LMFDB - Embedded newform 234.2.y.a.11.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [234,2,Mod(11,234)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(234, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([2, 7]))

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

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

chi := DirichletCharacter("234.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 234 = 2 \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	234.y (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:	$1.86849940730$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			11.7
Character	$\chi$	$=$	234.11
Dual form			234.2.y.a.149.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.707107 + 0.707107i) q^{2} +(1.67398 - 0.444746i) q^{3} -1.00000i q^{4} +(3.83221 + 1.02684i) q^{5} +(-0.869198 + 1.49816i) q^{6} +(-1.55176 - 0.415793i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.60440 - 1.48899i) q^{9} +(-3.43586 + 1.98370i) q^{10} +(-3.50976 - 3.50976i) q^{11} +(-0.444746 - 1.67398i) q^{12} +(-1.03908 + 3.45258i) q^{13} +(1.39127 - 0.803251i) q^{14} +(6.87171 + 0.0145410i) q^{15} -1.00000 q^{16} +(0.584080 - 1.01166i) q^{17} +(-0.788714 + 2.89447i) q^{18} +(-4.16646 + 1.11640i) q^{19} +(1.02684 - 3.83221i) q^{20} +(-2.78254 - 0.00588804i) q^{21} +4.96355 q^{22} +(1.63500 - 2.83190i) q^{23} +(1.49816 + 0.869198i) q^{24} +(9.30128 + 5.37010i) q^{25} +(-1.70661 - 3.17608i) q^{26} +(3.69749 - 3.65084i) q^{27} +(-0.415793 + 1.55176i) q^{28} +7.50570i q^{29} +(-4.86931 + 4.84875i) q^{30} +(-1.94388 + 7.25468i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-7.43622 - 4.31431i) q^{33} +(0.302342 + 1.12836i) q^{34} +(-5.51972 - 3.18681i) q^{35} +(-1.48899 - 2.60440i) q^{36} +(-4.28775 - 1.14890i) q^{37} +(2.15672 - 3.73555i) q^{38} +(-0.203868 + 6.24167i) q^{39} +(1.98370 + 3.43586i) q^{40} +(-1.44991 - 5.41115i) q^{41} +(1.97171 - 1.96339i) q^{42} +(-0.770434 + 0.444811i) q^{43} +(-3.50976 + 3.50976i) q^{44} +(11.5096 - 3.03183i) q^{45} +(0.846338 + 3.15858i) q^{46} +(2.43773 - 0.653187i) q^{47} +(-1.67398 + 0.444746i) q^{48} +(-3.82710 - 2.20958i) q^{49} +(-10.3742 + 2.77977i) q^{50} +(0.527807 - 1.95326i) q^{51} +(3.45258 + 1.03908i) q^{52} -6.60181i q^{53} +(-0.0329860 + 5.19605i) q^{54} +(-9.84618 - 17.0541i) q^{55} +(-0.803251 - 1.39127i) q^{56} +(-6.47805 + 3.72185i) q^{57} +(-5.30733 - 5.30733i) q^{58} +(5.81273 + 5.81273i) q^{59} +(0.0145410 - 6.87171i) q^{60} +(-7.05927 - 12.2270i) q^{61} +(-3.75530 - 6.50436i) q^{62} +(-4.66052 + 1.22767i) q^{63} +1.00000i q^{64} +(-7.52719 + 12.1640i) q^{65} +(8.30888 - 2.20752i) q^{66} +(-3.19229 + 0.855370i) q^{67} +(-1.01166 - 0.584080i) q^{68} +(1.47747 - 5.46770i) q^{69} +(6.15644 - 1.64961i) q^{70} +(0.942701 + 3.51821i) q^{71} +(2.89447 + 0.788714i) q^{72} +(-3.33343 + 3.33343i) q^{73} +(3.84429 - 2.21950i) q^{74} +(17.9585 + 4.85271i) q^{75} +(1.11640 + 4.16646i) q^{76} +(3.98698 + 6.90565i) q^{77} +(-4.26937 - 4.55768i) q^{78} +(-1.16902 + 2.02480i) q^{79} +(-3.83221 - 1.02684i) q^{80} +(4.56581 - 7.75586i) q^{81} +(4.85151 + 2.80102i) q^{82} +(-2.82772 - 10.5532i) q^{83} +(-0.00588804 + 2.78254i) q^{84} +(3.27712 - 3.27712i) q^{85} +(0.230251 - 0.859308i) q^{86} +(3.33813 + 12.5644i) q^{87} -4.96355i q^{88} +(-1.78297 + 6.65415i) q^{89} +(-5.99466 + 10.2823i) q^{90} +(3.04796 - 4.92554i) q^{91} +(-2.83190 - 1.63500i) q^{92} +(-0.0275273 + 13.0087i) q^{93} +(-1.26186 + 2.18561i) q^{94} -17.1131 q^{95} +(0.869198 - 1.49816i) q^{96} +(-1.65585 + 6.17970i) q^{97} +(4.26857 - 1.14376i) q^{98} +(-14.3668 - 3.91482i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 4 q^{7} + 24 q^{15} - 56 q^{16} - 8 q^{19} + 36 q^{27} - 4 q^{28} + 8 q^{31} - 36 q^{33} + 24 q^{35} - 24 q^{36} - 4 q^{37} - 36 q^{38} - 24 q^{39} - 48 q^{41} + 36 q^{42} + 12 q^{43} - 36 q^{45}+ \cdots - 24 q^{99}+O(q^{100}) $ 56 * q + 4 * q^7 + 24 * q^15 - 56 * q^16 - 8 * q^19 + 36 * q^27 - 4 * q^28 + 8 * q^31 - 36 * q^33 + 24 * q^35 - 24 * q^36 - 4 * q^37 - 36 * q^38 - 24 * q^39 - 48 * q^41 + 36 * q^42 + 12 * q^43 - 36 * q^45 + 60 * q^47 - 24 * q^50 - 4 * q^52 + 24 * q^57 - 60 * q^63 - 120 * q^65 - 56 * q^67 - 36 * q^69 + 24 * q^71 + 28 * q^73 + 48 * q^74 + 4 * q^76 - 24 * q^77 + 36 * q^78 - 24 * q^79 - 120 * q^81 - 60 * q^83 + 24 * q^84 + 48 * q^86 + 48 * q^87 + 4 * q^91 - 24 * q^92 + 20 * q^97 - 48 * q^98 - 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/234\mathbb{Z}\right)^\times$.

$n$	$145$	$209$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	1.67398	−	0.444746i	0.966471	−	0.256775i
$3$	1.67398	−	0.444746i	0.966471	−	0.256775i
$4$		−	1.00000i		−	0.500000i
$5$	3.83221	+	1.02684i	1.71381	+	0.459215i	0.976354	−	0.216176i	$-0.0693584\pi$
$5$	3.83221	+	1.02684i	1.71381	+	0.459215i	0.737460	+	0.675391i	$0.236025\pi$
$6$	−0.869198	+	1.49816i	−0.354848	+	0.611623i
$7$	−1.55176	−	0.415793i	−0.586511	−	0.157155i	−0.0466526	−	0.998911i	$-0.514855\pi$
$7$	−1.55176	−	0.415793i	−0.586511	−	0.157155i	−0.539858	+	0.841756i	$0.681522\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	2.60440	−	1.48899i	0.868134	−	0.496330i
$10$	−3.43586	+	1.98370i	−1.08651	+	0.627300i
$11$	−3.50976	−	3.50976i	−1.05823	−	1.05823i	−0.998196	−	0.0600368i	$-0.980878\pi$
$11$	−3.50976	−	3.50976i	−1.05823	−	1.05823i	−0.0600368	−	0.998196i	$-0.519122\pi$
$12$	−0.444746	−	1.67398i	−0.128387	−	0.483236i
$13$	−1.03908	+	3.45258i	−0.288188	+	0.957574i
$13$	−1.03908	+	3.45258i	−0.288188	+	0.957574i
$14$	1.39127	−	0.803251i	0.371833	−	0.214678i
$15$	6.87171	+	0.0145410i	1.77427	+	0.00375447i
$16$	−1.00000			−0.250000
$17$	0.584080	−	1.01166i	0.141660	−	0.245363i	−0.786462	−	0.617639i	$-0.788089\pi$
$17$	0.584080	−	1.01166i	0.141660	−	0.245363i	0.928122	+	0.372276i	$0.121423\pi$
$18$	−0.788714	+	2.89447i	−0.185902	+	0.682232i
$19$	−4.16646	+	1.11640i	−0.955853	+	0.256120i	−0.702844	−	0.711344i	$-0.748087\pi$
$19$	−4.16646	+	1.11640i	−0.955853	+	0.256120i	−0.253009	+	0.967464i	$0.581420\pi$
$20$	1.02684	−	3.83221i	0.229608	−	0.856907i
$21$	−2.78254	−	0.00588804i	−0.607199	−	0.00128488i
$22$	4.96355			1.05823
$23$	1.63500	−	2.83190i	0.340921	−	0.590492i	−0.643683	−	0.765292i	$-0.722594\pi$
$23$	1.63500	−	2.83190i	0.340921	−	0.590492i	0.984604	+	0.174800i	$0.0559278\pi$
$24$	1.49816	+	0.869198i	0.305811	+	0.177424i
$25$	9.30128	+	5.37010i	1.86026	+	1.07402i
$26$	−1.70661	−	3.17608i	−0.334693	−	0.622881i
$27$	3.69749	−	3.65084i	0.711581	−	0.702604i
$28$	−0.415793	+	1.55176i	−0.0785775	+	0.293255i
$29$			7.50570i			1.39377i	0.717182	+	0.696886i	$0.245432\pi$
$29$			7.50570i			1.39377i	−0.717182	+	0.696886i	$0.754568\pi$
$30$	−4.86931	+	4.84875i	−0.889011	+	0.885256i
$31$	−1.94388	+	7.25468i	−0.349132	+	1.30298i	0.538578	+	0.842576i	$0.318962\pi$
$31$	−1.94388	+	7.25468i	−0.349132	+	1.30298i	−0.887710	+	0.460403i	$0.847705\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	−7.43622	−	4.31431i	−1.29448	−	0.751025i
$34$	0.302342	+	1.12836i	0.0518513	+	0.193512i
$35$	−5.51972	−	3.18681i	−0.933002	−	0.538669i
$36$	−1.48899	−	2.60440i	−0.248165	−	0.434067i
$37$	−4.28775	−	1.14890i	−0.704902	−	0.188878i	−0.111477	−	0.993767i	$-0.535558\pi$
$37$	−4.28775	−	1.14890i	−0.704902	−	0.188878i	−0.593425	+	0.804889i	$0.702225\pi$
$38$	2.15672	−	3.73555i	0.349866	−	0.605986i
$39$	−0.203868	+	6.24167i	−0.0326449	+	0.999467i
$40$	1.98370	+	3.43586i	0.313650	+	0.543257i
$41$	−1.44991	−	5.41115i	−0.226439	−	0.845080i	−0.981823	−	0.189799i	$-0.939217\pi$
$41$	−1.44991	−	5.41115i	−0.226439	−	0.845080i	0.755384	−	0.655282i	$-0.227450\pi$
$42$	1.97171	−	1.96339i	0.304242	−	0.302957i
$43$	−0.770434	+	0.444811i	−0.117490	+	0.0678330i	−0.557593	−	0.830114i	$-0.688275\pi$
$43$	−0.770434	+	0.444811i	−0.117490	+	0.0678330i	0.440103	+	0.897947i	$0.354942\pi$
$44$	−3.50976	+	3.50976i	−0.529116	+	0.529116i
$45$	11.5096	−	3.03183i	1.71574	−	0.451958i
$46$	0.846338	+	3.15858i	0.124786	+	0.465707i
$47$	2.43773	−	0.653187i	0.355579	−	0.0952772i	−0.0766074	−	0.997061i	$-0.524409\pi$
