LMFDB - Embedded newform 228.2.w.b.67.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [228,2,Mod(67,228)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(228, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 0, 17])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("228.67"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 228 = 2^{2} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	228.w (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [60,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.82058916609$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$10$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			67.8
Character	$\chi$	$=$	228.67
Dual form			228.2.w.b.211.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.814750 + 1.15593i) q^{2} +(0.766044 - 0.642788i) q^{3} +(-0.672365 + 1.88359i) q^{4} +(3.29537 + 1.19942i) q^{5} +(1.36715 + 0.361785i) q^{6} +(-2.21173 - 1.27694i) q^{7} +(-2.72512 + 0.757450i) q^{8} +(0.173648 - 0.984808i) q^{9} +(1.29846 + 4.78645i) q^{10} +(0.00324770 - 0.00187506i) q^{11} +(0.695690 + 1.87510i) q^{12} +(0.382681 - 0.456062i) q^{13} +(-0.325947 - 3.59701i) q^{14} +(3.29537 - 1.19942i) q^{15} +(-3.09585 - 2.53292i) q^{16} +(-0.634319 - 3.59740i) q^{17} +(1.27985 - 0.601646i) q^{18} +(-2.19475 + 3.76604i) q^{19} +(-4.47490 + 5.40069i) q^{20} +(-2.51509 + 0.443478i) q^{21} +(0.00481351 + 0.00222642i) q^{22} +(0.471769 + 1.29618i) q^{23} +(-1.60068 + 2.33191i) q^{24} +(5.59064 + 4.69110i) q^{25} +(0.838966 + 0.0707777i) q^{26} +(-0.500000 - 0.866025i) q^{27} +(3.89234 - 3.30743i) q^{28} +(-4.56231 - 0.804457i) q^{29} +(4.07135 + 2.83200i) q^{30} +(4.50482 - 7.80257i) q^{31} +(0.405545 - 5.64230i) q^{32} +(0.00128262 - 0.00352396i) q^{33} +(3.64155 - 3.66421i) q^{34} +(-5.75689 - 6.86079i) q^{35} +(1.73822 + 0.989232i) q^{36} +11.9654i q^{37} +(-6.14147 + 0.531404i) q^{38} -0.595346i q^{39} +(-9.88877 - 0.772475i) q^{40} +(-6.76233 - 8.05903i) q^{41} +(-2.56180 - 2.54595i) q^{42} +(1.12571 - 3.09286i) q^{43} +(0.00134821 + 0.00737807i) q^{44} +(1.75343 - 3.03703i) q^{45} +(-1.11392 + 1.60139i) q^{46} +(1.35380 + 0.238711i) q^{47} +(-3.99969 + 0.0496434i) q^{48} +(-0.238826 - 0.413659i) q^{49} +(-0.867630 + 10.2845i) q^{50} +(-2.79828 - 2.34804i) q^{51} +(0.601734 + 1.02746i) q^{52} +(-2.00076 - 5.49705i) q^{53} +(0.593693 - 1.28356i) q^{54} +(0.0129513 - 0.00228367i) q^{55} +(6.99445 + 1.80455i) q^{56} +(0.739493 + 4.29571i) q^{57} +(-2.78724 - 5.92915i) q^{58} +(-1.05912 - 6.00657i) q^{59} +(0.0435239 + 7.01358i) q^{60} +(10.1552 - 3.69618i) q^{61} +(12.6896 - 1.14988i) q^{62} +(-1.64161 + 1.95639i) q^{63} +(6.85254 - 4.12828i) q^{64} +(1.80808 - 1.04390i) q^{65} +(0.00511847 - 0.00138853i) q^{66} +(-2.79523 + 15.8525i) q^{67} +(7.20254 + 1.22397i) q^{68} +(1.19456 + 0.689680i) q^{69} +(3.24019 - 12.2444i) q^{70} +(9.17413 + 3.33911i) q^{71} +(0.272730 + 2.81525i) q^{72} +(-8.53345 + 7.16041i) q^{73} +(-13.8312 + 9.74884i) q^{74} +7.29806 q^{75} +(-5.61803 - 6.66617i) q^{76} -0.00957739 q^{77} +(0.688181 - 0.485058i) q^{78} +(-1.45560 + 1.22139i) q^{79} +(-7.16395 - 12.0601i) q^{80} +(-0.939693 - 0.342020i) q^{81} +(3.80609 - 14.3829i) q^{82} +(6.90065 + 3.98409i) q^{83} +(0.855724 - 5.03559i) q^{84} +(2.22447 - 12.6156i) q^{85} +(4.49232 - 1.21866i) q^{86} +(-4.01202 + 2.31634i) q^{87} +(-0.00743010 + 0.00756973i) q^{88} +(-9.76573 + 11.6383i) q^{89} +(4.93921 - 0.447572i) q^{90} +(-1.42875 + 0.520024i) q^{91} +(-2.75867 + 0.0171194i) q^{92} +(-1.56451 - 8.87276i) q^{93} +(0.827074 + 1.75939i) q^{94} +(-11.7496 + 9.77809i) q^{95} +(-3.31613 - 4.58293i) q^{96} +(1.06007 - 0.186919i) q^{97} +(0.283579 - 0.613096i) q^{98} +(-0.00128262 - 0.00352396i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 3 q^{2} - 3 q^{4} + 3 q^{6} - 3 q^{8} - 6 q^{10} - 6 q^{13} - 9 q^{14} + 21 q^{16} + 18 q^{19} + 30 q^{20} - 6 q^{21} - 12 q^{22} - 18 q^{24} - 30 q^{27} - 18 q^{28} - 12 q^{31} + 33 q^{32} - 15 q^{34}+ \cdots - 105 q^{98}+O(q^{100}) $ 60 * q + 3 * q^2 - 3 * q^4 + 3 * q^6 - 3 * q^8 - 6 * q^10 - 6 * q^13 - 9 * q^14 + 21 * q^16 + 18 * q^19 + 30 * q^20 - 6 * q^21 - 12 * q^22 - 18 * q^24 - 30 * q^27 - 18 * q^28 - 12 * q^31 + 33 * q^32 - 15 * q^34 - 3 * q^36 - 84 * q^38 - 87 * q^40 - 12 * q^41 + 9 * q^42 - 18 * q^43 - 51 * q^44 - 21 * q^46 + 18 * q^48 + 30 * q^49 - 27 * q^50 - 3 * q^52 + 12 * q^53 + 3 * q^54 + 42 * q^56 - 36 * q^58 + 15 * q^60 + 105 * q^62 - 12 * q^63 + 21 * q^64 - 36 * q^65 + 24 * q^66 + 42 * q^67 - 15 * q^68 - 72 * q^69 - 96 * q^70 + 24 * q^71 + 18 * q^72 + 18 * q^73 + 69 * q^74 + 60 * q^75 + 54 * q^76 - 72 * q^77 + 57 * q^78 + 12 * q^79 - 12 * q^80 + 75 * q^82 + 39 * q^84 - 60 * q^85 + 21 * q^86 + 36 * q^88 - 12 * q^89 + 15 * q^90 - 84 * q^91 + 99 * q^92 - 12 * q^93 - 24 * q^95 + 12 * q^97 - 105 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/228\mathbb{Z}\right)^\times$.

$n$	$77$	$97$	$115$
$\chi(n)$	$1$	$e\left(\frac{17}{18}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.814750	+	1.15593i	0.576115	+	0.817368i
$2$	0.814750	+	1.15593i	0.576115	+	0.817368i
$3$	0.766044	−	0.642788i	0.442276	−	0.371114i
$3$	0.766044	−	0.642788i	0.442276	−	0.371114i
$4$	−0.672365	+	1.88359i	−0.336182	+	0.941797i
$5$	3.29537	+	1.19942i	1.47373	+	0.536395i	0.949112	−	0.314940i	$-0.101984\pi$
$5$	3.29537	+	1.19942i	1.47373	+	0.536395i	0.524622	+	0.851335i	$0.324207\pi$
$6$	1.36715	+	0.361785i	0.558138	+	0.147698i
$7$	−2.21173	−	1.27694i	−0.835956	−	0.482640i	0.0199314	−	0.999801i	$-0.493655\pi$
$7$	−2.21173	−	1.27694i	−0.835956	−	0.482640i	−0.855888	+	0.517162i	$0.826989\pi$
$8$	−2.72512	+	0.757450i	−0.963475	+	0.267799i
$9$	0.173648	−	0.984808i	0.0578827	−	0.328269i
$10$	1.29846	+	4.78645i	0.410608	+	1.51361i
$11$	0.00324770	−	0.00187506i	0.000979218	−	0.000565352i	−0.499510	−	0.866308i	$-0.666487\pi$
$11$	0.00324770	−	0.00187506i	0.000979218	−	0.000565352i	0.500490	+	0.865743i	$0.333153\pi$
$12$	0.695690	+	1.87510i	0.200828	+	0.541296i
$13$	0.382681	−	0.456062i	0.106137	−	0.126489i	−0.710361	−	0.703838i	$-0.751468\pi$
$13$	0.382681	−	0.456062i	0.106137	−	0.126489i	0.816498	+	0.577349i	$0.195913\pi$
$14$	−0.325947	−	3.59701i	−0.0871129	−	0.961340i
$15$	3.29537	−	1.19942i	0.850861	−	0.309688i
$16$	−3.09585	−	2.53292i	−0.773963	−	0.633231i
$17$	−0.634319	−	3.59740i	−0.153845	−	0.872498i	−0.959834	−	0.280568i	$-0.909477\pi$
$17$	−0.634319	−	3.59740i	−0.153845	−	0.872498i	0.805989	−	0.591930i	$-0.201634\pi$
$18$	1.27985	−	0.601646i	0.301664	−	0.141809i
$19$	−2.19475	+	3.76604i	−0.503509	+	0.863990i
$19$	−2.19475	+	3.76604i	−0.503509	+	0.863990i
$20$	−4.47490	+	5.40069i	−1.00062	+	1.20763i
$21$	−2.51509	+	0.443478i	−0.548838	+	0.0967749i
$22$	0.00481351	+	0.00222642i	0.00102624	+	0.000474674i
$23$	0.471769	+	1.29618i	0.0983707	+	0.270271i	0.979110	−	0.203329i	$-0.0651762\pi$
$23$	0.471769	+	1.29618i	0.0983707	+	0.270271i	−0.880740	+	0.473601i	$0.842954\pi$
$24$	−1.60068	+	2.33191i	−0.326738	+	0.476000i
$25$	5.59064	+	4.69110i	1.11813	+	0.938221i
$26$	0.838966	+	0.0707777i	0.164535	+	0.0138806i
$27$	−0.500000	−	0.866025i	−0.0962250	−	0.166667i
$28$	3.89234	−	3.30743i	0.735582	−	0.625046i
$29$	−4.56231	−	0.804457i	−0.847199	−	0.149384i	−0.266836	−	0.963742i	$-0.585978\pi$
$29$	−4.56231	−	0.804457i	−0.847199	−	0.149384i	−0.580363	+	0.814358i	$0.697089\pi$
$30$	4.07135	+	2.83200i	0.743323	+	0.517051i
$31$	4.50482	−	7.80257i	0.809089	−	1.40138i	−0.104407	−	0.994535i	$-0.533294\pi$
$31$	4.50482	−	7.80257i	0.809089	−	1.40138i	0.913496	−	0.406848i	$-0.133372\pi$
$32$	0.405545	−	5.64230i	0.0716910	−	0.997427i
$33$	0.00128262	−	0.00352396i	0.000223275	−	0.000613443i
$34$	3.64155	−	3.66421i	0.624520	−	0.628408i
$35$	−5.75689	−	6.86079i	−0.973092	−	1.15969i
$36$	1.73822	+	0.989232i	0.289704	+	0.164872i
$37$			11.9654i			1.96711i	0.180622	+	0.983553i	$0.442189\pi$
$37$			11.9654i			1.96711i	−0.180622	+	0.983553i	$0.557811\pi$
$38$	−6.14147	+	0.531404i	−0.996277	+	0.0862051i
$39$		−	0.595346i		−	0.0953317i
$40$	−9.88877	−	0.772475i	−1.56355	−	0.122139i
$41$	−6.76233	−	8.05903i	−1.05610	−	1.25861i	−0.964856	−	0.262780i	$-0.915361\pi$
$41$	−6.76233	−	8.05903i	−1.05610	−	1.25861i	−0.0912419	−	0.995829i	$-0.529084\pi$
$42$	−2.56180	−	2.54595i	−0.395294	−	0.392849i
$43$	1.12571	−	3.09286i	0.171669	−	0.471657i	−0.823785	−	0.566903i	$-0.808141\pi$
$43$	1.12571	−	3.09286i	0.171669	−	0.471657i	0.995454	+	0.0952458i	$0.0303637\pi$
$44$	0.00134821	+	0.00737807i	0.000203251	+	0.00111229i
$45$	1.75343	−	3.03703i	0.261386	−	0.452734i
$46$	−1.11392	+	1.60139i	−0.164238	+	0.236112i
$47$	1.35380	+	0.238711i	0.197472	+	0.0348196i	0.271509	−	0.962436i	$-0.412477\pi$
$47$	1.35380	+	0.238711i	0.197472	+	0.0348196i	−0.0740373	+	0.997255i	$0.523588\pi$
$48$	−3.99969	+	0.0496434i	−0.577306	+	0.00716540i
$49$	−0.238826	−	0.413659i	−0.0341180	−	0.0590942i
$50$	−0.867630	+	10.2845i	−0.122701	+	1.45445i
$51$	−2.79828	−	2.34804i	−0.391838	−	0.328791i
$52$	0.601734	+	1.02746i	0.0834455	+	0.142482i
$53$	−2.00076	−	5.49705i	−0.274826	−	0.755078i	−0.997928	−	0.0643373i	$-0.979507\pi$
$53$	−2.00076	−	5.49705i	−0.274826	−	0.755078i	0.723102	−	0.690741i	$-0.242716\pi$
$54$	0.593693	−	1.28356i	0.0807913	−	0.174671i
$55$	0.0129513	−	0.00228367i	0.00174636	−	0.000307930i
$56$	6.99445	+	1.80455i	0.934673	+	0.241143i
$57$	0.739493	+	4.29571i	0.0979482	+	0.568981i
$58$	−2.78724	−	5.92915i	−0.365982	−	0.778536i
$59$	−1.05912	−	6.00657i	−0.137886	−	0.781989i	−0.972807	−	0.231619i	$-0.925598\pi$
$59$	−1.05912	−	6.00657i	−0.137886	−	0.781989i	0.834921	−	0.550370i	$-0.185513\pi$
$60$	0.0435239	+	7.01358i	0.00561891	+	0.905450i
$61$	10.1552	−	3.69618i	1.30024	−	0.473248i	0.403164	−	0.915128i	$-0.367911\pi$
