−9.53234	−	3.09725i	−0.388832	−	0.126339i	0.108075	−	0.994143i	$-0.465531\pi$
$601$	−9.53234	−	3.09725i	−0.388832	−	0.126339i	−0.496908	+	0.867803i	$0.665531\pi$
$602$	10.2119	−	19.5516i	0.416205	−	0.796866i
$603$	−11.6757	−	1.84925i	−0.475471	−	0.0753072i
$604$	−4.37668	+	2.52688i	−0.178084	+	0.102817i
$605$	−15.4908	+	19.1059i	−0.629791	+	0.776765i
$606$	−13.0439	+	22.5927i	−0.529871	+	0.917764i
$607$	−16.2302	−	42.2811i	−0.658763	−	1.71614i	−0.697202	−	0.716875i	$-0.745572\pi$
$607$	−16.2302	−	42.2811i	−0.658763	−	1.71614i	0.0384389	−	0.999261i	$-0.487762\pi$
$608$	−3.07510	−	1.56684i	−0.124712	−	0.0635438i
$609$	10.9866	+	54.3809i	0.445201	+	2.20362i
$610$	0.368691	−	0.193243i	0.0149279	−	0.00782417i
$611$	1.09052	−	10.3756i	0.0441177	−	0.419752i
$612$	−1.95727	+	37.3470i	−0.0791180	+	1.50966i
$613$	13.3165	+	20.5056i	0.537848	+	0.828213i	0.998228	−	0.0595090i	$-0.0189535\pi$
$613$	13.3165	+	20.5056i	0.537848	+	0.828213i	−0.460380	+	0.887722i	$0.652287\pi$
$614$	5.28345	+	2.35234i	0.213223	+	0.0949329i
$615$	20.5835	−	41.5753i	0.830006	−	1.67648i
$616$	1.73831	−	8.60106i	0.0700384	−	0.346547i
$617$	−16.3626	+	16.3626i	−0.658734	+	0.658734i	−0.955080	−	0.296347i	$-0.904232\pi$
$617$	−16.3626	+	16.3626i	−0.658734	+	0.658734i	0.296347	+	0.955080i	$0.404232\pi$
$618$	11.8000	+	30.7401i	0.474666	+	1.23655i
$619$	3.04100	+	0.646384i	0.122228	+	0.0259804i	0.268620	−	0.963246i	$-0.413433\pi$
$619$	3.04100	+	0.646384i	0.122228	+	0.0259804i	−0.146391	+	0.989227i	$0.546766\pi$
$620$	−11.5899	+	20.6197i	−0.465463	+	0.828106i
$621$	−76.9674	−	8.08960i	−3.08859	−	0.324624i
$622$	−1.33009	−	8.39784i	−0.0533317	−	0.336723i
$623$	4.63255	−	2.30181i	0.185599	−	0.0922202i
$624$	−8.80136	+	2.85974i	−0.352336	+	0.114481i
$625$	15.8541	−	19.3299i	0.634165	−	0.773197i
$626$	4.98014	+	2.87528i	0.199046	+	0.114919i
$627$	−36.2658	+	6.49417i	−1.44832	+	0.259352i
$628$	8.27475	+	2.21721i	0.330199	+	0.0884765i
$629$	37.4825	−	27.2326i	1.49452	−	1.08583i
$630$	43.2964	−	4.61349i	1.72497	−	0.183806i
$631$	−0.989734	+	3.04609i	−0.0394007	+	0.121263i	−0.968822	−	0.247757i	$-0.920307\pi$
$631$	−0.989734	+	3.04609i	−0.0394007	+	0.121263i	0.929422	+	0.369020i	$0.120307\pi$
$632$	−0.123144	−	0.152070i	−0.00489841	−	0.00604903i
$633$	−1.70910	+	4.45236i	−0.0679307	+	0.176966i
$634$	−9.40923	+	8.47211i	−0.373688	+	0.336471i
$635$	−42.9431	+	17.0548i	−1.70415	+	0.676801i
$636$	4.86885	+	6.70139i	0.193062	+	0.265727i
$637$	5.60037	−	19.3315i	0.221895	−	0.765940i
$638$	8.14756	+	20.0125i	0.322565	+	0.792302i
$639$	20.9676	−	12.1056i	0.829464	−	0.478891i
$640$	2.09665	+	0.777218i	0.0828773	+	0.0307223i
$641$	−15.7535	−	3.34852i	−0.622228	−	0.132259i	−0.113999	−	0.993481i	$-0.536366\pi$
$641$	−15.7535	−	3.34852i	−0.622228	−	0.132259i	−0.508229	+	0.861222i	$0.669699\pi$
$642$	−9.97926	−	6.48061i	−0.393850	−	0.255769i
$643$	−20.2946	+	3.21435i	−0.800342	+	0.126762i	−0.543190	−	0.839610i	$-0.682784\pi$
$643$	−20.2946	+	3.21435i	−0.800342	+	0.126762i	−0.257151	+	0.966371i	$0.582784\pi$
$644$	13.3890	−	5.79997i	0.527599	−	0.228551i
$645$	59.9995	−	0.691671i	2.36248	−	0.0272345i
$646$	−11.7347	+	13.0327i	−0.461695	+	0.512764i
$647$	−6.88191	+	8.49845i	−0.270556	+	0.334109i	−0.894257	−	0.447555i	$-0.852295\pi$
$647$	−6.88191	+	8.49845i	−0.270556	+	0.334109i	0.623701	+	0.781663i	$0.285628\pi$
$648$	22.3012	−	5.97559i	0.876075	−	0.234743i
$649$	9.78737	−	17.7682i	0.384188	−	0.697463i
$650$	−8.71584	−	11.4325i	−0.341863	−	0.448420i
$651$	−52.2110	−	73.4089i	−2.04631	−	2.87712i
$652$	−4.23273	−	2.15668i	−0.165767	−	0.0844623i
$653$	20.7060	+	13.4466i	0.810289	+	0.526208i	0.882018	−	0.471216i	$-0.156185\pi$
$653$	20.7060	+	13.4466i	0.810289	+	0.526208i	−0.0717285	+	0.997424i	$0.522852\pi$
$654$	−43.4287	+	19.3357i	−1.69819	+	0.756085i
$655$	32.4113	−	29.8669i	1.26641	−	1.16700i
$656$	1.34016	+	6.30496i	0.0523245	+	0.246167i
$657$	7.09408	−	13.9229i	0.276767	−	0.543185i