$47$	2.43773	−	0.653187i	0.355579	−	0.0952772i	0.432187	+	0.901784i	$0.357742\pi$
$48$	−1.67398	+	0.444746i	−0.241618	+	0.0641936i
$49$	−3.82710	−	2.20958i	−0.546728	−	0.315654i
$50$	−10.3742	+	2.77977i	−1.46714	+	0.393118i
$51$	0.527807	−	1.95326i	0.0739077	−	0.273511i
$52$	3.45258	+	1.03908i	0.478787	+	0.144094i
$53$		−	6.60181i		−	0.906828i	−0.891300	−	0.453414i	$-0.850206\pi$
$53$		−	6.60181i		−	0.906828i	0.891300	−	0.453414i	$-0.149794\pi$
$54$	−0.0329860	+	5.19605i	−0.00448882	+	0.707093i
$55$	−9.84618	−	17.0541i	−1.32766	−	2.29957i
$56$	−0.803251	−	1.39127i	−0.107339	−	0.185916i
$57$	−6.47805	+	3.72185i	−0.858039	+	0.492971i
$58$	−5.30733	−	5.30733i	−0.696886	−	0.696886i
$59$	5.81273	+	5.81273i	0.756753	+	0.756753i	0.975730	−	0.218977i	$-0.0702719\pi$
$59$	5.81273	+	5.81273i	0.756753	+	0.756753i	−0.218977	+	0.975730i	$0.570272\pi$
$60$	0.0145410	−	6.87171i	0.00187724	−	0.887134i
$61$	−7.05927	−	12.2270i	−0.903847	−	1.56551i	−0.822457	−	0.568827i	$-0.807397\pi$
$61$	−7.05927	−	12.2270i	−0.903847	−	1.56551i	−0.0813898	−	0.996682i	$-0.525936\pi$
$62$	−3.75530	−	6.50436i	−0.476923	−	0.826055i
$63$	−4.66052	+	1.22767i	−0.587170	+	0.154671i
$64$			1.00000i			0.125000i
$65$	−7.52719	+	12.1640i	−0.933633	+	1.50876i
$66$	8.30888	−	2.20752i	1.02275	−	0.271727i
$67$	−3.19229	+	0.855370i	−0.390000	+	0.104500i	−0.448490	−	0.893788i	$-0.648038\pi$
$67$	−3.19229	+	0.855370i	−0.390000	+	0.104500i	0.0584902	+	0.998288i	$0.481371\pi$
$68$	−1.01166	−	0.584080i	−0.122681	−	0.0708301i
$69$	1.47747	−	5.46770i	0.177867	−	0.658234i
$70$	6.15644	−	1.64961i	0.735836	−	0.197167i
$71$	0.942701	+	3.51821i	0.111878	+	0.417534i	0.999034	−	0.0439344i	$-0.0139893\pi$
$71$	0.942701	+	3.51821i	0.111878	+	0.417534i	−0.887156	+	0.461469i	$0.847323\pi$
$72$	2.89447	+	0.788714i	0.341116	+	0.0929508i
$73$	−3.33343	+	3.33343i	−0.390149	+	0.390149i	−0.874741	−	0.484592i	$-0.838968\pi$
$73$	−3.33343	+	3.33343i	−0.390149	+	0.390149i	0.484592	+	0.874741i	$0.338968\pi$
$74$	3.84429	−	2.21950i	0.446890	−	0.258012i
$75$	17.9585	+	4.85271i	2.07366	+	0.560342i
$76$	1.11640	+	4.16646i	0.128060	+	0.477926i
$77$	3.98698	+	6.90565i	0.454358	+	0.786971i
$78$	−4.26937	−	4.55768i	−0.483411	−	0.516056i
$79$	−1.16902	+	2.02480i	−0.131525	+	0.227808i	−0.924265	−	0.381753i	$-0.875321\pi$
$79$	−1.16902	+	2.02480i	−0.131525	+	0.227808i	0.792740	+	0.609560i	$0.208654\pi$
$80$	−3.83221	−	1.02684i	−0.428454	−	0.114804i
$81$	4.56581	−	7.75586i	0.507312	−	0.861762i
$82$	4.85151	+	2.80102i	0.535760	+	0.309321i
$83$	−2.82772	−	10.5532i	−0.310383	−	1.15837i	−0.928212	−	0.372052i	$-0.878654\pi$
$83$	−2.82772	−	10.5532i	−0.310383	−	1.15837i	0.617829	−	0.786313i	$-0.288012\pi$
$84$	−0.00588804	+	2.78254i	−0.000642438	+	0.303600i
$85$	3.27712	−	3.27712i	0.355454	−	0.355454i
$86$	0.230251	−	0.859308i	0.0248286	−	0.0926616i
$87$	3.33813	+	12.5644i	0.357885	+	1.34704i
$88$		−	4.96355i		−	0.529116i
$89$	−1.78297	+	6.65415i	−0.188995	+	0.705338i	0.804745	+	0.593620i	$0.202302\pi$
$89$	−1.78297	+	6.65415i	−0.188995	+	0.705338i	−0.993740	+	0.111718i	$0.964365\pi$
$90$	−5.99466	+	10.2823i	−0.631892	+	1.08385i
$91$	3.04796	−	4.92554i	0.319513	−	0.516337i
$92$	−2.83190	−	1.63500i	−0.295246	−	0.170460i
$93$	−0.0275273	+	13.0087i	−0.00285445	+	1.34894i
$94$	−1.26186	+	2.18561i	−0.130151	+	0.225428i
$95$	−17.1131			−1.75577
$96$	0.869198	−	1.49816i	0.0887121	−	0.152906i
$97$	−1.65585	+	6.17970i	−0.168126	+	0.627453i	0.829495	+	0.558514i	$0.188628\pi$
$97$	−1.65585	+	6.17970i	−0.168126	+	0.627453i	−0.997621	+	0.0689395i	$0.978038\pi$
$98$	4.26857	−	1.14376i	0.431191	−	0.115537i
$99$	−14.3668	−	3.91482i	−1.44392	−	0.393455i
$100$	5.37010	−	9.30128i	0.537010	−	0.930128i
$101$	16.2961			1.62152			0.810762	−	0.585375i	$-0.199053\pi$
$101$	16.2961			1.62152			0.810762	+	0.585375i	$0.199053\pi$
$102$	1.00795	+	1.75438i	0.0998016	+	0.173709i
$103$	2.00231	−	1.15604i	0.197294	−	0.113908i	−0.398099	−	0.917343i	$-0.630330\pi$
$103$	2.00231	−	1.15604i	0.197294	−	0.113908i	0.595393	+	0.803435i	$0.296997\pi$
$104$	−3.17608	+	1.70661i	−0.311440	+	0.167346i
$105$	−10.6572	−	2.87977i	−1.04004	−	0.281037i
$106$	4.66818	+	4.66818i	0.453414	+	0.453414i
$107$	−8.90852	+	5.14333i	−0.861219	+	0.497225i	−0.864420	−	0.502770i	$-0.832314\pi$
$107$	−8.90852	+	5.14333i	−0.861219	+	0.497225i	0.00320143	+	0.999995i	$0.498981\pi$
$108$	−3.65084	−	3.69749i	−0.351302	−	0.355791i
$109$	5.93227	+	5.93227i	0.568208	+	0.568208i	0.931626	−	0.363418i	$-0.118390\pi$
$109$	5.93227	+	5.93227i	0.568208	+	0.568208i	−0.363418	+	0.931626i	$0.618390\pi$
$110$	19.0214	+	5.09676i	1.81361	+	0.485957i
$111$	−7.68857	−	0.0162696i	−0.729767	−	0.00154424i
$112$	1.55176	+	0.415793i	0.146628	+	0.0392888i
$113$			3.52980i			0.332055i	0.986121	+	0.166028i	$0.0530941\pi$
$113$			3.52980i			0.332055i	−0.986121	+	0.166028i	$0.946906\pi$
$114$	1.94893	−	7.21242i	0.182534	−	0.675505i
$115$	9.17355	−	9.17355i	0.855438	−	0.855438i
$116$	7.50570			0.696886
$117$	2.43469	+	10.5391i	0.225087	+	0.974339i
$118$	−8.22044			−0.756753
$119$	−1.32699	+	1.32699i	−0.121645	+	0.121645i
$120$	4.84875	+	4.86931i	0.442628	+	0.444505i
$121$			13.6369i			1.23971i
$122$	13.6375	+	3.65415i	1.23468	+	0.330831i
$123$	−4.83372	−	8.41331i	−0.435842	−	0.758602i
$124$	7.25468	+	1.94388i	0.651489	+	0.174566i
$125$	16.1034	+	16.1034i	1.44033	+	1.44033i
$126$	2.42739	−	4.16358i	0.216249	−	0.370921i
$127$	11.2191	−	6.47732i	0.995530	−	0.574769i	0.0886073	−	0.996067i	$-0.471758\pi$
$127$	11.2191	−	6.47732i	0.995530	−	0.574769i	0.906923	+	0.421297i	$0.138425\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	−1.09186	+	1.08725i	−0.0961331	+	0.0957271i
$130$	−3.27875	−	13.9238i	−0.287565	−	1.22120i
$131$	1.69814	−	0.980422i	0.148367	−	0.0856599i	−0.423979	−	0.905672i	$-0.639367\pi$
$131$	1.69814	−	0.980422i	0.148367	−	0.0856599i	0.572346	+	0.820012i	$0.306033\pi$
$132$	−4.31431	+	7.43622i	−0.375512	+	0.647240i
$133$	6.92955			0.600868
$134$	1.65245	−	2.86212i	0.142750	−	0.247250i
$135$	17.9183	−	10.1940i	1.54216	−	0.877363i
$136$	1.12836	−	0.302342i	0.0967558	−	0.0259256i
$137$	4.35359	−	16.2478i	0.371953	−	1.38815i	−0.485794	−	0.874073i	$-0.661470\pi$
$137$	4.35359	−	16.2478i	0.371953	−	1.38815i	0.857747	−	0.514073i	$-0.171864\pi$
$138$	2.82152	+	4.91098i	0.240183	+	0.418050i
$139$	16.0718			1.36319			0.681597	−	0.731728i	$-0.261286\pi$
$139$	16.0718			1.36319			0.681597	+	0.731728i	$0.261286\pi$
$140$	−3.18681	+	5.51972i	−0.269335	+	0.466501i
$141$	3.79020	−	2.17759i	0.319192	−	0.183386i
$142$	−3.15434	−	1.82116i	−0.264706	−	0.152828i
$143$	15.7647	−	8.47083i	1.31831	−	0.708366i
$144$	−2.60440	+	1.48899i	−0.217033	+	0.124083i
$145$	−7.70712	+	28.7634i	−0.640042	+	2.38867i
$146$		−	4.71419i		−	0.390149i
$147$	−7.38918	−	1.99669i	−0.609449	−	0.164684i
$148$	−1.14890	+	4.28775i	−0.0944390	+	0.352451i
$149$	−2.01440	+	2.01440i	−0.165026	+	0.165026i	−0.784789	−	0.619763i	$-0.787229\pi$
$149$	−2.01440	+	2.01440i	−0.165026	+	0.165026i	0.619763	+	0.784789i	$0.287229\pi$
$150$	−16.1299	+	9.26717i	−1.31700	+	0.756661i
$151$	−1.23214	−	4.59840i	−0.100270	−	0.374213i	0.897496	−	0.441023i	$-0.145384\pi$
$151$	−1.23214	−	4.59840i	−0.100270	−	0.374213i	−0.997766	+	0.0668104i	$0.978718\pi$
$152$	−3.73555	−	2.15672i	−0.302993	−	0.174933i
$153$	0.0148314	−	3.50445i	0.00119905	−	0.283318i
$154$	−7.70225	−	2.06381i	−0.620665	−	0.166307i
$155$	−14.8987	+	25.8054i	−1.19669	+	2.07274i
$156$	6.24167	+	0.203868i	0.499734	+	0.0163225i
$157$	3.96212	+	6.86259i	0.316211	+	0.547694i	0.979694	−	0.200497i	$-0.0642558\pi$
$157$	3.96212	+	6.86259i	0.316211	+	0.547694i	−0.663483	+	0.748192i	$0.730922\pi$
$158$	−0.605128	−	2.25837i	−0.0481414	−	0.179666i
$159$	−2.93613	−	11.0513i	−0.232850	−	0.876423i
$160$	3.43586	−	1.98370i	0.271629	−	0.156825i
$161$	−3.71461	+	3.71461i	−0.292753	+	0.292753i
$162$	2.25571	+	8.71274i	0.177225	+	0.684537i
$163$	−4.59427	−	17.1461i	−0.359851	−	1.34298i	−0.874268	−	0.485443i	$-0.838658\pi$
