LMFDB - Embedded newform 380.2.be.b.51.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(51,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 0, 5]))

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

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

chi := DirichletCharacter("380.51");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.be (of order $18$, degree $6$, 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:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$20$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			51.12
Character	$\chi$	$=$	380.51
Dual form			380.2.be.b.231.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.528488 - 1.31175i) q^{2} +(-0.385053 - 0.140148i) q^{3} +(-1.44140 - 1.38649i) q^{4} +(-0.173648 - 0.984808i) q^{5} +(-0.387335 + 0.431029i) q^{6} +(0.799236 + 0.461439i) q^{7} +(-2.58050 + 1.15802i) q^{8} +(-2.16951 - 1.82043i) q^{9} +O(q^{10})$	\(q+(0.528488 - 1.31175i) q^{2} +(-0.385053 - 0.140148i) q^{3} +(-1.44140 - 1.38649i) q^{4} +(-0.173648 - 0.984808i) q^{5} +(-0.387335 + 0.431029i) q^{6} +(0.799236 + 0.461439i) q^{7} +(-2.58050 + 1.15802i) q^{8} +(-2.16951 - 1.82043i) q^{9} +(-1.38360 - 0.292675i) q^{10} +(-0.765458 + 0.441937i) q^{11} +(0.360702 + 0.735882i) q^{12} +(-2.15996 - 5.93445i) q^{13} +(1.02768 - 0.804537i) q^{14} +(-0.0711549 + 0.403539i) q^{15} +(0.155277 + 3.99698i) q^{16} +(-2.58185 + 2.16643i) q^{17} +(-3.53452 + 1.88379i) q^{18} +(0.294141 - 4.34896i) q^{19} +(-1.11513 + 1.66027i) q^{20} +(-0.243078 - 0.289690i) q^{21} +(0.175178 + 1.23765i) q^{22} +(5.25895 + 0.927295i) q^{23} +(1.15592 - 0.0842479i) q^{24} +(-0.939693 + 0.342020i) q^{25} +(-8.92605 - 0.302941i) q^{26} +(1.19489 + 2.06962i) q^{27} +(-0.512238 - 1.77325i) q^{28} +(0.517190 - 0.616364i) q^{29} +(0.491740 + 0.306603i) q^{30} +(-4.76017 + 8.24486i) q^{31} +(5.32513 + 1.90867i) q^{32} +(0.356678 - 0.0628920i) q^{33} +(1.47735 + 4.53169i) q^{34} +(0.315643 - 0.867222i) q^{35} +(0.603115 + 5.63198i) q^{36} -4.07725i q^{37} +(-5.54932 - 2.68421i) q^{38} +2.58779i q^{39} +(1.58853 + 2.34021i) q^{40} +(3.75939 - 10.3289i) q^{41} +(-0.508466 + 0.165762i) q^{42} +(-2.37964 + 0.419595i) q^{43} +(1.71608 + 0.424293i) q^{44} +(-1.41605 + 2.45266i) q^{45} +(3.99567 - 6.40839i) q^{46} +(5.18564 - 6.18000i) q^{47} +(0.500379 - 1.56081i) q^{48} +(-3.07415 - 5.32458i) q^{49} +(-0.0479694 + 1.41340i) q^{50} +(1.29777 - 0.472350i) q^{51} +(-5.11469 + 11.5487i) q^{52} +(10.8012 + 1.90454i) q^{53} +(3.34631 - 0.473640i) q^{54} +(0.568144 + 0.677087i) q^{55} +(-2.59679 - 0.265212i) q^{56} +(-0.722757 + 1.63336i) q^{57} +(-0.535189 - 1.00417i) q^{58} +(6.63590 - 5.56818i) q^{59} +(0.662067 - 0.483007i) q^{60} +(0.00816087 - 0.0462826i) q^{61} +(8.29954 + 10.6015i) q^{62} +(-0.893930 - 2.45605i) q^{63} +(5.31797 - 5.97655i) q^{64} +(-5.46921 + 3.15765i) q^{65} +(0.106001 - 0.501112i) q^{66} +(10.7236 + 8.99818i) q^{67} +(6.72523 + 0.457021i) q^{68} +(-1.89502 - 1.09409i) q^{69} +(-0.970769 - 0.872362i) q^{70} +(-0.988117 - 5.60389i) q^{71} +(7.70652 + 2.18529i) q^{72} +(8.95524 + 3.25944i) q^{73} +(-5.34836 - 2.15478i) q^{74} +0.409765 q^{75} +(-6.45378 + 5.86078i) q^{76} -0.815709 q^{77} +(3.39454 + 1.36761i) q^{78} +(-15.1537 - 5.51548i) q^{79} +(3.90930 - 0.846987i) q^{80} +(1.30532 + 7.40283i) q^{81} +(-11.5621 - 10.3901i) q^{82} +(-2.88323 - 1.66463i) q^{83} +(-0.0512788 + 0.754586i) q^{84} +(2.58185 + 2.16643i) q^{85} +(-0.707205 + 3.34325i) q^{86} +(-0.285528 + 0.164849i) q^{87} +(1.46349 - 2.02684i) q^{88} +(-0.400871 - 1.10138i) q^{89} +(2.46893 + 3.15371i) q^{90} +(1.01207 - 5.73971i) q^{91} +(-6.29457 - 8.62810i) q^{92} +(2.98842 - 2.50758i) q^{93} +(-5.36610 - 10.0683i) q^{94} +(-4.33397 + 0.465518i) q^{95} +(-1.78296 - 1.48124i) q^{96} +(6.26962 + 7.47184i) q^{97} +(-8.60919 + 1.21855i) q^{98} +(2.46519 + 0.434679i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 3 q^{2} - 3 q^{4} + 3 q^{6} - 36 q^{8} + 6 q^{9}+O(q^{10}) $ 120 * q + 3 * q^2 - 3 * q^4 + 3 * q^6 - 36 * q^8 + 6 * q^9	$ 120 q + 3 q^{2} - 3 q^{4} + 3 q^{6} - 36 q^{8} + 6 q^{9} + 3 q^{10} - 12 q^{13} - 18 q^{14} + 9 q^{16} + 48 q^{17} - 12 q^{21} - 18 q^{24} - 24 q^{26} + 69 q^{28} - 12 q^{30} - 27 q^{32} + 6 q^{33} - 18 q^{34} - 72 q^{36} - 48 q^{38} - 36 q^{41} - 27 q^{42} - 99 q^{44} + 60 q^{45} + 27 q^{46} - 63 q^{48} + 60 q^{49} + 33 q^{52} - 24 q^{53} + 21 q^{54} - 48 q^{57} + 6 q^{60} - 24 q^{61} + 54 q^{62} + 84 q^{64} - 18 q^{65} - 132 q^{66} + 66 q^{68} - 72 q^{69} + 36 q^{70} - 42 q^{72} + 66 q^{74} + 180 q^{76} + 60 q^{77} + 114 q^{78} + 27 q^{80} - 66 q^{81} + 33 q^{82} - 144 q^{84} - 48 q^{85} + 75 q^{86} + 9 q^{88} - 3 q^{90} - 42 q^{92} - 144 q^{93} + 78 q^{96} + 42 q^{97} - 87 q^{98}+O(q^{100}) $ 120 * q + 3 * q^2 - 3 * q^4 + 3 * q^6 - 36 * q^8 + 6 * q^9 + 3 * q^10 - 12 * q^13 - 18 * q^14 + 9 * q^16 + 48 * q^17 - 12 * q^21 - 18 * q^24 - 24 * q^26 + 69 * q^28 - 12 * q^30 - 27 * q^32 + 6 * q^33 - 18 * q^34 - 72 * q^36 - 48 * q^38 - 36 * q^41 - 27 * q^42 - 99 * q^44 + 60 * q^45 + 27 * q^46 - 63 * q^48 + 60 * q^49 + 33 * q^52 - 24 * q^53 + 21 * q^54 - 48 * q^57 + 6 * q^60 - 24 * q^61 + 54 * q^62 + 84 * q^64 - 18 * q^65 - 132 * q^66 + 66 * q^68 - 72 * q^69 + 36 * q^70 - 42 * q^72 + 66 * q^74 + 180 * q^76 + 60 * q^77 + 114 * q^78 + 27 * q^80 - 66 * q^81 + 33 * q^82 - 144 * q^84 - 48 * q^85 + 75 * q^86 + 9 * q^88 - 3 * q^90 - 42 * q^92 - 144 * q^93 + 78 * q^96 + 42 * q^97 - 87 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$1$	$-1$

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 $

$2$	0.528488	−	1.31175i	0.373697	−	0.927551i
$2$	0.528488	−	1.31175i	0.373697	−	0.927551i
$3$	−0.385053	−	0.140148i	−0.222310	−	0.0809144i	0.228464	−	0.973552i	$-0.426630\pi$
$3$	−0.385053	−	0.140148i	−0.222310	−	0.0809144i	−0.450774	+	0.892638i	$0.648852\pi$
$4$	−1.44140	−	1.38649i	−0.720701	−	0.693246i
$5$	−0.173648	−	0.984808i	−0.0776578	−	0.440419i
$5$	−0.173648	−	0.984808i	−0.0776578	−	0.440419i
$6$	−0.387335	+	0.431029i	−0.158129	+	0.175967i
$7$	0.799236	+	0.461439i	0.302083	+	0.174408i	0.643378	−	0.765548i	$-0.277532\pi$
$7$	0.799236	+	0.461439i	0.302083	+	0.174408i	−0.341295	+	0.939956i	$0.610866\pi$
$8$	−2.58050	+	1.15802i	−0.912345	+	0.409422i
$9$	−2.16951	−	1.82043i	−0.723170	−	0.606811i
$10$	−1.38360	−	0.292675i	−0.437532	−	0.0925519i
$11$	−0.765458	+	0.441937i	−0.230794	+	0.133249i	−0.610938	−	0.791678i	$-0.709208\pi$
$11$	−0.765458	+	0.441937i	−0.230794	+	0.133249i	0.380144	+	0.924927i	$0.375874\pi$
$12$	0.360702	+	0.735882i	0.104126	+	0.212431i
$13$	−2.15996	−	5.93445i	−0.599066	−	1.64592i	−0.753140	−	0.657860i	$-0.771462\pi$
$13$	−2.15996	−	5.93445i	−0.599066	−	1.64592i	0.154075	−	0.988059i	$-0.450760\pi$
$14$	1.02768	−	0.804537i	0.274659	−	0.215022i
$15$	−0.0711549	+	0.403539i	−0.0183721	+	0.104193i
$16$	0.155277	+	3.99698i	0.0388193	+	0.999246i
$17$	−2.58185	+	2.16643i	−0.626191	+	0.525437i	−0.899743	−	0.436420i	$-0.856246\pi$
$17$	−2.58185	+	2.16643i	−0.626191	+	0.525437i	0.273552	+	0.961857i	$0.411802\pi$
$18$	−3.53452	+	1.88379i	−0.833095	+	0.444013i
$19$	0.294141	−	4.34896i	0.0674805	−	0.997721i
$19$	0.294141	−	4.34896i	0.0674805	−	0.997721i
$20$	−1.11513	+	1.66027i	−0.249351	+	0.371247i
$21$	−0.243078	−	0.289690i	−0.0530441	−	0.0632155i
$22$	0.175178	+	1.23765i	0.0373482	+	0.263868i
$23$	5.25895	+	0.927295i	1.09657	+	0.193354i	0.692531	−	0.721389i	$-0.256496\pi$
$23$	5.25895	+	0.927295i	1.09657	+	0.193354i	0.404036	+	0.914743i	$0.367607\pi$
$24$	1.15592	−	0.0842479i	0.235952	−	0.0171970i
$25$	−0.939693	+	0.342020i	−0.187939	+	0.0684040i
$26$	−8.92605	−	0.302941i	−1.75054	−	0.0594117i
$27$	1.19489	+	2.06962i	0.229957	+	0.398298i
$28$	−0.512238	−	1.77325i	−0.0968039	−	0.335114i
$29$	0.517190	−	0.616364i	0.0960399	−	0.114456i	−0.715884	−	0.698219i	$-0.753976\pi$
$29$	0.517190	−	0.616364i	0.0960399	−	0.114456i	0.811924	+	0.583763i	$0.198420\pi$
$30$	0.491740	+	0.306603i	0.0897791	+	0.0559779i
$31$	−4.76017	+	8.24486i	−0.854952	+	1.48082i	0.0217379	+	0.999764i	$0.493080\pi$
$31$	−4.76017	+	8.24486i	−0.854952	+	1.48082i	−0.876690	+	0.481056i	$0.840253\pi$
$32$	5.32513	+	1.90867i	0.941358	+	0.337409i
$33$	0.356678	−	0.0628920i	0.0620897	−	0.0109481i
$34$	1.47735	+	4.53169i	0.253363	+	0.777179i
$35$	0.315643	−	0.867222i	0.0533534	−	0.146587i
$36$	0.603115	+	5.63198i	0.100519	+	0.938664i
$37$		−	4.07725i		−	0.670296i	−0.942165	−	0.335148i	$-0.891214\pi$
$37$		−	4.07725i		−	0.670296i	0.942165	−	0.335148i	$-0.108786\pi$
$38$	−5.54932	−	2.68421i	−0.900219	−	0.435437i
$39$			2.58779i			0.414378i
$40$	1.58853	+	2.34021i	0.251168	+	0.370020i
$41$	3.75939	−	10.3289i	0.587119	−	1.61310i	−0.188626	−	0.982049i	$-0.560403\pi$
$41$	3.75939	−	10.3289i	0.587119	−	1.61310i	0.775745	−	0.631047i	$-0.217374\pi$
$42$	−0.508466	+	0.165762i	−0.0784580	+	0.0255776i
$43$	−2.37964	+	0.419595i	−0.362892	+	0.0639876i	−0.352121	−	0.935954i	$-0.614540\pi$
$43$	−2.37964	+	0.419595i	−0.362892	+	0.0639876i	−0.0107704	+	0.999942i	$0.503428\pi$
$44$	1.71608	+	0.424293i	0.258708	+	0.0639645i
$45$	−1.41605	+	2.45266i	−0.211092	+	0.365622i
$46$	3.99567	−	6.40839i	0.589130	−	0.944866i
$47$	5.18564	−	6.18000i	0.756403	−	0.901446i	−0.241212	−	0.970473i	$-0.577545\pi$
$47$	5.18564	−	6.18000i	0.756403	−	0.901446i	0.997615	+	0.0690262i	$0.0219892\pi$
$48$	0.500379	−	1.56081i	0.0722234	−	0.225284i
$49$	−3.07415	−	5.32458i	−0.439164	−	0.760654i
$50$	−0.0479694	+	1.41340i	−0.00678389	+	0.199885i
$51$	1.29777	−	0.472350i	0.181724	−	0.0661422i
$52$	−5.11469	+	11.5487i	−0.709280	+	1.60152i
$53$	10.8012	+	1.90454i	1.48366	+	0.261609i	0.856039	−	0.516911i	$-0.172918\pi$
$53$	10.8012	+	1.90454i	1.48366	+	0.261609i	0.627620	+	0.778520i	$0.284029\pi$
$54$	3.34631	−	0.473640i	0.455376	−	0.0644543i
