LMFDB - Embedded newform 648.2.t.a.613.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [648,2,Mod(37,648)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("648.37"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(648, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 9, 14])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 648 = 2^{3} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	648.t (of order $18$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$5.17430605098$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 216)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			613.3
Character	$\chi$	$=$	648.613
Dual form			648.2.t.a.37.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.39256 + 0.246516i) q^{2} +(1.87846 - 0.686578i) q^{4} +(-0.355965 + 0.978005i) q^{5} +(-0.272085 + 1.54307i) q^{7} +(-2.44662 + 1.41917i) q^{8} +(0.254609 - 1.44968i) q^{10} +(-1.44773 - 3.97760i) q^{11} +(-4.33941 - 5.17151i) q^{13} +(-0.00149657 - 2.21590i) q^{14} +(3.05722 - 2.57942i) q^{16} +(0.494959 + 0.857294i) q^{17} +(2.70129 + 1.55959i) q^{19} +(0.00281166 + 2.08154i) q^{20} +(2.99660 + 5.18217i) q^{22} +(-1.17888 - 6.68573i) q^{23} +(3.00044 + 2.51767i) q^{25} +(7.31776 + 6.13191i) q^{26} +(0.548339 + 3.08541i) q^{28} +(2.84964 - 3.39607i) q^{29} +(-0.409166 - 2.32049i) q^{31} +(-3.62150 + 4.34566i) q^{32} +(-0.900598 - 1.07182i) q^{34} +(-1.41228 - 0.815381i) q^{35} +(-3.19157 + 1.84266i) q^{37} +(-4.14618 - 1.50592i) q^{38} +(-0.517049 - 2.89798i) q^{40} +(2.44191 - 2.04900i) q^{41} +(-3.71087 - 10.1955i) q^{43} +(-5.45044 - 6.47779i) q^{44} +(3.28980 + 9.01969i) q^{46} +(0.155220 - 0.880296i) q^{47} +(4.27080 + 1.55445i) q^{49} +(-4.79894 - 2.76635i) q^{50} +(-11.7021 - 6.73512i) q^{52} +5.00251i q^{53} +4.40546 q^{55} +(-1.52420 - 4.16145i) q^{56} +(-3.13112 + 5.43173i) q^{58} +(3.85475 - 10.5908i) q^{59} +(-5.41575 - 0.954943i) q^{61} +(1.14183 + 3.13057i) q^{62} +(3.97189 - 6.94436i) q^{64} +(6.60244 - 2.40309i) q^{65} +(-0.467287 - 0.556891i) q^{67} +(1.51836 + 1.27056i) q^{68} +(2.16769 + 0.787319i) q^{70} +(2.52073 + 4.36603i) q^{71} +(7.01816 - 12.1558i) q^{73} +(3.99022 - 3.35279i) q^{74} +(6.14505 + 1.07498i) q^{76} +(6.53164 - 1.15170i) q^{77} +(-6.78017 - 5.68924i) q^{79} +(1.43442 + 3.90816i) q^{80} +(-2.89539 + 3.45533i) q^{82} +(4.03223 - 4.80543i) q^{83} +(-1.01463 + 0.178906i) q^{85} +(7.68099 + 13.2831i) q^{86} +(9.18695 + 7.67710i) q^{88} +(-4.02279 + 6.96768i) q^{89} +(9.16071 - 5.28894i) q^{91} +(-6.80475 - 11.7495i) q^{92} +(0.000853769 + 1.26413i) q^{94} +(-2.48685 + 2.08672i) q^{95} +(-10.1365 + 3.68937i) q^{97} +(-6.33056 - 1.11184i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q + 6 q^{2} - 6 q^{4} - 12 q^{7} + 3 q^{8} - 3 q^{10} + 21 q^{14} - 6 q^{16} + 6 q^{17} - 15 q^{20} - 6 q^{22} + 12 q^{23} - 12 q^{25} + 30 q^{26} - 12 q^{28} - 12 q^{31} + 36 q^{32} + 42 q^{38} - 21 q^{40}+ \cdots - 54 q^{98}+O(q^{100}) $ 204 * q + 6 * q^2 - 6 * q^4 - 12 * q^7 + 3 * q^8 - 3 * q^10 + 21 * q^14 - 6 * q^16 + 6 * q^17 - 15 * q^20 - 6 * q^22 + 12 * q^23 - 12 * q^25 + 30 * q^26 - 12 * q^28 - 12 * q^31 + 36 * q^32 + 42 * q^38 - 21 * q^40 + 24 * q^41 - 21 * q^44 - 3 * q^46 + 12 * q^47 - 12 * q^49 + 99 * q^50 - 33 * q^52 - 24 * q^55 - 99 * q^56 + 21 * q^58 + 36 * q^62 - 3 * q^64 + 12 * q^65 - 75 * q^68 + 9 * q^70 + 90 * q^71 - 6 * q^73 - 9 * q^74 - 18 * q^76 - 12 * q^79 - 78 * q^80 - 12 * q^82 + 30 * q^86 - 30 * q^88 + 6 * q^89 - 111 * q^92 - 33 * q^94 + 42 * q^95 - 12 * q^97 - 54 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/648\mathbb{Z}\right)^\times$.

$n$	$325$	$487$	$569$
$\chi(n)$	$-1$	$1$	$e\left(\frac{2}{9}\right)$

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 $

$2$	−1.39256	+	0.246516i	−0.984690	+	0.174313i
$2$	−1.39256	+	0.246516i	−0.984690	+	0.174313i
$3$		0			0
$3$		0			0
$4$	1.87846	−	0.686578i	0.939230	−	0.343289i
$5$	−0.355965	+	0.978005i	−0.159192	+	0.437377i	−0.993488	−	0.113941i	$-0.963653\pi$
$5$	−0.355965	+	0.978005i	−0.159192	+	0.437377i	0.834295	+	0.551318i	$0.185875\pi$
$6$		0			0
$7$	−0.272085	+	1.54307i	−0.102839	+	0.583227i	0.889223	+	0.457474i	$0.151246\pi$
$7$	−0.272085	+	1.54307i	−0.102839	+	0.583227i	−0.992062	+	0.125753i	$0.959865\pi$
$8$	−2.44662	+	1.41917i	−0.865011	+	0.501754i
$9$		0			0
$10$	0.254609	−	1.44968i	0.0805145	−	0.458430i
$11$	−1.44773	−	3.97760i	−0.436507	−	1.19929i	−0.941750	−	0.336315i	$-0.890819\pi$
$11$	−1.44773	−	3.97760i	−0.436507	−	1.19929i	0.505243	−	0.862977i	$-0.331403\pi$
$12$		0			0
$13$	−4.33941	−	5.17151i	−1.20354	−	1.43432i	−0.871039	−	0.491214i	$-0.836553\pi$
$13$	−4.33941	−	5.17151i	−1.20354	−	1.43432i	−0.332497	−	0.943104i	$-0.607891\pi$
$14$	−0.00149657	−	2.21590i	−0.000399976	−	0.592224i
$15$		0			0
$16$	3.05722	−	2.57942i	0.764305	−	0.644855i
$17$	0.494959	+	0.857294i	0.120045	+	0.207924i	0.919785	−	0.392422i	$-0.128363\pi$
$17$	0.494959	+	0.857294i	0.120045	+	0.207924i	−0.799740	+	0.600346i	$0.795029\pi$
$18$		0			0
$19$	2.70129	+	1.55959i	0.619719	+	0.357795i	0.776759	−	0.629797i	$-0.216862\pi$
$19$	2.70129	+	1.55959i	0.619719	+	0.357795i	−0.157041	+	0.987592i	$0.550195\pi$
$20$	0.00281166	+	2.08154i	0.000628707	+	0.465447i
$21$		0			0
$22$	2.99660	+	5.18217i	0.638876	+	1.10484i
$23$	−1.17888	−	6.68573i	−0.245812	−	1.39407i	−0.818598	−	0.574367i	$-0.805248\pi$
$23$	−1.17888	−	6.68573i	−0.245812	−	1.39407i	0.572786	−	0.819705i	$-0.305863\pi$
$24$		0			0
$25$	3.00044	+	2.51767i	0.600088	+	0.503533i
$26$	7.31776	+	6.13191i	1.43513	+	1.20257i
$27$		0			0
$28$	0.548339	+	3.08541i	0.103626	+	0.583088i
$29$	2.84964	−	3.39607i	0.529166	−	0.630635i	−0.433557	−	0.901126i	$-0.642742\pi$
$29$	2.84964	−	3.39607i	0.529166	−	0.630635i	0.962722	+	0.270491i	$0.0871861\pi$
$30$		0			0
$31$	−0.409166	−	2.32049i	−0.0734883	−	0.416773i	−0.999252	−	0.0386704i	$-0.987688\pi$
$31$	−0.409166	−	2.32049i	−0.0734883	−	0.416773i	0.925764	−	0.378103i	$-0.123423\pi$
$32$	−3.62150	+	4.34566i	−0.640197	+	0.768211i
$33$		0			0
$34$	−0.900598	−	1.07182i	−0.154451	−	0.183816i
$35$	−1.41228	−	0.815381i	−0.238719	−	0.137825i
$36$		0			0
$37$	−3.19157	+	1.84266i	−0.524691	+	0.302931i	−0.738852	−	0.673868i	$-0.764632\pi$
$37$	−3.19157	+	1.84266i	−0.524691	+	0.302931i	0.214161	+	0.976798i	$0.431298\pi$
$38$	−4.14618	−	1.50592i	−0.672599	−	0.244292i
$39$		0			0
$40$	−0.517049	−	2.89798i	−0.0817526	−	0.458211i
$41$	2.44191	−	2.04900i	0.381362	−	0.320000i	−0.431875	−	0.901933i	$-0.642148\pi$
$41$	2.44191	−	2.04900i	0.381362	−	0.320000i	0.813237	+	0.581933i	$0.197703\pi$
$42$		0			0
$43$	−3.71087	−	10.1955i	−0.565903	−	1.55481i	−0.810841	−	0.585267i	$-0.800990\pi$
$43$	−3.71087	−	10.1955i	−0.565903	−	1.55481i	0.244938	−	0.969539i	$-0.421233\pi$
$44$	−5.45044	−	6.47779i	−0.821684	−	0.976563i
$45$		0			0
$46$	3.28980	+	9.01969i	0.485054	+	1.32988i
$47$	0.155220	−	0.880296i	0.0226411	−	0.128404i	−0.971392	−	0.237481i	$-0.923678\pi$
$47$	0.155220	−	0.880296i	0.0226411	−	0.128404i	0.994033	+	0.109077i	$0.0347894\pi$
$48$		0			0
$49$	4.27080	+	1.55445i	0.610115	+	0.222064i
$50$	−4.79894	−	2.76635i	−0.678673	−	0.391221i
$51$		0			0
$52$	−11.7021	−	6.73512i	−1.62278	−	0.933994i
$53$			5.00251i			0.687148i	0.939126	+	0.343574i	$0.111638\pi$
$53$			5.00251i			0.687148i	−0.939126	+	0.343574i	$0.888362\pi$
$54$		0			0
$55$	4.40546			0.594032
$56$	−1.52420	−	4.16145i	−0.203680	−	0.556097i
$57$		0			0
$58$	−3.13112	+	5.43173i	−0.411136	+	0.713221i
$59$	3.85475	−	10.5908i	0.501846	−	1.37881i	−0.387625	−	0.921817i	$-0.626704\pi$
$59$	3.85475	−	10.5908i	0.501846	−	1.37881i	0.889470	−	0.456993i	$-0.151073\pi$
$60$		0			0
$61$	−5.41575	−	0.954943i	−0.693416	−	0.122268i	−0.184177	−	0.982893i	$-0.558962\pi$
$61$	−5.41575	−	0.954943i	−0.693416	−	0.122268i	−0.509239	+	0.860625i	$0.670073\pi$
$62$	1.14183	+	3.13057i	0.145012	+	0.397582i
$63$		0			0
$64$	3.97189	−	6.94436i	0.496487	−	0.868044i
