LMFDB - Embedded newform 546.2.q.i.335.1

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			335.1
Character	$\chi$	$=$	546.335
Dual form			546.2.q.i.251.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-1.72239 - 0.182725i) q^{3} +(-0.500000 + 0.866025i) q^{4} +3.28289i q^{5} +(0.702948 + 1.58299i) q^{6} +(-0.203837 - 2.63789i) q^{7} +1.00000 q^{8} +(2.93322 + 0.629446i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.72239 - 0.182725i) q^{3} +(-0.500000 + 0.866025i) q^{4} +3.28289i q^{5} +(0.702948 + 1.58299i) q^{6} +(-0.203837 - 2.63789i) q^{7} +1.00000 q^{8} +(2.93322 + 0.629446i) 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} +(0.599866 - 5.65440i) 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} +(-0.130923 + 4.58071i) q^{21} +(-2.08519 + 3.61166i) q^{22} +(-3.82560 + 2.20871i) q^{23} +(-1.72239 - 0.182725i) 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} +(-5.19679 + 2.30770i) q^{30} -6.97836 q^{31} +(-0.500000 + 0.866025i) q^{32} +(2.93156 + 6.60169i) q^{33} +7.69622 q^{34} +(8.65989 - 0.669174i) q^{35} +(-2.01173 + 2.22552i) q^{36} +(5.29343 - 3.05617i) q^{37} +2.52442 q^{38} +(-6.21700 - 0.590719i) q^{39} +3.28289i q^{40} +(-1.73761 + 1.00321i) q^{41} +(4.03247 - 2.17697i) q^{42} +(-4.64648 + 8.04793i) q^{43} +4.17039 q^{44} +(-2.06640 + 9.62945i) q^{45} +(3.82560 + 2.20871i) q^{46} +4.60624i q^{47} +(0.702948 + 1.58299i) 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} +(1.06549 + 5.08574i) 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} +(1.06251 - 7.86582i) 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} +(6.99275 - 3.10522i) q^{69} +(-4.90947 - 7.16510i) q^{70} +(-5.79343 + 10.0345i) q^{71} +(2.93322 + 0.629446i) q^{72} -1.12283 q^{73} +(-5.29343 - 3.05617i) q^{74} +(9.95084 + 1.05567i) q^{75} +(-1.26221 - 2.18621i) q^{76} +(-9.10211 + 6.23669i) q^{77} +(2.59692 + 5.67944i) q^{78} +2.20387 q^{79} +(2.84307 - 1.64144i) q^{80} +(8.20759 + 3.69261i) q^{81} +(1.73761 + 1.00321i) q^{82} +5.80900i q^{83} +(-3.90155 - 2.40373i) q^{84} +(-21.8809 - 12.6329i) q^{85} +9.29295 q^{86} +(6.49333 - 2.88345i) 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} +(12.0194 + 1.27512i) 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} - 12 q^{9}+O(q^{10}) $ 24 * q - 12 * q^2 - 12 * q^4 - 18 * q^7 + 24 * q^8 - 12 * q^9	$ 24 q - 12 q^{2} - 12 q^{4} - 18 q^{7} + 24 q^{8} - 12 q^{9} + 6 q^{15} - 12 q^{16} + 6 q^{18} - 12 q^{21} + 36 q^{23} - 12 q^{25} + 18 q^{28} - 12 q^{30} - 12 q^{32} + 36 q^{35} + 6 q^{36} + 36 q^{37} + 12 q^{39} + 24 q^{42} - 42 q^{43} - 36 q^{46} + 6 q^{50} + 12 q^{51} - 18 q^{56} + 36 q^{57} + 6 q^{60} + 24 q^{63} + 24 q^{64} - 66 q^{65} - 54 q^{67} - 48 q^{71} - 12 q^{72} - 36 q^{74} - 42 q^{78} - 48 q^{79} + 84 q^{81} - 12 q^{84} + 84 q^{86} + 36 q^{91} - 18 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 - 12 * q^9 + 6 * q^15 - 12 * q^16 + 6 * q^18 - 12 * q^21 + 36 * q^23 - 12 * q^25 + 18 * q^28 - 12 * q^30 - 12 * q^32 + 36 * q^35 + 6 * q^36 + 36 * q^37 + 12 * q^39 + 24 * q^42 - 42 * q^43 - 36 * q^46 + 6 * q^50 + 12 * q^51 - 18 * q^56 + 36 * q^57 + 6 * q^60 + 24 * q^63 + 24 * q^64 - 66 * q^65 - 54 * q^67 - 48 * q^71 - 12 * q^72 - 36 * q^74 - 42 * q^78 - 48 * q^79 + 84 * q^81 - 12 * q^84 + 84 * q^86 + 36 * q^91 - 18 * 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
$3$	−1.72239	−	0.182725i	−0.994420	−	0.105496i
$3$	−1.72239	−	0.182725i	−0.994420	−	0.105496i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$			3.28289i			1.46815i	0.679067	+	0.734076i	$0.262385\pi$
$5$			3.28289i			1.46815i	−0.679067	+	0.734076i	$0.737615\pi$
$6$	0.702948	+	1.58299i	0.286977	+	0.646254i
$7$	−0.203837	−	2.63789i	−0.0770431	−	0.997028i
$7$	−0.203837	−	2.63789i	−0.0770431	−	0.997028i
$8$	1.00000			0.353553
$9$	2.93322	+	0.629446i	0.977741	+	0.209815i
$10$	2.84307	−	1.64144i	0.899056	−	0.519070i
$11$	−2.08519	−	3.61166i	−0.628709	−	1.08896i	−0.987811	−	0.155658i	$-0.950250\pi$
$11$	−2.08519	−	3.61166i	−0.628709	−	1.08896i	0.359102	−	0.933298i	$-0.383083\pi$
$12$	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
$15$	0.599866	−	5.65440i	0.154885	−	1.45996i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−3.84811	+	6.66512i	−0.933304	+	1.61653i	−0.155672	+	0.987809i	$0.549754\pi$
$17$	−3.84811	+	6.66512i	−0.933304	+	1.61653i	−0.777631	+	0.628720i	$0.783579\pi$
$18$	−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
$21$	−0.130923	+	4.58071i	−0.0285697	+	0.999592i
$22$	−2.08519	+	3.61166i	−0.444565	+	0.770009i
$23$	−3.82560	+	2.20871i	−0.797693	+	0.460548i	−0.842664	−	0.538440i	$-0.819014\pi$
$23$	−3.82560	+	2.20871i	−0.797693	+	0.460548i	0.0449707	+	0.998988i	$0.485681\pi$
$24$	−1.72239	−	0.182725i	−0.351580	−	0.0372986i
$25$	−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	−0.792147	−	0.610330i	$-0.791037\pi$
$29$	−3.55238	+	2.05097i	−0.659660	+	0.380855i	0.132487	+	0.991185i	$0.457704\pi$
$30$	−5.19679	+	2.30770i	−0.948799	+	0.421327i
$31$	−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
$33$	2.93156	+	6.60169i	0.510320	+	1.14921i
$34$	7.69622			1.31989
$35$	8.65989	−	0.669174i	1.46379	−	0.113111i
$36$	−2.01173	+	2.22552i	−0.335288	+	0.370920i
$37$	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
$39$	−6.21700	−	0.590719i	−0.995516	−	0.0945907i
$40$			3.28289i			0.519070i
$41$	−1.73761	+	1.00321i	−0.271370	+	0.156675i	−0.629510	−	0.776992i	$-0.716744\pi$
$41$	−1.73761	+	1.00321i	−0.271370	+	0.156675i	0.358140	+	0.933668i	$0.383411\pi$
$42$	4.03247	−	2.17697i	0.622223	−	0.335914i
$43$	−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
$45$	−2.06640	+	9.62945i	−0.308041	+	1.43547i
$46$	3.82560	+	2.20871i	0.564054	+	0.325657i
$47$			4.60624i			0.671889i	0.941882	+	0.335945i	$0.109055\pi$
$47$			4.60624i			0.671889i	−0.941882	+	0.335945i	$0.890945\pi$
$48$	0.702948	+	1.58299i	0.101462	+	0.228485i
$49$	−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	$-0.900257\pi$
$53$		−	4.48819i		−	0.616500i	0.951305	−	0.308250i	$-0.0997434\pi$
