LMFDB - Embedded newform 273.2.cg.b.19.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(19,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 10, 5]))

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

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

chi := DirichletCharacter("273.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.cg (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			19.8
Character	$\chi$	$=$	273.19
Dual form			273.2.cg.b.115.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.41061 + 0.377973i) q^{2} +1.00000i q^{3} +(0.114915 + 0.0663464i) q^{4} +(1.70489 - 0.456824i) q^{5} +(-0.377973 + 1.41061i) q^{6} +(1.96341 + 1.77342i) q^{7} +(-1.92826 - 1.92826i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(1.41061 + 0.377973i) q^{2} +1.00000i q^{3} +(0.114915 + 0.0663464i) q^{4} +(1.70489 - 0.456824i) q^{5} +(-0.377973 + 1.41061i) q^{6} +(1.96341 + 1.77342i) q^{7} +(-1.92826 - 1.92826i) q^{8} -1.00000 q^{9} +2.57761 q^{10} +(1.59480 + 1.59480i) q^{11} +(-0.0663464 + 0.114915i) q^{12} +(2.06370 + 2.95654i) q^{13} +(2.09931 + 3.24373i) q^{14} +(0.456824 + 1.70489i) q^{15} +(-2.12389 - 3.67868i) q^{16} +(0.813654 - 1.40929i) q^{17} +(-1.41061 - 0.377973i) q^{18} +(-5.08160 - 5.08160i) q^{19} +(0.226226 + 0.0606172i) q^{20} +(-1.77342 + 1.96341i) q^{21} +(1.64685 + 2.85244i) q^{22} +(-5.63098 + 3.25105i) q^{23} +(1.92826 - 1.92826i) q^{24} +(-1.63217 + 0.942332i) q^{25} +(1.79359 + 4.95056i) q^{26} -1.00000i q^{27} +(0.107966 + 0.334058i) q^{28} +(3.90230 - 6.75898i) q^{29} +2.57761i q^{30} +(1.68884 - 6.30283i) q^{31} +(-0.193962 - 0.723875i) q^{32} +(-1.59480 + 1.59480i) q^{33} +(1.68042 - 1.68042i) q^{34} +(4.15754 + 2.12655i) q^{35} +(-0.114915 - 0.0663464i) q^{36} +(-0.545268 + 2.03497i) q^{37} +(-5.24746 - 9.08887i) q^{38} +(-2.95654 + 2.06370i) q^{39} +(-4.16834 - 2.40659i) q^{40} +(6.84645 - 1.83450i) q^{41} +(-3.24373 + 2.09931i) q^{42} +(-9.48195 + 5.47441i) q^{43} +(0.0774577 + 0.289076i) q^{44} +(-1.70489 + 0.456824i) q^{45} +(-9.17195 + 2.45762i) q^{46} +(-3.34284 - 12.4756i) q^{47} +(3.67868 - 2.12389i) q^{48} +(0.709963 + 6.96390i) q^{49} +(-2.65853 + 0.712352i) q^{50} +(1.40929 + 0.813654i) q^{51} +(0.0409944 + 0.476671i) q^{52} +(-3.00939 - 5.21242i) q^{53} +(0.377973 - 1.41061i) q^{54} +(3.44750 + 1.99041i) q^{55} +(-0.366351 - 7.20557i) q^{56} +(5.08160 - 5.08160i) q^{57} +(8.05934 - 8.05934i) q^{58} +(2.02441 + 7.55521i) q^{59} +(-0.0606172 + 0.226226i) q^{60} -6.26701i q^{61} +(4.76460 - 8.25252i) q^{62} +(-1.96341 - 1.77342i) q^{63} +7.40114i q^{64} +(4.86900 + 4.09784i) q^{65} +(-2.85244 + 1.64685i) q^{66} +(-3.75123 + 3.75123i) q^{67} +(0.187002 - 0.107966i) q^{68} +(-3.25105 - 5.63098i) q^{69} +(5.06090 + 4.57118i) q^{70} +(6.88920 + 1.84596i) q^{71} +(1.92826 + 1.92826i) q^{72} +(-4.55425 - 1.22031i) q^{73} +(-1.53832 + 2.66446i) q^{74} +(-0.942332 - 1.63217i) q^{75} +(-0.246808 - 0.921099i) q^{76} +(0.302997 + 5.95950i) q^{77} +(-4.95056 + 1.79359i) q^{78} +(-4.67565 + 8.09846i) q^{79} +(-5.30151 - 5.30151i) q^{80} +1.00000 q^{81} +10.3511 q^{82} +(3.82650 + 3.82650i) q^{83} +(-0.334058 + 0.107966i) q^{84} +(0.743393 - 2.77438i) q^{85} +(-15.4445 + 4.13835i) q^{86} +(6.75898 + 3.90230i) q^{87} -6.15037i q^{88} +(4.91594 + 1.31722i) q^{89} -2.57761 q^{90} +(-1.19131 + 9.46471i) q^{91} -0.862782 q^{92} +(6.30283 + 1.68884i) q^{93} -18.8618i q^{94} +(-10.9850 - 6.34217i) q^{95} +(0.723875 - 0.193962i) q^{96} +(-2.57958 + 9.62711i) q^{97} +(-1.63068 + 10.0917i) q^{98} +(-1.59480 - 1.59480i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 8 q^{7} - 40 q^{9}+O(q^{10}) $ 40 * q - 8 * q^7 - 40 * q^9	$ 40 q - 8 q^{7} - 40 q^{9} + 4 q^{11} - 24 q^{12} - 18 q^{14} + 32 q^{16} + 4 q^{17} + 14 q^{19} + 14 q^{20} + 2 q^{21} + 4 q^{22} + 12 q^{23} + 24 q^{25} - 32 q^{26} + 16 q^{28} + 8 q^{29} + 14 q^{31} - 26 q^{32} - 4 q^{33} - 24 q^{34} + 26 q^{35} + 36 q^{37} - 8 q^{38} + 18 q^{39} - 30 q^{40} - 2 q^{41} - 66 q^{43} - 32 q^{44} - 26 q^{46} - 4 q^{47} + 24 q^{48} - 14 q^{49} - 20 q^{50} + 2 q^{52} - 8 q^{53} - 42 q^{55} + 46 q^{56} - 14 q^{57} + 24 q^{58} + 14 q^{59} + 2 q^{60} + 24 q^{62} + 8 q^{63} + 28 q^{65} - 18 q^{66} - 44 q^{67} - 18 q^{68} + 4 q^{69} - 4 q^{70} - 6 q^{71} + 14 q^{73} - 20 q^{74} + 24 q^{75} - 64 q^{76} + 24 q^{77} + 8 q^{78} + 20 q^{80} + 40 q^{81} + 48 q^{82} - 12 q^{83} + 22 q^{84} + 2 q^{85} - 60 q^{86} + 18 q^{87} - 2 q^{89} - 14 q^{91} + 236 q^{92} - 8 q^{93} + 24 q^{95} + 16 q^{96} - 62 q^{97} - 88 q^{98} - 4 q^{99}+O(q^{100}) $ 40 * q - 8 * q^7 - 40 * q^9 + 4 * q^11 - 24 * q^12 - 18 * q^14 + 32 * q^16 + 4 * q^17 + 14 * q^19 + 14 * q^20 + 2 * q^21 + 4 * q^22 + 12 * q^23 + 24 * q^25 - 32 * q^26 + 16 * q^28 + 8 * q^29 + 14 * q^31 - 26 * q^32 - 4 * q^33 - 24 * q^34 + 26 * q^35 + 36 * q^37 - 8 * q^38 + 18 * q^39 - 30 * q^40 - 2 * q^41 - 66 * q^43 - 32 * q^44 - 26 * q^46 - 4 * q^47 + 24 * q^48 - 14 * q^49 - 20 * q^50 + 2 * q^52 - 8 * q^53 - 42 * q^55 + 46 * q^56 - 14 * q^57 + 24 * q^58 + 14 * q^59 + 2 * q^60 + 24 * q^62 + 8 * q^63 + 28 * q^65 - 18 * q^66 - 44 * q^67 - 18 * q^68 + 4 * q^69 - 4 * q^70 - 6 * q^71 + 14 * q^73 - 20 * q^74 + 24 * q^75 - 64 * q^76 + 24 * q^77 + 8 * q^78 + 20 * q^80 + 40 * q^81 + 48 * q^82 - 12 * q^83 + 22 * q^84 + 2 * q^85 - 60 * q^86 + 18 * q^87 - 2 * q^89 - 14 * q^91 + 236 * q^92 - 8 * q^93 + 24 * q^95 + 16 * q^96 - 62 * q^97 - 88 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	1.41061	+	0.377973i	0.997454	+	0.267267i	0.720379	−	0.693581i	$-0.243968\pi$
$2$	1.41061	+	0.377973i	0.997454	+	0.267267i	0.277076	+	0.960848i	$0.410635\pi$
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	0.114915	+	0.0663464i	0.0574576	+	0.0331732i
$5$	1.70489	−	0.456824i	0.762450	−	0.204298i	0.143416	−	0.989662i	$-0.454191\pi$
$5$	1.70489	−	0.456824i	0.762450	−	0.204298i	0.619033	+	0.785365i	$0.287525\pi$
$6$	−0.377973	+	1.41061i	−0.154307	+	0.575880i
$7$	1.96341	+	1.77342i	0.742100	+	0.670290i
$7$	1.96341	+	1.77342i	0.742100	+	0.670290i
$8$	−1.92826	−	1.92826i	−0.681742	−	0.681742i
$9$	−1.00000			−0.333333
$10$	2.57761			0.815111
$11$	1.59480	+	1.59480i	0.480850	+	0.480850i	0.905403	−	0.424553i	$-0.139569\pi$
$11$	1.59480	+	1.59480i	0.480850	+	0.480850i	−0.424553	+	0.905403i	$0.639569\pi$
$12$	−0.0663464	+	0.114915i	−0.0191525	+	0.0331732i
$13$	2.06370	+	2.95654i	0.572367	+	0.819998i
$13$	2.06370	+	2.95654i	0.572367	+	0.819998i
$14$	2.09931	+	3.24373i	0.561064	+	0.866922i
$15$	0.456824	+	1.70489i	0.117951	+	0.440201i
$16$	−2.12389	−	3.67868i	−0.530972	−	0.919671i
$17$	0.813654	−	1.40929i	0.197340	−	0.341803i	−0.750325	−	0.661069i	$-0.770103\pi$
$17$	0.813654	−	1.40929i	0.197340	−	0.341803i	0.947665	+	0.319266i	$0.103436\pi$
$18$	−1.41061	−	0.377973i	−0.332485	−	0.0890890i
$19$	−5.08160	−	5.08160i	−1.16580	−	1.16580i	−0.983185	−	0.182614i	$-0.941544\pi$
$19$	−5.08160	−	5.08160i	−1.16580	−	1.16580i	−0.182614	−	0.983185i	$-0.558456\pi$
$20$	0.226226	+	0.0606172i	0.0505858	+	0.0135544i
$21$	−1.77342	+	1.96341i	−0.386992	+	0.428451i
$22$	1.64685	+	2.85244i	0.351111	+	0.608141i
$23$	−5.63098	+	3.25105i	−1.17414	+	0.677891i	−0.954652	−	0.297724i	$-0.903773\pi$
$23$	−5.63098	+	3.25105i	−1.17414	+	0.677891i	−0.219490	+	0.975615i	$0.570439\pi$
$24$	1.92826	−	1.92826i	0.393604	−	0.393604i
$25$	−1.63217	+	0.942332i	−0.326433	+	0.188466i
$26$	1.79359	+	4.95056i	0.351751	+	0.970885i
$27$		−	1.00000i		−	0.192450i
$28$	0.107966	+	0.334058i	0.0204036	+	0.0631311i
$29$	3.90230	−	6.75898i	0.724638	−	1.25511i	−0.234484	−	0.972120i	$-0.575340\pi$
$29$	3.90230	−	6.75898i	0.724638	−	1.25511i	0.959123	−	0.282991i	$-0.0913266\pi$
$30$			2.57761i			0.470604i
$31$	1.68884	−	6.30283i	0.303324	−	1.13202i	−0.631054	−	0.775739i	$-0.717377\pi$
$31$	1.68884	−	6.30283i	0.303324	−	1.13202i	0.934378	−	0.356283i	$-0.115956\pi$
$32$	−0.193962	−	0.723875i	−0.0342879	−	0.127964i
$33$	−1.59480	+	1.59480i	−0.277619	+	0.277619i
$34$	1.68042	−	1.68042i	0.288190	−	0.288190i
$35$	4.15754	+	2.12655i	0.702752	+	0.359453i
$36$	−0.114915	−	0.0663464i	−0.0191525	−	0.0110577i
$37$	−0.545268	+	2.03497i	−0.0896415	+	0.334547i	−0.996153	−	0.0876352i	$-0.972069\pi$
$37$	−0.545268	+	2.03497i	−0.0896415	+	0.334547i	0.906511	+	0.422182i	$0.138736\pi$
$38$	−5.24746	−	9.08887i	−0.851251	−	1.47441i
$39$	−2.95654	+	2.06370i	−0.473426	+	0.330456i
$40$	−4.16834	−	2.40659i	−0.659072	−	0.380516i
$41$	6.84645	−	1.83450i	1.06924	−	0.286501i	0.319057	−	0.947736i	$-0.396634\pi$
$41$	6.84645	−	1.83450i	1.06924	−	0.286501i	0.750179	+	0.661235i	$0.229967\pi$
$42$	−3.24373	+	2.09931i	−0.500518	+	0.323930i
$43$	−9.48195	+	5.47441i	−1.44598	+	0.834839i	−0.998239	−	0.0593222i	$-0.981106\pi$
$43$	−9.48195	+	5.47441i	−1.44598	+	0.834839i	−0.447745	+	0.894161i	$0.647773\pi$
$44$	0.0774577	+	0.289076i	0.0116772	+	0.0435799i
$45$	−1.70489	+	0.456824i	−0.254150	+	0.0680993i
$46$	−9.17195	+	2.45762i	−1.35233	+	0.362356i
$47$	−3.34284	−	12.4756i	−0.487603	−	1.81976i	−0.568043	−	0.822999i	$-0.692299\pi$
$47$	−3.34284	−	12.4756i	−0.487603	−	1.81976i	0.0804402	−	0.996759i	$-0.474367\pi$
$48$	3.67868	−	2.12389i	0.530972	−	0.306557i
$49$	0.709963	+	6.96390i	0.101423	+	0.994843i
$50$	−2.65853	+	0.712352i	−0.375973	+	0.100742i
$51$	1.40929	+	0.813654i	0.197340	+	0.113934i
$52$	0.0409944	+	0.476671i	0.00568490	+	0.0661024i
$53$	−3.00939	−	5.21242i	−0.413371	−	0.715980i	0.581884	−	0.813271i	$-0.302316\pi$
$53$	−3.00939	−	5.21242i	−0.413371	−	0.715980i	−0.995256	+	0.0972910i	$0.968982\pi$
$54$	0.377973	−	1.41061i	0.0514356	−	0.191960i
