LMFDB - Embedded newform 648.2.t.a.37.17

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			37.17
Character	$\chi$	$=$	648.37
Dual form			648.2.t.a.613.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.000955132 + 1.41421i) q^{2} +(-2.00000 + 0.00270152i) q^{4} +(0.355965 + 0.978005i) q^{5} +(-0.272085 - 1.54307i) q^{7} +(-0.00573079 - 2.82842i) q^{8} +(-1.38277 + 0.504344i) q^{10} +(1.44773 - 3.97760i) q^{11} +(4.33941 - 5.17151i) q^{13} +(2.18198 - 0.386261i) q^{14} +(3.99999 - 0.0108061i) q^{16} +(0.494959 - 0.857294i) q^{17} +(-2.70129 + 1.55959i) q^{19} +(-0.714571 - 1.95505i) q^{20} +(5.62656 + 2.04360i) q^{22} +(-1.17888 + 6.68573i) q^{23} +(3.00044 - 2.51767i) q^{25} +(7.31776 + 6.13191i) q^{26} +(0.548339 + 3.08541i) q^{28} +(-2.84964 - 3.39607i) q^{29} +(-0.409166 + 2.32049i) q^{31} +(0.0191026 + 5.65682i) q^{32} +(1.21287 + 0.699158i) q^{34} +(1.41228 - 0.815381i) q^{35} +(3.19157 + 1.84266i) q^{37} +(-2.20817 - 3.81871i) q^{38} +(2.76417 - 1.01242i) q^{40} +(2.44191 + 2.04900i) q^{41} +(3.71087 - 10.1955i) q^{43} +(-2.88471 + 7.95911i) q^{44} +(-9.45618 - 1.66079i) q^{46} +(0.155220 + 0.880296i) q^{47} +(4.27080 - 1.55445i) q^{49} +(3.56338 + 4.24086i) q^{50} +(-8.66484 + 10.3547i) q^{52} +5.00251i q^{53} +4.40546 q^{55} +(-4.36290 + 0.778415i) q^{56} +(4.80005 - 4.03325i) q^{58} +(-3.85475 - 10.5908i) q^{59} +(5.41575 - 0.954943i) q^{61} +(-3.28206 - 0.576431i) q^{62} +(-7.99993 + 0.0324182i) q^{64} +(6.60244 + 2.40309i) q^{65} +(0.467287 - 0.556891i) q^{67} +(-0.987601 + 1.71592i) q^{68} +(1.15447 + 1.99649i) q^{70} +(2.52073 - 4.36603i) q^{71} +(7.01816 + 12.1558i) q^{73} +(-2.60286 + 4.51532i) q^{74} +(5.39836 - 3.12648i) q^{76} +(-6.53164 - 1.15170i) q^{77} +(-6.78017 + 5.68924i) q^{79} +(1.43442 + 3.90816i) q^{80} +(-2.89539 + 3.45533i) q^{82} +(-4.03223 - 4.80543i) q^{83} +(1.01463 + 0.178906i) q^{85} +(14.4222 + 5.23823i) q^{86} +(-11.2586 - 4.07199i) q^{88} +(-4.02279 - 6.96768i) q^{89} +(-9.16071 - 5.28894i) q^{91} +(2.33969 - 13.3746i) q^{92} +(-1.24478 + 0.220355i) q^{94} +(-2.48685 - 2.08672i) q^{95} +(-10.1365 - 3.68937i) q^{97} +(2.20240 + 6.03834i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/648\mathbb{Z}\right)^\times$.

$n$	$325$	$487$	$569$
$\chi(n)$	$-1$	$1$	$e\left(\frac{7}{9}\right)$

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 $

$2$	0.000955132		1.41421i	0.000675380		1.00000i
$2$	0.000955132		1.41421i	0.000675380		1.00000i
$3$		0			0
$3$		0			0
$4$	−2.00000	+	0.00270152i	−0.999999	+	0.00135076i
$5$	0.355965	+	0.978005i	0.159192	+	0.437377i	0.993488	−	0.113941i	$-0.0363474\pi$
$5$	0.355965	+	0.978005i	0.159192	+	0.437377i	−0.834295	+	0.551318i	$0.814125\pi$
$6$		0			0
$7$	−0.272085	−	1.54307i	−0.102839	−	0.583227i	−0.992062	−	0.125753i	$-0.959865\pi$
$7$	−0.272085	−	1.54307i	−0.102839	−	0.583227i	0.889223	−	0.457474i	$-0.151246\pi$
$8$	−0.00573079	−	2.82842i	−0.00202614	−	0.999998i
$9$		0			0
$10$	−1.38277	+	0.504344i	−0.437270	+	0.159488i
$11$	1.44773	−	3.97760i	0.436507	−	1.19929i	−0.505243	−	0.862977i	$-0.668597\pi$
$11$	1.44773	−	3.97760i	0.436507	−	1.19929i	0.941750	−	0.336315i	$-0.109181\pi$
$12$		0			0
$13$	4.33941	−	5.17151i	1.20354	−	1.43432i	0.332497	−	0.943104i	$-0.392109\pi$
$13$	4.33941	−	5.17151i	1.20354	−	1.43432i	0.871039	−	0.491214i	$-0.163447\pi$
$14$	2.18198	−	0.386261i	0.583157	−	0.103233i
$15$		0			0
$16$	3.99999	−	0.0108061i	0.999996	−	0.00270152i
$17$	0.494959	−	0.857294i	0.120045	−	0.207924i	−0.799740	−	0.600346i	$-0.795029\pi$
$17$	0.494959	−	0.857294i	0.120045	−	0.207924i	0.919785	+	0.392422i	$0.128363\pi$
$18$		0			0
$19$	−2.70129	+	1.55959i	−0.619719	+	0.357795i	−0.776759	−	0.629797i	$-0.783138\pi$
$19$	−2.70129	+	1.55959i	−0.619719	+	0.357795i	0.157041	+	0.987592i	$0.449805\pi$
$20$	−0.714571	−	1.95505i	−0.159783	−	0.437162i
$21$		0			0
$22$	5.62656	+	2.04360i	1.19959	+	0.435697i
$23$	−1.17888	+	6.68573i	−0.245812	+	1.39407i	0.572786	+	0.819705i	$0.305863\pi$
$23$	−1.17888	+	6.68573i	−0.245812	+	1.39407i	−0.818598	+	0.574367i	$0.805248\pi$
$24$		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	$-0.357258\pi$
$29$	−2.84964	−	3.39607i	−0.529166	−	0.630635i	−0.962722	+	0.270491i	$0.912814\pi$
$30$		0			0
$31$	−0.409166	+	2.32049i	−0.0734883	+	0.416773i	0.925764	+	0.378103i	$0.123423\pi$
$31$	−0.409166	+	2.32049i	−0.0734883	+	0.416773i	−0.999252	+	0.0386704i	$0.987688\pi$
$32$	0.0191026	+	5.65682i	0.00337689	+	0.999994i
$33$		0			0
$34$	1.21287	+	0.699158i	0.208005	+	0.119905i
$35$	1.41228	−	0.815381i	0.238719	−	0.137825i
$36$		0			0
$37$	3.19157	+	1.84266i	0.524691	+	0.302931i	0.738852	−	0.673868i	$-0.235368\pi$
$37$	3.19157	+	1.84266i	0.524691	+	0.302931i	−0.214161	+	0.976798i	$0.568702\pi$
$38$	−2.20817	−	3.81871i	−0.358213	−	0.619477i
$39$		0			0
$40$	2.76417	−	1.01242i	0.437054	−	0.160078i
$41$	2.44191	+	2.04900i	0.381362	+	0.320000i	0.813237	−	0.581933i	$-0.197703\pi$
$41$	2.44191	+	2.04900i	0.381362	+	0.320000i	−0.431875	+	0.901933i	$0.642148\pi$
$42$		0			0
$43$	3.71087	−	10.1955i	0.565903	−	1.55481i	−0.244938	−	0.969539i	$-0.578767\pi$
$43$	3.71087	−	10.1955i	0.565903	−	1.55481i	0.810841	−	0.585267i	$-0.199010\pi$
$44$	−2.88471	+	7.95911i	−0.434886	+	1.19988i
$45$		0			0
$46$	−9.45618	−	1.66079i	−1.39424	−	0.244871i
$47$	0.155220	+	0.880296i	0.0226411	+	0.128404i	0.994033	−	0.109077i	$-0.0347894\pi$
$47$	0.155220	+	0.880296i	0.0226411	+	0.128404i	−0.971392	+	0.237481i	$0.923678\pi$
$48$		0			0
$49$	4.27080	−	1.55445i	0.610115	−	0.222064i
$50$	3.56338	+	4.24086i	0.503939	+	0.599748i
$51$		0			0
$52$	−8.66484	+	10.3547i	−1.20160	+	1.43594i
$53$			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
$56$	−4.36290	+	0.778415i	−0.583017	+	0.104020i
$57$		0			0
$58$	4.80005	−	4.03325i	0.630278	−	0.529591i
$59$	−3.85475	−	10.5908i	−0.501846	−	1.37881i	−0.889470	−	0.456993i	$-0.848927\pi$
$59$	−3.85475	−	10.5908i	−0.501846	−	1.37881i	0.387625	−	0.921817i	$-0.373296\pi$
$60$		0			0
$61$	5.41575	−	0.954943i	0.693416	−	0.122268i	0.184177	−	0.982893i	$-0.441038\pi$
$61$	5.41575	−	0.954943i	0.693416	−	0.122268i	0.509239	+	0.860625i	$0.329927\pi$
$62$	−3.28206	−	0.576431i	−0.416823	−	0.0732068i
$63$		0			0
$64$	−7.99993	+	0.0324182i	−0.999992	+	0.00405227i
$65$	6.60244	+	2.40309i	0.818932	+	0.298067i
$66$		0			0
$67$	0.467287	−	0.556891i	0.0570882	−	0.0680351i	−0.736745	−	0.676171i	$-0.763638\pi$
$67$	0.467287	−	0.556891i	0.0570882	−	0.0680351i	0.793833	+	0.608136i	$0.208082\pi$
$68$	−0.987601	+	1.71592i	−0.119764	+	0.208086i
$69$		0			0
$70$	1.15447	+	1.99649i	0.137986	+	0.238626i
$71$	2.52073	−	4.36603i	0.299155	−	0.518152i	−0.676788	−	0.736178i	$-0.736628\pi$
$71$	2.52073	−	4.36603i	0.299155	−	0.518152i	0.975943	+	0.218026i	$0.0699618\pi$
$72$		0			0
$73$	7.01816	+	12.1558i	0.821413	+	1.42273i	0.904630	+	0.426198i	$0.140147\pi$
$73$	7.01816	+	12.1558i	0.821413	+	1.42273i	−0.0832165	+	0.996531i	$0.526519\pi$
$74$	−2.60286	+	4.51532i	−0.302576	+	0.524896i
$75$		0			0
