LMFDB - Embedded newform 546.2.q.i.251.12

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			251.12
Character	$\chi$	$=$	546.251
Dual form			546.2.q.i.335.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(1.72239 - 0.182725i) q^{3} +(-0.500000 - 0.866025i) q^{4} +3.28289i q^{5} +(-0.702948 + 1.58299i) q^{6} +(-2.38640 - 1.14242i) q^{7} +1.00000 q^{8} +(2.93322 - 0.629446i) q^{9} +O(q^{10})$	\(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} +(-2.38640 - 1.14242i) 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} +(-4.31904 - 1.53163i) 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} +(0.203837 + 2.63789i) 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} +(3.75042 - 7.83427i) 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} +(3.48595 - 2.97459i) 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} +(4.38977 + 5.45251i) 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} +(-2.38640 - 1.14242i) 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} +(-7.71892 - 1.84885i) 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} +(0.833094 + 4.50621i) 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} +(8.55861 + 4.21310i) 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} +(-6.91690 + 1.07540i) 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 $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−0.500000	+	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
$7$	−2.38640	−	1.14242i	−0.901973	−	0.431793i
$7$	−2.38640	−	1.14242i	−0.901973	−	0.431793i
$8$	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	0.359102	+	0.933298i	$0.383083\pi$
$11$	−2.08519	+	3.61166i	−0.628709	+	1.08896i	−0.987811	+	0.155658i	$0.950250\pi$
$12$	−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	0.777631	+	0.628720i	$0.216421\pi$
$17$	3.84811	+	6.66512i	0.933304	+	1.61653i	0.155672	+	0.987809i	$0.450246\pi$
$18$	−0.921495	+	2.85497i	−0.217198	+	0.672923i
$19$	1.26221	+	2.18621i	0.289571	+	0.501552i	0.973707	−	0.227802i	$-0.0731540\pi$
$19$	1.26221	+	2.18621i	0.289571	+	0.501552i	−0.684136	+	0.729354i	$0.739821\pi$
$20$	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	$-0.485681\pi$
$23$	−3.82560	−	2.20871i	−0.797693	−	0.460548i	−0.842664	+	0.538440i	$0.819014\pi$
$24$	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
$28$	0.203837	+	2.63789i	0.0385216	+	0.498514i
$29$	−3.55238	−	2.05097i	−0.659660	−	0.380855i	0.132487	−	0.991185i	$-0.457704\pi$
$29$	−3.55238	−	2.05097i	−0.659660	−	0.380855i	−0.792147	+	0.610330i	$0.791037\pi$
$30$	−5.19679	−	2.30770i	−0.948799	−	0.421327i
$31$	6.97836			1.25335			0.626675	−	0.779281i	$-0.284415\pi$
$31$	6.97836			1.25335			0.626675	+	0.779281i	$0.284415\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−2.93156	+	6.60169i	−0.510320	+	1.14921i
$34$	−7.69622			−1.31989
$35$	3.75042	−	7.83427i	0.633937	−	1.32423i
$36$	−2.01173	−	2.22552i	−0.335288	−	0.370920i
$37$	5.29343	+	3.05617i	0.870235	+	0.502431i	0.867426	−	0.497566i	$-0.165773\pi$
$37$	5.29343	+	3.05617i	0.870235	+	0.502431i	0.00280878	+	0.999996i	$0.499106\pi$
$38$	−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	$-0.283256\pi$
$41$	1.73761	+	1.00321i	0.271370	+	0.156675i	−0.358140	+	0.933668i	$0.616589\pi$
$42$	3.48595	−	2.97459i	0.537893	−	0.458989i
$43$	−4.64648	−	8.04793i	−0.708581	−	1.22730i	−0.965384	−	0.260835i	$-0.916002\pi$
$43$	−4.64648	−	8.04793i	−0.708581	−	1.22730i	0.256802	−	0.966464i	$-0.417331\pi$
$44$	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
$49$	4.38977	+	5.45251i	0.627110	+	0.778930i
$50$	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	$0.900257\pi$
$54$	−1.06549	+	5.08574i	−0.144996	+	0.692081i
$55$	−11.8567	−	6.84546i	−1.59875	−	0.923041i
$56$	−2.38640	−	1.14242i	−0.318896	−	0.152662i
$57$	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	$-0.625996\pi$
$59$	1.69525	−	0.978752i	0.220703	−	0.127423i	0.606276	+	0.795255i	$0.292663\pi$
$60$	4.59692	−	3.34670i	0.593460	−	0.432057i
$61$	6.38756	−	3.68786i	0.817843	−	0.472182i	−0.0318291	−	0.999493i	$-0.510133\pi$
$61$	6.38756	−	3.68786i	0.817843	−	0.472182i	0.849672	+	0.527311i	$0.176800\pi$
$62$	−3.48918	+	6.04343i	−0.443126	+	0.767517i
$63$	−7.71892	−	1.84885i	−0.972493	−	0.232933i
$64$	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	0.493423	−	0.869789i	$-0.335745\pi$
$67$	−0.107427	−	0.0620231i	−0.0131243	−	0.00757733i	−0.506548	+	0.862212i	$0.669079\pi$
$68$	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	−0.972627	−	0.232373i	$-0.925351\pi$
$71$	−5.79343	−	10.0345i	−0.687554	−	1.19088i	0.285073	−	0.958506i	$-0.407982\pi$
$72$	2.93322	−	0.629446i	0.345684	−	0.0741810i
$73$	1.12283			0.131418			0.0657088	−	0.997839i	$-0.479069\pi$
$73$	1.12283			0.131418			0.0657088	+	0.997839i	$0.479069\pi$