$55$	3.44750	+	1.99041i	0.464861	+	0.268387i
$56$	−0.366351	−	7.20557i	−0.0489557	−	0.962885i
$57$	5.08160	−	5.08160i	0.673074	−	0.673074i
$58$	8.05934	−	8.05934i	1.05824	−	1.05824i
$59$	2.02441	+	7.55521i	0.263556	+	0.983604i	0.963128	+	0.269042i	$0.0867072\pi$
$59$	2.02441	+	7.55521i	0.263556	+	0.983604i	−0.699572	+	0.714562i	$0.746626\pi$
$60$	−0.0606172	+	0.226226i	−0.00782565	+	0.0292057i
$61$		−	6.26701i		−	0.802408i	−0.915989	−	0.401204i	$-0.868592\pi$
$61$		−	6.26701i		−	0.802408i	0.915989	−	0.401204i	$-0.131408\pi$
$62$	4.76460	−	8.25252i	0.605104	−	1.04807i
$63$	−1.96341	−	1.77342i	−0.247367	−	0.223430i
$64$			7.40114i			0.925142i
$65$	4.86900	+	4.09784i	0.603925	+	0.508274i
$66$	−2.85244	+	1.64685i	−0.351111	+	0.202714i
$67$	−3.75123	+	3.75123i	−0.458285	+	0.458285i	−0.898092	−	0.439807i	$-0.855047\pi$
$67$	−3.75123	+	3.75123i	−0.458285	+	0.458285i	0.439807	+	0.898092i	$0.355047\pi$
$68$	0.187002	−	0.107966i	0.0226774	−	0.0130928i
$69$	−3.25105	−	5.63098i	−0.391381	−	0.677891i
$70$	5.06090	+	4.57118i	0.604893	+	0.546360i
$71$	6.88920	+	1.84596i	0.817598	+	0.219075i	0.643296	−	0.765617i	$-0.277566\pi$
$71$	6.88920	+	1.84596i	0.817598	+	0.219075i	0.174302	+	0.984692i	$0.444233\pi$
$72$	1.92826	+	1.92826i	0.227247	+	0.227247i
$73$	−4.55425	−	1.22031i	−0.533035	−	0.142826i	−0.0177454	−	0.999843i	$-0.505649\pi$
$73$	−4.55425	−	1.22031i	−0.533035	−	0.142826i	−0.515289	+	0.857016i	$0.672315\pi$
$74$	−1.53832	+	2.66446i	−0.178827	+	0.309737i
$75$	−0.942332	−	1.63217i	−0.108811	−	0.188466i
$76$	−0.246808	−	0.921099i	−0.0283108	−	0.105657i
$77$	0.302997	+	5.95950i	0.0345297	+	0.679148i
$78$	−4.95056	+	1.79359i	−0.560541	+	0.203084i
$79$	−4.67565	+	8.09846i	−0.526052	+	0.911148i	0.473488	+	0.880800i	$0.342995\pi$
$79$	−4.67565	+	8.09846i	−0.526052	+	0.911148i	−0.999539	+	0.0303476i	$0.990339\pi$
$80$	−5.30151	−	5.30151i	−0.592726	−	0.592726i
$81$	1.00000			0.111111
$82$	10.3511			1.14309
$83$	3.82650	+	3.82650i	0.420013	+	0.420013i	0.885208	−	0.465195i	$-0.154016\pi$
$83$	3.82650	+	3.82650i	0.420013	+	0.420013i	−0.465195	+	0.885208i	$0.654016\pi$
$84$	−0.334058	+	0.107966i	−0.0364487	+	0.0117800i
$85$	0.743393	−	2.77438i	0.0806322	−	0.300924i
$86$	−15.4445	+	4.13835i	−1.66543	+	0.446250i
$87$	6.75898	+	3.90230i	0.724638	+	0.418370i
$88$		−	6.15037i		−	0.655631i
$89$	4.91594	+	1.31722i	0.521089	+	0.139625i	0.509770	−	0.860311i	$-0.329730\pi$
$89$	4.91594	+	1.31722i	0.521089	+	0.139625i	0.0113186	+	0.999936i	$0.496397\pi$
$90$	−2.57761			−0.271704
$91$	−1.19131	+	9.46471i	−0.124883	+	0.992171i
$92$	−0.862782			−0.0899512
$93$	6.30283	+	1.68884i	0.653573	+	0.175124i
$94$		−	18.8618i		−	1.94545i
$95$	−10.9850	−	6.34217i	−1.12703	−	0.650693i
$96$	0.723875	−	0.193962i	0.0738802	−	0.0197961i
$97$	−2.57958	+	9.62711i	−0.261916	+	0.977485i	0.702195	+	0.711985i	$0.252204\pi$
$97$	−2.57958	+	9.62711i	−0.261916	+	0.977485i	−0.964111	+	0.265500i	$0.914463\pi$
$98$	−1.63068	+	10.0917i	−0.164724	+	1.01942i
$99$	−1.59480	−	1.59480i	−0.160283	−	0.160283i
$100$	−0.250081			−0.0250081
$101$	6.81498			0.678115			0.339058	−	0.940766i	$-0.389892\pi$
$101$	6.81498			0.678115			0.339058	+	0.940766i	$0.389892\pi$
$102$	1.68042	+	1.68042i	0.166387	+	0.166387i
$103$	−5.66334	+	9.80919i	−0.558025	+	0.966528i	0.439636	+	0.898176i	$0.355107\pi$
$103$	−5.66334	+	9.80919i	−0.558025	+	0.966528i	−0.997661	+	0.0683520i	$0.978226\pi$
$104$	1.72164	−	9.68032i	0.168821	−	0.949233i
$105$	−2.12655	+	4.15754i	−0.207530	+	0.405734i
$106$	−2.27493	−	8.49017i	−0.220961	−	0.824638i
$107$	2.27413	+	3.93890i	0.219848	+	0.380788i	0.954761	−	0.297373i	$-0.0961105\pi$
$107$	2.27413	+	3.93890i	0.219848	+	0.380788i	−0.734913	+	0.678161i	$0.762777\pi$
$108$	0.0663464	−	0.114915i	0.00638418	−	0.0110577i
$109$	−2.02887	−	0.543633i	−0.194330	−	0.0520706i	0.160341	−	0.987062i	$-0.448741\pi$
$109$	−2.02887	−	0.543633i	−0.194330	−	0.0520706i	−0.354671	+	0.934991i	$0.615407\pi$
$110$	4.11077	+	4.11077i	0.391946	+	0.391946i
$111$	−2.03497	−	0.545268i	−0.193151	−	0.0517546i
$112$	2.35378	−	10.9893i	0.222412	−	1.03839i
$113$	−3.95721	−	6.85409i	−0.372263	−	0.644779i	0.617650	−	0.786453i	$-0.288085\pi$
$113$	−3.95721	−	6.85409i	−0.372263	−	0.644779i	−0.989913	+	0.141674i	$0.954751\pi$
$114$	9.08887	−	5.24746i	0.851251	−	0.491470i
$115$	−8.11505	+	8.11505i	−0.756732	+	0.756732i
$116$	0.896867	−	0.517807i	0.0832720	−	0.0480771i
$117$	−2.06370	−	2.95654i	−0.190789	−	0.273333i
$118$			11.4226i			1.05154i
$119$	4.09680	−	1.32406i	0.375553	−	0.121377i
$120$	2.40659	−	4.16834i	0.219691	−	0.380516i
$121$		−	5.91323i		−	0.537566i
$122$	2.36876	−	8.84032i	0.214457	−	0.800365i
$123$	1.83450	+	6.84645i	0.165411	+	0.617324i
$124$	0.612243	−	0.612243i	0.0549811	−	0.0549811i
$125$	−8.59251	+	8.59251i	−0.768538	+	0.768538i
$126$	−2.09931	−	3.24373i	−0.187021	−	0.288974i
$127$	14.3203	+	8.26781i	1.27072	+	0.733650i	0.975123	−	0.221664i	$-0.0711487\pi$
$127$	14.3203	+	8.26781i	1.27072	+	0.733650i	0.295595	+	0.955313i	$0.404482\pi$
$128$	−3.18535	+	11.8879i	−0.281548	+	1.05075i
$129$	−5.47441	−	9.48195i	−0.481995	−	0.834839i
$130$	5.31940	+	7.62081i	0.466542	+	0.668389i
$131$	11.0979	+	6.40737i	0.969628	+	0.559815i	0.899123	−	0.437697i	$-0.144206\pi$
$131$	11.0979	+	6.40737i	0.969628	+	0.559815i	0.0705050	+	0.997511i	$0.477539\pi$
$132$	−0.289076	+	0.0774577i	−0.0251608	+	0.00674183i
$133$	−0.965457	−	18.9891i	−0.0837157	−	1.64656i
$134$	−6.70939	+	3.87367i	−0.579603	+	0.334634i
$135$	−0.456824	−	1.70489i	−0.0393171	−	0.146734i
$136$	−4.28641	+	1.14854i	−0.367556	+	0.0984864i
$137$	8.51271	−	2.28097i	0.727290	−	0.194877i	0.123868	−	0.992299i	$-0.460470\pi$
$137$	8.51271	−	2.28097i	0.727290	−	0.194877i	0.603422	+	0.797422i	$0.293803\pi$
$138$	−2.45762	−	9.17195i	−0.209206	−	0.780768i
$139$	10.9213	−	6.30540i	0.926330	−	0.534817i	0.0406813	−	0.999172i	$-0.487047\pi$
$139$	10.9213	−	6.30540i	0.926330	−	0.534817i	0.885649	+	0.464355i	$0.153714\pi$
$140$	0.336676	+	0.520211i	0.0284543	+	0.0439659i
$141$	12.4756	−	3.34284i	1.05064	−	0.281518i
$142$	9.02028	+	5.20786i	0.756965	+	0.437034i
$143$	−1.42391	+	8.00628i	−0.119074	+	0.669519i
$144$	2.12389	+	3.67868i	0.176991	+	0.306557i
$145$	3.56532	−	13.3060i	0.296084	−	1.10500i
$146$	−5.96304	−	3.44276i	−0.493505	−	0.284925i
$147$	−6.96390	+	0.709963i	−0.574373	+	0.0585568i
$148$	−0.197672	+	0.197672i	−0.0162486	+	0.0162486i
$149$	5.24546	−	5.24546i	0.429725	−	0.429725i	−0.458810	−	0.888535i	$-0.651724\pi$
$149$	5.24546	−	5.24546i	0.429725	−	0.429725i	0.888535	+	0.458810i	$0.151724\pi$
$150$	−0.712352	−	2.65853i	−0.0581633	−	0.217068i
$151$	−3.65054	+	13.6240i	−0.297077	+	1.10871i	0.642477	+	0.766305i	$0.277907\pi$
$151$	−3.65054	+	13.6240i	−0.297077	+	1.10871i	−0.939554	+	0.342401i	$0.888760\pi$
$152$			19.5973i			1.58955i
$153$	−0.813654	+	1.40929i	−0.0657800	+	0.113934i
$154$	−1.82511	+	8.52107i	−0.147072	+	0.686647i
$155$		−	11.5171i		−	0.925078i
$156$	−0.476671	+	0.0409944i	−0.0381642	+	0.00328218i
$157$	−4.64586	+	2.68229i	−0.370780	+	0.214070i	−0.673799	−	0.738915i	$-0.735339\pi$
$157$	−4.64586	+	2.68229i	−0.370780	+	0.214070i	0.303019	+	0.952984i	$0.402005\pi$
$158$	−9.65653	+	9.65653i	−0.768232	+	0.768232i
$159$	5.21242	−	3.00939i	0.413371	−	0.238660i
$160$	−0.661367	−	1.14552i	−0.0522856	−	0.0905614i
$161$	−16.8214	−	3.60295i	−1.32571	−	0.283952i
$162$	1.41061	+	0.377973i	0.110828	+	0.0296963i
$163$	−11.3721	−	11.3721i	−0.890731	−	0.890731i	0.103861	−	0.994592i	$-0.466880\pi$
$163$	−11.3721	−	11.3721i	−0.890731	−	0.890731i	−0.994592	+	0.103861i	$0.966880\pi$
$164$	0.908474	+	0.243425i	0.0709399	+	0.0190083i
$165$	−1.99041	+	3.44750i	−0.154954	+	0.268387i
$166$	3.95140	+	6.84402i	0.306688	+	0.531199i
$167$	1.36025	+	5.07654i	0.105260	+	0.392834i	0.998375	−	0.0569944i	$-0.0181517\pi$
$167$	1.36025	+	5.07654i	0.105260	+	0.392834i	−0.893115	+	0.449829i	$0.851485\pi$
$168$	7.20557	−	0.366351i	0.555922	−	0.0282646i
$169$	−4.48231	+	12.2028i	−0.344793	+	0.938679i
$170$	2.09728	−	3.63259i	0.160854	−	0.278607i
$171$	5.08160	+	5.08160i	0.388600	+	0.388600i
$172$	−1.45283			−0.110777
$173$	5.71254			0.434316			0.217158	−	0.976136i	$-0.430321\pi$
$173$	5.71254			0.434316			0.217158	+	0.976136i	$0.430321\pi$
$174$	8.05934	+	8.05934i	0.610977	+	0.610977i
$175$	−4.87576	−	1.04433i	−0.368573	−	0.0789441i
$176$	2.47959	−	9.25394i	0.186906	−	0.697542i
$177$	−7.55521	+	2.02441i	−0.567884	+	0.152164i
$178$	6.43662	+	3.71618i	0.482445	+	0.278540i
$179$		−	5.98541i		−	0.447371i	−0.974661	−	0.223685i	$-0.928191\pi$
$179$		−	5.98541i		−	0.447371i	0.974661	−	0.223685i	$-0.0718088\pi$
$180$	−0.226226	−	0.0606172i	−0.0168619	−	0.00451814i
$181$	14.3000			1.06291			0.531455	−	0.847086i	$-0.321645\pi$
$181$	14.3000			1.06291			0.531455	+	0.847086i	$0.321645\pi$
$182$	−5.25788	+	12.9008i	−0.389740	+	0.956268i
$183$	6.26701			0.463270
$184$	17.1268	+	4.58913i	1.26261	+	0.338315i
$185$			3.71849i			0.273389i
$186$	8.25252	+	4.76460i	0.605104	+	0.349357i
$187$	3.54515	−	0.949920i	0.259247	−	0.0694650i
$188$	0.443570	−	1.65543i	0.0323507	−	0.120734i
$189$	1.77342	−	1.96341i	0.128997	−	0.142817i
$190$	−13.0984	−	13.0984i	−0.950255	−	0.950255i
$191$	−7.65775			−0.554096			−0.277048	−	0.960856i	$-0.589356\pi$
$191$	−7.65775			−0.554096			−0.277048	+	0.960856i	$0.589356\pi$
$192$	−7.40114			−0.534131
$193$	−4.55803	−	4.55803i	−0.328094	−	0.328094i	0.523767	−	0.851861i	$-0.324526\pi$
$193$	−4.55803	−	4.55803i	−0.328094	−	0.328094i	−0.851861	+	0.523767i	$0.824526\pi$
$194$	−7.27757	+	12.6051i	−0.522499	+	0.904995i
