LMFDB - Embedded newform 546.2.q.j.335.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(251,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1]))

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

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

chi := DirichletCharacter("546.251");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.q (of order $6$, degree $2$, 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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			335.5
Character	$\chi$	$=$	546.335
Dual form			546.2.q.j.251.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.702948 + 1.58299i) q^{3} +(-0.500000 + 0.866025i) q^{4} -3.28289i q^{5} +(-1.72239 + 0.182725i) q^{6} +(-0.203837 - 2.63789i) q^{7} -1.00000 q^{8} +(-2.01173 - 2.22552i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.702948 + 1.58299i) q^{3} +(-0.500000 + 0.866025i) q^{4} -3.28289i q^{5} +(-1.72239 + 0.182725i) q^{6} +(-0.203837 - 2.63789i) q^{7} -1.00000 q^{8} +(-2.01173 - 2.22552i) q^{9} +(2.84307 - 1.64144i) q^{10} +(2.08519 + 3.61166i) q^{11} +(-1.01944 - 1.40027i) q^{12} +(3.60533 - 0.0395188i) q^{13} +(2.18256 - 1.49547i) q^{14} +(5.19679 + 2.30770i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.84811 - 6.66512i) q^{17} +(0.921495 - 2.85497i) q^{18} +(-1.26221 + 2.18621i) q^{19} +(2.84307 + 1.64144i) q^{20} +(4.31904 + 1.53163i) q^{21} +(-2.08519 + 3.61166i) q^{22} +(3.82560 - 2.20871i) q^{23} +(0.702948 - 1.58299i) q^{24} -5.77736 q^{25} +(1.83689 + 3.10255i) q^{26} +(4.93712 - 1.62012i) q^{27} +(2.38640 + 1.14242i) q^{28} +(3.55238 - 2.05097i) q^{29} +(0.599866 + 5.65440i) q^{30} -6.97836 q^{31} +(0.500000 - 0.866025i) q^{32} +(-7.18301 + 0.762034i) q^{33} +7.69622 q^{34} +(-8.65989 + 0.669174i) q^{35} +(2.93322 - 0.629446i) q^{36} +(5.29343 - 3.05617i) q^{37} -2.52442 q^{38} +(-2.47181 + 5.73500i) q^{39} +3.28289i q^{40} +(1.73761 - 1.00321i) q^{41} +(0.833094 + 4.50621i) q^{42} +(-4.64648 + 8.04793i) q^{43} -4.17039 q^{44} +(-7.30614 + 6.60428i) q^{45} +(3.82560 + 2.20871i) q^{46} -4.60624i q^{47} +(1.72239 - 0.182725i) q^{48} +(-6.91690 + 1.07540i) q^{49} +(-2.88868 - 5.00334i) q^{50} +(7.84581 + 10.7768i) q^{51} +(-1.76844 + 3.14207i) q^{52} +4.48819i q^{53} +(3.87163 + 3.46561i) q^{54} +(11.8567 - 6.84546i) q^{55} +(0.203837 + 2.63789i) q^{56} +(-2.57349 - 3.53487i) q^{57} +(3.55238 + 2.05097i) q^{58} +(1.69525 + 0.978752i) q^{59} +(-4.59692 + 3.34670i) q^{60} +(-6.38756 - 3.68786i) q^{61} +(-3.48918 - 6.04343i) q^{62} +(-5.46061 + 5.76036i) q^{63} +1.00000 q^{64} +(-0.129736 - 11.8359i) q^{65} +(-4.25145 - 5.83965i) q^{66} +(-0.107427 + 0.0620231i) q^{67} +(3.84811 + 6.66512i) q^{68} +(0.807175 + 7.60851i) q^{69} +(-4.90947 - 7.16510i) q^{70} +(5.79343 - 10.0345i) q^{71} +(2.01173 + 2.22552i) q^{72} -1.12283 q^{73} +(5.29343 + 3.05617i) q^{74} +(4.06118 - 9.14552i) q^{75} +(-1.26221 - 2.18621i) q^{76} +(9.10211 - 6.23669i) q^{77} +(-6.20255 + 0.726852i) q^{78} +2.20387 q^{79} +(-2.84307 + 1.64144i) q^{80} +(-0.905901 + 8.95429i) q^{81} +(1.73761 + 1.00321i) q^{82} -5.80900i q^{83} +(-3.48595 + 2.97459i) q^{84} +(-21.8809 - 12.6329i) q^{85} -9.29295 q^{86} +(0.749526 + 7.06511i) q^{87} +(-2.08519 - 3.61166i) q^{88} +(-5.51516 + 3.18418i) q^{89} +(-9.37255 - 3.02517i) q^{90} +(-0.839146 - 9.50241i) q^{91} +4.41743i q^{92} +(4.90542 - 11.0467i) q^{93} +(3.98912 - 2.30312i) q^{94} +(7.17710 + 4.14370i) q^{95} +(1.01944 + 1.40027i) q^{96} +(-3.26777 + 5.65995i) q^{97} +(-4.38977 - 5.45251i) q^{98} +(3.84299 - 11.9063i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{2} - 12 q^{4} - 18 q^{7} - 24 q^{8} + 6 q^{9}+O(q^{10}) $ 24 * q + 12 * q^2 - 12 * q^4 - 18 * q^7 - 24 * q^8 + 6 * q^9	$ 24 q + 12 q^{2} - 12 q^{4} - 18 q^{7} - 24 q^{8} + 6 q^{9} + 12 q^{15} - 12 q^{16} - 6 q^{18} + 12 q^{21} - 36 q^{23} - 12 q^{25} + 18 q^{28} + 6 q^{30} + 12 q^{32} - 36 q^{35} - 12 q^{36} + 36 q^{37} + 12 q^{39} - 12 q^{42} - 42 q^{43} - 36 q^{46} - 6 q^{50} + 12 q^{51} + 18 q^{56} - 36 q^{57} - 6 q^{60} + 66 q^{63} + 24 q^{64} + 66 q^{65} - 54 q^{67} + 48 q^{71} - 6 q^{72} + 36 q^{74} - 12 q^{78} - 48 q^{79} - 6 q^{81} - 24 q^{84} - 84 q^{86} + 36 q^{91} + 54 q^{93} - 36 q^{95} + 36 q^{99}+O(q^{100}) $ 24 * q + 12 * q^2 - 12 * q^4 - 18 * q^7 - 24 * q^8 + 6 * q^9 + 12 * q^15 - 12 * q^16 - 6 * q^18 + 12 * q^21 - 36 * q^23 - 12 * q^25 + 18 * q^28 + 6 * q^30 + 12 * q^32 - 36 * q^35 - 12 * q^36 + 36 * q^37 + 12 * q^39 - 12 * q^42 - 42 * q^43 - 36 * q^46 - 6 * q^50 + 12 * q^51 + 18 * q^56 - 36 * q^57 - 6 * q^60 + 66 * q^63 + 24 * q^64 + 66 * q^65 - 54 * q^67 + 48 * q^71 - 6 * q^72 + 36 * q^74 - 12 * q^78 - 48 * q^79 - 6 * q^81 - 24 * q^84 - 84 * q^86 + 36 * q^91 + 54 * q^93 - 36 * q^95 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	−0.702948	+	1.58299i	−0.405847	+	0.913941i
$3$	−0.702948	+	1.58299i	−0.405847	+	0.913941i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$		−	3.28289i		−	1.46815i	−0.679067	−	0.734076i	$-0.737615\pi$
$5$		−	3.28289i		−	1.46815i	0.679067	−	0.734076i	$-0.262385\pi$
$6$	−1.72239	+	0.182725i	−0.703161	+	0.0745972i
$7$	−0.203837	−	2.63789i	−0.0770431	−	0.997028i
$7$	−0.203837	−	2.63789i	−0.0770431	−	0.997028i
$8$	−1.00000			−0.353553
$9$	−2.01173	−	2.22552i	−0.670576	−	0.741841i
$10$	2.84307	−	1.64144i	0.899056	−	0.519070i
$11$	2.08519	+	3.61166i	0.628709	+	1.08896i	0.987811	+	0.155658i	$0.0497498\pi$
$11$	2.08519	+	3.61166i	0.628709	+	1.08896i	−0.359102	+	0.933298i	$0.616917\pi$
$12$	−1.01944	−	1.40027i	−0.294286	−	0.404222i
$13$	3.60533	−	0.0395188i	0.999940	−	0.0109605i
$13$	3.60533	−	0.0395188i	0.999940	−	0.0109605i
$14$	2.18256	−	1.49547i	0.583313	−	0.399682i
$15$	5.19679	+	2.30770i	1.34180	+	0.595846i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	3.84811	−	6.66512i	0.933304	−	1.61653i	0.155672	−	0.987809i	$-0.450246\pi$
$17$	3.84811	−	6.66512i	0.933304	−	1.61653i	0.777631	−	0.628720i	$-0.216421\pi$
$18$	0.921495	−	2.85497i	0.217198	−	0.672923i
$19$	−1.26221	+	2.18621i	−0.289571	+	0.501552i	−0.973707	−	0.227802i	$-0.926846\pi$
$19$	−1.26221	+	2.18621i	−0.289571	+	0.501552i	0.684136	+	0.729354i	$0.260179\pi$
$20$	2.84307	+	1.64144i	0.635729	+	0.367038i
$21$	4.31904	+	1.53163i	0.942492	+	0.334228i
$22$	−2.08519	+	3.61166i	−0.444565	+	0.770009i
$23$	3.82560	−	2.20871i	0.797693	−	0.460548i	−0.0449707	−	0.998988i	$-0.514319\pi$
$23$	3.82560	−	2.20871i	0.797693	−	0.460548i	0.842664	+	0.538440i	$0.180986\pi$
$24$	0.702948	−	1.58299i	0.143489	−	0.323127i
$25$	−5.77736			−1.15547
$26$	1.83689	+	3.10255i	0.360244	+	0.608461i
$27$	4.93712	−	1.62012i	0.950150	−	0.311793i
$28$	2.38640	+	1.14242i	0.450986	+	0.215896i
$29$	3.55238	−	2.05097i	0.659660	−	0.380855i	−0.132487	−	0.991185i	$-0.542296\pi$
$29$	3.55238	−	2.05097i	0.659660	−	0.380855i	0.792147	+	0.610330i	$0.208963\pi$
$30$	0.599866	+	5.65440i	0.109520	+	1.03235i
$31$	−6.97836			−1.25335			−0.626675	−	0.779281i	$-0.715585\pi$
$31$	−6.97836			−1.25335			−0.626675	+	0.779281i	$0.715585\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−7.18301	+	0.762034i	−1.25040	+	0.132653i
$34$	7.69622			1.31989
$35$	−8.65989	+	0.669174i	−1.46379	+	0.113111i
$36$	2.93322	−	0.629446i	0.488871	−	0.104908i
$37$	5.29343	−	3.05617i	0.870235	−	0.502431i	0.00280878	−	0.999996i	$-0.499106\pi$
$37$	5.29343	−	3.05617i	0.870235	−	0.502431i	0.867426	+	0.497566i	$0.165773\pi$
$38$	−2.52442			−0.409516
$39$	−2.47181	+	5.73500i	−0.395806	+	0.918334i
$40$			3.28289i			0.519070i
$41$	1.73761	−	1.00321i	0.271370	−	0.156675i	−0.358140	−	0.933668i	$-0.616589\pi$
$41$	1.73761	−	1.00321i	0.271370	−	0.156675i	0.629510	+	0.776992i	$0.283256\pi$
$42$	0.833094	+	4.50621i	0.128549	+	0.695324i
$43$	−4.64648	+	8.04793i	−0.708581	+	1.22730i	0.256802	+	0.966464i	$0.417331\pi$
$43$	−4.64648	+	8.04793i	−0.708581	+	1.22730i	−0.965384	+	0.260835i	$0.916002\pi$
$44$	−4.17039			−0.628709
$45$	−7.30614	+	6.60428i	−1.08914	+	0.984508i
$46$	3.82560	+	2.20871i	0.564054	+	0.325657i
$47$		−	4.60624i		−	0.671889i	−0.941882	−	0.335945i	$-0.890945\pi$
$47$		−	4.60624i		−	0.671889i	0.941882	−	0.335945i	$-0.109055\pi$
$48$	1.72239	−	0.182725i	0.248605	−	0.0263741i
$49$	−6.91690	+	1.07540i	−0.988129	+	0.153628i
$50$	−2.88868	−	5.00334i	−0.408521	−	0.707579i
$51$	7.84581	+	10.7768i	1.09863	+	1.50905i
$52$	−1.76844	+	3.14207i	−0.245239	+	0.435727i
$53$			4.48819i			0.616500i	0.951305	+	0.308250i	$0.0997434\pi$
$53$			4.48819i			0.616500i	−0.951305	+	0.308250i	$0.900257\pi$
$54$	3.87163	+	3.46561i	0.526862	+	0.471610i
$55$	11.8567	−	6.84546i	1.59875	−	0.923041i
$56$	0.203837	+	2.63789i	0.0272389	+	0.352503i
$57$	−2.57349	−	3.53487i	−0.340867	−	0.468205i
$58$	3.55238	+	2.05097i	0.466450	+	0.269305i
$59$	1.69525	+	0.978752i	0.220703	+	0.127423i	0.606276	−	0.795255i	$-0.292663\pi$
$59$	1.69525	+	0.978752i	0.220703	+	0.127423i	−0.385573	+	0.922677i	$0.625996\pi$
$60$	−4.59692	+	3.34670i	−0.593460	+	0.432057i
$61$	−6.38756	−	3.68786i	−0.817843	−	0.472182i	0.0318291	−	0.999493i	$-0.489867\pi$
$61$	−6.38756	−	3.68786i	−0.817843	−	0.472182i	−0.849672	+	0.527311i	$0.823200\pi$
$62$	−3.48918	−	6.04343i	−0.443126	−	0.767517i