$65$	6.60244	−	2.40309i	0.818932	−	0.298067i
$66$		0			0
$67$	−0.467287	−	0.556891i	−0.0570882	−	0.0680351i	0.736745	−	0.676171i	$-0.236362\pi$
$67$	−0.467287	−	0.556891i	−0.0570882	−	0.0680351i	−0.793833	+	0.608136i	$0.791918\pi$
$68$	1.51836	+	1.27056i	0.184128	+	0.154078i
$69$		0			0
$70$	2.16769	+	0.787319i	0.259089	+	0.0941026i
$71$	2.52073	+	4.36603i	0.299155	+	0.518152i	0.975943	−	0.218026i	$-0.0699618\pi$
$71$	2.52073	+	4.36603i	0.299155	+	0.518152i	−0.676788	+	0.736178i	$0.736628\pi$
$72$		0			0
$73$	7.01816	−	12.1558i	0.821413	−	1.42273i	−0.0832165	−	0.996531i	$-0.526519\pi$
$73$	7.01816	−	12.1558i	0.821413	−	1.42273i	0.904630	−	0.426198i	$-0.140147\pi$
$74$	3.99022	−	3.35279i	0.463854	−	0.389753i
$75$		0			0
$76$	6.14505	+	1.07498i	0.704885	+	0.123309i
$77$	6.53164	−	1.15170i	0.744349	−	0.131249i
$78$		0			0
$79$	−6.78017	−	5.68924i	−0.762829	−	0.640090i	0.176032	−	0.984384i	$-0.443674\pi$
$79$	−6.78017	−	5.68924i	−0.762829	−	0.640090i	−0.938862	+	0.344295i	$0.888118\pi$
$80$	1.43442	+	3.90816i	0.160373	+	0.436946i
$81$		0			0
$82$	−2.89539	+	3.45533i	−0.319743	+	0.381578i
$83$	4.03223	−	4.80543i	0.442595	−	0.527464i	−0.497917	−	0.867225i	$-0.665902\pi$
$83$	4.03223	−	4.80543i	0.442595	−	0.527464i	0.940512	+	0.339760i	$0.110346\pi$
$84$		0			0
$85$	−1.01463	+	0.178906i	−0.110052	+	0.0194051i
$86$	7.68099	+	13.2831i	0.828262	+	1.43236i
$87$		0			0
$88$	9.18695	+	7.67710i	0.979332	+	0.818382i
$89$	−4.02279	+	6.96768i	−0.426415	+	0.738573i	−0.996551	−	0.0829775i	$-0.973557\pi$
$89$	−4.02279	+	6.96768i	−0.426415	+	0.738573i	0.570136	+	0.821550i	$0.306890\pi$
$90$		0			0
$91$	9.16071	−	5.28894i	0.960303	−	0.554431i
$92$	−6.80475	−	11.7495i	−0.709444	−	1.22497i
$93$		0			0
$94$	0.000853769		1.26413i	8.80595e−5		0.130385i
$95$	−2.48685	+	2.08672i	−0.255146	+	0.214093i
$96$		0			0
$97$	−10.1365	+	3.68937i	−1.02920	+	0.374599i	−0.800777	−	0.598963i	$-0.795580\pi$
$97$	−10.1365	+	3.68937i	−1.02920	+	0.374599i	−0.228425	+	0.973561i	$0.573358\pi$
$98$	−6.33056	−	1.11184i	−0.639483	−	0.112313i
$99$		0			0
$100$	7.36478	+	2.66930i	0.736478	+	0.266930i
$101$	−6.50659	−	1.14729i	−0.647430	−	0.114159i	−0.159716	−	0.987163i	$-0.551058\pi$
$101$	−6.50659	−	1.14729i	−0.647430	−	0.114159i	−0.487714	+	0.873004i	$0.662169\pi$
$102$		0			0
$103$	−14.9315	−	5.43464i	−1.47125	−	0.535491i	−0.522809	−	0.852450i	$-0.675116\pi$
$103$	−14.9315	−	5.43464i	−1.47125	−	0.535491i	−0.948439	+	0.316959i	$0.897338\pi$
$104$	17.9562	+	6.49433i	1.76075	+	0.636822i
$105$		0			0
$106$	−1.23320	−	6.96631i	−0.119779	−	0.676628i
$107$		−	3.85513i		−	0.372689i	−0.982484	−	0.186345i	$-0.940336\pi$
$107$		−	3.85513i		−	0.372689i	0.982484	−	0.186345i	$-0.0596641\pi$
$108$		0			0
$109$			3.32803i			0.318767i	0.987217	+	0.159384i	$0.0509507\pi$
$109$			3.32803i			0.318767i	−0.987217	+	0.159384i	$0.949049\pi$
$110$	−6.13487	+	1.08602i	−0.584937	+	0.103548i
$111$		0			0
$112$	3.14841	+	5.41934i	0.297497	+	0.512079i
$113$	−7.85208	−	2.85792i	−0.738662	−	0.268851i	−0.0548351	−	0.998495i	$-0.517463\pi$
$113$	−7.85208	−	2.85792i	−0.738662	−	0.268851i	−0.683827	+	0.729645i	$0.739686\pi$
$114$		0			0
$115$	6.95832	+	1.22694i	0.648867	+	0.114413i
$116$	3.02127	−	8.33589i	0.280518	−	0.773968i
$117$		0			0
$118$	−2.75717	+	15.6987i	−0.253818	+	1.44518i
$119$	−1.45754	+	0.530501i	−0.133612	+	0.0486309i
$120$		0			0
$121$	−5.29891	+	4.44632i	−0.481719	+	0.404211i
$122$	7.77718	−	0.00525255i	0.704112	−	0.000475544i
$123$		0			0
$124$	−2.36180	−	4.07803i	−0.212096	−	0.366218i
$125$	−8.03702	+	4.64017i	−0.718853	+	0.415030i
$126$		0			0
$127$	1.83012	−	3.16986i	0.162397	−	0.281280i	−0.773331	−	0.634003i	$-0.781411\pi$
$127$	1.83012	−	3.16986i	0.162397	−	0.281280i	0.935728	+	0.352723i	$0.114744\pi$
$128$	−3.81921	+	10.6496i	−0.337574	+	0.941299i
$129$		0			0
$130$	−8.60191	+	4.97406i	−0.754437	+	0.436254i
$131$	−9.66082	+	1.70346i	−0.844070	+	0.148832i	−0.578930	−	0.815378i	$-0.696529\pi$
$131$	−9.66082	+	1.70346i	−0.844070	+	0.148832i	−0.265140	+	0.964210i	$0.585418\pi$
$132$		0			0
$133$	−3.14155	+	3.74395i	−0.272407	+	0.324641i
$134$	0.788009	+	0.660312i	0.0680736	+	0.0570423i
$135$		0			0
$136$	−2.42762	−	1.39504i	−0.208167	−	0.119624i
$137$	16.9231	+	14.2001i	1.44583	+	1.21320i	0.935550	+	0.353193i	$0.114904\pi$
$137$	16.9231	+	14.2001i	1.44583	+	1.21320i	0.510284	+	0.860006i	$0.329540\pi$
$138$		0			0
$139$	−4.68849	+	0.826707i	−0.397672	+	0.0701203i	−0.368908	−	0.929466i	$-0.620268\pi$
$139$	−4.68849	+	0.826707i	−0.397672	+	0.0701203i	−0.0287641	+	0.999586i	$0.509157\pi$
$140$	−3.21274	−	0.562019i	−0.271526	−	0.0474992i
$141$		0			0
$142$	−4.58657	−	5.45856i	−0.384896	−	0.458073i
$143$	−14.2879	+	24.7474i	−1.19482	+	2.06948i
$144$		0			0
$145$	2.30701	+	3.99585i	0.191586	+	0.331837i
$146$	−6.77662	+	18.6578i	−0.560837	+	1.54413i
$147$		0			0
$148$	−4.73011	+	5.65262i	−0.388813	+	0.464642i
$149$	14.7916	+	17.6280i	1.21178	+	1.44414i	0.861700	+	0.507418i	$0.169400\pi$
$149$	14.7916	+	17.6280i	1.21178	+	1.44414i	0.350076	+	0.936721i	$0.386156\pi$
$150$		0			0
$151$	18.6779	−	6.79819i	1.51998	−	0.553229i	0.558840	−	0.829276i	$-0.311247\pi$
$151$	18.6779	−	6.79819i	1.51998	−	0.553229i	0.961144	+	0.276047i	$0.0890245\pi$
$152$	−8.82236	+	0.0178754i	−0.715588	+	0.00144988i
$153$		0			0
$154$	−8.81180	+	3.21397i	−0.710075	+	0.258989i
$155$	2.41510	+	0.425848i	0.193986	+	0.0342049i
$156$		0			0
$157$	−1.67263	+	4.59552i	−0.133491	+	0.366762i	−0.988371	−	0.152063i	$-0.951408\pi$
$157$	−1.67263	+	4.59552i	−0.133491	+	0.366762i	0.854880	+	0.518825i	$0.173631\pi$
$158$	10.8443	+	6.25120i	0.862727	+	0.497319i
$159$		0			0
$160$	−2.96095	−	5.08875i	−0.234083	−	0.402301i
$161$	10.6373			0.838339
$162$		0			0
$163$			4.18081i			0.327466i	0.986505	+	0.163733i	$0.0523536\pi$
$163$			4.18081i			0.327466i	−0.986505	+	0.163733i	$0.947646\pi$
$164$	3.18022	−	5.52553i	0.248334	−	0.431471i
$165$		0			0
$166$	−4.43052	+	7.68587i	−0.343875	+	0.596539i
$167$	−5.72775	−	2.08473i	−0.443227	−	0.161321i	0.110759	−	0.993847i	$-0.464672\pi$
$167$	−5.72775	−	2.08473i	−0.443227	−	0.161321i	−0.553986	+	0.832526i	$0.686894\pi$
$168$		0			0
$169$	−5.65659	+	32.0801i	−0.435122	+	2.46770i
$170$	1.36883	−	0.499259i	0.104984	−	0.0382914i
$171$		0			0
$172$	−13.9708	−	16.6041i	−1.06526	−	1.26605i
$173$	0.453627	+	1.24633i	0.0344886	+	0.0947567i	0.955742	−	0.294207i	$-0.0950554\pi$
$173$	0.453627	+	1.24633i	0.0344886	+	0.0947567i	−0.921253	+	0.388964i	$0.872833\pi$
$174$		0			0
$175$	−4.70132	+	3.94488i	−0.355386	+	0.298205i
$176$	−14.6859	−	8.42611i	−1.10699	−	0.635142i
$177$		0			0
$178$	3.88434	−	10.6946i	0.291144	−	0.801595i
$179$	9.68622	−	5.59234i	0.723982	−	0.417991i	−0.0922343	−	0.995737i	$-0.529401\pi$
$179$	9.68622	−	5.59234i	0.723982	−	0.417991i	0.816217	+	0.577746i	$0.196068\pi$
$180$		0			0
$181$	3.21058	+	1.85363i	0.238641	+	0.137779i	0.614552	−	0.788876i	$-0.289337\pi$
$181$	3.21058	+	1.85363i	0.238641	+	0.137779i	−0.375911	+	0.926656i	$0.622670\pi$
$182$	−11.4530	+	9.62344i	−0.848956	+	0.713337i
$183$		0			0
$184$	12.3725	+	14.6844i	0.912111	+	1.08255i
$185$	−0.666039	−	3.77730i	−0.0489682	−	0.277712i
$186$		0			0
$187$	2.69341	−	3.20988i	0.196961	−	0.234730i
$188$	−0.312818	−	1.76017i	−0.0228146	−	0.128374i
$189$		0			0
$190$	2.94869	−	3.51893i	0.213920	−	0.255290i
$191$	−13.8306	−	11.6053i	−1.00075	−	0.839729i	−0.0136618	−	0.999907i	$-0.504349\pi$
$191$	−13.8306	−	11.6053i	−1.00075	−	0.839729i	−0.987088	+	0.160178i	$0.948793\pi$
$192$		0			0
$193$	0.770660	+	4.37063i	0.0554733	+	0.314605i	0.999900	−	0.0141163i	$-0.00449352\pi$
$193$	0.770660	+	4.37063i	0.0554733	+	0.314605i	−0.944427	+	0.328721i	$0.893382\pi$
$194$	13.2062	−	7.63648i	0.948148	−	0.548268i
$195$		0			0
$196$	9.08978	−	0.0122781i	0.649270	−	0.000877008i
$197$	−14.1519	−	8.17063i	−1.00828	−	0.582133i	−0.0975957	−	0.995226i	$-0.531115\pi$