$76$	5.39836	−	3.12648i	0.619235	−	0.358631i
$77$	−6.53164	−	1.15170i	−0.744349	−	0.131249i
$78$		0			0
$79$	−6.78017	+	5.68924i	−0.762829	+	0.640090i	−0.938862	−	0.344295i	$-0.888118\pi$
$79$	−6.78017	+	5.68924i	−0.762829	+	0.640090i	0.176032	+	0.984384i	$0.443674\pi$
$80$	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	$-0.334098\pi$
$83$	−4.03223	−	4.80543i	−0.442595	−	0.527464i	−0.940512	+	0.339760i	$0.889654\pi$
$84$		0			0
$85$	1.01463	+	0.178906i	0.110052	+	0.0194051i
$86$	14.4222	+	5.23823i	1.55519	+	0.564853i
$87$		0			0
$88$	−11.2586	−	4.07199i	−1.20017	−	0.434076i
$89$	−4.02279	−	6.96768i	−0.426415	−	0.738573i	0.570136	−	0.821550i	$-0.306890\pi$
$89$	−4.02279	−	6.96768i	−0.426415	−	0.738573i	−0.996551	+	0.0829775i	$0.973557\pi$
$90$		0			0
$91$	−9.16071	−	5.28894i	−0.960303	−	0.554431i
$92$	2.33969	−	13.3746i	0.243929	−	1.39440i
$93$		0			0
$94$	−1.24478	+	0.220355i	−0.128389	+	0.0227279i
$95$	−2.48685	−	2.08672i	−0.255146	−	0.214093i
$96$		0			0
$97$	−10.1365	−	3.68937i	−1.02920	−	0.374599i	−0.228425	−	0.973561i	$-0.573358\pi$
$97$	−10.1365	−	3.68937i	−1.02920	−	0.374599i	−0.800777	+	0.598963i	$0.795580\pi$
$98$	2.20240	+	6.03834i	0.222476	+	0.609965i
$99$		0			0
$100$	−5.99407	+	5.04344i	−0.599407	+	0.504344i
$101$	6.50659	−	1.14729i	0.647430	−	0.114159i	0.159716	−	0.987163i	$-0.448942\pi$
$101$	6.50659	−	1.14729i	0.647430	−	0.114159i	0.487714	+	0.873004i	$0.337831\pi$
$102$		0			0
$103$	−14.9315	+	5.43464i	−1.47125	+	0.535491i	−0.948439	−	0.316959i	$-0.897338\pi$
$103$	−14.9315	+	5.43464i	−1.47125	+	0.535491i	−0.522809	+	0.852450i	$0.675116\pi$
$104$	−14.6521	−	12.2440i	−1.43675	−	1.20063i
$105$		0			0
$106$	−7.07462	+	0.00477806i	−0.687148	+	0.000464086i
$107$		−	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	$0.949049\pi$
$110$	0.00420779	+	6.23026i	0.000401197	+	0.594032i
$111$		0			0
$112$	−1.10501	−	6.16933i	−0.104414	−	0.582947i
$113$	−7.85208	+	2.85792i	−0.738662	+	0.268851i	−0.683827	−	0.729645i	$-0.739686\pi$
$113$	−7.85208	+	2.85792i	−0.738662	+	0.268851i	−0.0548351	+	0.998495i	$0.517463\pi$
$114$		0			0
$115$	−6.95832	+	1.22694i	−0.648867	+	0.114413i
$116$	5.70846	+	6.78444i	0.530017	+	0.629920i
$117$		0			0
$118$	14.9740	−	5.46156i	1.37847	−	0.502777i
$119$	−1.45754	−	0.530501i	−0.133612	−	0.0486309i
$120$		0			0
$121$	−5.29891	−	4.44632i	−0.481719	−	0.404211i
$122$	1.35567	+	7.65811i	0.122736	+	0.693333i
$123$		0			0
$124$	0.812062	−	4.64209i	0.0729253	−	0.416872i
$125$	8.03702	+	4.64017i	0.718853	+	0.415030i
$126$		0			0
$127$	1.83012	+	3.16986i	0.162397	+	0.281280i	0.935728	−	0.352723i	$-0.114744\pi$
$127$	1.83012	+	3.16986i	0.162397	+	0.281280i	−0.773331	+	0.634003i	$0.781411\pi$
$128$	−0.0534872	−	11.3136i	−0.00472764	−	0.999989i
$129$		0			0
$130$	−3.39218	+	9.33955i	−0.297514	+	0.819133i
$131$	9.66082	+	1.70346i	0.844070	+	0.148832i	0.578930	−	0.815378i	$-0.303471\pi$
$131$	9.66082	+	1.70346i	0.844070	+	0.148832i	0.265140	+	0.964210i	$0.414582\pi$
$132$		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	0.510284	−	0.860006i	$-0.329540\pi$
$137$	16.9231	−	14.2001i	1.44583	−	1.21320i	0.935550	−	0.353193i	$-0.114904\pi$
$138$		0			0
$139$	4.68849	+	0.826707i	0.397672	+	0.0701203i	0.368908	−	0.929466i	$-0.379732\pi$
$139$	4.68849	+	0.826707i	0.397672	+	0.0701203i	0.0287641	+	0.999586i	$0.490843\pi$
$140$	−2.82236	+	1.63458i	−0.238533	+	0.138147i
$141$		0			0
$142$	6.17690	+	3.56068i	0.518354	+	0.298805i
$143$	−14.2879	−	24.7474i	−1.19482	−	2.06948i
$144$		0			0
$145$	2.30701	−	3.99585i	0.191586	−	0.331837i
$146$	−17.1842	+	9.93678i	−1.42217	+	0.822374i
$147$		0			0
$148$	−6.38812	−	3.67668i	−0.525100	−	0.302222i
$149$	−14.7916	+	17.6280i	−1.21178	+	1.44414i	−0.350076	+	0.936721i	$0.613844\pi$
$149$	−14.7916	+	17.6280i	−1.21178	+	1.44414i	−0.861700	+	0.507418i	$0.830600\pi$
$150$		0			0
$151$	18.6779	+	6.79819i	1.51998	+	0.553229i	0.961144	−	0.276047i	$-0.0890245\pi$
$151$	18.6779	+	6.79819i	1.51998	+	0.553229i	0.558840	+	0.829276i	$0.311247\pi$
$152$	4.42666	+	7.63145i	0.359050	+	0.618992i
$153$		0			0
$154$	1.62252	−	9.23823i	0.130746	−	0.744438i
$155$	−2.41510	+	0.425848i	−0.193986	+	0.0342049i
$156$		0			0
$157$	1.67263	+	4.59552i	0.133491	+	0.366762i	0.988371	−	0.152063i	$-0.0485917\pi$
$157$	1.67263	+	4.59552i	0.133491	+	0.366762i	−0.854880	+	0.518825i	$0.826369\pi$
$158$	−8.05228	−	9.58318i	−0.640605	−	0.762397i
$159$		0			0
$160$	−5.52560	+	2.03231i	−0.436837	+	0.160668i
$161$	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	$0.947646\pi$
$164$	−4.88934	−	4.09140i	−0.381794	−	0.319485i
$165$		0			0
$166$	6.79205	−	5.70703i	0.527165	−	0.442951i
$167$	−5.72775	+	2.08473i	−0.443227	+	0.161321i	−0.553986	−	0.832526i	$-0.686894\pi$
$167$	−5.72775	+	2.08473i	−0.443227	+	0.161321i	0.110759	+	0.993847i	$0.464672\pi$
$168$		0			0
$169$	−5.65659	−	32.0801i	−0.435122	−	2.46770i
$170$	−0.252042	+	1.43507i	−0.0193307	+	0.110065i
$171$		0			0
$172$	−7.39420	+	20.4011i	−0.563802	+	1.55557i
$173$	−0.453627	+	1.24633i	−0.0344886	+	0.0947567i	−0.955742	−	0.294207i	$-0.904945\pi$
$173$	−0.453627	+	1.24633i	−0.0344886	+	0.0947567i	0.921253	+	0.388964i	$0.127167\pi$
$174$		0			0
$175$	−4.70132	−	3.94488i	−0.355386	−	0.298205i
$176$	5.74791	−	15.9260i	0.433265	−	1.20047i
$177$		0			0
$178$	9.84994	−	5.69574i	0.738284	−	0.426914i
$179$	−9.68622	−	5.59234i	−0.723982	−	0.417991i	0.0922343	−	0.995737i	$-0.470599\pi$
$179$	−9.68622	−	5.59234i	−0.723982	−	0.417991i	−0.816217	+	0.577746i	$0.803932\pi$
$180$		0			0
$181$	−3.21058	+	1.85363i	−0.238641	+	0.137779i	−0.614552	−	0.788876i	$-0.710663\pi$
$181$	−3.21058	+	1.85363i	−0.238641	+	0.137779i	0.375911	+	0.926656i	$0.377330\pi$
$182$	7.47093	−	12.9602i	0.553783	−	0.960677i
$183$		0			0
$184$	18.9168	+	3.29604i	1.39457	+	0.242987i
$185$	−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	−0.987088	−	0.160178i	$-0.948793\pi$
$191$	−13.8306	+	11.6053i	−1.00075	+	0.839729i	−0.0136618	+	0.999907i	$0.504349\pi$
$192$		0			0
$193$	0.770660	−	4.37063i	0.0554733	−	0.314605i	−0.944427	−	0.328721i	$-0.893382\pi$
$193$	0.770660	−	4.37063i	0.0554733	−	0.314605i	0.999900	+	0.0141163i	$0.00449352\pi$
$194$	5.20788	−	14.3386i	0.373904	−	1.02945i
$195$		0			0
$196$	−8.53740	+	3.12043i	−0.609814	+	0.222888i
$197$	14.1519	−	8.17063i	1.00828	−	0.582133i	0.0975957	−	0.995226i	$-0.468885\pi$
$197$	14.1519	−	8.17063i	1.00828	−	0.582133i	0.910689	+	0.413093i	$0.135551\pi$
$198$		0			0
$199$	−0.458824	+	0.794707i	−0.0325252	+	0.0563353i	−0.881830	−	0.471568i	$-0.843688\pi$
$199$	−0.458824	+	0.794707i	−0.0325252	+	0.0563353i	0.849305	+	0.527903i	$0.177022\pi$
$200$	−7.13822	−	8.47208i	−0.504748	−	0.599066i
$201$		0			0
$202$	1.62872	+	9.20061i	0.114597	+	0.647352i
$203$	−4.46504	+	5.32123i	−0.313385	+	0.373477i
$204$		0			0
$205$	−1.13470	+	3.11757i	−0.0792511	+	0.217741i
$206$	−7.70000	−	21.1112i	−0.536484	−	1.47089i
$207$		0			0
$208$	17.3017	−	20.7328i	1.19966	−	1.43756i
$209$	2.29270	+	13.0025i	0.158589	+	0.899403i
$210$		0			0
