LMFDB - Embedded newform 261.2.x.a.14.4

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			14.4
Character	$\chi$	$=$	261.14
Dual form			261.2.x.a.56.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.38565 - 1.87749i) q^{2} +(-1.25257 - 1.19627i) q^{3} +(-1.01543 + 3.29194i) q^{4} +(-0.859785 - 2.19070i) q^{5} +(-0.510352 + 4.00930i) q^{6} +(-1.60836 + 0.496115i) q^{7} +(3.18260 - 1.11364i) q^{8} +(0.137883 + 2.99683i) q^{9} +(-2.92165 + 4.64977i) q^{10} +(-0.242992 - 1.28424i) q^{11} +(5.20995 - 2.90867i) q^{12} +(-3.83068 - 0.287070i) q^{13} +(3.16008 + 2.33224i) q^{14} +(-1.54372 + 3.77254i) q^{15} +(-0.808051 - 0.550920i) q^{16} +(1.97828 + 1.97828i) q^{17} +(5.43546 - 4.41143i) q^{18} +(2.81485 + 1.76869i) q^{19} +(8.08469 - 0.605864i) q^{20} +(2.60808 + 1.30262i) q^{21} +(-2.07445 + 2.23572i) q^{22} +(-0.414857 - 2.75239i) q^{23} +(-5.31866 - 2.41233i) q^{24} +(-0.394657 + 0.366189i) q^{25} +(4.76902 + 7.58985i) q^{26} +(3.41230 - 3.91870i) q^{27} -5.79841i q^{28} +(-5.38506 - 0.0330917i) q^{29} +(9.22196 - 2.32911i) q^{30} +(-4.01779 - 1.75294i) q^{31} +(-0.166823 - 4.45843i) q^{32} +(-1.23193 + 1.89929i) q^{33} +(0.972996 - 6.45540i) q^{34} +(2.46968 + 3.09688i) q^{35} +(-10.0054 - 2.58917i) q^{36} +(3.31464 + 9.47271i) q^{37} +(-0.579706 - 7.73563i) q^{38} +(4.45480 + 4.94210i) q^{39} +(-5.17600 - 6.01462i) q^{40} +(2.94155 + 10.9780i) q^{41} +(-1.16824 - 6.70161i) q^{42} +(-1.53830 - 3.52582i) q^{43} +(4.47439 + 0.504142i) q^{44} +(6.44659 - 2.87869i) q^{45} +(-4.59274 + 4.59274i) q^{46} +(-9.97238 + 1.88688i) q^{47} +(0.353096 + 1.65671i) q^{48} +(-3.44297 + 2.34737i) q^{49} +(1.23437 + 0.233556i) q^{50} +(-0.111388 - 4.84450i) q^{51} +(4.83481 - 12.3189i) q^{52} +(-8.87369 - 7.07653i) q^{53} +(-12.0856 - 0.976624i) q^{54} +(-2.60446 + 1.63649i) q^{55} +(-4.56629 + 3.37008i) q^{56} +(-1.40998 - 5.58273i) q^{57} +(7.39968 + 10.1563i) q^{58} +(0.0424144 + 0.0244880i) q^{59} +(-10.8514 - 8.91257i) q^{60} +(-2.71896 + 5.14453i) q^{61} +(2.27612 + 9.97231i) q^{62} +(-1.70854 - 4.75159i) q^{63} +(-9.66874 + 7.71056i) q^{64} +(2.66468 + 8.63868i) q^{65} +(5.27292 - 0.318812i) q^{66} +(-3.53635 - 5.18687i) q^{67} +(-8.52118 + 4.50358i) q^{68} +(-2.77296 + 3.94386i) q^{69} +(2.39225 - 8.92800i) q^{70} +(-10.7697 + 5.18640i) q^{71} +(3.77622 + 9.38417i) q^{72} +(0.169595 - 1.50520i) q^{73} +(13.1920 - 19.3491i) q^{74} +(0.932397 + 0.0134380i) q^{75} +(-8.68070 + 7.47034i) q^{76} +(1.02795 + 1.94498i) q^{77} +(3.10595 - 15.2119i) q^{78} +(-4.41480 - 3.79924i) q^{79} +(-0.512148 + 2.24387i) q^{80} +(-8.96198 + 0.826423i) q^{81} +(16.5352 - 20.7344i) q^{82} +(-2.49024 - 2.68384i) q^{83} +(-6.93645 + 7.26294i) q^{84} +(2.63291 - 6.03470i) q^{85} +(-4.48815 + 7.77370i) q^{86} +(6.70560 + 6.48343i) q^{87} +(-2.20353 - 3.81662i) q^{88} +(-1.07453 + 0.121070i) q^{89} +(-14.3374 - 8.11455i) q^{90} +(6.30355 - 1.43874i) q^{91} +(9.48198 + 1.42918i) q^{92} +(2.93558 + 7.00204i) q^{93} +(17.3608 + 16.1085i) q^{94} +(1.45449 - 7.68717i) q^{95} +(-5.12452 + 5.78408i) q^{96} +(12.7275 + 0.476228i) q^{97} +(9.17792 + 3.21149i) q^{98} +(3.81515 - 0.905279i) 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 $\left(\mathbb{Z}/261\mathbb{Z}\right)^\times$.

$n$	$118$	$146$
$\chi(n)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−1.38565	−	1.87749i	−0.979803	−	1.32759i	−0.944607	−	0.328205i	$-0.893556\pi$
$2$	−1.38565	−	1.87749i	−0.979803	−	1.32759i	−0.0351961	−	0.999380i	$-0.511206\pi$
$3$	−1.25257	−	1.19627i	−0.723174	−	0.690666i
$3$	−1.25257	−	1.19627i	−0.723174	−	0.690666i
$4$	−1.01543	+	3.29194i	−0.507715	+	1.64597i
$5$	−0.859785	−	2.19070i	−0.384507	−	0.979709i	−0.983815	−	0.179190i	$-0.942652\pi$
$5$	−0.859785	−	2.19070i	−0.384507	−	0.979709i	0.599307	−	0.800519i	$-0.295443\pi$
$6$	−0.510352	+	4.00930i	−0.208350	+	1.63679i
$7$	−1.60836	+	0.496115i	−0.607904	+	0.187514i	−0.583399	−	0.812186i	$-0.698277\pi$
$7$	−1.60836	+	0.496115i	−0.607904	+	0.187514i	−0.0245059	+	0.999700i	$0.507801\pi$
$8$	3.18260	−	1.11364i	1.12522	−	0.393732i
$9$	0.137883	+	2.99683i	0.0459610	+	0.998943i
$10$	−2.92165	+	4.64977i	−0.923906	+	1.47039i
$11$	−0.242992	−	1.28424i	−0.0732647	−	0.387213i	−0.999936	−	0.0113398i	$-0.996390\pi$
$11$	−0.242992	−	1.28424i	−0.0732647	−	0.387213i	0.926671	−	0.375873i	$-0.122657\pi$
$12$	5.20995	−	2.90867i	1.50398	−	0.839662i
$13$	−3.83068	−	0.287070i	−1.06244	−	0.0796189i	−0.467976	−	0.883741i	$-0.655017\pi$
$13$	−3.83068	−	0.287070i	−1.06244	−	0.0796189i	−0.594464	+	0.804122i	$0.702636\pi$
$14$	3.16008	+	2.33224i	0.844567	+	0.623319i
$15$	−1.54372	+	3.77254i	−0.398586	+	0.974066i
$16$	−0.808051	−	0.550920i	−0.202013	−	0.137730i
$17$	1.97828	+	1.97828i	0.479803	+	0.479803i	0.905069	−	0.425265i	$-0.139819\pi$
$17$	1.97828	+	1.97828i	0.479803	+	0.479803i	−0.425265	+	0.905069i	$0.639819\pi$
$18$	5.43546	−	4.41143i	1.28115	−	1.03978i
$19$	2.81485	+	1.76869i	0.645771	+	0.405765i	0.814716	−	0.579861i	$-0.196893\pi$
$19$	2.81485	+	1.76869i	0.645771	+	0.405765i	−0.168945	+	0.985626i	$0.554036\pi$
$20$	8.08469	−	0.605864i	1.80779	−	0.135475i
$21$	2.60808	+	1.30262i	0.569130	+	0.284254i
$22$	−2.07445	+	2.23572i	−0.442274	+	0.476658i
$23$	−0.414857	−	2.75239i	−0.0865036	−	0.573914i	−0.989530	−	0.144328i	$-0.953898\pi$
$23$	−0.414857	−	2.75239i	−0.0865036	−	0.573914i	0.903026	−	0.429585i	$-0.141340\pi$
$24$	−5.31866	−	2.41233i	−1.08567	−	0.492415i
$25$	−0.394657	+	0.366189i	−0.0789315	+	0.0732377i
$26$	4.76902	+	7.58985i	0.935281	+	1.48849i
$27$	3.41230	−	3.91870i	0.656698	−	0.754153i
$28$		−	5.79841i		−	1.09580i
$29$	−5.38506	−	0.0330917i	−0.999981	−	0.00614498i
$29$	−5.38506	−	0.0330917i	−0.999981	−	0.00614498i
$30$	9.22196	−	2.32911i	1.68369	−	0.425236i
$31$	−4.01779	−	1.75294i	−0.721616	−	0.314838i	0.00679655	−	0.999977i	$-0.497837\pi$
$31$	−4.01779	−	1.75294i	−0.721616	−	0.314838i	−0.728412	+	0.685139i	$0.759741\pi$
$32$	−0.166823	−	4.45843i	−0.0294904	−	0.788147i
$33$	−1.23193	+	1.89929i	−0.214452	+	0.330624i
$34$	0.972996	−	6.45540i	0.166867	−	1.10709i
$35$	2.46968	+	3.09688i	0.417453	+	0.523469i
$36$	−10.0054	−	2.58917i	−1.66757	−	0.431528i
$37$	3.31464	+	9.47271i	0.544924	+	1.55730i	0.805957	+	0.591973i	$0.201651\pi$
$37$	3.31464	+	9.47271i	0.544924	+	1.55730i	−0.261033	+	0.965330i	$0.584063\pi$
$38$	−0.579706	−	7.73563i	−0.0940407	−	1.25489i
$39$	4.45480	+	4.94210i	0.713339	+	0.791370i
$40$	−5.17600	−	6.01462i	−0.818398	−	0.950995i
$41$	2.94155	+	10.9780i	0.459394	+	1.71448i	0.674840	+	0.737964i	$0.264213\pi$
$41$	2.94155	+	10.9780i	0.459394	+	1.71448i	−0.215446	+	0.976516i	$0.569121\pi$
$42$	−1.16824	−	6.70161i	−0.180264	−	1.03408i
$43$	−1.53830	−	3.52582i	−0.234589	−	0.537683i	0.758954	−	0.651145i	$-0.225711\pi$
$43$	−1.53830	−	3.52582i	−0.234589	−	0.537683i	−0.993542	+	0.113462i	$0.963806\pi$
$44$	4.47439	+	0.504142i	0.674539	+	0.0760023i
$45$	6.44659	−	2.87869i	0.961001	−	0.429129i
$46$	−4.59274	+	4.59274i	−0.677163	+	0.677163i
$47$	−9.97238	+	1.88688i	−1.45462	+	0.275229i	−0.852312	−	0.523034i	$-0.824800\pi$
$47$	−9.97238	+	1.88688i	−1.45462	+	0.275229i	−0.602309	+	0.798263i	$0.705752\pi$
$48$	0.353096	+	1.65671i	0.0509650	+	0.239126i
$49$	−3.44297	+	2.34737i	−0.491852	+	0.335339i
$50$	1.23437	+	0.233556i	0.174567	+	0.0330298i
$51$	−0.111388	−	4.84450i	−0.0155974	−	0.678365i
$52$	4.83481	−	12.3189i	0.670467	−	1.70832i
$53$	−8.87369	−	7.07653i	−1.21889	−	0.972036i	−0.218902	−	0.975747i	$-0.570247\pi$
$53$	−8.87369	−	7.07653i	−1.21889	−	0.972036i	−0.999993	+	0.00371068i	$0.998819\pi$
$54$	−12.0856	−	0.976624i	−1.64464	−	0.132902i
$55$	−2.60446	+	1.63649i	−0.351185	+	0.220664i
$56$	−4.56629	+	3.37008i	−0.610196	+	0.450345i
$57$	−1.40998	−	5.58273i	−0.186757	−	0.739451i
$58$	7.39968	+	10.1563i	0.971626	+	1.33358i
$59$	0.0424144	+	0.0244880i	0.00552189	+	0.00318807i	0.502758	−	0.864427i	$-0.332319\pi$
$59$	0.0424144	+	0.0244880i	0.00552189	+	0.00318807i	−0.497237	+	0.867615i	$0.665652\pi$
$60$	−10.8514	−	8.91257i	−1.40092	−	1.15061i
$61$	−2.71896	+	5.14453i	−0.348127	+	0.658689i	−0.994547	−	0.104293i	$-0.966742\pi$
$61$	−2.71896	+	5.14453i	−0.348127	+	0.658689i	0.646419	+	0.762982i	$0.276266\pi$
$62$	2.27612	+	9.97231i	0.289067	+	1.26649i
$63$	−1.70854	−	4.75159i	−0.215255	−	0.598644i
$64$	−9.66874	+	7.71056i	−1.20859	+	0.963821i
$65$	2.66468	+	8.63868i	0.330513	+	1.07150i
$66$	5.27292	−	0.318812i	0.649052	−	0.0392430i
$67$	−3.53635	−	5.18687i	−0.432034	−	0.633677i	0.547058	−	0.837095i	$-0.315748\pi$
$67$	−3.53635	−	5.18687i	−0.432034	−	0.633677i	−0.979092	+	0.203417i	$0.934795\pi$
$68$	−8.52118	+	4.50358i	−1.03335	+	0.546139i
$69$	−2.77296	+	3.94386i	−0.333826	+	0.474785i
$70$	2.39225	−	8.92800i	0.285929	−	1.06710i
$71$	−10.7697	+	5.18640i	−1.27812	+	0.615512i	−0.944907	−	0.327338i	$-0.893848\pi$
$71$	−10.7697	+	5.18640i	−1.27812	+	0.615512i	−0.333217	+	0.942850i	$0.608134\pi$
$72$	3.77622	+	9.38417i	0.445032	+	1.10593i
$73$	0.169595	−	1.50520i	0.0198496	−	0.176170i	−0.979876	−	0.199609i	$-0.936033\pi$
$73$	0.169595	−	1.50520i	0.0198496	−	0.176170i	0.999725	+	0.0234387i	$0.00746145\pi$
$74$	13.1920	−	19.3491i	1.53354	−	2.24928i
$75$	0.932397	+	0.0134380i	0.107664	+	0.00155169i
$76$	−8.68070	+	7.47034i	−0.995744	+	0.856907i
$77$	1.02795	+	1.94498i	0.117146	+	0.221651i
$78$	3.10595	−	15.2119i	0.351679	−	1.72240i