$197$	−14.1519	−	8.17063i	−1.00828	−	0.582133i	−0.910689	+	0.413093i	$0.864449\pi$
$198$		0			0
$199$	−0.458824	−	0.794707i	−0.0325252	−	0.0563353i	0.849305	−	0.527903i	$-0.177022\pi$
$199$	−0.458824	−	0.794707i	−0.0325252	−	0.0563353i	−0.881830	+	0.471568i	$0.843688\pi$
$200$	−10.9139	−	1.90163i	−0.771732	−	0.134465i
$201$		0			0
$202$	9.34365	−	0.00631052i	0.657417	−	0.000444006i
$203$	4.46504	+	5.32123i	0.313385	+	0.373477i
$204$		0			0
$205$	1.13470	+	3.11757i	0.0792511	+	0.217741i
$206$	22.1328	+	3.88720i	1.54207	+	0.270834i
$207$		0			0
$208$	−26.6060	−	4.61728i	−1.84480	−	0.320151i
$209$	2.29270	−	13.0025i	0.158589	−	0.899403i
$210$		0			0
$211$	−2.09734	+	5.76240i	−0.144387	+	0.396700i	−0.990714	−	0.135964i	$-0.956587\pi$
$211$	−2.09734	+	5.76240i	−0.144387	+	0.396700i	0.846327	+	0.532664i	$0.178809\pi$
$212$	3.43462	+	9.39702i	0.235891	+	0.645390i
$213$		0			0
$214$	0.950351	+	5.36850i	0.0649647	+	0.366983i
$215$	11.2922			0.770124
$216$		0			0
$217$	3.69202			0.250631
$218$	−0.820412	−	4.63448i	−0.0555653	−	0.313887i
$219$		0			0
$220$	8.27547	−	3.02469i	0.557932	−	0.203925i
$221$	2.28567	−	6.27983i	0.153751	−	0.422427i
$222$		0			0
$223$	−3.72326	+	21.1156i	−0.249328	+	1.41401i	0.560896	+	0.827887i	$0.310457\pi$
$223$	−3.72326	+	21.1156i	−0.249328	+	1.41401i	−0.810223	+	0.586121i	$0.800654\pi$
$224$	−5.72031	−	6.77063i	−0.382204	−	0.452382i
$225$		0			0
$226$	11.6390	+	2.04417i	0.774217	+	0.135976i
$227$	6.36438	+	17.4860i	0.422419	+	1.16059i	0.950319	+	0.311279i	$0.100757\pi$
$227$	6.36438	+	17.4860i	0.422419	+	1.16059i	−0.527900	+	0.849307i	$0.677020\pi$
$228$		0			0
$229$	5.70813	+	6.80268i	0.377204	+	0.449534i	0.920930	−	0.389729i	$-0.127431\pi$
$229$	5.70813	+	6.80268i	0.377204	+	0.449534i	−0.543726	+	0.839263i	$0.682987\pi$
$230$	−9.99235	+	0.00674864i	−0.658876	+	0.000444992i
$231$		0			0
$232$	−2.15238	+	12.3530i	−0.141310	+	0.811017i
$233$	−9.39731	−	16.2766i	−0.615638	−	1.06632i	−0.990272	−	0.139144i	$-0.955565\pi$
$233$	−9.39731	−	16.2766i	−0.615638	−	1.06632i	0.374634	−	0.927173i	$-0.377768\pi$
$234$		0			0
$235$	0.805681	+	0.465160i	0.0525568	+	0.0303437i
$236$	−0.0304476	−	22.5411i	−0.00198197	−	1.46730i
$237$		0			0
$238$	1.89894	−	1.09806i	0.123090	−	0.0711768i
$239$	−3.56653	−	20.2268i	−0.230700	−	1.30836i	−0.851483	−	0.524382i	$-0.824297\pi$
$239$	−3.56653	−	20.2268i	−0.230700	−	1.30836i	0.620784	−	0.783982i	$-0.286815\pi$
$240$		0			0
$241$	−10.5529	−	8.85497i	−0.679775	−	0.570399i	0.236166	−	0.971713i	$-0.424109\pi$
$241$	−10.5529	−	8.85497i	−0.679775	−	0.570399i	−0.915941	+	0.401314i	$0.868554\pi$
$242$	6.28298	−	7.49804i	0.403885	−	0.481992i
$243$		0			0
$244$	−10.8289	+	1.92451i	−0.693250	+	0.123204i
$245$	−3.04051	+	3.62354i	−0.194251	+	0.231499i
$246$		0			0
$247$	−3.65657	−	20.7374i	−0.232662	−	1.31949i
$248$	4.29426	+	5.09669i	0.272686	+	0.323640i
$249$		0			0
$250$	10.0482	−	8.44298i	0.635502	−	0.533981i
$251$	0.419101	+	0.241968i	0.0264534	+	0.0152729i	0.513168	−	0.858288i	$-0.328472\pi$
$251$	0.419101	+	0.241968i	0.0264534	+	0.0152729i	−0.486715	+	0.873561i	$0.661805\pi$
$252$		0			0
$253$	−24.8865	+	14.3682i	−1.56460	+	0.903323i
$254$	−1.76713	+	4.86538i	−0.110880	+	0.305281i
$255$		0			0
$256$	2.69320	−	15.7717i	0.168325	−	0.985732i
$257$	−13.5896	+	11.4030i	−0.847695	+	0.711300i	−0.959281	−	0.282454i	$-0.908851\pi$
$257$	−13.5896	+	11.4030i	−0.847695	+	0.711300i	0.111586	+	0.993755i	$0.464407\pi$
$258$		0			0
$259$	−1.97497	−	5.42619i	−0.122719	−	0.337167i
$260$	10.7525	−	9.04720i	0.666842	−	0.561084i
$261$		0			0
$262$	13.0334	−	4.75373i	0.805204	−	0.293686i
$263$	−1.39832	+	7.93029i	−0.0862243	+	0.489002i	0.910861	+	0.412712i	$0.135419\pi$
$263$	−1.39832	+	7.93029i	−0.0862243	+	0.489002i	−0.997086	+	0.0762899i	$0.975693\pi$
$264$		0			0
$265$	−4.89249	−	1.78072i	−0.300543	−	0.109389i
$266$	3.45185	−	5.98812i	0.211647	−	0.367155i
$267$		0			0
$268$	−1.26013	−	0.725268i	−0.0769747	−	0.0443028i
$269$			6.56538i			0.400298i	0.979765	+	0.200149i	$0.0641426\pi$
$269$			6.56538i			0.400298i	−0.979765	+	0.200149i	$0.935857\pi$
$270$		0			0
$271$	10.8623			0.659839			0.329919	−	0.944009i	$-0.392978\pi$
$271$	10.8623			0.659839			0.329919	+	0.944009i	$0.392978\pi$
$272$	3.72452	+	1.34423i	0.225832	+	0.0815059i
$273$		0			0
$274$	−27.0670	−	15.6028i	−1.63518	−	0.942597i
$275$	5.67046	−	15.5795i	0.341941	−	0.939476i
$276$		0			0
$277$	31.2235	+	5.50555i	1.87604	+	0.330796i	0.990907	−	0.134546i	$-0.0429575\pi$
$277$	31.2235	+	5.50555i	1.87604	+	0.330796i	0.885131	+	0.465342i	$0.154069\pi$
$278$	6.32521	−	2.30703i	0.379361	−	0.138366i
$279$		0			0
$280$	4.61248	−	0.00934555i	0.275649	−	0.000558503i
$281$	18.4488	−	6.71481i	1.10056	−	0.400572i	0.273039	−	0.962003i	$-0.411971\pi$
$281$	18.4488	−	6.71481i	1.10056	−	0.400572i	0.827523	+	0.561431i	$0.189749\pi$
$282$		0			0
$283$	12.6768	+	15.1076i	0.753556	+	0.898053i	0.997422	−	0.0717558i	$-0.0228602\pi$
$283$	12.6768	+	15.1076i	0.753556	+	0.898053i	−0.243866	+	0.969809i	$0.578416\pi$
$284$	7.73270	+	6.47073i	0.458851	+	0.383967i
$285$		0			0
$286$	13.7962	−	37.9845i	0.815785	−	2.24607i
$287$	2.49735	+	4.32554i	0.147414	+	0.255329i
$288$		0			0
$289$	8.01003	−	13.8738i	0.471178	−	0.816105i
$290$	−4.19769	−	4.99576i	−0.246497	−	0.293361i
$291$		0			0
$292$	4.83741	−	27.6527i	0.283088	−	1.61825i
$293$	−26.1866	+	4.61741i	−1.52984	+	0.269752i	−0.874292	−	0.485401i	$-0.838674\pi$
$293$	−26.1866	+	4.61741i	−1.52984	+	0.269752i	−0.655549	+	0.755153i	$0.727563\pi$
$294$		0			0
$295$	8.98574	+	7.53993i	0.523170	+	0.438992i
$296$	5.19351	−	9.03767i	0.301867	−	0.525304i
$297$		0			0
$298$	−24.9438	−	20.9017i	−1.44496	−	1.21080i
$299$	−29.4597	+	35.1087i	−1.70370	+	2.03039i
$300$		0			0
$301$	16.7421	−	2.95209i	0.965001	−	0.170156i
$302$	−24.3342	+	14.0713i	−1.40028	+	0.809712i
$303$		0			0
$304$	12.2813	−	2.19975i	0.704380	−	0.126164i
$305$	2.86175	−	4.95671i	0.163864	−	0.283820i
$306$		0			0
$307$	20.0407	−	11.5705i	1.14379	−	0.660365i	0.196420	−	0.980520i	$-0.437068\pi$
$307$	20.0407	−	11.5705i	1.14379	−	0.660365i	0.947365	+	0.320155i	$0.103735\pi$
$308$	11.4787	−	6.64791i	0.654059	−	0.378800i
$309$		0			0
$310$	−3.46816	+	0.00234233i	−0.196978	+	0.000133035i
$311$	18.6806	−	15.6749i	1.05928	−	0.888842i	0.0652424	−	0.997869i	$-0.479218\pi$
$311$	18.6806	−	15.6749i	1.05928	−	0.888842i	0.994039	+	0.109027i	$0.0347735\pi$
$312$		0			0
$313$	24.2156	−	8.81377i	1.36875	−	0.498184i	0.450000	−	0.893028i	$-0.351424\pi$
$313$	24.2156	−	8.81377i	1.36875	−	0.498184i	0.918748	+	0.394845i	$0.129202\pi$
$314$	1.19637	−	6.81188i	0.0675153	−	0.384417i
$315$		0			0
$316$	−16.6424	−	6.03189i	−0.936208	−	0.339320i
$317$	18.1371	+	3.19806i	1.01868	+	0.179621i	0.657960	−	0.753053i	$-0.271420\pi$
$317$	18.1371	+	3.19806i	1.01868	+	0.179621i	0.360721	+	0.932674i	$0.382531\pi$
$318$		0			0
$319$	−17.6337	−	6.41816i	−0.987300	−	0.359348i
$320$	5.37776	+	6.35648i	0.300626	+	0.355338i
$321$		0			0
$322$	−14.8131	+	2.62227i	−0.825504	+	0.146134i
$323$			3.08773i			0.171806i
$324$		0			0
$325$		−	26.4420i		−	1.46674i
$326$	−1.03064	−	5.82204i	−0.0570817	−	0.322453i
$327$		0			0
$328$	−3.06652	+	8.47862i	−0.169320	+	0.468153i
$329$	1.31613	+	0.479031i	0.0725605	+	0.0264099i
$330$		0			0
$331$	−15.2370	−	2.68670i	−0.837502	−	0.147674i	−0.261583	−	0.965181i	$-0.584245\pi$
$331$	−15.2370	−	2.68670i	−0.837502	−	0.147674i	−0.575919	+	0.817507i	$0.695356\pi$
$332$	4.27508	−	11.7952i	0.234626	−	0.647348i
$333$		0			0
$334$	8.49017	+	1.49113i	0.464561	+	0.0815912i
$335$	0.710980	−	0.258776i	0.0388450	−	0.0141384i
$336$		0			0
$337$	9.32566	−	7.82516i	0.508001	−	0.426264i	−0.352424	−	0.935840i	$-0.614643\pi$
$337$	9.32566	−	7.82516i	0.508001	−	0.426264i	0.860425	+	0.509577i	$0.170198\pi$
$338$	−0.0311134	−	46.0680i	−0.00169235	−	2.50577i
$339$		0			0
$340$	−1.78310	+	1.03269i	−0.0967022	+	0.0560053i
