LMFDB - Embedded newform 210.2.x.a.107.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [210,2,Mod(23,210)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(210, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 9, 4]))

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

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

chi := DirichletCharacter("210.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 210 = 2 \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	210.x (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:	$1.67685844245$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			107.14
Character	$\chi$	$=$	210.107
Dual form			210.2.x.a.53.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 + 0.965926i) q^{2} +(0.680155 + 1.59292i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(1.30445 + 1.81616i) q^{5} +(-1.36260 + 1.06926i) q^{6} +(-2.54122 - 0.736347i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.07478 + 2.16686i) q^{9} +O(q^{10})$	\(q+(0.258819 + 0.965926i) q^{2} +(0.680155 + 1.59292i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(1.30445 + 1.81616i) q^{5} +(-1.36260 + 1.06926i) q^{6} +(-2.54122 - 0.736347i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.07478 + 2.16686i) q^{9} +(-1.41666 + 1.73005i) q^{10} +(1.83587 - 1.05994i) q^{11} +(-1.38549 - 1.03943i) q^{12} +(3.28206 - 3.28206i) q^{13} +(0.0535403 - 2.64521i) q^{14} +(-2.00576 + 3.31314i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-1.40048 - 0.375258i) q^{17} +(-2.63002 - 1.44326i) q^{18} +(4.72549 + 2.72826i) q^{19} +(-2.03776 - 0.920615i) q^{20} +(-0.555484 - 4.54878i) q^{21} +(1.49898 + 1.49898i) q^{22} +(-5.50010 + 1.47375i) q^{23} +(0.645421 - 1.60731i) q^{24} +(-1.59685 + 4.73815i) q^{25} +(4.01969 + 2.32077i) q^{26} +(-4.86281 - 1.83115i) q^{27} +(2.56893 - 0.632915i) q^{28} +7.20525 q^{29} +(-3.71938 - 1.07991i) q^{30} +(-0.528063 - 0.914632i) q^{31} +(0.965926 + 0.258819i) q^{32} +(2.93707 + 2.20346i) q^{33} -1.44989i q^{34} +(-1.97756 - 5.57577i) q^{35} +(0.713378 - 2.91395i) q^{36} +(6.22550 - 1.66812i) q^{37} +(-1.41225 + 5.27060i) q^{38} +(7.46037 + 2.99575i) q^{39} +(0.361834 - 2.20660i) q^{40} -1.86758i q^{41} +(4.25002 - 1.71387i) q^{42} +(1.79293 - 1.79293i) q^{43} +(-1.05994 + 1.83587i) q^{44} +(-6.64180 - 0.941565i) q^{45} +(-2.84706 - 4.93126i) q^{46} +(-2.87830 - 10.7419i) q^{47} +(1.71959 + 0.207427i) q^{48} +(5.91559 + 3.74244i) q^{49} +(-4.99000 - 0.316111i) q^{50} +(-0.354790 - 2.48609i) q^{51} +(-1.20132 + 4.48338i) q^{52} +(-1.73562 + 6.47741i) q^{53} +(0.510166 - 5.17105i) q^{54} +(4.31980 + 1.95159i) q^{55} +(1.27624 + 2.31759i) q^{56} +(-1.13183 + 9.38296i) q^{57} +(1.86485 + 6.95973i) q^{58} +(-2.63659 - 4.56671i) q^{59} +(0.0804705 - 3.87215i) q^{60} +(4.11857 - 7.13357i) q^{61} +(0.746794 - 0.746794i) q^{62} +(6.86803 - 3.97872i) q^{63} +1.00000i q^{64} +(10.2420 + 1.67947i) q^{65} +(-1.36821 + 3.40729i) q^{66} +(-2.43944 + 9.10412i) q^{67} +(1.40048 - 0.375258i) q^{68} +(-6.08848 - 7.75883i) q^{69} +(4.87395 - 3.35329i) q^{70} -1.75938i q^{71} +(2.99929 - 0.0651145i) q^{72} +(-1.20699 - 0.323412i) q^{73} +(3.22256 + 5.58163i) q^{74} +(-8.63359 + 0.679034i) q^{75} -5.45653 q^{76} +(-5.44582 + 1.34170i) q^{77} +(-0.962782 + 7.98152i) q^{78} +(-13.8415 - 7.99137i) q^{79} +(2.22506 - 0.221605i) q^{80} +(-0.390595 - 8.99152i) q^{81} +(1.80394 - 0.483365i) q^{82} +(-9.47707 - 9.47707i) q^{83} +(2.75545 + 3.66162i) q^{84} +(-1.14532 - 3.03300i) q^{85} +(2.19589 + 1.26779i) q^{86} +(4.90069 + 11.4774i) q^{87} +(-2.04764 - 0.548664i) q^{88} +(0.199936 - 0.346299i) q^{89} +(-0.809541 - 6.65918i) q^{90} +(-10.7572 + 5.92370i) q^{91} +(4.02635 - 4.02635i) q^{92} +(1.09777 - 1.46325i) q^{93} +(9.63096 - 5.56044i) q^{94} +(1.20919 + 12.1411i) q^{95} +(0.244702 + 1.71468i) q^{96} +(-8.63390 - 8.63390i) q^{97} +(-2.08385 + 6.68263i) q^{98} +(-1.51227 + 6.17721i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 8 q^{6} + 4 q^{7}+O(q^{10}) $ 64 * q + 8 * q^6 + 4 * q^7	$ 64 q + 8 q^{6} + 4 q^{7} + 4 q^{10} - 24 q^{15} + 32 q^{16} - 8 q^{18} + 12 q^{21} - 24 q^{22} - 8 q^{25} - 72 q^{27} + 4 q^{28} - 12 q^{30} + 32 q^{31} - 20 q^{33} - 24 q^{36} - 8 q^{37} - 40 q^{42} - 64 q^{43} - 28 q^{45} + 24 q^{46} - 16 q^{55} + 24 q^{57} - 28 q^{58} + 8 q^{60} + 24 q^{61} - 88 q^{63} - 16 q^{67} - 12 q^{70} + 8 q^{72} - 56 q^{73} + 8 q^{75} - 32 q^{76} - 16 q^{78} + 4 q^{81} + 16 q^{82} + 32 q^{85} + 76 q^{87} + 12 q^{88} + 40 q^{90} - 48 q^{91} + 84 q^{93} + 4 q^{96} + 104 q^{97}+O(q^{100}) $ 64 * q + 8 * q^6 + 4 * q^7 + 4 * q^10 - 24 * q^15 + 32 * q^16 - 8 * q^18 + 12 * q^21 - 24 * q^22 - 8 * q^25 - 72 * q^27 + 4 * q^28 - 12 * q^30 + 32 * q^31 - 20 * q^33 - 24 * q^36 - 8 * q^37 - 40 * q^42 - 64 * q^43 - 28 * q^45 + 24 * q^46 - 16 * q^55 + 24 * q^57 - 28 * q^58 + 8 * q^60 + 24 * q^61 - 88 * q^63 - 16 * q^67 - 12 * q^70 + 8 * q^72 - 56 * q^73 + 8 * q^75 - 32 * q^76 - 16 * q^78 + 4 * q^81 + 16 * q^82 + 32 * q^85 + 76 * q^87 + 12 * q^88 + 40 * q^90 - 48 * q^91 + 84 * q^93 + 4 * q^96 + 104 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$.

$n$	$31$	$71$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.258819	+	0.965926i	0.183013	+	0.683013i
$2$	0.258819	+	0.965926i	0.183013	+	0.683013i
$3$	0.680155	+	1.59292i	0.392688	+	0.919672i
$3$	0.680155	+	1.59292i	0.392688	+	0.919672i
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$	1.30445	+	1.81616i	0.583366	+	0.812210i
$5$	1.30445	+	1.81616i	0.583366	+	0.812210i
$6$	−1.36260	+	1.06926i	−0.556281	+	0.436522i
$7$	−2.54122	−	0.736347i	−0.960490	−	0.278313i
$7$	−2.54122	−	0.736347i	−0.960490	−	0.278313i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	−2.07478	+	2.16686i	−0.691593	+	0.722288i
$10$	−1.41666	+	1.73005i	−0.447986	+	0.547091i
$11$	1.83587	−	1.05994i	0.553535	−	0.319583i	−0.197012	−	0.980401i	$-0.563124\pi$
$11$	1.83587	−	1.05994i	0.553535	−	0.319583i	0.750546	+	0.660818i	$0.229790\pi$
$12$	−1.38549	−	1.03943i	−0.399957	−	0.300058i
$13$	3.28206	−	3.28206i	0.910280	−	0.910280i	−0.0860135	−	0.996294i	$-0.527413\pi$
$13$	3.28206	−	3.28206i	0.910280	−	0.910280i	0.996294	+	0.0860135i	$0.0274128\pi$
$14$	0.0535403	−	2.64521i	0.0143092	−	0.706962i
$15$	−2.00576	+	3.31314i	−0.517886	+	0.855450i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−1.40048	−	0.375258i	−0.339667	−	0.0910134i	0.0849537	−	0.996385i	$-0.472926\pi$
$17$	−1.40048	−	0.375258i	−0.339667	−	0.0910134i	−0.424620	+	0.905371i	$0.639592\pi$
$18$	−2.63002	−	1.44326i	−0.619902	−	0.340179i
$19$	4.72549	+	2.72826i	1.08410	+	0.625906i	0.932000	−	0.362458i	$-0.118063\pi$
$19$	4.72549	+	2.72826i	1.08410	+	0.625906i	0.152102	+	0.988365i	$0.451396\pi$
$20$	−2.03776	−	0.920615i	−0.455657	−	0.205856i
$21$	−0.555484	−	4.54878i	−0.121216	−	0.992626i
$22$	1.49898	+	1.49898i	0.319583	+	0.319583i
$23$	−5.50010	+	1.47375i	−1.14685	+	0.307298i	−0.781702	−	0.623652i	$-0.785648\pi$
$23$	−5.50010	+	1.47375i	−1.14685	+	0.307298i	−0.365148	+	0.930949i	$0.618982\pi$
$24$	0.645421	−	1.60731i	0.131746	−	0.328090i
$25$	−1.59685	+	4.73815i	−0.319369	+	0.947630i
$26$	4.01969	+	2.32077i	0.788326	+	0.455140i
$27$	−4.86281	−	1.83115i	−0.935848	−	0.352405i
$28$	2.56893	−	0.632915i	0.485483	−	0.119610i
$29$	7.20525			1.33798			0.668990	−	0.743271i	$-0.266727\pi$
$29$	7.20525			1.33798			0.668990	+	0.743271i	$0.266727\pi$
$30$	−3.71938	−	1.07991i	−0.679063	−	0.197164i
$31$	−0.528063	−	0.914632i	−0.0948429	−	0.164273i	0.814700	−	0.579882i	$-0.196902\pi$
$31$	−0.528063	−	0.914632i	−0.0948429	−	0.164273i	−0.909543	+	0.415610i	$0.863568\pi$
$32$	0.965926	+	0.258819i	0.170753	+	0.0457532i
$33$	2.93707	+	2.20346i	0.511278	+	0.383574i
$34$		−	1.44989i		−	0.248653i
$35$	−1.97756	−	5.57577i	−0.334269	−	0.942478i
$36$	0.713378	−	2.91395i	0.118896	−	0.485658i
$37$	6.22550	−	1.66812i	1.02347	−	0.274237i	0.292221	−	0.956351i	$-0.405606\pi$
$37$	6.22550	−	1.66812i	1.02347	−	0.274237i	0.731246	+	0.682114i	$0.238939\pi$
$38$	−1.41225	+	5.27060i	−0.229098	+	0.855004i
$39$	7.46037	+	2.99575i	1.19462	+	0.479703i
$40$	0.361834	−	2.20660i	0.0572110	−	0.348894i
$41$		−	1.86758i		−	0.291667i	−0.989309	−	0.145833i	$-0.953414\pi$
$41$		−	1.86758i		−	0.291667i	0.989309	−	0.145833i	$-0.0465863\pi$
$42$	4.25002	−	1.71387i	0.655792	−	0.264456i
$43$	1.79293	−	1.79293i	0.273420	−	0.273420i	−0.557056	−	0.830475i	$-0.688069\pi$
$43$	1.79293	−	1.79293i	0.273420	−	0.273420i	0.830475	+	0.557056i	$0.188069\pi$
$44$	−1.05994	+	1.83587i	−0.159792	+	0.276767i
$45$	−6.64180	−	0.941565i	−0.990100	−	0.140360i
$46$	−2.84706	−	4.93126i	−0.419776	−	0.727074i
$47$	−2.87830	−	10.7419i	−0.419843	−	1.56687i	−0.774934	−	0.632042i	$-0.782217\pi$
$47$	−2.87830	−	10.7419i	−0.419843	−	1.56687i	0.355091	−	0.934832i	$-0.384450\pi$
$48$	1.71959	+	0.207427i	0.248201	+	0.0299396i
$49$	5.91559	+	3.74244i	0.845084	+	0.534634i
$50$	−4.99000	−	0.316111i	−0.705692	−	0.0447048i
$51$	−0.354790	−	2.48609i	−0.0496805	−	0.348122i
$52$	−1.20132	+	4.48338i	−0.166593	+	0.621733i
$53$	−1.73562	+	6.47741i	−0.238405	+	0.889741i	0.738179	+	0.674605i	$0.235686\pi$
$53$	−1.73562	+	6.47741i	−0.238405	+	0.889741i	−0.976584	+	0.215136i	$0.930981\pi$
$54$	0.510166	−	5.17105i	0.0694248	−	0.703690i
$55$	4.31980	+	1.95159i	0.582482	+	0.263152i
$56$	1.27624	+	2.31759i	0.170544	+	0.309701i
$57$	−1.13183	+	9.38296i	−0.149915	+	1.24280i
$58$	1.86485	+	6.95973i	0.244867	+	0.913858i
$59$	−2.63659	−	4.56671i	−0.343255	−	0.594535i	0.641780	−	0.766889i	$-0.278196\pi$
$59$	−2.63659	−	4.56671i	−0.343255	−	0.594535i	−0.985035	+	0.172354i	$0.944863\pi$