$63$	−5.46061	+	5.76036i	−0.687973	+	0.725737i
$64$	1.00000			0.125000
$65$	−0.129736	−	11.8359i	−0.0160917	−	1.46806i
$66$	−4.25145	−	5.83965i	−0.523317	−	0.718812i
$67$	−0.107427	+	0.0620231i	−0.0131243	+	0.00757733i	−0.506548	−	0.862212i	$-0.669079\pi$
$67$	−0.107427	+	0.0620231i	−0.0131243	+	0.00757733i	0.493423	+	0.869789i	$0.335745\pi$
$68$	3.84811	+	6.66512i	0.466652	+	0.808265i
$69$	0.807175	+	7.60851i	0.0971724	+	0.915957i
$70$	−4.90947	−	7.16510i	−0.586794	−	0.856393i
$71$	5.79343	−	10.0345i	0.687554	−	1.19088i	−0.285073	−	0.958506i	$-0.592018\pi$
$71$	5.79343	−	10.0345i	0.687554	−	1.19088i	0.972627	−	0.232373i	$-0.0746489\pi$
$72$	2.01173	+	2.22552i	0.237084	+	0.262280i
$73$	−1.12283			−0.131418			−0.0657088	−	0.997839i	$-0.520931\pi$
$73$	−1.12283			−0.131418			−0.0657088	+	0.997839i	$0.520931\pi$
$74$	5.29343	+	3.05617i	0.615349	+	0.355272i
$75$	4.06118	−	9.14552i	0.468945	−	1.05603i
$76$	−1.26221	−	2.18621i	−0.144786	−	0.250776i
$77$	9.10211	−	6.23669i	1.03728	−	0.710737i
$78$	−6.20255	+	0.726852i	−0.702301	+	0.0822998i
$79$	2.20387			0.247955			0.123977	−	0.992285i	$-0.460435\pi$
$79$	2.20387			0.247955			0.123977	+	0.992285i	$0.460435\pi$
$80$	−2.84307	+	1.64144i	−0.317864	+	0.183519i
$81$	−0.905901	+	8.95429i	−0.100656	+	0.994921i
$82$	1.73761	+	1.00321i	0.191887	+	0.110786i
$83$		−	5.80900i		−	0.637621i	−0.947818	−	0.318811i	$-0.896717\pi$
$83$		−	5.80900i		−	0.637621i	0.947818	−	0.318811i	$-0.103283\pi$
$84$	−3.48595	+	2.97459i	−0.380348	+	0.324554i
$85$	−21.8809	−	12.6329i	−2.37331	−	1.37023i
$86$	−9.29295			−1.00209
$87$	0.749526	+	7.06511i	0.0803577	+	0.757459i
$88$	−2.08519	−	3.61166i	−0.222282	−	0.385004i
$89$	−5.51516	+	3.18418i	−0.584606	+	0.337523i	−0.762962	−	0.646444i	$-0.776256\pi$
$89$	−5.51516	+	3.18418i	−0.584606	+	0.337523i	0.178356	+	0.983966i	$0.442922\pi$
$90$	−9.37255	−	3.02517i	−0.987953	−	0.318880i
$91$	−0.839146	−	9.50241i	−0.0879664	−	0.996123i
$92$			4.41743i			0.460548i
$93$	4.90542	−	11.0467i	0.508669	−	1.14549i
$94$	3.98912	−	2.30312i	0.411446	−	0.237549i
$95$	7.17710	+	4.14370i	0.736355	+	0.425135i
$96$	1.01944	+	1.40027i	0.104046	+	0.142914i
$97$	−3.26777	+	5.65995i	−0.331792	+	0.574681i	−0.982863	−	0.184336i	$-0.940987\pi$
$97$	−3.26777	+	5.65995i	−0.331792	+	0.574681i	0.651071	+	0.759017i	$0.274320\pi$
$98$	−4.38977	−	5.45251i	−0.443434	−	0.550787i
$99$	3.84299	−	11.9063i	0.386235	−	1.19663i
$100$	2.88868	−	5.00334i	0.288868	−	0.500334i
$101$	8.77084	+	15.1915i	0.872731	+	1.51161i	0.859160	+	0.511707i	$0.170987\pi$
$101$	8.77084	+	15.1915i	0.872731	+	1.51161i	0.0135712	+	0.999908i	$0.495680\pi$
$102$	−5.41004	+	12.1831i	−0.535674	+	1.20630i
$103$			2.07167i			0.204127i	0.994778	+	0.102064i	$0.0325446\pi$
$103$			2.07167i			0.204127i	−0.994778	+	0.102064i	$0.967455\pi$
$104$	−3.60533	+	0.0395188i	−0.353532	+	0.00387514i
$105$	5.02816	−	14.1789i	0.490698	−	1.38372i
$106$	−3.88689	+	2.24410i	−0.377528	+	0.217966i
$107$	−3.22341	+	1.86104i	−0.311619	+	0.179913i	−0.647651	−	0.761937i	$-0.724248\pi$
$107$	−3.22341	+	1.86104i	−0.311619	+	0.179913i	0.336032	+	0.941851i	$0.390915\pi$
$108$	−1.06549	+	5.08574i	−0.102527	+	0.489375i
$109$		−	10.3186i		−	0.988347i	−0.869363	−	0.494174i	$-0.835471\pi$
$109$		−	10.3186i		−	0.988347i	0.869363	−	0.494174i	$-0.164529\pi$
$110$	11.8567	+	6.84546i	1.13049	+	0.652689i
$111$	1.11688	+	10.5278i	0.106009	+	0.999254i
$112$	−2.18256	+	1.49547i	−0.206232	+	0.141309i
$113$	−5.85794	−	3.38208i	−0.551068	−	0.318160i	0.198484	−	0.980104i	$-0.436398\pi$
$113$	−5.85794	−	3.38208i	−0.551068	−	0.318160i	−0.749553	+	0.661945i	$0.769731\pi$
$114$	1.77454	−	3.99614i	0.166201	−	0.374273i
$115$	−7.25096	−	12.5590i	−0.676155	−	1.17114i
$116$			4.10193i			0.380855i
$117$	−7.34090	−	7.94425i	−0.678667	−	0.734446i
$118$			1.95750i			0.180203i
$119$	−18.3662	−	8.79228i	−1.68363	−	0.805987i
$120$	−5.19679	−	2.30770i	−0.474400	−	0.210663i
$121$	−3.19606	+	5.53574i	−0.290551	+	0.503249i
$122$		−	7.37572i		−	0.667766i
$123$	0.366624	+	3.45584i	0.0330574	+	0.311602i
$124$	3.48918	−	6.04343i	0.313337	−	0.542716i
$125$			2.55199i			0.228257i
$126$	−7.71892	−	1.84885i	−0.687656	−	0.164709i
$127$	10.4721	+	18.1382i	0.929247	+	1.60950i	0.784585	+	0.620022i	$0.212876\pi$
$127$	10.4721	+	18.1382i	0.929247	+	1.60950i	0.144662	+	0.989481i	$0.453790\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−9.47358	−	13.0126i	−0.834103	−	1.14570i
$130$	10.1853	−	6.03031i	0.893313	−	0.528893i
$131$	10.6372			0.929375			0.464688	−	0.885475i	$-0.346167\pi$
$131$	10.6372			0.929375			0.464688	+	0.885475i	$0.346167\pi$
$132$	2.93156	−	6.60169i	0.255160	−	0.574603i
$133$	6.02427	+	2.88394i	0.522371	+	0.250069i
$134$	−0.107427	−	0.0620231i	−0.00928030	−	0.00535798i
$135$	−5.31868	−	16.2080i	−0.457759	−	1.39497i
$136$	−3.84811	+	6.66512i	−0.329973	+	0.571529i
$137$	−0.970884	+	1.68162i	−0.0829483	+	0.143671i	−0.904515	−	0.426442i	$-0.859767\pi$
$137$	−0.970884	+	1.68162i	−0.0829483	+	0.143671i	0.821567	+	0.570112i	$0.193100\pi$
$138$	−6.18557	+	4.50329i	−0.526551	+	0.383345i
$139$	−6.89520	−	3.98095i	−0.584843	−	0.337659i	0.178213	−	0.983992i	$-0.442969\pi$
$139$	−6.89520	−	3.98095i	−0.584843	−	0.337659i	−0.763056	+	0.646333i	$0.776302\pi$
$140$	3.75042	−	7.83427i	0.316969	−	0.662117i
$141$	7.29164	+	3.23795i	0.614067	+	0.272684i
$142$	11.5869			0.972348
$143$	7.66055	+	12.9388i	0.640607	+	1.08200i
$144$	−0.921495	+	2.85497i	−0.0767913	+	0.237914i
$145$	−6.73310	−	11.6621i	−0.559153	−	0.968482i
$146$	−0.561416	−	0.972402i	−0.0464631	−	0.0804765i
$147$	3.15988	−	11.7053i	0.260622	−	0.965441i
$148$			6.11233i			0.502431i
$149$	−1.78627	+	3.09390i	−0.146337	+	0.253463i	−0.929871	−	0.367886i	$-0.880082\pi$
$149$	−1.78627	+	3.09390i	−0.146337	+	0.253463i	0.783534	+	0.621349i	$0.213415\pi$
$150$	9.95084	−	1.05567i	0.812483	−	0.0861950i
$151$			14.8630i			1.20954i	0.796401	+	0.604768i	$0.206734\pi$
$151$			14.8630i			1.20954i	−0.796401	+	0.604768i	$0.793266\pi$
$152$	1.26221	−	2.18621i	0.102379	−	0.177325i
$153$	−22.5747	+	4.84436i	−1.82506	+	0.391643i
$154$	9.95219	+	4.76432i	0.801971	+	0.383919i
$155$			22.9092i			1.84011i
$156$	−3.73075	−	5.00814i	−0.298699	−	0.400972i
$157$			18.7474i			1.49620i	0.663585	+	0.748101i	$0.269034\pi$
$157$			18.7474i			1.49620i	−0.663585	+	0.748101i	$0.730966\pi$
$158$	1.10193	+	1.90861i	0.0876652	+	0.151841i
$159$	−7.10477	−	3.15496i	−0.563445	−	0.250205i
$160$	−2.84307	−	1.64144i	−0.224764	−	0.129768i
$161$	−6.60613	−	9.64129i	−0.520636	−	0.759840i
$162$	−8.20759	+	3.69261i	−0.644850	+	0.290119i
$163$	15.4012	+	8.89189i	1.20632	+	0.696467i	0.961952	−	0.273217i	$-0.0880878\pi$
$163$	15.4012	+	8.89189i	1.20632	+	0.696467i	0.244363	+	0.969684i	$0.421421\pi$
$164$			2.00642i			0.156675i
$165$	2.50167	+	23.5810i	0.194755	+	1.83578i
$166$	5.03074	−	2.90450i	0.390462	−	0.225433i
$167$	−9.41884	+	5.43797i	−0.728852	+	0.420803i	−0.818002	−	0.575215i	$-0.804918\pi$
$167$	−9.41884	+	5.43797i	−0.728852	+	0.420803i	0.0891502	+	0.996018i	$0.471585\pi$
$168$	−4.31904	−	1.53163i	−0.333221	−	0.118167i
$169$	12.9969	−	0.284957i	0.999760	−	0.0219198i
$170$		−	25.2658i		−	1.93780i
$171$	7.40470	−	1.58899i	0.566251	−	0.121513i
$172$	−4.64648	−	8.04793i	−0.354291	−	0.613649i
$173$	−6.13026	+	10.6179i	−0.466075	+	0.807266i	−0.999249	−	0.0387398i	$-0.987666\pi$
$173$	−6.13026	+	10.6179i	−0.466075	+	0.807266i	0.533174	+	0.846005i	$0.320999\pi$
$174$	−5.74380	+	4.18166i	−0.435436	+	0.317011i
$175$	1.17764	+	15.2400i	0.0890212	+	1.15204i
$176$	2.08519	−	3.61166i	0.157177	−	0.272239i
$177$	−2.74103	+	1.99555i	−0.206028	+	0.149995i
$178$	−5.51516	−	3.18418i	−0.413379	−	0.238664i
$179$	−16.7712	+	9.68288i	−1.25354	+	0.723733i	−0.971811	−	0.235761i	$-0.924242\pi$
$179$	−16.7712	+	9.68288i	−1.25354	+	0.723733i	−0.281731	+	0.959493i	$0.590909\pi$
$180$	−2.06640	−	9.62945i	−0.154021	−	0.717737i
$181$		−	1.02727i		−	0.0763566i	−0.999271	−	0.0381783i	$-0.987845\pi$
$181$		−	1.02727i		−	0.0763566i	0.999271	−	0.0381783i	$-0.0121555\pi$
$182$	7.80976	−	5.47793i	0.578898	−	0.406051i
$183$	10.3280	−	7.51908i	0.763466	−	0.555826i
$184$	−3.82560	+	2.20871i	−0.282027	+	0.162828i
$185$	−10.0331	−	17.3778i	−0.737645	−	1.27764i
$186$	12.0194	−	1.27512i	0.881307	−	0.0934964i
$187$	32.0962			2.34711
$188$	3.98912	+	2.30312i	0.290936	+	0.167972i
$189$	−5.28007	−	12.6933i	−0.384069	−	0.923305i
$190$			8.28740i			0.601231i
$191$	7.18621	+	4.14896i	0.519976	+	0.300208i	0.736925	−	0.675975i	$-0.236277\pi$
$191$	7.18621	+	4.14896i	0.519976	+	0.300208i	−0.216949	+	0.976183i	$0.569610\pi$
$192$	−0.702948	+	1.58299i	−0.0507309	+	0.114243i
$193$	−10.2886	+	5.94013i	−0.740590	+	0.427580i	−0.822284	−	0.569077i	$-0.807300\pi$
$193$	−10.2886	+	5.94013i	−0.740590	+	0.427580i	0.0816936	+	0.996657i	$0.473967\pi$
$194$	−6.53554			−0.469225
$195$	18.8274	+	8.11466i	1.34825	+	0.581103i
$196$	2.52713	−	6.52791i	0.180509	−	0.466279i
$197$	4.57466	+	7.92354i	0.325931	+	0.564529i	0.981700	−	0.190432i	$-0.0609889\pi$
$197$	4.57466	+	7.92354i	0.325931	+	0.564529i	−0.655769	+	0.754961i	$0.727656\pi$
$198$	12.2327	−	2.62503i	0.869338	−	0.186553i