$341$	−8.63764	+	4.98695i	−0.467755	+	0.270058i
$342$		0			0
$343$	−9.04472	+	15.6659i	−0.488369	+	0.845880i
$344$	23.5483	+	19.6782i	1.26964	+	1.06098i
$345$		0			0
$346$	−0.938945	−	1.62377i	−0.0504780	−	0.0872942i
$347$	−23.2143	+	4.09332i	−1.24621	+	0.219741i	−0.757576	−	0.652747i	$-0.773616\pi$
$347$	−23.2143	+	4.09332i	−1.24621	+	0.219741i	−0.488636	+	0.872488i	$0.662505\pi$
$348$		0			0
$349$	−14.7087	+	17.5291i	−0.787338	+	0.938312i	−0.999240	−	0.0389784i	$-0.987590\pi$
$349$	−14.7087	+	17.5291i	−0.787338	+	0.938312i	0.211902	+	0.977291i	$0.432034\pi$
$350$	5.57441	−	6.65244i	0.297965	−	0.355588i
$351$		0			0
$352$	22.5282	+	8.11356i	1.20076	+	0.432454i
$353$	−0.541929	−	0.454733i	−0.0288440	−	0.0242030i	0.628252	−	0.778010i	$-0.283771\pi$
$353$	−0.541929	−	0.454733i	−0.0288440	−	0.0242030i	−0.657096	+	0.753807i	$0.728215\pi$
$354$		0			0
$355$	−5.16729	+	0.911132i	−0.274251	+	0.0483579i
$356$	−2.77279	+	15.8505i	−0.146958	+	0.840073i
$357$		0			0
$358$	−12.1101	+	10.1755i	−0.640037	+	0.537792i
$359$	5.07907	−	8.79721i	0.268063	−	0.464299i	−0.700298	−	0.713850i	$-0.746950\pi$
$359$	5.07907	−	8.79721i	0.268063	−	0.464299i	0.968362	+	0.249551i	$0.0802831\pi$
$360$		0			0
$361$	−4.63535	−	8.02867i	−0.243966	−	0.422561i
$362$	−4.92789	−	1.78984i	−0.259004	−	0.0940717i
$363$		0			0
$364$	13.5767	−	16.2246i	0.711615	−	0.850400i
$365$	9.39023	+	11.1908i	0.491507	+	0.585755i
$366$		0			0
$367$	−1.79478	+	0.653245i	−0.0936866	+	0.0340991i	−0.388438	−	0.921475i	$-0.626985\pi$
$367$	−1.79478	+	0.653245i	−0.0936866	+	0.0340991i	0.294752	+	0.955574i	$0.404763\pi$
$368$	−20.8494	−	17.3989i	−1.08685	−	0.906983i
$369$		0			0
$370$	1.85867	+	5.09593i	0.0966274	+	0.264925i
$371$	−7.71925	−	1.36111i	−0.400763	−	0.0706654i
$372$		0			0
$373$	11.8307	−	32.5046i	0.612571	−	1.68303i	−0.111899	−	0.993720i	$-0.535693\pi$
$373$	11.8307	−	32.5046i	0.612571	−	1.68303i	0.724470	−	0.689306i	$-0.242084\pi$
$374$	−2.95945	+	5.13392i	−0.153030	+	0.265469i
$375$		0			0
$376$	0.869528	+	2.37403i	0.0448425	+	0.122431i
$377$	−29.9286			−1.54140
$378$		0			0
$379$			27.1937i			1.39685i	0.715685	+	0.698423i	$0.246114\pi$
$379$			27.1937i			1.39685i	−0.715685	+	0.698423i	$0.753886\pi$
$380$	−3.23876	+	5.62723i	−0.166145	+	0.288671i
$381$		0			0
$382$	22.1209	+	12.7516i	1.13180	+	0.652429i
$383$	5.67775	+	2.06653i	0.290120	+	0.105595i	0.482980	−	0.875631i	$-0.339554\pi$
$383$	5.67775	+	2.06653i	0.290120	+	0.105595i	−0.192861	+	0.981226i	$0.561777\pi$
$384$		0			0
$385$	−1.19866	+	6.79794i	−0.0610894	+	0.346455i
$386$	−2.15062	−	5.89639i	−0.109464	−	0.300118i
$387$		0			0
$388$	−16.5079	+	13.8898i	−0.838062	+	0.705148i
$389$	−3.99747	−	10.9830i	−0.202680	−	0.556858i	0.796156	−	0.605091i	$-0.206863\pi$
$389$	−3.99747	−	10.9830i	−0.202680	−	0.556858i	−0.998836	+	0.0482330i	$0.984641\pi$
$390$		0			0
$391$	5.14814	−	4.31980i	0.260353	−	0.218462i
$392$	−12.6551	+	2.25788i	−0.639177	+	0.114040i
$393$		0			0
$394$	21.7217	+	7.88943i	1.09432	+	0.397464i
$395$	7.97761	−	4.60588i	0.401397	−	0.231747i
$396$		0			0
$397$	−2.31327	−	1.33556i	−0.116099	−	0.0670301i	0.440826	−	0.897593i	$-0.354686\pi$
$397$	−2.31327	−	1.33556i	−0.116099	−	0.0670301i	−0.556925	+	0.830563i	$0.688019\pi$
$398$	0.834849	+	0.993571i	0.0418472	+	0.0498032i
$399$		0			0
$400$	15.6671	−	0.0423251i	0.783356	−	0.00211626i
$401$	2.15776	+	12.2372i	0.107753	+	0.611099i	0.990085	+	0.140470i	$0.0448615\pi$
$401$	2.15776	+	12.2372i	0.107753	+	0.611099i	−0.882332	+	0.470628i	$0.844027\pi$
$402$		0			0
$403$	−10.2249	+	12.1856i	−0.509339	+	0.607007i
$404$	−13.0101	+	2.31215i	−0.647275	+	0.115034i
$405$		0			0
$406$	−7.52962	−	6.30944i	−0.373689	−	0.313132i
$407$	11.9499	+	10.0271i	0.592334	+	0.497027i
$408$		0			0
$409$	−0.895032	−	5.07598i	−0.0442565	−	0.250991i	0.954651	−	0.297728i	$-0.0962288\pi$
$409$	−0.895032	−	5.07598i	−0.0442565	−	0.250991i	−0.998907	+	0.0467370i	$0.985118\pi$
$410$	−2.34868	−	4.06169i	−0.115993	−	0.200592i
$411$		0			0
$412$	−31.7796	+	0.0429266i	−1.56567	+	0.00211484i
$413$	15.2936	+	8.82978i	0.752550	+	0.434485i
$414$		0			0
$415$	3.26440	+	5.65411i	0.160243	+	0.277549i
$416$	38.1888	−	0.128960i	1.87236	−	0.00632279i
$417$		0			0
$418$	0.0126107	+	18.6720i	0.000616810	+	0.913278i
$419$	−1.84481	−	2.19856i	−0.0901248	−	0.107407i	0.719097	−	0.694909i	$-0.244556\pi$
$419$	−1.84481	−	2.19856i	−0.0901248	−	0.107407i	−0.809222	+	0.587503i	$0.800111\pi$
$420$		0			0
$421$	4.61049	+	12.6672i	0.224701	+	0.617362i	0.999897	−	0.0143594i	$-0.00457089\pi$
$421$	4.61049	+	12.6672i	0.224701	+	0.617362i	−0.775195	+	0.631721i	$0.782349\pi$
$422$	1.50016	−	8.54154i	0.0730264	−	0.415795i
$423$		0			0
$424$	−7.09944	−	12.2392i	−0.344779	−	0.594390i
$425$	−0.673287	+	3.81840i	−0.0326592	+	0.185220i
$426$		0			0
$427$	2.94709	−	8.09707i	0.142620	−	0.391845i
$428$	−2.64685	−	7.24170i	−0.127940	−	0.350041i
$429$		0			0
$430$	−15.7251	+	2.78372i	−0.758334	+	0.134243i
$431$	−25.2153			−1.21458			−0.607290	−	0.794480i	$-0.707743\pi$
$431$	−25.2153			−1.21458			−0.607290	+	0.794480i	$0.707743\pi$
$432$		0			0
$433$	−15.5658			−0.748046			−0.374023	−	0.927419i	$-0.622022\pi$
$433$	−15.5658			−0.748046			−0.374023	+	0.927419i	$0.622022\pi$
$434$	−5.14137	+	0.910143i	−0.246794	+	0.0436883i
$435$		0			0
$436$	2.28495	+	6.25156i	0.109429	+	0.299396i
$437$	7.24252	−	19.8987i	0.346457	−	0.951882i
$438$		0			0
$439$	5.53290	−	31.3787i	0.264071	−	1.49762i	−0.507596	−	0.861595i	$-0.669466\pi$
$439$	5.53290	−	31.3787i	0.264071	−	1.49762i	0.771667	−	0.636026i	$-0.219423\pi$
$440$	−10.7785	+	6.25211i	−0.513844	+	0.298058i
$441$		0			0
$442$	−1.63486	+	9.30851i	−0.0777624	+	0.442761i
$443$	−2.16330	−	5.94362i	−0.102782	−	0.282390i	0.877634	−	0.479332i	$-0.159121\pi$
$443$	−2.16330	−	5.94362i	−0.102782	−	0.282390i	−0.980415	+	0.196942i	$0.936899\pi$
$444$		0			0
$445$	−5.38246	−	6.41456i	−0.255153	−	0.304079i
$446$	−0.0204793	−	30.3227i	−0.000969725	−	1.43582i
$447$		0			0
$448$	9.63496	+	8.01838i	0.455209	+	0.378833i
$449$	4.18149	+	7.24256i	0.197337	+	0.341797i	0.947664	−	0.319269i	$-0.103437\pi$
$449$	4.18149	+	7.24256i	0.197337	+	0.341797i	−0.750327	+	0.661067i	$0.770104\pi$
$450$		0			0
$451$	−11.6853	−	6.74653i	−0.550241	−	0.317682i
$452$	−16.7120	+	0.0225739i	−0.786067	+	0.00106179i
$453$		0			0
$454$	−13.1734	−	22.7814i	−0.618257	−	1.06918i
$455$	1.91172	+	10.8419i	0.0896228	+	0.508276i
$456$		0			0
$457$	−21.5741	−	18.1028i	−1.00919	−	0.846812i	−0.0209605	−	0.999780i	$-0.506672\pi$
$457$	−21.5741	−	18.1028i	−1.00919	−	0.846812i	−0.988231	+	0.152968i	$0.951117\pi$
$458$	−9.62589	−	8.06601i	−0.449788	−	0.376900i
$459$		0			0
$460$	13.9133	−	2.47267i	0.648712	−	0.115289i
$461$	16.8013	−	20.0230i	0.782513	−	0.932563i	−0.216531	−	0.976276i	$-0.569474\pi$
$461$	16.8013	−	20.0230i	0.782513	−	0.932563i	0.999044	+	0.0437126i	$0.0139186\pi$
$462$		0			0
$463$	3.84612	+	21.8124i	0.178744	+	1.01371i	0.933733	+	0.357971i	$0.116531\pi$
$463$	3.84612	+	21.8124i	0.178744	+	1.01371i	−0.754988	+	0.655738i	$0.772358\pi$
$464$	−0.0479061	−	17.7330i	−0.00222399	−	0.823233i
$465$		0			0
$466$	17.0988	+	20.3496i	0.792086	+	0.942678i
$467$	19.1663	+	11.0657i	0.886910	+	0.512058i	0.872930	−	0.487845i	$-0.162217\pi$
$467$	19.1663	+	11.0657i	0.886910	+	0.512058i	0.0139792	+	0.999902i	$0.495550\pi$
$468$		0			0
$469$	0.986466	−	0.569536i	0.0455508	−	0.0262987i
$470$	−1.23663	−	0.449151i	−0.0570415	−	0.0207178i
$471$		0			0
$472$	5.59913	+	31.3823i	0.257721	+	1.44449i
$473$	−35.1815	+	29.5208i	−1.61765	+	1.35737i
$474$		0			0
$475$	4.17853	+	11.4804i	0.191724	+	0.526757i
$476$	−2.37370	+	1.99724i	−0.108798	+	0.0915433i
$477$		0			0
$478$	9.95285	+	27.2879i	0.455233	+	1.24812i
$479$	2.06488	−	11.7105i	0.0943470	−	0.535068i	−0.900599	−	0.434652i	$-0.856871\pi$
$479$	2.06488	−	11.7105i	0.0943470	−	0.535068i	0.994946	−	0.100416i	$-0.0320175\pi$
$480$		0			0