$54$	1.06549	+	5.08574i	0.144996	+	0.692081i
$55$	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	0.385573	−	0.922677i	$-0.374004\pi$
$59$	−1.69525	−	0.978752i	−0.220703	−	0.127423i	−0.606276	+	0.795255i	$0.707337\pi$
$60$	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
$63$	1.06251	−	7.86582i	0.133864	−	0.991000i
$64$	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
$69$	6.99275	−	3.10522i	0.841828	−	0.373825i
$70$	−4.90947	−	7.16510i	−0.586794	−	0.856393i
$71$	−5.79343	+	10.0345i	−0.687554	+	1.19088i	0.285073	+	0.958506i	$0.407982\pi$
$71$	−5.79343	+	10.0345i	−0.687554	+	1.19088i	−0.972627	+	0.232373i	$0.925351\pi$
$72$	2.93322	+	0.629446i	0.345684	+	0.0741810i
$73$	−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
$75$	9.95084	+	1.05567i	1.14902	+	0.121898i
$76$	−1.26221	−	2.18621i	−0.144786	−	0.250776i
$77$	−9.10211	+	6.23669i	−1.03728	+	0.710737i
$78$	2.59692	+	5.67944i	0.294043	+	0.643070i
$79$	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
$81$	8.20759	+	3.69261i	0.911955	+	0.410290i
$82$	1.73761	+	1.00321i	0.191887	+	0.110786i
$83$			5.80900i			0.637621i	0.947818	+	0.318811i	$0.103283\pi$
$83$			5.80900i			0.637621i	−0.947818	+	0.318811i	$0.896717\pi$
$84$	−3.90155	−	2.40373i	−0.425694	−	0.262269i
$85$	−21.8809	−	12.6329i	−2.37331	−	1.37023i
$86$	9.29295			1.00209
$87$	6.49333	−	2.88345i	0.696158	−	0.309138i
$88$	−2.08519	−	3.61166i	−0.222282	−	0.385004i
$89$	5.51516	−	3.18418i	0.584606	−	0.337523i	−0.178356	−	0.983966i	$-0.557078\pi$
$89$	5.51516	−	3.18418i	0.584606	−	0.337523i	0.762962	+	0.646444i	$0.223744\pi$
$90$	9.37255	−	3.02517i	0.987953	−	0.318880i
$91$	−0.839146	−	9.50241i	−0.0879664	−	0.996123i
$92$		−	4.41743i		−	0.460548i
$93$	12.0194	+	1.27512i	1.24636	+	0.132224i
$94$	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	$-0.829013\pi$
$101$	−8.77084	−	15.1915i	−0.872731	−	1.51161i	−0.0135712	−	0.999908i	$-0.504320\pi$
$102$	−13.2559	−	1.40629i	−1.31253	−	0.139244i
$103$			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
$105$	−15.0379	−	0.429805i	−1.46755	−	0.0419446i
$106$	−3.88689	+	2.24410i	−0.377528	+	0.217966i
$107$	3.22341	−	1.86104i	0.311619	−	0.179913i	−0.336032	−	0.941851i	$-0.609085\pi$
$107$	3.22341	−	1.86104i	0.311619	−	0.179913i	0.647651	+	0.761937i	$0.275752\pi$
$108$	3.87163	−	3.46561i	0.372548	−	0.333479i
$109$		−	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
$111$	−9.67577	+	4.29665i	−0.918384	+	0.407820i
$112$	−2.18256	+	1.49547i	−0.206232	+	0.141309i
$113$	5.85794	+	3.38208i	0.551068	+	0.318160i	0.749553	−	0.661945i	$-0.230269\pi$
$113$	5.85794	+	3.38208i	0.551068	+	0.318160i	−0.198484	+	0.980104i	$0.563602\pi$
$114$	−4.34803	−	0.461276i	−0.407230	−	0.0432024i
$115$	−7.25096	−	12.5590i	−0.676155	−	1.17114i
$116$		−	4.10193i		−	0.380855i
$117$	10.6001	+	2.15345i	0.979982	+	0.199086i
$118$			1.95750i			0.180203i
$119$	18.3662	+	8.79228i	1.68363	+	0.805987i
$120$	0.599866	−	5.65440i	0.0547601	−	0.516174i
$121$	−3.19606	+	5.53574i	−0.290551	+	0.503249i
$122$			7.37572i			0.667766i
$123$	3.17615	−	1.41041i	0.286384	−	0.127173i
$124$	3.48918	−	6.04343i	0.313337	−	0.542716i
$125$		−	2.55199i		−	0.228257i
$126$	−7.34325	+	3.01275i	−0.654189	+	0.268397i
$127$	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	$-0.653833\pi$
$131$	−10.6372			−0.929375			−0.464688	+	0.885475i	$0.653833\pi$
$132$	−7.18301	−	0.762034i	−0.625201	−	0.0663266i
$133$	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	−0.821567	−	0.570112i	$-0.806900\pi$
$137$	0.970884	−	1.68162i	0.0829483	−	0.143671i	0.904515	+	0.426442i	$0.140233\pi$
$138$	−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
$141$	0.841676	−	7.93372i	0.0708819	−	0.668140i
$142$	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
$147$	12.1101	−	0.588357i	0.998822	−	0.0485269i
$148$			6.11233i			0.502431i
$149$	1.78627	−	3.09390i	0.146337	−	0.253463i	−0.783534	−	0.621349i	$-0.786585\pi$
$149$	1.78627	−	3.09390i	0.146337	−	0.253463i	0.929871	+	0.367886i	$0.119918\pi$
$150$	−4.06118	−	9.14552i	−0.331594	−	0.746728i
$151$			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
$153$	−15.4827	+	17.1281i	−1.25170	+	1.38473i
$154$	9.95219	+	4.76432i	0.801971	+	0.383919i
$155$		−	22.9092i		−	1.84011i
$156$	3.62008	−	5.08872i	0.289838	−	0.407424i
$157$			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
$159$	−0.820105	+	7.73039i	−0.0650386	+	0.613060i
$160$	−2.84307	−	1.64144i	−0.224764	−	0.129768i
$161$	6.60613	+	9.64129i	0.520636	+	0.759840i
$162$	−0.905901	−	8.95429i	−0.0711743	−	0.703516i
$163$	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
$165$	−21.6726	+	9.62400i	−1.68721	+	0.749228i
$166$	5.03074	−	2.90450i	0.390462	−	0.225433i
$167$	9.41884	−	5.43797i	0.728852	−	0.420803i	−0.0891502	−	0.996018i	$-0.528415\pi$
$167$	9.41884	−	5.43797i	0.728852	−	0.420803i	0.818002	+	0.575215i	$0.195082\pi$
$168$	−0.130923	+	4.58071i	−0.0101009	+	0.353409i
$169$	12.9969	−	0.284957i	0.999760	−	0.0219198i
$170$			25.2658i			1.93780i
$171$	−5.07845	+	5.61816i	−0.388359	+	0.429632i
$172$	−4.64648	−	8.04793i	−0.354291	−	0.613649i
$173$	6.13026	−	10.6179i	0.466075	−	0.807266i	−0.533174	−	0.846005i	$-0.679001\pi$
$173$	6.13026	−	10.6179i	0.466075	−	0.807266i	0.999249	+	0.0387398i	$0.0123343\pi$
$174$	−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	0.281731	−	0.959493i	$-0.409091\pi$
$179$	16.7712	−	9.68288i	1.25354	−	0.723733i	0.971811	+	0.235761i	$0.0757582\pi$
$180$	−7.30614	−	6.60428i	−0.544568	−	0.492254i
$181$		−	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
$186$	−4.90542	−	11.0467i	−0.359683	−	0.809982i
$187$	32.0962			2.34711
$188$	−3.98912	−	2.30312i	−0.290936	−	0.167972i
$189$	−3.26733	+	13.3538i	−0.237664	+	0.971348i
$190$			8.28740i			0.601231i
$191$	−7.18621	−	4.14896i	−0.519976	−	0.300208i	0.216949	−	0.976183i	$-0.430390\pi$
$191$	−7.18621	−	4.14896i	−0.519976	−	0.300208i	−0.736925	+	0.675975i	$0.763723\pi$
$192$	−1.72239	−	0.182725i	−0.124302	−	0.0131871i
