LMFDB - Embedded newform 276.2.c.a.47.22

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [276,2,Mod(47,276)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(276, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("276.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 276 = 2^{2} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	276.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.20387109579$
Analytic rank:	$0$
Dimension:	$22$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			47.22
Character	$\chi$	$=$	276.47
Dual form			276.2.c.a.47.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.33491 + 0.466911i) q^{2} +(1.38398 - 1.04144i) q^{3} +(1.56399 + 1.24657i) q^{4} -0.588622i q^{5} +(2.33376 - 0.744034i) q^{6} -0.538069i q^{7} +(1.50575 + 2.39431i) q^{8} +(0.830813 - 2.88266i) q^{9} +O(q^{10})$	\(q+(1.33491 + 0.466911i) q^{2} +(1.38398 - 1.04144i) q^{3} +(1.56399 + 1.24657i) q^{4} -0.588622i q^{5} +(2.33376 - 0.744034i) q^{6} -0.538069i q^{7} +(1.50575 + 2.39431i) q^{8} +(0.830813 - 2.88266i) q^{9} +(0.274834 - 0.785760i) q^{10} -5.85045 q^{11} +(3.46276 + 0.0964349i) q^{12} -1.97835 q^{13} +(0.251230 - 0.718276i) q^{14} +(-0.613014 - 0.814643i) q^{15} +(0.892120 + 3.89925i) q^{16} +7.26738i q^{17} +(2.45501 - 3.46019i) q^{18} -1.26862i q^{19} +(0.733760 - 0.920599i) q^{20} +(-0.560366 - 0.744678i) q^{21} +(-7.80985 - 2.73164i) q^{22} +1.00000 q^{23} +(4.57746 + 1.74553i) q^{24} +4.65352 q^{25} +(-2.64092 - 0.923711i) q^{26} +(-1.85229 - 4.85480i) q^{27} +(0.670742 - 0.841534i) q^{28} +4.53367i q^{29} +(-0.437955 - 1.37370i) q^{30} -9.26323i q^{31} +(-0.629697 + 5.62170i) q^{32} +(-8.09692 + 6.09288i) q^{33} +(-3.39322 + 9.70132i) q^{34} -0.316720 q^{35} +(4.89283 - 3.47279i) q^{36} -1.46453 q^{37} +(0.592330 - 1.69349i) q^{38} +(-2.73799 + 2.06032i) q^{39} +(1.40934 - 0.886319i) q^{40} -1.51641i q^{41} +(-0.400342 - 1.25572i) q^{42} +4.18790i q^{43} +(-9.15004 - 7.29301i) q^{44} +(-1.69680 - 0.489035i) q^{45} +(1.33491 + 0.466911i) q^{46} -8.82974 q^{47} +(5.29550 + 4.46740i) q^{48} +6.71048 q^{49} +(6.21205 + 2.17278i) q^{50} +(7.56852 + 10.0579i) q^{51} +(-3.09411 - 2.46615i) q^{52} -10.9312i q^{53} +(-0.205885 - 7.34558i) q^{54} +3.44371i q^{55} +(1.28830 - 0.810199i) q^{56} +(-1.32118 - 1.75574i) q^{57} +(-2.11682 + 6.05206i) q^{58} -1.30300 q^{59} +(0.0567637 - 2.03826i) q^{60} -2.25703 q^{61} +(4.32510 - 12.3656i) q^{62} +(-1.55107 - 0.447035i) q^{63} +(-3.46542 + 7.21047i) q^{64} +1.16450i q^{65} +(-13.6535 + 4.35293i) q^{66} +7.43470i q^{67} +(-9.05930 + 11.3661i) q^{68} +(1.38398 - 1.04144i) q^{69} +(-0.422793 - 0.147880i) q^{70} +3.93677 q^{71} +(8.15298 - 2.35135i) q^{72} +0.236426 q^{73} +(-1.95502 - 0.683805i) q^{74} +(6.44039 - 4.84636i) q^{75} +(1.58142 - 1.98410i) q^{76} +3.14795i q^{77} +(-4.61697 + 1.47196i) q^{78} -7.96230i q^{79} +(2.29518 - 0.525122i) q^{80} +(-7.61950 - 4.78991i) q^{81} +(0.708026 - 2.02427i) q^{82} -0.731670 q^{83} +(0.0518886 - 1.86320i) q^{84} +4.27774 q^{85} +(-1.95538 + 5.59049i) q^{86} +(4.72154 + 6.27452i) q^{87} +(-8.80933 - 14.0078i) q^{88} -3.18998i q^{89} +(-2.03675 - 1.44507i) q^{90} +1.06449i q^{91} +(1.56399 + 1.24657i) q^{92} +(-9.64709 - 12.8202i) q^{93} +(-11.7869 - 4.12270i) q^{94} -0.746736 q^{95} +(4.98316 + 8.43612i) q^{96} +12.6978 q^{97} +(8.95791 + 3.13320i) q^{98} +(-4.86063 + 16.8649i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 3 q^{6} - 9 q^{8} - 2 q^{9}+O(q^{10}) $ 22 * q - 3 * q^6 - 9 * q^8 - 2 * q^9	$ 22 q - 3 q^{6} - 9 q^{8} - 2 q^{9} + 4 q^{10} + 14 q^{12} - 4 q^{13} + 12 q^{14} + 4 q^{16} - 14 q^{18} - 14 q^{20} + 2 q^{22} + 22 q^{23} + 22 q^{24} - 18 q^{25} + 27 q^{26} + 12 q^{27} + 6 q^{28} - 24 q^{30} - 20 q^{32} - 8 q^{33} - 6 q^{34} - 8 q^{35} + 3 q^{36} - 4 q^{37} + 22 q^{38} - 24 q^{39} - 4 q^{40} - 38 q^{42} - 56 q^{44} + 8 q^{47} + 17 q^{48} - 14 q^{49} + 20 q^{50} + 16 q^{51} - 19 q^{52} - 54 q^{54} - 18 q^{56} + 12 q^{57} + 3 q^{58} - 72 q^{59} + 64 q^{60} + 12 q^{61} + 63 q^{62} - 20 q^{63} + 3 q^{64} - 18 q^{66} - 20 q^{68} + 40 q^{71} + 48 q^{72} - 4 q^{73} + 28 q^{74} + 48 q^{75} + 26 q^{76} - 46 q^{78} - 84 q^{80} + 10 q^{81} - 29 q^{82} - 8 q^{83} + 76 q^{84} + 8 q^{85} + 28 q^{86} - 48 q^{87} - 30 q^{88} - 26 q^{90} + 12 q^{93} - 13 q^{94} + 32 q^{95} + 18 q^{96} - 4 q^{97} + 64 q^{98} + 20 q^{99}+O(q^{100}) $ 22 * q - 3 * q^6 - 9 * q^8 - 2 * q^9 + 4 * q^10 + 14 * q^12 - 4 * q^13 + 12 * q^14 + 4 * q^16 - 14 * q^18 - 14 * q^20 + 2 * q^22 + 22 * q^23 + 22 * q^24 - 18 * q^25 + 27 * q^26 + 12 * q^27 + 6 * q^28 - 24 * q^30 - 20 * q^32 - 8 * q^33 - 6 * q^34 - 8 * q^35 + 3 * q^36 - 4 * q^37 + 22 * q^38 - 24 * q^39 - 4 * q^40 - 38 * q^42 - 56 * q^44 + 8 * q^47 + 17 * q^48 - 14 * q^49 + 20 * q^50 + 16 * q^51 - 19 * q^52 - 54 * q^54 - 18 * q^56 + 12 * q^57 + 3 * q^58 - 72 * q^59 + 64 * q^60 + 12 * q^61 + 63 * q^62 - 20 * q^63 + 3 * q^64 - 18 * q^66 - 20 * q^68 + 40 * q^71 + 48 * q^72 - 4 * q^73 + 28 * q^74 + 48 * q^75 + 26 * q^76 - 46 * q^78 - 84 * q^80 + 10 * q^81 - 29 * q^82 - 8 * q^83 + 76 * q^84 + 8 * q^85 + 28 * q^86 - 48 * q^87 - 30 * q^88 - 26 * q^90 + 12 * q^93 - 13 * q^94 + 32 * q^95 + 18 * q^96 - 4 * q^97 + 64 * q^98 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/276\mathbb{Z}\right)^\times$.

$n$	$97$	$139$	$185$
$\chi(n)$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	1.33491	+	0.466911i	0.943926	+	0.330156i
$2$	1.33491	+	0.466911i	0.943926	+	0.330156i
$3$	1.38398	−	1.04144i	0.799042	−	0.601275i
$3$	1.38398	−	1.04144i	0.799042	−	0.601275i
$4$	1.56399	+	1.24657i	0.781994	+	0.623286i
$5$		−	0.588622i		−	0.263240i	−0.991300	−	0.131620i	$-0.957982\pi$
$5$		−	0.588622i		−	0.263240i	0.991300	−	0.131620i	$-0.0420179\pi$
$6$	2.33376	−	0.744034i	0.952752	−	0.303751i
$7$		−	0.538069i		−	0.203371i	−0.994817	−	0.101686i	$-0.967576\pi$
$7$		−	0.538069i		−	0.203371i	0.994817	−	0.101686i	$-0.0324235\pi$
$8$	1.50575	+	2.39431i	0.532364	+	0.846516i
$9$	0.830813	−	2.88266i	0.276938	−	0.960888i
$10$	0.274834	−	0.785760i	0.0869102	−	0.248479i
$11$	−5.85045			−1.76398			−0.881989	−	0.471270i	$-0.843796\pi$
$11$	−5.85045			−1.76398			−0.881989	+	0.471270i	$0.843796\pi$
$12$	3.46276	+	0.0964349i	0.999612	+	0.0278384i
$13$	−1.97835			−0.548694			−0.274347	−	0.961631i	$-0.588462\pi$
$13$	−1.97835			−0.548694			−0.274347	+	0.961631i	$0.588462\pi$
$14$	0.251230	−	0.718276i	0.0671441	−	0.191967i
$15$	−0.613014	−	0.814643i	−0.158280	−	0.210340i
$16$	0.892120	+	3.89925i	0.223030	+	0.974812i
$17$			7.26738i			1.76260i	0.472559	+	0.881299i	$0.343330\pi$
$17$			7.26738i			1.76260i	−0.472559	+	0.881299i	$0.656670\pi$
$18$	2.45501	−	3.46019i	0.578651	−	0.815575i
$19$		−	1.26862i		−	0.291040i	−0.989355	−	0.145520i	$-0.953514\pi$
$19$		−	1.26862i		−	0.291040i	0.989355	−	0.145520i	$-0.0464856\pi$
$20$	0.733760	−	0.920599i	0.164074	−	0.205852i
$21$	−0.560366	−	0.744678i	−0.122282	−	0.162502i
$22$	−7.80985	−	2.73164i	−1.66507	−	0.582388i
$23$	1.00000			0.208514
$23$	1.00000			0.208514
$24$	4.57746	+	1.74553i	0.934370	+	0.356305i
$25$	4.65352			0.930705
$26$	−2.64092	−	0.923711i	−0.517927	−	0.181155i
$27$	−1.85229	−	4.85480i	−0.356473	−	0.934306i
$28$	0.670742	−	0.841534i	0.126758	−	0.159035i
$29$			4.53367i			0.841882i	0.907088	+	0.420941i	$0.138300\pi$
$29$			4.53367i			0.841882i	−0.907088	+	0.420941i	$0.861700\pi$
$30$	−0.437955	−	1.37370i	−0.0799593	−	0.250802i
$31$		−	9.26323i		−	1.66373i	−0.554981	−	0.831863i	$-0.687274\pi$
$31$		−	9.26323i		−	1.66373i	0.554981	−	0.831863i	$-0.312726\pi$
$32$	−0.629697	+	5.62170i	−0.111316	+	0.993785i
$33$	−8.09692	+	6.09288i	−1.40949	+	1.06064i
$34$	−3.39322	+	9.70132i	−0.581932	+	1.66376i
$35$	−0.316720			−0.0535354
$36$	4.89283	−	3.47279i	0.815471	−	0.578798i
$37$	−1.46453			−0.240767			−0.120384	−	0.992727i	$-0.538412\pi$
$37$	−1.46453			−0.240767			−0.120384	+	0.992727i	$0.538412\pi$
$38$	0.592330	−	1.69349i	0.0960887	−	0.274721i
$39$	−2.73799	+	2.06032i	−0.438430	+	0.329916i
$40$	1.40934	−	0.886319i	0.222837	−	0.140139i
$41$		−	1.51641i		−	0.236823i	−0.992965	−	0.118411i	$-0.962220\pi$
$41$		−	1.51641i		−	0.236823i	0.992965	−	0.118411i	$-0.0377802\pi$
$42$	−0.400342	−	1.25572i	−0.0617740	−	0.193762i
$43$			4.18790i			0.638649i	0.947645	+	0.319325i	$0.103456\pi$
$43$			4.18790i			0.638649i	−0.947645	+	0.319325i	$0.896544\pi$
$44$	−9.15004	−	7.29301i	−1.37942	−	1.09946i
$45$	−1.69680	−	0.489035i	−0.252944	−	0.0729010i
$46$	1.33491	+	0.466911i	0.196822	+	0.0688423i
$47$	−8.82974			−1.28795			−0.643975	−	0.765047i	$-0.722716\pi$
$47$	−8.82974			−1.28795			−0.643975	+	0.765047i	$0.722716\pi$
$48$	5.29550	+	4.46740i	0.764340	+	0.644814i