$211$	2.09734	+	5.76240i	0.144387	+	0.396700i	0.990714	−	0.135964i	$-0.0434131\pi$
$211$	2.09734	+	5.76240i	0.144387	+	0.396700i	−0.846327	+	0.532664i	$0.821191\pi$
$212$	−0.0135144	−	10.0050i	−0.000928172	−	0.687148i
$213$		0			0
$214$	5.45197	−	0.00368215i	0.372689	−	0.000251707i
$215$	11.2922			0.770124
$216$		0			0
$217$	3.69202			0.250631
$218$	−4.70654	+	0.00317870i	−0.318767	+	0.000215289i
$219$		0			0
$220$	−8.81091	+	0.0119014i	−0.594031	+	0.000802394i
$221$	−2.28567	−	6.27983i	−0.153751	−	0.422427i
$222$		0			0
$223$	−3.72326	−	21.1156i	−0.249328	−	1.41401i	−0.810223	−	0.586121i	$-0.800654\pi$
$223$	−3.72326	−	21.1156i	−0.249328	−	1.41401i	0.560896	−	0.827887i	$-0.310457\pi$
$224$	8.72369	−	1.56862i	0.582876	−	0.104808i
$225$		0			0
$226$	−4.04921	−	11.1018i	−0.269350	−	0.738480i
$227$	−6.36438	+	17.4860i	−0.422419	+	1.16059i	0.527900	+	0.849307i	$0.322980\pi$
$227$	−6.36438	+	17.4860i	−0.422419	+	1.16059i	−0.950319	+	0.311279i	$0.899243\pi$
$228$		0			0
$229$	−5.70813	+	6.80268i	−0.377204	+	0.449534i	−0.920930	−	0.389729i	$-0.872569\pi$
$229$	−5.70813	+	6.80268i	−0.377204	+	0.449534i	0.543726	+	0.839263i	$0.317013\pi$
$230$	−1.74180	−	9.83938i	−0.114851	−	0.648789i
$231$		0			0
$232$	−9.58920	+	8.07946i	−0.629562	+	0.530442i
$233$	−9.39731	+	16.2766i	−0.615638	+	1.06632i	0.374634	+	0.927173i	$0.377768\pi$
$233$	−9.39731	+	16.2766i	−0.615638	+	1.06632i	−0.990272	+	0.139144i	$0.955565\pi$
$234$		0			0
$235$	−0.805681	+	0.465160i	−0.0525568	+	0.0303437i
$236$	7.73811	+	21.1712i	0.503708	+	1.37813i
$237$		0			0
$238$	0.748849	−	2.06178i	0.0485407	−	0.133645i
$239$	−3.56653	+	20.2268i	−0.230700	+	1.30836i	0.620784	+	0.783982i	$0.286815\pi$
$239$	−3.56653	+	20.2268i	−0.230700	+	1.30836i	−0.851483	+	0.524382i	$0.824297\pi$
$240$		0			0
$241$	−10.5529	+	8.85497i	−0.679775	+	0.570399i	−0.915941	−	0.401314i	$-0.868554\pi$
$241$	−10.5529	+	8.85497i	−0.679775	+	0.570399i	0.236166	+	0.971713i	$0.424109\pi$
$242$	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
$248$	6.56568	+	1.14399i	0.416921	+	0.0726437i
$249$		0			0
$250$	−6.55452	+	11.3705i	−0.414544	+	0.719133i
$251$	−0.419101	+	0.241968i	−0.0264534	+	0.0152729i	−0.513168	−	0.858288i	$-0.671528\pi$
$251$	−0.419101	+	0.241968i	−0.0264534	+	0.0152729i	0.486715	+	0.873561i	$0.338195\pi$
$252$		0			0
$253$	24.8865	+	14.3682i	1.56460	+	0.903323i
$254$	−4.48111	+	2.59121i	−0.281170	+	0.162587i
$255$		0			0
$256$	15.9998	−	0.0864482i	0.999985	−	0.00540301i
$257$	−13.5896	−	11.4030i	−0.847695	−	0.711300i	0.111586	−	0.993755i	$-0.464407\pi$
$257$	−13.5896	−	11.4030i	−0.847695	−	0.711300i	−0.959281	+	0.282454i	$0.908851\pi$
$258$		0			0
$259$	1.97497	−	5.42619i	0.122719	−	0.337167i
$260$	−13.2114	−	4.78834i	−0.819334	−	0.296960i
$261$		0			0
$262$	−2.39983	+	13.6641i	−0.148262	+	0.844170i
$263$	−1.39832	−	7.93029i	−0.0862243	−	0.489002i	−0.997086	−	0.0762899i	$-0.975693\pi$
$263$	−1.39832	−	7.93029i	−0.0862243	−	0.489002i	0.910861	−	0.412712i	$-0.135419\pi$
$264$		0			0
$265$	−4.89249	+	1.78072i	−0.300543	+	0.109389i
$266$	−5.29174	+	4.44639i	−0.324457	+	0.272626i
$267$		0			0
$268$	−0.933069	+	1.11504i	−0.0569963	+	0.0681121i
$269$			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	$0.392978\pi$
$272$	1.97056	−	3.43451i	0.119483	−	0.208248i
$273$		0			0
$274$	20.0982	+	23.9193i	1.21418	+	1.44501i
$275$	−5.67046	−	15.5795i	−0.341941	−	0.939476i
$276$		0			0
$277$	−31.2235	+	5.50555i	−1.87604	+	0.330796i	−0.990907	−	0.134546i	$-0.957043\pi$
$277$	−31.2235	+	5.50555i	−1.87604	+	0.330796i	−0.885131	+	0.465342i	$0.845931\pi$
$278$	−1.16466	+	6.63131i	−0.0698517	+	0.397719i
$279$		0			0
$280$	−2.31433	−	3.98985i	−0.138308	−	0.238439i
$281$	18.4488	+	6.71481i	1.10056	+	0.400572i	0.827523	−	0.561431i	$-0.189749\pi$
$281$	18.4488	+	6.71481i	1.10056	+	0.400572i	0.273039	+	0.962003i	$0.411971\pi$
$282$		0			0
$283$	−12.6768	+	15.1076i	−0.753556	+	0.898053i	−0.997422	−	0.0717558i	$-0.977140\pi$
$283$	−12.6768	+	15.1076i	−0.753556	+	0.898053i	0.243866	+	0.969809i	$0.421584\pi$
$284$	−5.02965	+	8.73886i	−0.298455	+	0.518556i
$285$		0			0
$286$	34.9844	−	20.2298i	2.06867	−	1.19621i
$287$	2.49735	−	4.32554i	0.147414	−	0.255329i
$288$		0			0
$289$	8.01003	+	13.8738i	0.471178	+	0.816105i
$290$	5.65319	+	3.25878i	0.331967	+	0.191362i
$291$		0			0
$292$	−14.0691	−	24.2926i	−0.823334	−	1.42162i
$293$	26.1866	+	4.61741i	1.52984	+	0.269752i	0.874292	−	0.485401i	$-0.161326\pi$
$293$	26.1866	+	4.61741i	1.52984	+	0.269752i	0.655549	+	0.755153i	$0.272437\pi$
$294$		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
$302$	−9.59625	+	26.4210i	−0.552202	+	1.52036i
$303$		0			0
$304$	−10.7883	+	6.26753i	−0.618750	+	0.359468i
$305$	2.86175	+	4.95671i	0.163864	+	0.283820i
$306$		0			0
$307$	−20.0407	−	11.5705i	−1.14379	−	0.660365i	−0.196420	−	0.980520i	$-0.562932\pi$
$307$	−20.0407	−	11.5705i	−1.14379	−	0.660365i	−0.947365	+	0.320155i	$0.896265\pi$
$308$	13.0664	+	2.28576i	0.744526	+	0.130243i
$309$		0			0
$310$	−0.604547	−	3.41507i	−0.0343359	−	0.193963i
$311$	18.6806	+	15.6749i	1.05928	+	0.888842i	0.994039	−	0.109027i	$-0.0347735\pi$
$311$	18.6806	+	15.6749i	1.05928	+	0.888842i	0.0652424	+	0.997869i	$0.479218\pi$
$312$		0			0
$313$	24.2156	+	8.81377i	1.36875	+	0.498184i	0.918748	−	0.394845i	$-0.129202\pi$
$313$	24.2156	+	8.81377i	1.36875	+	0.498184i	0.450000	+	0.893028i	$0.351424\pi$
$314$	−6.49745	+	2.36985i	−0.366672	+	0.133738i
$315$		0			0
$316$	13.5450	−	11.3968i	0.761964	−	0.641120i
$317$	−18.1371	+	3.19806i	−1.01868	+	0.179621i	−0.657960	−	0.753053i	$-0.728580\pi$
$317$	−18.1371	+	3.19806i	−1.01868	+	0.179621i	−0.360721	+	0.932674i	$0.617469\pi$
$318$		0			0
$319$	−17.6337	+	6.41816i	−0.987300	+	0.359348i
$320$	−2.87940	−	7.81244i	−0.160963	−	0.436729i
$321$		0			0
$322$	0.0101601	+	15.0435i	0.000566198	+	0.838339i
$323$			3.08773i			0.171806i
$324$		0			0
$325$		−	26.4420i		−	1.46674i
$326$	−5.91256	+	0.00399322i	−0.327466	+	0.000221164i
$327$		0			0
$328$	5.78145	−	6.91848i	0.319227	−	0.382009i
$329$	1.31613	−	0.479031i	0.0725605	−	0.0264099i
$330$		0			0
$331$	15.2370	−	2.68670i	0.837502	−	0.147674i	0.261583	−	0.965181i	$-0.415755\pi$
$331$	15.2370	−	2.68670i	0.837502	−	0.147674i	0.575919	+	0.817507i	$0.304644\pi$
$332$	8.07744	+	9.59995i	0.443307	+	0.526866i
$333$		0			0
$334$	−2.95372	−	8.09827i	−0.161621	−	0.443118i
$335$	0.710980	+	0.258776i	0.0388450	+	0.0141384i
$336$		0			0
$337$	9.32566	+	7.82516i	0.508001	+	0.426264i	0.860425	−	0.509577i	$-0.170198\pi$
$337$	9.32566	+	7.82516i	0.508001	+	0.426264i	−0.352424	+	0.935840i	$0.614643\pi$
$338$	45.3627	−	8.03026i	2.46740	−	0.436788i
$339$		0			0
$340$	−2.02973	−	0.355070i	−0.110078	−	0.0192564i
$341$	8.63764	+	4.98695i	0.467755	+	0.270058i
$342$		0			0
$343$	−9.04472	−	15.6659i	−0.488369	−	0.845880i
$344$	−28.8586	−	10.4375i	−1.55595	−	0.562752i
$345$		0			0
$346$	−1.76301	−	0.640335i	−0.0947800	−	0.0344246i
$347$	23.2143	+	4.09332i	1.24621	+	0.219741i	0.757576	−	0.652747i	$-0.226384\pi$