$60$	0.0804705	−	3.87215i	0.0103887	−	0.499892i
$61$	4.11857	−	7.13357i	0.527328	−	0.913360i	−0.472164	−	0.881511i	$-0.656527\pi$
$61$	4.11857	−	7.13357i	0.527328	−	0.913360i	0.999493	−	0.0318490i	$-0.0101396\pi$
$62$	0.746794	−	0.746794i	0.0948429	−	0.0948429i
$63$	6.86803	−	3.97872i	0.865290	−	0.501272i
$64$			1.00000i			0.125000i
$65$	10.2420	+	1.67947i	1.27036	+	0.208312i
$66$	−1.36821	+	3.40729i	−0.168415	+	0.419408i
$67$	−2.43944	+	9.10412i	−0.298025	+	1.11225i	0.640760	+	0.767742i	$0.278620\pi$
$67$	−2.43944	+	9.10412i	−0.298025	+	1.11225i	−0.938785	+	0.344504i	$0.888047\pi$
$68$	1.40048	−	0.375258i	0.169833	−	0.0455067i
$69$	−6.08848	−	7.75883i	−0.732967	−	0.934054i
$70$	4.87395	−	3.35329i	0.582549	−	0.400795i
$71$		−	1.75938i		−	0.208800i	−0.994535	−	0.104400i	$-0.966708\pi$
$71$		−	1.75938i		−	0.208800i	0.994535	−	0.104400i	$-0.0332922\pi$
$72$	2.99929	−	0.0651145i	0.353470	−	0.00767382i
$73$	−1.20699	−	0.323412i	−0.141268	−	0.0378525i	0.187492	−	0.982266i	$-0.439964\pi$
$73$	−1.20699	−	0.323412i	−0.141268	−	0.0378525i	−0.328760	+	0.944414i	$0.606631\pi$
$74$	3.22256	+	5.58163i	0.374615	+	0.648852i
$75$	−8.63359	+	0.679034i	−0.996921	+	0.0784081i
$76$	−5.45653			−0.625906
$77$	−5.44582	+	1.34170i	−0.620609	+	0.152901i
$78$	−0.962782	+	7.98152i	−0.109014	+	0.903729i
$79$	−13.8415	−	7.99137i	−1.55728	−	0.899099i	−0.997515	−	0.0704506i	$-0.977556\pi$
$79$	−13.8415	−	7.99137i	−1.55728	−	0.899099i	−0.559770	−	0.828648i	$-0.689110\pi$
$80$	2.22506	−	0.221605i	0.248769	−	0.0247761i
$81$	−0.390595	−	8.99152i	−0.0433995	−	0.999058i
$82$	1.80394	−	0.483365i	0.199212	−	0.0533787i
$83$	−9.47707	−	9.47707i	−1.04024	−	1.04024i	−0.999156	−	0.0410882i	$-0.986918\pi$
$83$	−9.47707	−	9.47707i	−1.04024	−	1.04024i	−0.0410882	−	0.999156i	$-0.513082\pi$
$84$	2.75545	+	3.66162i	0.300645	+	0.399516i
$85$	−1.14532	−	3.03300i	−0.124228	−	0.328975i
$86$	2.19589	+	1.26779i	0.236788	+	0.136710i
$87$	4.90069	+	11.4774i	0.525409	+	1.23050i
$88$	−2.04764	−	0.548664i	−0.218280	−	0.0584878i
$89$	0.199936	−	0.346299i	0.0211931	−	0.0367076i	−0.855234	−	0.518242i	$-0.826587\pi$
$89$	0.199936	−	0.346299i	0.0211931	−	0.0367076i	0.876427	+	0.481534i	$0.159920\pi$
$90$	−0.809541	−	6.65918i	−0.0853331	−	0.701939i
$91$	−10.7572	+	5.92370i	−1.12766	+	0.620973i
$92$	4.02635	−	4.02635i	0.419776	−	0.419776i
$93$	1.09777	−	1.46325i	0.113833	−	0.151732i
$94$	9.63096	−	5.56044i	0.993358	−	0.573516i
$95$	1.20919	+	12.1411i	0.124060	+	1.24565i
$96$	0.244702	+	1.71468i	0.0249748	+	0.175004i
$97$	−8.63390	−	8.63390i	−0.876640	−	0.876640i	0.116546	−	0.993185i	$-0.462818\pi$
$97$	−8.63390	−	8.63390i	−0.876640	−	0.876640i	−0.993185	+	0.116546i	$0.962818\pi$
$98$	−2.08385	+	6.68263i	−0.210500	+	0.675048i
$99$	−1.51227	+	6.17721i	−0.151989	+	0.620833i
$100$	−0.986167	−	4.90178i	−0.0986167	−	0.490178i
$101$	3.82984	−	2.21116i	0.381084	−	0.220019i	−0.297206	−	0.954813i	$-0.596055\pi$
$101$	3.82984	−	2.21116i	0.381084	−	0.220019i	0.678290	+	0.734795i	$0.262721\pi$
$102$	2.30955	−	0.986147i	0.228679	−	0.0976431i
$103$	2.77123	+	10.3424i	0.273057	+	1.01906i	0.957132	+	0.289652i	$0.0935395\pi$
$103$	2.77123	+	10.3424i	0.273057	+	1.01906i	−0.684075	+	0.729412i	$0.739794\pi$
$104$	−4.64154			−0.455140
$105$	7.53670	−	6.94248i	0.735507	−	0.677517i
$106$	−6.70591			−0.651335
$107$	2.76314	+	10.3122i	0.267123	+	0.996917i	0.960938	+	0.276763i	$0.0892618\pi$
$107$	2.76314	+	10.3122i	0.267123	+	0.996917i	−0.693815	+	0.720153i	$0.744072\pi$
$108$	5.12689	−	0.845583i	0.493335	−	0.0813663i
$109$	−7.42120	+	4.28463i	−0.710822	+	0.410393i	−0.811365	−	0.584539i	$-0.801275\pi$
$109$	−7.42120	+	4.28463i	−0.710822	+	0.410393i	0.100543	+	0.994933i	$0.467942\pi$
$110$	−0.767044	+	4.67772i	−0.0731348	+	0.446003i
$111$	6.89149	+	8.78214i	0.654111	+	0.833564i
$112$	−1.90830	+	1.83259i	−0.180318	+	0.173163i
$113$	7.12484	+	7.12484i	0.670249	+	0.670249i	0.957773	−	0.287524i	$-0.0928322\pi$
$113$	7.12484	+	7.12484i	0.670249	+	0.670249i	−0.287524	+	0.957773i	$0.592832\pi$
$114$	−9.35618	+	1.33522i	−0.876287	+	0.125055i
$115$	−9.85113	−	8.06662i	−0.918623	−	0.752216i
$116$	−6.23993	+	3.60262i	−0.579363	+	0.334495i
$117$	0.302232	+	13.9213i	0.0279413	+	1.28703i
$118$	3.72870	−	3.72870i	0.343255	−	0.343255i
$119$	3.28261	+	1.98485i	0.300916	+	0.181951i
$120$	3.76103	−	0.924457i	0.343334	−	0.0843910i
$121$	−3.25306	+	5.63447i	−0.295733	+	0.512224i
$122$	7.95646	+	2.13193i	0.720344	+	0.193016i
$123$	2.97490	−	1.27024i	0.268238	−	0.114534i
$124$	0.914632	+	0.528063i	0.0821364	+	0.0474215i
$125$	−10.6882	+	3.28054i	−0.955984	+	0.293420i
$126$	5.62072	+	5.60424i	0.500734	+	0.499265i
$127$	−11.2870	−	11.2870i	−1.00156	−	1.00156i	−0.999999	−	0.00155629i	$-0.999505\pi$
$127$	−11.2870	−	11.2870i	−1.00156	−	1.00156i	−0.00155629	−	0.999999i	$-0.500495\pi$
$128$	−0.965926	+	0.258819i	−0.0853766	+	0.0228766i
$129$	4.07547	+	1.63652i	0.358825	+	0.144088i
$130$	1.02859	+	10.3277i	0.0902130	+	0.905799i
$131$	−5.01434	−	2.89503i	−0.438105	−	0.252940i	0.264689	−	0.964334i	$-0.414731\pi$
$131$	−5.01434	−	2.89503i	−0.438105	−	0.252940i	−0.702793	+	0.711394i	$0.748064\pi$
$132$	−3.64531	−	0.439721i	−0.317283	−	0.0382728i
$133$	−9.99956	−	10.4127i	−0.867072	−	0.902897i
$134$	−9.42528			−0.814220
$135$	−3.01762	−	11.2202i	−0.259715	−	0.965685i
$136$	0.724943	+	1.25564i	0.0621633	+	0.107670i
$137$	−10.8253	−	2.90062i	−0.924864	−	0.247816i	−0.235201	−	0.971947i	$-0.575575\pi$
$137$	−10.8253	−	2.90062i	−0.924864	−	0.247816i	−0.689663	+	0.724130i	$0.742241\pi$
$138$	5.91864	−	7.88916i	0.503828	−	0.671570i
$139$			20.1333i			1.70768i	0.520535	+	0.853841i	$0.325733\pi$
$139$			20.1333i			1.70768i	−0.520535	+	0.853841i	$0.674267\pi$
$140$	4.50050	+	3.83998i	0.380362	+	0.324538i
$141$	15.1534	−	11.8911i	1.27614	−	1.00141i
$142$	1.69943	−	0.455361i	0.142613	−	0.0382131i
$143$	2.54665	−	9.50422i	0.212961	−	0.794782i
$144$	0.839170	+	2.88024i	0.0699308	+	0.240020i
$145$	9.39885	+	13.0859i	0.780532	+	1.08672i
$146$		−	1.24957i		−	0.103415i
$147$	−1.93788	+	11.9685i	−0.159833	+	0.987144i
$148$	−4.55738	+	4.55738i	−0.374615	+	0.374615i
$149$	5.90510	−	10.2279i	0.483765	−	0.837905i	−0.516061	−	0.856552i	$-0.672602\pi$
$149$	5.90510	−	10.2279i	0.483765	−	0.837905i	0.999826	+	0.0186464i	$0.00593567\pi$
$150$	−2.89043	−	8.16366i	−0.236003	−	0.666560i
$151$	4.33354	+	7.50591i	0.352658	+	0.610822i	0.986714	−	0.162465i	$-0.0519445\pi$
$151$	4.33354	+	7.50591i	0.352658	+	0.610822i	−0.634056	+	0.773287i	$0.718611\pi$
$152$	−1.41225	−	5.27060i	−0.114549	−	0.427502i
$153$	3.71882	−	2.25608i	0.300649	−	0.182393i
$154$	−2.70547	−	4.91300i	−0.218013	−	0.395901i
$155$	0.972285	−	2.15213i	0.0780958	−	0.172863i
$156$	−7.95874	+	1.13579i	−0.637209	+	0.0909362i
$157$	4.51828	−	16.8625i	0.360598	−	1.34577i	−0.512693	−	0.858572i	$-0.671352\pi$
$157$	4.51828	−	16.8625i	0.360598	−	1.34577i	0.873291	−	0.487198i	$-0.161981\pi$
$158$	4.13664	−	15.4381i	0.329093	−	1.22819i
$159$	−11.4985	+	1.64095i	−0.911888	+	0.130136i
$160$	0.789941	+	2.09189i	0.0624504	+	0.165378i
$161$	15.0621	+	0.304865i	1.18706	+	0.0240267i
$162$	8.58405	−	2.70446i	0.674427	−	0.212483i
$163$	1.34945	+	5.03620i	0.105697	+	0.394466i	0.998423	−	0.0561330i	$-0.0178771\pi$
$163$	1.34945	+	5.03620i	0.105697	+	0.394466i	−0.892726	+	0.450599i	$0.851210\pi$
$164$	0.933789	+	1.61737i	0.0729167	+	0.126295i
$165$	−0.170587	+	8.20847i	−0.0132802	+	0.639029i
$166$	6.70130	−	11.6070i	0.520122	−	0.900877i
$167$	5.99458	−	5.99458i	0.463874	−	0.463874i	−0.436049	−	0.899923i	$-0.643623\pi$
$167$	5.99458	−	5.99458i	0.463874	−	0.463874i	0.899923	+	0.436049i	$0.143623\pi$
$168$	−2.82369	+	3.60926i	−0.217852	+	0.278461i
$169$		−	8.54387i		−	0.657221i
$170$	2.63322	−	1.89130i	0.201959	−	0.145056i
$171$	−15.7161	+	4.57895i	−1.20184	+	0.350161i
$172$	−0.656259	+	2.44919i	−0.0500393	+	0.186749i
$173$	−4.84235	+	1.29750i	−0.368157	+	0.0986474i	−0.438154	−	0.898900i	$-0.644368\pi$
$173$	−4.84235	+	1.29750i	−0.368157	+	0.0986474i	0.0699972	+	0.997547i	$0.477701\pi$
$174$	−9.81790	+	7.70426i	−0.744293	+	0.584059i
$175$	7.54686	−	10.8648i	0.570489	−	0.821305i
$176$		−	2.11988i		−	0.159792i
$177$	5.48110	−	7.30595i	0.411985	−	0.549148i
$178$	0.386246	+	0.103494i	0.0289504	+	0.00775723i
$179$	−4.04588	−	7.00767i	−0.302403	−	0.523778i	0.674277	−	0.738479i	$-0.264456\pi$
$179$	−4.04588	−	7.00767i	−0.302403	−	0.523778i	−0.976680	+	0.214701i	$0.931122\pi$
$180$	6.22275	−	2.50548i	0.463816	−	0.186747i
$181$	10.6946			0.794924			0.397462	−	0.917619i	$-0.369891\pi$
$181$	10.6946			0.794924			0.397462	+	0.917619i	$0.369891\pi$
$182$	−8.50602	−	8.85747i	−0.630508	−	0.656559i
$183$	14.1645	+	1.70861i	1.04707	+	0.126304i
$184$	4.93126	+	2.84706i	0.363537	+	0.209888i
$185$	11.1504	+	9.13052i	0.819793	+	0.671289i
$186$	1.69752	+	0.681646i	0.124468	+	0.0499807i
$187$	−2.96885	+	0.795501i	−0.217104	+	0.0581728i
$188$	7.86365	+	7.86365i	0.573516	+	0.573516i
$189$	11.0091	+	8.23406i	0.800794	+	0.598940i
$190$	−11.4144	+	4.31034i	−0.828090	+	0.312705i
$191$	−0.647671	−	0.373933i	−0.0468638	−	0.0270569i	0.476385	−	0.879237i	$-0.341947\pi$
$191$	−0.647671	−	0.373933i	−0.0468638	−	0.0270569i	−0.523249	+	0.852180i	$0.675280\pi$
$192$	−1.59292	+	0.680155i	−0.114959	+	0.0490860i
$193$	−8.94254	−	2.39615i	−0.643698	−	0.172478i	−0.0778200	−	0.996967i	$-0.524796\pi$
$193$	−8.94254	−	2.39615i	−0.643698	−	0.172478i	−0.565878	+	0.824489i	$0.691463\pi$
$194$	6.10509	−	10.5743i	0.438320	−	0.759192i
$195$	4.29090	+	17.4570i	0.307278	+	1.25012i