$55$	0.568144	+	0.677087i	0.0766085	+	0.0912984i
$56$	−2.59679	−	0.265212i	−0.347010	−	0.0354404i
$57$	−0.722757	+	1.63336i	−0.0957315	+	0.216343i
$58$	−0.535189	−	1.00417i	−0.0702738	−	0.131854i
$59$	6.63590	−	5.56818i	0.863920	−	0.724915i	−0.0988885	−	0.995099i	$-0.531529\pi$
$59$	6.63590	−	5.56818i	0.863920	−	0.724915i	0.962809	+	0.270183i	$0.0870843\pi$
$60$	0.662067	−	0.483007i	0.0854725	−	0.0623559i
$61$	0.00816087	−	0.0462826i	0.00104489	−	0.00592588i	−0.984281	−	0.176610i	$-0.943487\pi$
$61$	0.00816087	−	0.0462826i	0.00104489	−	0.00592588i	0.985326	+	0.170684i	$0.0545979\pi$
$62$	8.29954	+	10.6015i	1.05404	+	1.34639i
$63$	−0.893930	−	2.45605i	−0.112625	−	0.309434i
$64$	5.31797	−	5.97655i	0.664747	−	0.747069i
$65$	−5.46921	+	3.15765i	−0.678373	+	0.391659i
$66$	0.106001	−	0.501112i	0.0130478	−	0.0616827i
$67$	10.7236	+	8.99818i	1.31010	+	1.09930i	0.988305	+	0.152492i	$0.0487298\pi$
$67$	10.7236	+	8.99818i	1.31010	+	1.09930i	0.321793	+	0.946810i	$0.395715\pi$
$68$	6.72523	+	0.457021i	0.815554	+	0.0554220i
$69$	−1.89502	−	1.09409i	−0.228133	−	0.131713i
$70$	−0.970769	−	0.872362i	−0.116029	−	0.104267i
$71$	−0.988117	−	5.60389i	−0.117268	−	0.665060i	−0.985602	−	0.169080i	$-0.945920\pi$
$71$	−0.988117	−	5.60389i	−0.117268	−	0.665060i	0.868334	−	0.495979i	$-0.165191\pi$
$72$	7.70652	+	2.18529i	0.908222	+	0.257539i
$73$	8.95524	+	3.25944i	1.04813	+	0.381489i	0.807957	−	0.589241i	$-0.200573\pi$
$73$	8.95524	+	3.25944i	1.04813	+	0.381489i	0.240174	+	0.970730i	$0.422795\pi$
$74$	−5.34836	−	2.15478i	−0.621734	−	0.250488i
$75$	0.409765			0.0473156
$76$	−6.45378	+	5.86078i	−0.740299	+	0.672277i
$77$	−0.815709			−0.0929587
$78$	3.39454	+	1.36761i	0.384357	+	0.154852i
$79$	−15.1537	−	5.51548i	−1.70492	−	0.620540i	−0.708550	−	0.705661i	$-0.750650\pi$
$79$	−15.1537	−	5.51548i	−1.70492	−	0.620540i	−0.996371	+	0.0851204i	$0.972873\pi$
$80$	3.90930	−	0.846987i	0.437073	−	0.0946961i
$81$	1.30532	+	7.40283i	0.145035	+	0.822536i
$82$	−11.5621	−	10.3901i	−1.27682	−	1.14739i
$83$	−2.88323	−	1.66463i	−0.316476	−	0.182717i	0.333345	−	0.942805i	$-0.391823\pi$
$83$	−2.88323	−	1.66463i	−0.316476	−	0.182717i	−0.649821	+	0.760088i	$0.725156\pi$
$84$	−0.0512788	+	0.754586i	−0.00559498	+	0.0823320i
$85$	2.58185	+	2.16643i	0.280041	+	0.234983i
$86$	−0.707205	+	3.34325i	−0.0762599	+	0.360512i
$87$	−0.285528	+	0.164849i	−0.0306118	+	0.0176737i
$88$	1.46349	−	2.02684i	0.156009	−	0.216062i
$89$	−0.400871	−	1.10138i	−0.0424922	−	0.116746i	0.916632	−	0.399733i	$-0.130897\pi$
$89$	−0.400871	−	1.10138i	−0.0424922	−	0.116746i	−0.959124	+	0.282986i	$0.908675\pi$
$90$	2.46893	+	3.15371i	0.260248	+	0.332430i
$91$	1.01207	−	5.73971i	0.106093	−	0.601686i
$92$	−6.29457	−	8.62810i	−0.656255	−	0.899542i
$93$	2.98842	−	2.50758i	0.309884	−	0.260024i
$94$	−5.36610	−	10.0683i	−0.553471	−	1.03847i
$95$	−4.33397	+	0.465518i	−0.444656	+	0.0477611i
$96$	−1.78296	−	1.48124i	−0.181972	−	0.151179i
$97$	6.26962	+	7.47184i	0.636583	+	0.758650i	0.983826	−	0.179125i	$-0.0573266\pi$
$97$	6.26962	+	7.47184i	0.636583	+	0.758650i	−0.347243	+	0.937775i	$0.612882\pi$
$98$	−8.60919	+	1.21855i	−0.869660	+	0.123092i
$99$	2.46519	+	0.434679i	0.247761	+	0.0436869i
$100$	1.82868	+	0.809888i	0.182868	+	0.0809888i
$101$	1.63141	−	0.593786i	0.162332	−	0.0590839i	−0.259576	−	0.965723i	$-0.583583\pi$
$101$	1.63141	−	0.593786i	0.162332	−	0.0590839i	0.421908	+	0.906639i	$0.361361\pi$
$102$	0.0662485	−	1.95199i	0.00655958	−	0.193276i
$103$	4.79758	+	8.30966i	0.472720	+	0.818775i	0.999513	−	0.0312188i	$-0.00993888\pi$
$103$	4.79758	+	8.30966i	0.472720	+	0.818775i	−0.526793	+	0.849994i	$0.676606\pi$
$104$	12.4460	+	12.8126i	1.22043	+	1.25638i
$105$	−0.243078	+	0.289690i	−0.0237220	+	0.0282708i
$106$	8.20660	−	13.1620i	0.797095	−	1.27841i
$107$	5.95469	−	10.3138i	0.575661	−	0.997075i	−0.420308	−	0.907381i	$-0.638078\pi$
$107$	5.95469	−	10.3138i	0.575661	−	0.997075i	0.995969	−	0.0896931i	$-0.0285886\pi$
$108$	1.14719	−	4.63986i	0.110388	−	0.446470i
$109$	−4.50815	+	0.794909i	−0.431803	+	0.0761385i	−0.385325	−	0.922781i	$-0.625911\pi$
$109$	−4.50815	+	0.794909i	−0.431803	+	0.0761385i	−0.0464775	+	0.998919i	$0.514800\pi$
$110$	1.18843	−	0.387433i	0.113312	−	0.0369403i
$111$	−0.571418	+	1.56996i	−0.0542366	+	0.149014i
$112$	−1.72026	+	3.26619i	−0.162550	+	0.308626i
$113$		−	3.61858i		−	0.340408i	−0.985409	−	0.170204i	$-0.945557\pi$
$113$		−	3.61858i		−	0.340408i	0.985409	−	0.170204i	$-0.0544426\pi$
$114$	1.76060	+	1.81129i	0.164895	+	0.169643i
$115$		−	5.34008i		−	0.497965i
$116$	−1.60006	+	0.171347i	−0.148562	+	0.0159091i
$117$	−6.11721	+	16.8069i	−0.565536	+	1.55380i
$118$	−3.79710	−	11.6474i	−0.349551	−	1.07223i
$119$	−3.06319	+	0.540123i	−0.280802	+	0.0495129i
$120$	−0.283692	−	1.12373i	−0.0258974	−	0.102582i
$121$	−5.10938	+	8.84971i	−0.464489	+	0.804519i
$122$	−0.0563985	−	0.0351648i	−0.00510608	−	0.00318367i
$123$	−2.89513	+	3.45028i	−0.261045	+	0.311102i
$124$	18.2927	−	5.28421i	1.64274	−	0.474536i
$125$	0.500000	+	0.866025i	0.0447214	+	0.0774597i
$126$	−3.69417	−	0.125376i	−0.329103	−	0.0111694i
$127$	−14.2739	+	5.19526i	−1.26660	+	0.461005i	−0.885979	−	0.463726i	$-0.846512\pi$
$127$	−14.2739	+	5.19526i	−1.26660	+	0.461005i	−0.380622	+	0.924731i	$0.624290\pi$
$128$	−5.02929	−	10.1344i	−0.444530	−	0.895764i
$129$	0.975092	+	0.171935i	0.0858521	+	0.0151380i
$130$	1.25165	+	8.84305i	0.109777	+	0.775587i
$131$	2.43278	+	2.89927i	0.212553	+	0.253310i	0.861778	−	0.507286i	$-0.169351\pi$
$131$	2.43278	+	2.89927i	0.212553	+	0.253310i	−0.649225	+	0.760596i	$0.724907\pi$
$132$	−0.601316	−	0.403879i	−0.0523378	−	0.0351532i
$133$	2.24187	−	3.34012i	0.194395	−	0.289625i
$134$	17.4707	−	9.31132i	1.50924	−	0.804376i
$135$	1.83068	−	1.53612i	0.157560	−	0.132209i
$136$	4.15370	−	8.58032i	0.356177	−	0.735756i
$137$	1.20274	−	6.82110i	0.102757	−	0.582766i	−0.889335	−	0.457256i	$-0.848832\pi$
$137$	1.20274	−	6.82110i	0.102757	−	0.582766i	0.992092	−	0.125510i	$-0.0400567\pi$
$138$	−2.43667	+	1.90758i	−0.207423	+	0.162384i
$139$	−5.36057	−	14.7281i	−0.454678	−	1.24922i	−0.929397	−	0.369080i	$-0.879673\pi$
$139$	−5.36057	−	14.7281i	−0.454678	−	1.24922i	0.474719	−	0.880137i	$-0.342550\pi$
$140$	−1.65737	+	0.812379i	−0.140073	+	0.0686585i
$141$	−2.86286	+	1.65287i	−0.241096	+	0.139197i
$142$	−7.87314	−	1.66542i	−0.660699	−	0.139759i
$143$	4.27601	+	3.58800i	0.357578	+	0.300044i
$144$	6.93937	−	8.95417i	0.578281	−	0.746181i
$145$	−0.696809	−	0.402303i	−0.0578668	−	0.0334094i
$146$	9.00832	−	10.0245i	0.745534	−	0.829634i
$147$	0.437481	+	2.48108i	0.0360828	+	0.204636i
$148$	−5.65308	+	5.87696i	−0.464680	+	0.483083i
$149$	−3.84885	−	1.40087i	−0.315310	−	0.114764i	0.179517	−	0.983755i	$-0.442546\pi$
$149$	−3.84885	−	1.40087i	−0.315310	−	0.114764i	−0.494827	+	0.868991i	$0.664769\pi$
$150$	0.216556	−	0.537511i	0.0176817	−	0.0438876i
$151$	−1.52291			−0.123932			−0.0619662	−	0.998078i	$-0.519737\pi$
$151$	−1.52291			−0.123932			−0.0619662	+	0.998078i	$0.519737\pi$
$152$	4.27716	+	11.5631i	0.346924	+	0.937893i
$153$	9.54520			0.771684
$154$	−0.431092	+	1.07001i	−0.0347384	+	0.0862239i
$155$	8.94619	+	3.25615i	0.718576	+	0.261540i
$156$	3.58795	−	3.73004i	0.287266	−	0.298642i
$157$	0.593780	+	3.36749i	0.0473888	+	0.268755i	0.999291	−	0.0376464i	$-0.0119861\pi$
$157$	0.593780	+	3.36749i	0.0473888	+	0.268755i	−0.951902	+	0.306402i	$0.900875\pi$
$158$	−15.2435	+	16.9630i	−1.21271	+	1.34951i
$159$	−3.89212	−	2.24711i	−0.308665	−	0.178208i
$160$	0.954976	−	5.57566i	0.0754975	−	0.440795i
$161$	3.77525	+	3.16781i	0.297532	+	0.249659i
$162$	10.4005	+	2.20005i	0.817144	+	0.172852i
$163$	−8.76505	+	5.06050i	−0.686532	+	0.396369i	−0.802311	−	0.596906i	$-0.796397\pi$
$163$	−8.76505	+	5.06050i	−0.686532	+	0.396369i	0.115780	+	0.993275i	$0.463063\pi$
$164$	−19.7397	+	9.67565i	−1.54141	+	0.755541i
$165$	−0.123873	−	0.340339i	−0.00964351	−	0.0264953i
$166$	−3.70735	+	2.90235i	−0.287746	+	0.225266i
$167$	−2.94699	+	16.7132i	−0.228045	+	1.29331i	0.628734	+	0.777621i	$0.283574\pi$
$167$	−2.94699	+	16.7132i	−0.228045	+	1.29331i	−0.856778	+	0.515685i	$0.827538\pi$
$168$	0.962731	+	0.466054i	0.0742763	+	0.0359569i
$169$	−20.5936	+	17.2801i	−1.58413	+	1.32924i
$170$	4.20630	−	2.24183i	0.322609	−	0.171940i
$171$	−8.55514	+	8.89965i	−0.654228	+	0.680573i
$172$	4.01178	+	2.69455i	0.305895	+	0.205457i
$173$	−0.433288	−	0.516372i	−0.0329422	−	0.0392590i	0.749322	−	0.662206i	$-0.230380\pi$
$173$	−0.433288	−	0.516372i	−0.0329422	−	0.0392590i	−0.782264	+	0.622947i	$0.785935\pi$
$174$	0.0653442	+	0.461663i	0.00495373	+	0.0349986i
$175$	−0.908858	−	0.160256i	−0.0687032	−	0.0121142i
$176$	−1.88528	−	2.99090i	−0.142108	−	0.225448i
$177$	−3.33554	+	1.21404i	−0.250715	+	0.0912526i
$178$	−1.65660	−	0.0562233i	−0.124167	−	0.00421412i
$179$	4.06746	+	7.04505i	0.304016	+	0.526572i	0.977042	−	0.213048i	$-0.0683390\pi$
$179$	4.06746	+	7.04505i	0.304016	+	0.526572i	−0.673026	+	0.739619i	$0.735006\pi$
$180$	5.44169	−	1.57194i	0.405600	−	0.117165i
$181$	8.45431	−	10.0755i	0.628404	−	0.748902i	−0.354087	−	0.935212i	$-0.615208\pi$
$181$	8.45431	−	10.0755i	0.628404	−	0.748902i	0.982491	+	0.186310i	$0.0596529\pi$
$182$	−6.99423	−	4.36095i	−0.518447	−	0.323255i
$183$	−0.00962877	+	0.0166775i	−0.000711779	+	0.00123284i
$184$	−14.6446	+	3.69709i	−1.07961	+	0.272553i
$185$	−4.01531	+	0.708008i	−0.295212	+	0.0520538i
$186$	−1.70999	−	5.24529i	−0.125382	−	0.384604i
$187$	1.01887	−	2.79933i	0.0745074	−	0.204707i
$188$	−16.0431	+	1.71802i	−1.17006	+	0.125299i
$189$			2.20548i			0.160425i
$190$	−1.67980	+	5.93113i	−0.121866	+	0.430289i
$191$			12.0252i			0.870116i	0.900402	+	0.435058i	$0.143272\pi$
$191$			12.0252i			0.870116i	−0.900402	+	0.435058i	$0.856728\pi$
$192$	−2.88530	+	1.55599i	−0.208229	+	0.112294i