$199$	3.46152	+	1.99851i	0.245381	+	0.141671i	0.617647	−	0.786455i	$-0.288086\pi$
$199$	3.46152	+	1.99851i	0.245381	+	0.141671i	−0.372267	+	0.928126i	$0.621419\pi$
$200$	5.77736			0.408521
$201$	−0.0226664	−	0.213656i	−0.00159876	−	0.0150701i
$202$	−8.77084	+	15.1915i	−0.617114	+	1.06887i
$203$	−6.13432	−	8.95271i	−0.430545	−	0.628357i
$204$	−13.2559	+	1.40629i	−0.928095	+	0.0984602i
$205$	−3.29343	−	5.70439i	−0.230023	−	0.398412i
$206$	−1.79412	+	1.03583i	−0.125002	+	0.0721700i
$207$	−12.6116	−	4.07064i	−0.876568	−	0.282929i
$208$	−1.83689	−	3.10255i	−0.127366	−	0.215123i
$209$	−10.5278			−0.728225
$210$	14.7934	−	2.73496i	1.02084	−	0.188730i
$211$	−13.9918	−	24.2346i	−0.963238	−	1.66838i	−0.714277	−	0.699863i	$-0.753244\pi$
$211$	−13.9918	−	24.2346i	−0.963238	−	1.66838i	−0.248961	−	0.968514i	$-0.580089\pi$
$212$	−3.88689	−	2.24410i	−0.266952	−	0.154125i
$213$	11.8121	+	16.2247i	0.809351	+	1.11170i
$214$	−3.22341	−	1.86104i	−0.220348	−	0.127218i
$215$	26.4205	+	15.2539i	1.80186	+	1.04031i
$216$	−4.93712	+	1.62012i	−0.335929	+	0.110235i
$217$	1.42245	+	18.4081i	0.0965620	+	1.24962i
$218$	8.93621	−	5.15932i	0.605237	−	0.349434i
$219$	0.789293	−	1.77744i	0.0533355	−	0.120108i
$220$			13.6909i			0.923041i
$221$	13.6103	−	24.1821i	0.915529	−	1.62666i
$222$	−8.55889	+	6.23114i	−0.574435	+	0.418207i
$223$	−8.69542	−	15.0609i	−0.582288	−	1.00855i	−0.995208	−	0.0977852i	$-0.968824\pi$
$223$	−8.69542	−	15.0609i	−0.582288	−	1.00855i	0.412919	−	0.910768i	$-0.364509\pi$
$224$	−2.38640	−	1.14242i	−0.159448	−	0.0763309i
$225$	11.6225	+	12.8576i	0.774832	+	0.857176i
$226$		−	6.76416i		−	0.449946i
$227$	−20.7722	−	11.9929i	−1.37870	−	0.795994i	−0.386699	−	0.922206i	$-0.626385\pi$
$227$	−20.7722	−	11.9929i	−1.37870	−	0.795994i	−0.992003	+	0.126212i	$0.959718\pi$
$228$	4.34803	−	0.461276i	0.287955	−	0.0305487i
$229$	−2.89589			−0.191366			−0.0956830	−	0.995412i	$-0.530504\pi$
$229$	−2.89589			−0.191366			−0.0956830	+	0.995412i	$0.530504\pi$
$230$	7.25096	−	12.5590i	0.478114	−	0.828118i
$231$	3.47432	+	18.7926i	0.228594	+	1.23647i
$232$	−3.55238	+	2.05097i	−0.233225	+	0.134653i
$233$			13.1948i			0.864422i	0.901772	+	0.432211i	$0.142266\pi$
$233$			13.1948i			0.864422i	−0.901772	+	0.432211i	$0.857734\pi$
$234$	3.20947	−	10.3295i	0.209810	−	0.675263i
$235$	−15.1218			−0.986436
$236$	−1.69525	+	0.978752i	−0.110351	+	0.0637114i
$237$	−1.54921	+	3.48871i	−0.100632	+	0.226616i
$238$	−1.56877	−	20.3018i	−0.101688	−	1.31597i
$239$	−23.6780			−1.53160			−0.765800	−	0.643079i	$-0.777657\pi$
$239$	−23.6780			−1.53160			−0.765800	+	0.643079i	$0.777657\pi$
$240$	−0.599866	−	5.65440i	−0.0387212	−	0.364990i
$241$	6.15543	−	10.6615i	0.396506	−	0.686769i	−0.596786	−	0.802400i	$-0.703556\pi$
$241$	6.15543	−	10.6615i	0.396506	−	0.686769i	0.993292	+	0.115632i	$0.0368892\pi$
$242$	−6.39212			−0.410901
$243$	−13.5378	−	7.72844i	−0.868448	−	0.495779i
$244$	6.38756	−	3.68786i	0.408921	−	0.236091i
$245$	3.53041	+	22.7074i	0.225550	+	1.45072i
$246$	−2.80953	+	2.04542i	−0.179129	+	0.130411i
$247$	−4.46430	+	7.93192i	−0.284057	+	0.504696i
$248$	6.97836			0.443126
$249$	9.19561	+	4.08343i	0.582748	+	0.258777i
$250$	−2.21009	+	1.27599i	−0.139778	+	0.0807010i
$251$	2.06908	−	3.58374i	0.130599	−	0.226204i	−0.793309	−	0.608820i	$-0.791643\pi$
$251$	2.06908	−	3.58374i	0.130599	−	0.226204i	0.923908	+	0.382616i	$0.124977\pi$
$252$	−2.25831	−	7.60921i	−0.142260	−	0.479335i
$253$	15.9542	+	9.21118i	1.00303	+	0.579102i
$254$	−10.4721	+	18.1382i	−0.657077	+	1.13809i
$255$	35.3789	−	25.7569i	2.21551	−	1.61296i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	8.37891	+	14.5127i	0.522662	+	0.905277i	0.999652	+	0.0263687i	$0.00839441\pi$
$257$	8.37891	+	14.5127i	0.522662	+	0.905277i	−0.476990	+	0.878909i	$0.658272\pi$
$258$	6.53246	−	14.7107i	0.406693	−	0.915847i
$259$	−9.14082	−	13.3405i	−0.567983	−	0.828940i
$260$	10.3151	+	5.80560i	0.639713	+	0.360048i
$261$	−11.7109	−	3.77991i	−0.724886	−	0.233971i
$262$	5.31859	+	9.21207i	0.328584	+	0.569124i
$263$	14.4457	−	8.34021i	0.890758	−	0.514279i	0.0165676	−	0.999863i	$-0.494726\pi$
$263$	14.4457	−	8.34021i	0.890758	−	0.514279i	0.874190	+	0.485583i	$0.161393\pi$
$264$	7.18301	−	0.762034i	0.442084	−	0.0469000i
$265$	14.7342			0.905117
$266$	0.514571	+	6.65914i	0.0315504	+	0.408298i
$267$	−1.16366	−	10.9688i	−0.0712148	−	0.671278i
$268$		−	0.124046i		−	0.00757733i
$269$	6.61911	−	11.4646i	0.403574	−	0.699011i	−0.590580	−	0.806979i	$-0.701101\pi$
$269$	6.61911	−	11.4646i	0.403574	−	0.699011i	0.994154	+	0.107968i	$0.0344344\pi$
$270$	11.3772	−	12.7101i	0.692396	−	0.773514i
$271$	10.0373	+	17.3851i	0.609723	+	1.05607i	0.991286	+	0.131728i	$0.0420525\pi$
$271$	10.0373	+	17.3851i	0.609723	+	1.05607i	−0.381563	+	0.924343i	$0.624614\pi$
$272$	−7.69622			−0.466652
$273$	15.6321	+	5.35134i	0.946099	+	0.323878i
$274$	−1.94177			−0.117307
$275$	−12.0469	−	20.8659i	−0.726456	−	1.25826i
$276$	−6.99275	−	3.10522i	−0.420914	−	0.186912i
$277$	−14.9253	+	25.8514i	−0.896776	+	1.55326i	−0.0651838	+	0.997873i	$0.520763\pi$
$277$	−14.9253	+	25.8514i	−0.896776	+	1.55326i	−0.831592	+	0.555387i	$0.812570\pi$
$278$		−	7.96189i		−	0.477522i
$279$	14.0386	+	15.5305i	0.840466	+	0.929786i
$280$	8.65989	−	0.669174i	0.517528	−	0.0399908i
$281$	8.32376			0.496554			0.248277	−	0.968689i	$-0.420136\pi$
$281$	8.32376			0.496554			0.248277	+	0.968689i	$0.420136\pi$
$282$	0.841676	+	7.93372i	0.0501211	+	0.472446i
$283$	14.7753	−	8.53050i	0.878298	−	0.507086i	0.00820138	−	0.999966i	$-0.497389\pi$
$283$	14.7753	−	8.53050i	0.878298	−	0.507086i	0.870097	+	0.492881i	$0.164056\pi$
$284$	5.79343	+	10.0345i	0.343777	+	0.595439i
$285$	−11.6046	+	8.44849i	−0.687396	+	0.500445i
$286$	−7.37509	+	13.1036i	−0.436098	+	0.774835i
$287$	−3.00055	−	4.37914i	−0.177117	−	0.258492i
$288$	−2.93322	+	0.629446i	−0.172842	+	0.0370905i
$289$	−21.1159	−	36.5738i	−1.24211	−	2.15140i
$290$	6.73310	−	11.6621i	0.395381	−	0.684820i
$291$	−6.66258	−	9.15151i	−0.390567	−	0.536471i
$292$	0.561416	−	0.972402i	0.0328544	−	0.0569055i
$293$	−19.1141	−	11.0355i	−1.11665	−	0.644701i	−0.176110	−	0.984370i	$-0.556351\pi$
$293$	−19.1141	−	11.0355i	−1.11665	−	0.644701i	−0.940545	+	0.339669i	$0.889685\pi$
$294$	11.7171	−	3.11614i	0.683353	−	0.181737i
$295$	3.21314	−	5.56531i	0.187076	−	0.324025i
$296$	−5.29343	+	3.05617i	−0.307675	+	0.177636i
$297$	16.1462	+	14.4529i	0.936897	+	0.838645i
$298$	−3.57253			−0.206951
$299$	13.7053	−	8.11433i	0.792597	−	0.469264i
$300$	5.88966	+	8.08985i	0.340040	+	0.467068i
$301$	22.1767	+	10.6164i	1.27824	+	0.611920i
$302$	−12.8718	+	7.43152i	−0.740687	+	0.427636i
$303$	−30.2135	+	3.20531i	−1.73572	+	0.184140i
$304$	2.52442			0.144786
$305$	−12.1068	+	20.9696i	−0.693235	+	1.20072i
$306$	−15.4827	−	17.1281i	−0.885087	−	0.979149i
$307$	−11.3953			−0.650362			−0.325181	−	0.945652i	$-0.605425\pi$
$307$	−11.3953			−0.650362			−0.325181	+	0.945652i	$0.605425\pi$
$308$	0.850079	+	11.0010i	0.0484377	+	0.626841i
$309$	−3.27943	−	1.45627i	−0.186560	−	0.0828446i
$310$	−19.8399	+	11.4546i	−1.12683	+	0.650577i
$311$	1.56464			0.0887226			0.0443613	−	0.999016i	$-0.485875\pi$
$311$	1.56464			0.0887226			0.0443613	+	0.999016i	$0.485875\pi$
$312$	2.47181	−	5.73500i	0.139938	−	0.324680i
$313$			31.0575i			1.75548i	0.479141	+	0.877738i	$0.340948\pi$
$313$			31.0575i			1.75548i	−0.479141	+	0.877738i	$0.659052\pi$
$314$	−16.2357	+	9.37368i	−0.916233	+	0.528987i
$315$	18.9106	+	17.9266i	1.06549	+	1.01005i
$316$	−1.10193	+	1.90861i	−0.0619887	+	0.107368i
$317$	16.1815			0.908844			0.454422	−	0.890786i	$-0.349846\pi$
$317$	16.1815			0.908844			0.454422	+	0.890786i	$0.349846\pi$
$318$	−0.820105	−	7.73039i	−0.0459892	−	0.433499i
$319$	14.8148	+	8.55332i	0.829469	+	0.478894i
$320$		−	3.28289i		−	0.183519i
$321$	−0.680116	−	6.41085i	−0.0379604	−	0.357818i
$322$	5.04654	−	10.5417i	0.281232	−	0.587467i
$323$	9.71426	+	16.8256i	0.540516	+	0.936201i
$324$	−7.30169	−	5.26168i	−0.405650	−	0.292316i
$325$	−20.8293	+	0.228314i	−1.15540	+	0.0126646i
$326$			17.7838i			0.984952i
$327$	16.3343	+	7.25347i	0.903291	+	0.401118i
$328$	−1.73761	+	1.00321i	−0.0959437	+	0.0553931i
$329$	−12.1507	+	0.938922i	−0.669892	+	0.0517644i
$330$	−19.1709	+	13.9570i	−1.05533	+	0.768309i
$331$	28.0842	+	16.2144i	1.54365	+	0.891226i	0.998604	+	0.0528184i	$0.0168204\pi$
$331$	28.0842	+	16.2144i	1.54365	+	0.891226i	0.545044	+	0.838407i	$0.316513\pi$
$332$	5.03074	+	2.90450i	0.276098	+	0.159405i
$333$	−17.4505	−	5.63248i	−0.956282	−	0.308658i
$334$	−9.41884	−	5.43797i	−0.515376	−	0.297552i
$335$	0.203615	+	0.352672i	0.0111247	+	0.0192685i
$336$	−0.833094	−	4.50621i	−0.0454490	−	0.245834i
$337$	−8.07834			−0.440055			−0.220028	−	0.975494i	$-0.570615\pi$
$337$	−8.07834			−0.440055			−0.220028	+	0.975494i	$0.570615\pi$
$338$	6.74522	+	11.1131i	0.366892	+	0.604475i
$339$	9.47164	−	6.89564i	0.514429	−	0.374520i
$340$	21.8809	−	12.6329i	1.18666	−	0.685116i
$341$	−14.5512	−	25.2035i	−0.787993	−	1.36484i
$342$	5.07845	+	5.61816i	0.274611	+	0.303795i
$343$	4.24670	+	18.0268i	0.229300	+	0.973356i
$344$	4.64648	−	8.04793i	0.250521	−	0.433916i