$481$	23.3788	+	8.50920i	1.06598	+	0.387986i
$482$	16.8785	+	9.72963i	0.768796	+	0.443172i
$483$		0			0
$484$	−6.90105	+	11.9903i	−0.313684	+	0.545016i
$485$		−	11.2268i		−	0.509783i
$486$		0			0
$487$	22.1183			1.00228			0.501138	−	0.865367i	$-0.332915\pi$
$487$	22.1183			1.00228			0.501138	+	0.865367i	$0.332915\pi$
$488$	14.6055	−	5.34951i	0.661160	−	0.242161i
$489$		0			0
$490$	3.34084	−	5.79554i	0.150924	−	0.261816i
$491$	−2.55319	+	7.01484i	−0.115224	+	0.316575i	−0.983877	−	0.178845i	$-0.942764\pi$
$491$	−2.55319	+	7.01484i	−0.115224	+	0.316575i	0.868653	+	0.495421i	$0.164986\pi$
$492$		0			0
$493$	4.32189	+	0.762066i	0.194648	+	0.0343217i
$494$	10.2041	+	27.9768i	0.459105	+	1.25874i
$495$		0			0
$496$	−7.23644	−	6.03885i	−0.324926	−	0.271153i
$497$	−7.42295	+	2.70173i	−0.332965	+	0.121189i
$498$		0			0
$499$	−6.65452	−	7.93054i	−0.297897	−	0.355020i	0.596246	−	0.802802i	$-0.296658\pi$
$499$	−6.65452	−	7.93054i	−0.297897	−	0.355020i	−0.894143	+	0.447782i	$0.852214\pi$
$500$	−11.9114	+	14.2344i	−0.532692	+	0.636582i
$501$		0			0
$502$	−0.643273	−	0.233640i	−0.0287107	−	0.0104279i
$503$	16.9435	+	29.3471i	0.755475	+	1.30852i	0.945138	+	0.326672i	$0.105927\pi$
$503$	16.9435	+	29.3471i	0.755475	+	1.30852i	−0.189663	+	0.981849i	$0.560739\pi$
$504$		0			0
$505$	3.43817	−	5.95508i	0.152997	−	0.264998i
$506$	31.1140	−	26.1436i	1.38319	−	1.16222i
$507$		0			0
$508$	1.26145	−	7.21098i	0.0559678	−	0.319935i
$509$	−16.7517	+	2.95378i	−0.742508	+	0.130924i	−0.532090	−	0.846688i	$-0.678593\pi$
$509$	−16.7517	+	2.95378i	−0.742508	+	0.130924i	−0.210417	+	0.977612i	$0.567482\pi$
$510$		0			0
$511$	16.8478	+	14.1370i	0.745301	+	0.625382i
$512$	0.137538	+	22.6270i	0.00607838	+	0.999982i
$513$		0			0
$514$	16.1133	−	19.2295i	0.710728	−	0.848175i
$515$	10.6302	−	12.6686i	0.468423	−	0.558245i
$516$		0			0
$517$	−3.72618	+	0.657026i	−0.163877	+	0.0288960i
$518$	4.08791	+	7.06945i	0.179613	+	0.310614i
$519$		0			0
$520$	−12.7433	+	15.2495i	−0.558829	+	0.668733i
$521$	14.6553	−	25.3837i	0.642060	−	1.11208i	−0.342912	−	0.939368i	$-0.611413\pi$
$521$	14.6553	−	25.3837i	0.642060	−	1.11208i	0.984972	−	0.172714i	$-0.0552535\pi$
$522$		0			0
$523$	−3.33680	+	1.92651i	−0.145908	+	0.0842402i	−0.571177	−	0.820827i	$-0.693513\pi$
$523$	−3.33680	+	1.92651i	−0.145908	+	0.0842402i	0.425269	+	0.905067i	$0.360180\pi$
$524$	−16.9779	+	9.83280i	−0.741683	+	0.429548i
$525$		0			0
$526$	−0.00769131	−	11.3881i	−0.000335357	−	0.496546i
$527$	1.78683	−	1.49932i	0.0778353	−	0.0653116i
$528$		0			0
$529$	−21.6963	+	7.89682i	−0.943319	+	0.343340i
$530$	7.25207	+	1.27369i	0.315010	+	0.0553254i
$531$		0			0
$532$	−3.33075	+	9.18977i	−0.144406	+	0.398427i
$533$	−21.1929	−	3.73687i	−0.917965	−	0.161862i
$534$		0			0
$535$	3.77033	+	1.37229i	0.163006	+	0.0593292i
$536$	1.93360	+	0.699339i	0.0835188	+	0.0302068i
$537$		0			0
$538$	−1.61847	−	9.14269i	−0.0697773	−	0.394170i
$539$		−	19.2380i		−	0.828638i
$540$		0			0
$541$		−	4.51542i		−	0.194133i	−0.995278	−	0.0970665i	$-0.969054\pi$
$541$		−	4.51542i		−	0.194133i	0.995278	−	0.0970665i	$-0.0309460\pi$
$542$	−15.1265	+	2.67774i	−0.649737	+	0.115019i
$543$		0			0
$544$	−5.51800	−	0.953770i	−0.236582	−	0.0408926i
$545$	−3.25483	−	1.18466i	−0.139421	−	0.0507453i
$546$		0			0
$547$	−12.3037	−	2.16948i	−0.526069	−	0.0927602i	−0.0956949	−	0.995411i	$-0.530507\pi$
$547$	−12.3037	−	2.16948i	−0.526069	−	0.0927602i	−0.430374	+	0.902651i	$0.641618\pi$
$548$	41.5388	+	15.0554i	1.77445	+	0.643134i
$549$		0			0
$550$	−4.05588	+	23.0932i	−0.172943	+	0.984698i
$551$	12.9942	−	4.72950i	0.553572	−	0.201484i
$552$		0			0
$553$	10.6237	−	8.91435i	0.451766	−	0.379077i
$554$	−44.8379	+	0.0302826i	−1.90498	+	0.00128658i
$555$		0			0
$556$	−8.23953	+	4.77195i	−0.349434	+	0.202376i
$557$	3.03004	−	1.74940i	0.128387	−	0.0741243i	−0.434431	−	0.900705i	$-0.643051\pi$
$557$	3.03004	−	1.74940i	0.128387	−	0.0741243i	0.562818	+	0.826581i	$0.309717\pi$
$558$		0			0
$559$	−36.6233	+	63.4335i	−1.54900	+	2.68295i
$560$	−6.42086	+	1.15007i	−0.271331	+	0.0485991i
$561$		0			0
$562$	−24.0358	+	13.8987i	−1.01389	+	0.586282i
$563$	−26.9436	+	4.75088i	−1.13554	+	0.200226i	−0.709653	−	0.704552i	$-0.751148\pi$
$563$	−26.9436	+	4.75088i	−1.13554	+	0.200226i	−0.425885	+	0.904777i	$0.640037\pi$
$564$		0			0
$565$	5.59013	−	6.66206i	0.235179	−	0.280275i
$566$	−21.3775	−	17.9132i	−0.898562	−	0.752949i
$567$		0			0
$568$	−12.3634	−	7.10466i	−0.518757	−	0.298105i
$569$	−3.15771	−	2.64963i	−0.132378	−	0.111078i	0.574195	−	0.818719i	$-0.305315\pi$
$569$	−3.15771	−	2.64963i	−0.132378	−	0.111078i	−0.706573	+	0.707640i	$0.749760\pi$
$570$		0			0
$571$	2.91629	−	0.514220i	0.122043	−	0.0215194i	−0.112293	−	0.993675i	$-0.535820\pi$
$571$	2.91629	−	0.514220i	0.122043	−	0.0215194i	0.234336	+	0.972156i	$0.424708\pi$
$572$	−9.84825	+	56.2967i	−0.411776	+	2.35389i
$573$		0			0
$574$	−4.54404	−	5.40795i	−0.189664	−	0.225724i
$575$	13.2953	−	23.0281i	0.554453	−	0.960340i
$576$		0			0
$577$	−4.23106	−	7.32841i	−0.176141	−	0.305086i	0.764414	−	0.644725i	$-0.223028\pi$
$577$	−4.23106	−	7.32841i	−0.176141	−	0.305086i	−0.940556	+	0.339640i	$0.889695\pi$
$578$	−7.73436	+	21.2947i	−0.321707	+	0.885743i
$579$		0			0
$580$	7.07708	+	5.92210i	0.293860	+	0.245902i
$581$	6.31802	+	7.52952i	0.262115	+	0.312377i
$582$		0			0
$583$	19.8980	−	7.24228i	0.824092	−	0.299945i
$584$	0.0804391	+	39.7006i	0.00332859	+	1.64282i
$585$		0			0
$586$	35.3283	−	12.8855i	1.45940	−	0.532294i
$587$	45.4714	+	8.01784i	1.87681	+	0.330932i	0.991079	−	0.133275i	$-0.0425493\pi$
$587$	45.4714	+	8.01784i	1.87681	+	0.330932i	0.885727	+	0.464206i	$0.153660\pi$
$588$		0			0
$589$	2.51375	−	6.90646i	0.103577	−	0.284576i
$590$	−14.3719	−	8.28470i	−0.591683	−	0.341076i
$591$		0			0
$592$	−5.00436	+	13.8658i	−0.205678	+	0.569881i
$593$	−22.0816			−0.906784			−0.453392	−	0.891311i	$-0.649786\pi$
$593$	−22.0816			−0.906784			−0.453392	+	0.891311i	$0.649786\pi$
$594$		0			0
$595$		−	1.61432i		−	0.0661807i
$596$	39.8884	+	22.9578i	1.63389	+	0.940389i
$597$		0			0
$598$	32.3696	−	56.1533i	1.32369	−	2.29628i
$599$	23.2555	+	8.46431i	0.950194	+	0.345842i	0.770184	−	0.637822i	$-0.220165\pi$
$599$	23.2555	+	8.46431i	0.950194	+	0.345842i	0.180010	+	0.983665i	$0.442387\pi$
$600$		0			0
$601$	2.55983	−	14.5175i	0.104418	−	0.592182i	−0.887034	−	0.461705i	$-0.847238\pi$
$601$	2.55983	−	14.5175i	0.104418	−	0.592182i	0.991451	−	0.130477i	$-0.0416509\pi$
$602$	−22.5867	+	8.23818i	−0.920567	+	0.335763i
$603$		0			0
$604$	30.4181	−	25.5939i	1.23770	−	1.04140i
$605$	−2.46229	−	6.76510i	−0.100107	−	0.275040i
$606$		0			0
$607$	−23.2768	+	19.5315i	−0.944775	+	0.792761i	−0.978410	−	0.206674i	$-0.933736\pi$
$607$	−23.2768	+	19.5315i	−0.944775	+	0.792761i	0.0336346	+	0.999434i	$0.489292\pi$
$608$	−16.5602	+	6.09082i	−0.671604	+	0.247015i
$609$		0			0
$610$	−2.76326	+	7.60799i	−0.111881	+	0.308038i
$611$	−5.22602	+	3.01724i	−0.211422	+	0.122065i
$612$		0			0
$613$	8.97166	+	5.17979i	0.362362	+	0.209210i	0.670116	−	0.742256i	$-0.266244\pi$
$613$	8.97166	+	5.17979i	0.362362	+	0.209210i	−0.307754	+	0.951466i	$0.599578\pi$
$614$	−25.0556	+	21.0530i	−1.01116	+	0.849631i
$615$		0			0
$616$	−14.3460	+	12.0873i	−0.578015	+	0.487012i
$617$	−2.09885	−	11.9032i	−0.0844965	−	0.479204i	−0.997464	−	0.0711715i	$-0.977326\pi$
$617$	−2.09885	−	11.9032i	−0.0844965	−	0.479204i	0.912968	−	0.408032i	$-0.133785\pi$
$618$		0			0
$619$	−1.25371	+	1.49411i	−0.0503908	+	0.0600535i	−0.790651	−	0.612267i	$-0.790258\pi$
$619$	−1.25371	+	1.49411i	−0.0503908	+	0.0600535i	0.740260	+	0.672320i	$0.234702\pi$
$620$	4.82905	−	0.858220i	0.193939	−	0.0344669i
$621$		0			0
$622$	−22.1498	+	26.4334i	−0.888127	+	1.05988i
$623$	−9.65710	−	8.10327i	−0.386904	−	0.324651i
$624$		0			0
$625$	1.72350	+	9.77447i	0.0689401	+	0.390979i
$626$	−31.5490	+	18.2433i	−1.26095	+	0.729147i
$627$		0			0
$628$	0.0132116	+	9.78089i	0.000527202	+	0.390300i
