LMFDB - Embedded newform 429.2.bs.a.85.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [429,2,Mod(7,429)] 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("429.7"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(429, base_ring=CyclotomicField(60)) chi = DirichletCharacter(H, H._module([0, 42, 55])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.bs (of order $60$, degree $16$, minimal)

Newform invariants

comment:select newform

sage:traces = [224,0,-28] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$14$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			85.10
Character	$\chi$	$=$	429.85
Dual form			429.2.bs.a.106.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.997265 + 0.807569i) q^{2} +(0.978148 + 0.207912i) q^{3} +(-0.0734543 - 0.345575i) q^{4} +(-0.322223 - 2.03444i) q^{5} +(0.807569 + 0.997265i) q^{6} +(-2.56603 - 1.66640i) q^{7} +(1.37098 - 2.69070i) q^{8} +(0.913545 + 0.406737i) q^{9} +(1.32161 - 2.28909i) q^{10} +(-1.16790 - 3.10419i) q^{11} -0.353296i q^{12} +(2.35894 - 2.72679i) q^{13} +(-1.21328 - 3.73408i) q^{14} +(0.107801 - 2.05697i) q^{15} +(2.89465 - 1.28878i) q^{16} +(-0.739265 + 7.03364i) q^{17} +(0.582579 + 1.14338i) q^{18} +(0.296316 + 5.65404i) q^{19} +(-0.679382 + 0.260790i) q^{20} +(-2.16349 - 2.16349i) q^{21} +(1.34214 - 4.03886i) q^{22} +(4.88228 + 2.81878i) q^{23} +(1.90045 - 2.34686i) q^{24} +(0.720175 - 0.233999i) q^{25} +(4.55456 - 0.814326i) q^{26} +(0.809017 + 0.587785i) q^{27} +(-0.387380 + 1.00916i) q^{28} +(-0.399802 + 0.359984i) q^{29} +(1.76865 - 1.96429i) q^{30} +(-2.41772 - 0.382929i) q^{31} +(-1.90637 - 0.510811i) q^{32} +(-0.496982 - 3.27918i) q^{33} +(-6.41739 + 6.41739i) q^{34} +(-2.56335 + 5.75737i) q^{35} +(0.0734543 - 0.345575i) q^{36} +(-8.25282 - 0.432512i) q^{37} +(-4.27052 + 5.87787i) q^{38} +(2.87432 - 2.17675i) q^{39} +(-5.91582 - 1.92217i) q^{40} +(6.45151 - 4.18966i) q^{41} +(-0.410404 - 3.90474i) q^{42} +(2.07444 + 3.59304i) q^{43} +(-0.986944 + 0.631614i) q^{44} +(0.533115 - 1.98961i) q^{45} +(2.59256 + 6.75385i) q^{46} +(12.0849 + 6.15757i) q^{47} +(3.09935 - 0.658787i) q^{48} +(0.960454 + 2.15721i) q^{49} +(0.907176 + 0.348232i) q^{50} +(-2.18549 + 6.72623i) q^{51} +(-1.11559 - 0.614897i) q^{52} +(8.73690 - 6.34773i) q^{53} +(0.332127 + 1.23951i) q^{54} +(-5.93896 + 3.37626i) q^{55} +(-8.00174 + 4.61981i) q^{56} +(-0.885701 + 5.59209i) q^{57} +(-0.689420 + 0.0361310i) q^{58} +(-2.18515 + 3.36484i) q^{59} +(-0.718758 + 0.113840i) q^{60} +(7.05955 + 0.741989i) q^{61} +(-2.10186 - 2.33436i) q^{62} +(-1.66640 - 2.56603i) q^{63} +(-5.21355 - 7.17583i) q^{64} +(-6.30759 - 3.92048i) q^{65} +(2.15254 - 3.67156i) q^{66} +(-7.03137 + 1.88405i) q^{67} +(2.48495 - 0.261179i) q^{68} +(4.18953 + 3.77227i) q^{69} +(-7.20581 + 3.67154i) q^{70} +(8.05784 - 6.52511i) q^{71} +(2.34686 - 1.90045i) q^{72} +(-0.976074 + 0.497335i) q^{73} +(-7.88096 - 7.09605i) q^{74} +(0.753089 - 0.0791528i) q^{75} +(1.93213 - 0.517713i) q^{76} +(-2.17595 + 9.91162i) q^{77} +(4.62434 + 0.150415i) q^{78} +(-5.31037 - 7.30909i) q^{79} +(-3.55467 - 5.47371i) q^{80} +(0.669131 + 0.743145i) q^{81} +(9.81731 + 1.03184i) q^{82} +(-12.2243 + 1.93613i) q^{83} +(-0.588730 + 0.906565i) q^{84} +(14.5477 - 0.762413i) q^{85} +(-0.832859 + 5.25846i) q^{86} +(-0.465910 + 0.268993i) q^{87} +(-9.95362 - 1.11331i) q^{88} +(0.294790 + 1.10017i) q^{89} +(2.13840 - 1.55364i) q^{90} +(-10.5970 + 3.06609i) q^{91} +(0.615478 - 1.89425i) q^{92} +(-2.28527 - 0.877233i) q^{93} +(7.07920 + 15.9001i) q^{94} +(11.4073 - 2.42470i) q^{95} +(-1.75851 - 0.896006i) q^{96} +(-3.83385 - 9.98753i) q^{97} +(-0.784273 + 2.92695i) q^{98} +(0.195658 - 3.31085i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q - 28 q^{3} - 6 q^{5} + 28 q^{9} - 16 q^{11} - 10 q^{13} - 36 q^{14} + 8 q^{15} - 24 q^{16} + 50 q^{20} + 10 q^{22} - 48 q^{23} - 30 q^{24} + 10 q^{26} + 56 q^{27} + 20 q^{29} + 12 q^{31} - 32 q^{33}+ \cdots - 6 q^{99}+O(q^{100}) $ 224 * q - 28 * q^3 - 6 * q^5 + 28 * q^9 - 16 * q^11 - 10 * q^13 - 36 * q^14 + 8 * q^15 - 24 * q^16 + 50 * q^20 + 10 * q^22 - 48 * q^23 - 30 * q^24 + 10 * q^26 + 56 * q^27 + 20 * q^29 + 12 * q^31 - 32 * q^33 - 104 * q^34 + 20 * q^35 + 12 * q^37 + 20 * q^39 - 80 * q^40 + 190 * q^41 + 32 * q^42 - 24 * q^44 + 4 * q^45 - 40 * q^46 - 10 * q^47 + 44 * q^48 - 24 * q^49 - 180 * q^50 - 110 * q^52 + 28 * q^53 - 62 * q^55 - 72 * q^56 + 20 * q^58 - 118 * q^59 + 88 * q^60 - 20 * q^61 + 120 * q^62 - 20 * q^66 - 156 * q^67 - 60 * q^68 + 12 * q^69 - 20 * q^70 + 64 * q^71 - 30 * q^72 + 10 * q^73 - 60 * q^74 - 12 * q^75 + 84 * q^78 + 200 * q^79 + 188 * q^80 + 28 * q^81 - 138 * q^82 - 80 * q^83 - 60 * q^84 + 40 * q^85 - 42 * q^86 - 18 * q^88 + 216 * q^89 - 88 * q^91 + 16 * q^92 + 12 * q^93 - 40 * q^94 - 300 * q^95 - 100 * q^96 + 18 * q^97 - 6 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{3}{10}\right)$	$1$

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 $

$2$	0.997265	+	0.807569i	0.705173	+	0.571038i	0.913410	−	0.407041i	$-0.133439\pi$
$2$	0.997265	+	0.807569i	0.705173	+	0.571038i	−0.208237	+	0.978078i	$0.566773\pi$
$3$	0.978148	+	0.207912i	0.564734	+	0.120038i
$3$	0.978148	+	0.207912i	0.564734	+	0.120038i
$4$	−0.0734543	−	0.345575i	−0.0367271	−	0.172788i
$5$	−0.322223	−	2.03444i	−0.144103	−	0.909828i	−0.948739	−	0.316060i	$-0.897640\pi$
$5$	−0.322223	−	2.03444i	−0.144103	−	0.909828i	0.804636	−	0.593768i	$-0.202360\pi$
$6$	0.807569	+	0.997265i	0.329689	+	0.407132i
$7$	−2.56603	−	1.66640i	−0.969867	−	0.629839i	−0.0405714	−	0.999177i	$-0.512918\pi$
$7$	−2.56603	−	1.66640i	−0.969867	−	0.629839i	−0.929295	+	0.369338i	$0.879584\pi$
$8$	1.37098	−	2.69070i	0.484715	−	0.951306i
$9$	0.913545	+	0.406737i	0.304515	+	0.135579i
$10$	1.32161	−	2.28909i	0.417929	−	0.723874i
$11$	−1.16790	−	3.10419i	−0.352135	−	0.935949i
$11$	−1.16790	−	3.10419i	−0.352135	−	0.935949i
$12$		−	0.353296i		−	0.101988i
$13$	2.35894	−	2.72679i	0.654253	−	0.756276i
$13$	2.35894	−	2.72679i	0.654253	−	0.756276i
$14$	−1.21328	−	3.73408i	−0.324262	−	0.997975i
$15$	0.107801	−	2.05697i	0.0278342	−	0.531108i
$16$	2.89465	−	1.28878i	0.723663	−	0.322196i
$17$	−0.739265	+	7.03364i	−0.179298	+	1.70591i	0.421765	+	0.906705i	$0.361411\pi$
$17$	−0.739265	+	7.03364i	−0.179298	+	1.70591i	−0.601063	+	0.799202i	$0.705256\pi$
$18$	0.582579	+	1.14338i	0.137315	+	0.269496i
$19$	0.296316	+	5.65404i	0.0679795	+	1.29713i	0.793349	+	0.608767i	$0.208335\pi$
$19$	0.296316	+	5.65404i	0.0679795	+	1.29713i	−0.725370	+	0.688359i	$0.758331\pi$
$20$	−0.679382	+	0.260790i	−0.151915	+	0.0583145i
$21$	−2.16349	−	2.16349i	−0.472112	−	0.472112i
$22$	1.34214	−	4.03886i	0.286146	−	0.861088i
$23$	4.88228	+	2.81878i	1.01803	+	0.587757i	0.913531	−	0.406768i	$-0.133344\pi$
$23$	4.88228	+	2.81878i	1.01803	+	0.587757i	0.104494	+	0.994526i	$0.466678\pi$
$24$	1.90045	−	2.34686i	0.387927	−	0.479050i
$25$	0.720175	−	0.233999i	0.144035	−	0.0467998i
$26$	4.55456	−	0.814326i	0.893223	−	0.159702i
$27$	0.809017	+	0.587785i	0.155695	+	0.113119i
$28$	−0.387380	+	1.00916i	−0.0732079	+	0.190713i
$29$	−0.399802	+	0.359984i	−0.0742414	+	0.0668473i	−0.705416	−	0.708794i	$-0.749240\pi$
$29$	−0.399802	+	0.359984i	−0.0742414	+	0.0668473i	0.631175	+	0.775641i	$0.282573\pi$
$30$	1.76865	−	1.96429i	0.322911	−	0.358629i
$31$	−2.41772	−	0.382929i	−0.434235	−	0.0687761i	−0.0645095	−	0.997917i	$-0.520548\pi$
$31$	−2.41772	−	0.382929i	−0.434235	−	0.0687761i	−0.369726	+	0.929141i	$0.620548\pi$
$32$	−1.90637	−	0.510811i	−0.337002	−	0.0902995i
$33$	−0.496982	−	3.27918i	−0.0865134	−	0.570832i
$34$	−6.41739	+	6.41739i	−1.10057	+	1.10057i
$35$	−2.56335	+	5.75737i	−0.433285	+	0.973173i
$36$	0.0734543	−	0.345575i	0.0122424	−	0.0575959i
$37$	−8.25282	−	0.432512i	−1.35676	−	0.0711045i	−0.639971	−	0.768399i	$-0.721054\pi$
$37$	−8.25282	−	0.432512i	−1.35676	−	0.0711045i	−0.716785	+	0.697295i	$0.754387\pi$
$38$	−4.27052	+	5.87787i	−0.692770	+	0.953517i
$39$	2.87432	−	2.17675i	0.460260	−	0.348560i
$40$	−5.91582	−	1.92217i	−0.935373	−	0.303921i
$41$	6.45151	−	4.18966i	1.00756	−	0.654315i	0.0683483	−	0.997662i	$-0.478227\pi$
$41$	6.45151	−	4.18966i	1.00756	−	0.654315i	0.939209	+	0.343346i	$0.111560\pi$
$42$	−0.410404	−	3.90474i	−0.0633268	−	0.602514i
$43$	2.07444	+	3.59304i	0.316349	+	0.547933i	0.979723	−	0.200355i	$-0.0642095\pi$
$43$	2.07444	+	3.59304i	0.316349	+	0.547933i	−0.663374	+	0.748288i	$0.730876\pi$
$44$	−0.986944	+	0.631614i	−0.148787	+	0.0952194i
$45$	0.533115	−	1.98961i	0.0794720	−	0.296594i
$46$	2.59256	+	6.75385i	0.382252	+	0.995801i
$47$	12.0849	+	6.15757i	1.76277	+	0.898175i	0.947927	+	0.318489i	$0.103175\pi$
$47$	12.0849	+	6.15757i	1.76277	+	0.898175i	0.814840	+	0.579685i	$0.196825\pi$
$48$	3.09935	−	0.658787i	0.447353	−	0.0950877i
$49$	0.960454	+	2.15721i	0.137208	+	0.308173i
$50$	0.907176	+	0.348232i	0.128294	+	0.0492474i
$51$	−2.18549	+	6.72623i	−0.306029	+	0.941861i
$52$	−1.11559	−	0.614897i	−0.154704	−	0.0852709i
$53$	8.73690	−	6.34773i	1.20011	−	0.871928i	0.205811	−	0.978592i	$-0.434017\pi$
$53$	8.73690	−	6.34773i	1.20011	−	0.871928i	0.994295	+	0.106664i	$0.0340168\pi$
$54$	0.332127	+	1.23951i	0.0451967	+	0.168677i
$55$	−5.93896	+	3.37626i	−0.800809	+	0.455255i
$56$	−8.00174	+	4.61981i	−1.06928	+	0.617348i
$57$	−0.885701	+	5.59209i	−0.117314	+	0.740691i
$58$	−0.689420	+	0.0361310i	−0.0905253	+	0.00474423i
$59$	−2.18515	+	3.36484i	−0.284483	+	0.438065i	−0.951805	−	0.306704i	$-0.900774\pi$
$59$	−2.18515	+	3.36484i	−0.284483	+	0.438065i	0.667322	+	0.744769i	$0.267440\pi$
$60$	−0.718758	+	0.113840i	−0.0927912	+	0.0146967i
$61$	7.05955	+	0.741989i	0.903883	+	0.0950019i	0.545053	−	0.838401i	$-0.316509\pi$