$163$	−4.59427	−	17.1461i	−0.359851	−	1.34298i	0.514417	−	0.857540i	$-0.328008\pi$
$164$	−5.41115	+	1.44991i	−0.422540	+	0.113219i
$165$	−24.0670	−	24.1691i	−1.87361	−	1.88156i
$166$	9.46175	+	5.46274i	0.734374	+	0.423991i
$167$	10.9578	−	2.93613i	0.847938	−	0.227204i	0.191414	−	0.981509i	$-0.438693\pi$
$167$	10.9578	−	2.93613i	0.847938	−	0.227204i	0.656524	+	0.754305i	$0.272026\pi$
$168$	−1.96339	−	1.97171i	−0.151479	−	0.152121i
$169$	−10.8406	−	7.17499i	−0.833895	−	0.551923i
$170$			4.63455i			0.355454i
$171$	−9.18883	+	9.11139i	−0.702688	+	0.696765i
$172$	0.444811	+	0.770434i	0.0339165	+	0.0587451i
$173$	−8.37298	−	14.5024i	−0.636586	−	1.10260i	−0.986177	−	0.165697i	$-0.947013\pi$
$173$	−8.37298	−	14.5024i	−0.636586	−	1.10260i	0.349591	−	0.936903i	$-0.386321\pi$
$174$	−11.2448	−	6.52393i	−0.852463	−	0.494578i
$175$	−12.2005	−	12.2005i	−0.922272	−	0.922272i
$176$	3.50976	+	3.50976i	0.264558	+	0.264558i
$177$	12.3156	+	7.14519i	0.925695	+	0.537065i
$178$	−3.44444	−	5.96594i	−0.258172	−	0.447166i
$179$	2.08607	+	3.61317i	0.155920	+	0.270061i	0.933394	−	0.358854i	$-0.116832\pi$
$179$	2.08607	+	3.61317i	0.155920	+	0.270061i	−0.777474	+	0.628916i	$0.783499\pi$
$180$	−3.03183	−	11.5096i	−0.225979	−	0.857871i
$181$		−	7.52589i		−	0.559395i	−0.960088	−	0.279698i	$-0.909766\pi$
$181$		−	7.52589i		−	0.559395i	0.960088	−	0.279698i	$-0.0902342\pi$
$182$	1.32765	+	5.63812i	0.0984120	+	0.417925i
$183$	−17.2550	−	17.3282i	−1.27553	−	1.28093i
$184$	3.15858	−	0.846338i	0.232853	−	0.0623929i
$185$	−15.2518	−	8.80564i	−1.12134	−	0.647404i
$186$	−9.17908	−	9.21801i	−0.673042	−	0.675897i
$187$	−5.60066	+	1.50069i	−0.409561	+	0.109741i
$188$	−0.653187	−	2.43773i	−0.0476386	−	0.177790i
$189$	−7.25561	+	4.12784i	−0.527768	+	0.300256i
$190$	12.1008	−	12.1008i	0.877884	−	0.877884i
$191$	−10.4815	+	6.05149i	−0.758414	+	0.437871i	−0.828726	−	0.559655i	$-0.810934\pi$
$191$	−10.4815	+	6.05149i	−0.758414	+	0.437871i	0.0703120	+	0.997525i	$0.477601\pi$
$192$	0.444746	+	1.67398i	0.0320968	+	0.120809i
$193$	4.12614	+	15.3990i	0.297006	+	1.10844i	0.939611	+	0.342244i	$0.111187\pi$
$193$	4.12614	+	15.3990i	0.297006	+	1.10844i	−0.642605	+	0.766197i	$0.722146\pi$
$194$	−3.19885	−	5.54057i	−0.229664	−	0.397789i
$195$	−7.19044	+	23.7100i	−0.514918	+	1.69791i
$196$	−2.20958	+	3.82710i	−0.157827	+	0.273364i
$197$	12.3667	+	3.31364i	0.881090	+	0.236087i	0.670877	−	0.741568i	$-0.265918\pi$
$197$	12.3667	+	3.31364i	0.881090	+	0.236087i	0.210212	+	0.977656i	$0.432584\pi$
$198$	12.9271	−	7.39069i	0.918688	−	0.525233i
$199$	11.0194	+	6.36204i	0.781143	+	0.450993i	0.836835	−	0.547455i	$-0.184403\pi$
$199$	11.0194	+	6.36204i	0.781143	+	0.450993i	−0.0556924	+	0.998448i	$0.517737\pi$
$200$	2.77977	+	10.3742i	0.196559	+	0.733569i
$201$	−4.96339	+	2.85163i	−0.350091	+	0.201138i
$202$	−11.5231	+	11.5231i	−0.810762	+	0.810762i
$203$	3.12082	−	11.6470i	0.219038	−	0.817462i
$204$	−1.95326	−	0.527807i	−0.136755	−	0.0369538i
$205$		−	22.2255i		−	1.55230i
$206$	−0.598408	+	2.23329i	−0.0416931	+	0.155601i
$207$	0.0415171	−	9.80991i	0.00288564	−	0.681836i
$208$	1.03908	−	3.45258i	0.0720470	−	0.239393i
$209$	18.5416	+	10.7050i	1.28255	+	0.740480i
$210$	9.57209	−	5.49947i	0.660537	−	0.379500i
$211$	−7.86486	+	13.6223i	−0.541439	+	0.937800i	0.457383	+	0.889270i	$0.348787\pi$
$211$	−7.86486	+	13.6223i	−0.541439	+	0.937800i	−0.998822	+	0.0485301i	$0.984546\pi$
$212$	−6.60181			−0.453414
$213$	3.14277	+	5.47014i	0.215339	+	0.374808i
$214$	2.66239	−	9.93616i	0.181997	−	0.679222i
$215$	−3.40921	+	0.913495i	−0.232506	+	0.0622999i
$216$	5.19605	+	0.0329860i	0.353546	+	0.00224441i
$217$	6.03289	−	10.4493i	0.409539	−	0.709343i
$218$	−8.38949			−0.568208
$219$	−4.09756	+	7.06263i	−0.276887	+	0.477248i
$220$	−17.0541	+	9.84618i	−1.14979	+	0.663829i
$221$	2.88592	+	3.06777i	0.194128	+	0.206361i
$222$	5.44815	−	5.42514i	0.365656	−	0.364111i
$223$	0.129240	+	0.129240i	0.00865452	+	0.00865452i	0.711421	−	0.702766i	$-0.248052\pi$
$223$	0.129240	+	0.129240i	0.00865452	+	0.00865452i	−0.702766	+	0.711421i	$0.748052\pi$
$224$	−1.39127	+	0.803251i	−0.0929582	+	0.0536694i
$225$	32.2203	+	0.136361i	2.14802	+	0.00909076i
$226$	−2.49594	−	2.49594i	−0.166028	−	0.166028i
$227$	−12.8172	−	3.43437i	−0.850710	−	0.227947i	−0.192982	−	0.981202i	$-0.561816\pi$
$227$	−12.8172	−	3.43437i	−0.850710	−	0.227947i	−0.657728	+	0.753255i	$0.728483\pi$
$228$	3.72185	+	6.47805i	0.246486	+	0.429020i
$229$	−8.72905	−	2.33894i	−0.576832	−	0.154562i	−0.0414037	−	0.999142i	$-0.513183\pi$
$229$	−8.72905	−	2.33894i	−0.576832	−	0.154562i	−0.535428	+	0.844581i	$0.679850\pi$
$230$			12.9734i			0.855438i
$231$	9.74537	+	9.78670i	0.641198	+	0.643918i
$232$	−5.30733	+	5.30733i	−0.348443	+	0.348443i
$233$	5.07704			0.332608			0.166304	−	0.986075i	$-0.446817\pi$
$233$	5.07704			0.332608			0.166304	+	0.986075i	$0.446817\pi$
$234$	−9.17384	−	5.73067i	−0.599713	−	0.374626i
$235$	10.0126			0.653150
$236$	5.81273	−	5.81273i	0.378377	−	0.378377i
$237$	−1.05639	+	3.90938i	−0.0686198	+	0.253942i
$238$		−	1.87665i		−	0.121645i
$239$	29.0366	+	7.78032i	1.87822	+	0.503267i	0.999672	+	0.0256107i	$0.00815302\pi$
$239$	29.0366	+	7.78032i	1.87822	+	0.503267i	0.878547	+	0.477657i	$0.158514\pi$
$240$	−6.87171	−	0.0145410i	−0.443567	−	0.000938618i
$241$	16.9189	+	4.53340i	1.08984	+	0.292022i	0.758621	−	0.651532i	$-0.225874\pi$
$241$	16.9189	+	4.53340i	1.08984	+	0.292022i	0.331219	+	0.943554i	$0.392540\pi$
$242$	−9.64271	−	9.64271i	−0.619857	−	0.619857i
$243$	4.19367	−	15.0138i	0.269024	−	0.963133i
$244$	−12.2270	+	7.05927i	−0.782755	+	0.451924i
$245$	−12.3974	−	12.3974i	−0.792038	−	0.792038i
$246$	9.36706	+	2.53115i	0.597222	+	0.161380i
$247$	0.474812	−	15.5451i	0.0302116	−	0.989110i
$248$	−6.50436	+	3.75530i	−0.413028	+	0.238462i
$249$	−9.42705	−	16.4082i	−0.597415	−	1.03983i
$250$	−22.7736			−1.44033
$251$	−12.2713	+	21.2544i	−0.774555	+	1.34157i	0.160489	+	0.987038i	$0.448693\pi$
$251$	−12.2713	+	21.2544i	−0.774555	+	1.34157i	−0.935044	+	0.354531i	$0.884640\pi$
$252$	1.22767	+	4.66052i	0.0773357	+	0.293585i
$253$	−15.6778	+	4.20084i	−0.985652	+	0.264105i
$254$	−3.35291	+	12.5132i	−0.210380	+	0.785150i
$255$	4.02834	−	6.94332i	0.252264	−	0.434807i
$256$	1.00000			0.0625000
$257$	10.5671	−	18.3027i	0.659156	−	1.14169i	−0.321678	−	0.946849i	$-0.604247\pi$
$257$	10.5671	−	18.3027i	0.659156	−	1.14169i	0.980834	−	0.194843i	$-0.0624197\pi$
$258$	0.00326058	−	1.54087i	0.000202995	−	0.0959301i
$259$	6.17586	+	3.56564i	0.383750	+	0.221558i
$260$	12.1640	+	7.52719i	0.754382	+	0.466817i
$261$	11.1759	+	19.5478i	0.691772	+	1.20998i
$262$	−0.507504	+	1.89403i	−0.0313537	+	0.117014i
$263$			1.30808i			0.0806599i	0.999186	+	0.0403299i	$0.0128409\pi$
$263$			1.30808i			0.0806599i	−0.999186	+	0.0403299i	$0.987159\pi$
$264$	−2.20752	−	8.30888i	−0.135864	−	0.511376i
$265$	6.77898	−	25.2995i	0.416429	−	1.55413i
$266$	−4.89993	+	4.89993i	−0.300434	+	0.300434i
$267$	−0.0252486	+	11.9319i	−0.00154519	+	0.730218i
$268$	0.855370	+	3.19229i	0.0522501	+	0.195000i
$269$	24.6923	+	14.2561i	1.50552	+	0.869210i	0.999979	+	0.00640436i	$0.00203859\pi$
$269$	24.6923	+	14.2561i	1.50552	+	0.869210i	0.505536	+	0.862805i	$0.331295\pi$
$270$	−5.46190	+	19.8785i	−0.332401	+	1.20976i
$271$	1.05690	+	0.283196i	0.0642021	+	0.0172029i	0.290777	−	0.956791i	$-0.406086\pi$
$271$	1.05690	+	0.283196i	0.0642021	+	0.0172029i	−0.226575	+	0.973994i	$0.572753\pi$
$272$	−0.584080	+	1.01166i	−0.0354151	+	0.0613407i
$273$	2.91160	−	9.60081i	0.176218	−	0.581068i
$274$	8.41050	+	14.5674i	0.508097	+	0.880049i
$275$	−13.7975	−	51.4930i	−0.832021	−	3.10515i
$276$	−5.46770	−	1.47747i	−0.329117	−	0.0889335i
$277$	−11.9296	+	6.88754i	−0.716779	+	0.413832i	−0.813566	−	0.581473i	$-0.802477\pi$
$277$	−11.9296	+	6.88754i	−0.716779	+	0.413832i	0.0967872	+	0.995305i	$0.469143\pi$
$278$	−11.3645	+	11.3645i	−0.681597	+	0.681597i
$279$	5.73949	+	21.7885i	0.343615	+	1.30444i
$280$	−1.64961	−	6.15644i	−0.0985833	−	0.367918i
$281$	−4.37098	+	1.17120i	−0.260751	+	0.0698680i	−0.386826	−	0.922153i	$-0.626429\pi$