$345$	24.9779	−	2.64987i	1.34476	−	0.142664i
$346$	−12.2605			−0.659130
$347$	21.6745	+	12.5138i	1.16355	+	0.671773i	0.952151	−	0.305628i	$-0.0988662\pi$
$347$	21.6745	+	12.5138i	1.16355	+	0.671773i	0.211394	+	0.977401i	$0.432200\pi$
$348$	−6.49333	−	2.88345i	−0.348079	−	0.154569i
$349$	8.66298	+	15.0047i	0.463718	+	0.803184i	0.999143	−	0.0413993i	$-0.0131816\pi$
$349$	8.66298	+	15.0047i	0.463718	+	0.803184i	−0.535424	+	0.844583i	$0.679848\pi$
$350$	−12.6094	+	8.63988i	−0.674002	+	0.461821i
$351$	17.7360	−	6.03619i	0.946676	−	0.322188i
$352$	4.17039			0.222282
$353$	0.964341	−	0.556762i	0.0513267	−	0.0296335i	−0.474117	−	0.880462i	$-0.657233\pi$
$353$	0.964341	−	0.556762i	0.0513267	−	0.0296335i	0.525444	+	0.850828i	$0.323899\pi$
$354$	−3.09871	−	1.37602i	−0.164695	−	0.0731349i
$355$	−32.9422	−	19.0192i	−1.74839	−	1.00943i
$356$		−	6.36836i		−	0.337523i
$357$	26.8286	−	22.8931i	1.41992	−	1.21163i
$358$	−16.7712	−	9.68288i	−0.886388	−	0.511756i
$359$	14.5551			0.768189			0.384095	−	0.923294i	$-0.374514\pi$
$359$	14.5551			0.768189			0.384095	+	0.923294i	$0.374514\pi$
$360$	7.30614	−	6.60428i	0.385068	−	0.348076i
$361$	6.31364	+	10.9356i	0.332297	+	0.575555i
$362$	0.889644	−	0.513636i	0.0467587	−	0.0269961i
$363$	−6.51637	−	8.95067i	−0.342021	−	0.469789i
$364$	8.64890	+	4.02448i	0.453326	+	0.210940i
$365$			3.68613i			0.192941i
$366$	11.6757	+	5.18475i	0.610299	+	0.271011i
$367$	−12.1645	+	7.02320i	−0.634984	+	0.366608i	−0.782680	−	0.622425i	$-0.786148\pi$
$367$	−12.1645	+	7.02320i	−0.634984	+	0.366608i	0.147696	+	0.989033i	$0.452814\pi$
$368$	−3.82560	−	2.20871i	−0.199423	−	0.115137i
$369$	−5.72828	−	1.84891i	−0.298202	−	0.0962504i
$370$	10.0331	−	17.3778i	0.521594	−	0.903427i
$371$	11.8393	−	0.914859i	0.614668	−	0.0474971i
$372$	7.11400	+	9.77156i	0.368844	+	0.506632i
$373$	18.3519	−	31.7864i	0.950224	−	1.64584i	0.205288	−	0.978702i	$-0.434187\pi$
$373$	18.3519	−	31.7864i	0.950224	−	1.64584i	0.744937	−	0.667135i	$-0.232480\pi$
$374$	16.0481	+	27.7961i	0.829828	+	1.43730i
$375$	−4.03978	−	1.79392i	−0.208613	−	0.0926374i
$376$			4.60624i			0.237549i
$377$	12.7265	−	7.53481i	0.655446	−	0.388062i
$378$	8.35272	−	10.9193i	0.429618	−	0.561630i
$379$	−0.706667	+	0.407994i	−0.0362990	+	0.0209573i	−0.518040	−	0.855357i	$-0.673338\pi$
$379$	−0.706667	+	0.407994i	−0.0362990	+	0.0209573i	0.481741	+	0.876314i	$0.340005\pi$
$380$	−7.17710	+	4.14370i	−0.368177	+	0.212567i
$381$	−36.0739	+	3.82702i	−1.84812	+	0.196064i
$382$			8.29792i			0.424559i
$383$	7.37148	+	4.25593i	0.376665	+	0.217468i	0.676366	−	0.736565i	$-0.263554\pi$
$383$	7.37148	+	4.25593i	0.376665	+	0.217468i	−0.299701	+	0.954033i	$0.596887\pi$
$384$	−1.72239	+	0.182725i	−0.0878951	+	0.00932465i
$385$	−20.4744	−	29.8812i	−1.04347	−	1.52289i
$386$	−10.2886	−	5.94013i	−0.523676	−	0.302345i
$387$	27.2583	−	5.84942i	1.38562	−	0.297343i
$388$	−3.26777	−	5.65995i	−0.165896	−	0.287340i
$389$			25.1319i			1.27424i	0.770765	+	0.637119i	$0.219874\pi$
$389$			25.1319i			1.27424i	−0.770765	+	0.637119i	$0.780126\pi$
$390$	2.38617	+	20.3623i	0.120829	+	1.03109i
$391$		−	33.9975i		−	1.71933i
$392$	6.91690	−	1.07540i	0.349356	−	0.0543158i
$393$	−7.47739	+	16.8386i	−0.377184	+	0.849394i
$394$	−4.57466	+	7.92354i	−0.230468	+	0.399182i
$395$		−	7.23506i		−	0.364035i
$396$	8.38968	+	9.28129i	0.421597	+	0.466402i
$397$	7.48939	−	12.9720i	0.375882	−	0.651046i	−0.614577	−	0.788857i	$-0.710673\pi$
$397$	7.48939	−	12.9720i	0.375882	−	0.651046i	0.990459	+	0.137811i	$0.0440065\pi$
$398$			3.99702i			0.200352i
$399$	−8.80001	+	7.50912i	−0.440551	+	0.375926i
$400$	2.88868	+	5.00334i	0.144434	+	0.250167i
$401$	−11.2625	−	19.5072i	−0.562422	−	0.974144i	−0.997284	−	0.0736470i	$-0.976536\pi$
$401$	−11.2625	−	19.5072i	−0.562422	−	0.974144i	0.434862	−	0.900497i	$-0.356797\pi$
$402$	0.173698	−	0.126457i	0.00866327	−	0.00630712i
$403$	−25.1593	+	0.275776i	−1.25327	+	0.0137374i
$404$	−17.5417			−0.872731
$405$	29.3959	+	2.97397i	1.46070	+	0.147778i
$406$	4.68611	−	9.78884i	0.232568	−	0.485812i
$407$	22.0757	+	12.7454i	1.09425	+	0.631766i
$408$	−7.84581	−	10.7768i	−0.388426	−	0.533529i
$409$	14.8936	−	25.7964i	0.736439	−	1.27555i	−0.217649	−	0.976027i	$-0.569839\pi$
$409$	14.8936	−	25.7964i	0.736439	−	1.27555i	0.954089	−	0.299524i	$-0.0968277\pi$
$410$	3.29343	−	5.70439i	0.162651	−	0.281720i
$411$	−1.97951	−	2.71899i	−0.0976421	−	0.134118i
$412$	−1.79412	−	1.03583i	−0.0883898	−	0.0510319i
$413$	2.23628	−	4.67138i	0.110040	−	0.229864i
$414$	−2.78053	−	12.9573i	−0.136656	−	0.636816i
$415$	−19.0703			−0.936125
$416$	1.76844	−	3.14207i	0.0867051	−	0.154053i
$417$	11.1488	−	8.11665i	0.545958	−	0.397474i
$418$	−5.26391	−	9.11736i	−0.257466	−	0.445945i
$419$	6.27014	+	10.8602i	0.306316	+	0.530555i	0.977554	−	0.210687i	$-0.0675702\pi$
$419$	6.27014	+	10.8602i	0.306316	+	0.530555i	−0.671237	+	0.741243i	$0.734237\pi$
$420$	9.76524	+	11.4440i	0.476495	+	0.558409i
$421$		−	7.92498i		−	0.386240i	−0.981175	−	0.193120i	$-0.938139\pi$
$421$		−	7.92498i		−	0.386240i	0.981175	−	0.193120i	$-0.0618606\pi$
$422$	13.9918	−	24.2346i	0.681112	−	1.17972i
$423$	−10.2513	+	9.26650i	−0.498435	+	0.450553i
$424$		−	4.48819i		−	0.217966i
$425$	−22.2319	+	38.5068i	−1.07841	+	1.86785i
$426$	−8.14497	+	18.3419i	−0.394625	+	0.888669i
$427$	−8.42613	+	17.6014i	−0.407769	+	0.851790i
$428$		−	3.72207i		−	0.179913i
$429$	−25.8670	+	3.03125i	−1.24887	+	0.146350i
$430$			30.5077i			1.47121i
$431$	−8.21994	−	14.2374i	−0.395941	−	0.685789i	0.597280	−	0.802033i	$-0.296248\pi$
$431$	−8.21994	−	14.2374i	−0.395941	−	0.685789i	−0.993221	+	0.116243i	$0.962915\pi$
$432$	−3.87163	−	3.46561i	−0.186274	−	0.166739i
$433$	15.7567	+	9.09714i	0.757219	+	0.437181i	0.828296	−	0.560290i	$-0.189310\pi$
$433$	15.7567	+	9.09714i	0.757219	+	0.437181i	−0.0710771	+	0.997471i	$0.522644\pi$
$434$	−15.2307	+	10.4359i	−0.731096	+	0.500941i
$435$	23.1940	−	2.46061i	1.11207	−	0.117977i
$436$	8.93621	+	5.15932i	0.427967	+	0.247087i
$437$			11.1515i			0.533446i
$438$	1.93395	−	0.205170i	0.0924077	−	0.00980339i
$439$	−18.2471	+	10.5350i	−0.870886	+	0.502807i	−0.867643	−	0.497188i	$-0.834366\pi$
$439$	−18.2471	+	10.5350i	−0.870886	+	0.502807i	−0.00324376	+	0.999995i	$0.501033\pi$
$440$	−11.8567	+	6.84546i	−0.565245	+	0.326344i
$441$	16.3082	+	13.2303i	0.776583	+	0.630015i
$442$	27.7474	−	0.304145i	1.31981	−	0.0144667i
$443$		−	5.49826i		−	0.261230i	−0.991433	−	0.130615i	$-0.958305\pi$
$443$		−	5.49826i		−	0.261230i	0.991433	−	0.130615i	$-0.0416952\pi$
$444$	−9.67577	−	4.29665i	−0.459192	−	0.203910i
$445$	10.4533	+	18.1057i	0.495535	+	0.858291i
$446$	8.69542	−	15.0609i	0.411740	−	0.713154i
$447$	−3.64197	−	5.00250i	−0.172259	−	0.236610i
$448$	−0.203837	−	2.63789i	−0.00963039	−	0.124628i
$449$	5.64836	−	9.78324i	0.266562	−	0.461700i	−0.701409	−	0.712759i	$-0.747445\pi$
$449$	5.64836	−	9.78324i	0.266562	−	0.461700i	0.967972	+	0.251059i	$0.0807788\pi$
$450$	−5.32381	+	16.4942i	−0.250967	+	0.777543i
$451$	7.24652	+	4.18378i	0.341225	+	0.197007i
$452$	5.85794	−	3.38208i	0.275534	−	0.159080i
$453$	−23.5281	−	10.4479i	−1.10545	−	0.490887i
$454$		−	23.9857i		−	1.12571i
$455$	−31.1954	+	2.75482i	−1.46246	+	0.129148i
$456$	2.57349	+	3.53487i	0.120515	+	0.165535i
$457$	−20.4295	+	11.7950i	−0.955651	+	0.551745i	−0.894832	−	0.446404i	$-0.852705\pi$
$457$	−20.4295	+	11.7950i	−0.955651	+	0.551745i	−0.0608191	+	0.998149i	$0.519371\pi$
$458$	−1.44795	−	2.50792i	−0.0676581	−	0.117187i
$459$	8.20028	−	39.1409i	0.382756	−	1.82694i
$460$	14.5019			0.676155
$461$	−8.76660	−	5.06140i	−0.408301	−	0.235733i	0.281758	−	0.959485i	$-0.409082\pi$
$461$	−8.76660	−	5.06140i	−0.408301	−	0.235733i	−0.690060	+	0.723753i	$0.742416\pi$
$462$	−14.5377	+	12.4052i	−0.676357	+	0.577141i
$463$		−	18.9145i		−	0.879032i	−0.898235	−	0.439516i	$-0.855150\pi$
$463$		−	18.9145i		−	0.879032i	0.898235	−	0.439516i	$-0.144850\pi$
$464$	−3.55238	−	2.05097i	−0.164915	−	0.0952137i
$465$	−36.2650	−	16.1040i	−1.68175	−	0.746803i
$466$	−11.4271	+	6.59742i	−0.529348	+	0.305619i
$467$	16.2055			0.749899			0.374950	−	0.927045i	$-0.377660\pi$
$467$	16.2055			0.749899			0.374950	+	0.927045i	$0.377660\pi$
$468$	10.5504	−	2.38528i	0.487691	−	0.110260i
$469$	0.185508	+	0.270738i	0.00856595	+	0.0125015i
$470$	−7.56089	−	13.0958i	−0.348758	−	0.604066i
$471$	−29.6769	−	13.1784i	−1.36744	−	0.607230i
$472$	−1.69525	−	0.978752i	−0.0780302	−	0.0450507i
$473$	−38.7552			−1.78197
$474$	−3.79591	+	0.402702i	−0.174352	+	0.0184967i
$475$	7.29225	−	12.6306i	0.334591	−	0.579529i
$476$	16.7975	−	11.5095i	0.769910	−	0.527536i
$477$	9.98857	−	9.02902i	0.457345	−	0.413410i
$478$	−11.8390	−	20.5057i	−0.541502	−	0.937909i
$479$	−28.4451	+	16.4228i	−1.29969	+	0.750376i	−0.980350	−	0.197265i	$-0.936794\pi$
$479$	−28.4451	+	16.4228i	−1.29969	+	0.750376i	−0.319338	+	0.947641i	$0.603461\pi$
$480$	4.59692	−	3.34670i	0.209820	−	0.152755i
$481$	18.9638	−	11.2277i	0.864676	−	0.511939i
$482$	12.3109			0.560744
$483$	19.9059	−	3.68013i	0.905748	−	0.167452i
$484$	−3.19606	−	5.53574i	−0.145275	−	0.251624i
$485$	18.5810	+	10.7277i	0.843719	+	0.487121i
$486$	−0.0758638	−	15.5883i	−0.00344125	−	0.707098i
