LMFDB - Embedded newform 558.2.ba.e.541.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [558,2,Mod(19,558)] 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("558.19"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(558, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([0, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 558 = 2 \cdot 3^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	558.ba (of order $15$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,2,0,-2,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$4.45565243279$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\Q(\zeta_{15})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1 $ x^8 - x^7 + x^5 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 186)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			541.1
Root			$-0.978148 + 0.207912i$ of defining polynomial
Character	$\chi$	$=$	558.541
Dual form			558.2.ba.e.361.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.309017 + 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(-0.360114 + 0.623735i) q^{5} +(0.173699 - 1.65264i) q^{7} +(0.809017 - 0.587785i) q^{8} +(-0.481926 - 0.535233i) q^{10} +(1.28716 - 0.573083i) q^{11} +(2.72256 + 0.578699i) q^{13} +(1.51807 + 0.675890i) q^{14} +(0.309017 + 0.951057i) q^{16} +(0.388870 + 0.173136i) q^{17} +(2.25638 - 0.479607i) q^{19} +(0.657960 - 0.292943i) q^{20} +(0.147278 + 1.40126i) q^{22} +(4.74803 - 3.44964i) q^{23} +(2.24064 + 3.88090i) q^{25} +(-1.39169 + 2.41048i) q^{26} +(-1.11192 + 1.23491i) q^{28} +(-0.0752842 + 0.231701i) q^{29} +(4.91949 + 2.60741i) q^{31} -1.00000 q^{32} +(-0.284829 + 0.316335i) q^{34} +(0.968255 + 0.703479i) q^{35} +(1.38479 + 2.39853i) q^{37} +(-0.241125 + 2.29415i) q^{38} +(0.0752842 + 0.716282i) q^{40} +(-3.38286 - 3.75704i) q^{41} +(-2.77823 + 0.590530i) q^{43} +(-1.37819 - 0.292943i) q^{44} +(1.81359 + 5.58164i) q^{46} +(2.12920 + 6.55302i) q^{47} +(4.14600 + 0.881260i) q^{49} +(-4.38335 + 0.931709i) q^{50} +(-1.86245 - 2.06846i) q^{52} +(-0.501380 - 4.77031i) q^{53} +(-0.106074 + 1.00922i) q^{55} +(-0.830869 - 1.43911i) q^{56} +(-0.197097 - 0.143199i) q^{58} +(8.08107 - 8.97493i) q^{59} -2.61994 q^{61} +(-4.00000 + 3.87298i) q^{62} +(0.309017 - 0.951057i) q^{64} +(-1.34139 + 1.48976i) q^{65} +(2.62464 - 4.54600i) q^{67} +(-0.212835 - 0.368642i) q^{68} +(-0.968255 + 0.703479i) q^{70} +(1.12618 + 10.7149i) q^{71} +(-5.42610 + 2.41585i) q^{73} +(-2.70906 + 0.575828i) q^{74} +(-2.10735 - 0.938254i) q^{76} +(-0.723518 - 2.22676i) q^{77} +(-12.2359 - 5.44777i) q^{79} +(-0.704489 - 0.149744i) q^{80} +(4.61852 - 2.05630i) q^{82} +(4.01038 + 4.45398i) q^{83} +(-0.248028 + 0.180203i) q^{85} +(0.296892 - 2.82474i) q^{86} +(0.704489 - 1.22021i) q^{88} +(0.481926 + 0.350140i) q^{89} +(1.42928 - 4.39888i) q^{91} -5.86889 q^{92} -6.89025 q^{94} +(-0.513403 + 1.58009i) q^{95} +(-4.23452 - 3.07656i) q^{97} +(-2.11931 + 3.67076i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} - 2 q^{4} - 3 q^{5} - 4 q^{7} + 2 q^{8} - 12 q^{10} - 3 q^{11} + 11 q^{13} + 4 q^{14} - 2 q^{16} + 2 q^{19} - 3 q^{20} - 12 q^{22} + 6 q^{23} - q^{25} + 4 q^{26} + 6 q^{28} - 3 q^{29} - 8 q^{31}+ \cdots + 11 q^{98}+O(q^{100}) $ 8 * q + 2 * q^2 - 2 * q^4 - 3 * q^5 - 4 * q^7 + 2 * q^8 - 12 * q^10 - 3 * q^11 + 11 * q^13 + 4 * q^14 - 2 * q^16 + 2 * q^19 - 3 * q^20 - 12 * q^22 + 6 * q^23 - q^25 + 4 * q^26 + 6 * q^28 - 3 * q^29 - 8 * q^31 - 8 * q^32 - 24 * q^35 + 8 * q^37 + 18 * q^38 + 3 * q^40 + 3 * q^41 - 15 * q^43 - 3 * q^44 + 9 * q^46 + 12 * q^47 + 39 * q^49 - 4 * q^50 - 4 * q^52 + 36 * q^53 - 6 * q^55 - 11 * q^56 - 12 * q^58 - 21 * q^59 - 70 * q^61 - 32 * q^62 - 2 * q^64 + 27 * q^65 + 17 * q^67 - 15 * q^68 + 24 * q^70 + 12 * q^71 - q^73 - 18 * q^74 - 3 * q^76 - 24 * q^77 - 33 * q^79 - 3 * q^80 + 27 * q^82 + 54 * q^83 + 30 * q^85 - 35 * q^86 + 3 * q^88 + 12 * q^89 + 8 * q^91 + 6 * q^92 - 12 * q^94 - 18 * q^95 - 9 * q^97 + 11 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/558\mathbb{Z}\right)^\times$.

$n$	$127$	$497$
$\chi(n)$	$e\left(\frac{11}{15}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.309017	+	0.951057i	−0.218508	+	0.672499i
$2$	−0.309017	+	0.951057i	−0.218508	+	0.672499i
$3$		0			0
$3$		0			0
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$	−0.360114	+	0.623735i	−0.161048	+	0.278943i	−0.935245	−	0.354002i	$-0.884821\pi$
$5$	−0.360114	+	0.623735i	−0.161048	+	0.278943i	0.774197	+	0.632945i	$0.218154\pi$
$6$		0			0
$7$	0.173699	−	1.65264i	0.0656521	−	0.624638i	−0.911383	−	0.411559i	$-0.864984\pi$
$7$	0.173699	−	1.65264i	0.0656521	−	0.624638i	0.977035	−	0.213078i	$-0.0683490\pi$
$8$	0.809017	−	0.587785i	0.286031	−	0.207813i
$9$		0			0
$10$	−0.481926	−	0.535233i	−0.152398	−	0.169256i
$11$	1.28716	−	0.573083i	0.388095	−	0.172791i	−0.203408	−	0.979094i	$-0.565202\pi$
$11$	1.28716	−	0.573083i	0.388095	−	0.172791i	0.591502	+	0.806303i	$0.298535\pi$
$12$		0			0
$13$	2.72256	+	0.578699i	0.755103	+	0.160502i	0.569351	−	0.822095i	$-0.307195\pi$
$13$	2.72256	+	0.578699i	0.755103	+	0.160502i	0.185752	+	0.982597i	$0.440528\pi$
$14$	1.51807	+	0.675890i	0.405722	+	0.180639i
$15$		0			0
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	0.388870	+	0.173136i	0.0943147	+	0.0419916i	0.453352	−	0.891332i	$-0.350228\pi$
$17$	0.388870	+	0.173136i	0.0943147	+	0.0419916i	−0.359037	+	0.933323i	$0.616895\pi$
$18$		0			0
$19$	2.25638	−	0.479607i	0.517648	−	0.110029i	0.0583230	−	0.998298i	$-0.481425\pi$
$19$	2.25638	−	0.479607i	0.517648	−	0.110029i	0.459325	+	0.888268i	$0.348091\pi$
$20$	0.657960	−	0.292943i	0.147124	−	0.0655040i
$21$		0			0
$22$	0.147278	+	1.40126i	0.0313998	+	0.298749i
$23$	4.74803	−	3.44964i	0.990032	−	0.719301i	0.0301042	−	0.999547i	$-0.490416\pi$
$23$	4.74803	−	3.44964i	0.990032	−	0.719301i	0.959928	+	0.280246i	$0.0904161\pi$
$24$		0			0
$25$	2.24064	+	3.88090i	0.448127	+	0.776179i
$26$	−1.39169	+	2.41048i	−0.272933	+	0.472735i
$27$		0			0
$28$	−1.11192	+	1.23491i	−0.210133	+	0.233377i
$29$	−0.0752842	+	0.231701i	−0.0139799	+	0.0430258i	−0.957803	−	0.287425i	$-0.907201\pi$
$29$	−0.0752842	+	0.231701i	−0.0139799	+	0.0430258i	0.943823	+	0.330451i	$0.107201\pi$
$30$		0			0
$31$	4.91949	+	2.60741i	0.883567	+	0.468304i
$31$	4.91949	+	2.60741i	0.883567	+	0.468304i
$32$	−1.00000			−0.176777
$33$		0			0
$34$	−0.284829	+	0.316335i	−0.0488478	+	0.0542510i
$35$	0.968255	+	0.703479i	0.163665	+	0.118910i
$36$		0			0
$37$	1.38479	+	2.39853i	0.227658	+	0.394315i	0.957114	−	0.289713i	$-0.0935599\pi$
$37$	1.38479	+	2.39853i	0.227658	+	0.394315i	−0.729456	+	0.684028i	$0.760227\pi$
$38$	−0.241125	+	2.29415i	−0.0391156	+	0.372160i
$39$		0			0
$40$	0.0752842	+	0.716282i	0.0119035	+	0.113254i
$41$	−3.38286	−	3.75704i	−0.528314	−	0.586752i	0.418628	−	0.908158i	$-0.362511\pi$
$41$	−3.38286	−	3.75704i	−0.528314	−	0.586752i	−0.946941	+	0.321406i	$0.895845\pi$
$42$		0			0
$43$	−2.77823	+	0.590530i	−0.423676	+	0.0900551i	−0.414815	−	0.909906i	$-0.636154\pi$
$43$	−2.77823	+	0.590530i	−0.423676	+	0.0900551i	−0.00886054	+	0.999961i	$0.502820\pi$
$44$	−1.37819	−	0.292943i	−0.207770	−	0.0441628i
$45$		0			0
$46$	1.81359	+	5.58164i	0.267399	+	0.822968i
$47$	2.12920	+	6.55302i	0.310576	+	0.955856i	0.977537	+	0.210763i	$0.0675948\pi$
$47$	2.12920	+	6.55302i	0.310576	+	0.955856i	−0.666961	+	0.745093i	$0.732405\pi$
$48$		0			0
$49$	4.14600	+	0.881260i	0.592286	+	0.125894i
$50$	−4.38335	+	0.931709i	−0.619899	+	0.131764i
$51$		0			0
$52$	−1.86245	−	2.06846i	−0.258275	−	0.286844i
$53$	−0.501380	−	4.77031i	−0.0688699	−	0.655253i	−0.973442	−	0.228933i	$-0.926476\pi$
$53$	−0.501380	−	4.77031i	−0.0688699	−	0.655253i	0.904572	−	0.426320i	$-0.140190\pi$
$54$		0			0
$55$	−0.106074	+	1.00922i	−0.0143030	+	0.136084i
$56$	−0.830869	−	1.43911i	−0.111030	−	0.192309i
$57$		0			0
$58$	−0.197097	−	0.143199i	−0.0258801	−	0.0188030i
$59$	8.08107	−	8.97493i	1.05207	−	1.16844i	0.0667365	−	0.997771i	$-0.478741\pi$