$79$	−4.41480	−	3.79924i	−0.496704	−	0.427448i	0.367928	−	0.929854i	$-0.380067\pi$
$79$	−4.41480	−	3.79924i	−0.496704	−	0.427448i	−0.864632	+	0.502406i	$0.832448\pi$
$80$	−0.512148	+	2.24387i	−0.0572599	+	0.250872i
$81$	−8.96198	+	0.826423i	−0.995775	+	0.0918248i
$82$	16.5352	−	20.7344i	1.82600	−	2.28974i
$83$	−2.49024	−	2.68384i	−0.273340	−	0.294590i	0.581431	−	0.813596i	$-0.302493\pi$
$83$	−2.49024	−	2.68384i	−0.273340	−	0.294590i	−0.854771	+	0.519005i	$0.826302\pi$
$84$	−6.93645	+	7.26294i	−0.756829	+	0.792451i
$85$	2.63291	−	6.03470i	0.285580	−	0.654555i
$86$	−4.48815	+	7.77370i	−0.483969	+	0.838260i
$87$	6.70560	+	6.48343i	0.718916	+	0.695097i
$88$	−2.20353	−	3.81662i	−0.234897	−	0.406854i
$89$	−1.07453	+	0.121070i	−0.113900	+	0.0128334i	−0.168730	−	0.985662i	$-0.553967\pi$
$89$	−1.07453	+	0.121070i	−0.113900	+	0.0128334i	0.0548307	+	0.998496i	$0.482538\pi$
$90$	−14.3374	−	8.11455i	−1.51130	−	0.855349i
$91$	6.30355	−	1.43874i	0.660792	−	0.150821i
$92$	9.48198	+	1.42918i	0.988564	+	0.149002i
$93$	2.93558	+	7.00204i	0.304406	+	0.726078i
$94$	17.3608	+	16.1085i	1.79063	+	1.66146i
$95$	1.45449	−	7.68717i	0.149228	−	0.788687i
$96$	−5.12452	+	5.78408i	−0.523019	+	0.590335i
$97$	12.7275	+	0.476228i	1.29228	+	0.0483536i	0.674662	−	0.738127i	$-0.264289\pi$
$97$	12.7275	+	0.476228i	1.29228	+	0.0483536i	0.617615	+	0.786481i	$0.288099\pi$
$98$	9.17792	+	3.21149i	0.927110	+	0.324410i
$99$	3.81515	−	0.905279i	0.383437	−	0.0909840i
$100$	−0.804724	−	1.67103i	−0.0804724	−	0.167103i
$101$	11.8424	−	5.16677i	1.17836	−	0.514113i	0.282853	−	0.959163i	$-0.408719\pi$
$101$	11.8424	−	5.16677i	1.17836	−	0.514113i	0.895505	+	0.445051i	$0.146814\pi$
$102$	−8.94115	+	6.92191i	−0.885305	+	0.685371i
$103$	−0.309160	+	4.12545i	−0.0304624	+	0.406492i	0.961040	+	0.276408i	$0.0891440\pi$
$103$	−0.309160	+	4.12545i	−0.0304624	+	0.406492i	−0.991503	+	0.130085i	$0.958475\pi$
$104$	−12.5112	+	3.35238i	−1.22683	+	0.328728i
$105$	0.611245	−	6.83348i	0.0596514	−	0.666879i
$106$	−0.990282	+	26.4659i	−0.0961847	+	2.57059i
$107$	4.39231	−	9.12072i	0.424620	−	0.881733i	−0.573426	−	0.819257i	$-0.694386\pi$
$107$	4.39231	−	9.12072i	0.424620	−	0.881733i	0.998046	−	0.0624758i	$-0.0198996\pi$
$108$	9.43516	+	15.2123i	0.907899	+	1.46380i
$109$	7.21361	+	1.64646i	0.690938	+	0.157702i	0.553551	−	0.832815i	$-0.313272\pi$
$109$	7.21361	+	1.64646i	0.690938	+	0.157702i	0.137387	+	0.990517i	$0.456130\pi$
$110$	6.68137	+	2.62224i	0.637043	+	0.250021i
$111$	7.18006	−	15.8305i	0.681502	−	1.50256i
$112$	1.57296	+	0.485194i	0.148631	+	0.0458465i
$113$	−18.7710	+	0.702363i	−1.76583	+	0.0660727i	−0.900428	−	0.435005i	$-0.856747\pi$
$113$	−18.7710	+	0.702363i	−1.76583	+	0.0660727i	−0.865402	+	0.501078i	$0.832937\pi$
$114$	−8.52777	+	10.3829i	−0.798699	+	0.972451i
$115$	−5.67297	+	3.27529i	−0.529007	+	0.305422i
$116$	5.57709	−	17.6937i	0.517820	−	1.64282i
$117$	0.332114	−	11.5195i	0.0307040	−	1.06498i
$118$	−0.0127956	−	0.113564i	−0.00117793	−	0.0104545i
$119$	−4.16325	−	2.20034i	−0.381644	−	0.201705i
$120$	−0.711780	+	13.7256i	−0.0649763	+	1.25297i
$121$	8.64938	−	3.39463i	0.786307	−	0.308603i
$122$	13.4263	−	2.02369i	1.21556	−	0.183217i
$123$	9.44816	−	17.2697i	0.851912	−	1.55715i
$124$	9.85036	−	11.4463i	0.884588	−	1.02791i
$125$	−9.46006	−	4.55573i	−0.846134	−	0.407476i
$126$	−6.55362	+	9.79180i	−0.583843	+	0.872323i
$127$	0.860520	−	2.45923i	0.0763588	−	0.218221i	−0.899376	−	0.437175i	$-0.855979\pi$
$127$	0.860520	−	2.45923i	0.0763588	−	0.218221i	0.975735	+	0.218954i	$0.0702646\pi$
$128$	19.2549	+	5.15935i	1.70191	+	0.456026i
$129$	−2.29100	+	6.25657i	−0.201711	+	0.550861i
$130$	12.5267	−	16.9731i	1.09867	−	1.48864i
$131$	5.79132	−	7.84696i	0.505990	−	0.685592i	−0.474926	−	0.880026i	$-0.657525\pi$
$131$	5.79132	−	7.84696i	0.505990	−	0.685592i	0.980916	+	0.194434i	$0.0622869\pi$
$132$	−5.00141	−	5.98404i	−0.435317	−	0.520844i
$133$	−5.40478	−	1.44821i	−0.468654	−	0.125575i
$134$	−4.83815	+	13.8267i	−0.417953	+	1.19444i
$135$	−11.5185	−	4.10609i	−0.991356	−	0.353396i
$136$	8.49917	+	4.09299i	0.728798	+	0.350971i
$137$	−6.95255	+	8.07901i	−0.593996	+	0.690236i	−0.971842	−	0.235632i	$-0.924284\pi$
$137$	−6.95255	+	8.07901i	−0.593996	+	0.690236i	0.377846	+	0.925868i	$0.376665\pi$
$138$	11.2469	−	0.258596i	0.957400	−	0.0220132i
$139$	10.4197	−	1.57052i	0.883786	−	0.133209i	0.308561	−	0.951204i	$-0.400153\pi$
$139$	10.4197	−	1.57052i	0.883786	−	0.133209i	0.575225	+	0.817995i	$0.304914\pi$
$140$	−12.7025	+	4.98538i	−1.07356	+	0.421342i
$141$	14.7483	+	9.56619i	1.24204	+	0.805619i
$142$	24.6604	+	13.0334i	2.06945	+	1.09374i
$143$	0.562156	+	4.98928i	0.0470099	+	0.417224i
$144$	1.53960	−	2.49755i	0.128300	−	0.208130i
$145$	4.55750	+	11.8255i	0.378480	+	0.982053i
$146$	−3.06099	+	1.76726i	−0.253329	+	0.146260i
$147$	7.12066	+	1.17845i	0.587302	+	0.0971971i
$148$	−34.5494	+	1.29275i	−2.83994	+	0.106263i
$149$	−7.29896	−	2.25143i	−0.597954	−	0.184444i	−0.0190205	−	0.999819i	$-0.506055\pi$
$149$	−7.29896	−	2.25143i	−0.597954	−	0.184444i	−0.578934	+	0.815375i	$0.696531\pi$
$150$	−1.26675	−	1.76919i	−0.103429	−	0.144453i
$151$	−19.3503	−	7.59442i	−1.57470	−	0.618025i	−0.592453	−	0.805605i	$-0.701840\pi$
$151$	−19.3503	−	7.59442i	−1.57470	−	0.618025i	−0.982249	+	0.187580i	$0.939936\pi$
$152$	10.9282	+	2.49430i	0.886397	+	0.202314i
$153$	−5.65580	+	6.20134i	−0.457244	+	0.501349i
$154$	2.22729	−	4.62502i	0.179480	−	0.372695i
$155$	−0.385732	+	10.3089i	−0.0309827	+	0.828030i
$156$	−20.7926	+	9.64659i	−1.66474	+	0.772345i
$157$	16.8301	−	4.50960i	1.34318	−	0.359905i	0.485570	−	0.874198i	$-0.338612\pi$
$157$	16.8301	−	4.50960i	1.34318	−	0.359905i	0.857615	+	0.514293i	$0.171945\pi$
$158$	−1.01567	+	13.5532i	−0.0808023	+	1.07823i
$159$	2.64952	+	19.4792i	0.210121	+	1.54480i
$160$	−9.62363	+	4.19875i	−0.760815	+	0.331940i
$161$	2.03274	+	4.22104i	0.160203	+	0.332664i
$162$	13.9698	+	15.6809i	1.09757	+	1.23201i
$163$	−18.4979	−	6.47271i	−1.44887	−	0.506982i	−0.512713	−	0.858560i	$-0.671359\pi$
$163$	−18.4979	−	6.47271i	−1.44887	−	0.506982i	−0.936158	+	0.351578i	$0.885645\pi$
$164$	−39.1260	−	1.46399i	−3.05522	−	0.114318i
$165$	5.21996	+	1.06581i	0.406374	+	0.0829731i
$166$	−1.58828	+	8.39427i	−0.123275	+	0.651522i
$167$	2.37685	+	2.20540i	0.183926	+	0.170659i	0.766762	−	0.641931i	$-0.221867\pi$
$167$	2.37685	+	2.20540i	0.183926	+	0.170659i	−0.582836	+	0.812590i	$0.698057\pi$
$168$	9.75113	+	1.24124i	0.752316	+	0.0957638i
$169$	1.73693	+	0.261800i	0.133610	+	0.0201384i
$170$	−14.9784	+	3.41872i	−1.14879	+	0.262204i
$171$	−4.91234	+	8.67950i	−0.375656	+	0.663738i
$172$	13.1688	−	1.48377i	1.00411	−	0.113137i
$173$	0.375704	+	0.650739i	0.0285643	+	0.0494747i	0.879954	−	0.475059i	$-0.157573\pi$
$173$	0.375704	+	0.650739i	0.0285643	+	0.0494747i	−0.851390	+	0.524533i	$0.824240\pi$
$174$	2.88095	−	21.5735i	0.218405	−	1.63548i
$175$	0.453081	−	0.784760i	0.0342497	−	0.0593223i
$176$	−0.511165	+	1.17160i	−0.0385305	+	0.0883128i
$177$	−0.0238330	−	0.0814121i	−0.00179140	−	0.00611931i
$178$	1.71623	+	1.84965i	0.128637	+	0.138637i
$179$	11.3740	−	14.2625i	0.850131	−	1.06603i	−0.146909	−	0.989150i	$-0.546932\pi$
$179$	11.3740	−	14.2625i	0.850131	−	1.06603i	0.997040	−	0.0768811i	$-0.0244962\pi$
$180$	2.93041	+	24.1449i	0.218420	+	1.79965i
$181$	1.49303	−	6.54140i	0.110976	−	0.486219i	−0.888642	−	0.458601i	$-0.848351\pi$
$181$	1.49303	−	6.54140i	0.110976	−	0.486219i	0.999619	−	0.0276176i	$-0.00879209\pi$
$182$	−11.4357	−	9.84126i	−0.847674	−	0.729482i
$183$	9.55994	−	3.19129i	0.706691	−	0.235907i
$184$	−4.38550	−	8.29778i	−0.323304	−	0.611720i
$185$	17.9019	−	15.4059i	1.31618	−	1.13266i
$186$	9.07856	−	15.2139i	0.665672	−	1.11554i
$187$	2.05988	−	3.02129i	0.150634	−	0.220939i
$188$	3.91476	−	34.7445i	0.285513	−	2.53400i
$189$	−3.54411	+	7.99558i	−0.257796	+	0.581593i
$190$	−16.4480	+	7.92094i	−1.19326	+	0.574645i
$191$	−6.10725	+	22.7926i	−0.441905	+	1.64921i	0.282075	+	0.959392i	$0.408977\pi$
$191$	−6.10725	+	22.7926i	−0.441905	+	1.64921i	−0.723980	+	0.689821i	$0.757689\pi$
$192$	21.3347	+	1.90836i	1.53970	+	0.137724i
$193$	−5.15493	+	2.72446i	−0.371060	+	0.196111i	−0.642394	−	0.766374i	$-0.722059\pi$
$193$	−5.15493	+	2.72446i	−0.371060	+	0.196111i	0.271334	+	0.962485i	$0.412535\pi$
$194$	−16.7417	−	24.5555i	−1.20198	−	1.76299i
$195$	6.99647	−	14.0083i	0.501028	−	1.00315i
$196$	−4.23133	−	13.7176i	−0.302238	−	0.979831i
$197$	−16.0333	+	12.7861i	−1.14232	+	0.910973i	−0.996922	−	0.0783998i	$-0.975019\pi$
$197$	−16.0333	+	12.7861i	−1.14232	+	0.910973i	−0.145402	+	0.989373i	$0.546448\pi$
$198$	−6.98611	−	5.90850i	−0.496481	−	0.419899i
$199$	−3.99458	−	17.5014i	−0.283168	−	1.24064i	−0.893706	−	0.448653i	$-0.851904\pi$
$199$	−3.99458	−	17.5014i	−0.283168	−	1.24064i	0.610538	−	0.791987i	$-0.290953\pi$
$200$	−0.848235	+	1.60494i	−0.0599793	+	0.113486i
$201$	−1.77535	+	10.7274i	−0.125224	+	0.756650i
$202$	−26.1099	−	15.0746i	−1.83709	−	1.06064i
$203$	8.67756	−	2.61838i	0.609045	−	0.183775i
$204$	16.0609	+	4.55256i	1.12449	+	0.318743i
$205$	21.5204	−	15.8828i	1.50305	−	1.10930i
$206$	8.17387	−	5.13598i	0.569501	−	0.357841i
$207$	8.19126	−	1.62276i	0.569332	−	0.112790i
$208$	2.93724	+	2.34237i	0.203661	+	0.162414i
$209$	1.58744	−	4.04472i	0.109805	−	0.279779i
$210$	−13.6768	+	8.32121i	−0.943786	+	0.574218i
$211$	−25.6180	−	4.84718i	−1.76361	−	0.333694i	−0.799800	−	0.600267i	$-0.795061\pi$
