LMFDB - Embedded newform 684.2.cc.a.211.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,2,Mod(211,684)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(684, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 6, 1]))

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

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

chi := DirichletCharacter("684.211");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	684.cc (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:	$5.46176749826$
Analytic rank:	$0$
Dimension:	$696$
Relative dimension:	$116$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			211.5
Character	$\chi$	$=$	684.211
Dual form			684.2.cc.a.295.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.40991 - 0.110292i) q^{2} +(-0.721709 - 1.57453i) q^{3} +(1.97567 + 0.311003i) q^{4} +(0.251320 - 1.42531i) q^{5} +(0.843885 + 2.29953i) q^{6} +(-0.441456 - 0.254875i) q^{7} +(-2.75121 - 0.656387i) q^{8} +(-1.95827 + 2.27270i) q^{9} +(-0.511538 + 1.98183i) q^{10} +6.08777i q^{11} +(-0.936178 - 3.33520i) q^{12} +(5.27874 - 0.930784i) q^{13} +(0.594301 + 0.408039i) q^{14} +(-2.42556 + 0.632947i) q^{15} +(3.80655 + 1.22888i) q^{16} +(-0.986905 + 5.59702i) q^{17} +(3.01164 - 2.98831i) q^{18} +(-3.04870 + 3.11535i) q^{19} +(0.939800 - 2.73778i) q^{20} +(-0.0827042 + 0.879030i) q^{21} +(0.671433 - 8.58318i) q^{22} +(1.55775 + 1.85645i) q^{23} +(0.952076 + 4.80558i) q^{24} +(2.73013 + 0.993685i) q^{25} +(-7.54519 + 0.730115i) q^{26} +(4.99173 + 1.44312i) q^{27} +(-0.792905 - 0.640843i) q^{28} +(-2.23770 - 2.66679i) q^{29} +(3.48963 - 0.624875i) q^{30} -1.67203 q^{31} +(-5.23135 - 2.15244i) q^{32} +(9.58536 - 4.39360i) q^{33} +(2.00875 - 7.78242i) q^{34} +(-0.474221 + 0.565155i) q^{35} +(-4.57572 + 3.88108i) q^{36} +1.85269i q^{37} +(4.64198 - 4.05610i) q^{38} +(-5.27526 - 7.63976i) q^{39} +(-1.62699 + 3.75635i) q^{40} +(2.19995 + 6.04432i) q^{41} +(0.213555 - 1.23023i) q^{42} +(1.67388 - 1.99486i) q^{43} +(-1.89332 + 12.0274i) q^{44} +(2.74714 + 3.36231i) q^{45} +(-1.99153 - 2.78923i) q^{46} +(-8.71774 - 10.3894i) q^{47} +(-0.812320 - 6.88042i) q^{48} +(-3.37008 - 5.83715i) q^{49} +(-3.73963 - 1.70211i) q^{50} +(9.52491 - 2.48551i) q^{51} +(10.7185 - 0.197218i) q^{52} +(-0.284836 + 0.782580i) q^{53} +(-6.87871 - 2.58521i) q^{54} +(8.67693 + 1.52998i) q^{55} +(1.04724 + 0.990980i) q^{56} +(7.10548 + 2.55189i) q^{57} +(2.86083 + 4.00673i) q^{58} +(6.53719 + 5.48535i) q^{59} +(-4.98896 + 0.496137i) q^{60} +(1.63700 + 9.28391i) q^{61} +(2.35741 + 0.184412i) q^{62} +(1.44374 - 0.504184i) q^{63} +(7.13831 + 3.61171i) q^{64} -7.75774i q^{65} +(-13.9990 + 5.13737i) q^{66} +(8.19960 + 2.98441i) q^{67} +(-3.69049 + 10.7509i) q^{68} +(1.79879 - 3.79254i) q^{69} +(0.730940 - 0.744512i) q^{70} +(9.26102 - 3.37073i) q^{71} +(6.87939 - 4.96730i) q^{72} +(8.37450 + 7.02704i) q^{73} +(0.204337 - 2.61212i) q^{74} +(-0.405775 - 5.01581i) q^{75} +(-6.99212 + 5.20675i) q^{76} +(1.55162 - 2.68748i) q^{77} +(6.59502 + 11.3532i) q^{78} +(-0.353877 + 2.00694i) q^{79} +(2.70819 - 5.11666i) q^{80} +(-1.33035 - 8.90113i) q^{81} +(-2.43508 - 8.76456i) q^{82} +(3.65110 + 2.10796i) q^{83} +(-0.436777 + 1.71095i) q^{84} +(7.72943 + 2.81328i) q^{85} +(-2.58004 + 2.62794i) q^{86} +(-2.58396 + 5.44797i) q^{87} +(3.99593 - 16.7487i) q^{88} +(-0.704285 - 0.839334i) q^{89} +(-3.50238 - 5.04353i) q^{90} +(-2.56756 - 0.934517i) q^{91} +(2.50024 + 4.15221i) q^{92} +(1.20672 + 2.63266i) q^{93} +(11.1453 + 15.6096i) q^{94} +(3.67413 + 5.12828i) q^{95} +(0.386439 + 9.79034i) q^{96} +(3.73268 + 10.2555i) q^{97} +(4.10770 + 8.60152i) q^{98} +(-13.8357 - 11.9215i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 696 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 6 q^{6} - 18 q^{8} - 12 q^{10} - 9 q^{12} - 6 q^{13} - 15 q^{14} - 3 q^{16} - 24 q^{17} - 6 q^{20} - 30 q^{21} + 21 q^{22} + 24 q^{24} - 6 q^{25} - 30 q^{26} - 6 q^{29}+ \cdots - 63 q^{98}+O(q^{100}) $ 696 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 - 6 * q^6 - 18 * q^8 - 12 * q^10 - 9 * q^12 - 6 * q^13 - 15 * q^14 - 3 * q^16 - 24 * q^17 - 6 * q^20 - 30 * q^21 + 21 * q^22 + 24 * q^24 - 6 * q^25 - 30 * q^26 - 6 * q^29 - 21 * q^30 - 3 * q^32 + 36 * q^33 + 33 * q^34 + 54 * q^36 - 3 * q^38 - 33 * q^40 + 54 * q^41 - 87 * q^42 - 33 * q^44 - 6 * q^45 - 18 * q^46 + 6 * q^48 + 282 * q^49 - 3 * q^52 - 24 * q^53 - 51 * q^54 - 63 * q^56 - 12 * q^57 - 6 * q^58 - 27 * q^60 - 6 * q^61 - 18 * q^62 - 24 * q^64 - 30 * q^66 + 3 * q^68 - 18 * q^69 - 45 * q^70 + 12 * q^72 - 60 * q^73 + 3 * q^74 - 3 * q^76 + 72 * q^77 - 81 * q^78 - 12 * q^80 - 72 * q^81 - 12 * q^82 - 9 * q^84 - 6 * q^85 - 57 * q^86 - 9 * q^88 - 24 * q^89 + 39 * q^90 + 81 * q^92 - 48 * q^93 + 15 * q^96 + 30 * q^97 - 63 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/684\mathbb{Z}\right)^\times$.

$n$	$325$	$343$	$533$
$\chi(n)$	$e\left(\frac{1}{18}\right)$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−1.40991	−	0.110292i	−0.996954	−	0.0779883i
$2$	−1.40991	−	0.110292i	−0.996954	−	0.0779883i
$3$	−0.721709	−	1.57453i	−0.416679	−	0.909054i
$3$	−0.721709	−	1.57453i	−0.416679	−	0.909054i
$4$	1.97567	+	0.311003i	0.987836	+	0.155502i
$5$	0.251320	−	1.42531i	0.112394	−	0.637416i	−0.875614	−	0.483012i	$-0.839543\pi$
$5$	0.251320	−	1.42531i	0.112394	−	0.637416i	0.988008	−	0.154405i	$-0.0493460\pi$
$6$	0.843885	+	2.29953i	0.344514	+	0.938781i
$7$	−0.441456	−	0.254875i	−0.166855	−	0.0963336i	0.414247	−	0.910164i	$-0.364045\pi$
$7$	−0.441456	−	0.254875i	−0.166855	−	0.0963336i	−0.581102	+	0.813831i	$0.697378\pi$
$8$	−2.75121	−	0.656387i	−0.972700	−	0.232068i
$9$	−1.95827	+	2.27270i	−0.652757	+	0.757567i
$10$	−0.511538	+	1.98183i	−0.161762	+	0.626709i
$11$			6.08777i			1.83553i	0.397123	+	0.917766i	$0.370009\pi$
$11$			6.08777i			1.83553i	−0.397123	+	0.917766i	$0.629991\pi$
$12$	−0.936178	−	3.33520i	−0.270251	−	0.962790i
$13$	5.27874	−	0.930784i	1.46406	−	0.258153i	0.615870	−	0.787847i	$-0.288804\pi$
$13$	5.27874	−	0.930784i	1.46406	−	0.258153i	0.848189	+	0.529694i	$0.177693\pi$
$14$	0.594301	+	0.408039i	0.158834	+	0.109053i
$15$	−2.42556	+	0.632947i	−0.626278	+	0.163426i
$16$	3.80655	+	1.22888i	0.951638	+	0.307220i
$17$	−0.986905	+	5.59702i	−0.239360	+	1.35748i	0.593875	+	0.804557i	$0.297597\pi$
$17$	−0.986905	+	5.59702i	−0.239360	+	1.35748i	−0.833235	+	0.552919i	$0.813514\pi$
$18$	3.01164	−	2.98831i	0.709850	−	0.704353i
$19$	−3.04870	+	3.11535i	−0.699420	+	0.714711i
$19$	−3.04870	+	3.11535i	−0.699420	+	0.714711i
$20$	0.939800	−	2.73778i	0.210146	−	0.612185i
$21$	−0.0827042	+	0.879030i	−0.0180475	+	0.191820i
$22$	0.671433	−	8.58318i	0.143150	−	1.82994i
$23$	1.55775	+	1.85645i	0.324813	+	0.387097i	0.903597	−	0.428384i	$-0.140917\pi$
$23$	1.55775	+	1.85645i	0.324813	+	0.387097i	−0.578784	+	0.815481i	$0.696472\pi$
$24$	0.952076	+	4.80558i	0.194342	+	0.980934i
$25$	2.73013	+	0.993685i	0.546025	+	0.198737i
$26$	−7.54519	+	0.730115i	−1.47973	+	0.143187i
$27$	4.99173	+	1.44312i	0.960660	+	0.277729i
$28$	−0.792905	−	0.640843i	−0.149845	−	0.121108i
$29$	−2.23770	−	2.66679i	−0.415531	−	0.495211i	0.517159	−	0.855889i	$-0.326990\pi$
$29$	−2.23770	−	2.66679i	−0.415531	−	0.495211i	−0.932690	+	0.360679i	$0.882545\pi$
$30$	3.48963	−	0.624875i	0.637116	−	0.114086i
$31$	−1.67203			−0.300306			−0.150153	−	0.988663i	$-0.547977\pi$
$31$	−1.67203			−0.300306			−0.150153	+	0.988663i	$0.547977\pi$
$32$	−5.23135	−	2.15244i	−0.924780	−	0.380501i
$33$	9.58536	−	4.39360i	1.66860	−	0.764828i
$34$	2.00875	−	7.78242i	0.344498	−	1.33467i
$35$	−0.474221	+	0.565155i	−0.0801580	+	0.0955286i
$36$	−4.57572	+	3.88108i	−0.762620	+	0.646847i
$37$			1.85269i			0.304580i	0.988336	+	0.152290i	$0.0486648\pi$
$37$			1.85269i			0.304580i	−0.988336	+	0.152290i	$0.951335\pi$
$38$	4.64198	−	4.05610i	0.753029	−	0.657987i
$39$	−5.27526	−	7.63976i	−0.844718	−	1.22334i
$40$	−1.62699	+	3.75635i	−0.257249	+	0.593932i
$41$	2.19995	+	6.04432i	0.343575	+	0.943964i	0.984348	+	0.176234i	$0.0563915\pi$
$41$	2.19995	+	6.04432i	0.343575	+	0.943964i	−0.640774	+	0.767730i	$0.721386\pi$
$42$	0.213555	−	1.23023i	0.0329523	−	0.189828i
$43$	1.67388	−	1.99486i	0.255265	−	0.304213i	−0.623159	−	0.782095i	$-0.714151\pi$
$43$	1.67388	−	1.99486i	0.255265	−	0.304213i	0.878424	+	0.477882i	$0.158595\pi$
$44$	−1.89332	+	12.0274i	−0.285428	+	1.81320i
$45$	2.74714	+	3.36231i	0.409520	+	0.501224i
$46$	−1.99153	−	2.78923i	−0.293635	−	0.411250i
$47$	−8.71774	−	10.3894i	−1.27161	−	1.51545i	−0.748402	−	0.663245i	$-0.769179\pi$
$47$	−8.71774	−	10.3894i	−1.27161	−	1.51545i	−0.523210	−	0.852204i	$-0.675266\pi$
$48$	−0.812320	−	6.88042i	−0.117248	−	0.993103i
$49$	−3.37008	−	5.83715i	−0.481440	−	0.833878i
$50$	−3.73963	−	1.70211i	−0.528863	−	0.240715i
$51$	9.52491	−	2.48551i	1.33375	−	0.348041i
$52$	10.7185	−	0.197218i	1.48639	−	0.0273493i
$53$	−0.284836	+	0.782580i	−0.0391252	+	0.107496i	−0.957717	−	0.287712i	$-0.907105\pi$
$53$	−0.284836	+	0.782580i	−0.0391252	+	0.107496i	0.918592	+	0.395208i	$0.129328\pi$
$54$	−6.87871	−	2.58521i	−0.936074	−	0.351803i
$55$	8.67693	+	1.52998i	1.17000	+	0.206302i
$56$	1.04724	+	0.990980i	0.139944	+	0.132425i
$57$	7.10548	+	2.55189i	0.941144	+	0.338006i
$58$	2.86083	+	4.00673i	0.375645	+	0.526109i
$59$	6.53719	+	5.48535i	0.851069	+	0.714132i	0.960025	−	0.279915i	$-0.0903062\pi$
$59$	6.53719	+	5.48535i	0.851069	+	0.714132i	−0.108956	+	0.994047i	$0.534751\pi$
$60$	−4.98896	+	0.496137i	−0.644072	+	0.0640510i
$61$	1.63700	+	9.28391i	0.209597	+	1.18868i	0.890040	+	0.455882i	$0.150676\pi$
$61$	1.63700	+	9.28391i	0.209597	+	1.18868i	−0.680443	+	0.732801i	$0.738213\pi$