$61$	7.05955	+	0.741989i	0.903883	+	0.0950019i	0.358829	+	0.933403i	$0.383176\pi$
$62$	−2.10186	−	2.33436i	−0.266937	−	0.296464i
$63$	−1.66640	−	2.56603i	−0.209946	−	0.323289i
$64$	−5.21355	−	7.17583i	−0.651693	−	0.896979i
$65$	−6.30759	−	3.92048i	−0.782361	−	0.486276i
$66$	2.15254	−	3.67156i	0.264959	−	0.451937i
$67$	−7.03137	+	1.88405i	−0.859019	+	0.230173i	−0.661333	−	0.750092i	$-0.730009\pi$
$67$	−7.03137	+	1.88405i	−0.859019	+	0.230173i	−0.197685	+	0.980266i	$0.563342\pi$
$68$	2.48495	−	0.261179i	0.301345	−	0.0316726i
$69$	4.18953	+	3.77227i	0.504360	+	0.454128i
$70$	−7.20581	+	3.67154i	−0.861259	+	0.438833i
$71$	8.05784	−	6.52511i	0.956289	−	0.774388i	−0.0179651	−	0.999839i	$-0.505719\pi$
$71$	8.05784	−	6.52511i	0.956289	−	0.774388i	0.974255	+	0.225451i	$0.0723854\pi$
$72$	2.34686	−	1.90045i	0.276580	−	0.223970i
$73$	−0.976074	+	0.497335i	−0.114241	+	0.0582086i	−0.510177	−	0.860069i	$-0.670420\pi$
$73$	−0.976074	+	0.497335i	−0.114241	+	0.0582086i	0.395936	+	0.918278i	$0.370420\pi$
$74$	−7.88096	−	7.09605i	−0.916144	−	0.824899i
$75$	0.753089	−	0.0791528i	0.0869592	−	0.00913978i
$76$	1.93213	−	0.517713i	0.221631	−	0.0593857i
$77$	−2.17595	+	9.91162i	−0.247973	+	1.12953i
$78$	4.62434	+	0.150415i	0.523604	+	0.0170312i
$79$	−5.31037	−	7.30909i	−0.597463	−	0.822337i	0.398010	−	0.917381i	$-0.369701\pi$
$79$	−5.31037	−	7.30909i	−0.597463	−	0.822337i	−0.995473	+	0.0950437i	$0.969701\pi$
$80$	−3.55467	−	5.47371i	−0.397424	−	0.611980i
$81$	0.669131	+	0.743145i	0.0743478	+	0.0825716i
$82$	9.81731	+	1.03184i	1.08414	+	0.113948i
$83$	−12.2243	+	1.93613i	−1.34179	+	0.212518i	−0.785701	−	0.618607i	$-0.787697\pi$
$83$	−12.2243	+	1.93613i	−1.34179	+	0.212518i	−0.556086	+	0.831125i	$0.687697\pi$
$84$	−0.588730	+	0.906565i	−0.0642358	+	0.0989144i
$85$	14.5477	−	0.762413i	1.57792	−	0.0826953i
$86$	−0.832859	+	5.25846i	−0.0898095	+	0.567035i
$87$	−0.465910	+	0.268993i	−0.0499508	+	0.0288391i
$88$	−9.95362	−	1.11331i	−1.06106	−	0.118680i
$89$	0.294790	+	1.10017i	0.0312476	+	0.116618i	0.979788	−	0.200038i	$-0.0641066\pi$
$89$	0.294790	+	1.10017i	0.0312476	+	0.116618i	−0.948540	+	0.316656i	$0.897440\pi$
$90$	2.13840	−	1.55364i	0.225408	−	0.163768i
$91$	−10.5970	+	3.06609i	−1.11087	+	0.321413i
$92$	0.615478	−	1.89425i	0.0641680	−	0.197489i
$93$	−2.28527	−	0.877233i	−0.236971	−	0.0909648i
$94$	7.07920	+	15.9001i	0.730164	+	1.63997i
$95$	11.4073	−	2.42470i	1.17037	−	0.248769i
$96$	−1.75851	−	0.896006i	−0.179477	−	0.0914482i
$97$	−3.83385	−	9.98753i	−0.389269	−	1.01408i	−0.978524	−	0.206133i	$-0.933912\pi$
$97$	−3.83385	−	9.98753i	−0.389269	−	1.01408i	0.589255	−	0.807947i	$-0.299421\pi$
$98$	−0.784273	+	2.92695i	−0.0792235	+	0.295666i
$99$	0.195658	−	3.31085i	0.0196644	−	0.332753i
$100$	−0.133764	−	0.231686i	−0.0133764	−	0.0231686i
$101$	0.926613	+	8.81614i	0.0922015	+	0.877238i	0.938674	+	0.344806i	$0.112055\pi$
$101$	0.926613	+	8.81614i	0.0922015	+	0.877238i	−0.846473	+	0.532432i	$0.821278\pi$
$102$	−7.61140	+	4.94290i	−0.753641	+	0.489420i
$103$	−1.61508	−	0.524772i	−0.159139	−	0.0517073i	0.228364	−	0.973576i	$-0.426662\pi$
$103$	−1.61508	−	0.524772i	−0.159139	−	0.0517073i	−0.387503	+	0.921868i	$0.626662\pi$
$104$	−4.10292	−	10.0856i	−0.402324	−	0.988972i
$105$	−3.70436	+	5.09861i	−0.361508	+	0.497573i
$106$	13.8392	+	0.725284i	1.34419	+	0.0704458i
$107$	−1.35509	+	6.37518i	−0.131001	+	0.616312i	0.862838	+	0.505480i	$0.168685\pi$
$107$	−1.35509	+	6.37518i	−0.131001	+	0.616312i	−0.993839	+	0.110832i	$0.964649\pi$
$108$	0.143698	−	0.322752i	0.0138274	−	0.0310568i
$109$	−5.93194	+	5.93194i	−0.568177	+	0.568177i	−0.931617	−	0.363441i	$-0.881602\pi$
$109$	−5.93194	+	5.93194i	−0.568177	+	0.568177i	0.363441	+	0.931617i	$0.381602\pi$
$110$	−8.64928	−	1.42909i	−0.824676	−	0.136258i
$111$	−7.98255	−	2.13892i	−0.757670	−	0.203017i
$112$	−9.57537	−	1.51659i	−0.904788	−	0.143304i
$113$	3.17953	−	3.53123i	0.299105	−	0.332190i	−0.574793	−	0.818299i	$-0.694917\pi$
$113$	3.17953	−	3.53123i	0.299105	−	0.332190i	0.873898	+	0.486109i	$0.161584\pi$
$114$	−5.39928	+	4.86153i	−0.505689	+	0.455324i
$115$	4.16146	−	10.8410i	0.388058	−	1.01093i
$116$	0.153769	+	0.111719i	0.0142771	+	0.0103729i
$117$	3.26409	−	1.53158i	0.301765	−	0.141595i
$118$	−4.89652	+	1.59097i	−0.450761	+	0.146461i
$119$	13.6178	−	16.8166i	1.24834	−	1.54157i
$120$	−5.38691	−	3.11013i	−0.491755	−	0.283915i
$121$	−8.27202	+	7.25078i	−0.752001	+	0.659161i
$122$	6.44103	+	6.44103i	0.583144	+	0.583144i
$123$	7.18161	−	2.75676i	0.647544	−	0.248569i
$124$	0.0452610	+	0.863631i	0.00406456	+	0.0775564i
$125$	−5.38375	−	10.5662i	−0.481538	−	0.945071i
$126$	0.410404	−	3.90474i	0.0365617	−	0.347862i
$127$	−18.1690	+	8.08934i	−1.61223	+	0.717813i	−0.997483	−	0.0709083i	$-0.977410\pi$
$127$	−18.1690	+	8.08934i	−1.61223	+	0.717813i	−0.614751	+	0.788721i	$0.710744\pi$
$128$	0.389110	−	7.42466i	0.0343928	−	0.656254i
$129$	1.28208	+	3.94582i	0.112880	+	0.347410i
$130$	−3.12428	−	9.00358i	−0.274018	−	0.789666i
$131$		−	2.89998i		−	0.253372i	−0.991943	−	0.126686i	$-0.959566\pi$
$131$		−	2.89998i		−	0.253372i	0.991943	−	0.126686i	$-0.0404341\pi$
$132$	−1.09670	+	0.412614i	−0.0954552	+	0.0359135i
$133$	8.66152	−	15.0022i	0.751049	−	1.30086i
$134$	−8.53364	−	3.79942i	−0.737194	−	0.328220i
$135$	0.935128	−	1.83529i	0.0804830	−	0.157957i
$136$	17.9119	+	11.6321i	1.53593	+	0.997445i
$137$	1.99265	+	2.46072i	0.170244	+	0.210234i	0.855126	−	0.518420i	$-0.173480\pi$
$137$	1.99265	+	2.46072i	0.170244	+	0.210234i	−0.684882	+	0.728654i	$0.740146\pi$
$138$	1.13170	+	7.14529i	0.0963369	+	0.608247i
$139$	3.48367	+	16.3894i	0.295481	+	1.39013i	0.835968	+	0.548778i	$0.184907\pi$
$139$	3.48367	+	16.3894i	0.295481	+	1.39013i	−0.540487	+	0.841352i	$0.681760\pi$
$140$	2.17789	+	0.462925i	0.184066	+	0.0391243i
$141$	10.5406	+	8.53561i	0.887679	+	0.718828i
$142$	13.3053			1.11655
$143$	−11.2195	−	4.13798i	−0.938221	−	0.346035i
$144$	3.16859			0.264049
$145$	0.861189	+	0.697377i	0.0715179	+	0.0579140i
$146$	−1.37504	−	0.292273i	−0.113799	−	0.0241887i
$147$	0.490955	+	2.30976i	0.0404933	+	0.190506i
$148$	0.456740	+	2.88374i	0.0375438	+	0.237042i
$149$	13.1975	+	16.2976i	1.08118	+	1.33515i	0.938460	+	0.345387i	$0.112252\pi$
$149$	13.1975	+	16.2976i	1.08118	+	1.33515i	0.142722	+	0.989763i	$0.454414\pi$
$150$	0.814950	+	0.529235i	0.0665404	+	0.0432118i
$151$	−3.88964	+	7.63385i	−0.316534	+	0.621234i	−0.993378	−	0.114893i	$-0.963347\pi$
$151$	−3.88964	+	7.63385i	−0.316534	+	0.621234i	0.676844	+	0.736127i	$0.263347\pi$
$152$	15.6196	+	6.95428i	1.26691	+	0.564067i
$153$	−3.53619	+	6.12486i	−0.285884	+	0.495166i
$154$	−10.1743	+	8.12728i	−0.819870	+	0.654915i
$155$			5.04209i			0.404990i
$156$	−0.963364	−	0.833403i	−0.0771308	−	0.0667257i
$157$	−3.11126	−	9.57546i	−0.248305	−	0.764205i	−0.995075	−	0.0991225i	$-0.968396\pi$
$157$	−3.11126	−	9.57546i	−0.248305	−	0.764205i	0.746770	−	0.665082i	$-0.231604\pi$
$158$	0.606756	−	11.5776i	0.0482709	−	0.921064i
$159$	9.86575	−	4.39251i	0.782405	−	0.348349i
$160$	−0.424936	+	4.04299i	−0.0335941	+	0.319627i
$161$	−7.83084	−	15.3689i	−0.617156	−	1.21124i
$162$	0.0671596	+	1.28148i	0.00527656	+	0.100683i
$163$	−3.98262	+	1.52878i	−0.311943	+	0.119744i	−0.509303	−	0.860587i	$-0.670097\pi$
$163$	−3.98262	+	1.52878i	−0.311943	+	0.119744i	0.197360	+	0.980331i	$0.436763\pi$
$164$	−1.92173	−	1.92173i	−0.150062	−	0.150062i
$165$	−6.51114	+	2.06771i	−0.506892	+	0.160971i
$166$	−13.7544	−	7.94109i	−1.06755	−	0.616348i
$167$	6.53846	−	8.07432i	0.505961	−	0.624810i	−0.458609	−	0.888638i	$-0.651652\pi$
$167$	6.53846	−	8.07432i	0.505961	−	0.624810i	0.964570	+	0.263829i	$0.0849854\pi$
$168$	−8.78740	+	2.85520i	−0.677962	+	0.220283i
$169$	−1.87079	−	12.8647i	−0.143907	−	0.989591i
$170$	15.1236	+	10.9879i	1.15993	+	0.842737i
$171$	−2.02901	+	5.28575i	−0.155162	+	0.404211i
$172$	1.08929	−	0.980799i	0.0830574	−	0.0747853i
$173$	−1.59920	+	1.77609i	−0.121585	+	0.135033i	−0.800864	−	0.598847i	$-0.795626\pi$
$173$	−1.59920	+	1.77609i	−0.121585	+	0.135033i	0.679279	+	0.733880i	$0.262293\pi$
$174$	−0.681867	−	0.107997i	−0.0516922	−	0.00818724i
$175$	−2.23792	−	0.599650i	−0.169171	−	0.0453293i
$176$	−7.38129	−	7.48039i	−0.556386	−	0.563855i
$177$	−2.83699	+	2.83699i	−0.213241	+	0.213241i
$178$	−0.594480	+	1.33522i	−0.0445582	+	0.100079i
$179$	0.308686	−	1.45225i	0.0230722	−	0.108546i	−0.965105	−	0.261865i	$-0.915663\pi$
$179$	0.308686	−	1.45225i	0.0230722	−	0.108546i	0.988177	+	0.153318i	$0.0489959\pi$
$180$	−0.726720	−	0.0380858i	−0.0541665	−	0.00283875i
$181$	−7.81851	+	10.7613i	−0.581145	+	0.799878i	−0.993820	−	0.111000i	$-0.964595\pi$
$181$	−7.81851	+	10.7613i	−0.581145	+	0.799878i	0.412675	+	0.910878i	$0.364595\pi$
$182$	−13.0441	−	5.50012i	−0.966894	−	0.407696i
$183$	6.75101	+	2.19354i	0.499049	+	0.162151i
$184$	14.2780	−	9.27224i	1.05259	−	0.683559i
$185$	1.77933	+	16.9292i	0.130819	+	1.24466i
$186$	−1.57059	−	2.72035i	−0.115161	−	0.199466i
$187$	22.6971	−	5.91977i	1.65978	−	0.432896i
$188$	1.24022	−	4.62855i	0.0904521	−	0.337572i
$189$	−1.09648	−	2.85642i	−0.0797568	−	0.207774i
$190$	13.3342	+	6.79412i	0.967366	+	0.492898i
$191$	−16.4517	+	3.49692i	−1.19040	+	0.253028i	−0.760191	−	0.649699i	$-0.774895\pi$
$191$	−16.4517	+	3.49692i	−1.19040	+	0.253028i	−0.430213	+	0.902727i	$0.641562\pi$
$192$	−3.60768	−	8.10298i	−0.260362	−	0.584782i
$193$	16.9088	+	6.49068i	1.21712	+	0.467210i	0.880327	−	0.474368i	$-0.157323\pi$
$193$	16.9088	+	6.49068i	1.21712	+	0.467210i	0.336796	+	0.941578i	$0.390657\pi$
$194$	4.24225	−	13.0563i	0.304576	−	0.937389i
$195$	−5.35464	−	5.14623i	−0.383454	−	0.368529i
$196$	0.674930	−	0.490366i	0.0482093	−	0.0350261i
$197$	3.78800	+	14.1370i	0.269884	+	1.00722i	0.959193	+	0.282752i	$0.0912474\pi$