$74$	−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	$0.896717\pi$
$84$	0.833094	+	4.50621i	0.0908980	+	0.491668i
$85$	−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	$-0.442922\pi$
$89$	−5.51516	−	3.18418i	−0.584606	−	0.337523i	−0.762962	+	0.646444i	$0.776256\pi$
$90$	−9.37255	−	3.02517i	−0.987953	−	0.318880i
$91$	8.55861	+	4.21310i	0.897186	+	0.441653i
$92$			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	$-0.0590135\pi$
$97$	3.26777	+	5.65995i	0.331792	+	0.574681i	−0.651071	+	0.759017i	$0.725680\pi$
$98$	−6.91690	+	1.07540i	−0.698713	+	0.108632i
$99$	−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	0.0135712	−	0.999908i	$-0.495680\pi$
$101$	8.77084	−	15.1915i	0.872731	−	1.51161i	0.859160	−	0.511707i	$-0.170987\pi$
$102$	−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
$105$	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	$-0.275752\pi$
$107$	3.22341	+	1.86104i	0.311619	+	0.179913i	−0.336032	+	0.941851i	$0.609085\pi$
$108$	−3.87163	−	3.46561i	−0.372548	−	0.333479i
$109$			10.3186i			0.988347i	0.869363	+	0.494174i	$0.164529\pi$
$109$			10.3186i			0.988347i	−0.869363	+	0.494174i	$0.835471\pi$
$110$	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	−0.198484	−	0.980104i	$-0.563602\pi$
$113$	5.85794	−	3.38208i	0.551068	−	0.318160i	0.749553	+	0.661945i	$0.230269\pi$
$114$	−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
$119$	−1.56877	−	20.3018i	−0.143809	−	1.86106i
$120$	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
$126$	5.46061	−	5.76036i	0.486470	−	0.513173i
$127$	10.4721	−	18.1382i	0.929247	−	1.60950i	0.144662	−	0.989481i	$-0.453790\pi$
$127$	10.4721	−	18.1382i	0.929247	−	1.60950i	0.784585	−	0.620022i	$-0.212876\pi$
$128$	−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	$0.346167\pi$
$132$	7.18301	−	0.762034i	0.625201	−	0.0663266i
$133$	−0.514571	−	6.65914i	−0.0446189	−	0.577421i
$134$	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	$-0.140233\pi$
$137$	0.970884	+	1.68162i	0.0829483	+	0.143671i	−0.821567	+	0.570112i	$0.806900\pi$
$138$	6.18557	−	4.50329i	0.526551	−	0.383345i
$139$	6.89520	−	3.98095i	0.584843	−	0.337659i	−0.178213	−	0.983992i	$-0.557031\pi$
$139$	6.89520	−	3.98095i	0.584843	−	0.337659i	0.763056	+	0.646333i	$0.223698\pi$
$140$	−8.65989	+	0.669174i	−0.731894	+	0.0565555i
$141$	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
$147$	8.55719	+	8.58921i	0.705785	+	0.708426i
$148$		−	6.11233i		−	0.502431i
$149$	1.78627	+	3.09390i	0.146337	+	0.253463i	0.929871	−	0.367886i	$-0.119918\pi$
$149$	1.78627	+	3.09390i	0.146337	+	0.253463i	−0.783534	+	0.621349i	$0.786585\pi$
$150$	4.06118	−	9.14552i	0.331594	−	0.746728i
$151$		−	14.8630i		−	1.20954i	−0.796401	−	0.604768i	$-0.793266\pi$
$151$		−	14.8630i		−	1.20954i	0.796401	−	0.604768i	$-0.206734\pi$
$152$	1.26221	+	2.18621i	0.102379	+	0.177325i
$153$	15.4827	+	17.1281i	1.25170	+	1.38473i
$154$	0.850079	+	11.0010i	0.0685013	+	0.886487i
$155$			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	0.244363	−	0.969684i	$-0.421421\pi$
$163$	15.4012	−	8.89189i	1.20632	−	0.696467i	0.961952	+	0.273217i	$0.0880878\pi$
$164$		−	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	$-0.471585\pi$
$167$	−9.41884	−	5.43797i	−0.728852	−	0.420803i	−0.818002	+	0.575215i	$0.804918\pi$
$168$	−4.31904	−	1.53163i	−0.333221	−	0.118167i
$169$	12.9969	+	0.284957i	0.999760	+	0.0219198i
$170$		−	25.2658i		−	1.93780i
$171$	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	$-0.320999\pi$
$173$	−6.13026	−	10.6179i	−0.466075	−	0.807266i	−0.999249	+	0.0387398i	$0.987666\pi$
$174$	5.74380	−	4.18166i	0.435436	−	0.317011i
$175$	13.7871	+	6.60015i	1.04220	+	0.498924i
$176$	−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	$-0.0757582\pi$
$179$	16.7712	+	9.68288i	1.25354	+	0.723733i	0.281731	+	0.959493i	$0.409091\pi$
$180$	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	$-0.0121555\pi$
$182$	−7.92796	+	5.30542i	−0.587659	+	0.393264i
$183$	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
$189$	−13.6328	−	1.77400i	−0.991639	−	0.129039i
$190$		−	8.28740i		−	0.601231i
$191$	−7.18621	+	4.14896i	−0.519976	+	0.300208i	−0.736925	−	0.675975i	$-0.763723\pi$
$191$	−7.18621	+	4.14896i	−0.519976	+	0.300208i	0.216949	+	0.976183i	$0.430390\pi$
$192$	1.72239	−	0.182725i	0.124302	−	0.0131871i
$193$	−10.2886	−	5.94013i	−0.740590	−	0.427580i	0.0816936	−	0.996657i	$-0.473967\pi$
$193$	−10.2886	−	5.94013i	−0.740590	−	0.427580i	−0.822284	+	0.569077i	$0.807300\pi$
$194$	−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	−0.981700	−	0.190432i	$-0.939011\pi$
$197$	−4.57466	+	7.92354i	−0.325931	+	0.564529i	0.655769	+	0.754961i	$0.272344\pi$
$198$	−8.38968	−	9.28129i	−0.596229	−	0.659592i
$199$	−3.46152	+	1.99851i	−0.245381	+	0.141671i	−0.617647	−	0.786455i	$-0.711914\pi$