$62$	2.35741	+	0.184412i	0.299391	+	0.0234204i
$63$	1.44374	−	0.504184i	0.181895	−	0.0635212i
$64$	7.13831	+	3.61171i	0.892289	+	0.451464i
$65$		−	7.75774i		−	0.962230i
$66$	−13.9990	+	5.13737i	−1.72316	+	0.632367i
$67$	8.19960	+	2.98441i	1.00174	+	0.364604i	0.790256	−	0.612777i	$-0.209948\pi$
$67$	8.19960	+	2.98441i	1.00174	+	0.364604i	0.211485	+	0.977381i	$0.432170\pi$
$68$	−3.69049	+	10.7509i	−0.447538	+	1.30374i
$69$	1.79879	−	3.79254i	0.216549	−	0.456568i
$70$	0.730940	−	0.744512i	0.0873640	−	0.0889863i
$71$	9.26102	−	3.37073i	1.09908	−	0.400033i	0.272103	−	0.962268i	$-0.412281\pi$
$71$	9.26102	−	3.37073i	1.09908	−	0.400033i	0.826977	+	0.562235i	$0.190059\pi$
$72$	6.87939	−	4.96730i	0.810743	−	0.585402i
$73$	8.37450	+	7.02704i	0.980161	+	0.822453i	0.984114	−	0.177539i	$-0.0568137\pi$
$73$	8.37450	+	7.02704i	0.980161	+	0.822453i	−0.00395242	+	0.999992i	$0.501258\pi$
$74$	0.204337	−	2.61212i	0.0237537	−	0.303653i
$75$	−0.405775	−	5.01581i	−0.0468548	−	0.579176i
$76$	−6.99212	+	5.20675i	−0.802051	+	0.597256i
$77$	1.55162	−	2.68748i	0.176823	−	0.306267i
$78$	6.59502	+	11.3532i	0.746739	+	1.28549i
$79$	−0.353877	+	2.00694i	−0.0398143	+	0.225798i	−0.998222	−	0.0596042i	$-0.981016\pi$
$79$	−0.353877	+	2.00694i	−0.0398143	+	0.225798i	0.958408	+	0.285402i	$0.0921273\pi$
$80$	2.70819	−	5.11666i	0.302785	−	0.572060i
$81$	−1.33035	−	8.90113i	−0.147817	−	0.989015i
$82$	−2.43508	−	8.76456i	−0.268910	−	0.967883i
$83$	3.65110	+	2.10796i	0.400760	+	0.231379i	0.686812	−	0.726835i	$-0.259010\pi$
$83$	3.65110	+	2.10796i	0.400760	+	0.231379i	−0.286052	+	0.958214i	$0.592343\pi$
$84$	−0.436777	+	1.71095i	−0.0476563	+	0.186680i
$85$	7.72943	+	2.81328i	0.838375	+	0.305143i
$86$	−2.58004	+	2.62794i	−0.278212	+	0.283379i
$87$	−2.58396	+	5.44797i	−0.277030	+	0.584084i
$88$	3.99593	−	16.7487i	0.425967	−	1.78542i
$89$	−0.704285	−	0.839334i	−0.0746541	−	0.0889692i	0.727425	−	0.686188i	$-0.240717\pi$
$89$	−0.704285	−	0.839334i	−0.0746541	−	0.0889692i	−0.802079	+	0.597218i	$0.796273\pi$
$90$	−3.50238	−	5.04353i	−0.369183	−	0.531635i
$91$	−2.56756	−	0.934517i	−0.269154	−	0.0979640i
$92$	2.50024	+	4.15221i	0.260668	+	0.432897i
$93$	1.20672	+	2.63266i	0.125131	+	0.272994i
$94$	11.1453	+	15.6096i	1.14955	+	1.61000i
$95$	3.67413	+	5.12828i	0.376958	+	0.526151i
$96$	0.386439	+	9.79034i	0.0394408	+	0.999222i
$97$	3.73268	+	10.2555i	0.378996	+	1.04128i	0.971773	+	0.235917i	$0.0758093\pi$
$97$	3.73268	+	10.2555i	0.378996	+	1.04128i	−0.592777	+	0.805367i	$0.701968\pi$
$98$	4.10770	+	8.60152i	0.414941	+	0.868885i
$99$	−13.8357	−	11.9215i	−1.39054	−	1.19816i
$100$	5.08479	+	2.81227i	0.508479	+	0.281227i
$101$	−12.7044	−	4.62404i	−1.26414	−	0.460109i	−0.378983	−	0.925404i	$-0.623726\pi$
$101$	−12.7044	−	4.62404i	−1.26414	−	0.460109i	−0.885156	+	0.465294i	$0.845948\pi$
$102$	−13.7034	+	2.45381i	−1.35684	+	0.242964i
$103$	−5.83768	−	10.1112i	−0.575203	−	0.996281i	−0.996020	−	0.0891354i	$-0.971590\pi$
$103$	−5.83768	−	10.1112i	−0.575203	−	0.996281i	0.420816	−	0.907146i	$-0.361744\pi$
$104$	−15.1339	−	0.904111i	−1.48400	−	0.0886554i
$105$	1.23210	+	0.338797i	0.120241	+	0.0330632i
$106$	0.487904	−	1.07195i	0.0473895	−	0.104117i
$107$	1.05031	+	1.81920i	0.101538	+	0.175868i	0.912318	−	0.409482i	$-0.134290\pi$
$107$	1.05031	+	1.81920i	0.101538	+	0.175868i	−0.810781	+	0.585350i	$0.800957\pi$
$108$	9.41321	+	4.40358i	0.905787	+	0.423734i
$109$	0.0732296	+	0.201197i	0.00701412	+	0.0192711i	0.943150	−	0.332367i	$-0.107847\pi$
$109$	0.0732296	+	0.201197i	0.00701412	+	0.0192711i	−0.936136	+	0.351638i	$0.885625\pi$
$110$	−12.0649	−	3.11412i	−1.15034	−	0.296920i
$111$	2.91711	−	1.33710i	0.276880	−	0.126912i
$112$	−1.36722	−	1.51269i	−0.129190	−	0.142936i
$113$	−3.80495	−	2.19679i	−0.357939	−	0.206656i	0.310237	−	0.950659i	$-0.399592\pi$
$113$	−3.80495	−	2.19679i	−0.357939	−	0.206656i	−0.668176	+	0.744003i	$0.732925\pi$
$114$	−9.73661	−	4.38160i	−0.911917	−	0.410374i
$115$	3.03751	−	1.75371i	0.283249	−	0.163534i
$116$	−3.59159	−	5.96464i	−0.333470	−	0.553803i
$117$	−8.22181	+	13.8197i	−0.760106	+	1.27763i
$118$	−8.61183	−	8.45483i	−0.792783	−	0.778330i
$119$	1.86221	−	2.21930i	0.170709	−	0.203443i
$120$	7.08869	−	0.149263i	0.647106	−	0.0136258i
$121$	−26.0609			−2.36917
$122$	−1.28408	−	13.2700i	−0.116255	−	1.20141i
$123$	7.92921	−	7.82612i	0.714953	−	0.705658i
$124$	−3.30339	−	0.520008i	−0.296653	−	0.0466981i
$125$	5.72068	−	9.90850i	0.511673	−	0.886243i
$126$	−2.09115	+	0.551619i	−0.186295	+	0.0491421i
$127$	6.98874	−	5.86425i	0.620150	−	0.520368i	−0.277701	−	0.960668i	$-0.589572\pi$
$127$	6.98874	−	5.86425i	0.620150	−	0.520368i	0.897851	+	0.440300i	$0.145128\pi$
$128$	−9.66601	−	5.87948i	−0.854363	−	0.519677i
$129$	−4.34901	−	1.19587i	−0.382909	−	0.105290i
$130$	−0.855619	+	10.9377i	−0.0750427	+	0.959299i
$131$	−2.97043	+	3.54002i	−0.259527	+	0.309293i	−0.880036	−	0.474907i	$-0.842482\pi$
$131$	−2.97043	+	3.54002i	−0.259527	+	0.309293i	0.620509	+	0.784200i	$0.286926\pi$
$132$	20.3039	−	5.69923i	1.76723	−	0.496054i
$133$	2.13989	−	0.598253i	0.185552	−	0.0518751i
$134$	−11.2315	−	5.11209i	−0.970255	−	0.441618i
$135$	3.31141	−	6.75206i	0.285001	−	0.581125i
$136$	6.38899	−	14.7508i	0.547851	−	1.26487i
$137$	2.18296	+	12.3802i	0.186503	+	1.05771i	0.924009	+	0.382371i	$0.124892\pi$
$137$	2.18296	+	12.3802i	0.186503	+	1.05771i	−0.737506	+	0.675341i	$0.763997\pi$
$138$	−2.95442	+	5.14873i	−0.251497	+	0.438289i
$139$	−22.7058	+	4.00365i	−1.92588	+	0.339585i	−0.999331	−	0.0365831i	$-0.988353\pi$
$139$	−22.7058	+	4.00365i	−1.92588	+	0.339585i	−0.926551	+	0.376168i	$0.877242\pi$
$140$	−1.11267	+	0.969076i	−0.0940378	+	0.0819019i
$141$	−10.0667	+	21.2244i	−0.847770	+	1.78742i
$142$	−13.4289	+	3.73100i	−1.12693	+	0.313099i
$143$	5.66640	+	32.1357i	0.473848	+	2.68733i
$144$	−10.2471	+	6.24468i	−0.853929	+	0.520390i
$145$	−4.36337	+	2.51919i	−0.362358	+	0.209208i
$146$	−11.0322	−	10.8311i	−0.913034	−	0.896389i
$147$	−6.75853	+	9.51900i	−0.557434	+	0.785114i
$148$	−0.576193	+	3.66031i	−0.0473628	+	0.300875i
$149$	12.1751	−	4.43138i	0.997425	−	0.363033i	0.208834	−	0.977951i	$-0.433033\pi$
$149$	12.1751	−	4.43138i	0.997425	−	0.363033i	0.788591	+	0.614918i	$0.210811\pi$
$150$	0.0188994	+	7.11658i	0.00154313	+	0.581066i
$151$	−4.03534	−	6.98942i	−0.328392	−	0.568791i	0.653801	−	0.756666i	$-0.273173\pi$
$151$	−4.03534	−	6.98942i	−0.328392	−	0.568791i	−0.982193	+	0.187875i	$0.939840\pi$
$152$	10.4325	−	6.56986i	0.846187	−	0.532886i
$153$	−10.7877	−	13.2034i	−0.872136	−	1.06743i
$154$	−2.48404	+	3.61797i	−0.200170	+	0.291544i
$155$	−0.420215	+	2.38316i	−0.0337525	+	0.191420i
$156$	−8.04619	−	16.7343i	−0.644211	−	1.33981i
$157$	−2.50469	+	14.2048i	−0.199896	+	1.13367i	0.705376	+	0.708833i	$0.250778\pi$
$157$	−2.50469	+	14.2048i	−0.199896	+	1.13367i	−0.905272	+	0.424833i	$0.860333\pi$
$158$	0.720284	−	2.79057i	0.0573027	−	0.222005i
$159$	1.43776	−	0.116314i	0.114022	−	0.00922428i
$160$	−4.38263	+	6.91532i	−0.346477	+	0.546704i
$161$	−0.214515	−	1.21657i	−0.0169061	−	0.0958794i
$162$	0.893943	+	12.6965i	0.0702348	+	0.997530i
$163$	2.86012	+	1.65129i	0.224022	+	0.129339i	0.607811	−	0.794082i	$-0.292048\pi$
$163$	2.86012	+	1.65129i	0.224022	+	0.129339i	−0.383789	+	0.923421i	$0.625381\pi$
$164$	2.46658	+	12.6258i	0.192607	+	0.985907i
$165$	−3.85323	−	14.7663i	−0.299974	−	1.14955i
$166$	−4.91521	−	3.37471i	−0.381494	−	0.261929i
$167$	12.0851	−	10.1406i	0.935173	−	0.784704i	−0.0415655	−	0.999136i	$-0.513235\pi$
$167$	12.0851	−	10.1406i	0.935173	−	0.784704i	0.976739	+	0.214432i	$0.0687901\pi$
$168$	0.804520	−	2.36411i	0.0620701	−	0.182395i
$169$	14.7827	−	5.38047i	1.13713	−	0.413883i
$170$	−10.5875	−	4.81896i	−0.812024	−	0.369598i
$171$	−1.11008	−	13.0295i	−0.0848898	−	0.996390i
$172$	3.92745	−	3.42060i	0.299465	−	0.260818i
$173$	5.91601	+	16.2541i	0.449786	+	1.23578i	0.932873	+	0.360205i	$0.117293\pi$
$173$	5.91601	+	16.2541i	0.449786	+	1.23578i	−0.483087	+	0.875572i	$0.660485\pi$
$174$	4.24401	−	7.39614i	0.321738	−	0.560700i
$175$	−0.951966	−	1.13451i	−0.0719618	−	0.0857608i
$176$	−7.48114	+	23.1734i	−0.563912	+	1.74676i
$177$	3.91888	−	14.2518i	0.294561	−	1.07123i
$178$	0.900404	+	1.26106i	0.0674881	+	0.0945204i
$179$	−8.60361	+	14.9019i	−0.643064	+	1.11382i	0.341681	+	0.939816i	$0.389004\pi$
$179$	−8.60361	+	14.9019i	−0.643064	+	1.11382i	−0.984745	+	0.174003i	$0.944330\pi$
$180$	4.38176	+	7.49719i	0.326597	+	0.558808i
$181$	−18.3416	+	3.23412i	−1.36332	+	0.240390i	−0.806987	−	0.590569i	$-0.798903\pi$
$181$	−18.3416	+	3.23412i	−1.36332	+	0.240390i	−0.556333	+	0.830960i	$0.687792\pi$
$182$	3.51696	+	1.60076i	0.260694	+	0.118657i
$183$	13.4363	−	9.27779i	0.993242	−	0.685834i
$184$	−3.06714	−	6.12998i	−0.226113	−	0.451908i
$185$	2.64065	+	0.465618i	0.194145	+	0.0342329i
$186$	−1.41100	−	3.84490i	−0.103460	−	0.281922i
$187$	−34.0733	−	6.00805i	−2.49169	−	0.439352i
$188$	−13.9922	−	23.2373i	−1.02049	−	1.69475i
$189$	−1.83582	−	1.90934i	−0.133536	−	0.138884i
$190$	−4.61457	−	7.63563i	−0.334776	−	0.553947i
$191$	10.3586	−	5.98056i	0.749524	−	0.432738i	−0.0759980	−	0.997108i	$-0.524214\pi$
$191$	10.3586	−	5.98056i	0.749524	−	0.432738i	0.825522	+	0.564370i	$0.190881\pi$
$192$	0.534954	−	13.8461i	0.0386070	−	0.999254i
$193$	−1.05420	−	2.89639i	−0.0758830	−	0.208487i	0.895951	−	0.444153i	$-0.146495\pi$
$193$	−1.05420	−	2.89639i	−0.0758830	−	0.208487i	−0.971834	+	0.235666i	$0.924273\pi$
$194$	−4.13163	−	14.8709i	−0.296634	−	1.06767i
$195$	−12.2148	+	5.59884i	−0.874719	+	0.400941i
$196$	−4.84279	−	12.5804i	−0.345914	−	0.898599i
$197$	0.643600	+	1.11475i	0.0458546	+	0.0794224i	0.888042	−	0.459763i	$-0.152066\pi$