$347$	23.2143	+	4.09332i	1.24621	+	0.219741i	0.488636	+	0.872488i	$0.337495\pi$
$348$		0			0
$349$	14.7087	+	17.5291i	0.787338	+	0.938312i	0.999240	−	0.0389784i	$-0.0124104\pi$
$349$	14.7087	+	17.5291i	0.787338	+	0.938312i	−0.211902	+	0.977291i	$0.567966\pi$
$350$	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	−0.657096	−	0.753807i	$-0.728215\pi$
$353$	−0.541929	+	0.454733i	−0.0288440	+	0.0242030i	0.628252	+	0.778010i	$0.283771\pi$
$354$		0			0
$355$	5.16729	+	0.911132i	0.274251	+	0.0483579i
$356$	8.06440	+	13.9245i	0.427412	+	0.737996i
$357$		0			0
$358$	7.89952	−	13.7037i	0.417502	−	0.724265i
$359$	5.07907	+	8.79721i	0.268063	+	0.464299i	0.968362	−	0.249551i	$-0.0802831\pi$
$359$	5.07907	+	8.79721i	0.268063	+	0.464299i	−0.700298	+	0.713850i	$0.746950\pi$
$360$		0			0
$361$	−4.63535	+	8.02867i	−0.243966	+	0.422561i
$362$	−2.62450	−	4.53868i	−0.137940	−	0.238548i
$363$		0			0
$364$	18.3357	+	10.5531i	0.961051	+	0.553134i
$365$	−9.39023	+	11.1908i	−0.491507	+	0.585755i
$366$		0			0
$367$	−1.79478	−	0.653245i	−0.0936866	−	0.0340991i	0.294752	−	0.955574i	$-0.404763\pi$
$367$	−1.79478	−	0.653245i	−0.0936866	−	0.0340991i	−0.388438	+	0.921475i	$0.626985\pi$
$368$	−4.64324	+	26.7556i	−0.242045	+	1.39473i
$369$		0			0
$370$	−5.34254	−	0.938313i	−0.277745	−	0.0487806i
$371$	7.71925	−	1.36111i	0.400763	−	0.0706654i
$372$		0			0
$373$	−11.8307	−	32.5046i	−0.612571	−	1.68303i	−0.724470	−	0.689306i	$-0.757916\pi$
$373$	−11.8307	−	32.5046i	−0.612571	−	1.68303i	0.111899	−	0.993720i	$-0.464307\pi$
$374$	4.53688	−	3.81212i	0.234596	−	0.197120i
$375$		0			0
$376$	2.48896	−	0.444072i	0.128358	−	0.0229013i
$377$	−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	$0.753886\pi$
$380$	4.97934	+	4.16671i	0.255435	+	0.213748i
$381$		0			0
$382$	−16.4256	−	19.5484i	−0.840405	−	1.00018i
$383$	5.67775	−	2.06653i	0.290120	−	0.105595i	−0.192861	−	0.981226i	$-0.561777\pi$
$383$	5.67775	−	2.06653i	0.290120	−	0.105595i	0.482980	+	0.875631i	$0.339554\pi$
$384$		0			0
$385$	−1.19866	−	6.79794i	−0.0610894	−	0.346455i
$386$	6.18174	+	1.08570i	0.314642	+	0.0552608i
$387$		0			0
$388$	20.2829	+	7.35135i	1.02971	+	0.373208i
$389$	3.99747	−	10.9830i	0.202680	−	0.556858i	−0.796156	−	0.605091i	$-0.793137\pi$
$389$	3.99747	−	10.9830i	0.202680	−	0.556858i	0.998836	+	0.0482330i	$0.0153590\pi$
$390$		0			0
$391$	5.14814	+	4.31980i	0.260353	+	0.218462i
$392$	−4.42110	−	12.0707i	−0.223299	−	0.609664i
$393$		0			0
$394$	11.5685	+	20.0061i	0.582814	+	1.00789i
$395$	−7.97761	−	4.60588i	−0.401397	−	0.231747i
$396$		0			0
$397$	2.31327	−	1.33556i	0.116099	−	0.0670301i	−0.440826	−	0.897593i	$-0.645314\pi$
$397$	2.31327	−	1.33556i	0.116099	−	0.0670301i	0.556925	+	0.830563i	$0.311981\pi$
$398$	−1.12432	−	0.648116i	−0.0563572	−	0.0324871i
$399$		0			0
$400$	11.9745	−	10.1031i	0.598725	−	0.505153i
$401$	2.15776	−	12.2372i	0.107753	−	0.611099i	−0.882332	−	0.470628i	$-0.844027\pi$
$401$	2.15776	−	12.2372i	0.107753	−	0.611099i	0.990085	−	0.140470i	$-0.0448615\pi$
$402$		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	−0.998907	−	0.0467370i	$-0.985118\pi$
$409$	−0.895032	+	5.07598i	−0.0442565	+	0.250991i	0.954651	+	0.297728i	$0.0962288\pi$
$410$	−4.40999	−	1.60173i	−0.217794	−	0.0791040i
$411$		0			0
$412$	29.8484	−	10.9096i	1.47052	−	0.537478i
$413$	−15.2936	+	8.82978i	−0.752550	+	0.434485i
$414$		0			0
$415$	3.26440	−	5.65411i	0.160243	−	0.277549i
$416$	29.3372	+	24.4485i	1.43837	+	1.19869i
$417$		0			0
$418$	−18.3862	+	3.25478i	−0.899296	+	0.159196i
$419$	1.84481	−	2.19856i	0.0901248	−	0.107407i	−0.719097	−	0.694909i	$-0.755444\pi$
$419$	1.84481	−	2.19856i	0.0901248	−	0.107407i	0.809222	+	0.587503i	$0.199889\pi$
$420$		0			0
$421$	−4.61049	+	12.6672i	−0.224701	+	0.617362i	−0.999897	−	0.0143594i	$-0.995429\pi$
$421$	−4.61049	+	12.6672i	−0.224701	+	0.617362i	0.775195	+	0.631721i	$0.217651\pi$
$422$	−8.14726	+	2.97159i	−0.396603	+	0.144655i
$423$		0			0
$424$	14.1492	−	0.0286683i	0.687147	−	0.00139226i
$425$	−0.673287	−	3.81840i	−0.0326592	−	0.185220i
$426$		0			0
$427$	−2.94709	−	8.09707i	−0.142620	−	0.391845i
$428$	0.0104147	+	7.71025i	0.000503414	+	0.372689i
$429$		0			0
$430$	0.0107856	+	15.9696i	0.000520126	+	0.770124i
$431$	−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	$0.622022\pi$
$434$	0.00352637	+	5.22131i	0.000169271	+	0.250631i
$435$		0			0
$436$	−0.00899073	−	6.65605i	−0.000430578	−	0.318767i
$437$	−7.24252	−	19.8987i	−0.346457	−	0.951882i
$438$		0			0
$439$	5.53290	+	31.3787i	0.264071	+	1.49762i	0.771667	+	0.636026i	$0.219423\pi$
$439$	5.53290	+	31.3787i	0.264071	+	1.49762i	−0.507596	+	0.861595i	$0.669466\pi$
$440$	−0.0252467	−	12.4605i	−0.00120359	−	0.594030i
$441$		0			0
$442$	8.87884	−	3.23843i	0.422323	−	0.154036i
$443$	2.16330	−	5.94362i	0.102782	−	0.282390i	−0.877634	−	0.479332i	$-0.840879\pi$
$443$	2.16330	−	5.94362i	0.102782	−	0.282390i	0.980415	+	0.196942i	$0.0631011\pi$
$444$		0			0
$445$	5.38246	−	6.41456i	0.255153	−	0.304079i
$446$	29.8585	−	5.28565i	1.41384	−	0.250283i
$447$		0			0
$448$	2.22669	+	12.3357i	0.105201	+	0.582805i
$449$	4.18149	−	7.24256i	0.197337	−	0.341797i	−0.750327	−	0.661067i	$-0.770104\pi$
$449$	4.18149	−	7.24256i	0.197337	−	0.341797i	0.947664	+	0.319269i	$0.103437\pi$
$450$		0			0
$451$	11.6853	−	6.74653i	0.550241	−	0.317682i
$452$	15.6964	−	5.73706i	0.738298	−	0.269848i
$453$		0			0
$454$	−24.7350	−	8.98389i	−1.16087	−	0.421635i
$455$	1.91172	−	10.8419i	0.0896228	−	0.508276i
$456$		0			0
$457$	−21.5741	+	18.1028i	−1.00919	+	0.846812i	−0.988231	−	0.152968i	$-0.951117\pi$
$457$	−21.5741	+	18.1028i	−1.00919	+	0.846812i	−0.0209605	+	0.999780i	$0.506672\pi$
$458$	−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	$-0.430526\pi$
$461$	−16.8013	−	20.0230i	−0.782513	−	0.932563i	−0.999044	+	0.0437126i	$0.986081\pi$
$462$		0			0
$463$	3.84612	−	21.8124i	0.178744	−	1.01371i	−0.754988	−	0.655738i	$-0.772358\pi$
$463$	3.84612	−	21.8124i	0.178744	−	1.01371i	0.933733	−	0.357971i	$-0.116531\pi$
$464$	−11.4352	−	13.5535i	−0.530867	−	0.629203i
$465$		0			0
$466$	−23.0276	−	13.2743i	−1.06673	−	0.614918i
$467$	−19.1663	+	11.0657i	−0.886910	+	0.512058i	−0.872930	−	0.487845i	$-0.837783\pi$
$467$	−19.1663	+	11.0657i	−0.886910	+	0.512058i	−0.0139792	+	0.999902i	$0.504450\pi$
$468$		0			0
$469$	−0.986466	−	0.569536i	−0.0455508	−	0.0262987i
$470$	−0.658605	−	1.13896i	−0.0303792	−	0.0525363i
$471$		0			0
$472$	−29.9333	+	10.9636i	−1.37779	+	0.504638i
$473$	−35.1815	−	29.5208i	−1.61765	−	1.35737i
$474$		0			0
$475$	−4.17853	+	11.4804i	−0.191724	+	0.526757i
$476$	2.91651	+	1.05706i	0.133678	+	0.0484504i
$477$		0			0
$478$	−28.6084	−	5.02452i	−1.30852	−	0.229816i
$479$	2.06488	+	11.7105i	0.0943470	+	0.535068i	0.994946	+	0.100416i	$0.0320175\pi$
$479$	2.06488	+	11.7105i	0.0943470	+	0.535068i	−0.900599	+	0.434652i	$0.856871\pi$
$480$		0			0
$481$	23.3788	−	8.50920i	1.06598	−	0.387986i
$482$	−12.5329	−	14.9157i	−0.570858	−	0.679389i
$483$		0			0
$484$	10.6098	+	8.87831i	0.482265	+	0.403560i