$59$	8.08107	−	8.97493i	1.05207	−	1.16844i	0.985329	−	0.170666i	$-0.0545920\pi$
$60$		0			0
$61$	−2.61994			−0.335449			−0.167725	−	0.985834i	$-0.553642\pi$
$61$	−2.61994			−0.335449			−0.167725	+	0.985834i	$0.553642\pi$
$62$	−4.00000	+	3.87298i	−0.508001	+	0.491869i
$63$		0			0
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	−1.34139	+	1.48976i	−0.166379	+	0.184782i
$66$		0			0
$67$	2.62464	−	4.54600i	0.320650	−	0.555383i	−0.659972	−	0.751290i	$-0.729432\pi$
$67$	2.62464	−	4.54600i	0.320650	−	0.555383i	0.980622	+	0.195908i	$0.0627652\pi$
$68$	−0.212835	−	0.368642i	−0.0258101	−	0.0447044i
$69$		0			0
$70$	−0.968255	+	0.703479i	−0.115729	+	0.0840818i
$71$	1.12618	+	10.7149i	0.133653	+	1.27162i	0.831560	+	0.555436i	$0.187448\pi$
$71$	1.12618	+	10.7149i	0.133653	+	1.27162i	−0.697906	+	0.716189i	$0.745885\pi$
$72$		0			0
$73$	−5.42610	+	2.41585i	−0.635076	+	0.282754i	−0.698914	−	0.715206i	$-0.746333\pi$
$73$	−5.42610	+	2.41585i	−0.635076	+	0.282754i	0.0638372	+	0.997960i	$0.479666\pi$
$74$	−2.70906	+	0.575828i	−0.314921	+	0.0669386i
$75$		0			0
$76$	−2.10735	−	0.938254i	−0.241730	−	0.107625i
$77$	−0.723518	−	2.22676i	−0.0824525	−	0.253763i
$78$		0			0
$79$	−12.2359	−	5.44777i	−1.37665	−	0.612923i	−0.420898	−	0.907108i	$-0.638285\pi$
$79$	−12.2359	−	5.44777i	−1.37665	−	0.612923i	−0.955748	+	0.294185i	$0.904952\pi$
$80$	−0.704489	−	0.149744i	−0.0787642	−	0.0167419i
$81$		0			0
$82$	4.61852	−	2.05630i	0.510030	−	0.227080i
$83$	4.01038	+	4.45398i	0.440196	+	0.488888i	0.921890	−	0.387452i	$-0.126645\pi$
$83$	4.01038	+	4.45398i	0.440196	+	0.488888i	−0.481693	+	0.876340i	$0.659978\pi$
$84$		0			0
$85$	−0.248028	+	0.180203i	−0.0269024	+	0.0195458i
$86$	0.296892	−	2.82474i	0.0320146	−	0.304599i
$87$		0			0
$88$	0.704489	−	1.22021i	0.0750987	−	0.130075i
$89$	0.481926	+	0.350140i	0.0510841	+	0.0371147i	0.613034	−	0.790056i	$-0.289949\pi$
$89$	0.481926	+	0.350140i	0.0510841	+	0.0371147i	−0.561950	+	0.827171i	$0.689949\pi$
$90$		0			0
$91$	1.42928	−	4.39888i	0.149830	−	0.461128i
$92$	−5.86889			−0.611874
$93$		0			0
$94$	−6.89025			−0.710675
$95$	−0.513403	+	1.58009i	−0.0526741	+	0.162114i
$96$		0			0
$97$	−4.23452	−	3.07656i	−0.429951	−	0.312377i	0.351679	−	0.936121i	$-0.385611\pi$
$97$	−4.23452	−	3.07656i	−0.429951	−	0.312377i	−0.781629	+	0.623743i	$0.785611\pi$
$98$	−2.11931	+	3.67076i	−0.214083	+	0.370802i
$99$		0			0
$100$	0.468421	−	4.45672i	0.0468421	−	0.445672i
$101$	−8.02685	+	5.83184i	−0.798701	+	0.580290i	−0.910533	−	0.413437i	$-0.864328\pi$
$101$	−8.02685	+	5.83184i	−0.798701	+	0.580290i	0.111832	+	0.993727i	$0.464328\pi$
$102$		0			0
$103$	−12.2525	−	13.6078i	−1.20728	−	1.34082i	−0.924288	−	0.381695i	$-0.875340\pi$
$103$	−12.2525	−	13.6078i	−1.20728	−	1.34082i	−0.282990	−	0.959123i	$-0.591326\pi$
$104$	2.54275	−	1.13211i	0.249337	−	0.111012i
$105$		0			0
$106$	4.69177	+	0.997267i	0.455705	+	0.0968631i
$107$	4.08531	+	1.81890i	0.394942	+	0.175840i	0.594592	−	0.804028i	$-0.297314\pi$
$107$	4.08531	+	1.81890i	0.394942	+	0.175840i	−0.199650	+	0.979867i	$0.563980\pi$
$108$		0			0
$109$	−3.04131	−	9.36018i	−0.291304	−	0.896543i	−0.984438	−	0.175733i	$-0.943770\pi$
$109$	−3.04131	−	9.36018i	−0.291304	−	0.896543i	0.693133	−	0.720809i	$-0.256230\pi$
$110$	−0.927051	−	0.412750i	−0.0883908	−	0.0393541i
$111$		0			0
$112$	1.62543	−	0.345495i	0.153588	−	0.0326462i
$113$	10.0295	−	4.46541i	0.943494	−	0.420071i	0.123437	−	0.992352i	$-0.460608\pi$
$113$	10.0295	−	4.46541i	0.943494	−	0.420071i	0.820057	+	0.572282i	$0.193942\pi$
$114$		0			0
$115$	0.441835	+	4.20378i	0.0412013	+	0.392004i
$116$	0.197097	−	0.143199i	0.0183000	−	0.0132957i
$117$		0			0
$118$	6.03848	+	10.4590i	0.555887	+	0.962825i
$119$	0.353677	−	0.612586i	0.0324215	−	0.0561557i
$120$		0			0
$121$	−6.03207	+	6.69929i	−0.548370	+	0.609026i
$122$	0.809607	−	2.49171i	0.0732984	−	0.225589i
$123$		0			0
$124$	−2.44736	−	5.00104i	−0.219779	−	0.449107i
$125$	−6.82867			−0.610775
$126$		0			0
$127$	10.9291	−	12.1380i	0.969799	−	1.07707i	−0.0271975	−	0.999630i	$-0.508658\pi$
$127$	10.9291	−	12.1380i	0.969799	−	1.07707i	0.996997	−	0.0774413i	$-0.0246750\pi$
$128$	0.809017	+	0.587785i	0.0715077	+	0.0519534i
$129$		0			0
$130$	−1.00234	−	1.73610i	−0.0879106	−	0.152266i
$131$	0.744436	−	7.08284i	0.0650417	−	0.618830i	−0.912644	−	0.408756i	$-0.865963\pi$
$131$	0.744436	−	7.08284i	0.0650417	−	0.618830i	0.977685	−	0.210074i	$-0.0673706\pi$
$132$		0			0
$133$	−0.400686	−	3.81227i	−0.0347439	−	0.330566i
$134$	3.51245	+	3.90097i	0.303429	+	0.336992i
$135$		0			0
$136$	0.416369	−	0.0885019i	0.0357033	−	0.00758898i
$137$	−14.1799	−	3.01403i	−1.21147	−	0.257506i	−0.442486	−	0.896775i	$-0.645903\pi$
$137$	−14.1799	−	3.01403i	−1.21147	−	0.257506i	−0.768982	+	0.639270i	$0.779237\pi$
$138$		0			0
$139$	6.35170	+	19.5485i	0.538744	+	1.65808i	0.735416	+	0.677616i	$0.236987\pi$
$139$	6.35170	+	19.5485i	0.538744	+	1.65808i	−0.196672	+	0.980469i	$0.563013\pi$
$140$	−0.369841	−	1.13825i	−0.0312572	−	0.0961999i
$141$		0			0
$142$	−10.5385	−	2.24002i	−0.884370	−	0.187979i
$143$	3.83603	−	0.815373i	0.320785	−	0.0681849i
$144$		0			0
$145$	−0.117409	−	0.130396i	−0.00975030	−	0.0108288i
$146$	−0.620857	−	5.90706i	−0.0513825	−	0.488872i
$147$		0			0
$148$	0.289500	−	2.75441i	0.0237967	−	0.226411i
$149$	−10.2156	−	17.6939i	−0.836894	−	1.44954i	−0.892479	−	0.451089i	$-0.851036\pi$
$149$	−10.2156	−	17.6939i	−0.836894	−	1.44954i	0.0555846	−	0.998454i	$-0.482298\pi$
$150$		0			0
$151$	−0.849699	−	0.617342i	−0.0691475	−	0.0502386i	0.552675	−	0.833397i	$-0.313607\pi$
$151$	−0.849699	−	0.617342i	−0.0691475	−	0.0502386i	−0.621822	+	0.783159i	$0.713607\pi$
$152$	1.54354	−	1.71427i	0.125198	−	0.139046i
$153$		0			0
$154$	2.34135			0.188672
$155$	−3.39791	+	2.12950i	−0.272927	+	0.171045i
$156$		0			0
$157$	4.50614	−	13.8685i	0.359629	−	1.10682i	−0.593648	−	0.804725i	$-0.702313\pi$
$157$	4.50614	−	13.8685i	0.359629	−	1.10682i	0.953277	−	0.302099i	$-0.0976872\pi$
$158$	8.96224	−	9.95358i	0.712998	−	0.791864i
$159$		0			0
$160$	0.360114	−	0.623735i	0.0284695	−	0.0493106i
$161$	−4.87628	−	8.44596i	−0.384304	−	0.665635i
$162$		0			0
$163$	−3.95554	+	2.87387i	−0.309822	+	0.225099i	−0.731820	−	0.681498i	$-0.761329\pi$
$163$	−3.95554	+	2.87387i	−0.309822	+	0.225099i	0.421998	+	0.906597i	$0.361329\pi$
$164$	0.528454	+	5.02791i	0.0412653	+	0.392614i
$165$		0			0
$166$	−5.47526	+	2.43774i	−0.424963	+	0.189206i
$167$	12.2190	−	2.59723i	0.945535	−	0.200980i	0.290754	−	0.956798i	$-0.406094\pi$
$167$	12.2190	−	2.59723i	0.945535	−	0.200980i	0.654782	+	0.755818i	$0.272761\pi$
$168$		0			0
$169$	−4.79864	−	2.13649i	−0.369126	−	0.164345i
$170$	−0.0947383	−	0.291575i	−0.00726610	−	0.0223628i
$171$		0			0
$172$	2.59474	+	1.15525i	0.197847	+	0.0880871i
$173$	−4.97591	−	1.05766i	−0.378312	−	0.0804126i	0.0148312	−	0.999890i	$-0.495279\pi$
$173$	−4.97591	−	1.05766i	−0.378312	−	0.0804126i	−0.393143	+	0.919477i	$0.628612\pi$
$174$		0			0
$175$	6.80290	−	3.02885i	0.514251	−	0.228959i
$176$	0.942790	+	1.04707i	0.0710654	+	0.0789262i
$177$		0			0
$178$	−0.481926	+	0.350140i	−0.0361219	+	0.0262441i
$179$	1.48412	−	14.1204i	0.110928	−	1.05541i	−0.787507	−	0.616305i	$-0.788629\pi$
$179$	1.48412	−	14.1204i	0.110928	−	1.05541i	0.898435	−	0.439106i	$-0.144705\pi$
$180$		0			0
$181$	−8.41115	+	14.5685i	−0.625196	+	1.08287i	0.363307	+	0.931669i	$0.381647\pi$
$181$	−8.41115	+	14.5685i	−0.625196	+	1.08287i	−0.988503	+	0.151201i	$0.951686\pi$
$182$	3.74191	+	2.71866i	0.277369	+	0.201520i
$183$		0			0
$184$	1.81359	−	5.58164i	0.133699	−	0.411484i
$185$	−1.99473			−0.146655
$186$		0			0
$187$	0.599760			0.0438588
$188$	2.12920	−	6.55302i	0.155288	−	0.477928i
$189$		0			0
$190$	−1.34411	−	0.976551i	−0.0975118	−	0.0708465i
$191$	−12.2441	+	21.2073i	−0.885948	+	1.53451i	−0.0413256	+	0.999146i	$0.513158\pi$
$191$	−12.2441	+	21.2073i	−0.885948	+	1.53451i	−0.844623	+	0.535362i	$0.820175\pi$
$192$		0			0
$193$	−1.25433	+	11.9341i	−0.0902885	+	0.859038i	0.851844	+	0.523796i	$0.175485\pi$