$49$	6.71048			0.958640
$50$	6.21205	+	2.17278i	0.878517	+	0.307278i
$51$	7.56852	+	10.0579i	1.05981	+	1.40839i
$52$	−3.09411	−	2.46615i	−0.429076	−	0.341993i
$53$		−	10.9312i		−	1.50152i	−0.660574	−	0.750761i	$-0.729687\pi$
$53$		−	10.9312i		−	1.50152i	0.660574	−	0.750761i	$-0.270313\pi$
$54$	−0.205885	−	7.34558i	−0.0280175	−	0.999607i
$55$			3.44371i			0.464349i
$56$	1.28830	−	0.810199i	0.172157	−	0.108267i
$57$	−1.32118	−	1.75574i	−0.174995	−	0.232554i
$58$	−2.11682	+	6.05206i	−0.277952	+	0.794674i
$59$	−1.30300			−0.169637			−0.0848183	−	0.996396i	$-0.527031\pi$
$59$	−1.30300			−0.169637			−0.0848183	+	0.996396i	$0.527031\pi$
$60$	0.0567637	−	2.03826i	0.00732817	−	0.263138i
$61$	−2.25703			−0.288984			−0.144492	−	0.989506i	$-0.546155\pi$
$61$	−2.25703			−0.288984			−0.144492	+	0.989506i	$0.546155\pi$
$62$	4.32510	−	12.3656i	0.549289	−	1.57043i
$63$	−1.55107	−	0.447035i	−0.195417	−	0.0563211i
$64$	−3.46542	+	7.21047i	−0.433178	+	0.901308i
$65$			1.16450i			0.144438i
$66$	−13.6535	+	4.35293i	−1.68063	+	0.535809i
$67$			7.43470i			0.908293i	0.890927	+	0.454146i	$0.150056\pi$
$67$			7.43470i			0.908293i	−0.890927	+	0.454146i	$0.849944\pi$
$68$	−9.05930	+	11.3661i	−1.09860	+	1.37834i
$69$	1.38398	−	1.04144i	0.166612	−	0.125374i
$70$	−0.422793	−	0.147880i	−0.0505335	−	0.0176750i
$71$	3.93677			0.467209			0.233604	−	0.972332i	$-0.424948\pi$
$71$	3.93677			0.467209			0.233604	+	0.972332i	$0.424948\pi$
$72$	8.15298	−	2.35135i	0.960838	−	0.277110i
$73$	0.236426			0.0276716			0.0138358	−	0.999904i	$-0.495596\pi$
$73$	0.236426			0.0276716			0.0138358	+	0.999904i	$0.495596\pi$
$74$	−1.95502	−	0.683805i	−0.227267	−	0.0794908i
$75$	6.44039	−	4.84636i	0.743673	−	0.559609i
$76$	1.58142	−	1.98410i	0.181401	−	0.227592i
$77$			3.14795i			0.358742i
$78$	−4.61697	+	1.47196i	−0.522769	+	0.166666i
$79$		−	7.96230i		−	0.895829i	−0.894076	−	0.447915i	$-0.852167\pi$
$79$		−	7.96230i		−	0.895829i	0.894076	−	0.447915i	$-0.147833\pi$
$80$	2.29518	−	0.525122i	0.256609	−	0.0587104i
$81$	−7.61950	−	4.78991i	−0.846611	−	0.532212i
$82$	0.708026	−	2.02427i	0.0781884	−	0.223543i
$83$	−0.731670			−0.0803112			−0.0401556	−	0.999193i	$-0.512785\pi$
$83$	−0.731670			−0.0803112			−0.0401556	+	0.999193i	$0.512785\pi$
$84$	0.0518886	−	1.86320i	0.00566151	−	0.203292i
$85$	4.27774			0.463986
$86$	−1.95538	+	5.59049i	−0.210854	+	0.602838i
$87$	4.72154	+	6.27452i	0.506202	+	0.672699i
$88$	−8.80933	−	14.0078i	−0.939078	−	1.49323i
$89$		−	3.18998i		−	0.338138i	−0.985604	−	0.169069i	$-0.945924\pi$
$89$		−	3.18998i		−	0.338138i	0.985604	−	0.169069i	$-0.0540760\pi$
$90$	−2.03675	−	1.44507i	−0.214692	−	0.152324i
$91$			1.06449i			0.111588i
$92$	1.56399	+	1.24657i	0.163057	+	0.129964i
$93$	−9.64709	−	12.8202i	−1.00036	−	1.32939i
$94$	−11.7869	−	4.12270i	−1.21573	−	0.425224i
$95$	−0.746736			−0.0766135
$96$	4.98316	+	8.43612i	0.508592	+	0.861008i
$97$	12.6978			1.28926			0.644631	−	0.764494i	$-0.277011\pi$
$97$	12.6978			1.28926			0.644631	+	0.764494i	$0.277011\pi$
$98$	8.95791	+	3.13320i	0.904886	+	0.316501i
$99$	−4.86063	+	16.8649i	−0.488512	+	1.69498i
$100$	7.27806	+	5.80095i	0.727806	+	0.580095i
$101$			0.284287i			0.0282876i	0.999900	+	0.0141438i	$0.00450227\pi$
$101$			0.284287i			0.0282876i	−0.999900	+	0.0141438i	$0.995498\pi$
$102$	5.40717	+	16.9603i	0.535390	+	1.67932i
$103$		−	15.7661i		−	1.55348i	−0.629820	−	0.776741i	$-0.716871\pi$
$103$		−	15.7661i		−	1.55348i	0.629820	−	0.776741i	$-0.283129\pi$
$104$	−2.97890	−	4.73677i	−0.292105	−	0.464478i
$105$	−0.438334	+	0.329844i	−0.0427770	+	0.0321895i
$106$	5.10392	−	14.5923i	0.495736	−	1.41733i
$107$	8.26461			0.798970			0.399485	−	0.916740i	$-0.369189\pi$
$107$	8.26461			0.798970			0.399485	+	0.916740i	$0.369189\pi$
$108$	3.15489	−	9.90185i	0.303580	−	0.952806i
$109$	−12.1870			−1.16731			−0.583653	−	0.812003i	$-0.698377\pi$
$109$	−12.1870			−1.16731			−0.583653	+	0.812003i	$0.698377\pi$
$110$	−1.60790	+	4.59705i	−0.153308	+	0.438312i
$111$	−2.02688	+	1.52522i	−0.192383	+	0.144767i
$112$	2.09806	−	0.480022i	0.198248	−	0.0453578i
$113$		−	7.96068i		−	0.748877i	−0.927252	−	0.374439i	$-0.877835\pi$
$113$		−	7.96068i		−	0.748877i	0.927252	−	0.374439i	$-0.122165\pi$
$114$	−0.943893	−	2.96064i	−0.0884037	−	0.277289i
$115$		−	0.588622i		−	0.0548893i
$116$	−5.65155	+	7.09061i	−0.524733	+	0.658347i
$117$	−1.64363	+	5.70290i	−0.151954	+	0.527234i
$118$	−1.73940	−	0.608387i	−0.160125	−	0.0560065i
$119$	3.91035			0.358461
$120$	1.02746	−	2.69439i	0.0937938	−	0.245963i
$121$	23.2278			2.11162
$122$	−3.01295	−	1.05383i	−0.272779	−	0.0954097i
$123$	−1.57924	−	2.09868i	−0.142396	−	0.189231i
$124$	11.5473	−	14.4876i	1.03698	−	1.30102i
$125$		−	5.68228i		−	0.508239i
$126$	−1.86182	−	1.32097i	−0.165864	−	0.117681i
$127$			6.82558i			0.605672i	0.953043	+	0.302836i	$0.0979334\pi$
$127$			6.82558i			0.605672i	−0.953043	+	0.302836i	$0.902067\pi$
$128$	−7.99269	+	8.00731i	−0.706460	+	0.707753i
$129$	4.36144	+	5.79598i	0.384004	+	0.510308i
$130$	−0.543717	+	1.55450i	−0.0476871	+	0.136339i
$131$	16.7453			1.46304			0.731522	−	0.681818i	$-0.238810\pi$
$131$	16.7453			1.46304			0.731522	+	0.681818i	$0.238810\pi$
$132$	−20.2587	−	0.564188i	−1.76329	−	0.0491062i
$133$	−0.682603			−0.0591892
$134$	−3.47134	+	9.92468i	−0.299878	+	0.857362i
$135$	−2.85764	+	1.09030i	−0.245947	+	0.0938378i
$136$	−17.4003	+	10.9429i	−1.49207	+	0.938343i
$137$			13.4873i			1.15230i	0.817344	+	0.576150i	$0.195446\pi$
$137$			13.4873i			1.15230i	−0.817344	+	0.576150i	$0.804554\pi$
$138$	2.33376	−	0.744034i	0.198662	−	0.0633364i
$139$			8.61521i			0.730733i	0.930864	+	0.365366i	$0.119056\pi$
$139$			8.61521i			0.730733i	−0.930864	+	0.365366i	$0.880944\pi$
$140$	−0.495346	−	0.394813i	−0.0418644	−	0.0333678i
$141$	−12.2202	+	9.19563i	−1.02913	+	0.774411i
$142$	5.25525	+	1.83812i	0.441011	+	0.154252i
$143$	11.5742			0.967884
$144$	11.9814	+	0.667862i	0.998450	+	0.0556551i
$145$	2.66862			0.221617
$146$	0.315608	+	0.110390i	0.0261199	+	0.00913593i
$147$	9.28719	−	6.98855i	0.765994	−	0.576406i
$148$	−2.29051	−	1.82564i	−0.188279	−	0.150067i
$149$			12.0473i			0.986953i	0.869759	+	0.493477i	$0.164274\pi$
$149$			12.0473i			0.986953i	−0.869759	+	0.493477i	$0.835726\pi$
$150$	10.8602	−	3.46238i	0.886730	−	0.282702i
$151$			12.1654i			0.990003i	0.868892	+	0.495002i	$0.164833\pi$
$151$			12.1654i			0.990003i	−0.868892	+	0.495002i	$0.835167\pi$
$152$	3.03746	−	1.91022i	0.246370	−	0.154939i
$153$	20.9494	+	6.03783i	1.69366	+	0.488130i
$154$	−1.46981	+	4.20224i	−0.118441	+	0.338626i
$155$	−5.45255			−0.437959
$156$	−6.85053	−	0.190782i	−0.548482	−	0.0152747i
$157$	15.3094			1.22182			0.610912	−	0.791699i	$-0.290803\pi$
$157$	15.3094			1.22182			0.610912	+	0.791699i	$0.290803\pi$
$158$	3.71769	−	10.6290i	0.295763	−	0.845597i
$159$	−11.3842	−	15.1286i	−0.902827	−	1.19978i
$160$	3.30906	+	0.370654i	0.261604	+	0.0293028i
$161$		−	0.538069i		−	0.0424058i
$162$	−7.93491	−	9.95174i	−0.623426	−	0.781883i
$163$			13.4878i			1.05644i	0.849107	+	0.528221i	$0.177141\pi$
$163$			13.4878i			1.05644i	−0.849107	+	0.528221i	$0.822859\pi$
$164$	1.89031	−	2.37164i	0.147608	−	0.185194i
$165$	3.58641	+	4.76603i	0.279202	+	0.371035i
$166$	−0.976717	−	0.341625i	−0.0758079	−	0.0265152i
$167$	18.8899			1.46174			0.730871	−	0.682515i	$-0.239114\pi$
$167$	18.8899			1.46174			0.730871	+	0.682515i	$0.239114\pi$
$168$	0.939217	−	2.46299i	0.0724622	−	0.190024i
$169$	−9.08615			−0.698935
$170$	5.71041	+	1.99732i	0.437969	+	0.153188i
$171$	−3.65699	−	1.05398i	−0.279657	−	0.0806000i
$172$	−5.22052	+	6.54983i	−0.398061	+	0.499420i
$173$		−	19.9776i		−	1.51887i	−0.650585	−	0.759433i	$-0.725476\pi$
$173$		−	19.9776i		−	1.51887i	0.650585	−	0.759433i	$-0.274524\pi$
$174$	3.37321	+	10.5805i	0.255722	+	0.802104i
$175$		−	2.50392i		−	0.189278i
$176$	−5.21931	−	22.8124i	−0.393420	−	1.71955i
$177$	−1.80333	+	1.35700i	−0.135547	+	0.101998i
$178$	1.48944	−	4.25835i	0.111638	−	0.319177i
$179$	−10.1914			−0.761740			−0.380870	−	0.924629i	$-0.624376\pi$
$179$	−10.1914			−0.761740			−0.380870	+	0.924629i	$0.624376\pi$
$180$	−2.04416	−	2.88003i	−0.152363	−	0.214665i
$181$	−9.16582			−0.681290			−0.340645	−	0.940192i	$-0.610645\pi$
$181$	−9.16582			−0.681290			−0.340645	+	0.940192i	$0.610645\pi$
$182$	−0.497020	+	1.42100i	−0.0368416	+	0.105331i
$183$	−3.12370	+	2.35056i	−0.230910	+	0.173759i
$184$	1.50575	+	2.39431i	0.111005	+	0.176511i
$185$			0.862056i			0.0633796i
$186$	−6.89216	−	21.6181i	−0.505358	−	1.58512i
$187$		−	42.5174i		−	3.10918i
$188$	−13.8096	−	11.0069i	−1.00717	−	0.802761i
$189$	−2.61222	+	0.996658i	−0.190011	+	0.0724962i
$190$	−0.996827	−	0.348659i	−0.0723175	−	0.0252944i