$61$	10.1552	−	3.69618i	1.30024	−	0.473248i	0.897074	+	0.441880i	$0.145688\pi$
$62$	12.6896	−	1.14988i	1.61157	−	0.146035i
$63$	−1.64161	+	1.95639i	−0.206823	+	0.246482i
$64$	6.85254	−	4.12828i	0.856568	−	0.516035i
$65$	1.80808	−	1.04390i	0.224265	−	0.129480i
$66$	0.00511847	−	0.00138853i	0.000630041	−	0.000170916i
$67$	−2.79523	+	15.8525i	−0.341492	+	1.93670i	0.00855120	+	0.999963i	$0.497278\pi$
$67$	−2.79523	+	15.8525i	−0.341492	+	1.93670i	−0.350043	+	0.936734i	$0.613833\pi$
$68$	7.20254	+	1.22397i	0.873436	+	0.148428i
$69$	1.19456	+	0.689680i	0.143808	+	0.0830278i
$70$	3.24019	−	12.2444i	0.387277	−	1.46349i
$71$	9.17413	+	3.33911i	1.08877	+	0.396279i	0.823165	−	0.567803i	$-0.192206\pi$
$71$	9.17413	+	3.33911i	1.08877	+	0.396279i	0.265604	+	0.964082i	$0.414429\pi$
$72$	0.272730	+	2.81525i	0.0321416	+	0.331780i
$73$	−8.53345	+	7.16041i	−0.998764	+	0.838063i	−0.986813	−	0.161866i	$-0.948249\pi$
$73$	−8.53345	+	7.16041i	−0.998764	+	0.838063i	−0.0119514	+	0.999929i	$0.503804\pi$
$74$	−13.8312	+	9.74884i	−1.60785	+	1.13328i
$75$	7.29806			0.842707
$76$	−5.61803	−	6.66617i	−0.644432	−	0.764662i
$77$	−0.00957739			−0.00109144
$78$	0.688181	−	0.485058i	0.0779211	−	0.0549220i
$79$	−1.45560	+	1.22139i	−0.163767	+	0.137417i	−0.720989	−	0.692947i	$-0.756312\pi$
$79$	−1.45560	+	1.22139i	−0.163767	+	0.137417i	0.557221	+	0.830364i	$0.311868\pi$
$80$	−7.16395	−	12.0601i	−0.800954	−	1.34836i
$81$	−0.939693	−	0.342020i	−0.104410	−	0.0380022i
$82$	3.80609	−	14.3829i	0.420313	−	1.58832i
$83$	6.90065	+	3.98409i	0.757445	+	0.437311i	0.828378	−	0.560170i	$-0.189264\pi$
$83$	6.90065	+	3.98409i	0.757445	+	0.437311i	−0.0709327	+	0.997481i	$0.522598\pi$
$84$	0.855724	−	5.03559i	0.0933672	−	0.549427i
$85$	2.22447	−	12.6156i	0.241277	−	1.36835i
$86$	4.49232	−	1.21866i	0.484419	−	0.131412i
$87$	−4.01202	+	2.31634i	−0.430134	+	0.248338i
$88$	−0.00743010	+	0.00756973i	−0.000792051	+	0.000806936i
$89$	−9.76573	+	11.6383i	−1.03517	+	1.23366i	−0.0633322	+	0.997993i	$0.520173\pi$
$89$	−9.76573	+	11.6383i	−1.03517	+	1.23366i	−0.971833	+	0.235670i	$0.924272\pi$
$90$	4.93921	−	0.447572i	0.520639	−	0.0471782i
$91$	−1.42875	+	0.520024i	−0.149774	+	0.0545133i
$92$	−2.75867	+	0.0171194i	−0.287611	+	0.00178482i
$93$	−1.56451	−	8.87276i	−0.162232	−	0.920062i
$94$	0.827074	+	1.75939i	0.0853061	+	0.181467i
$95$	−11.7496	+	9.77809i	−1.20548	+	1.00321i
$96$	−3.31613	−	4.58293i	−0.338451	−	0.467743i
$97$	1.06007	−	0.186919i	0.107634	−	0.0189788i	−0.119572	−	0.992826i	$-0.538152\pi$
$97$	1.06007	−	0.186919i	0.107634	−	0.0189788i	0.227206	+	0.973847i	$0.427041\pi$
$98$	0.283579	−	0.613096i	0.0286458	−	0.0619320i
$99$	−0.00128262	−	0.00352396i	−0.000128908	−	0.000354171i
$100$	−12.5951	+	7.37636i	−1.25951	+	0.737636i
$101$	4.30721	+	3.61418i	0.428583	+	0.359624i	0.831417	−	0.555649i	$-0.187530\pi$
$101$	4.30721	+	3.61418i	0.428583	+	0.359624i	−0.402834	+	0.915273i	$0.631975\pi$
$102$	0.434275	−	5.14769i	0.0429996	−	0.509698i
$103$	4.25392	+	7.36801i	0.419151	+	0.725992i	0.995854	−	0.0909623i	$-0.0289943\pi$
$103$	4.25392	+	7.36801i	0.419151	+	0.725992i	−0.576703	+	0.816954i	$0.695661\pi$
$104$	−0.697408	+	1.53268i	−0.0683865	+	0.150292i
$105$	−8.82006	−	1.55522i	−0.860750	−	0.151773i
$106$	4.72411	−	6.79148i	0.458846	−	0.659646i
$107$	−4.01613	+	6.95614i	−0.388254	+	0.672475i	−0.992215	−	0.124539i	$-0.960255\pi$
$107$	−4.01613	+	6.95614i	−0.388254	+	0.672475i	0.603961	+	0.797014i	$0.293588\pi$
$108$	1.96742	−	0.359512i	0.189315	−	0.0345941i
$109$	−1.20572	+	3.31268i	−0.115487	+	0.317298i	−0.983947	−	0.178462i	$-0.942888\pi$
$109$	−1.20572	+	3.31268i	−0.115487	+	0.317298i	0.868460	+	0.495759i	$0.165110\pi$
$110$	0.0131919	+	0.0131103i	0.00125780	+	0.00125002i
$111$	7.69123	+	9.16605i	0.730019	+	0.870003i
$112$	3.61279	+	9.55538i	0.341377	+	0.902899i
$113$			0.762117i			0.0716939i	0.999357	+	0.0358470i	$0.0114129\pi$
$113$			0.762117i			0.0716939i	−0.999357	+	0.0358470i	$0.988587\pi$
$114$	−4.36306	+	4.35474i	−0.408638	+	0.407859i
$115$			4.83722i			0.451074i
$116$	4.58280	−	8.05264i	0.425503	−	0.747669i
$117$	−0.382681	−	0.456062i	−0.0353789	−	0.0421629i
$118$	6.08028	−	6.11813i	0.559735	−	0.563219i
$119$	−3.19074	+	8.76648i	−0.292495	+	0.803622i
$120$	−8.07177	+	5.76463i	−0.736849	+	0.526236i
$121$	−5.49999	+	9.52627i	−0.499999	+	0.866024i
$122$	12.5465	+	8.72725i	1.13590	+	0.790128i
$123$	−10.3605	−	1.82683i	−0.934173	−	0.164720i
$124$	11.6680	+	13.7314i	1.04782	+	1.23312i
$125$	4.02949	+	6.97928i	0.360408	+	0.624246i
$126$	−3.59896	−	0.303619i	−0.320621	−	0.0270485i
$127$	−8.71951	−	7.31654i	−0.773731	−	0.649237i	0.167930	−	0.985799i	$-0.446292\pi$
$127$	−8.71951	−	7.31654i	−0.773731	−	0.649237i	−0.941662	+	0.336561i	$0.890736\pi$
$128$	10.3551	+	4.55756i	0.915272	+	0.402836i
$129$	−1.12571	−	3.09286i	−0.0991132	−	0.272311i
$130$	2.67981	+	1.23951i	0.235035	+	0.108712i
$131$	9.96414	−	1.75695i	0.870571	−	0.153505i	0.279521	−	0.960140i	$-0.409824\pi$
$131$	9.96414	−	1.75695i	0.870571	−	0.153505i	0.591051	+	0.806635i	$0.298713\pi$
$132$	0.00577532	+	0.00478531i	0.000502677	+	0.000416508i
$133$	9.66322	−	5.52691i	0.837908	−	0.479244i
$134$	−20.6019	+	9.68476i	−1.77973	+	0.836636i
$135$	−0.608960	−	3.45358i	−0.0524109	−	0.297237i
$136$	4.45345	+	9.32288i	0.381880	+	0.799431i
$137$	9.14251	−	3.32760i	0.781097	−	0.284296i	0.0794670	−	0.996837i	$-0.474678\pi$
$137$	9.14251	−	3.32760i	0.781097	−	0.284296i	0.701630	+	0.712541i	$0.252456\pi$
$138$	0.176044	+	1.94275i	0.0149859	+	0.165378i
$139$	−2.45569	+	2.92658i	−0.208289	+	0.248229i	−0.860068	−	0.510180i	$-0.829579\pi$
$139$	−2.45569	+	2.92658i	−0.208289	+	0.248229i	0.651778	+	0.758409i	$0.274023\pi$
$140$	16.7937	−	6.23069i	1.41932	−	0.526589i
$141$	1.19051	−	0.687342i	0.100259	−	0.0578846i
$142$	3.61483	+	13.3252i	0.303350	+	1.11823i
$143$	0.000387690	−	0.00219870i	3.24203e−5	−	0.000183865i
$144$	−3.03203	+	2.60898i	−0.252669	+	0.217415i
$145$	−14.0696	−	8.12309i	−1.16842	−	0.674586i
$146$	−15.2296	−	4.03015i	−1.26041	−	0.333538i
$147$	−0.448846	−	0.163367i	−0.0370202	−	0.0134743i
$148$	−22.5380	−	8.04513i	−1.85261	−	0.661306i
$149$	4.17418	−	3.50256i	0.341962	−	0.286941i	−0.455591	−	0.890189i	$-0.650572\pi$
$149$	4.17418	−	3.50256i	0.341962	−	0.286941i	0.797553	+	0.603249i	$0.206127\pi$
$150$	5.94610	+	8.43607i	0.485497	+	0.688802i
$151$	2.19768			0.178844			0.0894222	−	0.995994i	$-0.471498\pi$
$151$	2.19768			0.178844			0.0894222	+	0.995994i	$0.471498\pi$
$152$	3.12836	−	11.9253i	0.253743	−	0.967272i
$153$	−3.65290			−0.295319
$154$	−0.00780318	−	0.0110708i	−0.000628798	−	0.000892112i
$155$	24.2036	−	20.3092i	1.94408	−	1.63127i
$156$	1.12139	+	0.400290i	0.0897831	+	0.0320488i
$157$	10.0294	+	3.65039i	0.800431	+	0.291333i	0.709665	−	0.704539i	$-0.248846\pi$
$157$	10.0294	+	3.65039i	0.800431	+	0.291333i	0.0907657	+	0.995872i	$0.471069\pi$
$158$	−2.59779	−	0.687445i	−0.206669	−	0.0546902i
$159$	−5.06611	−	2.92492i	−0.401769	−	0.231961i
$160$	8.10389	−	18.1070i	0.640669	−	1.43149i
$161$	0.611716	−	3.46922i	0.0482100	−	0.273413i
$162$	−0.370262	−	1.36488i	−0.0290905	−	0.107235i
$163$	−9.37371	+	5.41192i	−0.734206	+	0.423894i	−0.819959	−	0.572422i	$-0.806004\pi$
$163$	−9.37371	+	5.41192i	−0.734206	+	0.423894i	0.0857529	+	0.996316i	$0.472670\pi$
$164$	19.7267	−	7.31887i	1.54039	−	0.571508i
$165$	0.00845339	−	0.0100744i	0.000658095	−	0.000784288i
$166$	1.01696	+	11.2227i	0.0789314	+	0.871053i
$167$	−9.25815	+	3.36969i	−0.716417	+	0.260755i	−0.674404	−	0.738362i	$-0.735599\pi$
$167$	−9.25815	+	3.36969i	−0.716417	+	0.260755i	−0.0420132	+	0.999117i	$0.513377\pi$
$168$	6.51800	−	3.11358i	0.502875	−	0.240218i
$169$	2.19588	+	12.4534i	0.168914	+	0.957958i
$170$	16.3952	−	7.70721i	1.25745	−	0.591116i
$171$	3.32772	+	2.81537i	0.254477	+	0.215297i
$172$	5.06881	+	4.19991i	0.386493	+	0.320240i
$173$	21.2004	−	3.73820i	1.61184	−	0.284210i	0.706120	−	0.708093i	$-0.250444\pi$
$173$	21.2004	−	3.73820i	1.61184	−	0.284210i	0.905717	+	0.423882i	$0.139333\pi$
$174$	−5.94634	−	2.75039i	−0.450791	−	0.208507i
$175$	−6.37472	−	17.5144i	−0.481884	−	1.32396i
$176$	−0.0148038	−	0.00242126i	−0.00111588	−	0.000182510i
$177$	−4.67228	−	3.92051i	−0.351190	−	0.294684i
$178$	−21.4098	−	1.80619i	−1.60473	−	0.135380i
$179$	−10.0713	−	17.4439i	−0.752762	−	1.30382i	−0.946480	−	0.322764i	$-0.895388\pi$
$179$	−10.0713	−	17.4439i	−0.752762	−	1.30382i	0.193718	−	0.981057i	$-0.437945\pi$
$180$	4.54159	+	5.34474i	0.338510	+	0.398373i
$181$	−7.45770	−	1.31499i	−0.554327	−	0.0977428i	−0.110534	−	0.993872i	$-0.535256\pi$
$181$	−7.45770	−	1.31499i	−0.554327	−	0.0977428i	−0.443793	+	0.896130i	$0.646367\pi$
$182$	−1.76519	−	1.22785i	−0.130845	−	0.0910147i
$183$	5.40346	−	9.35907i	0.399435	−	0.691842i
$184$	−2.26741	−	3.17489i	−0.167156	−	0.234056i
$185$	−14.3515	+	39.4305i	−1.05515	+	2.89899i
$186$	8.98163	−	9.03754i	0.658565	−	0.662665i
$187$	−0.00880542	−	0.0104939i	−0.000643916	−	0.000767389i
$188$	−1.35988	+	2.38951i	−0.0991796	+	0.174273i
$189$			2.55389i			0.185768i
$190$	−20.8758	−	5.61500i	−1.51449	−	0.407355i
$191$			8.80175i			0.636872i	0.947944	+	0.318436i	$0.103158\pi$
$191$			8.80175i			0.636872i	−0.947944	+	0.318436i	$0.896842\pi$
$192$	2.59574	−	7.56717i	0.187332	−	0.546114i
$193$	−2.08205	−	2.48129i	−0.149869	−	0.178607i	0.685887	−	0.727708i	$-0.259415\pi$
$193$	−2.08205	−	2.48129i	−0.149869	−	0.178607i	−0.835756	+	0.549101i	$0.814970\pi$
$194$	1.07976	+	1.07308i	0.0775222	+	0.0770426i
$195$	0.714068	−	1.96189i	0.0511355	−	0.140494i
$196$	0.939744	−	0.171722i	0.0671246	−	0.0122658i
$197$	8.33206	−	14.4315i	0.593634	−	1.02821i	−0.400104	−	0.916470i	$-0.631026\pi$