$197$	0.643600	+	1.11475i	0.0458546	+	0.0794224i	−0.842187	+	0.539185i	$0.818732\pi$
$198$	18.1922	+	18.3342i	1.29286	+	1.30295i
$199$	13.8144	−	2.43585i	0.979277	−	0.172673i	0.338974	−	0.940796i	$-0.389920\pi$
$199$	13.8144	−	2.43585i	0.979277	−	0.172673i	0.640303	+	0.768123i	$0.278809\pi$
$200$	−6.85891	−	4.52585i	−0.484998	−	0.320026i
$201$	−1.21869	−	15.0644i	−0.0859601	−	1.06256i
$202$	17.4021	+	7.92066i	1.22441	+	0.557296i
$203$	0.308150	+	1.74761i	0.0216279	+	0.122658i
$204$	19.5911	−	1.94827i	1.37165	−	0.136406i
$205$	9.16789	−	1.61655i	0.640313	−	0.112905i
$206$	7.11539	+	14.8996i	0.495753	+	1.03811i
$207$	−7.26966	−	0.0951386i	−0.505276	−	0.00661259i
$208$	21.2376	+	2.94386i	1.47256	+	0.204120i
$209$	−18.9655	−	18.5598i	−1.31187	−	1.28381i
$210$	−1.69978	−	0.613563i	−0.117296	−	0.0423398i
$211$	−7.74945	−	6.50256i	−0.533494	−	0.447655i	0.335812	−	0.941929i	$-0.390989\pi$
$211$	−7.74945	−	6.50256i	−0.533494	−	0.447655i	−0.869306	+	0.494274i	$0.835434\pi$
$212$	−0.806127	+	1.45754i	−0.0553650	+	0.100104i
$213$	−11.9911	−	12.1490i	−0.821615	−	0.832438i
$214$	−1.28020	−	2.68074i	−0.0875127	−	0.183251i
$215$	−2.42260	−	2.88714i	−0.165220	−	0.196902i
$216$	−12.7861	−	7.24683i	−0.869981	−	0.493085i
$217$	0.738129	+	0.426159i	0.0501075	+	0.0289296i
$218$	−0.0810565	−	0.291745i	−0.00548984	−	0.0197595i
$219$	5.02031	−	18.2574i	0.339241	−	1.23372i
$220$	16.6669	+	5.72129i	1.12368	+	0.385729i
$221$			30.4638i			2.04922i
$222$	−4.26033	+	1.56346i	−0.285934	+	0.104932i
$223$	−1.34563	−	1.12912i	−0.0901103	−	0.0756115i	0.596620	−	0.802524i	$-0.296510\pi$
$223$	−1.34563	−	1.12912i	−0.0901103	−	0.0756115i	−0.686730	+	0.726913i	$0.740955\pi$
$224$	1.76081	+	2.28355i	0.117649	+	0.152576i
$225$	−7.60468	+	4.25886i	−0.506979	+	0.283924i
$226$	5.12233	+	3.51692i	0.340732	+	0.233942i
$227$	−3.98593	−	6.90384i	−0.264556	−	0.458224i	0.702892	−	0.711297i	$-0.251892\pi$
$227$	−3.98593	−	6.90384i	−0.264556	−	0.458224i	−0.967447	+	0.253073i	$0.918559\pi$
$228$	13.2445	+	7.25152i	0.877135	+	0.480243i
$229$	5.14847	−	8.91740i	0.340220	−	0.589279i	−0.644253	−	0.764812i	$-0.722832\pi$
$229$	5.14847	−	8.91740i	0.340220	−	0.589279i	0.984473	+	0.175534i	$0.0561651\pi$
$230$	−4.47602	+	2.13755i	−0.295140	+	0.140946i
$231$	−5.35133	−	0.503484i	−0.352092	−	0.0331268i
$232$	4.40595	+	8.80570i	0.289265	+	0.578123i
$233$	19.4230	−	7.06941i	1.27245	−	0.463132i	0.384519	−	0.923117i	$-0.374367\pi$
$233$	19.4230	−	7.06941i	1.27245	−	0.463132i	0.887927	+	0.459985i	$0.152145\pi$
$234$	13.1162	−	18.5777i	0.857432	−	1.21446i
$235$	−16.9990	+	9.81438i	−1.10889	+	0.640220i
$236$	11.2094	+	12.8703i	0.729668	+	0.837788i
$237$	3.41538	−	0.891237i	0.221853	−	0.0578921i
$238$	−2.87032	+	2.92362i	−0.186055	+	0.189510i
$239$	−11.6356	+	6.71782i	−0.752645	+	0.434540i	−0.826649	−	0.562718i	$-0.809756\pi$
$239$	−11.6356	+	6.71782i	−0.752645	+	0.434540i	0.0740041	+	0.997258i	$0.476422\pi$
$240$	−10.0109	−	0.571381i	−0.646198	−	0.0368825i
$241$	0.323067	−	0.887620i	0.0208106	−	0.0571766i	−0.928852	−	0.370450i	$-0.879203\pi$
$241$	0.323067	−	0.887620i	0.0208106	−	0.0571766i	0.949663	+	0.313274i	$0.101426\pi$
$242$	36.7435	+	2.87432i	2.36196	+	0.184768i
$243$	−13.0549	+	8.51870i	−0.837475	+	0.546475i
$244$	0.346855	+	18.8511i	0.0222051	+	1.20682i
$245$	−9.16669	+	3.33640i	−0.585638	+	0.213155i
$246$	−12.0426	+	10.1596i	−0.767809	+	0.647751i
$247$	−13.1936	+	19.2828i	−0.839488	+	1.22694i
$248$	4.60011	+	1.09750i	0.292108	+	0.0696913i
$249$	0.684012	−	7.27008i	0.0433475	−	0.460723i
$250$	−9.15845	+	13.3391i	−0.579231	+	0.843639i
$251$	−6.06885	+	16.6740i	−0.383063	+	1.05246i	0.586997	+	0.809589i	$0.300310\pi$
$251$	−6.06885	+	16.6740i	−0.383063	+	1.05246i	−0.970060	+	0.242867i	$0.921912\pi$
$252$	3.00917	−	0.547093i	0.189560	−	0.0344636i
$253$	−11.3017	+	9.48322i	−0.710529	+	0.596205i
$254$	−10.5002	+	7.49724i	−0.658844	+	0.470418i
$255$	−1.14881	−	14.2006i	−0.0719415	−	0.889274i
$256$	12.9797	+	9.35560i	0.811232	+	0.584725i
$257$	8.53782	−	23.4575i	0.532575	−	1.46324i	−0.323422	−	0.946255i	$-0.604833\pi$
$257$	8.53782	−	23.4575i	0.532575	−	1.46324i	0.855996	−	0.516982i	$-0.172945\pi$
$258$	5.99981	+	2.16572i	0.373532	+	0.134832i
$259$	0.472204	−	0.817881i	0.0293413	−	0.0508207i
$260$	2.41268	−	15.3268i	0.149628	−	0.950525i
$261$	10.4429	+	0.136666i	0.646396	+	0.00845944i
$262$	4.57846	−	4.66348i	0.282858	−	0.288111i
$263$	5.85830	+	1.03298i	0.361238	+	0.0636960i	0.351322	−	0.936255i	$-0.385732\pi$
$263$	5.85830	+	1.03298i	0.361238	+	0.0636960i	0.00991636	+	0.999951i	$0.496843\pi$
$264$	−29.2552	+	5.79602i	−1.80053	+	0.356720i
$265$	1.04383	+	0.602656i	0.0641221	+	0.0370209i
$266$	−3.08303	+	0.607467i	−0.189033	+	0.0372462i
$267$	−0.813265	+	1.71467i	−0.0497710	+	0.104936i
$268$	15.2716	+	8.44632i	0.932859	+	0.515941i
$269$	10.0045	−	11.9229i	0.609985	−	0.726952i	−0.369329	−	0.929299i	$-0.620412\pi$
$269$	10.0045	−	11.9229i	0.609985	−	0.726952i	0.979314	+	0.202347i	$0.0648568\pi$
$270$	−5.41348	+	9.15455i	−0.329454	+	0.557128i
$271$	10.6818	+	29.3479i	0.648871	+	1.78276i	0.621866	+	0.783124i	$0.286375\pi$
$271$	10.6818	+	29.3479i	0.648871	+	1.78276i	0.0270058	+	0.999635i	$0.491403\pi$
$272$	−10.6348	+	20.0926i	−0.644828	+	1.21829i
$273$	0.381613	+	4.71715i	0.0230963	+	0.285495i
$274$	−1.71233	−	17.6957i	−0.103446	−	1.06903i
$275$	−6.04932	+	16.6204i	−0.364788	+	1.00225i
$276$	4.73332	−	6.93338i	0.284912	−	0.417340i
$277$	10.7958			0.648657			0.324328	−	0.945945i	$-0.394862\pi$
$277$	10.7958			0.648657			0.324328	+	0.945945i	$0.394862\pi$
$278$	32.4546	−	3.14049i	1.94650	−	0.188354i
$279$	3.27429	−	3.80003i	0.196027	−	0.227502i
$280$	1.67564	−	1.24359i	0.100139	−	0.0743185i
$281$	18.7702	−	3.30968i	1.11973	−	0.197439i	0.417010	−	0.908902i	$-0.363078\pi$
$281$	18.7702	−	3.30968i	1.11973	−	0.197439i	0.702724	+	0.711463i	$0.251967\pi$
$282$	16.5340	−	28.8142i	0.984586	−	1.71586i
$283$	−10.3833	+	12.3744i	−0.617224	+	0.735579i	−0.980590	−	0.196067i	$-0.937183\pi$
$283$	−10.3833	+	12.3744i	−0.617224	+	0.735579i	0.363366	+	0.931646i	$0.381627\pi$
$284$	19.3450	−	3.77926i	1.14792	−	0.224258i
$285$	5.42297	−	9.48615i	0.321229	−	0.561911i
$286$	−4.44477	−	45.9333i	−0.262825	−	2.71610i
$287$	0.569362	−	3.22901i	0.0336084	−	0.190603i
$288$	15.1363	−	7.67424i	0.891912	−	0.452209i
$289$	−14.3778	−	5.23310i	−0.845755	−	0.307830i
$290$	6.42980	−	3.07058i	0.377571	−	0.180311i
$291$	13.4536	−	13.2787i	0.788663	−	0.778409i
$292$	14.3598	+	16.4876i	0.840345	+	0.964865i
$293$	−28.8926	+	16.6811i	−1.68792	+	0.974523i	−0.731818	+	0.681500i	$0.761328\pi$
$293$	−28.8926	+	16.6811i	−1.68792	+	0.974523i	−0.956106	+	0.293022i	$0.905339\pi$
$294$	10.5788	−	12.6755i	0.616966	−	0.739249i
$295$	9.46123	−	7.93891i	0.550854	−	0.462221i
$296$	1.21608	−	5.09714i	0.0706833	−	0.296265i
$297$	−8.78538	+	30.3885i	−0.509780	+	1.76332i
$298$	−17.6545	+	4.90501i	−1.02270	+	0.284140i
$299$	9.95091	+	8.34980i	0.575476	+	0.482882i
$300$	0.758256	−	10.0358i	0.0437780	−	0.579417i
$301$	−1.24738	+	0.454011i	−0.0718980	+	0.0261687i
$302$	4.91858	+	10.2995i	0.283032	+	0.592669i
$303$	1.88824	+	23.3407i	0.108477	+	1.34089i
$304$	−15.4334	+	8.11226i	−0.885169	+	0.465270i
$305$	13.6438			0.781243
$306$	13.7534	+	19.8054i	0.786232	+	1.13220i
$307$	−3.39765	−	2.85096i	−0.193914	−	0.162713i	0.540661	−	0.841240i	$-0.318174\pi$
$307$	−3.39765	−	2.85096i	−0.193914	−	0.162713i	−0.734575	+	0.678527i	$0.762619\pi$
$308$	3.90130	−	4.82702i	0.222297	−	0.275045i
$309$	−11.7072	+	16.4889i	−0.665998	+	0.938020i
$310$	0.855308	−	3.31368i	0.0485782	−	0.188205i
$311$		−	0.342584i		−	0.0194262i	−0.999953	−	0.00971309i	$-0.996908\pi$
$311$		−	0.342584i		−	0.0194262i	0.999953	−	0.00971309i	$-0.00309182\pi$
$312$	9.49871	+	24.4812i	0.537759	+	1.38598i
$313$	5.20981	−	4.37155i	0.294476	−	0.247095i	−0.483565	−	0.875309i	$-0.660658\pi$
$313$	5.20981	−	4.37155i	0.294476	−	0.247095i	0.778041	+	0.628214i	$0.216214\pi$
$314$	5.09805	−	19.7512i	0.287700	−	1.11462i
$315$	−0.355775	−	2.18449i	−0.0200456	−	0.123082i
$316$	−1.32331	+	3.85499i	−0.0744420	+	0.216860i
$317$	9.37903	−	25.7687i	0.526779	−	1.44731i	−0.336064	−	0.941839i	$-0.609096\pi$
$317$	9.37903	−	25.7687i	0.526779	−	1.44731i	0.862842	−	0.505473i	$-0.168682\pi$
$318$	−2.03994	+	0.00541743i	−0.114394	+	0.000303794i
$319$	16.2348	−	13.6226i	0.908975	−	0.762720i
$320$	6.94180	−	9.26659i	0.388058	−	0.518018i
$321$	2.10635	−	2.96668i	0.117565	−	0.165584i
$322$	0.168267	+	1.73891i	0.00937716	+	0.0969059i
$323$	−14.4279	−	20.1382i	−0.802789	−	1.12052i
$324$	0.139948	−	17.9995i	0.00777491	−	0.999970i
$325$	15.3365	+	2.70425i	0.850718	+	0.150005i
$326$	−3.85038	−	2.64362i	−0.213253	−	0.146416i
$327$	0.263939	−	0.260508i	0.0145959	−	0.0144061i
$328$	−2.08512	−	18.0732i	−0.115132	−	0.997926i
$329$	1.20050	+	6.80839i	0.0661859	+	0.375359i
$330$	3.80409	+	21.2440i	0.209409	+	1.16945i
$331$	25.1987			1.38505			0.692523	−	0.721396i	$-0.256499\pi$
$331$	25.1987			1.38505			0.692523	+	0.721396i	$0.256499\pi$
$332$	6.55778	+	5.30014i	0.359905	+	0.290883i
$333$	−4.21061	−	3.62807i	−0.230740	−	0.198817i
$334$	−18.1573	+	12.9644i	−0.993523	+	0.709381i
$335$	6.31442	−	10.9369i	0.344994	−	0.597547i
$336$	−1.39504	+	3.24444i	−0.0761057	+	0.176999i
$337$	−23.0873	−	4.07092i	−1.25765	−	0.221757i	−0.495183	−	0.868789i	$-0.664899\pi$
$337$	−23.0873	−	4.07092i	−1.25765	−	0.221757i	−0.762463	+	0.647032i	$0.776010\pi$
$338$	−21.4357	+	5.95554i	−1.16595	+	0.323939i
$339$	−0.712835	+	7.57643i	−0.0387159	+	0.411495i
$340$	14.3959	+	7.96200i	0.780726	+	0.431800i
$341$		−	10.1790i		−	0.551221i
$342$	0.128055	+	18.4928i	0.00692444	+	0.999976i