$199$	−3.46152	+	1.99851i	−0.245381	+	0.141671i	0.372267	+	0.928126i	$0.378581\pi$
$200$	−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
$210$	9.76524	+	11.4440i	0.673866	+	0.789710i
$211$	−13.9918	+	24.2346i	−0.963238	+	1.66838i	−0.248961	+	0.968514i	$0.580089\pi$
$211$	−13.9918	+	24.2346i	−0.963238	+	1.66838i	−0.714277	+	0.699863i	$0.753244\pi$
$212$	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
$217$	−16.6531	−	7.97218i	−1.13049	−	0.541187i
$218$	−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	−0.412919	−	0.910768i	$-0.635491\pi$
$223$	8.69542	−	15.0609i	0.582288	−	1.00855i	0.995208	−	0.0977852i	$-0.0311758\pi$
$224$	0.203837	+	2.63789i	0.0136194	+	0.176251i
$225$	−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	$-0.959718\pi$
$227$	−20.7722	+	11.9929i	−1.37870	+	0.795994i	−0.386699	+	0.922206i	$0.626385\pi$
$228$	1.77454	−	3.99614i	0.117522	−	0.264651i
$229$	2.89589			0.191366			0.0956830	−	0.995412i	$-0.469496\pi$
$229$	2.89589			0.191366			0.0956830	+	0.995412i	$0.469496\pi$
$230$	7.25096	+	12.5590i	0.478114	+	0.828118i
$231$	14.5377	−	12.4052i	0.956514	−	0.816201i
$232$	−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	$0.857734\pi$
$234$	3.43512	−	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
$238$	18.3662	+	8.79228i	1.19051	+	0.569919i
$239$	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	$-0.296444\pi$
$241$	−6.15543	−	10.6615i	−0.396506	−	0.686769i	−0.993292	+	0.115632i	$0.963111\pi$
$242$	6.39212			0.410901
$243$	13.4619	−	7.85984i	0.863582	−	0.504209i
$244$	−6.38756	−	3.68786i	−0.408921	−	0.236091i
$245$	−17.9000	+	14.4111i	−1.14359	+	0.920694i
$246$	−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	$-0.124977\pi$
$251$	2.06908	+	3.58374i	0.130599	+	0.226204i	−0.793309	+	0.608820i	$0.791643\pi$
$252$	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	−0.476990	−	0.878909i	$-0.658272\pi$
$257$	8.37891	−	14.5127i	0.522662	−	0.905277i	0.999652	−	0.0263687i	$-0.00839441\pi$
$258$	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	−0.0165676	−	0.999863i	$-0.505274\pi$
$263$	−14.4457	−	8.34021i	−0.890758	−	0.514279i	−0.874190	+	0.485583i	$0.838607\pi$
$264$	−2.93156	+	6.60169i	−0.180425	+	0.406306i
$265$	−14.7342			−0.905117
$266$	6.02427	+	2.88394i	0.369372	+	0.176826i
$267$	−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	$-0.0344344\pi$
$269$	6.61911	+	11.4646i	0.403574	+	0.699011i	−0.590580	+	0.806979i	$0.701101\pi$
$270$	−16.6959	−	3.49790i	−1.01608	−	0.212876i
$271$	−10.0373	+	17.3851i	−0.609723	+	1.05607i	0.381563	+	0.924343i	$0.375386\pi$
$271$	−10.0373	+	17.3851i	−0.609723	+	1.05607i	−0.991286	+	0.131728i	$0.957948\pi$
$272$	−7.69622			−0.466652
$273$	15.5111	+	5.69271i	0.938772	+	0.344538i
$274$	−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	−0.831592	−	0.555387i	$-0.812570\pi$
$277$	−14.9253	−	25.8514i	−0.896776	−	1.55326i	−0.0651838	−	0.997873i	$-0.520763\pi$
$278$			7.96189i			0.477522i
$279$	20.4691	−	4.39250i	1.22545	−	0.262972i
$280$	3.75042	−	7.83427i	0.224131	−	0.468187i
$281$	−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	$-0.502611\pi$
$283$	−14.7753	−	8.53050i	−0.878298	−	0.507086i	−0.870097	+	0.492881i	$0.835944\pi$
$284$	−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	$-0.889685\pi$
$293$	−19.1141	+	11.0355i	−1.11665	+	0.644701i	−0.176110	+	0.984370i	$0.556351\pi$
$294$	−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
$297$	−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
$301$	1.89425	+	24.5138i	0.109183	+	1.41295i
$302$	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	$-0.394575\pi$
$307$	11.3953			0.650362			0.325181	+	0.945652i	$0.394575\pi$
$308$	−9.95219	−	4.76432i	−0.567079	−	0.271472i
$309$	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	$-0.485875\pi$
$311$	1.56464			0.0887226			0.0443613	+	0.999016i	$0.485875\pi$
$312$	−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
$315$	6.06958	−	25.3404i	0.341982	−	1.42777i
$316$	−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
$322$	−11.6527	+	0.900434i	−0.649378	+	0.0501792i
$323$	−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
$329$	5.26224	−	10.9923i	0.290117	−	0.606026i
$330$	19.1709	−	13.9570i	1.05533	−	0.768309i
$331$	28.0842	−	16.2144i	1.54365	−	0.891226i	0.545044	−	0.838407i	$-0.316513\pi$
$331$	28.0842	−	16.2144i	1.54365	−	0.891226i	0.998604	−	0.0528184i	$-0.0168204\pi$
$332$	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
$336$	3.48595	−	2.97459i	0.190174	−	0.162277i
$337$	−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	−0.952151	−	0.305628i	$-0.901134\pi$
$347$	−21.6745	+	12.5138i	−1.16355	+	0.671773i	−0.211394	+	0.977401i	$0.567800\pi$
$348$	0.749526	+	7.06511i	0.0401788	+	0.378730i
$349$	−8.66298	+	15.0047i	−0.463718	+	0.803184i	−0.999143	−	0.0413993i	$-0.986818\pi$