$629$	−3.15939	−	1.82408i	−0.125973	−	0.0727307i
$630$		0			0
$631$	−6.64702	−	11.5130i	−0.264614	−	0.458325i	0.702849	−	0.711340i	$-0.251911\pi$
$631$	−6.64702	−	11.5130i	−0.264614	−	0.458325i	−0.967462	+	0.253015i	$0.918578\pi$
$632$	24.6625	+	4.29716i	0.981023	+	0.170932i
$633$		0			0
$634$	−26.0454	+	0.0175906i	−1.03440	+	0.000698610i
$635$	2.44868	+	2.91823i	0.0971730	+	0.115806i
$636$		0			0
$637$	−10.4939	−	28.8319i	−0.415785	−	1.14236i
$638$	26.1383	+	4.59068i	1.03482	+	0.181747i
$639$		0			0
$640$	−9.05584	−	7.52609i	−0.357964	−	0.297495i
$641$	−4.99251	+	28.3139i	−0.197192	+	1.11833i	0.712069	+	0.702109i	$0.247758\pi$
$641$	−4.99251	+	28.3139i	−0.197192	+	1.11833i	−0.909262	+	0.416225i	$0.863353\pi$
$642$		0			0
$643$	−12.8078	+	35.1891i	−0.505090	+	1.38772i	0.381157	+	0.924510i	$0.375526\pi$
$643$	−12.8078	+	35.1891i	−0.505090	+	1.38772i	−0.886247	+	0.463213i	$0.846697\pi$
$644$	19.9818	−	7.30336i	0.787393	−	0.287793i
$645$		0			0
$646$	−0.761176	−	4.29986i	−0.0299481	−	0.169176i
$647$	23.8383			0.937182			0.468591	−	0.883415i	$-0.344762\pi$
$647$	23.8383			0.937182			0.468591	+	0.883415i	$0.344762\pi$
$648$		0			0
$649$	−47.7068			−1.87266
$650$	6.51838	+	36.8221i	0.255672	+	1.44428i
$651$		0			0
$652$	2.87045	+	7.85348i	0.112416	+	0.307566i
$653$	16.8138	−	46.1955i	0.657974	−	1.80777i	0.0720526	−	0.997401i	$-0.477045\pi$
$653$	16.8138	−	46.1955i	0.657974	−	1.80777i	0.585921	−	0.810368i	$-0.300733\pi$
$654$		0			0
$655$	1.77292	−	10.0547i	0.0692736	−	0.392870i
$656$	2.18021	−	12.5630i	0.0851229	−	0.490501i
$657$		0			0
$658$	−1.95088	−	0.342634i	−0.0760532	−	0.0133573i
$659$	9.01137	+	24.7585i	0.351033	+	0.964456i	0.982039	+	0.188678i	$0.0604202\pi$
$659$	9.01137	+	24.7585i	0.351033	+	0.964456i	−0.631006	+	0.775778i	$0.717358\pi$
$660$		0			0
$661$	0.937603	+	1.11739i	0.0364685	+	0.0434615i	0.783970	−	0.620798i	$-0.213191\pi$
$661$	0.937603	+	1.11739i	0.0364685	+	0.0434615i	−0.747502	+	0.664260i	$0.768747\pi$
$662$	21.8808	−	0.0147779i	0.850422	−	0.000574358i
$663$		0			0
$664$	−3.04560	+	17.4795i	−0.118192	+	0.678336i
$665$	−2.54332	−	4.40516i	−0.0986258	−	0.170825i
$666$		0			0
$667$	−26.0646	−	15.0484i	−1.00923	−	0.582677i
$668$	−12.1907	+	0.0164667i	−0.471672	+	0.000637115i
$669$		0			0
$670$	−0.926292	+	0.535629i	−0.0357858	+	0.0206932i
$671$	4.04215	+	22.9242i	0.156046	+	0.884979i
$672$		0			0
$673$	14.2562	+	11.9623i	0.549534	+	0.461114i	0.874783	−	0.484514i	$-0.161004\pi$
$673$	14.2562	+	11.9623i	0.549534	+	0.461114i	−0.325249	+	0.945628i	$0.605448\pi$
$674$	−11.0575	+	13.1959i	−0.425920	+	0.508289i
$675$		0			0
$676$	11.3998	+	64.1448i	0.438455	+	2.46711i
$677$	2.04257	−	2.43424i	0.0785022	−	0.0935553i	−0.725364	−	0.688366i	$-0.758328\pi$
$677$	2.04257	−	2.43424i	0.0785022	−	0.0935553i	0.803866	+	0.594810i	$0.202773\pi$
$678$		0			0
$679$	−2.93499	−	16.6451i	−0.112634	−	0.638782i
$680$	2.22850	−	1.87764i	0.0854593	−	0.0720044i
$681$		0			0
$682$	10.7991	−	9.07395i	0.413519	−	0.347460i
$683$	7.95770	+	4.59438i	0.304493	+	0.175799i	0.644459	−	0.764639i	$-0.277082\pi$
$683$	7.95770	+	4.59438i	0.304493	+	0.175799i	−0.339967	+	0.940437i	$0.610416\pi$
$684$		0			0
$685$	−19.9118	+	11.4961i	−0.760792	+	0.439243i
$686$	8.73343	−	24.0454i	0.333444	−	0.918059i
$687$		0			0
$688$	−37.6435	−	21.5981i	−1.43515	−	0.823421i
$689$	25.8705	−	21.7080i	0.985589	−	0.827008i
$690$		0			0
$691$	−6.14708	−	16.8890i	−0.233846	−	0.642487i	0.766154	−	0.642657i	$-0.222168\pi$
$691$	−6.14708	−	16.8890i	−0.233846	−	0.642487i	−1.00000		0.000170287i	$0.999946\pi$
$692$	1.70782	+	2.02973i	0.0649217	+	0.0771588i
$693$		0			0
$694$	31.3184	−	11.4229i	1.18883	−	0.433608i
$695$	0.860413	−	4.87964i	0.0326373	−	0.185095i
$696$		0			0
$697$	2.96524	+	1.07926i	0.112316	+	0.0408799i
$698$	16.1615	−	28.0363i	0.611723	−	1.06119i
$699$		0			0
$700$	−6.12277	+	10.6381i	−0.231419	+	0.402083i
$701$		−	19.1567i		−	0.723538i	−0.932268	−	0.361769i	$-0.882173\pi$
$701$		−	19.1567i		−	0.723538i	0.932268	−	0.361769i	$-0.117827\pi$
$702$		0			0
$703$	−11.4952			−0.433548
$704$	−33.3721	−	5.74506i	−1.25776	−	0.216525i
$705$		0			0
$706$	0.866769	+	0.499649i	0.0326213	+	0.0188045i
$707$	3.54070	−	9.72798i	0.133162	−	0.365858i
$708$		0			0
$709$	−9.23990	−	1.62924i	−0.347012	−	0.0611875i	−0.00257396	−	0.999997i	$-0.500819\pi$
$709$	−9.23990	−	1.62924i	−0.347012	−	0.0611875i	−0.344438	+	0.938809i	$0.611930\pi$
$710$	6.97116	−	2.54263i	0.261623	−	0.0954231i
$711$		0			0
$712$	−0.0461075	−	22.7563i	−0.00172795	−	0.852828i
$713$	−15.0318	+	5.47115i	−0.562947	+	0.204896i
$714$		0			0
$715$	−19.1171	−	22.7829i	−0.714938	−	0.852031i
$716$	14.3556	−	17.1553i	0.536494	−	0.641125i
$717$		0			0
$718$	−4.90427	+	13.5027i	−0.183026	+	0.503918i
$719$	−10.7417	−	18.6051i	−0.400596	−	0.693853i	0.593202	−	0.805054i	$-0.297864\pi$
$719$	−10.7417	−	18.6051i	−0.400596	−	0.693853i	−0.993798	+	0.111201i	$0.964530\pi$
$720$		0			0
$721$	12.4487	−	21.5618i	0.463614	−	0.803003i
$722$	8.43421	+	10.0377i	0.313889	+	0.373566i
$723$		0			0
$724$	7.30361	+	1.27765i	0.271437	+	0.0474836i
$725$	17.1004	−	3.01526i	0.635092	−	0.111984i
$726$		0			0
$727$	−22.5451	−	18.9176i	−0.836151	−	0.701614i	0.120543	−	0.992708i	$-0.461536\pi$
$727$	−22.5451	−	18.9176i	−0.836151	−	0.701614i	−0.956694	+	0.291094i	$0.905981\pi$
$728$	−14.9068	+	25.9406i	−0.552484	+	0.961424i
$729$		0			0
$730$	−15.8352	−	13.2691i	−0.586087	−	0.491111i
$731$	6.90385	−	8.22768i	0.255348	−	0.304312i
$732$		0			0
$733$	43.1488	−	7.60829i	1.59374	−	0.281019i	0.694835	−	0.719170i	$-0.255478\pi$
$733$	43.1488	−	7.60829i	1.59374	−	0.281019i	0.898901	+	0.438151i	$0.144366\pi$
$734$	2.33830	−	1.35213i	0.0863083	−	0.0499079i
$735$		0			0
$736$	33.3232	+	19.0894i	1.22831	+	0.703645i
$737$	−1.53859	+	2.66491i	−0.0566746	+	0.0981632i
$738$		0			0
$739$	21.9574	−	12.6771i	0.807716	−	0.466335i	−0.0384462	−	0.999261i	$-0.512241\pi$
$739$	21.9574	−	12.6771i	0.807716	−	0.466335i	0.846162	+	0.532926i	$0.178907\pi$
$740$	−3.84454	−	6.63821i	−0.141328	−	0.244025i
$741$		0			0
$742$	11.0851	−	0.00748664i	0.406946	−	0.000274843i
$743$	3.44991	−	2.89482i	0.126565	−	0.106201i	−0.577308	−	0.816526i	$-0.695897\pi$
$743$	3.44991	−	2.89482i	0.126565	−	0.106201i	0.703873	+	0.710326i	$0.251452\pi$
$744$		0			0
$745$	−22.5055	+	8.19135i	−0.824539	+	0.300108i
$746$	−8.46209	+	48.1812i	−0.309819	+	1.76404i
$747$		0			0
$748$	2.85562	−	7.87886i	0.104412	−	0.288080i
$749$	5.94874	+	1.04892i	0.217362	+	0.0383268i
$750$		0			0
$751$	36.9941	+	13.4647i	1.34993	+	0.491335i	0.912927	−	0.408124i	$-0.133817\pi$
$751$	36.9941	+	13.4647i	1.34993	+	0.491335i	0.437006	+	0.899459i	$0.356039\pi$
$752$	−1.79611	−	3.09163i	−0.0654974	−	0.112740i
$753$		0			0
$754$	41.6774	−	7.37788i	1.51780	−	0.268687i
$755$			20.6870i			0.752876i
$756$		0			0
$757$		−	33.7213i		−	1.22562i	−0.790229	−	0.612811i	$-0.790039\pi$
$757$		−	33.7213i		−	1.22562i	0.790229	−	0.612811i	$-0.209961\pi$
$758$	−6.70368	−	37.8689i	−0.243489	−	1.37546i
$759$		0			0
$760$	3.12297	−	8.63468i	0.113282	−	0.313213i
$761$	34.7776	+	12.6580i	1.26069	+	0.458852i	0.883999	−	0.467489i	$-0.154841\pi$
$761$	34.7776	+	12.6580i	1.26069	+	0.458852i	0.376687	+	0.926341i	$0.377063\pi$
$762$		0			0
$763$	−5.13539	−	0.905508i	−0.185914	−	0.0327816i
$764$	−33.9482	−	12.3042i	−1.22820	−	0.445152i
$765$		0			0
$766$	−8.41606	−	1.47812i	−0.304085	−	0.0534066i
$767$	−71.4980	+	26.0231i	−2.58164	+	0.939641i
$768$		0			0
$769$	−4.44297	+	3.72810i	−0.160218	+	0.134439i	−0.719372	−	0.694625i	$-0.755570\pi$
$769$	−4.44297	+	3.72810i	−0.160218	+	0.134439i	0.559154	+	0.829064i	$0.311126\pi$
$770$	−0.00659309	−	9.76205i	−0.000237599	−	0.351800i
$771$		0			0
$772$	4.44843	+	7.68093i	0.160103	+	0.276443i
$773$	36.8149	−	21.2551i	1.32414	−	0.764492i	0.339753	−	0.940515i	$-0.389656\pi$
$773$	36.8149	−	21.2551i	1.32414	−	0.764492i	0.984386	+	0.176022i	$0.0563231\pi$