$343$			7.00404i			0.378182i
$344$	−5.91460	+	4.38955i	−0.318894	+	0.236669i
$345$	−4.95345	−	3.51697i	−0.266685	−	0.189347i
$346$	−6.54832	−	23.5693i	−0.352040	−	1.26709i
$347$	12.2517	+	2.16031i	0.657707	+	0.115971i	0.492534	−	0.870293i	$-0.336071\pi$
$347$	12.2517	+	2.16031i	0.657707	+	0.115971i	0.165173	+	0.986265i	$0.447182\pi$
$348$	−6.79940	+	9.95978i	−0.364486	+	0.533900i
$349$	−10.4322	+	18.0692i	−0.558425	+	0.967220i	0.439204	+	0.898388i	$0.355261\pi$
$349$	−10.4322	+	18.0692i	−0.558425	+	0.967220i	−0.997628	+	0.0688322i	$0.978073\pi$
$350$	1.21705	+	1.70455i	0.0650543	+	0.0911118i
$351$	27.6933	+	2.97163i	1.47816	+	0.158614i
$352$	13.1036	−	31.8472i	0.698422	−	1.69746i
$353$	−9.83091			−0.523247			−0.261623	−	0.965170i	$-0.584258\pi$
$353$	−9.83091			−0.523247			−0.261623	+	0.965170i	$0.584258\pi$
$354$	−7.09712	+	19.6615i	−0.377208	+	1.04500i
$355$	−2.47685	−	14.0469i	−0.131458	−	0.745533i
$356$	−1.13040	−	1.87728i	−0.0599111	−	0.0994958i
$357$	−4.83832	−	1.33042i	−0.256071	−	0.0704131i
$358$	13.7738	−	20.0613i	0.727970	−	1.06028i
$359$	16.4503	+	2.90063i	0.868213	+	0.153089i	0.589974	−	0.807422i	$-0.299138\pi$
$359$	16.4503	+	2.90063i	0.868213	+	0.153089i	0.278239	+	0.960512i	$0.410249\pi$
$360$	−5.35099	−	11.0536i	−0.282022	−	0.582577i
$361$	−0.410823	−	18.9956i	−0.0216223	−	0.999766i
$362$	26.2166	−	2.53687i	1.37791	−	0.133335i
$363$	18.8084	+	41.0336i	0.987186	+	2.15371i
$364$	−4.78203	−	2.64482i	−0.250646	−	0.138626i
$365$	12.1204	−	10.1702i	0.634409	−	0.532332i
$366$	−19.9672	+	11.5989i	−1.04370	+	0.606284i
$367$	−5.47614	+	15.0456i	−0.285852	+	0.785372i	0.710783	+	0.703411i	$0.248341\pi$
$367$	−5.47614	+	15.0456i	−0.285852	+	0.785372i	−0.996636	+	0.0819613i	$0.973882\pi$
$368$	3.64830	+	8.98098i	0.190181	+	0.468166i
$369$	−18.0450	−	6.83658i	−0.939387	−	0.355898i
$370$	−3.67172	−	0.947721i	−0.190883	−	0.0492697i
$371$	0.325202	−	0.272877i	0.0168837	−	0.0141671i
$372$	1.56532	+	5.57657i	0.0811581	+	0.289132i
$373$		−	33.8352i		−	1.75192i	−0.482384	−	0.875960i	$-0.660229\pi$
$373$		−	33.8352i		−	1.75192i	0.482384	−	0.875960i	$-0.339771\pi$
$374$	47.3776	+	12.2288i	2.44984	+	0.632337i
$375$	−19.7299	−	1.85630i	−1.01885	−	0.0958589i
$376$	17.1649	+	34.3056i	0.885210	+	1.76918i
$377$	−14.2945	−	11.9945i	−0.736202	−	0.617747i
$378$	2.37774	+	2.89447i	0.122298	+	0.148875i
$379$	16.7594			0.860873			0.430436	−	0.902621i	$-0.358360\pi$
$379$	16.7594			0.860873			0.430436	+	0.902621i	$0.358360\pi$
$380$	5.66396	+	11.2745i	0.290555	+	0.578368i
$381$	−14.2773	−	6.77167i	−0.731446	−	0.346923i
$382$	−15.2643	+	7.28955i	−0.780990	+	0.372966i
$383$	−9.49988	+	3.45767i	−0.485421	+	0.176679i	−0.573125	−	0.819468i	$-0.694269\pi$
$383$	−9.49988	+	3.45767i	−0.485421	+	0.176679i	0.0877043	+	0.996147i	$0.472047\pi$
$384$	−2.28135	+	19.4627i	−0.116420	+	0.993200i
$385$	−3.44053	−	2.88695i	−0.175346	−	0.147133i
$386$	1.16687	+	4.19991i	0.0593923	+	0.213770i
$387$	1.25580	+	7.71071i	0.0638358	+	0.391957i
$388$	4.18507	+	21.4223i	0.212465	+	1.08755i
$389$	−11.2274	+	9.42092i	−0.569253	+	0.477660i	−0.881398	−	0.472375i	$-0.843397\pi$
$389$	−11.2274	+	9.42092i	−0.569253	+	0.477660i	0.312145	+	0.950034i	$0.398952\pi$
$390$	17.8392	−	6.54664i	0.903323	−	0.331502i
$391$	−11.9279	+	6.88660i	−0.603222	+	0.348271i
$392$	5.44037	+	18.2713i	0.274780	+	0.922839i
$393$	7.71764	+	2.12215i	0.389303	+	0.107049i
$394$	−0.784467	−	1.64267i	−0.0395209	−	0.0827567i
$395$	2.77157	+	1.00877i	0.139453	+	0.0507566i
$396$	−23.6271	−	27.8559i	−1.18731	−	1.39981i
$397$	−0.399761	+	2.26716i	−0.0200634	+	0.113785i	−0.993195	−	0.116466i	$-0.962844\pi$
$397$	−0.399761	+	2.26716i	−0.0200634	+	0.113785i	0.973131	+	0.230251i	$0.0739547\pi$
$398$	−19.7457	+	1.91070i	−0.989761	+	0.0957749i
$399$	−2.48635	−	2.93755i	−0.124473	−	0.147062i
$400$	9.17126	+	7.13752i	0.458563	+	0.356876i
$401$	12.6852	−	15.1177i	0.633470	−	0.754940i	−0.349853	−	0.936804i	$-0.613769\pi$
$401$	12.6852	−	15.1177i	0.633470	−	0.754940i	0.983324	+	0.181864i	$0.0582131\pi$
$402$	0.0567619	+	21.3738i	0.00283103	+	1.06603i
$403$	−8.82623	+	1.55630i	−0.439666	+	0.0775249i
$404$	−23.6617	−	13.0867i	−1.17721	−	0.651088i
$405$	−13.0212	−	0.340877i	−0.647028	−	0.0169383i
$406$	−0.241715	−	2.49795i	−0.0119961	−	0.123971i
$407$	−11.2787			−0.559067
$408$	−27.8365	+	0.586138i	−1.37811	+	0.0290182i
$409$	−0.722167	+	1.98414i	−0.0357089	+	0.0981093i	−0.956266	−	0.292499i	$-0.905513\pi$
$409$	−0.722167	+	1.98414i	−0.0357089	+	0.0981093i	0.920557	+	0.390608i	$0.127735\pi$
$410$	−13.1042	+	1.26803i	−0.647168	+	0.0626237i
$411$	17.9175	−	12.3720i	0.883804	−	0.610267i
$412$	−8.38873	−	21.7918i	−0.413283	−	1.07361i
$413$	−1.48780	−	4.08770i	−0.0732100	−	0.201143i
$414$	10.2390	+	0.935923i	0.503222	+	0.0459981i
$415$	3.92208	−	4.67416i	0.192527	−	0.229445i
$416$	−29.6184	−	6.49291i	−1.45216	−	0.318341i
$417$	22.6909	+	32.8614i	1.11118	+	1.60923i
$418$	24.6926	+	28.2593i	1.20776	+	1.38221i
$419$	−9.71994	−	5.61181i	−0.474850	−	0.274155i	0.243418	−	0.969922i	$-0.421731\pi$
$419$	−9.71994	−	5.61181i	−0.474850	−	0.274155i	−0.718268	+	0.695767i	$0.755065\pi$
$420$	2.32886	+	1.05254i	0.113637	+	0.0513586i
$421$	−7.55318	−	1.33183i	−0.368120	−	0.0649094i	−0.0134715	−	0.999909i	$-0.504288\pi$
$421$	−7.55318	−	1.33183i	−0.368120	−	0.0649094i	−0.354648	+	0.935000i	$0.615399\pi$
$422$	10.2088	+	10.0227i	0.496958	+	0.487898i
$423$	40.6837	+	0.532431i	1.97811	+	0.0258877i
$424$	1.29732	−	1.96608i	0.0630034	−	0.0954813i
$425$	−8.25605	+	14.2999i	−0.400477	+	0.693647i
$426$	15.5663	+	18.4515i	0.754192	+	0.893979i
$427$	1.64357	−	4.51567i	0.0795379	−	0.218529i
$428$	1.50930	+	3.92078i	0.0729547	+	0.189518i
$429$	46.5091	−	32.1146i	2.24548	−	1.55051i
$430$	3.09721	+	4.33780i	0.149361	+	0.209187i
$431$	9.18044	−	7.70330i	0.442206	−	0.371055i	−0.394328	−	0.918970i	$-0.629023\pi$
$431$	9.18044	−	7.70330i	0.442206	−	0.371055i	0.836534	+	0.547915i	$0.184578\pi$
$432$	17.2279	+	11.6276i	0.828877	+	0.559431i
$433$	−5.20895	+	14.3115i	−0.250326	+	0.687765i	0.749346	+	0.662178i	$0.230368\pi$
$433$	−5.20895	+	14.3115i	−0.250326	+	0.687765i	−0.999673	+	0.0255873i	$0.991854\pi$
$434$	−0.993691	−	0.682254i	−0.0476987	−	0.0327492i
$435$	7.11563	+	5.05212i	0.341168	+	0.242231i
$436$	0.0821048	+	0.420273i	0.00393211	+	0.0201274i
$437$	−10.5326	−	0.806838i	−0.503843	−	0.0385963i
$438$	−9.09181	+	25.1875i	−0.434424	+	1.20350i
$439$	−25.5511	+	9.29983i	−1.21949	+	0.443857i	−0.869985	−	0.493079i	$-0.835871\pi$
$439$	−25.5511	+	9.29983i	−1.21949	+	0.443857i	−0.349502	+	0.936936i	$0.613649\pi$
$440$	−22.8678	−	9.90471i	−1.09018	−	0.472189i
$441$	19.8656	+	3.77153i	0.945982	+	0.179597i
$442$	3.35992	−	42.9511i	0.159815	−	2.04297i
$443$	10.7206	−	29.4546i	0.509351	−	1.39943i	−0.372558	−	0.928009i	$-0.621519\pi$
$443$	10.7206	−	29.4546i	0.509351	−	1.39943i	0.881909	−	0.471420i	$-0.156259\pi$
$444$	6.17910	−	1.73445i	0.293247	−	0.0823132i
$445$	−1.37331	+	0.792880i	−0.0651011	+	0.0375861i
$446$	1.77268	+	1.74037i	0.0839390	+	0.0824087i
$447$	−15.7642	−	15.9719i	−0.745623	−	0.755445i
$448$	−2.23072	−	3.41379i	−0.105391	−	0.161286i
$449$	−5.73035	+	3.30842i	−0.270432	+	0.156134i	−0.629084	−	0.777337i	$-0.716570\pi$
$449$	−5.73035	+	3.30842i	−0.270432	+	0.156134i	0.358652	+	0.933471i	$0.383236\pi$
$450$	11.1916	−	5.16586i	0.527577	−	0.243521i
$451$	−36.7964	+	13.3928i	−1.73267	+	0.630642i
$452$	−6.83412	−	5.52348i	−0.321450	−	0.259803i
$453$	−8.09268	+	11.3981i	−0.380227	+	0.535529i
$454$	4.85835	+	10.1734i	0.228014	+	0.477460i
$455$	−1.97725	+	3.42470i	−0.0926951	+	0.160553i
$456$	−17.8736	−	11.6847i	−0.837010	−	0.547187i
$457$	0.121907	+	0.211149i	0.00570256	+	0.00987712i	0.868863	−	0.495053i	$-0.164851\pi$
$457$	0.121907	+	0.211149i	0.00570256	+	0.00987712i	−0.863160	+	0.504930i	$0.831518\pi$
$458$	−8.24237	+	12.0049i	−0.385141	+	0.560951i
$459$	−13.0035	+	26.5146i	−0.606953	+	1.23760i
$460$	6.54652	−	2.52007i	0.305233	−	0.117499i
$461$	−5.23687	−	4.39426i	−0.243906	−	0.204661i	0.512637	−	0.858605i	$-0.328669\pi$
$461$	−5.23687	−	4.39426i	−0.243906	−	0.204661i	−0.756543	+	0.653944i	$0.773113\pi$
$462$	7.48934	+	1.30008i	0.348436	+	0.0604850i
$463$			5.97934i			0.277884i	0.990301	+	0.138942i	$0.0443701\pi$
$463$			5.97934i			0.277884i	−0.990301	+	0.138942i	$0.955630\pi$
$464$	−5.24077	−	12.9012i	−0.243297	−	0.598921i
$465$	4.05562	−	1.05831i	0.188075	−	0.0490779i
$466$	−28.1644	+	7.82499i	−1.30469	+	0.362486i
$467$	−15.9547	−	9.21147i	−0.738297	−	0.426256i	0.0831528	−	0.996537i	$-0.473501\pi$
$467$	−15.9547	−	9.21147i	−0.738297	−	0.426256i	−0.821450	+	0.570281i	$0.806834\pi$
$468$	−20.5416	+	24.7462i	−0.949534	+	1.14390i
$469$	−2.85911	−	3.40736i	−0.132022	−	0.157337i
$470$	25.0495	−	11.9625i	1.15545	−	0.551789i
$471$	24.1735	−	6.30803i	1.11386	−	0.290659i
$472$	−14.3847	−	19.3823i	−0.662108	−	0.892142i
$473$	12.1442	+	10.1902i	0.558392	+	0.468547i
$474$	−4.91366	+	0.879871i	−0.225692	+	0.0404138i
$475$	−11.4190	+	5.47585i	−0.523941	+	0.251249i
$476$	4.36933	−	3.80545i	0.200268	−	0.174423i
$477$	−1.22079	−	2.17985i	−0.0558959	−	0.0998085i
$478$	17.1460	−	8.18818i	0.784241	−	0.374519i
$479$	−5.34811	+	0.943016i	−0.244361	+	0.0430875i	−0.294487	−	0.955655i	$-0.595149\pi$
$479$	−5.34811	+	0.943016i	−0.244361	+	0.0430875i	0.0501259	+	0.998743i	$0.484038\pi$
$480$	14.0513	+	1.90971i	0.641353	+	0.0871660i
$481$	1.72446	+	9.77987i	0.0786284	+	0.445924i
$482$	−0.553392	+	1.21583i	−0.0252063	+	0.0553795i
$483$	−1.76071	+	1.21577i	−0.0801151	+	0.0553195i
$484$	−51.4878	−	8.10503i	−2.34036	−	0.368411i
$485$	15.5553	−	2.74281i	0.706328	−	0.124545i