$658$	−3.34979	−	8.99684i	−0.130588	−	0.350733i
$659$		−	1.99542i		−	0.0777306i	−0.999244	−	0.0388653i	$-0.987626\pi$
$659$		−	1.99542i		−	0.0777306i	0.999244	−	0.0388653i	$-0.0123743\pi$
$660$	22.8500	−	6.90442i	0.889434	−	0.268754i
$661$	−4.59982	−	2.65570i	−0.178912	−	0.103295i	0.407869	−	0.913040i	$-0.366272\pi$
$661$	−4.59982	−	2.65570i	−0.178912	−	0.103295i	−0.586781	+	0.809745i	$0.699605\pi$
$662$	−16.4313	−	13.3058i	−0.638620	−	0.517145i
$663$	2.46108	+	46.9602i	0.0955804	+	1.82378i
$664$	0.0841688	−	0.259045i	0.00326638	−	0.0100529i
$665$	17.1399	+	11.0958i	0.664657	+	0.430278i
$666$	−54.2895	−	39.4436i	−2.10367	−	1.52841i
$667$	−19.5686	+	30.1330i	−0.757698	+	1.16675i
$668$	−0.492430	+	0.319788i	−0.0190527	+	0.0123730i
$669$	54.2813	−	5.70520i	2.09864	−	0.220576i
$670$	2.69654	+	2.37227i	0.104177	+	0.0916488i
$671$	0.140489	+	0.601223i	0.00542352	+	0.0232100i
$672$	−6.08205	+	5.96051i	−0.234620	+	0.229932i
$673$	23.1127	+	3.66070i	0.890931	+	0.141110i	0.585086	−	0.810972i	$-0.301061\pi$
$673$	23.1127	+	3.66070i	0.890931	+	0.141110i	0.305845	+	0.952081i	$0.401061\pi$
$674$	−10.5698	−	9.51710i	−0.407134	−	0.366585i
$675$	39.5609	+	57.9485i	1.52270	+	2.23044i
$676$	4.32406	−	1.92520i	0.166310	−	0.0740460i
$677$	12.3553	−	10.0051i	0.474854	−	0.384529i	−0.361805	−	0.932254i	$-0.617839\pi$
$677$	12.3553	−	10.0051i	0.474854	−	0.384529i	0.836658	+	0.547725i	$0.184506\pi$
$678$	−3.98449	−	7.82001i	−0.153024	−	0.300326i
$679$	6.09229	−	27.3041i	0.233801	−	1.04784i
$680$	6.57219	−	9.26868i	0.252032	−	0.355438i
$681$	23.8443	+	41.2995i	0.913714	+	1.58260i
$682$	−25.3022	−	24.3043i	−0.968869	−	0.930658i
$683$	−11.8737	+	3.18155i	−0.454335	+	0.121739i	−0.478727	−	0.877964i	$-0.658902\pi$
$683$	−11.8737	+	3.18155i	−0.454335	+	0.121739i	0.0243920	+	0.999702i	$0.492235\pi$
$684$	23.2048	+	10.3314i	0.887258	+	0.395033i
$685$	0.267745	−	1.82651i	0.0102300	−	0.0697872i
$686$	−3.30045	−	18.2238i	−0.126012	−	0.695788i
$687$	23.9270	−	3.78967i	0.912874	−	0.144585i
$688$	−6.47914	+	5.24670i	−0.247015	+	0.200029i
$689$	4.95117	+	5.49883i	0.188625	+	0.209489i
$690$	31.1325	+	24.6219i	1.18519	+	0.937338i
$691$	−4.44860	+	9.99172i	−0.169233	+	0.380103i	−0.978174	−	0.207786i	$-0.933374\pi$
$691$	−4.44860	+	9.99172i	−0.169233	+	0.380103i	0.808942	+	0.587889i	$0.200041\pi$
$692$	−9.76832	−	9.76832i	−0.371336	−	0.371336i
$693$	−9.46317	+	63.8854i	−0.359476	+	2.42681i
$694$			6.09347i			0.231305i
$695$	−2.05558	+	21.9935i	−0.0779727	+	0.834262i
$696$	4.35976	−	20.5111i	0.165256	−	0.777470i
$697$	32.7087	+	1.71419i	1.23893	+	0.0649297i
$698$	−5.28429	−	6.52556i	−0.200013	−	0.246996i
$699$	20.7990	+	15.1114i	0.786691	+	0.571565i
$700$	−11.8638	−	5.85243i	−0.448408	−	0.221201i
$701$	−0.100111	−	0.308109i	−0.00378113	−	0.0116371i	0.949148	−	0.314830i	$-0.101947\pi$
$701$	−0.100111	−	0.308109i	−0.00378113	−	0.0116371i	−0.952929	+	0.303193i	$0.901947\pi$
$702$	37.6676	−	14.4592i	1.42167	−	0.545728i
$703$	−8.14448	−	30.3956i	−0.307175	−	1.14639i
$704$	−1.89510	+	2.72187i	−0.0714244	+	0.102584i
$705$	17.2496	−	19.6076i	0.649659	−	0.738463i
$706$	−2.19964	−	3.02755i	−0.0827847	−	0.113943i
$707$	0.906135	+	21.4250i	0.0340787	+	0.805770i
$708$	−17.5407	+	8.93744i	−0.659220	+	0.335889i
$709$	−34.9403	−	3.67237i	−1.31221	−	0.137919i	−0.577551	−	0.816355i	$-0.695991\pi$
$709$	−34.9403	−	3.67237i	−1.31221	−	0.137919i	−0.734659	+	0.678436i	$0.762658\pi$
$710$	−7.34972	−	0.300274i	−0.275830	−	0.0112691i
$711$	0.963656	+	1.07025i	0.0361399	+	0.0401375i
$712$	−1.95249	+	0.102326i	−0.0731727	+	0.00383482i
$713$	9.12620	−	57.6205i	0.341779	−	2.15791i
$714$	21.2568	+	37.6911i	0.795514	+	1.41056i
$715$	19.6550	−	8.26741i	0.735056	−	0.309184i
$716$	3.32896	+	5.76592i	0.124409	+	0.215483i
$717$	13.8332	−	17.0826i	0.516612	−	0.637963i
$718$	9.72189	+	14.9704i	0.362818	+	0.558690i
$719$	−4.87830	+	1.03692i	−0.181930	+	0.0386704i	−0.297976	−	0.954573i	$-0.596311\pi$