$195$	−4.09784	+	4.86900i	−0.293452	+	0.348676i
$196$	−0.380444	+	0.847362i	−0.0271746	+	0.0605259i
$197$	5.31612	+	19.8400i	0.378758	+	1.41354i	0.847775	+	0.530355i	$0.177941\pi$
$197$	5.31612	+	19.8400i	0.378758	+	1.41354i	−0.469017	+	0.883189i	$0.655392\pi$
$198$	−1.64685	−	2.85244i	−0.117037	−	0.202714i
$199$	3.37252	−	5.84137i	0.239071	−	0.414084i	−0.721377	−	0.692543i	$-0.756490\pi$
$199$	3.37252	−	5.84137i	0.239071	−	0.414084i	0.960448	+	0.278459i	$0.0898237\pi$
$200$	4.96430	+	1.33018i	0.351029	+	0.0940579i
$201$	−3.75123	−	3.75123i	−0.264591	−	0.264591i
$202$	9.61329	+	2.57587i	0.676389	+	0.181238i
$203$	19.6483	−	6.35024i	1.37904	−	0.445699i
$204$	0.107966	+	0.187002i	0.00755913	+	0.0130928i
$205$	10.8344	−	6.25524i	0.756707	−	0.436885i
$206$	−11.6964	+	11.6964i	−0.814926	+	0.814926i
$207$	5.63098	−	3.25105i	0.391381	−	0.225964i
$208$	6.49313	−	13.8711i	0.450217	−	0.961785i
$209$		−	16.2083i		−	1.12115i
$210$	−4.57118	+	5.06090i	−0.315441	+	0.349235i
$211$	8.08382	−	14.0016i	0.556513	−	0.963910i	−0.441271	−	0.897374i	$-0.645472\pi$
$211$	8.08382	−	14.0016i	0.556513	−	0.963910i	0.997784	−	0.0665355i	$-0.0211946\pi$
$212$		−	0.798648i		−	0.0548514i
$213$	−1.84596	+	6.88920i	−0.126483	+	0.472041i
$214$	1.71911	+	6.41582i	0.117516	+	0.438577i
$215$	−13.6648	+	13.6648i	−0.931934	+	0.931934i
$216$	−1.92826	+	1.92826i	−0.131201	+	0.131201i
$217$	14.4935	−	9.38003i	0.983879	−	0.636758i
$218$	−2.65647	−	1.53371i	−0.179919	−	0.103876i
$219$	1.22031	−	4.55425i	0.0824607	−	0.307748i
$220$	0.264114	+	0.457458i	0.0178065	+	0.0308418i
$221$	5.84576	−	0.502744i	0.393228	−	0.0338182i
$222$	−2.66446	−	1.53832i	−0.178827	−	0.103246i
$223$	6.29395	−	1.68646i	0.421474	−	0.112934i	−0.0418472	−	0.999124i	$-0.513324\pi$
$223$	6.29395	−	1.68646i	0.421474	−	0.112934i	0.463321	+	0.886190i	$0.346658\pi$
$224$	0.902908	−	1.76524i	0.0603281	−	0.117945i
$225$	1.63217	−	0.942332i	0.108811	−	0.0628221i
$226$	−2.99144	−	11.1642i	−0.198987	−	0.742631i
$227$	−10.1500	+	2.71970i	−0.673682	+	0.180513i	−0.579413	−	0.815034i	$-0.696718\pi$
$227$	−10.1500	+	2.71970i	−0.673682	+	0.180513i	−0.0942692	+	0.995547i	$0.530051\pi$
$228$	0.921099	−	0.246808i	0.0610013	−	0.0163452i
$229$	1.12133	+	4.18487i	0.0740997	+	0.276544i	0.993028	−	0.117881i	$-0.0376103\pi$
$229$	1.12133	+	4.18487i	0.0740997	+	0.276544i	−0.918928	+	0.394425i	$0.870944\pi$
$230$	−14.5145	+	8.37993i	−0.957055	+	0.552556i
$231$	−5.95950	+	0.302997i	−0.392106	+	0.0199358i
$232$	−20.5577	+	5.50841i	−1.34968	+	0.361645i
$233$	−13.8386	−	7.98973i	−0.906598	−	0.523425i	−0.0272631	−	0.999628i	$-0.508679\pi$
$233$	−13.8386	−	7.98973i	−0.906598	−	0.523425i	−0.879335	+	0.476204i	$0.842013\pi$
$234$	−1.79359	−	4.95056i	−0.117250	−	0.323628i
$235$	−11.3983	−	19.7425i	−0.743545	−	1.28786i
$236$	−0.268625	+	1.00252i	−0.0174860	+	0.0652586i
$237$	−8.09846	−	4.67565i	−0.526052	−	0.303716i
$238$	6.27946	−	0.319265i	0.407037	−	0.0206949i
$239$	−1.84753	+	1.84753i	−0.119507	+	0.119507i	−0.764331	−	0.644824i	$-0.776931\pi$
$239$	−1.84753	+	1.84753i	−0.119507	+	0.119507i	0.644824	+	0.764331i	$0.276931\pi$
$240$	5.30151	−	5.30151i	0.342211	−	0.342211i
$241$	−5.09222	−	19.0044i	−0.328019	−	1.22418i	−0.911242	−	0.411871i	$-0.864875\pi$
$241$	−5.09222	−	19.0044i	−0.328019	−	1.22418i	0.583223	−	0.812312i	$-0.301791\pi$
$242$	2.23504	−	8.34128i	0.143674	−	0.536198i
$243$			1.00000i			0.0641500i
$244$	0.415793	−	0.720175i	0.0266184	−	0.0461045i
$245$	4.39169	+	11.5484i	0.280575	+	0.737797i
$246$			10.3511i			0.659961i
$247$	4.53709	−	25.5108i	0.288688	−	1.62322i
$248$	−15.4100	+	8.89696i	−0.978536	+	0.564958i
$249$	−3.82650	+	3.82650i	−0.242494	+	0.242494i
$250$	−15.3684	+	8.87298i	−0.971986	+	0.561176i
$251$	−3.65679	−	6.33375i	−0.230815	−	0.399783i	0.727234	−	0.686390i	$-0.240806\pi$
$251$	−3.65679	−	6.33375i	−0.230815	−	0.399783i	−0.958048	+	0.286608i	$0.907472\pi$
$252$	−0.107966	−	0.334058i	−0.00680121	−	0.0210437i
$253$	−14.1651	−	3.79552i	−0.890550	−	0.238622i
$254$	17.0754	+	17.0754i	1.07140	+	1.07140i
$255$	2.77438	+	0.743393i	0.173738	+	0.0465530i
$256$	−1.58546	+	2.74610i	−0.0990912	+	0.171631i
$257$	4.71541	+	8.16733i	0.294139	+	0.509464i	0.974784	−	0.223149i	$-0.0716338\pi$
$257$	4.71541	+	8.16733i	0.294139	+	0.509464i	−0.680645	+	0.732613i	$0.738300\pi$
$258$	−4.13835	−	15.4445i	−0.257643	−	0.961535i
$259$	−4.67944	+	3.02849i	−0.290766	+	0.188181i
$260$	0.287645	+	0.793944i	0.0178390	+	0.0492383i
$261$	−3.90230	+	6.75898i	−0.241546	+	0.418370i
$262$	13.2330	+	13.2330i	0.817539	+	0.817539i
$263$	−4.60736			−0.284102			−0.142051	−	0.989859i	$-0.545370\pi$
$263$	−4.60736			−0.284102			−0.142051	+	0.989859i	$0.545370\pi$
$264$	6.15037			0.378529
$265$	−7.51183	−	7.51183i	−0.461448	−	0.461448i
$266$	5.81546	−	27.1512i	0.356569	−	1.66474i
$267$	−1.31722	+	4.91594i	−0.0806127	+	0.300851i
$268$	−0.679954	+	0.182193i	−0.0415348	+	0.0111292i
$269$	−11.7137	−	6.76289i	−0.714195	−	0.412341i	0.0984174	−	0.995145i	$-0.468622\pi$
$269$	−11.7137	−	6.76289i	−0.714195	−	0.412341i	−0.812612	+	0.582805i	$0.801955\pi$
$270$		−	2.57761i		−	0.156868i
$271$	−17.1433	−	4.59354i	−1.04138	−	0.279038i	−0.302697	−	0.953087i	$-0.597887\pi$
$271$	−17.1433	−	4.59354i	−1.04138	−	0.279038i	−0.738687	+	0.674049i	$0.764554\pi$
$272$	−6.91244			−0.419128
$273$	−9.46471	−	1.19131i	−0.572830	−	0.0721013i
$274$	12.8703			0.777522
$275$	−4.10581	−	1.10015i	−0.247590	−	0.0663415i
$276$		−	0.862782i		−	0.0519334i
$277$	10.0049	+	5.77632i	0.601135	+	0.347065i	0.769488	−	0.638661i	$-0.220511\pi$
$277$	10.0049	+	5.77632i	0.601135	+	0.347065i	−0.168353	+	0.985727i	$0.553845\pi$
$278$	17.7890	−	4.76654i	1.06691	−	0.285878i
$279$	−1.68884	+	6.30283i	−0.101108	+	0.377341i
$280$	−3.91626	−	12.1173i	−0.234042	−	0.724150i
$281$	−11.8978	−	11.8978i	−0.709764	−	0.709764i	0.256721	−	0.966486i	$-0.417358\pi$
$281$	−11.8978	−	11.8978i	−0.709764	−	0.709764i	−0.966486	+	0.256721i	$0.917358\pi$
$282$	18.8618			1.12320
$283$	21.6412			1.28644			0.643219	−	0.765682i	$-0.277598\pi$
$283$	21.6412			1.28644			0.643219	+	0.765682i	$0.277598\pi$
$284$	0.669202	+	0.669202i	0.0397099	+	0.0397099i
$285$	6.34217	−	10.9850i	0.375678	−	0.650693i
$286$	−5.03474	+	10.7556i	−0.297711	+	0.635990i
$287$	16.6957	+	8.53975i	0.985518	+	0.504086i
$288$	0.193962	+	0.723875i	0.0114293	+	0.0426548i
$289$	7.17594	+	12.4291i	0.422114	+	0.731123i
$290$	10.0586	−	17.4220i	0.590661	−	1.02305i
$291$	−9.62711	−	2.57958i	−0.564351	−	0.151217i
$292$	−0.442390	−	0.442390i	−0.0258889	−	0.0258889i
$293$	9.50719	+	2.54744i	0.555416	+	0.148823i	0.525600	−	0.850732i	$-0.323841\pi$
$293$	9.50719	+	2.54744i	0.555416	+	0.148823i	0.0298165	+	0.999555i	$0.490508\pi$
$294$	−10.0917	−	1.63068i	−0.588561	−	0.0951033i
$295$	6.90280	+	11.9560i	0.401896	+	0.696105i
$296$	4.97536	−	2.87253i	0.289187	−	0.166962i
$297$	1.59480	−	1.59480i	0.0925397	−	0.0925397i
$298$	9.38196	−	5.41668i	0.543482	−	0.313780i
$299$	−21.2325	−	9.93907i	−1.22791	−	0.574791i
$300$		−	0.250081i		−	0.0144384i
$301$	−28.3254	−	6.06697i	−1.63265	−	0.349694i
$302$	−10.2990	+	17.8384i	−0.592641	+	1.02648i
$303$			6.81498i			0.391510i
$304$	−7.90084	+	29.4863i	−0.453144	+	1.69116i
$305$	−2.86292	−	10.6846i	−0.163930	−	0.611796i
$306$	−1.68042	+	1.68042i	−0.0960634	+	0.0960634i
$307$	−16.2375	+	16.2375i	−0.926725	+	0.926725i	−0.997493	−	0.0707682i	$-0.977455\pi$
$307$	−16.2375	+	16.2375i	−0.926725	+	0.926725i	0.0707682	+	0.997493i	$0.477455\pi$
$308$	−0.360572	+	0.704940i	−0.0205455	+	0.0401677i
$309$	−9.80919	−	5.66334i	−0.558025	−	0.322176i
$310$	4.35316	−	16.2462i	0.247243	−	0.922723i
$311$	−6.35536	−	11.0078i	−0.360379	−	0.624195i	0.627644	−	0.778501i	$-0.284019\pi$
$311$	−6.35536	−	11.0078i	−0.360379	−	0.624195i	−0.988023	+	0.154305i	$0.950686\pi$
$312$	9.68032	+	1.72164i	0.548040	+	0.0974686i
$313$	1.51101	+	0.872380i	0.0854072	+	0.0493099i	0.542095	−	0.840317i	$-0.317631\pi$
$313$	1.51101	+	0.872380i	0.0854072	+	0.0493099i	−0.456688	+	0.889627i	$0.650964\pi$
$314$	−7.56734	+	2.02766i	−0.427049	+	0.114428i
$315$	−4.15754	−	2.12655i	−0.234251	−	0.119818i
$316$	−1.07461	+	0.620425i	−0.0604514	+	0.0349016i
$317$	−6.21636	−	23.1998i	−0.349146	−	1.30303i	−0.887694	−	0.460434i	$-0.847694\pi$
$317$	−6.21636	−	23.1998i	−0.349146	−	1.30303i	0.538548	−	0.842595i	$-0.318973\pi$
$318$	8.49017	−	2.27493i	0.476105	−	0.127572i
$319$	17.0026	−	4.55583i	0.951963	−	0.255078i
$320$	3.38101	+	12.6181i	0.189004	+	0.705374i
$321$	−3.93890	+	2.27413i	−0.219848	+	0.126929i
$322$	−22.3667	−	11.4404i	−1.24645	−	0.637549i
$323$	−11.2961	+	3.02678i	−0.628532	+	0.168415i
$324$	0.114915	+	0.0663464i	0.00638418	+	0.00368591i
$325$	−6.15435	−	2.88089i	−0.341382	−	0.159803i
$326$	−11.7433	−	20.3400i	−0.650400	−	1.12653i
$327$	0.543633	−	2.02887i	0.0300630	−	0.112197i
$328$	−16.7391	−	9.66433i	−0.924263	−	0.533623i
$329$	15.5612	−	30.4230i	0.857916	−	1.67728i
$330$	−4.11077	+	4.11077i	−0.226290	+	0.226290i
$331$	−10.9866	+	10.9866i	−0.603879	+	0.603879i	−0.941340	−	0.337461i	$-0.890432\pi$
$331$	−10.9866	+	10.9866i	−0.603879	+	0.603879i	0.337461	+	0.941340i	$0.390432\pi$
$332$	0.185849	+	0.693597i	0.0101998	+	0.0380661i
$333$	0.545268	−	2.03497i	0.0298805	−	0.111516i
$334$			7.67517i			0.419967i
$335$	−4.68178	+	8.10908i	−0.255793	+	0.443046i
$336$	10.9893	+	2.35378i	0.599516	+	0.128409i
$337$		−	4.66674i		−	0.254213i	−0.991889	−	0.127107i	$-0.959431\pi$
$337$		−	4.66674i		−	0.254213i	0.991889	−	0.127107i	$-0.0405691\pi$
$338$	−10.9351	+	15.5193i	−0.594793	+	0.844137i