$485$		−	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	$0.332915\pi$
$488$	−2.73202	−	15.3125i	−0.123673	−	0.693166i
$489$		0			0
$490$	−5.12155	+	4.30339i	−0.231368	+	0.194407i
$491$	2.55319	+	7.01484i	0.115224	+	0.316575i	0.983877	−	0.178845i	$-0.0572362\pi$
$491$	2.55319	+	7.01484i	0.115224	+	0.316575i	−0.868653	+	0.495421i	$0.835014\pi$
$492$		0			0
$493$	−4.32189	+	0.762066i	−0.194648	+	0.0343217i
$494$	−29.3307	−	5.15137i	−1.31965	−	0.231771i
$495$		0			0
$496$	−1.61158	+	9.28636i	−0.0723622	+	0.416970i
$497$	−7.42295	−	2.70173i	−0.332965	−	0.121189i
$498$		0			0
$499$	6.65452	−	7.93054i	0.297897	−	0.355020i	−0.596246	−	0.802802i	$-0.703342\pi$
$499$	6.65452	−	7.93054i	0.297897	−	0.355020i	0.894143	+	0.447782i	$0.147786\pi$
$500$	−16.0866	−	9.25863i	−0.719412	−	0.414058i
$501$		0			0
$502$	−0.342595	−	0.592467i	−0.0152908	−	0.0264431i
$503$	16.9435	−	29.3471i	0.755475	−	1.30852i	−0.189663	−	0.981849i	$-0.560739\pi$
$503$	16.9435	−	29.3471i	0.755475	−	1.30852i	0.945138	−	0.326672i	$-0.105927\pi$
$504$		0			0
$505$	3.43817	+	5.95508i	0.152997	+	0.264998i
$506$	−20.2960	+	35.2085i	−0.902266	+	1.56521i
$507$		0			0
$508$	−3.66880	−	6.33477i	−0.162777	−	0.281060i
$509$	16.7517	+	2.95378i	0.742508	+	0.130924i	0.532090	−	0.846688i	$-0.321407\pi$
$509$	16.7517	+	2.95378i	0.742508	+	0.130924i	0.210417	+	0.977612i	$0.432518\pi$
$510$		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
$518$	7.67568	+	2.78785i	0.337250	+	0.122491i
$519$		0			0
$520$	6.75912	−	18.6883i	0.296407	−	0.819534i
$521$	14.6553	+	25.3837i	0.642060	+	1.11208i	0.984972	+	0.172714i	$0.0552535\pi$
$521$	14.6553	+	25.3837i	0.642060	+	1.11208i	−0.342912	+	0.939368i	$0.611413\pi$
$522$		0			0
$523$	3.33680	+	1.92651i	0.145908	+	0.0842402i	0.571177	−	0.820827i	$-0.306487\pi$
$523$	3.33680	+	1.92651i	0.145908	+	0.0842402i	−0.425269	+	0.905067i	$0.639820\pi$
$524$	−19.3262	−	3.38083i	−0.844270	−	0.147692i
$525$		0			0
$526$	11.2138	−	1.98510i	0.488944	−	0.0865545i
$527$	1.78683	+	1.49932i	0.0778353	+	0.0653116i
$528$		0			0
$529$	−21.6963	−	7.89682i	−0.943319	−	0.343340i
$530$	−2.52299	−	6.91732i	−0.109592	−	0.300469i
$531$		0			0
$532$	−6.29320	−	7.47940i	−0.272845	−	0.324273i
$533$	21.1929	−	3.73687i	0.917965	−	0.161862i
$534$		0			0
$535$	3.77033	−	1.37229i	0.163006	−	0.0593292i
$536$	−1.57780	−	1.31849i	−0.0681506	−	0.0569502i
$537$		0			0
$538$	−9.28484	+	0.00627080i	−0.400298	+	0.000270353i
$539$		−	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	$-0.0309460\pi$
$542$	0.0103749	+	15.3616i	0.000445642	+	0.659839i
$543$		0			0
$544$	4.85901	+	2.78352i	0.208328	+	0.119342i
$545$	−3.25483	+	1.18466i	−0.139421	+	0.0507453i
$546$		0			0
$547$	12.3037	−	2.16948i	0.526069	−	0.0927602i	0.0956949	−	0.995411i	$-0.469493\pi$
$547$	12.3037	−	2.16948i	0.526069	−	0.0927602i	0.430374	+	0.902651i	$0.358382\pi$
$548$	−33.8077	+	28.4460i	−1.44419	+	1.21515i
$549$		0			0
$550$	22.0273	−	8.03412i	0.939245	−	0.342576i
$551$	12.9942	+	4.72950i	0.553572	+	0.201484i
$552$		0			0
$553$	10.6237	+	8.91435i	0.451766	+	0.379077i
$554$	−7.81584	−	44.1514i	−0.332063	−	1.87581i
$555$		0			0
$556$	−9.37920	−	1.64075i	−0.397767	−	0.0695831i
$557$	−3.03004	−	1.74940i	−0.128387	−	0.0741243i	0.434431	−	0.900705i	$-0.356949\pi$
$557$	−3.03004	−	1.74940i	−0.128387	−	0.0741243i	−0.562818	+	0.826581i	$0.690283\pi$
$558$		0			0
$559$	−36.6233	−	63.4335i	−1.54900	−	2.68295i
$560$	5.64029	−	3.27677i	0.238346	−	0.138469i
$561$		0			0
$562$	−9.47855	+	26.0969i	−0.399828	+	1.10083i
$563$	26.9436	+	4.75088i	1.13554	+	0.200226i	0.709653	−	0.704552i	$-0.248852\pi$
$563$	26.9436	+	4.75088i	1.13554	+	0.200226i	0.425885	+	0.904777i	$0.359963\pi$
$564$		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	−0.706573	−	0.707640i	$-0.749760\pi$
$569$	−3.15771	+	2.64963i	−0.132378	+	0.111078i	0.574195	+	0.818719i	$0.305315\pi$
$570$		0			0
$571$	−2.91629	−	0.514220i	−0.122043	−	0.0215194i	0.112293	−	0.993675i	$-0.464180\pi$
$571$	−2.91629	−	0.514220i	−0.122043	−	0.0215194i	−0.234336	+	0.972156i	$0.575292\pi$
$572$	28.6427	+	49.4561i	1.19761	+	2.06787i
$573$		0			0
$574$	6.11963	+	3.52766i	0.255428	+	0.147242i
$575$	13.2953	+	23.0281i	0.554453	+	0.960340i
$576$		0			0
$577$	−4.23106	+	7.32841i	−0.176141	+	0.305086i	−0.940556	−	0.339640i	$-0.889695\pi$
$577$	−4.23106	+	7.32841i	−0.176141	+	0.305086i	0.764414	+	0.644725i	$0.223028\pi$
$578$	−19.6128	+	11.3411i	−0.815786	+	0.471729i
$579$		0			0
$580$	−4.60321	+	7.99793i	−0.191138	+	0.332096i
$581$	−6.31802	+	7.52952i	−0.262115	+	0.312377i
$582$		0			0
$583$	19.8980	+	7.24228i	0.824092	+	0.299945i
$584$	34.3415	−	19.9200i	1.42106	−	0.824294i
$585$		0			0
$586$	−6.50499	+	37.0379i	−0.268719	+	1.53002i
$587$	−45.4714	+	8.01784i	−1.87681	+	0.330932i	−0.991079	−	0.133275i	$-0.957451\pi$
$587$	−45.4714	+	8.01784i	−1.87681	+	0.330932i	−0.885727	+	0.464206i	$0.846340\pi$
$588$		0			0
$589$	−2.51375	−	6.90646i	−0.103577	−	0.284576i
$590$	10.6717	+	12.7006i	0.439345	+	0.522874i
$591$		0			0
$592$	12.7862	+	7.33611i	0.525508	+	0.301512i
$593$	−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
$596$	29.5356	−	35.2959i	1.20982	−	1.44577i
$597$		0			0
$598$	−49.6230	+	41.6958i	−2.02924	+	1.70507i
$599$	23.2555	−	8.46431i	0.950194	−	0.345842i	0.180010	−	0.983665i	$-0.442387\pi$
$599$	23.2555	−	8.46431i	0.950194	−	0.345842i	0.770184	+	0.637822i	$0.220165\pi$
$600$		0			0
$601$	2.55983	+	14.5175i	0.104418	+	0.592182i	0.991451	+	0.130477i	$0.0416509\pi$
$601$	2.55983	+	14.5175i	0.104418	+	0.592182i	−0.887034	+	0.461705i	$0.847238\pi$
$602$	4.15890	−	23.6798i	0.169504	−	0.965116i
$603$		0			0
$604$	−37.3741	−	13.5459i	−1.52073	−	0.551175i
$605$	2.46229	−	6.76510i	0.100107	−	0.275040i
$606$		0			0
$607$	−23.2768	−	19.5315i	−0.944775	−	0.792761i	0.0336346	−	0.999434i	$-0.489292\pi$
$607$	−23.2768	−	19.5315i	−0.944775	−	0.792761i	−0.978410	+	0.206674i	$0.933736\pi$
$608$	−8.87393	−	15.2509i	−0.359885	−	0.618507i
$609$		0			0
$610$	−7.00710	+	4.05187i	−0.283709	+	0.164055i
$611$	5.22602	+	3.01724i	0.211422	+	0.122065i
$612$		0			0
$613$	−8.97166	+	5.17979i	−0.362362	+	0.209210i	−0.670116	−	0.742256i	$-0.733756\pi$
$613$	−8.97166	+	5.17979i	−0.362362	+	0.209210i	0.307754	+	0.951466i	$0.400422\pi$
$614$	16.3440	−	28.3529i	0.659592	−	1.14423i
$615$		0			0
$616$	−3.22007	+	18.4808i	−0.129740	+	0.744614i
$617$	−2.09885	+	11.9032i	−0.0844965	+	0.479204i	0.912968	+	0.408032i	$0.133785\pi$
$617$	−2.09885	+	11.9032i	−0.0844965	+	0.479204i	−0.997464	+	0.0711715i	$0.977326\pi$
$618$		0			0
$619$	1.25371	+	1.49411i	0.0503908	+	0.0600535i	0.790651	−	0.612267i	$-0.209742\pi$
$619$	1.25371	+	1.49411i	0.0503908	+	0.0600535i	−0.740260	+	0.672320i	$0.765298\pi$
$620$	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
$626$	−12.4414	+	34.2545i	−0.497259	+	1.36908i
$627$		0			0
$628$	−3.35768	−	9.18651i	−0.133986	−	0.366582i
$629$	3.15939	−	1.82408i	0.125973	−	0.0727307i
$630$		0			0