$719$	−4.87830	+	1.03692i	−0.181930	+	0.0386704i	0.116046	+	0.993244i	$0.462978\pi$
$720$	−15.7093	−	4.90478i	−0.585449	−	0.182790i
$721$	21.7353	+	16.1292i	0.809463	+	0.600683i
$722$	−3.21823	−	6.31613i	−0.119770	−	0.235062i
$723$	4.22660	−	0.221507i	0.157189	−	0.00823792i
$724$	1.09491	+	10.4174i	0.0406921	+	0.387159i
$725$	32.3089	−	4.15087i	1.19992	−	0.154160i
$726$	1.42387	+	35.3768i	0.0528447	+	1.31295i
$727$	34.6791	+	34.6791i	1.28618	+	1.28618i	0.937090	+	0.349089i	$0.113509\pi$
$727$	34.6791	+	34.6791i	1.28618	+	1.28618i	0.349089	+	0.937090i	$0.386491\pi$
$728$	−4.84668	+	5.86317i	−0.179630	+	0.217303i
$729$	−32.7366	+	10.6368i	−1.21247	+	0.393955i
$730$	−4.08382	+	2.42099i	−0.151149	+	0.0896047i
$731$	17.2310	+	38.7014i	0.637310	+	1.43142i
$732$	0.214729	−	0.559387i	0.00793660	−	0.0206755i
$733$	−4.00511	+	6.16733i	−0.147932	+	0.227796i	−0.904867	−	0.425695i	$-0.860030\pi$
$733$	−4.00511	+	6.16733i	−0.147932	+	0.227796i	0.756934	+	0.653491i	$0.226696\pi$
$734$	4.66751	+	14.3651i	0.172281	+	0.530226i
$735$	39.4257	−	31.3652i	1.45424	−	1.15692i
$736$	−5.51497			−0.203284
$737$	−4.40841	+	2.99061i	−0.162386	+	0.110160i
$738$	−12.2784	−	45.8238i	−0.451976	−	1.68680i
$739$	−21.6274	+	2.27313i	−0.795576	+	0.0836184i	−0.493591	−	0.869694i	$-0.664316\pi$
$739$	−21.6274	+	2.27313i	−0.795576	+	0.0836184i	−0.301985	+	0.953313i	$0.597649\pi$
$740$	7.52531	+	18.9483i	0.276636	+	0.696554i
$741$	30.3758	+	9.86971i	1.11588	+	0.362573i
$742$	6.33174	+	2.50413i	0.232446	+	0.0919295i
$743$	4.22017	+	26.6451i	0.154823	+	0.977513i	0.935692	+	0.352818i	$0.114777\pi$
$743$	4.22017	+	26.6451i	0.154823	+	0.977513i	−0.780869	+	0.624695i	$0.785223\pi$
$744$	7.07897	+	33.3039i	0.259528	+	1.22098i
$745$	−15.6235	+	1.82442i	−0.572402	+	0.0668415i
$746$	1.58802	+	15.1090i	0.0581416	+	0.553180i
$747$	−0.518841	+	1.93634i	−0.0189834	+	0.0708470i
$748$	10.8672	+	12.8813i	0.397345	+	0.470987i
$749$	−9.78041	−	0.0987045i	−0.357368	−	0.00360658i
$750$	−1.24423	−	35.9643i	−0.0454327	−	1.31323i
$751$	26.2054	−	29.1041i	0.956249	−	1.06202i	−0.0417709	−	0.999127i	$-0.513300\pi$
$751$	26.2054	−	29.1041i	0.956249	−	1.06202i	0.998020	−	0.0628952i	$-0.0200334\pi$
$752$	−0.189903	+	3.62357i	−0.00692506	+	0.132138i
$753$	18.0185	+	6.91667i	0.656632	+	0.252057i
$754$	1.95798	−	18.6289i	0.0713055	−	0.678426i
$755$	−11.2998	+	0.130263i	−0.411241	+	0.00474077i
$756$	25.1205	−	27.3392i	0.913622	−	0.994315i
$757$	−5.65185	+	35.6844i	−0.205420	+	1.29697i	0.642270	+	0.766479i	$0.277993\pi$
$757$	−5.65185	+	35.6844i	−0.205420	+	1.29697i	−0.847690	+	0.530492i	$0.822007\pi$
$758$	−8.70841	+	32.5002i	−0.316304	+	1.18046i
$759$	−46.9237	+	35.5556i	−1.70322	+	1.29059i
$760$	−4.27745	−	6.42336i	−0.155159	−	0.233000i
$761$	−18.4381	+	41.4126i	−0.668380	+	1.50121i	0.186541	+	0.982447i	$0.440272\pi$
$761$	−18.4381	+	41.4126i	−0.668380	+	1.50121i	−0.854921	+	0.518759i	$0.826394\pi$
$762$	−30.1950	+	59.2611i	−1.09385	+	2.14680i
$763$	−21.6124	+	32.5561i	−0.782420	+	1.17861i
$764$	15.4035	−	21.2011i	0.557279	−	0.767029i
$765$	−44.7340	+	70.6542i	−1.61736	+	2.55451i
$766$	−22.1173	+	19.9145i	−0.799129	+	0.719539i
$767$	−14.7485	+	9.57778i	−0.532537	+	0.345834i
$768$	3.00489	−	1.15347i	0.108430	−	0.0416222i
$769$	−2.49217			−0.0898701			−0.0449350	−	0.998990i	$-0.514308\pi$
$769$	−2.49217			−0.0898701			−0.0449350	+	0.998990i	$0.514308\pi$
$770$	12.8120	−	14.8611i	0.461714	−	0.535556i
$771$	68.4451			2.46499
$772$	−25.3335	+	9.72461i	−0.911771	+	0.349996i
$773$	−28.9554	+	18.8039i	−1.04145	+	0.676329i	−0.947666	−	0.319264i	$-0.896564\pi$
$773$	−28.9554	+	18.8039i	−1.04145	+	0.676329i	−0.0937886	+	0.995592i	$0.529898\pi$
$774$	45.5992	−	41.0577i	1.63903	−	1.47579i
$775$	−45.1834	+	27.4946i	−1.62304	+	0.987634i
$776$	−6.21510	+	8.55435i	−0.223109	+	0.307083i
$777$	−77.4938	−	4.84592i	−2.78008	−	0.173846i
$778$	13.1986	−	25.9037i	0.473192	−	0.928692i
$779$	9.04835	−	20.3229i	0.324191	−	0.728145i