$349$	−8.66298	+	15.0047i	−0.463718	+	0.803184i	0.535424	+	0.844583i	$0.320152\pi$
$350$	−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	$-0.323899\pi$
$353$	0.964341	+	0.556762i	0.0513267	+	0.0296335i	−0.474117	+	0.880462i	$0.657233\pi$
$354$	0.357685	+	3.37158i	0.0190108	+	0.179197i
$355$	32.9422	−	19.0192i	1.74839	−	1.00943i
$356$			6.36836i			0.337523i
$357$	−6.41167	−	34.6808i	−0.339342	−	1.83550i
$358$	−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
$364$	−0.630654	−	9.51852i	−0.0330553	−	0.498906i
$365$			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	$-0.213852\pi$
$367$	12.1645	+	7.02320i	0.634984	+	0.366608i	−0.147696	+	0.989033i	$0.547186\pi$
$368$	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
$371$	5.12738	−	10.7106i	0.266200	−	0.556067i
$372$	−7.11400	−	9.77156i	−0.368844	−	0.506632i
$373$	18.3519	+	31.7864i	0.950224	+	1.64584i	0.744937	+	0.667135i	$0.232480\pi$
$373$	18.3519	+	31.7864i	0.950224	+	1.64584i	0.205288	+	0.978702i	$0.434187\pi$
$374$	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
$378$	8.35272	−	10.9193i	0.429618	−	0.561630i
$379$	−0.706667	−	0.407994i	−0.0362990	−	0.0209573i	0.481741	−	0.876314i	$-0.340005\pi$
$379$	−0.706667	−	0.407994i	−0.0362990	−	0.0209573i	−0.518040	+	0.855357i	$0.673338\pi$
$380$	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	$-0.596887\pi$
$383$	7.37148	−	4.25593i	0.376665	−	0.217468i	0.676366	+	0.736565i	$0.263554\pi$
$384$	−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	$0.219874\pi$
$389$			25.1319i			1.27424i	−0.770765	+	0.637119i	$0.780126\pi$
$390$	18.6450	+	8.52540i	0.944124	+	0.431701i
$391$		−	33.9975i		−	1.71933i
$392$	4.38977	+	5.45251i	0.221717	+	0.275394i
$393$	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	$-0.289327\pi$
$397$	−7.48939	−	12.9720i	−0.375882	−	0.651046i	−0.990459	+	0.137811i	$0.955993\pi$
$398$		−	3.99702i		−	0.200352i
$399$	−2.10308	−	11.3756i	−0.105286	−	0.569492i
$400$	2.88868	−	5.00334i	0.144434	−	0.250167i
$401$	11.2625	−	19.5072i	0.562422	−	0.974144i	−0.434862	−	0.900497i	$-0.643203\pi$
$401$	11.2625	−	19.5072i	0.562422	−	0.974144i	0.997284	−	0.0736470i	$-0.0234638\pi$
$402$	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
$406$	−10.8204	+	0.836125i	−0.537009	+	0.0414962i
$407$	−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	−0.954089	−	0.299524i	$-0.903172\pi$
$409$	−14.8936	−	25.7964i	−0.736439	−	1.27555i	0.217649	−	0.976027i	$-0.430161\pi$
$410$	−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
$413$	−5.16368	+	0.399012i	−0.254088	+	0.0196341i
$414$	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	$-0.734237\pi$
$419$	6.27014	−	10.8602i	0.306316	−	0.530555i	0.977554	+	0.210687i	$0.0675702\pi$
$420$	−14.7934	+	2.73496i	−0.721844	+	0.133452i
$421$			7.92498i			0.386240i	0.981175	+	0.193120i	$0.0618606\pi$
$421$			7.92498i			0.386240i	−0.981175	+	0.193120i	$0.938139\pi$
$422$	−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
$427$	−19.4563	+	1.50344i	−0.941557	+	0.0727567i
$428$		−	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	−0.597280	−	0.802033i	$-0.703752\pi$
$431$	8.21994	−	14.2374i	0.395941	−	0.685789i	0.993221	+	0.116243i	$0.0370852\pi$
$432$	−1.06549	+	5.08574i	−0.0512637	+	0.244688i
$433$	−15.7567	+	9.09714i	−0.757219	+	0.437181i	−0.828296	−	0.560290i	$-0.810690\pi$
$433$	−15.7567	+	9.09714i	−0.757219	+	0.437181i	0.0710771	+	0.997471i	$0.477356\pi$
$434$	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	$-0.165634\pi$
$439$	18.2471	+	10.5350i	0.870886	+	0.502807i	0.00324376	+	0.999995i	$0.498967\pi$
$440$	−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	$-0.0416952\pi$
$444$	−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
$448$	−2.38640	−	1.14242i	−0.112747	−	0.0539741i
$449$	−5.64836	−	9.78324i	−0.266562	−	0.461700i	0.701409	−	0.712759i	$-0.252555\pi$
$449$	−5.64836	−	9.78324i	−0.266562	−	0.461700i	−0.967972	+	0.251059i	$0.919221\pi$
$450$	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
$455$	−13.8311	+	28.0970i	−0.648414	+	1.31721i
$456$	2.57349	+	3.53487i	0.120515	+	0.165535i
$457$	−20.4295	−	11.7950i	−0.955651	−	0.551745i	−0.0608191	−	0.998149i	$-0.519371\pi$
$457$	−20.4295	−	11.7950i	−0.955651	−	0.551745i	−0.894832	+	0.446404i	$0.852705\pi$
$458$	−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	$-0.742416\pi$
$461$	−8.76660	+	5.06140i	−0.408301	+	0.235733i	0.281758	+	0.959485i	$0.409082\pi$
$462$	3.47432	+	18.7926i	0.161640	+	0.874313i
$463$			18.9145i			0.879032i	0.898235	+	0.439516i	$0.144850\pi$
$463$			18.9145i			0.879032i	−0.898235	+	0.439516i	$0.855150\pi$
$464$	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	$-0.377660\pi$
$467$	16.2055			0.749899			0.374950	+	0.927045i	$0.377660\pi$
$468$	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	$-0.603461\pi$