$197$	8.33206	−	14.4315i	0.593634	−	1.02821i	0.993738	−	0.111735i	$-0.0356408\pi$
$198$	0.00302845	−	0.00435377i	0.000215223	−	0.000309409i
$199$	24.7689	+	4.36743i	1.75582	+	0.309599i	0.956593	−	0.291426i	$-0.0941298\pi$
$199$	24.7689	+	4.36743i	1.75582	+	0.309599i	0.799230	+	0.601025i	$0.205241\pi$
$200$	−18.7884	−	8.54918i	−1.32854	−	0.604519i
$201$	8.04855	+	13.9405i	0.567701	+	0.983287i
$202$	−0.668450	+	7.92349i	−0.0470319	+	0.557495i
$203$	9.06335	+	7.60505i	0.636123	+	0.533770i
$204$	6.30422	−	3.69209i	0.441383	−	0.258498i
$205$	−12.6182	−	34.6683i	−0.881296	−	2.42134i
$206$	−5.05105	+	10.9203i	−0.351923	+	0.760856i
$207$	1.35841	−	0.239524i	0.0944157	−	0.0166480i
$208$	−2.33989	+	0.442597i	−0.162242	+	0.0306886i
$209$	−6.63182e−5		0.0163463i	−4.58732e−6		0.00113069i
$210$	−5.38842	−	11.4625i	−0.371837	−	0.790989i
$211$	0.195718	+	1.10997i	0.0134738	+	0.0764136i	0.990803	−	0.135311i	$-0.0432032\pi$
$211$	0.195718	+	1.10997i	0.0134738	+	0.0764136i	−0.977329	+	0.211724i	$0.932092\pi$
$212$	11.6995	−	0.0726028i	0.803522	−	0.00498638i
$213$	9.17413	−	3.33911i	0.628601	−	0.228792i
$214$	−11.3130	+	1.02514i	−0.773339	+	0.0700769i
$215$	7.41926	−	8.84193i	0.505989	−	0.603015i
$216$	2.01853	+	1.98130i	0.137344	+	0.134810i
$217$	−19.9269	+	11.5048i	−1.35273	+	0.780997i
$218$	−4.81160	+	1.30528i	−0.325883	+	0.0884047i
$219$	−1.93437	+	10.9704i	−0.130713	+	0.741310i
$220$	−0.00440651	+	0.0259305i	−0.000297087	+	0.00174824i
$221$	−1.88338	−	1.08737i	−0.126690	−	0.0731444i
$222$	−4.32892	+	16.3586i	−0.290538	+	1.09792i
$223$	−18.9083	−	6.88205i	−1.26619	−	0.460856i	−0.380350	−	0.924843i	$-0.624196\pi$
$223$	−18.9083	−	6.88205i	−1.26619	−	0.460856i	−0.885842	+	0.463987i	$0.846419\pi$
$224$	−8.10186	+	11.9614i	−0.541328	+	0.799204i
$225$	5.59064	−	4.69110i	0.372709	−	0.312740i
$226$	−0.880957	+	0.620935i	−0.0586004	+	0.0413040i
$227$	−16.1679			−1.07310			−0.536552	−	0.843867i	$-0.680274\pi$
$227$	−16.1679			−1.07310			−0.536552	+	0.843867i	$0.680274\pi$
$228$	−8.58859	−	1.49538i	−0.568793	−	0.0990340i
$229$	10.8224			0.715167			0.357583	−	0.933881i	$-0.383601\pi$
$229$	10.8224			0.715167			0.357583	+	0.933881i	$0.383601\pi$
$230$	−5.59151	+	3.94113i	−0.368693	+	0.259870i
$231$	−0.00733670	+	0.00615623i	−0.000482720	+	0.000405050i
$232$	13.0422	−	1.26347i	0.856260	−	0.0829512i
$233$	−13.5192	−	4.92057i	−0.885669	−	0.322357i	−0.141174	−	0.989985i	$-0.545088\pi$
$233$	−13.5192	−	4.92057i	−0.885669	−	0.322357i	−0.744495	+	0.667628i	$0.767310\pi$
$234$	0.215387	−	0.813930i	0.0140803	−	0.0532083i
$235$	4.17495	+	2.41041i	0.272344	+	0.157238i
$236$	12.0261	+	2.04365i	0.782829	+	0.133030i
$237$	−0.329957	+	1.87128i	−0.0214330	+	0.121553i
$238$	−12.7331	+	3.45421i	−0.825366	+	0.223903i
$239$	17.1433	−	9.89769i	1.10891	−	0.640228i	0.170362	−	0.985382i	$-0.445506\pi$
$239$	17.1433	−	9.89769i	1.10891	−	0.640228i	0.938546	+	0.345153i	$0.112173\pi$
$240$	−13.2400	−	4.63370i	−0.854639	−	0.299104i
$241$	11.2387	−	13.3938i	0.723951	−	0.862771i	−0.271057	−	0.962563i	$-0.587373\pi$
$241$	11.2387	−	13.3938i	0.723951	−	0.862771i	0.995008	+	0.0997922i	$0.0318178\pi$
$242$	−15.4929	+	1.40390i	−0.995918	+	0.0902462i
$243$	−0.939693	+	0.342020i	−0.0602813	+	0.0219406i
$244$	0.134125	+	21.6134i	0.00858650	+	1.38366i
$245$	−0.290871	−	1.64961i	−0.0185831	−	0.105390i
$246$	−6.32951	−	13.4644i	−0.403555	−	0.858461i
$247$	0.877660	+	2.44213i	0.0558442	+	0.155389i
$248$	−6.36610	+	24.6751i	−0.404248	+	1.56687i
$249$	7.84713	−	1.38366i	0.497292	−	0.0876859i
$250$	−4.78456	+	10.3442i	−0.302602	+	0.654224i
$251$	−8.15333	−	22.4011i	−0.514634	−	1.41394i	−0.876359	−	0.481659i	$-0.840034\pi$
$251$	−8.15333	−	22.4011i	−0.514634	−	1.41394i	0.361725	−	0.932285i	$-0.382188\pi$
$252$	−2.58129	−	4.40753i	−0.162606	−	0.277648i
$253$	0.00396257	+	0.00332499i	0.000249125	+	0.000209040i
$254$	1.35321	−	16.0403i	0.0849079	−	1.00646i
$255$	−6.40510	−	11.0940i	−0.401103	−	0.694731i
$256$	3.16860	+	15.6831i	0.198037	+	0.980194i
$257$	−17.1342	−	3.02122i	−1.06880	−	0.188458i	−0.388543	−	0.921431i	$-0.627021\pi$
$257$	−17.1342	−	3.02122i	−1.06880	−	0.188458i	−0.680259	+	0.732972i	$0.738132\pi$
$258$	2.65797	−	3.82116i	0.165478	−	0.237895i
$259$	15.2792	−	26.4643i	0.949403	−	1.64441i
$260$	0.750588	+	4.10758i	0.0465495	+	0.254741i
$261$	−1.58447	+	4.35330i	−0.0980763	+	0.269463i
$262$	10.1492	+	10.0864i	0.627020	+	0.623141i
$263$	−12.8586	−	15.3242i	−0.792892	−	0.944932i	0.206546	−	0.978437i	$-0.433778\pi$
$263$	−12.8586	−	15.3242i	−0.792892	−	0.944932i	−0.999439	+	0.0335045i	$0.989333\pi$
$264$	−0.000826059		0.0105747i	−5.08404e−5		0.000650829i
$265$		−	20.5146i		−	1.26020i
$266$	14.2619	+	6.66699i	0.874450	+	0.408779i
$267$			15.1928i			0.929783i
$268$	−27.9803	−	15.9238i	−1.70917	−	0.972699i
$269$	5.35478	+	6.38158i	0.326487	+	0.389092i	0.904172	−	0.427168i	$-0.140489\pi$
$269$	5.35478	+	6.38158i	0.326487	+	0.389092i	−0.577686	+	0.816259i	$0.696044\pi$
$270$	3.49596	−	3.51772i	0.212757	−	0.214082i
$271$	6.32735	−	17.3842i	0.384359	−	1.05602i	−0.585142	−	0.810931i	$-0.698961\pi$
$271$	6.32735	−	17.3842i	0.384359	−	1.05602i	0.969501	−	0.245087i	$-0.0788164\pi$
$272$	−7.14819	+	12.7437i	−0.433423	+	0.772701i
$273$	−0.760224	+	1.31675i	−0.0460108	+	0.0796931i
$274$	11.2953	+	7.85697i	0.682377	+	0.474657i
$275$	0.0269528	+	0.00475251i	0.00162532	+	0.000286587i
$276$	−2.10226	+	1.78635i	−0.126541	+	0.107526i
$277$	9.63808	+	16.6936i	0.579096	+	1.00302i	0.995583	+	0.0938823i	$0.0299277\pi$
$277$	9.63808	+	16.6936i	0.579096	+	1.00302i	−0.416487	+	0.909142i	$0.636739\pi$
$278$	−5.38371	−	0.454185i	−0.322893	−	0.0272402i
$279$	−6.90178	−	5.79128i	−0.413199	−	0.346715i
$280$	20.8849	+	14.3359i	1.24811	+	0.856735i
$281$	−3.74181	−	10.2805i	−0.223218	−	0.613286i	0.776644	−	0.629940i	$-0.216921\pi$
$281$	−3.74181	−	10.2805i	−0.223218	−	0.613286i	−0.999861	+	0.0166547i	$0.994698\pi$
$282$	1.76449	+	0.816140i	0.105074	+	0.0486004i
$283$	8.46982	−	1.49346i	0.503479	−	0.0887769i	0.0838603	−	0.996478i	$-0.473275\pi$
$283$	8.46982	−	1.49346i	0.503479	−	0.0887769i	0.419618	+	0.907701i	$0.362164\pi$
$284$	−12.4579	+	15.0352i	−0.739239	+	0.892177i
$285$	−2.71545	+	15.0429i	−0.160849	+	0.891066i
$286$	0.00285742	−	0.00134325i	0.000168963	−	7.94279e-5i
$287$	4.66553	+	26.4595i	0.275397	+	1.56186i
$288$	−5.48616	−	1.37916i	−0.323275	−	0.0812677i
$289$	3.43583	−	1.25054i	0.202108	−	0.0735612i
$290$	−2.07346	−	22.8818i	−0.121758	−	1.34367i
$291$	0.691912	−	0.824589i	0.0405606	−	0.0483383i
$292$	−7.74972	−	20.8880i	−0.453518	−	1.22237i
$293$	−11.0763	+	6.39490i	−0.647084	+	0.373594i	−0.787338	−	0.616522i	$-0.788541\pi$
$293$	−11.0763	+	6.39490i	−0.647084	+	0.373594i	0.140254	+	0.990116i	$0.455208\pi$
$294$	−0.176857	−	0.651940i	−0.0103145	−	0.0380219i
$295$	3.71419	−	21.0642i	0.216248	−	1.22640i
$296$	−9.06321	−	32.6072i	−0.526789	−	1.89526i
$297$	−0.00324770	−	0.00187506i	−0.000188451	−	0.000108802i
$298$	7.44964	+	1.97137i	0.431546	+	0.114198i
$299$	0.771673	+	0.280866i	0.0446270	+	0.0162429i
$300$	−4.90696	+	13.7466i	−0.283303	+	0.793659i
$301$	−6.43918	+	5.40312i	−0.371148	+	0.311430i
$302$	1.79056	+	2.54037i	0.103035	+	0.146182i
$303$	5.62266			0.323013
$304$	16.3337	−	6.09999i	0.936803	−	0.349858i
$305$	37.8983			2.17005
$306$	−2.97620	−	4.22251i	−0.170138	−	0.241385i
$307$	−14.4522	+	12.1269i	−0.824833	+	0.692117i	−0.954098	−	0.299493i	$-0.903182\pi$
$307$	−14.4522	+	12.1269i	−0.824833	+	0.692117i	0.129266	+	0.991610i	$0.458738\pi$
$308$	0.00643950	−	0.0180399i	0.000366924	−	0.00102792i
$309$	7.99476	+	2.90985i	0.454806	+	0.165536i
$310$	43.1959	+	11.4308i	2.45336	+	0.649225i
$311$	−17.5045	−	10.1062i	−0.992587	−	0.573070i	−0.0865403	−	0.996248i	$-0.527581\pi$
$311$	−17.5045	−	10.1062i	−0.992587	−	0.573070i	−0.906047	+	0.423178i	$0.860914\pi$
$312$	0.450945	+	1.62239i	0.0255297	+	0.0918497i
$313$	0.692923	−	3.92976i	0.0391664	−	0.222123i	−0.958942	−	0.283602i	$-0.908471\pi$
$313$	0.692923	−	3.92976i	0.0391664	−	0.222123i	0.998108	+	0.0614787i	$0.0195816\pi$
$314$	3.95182	+	14.5674i	0.223014	+	0.822088i
$315$	−7.75623	+	4.47806i	−0.437014	+	0.252310i
$316$	−1.32191	−	3.56297i	−0.0743634	−	0.200433i
$317$	11.1384	−	13.2743i	0.625596	−	0.745557i	−0.356425	−	0.934324i	$-0.616005\pi$
$317$	11.1384	−	13.2743i	0.625596	−	0.745557i	0.982022	+	0.188767i	$0.0604491\pi$
$318$	−0.746601	−	8.23917i	−0.0418673	−	0.462030i
$319$	−0.0163254	+	0.00594196i	−0.000914047	+	0.000332686i
$320$	27.5332	−	5.38516i	1.53915	−	0.301040i
$321$	1.39479	+	7.91023i	0.0778494	+	0.441506i
$322$	4.50858	−	2.11944i	0.251253	−	0.118112i
$323$	14.9401	+	5.50651i	0.831292	+	0.306391i
$324$	1.27604	−	1.54004i	0.0708913	−	0.0855576i
$325$	4.27886	−	0.754479i	0.237349	−	0.0418510i
$326$	−13.8931	−	6.42603i	−0.769465	−	0.355905i
$327$	1.20572	+	3.31268i	0.0666764	+	0.183192i
$328$	24.5324	+	16.8397i	1.35458	+	0.929816i
$329$	−2.68942	−	2.25669i	−0.148273	−	0.124415i
$330$	0.0185327	+	0.00156347i	0.00102019	+	8.60663e-5i
$331$	−2.53054	−	4.38302i	−0.139091	−	0.240913i	0.788062	−	0.615596i	$-0.211085\pi$
$331$	−2.53054	−	4.38302i	−0.139091	−	0.240913i	−0.927153	+	0.374683i	$0.877751\pi$
$332$	−12.1442	+	10.3193i	−0.666498	+	0.566343i
$333$	11.7837	+	2.07778i	0.645740	+	0.113861i
$334$	−11.4382	−	7.95635i	−0.625872	−	0.435352i
$335$	−28.2251	+	48.8874i	−1.54210	+	2.67100i
$336$	8.90964	+	4.99759i	0.486061	+	0.272641i
$337$	1.59075	−	4.37055i	0.0866537	−	0.238079i	−0.888795	−	0.458304i	$-0.848457\pi$
$337$	1.59075	−	4.37055i	0.0866537	−	0.238079i	0.975449	+	0.220225i	$0.0706792\pi$
$338$	−12.6063	+	12.6847i	−0.685690	+	0.689959i
$339$	0.489879	+	0.583816i	0.0266066	+	0.0317085i
$340$	22.2670	+	12.6723i	1.20760	+	0.687250i
