LMFDB - Embedded newform 261.2.x.a.101.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [261,2,Mod(2,261)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(261, base_ring=CyclotomicField(84)) chi = DirichletCharacter(H, H._module([14, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("261.2"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 261 = 3^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	261.x (of order $84$, degree $24$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$2.08409549276$
Analytic rank:	$0$
Dimension:	$672$
Relative dimension:	$28$ over $\Q(\zeta_{84})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{84}]$

Embedding invariants

Embedding label			101.10
Character	$\chi$	$=$	261.101
Dual form			261.2.x.a.230.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.347486 + 0.796446i) q^{2} +(0.982997 + 1.42608i) q^{3} +(0.846766 + 0.912597i) q^{4} +(-3.93941 - 0.593771i) q^{5} +(-1.47738 + 0.287360i) q^{6} +(-2.03501 - 1.88821i) q^{7} +(-2.66145 + 0.931280i) q^{8} +(-1.06743 + 2.80367i) q^{9} +(1.84180 - 2.93120i) q^{10} +(-2.36556 + 2.03573i) q^{11} +(-0.469071 + 2.10464i) q^{12} +(0.0455825 - 0.0668572i) q^{13} +(2.21099 - 0.964646i) q^{14} +(-3.02566 - 6.20161i) q^{15} +(-0.00296683 + 0.0395895i) q^{16} +(4.09498 + 4.09498i) q^{17} +(-1.86206 - 1.82439i) q^{18} +(2.30749 + 1.44989i) q^{19} +(-2.79389 - 4.09788i) q^{20} +(0.692341 - 4.75820i) q^{21} +(-0.799349 - 2.59142i) q^{22} +(7.85871 + 3.08432i) q^{23} +(-3.94428 - 2.88000i) q^{24} +(10.3885 + 3.20444i) q^{25} +(0.0374089 + 0.0595359i) q^{26} +(-5.04756 + 1.23375i) q^{27} -3.45601i q^{28} +(-2.02195 - 4.99116i) q^{29} +(5.99062 - 0.254806i) q^{30} +(-4.46827 + 3.29773i) q^{31} +(-5.01634 - 2.65121i) q^{32} +(-5.22845 - 1.37237i) q^{33} +(-4.68438 + 1.83848i) q^{34} +(6.89556 + 8.64676i) q^{35} +(-3.46249 + 1.39992i) q^{36} +(2.12109 + 6.06173i) q^{37} +(-1.95658 + 1.33398i) q^{38} +(0.140151 - 0.000715986i) q^{39} +(11.0375 - 2.08841i) q^{40} +(-4.77813 - 1.28030i) q^{41} +(3.54907 + 2.20482i) q^{42} +(-0.869673 + 1.17837i) q^{43} +(-3.86087 - 0.435016i) q^{44} +(5.86980 - 10.4110i) q^{45} +(-5.18728 + 5.18728i) q^{46} +(-1.64995 - 1.91728i) q^{47} +(-0.0593744 + 0.0346855i) q^{48} +(0.0528034 + 0.704612i) q^{49} +(-6.16203 + 7.16040i) q^{50} +(-1.81443 + 9.86514i) q^{51} +(0.0996113 - 0.0150140i) q^{52} +(0.457295 + 0.364681i) q^{53} +(0.771338 - 4.44882i) q^{54} +(10.5277 - 6.61497i) q^{55} +(7.17451 + 3.13021i) q^{56} +(0.200588 + 4.71592i) q^{57} +(4.67779 + 0.123987i) q^{58} +(6.12658 - 3.53718i) q^{59} +(3.09754 - 8.01252i) q^{60} +(-9.30117 + 0.348025i) q^{61} +(-1.07381 - 4.70465i) q^{62} +(7.46616 - 3.68996i) q^{63} +(3.79258 - 3.02448i) q^{64} +(-0.219266 + 0.236312i) q^{65} +(2.90983 - 3.68730i) q^{66} +(5.85402 - 0.438698i) q^{67} +(-0.269575 + 7.20455i) q^{68} +(3.32659 + 14.2391i) q^{69} +(-9.28279 + 2.48732i) q^{70} +(12.0733 - 5.81419i) q^{71} +(0.229911 - 8.45590i) q^{72} +(0.305465 - 2.71107i) q^{73} +(-5.56489 - 0.417031i) q^{74} +(5.64210 + 17.9649i) q^{75} +(0.630738 + 3.33353i) q^{76} +(8.65780 + 0.323952i) q^{77} +(-0.0481304 + 0.111872i) q^{78} +(-0.0611055 + 0.322950i) q^{79} +(0.0351947 - 0.154198i) q^{80} +(-6.72117 - 5.98547i) q^{81} +(2.68002 - 3.36064i) q^{82} +(-4.14511 + 13.4381i) q^{83} +(4.92856 - 3.39725i) q^{84} +(-13.7003 - 18.5633i) q^{85} +(-0.636305 - 1.10211i) q^{86} +(5.13025 - 7.78977i) q^{87} +(4.39997 - 7.62097i) q^{88} +(0.558973 - 0.0629811i) q^{89} +(6.25214 + 8.29265i) q^{90} +(-0.219001 + 0.0499855i) q^{91} +(3.83975 + 9.78352i) q^{92} +(-9.09514 - 3.13047i) q^{93} +(2.10034 - 0.647870i) q^{94} +(-8.22926 - 7.08185i) q^{95} +(-1.15019 - 9.75986i) q^{96} +(5.98574 + 11.3256i) q^{97} +(-0.579534 - 0.202788i) q^{98} +(-3.18244 - 8.80525i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 672 q - 36 q^{2} - 24 q^{3} - 14 q^{4} - 42 q^{5} - 28 q^{6} - 10 q^{7} - 28 q^{9} - 56 q^{10} - 48 q^{11} - 10 q^{12} - 14 q^{13} - 24 q^{14} - 20 q^{15} - 54 q^{16} - 50 q^{18} - 48 q^{19} - 30 q^{20}+ \cdots - 16 q^{99}+O(q^{100}) $ 672 * q - 36 * q^2 - 24 * q^3 - 14 * q^4 - 42 * q^5 - 28 * q^6 - 10 * q^7 - 28 * q^9 - 56 * q^10 - 48 * q^11 - 10 * q^12 - 14 * q^13 - 24 * q^14 - 20 * q^15 - 54 * q^16 - 50 * q^18 - 48 * q^19 - 30 * q^20 - 80 * q^21 - 14 * q^22 - 30 * q^23 - 16 * q^24 + 30 * q^25 + 36 * q^27 - 168 * q^30 - 12 * q^31 + 24 * q^32 - 70 * q^33 - 14 * q^34 + 128 * q^36 - 48 * q^37 - 42 * q^38 - 44 * q^39 - 2 * q^40 - 24 * q^41 - 28 * q^42 - 12 * q^43 + 24 * q^45 - 64 * q^46 - 42 * q^47 - 28 * q^48 + 22 * q^49 - 66 * q^50 - 28 * q^51 + 22 * q^52 - 36 * q^54 + 76 * q^55 - 42 * q^56 - 42 * q^58 - 132 * q^59 - 20 * q^60 - 28 * q^63 - 308 * q^64 - 66 * q^65 - 46 * q^66 - 14 * q^67 + 60 * q^68 - 64 * q^69 - 14 * q^70 + 56 * q^72 - 48 * q^73 + 66 * q^74 + 24 * q^75 - 28 * q^76 + 30 * q^77 + 72 * q^78 - 12 * q^79 + 140 * q^81 - 136 * q^82 + 246 * q^83 + 238 * q^84 + 34 * q^85 + 118 * q^87 + 8 * q^88 - 48 * q^90 - 56 * q^91 + 462 * q^92 + 28 * q^93 + 26 * q^94 - 246 * q^95 + 126 * q^96 - 36 * q^97 - 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/261\mathbb{Z}\right)^\times$.

$n$	$118$	$146$
$\chi(n)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−0.347486	+	0.796446i	−0.245710	+	0.563172i	−0.995091	−	0.0989666i	$-0.968446\pi$
$2$	−0.347486	+	0.796446i	−0.245710	+	0.563172i	0.749381	+	0.662139i	$0.230351\pi$
$3$	0.982997	+	1.42608i	0.567534	+	0.823350i
$3$	0.982997	+	1.42608i	0.567534	+	0.823350i
$4$	0.846766	+	0.912597i	0.423383	+	0.456298i
$5$	−3.93941	−	0.593771i	−1.76176	−	0.265542i	−0.813163	−	0.582036i	$-0.802256\pi$
$5$	−3.93941	−	0.593771i	−1.76176	−	0.265542i	−0.948595	+	0.316493i	$0.897495\pi$
$6$	−1.47738	+	0.287360i	−0.603136	+	0.117314i
$7$	−2.03501	−	1.88821i	−0.769160	−	0.713676i	0.194472	−	0.980908i	$-0.437701\pi$
$7$	−2.03501	−	1.88821i	−0.769160	−	0.713676i	−0.963632	+	0.267232i	$0.913891\pi$
$8$	−2.66145	+	0.931280i	−0.940963	+	0.329257i
$9$	−1.06743	+	2.80367i	−0.355811	+	0.934558i
$10$	1.84180	−	2.93120i	0.582427	−	0.926927i
$11$	−2.36556	+	2.03573i	−0.713242	+	0.613795i	−0.932202	−	0.361939i	$-0.882115\pi$
$11$	−2.36556	+	2.03573i	−0.713242	+	0.613795i	0.218959	+	0.975734i	$0.429734\pi$
$12$	−0.469071	+	2.10464i	−0.135409	+	0.607557i
$13$	0.0455825	−	0.0668572i	0.0126423	−	0.0185428i	−0.819866	−	0.572556i	$-0.805952\pi$
$13$	0.0455825	−	0.0668572i	0.0126423	−	0.0185428i	0.832508	+	0.554013i	$0.186904\pi$
$14$	2.21099	−	0.964646i	0.590913	−	0.257813i
$15$	−3.02566	−	6.20161i	−0.781223	−	1.60125i
$16$	−0.00296683	+	0.0395895i	−0.000741706	+	0.00989739i
$17$	4.09498	+	4.09498i	0.993179	+	0.993179i	0.999977	−	0.00679835i	$-0.00216400\pi$
$17$	4.09498	+	4.09498i	0.993179	+	0.993179i	−0.00679835	+	0.999977i	$0.502164\pi$
$18$	−1.86206	−	1.82439i	−0.438891	−	0.430013i
$19$	2.30749	+	1.44989i	0.529375	+	0.332628i	0.770056	−	0.637976i	$-0.220228\pi$
$19$	2.30749	+	1.44989i	0.529375	+	0.332628i	−0.240681	+	0.970604i	$0.577371\pi$
$20$	−2.79389	−	4.09788i	−0.624732	−	0.916313i
$21$	0.692341	−	4.75820i	0.151081	−	1.03832i
$22$	−0.799349	−	2.59142i	−0.170422	−	0.552494i
$23$	7.85871	+	3.08432i	1.63865	+	0.643124i	0.992739	−	0.120286i	$-0.0383810\pi$
$23$	7.85871	+	3.08432i	1.63865	+	0.643124i	0.645914	+	0.763410i	$0.276476\pi$
$24$	−3.94428	−	2.88000i	−0.805122	−	0.587878i
$25$	10.3885	+	3.20444i	2.07771	+	0.640887i
$26$	0.0374089	+	0.0595359i	0.00733648	+	0.0116759i
$27$	−5.04756	+	1.23375i	−0.971403	+	0.237436i
$28$		−	3.45601i		−	0.653125i
$29$	−2.02195	−	4.99116i	−0.375466	−	0.926836i
$29$	−2.02195	−	4.99116i	−0.375466	−	0.926836i
$30$	5.99062	−	0.254806i	1.09373	−	0.0465210i
$31$	−4.46827	+	3.29773i	−0.802524	+	0.592290i	−0.915967	−	0.401255i	$-0.868574\pi$
$31$	−4.46827	+	3.29773i	−0.802524	+	0.592290i	0.113442	+	0.993545i	$0.463812\pi$
$32$	−5.01634	−	2.65121i	−0.886772	−	0.468673i
$33$	−5.22845	−	1.37237i	−0.910157	−	0.238899i
$34$	−4.68438	+	1.83848i	−0.803364	+	0.315297i
$35$	6.89556	+	8.64676i	1.16556	+	1.46157i
$36$	−3.46249	+	1.39992i	−0.577082	+	0.233320i
$37$	2.12109	+	6.06173i	0.348705	+	0.996543i	0.976002	+	0.217762i	$0.0698757\pi$
$37$	2.12109	+	6.06173i	0.348705	+	0.996543i	−0.627296	+	0.778781i	$0.715839\pi$
$38$	−1.95658	+	1.33398i	−0.317400	+	0.216399i
$39$	0.140151		0.000715986i	0.0224422		0.000114650i
$40$	11.0375	−	2.08841i	1.74518	−	0.330206i
$41$	−4.77813	−	1.28030i	−0.746219	−	0.199949i	−0.134379	−	0.990930i	$-0.542904\pi$
$41$	−4.77813	−	1.28030i	−0.746219	−	0.199949i	−0.611840	+	0.790981i	$0.709570\pi$
$42$	3.54907	+	2.20482i	0.547633	+	0.340211i
$43$	−0.869673	+	1.17837i	−0.132624	+	0.179699i	−0.865877	−	0.500257i	$-0.833239\pi$
$43$	−0.869673	+	1.17837i	−0.132624	+	0.179699i	0.733253	+	0.679956i	$0.238001\pi$
$44$	−3.86087	−	0.435016i	−0.582048	−	0.0655811i
$45$	5.86980	−	10.4110i	0.875018	−	1.55198i
$46$	−5.18728	+	5.18728i	−0.764823	+	0.764823i
$47$	−1.64995	−	1.91728i	−0.240670	−	0.279664i	0.624627	−	0.780923i	$-0.285251\pi$
$47$	−1.64995	−	1.91728i	−0.240670	−	0.279664i	−0.865297	+	0.501260i	$0.832870\pi$
$48$	−0.0593744	+	0.0346855i	−0.00856996	+	0.00500641i
$49$	0.0528034	+	0.704612i	0.00754334	+	0.100659i
$50$	−6.16203	+	7.16040i	−0.871442	+	1.01263i
$51$	−1.81443	+	9.86514i	−0.254072	+	1.38140i
$52$	0.0996113	−	0.0150140i	0.0138136	−	0.00208207i
$53$	0.457295	+	0.364681i	0.0628143	+	0.0500927i	0.654394	−	0.756154i	$-0.272924\pi$
$53$	0.457295	+	0.364681i	0.0628143	+	0.0500927i	−0.591579	+	0.806247i	$0.701495\pi$
$54$	0.771338	−	4.44882i	0.104966	−	0.605408i
$55$	10.5277	−	6.61497i	1.41955	−	0.891962i
$56$	7.17451	+	3.13021i	0.958734	+	0.418292i
$57$	0.200588	+	4.71592i	0.0265685	+	0.624639i
$58$	4.67779	+	0.123987i	0.614224	+	0.0162802i
$59$	6.12658	−	3.53718i	0.797612	−	0.460502i	−0.0450232	−	0.998986i	$-0.514336\pi$