$486$	19.3458	−	10.5707i	0.877543	−	0.479497i
$487$	−6.15401	−	10.6591i	−0.278865	−	0.483008i	0.692238	−	0.721669i	$-0.256625\pi$
$487$	−6.15401	−	10.6591i	−0.278865	−	0.483008i	−0.971103	+	0.238661i	$0.923291\pi$
$488$	1.59009	−	26.6165i	0.0719801	−	1.20487i
$489$	0.535827	−	5.69509i	0.0242309	−	0.257541i
$490$	13.2921	−	3.69300i	0.600478	−	0.166833i
$491$	−2.13505	−	5.86601i	−0.0963536	−	0.264729i	0.882147	−	0.470975i	$-0.156098\pi$
$491$	−2.13505	−	5.86601i	−0.0963536	−	0.264729i	−0.978500	+	0.206245i	$0.933875\pi$
$492$	18.0995	−	12.9958i	0.815987	−	0.585898i
$493$	17.1345	−	9.89259i	0.771698	−	0.445540i
$494$	20.7285	−	25.7318i	0.932618	−	1.15773i
$495$	−20.4690	+	16.7240i	−0.920012	+	0.751687i
$496$	−6.36468	−	2.05473i	−0.285783	−	0.0922600i
$497$	−4.94745	−	0.872368i	−0.221923	−	0.0391311i
$498$	−1.76623	+	10.1747i	−0.0791465	+	0.455939i
$499$	−12.6061	−	2.22280i	−0.564329	−	0.0995064i	−0.115796	−	0.993273i	$-0.536942\pi$
$499$	−12.6061	−	2.22280i	−0.564329	−	0.0995064i	−0.448532	+	0.893767i	$0.648053\pi$
$500$	14.3837	−	17.7968i	0.643261	−	0.795897i
$501$	−24.6886	−	11.7098i	−1.10300	−	0.523153i
$502$	10.3955	−	22.8395i	0.463975	−	1.01938i
$503$	34.6343	−	6.10696i	1.54427	−	0.272296i	0.664349	−	0.747423i	$-0.268709\pi$
$503$	34.6343	−	6.10696i	1.54427	−	0.272296i	0.879917	+	0.475127i	$0.157598\pi$
$504$	−4.30298	+	0.439462i	−0.191670	+	0.0195752i
$505$	−9.78355	+	16.9456i	−0.435362	+	0.754070i
$506$	16.9802	−	12.1240i	0.754862	−	0.538976i
$507$	−19.1405	−	19.3927i	−0.850061	−	0.861259i
$508$	15.6312	−	9.41230i	0.693525	−	0.417604i
$509$	11.1463	+	13.2836i	0.494051	+	0.588787i	0.954243	−	0.299032i	$-0.0966638\pi$
$509$	11.1463	+	13.2836i	0.494051	+	0.588787i	−0.460192	+	0.887820i	$0.652219\pi$
$510$	0.0535071	+	20.1482i	0.00236934	+	0.892177i
$511$	−1.90596	−	5.23658i	−0.0843146	−	0.231653i
$512$	−17.2683	−	14.6221i	−0.763159	−	0.646211i
$513$	−19.7141	+	11.1514i	−0.870400	+	0.492344i
$514$	−14.6247	+	32.1312i	−0.645068	+	1.41725i
$515$	−15.8786	+	5.77934i	−0.699695	+	0.254668i
$516$	−8.22030	−	3.71520i	−0.361879	−	0.163553i
$517$	63.2482	−	53.0716i	2.78165	−	2.33408i
$518$	−0.755969	+	1.10106i	−0.0332154	+	0.0483776i
$519$	21.3229	−	21.0457i	0.935971	−	0.923802i
$520$	−5.09208	+	21.3432i	−0.223302	+	0.935961i
$521$	−1.37049	−	0.791252i	−0.0600422	−	0.0346654i	0.469678	−	0.882838i	$-0.344370\pi$
$521$	−1.37049	−	0.791252i	−0.0600422	−	0.0346654i	−0.529721	+	0.848172i	$0.677703\pi$
$522$	−14.7084	−	1.34445i	−0.643768	−	0.0588451i
$523$	−1.44382	−	8.18832i	−0.0631339	−	0.358050i	−0.999966	−	0.00827026i	$-0.997367\pi$
$523$	−1.44382	−	8.18832i	−0.0631339	−	0.358050i	0.936832	−	0.349780i	$-0.113744\pi$
$524$	−6.96955	+	6.07010i	−0.304466	+	0.265174i
$525$	−1.09927	+	2.31768i	−0.0479762	+	0.101152i
$526$	−8.14572	−	2.10252i	−0.355170	−	0.0916744i
$527$	1.65014	−	9.35840i	0.0718811	−	0.407658i
$528$	41.8864	−	4.94522i	1.82287	−	0.215213i
$529$	2.97407	−	16.8668i	0.129307	−	0.733339i
$530$	−1.40524	−	0.964816i	−0.0610396	−	0.0419089i
$531$	−25.2682	+	4.11527i	−1.09654	+	0.178588i
$532$	4.41378	−	0.516438i	0.191362	−	0.0223904i
$533$	17.2389	+	29.8587i	0.746701	+	1.29332i
$534$	1.33574	−	2.32783i	0.0578032	−	0.100735i
$535$	2.85688	−	1.03982i	0.123513	−	0.0449552i
$536$	−20.5999	−	13.5929i	−0.889780	−	0.587122i
$537$	29.6727	+	2.79178i	1.28047	+	0.120474i
$538$	−15.4204	+	15.7068i	−0.664821	+	0.677166i
$539$	35.5352	−	20.5163i	1.53061	−	0.883698i
$540$	8.64217	−	12.3100i	0.371900	−	0.529738i
$541$	3.97900	+	22.5660i	0.171071	+	0.970189i	0.942582	+	0.333974i	$0.108390\pi$
$541$	3.97900	+	22.5660i	0.171071	+	0.970189i	−0.771512	+	0.636215i	$0.780499\pi$
$542$	−11.8234	−	42.5559i	−0.507861	−	1.82793i
$543$	18.3295	+	26.5452i	0.786594	+	1.13917i
$544$	17.2101	−	27.1557i	0.737876	−	1.16429i
$545$	0.305171	−	0.0538099i	0.0130721	−	0.00230496i
$546$	−0.0177740	−	6.69283i	−0.000760657	−	0.286427i
$547$	2.86043	+	16.2223i	0.122303	+	0.693616i	0.982873	+	0.184283i	$0.0589964\pi$
$547$	2.86043	+	16.2223i	0.122303	+	0.693616i	−0.860570	+	0.509332i	$0.829892\pi$
$548$	0.462535	+	25.1381i	0.0197585	+	1.07385i
$549$	−24.3053	−	14.4600i	−1.03732	−	0.617137i
$550$	10.3621	−	22.7660i	0.441840	−	0.970745i
$551$	15.1301	+	1.15902i	0.644563	+	0.0493760i
$552$	−7.43823	+	9.25336i	−0.316592	+	0.393849i
$553$	0.667739	−	0.795781i	0.0283952	−	0.0338400i
$554$	−15.2211	−	1.19069i	−0.646681	−	0.0505877i
$555$	−1.17265	−	4.49382i	−0.0497764	−	0.190752i
$556$	−46.1044	+	0.848309i	−1.95526	+	0.0359763i
$557$	−28.5604	+	23.9650i	−1.21014	+	1.01543i	−0.210860	+	0.977516i	$0.567626\pi$
$557$	−28.5604	+	23.9650i	−1.21014	+	1.01543i	−0.999281	+	0.0379127i	$0.987929\pi$
$558$	−5.03556	+	4.99656i	−0.213172	+	0.211521i
$559$	6.97921	−	12.0884i	0.295189	−	0.511283i
$560$	−2.49966	+	1.56853i	−0.105630	+	0.0662825i
$561$	15.1312	+	57.9855i	0.638840	+	2.44815i
$562$	−26.8292	+	2.59614i	−1.13172	+	0.109512i
$563$	38.0448			1.60340			0.801698	−	0.597729i	$-0.203930\pi$
$563$	38.0448			1.60340			0.801698	+	0.597729i	$0.203930\pi$
$564$	−26.4894	+	38.8017i	−1.11540	+	1.63385i
$565$	−4.08735	+	4.87112i	−0.171956	+	0.204929i
$566$	16.0043	−	16.3015i	0.672711	−	0.685203i
$567$	−1.68138	+	4.26853i	−0.0706115	+	0.179261i
$568$	−27.6915	+	3.19479i	−1.16191	+	0.134050i
$569$	12.9035	−	7.44983i	0.540942	−	0.312313i	−0.204519	−	0.978863i	$-0.565563\pi$
$569$	12.9035	−	7.44983i	0.540942	−	0.312313i	0.745461	+	0.666550i	$0.232230\pi$
$570$	−8.69213	+	12.7765i	−0.364073	+	0.535147i
$571$	17.8598	+	10.3114i	0.747411	+	0.431518i	0.824758	−	0.565486i	$-0.191311\pi$
$571$	17.8598	+	10.3114i	0.747411	+	0.431518i	−0.0773464	+	0.997004i	$0.524645\pi$
$572$	1.20062	+	65.2519i	0.0502004	+	2.72832i
$573$	−16.8925	−	11.9937i	−0.705693	−	0.501045i
$574$	−1.15888	+	4.48981i	−0.0483708	+	0.187401i
$575$	2.40812	+	6.61626i	0.100426	+	0.275917i
$576$	−22.1871	+	9.15054i	−0.924463	+	0.381273i
$577$	−22.6278	−	39.1926i	−0.942010	−	1.63161i	−0.761631	−	0.648011i	$-0.775601\pi$
$577$	−22.6278	−	39.1926i	−0.942010	−	1.63161i	−0.180379	−	0.983597i	$-0.557732\pi$
$578$	19.6942	+	8.96395i	0.819172	+	0.372851i
$579$	−3.79962	+	3.75022i	−0.157907	+	0.155854i
$580$	−9.40407	+	3.62008i	−0.390483	+	0.150316i
$581$	−1.07453	−	1.86114i	−0.0445791	−	0.0772133i
$582$	−20.4328	+	17.2378i	−0.846968	+	0.714532i
$583$	−4.76417	−	1.73402i	−0.197312	−	0.0718156i
$584$	−18.4276	−	24.8298i	−0.762538	−	1.02746i
$585$	17.6310	+	15.1918i	0.728954	+	0.628102i
$586$	42.5756	−	20.3322i	1.75878	−	0.839916i
$587$	−12.1847	−	33.4772i	−0.502917	−	1.38175i	−0.888414	−	0.459043i	$-0.848192\pi$
$587$	−12.1847	−	33.4772i	−0.502917	−	1.38175i	0.385497	−	0.922709i	$-0.374030\pi$
$588$	−16.3131	+	16.7045i	−0.672740	+	0.688882i
$589$	5.09753	−	5.20897i	0.210040	−	0.214632i
$590$	−14.2150	+	10.1496i	−0.585224	+	0.417853i
$591$	1.29071	−	1.81789i	0.0530926	−	0.0747779i
$592$	−2.27674	+	7.05237i	−0.0935732	+	0.289850i
$593$	2.59323	+	0.943859i	0.106491	+	0.0387596i	0.394716	−	0.918803i	$-0.370843\pi$
$593$	2.59323	+	0.943859i	0.106491	+	0.0387596i	−0.288225	+	0.957563i	$0.593065\pi$
$594$	15.7382	−	41.8760i	0.645745	−	1.71819i
$595$	−2.69517	−	3.21198i	−0.110491	−	0.131678i
$596$	25.4322	−	4.96845i	1.04174	−	0.203516i
$597$	−13.8053	−	19.9932i	−0.565013	−	0.818266i
$598$	−13.1089	−	12.8699i	−0.536064	−	0.526291i
$599$	−27.9992	−	10.1909i	−1.14402	−	0.416388i	−0.300655	−	0.953733i	$-0.597205\pi$
$599$	−27.9992	−	10.1909i	−1.14402	−	0.416388i	−0.843363	+	0.537345i	$0.819427\pi$
$600$	−2.17594	+	14.0659i	−0.0888324	+	0.574238i
$601$	8.24759	+	4.76175i	0.336426	+	0.194236i	0.658691	−	0.752414i	$-0.271111\pi$
$601$	8.24759	+	4.76175i	0.336426	+	0.194236i	−0.322264	+	0.946650i	$0.604444\pi$
$602$	1.80877	−	0.502536i	0.0737199	−	0.0204818i
$603$	−22.8397	+	12.7910i	−0.930105	+	0.520889i
$604$	−5.79878	−	15.0638i	−0.235949	−	0.612937i
$605$	−6.54963	+	37.1448i	−0.266280	+	1.51015i
$606$	−0.0879467	−	33.1165i	−0.00357259	−	1.34526i
$607$	19.6784	−	34.0839i	0.798721	−	1.38342i	−0.121729	−	0.992563i	$-0.538844\pi$
$607$	19.6784	−	34.0839i	0.798721	−	1.38342i	0.920450	−	0.390861i	$-0.127823\pi$
$608$	22.6544	−	9.73534i	0.918758	−	0.394820i
$609$	2.52926	−	1.74645i	0.102491	−	0.0707699i
$610$	−19.2365	−	1.50481i	−0.778864	−	0.0609279i
$611$	−55.6889	−	46.7286i	−2.25293	−	1.89044i
$612$	−17.2067	−	29.4406i	−0.695539	−	1.19007i
$613$	40.3552	−	14.6881i	1.62993	−	0.593247i	0.644695	−	0.764440i	$-0.276984\pi$
$613$	40.3552	−	14.6881i	1.62993	−	0.593247i	0.985237	+	0.171193i	$0.0547622\pi$
$614$	4.47592	+	4.39433i	0.180634	+	0.177341i
$615$	−9.16185	−	13.2684i	−0.369442	−	0.535034i
$616$	−6.03285	+	6.37536i	−0.243071	+	0.256871i
$617$	−17.3362	−	6.30987i	−0.697930	−	0.254026i	−0.0314033	−	0.999507i	$-0.509998\pi$
$617$	−17.3362	−	6.30987i	−0.697930	−	0.254026i	−0.666527	+	0.745481i	$0.732220\pi$
$618$	18.3246	−	21.9566i	0.737124	−	0.883223i
$619$		−	5.40986i		−	0.217441i	−0.994072	−	0.108720i	$-0.965325\pi$
$619$		−	5.40986i		−	0.217441i	0.994072	−	0.108720i	$-0.0346753\pi$
$620$	−1.57138	+	4.57765i	−0.0631080	+	0.183843i
$621$	5.09678	+	11.5149i	0.204527	+	0.462079i
$622$	−0.0377844	+	0.483012i	−0.00151502	+	0.0193670i
$623$	0.0969858	+	0.550034i	0.00388565	+	0.0220366i
$624$	−10.6922	−	35.5638i	−0.428031	−	1.42369i
$625$	−1.55683	−	1.30633i	−0.0622731	−	0.0522533i
$626$	−7.82749	+	5.58888i	−0.312850	+	0.223376i
$627$	−15.5353	+	43.2565i	−0.620420	+	1.72750i
$628$	−9.36618	+	27.2850i	−0.373751	+	1.08879i
$629$	−10.3695	−	1.82843i	−0.413461	−	0.0729043i
$630$	0.260677	+	3.11916i	0.0103856	+	0.124271i
$631$	−3.59617	+	9.88041i	−0.143161	+	0.393333i	−0.990463	−	0.137779i	$-0.956003\pi$