$193$	−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
$195$	1.93926	−	20.4097i	0.138874	−	1.46157i
$196$	2.52713	−	6.52791i	0.180509	−	0.466279i
$197$	−4.57466	−	7.92354i	−0.325931	−	0.564529i	0.655769	−	0.754961i	$-0.272344\pi$
$197$	−4.57466	−	7.92354i	−0.325931	−	0.564529i	−0.981700	+	0.190432i	$0.939011\pi$
$198$	−8.38968	+	9.28129i	−0.596229	+	0.659592i
$199$	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
$201$	0.196364	−	0.0871981i	0.0138505	−	0.00615048i
$202$	−8.77084	+	15.1915i	−0.617114	+	1.06887i
$203$	6.13432	+	8.95271i	0.430545	+	0.628357i
$204$	5.41004	+	12.1831i	0.378779	+	0.852984i
$205$	−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
$210$	7.14675	+	13.2381i	0.493173	+	0.913519i
$211$	−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
$219$	1.93395	+	0.205170i	0.130684	+	0.0138641i
$220$			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
$225$	−16.9463	−	3.63654i	−1.12975	−	0.242436i
$226$		−	6.76416i		−	0.449946i
$227$	20.7722	+	11.9929i	1.37870	+	0.795994i	0.992003	−	0.126212i	$-0.0402820\pi$
$227$	20.7722	+	11.9929i	1.37870	+	0.795994i	0.386699	+	0.922206i	$0.373615\pi$
$228$	1.77454	+	3.99614i	0.117522	+	0.264651i
$229$	−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
$231$	16.8169	−	9.07881i	1.10647	−	0.597342i
$232$	−3.55238	+	2.05097i	−0.233225	+	0.134653i
$233$		−	13.1948i		−	0.864422i	−0.901772	−	0.432211i	$-0.857734\pi$
$233$		−	13.1948i		−	0.864422i	0.901772	−	0.432211i	$-0.142266\pi$
$234$	−3.43512	−	10.2567i	−0.224561	−	0.670502i
$235$	−15.1218			−0.986436
$236$	1.69525	−	0.978752i	0.110351	−	0.0637114i
$237$	−3.79591	−	0.402702i	−0.246571	−	0.0261583i
$238$	−1.56877	−	20.3018i	−0.101688	−	1.31597i
$239$	23.6780			1.53160			0.765800	−	0.643079i	$-0.222343\pi$
$239$	23.6780			1.53160			0.765800	+	0.643079i	$0.222343\pi$
$240$	−5.19679	+	2.30770i	−0.335451	+	0.148961i
$241$	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
$243$	−13.4619	−	7.85984i	−0.863582	−	0.504209i
$244$	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
$249$	1.06145	−	10.0053i	0.0672667	−	0.634063i
$250$	−2.21009	+	1.27599i	−0.139778	+	0.0807010i
$251$	−2.06908	+	3.58374i	−0.130599	+	0.226204i	−0.923908	−	0.382616i	$-0.875023\pi$
$251$	−2.06908	+	3.58374i	−0.130599	+	0.226204i	0.793309	+	0.608820i	$0.208357\pi$
$252$	6.28074	+	4.85307i	0.395650	+	0.305715i
$253$	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	$-0.991606\pi$
$257$	−8.37891	−	14.5127i	−0.522662	−	0.905277i	0.476990	−	0.878909i	$-0.341728\pi$
$258$	−16.0060	−	1.69806i	−0.996493	−	0.105716i
$259$	−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	−0.874190	−	0.485583i	$-0.838607\pi$
$263$	−14.4457	+	8.34021i	−0.890758	+	0.514279i	−0.0165676	+	0.999863i	$0.505274\pi$
$264$	2.93156	+	6.60169i	0.180425	+	0.406306i
$265$	14.7342			0.905117
$266$	−0.514571	−	6.65914i	−0.0315504	−	0.408298i
$267$	−10.0811	+	4.47663i	−0.616951	+	0.273965i
$268$		−	0.124046i		−	0.00757733i
$269$	−6.61911	+	11.4646i	−0.403574	+	0.699011i	−0.994154	−	0.107968i	$-0.965566\pi$
$269$	−6.61911	+	11.4646i	−0.403574	+	0.699011i	0.590580	+	0.806979i	$0.298899\pi$
$270$	−16.6959	+	3.49790i	−1.01608	+	0.212876i
$271$	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
$273$	−0.290996	+	16.5201i	−0.0176119	+	0.999845i
$274$	−1.94177			−0.117307
$275$	12.0469	+	20.8659i	0.726456	+	1.25826i
$276$	−0.807175	+	7.60851i	−0.0485862	+	0.457978i
$277$	−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
$279$	−20.4691	−	4.39250i	−1.22545	−	0.262972i
$280$	8.65989	−	0.669174i	0.517528	−	0.0399908i
$281$	−8.32376			−0.496554			−0.248277	−	0.968689i	$-0.579864\pi$
$281$	−8.32376			−0.496554			−0.248277	+	0.968689i	$0.579864\pi$
$282$	−7.29164	+	3.23795i	−0.434211	+	0.192817i
$283$	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
$288$	−2.01173	+	2.22552i	−0.118542	+	0.131140i
$289$	−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	0.940545	−	0.339669i	$-0.110315\pi$
$293$	19.1141	+	11.0355i	1.11665	+	0.644701i	0.176110	+	0.984370i	$0.443649\pi$
$294$	−6.56457	−	10.1935i	−0.382853	−	0.594494i
$295$	3.21314	−	5.56531i	0.187076	−	0.324025i
$296$	5.29343	−	3.05617i	0.307675	−	0.177636i
$297$	4.44353	+	21.2095i	0.257839	+	1.23070i
$298$	−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
$303$	12.3309	+	27.7683i	0.708391	+	1.59525i
$304$	2.52442			0.144786
$305$	12.1068	−	20.9696i	0.693235	−	1.20072i
$306$	22.5747	+	4.84436i	1.29051	+	0.276933i
$307$	−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
$309$	0.378546	−	3.56821i	0.0215347	−	0.202988i
$310$	−19.8399	+	11.4546i	−1.12683	+	0.650577i
$311$	−1.56464			−0.0887226			−0.0443613	−	0.999016i	$-0.514125\pi$
$311$	−1.56464			−0.0887226			−0.0443613	+	0.999016i	$0.514125\pi$
$312$	−6.21700	−	0.590719i	−0.351968	−	0.0334429i
$313$			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
$315$	25.8226	+	3.48810i	1.45494	+	0.196532i
$316$	−1.10193	+	1.90861i	−0.0619887	+	0.107368i
$317$	−16.1815			−0.908844			−0.454422	−	0.890786i	$-0.650154\pi$
$317$	−16.1815			−0.908844			−0.454422	+	0.890786i	$0.650154\pi$
$318$	7.10477	−	3.15496i	0.398416	−	0.176922i
$319$	14.8148	+	8.55332i	0.829469	+	0.478894i
$320$			3.28289i			0.183519i
$321$	−5.89201	+	2.61642i	−0.328860	+	0.146035i
$322$	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
$327$	−1.88548	+	17.7727i	−0.104267	+	0.982832i
$328$	−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
$336$	4.03247	−	2.17697i	0.219989	−	0.118763i
$337$	−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
$342$	7.40470	+	1.58899i	0.400400	+	0.0859227i
$343$	4.24670	+	18.0268i	0.229300	+	0.973356i
$344$	−4.64648	+	8.04793i	−0.250521	+	0.433916i
$345$	10.1941	+	22.9564i	0.548832	+	1.23593i
$346$	−12.2605			−0.659130
$347$	−21.6745	−	12.5138i	−1.16355	−	0.671773i	−0.211394	−	0.977401i	$-0.567800\pi$
$347$	−21.6745	−	12.5138i	−1.16355	−	0.671773i	−0.952151	+	0.305628i	$0.901134\pi$
$348$	−0.749526	+	7.06511i	−0.0401788	+	0.378730i