$631$	−6.64702	+	11.5130i	−0.264614	+	0.458325i	−0.967462	−	0.253015i	$-0.918578\pi$
$631$	−6.64702	+	11.5130i	−0.264614	+	0.458325i	0.702849	+	0.711340i	$0.251911\pi$
$632$	16.1304	+	19.1446i	0.641634	+	0.761531i
$633$		0			0
$634$	−4.54006	−	25.6467i	−0.180309	−	1.01856i
$635$	−2.44868	+	2.91823i	−0.0971730	+	0.115806i
$636$		0			0
$637$	10.4939	−	28.8319i	0.415785	−	1.14236i
$638$	−9.09349	−	24.9317i	−0.360015	−	0.987057i
$639$		0			0
$640$	11.0457	−	4.07955i	0.436620	−	0.161258i
$641$	−4.99251	−	28.3139i	−0.197192	−	1.11833i	−0.909262	−	0.416225i	$-0.863353\pi$
$641$	−4.99251	−	28.3139i	−0.197192	−	1.11833i	0.712069	−	0.702109i	$-0.247758\pi$
$642$		0			0
$643$	12.8078	+	35.1891i	0.505090	+	1.38772i	0.886247	+	0.463213i	$0.153303\pi$
$643$	12.8078	+	35.1891i	0.505090	+	1.38772i	−0.381157	+	0.924510i	$0.624474\pi$
$644$	−21.2746	+	0.0287370i	−0.838338	+	0.00113239i
$645$		0			0
$646$	−4.36671	+	0.00294919i	−0.171806	+	0.000116034i
$647$	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
$650$	37.3946	−	0.0252556i	1.46674	−	0.000990605i
$651$		0			0
$652$	−0.0112945	−	8.36161i	−0.000442328	−	0.327466i
$653$	−16.8138	−	46.1955i	−0.657974	−	1.80777i	−0.585921	−	0.810368i	$-0.699267\pi$
$653$	−16.8138	−	46.1955i	−0.657974	−	1.80777i	−0.0720526	−	0.997401i	$-0.522955\pi$
$654$		0			0
$655$	1.77292	+	10.0547i	0.0692736	+	0.392870i
$656$	9.78973	+	8.16959i	0.382225	+	0.318969i
$657$		0			0
$658$	0.678710	+	1.86083i	0.0264589	+	0.0725426i
$659$	−9.01137	+	24.7585i	−0.351033	+	0.964456i	0.631006	+	0.775778i	$0.282642\pi$
$659$	−9.01137	+	24.7585i	−0.351033	+	0.964456i	−0.982039	+	0.188678i	$0.939580\pi$
$660$		0			0
$661$	−0.937603	+	1.11739i	−0.0364685	+	0.0434615i	−0.783970	−	0.620798i	$-0.786809\pi$
$661$	−0.937603	+	1.11739i	−0.0364685	+	0.0434615i	0.747502	+	0.664260i	$0.231253\pi$
$662$	3.81412	+	21.5458i	0.148240	+	0.837402i
$663$		0			0
$664$	−13.5687	+	11.4324i	−0.526566	+	0.443663i
$665$	−2.54332	+	4.40516i	−0.0986258	+	0.170825i
$666$		0			0
$667$	26.0646	−	15.0484i	1.00923	−	0.582677i
$668$	11.4499	−	4.18493i	0.443008	−	0.161920i
$669$		0			0
$670$	−0.365285	+	1.00572i	−0.0141122	+	0.0388545i
$671$	4.04215	−	22.9242i	0.156046	−	0.884979i
$672$		0			0
$673$	14.2562	−	11.9623i	0.549534	−	0.461114i	−0.325249	−	0.945628i	$-0.605448\pi$
$673$	14.2562	−	11.9623i	0.549534	−	0.461114i	0.874783	+	0.484514i	$0.161004\pi$
$674$	−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	$-0.241672\pi$
$677$	−2.04257	−	2.43424i	−0.0785022	−	0.0935553i	−0.803866	+	0.594810i	$0.797227\pi$
$678$		0			0
$679$	−2.93499	+	16.6451i	−0.112634	+	0.638782i
$680$	0.500207	−	2.87081i	0.0191821	−	0.110091i
$681$		0			0
$682$	−7.04435	+	12.2202i	−0.269742	+	0.467937i
$683$	−7.95770	+	4.59438i	−0.304493	+	0.175799i	−0.644459	−	0.764639i	$-0.722918\pi$
$683$	−7.95770	+	4.59438i	−0.304493	+	0.175799i	0.339967	+	0.940437i	$0.389584\pi$
$684$		0			0
$685$	19.9118	+	11.4961i	0.760792	+	0.439243i
$686$	22.1463	−	12.8061i	0.845550	−	0.488940i
$687$		0			0
$688$	14.7333	−	40.8221i	0.561701	−	1.55633i
$689$	25.8705	+	21.7080i	0.985589	+	0.827008i
$690$		0			0
$691$	6.14708	−	16.8890i	0.233846	−	0.642487i	−0.766154	−	0.642657i	$-0.777832\pi$
$691$	6.14708	−	16.8890i	0.233846	−	0.642487i	1.00000		0.000170287i	$5.42042e-5\pi$
$692$	0.903886	−	2.49388i	0.0343606	−	0.0948032i
$693$		0			0
$694$	−5.76665	+	32.8339i	−0.218899	+	1.24636i
$695$	0.860413	+	4.87964i	0.0326373	+	0.185095i
$696$		0			0
$697$	2.96524	−	1.07926i	0.112316	−	0.0408799i
$698$	−24.7759	+	20.8180i	−0.937780	+	0.787971i
$699$		0			0
$700$	9.41329	+	7.87705i	0.355789	+	0.297724i
$701$		−	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
$704$	−11.4528	+	31.8675i	−0.431643	+	1.20105i
$705$		0			0
$706$	−0.643607	−	0.765969i	−0.0242225	−	0.0288276i
$707$	−3.54070	−	9.72798i	−0.133162	−	0.365858i
$708$		0			0
$709$	9.23990	−	1.62924i	0.347012	−	0.0611875i	0.00257396	−	0.999997i	$-0.499181\pi$
$709$	9.23990	−	1.62924i	0.347012	−	0.0611875i	0.344438	+	0.938809i	$0.388070\pi$
$710$	−1.28360	+	7.30852i	−0.0481726	+	0.274284i
$711$		0			0
$712$	−19.6845	+	11.4181i	−0.737707	+	0.427911i
$713$	−15.0318	−	5.47115i	−0.562947	−	0.204896i
$714$		0			0
$715$	19.1171	−	22.7829i	0.714938	−	0.852031i
$716$	19.3875	+	11.1585i	0.724546	+	0.417013i
$717$		0			0
$718$	−12.4363	+	7.19129i	−0.464118	+	0.268377i
$719$	−10.7417	+	18.6051i	−0.400596	+	0.693853i	−0.993798	−	0.111201i	$-0.964530\pi$
$719$	−10.7417	+	18.6051i	−0.400596	+	0.693853i	0.593202	+	0.805054i	$0.297864\pi$
$720$		0			0
$721$	12.4487	+	21.5618i	0.463614	+	0.803003i
$722$	−11.3587	−	6.54771i	−0.422726	−	0.243681i
$723$		0			0
$724$	6.41615	−	3.71593i	0.238454	−	0.138102i
$725$	−17.1004	−	3.01526i	−0.635092	−	0.111984i
$726$		0			0
$727$	−22.5451	+	18.9176i	−0.836151	+	0.701614i	−0.956694	−	0.291094i	$-0.905981\pi$
$727$	−22.5451	+	18.9176i	−0.836151	+	0.701614i	0.120543	+	0.992708i	$0.461536\pi$
$728$	−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	$-0.744522\pi$
$733$	−43.1488	−	7.60829i	−1.59374	−	0.281019i	−0.898901	+	0.438151i	$0.855634\pi$
$734$	0.922114	−	2.53882i	0.0340358	−	0.0937096i
$735$		0			0
$736$	−37.8425	−	6.54097i	−1.39489	−	0.241103i
$737$	−1.53859	−	2.66491i	−0.0566746	−	0.0981632i
$738$		0			0
$739$	−21.9574	−	12.6771i	−0.807716	−	0.466335i	0.0384462	−	0.999261i	$-0.487759\pi$
$739$	−21.9574	−	12.6771i	−0.807716	−	0.466335i	−0.846162	+	0.532926i	$0.821093\pi$
$740$	1.32187	−	7.55638i	0.0485930	−	0.277778i
$741$		0			0
$742$	1.93227	+	10.9154i	0.0709360	+	0.400716i
$743$	3.44991	+	2.89482i	0.126565	+	0.106201i	0.703873	−	0.710326i	$-0.251452\pi$
$743$	3.44991	+	2.89482i	0.126565	+	0.106201i	−0.577308	+	0.816526i	$0.695897\pi$
$744$		0			0
$745$	−22.5055	−	8.19135i	−0.824539	−	0.300108i
$746$	45.9572	−	16.7622i	1.68261	−	0.613708i
$747$		0			0
$748$	5.39548	+	6.41247i	0.197278	+	0.234463i
$749$	−5.94874	+	1.04892i	−0.217362	+	0.0383268i
$750$		0			0
$751$	36.9941	−	13.4647i	1.34993	−	0.491335i	0.437006	−	0.899459i	$-0.356039\pi$
$751$	36.9941	−	13.4647i	1.34993	−	0.491335i	0.912927	+	0.408124i	$0.133817\pi$
$752$	0.630390	+	3.51949i	0.0229879	+	0.128343i
$753$		0			0
$754$	−0.0285857	−	42.3254i	−0.00104103	−	1.54140i
$755$			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	$-0.209961\pi$
$758$	−38.4577	+	0.0259735i	−1.39685	+	0.000943402i
$759$		0			0
$760$	−5.88786	+	7.04583i	−0.213575	+	0.255579i
$761$	34.7776	−	12.6580i	1.26069	−	0.458852i	0.376687	−	0.926341i	$-0.377063\pi$
$761$	34.7776	−	12.6580i	1.26069	−	0.458852i	0.883999	+	0.467489i	$0.154841\pi$
$762$		0			0
$763$	5.13539	−	0.905508i	0.185914	−	0.0327816i
$764$	27.6299	−	23.2479i	0.999615	−	0.841080i
$765$		0			0
$766$	2.92794	+	8.02758i	0.105791	+	0.290048i
$767$	−71.4980	−	26.0231i	−2.58164	−	0.939641i
$768$		0			0
$769$	−4.44297	−	3.72810i	−0.160218	−	0.134439i	0.559154	−	0.829064i	$-0.311126\pi$
$769$	−4.44297	−	3.72810i	−0.160218	−	0.134439i	−0.719372	+	0.694625i	$0.755570\pi$
$770$	9.61260	−	1.70166i	0.346414	−	0.0613234i
$771$		0			0