$211$	−25.6180	−	4.84718i	−1.76361	−	0.333694i	−0.963815	+	0.266573i	$0.914109\pi$
$212$	32.3061	−	22.0259i	2.21879	−	1.51275i
$213$	19.6941	+	6.38707i	1.34942	+	0.437635i
$214$	−23.2102	+	4.39162i	−1.58662	+	0.300205i
$215$	−6.40140	+	6.40140i	−0.436572	+	0.436572i
$216$	6.49599	−	16.2717i	0.441996	−	1.10715i
$217$	7.33172	+	0.826087i	0.497710	+	0.0560784i
$218$	−6.90433	−	15.8249i	−0.467620	−	1.07180i
$219$	−2.01305	+	1.68249i	−0.136029	+	0.113692i
$220$	−2.74259	−	10.2355i	−0.184905	−	0.690075i
$221$	−7.01026	−	8.14607i	−0.471561	−	0.547964i
$222$	−39.6706	+	8.45500i	−2.66252	+	0.567462i
$223$	1.27606	+	17.0279i	0.0854515	+	1.14027i	0.860870	+	0.508824i	$0.169920\pi$
$223$	1.27606	+	17.0279i	0.0854515	+	1.14027i	−0.775419	+	0.631447i	$0.782461\pi$
$224$	2.48020	+	7.08802i	0.165716	+	0.473588i
$225$	−1.15182	−	1.13223i	−0.0767881	−	0.0754820i
$226$	27.3288	+	34.2692i	1.81788	+	2.27955i
$227$	−1.65290	+	10.9663i	−0.109707	+	0.727858i	0.864571	+	0.502510i	$0.167590\pi$
$227$	−1.65290	+	10.9663i	−0.109707	+	0.727858i	−0.974278	+	0.225348i	$0.927648\pi$
$228$	19.8098	+	1.02729i	1.31193	+	0.0680338i
$229$	−0.210341	−	5.62149i	−0.0138998	−	0.371479i	−0.988837	−	0.149000i	$-0.952395\pi$
$229$	−0.210341	−	5.62149i	−0.0138998	−	0.371479i	0.974937	−	0.222479i	$-0.0714149\pi$
$230$	14.0101	+	6.11253i	0.923797	+	0.403049i
$231$	1.03913	−	3.66593i	0.0683697	−	0.241200i
$232$	−17.1754	+	5.89171i	−1.12762	+	0.386810i
$233$		−	20.9159i		−	1.37025i	−0.728427	−	0.685123i	$-0.759748\pi$
$233$		−	20.9159i		−	1.37025i	0.728427	−	0.685123i	$-0.240252\pi$
$234$	−22.0879	+	15.3384i	−1.44393	+	1.00271i
$235$	12.7077	+	20.2241i	0.828957	+	1.31928i
$236$	−0.123682	+	0.114760i	−0.00805101	+	0.00747024i
$237$	0.984949	+	10.0401i	0.0639793	+	0.652176i
$238$	1.63769	+	10.8654i	0.106156	+	0.704296i
$239$	10.3748	−	11.1814i	0.671090	−	0.723264i	−0.302097	−	0.953277i	$-0.597687\pi$
$239$	10.3748	−	11.1814i	0.671090	−	0.723264i	0.973187	+	0.230014i	$0.0738771\pi$
$240$	3.32577	−	2.19794i	0.214678	−	0.141877i
$241$	−15.7065	+	1.17704i	−1.01174	+	0.0758197i	−0.570272	−	0.821456i	$-0.693162\pi$
$241$	−15.7065	+	1.17704i	−1.01174	+	0.0758197i	−0.441471	+	0.897275i	$0.645543\pi$
$242$	−18.3584	−	11.5353i	−1.18012	−	0.741520i
$243$	12.2142	+	9.68577i	0.783539	+	0.621343i
$244$	−14.1746	−	14.1746i	−0.907434	−	0.907434i
$245$	8.10259	+	5.52425i	0.517656	+	0.352932i
$246$	−45.5155	+	6.19092i	−2.90196	+	0.394719i
$247$	−10.2751	−	7.58334i	−0.653787	−	0.482517i
$248$	−14.7392	−	1.10455i	−0.935938	−	0.0701389i
$249$	−0.0913844	+	6.34071i	−0.00579125	+	0.401826i
$250$	4.55501	+	24.0738i	0.288084	+	1.52256i
$251$	4.32360	−	6.88097i	0.272903	−	0.434323i	−0.681951	−	0.731398i	$-0.738868\pi$
$251$	4.32360	−	6.88097i	0.272903	−	0.434323i	0.954854	+	0.297075i	$0.0960111\pi$
$252$	17.3768	−	0.799501i	1.09464	−	0.0503639i
$253$	−3.43393	+	1.20158i	−0.215889	+	0.0755430i
$254$	−5.80955	+	1.79201i	−0.364524	+	0.112441i
$255$	−10.5170	+	4.40924i	−0.658603	+	0.276117i
$256$	−7.95781	−	20.2762i	−0.497363	−	1.26726i
$257$	−4.13274	+	13.3980i	−0.257793	+	0.835744i	0.730465	+	0.682950i	$0.239303\pi$
$257$	−4.13274	+	13.3980i	−0.257793	+	0.835744i	−0.988258	+	0.152794i	$0.951173\pi$
$258$	14.9212	−	4.36810i	0.928951	−	0.271946i
$259$	−10.0307	−	13.5911i	−0.623277	−	0.844511i
$260$	−31.1438			−1.93146
$261$	−0.643338	−	16.1427i	−0.0398216	−	0.999207i
$262$	−22.7573			−1.40595
$263$	3.55388	+	4.81534i	0.219142	+	0.296927i	0.900353	−	0.435160i	$-0.143308\pi$
$263$	3.55388	+	4.81534i	0.219142	+	0.296927i	−0.681211	+	0.732087i	$0.738546\pi$
$264$	−1.80562	+	7.41662i	−0.111129	+	0.456461i
$265$	−7.87306	+	25.5238i	−0.483638	+	1.56792i
$266$	4.77014	+	12.1541i	0.292476	+	0.745217i
$267$	1.49076	+	1.13377i	0.0912328	+	0.0693858i
$268$	20.6658	−	6.37455i	1.26236	−	0.389388i
$269$	3.24155	−	1.13427i	0.197641	−	0.0691574i	−0.229644	−	0.973275i	$-0.573756\pi$
$269$	3.24155	−	1.13427i	0.197641	−	0.0691574i	0.427284	+	0.904117i	$0.359470\pi$
$270$	8.25150	+	27.3155i	0.502170	+	1.66237i
$271$	10.9634	−	17.4482i	0.665980	−	1.05990i	−0.327384	−	0.944891i	$-0.606167\pi$
$271$	10.9634	−	17.4482i	0.665980	−	1.05990i	0.993364	−	0.115010i	$-0.0366901\pi$
$272$	−0.508678	−	2.68843i	−0.0308431	−	0.163010i
$273$	−9.61679	−	5.73861i	−0.582035	−	0.347316i
$274$	24.8020	+	1.85866i	1.49835	+	0.112286i
$275$	0.566173	+	0.417855i	0.0341415	+	0.0251976i
$276$	−10.1672	−	13.1331i	−0.611993	−	0.790522i
$277$	21.2986	+	14.5211i	1.27971	+	0.872490i	0.996252	−	0.0864953i	$-0.0275668\pi$
$277$	21.2986	+	14.5211i	1.27971	+	0.872490i	0.283456	+	0.958985i	$0.408519\pi$
$278$	−17.3867	−	17.3867i	−1.04278	−	1.04278i
$279$	4.69928	−	12.2823i	0.281339	−	0.735323i
$280$	11.3088	+	7.10581i	0.675832	+	0.424654i
$281$	9.22816	−	0.691555i	0.550506	−	0.0412547i	0.203426	−	0.979090i	$-0.434792\pi$
$281$	9.22816	−	0.691555i	0.550506	−	0.0412547i	0.347080	+	0.937836i	$0.387173\pi$
$282$	−2.47563	−	40.9453i	−0.147422	−	2.43825i
$283$	−11.0664	+	11.9268i	−0.657832	+	0.708974i	−0.970558	−	0.240870i	$-0.922567\pi$
$283$	−11.0664	+	11.9268i	−0.657832	+	0.708974i	0.312726	+	0.949843i	$0.398758\pi$
$284$	−6.13748	−	40.7195i	−0.364192	−	2.41626i
$285$	−11.0178	+	7.88879i	−0.652637	+	0.467291i
$286$	8.58836	−	7.96883i	0.507840	−	0.471207i
$287$	−10.1774	−	16.1973i	−0.600756	−	0.956097i
$288$	13.3382	−	1.11468i	0.785958	−	0.0656832i
$289$		−	9.17282i		−	0.539577i
$290$	15.8871	−	24.9426i	0.932924	−	1.46468i
$291$	−15.3724	−	15.8220i	−0.901145	−	0.927500i
$292$	4.78281	+	2.08672i	0.279893	+	0.122116i
$293$	0.930764	+	24.8752i	0.0543758	+	1.45322i	0.713218	+	0.700942i	$0.247237\pi$
$293$	0.930764	+	24.8752i	0.0543758	+	1.45322i	−0.658842	+	0.752281i	$0.728953\pi$
$294$	−7.65421	−	15.0019i	−0.446403	−	0.874928i
$295$	0.0171784	−	0.113972i	0.00100017	−	0.00663568i
$296$	21.0984	+	26.4565i	1.22632	+	1.53776i
$297$	−5.86171	−	3.43001i	−0.340131	−	0.199029i
$298$	5.88677	+	16.8234i	0.341011	+	0.974554i
$299$	0.799055	+	10.6626i	0.0462105	+	0.616637i
$300$	−0.991021	+	3.05575i	−0.0572166	+	0.176424i
$301$	4.22336	+	4.90763i	0.243430	+	0.282871i
$302$	12.5543	+	46.8531i	0.722416	+	2.69609i
$303$	−21.0143	−	7.69488i	−1.20724	−	0.442059i
$304$	−1.30014	−	2.97995i	−0.0745680	−	0.170912i
$305$	13.6078	+	1.53323i	0.779181	+	0.0877926i
$306$	19.4799	+	2.02581i	1.11359	+	0.115808i
$307$	4.95541	−	4.95541i	0.282820	−	0.282820i	−0.551412	−	0.834233i	$-0.685911\pi$
$307$	4.95541	−	4.95541i	0.282820	−	0.282820i	0.834233	+	0.551412i	$0.185911\pi$
$308$	−7.44655	+	1.40896i	−0.424307	+	0.0802832i
$309$	5.32239	−	4.79759i	0.302780	−	0.272925i
$310$	19.8893	−	13.5603i	1.12964	−	0.770174i
$311$	24.0130	+	4.54351i	1.36165	+	0.257639i	0.814874	−	0.579638i	$-0.196806\pi$
$311$	24.0130	+	4.54351i	1.36165	+	0.257639i	0.546780	+	0.837277i	$0.315854\pi$
$312$	19.6816	+	10.7677i	1.11425	+	0.609601i
$313$	1.85759	−	4.73307i	0.104997	−	0.267529i	−0.868714	−	0.495314i	$-0.835053\pi$
$313$	1.85759	−	4.73307i	0.104997	−	0.267529i	0.973711	+	0.227785i	$0.0731483\pi$
$314$	−31.7873	−	25.3495i	−1.79386	−	1.43056i
$315$	−8.94031	+	7.82822i	−0.503729	+	0.441071i
$316$	16.9898	−	10.6754i	0.955751	−	0.600538i
$317$	2.78312	−	2.05404i	0.156316	−	0.115366i	−0.512854	−	0.858476i	$-0.671412\pi$
$317$	2.78312	−	2.05404i	0.156316	−	0.115366i	0.669170	+	0.743110i	$0.266650\pi$
$318$	32.9007	−	31.9658i	1.84498	−	1.79255i
$319$	1.26603	+	6.92376i	0.0708839	+	0.387656i
$320$	25.2045	+	14.5518i	1.40898	+	0.813473i
$321$	−16.4125	+	6.16999i	−0.916057	+	0.344376i
$322$	5.10828	−	9.66533i	0.284673	−	0.538628i
$323$	2.06960	+	9.06752i	0.115156	+	0.504530i
$324$	6.37972	−	30.3415i	0.354429	−	1.68564i
$325$	1.61693	−	1.28946i	0.0896911	−	0.0715263i
$326$	13.4792	+	43.6986i	0.746546	+	2.42024i
$327$	−7.06597	−	10.6917i	−0.390749	−	0.591254i
$328$	21.5874	+	31.6629i	1.19196	+	1.74829i
$329$	15.1031	−	7.98222i	0.832661	−	0.440074i
$330$	−5.23200	−	11.2773i	−0.288012	−	0.620793i
$331$	9.08957	−	33.9227i	0.499608	−	1.86456i	−0.00290946	−	0.999996i	$-0.500926\pi$
$331$	9.08957	−	33.9227i	0.499608	−	1.86456i	0.502518	−	0.864567i	$-0.332407\pi$
$332$	11.3637	−	5.47248i	0.623665	−	0.300341i
$333$	−27.9311	+	11.2395i	−1.53061	+	0.615923i
$334$	0.847122	−	7.51842i	0.0463525	−	0.411390i
$335$	−8.32236	+	12.2067i	−0.454699	+	0.666921i
$336$	−1.38983	−	2.48942i	−0.0758213	−	0.135809i
$337$	−5.08358	+	4.37478i	−0.276920	+	0.238309i	−0.779772	−	0.626063i	$-0.784665\pi$
$337$	−5.08358	+	4.37478i	−0.276920	+	0.238309i	0.502852	+	0.864373i	$0.332284\pi$
$338$	−1.91525	−	3.62382i	−0.104176	−	0.197110i
$339$	24.3523	+	21.5754i	1.32264	+	1.17182i
$340$	17.1923	+	14.7952i	0.932386	+	0.802383i
$341$	−1.27491	+	5.58575i	−0.0690404	+	0.302486i
$342$	23.1024	−	2.80389i	1.24924	−	0.151617i
$343$	11.7189	−	14.6951i	0.632763	−	0.793459i
$344$	−8.82230	−	9.50818i	−0.475667	−	0.512647i
$345$	11.0239	+	2.68385i	0.593509	+	0.144494i
$346$	0.701160	−	1.60708i	0.0376946	−	0.0863970i
$347$	3.15915	−	5.47181i	0.169592	−	0.293742i	−0.768684	−	0.639628i	$-0.779088\pi$
$347$	3.15915	−	5.47181i	0.169592	−	0.293742i	0.938276	+	0.345886i	$0.112422\pi$
$348$	−28.1521	+	15.4910i	−1.50911	+	0.830404i
$349$	−4.78605	−	8.28968i	−0.256191	−	0.443736i	0.709027	−	0.705181i	$-0.249134\pi$
$349$	−4.78605	−	8.28968i	−0.256191	−	0.443736i	−0.965218	+	0.261445i	$0.915801\pi$