$780$	−20.2893	−	4.06876i	−0.726473	−	0.145685i
$781$	3.16215	−	10.4422i	0.113151	−	0.373651i
$782$	−7.25306	+	27.0688i	−0.259369	+	0.967977i
$783$	−14.3017	+	90.2976i	−0.511102	+	3.22697i
$784$	−1.59327	+	6.81627i	−0.0569026	+	0.243438i
$785$	13.7003	+	13.3880i	0.488985	+	0.477840i
$786$	6.63147	−	63.0942i	0.236537	−	2.25050i
$787$	33.6467	+	12.9158i	1.19938	+	0.460397i	0.874345	−	0.485306i	$-0.161292\pi$
$787$	33.6467	+	12.9158i	1.19938	+	0.460397i	0.325032	+	0.945703i	$0.394625\pi$
$788$	0.713030	−	13.6054i	0.0254006	−	0.484673i
$789$	−4.11717	+	4.57258i	−0.146575	+	0.162788i
$790$	−0.0734248	−	0.431345i	−0.00261234	−	0.0153466i
$791$	−6.21111	−	3.67005i	−0.220842	−	0.130492i
$792$	12.8802	−	20.7351i	0.457676	−	0.736789i
$793$	0.138531	−	0.517004i	0.00491938	−	0.0183594i
$794$	1.56226	+	14.8639i	0.0554426	+	0.527501i
$795$	2.14831	+	18.3972i	0.0761926	+	0.652481i
$796$	1.03193	+	4.85487i	0.0365760	+	0.172076i
$797$	3.92245	+	24.7654i	0.138940	+	0.877235i	0.954424	+	0.298455i	$0.0964712\pi$
$797$	3.92245	+	24.7654i	0.138940	+	0.877235i	−0.815483	+	0.578781i	$0.803529\pi$
$798$	29.0734	−	4.30448i	1.02919	−	0.152377i
$799$	17.5356	+	5.69766i	0.620365	+	0.201569i
$800$	3.23534	+	3.81216i	0.114387	+	0.134780i
$801$	14.3109	−	1.50414i	0.505652	−	0.0531462i
$802$	−8.19698	−	30.5915i	−0.289445	−	1.08022i
$803$	−1.95895	−	6.76371i	−0.0691299	−	0.238686i
$804$	5.16976			0.182323
$805$	32.4531	+	3.36386i	1.14382	+	0.118560i
$806$	9.39860	+	28.9259i	0.331052	+	1.01887i
$807$	33.0968	−	50.9646i	1.16506	−	1.79404i
$808$	2.90462	−	7.56679i	0.102184	−	0.266199i
$809$	13.6121	+	30.5732i	0.478575	+	1.07490i	0.978012	+	0.208548i	$0.0668737\pi$
$809$	13.6121	+	30.5732i	0.478575	+	1.07490i	−0.499437	+	0.866350i	$0.666460\pi$
$810$	50.0178	+	12.7861i	1.75744	+	0.449258i
$811$	−3.36794	+	1.09431i	−0.118264	+	0.0384264i	−0.367551	−	0.930003i	$-0.619804\pi$
$811$	−3.36794	+	1.09431i	−0.118264	+	0.0384264i	0.249287	+	0.968430i	$0.419804\pi$
$812$	−6.01440	−	16.1534i	−0.211064	−	0.566875i
$813$	−31.6573	−	31.6573i	−1.11027	−	1.11027i
$814$	−30.0049	+	3.76519i	−1.05167	+	0.131970i
$815$	−5.88771	−	8.84146i	−0.206238	−	0.309703i
$816$	−1.70959	−	16.2657i	−0.0598478	−	0.569414i
$817$	28.7341	−	1.50589i	1.00528	−	0.0526844i
$818$	15.6445	+	30.7040i	0.546996	+	1.07354i
$819$	33.3636	−	44.9598i	1.16582	−	1.57102i
$820$	−4.29564	+	13.7583i	−0.150010	+	0.480460i
$821$	−51.7226	+	10.9940i	−1.80513	+	0.383693i	−0.982705	−	0.185178i	$-0.940714\pi$
$821$	−51.7226	+	10.9940i	−1.80513	+	0.383693i	−0.822427	+	0.568871i	$0.807380\pi$
$822$	−1.44723	−	2.22854i	−0.0504780	−	0.0777293i
$823$	−12.1808	+	15.0420i	−0.424594	+	0.524330i	−0.943888	−	0.330266i	$-0.892862\pi$
$823$	−12.1808	+	15.0420i	−0.424594	+	0.524330i	0.519294	+	0.854596i	$0.326195\pi$
$824$	−5.11501	−	8.85945i	−0.178190	−	0.308634i
$825$	52.1051	+	11.5768i	1.81407	+	0.403053i
$826$	−8.23213	+	13.9319i	−0.286432	+	0.484751i
$827$	−2.20713	+	13.9353i	−0.0767494	+	0.484576i	0.919135	+	0.393943i	$0.128889\pi$
$827$	−2.20713	+	13.9353i	−0.0767494	+	0.484576i	−0.995884	+	0.0906336i	$0.971111\pi$
$828$	40.5338	−	2.12428i	1.40865	−	0.0738240i
$829$	−27.6883	−	30.7509i	−0.961653	−	1.06802i	−0.997639	−	0.0686714i	$-0.978124\pi$
$829$	−27.6883	−	30.7509i	−0.961653	−	1.06802i	0.0359865	−	0.999352i	$-0.488543\pi$
$830$	0.447885	−	0.412725i	0.0155463	−	0.0143259i
$831$	10.6357	+	1.11786i	0.368948	+	0.0387780i
$832$	2.56181	−	1.30531i	0.0888149	−	0.0452535i
$833$	31.3604	+	16.7846i	1.08657	+	0.581553i
$834$	18.6893	+	25.7237i	0.647159	+	0.890738i
$835$	−1.31024	+	0.0838219i	−0.0453428	+	0.00290078i
$836$	10.8130	−	3.75541i	0.373975	−	0.129884i
$837$	−38.4202	−	143.386i	−1.32800	−	4.95615i
$838$	−19.6660	+	7.54907i	−0.679350	+	0.260778i
$839$	−9.55790	−	29.4162i	−0.329975	−	1.01556i	−0.969144	−	0.246493i	$-0.920722\pi$
$839$	−9.55790	−	29.4162i	−0.329975	−	1.01556i	0.639169	−	0.769066i	$-0.279278\pi$