$487$	−26.2146	−	15.1350i	−1.18790	−	0.685833i	−0.230069	−	0.973174i	$-0.573895\pi$
$487$	−26.2146	−	15.1350i	−1.18790	−	0.685833i	−0.957828	+	0.287342i	$0.907228\pi$
$488$	6.38756	+	3.68786i	0.289151	+	0.166941i
$489$	−24.9020	+	18.1294i	−1.12611	+	0.819842i
$490$	−17.9000	+	14.4111i	−0.808639	+	0.651029i
$491$	−16.9520	+	9.78727i	−0.765035	+	0.441693i	−0.831101	−	0.556122i	$-0.812289\pi$
$491$	−16.9520	+	9.78727i	−0.765035	+	0.441693i	0.0660655	+	0.997815i	$0.478955\pi$
$492$	−3.17615	−	1.41041i	−0.143192	−	0.0635863i
$493$		−	31.5694i		−	1.42181i
$494$	−9.10139	+	0.0997622i	−0.409491	+	0.00448851i
$495$	−39.0871	−	12.6161i	−1.75684	−	0.567052i
$496$	3.48918	+	6.04343i	0.156669	+	0.271358i
$497$	−27.6509	−	13.2370i	−1.24031	−	0.593762i
$498$	1.06145	+	10.0053i	0.0475648	+	0.448350i
$499$			3.88687i			0.174000i	0.996208	+	0.0870001i	$0.0277280\pi$
$499$			3.88687i			0.174000i	−0.996208	+	0.0870001i	$0.972272\pi$
$500$	−2.21009	−	1.27599i	−0.0988381	−	0.0570642i
$501$	−1.98731	−	18.7326i	−0.0887864	−	0.836909i
$502$	4.13815			0.184695
$503$	−3.70474	+	6.41680i	−0.165186	+	0.286111i	−0.936721	−	0.350076i	$-0.886156\pi$
$503$	−3.70474	+	6.41680i	−0.165186	+	0.286111i	0.771535	+	0.636187i	$0.219489\pi$
$504$	5.46061	−	5.76036i	0.243235	−	0.256587i
$505$	49.8721	−	28.7937i	2.21928	−	1.28130i
$506$			18.4224i			0.818974i
$507$	−8.68504	+	20.7743i	−0.385716	+	0.922617i
$508$	−20.9442			−0.929247
$509$	22.8313	−	13.1817i	1.01198	−	0.584267i	0.100209	−	0.994966i	$-0.468049\pi$
$509$	22.8313	−	13.1817i	1.01198	−	0.584267i	0.911771	+	0.410700i	$0.134716\pi$
$510$	39.9956	+	17.7606i	1.77104	+	0.786451i
$511$	0.228875	+	2.96191i	0.0101248	+	0.131027i
$512$	−1.00000			−0.0441942
$513$	−2.68976	+	12.8386i	−0.118756	+	0.566836i
$514$	−8.37891	+	14.5127i	−0.369578	+	0.640128i
$515$	6.80105			0.299690
$516$	16.0060	−	1.69806i	0.704627	−	0.0747528i
$517$	16.6362	−	9.60490i	0.731658	−	0.422423i
$518$	6.98282	−	14.5864i	0.306808	−	0.640891i
$519$	−12.4988	−	17.1680i	−0.548638	−	0.753592i
$520$	0.129736	+	11.8359i	0.00568929	+	0.519039i
$521$	18.3528			0.804051			0.402026	−	0.915628i	$-0.368306\pi$
$521$	18.3528			0.804051			0.402026	+	0.915628i	$0.368306\pi$
$522$	−2.58195	−	12.0319i	−0.113009	−	0.526621i
$523$	−20.8475	+	12.0363i	−0.911598	+	0.526311i	−0.880945	−	0.473219i	$-0.843092\pi$
$523$	−20.8475	+	12.0363i	−0.911598	+	0.526311i	−0.0306528	+	0.999530i	$0.509759\pi$
$524$	−5.31859	+	9.21207i	−0.232344	+	0.402431i
$525$	−24.9527	−	8.84875i	−1.08902	−	0.386191i
$526$	14.4457	+	8.34021i	0.629861	+	0.363650i
$527$	−26.8535	+	46.5116i	−1.16976	+	2.02608i
$528$	4.25145	+	5.83965i	0.185020	+	0.254138i
$529$	−1.74318	+	3.01927i	−0.0757903	+	0.131273i
$530$	7.36712	+	12.7602i	0.320007	+	0.554268i
$531$	−1.23214	−	5.74180i	−0.0534705	−	0.249173i
$532$	−5.50970	+	3.77520i	−0.238876	+	0.163676i
$533$	6.22504	−	3.68558i	0.269636	−	0.159640i
$534$	8.91741	−	6.49215i	0.385894	−	0.280943i
$535$	6.10958	+	10.5821i	0.264140	+	0.457504i
$536$	0.107427	−	0.0620231i	0.00464015	−	0.00267899i
$537$	−3.53861	−	33.3553i	−0.152702	−	1.43939i
$538$	13.2382			0.570740
$539$	−18.3070	−	22.7391i	−0.788540	−	0.979442i
$540$	16.6959	+	3.49790i	0.718478	+	0.150526i
$541$		−	9.09344i		−	0.390958i	−0.980708	−	0.195479i	$-0.937374\pi$
$541$		−	9.09344i		−	0.390958i	0.980708	−	0.195479i	$-0.0626261\pi$
$542$	−10.0373	+	17.3851i	−0.431139	+	0.746755i
$543$	1.62616	+	0.722119i	0.0697854	+	0.0309891i
$544$	−3.84811	−	6.66512i	−0.164986	−	0.285765i
$545$	−33.8750			−1.45104
$546$	3.18166	+	16.2135i	0.136163	+	0.693873i
$547$	35.2496			1.50716			0.753582	−	0.657354i	$-0.228324\pi$
$547$	35.2496			1.50716			0.753582	+	0.657354i	$0.228324\pi$
$548$	−0.970884	−	1.68162i	−0.0414741	−	0.0718353i
$549$	4.64262	+	21.6346i	0.198142	+	0.923343i
$550$	12.0469	−	20.8659i	0.513682	−	0.889723i
$551$			10.3550i			0.441139i
$552$	−0.807175	−	7.60851i	−0.0343556	−	0.323840i
$553$	−0.449230	−	5.81356i	−0.0191032	−	0.247218i
$554$	−29.8506			−1.26823
$555$	34.5616	−	3.66658i	1.46706	−	0.155638i
$556$	6.89520	−	3.98095i	0.292422	−	0.168830i
$557$	−7.03801	−	12.1902i	−0.298210	−	0.516515i	0.677517	−	0.735507i	$-0.263056\pi$
$557$	−7.03801	−	12.1902i	−0.298210	−	0.516515i	−0.975726	+	0.218993i	$0.929723\pi$
$558$	−6.43052	+	19.9230i	−0.272226	+	0.843407i
$559$	−16.4341	+	29.1991i	−0.695087	+	1.23499i
$560$	4.90947	+	7.16510i	0.207463	+	0.302781i
$561$	−22.5620	+	50.8080i	−0.952567	+	2.14512i
$562$	4.16188	+	7.20858i	0.175558	+	0.304076i
$563$	−7.86426	+	13.6213i	−0.331439	+	0.574069i	−0.982794	−	0.184704i	$-0.940867\pi$
$563$	−7.86426	+	13.6213i	−0.331439	+	0.574069i	0.651355	+	0.758773i	$0.274201\pi$
$564$	−6.44996	+	4.69577i	−0.271593	+	0.197728i
$565$	−11.1030	+	19.2310i	−0.467107	+	0.809053i
$566$	14.7753	+	8.53050i	0.621051	+	0.358564i
$567$	23.8051	+	0.564450i	0.999719	+	0.0237047i
$568$	−5.79343	+	10.0345i	−0.243087	+	0.421039i
$569$	23.2297	−	13.4117i	0.973838	−	0.562246i	0.0734341	−	0.997300i	$-0.476604\pi$
$569$	23.2297	−	13.4117i	0.973838	−	0.562246i	0.900404	+	0.435054i	$0.143271\pi$
$570$	−13.1189	−	5.82561i	−0.549490	−	0.244008i
$571$	16.7595			0.701363			0.350682	−	0.936495i	$-0.385950\pi$
$571$	16.7595			0.701363			0.350682	+	0.936495i	$0.385950\pi$
$572$	−15.0356	+	0.164809i	−0.628672	+	0.00689099i
$573$	−11.6193	+	8.45921i	−0.485403	+	0.353389i
$574$	2.29217	−	4.78812i	0.0956734	−	0.199852i
$575$	−22.1019	+	12.7605i	−0.921712	+	0.532151i
$576$	−2.01173	−	2.22552i	−0.0838220	−	0.0927301i
$577$	10.6399			0.442946			0.221473	−	0.975166i	$-0.428913\pi$
$577$	10.6399			0.442946			0.221473	+	0.975166i	$0.428913\pi$
$578$	21.1159	−	36.5738i	0.878305	−	1.52127i
$579$	−2.17082	−	20.4624i	−0.0902163	−	0.850388i
$580$	13.4662			0.559153
$581$	−15.3235	+	1.18409i	−0.635726	+	0.0491243i
$582$	4.59415	−	10.3457i	0.190434	−	0.428844i
$583$	−16.2098	+	9.35874i	−0.671342	+	0.387600i
$584$	1.12283			0.0464631
$585$	−26.0801	+	24.0994i	−1.07828	+	0.996386i
$586$		−	22.0710i		−	0.911745i
$587$	−21.6686	+	12.5103i	−0.894357	+	0.516357i	−0.875365	−	0.483462i	$-0.839379\pi$
$587$	−21.6686	+	12.5103i	−0.894357	+	0.516357i	−0.0189918	+	0.999820i	$0.506046\pi$
$588$	8.55719	+	8.58921i	0.352893	+	0.354213i
$589$	8.80816	−	15.2562i	0.362934	−	0.628620i
$590$	6.42627			0.264565
$591$	−15.7587	+	1.67181i	−0.648225	+	0.0687691i
$592$	−5.29343	−	3.05617i	−0.217559	−	0.125608i
$593$			47.2978i			1.94229i	0.238497	+	0.971143i	$0.423345\pi$
$593$			47.2978i			1.94229i	−0.238497	+	0.971143i	$0.576655\pi$
$594$	−4.44353	+	21.2095i	−0.182320	+	0.870236i
$595$	−28.8641	+	60.2943i	−1.18331	+	2.47182i
$596$	−1.78627	−	3.09390i	−0.0731683	−	0.126731i
$597$	−5.59689	+	4.07471i	−0.229066	+	0.166767i
$598$	13.8799	+	7.81197i	0.567590	+	0.319455i
$599$		−	37.9705i		−	1.55143i	−0.631081	−	0.775717i	$-0.717388\pi$
$599$		−	37.9705i		−	1.55143i	0.631081	−	0.775717i	$-0.282612\pi$
$600$	−4.06118	+	9.14552i	−0.165797	+	0.373364i
$601$	−20.2283	+	11.6788i	−0.825131	+	0.476390i	−0.852183	−	0.523244i	$-0.824721\pi$
$601$	−20.2283	+	11.6788i	−0.825131	+	0.476390i	0.0270517	+	0.999634i	$0.491388\pi$
$602$	1.89425	+	24.5138i	0.0772037	+	0.999107i
$603$	0.354148	+	0.114308i	0.0144220	+	0.00465498i
$604$	−12.8718	−	7.43152i	−0.523745	−	0.302384i
$605$	18.1732	+	10.4923i	0.738846	+	0.426573i
$606$	−17.8826	−	24.5630i	−0.726433	−	0.997805i
$607$	26.4502	+	15.2710i	1.07358	+	0.619833i	0.929158	−	0.369683i	$-0.120534\pi$
$607$	26.4502	+	15.2710i	1.07358	+	0.619833i	0.144424	+	0.989516i	$0.453867\pi$
$608$	1.26221	+	2.18621i	0.0511894	+	0.0886627i
$609$	18.4842	−	3.41730i	0.749017	−	0.138476i
$610$	−24.2137			−0.980382
$611$	−0.182033	−	16.6070i	−0.00736427	−	0.671849i
$612$	7.09203	−	21.9725i	0.286678	−	0.888184i
$613$	24.7422	−	14.2849i	0.999328	−	0.576962i	0.0912784	−	0.995825i	$-0.470905\pi$
$613$	24.7422	−	14.2849i	0.999328	−	0.576962i	0.908049	+	0.418863i	$0.137571\pi$
$614$	−5.69763	−	9.86859i	−0.229938	−	0.398264i
$615$	11.3451	−	1.20359i	0.457480	−	0.0485333i
$616$	−9.10211	+	6.23669i	−0.366735	+	0.251284i
$617$	8.53339	−	14.7803i	0.343541	−	0.595031i	−0.641546	−	0.767084i	$-0.721707\pi$
$617$	8.53339	−	14.7803i	0.343541	−	0.595031i	0.985088	+	0.172053i	$0.0550401\pi$
$618$	−0.378546	−	3.56821i	−0.0152273	−	0.143534i
$619$	−22.3781			−0.899453			−0.449727	−	0.893166i	$-0.648479\pi$
$619$	−22.3781			−0.899453			−0.449727	+	0.893166i	$0.648479\pi$
$620$	−19.8399	−	11.4546i	−0.796790	−	0.460027i
$621$	15.3091	−	17.1026i	0.614333	−	0.686305i
$622$	0.782320	+	1.35502i	0.0313682	+	0.0543313i
$623$	9.52371	+	13.8993i	0.381559	+	0.556865i
$624$	6.20255	−	0.726852i	0.248301	−	0.0290974i
$625$	−20.5089			−0.820356
$626$	−26.8966	+	15.5288i	−1.07501	+	0.620655i
$627$	7.40051	−	16.6655i	0.295548	−	0.665554i
$628$	−16.2357	−	9.37368i	−0.647875	−	0.374051i
$629$		−	47.0418i		−	1.87568i
$630$	−6.06958	+	25.3404i	−0.241818	+	1.00958i
$631$	−11.2407	−	6.48982i	−0.447485	−	0.258356i	0.259282	−	0.965802i	$-0.416514\pi$
$631$	−11.2407	−	6.48982i	−0.447485	−	0.258356i	−0.706768	+	0.707446i	$0.749847\pi$
$632$	−2.20387			−0.0876652