$59$	6.12658	−	3.53718i	0.797612	−	0.460502i	0.842636	+	0.538484i	$0.181003\pi$
$60$	3.09754	−	8.01252i	0.399890	−	1.03441i
$61$	−9.30117	+	0.348025i	−1.19089	+	0.0445600i	−0.625475	−	0.780245i	$-0.715095\pi$
$61$	−9.30117	+	0.348025i	−1.19089	+	0.0445600i	−0.565418	+	0.824805i	$0.691285\pi$
$62$	−1.07381	−	4.70465i	−0.136373	−	0.597491i
$63$	7.46616	−	3.68996i	0.940648	−	0.464891i
$64$	3.79258	−	3.02448i	0.474072	−	0.378060i
$65$	−0.219266	+	0.236312i	−0.0271966	+	0.0293109i
$66$	2.90983	−	3.68730i	0.358176	−	0.453875i
$67$	5.85402	−	0.438698i	0.715183	−	0.0535955i	0.287831	−	0.957681i	$-0.407066\pi$
$67$	5.85402	−	0.438698i	0.715183	−	0.0535955i	0.427351	+	0.904086i	$0.359447\pi$
$68$	−0.269575	+	7.20455i	−0.0326908	+	0.873681i
$69$	3.32659	+	14.2391i	0.400475	+	1.71418i
$70$	−9.28279	+	2.48732i	−1.10951	+	0.297291i
$71$	12.0733	−	5.81419i	1.43283	−	0.690017i	0.453312	−	0.891352i	$-0.350242\pi$
$71$	12.0733	−	5.81419i	1.43283	−	0.690017i	0.979522	+	0.201335i	$0.0645279\pi$
$72$	0.229911	−	8.45590i	0.0270952	−	0.996538i
$73$	0.305465	−	2.71107i	0.0357519	−	0.317307i	−0.963089	−	0.269182i	$-0.913247\pi$
$73$	0.305465	−	2.71107i	0.0357519	−	0.317307i	0.998841	−	0.0481253i	$-0.0153247\pi$
$74$	−5.56489	−	0.417031i	−0.646905	−	0.0484789i
$75$	5.64210	+	17.9649i	0.651493	+	2.07440i
$76$	0.630738	+	3.33353i	0.0723506	+	0.382382i
$77$	8.65780	+	0.323952i	0.986648	+	0.0369178i
$78$	−0.0481304	+	0.111872i	−0.00544969	+	0.0126670i
$79$	−0.0611055	+	0.322950i	−0.00687490	+	0.0363347i	−0.985836	−	0.167712i	$-0.946362\pi$
$79$	−0.0611055	+	0.322950i	−0.00687490	+	0.0363347i	0.978961	+	0.204047i	$0.0654096\pi$
$80$	0.0351947	−	0.154198i	0.00393488	−	0.0172398i
$81$	−6.72117	−	5.98547i	−0.746797	−	0.665052i
$82$	2.68002	−	3.36064i	0.295959	−	0.371120i
$83$	−4.14511	+	13.4381i	−0.454985	+	1.47503i	0.380121	+	0.924937i	$0.375882\pi$
$83$	−4.14511	+	13.4381i	−0.454985	+	1.47503i	−0.835106	+	0.550089i	$0.814594\pi$
$84$	4.92856	−	3.39725i	0.537750	−	0.370670i
$85$	−13.7003	−	18.5633i	−1.48601	−	2.01347i
$86$	−0.636305	−	1.10211i	−0.0686145	−	0.118844i
$87$	5.13025	−	7.78977i	0.550021	−	0.835151i
$88$	4.39997	−	7.62097i	0.469038	−	0.812398i
$89$	0.558973	−	0.0629811i	0.0592510	−	0.00667598i	−0.0822892	−	0.996608i	$-0.526223\pi$
$89$	0.558973	−	0.0629811i	0.0592510	−	0.00667598i	0.141540	+	0.989933i	$0.454795\pi$
$90$	6.25214	+	8.29265i	0.659033	+	0.874122i
$91$	−0.219001	+	0.0499855i	−0.0229575	+	0.00523991i
$92$	3.83975	+	9.78352i	0.400322	+	1.02000i
$93$	−9.09514	−	3.13047i	−0.943122	−	0.324614i
$94$	2.10034	−	0.647870i	0.216634	−	0.0668227i
$95$	−8.22926	−	7.08185i	−0.844304	−	0.726582i
$96$	−1.15019	−	9.75986i	−0.117391	−	0.996111i
$97$	5.98574	+	11.3256i	0.607760	+	1.14994i	0.975498	+	0.220008i	$0.0706084\pi$
$97$	5.98574	+	11.3256i	0.607760	+	1.14994i	−0.367738	+	0.929929i	$0.619868\pi$
$98$	−0.579534	−	0.202788i	−0.0585417	−	0.0204846i
$99$	−3.18244	−	8.80525i	−0.319847	−	0.884961i
$100$	5.87229	+	12.1939i	0.587229	+	1.21939i
$101$	−0.483604	−	0.356916i	−0.0481204	−	0.0355145i	0.569494	−	0.821995i	$-0.307139\pi$
$101$	−0.483604	−	0.356916i	−0.0481204	−	0.0355145i	−0.617615	+	0.786481i	$0.711901\pi$
$102$	−7.22656	−	4.87309i	−0.715536	−	0.482508i
$103$	−5.35650	−	3.65200i	−0.527792	−	0.359842i	0.269919	−	0.962883i	$-0.413003\pi$
$103$	−5.35650	−	3.65200i	−0.527792	−	0.359842i	−0.797710	+	0.603041i	$0.793956\pi$
$104$	−0.0590525	+	0.220387i	−0.00579057	+	0.0216107i
$105$	−5.55269	+	18.3334i	−0.541887	+	1.78916i
$106$	−0.449352	+	0.237489i	−0.0436449	+	0.0230670i
$107$	−3.51923	+	7.30776i	−0.340217	+	0.706468i	−0.998945	−	0.0459129i	$-0.985380\pi$
$107$	−3.51923	+	7.30776i	−0.340217	+	0.706468i	0.658728	+	0.752381i	$0.271095\pi$
$108$	−5.40002	−	3.56169i	−0.519617	−	0.342723i
$109$	3.18652	+	0.727303i	0.305213	+	0.0696630i	0.372385	−	0.928078i	$-0.378540\pi$
$109$	3.18652	+	0.727303i	0.305213	+	0.0696630i	−0.0671712	+	0.997741i	$0.521397\pi$
$110$	1.61025	+	10.6833i	0.153531	+	1.01861i
$111$	−6.55952	+	8.98352i	−0.622602	+	0.852678i
$112$	0.0807909	−	0.0749630i	0.00763402	−	0.00708334i
$113$	−3.31019	+	6.26318i	−0.311396	+	0.589191i	−0.989289	−	0.145970i	$-0.953370\pi$
$113$	−3.31019	+	6.26318i	−0.311396	+	0.589191i	0.677893	+	0.735161i	$0.262893\pi$
$114$	−3.82568	−	1.47896i	−0.358307	−	0.138517i
$115$	−29.1273	−	16.8167i	−2.71613	−	1.56816i
$116$	2.84280	−	6.07157i	0.263948	−	0.563731i
$117$	0.138789	+	0.199164i	0.0128311	+	0.0184127i
$118$	0.688275	+	6.10861i	0.0633608	+	0.562343i
$119$	−0.601128	−	16.0655i	−0.0551053	−	1.47272i
$120$	13.8281	+	13.6875i	1.26232	+	1.24949i
$121$	−0.187786	+	1.24588i	−0.0170715	+	0.113262i
$122$	2.95484	−	7.52881i	0.267519	−	0.681626i
$123$	−2.87108	−	8.07255i	−0.258876	−	0.727877i
$124$	−6.79307	−	1.28532i	−0.610036	−	0.115425i
$125$	−21.0751	−	10.1492i	−1.88501	−	0.907775i
$126$	0.344466	+	7.22860i	0.0306874	+	0.643975i
$127$	−3.43221	+	9.80870i	−0.304560	+	0.870381i	0.685291	+	0.728269i	$0.259675\pi$
$127$	−3.43221	+	9.80870i	−0.304560	+	0.870381i	−0.989851	+	0.142112i	$0.954611\pi$
$128$	−1.84603	−	6.88949i	−0.163168	−	0.608951i
$129$	−2.53533	−	0.0818977i	−0.223224	−	0.00721069i
$130$	−0.112018	−	0.256749i	−0.00982465	−	0.0225183i
$131$	−3.54474	−	8.12462i	−0.309705	−	0.709852i	0.690200	−	0.723619i	$-0.257522\pi$
$131$	−3.54474	−	8.12462i	−0.309705	−	0.709852i	−0.999905	+	0.0137669i	$0.995618\pi$
$132$	−3.17486	−	5.93355i	−0.276336	−	0.516449i
$133$	−1.95806	−	7.30757i	−0.169785	−	0.633647i
$134$	−1.68479	+	4.81485i	−0.145544	+	0.415940i
$135$	20.6170	−	1.86317i	1.77443	−	0.160356i
$136$	−14.7121	−	7.08499i	−1.26156	−	0.607533i
$137$	20.6642	+	3.90988i	1.76546	+	0.334044i	0.964382	−	0.264512i	$-0.0852109\pi$
$137$	20.6642	+	3.90988i	1.76546	+	0.334044i	0.801081	+	0.598556i	$0.204259\pi$
$138$	−12.4966	−	2.29842i	−1.06378	−	0.195654i
$139$	6.91346	−	17.6152i	0.586392	−	1.49410i	−0.262177	−	0.965020i	$-0.584441\pi$
$139$	6.91346	−	17.6152i	0.586392	−	1.49410i	0.848570	−	0.529084i	$-0.177464\pi$
$140$	−2.05208	+	13.6146i	−0.173432	+	1.15065i
$141$	1.11230	−	4.23765i	0.0936728	−	0.356874i
$142$	0.435391	+	11.6361i	0.0365372	+	0.976476i
$143$	0.0282750	+	0.250948i	0.00236448	+	0.0209853i
$144$	−0.107829	−	0.0505772i	−0.00898577	−	0.00421477i
$145$	5.00168	+	20.8628i	0.415367	+	1.73256i
$146$	2.05308	+	1.18535i	0.169914	+	0.0980999i
$147$	−0.952930	+	0.767933i	−0.0785964	+	0.0633381i
$148$	−3.73585	+	7.06857i	−0.307085	+	0.581033i
$149$	2.79886	−	2.59696i	0.229292	−	0.212751i	−0.557157	−	0.830407i	$-0.688108\pi$
$149$	2.79886	−	2.59696i	0.229292	−	0.212751i	0.786449	+	0.617656i	$0.211917\pi$
$150$	−16.2686	−	1.74891i	−1.32833	−	0.142798i
$151$	1.37710	+	9.13649i	0.112067	+	0.743517i	0.972321	+	0.233651i	$0.0750672\pi$
$151$	1.37710	+	9.13649i	0.112067	+	0.743517i	−0.860253	+	0.509867i	$0.829695\pi$
$152$	−7.49152	−	1.70989i	−0.607643	−	0.138691i
$153$	−15.8521	+	7.10987i	−1.28157	+	0.574799i
$154$	−3.26647	+	6.78290i	−0.263220	+	0.546582i
$155$	19.5604	−	10.3380i	1.57113	−	0.830368i
$156$	0.119329	+	0.127295i	0.00955395	+	0.0101918i
$157$	−3.53862	+	13.2063i	−0.282413	+	1.05398i	0.668296	+	0.743895i	$0.267024\pi$
$157$	−3.53862	+	13.2063i	−0.282413	+	1.05398i	−0.950709	+	0.310084i	$0.899643\pi$
$158$	−0.235979	−	0.160888i	−0.0187735	−	0.0127995i
$159$	−0.0705457	+	1.01062i	−0.00559463	+	0.0801475i
$160$	18.1872	+	13.4228i	1.43782	+	1.06116i
$161$	−10.1687	−	21.1155i	−0.801405	−	1.66413i
$162$	7.10261	−	3.27318i	0.558034	−	0.257166i
$163$	−8.35161	−	2.92235i	−0.654148	−	0.228896i	−0.0172583	−	0.999851i	$-0.505494\pi$
$163$	−8.35161	−	2.92235i	−0.654148	−	0.228896i	−0.636890	+	0.770955i	$0.719779\pi$
$164$	−2.87757	−	5.44462i	−0.224700	−	0.425153i
$165$	19.7822	+	8.51084i	1.54004	+	0.662568i
$166$	−9.26237	−	7.97091i	−0.718899	−	0.618663i
$167$	21.6606	−	6.68140i	1.67614	−	0.517022i	0.696465	−	0.717591i	$-0.254755\pi$
$167$	21.6606	−	6.68140i	1.67614	−	0.517022i	0.979680	+	0.200569i	$0.0642790\pi$
$168$	2.58858	+	13.3084i	0.199714	+	1.02677i
$169$	4.74704	+	12.0953i	0.365157	+	0.930405i
$170$	19.5453	−	4.46109i	1.49906	−	0.342150i
$171$	−6.52812	+	4.92179i	−0.499218	+	0.376379i
$172$	−1.81178	+	0.204139i	−0.138147	+	0.0155654i
$173$	1.87569	−	3.24880i	0.142606	−	0.247001i	−0.785871	−	0.618390i	$-0.787785\pi$
$173$	1.87569	−	3.24880i	0.142606	−	0.247001i	0.928477	+	0.371389i	$0.121118\pi$
$174$	4.42144	+	6.79280i	0.335188	+	0.514961i
$175$	−15.0901	−	26.1368i	−1.14070	−	1.97575i
$176$	−0.0735753	−	0.0996910i	−0.00554595	−	0.00751449i
$177$	11.0667	+	5.25998i	0.831826	+	0.395364i
$178$	−0.144074	+	0.467076i	−0.0107988	+	0.0350089i
$179$	0.801836	−	1.00547i	0.0599321	−	0.0751524i	−0.750962	−	0.660345i	$-0.770410\pi$
$179$	0.801836	−	1.00547i	0.0599321	−	0.0751524i	0.810894	+	0.585193i	$0.198981\pi$
$180$	14.4714	−	3.45893i	1.07863	−	0.257814i
$181$	1.89559	−	8.30511i	0.140898	−	0.617314i	−0.854330	−	0.519731i	$-0.826032\pi$
$181$	1.89559	−	8.30511i	0.140898	−	0.617314i	0.995227	−	0.0975821i	$-0.0311109\pi$
$182$	0.0362889	−	0.191792i	0.00268992	−	0.0142165i
$183$	−9.63933	−	12.9221i	−0.712560	−	0.955232i
$184$	−23.7879	−	0.890080i	−1.75367	−	0.0656176i
$185$	−4.75657	−	25.1391i	−0.349710	−	1.84826i
$186$	5.65368	−	6.15599i	0.414548	−	0.451379i
$187$	−18.0232	−	1.35065i	−1.31798	−	0.0987693i
$188$	0.352579	−	3.12923i	0.0257145	−	0.228222i
$189$	12.6014	+	7.02016i	0.916617	+	0.510641i
$190$	8.49986	−	4.09332i	0.616645	−	0.296960i
$191$	7.32698	−	1.96326i	0.530162	−	0.142056i	0.0161989	−	0.999869i	$-0.494844\pi$
$191$	7.32698	−	1.96326i	0.530162	−	0.142056i	0.513963	+	0.857812i	$0.328177\pi$
$192$	8.04125	+	2.43548i	0.580327	+	0.175766i
$193$	−0.408584	+	10.9196i	−0.0294105	+	0.786012i	0.904070	+	0.427384i	$0.140565\pi$
$193$	−0.408584	+	10.9196i	−0.0294105	+	0.786012i	−0.933481	+	0.358628i	$0.883245\pi$
$194$	−11.1002	+	0.831842i	−0.796945	+	0.0597228i