$193$	−1.25433	+	11.9341i	−0.0902885	+	0.859038i	−0.942132	+	0.335242i	$0.891182\pi$
$194$	4.23452	−	3.07656i	0.304021	−	0.220884i
$195$		0			0
$196$	−2.83619	−	3.14991i	−0.202585	−	0.224994i
$197$	−12.2437	+	5.45125i	−0.872327	+	0.388385i	−0.793549	−	0.608507i	$-0.791769\pi$
$197$	−12.2437	+	5.45125i	−0.872327	+	0.388385i	−0.0787788	+	0.996892i	$0.525102\pi$
$198$		0			0
$199$	1.02057	+	0.216930i	0.0723466	+	0.0153777i	0.243943	−	0.969790i	$-0.421559\pi$
$199$	1.02057	+	0.216930i	0.0723466	+	0.0153777i	−0.171596	+	0.985167i	$0.554892\pi$
$200$	4.09385	+	1.82270i	0.289479	+	0.128884i
$201$		0			0
$202$	−3.06598	−	9.43612i	−0.215722	−	0.663923i
$203$	0.369841	+	0.164664i	0.0259577	+	0.0115571i
$204$		0			0
$205$	3.56161	−	0.757044i	0.248754	−	0.0528743i
$206$	16.7280	−	7.44781i	1.16550	−	0.518913i
$207$		0			0
$208$	0.290943	+	2.76814i	0.0201733	+	0.191936i
$209$	2.62947	−	1.91042i	0.181884	−	0.132147i
$210$		0			0
$211$	8.20101	+	14.2046i	0.564581	+	0.977883i	0.997089	+	0.0762526i	$0.0242955\pi$
$211$	8.20101	+	14.2046i	0.564581	+	0.977883i	−0.432508	+	0.901630i	$0.642371\pi$
$212$	−2.39829	+	4.15397i	−0.164716	+	0.285296i
$213$		0			0
$214$	−2.99231	+	3.32329i	−0.204550	+	0.227176i
$215$	0.632143	−	1.94554i	0.0431118	−	0.132684i
$216$		0			0
$217$	5.16361	−	7.67723i	0.350528	−	0.521164i
$218$	9.84187			0.666576
$219$		0			0
$220$	0.679023	−	0.754131i	0.0457797	−	0.0508435i
$221$	0.958528	+	0.696412i	0.0644776	+	0.0468457i
$222$		0			0
$223$	10.9262	+	18.9248i	0.731675	+	1.26730i	0.956167	+	0.292822i	$0.0945943\pi$
$223$	10.9262	+	18.9248i	0.731675	+	1.26730i	−0.224492	+	0.974476i	$0.572072\pi$
$224$	−0.173699	+	1.65264i	−0.0116058	+	0.110421i
$225$		0			0
$226$	1.14758	+	10.9185i	0.0763359	+	0.726287i
$227$	−7.72368	−	8.57801i	−0.512638	−	0.569343i	0.430140	−	0.902762i	$-0.358464\pi$
$227$	−7.72368	−	8.57801i	−0.512638	−	0.569343i	−0.942779	+	0.333420i	$0.891797\pi$
$228$		0			0
$229$	−20.4055	+	4.33731i	−1.34843	+	0.286618i	−0.824847	−	0.565356i	$-0.808739\pi$
$229$	−20.4055	+	4.33731i	−1.34843	+	0.286618i	−0.523584	+	0.851974i	$0.675405\pi$
$230$	−4.13456	−	0.878828i	−0.272625	−	0.0579482i
$231$		0			0
$232$	0.0752842	+	0.231701i	0.00494265	+	0.0152119i
$233$	8.46951	+	26.0665i	0.554856	+	1.70767i	0.696323	+	0.717729i	$0.254818\pi$
$233$	8.46951	+	26.0665i	0.554856	+	1.70767i	−0.141467	+	0.989943i	$0.545182\pi$
$234$		0			0
$235$	−4.85410	−	1.03177i	−0.316647	−	0.0673053i
$236$	−11.8131	+	2.51094i	−0.768964	+	0.163448i
$237$		0			0
$238$	0.473312	+	0.525666i	0.0306803	+	0.0340739i
$239$	0.491653	+	4.67777i	0.0318024	+	0.302580i	0.998848	+	0.0479779i	$0.0152777\pi$
$239$	0.491653	+	4.67777i	0.0318024	+	0.302580i	−0.967046	+	0.254602i	$0.918056\pi$
$240$		0			0
$241$	−1.18509	+	11.2754i	−0.0763387	+	0.726314i	0.887677	+	0.460467i	$0.152318\pi$
$241$	−1.18509	+	11.2754i	−0.0763387	+	0.726314i	−0.964015	+	0.265847i	$0.914349\pi$
$242$	−4.50739	−	7.80703i	−0.289746	−	0.501855i
$243$		0			0
$244$	2.11958	+	1.53996i	0.135692	+	0.0985861i
$245$	−2.04270	+	2.26865i	−0.130504	+	0.144939i
$246$		0			0
$247$	6.42067			0.408537
$248$	5.51255	−	0.782168i	0.350047	−	0.0496677i
$249$		0			0
$250$	2.11018	−	6.49445i	0.133459	−	0.410745i
$251$	−0.676301	+	0.751109i	−0.0426878	+	0.0474096i	−0.764111	−	0.645085i	$-0.776822\pi$
$251$	−0.676301	+	0.751109i	−0.0426878	+	0.0474096i	0.721423	+	0.692495i	$0.243488\pi$
$252$		0			0
$253$	4.13456	−	7.16127i	0.259938	−	0.450225i
$254$	8.16663	+	14.1450i	0.512420	+	0.887537i
$255$		0			0
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	3.20124	+	30.4577i	0.199688	+	1.89990i	0.394237	+	0.919009i	$0.371009\pi$
$257$	3.20124	+	30.4577i	0.199688	+	1.89990i	−0.194549	+	0.980893i	$0.562324\pi$
$258$		0			0
$259$	4.20443	−	1.87193i	0.261250	−	0.116316i
$260$	1.96086	−	0.416794i	0.121608	−	0.0258485i
$261$		0			0
$262$	6.50614	+	2.89672i	0.401950	+	0.178960i
$263$	1.80632	+	5.55927i	0.111382	+	0.342799i	0.991175	−	0.132558i	$-0.0423189\pi$
$263$	1.80632	+	5.55927i	0.111382	+	0.342799i	−0.879793	+	0.475357i	$0.842319\pi$
$264$		0			0
$265$	3.15597	+	1.40513i	0.193869	+	0.0863162i
$266$	3.74951	+	0.796982i	0.229897	+	0.0488661i
$267$		0			0
$268$	−4.79545	+	2.13507i	−0.292929	+	0.130420i
$269$	−0.304971	−	0.338705i	−0.0185944	−	0.0206512i	0.733776	−	0.679392i	$-0.237756\pi$
$269$	−0.304971	−	0.338705i	−0.0185944	−	0.0206512i	−0.752370	+	0.658740i	$0.771090\pi$
$270$		0			0
$271$	2.08363	−	1.51385i	0.126572	−	0.0919596i	−0.522698	−	0.852518i	$-0.675075\pi$
$271$	2.08363	−	1.51385i	0.126572	−	0.0919596i	0.649270	+	0.760558i	$0.275075\pi$
$272$	−0.0444947	+	0.423339i	−0.00269789	+	0.0256687i
$273$		0			0
$274$	7.24833	−	12.5545i	0.437888	−	0.758444i
$275$	5.10814	+	3.71128i	0.308033	+	0.223799i
$276$		0			0
$277$	7.23820	−	22.2769i	0.434901	−	1.33849i	−0.458287	−	0.888804i	$-0.651537\pi$
$277$	7.23820	−	22.2769i	0.434901	−	1.33849i	0.893188	−	0.449684i	$-0.148463\pi$
$278$	−20.5545			−1.23278
$279$		0			0
$280$	1.19683			0.0715242
$281$	−9.06598	+	27.9022i	−0.540831	+	1.66451i	0.189870	+	0.981809i	$0.439193\pi$
$281$	−9.06598	+	27.9022i	−0.540831	+	1.66451i	−0.730701	+	0.682698i	$0.760807\pi$
$282$		0			0
$283$	8.80869	+	6.39989i	0.523622	+	0.380434i	0.817967	−	0.575266i	$-0.195101\pi$
$283$	8.80869	+	6.39989i	0.523622	+	0.380434i	−0.294345	+	0.955699i	$0.595101\pi$
$284$	5.38696	−	9.33049i	0.319657	−	0.553663i
$285$		0			0
$286$	−0.409932	+	3.90024i	−0.0242398	+	0.230626i
$287$	−6.79662	+	4.93804i	−0.401192	+	0.291483i
$288$		0			0
$289$	−11.2540	−	12.4988i	−0.661999	−	0.735224i
$290$	0.160296	−	0.0713682i	0.00941288	−	0.00419088i
$291$		0			0
$292$	5.80981	+	1.23491i	0.339993	+	0.0722678i
$293$	−10.0783	−	4.48715i	−0.588781	−	0.262142i	0.0906485	−	0.995883i	$-0.471106\pi$
$293$	−10.0783	−	4.48715i	−0.588781	−	0.262142i	−0.679430	+	0.733741i	$0.737773\pi$
$294$		0			0
$295$	2.68788	+	8.27244i	0.156494	+	0.481640i
$296$	2.53014	+	1.12649i	0.147061	+	0.0654759i
$297$		0			0
$298$	19.9847	−	4.24788i	1.15768	−	0.246073i
$299$	14.9231	−	6.64420i	0.863026	−	0.384244i
$300$		0			0
$301$	0.493356	+	4.69397i	0.0284366	+	0.270556i
$302$	0.849699	−	0.617342i	0.0488947	−	0.0355241i
$303$		0			0
$304$	1.15339	+	1.99773i	0.0661516	+	0.114578i
$305$	0.943478	−	1.63415i	0.0540234	−	0.0935712i
$306$		0			0
$307$	−5.03883	+	5.59619i	−0.287581	+	0.319392i	−0.869574	−	0.493802i	$-0.835607\pi$
$307$	−5.03883	+	5.59619i	−0.287581	+	0.319392i	0.581993	+	0.813194i	$0.302273\pi$
$308$	−0.723518	+	2.22676i	−0.0412262	+	0.126881i
$309$		0			0
$310$	−0.975261	−	3.88965i	−0.0553911	−	0.220918i
$311$	13.9560			0.791370			0.395685	−	0.918386i	$-0.370507\pi$
$311$	13.9560			0.791370			0.395685	+	0.918386i	$0.370507\pi$
$312$		0			0
$313$	16.7885	−	18.6455i	0.948943	−	1.05391i	−0.0495358	−	0.998772i	$-0.515774\pi$
$313$	16.7885	−	18.6455i	0.948943	−	1.05391i	0.998479	−	0.0551357i	$-0.0175591\pi$
$314$	11.7972	+	8.57118i	0.665755	+	0.483700i
$315$		0			0
$316$	6.69693	+	11.5994i	0.376732	+	0.652519i
$317$	−1.44088	+	13.7091i	−0.0809279	+	0.769977i	0.876519	+	0.481367i	$0.159860\pi$
$317$	−1.44088	+	13.7091i	−0.0809279	+	0.769977i	−0.957447	+	0.288610i	$0.906807\pi$
$318$		0			0
$319$	0.0358806	+	0.341382i	0.00200893	+	0.0191137i
$320$	0.481926	+	0.535233i	0.0269405	+	0.0299204i
$321$		0			0
$322$	9.53944	−	2.02767i	0.531612	−	0.112998i
$323$	0.960473	+	0.204155i	0.0534421	+	0.0113595i
$324$		0			0
$325$	3.85440	+	11.8626i	0.213804	+	0.658021i
$326$	−1.51088	−	4.65002i	−0.0836800	−	0.257541i
$327$		0			0
$328$	−4.94512	−	1.05112i	−0.273049	−	0.0580383i
$329$	11.1996	−	2.38055i	0.617453	−	0.131244i
$330$		0			0
$331$	0.242751	+	0.269602i	0.0133428	+	0.0148187i	0.749779	−	0.661688i	$-0.230160\pi$
$331$	0.242751	+	0.269602i	0.0133428	+	0.0148187i	−0.736436	+	0.676507i	$0.763493\pi$
$332$	−0.626483	−	5.96059i	−0.0343827	−	0.327130i
$333$		0			0
$334$	−1.30577	+	12.4236i	−0.0714485	+	0.679787i