$197$	3.78800	+	14.1370i	0.269884	+	1.00722i	−0.689309	+	0.724467i	$0.742086\pi$
$198$	2.86886	−	3.14378i	0.203881	−	0.223419i
$199$	4.01962	−	2.32073i	0.284943	−	0.164512i	−0.350716	−	0.936482i	$-0.614062\pi$
$199$	4.01962	−	2.32073i	0.284943	−	0.164512i	0.635659	+	0.771970i	$0.280728\pi$
$200$	0.357724	−	2.25858i	0.0252949	−	0.159706i
$201$	−7.26943	+	0.380975i	−0.512746	+	0.0268719i
$202$	−6.19556	+	9.54032i	−0.435918	+	0.671255i
$203$	1.62578	−	0.257498i	0.114107	−	0.0180728i
$204$	2.48495	+	0.261179i	0.173981	+	0.0182862i
$205$	−10.6024	−	11.7752i	−0.740506	−	0.822415i
$206$	−1.18688	−	1.82763i	−0.0826935	−	0.127337i
$207$	3.31368	+	4.56089i	0.230317	+	0.317004i
$208$	3.31407	−	10.9333i	0.229790	−	0.758086i
$209$	17.2052	−	7.52318i	1.19011	−	0.520389i
$210$	−7.81170	+	2.09314i	−0.539059	+	0.144440i
$211$	−16.8462	+	1.77060i	−1.15974	+	0.121893i	−0.664791	−	0.747029i	$-0.731479\pi$
$211$	−16.8462	+	1.77060i	−1.15974	+	0.121893i	−0.494948	+	0.868923i	$0.664813\pi$
$212$	−2.83538	−	2.55299i	−0.194735	−	0.175340i
$213$	9.23840	−	4.70720i	0.633005	−	0.322532i
$214$	−6.49978	+	5.26342i	−0.444316	+	0.359800i
$215$	6.64138	−	5.37808i	0.452938	−	0.366782i
$216$	2.69070	−	1.37098i	0.183079	−	0.0932834i
$217$	5.56582	+	5.01148i	0.377832	+	0.340202i
$218$	−10.7062	+	1.12526i	−0.725113	+	0.0762124i
$219$	−1.05815	+	0.283529i	−0.0715029	+	0.0191591i
$220$	1.60300	+	1.80436i	0.108074	+	0.121650i
$221$	17.4354	+	18.6078i	1.17283	+	1.25169i
$222$	−6.23339	−	8.57953i	−0.418358	−	0.575820i
$223$	6.16909	+	9.49957i	0.413113	+	0.636138i	0.982572	−	0.185881i	$-0.0595140\pi$
$223$	6.16909	+	9.49957i	0.413113	+	0.636138i	−0.569459	+	0.822020i	$0.692847\pi$
$224$	4.04059	+	4.48753i	0.269973	+	0.299836i
$225$	0.753089	+	0.0791528i	0.0502059	+	0.00527685i
$226$	6.02255	−	0.953878i	0.400614	−	0.0634510i
$227$	−5.28463	+	8.13761i	−0.350753	+	0.540112i	−0.969378	−	0.245574i	$-0.921023\pi$
$227$	−5.28463	+	8.13761i	−0.350753	+	0.540112i	0.618625	+	0.785687i	$0.287690\pi$
$228$	1.99755	−	0.104687i	0.132291	−	0.00693307i
$229$	2.05049	−	12.9463i	0.135500	−	0.855515i	−0.822504	−	0.568760i	$-0.807423\pi$
$229$	2.05049	−	12.9463i	0.135500	−	0.855515i	0.958004	−	0.286755i	$-0.0925766\pi$
$230$	12.9049	−	7.45065i	0.850924	−	0.491281i
$231$	−4.18914	+	9.24262i	−0.275625	+	0.608120i
$232$	0.420487	+	1.56928i	0.0276063	+	0.103028i
$233$	3.35937	−	2.44072i	0.220079	−	0.159897i	−0.472283	−	0.881447i	$-0.656570\pi$
$233$	3.35937	−	2.44072i	0.220079	−	0.159897i	0.692362	+	0.721550i	$0.256570\pi$
$234$	4.49202	+	1.10858i	0.293652	+	0.0724703i
$235$	8.63316	−	26.5701i	0.563165	−	1.73324i
$236$	1.32331	+	0.507973i	0.0861404	+	0.0330662i
$237$	−3.67468	−	8.25346i	−0.238696	−	0.536120i
$238$	27.1611	−	5.77327i	1.76059	−	0.374226i
$239$	−12.5262	−	6.38242i	−0.810253	−	0.412845i	−0.000778821	−	1.00000i	$-0.500248\pi$
$239$	−12.5262	−	6.38242i	−0.810253	−	0.412845i	−0.809475	+	0.587155i	$0.800248\pi$
$240$	−2.33894	−	6.09316i	−0.150978	−	0.393312i
$241$	6.70698	−	25.0308i	0.432035	−	1.61237i	−0.316030	−	0.948749i	$-0.602350\pi$
$241$	6.70698	−	25.0308i	0.432035	−	1.61237i	0.748065	−	0.663626i	$-0.230983\pi$
$242$	−14.1049	+	0.550720i	−0.906697	+	0.0354016i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−0.262141	−	2.49411i	−0.0167819	−	0.159669i
$245$	4.07924	−	2.64909i	0.260613	−	0.169244i
$246$	9.38824	+	3.05043i	0.598573	+	0.194488i
$247$	16.1164	+	12.5296i	1.02546	+	0.797237i
$248$	−4.34499	+	5.98037i	−0.275907	+	0.379754i
$249$	−12.3597	−	0.647743i	−0.783262	−	0.0410490i
$250$	3.16392	−	14.8851i	0.200104	−	0.941414i
$251$	−10.0469	+	22.5658i	−0.634157	+	1.42434i	0.255091	+	0.966917i	$0.417894\pi$
$251$	−10.0469	+	22.5658i	−0.634157	+	1.42434i	−0.889249	+	0.457424i	$0.848772\pi$
$252$	−0.764351	+	0.764351i	−0.0481496	+	0.0481496i
$253$	3.04803	−	18.4476i	0.191628	−	1.15979i
$254$	−24.6520	−	6.60547i	−1.54680	−	0.414464i
$255$	14.3883	+	2.27888i	0.901031	+	0.142709i
$256$	−5.48615	+	6.09299i	−0.342885	+	0.380812i
$257$	−1.34187	+	1.20822i	−0.0837035	+	0.0753670i	−0.709920	−	0.704282i	$-0.751269\pi$
$257$	−1.34187	+	1.20822i	−0.0837035	+	0.0753670i	0.626217	+	0.779649i	$0.284602\pi$
$258$	−1.90795	+	4.97039i	−0.118784	+	0.309443i
$259$	20.4562	+	14.8623i	1.27109	+	0.923499i
$260$	−0.891502	+	2.46772i	−0.0552886	+	0.153042i
$261$	−0.511656	+	0.166247i	−0.0316707	+	0.0102904i
$262$	2.34193	−	2.89205i	0.144685	−	0.178671i
$263$	7.29902	+	4.21409i	0.450077	+	0.259852i	0.707863	−	0.706350i	$-0.249660\pi$
$263$	7.29902	+	4.21409i	0.450077	+	0.259852i	−0.257786	+	0.966202i	$0.582993\pi$
$264$	−9.50463	−	3.15846i	−0.584970	−	0.194390i
$265$	−15.7293	−	15.7293i	−0.966243	−	0.966243i
$266$	20.7531	−	7.96638i	1.27246	−	0.488450i
$267$	0.0596096	+	1.13742i	0.00364805	+	0.0696089i
$268$	1.16757	+	2.29148i	0.0713204	+	0.139974i
$269$	1.57491	−	14.9842i	0.0960238	−	0.913606i	−0.835393	−	0.549652i	$-0.814760\pi$
$269$	1.57491	−	14.9842i	0.0960238	−	0.913606i	0.931417	−	0.363953i	$-0.118573\pi$
$270$	2.41470	−	1.07509i	0.146954	−	0.0654280i
$271$	1.30016	−	24.8086i	0.0789794	−	1.50702i	−0.615862	−	0.787854i	$-0.711192\pi$
$271$	1.30016	−	24.8086i	0.0789794	−	1.50702i	0.694842	−	0.719163i	$-0.255474\pi$
$272$	6.92491	+	21.3127i	0.419884	+	1.29227i
$273$	−11.0029	+	0.795842i	−0.665927	+	0.0481666i
$274$			4.06319i			0.245466i
$275$	−1.56747	−	1.96227i	−0.0945221	−	0.118330i
$276$	0.995864	−	1.72489i	0.0599440	−	0.103826i
$277$	15.4521	+	6.87970i	0.928424	+	0.413361i	0.814523	−	0.580131i	$-0.196999\pi$
$277$	15.4521	+	6.87970i	0.928424	+	0.413361i	0.113901	+	0.993492i	$0.463665\pi$
$278$	−9.76142	+	19.1579i	−0.585451	+	1.14901i
$279$	−2.05294	−	1.33320i	−0.122907	−	0.0798165i
$280$	11.9771	+	14.7904i	0.715766	+	0.883897i
$281$	3.25860	+	20.5740i	0.194392	+	1.22734i	0.871106	+	0.491094i	$0.163403\pi$
$281$	3.25860	+	20.5740i	0.194392	+	1.22734i	−0.676715	+	0.736245i	$0.736597\pi$
$282$	3.61868	+	17.0245i	0.215489	+	1.01380i
$283$	11.4041	+	2.42402i	0.677904	+	0.144093i	0.533982	−	0.845496i	$-0.320695\pi$
$283$	11.4041	+	2.42402i	0.677904	+	0.144093i	0.143923	+	0.989589i	$0.454028\pi$
$284$	−2.84680	−	2.30529i	−0.168926	−	0.136794i
$285$	11.6622			0.690807
$286$	−7.84710	−	13.1872i	−0.464009	−	0.779774i
$287$	−23.5364			−1.38931
$288$	−1.53379	−	1.24204i	−0.0903796	−	0.0731880i
$289$	−32.2970	−	6.86494i	−1.89982	−	0.403820i
$290$	0.295653	+	1.39094i	0.0173614	+	0.0816788i
$291$	−1.67355	−	10.5664i	−0.0981053	−	0.619412i
$292$	0.243563	+	0.300776i	0.0142535	+	0.0176016i
$293$	2.23439	+	1.45103i	0.130534	+	0.0847699i	0.608254	−	0.793742i	$-0.291870\pi$
$293$	2.23439	+	1.45103i	0.130534	+	0.0847699i	−0.477720	+	0.878512i	$0.658537\pi$
$294$	−1.37568	+	2.69993i	−0.0802313	+	0.157463i
$295$	7.54966	+	3.36133i	0.439558	+	0.195704i
$296$	−12.4782	+	21.6129i	−0.725281	+	1.25622i
$297$	0.879747	−	3.19782i	0.0510481	−	0.185556i
$298$			26.9109i			1.55891i
$299$	19.2032	−	6.66361i	1.11055	−	0.385367i
$300$	−0.0826708	−	0.254435i	−0.00477300	−	0.0146898i
$301$	0.664356	−	12.6767i	0.0382928	−	0.730671i
$302$	−10.0439	+	4.47181i	−0.577959	+	0.257324i
$303$	−0.926613	+	8.81614i	−0.0532325	+	0.506474i
$304$	8.14456	+	15.9846i	0.467122	+	0.916779i
$305$	−0.765222	−	14.6013i	−0.0438165	−	0.836068i
$306$	−8.47276	+	3.25239i	−0.484356	+	0.185927i
$307$	8.60217	+	8.60217i	0.490952	+	0.490952i	0.908606	−	0.417654i	$-0.137148\pi$
$307$	8.60217	+	8.60217i	0.490952	+	0.490952i	−0.417654	+	0.908606i	$0.637148\pi$
$308$	3.58504	+	0.0239038i	0.204277	+	0.00136205i
$309$	−1.47068	−	0.849099i	−0.0836642	−	0.0483036i
$310$	−4.07183	+	5.02829i	−0.231265	+	0.285588i
$311$	16.6030	−	5.39465i	0.941471	−	0.305902i	0.202226	−	0.979339i	$-0.435183\pi$
$311$	16.6030	−	5.39465i	0.941471	−	0.305902i	0.739245	+	0.673436i	$0.235183\pi$
$312$	−1.91635	−	10.7182i	−0.108492	−	0.606800i
$313$	−0.271759	−	0.197444i	−0.0153607	−	0.0111602i	0.580078	−	0.814561i	$-0.303022\pi$
$313$	−0.271759	−	0.197444i	−0.0153607	−	0.0111602i	−0.595439	+	0.803400i	$0.703022\pi$
$314$	4.63010	−	12.0618i	0.261292	−	0.680688i
$315$	−4.68347	+	4.21701i	−0.263883	+	0.237602i
$316$	−2.13577	+	2.37202i	−0.120147	+	0.133436i
$317$	−3.11197	−	0.492887i	−0.174786	−	0.0276833i	0.0684281	−	0.997656i	$-0.478202\pi$
$317$	−3.11197	−	0.492887i	−0.174786	−	0.0276833i	−0.243214	+	0.969973i	$0.578202\pi$
$318$	13.3860	+	3.58677i	0.750651	+	0.201136i
$319$	1.58439	+	0.820638i	0.0887087	+	0.0459469i
$320$	−12.9189	+	12.9189i	−0.722186	+	0.722186i
$321$	−2.65095	+	5.95413i	−0.147962	+	0.332327i
$322$	4.60202	−	21.6508i	0.256460	−	1.20655i
$323$	−39.9875	−	2.09566i	−2.22497	−	0.116605i
$324$	0.207662	−	0.285822i	0.0115368	−	0.0158790i
$325$	1.06078	−	2.51576i	0.0588417	−	0.139549i
$326$	−5.20632	−	1.69164i	−0.288352	−	0.0936911i
$327$	−7.03563	+	4.56899i	−0.389071	+	0.252666i
$328$	−2.42823	−	23.1030i	−0.134076	−	1.27565i
$329$	−20.7493	−	35.9388i	−1.14394	−	1.98137i
$330$	−8.16315	−	3.19615i	−0.449366	−	0.175942i
$331$	−5.32190	+	19.8616i	−0.292518	+	1.09169i	0.650650	+	0.759377i	$0.274496\pi$
$331$	−5.32190	+	19.8616i	−0.292518	+	1.09169i	−0.943168	+	0.332315i	$0.892170\pi$
$332$	1.56700	+	4.08218i	0.0860005	+	0.224039i
$333$	−7.36341	−	3.75184i	−0.403512	−	0.205600i
$334$	13.0411	−	2.77198i	0.713579	−	0.151676i
$335$	6.09865	+	13.6978i	0.333205	+	0.748391i
$336$	−9.05081	−	3.47428i	−0.493762	−	0.189538i
$337$	8.97633	−	27.6263i	0.488972	−	1.50490i	−0.337173	−	0.941443i	$-0.609471\pi$
$337$	8.97633	−	27.6263i	0.488972	−	1.50490i	0.826145	−	0.563458i	$-0.190529\pi$
$338$	8.52344	−	14.3403i	0.463614	−	0.780009i
$339$	3.84424	−	2.79300i	0.208790	−	0.151695i
$340$	−1.33206	−	4.97132i	−0.0722412	−	0.269608i