$631$	−3.59617	+	9.88041i	−0.143161	+	0.393333i	0.847302	+	0.531112i	$0.178226\pi$
$632$	2.29092	−	5.28923i	0.0911279	−	0.210394i
$633$	−4.64561	+	16.8947i	−0.184646	+	0.671503i
$634$	−16.0656	+	35.2970i	−0.638048	+	1.40182i
$635$	−6.60194	−	11.4349i	−0.261990	−	0.453780i
$636$	2.87672	+	0.217351i	0.114069	+	0.00861854i
$637$	−23.2229	−	27.6760i	−0.920124	−	1.09656i
$638$	−24.3920	+	17.4160i	−0.965690	+	0.689508i
$639$	−10.4749	+	27.6483i	−0.414381	+	1.09375i
$640$	−10.8093	+	12.2994i	−0.427276	+	0.486176i
$641$	10.6578	−	12.7014i	0.420956	−	0.501676i	−0.513334	−	0.858189i	$-0.671590\pi$
$641$	10.6578	−	12.7014i	0.420956	−	0.501676i	0.934291	+	0.356512i	$0.116034\pi$
$642$	−3.29696	+	3.95042i	−0.130121	+	0.155911i
$643$	−0.634481	−	1.74322i	−0.0250215	−	0.0687460i	0.926553	−	0.376164i	$-0.122757\pi$
$643$	−0.634481	−	1.74322i	−0.0250215	−	0.0687460i	−0.951574	+	0.307418i	$0.900535\pi$
$644$	−0.0454522	−	2.47026i	−0.00179107	−	0.0973420i
$645$	−2.79747	+	5.89813i	−0.110150	+	0.232239i
$646$	18.1209	+	29.9842i	0.712957	+	1.17971i
$647$			1.28085i			0.0503554i	0.999683	+	0.0251777i	$0.00801515\pi$
$647$			1.28085i			0.0503554i	−0.999683	+	0.0251777i	$0.991985\pi$
$648$	−2.18251	+	25.3621i	−0.0857372	+	0.996318i
$649$	−33.3935	+	39.7969i	−1.31081	+	1.56216i
$650$	−21.3248	−	5.50423i	−0.836428	−	0.215894i
$651$	0.138284	−	1.46977i	0.00541978	−	0.0576047i
$652$	5.13710	+	4.15192i	0.201184	+	0.162602i
$653$	8.83697			0.345817			0.172909	−	0.984938i	$-0.444683\pi$
$653$	8.83697			0.345817			0.172909	+	0.984938i	$0.444683\pi$
$654$	−0.400861	+	0.338181i	−0.0156749	+	0.0132239i
$655$	4.29908	+	5.12345i	0.167979	+	0.200190i
$656$	0.946491	+	25.7115i	0.0369543	+	1.00387i
$657$	−32.3699	+	5.27190i	−1.26287	+	0.205676i
$658$	−0.941684	−	9.73160i	−0.0367107	−	0.379377i
$659$	−9.41172	−	3.42559i	−0.366629	−	0.133442i	0.152135	−	0.988360i	$-0.451385\pi$
$659$	−9.41172	−	3.42559i	−0.366629	−	0.133442i	−0.518763	+	0.854918i	$0.673607\pi$
$660$	−3.02037	−	30.3717i	−0.117568	−	1.18222i
$661$	1.44531	+	1.72246i	0.0562162	+	0.0669958i	0.793420	−	0.608675i	$-0.208299\pi$
$661$	1.44531	+	1.72246i	0.0562162	+	0.0669958i	−0.737204	+	0.675671i	$0.763854\pi$
$662$	−35.5278	−	2.77922i	−1.38083	−	0.108017i
$663$	47.9661	−	21.9860i	1.86285	−	0.853866i
$664$	−8.66129	−	8.19597i	−0.336123	−	0.318065i
$665$	−0.314896	−	3.20035i	−0.0122111	−	0.124104i
$666$	5.53642	+	5.57964i	0.214532	+	0.216207i
$667$	1.46499	−	8.30838i	0.0567247	−	0.321702i
$668$	27.0300	−	16.2760i	1.04582	−	0.629737i
$669$	−0.806674	+	2.93363i	−0.0311878	+	0.113421i
$670$	−10.1090	+	14.7236i	−0.390545	+	0.568821i
$671$	−56.5183	+	9.96570i	−2.18186	+	0.384722i
$672$	2.32471	−	4.42050i	0.0896778	−	0.170524i
$673$			17.2305i			0.664188i	0.943246	+	0.332094i	$0.107755\pi$
$673$			17.2305i			0.664188i	−0.943246	+	0.332094i	$0.892245\pi$
$674$	32.1020	+	8.28596i	1.23652	+	0.319163i
$675$	12.1941	+	8.90011i	0.469350	+	0.342565i
$676$	30.8792	−	6.03257i	1.18766	−	0.232022i
$677$	−3.26345	−	1.88416i	−0.125425	−	0.0724140i	0.435975	−	0.899959i	$-0.356404\pi$
$677$	−3.26345	−	1.88416i	−0.125425	−	0.0724140i	−0.561400	+	0.827545i	$0.689737\pi$
$678$	1.84065	−	10.6034i	0.0706898	−	0.407223i
$679$	0.966042	−	5.47870i	0.0370733	−	0.210253i
$680$	−19.4187	−	12.8134i	−0.744673	−	0.491373i
$681$	−7.99359	+	11.2585i	−0.306315	+	0.431427i
$682$	−1.12266	+	14.3514i	−0.0429888	+	0.549542i
$683$	−2.98686			−0.114289			−0.0571444	−	0.998366i	$-0.518200\pi$
$683$	−2.98686			−0.114289			−0.0571444	+	0.998366i	$0.518200\pi$
$684$	1.85907	−	26.0872i	0.0710831	−	0.997470i
$685$	18.1942			0.695164
$686$	0.772490	−	9.87503i	0.0294938	−	0.377031i
$687$	−17.7564	−	1.67062i	−0.677449	−	0.0637383i
$688$	8.82317	−	5.53653i	0.336380	−	0.211078i
$689$	−0.775161	+	4.39616i	−0.0295313	+	0.167480i
$690$	6.59601	+	5.50493i	0.251106	+	0.209569i
$691$	39.1998	+	22.6320i	1.49123	+	0.860963i	0.999950	−	0.0100381i	$-0.00319528\pi$
$691$	39.1998	+	22.6320i	1.49123	+	0.860963i	0.491282	+	0.871001i	$0.336529\pi$
$692$	6.63302	+	33.9527i	0.252149	+	1.29069i
$693$	3.06936	+	8.78918i	0.116595	+	0.333873i
$694$	−17.0355	−	4.39710i	−0.646659	−	0.166912i
$695$			33.3689i			1.26576i
$696$	10.6850	−	13.2924i	0.405014	−	0.503849i
$697$	−36.0013	+	6.34800i	−1.36365	+	0.240448i
$698$	16.7014	−	24.3252i	0.632156	−	0.920723i
$699$	−25.1488	−	25.4800i	−0.951213	−	0.963743i
$700$	−1.52794	−	2.53748i	−0.0577505	−	0.0959077i
$701$	−5.97162	+	33.8668i	−0.225545	+	1.27913i	0.636095	+	0.771611i	$0.280549\pi$
$701$	−5.97162	+	33.8668i	−0.225545	+	1.27913i	−0.861640	+	0.507519i	$0.830563\pi$
$702$	−38.7172	−	7.24407i	−1.46129	−	0.273410i
$703$	−5.77178	−	5.64830i	−0.217687	−	0.213030i
$704$	−21.9873	+	43.4564i	−0.828677	+	1.63782i
$705$	27.7214	+	19.6823i	1.04405	+	0.741277i
$706$	13.8607	+	1.08427i	0.521653	+	0.0408071i
$707$	4.42990	+	5.27935i	0.166604	+	0.198550i
$708$	12.1748	−	26.9381i	0.457556	−	1.01240i
$709$	7.31816	+	2.66359i	0.274839	+	0.100033i	0.475763	−	0.879574i	$-0.342172\pi$
$709$	7.31816	+	2.66359i	0.274839	+	0.100033i	−0.200924	+	0.979607i	$0.564394\pi$
$710$	1.94286	+	20.0780i	0.0729143	+	0.753514i
$711$	−3.86819	−	4.73439i	−0.145068	−	0.177553i
$712$	1.38671	+	2.77147i	0.0519691	+	0.103865i
$713$	−2.60461	−	3.10405i	−0.0975433	−	0.116248i
$714$	6.67485	+	2.40939i	0.249800	+	0.0901692i
$715$	47.2274			1.76620
$716$	−21.6324	+	26.7655i	−0.808442	+	1.00027i
$717$	18.9749	+	13.4723i	0.708631	+	0.503131i
$718$	−22.8734	−	5.90395i	−0.853629	−	0.220334i
$719$	3.17730	−	3.78656i	0.118493	−	0.141215i	−0.703537	−	0.710659i	$-0.748397\pi$
$719$	3.17730	−	3.78656i	0.118493	−	0.141215i	0.822030	+	0.569444i	$0.192841\pi$
$720$	6.32527	+	16.1747i	0.235729	+	0.602797i
$721$			5.95150i			0.221646i
$722$	−1.51584	+	26.8273i	−0.0564137	+	0.998407i
$723$	−1.63074	+	0.131926i	−0.0606480	+	0.00490636i
$724$	−37.2428	+	0.685258i	−1.38412	+	0.0254674i
$725$	−3.45926	−	9.50425i	−0.128474	−	0.352979i
$726$	−21.9924	−	59.9280i	−0.816215	−	2.22414i
$727$	23.7186	−	28.2668i	0.879675	−	1.04836i	−0.118787	−	0.992920i	$-0.537901\pi$
$727$	23.7186	−	28.2668i	0.879675	−	1.04836i	0.998462	−	0.0554363i	$-0.0176550\pi$
$728$	6.45050	+	4.25637i	0.239072	+	0.157751i
$729$	22.8348	+	14.4073i	0.845734	+	0.533605i
$730$	−18.2103	+	13.0022i	−0.673992	+	0.481234i
$731$	9.51328	+	11.3375i	0.351861	+	0.419332i
$732$	29.4312	−	14.1511i	1.08781	−	0.523041i
$733$	−16.6060	−	28.7625i	−0.613358	−	1.06237i	−0.990670	−	0.136281i	$-0.956485\pi$
$733$	−16.6060	−	28.7625i	−0.613358	−	1.06237i	0.377312	−	0.926086i	$-0.376848\pi$
$734$	9.38025	−	20.6089i	0.346231	−	0.760687i
$735$	11.8689	+	12.0253i	0.437792	+	0.443559i
$736$	−4.15323	−	13.0647i	−0.153090	−	0.481572i
$737$	−18.1684	+	49.9173i	−0.669242	+	1.83873i
$738$	24.6878	+	11.6292i	0.908770	+	0.428075i
$739$	23.9715	+	4.22682i	0.881805	+	0.155486i	0.596176	−	0.802854i	$-0.296686\pi$
$739$	23.9715	+	4.22682i	0.881805	+	0.155486i	0.285630	+	0.958340i	$0.407797\pi$
$740$	5.07225	+	1.74116i	0.186460	+	0.0640063i
$741$	39.8832	+	6.85708i	1.46515	+	0.251901i
$742$	−0.488601	+	0.348864i	−0.0179371	+	0.0128072i
$743$	10.9079	+	9.15281i	0.400172	+	0.335784i	0.820560	−	0.571560i	$-0.193662\pi$
$743$	10.9079	+	9.15281i	0.400172	+	0.335784i	−0.420388	+	0.907344i	$0.638106\pi$
$744$	−1.59190	−	8.03508i	−0.0583620	−	0.294580i
$745$	−3.25623	−	18.4670i	−0.119299	−	0.676578i
$746$	−3.73176	+	47.7045i	−0.136629	+	1.74658i
$747$	−11.9406	+	4.16989i	−0.436884	+	0.152568i
$748$	−65.4492	−	22.4668i	−2.39306	−	0.821469i
$749$		−	1.07079i		−	0.0391259i
$750$	27.6125	+	4.79326i	1.00827	+	0.175025i
$751$	−32.5289	−	11.8396i	−1.18700	−	0.432031i	−0.328329	−	0.944564i	$-0.606485\pi$
$751$	−32.5289	−	11.8396i	−1.18700	−	0.432031i	−0.858668	+	0.512532i	$0.828708\pi$
$752$	−20.4172	−	50.2608i	−0.744539	−	1.83282i
$753$	30.6337	−	2.47824i	1.11635	−	0.0903119i
$754$	18.8310	+	18.4877i	0.685783	+	0.673281i
$755$	−10.9762	+	3.99502i	−0.399466	+	0.145394i
$756$	−3.03316	−	4.34317i	−0.110315	−	0.157960i
$757$	−11.7683	−	9.87475i	−0.427725	−	0.358904i	0.403367	−	0.915038i	$-0.367840\pi$
$757$	−11.7683	−	9.87475i	−0.427725	−	0.358904i	−0.831093	+	0.556134i	$0.812284\pi$
$758$	−23.6292	−	1.84843i	−0.858251	−	0.0671380i
$759$	23.0881	+	10.9506i	0.838045	+	0.397483i
$760$	−6.74216	−	16.5206i	−0.244564	−	0.599266i
$761$	5.29134	−	9.16487i	0.191811	−	0.332226i	−0.754039	−	0.656829i	$-0.771897\pi$
$761$	5.29134	−	9.16487i	0.191811	−	0.332226i	0.945850	+	0.324603i	$0.105231\pi$
$762$	19.3827	+	11.1221i	0.702162	+	0.402911i
$763$	0.0189523	−	0.107484i	0.000686119	−	0.00389118i
$764$	22.3252	−	8.59404i	0.807698	−	0.310922i
$765$	−21.5301	+	12.0575i	−0.778422	+	0.435941i
$766$	13.7753	−	3.82723i	0.497721	−	0.138283i
$767$	39.6138	+	22.8710i	1.43037	+	0.825825i
$768$	5.36307	−	27.1889i	0.193523	−	0.981096i
$769$	−1.39110	−	0.506319i	−0.0501643	−	0.0182583i	0.316816	−	0.948487i	$-0.397386\pi$
$769$	−1.39110	−	0.506319i	−0.0501643	−	0.0182583i	−0.366980	+	0.930229i	$0.619608\pi$
$770$	4.53242	+	4.44979i	0.163337	+	0.160359i
$771$	−43.0962	+	3.48645i	−1.55207	+	0.125561i
$772$	−1.18197	−	6.05018i	−0.0425399	−	0.217751i
$773$	6.07608	+	7.24119i	0.218541	+	0.260448i	0.864165	−	0.503208i	$-0.167847\pi$
$773$	6.07608	+	7.24119i	0.218541	+	0.260448i	−0.645624	+	0.763656i	$0.723403\pi$
$774$	−0.920126	−	11.0099i	−0.0330732	−	0.395742i
$775$	−4.56486	−	1.66147i	−0.163975	−	0.0596819i
$776$	−3.53784	−	30.6650i	−0.127001	−	1.10081i
$777$	−1.62857	−	0.153225i	−0.0584246	−	0.00549693i
$778$	16.8687	−	12.0443i	0.604771	−	0.431810i
$779$	−25.5372	−	11.5737i	−0.914964	−	0.414671i