$350$	−2.10119	+	0.236747i	−0.112313	+	0.0126547i
$351$	−14.1964	+	14.0317i	−0.757748	+	0.748957i
$352$	−5.68516	+	1.29760i	−0.303020	+	0.0691624i
$353$	−3.69581	−	0.557054i	−0.196708	−	0.0296490i	0.0499491	−	0.998752i	$-0.484094\pi$
$353$	−3.69581	−	0.557054i	−0.196708	−	0.0296490i	−0.246657	+	0.969103i	$0.579332\pi$
$354$	−0.119826	+	0.157555i	−0.00636869	+	0.00837395i
$355$	20.6214	+	19.1339i	1.09447	+	1.01552i
$356$	0.692550	−	3.66022i	0.0367051	−	0.193991i
$357$	2.58258	+	7.73645i	0.136684	+	0.409456i
$358$	−42.5381	−	1.59166i	−2.24821	−	0.0841220i
$359$	11.8233	+	4.13714i	0.624009	+	0.218350i	0.623717	−	0.781650i	$-0.285622\pi$
$359$	11.8233	+	4.13714i	0.624009	+	0.218350i	0.000291213		1.00000i	$0.499907\pi$
$360$	17.3111	−	16.3409i	0.912376	−	0.861242i
$361$	−3.44866	−	7.16122i	−0.181509	−	0.376907i
$362$	−14.3502	+	6.26094i	−0.754231	+	0.329068i
$363$	−14.8949	−	6.09496i	−0.781778	−	0.319902i
$364$	−1.66455	+	22.2119i	−0.0872461	+	1.16422i
$365$	−3.44324	+	0.922615i	−0.180228	+	0.0482919i
$366$	−19.2383	−	13.5267i	−1.00560	−	0.707050i
$367$	0.491400	−	13.1329i	0.0256509	−	0.685534i	−0.925851	−	0.377890i	$-0.876650\pi$
$367$	0.491400	−	13.1329i	0.0256509	−	0.685534i	0.951502	−	0.307644i	$-0.0995406\pi$
$368$	−1.18112	+	2.45263i	−0.0615703	+	0.127852i
$369$	−32.4937	+	10.3290i	−1.69155	+	0.537707i
$370$	−53.7302	−	12.2636i	−2.79330	−	0.637552i
$371$	17.7829	+	6.97927i	0.923242	+	0.362346i
$372$	−26.0312	+	2.55369i	−1.34965	+	0.132403i
$373$	−32.0490	−	9.88580i	−1.65943	−	0.511867i	−0.683502	−	0.729949i	$-0.739544\pi$
$373$	−32.0490	−	9.88580i	−1.65943	−	0.511867i	−0.975931	+	0.218081i	$0.930020\pi$
$374$	−8.52672	+	0.319047i	−0.440906	+	0.0164976i
$375$	6.39956	+	17.0232i	0.330472	+	0.879072i
$376$	−29.6368	+	17.1108i	−1.52840	+	0.882423i
$377$	20.6190	+	1.67265i	1.06193	+	0.0861461i
$378$	19.9225	−	4.42506i	1.02470	−	0.227601i
$379$	3.11951	+	27.6864i	0.160239	+	1.42216i	0.774260	+	0.632868i	$0.218122\pi$
$379$	3.11951	+	27.6864i	0.160239	+	1.42216i	−0.614021	+	0.789289i	$0.710449\pi$
$380$	23.8288	+	12.5939i	1.22239	+	0.646052i
$381$	−4.01976	+	2.05095i	−0.205939	+	0.105073i
$382$	51.2553	−	20.1162i	2.62245	−	1.02924i
$383$	−6.22952	+	0.938949i	−0.318314	+	0.0479781i	−0.306256	−	0.951949i	$-0.599076\pi$
$383$	−6.22952	+	0.938949i	−0.318314	+	0.0479781i	−0.0120578	+	0.999927i	$0.503838\pi$
$384$	−17.9463	−	29.4965i	−0.915817	−	1.50524i
$385$	3.37703	−	3.92418i	0.172110	−	0.199995i
$386$	12.2581	+	5.90318i	0.623920	+	0.300464i
$387$	10.3542	−	5.09618i	0.526333	−	0.259053i
$388$	−14.4915	+	41.4144i	−0.735697	+	2.10250i
$389$	−4.51113	−	1.20875i	−0.228724	−	0.0612863i	0.142637	−	0.989775i	$-0.454442\pi$
$389$	−4.51113	−	1.20875i	−0.228724	−	0.0612863i	−0.371360	+	0.928489i	$0.621109\pi$
$390$	−35.9950	+	6.27474i	−1.82268	+	0.317734i
$391$	4.62430	−	6.26571i	0.233861	−	0.316871i
$392$	−8.34346	+	11.3050i	−0.421409	+	0.570988i
$393$	−16.6411	+	2.90092i	−0.839434	+	0.146332i
$394$	46.2223	+	12.3852i	2.32865	+	0.623959i
$395$	−4.52721	+	12.9380i	−0.227788	+	0.650982i
$396$	−0.893887	+	13.4785i	−0.0449195	+	0.677319i
$397$	−26.3027	−	12.6667i	−1.32009	−	0.635723i	−0.364718	−	0.931118i	$-0.618834\pi$
$397$	−26.3027	−	12.6667i	−1.32009	−	0.635723i	−0.955375	+	0.295395i	$0.904549\pi$
$398$	−27.3236	+	31.7506i	−1.36961	+	1.59151i
$399$	5.03744	+	8.27955i	0.252187	+	0.414496i
$400$	0.520644	−	0.0784745i	0.0260322	−	0.00392372i
$401$	−18.7900	+	7.37451i	−0.938326	+	0.368266i	−0.784709	−	0.619865i	$-0.787187\pi$
$401$	−18.7900	+	7.37451i	−0.938326	+	0.368266i	−0.153617	+	0.988130i	$0.549092\pi$
$402$	22.6005	−	11.5312i	1.12721	−	0.575123i
$403$	14.8876	+	7.86835i	0.741607	+	0.391950i
$404$	4.98362	+	44.2308i	0.247944	+	2.20057i
$405$	9.51581	+	18.9224i	0.472844	+	0.940262i
$406$	−16.9400	−	12.6639i	−0.840721	−	0.628497i
$407$	11.3598	−	6.55859i	0.563085	−	0.325097i
$408$	−5.74953	−	15.2941i	−0.284644	−	0.757169i
$409$	12.3158	−	0.460823i	0.608975	−	0.0227862i	0.268874	−	0.963175i	$-0.413348\pi$
$409$	12.3158	−	0.460823i	0.608975	−	0.0227862i	0.340101	+	0.940389i	$0.389539\pi$
$410$	−59.6395	−	18.3964i	−2.94539	−	0.908531i
$411$	18.3732	−	1.80244i	0.906285	−	0.0889078i
$412$	−13.2668	−	5.20684i	−0.653608	−	0.256522i
$413$	−0.0803667	−	0.0183432i	−0.00395459	−	0.000902609i
$414$	−14.3969	−	13.1304i	−0.707571	−	0.645325i
$415$	−3.73841	+	7.76289i	−0.183511	+	0.381065i
$416$	−0.640837	+	17.1267i	−0.0314196	+	0.839707i
$417$	−14.9302	−	10.4976i	−0.731134	−	0.514068i
$418$	−9.79356	+	2.62418i	−0.479018	+	0.128353i
$419$	−2.64028	+	35.2321i	−0.128986	+	1.72120i	0.439276	+	0.898352i	$0.355235\pi$
$419$	−2.64028	+	35.2321i	−0.128986	+	1.72120i	−0.568262	+	0.822848i	$0.692384\pi$
$420$	21.8747	+	8.95110i	1.06738	+	0.436769i
$421$	−0.0737881	+	0.0321934i	−0.00359621	+	0.00156901i	−0.401689	−	0.915776i	$-0.631577\pi$
$421$	−0.0737881	+	0.0321934i	−0.00359621	+	0.00156901i	0.398093	+	0.917345i	$0.369672\pi$
$422$	26.3970	+	54.8140i	1.28499	+	2.66830i
$423$	−7.02966	−	29.6253i	−0.341794	−	1.44043i
$424$	−36.1221	−	12.6397i	−1.75425	−	0.613837i
$425$	−1.50517	−	0.0563194i	−0.0730113	−	0.00273189i
$426$	−15.2975	−	45.8257i	−0.741167	−	2.22026i
$427$	1.82081	−	9.62319i	0.0881150	−	0.465699i
$428$	25.5648	+	23.7207i	1.23572	+	1.14658i
$429$	5.26437	−	6.92193i	0.254166	−	0.334194i
$430$	20.8886	+	3.14846i	1.00734	+	0.151832i
$431$	−0.724552	+	0.165374i	−0.0349004	+	0.00796580i	−0.239936	−	0.970789i	$-0.577126\pi$
$431$	−0.724552	+	0.165374i	−0.0349004	+	0.00796580i	0.205035	+	0.978755i	$0.434269\pi$
$432$	−4.91621	+	1.28660i	−0.236531	+	0.0619016i
$433$	−12.4102	+	1.39830i	−0.596398	+	0.0671980i	−0.405003	−	0.914315i	$-0.632730\pi$
$433$	−12.4102	+	1.39830i	−0.596398	+	0.0671980i	−0.191395	+	0.981513i	$0.561301\pi$
$434$	−8.60823	−	14.9099i	−0.413208	−	0.715698i
$435$	8.43785	−	20.2643i	0.404564	−	0.971598i
$436$	−12.7450	+	22.0749i	−0.610372	+	1.05720i
$437$	3.70037	−	8.48133i	0.177013	−	0.405717i
$438$	5.94824	+	1.44814i	0.284218	+	0.0691948i
$439$	−22.3111	−	24.0457i	−1.06485	−	1.14764i	−0.988602	−	0.150550i	$-0.951896\pi$
$439$	−22.3111	−	24.0457i	−1.06485	−	1.14764i	−0.0762503	−	0.997089i	$-0.524295\pi$
$440$	−6.46650	+	8.10874i	−0.308278	+	0.386569i
$441$	−7.50941	−	9.99432i	−0.357591	−	0.475920i
$442$	−5.58039	+	24.4493i	−0.265432	+	1.16293i
$443$	−4.46776	−	3.84481i	−0.212269	−	0.182673i	0.539726	−	0.841841i	$-0.318528\pi$
$443$	−4.46776	−	3.84481i	−0.212269	−	0.182673i	−0.751996	+	0.659168i	$0.770909\pi$
$444$	44.8221	+	39.7111i	2.12716	+	1.88460i
$445$	1.18909	+	2.24987i	0.0563682	+	0.106654i
$446$	30.2015	−	25.9905i	1.43008	−	1.23068i
$447$	6.44917	+	11.5516i	0.305035	+	0.546372i
$448$	11.7255	−	17.1982i	0.553979	−	0.812538i
$449$	−1.91729	+	17.0164i	−0.0904825	+	0.803055i	0.863736	+	0.503944i	$0.168118\pi$
$449$	−1.91729	+	17.0164i	−0.0904825	+	0.803055i	−0.954219	+	0.299110i	$0.903310\pi$
$450$	−0.529728	+	3.73141i	−0.0249716	+	0.175900i
$451$	13.3837	−	6.44523i	0.630212	−	0.303494i
$452$	16.7485	−	62.5063i	0.787784	−	2.94005i
$453$	15.1527	+	32.6607i	0.711935	+	1.53453i
$454$	22.8794	−	12.0921i	1.07378	−	0.567512i
$455$	−8.57155	−	12.5722i	−0.401840	−	0.589392i
$456$	−10.7046	−	16.1974i	−0.501288	−	0.758513i
$457$	−0.849114	−	2.75276i	−0.0397199	−	0.128769i	0.933541	−	0.358470i	$-0.116701\pi$
$457$	−0.849114	−	2.75276i	−0.0397199	−	0.128769i	−0.973261	+	0.229701i	$0.926225\pi$
$458$	−10.2628	+	8.18434i	−0.479551	+	0.382429i
$459$	14.5028	−	1.00178i	0.676931	−	0.0467592i
$460$	−5.02156	−	22.0009i	−0.234132	−	1.02580i
$461$	10.3836	−	19.6467i	0.483612	−	0.915038i	−0.514723	−	0.857356i	$-0.672105\pi$
$461$	10.3836	−	19.6467i	0.483612	−	0.915038i	0.998335	−	0.0576818i	$-0.0183709\pi$
$462$	−8.32261	+	3.12874i	−0.387203	+	0.145562i
$463$	16.4210	+	9.48066i	0.763148	+	0.440604i	0.830425	−	0.557131i	$-0.188098\pi$
$463$	16.4210	+	9.48066i	0.763148	+	0.440604i	−0.0672769	+	0.997734i	$0.521431\pi$
$464$	4.33318	+	2.99348i	0.201163	+	0.138969i
$465$	12.8154	−	12.4512i	0.594298	−	0.577411i
$466$	−39.2694	+	28.9821i	−1.81912	+	1.34257i
$467$	−5.50558	+	3.45939i	−0.254768	+	0.160081i	−0.653361	−	0.757047i	$-0.726642\pi$
$467$	−5.50558	+	3.45939i	−0.254768	+	0.160081i	0.398593	+	0.917128i	$0.369499\pi$
$468$	37.5842	+	12.7905i	1.73733	+	0.591242i
$469$	8.26102	+	6.58795i	0.381459	+	0.304203i
$470$	20.3622	−	51.8821i	0.939239	−	2.39314i
$471$	−26.4756	−	14.4847i	−1.21993	−	0.667418i
$472$	0.162259	+	0.0307011i	0.00746858	+	0.00141313i
$473$	−4.15421	+	2.83229i	−0.191011	+	0.130229i
$474$	17.4854	−	15.7613i	0.803132	−	0.723942i
$475$	−1.75857	+	0.332740i	−0.0806890	+	0.0152672i
$476$	11.4709	−	11.4709i	0.525767	−	0.525767i
$477$	19.9836	−	27.5687i	0.914987	−	1.26228i
$478$	−35.3688	−	3.98510i	−1.61773	−	0.182274i
$479$	2.99951	+	6.87496i	0.137051	+	0.314125i	0.971531	−	0.236914i	$-0.0761361\pi$
$479$	2.99951	+	6.87496i	0.137051	+	0.314125i	−0.834479	+	0.551039i	$0.814231\pi$
$480$	17.0771	+	6.25321i	0.779461	+	0.285419i
$481$	−9.97802	−	37.2385i	−0.454958	−	1.69793i
$482$	23.9736	+	27.8578i	1.09197	+	1.26889i
$483$	2.50333	−	7.71887i	0.113905	−	0.351221i
$484$	2.39209	+	31.9203i	0.108731	+	1.45092i
$485$	−9.89960	−	28.2914i	−0.449518	−	1.28465i
$486$	1.26038	−	36.3531i	0.0571721	−	1.64901i
$487$	17.3852	+	21.8003i	0.787797	+	0.987866i	0.999944	+	0.0106282i	$0.00338311\pi$