$840$	−18.3860	+	4.95482i	−0.634377	+	0.170957i
$841$	10.8763	+	7.90208i	0.375044	+	0.272486i
$842$	−13.3185	−	16.4470i	−0.458987	−	0.566802i
$843$	1.77441	+	0.0929930i	0.0611140	+	0.00320285i
$844$	0.308064	−	1.44933i	0.0106040	−	0.0498879i
$845$	10.5380	+	0.984914i	0.362518	+	0.0338821i
$846$		−	26.7056i		−	0.918156i
$847$	16.5790	+	23.9194i	0.569661	+	0.821879i
$848$	−1.81977	−	1.81977i	−0.0624910	−	0.0624910i
$849$	−1.61812	+	3.63437i	−0.0555339	+	0.124731i
$850$	22.9660	−	10.8662i	0.787726	−	0.372709i
$851$	−33.6467	−	37.3685i	−1.15339	−	1.28097i
$852$	−8.22863	+	6.66341i	−0.281908	+	0.228285i
$853$	4.39683	−	0.696389i	0.150545	−	0.0238439i	−0.0807073	−	0.996738i	$-0.525718\pi$
$853$	4.39683	−	0.696389i	0.150545	−	0.0238439i	0.231252	+	0.972894i	$0.425718\pi$
$854$	−0.0975358	−	0.482776i	−0.00333761	−	0.0165203i
$855$	33.9125	+	45.5626i	1.15978	+	1.55821i
$856$	3.37723	+	1.50364i	0.115431	+	0.0513933i
$857$	−22.0393	+	5.90540i	−0.752847	+	0.201725i	−0.614781	−	0.788698i	$-0.710755\pi$
$857$	−22.0393	+	5.90540i	−0.752847	+	0.201725i	−0.138066	+	0.990423i	$0.544089\pi$
$858$	13.3815	−	27.6224i	0.456837	−	0.943014i
$859$	−6.96173	−	12.0581i	−0.237531	−	0.411416i	0.722474	−	0.691398i	$-0.243005\pi$
$859$	−6.96173	−	12.0581i	−0.237531	−	0.411416i	−0.960005	+	0.279982i	$0.909672\pi$
$860$	−18.3779	+	3.12835i	−0.626683	+	0.106676i
$861$	−40.4195	−	37.1392i	−1.37749	−	1.26570i
$862$	−3.99749	−	7.84551i	−0.136155	−	0.267219i
$863$	3.04042	−	2.46209i	0.103497	−	0.0838104i	−0.576175	−	0.817326i	$-0.695455\pi$
$863$	3.04042	−	2.46209i	0.103497	−	0.0838104i	0.679672	+	0.733516i	$0.262122\pi$
$864$	−12.8197	+	5.70772i	−0.436136	+	0.194180i
$865$	−8.33837	−	29.7434i	−0.283513	−	1.01131i
$866$	23.0228	+	20.7298i	0.782346	+	0.704428i
$867$	−28.0405	−	4.44118i	−0.952306	−	0.150831i
$868$	19.5894	+	19.9888i	0.664907	+	0.678465i
$869$	0.646669	+	0.0548432i	0.0219367	+	0.00186043i
$870$	30.9710	−	35.2045i	1.05001	−	1.19354i
$871$	4.59277	−	0.482719i	0.155620	−	0.0163563i
$872$	12.3868	−	8.04411i	0.419472	−	0.272408i
$873$	42.3845	−	65.2664i	1.43450	−	2.20893i
$874$	15.3985	+	11.1877i	0.520863	+	0.378429i
$875$	−16.7133	−	24.4063i	−0.565013	−	0.825082i
$876$	−2.11173	+	6.49925i	−0.0713489	+	0.219589i
$877$	−2.46075	−	46.9539i	−0.0830935	−	1.58552i	−0.648830	−	0.760933i	$-0.724741\pi$
$877$	−2.46075	−	46.9539i	−0.0830935	−	1.58552i	0.565737	−	0.824586i	$-0.308592\pi$
$878$	0.682090	+	0.552346i	0.0230194	+	0.0186408i
$879$	−37.4450	−	21.6189i	−1.26299	−	0.729187i
$880$	−6.67622	+	3.22926i	−0.225055	+	0.108858i
$881$		−	25.7685i		−	0.868164i	−0.900873	−	0.434082i	$-0.857073\pi$
$881$		−	25.7685i		−	0.868164i	0.900873	−	0.434082i	$-0.142927\pi$
$882$	9.08466	−	50.7117i	0.305897	−	1.70755i
$883$	22.6094	−	44.3735i	0.760867	−	1.49329i	−0.105793	−	0.994388i	$-0.533738\pi$
$883$	22.6094	−	44.3735i	0.760867	−	1.49329i	0.866661	−	0.498898i	$-0.166262\pi$
$884$	−3.03758	−	14.2907i	−0.102165	−	0.480647i
$885$	−43.9834	−	1.79695i	−1.47849	−	0.0604038i
$886$	−19.5973	+	8.72527i	−0.658383	+	0.293131i
$887$	−26.8676	−	17.4480i	−0.902124	−	0.585846i	0.00809776	−	0.999967i	$-0.497422\pi$
$887$	−26.8676	−	17.4480i	−0.902124	−	0.585846i	−0.910222	+	0.414121i	$0.864089\pi$
$888$	26.1485	+	13.3233i	0.877486	+	0.447101i
$889$	5.16574	+	54.4269i	0.173253	+	1.82542i
$890$	−3.91801	−	1.93976i	−0.131332	−	0.0650210i
$891$	−36.9455	+	67.0716i	−1.23772	+	2.24698i
$892$	−16.3796	+	4.38890i	−0.548429	+	0.146951i
$893$	7.88102	−	9.73225i	0.263728	−	0.325677i
$894$	−15.1504	+	16.8262i	−0.506704	+	0.562752i
$895$	0.171611	+	14.8866i	0.00573634	+	0.497603i
$896$	1.57665	−	2.12466i	0.0526723	−	0.0709797i
$897$	50.4088	−	7.98397i	1.68310	−	0.266577i
$898$	7.19273	+	4.67101i	0.240025	+	0.155874i
$899$	−67.4103	−	14.3285i	−2.24826	−	0.477882i
$900$	−25.2474	−	26.7723i	−0.841580	−	0.892410i
$901$	−11.3251	+	6.53856i	−0.377294	+	0.217831i