$339$	6.85409	−	3.95721i	0.372263	−	0.214926i
$340$	0.269497	−	0.269497i	0.0146155	−	0.0146155i
$341$	12.7451	−	7.35839i	0.690187	−	0.398479i
$342$	5.24746	+	9.08887i	0.283750	+	0.491470i
$343$	−10.9560	+	14.9321i	−0.591567	+	0.806256i
$344$	28.8397	+	7.72757i	1.55493	+	0.416643i
$345$	−8.11505	−	8.11505i	−0.436900	−	0.436900i
$346$	8.05818	+	2.15918i	0.433211	+	0.116078i
$347$	16.7637	−	29.0355i	0.899921	−	1.55871i	0.0723277	−	0.997381i	$-0.476957\pi$
$347$	16.7637	−	29.0355i	0.899921	−	1.55871i	0.827593	−	0.561328i	$-0.189709\pi$
$348$	0.517807	+	0.896867i	0.0277573	+	0.0480771i
$349$	1.15161	+	4.29785i	0.0616440	+	0.230059i	0.989874	−	0.141948i	$-0.0453365\pi$
$349$	1.15161	+	4.29785i	0.0616440	+	0.230059i	−0.928230	+	0.372007i	$0.878670\pi$
$350$	−6.48309	−	3.31606i	−0.346536	−	0.177251i
$351$	2.95654	−	2.06370i	0.157809	−	0.110152i
$352$	0.845106	−	1.46377i	0.0450443	−	0.0780190i
$353$	19.3433	+	19.3433i	1.02954	+	1.02954i	0.999550	+	0.0299886i	$0.00954711\pi$
$353$	19.3433	+	19.3433i	1.02954	+	1.02954i	0.0299886	+	0.999550i	$0.490453\pi$
$354$	−11.4226			−0.607107
$355$	12.5886			0.668134
$356$	0.477524	+	0.477524i	0.0253087	+	0.0253087i
$357$	1.32406	+	4.09680i	0.0700769	+	0.216826i
$358$	2.26232	−	8.44310i	0.119567	−	0.446232i
$359$	−31.7614	+	8.51045i	−1.67630	+	0.449164i	−0.966799	−	0.255537i	$-0.917748\pi$
$359$	−31.7614	+	8.51045i	−1.67630	+	0.449164i	−0.709505	+	0.704701i	$0.751081\pi$
$360$	4.16834	+	2.40659i	0.219691	+	0.126839i
$361$			32.6453i			1.71817i
$362$	20.1718	+	5.40501i	1.06020	+	0.284081i
$363$	5.91323			0.310364
$364$	−0.764849	+	1.00860i	−0.0400890	+	0.0528651i
$365$	−8.32196			−0.435591
$366$	8.84032	+	2.36876i	0.462091	+	0.123817i
$367$			13.1452i			0.686173i	0.939304	+	0.343086i	$0.111472\pi$
$367$			13.1452i			0.686173i	−0.939304	+	0.343086i	$0.888528\pi$
$368$	23.9192	+	13.8097i	1.24687	+	0.719883i
$369$	−6.84645	+	1.83450i	−0.356412	+	0.0955003i
$370$	−1.40549	+	5.24535i	−0.0730678	+	0.272693i
$371$	3.33513	−	15.5710i	0.173152	−	0.808407i
$372$	0.612243	+	0.612243i	0.0317433	+	0.0317433i
$373$	−13.5493			−0.701556			−0.350778	−	0.936459i	$-0.614083\pi$
$373$	−13.5493			−0.701556			−0.350778	+	0.936459i	$0.614083\pi$
$374$	5.35988			0.277153
$375$	−8.59251	−	8.59251i	−0.443715	−	0.443715i
$376$	−17.6104	+	30.5021i	−0.908186	+	1.57302i
$377$	28.0364	−	2.41117i	1.44395	−	0.124181i
$378$	3.24373	−	2.09931i	0.166839	−	0.107977i
$379$	3.10819	+	11.5999i	0.159657	+	0.595848i	0.998661	+	0.0517233i	$0.0164714\pi$
$379$	3.10819	+	11.5999i	0.159657	+	0.595848i	−0.839005	+	0.544124i	$0.816862\pi$
$380$	−0.841560	−	1.45762i	−0.0431711	−	0.0747745i
$381$	−8.26781	+	14.3203i	−0.423573	+	0.733650i
$382$	−10.8021	−	2.89442i	−0.552685	−	0.148091i
$383$	5.62895	+	5.62895i	0.287626	+	0.287626i	0.836141	−	0.548515i	$-0.184807\pi$
$383$	5.62895	+	5.62895i	0.287626	+	0.287626i	−0.548515	+	0.836141i	$0.684807\pi$
$384$	−11.8879	−	3.18535i	−0.606651	−	0.162552i
$385$	3.23902	+	10.0219i	0.165076	+	0.510762i
$386$	−4.70680	−	8.15242i	−0.239570	−	0.414947i
$387$	9.48195	−	5.47441i	0.481995	−	0.278280i
$388$	−0.935156	+	0.935156i	−0.0474754	+	0.0474754i
$389$	26.9226	−	15.5438i	1.36503	−	0.788100i	0.374742	−	0.927129i	$-0.377731\pi$
$389$	26.9226	−	15.5438i	1.36503	−	0.788100i	0.990288	+	0.139029i	$0.0443981\pi$
$390$	−7.62081	+	5.31940i	−0.385895	+	0.269358i
$391$			10.5809i			0.535100i
$392$	12.0592	−	14.7972i	0.609082	−	0.747371i
$393$	−6.40737	+	11.0979i	−0.323209	+	0.559815i
$394$			29.9960i			1.51118i
$395$	−4.27189	+	15.9429i	−0.214942	+	0.802176i
$396$	−0.0774577	−	0.289076i	−0.00389240	−	0.0145266i
$397$	−5.72844	+	5.72844i	−0.287502	+	0.287502i	−0.836092	−	0.548590i	$-0.815165\pi$
$397$	−5.72844	+	5.72844i	−0.287502	+	0.287502i	0.548590	+	0.836092i	$0.315165\pi$
$398$	6.96519	−	6.96519i	0.349134	−	0.349134i
$399$	18.9891	−	0.965457i	0.950643	−	0.0483333i
$400$	6.93308	+	4.00282i	0.346654	+	0.200141i
$401$	−4.32020	+	16.1232i	−0.215740	+	0.805154i	0.770164	+	0.637846i	$0.220174\pi$
$401$	−4.32020	+	16.1232i	−0.215740	+	0.805154i	−0.985905	+	0.167309i	$0.946492\pi$
$402$	−3.87367	−	6.70939i	−0.193201	−	0.334634i
$403$	22.1199	−	8.01401i	1.10187	−	0.399206i
$404$	0.783145	+	0.452149i	0.0389629	+	0.0224952i
$405$	1.70489	−	0.456824i	0.0847166	−	0.0226998i
$406$	30.1164	−	1.53120i	1.49465	−	0.0759922i
$407$	−4.11496	+	2.37577i	−0.203971	+	0.117763i
$408$	−1.14854	−	4.28641i	−0.0568611	−	0.212209i
$409$	16.8910	−	4.52593i	0.835206	−	0.223793i	0.184223	−	0.982885i	$-0.441023\pi$
$409$	16.8910	−	4.52593i	0.835206	−	0.223793i	0.650984	+	0.759092i	$0.274357\pi$
$410$	17.6475	−	4.72862i	0.871546	−	0.233530i
$411$	2.28097	+	8.51271i	0.112512	+	0.419901i
$412$	−1.30161	+	0.751484i	−0.0641256	+	0.0370229i
$413$	−9.42380	+	18.4241i	−0.463715	+	0.906591i
$414$	9.17195	−	2.45762i	0.450777	−	0.120785i
$415$	8.27179	+	4.77572i	0.406046	+	0.234431i
$416$	1.73989	−	2.06732i	0.0853052	−	0.101359i
$417$	6.30540	+	10.9213i	0.308777	+	0.534817i
$418$	6.12628	−	22.8636i	0.299646	−	1.11829i
$419$	12.1131	+	6.99350i	0.591764	+	0.341655i	0.765795	−	0.643085i	$-0.222346\pi$
$419$	12.1131	+	6.99350i	0.591764	+	0.341655i	−0.174031	+	0.984740i	$0.555679\pi$
$420$	−0.520211	+	0.336676i	−0.0253837	+	0.0164281i
$421$	11.2239	−	11.2239i	0.547020	−	0.547020i	−0.378558	−	0.925578i	$-0.623580\pi$
$421$	11.2239	−	11.2239i	0.547020	−	0.547020i	0.925578	+	0.378558i	$0.123580\pi$
$422$	16.6954	−	16.6954i	0.812718	−	0.812718i
$423$	3.34284	+	12.4756i	0.162534	+	0.606586i
$424$	−4.24800	+	15.8538i	−0.206301	+	0.769926i
$425$			3.06693i			0.148768i
$426$	−5.20786	+	9.02028i	−0.252322	+	0.437034i
$427$	11.1140	−	12.3047i	0.537846	−	0.595467i
$428$			0.603520i			0.0291722i
$429$	−8.00628	−	1.42391i	−0.386547	−	0.0687471i
$430$	−24.4407	+	14.1109i	−1.17864	+	0.680486i
$431$	−20.5510	+	20.5510i	−0.989905	+	0.989905i	−0.999950	−	0.0100445i	$-0.996803\pi$
$431$	−20.5510	+	20.5510i	−0.989905	+	0.989905i	0.0100445	+	0.999950i	$0.496803\pi$
$432$	−3.67868	+	2.12389i	−0.176991	+	0.102186i
$433$	−14.2229	−	24.6348i	−0.683508	−	1.18387i	−0.973903	−	0.226964i	$-0.927120\pi$
$433$	−14.2229	−	24.6348i	−0.683508	−	1.18387i	0.290395	−	0.956907i	$-0.406213\pi$
$434$	23.9900	−	7.75346i	1.15156	−	0.372178i
$435$	13.3060	+	3.56532i	0.637972	+	0.170944i
$436$	−0.197080	−	0.197080i	−0.00943841	−	0.00943841i
$437$	45.1349	+	12.0939i	2.15910	+	0.578528i
$438$	3.44276	−	5.96304i	0.164502	−	0.284925i
$439$	−16.3048	−	28.2408i	−0.778186	−	1.34786i	−0.932986	−	0.359912i	$-0.882807\pi$
$439$	−16.3048	−	28.2408i	−0.778186	−	1.34786i	0.154800	−	0.987946i	$-0.450527\pi$
$440$	−2.80963	−	10.4857i	−0.133944	−	0.499886i
$441$	−0.709963	−	6.96390i	−0.0338078	−	0.331614i
$442$	8.43613	+	1.50036i	0.401266	+	0.0713649i
$443$	−6.08812	+	10.5449i	−0.289255	+	0.501005i	−0.973632	−	0.228124i	$-0.926741\pi$
$443$	−6.08812	+	10.5449i	−0.289255	+	0.501005i	0.684377	+	0.729128i	$0.260074\pi$
$444$	−0.197672	−	0.197672i	−0.00938112	−	0.00938112i
$445$	8.98287			0.425829
$446$	9.51577			0.450585
$447$	5.24546	+	5.24546i	0.248102	+	0.248102i
$448$	−13.1253	+	14.5315i	−0.620113	+	0.686547i
$449$	−0.322297	+	1.20283i	−0.0152101	+	0.0567650i	−0.973114	−	0.230325i	$-0.926021\pi$
$449$	−0.322297	+	1.20283i	−0.0152101	+	0.0567650i	0.957904	+	0.287090i	$0.0926878\pi$
$450$	2.65853	−	0.712352i	0.125324	−	0.0335806i
$451$	13.8444	+	7.99306i	0.651906	+	0.376378i
$452$		−	1.05019i		−	0.0493966i
$453$	−13.6240	−	3.65054i	−0.640112	−	0.171517i
$454$	−15.3458			−0.720212
$455$	2.29265	+	16.6805i	0.107481	+	0.781994i
$456$	−19.5973			−0.917726
$457$	−7.36967	−	1.97470i	−0.344738	−	0.0923724i	0.0822955	−	0.996608i	$-0.473775\pi$
$457$	−7.36967	−	1.97470i	−0.344738	−	0.0923724i	−0.427034	+	0.904236i	$0.640442\pi$
$458$			6.32707i			0.295644i
$459$	−1.40929	−	0.813654i	−0.0657800	−	0.0379781i
$460$	−1.47095	+	0.394139i	−0.0685833	+	0.0183768i
$461$	0.143143	−	0.534215i	0.00666682	−	0.0248809i	−0.962512	−	0.271238i	$-0.912567\pi$
$461$	0.143143	−	0.534215i	0.00666682	−	0.0248809i	0.969179	+	0.246357i	$0.0792336\pi$
$462$	−8.52107	−	1.82511i	−0.396436	−	0.0849120i
$463$	28.5117	+	28.5117i	1.32505	+	1.32505i	0.909627	+	0.415426i	$0.136367\pi$
$463$	28.5117	+	28.5117i	1.32505	+	1.32505i	0.415426	+	0.909627i	$0.363633\pi$
$464$	−33.1522			−1.53905
$465$	11.5171			0.534094
$466$	−16.5010	−	16.5010i	−0.764396	−	0.764396i
$467$	15.3705	−	26.6225i	0.711262	−	1.23194i	−0.253121	−	0.967435i	$-0.581457\pi$
$467$	15.3705	−	26.6225i	0.711262	−	1.23194i	0.964384	−	0.264508i	$-0.0852095\pi$
$468$	−0.0409944	−	0.476671i	−0.00189497	−	0.0220341i
$469$	−14.0177	+	0.712699i	−0.647277	+	0.0329094i
$470$	−8.61652	−	32.1573i	−0.397450	−	1.48330i
$471$	−2.68229	−	4.64586i	−0.123593	−	0.214070i
$472$	10.6648	−	18.4720i	0.490887	−	0.850241i
$473$	−23.8524	−	6.39123i	−1.09673	−	0.293869i
$474$	−9.65653	−	9.65653i	−0.443539	−	0.443539i
$475$	13.0826	+	3.50546i	0.600269	+	0.160842i
$476$	0.558632	+	0.119652i	0.0256048	+	0.00548426i
$477$	3.00939	+	5.21242i	0.137790	+	0.238660i
$478$	−3.30447	+	1.90784i	−0.151143	+	0.0872624i
$479$	3.20616	−	3.20616i	0.146493	−	0.146493i	−0.630056	−	0.776550i	$-0.716968\pi$
$479$	3.20616	−	3.20616i	0.146493	−	0.146493i	0.776550	+	0.630056i	$0.216968\pi$
$480$	1.14552	−	0.661367i	0.0522856	−	0.0301871i
$481$	−7.14174	+	2.58745i	−0.325635	+	0.117978i
$482$		−	28.7326i		−	1.30873i
$483$	3.60295	−	16.8214i	0.163940	−	0.765401i
$484$	0.392321	−	0.679520i	0.0178328	−	0.0308873i
$485$			17.5916i			0.798792i
$486$	−0.377973	+	1.41061i	−0.0171452	+	0.0639867i