$487$	17.3852	+	21.8003i	0.787797	+	0.987866i	−0.212147	+	0.977238i	$0.568045\pi$
$488$	−2.92422	+	19.4009i	−0.132373	+	0.878239i
$489$	15.4269	+	30.2361i	0.697631	+	1.36732i
$490$	−0.855631	−	22.8672i	−0.0386535	−	1.03304i
$491$	−12.7909	−	5.58062i	−0.577246	−	0.251850i	0.0909247	−	0.995858i	$-0.471018\pi$
$491$	−12.7909	−	5.58062i	−0.577246	−	0.251850i	−0.668171	+	0.744008i	$0.732922\pi$
$492$	47.2568	+	48.6389i	2.13050	+	2.19281i
$493$	−10.5877	−	10.7186i	−0.476846	−	0.482743i
$494$			29.7992i			1.34073i
$495$	−5.26340	−	7.57948i	−0.236572	−	0.340672i
$496$	2.28085	+	3.62995i	0.102413	+	0.162989i
$497$	14.7485	−	13.6846i	0.661560	−	0.613838i
$498$	12.0312	−	8.61444i	0.539133	−	0.386022i
$499$	1.57227	+	10.4313i	0.0703846	+	0.466971i	0.996062	+	0.0886577i	$0.0282577\pi$
$499$	1.57227	+	10.4313i	0.0703846	+	0.466971i	−0.925678	+	0.378313i	$0.876504\pi$
$500$	24.6032	−	26.5159i	1.10029	−	1.18583i
$501$	−0.338936	−	5.60577i	−0.0151426	−	0.250447i
$502$	−18.9099	+	1.41710i	−0.843992	+	0.0632485i
$503$	−1.03102	−	0.647834i	−0.0459710	−	0.0288855i	0.508851	−	0.860855i	$-0.330071\pi$
$503$	−1.03102	−	0.647834i	−0.0459710	−	0.0288855i	−0.554822	+	0.831969i	$0.687213\pi$
$504$	−10.7292	−	13.2197i	−0.477915	−	0.588853i
$505$	−21.5007	−	21.5007i	−0.956768	−	0.956768i
$506$	7.01419	+	4.78219i	0.311819	+	0.212594i
$507$	−1.86245	−	2.40575i	−0.0827141	−	0.106843i
$508$	7.22183	+	5.32995i	0.320417	+	0.236478i
$509$	−16.9433	−	1.26972i	−0.750997	−	0.0562795i	−0.306269	−	0.951945i	$-0.599081\pi$
$509$	−16.9433	−	1.26972i	−0.750997	−	0.0562795i	−0.444728	+	0.895666i	$0.646700\pi$
$510$	22.8512	+	13.6360i	1.01187	+	0.603811i
$511$	0.473980	+	2.50504i	0.0209676	+	0.110817i
$512$	−5.83029	+	9.27886i	−0.257665	+	0.410071i
$513$	16.5361	−	4.99524i	0.730086	−	0.220545i
$514$	30.8811	−	10.8058i	1.36211	−	0.476622i
$515$	9.30341	−	2.86972i	0.409957	−	0.126455i
$516$	−18.2699	−	13.8949i	−0.804289	−	0.611690i
$517$	4.84641	+	12.3484i	0.213145	+	0.543084i
$518$	−11.6181	+	37.6651i	−0.510471	+	1.65491i
$519$	0.307861	−	1.26454i	0.0135136	−	0.0555072i
$520$	18.1010	+	24.5260i	0.793782	+	1.07554i
$521$	−31.1681			−1.36550			−0.682749	−	0.730653i	$-0.739216\pi$
$521$	−31.1681			−1.36550			−0.682749	+	0.730653i	$0.739216\pi$
$522$	−29.4163	+	23.5760i	−1.28752	+	1.03189i
$523$	−17.5458			−0.767226			−0.383613	−	0.923494i	$-0.625320\pi$
$523$	−17.5458			−0.767226			−0.383613	+	0.923494i	$0.625320\pi$
$524$	19.9511	+	27.0327i	0.871566	+	1.18093i
$525$	−1.50630	+	0.440963i	−0.0657404	+	0.0192452i
$526$	4.11631	−	13.3448i	0.179480	−	0.581859i
$527$	−4.48049	−	11.4161i	−0.195173	−	0.497294i
$528$	2.04182	−	0.856028i	0.0888589	−	0.0372538i
$529$	14.5746	−	4.49567i	0.633679	−	0.195464i
$530$	58.8300	−	20.5855i	2.55541	−	0.894178i
$531$	−0.0675381	+	0.130485i	−0.00293090	+	0.00566258i
$532$	10.2556	−	16.3217i	0.444636	−	0.707633i
$533$	−8.11670	−	42.8978i	−0.351573	−	1.85811i
$534$	0.0629803	−	4.36989i	0.00272542	−	0.189104i
$535$	−23.7571	−	1.78035i	−1.02711	−	0.0769713i
$536$	−17.0311	−	12.5695i	−0.735632	−	0.542921i
$537$	−31.3086	+	4.25853i	−1.35106	+	0.183769i
$538$	−6.62122	−	4.51427i	−0.285461	−	0.194624i
$539$	3.85121	+	3.85121i	0.165883	+	0.165883i
$540$	25.2132	−	33.7488i	1.08500	−	1.45232i
$541$	22.4738	+	14.1213i	0.966226	+	0.607120i	0.920045	−	0.391813i	$-0.128152\pi$
$541$	22.4738	+	14.1213i	0.966226	+	0.607120i	0.0461812	+	0.998933i	$0.485295\pi$
$542$	−47.9502	+	3.59337i	−2.05964	+	0.154349i
$543$	−9.69541	+	6.40752i	−0.416070	+	0.274973i
$544$	8.49000	−	9.15005i	0.364006	−	0.392305i
$545$	−2.59526	−	17.2184i	−0.111169	−	0.737556i
$546$	2.55133	+	26.0071i	0.109187	+	1.11300i
$547$	−11.6750	+	10.8328i	−0.499186	+	0.463177i	−0.889126	−	0.457663i	$-0.848686\pi$
$547$	−11.6750	+	10.8328i	−0.499186	+	0.463177i	0.389939	+	0.920841i	$0.372496\pi$
$548$	−19.5358	−	31.0910i	−0.834528	−	1.32814i
$549$	−15.7922	−	7.43892i	−0.673993	−	0.317486i
$550$		−	1.64198i		−	0.0700144i
$551$	−15.0996	−	9.61764i	−0.643265	−	0.409725i
$552$	−4.43320	+	15.6398i	−0.188690	+	0.665675i
$553$	8.98546	+	3.92032i	0.382101	+	0.166709i
$554$	−2.24912	−	60.1091i	−0.0955561	−	2.55379i
$555$	−40.8530	−	2.11854i	−1.73412	−	0.0899271i
$556$	−5.41041	+	35.8957i	−0.229453	+	1.52232i
$557$	−16.0211	−	20.0899i	−0.678837	−	0.851235i	0.316409	−	0.948623i	$-0.397523\pi$
$557$	−16.0211	−	20.0899i	−0.678837	−	0.851235i	−0.995247	+	0.0973878i	$0.968951\pi$
$558$	−29.5715	+	8.19614i	−1.25186	+	0.346970i
$559$	4.88058	+	13.9479i	0.206427	+	0.589934i
$560$	−0.289495	−	3.86304i	−0.0122334	−	0.163243i
$561$	−6.19443	+	1.32022i	−0.261529	+	0.0557397i
$562$	−14.0854	−	16.3675i	−0.594156	−	0.690422i
$563$	1.05075	+	3.92147i	0.0442840	+	0.165270i	0.984527	−	0.175235i	$-0.0560686\pi$
$563$	1.05075	+	3.92147i	0.0442840	+	0.165270i	−0.940243	+	0.340505i	$0.889402\pi$
$564$	−46.4672	+	38.8369i	−1.95662	+	1.63533i
$565$	17.6777	+	40.5177i	0.743707	+	1.70459i
$566$	37.7266	+	4.25077i	1.58577	+	0.178673i
$567$	14.0041	−	5.77536i	0.588118	−	0.242542i
$568$	−28.4998	+	28.4998i	−1.19582	+	1.19582i
$569$	44.5823	−	8.43543i	1.86899	−	0.353632i	0.877054	−	0.480391i	$-0.159505\pi$
$569$	44.5823	−	8.43543i	1.86899	−	0.353632i	0.991933	+	0.126760i	$0.0404578\pi$
$570$	30.0779	+	9.75466i	1.25982	+	0.408578i
$571$	18.7706	−	12.7976i	0.785526	−	0.535563i	−0.102840	−	0.994698i	$-0.532793\pi$
$571$	18.7706	−	12.7976i	0.785526	−	0.535563i	0.888366	+	0.459135i	$0.151841\pi$
$572$	−16.9952	−	3.21567i	−0.710606	−	0.134454i
$573$	34.9158	−	21.2435i	1.45863	−	0.887459i
$574$	−16.3079	+	41.5519i	−0.680679	+	1.73434i
$575$	1.17162	+	0.934337i	0.0488600	+	0.0389645i
$576$	−24.4404	−	27.9124i	−1.01835	−	1.16302i
$577$	−18.1390	+	11.3975i	−0.755136	+	0.474484i	−0.853777	−	0.520640i	$-0.825694\pi$
$577$	−18.1390	+	11.3975i	−0.755136	+	0.474484i	0.0986403	+	0.995123i	$0.468551\pi$
$578$	−17.2219	+	12.7103i	−0.716335	+	0.528679i
$579$	9.71612	+	2.75409i	0.403788	+	0.114456i
$580$	−43.5566	+	2.99508i	−1.80859	+	0.124364i
$581$	5.33671	+	3.08115i	0.221404	+	0.127828i
$582$	−8.40482	+	50.7852i	−0.348391	+	2.10511i
$583$	−6.93174	+	13.1155i	−0.287083	+	0.543188i
$584$	−1.13650	−	4.97931i	−0.0470285	−	0.206046i
$585$	−25.5212	+	9.17672i	−1.05517	+	0.379411i
$586$	45.4132	−	36.2158i	1.87600	−	1.49606i
$587$	4.51122	+	14.6250i	0.186198	+	0.603638i	0.999755	+	0.0221529i	$0.00705207\pi$
$587$	4.51122	+	14.6250i	0.186198	+	0.603638i	−0.813557	+	0.581485i	$0.802472\pi$
$588$	−11.1099	+	22.2442i	−0.458166	+	0.917334i
$589$	−8.20906	−	12.0405i	−0.338248	−	0.496119i
$590$	−0.237784	+	0.125672i	−0.00978940	+	0.00517385i
$591$	35.3785	+	3.16456i	1.45528	+	0.130172i
$592$	2.54030	−	9.48054i	0.104406	−	0.389648i
$593$	14.7013	−	7.07979i	0.603712	−	0.290732i	−0.106952	−	0.994264i	$-0.534109\pi$
$593$	14.7013	−	7.07979i	0.603712	−	0.290732i	0.710664	+	0.703532i	$0.248395\pi$
$594$	1.68247	+	15.7581i	0.0690326	+	0.646563i
$595$	−1.24078	+	11.0122i	−0.0508670	+	0.451457i
$596$	14.8232	−	21.7416i	0.607180	−	0.890570i
$597$	−15.9329	+	26.7004i	−0.652088	+	1.09277i
$598$	18.9118	−	16.2749i	0.773361	−	0.665531i
$599$	4.27140	+	8.08188i	0.174525	+	0.330217i	0.955824	−	0.293940i	$-0.0949666\pi$
$599$	4.27140	+	8.08188i	0.174525	+	0.330217i	−0.781299	+	0.624157i	$0.785443\pi$
$600$	2.98242	−	0.995588i	0.121757	−	0.0406447i
$601$	22.0191	+	18.9490i	0.898178	+	0.772945i	0.974558	−	0.224134i	$-0.0719553\pi$
$601$	22.0191	+	18.9490i	0.898178	+	0.772945i	−0.0763802	+	0.997079i	$0.524336\pi$
$602$	3.36193	−	14.7296i	0.137022	−	0.600333i
$603$	15.0566	−	11.3130i	0.613151	−	0.460702i
$604$	44.6492	−	55.9883i	1.81675	−	2.27813i
$605$	−14.8732	−	16.0295i	−0.604682	−	0.651692i
$606$	14.6714	+	50.1165i	0.595984	+	2.03584i
$607$	−3.76363	+	8.62633i	−0.152761	+	0.350132i	−0.976068	−	0.217464i	$-0.930222\pi$
$607$	−3.76363	+	8.62633i	−0.152761	+	0.350132i	0.823307	+	0.567596i	$0.192126\pi$
$608$	7.41599	−	12.8449i	0.300758	−	0.520928i
$609$	−14.0016	−	7.10097i	−0.567372	−	0.287746i
$610$	−15.9770	−	27.6731i	−0.646892	−	1.12045i
$611$	38.7427	−	4.36525i	1.56736	−	0.176599i
$612$	−14.6714	−	24.9156i	−0.593055	−	1.00715i
$613$	29.2534	−	6.67690i	1.18153	−	0.269677i	0.413753	−	0.910389i	$-0.364218\pi$
$613$	29.2534	−	6.67690i	1.18153	−	0.269677i	0.767782	+	0.640712i	$0.221361\pi$
$614$	−16.1702	−	2.43727i	−0.652576	−	0.0983601i
$615$	−45.9560	−	5.84983i	−1.85312	−	0.235888i
$616$	5.43756	+	5.04532i	0.219086	+	0.203282i
$617$	2.18228	−	11.5336i	0.0878553	−	0.464326i	−0.910817	−	0.412811i	$-0.864547\pi$
$617$	2.18228	−	11.5336i	0.0878553	−	0.464326i	0.998672	−	0.0515158i	$-0.0164052\pi$
$618$	−16.3824	−	3.34495i	−0.658996	−	0.134553i
$619$	−13.8594	−	0.518582i	−0.557056	−	0.0208436i	−0.242619	−	0.970122i	$-0.578006\pi$
$619$	−13.8594	−	0.518582i	−0.557056	−	0.0208436i	−0.314438	+	0.949278i	$0.601816\pi$
$620$	−33.5446	−	11.7378i	−1.34718	−	0.471400i
$621$	−12.2014	−	7.76631i	−0.489626	−	0.311651i
$622$	−24.7433	−	51.3799i	−0.992114	−	2.06015i
$623$	1.66817	−	0.727813i	0.0668336	−	0.0291592i
$624$	−0.877005	−	6.44771i	−0.0351083	−	0.258115i
$625$	−2.04776	+	27.3254i	−0.0819103	+	1.09302i
$626$	−11.4603	+	3.07077i	−0.458044	+	0.122733i
$627$	−6.82696	+	3.16731i	−0.272642	+	0.126490i
$628$	−2.24440	+	59.9827i	−0.0895611	+	2.39357i
$629$	−12.1824	+	25.2970i	−0.485743	+	1.00866i
$630$	27.0855	+	5.93815i	1.07911	+	0.236581i