$774$		0			0
$775$	4.61456	−	7.99264i	0.165760	−	0.287104i
$776$	19.5642	−	23.4119i	0.702314	−	0.840438i
$777$		0			0
$778$	8.27420	+	14.3090i	0.296644	+	0.513003i
$779$	9.79190	−	1.72658i	0.350831	−	0.0618610i
$780$		0			0
$781$	13.7170	−	16.3473i	0.490833	−	0.584951i
$782$	−6.10421	+	7.28470i	−0.218286	+	0.260500i
$783$		0			0
$784$	17.0664	−	6.26391i	0.609513	−	0.223711i
$785$	−3.89904	−	3.27169i	−0.139163	−	0.116771i
$786$		0			0
$787$	−16.8983	+	2.97963i	−0.602359	+	0.106212i	−0.466508	−	0.884517i	$-0.654488\pi$
$787$	−16.8983	+	2.97963i	−0.602359	+	0.106212i	−0.135851	+	0.990729i	$0.543377\pi$
$788$	−32.1936	−	5.63178i	−1.14685	−	0.200624i
$789$		0			0
$790$	−9.97390	+	8.38058i	−0.354855	+	0.298168i
$791$	6.54642	−	11.3387i	0.232764	−	0.403159i
$792$		0			0
$793$	18.5627	+	32.1515i	0.659179	+	1.14173i
$794$	3.55060	+	1.28960i	0.126006	+	0.0457662i
$795$		0			0
$796$	−1.40751	−	1.17781i	−0.0498879	−	0.0417462i
$797$	4.53298	+	5.40220i	0.160567	+	0.191356i	0.840329	−	0.542076i	$-0.182362\pi$
$797$	4.53298	+	5.40220i	0.160567	+	0.191356i	−0.679763	+	0.733432i	$0.737917\pi$
$798$		0			0
$799$	0.831499	−	0.302641i	0.0294163	−	0.0107067i
$800$	−21.8070	+	3.92114i	−0.770994	+	0.138633i
$801$		0			0
$802$	−6.02149	−	16.5092i	−0.212626	−	0.582960i
$803$	−58.5114	−	10.3171i	−2.06482	−	0.364084i
$804$		0			0
$805$	−3.78652	+	10.4034i	−0.133457	+	0.366670i
$806$	11.2349	−	19.4898i	0.395732	−	0.686499i
$807$		0			0
$808$	17.5473	−	6.42700i	0.617313	−	0.226101i
$809$	34.2649			1.20469			0.602345	−	0.798236i	$-0.294233\pi$
$809$	34.2649			1.20469			0.602345	+	0.798236i	$0.294233\pi$
$810$		0			0
$811$		−	5.06146i		−	0.177732i	−0.996044	−	0.0888659i	$-0.971676\pi$
$811$		−	5.06146i		−	0.177732i	0.996044	−	0.0888659i	$-0.0283243\pi$
$812$	12.0408	+	6.93012i	0.422551	+	0.243199i
$813$		0			0
$814$	−19.1128	−	11.0176i	−0.669904	−	0.386166i
$815$	−4.08885	−	1.48822i	−0.143226	−	0.0521301i
$816$		0			0
$817$	5.87673	−	33.3286i	0.205601	−	1.16602i
$818$	2.49770	+	6.84797i	0.0873300	+	0.239434i
$819$		0			0
$820$	4.27195	+	5.07717i	0.149183	+	0.177302i
$821$	−5.19050	−	14.2608i	−0.181150	−	0.497705i	0.815568	−	0.578661i	$-0.196425\pi$
$821$	−5.19050	−	14.2608i	−0.181150	−	0.497705i	−0.996718	+	0.0809566i	$0.974202\pi$
$822$		0			0
$823$	22.8496	−	19.1731i	0.796487	−	0.668332i	−0.150855	−	0.988556i	$-0.548203\pi$
$823$	22.8496	−	19.1731i	0.796487	−	0.668332i	0.947342	+	0.320224i	$0.103758\pi$
$824$	44.2445	−	7.89396i	1.54133	−	0.274999i
$825$		0			0
$826$	−23.4740	−	8.52589i	−0.816765	−	0.296654i
$827$	7.24554	−	4.18322i	0.251952	−	0.145465i	−0.368706	−	0.929546i	$-0.620199\pi$
$827$	7.24554	−	4.18322i	0.251952	−	0.145465i	0.620658	+	0.784082i	$0.286866\pi$
$828$		0			0
$829$	26.4946	+	15.2967i	0.920196	+	0.531276i	0.883698	−	0.468058i	$-0.155046\pi$
$829$	26.4946	+	15.2967i	0.920196	+	0.531276i	0.0364987	+	0.999334i	$0.488380\pi$
$830$	−5.93971	−	7.06897i	−0.206170	−	0.245368i
$831$		0			0
$832$	−53.1485	+	9.59374i	−1.84259	+	0.332603i
$833$	0.781255	+	4.43072i	0.0270689	+	0.153515i
$834$		0			0
$835$	4.07776	−	4.85968i	0.141117	−	0.168176i
$836$	−4.62051	−	25.9988i	−0.159804	−	0.899188i
$837$		0			0
$838$	3.11099	+	2.60685i	0.107467	+	0.0900522i
$839$	−5.60536	−	4.70346i	−0.193519	−	0.162381i	0.540880	−	0.841100i	$-0.318091\pi$
$839$	−5.60536	−	4.70346i	−0.193519	−	0.162381i	−0.734399	+	0.678718i	$0.762536\pi$
$840$		0			0
$841$	1.62295	+	9.20422i	0.0559639	+	0.317387i
$842$	−9.54306	−	16.5033i	−0.328876	−	0.568742i
$843$		0			0
$844$	0.0165663	+	12.2644i	0.000570236	+	0.422159i
$845$	−29.3610	−	16.9516i	−1.01005	−	0.583151i
$846$		0			0
$847$	−5.41924	−	9.38639i	−0.186207	−	0.322520i
$848$	12.9036	+	15.2938i	0.443111	+	0.525191i
$849$		0			0
$850$	−0.00370334	−	5.48333i	−0.000127023	−	0.188077i
$851$	16.0820	+	19.1657i	0.551283	+	0.656993i
$852$		0			0
$853$	15.5473	+	42.7160i	0.532331	+	1.46257i	0.856290	+	0.516496i	$0.172764\pi$
$853$	15.5473	+	42.7160i	0.532331	+	1.46257i	−0.323959	+	0.946071i	$0.605014\pi$
$854$	−2.10795	+	12.0022i	−0.0721326	+	0.410706i
$855$		0			0
$856$	5.47109	+	9.43203i	0.186998	+	0.322380i
$857$	3.84017	−	21.7787i	0.131178	−	0.743946i	−0.846268	−	0.532758i	$-0.821156\pi$
$857$	3.84017	−	21.7787i	0.131178	−	0.743946i	0.977445	−	0.211188i	$-0.0677333\pi$
$858$		0			0
$859$	−10.5655	+	29.0285i	−0.360491	+	0.990441i	0.618365	+	0.785891i	$0.287795\pi$
$859$	−10.5655	+	29.0285i	−0.360491	+	0.990441i	−0.978856	+	0.204550i	$0.934427\pi$
$860$	21.2120	−	7.75300i	0.723324	−	0.264375i
$861$		0			0
$862$	35.1139	−	6.21599i	1.19598	−	0.211717i
$863$	27.4661			0.934956			0.467478	−	0.884005i	$-0.345163\pi$
$863$	27.4661			0.934956			0.467478	+	0.884005i	$0.345163\pi$
$864$		0			0
$865$	−1.38039			−0.0469348
$866$	21.6764	−	3.83723i	0.736594	−	0.130394i
$867$		0			0
$868$	6.93531	−	2.53486i	0.235400	−	0.0860388i
$869$	−12.8137	+	35.2053i	−0.434675	+	1.19426i
$870$		0			0
$871$	−0.852216	+	4.83316i	−0.0288762	+	0.163765i
$872$	−4.72305	−	8.14241i	−0.159943	−	0.275737i
$873$		0			0
$874$	−5.18032	+	29.4955i	−0.175227	+	0.997701i
$875$	−4.97337	−	13.6642i	−0.168131	−	0.461935i
$876$		0			0
$877$	−7.68788	−	9.16206i	−0.259601	−	0.309381i	0.620463	−	0.784236i	$-0.286945\pi$
$877$	−7.68788	−	9.16206i	−0.259601	−	0.309381i	−0.880064	+	0.474855i	$0.842500\pi$
$878$	0.0304331	+	45.0607i	0.00102707	+	1.52072i
$879$		0			0
$880$	13.4685	−	11.3635i	0.454021	−	0.383064i
$881$	−18.8243	−	32.6046i	−0.634205	−	1.09848i	−0.986683	−	0.162655i	$-0.947994\pi$
$881$	−18.8243	−	32.6046i	−0.634205	−	1.09848i	0.352478	−	0.935820i	$-0.385339\pi$
$882$		0			0
$883$	−19.8345	−	11.4515i	−0.667485	−	0.385373i	0.127638	−	0.991821i	$-0.459261\pi$
$883$	−19.8345	−	11.4515i	−0.667485	−	0.385373i	−0.795123	+	0.606448i	$0.792594\pi$
$884$	−0.0180539	−	13.3657i	−0.000607217	−	0.449537i
$885$		0			0
$886$	4.47773	+	7.74358i	0.150432	+	0.260151i
$887$	−0.995710	−	5.64695i	−0.0334327	−	0.189606i	0.963518	−	0.267645i	$-0.0862454\pi$
$887$	−0.995710	−	5.64695i	−0.0334327	−	0.189606i	−0.996950	+	0.0780387i	$0.975134\pi$
$888$		0			0
$889$	4.39338	+	3.68648i	0.147349	+	0.123641i
$890$	9.07670	+	7.60581i	0.304252	+	0.254947i
$891$		0			0
$892$	7.50355	+	42.2212i	0.251237	+	1.41367i
$893$	1.79219	−	2.13585i	0.0599735	−	0.0714737i
$894$		0			0
$895$	2.02139	+	11.4639i	0.0675675	+	0.383194i
$896$	−15.3939	−	8.79092i	−0.514275	−	0.293684i
$897$		0			0
$898$	−7.60840	−	9.05491i	−0.253895	−	0.302166i
$899$	−9.04655	−	5.22303i	−0.301719	−	0.174198i
$900$		0			0
$901$	−4.28862	+	2.47604i	−0.142875	+	0.0824888i
$902$	17.9357	+	6.51434i	0.597193	+	0.216904i
$903$		0			0
$904$	23.2669	−	4.15122i	0.773847	−	0.138067i
$905$	−2.95572	+	2.48014i	−0.0982513	+	0.0824426i
$906$		0			0
$907$	−8.42248	−	23.1406i	−0.279664	−	0.768370i	−0.997401	−	0.0720557i	$-0.977044\pi$
$907$	−8.42248	−	23.1406i	−0.279664	−	0.768370i	0.717737	−	0.696315i	$-0.245178\pi$
$908$	23.9607	+	28.4771i	0.795165	+	0.945045i
$909$		0			0
$910$	−5.33489	−	14.6267i	−0.176850	−	0.484872i
$911$	−6.32793	+	35.8875i	−0.209654	+	1.18901i	0.680293	+	0.732940i	$0.261853\pi$
$911$	−6.32793	+	35.8875i	−0.209654	+	1.18901i	−0.889947	+	0.456065i	$0.849259\pi$
$912$		0			0
$913$	−24.9517	−	9.08166i	−0.825780	−	0.300559i
$914$	34.5058	+	19.8909i	1.14135	+	0.657932i
$915$		0			0
$916$	15.3931	+	8.85948i	0.508601	+	0.292726i
$917$		−	15.3708i		−	0.507590i
$918$		0			0
$919$	27.8245			0.917845			0.458923	−	0.888476i	$-0.348236\pi$
$919$	27.8245			0.917845			0.458923	+	0.888476i	$0.348236\pi$
$920$	−18.7656	+	6.87321i	−0.618684	+	0.226603i
$921$		0			0
$922$	−18.4608	+	32.0250i	−0.607975	+	1.05469i
$923$	11.6405	−	31.9819i	0.383151	−	1.05270i
$924$		0			0
$925$	−14.2153	−	2.50654i	−0.467397	−	0.0824146i
$926$	−10.7331	−	29.4270i	−0.352711	−	0.967032i
$927$		0			0
$928$	4.43818	+	24.6825i	0.145690	+	0.810241i