$487$	5.72908	+	21.3812i	0.259609	+	0.968876i	0.965468	+	0.260523i	$0.0838949\pi$
$487$	5.72908	+	21.3812i	0.259609	+	0.968876i	−0.705858	+	0.708353i	$0.749438\pi$
$488$	−12.0844	+	12.0844i	−0.547035	+	0.547035i
$489$	11.3721	−	11.3721i	0.514264	−	0.514264i
$490$	1.83001	+	17.9502i	0.0826713	+	0.810907i
$491$	−23.7750	−	13.7265i	−1.07295	−	0.619469i	−0.143965	−	0.989583i	$-0.545985\pi$
$491$	−23.7750	−	13.7265i	−1.07295	−	0.619469i	−0.928986	+	0.370114i	$0.879319\pi$
$492$	−0.243425	+	0.908474i	−0.0109744	+	0.0409572i
$493$	−6.35024	−	10.9989i	−0.286000	−	0.495367i
$494$	16.0425	−	34.2710i	0.721785	−	1.54193i
$495$	−3.44750	−	1.99041i	−0.154954	−	0.0894625i
$496$	−26.7730	+	7.17381i	−1.20214	+	0.322114i
$497$	10.2527	+	15.8418i	0.459896	+	0.710603i
$498$	−6.84402	+	3.95140i	−0.306688	+	0.177066i
$499$	8.08079	+	30.1579i	0.361746	+	1.35005i	0.871779	+	0.489900i	$0.162967\pi$
$499$	8.08079	+	30.1579i	0.361746	+	1.35005i	−0.510033	+	0.860155i	$0.670367\pi$
$500$	−1.55749	+	0.417329i	−0.0696532	+	0.0186635i
$501$	−5.07654	+	1.36025i	−0.226803	+	0.0607717i
$502$	−2.76433	−	10.3166i	−0.123378	−	0.460454i
$503$	−33.4708	+	19.3244i	−1.49239	+	0.861633i	−0.999962	−	0.00871978i	$-0.997224\pi$
$503$	−33.4708	+	19.3244i	−1.49239	+	0.861633i	−0.492429	+	0.870352i	$0.663891\pi$
$504$	0.366351	+	7.20557i	0.0163186	+	0.320962i
$505$	11.6188	−	3.11324i	0.517029	−	0.138537i
$506$	−18.5468	−	10.7080i	−0.824507	−	0.476029i
$507$	−12.2028	−	4.48231i	−0.541946	−	0.199066i
$508$	1.09708	+	1.90020i	0.0486750	+	0.0843076i
$509$	2.14731	−	8.01388i	0.0951779	−	0.355209i	−0.901868	−	0.432011i	$-0.857804\pi$
$509$	2.14731	−	8.01388i	0.0951779	−	0.355209i	0.997046	+	0.0768019i	$0.0244709\pi$
$510$	3.63259	+	2.09728i	0.160854	+	0.0928691i
$511$	−6.77775	−	10.4726i	−0.299830	−	0.463279i
$512$	14.1307	−	14.1307i	0.624493	−	0.624493i
$513$	−5.08160	+	5.08160i	−0.224358	+	0.224358i
$514$	3.56459	+	13.3032i	0.157227	+	0.586781i
$515$	−5.17429	+	19.3107i	−0.228007	+	0.850932i
$516$		−	1.45283i		−	0.0639572i
$517$	14.5650	−	25.2273i	0.640567	−	1.10950i
$518$	−7.74556	+	2.50333i	−0.340321	+	0.109990i
$519$			5.71254i			0.250753i
$520$	−1.48699	−	17.2904i	−0.0652090	−	0.758232i
$521$	23.3799	−	13.4984i	1.02429	−	0.591375i	0.108948	−	0.994047i	$-0.465252\pi$
$521$	23.3799	−	13.4984i	1.02429	−	0.591375i	0.915344	+	0.402672i	$0.131918\pi$
$522$	−8.05934	+	8.05934i	−0.352748	+	0.352748i
$523$	5.97993	−	3.45251i	0.261484	−	0.150968i	−0.363527	−	0.931584i	$-0.618428\pi$
$523$	5.97993	−	3.45251i	0.261484	−	0.150968i	0.625011	+	0.780616i	$0.285094\pi$
$524$	0.850212	+	1.47261i	0.0371417	+	0.0643313i
$525$	1.04433	−	4.87576i	0.0455784	−	0.212796i
$526$	−6.49920	−	1.74145i	−0.283378	−	0.0759310i
$527$	−7.50838	−	7.50838i	−0.327070	−	0.327070i
$528$	9.25394	+	2.47959i	0.402726	+	0.107910i
$529$	9.63866	−	16.6946i	0.419072	−	0.725854i
$530$	−7.75702	−	13.4356i	−0.336944	−	0.583603i
$531$	−2.02441	−	7.55521i	−0.0878520	−	0.327868i
$532$	1.14891	−	2.24619i	0.0498116	−	0.0973847i
$533$	19.5528	+	16.4560i	0.846925	+	0.712788i
$534$	−3.71618	+	6.43662i	−0.160815	+	0.278540i
$535$	5.67652	+	5.67652i	0.245417	+	0.245417i
$536$	14.4667			0.624865
$537$	5.98541			0.258290
$538$	−13.9673	−	13.9673i	−0.602172	−	0.602172i
$539$	−9.97378	+	12.2383i	−0.429601	+	0.527140i
$540$	0.0606172	−	0.226226i	0.00260855	−	0.00973524i
$541$	3.68111	−	0.986350i	0.158263	−	0.0424065i	−0.178817	−	0.983882i	$-0.557227\pi$
$541$	3.68111	−	0.986350i	0.158263	−	0.0424065i	0.337081	+	0.941476i	$0.390560\pi$
$542$	−22.4464	−	12.9594i	−0.964155	−	0.556655i
$543$			14.3000i			0.613672i
$544$	−1.17797	−	0.315635i	−0.0505049	−	0.0135328i
$545$	−3.70734			−0.158805
$546$	−12.9008	−	5.25788i	−0.552102	−	0.225016i
$547$	6.54169			0.279702			0.139851	−	0.990173i	$-0.455338\pi$
$547$	6.54169			0.279702			0.139851	+	0.990173i	$0.455338\pi$
$548$	1.12957	+	0.302669i	0.0482530	+	0.0129294i
$549$			6.26701i			0.267469i
$550$	−5.37588	−	3.10377i	−0.229228	−	0.132345i
$551$	−54.1763	+	14.5165i	−2.30799	+	0.618424i
$552$	−4.58913	+	17.1268i	−0.195326	+	0.728967i
$553$	−23.5422	+	7.60872i	−1.00112	+	0.323556i
$554$	11.9297	+	11.9297i	0.506845	+	0.506845i
$555$	−3.71849			−0.157841
$556$	1.67336			0.0709664
$557$	0.230073	+	0.230073i	0.00974850	+	0.00974850i	0.711964	−	0.702216i	$-0.247806\pi$
$557$	0.230073	+	0.230073i	0.00974850	+	0.00974850i	−0.702216	+	0.711964i	$0.747806\pi$
$558$	−4.76460	+	8.25252i	−0.201701	+	0.349357i
$559$	−35.7532	−	16.7363i	−1.51220	−	0.707870i
$560$	−1.00724	−	19.8108i	−0.0425635	−	0.837160i
$561$	0.949920	+	3.54515i	0.0401056	+	0.149676i
$562$	−12.2862	−	21.2803i	−0.518261	−	0.897654i
$563$	1.18117	−	2.04585i	0.0497804	−	0.0862222i	−0.840062	−	0.542491i	$-0.817481\pi$
$563$	1.18117	−	2.04585i	0.0497804	−	0.0862222i	0.889842	+	0.456269i	$0.150815\pi$
$564$	1.65543	+	0.443570i	0.0697060	+	0.0186777i
$565$	−9.87772	−	9.87772i	−0.415559	−	0.415559i
$566$	30.5274	+	8.17980i	1.28316	+	0.343823i
$567$	1.96341	+	1.77342i	0.0824555	+	0.0744766i
$568$	−9.72468	−	16.8436i	−0.408038	−	0.706743i
$569$	−5.30051	+	3.06025i	−0.222209	+	0.128292i	−0.606973	−	0.794723i	$-0.707616\pi$
$569$	−5.30051	+	3.06025i	−0.222209	+	0.128292i	0.384764	+	0.923015i	$0.374283\pi$
$570$	13.0984	−	13.0984i	0.548630	−	0.548630i
$571$	34.6029	−	19.9780i	1.44808	−	0.836052i	0.449718	−	0.893171i	$-0.351525\pi$
$571$	34.6029	−	19.9780i	1.44808	−	0.836052i	0.998367	+	0.0571186i	$0.0181913\pi$
$572$	−0.694817	+	0.825573i	−0.0290518	+	0.0345189i
$573$		−	7.65775i		−	0.319907i
$574$	20.3234	+	18.3568i	0.848284	+	0.766199i
$575$	6.12714	−	10.6125i	0.255519	−	0.442572i
$576$		−	7.40114i		−	0.308381i
$577$	−5.69221	+	21.2436i	−0.236970	+	0.884383i	0.740281	+	0.672297i	$0.234692\pi$
$577$	−5.69221	+	21.2436i	−0.236970	+	0.884383i	−0.977251	+	0.212086i	$0.931974\pi$
$578$	5.42461	+	20.2449i	0.225634	+	0.842078i
$579$	4.55803	−	4.55803i	0.189425	−	0.189425i
$580$	1.29251	−	1.29251i	0.0536687	−	0.0536687i
$581$	0.726999	+	14.2990i	0.0301610	+	0.593221i
$582$	−12.6051	−	7.27757i	−0.522499	−	0.301665i
$583$	3.51339	−	13.1121i	0.145510	−	0.543049i
$584$	6.42870	+	11.1348i	0.266021	+	0.460763i
$585$	−4.86900	−	4.09784i	−0.201308	−	0.169425i
$586$	12.4481	+	7.18692i	0.514226	+	0.296889i
$587$	−24.8029	+	6.64591i	−1.02372	+	0.274306i	−0.731353	−	0.681999i	$-0.761111\pi$
$587$	−24.8029	+	6.64591i	−1.02372	+	0.274306i	−0.292371	+	0.956305i	$0.594444\pi$
$588$	−0.847362	−	0.380444i	−0.0349446	−	0.0156892i
$589$	−40.6105	+	23.4465i	−1.67332	+	0.966094i
$590$	5.21814	+	19.4743i	0.214827	+	0.801746i
$591$	−19.8400	+	5.31612i	−0.816110	+	0.218676i
$592$	8.64409	−	2.31618i	0.355270	−	0.0951943i
$593$	0.190725	+	0.711795i	0.00783213	+	0.0292299i	0.969731	−	0.244174i	$-0.0785170\pi$
$593$	0.190725	+	0.711795i	0.00783213	+	0.0292299i	−0.961899	+	0.273404i	$0.911850\pi$
$594$	2.85244	−	1.64685i	0.117037	−	0.0675713i
$595$	6.37972	−	4.12890i	0.261543	−	0.169268i
$596$	0.950801	−	0.254766i	0.0389463	−	0.0104356i
$597$	5.84137	+	3.37252i	0.239071	+	0.138028i
$598$	−26.1942	−	22.0455i	−1.07116	−	0.901507i
$599$	−8.17923	−	14.1669i	−0.334194	−	0.578842i	0.649135	−	0.760673i	$-0.275131\pi$
$599$	−8.17923	−	14.1669i	−0.334194	−	0.578842i	−0.983330	+	0.181831i	$0.941798\pi$
$600$	−1.33018	+	4.96430i	−0.0543043	+	0.202667i
$601$	2.40336	+	1.38758i	0.0980349	+	0.0566005i	0.548216	−	0.836337i	$-0.315307\pi$
$601$	2.40336	+	1.38758i	0.0980349	+	0.0566005i	−0.450181	+	0.892937i	$0.648641\pi$
$602$	−37.6630	−	19.2644i	−1.53503	−	0.785157i
$603$	3.75123	−	3.75123i	0.152762	−	0.152762i
$604$	−1.32341	+	1.32341i	−0.0538486	+	0.0538486i
$605$	−2.70130	−	10.0814i	−0.109824	−	0.409867i
$606$	−2.57587	+	9.61329i	−0.104638	+	0.390513i
$607$		−	1.50128i		−	0.0609351i	−0.999536	−	0.0304676i	$-0.990300\pi$
$607$		−	1.50128i		−	0.0609351i	0.999536	−	0.0304676i	$-0.00969963\pi$
$608$	−2.69281	+	4.66408i	−0.109208	+	0.189153i
$609$	6.35024	+	19.6483i	0.257325	+	0.796190i
$610$		−	16.1539i		−	0.654051i
$611$	29.9862	−	35.6292i	1.21311	−	1.44140i
$612$	−0.187002	+	0.107966i	−0.00755913	+	0.00436426i
$613$	0.0719018	−	0.0719018i	0.00290408	−	0.00290408i	−0.705653	−	0.708557i	$-0.749346\pi$
$613$	0.0719018	−	0.0719018i	0.00290408	−	0.00290408i	0.708557	+	0.705653i	$0.249346\pi$
$614$	−29.0422	+	16.7675i	−1.17205	+	0.676682i
$615$	6.25524	+	10.8344i	0.252236	+	0.436885i
$616$	10.9072	−	12.0757i	0.439463	−	0.486544i
$617$	−33.4006	−	8.94965i	−1.34466	−	0.360299i	−0.486496	−	0.873683i	$-0.661725\pi$
$617$	−33.4006	−	8.94965i	−1.34466	−	0.360299i	−0.858159	+	0.513383i	$0.828392\pi$
$618$	−11.6964	−	11.6964i	−0.470498	−	0.470498i
$619$	4.56014	+	1.22189i	0.183287	+	0.0491117i	0.349295	−	0.937013i	$-0.386421\pi$
$619$	4.56014	+	1.22189i	0.183287	+	0.0491117i	−0.166008	+	0.986124i	$0.553088\pi$
$620$	0.764120	−	1.32349i	0.0306878	−	0.0531528i
$621$	3.25105	+	5.63098i	0.130460	+	0.225964i
$622$	−4.80430	−	17.9299i	−0.192635	−	0.718924i
$623$	7.31602	+	11.3043i	0.293110	+	0.452896i
$624$	13.8711	+	6.49313i	0.555287	+	0.259933i
$625$	−6.01236	+	10.4137i	−0.240494	+	0.416549i
$626$	1.80171	+	1.80171i	0.0720108	+	0.0720108i
$627$	16.2083			0.647296
$628$	−0.711840			−0.0284055
$629$	2.42420	+	2.42420i	0.0966592	+	0.0966592i
$630$	−5.06090	−	4.57118i	−0.201631	−	0.182120i
$631$	4.26964	−	15.9345i	0.169972	−	0.634343i	−0.827382	−	0.561640i	$-0.810171\pi$
$631$	4.26964	−	15.9345i	0.169972	−	0.634343i	0.997354	−	0.0727032i	$-0.0231626\pi$
$632$	24.6318	−	6.60006i	0.979799	−	0.262536i
$633$	14.0016	+	8.08382i	0.556513	+	0.321303i