$195$	−0.552539	−	0.0803972i	−0.0395681	−	0.00575737i
$196$	−0.598314	+	0.644829i	−0.0427367	+	0.0460592i
$197$	−17.2916	+	13.7896i	−1.23198	+	0.982469i	−0.232025	+	0.972710i	$0.574535\pi$
$197$	−17.2916	+	13.7896i	−1.23198	+	0.982469i	−0.999952	+	0.00975941i	$0.996893\pi$
$198$	8.11876	+	0.525061i	0.576975	+	0.0373144i
$199$	−1.76743	−	7.74363i	−0.125290	−	0.548931i	−0.998141	−	0.0609447i	$-0.980589\pi$
$199$	−1.76743	−	7.74363i	−0.125290	−	0.548931i	0.872851	−	0.487986i	$-0.162268\pi$
$200$	−30.6327	+	1.14620i	−2.16606	+	0.0810483i
$201$	6.38011	+	7.91709i	0.450018	+	0.558428i
$202$	0.452310	−	0.261141i	0.0318244	−	0.0183738i
$203$	−5.30969	+	13.9749i	−0.372667	+	0.980847i
$204$	−10.5393	+	6.69762i	−0.737898	+	0.468927i
$205$	18.0628	+	7.88073i	1.26156	+	0.550414i
$206$	4.76993	−	2.99715i	0.332337	−	0.208821i
$207$	−17.0361	+	18.7409i	−1.18409	+	1.30259i
$208$	0.00251161	+	0.00200294i	0.000174149	+	0.000138879i
$209$	−8.41009	+	1.26762i	−0.581738	+	0.0876830i
$210$	−12.6721	−	10.7930i	−0.874456	−	0.744789i
$211$	7.48188	−	8.69410i	0.515074	−	0.598527i	−0.438856	−	0.898558i	$-0.644616\pi$
$211$	7.48188	−	8.69410i	0.515074	−	0.598527i	0.953930	+	0.300031i	$0.0969970\pi$
$212$	0.0544155	+	0.726125i	0.00373727	+	0.0498705i
$213$	20.1595	+	11.5022i	1.38131	+	0.788117i
$214$	−4.59735	−	5.34222i	−0.314269	−	0.365187i
$215$	4.12568	−	4.12568i	0.281369	−	0.281369i
$216$	12.2848	−	7.98426i	0.835877	−	0.543260i
$217$	15.3198	+	1.72612i	1.03997	+	0.117177i
$218$	−1.68653	+	2.28516i	−0.114226	+	0.154771i
$219$	4.16649	−	2.22936i	0.281545	−	0.150646i
$220$	14.9513	+	4.00618i	1.00801	+	0.270096i
$221$	0.460438	−	0.0871196i	0.0309724	−	0.00586030i
$222$	−4.87555	−	8.34595i	−0.327226	−	0.560143i
$223$	4.86048	−	3.31382i	0.325482	−	0.221910i	−0.389544	−	0.921008i	$-0.627367\pi$
$223$	4.86048	−	3.31382i	0.325482	−	0.221910i	0.715026	+	0.699098i	$0.246415\pi$
$224$	5.20224	+	14.8671i	0.347589	+	0.993352i
$225$	−20.0733	+	25.7055i	−1.33822	+	1.71370i
$226$	−3.83804	−	4.81275i	−0.255303	−	0.320140i
$227$	0.984002	−	0.386192i	0.0653105	−	0.0256325i	−0.332461	−	0.943117i	$-0.607879\pi$
$227$	0.984002	−	0.386192i	0.0653105	−	0.0256325i	0.397771	+	0.917485i	$0.369784\pi$
$228$	−4.13388	+	4.17634i	−0.273773	+	0.276585i
$229$	6.70935	+	3.54599i	0.443366	+	0.234326i	0.674025	−	0.738709i	$-0.264564\pi$
$229$	6.70935	+	3.54599i	0.443366	+	0.234326i	−0.230658	+	0.973035i	$0.574088\pi$
$230$	23.5149	−	17.3548i	1.55053	−	1.14434i
$231$	8.04861	+	12.6652i	0.529560	+	0.833309i
$232$	10.0295	+	11.4007i	0.658467	+	0.748494i
$233$			0.401155i			0.0262806i	0.999914	+	0.0131403i	$0.00418280\pi$
$233$			0.401155i			0.0262806i	−0.999914	+	0.0131403i	$0.995817\pi$
$234$	−0.206851	+	0.0413317i	−0.0135222	+	0.00270194i
$235$	5.36141	+	8.53264i	0.349740	+	0.556608i
$236$	8.41580	+	2.59593i	0.547822	+	0.168981i
$237$	−0.520621	+	0.230318i	−0.0338180	+	0.0149607i
$238$	13.0042	+	5.10376i	0.842936	+	0.330828i
$239$	2.28795	+	7.41734i	0.147995	+	0.479788i	0.998968	−	0.0454217i	$-0.0144632\pi$
$239$	2.28795	+	7.41734i	0.147995	+	0.479788i	−0.850973	+	0.525209i	$0.823987\pi$
$240$	0.254495	−	0.101385i	0.0164276	−	0.00654441i
$241$	−3.60770	−	5.29152i	−0.232392	−	0.340857i	0.692275	−	0.721634i	$-0.256609\pi$
$241$	−3.60770	−	5.29152i	−0.232392	−	0.340857i	−0.924667	+	0.380778i	$0.875656\pi$
$242$	−0.927024	−	0.582487i	−0.0595913	−	0.0374437i
$243$	1.92889	−	15.4687i	0.123739	−	0.992315i
$244$	−8.19352	−	8.19352i	−0.524536	−	0.524536i
$245$	0.210364	−	2.80711i	0.0134396	−	0.179340i
$246$	7.42701	+	0.518437i	0.473529	+	0.0330543i
$247$	0.202117	−	0.0881828i	0.0128604	−	0.00561093i
$248$	8.82094	−	12.9379i	0.560130	−	0.821560i
$249$	−23.2385	+	7.29835i	−1.47268	+	0.462514i
$250$	15.4066	−	13.2585i	0.974400	−	0.838539i
$251$	−1.19486	+	1.90160i	−0.0754186	+	0.120028i	−0.882304	−	0.470680i	$-0.844009\pi$
$251$	−1.19486	+	1.90160i	−0.0754186	+	0.120028i	0.806885	+	0.590708i	$0.201151\pi$
$252$	9.68953	+	3.68906i	0.610383	+	0.232389i
$253$	−24.8690	+	8.70206i	−1.56350	+	0.547094i
$254$	−6.61945	−	6.14196i	−0.415341	−	0.385381i
$255$	13.0054	−	37.7855i	0.814432	−	2.36622i
$256$	15.7220	+	2.36971i	0.982624	+	0.148107i
$257$	5.80996	+	6.26165i	0.362416	+	0.390591i	0.887766	−	0.460295i	$-0.152256\pi$
$257$	5.80996	+	6.26165i	0.362416	+	0.390591i	−0.525351	+	0.850886i	$0.676066\pi$
$258$	0.946220	−	1.99080i	0.0589091	−	0.123942i
$259$	7.12939	−	16.3407i	0.442999	−	1.01536i
$260$	−0.401325			−0.0248891
$261$	16.1519	−	0.341146i	0.999777	−	0.0211164i
$262$	7.70257			0.475866
$263$	2.82699	−	6.47952i	0.174319	−	0.399544i	−0.807367	−	0.590050i	$-0.799108\pi$
$263$	2.82699	−	6.47952i	0.174319	−	0.399544i	0.981686	+	0.190506i	$0.0610128\pi$
$264$	15.1933	−	1.21666i	0.935084	−	0.0748805i
$265$	−1.58494	−	1.70815i	−0.0973618	−	0.104931i
$266$	6.50048	+	0.979790i	0.398570	+	0.0600748i
$267$	0.639285	+	0.735232i	0.0391236	+	0.0449955i
$268$	5.35734	+	4.97089i	0.327252	+	0.303645i
$269$	−21.2967	+	7.45203i	−1.29848	+	0.454358i	−0.888978	−	0.457950i	$-0.848584\pi$
$269$	−21.2967	+	7.45203i	−1.29848	+	0.454358i	−0.409504	+	0.912309i	$0.634298\pi$
$270$	−5.68019	+	17.0677i	−0.345686	+	1.03871i
$271$	10.7505	−	17.1093i	0.653044	−	1.03931i	−0.341983	−	0.939706i	$-0.611098\pi$
$271$	10.7505	−	17.1093i	0.653044	−	1.03931i	0.995027	−	0.0996073i	$-0.0317587\pi$
$272$	−0.174267	+	0.149969i	−0.0105665	+	0.00909322i
$273$	−0.286561	−	0.263178i	−0.0173435	−	0.0159283i
$274$	−10.2945	+	15.0993i	−0.621915	+	0.912182i
$275$	−31.0980	+	13.5679i	−1.87528	+	0.818177i
$276$	−10.1777	+	15.0930i	−0.612624	+	0.908491i
$277$	1.22682	−	16.3707i	0.0737122	−	0.983621i	−0.830633	−	0.556820i	$-0.812021\pi$
$277$	1.22682	−	16.3707i	0.0737122	−	0.983621i	0.904346	−	0.426801i	$-0.140360\pi$
$278$	11.6272	+	11.6272i	0.697355	+	0.697355i
$279$	−4.47618	−	16.0477i	−0.267982	−	0.960749i
$280$	−26.4047	−	16.5912i	−1.57798	−	0.991513i
$281$	0.123893	+	0.181718i	0.00739087	+	0.0108404i	0.829916	−	0.557888i	$-0.188388\pi$
$281$	0.123893	+	0.181718i	0.00739087	+	0.0108404i	−0.822526	+	0.568728i	$0.807436\pi$
$282$	2.98855	+	2.35841i	0.177965	+	0.140441i
$283$	−8.70565	−	28.2230i	−0.517497	−	1.67768i	−0.716420	−	0.697669i	$-0.754221\pi$
$283$	−8.70565	−	28.2230i	−0.517497	−	1.67768i	0.198923	−	0.980015i	$-0.436256\pi$
$284$	15.5292	+	6.09478i	0.921491	+	0.361659i
$285$	2.00998	−	18.6971i	0.119061	−	1.10752i
$286$	−0.209692	−	0.0646813i	−0.0123993	−	0.00382469i
$287$	7.30606	+	11.6275i	0.431263	+	0.686351i
$288$	12.7877	−	11.2342i	0.753525	−	0.661981i
$289$			16.5377i			0.972807i
$290$	−18.3541	−	3.26597i	−1.07779	−	0.191784i
$291$	−10.2673	+	19.6692i	−0.601877	+	1.15303i
$292$	2.73277	−	2.01688i	0.159923	−	0.118029i
$293$	4.77822	+	2.52536i	0.279146	+	0.147533i	0.600982	−	0.799262i	$-0.294776\pi$
$293$	4.77822	+	2.52536i	0.279146	+	0.147533i	−0.321836	+	0.946795i	$0.604300\pi$
$294$	−0.280488	−	1.02580i	−0.0163584	−	0.0598261i
$295$	−26.2354	+	10.2966i	−1.52748	+	0.599493i
$296$	−11.2903	−	14.1576i	−0.656238	−	0.822896i
$297$	9.42871	−	13.1940i	0.547109	−	0.765592i
$298$	1.09578	+	3.13155i	0.0634766	+	0.181406i
$299$	0.564428	−	0.384820i	0.0326417	−	0.0222547i
$300$	−11.6171	+	20.3610i	−0.670716	+	1.17554i
$301$	3.99479	−	0.755855i	0.230256	−	0.0435668i
$302$	−7.75525	−	2.07801i	−0.446264	−	0.119576i
$303$	0.0336110	−	1.04051i	0.00193090	−	0.0597756i
$304$	−0.0642466	+	0.0870510i	−0.00368479	+	0.00499272i
$305$	36.8478	+	4.15175i	2.10990	+	0.237728i
$306$	−0.154244	−	15.0959i	−0.00881754	−	0.862976i
$307$	12.7920	−	12.7920i	0.730079	−	0.730079i	−0.240556	−	0.970635i	$-0.577330\pi$
$307$	12.7920	−	12.7920i	0.730079	−	0.730079i	0.970635	+	0.240556i	$0.0773299\pi$
$308$	7.03550	+	8.17539i	0.400885	+	0.465836i
$309$	−0.0573638	−	11.2287i	−0.00326331	−	0.638780i
$310$	1.43668	+	19.1711i	0.0815978	+	1.08885i
$311$	9.01041	−	10.4703i	0.510933	−	0.593715i	−0.441955	−	0.897037i	$-0.645715\pi$
$311$	9.01041	−	10.4703i	0.510933	−	0.593715i	0.952888	+	0.303322i	$0.0980958\pi$
$312$	−0.372339	+	0.132426i	−0.0210795	+	0.00749713i
$313$	−4.98699	+	0.751667i	−0.281881	+	0.0424867i	−0.288461	−	0.957492i	$-0.593144\pi$
$313$	−4.98699	+	0.751667i	−0.281881	+	0.0424867i	0.00657999	+	0.999978i	$0.497906\pi$
$314$	−9.28850	−	7.40733i	−0.524180	−	0.418020i
$315$	−31.6033	+	10.1031i	−1.78064	+	0.569243i
$316$	−0.346465	+	0.217699i	−0.0194902	+	0.0122465i
$317$	25.9024	+	11.3011i	1.45483	+	0.634734i	0.970707	−	0.240268i	$-0.0772354\pi$
$317$	25.9024	+	11.3011i	1.45483	+	0.634734i	0.484119	+	0.875002i	$0.339140\pi$
$318$	−0.780391	−	0.407362i	−0.0437622	−	0.0228437i
$319$	14.9437	+	7.69075i	0.836686	+	0.430600i
$320$	−16.7364	+	9.66274i	−0.935591	+	0.540164i
$321$	−13.8809	+	2.16479i	−0.774755	+	0.120827i
$322$	20.3508	−	0.761474i	1.13411	−	0.0424353i
$323$	3.51185	+	15.3864i	0.195405	+	0.856123i
$324$	−0.228939	−	11.2020i	−0.0127188	−	0.622334i
$325$	0.687774	−	0.548482i	0.0381509	−	0.0304243i
$326$	5.22956	−	5.63613i	0.289639	−	0.312156i
$327$	2.09515	+	5.25919i	0.115862	+	0.290834i
$328$	13.9091	−	1.04234i	0.767999	−	0.0575536i
$329$	−0.262562	+	7.01713i	−0.0144755	+	0.386867i
$330$	−13.6524	+	12.7980i	−0.751542	+	0.704508i
$331$	−16.8629	+	4.51841i	−0.926870	+	0.248354i	−0.690520	−	0.723314i	$-0.742618\pi$
$331$	−16.8629	+	4.51841i	−0.926870	+	0.248354i	−0.236351	+	0.971668i	$0.575951\pi$
$332$	−15.7735	+	7.59613i	−0.865684	+	0.416892i
$333$	−19.2592	−	0.523647i	−1.05540	−	0.0286957i
$334$	−2.20536	+	19.5732i	−0.120672	+	1.07100i
$335$	−23.3219	−	1.74773i	−1.27421	−	0.0954889i
$336$	0.186321	+	0.0415262i	0.0101646	+	0.00226544i
$337$	1.59662	+	8.43836i	0.0869736	+	0.459667i	0.998795	+	0.0490792i	$0.0156287\pi$
$337$	1.59662	+	8.43836i	0.0869736	+	0.459667i	−0.911821	+	0.410587i	$0.865324\pi$
$338$	−11.2828	−	0.422171i	−0.613701	−	0.0229631i