$633$	48.1987	−	5.11332i	1.91573	−	0.203236i
$634$	8.09076	+	14.0136i	0.321325	+	0.556551i
$635$	59.5456	−	34.3787i	2.36300	−	1.36428i
$636$	6.28466	−	4.57543i	0.249203	−	0.181428i
$637$	−24.8952	+	4.15052i	−0.986386	+	0.164449i
$638$			17.1066i			0.677259i
$639$	−33.9869	+	7.29331i	−1.34450	+	0.288519i
$640$	2.84307	−	1.64144i	0.112382	−	0.0648838i
$641$	−10.4824	−	6.05200i	−0.414029	−	0.239040i	0.278490	−	0.960439i	$-0.410166\pi$
$641$	−10.4824	−	6.05200i	−0.414029	−	0.239040i	−0.692519	+	0.721399i	$0.743499\pi$
$642$	5.21190	−	3.79442i	0.205697	−	0.149754i
$643$	2.90522	−	5.03200i	0.114571	−	0.198443i	−0.803037	−	0.595929i	$-0.796784\pi$
$643$	2.90522	−	5.03200i	0.114571	−	0.198443i	0.917608	+	0.397486i	$0.130117\pi$
$644$	11.6527	−	0.900434i	0.459180	−	0.0354821i
$645$	−42.7190	+	31.1007i	−1.68206	+	1.22459i
$646$	−9.71426	+	16.8256i	−0.382202	+	0.661994i
$647$	−9.24194	−	16.0075i	−0.363338	−	0.629320i	0.625170	−	0.780489i	$-0.285030\pi$
$647$	−9.24194	−	16.0075i	−0.363338	−	0.629320i	−0.988508	+	0.151169i	$0.951696\pi$
$648$	0.905901	−	8.95429i	0.0355872	−	0.351758i
$649$			8.16355i			0.320447i
$650$	−10.6124	−	17.9246i	−0.416252	−	0.703059i
$651$	−30.1398	−	10.6882i	−1.18127	−	0.418905i
$652$	−15.4012	+	8.89189i	−0.603158	+	0.348233i
$653$	11.3924	−	6.57741i	0.445819	−	0.257394i	−0.260244	−	0.965543i	$-0.583803\pi$
$653$	11.3924	−	6.57741i	0.445819	−	0.257394i	0.706063	+	0.708149i	$0.250470\pi$
$654$	1.88548	+	17.7727i	0.0737280	+	0.694967i
$655$		−	34.9207i		−	1.36446i
$656$	−1.73761	−	1.00321i	−0.0678424	−	0.0391688i
$657$	2.25883	+	2.49889i	0.0881255	+	0.0974910i
$658$	−6.88850	−	10.0534i	−0.268542	−	0.391922i
$659$	11.9839	+	6.91891i	0.466827	+	0.269523i	0.714910	−	0.699216i	$-0.246467\pi$
$659$	11.9839	+	6.91891i	0.466827	+	0.269523i	−0.248084	+	0.968739i	$0.579801\pi$
$660$	−21.6726	−	9.62400i	−0.843605	−	0.374614i
$661$	−18.7710	−	32.5124i	−0.730108	−	1.26458i	−0.956837	−	0.290626i	$-0.906136\pi$
$661$	−18.7710	−	32.5124i	−0.730108	−	1.26458i	0.226729	−	0.973958i	$-0.427197\pi$
$662$			32.4289i			1.26038i
$663$	28.7127	+	38.5438i	1.11511	+	1.49692i
$664$			5.80900i			0.225433i
$665$	9.46766	−	19.7770i	0.367140	−	0.766920i
$666$	−3.84738	−	17.9288i	−0.149083	−	0.694728i
$667$	9.05999	−	15.6924i	0.350804	−	0.607611i
$668$		−	10.8759i		−	0.420803i
$669$	29.9537	−	3.17774i	1.15808	−	0.122859i
$670$	−0.203615	+	0.352672i	−0.00786634	+	0.0136249i
$671$		−	30.7596i		−	1.18746i
$672$	3.48595	−	2.97459i	0.134473	−	0.114747i
$673$	−6.25166	−	10.8282i	−0.240984	−	0.417396i	0.720011	−	0.693963i	$-0.244137\pi$
$673$	−6.25166	−	10.8282i	−0.240984	−	0.417396i	−0.960995	+	0.276567i	$0.910803\pi$
$674$	−4.03917	−	6.99605i	−0.155583	−	0.269478i
$675$	−28.5236	+	9.36003i	−1.09787	+	0.360268i
$676$	−6.25166	+	11.3981i	−0.240448	+	0.438389i
$677$	23.5823			0.906340			0.453170	−	0.891424i	$-0.350293\pi$
$677$	23.5823			0.906340			0.453170	+	0.891424i	$0.350293\pi$
$678$	10.7076	+	4.75486i	0.411224	+	0.182609i
$679$	15.5964	+	7.46631i	0.598535	+	0.286531i
$680$	21.8809	+	12.6329i	0.839092	+	0.484450i
$681$	33.5864	−	24.4519i	1.28703	−	0.937000i
$682$	14.5512	−	25.2035i	0.557195	−	0.965090i
$683$	3.38165	−	5.85720i	0.129395	−	0.224119i	−0.794047	−	0.607856i	$-0.792030\pi$
$683$	3.38165	−	5.85720i	0.129395	−	0.224119i	0.923442	+	0.383737i	$0.125363\pi$
$684$	−2.32624	+	7.20715i	−0.0889461	+	0.275572i
$685$	5.52058	+	3.18731i	0.210930	+	0.121781i
$686$	−13.4883	+	12.6911i	−0.514986	+	0.484550i
$687$	2.03566	−	4.58418i	0.0776654	−	0.174897i
$688$	9.29295			0.354291
$689$	0.177368	+	16.1814i	0.00675718	+	0.616463i
$690$	14.7838	+	20.3066i	0.562809	+	0.773057i
$691$	1.69532	+	2.93638i	0.0644929	+	0.111705i	0.896469	−	0.443107i	$-0.146124\pi$
$691$	1.69532	+	2.93638i	0.0644929	+	0.111705i	−0.831976	+	0.554812i	$0.812790\pi$
$692$	−6.13026	−	10.6179i	−0.233038	−	0.403633i
$693$	−32.1909	−	7.71043i	−1.22283	−	0.292895i
$694$			25.0275i			0.950031i
$695$	−13.0690	+	22.6362i	−0.495735	+	0.858639i
$696$	−0.749526	−	7.06511i	−0.0284107	−	0.267802i
$697$		−	15.4419i		−	0.584903i
$698$	−8.66298	+	15.0047i	−0.327898	+	0.567937i
$699$	−20.8873	−	9.27528i	−0.790031	−	0.350823i
$700$	−13.7871	−	6.60015i	−0.521102	−	0.249462i
$701$		−	43.1581i		−	1.63006i	−0.579419	−	0.815030i	$-0.696721\pi$
$701$		−	43.1581i		−	1.63006i	0.579419	−	0.815030i	$-0.303279\pi$
$702$	14.0955	+	12.3417i	0.532000	+	0.465807i
$703$			15.4301i			0.581958i
$704$	2.08519	+	3.61166i	0.0785887	+	0.136120i
$705$	10.6298	−	23.9376i	0.400342	−	0.901544i
$706$	0.964341	+	0.556762i	0.0362934	+	0.0209540i
$707$	38.2858	−	26.2331i	1.43988	−	0.986597i
$708$	−0.357685	−	3.37158i	−0.0134426	−	0.126712i
$709$	16.9511	+	9.78671i	0.636611	+	0.367548i	0.783308	−	0.621634i	$-0.213531\pi$
$709$	16.9511	+	9.78671i	0.636611	+	0.367548i	−0.146697	+	0.989182i	$0.546864\pi$
$710$		−	38.0384i		−	1.42756i
$711$	−4.43359	−	4.90476i	−0.166272	−	0.183943i
$712$	5.51516	−	3.18418i	0.206689	−	0.119332i
$713$	−26.6964	+	15.4132i	−0.999789	+	0.577228i
$714$	33.2403	+	11.7877i	1.24399	+	0.441145i
$715$	42.4768	−	25.1487i	1.58854	−	0.940509i
$716$		−	19.3658i		−	0.723733i
$717$	16.6444	−	37.4820i	0.621596	−	1.39979i
$718$	7.27755	+	12.6051i	0.271596	+	0.470418i
$719$	−8.87175	+	15.3663i	−0.330860	+	0.573067i	−0.982681	−	0.185306i	$-0.940672\pi$
$719$	−8.87175	+	15.3663i	−0.330860	+	0.573067i	0.651820	+	0.758373i	$0.274006\pi$
$720$	9.37255	+	3.02517i	0.349294	+	0.112741i
$721$	5.46483	−	0.422282i	0.203521	−	0.0157266i
$722$	−6.31364	+	10.9356i	−0.234969	+	0.406979i
$723$	12.5502	+	17.2385i	0.466745	+	0.641107i
$724$	0.889644	+	0.513636i	0.0330634	+	0.0190891i
$725$	−20.5234	+	11.8492i	−0.762219	+	0.440067i
$726$	4.49333	−	10.1187i	0.166763	−	0.375539i
$727$			16.4693i			0.610814i	0.952222	+	0.305407i	$0.0987925\pi$
$727$			16.4693i			0.610814i	−0.952222	+	0.305407i	$0.901207\pi$
$728$	0.839146	+	9.50241i	0.0311008	+	0.352183i
$729$	21.7504	−	15.9975i	0.805571	−	0.592500i
$730$	−3.19229	+	1.84307i	−0.118152	+	0.0682150i
$731$	35.7603	+	61.9387i	1.32264	+	2.29088i
$732$	1.34773	+	12.7038i	0.0498135	+	0.469547i
$733$	4.62622			0.170873			0.0854367	−	0.996344i	$-0.472771\pi$
$733$	4.62622			0.170873			0.0854367	+	0.996344i	$0.472771\pi$
$734$	−12.1645	−	7.02320i	−0.449002	−	0.259231i
$735$	−38.4274	−	10.3735i	−1.41741	−	0.382633i
$736$		−	4.41743i		−	0.162828i
$737$	−0.448013	−	0.258660i	−0.0165028	−	0.00952788i
$738$	−1.26294	−	5.88529i	−0.0464893	−	0.216640i
$739$	−4.63110	+	2.67377i	−0.170358	+	0.0983562i	−0.582755	−	0.812648i	$-0.698025\pi$
$739$	−4.63110	+	2.67377i	−0.170358	+	0.0983562i	0.412397	+	0.911004i	$0.364692\pi$
$740$	20.0661			0.737645
$741$	−9.41799	−	12.6427i	−0.345979	−	0.464440i
$742$	6.71196	+	9.79574i	0.246404	+	0.359613i
$743$	−15.9338	−	27.5981i	−0.584553	−	1.01247i	−0.994931	−	0.100560i	$-0.967937\pi$
$743$	−15.9338	−	27.5981i	−0.584553	−	1.01247i	0.410378	−	0.911915i	$-0.365397\pi$
$744$	−4.90542	+	11.0467i	−0.179841	+	0.404991i
$745$	10.1569	+	5.86411i	0.372122	+	0.214845i
$746$	36.7038			1.34382
$747$	−12.9281	+	11.6861i	−0.473013	+	0.427573i
$748$	−16.0481	+	27.7961i	−0.586777	+	1.01633i
$749$	5.56626	+	8.12365i	0.203387	+	0.296832i
$750$	−0.466312	−	4.39551i	−0.0170273	−	0.160501i
$751$	12.5881	+	21.8033i	0.459347	+	0.795613i	0.998927	−	0.0463220i	$-0.0147500\pi$
$751$	12.5881	+	21.8033i	0.459347	+	0.795613i	−0.539579	+	0.841935i	$0.681417\pi$
$752$	−3.98912	+	2.30312i	−0.145468	+	0.0839861i
$753$	4.21859	+	5.79452i	0.153734	+	0.211164i
$754$	12.8886	+	7.25404i	0.469374	+	0.264176i
$755$	48.7937			1.77578
$756$	13.6328	+	1.77400i	0.495820	+	0.0645196i
$757$	8.82099	+	15.2784i	0.320604	+	0.555303i	0.980613	−	0.195955i	$-0.0627807\pi$
$757$	8.82099	+	15.2784i	0.320604	+	0.555303i	−0.660009	+	0.751258i	$0.729447\pi$
$758$	−0.706667	−	0.407994i	−0.0256673	−	0.0148190i
$759$	−25.7962	+	18.7805i	−0.936344	+	0.681687i
$760$	−7.17710	−	4.14370i	−0.260341	−	0.150308i
$761$	19.7704	+	11.4144i	0.716676	+	0.413773i	0.813528	−	0.581526i	$-0.197544\pi$
$761$	19.7704	+	11.4144i	0.716676	+	0.413773i	−0.0968519	+	0.995299i	$0.530877\pi$
$762$	−21.3513	−	29.3274i	−0.773474	−	1.06242i
$763$	−27.2194	+	2.10332i	−0.985410	+	0.0761453i
$764$	−7.18621	+	4.14896i	−0.259988	+	0.150104i
$765$	15.9035	+	74.1103i	0.574992	+	2.67946i
$766$			8.51185i			0.307546i
$767$	6.15062	+	3.46174i	0.222086	+	0.124996i
$768$	−1.01944	−	1.40027i	−0.0367858	−	0.0505278i
$769$	−5.98667	−	10.3692i	−0.215885	−	0.373923i	0.737661	−	0.675171i	$-0.235930\pi$
$769$	−5.98667	−	10.3692i	−0.215885	−	0.373923i	−0.953546	+	0.301248i	$0.902597\pi$
$770$	15.6407	−	32.6719i	0.563652	−	1.17742i
$771$	−28.8634	+	3.06208i	−1.03949	+	0.110278i
$772$		−	11.8803i		−	0.427580i
$773$	6.95873	+	4.01762i	0.250288	+	0.144504i	0.619896	−	0.784684i	$-0.287175\pi$
$773$	6.95873	+	4.01762i	0.250288	+	0.144504i	−0.369608	+	0.929188i	$0.620508\pi$
$774$	18.6949	+	20.6817i	0.671974	+	0.743388i
$775$	40.3165			1.44821
$776$	3.26777	−	5.65995i	0.117306	−	0.203180i
$777$	27.5435	−	5.09215i	0.988116	−	0.182680i
$778$	−21.7649	+	12.5660i	−0.780308	+	0.450511i