$634$		−	35.0755i		−	1.39303i
$635$	28.1914	+	7.55386i	1.11874	+	0.299766i
$636$	0.798648			0.0316685
$637$	−19.1239	+	16.4704i	−0.757718	+	0.652582i
$638$	25.7061			1.01771
$639$	−6.88920	−	1.84596i	−0.272533	−	0.0730249i
$640$			21.7227i			0.858664i
$641$	−9.72481	−	5.61462i	−0.384107	−	0.221764i	0.295497	−	0.955344i	$-0.404515\pi$
$641$	−9.72481	−	5.61462i	−0.384107	−	0.221764i	−0.679604	+	0.733580i	$0.737848\pi$
$642$	−6.41582	+	1.71911i	−0.253212	+	0.0678480i
$643$	10.7511	−	40.1236i	0.423982	−	1.58232i	−0.342155	−	0.939644i	$-0.611157\pi$
$643$	10.7511	−	40.1236i	0.423982	−	1.58232i	0.766136	−	0.642678i	$-0.222177\pi$
$644$	−1.69399	−	1.53007i	−0.0667527	−	0.0602934i
$645$	−13.6648	−	13.6648i	−0.538052	−	0.538052i
$646$	−17.0785			−0.671944
$647$	−28.7294			−1.12947			−0.564735	−	0.825273i	$-0.691021\pi$
$647$	−28.7294			−1.12947			−0.564735	+	0.825273i	$0.691021\pi$
$648$	−1.92826	−	1.92826i	−0.0757491	−	0.0757491i
$649$	−8.82051	+	15.2776i	−0.346235	+	0.599697i
$650$	−7.59250	−	6.38999i	−0.297803	−	0.250636i
$651$	9.38003	+	14.4935i	0.367632	+	0.568043i
$652$	−0.552330	−	2.06132i	−0.0216309	−	0.0807277i
$653$	8.47378	+	14.6770i	0.331605	+	0.574356i	0.982827	−	0.184531i	$-0.0590766\pi$
$653$	8.47378	+	14.6770i	0.331605	+	0.574356i	−0.651222	+	0.758887i	$0.725743\pi$
$654$	1.53371	−	2.65647i	0.0599729	−	0.103876i
$655$	21.8477	+	5.85408i	0.853661	+	0.228738i
$656$	−21.2897	−	21.2897i	−0.831221	−	0.831221i
$657$	4.55425	+	1.22031i	0.177678	+	0.0476087i
$658$	33.4499	−	37.0335i	1.30401	−	1.44371i
$659$	6.53667	+	11.3218i	0.254632	+	0.441036i	0.964796	−	0.263001i	$-0.0847122\pi$
$659$	6.53667	+	11.3218i	0.254632	+	0.441036i	−0.710163	+	0.704037i	$0.751379\pi$
$660$	−0.457458	+	0.264114i	−0.0178065	+	0.0102806i
$661$	−9.42539	+	9.42539i	−0.366605	+	0.366605i	−0.866238	−	0.499632i	$-0.833468\pi$
$661$	−9.42539	+	9.42539i	−0.366605	+	0.366605i	0.499632	+	0.866238i	$0.333468\pi$
$662$	−19.6505	+	11.3452i	−0.763739	+	0.440945i
$663$	0.502744	+	5.84576i	0.0195249	+	0.227031i
$664$		−	14.7569i		−	0.572680i
$665$	−10.3207	−	31.9332i	−0.400218	−	1.23832i
$666$	1.53832	−	2.66446i	0.0596089	−	0.103246i
$667$			50.7463i			1.96490i
$668$	−0.180496	+	0.673620i	−0.00698360	+	0.0260631i
$669$	1.68646	+	6.29395i	0.0652023	+	0.243338i
$670$	−9.66919	+	9.66919i	−0.373553	+	0.373553i
$671$	9.99462	−	9.99462i	0.385838	−	0.385838i
$672$	1.76524	+	0.902908i	0.0680956	+	0.0348304i
$673$	26.6155	+	15.3665i	1.02595	+	0.592334i	0.915823	−	0.401583i	$-0.131540\pi$
$673$	26.6155	+	15.3665i	1.02595	+	0.592334i	0.110130	+	0.993917i	$0.464873\pi$
$674$	1.76390	−	6.58296i	0.0679429	−	0.253566i
$675$	0.942332	+	1.63217i	0.0362704	+	0.0628221i
$676$	−1.32470	+	1.10491i	−0.0509500	+	0.0424964i
$677$	8.46296	+	4.88609i	0.325258	+	0.187788i	0.653734	−	0.756725i	$-0.273202\pi$
$677$	8.46296	+	4.88609i	0.325258	+	0.187788i	−0.328476	+	0.944512i	$0.606535\pi$
$678$	11.1642	−	2.99144i	0.428758	−	0.114885i
$679$	−22.1377	+	14.3273i	−0.849566	+	0.549831i
$680$	−6.78317	+	3.91626i	−0.260123	+	0.150182i
$681$	−2.71970	−	10.1500i	−0.104219	−	0.388951i
$682$	20.7597	−	5.56254i	0.794930	−	0.213001i
$683$	23.6182	−	6.32848i	0.903726	−	0.242153i	0.223110	−	0.974793i	$-0.428379\pi$
$683$	23.6182	−	6.32848i	0.903726	−	0.242153i	0.680616	+	0.732640i	$0.261712\pi$
$684$	0.246808	+	0.921099i	0.00943693	+	0.0352191i
$685$	13.4712	−	7.77761i	0.514709	−	0.297167i
$686$	−21.0986	+	16.9223i	−0.805547	+	0.646097i
$687$	−4.18487	+	1.12133i	−0.159663	+	0.0427815i
$688$	40.2772	+	23.2541i	1.53555	+	0.886553i
$689$	9.20027	−	19.6542i	0.350502	−	0.748767i
$690$	−8.37993	−	14.5145i	−0.319018	−	0.552556i
$691$	9.73031	−	36.3140i	0.370158	−	1.38145i	−0.490133	−	0.871648i	$-0.663052\pi$
$691$	9.73031	−	36.3140i	0.370158	−	1.38145i	0.860291	−	0.509803i	$-0.170282\pi$
$692$	0.656458	+	0.379006i	0.0249548	+	0.0144077i
$693$	−0.302997	−	5.95950i	−0.0115099	−	0.226383i
$694$	34.6217	−	34.6217i	1.31422	−	1.31422i
$695$	15.7391	−	15.7391i	0.597018	−	0.597018i
$696$	−5.50841	−	20.5577i	−0.208796	−	0.779237i
$697$	2.98530	−	11.1413i	0.113076	−	0.422006i
$698$			6.49788i			0.245948i
$699$	7.98973	−	13.8386i	0.302199	−	0.523425i
$700$	−0.491012	−	0.443499i	−0.0185585	−	0.0167627i
$701$			41.9982i			1.58625i	0.609058	+	0.793125i	$0.291548\pi$
$701$			41.9982i			1.58625i	−0.609058	+	0.793125i	$0.708452\pi$
$702$	4.95056	−	1.79359i	0.186847	−	0.0676945i
$703$	13.1117	−	7.57006i	0.494518	−	0.285510i
$704$	−11.8033	+	11.8033i	−0.444855	+	0.444855i
$705$	19.7425	−	11.3983i	0.743545	−	0.429286i
$706$	19.9747	+	34.5971i	0.751756	+	1.30208i
$707$	13.3806	+	12.0858i	0.503229	+	0.454534i
$708$	−1.00252	−	0.268625i	−0.0376770	−	0.0100955i
$709$	13.5329	+	13.5329i	0.508238	+	0.508238i	0.913985	−	0.405748i	$-0.132989\pi$
$709$	13.5329	+	13.5329i	0.508238	+	0.508238i	−0.405748	+	0.913985i	$0.632989\pi$
$710$	17.7577	+	4.75815i	0.666433	+	0.178570i
$711$	4.67565	−	8.09846i	0.175351	−	0.303716i
$712$	−6.93925	−	12.0191i	−0.260060	−	0.450436i
$713$	10.9810	+	40.9816i	0.411242	+	1.53477i
$714$	0.319265	+	6.27946i	0.0119482	+	0.235003i
$715$	1.22985	+	14.3003i	0.0459936	+	0.534801i
$716$	0.397111	−	0.687816i	0.0148407	−	0.0257049i
$717$	−1.84753	−	1.84753i	−0.0689973	−	0.0689973i
$718$	−48.0198			−1.79208
$719$	12.7618			0.475934			0.237967	−	0.971273i	$-0.423519\pi$
$719$	12.7618			0.475934			0.237967	+	0.971273i	$0.423519\pi$
$720$	5.30151	+	5.30151i	0.197575	+	0.197575i
$721$	−28.5153	+	9.21599i	−1.06196	+	0.343221i
$722$	−12.3390	+	46.0499i	−0.459211	+	1.71380i
$723$	19.0044	−	5.09222i	0.706782	−	0.189382i
$724$	1.64329	+	0.948753i	0.0610723	+	0.0352601i
$725$			14.7090i			0.546280i
$726$	8.34128	+	2.23504i	0.309574	+	0.0829500i
$727$	3.92873			0.145708			0.0728542	−	0.997343i	$-0.476789\pi$
$727$	3.92873			0.145708			0.0728542	+	0.997343i	$0.476789\pi$
$728$	20.5475	−	15.9532i	0.761543	−	0.591267i
$729$	−1.00000			−0.0370370
$730$	−11.7391	−	3.14547i	−0.434482	−	0.116419i
$731$			17.8171i			0.658989i
$732$	0.720175	+	0.415793i	0.0266184	+	0.0153682i
$733$	30.7075	−	8.22804i	1.13421	−	0.303910i	0.357587	−	0.933880i	$-0.383600\pi$
$733$	30.7075	−	8.22804i	1.13421	−	0.303910i	0.776619	+	0.629970i	$0.216933\pi$
$734$	−4.96852	+	18.5428i	−0.183391	+	0.684426i
$735$	−11.5484	+	4.39169i	−0.425968	+	0.161990i
$736$	3.44555	+	3.44555i	0.127005	+	0.127005i
$737$	−11.9649			−0.440733
$738$	−10.3511			−0.381029
$739$	−18.1407	−	18.1407i	−0.667317	−	0.667317i	0.289777	−	0.957094i	$-0.406419\pi$
$739$	−18.1407	−	18.1407i	−0.667317	−	0.667317i	−0.957094	+	0.289777i	$0.906419\pi$
$740$	−0.246708	+	0.427311i	−0.00906917	+	0.0157083i
$741$	25.5108	+	4.53709i	0.937164	+	0.166674i
$742$	10.5900	−	20.7041i	0.388771	−	0.760072i
$743$	−3.90299	−	14.5661i	−0.143187	−	0.534380i	−0.999829	−	0.0184698i	$-0.994121\pi$
$743$	−3.90299	−	14.5661i	−0.143187	−	0.534380i	0.856643	−	0.515910i	$-0.172546\pi$
$744$	−8.89696	−	15.4100i	−0.326179	−	0.564958i
$745$	6.54668	−	11.3392i	0.239852	−	0.415436i
$746$	−19.1128	−	5.12126i	−0.699770	−	0.187503i
$747$	−3.82650	−	3.82650i	−0.140004	−	0.140004i
$748$	0.470416	+	0.126047i	0.0172001	+	0.00460875i
$749$	−2.52028	+	11.7667i	−0.0920891	+	0.429944i
$750$	−8.87298	−	15.3684i	−0.323995	−	0.561176i
$751$	−40.3147	+	23.2757i	−1.47110	+	0.849341i	−0.999473	−	0.0324554i	$-0.989667\pi$
$751$	−40.3147	+	23.2757i	−1.47110	+	0.849341i	−0.471629	+	0.881797i	$0.656334\pi$
$752$	−38.7941	+	38.7941i	−1.41468	+	1.41468i
$753$	6.33375	−	3.65679i	0.230815	−	0.133261i
$754$	40.4598	+	7.19576i	1.47346	+	0.262054i
$755$			24.8951i			0.906025i
$756$	0.334058	−	0.107966i	0.0121496	−	0.00392668i
$757$	1.12340	−	1.94578i	0.0408306	−	0.0707207i	−0.844888	−	0.534943i	$-0.820333\pi$
$757$	1.12340	−	1.94578i	0.0408306	−	0.0707207i	0.885719	+	0.464223i	$0.153666\pi$
$758$			17.5378i			0.637002i
$759$	3.79552	−	14.1651i	0.137769	−	0.514159i
$760$	8.95249	+	33.4112i	0.324741	+	1.21195i
$761$	−29.4999	+	29.4999i	−1.06937	+	1.06937i	−0.0719617	+	0.997407i	$0.522926\pi$
$761$	−29.4999	+	29.4999i	−1.06937	+	1.06937i	−0.997407	+	0.0719617i	$0.977074\pi$
$762$	−17.0754	+	17.0754i	−0.618575	+	0.618575i
$763$	−3.01941	−	4.66541i	−0.109310	−	0.168899i
$764$	−0.879993	−	0.508064i	−0.0318370	−	0.0183811i
$765$	−0.743393	+	2.77438i	−0.0268774	+	0.100308i
$766$	5.81268	+	10.0679i	0.210021	+	0.363766i
$767$	−18.1595	+	21.5769i	−0.655703	+	0.779097i
$768$	−2.74610	−	1.58546i	−0.0990912	−	0.0572103i
$769$	−30.8135	+	8.25646i	−1.11116	+	0.297736i	−0.767303	−	0.641285i	$-0.778402\pi$
$769$	−30.8135	+	8.25646i	−1.11116	+	0.297736i	−0.343861	+	0.939020i	$0.611735\pi$
$770$	0.781008	+	15.3612i	0.0281456	+	0.553581i
$771$	−8.16733	+	4.71541i	−0.294139	+	0.169821i
$772$	−0.221378	−	0.826196i	−0.00796758	−	0.0297354i
$773$	31.6927	−	8.49203i	1.13991	−	0.305437i	0.360993	−	0.932569i	$-0.382438\pi$
$773$	31.6927	−	8.49203i	1.13991	−	0.305437i	0.778913	+	0.627132i	$0.215771\pi$
$774$	15.4445	−	4.13835i	0.555143	−	0.148750i
$775$	3.18289	+	11.8787i	0.114333	+	0.426696i
$776$	23.5376	−	13.5895i	0.844951	−	0.487833i
$777$	−3.02849	−	4.67944i	−0.108646	−	0.167874i
$778$	43.8525	−	11.7502i	1.57219	−	0.421267i
$779$	−44.1131	−	25.4687i	−1.58052	−	0.912511i
$780$	−0.793944	+	0.287645i	−0.0284278	+	0.0102994i
$781$	8.04297	+	13.9308i	0.287800	+	0.498484i
$782$	−3.99930	+	14.9256i	−0.143015	+	0.533738i
$783$	−6.75898	−	3.90230i	−0.241546	−	0.139457i
$784$	24.1101	−	17.4023i	0.861076	−	0.621510i
$785$	−6.69534	+	6.69534i	−0.238967	+	0.238967i
$786$	−13.2330	+	13.2330i	−0.472006	+	0.472006i