$196$	−6.99427	−	0.283250i	−0.499590	−	0.0202322i
$197$	−2.71376	+	2.71376i	−0.193348	+	0.193348i	−0.797141	−	0.603793i	$-0.793655\pi$
$197$	−2.71376	+	2.71376i	−0.193348	+	0.193348i	0.603793	+	0.797141i	$0.293655\pi$
$198$	−6.35813	+	0.138035i	−0.451853	+	0.00980971i
$199$	4.85488	−	2.80297i	0.344153	−	0.198697i	−0.317954	−	0.948106i	$-0.602996\pi$
$199$	4.85488	−	2.80297i	0.344153	−	0.198697i	0.662107	+	0.749409i	$0.269662\pi$
$200$	4.47952	−	2.22124i	0.316750	−	0.157065i
$201$	−16.1613	+	2.30638i	−1.13993	+	0.162680i
$202$	3.12705	+	3.12705i	0.220019	+	0.220019i
$203$	−18.3101	−	5.30556i	−1.28512	−	0.372377i
$204$	1.55030	+	1.97562i	0.108543	+	0.138321i
$205$	3.39181	−	2.43615i	0.236895	−	0.170148i
$206$	−9.27271	+	5.35360i	−0.646060	+	0.373003i
$207$	8.21808	−	14.9757i	0.571196	−	1.04088i
$208$	−1.20132	−	4.48338i	−0.0832964	−	0.310867i
$209$	11.5672			0.800117
$210$	8.65657	+	5.48305i	0.597360	+	0.378366i
$211$	14.8448			1.02196			0.510978	−	0.859594i	$-0.329283\pi$
$211$	14.8448			1.02196			0.510978	+	0.859594i	$0.329283\pi$
$212$	−1.73562	−	6.47741i	−0.119203	−	0.444870i
$213$	2.80255	−	1.19665i	0.192028	−	0.0819932i
$214$	−9.24565	+	5.33798i	−0.632020	+	0.364897i
$215$	5.59503	+	0.917463i	0.381578	+	0.0625705i
$216$	2.14371	+	4.73334i	0.145861	+	0.322063i
$217$	0.668438	+	2.71312i	0.0453765	+	0.184178i
$218$	−6.05939	−	6.05939i	−0.410393	−	0.410393i
$219$	−0.305772	−	2.14261i	−0.0206622	−	0.144784i
$220$	−4.71685	+	0.469774i	−0.318010	+	0.0316722i
$221$	−5.82809	+	3.36485i	−0.392040	+	0.226344i
$222$	−6.69925	+	8.92965i	−0.449624	+	0.599319i
$223$	5.02812	−	5.02812i	0.336708	−	0.336708i	−0.518419	−	0.855127i	$-0.673479\pi$
$223$	5.02812	−	5.02812i	0.336708	−	0.336708i	0.855127	+	0.518419i	$0.173479\pi$
$224$	−2.26405	−	1.36897i	−0.151273	−	0.0914683i
$225$	−6.95383	−	13.2908i	−0.463589	−	0.886051i
$226$	−5.03803	+	8.72612i	−0.335124	+	0.580453i
$227$	11.2410	+	3.01201i	0.746089	+	0.199914i	0.611783	−	0.791026i	$-0.290453\pi$
$227$	11.2410	+	3.01201i	0.746089	+	0.199914i	0.134307	+	0.990940i	$0.457119\pi$
$228$	−3.71128	−	8.69180i	−0.245786	−	0.575628i
$229$	3.58186	+	2.06799i	0.236696	+	0.136657i	0.613657	−	0.789572i	$-0.289698\pi$
$229$	3.58186	+	2.06799i	0.236696	+	0.136657i	−0.376961	+	0.926229i	$0.623031\pi$
$230$	5.24209	−	11.6033i	0.345653	−	0.765096i
$231$	−5.84122	−	7.76218i	−0.384324	−	0.510714i
$232$	−5.09488	−	5.09488i	−0.334495	−	0.334495i
$233$	−21.9305	+	5.87626i	−1.43671	+	0.384967i	−0.891382	−	0.453253i	$-0.850263\pi$
$233$	−21.9305	+	5.87626i	−1.43671	+	0.384967i	−0.545333	+	0.838220i	$0.683597\pi$
$234$	−13.3688	+	3.89504i	−0.873943	+	0.254627i
$235$	15.7545	−	19.2397i	1.02771	−	1.25506i
$236$	4.56671	+	2.63659i	0.297267	+	0.171627i
$237$	3.31526	−	27.4837i	0.215349	−	1.78526i
$238$	−1.06762	+	3.68448i	−0.0692034	+	0.238829i
$239$	10.6159			0.686682			0.343341	−	0.939211i	$-0.388441\pi$
$239$	10.6159			0.686682			0.343341	+	0.939211i	$0.388441\pi$
$240$	1.86638	+	3.39361i	0.120475	+	0.219057i
$241$	10.0635	+	17.4304i	0.648245	+	1.12279i	0.983542	+	0.180680i	$0.0578300\pi$
$241$	10.0635	+	17.4304i	0.648245	+	1.12279i	−0.335297	+	0.942112i	$0.608837\pi$
$242$	−6.28443	−	1.68391i	−0.403979	−	0.108246i
$243$	14.0571	−	6.73782i	0.901763	−	0.432231i
$244$			8.23713i			0.527328i
$245$	0.919713	+	15.6254i	0.0587583	+	0.998272i
$246$	1.99692	+	2.54477i	0.127319	+	0.162249i
$247$	24.4637	−	6.55502i	1.55659	−	0.417086i
$248$	−0.273346	+	1.02014i	−0.0173575	+	0.0647789i
$249$	8.65032	−	21.5421i	0.548192	−	1.36517i
$250$	−5.93507	−	9.47496i	−0.375367	−	0.599249i
$251$			17.8395i			1.12602i	0.826450	+	0.563010i	$0.190357\pi$
$251$			17.8395i			1.12602i	−0.826450	+	0.563010i	$0.809643\pi$
$252$	−3.95853	+	6.87969i	−0.249364	+	0.433379i
$253$	−8.53537	+	8.53537i	−0.536614	+	0.536614i
$254$	7.98108	−	13.8236i	0.500778	−	0.867372i
$255$	4.05232	−	3.88732i	0.253766	−	0.243433i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	0.258140	+	0.963390i	0.0161023	+	0.0600946i	0.973510	−	0.228646i	$-0.0734300\pi$
$257$	0.258140	+	0.963390i	0.0161023	+	0.0600946i	−0.957407	+	0.288741i	$0.906763\pi$
$258$	−0.525951	+	4.36016i	−0.0327443	+	0.271452i
$259$	−17.0487	−	0.345073i	−1.05935	−	0.0214418i
$260$	−9.70957	+	3.66654i	−0.602162	+	0.227389i
$261$	−14.9493	+	15.6128i	−0.925337	+	0.966407i
$262$	1.49858	−	5.59277i	0.0925824	−	0.345522i
$263$	4.46730	−	16.6722i	0.275466	−	1.02805i	−0.680063	−	0.733153i	$-0.738048\pi$
$263$	4.46730	−	16.6722i	0.275466	−	1.02805i	0.955529	−	0.294898i	$-0.0952857\pi$
$264$	−0.518738	−	3.63491i	−0.0319261	−	0.223713i
$265$	−14.0280	+	5.29728i	−0.861733	+	0.325409i
$266$	7.46983	−	12.3538i	0.458005	−	0.757462i
$267$	0.687613	+	0.0829443i	0.0420812	+	0.00507611i
$268$	−2.43944	−	9.10412i	−0.149013	−	0.556123i
$269$	−13.8205	−	23.9379i	−0.842653	−	1.45952i	−0.887644	−	0.460531i	$-0.847659\pi$
$269$	−13.8205	−	23.9379i	−0.842653	−	1.45952i	0.0449907	−	0.998987i	$-0.485674\pi$
$270$	10.0569	−	5.81881i	0.612044	−	0.354121i
$271$	−2.56520	+	4.44305i	−0.155825	+	0.269896i	−0.933359	−	0.358944i	$-0.883137\pi$
$271$	−2.56520	+	4.44305i	−0.155825	+	0.269896i	0.777534	+	0.628840i	$0.216470\pi$
$272$	−1.02522	+	1.02522i	−0.0621633	+	0.0621633i
$273$	−16.7525	−	13.1063i	−1.01391	−	0.793227i
$274$		−	11.2071i		−	0.677047i
$275$	2.09055	+	10.3912i	0.126065	+	0.626611i
$276$	9.15220	+	3.67511i	0.550898	+	0.221215i
$277$	−7.12965	+	26.6082i	−0.428379	+	1.59873i	0.328053	+	0.944659i	$0.393608\pi$
$277$	−7.12965	+	26.6082i	−0.428379	+	1.59873i	−0.756432	+	0.654073i	$0.773059\pi$
$278$	−19.4472	+	5.21087i	−1.16637	+	0.312527i
$279$	3.07750	+	0.753417i	0.184245	+	0.0451059i
$280$	−2.54432	+	5.34101i	−0.152052	+	0.319187i
$281$			19.8830i			1.18612i	0.805157	+	0.593062i	$0.202081\pi$
$281$			19.8830i			1.18612i	−0.805157	+	0.593062i	$0.797919\pi$
$282$	15.4079	+	11.5594i	0.917526	+	0.688351i
$283$	−5.11082	−	1.36944i	−0.303807	−	0.0814048i	0.103695	−	0.994609i	$-0.466933\pi$
$283$	−5.11082	−	1.36944i	−0.303807	−	0.0814048i	−0.407502	+	0.913204i	$0.633600\pi$
$284$	0.879690	+	1.52367i	0.0522000	+	0.0904131i
$285$	−18.5173	+	10.1840i	−1.09687	+	0.603246i
$286$	9.83949			0.581821
$287$	−1.37518	+	4.74593i	−0.0811746	+	0.280143i
$288$	−2.56491	+	1.55604i	−0.151139	+	0.0916904i
$289$	−12.9019	−	7.44892i	−0.758935	−	0.438172i
$290$	−10.2074	+	12.4655i	−0.599397	+	0.731997i
$291$	7.88070	−	19.6255i	0.461975	−	1.15047i
$292$	1.20699	−	0.323412i	0.0706338	−	0.0189263i
$293$	21.3392	+	21.3392i	1.24665	+	1.24665i	0.957191	+	0.289456i	$0.0934744\pi$
$293$	21.3392	+	21.3392i	1.24665	+	1.24665i	0.289456	+	0.957191i	$0.406526\pi$
$294$	−12.0622	+	1.22583i	−0.703483	+	0.0714917i
$295$	4.85457	−	10.7455i	0.282644	−	0.625626i
$296$	−5.58163	−	3.22256i	−0.324426	−	0.187307i
$297$	−10.8684	+	1.79253i	−0.630647	+	0.104013i
$298$	11.4078	+	3.05671i	0.660835	+	0.177070i
$299$	−13.2147	+	22.8886i	−0.764228	+	1.32368i
$300$	7.13739	−	4.90486i	0.412078	−	0.283182i
$301$	−5.87645	+	3.23601i	−0.338713	+	0.186521i
$302$	−6.12855	+	6.12855i	−0.352658	+	0.352658i
$303$	6.12709	+	4.59670i	0.351992	+	0.264073i
$304$	4.72549	−	2.72826i	0.271025	−	0.156477i
$305$	18.3281	−	1.82539i	1.04946	−	0.104521i
$306$	3.14170	+	3.00819i	0.179599	+	0.171967i
$307$	17.8595	+	17.8595i	1.01929	+	1.01929i	0.999810	+	0.0194830i	$0.00620203\pi$
$307$	17.8595	+	17.8595i	1.01929	+	1.01929i	0.0194830	+	0.999810i	$0.493798\pi$
$308$	4.04537	−	3.88486i	0.230506	−	0.221360i
$309$	−14.5897	+	11.4488i	−0.829978	+	0.651297i
$310$	2.33045	+	0.382143i	0.132360	+	0.0217042i
$311$	−13.1923	+	7.61659i	−0.748068	+	0.431897i	−0.824996	−	0.565139i	$-0.808822\pi$
$311$	−13.1923	+	7.61659i	−0.748068	+	0.431897i	0.0769272	+	0.997037i	$0.475489\pi$
$312$	−3.15697	−	7.39359i	−0.178728	−	0.418580i
$313$	−5.90424	−	22.0349i	−0.333727	−	1.24549i	−0.905243	−	0.424895i	$-0.860311\pi$
$313$	−5.90424	−	22.0349i	−0.333727	−	1.24549i	0.571515	−	0.820591i	$-0.306356\pi$
$314$	17.4573			0.985172
$315$	16.1849	+	7.28339i	0.911918	+	0.410372i
$316$	15.9827			0.899099
$317$	1.27984	+	4.77643i	0.0718830	+	0.268271i	0.992508	−	0.122176i	$-0.0389872\pi$
$317$	1.27984	+	4.77643i	0.0718830	+	0.268271i	−0.920625	+	0.390447i	$0.872321\pi$
$318$	−4.56106	−	10.6820i	−0.255771	−	0.599015i
$319$	13.2279	−	7.63712i	0.740619	−	0.427596i
$320$	−1.81616	+	1.30445i	−0.101526	+	0.0729207i
$321$	−14.5471	+	11.4153i	−0.811940	+	0.637142i
$322$	3.60389	+	14.6278i	0.200837	+	0.815177i
$323$	−5.59416	−	5.59416i	−0.311267	−	0.311267i
$324$	4.83403	+	7.59159i	0.268557	+	0.421755i
$325$	10.3100	+	20.7919i	0.571894	+	1.15332i
$326$	−4.51534	+	2.60693i	−0.250081	+	0.144385i
$327$	−11.8726	−	8.90715i	−0.656558	−	0.492567i
$328$	−1.32058	+	1.32058i	−0.0729167	+	0.0729167i
$329$	−0.595415	+	29.4171i	−0.0328263	+	1.62181i
$330$	−7.97293	+	1.95973i	−0.438895	+	0.107880i
$331$	0.118156	−	0.204653i	0.00649446	−	0.0112487i	−0.862760	−	0.505614i	$-0.831266\pi$
$331$	0.118156	−	0.204653i	0.00649446	−	0.0112487i	0.869254	+	0.494365i	$0.164599\pi$
$332$	12.9459	+	3.46885i	0.710500	+	0.190378i
$333$	−9.30195	+	16.9508i	−0.509744	+	0.928898i
$334$	7.34183	+	4.23880i	0.401727	+	0.231937i
$335$	−19.7166	+	7.44542i	−1.07723	+	0.406787i
$336$	−4.21710	−	1.79333i	−0.230062	−	0.0978341i
$337$	−0.442376	−	0.442376i	−0.0240977	−	0.0240977i	0.694955	−	0.719053i	$-0.255424\pi$
$337$	−0.442376	−	0.442376i	−0.0240977	−	0.0240977i	−0.719053	+	0.694955i	$0.755424\pi$
$338$	8.25275	−	2.21132i	0.448890	−	0.120280i
$339$	−6.50329	+	16.1953i	−0.353210	+	0.879608i