$281$	−4.37098	+	1.17120i	−0.260751	+	0.0698680i	0.126075	+	0.992021i	$0.459762\pi$
$282$	−1.14029	+	4.21987i	−0.0679030	+	0.251289i
$283$	−3.36340	−	1.94186i	−0.199933	−	0.115432i	0.396691	−	0.917952i	$-0.370158\pi$
$283$	−3.36340	−	1.94186i	−0.199933	−	0.115432i	−0.596624	+	0.802521i	$0.703492\pi$
$284$	3.51821	−	0.942701i	0.208767	−	0.0559390i
$285$	−28.6470	+	7.61100i	−1.69690	+	0.450836i
$286$	−5.15751	+	17.1371i	−0.304970	+	1.01334i
$287$			8.99968i			0.531235i
$288$	0.788714	−	2.89447i	0.0464754	−	0.170558i
$289$	7.81770	+	13.5407i	0.459865	+	0.796509i
$290$	−14.8890	−	25.7885i	−0.874313	−	1.51435i
$291$	−0.0234484	+	11.0811i	−0.00137457	+	0.649586i
$292$	3.33343	+	3.33343i	0.195074	+	0.195074i
$293$	−3.87378	−	3.87378i	−0.226309	−	0.226309i	0.584840	−	0.811149i	$-0.301157\pi$
$293$	−3.87378	−	3.87378i	−0.226309	−	0.226309i	−0.811149	+	0.584840i	$0.801157\pi$
$294$	6.63681	−	3.81306i	0.387067	−	0.222382i
$295$	16.3069	+	28.2443i	0.949422	+	1.64445i
$296$	−2.21950	−	3.84429i	−0.129006	−	0.223445i
$297$	−25.7909	−	0.163728i	−1.49654	−	0.00950044i
$298$		−	2.84880i		−	0.165026i
$299$	8.07848	+	8.58753i	0.467191	+	0.496630i
$300$	4.85271	−	17.9585i	0.280171	−	1.03683i
$301$	1.38048	−	0.369898i	0.0795695	−	0.0213206i
$302$	4.12282	+	2.38031i	0.237241	+	0.136971i
$303$	27.2793	−	7.24764i	1.56716	−	0.416366i
$304$	4.16646	−	1.11640i	0.238963	−	0.0640300i
$305$	−14.4974	−	54.1052i	−0.830121	−	3.09805i
$306$	2.46753	+	2.48851i	0.141060	+	0.142259i
$307$	0.236798	−	0.236798i	0.0135148	−	0.0135148i	−0.700317	−	0.713832i	$-0.746958\pi$
$307$	0.236798	−	0.236798i	0.0135148	−	0.0135148i	0.713832	+	0.700317i	$0.246958\pi$
$308$	6.90565	−	3.98698i	0.393486	−	0.227179i
$309$	2.83768	−	2.82570i	0.161430	−	0.160748i
$310$	−7.71215	−	28.7821i	−0.438021	−	1.63472i
$311$	−7.57359	−	13.1178i	−0.429459	−	0.743844i	0.567366	−	0.823465i	$-0.307962\pi$
$311$	−7.57359	−	13.1178i	−0.429459	−	0.743844i	−0.996825	+	0.0796211i	$0.974629\pi$
$312$	−4.55768	+	4.26937i	−0.258028	+	0.241706i
$313$	−6.19713	+	10.7337i	−0.350282	+	0.606707i	−0.986299	−	0.164969i	$-0.947248\pi$
$313$	−6.19713	+	10.7337i	−0.350282	+	0.606707i	0.636016	+	0.771675i	$0.280581\pi$
$314$	−7.65422	−	2.05094i	−0.431953	−	0.115741i
$315$	−19.1207	−	0.0809218i	−1.07733	−	0.00455942i
$316$	2.02480	+	1.16902i	0.113904	+	0.0657624i
$317$	−3.26964	−	12.2024i	−0.183641	−	0.685358i	−0.994917	−	0.100695i	$-0.967893\pi$
$317$	−3.26964	−	12.2024i	−0.183641	−	0.685358i	0.811276	−	0.584663i	$-0.198773\pi$
$318$	9.89059	+	5.73828i	0.554637	+	0.321786i
$319$	26.3432	−	26.3432i	1.47494	−	1.47494i
$320$	−1.02684	+	3.83221i	−0.0574019	+	0.214227i
$321$	−12.6252	+	12.5719i	−0.704669	+	0.701693i
$322$		−	5.25326i		−	0.292753i
$323$	−1.30414	+	4.86710i	−0.0725640	+	0.270813i
$324$	−7.75586	−	4.56581i	−0.430881	−	0.253656i
$325$	−28.2054	+	26.5335i	−1.56456	+	1.47181i
$326$	15.3727	+	8.87545i	0.851417	+	0.491566i
$327$	12.5688	+	7.29212i	0.695058	+	0.403255i
$328$	2.80102	−	4.85151i	0.154660	−	0.267880i
$329$	−4.05436			−0.223524
$330$	34.1081	+	0.0721751i	1.87759	+	0.00397311i
$331$	−0.372128	+	1.38880i	−0.0204540	+	0.0763353i	−0.975398	−	0.220449i	$-0.929248\pi$
$331$	−0.372128	+	1.38880i	−0.0204540	+	0.0763353i	0.954944	+	0.296785i	$0.0959143\pi$
$332$	−10.5532	+	2.82772i	−0.579183	+	0.155191i
$333$	−12.8777	+	3.39223i	−0.705695	+	0.185893i
$334$	−5.67216	+	9.82447i	−0.310367	+	0.537571i
$335$	−13.1118			−0.716375
$336$	2.78254	+	0.00588804i	0.151800	+	0.000321219i
$337$	16.5630	−	9.56266i	0.902245	−	0.520911i	0.0243169	−	0.999704i	$-0.492259\pi$
$337$	16.5630	−	9.56266i	0.902245	−	0.520911i	0.877928	+	0.478793i	$0.158926\pi$
$338$	12.7390	−	2.59200i	0.692909	−	0.140986i
$339$	1.56986	+	5.90880i	0.0852633	+	0.320922i
$340$	−3.27712	−	3.27712i	−0.177727	−	0.177727i
$341$	32.2848	−	18.6396i	1.74832	−	1.00939i
$342$	0.0547650	−	12.9402i	0.00296135	−	0.699726i
$343$	12.9718	+	12.9718i	0.700411	+	0.700411i
$344$	−0.859308	−	0.230251i	−0.0463308	−	0.0124143i
$345$	11.2764	−	19.4362i	0.607102	−	1.04641i
$346$	16.1754	+	4.33418i	0.869593	+	0.233007i
$347$			30.2389i			1.62331i	0.584137	+	0.811655i	$0.301433\pi$
$347$			30.2389i			1.62331i	−0.584137	+	0.811655i	$0.698567\pi$
$348$	12.5644	−	3.33813i	0.673521	−	0.178943i
$349$	13.0186	−	13.0186i	0.696868	−	0.696868i	−0.266865	−	0.963734i	$-0.585988\pi$
$349$	13.0186	−	13.0186i	0.696868	−	0.696868i	0.963734	+	0.266865i	$0.0859879\pi$
$350$	17.2541			0.922272
$351$	8.76284	+	16.5594i	0.467726	+	0.883874i
$352$	−4.96355			−0.264558
$353$	13.6207	−	13.6207i	0.724955	−	0.724955i	−0.244655	−	0.969610i	$-0.578675\pi$
$353$	13.6207	−	13.6207i	0.724955	−	0.724955i	0.969610	+	0.244655i	$0.0786747\pi$
$354$	−13.7608	+	3.65601i	−0.731380	+	0.194315i
$355$			14.4505i			0.766953i
$356$	6.65415	+	1.78297i	0.352669	+	0.0944974i
$357$	−1.63118	+	2.81153i	−0.0863313	+	0.148802i
$358$	−4.02997	−	1.07983i	−0.212991	−	0.0570707i
$359$	−14.9056	−	14.9056i	−0.786685	−	0.786685i	0.194264	−	0.980949i	$-0.437768\pi$
$359$	−14.9056	−	14.9056i	−0.786685	−	0.786685i	−0.980949	+	0.194264i	$0.937768\pi$
$360$	10.2823	+	5.99466i	0.541925	+	0.315946i
$361$	−0.341404	+	0.197110i	−0.0179686	+	0.0103742i
$362$	5.32161	+	5.32161i	0.279698	+	0.279698i
$363$	6.06494	+	22.8278i	0.318327	+	1.19815i
$364$	−4.92554	−	3.04796i	−0.258168	−	0.159756i
$365$	−16.1973	+	9.35151i	−0.847805	+	0.489480i
$366$	24.4540	+	0.0517463i	1.27823	+	0.00270482i
$367$	21.2676			1.11016			0.555079	−	0.831798i	$-0.312688\pi$
$367$	21.2676			1.11016			0.555079	+	0.831798i	$0.312688\pi$
$368$	−1.63500	+	2.83190i	−0.0852302	+	0.147623i
$369$	−11.8333	−	11.9339i	−0.616018	−	0.621254i
$370$	17.0112	−	4.55814i	0.884370	−	0.236966i
$371$	−2.74499	+	10.2444i	−0.142513	+	0.531864i
$372$	13.0087	+	0.0275273i	0.674470	+	0.00142722i
$373$	−19.9407			−1.03249			−0.516246	−	0.856440i	$-0.672671\pi$
$373$	−19.9407			−1.03249			−0.516246	+	0.856440i	$0.672671\pi$
$374$	2.89911	−	5.02141i	0.149910	−	0.259651i
$375$	34.1186	+	19.7947i	1.76187	+	1.02220i
$376$	2.18561	+	1.26186i	0.112714	+	0.0650755i
$377$	−25.9140	−	7.79899i	−1.33464	−	0.401669i
$378$	2.21167	−	8.04931i	0.113756	−	0.414012i
$379$	−7.46317	+	27.8529i	−0.383357	+	1.43071i	0.457383	+	0.889270i	$0.348787\pi$
$379$	−7.46317	+	27.8529i	−0.383357	+	1.43071i	−0.840740	+	0.541439i	$0.817880\pi$
$380$			17.1131i			0.877884i
$381$	15.8997	−	15.8325i	0.814565	−	0.811125i
$382$	3.13248	−	11.6906i	0.160272	−	0.598142i
$383$	−13.9292	+	13.9292i	−0.711750	+	0.711750i	−0.966901	−	0.255151i	$-0.917875\pi$
$383$	−13.9292	+	13.9292i	−0.711750	+	0.711750i	0.255151	+	0.966901i	$0.417875\pi$
$384$	−1.49816	−	0.869198i	−0.0764529	−	0.0443561i
$385$	8.18795	+	30.5578i	0.417296	+	1.55737i
$386$	−13.8063	−	7.97109i	−0.702724	−	0.405718i
$387$	−1.34420	+	2.30564i	−0.0683296	+	0.117202i
$388$	6.17970	+	1.65585i	0.313727	+	0.0840628i
$389$	1.75344	−	3.03705i	0.0889030	−	0.153984i	−0.818145	−	0.575012i	$-0.804997\pi$
$389$	1.75344	−	3.03705i	0.0889030	−	0.153984i	0.907048	+	0.421028i	$0.138331\pi$
$390$	−11.6811	−	21.8499i	−0.591496	−	1.10641i
$391$	−1.90994	−	3.30812i	−0.0965899	−	0.167299i
$392$	−1.14376	−	4.26857i	−0.0577687	−	0.215596i
$393$	2.40661	−	2.39645i	0.121397	−	0.120885i
$394$	−11.0877	+	6.40147i	−0.558588	+	0.322501i
$395$	−6.55906	+	6.55906i	−0.330022	+	0.330022i
$396$	−3.91482	+	14.3668i	−0.196727	+	0.721960i
$397$	−3.67258	−	13.7062i	−0.184321	−	0.687896i	−0.994775	−	0.102093i	$-0.967446\pi$
$397$	−3.67258	−	13.7062i	−0.184321	−	0.687896i	0.810454	−	0.585803i	$-0.199221\pi$
$398$	−12.2905	+	3.29323i	−0.616068	+	0.165075i
$399$	11.5999	−	3.08189i	0.580722	−	0.154288i
$400$	−9.30128	−	5.37010i	−0.465064	−	0.268505i
$401$	−29.5314	+	7.91291i	−1.47473	+	0.395152i	−0.904549	−	0.426370i	$-0.859792\pi$
$401$	−29.5314	+	7.91291i	−1.47473	+	0.395152i	−0.570177	+	0.821522i	$0.693125\pi$
$402$	1.49324	−	5.52605i	0.0744761	−	0.275614i
$403$	−23.0275	−	14.2496i	−1.14708	−	0.709822i