$479$	−28.4451	−	16.4228i	−1.29969	−	0.750376i	−0.980350	+	0.197265i	$0.936794\pi$
$480$	4.59692	−	3.34670i	0.209820	−	0.152755i
$481$	−18.9638	−	11.2277i	−0.864676	−	0.511939i
$482$	12.3109			0.560744
$483$	13.1400	+	15.3989i	0.597891	+	0.700675i
$484$	−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	−0.957828	−	0.287342i	$-0.907228\pi$
$487$	−26.2146	+	15.1350i	−1.18790	+	0.685833i	−0.230069	+	0.973174i	$0.573895\pi$
$488$	6.38756	−	3.68786i	0.289151	−	0.166941i
$489$	24.9020	−	18.1294i	1.12611	−	0.819842i
$490$	−3.53041	−	22.7074i	−0.159488	−	1.02582i
$491$	16.9520	+	9.78727i	0.765035	+	0.441693i	0.831101	−	0.556122i	$-0.187711\pi$
$491$	16.9520	+	9.78727i	0.765035	+	0.441693i	−0.0660655	+	0.997815i	$0.521045\pi$
$492$	−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
$497$	2.36183	+	30.5649i	0.105943	+	1.37102i
$498$	−9.19561	−	4.08343i	−0.412065	−	0.182983i
$499$		−	3.88687i		−	0.174000i	−0.996208	−	0.0870001i	$-0.972272\pi$
$499$		−	3.88687i		−	0.174000i	0.996208	−	0.0870001i	$-0.0277280\pi$
$500$	−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	$-0.219489\pi$
$503$	−3.70474	−	6.41680i	−0.165186	−	0.286111i	−0.936721	+	0.350076i	$0.886156\pi$
$504$	−7.71892	−	1.84885i	−0.343828	−	0.0823544i
$505$	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	$-0.134716\pi$
$509$	22.8313	+	13.1817i	1.01198	+	0.584267i	0.100209	+	0.994966i	$0.468049\pi$
$510$	−4.61670	−	43.5175i	−0.204431	−	1.92699i
$511$	−2.67952	−	1.28274i	−0.118535	−	0.0567452i
$512$	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
$518$	16.1236	−	1.24592i	0.708432	−	0.0547425i
$519$	−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	$0.368306\pi$
$522$	9.12894	−	8.25197i	0.399563	−	0.361179i
$523$	20.8475	+	12.0363i	0.911598	+	0.526311i	0.880945	−	0.473219i	$-0.156908\pi$
$523$	20.8475	+	12.0363i	0.911598	+	0.526311i	0.0306528	+	0.999530i	$0.490241\pi$
$524$	−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
$531$	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
$539$	−28.8461	+	4.48482i	−1.24249	+	0.193175i
$540$	11.3772	−	12.7101i	0.489598	−	0.546957i
$541$			9.09344i			0.390958i	0.980708	+	0.195479i	$0.0626261\pi$
$541$			9.09344i			0.390958i	−0.980708	+	0.195479i	$0.937374\pi$
$542$	−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
$546$	−12.6856	+	10.5866i	−0.542892	+	0.453066i
$547$	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
$553$	−5.25930	−	2.51773i	−0.223648	−	0.107065i
$554$	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	−0.677517	−	0.735507i	$-0.736944\pi$
$557$	7.03801	−	12.1902i	0.298210	−	0.516515i	0.975726	+	0.218993i	$0.0702771\pi$
$558$	−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	$-0.274201\pi$
$563$	−7.86426	−	13.6213i	−0.331439	−	0.574069i	−0.982794	+	0.184704i	$0.940867\pi$
$564$	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	$-0.523396\pi$
$569$	−23.2297	−	13.4117i	−0.973838	−	0.562246i	−0.900404	+	0.435054i	$0.856729\pi$
$570$	−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
$574$	5.29272	−	0.408983i	0.220914	−	0.0170706i
$575$	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	$-0.571087\pi$
$577$	−10.6399			−0.442946			−0.221473	+	0.975166i	$0.571087\pi$
$578$	−21.1159	−	36.5738i	−0.878305	−	1.52127i
$579$	−18.8064	−	8.35121i	−0.781566	−	0.347064i
$580$	−13.4662			−0.559153
$581$	6.63630	−	13.8626i	0.275320	−	0.575117i
$582$	−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	$-0.506046\pi$
$587$	−21.6686	−	12.5103i	−0.894357	−	0.516357i	−0.875365	+	0.483462i	$0.839379\pi$
$588$	3.15988	−	11.7053i	0.130311	−	0.482720i
$589$	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
$595$	66.6484	−	5.15011i	2.73232	−	0.211134i
$596$	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	$-0.282612\pi$
$600$	−9.95084	+	1.05567i	−0.406241	+	0.0430975i
$601$	20.2283	+	11.6788i	0.825131	+	0.476390i	0.852183	−	0.523244i	$-0.175279\pi$
$601$	20.2283	+	11.6788i	0.825131	+	0.476390i	−0.0270517	+	0.999634i	$0.508612\pi$
$602$	−22.1767	−	10.6164i	−0.903854	−	0.432693i
$603$	−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	$-0.879466\pi$
$607$	−26.4502	+	15.2710i	−1.07358	+	0.619833i	−0.144424	+	0.989516i	$0.546133\pi$
$608$	1.26221	−	2.18621i	0.0511894	−	0.0886627i
$609$	12.2016	+	14.2991i	0.494432	+	0.579430i
$610$	−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	0.908049	−	0.418863i	$-0.137571\pi$
$613$	24.7422	+	14.2849i	0.999328	+	0.576962i	0.0912784	+	0.995825i	$0.470905\pi$
$614$	−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	0.641546	−	0.767084i	$-0.278293\pi$
$617$	−8.53339	−	14.7803i	−0.343541	−	0.595031i	−0.985088	+	0.172053i	$0.944960\pi$
$618$	−3.27943	−	1.45627i	−0.131918	−	0.0585800i
$619$	22.3781			0.899453			0.449727	−	0.893166i	$-0.351521\pi$