$191$	10.3694			0.750300			0.375150	−	0.926964i	$-0.377591\pi$
$191$	10.3694			0.750300			0.375150	+	0.926964i	$0.377591\pi$
$192$	2.71317	+	13.5882i	0.195806	+	0.980643i
$193$	−16.4898			−1.18696			−0.593481	−	0.804848i	$-0.702247\pi$
$193$	−16.4898			−1.18696			−0.593481	+	0.804848i	$0.702247\pi$
$194$	16.9504	+	5.92872i	1.21697	+	0.425657i
$195$	1.21275	+	1.61164i	0.0868470	+	0.115412i
$196$	10.4951	+	8.36509i	0.749651	+	0.597507i
$197$		−	8.11579i		−	0.578226i	−0.957295	−	0.289113i	$-0.906640\pi$
$197$		−	8.11579i		−	0.578226i	0.957295	−	0.289113i	$-0.0933604\pi$
$198$	−14.3629	+	20.2437i	−1.02073	+	1.43866i
$199$			16.2062i			1.14883i	0.818564	+	0.574415i	$0.194770\pi$
$199$			16.2062i			1.14883i	−0.818564	+	0.574415i	$0.805230\pi$
$200$	7.00705	+	11.1420i	0.495473	+	0.787856i
$201$	7.74278	+	10.2895i	0.546134	+	0.725765i
$202$	−0.132737	+	0.379499i	−0.00933933	+	0.0267014i
$203$	2.43943			0.171214
$204$	−0.700829	+	25.1652i	−0.0490678	+	1.76191i
$205$	−0.892590			−0.0623412
$206$	7.36137	−	21.0464i	0.512891	−	1.46637i
$207$	0.830813	−	2.88266i	0.0577455	−	0.200359i
$208$	−1.76492	−	7.71405i	−0.122375	−	0.534873i
$209$			7.42198i			0.513389i
$210$	−0.739146	+	0.235650i	−0.0510059	+	0.0162614i
$211$		−	12.6189i		−	0.868721i	−0.900739	−	0.434360i	$-0.856974\pi$
$211$		−	12.6189i		−	0.868721i	0.900739	−	0.434360i	$-0.143026\pi$
$212$	13.6266	−	17.0963i	0.935877	−	1.17418i
$213$	5.44842	−	4.09990i	0.373320	−	0.280921i
$214$	11.0325	+	3.85884i	0.754169	+	0.263785i
$215$	2.46509			0.168118
$216$	8.83479	−	11.7451i	0.601131	−	0.799150i
$217$	−4.98426			−0.338354
$218$	−16.2686	−	5.69026i	−1.10185	−	0.385393i
$219$	0.327209	−	0.246223i	0.0221107	−	0.0166382i
$220$	−4.29283	+	5.38592i	−0.289422	+	0.363119i
$221$		−	14.3774i		−	0.967127i
$222$	−3.41786	+	1.08966i	−0.229392	+	0.0731332i
$223$			19.5344i			1.30812i	0.756444	+	0.654059i	$0.226935\pi$
$223$			19.5344i			1.30812i	−0.756444	+	0.654059i	$0.773065\pi$
$224$	3.02486	+	0.338821i	0.202107	+	0.0226384i
$225$	3.86621	−	13.4145i	0.257747	−	0.894303i
$226$	3.71693	−	10.6268i	0.247246	−	0.706885i
$227$	−13.8874			−0.921739			−0.460869	−	0.887468i	$-0.652462\pi$
$227$	−13.8874			−0.921739			−0.460869	+	0.887468i	$0.652462\pi$
$228$	0.122339	−	4.39291i	0.00810209	−	0.290928i
$229$	−5.18923			−0.342914			−0.171457	−	0.985192i	$-0.554847\pi$
$229$	−5.18923			−0.342914			−0.171457	+	0.985192i	$0.554847\pi$
$230$	0.274834	−	0.785760i	0.0181220	−	0.0518115i
$231$	3.27839	+	4.35670i	0.215702	+	0.286650i
$232$	−10.8550	+	6.82658i	−0.712666	+	0.448187i
$233$			21.5429i			1.41132i	0.708550	+	0.705661i	$0.249350\pi$
$233$			21.5429i			1.41132i	−0.708550	+	0.705661i	$0.750650\pi$
$234$	−4.85686	+	6.84545i	−0.317503	+	0.447501i
$235$			5.19738i			0.339040i
$236$	−2.03788	−	1.62429i	−0.132655	−	0.105732i
$237$	−8.29225	−	11.0197i	−0.538639	−	0.715806i
$238$	5.21998	+	1.82579i	0.338361	+	0.118348i
$239$	−13.0339			−0.843092			−0.421546	−	0.906807i	$-0.638512\pi$
$239$	−13.0339			−0.843092			−0.421546	+	0.906807i	$0.638512\pi$
$240$	2.62961	−	3.11705i	0.169741	−	0.201205i
$241$	13.6388			0.878550			0.439275	−	0.898353i	$-0.355235\pi$
$241$	13.6388			0.878550			0.439275	+	0.898353i	$0.355235\pi$
$242$	31.0071	+	10.8453i	1.99321	+	0.697163i
$243$	−15.5336	+	1.30609i	−0.996484	+	0.0837859i
$244$	−3.52998	−	2.81355i	−0.225984	−	0.180119i
$245$		−	3.94994i		−	0.252352i
$246$	−1.12826	−	3.53892i	−0.0719350	−	0.225633i
$247$			2.50976i			0.159692i
$248$	22.1790	−	13.9481i	1.40837	−	0.885707i
$249$	−1.01262	+	0.761989i	−0.0641721	+	0.0482891i
$250$	2.65312	−	7.58535i	0.167798	−	0.479740i
$251$	−13.8504			−0.874229			−0.437115	−	0.899406i	$-0.644000\pi$
$251$	−13.8504			−0.874229			−0.437115	+	0.899406i	$0.644000\pi$
$252$	−1.86860	−	2.63268i	−0.117711	−	0.165843i
$253$	−5.85045			−0.367815
$254$	−3.18694	+	9.11155i	−0.199966	+	0.571710i
$255$	5.92032	−	4.45500i	0.370745	−	0.278983i
$256$	−14.4082	+	6.95719i	−0.900515	+	0.434824i
$257$			12.4696i			0.777830i	0.921274	+	0.388915i	$0.127150\pi$
$257$			12.4696i			0.777830i	−0.921274	+	0.388915i	$0.872850\pi$
$258$	3.11594	+	9.77354i	0.193990	+	0.608474i
$259$			0.788019i			0.0489651i
$260$	−1.45163	+	1.82126i	−0.0900263	+	0.112950i
$261$	13.0691	+	3.76663i	0.808954	+	0.233149i
$262$	22.3535	+	7.81856i	1.38101	+	0.483032i
$263$	−12.5953			−0.776659			−0.388330	−	0.921521i	$-0.626948\pi$
$263$	−12.5953			−0.776659			−0.388330	+	0.921521i	$0.626948\pi$
$264$	−26.7802	−	10.2122i	−1.64821	−	0.628515i
$265$	−6.43437			−0.395260
$266$	−0.911216	−	0.318715i	−0.0558702	−	0.0195417i
$267$	−3.32217	−	4.41488i	−0.203314	−	0.270186i
$268$	−9.26788	+	11.6278i	−0.566126	+	0.710280i
$269$		−	26.4922i		−	1.61526i	−0.589690	−	0.807629i	$-0.700750\pi$
$269$		−	26.4922i		−	1.61526i	0.589690	−	0.807629i	$-0.299250\pi$
$270$	−4.32378	+	0.121189i	−0.263137	+	0.00737532i
$271$			10.5644i			0.641741i	0.947123	+	0.320871i	$0.103976\pi$
$271$			10.5644i			0.641741i	−0.947123	+	0.320871i	$0.896024\pi$
$272$	−28.3373	+	6.48337i	−1.71820	+	0.393112i
$273$	1.10860	+	1.47323i	0.0670953	+	0.0891639i
$274$	−6.29738	+	18.0044i	−0.380439	+	1.08769i
$275$	−27.2252			−1.64174
$276$	3.46276	+	0.0964349i	0.208434	+	0.00580470i
$277$	−25.7333			−1.54617			−0.773083	−	0.634304i	$-0.781287\pi$
$277$	−25.7333			−1.54617			−0.773083	+	0.634304i	$0.781287\pi$
$278$	−4.02254	+	11.5006i	−0.241256	+	0.689758i
$279$	−26.7028	−	7.69601i	−1.59865	−	0.460748i
$280$	−0.476901	−	0.758324i	−0.0285003	−	0.0453185i
$281$		−	11.9567i		−	0.713274i	−0.934243	−	0.356637i	$-0.883923\pi$
$281$		−	11.9567i		−	0.713274i	0.934243	−	0.356637i	$-0.116077\pi$
$282$	−20.6064	+	6.56962i	−1.22710	+	0.391215i
$283$			14.7565i			0.877182i	0.898687	+	0.438591i	$0.144522\pi$
$283$			14.7565i			0.877182i	−0.898687	+	0.438591i	$0.855478\pi$
$284$	6.15706	+	4.90747i	0.365355	+	0.291204i
$285$	−1.03347	+	0.777679i	−0.0612174	+	0.0460657i
$286$	15.4506	+	5.40413i	0.913612	+	0.319553i
$287$	−0.815931			−0.0481629
$288$	15.6823	+	6.48578i	0.924089	+	0.382178i
$289$	−35.8148			−2.10675
$290$	3.56238	+	1.24601i	0.209190	+	0.0731681i
$291$	17.5735	−	13.2239i	1.03017	−	0.775200i
$292$	0.369767	+	0.294722i	0.0216390	+	0.0172473i
$293$		−	21.2613i		−	1.24210i	−0.783772	−	0.621049i	$-0.786707\pi$
$293$		−	21.2613i		−	1.24210i	0.783772	−	0.621049i	$-0.213293\pi$
$294$	15.6606	−	4.99283i	0.913346	−	0.291187i
$295$			0.766977i			0.0446552i
$296$	−2.20522	−	3.50654i	−0.128176	−	0.203813i
$297$	10.8367	+	28.4027i	0.628810	+	1.64809i
$298$	−5.62501	+	16.0821i	−0.325848	+	0.931611i
$299$	−1.97835			−0.114411
$300$	16.1140	+	0.448762i	0.930344	+	0.0259093i
$301$	2.25338			0.129883
$302$	−5.68014	+	16.2397i	−0.326855	+	0.934490i
$303$	0.296068	+	0.393448i	0.0170086	+	0.0226030i
$304$	4.94665	−	1.13176i	0.283710	−	0.0649107i
$305$			1.32854i			0.0760720i
$306$	25.1465	+	17.8415i	1.43753	+	1.01993i
$307$		−	21.6937i		−	1.23813i	−0.785341	−	0.619064i	$-0.787512\pi$
$307$		−	21.6937i		−	1.23813i	0.785341	−	0.619064i	$-0.212488\pi$
$308$	−3.92414	+	4.92335i	−0.223599	+	0.280534i
$309$	−16.4194	−	21.8200i	−0.934069	−	1.24130i
$310$	−7.27868	−	2.54585i	−0.413401	−	0.144595i
$311$	9.17585			0.520315			0.260157	−	0.965566i	$-0.416226\pi$
$311$	9.17585			0.520315			0.260157	+	0.965566i	$0.416226\pi$
$312$	−9.05579	−	3.45326i	−0.512683	−	0.195503i
$313$	−12.6850			−0.716996			−0.358498	−	0.933530i	$-0.616711\pi$
$313$	−12.6850			−0.716996			−0.358498	+	0.933530i	$0.616711\pi$
$314$	20.4367	+	7.14813i	1.15331	+	0.403392i
$315$	−0.263135	+	0.912996i	−0.0148260	+	0.0514415i
$316$	9.92558	−	12.4530i	0.558357	−	0.700533i
$317$			20.5340i			1.15330i	0.816990	+	0.576651i	$0.195641\pi$
$317$			20.5340i			1.15330i	−0.816990	+	0.576651i	$0.804359\pi$
$318$	−8.13321	−	25.5108i	−0.456088	−	1.43058i
$319$		−	26.5240i		−	1.48506i
$320$	4.24424	+	2.03983i	0.237260	+	0.114030i
$321$	11.4381	−	8.60708i	0.638411	−	0.480400i
$322$	0.251230	−	0.718276i	0.0140005	−	0.0400279i
$323$	9.21951			0.512987
$324$	−5.94585	−	16.9896i	−0.330325	−	0.943867i
$325$	−9.20628			−0.510672
$326$	−6.29758	+	18.0050i	−0.348791	+	0.997204i
$327$	−16.8666	+	12.6920i	−0.932727	+	0.701871i
$328$	3.63074	−	2.28333i	0.200474	−	0.126076i
$329$			4.75101i			0.261932i
$330$	2.56223	+	8.03677i	0.141046	+	0.442410i
$331$			7.09623i			0.390044i	0.980799	+	0.195022i	$0.0624778\pi$
$331$			7.09623i			0.390044i	−0.980799	+	0.195022i	$0.937522\pi$
$332$	−1.14432	−	0.912079i	−0.0628029	−	0.0500568i
$333$	−1.21675	+	4.22175i	−0.0666775	+	0.231350i
$334$	25.2164	+	8.81989i	1.37978	+	0.482603i
$335$	4.37623			0.239099
$336$	2.40377	−	2.84935i	0.131136	−	0.155445i