$787$	−9.81127	−	36.6162i	−0.349734	−	1.30523i	−0.886983	−	0.461802i	$-0.847203\pi$
$787$	−9.81127	−	36.6162i	−0.349734	−	1.30523i	0.537249	−	0.843424i	$-0.319464\pi$
$788$	−0.705411	+	2.63263i	−0.0251292	+	0.0937835i
$789$		−	4.60736i		−	0.164026i
$790$	−12.0520	+	20.8746i	−0.428790	+	0.742686i
$791$	4.38555	−	20.4752i	0.155932	−	0.728014i
$792$			6.15037i			0.218544i
$793$	18.5287	−	12.9332i	0.657973	−	0.459272i
$794$	−10.2458	+	5.91542i	−0.363610	+	0.209930i
$795$	7.51183	−	7.51183i	0.266417	−	0.266417i
$796$	0.775107	−	0.447508i	0.0274729	−	0.0158615i
$797$	−20.1772	−	34.9479i	−0.714712	−	1.23792i	−0.963071	−	0.269249i	$-0.913224\pi$
$797$	−20.1772	−	34.9479i	−0.714712	−	1.23792i	0.248358	−	0.968668i	$-0.420109\pi$
$798$	27.1512	+	5.81546i	0.961140	+	0.205865i
$799$	−20.3017	−	5.43982i	−0.718222	−	0.192447i
$800$	0.998709	+	0.998709i	0.0353097	+	0.0353097i
$801$	−4.91594	−	1.31722i	−0.173696	−	0.0465418i
$802$	−12.1883	+	21.1107i	−0.430382	+	0.745444i
$803$	−5.31697	−	9.20926i	−0.187632	−	0.324988i
$804$	−0.182193	−	0.679954i	−0.00642545	−	0.0239801i
$805$	−30.3246	+	1.54178i	−1.06880	+	0.0543408i
$806$	34.2316	−	2.94397i	1.20576	−	0.103697i
$807$	6.76289	−	11.7137i	0.238065	−	0.412341i
$808$	−13.1410	−	13.1410i	−0.462300	−	0.462300i
$809$	−21.1048			−0.742005			−0.371003	−	0.928632i	$-0.620986\pi$
$809$	−21.1048			−0.742005			−0.371003	+	0.928632i	$0.620986\pi$
$810$	2.57761			0.0905679
$811$	−12.9178	−	12.9178i	−0.453607	−	0.453607i	0.442943	−	0.896550i	$-0.353934\pi$
$811$	−12.9178	−	12.9178i	−0.453607	−	0.453607i	−0.896550	+	0.442943i	$0.853934\pi$
$812$	2.67921	+	0.573855i	0.0940217	+	0.0201384i
$813$	4.59354	−	17.1433i	0.161103	−	0.601243i
$814$	−6.70260	+	1.79596i	−0.234926	+	0.0629482i
$815$	−24.5832	−	14.1931i	−0.861112	−	0.497163i
$816$		−	6.91244i		−	0.241984i
$817$	76.0022	+	20.3647i	2.65898	+	0.712472i
$818$	25.5373			0.892892
$819$	1.19131	−	9.46471i	0.0416277	−	0.330724i
$820$	1.66005			0.0579715
$821$	47.4052	+	12.7022i	1.65445	+	0.443309i	0.960854	−	0.277054i	$-0.0893580\pi$
$821$	47.4052	+	12.7022i	1.65445	+	0.443309i	0.693598	+	0.720363i	$0.256025\pi$
$822$			12.8703i			0.448903i
$823$	17.3304	+	10.0057i	0.604100	+	0.348778i	0.770653	−	0.637255i	$-0.219930\pi$
$823$	17.3304	+	10.0057i	0.604100	+	0.348778i	−0.166553	+	0.986033i	$0.553264\pi$
$824$	29.8350	−	7.99427i	1.03935	−	0.278493i
$825$	1.10015	−	4.10581i	0.0383023	−	0.142946i
$826$	−20.2571	+	22.4273i	−0.704836	+	0.780347i
$827$	−33.6816	−	33.6816i	−1.17122	−	1.17122i	−0.981918	−	0.189306i	$-0.939376\pi$
$827$	−33.6816	−	33.6816i	−1.17122	−	1.17122i	−0.189306	−	0.981918i	$-0.560624\pi$
$828$	0.862782			0.0299837
$829$	−47.3709			−1.64526			−0.822629	−	0.568578i	$-0.807494\pi$
$829$	−47.3709			−1.64526			−0.822629	+	0.568578i	$0.807494\pi$
$830$	9.86320	+	9.86320i	0.342357	+	0.342357i
$831$	−5.77632	+	10.0049i	−0.200378	+	0.347065i
$832$	−21.8818	+	15.2737i	−0.758614	+	0.529520i
$833$	10.3918	+	4.66566i	0.360055	+	0.161656i
$834$	4.76654	+	17.7890i	0.165052	+	0.615981i
$835$	4.63817	+	8.03354i	0.160510	+	0.278012i
$836$	1.07536	−	1.86258i	0.0371921	−	0.0644186i
$837$	−6.30283	−	1.68884i	−0.217858	−	0.0583748i
$838$	14.4436	+	14.4436i	0.498944	+	0.498944i
$839$	−14.4591	−	3.87431i	−0.499184	−	0.133756i	0.000437384	−	1.00000i	$-0.499861\pi$
$839$	−14.4591	−	3.87431i	−0.499184	−	0.133756i	−0.499621	+	0.866244i	$0.666527\pi$
$840$	12.1173	−	3.91626i	0.418088	−	0.135124i
$841$	−15.9559	−	27.6363i	−0.550202	−	0.952977i
$842$	20.0749	−	11.5903i	0.691827	−	0.399427i
$843$	11.8978	−	11.8978i	0.409783	−	0.409783i
$844$	1.85791	−	1.07266i	0.0639519	−	0.0369226i
$845$	−2.06730	+	22.8521i	−0.0711173	+	0.786136i
$846$			18.8618i			0.648482i
$847$	10.4866	−	11.6101i	0.360325	−	0.398928i
$848$	−12.7832	+	22.1412i	−0.438978	+	0.760332i
$849$			21.6412i			0.742726i
$850$	−1.15921	+	4.32625i	−0.0397607	+	0.148389i
$851$	−3.54539	−	13.2316i	−0.121534	−	0.453572i
$852$	−0.669202	+	0.669202i	−0.0229265	+	0.0229265i
$853$	−4.30446	+	4.30446i	−0.147382	+	0.147382i	−0.776947	−	0.629565i	$-0.783233\pi$
$853$	−4.30446	+	4.30446i	−0.147382	+	0.147382i	0.629565	+	0.776947i	$0.283233\pi$
$854$	20.3284	−	13.1564i	0.695625	−	0.450202i
$855$	10.9850	+	6.34217i	0.375678	+	0.216898i
$856$	3.21012	−	11.9803i	0.109719	−	0.409479i
$857$	−2.53847	−	4.39675i	−0.0867124	−	0.150190i	0.819407	−	0.573212i	$-0.194303\pi$
$857$	−2.53847	−	4.39675i	−0.0867124	−	0.150190i	−0.906120	+	0.423022i	$0.860969\pi$
$858$	−10.7556	−	5.03474i	−0.367189	−	0.171883i
$859$	13.0902	+	7.55762i	0.446631	+	0.257863i	0.706406	−	0.707807i	$-0.250315\pi$
$859$	13.0902	+	7.55762i	0.446631	+	0.257863i	−0.259775	+	0.965669i	$0.583648\pi$
$860$	−2.47691	+	0.663686i	−0.0844620	+	0.0226315i
$861$	−8.53975	+	16.6957i	−0.291034	+	0.568989i
$862$	−36.7572	+	21.2218i	−1.25195	+	0.722816i
$863$	−8.82787	−	32.9461i	−0.300504	−	1.12150i	−0.936747	−	0.350008i	$-0.886179\pi$
$863$	−8.82787	−	32.9461i	−0.300504	−	1.12150i	0.636243	−	0.771489i	$-0.280488\pi$
$864$	−0.723875	+	0.193962i	−0.0246267	+	0.00659872i
$865$	9.73925	−	2.60962i	0.331144	−	0.0887298i
$866$	−10.7517	−	40.1260i	−0.365359	−	1.36354i
$867$	−12.4291	+	7.17594i	−0.422114	+	0.243708i
$868$	2.28785	−	0.116321i	0.0776547	−	0.00394818i
$869$	−20.3721	+	5.45870i	−0.691078	+	0.185174i
$870$	17.4220	+	10.0586i	0.590661	+	0.341018i
$871$	−18.8321	−	3.34927i	−0.638100	−	0.113486i
$872$	2.86391	+	4.96044i	0.0969843	+	0.167982i
$873$	2.57958	−	9.62711i	0.0873054	−	0.325828i
$874$	59.0968	+	34.1195i	1.99898	+	1.15411i
$875$	−32.1088	+	1.63250i	−1.08547	+	0.0551885i
$876$	0.442390	−	0.442390i	0.0149470	−	0.0149470i
$877$	11.9907	−	11.9907i	0.404897	−	0.404897i	−0.475058	−	0.879955i	$-0.657573\pi$
$877$	11.9907	−	11.9907i	0.404897	−	0.404897i	0.879955	+	0.475058i	$0.157573\pi$
$878$	−12.3255	−	45.9996i	−0.415967	−	1.55241i
$879$	−2.54744	+	9.50719i	−0.0859232	+	0.320670i
$880$		−	16.9097i		−	0.570025i
$881$	13.1115	−	22.7097i	0.441737	−	0.765111i	−0.556082	−	0.831128i	$-0.687696\pi$
$881$	13.1115	−	22.7097i	0.441737	−	0.765111i	0.997819	+	0.0660169i	$0.0210291\pi$
$882$	1.63068	−	10.0917i	0.0549079	−	0.339806i
$883$		−	46.6268i		−	1.56912i	−0.620054	−	0.784559i	$-0.712889\pi$
$883$		−	46.6268i		−	1.56912i	0.620054	−	0.784559i	$-0.287111\pi$
$884$	0.705123	+	0.330072i	0.0237158	+	0.0111015i
$885$	−11.9560	+	6.90280i	−0.401896	+	0.232035i
$886$	−12.5737	+	12.5737i	−0.422421	+	0.422421i
$887$	41.0807	−	23.7179i	1.37935	−	0.796371i	0.387273	−	0.921965i	$-0.373417\pi$
$887$	41.0807	−	23.7179i	1.37935	−	0.796371i	0.992082	+	0.125594i	$0.0400838\pi$
$888$	2.87253	+	4.97536i	0.0963956	+	0.166962i
$889$	13.4543	+	41.6290i	0.451242	+	1.39619i
$890$	12.6714	+	3.39528i	0.424745	+	0.113810i
$891$	1.59480	+	1.59480i	0.0534278	+	0.0534278i
$892$	0.835162	+	0.223781i	0.0279633	+	0.00749274i
$893$	−46.4092	+	80.3831i	−1.55303	+	2.68992i
$894$	5.41668	+	9.38196i	0.181161	+	0.313780i
$895$	−2.73428	−	10.2045i	−0.0913969	−	0.341098i
$896$	−27.3364	+	17.6918i	−0.913244	+	0.591043i
$897$	9.93907	−	21.2325i	0.331856	−	0.708933i
$898$	−0.909273	+	1.57491i	−0.0303428	+	0.0525553i
$899$	−36.0103	−	36.0103i	−1.20101	−	1.20101i
$900$	0.250081			0.00833604
$901$	−9.79440			−0.326299
$902$	16.5079	+	16.5079i	0.549653	+	0.549653i
$903$	6.06697	−	28.3254i	0.201896	−	0.942610i
$904$	−5.58593	+	20.8470i	−0.185785	+	0.693360i
$905$	24.3799	−	6.53258i	0.810416	−	0.217150i
$906$	−17.8384	−	10.2990i	−0.592641	−	0.342161i
$907$			28.3652i			0.941850i	0.882173	+	0.470925i	$0.156080\pi$
$907$			28.3652i			0.941850i	−0.882173	+	0.470925i	$0.843920\pi$
$908$	−1.34684	−	0.360884i	−0.0446964	−	0.0119764i
$909$	−6.81498			−0.226038
$910$	−3.07073	+	24.3963i	−0.101794	+	0.808730i
$911$	25.8520			0.856515			0.428258	−	0.903657i	$-0.359128\pi$
$911$	25.8520			0.856515			0.428258	+	0.903657i	$0.359128\pi$
$912$	−29.4863	−	7.90084i	−0.976390	−	0.261623i
$913$			12.2050i			0.403926i
$914$	−9.64937	−	5.57106i	−0.319173	−	0.184274i
$915$	10.6846	−	2.86292i	0.353220	−	0.0946451i
$916$	−0.148793	+	0.555302i	−0.00491625	+	0.0183477i
$917$	10.4268	+	32.2615i	0.344322	+	1.06537i
$918$	−1.68042	−	1.68042i	−0.0554622	−	0.0554622i
$919$	7.15708			0.236090			0.118045	−	0.993008i	$-0.462337\pi$
$919$	7.15708			0.236090			0.118045	+	0.993008i	$0.462337\pi$
$920$	31.2958			1.03179
$921$	−16.2375	−	16.2375i	−0.535045	−	0.535045i
$922$	0.403838	−	0.699467i	0.0132997	−	0.0230357i
$923$	8.75958	+	24.1777i	0.288325	+	0.795820i
$924$	−0.704940	−	0.360572i	−0.0231908	−	0.0118619i
$925$	−1.02765	−	3.83523i	−0.0337888	−	0.126102i
$926$	29.4424	+	50.9957i	0.967536	+	1.67582i
$927$	5.66334	−	9.80919i	0.186008	−	0.322176i
$928$	−5.64955	−	1.51379i	−0.185456	−	0.0496927i
$929$	−31.3926	−	31.3926i	−1.02996	−	1.02996i	−0.999537	−	0.0304195i	$-0.990316\pi$
$929$	−31.3926	−	31.3926i	−1.02996	−	1.02996i	−0.0304195	−	0.999537i	$-0.509684\pi$
$930$	16.2462	+	4.35316i	0.532734	+	0.142746i
$931$	31.7800	−	38.9955i	1.04155	−	1.27803i
$932$	−1.06018	−	1.83628i	−0.0347273	−	0.0601495i
$933$	11.0078	−	6.35536i	0.360379	−	0.208065i
$934$	31.7444	−	31.7444i	1.03871	−	1.03871i
$935$	5.61014	−	3.23902i	0.183471	−	0.105927i
$936$	−1.72164	+	9.68032i	−0.0562735	+	0.316411i
$937$			7.95395i			0.259844i	0.991524	+	0.129922i	$0.0414727\pi$
$937$			7.95395i			0.259844i	−0.991524	+	0.129922i	$0.958527\pi$
$938$	−20.0429	−	4.29297i	−0.654425	−	0.140170i
$939$	−0.872380	+	1.51101i	−0.0284691	+	0.0493099i
$940$		−	3.02495i		−	0.0986631i
$941$	−10.6078	+	39.5887i	−0.345803	+	1.29055i	0.545869	+	0.837871i	$0.316200\pi$