$339$	−12.1857	+	1.43608i	−0.661838	+	0.0779973i
$340$	5.33982	−	28.2216i	0.289592	−	1.53053i
$341$	3.85666	−	16.8971i	0.208850	−	0.915032i
$342$	−1.65151	−	6.90955i	−0.0893034	−	0.373626i
$343$	−10.8930	+	13.6594i	−0.588166	+	0.737536i
$344$	1.21720	−	3.94606i	0.0656270	−	0.212757i
$345$	−4.65008	−	58.0687i	−0.250352	−	3.12631i
$346$	1.93571	+	2.62280i	0.104065	+	0.141003i
$347$	1.32836	+	2.30079i	0.0713102	+	0.123513i	0.899476	−	0.436971i	$-0.143949\pi$
$347$	1.32836	+	2.30079i	0.0713102	+	0.123513i	−0.828166	+	0.560484i	$0.810615\pi$
$348$	11.4530	−	1.91426i	0.613947	−	0.102615i
$349$	−16.9620	+	29.3791i	−0.907956	+	1.57263i	−0.0910578	+	0.995846i	$0.529025\pi$
$349$	−16.9620	+	29.3791i	−0.907956	+	1.57263i	−0.816899	+	0.576781i	$0.804309\pi$
$350$	26.0601	−	2.93627i	1.39297	−	0.156950i
$351$	−0.147595	+	0.393703i	−0.00787803	+	0.0210143i
$352$	17.2636	−	3.94030i	0.920152	−	0.210019i
$353$	−6.95036	−	17.7092i	−0.369930	−	0.942567i	−0.987722	−	0.156225i	$-0.950068\pi$
$353$	−6.95036	−	17.7092i	−0.369930	−	0.942567i	0.617791	−	0.786342i	$-0.288028\pi$
$354$	−8.03482	+	6.98628i	−0.427046	+	0.371317i
$355$	−51.0139	+	15.7357i	−2.70754	+	0.835165i
$356$	0.530795	+	0.456786i	0.0281321	+	0.0242096i
$357$	22.3198	−	16.6496i	1.18129	−	0.881190i
$358$	0.522177	+	0.988006i	0.0275979	+	0.0522177i
$359$	3.97686	+	1.39156i	0.209891	+	0.0734440i	0.433177	−	0.901309i	$-0.357393\pi$
$359$	3.97686	+	1.39156i	0.209891	+	0.0734440i	−0.223286	+	0.974753i	$0.571678\pi$
$360$	−5.92658	+	33.1748i	−0.312358	+	1.74846i
$361$	−5.02146	−	10.4272i	−0.264287	−	0.548798i
$362$	5.95588	+	4.39564i	0.313034	+	0.231030i
$363$	−1.96132	+	0.956898i	−0.102943	+	0.0502241i
$364$	−0.231059	−	0.157534i	−0.0121108	−	0.00825700i
$365$	−2.81311	+	10.4987i	−0.147245	+	0.549525i
$366$	13.6413	−	3.18695i	0.713043	−	0.166584i
$367$	31.4852	−	16.6404i	1.64351	−	0.868622i	0.649379	−	0.760465i	$-0.275029\pi$
$367$	31.4852	−	16.6404i	1.64351	−	0.868622i	0.994134	−	0.108157i	$-0.0344949\pi$
$368$	−0.145422	+	0.301972i	−0.00758065	+	0.0157414i
$369$	8.68987	−	12.0297i	0.452377	−	0.626241i
$370$	21.6748	+	4.94713i	1.12682	+	0.257189i
$371$	−0.242005	−	1.60560i	−0.0125643	−	0.0833584i
$372$	−4.84460	−	10.9510i	−0.251181	−	0.567781i
$373$	4.34643	−	4.03290i	0.225050	−	0.208816i	−0.559587	−	0.828772i	$-0.689040\pi$
$373$	4.34643	−	4.03290i	0.225050	−	0.208816i	0.784636	+	0.619956i	$0.212850\pi$
$374$	7.33851	−	13.8851i	0.379466	−	0.717984i
$375$	−6.24310	−	40.0315i	−0.322392	−	2.06722i
$376$	6.17678	+	3.56616i	0.318543	+	0.183911i
$377$	−0.425861	−	0.0923278i	−0.0219329	−	0.00475512i
$378$	−9.96998	+	7.59693i	−0.512800	+	0.390744i
$379$	1.34409	+	11.9291i	0.0690412	+	0.612758i	0.979823	+	0.199869i	$0.0640516\pi$
$379$	1.34409	+	11.9291i	0.0690412	+	0.612758i	−0.910781	+	0.412889i	$0.864520\pi$
$380$	−0.505384	−	13.5067i	−0.0259256	−	0.692877i
$381$	−17.3619	+	4.74730i	−0.889477	+	0.243211i
$382$	−0.982393	+	6.51775i	−0.0502636	+	0.333477i
$383$	−5.34059	+	13.6076i	−0.272892	+	0.695317i	0.727070	+	0.686563i	$0.240882\pi$
$383$	−5.34059	+	13.6076i	−0.272892	+	0.695317i	−0.999962	+	0.00875328i	$0.997214\pi$
$384$	8.01035	−	9.40495i	0.408777	−	0.479945i
$385$	−33.9143	−	6.41693i	−1.72843	−	0.327037i
$386$	−8.55491	−	4.11983i	−0.435434	−	0.209694i
$387$	−2.37543	−	3.69611i	−0.120750	−	0.187884i
$388$	−5.26716	+	15.0527i	−0.267399	+	0.764184i
$389$	9.34356	+	34.8706i	0.473737	+	1.76801i	0.626159	+	0.779696i	$0.284626\pi$
$389$	9.34356	+	34.8706i	0.473737	+	1.76801i	−0.152422	+	0.988316i	$0.548707\pi$
$390$	0.256032	−	0.412131i	0.0129647	−	0.0208690i
$391$	19.5510	+	44.8115i	0.988739	+	2.26621i
$392$	−0.796724	−	1.82611i	−0.0402406	−	0.0922325i
$393$	8.10193	−	13.0416i	0.408688	−	0.657860i
$394$	−4.97408	−	18.5635i	−0.250591	−	0.935218i
$395$	0.432478	−	1.23595i	0.0217603	−	0.0621874i
$396$	5.34086	−	10.3603i	0.268389	−	0.520623i
$397$	−13.1741	−	6.34433i	−0.661191	−	0.318413i	0.0730239	−	0.997330i	$-0.476735\pi$
$397$	−13.1741	−	6.34433i	−0.661191	−	0.318413i	−0.734214	+	0.678918i	$0.762449\pi$
$398$	6.78154	+	1.28314i	0.339928	+	0.0643178i
$399$	8.49645	−	9.97568i	0.425355	−	0.499409i
$400$	−0.157683	+	0.401770i	−0.00788416	+	0.0200885i
$401$	−5.59671	+	37.1317i	−0.279486	+	1.85427i	0.204070	+	0.978956i	$0.434583\pi$
$401$	−5.59671	+	37.1317i	−0.279486	+	1.85427i	−0.483556	+	0.875313i	$0.660655\pi$
$402$	−8.52253	+	2.33033i	−0.425065	+	0.116226i
$403$	0.0168024	+	0.449054i	0.000836989	+	0.0223690i
$404$	−0.0837790	−	0.743560i	−0.00416816	−	0.0369935i
$405$	22.9235	+	27.5701i	1.13908	+	1.36997i
$406$	−9.28522	−	9.08496i	−0.460818	−	0.450879i
$407$	−17.3576	−	10.0214i	−0.860384	−	0.496743i
$408$	−4.35819	−	27.9453i	−0.215763	−	1.38350i
$409$	−0.178954	+	0.338597i	−0.00884870	+	0.0167426i	−0.888500	−	0.458876i	$-0.848252\pi$
$409$	−0.178954	+	0.338597i	−0.00884870	+	0.0167426i	0.879651	+	0.475619i	$0.157776\pi$
$410$	−12.5531	+	11.6476i	−0.619956	+	0.575235i
$411$	14.7370	+	33.3123i	0.726925	+	1.64318i
$412$	−1.20290	−	7.98072i	−0.0592626	−	0.393182i
$413$	−19.1466	−	4.37008i	−0.942141	−	0.215037i
$414$	−9.00636	−	20.0805i	−0.442639	−	0.986903i
$415$	24.3085	−	50.4770i	1.19326	−	2.47782i
$416$	−0.405910	+	0.214530i	−0.0199014	+	0.0105182i
$417$	31.9167	−	7.45653i	1.56297	−	0.365148i
$418$	1.91280	−	7.13866i	0.0935581	−	0.349163i
$419$	−11.7647	−	8.02105i	−0.574744	−	0.391854i	0.240778	−	0.970580i	$-0.422597\pi$
$419$	−11.7647	−	8.02105i	−0.574744	−	0.391854i	−0.815522	+	0.578727i	$0.803550\pi$
$420$	−21.4328	+	10.4567i	−1.04581	+	0.510236i
$421$	7.50558	+	5.53937i	0.365800	+	0.269973i	0.761174	−	0.648548i	$-0.224623\pi$
$421$	7.50558	+	5.53937i	0.365800	+	0.269973i	−0.395374	+	0.918520i	$0.629385\pi$
$422$	4.32454	+	8.97999i	0.210515	+	0.437139i
$423$	7.13664	−	2.57936i	0.346995	−	0.125413i
$424$	−1.55669	−	0.544708i	−0.0755993	−	0.0264533i
$425$	29.4187	+	55.6629i	1.42702	+	2.70005i
$426$	−16.1660	+	12.0591i	−0.783246	+	0.584266i
$427$	19.5851	+	16.8543i	0.947788	+	0.815638i
$428$	−9.64900	+	2.97632i	−0.466402	+	0.143866i
$429$	−0.330079	+	0.287004i	−0.0159363	+	0.0138567i
$430$	1.85226	+	4.71949i	0.0893241	+	0.227594i
$431$	−17.9643	+	4.10024i	−0.865311	+	0.197502i	−0.632064	−	0.774916i	$-0.717792\pi$
$431$	−17.9643	+	4.10024i	−0.865311	+	0.197502i	−0.233247	+	0.972418i	$0.574935\pi$
$432$	−0.0338685	−	0.203491i	−0.00162950	−	0.00979046i
$433$	−19.8277	+	2.23404i	−0.952857	+	0.107361i	−0.574685	−	0.818374i	$-0.694876\pi$
$433$	−19.8277	+	2.23404i	−0.952857	+	0.107361i	−0.378171	+	0.925736i	$0.623447\pi$
$434$	−6.69816	+	11.6016i	−0.321522	+	0.556893i
$435$	−24.8355	+	27.6409i	−1.19077	+	1.32528i
$436$	2.03450	+	3.52386i	0.0974351	+	0.168763i
$437$	13.6620	+	18.5113i	0.653541	+	0.885517i
$438$	0.327768	+	4.09305i	0.0156613	+	0.195574i
$439$	−0.327248	+	1.06091i	−0.0156187	+	0.0506345i	−0.963047	−	0.269334i	$-0.913196\pi$
$439$	−0.327248	+	1.06091i	−0.0156187	+	0.0506345i	0.947428	+	0.319969i	$0.103672\pi$
$440$	−21.8584	+	27.4096i	−1.04206	+	1.30670i
$441$	−2.03187	−	0.604083i	−0.0967555	−	0.0287659i
$442$	−0.0906096	+	0.396987i	−0.00430986	+	0.0188827i
$443$	−0.654241	+	3.45775i	−0.0310839	+	0.164282i	−0.994669	−	0.103120i	$-0.967118\pi$
$443$	−0.654241	+	3.45775i	−0.0310839	+	0.164282i	0.963585	+	0.267402i	$0.0861652\pi$
$444$	−13.7527	+	1.62075i	−0.652675	+	0.0769173i
$445$	−2.23942	−	0.0837931i	−0.106159	−	0.00397218i
$446$	0.950330	+	5.02262i	0.0449994	+	0.237828i
$447$	6.45476	+	1.43860i	0.305300	+	0.0680436i
$448$	−13.4288	−	1.00635i	−0.634449	−	0.0475454i
$449$	3.66667	−	32.5426i	0.173041	−	1.53578i	−0.544201	−	0.838955i	$-0.683167\pi$
$449$	3.66667	−	32.5426i	0.173041	−	1.53578i	0.717242	−	0.696825i	$-0.245404\pi$
$450$	−13.4979	−	24.9196i	−0.636296	−	1.17472i
$451$	13.9093	−	6.69836i	0.654963	−	0.315413i
$452$	−8.51871	+	2.28258i	−0.400687	+	0.107364i
$453$	−11.6757	+	10.9450i	−0.548573	+	0.514242i
$454$	−0.0343454	+	0.917901i	−0.00161191	+	0.0430792i
$455$	0.892415	−	0.0668772i	0.0418371	−	0.00313525i
$456$	−4.92570	−	12.3644i	−0.230667	−	0.579014i
$457$	10.8997	−	11.7470i	0.509865	−	0.549504i	−0.424683	−	0.905342i	$-0.639614\pi$
$457$	10.8997	−	11.7470i	0.509865	−	0.549504i	0.934547	+	0.355839i	$0.115805\pi$
$458$	−5.15560	+	4.11145i	−0.240905	+	0.192115i
$459$	−25.7218	−	15.6175i	−1.20059	−	0.728961i
$460$	−9.31718	−	40.8212i	−0.434416	−	1.90330i
$461$	−18.7652	+	0.702145i	−0.873983	+	0.0327021i	−0.470618	−	0.882337i	$-0.655969\pi$
$461$	−18.7652	+	0.702145i	−0.873983	+	0.0327021i	−0.403365	+	0.915039i	$0.632160\pi$
$462$	−12.8839	+	2.00931i	−0.599415	+	0.0934814i
$463$	18.6812	−	10.7856i	0.868189	−	0.501249i	0.00144300	−	0.999999i	$-0.499541\pi$
$463$	18.6812	−	10.7856i	0.868189	−	0.501249i	0.866746	+	0.498750i	$0.166207\pi$
$464$	0.203597	−	0.0652401i	0.00945174	−	0.00302869i
$465$	33.9707	+	17.7326i	1.57535	+	0.822330i
$466$	−0.319499	−	0.139396i	−0.0148005	−	0.00645739i
$467$	−5.37851	+	3.37954i	−0.248888	+	0.156386i	−0.650698	−	0.759336i	$-0.725524\pi$
$467$	−5.37851	+	3.37954i	−0.248888	+	0.156386i	0.401811	+	0.915723i	$0.368381\pi$
$468$	−0.0642341	+	0.295304i	−0.00296922	+	0.0136504i
$469$	−12.7413	−	10.1609i	−0.588340	−	0.469185i
$470$	−8.65880	+	1.30510i	−0.399401	+	0.0602000i
$471$	−22.3118	+	7.93540i	−1.02807	+	0.365644i
$472$	−13.0114	+	15.1196i	−0.598900	+	0.695935i
$473$	−0.341568	−	4.55791i	−0.0157053	−	0.209573i
$474$	−0.00252715	−	0.494678i	−0.000116076	−	0.0227213i
$475$	19.3254	+	22.4565i	0.886708	+	1.03037i
$476$	14.1523	−	14.1523i	0.648670	−	0.648670i
$477$	−1.51058	+	0.892834i	−0.0691646	+	0.0408800i
$478$	−6.70254	−	0.755195i	−0.306567	−	0.0345418i
$479$	10.4024	−	14.0947i	0.475297	−	0.644004i	−0.499707	−	0.866195i	$-0.666559\pi$
$479$	10.4024	−	14.0947i	0.475297	−	0.644004i	0.975003	+	0.222191i	$0.0713208\pi$
$480$	−1.26403	+	39.1310i	−0.0576949	+	1.78608i