$337$	20.4166			1.11216			0.556082	−	0.831127i	$-0.312304\pi$
$337$	20.4166			1.11216			0.556082	+	0.831127i	$0.312304\pi$
$338$	−12.1292	−	4.24242i	−0.659743	−	0.230757i
$339$	−8.29055	−	11.0174i	−0.450281	−	0.598385i
$340$	6.69034	+	5.33251i	0.362834	+	0.289196i
$341$			54.1941i			2.93478i
$342$	−4.38965	−	3.11446i	−0.237365	−	0.168411i
$343$		−	7.37719i		−	0.398331i
$344$	−10.0271	+	6.30594i	−0.540627	+	0.339994i
$345$	−0.613014	−	0.814643i	−0.0330036	−	0.0438589i
$346$	9.32774	−	26.6683i	0.501463	−	1.43370i
$347$	−14.8367			−0.796477			−0.398239	−	0.917282i	$-0.630378\pi$
$347$	−14.8367			−0.796477			−0.398239	+	0.917282i	$0.630378\pi$
$348$	−0.437204	+	15.6990i	−0.0234366	+	0.841555i
$349$	−13.5433			−0.724954			−0.362477	−	0.931993i	$-0.618069\pi$
$349$	−13.5433			−0.724954			−0.362477	+	0.931993i	$0.618069\pi$
$350$	1.16911	−	3.34251i	0.0624914	−	0.178665i
$351$	3.66446	+	9.60446i	0.195594	+	0.512648i
$352$	3.68401	−	32.8895i	0.196359	−	1.75301i
$353$		−	7.53844i		−	0.401231i	−0.979670	−	0.200615i	$-0.935706\pi$
$353$		−	7.53844i		−	0.401231i	0.979670	−	0.200615i	$-0.0642942\pi$
$354$	−3.04089	+	0.969479i	−0.161622	+	0.0515272i
$355$		−	2.31727i		−	0.122988i
$356$	3.97654	−	4.98910i	0.210756	−	0.264422i
$357$	5.41186	−	4.07239i	0.286426	−	0.215534i
$358$	−13.6046	−	4.75847i	−0.719027	−	0.251493i
$359$	3.01230			0.158983			0.0794914	−	0.996836i	$-0.474670\pi$
$359$	3.01230			0.158983			0.0794914	+	0.996836i	$0.474670\pi$
$360$	−1.38406	−	4.79903i	−0.0729464	−	0.252931i
$361$	17.3906			0.915295
$362$	−12.2356	−	4.27962i	−0.643088	−	0.224932i
$363$	32.1468	−	24.1903i	1.68727	−	1.26966i
$364$	−1.32696	+	1.66484i	−0.0695515	+	0.0872616i
$365$		−	0.139166i		−	0.00728426i
$366$	−5.26737	+	1.67931i	−0.275330	+	0.0877789i
$367$		−	15.7949i		−	0.824487i	−0.911074	−	0.412243i	$-0.864745\pi$
$367$		−	15.7949i		−	0.824487i	0.911074	−	0.412243i	$-0.135255\pi$
$368$	0.892120	+	3.89925i	0.0465050	+	0.203262i
$369$	−4.37129	−	1.25985i	−0.227560	−	0.0655851i
$370$	−0.402503	+	1.15077i	−0.0209251	+	0.0598257i
$371$	−5.88176			−0.305366
$372$	0.893299	−	32.0763i	0.0463154	−	1.66308i
$373$	30.9246			1.60122			0.800609	−	0.599187i	$-0.204510\pi$
$373$	30.9246			1.60122			0.800609	+	0.599187i	$0.204510\pi$
$374$	19.8519	−	56.7571i	1.02651	−	2.93484i
$375$	−5.91774	−	7.86417i	−0.305591	−	0.406104i
$376$	−13.2954	−	21.1411i	−0.685658	−	1.09027i
$377$		−	8.96917i		−	0.461936i
$378$	−3.95243	+	0.110781i	−0.203291	+	0.00569794i
$379$		−	6.90466i		−	0.354668i	−0.984151	−	0.177334i	$-0.943253\pi$
$379$		−	6.90466i		−	0.354668i	0.984151	−	0.177334i	$-0.0567474\pi$
$380$	−1.16789	−	0.930859i	−0.0599113	−	0.0477521i
$381$	7.10842	+	9.44647i	0.364175	+	0.483958i
$382$	13.8422	+	4.84156i	0.708228	+	0.247716i
$383$	10.2555			0.524029			0.262015	−	0.965064i	$-0.415613\pi$
$383$	10.2555			0.524029			0.262015	+	0.965064i	$0.415613\pi$
$384$	−2.72262	+	19.4059i	−0.138938	+	0.990301i
$385$	1.85295			0.0944352
$386$	−22.0125	−	7.69926i	−1.12040	−	0.391882i
$387$	12.0723	+	3.47936i	0.613671	+	0.176866i
$388$	19.8591	+	15.8287i	1.00820	+	0.803578i
$389$			34.2979i			1.73897i	0.493957	+	0.869486i	$0.335550\pi$
$389$			34.2979i			1.73897i	−0.493957	+	0.869486i	$0.664450\pi$
$390$	0.866426	+	2.71765i	0.0438732	+	0.137614i
$391$			7.26738i			0.367527i
$392$	10.1043	+	16.0670i	0.510345	+	0.811504i
$393$	23.1752	−	17.4392i	1.16903	−	0.879691i
$394$	3.78935	−	10.8339i	0.190905	−	0.545803i
$395$	−4.68679			−0.235818
$396$	−28.6253	+	20.3174i	−1.43847	+	1.02099i
$397$	17.2143			0.863962			0.431981	−	0.901883i	$-0.357815\pi$
$397$	17.2143			0.863962			0.431981	+	0.901883i	$0.357815\pi$
$398$	−7.56687	+	21.6339i	−0.379293	+	1.08441i
$399$	−0.944710	+	0.710889i	−0.0472947	+	0.0355890i
$400$	4.15150	+	18.1452i	0.207575	+	0.907262i
$401$		−	21.1161i		−	1.05449i	−0.849713	−	0.527245i	$-0.823225\pi$
$401$		−	21.1161i		−	1.05449i	0.849713	−	0.527245i	$-0.176775\pi$
$402$	5.53167	+	17.3508i	0.275894	+	0.865378i
$403$			18.3259i			0.912877i
$404$	−0.354384	+	0.444622i	−0.0176313	+	0.0221208i
$405$	−2.81945	+	4.48501i	−0.140099	+	0.222862i
$406$	3.25643	+	1.13900i	0.161614	+	0.0565274i
$407$	8.56817			0.424708
$408$	−12.6854	+	33.2661i	−0.628023	+	1.64692i
$409$	−7.91024			−0.391136			−0.195568	−	0.980690i	$-0.562655\pi$
$409$	−7.91024			−0.391136			−0.195568	+	0.980690i	$0.562655\pi$
$410$	−1.19153	−	0.416760i	−0.0588455	−	0.0205823i
$411$	14.0462	+	18.6662i	0.692849	+	0.920737i
$412$	19.6536	−	24.6580i	0.968263	−	1.21481i
$413$			0.701106i			0.0344992i
$414$	2.45501	−	3.46019i	0.120657	−	0.170059i
$415$			0.430677i			0.0211411i
$416$	1.24576	−	11.1217i	0.0610783	−	0.545284i
$417$	8.97221	+	11.9233i	0.439371	+	0.583887i
$418$	−3.46540	+	9.90770i	−0.169498	+	0.484601i
$419$	17.8462			0.871844			0.435922	−	0.899984i	$-0.356422\pi$
$419$	17.8462			0.871844			0.435922	+	0.899984i	$0.356422\pi$
$420$	−1.09672	−	0.0305428i	−0.0535146	−	0.00149034i
$421$	−27.8105			−1.35540			−0.677700	−	0.735338i	$-0.737023\pi$
$421$	−27.8105			−1.35540			−0.677700	+	0.735338i	$0.737023\pi$
$422$	5.89190	−	16.8451i	0.286813	−	0.820008i
$423$	−7.33586	+	25.4532i	−0.356682	+	1.23758i
$424$	26.1728	−	16.4597i	1.27106	−	0.799355i
$425$			33.8189i			1.64046i
$426$	9.18746	−	2.92909i	0.445134	−	0.141915i
$427$			1.21444i			0.0587709i
$428$	12.9258	+	10.3024i	0.624790	+	0.497987i
$429$	16.0185	−	12.0538i	0.773381	−	0.581964i
$430$	3.29069	+	1.15098i	0.158691	+	0.0555052i
$431$	−22.8918			−1.10266			−0.551329	−	0.834288i	$-0.685879\pi$
$431$	−22.8918			−1.10266			−0.551329	+	0.834288i	$0.685879\pi$
$432$	17.2776	−	11.5536i	0.831268	−	0.555872i
$433$	−16.0841			−0.772955			−0.386477	−	0.922299i	$-0.626308\pi$
$433$	−16.0841			−0.772955			−0.386477	+	0.922299i	$0.626308\pi$
$434$	−6.65356	−	2.32721i	−0.319381	−	0.111709i
$435$	3.69332	−	2.77920i	0.177081	−	0.133253i
$436$	−19.0604	−	15.1920i	−0.912826	−	0.727565i
$437$		−	1.26862i		−	0.0606861i
$438$	0.551760	−	0.175909i	0.0263641	−	0.00840525i
$439$		−	4.51769i		−	0.215618i	−0.994172	−	0.107809i	$-0.965617\pi$
$439$		−	4.51769i		−	0.215618i	0.994172	−	0.107809i	$-0.0343834\pi$
$440$	−8.24530	+	5.18537i	−0.393079	+	0.247203i
$441$	5.57515	−	19.3441i	0.265484	−	0.921146i
$442$	6.71295	−	19.1926i	0.319303	−	0.912897i
$443$	5.09237			0.241946			0.120973	−	0.992656i	$-0.461399\pi$
$443$	5.09237			0.241946			0.120973	+	0.992656i	$0.461399\pi$
$444$	−5.07132	−	0.141232i	−0.240674	−	0.00670257i
$445$	−1.87770			−0.0890113
$446$	−9.12081	+	26.0767i	−0.431883	+	1.23477i
$447$	12.5465	+	16.6732i	0.593430	+	0.788617i
$448$	3.87973	+	1.86464i	0.183300	+	0.0880958i
$449$		−	23.2680i		−	1.09808i	−0.835795	−	0.549041i	$-0.814993\pi$
$449$		−	23.2680i		−	1.09808i	0.835795	−	0.549041i	$-0.185007\pi$
$450$	11.4244	−	16.1021i	0.538554	−	0.759059i
$451$			8.87166i			0.417750i
$452$	9.92355	−	12.4504i	0.466765	−	0.585618i
$453$	12.6695	+	16.8366i	0.595264	+	0.791055i
$454$	−18.5385	−	6.48417i	−0.870053	−	0.304317i
$455$	0.626581			0.0293745
$456$	2.21441	−	5.80703i	0.103699	−	0.271939i
$457$	35.1278			1.64321			0.821605	−	0.570057i	$-0.193079\pi$
$457$	35.1278			1.64321			0.821605	+	0.570057i	$0.193079\pi$
$458$	−6.92718	−	2.42291i	−0.323686	−	0.113215i
$459$	35.2816	−	13.4613i	1.64681	−	0.628318i
$460$	0.733760	−	0.920599i	0.0342117	−	0.0429231i
$461$			4.35975i			0.203054i	0.994833	+	0.101527i	$0.0323728\pi$
$461$			4.35975i			0.203054i	−0.994833	+	0.101527i	$0.967627\pi$
$462$	2.34218	+	7.34654i	0.108968	+	0.341792i
$463$			29.3547i			1.36423i	0.731245	+	0.682115i	$0.238940\pi$
$463$			29.3547i			1.36423i	−0.731245	+	0.682115i	$0.761060\pi$
$464$	−17.6779	+	4.04458i	−0.820676	+	0.187765i
$465$	−7.54623	+	5.67849i	−0.349948	+	0.263334i
$466$	−10.0586	+	28.7579i	−0.465956	+	1.33218i
$467$	10.2477			0.474207			0.237104	−	0.971484i	$-0.423802\pi$
$467$	10.2477			0.474207			0.237104	+	0.971484i	$0.423802\pi$
$468$	−9.67970	+	6.87037i	−0.447444	+	0.317583i
$469$	4.00038			0.184720
$470$	−2.42671	+	6.93806i	−0.111936	+	0.320029i
$471$	21.1879	−	15.9438i	0.976289	−	0.734651i
$472$	−1.96200	−	3.11979i	−0.0903084	−	0.143600i
$473$		−	24.5011i		−	1.12656i
$474$	−5.92422	−	18.5821i	−0.272109	−	0.853503i
$475$		−	5.90353i		−	0.270873i
$476$	6.11574	+	4.87453i	0.280315	+	0.223424i
$477$	−31.5111	−	9.08181i	−1.44279	−	0.415828i
$478$	−17.3991	−	6.08566i	−0.795817	−	0.278352i
$479$	−25.9407			−1.18526			−0.592631	−	0.805474i	$-0.701911\pi$
$479$	−25.9407			−1.18526			−0.592631	+	0.805474i	$0.701911\pi$
$480$	4.96569	−	2.93320i	0.226652	−	0.133882i
$481$	2.89735			0.132108
$482$	18.2066	+	6.36809i	0.829287	+	0.290058i
$483$	−0.560366	−	0.744678i	−0.0254975	−	0.0338840i