$335$	1.89033	+	3.27415i	0.103280	+	0.178886i
$336$		0			0
$337$	10.8516	+	7.88415i	0.591124	+	0.429477i	0.842717	−	0.538356i	$-0.180954\pi$
$337$	10.8516	+	7.88415i	0.591124	+	0.429477i	−0.251593	+	0.967833i	$0.580954\pi$
$338$	3.51478	−	3.90356i	0.191179	−	0.212326i
$339$		0			0
$340$	0.306580			0.0166266
$341$	7.82646	+	0.536887i	0.423827	+	0.0290741i
$342$		0			0
$343$	5.77110	−	17.7616i	0.311610	−	0.959037i
$344$	−1.90053	+	2.11075i	−0.102470	+	0.113804i
$345$		0			0
$346$	2.54354	−	4.40554i	0.136742	−	0.236843i
$347$	−17.6702	−	30.6057i	−0.948585	−	1.64300i	−0.748409	−	0.663237i	$-0.769182\pi$
$347$	−17.6702	−	30.6057i	−0.948585	−	1.64300i	−0.200176	−	0.979760i	$-0.564151\pi$
$348$		0			0
$349$	−25.0879	+	18.2274i	−1.34293	+	0.975693i	−0.343595	+	0.939118i	$0.611645\pi$
$349$	−25.0879	+	18.2274i	−1.34293	+	0.975693i	−0.999331	+	0.0365750i	$0.988355\pi$
$350$	0.778393	+	7.40591i	0.0416068	+	0.395863i
$351$		0			0
$352$	−1.28716	+	0.573083i	−0.0686061	+	0.0305454i
$353$	23.7860	−	5.05587i	1.26600	−	0.269097i	0.474494	−	0.880259i	$-0.342631\pi$
$353$	23.7860	−	5.05587i	1.26600	−	0.269097i	0.791506	+	0.611162i	$0.209298\pi$
$354$		0			0
$355$	−7.08881	−	3.15614i	−0.376235	−	0.167511i
$356$	−0.184079	−	0.566538i	−0.00975619	−	0.0300265i
$357$		0			0
$358$	12.9707	+	5.77493i	0.685524	+	0.305215i
$359$	−19.0052	−	4.03968i	−1.00306	−	0.213206i	−0.323026	−	0.946390i	$-0.604700\pi$
$359$	−19.0052	−	4.03968i	−1.00306	−	0.213206i	−0.680031	+	0.733184i	$0.738034\pi$
$360$		0			0
$361$	−12.4962	+	5.56365i	−0.657693	+	0.292824i
$362$	−11.2563	−	12.5014i	−0.591619	−	0.657059i
$363$		0			0
$364$	−3.74191	+	2.71866i	−0.196130	+	0.142497i
$365$	0.447158	−	4.25443i	0.0234053	−	0.222687i
$366$		0			0
$367$	−9.63456	+	16.6876i	−0.502920	+	0.871083i	0.497074	+	0.867708i	$0.334408\pi$
$367$	−9.63456	+	16.6876i	−0.502920	+	0.871083i	−0.999994	+	0.00337510i	$0.998926\pi$
$368$	4.74803	+	3.44964i	0.247508	+	0.179825i
$369$		0			0
$370$	0.616404	−	1.89710i	0.0320453	−	0.0986254i
$371$	−7.97068			−0.413817
$372$		0			0
$373$	−4.38573			−0.227084			−0.113542	−	0.993533i	$-0.536220\pi$
$373$	−4.38573			−0.227084			−0.113542	+	0.993533i	$0.536220\pi$
$374$	−0.185336	+	0.570406i	−0.00958350	+	0.0294950i
$375$		0			0
$376$	5.57433	+	4.04999i	0.287474	+	0.208862i
$377$	−0.339051	+	0.587254i	−0.0174620	+	0.0302451i
$378$		0			0
$379$	−1.33865	+	12.7364i	−0.0687619	+	0.654226i	0.904805	+	0.425825i	$0.140016\pi$
$379$	−1.33865	+	12.7364i	−0.0687619	+	0.654226i	−0.973567	+	0.228401i	$0.926650\pi$
$380$	1.34411	−	0.976551i	0.0689513	−	0.0500960i
$381$		0			0
$382$	−16.3857	−	18.1982i	−0.838367	−	0.931101i
$383$	25.6906	−	11.4382i	1.31273	−	0.584464i	0.373459	−	0.927647i	$-0.378172\pi$
$383$	25.6906	−	11.4382i	1.31273	−	0.584464i	0.939269	+	0.343183i	$0.111505\pi$
$384$		0			0
$385$	1.64946	+	0.350603i	0.0840640	+	0.0178684i
$386$	−10.9624	−	4.88079i	−0.557973	−	0.248426i
$387$		0			0
$388$	1.61744	+	4.97798i	0.0821133	+	0.252719i
$389$	−2.14390	−	0.954527i	−0.108700	−	0.0483965i	0.351666	−	0.936126i	$-0.385615\pi$
$389$	−2.14390	−	0.954527i	−0.108700	−	0.0483965i	−0.460366	+	0.887729i	$0.652282\pi$
$390$		0			0
$391$	2.44362	−	0.519408i	0.123579	−	0.0262676i
$392$	3.87218	−	1.72400i	0.195574	−	0.0870753i
$393$		0			0
$394$	−1.40093	−	13.3290i	−0.0705779	−	0.671504i
$395$	7.80428	−	5.67014i	0.392676	−	0.285296i
$396$		0			0
$397$	−11.2870	−	19.5496i	−0.566477	−	0.981167i	−0.996911	−	0.0785449i	$-0.974973\pi$
$397$	−11.2870	−	19.5496i	−0.566477	−	0.981167i	0.430433	−	0.902622i	$-0.358361\pi$
$398$	−0.521687	+	0.903589i	−0.0261498	+	0.0452928i
$399$		0			0
$400$	−2.99856	+	3.33023i	−0.149928	+	0.166512i
$401$	6.51963	−	20.0654i	0.325575	−	1.00202i	−0.645606	−	0.763671i	$-0.723395\pi$
$401$	6.51963	−	20.0654i	0.325575	−	1.00202i	0.971180	−	0.238345i	$-0.0766050\pi$
$402$		0			0
$403$	11.8847	+	9.94574i	0.592020	+	0.495432i
$404$	9.92173			0.493624
$405$		0			0
$406$	−0.270892	+	0.300855i	−0.0134441	+	0.0149312i
$407$	3.15701	+	2.29370i	0.156487	+	0.113694i
$408$		0			0
$409$	10.7156	+	18.5600i	0.529852	+	0.917731i	0.999394	+	0.0348204i	$0.0110859\pi$
$409$	10.7156	+	18.5600i	0.529852	+	0.917731i	−0.469541	+	0.882910i	$0.655581\pi$
$410$	−0.380607	+	3.62124i	−0.0187968	+	0.178840i
$411$		0			0
$412$	1.91403	+	18.2108i	0.0942977	+	0.897182i
$413$	−13.4286	−	14.9140i	−0.660779	−	0.733870i
$414$		0			0
$415$	−4.22230	+	0.897477i	−0.207264	+	0.0440554i
$416$	−2.72256	−	0.578699i	−0.133485	−	0.0283730i
$417$		0			0
$418$	1.00437	+	3.09113i	0.0491253	+	0.151192i
$419$	−3.81826	−	11.7514i	−0.186534	−	0.574093i	0.813437	−	0.581652i	$-0.197594\pi$
$419$	−3.81826	−	11.7514i	−0.186534	−	0.574093i	−0.999971	+	0.00755981i	$0.997594\pi$
$420$		0			0
$421$	−23.4190	−	4.97785i	−1.14137	−	0.242606i	−0.401828	−	0.915715i	$-0.631625\pi$
$421$	−23.4190	−	4.97785i	−1.14137	−	0.242606i	−0.739543	+	0.673110i	$0.764958\pi$
$422$	−16.0436	+	3.41017i	−0.780990	+	0.166005i
$423$		0			0
$424$	−3.20955	−	3.56456i	−0.155869	−	0.173110i
$425$	0.199393	+	1.89710i	0.00967198	+	0.0920227i
$426$		0			0
$427$	−0.455082	+	4.32981i	−0.0220229	+	0.209534i
$428$	−2.23597	−	3.87281i	−0.108079	−	0.187199i
$429$		0			0
$430$	1.65497	+	1.20241i	0.0798098	+	0.0579852i
$431$	−8.43237	+	9.36510i	−0.406173	+	0.451101i	−0.911176	−	0.412016i	$-0.864825\pi$
$431$	−8.43237	+	9.36510i	−0.406173	+	0.451101i	0.505003	+	0.863117i	$0.331491\pi$
$432$		0			0
$433$	−16.5682			−0.796215			−0.398107	−	0.917339i	$-0.630333\pi$
$433$	−16.5682			−0.796215			−0.398107	+	0.917339i	$0.630333\pi$
$434$	5.70583	+	7.28328i	0.273889	+	0.349608i
$435$		0			0
$436$	−3.04131	+	9.36018i	−0.145652	+	0.448271i
$437$	9.05886	−	10.0609i	0.433344	−	0.481277i
$438$		0			0
$439$	8.16693	−	14.1455i	0.389786	−	0.675130i	−0.602634	−	0.798018i	$-0.705882\pi$
$439$	8.16693	−	14.1455i	0.389786	−	0.675130i	0.992421	+	0.122888i	$0.0392155\pi$
$440$	0.507392	+	0.878828i	0.0241890	+	0.0418965i
$441$		0			0
$442$	−0.958528	+	0.696412i	−0.0455925	+	0.0331249i
$443$	1.40254	+	13.3443i	0.0666367	+	0.634006i	0.975965	+	0.217927i	$0.0699294\pi$
$443$	1.40254	+	13.3443i	0.0666367	+	0.634006i	−0.909328	+	0.416079i	$0.863404\pi$
$444$		0			0
$445$	−0.391943	+	0.174504i	−0.0185799	+	0.00827229i
$446$	−21.3749	+	4.54338i	−1.01213	+	0.215135i
$447$		0			0
$448$	−1.51807	−	0.675890i	−0.0717223	−	0.0319328i
$449$	−1.57732	−	4.85448i	−0.0744382	−	0.229097i	0.906914	−	0.421316i	$-0.138432\pi$
$449$	−1.57732	−	4.85448i	−0.0744382	−	0.229097i	−0.981352	+	0.192219i	$0.938432\pi$
$450$		0			0
$451$	−6.50739	−	2.89728i	−0.306421	−	0.136427i
$452$	−10.7387	−	2.28259i	−0.505107	−	0.107364i
$453$		0			0
$454$	10.5449	−	4.69490i	0.494898	−	0.220343i
$455$	2.22903	+	2.47559i	0.104499	+	0.116058i
$456$		0			0
$457$	30.8490	−	22.4131i	1.44306	−	1.04844i	0.455665	−	0.890152i	$-0.349402\pi$
$457$	30.8490	−	22.4131i	1.44306	−	1.04844i	0.987393	−	0.158291i	$-0.0505984\pi$
$458$	2.18060	−	20.7470i	0.101893	−	0.969446i
$459$		0			0
$460$	2.11347	−	3.66063i	0.0985408	−	0.170678i
$461$	−11.0437	−	8.02372i	−0.514356	−	0.373702i	0.300117	−	0.953902i	$-0.402974\pi$
$461$	−11.0437	−	8.02372i	−0.514356	−	0.373702i	−0.814474	+	0.580201i	$0.802974\pi$
$462$		0			0
$463$	9.68783	−	29.8161i	0.450232	−	1.38567i	−0.426411	−	0.904529i	$-0.640222\pi$
$463$	9.68783	−	29.8161i	0.450232	−	1.38567i	0.876643	−	0.481142i	$-0.159778\pi$
$464$	−0.243625			−0.0113100
$465$		0			0
$466$	−27.4079			−1.26965
$467$	2.01215	−	6.19275i	0.0931110	−	0.286566i	−0.893646	−	0.448773i	$-0.851861\pi$
$467$	2.01215	−	6.19275i	0.0931110	−	0.286566i	0.986757	+	0.162207i	$0.0518612\pi$
$468$		0			0
$469$	−7.05699	−	5.12720i	−0.325861	−	0.236752i
$470$	2.48127	−	4.29769i	0.114453	−	0.198238i
$471$		0			0
$472$	1.26239	−	12.0108i	0.0581061	−	0.552842i
$473$	−3.23761	+	2.35226i	−0.148866	+	0.108157i
$474$		0			0
$475$	6.91702	+	7.68213i	0.317375	+	0.352480i