$772$	−1.52951	+	8.74333i	−0.0550483	+	0.314679i
$773$	−36.8149	−	21.2551i	−1.32414	−	0.764492i	−0.339753	−	0.940515i	$-0.610344\pi$
$773$	−36.8149	−	21.2551i	−1.32414	−	0.764492i	−0.984386	+	0.176022i	$0.943677\pi$
$774$		0			0
$775$	4.61456	+	7.99264i	0.165760	+	0.287104i
$776$	−10.3770	+	28.6913i	−0.372513	+	1.02996i
$777$		0			0
$778$	15.5361	+	5.64278i	0.556995	+	0.202304i
$779$	−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	$-0.345512\pi$
$787$	16.8983	+	2.97963i	0.602359	+	0.106212i	0.135851	+	0.990729i	$0.456623\pi$
$788$	−28.2818	+	16.3795i	−1.00750	+	0.583495i
$789$		0			0
$790$	6.50607	−	11.2864i	0.231476	−	0.401554i
$791$	6.54642	+	11.3387i	0.232764	+	0.403159i
$792$		0			0
$793$	18.5627	−	32.1515i	0.659179	−	1.14173i
$794$	1.89098	+	3.27017i	0.0671084	+	0.116054i
$795$		0			0
$796$	0.915501	−	1.59065i	0.0324491	−	0.0563791i
$797$	−4.53298	+	5.40220i	−0.160567	+	0.191356i	−0.840329	−	0.542076i	$-0.817638\pi$
$797$	−4.53298	+	5.40220i	−0.160567	+	0.191356i	0.679763	+	0.733432i	$0.262083\pi$
$798$		0			0
$799$	0.831499	+	0.302641i	0.0294163	+	0.0107067i
$800$	14.2993	+	16.9249i	0.505557	+	0.598384i
$801$		0			0
$802$	17.3081	+	3.03984i	0.611171	+	0.107340i
$803$	58.5114	−	10.3171i	2.06482	−	0.364084i
$804$		0			0
$805$	3.78652	+	10.4034i	0.133457	+	0.366670i
$806$	−17.2232	+	14.4719i	−0.606663	+	0.509749i
$807$		0			0
$808$	−3.28230	−	18.3968i	−0.115471	−	0.647197i
$809$	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	$-0.0283243\pi$
$812$	8.91571	−	10.6545i	0.312880	−	0.373900i
$813$		0			0
$814$	14.1919	+	16.8901i	0.497427	+	0.591998i
$815$	−4.08885	+	1.48822i	−0.143226	+	0.0521301i
$816$		0			0
$817$	5.87673	+	33.3286i	0.205601	+	1.16602i
$818$	−7.17937	−	1.26092i	−0.251021	−	0.0440869i
$819$		0			0
$820$	2.26098	−	6.23820i	0.0789569	−	0.217847i
$821$	5.19050	−	14.2608i	0.181150	−	0.497705i	−0.815568	−	0.578661i	$-0.803575\pi$
$821$	5.19050	−	14.2608i	0.181150	−	0.497705i	0.996718	+	0.0809566i	$0.0257975\pi$
$822$		0			0
$823$	22.8496	+	19.1731i	0.796487	+	0.668332i	0.947342	−	0.320224i	$-0.103758\pi$
$823$	22.8496	+	19.1731i	0.796487	+	0.668332i	−0.150855	+	0.988556i	$0.548203\pi$
$824$	15.4570	+	42.2015i	0.538471	+	1.47016i
$825$		0			0
$826$	−12.5018	−	21.6200i	−0.434993	−	0.752256i
$827$	−7.24554	−	4.18322i	−0.251952	−	0.145465i	0.368706	−	0.929546i	$-0.379801\pi$
$827$	−7.24554	−	4.18322i	−0.251952	−	0.145465i	−0.620658	+	0.784082i	$0.713134\pi$
$828$		0			0
$829$	−26.4946	+	15.2967i	−0.920196	+	0.531276i	−0.883698	−	0.468058i	$-0.844954\pi$
$829$	−26.4946	+	15.2967i	−0.920196	+	0.531276i	−0.0364987	+	0.999334i	$0.511620\pi$
$830$	7.99923	+	4.61116i	0.277657	+	0.160056i
$831$		0			0
$832$	−34.5473	+	41.5124i	−1.19771	+	1.43918i
$833$	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	−0.734399	−	0.678718i	$-0.762536\pi$
$839$	−5.60536	+	4.70346i	−0.193519	+	0.162381i	0.540880	+	0.841100i	$0.318091\pi$
$840$		0			0
$841$	1.62295	−	9.20422i	0.0559639	−	0.317387i
$842$	−17.9185	−	6.50811i	−0.617514	−	0.224284i
$843$		0			0
$844$	−4.21025	−	11.5191i	−0.144923	−	0.396505i
$845$	29.3610	−	16.9516i	1.01005	−	0.583151i
$846$		0			0
$847$	−5.41924	+	9.38639i	−0.186207	+	0.322520i
$848$	0.0540575	+	20.0100i	0.00185634	+	0.687146i
$849$		0			0
$850$	5.39939	−	0.955818i	0.185197	−	0.0327843i
$851$	−16.0820	+	19.1657i	−0.551283	+	0.656993i
$852$		0			0
$853$	−15.5473	+	42.7160i	−0.532331	+	1.46257i	0.323959	+	0.946071i	$0.394986\pi$
$853$	−15.5473	+	42.7160i	−0.532331	+	1.46257i	−0.856290	+	0.516496i	$0.827236\pi$
$854$	11.4482	−	4.17555i	0.391748	−	0.142884i
$855$		0			0
$856$	−10.9039	+	0.0220929i	−0.372688	+	0.000755120i
$857$	3.84017	+	21.7787i	0.131178	+	0.743946i	0.977445	+	0.211188i	$0.0677333\pi$
$857$	3.84017	+	21.7787i	0.131178	+	0.743946i	−0.846268	+	0.532758i	$0.821156\pi$
$858$		0			0
$859$	10.5655	+	29.0285i	0.360491	+	0.990441i	0.978856	+	0.204550i	$0.0655730\pi$
$859$	10.5655	+	29.0285i	0.360491	+	0.990441i	−0.618365	+	0.785891i	$0.712205\pi$
$860$	−22.5845	+	0.0305062i	−0.770123	+	0.00104025i
$861$		0			0
$862$	−0.0240840	−	35.6599i	−0.000820303	−	1.21458i
$863$	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
$866$	−0.0148674	−	22.0134i	−0.000505215	−	0.748046i
$867$		0			0
$868$	−7.38404	+	0.00997407i	−0.250631	+	0.000338542i
$869$	12.8137	+	35.2053i	0.434675	+	1.19426i
$870$		0			0
$871$	−0.852216	−	4.83316i	−0.0288762	−	0.163765i
$872$	9.41306	−	0.0190722i	0.318766	−	0.000645866i
$873$		0			0
$874$	28.1340	−	10.2615i	0.951648	−	0.347100i
$875$	4.97337	−	13.6642i	0.168131	−	0.461935i
$876$		0			0
$877$	7.68788	−	9.16206i	0.259601	−	0.309381i	−0.620463	−	0.784236i	$-0.713055\pi$
$877$	7.68788	−	9.16206i	0.259601	−	0.309381i	0.880064	+	0.474855i	$0.157500\pi$
$878$	−44.3708	+	7.85468i	−1.49744	+	0.265083i
$879$		0			0
$880$	17.6218	−	0.0476057i	0.594030	−	0.00160479i
$881$	−18.8243	+	32.6046i	−0.634205	+	1.09848i	0.352478	+	0.935820i	$0.385339\pi$
$881$	−18.8243	+	32.6046i	−0.634205	+	1.09848i	−0.986683	+	0.162655i	$0.947994\pi$
$882$		0			0
$883$	19.8345	−	11.4515i	0.667485	−	0.385373i	−0.127638	−	0.991821i	$-0.540739\pi$
$883$	19.8345	−	11.4515i	0.667485	−	0.385373i	0.795123	+	0.606448i	$0.207406\pi$
$884$	4.58831	+	12.5535i	0.154321	+	0.422219i
$885$		0			0
$886$	8.40762	+	3.05369i	0.282459	+	0.102591i
$887$	−0.995710	+	5.64695i	−0.0334327	+	0.189606i	−0.996950	−	0.0780387i	$-0.975134\pi$
$887$	−0.995710	+	5.64695i	−0.0334327	+	0.189606i	0.963518	+	0.267645i	$0.0862454\pi$
$888$		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
$896$	−17.4431	+	3.16080i	−0.582734	+	0.105595i
$897$		0			0
$898$	10.2465	+	5.90660i	0.341931	+	0.197106i
$899$	9.04655	−	5.22303i	0.301719	−	0.174198i
$900$		0			0
$901$	4.28862	+	2.47604i	0.142875	+	0.0824888i
$902$	9.55219	+	16.5191i	0.318053	+	0.550026i
$903$		0			0
$904$	8.12841	+	22.1926i	0.270347	+	0.738116i
$905$	−2.95572	−	2.48014i	−0.0982513	−	0.0824426i
$906$		0			0
$907$	8.42248	−	23.1406i	0.279664	−	0.768370i	−0.717737	−	0.696315i	$-0.754822\pi$
$907$	8.42248	−	23.1406i	0.279664	−	0.768370i	0.997401	−	0.0720557i	$-0.0229559\pi$
$908$	12.6815	−	34.9891i	0.420851	−	1.16116i
$909$		0			0
$910$	15.3346	+	2.69322i	0.508336	+	0.0892795i
$911$	−6.32793	−	35.8875i	−0.209654	−	1.18901i	−0.889947	−	0.456065i	$-0.849259\pi$
$911$	−6.32793	−	35.8875i	−0.209654	−	1.18901i	0.680293	−	0.732940i	$-0.261853\pi$
$912$		0			0
$913$	−24.9517	+	9.08166i	−0.825780	+	0.300559i
$914$	−25.6218	−	30.4930i	−0.847494	−	1.00862i
$915$		0			0
$916$	11.3979	−	13.6208i	0.376596	−	0.450043i
$917$		−	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	$0.348236\pi$
$920$	3.51018	+	19.6740i	0.115727	+	0.648634i
$921$		0			0
$922$	28.3007	−	23.7797i	0.932034	−	0.783143i
$923$	−11.6405	−	31.9819i	−0.383151	−	1.05270i
$924$		0			0
$925$	14.2153	−	2.50654i	0.467397	−	0.0824146i
$926$	30.8511	+	5.41840i	1.01383	+	0.178060i
$927$		0			0
$928$	19.1565	−	16.1848i	0.628845	−	0.531292i