$349$	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
$351$	−17.8640	−	5.64598i	−0.953510	−	0.301360i
$352$	4.17039			0.222282
$353$	−0.964341	+	0.556762i	−0.0513267	+	0.0296335i	−0.525444	−	0.850828i	$-0.676101\pi$
$353$	−0.964341	+	0.556762i	−0.0513267	+	0.0296335i	0.474117	+	0.880462i	$0.342767\pi$
$354$	0.357685	−	3.37158i	0.0190108	−	0.179197i
$355$	−32.9422	−	19.0192i	−1.74839	−	1.00943i
$356$			6.36836i			0.337523i
$357$	−30.0271	−	18.4997i	−1.58921	−	0.979106i
$358$	−16.7712	−	9.68288i	−0.886388	−	0.511756i
$359$	−14.5551			−0.768189			−0.384095	−	0.923294i	$-0.625486\pi$
$359$	−14.5551			−0.768189			−0.384095	+	0.923294i	$0.625486\pi$
$360$	−2.06640	+	9.62945i	−0.108909	+	0.507516i
$361$	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
$366$	1.34773	−	12.7038i	0.0704469	−	0.664040i
$367$	−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
$375$	−0.466312	+	4.39551i	−0.0240803	+	0.226983i
$376$			4.60624i			0.237549i
$377$	−12.7265	+	7.53481i	−0.655446	+	0.388062i
$378$	13.1984	−	3.84732i	0.678853	−	0.197885i
$379$	−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
$381$	−14.7227	−	33.1544i	−0.754265	−	1.69855i
$382$			8.29792i			0.424559i
$383$	−7.37148	−	4.25593i	−0.376665	−	0.217468i	0.299701	−	0.954033i	$-0.403113\pi$
$383$	−7.37148	−	4.25593i	−0.376665	−	0.217468i	−0.676366	+	0.736565i	$0.736446\pi$
$384$	0.702948	+	1.58299i	0.0358722	+	0.0807817i
$385$	−20.4744	−	29.8812i	−1.04347	−	1.52289i
$386$	10.2886	+	5.94013i	0.523676	+	0.302345i
$387$	−18.6949	+	20.6817i	−0.950315	+	1.05131i
$388$	−3.26777	−	5.65995i	−0.165896	−	0.287340i
$389$		−	25.1319i		−	1.27424i	−0.770765	−	0.637119i	$-0.780126\pi$
$389$		−	25.1319i		−	1.27424i	0.770765	−	0.637119i	$-0.219874\pi$
$390$	−18.6450	+	8.52540i	−0.944124	+	0.431701i
$391$		−	33.9975i		−	1.71933i
$392$	−6.91690	+	1.07540i	−0.349356	+	0.0543158i
$393$	18.3213	+	1.94368i	0.924189	+	0.0980458i
$394$	−4.57466	+	7.92354i	−0.230468	+	0.399182i
$395$			7.23506i			0.364035i
$396$	12.2327	+	2.62503i	0.614715	+	0.131913i
$397$	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
$399$	−9.84915	−	6.06804i	−0.493074	−	0.303782i
$400$	2.88868	+	5.00334i	0.144434	+	0.250167i
$401$	11.2625	+	19.5072i	0.562422	+	0.974144i	0.997284	+	0.0736470i	$0.0234638\pi$
$401$	11.2625	+	19.5072i	0.562422	+	0.974144i	−0.434862	+	0.900497i	$0.643203\pi$
$402$	−0.173698	−	0.126457i	−0.00866327	−	0.00630712i
$403$	−25.1593	+	0.275776i	−1.25327	+	0.0137374i
$404$	17.5417			0.872731
$405$	−12.1224	+	26.9446i	−0.602369	+	1.33889i
$406$	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
$414$	9.83108	+	8.88666i	0.483171	+	0.436755i
$415$	−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	0.671237	−	0.741243i	$-0.265763\pi$
$419$	−6.27014	−	10.8602i	−0.306316	−	0.530555i	−0.977554	+	0.210687i	$0.932430\pi$
$420$	7.89120	−	12.8083i	0.385051	−	0.624983i
$421$		−	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
$423$	−2.89938	+	13.5111i	−0.140973	+	0.656933i
$424$		−	4.48819i		−	0.217966i
$425$	22.2319	−	38.5068i	1.07841	−	1.86785i
$426$	−19.9571	−	2.11721i	−0.966922	−	0.102579i
$427$	−8.42613	+	17.6014i	−0.407769	+	0.851790i
$428$			3.72207i			0.179913i
$429$	10.8302	+	23.6854i	0.522885	+	1.14354i
$430$			30.5077i			1.47121i
$431$	8.21994	+	14.2374i	0.395941	+	0.685789i	0.993221	−	0.116243i	$-0.0370852\pi$
$431$	8.21994	+	14.2374i	0.395941	+	0.685789i	−0.597280	+	0.802033i	$0.703752\pi$
$432$	1.06549	+	5.08574i	0.0512637	+	0.244688i
$433$	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
$435$	9.46603	+	21.3169i	0.453862	+	1.02207i
$436$	8.93621	+	5.15932i	0.427967	+	0.247087i
$437$		−	11.1515i		−	0.533446i
$438$	−0.789293	−	1.77744i	−0.0377139	−	0.0849291i
$439$	−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
$441$	−20.9657	−	1.19944i	−0.998368	−	0.0571160i
$442$	27.7474	−	0.304145i	1.31981	−	0.0144667i
$443$			5.49826i			0.261230i	0.991433	+	0.130615i	$0.0416952\pi$
$443$			5.49826i			0.261230i	−0.991433	+	0.130615i	$0.958305\pi$
$444$	1.11688	−	10.5278i	0.0530046	−	0.499627i
$445$	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	−0.967972	−	0.251059i	$-0.919221\pi$
$449$	−5.64836	+	9.78324i	−0.266562	+	0.461700i	0.701409	+	0.712759i	$0.252555\pi$
$450$	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
$453$	2.71585	−	25.5999i	0.127602	−	1.20279i
$454$		−	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
$459$	29.7969	−	26.6721i	1.39080	−	1.24495i
$460$	14.5019			0.676155
$461$	8.76660	+	5.06140i	0.408301	+	0.235733i	0.690060	−	0.723753i	$-0.257584\pi$
$461$	8.76660	+	5.06140i	0.408301	+	0.235733i	−0.281758	+	0.959485i	$0.590918\pi$
$462$	−16.2710	−	10.0245i	−0.756993	−	0.466382i
$463$		−	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
$465$	−4.18608	+	39.4584i	−0.194125	+	1.82984i
$466$	−11.4271	+	6.59742i	−0.529348	+	0.305619i
$467$	−16.2055			−0.749899			−0.374950	−	0.927045i	$-0.622340\pi$
$467$	−16.2055			−0.749899			−0.374950	+	0.927045i	$0.622340\pi$
$468$	−7.16500	+	8.10325i	−0.331202	+	0.374573i
$469$	0.185508	+	0.270738i	0.00856595	+	0.0125015i
$470$	7.56089	+	13.0958i	0.348758	+	0.604066i
$471$	3.42561	−	32.2902i	0.157844	−	1.48785i
$472$	−1.69525	−	0.978752i	−0.0780302	−	0.0450507i
$473$	38.7552			1.78197
$474$	1.54921	+	3.48871i	0.0711574	+	0.160242i
$475$	7.29225	−	12.6306i	0.334591	−	0.579529i
$476$	−16.7975	+	11.5095i	−0.769910	+	0.527536i
$477$	2.82507	−	13.1649i	0.129351	−	0.602778i
$478$	−11.8390	−	20.5057i	−0.541502	−	0.937909i
$479$	28.4451	−	16.4228i	1.29969	−	0.750376i	0.319338	−	0.947641i	$-0.396539\pi$
$479$	28.4451	−	16.4228i	1.29969	−	0.750376i	0.980350	+	0.197265i	$0.0632060\pi$
$480$	4.59692	+	3.34670i	0.209820	+	0.152755i
$481$	18.9638	−	11.2277i	0.864676	−	0.511939i
$482$	−12.3109			−0.560744
$483$	−9.61660	−	17.8131i	−0.437571	−	0.810525i
$484$	−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	−0.0660655	−	0.997815i	$-0.521045\pi$
$491$	16.9520	−	9.78727i	0.765035	−	0.441693i	0.831101	+	0.556122i	$0.187711\pi$