$631$	−38.5453	−	8.79772i	−1.53447	−	0.350232i	−0.629937	−	0.776646i	$-0.716919\pi$
$631$	−38.5453	−	8.79772i	−1.53447	−	0.350232i	−0.904528	+	0.426414i	$0.859777\pi$
$632$	−18.2815	−	7.17498i	−0.727201	−	0.285405i
$633$	26.2899	+	36.7174i	1.04493	+	1.45939i
$634$	−7.71287	−	2.37911i	−0.306317	−	0.0944863i
$635$	−6.12728	+	0.229266i	−0.243154	+	0.00909816i
$636$	−66.8148	−	11.0577i	−2.64938	−	0.438466i
$637$	13.8628	−	8.00368i	0.549263	−	0.317117i
$638$	11.2450	−	11.9709i	0.445194	−	0.473931i
$639$	−17.0277	−	31.5597i	−0.673606	−	1.24848i
$640$	−5.25255	−	46.6176i	−0.207625	−	1.84272i
$641$	−31.2867	−	16.5355i	−1.23575	−	0.653112i	−0.283657	−	0.958926i	$-0.591548\pi$
$641$	−31.2867	−	16.5355i	−1.23575	−	0.653112i	−0.952091	+	0.305813i	$0.901072\pi$
$642$	34.3261	+	22.2649i	1.35474	+	0.878724i
$643$	−25.6240	+	10.0567i	−1.01051	+	0.396596i	−0.812097	−	0.583522i	$-0.801674\pi$
$643$	−25.6240	+	10.0567i	−1.01051	+	0.396596i	−0.198414	+	0.980118i	$0.563579\pi$
$644$	−15.9595	+	2.40551i	−0.628893	+	0.0947903i
$645$	15.6760	−	0.360433i	0.617242	−	0.0141920i
$646$	14.1564	−	16.4501i	0.556977	−	0.647219i
$647$	5.32845	+	2.56604i	0.209483	+	0.100882i	0.535683	−	0.844419i	$-0.320054\pi$
$647$	5.32845	+	2.56604i	0.209483	+	0.100882i	−0.326200	+	0.945301i	$0.605768\pi$
$648$	−27.6021	+	12.6106i	−1.08431	+	0.495391i
$649$	0.0211421	−	0.0604207i	0.000829901	−	0.00237172i
$650$	−4.66144	−	1.24903i	−0.182837	−	0.0489910i
$651$	−8.19530	−	9.80544i	−0.321199	−	0.384306i
$652$	40.0911	−	54.3216i	1.57009	−	2.12740i
$653$	14.4752	−	19.6132i	0.566458	−	0.767523i	−0.423952	−	0.905685i	$-0.639357\pi$
$653$	14.4752	−	19.6132i	0.566458	−	0.767523i	0.990410	+	0.138162i	$0.0441193\pi$
$654$	−10.2826	+	28.0813i	−0.402083	+	1.09806i
$655$	−22.1696	−	5.94032i	−0.866238	−	0.232108i
$656$	3.67109	−	10.4914i	0.143332	−	0.409619i
$657$	4.53421	+	0.300706i	0.176896	+	0.0117317i
$658$	−35.9142	−	17.2953i	−1.40008	−	0.674243i
$659$	2.39685	−	2.78519i	0.0933679	−	0.108496i	−0.709344	−	0.704862i	$-0.751009\pi$
$659$	2.39685	−	2.78519i	0.0933679	−	0.108496i	0.802712	+	0.596367i	$0.203390\pi$
$660$	−8.80908	+	16.1016i	−0.342893	+	0.626752i
$661$	−22.3903	+	3.37479i	−0.870882	+	0.131264i	−0.569254	−	0.822162i	$-0.692768\pi$
$661$	−22.3903	+	3.37479i	−0.870882	+	0.131264i	−0.301627	+	0.953426i	$0.597530\pi$
$662$	−76.2846	+	29.9395i	−2.96488	+	1.16363i
$663$	−0.964019	+	18.5897i	−0.0374394	+	0.721964i
$664$	−10.9143	−	5.76837i	−0.423557	−	0.223856i
$665$	1.47437	+	13.0854i	0.0571735	+	0.507429i
$666$	59.8048	+	36.8662i	2.31739	+	1.42854i
$667$	2.14295	+	14.8355i	0.0829753	+	0.574435i
$668$	−9.67356	+	5.58503i	−0.374281	+	0.216091i
$669$	18.7716	−	22.8552i	0.725750	−	0.883633i
$670$	34.4498	−	1.28902i	1.33091	−	0.0497991i
$671$	7.26750	+	2.24173i	0.280559	+	0.0865409i
$672$	5.37253	−	11.8453i	0.207250	−	0.456941i
$673$	3.65184	+	1.43324i	0.140768	+	0.0552474i	0.434679	−	0.900585i	$-0.356862\pi$
$673$	3.65184	+	1.43324i	0.140768	+	0.0552474i	−0.293911	+	0.955833i	$0.594957\pi$
$674$	15.2577	+	3.48246i	0.587703	+	0.134139i
$675$	0.0882902	+	2.79609i	0.00339829	+	0.107622i
$676$	−2.62555	+	5.45202i	−0.100983	+	0.209693i
$677$	−0.00126227	+	0.0337348i	−4.85129e−5	+	0.00129653i	−0.999325	−	0.0367429i	$-0.988302\pi$
$677$	−0.00126227	+	0.0337348i	−4.85129e−5	+	0.00129653i	0.999276	+	0.0380395i	$0.0121113\pi$
$678$	6.76385	−	75.6172i	0.259764	−	2.90406i
$679$	−20.7066	+	5.54833i	−0.794648	+	0.212925i
$680$	1.65903	−	22.1382i	0.0636208	−	0.848961i
$681$	15.1890	−	11.7588i	0.582044	−	0.450597i
$682$	12.2538	−	5.34627i	0.469221	−	0.204719i
$683$	−1.35821	−	2.82036i	−0.0519706	−	0.107918i	0.873366	−	0.487064i	$-0.161932\pi$
$683$	−1.35821	−	2.82036i	−0.0519706	−	0.107918i	−0.925337	+	0.379146i	$0.876218\pi$
$684$	−23.5843	−	24.9845i	−0.901767	−	0.955308i
$685$	23.6763	+	8.28471i	0.904626	+	0.316542i
$686$	−43.8282	−	1.63993i	−1.67337	−	0.0626130i
$687$	−6.46135	+	7.29296i	−0.246516	+	0.278244i
$688$	−0.699421	+	3.69653i	−0.0266652	+	0.140929i
$689$	31.9608	+	29.6553i	1.21761	+	1.12978i
$690$	−10.2364	−	24.4162i	−0.389694	−	0.929509i
$691$	17.4549	+	2.63090i	0.664016	+	0.100084i	0.472398	−	0.881385i	$-0.343388\pi$
$691$	17.4549	+	2.63090i	0.664016	+	0.100084i	0.191618	+	0.981470i	$0.438627\pi$
$692$	−2.52369	+	0.576017i	−0.0959365	+	0.0218969i
$693$	−5.68702	+	3.34877i	−0.216032	+	0.127209i
$694$	−14.6507	+	1.65074i	−0.556134	+	0.0626613i
$695$	−12.3992	−	21.4761i	−0.470329	−	0.814633i
$696$	28.5615	+	13.1666i	1.08262	+	0.499077i
$697$	−15.8984	+	27.5368i	−0.602195	+	1.04303i
$698$	−8.93200	+	20.4724i	−0.338081	+	0.774890i
$699$	−25.0210	+	26.1987i	−0.946383	+	0.990926i
$700$	2.12331	+	2.28838i	0.0802536	+	0.0864928i
$701$	2.79354	−	3.50299i	0.105510	−	0.132306i	−0.726273	−	0.687407i	$-0.758749\pi$
$701$	2.79354	−	3.50299i	0.105510	−	0.132306i	0.831783	+	0.555101i	$0.187320\pi$
$702$	46.0156	+	7.21054i	1.73675	+	0.272144i
$703$	−7.42403	+	32.5268i	−0.280003	+	1.22677i
$704$	12.2516	+	10.5434i	0.461751	+	0.397369i
$705$	8.27621	−	40.5340i	0.311700	−	1.52660i
$706$	4.07524	+	7.71072i	0.153374	+	0.290197i
$707$	−16.4835	+	14.1852i	−0.619926	+	0.533490i
$708$	0.292205	+	0.00421135i	0.0109817	+	0.000158272i
$709$	−27.8628	+	40.8673i	−1.04641	+	1.53480i	−0.216995	+	0.976173i	$0.569625\pi$
$709$	−27.8628	+	40.8673i	−1.04641	+	1.53480i	−0.829417	+	0.558631i	$0.811327\pi$
$710$	7.34958	−	65.2293i	0.275825	−	2.44801i
$711$	10.7770	−	13.7543i	0.404167	−	0.515825i
$712$	−3.28496	+	1.58196i	−0.123109	+	0.0592863i
$713$	−3.15798	+	11.7857i	−0.118267	+	0.441380i
$714$	10.9466	−	15.5688i	0.409665	−	0.582647i
$715$	10.4467	−	5.52122i	0.390683	−	0.206482i
$716$	35.4019	+	51.9251i	1.32303	+	1.94053i
$717$	−26.3712	+	1.59445i	−0.984849	+	0.0595459i
$718$	−8.61548	−	27.9307i	−0.321527	−	1.04236i
$719$	−32.1313	+	25.6239i	−1.19830	+	0.955610i	−0.999701	−	0.0244717i	$-0.992210\pi$
$719$	−32.1313	+	25.6239i	−1.19830	+	0.955610i	−0.198596	+	0.980081i	$0.563638\pi$
$720$	−6.79510	−	1.22543i	−0.253239	−	0.0456691i
$721$	−1.54945	−	6.78860i	−0.0577047	−	0.252821i
$722$	−8.66648	+	16.3978i	−0.322533	+	0.610262i
$723$	21.0816	+	17.3148i	0.784033	+	0.643946i
$724$	20.0178	+	11.5573i	0.743957	+	0.429524i
$725$	2.13737	−	1.95889i	0.0793800	−	0.0727513i
$726$	9.19588	+	36.4105i	0.341291	+	1.35132i
$727$	20.5002	−	15.1298i	0.760310	−	0.561134i	−0.143204	−	0.989693i	$-0.545741\pi$
$727$	20.5002	−	15.1298i	0.760310	−	0.561134i	0.903514	+	0.428559i	$0.140979\pi$
$728$	18.4595	−	11.5988i	0.684153	−	0.429882i
$729$	−3.71235	−	26.7436i	−0.137495	−	0.990503i
$730$	6.50333	+	5.18623i	0.240699	+	0.191951i
$731$	3.93187	−	10.0183i	0.145426	−	0.370538i
$732$	0.798104	+	34.7113i	0.0294988	+	1.28297i
$733$	43.0217	+	8.14014i	1.58904	+	0.300663i	0.903899	−	0.427746i	$-0.140692\pi$
$733$	43.0217	+	8.14014i	1.58904	+	0.300663i	0.685142	+	0.728409i	$0.259740\pi$
$734$	−25.3379	+	17.2751i	−0.935237	+	0.637634i
$735$	−3.54060	−	16.6124i	−0.130597	−	0.612758i
$736$	−12.2022	+	2.30877i	−0.449777	+	0.0851025i
$737$	−5.80189	+	5.80189i	−0.213715	+	0.213715i
$738$	64.4175	+	46.6942i	2.37124	+	1.71884i
$739$	7.63712	+	0.860496i	0.280936	+	0.0316539i	0.251308	−	0.967907i	$-0.419139\pi$
$739$	7.63712	+	0.860496i	0.280936	+	0.0316539i	0.0296277	+	0.999561i	$0.490568\pi$
$740$	32.5370	+	74.5757i	1.19609	+	2.74146i
$741$	3.79856	+	21.7904i	0.139544	+	0.800492i
$742$	−11.5374	−	43.0580i	−0.423550	−	1.58071i
$743$	−25.0504	−	29.1091i	−0.919010	−	1.06791i	−0.997477	−	0.0709919i	$-0.977384\pi$
$743$	−25.0504	−	29.1091i	−0.919010	−	1.06791i	0.0784672	−	0.996917i	$-0.474997\pi$
$744$	17.1406	+	19.0155i	0.628403	+	0.697143i
$745$	1.34333	+	17.9255i	0.0492159	+	0.656741i
$746$	25.8482	+	73.8698i	0.946369	+	2.70457i
$747$	7.69966	−	7.83289i	0.281716	−	0.286591i
$748$	7.85425	+	9.84892i	0.287180	+	0.360112i
$749$	−2.53951	+	16.8485i	−0.0927915	+	0.615631i
$750$	23.0933	−	35.6032i	0.843246	−	1.30005i
$751$	−0.322301	−	8.61366i	−0.0117609	−	0.314317i	−0.992746	−	0.120233i	$-0.961636\pi$
$751$	−0.322301	−	8.61366i	−0.0117609	−	0.314317i	0.980985	−	0.194084i	$-0.0621736\pi$
$752$	9.09771	+	3.96929i	0.331759	+	0.144745i
$753$	−13.6471	+	3.44674i	−0.497329	+	0.125606i
$754$	−25.4303	−	41.0296i	−0.926117	−	1.49421i
$755$			48.9201i			1.78039i
$756$	−22.7222	−	19.7859i	−0.826398	−	0.719608i
$757$	4.88050	+	7.76727i	0.177385	+	0.282306i	0.923568	−	0.383434i	$-0.125259\pi$
$757$	4.88050	+	7.76727i	0.177385	+	0.282306i	−0.746183	+	0.665740i	$0.768116\pi$
$758$	47.6584	−	44.2206i	1.73103	−	1.60616i
$759$	5.73867	+	2.60283i	0.208301	+	0.0944768i
$760$	−3.93168	−	26.0850i	−0.142617	−	0.946202i
$761$	13.4170	−	14.4600i	0.486364	−	0.524176i	−0.441416	−	0.897302i	$-0.645524\pi$
$761$	13.4170	−	14.4600i	0.486364	−	0.524176i	0.927781	+	0.373126i	$0.121714\pi$
$762$	9.42061	+	4.70516i	0.341273	+	0.170450i
$763$	−12.4189	+	0.930671i	−0.449596	+	0.0336925i
$764$	−68.8304	−	43.2490i	−2.49019	−	1.56469i
$765$	18.4480	+	7.05831i	0.666989	+	0.255194i
$766$	10.3948	+	10.3948i	0.375579	+	0.375579i
$767$	−0.155447	−	0.105982i	−0.00561285	−	0.00382678i
$768$	−14.2880	+	34.9171i	−0.515574	+	1.25996i
$769$	20.6468	+	15.2381i	0.744544	+	0.549499i	0.898708	−	0.438547i	$-0.144507\pi$
$769$	20.6468	+	15.2381i	0.744544	+	0.549499i	−0.154164	+	0.988045i	$0.549269\pi$
$770$	−12.0470	−	0.902798i	−0.434144	−	0.0325346i