$341$		−	0.0337872i		−	0.00182968i
$342$	−0.543124	+	6.14044i	−0.0293688	+	0.332037i
$343$			19.0971i			1.03115i
$344$	−0.725005	+	9.28108i	−0.0390897	+	0.500403i
$345$	3.10931	+	3.70553i	0.167400	+	0.199499i
$346$	21.5941	+	21.4606i	1.16091	+	1.15373i
$347$	−6.38901	+	17.5537i	−0.342980	+	0.942330i	0.641545	+	0.767086i	$0.278294\pi$
$347$	−6.38901	+	17.5537i	−0.342980	+	0.942330i	−0.984525	+	0.175245i	$0.943928\pi$
$348$	−1.66551	−	9.11445i	−0.0892806	−	0.488586i
$349$	−13.3174	+	23.0664i	−0.712865	+	1.23472i	0.250912	+	0.968010i	$0.419269\pi$
$349$	−13.3174	+	23.0664i	−0.712865	+	1.23472i	−0.963777	+	0.266708i	$0.914064\pi$
$350$	15.0517	−	21.6386i	0.804546	−	1.15663i
$351$	−0.586302	−	0.103381i	−0.0312945	−	0.00551806i
$352$	−0.00926256	−	0.0190849i	−0.000493696	−	0.00101723i
$353$	14.4069	+	24.9535i	0.766802	+	1.32814i	0.939289	+	0.343128i	$0.111486\pi$
$353$	14.4069	+	24.9535i	0.766802	+	1.32814i	−0.172487	+	0.985012i	$0.555180\pi$
$354$	0.725107	−	8.59508i	0.0385390	−	0.456823i
$355$	26.2272	+	22.0072i	1.39199	+	1.16802i
$356$	−15.3558	−	26.2199i	−0.813855	−	1.38965i
$357$	3.19074	+	8.76648i	0.168872	+	0.463971i
$358$	11.9585	−	25.8542i	0.632025	−	1.36643i
$359$	−5.54418	+	0.977588i	−0.292610	+	0.0515951i	−0.318026	−	0.948082i	$-0.603020\pi$
$359$	−5.54418	+	0.977588i	−0.292610	+	0.0515951i	0.0254160	+	0.999677i	$0.491909\pi$
$360$	−2.47791	+	9.60440i	−0.130597	+	0.506196i
$361$	−9.36617	−	16.5310i	−0.492957	−	0.870054i
$362$	−4.55612	−	9.69200i	−0.239464	−	0.509400i
$363$	1.91013	+	10.8329i	0.100256	+	0.568578i
$364$	−0.0188704	−	3.04084i	−0.000989078	−	0.159383i
$365$	−36.7092	+	13.3610i	−1.92145	+	0.699349i
$366$	15.2209	−	1.37926i	0.795611	−	0.0720951i
$367$	−0.856254	+	1.02044i	−0.0446961	+	0.0532667i	−0.787929	−	0.615766i	$-0.788847\pi$
$367$	−0.856254	+	1.02044i	−0.0446961	+	0.0532667i	0.743233	+	0.669032i	$0.233291\pi$
$368$	1.82259	−	5.20772i	0.0950088	−	0.271471i
$369$	−9.11086	+	5.26016i	−0.474292	+	0.273833i
$370$	−57.2720	+	15.5366i	−2.97743	+	0.807709i
$371$	−2.59428	+	14.7129i	−0.134688	+	0.763855i
$372$	17.7646	+	3.01883i	0.921051	+	0.156519i
$373$	2.69212	+	1.55430i	0.139393	+	0.0804785i	0.568075	−	0.822977i	$-0.307689\pi$
$373$	2.69212	+	1.55430i	0.139393	+	0.0804785i	−0.428682	+	0.903456i	$0.641022\pi$
$374$	0.00495602	−	0.0187284i	0.000256270	−	0.000968422i
$375$	7.57296	+	2.75633i	0.391066	+	0.142336i
$376$	−3.87007	+	0.374918i	−0.199584	+	0.0193349i
$377$	−2.11279	+	1.77284i	−0.108814	+	0.0913060i
$378$	−2.95213	+	2.08078i	−0.151841	+	0.107024i
$379$	25.2168			1.29530			0.647650	−	0.761938i	$-0.275752\pi$
$379$	25.2168			1.29530			0.647650	+	0.761938i	$0.275752\pi$
$380$	−10.5180	−	28.7058i	−0.539560	−	1.47258i
$381$	−11.3825			−0.583144
$382$	−10.1742	+	7.17122i	−0.520559	+	0.366912i
$383$	0.227120	−	0.190577i	0.0116053	−	0.00973802i	−0.636967	−	0.770891i	$-0.719811\pi$
$383$	0.227120	−	0.190577i	0.0116053	−	0.00973802i	0.648572	+	0.761153i	$0.275367\pi$
$384$	10.8620	−	3.16485i	0.554301	−	0.161506i
$385$	−0.0315610	−	0.0114873i	−0.00160850	−	0.000585446i
$386$	1.17186	−	4.42835i	0.0596460	−	0.225397i
$387$	−2.85040	−	1.64568i	−0.144894	−	0.0836545i
$388$	−0.360675	+	2.12242i	−0.0183105	+	0.107750i
$389$	5.15872	−	29.2565i	0.261557	−	1.48336i	−0.517105	−	0.855922i	$-0.672990\pi$
$389$	5.15872	−	29.2565i	0.261557	−	1.48336i	0.778663	−	0.627443i	$-0.215898\pi$
$390$	2.84960	−	0.773032i	0.144295	−	0.0391440i
$391$	4.36361	−	2.51933i	0.220677	−	0.127408i
$392$	0.964156	+	0.946371i	0.0486972	+	0.0477990i
$393$	6.50363	−	7.75073i	0.328065	−	0.390972i
$394$	23.4705	−	2.12680i	1.18242	−	0.107147i
$395$	−6.26169	+	2.27907i	−0.315060	+	0.114672i
$396$	0.00750009		4.65430e-5i	0.000376894		2.33887e-6i
$397$	−2.71559	−	15.4009i	−0.136291	−	0.772947i	−0.973952	−	0.226755i	$-0.927188\pi$
$397$	−2.71559	−	15.4009i	−0.136291	−	0.772947i	0.837660	−	0.546191i	$-0.183923\pi$
$398$	15.1320	+	32.1896i	0.758500	+	1.61352i
$399$	3.84983	−	10.4453i	0.192732	−	0.522917i
$400$	−5.42559	−	28.6836i	−0.271279	−	1.43418i
$401$	7.90035	−	1.39304i	0.394525	−	0.0695653i	0.0271334	−	0.999632i	$-0.491362\pi$
$401$	7.90035	−	1.39304i	0.394525	−	0.0695653i	0.367391	+	0.930066i	$0.380251\pi$
$402$	−9.55673	+	20.6616i	−0.476646	+	1.03051i
$403$	−1.83454	−	5.04037i	−0.0913852	−	0.251079i
$404$	−9.70365	+	5.68299i	−0.482775	+	0.282739i
$405$	−2.68641	−	2.25417i	−0.133489	−	0.112010i
$406$	−1.40657	+	16.6729i	−0.0698069	+	0.827460i
$407$	0.0224359	+	0.0388601i	0.00111211	+	0.00192622i
$408$	9.40417	+	4.27912i	0.465576	+	0.211848i
$409$	−7.37540	−	1.30048i	−0.364690	−	0.0643047i	−0.0116995	−	0.999932i	$-0.503724\pi$
$409$	−7.37540	−	1.30048i	−0.364690	−	0.0643047i	−0.352991	+	0.935627i	$0.614835\pi$
$410$	29.7936	−	42.8319i	1.47140	−	2.11531i
$411$	4.86463	−	8.42578i	0.239954	−	0.415613i
$412$	−16.7385	+	3.05867i	−0.824648	+	0.150690i
$413$	−5.32756	+	14.6374i	−0.262152	+	0.720257i
$414$	1.38363	+	1.37507i	0.0680019	+	0.0675812i
$415$	17.9616	+	21.4058i	0.881701	+	1.05077i
$416$	−2.41804	−	2.34416i	−0.118554	−	0.114932i
$417$			3.82038i			0.187085i
$418$	−0.0189492	+	0.0132415i	−0.000926837	+	0.000647661i
$419$		−	15.6423i		−	0.764176i	−0.924126	−	0.382088i	$-0.875205\pi$
$419$		−	15.6423i		−	0.764176i	0.924126	−	0.382088i	$-0.124795\pi$
$420$	8.85969	−	15.5677i	0.432309	−	0.759628i
$421$	−16.8520	−	20.0835i	−0.821318	−	0.978808i	0.178669	−	0.983909i	$-0.442821\pi$
$421$	−16.8520	−	20.0835i	−0.821318	−	0.978808i	−0.999987	+	0.00510082i	$0.998376\pi$
$422$	−1.12359	+	1.13059i	−0.0546956	+	0.0550361i
$423$	0.470170	−	1.29178i	0.0228604	−	0.0628085i
$424$	9.61606	+	13.4646i	0.466997	+	0.653901i
$425$	13.3295	−	23.0874i	0.646578	−	1.11991i
$426$	11.3344	+	7.88414i	0.549154	+	0.381988i
$427$	−27.1804	−	4.79263i	−1.31535	−	0.231932i
$428$	−10.4022	−	12.2418i	−0.502811	−	0.591730i
$429$	−0.00111631	−	0.00193351i	−5.38959e−5	−	9.33505e-5i
$430$	16.2655	+	1.37221i	0.784393	+	0.0661737i
$431$	−3.64600	−	3.05936i	−0.175622	−	0.147364i	0.550740	−	0.834677i	$-0.314346\pi$
$431$	−3.64600	−	3.05936i	−0.175622	−	0.147364i	−0.726361	+	0.687313i	$0.758790\pi$
$432$	−0.645650	+	3.94755i	−0.0310639	+	0.189926i
$433$	1.71821	+	4.72075i	0.0825720	+	0.226865i	0.974107	−	0.226087i	$-0.0725933\pi$
$433$	1.71821	+	4.72075i	0.0825720	+	0.226865i	−0.891535	+	0.452952i	$0.850371\pi$
$434$	−29.5342	−	13.6606i	−1.41769	−	0.655731i
$435$	−15.9994	+	2.82112i	−0.767111	+	0.135262i
$436$	−5.42907	−	4.49842i	−0.260005	−	0.215435i
$437$	−5.91687	−	1.06807i	−0.283042	−	0.0510928i
$438$	−14.2571	+	6.70211i	−0.681229	+	0.320239i
$439$	1.33326	+	7.56129i	0.0636330	+	0.360881i	0.999953	+	0.00973175i	$0.00309776\pi$
$439$	1.33326	+	7.56129i	0.0636330	+	0.360881i	−0.936320	+	0.351149i	$0.885791\pi$
$440$	−0.0335642	+	0.0160333i	−0.00160011	+	0.000764356i
$441$	−0.448846	+	0.163367i	−0.0213736	+	0.00777937i
$442$	−0.277557	−	3.06300i	−0.0132020	−	0.145692i
$443$	10.1596	−	12.1078i	0.482698	−	0.575258i	−0.468646	−	0.883386i	$-0.655258\pi$
$443$	10.1596	−	12.1078i	0.482698	−	0.575258i	0.951345	+	0.308128i	$0.0997026\pi$
$444$	−22.4364	+	8.32423i	−1.06479	+	0.395050i
$445$	−46.1409	+	26.6395i	−2.18729	+	1.26283i
$446$	−7.45033	−	27.4639i	−0.352783	−	1.30045i
$447$	0.946211	−	5.36623i	0.0447542	−	0.253814i
$448$	−20.4276	+	0.380339i	−0.965112	+	0.0179693i
$449$	−0.961162	−	0.554927i	−0.0453600	−	0.0261886i	0.477148	−	0.878823i	$-0.341670\pi$
$449$	−0.961162	−	0.554927i	−0.0453600	−	0.0261886i	−0.522509	+	0.852634i	$0.675004\pi$
$450$	9.97758	+	2.64033i	0.470347	+	0.124466i
$451$	−0.0370731	−	0.0134935i	−0.00174571	−	0.000635385i
$452$	−1.43552	−	0.512420i	−0.0675211	−	0.0241022i
$453$	1.68352	−	1.41264i	0.0790985	−	0.0663716i
$454$	−13.1728	−	18.6891i	−0.618232	−	0.877122i
$455$	−5.33200			−0.249968
$456$	−5.26899	−	11.1462i	−0.246743	−	0.521969i
$457$	−2.71901			−0.127190			−0.0635949	−	0.997976i	$-0.520257\pi$
$457$	−2.71901			−0.127190			−0.0635949	+	0.997976i	$0.520257\pi$
$458$	8.81758	+	12.5100i	0.412019	+	0.584555i
$459$	−2.79828	+	2.34804i	−0.130613	+	0.109597i
$460$	−9.11137	−	3.25238i	−0.424820	−	0.151643i
$461$	9.32484	+	3.39396i	0.434301	+	0.158073i	0.549913	−	0.835222i	$-0.314661\pi$
$461$	9.32484	+	3.39396i	0.434301	+	0.158073i	−0.115612	+	0.993294i	$0.536883\pi$
$462$	−0.0130938	−	0.00346496i	−0.000609177	−	0.000161204i
$463$	−9.46007	−	5.46177i	−0.439647	−	0.253830i	0.263801	−	0.964577i	$-0.415024\pi$
$463$	−9.46007	−	5.46177i	−0.439647	−	0.253830i	−0.703448	+	0.710747i	$0.748357\pi$
$464$	12.0866	+	14.0465i	0.561106	+	0.652090i
$465$	5.48650	−	31.1155i	0.254430	−	1.44295i
$466$	−5.32688	−	19.6363i	−0.246763	−	0.909633i
$467$	2.92071	−	1.68627i	0.135154	−	0.0780314i	−0.430898	−	0.902400i	$-0.641803\pi$
$467$	2.92071	−	1.68627i	0.135154	−	0.0780314i	0.566053	+	0.824369i	$0.308470\pi$
$468$	1.11634	−	0.414176i	0.0516027	−	0.0191453i
$469$	26.4251	−	31.4922i	1.22020	−	1.45418i
$470$	0.615270	+	6.78985i	0.0283803	+	0.313193i
$471$	10.0294	−	3.65039i	0.462129	−	0.168201i
$472$	7.43590	+	15.5664i	0.342265	+	0.716501i
$473$	−0.00214334	−	0.0121555i	−9.85507e−5	−	0.000558909i
$474$	−2.43191	+	1.14322i	−0.111701	+	0.0525097i
$475$	−29.9369	+	10.7588i	−1.37360	+	0.493648i
$476$	−14.3672	−	11.9043i	−0.658517	−	0.545634i
$477$	−5.76097	+	1.01581i	−0.263777	+	0.0465110i
$478$	25.4086	+	11.7524i	1.16216	+	0.537541i
$479$	8.89289	+	24.4330i	0.406326	+	1.11637i	0.959106	+	0.283046i	$0.0913448\pi$
$479$	8.89289	+	24.4330i	0.406326	+	1.11637i	−0.552780	+	0.833327i	$0.686433\pi$
$480$	−5.43104	−	19.0799i	−0.247892	−	0.870873i
$481$	5.45698	+	4.57895i	0.248817	+	0.208782i
$482$	24.6391	+	2.07863i	1.12228	+	0.0946789i