$492$	−0.366624	+	3.45584i	−0.0165287	+	0.155801i
$493$		−	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
$498$	−9.19561	+	4.08343i	−0.412065	+	0.182983i
$499$			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
$501$	−17.2165	+	7.64522i	−0.769178	+	0.341563i
$502$	4.13815			0.184695
$503$	3.70474	−	6.41680i	0.165186	−	0.286111i	−0.771535	−	0.636187i	$-0.780511\pi$
$503$	3.70474	−	6.41680i	0.165186	−	0.286111i	0.936721	+	0.350076i	$0.113844\pi$
$504$	1.06251	−	7.86582i	0.0473279	−	0.350371i
$505$	49.8721	−	28.7937i	2.21928	−	1.28130i
$506$		−	18.4224i		−	0.818974i
$507$	−22.4377	−	1.88405i	−0.996493	−	0.0836736i
$508$	−20.9442			−0.929247
$509$	−22.8313	+	13.1817i	−1.01198	+	0.584267i	−0.911771	−	0.410700i	$-0.865284\pi$
$509$	−22.8313	+	13.1817i	−1.01198	+	0.584267i	−0.100209	+	0.994966i	$0.531951\pi$
$510$	4.61670	−	43.5175i	0.204431	−	1.92699i
$511$	0.228875	+	2.96191i	0.0101248	+	0.131027i
$512$	1.00000			0.0441942
$513$	9.77363	−	8.74868i	0.431516	−	0.386264i
$514$	−8.37891	+	14.5127i	−0.369578	+	0.640128i
$515$	−6.80105			−0.299690
$516$	6.53246	+	14.7107i	0.287576	+	0.647601i
$517$	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	$-0.631694\pi$
$521$	−18.3528			−0.804051			−0.402026	+	0.915628i	$0.631694\pi$
$522$	9.12894	+	8.25197i	0.399563	+	0.361179i
$523$	−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
$525$	0.756388	−	26.4644i	0.0330115	−	1.15500i
$526$	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
$531$	−4.35647	−	3.93797i	−0.189055	−	0.170893i
$532$	−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
$537$	−30.6559	+	13.6131i	−1.32290	+	0.587450i
$538$	13.2382			0.570740
$539$	18.3070	+	22.7391i	0.788540	+	0.979442i
$540$	11.3772	+	12.7101i	0.489598	+	0.546957i
$541$		−	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
$543$	−0.187709	+	1.76936i	−0.00805535	+	0.0759305i
$544$	−3.84811	−	6.66512i	−0.164986	−	0.285765i
$545$	33.8750			1.45104
$546$	14.4524	−	8.00806i	0.618504	−	0.342714i
$547$	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
$549$	−16.4148	−	14.8379i	−0.700568	−	0.633268i
$550$	12.0469	−	20.8659i	0.513682	−	0.889723i
$551$		−	10.3550i		−	0.441139i
$552$	6.99275	−	3.10522i	0.297631	−	0.132167i
$553$	−0.449230	−	5.81356i	−0.0191032	−	0.247218i
$554$	29.8506			1.26823
$555$	−14.1054	−	31.7645i	−0.598742	−	1.34833i
$556$	6.89520	−	3.98095i	0.292422	−	0.168830i
$557$	7.03801	+	12.1902i	0.298210	+	0.516515i	0.975726	−	0.218993i	$-0.0702771\pi$
$557$	7.03801	+	12.1902i	0.298210	+	0.516515i	−0.677517	+	0.735507i	$0.736944\pi$
$558$	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
$561$	−55.2820	−	5.86478i	−2.33401	−	0.247611i
$562$	4.16188	+	7.20858i	0.175558	+	0.304076i
$563$	7.86426	−	13.6213i	0.331439	−	0.574069i	−0.651355	−	0.758773i	$-0.725799\pi$
$563$	7.86426	−	13.6213i	0.331439	−	0.574069i	0.982794	+	0.184704i	$0.0591326\pi$
$564$	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
$567$	8.06769	−	22.4034i	0.338811	−	0.940854i
$568$	−5.79343	+	10.0345i	−0.243087	+	0.421039i
$569$	−23.2297	+	13.4117i	−0.973838	+	0.562246i	−0.900404	−	0.435054i	$-0.856729\pi$
$569$	−23.2297	+	13.4117i	−0.973838	+	0.562246i	−0.0734341	+	0.997300i	$0.523396\pi$
$570$	1.51432	−	14.2741i	0.0634278	−	0.597876i
$571$	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
$576$	2.93322	+	0.629446i	0.122218	+	0.0262269i
$577$	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
$579$	18.8064	−	8.35121i	0.781566	−	0.347064i
$580$	13.4662			0.559153
$581$	15.3235	−	1.18409i	0.635726	−	0.0491243i
$582$	−11.2567	−	1.19421i	−0.466606	−	0.0495015i
$583$	−16.2098	+	9.35874i	−0.671342	+	0.387600i
$584$	−1.12283			−0.0464631
$585$	−7.06953	+	34.7990i	−0.292289	+	1.43876i
$586$		−	22.0710i		−	0.911745i
$587$	21.6686	−	12.5103i	0.894357	−	0.516357i	0.0189918	−	0.999820i	$-0.493954\pi$
$587$	21.6686	−	12.5103i	0.894357	−	0.516357i	0.875365	+	0.483462i	$0.160621\pi$
$588$	−5.54550	+	10.7818i	−0.228693	+	0.444634i
$589$	8.80816	−	15.2562i	0.362934	−	0.628620i
$590$	−6.42627			−0.264565
$591$	6.43150	+	14.4833i	0.264556	+	0.595763i
$592$	−5.29343	−	3.05617i	−0.217559	−	0.125608i
$593$		−	47.2978i		−	1.94229i	−0.238497	−	0.971143i	$-0.576655\pi$
$593$		−	47.2978i		−	1.94229i	0.238497	−	0.971143i	$-0.423345\pi$
$594$	16.1462	−	14.4529i	0.662486	−	0.593012i
$595$	−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	$0.282612\pi$
$599$			37.9705i			1.55143i	−0.631081	+	0.775717i	$0.717388\pi$
$600$	9.95084	+	1.05567i	0.406241	+	0.0430975i
$601$	−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
$609$	−8.92979	−	16.5409i	−0.361853	−	0.670272i
$610$	−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
$615$	4.63023	+	10.4270i	0.186709	+	0.420456i
$616$	−9.10211	+	6.23669i	−0.366735	+	0.251284i
$617$	−8.53339	+	14.7803i	−0.343541	+	0.595031i	−0.985088	−	0.172053i	$-0.944960\pi$
$617$	−8.53339	+	14.7803i	−0.343541	+	0.595031i	0.641546	+	0.767084i	$0.278293\pi$
$618$	−3.27943	+	1.45627i	−0.131918	+	0.0585800i
$619$	−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
$621$	22.4659	−	4.70674i	0.901524	−	0.188875i
$622$	0.782320	+	1.35502i	0.0313682	+	0.0543313i
$623$	−9.52371	−	13.8993i	−0.381559	−	0.556865i
$624$	2.59692	+	5.67944i	0.103960	+	0.227359i
$625$	−20.5089			−0.820356
$626$	26.8966	−	15.5288i	1.07501	−	0.620655i
$627$	−18.1330	−	1.92370i	−0.724161	−	0.0768251i
$628$	−16.2357	−	9.37368i	−0.647875	−	0.374051i
$629$			47.0418i			1.87568i
$630$	−9.89052	−	24.1071i	−0.394048	−	0.960449i
$631$	−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
$633$	19.6711	+	44.2979i	0.781855	+	1.76068i
$634$	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
$639$	−23.3096	+	25.7868i	−0.922115	+	1.02011i
$640$	2.84307	−	1.64144i	0.112382	−	0.0648838i
$641$	10.4824	+	6.05200i	0.414029	+	0.239040i	0.692519	−	0.721399i	$-0.256501\pi$
$641$	10.4824	+	6.05200i	0.414029	+	0.239040i	−0.278490	+	0.960439i	$0.589834\pi$