$929$	−14.0864	−	5.12703i	−0.462160	−	0.168212i	0.100438	−	0.994943i	$-0.467976\pi$
$929$	−14.0864	−	5.12703i	−0.462160	−	0.168212i	−0.562598	+	0.826731i	$0.690198\pi$
$930$		0			0
$931$	−9.11238	+	10.8597i	−0.298646	+	0.355913i
$932$	18.7506	−	32.5786i	0.614197	−	1.06715i
$933$		0			0
$934$	−15.6675	−	27.0946i	−0.512656	−	0.886564i
$935$	2.18052	−	3.77677i	0.0713106	−	0.123514i
$936$		0			0
$937$	−9.57278	−	16.5805i	−0.312729	−	0.541663i	0.666223	−	0.745753i	$-0.267910\pi$
$937$	−9.57278	−	16.5805i	−0.312729	−	0.541663i	−0.978952	+	0.204090i	$0.934577\pi$
$938$	0.804504	−	1.39562i	0.0262680	−	0.0455685i
$939$		0			0
$940$	1.61010	−	0.932496i	0.0525158	−	0.0304147i
$941$	36.4053	+	6.41923i	1.18678	+	0.209261i	0.731975	−	0.681331i	$-0.238599\pi$
$941$	36.4053	+	6.41923i	1.18678	+	0.209261i	0.454803	+	0.890592i	$0.349710\pi$
$942$		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	$-0.355110\pi$
$947$	−16.0406	−	19.1164i	−0.521248	−	0.621199i	−0.960875	+	0.276981i	$0.910666\pi$
$948$		0			0
$949$	93.3185	+	16.4546i	3.02925	+	0.534138i
$950$	−16.2397	−	5.89836i	−0.526887	−	0.191368i
$951$		0			0
$952$	−1.49213	+	4.12557i	−0.0483601	+	0.133711i
$953$	7.31014	+	12.6615i	0.236799	+	0.410147i	0.959794	−	0.280706i	$-0.0905685\pi$
$953$	7.31014	+	12.6615i	0.236799	+	0.410147i	−0.722995	+	0.690853i	$0.757235\pi$
$954$		0			0
$955$	−16.2733	−	9.39537i	−0.526590	−	0.304027i
$956$	7.07841	−	40.4632i	0.228932	−	1.30867i
$957$		0			0
$958$	−16.5592	+	2.93137i	−0.535004	+	0.0947083i
$959$	−26.5164	−	22.2499i	−0.856258	−	0.718486i
$960$		0			0
$961$	23.9132	+	8.70369i	0.771393	+	0.280764i
$962$	12.0562	+	33.0545i	0.388706	+	1.06572i
$963$		0			0
$964$	21.0819	−	17.7384i	0.679004	−	0.571316i
$965$	4.54883	−	0.802081i	0.146432	−	0.0258199i
$966$		0			0
$967$	48.8192	−	17.7687i	1.56992	−	0.571404i	0.596937	−	0.802288i	$-0.296384\pi$
$967$	48.8192	−	17.7687i	1.56992	−	0.571404i	0.972981	+	0.230884i	$0.0741619\pi$
$968$	−12.5457	+	15.0130i	−0.403234	+	0.482537i
$969$		0			0
$970$	15.8771	−	0.0107231i	0.509783	−	0.000344297i
$971$			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
$974$	0.0211259	+	31.2800i	0.000676918	+	1.00228i
$975$		0			0
$976$	21.6526	−	3.87828i	0.693083	−	0.124141i
$977$	7.72505	−	2.81169i	0.247146	−	0.0899539i	−0.215477	−	0.976509i	$-0.569131\pi$
$977$	7.72505	−	2.81169i	0.247146	−	0.0899539i	0.462623	+	0.886555i	$0.346908\pi$
$978$		0			0
$979$	−33.5386	+	5.91376i	−1.07190	+	0.189004i
$980$	−6.09081	−	7.23886i	−0.194564	−	0.231237i
$981$		0			0
$982$	−9.91804	+	3.61746i	−0.316497	+	0.115438i
$983$	22.5289	+	8.19984i	0.718559	+	0.261534i	0.675314	−	0.737530i	$-0.264008\pi$
$983$	22.5289	+	8.19984i	0.718559	+	0.261534i	0.0432453	+	0.999064i	$0.486230\pi$
$984$		0			0
$985$	13.0285	+	10.9322i	0.415123	+	0.348330i
$986$	−1.08185	−	6.11135i	−0.0344532	−	0.194625i
$987$		0			0
$988$	7.25711	−	41.4847i	0.230880	−	1.31981i
$989$	63.7900	+	36.8292i	2.02840	+	1.17110i
$990$		0			0
$991$	8.43544	+	14.6106i	0.267960	+	0.464121i	0.968335	−	0.249654i	$-0.0803170\pi$
$991$	8.43544	+	14.6106i	0.267960	+	0.464121i	−0.700375	+	0.713776i	$0.746984\pi$
$992$	−13.1344	−	2.27025i	−0.417019	−	0.0720805i
$993$		0			0
$994$	3.81374	−	10.5002i	0.120964	−	0.333047i
$995$	−0.940553	−	0.165845i	−0.0298175	−	0.00525763i
$996$		0			0
$997$	−21.3234	−	25.4122i	−0.675317	−	0.804812i	0.314180	−	0.949363i	$-0.398270\pi$
$997$	−21.3234	−	25.4122i	−0.675317	−	0.804812i	−0.989497	+	0.144552i	$0.953826\pi$
$998$	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.37.17		204
3.2	odd	2		216.2.t.a.157.18	✓	204
8.5	even	2	inner	648.2.t.a.37.3		204
12.11	even	2		864.2.bf.a.49.15		204
24.5	odd	2		216.2.t.a.157.32	yes	204
24.11	even	2		864.2.bf.a.49.20		204
27.11	odd	18		216.2.t.a.205.32	yes	204
27.16	even	9	inner	648.2.t.a.613.3		204
108.11	even	18		864.2.bf.a.529.20		204
216.11	even	18		864.2.bf.a.529.15		204
216.173	odd	18		216.2.t.a.205.18	yes	204
216.205	even	18	inner	648.2.t.a.613.17		204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.t.a.157.18	✓	204	3.2	odd	2
216.2.t.a.157.32	yes	204	24.5	odd	2
216.2.t.a.205.18	yes	204	216.173	odd	18
216.2.t.a.205.32	yes	204	27.11	odd	18
648.2.t.a.37.3		204	8.5	even	2	inner
648.2.t.a.37.17		204	1.1	even	1	trivial
648.2.t.a.613.3		204	27.16	even	9	inner
648.2.t.a.613.17		204	216.205	even	18	inner
864.2.bf.a.49.15		204	12.11	even	2
864.2.bf.a.49.20		204	24.11	even	2
864.2.bf.a.529.15		204	216.11	even	18
864.2.bf.a.529.20		204	108.11	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:	\( N \)	\(=\)	\( 648 = 2^{3} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	648.t (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.000955132 + 1.41421i) q^{2} +(-2.00000 + 0.00270152i) q^{4} +(0.355965 + 0.978005i) q^{5} +(-0.272085 - 1.54307i) q^{7} +(-0.00573079 - 2.82842i) q^{8} +(-1.38277 + 0.504344i) q^{10} +(1.44773 - 3.97760i) q^{11} +(4.33941 - 5.17151i) q^{13} +(2.18198 - 0.386261i) q^{14} +(3.99999 - 0.0108061i) q^{16} +(0.494959 - 0.857294i) q^{17} +(-2.70129 + 1.55959i) q^{19} +(-0.714571 - 1.95505i) q^{20} +(5.62656 + 2.04360i) q^{22} +(-1.17888 + 6.68573i) q^{23} +(3.00044 - 2.51767i) q^{25} +(7.31776 + 6.13191i) q^{26} +(0.548339 + 3.08541i) q^{28} +(-2.84964 - 3.39607i) q^{29} +(-0.409166 + 2.32049i) q^{31} +(0.0191026 + 5.65682i) q^{32} +(1.21287 + 0.699158i) q^{34} +(1.41228 - 0.815381i) q^{35} +(3.19157 + 1.84266i) q^{37} +(-2.20817 - 3.81871i) q^{38} +(2.76417 - 1.01242i) q^{40} +(2.44191 + 2.04900i) q^{41} +(3.71087 - 10.1955i) q^{43} +(-2.88471 + 7.95911i) q^{44} +(-9.45618 - 1.66079i) q^{46} +(0.155220 + 0.880296i) q^{47} +(4.27080 - 1.55445i) q^{49} +(3.56338 + 4.24086i) q^{50} +(-8.66484 + 10.3547i) q^{52} +5.00251i q^{53} +4.40546 q^{55} +(-4.36290 + 0.778415i) q^{56} +(4.80005 - 4.03325i) q^{58} +(-3.85475 - 10.5908i) q^{59} +(5.41575 - 0.954943i) q^{61} +(-3.28206 - 0.576431i) q^{62} +(-7.99993 + 0.0324182i) q^{64} +(6.60244 + 2.40309i) q^{65} +(0.467287 - 0.556891i) q^{67} +(-0.987601 + 1.71592i) q^{68} +(1.15447 + 1.99649i) q^{70} +(2.52073 - 4.36603i) q^{71} +(7.01816 + 12.1558i) q^{73} +(-2.60286 + 4.51532i) q^{74} +(5.39836 - 3.12648i) q^{76} +(-6.53164 - 1.15170i) q^{77} +(-6.78017 + 5.68924i) q^{79} +(1.43442 + 3.90816i) q^{80} +(-2.89539 + 3.45533i) q^{82} +(-4.03223 - 4.80543i) q^{83} +(1.01463 + 0.178906i) q^{85} +(14.4222 + 5.23823i) q^{86} +(-11.2586 - 4.07199i) q^{88} +(-4.02279 - 6.96768i) q^{89} +(-9.16071 - 5.28894i) q^{91} +(2.33969 - 13.3746i) q^{92} +(-1.24478 + 0.220355i) q^{94} +(-2.48685 - 2.08672i) q^{95} +(-10.1365 - 3.68937i) q^{97} +(2.20240 + 6.03834i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q + 6 q^{2} - 6 q^{4} - 12 q^{7} + 3 q^{8} - 3 q^{10} + 21 q^{14} - 6 q^{16} + 6 q^{17} - 15 q^{20} - 6 q^{22} + 12 q^{23} - 12 q^{25} + 30 q^{26} - 12 q^{28} - 12 q^{31} + 36 q^{32} + 42 q^{38} - 21 q^{40}+ \cdots - 54 q^{98}+O(q^{100}) \) 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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