$481$	0.501955	+	0.134498i	0.0228872	+	0.00613260i
$482$	5.46803	−	1.03461i	0.249062	−	0.0471251i
$483$	20.1167	−	35.2579i	0.915341	−	1.60429i
$484$	−1.29600	+	0.883596i	−0.0589090	+	0.0401635i
$485$	−16.8555	−	48.1702i	−0.765369	−	2.18730i
$486$	11.6497	+	6.91140i	0.528440	+	0.313507i
$487$	8.12615	+	10.1899i	0.368231	+	0.461747i	0.931081	−	0.364812i	$-0.118867\pi$
$487$	8.12615	+	10.1899i	0.368231	+	0.461747i	−0.562850	+	0.826559i	$0.690295\pi$
$488$	24.4304	−	9.58824i	1.10591	−	0.434039i
$489$	−4.04208	−	14.7828i	−0.182789	−	0.668500i
$490$	2.16261	+	1.14297i	0.0976968	+	0.0516343i
$491$	4.05537	−	2.99300i	0.183016	−	0.135072i	−0.498459	−	0.866913i	$-0.666101\pi$
$491$	4.05537	−	2.99300i	0.183016	−	0.135072i	0.681475	+	0.731841i	$0.261339\pi$
$492$	4.93585	−	9.45570i	0.222525	−	0.426296i
$493$	12.1589	−	28.7186i	0.547609	−	1.29342i
$494$			0.191617i			0.00862128i
$495$	7.30863	+	36.5772i	0.328499	+	1.64402i
$496$	−0.117299	−	0.186680i	−0.00526688	−	0.00838220i
$497$	−35.5476	−	10.9650i	−1.59453	−	0.491847i
$498$	2.26231	−	21.0443i	0.101377	−	0.943018i
$499$	−8.08145	−	3.17174i	−0.361775	−	0.141986i	0.177489	−	0.984123i	$-0.443202\pi$
$499$	−8.08145	−	3.17174i	−0.361775	−	0.141986i	−0.539265	+	0.842136i	$0.681298\pi$
$500$	−8.58352	−	27.8271i	−0.383867	−	1.24447i
$501$	30.8205	+	24.3220i	1.37696	+	1.08663i
$502$	−1.09933	−	1.61242i	−0.0490654	−	0.0719657i
$503$	0.126985	+	0.0797902i	0.00566200	+	0.00355767i	0.534860	−	0.844941i	$-0.320364\pi$
$503$	0.126985	+	0.0797902i	0.00566200	+	0.00355767i	−0.529198	+	0.848498i	$0.677507\pi$
$504$	−16.4344	+	16.7737i	−0.732046	+	0.747160i
$505$	1.69319	+	1.69319i	0.0753459	+	0.0753459i
$506$	1.71092	−	22.8307i	0.0760598	−	1.01495i
$507$	−12.5825	+	18.6593i	−0.558810	+	0.828688i
$508$	−11.8577	+	5.17345i	−0.526099	+	0.229535i
$509$	−20.6064	+	30.2240i	−0.913361	+	1.33966i	0.0270563	+	0.999634i	$0.491387\pi$
$509$	−20.6064	+	30.2240i	−0.913361	+	1.33966i	−0.940418	+	0.340021i	$0.889566\pi$
$510$	25.5749	+	23.4880i	1.13248	+	1.04007i
$511$	−5.74070	+	4.94027i	−0.253954	+	0.218545i
$512$	0.238957	−	0.380298i	0.0105605	−	0.0168070i
$513$	−13.4360	−	4.47155i	−0.593215	−	0.197424i
$514$	−7.00595	+	2.45149i	−0.309019	+	0.108130i
$515$	18.9330	+	17.5673i	0.834288	+	0.774106i
$516$	−2.07209	−	2.38309i	−0.0912189	−	0.104909i
$517$	7.80611	+	1.17658i	0.343312	+	0.0517460i
$518$	10.5371	+	11.3563i	0.462976	+	0.498969i
$519$	6.47686	−	0.518660i	0.284303	−	0.0227667i
$520$	0.363491	−	0.833131i	0.0159401	−	0.0365352i
$521$	17.4505			0.764521			0.382260	−	0.924055i	$-0.375146\pi$
$521$	17.4505			0.764521			0.382260	+	0.924055i	$0.375146\pi$
$522$	−5.34085	+	12.9827i	−0.233763	+	0.568235i
$523$	39.2379			1.71575			0.857877	−	0.513856i	$-0.171783\pi$
$523$	39.2379			1.71575			0.857877	+	0.513856i	$0.171783\pi$
$524$	4.41294	−	10.1146i	0.192780	−	0.441857i
$525$	22.4397	−	47.2121i	0.979351	−	2.06050i
$526$	4.17825	+	4.50308i	0.182180	+	0.196344i
$527$	−31.8016	−	4.79332i	−1.38530	−	0.208800i
$528$	0.0698435	−	0.202921i	0.00303955	−	0.00883098i
$529$	35.3861	+	32.8335i	1.53853	+	1.42754i
$530$	1.91120	−	0.668756i	0.0830170	−	0.0290489i
$531$	3.37739	+	20.9526i	0.146566	+	0.909267i
$532$	5.01085	−	7.97472i	0.217248	−	0.345748i
$533$	−0.303396	+	0.261093i	−0.0131415	+	0.0113092i
$534$	−0.807715	+	0.253673i	−0.0349532	+	0.0109775i
$535$	18.2028	−	26.6987i	0.786977	−	1.15428i
$536$	−15.1716	+	6.61931i	−0.655314	+	0.285910i
$537$	2.22209	+	0.155111i	0.0958902	+	0.00669355i
$538$	1.46515	−	19.5511i	0.0631673	−	0.842909i
$539$	−1.55931	−	1.55931i	−0.0671641	−	0.0671641i
$540$	19.1581	+	17.2373i	0.824432	+	0.741776i
$541$	−17.2608	−	10.8457i	−0.742100	−	0.466293i	0.107177	−	0.994240i	$-0.465819\pi$
$541$	−17.2608	−	10.8457i	−0.742100	−	0.466293i	−0.849277	+	0.527947i	$0.822962\pi$
$542$	9.89097	+	14.5074i	0.424853	+	0.623145i
$543$	13.7071	−	5.46063i	0.588230	−	0.234338i
$544$	−9.68515	−	31.3985i	−0.415247	−	1.34620i
$545$	−12.1212	−	4.75721i	−0.519214	−	0.203776i
$546$	0.309183	−	0.136780i	0.0132318	−	0.00585363i
$547$	38.8739	+	11.9910i	1.66213	+	0.512699i	0.976549	−	0.215297i	$-0.0690720\pi$
$547$	38.8739	+	11.9910i	1.66213	+	0.512699i	0.685581	+	0.727996i	$0.259548\pi$
$548$	13.9296	+	22.1689i	0.595044	+	0.947006i
$549$	8.95263	−	26.4489i	0.382089	−	1.12881i
$550$		−	29.4826i		−	1.25714i
$551$	2.57103	−	14.4487i	0.109529	−	0.615535i
$552$	−22.1141	−	34.7985i	−0.941238	−	1.48112i
$553$	0.734148	−	0.541826i	0.0312191	−	0.0230408i
$554$	12.6121	+	6.66568i	0.535836	+	0.283198i
$555$	31.1748	−	31.4949i	1.32330	−	1.33689i
$556$	21.9297	−	8.60676i	0.930025	−	0.365008i
$557$	−19.7968	−	24.8244i	−0.838819	−	1.05185i	−0.997912	−	0.0645817i	$-0.979429\pi$
$557$	−19.7968	−	24.8244i	−0.838819	−	1.05185i	0.159094	−	0.987263i	$-0.449143\pi$
$558$	14.3365	+	2.01130i	0.606913	+	0.0851451i
$559$	0.0391403	+	0.111857i	0.00165546	+	0.00473103i
$560$	−0.362779	+	0.247339i	−0.0153302	+	0.0104520i
$561$	−15.7906	−	27.0302i	−0.666679	−	1.14122i
$562$	−0.187780	+	0.0355299i	−0.00792102	+	0.00149874i
$563$	22.8976	+	6.13540i	0.965020	+	0.258576i	0.706724	−	0.707490i	$-0.250172\pi$
$563$	22.8976	+	6.13540i	0.965020	+	0.258576i	0.258296	+	0.966066i	$0.416839\pi$
$564$	4.80912	−	2.57321i	0.202501	−	0.108352i
$565$	16.7591	−	22.7078i	0.705060	−	0.955323i
$566$	25.5032	+	2.87352i	1.07198	+	0.120783i
$567$	2.37580	+	24.8715i	0.0997743	+	1.04450i
$568$	−26.7177	+	26.7177i	−1.12105	+	1.12105i
$569$	−25.1510	−	29.2260i	−1.05439	−	1.22522i	−0.973546	−	0.228492i	$-0.926620\pi$
$569$	−25.1510	−	29.2260i	−1.05439	−	1.22522i	−0.0808405	−	0.996727i	$-0.525760\pi$
$570$	14.1928	+	8.09780i	0.594469	+	0.339179i
$571$	−0.0796671	−	1.06308i	−0.00333396	−	0.0444886i	0.995289	−	0.0969558i	$-0.0309106\pi$
$571$	−0.0796671	−	1.06308i	−0.00333396	−	0.0444886i	−0.998623	+	0.0524672i	$0.983292\pi$
$572$	−0.205072	+	0.238298i	−0.00857449	+	0.00996373i
$573$	10.0022	+	8.51902i	0.417847	+	0.355887i
$574$	−11.7994	+	1.77848i	−0.492499	+	0.0742324i
$575$	71.7569	+	57.2242i	2.99247	+	2.38642i
$576$	4.43133	+	13.8616i	0.184639	+	0.577565i
$577$	15.0505	−	9.45687i	0.626561	−	0.393695i	−0.180996	−	0.983484i	$-0.557932\pi$
$577$	15.0505	−	9.45687i	0.626561	−	0.393695i	0.807557	+	0.589789i	$0.200789\pi$
$578$	−13.1714	−	5.74662i	−0.547858	−	0.239028i
$579$	−15.9739	+	10.1513i	−0.663854	+	0.421873i
$580$	−14.8041	+	22.2304i	−0.614706	+	0.923069i
$581$	33.8093	−	19.5198i	1.40265	−	0.809819i
$582$	−12.0977	−	15.0121i	−0.501466	−	0.622270i
$583$	−1.82415	+	0.0682548i	−0.0755485	+	0.00282682i
$584$	1.71179	+	7.49985i	0.0708344	+	0.310346i
$585$	−0.428491	−	0.866998i	−0.0177159	−	0.0358459i
$586$	−3.67167	+	2.92806i	−0.151675	+	0.120957i
$587$	31.1873	−	33.6119i	1.28724	−	1.38731i	0.406537	−	0.913634i	$-0.366736\pi$
$587$	31.1873	−	33.6119i	1.28724	−	1.38731i	0.880699	−	0.473676i	$-0.157073\pi$
$588$	−1.50772	−	0.219381i	−0.0621774	−	0.00904713i
$589$	−15.0919	+	1.13098i	−0.621849	+	0.0466011i
$590$	0.915715	−	24.4730i	0.0376994	−	1.00754i
$591$	−36.6628	−	11.1042i	−1.50810	−	0.456765i
$592$	−0.246274	+	0.0659890i	−0.0101218	+	0.00271213i
$593$	1.51209	−	0.728185i	0.0620941	−	0.0299030i	−0.402579	−	0.915385i	$-0.631886\pi$
$593$	1.51209	−	0.728185i	0.0620941	−	0.0299030i	0.464673	+	0.885482i	$0.346172\pi$
$594$	7.23194	+	12.0942i	0.296730	+	0.496230i
$595$	−7.17113	+	63.6455i	−0.293988	+	2.60921i
$596$	4.73996	+	0.355211i	0.194156	+	0.0145500i
$597$	9.30569	−	10.1325i	0.380856	−	0.414694i
$598$	0.110358	+	0.583256i	0.00451287	+	0.0238511i
$599$	−8.39998	−	0.314305i	−0.343214	−	0.0128422i	−0.134771	−	0.990877i	$-0.543030\pi$
$599$	−8.39998	−	0.314305i	−0.343214	−	0.0128422i	−0.208443	+	0.978035i	$0.566839\pi$
$600$	−31.7465	−	42.5582i	−1.29604	−	1.73743i
$601$	−5.66715	+	29.9516i	−0.231168	+	1.22175i	0.654006	+	0.756490i	$0.273087\pi$
$601$	−5.66715	+	29.9516i	−0.231168	+	1.22175i	−0.885173	+	0.465261i	$0.845960\pi$
$602$	−0.786135	+	3.44428i	−0.0320405	+	0.140378i
$603$	−5.01881	+	16.8810i	−0.204382	+	0.687449i
$604$	−7.17185	+	8.99321i	−0.291818	+	0.365929i
$605$	1.47953	−	4.79653i	0.0601516	−	0.195007i
$606$	0.817028	+	0.388331i	0.0331895	+	0.0157749i
$607$	8.69422	+	11.7802i	0.352887	+	0.478145i	0.944703	−	0.327928i	$-0.106350\pi$
$607$	8.69422	+	11.7802i	0.352887	+	0.478145i	−0.591815	+	0.806074i	$0.701589\pi$
$608$	−7.73119	−	13.3908i	−0.313541	−	0.543069i
$609$	−25.1488	+	6.16523i	−1.01908	+	0.249828i
$610$	−16.1107	+	27.9046i	−0.652304	+	1.12982i
$611$	−0.203393	+	0.0229168i	−0.00822839	+	0.000927116i
$612$	−19.9115	−	8.44618i	−0.804873	−	0.341417i
$613$	9.02711	−	2.06038i	0.364601	−	0.0832179i	−0.0362954	−	0.999341i	$-0.511556\pi$
$613$	9.02711	−	2.06038i	0.364601	−	0.0832179i	0.400897	+	0.916123i	$0.368699\pi$
$614$	5.74310	+	14.6332i	0.231773	+	0.590547i
$615$	6.51712	+	33.5058i	0.262796	+	1.35109i
$616$	−23.3440	+	7.20066i	−0.940555	+	0.290123i
$617$	−15.0831	−	12.9801i	−0.607223	−	0.522558i	0.294061	−	0.955787i	$-0.404993\pi$
$617$	−15.0831	−	12.9801i	−0.607223	−	0.522558i	−0.901284	+	0.433229i	$0.857374\pi$
$618$	8.96301	+	3.85614i	0.360545	+	0.155117i
$619$	−0.110071	−	0.208265i	−0.00442413	−	0.00837086i	0.881893	−	0.471449i	$-0.156269\pi$
$619$	−0.110071	−	0.208265i	−0.00442413	−	0.00837086i	−0.886318	+	0.463078i	$0.846745\pi$
$620$	25.9975	+	9.09693i	1.04409	+	0.365341i
$621$	−43.4726	−	5.87256i	−1.74449	−	0.235658i
$622$	5.20802	+	10.8146i	0.208823	+	0.433625i
$623$	−1.25643	−	0.927291i	−0.0503380	−	0.0371511i
$624$	−0.000387459		0.00555065i	−1.55108e−5		0.000222204i
$625$	32.0848	+	21.8750i	1.28339	+	0.875002i
$626$	1.13424	−	4.23306i	0.0453335	−	0.169187i
$627$	−10.0748	−	10.7474i	−0.402350	−	0.429211i
$628$	−15.0484	+	7.95333i	−0.600498	+	0.317372i
$629$	−16.1368	+	33.5085i	−0.643418	+	1.33607i
$630$	2.93514	−	28.6809i	0.116939	−	1.14268i
$631$	−3.93806	−	0.898837i	−0.156772	−	0.0357821i	0.143415	−	0.989663i	$-0.454192\pi$