$484$	36.3280	+	28.9551i	1.65127	+	1.31614i
$485$		−	7.47418i		−	0.339385i
$486$	−21.3459	−	5.50931i	−0.968270	−	0.249907i
$487$		−	7.35677i		−	0.333367i	−0.986010	−	0.166683i	$-0.946694\pi$
$487$		−	7.35677i		−	0.333367i	0.986010	−	0.166683i	$-0.0533058\pi$
$488$	−3.39853	−	5.40404i	−0.153844	−	0.244629i
$489$	14.0467	+	18.6668i	0.635212	+	0.844143i
$490$	1.84427	−	5.27283i	0.0833156	−	0.238202i
$491$	−9.47717			−0.427699			−0.213849	−	0.976867i	$-0.568600\pi$
$491$	−9.47717			−0.427699			−0.213849	+	0.976867i	$0.568600\pi$
$492$	0.146234	−	5.25095i	0.00659276	−	0.236731i
$493$	−32.9479			−1.48390
$494$	−1.17183	+	3.35031i	−0.0527233	+	0.150738i
$495$	9.92705	+	2.86108i	0.446188	+	0.128596i
$496$	36.1196	−	8.26392i	1.62182	−	0.371061i
$497$		−	2.11825i		−	0.0950167i
$498$	−1.70754	+	0.544387i	−0.0765167	+	0.0243946i
$499$		−	8.06021i		−	0.360825i	−0.983591	−	0.180412i	$-0.942257\pi$
$499$		−	8.06021i		−	0.360825i	0.983591	−	0.180412i	$-0.0577432\pi$
$500$	7.08337	−	8.88702i	0.316778	−	0.397440i
$501$	26.1432	−	19.6726i	1.16799	−	0.878909i
$502$	−18.4891	−	6.46690i	−0.825208	−	0.288632i
$503$	35.7599			1.59445			0.797227	−	0.603680i	$-0.206299\pi$
$503$	35.7599			1.59445			0.797227	+	0.603680i	$0.206299\pi$
$504$	−1.26519	−	4.38687i	−0.0563561	−	0.195407i
$505$	0.167338			0.00744643
$506$	−7.80985	−	2.73164i	−0.347190	−	0.121436i
$507$	−12.5751	+	9.46266i	−0.558478	+	0.420252i
$508$	−8.50857	+	10.6751i	−0.377507	+	0.473632i
$509$		−	24.5359i		−	1.08753i	−0.839236	−	0.543767i	$-0.816997\pi$
$509$		−	24.5359i		−	1.08753i	0.839236	−	0.543767i	$-0.183003\pi$
$510$	9.98320	−	3.18278i	0.442063	−	0.140936i
$511$		−	0.127213i		−	0.00562759i
$512$	−22.4821	+	2.55988i	−0.993580	+	0.113132i
$513$	−6.15887	+	2.34984i	−0.271921	+	0.103748i
$514$	−5.82217	+	16.6458i	−0.256805	+	0.734214i
$515$	−9.28029			−0.408939
$516$	−0.403860	+	14.5017i	−0.0177790	+	0.638402i
$517$	51.6580			2.27191
$518$	−0.367935	+	1.05194i	−0.0161661	+	0.0462195i
$519$	−20.8054	−	27.6486i	−0.913256	−	1.21364i
$520$	−2.78817	+	1.75345i	−0.122269	+	0.0768937i
$521$			39.9339i			1.74954i	0.484542	+	0.874768i	$0.338986\pi$
$521$			39.9339i			1.74954i	−0.484542	+	0.874768i	$0.661014\pi$
$522$	15.6874	+	11.1302i	0.686618	+	0.487156i
$523$			8.29628i			0.362771i	0.983412	+	0.181385i	$0.0580582\pi$
$523$			8.29628i			0.362771i	−0.983412	+	0.181385i	$0.941942\pi$
$524$	26.1895	+	20.8742i	1.14409	+	0.911894i
$525$	−2.60768	−	3.46538i	−0.113808	−	0.151241i
$526$	−16.8136	−	5.88088i	−0.733109	−	0.256419i
$527$	67.3194			2.93248
$528$	−30.9811	−	26.1363i	−1.34828	−	1.13744i
$529$	1.00000			0.0434783
$530$	−8.58933	−	3.00428i	−0.373097	−	0.130498i
$531$	−1.08255	+	3.75612i	−0.0469788	+	0.163002i
$532$	−1.06758	−	0.850913i	−0.0462856	−	0.0368918i
$533$			2.99997i			0.129943i
$534$	−2.37346	−	7.44464i	−0.102709	−	0.322161i
$535$		−	4.86474i		−	0.210321i
$536$	−17.8010	+	11.1948i	−0.768884	+	0.483542i
$537$	−14.1047	+	10.6137i	−0.608663	+	0.458015i
$538$	12.3695	−	35.3648i	0.533287	−	1.52469i
$539$	−39.2594			−1.69102
$540$	−5.82845	−	1.85704i	−0.250817	−	0.0799143i
$541$	−43.2364			−1.85888			−0.929440	−	0.368973i	$-0.879709\pi$
$541$	−43.2364			−1.85888			−0.929440	+	0.368973i	$0.879709\pi$
$542$	−4.93263	+	14.1026i	−0.211875	+	0.605757i
$543$	−12.6853	+	9.54564i	−0.544380	+	0.409643i
$544$	−40.8550	−	4.57625i	−1.75164	−	0.196205i
$545$			7.17356i			0.307281i
$546$	0.792014	+	2.48425i	0.0338951	+	0.106316i
$547$			38.5471i			1.64815i	0.566477	+	0.824077i	$0.308306\pi$
$547$			38.5471i			1.64815i	−0.566477	+	0.824077i	$0.691694\pi$
$548$	−16.8129	+	21.0940i	−0.718213	+	0.901093i
$549$	−1.87517	+	6.50627i	−0.0800304	+	0.277681i
$550$	−36.3433	−	12.7118i	−1.54968	−	0.542031i
$551$	5.75149			0.245022
$552$	4.57746	+	1.74553i	0.194830	+	0.0742948i
$553$	−4.28427			−0.182186
$554$	−34.3518	−	12.0152i	−1.45947	−	0.510476i
$555$	0.897778	+	1.19307i	0.0381085	+	0.0506430i
$556$	−10.7395	+	13.4741i	−0.455455	+	0.571429i
$557$		−	16.4418i		−	0.696662i	−0.937372	−	0.348331i	$-0.886748\pi$
$557$		−	16.4418i		−	0.696662i	0.937372	−	0.348331i	$-0.113252\pi$
$558$	−32.0526	−	22.7413i	−1.35689	−	0.962717i
$559$		−	8.28512i		−	0.350423i
$560$	−0.282552	−	1.23497i	−0.0119400	−	0.0521869i
$561$	−44.2793	−	58.8434i	−1.86947	−	2.48437i
$562$	5.58269	−	15.9611i	0.235492	−	0.673278i
$563$	−7.65317			−0.322542			−0.161271	−	0.986910i	$-0.551559\pi$
$563$	−7.65317			−0.322542			−0.161271	+	0.986910i	$0.551559\pi$
$564$	−30.5753	−	0.851495i	−1.28745	−	0.0358544i
$565$	−4.68583			−0.197134
$566$	−6.88996	+	19.6986i	−0.289607	+	0.827995i
$567$	−2.57730	+	4.09982i	−0.108236	+	0.172176i
$568$	5.92780	+	9.42584i	0.248725	+	0.395500i
$569$			13.2613i			0.555942i	0.960590	+	0.277971i	$0.0896619\pi$
$569$			13.2613i			0.555942i	−0.960590	+	0.277971i	$0.910338\pi$
$570$	−1.74270	+	0.555597i	−0.0729936	+	0.0232714i
$571$		−	19.1048i		−	0.799512i	−0.916622	−	0.399756i	$-0.869095\pi$
$571$		−	19.1048i		−	0.799512i	0.916622	−	0.399756i	$-0.130905\pi$
$572$	18.1019	+	14.4281i	0.756880	+	0.603268i
$573$	14.3510	−	10.7990i	0.599522	−	0.451136i
$574$	−1.08920	−	0.380967i	−0.0454622	−	0.0159013i
$575$	4.65352			0.194065
$576$	17.9062	+	15.9802i	0.746093	+	0.665842i
$577$	−42.8506			−1.78390			−0.891948	−	0.452138i	$-0.850661\pi$
$577$	−42.8506			−1.78390			−0.891948	+	0.452138i	$0.850661\pi$
$578$	−47.8096	−	16.7223i	−1.98862	−	0.695556i
$579$	−22.8216	+	17.1731i	−0.948433	+	0.713690i
$580$	4.17369	+	3.32663i	0.173303	+	0.138131i
$581$			0.393689i			0.0163330i
$582$	29.6334	−	9.44756i	1.22835	−	0.391614i
$583$			63.9527i			2.64865i
$584$	0.355999	+	0.566076i	0.0147313	+	0.0234244i
$585$	3.35686	+	0.967480i	0.138789	+	0.0400004i
$586$	9.92713	−	28.3820i	0.410086	−	1.17245i
$587$	−12.7842			−0.527659			−0.263829	−	0.964569i	$-0.584986\pi$
$587$	−12.7842			−0.527659			−0.263829	+	0.964569i	$0.584986\pi$
$588$	23.2368	+	0.647125i	0.958269	+	0.0266870i
$589$	−11.7515			−0.484211
$590$	−0.358110	+	1.02385i	−0.0147432	+	0.0421512i
$591$	−8.45209	−	11.2321i	−0.347673	−	0.462027i
$592$	−1.30654	−	5.71057i	−0.0536984	−	0.234703i
$593$		−	18.7122i		−	0.768418i	−0.923246	−	0.384209i	$-0.874474\pi$
$593$		−	18.7122i		−	0.768418i	0.923246	−	0.384209i	$-0.125526\pi$
$594$	1.20452	+	42.9750i	0.0494222	+	1.76329i
$595$		−	2.30172i		−	0.0943613i
$596$	−15.0178	+	18.8418i	−0.615154	+	0.771792i
$597$	16.8778	+	22.4292i	0.690763	+	0.917964i
$598$	−2.64092	−	0.923711i	−0.107995	−	0.0377733i
$599$	−30.2396			−1.23556			−0.617779	−	0.786352i	$-0.711967\pi$
$599$	−30.2396			−1.23556			−0.617779	+	0.786352i	$0.711967\pi$
$600$	21.3013	+	8.12287i	0.869622	+	0.331615i
$601$	5.03298			0.205300			0.102650	−	0.994718i	$-0.467268\pi$
$601$	5.03298			0.205300			0.102650	+	0.994718i	$0.467268\pi$
$602$	3.00807	+	1.05213i	0.122600	+	0.0428816i
$603$	21.4317	+	6.17684i	0.872768	+	0.251540i
$604$	−15.1650	+	19.0265i	−0.617055	+	0.774177i
$605$		−	13.6724i		−	0.555862i
$606$	0.211519	+	0.663457i	0.00859238	+	0.0269511i
$607$		−	20.9083i		−	0.848641i	−0.905512	−	0.424320i	$-0.860513\pi$
$607$		−	20.9083i		−	0.848641i	0.905512	−	0.424320i	$-0.139487\pi$
$608$	7.13177	+	0.798844i	0.289232	+	0.0323974i
$609$	3.37613	−	2.54051i	0.136808	−	0.102947i
$610$	−0.620310	+	1.77349i	−0.0251156	+	0.0718064i
$611$	17.4683			0.706691
$612$	25.2380	+	35.5580i	1.02019	+	1.43735i
$613$	−3.56369			−0.143936			−0.0719680	−	0.997407i	$-0.522928\pi$
$613$	−3.56369			−0.143936			−0.0719680	+	0.997407i	$0.522928\pi$
$614$	10.1290	−	28.9593i	0.408775	−	1.16870i
$615$	−1.23533	+	0.929578i	−0.0498133	+	0.0374842i
$616$	−7.53716	+	4.74003i	−0.303681	+	0.190981i
$617$		−	45.3619i		−	1.82620i	−0.407732	−	0.913102i	$-0.633680\pi$
$617$		−	45.3619i		−	1.82620i	0.407732	−	0.913102i	$-0.366320\pi$
$618$	−11.7305	−	36.7943i	−0.471871	−	1.48008i
$619$		−	10.1501i		−	0.407967i	−0.978974	−	0.203984i	$-0.934611\pi$
$619$		−	10.1501i		−	0.407967i	0.978974	−	0.203984i	$-0.0653889\pi$
$620$	−8.52772	−	6.79699i	−0.342482	−	0.272974i
$621$	−1.85229	−	4.85480i	−0.0743297	−	0.194816i
$622$	12.2490	+	4.28430i	0.491139	+	0.171785i
$623$	−1.71643			−0.0687674
$624$	−10.4763	−	8.83806i	−0.419389	−	0.353805i
$625$	19.9229			0.796916
$626$	−16.9333	−	5.92274i	−0.676791	−	0.236720i
$627$	7.72953	+	10.2719i	0.308688	+	0.410219i
$628$	23.9437	+	19.0843i	0.955459	+	0.761545i
$629$		−	10.6433i		−	0.424376i
$630$	−0.777550	+	1.09591i	−0.0309783	+	0.0436621i
$631$			30.2545i			1.20441i	0.798340	+	0.602207i	$0.205712\pi$
$631$			30.2545i			1.20441i	−0.798340	+	0.602207i	$0.794288\pi$
$632$	19.0642	−	11.9893i	0.758334	−	0.476907i
$633$	−13.1418	−	17.4643i	−0.522340	−	0.694145i