$619$	22.3781			0.899453			0.449727	+	0.893166i	$0.351521\pi$
$620$	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
$630$	18.9106	+	17.9266i	0.753417	+	0.714212i
$631$	−11.2407	+	6.48982i	−0.447485	+	0.258356i	−0.706768	−	0.707446i	$-0.749847\pi$
$631$	−11.2407	+	6.48982i	−0.447485	+	0.258356i	0.259282	+	0.965802i	$0.416514\pi$
$632$	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
$637$	−15.6111	−	19.8316i	−0.618535	−	0.785757i
$638$			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	−0.278490	−	0.960439i	$-0.589834\pi$
$641$	10.4824	−	6.05200i	0.414029	−	0.239040i	0.692519	+	0.721399i	$0.256501\pi$
$642$	−5.21190	+	3.79442i	−0.205697	+	0.149754i
$643$	−2.90522	−	5.03200i	−0.114571	−	0.198443i	0.803037	−	0.595929i	$-0.203216\pi$
$643$	−2.90522	−	5.03200i	−0.114571	−	0.198443i	−0.917608	+	0.397486i	$0.869883\pi$
$644$	5.04654	−	10.5417i	0.198861	−	0.415402i
$645$	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	$-0.951696\pi$
$647$	−9.24194	+	16.0075i	−0.363338	+	0.629320i	0.625170	+	0.780489i	$0.285030\pi$
$648$	8.20759	−	3.69261i	0.322425	−	0.145060i
$649$			8.16355i			0.320447i
$650$	−10.6124	+	17.9246i	−0.416252	+	0.703059i
$651$	−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	$-0.416197\pi$
$653$	−11.3924	−	6.57741i	−0.445819	−	0.257394i	−0.706063	+	0.708149i	$0.749530\pi$
$654$	−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	−0.714910	−	0.699216i	$-0.753533\pi$
$659$	−11.9839	+	6.91891i	−0.466827	+	0.269523i	0.248084	+	0.968739i	$0.420199\pi$
$660$	2.50167	+	23.5810i	0.0973775	+	0.917890i
$661$	18.7710	−	32.5124i	0.730108	−	1.26458i	−0.226729	−	0.973958i	$-0.572803\pi$
$661$	18.7710	−	32.5124i	0.730108	−	1.26458i	0.956837	−	0.290626i	$-0.0938636\pi$
$662$			32.4289i			1.26038i
$663$	−27.8609	−	39.1639i	−1.08203	−	1.52100i
$664$			5.80900i			0.225433i
$665$	21.8612	−	1.68928i	0.847742	−	0.0655074i
$666$	−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
$672$	0.833094	+	4.50621i	0.0321373	+	0.173831i
$673$	−6.25166	+	10.8282i	−0.240984	+	0.417396i	−0.960995	−	0.276567i	$-0.910803\pi$
$673$	−6.25166	+	10.8282i	−0.240984	+	0.417396i	0.720011	+	0.693963i	$0.244137\pi$
$674$	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	$0.350293\pi$
$678$	1.23598	+	11.6505i	0.0474676	+	0.447435i
$679$	−1.33218	−	17.2400i	−0.0511246	−	0.661612i
$680$	−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	$-0.207970\pi$
$683$	−3.38165	−	5.85720i	−0.129395	−	0.224119i	−0.923442	+	0.383737i	$0.874637\pi$
$684$	2.32624	−	7.20715i	0.0889461	−	0.275572i
$685$	−5.52058	+	3.18731i	−0.210930	+	0.121781i
$686$	17.7350	+	5.33565i	0.677126	+	0.203716i
$687$	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	$-0.853876\pi$
$691$	−1.69532	+	2.93638i	−0.0644929	+	0.111705i	0.831976	+	0.554812i	$0.187210\pi$
$692$	−6.13026	+	10.6179i	−0.233038	+	0.403633i
$693$	22.7729	−	24.0229i	0.865070	−	0.912555i
$694$		−	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
$700$	−1.17764	−	15.2400i	−0.0445106	−	0.576019i
$701$		−	43.1581i		−	1.63006i	−0.579419	−	0.815030i	$-0.696721\pi$
$701$		−	43.1581i		−	1.63006i	0.579419	−	0.815030i	$-0.303279\pi$
$702$	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	−0.146697	−	0.989182i	$-0.546864\pi$
$709$	16.9511	−	9.78671i	0.636611	−	0.367548i	0.783308	+	0.621634i	$0.213531\pi$
$710$			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
$714$	33.2403	+	11.7877i	1.24399	+	0.441145i
$715$	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	$-0.274006\pi$
$719$	−8.87175	−	15.3663i	−0.330860	−	0.573067i	−0.982681	+	0.185306i	$0.940672\pi$
$720$	−9.37255	−	3.02517i	−0.349294	−	0.112741i
$721$	2.36671	−	4.94382i	0.0881407	−	0.184117i
$722$	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	$0.901207\pi$
$728$	8.55861	+	4.21310i	0.317203	+	0.156148i
$729$	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	$-0.527229\pi$
$733$	−4.62622			−0.170873			−0.0854367	+	0.996344i	$0.527229\pi$
$734$	−12.1645	+	7.02320i	−0.449002	+	0.259231i
$735$	−28.1974	+	28.0923i	−1.04008	+	1.03620i
$736$			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	0.412397	−	0.911004i	$-0.364692\pi$
$739$	−4.63110	−	2.67377i	−0.170358	−	0.0983562i	−0.582755	+	0.812648i	$0.698025\pi$
$740$	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	−0.410378	−	0.911915i	$-0.634603\pi$
$743$	15.9338	−	27.5981i	0.584553	−	1.01247i	0.994931	−	0.100560i	$-0.0320633\pi$
$744$	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	−0.539579	−	0.841935i	$-0.681417\pi$
$751$	12.5881	−	21.8033i	0.459347	−	0.795613i	0.998927	+	0.0463220i	$0.0147500\pi$
$752$	−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
$756$	5.28007	+	12.6933i	0.192034	+	0.461652i
$757$	8.82099	−	15.2784i	0.320604	−	0.555303i	−0.660009	−	0.751258i	$-0.729447\pi$