$631$	−3.93806	−	0.898837i	−0.156772	−	0.0357821i	−0.300186	+	0.953881i	$0.597049\pi$
$632$	−0.138128	−	0.916421i	−0.00549445	−	0.0364533i
$633$	19.7532	+	2.12352i	0.785119	+	0.0844022i
$634$	−18.0015	+	16.7029i	−0.714929	+	0.663357i
$635$	19.3450	−	36.6026i	0.767683	−	1.45253i
$636$	−0.982025	+	0.791380i	−0.0389398	+	0.0313802i
$637$	0.0495153	+	0.0285877i	0.00196187	+	0.00113268i
$638$	−11.3180	+	9.22941i	−0.448083	+	0.365396i
$639$	3.41365	+	40.0558i	0.135042	+	1.58458i
$640$	3.18151	+	28.2367i	0.125760	+	1.11615i
$641$	0.190839	+	5.10028i	0.00753769	+	0.201449i	0.997980	+	0.0635238i	$0.0202339\pi$
$641$	0.190839	+	5.10028i	0.00753769	+	0.201449i	−0.990443	+	0.137925i	$0.955957\pi$
$642$	3.09927	−	11.8076i	0.122319	−	0.466009i
$643$	−2.45179	+	16.2665i	−0.0966890	+	0.641490i	0.887021	+	0.461729i	$0.152771\pi$
$643$	−2.45179	+	16.2665i	−0.0966890	+	0.641490i	−0.983710	+	0.179761i	$0.942468\pi$
$644$	10.6594	−	27.1598i	0.420040	−	1.07025i
$645$	9.93909	+	1.82804i	0.391351	+	0.0719788i
$646$	−13.4748	−	2.54956i	−0.530158	−	0.100311i
$647$	12.1314	+	5.84216i	0.476934	+	0.229679i	0.656877	−	0.753998i	$-0.271877\pi$
$647$	12.1314	+	5.84216i	0.476934	+	0.229679i	−0.179943	+	0.983677i	$0.557591\pi$
$648$	23.4622	+	9.67071i	0.921682	+	0.379901i
$649$	−7.29204	+	20.8394i	−0.286237	+	0.818020i
$650$	0.197844	+	0.738365i	0.00776009	+	0.0289610i
$651$	12.5977	+	23.5440i	0.493742	+	0.922764i
$652$	−4.40493	−	10.0962i	−0.172510	−	0.395398i
$653$	−6.28363	−	14.4022i	−0.245897	−	0.563603i	0.749218	−	0.662324i	$-0.230430\pi$
$653$	−6.28363	−	14.4022i	−0.245897	−	0.563603i	−0.995115	+	0.0987210i	$0.968525\pi$
$654$	−4.91669	−	0.158822i	−0.192258	−	0.00621041i
$655$	9.14001	+	34.1110i	0.357130	+	1.33283i
$656$	0.0648622	−	0.185366i	0.00253245	−	0.00723731i
$657$	7.27490	+	3.75031i	0.283821	+	0.146314i
$658$	−5.49753	−	2.64747i	−0.214316	−	0.103209i
$659$	−9.28490	−	1.75680i	−0.361688	−	0.0684351i	0.00189141	−	0.999998i	$-0.499398\pi$
$659$	−9.28490	−	1.75680i	−0.361688	−	0.0684351i	−0.363580	+	0.931563i	$0.618446\pi$
$660$	8.98389	+	25.2598i	0.349698	+	0.983237i
$661$	2.66509	−	6.79054i	0.103660	−	0.264121i	−0.869629	−	0.493707i	$-0.835642\pi$
$661$	2.66509	−	6.79054i	0.103660	−	0.264121i	0.973289	+	0.229585i	$0.0737369\pi$
$662$	2.26096	−	15.0005i	0.0878747	−	0.583011i
$663$	0.576849	+	0.570985i	0.0224030	+	0.0221752i
$664$	−1.48267	−	39.6251i	−0.0575386	−	1.53775i
$665$	3.37457	+	29.9502i	0.130860	+	1.16142i
$666$	7.10937	−	15.1570i	0.275482	−	0.587321i
$667$	−0.495572	−	45.4604i	−0.0191886	−	1.76023i
$668$	24.4388	+	14.1098i	0.945567	+	0.545924i
$669$	9.50363	+	3.67398i	0.367431	+	0.142044i
$670$	9.49600	−	17.9673i	0.366862	−	0.694137i
$671$	21.2940	−	19.7579i	0.822044	−	0.762746i
$672$	−16.0880	+	22.0332i	−0.620608	+	0.849948i
$673$	−5.12916	−	34.0297i	−0.197715	−	1.31175i	−0.838867	−	0.544337i	$-0.816781\pi$
$673$	−5.12916	−	34.0297i	−0.197715	−	1.31175i	0.641152	−	0.767414i	$-0.278457\pi$
$674$	−7.27550	−	1.66058i	−0.280242	−	0.0639633i
$675$	−56.3902	−	3.35771i	−2.17046	−	0.129238i
$676$	−7.01846	+	14.5740i	−0.269941	+	0.560538i
$677$	−43.7951	+	23.1464i	−1.68318	+	0.889588i	−0.698420	+	0.715688i	$0.746113\pi$
$677$	−43.7951	+	23.1464i	−1.68318	+	0.889588i	−0.984763	+	0.173900i	$0.944363\pi$
$678$	3.09061	−	10.2043i	0.118694	−	0.391894i
$679$	9.20404	−	34.3499i	0.353219	−	1.31823i
$680$	53.7503	+	36.6463i	2.06123	+	1.40532i
$681$	1.51801	+	1.02364i	0.0581704	+	0.0392261i
$682$	12.1175	+	8.94314i	0.464004	+	0.342451i
$683$	−16.6673	−	34.6100i	−0.637756	−	1.32431i	−0.929855	−	0.367927i	$-0.880068\pi$
$683$	−16.6673	−	34.6100i	−0.637756	−	1.32431i	0.292098	−	0.956388i	$-0.405647\pi$
$684$	−10.0194	−	1.78994i	−0.383101	−	0.0684400i
$685$	−79.0833	−	27.6724i	−3.02162	−	1.05731i
$686$	−7.09379	−	13.4221i	−0.270842	−	0.512458i
$687$	1.53838	+	13.0538i	0.0586930	+	0.498034i
$688$	−0.0440708	−	0.0379260i	−0.00168018	−	0.00144591i
$689$	0.0452261	−	0.0139504i	0.00172298	−	0.000531469i
$690$	47.8644	+	16.4745i	1.82217	+	0.627174i
$691$	−3.17749	−	8.09610i	−0.120877	−	0.307990i	0.857609	−	0.514302i	$-0.171949\pi$
$691$	−3.17749	−	8.09610i	−0.120877	−	0.307990i	−0.978486	+	0.206312i	$0.933854\pi$
$692$	4.55311	−	1.03922i	0.173083	−	0.0395052i
$693$	−10.1499	+	23.9279i	−0.385562	+	0.908944i
$694$	−2.29404	+	0.258476i	−0.0870806	+	0.00981163i
$695$	−37.6944	+	65.2886i	−1.42983	+	2.47654i
$696$	−6.39943	+	25.5097i	−0.242570	+	0.966945i
$697$	−14.3236	−	24.8091i	−0.542544	−	0.939713i
$698$	−17.5048	−	23.7182i	−0.662566	−	0.897745i
$699$	−0.572082	+	0.394335i	−0.0216381	+	0.0149151i
$700$	11.0746	−	35.9029i	0.418579	−	1.35700i
$701$	10.7810	−	13.5190i	0.407194	−	0.510605i	−0.535376	−	0.844614i	$-0.679830\pi$
$701$	10.7810	−	13.5190i	0.407194	−	0.510605i	0.942570	+	0.334009i	$0.108401\pi$
$702$	−0.262276	−	0.254358i	−0.00989897	−	0.00960011i
$703$	−3.89446	+	17.0628i	−0.146883	+	0.643534i
$704$	−2.81454	+	14.8752i	−0.106077	+	0.560631i
$705$	−6.89801	+	16.0334i	−0.259794	+	0.603852i
$706$	16.5196	+	0.618119i	0.621723	+	0.0232632i
$707$	0.310205	+	1.63947i	0.0116665	+	0.0616587i
$708$	4.57069	+	14.5534i	0.171777	+	0.546951i
$709$	25.3230	+	1.89769i	0.951024	+	0.0712694i	0.541199	−	0.840895i	$-0.317971\pi$
$709$	25.3230	+	1.89769i	0.951024	+	0.0712694i	0.409825	+	0.912164i	$0.365590\pi$
$710$	5.19397	−	46.0977i	0.194926	−	1.73002i
$711$	−0.840221	−	0.516048i	−0.0315108	−	0.0193533i
$712$	−1.42902	+	0.688181i	−0.0535549	+	0.0257907i
$713$	−45.2860	+	12.1344i	−1.69598	+	0.454435i
$714$	5.50467	+	23.5620i	0.206007	+	0.881787i
$715$	0.0376185	−	1.00538i	0.00140685	−	0.0375989i
$716$	1.59656	−	0.119645i	0.0596661	−	0.00447136i
$717$	−8.32871	+	10.5540i	−0.311041	+	0.394147i
$718$	−2.49021	+	2.68381i	−0.0929338	+	0.100159i
$719$	−33.7560	+	26.9195i	−1.25889	+	1.00393i	−0.259617	+	0.965712i	$0.583596\pi$
$719$	−33.7560	+	26.9195i	−1.25889	+	1.00393i	−0.999269	+	0.0382169i	$0.987832\pi$
$720$	0.394752	+	0.263270i	0.0147116	+	0.00981150i
$721$	4.00477	+	17.5460i	0.149145	+	0.653449i
$722$	10.0496	−	0.376028i	0.374006	−	0.0139943i
$723$	3.99980	−	10.3464i	0.148754	−	0.384788i
$724$	9.18433	−	5.30257i	0.341333	−	0.197069i
$725$	−5.01119	−	58.3301i	−0.186111	−	2.16632i
$726$	−0.0805851	−	1.89460i	−0.00299079	−	0.0703151i
$727$	−1.26020	−	0.549818i	−0.0467381	−	0.0203916i	0.376393	−	0.926460i	$-0.377164\pi$
$727$	−1.26020	−	0.549818i	−0.0467381	−	0.0203916i	−0.423131	+	0.906068i	$0.639069\pi$
$728$	0.536309	−	0.336985i	0.0198769	−	0.0124895i
$729$	23.9557	−	12.4549i	0.887248	−	0.461292i
$730$	−7.38410	−	5.88862i	−0.273298	−	0.217948i
$731$	−8.38667	+	1.26409i	−0.310192	+	0.0467540i
$732$	3.63044	−	19.7389i	0.134185	−	0.729569i
$733$	4.79773	−	5.57506i	0.177208	−	0.205919i	−0.662342	−	0.749201i	$-0.730438\pi$
$733$	4.79773	−	5.57506i	0.177208	−	0.205919i	0.839550	+	0.543282i	$0.182819\pi$
$734$	2.31253	+	30.8585i	0.0853570	+	1.13901i
$735$	4.20996	−	2.45938i	0.155287	−	0.0907157i
$736$	−31.2448	−	36.3071i	−1.15170	−	1.33830i
$737$	−12.9550	+	12.9550i	−0.477202	+	0.477202i
$738$	6.56139	+	11.1012i	0.241528	+	0.408639i
$739$	38.4772	+	4.33534i	1.41541	+	0.159478i	0.786301	−	0.617843i	$-0.211993\pi$
$739$	38.4772	+	4.33534i	1.41541	+	0.159478i	0.629104	+	0.777321i	$0.283422\pi$
$740$	18.9142	−	25.6278i	0.695298	−	0.942095i
$741$	0.324436	+	0.201553i	0.0119185	+	0.00740422i
$742$	1.36286	+	0.365178i	0.0500323	+	0.0134061i
$743$	23.1647	−	4.38300i	0.849830	−	0.160797i	0.257287	−	0.966335i	$-0.417171\pi$
$743$	23.1647	−	4.38300i	0.849830	−	0.160797i	0.592543	+	0.805539i	$0.298124\pi$
$744$	27.1216	−	0.138555i	0.994324	−	0.00507967i
$745$	−12.5679	+	8.56862i	−0.460451	+	0.313930i
$746$	1.70166	+	4.86307i	0.0623023	+	0.178050i
$747$	−33.2515	−	25.9658i	−1.21661	−	0.950040i
$748$	−14.0288	−	17.5916i	−0.512944	−	0.643212i
$749$	20.9602	−	8.22629i	0.765871	−	0.300582i
$750$	34.0523	+	8.93810i	1.24342	+	0.326373i
$751$	−40.7007	−	21.5110i	−1.48519	−	0.784947i	−0.489012	−	0.872277i	$-0.662643\pi$
$751$	−40.7007	−	21.5110i	−1.48519	−	0.784947i	−0.996179	+	0.0873305i	$0.972166\pi$
$752$	0.0807993	−	0.0596326i	0.00294645	−	0.00217458i
$753$	−3.88638	+	0.165304i	−0.141628	+	0.00602401i
$754$	0.221515	−	0.307092i	0.00806709	−	0.0111836i
$755$		−	36.8101i		−	1.33966i
$756$	4.26386	+	17.4444i	0.155075	+	0.634448i
$757$	28.7632	+	45.7764i	1.04542	+	1.66377i	0.680528	+	0.732722i	$0.261751\pi$
$757$	28.7632	+	45.7764i	1.04542	+	1.66377i	0.364890	+	0.931051i	$0.381107\pi$
$758$	−9.96795	−	3.07471i	−0.362052	−	0.111678i
$759$	−36.8561	−	26.9113i	−1.33779	−	0.976817i
$760$	28.4969	+	11.1842i	1.03369	+	0.405694i
$761$	2.03992	+	6.61325i	0.0739469	+	0.239730i	0.984999	−	0.172562i	$-0.0552045\pi$
$761$	2.03992	+	6.61325i	0.0739469	+	0.239730i	−0.911052	+	0.412292i	$0.864728\pi$
$762$	2.25204	−	15.4774i	0.0815829	−	0.560688i
$763$	−5.11129	−	7.49689i	−0.185041	−	0.271406i
$764$	7.99590	+	5.02416i	0.289282	+	0.181768i
$765$	66.6696	−	18.5962i	2.41044	−	0.672346i
$766$	−8.98195	−	8.98195i	−0.324531	−	0.324531i
$767$	0.0427785	−	0.570839i	0.00154464	−	0.0206118i
$768$	12.0753	+	24.7503i	0.435729	+	0.893100i
$769$	13.4554	−	5.87053i	0.485214	−	0.211697i	−0.143022	−	0.989720i	$-0.545682\pi$
$769$	13.4554	−	5.87053i	0.485214	−	0.211697i	0.628236	+	0.778023i	$0.283777\pi$
$770$	16.8955	−	24.7811i	0.608871	−	0.893049i
$771$	−3.21847	+	14.4407i	−0.115910	+	0.520069i
$772$	−10.3112	+	8.87349i	−0.371108	+	0.319364i
$773$	−18.7645	+	29.8635i	−0.674911	+	1.07411i	0.317152	+	0.948375i	$0.397273\pi$
$773$	−18.7645	+	29.8635i	−0.674911	+	1.07411i	−0.992063	+	0.125740i	$0.959869\pi$
$774$	3.76918	−	0.607560i	0.135480	−	0.0218383i
$775$	−56.9861	+	19.9403i	−2.04700	+	0.716277i
$776$	−26.4780	−	24.5680i	−0.950505	−	0.881940i
$777$	30.3114	−	5.89578i	1.08742	−	0.211510i