$340$	2.50838	+	2.05399i	0.136036	+	0.111393i
$341$	−1.93891	−	1.11943i	−0.104998	−	0.0606204i
$342$	−8.49056	−	13.9955i	−0.459117	−	0.756789i
$343$	−12.2771	−	13.8663i	−0.662900	−	0.748708i
$344$	−2.53559			−0.136710
$345$	6.14916	−	21.1786i	0.331060	−	1.14022i
$346$	−2.50658	−	4.34153i	−0.134755	−	0.233402i
$347$	3.94296	+	1.05651i	0.211669	+	0.0567166i	0.363095	−	0.931752i	$-0.381720\pi$
$347$	3.94296	+	1.05651i	0.211669	+	0.0567166i	−0.151426	+	0.988469i	$0.548387\pi$
$348$	−9.98280	−	7.48935i	−0.535134	−	0.401471i
$349$		−	11.9140i		−	0.637743i	−0.947798	−	0.318871i	$-0.896696\pi$
$349$		−	11.9140i		−	0.637743i	0.947798	−	0.318871i	$-0.103304\pi$
$350$	12.4479	+	4.47767i	0.665369	+	0.239342i
$351$	−21.9700	+	9.95010i	−1.17267	+	0.531097i
$352$	2.04764	−	0.548664i	0.109140	−	0.0292439i
$353$	−1.82988	+	6.82920i	−0.0973946	+	0.363482i	−0.997372	−	0.0724557i	$-0.976916\pi$
$353$	−1.82988	+	6.82920i	−0.0973946	+	0.363482i	0.899977	+	0.435937i	$0.143583\pi$
$354$	8.47562	+	3.40342i	0.450474	+	0.180890i
$355$	3.19531	−	2.29502i	0.169589	−	0.121807i
$356$			0.399872i			0.0211931i
$357$	−0.929023	+	6.57894i	−0.0491691	+	0.348194i
$358$	5.72174	−	5.72174i	0.302403	−	0.302403i
$359$	−4.55001	+	7.88085i	−0.240140	+	0.415935i	−0.960754	−	0.277401i	$-0.910527\pi$
$359$	−4.55001	+	7.88085i	−0.240140	+	0.415935i	0.720614	+	0.693337i	$0.243860\pi$
$360$	4.03067	+	5.36225i	0.212435	+	0.282615i
$361$	5.38683	+	9.33027i	0.283518	+	0.491067i
$362$	2.76797	+	10.3302i	0.145481	+	0.542943i
$363$	−11.1878	−	1.34955i	−0.587209	−	0.0708329i
$364$	6.35414	−	10.5087i	0.333047	−	0.550804i
$365$	−0.987086	−	2.61396i	−0.0516665	−	0.136821i
$366$	2.01564	+	14.1240i	0.105359	+	0.738275i
$367$	2.86001	−	10.6737i	0.149291	−	0.557163i	−0.850235	−	0.526403i	$-0.823540\pi$
$367$	2.86001	−	10.6737i	0.149291	−	0.557163i	0.999527	−	0.0307603i	$-0.00979286\pi$
$368$	−1.47375	+	5.50010i	−0.0768244	+	0.286713i
$369$	4.04679	+	3.87481i	0.210667	+	0.201715i
$370$	−5.93347	+	13.1336i	−0.308466	+	0.682784i
$371$	9.18020	−	15.1825i	0.476612	−	0.788236i
$372$	−0.219070	+	1.81610i	−0.0113582	+	0.0941603i
$373$	8.87861	+	33.1354i	0.459717	+	1.71569i	0.673837	+	0.738880i	$0.264645\pi$
$373$	8.87861	+	33.1354i	0.459717	+	1.71569i	−0.214120	+	0.976807i	$0.568688\pi$
$374$	−1.53679	−	2.66180i	−0.0794655	−	0.137638i
$375$	−12.4953	−	14.7942i	−0.645253	−	0.763969i
$376$	−5.56044	+	9.63096i	−0.286758	+	0.496679i
$377$	23.6481	−	23.6481i	1.21794	−	1.21794i
$378$	−5.10413	+	12.7651i	−0.262528	+	0.656566i
$379$			17.2109i			0.884063i	0.897000	+	0.442031i	$0.145742\pi$
$379$			17.2109i			0.884063i	−0.897000	+	0.442031i	$0.854258\pi$
$380$	−7.11774	−	9.90990i	−0.365132	−	0.508367i
$381$	10.3023	−	25.6561i	0.527804	−	1.31440i
$382$	0.193562	−	0.722383i	0.00990350	−	0.0369604i
$383$	18.3791	−	4.92466i	0.939128	−	0.251639i	0.243385	−	0.969930i	$-0.421742\pi$
$383$	18.3791	−	4.92466i	0.939128	−	0.251639i	0.695743	+	0.718291i	$0.255075\pi$
$384$	−1.06926	−	1.36260i	−0.0545653	−	0.0695351i
$385$	−9.54051	−	8.14029i	−0.486230	−	0.414867i
$386$		−	9.25799i		−	0.471220i
$387$	0.165104	+	7.60498i	0.00839270	+	0.386583i
$388$	11.7941	+	3.16023i	0.598756	+	0.160436i
$389$	−18.4175	−	31.9000i	−0.933804	−	1.61740i	−0.776752	−	0.629806i	$-0.783134\pi$
$389$	−18.4175	−	31.9000i	−0.933804	−	1.61740i	−0.157052	−	0.987590i	$-0.550199\pi$
$390$	−15.7516	+	8.66289i	−0.797612	+	0.438663i
$391$	8.25583			0.417515
$392$	−1.53665	−	6.82925i	−0.0776126	−	0.344929i
$393$	1.20102	−	9.95650i	0.0605833	−	0.502239i
$394$	−3.32367	−	1.91892i	−0.167444	−	0.0966739i
$395$	−3.54185	−	35.5625i	−0.178210	−	1.78935i
$396$	−1.77894	−	6.10576i	−0.0893949	−	0.306826i
$397$	19.3405	−	5.18227i	0.970672	−	0.260091i	0.261561	−	0.965187i	$-0.415763\pi$
$397$	19.3405	−	5.18227i	0.970672	−	0.260091i	0.709112	+	0.705096i	$0.249096\pi$
$398$	3.96399	+	3.96399i	0.198697	+	0.198697i
$399$	9.78535	−	23.0107i	0.489880	−	1.15198i
$400$	3.30494	+	3.75198i	0.165247	+	0.187599i
$401$	−9.00824	−	5.20091i	−0.449850	−	0.259721i	0.257917	−	0.966167i	$-0.416964\pi$
$401$	−9.00824	−	5.20091i	−0.449850	−	0.259721i	−0.707767	+	0.706446i	$0.750297\pi$
$402$	−6.41065	−	15.0137i	−0.319734	−	0.748815i
$403$	−4.73502	−	1.26874i	−0.235868	−	0.0632006i
$404$	−2.21116	+	3.82984i	−0.110009	+	0.190542i
$405$	15.8205	−	12.4383i	0.786127	−	0.618065i
$406$	0.385771	−	19.0594i	0.0191455	−	0.945901i
$407$	9.66109	−	9.66109i	0.478883	−	0.478883i
$408$	−1.50705	+	2.00880i	−0.0746103	+	0.0994506i
$409$	−13.4035	+	7.73849i	−0.662758	+	0.382644i	−0.793327	−	0.608796i	$-0.791653\pi$
$409$	−13.4035	+	7.73849i	−0.662758	+	0.382644i	0.130569	+	0.991439i	$0.458320\pi$
$410$	3.23101	+	2.64572i	0.159568	+	0.130663i
$411$	−2.74240	−	19.2166i	−0.135273	−	0.947886i
$412$	−7.57114	−	7.57114i	−0.373003	−	0.373003i
$413$	3.33747	+	13.5465i	0.164226	+	0.666577i
$414$	16.5924	+	4.06206i	0.815471	+	0.199640i
$415$	4.84952	−	29.5742i	0.238054	−	1.45174i
$416$	4.01969	−	2.32077i	0.197082	−	0.113785i
$417$	−32.0706	+	13.6937i	−1.57051	+	0.670586i
$418$	2.99380	+	11.1730i	0.146432	+	0.546490i
$419$	−14.9110			−0.728451			−0.364225	−	0.931311i	$-0.618666\pi$
$419$	−14.9110			−0.728451			−0.364225	+	0.931311i	$0.618666\pi$
$420$	−3.05574	+	9.78072i	−0.149105	+	0.477250i
$421$	−16.5292			−0.805586			−0.402793	−	0.915291i	$-0.631960\pi$
$421$	−16.5292			−0.805586			−0.402793	+	0.915291i	$0.631960\pi$
$422$	3.84211	+	14.3389i	0.187031	+	0.698009i
$423$	29.2482	+	16.0503i	1.42209	+	0.780391i
$424$	5.80749	−	3.35295i	0.282036	−	0.162834i
$425$	4.01438	−	6.03647i	0.194726	−	0.292812i
$426$	1.88123	+	2.39734i	0.0911459	+	0.116151i
$427$	−15.7190	+	15.0953i	−0.760694	+	0.730511i
$428$	−7.54904	−	7.54904i	−0.364897	−	0.364897i
$429$	16.8716	−	2.40774i	0.814566	−	0.116247i
$430$	0.561898	+	5.64184i	0.0270971	+	0.272074i
$431$	6.60065	−	3.81089i	0.317942	−	0.183564i	−0.332533	−	0.943092i	$-0.607903\pi$
$431$	6.60065	−	3.81089i	0.317942	−	0.183564i	0.650475	+	0.759528i	$0.274570\pi$
$432$	−4.01722	+	3.29574i	−0.193279	+	0.158566i
$433$	−7.94117	+	7.94117i	−0.381628	+	0.381628i	−0.871689	−	0.490060i	$-0.836975\pi$
$433$	−7.94117	+	7.94117i	−0.381628	+	0.381628i	0.490060	+	0.871689i	$0.336975\pi$
$434$	−2.44767	+	1.34787i	−0.117492	+	0.0646997i
$435$	−14.4520	+	23.8720i	−0.692921	+	1.14458i
$436$	4.28463	−	7.42120i	0.205197	−	0.355411i
$437$	−30.0114	−	8.04154i	−1.43564	−	0.384679i
$438$	1.99046	−	0.849901i	0.0951079	−	0.0406098i
$439$	−11.5080	−	6.64413i	−0.549245	−	0.317107i	0.199572	−	0.979883i	$-0.436045\pi$
$439$	−11.5080	−	6.64413i	−0.549245	−	0.317107i	−0.748818	+	0.662776i	$0.769378\pi$
$440$	−1.67458	−	4.43454i	−0.0798324	−	0.211409i
$441$	−20.3829	+	5.05355i	−0.970613	+	0.240645i
$442$	−4.75862	−	4.75862i	−0.226344	−	0.226344i
$443$	23.7141	−	6.35418i	1.12669	−	0.301896i	0.353104	−	0.935584i	$-0.385126\pi$
$443$	23.7141	−	6.35418i	1.12669	−	0.301896i	0.773589	+	0.633688i	$0.218460\pi$
$444$	−10.3593	−	4.15981i	−0.491629	−	0.197416i
$445$	0.889738	−	0.0886134i	0.0421776	−	0.00420068i
$446$	6.15816	+	3.55542i	0.291597	+	0.168354i
$447$	20.3087	+	2.44976i	0.960566	+	0.115870i
$448$	0.736347	−	2.54122i	0.0347891	−	0.120061i
$449$	5.93549			0.280113			0.140056	−	0.990144i	$-0.455272\pi$
$449$	5.93549			0.280113			0.140056	+	0.990144i	$0.455272\pi$
$450$	11.0381	−	10.1568i	0.520341	−	0.478795i
$451$	−1.97952	−	3.42863i	−0.0932119	−	0.161448i
$452$	−9.73272	−	2.60787i	−0.457789	−	0.122664i
$453$	−9.00882	+	12.0082i	−0.423271	+	0.564192i
$454$			11.6375i			0.546175i
$455$	−24.7905	−	11.8096i	−1.16220	−	0.553641i
$456$	7.43508	−	5.83443i	0.348180	−	0.273222i
$457$	10.0583	−	2.69512i	0.470508	−	0.126072i	−0.0157712	−	0.999876i	$-0.505020\pi$
$457$	10.0583	−	2.69512i	0.470508	−	0.126072i	0.486280	+	0.873803i	$0.338354\pi$
$458$	−1.07047	+	3.99505i	−0.0500198	+	0.186676i
$459$	6.12312	+	4.38930i	0.285803	+	0.204875i
$460$	12.5646	+	2.06033i	0.585829	+	0.0960633i
$461$		−	32.7232i		−	1.52407i	−0.647535	−	0.762035i	$-0.724200\pi$
$461$		−	32.7232i		−	1.52407i	0.647535	−	0.762035i	$-0.275800\pi$
$462$	5.98587	−	7.65119i	0.278488	−	0.355966i
$463$	6.59995	−	6.59995i	0.306726	−	0.306726i	−0.536912	−	0.843638i	$-0.680409\pi$
$463$	6.59995	−	6.59995i	0.306726	−	0.306726i	0.843638	+	0.536912i	$0.180409\pi$
$464$	3.60262	−	6.23993i	0.167248	−	0.289681i
$465$	4.08948	+	0.0849870i	0.189645	+	0.00394118i
$466$	−11.3521	−	19.6623i	−0.525874	−	0.910841i
$467$	0.208078	+	0.776556i	0.00962868	+	0.0359347i	0.970573	−	0.240807i	$-0.0774121\pi$
$467$	0.208078	+	0.776556i	0.00962868	+	0.0359347i	−0.960944	+	0.276742i	$0.910745\pi$
$468$	−7.22241	−	11.9051i	−0.333856	−	0.550314i
$469$	12.9029	−	21.3393i	0.595803	−	0.985357i
$470$	22.6617	+	10.2380i	1.04531	+	0.472246i
$471$	29.9336	−	4.27183i	1.37927	−	0.196836i
$472$	−1.36480	+	5.09350i	−0.0628200	+	0.234447i
$473$	1.39119	−	5.19198i	0.0639669	−	0.238728i
$474$	27.4052	−	3.91100i	1.25876	−	0.179638i
$475$	−20.4728	+	18.0335i	−0.939357	+	0.827432i
$476$	−3.83525	−	0.0776272i	−0.175788	−	0.00355804i
$477$	−10.4346	−	17.2000i	−0.477770	−	0.787535i
$478$	2.74758	+	10.2541i	0.125672	+	0.469013i
$479$	8.48718	+	14.7002i	0.387789	+	0.671670i	0.992152	−	0.125039i	$-0.0399056\pi$
$479$	8.48718	+	14.7002i	0.387789	+	0.671670i	−0.604363	+	0.796709i	$0.706572\pi$
$480$	−2.79492	+	2.68112i	−0.127570	+	0.122376i
$481$	14.9576	−	25.9074i	0.682009	−	1.18127i
$482$	−14.2319	+	14.2319i	−0.648245	+	0.648245i
$483$	9.75897	+	24.2001i	0.444049	+	1.10114i
$484$		−	6.50612i		−	0.295733i
$485$	4.41806	−	26.9430i	0.200614	−	1.22342i