$642$	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	0.988508	−	0.151169i	$-0.0483037\pi$
$647$	9.24194	+	16.0075i	0.363338	+	0.629320i	−0.625170	+	0.780489i	$0.714970\pi$
$648$	8.20759	+	3.69261i	0.322425	+	0.145060i
$649$			8.16355i			0.320447i
$650$	10.6124	+	17.9246i	0.416252	+	0.703059i
$651$	0.913625	−	31.9658i	0.0358078	−	1.25284i
$652$	−15.4012	+	8.89189i	−0.603158	+	0.348233i
$653$	−11.3924	+	6.57741i	−0.445819	+	0.257394i	−0.706063	−	0.708149i	$-0.749530\pi$
$653$	−11.3924	+	6.57741i	−0.445819	+	0.257394i	0.260244	+	0.965543i	$0.416197\pi$
$654$	16.3343	−	7.25347i	0.638723	−	0.283633i
$655$		−	34.9207i		−	1.36446i
$656$	1.73761	+	1.00321i	0.0678424	+	0.0391688i
$657$	−3.29352	−	0.706763i	−0.128492	−	0.0275734i
$658$	−6.88850	−	10.0534i	−0.268542	−	0.391922i
$659$	−11.9839	−	6.91891i	−0.466827	−	0.269523i	0.248084	−	0.968739i	$-0.420199\pi$
$659$	−11.9839	−	6.91891i	−0.466827	−	0.269523i	−0.714910	+	0.699216i	$0.753533\pi$
$660$	2.50167	−	23.5810i	0.0973775	−	0.917890i
$661$	−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
$663$	27.8609	−	39.1639i	1.08203	−	1.52100i
$664$			5.80900i			0.225433i
$665$	−9.46766	+	19.7770i	−0.367140	+	0.766920i
$666$	−13.6031	−	12.2963i	−0.527111	−	0.476474i
$667$	9.05999	−	15.6924i	0.350804	−	0.607611i
$668$			10.8759i			0.420803i
$669$	12.2249	+	27.5296i	0.472640	+	1.06435i
$670$	−0.203615	+	0.352672i	−0.00786634	+	0.0136249i
$671$			30.7596i			1.18746i
$672$	−3.90155	−	2.40373i	−0.150505	−	0.0927261i
$673$	−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	$-0.649707\pi$
$677$	−23.5823			−0.906340			−0.453170	+	0.891424i	$0.649707\pi$
$678$	−1.23598	+	11.6505i	−0.0474676	+	0.447435i
$679$	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	−0.923442	−	0.383737i	$-0.874637\pi$
$683$	−3.38165	+	5.85720i	−0.129395	+	0.224119i	0.794047	+	0.607856i	$0.207970\pi$
$684$	−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
$687$	4.98785	+	0.529153i	0.190298	+	0.0201884i
$688$	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
$693$	−30.6242	+	12.5643i	−1.16332	+	0.477279i
$694$			25.0275i			0.950031i
$695$	13.0690	−	22.6362i	0.495735	−	0.858639i
$696$	6.49333	−	2.88345i	0.246129	−	0.109297i
$697$		−	15.4419i		−	0.584903i
$698$	8.66298	−	15.0047i	0.327898	−	0.567937i
$699$	−2.41103	+	22.7266i	−0.0911935	+	0.859599i
$700$	−13.7871	−	6.60015i	−0.521102	−	0.249462i
$701$			43.1581i			1.63006i	0.579419	+	0.815030i	$0.303279\pi$
$701$			43.1581i			1.63006i	−0.579419	+	0.815030i	$0.696721\pi$
$702$	4.04245	+	18.2937i	0.152572	+	0.690450i
$703$			15.4301i			0.581958i
$704$	−2.08519	−	3.61166i	−0.0785887	−	0.136120i
$705$	26.0455	+	2.76313i	0.980931	+	0.104065i
$706$	0.964341	+	0.556762i	0.0362934	+	0.0209540i
$707$	−38.2858	+	26.2331i	−1.43988	+	0.986597i
$708$	−3.09871	+	1.37602i	−0.116457	+	0.0517142i
$709$	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
$711$	6.46444	+	1.38722i	0.242435	+	0.0520247i
$712$	5.51516	−	3.18418i	0.206689	−	0.119332i
$713$	26.6964	−	15.4132i	0.999789	−	0.577228i
$714$	−1.00761	+	35.2541i	−0.0377088	+	1.31935i
$715$	42.4768	−	25.1487i	1.58854	−	0.940509i
$716$			19.3658i			0.723733i
$717$	−40.7826	−	4.32656i	−1.52305	−	0.161578i
$718$	7.27755	+	12.6051i	0.271596	+	0.470418i
$719$	8.87175	−	15.3663i	0.330860	−	0.573067i	−0.651820	−	0.758373i	$-0.725994\pi$
$719$	8.87175	−	15.3663i	0.330860	−	0.573067i	0.982681	+	0.185306i	$0.0593277\pi$
$720$	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
$726$	−11.0097	−	1.16800i	−0.408608	−	0.0433486i
$727$			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
$732$	−11.6757	+	5.18475i	−0.431546	+	0.191634i
$733$	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
$735$	1.93151	+	39.7560i	0.0712449	+	1.46642i
$736$		−	4.41743i		−	0.162828i
$737$	0.448013	+	0.258660i	0.0165028	+	0.00952788i
$738$	4.46534	+	4.03638i	0.164372	+	0.148581i
$739$	−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
$741$	9.13860	−	12.8461i	0.335715	−	0.471912i
$742$	6.71196	+	9.79574i	0.246404	+	0.359613i
$743$	15.9338	+	27.5981i	0.584553	+	1.01247i	0.994931	+	0.100560i	$0.0320633\pi$
$743$	15.9338	+	27.5981i	0.584553	+	1.01247i	−0.410378	+	0.911915i	$0.634603\pi$
$744$	12.0194	+	1.27512i	0.440653	+	0.0467482i
$745$	10.1569	+	5.86411i	0.372122	+	0.214845i
$746$	−36.7038			−1.34382
$747$	−3.65646	+	17.0391i	−0.133783	+	0.623428i
$748$	−16.0481	+	27.7961i	−0.586777	+	1.01633i
$749$	−5.56626	−	8.12365i	−0.203387	−	0.296832i
$750$	4.03978	−	1.79392i	0.147512	−	0.0655045i
$751$	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
$756$	−9.93108	−	9.50650i	−0.361190	−	0.345748i
$757$	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	0.0968519	−	0.995299i	$-0.469123\pi$
$761$	−19.7704	−	11.4144i	−0.716676	−	0.413773i	−0.813528	+	0.581526i	$0.802456\pi$
$762$	−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
$765$	−56.2297	−	50.8280i	−2.03299	−	1.83769i
$766$			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
$771$	11.7799	+	26.5275i	0.424242	+	0.955365i
$772$		−	11.8803i		−	0.427580i
$773$	−6.95873	−	4.01762i	−0.250288	−	0.144504i	0.369608	−	0.929188i	$-0.379492\pi$
$773$	−6.95873	−	4.01762i	−0.250288	−	0.144504i	−0.619896	+	0.784684i	$0.712825\pi$
$774$	27.2583	+	5.84942i	0.979780	+	0.210253i
$775$	40.3165			1.44821
$776$	−3.26777	+	5.65995i	−0.117306	+	0.203180i
$777$	13.3064	+	24.6478i	0.477363	+	0.884234i
$778$	−21.7649	+	12.5660i	−0.780308	+	0.450511i
$779$		−	5.06506i		−	0.181475i
$780$	16.7057	+	11.8843i	0.598160	+	0.425526i
$781$	48.3217			1.72909
$782$	−29.4427	+	16.9987i	−1.05287	+	0.607873i
$783$	20.8614	−	4.37059i	0.745524	−	0.156192i
$784$	4.38977	+	5.45251i	0.156778	+	0.194733i
$785$	−61.5455			−2.19665
$786$	−7.47739	−	16.8386i	−0.266710	−	0.600612i
$787$	−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
$789$	26.4050	−	11.7255i	0.940042	−	0.417438i
$790$	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
$795$	−25.3780	−	2.69231i	−0.900066	−	0.0954866i
$796$	−3.46152	+	1.99851i	−0.122690	+	0.0708353i