$193$	2.79421	−	7.67702i	0.201131	−	0.552604i	−0.797588	−	0.603203i	$-0.793891\pi$
$193$	2.79421	−	7.67702i	0.201131	−	0.552604i	0.998719	+	0.0505991i	$0.0161131\pi$
$194$	13.1146	−	4.27543i	0.941576	−	0.306958i
$195$	2.54847	−	0.449365i	0.182500	−	0.0321797i
$196$	−2.95141	+	11.9371i	−0.210815	+	0.852653i
$197$	−0.688222	+	1.19204i	−0.0490338	+	0.0849291i	−0.889501	−	0.456934i	$-0.848948\pi$
$197$	−0.688222	+	1.19204i	−0.0490338	+	0.0849291i	0.840467	+	0.541863i	$0.182281\pi$
$198$	1.87301	−	3.00400i	0.133109	−	0.213485i
$199$	−12.1103	+	14.4325i	−0.858476	+	1.02309i	0.140977	+	0.990013i	$0.454976\pi$
$199$	−12.1103	+	14.4325i	−0.858476	+	1.02309i	−0.999453	+	0.0330792i	$0.989469\pi$
$200$	2.02881	−	1.97077i	0.143459	−	0.139354i
$201$	−2.86808	−	4.96766i	−0.202299	−	0.350392i
$202$	0.0832802	−	2.45382i	0.00585958	−	0.172650i
$203$	0.697772	−	0.253968i	0.0489740	−	0.0178251i
$204$	−2.52552	−	1.11850i	−0.176822	−	0.0783109i
$205$	−10.8247	−	1.90869i	−0.756033	−	0.133309i
$206$	13.4357	−	1.90170i	0.936110	−	0.132498i
$207$	−9.72126	−	11.5853i	−0.675674	−	0.805237i
$208$	23.3845	−	9.55482i	1.62142	−	0.662507i
$209$	1.69682	+	3.45894i	0.117371	+	0.239260i
$210$	0.251538	+	0.471957i	0.0173578	+	0.0325681i
$211$	20.4389	−	17.1503i	1.40707	−	1.18068i	0.449220	−	0.893421i	$-0.351702\pi$
$211$	20.4389	−	17.1503i	1.40707	−	1.18068i	0.957854	−	0.287254i	$-0.0927424\pi$
$212$	−12.9282	−	17.7210i	−0.887915	−	1.21708i
$213$	−0.404896	+	2.29628i	−0.0277430	+	0.157338i
$214$	−10.3822	−	13.2618i	−0.709714	−	0.906559i
$215$	0.826440	+	2.27063i	0.0563627	+	0.154855i
$216$	−5.48008	−	3.95693i	−0.372872	−	0.269235i
$217$	−7.60900	+	4.39306i	−0.516533	+	0.298220i
$218$	−1.33978	+	6.33369i	−0.0907412	+	0.428972i
$219$	−2.99144	−	2.51011i	−0.202143	−	0.169618i
$220$	0.119853	−	1.76368i	0.00808050	−	0.118907i
$221$	18.4333	+	10.6425i	1.23996	+	0.715889i
$222$	1.75741	+	1.57926i	0.117950	+	0.105993i
$223$	−0.404250	−	2.29262i	−0.0270706	−	0.153525i	0.968276	−	0.249882i	$-0.0803919\pi$
$223$	−0.404250	−	2.29262i	−0.0270706	−	0.153525i	−0.995347	+	0.0963574i	$0.969281\pi$
$224$	3.37530	+	3.98270i	0.225522	+	0.266105i
$225$	2.66130	+	0.968633i	0.177420	+	0.0645755i
$226$	−4.74669	−	1.91238i	−0.315745	−	0.127209i
$227$	−5.93868			−0.394164			−0.197082	−	0.980387i	$-0.563147\pi$
$227$	−5.93868			−0.394164			−0.197082	+	0.980387i	$0.563147\pi$
$228$	3.30642	−	1.35223i	0.218973	−	0.0895534i
$229$	−17.8878			−1.18206			−0.591028	−	0.806651i	$-0.701278\pi$
$229$	−17.8878			−1.18206			−0.591028	+	0.806651i	$0.701278\pi$
$230$	−7.00487	−	2.82217i	−0.461888	−	0.186088i
$231$	0.314091	+	0.114320i	0.0206657	+	0.00752169i
$232$	−0.620848	+	2.18944i	−0.0407607	+	0.143744i
$233$	2.50860	+	14.2270i	0.164344	+	0.932039i	0.949739	+	0.313044i	$0.101349\pi$
$233$	2.50860	+	14.2270i	0.164344	+	0.932039i	−0.785395	+	0.618995i	$0.787540\pi$
$234$	18.8137	+	16.9065i	1.22989	+	1.10521i
$235$	−6.98659	−	4.03371i	−0.455755	−	0.263130i
$236$	−17.2852	−	1.17464i	−1.12517	−	0.0764626i
$237$	5.06198	+	4.24751i	0.328811	+	0.275905i
$238$	−0.910348	+	4.30360i	−0.0590091	+	0.278961i
$239$	−5.47735	+	3.16235i	−0.354301	+	0.204555i	−0.666578	−	0.745436i	$-0.732242\pi$
$239$	−5.47735	+	3.16235i	−0.354301	+	0.204555i	0.312277	+	0.949991i	$0.398908\pi$
$240$	−1.62399	−	0.221745i	−0.104828	−	0.0143136i
$241$	−6.18671	−	16.9979i	−0.398521	−	1.09493i	−0.963005	−	0.269484i	$-0.913147\pi$
$241$	−6.18671	−	16.9979i	−0.398521	−	1.09493i	0.564484	−	0.825444i	$-0.309075\pi$
$242$	8.90840	+	11.3792i	0.572654	+	0.731484i
$243$	1.77982	−	10.0939i	0.114175	−	0.647521i
$244$	−0.0759335	+	0.0553968i	−0.00486115	+	0.00354642i
$245$	−4.70987	+	3.95205i	−0.300902	+	0.252487i
$246$	2.99588	+	5.62113i	0.191011	+	0.358390i
$247$	−26.4440	+	7.64803i	−1.68259	+	0.486633i
$248$	2.73590	−	26.7882i	0.173730	−	1.70106i
$249$	0.876902	+	1.04505i	0.0555714	+	0.0662274i
$250$	1.40026	−	0.198194i	0.0885600	−	0.0125349i
$251$	17.3282	+	3.05544i	1.09375	+	0.192858i	0.691288	−	0.722579i	$-0.257044\pi$
$251$	17.3282	+	3.05544i	1.09375	+	0.192858i	0.402461	+	0.915437i	$0.368155\pi$
$252$	−2.11679	+	4.77959i	−0.133345	+	0.301086i
$253$	−4.43531	+	1.61432i	−0.278846	+	0.101492i
$254$	−0.728651	+	21.4694i	−0.0457197	+	1.34711i
$255$	−0.690529	−	1.19603i	−0.0432426	−	0.0748984i
$256$	−15.9518	+	1.24128i	−0.996986	+	0.0775800i
$257$	16.0918	−	19.1775i	1.00378	−	1.19626i	0.0232817	−	0.999729i	$-0.492589\pi$
$257$	16.0918	−	19.1775i	1.00378	−	1.19626i	0.980498	−	0.196529i	$-0.0629670\pi$
$258$	0.740861	−	1.18822i	0.0461240	−	0.0739751i
$259$	1.88140	−	3.25869i	0.116905	−	0.202485i
$260$	12.2614	+	3.03158i	0.760420	+	0.188011i
$261$	−2.24410	+	0.395695i	−0.138906	+	0.0244929i
$262$	5.08882	−	1.65898i	0.314388	−	0.102492i
$263$	−9.00340	+	24.7366i	−0.555174	+	1.52533i	0.271382	+	0.962472i	$0.412519\pi$
$263$	−9.00340	+	24.7366i	−0.555174	+	1.52533i	−0.826556	+	0.562855i	$0.809703\pi$
$264$	−0.847579	+	0.575334i	−0.0521649	+	0.0354094i
$265$		−	10.9678i		−	0.673748i
$266$	−3.19662	−	4.70600i	−0.195997	−	0.288543i
$267$			0.480272i			0.0293921i
$268$	−2.98112	−	27.8382i	−0.182101	−	1.70049i
$269$	−0.156279	+	0.429373i	−0.00952850	+	0.0261793i	−0.944366	−	0.328897i	$-0.893323\pi$
$269$	−0.156279	+	0.429373i	−0.00952850	+	0.0261793i	0.934837	+	0.355077i	$0.115545\pi$
$270$	−1.04753	−	3.21323i	−0.0637504	−	0.195551i
$271$	6.33388	−	1.11683i	0.384756	−	0.0678428i	0.0220750	−	0.999756i	$-0.492973\pi$
$271$	6.33388	−	1.11683i	0.384756	−	0.0678428i	0.362681	+	0.931914i	$0.381862\pi$
$272$	−9.06010	−	9.98323i	−0.549349	−	0.605322i
$273$	−1.19411	+	2.06825i	−0.0722707	+	0.125176i
$274$	−8.31198	−	5.18257i	−0.502145	−	0.313091i
$275$	0.568144	−	0.677087i	0.0342604	−	0.0408299i
$276$	1.21453	+	4.20444i	0.0731064	+	0.253078i
$277$	−0.377151	−	0.653246i	−0.0226608	−	0.0392497i	0.854473	−	0.519496i	$-0.173880\pi$
$277$	−0.377151	−	0.653246i	−0.0226608	−	0.0392497i	−0.877133	+	0.480247i	$0.840547\pi$
$278$	−22.1526	−	0.751837i	−1.32862	−	0.0450922i
$279$	25.3365	−	9.22171i	1.51685	−	0.552090i
$280$	0.189744	+	2.60339i	0.0113394	+	0.155582i
$281$	23.9307	+	4.21964i	1.42759	+	0.251722i	0.833430	−	0.552626i	$-0.186374\pi$
$281$	23.9307	+	4.21964i	1.42759	+	0.251722i	0.594159	+	0.804348i	$0.297485\pi$
$282$	0.655178	+	4.62889i	0.0390153	+	0.275647i
$283$	−6.77738	−	8.07697i	−0.402873	−	0.480126i	0.526020	−	0.850472i	$-0.323684\pi$
$283$	−6.77738	−	8.07697i	−0.402873	−	0.480126i	−0.928894	+	0.370346i	$0.879239\pi$
$284$	−6.34548	+	9.44748i	−0.376535	+	0.560605i
$285$	1.73405	+	0.428147i	0.102716	+	0.0253613i
$286$	6.96640	−	3.71287i	0.411932	−	0.219546i
$287$	7.77078	−	6.52046i	0.458695	−	0.384891i
$288$	−8.07830	−	13.8349i	−0.476018	−	0.815231i
$289$	−0.979481	+	5.55491i	−0.0576166	+	0.326760i
$290$	−0.895977	+	0.701430i	−0.0526136	+	0.0411894i
$291$	−1.36697	−	3.75573i	−0.0801333	−	0.220165i
$292$	−8.38890	−	17.1145i	−0.490924	−	1.00155i
$293$	9.11646	−	5.26339i	0.532589	−	0.307490i	−0.209481	−	0.977813i	$-0.567177\pi$
$293$	9.11646	−	5.26339i	0.532589	−	0.307490i	0.742070	+	0.670322i	$0.233844\pi$
$294$	3.48577	+	0.737352i	0.203294	+	0.0430032i
$295$	−6.63590	−	5.56818i	−0.386357	−	0.324192i
$296$	4.72155	+	10.5214i	0.274434	+	0.611542i
$297$	−1.82928	−	1.05614i	−0.106146	−	0.0612832i
$298$	−3.87167	+	4.30841i	−0.224280	+	0.249580i
$299$	−5.85615	−	33.2119i	−0.338670	−	1.92069i
$300$	−0.590635	−	0.568136i	−0.0341004	−	0.0328013i
$301$	−2.09551	−	0.762704i	−0.120783	−	0.0439615i
$302$	−0.804837	+	1.99768i	−0.0463132	+	0.114954i
$303$	−0.711398			−0.0408687
$304$	17.4284	+	0.500381i	0.999588	+	0.0286988i
$305$	−0.0469966			−0.00269102
$306$	5.04452	−	12.5210i	0.288376	−	0.715776i
$307$	31.2023	+	11.3567i	1.78081	+	0.648161i	0.999718	+	0.0237406i	$0.00755757\pi$
$307$	31.2023	+	11.3567i	1.78081	+	0.648161i	0.781089	+	0.624420i	$0.214665\pi$
$308$	1.17576	+	1.13097i	0.0669954	+	0.0644433i
$309$	−0.682743	−	3.87203i	−0.0388399	−	0.220272i
$310$	8.99922	−	10.0144i	0.511121	−	0.568779i
$311$	−13.6581	−	7.88551i	−0.774480	−	0.447146i	0.0599902	−	0.998199i	$-0.480893\pi$
$311$	−13.6581	−	7.88551i	−0.774480	−	0.447146i	−0.834471	+	0.551052i	$0.814226\pi$
$312$	−2.99672	−	6.67779i	−0.169656	−	0.378056i
$313$	−4.28991	−	3.59967i	−0.242480	−	0.203465i	0.513446	−	0.858122i	$-0.328369\pi$
$313$	−4.28991	−	3.59967i	−0.242480	−	0.203465i	−0.755926	+	0.654657i	$0.772813\pi$
$314$	4.73113	+	1.00078i	0.266993	+	0.0564776i
$315$	−2.26351	+	1.30684i	−0.127534	+	0.0736320i
$316$	14.1953	+	28.9605i	0.798550	+	1.62915i
$317$	−6.09270	−	16.7396i	−0.342200	−	0.940187i	−0.984755	−	0.173947i	$-0.944348\pi$
$317$	−6.09270	−	16.7396i	−0.342200	−	0.940187i	0.642555	−	0.766240i	$-0.277874\pi$
$318$	−5.00460	+	3.91793i	−0.280644	+	0.219707i
$319$	−0.123493	+	0.700366i	−0.00691431	+	0.0392130i
$320$	−6.80921	−	4.19936i	−0.380646	−	0.234752i
$321$	−3.73833	+	3.13683i	−0.208653	+	0.175081i
$322$	6.15057	−	3.27806i	0.342758	−	0.182679i
$323$	8.66230	+	11.8656i	0.481984	+	0.660221i
$324$	8.38248	−	12.4803i	0.465693	−	0.693348i
$325$	4.05940	+	4.83780i	0.225175	+	0.268353i
$326$	2.00592	+	14.1720i	0.111098	+	0.784915i
$327$	1.84728	+	0.325726i	0.102155	+	0.0180127i
$328$	2.25991	+	31.0071i	0.124783	+	1.71208i
$329$	6.99625	−	2.54643i	0.385716	−	0.140389i
$330$	−0.511906	−	0.0173736i	−0.0281795	−	0.000956384i
$331$	2.60179	+	4.50644i	0.143008	+	0.247696i	0.928628	−	0.371013i	$-0.120989\pi$
$331$	2.60179	+	4.50644i	0.143008	+	0.247696i	−0.785620	+	0.618709i	$0.787656\pi$
$332$	1.84789	+	6.39699i	0.101416	+	0.351080i
$333$	−7.42237	+	8.84564i	−0.406744	+	0.484738i
$334$	20.3662	+	12.6984i	1.11439	+	0.694828i
$335$	6.99934	−	12.1232i	0.382415	−	0.662362i
$336$	1.12014	−	1.01656i	0.0611087	−	0.0554581i