$404$		−	16.2961i		−	0.810762i
$405$	25.4611	−	25.0337i	1.26517	−	1.24394i
$406$	6.02895	+	10.4425i	0.299212	+	0.518250i
$407$	11.0166	+	19.0814i	0.546074	+	0.945828i
$408$	1.75438	−	1.00795i	0.0868546	−	0.0499008i
$409$	−13.2956	−	13.2956i	−0.657426	−	0.657426i	0.297344	−	0.954770i	$-0.403899\pi$
$409$	−13.2956	−	13.2956i	−0.657426	−	0.657426i	−0.954770	+	0.297344i	$0.903899\pi$
$410$	15.7158	+	15.7158i	0.776148	+	0.776148i
$411$	0.0616511	−	29.1347i	0.00304103	−	1.43711i
$412$	−1.15604	−	2.00231i	−0.0569538	−	0.0986469i
$413$	−6.60308	−	11.4369i	−0.324916	−	0.562771i
$414$	6.90730	+	6.96601i	0.339475	+	0.342361i
$415$		−	43.3457i		−	2.12776i
$416$	1.70661	+	3.17608i	0.0836732	+	0.155720i
$417$	26.9039	−	7.14789i	1.31749	−	0.350033i
$418$	−20.6805	+	5.54131i	−1.01151	+	0.271035i
$419$	3.91273	+	2.25902i	0.191149	+	0.110360i	0.592520	−	0.805555i	$-0.298133\pi$
$419$	3.91273	+	2.25902i	0.191149	+	0.110360i	−0.401371	+	0.915915i	$0.631466\pi$
$420$	−2.87977	+	10.6572i	−0.140519	+	0.520018i
$421$	−31.8142	+	8.52459i	−1.55053	+	0.415463i	−0.929650	−	0.368444i	$-0.879891\pi$
$421$	−31.8142	+	8.52459i	−1.55053	+	0.415463i	−0.620879	+	0.783907i	$0.713224\pi$
$422$	−4.07115	−	15.1937i	−0.198180	−	0.739620i
$423$	5.37623	−	5.33092i	0.261401	−	0.259198i
$424$	4.66818	−	4.66818i	0.226707	−	0.226707i
$425$	10.8654	−	6.27313i	0.527049	−	0.304292i
$426$	−6.09025	−	1.64570i	−0.295073	−	0.0797343i
$427$	5.87039	+	21.9086i	0.284088	+	1.06023i
$428$	5.14333	+	8.90852i	0.248612	+	0.430609i
$429$	22.6223	−	21.1912i	1.09221	−	1.02312i
$430$	1.76474	−	3.05661i	0.0851032	−	0.147403i
$431$	10.5837	+	2.83588i	0.509797	+	0.136600i	0.504543	−	0.863386i	$-0.331661\pi$
$431$	10.5837	+	2.83588i	0.509797	+	0.136600i	0.00525390	+	0.999986i	$0.498328\pi$
$432$	−3.69749	+	3.65084i	−0.177895	+	0.175651i
$433$	−7.59434	−	4.38459i	−0.364960	−	0.210710i	0.306294	−	0.951937i	$-0.400911\pi$
$433$	−7.59434	−	4.38459i	−0.364960	−	0.210710i	−0.671255	+	0.741227i	$0.734244\pi$
$434$	3.12285	+	11.6546i	0.149902	+	0.559441i
$435$	−0.109140	+	51.5769i	−0.00523288	+	2.47293i
$436$	5.93227	−	5.93227i	0.284104	−	0.284104i
$437$	−3.65063	+	13.6243i	−0.174633	+	0.651740i
$438$	−2.09662	−	7.89144i	−0.100180	−	0.377068i
$439$			32.7658i			1.56383i	0.623387	+	0.781913i	$0.285756\pi$
$439$			32.7658i			1.56383i	−0.623387	+	0.781913i	$0.714244\pi$
$440$	5.09676	−	19.0214i	0.242978	−	0.906807i
$441$	−13.2573	−	0.0561072i	−0.631302	−	0.00267177i
$442$	−4.20990	−	0.128588i	−0.200245	−	0.00611630i
$443$	−25.8748	−	14.9388i	−1.22935	−	0.709766i	−0.262457	−	0.964944i	$-0.584533\pi$
$443$	−25.8748	−	14.9388i	−1.22935	−	0.709766i	−0.966894	+	0.255178i	$0.917866\pi$
$444$	−0.0162696	+	7.68857i	−0.000772119	+	0.364883i
$445$	−13.6654	+	23.6692i	−0.647804	+	1.12203i
$446$	−0.182772			−0.00865452
$447$	−2.47617	+	4.26797i	−0.117119	+	0.201868i
$448$	0.415793	−	1.55176i	0.0196444	−	0.0733138i
$449$	−14.4946	+	3.88382i	−0.684043	+	0.183289i	−0.584072	−	0.811702i	$-0.698542\pi$
$449$	−14.4946	+	3.88382i	−0.684043	+	0.183289i	−0.0999708	+	0.994990i	$0.531875\pi$
$450$	−22.8796	+	22.6868i	−1.07855	+	1.06946i
$451$	−13.9030	+	24.0807i	−0.654667	+	1.13392i
$452$	3.52980			0.166028
$453$	−4.10770	−	7.14964i	−0.192996	−	0.335919i
$454$	11.4916	−	6.63469i	0.539329	−	0.311382i
$455$	16.7381	−	15.7459i	0.784696	−	0.738181i
$456$	−7.21242	−	1.94893i	−0.337753	−	0.0912670i
$457$	2.55074	+	2.55074i	0.119318	+	0.119318i	0.764245	−	0.644926i	$-0.223112\pi$
$457$	2.55074	+	2.55074i	0.119318	+	0.119318i	−0.644926	+	0.764245i	$0.723112\pi$
$458$	7.82625	−	4.51849i	0.365697	−	0.211135i
$459$	−1.53376	−	5.87297i	−0.0715900	−	0.274127i
$460$	−9.17355	−	9.17355i	−0.427719	−	0.427719i
$461$	32.0555	+	8.58926i	1.49298	+	0.400042i	0.910741	−	0.412979i	$-0.135512\pi$
$461$	32.0555	+	8.58926i	1.49298	+	0.400042i	0.582235	+	0.813021i	$0.302178\pi$
$462$	−13.8113	−	0.0292256i	−0.642558	−	0.00135970i
$463$	3.54265	+	0.949249i	0.164641	+	0.0441154i	0.340198	−	0.940354i	$-0.389506\pi$
$463$	3.54265	+	0.949249i	0.164641	+	0.0441154i	−0.175557	+	0.984469i	$0.556173\pi$
$464$		−	7.50570i		−	0.348443i
$465$	−13.4633	+	49.8237i	−0.624345	+	2.31052i
$466$	−3.59001	+	3.59001i	−0.166304	+	0.166304i
$467$	−5.90589			−0.273292			−0.136646	−	0.990620i	$-0.543632\pi$
$467$	−5.90589			−0.273292			−0.136646	+	0.990620i	$0.543632\pi$
$468$	10.5391	−	2.43469i	0.487169	−	0.112544i
$469$	5.30932			0.245162
$470$	−7.07997	+	7.07997i	−0.326575	+	0.326575i
$471$	9.68461	+	9.72568i	0.446243	+	0.448136i
$472$			8.22044i			0.378377i
$473$	4.26522	+	1.14286i	0.196115	+	0.0525489i
$474$	−2.01737	−	3.51133i	−0.0926610	−	0.161281i
$475$	−44.7486	−	11.9904i	−2.05321	−	0.550155i
$476$	1.32699	+	1.32699i	0.0608226	+	0.0608226i
$477$	−9.83003	−	17.1938i	−0.450086	−	0.787248i
$478$	−26.0335	+	15.0304i	−1.19074	+	0.687476i
$479$	−15.1937	−	15.1937i	−0.694217	−	0.694217i	0.268940	−	0.963157i	$-0.413327\pi$
$479$	−15.1937	−	15.1937i	−0.694217	−	0.694217i	−0.963157	+	0.268940i	$0.913327\pi$
$480$	4.86931	−	4.84875i	0.222253	−	0.221314i
$481$	8.42198	−	13.6100i	0.384009	−	0.620564i
$482$	−15.1690	+	8.75785i	−0.690931	+	0.398909i
$483$	−4.56612	+	7.87024i	−0.207766	+	0.358108i
$484$	13.6369			0.619857
$485$	−12.6911	+	21.9816i	−0.576272	+	0.998133i
$486$	7.65096	+	13.5817i	0.347055	+	0.616079i
$487$	41.0392	−	10.9964i	1.85966	−	0.498295i	0.859741	−	0.510730i	$-0.170625\pi$
$487$	41.0392	−	10.9964i	1.85966	−	0.498295i	0.999923	+	0.0124347i	$0.00395819\pi$
$488$	3.65415	−	13.6375i	0.165416	−	0.617339i
$489$	−15.3164	−	26.6588i	−0.692630	−	1.20555i
$490$	17.5325			0.792038
$491$	10.2924	−	17.8270i	0.464490	−	0.804521i	−0.534688	−	0.845050i	$-0.679571\pi$
$491$	10.2924	−	17.8270i	0.464490	−	0.804521i	0.999178	+	0.0405286i	$0.0129042\pi$
$492$	−8.41331	+	4.83372i	−0.379301	+	0.217921i
$493$	7.59319	+	4.38393i	0.341980	+	0.197442i
$494$	10.6563	+	11.3278i	0.479449	+	0.509661i
$495$	−51.0368	−	29.7548i	−2.29393	−	1.33738i
$496$	1.94388	−	7.25468i	0.0872830	−	0.325745i
$497$		−	5.85139i		−	0.262471i
$498$	18.2683	+	4.93643i	0.818622	+	0.221207i
$499$	5.19060	−	19.3716i	0.232363	−	0.867190i	−0.746957	−	0.664872i	$-0.768486\pi$
$499$	5.19060	−	19.3716i	0.232363	−	0.867190i	0.979320	−	0.202318i	$-0.0648474\pi$
$500$	16.1034	−	16.1034i	0.720164	−	0.720164i
$501$	17.0372	−	9.78844i	0.761168	−	0.437315i
$502$	−6.35207	−	23.7063i	−0.283507	−	1.05806i
$503$	−12.7223	−	7.34523i	−0.567260	−	0.327508i	0.188794	−	0.982017i	$-0.439542\pi$
$503$	−12.7223	−	7.34523i	−0.567260	−	0.327508i	−0.756054	+	0.654509i	$0.772875\pi$
$504$	−4.16358	−	2.42739i	−0.185460	−	0.108125i
$505$	62.4501	+	16.7335i	2.77899	+	0.744629i
$506$	8.11541	−	14.0563i	0.360774	−	0.624879i
$507$	−21.3380	−	7.18944i	−0.947656	−	0.319294i
$508$	−6.47732	−	11.2191i	−0.287385	−	0.497765i
$509$	−2.01708	−	7.52784i	−0.0894055	−	0.333666i	0.906706	−	0.421762i	$-0.138588\pi$
$509$	−2.01708	−	7.52784i	−0.0894055	−	0.333666i	−0.996112	+	0.0880964i	$0.971922\pi$
$510$	2.06120	+	7.75813i	0.0912715	+	0.343536i
$511$	6.55871	−	3.78667i	0.290140	−	0.167513i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−11.3296	+	19.3390i	−0.500216	+	0.853836i
$514$	5.46992	+	20.4140i	0.241268	+	0.900424i
$515$	8.86034	−	2.37412i	0.390433	−	0.104616i
$516$	1.08725	+	1.09186i	0.0478635	+	0.0480665i
$517$	−10.8484	−	6.26331i	−0.477111	−	0.275460i
$518$	−6.88828	+	1.84571i	−0.302654	+	0.0810958i
$519$	−20.4661	−	20.5529i	−0.898362	−	0.902172i
$520$	−13.9238	+	3.27875i	−0.610599	+	0.143783i
$521$		−	2.05915i		−	0.0902131i	−0.998982	−	0.0451065i	$-0.985637\pi$
$521$		−	2.05915i		−	0.0902131i	0.998982	−	0.0451065i	$-0.0143627\pi$
$522$	−21.7250	−	5.91985i	−0.950876	−	0.259105i
$523$	−10.5734	−	18.3136i	−0.462342	−	0.800800i	0.536735	−	0.843751i	$-0.319657\pi$
$523$	−10.5734	−	18.3136i	−0.462342	−	0.800800i	−0.999077	+	0.0429511i	$0.986324\pi$
$524$	−0.980422	−	1.69814i	−0.0428299	−	0.0741836i
$525$	−25.8495	−	14.9972i	−1.12817	−	0.654534i
$526$	−0.924955	−	0.924955i	−0.0403299	−	0.0403299i