$771$	21.2042	−	11.8381i	0.763649	−	0.426340i
$772$	−3.73430	−	19.7362i	−0.134400	−	0.710322i
$773$	15.8305	−	25.1941i	0.569383	−	0.906167i	−0.430611	−	0.902538i	$-0.641702\pi$
$773$	15.8305	−	25.1941i	0.569383	−	0.906167i	0.999993	−	0.00362949i	$-0.00115530\pi$
$774$	−23.9153	−	12.3784i	−0.859617	−	0.444931i
$775$	2.22756	−	0.779456i	0.0800162	−	0.0279989i
$776$	41.0368	−	12.6582i	1.47313	−	0.454402i
$777$	−3.69443	+	29.0233i	−0.132537	+	1.04120i
$778$	3.98143	+	10.1445i	0.142741	+	0.363699i
$779$	−11.1367	+	36.1042i	−0.399013	+	1.29357i
$780$	39.0099	+	37.2564i	1.39678	+	1.33399i
$781$	9.27752	+	12.5706i	0.331976	+	0.449811i
$782$	−18.1715			−0.649810
$783$	−18.5052	+	20.9895i	−0.661320	+	0.750104i
$784$	4.07531			0.145547
$785$	−24.3494	−	32.9922i	−0.869067	−	1.17754i
$786$	28.5052	+	27.2239i	1.01675	+	0.971044i
$787$	−3.92090	+	12.7112i	−0.139765	+	0.453107i	−0.998210	−	0.0597980i	$-0.980954\pi$
$787$	−3.92090	+	12.7112i	−0.139765	+	0.453107i	0.858446	+	0.512905i	$0.171431\pi$
$788$	−25.8105	−	65.7640i	−0.919460	−	2.34275i
$789$	1.30894	−	10.2830i	0.0465995	−	0.366084i
$790$	30.5641	−	9.42778i	1.08742	−	0.335425i
$791$	29.8422	−	10.4422i	1.06107	−	0.371283i
$792$	11.1339	−	7.12985i	0.395627	−	0.253348i
$793$	11.8923	−	18.9265i	0.422309	−	0.672101i
$794$	12.6647	+	66.9346i	0.449454	+	2.37542i
$795$	40.3950	−	22.5522i	1.43266	−	0.799844i
$796$	61.6697	+	4.62151i	2.18583	+	0.163805i
$797$	18.8188	+	13.8889i	0.666595	+	0.491970i	0.873773	−	0.486334i	$-0.161666\pi$
$797$	18.8188	+	13.8889i	0.666595	+	0.491970i	−0.207178	+	0.978303i	$0.566428\pi$
$798$	8.56463	−	20.9303i	0.303185	−	0.740924i
$799$	−23.4609	−	15.9954i	−0.829988	−	0.565876i
$800$	1.69846	+	1.69846i	0.0600498	+	0.0600498i
$801$	−0.510985	−	3.20348i	−0.0180548	−	0.113189i
$802$	39.8819	+	25.0594i	1.40828	+	0.884880i
$803$	−1.97425	+	0.147949i	−0.0696697	+	0.00522102i
$804$	−33.5111	−	16.7372i	−1.18185	−	0.590277i
$805$	7.49928	−	8.08230i	0.264315	−	0.284864i
$806$	−5.85633	−	38.8542i	−0.206280	−	1.36858i
$807$	−5.41716	−	2.45701i	−0.190693	−	0.0864908i
$808$	31.9356	−	29.6319i	1.12349	−	1.04245i
$809$	−7.24272	−	11.5267i	−0.254640	−	0.405258i	0.694801	−	0.719202i	$-0.255492\pi$
$809$	−7.24272	−	11.5267i	−0.254640	−	0.405258i	−0.949442	+	0.313944i	$0.898350\pi$
$810$	22.3410	−	44.0857i	0.784984	−	1.54901i
$811$			28.8853i			1.01430i	0.861857	+	0.507151i	$0.169301\pi$
$811$			28.8853i			1.01430i	−0.861857	+	0.507151i	$0.830699\pi$
$812$	−0.191879	+	31.2248i	−0.00673364	+	1.09578i
$813$	−34.6052	+	8.73995i	−1.21366	+	0.306523i
$814$	−28.0544	−	12.2400i	−0.983306	−	0.429012i
$815$	1.72451	+	46.0885i	0.0604070	+	1.61441i
$816$	−2.57892	+	3.97597i	−0.0902804	+	0.139187i
$817$	1.90599	−	12.6454i	0.0666823	−	0.442408i
$818$	−17.9305	−	22.4842i	−0.626926	−	0.786140i
$819$	5.18083	+	18.6923i	0.181033	+	0.653162i
$820$	30.4327	+	86.9718i	1.06276	+	3.03719i
$821$	−0.145373	−	1.93987i	−0.00507356	−	0.0677019i	0.994092	−	0.108538i	$-0.0346169\pi$
$821$	−0.145373	−	1.93987i	−0.00507356	−	0.0677019i	−0.999166	+	0.0408361i	$0.986998\pi$
$822$	−28.8429	−	31.9980i	−1.00601	−	1.11606i
$823$	17.3811	+	20.1972i	0.605867	+	0.704030i	0.974206	−	0.225662i	$-0.0724543\pi$
$823$	17.3811	+	20.1972i	0.605867	+	0.704030i	−0.368339	+	0.929692i	$0.620073\pi$
$824$	3.61034	+	13.4740i	0.125772	+	0.469387i
$825$	−0.209307	−	1.20069i	−0.00728714	−	0.0418026i
$826$	0.0769210	+	0.176305i	0.00267643	+	0.00613443i
$827$	−14.3371	−	1.61540i	−0.498548	−	0.0561729i	−0.140890	−	0.990025i	$-0.544996\pi$
$827$	−14.3371	−	1.61540i	−0.498548	−	0.0561729i	−0.357659	+	0.933852i	$0.616425\pi$
$828$	−2.97560	+	28.6129i	−0.103409	+	0.994368i
$829$	6.48996	−	6.48996i	0.225406	−	0.225406i	−0.585365	−	0.810770i	$-0.699049\pi$
$829$	6.48996	−	6.48996i	0.225406	−	0.225406i	0.810770	+	0.585365i	$0.199049\pi$
$830$	19.7549	−	3.73782i	0.685702	−	0.129742i
$831$	−9.30688	−	43.6676i	−0.322852	−	1.51481i
$832$	39.2514	−	26.7611i	1.36080	−	0.927775i
$833$	−11.4549	−	2.16739i	−0.396889	−	0.0750955i
$834$	0.978962	+	42.5772i	0.0338987	+	1.47433i
$835$	2.78777	−	7.10312i	0.0964748	−	0.245814i
$836$	11.7031	+	9.33288i	0.404759	+	0.322784i
$837$	−20.5792	+	9.76291i	−0.711320	+	0.337455i
$838$	69.8064	−	43.8622i	2.41142	−	1.51520i
$839$	−6.80315	+	5.02095i	−0.234871	+	0.173343i	−0.704897	−	0.709310i	$-0.749007\pi$
$839$	−6.80315	+	5.02095i	−0.234871	+	0.173343i	0.470026	+	0.882653i	$0.344245\pi$
$840$	−5.66469	−	22.4290i	−0.195450	−	0.773873i
$841$	28.9978	+	0.356402i	0.999924	+	0.0122897i
$842$	0.162687	+	0.0939276i	0.00560658	+	0.00323696i
$843$	−12.3862	−	10.1731i	−0.426605	−	0.350381i
$844$	41.9699	−	79.4109i	1.44466	−	2.73344i
$845$	−0.919860	−	4.03017i	−0.0316441	−	0.138642i
$846$	−45.8806	+	54.2485i	−1.57741	+	1.86510i
$847$	−12.2272	+	9.75089i	−0.420132	+	0.335044i
$848$	3.27179	+	10.6069i	0.112354	+	0.364242i
$849$	28.1292	−	1.70075i	0.965391	−	0.0583695i
$850$	1.97990	+	2.90397i	0.0679098	+	0.0996054i
$851$	24.6975	−	13.0530i	0.846620	−	0.447452i
$852$	−41.0238	+	58.3463i	−1.40545	+	1.99891i
$853$	0.123128	−	0.459519i	0.00421581	−	0.0157336i	−0.963786	−	0.266677i	$-0.914074\pi$
$853$	0.123128	−	0.459519i	0.00421581	−	0.0157336i	0.968002	+	0.250944i	$0.0807409\pi$
$854$	−20.5904	+	9.91583i	−0.704590	+	0.339313i
$855$	23.2377	+	3.29893i	0.794712	+	0.112821i
$856$	3.82176	−	33.9191i	0.130625	−	1.15933i
$857$	6.43626	−	9.44025i	0.219858	−	0.322473i	−0.700425	−	0.713726i	$-0.747006\pi$
$857$	6.43626	−	9.44025i	0.219858	−	0.322473i	0.920283	+	0.391253i	$0.127958\pi$
$858$	−20.2904	−	0.292432i	−0.692704	−	0.00998347i
$859$	−11.7350	+	10.0987i	−0.400391	+	0.344565i	−0.829320	−	0.558774i	$-0.811272\pi$
$859$	−11.7350	+	10.0987i	−0.400391	+	0.344565i	0.428929	+	0.903338i	$0.358891\pi$
$860$	−14.5729	−	27.5732i	−0.496930	−	0.940238i
$861$	−6.62833	+	32.4633i	−0.225893	+	1.10635i
$862$	1.31446	+	1.13119i	0.0447708	+	0.0385284i
$863$	−4.86782	+	21.3273i	−0.165702	+	0.725990i	0.821980	+	0.569517i	$0.192870\pi$
$863$	−4.86782	+	21.3273i	−0.165702	+	0.725990i	−0.987682	+	0.156473i	$0.949988\pi$
$864$	−18.0405	−	14.5598i	−0.613750	−	0.495334i
$865$	1.10255	−	1.38255i	0.0374877	−	0.0470081i
$866$	19.8216	+	21.3626i	0.673564	+	0.725929i
$867$	−10.9732	+	11.4896i	−0.372668	+	0.390208i
$868$	−10.1643	+	23.2968i	−0.344998	+	0.790744i
$869$	−3.80638	+	6.59285i	−0.129123	+	0.223647i
$870$	−49.7379	+	12.2372i	−1.68627	+	0.414881i
$871$	12.0576	+	20.8845i	0.408558	+	0.707643i
$872$	24.7916	−	2.79334i	0.839550	−	0.0945946i
$873$	0.327725	+	38.2077i	0.0110918	+	1.29313i
$874$	−21.0510	+	4.80476i	−0.712061	+	0.162523i
$875$	17.4754	+	2.63399i	0.590776	+	0.0890451i
$876$	−3.49455	−	8.33529i	−0.118070	−	0.281624i
$877$	−33.4615	−	31.0477i	−1.12991	−	1.04841i	−0.998369	−	0.0570957i	$-0.981816\pi$
$877$	−33.4615	−	31.0477i	−1.12991	−	1.04841i	−0.131544	−	0.991310i	$-0.541994\pi$
$878$	−14.2301	+	75.2078i	−0.480242	+	2.53814i
$879$	28.5915	−	32.2714i	0.964369	−	1.08849i
$880$	3.00611	+	0.112481i	0.101336	+	0.00379173i
$881$	20.5310	+	7.18410i	0.691707	+	0.242039i	0.653162	−	0.757218i	$-0.273442\pi$
$881$	20.5310	+	7.18410i	0.691707	+	0.242039i	0.0385447	+	0.999257i	$0.487728\pi$
$882$	−8.35882	+	27.9475i	−0.281456	+	0.941040i
$883$	0.902933	+	1.87496i	0.0303861	+	0.0630974i	0.915609	−	0.402069i	$-0.131709\pi$
$883$	0.902933	+	1.87496i	0.0303861	+	0.0630974i	−0.885223	+	0.465166i	$0.845995\pi$
$884$	33.9348	−	14.8056i	1.14135	−	0.497966i
$885$	−0.157858	+	0.122208i	−0.00530633	+	0.00410797i
$886$	−1.02785	+	13.7157i	−0.0345314	+	0.460789i
$887$	−38.3136	+	10.2661i	−1.28645	+	0.344702i	−0.836309	−	0.548258i	$-0.815291\pi$
$887$	−38.3136	+	10.2661i	−1.28645	+	0.344702i	−0.450136	+	0.892960i	$0.648625\pi$
$888$	5.22184	−	58.3781i	0.175233	−	1.95904i
$889$	−0.163972	+	4.38225i	−0.00549945	+	0.146976i
$890$	2.57644	−	5.35003i	0.0863624	−	0.179333i
$891$	3.23901	+	11.3085i	0.108511	+	0.378850i
$892$	−57.3505	−	13.0899i	−1.92024	−	0.438282i
$893$	−31.4080	−	12.3267i	−1.05103	−	0.412499i
$894$	12.7517	−	28.1147i	0.426481	−	0.940297i
$895$	−41.0240	−	12.6542i	−1.37128	−	0.422984i
$896$	−33.5286	+	1.25455i	−1.12011	+	0.0419116i
$897$	11.7545	−	14.3116i	0.392472	−	0.477852i
$898$	34.6048	−	19.9791i	1.15478	−	0.666712i
$899$	21.5780	+	9.57266i	0.719667	+	0.319266i
$900$	4.89683	−	2.64203i	0.163228	−	0.0880676i
$901$	−3.55528	−	31.5540i	−0.118444	−	1.05122i
$902$	−30.6459	−	16.1968i	−1.02040	−	0.539296i
$903$	0.580777	−	11.1994i	0.0193270	−	0.372694i
$904$	−58.9586	+	23.1395i	−1.96093	+	0.769610i
$905$	−15.6139	+	2.35342i	−0.519024	+	0.0782302i
$906$	40.3238	−	73.7053i	1.33967	−	2.44869i
$907$	27.3055	−	31.7296i	0.906665	−	1.05356i	−0.0916643	−	0.995790i	$-0.529219\pi$
$907$	27.3055	−	31.7296i	0.906665	−	1.05356i	0.998330	−	0.0577743i	$-0.0184004\pi$
$908$	−34.4220	−	16.5767i	−1.14233	−	0.550119i
$909$	17.1168	+	34.7771i	0.567728	+	1.15348i
$910$	−11.7269	+	33.5136i	−0.388743	+	1.11096i
$911$	−40.9059	−	10.9607i	−1.35527	−	0.363144i	−0.493194	−	0.869919i	$-0.664171\pi$
$911$	−40.9059	−	10.9607i	−1.35527	−	0.363144i	−0.862078	+	0.506775i	$0.830837\pi$
$912$	−1.93630	+	5.28792i	−0.0641173	+	0.175101i
$913$	−2.84159	+	3.85022i	−0.0940431	+	0.127424i
$914$	−3.99170	+	5.40856i	−0.132034	+	0.178899i
$915$	−15.2106	−	18.1991i	−0.502848	−	0.601643i
$916$	18.7192	+	5.01580i	0.618500	+	0.165727i