$341$	1.63497	+	7.95229i	0.0885386	+	0.430640i
$342$	−6.29206	+	3.63272i	−0.340236	+	0.196435i
$343$	−2.22020	+	14.0178i	−0.119880	+	0.756890i
$344$	12.5118	−	0.655716i	0.674591	−	0.0353538i
$345$	6.32448	−	9.73885i	0.340499	−	0.524322i
$346$	−3.02914	+	0.479768i	−0.162847	+	0.0257925i
$347$	−17.7649	−	1.86717i	−0.953670	−	0.100235i	−0.385105	−	0.922873i	$-0.625835\pi$
$347$	−17.7649	−	1.86717i	−0.953670	−	0.100235i	−0.568565	+	0.822638i	$0.692501\pi$
$348$	0.127181	+	0.141248i	0.00681759	+	0.00757171i
$349$	−11.0671	−	17.0419i	−0.592409	−	0.912230i	0.407591	−	0.913165i	$-0.366369\pi$
$349$	−11.0671	−	17.0419i	−0.592409	−	0.912230i	−1.00000		0.000935016i	$0.999702\pi$
$350$	−1.74754	−	2.40529i	−0.0934101	−	0.128568i
$351$	3.51119	−	0.819471i	0.187414	−	0.0437401i
$352$	0.640799	+	6.51433i	0.0341547	+	0.347215i
$353$	12.7379	−	3.41312i	0.677971	−	0.181662i	0.0966283	−	0.995321i	$-0.469194\pi$
$353$	12.7379	−	3.41312i	0.677971	−	0.181662i	0.581343	+	0.813659i	$0.302528\pi$
$354$	−5.12030	+	0.538165i	−0.272141	+	0.0286031i
$355$	−15.8713	−	14.2906i	−0.842364	−	0.758468i
$356$	0.358538	−	0.182684i	0.0190025	−	0.00968224i
$357$	16.8166	−	13.6178i	0.890028	−	0.720730i
$358$	1.48063	−	1.19899i	0.0782540	−	0.0633688i
$359$	11.6616	−	5.94186i	0.615473	−	0.313599i	−0.118316	−	0.992976i	$-0.537750\pi$
$359$	11.6616	−	5.94186i	0.615473	−	0.313599i	0.733790	+	0.679377i	$0.237750\pi$
$360$	−4.62256	−	4.16217i	−0.243630	−	0.219366i
$361$	−12.9845	+	1.36472i	−0.683393	+	0.0718275i
$362$	−16.4876	+	4.41783i	−0.866568	+	0.232196i
$363$	−9.59877	+	5.37248i	−0.503805	+	0.281982i
$364$	1.83796	+	3.43685i	0.0963353	+	0.180140i
$365$	1.32631	+	1.82551i	0.0694222	+	0.0955515i
$366$	4.96112	+	7.63945i	0.259322	+	0.399320i
$367$	7.26072	+	8.06384i	0.379006	+	0.420929i	0.902223	−	0.431271i	$-0.141935\pi$
$367$	7.26072	+	8.06384i	0.379006	+	0.420929i	−0.523216	+	0.852200i	$0.675268\pi$
$368$	17.7653	+	1.86721i	0.926080	+	0.0973349i
$369$	7.59784	−	1.20338i	0.395528	−	0.0626454i
$370$	−11.8970	+	18.3198i	−0.618498	+	0.952403i
$371$	−32.9970	+	1.72930i	−1.71312	+	0.0897806i
$372$	−0.135287	+	0.854169i	−0.00701431	+	0.0442866i
$373$	9.00684	−	5.20010i	0.466357	−	0.269251i	−0.248357	−	0.968669i	$-0.579891\pi$
$373$	9.00684	−	5.20010i	0.466357	−	0.269251i	0.714713	+	0.699418i	$0.246557\pi$
$374$	27.4157	+	12.4259i	1.41763	+	0.642530i
$375$	−3.06927	−	11.4547i	−0.158496	−	0.591516i
$376$	33.1364	−	24.0750i	1.70888	−	1.24157i
$377$	0.0384906	+	1.93936i	0.00198236	+	0.0998820i
$378$	1.21328	−	3.73408i	0.0624042	−	0.192060i
$379$	−25.0236	−	9.60567i	−1.28538	−	0.493410i	−0.382757	−	0.923849i	$-0.625025\pi$
$379$	−25.0236	−	9.60567i	−1.28538	−	0.493410i	−0.902620	+	0.430439i	$0.858359\pi$
$380$	−1.67583	−	3.76398i	−0.0859684	−	0.193088i
$381$	−19.4538	+	4.13503i	−0.996648	+	0.211844i
$382$	−19.2307	−	9.79854i	−0.983929	−	0.501337i
$383$	5.71385	+	14.8851i	0.291964	+	0.760593i	0.998594	+	0.0530092i	$0.0168813\pi$
$383$	5.71385	+	14.8851i	0.291964	+	0.760593i	−0.706630	+	0.707583i	$0.749785\pi$
$384$	1.92428	−	7.18152i	0.0981981	−	0.366480i
$385$	20.8657	+	1.23308i	1.06342	+	0.0628437i
$386$	11.6209	+	20.1280i	0.591487	+	1.02449i
$387$	0.433676	+	4.12615i	0.0220450	+	0.209744i
$388$	−3.16983	+	2.05851i	−0.160924	+	0.104505i
$389$	−30.7342	−	9.98615i	−1.55829	−	0.506318i	−0.601937	−	0.798543i	$-0.705604\pi$
$389$	−30.7342	−	9.98615i	−1.55829	−	0.506318i	−0.956349	+	0.292225i	$0.905604\pi$
$390$	−1.18406	−	9.45640i	−0.0599572	−	0.478843i
$391$	−23.4356	+	32.2563i	−1.18519	+	1.63127i
$392$	7.12118	+	0.373205i	0.359674	+	0.0188497i
$393$	0.602940	−	2.83661i	0.0304143	−	0.143088i
$394$	−7.63896	+	17.1574i	−0.384845	+	0.864377i
$395$	−13.1588	+	13.1588i	−0.662090	+	0.662090i
$396$	−1.15852	+	0.175581i	−0.0582178	+	0.00882330i
$397$	26.8390	+	7.19150i	1.34701	+	0.360931i	0.859031	−	0.511923i	$-0.171067\pi$
$397$	26.8390	+	7.19150i	1.34701	+	0.360931i	0.487981	+	0.872854i	$0.337733\pi$
$398$	5.88277	+	0.931739i	0.294877	+	0.0467039i
$399$	11.5914	−	12.8735i	0.580295	−	0.644483i
$400$	1.78308	−	1.60549i	0.0891541	−	0.0802747i
$401$	−2.30081	+	5.99382i	−0.114897	+	0.299317i	−0.978955	−	0.204075i	$-0.934581\pi$
$401$	−2.30081	+	5.99382i	−0.114897	+	0.299317i	0.864058	+	0.503392i	$0.167915\pi$
$402$	−7.55721	−	5.49064i	−0.376920	−	0.273848i
$403$	−6.74742	+	5.68931i	−0.336113	+	0.283405i
$404$	2.97857	−	0.967797i	0.148190	−	0.0481497i
$405$	1.29627	−	1.60076i	0.0644123	−	0.0795425i
$406$	1.82928	+	1.05613i	0.0907856	+	0.0524151i
$407$	8.29588	+	26.1235i	0.411211	+	1.29489i
$408$	15.1020	+	15.1020i	0.747661	+	0.747661i
$409$	−27.3327	+	10.4920i	−1.35152	+	0.518798i	−0.923022	−	0.384747i	$-0.874289\pi$
$409$	−27.3327	+	10.4920i	−1.35152	+	0.518798i	−0.428493	+	0.903545i	$0.640955\pi$
$410$	−1.06415	−	20.3052i	−0.0525546	−	1.00280i
$411$	1.43750	+	2.82124i	0.0709064	+	0.139162i
$412$	−0.0627135	+	0.596679i	−0.00308967	+	0.0293963i
$413$	11.2143	−	4.99293i	0.551820	−	0.245686i
$414$	−0.378617	+	7.22444i	−0.0186080	+	0.355062i
$415$	7.87788	+	24.2456i	0.386710	+	1.19017i
$416$	−5.88990	+	3.99331i	−0.288776	+	0.195788i
$417$			16.7555i			0.820522i
$418$	23.2336	+	6.39175i	1.13639	+	0.312631i
$419$	9.05637	−	15.6861i	0.442433	−	0.766316i	−0.555437	−	0.831559i	$-0.687449\pi$
$419$	9.05637	−	15.6861i	0.442433	−	0.766316i	0.997869	+	0.0652431i	$0.0207823\pi$
$420$	2.03405	+	0.905619i	0.0992516	+	0.0441897i
$421$	−5.85364	+	11.4884i	−0.285289	+	0.559911i	−0.988527	−	0.151043i	$-0.951737\pi$
$421$	−5.85364	+	11.4884i	−0.285289	+	0.559911i	0.703238	+	0.710954i	$0.251737\pi$
$422$	−18.2300	−	11.8387i	−0.887422	−	0.576298i
$423$	8.53561	+	10.5406i	0.415016	+	0.512502i
$424$	−5.10172	−	32.2110i	−0.247761	−	1.56430i
$425$	1.11346	+	5.23844i	0.0540109	+	0.254102i
$426$	13.0145	+	2.76632i	0.630556	+	0.134029i
$427$	−16.8785	−	13.6680i	−0.816810	−	0.661440i
$428$	2.30264			0.111302
$429$	−10.1140	−	6.38022i	−0.488308	−	0.308040i
$430$	10.9664			0.528846
$431$	−6.15094	−	4.98093i	−0.296280	−	0.239923i	0.469641	−	0.882858i	$-0.344383\pi$
$431$	−6.15094	−	4.98093i	−0.296280	−	0.239923i	−0.765921	+	0.642935i	$0.777717\pi$
$432$	3.09935	+	0.658787i	0.149118	+	0.0316959i
$433$	−2.30381	−	10.8386i	−0.110714	−	0.520868i	−0.998197	−	0.0600274i	$-0.980881\pi$
$433$	−2.30381	−	10.8386i	−0.110714	−	0.520868i	0.887483	−	0.460841i	$-0.152452\pi$
$434$	1.50347	+	9.49256i	0.0721690	+	0.455657i
$435$	0.697377	+	0.861189i	0.0334367	+	0.0412909i
$436$	2.48566	+	1.61420i	0.119041	+	0.0773064i
$437$	−14.4908	+	28.4398i	−0.693190	+	1.36046i
$438$	−1.28422	−	0.571772i	−0.0613625	−	0.0273203i
$439$	−17.2284	+	29.8405i	−0.822267	+	1.42421i	0.0817226	+	0.996655i	$0.473958\pi$
$439$	−17.2284	+	29.8405i	−0.822267	+	1.42421i	−0.903990	+	0.427554i	$0.859375\pi$
$440$	0.942317	+	20.6087i	0.0449232	+	0.982483i
$441$			2.36136i			0.112446i
$442$	2.36065	+	32.6371i	0.112284	+	1.55239i
$443$	−5.24384	−	16.1389i	−0.249142	−	0.766782i	−0.994927	−	0.100595i	$-0.967925\pi$
$443$	−5.24384	−	16.1389i	−0.249142	−	0.766782i	0.745785	−	0.666187i	$-0.232075\pi$
$444$	−0.152805	+	2.91569i	−0.00725179	+	0.138372i
$445$	2.14324	−	0.954232i	0.101599	−	0.0452349i
$446$	−1.51934	+	14.4555i	−0.0719428	+	0.684490i
$447$	9.52066	+	18.6854i	0.450312	+	0.883787i
$448$	1.42031	+	27.1012i	0.0671035	+	1.28041i
$449$	−17.8493	+	6.85171i	−0.842361	+	0.323352i	−0.741006	−	0.671498i	$-0.765651\pi$
$449$	−17.8493	+	6.85171i	−0.842361	+	0.323352i	−0.101355	+	0.994850i	$0.532318\pi$
$450$	0.687107	+	0.687107i	0.0323906	+	0.0323906i
$451$	−20.5402	−	15.1336i	−0.967202	−	0.712615i
$452$	−1.45386	−	0.839384i	−0.0683836	−	0.0394813i
$453$	−5.39181	+	6.65833i	−0.253329	+	0.312835i
$454$	−11.8419	+	3.84765i	−0.555766	+	0.180579i
$455$	9.65237	+	20.5710i	0.452510	+	0.964384i
$456$	13.8324	+	10.0498i	0.647760	+	0.470625i
$457$	5.67586	−	14.7861i	0.265505	−	0.691665i	−0.734411	−	0.678705i	$-0.762541\pi$
$457$	5.67586	−	14.7861i	0.265505	−	0.691665i	0.999916	−	0.0129598i	$-0.00412534\pi$
$458$	12.4999	−	11.2550i	0.584082	−	0.525910i
$459$	−4.73235	+	5.25580i	−0.220887	+	0.245320i
$460$	−4.05205	−	0.641781i	−0.188928	−	0.0299232i
$461$	−35.1894	−	9.42897i	−1.63893	−	0.439151i	−0.682449	−	0.730933i	$-0.739085\pi$
$461$	−35.1894	−	9.42897i	−1.63893	−	0.439151i	−0.956485	+	0.291782i	$0.905752\pi$
$462$	−11.6417	+	5.83432i	−0.541623	+	0.271437i
$463$	13.4280	−	13.4280i	0.624054	−	0.624054i	−0.322512	−	0.946565i	$-0.604527\pi$
$463$	13.4280	−	13.4280i	0.624054	−	0.624054i	0.946565	+	0.322512i	$0.104527\pi$
$464$	−0.693348	+	1.55728i	−0.0321879	+	0.0722951i
$465$	−1.04831	+	4.93190i	−0.0486141	+	0.228712i
$466$	5.32123	+	0.278874i	0.246501	+	0.0129186i
$467$	5.80785	−	7.99381i	0.268755	−	0.369910i	−0.653214	−	0.757173i	$-0.726580\pi$
$467$	5.80785	−	7.99381i	0.268755	−	0.369910i	0.921969	+	0.387264i	$0.126580\pi$
$468$	−0.769038	−	1.01549i	−0.0355488	−	0.0469409i
$469$	21.1823	+	6.88253i	0.978106	+	0.317806i
$470$	30.0668	−	19.5256i	1.38688	−	0.900648i
$471$	−1.05242	−	10.0131i	−0.0484928	−	0.461378i
$472$	6.05797	+	10.4927i	0.278841	+	0.482966i
$473$	8.73074	−	10.6358i	0.401440	−	0.489033i
$474$	3.00061	−	11.1984i	0.137823	−	0.514361i
$475$	1.53644	+	4.00256i	0.0704967	+	0.183650i
$476$	−6.81168	−	3.47072i	−0.312213	−	0.159080i
$477$	10.5634	−	2.24532i	0.483665	−	0.102806i
$478$	−7.33770	−	16.4807i	−0.335619	−	0.753812i
$479$	−23.4425	−	8.99872i	−1.07111	−	0.411162i	−0.242019	−	0.970271i	$-0.577810\pi$
$479$	−23.4425	−	8.99872i	−1.07111	−	0.411162i	−0.829094	+	0.559110i	$0.811143\pi$
$480$	−1.25624	+	3.86629i	−0.0573390	+	0.176471i
$481$	−20.6473	+	21.4835i	−0.941435	+	0.979562i