$527$	6.20386	+	6.20386i	0.270244	+	0.270244i
$528$	7.43622	+	4.31431i	0.323620	+	0.187756i
$529$	6.15355	+	10.6583i	0.267546	+	0.463403i
$530$	13.0960	+	22.6829i	0.568853	+	0.985282i
$531$	23.7938	+	6.48358i	1.03256	+	0.281363i
$532$		−	6.92955i		−	0.300434i
$533$	20.1890	+	0.616657i	0.874484	+	0.0267104i
$534$	−8.41925	−	8.45495i	−0.364336	−	0.365882i
$535$	−39.4206	+	10.5627i	−1.70430	+	0.456666i
$536$	−2.86212	−	1.65245i	−0.123625	−	0.0713749i
$537$	5.09898	+	5.12060i	0.220037	+	0.220970i
$538$	−27.5407	+	7.37950i	−1.18736	+	0.318153i
$539$	5.67712	+	21.1873i	0.244531	+	0.912601i
$540$	−10.1940	−	17.9183i	−0.438682	−	0.771082i
$541$	−5.41302	+	5.41302i	−0.232724	+	0.232724i	−0.813829	−	0.581105i	$-0.802621\pi$
$541$	−5.41302	+	5.41302i	−0.232724	+	0.232724i	0.581105	+	0.813829i	$0.302621\pi$
$542$	−0.947591	+	0.547092i	−0.0407025	+	0.0234996i
$543$	−3.34711	−	12.5982i	−0.143638	−	0.540639i
$544$	−0.302342	−	1.12836i	−0.0129628	−	0.0483779i
$545$	16.6422	+	28.8251i	0.712873	+	1.23473i
$546$	4.72999	+	8.84761i	0.202425	+	0.378643i
$547$	10.3483	−	17.9238i	0.442461	−	0.766365i	−0.555411	−	0.831576i	$-0.687439\pi$
$547$	10.3483	−	17.9238i	0.442461	−	0.766365i	0.997871	+	0.0652117i	$0.0207723\pi$
$548$	−16.2478	−	4.35359i	−0.694073	−	0.185976i
$549$	−36.5911	−	21.3329i	−1.56167	−	0.910464i
$550$	46.1674	+	26.6548i	1.96858	+	1.13656i
$551$	−8.37937	−	31.2722i	−0.356973	−	1.33224i
$552$	4.91098	−	2.82152i	0.209025	−	0.120092i
$553$	2.65593	−	2.65593i	0.112942	−	0.112942i
$554$	3.56526	−	13.3057i	0.151473	−	0.565306i
$555$	−29.4475	−	7.95725i	−1.24998	−	0.337767i
$556$		−	16.0718i		−	0.681597i
$557$	−2.69183	+	10.0460i	−0.114056	+	0.425664i	−0.999215	−	0.0396260i	$-0.987383\pi$
$557$	−2.69183	+	10.0460i	−0.114056	+	0.425664i	0.885158	+	0.465290i	$0.154050\pi$
$558$	−19.4652	−	11.3484i	−0.824029	−	0.480415i
$559$	−0.735204	−	3.12218i	−0.0310958	−	0.132054i
$560$	5.51972	+	3.18681i	0.233251	+	0.134667i
$561$	−8.70795	+	5.00300i	−0.367650	+	0.211227i
$562$	2.26259	−	3.91892i	0.0954415	−	0.165310i
$563$	12.0716			0.508759			0.254379	−	0.967104i	$-0.418129\pi$
$563$	12.0716			0.508759			0.254379	+	0.967104i	$0.418129\pi$
$564$	−2.17759	−	3.79020i	−0.0916932	−	0.159596i
$565$	−3.62452	+	13.5269i	−0.152485	+	0.569081i
$566$	3.75139	−	1.00518i	0.157683	−	0.0422509i
$567$	−10.3099	+	10.1368i	−0.432974	+	0.425706i
$568$	−1.82116	+	3.15434i	−0.0764141	+	0.132353i
$569$	3.09992			0.129955			0.0649777	−	0.997887i	$-0.479302\pi$
$569$	3.09992			0.129955			0.0649777	+	0.997887i	$0.479302\pi$
$570$	14.8747	−	25.6382i	0.623032	−	1.07387i
$571$	−16.8061	+	9.70302i	−0.703314	+	0.406059i	−0.808581	−	0.588385i	$-0.799764\pi$
$571$	−16.8061	+	9.70302i	−0.703314	+	0.406059i	0.105266	+	0.994444i	$0.466431\pi$
$572$	−8.47083	−	15.7647i	−0.354183	−	0.659153i
$573$	−14.8544	+	14.7917i	−0.620551	+	0.617931i
$574$	−6.36374	−	6.36374i	−0.265617	−	0.265617i
$575$	30.4152	−	17.5602i	1.26840	−	0.732311i
$576$	1.48899	+	2.60440i	0.0620413	+	0.108517i
$577$	−13.0940	−	13.0940i	−0.545109	−	0.545109i	0.379913	−	0.925022i	$-0.375954\pi$
$577$	−13.0940	−	13.0940i	−0.545109	−	0.545109i	−0.925022	+	0.379913i	$0.875954\pi$
$578$	−15.1026	−	4.04674i	−0.628187	−	0.168322i
$579$	13.7557	+	23.9424i	0.571667	+	0.995013i
$580$	28.7634	+	7.70712i	1.19433	+	0.320021i
$581$			17.5518i			0.728172i
$582$	−7.81895	−	7.85211i	−0.324106	−	0.325480i
$583$	−23.1708	+	23.1708i	−0.959635	+	0.959635i
$584$	−4.71419			−0.195074
$585$	−1.49168	+	42.8880i	−0.0616733	+	1.77320i
$586$	5.47836			0.226309
$587$	3.53264	−	3.53264i	0.145808	−	0.145808i	−0.630435	−	0.776242i	$-0.717123\pi$
$587$	3.53264	−	3.53264i	0.145808	−	0.145808i	0.776242	+	0.630435i	$0.217123\pi$
$588$	−1.99669	+	7.38918i	−0.0823422	+	0.304725i
$589$		−	32.3965i		−	1.33487i
$590$	−31.5024	−	8.44105i	−1.29693	−	0.347513i
$591$	22.1753	+	0.0469244i	0.912169	+	0.00193021i
$592$	4.28775	+	1.14890i	0.176226	+	0.0472195i
$593$	−6.13688	−	6.13688i	−0.252012	−	0.252012i	0.569783	−	0.821795i	$-0.307027\pi$
$593$	−6.13688	−	6.13688i	−0.252012	−	0.252012i	−0.821795	+	0.569783i	$0.807027\pi$
$594$	18.3527	−	18.1211i	0.753019	−	0.743518i
$595$	−6.44792	+	3.72271i	−0.264339	+	0.152616i
$596$	2.01440	+	2.01440i	0.0825132	+	0.0825132i
$597$	21.2757	+	5.74908i	0.870756	+	0.235294i
$598$	−11.7847	−	0.359953i	−0.481910	−	0.0147196i
$599$	−14.0676	+	8.12194i	−0.574787	+	0.331853i	−0.759059	−	0.651022i	$-0.774341\pi$
$599$	−14.0676	+	8.12194i	−0.574787	+	0.331853i	0.184272	+	0.982875i	$0.441007\pi$
$600$	9.26717	+	16.1299i	0.378331	+	0.658502i
$601$	−12.6796			−0.517213			−0.258607	−	0.965983i	$-0.583263\pi$
$601$	−12.6796			−0.517213			−0.258607	+	0.965983i	$0.583263\pi$
$602$	−0.714589	+	1.23770i	−0.0291245	+	0.0504450i
$603$	−7.04035	+	6.98101i	−0.286705	+	0.284289i
$604$	−4.59840	+	1.23214i	−0.187106	+	0.0501350i
$605$	−14.0028	+	52.2592i	−0.569296	+	2.12464i
$606$	−14.1646	+	24.4143i	−0.575396	+	0.991762i
$607$	10.0497			0.407903			0.203951	−	0.978981i	$-0.434622\pi$
$607$	10.0497			0.407903			0.203951	+	0.978981i	$0.434622\pi$
$608$	−2.15672	+	3.73555i	−0.0874666	+	0.151497i
$609$	0.0441938	−	20.8849i	0.00179082	−	0.846297i
$610$	48.5094	+	28.0069i	1.96409	+	1.13397i
$611$	−0.277804	+	9.09517i	−0.0112388	+	0.367951i
$612$	−3.50445	−	0.0148314i	−0.141659	−	0.000599523i
$613$	−1.97714	+	7.37880i	−0.0798561	+	0.298027i	−0.994290	−	0.106707i	$-0.965969\pi$
$613$	−1.97714	+	7.37880i	−0.0798561	+	0.298027i	0.914434	+	0.404734i	$0.132636\pi$
$614$			0.334882i			0.0135148i
$615$	−9.88471	−	37.2050i	−0.398590	−	1.50025i
$616$	−2.06381	+	7.70225i	−0.0831533	+	0.310332i
$617$	25.8657	−	25.8657i	1.04131	−	1.04131i	0.0422041	−	0.999109i	$-0.486562\pi$
$617$	25.8657	−	25.8657i	1.04131	−	1.04131i	0.999109	−	0.0422041i	$-0.0134380\pi$
$618$	−0.00847405	+	4.00462i	−0.000340876	+	0.161089i
$619$	−11.4452	−	42.7139i	−0.460020	−	1.71682i	−0.672896	−	0.739737i	$-0.734950\pi$
$619$	−11.4452	−	42.7139i	−0.460020	−	1.71682i	0.212877	−	0.977079i	$-0.431717\pi$
$620$	25.8054	+	14.8987i	1.03637	+	0.598347i
$621$	−4.29342	−	16.4400i	−0.172289	−	0.659716i
$622$	14.6310	+	3.92038i	0.586652	+	0.157193i
$623$	5.53350	−	9.58430i	0.221695	−	0.383987i
$624$	0.203868	−	6.24167i	0.00816124	−	0.249867i
$625$	18.3254	+	31.7405i	0.733015	+	1.26962i
$626$	−3.20787	−	11.9719i	−0.128212	−	0.478495i
$627$	35.7992	+	9.67361i	1.42968	+	0.386327i
$628$	6.86259	−	3.96212i	0.273847	−	0.158106i
$629$	−3.66669	+	3.66669i	−0.146200	+	0.146200i
$630$	13.5776	−	13.4631i	0.540944	−	0.536385i
$631$	5.78419	+	21.5869i	0.230265	+	0.859360i	0.980226	+	0.197879i	$0.0634053\pi$
$631$	5.78419	+	21.5869i	0.230265	+	0.859360i	−0.749962	+	0.661481i	$0.769928\pi$
$632$	−2.25837	+	0.605128i	−0.0898331	+	0.0240707i
$633$	−7.10711	+	26.3013i	−0.282482	+	1.04538i
$634$	10.9404	+	6.31645i	0.434499	+	0.250858i
$635$	49.6449	−	13.3023i	1.97010	−	0.527886i
$636$	−11.0513	+	2.93613i	−0.438212	+	0.116425i
$637$	11.6054	−	10.9175i	0.459822	−	0.432565i
$638$			37.2549i			1.47494i
$639$	7.69375	+	7.75915i	0.304360	+	0.306947i
$640$	−1.98370	−	3.43586i	−0.0784124	−	0.135814i
$641$	1.06735	+	1.84870i	0.0421577	+	0.0730192i	0.886334	−	0.463046i	$-0.153243\pi$
$641$	1.06735	+	1.84870i	0.0421577	+	0.0730192i	−0.844177	+	0.536065i	$0.819910\pi$
$642$	0.0377020	−	17.8170i	0.00148798	−	0.703181i
$643$	−8.55199	−	8.55199i	−0.337258	−	0.337258i	0.518077	−	0.855334i	$-0.326648\pi$
$643$	−8.55199	−	8.55199i	−0.337258	−	0.337258i	−0.855334	+	0.518077i	$0.826648\pi$
$644$	3.71461	+	3.71461i	0.146376	+	0.146376i
$645$	−5.30067	+	3.04540i	−0.208714	+	0.119913i
$646$	−2.51940	−	4.36372i	−0.0991243	−	0.171688i
$647$	−0.758934	−	1.31451i	−0.0298368	−	0.0516788i	0.850721	−	0.525617i	$-0.176165\pi$
$647$	−0.758934	−	1.31451i	−0.0298368	−	0.0516788i	−0.880558	+	0.473938i	$0.842832\pi$
$648$	8.71274	−	2.25571i	0.342269	−	0.0886125i
$649$		−	40.8026i		−	1.60164i
$650$	1.18225	−	38.7063i	0.0463717	−	1.51818i
$651$	5.45164	−	20.1749i	0.213667	−	0.790719i