$778$	−31.0193	−	4.67541i	−1.11210	−	0.167622i
$779$	−9.16921	−	9.88206i	−0.328521	−	0.354062i
$780$	−0.394501	−	0.572323i	−0.0141254	−	0.0204924i
$781$	−16.7239	+	38.3317i	−0.598430	+	1.37162i
$782$	−42.4836			−1.51921
$783$	16.3638	+	22.6986i	0.584793	+	0.811182i
$784$	−0.0280519			−0.00100185
$785$	21.7816	−	49.9240i	0.777419	−	1.78186i
$786$	7.57160	+	10.9845i	0.270070	+	0.391805i
$787$	−16.6300	−	17.9229i	−0.592797	−	0.638883i	0.363391	−	0.931637i	$-0.381619\pi$
$787$	−16.6300	−	17.9229i	−0.592797	−	0.638883i	−0.956188	+	0.292754i	$0.905428\pi$
$788$	−27.2263	−	4.10371i	−0.969897	−	0.146188i
$789$	12.0193	−	2.33783i	0.427897	−	0.0832289i
$790$	0.834088	+	0.773921i	0.0296755	+	0.0275349i
$791$	18.5625	−	6.49529i	0.660005	−	0.230946i
$792$	16.6700	+	20.4710i	0.592344	+	0.727404i
$793$	−0.400702	+	0.637714i	−0.0142293	+	0.0226459i
$794$	9.63073	−	8.28792i	0.341782	−	0.294127i
$795$	0.877985	−	3.93936i	0.0311389	−	0.139715i
$796$	5.57021	−	8.16999i	0.197431	−	0.289578i
$797$	−7.18843	+	3.13628i	−0.254627	+	0.111093i	−0.523329	−	0.852131i	$-0.675310\pi$
$797$	−7.18843	+	3.13628i	−0.254627	+	0.111093i	0.268702	+	0.963223i	$0.413405\pi$
$798$	4.99269	+	10.2334i	0.176739	+	0.362257i
$799$	1.09470	−	14.6077i	0.0387276	−	0.516784i
$800$	−43.6167	−	43.6167i	−1.54208	−	1.54208i
$801$	−0.420088	+	1.63440i	−0.0148431	+	0.0577489i
$802$	−27.6286	−	17.3602i	−0.975601	−	0.613011i
$803$	4.79641	+	7.03504i	0.169262	+	0.248261i
$804$	−1.82265	+	12.5264i	−0.0642800	+	0.441772i
$805$	27.5209	+	89.2205i	0.969983	+	3.14461i
$806$	−0.363486	−	0.142658i	−0.0128033	−	0.00502491i
$807$	−31.5618	−	23.0455i	−1.11103	−	0.811241i
$808$	1.61947	+	0.499542i	0.0569729	+	0.0175738i
$809$	1.95860	+	3.11709i	0.0688605	+	0.109591i	0.879380	−	0.476121i	$-0.157958\pi$
$809$	1.95860	+	3.11709i	0.0688605	+	0.109591i	−0.810519	+	0.585712i	$0.800815\pi$
$810$	−29.9236	+	8.67709i	−1.05141	+	0.304882i
$811$		−	51.5173i		−	1.80902i	−0.426456	−	0.904508i	$-0.640238\pi$
$811$		−	51.5173i		−	1.80902i	0.426456	−	0.904508i	$-0.359762\pi$
$812$	−17.2495	+	6.98788i	−0.605340	+	0.245226i
$813$	34.9669	−	1.48729i	1.22634	−	0.0521615i
$814$	14.0130	−	10.3421i	0.491157	−	0.362490i
$815$	31.1652	+	16.4713i	1.09167	+	0.576964i
$816$	−0.385173	−	0.101101i	−0.0134838	−	0.00353923i
$817$	−3.71527	+	1.45814i	−0.129981	+	0.0510137i
$818$	−0.207490	−	0.260185i	−0.00725473	−	0.00909715i
$819$	0.0936258	−	0.667364i	0.00327155	−	0.0233196i
$820$	8.10306	+	23.1572i	0.282971	+	0.808685i
$821$	−16.7750	+	11.4370i	−0.585453	+	0.399155i	−0.819507	−	0.573068i	$-0.805753\pi$
$821$	−16.7750	+	11.4370i	−0.585453	+	0.399155i	0.234055	+	0.972223i	$0.424801\pi$
$822$	−31.6524	+	0.161701i	−1.10400	+	0.00563998i
$823$	−41.2962	+	7.81367i	−1.43950	+	0.272367i	−0.846307	−	0.532696i	$-0.821179\pi$
$823$	−41.2962	+	7.81367i	−1.43950	+	0.272367i	−0.593189	+	0.805063i	$0.702131\pi$
$824$	17.6571	+	4.73120i	0.615113	+	0.164819i
$825$	−49.9183	−	31.0112i	−1.73793	−	1.07967i
$826$	10.1337	−	13.7307i	0.352596	−	0.477751i
$827$	−22.0558	−	2.48509i	−0.766955	−	0.0864150i	−0.280186	−	0.959946i	$-0.590396\pi$
$827$	−22.0558	−	2.48509i	−0.766955	−	0.0864150i	−0.486769	+	0.873531i	$0.661825\pi$
$828$	−31.5285	+	0.322145i	−1.09569	+	0.0111953i
$829$	32.5068	−	32.5068i	1.12901	−	1.12901i	0.138670	−	0.990339i	$-0.455717\pi$
$829$	32.5068	−	32.5068i	1.12901	−	1.12901i	0.990339	−	0.138670i	$-0.0442826\pi$
$830$	31.7554	+	36.9004i	1.10225	+	1.28083i
$831$	24.5520	−	14.3428i	0.851699	−	0.497547i
$832$	−0.0293332	−	0.391424i	−0.00101694	−	0.0135702i
$833$	−2.66914	+	3.10160i	−0.0924803	+	0.107464i
$834$	−5.15188	+	28.0110i	−0.178395	+	0.969940i
$835$	−89.2971	+	13.4594i	−3.09025	+	0.465781i
$836$	−8.27821	−	6.60165i	−0.286308	−	0.228323i
$837$	18.4853	−	22.1582i	0.638944	−	0.765900i
$838$	10.4764	−	6.58276i	0.361901	−	0.227398i
$839$	−34.2892	−	14.9602i	−1.18379	−	0.516484i	−0.286569	−	0.958060i	$-0.592515\pi$
$839$	−34.2892	−	14.9602i	−1.18379	−	0.516484i	−0.897224	+	0.441576i	$0.854420\pi$
$840$	−2.29533	−	53.9644i	−0.0791965	−	1.86195i
$841$	−20.8235	+	20.1838i	−0.718050	+	0.695991i
$842$	−7.01989	+	4.05294i	−0.241922	+	0.139673i
$843$	−0.137359	+	0.355311i	−0.00473089	+	0.0122376i
$844$	14.2696	−	0.533931i	0.491180	−	0.0183787i
$845$	−11.5187	−	50.4669i	−0.396256	−	1.73611i
$846$	−0.425560	+	6.58023i	−0.0146311	+	0.226233i
$847$	2.73463	−	2.18080i	0.0939630	−	0.0749330i
$848$	−0.0157943	+	0.0170222i	−0.000542377	+	0.000584543i
$849$	31.6908	−	40.1581i	1.08762	−	1.37822i
$850$	−54.5551	+	4.08834i	−1.87122	+	0.140229i
$851$	−2.02725	+	54.1795i	−0.0694934	+	1.85725i
$852$	6.57353	+	28.1372i	0.225206	+	0.963964i
$853$	−12.0991	+	3.24195i	−0.414266	+	0.111002i	−0.459931	−	0.887954i	$-0.652126\pi$
$853$	−12.0991	+	3.24195i	−0.414266	+	0.111002i	0.0456650	+	0.998957i	$0.485459\pi$
$854$	−20.2291	+	9.74182i	−0.692225	+	0.333358i
$855$	28.6394	−	15.5127i	0.979446	−	0.530525i
$856$	2.56067	−	22.7266i	0.0875220	−	0.776779i
$857$	39.1514	+	2.93399i	1.33739	+	0.100223i	0.724132	−	0.689662i	$-0.242241\pi$
$857$	39.1514	+	2.93399i	1.33739	+	0.100223i	0.613255	+	0.789885i	$0.289860\pi$
$858$	−0.113885	−	0.362619i	−0.00388798	−	0.0123796i
$859$	2.58522	+	13.6632i	0.0882067	+	0.466184i	0.998622	+	0.0524872i	$0.0167149\pi$
$859$	2.58522	+	13.6632i	0.0882067	+	0.466184i	−0.910415	+	0.413696i	$0.864238\pi$
$860$	7.25856	+	0.271596i	0.247515	+	0.00926136i
$861$	−9.40000	+	21.8489i	−0.320351	+	0.744608i
$862$	2.97673	−	15.7324i	0.101388	−	0.535847i
$863$	10.0560	−	44.0582i	0.342310	−	1.49976i	−0.451874	−	0.892082i	$-0.649244\pi$
$863$	10.0560	−	44.0582i	0.342310	−	1.49976i	0.794184	−	0.607677i	$-0.207898\pi$
$864$	28.5912	+	7.19323i	0.972693	+	0.244719i
$865$	−9.31817	+	11.6846i	−0.316827	+	0.397289i
$866$	5.11054	−	16.5680i	0.173663	−	0.563002i
$867$	−23.5842	+	16.2565i	−0.800961	+	0.552101i
$868$	11.3970	+	15.4424i	0.386839	+	0.524149i
$869$	−0.512890	−	0.888351i	−0.0173986	−	0.0301353i
$870$	−13.3845	−	29.3850i	−0.453777	−	0.996243i
$871$	0.237511	−	0.411380i	0.00804774	−	0.0139391i
$872$	−9.15808	+	1.03187i	−0.310132	+	0.0349434i
$873$	−38.1426	+	4.69276i	−1.29093	+	0.158826i
$874$	−19.4906	+	4.44861i	−0.659280	+	0.150476i
$875$	23.7241	+	60.4480i	0.802020	+	2.04351i
$876$	5.56255	+	1.91458i	0.187941	+	0.0646877i
$877$	−44.8756	+	13.8423i	−1.51534	+	0.467421i	−0.937282	−	0.348573i	$-0.886666\pi$
$877$	−44.8756	+	13.8423i	−1.51534	+	0.467421i	−0.578060	+	0.815994i	$0.696190\pi$
$878$	−0.731244	−	0.629286i	−0.0246783	−	0.0212374i
$879$	1.09559	+	9.29656i	0.0369535	+	0.313565i
$880$	0.230650	+	0.436411i	0.00777520	+	0.0147114i
$881$	19.2525	+	6.73675i	0.648634	+	0.226967i	0.634488	−	0.772933i	$-0.281211\pi$
$881$	19.2525	+	6.73675i	0.648634	+	0.226967i	0.0141464	+	0.999900i	$0.495497\pi$
$882$	1.18716	−	1.40836i	0.0399739	−	0.0474220i
$883$	8.34381	+	17.3261i	0.280792	+	0.583070i	0.992893	−	0.119006i	$-0.0379709\pi$
$883$	8.34381	+	17.3261i	0.280792	+	0.583070i	−0.712102	+	0.702076i	$0.752257\pi$
$884$	0.469388	+	0.346424i	0.0157872	+	0.0116515i
$885$	−40.4732	−	27.2923i	−1.36049	−	0.917421i
$886$	−2.52657	−	1.72258i	−0.0848817	−	0.0578714i
$887$	−0.411184	+	1.53456i	−0.0138062	+	0.0515255i	−0.972485	−	0.232964i	$-0.925157\pi$
$887$	−0.411184	+	1.53456i	−0.0138062	+	0.0515255i	0.958679	+	0.284490i	$0.0918242\pi$
$888$	9.09162	−	30.0179i	0.305095	−	1.00733i
$889$	25.5055	−	13.4800i	0.855426	−	0.452106i
$890$	0.844903	−	1.75446i	0.0283212	−	0.0588096i
$891$	28.0841	+	0.476505i	0.940853	+	0.0159635i
$892$	7.13987	+	1.62963i	0.239061	+	0.0545640i
$893$	−1.02740	−	6.81636i	−0.0343807	−	0.228101i
$894$	−3.38871	+	4.64097i	−0.113335	+	0.155217i
$895$	−3.75578	+	3.48486i	−0.125542	+	0.116486i
$896$	−9.25212	+	17.5059i	−0.309092	+	0.584830i
$897$	1.10362	+	0.426644i	0.0368487	+	0.0142452i
$898$	24.6443	+	14.2284i	0.822391	+	0.474807i
$899$	25.4941	+	15.6340i	0.850277	+	0.521424i
$900$	−40.4561	+	3.44777i	−1.34854	+	0.114926i
$901$	0.379254	+	3.36597i	0.0126348	+	0.112137i
$902$	0.501601	+	13.4056i	0.0167015	+	0.446357i
$903$	5.00478	+	4.95391i	0.166549	+	0.164856i
$904$	2.97711	−	19.7518i	0.0990172	−	0.656936i
$905$	−12.3988	+	31.5917i	−0.412151	+	1.05014i
$906$	−4.65996	−	13.1023i	−0.154817	−	0.435295i
$907$	23.3352	+	4.41526i	0.774832	+	0.146606i	0.558266	−	0.829662i	$-0.311467\pi$
$907$	23.3352	+	4.41526i	0.774832	+	0.146606i	0.216566	+	0.976268i	$0.430514\pi$
$908$	1.18566	+	0.570982i	0.0393474	+	0.0189487i
$909$	1.51689	−	0.974884i	0.0503121	−	0.0323348i
$910$	−0.256837	+	0.733999i	−0.00851407	+	0.0243318i
$911$	−9.59919	−	35.8247i	−0.318035	−	1.18692i	−0.921130	−	0.389255i	$-0.872733\pi$
$911$	−9.59919	−	35.8247i	−0.318035	−	1.18692i	0.603095	−	0.797670i	$-0.293934\pi$
$912$	−0.187296	−	0.00605014i	−0.00620200	−	0.000200340i
$913$	−17.5508	−	40.2270i	−0.580848	−	1.33132i
$914$	5.56841	+	12.7629i	0.184187	+	0.422160i
$915$	30.3005	+	56.6292i	1.00170	+	1.87210i
$916$	2.44519	+	9.12556i	0.0807912	+	0.301517i
$917$	−8.12743	+	23.2269i	−0.268391	+	0.767019i
$918$	21.3764	−	15.0592i	0.705528	−	0.497028i
$919$	33.3922	+	16.0808i	1.10151	+	0.530458i	0.894132	−	0.447804i	$-0.147794\pi$
$919$	33.3922	+	16.0808i	1.10151	+	0.530458i	0.207375	+	0.978262i	$0.433508\pi$
$920$	93.1817	+	17.6309i	3.07211	+	0.581275i
$921$	30.8170	+	5.66798i	1.01545	+	0.186766i
$922$	5.96143	−	15.1895i	0.196329	−	0.500238i
$923$	0.161610	−	1.07221i	0.00531945	−	0.0352922i
$924$	−4.74293	+	18.0696i	−0.156031	+	0.594446i
$925$	2.61059	+	69.7694i	0.0858356	+	2.29400i
$926$	2.09869	+	18.6264i	0.0689673	+	0.612102i
$927$	15.9567	−	11.1196i	0.524088	−	0.365216i
$928$	−3.08986	+	30.3980i	−0.101430	+	0.997863i
$929$	−13.4023	−	7.73784i	−0.439716	−	0.253870i	0.263761	−	0.964588i	$-0.415037\pi$
$929$	−13.4023	−	7.73784i	−0.439716	−	0.253870i	−0.703477	+	0.710718i	$0.748370\pi$
$930$	−25.9274	+	20.8940i	−0.850193	+	0.685141i