$476$	−0.646200	+	0.287707i	−0.0296185	+	0.0131870i
$477$		0			0
$478$	−4.60075	−	0.977920i	−0.210433	−	0.0447290i
$479$	−11.5783	−	5.15499i	−0.529026	−	0.235538i	0.124801	−	0.992182i	$-0.460171\pi$
$479$	−11.5783	−	5.15499i	−0.529026	−	0.235538i	−0.653827	+	0.756644i	$0.726838\pi$
$480$		0			0
$481$	2.38215	+	7.33151i	0.108617	+	0.334288i
$482$	−10.3574	−	4.61139i	−0.471764	−	0.210043i
$483$		0			0
$484$	8.81779	−	1.87428i	0.400809	−	0.0851945i
$485$	3.44387	−	1.53331i	0.156378	−	0.0696240i
$486$		0			0
$487$	−1.58887	−	15.1171i	−0.0719984	−	0.685019i	−0.969681	−	0.244376i	$-0.921417\pi$
$487$	−1.58887	−	15.1171i	−0.0719984	−	0.685019i	0.897682	−	0.440643i	$-0.145250\pi$
$488$	−2.11958	+	1.53996i	−0.0959488	+	0.0697109i
$489$		0			0
$490$	−1.52639	−	2.64378i	−0.0689551	−	0.119434i
$491$	−13.4000	+	23.2095i	−0.604734	+	1.04743i	0.387359	+	0.921929i	$0.373387\pi$
$491$	−13.4000	+	23.2095i	−0.604734	+	1.04743i	−0.992093	+	0.125501i	$0.959946\pi$
$492$		0			0
$493$	−0.0693915	+	0.0770671i	−0.00312524	+	0.00347093i
$494$	−1.98410	+	6.10642i	−0.0892687	+	0.274741i
$495$		0			0
$496$	−0.959585	+	5.48445i	−0.0430867	+	0.246259i
$497$	17.9034			0.803079
$498$		0			0
$499$	21.4480	−	23.8204i	0.960143	−	1.06635i	−0.0376063	−	0.999293i	$-0.511973\pi$
$499$	21.4480	−	23.8204i	0.960143	−	1.06635i	0.997749	−	0.0670542i	$-0.0213600\pi$
$500$	5.52451	+	4.01379i	0.247064	+	0.179502i
$501$		0			0
$502$	−0.505358	−	0.875306i	−0.0225552	−	0.0390668i
$503$	1.22023	−	11.6097i	0.0544074	−	0.517652i	−0.933048	−	0.359753i	$-0.882861\pi$
$503$	1.22023	−	11.6097i	0.0544074	−	0.517652i	0.987455	−	0.157900i	$-0.0504722\pi$
$504$		0			0
$505$	−0.746950	−	7.10675i	−0.0332388	−	0.316246i
$506$	5.53312	+	6.14516i	0.245977	+	0.273186i
$507$		0			0
$508$	−15.9763	+	3.39588i	−0.708835	+	0.150668i
$509$	−17.8948	−	3.80365i	−0.793172	−	0.168594i	−0.206530	−	0.978440i	$-0.566217\pi$
$509$	−17.8948	−	3.80365i	−0.793172	−	0.168594i	−0.586642	+	0.809846i	$0.699550\pi$
$510$		0			0
$511$	3.05002	+	9.38699i	0.134925	+	0.415256i
$512$	−0.309017	−	0.951057i	−0.0136568	−	0.0420312i
$513$		0			0
$514$	−29.9563	−	6.36740i	−1.32131	−	0.280854i
$515$	12.9000	−	2.74197i	0.568441	−	0.120826i
$516$		0			0
$517$	6.49606	+	7.21460i	0.285696	+	0.317298i
$518$	0.481073	+	4.57710i	0.0211371	+	0.201106i
$519$		0			0
$520$	−0.209545	+	1.99369i	−0.00918916	+	0.0874290i
$521$	13.3850	+	23.1836i	0.586410	+	1.01569i	0.994698	+	0.102838i	$0.0327924\pi$
$521$	13.3850	+	23.1836i	0.586410	+	1.01569i	−0.408288	+	0.912853i	$0.633874\pi$
$522$		0			0
$523$	−19.1778	−	13.9335i	−0.838588	−	0.609270i	0.0833876	−	0.996517i	$-0.473426\pi$
$523$	−19.1778	−	13.9335i	−0.838588	−	0.609270i	−0.921976	+	0.387247i	$0.873426\pi$
$524$	−4.76545	+	5.29257i	−0.208180	+	0.231207i
$525$		0			0
$526$	−5.84536			−0.254870
$527$	1.46161	+	1.86568i	0.0636685	+	0.0812704i
$528$		0			0
$529$	3.53633	−	10.8837i	0.153754	−	0.473205i
$530$	−2.31160	+	2.56729i	−0.100410	+	0.111516i
$531$		0			0
$532$	−1.91664	+	3.31971i	−0.0830967	+	0.143928i
$533$	−7.03585	−	12.1864i	−0.304756	−	0.527853i
$534$		0			0
$535$	−2.60569	+	1.89314i	−0.112654	+	0.0818477i
$536$	−0.548698	−	5.22052i	−0.0237002	−	0.225492i
$537$		0			0
$538$	0.416369	−	0.185379i	0.0179509	−	0.00799227i
$539$	5.84162	−	1.24167i	0.251616	−	0.0534827i
$540$		0			0
$541$	−12.2004	−	5.43195i	−0.524534	−	0.233538i	0.127348	−	0.991858i	$-0.459354\pi$
$541$	−12.2004	−	5.43195i	−0.524534	−	0.233538i	−0.651882	+	0.758320i	$0.726020\pi$
$542$	0.795876	+	2.44946i	0.0341858	+	0.105213i
$543$		0			0
$544$	−0.388870	−	0.173136i	−0.0166726	−	0.00742314i
$545$	6.93349	+	1.47376i	0.296998	+	0.0631289i
$546$		0			0
$547$	0.889972	−	0.396241i	0.0380525	−	0.0169420i	−0.387622	−	0.921818i	$-0.626703\pi$
$547$	0.889972	−	0.396241i	0.0380525	−	0.0169420i	0.425675	+	0.904876i	$0.360037\pi$
$548$	9.70016	+	10.7731i	0.414370	+	0.460205i
$549$		0			0
$550$	−5.10814	+	3.71128i	−0.217812	+	0.158250i
$551$	−0.0587440	+	0.558911i	−0.00250258	+	0.0238104i
$552$		0			0
$553$	−11.1286	+	19.2752i	−0.473234	+	0.819666i
$554$	18.9499	+	13.7679i	0.805102	+	0.584941i
$555$		0			0
$556$	6.35170	−	19.5485i	0.269372	−	0.829042i
$557$	4.59258			0.194594			0.0972969	−	0.995255i	$-0.468980\pi$
$557$	4.59258			0.194594			0.0972969	+	0.995255i	$0.468980\pi$
$558$		0			0
$559$	−7.90564			−0.334373
$560$	−0.369841	+	1.13825i	−0.0156286	+	0.0480999i
$561$		0			0
$562$	−23.7350	−	17.2445i	−1.00120	−	0.727416i
$563$	−15.1698	+	26.2748i	−0.639329	+	1.10735i	0.346251	+	0.938142i	$0.387455\pi$
$563$	−15.1698	+	26.2748i	−0.639329	+	1.10735i	−0.985580	+	0.169209i	$0.945879\pi$
$564$		0			0
$565$	−0.826518	+	7.86380i	−0.0347719	+	0.330832i
$566$	−8.80869	+	6.39989i	−0.370257	+	0.269007i
$567$		0			0
$568$	7.20916	+	8.00658i	0.302490	+	0.335949i
$569$	−28.2730	+	12.5879i	−1.18526	+	0.527714i	−0.902171	−	0.431379i	$-0.858027\pi$
$569$	−28.2730	+	12.5879i	−1.18526	+	0.527714i	−0.283093	+	0.959092i	$0.591361\pi$
$570$		0			0
$571$	−37.4030	−	7.95025i	−1.56527	−	0.332707i	−0.657918	−	0.753089i	$-0.728563\pi$
$571$	−37.4030	−	7.95025i	−1.56527	−	0.332707i	−0.907347	+	0.420382i	$0.861896\pi$
$572$	−3.58268	−	1.59511i	−0.149799	−	0.0666949i
$573$		0			0
$574$	−2.59608	−	7.98991i	−0.108358	−	0.333492i
$575$	24.0263	+	10.6972i	1.00197	+	0.446104i
$576$		0			0
$577$	21.1652	−	4.49879i	0.881117	−	0.187287i	0.254930	−	0.966960i	$-0.417948\pi$
$577$	21.1652	−	4.49879i	0.881117	−	0.187287i	0.626188	+	0.779672i	$0.284614\pi$
$578$	15.3647	−	6.84082i	0.639089	−	0.284541i
$579$		0			0
$580$	0.0183411	+	0.174504i	0.000761574	+	0.00724589i
$581$	8.05740	−	5.85405i	0.334277	−	0.242867i
$582$		0			0
$583$	−3.37914	−	5.85285i	−0.139950	−	0.242400i
$584$	−2.96980	+	5.14385i	−0.122891	+	0.212854i
$585$		0			0
$586$	7.38190	−	8.19843i	0.304944	−	0.338674i
$587$	13.0613	−	40.1986i	0.539098	−	1.65917i	−0.195526	−	0.980699i	$-0.562641\pi$
$587$	13.0613	−	40.1986i	0.539098	−	1.65917i	0.734624	−	0.678475i	$-0.237359\pi$
$588$		0			0
$589$	12.3508	+	3.52387i	0.508904	+	0.145198i
$590$	−8.69816			−0.358098
$591$		0			0
$592$	−1.85321	+	2.05820i	−0.0761665	+	0.0845914i
$593$	−7.75392	−	5.63355i	−0.318415	−	0.231342i	0.417084	−	0.908868i	$-0.363052\pi$
$593$	−7.75392	−	5.63355i	−0.318415	−	0.231342i	−0.735499	+	0.677526i	$0.763052\pi$
$594$		0			0
$595$	0.254728	+	0.441201i	0.0104428	+	0.0180875i
$596$	−2.13564	+	20.3193i	−0.0874793	+	0.832310i
$597$		0			0
$598$	1.70751	+	16.2459i	0.0698253	+	0.664344i
$599$	−24.0714	−	26.7340i	−0.983530	−	1.09232i	−0.995722	−	0.0923950i	$-0.970548\pi$
$599$	−24.0714	−	26.7340i	−0.983530	−	1.09232i	0.0121925	−	0.999926i	$-0.496119\pi$
$600$		0			0
$601$	17.8089	−	3.78540i	0.726440	−	0.154410i	0.170174	−	0.985414i	$-0.445567\pi$
$601$	17.8089	−	3.78540i	0.726440	−	0.154410i	0.556266	+	0.831005i	$0.312234\pi$
$602$	−4.61669	−	0.981307i	−0.188162	−	0.0399951i
$603$		0			0
$604$	0.324556	+	0.998881i	0.0132060	+	0.0406439i
$605$	−2.00635	−	6.17492i	−0.0815698	−	0.251046i
$606$		0			0
$607$	−19.4096	−	4.12563i	−0.787810	−	0.167454i	−0.203597	−	0.979055i	$-0.565263\pi$
$607$	−19.4096	−	4.12563i	−0.787810	−	0.167454i	−0.584213	+	0.811601i	$0.698597\pi$
$608$	−2.25638	+	0.479607i	−0.0915081	+	0.0194506i
$609$		0			0
$610$	1.26262	+	1.40228i	0.0511220	+	0.0567767i
$611$	2.00467	+	19.0732i	0.0811003	+	0.771618i
$612$		0			0
$613$	2.27329	−	21.6290i	0.0918175	−	0.873585i	−0.847560	−	0.530700i	$-0.821929\pi$
$613$	2.27329	−	21.6290i	0.0918175	−	0.873585i	0.939377	−	0.342885i	$-0.111404\pi$
$614$	−3.76521	−	6.52154i	−0.151952	−	0.263188i
$615$		0			0
$616$	−1.89419	−	1.37621i	−0.0763192	−	0.0554492i
$617$	−0.452250	+	0.502274i	−0.0182069	+	0.0202208i	−0.752179	−	0.658958i	$-0.770997\pi$
$617$	−0.452250	+	0.502274i	−0.0182069	+	0.0202208i	0.733973	+	0.679179i	$0.237664\pi$
$618$		0			0
$619$	10.7141			0.430634			0.215317	−	0.976544i	$-0.430921\pi$
$619$	10.7141			0.430634			0.215317	+	0.976544i	$0.430921\pi$