$779$			5.06506i			0.181475i
$780$	−16.4412	+	12.2476i	−0.588689	+	0.438536i
$781$	48.3217			1.72909
$782$	29.4427	−	16.9987i	1.05287	−	0.607873i
$783$	14.2157	−	15.8812i	0.508028	−	0.567547i
$784$	4.38977	+	5.45251i	0.156778	+	0.194733i
$785$	61.5455			2.19665
$786$	−18.3213	+	1.94368i	−0.653500	+	0.0693288i
$787$	−5.23675	+	9.07032i	−0.186670	+	0.323322i	−0.944138	−	0.329550i	$-0.893103\pi$
$787$	−5.23675	+	9.07032i	−0.186670	+	0.323322i	0.757468	+	0.652872i	$0.226436\pi$
$788$	−9.14932			−0.325931
$789$	3.04793	+	28.7301i	0.108509	+	1.02282i
$790$	6.26574	−	3.61753i	0.222925	−	0.128706i
$791$	−7.72749	+	16.1420i	−0.274758	+	0.573943i
$792$	−3.84299	+	11.9063i	−0.136555	+	0.423073i
$793$	−23.1750	−	13.0435i	−0.822969	−	0.463189i
$794$	14.9788			0.531577
$795$	−10.3574	+	23.3242i	−0.367339	+	0.827223i
$796$	−3.46152	+	1.99851i	−0.122690	+	0.0708353i
$797$	11.3604	−	19.6768i	0.402406	−	0.696988i	−0.591609	−	0.806225i	$-0.701507\pi$
$797$	11.3604	−	19.6768i	0.402406	−	0.696988i	0.994016	+	0.109236i	$0.0348405\pi$
$798$	−10.9031	−	3.86647i	−0.385965	−	0.136872i
$799$	−30.7011	−	17.7253i	−1.08613	−	0.627076i
$800$	−2.88868	+	5.00334i	−0.102130	+	0.176895i
$801$	18.1815	+	5.86841i	0.642411	+	0.207350i
$802$	11.2625	−	19.5072i	0.397693	−	0.688824i
$803$	−2.34132	−	4.05529i	−0.0826235	−	0.143108i
$804$	0.196364	+	0.0871981i	0.00692523	+	0.00307524i
$805$	−31.6513	+	21.6872i	−1.11556	+	0.764374i
$806$	−12.8185	−	21.6507i	−0.451512	−	0.762614i
$807$	13.4955	+	18.5370i	0.475065	+	0.652535i
$808$	−8.77084	−	15.1915i	−0.308557	−	0.534437i
$809$	−12.4690	+	7.19898i	−0.438387	+	0.253103i	−0.702913	−	0.711276i	$-0.748118\pi$
$809$	−12.4690	+	7.19898i	−0.438387	+	0.253103i	0.264526	+	0.964378i	$0.414784\pi$
$810$	12.1224	+	26.9446i	0.425939	+	0.946738i
$811$	−22.5924			−0.793325			−0.396662	−	0.917965i	$-0.629832\pi$
$811$	−22.5924			−0.793325			−0.396662	+	0.917965i	$0.629832\pi$
$812$	10.8204	−	0.836125i	0.379723	−	0.0293422i
$813$	−34.5762	+	3.66813i	−1.21264	+	0.128647i
$814$			25.4908i			0.893451i
$815$	29.1911	−	50.5604i	1.02252	−	1.77106i
$816$	5.41004	−	12.1831i	0.189389	−	0.426492i
$817$	−11.7297	−	20.3164i	−0.410369	−	0.710781i
$818$	29.7871			1.04148
$819$	−19.4597	+	20.9838i	−0.679977	+	0.733234i
$820$	6.58687			0.230023
$821$	0.821661	+	1.42316i	0.0286762	+	0.0496686i	0.880007	−	0.474960i	$-0.157538\pi$
$821$	0.821661	+	1.42316i	0.0286762	+	0.0496686i	−0.851331	+	0.524629i	$0.824204\pi$
$822$	1.36496	−	3.07380i	0.0476085	−	0.107211i
$823$	6.07905	−	10.5292i	0.211903	−	0.367026i	−0.740407	−	0.672158i	$-0.765367\pi$
$823$	6.07905	−	10.5292i	0.211903	−	0.367026i	0.952310	+	0.305132i	$0.0987007\pi$
$824$		−	2.07167i		−	0.0721700i
$825$	41.4989	−	4.40255i	1.44480	−	0.153277i
$826$	5.16368	−	0.399012i	0.179667	−	0.0138834i
$827$	36.4788			1.26849			0.634246	−	0.773132i	$-0.281311\pi$
$827$	36.4788			1.26849			0.634246	+	0.773132i	$0.281311\pi$
$828$	9.83108	−	8.88666i	0.341654	−	0.308833i
$829$	−47.8785	+	27.6427i	−1.66289	+	0.960070i	−0.691565	+	0.722314i	$0.743078\pi$
$829$	−47.8785	+	27.6427i	−1.66289	+	0.960070i	−0.971325	+	0.237756i	$0.923588\pi$
$830$	−9.53516	−	16.5154i	−0.330970	−	0.573257i
$831$	−30.4309	−	41.7989i	−1.05563	−	1.44999i
$832$	3.60533	−	0.0395188i	0.124992	−	0.00137007i
$833$	−19.4493	+	50.2402i	−0.673880	+	1.74072i
$834$	12.6036	+	5.59680i	0.436427	+	0.193801i
$835$	17.8523	+	30.9210i	0.617803	+	1.07007i
$836$	5.26391	−	9.11736i	0.182056	−	0.315330i
$837$	−34.4530	+	11.3058i	−1.19087	+	0.390785i
$838$	−6.27014	+	10.8602i	−0.216598	+	0.375159i
$839$	−8.53828	−	4.92958i	−0.294774	−	0.170188i	0.345319	−	0.938485i	$-0.387771\pi$
$839$	−8.53828	−	4.92958i	−0.294774	−	0.170188i	−0.640093	+	0.768297i	$0.721104\pi$
$840$	−5.02816	+	14.1789i	−0.173488	+	0.489220i
$841$	−6.08707	+	10.5431i	−0.209899	+	0.363556i
$842$	6.86323	−	3.96249i	0.236523	−	0.136556i
$843$	−5.85117	+	13.1764i	−0.201525	+	0.453821i
$844$	27.9837			0.963238
$845$	−0.935482	−	42.6673i	−0.0321816	−	1.46780i
$846$	−13.1507	−	4.24463i	−0.452129	−	0.145933i
$847$	15.2541	+	7.30246i	0.524138	+	0.250915i
$848$	3.88689	−	2.24410i	0.133476	−	0.0770625i
$849$	3.11748	+	29.3856i	0.106991	+	1.00851i
$850$	−44.4638			−1.52510
$851$	13.5004	−	23.3833i	0.462787	−	0.801571i
$852$	−19.9571	+	2.11721i	−0.683717	+	0.0725345i
$853$	50.9055			1.74297			0.871485	−	0.490422i	$-0.163157\pi$
$853$	50.9055			1.74297			0.871485	+	0.490422i	$0.163157\pi$
$854$	−19.4563	+	1.50344i	−0.665781	+	0.0514468i
$855$	−5.21647	−	24.3088i	−0.178400	−	0.831343i
$856$	3.22341	−	1.86104i	0.110174	−	0.0636089i
$857$	37.6517			1.28616			0.643078	−	0.765800i	$-0.277657\pi$
$857$	37.6517			1.28616			0.643078	+	0.765800i	$0.277657\pi$
$858$	−15.5587	−	20.8859i	−0.531164	−	0.713033i
$859$		−	35.0983i		−	1.19754i	−0.800922	−	0.598769i	$-0.795657\pi$
$859$		−	35.0983i		−	1.19754i	0.800922	−	0.598769i	$-0.204343\pi$
$860$	−26.4205	+	15.2539i	−0.900931	+	0.520153i
$861$	9.04137	−	1.67154i	0.308129	−	0.0569659i
$862$	8.21994	−	14.2374i	0.279972	−	0.484926i
$863$	−37.0070			−1.25973			−0.629867	−	0.776703i	$-0.716891\pi$
$863$	−37.0070			−1.25973			−0.629867	+	0.776703i	$0.716891\pi$
$864$	1.06549	−	5.08574i	0.0362489	−	0.173020i
$865$	34.8575	+	20.1250i	1.18519	+	0.684269i
$866$			18.1943i			0.618267i
$867$	72.7394	−	7.71681i	2.47036	−	0.262077i
$868$	−16.6531	−	7.97218i	−0.565244	−	0.270594i
$869$	4.59549	+	7.95963i	0.155891	+	0.270012i
$870$	13.7279	+	18.8563i	0.465421	+	0.639287i
$871$	−0.384860	+	0.227860i	−0.0130405	+	0.00772073i
$872$			10.3186i			0.349434i
$873$	19.1702	−	4.11377i	0.648813	−	0.139230i
$874$	−9.65744	+	5.57573i	−0.326668	+	0.188602i
$875$	6.73186	−	0.520189i	0.227578	−	0.0175856i
$876$	1.14466	+	1.57227i	0.0386744	+	0.0531219i
$877$	11.3397	+	6.54696i	0.382913	+	0.221075i	0.679085	−	0.734060i	$-0.262377\pi$
$877$	11.3397	+	6.54696i	0.382913	+	0.221075i	−0.296172	+	0.955135i	$0.595710\pi$
$878$	−18.2471	−	10.5350i	−0.615810	−	0.355538i
$879$	30.9053	−	22.5000i	1.04241	−	0.758907i
$880$	−11.8567	−	6.84546i	−0.399689	−	0.230760i
$881$	4.51600	+	7.82195i	0.152148	+	0.263528i	0.932017	−	0.362415i	$-0.118048\pi$
$881$	4.51600	+	7.82195i	0.152148	+	0.263528i	−0.779869	+	0.625943i	$0.784714\pi$
$882$	−3.30366	+	20.7385i	−0.111240	+	0.698302i
$883$	−45.8128			−1.54172			−0.770861	−	0.637003i	$-0.780174\pi$
$883$	−45.8128			−1.54172			−0.770861	+	0.637003i	$0.780174\pi$
$884$	14.1371	+	23.8779i	0.475483	+	0.803101i
$885$	6.55118	+	8.99849i	0.220216	+	0.302481i
$886$	4.76164	−	2.74913i	0.159970	−	0.0923589i
$887$	−13.0463	−	22.5968i	−0.438051	−	0.758726i	0.559488	−	0.828838i	$-0.310998\pi$
$887$	−13.0463	−	22.5968i	−0.438051	−	0.758726i	−0.997539	+	0.0701120i	$0.977664\pi$
$888$	−1.11688	−	10.5278i	−0.0374799	−	0.353289i
$889$	45.7119	−	31.3214i	1.53313	−	1.05049i
$890$	−10.4533	+	18.1057i	−0.350396	+	0.606903i
$891$	−34.2288	+	15.3996i	−1.14671	+	0.515907i
$892$	17.3908			0.582288
$893$	10.0702	+	5.81405i	0.336987	+	0.194560i
$894$	2.51131	−	5.65529i	0.0839906	−	0.189141i
$895$	31.7878	+	55.0581i	1.06255	+	1.84039i
$896$	2.18256	−	1.49547i	0.0729142	−	0.0499602i
$897$	3.21081	+	27.3993i	0.107206	+	0.914837i
$898$	11.2967			0.376976
$899$	−24.7898	+	14.3124i	−0.826785	+	0.477344i
$900$	−16.9463	+	3.63654i	−0.564876	+	0.121218i
$901$	29.9143	+	17.2710i	0.996591	+	0.575382i
$902$			8.36756i			0.278609i
$903$	−32.3948	+	27.6427i	−1.07803	+	0.919892i
$904$	5.85794	+	3.38208i	0.194832	+	0.112486i
$905$	−3.37242			−0.112103
$906$	−2.71585	−	25.5999i	−0.0902281	−	0.850499i
$907$	0.495632	+	0.858461i	0.0164572	+	0.0285047i	0.874137	−	0.485680i	$-0.161428\pi$
$907$	0.495632	+	0.858461i	0.0164572	+	0.0285047i	−0.857680	+	0.514185i	$0.828095\pi$
$908$	20.7722	−	11.9929i	0.689351	−	0.397997i
$909$	16.1646	−	50.0810i	0.536145	−	1.66108i
$910$	−17.9834	−	25.6386i	−0.596145	−	0.849910i
$911$		−	4.92531i		−	0.163183i	−0.996666	−	0.0815914i	$-0.974000\pi$
$911$		−	4.92531i		−	0.163183i	0.996666	−	0.0815914i	$-0.0260003\pi$
$912$	−1.77454	+	3.99614i	−0.0587608	+	0.132325i
$913$	20.9801	−	12.1129i	0.694342	−	0.400878i
$914$	−20.4295	−	11.7950i	−0.675747	−	0.390143i
$915$	−24.6843	−	33.9056i	−0.816038	−	1.12088i
$916$	1.44795	−	2.50792i	0.0478415	−	0.0828639i
$917$	−2.16825	−	28.0597i	−0.0716020	−	0.926613i
$918$	37.9972	−	12.4688i	1.25409	−	0.411532i
$919$	3.16943	−	5.48962i	0.104550	−	0.181086i	−0.809004	−	0.587803i	$-0.799993\pi$
$919$	3.16943	−	5.48962i	0.104550	−	0.181086i	0.913554	+	0.406717i	$0.133326\pi$
$920$	7.25096	+	12.5590i	0.239057	+	0.414059i
$921$	8.01028	−	18.0386i	0.263948	−	0.594393i
$922$		−	10.1228i		−	0.333376i
$923$	20.4907	−	36.4068i	0.674460	−	1.19834i
$924$	−18.0121	−	6.38747i	−0.592554	−	0.210132i
$925$	−30.5821	+	17.6566i	−1.00553	+	0.580544i
$926$	16.3804	−	9.45726i	0.538295	−	0.310785i
$927$	4.61054	−	4.16763i	0.151430	−	0.136883i
$928$		−	4.10193i		−	0.134653i
$929$	−0.544018	−	0.314089i	−0.0178486	−	0.0103049i	0.491049	−	0.871132i	$-0.336614\pi$
$929$	−0.544018	−	0.314089i	−0.0178486	−	0.0103049i	−0.508898	+	0.860827i	$0.669947\pi$
$930$	−4.18608	−	39.4584i	−0.137267	−	1.29389i