$652$	−17.1461	+	4.59427i	−0.671492	+	0.179926i
$653$	4.79770	+	2.76995i	0.187748	+	0.108397i	0.590928	−	0.806724i	$-0.298762\pi$
$653$	4.79770	+	2.76995i	0.187748	+	0.108397i	−0.403180	+	0.915121i	$0.632095\pi$
$654$	−14.0438	+	3.73120i	−0.549157	+	0.145901i
$655$	7.51436	−	2.01347i	0.293610	−	0.0786726i
$656$	1.44991	+	5.41115i	0.0566097	+	0.211270i
$657$	−3.71815	+	13.6451i	−0.145059	+	0.532344i
$658$	2.86687	−	2.86687i	0.111762	−	0.111762i
$659$	−26.0385	+	15.0334i	−1.01432	+	0.585616i	−0.912453	−	0.409182i	$-0.865814\pi$
$659$	−26.0385	+	15.0334i	−1.01432	+	0.585616i	−0.101865	+	0.994798i	$0.532481\pi$
$660$	−24.1691	+	24.0670i	−0.940781	+	0.936807i
$661$	−7.83198	−	29.2293i	−0.304629	−	1.13689i	−0.933264	−	0.359190i	$-0.883053\pi$
$661$	−7.83198	−	29.2293i	−0.304629	−	1.13689i	0.628636	−	0.777700i	$-0.283614\pi$
$662$	−0.718896	−	1.24516i	−0.0279407	−	0.0483947i
$663$	6.19535	+	3.85188i	0.240608	+	0.149595i
$664$	5.46274	−	9.46175i	0.211996	−	0.367187i
$665$	26.5555	+	7.11551i	1.02978	+	0.275928i
$666$	6.70726	−	11.5046i	0.259901	−	0.445794i
$667$	21.2554	+	12.2718i	0.823012	+	0.475166i
$668$	−2.93613	−	10.9578i	−0.113602	−	0.423969i
$669$	0.273823	+	0.158865i	0.0105866	+	0.00614209i
$670$	9.27146	−	9.27146i	0.358188	−	0.358188i
$671$	−18.1376	+	67.6903i	−0.700193	+	2.61315i
$672$	−1.97171	+	1.96339i	−0.0760605	+	0.0757393i
$673$		−	27.8812i		−	1.07474i	−0.843346	−	0.537371i	$-0.819418\pi$
$673$		−	27.8812i		−	1.07474i	0.843346	−	0.537371i	$-0.180582\pi$
$674$	−4.95000	+	18.4736i	−0.190667	+	0.711578i
$675$	53.9967	−	14.1016i	2.07833	−	0.542771i
$676$	−7.17499	+	10.8406i	−0.275961	+	0.416948i
$677$	−33.3037	−	19.2279i	−1.27997	−	0.738989i	−0.303124	−	0.952951i	$-0.598030\pi$
$677$	−33.3037	−	19.2279i	−1.27997	−	0.738989i	−0.976842	+	0.213962i	$0.931363\pi$
$678$	−5.28821	−	3.06809i	−0.203093	−	0.117829i
$679$	5.13895	−	8.90093i	0.197215	−	0.341586i
$680$	4.63455			0.177727
$681$	−22.9832	−	0.0486340i	−0.880718	−	0.00186366i
$682$	−9.64857	+	36.0090i	−0.369463	+	1.37885i
$683$	27.1625	−	7.27817i	1.03934	−	0.278491i	0.301502	−	0.953465i	$-0.402512\pi$
$683$	27.1625	−	7.27817i	1.03934	−	0.278491i	0.737841	+	0.674974i	$0.235845\pi$
$684$	9.11139	+	9.18883i	0.348383	+	0.351344i
$685$	33.3677	−	57.7946i	1.27492	−	2.20822i
$686$	−18.3449			−0.700411
$687$	−15.6525	−	0.0331217i	−0.597179	−	0.00126367i
$688$	0.770434	−	0.444811i	0.0293725	−	0.0169582i
$689$	22.7933	+	6.85979i	0.868355	+	0.261337i
$690$	5.76986	+	21.7171i	0.219655	+	0.826757i
$691$	−20.5446	−	20.5446i	−0.781554	−	0.781554i	0.198539	−	0.980093i	$-0.436380\pi$
$691$	−20.5446	−	20.5446i	−0.781554	−	0.781554i	−0.980093	+	0.198539i	$0.936380\pi$
$692$	−14.5024	+	8.37298i	−0.551300	+	0.318293i
$693$	20.6661	+	12.0485i	0.785042	+	0.457685i
$694$	−21.3821	−	21.3821i	−0.811655	−	0.811655i
$695$	61.5905	+	16.5031i	2.33626	+	0.625999i
$696$	−6.52393	+	11.2448i	−0.247289	+	0.426232i
$697$	−6.32110	−	1.69373i	−0.239429	−	0.0641547i
$698$			18.4110i			0.696868i
$699$	8.49885	−	2.25800i	0.321456	−	0.0854053i
$700$	−12.2005	+	12.2005i	−0.461136	+	0.461136i
$701$	−24.1668			−0.912769			−0.456384	−	0.889783i	$-0.650856\pi$
$701$	−24.1668			−0.912769			−0.456384	+	0.889783i	$0.650856\pi$
$702$	−17.9055	−	5.51298i	−0.675800	−	0.208074i
$703$	19.1474			0.722158
$704$	3.50976	−	3.50976i	0.132279	−	0.132279i
$705$	16.7609	−	4.45307i	0.631250	−	0.167712i
$706$			19.2625i			0.724955i
$707$	−25.2877	−	6.77582i	−0.951041	−	0.254831i
$708$	7.14519	−	12.3156i	0.268533	−	0.462848i
$709$	46.0830	+	12.3479i	1.73068	+	0.463735i	0.980340	−	0.197316i	$-0.0632224\pi$
$709$	46.0830	+	12.3479i	1.73068	+	0.463735i	0.750342	+	0.661050i	$0.229889\pi$
$710$	−10.2180	−	10.2180i	−0.383476	−	0.383476i
$711$	−0.0296846	+	7.01405i	−0.00111326	+	0.263047i
$712$	−5.96594	+	3.44444i	−0.223583	+	0.129086i
$713$	17.3663	+	17.3663i	0.650372	+	0.650372i
$714$	−0.834634	−	3.14147i	−0.0312354	−	0.117567i
$715$	69.1115	−	16.2742i	2.58462	−	0.608622i
$716$	3.61317	−	2.08607i	0.135031	−	0.0779600i
$717$	52.0668	+	0.110177i	1.94447	+	0.00411463i
$718$	21.0796			0.786685
$719$	−22.5283	+	39.0202i	−0.840165	+	1.45521i	0.0495902	+	0.998770i	$0.484208\pi$
$719$	−22.5283	+	39.0202i	−0.840165	+	1.45521i	−0.889755	+	0.456438i	$0.849125\pi$
$720$	−11.5096	+	3.03183i	−0.428936	+	0.112989i
$721$	−3.58778	+	0.961344i	−0.133616	+	0.0358023i
$722$	0.102031	−	0.380787i	0.00379722	−	0.0141714i
$723$	30.3380	+	0.0641973i	1.12828	+	0.00238752i
$724$	−7.52589			−0.279698
$725$	−40.3063	+	69.8126i	−1.49694	+	2.59277i
$726$	−20.4302	−	11.8531i	−0.758238	−	0.439911i
$727$	−41.1027	−	23.7307i	−1.52442	−	0.880122i	−0.999582	−	0.0289169i	$-0.990794\pi$
$727$	−41.1027	−	23.7307i	−1.52442	−	0.880122i	−0.524834	−	0.851205i	$-0.675872\pi$
$728$	5.63812	−	1.32765i	0.208962	−	0.0492060i
$729$	0.342794	−	26.9978i	0.0126961	−	0.999919i
$730$	4.84070	−	18.0657i	0.179162	−	0.668643i
$731$			1.03922i			0.0384370i
$732$	−17.3282	+	17.2550i	−0.640467	+	0.637763i
$733$	−3.96299	+	14.7901i	−0.146377	+	0.546285i	0.853314	+	0.521398i	$0.174589\pi$
$733$	−3.96299	+	14.7901i	−0.146377	+	0.546285i	−0.999690	+	0.0248869i	$0.992077\pi$
$734$	−15.0384	+	15.0384i	−0.555079	+	0.555079i
$735$	−26.2666	−	15.2392i	−0.968857	−	0.562107i
$736$	−0.846338	−	3.15858i	−0.0311964	−	0.116427i
$737$	14.2063	+	8.20202i	0.523296	+	0.302125i
$738$	16.8060	+	0.0711255i	0.618636	+	0.00261817i
$739$	−39.2148	−	10.5076i	−1.44254	−	0.386527i	−0.549117	−	0.835746i	$-0.685036\pi$
$739$	−39.2148	−	10.5076i	−1.44254	−	0.386527i	−0.893422	+	0.449218i	$0.851702\pi$
$740$	−8.80564	+	15.2518i	−0.323702	+	0.560668i
$741$	−6.11880	−	26.2333i	−0.224780	−	0.963704i
$742$	−5.30291	−	9.18490i	−0.194676	−	0.337188i
$743$	−5.31877	−	19.8499i	−0.195127	−	0.728223i	−0.992234	−	0.124385i	$-0.960304\pi$
$743$	−5.31877	−	19.8499i	−0.195127	−	0.728223i	0.797107	−	0.603838i	$-0.206363\pi$
$744$	−9.21801	+	9.17908i	−0.337948	+	0.336521i
$745$	−9.78808	+	5.65115i	−0.358607	+	0.207042i
$746$	14.1002	−	14.1002i	0.516246	−	0.516246i
$747$	−23.0782	−	23.2743i	−0.844386	−	0.851563i
$748$	1.50069	+	5.60066i	0.0548707	+	0.204780i
$749$	15.9625	−	4.27713i	0.583255	−	0.156283i
$750$	−38.1225	+	10.1285i	−1.39204	+	0.369839i
$751$	2.70228	+	1.56016i	0.0986078	+	0.0569312i	0.548493	−	0.836155i	$-0.315202\pi$
$751$	2.70228	+	1.56016i	0.0986078	+	0.0569312i	−0.449885	+	0.893086i	$0.648535\pi$
$752$	−2.43773	+	0.653187i	−0.0888948	+	0.0238193i
$753$	−11.0890	+	41.0371i	−0.404105	+	1.49547i
$754$	23.8387	−	12.8093i	0.868154	−	0.466486i
$755$		−	18.8872i		−	0.687377i
$756$	4.12784	+	7.25561i	0.150128	+	0.263884i
$757$	16.5089	+	28.5942i	0.600026	+	1.03928i	0.992816	+	0.119647i	$0.0381764\pi$
$757$	16.5089	+	28.5942i	0.600026	+	1.03928i	−0.392791	+	0.919628i	$0.628490\pi$
$758$	−14.4177	−	24.9723i	−0.523676	−	0.907033i
$759$	−24.3759	+	14.0047i	−0.884789	+	0.508340i
$760$	−12.1008	−	12.1008i	−0.438942	−	0.438942i
$761$	−1.09462	−	1.09462i	−0.0396798	−	0.0396798i	0.686988	−	0.726668i	$-0.258932\pi$
$761$	−1.09462	−	1.09462i	−0.0396798	−	0.0396798i	−0.726668	+	0.686988i	$0.758932\pi$
$762$	−0.0474805	+	22.4381i	−0.00172004	+	0.812845i
$763$	−6.73886	−	11.6721i	−0.243963	−	0.422557i
$764$	6.05149	+	10.4815i	0.218935	+	0.379207i
$765$	3.65533	−	13.4145i	0.132159	−	0.485004i
$766$		−	19.6989i		−	0.711750i
$767$	−26.1088	+	14.0291i	−0.942734	+	0.506560i
$768$	1.67398	−	0.444746i	0.0604045	−	0.0160484i
$769$	41.6581	−	11.1623i	1.50223	−	0.402522i	0.588385	−	0.808581i	$-0.299764\pi$
$769$	41.6581	−	11.1623i	1.50223	−	0.402522i	0.913847	+	0.406060i	$0.133097\pi$
$770$	−27.3974	−	15.8179i	−0.987334	−	0.570037i
$771$	9.54898	−	35.3380i	0.343898	−	1.27267i
$772$	15.3990	−	4.12614i	0.554221	−	0.148503i
$773$	1.57719	+	5.88615i	0.0567275	+	0.211710i	0.988472	−	0.151405i	$-0.0483798\pi$
$773$	1.57719	+	5.88615i	0.0567275	+	0.211710i	−0.931744	+	0.363115i	$0.881713\pi$
$774$	−0.679836	−	2.58082i	−0.0244362	−	0.0927658i
$775$	−57.0389	+	57.0389i	−2.04890	+	2.04890i
$776$	−5.54057	+	3.19885i	−0.198895	+	0.114832i