$620$	4.00065	+	0.274441i	0.160670	+	0.0110218i
$621$		0			0
$622$	−4.31263	+	13.2729i	−0.172921	+	0.532195i
$623$	0.662364	−	0.735629i	0.0265370	−	0.0294724i
$624$		0			0
$625$	−8.74408	+	15.1452i	−0.349763	+	0.605808i
$626$	12.5450	+	21.7286i	0.501400	+	0.868450i
$627$		0			0
$628$	−11.7972	+	8.57118i	−0.470760	+	0.342027i
$629$	0.123232	+	1.17247i	0.00491357	+	0.0467495i
$630$		0			0
$631$	−21.8136	+	9.71204i	−0.868386	+	0.386630i	−0.792053	−	0.610452i	$-0.790988\pi$
$631$	−21.8136	+	9.71204i	−0.868386	+	0.386630i	−0.0763328	+	0.997082i	$0.524321\pi$
$632$	−13.1012	+	2.78474i	−0.521137	+	0.110771i
$633$		0			0
$634$	−12.5928	−	5.60669i	−0.500125	−	0.222670i
$635$	3.63517	+	11.1879i	0.144257	+	0.443978i
$636$		0			0
$637$	10.7778	+	4.79857i	0.427030	+	0.190126i
$638$	−0.335761	−	0.0713682i	−0.0132929	−	0.00282549i
$639$		0			0
$640$	−0.657960	+	0.292943i	−0.0260082	+	0.0115796i
$641$	−2.47779	−	2.75186i	−0.0978668	−	0.108692i	0.692222	−	0.721685i	$-0.256632\pi$
$641$	−2.47779	−	2.75186i	−0.0978668	−	0.108692i	−0.790088	+	0.612993i	$0.789965\pi$
$642$		0			0
$643$	12.3157	−	8.94790i	0.485685	−	0.352871i	−0.317838	−	0.948145i	$-0.602957\pi$
$643$	12.3157	−	8.94790i	0.485685	−	0.352871i	0.803522	+	0.595275i	$0.202957\pi$
$644$	−1.01942	+	9.69913i	−0.0401708	+	0.382199i
$645$		0			0
$646$	−0.490965	+	0.850377i	−0.0193168	+	0.0334576i
$647$	−6.01834	−	4.37258i	−0.236605	−	0.171904i	0.463164	−	0.886272i	$-0.346714\pi$
$647$	−6.01834	−	4.37258i	−0.236605	−	0.171904i	−0.699770	+	0.714369i	$0.746714\pi$
$648$		0			0
$649$	5.25829	−	16.1833i	0.206406	−	0.635252i
$650$	−12.4731			−0.489236
$651$		0			0
$652$	4.88932			0.191480
$653$	−2.92571	+	9.00441i	−0.114492	+	0.352370i	−0.991841	−	0.127483i	$-0.959310\pi$
$653$	−2.92571	+	9.00441i	−0.114492	+	0.352370i	0.877349	+	0.479853i	$0.159310\pi$
$654$		0			0
$655$	4.14973	+	3.01496i	0.162143	+	0.117804i
$656$	2.52780	−	4.37828i	0.0986940	−	0.170943i
$657$		0			0
$658$	−1.19683	+	11.3871i	−0.0466573	+	0.443914i
$659$	−17.7973	+	12.9305i	−0.693285	+	0.503701i	−0.877738	−	0.479140i	$-0.840949\pi$
$659$	−17.7973	+	12.9305i	−0.693285	+	0.503701i	0.184453	+	0.982841i	$0.440949\pi$
$660$		0			0
$661$	12.7080	+	14.1136i	0.494283	+	0.548957i	0.937740	−	0.347339i	$-0.112915\pi$
$661$	12.7080	+	14.1136i	0.494283	+	0.548957i	−0.443456	+	0.896296i	$0.646248\pi$
$662$	−0.331421	+	0.147558i	−0.0128810	+	0.00573500i
$663$		0			0
$664$	5.86245	+	1.24610i	0.227507	+	0.0483581i
$665$	2.52214	+	1.12293i	0.0978044	+	0.0435453i
$666$		0			0
$667$	0.441835	+	1.35983i	0.0171079	+	0.0526527i
$668$	−11.4120	−	5.08095i	−0.441544	−	0.196588i
$669$		0			0
$670$	−3.69805	+	0.786045i	−0.142868	+	0.0303676i
$671$	−3.37230	+	1.50144i	−0.130186	+	0.0579626i
$672$		0			0
$673$	−1.65577	−	15.7536i	−0.0638252	−	0.607256i	−0.978952	−	0.204090i	$-0.934576\pi$
$673$	−1.65577	−	15.7536i	−0.0638252	−	0.607256i	0.915127	−	0.403166i	$-0.132090\pi$
$674$	−10.8516	+	7.88415i	−0.417988	+	0.303686i
$675$		0			0
$676$	2.62638	+	4.54903i	0.101015	+	0.174963i
$677$	18.1168	−	31.3792i	0.696284	−	1.20600i	−0.273462	−	0.961883i	$-0.588169\pi$
$677$	18.1168	−	31.3792i	0.696284	−	1.20600i	0.969746	−	0.244116i	$-0.0784979\pi$
$678$		0			0
$679$	−5.81997	+	6.46373i	−0.223350	+	0.248055i
$680$	−0.0947383	+	0.291575i	−0.00363305	+	0.0111814i
$681$		0			0
$682$	−2.92912	+	7.27750i	−0.112162	+	0.278670i
$683$	−21.4383			−0.820312			−0.410156	−	0.912015i	$-0.634526\pi$
$683$	−21.4383			−0.820312			−0.410156	+	0.912015i	$0.634526\pi$
$684$		0			0
$685$	6.98632	−	7.75909i	0.266934	−	0.296460i
$686$	15.1089	+	10.9773i	0.576861	+	0.419114i
$687$		0			0
$688$	−1.42015	−	2.45977i	−0.0541426	−	0.0937778i
$689$	1.39553	−	13.2776i	0.0531656	−	0.505837i
$690$		0			0
$691$	2.61859	+	24.9142i	0.0996158	+	0.947781i	0.924166	+	0.381992i	$0.124762\pi$
$691$	2.61859	+	24.9142i	0.0996158	+	0.947781i	−0.824550	+	0.565789i	$0.808572\pi$
$692$	3.40392	+	3.78044i	0.129398	+	0.143711i
$693$		0			0
$694$	34.5681	−	7.34767i	1.31219	−	0.278914i
$695$	−14.4804	−	3.07791i	−0.549274	−	0.116752i
$696$		0			0
$697$	−0.665011	−	2.04669i	−0.0251891	−	0.0775241i
$698$	−9.58274	−	29.4926i	−0.362712	−	1.11631i
$699$		0			0
$700$	−7.28398	−	1.54826i	−0.275308	−	0.0585186i
$701$	2.36301	−	0.502274i	0.0892498	−	0.0189706i	−0.163070	−	0.986614i	$-0.552140\pi$
$701$	2.36301	−	0.502274i	0.0892498	−	0.0189706i	0.252320	+	0.967644i	$0.418806\pi$
$702$		0			0
$703$	4.27495	+	4.74782i	0.161233	+	0.179067i
$704$	−0.147278	−	1.40126i	−0.00555076	−	0.0528119i
$705$		0			0
$706$	−2.54186	+	24.1842i	−0.0956641	+	0.910183i
$707$	8.24366	+	14.2784i	0.310035	+	0.536996i
$708$		0			0
$709$	29.2254	+	21.2335i	1.09758	+	0.797441i	0.980664	−	0.195700i	$-0.0626979\pi$
$709$	29.2254	+	21.2335i	1.09758	+	0.797441i	0.116920	+	0.993141i	$0.462698\pi$
$710$	5.19223	−	5.76656i	0.194861	−	0.216415i
$711$		0			0
$712$	0.595693			0.0223246
$713$	32.3525	−	4.59046i	1.21161	−	0.171914i
$714$		0			0
$715$	−0.872829	+	2.68629i	−0.0326420	+	0.100462i
$716$	−9.50046	+	10.5513i	−0.355049	+	0.394322i
$717$		0			0
$718$	9.71490	−	16.8267i	0.362557	−	0.627967i
$719$	13.2301	+	22.9152i	0.493399	+	0.854592i	0.999971	−	0.00760589i	$-0.00242105\pi$
$719$	13.2301	+	22.9152i	0.493399	+	0.854592i	−0.506572	+	0.862197i	$0.669088\pi$
$720$		0			0
$721$	−24.6170	+	17.8853i	−0.916786	+	0.666084i
$722$	−1.42982	−	13.6038i	−0.0532123	−	0.506282i
$723$		0			0
$724$	15.3679	−	6.84224i	0.571145	−	0.254290i
$725$	−1.06789	+	0.226988i	−0.0396605	+	0.00843011i
$726$		0			0
$727$	−6.46885	−	2.88012i	−0.239916	−	0.106818i	0.283257	−	0.959044i	$-0.408585\pi$
$727$	−6.46885	−	2.88012i	−0.239916	−	0.106818i	−0.523173	+	0.852227i	$0.675252\pi$
$728$	−1.42928	−	4.39888i	−0.0529728	−	0.163033i
$729$		0			0
$730$	3.90802	+	1.73996i	0.144642	+	0.0643989i
$731$	−1.18261	−	0.251372i	−0.0437404	−	0.00929731i
$732$		0			0
$733$	24.5259	−	10.9197i	0.905886	−	0.403327i	0.0997200	−	0.995016i	$-0.468205\pi$
$733$	24.5259	−	10.9197i	0.905886	−	0.403327i	0.806166	+	0.591689i	$0.201539\pi$
$734$	−12.8936	−	14.3198i	−0.475910	−	0.528552i
$735$		0			0
$736$	−4.74803	+	3.44964i	−0.175015	+	0.127156i
$737$	0.773103	−	7.35559i	0.0284776	−	0.270947i
$738$		0			0
$739$	−11.7031	+	20.2703i	−0.430505	+	0.745656i	−0.996917	−	0.0784659i	$-0.974998\pi$
$739$	−11.7031	+	20.2703i	−0.430505	+	0.745656i	0.566412	+	0.824122i	$0.308331\pi$
$740$	1.61377	+	1.17247i	0.0593233	+	0.0431009i
$741$		0			0
$742$	2.46308	−	7.58057i	0.0904223	−	0.278291i
$743$	15.2912			0.560979			0.280490	−	0.959857i	$-0.409503\pi$
$743$	15.2912			0.560979			0.280490	+	0.959857i	$0.409503\pi$
$744$		0			0
$745$	14.7151			0.539120
$746$	1.35526	−	4.17108i	0.0496198	−	0.152714i
$747$		0			0
$748$	−0.485216	−	0.352530i	−0.0177413	−	0.0128898i
$749$	3.71559	−	6.43559i	0.135765	−	0.235151i
$750$		0			0
$751$	2.22176	−	21.1387i	0.0810733	−	0.771361i	−0.876155	−	0.482029i	$-0.839900\pi$
$751$	2.22176	−	21.1387i	0.0810733	−	0.771361i	0.957229	−	0.289332i	$-0.0934333\pi$
$752$	−5.57433	+	4.04999i	−0.203275	+	0.147688i
$753$		0			0
$754$	−0.453739	−	0.503928i	−0.0165242	−	0.0183520i
$755$	0.691046	−	0.307674i	0.0251497	−	0.0111974i
$756$		0			0
$757$	−47.8122	−	10.1628i	−1.73776	−	0.369373i	−0.773392	−	0.633928i	$-0.781442\pi$
$757$	−47.8122	−	10.1628i	−1.73776	−	0.369373i	−0.964371	+	0.264555i	$0.914775\pi$
$758$	−11.6994	−	5.20890i	−0.424941	−	0.189196i
$759$		0			0
$760$	0.513403	+	1.58009i	0.0186231	+	0.0573160i
$761$	20.6350	+	9.18729i	0.748018	+	0.333039i	0.745096	−	0.666957i	$-0.232403\pi$
$761$	20.6350	+	9.18729i	0.748018	+	0.333039i	0.00292132	+	0.999996i	$0.499070\pi$
$762$		0			0
$763$	−15.9972	+	3.40032i	−0.579139	+	0.123100i
$764$	22.3710	−	9.96021i	0.809354	−	0.360348i
$765$		0			0
$766$	2.93953	+	27.9678i	0.106210	+	1.01052i
$767$	27.1950	−	19.7583i	0.981954	−	0.713432i
$768$		0			0
$769$	23.3506	+	40.4444i	0.842044	+	1.45846i	0.888163	+	0.459528i	$0.151981\pi$