$931$	−0.899769	+	1.70245i	−0.0294887	+	0.0557954i
$932$	−0.366093	+	0.339685i	−0.0119918	+	0.0111267i
$933$	23.7887	+	2.55734i	0.778807	+	0.0837237i
$934$	−0.822666	−	5.45803i	−0.0269185	−	0.178592i
$935$	70.1987	+	16.0224i	2.29574	+	0.523988i
$936$	−0.554858	−	0.400812i	−0.0181361	−	0.0131010i
$937$	18.4165	−	38.2422i	0.601639	−	1.24932i	−0.348447	−	0.937329i	$-0.613291\pi$
$937$	18.4165	−	38.2422i	0.601639	−	1.24932i	0.950086	−	0.311988i	$-0.100995\pi$
$938$	12.5200	−	6.61702i	0.408793	−	0.216053i
$939$	−5.97413	−	6.37298i	−0.194959	−	0.207974i
$940$	−3.24700	+	12.1180i	−0.105905	+	0.395244i
$941$	9.68530	+	6.60333i	0.315732	+	0.215262i	0.710808	−	0.703386i	$-0.248329\pi$
$941$	9.68530	+	6.60333i	0.315732	+	0.215262i	−0.395076	+	0.918648i	$0.629282\pi$
$942$	1.43291	−	20.5276i	0.0466868	−	0.668824i
$943$	−33.6011	−	24.7987i	−1.09420	−	0.807558i
$944$	0.121859	+	0.253043i	0.00396617	+	0.00823583i
$945$	−45.4737	−	35.1376i	−1.47926	−	1.14303i
$946$	3.74882	+	1.31177i	0.121885	+	0.0426492i
$947$	6.87763	+	13.0131i	0.223493	+	0.422869i	0.970208	−	0.242275i	$-0.0778937\pi$
$947$	6.87763	+	13.0131i	0.223493	+	0.422869i	−0.746715	+	0.665145i	$0.768370\pi$
$948$	−0.651031	−	0.280092i	−0.0211445	−	0.00909696i
$949$	−0.167331	−	0.144000i	−0.00543179	−	0.00467443i
$950$	−24.6007	+	7.58830i	−0.798151	+	0.246197i
$951$	9.34567	+	48.0480i	0.303054	+	1.55806i
$952$	16.5613	+	42.1976i	0.536756	+	1.36763i
$953$	40.6037	−	9.26753i	1.31528	−	0.300205i	0.493371	−	0.869819i	$-0.335765\pi$
$953$	40.6037	−	9.26753i	1.31528	−	0.300205i	0.821912	+	0.569614i	$0.192907\pi$
$954$	−0.186189	−	1.51334i	−0.00602811	−	0.0489962i
$955$	−30.0297	+	3.38354i	−0.971739	+	0.109489i
$956$	−4.83168	+	8.36872i	−0.156268	+	0.270664i
$957$	3.72193	+	28.8709i	0.120313	+	0.933265i
$958$	7.61100	+	13.1826i	0.245900	+	0.425912i
$959$	−34.6691	−	46.9750i	−1.11952	−	1.51690i
$960$	−30.2317	−	14.3690i	−0.975723	−	0.463758i
$961$	−0.0470302	+	0.152468i	−0.00151710	+	0.00491833i
$962$	−0.281543	+	0.353044i	−0.00907731	+	0.0113826i
$963$	−16.7320	−	17.6673i	−0.539182	−	0.569322i
$964$	1.77415	−	7.77305i	0.0571414	−	0.250353i
$965$	8.09333	−	42.7743i	0.260534	−	1.37695i
$966$	21.0907	+	28.2735i	0.678583	+	0.909684i
$967$	29.6728	+	1.11028i	0.954214	+	0.0357042i	0.509961	−	0.860197i	$-0.329660\pi$
$967$	29.6728	+	1.11028i	0.954214	+	0.0357042i	0.444252	+	0.895902i	$0.353469\pi$
$968$	−0.660481	−	3.49073i	−0.0212287	−	0.112196i
$969$	−18.4902	+	20.1330i	−0.593991	+	0.646765i
$970$	44.2220	+	3.31398i	1.41988	+	0.106406i
$971$	−3.12706	+	27.7534i	−0.100352	+	0.890650i	0.838165	+	0.545417i	$0.183629\pi$
$971$	−3.12706	+	27.7534i	−0.100352	+	0.890650i	−0.938517	+	0.345233i	$0.887800\pi$
$972$	15.7500	−	11.3380i	0.505180	−	0.363667i
$973$	−47.3302	+	22.7930i	−1.51734	+	0.730710i
$974$	−10.9394	+	2.93120i	−0.350521	+	0.0939218i
$975$	1.45826	+	0.441668i	0.0467017	+	0.0141447i
$976$	0.0138168	−	0.369261i	0.000442265	−	0.0118198i
$977$	6.82171	−	0.511216i	0.218246	−	0.0163553i	0.0348415	−	0.999393i	$-0.488907\pi$
$977$	6.82171	−	0.511216i	0.218246	−	0.0163553i	0.183404	+	0.983038i	$0.441288\pi$
$978$	13.1782	+	1.91750i	0.421393	+	0.0613149i
$979$	−1.19407	+	1.28690i	−0.0381626	+	0.0411295i
$980$	2.73989	−	2.18499i	0.0875225	−	0.0697968i
$981$	−5.44052	+	8.15762i	−0.173702	+	0.260453i
$982$	0.974577	+	4.26990i	0.0311000	+	0.136258i
$983$	22.3314	−	0.835582i	0.712261	−	0.0266509i	0.321194	−	0.947013i	$-0.395916\pi$
$983$	22.3314	−	0.835582i	0.712261	−	0.0266509i	0.391066	+	0.920362i	$0.372106\pi$
$984$	15.1590	+	18.8109i	0.483252	+	0.599669i
$985$	76.3067	−	44.0557i	2.43133	−	1.40373i
$986$	18.6477	+	19.6632i	0.593865	+	0.626203i
$987$	−10.2651	+	6.52338i	−0.326742	+	0.207641i
$988$	0.251621	+	0.109781i	0.00800513	+	0.00349260i
$989$	−10.4690	+	6.57808i	−0.332893	+	0.209171i
$990$	−31.6714	−	6.88911i	−1.00658	−	0.218950i
$991$	−11.1299	−	8.87580i	−0.353553	−	0.281949i	0.430567	−	0.902559i	$-0.358314\pi$
$991$	−11.1299	−	8.87580i	−0.353553	−	0.281949i	−0.784120	+	0.620610i	$0.786885\pi$
$992$	31.1573	−	4.69621i	0.989246	−	0.149105i
$993$	−23.0198	−	19.6064i	−0.730512	−	0.622189i
$994$	21.0853	−	24.5016i	0.668785	−	0.777142i
$995$	2.36470	+	31.5548i	0.0749661	+	1.00035i
$996$	−26.3380	−	15.0274i	−0.834553	−	0.476161i
$997$	−10.2839	−	11.9502i	−0.325696	−	0.378465i	0.571122	−	0.820865i	$-0.306508\pi$
$997$	−10.2839	−	11.9502i	−0.325696	−	0.378465i	−0.896818	+	0.442400i	$0.854127\pi$
$998$	5.33430	−	5.33430i	0.168854	−	0.168854i
$999$	−18.1850	−	27.9801i	−0.575349	−	0.885250i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	261.2.x.a.101.10	yes	672
3.2	odd	2		783.2.be.a.710.19		672
9.4	even	3		783.2.be.a.449.10		672
9.5	odd	6	inner	261.2.x.a.14.19	✓	672
29.27	odd	28	inner	261.2.x.a.56.19	yes	672
87.56	even	28		783.2.be.a.143.10		672
261.85	odd	84		783.2.be.a.665.19		672
261.230	even	84	inner	261.2.x.a.230.10	yes	672

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
261.2.x.a.14.19	✓	672	9.5	odd	6	inner
261.2.x.a.56.19	yes	672	29.27	odd	28	inner
261.2.x.a.101.10	yes	672	1.1	even	1	trivial
261.2.x.a.230.10	yes	672	261.230	even	84	inner
783.2.be.a.143.10		672	87.56	even	28
783.2.be.a.449.10		672	9.4	even	3
783.2.be.a.665.19		672	261.85	odd	84
783.2.be.a.710.19		672	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 261 = 3^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	261.x (of order \(84\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.347486 + 0.796446i) q^{2} +(0.982997 + 1.42608i) q^{3} +(0.846766 + 0.912597i) q^{4} +(-3.93941 - 0.593771i) q^{5} +(-1.47738 + 0.287360i) q^{6} +(-2.03501 - 1.88821i) q^{7} +(-2.66145 + 0.931280i) q^{8} +(-1.06743 + 2.80367i) q^{9} +(1.84180 - 2.93120i) q^{10} +(-2.36556 + 2.03573i) q^{11} +(-0.469071 + 2.10464i) q^{12} +(0.0455825 - 0.0668572i) q^{13} +(2.21099 - 0.964646i) q^{14} +(-3.02566 - 6.20161i) q^{15} +(-0.00296683 + 0.0395895i) q^{16} +(4.09498 + 4.09498i) q^{17} +(-1.86206 - 1.82439i) q^{18} +(2.30749 + 1.44989i) q^{19} +(-2.79389 - 4.09788i) q^{20} +(0.692341 - 4.75820i) q^{21} +(-0.799349 - 2.59142i) q^{22} +(7.85871 + 3.08432i) q^{23} +(-3.94428 - 2.88000i) q^{24} +(10.3885 + 3.20444i) q^{25} +(0.0374089 + 0.0595359i) q^{26} +(-5.04756 + 1.23375i) q^{27} -3.45601i q^{28} +(-2.02195 - 4.99116i) q^{29} +(5.99062 - 0.254806i) q^{30} +(-4.46827 + 3.29773i) q^{31} +(-5.01634 - 2.65121i) q^{32} +(-5.22845 - 1.37237i) q^{33} +(-4.68438 + 1.83848i) q^{34} +(6.89556 + 8.64676i) q^{35} +(-3.46249 + 1.39992i) q^{36} +(2.12109 + 6.06173i) q^{37} +(-1.95658 + 1.33398i) q^{38} +(0.140151 - 0.000715986i) q^{39} +(11.0375 - 2.08841i) q^{40} +(-4.77813 - 1.28030i) q^{41} +(3.54907 + 2.20482i) q^{42} +(-0.869673 + 1.17837i) q^{43} +(-3.86087 - 0.435016i) q^{44} +(5.86980 - 10.4110i) q^{45} +(-5.18728 + 5.18728i) q^{46} +(-1.64995 - 1.91728i) q^{47} +(-0.0593744 + 0.0346855i) q^{48} +(0.0528034 + 0.704612i) q^{49} +(-6.16203 + 7.16040i) q^{50} +(-1.81443 + 9.86514i) q^{51} +(0.0996113 - 0.0150140i) q^{52} +(0.457295 + 0.364681i) q^{53} +(0.771338 - 4.44882i) q^{54} +(10.5277 - 6.61497i) q^{55} +(7.17451 + 3.13021i) q^{56} +(0.200588 + 4.71592i) q^{57} +(4.67779 + 0.123987i) q^{58} +(6.12658 - 3.53718i) q^{59} +(3.09754 - 8.01252i) q^{60} +(-9.30117 + 0.348025i) q^{61} +(-1.07381 - 4.70465i) q^{62} +(7.46616 - 3.68996i) q^{63} +(3.79258 - 3.02448i) q^{64} +(-0.219266 + 0.236312i) q^{65} +(2.90983 - 3.68730i) q^{66} +(5.85402 - 0.438698i) q^{67} +(-0.269575 + 7.20455i) q^{68} +(3.32659 + 14.2391i) q^{69} +(-9.28279 + 2.48732i) q^{70} +(12.0733 - 5.81419i) q^{71} +(0.229911 - 8.45590i) q^{72} +(0.305465 - 2.71107i) q^{73} +(-5.56489 - 0.417031i) q^{74} +(5.64210 + 17.9649i) q^{75} +(0.630738 + 3.33353i) q^{76} +(8.65780 + 0.323952i) q^{77} +(-0.0481304 + 0.111872i) q^{78} +(-0.0611055 + 0.322950i) q^{79} +(0.0351947 - 0.154198i) q^{80} +(-6.72117 - 5.98547i) q^{81} +(2.68002 - 3.36064i) q^{82} +(-4.14511 + 13.4381i) q^{83} +(4.92856 - 3.39725i) q^{84} +(-13.7003 - 18.5633i) q^{85} +(-0.636305 - 1.10211i) q^{86} +(5.13025 - 7.78977i) q^{87} +(4.39997 - 7.62097i) q^{88} +(0.558973 - 0.0629811i) q^{89} +(6.25214 + 8.29265i) q^{90} +(-0.219001 + 0.0499855i) q^{91} +(3.83975 + 9.78352i) q^{92} +(-9.09514 - 3.13047i) q^{93} +(2.10034 - 0.647870i) q^{94} +(-8.22926 - 7.08185i) q^{95} +(-1.15019 - 9.75986i) q^{96} +(5.98574 + 11.3256i) q^{97} +(-0.579534 - 0.202788i) q^{98} +(-3.18244 - 8.80525i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 672 q - 36 q^{2} - 24 q^{3} - 14 q^{4} - 42 q^{5} - 28 q^{6} - 10 q^{7} - 28 q^{9} - 56 q^{10} - 48 q^{11} - 10 q^{12} - 14 q^{13} - 24 q^{14} - 20 q^{15} - 54 q^{16} - 50 q^{18} - 48 q^{19} - 30 q^{20}+ \cdots - 16 q^{99}+O(q^{100}) \) 672 * q - 36 * q^2 - 24 * q^3 - 14 * q^4 - 42 * q^5 - 28 * q^6 - 10 * q^7 - 28 * q^9 - 56 * q^10 - 48 * q^11 - 10 * q^12 - 14 * q^13 - 24 * q^14 - 20 * q^15 - 54 * q^16 - 50 * q^18 - 48 * q^19 - 30 * q^20 - 80 * q^21 - 14 * q^22 - 30 * q^23 - 16 * q^24 + 30 * q^25 + 36 * q^27 - 168 * q^30 - 12 * q^31 + 24 * q^32 - 70 * q^33 - 14 * q^34 + 128 * q^36 - 48 * q^37 - 42 * q^38 - 44 * q^39 - 2 * q^40 - 24 * q^41 - 28 * q^42 - 12 * q^43 + 24 * q^45 - 64 * q^46 - 42 * q^47 - 28 * q^48 + 22 * q^49 - 66 * q^50 - 28 * q^51 + 22 * q^52 - 36 * q^54 + 76 * q^55 - 42 * q^56 - 42 * q^58 - 132 * q^59 - 20 * q^60 - 28 * q^63 - 308 * q^64 - 66 * q^65 - 46 * q^66 - 14 * q^67 + 60 * q^68 - 64 * q^69 - 14 * q^70 + 56 * q^72 - 48 * q^73 + 66 * q^74 + 24 * q^75 - 28 * q^76 + 30 * q^77 + 72 * q^78 - 12 * q^79 + 140 * q^81 - 136 * q^82 + 246 * q^83 + 238 * q^84 + 34 * q^85 + 118 * q^87 + 8 * q^88 - 48 * q^90 - 56 * q^91 + 462 * q^92 + 28 * q^93 + 26 * q^94 - 246 * q^95 + 126 * q^96 - 36 * q^97 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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