$941$	−10.6078	+	39.5887i	−0.345803	+	1.29055i	−0.891671	+	0.452683i	$0.850467\pi$
$942$	−2.02766	−	7.56734i	−0.0660648	−	0.246557i
$943$	−32.5882	+	32.5882i	−1.06122	+	1.06122i
$944$	23.4936	−	23.4936i	0.764651	−	0.764651i
$945$	2.12655	−	4.15754i	0.0691767	−	0.135245i
$946$	−31.2308	−	18.0311i	−1.01540	−	0.586242i
$947$	13.6972	−	51.1188i	0.445100	−	1.66114i	−0.270571	−	0.962700i	$-0.587213\pi$
$947$	13.6972	−	51.1188i	0.445100	−	1.66114i	0.715672	−	0.698437i	$-0.246121\pi$
$948$	−0.620425	−	1.07461i	−0.0201505	−	0.0349016i
$949$	−5.79070	−	15.9832i	−0.187974	−	0.518836i
$950$	17.1295	+	9.88971i	0.555754	+	0.320864i
$951$	23.1998	−	6.21636i	0.752304	−	0.201579i
$952$	−10.4528	−	5.34654i	−0.338778	−	0.173282i
$953$	−32.1309	+	18.5508i	−1.04082	+	0.600920i	−0.920066	−	0.391763i	$-0.871865\pi$
$953$	−32.1309	+	18.5508i	−1.04082	+	0.600920i	−0.120757	+	0.992682i	$0.538532\pi$
$954$	2.27493	+	8.49017i	0.0736537	+	0.274879i
$955$	−13.0556	+	3.49824i	−0.422470	+	0.113201i
$956$	−0.334887	+	0.0897326i	−0.0108310	+	0.00290216i
$957$	4.55583	+	17.0026i	0.147269	+	0.549616i
$958$	5.73450	−	3.31081i	0.185273	−	0.106968i
$959$	20.7591	+	10.6181i	0.670345	+	0.342877i
$960$	−12.6181	+	3.38101i	−0.407248	+	0.109122i
$961$	−10.0267	−	5.78893i	−0.323442	−	0.186740i
$962$	−11.0522	+	0.950506i	−0.356338	+	0.0306456i
$963$	−2.27413	−	3.93890i	−0.0732827	−	0.126929i
$964$	0.675701	−	2.52175i	0.0217629	−	0.0812201i
$965$	−9.85315	−	5.68872i	−0.317184	−	0.183126i
$966$	11.4404	−	22.3667i	0.368089	−	0.719636i
$967$	−18.4234	+	18.4234i	−0.592456	+	0.592456i	−0.938294	−	0.345838i	$-0.887595\pi$
$967$	−18.4234	+	18.4234i	−0.592456	+	0.592456i	0.345838	+	0.938294i	$0.387595\pi$
$968$	−11.4022	+	11.4022i	−0.366481	+	0.366481i
$969$	−3.02678	−	11.2961i	−0.0972342	−	0.362883i
$970$	−6.64913	+	24.8149i	−0.213491	+	0.796758i
$971$		−	30.7246i		−	0.986000i	−0.870029	−	0.493000i	$-0.835900\pi$
$971$		−	30.7246i		−	0.986000i	0.870029	−	0.493000i	$-0.164100\pi$
$972$	−0.0663464	+	0.114915i	−0.00212806	+	0.00368591i
$973$	32.6251	+	6.98791i	1.04591	+	0.224022i
$974$			32.3261i			1.03579i
$975$	2.88089	−	6.15435i	0.0922622	−	0.197097i
$976$	−23.0543	+	13.3104i	−0.737951	+	0.426056i
$977$	6.55679	−	6.55679i	0.209770	−	0.209770i	−0.594400	−	0.804170i	$-0.702610\pi$
$977$	6.55679	−	6.55679i	0.209770	−	0.209770i	0.804170	+	0.594400i	$0.202610\pi$
$978$	20.3400	−	11.7433i	0.650400	−	0.375509i
$979$	5.73924	+	9.94065i	0.183427	+	0.317704i
$980$	−0.261520	+	1.61846i	−0.00835394	+	0.0516997i
$981$	2.02887	+	0.543633i	0.0647768	+	0.0173569i
$982$	−28.3491	−	28.3491i	−0.904656	−	0.904656i
$983$	31.3616	+	8.40332i	1.00028	+	0.268024i	0.721563	−	0.692349i	$-0.243424\pi$
$983$	31.3616	+	8.40332i	1.00028	+	0.268024i	0.278718	+	0.960373i	$0.410091\pi$
$984$	9.66433	−	16.7391i	0.308088	−	0.533623i
$985$	18.1268	+	31.3965i	0.577568	+	1.00038i
$986$	−4.80043	−	17.9155i	−0.152877	−	0.570544i
$987$	30.4230	+	15.5612i	0.968376	+	0.495318i
$988$	2.21393	−	2.63057i	0.0704346	−	0.0836895i
$989$	35.5951	−	61.6526i	1.13186	−	1.96044i
$990$	−4.11077	−	4.11077i	−0.130649	−	0.130649i
$991$	−23.8883			−0.758836			−0.379418	−	0.925225i	$-0.623876\pi$
$991$	−23.8883			−0.758836			−0.379418	+	0.925225i	$0.623876\pi$
$992$	−4.89003			−0.155259
$993$	−10.9866	−	10.9866i	−0.348650	−	0.348650i
$994$	8.47479	+	26.2219i	0.268804	+	0.831709i
$995$	3.08129	−	11.4995i	0.0976835	−	0.364560i
$996$	−0.693597	+	0.185849i	−0.0219775	+	0.00588885i
$997$	−16.3534	−	9.44164i	−0.517918	−	0.299020i	0.218165	−	0.975912i	$-0.429993\pi$
$997$	−16.3534	−	9.44164i	−0.517918	−	0.299020i	−0.736082	+	0.676892i	$0.763326\pi$
$998$			45.5955i			1.44330i
$999$	2.03497	+	0.545268i	0.0643836	+	0.0172515i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.cg.b.19.8	yes	40
3.2	odd	2		819.2.gh.d.19.3		40
7.3	odd	6		273.2.bt.b.136.3	✓	40
13.11	odd	12		273.2.bt.b.271.3	yes	40
21.17	even	6		819.2.et.d.136.8		40
39.11	even	12		819.2.et.d.271.8		40
91.24	even	12	inner	273.2.cg.b.115.8	yes	40
273.206	odd	12		819.2.gh.d.388.3		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bt.b.136.3	✓	40	7.3	odd	6
273.2.bt.b.271.3	yes	40	13.11	odd	12
273.2.cg.b.19.8	yes	40	1.1	even	1	trivial
273.2.cg.b.115.8	yes	40	91.24	even	12	inner
819.2.et.d.136.8		40	21.17	even	6
819.2.et.d.271.8		40	39.11	even	12
819.2.gh.d.19.3		40	3.2	odd	2
819.2.gh.d.388.3		40	273.206	odd	12

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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.cg (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.41061 + 0.377973i) q^{2} +1.00000i q^{3} +(0.114915 + 0.0663464i) q^{4} +(1.70489 - 0.456824i) q^{5} +(-0.377973 + 1.41061i) q^{6} +(1.96341 + 1.77342i) q^{7} +(-1.92826 - 1.92826i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(1.41061 + 0.377973i) q^{2} +1.00000i q^{3} +(0.114915 + 0.0663464i) q^{4} +(1.70489 - 0.456824i) q^{5} +(-0.377973 + 1.41061i) q^{6} +(1.96341 + 1.77342i) q^{7} +(-1.92826 - 1.92826i) q^{8} -1.00000 q^{9} +2.57761 q^{10} +(1.59480 + 1.59480i) q^{11} +(-0.0663464 + 0.114915i) q^{12} +(2.06370 + 2.95654i) q^{13} +(2.09931 + 3.24373i) q^{14} +(0.456824 + 1.70489i) q^{15} +(-2.12389 - 3.67868i) q^{16} +(0.813654 - 1.40929i) q^{17} +(-1.41061 - 0.377973i) q^{18} +(-5.08160 - 5.08160i) q^{19} +(0.226226 + 0.0606172i) q^{20} +(-1.77342 + 1.96341i) q^{21} +(1.64685 + 2.85244i) q^{22} +(-5.63098 + 3.25105i) q^{23} +(1.92826 - 1.92826i) q^{24} +(-1.63217 + 0.942332i) q^{25} +(1.79359 + 4.95056i) q^{26} -1.00000i q^{27} +(0.107966 + 0.334058i) q^{28} +(3.90230 - 6.75898i) q^{29} +2.57761i q^{30} +(1.68884 - 6.30283i) q^{31} +(-0.193962 - 0.723875i) q^{32} +(-1.59480 + 1.59480i) q^{33} +(1.68042 - 1.68042i) q^{34} +(4.15754 + 2.12655i) q^{35} +(-0.114915 - 0.0663464i) q^{36} +(-0.545268 + 2.03497i) q^{37} +(-5.24746 - 9.08887i) q^{38} +(-2.95654 + 2.06370i) q^{39} +(-4.16834 - 2.40659i) q^{40} +(6.84645 - 1.83450i) q^{41} +(-3.24373 + 2.09931i) q^{42} +(-9.48195 + 5.47441i) q^{43} +(0.0774577 + 0.289076i) q^{44} +(-1.70489 + 0.456824i) q^{45} +(-9.17195 + 2.45762i) q^{46} +(-3.34284 - 12.4756i) q^{47} +(3.67868 - 2.12389i) q^{48} +(0.709963 + 6.96390i) q^{49} +(-2.65853 + 0.712352i) q^{50} +(1.40929 + 0.813654i) q^{51} +(0.0409944 + 0.476671i) q^{52} +(-3.00939 - 5.21242i) q^{53} +(0.377973 - 1.41061i) q^{54} +(3.44750 + 1.99041i) q^{55} +(-0.366351 - 7.20557i) q^{56} +(5.08160 - 5.08160i) q^{57} +(8.05934 - 8.05934i) q^{58} +(2.02441 + 7.55521i) q^{59} +(-0.0606172 + 0.226226i) q^{60} -6.26701i q^{61} +(4.76460 - 8.25252i) q^{62} +(-1.96341 - 1.77342i) q^{63} +7.40114i q^{64} +(4.86900 + 4.09784i) q^{65} +(-2.85244 + 1.64685i) q^{66} +(-3.75123 + 3.75123i) q^{67} +(0.187002 - 0.107966i) q^{68} +(-3.25105 - 5.63098i) q^{69} +(5.06090 + 4.57118i) q^{70} +(6.88920 + 1.84596i) q^{71} +(1.92826 + 1.92826i) q^{72} +(-4.55425 - 1.22031i) q^{73} +(-1.53832 + 2.66446i) q^{74} +(-0.942332 - 1.63217i) q^{75} +(-0.246808 - 0.921099i) q^{76} +(0.302997 + 5.95950i) q^{77} +(-4.95056 + 1.79359i) q^{78} +(-4.67565 + 8.09846i) q^{79} +(-5.30151 - 5.30151i) q^{80} +1.00000 q^{81} +10.3511 q^{82} +(3.82650 + 3.82650i) q^{83} +(-0.334058 + 0.107966i) q^{84} +(0.743393 - 2.77438i) q^{85} +(-15.4445 + 4.13835i) q^{86} +(6.75898 + 3.90230i) q^{87} -6.15037i q^{88} +(4.91594 + 1.31722i) q^{89} -2.57761 q^{90} +(-1.19131 + 9.46471i) q^{91} -0.862782 q^{92} +(6.30283 + 1.68884i) q^{93} -18.8618i q^{94} +(-10.9850 - 6.34217i) q^{95} +(0.723875 - 0.193962i) q^{96} +(-2.57958 + 9.62711i) q^{97} +(-1.63068 + 10.0917i) q^{98} +(-1.59480 - 1.59480i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 8 q^{7} - 40 q^{9}+O(q^{10}) \) 40 * q - 8 * q^7 - 40 * q^9	\( 40 q - 8 q^{7} - 40 q^{9} + 4 q^{11} - 24 q^{12} - 18 q^{14} + 32 q^{16} + 4 q^{17} + 14 q^{19} + 14 q^{20} + 2 q^{21} + 4 q^{22} + 12 q^{23} + 24 q^{25} - 32 q^{26} + 16 q^{28} + 8 q^{29} + 14 q^{31} - 26 q^{32} - 4 q^{33} - 24 q^{34} + 26 q^{35} + 36 q^{37} - 8 q^{38} + 18 q^{39} - 30 q^{40} - 2 q^{41} - 66 q^{43} - 32 q^{44} - 26 q^{46} - 4 q^{47} + 24 q^{48} - 14 q^{49} - 20 q^{50} + 2 q^{52} - 8 q^{53} - 42 q^{55} + 46 q^{56} - 14 q^{57} + 24 q^{58} + 14 q^{59} + 2 q^{60} + 24 q^{62} + 8 q^{63} + 28 q^{65} - 18 q^{66} - 44 q^{67} - 18 q^{68} + 4 q^{69} - 4 q^{70} - 6 q^{71} + 14 q^{73} - 20 q^{74} + 24 q^{75} - 64 q^{76} + 24 q^{77} + 8 q^{78} + 20 q^{80} + 40 q^{81} + 48 q^{82} - 12 q^{83} + 22 q^{84} + 2 q^{85} - 60 q^{86} + 18 q^{87} - 2 q^{89} - 14 q^{91} + 236 q^{92} - 8 q^{93} + 24 q^{95} + 16 q^{96} - 62 q^{97} - 88 q^{98} - 4 q^{99}+O(q^{100}) \) 40 * q - 8 * q^7 - 40 * q^9 + 4 * q^11 - 24 * q^12 - 18 * q^14 + 32 * q^16 + 4 * q^17 + 14 * q^19 + 14 * q^20 + 2 * q^21 + 4 * q^22 + 12 * q^23 + 24 * q^25 - 32 * q^26 + 16 * q^28 + 8 * q^29 + 14 * q^31 - 26 * q^32 - 4 * q^33 - 24 * q^34 + 26 * q^35 + 36 * q^37 - 8 * q^38 + 18 * q^39 - 30 * q^40 - 2 * q^41 - 66 * q^43 - 32 * q^44 - 26 * q^46 - 4 * q^47 + 24 * q^48 - 14 * q^49 - 20 * q^50 + 2 * q^52 - 8 * q^53 - 42 * q^55 + 46 * q^56 - 14 * q^57 + 24 * q^58 + 14 * q^59 + 2 * q^60 + 24 * q^62 + 8 * q^63 + 28 * q^65 - 18 * q^66 - 44 * q^67 - 18 * q^68 + 4 * q^69 - 4 * q^70 - 6 * q^71 + 14 * q^73 - 20 * q^74 + 24 * q^75 - 64 * q^76 + 24 * q^77 + 8 * q^78 + 20 * q^80 + 40 * q^81 + 48 * q^82 - 12 * q^83 + 22 * q^84 + 2 * q^85 - 60 * q^86 + 18 * q^87 - 2 * q^89 - 14 * q^91 + 236 * q^92 - 8 * q^93 + 24 * q^95 + 16 * q^96 - 62 * q^97 - 88 * q^98 - 4 * q^99

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