$757$	8.82099	−	15.2784i	0.320604	−	0.555303i	0.980613	+	0.195955i	$0.0627807\pi$
$758$	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	$-0.530877\pi$
$761$	19.7704	−	11.4144i	0.716676	−	0.413773i	0.813528	+	0.581526i	$0.197544\pi$
$762$	21.3513	+	29.3274i	0.773474	+	1.06242i
$763$	11.7882	−	24.6244i	0.426761	−	0.891462i
$764$	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	$-0.764070\pi$
$769$	5.98667	−	10.3692i	0.215885	−	0.373923i	0.953546	+	0.301248i	$0.0974031\pi$
$770$	−36.1151	+	2.79071i	−1.30150	+	0.100570i
$771$	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	$-0.620508\pi$
$773$	6.95873	−	4.01762i	0.250288	−	0.144504i	0.619896	+	0.784684i	$0.287175\pi$
$774$	27.2583	−	5.84942i	0.979780	−	0.210253i
$775$	−40.3165			−1.44821
$776$	3.26777	+	5.65995i	0.117306	+	0.203180i
$777$	−18.1817	−	21.3073i	−0.652263	−	0.764394i
$778$	−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
$784$	−6.91690	+	1.07540i	−0.247032	+	0.0384071i
$785$	−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	$-0.106897\pi$
$787$	5.23675	+	9.07032i	0.186670	+	0.323322i	−0.757468	+	0.652872i	$0.773564\pi$
$788$	9.14932			0.325931
$789$	−26.4050	−	11.7255i	−0.940042	−	0.417438i
$790$	−6.26574	−	3.61753i	−0.222925	−	0.128706i
$791$	−17.8431	+	1.37879i	−0.634428	+	0.0490240i
$792$	−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	$-0.0348405\pi$
$797$	11.3604	+	19.6768i	0.402406	+	0.696988i	−0.591609	+	0.806225i	$0.701507\pi$
$798$	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
$804$	0.0226664	+	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	0.702913	−	0.711276i	$-0.251882\pi$
$809$	12.4690	+	7.19898i	0.438387	+	0.253103i	−0.264526	+	0.964378i	$0.585216\pi$
$810$	−29.3959	−	2.97397i	−1.03287	−	0.104495i
$811$	22.5924			0.793325			0.396662	−	0.917965i	$-0.370168\pi$
$811$	22.5924			0.793325			0.396662	+	0.917965i	$0.370168\pi$
$812$	4.68611	−	9.78884i	0.164450	−	0.343521i
$813$	−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
$819$	27.7562	+	6.97077i	0.969881	+	0.243579i
$820$	6.58687			0.230023
$821$	−0.821661	+	1.42316i	−0.0286762	+	0.0496686i	−0.880007	−	0.474960i	$-0.842462\pi$
$821$	−0.821661	+	1.42316i	−0.0286762	+	0.0496686i	0.851331	+	0.524629i	$0.175796\pi$
$822$	−3.34447	+	0.354810i	−0.116652	+	0.0123754i
$823$	6.07905	+	10.5292i	0.211903	+	0.367026i	0.952310	−	0.305132i	$-0.0987007\pi$
$823$	6.07905	+	10.5292i	0.211903	+	0.367026i	−0.740407	+	0.672158i	$0.765367\pi$
$824$			2.07167i			0.0721700i
$825$	16.9367	−	38.1403i	0.589660	−	1.32788i
$826$	2.23628	−	4.67138i	0.0778103	−	0.162538i
$827$	−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	0.971325	+	0.237756i	$0.0764117\pi$
$829$	47.8785	+	27.6427i	1.66289	+	0.960070i	0.691565	+	0.722314i	$0.256922\pi$
$830$	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	$-0.721104\pi$
$839$	−8.53828	+	4.92958i	−0.294774	+	0.170188i	0.345319	+	0.938485i	$0.387771\pi$
$840$	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
$843$	−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
$847$	1.30295	+	16.8617i	0.0447699	+	0.579375i
$848$	−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	$-0.836843\pi$
$853$	−50.9055			−1.74297			−0.871485	+	0.490422i	$0.836843\pi$
$854$	8.42613	−	17.6014i	0.288336	−	0.602307i
$855$	−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	$-0.277657\pi$
$857$	37.6517			1.28616			0.643078	+	0.765800i	$0.277657\pi$
$858$	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
$861$	−5.96828	−	6.99429i	−0.203399	−	0.238365i
$862$	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
$868$	1.42245	+	18.4081i	0.0482810	+	0.624812i
$869$	−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
$875$	−2.91543	+	6.09006i	−0.0985596	+	0.205881i
$876$	−1.14466	−	1.57227i	−0.0386744	−	0.0531219i
$877$	11.3397	−	6.54696i	0.382913	−	0.221075i	−0.296172	−	0.955135i	$-0.595710\pi$
$877$	11.3397	−	6.54696i	0.382913	−	0.221075i	0.679085	+	0.734060i	$0.262377\pi$
$878$	−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	$-0.784714\pi$
$881$	4.51600	−	7.82195i	0.152148	−	0.263528i	0.932017	+	0.362415i	$0.118048\pi$
$882$	−19.6119	+	7.50820i	−0.660367	+	0.252814i
$883$	−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	$-0.977664\pi$
$887$	−13.0463	+	22.5968i	−0.438051	+	0.758726i	0.559488	+	0.828838i	$0.310998\pi$
$888$	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
$903$	7.74191	+	41.8760i	0.257634	+	1.39355i
$904$	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	−0.857680	−	0.514185i	$-0.828095\pi$
$907$	0.495632	−	0.858461i	0.0164572	−	0.0285047i	0.874137	+	0.485680i	$0.161428\pi$
$908$	20.7722	+	11.9929i	0.689351	+	0.397997i
$909$	16.1646	−	50.0810i	0.536145	−	1.66108i
$910$	−17.4171	−	26.0266i	−0.577372	−	0.862773i
$911$		−	4.92531i		−	0.163183i	−0.996666	−	0.0815914i	$-0.974000\pi$