$780$	−25.8736	+	7.26263i	−0.926425	+	0.260044i
$781$	20.5202	+	56.3789i	0.734272	+	2.01740i
$782$	17.5768	−	8.39391i	0.628546	−	0.300165i
$783$	−7.32152	−	16.5412i	−0.261650	−	0.591134i
$784$	−5.65523	−	26.3608i	−0.201972	−	0.941458i
$785$	19.6167	+	7.13990i	0.700150	+	0.254834i
$786$	−10.6471	−	3.84323i	−0.379769	−	0.137084i
$787$	11.5030	+	19.9238i	0.410038	+	0.710206i	0.994893	−	0.100931i	$-0.0321822\pi$
$787$	11.5030	+	19.9238i	0.410038	+	0.710206i	−0.584856	+	0.811137i	$0.698849\pi$
$788$	0.924851	+	2.40254i	0.0329465	+	0.0855868i
$789$	−2.60154	−	9.96955i	−0.0926173	−	0.354926i
$790$	−3.79639	−	1.72795i	−0.135069	−	0.0614777i
$791$	1.11981	+	1.93957i	0.0398159	+	0.0689631i
$792$	30.2398	+	41.8801i	1.07452	+	1.48814i
$793$	17.2826	+	47.4837i	0.613724	+	1.68619i
$794$	0.813675	−	3.15239i	0.0288762	−	0.111874i
$795$	0.195556	−	2.07848i	0.00693565	−	0.0737162i
$796$	28.0503	−	0.516118i	0.994216	−	0.0182933i
$797$	−44.4533	−	25.6651i	−1.57462	−	0.909105i	−0.995591	−	0.0937955i	$-0.970100\pi$
$797$	−44.4533	−	25.6651i	−1.57462	−	0.909105i	−0.579025	−	0.815310i	$-0.696567\pi$
$798$	3.18153	+	4.41590i	0.112625	+	0.156321i
$799$	66.7532	−	38.5400i	2.36156	−	1.36345i
$800$	−12.1434	−	11.0747i	−0.429334	−	0.391551i
$801$	3.28674	+	0.0430138i	0.116131	+	0.00151982i
$802$	−19.5523	+	19.9154i	−0.690417	+	0.703238i
$803$	−42.7790	+	50.9820i	−1.50964	+	1.79912i
$804$	2.27733	−	30.1413i	0.0803153	−	1.06300i
$805$	−1.78790			−0.0630152
$806$	12.6158	−	1.22078i	0.444373	−	0.0430000i
$807$	−25.9933	−	7.14749i	−0.915007	−	0.251604i
$808$	31.9174	+	21.0607i	1.12285	+	0.740914i
$809$	9.74629	−	16.8811i	0.342661	−	0.593507i	−0.642265	−	0.766483i	$-0.722005\pi$
$809$	9.74629	−	16.8811i	0.342661	−	0.593507i	0.984926	+	0.172976i	$0.0553384\pi$
$810$	18.3211	+	1.91674i	0.643736	+	0.0673473i
$811$	34.7698	−	29.1753i	1.22093	−	1.02448i	0.222156	−	0.975011i	$-0.428691\pi$
$811$	34.7698	−	29.1753i	1.22093	−	1.02448i	0.998776	−	0.0494718i	$-0.0157538\pi$
$812$	0.0652921	+	3.54853i	0.00229130	+	0.124529i
$813$	38.5000	−	37.9994i	1.35025	−	1.33270i
$814$	15.9020	+	1.24396i	0.557364	+	0.0436007i
$815$	3.07240	−	3.66155i	0.107622	−	0.128258i
$816$	39.3115	+	2.24375i	1.37618	+	0.0785469i
$817$	1.11151	+	11.2965i	0.0388867	+	0.395213i
$818$	1.23702	−	2.71780i	0.0432515	−	0.0950256i
$819$	7.15187	−	4.00527i	0.249906	−	0.139956i
$820$	18.6155	−	0.342521i	0.650081	−	0.0119613i
$821$	4.58748	+	26.0169i	0.160104	+	0.907995i	0.953970	+	0.299902i	$0.0969541\pi$
$821$	4.58748	+	26.0169i	0.160104	+	0.907995i	−0.793866	+	0.608093i	$0.791935\pi$
$822$	−26.6265	+	15.4673i	−0.928706	+	0.539482i
$823$	−27.6532	+	4.87600i	−0.963929	+	0.169967i	−0.633396	−	0.773828i	$-0.718340\pi$
$823$	−27.6532	+	4.87600i	−0.963929	+	0.169967i	−0.330533	+	0.943794i	$0.607229\pi$
$824$	9.42385	+	31.6497i	0.328295	+	1.10257i
$825$	30.5351	−	2.47026i	1.06310	−	0.0860035i
$826$	1.64682	+	5.92737i	0.0573002	+	0.206240i
$827$	4.66772	+	26.4719i	0.162312	+	0.920519i	0.951792	+	0.306743i	$0.0992392\pi$
$827$	4.66772	+	26.4719i	0.162312	+	0.920519i	−0.789480	+	0.613776i	$0.789650\pi$
$828$	−14.3329	−	2.44885i	−0.498102	−	0.0851034i
$829$	−40.9937	+	23.6677i	−1.42377	+	0.822014i	−0.996619	−	0.0821662i	$-0.973816\pi$
$829$	−40.9937	+	23.6677i	−1.42377	+	0.822014i	−0.427151	+	0.904180i	$0.640483\pi$
$830$	−6.04529	+	6.15755i	−0.209835	+	0.213732i
$831$	−7.79143	−	16.9983i	−0.270282	−	0.589664i
$832$	41.0430	+	12.4211i	1.42291	+	0.430623i
$833$	35.9965	−	13.1017i	1.24721	−	0.453946i
$834$	−28.3676	−	48.8342i	−0.982290	−	1.69099i
$835$	−11.4162	−	19.7735i	−0.395075	−	0.684290i
$836$	−31.6975	−	42.5664i	−1.09628	−	1.47219i
$837$	−8.34634	−	2.41294i	−0.288492	−	0.0834036i
$838$	13.0853	+	8.98416i	0.452023	+	0.310352i
$839$	4.95418	−	28.0966i	0.171037	−	0.970001i	−0.771581	−	0.636131i	$-0.780534\pi$
$839$	4.95418	−	28.0966i	0.171037	−	0.970001i	0.942619	−	0.333871i	$-0.108355\pi$
$840$	−3.16739	−	1.74084i	−0.109285	−	0.0600645i
$841$	2.93134	−	16.6244i	0.101081	−	0.573257i
$842$	10.5024	+	2.71081i	0.361936	+	0.0934208i
$843$	−18.7578	−	27.1655i	−0.646052	−	0.935629i
$844$	−13.2881	−	15.2570i	−0.457394	−	0.525169i
$845$	−3.95363	−	22.4221i	−0.136009	−	0.771345i
$846$	−57.3015	−	5.23777i	−1.97006	−	0.180078i
$847$	11.5047	+	6.64227i	0.395308	+	0.228231i
$848$	−2.04594	+	2.62890i	−0.0702579	+	0.0902770i
$849$	26.9775	+	7.41813i	0.925866	+	0.254589i
$850$	13.2174	−	19.2509i	0.453354	−	0.660301i
$851$	−3.43943	+	2.88603i	−0.117902	+	0.0989317i
$852$	−19.9120	−	27.7318i	−0.682175	−	0.950074i
$853$	29.2013	−	10.6284i	0.999834	−	0.363910i	0.210313	−	0.977634i	$-0.432552\pi$
$853$	29.2013	−	10.6284i	0.999834	−	0.363910i	0.789520	+	0.613724i	$0.210329\pi$
$854$	−2.81532	+	6.18540i	−0.0963383	+	0.211660i
$855$	−18.8500	−	1.69237i	−0.644657	−	0.0578778i
$856$	−1.69554	−	5.69440i	−0.0579522	−	0.194631i
$857$	−17.1733	−	47.1833i	−0.586629	−	1.61175i	−0.776624	−	0.629965i	$-0.783069\pi$
$857$	−17.1733	−	47.1833i	−0.586629	−	1.61175i	0.189995	−	0.981785i	$-0.439153\pi$
$858$	−69.1155	+	40.1489i	−2.35956	+	1.37066i
$859$	18.1537	+	21.6348i	0.619397	+	0.738169i	0.980967	−	0.194176i	$-0.0622034\pi$
$859$	18.1537	+	21.6348i	0.619397	+	0.738169i	−0.361569	+	0.932345i	$0.617759\pi$
$860$	−3.88835	−	6.45748i	−0.132592	−	0.220198i
$861$	−5.49508	+	1.43393i	−0.187272	+	0.0488683i
$862$	−13.7932	+	9.84840i	−0.469797	+	0.335438i
$863$	20.8454	−	36.1052i	0.709584	−	1.22904i	−0.255427	−	0.966828i	$-0.582216\pi$
$863$	20.8454	−	36.1052i	0.709584	−	1.22904i	0.965011	−	0.262208i	$-0.0844505\pi$
$864$	−23.0073	−	18.2939i	−0.782723	−	0.622370i
$865$	24.6539	−	4.34715i	0.838258	−	0.147807i
$866$	8.92257	−	19.6033i	0.303201	−	0.666148i
$867$	2.13696	+	26.4151i	0.0725748	+	0.897103i
$868$	1.32576	+	1.07151i	0.0449993	+	0.0363694i
$869$	−12.2178	−	2.15432i	−0.414460	−	0.0730804i
$870$	−9.47516	−	7.90782i	−0.321238	−	0.268100i
$871$	46.0614	+	8.12187i	1.56073	+	0.275199i
$872$	−0.0694072	−	0.601601i	−0.00235043	−	0.0203728i
$873$	−30.6172	−	11.5997i	−1.03623	−	0.392590i
$874$	14.7610	+	2.29923i	0.499299	+	0.0777727i
$875$	−5.05085	+	2.91611i	−0.170750	+	0.0985825i
$876$	15.5966	−	34.5092i	0.526960	−	1.16596i
$877$	−0.995479	−	2.73506i	−0.0336149	−	0.0923563i	0.921750	−	0.387785i	$-0.126760\pi$
$877$	−0.995479	−	2.73506i	−0.0336149	−	0.0923563i	−0.955365	+	0.295429i	$0.904537\pi$
$878$	37.0503	−	10.2938i	1.25039	−	0.347399i
$879$	47.1170	+	33.4532i	1.58922	+	1.12835i
$880$	31.1491	+	16.4869i	1.05003	+	0.555772i
$881$	−11.5651	−	20.0313i	−0.389637	−	0.674870i	0.602764	−	0.797920i	$-0.294066\pi$
$881$	−11.5651	−	20.0313i	−0.389637	−	0.674870i	−0.992401	+	0.123049i	$0.960733\pi$
$882$	−27.5927	−	7.50853i	−0.929094	−	0.252825i
$883$	−15.4785	+	2.72927i	−0.520891	+	0.0918472i	−0.427911	−	0.903821i	$-0.640750\pi$
$883$	−15.4785	+	2.72927i	−0.520891	+	0.0918472i	−0.0929801	+	0.995668i	$0.529639\pi$
$884$	−9.47434	+	60.1864i	−0.318656	+	2.02429i
$885$	−19.3283	−	9.16737i	−0.649714	−	0.308158i
$886$	−18.3636	+	40.3458i	−0.616938	+	1.35544i
$887$	−7.37049	−	41.8001i	−0.247477	−	1.40351i	−0.814669	−	0.579926i	$-0.803082\pi$
$887$	−7.37049	−	41.8001i	−0.247477	−	1.40351i	0.567193	−	0.823585i	$-0.308029\pi$
$888$	−8.90324	+	1.76390i	−0.298773	+	0.0591927i
$889$	−4.57987	+	0.807554i	−0.153604	+	0.0270845i
$890$	2.02369	−	0.966422i	0.0678341	−	0.0323945i
$891$	54.1880	−	8.09886i	1.81537	−	0.271322i
$892$	−2.30737	−	2.64927i	−0.0772564	−	0.0887040i
$893$	58.9444	+	4.51536i	1.97250	+	0.151101i
$894$	20.4645	+	24.2575i	0.684436	+	0.811294i
$895$	19.0775	+	16.0079i	0.637690	+	0.535086i
$896$	2.76859	+	5.05915i	0.0924920	+	0.169014i
$897$	5.96533	−	21.6941i	0.199176	−	0.724345i
$898$	8.44414	−	4.03254i	0.281785	−	0.134568i
$899$	3.74151	+	4.45896i	0.124786	+	0.148715i
$900$	−16.3489	+	6.04903i	−0.544962	+	0.201634i
$901$	−4.09901	−	2.36656i	−0.136558	−	0.0788417i
$902$	53.3566	−	14.8242i	1.77658	−	0.493593i
$903$	1.61510	+	1.63638i	0.0537472	+	0.0544552i
$904$	9.02627	+	8.54134i	0.300209	+	0.284081i
$905$			26.9552i			0.896020i
$906$	12.6670	−	15.1777i	0.420834	−	0.504244i
$907$	−21.5528	−	18.0849i	−0.715648	−	0.600500i	0.210529	−	0.977588i	$-0.432481\pi$
$907$	−21.5528	−	18.0849i	−0.715648	−	0.600500i	−0.926178	+	0.377087i	$0.876926\pi$
$908$	−5.72777	−	14.8793i	−0.190083	−	0.493788i
$909$	35.3878	−	19.8183i	1.17374	−	0.657331i
$910$	3.16546	−	4.61043i	0.104934	−	0.152834i
$911$	−17.2910	−	29.9488i	−0.572875	−	0.992249i	−0.996269	−	0.0863032i	$-0.972495\pi$
$911$	−17.2910	−	29.9488i	−0.572875	−	0.992249i	0.423394	−	0.905946i	$-0.360839\pi$
$912$	23.9114	+	18.4457i	0.791787	+	0.610798i
$913$	−12.8328	+	22.2270i	−0.424703	+	0.735607i
$914$	−0.148589	−	0.311145i	−0.00491489	−	0.0102918i
$915$	−9.84688	−	21.4826i	−0.325528	−	0.710192i
$916$	12.9450	−	16.0167i	0.427715	−	0.529206i
$917$	2.21357	−	0.805675i	0.0730987	−	0.0266057i
$918$	21.2581	−	35.9489i	0.701622	−	1.18649i
$919$	−6.53562	+	3.77334i	−0.215590	+	0.124471i	−0.603907	−	0.797055i	$-0.706390\pi$
$919$	−6.53562	+	3.77334i	−0.215590	+	0.124471i	0.388316	+	0.921526i	$0.373057\pi$
$920$	−9.50793	+	2.83103i	−0.313467	+	0.0933364i
$921$	−2.03681	+	7.40725i	−0.0671151	+	0.244077i
$922$	6.89885	+	6.77308i	0.227202	+	0.223060i
$923$	45.7491	−	26.4132i	1.50585	−	0.869402i
$924$	−10.4159	−	2.65900i	−0.342657	−	0.0874747i
$925$	−1.84099	+	5.05808i	−0.0605314	+	0.166309i
$926$	0.659475	−	8.43031i	0.0216717	−	0.277037i
$927$	34.4114	+	6.53308i	1.13022	+	0.214574i
$928$	5.96610	+	18.7674i	0.195847	+	0.616071i
$929$	14.0624	−	5.11829i	0.461372	−	0.167926i	−0.100868	−	0.994900i	$-0.532162\pi$