$902$	−18.1599	−	11.2805i	−0.604660	−	0.375600i
$903$	19.0665	−	68.3890i	0.634494	−	2.27584i
$904$	1.60276	+	2.20601i	0.0533070	+	0.0733707i
$905$	−9.27943	+	21.5057i	−0.308459	+	0.714875i
$906$	−12.0883	+	10.8843i	−0.401606	+	0.361608i
$907$	8.29621	−	21.6124i	0.275471	−	0.717627i	−0.724138	−	0.689655i	$-0.757762\pi$
$907$	8.29621	−	21.6124i	0.275471	−	0.717627i	0.999609	−	0.0279712i	$-0.00890468\pi$
$908$	−9.32414	−	11.5144i	−0.309432	−	0.382117i
$909$	−18.4337	+	56.7330i	−0.611406	+	1.88171i
$910$	−15.8713	+	6.11858i	−0.526129	+	0.202829i
$911$	−15.4873	+	11.2522i	−0.513119	+	0.372802i	−0.814005	−	0.580857i	$-0.802717\pi$
$911$	−15.4873	+	11.2522i	−0.513119	+	0.372802i	0.300887	+	0.953660i	$0.402717\pi$
$912$	−10.7300	−	2.87509i	−0.355305	−	0.0952038i
$913$	0.426226	+	0.796496i	0.0141060	+	0.0263602i
$914$	17.1252	+	9.88726i	0.566453	+	0.327042i
$915$	1.03145	−	0.855121i	0.0340985	−	0.0282694i
$916$	−7.15811	+	2.32581i	−0.236511	+	0.0768470i
$917$	−23.2051	−	46.7018i	−0.766300	−	1.54223i
$918$	11.1548	+	70.4289i	0.368164	+	2.32450i
$919$	4.23682	+	0.445308i	0.139760	+	0.0146893i	0.174150	−	0.984719i	$-0.444282\pi$
$919$	4.23682	+	0.445308i	0.139760	+	0.0146893i	−0.0343902	+	0.999408i	$0.510949\pi$
$920$	−10.7501	−	6.04241i	−0.354419	−	0.199212i
$921$	18.2083	+	3.87029i	0.599983	+	0.127530i
$922$	6.11267	+	15.9240i	0.201310	+	0.524430i
$923$	−6.68805	+	6.68805i	−0.220140	+	0.220140i
$924$	−0.283048	−	28.2423i	−0.00931159	−	0.929104i
$925$	−6.09176	+	45.1800i	−0.200296	+	1.48551i
$926$	−8.13331	−	3.62118i	−0.267277	−	0.118999i
$927$	41.0067	+	63.1447i	1.34684	+	2.07394i
$928$	−0.340963	+	6.50596i	−0.0111927	+	0.213569i
$929$	3.31936	−	31.5816i	0.108905	−	1.03616i	−0.794469	−	0.607305i	$-0.792251\pi$
$929$	3.31936	−	31.5816i	0.108905	−	1.03616i	0.903373	−	0.428855i	$-0.141083\pi$
$930$	−22.6904	+	72.6737i	−0.744046	+	2.38306i
$931$	18.2761	−	15.7998i	0.598976	−	0.517818i
$932$	−7.11688	−	3.62623i	−0.233121	−	0.118781i
$933$	−9.80740	−	25.5492i	−0.321080	−	0.836442i
$934$	11.3989	−	19.7435i	0.372983	−	0.646026i
$935$	7.06970	+	37.0154i	0.231204	+	1.21053i
$936$	−18.3260	+	10.5805i	−0.599003	+	0.345834i
$937$	−28.0462	−	4.44209i	−0.916230	−	0.145117i	−0.319526	−	0.947578i	$-0.603524\pi$
$937$	−28.0462	−	4.44209i	−0.916230	−	0.145117i	−0.596705	+	0.802461i	$0.703524\pi$
$938$	3.58714	−	2.27838i	0.117124	−	0.0743919i
$939$	17.6033	+	5.71966i	0.574462	+	0.186654i
$940$	−4.34029	+	6.85518i	−0.141565	+	0.223591i
$941$	−12.3388	−	27.7135i	−0.402235	−	0.903434i	−0.995168	−	0.0981826i	$-0.968697\pi$
$941$	−12.3388	−	27.7135i	−0.402235	−	0.903434i	0.592934	−	0.805251i	$-0.297970\pi$
$942$	27.5355	+	1.44307i	0.897154	+	0.0470179i
$943$	−1.86046	−	35.4997i	−0.0605850	−	1.15603i
$944$	4.94820	−	3.59508i	0.161050	−	0.117010i
$945$	78.9199	−	25.7679i	2.56726	−	0.838231i
$946$	2.33666	−	27.5521i	0.0759713	−	0.895796i
$947$	−21.5310	−	5.76922i	−0.699664	−	0.187474i	−0.108584	−	0.994087i	$-0.534632\pi$
$947$	−21.5310	−	5.76922i	−0.699664	−	0.187474i	−0.591080	+	0.806613i	$0.701298\pi$
$948$	−0.489465	−	0.396361i	−0.0158971	−	0.0128732i
$949$	−1.26919	+	5.97106i	−0.0411996	+	0.193829i
$950$	−1.30015	−	17.2073i	−0.0421824	−	0.558278i
$951$	−23.9539	+	32.9697i	−0.776759	+	1.06912i
$952$	−8.35476	−	10.5329i	−0.270779	−	0.341372i
$953$	−9.10226	+	4.63783i	−0.294851	+	0.150234i	−0.595159	−	0.803608i	$-0.702911\pi$
$953$	−9.10226	+	4.63783i	−0.294851	+	0.150234i	0.300307	+	0.953842i	$0.402911\pi$
$954$	14.0758	+	12.6739i	0.455721	+	0.410333i
$955$	53.2540	−	24.4496i	1.72326	−	0.791170i
$956$	−3.41464	+	5.91434i	−0.110437	+	0.191283i
$957$	39.0436	+	57.5537i	1.26210	+	1.86045i
$958$	−12.0707	+	12.0707i	−0.389988	+	0.389988i
$959$	−1.98634	−	0.908505i	−0.0641423	−	0.0293371i
$960$	7.12107	+	1.04387i	0.229832	+	0.0336907i
$961$	79.1318	−	16.8200i	2.55264	−	0.542580i
$962$	24.4741	+	9.39474i	0.789077	+	0.302898i
$963$	−25.4010	−	9.75054i	−0.818537	−	0.314207i