$486$	10.1465	+	11.8342i	0.460253	+	0.536812i
$487$	−4.13903	+	15.4471i	−0.187557	+	0.699974i	0.806511	+	0.591219i	$0.201353\pi$
$487$	−4.13903	+	15.4471i	−0.187557	+	0.699974i	−0.994069	+	0.108755i	$0.965314\pi$
$488$	−7.95646	+	2.13193i	−0.360172	+	0.0965078i
$489$	−7.10443	+	5.57496i	−0.321273	+	0.252108i
$490$	−14.8550	+	4.93253i	−0.671079	+	0.222829i
$491$		−	6.87591i		−	0.310305i	−0.987891	−	0.155153i	$-0.950413\pi$
$491$		−	6.87591i		−	0.310305i	0.987891	−	0.155153i	$-0.0495869\pi$
$492$	−1.94122	+	2.58751i	−0.0875168	+	0.116654i
$493$	−10.0908	−	2.70383i	−0.454468	−	0.121774i
$494$	12.6633	+	21.9335i	0.569750	+	0.986837i
$495$	−13.1915	+	5.31131i	−0.592912	+	0.238725i
$496$	−1.05613			−0.0474215
$497$	−1.29551	+	4.47097i	−0.0581117	+	0.200550i
$498$	23.0469	+	2.78007i	1.03276	+	0.124578i
$499$	26.8381	+	15.4950i	1.20144	+	0.693651i	0.960875	−	0.276982i	$-0.0893343\pi$
$499$	26.8381	+	15.4950i	1.20144	+	0.693651i	0.240564	+	0.970633i	$0.422668\pi$
$500$	7.61600	−	8.18514i	0.340598	−	0.366051i
$501$	13.6261	+	5.47163i	0.608770	+	0.244454i
$502$	−17.2316	+	4.61720i	−0.769085	+	0.206076i
$503$	19.3755	+	19.3755i	0.863913	+	0.863913i	0.991790	−	0.127877i	$-0.0408164\pi$
$503$	19.3755	+	19.3755i	0.863913	+	0.863913i	−0.127877	+	0.991790i	$0.540816\pi$
$504$	−7.66981	−	2.04305i	−0.341640	−	0.0910046i
$505$	9.01164	+	4.07126i	0.401013	+	0.181168i
$506$	−10.4537	−	6.03542i	−0.464722	−	0.268307i
$507$	13.6097	−	5.81116i	0.604428	−	0.258083i
$508$	15.4183	+	4.13131i	0.684075	+	0.183297i
$509$	−10.4397	+	18.0821i	−0.462733	+	0.801477i	−0.999096	−	0.0425105i	$-0.986464\pi$
$509$	−10.4397	+	18.0821i	−0.462733	+	0.801477i	0.536363	+	0.843987i	$0.319798\pi$
$510$	4.80368	+	2.90813i	0.212710	+	0.128774i
$511$	2.82909	+	1.71063i	0.125151	+	0.0756736i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−17.9833	−	21.9201i	−0.793982	−	0.967795i
$514$	−0.863752	+	0.498688i	−0.0380985	+	0.0219962i
$515$	−15.1684	+	18.5240i	−0.668401	+	0.816266i
$516$	−4.34772	+	0.620464i	−0.191398	+	0.0273144i
$517$	−16.6700	−	16.6700i	−0.733144	−	0.733144i
$518$	−4.07921	−	16.5571i	−0.179230	−	0.727476i
$519$	−5.36037	−	6.83096i	−0.235294	−	0.299846i
$520$	−6.05463	−	8.42976i	−0.265513	−	0.369669i
$521$	−18.9520	+	10.9419i	−0.830300	+	0.479374i	−0.853956	−	0.520346i	$-0.825803\pi$
$521$	−18.9520	+	10.9419i	−0.830300	+	0.479374i	0.0236551	+	0.999720i	$0.492470\pi$
$522$	−18.9500	−	10.3990i	−0.829417	−	0.455152i
$523$	−3.39310	−	12.6632i	−0.148370	−	0.553724i	−0.999582	−	0.0289028i	$-0.990799\pi$
$523$	−3.39310	−	12.6632i	−0.148370	−	0.553724i	0.851212	−	0.524822i	$-0.175868\pi$
$524$	5.79006			0.252940
$525$	22.4399	+	4.63174i	0.979355	+	0.202146i
$526$	17.2603			0.752586
$527$	0.396320	+	1.47909i	0.0172640	+	0.0644300i
$528$	3.37679	−	1.44185i	0.146956	−	0.0627483i
$529$	8.16059	−	4.71152i	0.354808	−	0.204849i
$530$	−8.74749	−	12.1790i	−0.379967	−	0.529021i
$531$	15.3658	+	3.76177i	0.666818	+	0.163247i
$532$	13.8662	+	4.01789i	0.601177	+	0.174198i
$533$	−6.12951	−	6.12951i	−0.265499	−	0.265499i
$534$	0.0978493	+	0.685651i	0.00423435	+	0.0296710i
$535$	−15.1242	+	18.4700i	−0.653875	+	0.798527i
$536$	8.16253	−	4.71264i	0.352568	−	0.203555i
$537$	8.41082	−	11.2111i	0.362954	−	0.483793i
$538$	19.5452	−	19.5452i	0.842653	−	0.842653i
$539$	14.8270	+	0.600456i	0.638643	+	0.0258635i
$540$	8.22346	+	8.20821i	0.353881	+	0.353225i
$541$	−11.6807	+	20.2316i	−0.502194	+	0.869826i	0.497803	+	0.867290i	$0.334140\pi$
$541$	−11.6807	+	20.2316i	−0.502194	+	0.869826i	−0.999997	+	0.00253553i	$0.999193\pi$
$542$	−4.95558	−	1.32784i	−0.212860	−	0.0570358i
$543$	7.27399	+	17.0356i	0.312157	+	0.731069i
$544$	−1.25564	−	0.724943i	−0.0538350	−	0.0310817i
$545$	−17.4621	−	7.88899i	−0.747995	−	0.337927i
$546$	8.32381	−	19.5738i	0.356226	−	0.837683i
$547$	−2.60152	−	2.60152i	−0.111233	−	0.111233i	0.649300	−	0.760533i	$-0.275062\pi$
$547$	−2.60152	−	2.60152i	−0.111233	−	0.111233i	−0.760533	+	0.649300i	$0.775062\pi$
$548$	10.8253	−	2.90062i	0.462432	−	0.123908i
$549$	6.91236	+	23.7249i	0.295012	+	1.01256i
$550$	−9.49603	+	4.70875i	−0.404912	+	0.200782i
$551$	34.0483	+	19.6578i	1.45051	+	0.837451i
$552$	−1.18112	+	9.79153i	−0.0502717	+	0.416755i
$553$	29.2897	+	30.4999i	1.24553	+	1.29699i
$554$	−27.5468			−1.17035
$555$	−6.96017	+	23.9718i	−0.295443	+	1.01755i
$556$	−10.0666	−	17.4359i	−0.426920	−	0.739448i
$557$	36.8670	+	9.87848i	1.56211	+	0.418565i	0.933329	−	0.359022i	$-0.116890\pi$
$557$	36.8670	+	9.87848i	1.56211	+	0.418565i	0.628776	+	0.777587i	$0.283556\pi$
$558$	0.0687692	+	3.16763i	0.00291123	+	0.134097i
$559$		−	11.7690i		−	0.497777i
$560$	−5.81754	−	1.07527i	−0.245836	−	0.0454384i
$561$	−3.28645	−	4.18807i	−0.138754	−	0.176820i
$562$	−19.2055	+	5.14611i	−0.810137	+	0.217076i
$563$	−1.02963	+	3.84263i	−0.0433937	+	0.161948i	−0.984223	−	0.176934i	$-0.943382\pi$
$563$	−1.02963	+	3.84263i	−0.0433937	+	0.161948i	0.940829	+	0.338882i	$0.110049\pi$
$564$	−7.17765	+	17.8747i	−0.302234	+	0.752659i
$565$	−3.64586	+	22.2338i	−0.153383	+	0.935383i
$566$		−	5.29112i		−	0.222402i
$567$	−5.62829	+	23.1370i	−0.236366	+	0.971664i
$568$	−1.24407	+	1.24407i	−0.0522000	+	0.0522000i
$569$	−2.50482	+	4.33847i	−0.105007	+	0.181878i	−0.913741	−	0.406297i	$-0.866820\pi$
$569$	−2.50482	+	4.33847i	−0.105007	+	0.181878i	0.808734	+	0.588175i	$0.200153\pi$
$570$	−14.6296	−	15.2506i	−0.612767	−	0.638776i
$571$	−16.4609	−	28.5111i	−0.688867	−	1.19315i	−0.972205	−	0.234132i	$-0.924775\pi$
$571$	−16.4609	−	28.5111i	−0.688867	−	1.19315i	0.283338	−	0.959020i	$-0.408558\pi$
$572$	2.54665	+	9.50422i	0.106481	+	0.397391i
$573$	0.155128	−	1.28602i	0.00648057	−	0.0537243i
$574$	−4.94014	−	0.0999906i	−0.206197	−	0.00417353i
$575$	1.79997	−	28.4137i	0.0750641	−	1.18493i
$576$	−2.16686	−	2.07478i	−0.0902860	−	0.0864491i
$577$	5.90675	−	22.0443i	0.245901	−	0.917716i	−0.727027	−	0.686609i	$-0.759099\pi$
$577$	5.90675	−	22.0443i	0.245901	−	0.917716i	0.972928	−	0.231107i	$-0.0742347\pi$
$578$	3.85584	−	14.3902i	0.160382	−	0.598553i
$579$	−2.26545	−	15.8745i	−0.0941489	−	0.659721i
$580$	−14.6826	−	6.63326i	−0.609660	−	0.275431i
$581$	17.1049	+	31.0617i	0.709631	+	1.28866i
$582$	20.9964	+	2.53273i	0.870330	+	0.104985i
$583$	3.67929	+	13.7313i	0.152381	+	0.568693i
$584$	0.624785	+	1.08216i	0.0258538	+	0.0447800i
$585$	−24.8891	+	18.7085i	−1.02904	+	0.773502i
$586$	−15.0891	+	26.1350i	−0.623324	+	1.07963i
$587$	−29.3071	+	29.3071i	−1.20963	+	1.20963i	−0.238489	+	0.971145i	$0.576652\pi$
$587$	−29.3071	+	29.3071i	−1.20963	+	1.20963i	−0.971145	+	0.238489i	$0.923348\pi$
$588$	−4.30599	−	11.3340i	−0.177576	−	0.467404i
$589$		−	5.76278i		−	0.237451i
$590$	11.6358	+	1.90802i	0.479038	+	0.0785519i
$591$	−6.16859	−	2.47702i	−0.253742	−	0.101891i
$592$	1.66812	−	6.22550i	0.0685593	−	0.255867i
$593$	21.0623	−	5.64362i	0.864925	−	0.231756i	0.201033	−	0.979584i	$-0.435570\pi$
$593$	21.0623	−	5.64362i	0.864925	−	0.231756i	0.663892	+	0.747829i	$0.268904\pi$
$594$	−4.54439	−	10.0341i	−0.186459	−	0.411704i
$595$	0.677184	+	8.55087i	0.0277618	+	0.350551i
$596$			11.8102i			0.483765i
$597$	7.76697	+	5.82698i	0.317881	+	0.238482i
$598$	−25.5289	−	6.84045i	−1.04396	−	0.279727i
$599$	6.91835	+	11.9829i	0.282676	+	0.489610i	0.972043	−	0.234803i	$-0.0754445\pi$
$599$	6.91835	+	11.9829i	0.282676	+	0.489610i	−0.689367	+	0.724413i	$0.742111\pi$
$600$	6.58502	+	5.62472i	0.268832	+	0.229628i
$601$	7.92094			0.323102			0.161551	−	0.986864i	$-0.448350\pi$
$601$	7.92094			0.323102			0.161551	+	0.986864i	$0.448350\pi$
$602$	−4.64669	−	4.83868i	−0.189385	−	0.197210i
$603$	−14.6661	−	24.1750i	−0.597249	−	0.984481i
$604$	−7.50591	−	4.33354i	−0.305411	−	0.176329i
$605$	−14.4765	+	1.44179i	−0.588554	+	0.0586170i
$606$	−2.85426	+	7.10802i	−0.115946	+	0.288744i
$607$	−31.9387	+	8.55795i	−1.29635	+	0.347356i	−0.840070	−	0.542479i	$-0.817486\pi$
$607$	−31.9387	+	8.55795i	−1.29635	+	0.347356i	−0.456282	+	0.889835i	$0.650819\pi$
$608$	3.85835	+	3.85835i	0.156477	+	0.156477i
$609$	−4.00240	−	32.7751i	−0.162185	−	1.32811i
$610$	6.50685	+	17.2312i	0.263455	+	0.697669i
$611$	−44.7025	−	25.8090i	−1.80847	−	1.04412i
$612$	−2.09256	+	3.81323i	−0.0845866	+	0.154141i
$613$	−9.17128	−	2.45744i	−0.370424	−	0.0992549i	0.0688043	−	0.997630i	$-0.478082\pi$
$613$	−9.17128	−	2.45744i	−0.370424	−	0.0992549i	−0.439229	+	0.898375i	$0.644748\pi$
$614$	−12.6285	+	21.8733i	−0.509647	+	0.882734i
$615$	6.18755	+	3.74592i	0.249506	+	0.151050i
$616$	4.79950	+	2.90205i	0.193378	+	0.116927i
$617$	−13.7827	+	13.7827i	−0.554873	+	0.554873i	−0.927843	−	0.372971i	$-0.878339\pi$
$617$	−13.7827	+	13.7827i	−0.554873	+	0.554873i	0.372971	+	0.927843i	$0.378339\pi$
$618$	−14.8347	−	11.1294i	−0.596741	−	0.447690i
$619$	6.45537	−	3.72701i	0.259463	−	0.149801i	−0.364626	−	0.931154i	$-0.618803\pi$
$619$	6.45537	−	3.72701i	0.259463	−	0.149801i	0.624090	+	0.781353i	$0.285470\pi$
$620$	0.234042	+	2.34994i	0.00939937	+	0.0943760i
$621$	29.4446	+	2.90495i	1.18157	+	0.116571i
$622$	−10.7715	−	10.7715i	−0.431897	−	0.431897i
$623$	−0.763077	+	0.732799i	−0.0305720	+	0.0293590i
$624$	6.32458	−	4.96300i	0.253186	−	0.198679i
$625$	−19.9002	−	15.1322i	−0.796007	−	0.605288i
$626$	19.7560	−	11.4061i	0.789607	−	0.455880i
$627$	7.86747	+	18.4255i	0.314196	+	0.735845i
$628$	4.51828	+	16.8625i	0.180299	+	0.672885i
$629$	−9.34468			−0.372597
$630$	−2.84624	+	17.5185i	−0.113397	+	0.697955i
$631$	−49.0067			−1.95093			−0.975463	−	0.220162i	$-0.929342\pi$
$631$	−49.0067			−1.95093			−0.975463	+	0.220162i	$0.929342\pi$
$632$	4.13664	+	15.4381i	0.164547	+	0.614096i