$337$	14.6608	−	2.58510i	0.798626	−	0.140819i	0.240580	−	0.970629i	$-0.422662\pi$
$337$	14.6608	−	2.58510i	0.798626	−	0.140819i	0.558046	+	0.829810i	$0.311551\pi$
$338$	11.7838	+	36.1461i	0.640954	+	1.96609i
$339$	−0.507136	+	1.39335i	−0.0275439	+	0.0756762i
$340$	−0.717745	−	6.70242i	−0.0389252	−	0.363490i
$341$		−	8.41479i		−	0.455686i
$342$	7.15287	+	15.9256i	0.386783	+	0.861158i
$343$		−	12.1343i		−	0.655189i
$344$	5.65476	−	3.83844i	0.304884	−	0.206955i
$345$	−0.748400	+	2.05621i	−0.0402925	+	0.110703i
$346$	−0.906341	+	0.295471i	−0.0487252	+	0.0158846i
$347$	−11.9566	+	2.10828i	−0.641865	+	0.113178i	−0.485101	−	0.874458i	$-0.661217\pi$
$347$	−11.9566	+	2.10828i	−0.641865	+	0.113178i	−0.156764	+	0.987636i	$0.550106\pi$
$348$	0.640123	+	0.158268i	0.0343142	+	0.00848404i
$349$	−2.70216	+	4.68027i	−0.144643	+	0.250529i	−0.929240	−	0.369477i	$-0.879537\pi$
$349$	−2.70216	+	4.68027i	−0.144643	+	0.250529i	0.784597	+	0.620007i	$0.212870\pi$
$350$	−0.690537	+	1.10751i	−0.0369108	+	0.0591986i
$351$	9.70110	−	11.5613i	0.517806	−	0.617097i
$352$	−4.91967	+	0.892364i	−0.262220	+	0.0475632i
$353$	−11.7282	−	20.3139i	−0.624229	−	1.08120i	−0.988689	−	0.149978i	$-0.952080\pi$
$353$	−11.7282	−	20.3139i	−0.624229	−	1.08120i	0.364460	−	0.931219i	$-0.381254\pi$
$354$	−0.170272	+	5.01701i	−0.00904988	+	0.266651i
$355$	−5.34717	+	1.94621i	−0.283798	+	0.103294i
$356$	−0.949243	+	2.14334i	−0.0503098	+	0.113597i
$357$	1.25519	+	0.221323i	0.0664315	+	0.0117137i
$358$	11.3910	−	1.61229i	0.602032	−	0.0852122i
$359$	15.8317	+	18.8674i	0.835563	+	0.995786i	0.999956	+	0.00939060i	$0.00298916\pi$
$359$	15.8317	+	18.8674i	0.835563	+	0.995786i	−0.164393	+	0.986395i	$0.552566\pi$
$360$	0.813872	−	7.96892i	0.0428948	−	0.419999i
$361$	−18.8270	−	2.55841i	−0.990893	−	0.134653i
$362$	−8.74853	−	16.4147i	−0.459812	−	0.862739i
$363$	3.20765	−	2.69154i	0.168358	−	0.141269i
$364$	−9.41687	+	6.87001i	−0.493578	+	0.360086i
$365$	1.65486	−	9.38518i	0.0866194	−	0.491243i
$366$	0.0167881	+	0.0214444i	0.000877529	+	0.00112092i
$367$	−10.7805	−	29.6193i	−0.562740	−	1.54611i	−0.815603	−	0.578612i	$-0.803594\pi$
$367$	−10.7805	−	29.6193i	−0.562740	−	1.54611i	0.252863	−	0.967502i	$-0.418628\pi$
$368$	−2.88979	+	21.1639i	−0.150641	+	1.10325i
$369$	−26.9590	+	15.5648i	−1.40343	+	0.810271i
$370$	−1.19331	+	5.64128i	−0.0620372	+	0.293276i
$371$	7.75388	+	6.50628i	0.402561	+	0.337789i
$372$	−7.78425	−	0.528988i	−0.403594	−	0.0274268i
$373$	9.48035	+	5.47348i	0.490874	+	0.283406i	0.724937	−	0.688815i	$-0.241869\pi$
$373$	9.48035	+	5.47348i	0.490874	+	0.283406i	−0.234063	+	0.972221i	$0.575202\pi$
$374$	−3.13357	−	2.81592i	−0.162033	−	0.145608i
$375$	−0.0711549	−	0.403539i	−0.00367442	−	0.0208387i
$376$	−6.22497	+	21.9526i	−0.321028	+	1.13212i
$377$	−4.77489	−	1.73792i	−0.245919	−	0.0895073i
$378$	2.89305	+	1.16557i	0.148803	+	0.0599504i
$379$	16.2759			0.836038			0.418019	−	0.908438i	$-0.362724\pi$
$379$	16.2759			0.836038			0.418019	+	0.908438i	$0.362724\pi$
$380$	6.89243	+	5.33802i	0.353574	+	0.273835i
$381$	6.22430			0.318880
$382$	15.7742	+	6.35519i	0.807076	+	0.325160i
$383$	6.83718	+	2.48853i	0.349363	+	0.127158i	0.510741	−	0.859735i	$-0.329371\pi$
$383$	6.83718	+	2.48853i	0.349363	+	0.127158i	−0.161377	+	0.986893i	$0.551594\pi$
$384$	0.516226	+	4.60713i	0.0263436	+	0.235106i
$385$	0.141646	+	0.803317i	0.00721897	+	0.0409408i
$386$	−8.59367	−	7.72253i	−0.437406	−	0.393066i
$387$	5.92649	+	3.42166i	0.301261	+	0.173933i
$388$	1.32261	−	19.4627i	0.0671455	−	0.988069i
$389$	8.52277	+	7.15145i	0.432122	+	0.362593i	0.832752	−	0.553647i	$-0.186764\pi$
$389$	8.52277	+	7.15145i	0.432122	+	0.362593i	−0.400630	+	0.916240i	$0.631209\pi$
$390$	0.757381	−	3.58046i	0.0383515	−	0.181304i
$391$	−15.5868	+	8.99902i	−0.788256	+	0.455100i
$392$	14.0988	+	10.1802i	0.712098	+	0.514176i
$393$	−0.530421	−	1.45732i	−0.0267562	−	0.0735121i
$394$	1.19994	+	1.53276i	0.0604522	+	0.0772191i
$395$	−2.80028	+	15.8812i	−0.140898	+	0.799070i
$396$	−2.95064	−	4.04451i	−0.148275	−	0.203244i
$397$	24.2313	−	20.3325i	1.21613	−	1.02046i	0.217116	−	0.976146i	$-0.430335\pi$
$397$	24.2313	−	20.3325i	1.21613	−	1.02046i	0.999018	−	0.0443116i	$-0.0141094\pi$
$398$	12.5317	+	23.5131i	0.628160	+	1.17861i
$399$	−1.33135	+	0.971930i	−0.0666508	+	0.0486574i
$400$	−1.51296	−	3.70283i	−0.0756481	−	0.185141i
$401$	0.0950610	+	0.113289i	0.00474712	+	0.00565740i	0.768413	−	0.639955i	$-0.221047\pi$
$401$	0.0950610	+	0.113289i	0.00474712	+	0.00565740i	−0.763666	+	0.645612i	$0.776602\pi$
$402$	−8.03210	+	1.13687i	−0.400605	+	0.0567020i
$403$	59.2104	+	10.4404i	2.94948	+	0.520073i
$404$	−3.17480	−	1.40606i	−0.157952	−	0.0699540i
$405$	7.06370	−	2.57098i	0.350998	−	0.127753i
$406$	0.0356198	−	1.04952i	0.00176778	−	0.0520870i
$407$	1.80189	+	3.12097i	0.0893164	+	0.154701i
$408$	−2.80191	+	2.72175i	−0.138715	+	0.134746i
$409$	23.9187	−	28.5052i	1.18271	−	1.40949i	0.291092	−	0.956695i	$-0.405981\pi$
$409$	23.9187	−	28.5052i	1.18271	−	1.40949i	0.891613	−	0.452798i	$-0.149574\pi$
$410$	−8.22448	+	13.1907i	−0.406178	+	0.651442i
$411$	−1.41908	+	2.45792i	−0.0699982	+	0.121240i
$412$	4.60603	−	18.6294i	0.226923	−	0.917803i
$413$	7.87303	−	1.38823i	0.387406	−	0.0683102i
$414$	−20.3347	+	6.62920i	−0.999396	+	0.325807i
$415$	−1.13868	+	3.12849i	−0.0558955	+	0.153572i
$416$	−0.175160	−	35.7243i	−0.00858792	−	1.75153i
$417$			6.42235i			0.314504i
$418$	5.43403	−	0.397801i	0.265787	−	0.0194571i
$419$			14.6602i			0.716197i	0.933684	+	0.358099i	$0.116575\pi$
$419$			14.6602i			0.716197i	−0.933684	+	0.358099i	$0.883425\pi$
$420$	0.752026	−	0.0805326i	0.0366951	−	0.00392959i
$421$	−10.3539	+	28.4471i	−0.504618	+	1.38643i	0.382103	+	0.924120i	$0.375200\pi$
$421$	−10.3539	+	28.4471i	−0.504618	+	1.38643i	−0.886720	+	0.462306i	$0.847022\pi$
$422$	−11.6953	−	35.8746i	−0.569317	−	1.74635i
$423$	−22.5006	+	3.96746i	−1.09402	+	0.192905i
$424$	−30.0780	+	7.59335i	−1.46072	+	0.368766i
$425$	1.68518	−	2.91883i	0.0817435	−	0.141584i
$426$	2.79817	+	1.74468i	0.135572	+	0.0845299i
$427$	0.0278791	−	0.0332250i	0.00134916	−	0.00160787i
$428$	−22.8831	+	6.61023i	−1.10610	+	0.319517i
$429$	−1.14364	−	1.98084i	−0.0552155	−	0.0956360i
$430$	3.41527	+	0.115911i	0.164699	+	0.00558971i
$431$	−25.1574	+	9.15653i	−1.21179	+	0.441054i	−0.867323	−	0.497745i	$-0.834161\pi$
$431$	−25.1574	+	9.15653i	−1.21179	+	0.441054i	−0.344464	+	0.938800i	$0.611939\pi$
$432$	−8.08668	+	5.09733i	−0.389071	+	0.245246i
$433$	29.8436	+	5.26224i	1.43419	+	0.252887i	0.836116	−	0.548552i	$-0.184821\pi$
$433$	29.8436	+	5.26224i	1.43419	+	0.252887i	0.598077	+	0.801439i	$0.295932\pi$
$434$	1.74135	+	12.3028i	0.0835876	+	0.590554i
$435$	0.211926	+	0.252564i	0.0101611	+	0.0121095i
$436$	7.60019	+	5.10474i	0.363983	+	0.244473i
$437$	5.57964	−	22.5982i	0.266910	−	1.08102i
$438$	−4.87359	+	2.59747i	−0.232869	+	0.124112i
$439$	6.05779	−	5.08309i	0.289122	−	0.242603i	−0.486677	−	0.873582i	$-0.661791\pi$
$439$	6.05779	−	5.08309i	0.289122	−	0.242603i	0.775800	+	0.630979i	$0.217347\pi$
$440$	−2.25018	−	1.08930i	−0.107273	−	0.0519304i
$441$	−3.02366	+	17.1480i	−0.143984	+	0.816572i
$442$	23.7021	−	18.5555i	1.12739	−	0.882597i
$443$	−3.49819	−	9.61119i	−0.166204	−	0.456641i	0.828431	−	0.560091i	$-0.189234\pi$
$443$	−3.49819	−	9.61119i	−0.166204	−	0.456641i	−0.994635	+	0.103450i	$0.967012\pi$
$444$	3.00038	−	1.47067i	0.142392	−	0.0697951i
$445$	−1.01504	+	0.586033i	−0.0481175	+	0.0277807i
$446$	−3.22099	−	0.681342i	−0.152518	−	0.0322625i
$447$	1.28568	+	1.07882i	0.0608107	+	0.0510263i
$448$	7.00813	−	2.32275i	0.331103	−	0.109740i
$449$	−9.94278	−	5.74046i	−0.469229	−	0.270909i	0.246688	−	0.969095i	$-0.420658\pi$
$449$	−9.94278	−	5.74046i	−0.469229	−	0.270909i	−0.715917	+	0.698186i	$0.753991\pi$
$450$	2.67707	−	2.97906i	0.126198	−	0.140434i
$451$	1.68705	+	9.56772i	0.0794399	+	0.450526i
$452$	−5.01714	+	5.21583i	−0.235986	+	0.245332i
$453$	0.586400	+	0.213432i	0.0275515	+	0.0100279i
$454$	−3.13852	+	7.79009i	−0.147298	+	0.365607i
$455$	−5.82826			−0.273233
$456$	−0.0263872	−	5.05185i	−0.00123569	−	0.236575i
$457$	−2.51419			−0.117609			−0.0588045	−	0.998270i	$-0.518729\pi$
$457$	−2.51419			−0.117609			−0.0588045	+	0.998270i	$0.518729\pi$
$458$	−9.45346	+	23.4644i	−0.441731	+	1.09642i
$459$	−7.56872	−	2.75479i	−0.353277	−	0.128582i
$460$	−7.40398	+	7.69720i	−0.345212	+	0.358884i
$461$	−3.30768	−	18.7588i	−0.154054	−	0.873685i	−0.959645	−	0.281213i	$-0.909263\pi$
$461$	−3.30768	−	18.7588i	−0.154054	−	0.873685i	0.805591	−	0.592472i	$-0.201848\pi$
$462$	0.315953	−	0.351594i	0.0146995	−	0.0163576i
$463$	16.0106	+	9.24370i	0.744074	+	0.429591i	0.823549	−	0.567246i	$-0.191991\pi$
$463$	16.0106	+	9.24370i	0.744074	+	0.429591i	−0.0794748	+	0.996837i	$0.525324\pi$
$464$	2.54390	+	1.97150i	0.118098	+	0.0915244i
$465$	−2.98842	−	2.50758i	−0.138584	−	0.116286i
$466$	19.9880	+	4.22811i	0.925928	+	0.195863i
$467$	7.71330	−	4.45327i	0.356929	−	0.206073i	−0.310804	−	0.950474i	$-0.600598\pi$
$467$	7.71330	−	4.45327i	0.356929	−	0.206073i	0.667733	+	0.744401i	$0.267265\pi$
$468$	32.1200	−	15.7440i	1.48475	−	0.727768i
$469$	4.41858	+	12.1400i	0.204031	+	0.560571i
$470$	−8.98357	+	7.03293i	−0.414381	+	0.324405i
$471$	0.243310	−	1.37988i	0.0112111	−	0.0635815i
$472$	−10.6759	+	22.0532i	−0.491397	+	1.01508i
$473$	1.63608	−	1.37283i	0.0752270	−	0.0631230i
$474$	8.24688	−	4.39532i	0.378792	−	0.201884i
$475$	1.21103	+	4.18729i	0.0555659	+	0.192126i
$476$	5.16416	+	3.46855i	0.236699	+	0.158981i
$477$	−19.9662	−	23.7948i	−0.914190	−	1.08949i
$478$	1.25352	+	8.85621i	0.0573345	+	0.405074i
$479$	35.5420	+	6.26701i	1.62395	+	0.286347i	0.910237	−	0.414087i	$-0.135899\pi$
$479$	35.5420	+	6.26701i	1.62395	+	0.286347i	0.713717	+	0.700434i	$0.247010\pi$
$480$	−1.14913	+	2.01309i	−0.0524505	+	0.0918844i