$769$	23.3506	+	40.4444i	0.842044	+	1.45846i	−0.0461191	+	0.998936i	$0.514685\pi$
$770$	−0.843153	+	1.46038i	−0.0303851	+	0.0526286i
$771$		0			0
$772$	8.02948	−	8.91764i	0.288987	−	0.320953i
$773$	8.14908	−	25.0803i	0.293102	−	0.902076i	−0.690750	−	0.723094i	$-0.742720\pi$
$773$	8.14908	−	25.0803i	0.293102	−	0.902076i	0.983852	−	0.178982i	$-0.0572804\pi$
$774$		0			0
$775$	0.903716	+	24.9343i	0.0324624	+	0.895666i
$776$	−5.23416			−0.187895
$777$		0			0
$778$	1.57031	−	1.74401i	0.0562984	−	0.0625257i
$779$	−9.43490	−	6.85486i	−0.338040	−	0.245601i
$780$		0			0
$781$	7.59010	+	13.1464i	0.271595	+	0.470417i
$782$	−0.261134	+	2.48453i	−0.00933815	+	0.0888465i
$783$		0			0
$784$	0.443057	+	4.21540i	0.0158235	+	0.150550i
$785$	7.02752	+	7.80485i	0.250823	+	0.278567i
$786$		0			0
$787$	5.11735	−	1.08773i	0.182414	−	0.0387732i	−0.115799	−	0.993273i	$-0.536943\pi$
$787$	5.11735	−	1.08773i	0.182414	−	0.0387732i	0.298213	+	0.954499i	$0.403610\pi$
$788$	13.1095	+	2.78651i	0.467007	+	0.0992655i
$789$		0			0
$790$	2.98097	+	9.17449i	0.106058	+	0.326414i
$791$	−5.63759	−	17.3507i	−0.200450	−	0.616921i
$792$		0			0
$793$	−7.13296	−	1.51616i	−0.253299	−	0.0538403i
$794$	22.0807	−	4.69339i	0.783613	−	0.166562i
$795$		0			0
$796$	−0.698154	−	0.775378i	−0.0247454	−	0.0274826i
$797$	3.86920	+	36.8130i	0.137054	+	1.30398i	0.819513	+	0.573060i	$0.194244\pi$
$797$	3.86920	+	36.8130i	0.137054	+	1.30398i	−0.682459	+	0.730924i	$0.739090\pi$
$798$		0			0
$799$	−0.306580	+	2.91691i	−0.0108460	+	0.103193i
$800$	−2.24064	−	3.88090i	−0.0792185	−	0.137210i
$801$		0			0
$802$	17.0686	+	12.4011i	0.602714	+	0.437897i
$803$	−5.59979	+	6.21920i	−0.197612	+	0.219471i
$804$		0			0
$805$	7.02406			0.247565
$806$	−13.1315	+	8.22964i	−0.462539	+	0.289877i
$807$		0			0
$808$	−3.06598	+	9.43612i	−0.107861	+	0.331962i
$809$	15.5080	−	17.2234i	0.545233	−	0.605543i	−0.406054	−	0.913849i	$-0.633095\pi$
$809$	15.5080	−	17.2234i	0.545233	−	0.605543i	0.951287	+	0.308306i	$0.0997621\pi$
$810$		0			0
$811$	12.6198	−	21.8581i	0.443140	−	0.767542i	−0.554780	−	0.831997i	$-0.687198\pi$
$811$	12.6198	−	21.8581i	0.443140	−	0.767542i	0.997921	+	0.0644553i	$0.0205310\pi$
$812$	−0.202421	−	0.350603i	−0.00710357	−	0.0123037i
$813$		0			0
$814$	−3.15701	+	2.29370i	−0.110653	+	0.0803941i
$815$	−0.368088	−	3.50213i	−0.0128936	−	0.122674i
$816$		0			0
$817$	−5.98550	+	2.66492i	−0.209406	+	0.0932336i
$818$	−20.9629	+	4.45580i	−0.732950	+	0.155793i
$819$		0			0
$820$	−3.32639	−	1.48100i	−0.116162	−	0.0517188i
$821$	−3.92277	−	12.0730i	−0.136906	−	0.421352i	0.858976	−	0.512016i	$-0.171101\pi$
$821$	−3.92277	−	12.0730i	−0.136906	−	0.421352i	−0.995882	+	0.0906640i	$0.971101\pi$
$822$		0			0
$823$	−11.2280	−	4.99901i	−0.391382	−	0.174255i	0.201604	−	0.979467i	$-0.435385\pi$
$823$	−11.2280	−	4.99901i	−0.391382	−	0.174255i	−0.592986	+	0.805213i	$0.702051\pi$
$824$	−17.9110	−	3.80710i	−0.623959	−	0.132626i
$825$		0			0
$826$	18.3337	−	8.16270i	0.637912	−	0.284017i
$827$	19.2979	+	21.4325i	0.671053	+	0.745280i	0.978491	−	0.206288i	$-0.0661384\pi$
$827$	19.2979	+	21.4325i	0.671053	+	0.745280i	−0.307438	+	0.951568i	$0.599472\pi$
$828$		0			0
$829$	23.3372	−	16.9555i	0.810536	−	0.588889i	−0.103450	−	0.994635i	$-0.532988\pi$
$829$	23.3372	−	16.9555i	0.810536	−	0.588889i	0.913986	+	0.405746i	$0.132988\pi$
$830$	0.451210	−	4.29298i	0.0156617	−	0.149011i
$831$		0			0
$832$	1.39169	−	2.41048i	0.0482483	−	0.0835685i
$833$	1.45968	+	1.06052i	0.0505748	+	0.0367447i
$834$		0			0
$835$	−2.78025	+	8.55672i	−0.0962144	+	0.296118i
$836$	−3.25021			−0.112411
$837$		0			0
$838$	12.3561			0.426836
$839$	5.96488	−	18.3580i	0.205931	−	0.633789i	−0.793743	−	0.608253i	$-0.791871\pi$
$839$	5.96488	−	18.3580i	0.205931	−	0.633789i	0.999674	−	0.0255362i	$-0.00812932\pi$
$840$		0			0
$841$	23.4135	+	17.0109i	0.807361	+	0.586582i
$842$	11.9711	−	20.7345i	0.412551	−	0.714559i
$843$		0			0
$844$	1.71448	−	16.3122i	0.0590148	−	0.561488i
$845$	3.06066	−	2.22370i	0.105290	−	0.0764976i
$846$		0			0
$847$	10.0237	+	11.1325i	0.344419	+	0.382516i
$848$	4.38190	−	1.95095i	0.150475	−	0.0669959i
$849$		0			0
$850$	−1.86586	−	0.396601i	−0.0639986	−	0.0136033i
$851$	14.8491	+	6.61124i	0.509020	+	0.226630i
$852$		0			0
$853$	−1.60711	−	4.94618i	−0.0550264	−	0.169354i	0.919766	−	0.392467i	$-0.128378\pi$
$853$	−1.60711	−	4.94618i	−0.0550264	−	0.169354i	−0.974793	+	0.223113i	$0.928378\pi$
$854$	−3.97727	−	1.77079i	−0.136099	−	0.0605953i
$855$		0			0
$856$	4.37421	−	0.929767i	0.149507	−	0.0317788i
$857$	−6.13694	+	2.73234i	−0.209634	+	0.0933350i	−0.508867	−	0.860845i	$-0.669936\pi$
$857$	−6.13694	+	2.73234i	−0.209634	+	0.0933350i	0.299234	+	0.954180i	$0.403269\pi$
$858$		0			0
$859$	−4.98966	−	47.4734i	−0.170245	−	1.61977i	−0.662321	−	0.749220i	$-0.730428\pi$
$859$	−4.98966	−	47.4734i	−0.170245	−	1.61977i	0.492076	−	0.870552i	$-0.336238\pi$
$860$	−1.65497	+	1.20241i	−0.0564341	+	0.0410018i
$861$		0			0
$862$	−6.30099	−	10.9136i	−0.214613	−	0.371720i
$863$	−17.0047	+	29.4530i	−0.578846	+	1.00259i	0.416766	+	0.909014i	$0.363163\pi$
$863$	−17.0047	+	29.4530i	−0.578846	+	1.00259i	−0.995612	+	0.0935766i	$0.970170\pi$
$864$		0			0
$865$	2.45160	−	2.72277i	0.0833568	−	0.0925771i
$866$	5.11984	−	15.7573i	0.173979	−	0.535453i
$867$		0			0
$868$	−8.69001	+	3.17591i	−0.294958	+	0.107798i
$869$	−18.8716			−0.640177
$870$		0			0
$871$	9.77650	−	10.8579i	0.331264	−	0.367906i
$872$	−7.96224	−	5.78491i	−0.269636	−	0.195902i
$873$		0			0
$874$	6.76913	+	11.7245i	0.228969	+	0.396586i
$875$	−1.18613	+	11.2853i	−0.0400986	+	0.381513i
$876$		0			0
$877$	1.35364	+	12.8790i	0.0457090	+	0.434892i	0.993314	+	0.115447i	$0.0368300\pi$
$877$	1.35364	+	12.8790i	0.0457090	+	0.434892i	−0.947605	+	0.319445i	$0.896503\pi$
$878$	10.9295	+	12.1384i	0.368852	+	0.409652i
$879$		0			0
$880$	−0.992608	+	0.210985i	−0.0334608	+	0.00711232i
$881$	45.3854	+	9.64697i	1.52907	+	0.325015i	0.894224	−	0.447621i	$-0.147729\pi$
$881$	45.3854	+	9.64697i	1.52907	+	0.325015i	0.634850	+	0.772635i	$0.281062\pi$
$882$		0			0
$883$	5.68470	+	17.4957i	0.191306	+	0.588778i	1.00000		0.000548755i	$0.000174674\pi$
$883$	5.68470	+	17.4957i	0.191306	+	0.588778i	−0.808694	+	0.588229i	$0.799825\pi$
$884$	−0.366125	−	1.12682i	−0.0123141	−	0.0378990i
$885$		0			0
$886$	−13.1246	−	2.78971i	−0.440929	−	0.0937223i
$887$	−1.13016	+	0.240223i	−0.0379470	+	0.00806589i	−0.226846	−	0.973931i	$-0.572841\pi$
$887$	−1.13016	+	0.240223i	−0.0379470	+	0.00806589i	0.188899	+	0.981997i	$0.439508\pi$
$888$		0			0
$889$	−18.1613	−	20.1701i	−0.609110	−	0.676485i
$890$	−0.0448463	−	0.426684i	−0.00150325	−	0.0143025i
$891$		0			0
$892$	2.28420	−	21.7328i	0.0764808	−	0.727666i
$893$	7.94716	+	13.7649i	0.265942	+	0.460624i
$894$		0			0
$895$	8.27296	+	6.01066i	0.276535	+	0.200914i
$896$	1.11192	−	1.23491i	0.0371466	−	0.0412555i
$897$		0			0
$898$	5.10431			0.170333
$899$	−0.974500	+	0.943555i	−0.0325014	+	0.0314693i
$900$		0			0
$901$	0.630941	−	1.94184i	0.0210197	−	0.0646920i
$902$	4.76637	−	5.29359i	0.158703	−	0.176257i
$903$		0			0
$904$	5.48932	−	9.50778i	0.182572	−	0.316224i
$905$	−6.05794	−	10.4927i	−0.201373	−	0.348788i
$906$		0			0
$907$	−3.57748	+	2.59919i	−0.118788	+	0.0863048i	−0.645593	−	0.763681i	$-0.723390\pi$
$907$	−3.57748	+	2.59919i	−0.118788	+	0.0863048i	0.526805	+	0.849986i	$0.323390\pi$
$908$	1.20656	+	11.4796i	0.0400410	+	0.380965i
$909$		0			0
$910$	−3.04324	+	1.35494i	−0.100882	+	0.0449157i
$911$	−11.1228	+	2.36422i	−0.368514	+	0.0783301i	−0.388447	−	0.921471i	$-0.626988\pi$
$911$	−11.1228	+	2.36422i	−0.368514	+	0.0783301i	0.0199324	+	0.999801i	$0.493655\pi$
$912$		0			0
$913$	7.71452	+	3.43472i	0.255313	+	0.113673i
$914$	11.7833	+	36.2652i	0.389756	+	1.19955i
$915$		0			0
$916$	19.0578	+	8.48507i	0.629687	+	0.280354i
$917$	−11.5760	−	2.46056i	−0.382275	−	0.0812550i
$918$		0			0
$919$	21.3808	−	9.51934i	0.705287	−	0.314014i	−0.0225678	−	0.999745i	$-0.507184\pi$