$633$	10.0967	+	23.6465i	0.401310	+	0.939864i
$634$	−4.28243	+	2.47246i	−0.170077	+	0.0981940i
$635$	5.77566	−	35.2221i	0.229200	−	1.39775i
$636$	9.13750	−	7.17034i	0.362325	−	0.284322i
$637$	31.6982	−	7.13242i	1.25593	−	0.282597i
$638$	10.8005	+	10.8005i	0.427596	+	0.427596i
$639$	3.81234	+	3.65032i	0.150814	+	0.144405i
$640$	−1.73005	−	1.41666i	−0.0683864	−	0.0559983i
$641$	20.1256	−	11.6195i	0.794915	−	0.458944i	−0.0467751	−	0.998905i	$-0.514894\pi$
$641$	20.1256	−	11.6195i	0.794915	−	0.458944i	0.841690	+	0.539961i	$0.181561\pi$
$642$	−14.7914	−	11.0969i	−0.583772	−	0.437960i
$643$	15.5301	−	15.5301i	0.612445	−	0.612445i	−0.331137	−	0.943583i	$-0.607432\pi$
$643$	15.5301	−	15.5301i	0.612445	−	0.612445i	0.943583	+	0.331137i	$0.107432\pi$
$644$	−13.1966	+	7.26705i	−0.520020	+	0.286362i
$645$	2.34404	+	9.53644i	0.0922966	+	0.375497i
$646$	3.95567	−	6.85142i	0.155634	−	0.269565i
$647$	41.7186	+	11.1785i	1.64013	+	0.439471i	0.956825	−	0.290663i	$-0.0938760\pi$
$647$	41.7186	+	11.1785i	1.64013	+	0.439471i	0.683303	+	0.730135i	$0.260543\pi$
$648$	−6.08177	+	6.63416i	−0.238915	+	0.260614i
$649$	−9.68086	−	5.58925i	−0.380007	−	0.219397i
$650$	−17.4150	+	15.3400i	−0.683072	+	0.601684i
$651$	−3.86713	+	2.91011i	−0.151565	+	0.114056i
$652$	−3.68676	−	3.68676i	−0.144385	−	0.144385i
$653$	−24.1492	+	6.47076i	−0.945031	+	0.253220i	−0.698252	−	0.715852i	$-0.746039\pi$
$653$	−24.1492	+	6.47076i	−0.945031	+	0.253220i	−0.246778	+	0.969072i	$0.579372\pi$
$654$	5.53078	−	13.7734i	0.216271	−	0.538584i
$655$	−1.28310	−	12.8832i	−0.0501350	−	0.503389i
$656$	−1.61737	−	0.933789i	−0.0631477	−	0.0364583i
$657$	3.20503	−	1.94438i	0.125040	−	0.0758573i
$658$	−28.5688	+	7.03857i	−1.11373	+	0.274392i
$659$	20.0343			0.780425			0.390213	−	0.920725i	$-0.372401\pi$
$659$	20.0343			0.780425			0.390213	+	0.920725i	$0.372401\pi$
$660$	−3.95650	−	7.19404i	−0.154007	−	0.280028i
$661$	−6.62569	−	11.4760i	−0.257709	−	0.446366i	0.707918	−	0.706294i	$-0.249634\pi$
$661$	−6.62569	−	11.4760i	−0.257709	−	0.446366i	−0.965628	+	0.259928i	$0.916301\pi$
$662$	0.228261	+	0.0611622i	0.00887160	+	0.00237714i
$663$	−9.32394	−	6.99505i	−0.362112	−	0.271665i
$664$			13.4026i			0.520122i
$665$	5.86723	−	31.7436i	0.227522	−	1.23096i
$666$	−18.7807	−	4.59781i	−0.727739	−	0.178161i
$667$	−39.6296	+	10.6187i	−1.53446	+	0.411158i
$668$	−2.19417	+	8.18874i	−0.0848949	+	0.316832i
$669$	11.4293	+	4.58948i	0.441882	+	0.177440i
$670$	−12.2948	−	17.1178i	−0.474988	−	0.661318i
$671$		−	17.4617i		−	0.674102i
$672$	0.640756	−	4.53756i	0.0247177	−	0.175040i
$673$	−18.6445	+	18.6445i	−0.718692	+	0.718692i	−0.968337	−	0.249645i	$-0.919686\pi$
$673$	−18.6445	+	18.6445i	−0.718692	+	0.718692i	0.249645	+	0.968337i	$0.419686\pi$
$674$	0.312807	−	0.541798i	0.0120489	−	0.0208693i
$675$	16.4414	−	20.1167i	0.632830	−	0.774291i
$676$	4.27194	+	7.39921i	0.164305	+	0.284585i
$677$	−12.8090	−	47.8038i	−0.492290	−	1.83725i	−0.544709	−	0.838625i	$-0.683360\pi$
$677$	−12.8090	−	47.8038i	−0.492290	−	1.83725i	0.0524196	−	0.998625i	$-0.483307\pi$
$678$	−17.3266	−	2.09005i	−0.665425	−	0.0802679i
$679$	15.5831	+	28.2982i	0.598024	+	1.08598i
$680$	−1.33479	+	2.95452i	−0.0511867	+	0.113301i
$681$	2.84772	+	19.9546i	0.109125	+	0.764661i
$682$	0.579459	−	2.16257i	0.0221886	−	0.0828091i
$683$	−2.56877	+	9.58678i	−0.0982913	+	0.366828i	−0.997498	−	0.0706962i	$-0.977478\pi$
$683$	−2.56877	+	9.58678i	−0.0982913	+	0.366828i	0.899207	+	0.437524i	$0.144145\pi$
$684$	11.3211	−	11.8235i	0.432872	−	0.452085i
$685$	−8.85297	−	23.4440i	−0.338255	−	0.895751i
$686$	10.2162	−	15.4476i	0.390058	−	0.589792i
$687$	−0.857916	+	7.11217i	−0.0327315	+	0.271346i
$688$	−0.656259	−	2.44919i	−0.0250196	−	0.0933746i
$689$	15.5629	+	26.9557i	0.592898	+	1.02693i
$690$	22.0485	+	0.458209i	0.839371	+	0.0174437i
$691$	−3.42873	+	5.93874i	−0.130435	+	0.225920i	−0.923844	−	0.382768i	$-0.874971\pi$
$691$	−3.42873	+	5.93874i	−0.130435	+	0.225920i	0.793409	+	0.608689i	$0.208304\pi$
$692$	3.54485	−	3.54485i	0.134755	−	0.134755i
$693$	8.39159	−	14.5841i	0.318770	−	0.554004i
$694$			4.08205i			0.154953i
$695$	−36.5651	+	26.2627i	−1.38700	+	0.996202i
$696$	4.65042	−	11.5810i	0.176274	−	0.438978i
$697$	−0.700824	+	2.61551i	−0.0265456	+	0.0990695i
$698$	11.5081	−	3.08358i	0.435587	−	0.116715i
$699$	−24.2765	−	30.9367i	−0.918223	−	1.17013i
$700$	−1.10334	+	13.1827i	−0.0417025	+	0.498258i
$701$			28.8845i			1.09095i	0.838127	+	0.545476i	$0.183651\pi$
$701$			28.8845i			1.09095i	−0.838127	+	0.545476i	$0.816349\pi$
$702$	−15.2973	−	18.6461i	−0.577360	−	0.703752i
$703$	33.9696	+	9.10213i	1.28119	+	0.343293i
$704$	1.05994	+	1.83587i	0.0399479	+	0.0691918i
$705$	41.3628	+	12.0096i	1.55781	+	0.452307i
$706$	−7.07011			−0.266087
$707$	−11.3607	+	2.79895i	−0.427261	+	0.105265i
$708$	−1.09380	+	9.06769i	−0.0411076	+	0.340785i
$709$	−21.3823	−	12.3450i	−0.803027	−	0.463628i	0.0415013	−	0.999138i	$-0.486786\pi$
$709$	−21.3823	−	12.3450i	−0.803027	−	0.463628i	−0.844529	+	0.535510i	$0.820119\pi$
$710$	3.04382	+	2.49244i	0.114233	+	0.0935395i
$711$	46.0341	−	13.4122i	1.72641	−	0.502998i
$712$	−0.386246	+	0.103494i	−0.0144752	+	0.00387862i
$713$	4.25234	+	4.25234i	0.159251	+	0.159251i
$714$	−6.59522	+	0.805388i	−0.246820	+	0.0301409i
$715$	20.5831	−	7.77262i	0.769764	−	0.290679i
$716$	7.00767	+	4.04588i	0.261889	+	0.151202i
$717$	7.22043	+	16.9102i	0.269652	+	0.631522i
$718$	−8.78994	−	2.35526i	−0.328038	−	0.0878975i
$719$	11.2630	−	19.5080i	0.420038	−	0.727527i	−0.575905	−	0.817517i	$-0.695350\pi$
$719$	11.2630	−	19.5080i	0.420038	−	0.727527i	0.995943	+	0.0899900i	$0.0286835\pi$
$720$	−4.13632	+	5.28118i	−0.154151	+	0.196818i
$721$	0.573266	−	28.3228i	0.0213496	−	1.05480i
$722$	−7.61813	+	7.61813i	−0.283518	+	0.283518i
$723$	−20.9205	+	27.8857i	−0.778043	+	1.03708i
$724$	−9.26180	+	5.34730i	−0.344212	+	0.198731i
$725$	−11.5057	+	34.1396i	−0.427310	+	1.26791i
$726$	−1.59206	−	11.1559i	−0.0590869	−	0.414035i
$727$	6.61815	+	6.61815i	0.245454	+	0.245454i	0.819102	−	0.573648i	$-0.194472\pi$
$727$	6.61815	+	6.61815i	0.245454	+	0.245454i	−0.573648	+	0.819102i	$0.694472\pi$
$728$	11.7952	+	3.41778i	0.437158	+	0.126671i
$729$	20.2938	+	17.8090i	0.751622	+	0.659594i
$730$	2.26941	−	1.62999i	0.0839947	−	0.0603288i
$731$	−3.18378	+	1.83816i	−0.117756	+	0.0679867i
$732$	−13.1211	+	5.60253i	−0.484969	+	0.207075i
$733$	0.500074	+	1.86630i	0.0184707	+	0.0689334i	0.974546	−	0.224188i	$-0.0719728\pi$
$733$	0.500074	+	1.86630i	0.0184707	+	0.0689334i	−0.956075	+	0.293121i	$0.905306\pi$
$734$	11.0502			0.407872
$735$	−24.2645	+	12.0927i	−0.895009	+	0.446048i
$736$	−5.69412			−0.209888
$737$	5.17132	+	19.2996i	0.190488	+	0.710911i
$738$	−2.69539	+	4.91177i	−0.0992188	+	0.180805i
$739$	9.70996	−	5.60605i	0.357187	−	0.206222i	−0.310659	−	0.950521i	$-0.600550\pi$
$739$	9.70996	−	5.60605i	0.357187	−	0.206222i	0.667846	+	0.744299i	$0.267216\pi$
$740$	−14.2218	−	2.33206i	−0.522803	−	0.0857284i
$741$	27.0807	+	34.5102i	0.994835	+	1.26776i
$742$	17.0412	+	4.93787i	0.625601	+	0.181275i
$743$	11.6014	+	11.6014i	0.425613	+	0.425613i	0.887131	−	0.461518i	$-0.152695\pi$
$743$	11.6014	+	11.6014i	0.425613	+	0.425613i	−0.461518	+	0.887131i	$0.652695\pi$
$744$	−1.81092	+	0.258436i	−0.0663914	+	0.00947473i
$745$	26.2784	−	2.61720i	0.962767	−	0.0958866i
$746$	−29.7084	+	17.1522i	−1.08770	+	0.627985i
$747$	40.1983	−	0.872704i	1.47078	−	0.0319306i
$748$	2.17335	−	2.17335i	0.0794655	−	0.0794655i
$749$	0.571594	−	28.2401i	0.0208856	−	1.03187i
$750$	11.0561	−	15.8985i	0.403711	−	0.580532i
$751$	−6.85013	+	11.8648i	−0.249965	+	0.432952i	−0.963516	−	0.267652i	$-0.913752\pi$
$751$	−6.85013	+	11.8648i	−0.249965	+	0.432952i	0.713551	+	0.700603i	$0.247086\pi$
$752$	−10.7419	−	2.87830i	−0.391718	−	0.104961i
$753$	−28.4169	+	12.1336i	−1.03557	+	0.442174i
$754$	28.9629	+	16.7217i	1.05476	+	0.608969i
$755$	−7.97904	+	17.6614i	−0.290387	+	0.642765i
$756$	−13.6512	−	1.62635i	−0.496489	−	0.0591499i
$757$	28.3749	+	28.3749i	1.03130	+	1.03130i	0.999494	+	0.0318111i	$0.0101275\pi$
$757$	28.3749	+	28.3749i	1.03130	+	1.03130i	0.0318111	+	0.999494i	$0.489873\pi$
$758$	−16.6244	+	4.45450i	−0.603826	+	0.161795i
$759$	−19.4015	−	7.79077i	−0.704231	−	0.282787i
$760$	7.73002	−	9.44008i	0.280397	−	0.342428i
$761$	4.58035	+	2.64447i	0.166038	+	0.0958618i	0.580716	−	0.814106i	$-0.302773\pi$
$761$	4.58035	+	2.64447i	0.166038	+	0.0958618i	−0.414679	+	0.909968i	$0.636106\pi$
$762$	27.4483	+	3.31099i	0.994347	+	0.119945i
$763$	22.0139	−	5.42361i	0.796956	−	0.196348i
$764$	0.747866			0.0270569
$765$	8.94839	+	3.81103i	0.323530	+	0.137788i
$766$	9.51372	+	16.4782i	0.343745	+	0.595383i
$767$	−23.6417	−	6.33477i	−0.853652	−	0.228735i
$768$	1.03943	−	1.38549i	0.0375072	−	0.0499946i
$769$			0.931143i			0.0335779i	0.999859	+	0.0167889i	$0.00534434\pi$
$769$			0.931143i			0.0335779i	−0.999859	+	0.0167889i	$0.994656\pi$
$770$	5.39365	−	11.3223i	0.194374	−	0.408027i
$771$	−1.35903	+	1.06645i	−0.0489442	+	0.0384073i
$772$	8.94254	−	2.39615i	0.321849	−	0.0862392i
$773$	2.98432	−	11.1376i	0.107339	−	0.400593i	−0.891261	−	0.453490i	$-0.850179\pi$
$773$	2.98432	−	11.1376i	0.107339	−	0.400593i	0.998600	+	0.0528969i	$0.0168455\pi$
$774$	−7.30311	+	2.12779i	−0.262505	+	0.0764819i
$775$	5.17690	−	1.04152i	0.185960	−	0.0374124i
$776$			12.2102i			0.438320i
$777$	−11.0461	−	27.3919i	−0.396276	−	0.982678i
$778$	26.0463	−	26.0463i	0.933804	−	0.933804i
$779$	5.09524	−	8.82522i	0.182556	−	0.316196i
$780$	−12.4445	−	12.9727i	−0.445585	−	0.464499i
$781$	−1.86483	−	3.22999i	−0.0667290	−	0.115578i