$481$	−24.1962	+	8.80671i	−1.10325	+	0.401551i
$482$	−25.5666	−	0.867706i	−1.16453	−	0.0395229i
$483$	−1.00971	−	1.74887i	−0.0459434	−	0.0795763i
$484$	19.6347	−	5.67187i	0.892488	−	0.257812i
$485$	6.26962	−	7.47184i	0.284689	−	0.339279i
$486$	−12.3001	−	7.66916i	−0.557942	−	0.347880i
$487$	5.44016	−	9.42263i	0.246517	−	0.426980i	−0.716040	−	0.698059i	$-0.754047\pi$
$487$	5.44016	−	9.42263i	0.246517	−	0.426980i	0.962557	+	0.271079i	$0.0873806\pi$
$488$	0.0325371	+	0.128883i	0.00147288	+	0.00583425i
$489$	4.08423	−	0.720159i	0.184695	−	0.0325667i
$490$	2.69501	+	8.26680i	0.121748	+	0.373456i
$491$	4.22305	−	11.6027i	0.190583	−	0.523623i	−0.807192	−	0.590289i	$-0.799014\pi$
$491$	4.22305	−	11.6027i	0.190583	−	0.523623i	0.997775	+	0.0666655i	$0.0212360\pi$
$492$	8.95684	−	0.959166i	0.403805	−	0.0432425i
$493$			2.71182i			0.122134i
$494$	−3.94299	+	38.7300i	−0.177404	+	1.74254i
$495$		−	2.50322i		−	0.112511i
$496$	−33.6937	−	17.7461i	−1.51289	−	0.796823i
$497$	1.79612	−	4.93479i	0.0805668	−	0.221356i
$498$	1.83428	−	0.597984i	0.0821962	−	0.0267963i
$499$	−25.5992	+	4.51384i	−1.14598	+	0.202067i	−0.714220	−	0.699922i	$-0.753218\pi$
$499$	−25.5992	+	4.51384i	−1.14598	+	0.202067i	−0.431760	+	0.901989i	$0.642107\pi$
$500$	0.480037	−	1.94154i	0.0214679	−	0.0868282i
$501$	3.47706	−	6.02245i	0.155344	−	0.269063i
$502$	13.1657	−	21.1157i	0.587616	−	0.942438i
$503$	−12.9017	+	15.3756i	−0.575257	+	0.685565i	−0.972701	−	0.232062i	$-0.925453\pi$
$503$	−12.9017	+	15.3756i	−0.575257	+	0.685565i	0.397444	+	0.917626i	$0.369897\pi$
$504$	5.15095	+	5.30266i	0.229442	+	0.236199i
$505$	−0.868057	−	1.50352i	−0.0386280	−	0.0669057i
$506$	−0.226414	+	6.67119i	−0.0100653	+	0.296571i
$507$	10.3514	−	3.76760i	0.459722	−	0.167325i
$508$	27.7776	+	12.3021i	1.23243	+	0.545820i
$509$	−18.7605	−	3.30798i	−0.831544	−	0.146624i	−0.258359	−	0.966049i	$-0.583182\pi$
$509$	−18.7605	−	3.30798i	−0.831544	−	0.146624i	−0.573186	+	0.819425i	$0.694293\pi$
$510$	−1.93384	+	0.273717i	−0.0856317	+	0.0121204i
$511$	5.65332	+	6.73736i	0.250088	+	0.298043i
$512$	−6.80206	+	21.5808i	−0.300612	+	0.953747i
$513$	9.35215	−	4.58779i	0.412907	−	0.202556i
$514$	−16.6518	−	31.2436i	−0.734480	−	1.37809i
$515$	7.35032	−	6.16765i	0.323894	−	0.271779i
$516$	−1.16711	−	1.59979i	−0.0513793	−	0.0704266i
$517$	−1.23821	+	7.02226i	−0.0544566	+	0.308839i
$518$	−3.28030	−	4.19012i	−0.144128	−	0.184103i
$519$	0.0944702	+	0.259555i	0.00414678	+	0.0113932i
$520$	10.4567	−	14.4818i	0.458556	−	0.635069i
$521$	24.7319	−	14.2790i	1.08352	−	0.625572i	0.151678	−	0.988430i	$-0.451532\pi$
$521$	24.7319	−	14.2790i	1.08352	−	0.625572i	0.931845	+	0.362858i	$0.118199\pi$
$522$	−0.666923	+	3.15283i	−0.0291904	+	0.137996i
$523$	−27.6243	−	23.1796i	−1.20793	−	1.01357i	−0.999367	−	0.0355618i	$-0.988678\pi$
$523$	−27.6243	−	23.1796i	−1.20793	−	1.01357i	−0.208560	−	0.978010i	$-0.566878\pi$
$524$	0.513208	−	7.55204i	0.0224196	−	0.329912i
$525$	0.327499	+	0.189082i	0.0142932	+	0.00825219i
$526$	27.6902	+	24.8833i	1.20735	+	1.08496i
$527$	−5.57186	−	31.5996i	−0.242714	−	1.37650i
$528$	0.306762	+	1.41587i	0.0133501	+	0.0616179i
$529$	5.18375	+	1.88673i	0.225381	+	0.0820318i
$530$	−14.3871	−	5.79636i	−0.624936	−	0.251778i
$531$	−24.5331			−1.06465
$532$	−7.86249	+	1.70612i	−0.340882	+	0.0739697i
$533$	−69.4162			−3.00675
$534$	0.629999	+	0.253818i	0.0272627	+	0.0109838i
$535$	−11.1911	−	4.07325i	−0.483836	−	0.176102i
$536$	−38.0924	−	10.8016i	−1.64534	−	0.466560i
$537$	−0.578839	−	3.28276i	−0.0249788	−	0.141662i
$538$	0.480641	+	0.431918i	0.0207219	+	0.0186213i
$539$	4.70626	+	2.71716i	0.202713	+	0.117036i
$540$	−4.76857	−	0.324054i	−0.205207	−	0.0139451i
$541$	−21.6120	−	18.1346i	−0.929173	−	0.779669i	0.0464959	−	0.998918i	$-0.485195\pi$
$541$	−21.6120	−	18.1346i	−0.929173	−	0.779669i	−0.975669	+	0.219250i	$0.929639\pi$
$542$	1.88236	−	8.89872i	0.0808544	−	0.382233i
$543$	−4.66741	+	2.69473i	−0.200298	+	0.115642i
$544$	−17.8837	+	6.60861i	−0.766757	+	0.283342i
$545$	1.56566	+	4.30163i	0.0670657	+	0.184262i
$546$	2.08197	+	2.65942i	0.0891002	+	0.113813i
$547$	0.0602333	−	0.341600i	0.00257539	−	0.0146058i	−0.983493	−	0.180946i	$-0.942084\pi$
$547$	0.0602333	−	0.341600i	0.00257539	−	0.0146058i	0.986068	+	0.166341i	$0.0531951\pi$
$548$	−11.1910	+	8.16435i	−0.478058	+	0.348764i
$549$	−0.101959	+	0.0855542i	−0.00435152	+	0.00365136i
$550$	−0.587916	−	1.10310i	−0.0250688	−	0.0470362i
$551$	−2.52842	−	2.43054i	−0.107714	−	0.103544i
$552$	6.15707	+	0.628826i	0.262062	+	0.0267646i
$553$	−9.56630	−	11.4007i	−0.406800	−	0.484806i
$554$	−1.05622	+	0.149498i	−0.0448744	+	0.00635157i
$555$	1.64533	+	0.290117i	0.0698405	+	0.0123148i
$556$	−12.6936	+	28.6614i	−0.538329	+	1.21552i
$557$	−4.23896	+	1.54285i	−0.179610	+	0.0653728i	−0.430260	−	0.902705i	$-0.641578\pi$
$557$	−4.23896	+	1.54285i	−0.179610	+	0.0653728i	0.250649	+	0.968078i	$0.419356\pi$
$558$	1.29337	−	38.1088i	0.0547529	−	1.61327i
$559$	7.62999	+	13.2155i	0.322714	+	0.558957i
$560$	3.51529	+	1.12696i	0.148548	+	0.0476228i
$561$	−0.784640	+	0.935097i	−0.0331275	+	0.0394798i
$562$	18.1822	−	29.1612i	0.766971	−	1.23009i
$563$	3.58969	−	6.21753i	0.151287	−	0.262038i	−0.780414	−	0.625264i	$-0.784991\pi$
$563$	3.58969	−	6.21753i	0.151287	−	0.262038i	0.931701	+	0.363226i	$0.118325\pi$
$564$	6.41823	+	1.58688i	0.270256	+	0.0668197i
$565$	−3.56361	+	0.628360i	−0.149922	+	0.0264353i
$566$	−14.1768	+	4.62168i	−0.595894	+	0.194264i
$567$	−2.37270	+	6.51893i	−0.0996439	+	0.273769i
$568$	9.03926	+	13.3166i	0.379279	+	0.558752i
$569$			11.4331i			0.479300i	0.970859	+	0.239650i	$0.0770326\pi$
$569$			11.4331i			0.479300i	−0.970859	+	0.239650i	$0.922967\pi$
$570$	1.47805	−	2.04838i	0.0619086	−	0.0857970i
$571$		−	10.5655i		−	0.442151i	−0.975257	−	0.221076i	$-0.929043\pi$
$571$		−	10.5655i		−	0.442151i	0.975257	−	0.221076i	$-0.0709568\pi$
$572$	−1.18872	−	11.1004i	−0.0497027	−	0.464132i
$573$	1.68531	−	4.63035i	0.0704049	−	0.193436i
$574$	−4.44648	−	13.6393i	−0.185593	−	0.569295i
$575$	−5.25895	+	0.927295i	−0.219313	+	0.0386709i
$576$	−22.4173	+	3.28516i	−0.934055	+	0.136882i
$577$	−8.75717	+	15.1679i	−0.364566	+	0.631446i	−0.988706	−	0.149866i	$-0.952116\pi$
$577$	−8.75717	+	15.1679i	−0.364566	+	0.631446i	0.624141	+	0.781312i	$0.285449\pi$
$578$	6.76904	+	4.22054i	0.281555	+	0.175551i
$579$	−2.15183	+	2.56446i	−0.0894272	+	0.106575i
$580$	0.446592	+	1.54600i	0.0185437	+	0.0641942i
$581$	−1.53626	−	2.66087i	−0.0637346	−	0.110392i
$582$	−5.64902	−	0.191722i	−0.234159	−	0.00794713i
$583$	−9.10956	+	3.31561i	−0.377279	+	0.137318i
$584$	−26.8835	+	1.95937i	−1.11245	+	0.0810792i
$585$	17.6138	+	3.10579i	0.728241	+	0.128409i
$586$	−2.08634	−	14.7402i	−0.0861859	−	0.608912i
$587$	2.51371	+	2.99572i	0.103752	+	0.123647i	0.815422	−	0.578868i	$-0.196505\pi$
$587$	2.51371	+	2.99572i	0.103752	+	0.123647i	−0.711670	+	0.702514i	$0.752061\pi$
$588$	2.80941	−	4.18280i	0.115858	−	0.172496i
$589$	34.4564	+	23.1270i	1.41975	+	0.952929i
$590$	−10.8111	+	5.76196i	−0.445085	+	0.237216i
$591$	0.432063	−	0.362544i	0.0177727	−	0.0149131i
$592$	16.2967	−	0.633104i	0.669791	−	0.0260204i
$593$	−3.61020	+	20.4745i	−0.148253	+	0.840785i	0.816444	+	0.577424i	$0.195942\pi$
$593$	−3.61020	+	20.4745i	−0.148253	+	0.840785i	−0.964697	+	0.263361i	$0.915169\pi$
$594$	−2.35214	+	1.84141i	−0.0965096	+	0.0755541i
$595$	1.06383	+	2.92286i	0.0436129	+	0.119826i
$596$	3.60545	+	7.35562i	0.147685	+	0.301298i
$597$	6.68579	−	3.86004i	0.273631	−	0.157981i
$598$	−46.6607	−	9.87023i	−1.90810	−	0.403624i
$599$	10.3488	+	8.68368i	0.422841	+	0.354805i	0.829242	−	0.558889i	$-0.188772\pi$
$599$	10.3488	+	8.68368i	0.422841	+	0.354805i	−0.406402	+	0.913694i	$0.633217\pi$
$600$	−1.05740	+	0.474516i	−0.0431681	+	0.0193720i
$601$	−13.5011	−	7.79486i	−0.550721	−	0.317959i	0.198692	−	0.980062i	$-0.436331\pi$
$601$	−13.5011	−	7.79486i	−0.550721	−	0.317959i	−0.749413	+	0.662103i	$0.769664\pi$
$602$	−2.10793	+	2.34572i	−0.0859129	+	0.0956043i
$603$	−6.88438	−	39.0432i	−0.280354	−	1.58996i
$604$	2.19512	+	2.11150i	0.0893182	+	0.0859157i
$605$	9.60250	+	3.49502i	0.390397	+	0.142093i
$606$	−0.375965	+	0.933180i	−0.0152725	+	0.0379078i
$607$	−23.6232			−0.958837			−0.479418	−	0.877586i	$-0.659152\pi$
$607$	−23.6232			−0.958837			−0.479418	+	0.877586i	$0.659152\pi$
$608$	9.86708	−	22.5974i	0.400163	−	0.916444i
$609$	−0.304272			−0.0123297
$610$	−0.0248371	+	0.0616480i	−0.00100563	+	0.00249605i
$611$	−47.8757	−	17.4253i	−1.93684	−	0.704953i
$612$	−13.7585	−	13.2343i	−0.556153	−	0.534967i
$613$	2.04427	+	11.5936i	0.0825673	+	0.468262i	0.997855	+	0.0654618i	$0.0208520\pi$
$613$	2.04427	+	11.5936i	0.0825673	+	0.468262i	−0.915288	+	0.402800i	$0.868037\pi$
$614$	31.3872	−	34.9278i	1.26668	−	1.40957i
$615$	3.90060	+	2.25201i	0.157287	+	0.0908099i
$616$	2.10494	−	0.944609i	0.0848104	−	0.0380594i
$617$	−1.07542	−	0.902384i	−0.0432948	−	0.0363286i	0.620884	−	0.783903i	$-0.286774\pi$
$617$	−1.07542	−	0.902384i	−0.0432948	−	0.0363286i	−0.664178	+	0.747574i	$0.731218\pi$
$618$	−5.43997	−	1.15073i	−0.218828	−	0.0462891i
$619$	−6.20379	+	3.58176i	−0.249352	+	0.143963i	−0.619467	−	0.785022i	$-0.712651\pi$
$619$	−6.20379	+	3.58176i	−0.249352	+	0.143963i	0.370116	+	0.928986i	$0.379318\pi$
$620$	−8.38043	−	17.0972i	−0.336566	−	0.686642i
$621$	4.36474	+	11.9920i	0.175151	+	0.481223i
$622$	−17.5620	+	13.7487i	−0.704172	+	0.551273i
$623$	0.187831	−	1.06524i	0.00752529	−	0.0426780i
$624$	−10.3434	+	0.401824i	−0.414066	+	0.0160858i
$625$	0.766044	−	0.642788i	0.0306418	−	0.0257115i
$626$	−6.98905	+	3.72494i	−0.279338	+	0.148878i
$627$	−0.168602	−	1.56968i	−0.00673330	−	0.0626870i
$628$	3.81313	−	5.67718i	0.152160	−	0.226544i
$629$	8.83309	+	10.5269i	0.352198	+	0.419734i
$630$	0.518014	+	3.65982i	0.0206382	+	0.145811i