$483$	−1.76137	−	3.05078i	−0.0801450	−	0.138815i
$484$	−14.2456	−	16.7649i	−0.647528	−	0.762040i
$485$	3.71752	+	0.655499i	0.168804	+	0.0297647i
$486$	−1.16097	−	0.807561i	−0.0526625	−	0.0366317i
$487$	−18.5458	+	32.1223i	−0.840392	+	1.45560i	0.0491719	+	0.998790i	$0.484342\pi$
$487$	−18.5458	+	32.1223i	−0.840392	+	1.45560i	−0.889564	+	0.456811i	$0.848992\pi$
$488$	−24.8744	+	17.7646i	−1.12601	+	0.804165i
$489$	−3.70197	+	10.1711i	−0.167409	+	0.459952i
$490$	1.66985	−	1.68025i	0.0754363	−	0.0759059i
$491$	−4.42577	−	5.27443i	−0.199732	−	0.238032i	0.656876	−	0.753998i	$-0.271877\pi$
$491$	−4.42577	−	5.27443i	−0.199732	−	0.238032i	−0.856609	+	0.515967i	$0.827433\pi$
$492$	10.4070	−	18.2866i	0.469185	−	0.824426i
$493$			16.9227i			0.762161i
$494$	−2.10787	+	3.00425i	−0.0948376	+	0.135167i
$495$		−	0.0131511i		−	0.000591100i
$496$	−33.7096	+	12.7452i	−1.51360	+	0.572279i
$497$	−16.0269	−	19.1001i	−0.718903	−	0.856755i
$498$	7.99287	+	7.94342i	0.358169	+	0.355953i
$499$	13.7848	−	37.8735i	0.617093	−	1.69545i	−0.0968973	−	0.995294i	$-0.530892\pi$
$499$	13.7848	−	37.8735i	0.617093	−	1.69545i	0.713991	−	0.700155i	$-0.246886\pi$
$500$	−15.8554	+	2.89730i	−0.709076	+	0.129571i
$501$	−4.92616	+	8.53236i	−0.220085	+	0.381198i
$502$	19.2512	−	27.6760i	0.859225	−	1.23524i
$503$	25.1210	+	4.42950i	1.12009	+	0.197502i	0.702879	−	0.711309i	$-0.251897\pi$
$503$	25.1210	+	4.42950i	1.12009	+	0.197502i	0.417209	+	0.908811i	$0.363008\pi$
$504$	2.99171	−	6.57484i	0.133261	−	0.292866i
$505$	9.85894	+	17.0762i	0.438717	+	0.759880i
$506$	−0.000614964		0.00728950i	−2.73385e−5		0.000324058i
$507$	9.68706	+	8.12841i	0.430218	+	0.360995i
$508$	19.6441	−	11.5046i	0.871565	−	0.510435i
$509$	9.28177	+	25.5015i	0.411407	+	1.13033i	0.956443	+	0.291919i	$0.0942939\pi$
$509$	9.28177	+	25.5015i	0.411407	+	1.13033i	−0.545036	+	0.838413i	$0.683484\pi$
$510$	7.60532	−	16.4427i	0.336769	−	0.728094i
$511$	28.0171	−	4.94018i	1.23941	−	0.218541i
$512$	−15.5470	+	16.4405i	−0.687088	+	0.726575i
$513$	4.35886	+	0.0176843i	0.192449	+	0.000780780i
$514$	−10.4678	−	22.2675i	−0.461713	−	0.982178i
$515$	5.18094	+	29.3825i	0.228299	+	1.29475i
$516$	6.58258	−	0.0408493i	0.289782	−	0.00179829i
$517$	0.00484433	−	0.00176319i	0.000213053	−	7.75451e-5i
$518$	43.0397	−	3.90009i	1.89106	−	0.171360i
$519$	13.8376	−	16.4910i	0.607402	−	0.723874i
$520$	−4.13654	+	4.21428i	−0.181399	+	0.184808i
$521$	−13.1732	+	7.60552i	−0.577126	+	0.333204i	−0.759990	−	0.649934i	$-0.774796\pi$
$521$	−13.1732	+	7.60552i	−0.577126	+	0.333204i	0.182864	+	0.983138i	$0.441463\pi$
$522$	−6.32307	+	1.71531i	−0.276753	+	0.0750770i
$523$	5.85798	−	33.2223i	0.256152	−	1.45271i	−0.536947	−	0.843616i	$-0.680423\pi$
$523$	5.85798	−	33.2223i	0.256152	−	1.45271i	0.793099	−	0.609093i	$-0.208466\pi$
$524$	−3.39016	+	19.9497i	−0.148100	+	0.871507i
$525$	−16.1414	−	9.31922i	−0.704467	−	0.406724i
$526$	7.23728	−	27.3490i	0.315560	−	1.19248i
$527$	−30.9265	−	11.2563i	−1.34718	−	0.490333i
$528$	−0.0128967	+	0.00766089i	−0.000561257	+	0.000333397i
$529$	16.1615	−	13.5611i	0.702675	−	0.589614i
$530$	23.7135	−	16.7143i	1.03005	−	0.726021i
$531$	−6.09923			−0.264684
$532$	3.91325	+	21.9177i	0.169661	+	0.950252i
$533$	−6.26323			−0.271290
$534$	−17.5618	+	12.3783i	−0.759975	+	0.535662i
$535$	−21.5779	+	18.1060i	−0.932895	+	0.782792i
$536$	−4.39017	−	45.3173i	−0.189626	−	1.95741i
$537$	−18.9278	−	6.88915i	−0.816794	−	0.297289i
$538$	−3.01387	+	11.3892i	−0.129937	+	0.491022i
$539$	−0.00155127		0.000895627i	−6.68180e−5		3.85774e-5i
$540$	6.91459	+	1.17503i	0.297557	+	0.0505654i
$541$	−1.62382	+	9.20914i	−0.0698135	+	0.395932i	0.929798	+	0.368069i	$0.119981\pi$
$541$	−1.62382	+	9.20914i	−0.0698135	+	0.395932i	−0.999612	+	0.0278624i	$0.991130\pi$
$542$	25.2502	−	6.84982i	1.08459	−	0.294225i
$543$	−6.55820	+	3.78638i	−0.281439	+	0.162489i
$544$	−20.5549	+	2.12011i	−0.881283	+	0.0908989i
$545$	−7.94658	+	9.47036i	−0.340394	+	0.405666i
$546$	−2.14146	+	0.194051i	−0.0916462	+	0.00830462i
$547$	−16.5137	+	6.01049i	−0.706074	+	0.256990i	−0.670002	−	0.742359i	$-0.733707\pi$
$547$	−16.5137	+	6.01049i	−0.706074	+	0.256990i	−0.0360723	+	0.999349i	$0.511485\pi$
$548$	0.120750	+	19.4581i	0.00515821	+	0.831210i
$549$	−1.87660	−	10.6427i	−0.0800914	−	0.454221i
$550$	0.0164662	+	0.0350278i	0.000702122	+	0.00149359i
$551$	13.0427	−	15.4163i	0.555639	−	0.656755i
$552$	−3.77772	−	0.974641i	−0.160790	−	0.0414835i
$553$	4.77904	−	0.842674i	0.203225	−	0.0358341i
$554$	−11.4441	+	24.7421i	−0.486214	+	1.05119i
$555$	14.3515	+	39.4305i	0.609189	+	1.67373i
$556$	−3.86137	−	6.59326i	−0.163758	−	0.279616i
$557$	−24.6228	−	20.6610i	−1.04330	−	0.875436i	−0.0509300	−	0.998702i	$-0.516219\pi$
$557$	−24.6228	−	20.6610i	−1.04330	−	0.875436i	−0.992374	+	0.123267i	$0.960663\pi$
$558$	1.07111	−	12.6964i	0.0453437	−	0.537483i
$559$	−0.979748	−	1.69697i	−0.0414389	−	0.0717743i
$560$	0.444612	+	35.8218i	0.0187883	+	1.51375i
$561$	−0.0134907	−	0.00237877i	−0.000569577	−	0.000100432i
$562$	8.83498	−	12.7014i	0.372681	−	0.535774i
$563$	21.8457	−	37.8379i	0.920688	−	1.59468i	0.122334	−	0.992489i	$-0.460962\pi$
$563$	21.8457	−	37.8379i	0.920688	−	1.59468i	0.798354	−	0.602189i	$-0.205705\pi$
$564$	0.494216	+	2.70458i	0.0208102	+	0.113884i
$565$	−0.914096	+	2.51146i	−0.0384563	+	0.105658i
$566$	8.62713	+	8.57376i	0.362625	+	0.360382i
$567$	1.64161	+	1.95639i	0.0689411	+	0.0821608i
$568$	−27.5298	−	2.15053i	−1.15512	−	0.0902341i
$569$			21.4379i			0.898726i	0.893349	+	0.449363i	$0.148349\pi$
$569$			21.4379i			0.898726i	−0.893349	+	0.449363i	$0.851651\pi$
$570$	−19.6010	+	9.11735i	−0.820997	+	0.381884i
$571$		−	3.00361i		−	0.125697i	−0.998023	−	0.0628487i	$-0.979981\pi$
$571$		−	3.00361i		−	0.125697i	0.998023	−	0.0628487i	$-0.0200185\pi$
$572$	0.00388079	+	0.00220858i	0.000162264	+	9.23453e-5i
$573$	5.65765	+	6.74253i	0.236352	+	0.281673i
$574$	−26.7842	+	26.9509i	−1.11795	+	1.12491i
$575$	−3.44300	+	9.45957i	−0.143583	+	0.394491i
$576$	−2.87563	−	7.46530i	−0.119818	−	0.311054i
$577$	−1.51128	+	2.61761i	−0.0629154	+	0.108973i	−0.895767	−	0.444523i	$-0.853373\pi$
$577$	−1.51128	+	2.61761i	−0.0629154	+	0.108973i	0.832852	+	0.553496i	$0.186707\pi$
$578$	4.24488	+	2.95271i	0.176564	+	0.122817i
$579$	−3.18989	−	0.562463i	−0.132567	−	0.0233752i
$580$	24.7605	−	21.0397i	1.02812	−	0.873628i
$581$	−10.1749	−	17.6235i	−0.422127	−	0.731146i
$582$	1.51691	+	0.127971i	0.0628778	+	0.00530456i
$583$	−0.0168052	−	0.0141012i	−0.000696000	−	0.000584013i
$584$	17.8310	−	25.9766i	0.737852	−	1.07492i
$585$	−0.714068	−	1.96189i	−0.0295231	−	0.0811140i
$586$	−16.4165	−	7.59321i	−0.678159	−	0.313673i
$587$	39.0655	−	6.88830i	1.61241	−	0.284311i	0.706475	−	0.707738i	$-0.250284\pi$
$587$	39.0655	−	6.88830i	1.61241	−	0.284311i	0.905930	+	0.423427i	$0.139173\pi$
$588$	0.609505	−	0.735602i	0.0251356	−	0.0303357i
$589$	19.4979	+	34.0900i	0.803397	+	1.40465i
$590$	27.3749	−	12.8687i	1.12701	−	0.529796i
$591$	−2.89369	−	16.4109i	−0.119031	−	0.675056i
$592$	30.3075	−	37.0432i	1.24563	−	1.52247i
$593$	−2.55640	+	0.930453i	−0.104979	+	0.0382091i	−0.393975	−	0.919121i	$-0.628901\pi$
$593$	−2.55640	+	0.930453i	−0.104979	+	0.0382091i	0.288997	+	0.957330i	$0.406678\pi$
$594$	−0.000478618	−	0.00528183i	−1.96380e−5	−	0.000216716i
$595$	−21.0293	+	25.0618i	−0.862118	+	1.02743i
$596$	3.79082	+	10.2175i	0.155278	+	0.418524i
$597$	21.7814	−	12.5755i	0.891455	−	0.514682i
$598$	0.304058	+	1.12084i	0.0124339	+	0.0458345i
$599$	5.56492	−	31.5602i	0.227376	−	1.28952i	−0.630713	−	0.776016i	$-0.717238\pi$
$599$	5.56492	−	31.5602i	0.227376	−	1.28952i	0.858090	−	0.513500i	$-0.171651\pi$
$600$	−19.8881	+	5.52791i	−0.811927	+	0.225676i
$601$	27.9203	+	16.1198i	1.13889	+	0.657540i	0.946156	−	0.323710i	$-0.104930\pi$
$601$	27.9203	+	16.1198i	1.13889	+	0.657540i	0.192737	+	0.981250i	$0.438264\pi$
$602$	−11.4920	−	3.04108i	−0.468378	−	0.123945i
$603$	15.1263	+	5.50553i	0.615992	+	0.224203i
$604$	−1.47764	+	4.13953i	−0.0601243	+	0.168435i
$605$	−29.5505	+	24.7958i	−1.20140	+	1.00809i
$606$	4.58106	+	6.49942i	0.186093	+	0.264021i
$607$	−6.79373			−0.275749			−0.137874	−	0.990450i	$-0.544027\pi$
$607$	−6.79373			−0.275749			−0.137874	+	0.990450i	$0.544027\pi$
$608$	20.3591	+	13.9107i	0.825670	+	0.564154i
$609$	11.8314			0.479431
$610$	30.8777	+	43.8080i	1.25020	+	1.77373i
$611$	0.626941	−	0.526066i	0.0253633	−	0.0212823i
$612$	2.45608	−	6.88058i	0.0992811	−	0.278131i
$613$	14.5217	+	5.28548i	0.586528	+	0.213479i	0.618201	−	0.786020i	$-0.287862\pi$
$613$	14.5217	+	5.28548i	0.586528	+	0.213479i	−0.0316739	+	0.999498i	$0.510084\pi$
$614$	−25.7928	−	6.82546i	−1.04091	−	0.275453i
$615$	−31.9505	−	18.4466i	−1.28837	−	0.743840i
$616$	0.0260995	−	0.00725439i	0.00105158	−	0.000292288i
$617$	3.54117	−	20.0829i	0.142562	−	0.808509i	−0.826731	−	0.562598i	$-0.809802\pi$
$617$	3.54117	−	20.0829i	0.142562	−	0.808509i	0.969292	−	0.245911i	$-0.0790870\pi$
$618$	3.15013	+	11.6122i	0.126717	+	0.467112i
$619$	−30.5054	+	17.6123i	−1.22611	+	0.707897i	−0.966215	−	0.257738i	$-0.917023\pi$
$619$	−30.5054	+	17.6123i	−1.22611	+	0.707897i	−0.259899	+	0.965636i	$0.583689\pi$
$620$	21.9807	+	59.2449i	0.882765	+	2.37933i
$621$	0.886636	−	1.05665i	0.0355795	−	0.0424020i
$622$	−2.57966	−	28.4680i	−0.103435	−	1.14146i
$623$	36.4607	−	13.2706i	1.46077	−	0.531676i
$624$	−1.50797	+	1.84310i	−0.0603670	+	0.0737832i
$625$	−1.42888	−	8.10360i	−0.0571553	−	0.324144i
$626$	5.10711	−	2.40080i	0.204121	−	0.0959554i
$627$	0.0104564	+	0.0125646i	0.000417587	+	0.000501781i
$628$	−13.6192	+	16.4369i	−0.543467	+	0.655902i
$629$	43.0445	−	7.58990i	1.71630	−	0.302629i
$630$	−11.4957	−	5.31719i	−0.458001	−	0.211842i
$631$	−0.387450	−	1.06451i	−0.0154241	−	0.0423774i	0.931742	−	0.363122i	$-0.118289\pi$