$782$	2.13677	+	7.97452i	0.0764106	+	0.285168i
$783$	−35.0377	−	13.1939i	−1.25215	−	0.471510i
$784$	6.19884	−	3.25183i	0.221387	−	0.116137i
$785$	36.5187	−	13.7902i	1.30341	−	0.492195i
$786$	9.92809	−	1.41684i	0.354123	−	0.0505370i
$787$	5.10495	−	19.0519i	0.181972	−	0.679129i	−0.813287	−	0.581863i	$-0.802324\pi$
$787$	5.10495	−	19.0519i	0.181972	−	0.679129i	0.995258	−	0.0972652i	$-0.0310095\pi$
$788$	0.993307	−	3.70707i	0.0353851	−	0.132059i
$789$	29.5959	−	4.22363i	1.05364	−	0.150365i
$790$	33.4341	−	12.6254i	1.18953	−	0.449192i
$791$	−12.8594	−	23.3521i	−0.457229	−	0.830307i
$792$	5.43729	−	3.29861i	0.193206	−	0.117211i
$793$	−9.89542	−	36.9302i	−0.351397	−	1.31143i
$794$	10.0114	+	17.3402i	0.355291	+	0.615382i
$795$	−17.9793	−	18.7425i	−0.637662	−	0.664728i
$796$	−2.80297	+	4.85488i	−0.0993485	+	0.172077i
$797$	−13.9935	+	13.9935i	−0.495674	+	0.495674i	−0.910088	−	0.414414i	$-0.863986\pi$
$797$	−13.9935	+	13.9935i	−0.495674	+	0.495674i	0.414414	+	0.910088i	$0.363986\pi$
$798$	24.7593	+	3.49630i	0.876470	+	0.123768i
$799$			16.1240i			0.570426i
$800$	−2.76876	+	4.16341i	−0.0978904	+	0.147199i
$801$	0.335560	+	1.15173i	0.0118564	+	0.0406943i
$802$	2.69219	−	10.0474i	0.0950645	−	0.354786i
$803$	−2.55867	+	0.685594i	−0.0902936	+	0.0241941i
$804$	12.8429	−	10.0780i	0.452935	−	0.355425i
$805$	19.0941	+	27.7529i	0.672977	+	0.978161i
$806$		−	4.90205i		−	0.172667i
$807$	28.7310	−	38.2965i	1.01138	−	1.34810i
$808$	−4.27164	−	1.14458i	−0.150276	−	0.0402662i
$809$	−12.8197	−	22.2044i	−0.450717	−	0.780666i	0.547713	−	0.836666i	$-0.315498\pi$
$809$	−12.8197	−	22.2044i	−0.450717	−	0.780666i	−0.998431	+	0.0560005i	$0.982165\pi$
$810$	16.1091	+	12.0621i	0.566018	+	0.423821i
$811$	−11.0170			−0.386858			−0.193429	−	0.981114i	$-0.561961\pi$
$811$	−11.0170			−0.386858			−0.193429	+	0.981114i	$0.561961\pi$
$812$	18.5098	−	4.56031i	0.649567	−	0.160035i
$813$	−8.82215	−	1.06418i	−0.309406	−	0.0373226i
$814$	11.8324	+	6.83143i	0.414725	+	0.239441i
$815$	−7.38625	+	9.02026i	−0.258729	+	0.315966i
$816$	−2.33041	−	0.935787i	−0.0815806	−	0.0327591i
$817$	13.3641	−	3.58089i	0.467550	−	0.125280i
$818$	−10.9439	−	10.9439i	−0.382644	−	0.382644i
$819$	9.48289	−	35.5997i	0.331359	−	1.24395i
$820$	−1.71932	+	3.80568i	−0.0600413	+	0.132900i
$821$	−13.0985	−	7.56242i	−0.457141	−	0.263930i	0.253700	−	0.967283i	$-0.418352\pi$
$821$	−13.0985	−	7.56242i	−0.457141	−	0.263930i	−0.710841	+	0.703352i	$0.751686\pi$
$822$	17.8520	−	7.62258i	0.622661	−	0.265868i
$823$	−39.6086	−	10.6131i	−1.38067	−	0.369949i	−0.509305	−	0.860586i	$-0.670097\pi$
$823$	−39.6086	−	10.6131i	−1.38067	−	0.369949i	−0.871364	+	0.490637i	$0.836764\pi$
$824$	5.35360	−	9.27271i	0.186502	−	0.323030i
$825$	−15.1304	+	10.3977i	−0.526773	+	0.362001i
$826$	−12.2211	+	6.72983i	−0.425225	+	0.234161i
$827$	25.1800	−	25.1800i	0.875596	−	0.875596i	−0.117480	−	0.993075i	$-0.537482\pi$
$827$	25.1800	−	25.1800i	0.875596	−	0.875596i	0.993075	+	0.117480i	$0.0374815\pi$
$828$	0.370770	+	17.0783i	0.0128852	+	0.593514i
$829$	−25.3933	+	14.6608i	−0.881944	+	0.509191i	−0.871299	−	0.490752i	$-0.836722\pi$
$829$	−25.3933	+	14.6608i	−0.881944	+	0.509191i	−0.0106454	+	0.999943i	$0.503389\pi$
$830$	29.8216	−	2.97008i	1.03512	−	0.103093i
$831$	−47.2340	+	6.74076i	−1.63853	+	0.233835i
$832$	3.28206	+	3.28206i	0.113785	+	0.113785i
$833$	−6.88029	−	7.46108i	−0.238388	−	0.258511i
$834$	−21.5276	−	27.4337i	−0.745441	−	0.949950i
$835$	18.7067	+	3.06749i	0.647371	+	0.106155i
$836$	−10.0175	+	5.78358i	−0.346461	+	0.200029i
$837$	0.893043	+	5.41464i	0.0308681	+	0.187157i
$838$	−3.85925	−	14.4029i	−0.133316	−	0.497541i
$839$	−20.2876			−0.700407			−0.350203	−	0.936674i	$-0.613888\pi$
$839$	−20.2876			−0.700407			−0.350203	+	0.936674i	$0.613888\pi$
$840$	−10.2383	−	0.420177i	−0.353256	−	0.0144975i
$841$	22.9156			0.790192
$842$	−4.27808	−	15.9660i	−0.147432	−	0.550225i
$843$	−31.6721	+	13.5236i	−1.09084	+	0.465776i
$844$	−12.8559	+	7.42239i	−0.442520	+	0.255489i
$845$	15.5170	−	11.1450i	0.533801	−	0.383400i
$846$	−7.93340	+	32.4057i	−0.272756	+	1.11413i
$847$	12.4157	−	11.9230i	0.426607	−	0.409680i
$848$	4.74179	+	4.74179i	0.162834	+	0.162834i
$849$	−1.29475	−	9.07256i	−0.0444356	−	0.311369i
$850$	6.86978	+	2.31524i	0.235631	+	0.0794122i
$851$	−31.7825	+	18.3496i	−1.08949	+	0.629018i
$852$	−1.82875	+	2.43761i	−0.0626520	+	0.0835110i
$853$	−7.01032	+	7.01032i	−0.240029	+	0.240029i	−0.816862	−	0.576833i	$-0.804288\pi$
$853$	−7.01032	+	7.01032i	−0.240029	+	0.240029i	0.576833	+	0.816862i	$0.304288\pi$
$854$	−18.6493	−	11.2764i	−0.638165	−	0.385871i
$855$	−28.8169	−	22.5699i	−0.985517	−	0.771875i
$856$	5.33798	−	9.24565i	0.182448	−	0.316010i
$857$	−20.2170	−	5.41712i	−0.690599	−	0.185045i	−0.103583	−	0.994621i	$-0.533031\pi$
$857$	−20.2170	−	5.41712i	−0.690599	−	0.185045i	−0.587016	+	0.809575i	$0.699697\pi$
$858$	6.69238	+	15.6735i	0.228474	+	0.535084i
$859$	−11.7809	−	6.80172i	−0.401960	−	0.232072i	0.285369	−	0.958418i	$-0.407884\pi$
$859$	−11.7809	−	6.80172i	−0.401960	−	0.232072i	−0.687329	+	0.726346i	$0.741217\pi$
$860$	−5.30417	+	2.00297i	−0.180871	+	0.0683006i
$861$	−8.49521	+	1.03741i	−0.289516	+	0.0353548i
$862$	5.38941	+	5.38941i	0.183564	+	0.183564i
$863$	45.3947	−	12.1635i	1.54525	−	0.414050i	0.617296	−	0.786731i	$-0.288228\pi$
$863$	45.3947	−	12.1635i	1.54525	−	0.414050i	0.927959	+	0.372681i	$0.121562\pi$
$864$	−4.22318	−	3.02734i	−0.143675	−	0.102992i
$865$	−8.67305	−	7.10194i	−0.294892	−	0.241473i
$866$	−9.72591	−	5.61526i	−0.330500	−	0.190814i
$867$	3.09022	−	25.6181i	0.104949	−	0.870036i
$868$	−1.93544	−	2.01541i	−0.0656932	−	0.0684075i
$869$	−33.8814			−1.14935
$870$	−26.7990	−	7.78105i	−0.908573	−	0.263802i
$871$	21.8739	+	37.8867i	0.741169	+	1.28374i
$872$	8.27727	+	2.21789i	0.280304	+	0.0751072i
$873$	36.6219	−	0.795060i	1.23946	−	0.0269087i
$874$		−	31.0701i		−	1.05096i
$875$	29.5767	−	0.466331i	0.999876	−	0.0157649i
$876$	1.33611	+	1.70267i	0.0451430	+	0.0575278i
$877$	−21.4208	+	5.73970i	−0.723330	+	0.193816i	−0.601657	−	0.798754i	$-0.705493\pi$
$877$	−21.4208	+	5.73970i	−0.723330	+	0.193816i	−0.121673	+	0.992570i	$0.538826\pi$
$878$	3.43925	−	12.8355i	0.116069	−	0.433176i
$879$	−19.4776	+	48.5055i	−0.656963	+	1.63605i
$880$	3.85003	−	2.76526i	0.129784	−	0.0932170i
$881$		−	44.7263i		−	1.50687i	−0.657525	−	0.753433i	$-0.728396\pi$
$881$		−	44.7263i		−	1.50687i	0.657525	−	0.753433i	$-0.271604\pi$
$882$	−10.1568	−	18.3804i	−0.341998	−	0.618900i
$883$	−3.98957	+	3.98957i	−0.134260	+	0.134260i	−0.771043	−	0.636783i	$-0.780265\pi$
$883$	−3.98957	+	3.98957i	−0.134260	+	0.134260i	0.636783	+	0.771043i	$0.280265\pi$
$884$	3.36485	−	5.82809i	0.113172	−	0.196020i
$885$	20.4185	+	0.424335i	0.686362	+	0.0142639i
$886$	12.2753	+	21.2615i	0.412398	+	0.714295i
$887$	−7.97169	−	29.7508i	−0.267663	−	0.998933i	−0.960600	−	0.277935i	$-0.910350\pi$
$887$	−7.97169	−	29.7508i	−0.267663	−	0.998933i	0.692937	−	0.720998i	$-0.256317\pi$
$888$	1.33689	−	11.0829i	0.0448632	−	0.371919i
$889$	20.3715	+	36.9937i	0.683239	+	1.24073i
$890$	0.315875	+	0.836486i	0.0105882	+	0.0280391i
$891$	−10.2475	−	16.0932i	−0.343305	−	0.539143i
$892$	−1.84042	+	6.86854i	−0.0616218	+	0.229976i
$893$	15.7055	−	58.6137i	0.525564	−	1.96143i
$894$	2.88998	+	20.2507i	0.0966554	+	0.677285i
$895$	7.44939	−	16.4891i	0.249006	−	0.551169i
$896$	2.64521	+	0.0535403i	0.0883702	+	0.00178865i
$897$	−45.4478	−	5.48220i	−1.51746	−	0.183045i
$898$	1.53622	+	5.73324i	0.0512642	+	0.191321i
$899$	−3.80482	−	6.59015i	−0.126898	−	0.219794i
$900$	12.6676	+	8.03322i	0.422252	+	0.267774i
$901$	4.86140	−	8.42019i	0.161957	−	0.280517i
$902$	2.79946	−	2.79946i	0.0932119	−	0.0932119i
$903$	−9.15161	−	7.15972i	−0.304546	−	0.238261i
$904$		−	10.0761i		−	0.335124i
$905$	13.9505	+	19.4231i	0.463731	+	0.645645i
$906$	−13.9306	−	5.59391i	−0.462815	−	0.185845i
$907$	6.18534	−	23.0840i	0.205381	−	0.766491i	−0.783952	−	0.620821i	$-0.786799\pi$
$907$	6.18534	−	23.0840i	0.205381	−	0.766491i	0.989333	−	0.145670i	$-0.0465339\pi$
$908$	−11.2410	+	3.01201i	−0.373045	+	0.0999570i
$909$	−3.15479	+	12.8864i	−0.104638	+	0.427415i
$910$	4.99090	−	27.0023i	0.165447	−	0.895119i
$911$			27.2518i			0.902892i	0.892298	+	0.451446i	$0.149092\pi$
$911$			27.2518i			0.902892i	−0.892298	+	0.451446i	$0.850908\pi$
$912$	7.55997	+	5.67168i	0.250335	+	0.187808i
$913$	−27.4438	−	7.35353i	−0.908256	−	0.243366i
$914$	5.20657	+	9.01804i	0.172218	+	0.298290i
$915$	15.3737	+	27.9536i	0.508237	+	0.924119i
$916$	−4.13598			−0.136657
$917$	10.6108	+	11.0492i	0.350399	+	0.364876i
$918$	−2.65495	+	7.05051i	−0.0876266	+	0.232702i
$919$	8.37600	+	4.83589i	0.276299	+	0.159521i	0.631747	−	0.775175i	$-0.282338\pi$
$919$	8.37600	+	4.83589i	0.276299	+	0.159521i	−0.355448	+	0.934696i	$0.615672\pi$
$920$	1.26184	+	12.6698i	0.0416018	+	0.417710i
$921$	−16.3015	+	40.5959i	−0.537151	+	1.33768i
$922$	31.6082	−	8.46938i	1.04096	−	0.278924i
$923$	−5.77440	−	5.77440i	−0.190067	−	0.190067i
$924$	8.93974	+	3.80164i	0.294096	+	0.125065i
$925$	−2.03737	+	32.1611i	−0.0669883	+	1.05745i
$926$	8.08325	+	4.66687i	0.265632	+	0.153363i
$927$	−28.1602	−	15.4532i	−0.924902	−	0.507551i
$928$	6.95973	+	1.86485i	0.228464	+	0.0612169i
$929$	−15.3159	+	26.5279i	−0.502499	+	0.870353i	0.497497	+	0.867466i	$0.334252\pi$
$929$	−15.3159	+	26.5279i	−0.502499	+	0.870353i	−0.999996	+	0.00288755i	$0.999081\pi$
$930$	0.976343	+	3.97213i	0.0320155	+	0.130251i
$931$	17.7437	+	33.8241i	0.581526	+	1.10854i
$932$	16.0542	−	16.0542i	0.525874	−	0.525874i
$933$	−21.1054	−	15.8338i	−0.690961	−	0.518376i