$482$	26.9027	−	19.5460i	1.22539	−	0.890295i
$483$	−4.46434	−	16.6612i	−0.203135	−	0.758109i
$484$	3.11330	+	2.32600i	0.141514	+	0.105727i
$485$	−19.0836	+	11.0179i	−0.866544	+	0.500299i
$486$	−0.200743	+	1.26744i	−0.00910588	+	0.0574923i
$487$	−25.9841	+	1.36177i	−1.17745	+	0.0617077i	−0.631001	−	0.775782i	$-0.717355\pi$
$487$	−25.9841	+	1.36177i	−1.17745	+	0.0617077i	−0.546453	+	0.837490i	$0.684022\pi$
$488$	11.6750	−	17.9779i	0.528501	−	0.813820i
$489$	−4.21344	+	0.667344i	−0.190538	+	0.0301783i
$490$	6.20740	+	0.652424i	0.280422	+	0.0294735i
$491$	−6.32806	−	7.02802i	−0.285581	−	0.317170i	0.583236	−	0.812303i	$-0.301786\pi$
$491$	−6.32806	−	7.02802i	−0.285581	−	0.317170i	−0.868817	+	0.495133i	$0.835119\pi$
$492$	−1.48019	−	2.27929i	−0.0667321	−	0.102758i
$493$	−2.23643	−	3.07819i	−0.100724	−	0.138635i
$494$	5.95382	+	25.5104i	0.267875	+	1.14777i
$495$	−6.79876	+	0.668778i	−0.305582	+	0.0300593i
$496$	−7.49197	+	2.00747i	−0.336399	+	0.0901379i
$497$	−31.5500	+	3.31604i	−1.41521	+	0.148745i
$498$	−11.8028	−	10.6273i	−0.528895	−	0.476219i
$499$	13.1046	−	6.67713i	0.586643	−	0.298909i	−0.135363	−	0.990796i	$-0.543220\pi$
$499$	13.1046	−	6.67713i	0.586643	−	0.298909i	0.722006	+	0.691887i	$0.243220\pi$
$500$	−3.25596	+	2.63663i	−0.145611	+	0.117913i
$501$	8.07432	−	6.53846i	0.360734	−	0.292117i
$502$	−28.2429	+	14.3905i	−1.26054	+	0.642279i
$503$	4.50616	+	4.05736i	0.200920	+	0.180909i	0.763448	−	0.645869i	$-0.223505\pi$
$503$	4.50616	+	4.05736i	0.200920	+	0.180909i	−0.562529	+	0.826778i	$0.690171\pi$
$504$	−9.18900	+	0.965803i	−0.409311	+	0.0430203i
$505$	17.6373	−	4.72590i	0.784850	−	0.210300i
$506$	17.9374	−	15.9356i	0.797414	−	0.708425i
$507$	0.844805	−	12.9725i	0.0375191	−	0.576130i
$508$	4.13006	+	5.68454i	0.183242	+	0.252211i
$509$	−1.97368	−	3.03920i	−0.0874818	−	0.134710i	0.792221	−	0.610235i	$-0.208925\pi$
$509$	−1.97368	−	3.03920i	−0.0874818	−	0.134710i	−0.879702	+	0.475525i	$0.842258\pi$
$510$	12.5086	+	13.8922i	0.553890	+	0.615157i
$511$	3.33339	+	0.350353i	0.147460	+	0.0154987i
$512$	−25.0783	+	3.97201i	−1.10831	+	0.175540i
$513$	−3.08364	+	4.74839i	−0.136146	+	0.209646i
$514$	−2.31392	+	0.121268i	−0.102063	+	0.00534888i
$515$	−0.547199	+	3.45488i	−0.0241125	+	0.152240i
$516$	1.26940	−	0.732891i	0.0558824	−	0.0322637i
$517$	5.00031	−	44.7054i	0.219913	−	1.96614i
$518$	8.39792	+	31.3415i	0.368983	+	1.37706i
$519$	−1.93352	+	1.40478i	−0.0848721	+	0.0616632i
$520$	−19.1964	+	11.5969i	−0.841819	+	0.508559i
$521$	0.448919	−	1.38163i	0.0196675	−	0.0605304i	−0.940741	−	0.339126i	$-0.889869\pi$
$521$	0.448919	−	1.38163i	0.0196675	−	0.0605304i	0.960409	+	0.278595i	$0.0898688\pi$
$522$	−0.644512	−	0.247405i	−0.0282095	−	0.0108286i
$523$	4.17347	+	9.37377i	0.182493	+	0.409886i	0.981507	−	0.191426i	$-0.0613113\pi$
$523$	4.17347	+	9.37377i	0.182493	+	0.409886i	−0.799014	+	0.601313i	$0.794645\pi$
$524$	−1.00216	+	0.213016i	−0.0437796	+	0.00930564i
$525$	−2.06434	−	1.05184i	−0.0900954	−	0.0459059i
$526$	3.87589	+	10.0970i	0.168997	+	0.440251i
$527$	4.48072	−	16.7223i	0.195183	−	0.728433i
$528$	−5.66473	−	8.85158i	−0.246526	−	0.385216i
$529$	4.39109	+	7.60559i	0.190917	+	0.330678i
$530$	−2.98378	−	28.3888i	−0.129607	−	1.23313i
$531$	−3.36484	+	2.18515i	−0.146022	+	0.0948275i
$532$	−5.82061	−	1.89123i	−0.252356	−	0.0819953i
$533$	3.79440	−	27.4751i	0.164354	−	1.19008i
$534$	−0.859098	+	1.18245i	−0.0371768	+	0.0511695i
$535$	13.4065	+	0.702607i	0.579616	+	0.0303764i
$536$	−4.57046	+	21.5023i	−0.197414	+	0.928758i
$537$	0.603880	−	1.35634i	0.0260594	−	0.0585303i
$538$	13.6714	−	13.6714i	0.589416	−	0.589416i
$539$	5.57469	−	5.50084i	0.240119	−	0.236938i
$540$	−0.702921	−	0.188347i	−0.0302489	−	0.00810517i
$541$	16.0835	+	2.54738i	0.691485	+	0.109521i	0.492280	−	0.870437i	$-0.336164\pi$
$541$	16.0835	+	2.54738i	0.691485	+	0.109521i	0.199206	+	0.979958i	$0.436164\pi$
$542$	21.3313	−	23.6908i	0.916257	−	1.01761i
$543$	−9.88505	+	8.90054i	−0.424208	+	0.381959i
$544$	5.00217	−	13.0311i	0.214466	−	0.558704i
$545$	13.9796	+	10.1567i	0.598819	+	0.435067i
$546$	−11.6155	−	8.09196i	−0.497099	−	0.346304i
$547$	−7.89217	+	2.56432i	−0.337445	+	0.109643i	−0.472838	−	0.881149i	$-0.656770\pi$
$547$	−7.89217	+	2.56432i	−0.337445	+	0.109643i	0.135393	+	0.990792i	$0.456770\pi$
$548$	0.703995	−	0.869362i	0.0300732	−	0.0371373i
$549$	6.14743	+	3.54922i	0.262366	+	0.151477i
$550$	0.0214882	−	3.22275i	0.000916259	−	0.137418i
$551$	−2.15383	−	2.15383i	−0.0917562	−	0.0917562i
$552$	15.8938	−	6.10106i	0.676485	−	0.259678i
$553$	1.44669	+	27.6045i	0.0615195	+	1.17386i
$554$	9.85396	+	19.3395i	0.418655	+	0.821656i
$555$	−1.77933	+	16.9292i	−0.0755284	+	0.718605i
$556$	5.40788	−	2.40774i	0.229345	−	0.102111i
$557$	0.213355	−	4.07106i	0.00904014	−	0.172496i	−0.990378	−	0.138388i	$-0.955808\pi$
$557$	0.213355	−	4.07106i	0.00904014	−	0.172496i	0.999418	−	0.0341077i	$-0.0108589\pi$
$558$	−0.970680	−	2.98745i	−0.0410922	−	0.126469i
$559$	14.6910	+	2.81919i	0.621361	+	0.119239i
$560$			19.9692i			0.843852i
$561$	23.4319	−	1.07141i	0.989298	−	0.0452348i
$562$	−13.3652	+	23.1492i	−0.563777	+	0.976491i
$563$	1.99027	+	0.886126i	0.0838800	+	0.0373458i	0.448248	−	0.893909i	$-0.352048\pi$
$563$	1.99027	+	0.886126i	0.0838800	+	0.0373458i	−0.364368	+	0.931255i	$0.618715\pi$
$564$	2.17544	−	4.26955i	0.0916027	−	0.179780i
$565$	−8.20858	−	5.33072i	−0.345338	−	0.224265i
$566$	9.41536	+	11.6270i	0.395757	+	0.488719i
$567$	−0.478632	−	3.02197i	−0.0201007	−	0.126911i
$568$	−6.50997	−	30.6270i	−0.273152	−	1.28508i
$569$	11.0371	+	2.34600i	0.462698	+	0.0983495i	0.433362	−	0.901220i	$-0.357327\pi$
$569$	11.0371	+	2.34600i	0.462698	+	0.0983495i	0.0293363	+	0.999570i	$0.490661\pi$
$570$	11.6303	+	9.41800i	0.487138	+	0.394477i
$571$	−11.1501			−0.466616			−0.233308	−	0.972403i	$-0.574955\pi$
$571$	−11.1501			−0.466616			−0.233308	+	0.972403i	$0.574955\pi$
$572$	−0.605864	+	4.18113i	−0.0253325	+	0.174822i
$573$	−16.8193			−0.702634
$574$	−23.4720	−	19.0073i	−0.979703	−	0.793348i
$575$	4.17569	+	0.887570i	0.174138	+	0.0370142i
$576$	−1.84414	−	8.67599i	−0.0768391	−	0.361499i
$577$	−3.60276	−	22.7470i	−0.149985	−	0.946968i	−0.941792	−	0.336196i	$-0.890859\pi$
$577$	−3.60276	−	22.7470i	−0.149985	−	0.946968i	0.791807	−	0.610772i	$-0.209141\pi$
$578$	−26.6648	−	32.9282i	−1.10911	−	1.36963i
$579$	15.1898	+	9.86439i	0.631268	+	0.409950i
$580$	0.177738	−	0.348831i	0.00738018	−	0.0144844i
$581$	34.5941	+	15.4023i	1.43521	+	0.638995i
$582$	6.86411	−	11.8890i	0.284526	−	0.492814i
$583$	−29.9084	−	19.7075i	−1.23868	−	0.816201i
$584$			3.30816i			0.136893i
$585$	−4.16767	−	6.14707i	−0.172312	−	0.254150i
$586$	1.05647	+	3.25148i	0.0436424	+	0.134317i
$587$	−0.132638	+	2.53088i	−0.00547454	+	0.104461i	−1.00000		3.40607e-5i	$-0.999989\pi$
$587$	−0.132638	+	2.53088i	−0.00547454	+	0.104461i	0.994525	+	0.104495i	$0.0333225\pi$
$588$	0.762134	−	0.339324i	0.0314299	−	0.0139935i
$589$	1.44869	−	13.7833i	0.0596922	−	0.567933i
$590$	4.81451	+	9.44900i	0.198210	+	0.389009i
$591$	0.765973	+	14.6156i	0.0315079	+	0.601207i
$592$	−24.4465	+	9.38412i	−1.00474	+	0.385685i
$593$	11.9080	+	11.9080i	0.489004	+	0.489004i	0.907992	−	0.418988i	$-0.137615\pi$
$593$	11.9080	+	11.9080i	0.489004	+	0.489004i	−0.418988	+	0.907992i	$0.637615\pi$
$594$	3.45980	−	2.47862i	0.141957	−	0.101699i
$595$	−38.6003	−	22.2859i	−1.58246	−	0.913631i
$596$	4.66262	−	5.75786i	0.190989	−	0.235851i
$597$	4.41429	−	1.43429i	0.180665	−	0.0587015i
$598$	24.5320	+	8.86256i	1.00319	+	0.362417i
$599$	19.8401	+	14.4147i	0.810645	+	0.588968i	0.914018	−	0.405675i	$-0.132963\pi$
$599$	19.8401	+	14.4147i	0.810645	+	0.588968i	−0.103373	+	0.994643i	$0.532963\pi$
$600$	0.819493	−	2.13485i	0.0334557	−	0.0871550i
$601$	29.1179	−	26.2178i	1.18774	−	1.06945i	0.191620	−	0.981469i	$-0.438626\pi$
$601$	29.1179	−	26.2178i	1.18774	−	1.06945i	0.996122	−	0.0879787i	$-0.0280407\pi$
$602$	10.8998	−	12.1055i	0.444244	−	0.493383i
$603$	−7.18979	−	1.13875i	−0.292791	−	0.0463735i
$604$	2.92378	+	0.783424i	0.118967	+	0.0318771i
$605$	17.4167	+	14.4925i	0.708089	+	0.589205i
$606$	−8.04372	+	8.04372i	−0.326754	+	0.326754i
$607$	−1.12890	+	2.53555i	−0.0458206	+	0.102915i	−0.935005	−	0.354633i	$-0.884606\pi$
$607$	−1.12890	+	2.53555i	−0.0458206	+	0.102915i	0.889185	+	0.457548i	$0.151272\pi$
$608$	2.32326	−	10.9301i	0.0942206	−	0.443273i
$609$	1.64379	+	0.0861473i	0.0666096	+	0.00349086i
$610$	11.0284	−	15.1793i	0.446528	−	0.614593i
$611$	45.2980	−	18.4277i	1.83256	−	0.745506i
$612$	2.37635	+	0.772122i	0.0960582	+	0.0312112i
$613$	−18.5434	+	12.0422i	−0.748960	+	0.486380i	−0.861810	−	0.507232i	$-0.830669\pi$
$613$	−18.5434	+	12.0422i	−0.748960	+	0.486380i	0.112850	+	0.993612i	$0.464002\pi$
$614$	1.63179	+	15.5255i	0.0658539	+	0.626558i
$615$	−7.92254	−	13.7222i	−0.319468	−	0.553334i
$616$	23.6860	+	19.4435i	0.954337	+	0.783400i
$617$	12.6653	−	47.2677i	0.509887	−	1.90292i	0.0884123	−	0.996084i	$-0.471821\pi$
$617$	12.6653	−	47.2677i	0.509887	−	1.90292i	0.421475	−	0.906840i	$-0.361513\pi$
$618$	−0.780954	−	2.03445i	−0.0314146	−	0.0818378i
$619$	18.3984	+	9.37448i	0.739496	+	0.376792i	0.782803	−	0.622270i	$-0.213789\pi$
$619$	18.3984	+	9.37448i	0.739496	+	0.376792i	−0.0433069	+	0.999062i	$0.513789\pi$
$620$	1.74242	−	0.370363i	0.0699773	−	0.0148741i
$621$	2.29301	+	5.15018i	0.0920151	+	0.206669i
$622$	20.9142	+	8.02819i	0.838581	+	0.321901i
$623$	1.07688	−	3.31430i	0.0431444	−	0.132785i
$624$	5.51481	−	10.0053i	0.220769	−	0.400534i
$625$	−16.6984	+	12.1321i	−0.667938	+	0.485285i
$626$	−0.111566	−	0.416368i	−0.00445906	−	0.0166414i
$627$	18.3933	−	3.78163i	0.734559	−	0.151024i
$628$	−3.08051	+	1.77853i	−0.122926	+	0.0709711i