$911$		−	4.92531i		−	0.163183i	0.996666	−	0.0815914i	$-0.0260003\pi$
$912$	−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
$917$	−25.3845	−	12.1521i	−0.838271	−	0.401297i
$918$	−37.9972	+	12.4688i	−1.25409	+	0.411532i
$919$	3.16943	+	5.48962i	0.104550	+	0.181086i	0.913554	−	0.406717i	$-0.133326\pi$
$919$	3.16943	+	5.48962i	0.104550	+	0.181086i	−0.809004	+	0.587803i	$0.799993\pi$
$920$	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
$924$	−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
$927$	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	$-0.669947\pi$
$929$	−0.544018	+	0.314089i	−0.0178486	+	0.0103049i	0.491049	+	0.871132i	$0.336614\pi$
$930$	−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	$-0.176204\pi$
$938$	−0.327220	+	0.0252852i	−0.0106841	+	0.000825591i
$939$	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
$945$	5.82383	−	44.7549i	0.189449	−	1.45588i
$946$	−19.3776	+	33.5630i	−0.630020	+	1.09123i
$947$	−9.54333	+	16.5295i	−0.310116	+	0.537137i	−0.978387	−	0.206781i	$-0.933701\pi$
$947$	−9.54333	+	16.5295i	−0.310116	+	0.537137i	0.668271	+	0.743918i	$0.267035\pi$
$948$	−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
$952$	−1.56877	−	20.3018i	−0.0508442	−	0.657984i
$953$	47.2598	−	27.2854i	1.53089	−	0.883862i	0.531573	−	0.847012i	$-0.321601\pi$
$953$	47.2598	−	27.2854i	1.53089	−	0.883862i	0.999321	−	0.0368498i	$-0.0117323\pi$
$954$	−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
$959$	−0.395804	−	5.12217i	−0.0127812	−	0.165403i
$960$	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
$966$	−19.9059	+	3.68013i	−0.640461	+	0.118406i
$967$		−	53.5813i		−	1.72306i	−0.507708	−	0.861529i	$-0.669507\pi$
$967$		−	53.5813i		−	1.72306i	0.507708	−	0.861529i	$-0.330493\pi$
$968$	−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	−0.977220	−	0.212227i	$-0.931928\pi$
$971$	−20.9527	−	36.2911i	−0.672404	−	1.16464i	0.304816	−	0.952411i	$-0.401405\pi$
$972$	−13.5378	−	7.72844i	−0.434224	−	0.247890i
$973$	−21.0026	+	1.62293i	−0.673311	+	0.0520287i
$974$		−	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	−0.245508	−	0.969395i	$-0.578955\pi$
$977$	22.4040	−	38.8048i	0.716767	−	1.24148i	0.962274	−	0.272081i	$-0.0877120\pi$
$978$	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
$987$	7.05503	−	19.8945i	0.224564	−	0.633250i
$988$	−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	−0.334975	−	0.942227i	$-0.608728\pi$
$991$	20.4150	−	35.3599i	0.648505	−	1.12324i	0.983480	−	0.181016i	$-0.0579387\pi$
$992$	−3.48918	−	6.04343i	−0.110782	−	0.191879i
$993$	45.4091	−	33.0592i	1.44101	−	1.04910i
$994$	−27.6509	−	13.2370i	−0.877032	−	0.419853i
$995$	−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	$-0.920878\pi$
$997$	−39.1799	+	22.6206i	−1.24084	+	0.716400i	−0.271576	+	0.962417i	$0.587545\pi$
$998$	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.251.12	yes	24
3.2	odd	2		546.2.q.j.251.8	yes	24
7.6	odd	2	inner	546.2.q.i.251.1	✓	24
13.10	even	6		546.2.q.j.335.5	yes	24
21.20	even	2		546.2.q.j.251.5	yes	24
39.23	odd	6	inner	546.2.q.i.335.1	yes	24
91.62	odd	6		546.2.q.j.335.8	yes	24
273.62	even	6	inner	546.2.q.i.335.12	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.q.i.251.1	✓	24	7.6	odd	2	inner
546.2.q.i.251.12	yes	24	1.1	even	1	trivial
546.2.q.i.335.1	yes	24	39.23	odd	6	inner
546.2.q.i.335.12	yes	24	273.62	even	6	inner
546.2.q.j.251.5	yes	24	21.20	even	2
546.2.q.j.251.8	yes	24	3.2	odd	2
546.2.q.j.335.5	yes	24	13.10	even	6
546.2.q.j.335.8	yes	24	91.62	odd	6

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)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(1.72239 - 0.182725i) q^{3} +(-0.500000 - 0.866025i) q^{4} +3.28289i q^{5} +(-0.702948 + 1.58299i) q^{6} +(-2.38640 - 1.14242i) q^{7} +1.00000 q^{8} +(2.93322 - 0.629446i) q^{9} +O(q^{10})\)	\(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} +(-2.38640 - 1.14242i) 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} +(-4.31904 - 1.53163i) 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} +(0.203837 + 2.63789i) 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} +(3.75042 - 7.83427i) 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} +(3.48595 - 2.97459i) 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} +(4.38977 + 5.45251i) 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} +(-2.38640 - 1.14242i) 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} +(-7.71892 - 1.84885i) 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} +(0.833094 + 4.50621i) 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} +(8.55861 + 4.21310i) 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} +(-6.91690 + 1.07540i) 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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