$631$	−0.387450	−	1.06451i	−0.0154241	−	0.0423774i	−0.947166	+	0.320744i	$0.896067\pi$
$632$	3.04153	−	4.43098i	0.120986	−	0.176255i
$633$	0.863405	+	0.724483i	0.0343173	+	0.0287956i
$634$	24.4192	+	2.06008i	0.969810	+	0.0818161i
$635$	−19.9584	−	34.5690i	−0.792026	−	1.37183i
$636$	8.91564	−	7.57589i	0.353528	−	0.300403i
$637$	−0.280048	−	0.0493801i	−0.0110959	−	0.00195651i
$638$	−0.0201696	−	0.0140299i	−0.000798523	−	0.000555448i
$639$	4.88145	−	8.45492i	0.193107	−	0.334471i
$640$	28.6575	+	27.4390i	1.13279	+	1.08462i
$641$	7.36003	−	20.2215i	0.290704	−	0.798702i	−0.705260	−	0.708949i	$-0.749170\pi$
$641$	7.36003	−	20.2215i	0.290704	−	0.798702i	0.995964	−	0.0897537i	$-0.0286080\pi$
$642$	−8.00729	+	8.05714i	−0.316023	+	0.317990i
$643$	−11.3370	−	13.5109i	−0.447088	−	0.532819i	0.494683	−	0.869074i	$-0.335284\pi$
$643$	−11.3370	−	13.5109i	−0.447088	−	0.532819i	−0.941771	+	0.336254i	$0.890840\pi$
$644$	6.12330	+	3.48480i	0.241292	+	0.137320i
$645$		−	11.5423i		−	0.454478i
$646$	5.80732	+	21.7562i	0.228486	+	0.855988i
$647$			28.7307i			1.12952i	0.825255	+	0.564760i	$0.191031\pi$
$647$			28.7307i			1.12952i	−0.825255	+	0.564760i	$0.808969\pi$
$648$	2.81984	+	0.220276i	0.110774	+	0.00865324i
$649$	−0.0147024	−	0.0175216i	−0.000577119	−	0.000687783i
$650$	4.35833	+	4.33137i	0.170948	+	0.169890i
$651$	−7.86975	+	21.6219i	−0.308440	+	0.847431i
$652$	−3.89130	−	21.2951i	−0.152395	−	0.833979i
$653$	−16.1978	+	28.0554i	−0.633868	+	1.09789i	0.352886	+	0.935666i	$0.385200\pi$
$653$	−16.1978	+	28.0554i	−0.633868	+	1.09789i	−0.986754	+	0.162225i	$0.948133\pi$
$654$	−2.84688	+	4.09274i	−0.111322	+	0.160039i
$655$	34.9428	+	6.16137i	1.36533	+	0.240744i
$656$	0.522263	+	42.0780i	0.0203910	+	1.64287i
$657$	5.56981	+	9.64720i	0.217299	+	0.376373i
$658$	0.417380	−	4.94743i	0.0162712	−	0.192871i
$659$	−20.9657	−	17.5923i	−0.816707	−	0.685298i	0.135492	−	0.990778i	$-0.456739\pi$
$659$	−20.9657	−	17.5923i	−0.816707	−	0.685298i	−0.952198	+	0.305480i	$0.901183\pi$
$660$	0.0132922	+	0.0226964i	0.000517400	+	0.000883456i
$661$	−8.14296	−	22.3726i	−0.316724	−	0.870193i	−0.991257	−	0.131948i	$-0.957877\pi$
$661$	−8.14296	−	22.3726i	−0.316724	−	0.870193i	0.674532	−	0.738245i	$-0.264345\pi$
$662$	3.00473	−	6.49620i	0.116782	−	0.252482i
$663$	−2.14170	+	0.377640i	−0.0831767	+	0.0146663i
$664$	−21.8228	−	5.63023i	−0.846890	−	0.218495i
$665$	38.4730	−	6.62299i	1.49192	−	0.256829i
$666$	7.19896	+	15.3140i	0.278954	+	0.593405i
$667$	−1.10964	−	6.29307i	−0.0429653	−	0.243668i
$668$	−0.122278	−	19.7043i	−0.00473107	−	0.762381i
$669$	−18.9083	+	6.88205i	−0.731036	+	0.266075i
$670$	−79.5070	+	7.20461i	−3.07162	+	0.278338i
$671$	0.0260504	−	0.0310457i	0.00100566	−	0.00119850i
$672$	1.48225	+	14.3707i	0.0571792	+	0.554363i
$673$	12.0059	−	6.93159i	0.462792	−	0.267193i	−0.250425	−	0.968136i	$-0.580570\pi$
$673$	12.0059	−	6.93159i	0.462792	−	0.267193i	0.713218	+	0.700943i	$0.247237\pi$
$674$	6.34813	−	1.72211i	0.244521	−	0.0663330i
$675$	1.26729	−	7.18719i	0.0487782	−	0.276635i
$676$	−24.9337	−	4.23711i	−0.958987	−	0.162966i
$677$	27.0022	+	15.5897i	1.03778	+	0.599162i	0.919203	−	0.393783i	$-0.128834\pi$
$677$	27.0022	+	15.5897i	1.03778	+	0.599162i	0.118576	+	0.992945i	$0.462167\pi$
$678$	−0.275723	+	1.04193i	−0.0105891	+	0.0400151i
$679$	−2.58328	−	0.940237i	−0.0991372	−	0.0360830i
$680$	3.49373	+	36.0639i	0.133978	+	1.38299i
$681$	−12.3854	+	10.3926i	−0.474608	+	0.398244i
$682$	0.0390558	−	0.0275281i	0.00149552	−	0.00105411i
$683$	−13.4184			−0.513441			−0.256720	−	0.966486i	$-0.582642\pi$
$683$	−13.4184			−0.513441			−0.256720	+	0.966486i	$0.582642\pi$
$684$	−7.54045	+	4.37511i	−0.288316	+	0.167287i
$685$	34.1191			1.30362
$686$	−22.0750	+	15.5594i	−0.842826	+	0.594059i
$687$	8.29047	−	6.95653i	0.316301	−	0.265408i
$688$	−11.3190	+	6.72371i	−0.431533	+	0.256339i
$689$	−3.27265	−	1.19115i	−0.124678	−	0.0453791i
$690$	−1.75004	+	6.61323i	−0.0666227	+	0.251761i
$691$	23.7827	+	13.7310i	0.904738	+	0.522351i	0.878734	−	0.477311i	$-0.158389\pi$
$691$	23.7827	+	13.7310i	0.904738	+	0.522351i	0.0260037	+	0.999662i	$0.491722\pi$
$692$	−7.21314	+	42.4464i	−0.274203	+	1.61357i
$693$	−0.00166310	+	0.00943189i	−6.31758e−5	+	0.000358288i
$694$	−25.4963	+	6.91658i	−0.967827	+	0.262550i
$695$	−11.6026	+	6.69877i	−0.440112	+	0.254099i
$696$	9.17873	−	9.35121i	0.347919	−	0.354457i
$697$	−24.7021	+	29.4388i	−0.935658	+	1.11507i
$698$	−37.5136	+	3.39934i	−1.41991	+	0.128667i
$699$	−13.5192	+	4.92057i	−0.511341	+	0.186113i
$700$	37.2762	−	0.231323i	1.40891	−	0.00874319i
$701$	−3.07645	−	17.4474i	−0.116196	−	0.658980i	−0.986151	−	0.165849i	$-0.946963\pi$
$701$	−3.07645	−	17.4474i	−0.116196	−	0.658980i	0.869955	−	0.493131i	$-0.164148\pi$
$702$	−0.358188	−	0.761955i	−0.0135189	−	0.0287581i
$703$	−45.0623	−	26.2611i	−1.69956	−	0.990456i
$704$	0.0145142	−	0.0262563i	0.000547025	−	0.000989573i
$705$	4.74758	−	0.837127i	0.178804	−	0.0315280i
$706$	−17.1065	+	36.9843i	−0.643813	+	1.39192i
$707$	−4.91129	−	13.4937i	−0.184708	−	0.507481i
$708$	10.5261	−	6.16467i	0.395596	−	0.231682i
$709$	−1.95002	−	1.63626i	−0.0732344	−	0.0614509i	0.605436	−	0.795894i	$-0.292999\pi$
$709$	−1.95002	−	1.63626i	−0.0732344	−	0.0614509i	−0.678670	+	0.734443i	$0.737443\pi$
$710$	−4.07028	+	48.2472i	−0.152755	+	1.81069i
$711$	0.950074	+	1.64558i	0.0356305	+	0.0617139i
$712$	17.7973	−	39.1129i	0.666982	−	1.46582i
$713$	12.2387	+	2.15802i	0.458344	+	0.0808184i
$714$	−7.53382	+	10.8308i	−0.281946	+	0.405332i
$715$	0.00391474	−	0.00678053i	0.000146403	−	0.000253577i
$716$	39.6289	−	7.24148i	1.48100	−	0.270627i
$717$	6.77042	−	18.6016i	0.252846	−	0.694688i
$718$	−5.64715	−	5.61221i	−0.210750	−	0.209446i
$719$	18.2917	+	21.7992i	0.682164	+	0.812971i	0.990384	−	0.138344i	$-0.0441779\pi$
$719$	18.2917	+	21.7992i	0.682164	+	0.812971i	−0.308220	+	0.951315i	$0.599733\pi$
$720$	−13.1209	+	4.96089i	−0.488988	+	0.184881i
$721$		−	21.7281i		−	0.809196i
$722$	11.4777	−	24.2953i	0.427155	−	0.904179i
$723$		−	17.4844i		−	0.650251i
$724$	7.49121	−	13.1631i	0.278409	−	0.489204i
$725$	−21.7324	−	25.8997i	−0.807121	−	0.961890i
$726$	−10.9658	+	11.0341i	−0.406979	+	0.409513i
$727$	4.78434	−	13.1449i	0.177441	−	0.487516i	−0.818806	−	0.574071i	$-0.805363\pi$
$727$	4.78434	−	13.1449i	0.177441	−	0.487516i	0.996247	+	0.0865544i	$0.0275857\pi$
$728$	3.49963	−	2.49934i	0.129705	−	0.0926315i
$729$	−0.500000	+	0.866025i	−0.0185185	+	0.0320750i
$730$	−45.3533	−	31.5474i	−1.67860	−	1.16762i
$731$	−11.8403	−	2.08777i	−0.437930	−	0.0772190i
$732$	13.9956	+	16.4706i	0.517292	+	0.608772i
$733$	7.51394	+	13.0145i	0.277534	+	0.480702i	0.970771	−	0.240007i	$-0.0771497\pi$
$733$	7.51394	+	13.0145i	0.277534	+	0.480702i	−0.693238	+	0.720709i	$0.743816\pi$
$734$	−1.87720	−	0.158366i	−0.0692886	−	0.00584539i
$735$	−1.28317	−	1.07671i	−0.0473304	−	0.0397150i
$736$	7.50473	−	2.13621i	0.276628	−	0.0787416i
$737$	0.0206464	+	0.0567255i	0.000760520	+	0.00208951i
$738$	−13.5035	−	6.24583i	−0.497069	−	0.229912i
$739$	−6.78203	+	1.19586i	−0.249481	+	0.0439902i	−0.296990	−	0.954881i	$-0.595983\pi$
$739$	−6.78203	+	1.19586i	−0.249481	+	0.0439902i	0.0475090	+	0.998871i	$0.484872\pi$
$740$	−64.6216	−	53.5442i	−2.37554	−	1.96832i
$741$	2.24210	+	1.30663i	0.0823656	+	0.0480004i
$742$	−19.1208	+	8.98851i	−0.701946	+	0.329978i
$743$	1.26270	+	7.16110i	0.0463238	+	0.262715i	0.999170	−	0.0407388i	$-0.0129712\pi$
$743$	1.26270	+	7.16110i	0.0463238	+	0.262715i	−0.952846	+	0.303454i	$0.901860\pi$
$744$	10.9841	+	22.9943i	0.402698	+	0.843011i
$745$	17.9565	−	6.53563i	0.657875	−	0.239447i
$746$	0.396742	+	4.37828i	0.0145258	+	0.160300i
$747$	5.12185	−	6.10398i	0.187399	−	0.223333i
$748$	0.0256867	−	0.00953012i	0.000939198	−	0.000348456i
$749$	17.7652	−	10.2567i	0.649126	−	0.374773i
$750$	2.98393	+	10.9996i	0.108958	+	0.401647i
$751$	−0.615511	+	3.49074i	−0.0224603	+	0.127379i	−0.993976	−	0.109595i	$-0.965045\pi$
$751$	−0.615511	+	3.49074i	−0.0224603	+	0.127379i	0.971516	+	0.236974i	$0.0761556\pi$
$752$	−3.58652	−	4.16808i	−0.130787	−	0.151994i
$753$	−20.6450	−	11.9194i	−0.752344	−	0.434366i
$754$	−3.77068	−	0.997822i	−0.137320	−	0.0363385i
$755$	7.24215	+	2.63593i	0.263569	+	0.0959313i
$756$	−4.81049	−	1.71714i	−0.174956	−	0.0624519i
$757$	−10.4718	+	8.78689i	−0.380604	+	0.319365i	−0.812940	−	0.582348i	$-0.802134\pi$
$757$	−10.4718	+	8.78689i	−0.380604	+	0.319365i	0.432335	+	0.901713i	$0.357690\pi$
$758$	20.5454	+	29.1489i	0.746242	+	1.05874i
$759$	0.00517277			0.000187760
$760$	24.6125	−	35.5462i	0.892790	−	1.28939i
$761$	4.54239			0.164662			0.0823308	−	0.996605i	$-0.473764\pi$
$761$	4.54239			0.164662			0.0823308	+	0.996605i	$0.473764\pi$
$762$	−9.27390	−	13.1574i	−0.335958	−	0.476643i
$763$	6.89684	−	5.78714i	0.249682	−	0.209508i
$764$	−16.5789	−	5.91798i	−0.599804	−	0.214105i
$765$	−12.0377	−	4.38135i	−0.435222	−	0.158408i
$766$	0.405340	+	0.107264i	0.0146455	+	0.00387560i
$767$	−3.14467	−	1.81558i	−0.113547	−	0.0655567i
$768$	12.5082	+	9.97722i	0.451351	+	0.360022i
$769$	−7.07178	+	40.1061i	−0.255015	+	1.44626i	0.541019	+	0.841010i	$0.318039\pi$
$769$	−7.07178	+	40.1061i	−0.255015	+	1.44626i	−0.796034	+	0.605252i	$0.793073\pi$
$770$	−0.0124358	−	0.0458417i	−0.000448156	−	0.00165202i
$771$	−15.0676	+	8.69925i	−0.542645	+	0.313296i
$772$	6.07365	−	2.25341i	0.218595	−	0.0811019i
$773$	−11.1116	+	13.2423i	−0.399658	+	0.476294i	−0.927916	−	0.372790i	$-0.878401\pi$
$773$	−11.1116	+	13.2423i	−0.399658	+	0.476294i	0.528258	+	0.849084i	$0.322846\pi$
$774$	−0.420068	−	4.63569i	−0.0150990	−	0.166626i
$775$	61.7875	−	22.4888i	2.21947	−	0.807821i
$776$	−2.74724	+	1.31233i	−0.0986201	+	0.0471098i