$629$	9.14315	−	57.7276i	0.364561	−	2.30175i
$630$	−8.07618	+	0.423255i	−0.321763	+	0.0168629i
$631$	−1.80336	+	2.77694i	−0.0717907	+	0.110548i	−0.872742	−	0.488181i	$-0.837661\pi$
$631$	−1.80336	+	2.77694i	−0.0717907	+	0.110548i	0.800952	+	0.598729i	$0.204327\pi$
$632$	−26.9470	+	4.26798i	−1.07189	+	0.169771i
$633$	−16.8462	−	1.77060i	−0.669576	−	0.0703752i
$634$	−2.70542	−	3.00467i	−0.107446	−	0.119331i
$635$	22.3117	+	34.3570i	0.885413	+	1.36342i
$636$	−2.24263	−	3.08671i	−0.0889259	−	0.122396i
$637$	8.14793	+	2.46978i	0.322833	+	0.0978564i
$638$	0.917332	+	2.09789i	0.0363175	+	0.0830565i
$639$	10.0152	−	2.68357i	0.396195	−	0.106160i
$640$	−15.2304	+	1.60078i	−0.602034	+	0.0632763i
$641$	−18.9242	−	17.0394i	−0.747461	−	0.673017i	0.204627	−	0.978840i	$-0.434402\pi$
$641$	−18.9242	−	17.0394i	−0.747461	−	0.673017i	−0.952088	+	0.305823i	$0.901069\pi$
$642$	−7.45207	+	3.79702i	−0.294110	+	0.149856i
$643$	−21.8837	+	17.7211i	−0.863011	+	0.698852i	−0.954903	−	0.296917i	$-0.904042\pi$
$643$	−21.8837	+	17.7211i	−0.863011	+	0.698852i	0.0918927	+	0.995769i	$0.470708\pi$
$644$	−4.73590	+	3.83505i	−0.186620	+	0.151122i
$645$	7.61441	−	3.87974i	0.299817	−	0.152764i
$646$	−38.1858	−	34.3826i	−1.50240	−	1.35277i
$647$	31.8050	−	3.34284i	1.25038	−	0.131420i	0.543899	−	0.839151i	$-0.316947\pi$
$647$	31.8050	−	3.34284i	1.25038	−	0.131420i	0.706483	+	0.707730i	$0.250281\pi$
$648$	2.91694	−	0.781593i	0.114588	−	0.0307039i
$649$	12.9971	+	2.85333i	0.510183	+	0.112003i
$650$	3.08953	−	1.65222i	0.121181	−	0.0648054i
$651$	4.40224	+	6.05917i	0.172538	+	0.237478i
$652$	0.820850	+	1.26400i	0.0321470	+	0.0495020i
$653$	7.81785	+	8.68260i	0.305936	+	0.339776i	0.876433	−	0.481523i	$-0.159916\pi$
$653$	7.81785	+	8.68260i	0.305936	+	0.339776i	−0.570497	+	0.821299i	$0.693250\pi$
$654$	−10.7062	−	1.12526i	−0.418644	−	0.0440013i
$655$	−5.89983	+	0.934441i	−0.230525	+	0.0365116i
$656$	13.2753	−	20.4422i	0.518314	−	0.798134i
$657$	−1.09397	+	0.0573327i	−0.0426799	+	0.00223676i
$658$	8.33053	−	52.5969i	0.324758	−	2.05044i
$659$	−27.2104	+	15.7099i	−1.05997	+	0.611972i	−0.925423	−	0.378936i	$-0.876290\pi$
$659$	−27.2104	+	15.7099i	−1.05997	+	0.611972i	−0.134543	+	0.990908i	$0.542957\pi$
$660$	1.19282	+	2.09821i	0.0464304	+	0.0816726i
$661$	6.70256	+	25.0143i	0.260699	+	0.972944i	0.964830	+	0.262873i	$0.0846701\pi$
$661$	6.70256	+	25.0143i	0.260699	+	0.972944i	−0.704131	+	0.710070i	$0.748663\pi$
$662$	−21.3470	+	15.5095i	−0.829673	+	0.602793i
$663$	13.1856	+	21.8262i	0.512087	+	0.847657i
$664$	−11.5497	+	35.5462i	−0.448214	+	1.37946i
$665$	−33.3120	−	12.7873i	−1.29178	−	0.495869i
$666$	−4.31339	−	9.68804i	−0.167141	−	0.375404i
$667$	−2.96666	+	0.630583i	−0.114870	+	0.0244163i
$668$	−3.27056	−	1.66643i	−0.126542	−	0.0644763i
$669$	4.05921	+	10.5746i	0.156938	+	0.408838i
$670$	−4.97995	+	18.5854i	−0.192392	+	0.718017i
$671$	−5.94158	−	22.7808i	−0.229372	−	0.879442i
$672$	3.01928	+	5.22955i	0.116471	+	0.201734i
$673$	0.829721	+	7.89427i	0.0319834	+	0.304302i	0.998806	+	0.0488529i	$0.0155565\pi$
$673$	0.829721	+	7.89427i	0.0319834	+	0.304302i	−0.966823	+	0.255449i	$0.917777\pi$
$674$	31.2619	−	20.3017i	1.20416	−	0.781993i
$675$	0.720175	+	0.233999i	0.0277196	+	0.00900663i
$676$	−4.30830	+	1.59147i	−0.165704	+	0.0612102i
$677$	10.4042	−	14.3202i	0.399867	−	0.550369i	−0.560844	−	0.827922i	$-0.689523\pi$
$677$	10.4042	−	14.3202i	0.399867	−	0.550369i	0.960711	+	0.277552i	$0.0895232\pi$
$678$	6.08926	+	0.319125i	0.233857	+	0.0122559i
$679$	−6.80542	+	32.0170i	−0.261168	+	1.22870i
$680$	17.8932	−	40.1887i	0.686172	−	1.54117i
$681$	−6.86105	+	6.86105i	−0.262916	+	0.262916i
$682$	−4.79152	+	9.25088i	−0.183477	+	0.354235i
$683$	−2.18542	−	0.585581i	−0.0836227	−	0.0224066i	0.216765	−	0.976224i	$-0.430449\pi$
$683$	−2.18542	−	0.585581i	−0.0836227	−	0.0224066i	−0.300388	+	0.953817i	$0.597116\pi$
$684$	1.97566	+	0.312914i	0.0755413	+	0.0119646i
$685$	4.36410	−	4.84683i	0.166744	−	0.185188i
$686$	−13.5345	+	12.1865i	−0.516748	+	0.465282i
$687$	4.69737	−	12.2371i	0.179216	−	0.466873i
$688$	10.6354	+	7.72709i	0.405472	+	0.294593i
$689$	3.30089	−	38.7976i	0.125754	−	1.47807i
$690$	14.1720	−	4.60475i	0.539518	−	0.175300i
$691$	−18.2986	+	22.5969i	−0.696112	+	0.859626i	−0.995525	−	0.0944970i	$-0.969876\pi$
$691$	−18.2986	+	22.5969i	−0.696112	+	0.859626i	0.299413	+	0.954123i	$0.403209\pi$
$692$	0.731240	+	0.422182i	0.0277976	+	0.0160489i
$693$	−6.01925	+	8.16968i	−0.228652	+	0.310340i
$694$	−16.2084	−	16.2084i	−0.615264	−	0.615264i
$695$	32.2207	−	12.3684i	1.22220	−	0.469158i
$696$	0.0850269	+	1.62241i	0.00322294	+	0.0614973i
$697$	24.6992	+	48.4749i	0.935548	+	1.83612i
$698$	2.72564	−	25.9327i	0.103167	−	0.981567i
$699$	3.79341	−	1.68893i	0.143480	−	0.0638814i
$700$	−0.0428390	+	0.817417i	−0.00161916	+	0.0308955i
$701$	−3.02398	−	9.30684i	−0.114214	−	0.351515i	0.877568	−	0.479452i	$-0.159164\pi$
$701$	−3.02398	−	9.30684i	−0.114214	−	0.351515i	−0.991782	+	0.127937i	$0.959164\pi$
$702$	4.16337	+	2.01830i	0.157136	+	0.0761758i
$703$		−	46.7900i		−	1.76472i
$704$	−16.1862	+	24.5645i	−0.610042	+	0.925810i
$705$	13.9687	−	24.1946i	0.526093	−	0.911220i
$706$	15.4594	+	6.88297i	0.581822	+	0.259044i
$707$	12.3135	−	24.1665i	0.463095	−	0.908876i
$708$	1.18878	+	0.772005i	0.0446772	+	0.0290137i
$709$	−4.08716	−	5.04722i	−0.153497	−	0.189552i	0.694597	−	0.719399i	$-0.255583\pi$
$709$	−4.08716	−	5.04722i	−0.153497	−	0.189552i	−0.848093	+	0.529847i	$0.822249\pi$
$710$	−4.28727	−	27.0687i	−0.160898	−	1.01587i
$711$	−1.87839	−	8.83711i	−0.0704450	−	0.331418i
$712$	3.36438	+	0.715121i	0.126085	+	0.0268003i
$713$	−10.7246	−	8.68459i	−0.401639	−	0.325241i
$714$	27.7679			1.03919
$715$	−4.80328	+	24.1587i	−0.179633	+	0.903485i
$716$	−0.524536			−0.0196028
$717$	−10.9255	−	8.84730i	−0.408020	−	0.330408i
$718$	16.4281	+	3.49190i	0.613092	+	0.130317i
$719$	−1.13074	−	5.31972i	−0.0421695	−	0.198392i	0.952020	−	0.306036i	$-0.0990027\pi$
$719$	−1.13074	−	5.31972i	−0.0421695	−	0.198392i	−0.994190	+	0.107644i	$0.965669\pi$
$720$	−1.02099	−	6.44630i	−0.0380502	−	0.240239i
$721$	3.26987	+	4.03795i	0.121776	+	0.150381i
$722$	−14.0511	−	9.12486i	−0.522926	−	0.339592i
$723$	11.7646	−	23.0893i	0.437531	−	0.858702i
$724$	4.29313	+	1.91142i	0.159553	+	0.0710375i
$725$	−0.203692	+	0.352804i	−0.00756492	+	0.0131028i
$726$	−13.9112	−	2.39389i	−0.516292	−	0.0888455i
$727$		−	39.0930i		−	1.44988i	−0.688812	−	0.724940i	$-0.741867\pi$
$727$		−	39.0930i		−	1.44988i	0.688812	−	0.724940i	$-0.258133\pi$
$728$	−6.27838	+	32.7169i	−0.232692	+	1.21257i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	−0.151542	+	2.89160i	−0.00560884	+	0.107023i
$731$	−26.8057	+	11.9347i	−0.991444	+	0.441419i
$732$	0.262141	−	2.49411i	0.00968902	−	0.0921849i
$733$	12.7241	+	24.9724i	0.469975	+	0.922378i	0.997351	+	0.0727455i	$0.0231761\pi$
$733$	12.7241	+	24.9724i	0.469975	+	0.922378i	−0.527376	+	0.849632i	$0.676824\pi$
$734$	0.728747	+	13.9053i	0.0268985	+	0.513254i
$735$	4.54087	−	1.74308i	0.167493	−	0.0642944i
$736$	−7.86758	−	7.86758i	−0.290003	−	0.290003i
$737$	14.0604	+	19.6263i	0.517921	+	0.722946i
$738$	8.54887	+	4.93569i	0.314688	+	0.181685i
$739$	7.32530	−	9.04599i	0.269466	−	0.332762i	−0.624394	−	0.781110i	$-0.714654\pi$
$739$	7.32530	−	9.04599i	0.269466	−	0.332762i	0.893859	+	0.448347i	$0.147987\pi$
$740$	5.71962	−	1.85842i	0.210257	−	0.0683167i
$741$	13.1592	+	15.6065i	0.483414	+	0.573321i
$742$	−34.3032	−	24.9228i	−1.25931	−	0.914943i
$743$	19.5306	−	50.8790i	0.716508	−	1.86657i	0.334731	−	0.942314i	$-0.391354\pi$
$743$	19.5306	−	50.8790i	0.716508	−	1.86657i	0.381777	−	0.924254i	$-0.375312\pi$
$744$	−5.49343	+	4.94631i	−0.201399	+	0.181340i
$745$	28.9039	−	32.1010i	1.05896	−	1.17609i
$746$	13.1816	+	2.08777i	0.482614	+	0.0764386i
$747$	−11.9549	−	3.20331i	−0.437407	−	0.117203i
$748$	−3.71293	−	7.40874i	−0.135758	−	0.270890i
$749$	14.1008	−	14.1008i	0.515231	−	0.515231i
$750$	6.18956	−	13.9020i	0.226011	−	0.507628i
$751$	3.32284	−	15.6327i	0.121252	−	0.570446i	−0.875013	−	0.484099i	$-0.839147\pi$
$751$	3.32284	−	15.6327i	0.121252	−	0.570446i	0.996265	−	0.0863469i	$-0.0275193\pi$
$752$	42.9174	+	2.24921i	1.56504	+	0.0820201i
$753$	−14.5191	+	19.9838i	−0.529105	+	0.728251i
$754$	−1.52778	+	1.96514i	−0.0556385	+	0.0715660i
$755$	16.7839	+	5.45342i	0.610829	+	0.198470i
$756$	−0.906565	+	0.588730i	−0.0329715	+	0.0214119i
$757$	3.69634	+	35.1683i	0.134346	+	1.27821i	0.829155	+	0.559019i	$0.188822\pi$
$757$	3.69634	+	35.1683i	0.134346	+	1.27821i	−0.694809	+	0.719194i	$0.744511\pi$
$758$	−17.1979	−	29.7877i	−0.624657	−	1.08194i
$759$	6.81689	−	17.4107i	0.247438	−	0.631970i
$760$	9.11506	−	34.0179i	0.330638	−	1.23396i
$761$	5.73760	+	14.9470i	0.207988	+	0.541827i	0.997402	−	0.0720337i	$-0.0229489\pi$
$761$	5.73760	+	14.9470i	0.207988	+	0.541827i	−0.789414	+	0.613861i	$0.789616\pi$
$762$	−22.7399	−	11.5866i	−0.823780	−	0.419737i
$763$	25.1065	−	5.33654i	0.908915	−	0.193196i
$764$	2.41690	+	5.42844i	0.0874403	+	0.196394i
$765$	13.6001	+	5.22058i	0.491712	+	0.188751i
$766$	−6.32252	+	19.4587i	−0.228442	+	0.703072i
$767$	4.02057	+	13.8959i	0.145174	+	0.501752i
$768$	−6.63307	+	4.81921i	−0.239350	+	0.173898i
$769$	10.9103	+	40.7178i	0.393435	+	1.46832i	0.824429	+	0.565966i	$0.191497\pi$
$769$	10.9103	+	40.7178i	0.393435	+	1.46832i	−0.430993	+	0.902355i	$0.641837\pi$
$770$	19.8128	+	18.0802i	0.714005	+	0.651566i
$771$	−1.56375	+	0.902831i	−0.0563171	+	0.0325147i
$772$	1.00100	−	6.32003i	0.0360266	−	0.227463i
$773$	1.45801	−	0.0764109i	0.0524409	−	0.00274831i	−0.0260975	−	0.999659i	$-0.508308\pi$
$773$	1.45801	−	0.0764109i	0.0524409	−	0.00274831i	0.0785383	+	0.996911i	$0.474975\pi$