$797$	−11.3604	+	19.6768i	−0.402406	+	0.696988i	−0.994016	−	0.109236i	$-0.965159\pi$
$797$	−11.3604	+	19.6768i	−0.402406	+	0.696988i	0.591609	+	0.806225i	$0.298493\pi$
$798$	−0.330504	+	11.5636i	−0.0116997	+	0.409348i
$799$	−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
$804$	−0.0226664	+	0.213656i	−0.000799382	+	0.00753505i
$805$	−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	−0.264526	−	0.964378i	$-0.585216\pi$
$809$	12.4690	−	7.19898i	0.438387	−	0.253103i	0.702913	+	0.711276i	$0.251882\pi$
$810$	29.3959	−	2.97397i	1.03287	−	0.104495i
$811$	−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
$813$	−14.1114	−	31.7779i	−0.494908	−	1.11450i
$814$			25.4908i			0.893451i
$815$	−29.1911	+	50.5604i	−1.02252	+	1.77106i
$816$	−13.2559	−	1.40629i	−0.464048	−	0.0492301i
$817$	−11.7297	−	20.3164i	−0.410369	−	0.710781i
$818$	−29.7871			−1.04148
$819$	3.51985	−	28.4009i	0.122994	−	0.992407i
$820$	6.58687			0.230023
$821$	−0.821661	−	1.42316i	−0.0286762	−	0.0496686i	0.851331	−	0.524629i	$-0.175796\pi$
$821$	−0.821661	−	1.42316i	−0.0286762	−	0.0496686i	−0.880007	+	0.474960i	$0.842462\pi$
$822$	3.34447	+	0.354810i	0.116652	+	0.0123754i
$823$	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
$825$	−16.9367	−	38.1403i	−0.589660	−	1.32788i
$826$	5.16368	−	0.399012i	0.179667	−	0.0138834i
$827$	−36.4788			−1.26849			−0.634246	−	0.773132i	$-0.718689\pi$
$827$	−36.4788			−1.26849			−0.634246	+	0.773132i	$0.718689\pi$
$828$	2.78053	−	12.9573i	0.0966302	−	0.450297i
$829$	−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
$834$	1.45484	−	13.7134i	0.0503769	−	0.474858i
$835$	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	0.640093	−	0.768297i	$-0.278896\pi$
$839$	8.53828	+	4.92958i	0.294774	+	0.170188i	−0.345319	+	0.938485i	$0.612229\pi$
$840$	−15.0379	−	0.429805i	−0.518858	−	0.0148297i
$841$	−6.08707	+	10.5431i	−0.209899	+	0.363556i
$842$	−6.86323	+	3.96249i	−0.236523	+	0.136556i
$843$	14.3367	+	1.52096i	0.493783	+	0.0523846i
$844$	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
$849$	−27.0074	+	11.9930i	−0.926893	+	0.411599i
$850$	−44.4638			−1.52510
$851$	−13.5004	+	23.3833i	−0.462787	+	0.801571i
$852$	8.14497	+	18.3419i	0.279042	+	0.628384i
$853$	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
$855$	−18.4438	−	16.6720i	−0.630765	−	0.570170i
$856$	3.22341	−	1.86104i	0.110174	−	0.0636089i
$857$	−37.6517			−1.28616			−0.643078	−	0.765800i	$-0.722343\pi$
$857$	−37.6517			−1.28616			−0.643078	+	0.765800i	$0.722343\pi$
$858$	15.0971	−	21.2219i	0.515407	−	0.724504i
$859$		−	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
$861$	−4.36793	−	8.09084i	−0.148858	−	0.275735i
$862$	8.21994	−	14.2374i	0.279972	−	0.484926i
$863$	37.0070			1.25973			0.629867	−	0.776703i	$-0.283109\pi$
$863$	37.0070			1.25973			0.629867	+	0.776703i	$0.283109\pi$
$864$	3.87163	−	3.46561i	0.131716	−	0.117903i
$865$	34.8575	+	20.1250i	1.18519	+	0.684269i
$866$		−	18.1943i		−	0.618267i
$867$	29.6867	+	66.8526i	1.00821	+	2.27043i
$868$	−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
$873$	−13.1477	+	14.5450i	−0.444983	+	0.492274i
$874$	−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	0.779869	−	0.625943i	$-0.215286\pi$
$881$	−4.51600	−	7.82195i	−0.152148	−	0.263528i	−0.932017	+	0.362415i	$0.881952\pi$
$882$	9.44412	+	18.7566i	0.318000	+	0.631566i
$883$	−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	0.997539	−	0.0701120i	$-0.0223357\pi$
$887$	13.0463	+	22.5968i	0.438051	+	0.758726i	−0.559488	+	0.828838i	$0.689002\pi$
$888$	−9.67577	+	4.29665i	−0.324698	+	0.144186i
$889$	45.7119	−	31.3214i	1.53313	−	1.05049i
$890$	10.4533	−	18.1057i	0.350396	−	0.606903i
$891$	−3.77796	−	37.3429i	−0.126566	−	1.25103i
$892$	17.3908			0.582288
$893$	−10.0702	−	5.81405i	−0.336987	−	0.194560i
$894$	6.15328	+	0.652792i	0.205796	+	0.0218326i
$895$	31.7878	+	55.0581i	1.06255	+	1.84039i
$896$	−2.18256	+	1.49547i	−0.0729142	+	0.0499602i
$897$	25.0885	−	11.4717i	0.837680	−	0.383029i
$898$	11.2967			0.376976
$899$	24.7898	−	14.3124i	0.826785	−	0.477344i
$900$	11.6225	−	12.8576i	0.387416	−	0.428588i
$901$	29.9143	+	17.2710i	0.996591	+	0.575382i
$902$		−	8.36756i		−	0.278609i
$903$	−36.2569	−	22.3378i	−1.20655	−	0.743355i
$904$	5.85794	+	3.38208i	0.194832	+	0.112486i
$905$	3.37242			0.112103
$906$	−23.5281	+	10.4479i	−0.781668	+	0.347110i
$907$	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	$0.0260003\pi$
$911$			4.92531i			0.163183i	−0.996666	+	0.0815914i	$0.974000\pi$
$912$	−4.34803	−	0.461276i	−0.143978	−	0.0152744i
$913$	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
$921$	19.6270	+	2.08220i	0.646733	+	0.0686109i
$922$		−	10.1228i		−	0.333376i
$923$	−20.4907	+	36.4068i	−0.674460	+	1.19834i
$924$	−0.545998	+	19.1033i	−0.0179620	+	0.628453i
$925$	−30.5821	+	17.6566i	−1.00553	+	0.580544i
$926$	−16.3804	+	9.45726i	−0.538295	+	0.310785i
$927$	−1.30400	+	6.07666i	−0.0428291	+	0.199584i
$928$		−	4.10193i		−	0.134653i
$929$	0.544018	+	0.314089i	0.0178486	+	0.0103049i	0.508898	−	0.860827i	$-0.330053\pi$
$929$	0.544018	+	0.314089i	0.0178486	+	0.0103049i	−0.491049	+	0.871132i	$0.663386\pi$
$930$	36.2650	−	16.1040i	1.18918	−	0.528070i
$931$	6.37954	−	16.4792i	0.209081	−	0.540084i
$932$	11.4271	+	6.59742i	0.374306	+	0.216106i
$933$	2.69491	+	0.285899i	0.0882275	+	0.00935992i
$934$	8.10273	+	14.0343i	0.265129	+	0.459218i
$935$			105.368i			3.44591i
$936$	10.6001	+	2.15345i	0.346476	+	0.0703876i
$937$		−	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
$939$	5.67499	−	53.4931i	0.185196	−	1.74568i
$940$	7.56089	−	13.0958i	0.246609	−	0.427139i
$941$		−	21.1091i		−	0.688138i	−0.938944	−	0.344069i	$-0.888195\pi$
$941$		−	21.1091i		−	0.688138i	0.938944	−	0.344069i	$-0.111805\pi$
$942$	−29.6769	+	13.1784i	−0.966926	+	0.429376i
$943$	4.43161	−	7.67578i	0.144313	−	0.249958i
$944$			1.95750i			0.0637114i
$945$	−43.8391	−	10.7263i	−1.42609	−	0.348926i
$946$	−19.3776	−	33.5630i	−0.630020	−	1.09123i