$777$	−5.30641	−	30.0941i	−0.190366	−	1.07962i
$778$	38.0217	−	17.8736i	1.36314	−	0.640801i
$779$	45.1922	−	7.77970i	1.61918	−	0.278737i
$780$	3.21528	+	2.66412i	0.115126	+	0.0953907i
$781$	0.0360558	−	0.00635761i	0.00129018	−	0.000227493i
$782$	6.46743	+	2.99142i	0.231275	+	0.106973i
$783$	1.58447	+	4.35330i	0.0566244	+	0.155574i
$784$	−0.308396	+	1.88556i	−0.0110142	+	0.0673413i
$785$	28.6721	+	24.0588i	1.02335	+	0.858694i
$786$	14.2582	+	1.20286i	0.508572	+	0.0429046i
$787$	16.5763	+	28.7110i	0.590882	+	1.02344i	0.994114	+	0.108340i	$0.0345534\pi$
$787$	16.5763	+	28.7110i	0.590882	+	1.02344i	−0.403232	+	0.915098i	$0.632113\pi$
$788$	21.5810	+	25.3975i	0.768791	+	0.904747i
$789$	−19.7004	−	3.47372i	−0.701354	−	0.123668i
$790$	−7.73616	−	5.38122i	−0.275240	−	0.191455i
$791$	0.973181	−	1.68560i	0.0346023	−	0.0599330i
$792$	0.00616450	+	0.00863169i	0.000219046	+	0.000306714i
$793$	2.20051	−	6.04585i	0.0781424	−	0.214694i
$794$	15.5898	−	15.6869i	0.553263	−	0.556707i
$795$	−13.1865	−	15.7151i	−0.467677	−	0.557356i
$796$	−24.8802	+	43.7181i	−0.881856	+	1.54955i
$797$			20.7949i			0.736592i	0.929709	+	0.368296i	$0.120059\pi$
$797$			20.7949i			0.736592i	−0.929709	+	0.368296i	$0.879941\pi$
$798$	15.2107	−	4.06013i	0.538452	−	0.143727i
$799$		−	5.02158i		−	0.177651i
$800$	28.7359	−	29.6416i	1.01597	−	1.04799i
$801$	9.76573	+	11.6383i	0.345055	+	0.411221i
$802$	8.04708	+	7.99729i	0.284152	+	0.282394i
$803$	−0.0142879	+	0.0392556i	−0.000504208	+	0.00138530i
$804$	−31.6698	+	5.78710i	−1.11691	+	0.204095i
$805$	6.17687	−	10.6986i	0.217706	−	0.377078i
$806$	4.33164	−	6.22725i	0.152575	−	0.219346i
$807$	8.20400	+	1.44659i	0.288794	+	0.0509223i
$808$	−14.4752	−	6.58656i	−0.509236	−	0.231715i
$809$	−17.4247	−	30.1805i	−0.612621	−	1.06109i	−0.990797	−	0.135357i	$-0.956782\pi$
$809$	−17.4247	−	30.1805i	−0.612621	−	1.06109i	0.378176	−	0.925734i	$-0.376552\pi$
$810$	0.416913	−	4.94189i	0.0146488	−	0.173640i
$811$	14.3667	+	12.0551i	0.504484	+	0.423312i	0.859183	−	0.511668i	$-0.170972\pi$
$811$	14.3667	+	12.0551i	0.504484	+	0.423312i	−0.354699	+	0.934980i	$0.615417\pi$
$812$	−20.4187	+	11.9583i	−0.716556	+	0.419654i
$813$	−6.32735	−	17.3842i	−0.221910	−	0.609692i
$814$	−0.0266401	+	0.0575957i	−0.000933734	+	0.00201873i
$815$	−37.3810	+	6.59128i	−1.30940	+	0.230882i
$816$	2.71567	+	14.3570i	0.0950674	+	0.502596i
$817$	9.17721	+	11.0275i	0.321070	+	0.385804i
$818$	−4.50584	−	9.58504i	−0.157543	−	0.335133i
$819$	0.264023	+	1.49735i	0.00922571	+	0.0523216i
$820$	73.7851	−	0.457885i	2.57669	−	0.0159900i
$821$	5.25655	−	1.91323i	0.183455	−	0.0667721i	−0.248659	−	0.968591i	$-0.579990\pi$
$821$	5.25655	−	1.91323i	0.183455	−	0.0667721i	0.432114	+	0.901819i	$0.357768\pi$
$822$	13.7031	−	1.24172i	0.477950	−	0.0433100i
$823$	−16.6976	+	19.8994i	−0.582040	+	0.693648i	−0.974055	−	0.226310i	$-0.927334\pi$
$823$	−16.6976	+	19.8994i	−0.582040	+	0.693648i	0.392015	+	0.919959i	$0.371778\pi$
$824$	−17.1733	−	16.8566i	−0.598262	−	0.587226i
$825$	0.0237019	−	0.0136843i	0.000825194	−	0.000476426i
$826$	−21.2604	+	5.76748i	−0.739746	+	0.200676i
$827$	−2.26042	+	12.8195i	−0.0786025	+	0.445777i	0.919952	+	0.392031i	$0.128227\pi$
$827$	−2.26042	+	12.8195i	−0.0786025	+	0.445777i	−0.998555	+	0.0537463i	$0.982884\pi$
$828$	−0.462179	+	2.71973i	−0.0160618	+	0.0945172i
$829$	−36.0310	−	20.8025i	−1.25141	−	0.722502i	−0.280020	−	0.959994i	$-0.590341\pi$
$829$	−36.0310	−	20.8025i	−1.25141	−	0.722502i	−0.971389	+	0.237492i	$0.923675\pi$
$830$	−10.1095	+	38.2028i	−0.350905	+	1.32604i
$831$	18.1137	+	6.59283i	0.628356	+	0.228703i
$832$	0.739588	−	4.70500i	0.0256406	−	0.163116i
$833$	−1.33661	+	1.12155i	−0.0463107	+	0.0388593i
$834$	−4.41610	+	3.11265i	−0.152917	+	0.107782i
$835$	−34.5507			−1.19568
$836$	−0.0307451	−	0.0111156i	−0.00106334	−	0.000384440i
$837$	−9.00963			−0.311418
$838$	18.0815	−	12.7446i	0.624613	−	0.440254i
$839$	8.14585	−	6.83518i	0.281226	−	0.235977i	−0.491253	−	0.871017i	$-0.663461\pi$
$839$	8.14585	−	6.83518i	0.281226	−	0.235977i	0.772479	+	0.635040i	$0.219016\pi$
$840$	25.2137	−	2.44261i	0.869956	−	0.0842780i
$841$	−7.08361	−	2.57822i	−0.244262	−	0.0889043i
$842$	9.48496	−	35.8428i	0.326873	−	1.23523i
$843$	−9.47460	−	5.47016i	−0.326322	−	0.188402i
$844$	−2.22233	−	0.377653i	−0.0764958	−	0.0129993i
$845$	−7.70064	+	43.6725i	−0.264910	+	1.50238i
$846$	1.87628	−	0.508993i	0.0645079	−	0.0174996i
$847$	24.3290	−	14.0464i	0.835955	−	0.482639i
$848$	−7.72955	+	22.0858i	−0.265434	+	0.758431i
$849$	5.52828	−	6.58835i	0.189730	−	0.226112i
$850$	37.5478	−	3.40243i	1.28788	−	0.116702i
$851$	−15.5093	+	5.64492i	−0.531652	+	0.193505i
$852$	0.121168	+	19.5254i	0.00415115	+	0.668930i
$853$	−3.43498	−	19.4807i	−0.117612	−	0.667008i	−0.985424	−	0.170116i	$-0.945586\pi$
$853$	−3.43498	−	19.4807i	−0.117612	−	0.667008i	0.867812	−	0.496892i	$-0.165525\pi$
$854$	−16.6052	−	35.3235i	−0.568220	−	1.20874i
$855$	7.58925	+	13.2690i	0.259547	+	0.453790i
$856$	5.67550	−	21.9983i	0.193985	−	0.751887i
$857$	4.78136	−	0.843082i	0.163328	−	0.0287991i	−0.0913861	−	0.995816i	$-0.529130\pi$
$857$	4.78136	−	0.843082i	0.163328	−	0.0287991i	0.254714	+	0.967016i	$0.418019\pi$
$858$	0.00132549	−	0.00286570i	4.52515e−5	−	9.78335e-5i
$859$	9.60567	+	26.3914i	0.327741	+	0.900462i	0.988682	+	0.150024i	$0.0479350\pi$
$859$	9.60567	+	26.3914i	0.327741	+	0.900462i	−0.660941	+	0.750438i	$0.729843\pi$
$860$	11.6662	+	19.9199i	0.397813	+	0.679262i
$861$	20.5819	+	17.2702i	0.701428	+	0.588568i
$862$	0.565835	−	6.70715i	0.0192724	−	0.228446i
$863$	17.5382	+	30.3771i	0.597007	+	1.03405i	0.993260	+	0.115906i	$0.0369770\pi$
$863$	17.5382	+	30.3771i	0.597007	+	1.03405i	−0.396253	+	0.918141i	$0.629690\pi$
$864$	−5.08915	+	2.46994i	−0.173136	+	0.0840290i
$865$	74.3468	+	13.1094i	2.52787	+	0.445731i
$866$	−4.05696	+	5.83237i	−0.137861	+	0.198192i
$867$	1.82817	−	3.16648i	0.0620878	−	0.107539i
$868$	−8.27223	−	45.2696i	−0.280778	−	1.53655i
$869$	−0.00243716	+	0.00669604i	−8.26750e−5	+	0.000227148i
$870$	−16.2965	−	16.1957i	−0.552503	−	0.549085i
$871$	6.16006	+	7.34127i	0.208726	+	0.248749i
$872$	0.776534	−	9.94073i	0.0262968	−	0.336636i
$873$		−	1.07642i		−	0.0364315i
$874$	−3.58615	−	7.70972i	−0.121303	−	0.260785i
$875$		−	20.5817i		−	0.695789i
$876$	−19.3631	−	11.0197i	−0.654220	−	0.372320i
$877$	−5.71112	−	6.80625i	−0.192851	−	0.229831i	0.660951	−	0.750429i	$-0.270153\pi$
$877$	−5.71112	−	6.80625i	−0.192851	−	0.229831i	−0.853802	+	0.520599i	$0.825709\pi$
$878$	−7.65407	+	7.70172i	−0.258312	+	0.259920i
$879$	−4.37437	+	12.0185i	−0.147544	+	0.405373i
$880$	−0.0458798	−	0.0257349i	−0.00154661	−	0.000867522i
$881$	−7.40571	+	12.8271i	−0.249505	+	0.432155i	−0.963388	−	0.268109i	$-0.913601\pi$
$881$	−7.40571	+	12.8271i	−0.249505	+	0.432155i	0.713884	+	0.700264i	$0.246934\pi$
$882$	−0.554539	−	0.385734i	−0.0186723	−	0.0129883i
$883$	45.1226	+	7.95634i	1.51850	+	0.267752i	0.869842	−	0.493330i	$-0.164221\pi$
$883$	45.1226	+	7.95634i	1.51850	+	0.267752i	0.648655	+	0.761082i	$0.275332\pi$
$884$	3.31448	−	2.81641i	0.111478	−	0.0947262i
$885$	−10.6946	−	18.5235i	−0.359494	−	0.622662i
$886$	22.2733	+	1.87904i	0.748287	+	0.0631277i
$887$	−39.4359	−	33.0906i	−1.32413	−	1.11107i	−0.985412	−	0.170185i	$-0.945563\pi$
$887$	−39.4359	−	33.0906i	−1.32413	−	1.11107i	−0.338715	−	0.940889i	$-0.609992\pi$
$888$	−27.9023	−	19.1529i	−0.936341	−	0.642728i
$889$	9.94241	+	27.3165i	0.333458	+	0.916167i
$890$	−68.3868	−	31.6313i	−2.29233	−	1.06028i
$891$	−0.00369315		0.000651201i	−0.000123725		2.18161e-5i
$892$	25.6762	−	30.9883i	0.859704	−	1.03756i
$893$	−3.87024	+	4.57456i	−0.129513	+	0.153082i
$894$	6.97393	−	3.27838i	0.233243	−	0.109645i
$895$	−12.2660	−	69.5639i	−0.410007	−	2.32526i
$896$	−17.0830	−	23.3030i	−0.570703	−	0.778500i
$897$	0.771673	−	0.280866i	0.0257654	−	0.00937784i
$898$	−0.141648	−	1.56317i	−0.00472685	−	0.0521635i
$899$	−26.8292	+	31.9738i	−0.894803	+	1.06639i
$900$	5.07719	+	13.6846i	0.169240	+	0.456154i
$901$	−18.5060	+	10.6844i	−0.616524	+	0.355950i
$902$	−0.0146077	−	0.0538479i	−0.000486384	−	0.00179294i
$903$	−1.45964	+	8.27805i	−0.0485739	+	0.275476i
$904$	−0.577265	−	2.07686i	−0.0191996	−	0.0690753i
$905$	−22.9987	−	13.2783i	−0.764502	−	0.441385i
$906$	3.00456	+	0.795086i	0.0998199	+	0.0264150i
$907$	−40.5085	−	14.7439i	−1.34506	−	0.489562i	−0.433659	−	0.901077i	$-0.642778\pi$
$907$	−40.5085	−	14.7439i	−1.34506	−	0.489562i	−0.911403	+	0.411515i	$0.865000\pi$
$908$	10.8708	−	30.4538i	0.360759	−	1.01065i
$909$	4.30721	−	3.61418i	0.142861	−	0.119875i
$910$	−4.34425	−	6.16343i	−0.144010	−	0.204316i
$911$	−5.19556			−0.172137			−0.0860684	−	0.996289i	$-0.527430\pi$
$911$	−5.19556			−0.172137			−0.0860684	+	0.996289i	$0.527430\pi$
$912$	8.59135	−	15.1720i	0.284488	−	0.502394i
$913$	0.0298816			0.000988938
$914$	−2.21531	−	3.14299i	−0.0732759	−	0.103961i
$915$	29.0318	−	24.3606i	0.959762	−	0.805336i
$916$	−7.27662	+	20.3851i	−0.240426	+	0.673542i
$917$	−24.2815	−	8.83776i	−0.801847	−	0.291848i
$918$	−4.99408	−	1.32156i	−0.164829	−	0.0436181i
$919$	−31.3210	−	18.0832i	−1.03318	−	0.596510i	−0.115290	−	0.993332i	$-0.536780\pi$
$919$	−31.3210	−	18.0832i	−1.03318	−	0.596510i	−0.917895	+	0.396822i	$0.870113\pi$
$920$	−3.66395	−	13.1820i	−0.120797	−	0.434598i
$921$	−3.27606	+	18.5794i	−0.107950	+	0.612213i
$922$	3.67422	+	13.5441i	0.121004	+	0.446052i
$923$	5.03360	−	2.90615i	0.165683	−	0.0956572i
$924$	−0.00666289	−	0.0179586i	−0.000219193	−	0.000590795i
$925$	−56.1311	+	66.8944i	−1.84558	+	2.19948i
$926$	−1.39415	−	15.3852i	−0.0458145	−	0.505589i
$927$	7.99476	−	2.90985i	0.262582	−	0.0955722i
$928$	−6.38921	+	25.4156i	−0.209736	+	0.834309i
$929$	−7.06350	−	40.0591i	−0.231746	−	1.31430i	−0.849360	−	0.527815i	$-0.823012\pi$