$919$	21.3808	−	9.51934i	0.705287	−	0.314014i	0.727855	+	0.685731i	$0.240517\pi$
$920$	2.82837	+	3.14122i	0.0932486	+	0.103563i
$921$		0			0
$922$	11.0437	−	8.02372i	0.363705	−	0.264247i
$923$	−3.13460	+	29.8237i	−0.103177	+	0.981659i
$924$		0			0
$925$	−6.20562	+	10.7484i	−0.204040	+	0.353407i
$926$	25.3631	+	18.4274i	0.833482	+	0.605560i
$927$		0			0
$928$	0.0752842	−	0.231701i	0.00247133	−	0.00760596i
$929$	33.5711			1.10143			0.550716	−	0.834692i	$-0.314355\pi$
$929$	33.5711			1.10143			0.550716	+	0.834692i	$0.314355\pi$
$930$		0			0
$931$	9.77759			0.320448
$932$	8.46951	−	26.0665i	0.277428	−	0.853836i
$933$		0			0
$934$	5.26787	+	3.82733i	0.172370	+	0.125234i
$935$	−0.215982	+	0.374092i	−0.00706336	+	0.0122341i
$936$		0			0
$937$	−0.582320	+	5.54040i	−0.0190236	+	0.180997i	−0.999908	−	0.0135962i	$-0.995672\pi$
$937$	−0.582320	+	5.54040i	−0.0190236	+	0.180997i	0.980884	+	0.194593i	$0.0623387\pi$
$938$	7.05699	−	5.12720i	0.230419	−	0.167409i
$939$		0			0
$940$	3.32059	+	3.68789i	0.108306	+	0.120286i
$941$	−40.6201	+	18.0852i	−1.32418	+	0.589561i	−0.942336	−	0.334667i	$-0.891376\pi$
$941$	−40.6201	+	18.0852i	−1.32418	+	0.589561i	−0.381840	+	0.924229i	$0.624709\pi$
$942$		0			0
$943$	−29.0224	−	6.16890i	−0.945098	−	0.200887i
$944$	11.0329	+	4.91214i	0.359089	+	0.159877i
$945$		0			0
$946$	−1.23666	−	3.80604i	−0.0402072	−	0.123745i
$947$	30.5374	+	13.5961i	0.992333	+	0.441815i	0.837684	−	0.546154i	$-0.183909\pi$
$947$	30.5374	+	13.5961i	0.992333	+	0.441815i	0.154648	+	0.987970i	$0.450576\pi$
$948$		0			0
$949$	−16.1709	+	3.43724i	−0.524931	+	0.111577i
$950$	−9.44362	+	4.20457i	−0.306391	+	0.136414i
$951$		0			0
$952$	−0.0739386	−	0.703479i	−0.00239636	−	0.0227999i
$953$	−21.5000	+	15.6206i	−0.696452	+	0.506002i	−0.878775	−	0.477237i	$-0.841638\pi$
$953$	−21.5000	+	15.6206i	−0.696452	+	0.506002i	0.182323	+	0.983239i	$0.441638\pi$
$954$		0			0
$955$	−8.81850	−	15.2741i	−0.285360	−	0.494258i
$956$	2.35177	−	4.07338i	0.0760616	−	0.131743i
$957$		0			0
$958$	8.48058	−	9.41864i	0.273995	−	0.304303i
$959$	−7.44411	+	22.9106i	−0.240383	+	0.739823i
$960$		0			0
$961$	17.4028	+	25.6543i	0.561382	+	0.827557i
$962$	−7.70881			−0.248542
$963$		0			0
$964$	7.58629	−	8.42543i	0.244338	−	0.271365i
$965$	−6.99204	−	5.08001i	−0.225082	−	0.163531i
$966$		0			0
$967$	−16.0045	−	27.7207i	−0.514671	−	0.891437i	−0.999855	−	0.0170246i	$-0.994581\pi$
$967$	−16.0045	−	27.7207i	−0.514671	−	0.891437i	0.485184	−	0.874412i	$-0.338753\pi$
$968$	−0.942301	+	8.96540i	−0.0302867	+	0.288159i
$969$		0			0
$970$	0.394050	+	3.74913i	0.0126522	+	0.120377i
$971$	−27.3662	−	30.3933i	−0.878224	−	0.975366i	0.121628	−	0.992576i	$-0.461188\pi$
$971$	−27.3662	−	30.3933i	−0.878224	−	0.975366i	−0.999852	+	0.0172096i	$0.994522\pi$
$972$		0			0
$973$	33.4099	−	7.10149i	1.07107	−	0.227663i
$974$	14.8682	+	3.16032i	0.476406	+	0.101263i
$975$		0			0
$976$	−0.809607	−	2.49171i	−0.0259149	−	0.0797579i
$977$	13.1578	+	40.4956i	0.420956	+	1.29557i	0.906814	+	0.421531i	$0.138507\pi$
$977$	13.1578	+	40.4956i	0.420956	+	1.29557i	−0.485858	+	0.874038i	$0.661493\pi$
$978$		0			0
$979$	0.820977	+	0.174504i	0.0262385	+	0.00557717i
$980$	2.98606	−	0.634707i	0.0953863	−	0.0202750i
$981$		0			0
$982$	−17.9327	−	19.9163i	−0.572256	−	0.635555i
$983$	−2.23926	−	21.3051i	−0.0714212	−	0.679527i	−0.970395	−	0.241524i	$-0.922353\pi$
$983$	−2.23926	−	21.3051i	−0.0714212	−	0.679527i	0.898974	−	0.438003i	$-0.144314\pi$
$984$		0			0
$985$	1.00899	−	9.59989i	0.0321491	−	0.305878i
$986$	−0.0518520	−	0.0898103i	−0.00165130	−	0.00286014i
$987$		0			0
$988$	−5.19443	−	3.77398i	−0.165257	−	0.120066i
$989$	−11.1540	+	12.3878i	−0.354676	+	0.393908i
$990$		0			0
$991$	−6.00211			−0.190663			−0.0953317	−	0.995446i	$-0.530391\pi$
$991$	−6.00211			−0.190663			−0.0953317	+	0.995446i	$0.530391\pi$
$992$	−4.91949	−	2.60741i	−0.156194	−	0.0827853i
$993$		0			0
$994$	−5.53247	+	17.0272i	−0.175479	+	0.540069i
$995$	−0.502829	+	0.558449i	−0.0159408	+	0.0177040i
$996$		0			0
$997$	−18.0916	+	31.3356i	−0.572968	+	0.992409i	0.423291	+	0.905994i	$0.360875\pi$
$997$	−18.0916	+	31.3356i	−0.572968	+	0.992409i	−0.996259	+	0.0864157i	$0.972459\pi$
$998$	16.0267	+	27.7591i	0.507318	+	0.878700i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	558.2.ba.e.541.1		8
3.2	odd	2		186.2.m.a.169.1	✓	8
31.20	even	15	inner	558.2.ba.e.361.1		8
93.20	odd	30		186.2.m.a.175.1	yes	8
93.50	odd	30		5766.2.a.bg.1.3		4
93.74	even	30		5766.2.a.bc.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
186.2.m.a.169.1	✓	8	3.2	odd	2
186.2.m.a.175.1	yes	8	93.20	odd	30
558.2.ba.e.361.1		8	31.20	even	15	inner
558.2.ba.e.541.1		8	1.1	even	1	trivial
5766.2.a.bc.1.3		4	93.74	even	30
5766.2.a.bg.1.3		4	93.50	odd	30

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:	\( N \)	\(=\)	\( 558 = 2 \cdot 3^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	558.ba (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 + 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(-0.360114 + 0.623735i) q^{5} +(0.173699 - 1.65264i) q^{7} +(0.809017 - 0.587785i) q^{8} +(-0.481926 - 0.535233i) q^{10} +(1.28716 - 0.573083i) q^{11} +(2.72256 + 0.578699i) q^{13} +(1.51807 + 0.675890i) q^{14} +(0.309017 + 0.951057i) q^{16} +(0.388870 + 0.173136i) q^{17} +(2.25638 - 0.479607i) q^{19} +(0.657960 - 0.292943i) q^{20} +(0.147278 + 1.40126i) q^{22} +(4.74803 - 3.44964i) q^{23} +(2.24064 + 3.88090i) q^{25} +(-1.39169 + 2.41048i) q^{26} +(-1.11192 + 1.23491i) q^{28} +(-0.0752842 + 0.231701i) q^{29} +(4.91949 + 2.60741i) q^{31} -1.00000 q^{32} +(-0.284829 + 0.316335i) q^{34} +(0.968255 + 0.703479i) q^{35} +(1.38479 + 2.39853i) q^{37} +(-0.241125 + 2.29415i) q^{38} +(0.0752842 + 0.716282i) q^{40} +(-3.38286 - 3.75704i) q^{41} +(-2.77823 + 0.590530i) q^{43} +(-1.37819 - 0.292943i) q^{44} +(1.81359 + 5.58164i) q^{46} +(2.12920 + 6.55302i) q^{47} +(4.14600 + 0.881260i) q^{49} +(-4.38335 + 0.931709i) q^{50} +(-1.86245 - 2.06846i) q^{52} +(-0.501380 - 4.77031i) q^{53} +(-0.106074 + 1.00922i) q^{55} +(-0.830869 - 1.43911i) q^{56} +(-0.197097 - 0.143199i) q^{58} +(8.08107 - 8.97493i) q^{59} -2.61994 q^{61} +(-4.00000 + 3.87298i) q^{62} +(0.309017 - 0.951057i) q^{64} +(-1.34139 + 1.48976i) q^{65} +(2.62464 - 4.54600i) q^{67} +(-0.212835 - 0.368642i) q^{68} +(-0.968255 + 0.703479i) q^{70} +(1.12618 + 10.7149i) q^{71} +(-5.42610 + 2.41585i) q^{73} +(-2.70906 + 0.575828i) q^{74} +(-2.10735 - 0.938254i) q^{76} +(-0.723518 - 2.22676i) q^{77} +(-12.2359 - 5.44777i) q^{79} +(-0.704489 - 0.149744i) q^{80} +(4.61852 - 2.05630i) q^{82} +(4.01038 + 4.45398i) q^{83} +(-0.248028 + 0.180203i) q^{85} +(0.296892 - 2.82474i) q^{86} +(0.704489 - 1.22021i) q^{88} +(0.481926 + 0.350140i) q^{89} +(1.42928 - 4.39888i) q^{91} -5.86889 q^{92} -6.89025 q^{94} +(-0.513403 + 1.58009i) q^{95} +(-4.23452 - 3.07656i) q^{97} +(-2.11931 + 3.67076i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} - 2 q^{4} - 3 q^{5} - 4 q^{7} + 2 q^{8} - 12 q^{10} - 3 q^{11} + 11 q^{13} + 4 q^{14} - 2 q^{16} + 2 q^{19} - 3 q^{20} - 12 q^{22} + 6 q^{23} - q^{25} + 4 q^{26} + 6 q^{28} - 3 q^{29} - 8 q^{31}+ \cdots + 11 q^{98}+O(q^{100}) \) 8 * q + 2 * q^2 - 2 * q^4 - 3 * q^5 - 4 * q^7 + 2 * q^8 - 12 * q^10 - 3 * q^11 + 11 * q^13 + 4 * q^14 - 2 * q^16 + 2 * q^19 - 3 * q^20 - 12 * q^22 + 6 * q^23 - q^25 + 4 * q^26 + 6 * q^28 - 3 * q^29 - 8 * q^31 - 8 * q^32 - 24 * q^35 + 8 * q^37 + 18 * q^38 + 3 * q^40 + 3 * q^41 - 15 * q^43 - 3 * q^44 + 9 * q^46 + 12 * q^47 + 39 * q^49 - 4 * q^50 - 4 * q^52 + 36 * q^53 - 6 * q^55 - 11 * q^56 - 12 * q^58 - 21 * q^59 - 70 * q^61 - 32 * q^62 - 2 * q^64 + 27 * q^65 + 17 * q^67 - 15 * q^68 + 24 * q^70 + 12 * q^71 - q^73 - 18 * q^74 - 3 * q^76 - 24 * q^77 - 33 * q^79 - 3 * q^80 + 27 * q^82 + 54 * q^83 + 30 * q^85 - 35 * q^86 + 3 * q^88 + 12 * q^89 + 8 * q^91 + 6 * q^92 - 12 * q^94 - 18 * q^95 - 9 * q^97 + 11 * q^98

Introduction

L-functions

Modular forms

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