$929$	−14.0864	+	5.12703i	−0.462160	+	0.168212i	−0.562598	−	0.826731i	$-0.690198\pi$
$929$	−14.0864	+	5.12703i	−0.462160	+	0.168212i	0.100438	+	0.994943i	$0.467976\pi$
$930$		0			0
$931$	9.11238	+	10.8597i	0.298646	+	0.355913i
$932$	−28.8276	−	24.1230i	−0.944281	−	0.790174i
$933$		0			0
$934$	−29.4181	−	10.6848i	−0.962590	−	0.349618i
$935$	2.18052	+	3.77677i	0.0713106	+	0.123514i
$936$		0			0
$937$	−9.57278	+	16.5805i	−0.312729	+	0.541663i	−0.978952	−	0.204090i	$-0.934577\pi$
$937$	−9.57278	+	16.5805i	−0.312729	+	0.541663i	0.666223	+	0.745753i	$0.267910\pi$
$938$	−1.23332	+	1.03629i	−0.0402692	+	0.0338362i
$939$		0			0
$940$	1.83281	+	0.320621i	0.0597796	+	0.0104575i
$941$	−36.4053	+	6.41923i	−1.18678	+	0.209261i	−0.731975	−	0.681331i	$-0.761401\pi$
$941$	−36.4053	+	6.41923i	−1.18678	+	0.209261i	−0.454803	+	0.890592i	$0.650290\pi$
$942$		0			0
$943$	−16.5778	−	13.9104i	−0.539847	−	0.452985i
$944$	−15.5334	−	42.3216i	−0.505569	−	1.37745i
$945$		0			0
$946$	41.7151	−	49.7823i	1.35627	−	1.61856i
$947$	16.0406	−	19.1164i	0.521248	−	0.621199i	−0.439627	−	0.898180i	$-0.644890\pi$
$947$	16.0406	−	19.1164i	0.521248	−	0.621199i	0.960875	+	0.276981i	$0.0893340\pi$
$948$		0			0
$949$	−93.3185	+	16.4546i	−3.02925	+	0.534138i
$950$	−8.64896	−	14.9571i	−0.280609	−	0.485273i
$951$		0			0
$952$	2.81317	−	3.36643i	0.0911753	−	0.109107i
$953$	7.31014	−	12.6615i	0.236799	−	0.410147i	−0.722995	−	0.690853i	$-0.757235\pi$
$953$	7.31014	−	12.6615i	0.236799	−	0.410147i	0.959794	+	0.280706i	$0.0905685\pi$
$954$		0			0
$955$	16.2733	−	9.39537i	0.526590	−	0.304027i
$956$	−20.5869	−	35.5465i	−0.665827	−	1.14966i
$957$		0			0
$958$	0.0113577	+	16.8167i	0.000366949	+	0.543322i
$959$	−26.5164	+	22.2499i	−0.856258	+	0.718486i
$960$		0			0
$961$	23.9132	−	8.70369i	0.771393	−	0.280764i
$962$	−34.6542	−	6.08633i	−1.11729	−	0.196231i
$963$		0			0
$964$	−25.9029	−	9.38828i	−0.834276	−	0.302376i
$965$	−4.54883	−	0.802081i	−0.146432	−	0.0258199i
$966$		0			0
$967$	48.8192	+	17.7687i	1.56992	+	0.571404i	0.972981	−	0.230884i	$-0.0741619\pi$
$967$	48.8192	+	17.7687i	1.56992	+	0.571404i	0.596937	+	0.802288i	$0.296384\pi$
$968$	6.65433	−	18.3985i	0.213878	−	0.591351i
$969$		0			0
$970$	2.76759	+	15.6340i	0.0888619	+	0.501978i
$971$			20.4952i			0.657724i	0.944378	+	0.328862i	$0.106665\pi$
$971$			20.4952i			0.657724i	−0.944378	+	0.328862i	$0.893335\pi$
$972$		0			0
$973$		−	7.45961i		−	0.239144i
$974$	−30.8011	+	5.45252i	−0.986932	+	0.174710i
$975$		0			0
$976$	−19.0203	+	11.0500i	−0.608826	+	0.353702i
$977$	7.72505	+	2.81169i	0.247146	+	0.0899539i	0.462623	−	0.886555i	$-0.346908\pi$
$977$	7.72505	+	2.81169i	0.247146	+	0.0899539i	−0.215477	+	0.976509i	$0.569131\pi$
$978$		0			0
$979$	33.5386	+	5.91376i	1.07190	+	0.189004i
$980$	−3.22363	+	8.89422i	−0.102975	+	0.284116i
$981$		0			0
$982$	1.82621	−	10.3980i	0.0582767	−	0.331814i
$983$	22.5289	−	8.19984i	0.718559	−	0.261534i	0.0432453	−	0.999064i	$-0.486230\pi$
$983$	22.5289	−	8.19984i	0.718559	−	0.261534i	0.675314	+	0.737530i	$0.264008\pi$
$984$		0			0
$985$	13.0285	−	10.9322i	0.415123	−	0.348330i
$986$	−6.20636	+	0.00419165i	−0.197651	+	0.000133489i
$987$		0			0
$988$	−21.1066	−	36.4439i	−0.671491	−	1.15944i
$989$	−63.7900	+	36.8292i	−2.02840	+	1.17110i
$990$		0			0
$991$	8.43544	−	14.6106i	0.267960	−	0.464121i	−0.700375	−	0.713776i	$-0.746984\pi$
$991$	8.43544	−	14.6106i	0.267960	−	0.464121i	0.968335	+	0.249654i	$0.0803170\pi$
$992$	11.5659	+	6.62558i	0.367217	+	0.210362i
$993$		0			0
$994$	9.67090	−	5.59221i	0.306742	−	0.177374i
$995$	0.940553	−	0.165845i	0.0298175	−	0.00525763i
$996$		0			0
$997$	21.3234	−	25.4122i	0.675317	−	0.804812i	−0.314180	−	0.949363i	$-0.601730\pi$
$997$	21.3234	−	25.4122i	0.675317	−	0.804812i	0.989497	+	0.144552i	$0.0461740\pi$
$998$	11.2218	+	9.40333i	0.355221	+	0.297657i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	648.2.t.a.613.3		204
3.2	odd	2		216.2.t.a.205.32	yes	204
8.5	even	2	inner	648.2.t.a.613.17		204
12.11	even	2		864.2.bf.a.529.20		204
24.5	odd	2		216.2.t.a.205.18	yes	204
24.11	even	2		864.2.bf.a.529.15		204
27.5	odd	18		216.2.t.a.157.18	✓	204
27.22	even	9	inner	648.2.t.a.37.17		204
108.59	even	18		864.2.bf.a.49.15		204
216.5	odd	18		216.2.t.a.157.32	yes	204
216.59	even	18		864.2.bf.a.49.20		204
216.157	even	18	inner	648.2.t.a.37.3		204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.t.a.157.18	✓	204	27.5	odd	18
216.2.t.a.157.32	yes	204	216.5	odd	18
216.2.t.a.205.18	yes	204	24.5	odd	2
216.2.t.a.205.32	yes	204	3.2	odd	2
648.2.t.a.37.3		204	216.157	even	18	inner
648.2.t.a.37.17		204	27.22	even	9	inner
648.2.t.a.613.3		204	1.1	even	1	trivial
648.2.t.a.613.17		204	8.5	even	2	inner
864.2.bf.a.49.15		204	108.59	even	18
864.2.bf.a.49.20		204	216.59	even	18
864.2.bf.a.529.15		204	24.11	even	2
864.2.bf.a.529.20		204	12.11	even	2

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:	\( N \)	\(=\)	\( 648 = 2^{3} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	648.t (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.39256 + 0.246516i) q^{2} +(1.87846 - 0.686578i) q^{4} +(-0.355965 + 0.978005i) q^{5} +(-0.272085 + 1.54307i) q^{7} +(-2.44662 + 1.41917i) q^{8} +(0.254609 - 1.44968i) q^{10} +(-1.44773 - 3.97760i) q^{11} +(-4.33941 - 5.17151i) q^{13} +(-0.00149657 - 2.21590i) q^{14} +(3.05722 - 2.57942i) q^{16} +(0.494959 + 0.857294i) q^{17} +(2.70129 + 1.55959i) q^{19} +(0.00281166 + 2.08154i) q^{20} +(2.99660 + 5.18217i) q^{22} +(-1.17888 - 6.68573i) q^{23} +(3.00044 + 2.51767i) q^{25} +(7.31776 + 6.13191i) q^{26} +(0.548339 + 3.08541i) q^{28} +(2.84964 - 3.39607i) q^{29} +(-0.409166 - 2.32049i) q^{31} +(-3.62150 + 4.34566i) q^{32} +(-0.900598 - 1.07182i) q^{34} +(-1.41228 - 0.815381i) q^{35} +(-3.19157 + 1.84266i) q^{37} +(-4.14618 - 1.50592i) q^{38} +(-0.517049 - 2.89798i) q^{40} +(2.44191 - 2.04900i) q^{41} +(-3.71087 - 10.1955i) q^{43} +(-5.45044 - 6.47779i) q^{44} +(3.28980 + 9.01969i) q^{46} +(0.155220 - 0.880296i) q^{47} +(4.27080 + 1.55445i) q^{49} +(-4.79894 - 2.76635i) q^{50} +(-11.7021 - 6.73512i) q^{52} +5.00251i q^{53} +4.40546 q^{55} +(-1.52420 - 4.16145i) q^{56} +(-3.13112 + 5.43173i) q^{58} +(3.85475 - 10.5908i) q^{59} +(-5.41575 - 0.954943i) q^{61} +(1.14183 + 3.13057i) q^{62} +(3.97189 - 6.94436i) q^{64} +(6.60244 - 2.40309i) q^{65} +(-0.467287 - 0.556891i) q^{67} +(1.51836 + 1.27056i) q^{68} +(2.16769 + 0.787319i) q^{70} +(2.52073 + 4.36603i) q^{71} +(7.01816 - 12.1558i) q^{73} +(3.99022 - 3.35279i) q^{74} +(6.14505 + 1.07498i) q^{76} +(6.53164 - 1.15170i) q^{77} +(-6.78017 - 5.68924i) q^{79} +(1.43442 + 3.90816i) q^{80} +(-2.89539 + 3.45533i) q^{82} +(4.03223 - 4.80543i) q^{83} +(-1.01463 + 0.178906i) q^{85} +(7.68099 + 13.2831i) q^{86} +(9.18695 + 7.67710i) q^{88} +(-4.02279 + 6.96768i) q^{89} +(9.16071 - 5.28894i) q^{91} +(-6.80475 - 11.7495i) q^{92} +(0.000853769 + 1.26413i) q^{94} +(-2.48685 + 2.08672i) q^{95} +(-10.1365 + 3.68937i) q^{97} +(-6.33056 - 1.11184i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q + 6 q^{2} - 6 q^{4} - 12 q^{7} + 3 q^{8} - 3 q^{10} + 21 q^{14} - 6 q^{16} + 6 q^{17} - 15 q^{20} - 6 q^{22} + 12 q^{23} - 12 q^{25} + 30 q^{26} - 12 q^{28} - 12 q^{31} + 36 q^{32} + 42 q^{38} - 21 q^{40}+ \cdots - 54 q^{98}+O(q^{100}) \) 204 * q + 6 * q^2 - 6 * q^4 - 12 * q^7 + 3 * q^8 - 3 * q^10 + 21 * q^14 - 6 * q^16 + 6 * q^17 - 15 * q^20 - 6 * q^22 + 12 * q^23 - 12 * q^25 + 30 * q^26 - 12 * q^28 - 12 * q^31 + 36 * q^32 + 42 * q^38 - 21 * q^40 + 24 * q^41 - 21 * q^44 - 3 * q^46 + 12 * q^47 - 12 * q^49 + 99 * q^50 - 33 * q^52 - 24 * q^55 - 99 * q^56 + 21 * q^58 + 36 * q^62 - 3 * q^64 + 12 * q^65 - 75 * q^68 + 9 * q^70 + 90 * q^71 - 6 * q^73 - 9 * q^74 - 18 * q^76 - 12 * q^79 - 78 * q^80 - 12 * q^82 + 30 * q^86 - 30 * q^88 + 6 * q^89 - 111 * q^92 - 33 * q^94 + 42 * q^95 - 12 * q^97 - 54 * q^98

Introduction

L-functions

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