$917$	−5.42156	+	15.4939i	−0.179036	+	0.511655i
$918$	−21.9766	−	25.8407i	−0.725336	−	0.852869i
$919$	8.05077	+	3.87705i	0.265570	+	0.127892i	0.561931	−	0.827184i	$-0.310059\pi$
$919$	8.05077	+	3.87705i	0.265570	+	0.127892i	−0.296361	+	0.955076i	$0.595773\pi$
$920$	−14.4073	+	16.7416i	−0.474995	+	0.551954i
$921$	−12.1350	+	0.279016i	−0.399863	+	0.00919390i
$922$	−51.2745	+	7.72839i	−1.68864	+	0.254521i
$923$	42.7440	−	16.7758i	1.40694	−	0.552182i
$924$	11.0129	+	7.14325i	0.362296	+	0.234996i
$925$	−4.77695	−	2.52469i	−0.157065	−	0.0830113i
$926$	−4.95390	−	43.9671i	−0.162795	−	1.44485i
$927$	−12.4059	−	0.357670i	−0.407463	−	0.0117474i
$928$	0.750814	+	24.0145i	0.0246467	+	0.788313i
$929$	21.7779	−	12.5735i	0.714510	−	0.412522i	−0.0982188	−	0.995165i	$-0.531315\pi$
$929$	21.7779	−	12.5735i	0.714510	−	0.412522i	0.812729	+	0.582642i	$0.197981\pi$
$930$	−41.1346	−	6.80768i	−1.34886	−	0.223233i
$931$	−13.8432	+	0.517976i	−0.453693	+	0.0169760i
$932$	68.8539	+	21.2386i	2.25539	+	0.695694i
$933$	−24.6428	−	34.4171i	−0.806770	−	1.12677i
$934$	14.1238	+	5.54317i	0.462144	+	0.181378i
$935$	−8.38979	−	1.91491i	−0.274375	−	0.0626244i
$936$	−11.7716	−	37.0318i	−0.384766	−	1.21042i
$937$	0.0247294	−	0.0513511i	0.000807873	−	0.00167757i	−0.900565	−	0.434722i	$-0.856847\pi$
$937$	0.0247294	−	0.0513511i	0.000807873	−	0.00167757i	0.901372	+	0.433045i	$0.142561\pi$
$938$	0.921910	−	24.6386i	0.0301014	−	0.804478i
$939$	−7.98879	+	3.70634i	−0.260704	+	0.120952i
$940$	−79.4804	+	21.2967i	−2.59236	+	0.694622i
$941$	2.98261	−	39.8002i	0.0972305	−	1.29745i	−0.708730	−	0.705480i	$-0.750731\pi$
$941$	2.98261	−	39.8002i	0.0972305	−	1.29745i	0.805960	−	0.591970i	$-0.201650\pi$
$942$	9.49110	+	69.7783i	0.309237	+	2.27350i
$943$	28.9955	−	12.6506i	0.944225	−	0.411961i
$944$	−0.0207821	−	0.0431545i	−0.000676401	−	0.00140456i
$945$	20.5631	+	0.889577i	0.668916	+	0.0289379i
$946$	11.0739	+	3.87492i	0.360043	+	0.125985i
$947$	−14.5457	−	0.544261i	−0.472671	−	0.0176861i	−0.200005	−	0.979795i	$-0.564096\pi$
$947$	−14.5457	−	0.544261i	−0.472671	−	0.0176861i	−0.272666	+	0.962109i	$0.587905\pi$
$948$	−34.0516	−	6.95264i	−1.10595	−	0.225811i
$949$	−1.08176	+	5.71725i	−0.0351155	+	0.185590i
$950$	3.06149	+	2.84064i	0.0993277	+	0.0921627i
$951$	−5.94325	−	0.756528i	−0.192723	−	0.0245321i
$952$	−15.7004	−	2.36645i	−0.508851	−	0.0766970i
$953$	26.3332	−	6.01039i	0.853017	−	0.194696i	0.226411	−	0.974032i	$-0.427301\pi$
$953$	26.3332	−	6.01039i	0.853017	−	0.194696i	0.626606	+	0.779336i	$0.284444\pi$
$954$	−79.4502	+	0.681481i	−2.57229	+	0.0220638i
$955$	55.1825	−	6.21758i	1.78566	−	0.201196i
$956$	26.2736	+	45.5072i	0.849748	+	1.47181i
$957$	6.69688	−	10.1870i	0.216480	−	0.329300i
$958$	8.75139	−	15.1578i	0.282744	−	0.489728i
$959$	7.17411	−	16.4432i	0.231664	−	0.530980i
$960$	−14.1626	−	48.3787i	−0.457097	−	1.56141i
$961$	−8.01556	−	8.63872i	−0.258566	−	0.278668i
$962$	−56.0888	+	70.3331i	−1.80838	+	2.26763i
$963$	27.9389	+	11.9054i	0.900317	+	0.383646i
$964$	12.0741	−	52.9000i	0.388880	−	1.70380i
$965$	10.4006	+	8.95043i	0.334807	+	0.288125i
$966$	−17.9608	+	5.99567i	−0.577880	+	0.192908i
$967$	10.7604	+	20.3597i	0.346031	+	0.654723i	0.994292	−	0.106696i	$-0.0340271\pi$
$967$	10.7604	+	20.3597i	0.346031	+	0.654723i	−0.648261	+	0.761418i	$0.724503\pi$
$968$	23.7471	−	20.4361i	0.763262	−	0.656840i
$969$	8.25486	−	13.8335i	0.265184	−	0.444397i
$970$	−39.3995	+	57.7884i	−1.26504	+	1.85547i
$971$	2.74782	−	24.3876i	0.0881818	−	0.782635i	−0.869328	−	0.494235i	$-0.835448\pi$
$971$	2.74782	−	24.3876i	0.0881818	−	0.782635i	0.957510	−	0.288400i	$-0.0931232\pi$
$972$	−44.2876	+	30.3731i	−1.42053	+	0.974217i
$973$	−15.9795	+	7.69532i	−0.512279	+	0.246701i
$974$	16.8401	−	62.8480i	0.539591	−	2.01378i
$975$	−3.56786	−	0.319140i	−0.114263	−	0.0102207i
$976$	5.03129	−	2.65911i	0.161048	−	0.0851161i
$977$	0.945524	+	1.38683i	0.0302500	+	0.0443686i	0.841066	−	0.540933i	$-0.181929\pi$
$977$	0.945524	+	1.38683i	0.0302500	+	0.0443686i	−0.810816	+	0.585301i	$0.800976\pi$
$978$	35.3915	−	70.8605i	1.13170	−	2.26587i
$979$	0.416584	+	1.35053i	0.0133141	+	0.0431632i
$980$	−26.4131	+	21.0638i	−0.843736	+	0.672857i
$981$	−3.93952	+	21.8450i	−0.125779	+	0.697456i
$982$	7.24618	+	31.7476i	0.231235	+	1.01311i
$983$	−8.11419	+	15.3528i	−0.258802	+	0.489678i	−0.978939	−	0.204155i	$-0.934555\pi$
$983$	−8.11419	+	15.3528i	−0.258802	+	0.489678i	0.720136	+	0.693833i	$0.244079\pi$
$984$	10.8375	−	65.4844i	0.345487	−	2.08757i
$985$	41.7956	+	24.1307i	1.33172	+	0.768869i
$986$	−5.45326	+	34.7306i	−0.173667	+	1.10605i
$987$	−28.4666	−	8.06904i	−0.906103	−	0.256840i
$988$	35.3975	−	26.1246i	1.12615	−	0.831133i
$989$	−9.06628	+	5.69672i	−0.288291	+	0.181145i
$990$	−6.93717	+	20.3845i	−0.220478	+	0.647861i
$991$	7.46784	+	5.95540i	0.237224	+	0.189180i	0.734885	−	0.678192i	$-0.237236\pi$
$991$	7.46784	+	5.95540i	0.237224	+	0.189180i	−0.497661	+	0.867372i	$0.665808\pi$
$992$	−7.14511	+	18.2054i	−0.226858	+	0.578024i
$993$	−51.9661	+	31.6172i	−1.64909	+	1.00334i
$994$	−46.1289	−	8.72807i	−1.46312	−	0.276837i
$995$	−34.9057	+	23.7983i	−1.10659	+	0.754458i
$996$	−20.7805	−	6.73938i	−0.658454	−	0.213545i
$997$	20.7421	−	3.92462i	0.656909	−	0.124294i	0.153238	−	0.988189i	$-0.451030\pi$
$997$	20.7421	−	3.92462i	0.656909	−	0.124294i	0.503671	+	0.863896i	$0.331982\pi$
$998$	17.4061	−	17.4061i	0.550981	−	0.550981i
$999$	48.4312	+	19.3347i	1.53230	+	0.611722i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	261.2.x.a.14.4	✓	672
3.2	odd	2		783.2.be.a.449.25		672
9.2	odd	6	inner	261.2.x.a.101.25	yes	672
9.7	even	3		783.2.be.a.710.4		672
29.27	odd	28	inner	261.2.x.a.230.25	yes	672
87.56	even	28		783.2.be.a.665.4		672
261.56	even	84	inner	261.2.x.a.56.4	yes	672
261.259	odd	84		783.2.be.a.143.25		672

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
261.2.x.a.14.4	✓	672	1.1	even	1	trivial
261.2.x.a.56.4	yes	672	261.56	even	84	inner
261.2.x.a.101.25	yes	672	9.2	odd	6	inner
261.2.x.a.230.25	yes	672	29.27	odd	28	inner
783.2.be.a.143.25		672	261.259	odd	84
783.2.be.a.449.25		672	3.2	odd	2
783.2.be.a.665.4		672	87.56	even	28
783.2.be.a.710.4		672	9.7	even	3

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+(-1.38565 - 1.87749i) q^{2} +(-1.25257 - 1.19627i) q^{3} +(-1.01543 + 3.29194i) q^{4} +(-0.859785 - 2.19070i) q^{5} +(-0.510352 + 4.00930i) q^{6} +(-1.60836 + 0.496115i) q^{7} +(3.18260 - 1.11364i) q^{8} +(0.137883 + 2.99683i) q^{9} +(-2.92165 + 4.64977i) q^{10} +(-0.242992 - 1.28424i) q^{11} +(5.20995 - 2.90867i) q^{12} +(-3.83068 - 0.287070i) q^{13} +(3.16008 + 2.33224i) q^{14} +(-1.54372 + 3.77254i) q^{15} +(-0.808051 - 0.550920i) q^{16} +(1.97828 + 1.97828i) q^{17} +(5.43546 - 4.41143i) q^{18} +(2.81485 + 1.76869i) q^{19} +(8.08469 - 0.605864i) q^{20} +(2.60808 + 1.30262i) q^{21} +(-2.07445 + 2.23572i) q^{22} +(-0.414857 - 2.75239i) q^{23} +(-5.31866 - 2.41233i) q^{24} +(-0.394657 + 0.366189i) q^{25} +(4.76902 + 7.58985i) q^{26} +(3.41230 - 3.91870i) q^{27} -5.79841i q^{28} +(-5.38506 - 0.0330917i) q^{29} +(9.22196 - 2.32911i) q^{30} +(-4.01779 - 1.75294i) q^{31} +(-0.166823 - 4.45843i) q^{32} +(-1.23193 + 1.89929i) q^{33} +(0.972996 - 6.45540i) q^{34} +(2.46968 + 3.09688i) q^{35} +(-10.0054 - 2.58917i) q^{36} +(3.31464 + 9.47271i) q^{37} +(-0.579706 - 7.73563i) q^{38} +(4.45480 + 4.94210i) q^{39} +(-5.17600 - 6.01462i) q^{40} +(2.94155 + 10.9780i) q^{41} +(-1.16824 - 6.70161i) q^{42} +(-1.53830 - 3.52582i) q^{43} +(4.47439 + 0.504142i) q^{44} +(6.44659 - 2.87869i) q^{45} +(-4.59274 + 4.59274i) q^{46} +(-9.97238 + 1.88688i) q^{47} +(0.353096 + 1.65671i) q^{48} +(-3.44297 + 2.34737i) q^{49} +(1.23437 + 0.233556i) q^{50} +(-0.111388 - 4.84450i) q^{51} +(4.83481 - 12.3189i) q^{52} +(-8.87369 - 7.07653i) q^{53} +(-12.0856 - 0.976624i) q^{54} +(-2.60446 + 1.63649i) q^{55} +(-4.56629 + 3.37008i) q^{56} +(-1.40998 - 5.58273i) q^{57} +(7.39968 + 10.1563i) q^{58} +(0.0424144 + 0.0244880i) q^{59} +(-10.8514 - 8.91257i) q^{60} +(-2.71896 + 5.14453i) q^{61} +(2.27612 + 9.97231i) q^{62} +(-1.70854 - 4.75159i) q^{63} +(-9.66874 + 7.71056i) q^{64} +(2.66468 + 8.63868i) q^{65} +(5.27292 - 0.318812i) q^{66} +(-3.53635 - 5.18687i) q^{67} +(-8.52118 + 4.50358i) q^{68} +(-2.77296 + 3.94386i) q^{69} +(2.39225 - 8.92800i) q^{70} +(-10.7697 + 5.18640i) q^{71} +(3.77622 + 9.38417i) q^{72} +(0.169595 - 1.50520i) q^{73} +(13.1920 - 19.3491i) q^{74} +(0.932397 + 0.0134380i) q^{75} +(-8.68070 + 7.47034i) q^{76} +(1.02795 + 1.94498i) q^{77} +(3.10595 - 15.2119i) q^{78} +(-4.41480 - 3.79924i) q^{79} +(-0.512148 + 2.24387i) q^{80} +(-8.96198 + 0.826423i) q^{81} +(16.5352 - 20.7344i) q^{82} +(-2.49024 - 2.68384i) q^{83} +(-6.93645 + 7.26294i) q^{84} +(2.63291 - 6.03470i) q^{85} +(-4.48815 + 7.77370i) q^{86} +(6.70560 + 6.48343i) q^{87} +(-2.20353 - 3.81662i) q^{88} +(-1.07453 + 0.121070i) q^{89} +(-14.3374 - 8.11455i) q^{90} +(6.30355 - 1.43874i) q^{91} +(9.48198 + 1.42918i) q^{92} +(2.93558 + 7.00204i) q^{93} +(17.3608 + 16.1085i) q^{94} +(1.45449 - 7.68717i) q^{95} +(-5.12452 + 5.78408i) q^{96} +(12.7275 + 0.476228i) q^{97} +(9.17792 + 3.21149i) q^{98} +(3.81515 - 0.905279i) 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

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Representations

Groups

Database

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