$631$	18.5248	+	3.26643i	0.737462	+	0.130034i	0.529748	−	0.848155i	$-0.322287\pi$
$631$	18.5248	+	3.26643i	0.737462	+	0.130034i	0.207714	+	0.978190i	$0.433398\pi$
$632$	45.4911	−	3.31556i	1.80954	−	0.131886i
$633$	−10.2736	+	3.73930i	−0.408341	+	0.148624i
$634$	−25.1781	−	0.854520i	−0.999950	−	0.0339373i
$635$	7.59497	+	13.1549i	0.301397	+	0.522035i
$636$	2.49450	+	8.63538i	0.0989132	+	0.342415i
$637$	−24.9584	+	29.7443i	−0.988887	+	1.17851i
$638$	0.853444	+	0.532128i	0.0337882	+	0.0210672i
$639$	−8.05779	+	13.9565i	−0.318761	+	0.552110i
$640$	−9.10712	+	6.71270i	−0.359991	+	0.265343i
$641$	35.8787	−	6.32639i	1.41712	−	0.249877i	0.587964	−	0.808887i	$-0.299930\pi$
$641$	35.8787	−	6.32639i	1.41712	−	0.249877i	0.829161	+	0.559010i	$0.188819\pi$
$642$	2.13909	+	6.56155i	0.0844232	+	0.258964i
$643$	0.119826	−	0.329218i	0.00472546	−	0.0129831i	−0.937307	−	0.348504i	$-0.886690\pi$
$643$	0.119826	−	0.329218i	0.00472546	−	0.0129831i	0.942033	+	0.335520i	$0.108912\pi$
$644$	−1.04951	−	9.80045i	−0.0413563	−	0.386192i
$645$		−	0.990135i		−	0.0389865i
$646$	20.1427	−	5.09199i	0.792504	−	0.200342i
$647$			45.8927i			1.80423i	0.431498	+	0.902114i	$0.357985\pi$
$647$			45.8927i			1.80423i	−0.431498	+	0.902114i	$0.642015\pi$
$648$	−11.9410	−	17.5914i	−0.469087	−	0.691056i
$649$	−2.61872	+	7.19486i	−0.102794	+	0.282423i
$650$	8.49136	−	2.76822i	0.333058	−	0.108578i
$651$	3.54554	−	0.625175i	0.138961	−	0.0245025i
$652$	19.6503	+	4.85846i	0.769565	+	0.190272i
$653$	−4.71566	+	8.16777i	−0.184538	+	0.319629i	−0.943421	−	0.331598i	$-0.892412\pi$
$653$	−4.71566	+	8.16777i	−0.184538	+	0.319629i	0.758883	+	0.651227i	$0.225746\pi$
$654$	1.40354	−	2.25104i	0.0548827	−	0.0880226i
$655$	2.43278	−	2.89927i	0.0950564	−	0.113284i
$656$	41.8680	+	13.4224i	1.63467	+	0.524057i
$657$	−13.4949	−	23.3738i	−0.526485	−	0.911899i
$658$	0.357144	−	10.5231i	0.0139229	−	0.410234i
$659$	−14.6436	+	5.32985i	−0.570435	+	0.207621i	−0.611103	−	0.791551i	$-0.709274\pi$
$659$	−14.6436	+	5.32985i	−0.570435	+	0.207621i	0.0406676	+	0.999173i	$0.487052\pi$
$660$	−0.293326	+	0.662314i	−0.0114177	+	0.0257805i
$661$	−13.9065	−	2.45209i	−0.540900	−	0.0953753i	−0.103478	−	0.994632i	$-0.532997\pi$
$661$	−13.9065	−	2.45209i	−0.540900	−	0.0953753i	−0.437422	+	0.899256i	$0.644108\pi$
$662$	7.28636	−	1.03132i	0.283192	−	0.0400833i
$663$	−5.60627	−	6.68129i	−0.217729	−	0.259480i
$664$	9.36787	+	0.956748i	0.363544	+	0.0371290i
$665$	−3.67867	−	1.62781i	−0.142653	−	0.0631236i
$666$	7.68068	+	14.4111i	0.297620	+	0.558421i
$667$	3.29143	−	2.76184i	0.127445	−	0.106939i
$668$	27.4205	−	20.0044i	1.06093	−	0.773995i
$669$	−0.165647	+	0.939433i	−0.00640430	+	0.0363206i
$670$	−12.2036	−	15.5884i	−0.471467	−	0.602232i
$671$	0.0142072	+	0.0390340i	0.000548463	+	0.00150689i
$672$	−0.741501	−	2.00659i	−0.0286040	−	0.0774059i
$673$	−24.9734	+	14.4184i	−0.962654	+	0.555789i	−0.896989	−	0.442053i	$-0.854250\pi$
$673$	−24.9734	+	14.4184i	−0.962654	+	0.555789i	−0.0656652	+	0.997842i	$0.520917\pi$
$674$	4.35705	−	20.5976i	0.167827	−	0.793390i
$675$	−1.83068	−	1.53612i	−0.0704630	−	0.0591255i
$676$	53.6424	+	3.64534i	2.06317	+	0.140205i
$677$	38.7057	+	22.3468i	1.48758	+	0.858856i	0.999900	−	0.0141659i	$-0.00450929\pi$
$677$	38.7057	+	22.3468i	1.48758	+	0.858856i	0.487682	+	0.873021i	$0.337843\pi$
$678$	1.55971	+	1.40160i	0.0599004	+	0.0538283i
$679$	1.56311	+	8.86481i	0.0599865	+	0.340200i
$680$	−9.17125	−	2.60064i	−0.351701	−	0.0997300i
$681$	2.28671	+	0.832293i	0.0876268	+	0.0318935i
$682$	−11.0381	−	4.44711i	−0.422672	−	0.170289i
$683$	34.5160			1.32072			0.660358	−	0.750951i	$-0.270404\pi$
$683$	34.5160			1.32072			0.660358	+	0.750951i	$0.270404\pi$
$684$	24.6707	−	0.966332i	0.943308	−	0.0369486i
$685$	−6.92633			−0.264641
$686$	−15.9172	−	6.41282i	−0.607721	−	0.244842i
$687$	6.88773	+	2.50693i	0.262783	+	0.0956453i
$688$	−2.04662	−	9.44623i	−0.0780265	−	0.360134i
$689$	−12.0278	−	68.2129i	−0.458222	−	2.59870i
$690$	2.30173	+	2.06840i	0.0876252	+	0.0787427i
$691$	15.6373	+	9.02822i	0.594872	+	0.343450i	0.767022	−	0.641621i	$-0.221738\pi$
$691$	15.6373	+	9.02822i	0.594872	+	0.343450i	−0.172149	+	0.985071i	$0.555071\pi$
$692$	−0.0914045	+	1.34505i	−0.00347468	+	0.0511311i
$693$	1.76969	+	1.48494i	0.0672249	+	0.0564084i
$694$	−3.55339	+	16.7984i	−0.134885	+	0.637657i
$695$	−13.5735	+	7.83664i	−0.514870	+	0.297261i
$696$	0.545905	−	0.756041i	0.0206925	−	0.0286577i
$697$	12.6705	+	34.8120i	0.479931	+	1.31860i
$698$	4.71131	+	6.01803i	0.178326	+	0.227786i
$699$	1.02793	−	5.82970i	0.0388800	−	0.220500i
$700$	1.08784	+	1.49112i	0.0411163	+	0.0563590i
$701$	−19.9231	+	16.7174i	−0.752484	+	0.631409i	−0.936159	−	0.351578i	$-0.885645\pi$
$701$	−19.9231	+	16.7174i	−0.752484	+	0.631409i	0.183675	+	0.982987i	$0.441201\pi$
$702$	−10.0387	−	18.8355i	−0.378886	−	0.710899i
$703$	−17.7318	−	1.19929i	−0.668769	−	0.0452319i
$704$	−1.42942	+	6.92501i	−0.0538734	+	0.260996i
$705$	2.12489	+	2.53235i	0.0800281	+	0.0953737i
$706$	−32.8450	+	4.64891i	−1.23614	+	0.174964i
$707$	1.57788	+	0.278223i	0.0593423	+	0.0104636i
$708$	6.49111	+	2.87479i	0.243951	+	0.108041i
$709$	38.3438	−	13.9560i	1.44003	−	0.524128i	0.500242	−	0.865886i	$-0.333244\pi$
$709$	38.3438	−	13.9560i	1.44003	−	0.524128i	0.939788	+	0.341758i	$0.111022\pi$
$710$	−0.272962	+	8.04273i	−0.0102441	+	0.301838i
$711$	22.8354	+	39.5521i	0.856396	+	1.48332i
$712$	2.30987	+	2.37790i	0.0865661	+	0.0891157i
$713$	−32.6789	+	38.9452i	−1.22383	+	1.45851i
$714$	0.953672	−	1.52953i	0.0356903	−	0.0572412i
$715$	2.79097	−	4.83410i	0.104376	−	0.180785i
$716$	3.90506	−	15.7942i	0.145939	−	0.590259i
$717$	2.55227	−	0.450034i	0.0953162	−	0.0168068i
$718$	33.1163	−	10.7961i	1.23589	−	0.402905i
$719$	5.85261	−	16.0799i	0.218266	−	0.599680i	−0.781439	−	0.623982i	$-0.785514\pi$
$719$	5.85261	−	16.0799i	0.218266	−	0.599680i	0.999705	+	0.0243017i	$0.00773623\pi$
$720$	−10.0231	−	5.27907i	−0.373540	−	0.196739i
$721$			8.85517i			0.329784i
$722$	−13.3058	+	23.3443i	−0.495192	+	0.868784i
$723$			7.41213i			0.275660i
$724$	−26.1556	+	2.80094i	−0.972065	+	0.104096i
$725$	−0.275191	+	0.756082i	−0.0102203	+	0.0280802i
$726$	−1.83543	−	5.63009i	−0.0681194	−	0.208952i
$727$	−6.91335	+	1.21901i	−0.256402	+	0.0452106i	−0.300372	−	0.953822i	$-0.597111\pi$
$727$	−6.91335	+	1.21901i	−0.256402	+	0.0452106i	0.0439695	+	0.999033i	$0.486000\pi$
$728$	4.03507	+	15.9833i	0.149550	+	0.592382i
$729$	9.17559	−	15.8926i	0.339837	−	0.588614i
$730$	−11.4365	−	7.13073i	−0.423283	−	0.263920i
$731$	5.23486	−	6.23866i	0.193618	−	0.230745i
$732$	0.0370022	−	0.0106888i	0.00136764	−	0.000395069i
$733$	8.98091	+	15.5554i	0.331717	+	0.574551i	0.982849	−	0.184414i	$-0.0590386\pi$
$733$	8.98091	+	15.5554i	0.331717	+	0.574551i	−0.651131	+	0.758965i	$0.725705\pi$
$734$	−44.5506	−	1.51200i	−1.64439	−	0.0558091i
$735$	2.36742	−	0.861670i	0.0873236	−	0.0317832i
$736$	26.2347	+	14.9756i	0.967023	+	0.552007i
$737$	−12.1851	−	2.14856i	−0.448844	−	0.0791433i
$738$	6.16969	+	43.5895i	0.227110	+	1.60455i
$739$	−6.76426	−	8.06133i	−0.248827	−	0.296541i	0.627145	−	0.778903i	$-0.284223\pi$
$739$	−6.76426	−	8.06133i	−0.248827	−	0.296541i	−0.875972	+	0.482362i	$0.839779\pi$
$740$	6.76932	+	4.54668i	0.248845	+	0.167139i
$741$	11.2542	+	0.761174i	0.413433	+	0.0279624i
$742$	12.6325	−	6.73270i	0.463753	−	0.247165i
$743$	12.0155	−	10.0822i	0.440806	−	0.369880i	−0.395205	−	0.918593i	$-0.629326\pi$
$743$	12.0155	−	10.0822i	0.440806	−	0.369880i	0.836011	+	0.548713i	$0.184882\pi$
$744$	−4.80778	+	9.93146i	−0.176262	+	0.364105i
$745$	−0.711239	+	4.03364i	−0.0260578	+	0.147781i
$746$	12.1901	−	9.54322i	0.446312	−	0.349402i
$747$	3.22484	+	8.86017i	0.117991	+	0.324177i
$748$	−5.34986	+	2.62230i	−0.195610	+	0.0958808i
$749$	9.51840	−	5.49545i	0.347795	−	0.200799i
$750$	−0.566949	−	0.119928i	−0.0207021	−	0.00437915i
$751$	8.47109	+	7.10809i	0.309114	+	0.259378i	0.784126	−	0.620602i	$-0.213112\pi$
$751$	8.47109	+	7.10809i	0.309114	+	0.259378i	−0.475012	+	0.879980i	$0.657556\pi$
$752$	25.5066	+	19.7673i	0.930130	+	0.720840i
$753$	−6.24408	−	3.60502i	−0.227547	−	0.131374i
$754$	−4.80319	+	5.34501i	−0.174922	+	0.194654i
$755$	0.264450	+	1.49977i	0.00962432	+	0.0545822i
$756$	3.05788	−	3.17899i	0.111214	−	0.115619i
$757$	3.05465	+	1.11180i	0.111023	+	0.0404091i	0.396934	−	0.917847i	$-0.370074\pi$
$757$	3.05465	+	1.11180i	0.111023	+	0.0404091i	−0.285911	+	0.958256i	$0.592296\pi$
$758$	8.60163	−	21.3500i	0.312425	−	0.775468i
$759$	1.93407			0.0702024
$760$	10.6447	−	6.22010i	0.386125	−	0.225627i
$761$	11.0953			0.402206			0.201103	−	0.979570i	$-0.435547\pi$
$761$	11.0953			0.402206			0.201103	+	0.979570i	$0.435547\pi$
$762$	3.28946	−	8.16475i	0.119165	−	0.295778i
$763$	−3.96988	−	1.44492i	−0.143719	−	0.0523096i
$764$	16.6729	−	17.3332i	0.603204	−	0.627093i
$765$	−1.65751	−	9.40019i	−0.0599273	−	0.339864i
$766$	6.87770	−	7.65354i	0.248502	−	0.276534i
$767$	−47.3774	−	27.3533i	−1.71070	−	0.987671i
$768$	6.31624	+	1.75765i	0.227918	+	0.0634236i
$769$	32.0838	+	26.9215i	1.15697	+	0.970816i	0.999859	−	0.0167648i	$-0.00533666\pi$
$769$	32.0838	+	26.9215i	1.15697	+	0.970816i	0.157114	+	0.987581i	$0.449781\pi$
$770$	1.12861	+	0.238738i	0.0406724	+	0.00860350i
$771$	−8.88388	+	5.12911i	−0.319945	+	0.184720i
$772$	−14.6717	+	7.19152i	−0.528046	+	0.258829i
$773$	−6.83653	−	18.7832i	−0.245893	−	0.675586i	−0.999826	−	0.0186346i	$-0.994068\pi$
$773$	−6.83653	−	18.7832i	−0.245893	−	0.675586i	0.753933	−	0.656951i	$-0.228154\pi$
$774$	7.62046	−	5.96580i	0.273912	−	0.214436i
$775$	1.65319	−	9.37571i	0.0593843	−	0.336785i
$776$	−24.8313	−	12.0207i	−0.891392	−	0.431519i
$777$	−1.18114	+	0.991093i	−0.0423731	+	0.0355553i
$778$	13.8851	−	7.40033i	0.497806	−	0.265315i
$779$	−43.8140	−	19.3876i	−1.56980	−	0.694633i