$774$	−2.89966	+	4.46509i	−0.104226	+	0.160494i
$775$	−1.83079	+	0.289968i	−0.0657638	+	0.0104160i
$776$	−32.1296	−	3.37695i	−1.15338	−	0.121226i
$777$	16.9192	+	18.7906i	0.606971	+	0.674110i
$778$	−22.5856	−	34.7788i	−0.809734	−	1.24688i
$779$	25.6002	+	35.2357i	0.917223	+	1.26245i
$780$	−1.38509	+	2.22845i	−0.0495941	+	0.0797911i
$781$	−29.6659	−	17.3924i	−1.06153	−	0.622349i
$782$	−49.4207	+	13.2422i	−1.76728	+	0.473542i
$783$	−0.535040	+	0.0562349i	−0.0191208	+	0.00200967i
$784$	5.56036	+	5.00657i	0.198584	+	0.178806i
$785$	−18.4782	+	9.41509i	−0.659514	+	0.336039i
$786$	2.89205	−	2.34193i	0.103156	−	0.0835340i
$787$	−0.945719	+	0.765828i	−0.0337112	+	0.0272988i	−0.646028	−	0.763314i	$-0.723571\pi$
$787$	−0.945719	+	0.765828i	−0.0337112	+	0.0272988i	0.612317	+	0.790613i	$0.290238\pi$
$788$	4.60715	−	2.34746i	0.164123	−	0.0836248i
$789$	6.26336	+	5.63956i	0.222982	+	0.200774i
$790$	−23.7494	+	2.49616i	−0.844965	+	0.0888094i
$791$	−14.0432	+	3.76286i	−0.499318	+	0.133792i
$792$	−8.64025	−	5.06556i	−0.307018	−	0.179997i
$793$	18.6763	−	17.4996i	0.663215	−	0.621430i
$794$	20.9580	+	28.8462i	0.743771	+	1.02371i
$795$	−12.1153	−	18.6559i	−0.429684	−	0.661656i
$796$	−1.09724	−	1.21861i	−0.0388908	−	0.0431926i
$797$	18.2165	+	1.91463i	0.645261	+	0.0678197i	0.421506	−	0.906826i	$-0.361502\pi$
$797$	18.2165	+	1.91463i	0.645261	+	0.0678197i	0.223755	+	0.974645i	$0.428168\pi$
$798$	21.9559	−	3.47748i	0.777232	−	0.123101i
$799$	−52.2441	+	80.4489i	−1.84826	+	2.84608i
$800$	−1.49245	+	0.0782161i	−0.0527661	+	0.00276536i
$801$	−0.178176	+	1.12496i	−0.00629553	+	0.0397484i
$802$	−7.13495	+	4.11936i	−0.251944	+	0.145460i
$803$	2.68378	+	2.44908i	0.0947085	+	0.0864263i
$804$	0.665627	+	2.48415i	0.0234748	+	0.0876093i
$805$	−28.7438	+	20.8836i	−1.01308	+	0.736049i
$806$	−11.3235	+	0.224738i	−0.398852	+	0.00791605i
$807$	4.65589	−	14.3294i	0.163895	−	0.504417i
$808$	24.9919	+	9.59351i	0.879213	+	0.337498i
$809$	−7.60201	−	17.0744i	−0.267272	−	0.600303i	0.729193	−	0.684308i	$-0.239896\pi$
$809$	−7.60201	−	17.0744i	−0.267272	−	0.600303i	−0.996465	+	0.0840046i	$0.973229\pi$
$810$	2.58545	−	0.549555i	0.0908436	−	0.0193094i
$811$	−7.28493	−	3.71186i	−0.255808	−	0.130341i	0.321384	−	0.946949i	$-0.395852\pi$
$811$	−7.28493	−	3.71186i	−0.255808	−	0.130341i	−0.577193	+	0.816608i	$0.695852\pi$
$812$	−0.208405	−	0.542914i	−0.00731359	−	0.0190526i
$813$	6.42976	−	23.9962i	0.225501	−	0.841583i
$814$	−12.8233	+	32.7515i	−0.449457	+	1.14794i
$815$	4.39351	+	7.60978i	0.153898	+	0.266559i
$816$	2.34243	+	22.2867i	0.0820014	+	0.780191i
$817$	−19.7005	+	12.7936i	−0.689233	+	0.447593i
$818$	−35.7310	−	11.6097i	−1.24930	−	0.405924i
$819$	−10.9280	−	1.50919i	−0.381853	−	0.0527352i
$820$	−3.29042	+	4.52888i	−0.114906	+	0.158155i
$821$	−32.3656	−	1.69621i	−1.12957	−	0.0591981i	−0.521622	−	0.853177i	$-0.674673\pi$
$821$	−32.3656	−	1.69621i	−1.12957	−	0.0591981i	−0.607946	+	0.793979i	$0.708006\pi$
$822$	−0.844785	+	3.97440i	−0.0294653	+	0.138623i
$823$	12.5009	−	28.0775i	0.435754	−	0.978720i	−0.553545	−	0.832819i	$-0.686725\pi$
$823$	12.5009	−	28.0775i	0.435754	−	0.978720i	0.989299	−	0.145901i	$-0.0466080\pi$
$824$	−3.62625	+	3.62625i	−0.126326	+	0.126326i
$825$	−1.12524	−	2.24529i	−0.0391758	−	0.0781709i
$826$	15.2158	+	4.07706i	0.529425	+	0.141859i
$827$	−13.9663	−	2.21205i	−0.485657	−	0.0769205i	−0.0911955	−	0.995833i	$-0.529069\pi$
$827$	−13.9663	−	2.21205i	−0.485657	−	0.0769205i	−0.394461	+	0.918913i	$0.629069\pi$
$828$	1.33273	−	1.48014i	0.0463154	−	0.0514385i
$829$	−8.76472	+	7.89179i	−0.304411	+	0.274093i	−0.807151	−	0.590344i	$-0.798992\pi$
$829$	−8.76472	+	7.89179i	−0.304411	+	0.274093i	0.502740	+	0.864438i	$0.332325\pi$
$830$	−11.7237	+	30.5412i	−0.406935	+	1.06010i
$831$	13.6840	+	9.94202i	0.474693	+	0.344885i
$832$	−31.8654	−	2.71110i	−1.10474	−	0.0939906i
$833$	−15.8831	+	5.16073i	−0.550316	+	0.178809i
$834$	−13.5313	+	16.7097i	−0.468549	+	0.578610i
$835$	−18.5335	−	10.7003i	−0.641380	−	0.370301i
$836$	−3.86362	−	5.39307i	−0.133626	−	0.186523i
$837$	−1.73090	−	1.73090i	−0.0598285	−	0.0598285i
$838$	21.6992	−	8.32954i	0.749586	−	0.287739i
$839$	2.36211	+	45.0718i	0.0815493	+	1.55605i	0.666823	+	0.745217i	$0.267654\pi$
$839$	2.36211	+	45.0718i	0.0815493	+	1.55605i	−0.585273	+	0.810836i	$0.699013\pi$
$840$	8.64022	+	16.9574i	0.298116	+	0.585086i
$841$	−3.00107	+	28.5533i	−0.103485	+	0.984596i
$842$	−15.1153	+	6.72977i	−0.520908	+	0.231923i
$843$	−1.09018	+	20.8019i	−0.0375478	+	0.716455i
$844$	1.84930	+	5.69156i	0.0636556	+	0.195912i
$845$	−25.5696	+	7.95131i	−0.879620	+	0.273534i
$846$			17.4049i			0.598392i
$847$	33.3089	−	4.82122i	1.14451	−	0.165659i
$848$	17.1095	−	29.6344i	0.587541	−	1.01765i
$849$	10.6509	+	4.74210i	0.365539	+	0.162748i
$850$	−3.11998	+	6.12331i	−0.107014	+	0.210028i
$851$	−39.0734	−	25.3746i	−1.33942	−	0.869829i
$852$	−2.30529	−	2.84680i	−0.0789780	−	0.0975297i
$853$	−5.16597	−	32.6167i	−0.176880	−	1.11677i	−0.903138	−	0.429351i	$-0.858742\pi$
$853$	−5.16597	−	32.6167i	−0.176880	−	1.11677i	0.726258	−	0.687422i	$-0.241258\pi$
$854$	−5.79454	−	27.2612i	−0.198285	−	0.932858i
$855$	11.4073	+	2.42470i	0.390122	+	0.0829230i
$856$	15.2959	+	12.3864i	0.522803	+	0.423358i
$857$	24.2200			0.827340			0.413670	−	0.910427i	$-0.364247\pi$
$857$	24.2200			0.827340			0.413670	+	0.910427i	$0.364247\pi$
$858$	−4.93385	−	14.5305i	−0.168439	−	0.496064i
$859$	2.33333			0.0796123			0.0398061	−	0.999207i	$-0.487326\pi$
$859$	2.33333			0.0796123			0.0398061	+	0.999207i	$0.487326\pi$
$860$	−2.34637	−	1.90005i	−0.0800105	−	0.0647912i
$861$	−23.0221	−	4.89349i	−0.784590	−	0.166770i
$862$	−2.11167	−	9.93461i	−0.0719236	−	0.338374i
$863$	4.73828	+	29.9163i	0.161293	+	1.01836i	0.926969	+	0.375137i	$0.122404\pi$
$863$	4.73828	+	29.9163i	0.161293	+	1.01836i	−0.765676	+	0.643226i	$0.777596\pi$
$864$	−1.24204	−	1.53379i	−0.0422551	−	0.0521807i
$865$	4.12864	+	2.68117i	0.140378	+	0.0911625i
$866$	6.45538	−	12.6694i	0.219363	−	0.430524i
$867$	−30.1639	−	13.4299i	−1.02442	−	0.456102i
$868$	1.32301	−	2.29152i	0.0449059	−	0.0777794i
$869$	−16.4868	+	25.0207i	−0.559278	+	0.848769i
$870$			1.42201i			0.0482108i
$871$	−11.4492	+	23.6175i	−0.387941	+	0.800247i
$872$	7.82850	+	24.0936i	0.265106	+	0.815913i
$873$	0.559895	−	10.6834i	0.0189496	−	0.361579i
$874$	−37.4183	+	16.6597i	−1.26569	+	0.563523i
$875$	−3.79265	+	36.0846i	−0.128215	+	1.21988i
$876$	0.175706	+	0.344843i	0.00593656	+	0.0116512i
$877$	−1.57388	−	30.0314i	−0.0531461	−	1.01409i	−0.886903	−	0.461956i	$-0.847148\pi$
$877$	−1.57388	−	30.0314i	−0.0531461	−	1.01409i	0.833757	−	0.552132i	$-0.186186\pi$
$878$	−41.2795	+	15.8457i	−1.39312	+	0.534768i
$879$	1.88387	+	1.88387i	0.0635415	+	0.0635415i
$880$	−12.8400	+	17.4271i	−0.432835	+	0.587469i
$881$	43.0702	+	24.8666i	1.45107	+	0.837776i	0.998542	−	0.0539742i	$-0.0171889\pi$
$881$	43.0702	+	24.8666i	1.45107	+	0.837776i	0.452528	+	0.891750i	$0.350522\pi$
$882$	−1.90696	+	2.35491i	−0.0642108	+	0.0792938i
$883$	32.8074	−	10.6598i	1.10406	−	0.358730i	0.300395	−	0.953815i	$-0.402881\pi$
$883$	32.8074	−	10.6598i	1.10406	−	0.358730i	0.803663	+	0.595085i	$0.202881\pi$
$884$	5.14968	−	7.39206i	0.173202	−	0.248622i
$885$	6.68582	+	4.85754i	0.224742	+	0.163284i
$886$	7.80377	−	20.3295i	0.262173	−	0.682983i
$887$	−0.539899	+	0.486127i	−0.0181280	+	0.0163226i	−0.678145	−	0.734928i	$-0.737216\pi$
$887$	−0.539899	+	0.486127i	−0.0181280	+	0.0163226i	0.660017	+	0.751251i	$0.270549\pi$
$888$	−16.6991	+	18.5462i	−0.560385	+	0.622371i
$889$	60.1020	+	9.51923i	2.01576	+	0.319265i
$890$	2.90798	+	0.779192i	0.0974759	+	0.0261186i
$891$	1.52539	−	2.94503i	0.0511024	−	0.0986622i
$892$	2.82967	−	2.82967i	0.0947443	−	0.0947443i
$893$	−31.2342	+	70.1532i	−1.04521	+	2.34759i
$894$	−5.59509	+	26.3228i	−0.187128	+	0.880367i
$895$	−3.05398	−	0.160052i	−0.102083	−	0.00534996i
$896$	−13.3709	+	18.4035i	−0.446690	+	0.614817i
$897$	20.1690	−	2.52542i	0.673425	−	0.0843212i
$898$	−23.3337	−	7.58158i	−0.778656	−	0.253001i
$899$	1.10446	−	0.717243i	0.0368357	−	0.0239214i
$900$	−0.0279643	−	0.266063i	−0.000932145	−	0.00886876i
$901$	38.1888	+	66.1449i	1.27225	+	2.20360i
$902$	−8.26261	−	31.6799i	−0.275115	−	1.05483i
$903$	3.28547	−	12.2615i	0.109333	−	0.408038i
$904$	−5.14240	−	13.3964i	−0.171034	−	0.445558i
$905$	24.4124	+	12.4387i	0.811496	+	0.413478i
$906$	−10.7541	+	2.28586i	−0.357282	+	0.0759425i
$907$	15.7572	+	35.3911i	0.523208	+	1.17514i	0.961121	+	0.276127i	$0.0890509\pi$
$907$	15.7572	+	35.3911i	0.523208	+	1.17514i	−0.437914	+	0.899017i	$0.644282\pi$
$908$	3.20034	+	1.22849i	0.106207	+	0.0407690i
$909$	−2.73934	+	8.43083i	−0.0908582	+	0.279633i
$910$	−6.98654	+	28.3097i	−0.231602	+	0.938457i
$911$	−16.6999	+	12.1332i	−0.553293	+	0.401991i	−0.828998	−	0.559251i	$-0.811089\pi$
$911$	−16.6999	+	12.1332i	−0.553293	+	0.401991i	0.275705	+	0.961242i	$0.411089\pi$
$912$	4.64320	+	17.3286i	0.153752	+	0.573809i
$913$	20.2868	+	35.6852i	0.671396	+	1.18101i
$914$	17.6011	−	10.1620i	0.582194	−	0.336130i
$915$	2.28728	−	14.4413i	0.0756152	−	0.477415i
$916$	−4.62453	+	0.242362i	−0.152799	+	0.00800785i
$917$	−4.83252	+	7.44142i	−0.159584	+	0.245737i
$918$	−8.96382	+	1.41973i	−0.295850	+	0.0468581i
$919$	−31.0611	−	3.26465i	−1.02461	−	0.107691i	−0.422713	−	0.906264i	$-0.638922\pi$
$919$	−31.0611	−	3.26465i	−1.02461	−	0.107691i	−0.601898	+	0.798573i	$0.705589\pi$
$920$	−23.4645	−	26.0600i	−0.773602	−	0.859172i
$921$	6.62570	+	10.2027i	0.218324	+	0.336190i
$922$	−27.4786	−	37.8210i	−0.904959	−	1.24557i
$923$	1.21535	−	37.3644i	0.0400036	−	1.22986i
$924$	3.50173	+	0.768754i	0.115199	+	0.0252901i
$925$	−6.04468	+	1.61967i	−0.198748	+	0.0532544i