$634$	−9.58753	+	27.4111i	−0.380770	+	1.08863i
$635$	4.01769			0.159437
$636$	1.05415	−	37.8523i	0.0417999	−	1.50094i
$637$	−13.2756			−0.526000
$638$	12.3844	−	35.4073i	0.490301	−	1.40179i
$639$	3.27072	−	11.3484i	0.129388	−	0.448935i
$640$	4.71328	+	4.70467i	0.186309	+	0.185969i
$641$			12.9590i			0.511849i	0.966697	+	0.255924i	$0.0823798\pi$
$641$			12.9590i			0.511849i	−0.966697	+	0.255924i	$0.917620\pi$
$642$	19.2876	−	6.14915i	0.761220	−	0.242688i
$643$			20.5803i			0.811606i	0.913961	+	0.405803i	$0.133008\pi$
$643$			20.5803i			0.811606i	−0.913961	+	0.405803i	$0.866992\pi$
$644$	0.670742	−	0.841534i	0.0264309	−	0.0331611i
$645$	3.41165	−	2.56724i	0.134333	−	0.101085i
$646$	12.3072	+	4.30469i	0.484222	+	0.169366i
$647$	48.9952			1.92620			0.963100	−	0.269142i	$-0.0867401\pi$
$647$	48.9952			1.92620			0.963100	+	0.269142i	$0.0867401\pi$
$648$	−0.00456109	−	25.4558i	−0.000179177	−	1.00000i
$649$	7.62316			0.299235
$650$	−12.2896	−	4.29851i	−0.482037	−	0.168601i
$651$	−6.89813	+	5.19080i	−0.270359	+	0.203443i
$652$	−16.8135	+	21.0947i	−0.658466	+	0.826132i
$653$			17.3346i			0.678356i	0.940722	+	0.339178i	$0.110149\pi$
$653$			17.3346i			0.678356i	−0.940722	+	0.339178i	$0.889851\pi$
$654$	−28.4415	+	9.06756i	−1.11215	+	0.354570i
$655$		−	9.85666i		−	0.385132i
$656$	5.91284	−	1.35282i	0.230858	−	0.0528186i
$657$	0.196426	−	0.681536i	0.00766329	−	0.0265893i
$658$	−2.21830	+	6.34219i	−0.0864783	+	0.247244i
$659$	−10.2660			−0.399906			−0.199953	−	0.979806i	$-0.564079\pi$
$659$	−10.2660			−0.399906			−0.199953	+	0.979806i	$0.564079\pi$
$660$	−0.332094	+	11.9247i	−0.0129267	+	0.464169i
$661$	14.7119			0.572227			0.286113	−	0.958196i	$-0.407637\pi$
$661$	14.7119			0.572227			0.286113	+	0.958196i	$0.407637\pi$
$662$	−3.31331	+	9.47285i	−0.128775	+	0.368173i
$663$	−14.9732	−	19.8980i	−0.581509	−	0.772776i
$664$	−1.10171	−	1.75184i	−0.0427548	−	0.0679847i
$665$			0.401795i			0.0155810i
$666$	−3.59544	+	5.06756i	−0.139320	+	0.196364i
$667$			4.53367i			0.175544i
$668$	29.5435	+	23.5476i	1.14307	+	0.911083i
$669$	20.3438	+	27.0352i	0.786538	+	1.04524i
$670$	5.84189	+	2.04331i	0.225692	+	0.0789399i
$671$	13.2047			0.509761
$672$	4.53922	−	2.68128i	0.175104	−	0.103433i
$673$	0.632994			0.0244001			0.0122001	−	0.999926i	$-0.496117\pi$
$673$	0.632994			0.0244001			0.0122001	+	0.999926i	$0.496117\pi$
$674$	27.2544	+	9.53274i	1.04980	+	0.367188i
$675$	−8.61966	−	22.5919i	−0.331771	−	0.869563i
$676$	−14.2106	−	11.3265i	−0.546563	−	0.435636i
$677$		−	9.33805i		−	0.358891i	−0.983768	−	0.179445i	$-0.942570\pi$
$677$		−	9.33805i		−	0.358891i	0.983768	−	0.179445i	$-0.0574303\pi$
$678$	−5.92301	−	18.5783i	−0.227472	−	0.713494i
$679$		−	6.83227i		−	0.262198i
$680$	6.44122	+	10.2422i	0.247009	+	0.392772i
$681$	−19.2199	+	14.4629i	−0.736508	+	0.554218i
$682$	−25.3038	+	72.3445i	−0.968933	+	2.77021i
$683$	17.5360			0.670995			0.335498	−	0.942041i	$-0.391096\pi$
$683$	17.5360			0.670995			0.335498	+	0.942041i	$0.391096\pi$
$684$	−4.40563	−	6.20712i	−0.168453	−	0.237335i
$685$	7.93895			0.303332
$686$	3.44449	−	9.84791i	0.131511	−	0.375995i
$687$	−7.18181	+	5.40427i	−0.274003	+	0.206186i
$688$	−16.3297	+	3.73611i	−0.622563	+	0.142438i
$689$			21.6258i			0.823876i
$690$	−0.437955	−	1.37370i	−0.0166727	−	0.0522959i
$691$		−	28.1823i		−	1.07210i	−0.844185	−	0.536052i	$-0.819915\pi$
$691$		−	28.1823i		−	1.07210i	0.844185	−	0.536052i	$-0.180085\pi$
$692$	24.9035	−	31.2447i	0.946688	−	1.18774i
$693$	9.07447	+	2.61536i	0.344711	+	0.0993491i
$694$	−19.8057	−	6.92743i	−0.751816	−	0.262962i
$695$	5.07111			0.192358
$696$	−7.91367	+	20.7527i	−0.299967	+	0.786629i
$697$	11.0203			0.417423
$698$	−18.0791	−	6.32350i	−0.684303	−	0.239348i
$699$	22.4356	+	29.8150i	0.848592	+	1.12771i
$700$	3.12131	−	3.91610i	0.117974	−	0.148015i
$701$			33.6545i			1.27111i	0.772055	+	0.635556i	$0.219229\pi$
$701$			33.6545i			1.27111i	−0.772055	+	0.635556i	$0.780771\pi$
$702$	0.407313	+	14.5321i	0.0153730	+	0.548479i
$703$			1.85793i			0.0700730i
$704$	20.2743	−	42.1845i	0.764116	−	1.58989i
$705$	5.41275	+	7.19308i	0.203856	+	0.270907i
$706$	3.51978	−	10.0632i	0.132469	−	0.378732i
$707$	0.152966			0.00575288
$708$	−4.51199	−	0.125655i	−0.169571	−	0.00472241i
$709$	41.0192			1.54051			0.770254	−	0.637737i	$-0.220129\pi$
$709$	41.0192			1.54051			0.770254	+	0.637737i	$0.220129\pi$
$710$	1.08196	−	3.09336i	0.0406052	−	0.116092i
$711$	−22.9526	−	6.61518i	−0.860791	−	0.248089i
$712$	7.63780	−	4.80332i	0.286239	−	0.180012i
$713$		−	9.26323i		−	0.346911i
$714$	9.12580	−	2.90943i	0.341525	−	0.108883i
$715$		−	6.81284i		−	0.254786i
$716$	−15.9392	−	12.7043i	−0.595677	−	0.474782i
$717$	−18.0387	+	13.5740i	−0.673666	+	0.506930i
$718$	4.02115	+	1.40647i	0.150068	+	0.0524891i
$719$	−44.0134			−1.64142			−0.820711	−	0.571344i	$-0.806422\pi$
$719$	−44.0134			−1.64142			−0.820711	+	0.571344i	$0.806422\pi$
$720$	0.393118	−	7.05252i	0.0146507	−	0.262832i
$721$	−8.48326			−0.315933
$722$	23.2150	+	8.11987i	0.863972	+	0.302190i
$723$	18.8758	−	14.2039i	0.701999	−	0.528250i
$724$	−14.3352	−	11.4259i	−0.532765	−	0.424638i
$725$			21.0975i			0.783543i
$726$	54.2080	−	17.2823i	2.01185	−	0.641405i
$727$			11.4368i			0.424166i	0.977252	+	0.212083i	$0.0680247\pi$
$727$			11.4368i			0.424166i	−0.977252	+	0.212083i	$0.931975\pi$
$728$	−2.54871	+	1.60285i	−0.0944614	+	0.0594057i
$729$	−20.1381	+	17.9849i	−0.745854	+	0.666109i
$730$	0.0649779	−	0.185774i	0.00240494	−	0.00687580i
$731$	−30.4351			−1.12568
$732$	−7.81557	−	0.217657i	−0.288872	−	0.00804483i
$733$	46.9599			1.73450			0.867251	−	0.497871i	$-0.165885\pi$
$733$	46.9599			1.73450			0.867251	+	0.497871i	$0.165885\pi$
$734$	7.37481	−	21.0848i	0.272209	−	0.778255i
$735$	−4.11362	−	5.46665i	−0.151733	−	0.201640i
$736$	−0.629697	+	5.62170i	−0.0232110	+	0.207219i
$737$		−	43.4963i		−	1.60221i
$738$	−5.24705	−	3.72279i	−0.193147	−	0.137038i
$739$			35.9669i			1.32306i	0.749917	+	0.661532i	$0.230093\pi$
$739$			35.9669i			1.32306i	−0.749917	+	0.661532i	$0.769907\pi$
$740$	−1.07461	+	1.34825i	−0.0395036	+	0.0495625i
$741$	2.61376	+	3.47346i	0.0960189	+	0.127601i
$742$	−7.85165	−	2.74626i	−0.288243	−	0.100818i
$743$	5.65631			0.207510			0.103755	−	0.994603i	$-0.466914\pi$
$743$	5.65631			0.207510			0.103755	+	0.994603i	$0.466914\pi$
$744$	16.1693	−	42.4021i	0.592794	−	1.55453i
$745$	7.09131			0.259805
$746$	41.2817	+	14.4391i	1.51143	+	0.528651i
$747$	−0.607881	+	2.10916i	−0.0222412	+	0.0771701i
$748$	53.0010	−	66.4968i	1.93791	−	2.43136i
$749$		−	4.44693i		−	0.162487i
$750$	−4.22781	−	13.2611i	−0.154378	−	0.484225i
$751$		−	2.11699i		−	0.0772501i	−0.999254	−	0.0386251i	$-0.987702\pi$
$751$		−	2.11699i		−	0.0772501i	0.999254	−	0.0386251i	$-0.0122978\pi$
$752$	−7.87719	−	34.4293i	−0.287251	−	1.25551i
$753$	−19.1687	+	14.4243i	−0.698546	+	0.525652i
$754$	4.18780	−	11.9731i	0.152511	−	0.436033i
$755$	7.16081			0.260608
$756$	−5.32788	−	1.69755i	−0.193773	−	0.0617393i
$757$	44.7705			1.62721			0.813606	−	0.581417i	$-0.197502\pi$
$757$	44.7705			1.62721			0.813606	+	0.581417i	$0.197502\pi$
$758$	3.22386	−	9.21712i	0.117096	−	0.334781i
$759$	−8.09692	+	6.09288i	−0.293900	+	0.221158i
$760$	−1.12440	−	1.78792i	−0.0407862	−	0.0648545i
$761$			26.1611i			0.948341i	0.880433	+	0.474170i	$0.157252\pi$
$761$			26.1611i			0.948341i	−0.880433	+	0.474170i	$0.842748\pi$
$762$	5.07846	+	15.9292i	0.183973	+	0.577055i
$763$			6.55746i			0.237396i
$764$	16.2175	+	12.9261i	0.586730	+	0.467651i
$765$	3.55400	−	12.3313i	0.128495	−	0.445839i
$766$	13.6901	+	4.78838i	0.494645	+	0.173011i
$767$	2.57779			0.0930787
$768$	−12.6953	+	24.6339i	−0.458101	+	0.888900i
$769$	−28.1354			−1.01459			−0.507295	−	0.861772i	$-0.669355\pi$
$769$	−28.1354			−1.01459			−0.507295	+	0.861772i	$0.669355\pi$
$770$	2.47353	+	0.865164i	0.0891399	+	0.0311783i
$771$	12.9863	+	17.2576i	0.467689	+	0.621519i
$772$	−25.7899	−	20.5557i	−0.928197	−	0.739816i
$773$		−	3.88847i		−	0.139859i	−0.997552	−	0.0699294i	$-0.977723\pi$
$773$		−	3.88847i		−	0.139859i	0.997552	−	0.0699294i	$-0.0222774\pi$
$774$	14.4910	+	10.2813i	0.520866	+	0.369555i
$775$		−	43.1067i		−	1.54844i
$776$	19.1197	+	30.4023i	0.686356	+	1.09138i
$777$	0.820673	+	1.09060i	0.0294415	+	0.0391252i
$778$	−16.0141	+	45.7847i	−0.574132	+	1.64146i
$779$	−1.92374			−0.0689250
$780$	−0.112298	+	4.03238i	−0.00402092	+	0.144382i
$781$	−23.0319			−0.824146
$782$	−3.39322	+	9.70132i	−0.121341	+	0.346918i
$783$	22.0100	−	8.39766i	0.786575	−	0.300108i
$784$	5.98656	+	26.1658i	0.213806	+	0.934494i
$785$		−	9.01146i		−	0.321633i
$786$	39.0794	−	12.4591i	1.39392	−	0.444400i
$787$		−	43.6834i		−	1.55715i	−0.627554	−	0.778573i	$-0.715944\pi$