$780$	−4.29642	−	2.88573i	−0.153836	−	0.103326i
$781$	3.23293	+	3.85286i	0.115683	+	0.137866i
$782$	3.56710	+	25.2019i	0.127559	+	0.901217i
$783$	1.89362	+	0.333897i	0.0676726	+	0.0119325i
$784$	20.8049	−	13.1141i	0.743033	−	0.468361i
$785$	3.21322	−	1.16952i	0.114685	−	0.0417419i
$786$	−2.19197	−	0.0743932i	−0.0781849	−	0.00265352i
$787$	2.72298	+	4.71635i	0.0970639	+	0.168120i	0.910468	−	0.413579i	$-0.135722\pi$
$787$	2.72298	+	4.71635i	0.0970639	+	0.168120i	−0.813404	+	0.581699i	$0.802388\pi$
$788$	2.64475	−	0.763988i	0.0942155	−	0.0272159i
$789$	6.93357	−	8.26311i	0.246842	−	0.294174i
$790$	19.3523	+	12.0663i	0.688525	+	0.429300i
$791$	1.66976	−	2.89210i	0.0593697	−	0.102831i
$792$	−6.86478	+	1.73305i	−0.243929	+	0.0615812i
$793$	−0.292289	+	0.0515384i	−0.0103795	+	0.00183018i
$794$	−13.8653	−	42.5310i	−0.492060	−	1.50937i
$795$	−1.53712	+	4.22319i	−0.0545159	+	0.149781i
$796$	37.4663	−	4.01218i	1.32796	−	0.142208i
$797$			20.7404i			0.734662i	0.930090	+	0.367331i	$0.119728\pi$
$797$			20.7404i			0.734662i	−0.930090	+	0.367331i	$0.880272\pi$
$798$	0.571332	+	2.26006i	0.0202249	+	0.0800051i
$799$			27.1902i			0.961920i
$800$	−5.65679	+	0.0277358i	−0.199998	+	0.000980608i
$801$	−1.13530	+	3.11922i	−0.0401139	+	0.110212i
$802$	0.198846	−	0.0648247i	0.00702151	−	0.00228904i
$803$	−8.29533	+	1.46269i	−0.292736	+	0.0516172i
$804$	−2.75357	+	11.1370i	−0.0971109	+	0.392771i
$805$	2.46412	−	4.26798i	0.0868489	−	0.150427i
$806$	44.9872	−	72.1520i	1.58461	−	2.54144i
$807$	0.120351	−	0.143429i	0.00423657	−	0.00504895i
$808$	−3.52225	+	3.42148i	−0.123912	+	0.120367i
$809$	22.9368	+	39.7277i	0.806414	+	1.39675i	0.915332	+	0.402700i	$0.131928\pi$
$809$	22.9368	+	39.7277i	0.806414	+	1.39675i	−0.108918	+	0.994051i	$0.534739\pi$
$810$	0.360587	−	10.6246i	0.0126697	−	0.373309i
$811$	−5.35173	+	1.94787i	−0.187925	+	0.0683990i	−0.434268	−	0.900784i	$-0.642993\pi$
$811$	−5.35173	+	1.94787i	−0.187925	+	0.0683990i	0.246344	+	0.969183i	$0.420771\pi$
$812$	−1.35789	−	0.601385i	−0.0476527	−	0.0211045i
$813$	−2.59540	−	0.457639i	−0.0910246	−	0.0160501i
$814$	5.04622	−	0.714247i	0.176870	−	0.0250343i
$815$	6.50566	+	7.75314i	0.227883	+	0.271581i
$816$	2.08949	+	5.11382i	0.0731468	+	0.179020i
$817$	1.12485	+	10.4724i	0.0393536	+	0.366382i
$818$	−24.7511	−	46.4402i	−0.865403	−	1.62374i
$819$	−12.6445	+	10.6100i	−0.441833	+	0.370742i
$820$	12.9564	+	17.7596i	0.452458	+	0.620193i
$821$	−3.29373	+	18.6797i	−0.114952	+	0.651926i	0.871822	+	0.489823i	$0.162939\pi$
$821$	−3.29373	+	18.6797i	−0.114952	+	0.651926i	−0.986774	+	0.162102i	$0.948172\pi$
$822$	2.47422	+	3.16047i	0.0862985	+	0.110234i
$823$	3.06655	+	8.42528i	0.106893	+	0.293687i	0.981595	−	0.190975i	$-0.0611649\pi$
$823$	3.06655	+	8.42528i	0.106893	+	0.293687i	−0.874702	+	0.484662i	$0.838943\pi$
$824$	−22.0029	−	15.8874i	−0.766508	−	0.553463i
$825$	−0.313658	+	0.181090i	−0.0109202	+	0.00630476i
$826$	2.33978	−	11.0611i	0.0814115	−	0.384866i
$827$	10.7634	+	9.03159i	0.374281	+	0.314059i	0.810452	−	0.585805i	$-0.199221\pi$
$827$	10.7634	+	9.03159i	0.374281	+	0.314059i	−0.436171	+	0.899864i	$0.643666\pi$
$828$	−2.05076	+	30.1776i	−0.0712687	+	1.04874i
$829$	30.9897	+	17.8919i	1.07632	+	0.621412i	0.929900	−	0.367811i	$-0.119893\pi$
$829$	30.9897	+	17.8919i	1.07632	+	0.621412i	0.146416	+	0.989223i	$0.453226\pi$
$830$	3.50204	+	3.14703i	0.121557	+	0.109235i
$831$	0.0536723	+	0.304391i	0.00186187	+	0.0105592i
$832$	−46.9541	−	18.6501i	−1.62784	−	0.646576i
$833$	19.4723	+	7.08735i	0.674676	+	0.245562i
$834$	8.42455	+	3.39413i	0.291718	+	0.117529i
$835$	16.9710			0.587306
$836$	2.35000	−	7.33835i	0.0812765	−	0.253802i
$837$	−22.7516			−0.786409
$838$	19.2306	+	7.74773i	0.664309	+	0.267641i
$839$	28.6550	+	10.4296i	0.989281	+	0.360069i	0.785442	−	0.618936i	$-0.212436\pi$
$839$	28.6550	+	10.4296i	0.989281	+	0.360069i	0.203839	+	0.979004i	$0.434658\pi$
$840$	0.291798	−	1.02903i	0.0100680	−	0.0355051i
$841$	4.92338	+	27.9219i	0.169772	+	0.962823i
$842$	31.8437	+	28.6157i	1.09741	+	0.986162i
$843$	−8.62323	−	4.97862i	−0.297000	−	0.171473i
$844$	−53.2395	−	3.61796i	−1.83258	−	0.124535i
$845$	20.5936	+	17.2801i	0.708443	+	0.594454i
$846$	−6.68695	+	31.6120i	−0.229902	+	1.08684i
$847$	−8.16721	+	4.71534i	−0.280629	+	0.162021i
$848$	−5.93525	+	43.4680i	−0.203817	+	1.49270i
$849$	1.47768	+	4.05989i	0.0507139	+	0.139335i
$850$	−2.93818	−	3.75311i	−0.100779	−	0.128731i
$851$	3.78082	−	21.4421i	0.129605	−	0.735025i
$852$	3.76739	−	2.74847i	0.129069	−	0.0941611i
$853$	16.4045	−	13.7650i	0.561680	−	0.471306i	−0.317193	−	0.948361i	$-0.602740\pi$
$853$	16.4045	−	13.7650i	0.561680	−	0.471306i	0.878873	+	0.477055i	$0.158296\pi$
$854$	−0.0288493	−	0.0541295i	−0.000987202	−	0.00185227i
$855$	10.2500	+	6.87976i	0.350544	+	0.235283i
$856$	−3.42245	+	33.5105i	−0.116977	+	1.14536i
$857$	−11.4787	−	13.6797i	−0.392104	−	0.467291i	0.533492	−	0.845805i	$-0.320880\pi$
$857$	−11.4787	−	13.6797i	−0.392104	−	0.467291i	−0.925595	+	0.378514i	$0.876435\pi$
$858$	−3.20278	+	0.453325i	−0.109341	+	0.0154763i
$859$	−10.8623	−	1.91532i	−0.370618	−	0.0653499i	−0.0147626	−	0.999891i	$-0.504699\pi$
$859$	−10.8623	−	1.91532i	−0.370618	−	0.0653499i	−0.355855	+	0.934541i	$0.615810\pi$
$860$	1.95697	−	4.41874i	0.0667322	−	0.150678i
$861$	−3.90599	+	1.42166i	−0.133116	+	0.0484502i
$862$	−1.28423	+	37.8394i	−0.0437411	+	1.28881i
$863$	−11.7325	−	20.3213i	−0.399380	−	0.691746i	0.594270	−	0.804266i	$-0.297441\pi$
$863$	−11.7325	−	20.3213i	−0.399380	−	0.691746i	−0.993650	+	0.112520i	$0.964108\pi$
$864$	2.41274	+	13.3016i	0.0820831	+	0.452530i
$865$	−0.433288	+	0.516372i	−0.0147322	+	0.0175572i
$866$	22.6747	−	36.3665i	0.770519	−	1.23578i
$867$	1.15566	−	2.00166i	0.0392483	−	0.0679801i
$868$	17.0586	+	4.21766i	0.579006	+	0.143157i
$869$	14.0370	−	2.47510i	0.476172	−	0.0839620i
$870$	0.443303	−	0.144518i	0.0150294	−	0.00489964i
$871$	30.2366	−	83.0744i	1.02453	−	2.81487i
$872$	10.7128	−	7.27180i	0.362780	−	0.246254i
$873$		−	27.6236i		−	0.934919i
$874$	−26.6946	−	19.2620i	−0.902957	−	0.651547i
$875$			0.922878i			0.0311990i
$876$	0.831608	+	7.76569i	0.0280974	+	0.262378i
$877$	−11.5525	+	31.7402i	−0.390099	+	1.07179i	0.576857	+	0.816845i	$0.304279\pi$
$877$	−11.5525	+	31.7402i	−0.390099	+	1.07179i	−0.966956	+	0.254944i	$0.917943\pi$
$878$	−3.46630	−	10.6327i	−0.116982	−	0.358836i
$879$	−4.24797	+	0.749032i	−0.143280	+	0.0252642i
$880$	−2.61809	+	2.37600i	−0.0882557	+	0.0800949i
$881$	−17.8632	+	30.9399i	−0.601825	+	1.04239i	0.390719	+	0.920510i	$0.372226\pi$
$881$	−17.8632	+	30.9399i	−0.601825	+	1.04239i	−0.992545	+	0.121882i	$0.961107\pi$
$882$	20.8960	+	13.0288i	0.703606	+	0.438703i
$883$	20.0846	−	23.9359i	0.675900	−	0.805506i	−0.313674	−	0.949531i	$-0.601560\pi$
$883$	20.0846	−	23.9359i	0.675900	−	0.805506i	0.989574	+	0.144024i	$0.0460044\pi$
$884$	−11.8141	−	40.8977i	−0.397350	−	1.37554i
$885$	1.77480	+	3.07405i	0.0596594	+	0.103333i
$886$	−14.4563	−	0.490631i	−0.485668	−	0.0164831i
$887$	40.3871	−	14.6997i	1.35606	−	0.493567i	0.441229	−	0.897394i	$-0.354543\pi$
$887$	40.3871	−	14.6997i	1.35606	−	0.493567i	0.914835	+	0.403827i	$0.132320\pi$
$888$	−0.343500	−	4.71299i	−0.0115271	−	0.158158i
$889$	−13.8055	−	2.43428i	−0.463021	−	0.0816431i
$890$	0.232296	+	1.64119i	0.00778659	+	0.0550130i
$891$	−4.27075	−	5.08969i	−0.143076	−	0.170511i
$892$	−2.59601	+	3.86507i	−0.0869207	+	0.129412i
$893$	−25.3513	−	24.3699i	−0.848349	−	0.815509i
$894$	2.09461	−	1.11636i	0.0700543	−	0.0373367i
$895$	6.23171	−	5.22903i	0.208303	−	0.174787i
$896$	0.656827	−	10.4205i	0.0219430	−	0.348124i
$897$	−2.39964	+	13.6091i	−0.0801218	+	0.454393i
$898$	−12.7847	+	10.0087i	−0.426632	+	0.333995i
$899$	2.61991	+	7.19816i	0.0873791	+	0.240072i
$900$	−2.49300	−	5.08606i	−0.0830998	−	0.169535i
$901$	−32.0132	+	18.4828i	−1.06651	+	0.615752i
$902$	13.4421	+	2.84343i	0.447572	+	0.0946758i
$903$	0.699991	+	0.587363i	0.0232943	+	0.0195462i
$904$	4.19040	+	9.33776i	0.139371	+	0.310569i
$905$	−11.3905	−	6.57628i	−0.378632	−	0.218603i
$906$	0.589875	−	0.656416i	0.0195973	−	0.0218080i
$907$	5.89270	+	33.4192i	0.195664	+	1.10966i	0.911470	+	0.411366i	$0.134948\pi$
$907$	5.89270	+	33.4192i	0.195664	+	1.10966i	−0.715806	+	0.698299i	$0.753941\pi$
$908$	8.56003	+	8.23394i	0.284074	+	0.273253i
$909$	−4.62031	−	1.68166i	−0.153246	−	0.0557770i
$910$	−3.08016	+	7.64525i	−0.102106	+	0.253437i
$911$	−51.5855			−1.70910			−0.854552	−	0.519366i	$-0.826168\pi$
$911$	−51.5855			−1.70910			−0.854552	+	0.519366i	$0.826168\pi$
$912$	−6.64073	−	2.63523i	−0.219897	−	0.0872611i
$913$	2.94266			0.0973878
$914$	−1.32872	+	3.29800i	−0.0439501	+	0.109088i
$915$	0.0180962	+	0.00658646i	0.000598241	+	0.000217742i
$916$	25.7834	+	24.8012i	0.851909	+	0.819456i
$917$	0.606526	+	3.43978i	0.0200292	+	0.113591i
$918$	−7.61358	+	8.47243i	−0.251286	+	0.279632i
$919$	11.2283	+	6.48268i	0.370389	+	0.213844i	0.673628	−	0.739070i	$-0.264735\pi$
$919$	11.2283	+	6.48268i	0.370389	+	0.213844i	−0.303240	+	0.952914i	$0.598068\pi$
$920$	6.18392	+	13.7801i	0.203878	+	0.454316i
$921$	−10.4229	−	8.74585i	−0.343446	−	0.288186i
$922$	−26.3550	−	5.57493i	−0.867957	−	0.183600i
$923$	−31.1217	+	17.9681i	−1.02438	+	0.591428i
$924$	−0.294228	−	0.600266i	−0.00967939	−	0.0197473i
$925$	1.39450	+	3.83137i	0.0458510	+	0.125975i
$926$	20.5869	−	16.1167i	0.676526	−	0.529629i
$927$	4.71879	−	26.7616i	0.154985	−	0.878965i
$928$	3.93054	−	2.29507i	0.129026	−	0.0753393i
$929$	18.5664	−	15.5790i	0.609143	−	0.511132i	−0.285227	−	0.958460i	$-0.592069\pi$
$929$	18.5664	−	15.5790i	0.609143	−	0.511132i	0.894370	+	0.447329i	$0.147625\pi$
$930$	−4.86867	+	2.59484i	−0.159650	+	0.0850883i
$931$	−24.0606	+	11.8032i	−0.788555	+	0.386834i
$932$	16.1097	−	23.9849i	0.527690	−	0.785652i
$933$	4.15396	+	4.95049i	0.135994	+	0.162072i