$947$	−9.54333	−	16.5295i	−0.310116	−	0.537137i	0.668271	−	0.743918i	$-0.267035\pi$
$947$	−9.54333	−	16.5295i	−0.310116	−	0.537137i	−0.978387	+	0.206781i	$0.933701\pi$
$948$	2.24671	−	3.08601i	0.0729696	−	0.100229i
$949$	−4.04819	+	0.0443730i	−0.131410	+	0.00144041i
$950$	−14.5845			−0.473184
$951$	27.8708	+	2.95677i	0.903773	+	0.0958798i
$952$	18.3662	+	8.79228i	0.595253	+	0.284959i
$953$	47.2598	+	27.2854i	1.53089	+	0.883862i	0.999321	+	0.0368498i	$0.0117323\pi$
$953$	47.2598	+	27.2854i	1.53089	+	0.883862i	0.531573	+	0.847012i	$0.321601\pi$
$954$	−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
$960$	0.599866	−	5.65440i	0.0193606	−	0.182495i
$961$	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
$966$	−10.6183	+	17.2348i	−0.341639	+	0.554520i
$967$			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
$969$	13.6572	+	30.7552i	0.438734	+	0.987999i
$970$			21.4555i			0.688893i
$971$	20.9527	−	36.2911i	0.672404	−	1.16464i	−0.304816	−	0.952411i	$-0.598595\pi$
$971$	20.9527	−	36.2911i	0.672404	−	1.16464i	0.977220	−	0.212227i	$-0.0680715\pi$
$972$	13.5378	−	7.72844i	0.434224	−	0.247890i
$973$	−9.09579	+	19.0002i	−0.291598	+	0.609119i
$974$			30.2700i			0.969914i
$975$	35.9178	+	3.41280i	1.15029	+	0.109297i
$976$			7.37572i			0.236091i
$977$	22.4040	+	38.8048i	0.716767	+	1.24148i	0.962274	+	0.272081i	$0.0877120\pi$
$977$	22.4040	+	38.8048i	0.716767	+	1.24148i	−0.245508	+	0.969395i	$0.578955\pi$
$978$	−3.24954	+	30.6305i	−0.103909	+	0.979456i
$979$	−23.0004	−	13.2793i	−0.735095	−	0.424407i
$980$	21.4304	+	8.29628i	0.684569	+	0.265015i
$981$	6.49504	−	30.2669i	0.207371	−	0.966348i
$982$	−16.9520	−	9.78727i	−0.540962	−	0.312324i
$983$			35.3442i			1.12731i	0.826012	+	0.563653i	$0.190604\pi$
$983$			35.3442i			1.12731i	−0.826012	+	0.563653i	$0.809396\pi$
$984$	3.17615	−	1.41041i	0.101252	−	0.0449623i
$985$	26.0121	−	15.0181i	0.828815	−	0.478517i
$986$	−27.3399	+	15.7847i	−0.870679	+	0.502687i
$987$	−21.0998	−	0.603061i	−0.671615	−	0.0191957i
$988$	−4.63709	−	7.83215i	−0.147526	−	0.249174i
$989$		−	41.0509i		−	1.30534i
$990$	−30.4694	−	27.5424i	−0.968382	−	0.875355i
$991$	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
$999$	−31.0857	+	6.51266i	−0.983508	+	0.206051i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.q.i.251.1	✓	24	273.251	even	6	inner
546.2.q.i.251.12	yes	24	39.17	odd	6	inner
546.2.q.i.335.1	yes	24	1.1	even	1	trivial
546.2.q.i.335.12	yes	24	7.6	odd	2	inner
546.2.q.j.251.5	yes	24	91.69	odd	6
546.2.q.j.251.8	yes	24	13.4	even	6
546.2.q.j.335.5	yes	24	3.2	odd	2
546.2.q.j.335.8	yes	24	21.20	even	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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.72239 - 0.182725i) q^{3} +(-0.500000 + 0.866025i) q^{4} +3.28289i q^{5} +(0.702948 + 1.58299i) q^{6} +(-0.203837 - 2.63789i) q^{7} +1.00000 q^{8} +(2.93322 + 0.629446i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.72239 - 0.182725i) q^{3} +(-0.500000 + 0.866025i) q^{4} +3.28289i q^{5} +(0.702948 + 1.58299i) q^{6} +(-0.203837 - 2.63789i) q^{7} +1.00000 q^{8} +(2.93322 + 0.629446i) 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} +(0.599866 - 5.65440i) 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} +(-0.130923 + 4.58071i) q^{21} +(-2.08519 + 3.61166i) q^{22} +(-3.82560 + 2.20871i) q^{23} +(-1.72239 - 0.182725i) 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} +(-5.19679 + 2.30770i) q^{30} -6.97836 q^{31} +(-0.500000 + 0.866025i) q^{32} +(2.93156 + 6.60169i) q^{33} +7.69622 q^{34} +(8.65989 - 0.669174i) q^{35} +(-2.01173 + 2.22552i) q^{36} +(5.29343 - 3.05617i) q^{37} +2.52442 q^{38} +(-6.21700 - 0.590719i) q^{39} +3.28289i q^{40} +(-1.73761 + 1.00321i) q^{41} +(4.03247 - 2.17697i) q^{42} +(-4.64648 + 8.04793i) q^{43} +4.17039 q^{44} +(-2.06640 + 9.62945i) q^{45} +(3.82560 + 2.20871i) q^{46} +4.60624i q^{47} +(0.702948 + 1.58299i) 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} +(1.06549 + 5.08574i) 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} +(1.06251 - 7.86582i) 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} +(6.99275 - 3.10522i) q^{69} +(-4.90947 - 7.16510i) q^{70} +(-5.79343 + 10.0345i) q^{71} +(2.93322 + 0.629446i) q^{72} -1.12283 q^{73} +(-5.29343 - 3.05617i) q^{74} +(9.95084 + 1.05567i) q^{75} +(-1.26221 - 2.18621i) q^{76} +(-9.10211 + 6.23669i) q^{77} +(2.59692 + 5.67944i) q^{78} +2.20387 q^{79} +(2.84307 - 1.64144i) q^{80} +(8.20759 + 3.69261i) q^{81} +(1.73761 + 1.00321i) q^{82} +5.80900i q^{83} +(-3.90155 - 2.40373i) q^{84} +(-21.8809 - 12.6329i) q^{85} +9.29295 q^{86} +(6.49333 - 2.88345i) 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} +(12.0194 + 1.27512i) 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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 12 q^{2} - 12 q^{4} - 18 q^{7} + 24 q^{8} - 12 q^{9}+O(q^{10}) \) 24 * q - 12 * q^2 - 12 * q^4 - 18 * q^7 + 24 * q^8 - 12 * q^9	\( 24 q - 12 q^{2} - 12 q^{4} - 18 q^{7} + 24 q^{8} - 12 q^{9} + 6 q^{15} - 12 q^{16} + 6 q^{18} - 12 q^{21} + 36 q^{23} - 12 q^{25} + 18 q^{28} - 12 q^{30} - 12 q^{32} + 36 q^{35} + 6 q^{36} + 36 q^{37} + 12 q^{39} + 24 q^{42} - 42 q^{43} - 36 q^{46} + 6 q^{50} + 12 q^{51} - 18 q^{56} + 36 q^{57} + 6 q^{60} + 24 q^{63} + 24 q^{64} - 66 q^{65} - 54 q^{67} - 48 q^{71} - 12 q^{72} - 36 q^{74} - 42 q^{78} - 48 q^{79} + 84 q^{81} - 12 q^{84} + 84 q^{86} + 36 q^{91} - 18 q^{93} + 36 q^{95} - 36 q^{99}+O(q^{100}) \) 24 * q - 12 * q^2 - 12 * q^4 - 18 * q^7 + 24 * q^8 - 12 * q^9 + 6 * q^15 - 12 * q^16 + 6 * q^18 - 12 * q^21 + 36 * q^23 - 12 * q^25 + 18 * q^28 - 12 * q^30 - 12 * q^32 + 36 * q^35 + 6 * q^36 + 36 * q^37 + 12 * q^39 + 24 * q^42 - 42 * q^43 - 36 * q^46 + 6 * q^50 + 12 * q^51 - 18 * q^56 + 36 * q^57 + 6 * q^60 + 24 * q^63 + 24 * q^64 - 66 * q^65 - 54 * q^67 - 48 * q^71 - 12 * q^72 - 36 * q^74 - 42 * q^78 - 48 * q^79 + 84 * q^81 - 12 * q^84 + 84 * q^86 + 36 * q^91 - 18 * q^93 + 36 * q^95 - 36 * q^99

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