$787$		−	43.6834i		−	1.55715i	0.627554	−	0.778573i	$-0.284056\pi$
$788$	10.1169	−	12.6930i	0.360400	−	0.452170i
$789$	−17.4317	+	13.1172i	−0.620584	+	0.466985i
$790$	−6.25646	−	2.18831i	−0.222595	−	0.0778567i
$791$	−4.28339			−0.152300
$792$	−47.6986	+	13.7565i	−1.69490	+	0.488815i
$793$	4.46519			0.158564
$794$	22.9796	+	8.03755i	0.815517	+	0.285242i
$795$	−8.90506	+	6.70100i	−0.315830	+	0.237660i
$796$	−20.2022	+	25.3464i	−0.716050	+	0.898379i
$797$		−	4.62544i		−	0.163842i	−0.996639	−	0.0819208i	$-0.973895\pi$
$797$		−	4.62544i		−	0.163842i	0.996639	−	0.0819208i	$-0.0261055\pi$
$798$	−1.59303	+	0.507880i	−0.0563926	+	0.0179787i
$799$		−	64.1690i		−	2.27014i
$800$	−2.93031	+	26.1607i	−0.103602	+	0.924920i
$801$	−9.19565	−	2.65028i	−0.324912	−	0.0936430i
$802$	9.85936	−	28.1882i	0.348146	−	0.995361i
$803$	−1.38320			−0.0488120
$804$	−0.716964	+	25.7446i	−0.0252854	+	0.907941i
$805$	−0.316720			−0.0111629
$806$	−8.55655	+	24.4635i	−0.301392	+	0.861689i
$807$	−27.5900	−	36.6648i	−0.971214	−	1.29066i
$808$	−0.680671	+	0.428066i	−0.0239459	+	0.0150593i
$809$		−	21.9130i		−	0.770419i	−0.922829	−	0.385210i	$-0.874129\pi$
$809$		−	21.9130i		−	0.770419i	0.922829	−	0.385210i	$-0.125871\pi$
$810$	−5.85782	+	4.67067i	−0.205823	+	0.164111i
$811$		−	18.1124i		−	0.636011i	−0.948089	−	0.318006i	$-0.896987\pi$
$811$		−	18.1124i		−	0.636011i	0.948089	−	0.318006i	$-0.103013\pi$
$812$	3.81524	+	3.04092i	0.133889	+	0.106715i
$813$	11.0022	+	14.6209i	0.385863	+	0.512779i
$814$	11.4378	+	4.00057i	0.400893	+	0.140220i
$815$	7.93920			0.278098
$816$	−32.4663	+	38.4844i	−1.13655	+	1.34722i
$817$	5.31284			0.185873
$818$	−10.5595	−	3.69338i	−0.369204	−	0.129136i
$819$	3.06856	+	0.884389i	0.107224	+	0.0309030i
$820$	−1.39600	−	1.11268i	−0.0487505	−	0.0388564i
$821$		−	23.3176i		−	0.813790i	−0.913475	−	0.406895i	$-0.866612\pi$
$821$		−	23.3176i		−	0.813790i	0.913475	−	0.406895i	$-0.133388\pi$
$822$	10.0350	+	31.4761i	0.350012	+	1.09786i
$823$		−	33.0487i		−	1.15200i	−0.817448	−	0.576002i	$-0.804612\pi$
$823$		−	33.0487i		−	1.15200i	0.817448	−	0.576002i	$-0.195388\pi$
$824$	37.7490	−	23.7399i	1.31505	−	0.827017i
$825$	−37.6792	+	28.3534i	−1.31182	+	0.987138i
$826$	−0.327354	+	0.935916i	−0.0113901	+	0.0325647i
$827$	−25.6575			−0.892199			−0.446099	−	0.894983i	$-0.647187\pi$
$827$	−25.6575			−0.892199			−0.446099	+	0.894983i	$0.647187\pi$
$828$	4.89283	−	3.47279i	0.170038	−	0.120688i
$829$	−28.8977			−1.00366			−0.501829	−	0.864967i	$-0.667339\pi$
$829$	−28.8977			−1.00366			−0.501829	+	0.864967i	$0.667339\pi$
$830$	−0.201088	+	0.574917i	−0.00697987	+	0.0199557i
$831$	−35.6145	+	26.7997i	−1.23545	+	0.929671i
$832$	6.85580	−	14.2648i	0.237682	−	0.494543i
$833$			48.7676i			1.68970i
$834$	6.41001	+	20.1058i	0.221960	+	0.696207i
$835$		−	11.1190i		−	0.384789i
$836$	−9.25202	+	11.6079i	−0.319988	+	0.401467i
$837$	−44.9711	+	17.1582i	−1.55443	+	0.593073i
$838$	23.8231	+	8.33259i	0.822957	+	0.287844i
$839$	4.45675			0.153864			0.0769320	−	0.997036i	$-0.475488\pi$
$839$	4.45675			0.153864			0.0769320	+	0.997036i	$0.475488\pi$
$840$	−1.44977	−	0.552844i	−0.0500218	−	0.0190749i
$841$	8.44582			0.291235
$842$	−37.1246	−	12.9850i	−1.27940	−	0.447493i
$843$	−12.4521	−	16.5478i	−0.428874	−	0.569936i
$844$	15.7304	−	19.7358i	0.541461	−	0.679335i
$845$			5.34831i			0.183988i
$846$	−21.6771	+	30.5526i	−0.745274	+	1.05042i
$847$		−	12.4982i		−	0.429442i
$848$	42.6236	−	9.75198i	1.46370	−	0.334884i
$849$	15.3680	+	20.4227i	0.527427	+	0.700905i
$850$	−15.7904	+	45.1453i	−0.541607	+	1.54847i
$851$	−1.46453			−0.0502035
$852$	13.6321	+	0.379642i	0.467028	+	0.0130063i
$853$	−2.82582			−0.0967542			−0.0483771	−	0.998829i	$-0.515405\pi$
$853$	−2.82582			−0.0967542			−0.0483771	+	0.998829i	$0.515405\pi$
$854$	−0.567036	+	1.62117i	−0.0194036	+	0.0554754i
$855$	−0.620397	+	2.15259i	−0.0212171	+	0.0736169i
$856$	12.4445	+	19.7880i	0.425343	+	0.676341i
$857$			13.5376i			0.462434i	0.972902	+	0.231217i	$0.0742708\pi$
$857$			13.5376i			0.462434i	−0.972902	+	0.231217i	$0.925729\pi$
$858$	27.0114	−	8.61161i	0.922153	−	0.293995i
$859$			17.4689i			0.596031i	0.954561	+	0.298015i	$0.0963247\pi$
$859$			17.4689i			0.596031i	−0.954561	+	0.298015i	$0.903675\pi$
$860$	3.85538	+	3.07292i	0.131467	+	0.104786i
$861$	−1.12923	+	0.849742i	−0.0384842	+	0.0289591i
$862$	−30.5585	−	10.6884i	−1.04083	−	0.364049i
$863$	−5.90488			−0.201004			−0.100502	−	0.994937i	$-0.532045\pi$
$863$	−5.90488			−0.201004			−0.100502	+	0.994937i	$0.532045\pi$
$864$	28.4586	−	7.35594i	0.968180	−	0.250254i
$865$	−11.7592			−0.399826
$866$	−21.4709	−	7.50986i	−0.729612	−	0.255196i
$867$	−49.5670	+	37.2989i	−1.68338	+	1.26674i
$868$	−7.79533	−	6.21324i	−0.264591	−	0.210891i
$869$			46.5831i			1.58022i
$870$	6.22791	−	1.98554i	0.211146	−	0.0673162i
$871$		−	14.7084i		−	0.498375i
$872$	−18.3506	−	29.1795i	−0.621431	−	0.988143i
$873$	10.5495	−	36.6034i	0.357045	−	1.23884i
$874$	0.592330	−	1.69349i	0.0200359	−	0.0572832i
$875$	−3.05746			−0.103361
$876$	0.818686	+	0.0227997i	0.0276608	+	0.000770331i
$877$	22.3348			0.754191			0.377096	−	0.926174i	$-0.376923\pi$
$877$	22.3348			0.754191			0.377096	+	0.926174i	$0.376923\pi$
$878$	2.10936	−	6.03073i	0.0711874	−	0.203527i
$879$	−22.1423	−	29.4253i	−0.746842	−	0.992489i
$880$	−13.4279	+	3.07220i	−0.452653	+	0.103564i
$881$		−	44.8167i		−	1.50991i	−0.655776	−	0.754956i	$-0.727658\pi$
$881$		−	44.8167i		−	1.50991i	0.655776	−	0.754956i	$-0.272342\pi$
$882$	16.4743	−	23.2196i	0.554719	−	0.781843i
$883$		−	31.1315i		−	1.04766i	−0.851823	−	0.523829i	$-0.824503\pi$
$883$		−	31.1315i		−	1.04766i	0.851823	−	0.523829i	$-0.175497\pi$
$884$	17.9224	−	22.4861i	0.602796	−	0.756288i
$885$	0.798760	+	1.06148i	0.0268500	+	0.0356814i
$886$	6.79787	+	2.37768i	0.228379	+	0.0798798i
$887$	25.0923			0.842516			0.421258	−	0.906941i	$-0.361589\pi$
$887$	25.0923			0.842516			0.421258	+	0.906941i	$0.361589\pi$
$888$	−6.70383	−	2.55639i	−0.224966	−	0.0857867i
$889$	3.67263			0.123176
$890$	−2.50656	−	0.876716i	−0.0840201	−	0.0293876i
$891$	44.5775	+	28.0231i	1.49340	+	0.938810i
$892$	−24.3510	+	30.5515i	−0.815331	+	1.02294i
$893$			11.2015i			0.374845i
$894$	8.96360	+	28.1154i	0.299787	+	0.940321i
$895$			5.99888i			0.200520i
$896$	4.30848	+	4.30062i	0.143936	+	0.143674i
$897$	−2.73799	+	2.06032i	−0.0914190	+	0.0687922i
$898$	10.8641	−	31.0607i	0.362538	−	1.03651i
$899$	41.9965			1.40066
$900$	22.7689	−	16.1607i	0.758963	−	0.538690i
$901$	79.4414			2.64658
$902$	−4.14227	+	11.8429i	−0.137923	+	0.394325i
$903$	3.11864	−	2.34676i	0.103782	−	0.0780952i
$904$	19.0603	−	11.9868i	0.633937	−	0.398675i
$905$			5.39521i			0.179343i
$906$	9.05144	+	28.3910i	0.300714	+	0.943227i
$907$			25.2718i			0.839136i	0.907724	+	0.419568i	$0.137818\pi$
$907$			25.2718i			0.839136i	−0.907724	+	0.419568i	$0.862182\pi$
$908$	−21.7197	−	17.3116i	−0.720794	−	0.574506i
$909$	0.819504	+	0.236189i	0.0271812	+	0.00783391i
$910$	0.836431	+	0.292557i	0.0277274	+	0.00969818i
$911$	−40.0503			−1.32693			−0.663463	−	0.748209i	$-0.730914\pi$
$911$	−40.0503			−1.32693			−0.663463	+	0.748209i	$0.730914\pi$
$912$	5.66741	−	6.71796i	0.187667	−	0.222454i
$913$	4.28060			0.141667
$914$	46.8926	+	16.4016i	1.55107	+	0.542515i
$915$	1.38359	+	1.83868i	0.0457402	+	0.0607848i
$916$	−8.11590	−	6.46875i	−0.268157	−	0.213734i
$917$		−	9.01013i		−	0.297541i
$918$	53.3831	−	1.49625i	1.76191	−	0.0493835i
$919$		−	2.59895i		−	0.0857314i	−0.999081	−	0.0428657i	$-0.986351\pi$
$919$		−	2.59895i		−	0.0857314i	0.999081	−	0.0428657i	$-0.0136488\pi$
$920$	1.40934	−	0.886319i	0.0464647	−	0.0292211i
$921$	−22.5927	−	30.0238i	−0.744455	−	0.989316i
$922$	−2.03561	+	5.81988i	−0.0670393	+	0.191668i
$923$	−7.78829			−0.256355
$924$	−0.303572	+	10.9006i	−0.00998679	+	0.358603i
$925$	−6.81523			−0.224083
$926$	−13.7060	+	39.1860i	−0.450408	+	1.28773i
$927$	−45.4484	−	13.0987i	−1.49272	−	0.430218i
$928$	−25.4869	−	2.85484i	−0.836650	−	0.0937147i
$929$		−	30.0541i		−	0.986042i	−0.870018	−	0.493021i	$-0.835893\pi$
$929$		−	30.0541i		−	0.986042i	0.870018	−	0.493021i	$-0.164107\pi$
$930$	−12.7249	+	4.05688i	−0.417266	+	0.133030i
$931$		−	8.51302i		−	0.279003i
$932$	−26.8548	+	33.6928i	−0.879657	+	1.10365i
$933$	12.6992	−	9.55608i	0.415753	−	0.312852i
$934$	13.6798	+	4.78477i	0.447617	+	0.156562i
$935$	−25.0267			−0.818461
$936$	−16.1294	+	4.65179i	−0.527206	+	0.152049i
$937$	34.7667			1.13578			0.567889	−	0.823105i	$-0.307760\pi$
$937$	34.7667			1.13578			0.567889	+	0.823105i	$0.307760\pi$
$938$	5.34016	+	1.86782i	0.174363	+	0.0609865i
$939$	−17.5557	+	13.2106i	−0.572910	+	0.431112i