$934$	−1.76522	−	12.4715i	−0.0577598	−	0.408078i
$935$	−2.93373	−	0.517295i	−0.0959431	−	0.0169174i
$936$	−3.67728	−	50.4541i	−0.120196	−	1.64914i
$937$	48.5056	−	17.6546i	1.58461	−	0.576750i	0.608408	−	0.793625i	$-0.291809\pi$
$937$	48.5056	−	17.6546i	1.58461	−	0.576750i	0.976199	+	0.216875i	$0.0695863\pi$
$938$	18.2598	+	0.619720i	0.596204	+	0.0202346i
$939$	1.14736	+	1.98728i	0.0374426	+	0.0648526i
$940$	4.47778	+	15.5011i	0.146049	+	0.505589i
$941$	27.9490	−	33.3083i	0.911111	−	1.08582i	−0.0848817	−	0.996391i	$-0.527051\pi$
$941$	27.9490	−	33.3083i	0.911111	−	1.08582i	0.995993	−	0.0894294i	$-0.0285043\pi$
$942$	−1.68148	−	1.04841i	−0.0547855	−	0.0341591i
$943$	29.3484	−	50.8328i	0.955714	−	1.65535i
$944$	23.2863	+	25.6590i	0.757906	+	0.835129i
$945$	2.17198	−	0.382978i	0.0706544	−	0.0124583i
$946$	−0.936174	−	2.87166i	−0.0304376	−	0.0933658i
$947$	−11.4222	+	31.3823i	−0.371173	+	1.01979i	0.603736	+	0.797184i	$0.293678\pi$
$947$	−11.4222	+	31.3823i	−0.371173	+	1.01979i	−0.974909	+	0.222604i	$0.928544\pi$
$948$	−1.40721	−	13.1408i	−0.0457041	−	0.426792i
$949$		−	60.1846i		−	1.95368i
$950$	6.13271	+	0.624355i	0.198972	+	0.0202568i
$951$			7.29949i			0.236702i
$952$	7.27908	−	4.94102i	0.235916	−	0.160139i
$953$	−2.07788	+	5.70893i	−0.0673092	+	0.184930i	−0.968787	−	0.247895i	$-0.920261\pi$
$953$	−2.07788	+	5.70893i	−0.0673092	+	0.184930i	0.901478	+	0.432826i	$0.142483\pi$
$954$	−41.7648	+	13.6155i	−1.35219	+	0.440819i
$955$	11.8425	−	2.08816i	0.383216	−	0.0675713i
$956$	12.2796	+	3.03609i	0.397152	+	0.0981942i
$957$	0.145706	−	0.252371i	0.00471002	−	0.00815799i
$958$	27.0043	−	43.3103i	0.872469	−	1.39929i
$959$	4.10880	−	4.89668i	0.132680	−	0.158122i
$960$	2.03337	+	2.57127i	0.0656269	+	0.0829875i
$961$	−29.8184	−	51.6471i	−0.961885	−	1.66603i
$962$	−1.23517	+	36.3938i	−0.0398234	+	1.17338i
$963$	−31.6944	+	11.5358i	−1.02134	+	0.371736i
$964$	−14.6499	+	33.0786i	−0.471840	+	1.06539i
$965$	−8.04560	−	1.41866i	−0.258997	−	0.0456682i
$966$	−2.82771	+	0.400236i	−0.0909800	+	0.0128774i
$967$	−20.7172	−	24.6898i	−0.666221	−	0.793971i	0.322043	−	0.946725i	$-0.395630\pi$
$967$	−20.7172	−	24.6898i	−0.666221	−	0.793971i	−0.988264	+	0.152754i	$0.951186\pi$
$968$	2.93661	−	28.7535i	0.0943864	−	0.924171i
$969$	−1.67251	−	5.78289i	−0.0537286	−	0.185773i
$970$	−6.48780	−	12.1730i	−0.208311	−	0.390851i
$971$	26.2840	−	22.0549i	0.843493	−	0.707775i	−0.114854	−	0.993382i	$-0.536640\pi$
$971$	26.2840	−	22.0549i	0.843493	−	0.707775i	0.958347	+	0.285608i	$0.0921954\pi$
$972$	−16.5605	+	12.0816i	−0.531178	+	0.387517i
$973$	2.51174	−	14.2448i	0.0805226	−	0.456667i
$974$	−9.48512	−	12.1159i	−0.303923	−	0.388218i
$975$	−0.885076	−	2.43173i	−0.0283451	−	0.0778776i
$976$	0.186258	+	0.0254322i	0.00596197	+	0.000814066i
$977$	−18.7469	+	10.8235i	−0.599765	+	0.346274i	−0.768949	−	0.639310i	$-0.779220\pi$
$977$	−18.7469	+	10.8235i	−0.599765	+	0.346274i	0.169184	+	0.985584i	$0.445887\pi$
$978$	1.21379	−	5.73810i	0.0388127	−	0.183484i
$979$	0.793592	+	0.665903i	0.0253633	+	0.0212823i
$980$	12.2683	+	0.833708i	0.391896	+	0.0266318i
$981$	11.2276	+	6.48223i	0.358468	+	0.206962i
$982$	−12.9881	−	11.6715i	−0.414467	−	0.372452i
$983$	−1.02555	−	5.81618i	−0.0327100	−	0.185507i	0.964075	−	0.265630i	$-0.0855799\pi$
$983$	−1.02555	−	5.81618i	−0.0327100	−	0.185507i	−0.996785	+	0.0801226i	$0.974469\pi$
$984$	3.47539	−	12.2561i	0.110791	−	0.390710i
$985$	1.29344	+	0.470772i	0.0412123	+	0.0150000i
$986$	3.55724	+	1.43316i	0.113286	+	0.0456412i
$987$	−3.05080			−0.0971081
$988$	48.7204	+	25.6405i	1.55000	+	0.815734i
$989$	−12.9035			−0.410307
$990$	−3.28361	−	1.32292i	−0.104360	−	0.0420451i
$991$	11.2099	+	4.08005i	0.356093	+	0.129607i	0.513871	−	0.857867i	$-0.328211\pi$
$991$	11.2099	+	4.08005i	0.356093	+	0.129607i	−0.157778	+	0.987475i	$0.550433\pi$
$992$	−41.0852	+	34.8193i	−1.30446	+	1.10551i
$993$	−0.370261	−	2.09985i	−0.0117499	−	0.0666368i
$994$	−5.52401	−	4.96404i	−0.175211	−	0.157450i
$995$	16.3162	+	9.42014i	0.517257	+	0.298638i
$996$	0.184988	−	2.72216i	0.00586156	−	0.0862548i
$997$	−37.5575	−	31.5145i	−1.18946	−	0.998073i	−0.999869	−	0.0162096i	$-0.994840\pi$
$997$	−37.5575	−	31.5145i	−1.18946	−	0.998073i	−0.189589	−	0.981864i	$-0.560715\pi$
$998$	−7.60783	+	35.9654i	−0.240822	+	1.13847i
$999$	8.43835	−	4.87188i	0.266977	−	0.154140i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.be.b.51.12	yes	120
4.3	odd	2	inner	380.2.be.b.51.2	✓	120
19.3	odd	18	inner	380.2.be.b.231.2	yes	120
76.3	even	18	inner	380.2.be.b.231.12	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.be.b.51.2	✓	120	4.3	odd	2	inner
380.2.be.b.51.12	yes	120	1.1	even	1	trivial
380.2.be.b.231.2	yes	120	19.3	odd	18	inner
380.2.be.b.231.12	yes	120	76.3	even	18	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:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.be (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.528488 - 1.31175i) q^{2} +(-0.385053 - 0.140148i) q^{3} +(-1.44140 - 1.38649i) q^{4} +(-0.173648 - 0.984808i) q^{5} +(-0.387335 + 0.431029i) q^{6} +(0.799236 + 0.461439i) q^{7} +(-2.58050 + 1.15802i) q^{8} +(-2.16951 - 1.82043i) q^{9} +O(q^{10})\)	\(q+(0.528488 - 1.31175i) q^{2} +(-0.385053 - 0.140148i) q^{3} +(-1.44140 - 1.38649i) q^{4} +(-0.173648 - 0.984808i) q^{5} +(-0.387335 + 0.431029i) q^{6} +(0.799236 + 0.461439i) q^{7} +(-2.58050 + 1.15802i) q^{8} +(-2.16951 - 1.82043i) q^{9} +(-1.38360 - 0.292675i) q^{10} +(-0.765458 + 0.441937i) q^{11} +(0.360702 + 0.735882i) q^{12} +(-2.15996 - 5.93445i) q^{13} +(1.02768 - 0.804537i) q^{14} +(-0.0711549 + 0.403539i) q^{15} +(0.155277 + 3.99698i) q^{16} +(-2.58185 + 2.16643i) q^{17} +(-3.53452 + 1.88379i) q^{18} +(0.294141 - 4.34896i) q^{19} +(-1.11513 + 1.66027i) q^{20} +(-0.243078 - 0.289690i) q^{21} +(0.175178 + 1.23765i) q^{22} +(5.25895 + 0.927295i) q^{23} +(1.15592 - 0.0842479i) q^{24} +(-0.939693 + 0.342020i) q^{25} +(-8.92605 - 0.302941i) q^{26} +(1.19489 + 2.06962i) q^{27} +(-0.512238 - 1.77325i) q^{28} +(0.517190 - 0.616364i) q^{29} +(0.491740 + 0.306603i) q^{30} +(-4.76017 + 8.24486i) q^{31} +(5.32513 + 1.90867i) q^{32} +(0.356678 - 0.0628920i) q^{33} +(1.47735 + 4.53169i) q^{34} +(0.315643 - 0.867222i) q^{35} +(0.603115 + 5.63198i) q^{36} -4.07725i q^{37} +(-5.54932 - 2.68421i) q^{38} +2.58779i q^{39} +(1.58853 + 2.34021i) q^{40} +(3.75939 - 10.3289i) q^{41} +(-0.508466 + 0.165762i) q^{42} +(-2.37964 + 0.419595i) q^{43} +(1.71608 + 0.424293i) q^{44} +(-1.41605 + 2.45266i) q^{45} +(3.99567 - 6.40839i) q^{46} +(5.18564 - 6.18000i) q^{47} +(0.500379 - 1.56081i) q^{48} +(-3.07415 - 5.32458i) q^{49} +(-0.0479694 + 1.41340i) q^{50} +(1.29777 - 0.472350i) q^{51} +(-5.11469 + 11.5487i) q^{52} +(10.8012 + 1.90454i) q^{53} +(3.34631 - 0.473640i) q^{54} +(0.568144 + 0.677087i) q^{55} +(-2.59679 - 0.265212i) q^{56} +(-0.722757 + 1.63336i) q^{57} +(-0.535189 - 1.00417i) q^{58} +(6.63590 - 5.56818i) q^{59} +(0.662067 - 0.483007i) q^{60} +(0.00816087 - 0.0462826i) q^{61} +(8.29954 + 10.6015i) q^{62} +(-0.893930 - 2.45605i) q^{63} +(5.31797 - 5.97655i) q^{64} +(-5.46921 + 3.15765i) q^{65} +(0.106001 - 0.501112i) q^{66} +(10.7236 + 8.99818i) q^{67} +(6.72523 + 0.457021i) q^{68} +(-1.89502 - 1.09409i) q^{69} +(-0.970769 - 0.872362i) q^{70} +(-0.988117 - 5.60389i) q^{71} +(7.70652 + 2.18529i) q^{72} +(8.95524 + 3.25944i) q^{73} +(-5.34836 - 2.15478i) q^{74} +0.409765 q^{75} +(-6.45378 + 5.86078i) q^{76} -0.815709 q^{77} +(3.39454 + 1.36761i) q^{78} +(-15.1537 - 5.51548i) q^{79} +(3.90930 - 0.846987i) q^{80} +(1.30532 + 7.40283i) q^{81} +(-11.5621 - 10.3901i) q^{82} +(-2.88323 - 1.66463i) q^{83} +(-0.0512788 + 0.754586i) q^{84} +(2.58185 + 2.16643i) q^{85} +(-0.707205 + 3.34325i) q^{86} +(-0.285528 + 0.164849i) q^{87} +(1.46349 - 2.02684i) q^{88} +(-0.400871 - 1.10138i) q^{89} +(2.46893 + 3.15371i) q^{90} +(1.01207 - 5.73971i) q^{91} +(-6.29457 - 8.62810i) q^{92} +(2.98842 - 2.50758i) q^{93} +(-5.36610 - 10.0683i) q^{94} +(-4.33397 + 0.465518i) q^{95} +(-1.78296 - 1.48124i) q^{96} +(6.26962 + 7.47184i) q^{97} +(-8.60919 + 1.21855i) q^{98} +(2.46519 + 0.434679i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 3 q^{2} - 3 q^{4} + 3 q^{6} - 36 q^{8} + 6 q^{9}+O(q^{10}) \) 120 * q + 3 * q^2 - 3 * q^4 + 3 * q^6 - 36 * q^8 + 6 * q^9	\( 120 q + 3 q^{2} - 3 q^{4} + 3 q^{6} - 36 q^{8} + 6 q^{9} + 3 q^{10} - 12 q^{13} - 18 q^{14} + 9 q^{16} + 48 q^{17} - 12 q^{21} - 18 q^{24} - 24 q^{26} + 69 q^{28} - 12 q^{30} - 27 q^{32} + 6 q^{33} - 18 q^{34} - 72 q^{36} - 48 q^{38} - 36 q^{41} - 27 q^{42} - 99 q^{44} + 60 q^{45} + 27 q^{46} - 63 q^{48} + 60 q^{49} + 33 q^{52} - 24 q^{53} + 21 q^{54} - 48 q^{57} + 6 q^{60} - 24 q^{61} + 54 q^{62} + 84 q^{64} - 18 q^{65} - 132 q^{66} + 66 q^{68} - 72 q^{69} + 36 q^{70} - 42 q^{72} + 66 q^{74} + 180 q^{76} + 60 q^{77} + 114 q^{78} + 27 q^{80} - 66 q^{81} + 33 q^{82} - 144 q^{84} - 48 q^{85} + 75 q^{86} + 9 q^{88} - 3 q^{90} - 42 q^{92} - 144 q^{93} + 78 q^{96} + 42 q^{97} - 87 q^{98}+O(q^{100}) \) 120 * q + 3 * q^2 - 3 * q^4 + 3 * q^6 - 36 * q^8 + 6 * q^9 + 3 * q^10 - 12 * q^13 - 18 * q^14 + 9 * q^16 + 48 * q^17 - 12 * q^21 - 18 * q^24 - 24 * q^26 + 69 * q^28 - 12 * q^30 - 27 * q^32 + 6 * q^33 - 18 * q^34 - 72 * q^36 - 48 * q^38 - 36 * q^41 - 27 * q^42 - 99 * q^44 + 60 * q^45 + 27 * q^46 - 63 * q^48 + 60 * q^49 + 33 * q^52 - 24 * q^53 + 21 * q^54 - 48 * q^57 + 6 * q^60 - 24 * q^61 + 54 * q^62 + 84 * q^64 - 18 * q^65 - 132 * q^66 + 66 * q^68 - 72 * q^69 + 36 * q^70 - 42 * q^72 + 66 * q^74 + 180 * q^76 + 60 * q^77 + 114 * q^78 + 27 * q^80 - 66 * q^81 + 33 * q^82 - 144 * q^84 - 48 * q^85 + 75 * q^86 + 9 * q^88 - 3 * q^90 - 42 * q^92 - 144 * q^93 + 78 * q^96 + 42 * q^97 - 87 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more