$931$	6.37954	−	16.4792i	0.209081	−	0.540084i
$932$	−11.4271	−	6.59742i	−0.374306	−	0.216106i
$933$	−1.09986	+	2.47681i	−0.0360078	+	0.0810872i
$934$	8.10273	+	14.0343i	0.265129	+	0.459218i
$935$		−	105.368i		−	3.44591i
$936$	7.34090	+	7.94425i	0.239945	+	0.259666i
$937$		−	32.1850i		−	1.05144i	−0.850658	−	0.525720i	$-0.823796\pi$
$937$		−	32.1850i		−	1.05144i	0.850658	−	0.525720i	$-0.176204\pi$
$938$	−0.141712	+	0.296024i	−0.00462708	+	0.00966551i
$939$	−49.1638	−	21.8318i	−1.60440	−	0.712455i
$940$	7.56089	−	13.0958i	0.246609	−	0.427139i
$941$			21.1091i			0.688138i	0.938944	+	0.344069i	$0.111805\pi$
$941$			21.1091i			0.688138i	−0.938944	+	0.344069i	$0.888195\pi$
$942$	−3.42561	−	32.2902i	−0.111613	−	1.05207i
$943$	4.43161	−	7.67578i	0.144313	−	0.249958i
$944$		−	1.95750i		−	0.0637114i
$945$	−41.6708	+	17.3339i	−1.35555	+	0.563871i
$946$	−19.3776	−	33.5630i	−0.630020	−	1.09123i
$947$	9.54333	+	16.5295i	0.310116	+	0.537137i	0.978387	−	0.206781i	$-0.0662986\pi$
$947$	9.54333	+	16.5295i	0.310116	+	0.537137i	−0.668271	+	0.743918i	$0.732965\pi$
$948$	−2.24671	−	3.08601i	−0.0729696	−	0.100229i
$949$	−4.04819	+	0.0443730i	−0.131410	+	0.00144041i
$950$	14.5845			0.473184
$951$	−11.3748	+	25.6152i	−0.368852	+	0.830630i
$952$	18.3662	+	8.79228i	0.595253	+	0.284959i
$953$	−47.2598	−	27.2854i	−1.53089	−	0.883862i	−0.999321	−	0.0368498i	$-0.988268\pi$
$953$	−47.2598	−	27.2854i	−1.53089	−	0.883862i	−0.531573	−	0.847012i	$-0.678399\pi$
$954$	12.8136	+	4.13585i	0.414857	+	0.133903i
$955$	13.6206	−	23.5915i	0.440752	−	0.763404i
$956$	11.8390	−	20.5057i	0.382900	−	0.663202i
$957$	−23.9539	+	17.4392i	−0.774319	+	0.563728i
$958$	−28.4451	−	16.4228i	−0.919019	−	0.530596i
$959$	4.63383	+	2.21831i	0.149634	+	0.0716329i
$960$	5.19679	+	2.30770i	0.167726	+	0.0744807i
$961$	17.6974			0.570885
$962$	19.2054	+	10.8093i	0.619206	+	0.348506i
$963$	10.6264	+	3.42987i	0.342431	+	0.110526i
$964$	6.15543	+	10.6615i	0.198253	+	0.343384i
$965$	19.5008	+	33.7764i	0.627753	+	1.08730i
$966$	13.1400	+	15.3989i	0.422773	+	0.495452i
$967$			53.5813i			1.72306i	0.507708	+	0.861529i	$0.330493\pi$
$967$			53.5813i			1.72306i	−0.507708	+	0.861529i	$0.669507\pi$
$968$	3.19606	−	5.53574i	0.102725	−	0.177925i
$969$	−33.4634	+	3.55008i	−1.07500	+	0.114045i
$970$			21.4555i			0.688893i
$971$	−20.9527	+	36.2911i	−0.672404	+	1.16464i	0.304816	+	0.952411i	$0.401405\pi$
$971$	−20.9527	+	36.2911i	−0.672404	+	1.16464i	−0.977220	+	0.212227i	$0.931928\pi$
$972$	13.4619	−	7.85984i	0.431791	−	0.252104i
$973$	−9.09579	+	19.0002i	−0.291598	+	0.609119i
$974$		−	30.2700i		−	0.969914i
$975$	14.2805	−	33.1331i	0.457342	−	1.06111i
$976$			7.37572i			0.236091i
$977$	−22.4040	−	38.8048i	−0.716767	−	1.24148i	−0.962274	−	0.272081i	$-0.912288\pi$
$977$	−22.4040	−	38.8048i	−0.716767	−	1.24148i	0.245508	−	0.969395i	$-0.421045\pi$
$978$	−28.1516	−	12.5011i	−0.900188	−	0.399740i
$979$	−23.0004	−	13.2793i	−0.735095	−	0.424407i
$980$	−21.4304	−	8.29628i	−0.684569	−	0.265015i
$981$	−22.9644	+	20.7583i	−0.733196	+	0.662762i
$982$	−16.9520	−	9.78727i	−0.540962	−	0.312324i
$983$		−	35.3442i		−	1.12731i	−0.826012	−	0.563653i	$-0.809396\pi$
$983$		−	35.3442i		−	1.12731i	0.826012	−	0.563653i	$-0.190604\pi$
$984$	−0.366624	−	3.45584i	−0.0116876	−	0.110168i
$985$	26.0121	−	15.0181i	0.828815	−	0.478517i
$986$	27.3399	−	15.7847i	0.870679	−	0.502687i
$987$	7.05503	−	19.8945i	0.224564	−	0.633250i
$988$	−4.63709	−	7.83215i	−0.147526	−	0.249174i
$989$			41.0509i			1.30534i
$990$	−8.61770	−	40.1585i	−0.273888	−	1.27632i
$991$	20.4150	+	35.3599i	0.648505	+	1.12324i	0.983480	+	0.181016i	$0.0579387\pi$
$991$	20.4150	+	35.3599i	0.648505	+	1.12324i	−0.334975	+	0.942227i	$0.608728\pi$
$992$	−3.48918	+	6.04343i	−0.110782	+	0.191879i
$993$	−45.4091	+	33.0592i	−1.44101	+	1.04910i
$994$	−2.36183	−	30.5649i	−0.0749127	−	0.969458i
$995$	6.56089	−	11.3638i	0.207994	−	0.360256i
$996$	−8.13416	+	5.92192i	−0.257741	+	0.187643i
$997$	39.1799	+	22.6206i	1.24084	+	0.716400i	0.969266	−	0.246017i	$-0.0791219\pi$
$997$	39.1799	+	22.6206i	1.24084	+	0.716400i	0.271576	+	0.962417i	$0.412455\pi$
$998$	−3.36613	+	1.94343i	−0.106553	+	0.0615184i
$999$	21.1830	−	23.6647i	0.670200	−	0.748717i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.q.j.335.5	yes	24
3.2	odd	2		546.2.q.i.335.1	yes	24
7.6	odd	2	inner	546.2.q.j.335.8	yes	24
13.4	even	6		546.2.q.i.251.12	yes	24
21.20	even	2		546.2.q.i.335.12	yes	24
39.17	odd	6	inner	546.2.q.j.251.8	yes	24
91.69	odd	6		546.2.q.i.251.1	✓	24
273.251	even	6	inner	546.2.q.j.251.5	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.q.i.251.1	✓	24	91.69	odd	6
546.2.q.i.251.12	yes	24	13.4	even	6
546.2.q.i.335.1	yes	24	3.2	odd	2
546.2.q.i.335.12	yes	24	21.20	even	2
546.2.q.j.251.5	yes	24	273.251	even	6	inner
546.2.q.j.251.8	yes	24	39.17	odd	6	inner
546.2.q.j.335.5	yes	24	1.1	even	1	trivial
546.2.q.j.335.8	yes	24	7.6	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.702948 + 1.58299i) q^{3} +(-0.500000 + 0.866025i) q^{4} -3.28289i q^{5} +(-1.72239 + 0.182725i) q^{6} +(-0.203837 - 2.63789i) q^{7} -1.00000 q^{8} +(-2.01173 - 2.22552i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.702948 + 1.58299i) q^{3} +(-0.500000 + 0.866025i) q^{4} -3.28289i q^{5} +(-1.72239 + 0.182725i) q^{6} +(-0.203837 - 2.63789i) q^{7} -1.00000 q^{8} +(-2.01173 - 2.22552i) q^{9} +(2.84307 - 1.64144i) q^{10} +(2.08519 + 3.61166i) q^{11} +(-1.01944 - 1.40027i) q^{12} +(3.60533 - 0.0395188i) q^{13} +(2.18256 - 1.49547i) q^{14} +(5.19679 + 2.30770i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.84811 - 6.66512i) q^{17} +(0.921495 - 2.85497i) q^{18} +(-1.26221 + 2.18621i) q^{19} +(2.84307 + 1.64144i) q^{20} +(4.31904 + 1.53163i) q^{21} +(-2.08519 + 3.61166i) q^{22} +(3.82560 - 2.20871i) q^{23} +(0.702948 - 1.58299i) q^{24} -5.77736 q^{25} +(1.83689 + 3.10255i) q^{26} +(4.93712 - 1.62012i) q^{27} +(2.38640 + 1.14242i) q^{28} +(3.55238 - 2.05097i) q^{29} +(0.599866 + 5.65440i) q^{30} -6.97836 q^{31} +(0.500000 - 0.866025i) q^{32} +(-7.18301 + 0.762034i) q^{33} +7.69622 q^{34} +(-8.65989 + 0.669174i) q^{35} +(2.93322 - 0.629446i) q^{36} +(5.29343 - 3.05617i) q^{37} -2.52442 q^{38} +(-2.47181 + 5.73500i) q^{39} +3.28289i q^{40} +(1.73761 - 1.00321i) q^{41} +(0.833094 + 4.50621i) q^{42} +(-4.64648 + 8.04793i) q^{43} -4.17039 q^{44} +(-7.30614 + 6.60428i) q^{45} +(3.82560 + 2.20871i) q^{46} -4.60624i q^{47} +(1.72239 - 0.182725i) q^{48} +(-6.91690 + 1.07540i) q^{49} +(-2.88868 - 5.00334i) q^{50} +(7.84581 + 10.7768i) q^{51} +(-1.76844 + 3.14207i) q^{52} +4.48819i q^{53} +(3.87163 + 3.46561i) q^{54} +(11.8567 - 6.84546i) q^{55} +(0.203837 + 2.63789i) q^{56} +(-2.57349 - 3.53487i) q^{57} +(3.55238 + 2.05097i) q^{58} +(1.69525 + 0.978752i) q^{59} +(-4.59692 + 3.34670i) q^{60} +(-6.38756 - 3.68786i) q^{61} +(-3.48918 - 6.04343i) q^{62} +(-5.46061 + 5.76036i) q^{63} +1.00000 q^{64} +(-0.129736 - 11.8359i) q^{65} +(-4.25145 - 5.83965i) q^{66} +(-0.107427 + 0.0620231i) q^{67} +(3.84811 + 6.66512i) q^{68} +(0.807175 + 7.60851i) q^{69} +(-4.90947 - 7.16510i) q^{70} +(5.79343 - 10.0345i) q^{71} +(2.01173 + 2.22552i) q^{72} -1.12283 q^{73} +(5.29343 + 3.05617i) q^{74} +(4.06118 - 9.14552i) q^{75} +(-1.26221 - 2.18621i) q^{76} +(9.10211 - 6.23669i) q^{77} +(-6.20255 + 0.726852i) q^{78} +2.20387 q^{79} +(-2.84307 + 1.64144i) q^{80} +(-0.905901 + 8.95429i) q^{81} +(1.73761 + 1.00321i) q^{82} -5.80900i q^{83} +(-3.48595 + 2.97459i) q^{84} +(-21.8809 - 12.6329i) q^{85} -9.29295 q^{86} +(0.749526 + 7.06511i) q^{87} +(-2.08519 - 3.61166i) q^{88} +(-5.51516 + 3.18418i) q^{89} +(-9.37255 - 3.02517i) q^{90} +(-0.839146 - 9.50241i) q^{91} +4.41743i q^{92} +(4.90542 - 11.0467i) q^{93} +(3.98912 - 2.30312i) q^{94} +(7.17710 + 4.14370i) q^{95} +(1.01944 + 1.40027i) q^{96} +(-3.26777 + 5.65995i) q^{97} +(-4.38977 - 5.45251i) q^{98} +(3.84299 - 11.9063i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{2} - 12 q^{4} - 18 q^{7} - 24 q^{8} + 6 q^{9}+O(q^{10}) \) 24 * q + 12 * q^2 - 12 * q^4 - 18 * q^7 - 24 * q^8 + 6 * q^9	\( 24 q + 12 q^{2} - 12 q^{4} - 18 q^{7} - 24 q^{8} + 6 q^{9} + 12 q^{15} - 12 q^{16} - 6 q^{18} + 12 q^{21} - 36 q^{23} - 12 q^{25} + 18 q^{28} + 6 q^{30} + 12 q^{32} - 36 q^{35} - 12 q^{36} + 36 q^{37} + 12 q^{39} - 12 q^{42} - 42 q^{43} - 36 q^{46} - 6 q^{50} + 12 q^{51} + 18 q^{56} - 36 q^{57} - 6 q^{60} + 66 q^{63} + 24 q^{64} + 66 q^{65} - 54 q^{67} + 48 q^{71} - 6 q^{72} + 36 q^{74} - 12 q^{78} - 48 q^{79} - 6 q^{81} - 24 q^{84} - 84 q^{86} + 36 q^{91} + 54 q^{93} - 36 q^{95} + 36 q^{99}+O(q^{100}) \) 24 * q + 12 * q^2 - 12 * q^4 - 18 * q^7 - 24 * q^8 + 6 * q^9 + 12 * q^15 - 12 * q^16 - 6 * q^18 + 12 * q^21 - 36 * q^23 - 12 * q^25 + 18 * q^28 + 6 * q^30 + 12 * q^32 - 36 * q^35 - 12 * q^36 + 36 * q^37 + 12 * q^39 - 12 * q^42 - 42 * q^43 - 36 * q^46 - 6 * q^50 + 12 * q^51 + 18 * q^56 - 36 * q^57 - 6 * q^60 + 66 * q^63 + 24 * q^64 + 66 * q^65 - 54 * q^67 + 48 * q^71 - 6 * q^72 + 36 * q^74 - 12 * q^78 - 48 * q^79 - 6 * q^81 - 24 * q^84 - 84 * q^86 + 36 * q^91 + 54 * q^93 - 36 * q^95 + 36 * q^99

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