$929$	14.0624	−	5.11829i	0.461372	−	0.167926i	0.562240	+	0.826974i	$0.309940\pi$
$930$	−5.83477	+	1.04481i	−0.191330	+	0.0342607i
$931$	28.4591	+	7.29675i	0.932710	+	0.239141i
$932$	40.5721	−	7.92620i	1.32898	−	0.259631i
$933$	−0.539408	+	0.247246i	−0.0176594	+	0.00809448i
$934$	21.4787	+	14.7470i	0.702805	+	0.482536i
$935$	−17.1266	+	47.0550i	−0.560100	+	1.53886i
$936$	31.6910	−	32.6243i	1.03585	−	1.06636i
$937$	4.09258	−	3.43408i	0.133699	−	0.112187i	−0.573486	−	0.819215i	$-0.694409\pi$
$937$	4.09258	−	3.43408i	0.133699	−	0.112187i	0.707185	+	0.707029i	$0.249965\pi$
$938$	3.65528	+	5.11939i	0.119349	+	0.167154i
$939$	−10.6431	−	5.04800i	−0.347324	−	0.164735i
$940$	−36.6368	+	14.1032i	−1.19496	+	0.459997i
$941$	−12.3010	+	33.7966i	−0.401000	+	1.10174i	0.560792	+	0.827957i	$0.310497\pi$
$941$	−12.3010	+	33.7966i	−0.401000	+	1.10174i	−0.961792	+	0.273782i	$0.911725\pi$
$942$	−34.7781	+	6.22759i	−1.13313	+	0.202906i
$943$	−7.79402	+	13.4996i	−0.253808	+	0.439609i
$944$	18.1433	+	28.9137i	0.590515	+	0.941061i
$945$	−3.18277	+	2.13674i	−0.103536	+	0.0695083i
$946$	−15.9983	−	15.7067i	−0.520150	−	0.510668i
$947$	−26.1582	−	4.61240i	−0.850028	−	0.149883i	−0.268370	−	0.963316i	$-0.586485\pi$
$947$	−26.1582	−	4.61240i	−0.850028	−	0.149883i	−0.581658	+	0.813433i	$0.697596\pi$
$948$	7.02484	−	0.698598i	0.228156	−	0.0226894i
$949$	50.7475	+	29.2991i	1.64733	+	0.951088i
$950$	16.7037	−	6.46101i	0.541939	−	0.209623i
$951$	−47.3424	+	3.82996i	−1.53518	+	0.124195i
$952$	−6.58006	+	4.88343i	−0.213261	+	0.158273i
$953$	−8.80218	+	10.4900i	−0.285131	+	0.339806i	−0.889531	−	0.456876i	$-0.848968\pi$
$953$	−8.80218	+	10.4900i	−0.285131	+	0.339806i	0.604400	+	0.796681i	$0.293413\pi$
$954$	1.48077	+	3.20803i	0.0479418	+	0.103864i
$955$	−5.92079	−	16.2672i	−0.191592	−	0.526396i
$956$	−25.0774	+	9.65349i	−0.811061	+	0.312216i
$957$	−33.1660	−	15.7306i	−1.07210	−	0.508497i
$958$	7.64434	−	0.739710i	0.246977	−	0.0238989i
$959$	2.19172	−	6.02169i	0.0707742	−	0.194451i
$960$	−19.6005	−	4.24227i	−0.632602	−	0.136919i
$961$	−28.2043			−0.909816
$962$	−1.35268	−	13.9789i	−0.0436120	−	0.450698i
$963$	−6.19129	−	1.17543i	−0.199511	−	0.0378777i
$964$	0.914327	−	1.65317i	0.0294485	−	0.0532450i
$965$	−4.39319	+	0.774637i	−0.141422	+	0.0249365i
$966$	2.61653	−	1.51993i	0.0841853	−	0.0489030i
$967$	−7.03703	+	8.38641i	−0.226296	+	0.269689i	−0.867231	−	0.497906i	$-0.834102\pi$
$967$	−7.03703	+	8.38641i	−0.226296	+	0.269689i	0.640935	+	0.767595i	$0.278547\pi$
$968$	71.6991	+	17.1060i	2.30450	+	0.549809i
$969$	−21.2954	+	37.2510i	−0.684106	+	1.19668i
$970$	−22.2340	+	2.15148i	−0.713890	+	0.0690800i
$971$	1.55755	−	8.83329i	0.0499841	−	0.283474i	−0.949563	−	0.313577i	$-0.898473\pi$
$971$	1.55755	−	8.83329i	0.0499841	−	0.283474i	0.999547	+	0.0301034i	$0.00958367\pi$
$972$	−28.4416	+	12.7700i	−0.912266	+	0.409599i
$973$	11.0440	+	4.01970i	0.354056	+	0.128866i
$974$	7.50096	+	15.7070i	0.240346	+	0.503285i
$975$	−6.81062	−	26.0995i	−0.218114	−	0.835852i
$976$	−5.17747	+	37.3514i	−0.165727	+	1.19559i
$977$	24.7284	−	14.2769i	0.791132	−	0.456760i	−0.0492292	−	0.998788i	$-0.515676\pi$
$977$	24.7284	−	14.2769i	0.791132	−	0.456760i	0.840361	+	0.542027i	$0.182343\pi$
$978$	−1.38359	+	7.97045i	−0.0442423	+	0.254867i
$979$	5.10967	−	4.28752i	0.163306	−	0.137030i
$980$	−19.1480	+	3.74076i	−0.611660	+	0.119494i
$981$	−0.600664	−	0.227569i	−0.0191777	−	0.00726570i
$982$	2.36325	+	8.50600i	0.0754143	+	0.271437i
$983$	8.46528	+	7.10321i	0.270000	+	0.226557i	0.767728	−	0.640776i	$-0.221387\pi$
$983$	8.46528	+	7.10321i	0.270000	+	0.226557i	−0.497727	+	0.867334i	$0.665832\pi$
$984$	−26.9519	+	16.3267i	−0.859195	+	0.520476i
$985$	1.75061	−	0.637168i	0.0557789	−	0.0203019i
$986$	−25.2491	+	12.0578i	−0.804095	+	0.384000i
$987$	9.85358	−	6.80390i	0.313643	−	0.216571i
$988$	−32.0632	+	33.9932i	−1.02007	+	1.08147i
$989$	6.31085			0.200673
$990$	30.7039	−	21.3217i	0.975832	−	0.677647i
$991$	−13.3786	−	11.2259i	−0.424984	−	0.356604i	0.405071	−	0.914285i	$-0.367247\pi$
$991$	−13.3786	−	11.2259i	−0.424984	−	0.356604i	−0.830055	+	0.557681i	$0.811691\pi$
$992$	8.74699	+	3.59895i	0.277717	+	0.114267i
$993$	−18.1861	−	39.6760i	−0.577120	−	1.25908i
$994$	6.87922	+	1.77562i	0.218196	+	0.0563193i
$995$		−	20.3019i		−	0.643615i
$996$	3.61240	−	14.1506i	0.114463	−	0.448378i
$997$	28.4533	−	23.8751i	0.901124	−	0.756133i	−0.0692855	−	0.997597i	$-0.522072\pi$
$997$	28.4533	−	23.8751i	0.901124	−	0.756133i	0.970410	+	0.241464i	$0.0776275\pi$
$998$	17.5283	+	4.52430i	0.554850	+	0.143214i
$999$	−2.67365	+	9.24814i	−0.0845907	+	0.292598i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.2.cc.a.211.5	yes	696
4.3	odd	2	inner	684.2.cc.a.211.88	yes	696
9.7	even	3		684.2.bt.a.439.74	yes	696
19.10	odd	18		684.2.bt.a.67.9	✓	696
36.7	odd	6		684.2.bt.a.439.9	yes	696
76.67	even	18		684.2.bt.a.67.74	yes	696
171.124	odd	18	inner	684.2.cc.a.295.88	yes	696
684.295	even	18	inner	684.2.cc.a.295.5	yes	696

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.2.bt.a.67.9	✓	696	19.10	odd	18
684.2.bt.a.67.74	yes	696	76.67	even	18
684.2.bt.a.439.9	yes	696	36.7	odd	6
684.2.bt.a.439.74	yes	696	9.7	even	3
684.2.cc.a.211.5	yes	696	1.1	even	1	trivial
684.2.cc.a.211.88	yes	696	4.3	odd	2	inner
684.2.cc.a.295.5	yes	696	684.295	even	18	inner
684.2.cc.a.295.88	yes	696	171.124	odd	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:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	684.cc (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40991 - 0.110292i) q^{2} +(-0.721709 - 1.57453i) q^{3} +(1.97567 + 0.311003i) q^{4} +(0.251320 - 1.42531i) q^{5} +(0.843885 + 2.29953i) q^{6} +(-0.441456 - 0.254875i) q^{7} +(-2.75121 - 0.656387i) q^{8} +(-1.95827 + 2.27270i) q^{9} +(-0.511538 + 1.98183i) q^{10} +6.08777i q^{11} +(-0.936178 - 3.33520i) q^{12} +(5.27874 - 0.930784i) q^{13} +(0.594301 + 0.408039i) q^{14} +(-2.42556 + 0.632947i) q^{15} +(3.80655 + 1.22888i) q^{16} +(-0.986905 + 5.59702i) q^{17} +(3.01164 - 2.98831i) q^{18} +(-3.04870 + 3.11535i) q^{19} +(0.939800 - 2.73778i) q^{20} +(-0.0827042 + 0.879030i) q^{21} +(0.671433 - 8.58318i) q^{22} +(1.55775 + 1.85645i) q^{23} +(0.952076 + 4.80558i) q^{24} +(2.73013 + 0.993685i) q^{25} +(-7.54519 + 0.730115i) q^{26} +(4.99173 + 1.44312i) q^{27} +(-0.792905 - 0.640843i) q^{28} +(-2.23770 - 2.66679i) q^{29} +(3.48963 - 0.624875i) q^{30} -1.67203 q^{31} +(-5.23135 - 2.15244i) q^{32} +(9.58536 - 4.39360i) q^{33} +(2.00875 - 7.78242i) q^{34} +(-0.474221 + 0.565155i) q^{35} +(-4.57572 + 3.88108i) q^{36} +1.85269i q^{37} +(4.64198 - 4.05610i) q^{38} +(-5.27526 - 7.63976i) q^{39} +(-1.62699 + 3.75635i) q^{40} +(2.19995 + 6.04432i) q^{41} +(0.213555 - 1.23023i) q^{42} +(1.67388 - 1.99486i) q^{43} +(-1.89332 + 12.0274i) q^{44} +(2.74714 + 3.36231i) q^{45} +(-1.99153 - 2.78923i) q^{46} +(-8.71774 - 10.3894i) q^{47} +(-0.812320 - 6.88042i) q^{48} +(-3.37008 - 5.83715i) q^{49} +(-3.73963 - 1.70211i) q^{50} +(9.52491 - 2.48551i) q^{51} +(10.7185 - 0.197218i) q^{52} +(-0.284836 + 0.782580i) q^{53} +(-6.87871 - 2.58521i) q^{54} +(8.67693 + 1.52998i) q^{55} +(1.04724 + 0.990980i) q^{56} +(7.10548 + 2.55189i) q^{57} +(2.86083 + 4.00673i) q^{58} +(6.53719 + 5.48535i) q^{59} +(-4.98896 + 0.496137i) q^{60} +(1.63700 + 9.28391i) q^{61} +(2.35741 + 0.184412i) q^{62} +(1.44374 - 0.504184i) q^{63} +(7.13831 + 3.61171i) q^{64} -7.75774i q^{65} +(-13.9990 + 5.13737i) q^{66} +(8.19960 + 2.98441i) q^{67} +(-3.69049 + 10.7509i) q^{68} +(1.79879 - 3.79254i) q^{69} +(0.730940 - 0.744512i) q^{70} +(9.26102 - 3.37073i) q^{71} +(6.87939 - 4.96730i) q^{72} +(8.37450 + 7.02704i) q^{73} +(0.204337 - 2.61212i) q^{74} +(-0.405775 - 5.01581i) q^{75} +(-6.99212 + 5.20675i) q^{76} +(1.55162 - 2.68748i) q^{77} +(6.59502 + 11.3532i) q^{78} +(-0.353877 + 2.00694i) q^{79} +(2.70819 - 5.11666i) q^{80} +(-1.33035 - 8.90113i) q^{81} +(-2.43508 - 8.76456i) q^{82} +(3.65110 + 2.10796i) q^{83} +(-0.436777 + 1.71095i) q^{84} +(7.72943 + 2.81328i) q^{85} +(-2.58004 + 2.62794i) q^{86} +(-2.58396 + 5.44797i) q^{87} +(3.99593 - 16.7487i) q^{88} +(-0.704285 - 0.839334i) q^{89} +(-3.50238 - 5.04353i) q^{90} +(-2.56756 - 0.934517i) q^{91} +(2.50024 + 4.15221i) q^{92} +(1.20672 + 2.63266i) q^{93} +(11.1453 + 15.6096i) q^{94} +(3.67413 + 5.12828i) q^{95} +(0.386439 + 9.79034i) q^{96} +(3.73268 + 10.2555i) q^{97} +(4.10770 + 8.60152i) q^{98} +(-13.8357 - 11.9215i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 696 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 6 q^{6} - 18 q^{8} - 12 q^{10} - 9 q^{12} - 6 q^{13} - 15 q^{14} - 3 q^{16} - 24 q^{17} - 6 q^{20} - 30 q^{21} + 21 q^{22} + 24 q^{24} - 6 q^{25} - 30 q^{26} - 6 q^{29}+ \cdots - 63 q^{98}+O(q^{100}) \) 696 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 - 6 * q^6 - 18 * q^8 - 12 * q^10 - 9 * q^12 - 6 * q^13 - 15 * q^14 - 3 * q^16 - 24 * q^17 - 6 * q^20 - 30 * q^21 + 21 * q^22 + 24 * q^24 - 6 * q^25 - 30 * q^26 - 6 * q^29 - 21 * q^30 - 3 * q^32 + 36 * q^33 + 33 * q^34 + 54 * q^36 - 3 * q^38 - 33 * q^40 + 54 * q^41 - 87 * q^42 - 33 * q^44 - 6 * q^45 - 18 * q^46 + 6 * q^48 + 282 * q^49 - 3 * q^52 - 24 * q^53 - 51 * q^54 - 63 * q^56 - 12 * q^57 - 6 * q^58 - 27 * q^60 - 6 * q^61 - 18 * q^62 - 24 * q^64 - 30 * q^66 + 3 * q^68 - 18 * q^69 - 45 * q^70 + 12 * q^72 - 60 * q^73 + 3 * q^74 - 3 * q^76 + 72 * q^77 - 81 * q^78 - 12 * q^80 - 72 * q^81 - 12 * q^82 - 9 * q^84 - 6 * q^85 - 57 * q^86 - 9 * q^88 - 24 * q^89 + 39 * q^90 + 81 * q^92 - 48 * q^93 + 15 * q^96 + 30 * q^97 - 63 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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