$940$	−6.47891	+	8.12864i	−0.211319	+	0.265127i
$941$		−	25.2393i		−	0.822779i	−0.911460	−	0.411389i	$-0.865044\pi$
$941$		−	25.2393i		−	0.822779i	0.911460	−	0.411389i	$-0.134956\pi$
$942$	35.7284	−	11.3907i	1.16409	−	0.371130i
$943$		−	1.51641i		−	0.0493810i
$944$	−1.16244	−	5.08073i	−0.0378341	−	0.165364i
$945$	0.586655	+	1.53761i	0.0190839	+	0.0500184i
$946$	11.4398	−	32.7069i	0.371941	−	1.06339i
$947$	46.1392			1.49932			0.749661	−	0.661822i	$-0.230216\pi$
$947$	46.1392			1.49932			0.749661	+	0.661822i	$0.230216\pi$
$948$	0.767844	−	27.5715i	0.0249384	−	0.895482i
$949$	−0.467732			−0.0151832
$950$	2.75642	−	7.88071i	0.0894302	−	0.255684i
$951$	21.3849	+	28.4186i	0.693451	+	0.921538i
$952$	5.88802	+	9.36258i	0.190832	+	0.303443i
$953$			11.4777i			0.371798i	0.982569	+	0.185899i	$0.0595198\pi$
$953$			11.4777i			0.371798i	−0.982569	+	0.185899i	$0.940480\pi$
$954$	−37.8242	−	26.8363i	−1.22460	−	0.868858i
$955$		−	6.10363i		−	0.197509i
$956$	−20.3848	−	16.2477i	−0.659293	−	0.525487i
$957$	−27.6231	−	36.7088i	−0.892929	−	1.18663i
$958$	−34.6287	−	12.1120i	−1.11880	−	0.391321i
$959$	7.25712			0.234345
$960$	7.99831	−	1.59703i	0.258144	−	0.0515441i
$961$	−54.8075			−1.76798
$962$	3.86771	+	1.35280i	0.124700	+	0.0436161i
$963$	6.86634	−	23.8241i	0.221265	−	0.767721i
$964$	21.3309	+	17.0017i	0.687021	+	0.547588i
$965$			9.70626i			0.312456i
$966$	−0.400342	−	1.25572i	−0.0128808	−	0.0404022i
$967$			33.7318i			1.08474i	0.840139	+	0.542372i	$0.182473\pi$
$967$			33.7318i			1.08474i	−0.840139	+	0.542372i	$0.817527\pi$
$968$	34.9753	+	55.6145i	1.12415	+	1.78752i
$969$	12.7596	−	9.60155i	0.409898	−	0.308446i
$970$	3.48978	−	9.97739i	0.112050	−	0.320355i
$971$	−30.9660			−0.993746			−0.496873	−	0.867823i	$-0.665519\pi$
$971$	−30.9660			−0.993746			−0.496873	+	0.867823i	$0.665519\pi$
$972$	−25.9226	−	17.3211i	−0.831467	−	0.555574i
$973$	4.63558			0.148610
$974$	3.43495	−	9.82065i	0.110063	−	0.314674i
$975$	−12.7413	+	9.58777i	−0.408049	+	0.307054i
$976$	−2.01355	−	8.80073i	−0.0644520	−	0.281705i
$977$		−	29.8693i		−	0.955604i	−0.878468	−	0.477802i	$-0.841434\pi$
$977$		−	29.8693i		−	0.955604i	0.878468	−	0.477802i	$-0.158566\pi$
$978$	10.0353	+	31.4771i	0.320895	+	1.00653i
$979$			18.6628i			0.596467i
$980$	4.92388	−	6.17766i	0.157288	−	0.197338i
$981$	−10.1251	+	35.1311i	−0.323271	+	1.12165i
$982$	−12.6512	−	4.42500i	−0.403716	−	0.141207i
$983$	0.0987496			0.00314962			0.00157481	−	0.999999i	$-0.499499\pi$
$983$	0.0987496			0.00314962			0.00157481	+	0.999999i	$0.499499\pi$
$984$	2.64693	−	6.94128i	0.0843812	−	0.221280i
$985$	−4.77714			−0.152212
$986$	−43.9826	−	15.3837i	−1.40069	−	0.489918i
$987$	4.94788	+	6.57531i	0.157493	+	0.209294i
$988$	−3.12859	+	3.92524i	−0.0995338	+	0.124878i
$989$			4.18790i			0.133168i
$990$	11.9159	+	8.45434i	0.378712	+	0.268696i
$991$		−	9.20919i		−	0.292539i	−0.989245	−	0.146270i	$-0.953273\pi$
$991$		−	9.20919i		−	0.292539i	0.989245	−	0.146270i	$-0.0467267\pi$
$992$	52.0751	+	5.83303i	1.65339	+	0.185199i
$993$	7.39029	+	9.82106i	0.234524	+	0.311662i
$994$	0.989036	−	2.82769i	0.0313703	−	0.0896888i
$995$	9.53936			0.302418
$996$	−2.53360	−	0.0705585i	−0.0802801	−	0.00223573i
$997$	0.0655187			0.00207500			0.00103750	−	0.999999i	$-0.499670\pi$
$997$	0.0655187			0.00207500			0.00103750	+	0.999999i	$0.499670\pi$
$998$	3.76340	−	10.7597i	0.119128	−	0.340592i
$999$	2.71273	+	7.11000i	0.0858270	+	0.224950i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	276.2.c.a.47.22	yes	22
3.2	odd	2		276.2.c.b.47.1	yes	22
4.3	odd	2		276.2.c.b.47.2	yes	22
12.11	even	2	inner	276.2.c.a.47.21	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
276.2.c.a.47.21	✓	22	12.11	even	2	inner
276.2.c.a.47.22	yes	22	1.1	even	1	trivial
276.2.c.b.47.1	yes	22	3.2	odd	2
276.2.c.b.47.2	yes	22	4.3	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 276 = 2^{2} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	276.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.33491 + 0.466911i) q^{2} +(1.38398 - 1.04144i) q^{3} +(1.56399 + 1.24657i) q^{4} -0.588622i q^{5} +(2.33376 - 0.744034i) q^{6} -0.538069i q^{7} +(1.50575 + 2.39431i) q^{8} +(0.830813 - 2.88266i) q^{9} +O(q^{10})\)	\(q+(1.33491 + 0.466911i) q^{2} +(1.38398 - 1.04144i) q^{3} +(1.56399 + 1.24657i) q^{4} -0.588622i q^{5} +(2.33376 - 0.744034i) q^{6} -0.538069i q^{7} +(1.50575 + 2.39431i) q^{8} +(0.830813 - 2.88266i) q^{9} +(0.274834 - 0.785760i) q^{10} -5.85045 q^{11} +(3.46276 + 0.0964349i) q^{12} -1.97835 q^{13} +(0.251230 - 0.718276i) q^{14} +(-0.613014 - 0.814643i) q^{15} +(0.892120 + 3.89925i) q^{16} +7.26738i q^{17} +(2.45501 - 3.46019i) q^{18} -1.26862i q^{19} +(0.733760 - 0.920599i) q^{20} +(-0.560366 - 0.744678i) q^{21} +(-7.80985 - 2.73164i) q^{22} +1.00000 q^{23} +(4.57746 + 1.74553i) q^{24} +4.65352 q^{25} +(-2.64092 - 0.923711i) q^{26} +(-1.85229 - 4.85480i) q^{27} +(0.670742 - 0.841534i) q^{28} +4.53367i q^{29} +(-0.437955 - 1.37370i) q^{30} -9.26323i q^{31} +(-0.629697 + 5.62170i) q^{32} +(-8.09692 + 6.09288i) q^{33} +(-3.39322 + 9.70132i) q^{34} -0.316720 q^{35} +(4.89283 - 3.47279i) q^{36} -1.46453 q^{37} +(0.592330 - 1.69349i) q^{38} +(-2.73799 + 2.06032i) q^{39} +(1.40934 - 0.886319i) q^{40} -1.51641i q^{41} +(-0.400342 - 1.25572i) q^{42} +4.18790i q^{43} +(-9.15004 - 7.29301i) q^{44} +(-1.69680 - 0.489035i) q^{45} +(1.33491 + 0.466911i) q^{46} -8.82974 q^{47} +(5.29550 + 4.46740i) q^{48} +6.71048 q^{49} +(6.21205 + 2.17278i) q^{50} +(7.56852 + 10.0579i) q^{51} +(-3.09411 - 2.46615i) q^{52} -10.9312i q^{53} +(-0.205885 - 7.34558i) q^{54} +3.44371i q^{55} +(1.28830 - 0.810199i) q^{56} +(-1.32118 - 1.75574i) q^{57} +(-2.11682 + 6.05206i) q^{58} -1.30300 q^{59} +(0.0567637 - 2.03826i) q^{60} -2.25703 q^{61} +(4.32510 - 12.3656i) q^{62} +(-1.55107 - 0.447035i) q^{63} +(-3.46542 + 7.21047i) q^{64} +1.16450i q^{65} +(-13.6535 + 4.35293i) q^{66} +7.43470i q^{67} +(-9.05930 + 11.3661i) q^{68} +(1.38398 - 1.04144i) q^{69} +(-0.422793 - 0.147880i) q^{70} +3.93677 q^{71} +(8.15298 - 2.35135i) q^{72} +0.236426 q^{73} +(-1.95502 - 0.683805i) q^{74} +(6.44039 - 4.84636i) q^{75} +(1.58142 - 1.98410i) q^{76} +3.14795i q^{77} +(-4.61697 + 1.47196i) q^{78} -7.96230i q^{79} +(2.29518 - 0.525122i) q^{80} +(-7.61950 - 4.78991i) q^{81} +(0.708026 - 2.02427i) q^{82} -0.731670 q^{83} +(0.0518886 - 1.86320i) q^{84} +4.27774 q^{85} +(-1.95538 + 5.59049i) q^{86} +(4.72154 + 6.27452i) q^{87} +(-8.80933 - 14.0078i) q^{88} -3.18998i q^{89} +(-2.03675 - 1.44507i) q^{90} +1.06449i q^{91} +(1.56399 + 1.24657i) q^{92} +(-9.64709 - 12.8202i) q^{93} +(-11.7869 - 4.12270i) q^{94} -0.746736 q^{95} +(4.98316 + 8.43612i) q^{96} +12.6978 q^{97} +(8.95791 + 3.13320i) q^{98} +(-4.86063 + 16.8649i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 3 q^{6} - 9 q^{8} - 2 q^{9}+O(q^{10}) \) 22 * q - 3 * q^6 - 9 * q^8 - 2 * q^9	\( 22 q - 3 q^{6} - 9 q^{8} - 2 q^{9} + 4 q^{10} + 14 q^{12} - 4 q^{13} + 12 q^{14} + 4 q^{16} - 14 q^{18} - 14 q^{20} + 2 q^{22} + 22 q^{23} + 22 q^{24} - 18 q^{25} + 27 q^{26} + 12 q^{27} + 6 q^{28} - 24 q^{30} - 20 q^{32} - 8 q^{33} - 6 q^{34} - 8 q^{35} + 3 q^{36} - 4 q^{37} + 22 q^{38} - 24 q^{39} - 4 q^{40} - 38 q^{42} - 56 q^{44} + 8 q^{47} + 17 q^{48} - 14 q^{49} + 20 q^{50} + 16 q^{51} - 19 q^{52} - 54 q^{54} - 18 q^{56} + 12 q^{57} + 3 q^{58} - 72 q^{59} + 64 q^{60} + 12 q^{61} + 63 q^{62} - 20 q^{63} + 3 q^{64} - 18 q^{66} - 20 q^{68} + 40 q^{71} + 48 q^{72} - 4 q^{73} + 28 q^{74} + 48 q^{75} + 26 q^{76} - 46 q^{78} - 84 q^{80} + 10 q^{81} - 29 q^{82} - 8 q^{83} + 76 q^{84} + 8 q^{85} + 28 q^{86} - 48 q^{87} - 30 q^{88} - 26 q^{90} + 12 q^{93} - 13 q^{94} + 32 q^{95} + 18 q^{96} - 4 q^{97} + 64 q^{98} + 20 q^{99}+O(q^{100}) \) 22 * q - 3 * q^6 - 9 * q^8 - 2 * q^9 + 4 * q^10 + 14 * q^12 - 4 * q^13 + 12 * q^14 + 4 * q^16 - 14 * q^18 - 14 * q^20 + 2 * q^22 + 22 * q^23 + 22 * q^24 - 18 * q^25 + 27 * q^26 + 12 * q^27 + 6 * q^28 - 24 * q^30 - 20 * q^32 - 8 * q^33 - 6 * q^34 - 8 * q^35 + 3 * q^36 - 4 * q^37 + 22 * q^38 - 24 * q^39 - 4 * q^40 - 38 * q^42 - 56 * q^44 + 8 * q^47 + 17 * q^48 - 14 * q^49 + 20 * q^50 + 16 * q^51 - 19 * q^52 - 54 * q^54 - 18 * q^56 + 12 * q^57 + 3 * q^58 - 72 * q^59 + 64 * q^60 + 12 * q^61 + 63 * q^62 - 20 * q^63 + 3 * q^64 - 18 * q^66 - 20 * q^68 + 40 * q^71 + 48 * q^72 - 4 * q^73 + 28 * q^74 + 48 * q^75 + 26 * q^76 - 46 * q^78 - 84 * q^80 + 10 * q^81 - 29 * q^82 - 8 * q^83 + 76 * q^84 + 8 * q^85 + 28 * q^86 - 48 * q^87 - 30 * q^88 - 26 * q^90 + 12 * q^93 - 13 * q^94 + 32 * q^95 + 18 * q^96 - 4 * q^97 + 64 * q^98 + 20 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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