$926$	24.2354	−	2.54724i	0.796424	−	0.0837075i
$927$	−1.26201	−	1.13632i	−0.0414498	−	0.0373215i
$928$	0.946056	−	0.482040i	0.0310558	−	0.0158237i
$929$	5.27648	−	4.27281i	0.173116	−	0.140186i	−0.538847	−	0.842404i	$-0.681140\pi$
$929$	5.27648	−	4.27281i	0.173116	−	0.140186i	0.711963	+	0.702217i	$0.247807\pi$
$930$	−5.02829	+	4.07183i	−0.164884	+	0.133521i
$931$	−11.9124	+	6.06966i	−0.390412	+	0.198925i
$932$	−1.09021	−	0.981632i	−0.0357111	−	0.0321544i
$933$	17.3618	−	1.82480i	0.568400	−	0.0597413i
$934$	12.2475	−	3.28171i	0.400751	−	0.107381i
$935$	−19.3569	−	44.2684i	−0.633040	−	1.44773i
$936$	0.353972	−	10.8824i	0.0115699	−	0.355704i
$937$	0.424380	+	0.584109i	0.0138639	+	0.0190820i	0.815893	−	0.578203i	$-0.196246\pi$
$937$	0.424380	+	0.584109i	0.0138639	+	0.0190820i	−0.802029	+	0.597285i	$0.796246\pi$
$938$	15.5662	+	23.9698i	0.508254	+	0.782643i
$939$	−0.224769	−	0.249632i	−0.00733507	−	0.00814642i
$940$	−9.81612	−	1.03172i	−0.320167	−	0.0336509i
$941$	18.0579	−	2.86009i	0.588670	−	0.0932361i	0.145008	−	0.989430i	$-0.453679\pi$
$941$	18.0579	−	2.86009i	0.588670	−	0.0932361i	0.443662	+	0.896194i	$0.353679\pi$
$942$	7.03671	−	10.8356i	0.229269	−	0.353043i
$943$	43.3078	−	2.26967i	1.41030	−	0.0739105i
$944$	−1.98871	+	12.5562i	−0.0647270	+	0.408670i
$945$	−5.45789	+	3.15111i	−0.177545	+	0.102506i
$946$	17.2960	−	3.55601i	0.562341	−	0.115616i
$947$	12.5952	+	47.0059i	0.409289	+	1.52749i	0.796006	+	0.605288i	$0.206942\pi$
$947$	12.5952	+	47.0059i	0.409289	+	1.52749i	−0.386717	+	0.922198i	$0.626391\pi$
$948$	−2.58227	+	1.87613i	−0.0838683	+	0.0609339i
$949$	−0.946373	+	3.83473i	−0.0307206	+	0.124481i
$950$	−1.70011	+	5.23239i	−0.0551588	+	0.169761i
$951$	−2.94149	−	1.12913i	−0.0953843	−	0.0366146i
$952$	−26.5786	−	59.6966i	−0.861419	−	1.93478i
$953$	−39.3772	+	8.36987i	−1.27555	+	0.271127i	−0.795414	−	0.606067i	$-0.792746\pi$
$953$	−39.3772	+	8.36987i	−1.27555	+	0.271127i	−0.480137	+	0.877193i	$0.659413\pi$
$954$	12.3478	+	6.29150i	0.399774	+	0.203695i
$955$	12.4154	+	32.3432i	0.401753	+	1.04660i
$956$	−1.28550	+	4.79756i	−0.0415762	+	0.155164i
$957$	1.37914	+	1.13212i	0.0445814	+	0.0365962i
$958$	−16.1112	−	27.9055i	−0.520531	−	0.901586i
$959$	−1.01266	−	9.63482i	−0.0327005	−	0.311125i
$960$	−15.3225	+	9.95056i	−0.494532	+	0.321153i
$961$	−23.7840	−	7.72790i	−0.767227	−	0.249287i
$962$	−37.9402	+	4.75059i	−1.22324	+	0.153165i
$963$	−3.83095	+	5.27285i	−0.123451	+	0.169915i
$964$	−9.14268	−	0.479147i	−0.294466	−	0.0154323i
$965$	7.75648	−	36.4914i	0.249690	−	1.17470i
$966$	9.00290	−	20.2208i	0.289664	−	0.650595i
$967$	39.2191	−	39.2191i	1.26120	−	1.26120i	0.310690	−	0.950511i	$-0.399440\pi$
$967$	39.2191	−	39.2191i	1.26120	−	1.26120i	0.950511	−	0.310690i	$-0.100560\pi$
$968$	8.16889	+	32.1982i	0.262558	+	1.03489i
$969$	−38.6780	−	10.3637i	−1.24252	−	0.332931i
$970$	−27.9292	−	4.42355i	−0.896753	−	0.142032i
$971$	20.1639	−	22.3942i	0.647089	−	0.718665i	−0.326951	−	0.945041i	$-0.606021\pi$
$971$	20.1639	−	22.3942i	0.647089	−	0.718665i	0.974040	+	0.226376i	$0.0726879\pi$
$972$	0.262550	−	0.236401i	0.00842129	−	0.00758256i
$973$	18.3720	−	47.8608i	0.588980	−	1.53435i
$974$	−27.0128	−	19.6259i	−0.865545	−	0.628855i
$975$	1.56066	−	2.24023i	0.0499811	−	0.0717449i
$976$	21.3912	−	6.95042i	0.684716	−	0.222478i
$977$	−31.0775	+	38.3775i	−0.994258	+	1.22781i	−0.0206013	+	0.999788i	$0.506558\pi$
$977$	−31.0775	+	38.3775i	−0.994258	+	1.22781i	−0.973657	+	0.228019i	$0.926775\pi$
$978$	−4.74084	−	2.73713i	−0.151595	−	0.0875237i
$979$	3.07085	−	2.19997i	0.0981449	−	0.0703115i
$980$	−1.21510	−	1.21510i	−0.0388148	−	0.0388148i
$981$	−7.83183	+	3.00636i	−0.250051	+	0.0959856i
$982$	−0.635137	−	12.1191i	−0.0202680	−	0.386737i
$983$	−3.31933	−	6.51455i	−0.105870	−	0.207782i	0.831994	−	0.554785i	$-0.187199\pi$
$983$	−3.31933	−	6.51455i	−0.105870	−	0.207782i	−0.937864	+	0.347003i	$0.887199\pi$
$984$	2.42823	−	23.1030i	0.0774090	−	0.736498i
$985$	27.5403	−	12.2617i	0.877505	−	0.390691i
$986$	0.255532	−	4.87584i	0.00813780	−	0.155278i
$987$	−12.8237	−	39.4674i	−0.408184	−	1.25626i
$988$	3.14609	−	6.48977i	0.100090	−	0.206467i
$989$			23.3896i			0.743746i
$990$	−7.32025	−	4.82352i	−0.232653	−	0.153301i
$991$	24.4552	−	42.3577i	0.776845	−	1.34554i	−0.156906	−	0.987613i	$-0.550152\pi$
$991$	24.4552	−	42.3577i	0.776845	−	1.34554i	0.933752	−	0.357922i	$-0.116515\pi$
$992$	4.41347	+	1.96500i	0.140128	+	0.0623889i
$993$	−9.33506	+	18.3211i	−0.296239	+	0.581402i
$994$	−34.1417	−	22.1719i	−1.08291	−	0.703249i
$995$	−6.01659	−	7.42987i	−0.190739	−	0.235543i
$996$	0.684027	+	4.31878i	0.0216742	+	0.136846i
$997$	8.53088	+	40.1346i	0.270176	+	1.27108i	0.878636	+	0.477492i	$0.158454\pi$
$997$	8.53088	+	40.1346i	0.270176	+	1.27108i	−0.608460	+	0.793584i	$0.708212\pi$
$998$	18.4610	+	3.92401i	0.584373	+	0.124212i
$999$	−6.42245	−	5.20080i	−0.203197	−	0.164546i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.bs.a.85.10	yes	224
11.7	odd	10	inner	429.2.bs.a.7.10	✓	224
13.2	odd	12	inner	429.2.bs.a.184.10	yes	224
143.106	even	60	inner	429.2.bs.a.106.10	yes	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.bs.a.7.10	✓	224	11.7	odd	10	inner
429.2.bs.a.85.10	yes	224	1.1	even	1	trivial
429.2.bs.a.106.10	yes	224	143.106	even	60	inner
429.2.bs.a.184.10	yes	224	13.2	odd	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.bs (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(0.997265 + 0.807569i) q^{2} +(0.978148 + 0.207912i) q^{3} +(-0.0734543 - 0.345575i) q^{4} +(-0.322223 - 2.03444i) q^{5} +(0.807569 + 0.997265i) q^{6} +(-2.56603 - 1.66640i) q^{7} +(1.37098 - 2.69070i) q^{8} +(0.913545 + 0.406737i) q^{9} +(1.32161 - 2.28909i) q^{10} +(-1.16790 - 3.10419i) q^{11} -0.353296i q^{12} +(2.35894 - 2.72679i) q^{13} +(-1.21328 - 3.73408i) q^{14} +(0.107801 - 2.05697i) q^{15} +(2.89465 - 1.28878i) q^{16} +(-0.739265 + 7.03364i) q^{17} +(0.582579 + 1.14338i) q^{18} +(0.296316 + 5.65404i) q^{19} +(-0.679382 + 0.260790i) q^{20} +(-2.16349 - 2.16349i) q^{21} +(1.34214 - 4.03886i) q^{22} +(4.88228 + 2.81878i) q^{23} +(1.90045 - 2.34686i) q^{24} +(0.720175 - 0.233999i) q^{25} +(4.55456 - 0.814326i) q^{26} +(0.809017 + 0.587785i) q^{27} +(-0.387380 + 1.00916i) q^{28} +(-0.399802 + 0.359984i) q^{29} +(1.76865 - 1.96429i) q^{30} +(-2.41772 - 0.382929i) q^{31} +(-1.90637 - 0.510811i) q^{32} +(-0.496982 - 3.27918i) q^{33} +(-6.41739 + 6.41739i) q^{34} +(-2.56335 + 5.75737i) q^{35} +(0.0734543 - 0.345575i) q^{36} +(-8.25282 - 0.432512i) q^{37} +(-4.27052 + 5.87787i) q^{38} +(2.87432 - 2.17675i) q^{39} +(-5.91582 - 1.92217i) q^{40} +(6.45151 - 4.18966i) q^{41} +(-0.410404 - 3.90474i) q^{42} +(2.07444 + 3.59304i) q^{43} +(-0.986944 + 0.631614i) q^{44} +(0.533115 - 1.98961i) q^{45} +(2.59256 + 6.75385i) q^{46} +(12.0849 + 6.15757i) q^{47} +(3.09935 - 0.658787i) q^{48} +(0.960454 + 2.15721i) q^{49} +(0.907176 + 0.348232i) q^{50} +(-2.18549 + 6.72623i) q^{51} +(-1.11559 - 0.614897i) q^{52} +(8.73690 - 6.34773i) q^{53} +(0.332127 + 1.23951i) q^{54} +(-5.93896 + 3.37626i) q^{55} +(-8.00174 + 4.61981i) q^{56} +(-0.885701 + 5.59209i) q^{57} +(-0.689420 + 0.0361310i) q^{58} +(-2.18515 + 3.36484i) q^{59} +(-0.718758 + 0.113840i) q^{60} +(7.05955 + 0.741989i) q^{61} +(-2.10186 - 2.33436i) q^{62} +(-1.66640 - 2.56603i) q^{63} +(-5.21355 - 7.17583i) q^{64} +(-6.30759 - 3.92048i) q^{65} +(2.15254 - 3.67156i) q^{66} +(-7.03137 + 1.88405i) q^{67} +(2.48495 - 0.261179i) q^{68} +(4.18953 + 3.77227i) q^{69} +(-7.20581 + 3.67154i) q^{70} +(8.05784 - 6.52511i) q^{71} +(2.34686 - 1.90045i) q^{72} +(-0.976074 + 0.497335i) q^{73} +(-7.88096 - 7.09605i) q^{74} +(0.753089 - 0.0791528i) q^{75} +(1.93213 - 0.517713i) q^{76} +(-2.17595 + 9.91162i) q^{77} +(4.62434 + 0.150415i) q^{78} +(-5.31037 - 7.30909i) q^{79} +(-3.55467 - 5.47371i) q^{80} +(0.669131 + 0.743145i) q^{81} +(9.81731 + 1.03184i) q^{82} +(-12.2243 + 1.93613i) q^{83} +(-0.588730 + 0.906565i) q^{84} +(14.5477 - 0.762413i) q^{85} +(-0.832859 + 5.25846i) q^{86} +(-0.465910 + 0.268993i) q^{87} +(-9.95362 - 1.11331i) q^{88} +(0.294790 + 1.10017i) q^{89} +(2.13840 - 1.55364i) q^{90} +(-10.5970 + 3.06609i) q^{91} +(0.615478 - 1.89425i) q^{92} +(-2.28527 - 0.877233i) q^{93} +(7.07920 + 15.9001i) q^{94} +(11.4073 - 2.42470i) q^{95} +(-1.75851 - 0.896006i) q^{96} +(-3.83385 - 9.98753i) q^{97} +(-0.784273 + 2.92695i) q^{98} +(0.195658 - 3.31085i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q - 28 q^{3} - 6 q^{5} + 28 q^{9} - 16 q^{11} - 10 q^{13} - 36 q^{14} + 8 q^{15} - 24 q^{16} + 50 q^{20} + 10 q^{22} - 48 q^{23} - 30 q^{24} + 10 q^{26} + 56 q^{27} + 20 q^{29} + 12 q^{31} - 32 q^{33}+ \cdots - 6 q^{99}+O(q^{100}) \) 224 * q - 28 * q^3 - 6 * q^5 + 28 * q^9 - 16 * q^11 - 10 * q^13 - 36 * q^14 + 8 * q^15 - 24 * q^16 + 50 * q^20 + 10 * q^22 - 48 * q^23 - 30 * q^24 + 10 * q^26 + 56 * q^27 + 20 * q^29 + 12 * q^31 - 32 * q^33 - 104 * q^34 + 20 * q^35 + 12 * q^37 + 20 * q^39 - 80 * q^40 + 190 * q^41 + 32 * q^42 - 24 * q^44 + 4 * q^45 - 40 * q^46 - 10 * q^47 + 44 * q^48 - 24 * q^49 - 180 * q^50 - 110 * q^52 + 28 * q^53 - 62 * q^55 - 72 * q^56 + 20 * q^58 - 118 * q^59 + 88 * q^60 - 20 * q^61 + 120 * q^62 - 20 * q^66 - 156 * q^67 - 60 * q^68 + 12 * q^69 - 20 * q^70 + 64 * q^71 - 30 * q^72 + 10 * q^73 - 60 * q^74 - 12 * q^75 + 84 * q^78 + 200 * q^79 + 188 * q^80 + 28 * q^81 - 138 * q^82 - 80 * q^83 - 60 * q^84 + 40 * q^85 - 42 * q^86 - 18 * q^88 + 216 * q^89 - 88 * q^91 + 16 * q^92 + 12 * q^93 - 40 * q^94 - 300 * q^95 - 100 * q^96 + 18 * q^97 - 6 * q^99

Introduction

L-functions

Modular forms

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Database

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