$929$	−7.06350	−	40.0591i	−0.231746	−	1.31430i	0.617614	−	0.786482i	$-0.288100\pi$
$930$	40.4376	−	19.0093i	1.32600	−	0.623340i
$931$	2.08202	+	0.00844694i	0.0682355	+	0.000276837i
$932$	18.3582	−	22.1562i	0.601341	−	0.725750i
$933$	−19.9053	+	3.50985i	−0.651671	+	0.114907i
$934$	4.32887	+	2.00225i	0.141645	+	0.0655158i
$935$	−0.0164306	−	0.0451426i	−0.000537337	−	0.00147632i
$936$	1.38830	+	0.952960i	0.0453778	+	0.0311485i
$937$	−18.1313	−	15.2140i	−0.592324	−	0.497019i	0.296644	−	0.954988i	$-0.404133\pi$
$937$	−18.1313	−	15.2140i	−0.592324	−	0.497019i	−0.888968	+	0.457969i	$0.848577\pi$
$938$	57.9328	+	4.88738i	1.89157	+	0.159579i
$939$	−1.99519	−	3.45578i	−0.0651107	−	0.112775i
$940$	−7.34733	+	6.24324i	−0.239643	+	0.203632i
$941$	−13.1762	−	2.32332i	−0.429532	−	0.0757382i	−0.0452976	−	0.998974i	$-0.514424\pi$
$941$	−13.1762	−	2.32332i	−0.429532	−	0.0757382i	−0.384235	+	0.923235i	$0.625535\pi$
$942$	12.3910	+	8.61912i	0.403722	+	0.280826i
$943$	7.25565	−	12.5672i	0.236277	−	0.409243i
$944$	−11.9353	+	21.2781i	−0.388461	+	0.692544i
$945$	−3.06318	+	8.41601i	−0.0996451	+	0.273773i
$946$	0.0123046	−	0.0123812i	0.000400058	−	0.000402548i
$947$	−3.99772	−	4.76429i	−0.129908	−	0.154819i	0.697169	−	0.716907i	$-0.254443\pi$
$947$	−3.99772	−	4.76429i	−0.129908	−	0.154819i	−0.827077	+	0.562088i	$0.809998\pi$
$948$	−3.30288	−	1.87969i	−0.107273	−	0.0610494i
$949$			6.63193i			0.215282i
$950$	−36.8276	−	25.8394i	−1.19484	−	0.838340i
$951$		−	17.3283i		−	0.561909i
$952$	2.05497	−	26.3065i	0.0666020	−	0.852599i
$953$	4.71849	+	5.62328i	0.152847	+	0.182156i	0.837034	−	0.547150i	$-0.184287\pi$
$953$	4.71849	+	5.62328i	0.152847	+	0.182156i	−0.684187	+	0.729306i	$0.739843\pi$
$954$	−5.86797	−	5.83166i	−0.189982	−	0.188807i
$955$	−10.5570	+	29.0050i	−0.341615	+	0.938580i
$956$	7.11668	+	38.9459i	0.230170	+	1.25960i
$957$	−0.00868656	+	0.0150456i	−0.000280797	+	0.000486354i
$958$	−20.9975	+	30.1864i	−0.678397	+	0.975278i
$959$	−24.4699	−	4.31471i	−0.790176	−	0.139329i
$960$	17.6301	−	21.8233i	0.569010	−	0.704343i
$961$	−25.0867	−	43.4515i	−0.809250	−	1.40166i
$962$	−0.846886	+	10.0386i	−0.0273047	+	0.323657i
$963$	6.15306	+	5.16303i	0.198280	+	0.166376i
$964$	17.6720	+	30.1747i	0.569176	+	0.971863i
$965$	−3.88503	−	10.6740i	−0.125063	−	0.343609i
$966$	2.09142	−	4.52164i	0.0672904	−	0.145482i
$967$	−33.6281	+	5.92954i	−1.08141	+	0.190681i	−0.685837	−	0.727755i	$-0.740564\pi$
$967$	−33.6281	+	5.92954i	−1.08141	+	0.190681i	−0.395570	+	0.918436i	$0.629453\pi$
$968$	7.77246	−	30.1262i	0.249816	−	0.968292i
$969$	14.9843	−	5.38511i	0.481366	−	0.172995i
$970$	2.27114	+	4.83128i	0.0729218	+	0.155123i
$971$	−1.61392	−	9.15301i	−0.0517932	−	0.293734i	0.947898	−	0.318573i	$-0.103204\pi$
$971$	−1.61392	−	9.15301i	−0.0517932	−	0.293734i	−0.999691	+	0.0248393i	$0.992093\pi$
$972$	−0.0124111	−	1.99996i	−0.000398085	−	0.0641488i
$973$	9.16841	−	3.33703i	0.293926	−	0.106980i
$974$	−52.2415	+	4.73392i	−1.67393	+	0.151685i
$975$	2.79283	−	3.32837i	0.0894422	−	0.106593i
$976$	−40.8011	−	14.2795i	−1.30601	−	0.457074i
$977$	−1.71104	+	0.987869i	−0.0547410	+	0.0316047i	−0.527121	−	0.849790i	$-0.676728\pi$
$977$	−1.71104	+	0.987869i	−0.0547410	+	0.0316047i	0.472380	+	0.881395i	$0.343395\pi$
$978$	−14.7733	+	4.00766i	−0.472397	+	0.128151i
$979$	−0.00989356	+	0.0561092i	−0.000316200	+	0.00179326i
$980$	3.30277	+	0.561257i	0.105503	+	0.0179287i
$981$	3.05299	+	1.76264i	0.0974744	+	0.0562768i
$982$	2.49099	−	9.41324i	0.0794907	−	0.300388i
$983$	15.7370	+	5.72779i	0.501931	+	0.182688i	0.580562	−	0.814216i	$-0.302833\pi$
$983$	15.7370	+	5.72779i	0.501931	+	0.182688i	−0.0786313	+	0.996904i	$0.525055\pi$
$984$	29.6173	−	2.86921i	0.944164	−	0.0914670i
$985$	44.7666	−	37.5637i	1.42638	−	1.19688i
$986$	−19.5616	+	13.7878i	−0.622967	+	0.439093i
$987$	−3.51079			−0.111750
$988$	−5.19010	+	0.0111510i	−0.165119	+	0.000354761i
$989$	4.53997			0.144363
$990$	0.0152018	−	0.0107149i	0.000483146	−	0.000340542i
$991$	−32.4691	+	27.2448i	−1.03142	+	0.865460i	−0.991019	−	0.133723i	$-0.957307\pi$
$991$	−32.4691	+	27.2448i	−1.03142	+	0.865460i	−0.0403967	+	0.999184i	$0.512862\pi$
$992$	−42.1975	−	28.5818i	−1.33977	−	0.907473i
$993$	−4.75586	−	1.73099i	−0.150923	−	0.0549313i
$994$	9.02052	−	34.0878i	0.286114	−	1.08120i
$995$	76.3844	+	44.1006i	2.42155	+	1.39808i
$996$	−2.66988	+	15.7111i	−0.0845983	+	0.497826i
$997$	−2.18396	+	12.3859i	−0.0691668	+	0.392264i	0.930496	+	0.366302i	$0.119376\pi$
$997$	−2.18396	+	12.3859i	−0.0691668	+	0.392264i	−0.999663	+	0.0259626i	$0.991735\pi$
$998$	55.0104	−	14.9231i	1.74132	−	0.472382i
$999$	10.3624	−	5.98272i	0.327851	−	0.189285i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	228.2.w.b.67.8	yes	60
3.2	odd	2		684.2.cf.b.523.3		60
4.3	odd	2		228.2.w.a.67.6	✓	60
12.11	even	2		684.2.cf.c.523.5		60
19.2	odd	18		228.2.w.a.211.6	yes	60
57.2	even	18		684.2.cf.c.667.5		60
76.59	even	18	inner	228.2.w.b.211.8	yes	60
228.59	odd	18		684.2.cf.b.667.3		60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
228.2.w.a.67.6	✓	60	4.3	odd	2
228.2.w.a.211.6	yes	60	19.2	odd	18
228.2.w.b.67.8	yes	60	1.1	even	1	trivial
228.2.w.b.211.8	yes	60	76.59	even	18	inner
684.2.cf.b.523.3		60	3.2	odd	2
684.2.cf.b.667.3		60	228.59	odd	18
684.2.cf.c.523.5		60	12.11	even	2
684.2.cf.c.667.5		60	57.2	even	18

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 228 = 2^{2} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	228.w (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.814750 + 1.15593i) q^{2} +(0.766044 - 0.642788i) q^{3} +(-0.672365 + 1.88359i) q^{4} +(3.29537 + 1.19942i) q^{5} +(1.36715 + 0.361785i) q^{6} +(-2.21173 - 1.27694i) q^{7} +(-2.72512 + 0.757450i) q^{8} +(0.173648 - 0.984808i) q^{9} +(1.29846 + 4.78645i) q^{10} +(0.00324770 - 0.00187506i) q^{11} +(0.695690 + 1.87510i) q^{12} +(0.382681 - 0.456062i) q^{13} +(-0.325947 - 3.59701i) q^{14} +(3.29537 - 1.19942i) q^{15} +(-3.09585 - 2.53292i) q^{16} +(-0.634319 - 3.59740i) q^{17} +(1.27985 - 0.601646i) q^{18} +(-2.19475 + 3.76604i) q^{19} +(-4.47490 + 5.40069i) q^{20} +(-2.51509 + 0.443478i) q^{21} +(0.00481351 + 0.00222642i) q^{22} +(0.471769 + 1.29618i) q^{23} +(-1.60068 + 2.33191i) q^{24} +(5.59064 + 4.69110i) q^{25} +(0.838966 + 0.0707777i) q^{26} +(-0.500000 - 0.866025i) q^{27} +(3.89234 - 3.30743i) q^{28} +(-4.56231 - 0.804457i) q^{29} +(4.07135 + 2.83200i) q^{30} +(4.50482 - 7.80257i) q^{31} +(0.405545 - 5.64230i) q^{32} +(0.00128262 - 0.00352396i) q^{33} +(3.64155 - 3.66421i) q^{34} +(-5.75689 - 6.86079i) q^{35} +(1.73822 + 0.989232i) q^{36} +11.9654i q^{37} +(-6.14147 + 0.531404i) q^{38} -0.595346i q^{39} +(-9.88877 - 0.772475i) q^{40} +(-6.76233 - 8.05903i) q^{41} +(-2.56180 - 2.54595i) q^{42} +(1.12571 - 3.09286i) q^{43} +(0.00134821 + 0.00737807i) q^{44} +(1.75343 - 3.03703i) q^{45} +(-1.11392 + 1.60139i) q^{46} +(1.35380 + 0.238711i) q^{47} +(-3.99969 + 0.0496434i) q^{48} +(-0.238826 - 0.413659i) q^{49} +(-0.867630 + 10.2845i) q^{50} +(-2.79828 - 2.34804i) q^{51} +(0.601734 + 1.02746i) q^{52} +(-2.00076 - 5.49705i) q^{53} +(0.593693 - 1.28356i) q^{54} +(0.0129513 - 0.00228367i) q^{55} +(6.99445 + 1.80455i) q^{56} +(0.739493 + 4.29571i) q^{57} +(-2.78724 - 5.92915i) q^{58} +(-1.05912 - 6.00657i) q^{59} +(0.0435239 + 7.01358i) q^{60} +(10.1552 - 3.69618i) q^{61} +(12.6896 - 1.14988i) q^{62} +(-1.64161 + 1.95639i) q^{63} +(6.85254 - 4.12828i) q^{64} +(1.80808 - 1.04390i) q^{65} +(0.00511847 - 0.00138853i) q^{66} +(-2.79523 + 15.8525i) q^{67} +(7.20254 + 1.22397i) q^{68} +(1.19456 + 0.689680i) q^{69} +(3.24019 - 12.2444i) q^{70} +(9.17413 + 3.33911i) q^{71} +(0.272730 + 2.81525i) q^{72} +(-8.53345 + 7.16041i) q^{73} +(-13.8312 + 9.74884i) q^{74} +7.29806 q^{75} +(-5.61803 - 6.66617i) q^{76} -0.00957739 q^{77} +(0.688181 - 0.485058i) q^{78} +(-1.45560 + 1.22139i) q^{79} +(-7.16395 - 12.0601i) q^{80} +(-0.939693 - 0.342020i) q^{81} +(3.80609 - 14.3829i) q^{82} +(6.90065 + 3.98409i) q^{83} +(0.855724 - 5.03559i) q^{84} +(2.22447 - 12.6156i) q^{85} +(4.49232 - 1.21866i) q^{86} +(-4.01202 + 2.31634i) q^{87} +(-0.00743010 + 0.00756973i) q^{88} +(-9.76573 + 11.6383i) q^{89} +(4.93921 - 0.447572i) q^{90} +(-1.42875 + 0.520024i) q^{91} +(-2.75867 + 0.0171194i) q^{92} +(-1.56451 - 8.87276i) q^{93} +(0.827074 + 1.75939i) q^{94} +(-11.7496 + 9.77809i) q^{95} +(-3.31613 - 4.58293i) q^{96} +(1.06007 - 0.186919i) q^{97} +(0.283579 - 0.613096i) q^{98} +(-0.00128262 - 0.00352396i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 3 q^{2} - 3 q^{4} + 3 q^{6} - 3 q^{8} - 6 q^{10} - 6 q^{13} - 9 q^{14} + 21 q^{16} + 18 q^{19} + 30 q^{20} - 6 q^{21} - 12 q^{22} - 18 q^{24} - 30 q^{27} - 18 q^{28} - 12 q^{31} + 33 q^{32} - 15 q^{34}+ \cdots - 105 q^{98}+O(q^{100}) \) 60 * q + 3 * q^2 - 3 * q^4 + 3 * q^6 - 3 * q^8 - 6 * q^10 - 6 * q^13 - 9 * q^14 + 21 * q^16 + 18 * q^19 + 30 * q^20 - 6 * q^21 - 12 * q^22 - 18 * q^24 - 30 * q^27 - 18 * q^28 - 12 * q^31 + 33 * q^32 - 15 * q^34 - 3 * q^36 - 84 * q^38 - 87 * q^40 - 12 * q^41 + 9 * q^42 - 18 * q^43 - 51 * q^44 - 21 * q^46 + 18 * q^48 + 30 * q^49 - 27 * q^50 - 3 * q^52 + 12 * q^53 + 3 * q^54 + 42 * q^56 - 36 * q^58 + 15 * q^60 + 105 * q^62 - 12 * q^63 + 21 * q^64 - 36 * q^65 + 24 * q^66 + 42 * q^67 - 15 * q^68 - 72 * q^69 - 96 * q^70 + 24 * q^71 + 18 * q^72 + 18 * q^73 + 69 * q^74 + 60 * q^75 + 54 * q^76 - 72 * q^77 + 57 * q^78 + 12 * q^79 - 12 * q^80 + 75 * q^82 + 39 * q^84 - 60 * q^85 + 21 * q^86 + 36 * q^88 - 12 * q^89 + 15 * q^90 - 84 * q^91 + 99 * q^92 - 12 * q^93 - 24 * q^95 + 12 * q^97 - 105 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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