$934$	−0.696241	+	0.401975i	−0.0227817	+	0.0131530i
$935$	−5.31745	−	4.35421i	−0.173899	−	0.142398i
$936$	9.63016	−	10.0576i	0.314772	−	0.328742i
$937$	−0.818219	−	0.818219i	−0.0267300	−	0.0267300i	0.693615	−	0.720345i	$-0.256017\pi$
$937$	−0.818219	−	0.818219i	−0.0267300	−	0.0267300i	−0.720345	+	0.693615i	$0.756017\pi$
$938$	23.9517	+	6.94027i	0.782051	+	0.226608i
$939$	31.0840	−	24.3921i	1.01439	−	0.796007i
$940$	−4.02392	+	24.5393i	−0.131246	+	0.800384i
$941$	39.7684	−	22.9603i	1.29641	−	0.748484i	0.316630	−	0.948549i	$-0.397449\pi$
$941$	39.7684	−	22.9603i	1.29641	−	0.748484i	0.979783	+	0.200065i	$0.0641154\pi$
$942$	11.8737	+	27.8080i	0.386865	+	0.906035i
$943$	2.75234	+	10.2719i	0.0896285	+	0.334498i
$944$	−5.27318			−0.171627
$945$	−0.593570	+	30.7351i	−0.0193088	+	0.999814i
$946$	5.37514			0.174761
$947$	8.20271	+	30.6129i	0.266552	+	0.994787i	0.961293	+	0.275527i	$0.0888524\pi$
$947$	8.20271	+	30.6129i	0.266552	+	0.994787i	−0.694741	+	0.719260i	$0.744481\pi$
$948$	10.8707	+	25.4592i	0.353065	+	0.826876i
$949$	−5.02288	+	2.89996i	−0.163050	+	0.0941367i
$950$	−22.7177	−	15.1078i	−0.737061	−	0.490162i
$951$	−6.73797	+	5.28739i	−0.218494	+	0.171456i
$952$	−0.917654	−	3.72466i	−0.0297413	−	0.120717i
$953$	−12.7159	−	12.7159i	−0.411908	−	0.411908i	0.470495	−	0.882403i	$-0.344076\pi$
$953$	−12.7159	−	12.7159i	−0.411908	−	0.411908i	−0.882403	+	0.470495i	$0.844076\pi$
$954$	13.9133	−	14.5308i	0.450459	−	0.470452i
$955$	−0.165731	−	1.66405i	−0.00536292	−	0.0538473i
$956$	−9.19360	+	5.30793i	−0.297342	+	0.171671i
$957$	21.1623	+	15.8765i	0.684080	+	0.513214i
$958$	−12.0027	+	12.0027i	−0.387789	+	0.387789i
$959$	25.3735	+	15.3422i	0.819352	+	0.495427i
$960$	−3.31314	−	2.00576i	−0.106931	−	0.0647357i
$961$	14.9423	−	25.8808i	0.482010	−	0.834865i
$962$	28.8959	+	7.74264i	0.931642	+	0.249633i
$963$	−28.0780	−	15.4081i	−0.904801	−	0.496520i
$964$	−17.4304	−	10.0635i	−0.561396	−	0.324122i
$965$	−7.31327	−	19.3667i	−0.235423	−	0.623436i
$966$	−20.8497	+	15.6899i	−0.670829	+	0.504814i
$967$	−3.87679	−	3.87679i	−0.124669	−	0.124669i	0.642019	−	0.766688i	$-0.278097\pi$
$967$	−3.87679	−	3.87679i	−0.124669	−	0.124669i	−0.766688	+	0.642019i	$0.778097\pi$
$968$	6.28443	−	1.68391i	0.201989	−	0.0541229i
$969$	5.10614	−	12.7159i	0.164033	−	0.408495i
$970$	27.1684	−	2.70583i	0.872324	−	0.0868790i
$971$	9.52298	+	5.49809i	0.305607	+	0.176442i	0.644959	−	0.764217i	$-0.276874\pi$
$971$	9.52298	+	5.49809i	0.305607	+	0.176442i	−0.339352	+	0.940659i	$0.610208\pi$
$972$	−8.80489	+	12.8637i	−0.282417	+	0.412602i
$973$	14.8251	−	51.1630i	0.475270	−	1.64021i
$974$	−15.9920			−0.512416
$975$	−26.1074	+	30.5646i	−0.836105	+	0.978851i
$976$	−4.11857	−	7.13357i	−0.131832	−	0.228340i
$977$	45.8432	+	12.2836i	1.46665	+	0.392988i	0.901782	−	0.432191i	$-0.142259\pi$
$977$	45.8432	+	12.2836i	1.46665	+	0.392988i	0.564870	+	0.825180i	$0.308926\pi$
$978$	−7.22376	−	5.41945i	−0.230990	−	0.173295i
$979$		−	0.847678i		−	0.0270919i
$980$	−8.60921	−	13.0722i	−0.275011	−	0.417575i
$981$	6.11313	−	24.9704i	0.195177	−	0.797243i
$982$	6.64162	−	1.77962i	0.211942	−	0.0567898i
$983$	7.87919	−	29.4055i	0.251307	−	0.937891i	−0.718801	−	0.695216i	$-0.755309\pi$
$983$	7.87919	−	29.4055i	0.251307	−	0.937891i	0.970108	−	0.242675i	$-0.0780247\pi$
$984$	−3.00177	−	1.20537i	−0.0956929	−	0.0384259i
$985$	−8.46858	−	1.38866i	−0.269831	−	0.0442465i
$986$		−	10.4468i		−	0.332693i
$987$	−47.2639	+	19.0597i	−1.50443	+	0.606678i
$988$	−17.9087	+	17.9087i	−0.569750	+	0.569750i
$989$	−7.21898	+	12.5036i	−0.229550	+	0.397593i
$990$	−8.54453	−	11.3673i	−0.271563	−	0.361277i
$991$	7.93677	+	13.7469i	0.252120	+	0.436684i	0.964109	−	0.265506i	$-0.0855389\pi$
$991$	7.93677	+	13.7469i	0.252120	+	0.436684i	−0.711989	+	0.702190i	$0.752206\pi$
$992$	−0.273346	−	1.02014i	−0.00867873	−	0.0323895i
$993$	0.406360	+	0.0490178i	0.0128954	+	0.00155553i
$994$	−4.65393	−	0.0941977i	−0.147614	−	0.00298777i
$995$	11.4236	+	5.16090i	0.362151	+	0.163612i
$996$	3.27964	+	22.9811i	0.103919	+	0.728186i
$997$	−7.23598	+	27.0051i	−0.229166	+	0.855259i	0.751527	+	0.659703i	$0.229318\pi$
$997$	−7.23598	+	27.0051i	−0.229166	+	0.855259i	−0.980693	+	0.195556i	$0.937349\pi$
$998$	−8.02080	+	29.9340i	−0.253894	+	0.947545i
$999$	−33.3280	−	3.28808i	−1.05445	−	0.104030i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.2.x.a.107.14	yes	64
3.2	odd	2	inner	210.2.x.a.107.7	yes	64
5.3	odd	4	inner	210.2.x.a.23.10	yes	64
7.4	even	3	inner	210.2.x.a.137.7	yes	64
15.8	even	4	inner	210.2.x.a.23.7	✓	64
21.11	odd	6	inner	210.2.x.a.137.10	yes	64
35.18	odd	12	inner	210.2.x.a.53.7	yes	64
105.53	even	12	inner	210.2.x.a.53.14	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.x.a.23.7	✓	64	15.8	even	4	inner
210.2.x.a.23.10	yes	64	5.3	odd	4	inner
210.2.x.a.53.7	yes	64	35.18	odd	12	inner
210.2.x.a.53.14	yes	64	105.53	even	12	inner
210.2.x.a.107.7	yes	64	3.2	odd	2	inner
210.2.x.a.107.14	yes	64	1.1	even	1	trivial
210.2.x.a.137.7	yes	64	7.4	even	3	inner
210.2.x.a.137.10	yes	64	21.11	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	210.x (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.258819 + 0.965926i) q^{2} +(0.680155 + 1.59292i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(1.30445 + 1.81616i) q^{5} +(-1.36260 + 1.06926i) q^{6} +(-2.54122 - 0.736347i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.07478 + 2.16686i) q^{9} +O(q^{10})\)	\(q+(0.258819 + 0.965926i) q^{2} +(0.680155 + 1.59292i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(1.30445 + 1.81616i) q^{5} +(-1.36260 + 1.06926i) q^{6} +(-2.54122 - 0.736347i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.07478 + 2.16686i) q^{9} +(-1.41666 + 1.73005i) q^{10} +(1.83587 - 1.05994i) q^{11} +(-1.38549 - 1.03943i) q^{12} +(3.28206 - 3.28206i) q^{13} +(0.0535403 - 2.64521i) q^{14} +(-2.00576 + 3.31314i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-1.40048 - 0.375258i) q^{17} +(-2.63002 - 1.44326i) q^{18} +(4.72549 + 2.72826i) q^{19} +(-2.03776 - 0.920615i) q^{20} +(-0.555484 - 4.54878i) q^{21} +(1.49898 + 1.49898i) q^{22} +(-5.50010 + 1.47375i) q^{23} +(0.645421 - 1.60731i) q^{24} +(-1.59685 + 4.73815i) q^{25} +(4.01969 + 2.32077i) q^{26} +(-4.86281 - 1.83115i) q^{27} +(2.56893 - 0.632915i) q^{28} +7.20525 q^{29} +(-3.71938 - 1.07991i) q^{30} +(-0.528063 - 0.914632i) q^{31} +(0.965926 + 0.258819i) q^{32} +(2.93707 + 2.20346i) q^{33} -1.44989i q^{34} +(-1.97756 - 5.57577i) q^{35} +(0.713378 - 2.91395i) q^{36} +(6.22550 - 1.66812i) q^{37} +(-1.41225 + 5.27060i) q^{38} +(7.46037 + 2.99575i) q^{39} +(0.361834 - 2.20660i) q^{40} -1.86758i q^{41} +(4.25002 - 1.71387i) q^{42} +(1.79293 - 1.79293i) q^{43} +(-1.05994 + 1.83587i) q^{44} +(-6.64180 - 0.941565i) q^{45} +(-2.84706 - 4.93126i) q^{46} +(-2.87830 - 10.7419i) q^{47} +(1.71959 + 0.207427i) q^{48} +(5.91559 + 3.74244i) q^{49} +(-4.99000 - 0.316111i) q^{50} +(-0.354790 - 2.48609i) q^{51} +(-1.20132 + 4.48338i) q^{52} +(-1.73562 + 6.47741i) q^{53} +(0.510166 - 5.17105i) q^{54} +(4.31980 + 1.95159i) q^{55} +(1.27624 + 2.31759i) q^{56} +(-1.13183 + 9.38296i) q^{57} +(1.86485 + 6.95973i) q^{58} +(-2.63659 - 4.56671i) q^{59} +(0.0804705 - 3.87215i) q^{60} +(4.11857 - 7.13357i) q^{61} +(0.746794 - 0.746794i) q^{62} +(6.86803 - 3.97872i) q^{63} +1.00000i q^{64} +(10.2420 + 1.67947i) q^{65} +(-1.36821 + 3.40729i) q^{66} +(-2.43944 + 9.10412i) q^{67} +(1.40048 - 0.375258i) q^{68} +(-6.08848 - 7.75883i) q^{69} +(4.87395 - 3.35329i) q^{70} -1.75938i q^{71} +(2.99929 - 0.0651145i) q^{72} +(-1.20699 - 0.323412i) q^{73} +(3.22256 + 5.58163i) q^{74} +(-8.63359 + 0.679034i) q^{75} -5.45653 q^{76} +(-5.44582 + 1.34170i) q^{77} +(-0.962782 + 7.98152i) q^{78} +(-13.8415 - 7.99137i) q^{79} +(2.22506 - 0.221605i) q^{80} +(-0.390595 - 8.99152i) q^{81} +(1.80394 - 0.483365i) q^{82} +(-9.47707 - 9.47707i) q^{83} +(2.75545 + 3.66162i) q^{84} +(-1.14532 - 3.03300i) q^{85} +(2.19589 + 1.26779i) q^{86} +(4.90069 + 11.4774i) q^{87} +(-2.04764 - 0.548664i) q^{88} +(0.199936 - 0.346299i) q^{89} +(-0.809541 - 6.65918i) q^{90} +(-10.7572 + 5.92370i) q^{91} +(4.02635 - 4.02635i) q^{92} +(1.09777 - 1.46325i) q^{93} +(9.63096 - 5.56044i) q^{94} +(1.20919 + 12.1411i) q^{95} +(0.244702 + 1.71468i) q^{96} +(-8.63390 - 8.63390i) q^{97} +(-2.08385 + 6.68263i) q^{98} +(-1.51227 + 6.17721i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 8 q^{6} + 4 q^{7}+O(q^{10}) \) 64 * q + 8 * q^6 + 4 * q^7	\( 64 q + 8 q^{6} + 4 q^{7} + 4 q^{10} - 24 q^{15} + 32 q^{16} - 8 q^{18} + 12 q^{21} - 24 q^{22} - 8 q^{25} - 72 q^{27} + 4 q^{28} - 12 q^{30} + 32 q^{31} - 20 q^{33} - 24 q^{36} - 8 q^{37} - 40 q^{42} - 64 q^{43} - 28 q^{45} + 24 q^{46} - 16 q^{55} + 24 q^{57} - 28 q^{58} + 8 q^{60} + 24 q^{61} - 88 q^{63} - 16 q^{67} - 12 q^{70} + 8 q^{72} - 56 q^{73} + 8 q^{75} - 32 q^{76} - 16 q^{78} + 4 q^{81} + 16 q^{82} + 32 q^{85} + 76 q^{87} + 12 q^{88} + 40 q^{90} - 48 q^{91} + 84 q^{93} + 4 q^{96} + 104 q^{97}+O(q^{100}) \) 64 * q + 8 * q^6 + 4 * q^7 + 4 * q^10 - 24 * q^15 + 32 * q^16 - 8 * q^18 + 12 * q^21 - 24 * q^22 - 8 * q^25 - 72 * q^27 + 4 * q^28 - 12 * q^30 + 32 * q^31 - 20 * q^33 - 24 * q^36 - 8 * q^37 - 40 * q^42 - 64 * q^43 - 28 * q^45 + 24 * q^46 - 16 * q^55 + 24 * q^57 - 28 * q^58 + 8 * q^60 + 24 * q^61 - 88 * q^63 - 16 * q^67 - 12 * q^70 + 8 * q^72 - 56 * q^73 + 8 * q^75 - 32 * q^76 - 16 * q^78 + 4 * q^81 + 16 * q^82 + 32 * q^85 + 76 * q^87 + 12 * q^88 + 40 * q^90 - 48 * q^91 + 84 * q^93 + 4 * q^96 + 104 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more