$964$	−1.28622	+	0.273394i	−0.0414262	+	0.00880542i
$965$	−60.0359	−	8.80060i	−1.93262	−	0.283301i
$966$	38.2717	−	27.2202i	1.23137	−	0.875794i
$967$	−32.7964	+	32.7964i	−1.05466	+	1.05466i	−0.0562427	+	0.998417i	$0.517912\pi$
$967$	−32.7964	+	32.7964i	−1.05466	+	1.05466i	−0.998417	+	0.0562427i	$0.982088\pi$
$968$	−2.15632	−	10.7866i	−0.0693067	−	0.346694i
$969$	−28.2232	+	48.8841i	−0.906661	+	1.57038i
$970$	−21.4872	+	9.86507i	−0.689914	+	0.316748i
$971$	−40.2042	−	36.2000i	−1.29021	−	1.16171i	−0.977283	−	0.211938i	$-0.932023\pi$
$971$	−40.2042	−	36.2000i	−1.29021	−	1.16171i	−0.312931	−	0.949776i	$-0.601311\pi$
$972$	28.7025	−	14.6247i	0.920634	−	0.469087i
$973$	24.3048	+	9.61225i	0.779175	+	0.308155i
$974$	17.0467	−	23.4627i	0.546210	−	0.751794i
$975$	−35.0910	−	30.1607i	−1.12381	−	0.965917i
$976$	−0.0387046	+	0.182091i	−0.00123890	+	0.00582859i
$977$	14.0727	+	11.3959i	0.450226	+	0.364586i	0.827453	−	0.561535i	$-0.189789\pi$
$977$	14.0727	+	11.3959i	0.450226	+	0.364586i	−0.377227	+	0.926121i	$0.623122\pi$
$978$	−14.7693	−	3.95743i	−0.472271	−	0.126545i
$979$	4.24122	−	4.90526i	0.135550	−	0.156773i
$980$	−10.5738	+	11.5410i	−0.337769	+	0.368663i
$981$	−87.9420	+	63.8936i	−2.80777	+	2.03997i
$982$	1.23148	+	23.4981i	0.0392982	+	0.749855i
$983$	19.4421	+	1.01892i	0.620107	+	0.0324984i	0.359803	−	0.933028i	$-0.382844\pi$
$983$	19.4421	+	1.01892i	0.620107	+	0.0324984i	0.260304	+	0.965527i	$0.416177\pi$
$984$	8.43855	+	18.9533i	0.269011	+	0.604209i
$985$	16.2965	−	25.7391i	0.519249	−	0.820117i
$986$	31.4844	+	10.2299i	1.00267	+	0.325786i
$987$	−16.5670	−	26.0834i	−0.527332	−	0.830244i
$988$	−9.80088	−	1.55231i	−0.311808	−	0.0493855i
$989$	39.8188	−	22.9894i	1.26616	−	0.731020i
$990$	47.8248	−	26.3059i	1.51997	−	0.836057i
$991$	5.47333	−	9.48008i	0.173866	−	0.301145i	−0.765902	−	0.642957i	$-0.777707\pi$
$991$	5.47333	−	9.48008i	0.173866	−	0.301145i	0.939768	+	0.341812i	$0.111041\pi$
$992$	−3.79091	−	9.87566i	−0.120362	−	0.313552i
$993$	−60.6355	−	30.8953i	−1.92421	−	0.980434i
$994$	−2.77294	+	8.25001i	−0.0879525	+	0.261675i
$995$	−3.30768	+	10.5940i	−0.104860	+	0.335852i
$996$	0.0916389	−	0.871886i	0.00290369	−	0.0276268i
$997$	−1.03376	+	19.7254i	−0.0327396	+	0.624708i	0.932153	+	0.362064i	$0.117928\pi$
$997$	−1.03376	+	19.7254i	−0.0327396	+	0.624708i	−0.964893	+	0.262644i	$0.915405\pi$
$998$	−12.8396	−	19.7712i	−0.406430	−	0.625848i
$999$	−116.887	−	52.0417i	−3.69816	−	1.64653i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.bv.a.3.1	✓	768
5.2	odd	4	inner	770.2.bv.a.157.24	yes	768
7.5	odd	6	inner	770.2.bv.a.663.48	yes	768
11.4	even	5	inner	770.2.bv.a.213.24	yes	768
35.12	even	12	inner	770.2.bv.a.47.24	yes	768
55.37	odd	20	inner	770.2.bv.a.367.48	yes	768
77.26	odd	30	inner	770.2.bv.a.103.24	yes	768
385.257	even	60	inner	770.2.bv.a.257.1	yes	768

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.bv.a.3.1	✓	768	1.1	even	1	trivial
770.2.bv.a.47.24	yes	768	35.12	even	12	inner
770.2.bv.a.103.24	yes	768	77.26	odd	30	inner
770.2.bv.a.157.24	yes	768	5.2	odd	4	inner
770.2.bv.a.213.24	yes	768	11.4	even	5	inner
770.2.bv.a.257.1	yes	768	385.257	even	60	inner
770.2.bv.a.367.48	yes	768	55.37	odd	20	inner
770.2.bv.a.663.48	yes	768	7.5	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.bv (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.933580 + 0.358368i) q^{2} +(-2.69941 + 1.75302i) q^{3} +(0.743145 - 0.669131i) q^{4} +(2.18170 - 0.490086i) q^{5} +(1.89189 - 2.60396i) q^{6} +(0.165124 - 2.64059i) q^{7} +(-0.453990 + 0.891007i) q^{8} +(2.99352 - 6.72356i) q^{9} +O(q^{10})\)	\(q+(-0.933580 + 0.358368i) q^{2} +(-2.69941 + 1.75302i) q^{3} +(0.743145 - 0.669131i) q^{4} +(2.18170 - 0.490086i) q^{5} +(1.89189 - 2.60396i) q^{6} +(0.165124 - 2.64059i) q^{7} +(-0.453990 + 0.891007i) q^{8} +(2.99352 - 6.72356i) q^{9} +(-1.86116 + 1.23939i) q^{10} +(-1.08813 - 3.13305i) q^{11} +(-0.833054 + 3.10900i) q^{12} +(-0.449779 + 2.83979i) q^{13} +(0.792148 + 2.52438i) q^{14} +(-5.03017 + 5.14749i) q^{15} +(0.104528 - 0.994522i) q^{16} +(-4.74388 - 1.82100i) q^{17} +(-0.385185 + 7.34977i) q^{18} +(-2.30935 + 2.56479i) q^{19} +(1.29339 - 1.82405i) q^{20} +(4.18326 + 7.41750i) q^{21} +(2.13864 + 2.53500i) q^{22} +(-1.42738 + 5.32705i) q^{23} +(-0.336443 - 3.20104i) q^{24} +(4.51963 - 2.13844i) q^{25} +(-0.597786 - 2.81236i) q^{26} +(2.19524 + 13.8602i) q^{27} +(-1.64419 - 2.07283i) q^{28} +(6.19603 + 2.01321i) q^{29} +(2.85137 - 6.60825i) q^{30} +(-10.5203 + 1.10573i) q^{31} +(0.258819 + 0.965926i) q^{32} +(8.42957 + 6.54987i) q^{33} +5.08138 q^{34} +(-0.933867 - 5.84191i) q^{35} +(-2.27432 - 6.99964i) q^{36} +(-4.96589 + 7.64681i) q^{37} +(1.23682 - 3.22203i) q^{38} +(-3.76406 - 8.45422i) q^{39} +(-0.553801 + 2.16640i) q^{40} +(-6.13033 + 1.99187i) q^{41} +(-6.56361 - 5.42569i) q^{42} +(-5.89521 - 5.89521i) q^{43} +(-2.90505 - 1.60021i) q^{44} +(3.23585 - 16.1359i) q^{45} +(-0.576471 - 5.48476i) q^{46} +(-3.62357 + 0.189903i) q^{47} +(1.46125 + 2.86786i) q^{48} +(-6.94547 - 0.872051i) q^{49} +(-3.45309 + 3.61610i) q^{50} +(15.9979 - 3.40046i) q^{51} +(1.56594 + 2.41134i) q^{52} +(1.61958 - 2.00001i) q^{53} +(-7.01648 - 12.1529i) q^{54} +(-3.90943 - 6.30209i) q^{55} +(2.27782 + 1.34593i) q^{56} +(1.73775 - 10.9717i) q^{57} +(-6.50596 + 0.340963i) q^{58} +(4.09261 + 4.54530i) q^{59} +(-0.293796 + 7.19117i) q^{60} +(-0.185139 - 0.0194589i) q^{61} +(9.42530 - 4.80243i) q^{62} +(-17.2599 - 9.01490i) q^{63} +(-0.587785 - 0.809017i) q^{64} +(0.410460 + 6.41601i) q^{65} +(-10.2169 - 3.09394i) q^{66} +(-0.415709 - 1.55145i) q^{67} +(-4.74388 + 1.82100i) q^{68} +(-5.48532 - 16.8821i) q^{69} +(2.96539 + 5.11922i) q^{70} +(2.66137 + 1.93360i) q^{71} +(4.63171 + 5.71968i) q^{72} +(2.12024 + 0.111117i) q^{73} +(1.89569 - 8.91853i) q^{74} +(-8.45160 + 13.6955i) q^{75} +3.45127i q^{76} +(-8.45278 + 2.35596i) q^{77} +(6.54378 + 6.54378i) q^{78} +(-0.0795894 + 0.178761i) q^{79} +(-0.259352 - 2.22098i) q^{80} +(-15.4488 - 17.1577i) q^{81} +(5.00934 - 4.05648i) q^{82} +(-0.269022 + 0.0426090i) q^{83} +(8.07205 + 2.71313i) q^{84} +(-11.2422 - 1.64798i) q^{85} +(7.61631 + 3.39100i) q^{86} +(-20.2548 + 5.42726i) q^{87} +(3.28556 + 0.452846i) q^{88} +(0.977585 + 1.69323i) q^{89} +(2.76166 + 16.2238i) q^{90} +(7.42447 + 1.65660i) q^{91} +(2.50374 + 4.91387i) q^{92} +(26.4602 - 21.4271i) q^{93} +(3.31484 - 1.47586i) q^{94} +(-3.78134 + 6.72738i) q^{95} +(-2.39194 - 2.15371i) q^{96} +(10.4436 + 1.65410i) q^{97} +(6.79667 - 1.67490i) q^{98} +(-24.3226 - 2.06277i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 768 q + 24 q^{5} + 4 q^{7}+O(q^{10}) \) 768 * q + 24 * q^5 + 4 * q^7	\( 768 q + 24 q^{5} + 4 q^{7} + 24 q^{10} + 12 q^{11} - 24 q^{15} - 96 q^{16} + 8 q^{22} + 8 q^{23} + 16 q^{25} - 24 q^{26} - 28 q^{28} - 16 q^{30} + 252 q^{33} - 40 q^{35} + 160 q^{36} - 8 q^{37} - 44 q^{42} + 80 q^{43} + 96 q^{45} - 8 q^{46} - 24 q^{47} + 64 q^{50} - 8 q^{51} + 40 q^{53} + 16 q^{56} + 64 q^{57} - 48 q^{58} - 164 q^{63} - 88 q^{65} + 32 q^{67} - 100 q^{70} + 32 q^{71} + 120 q^{73} - 336 q^{75} - 96 q^{77} - 36 q^{80} - 24 q^{81} + 48 q^{82} - 112 q^{85} - 24 q^{87} + 4 q^{88} - 12 q^{91} - 16 q^{92} - 88 q^{93} - 44 q^{95} + 32 q^{98}+O(q^{100}) \) 768 * q + 24 * q^5 + 4 * q^7 + 24 * q^10 + 12 * q^11 - 24 * q^15 - 96 * q^16 + 8 * q^22 + 8 * q^23 + 16 * q^25 - 24 * q^26 - 28 * q^28 - 16 * q^30 + 252 * q^33 - 40 * q^35 + 160 * q^36 - 8 * q^37 - 44 * q^42 + 80 * q^43 + 96 * q^45 - 8 * q^46 - 24 * q^47 + 64 * q^50 - 8 * q^51 + 40 * q^53 + 16 * q^56 + 64 * q^57 - 48 * q^58 - 164 * q^63 - 88 * q^65 + 32 * q^67 - 100 * q^70 + 32 * q^71 + 120 * q^73 - 336 * q^75 - 96 * q^77 - 36 * q^80 - 24 * q^81 + 48 * q^82 - 112 * q^85 - 24 * q^87 + 4 * q^88 - 12 * q^91 - 16 * q^92 - 88 * q^93 - 44 * q^95 + 32 * q^98

Introduction

L-functions

Modular forms

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