$777$	11.9241	+	3.22210i	0.427773	+	0.115592i
$778$	0.907648	+	3.38739i	0.0325407	+	0.121444i
$779$	12.0820	+	20.9267i	0.432884	+	0.749777i
$780$	23.7100	+	7.19044i	0.848955	+	0.257459i
$781$	9.03942	−	15.6567i	0.323456	−	0.560242i
$782$	3.68972	+	0.988659i	0.131944	+	0.0353544i
$783$	27.4021	+	27.7522i	0.979270	+	0.991783i
$784$	3.82710	+	2.20958i	0.136682	+	0.0789135i
$785$	8.13689	+	30.3673i	0.290418	+	1.08386i
$786$	−0.00718675	+	3.39627i	−0.000256343	+	0.121141i
$787$	−14.5671	+	14.5671i	−0.519261	+	0.519261i	−0.917348	−	0.398087i	$-0.869674\pi$
$787$	−14.5671	+	14.5671i	−0.519261	+	0.519261i	0.398087	+	0.917348i	$0.369674\pi$
$788$	3.31364	−	12.3667i	0.118044	−	0.440545i
$789$	0.581766	+	2.18970i	0.0207114	+	0.0779555i
$790$		−	9.27591i		−	0.330022i
$791$	1.46766	−	5.47740i	0.0521841	−	0.194754i
$792$	−7.39069	−	12.9271i	−0.262617	−	0.459344i
$793$	49.5499	−	11.6679i	1.75957	−	0.414339i
$794$	12.2887	+	7.09487i	0.436109	+	0.251788i
$795$	0.0959969	−	45.3657i	0.00340466	−	1.60896i
$796$	6.36204	−	11.0194i	0.225496	−	0.390571i
$797$	−13.9665			−0.494717			−0.247359	−	0.968924i	$-0.579563\pi$
$797$	−13.9665			−0.494717			−0.247359	+	0.968924i	$0.579563\pi$
$798$	−6.02315	+	10.3816i	−0.213217	+	0.367505i
$799$	0.763028	−	2.84766i	0.0269940	−	0.100743i
$800$	10.3742	−	2.77977i	0.366784	−	0.0982796i
$801$	5.26439	+	19.9849i	0.186008	+	0.706132i
$802$	15.2866	−	26.4771i	0.539787	−	0.934939i
$803$	23.3991			0.825737
$804$	2.85163	+	4.96339i	0.100569	+	0.175045i
$805$	−18.0495	+	10.4209i	−0.636160	+	0.367287i
$806$	26.3589	−	6.20693i	0.928452	−	0.218630i
$807$	47.6747	+	12.8826i	1.67823	+	0.453488i
$808$	11.5231	+	11.5231i	0.405381	+	0.405381i
$809$	−28.0310	+	16.1837i	−0.985516	+	0.568988i	−0.903931	−	0.427678i	$-0.859332\pi$
$809$	−28.0310	+	16.1837i	−0.985516	+	0.568988i	−0.0815852	+	0.996666i	$0.525998\pi$
$810$	−0.302226	+	35.7052i	−0.0106191	+	1.25455i
$811$	14.9344	+	14.9344i	0.524417	+	0.524417i	0.918902	−	0.394485i	$-0.129077\pi$
$811$	14.9344	+	14.9344i	0.524417	+	0.524417i	−0.394485	+	0.918902i	$0.629077\pi$
$812$	−11.6470	−	3.12082i	−0.408731	−	0.109519i
$813$	1.89518	+	0.00401033i	0.0664668	+	0.000140648i
$814$	−21.2825	−	5.70263i	−0.745951	−	0.199877i
$815$		−	70.4248i		−	2.46687i
$816$	−0.527807	+	1.95326i	−0.0184769	+	0.0683777i
$817$	2.71340	−	2.71340i	0.0949299	−	0.0949299i
$818$	18.8029			0.657426
$819$	0.604020	−	17.3665i	0.0211062	−	0.606833i
$820$	−22.2255			−0.776148
$821$	6.31879	−	6.31879i	0.220527	−	0.220527i	−0.588193	−	0.808720i	$-0.700161\pi$
$821$	6.31879	−	6.31879i	0.220527	−	0.220527i	0.808720	+	0.588193i	$0.200161\pi$
$822$	20.5578	+	20.6450i	0.717035	+	0.720076i
$823$			34.3205i			1.19634i	0.801371	+	0.598168i	$0.204104\pi$
$823$			34.3205i			1.19634i	−0.801371	+	0.598168i	$0.795896\pi$
$824$	2.23329	+	0.598408i	0.0778004	+	0.0208465i
$825$	−45.9981	−	80.0618i	−1.60145	−	2.78739i
$826$	12.7562	+	3.41800i	0.443844	+	0.118928i
$827$	38.5858	+	38.5858i	1.34176	+	1.34176i	0.894307	+	0.447454i	$0.147669\pi$
$827$	38.5858	+	38.5858i	1.34176	+	1.34176i	0.447454	+	0.894307i	$0.352331\pi$
$828$	−9.80991	−	0.0415171i	−0.340918	−	0.00144282i
$829$	−38.9919	+	22.5120i	−1.35425	+	0.781874i	−0.988841	−	0.148974i	$-0.952403\pi$
$829$	−38.9919	+	22.5120i	−1.35425	+	0.781874i	−0.365405	+	0.930849i	$0.619070\pi$
$830$	30.6500	+	30.6500i	1.06388	+	1.06388i
$831$	−16.9066	+	16.8352i	−0.586485	+	0.584008i
$832$	−3.45258	−	1.03908i	−0.119697	−	0.0360235i
$833$	−4.47067	+	2.58114i	−0.154899	+	0.0894312i
$834$	−13.9696	+	24.0782i	−0.483727	+	0.833761i
$835$	45.0074			1.55754
$836$	10.7050	−	18.5416i	0.370240	−	0.641275i
$837$	19.2981	+	33.9209i	0.667042	+	1.17248i
$838$	−4.36408	+	1.16935i	−0.150755	+	0.0403946i
$839$	3.93871	−	14.6995i	0.135979	−	0.507482i	−0.864012	−	0.503470i	$-0.832056\pi$
$839$	3.93871	−	14.6995i	0.135979	−	0.507482i	0.999992	−	0.00401195i	$-0.00127705\pi$
$840$	−5.49947	−	9.57209i	−0.189750	−	0.330268i
$841$	−27.3355			−0.942602
$842$	16.4682	−	28.5238i	0.567533	−	0.982996i
$843$	−6.79604	+	3.90455i	−0.234068	+	0.134480i
$844$	13.6223	+	7.86486i	0.468900	+	0.270720i
$845$	−34.1760	−	38.6276i	−1.17569	−	1.32883i
$846$	−0.0320421	+	7.57110i	−0.00110163	+	0.260300i
$847$	5.67011	−	21.1611i	0.194827	−	0.727105i
$848$			6.60181i			0.226707i
$849$	−6.49389	−	1.75477i	−0.222870	−	0.0602235i
$850$	−3.24721	+	12.1188i	−0.111378	+	0.415670i
$851$	−10.2640	+	10.2640i	−0.351847	+	0.351847i
$852$	5.47014	−	3.14277i	0.187404	−	0.107670i
$853$	3.70408	+	13.8238i	0.126825	+	0.473319i	0.999898	−	0.0142712i	$-0.00454281\pi$
$853$	3.70408	+	13.8238i	0.126825	+	0.473319i	−0.873073	+	0.487590i	$0.837876\pi$
$854$	−19.6427	−	11.3407i	−0.672160	−	0.388072i
$855$	−44.5694	+	25.4813i	−1.52424	+	0.871441i
$856$	−9.93616	−	2.66239i	−0.339611	−	0.0909985i
$857$	13.4960	−	23.3757i	0.461014	−	0.798500i	−0.537998	−	0.842946i	$-0.680819\pi$
$857$	13.4960	−	23.3757i	0.461014	−	0.798500i	0.999012	+	0.0444467i	$0.0141525\pi$
$858$	−1.01191	+	30.9809i	−0.0345460	+	1.05767i
$859$	15.9548	+	27.6345i	0.544371	+	0.942878i	0.998646	+	0.0520165i	$0.0165649\pi$
$859$	15.9548	+	27.6345i	0.544371	+	0.942878i	−0.454275	+	0.890861i	$0.650102\pi$
$860$	0.913495	+	3.40921i	0.0311499	+	0.116253i
$861$	4.00258	+	15.0653i	0.136407	+	0.513423i
$862$	−9.48905	+	5.47851i	−0.323198	+	0.186599i
$863$	28.8101	−	28.8101i	0.980707	−	0.980707i	−0.0191108	−	0.999817i	$-0.506084\pi$
$863$	28.8101	−	28.8101i	0.980707	−	0.980707i	0.999817	+	0.0191108i	$0.00608352\pi$
$864$	0.0329860	−	5.19605i	0.00112221	−	0.176773i
$865$	−17.1954	−	64.1740i	−0.584660	−	2.18198i
$866$	8.47038	−	2.26963i	0.287835	−	0.0771252i
$867$	19.1088	+	19.1899i	0.648969	+	0.651722i
$868$	−10.4493	−	6.03289i	−0.354671	−	0.204770i
$869$	11.2095	−	3.00359i	0.380258	−	0.101890i
$870$	−36.3932	−	36.5476i	−1.23385	−	1.23908i
$871$	0.363794	−	11.9104i	0.0123267	−	0.403569i
$872$			8.38949i			0.284104i
$873$	4.88903	+	18.5600i	0.165469	+	0.628159i
$874$	−7.05248	−	12.2152i	−0.238554	−	0.413187i
$875$	−18.2929	−	31.6842i	−0.618413	−	1.07112i
$876$	7.06263	+	4.09756i	0.238624	+	0.138444i
$877$	−25.7472	−	25.7472i	−0.869421	−	0.869421i	0.122987	−	0.992408i	$-0.460753\pi$
$877$	−25.7472	−	25.7472i	−0.869421	−	0.869421i	−0.992408	+	0.122987i	$0.960753\pi$
$878$	−23.1689	−	23.1689i	−0.781913	−	0.781913i
$879$	−8.20748	−	4.76178i	−0.276831	−	0.160611i
$880$	9.84618	+	17.0541i	0.331915	+	0.574893i
$881$	−22.3784	−	38.7605i	−0.753946	−	1.30587i	−0.945896	−	0.324469i	$-0.894815\pi$
$881$	−22.3784	−	38.7605i	−0.753946	−	1.30587i	0.191950	−	0.981405i	$-0.438519\pi$
$882$	9.41403	−	9.33468i	0.316987	−	0.314315i
$883$			22.3724i			0.752891i	0.926439	+	0.376445i	$0.122854\pi$
$883$			22.3724i			0.752891i	−0.926439	+	0.376445i	$0.877146\pi$
$884$	3.06777	−	2.88592i	0.103180	−	0.0970641i
$885$	39.8589	+	40.0279i	1.33984	+	1.34552i
$886$	28.8596	−	7.73292i	0.969558	−	0.259792i
$887$	−29.4782	−	17.0192i	−0.989781	−	0.571450i	−0.0845722	−	0.996417i	$-0.526952\pi$
$887$	−29.4782	−	17.0192i	−0.989781	−	0.571450i	−0.905209	+	0.424967i	$0.860286\pi$
$888$	−5.42514	−	5.44815i	−0.182056	−	0.182828i
$889$	−20.1025	+	5.38645i	−0.674217	+	0.180656i
$890$	−7.07375	−	26.3996i	−0.237113	−	0.884917i
$891$	−43.2461	+	11.1963i	−1.44880	+	0.375091i
$892$	0.129240	−	0.129240i	0.00432726	−	0.00432726i
$893$	−9.42749	+	5.44296i	−0.315479	+	0.182142i
$894$	−1.26699	−	4.76882i	−0.0423746	−	0.159493i
$895$	4.28410	+	15.9885i	0.143202	+	0.534436i
$896$	0.803251	+	1.39127i	0.0268347	+	0.0464791i
$897$	17.3425	+	10.7825i	0.579048	+	0.360016i
$898$	7.50297	−	12.9955i	0.250377	−	0.433666i
$899$	−54.4514	−	14.5902i	−1.81606	−	0.486611i
$900$	0.136361	−	32.2203i	0.00454538	−	1.07401i
$901$	−6.67876	−	3.85599i	−0.222502	−	0.128462i
$902$	−7.19673	−	26.8586i	−0.239625	−	0.894292i
$903$	2.14638	−	1.23316i	0.0714271	−	0.0410372i
$904$	−2.49594	+	2.49594i	−0.0830138	+	0.0830138i
$905$	7.72786	−	28.8408i	0.256883	−	0.958699i
$906$	7.96014	+	2.15098i	0.264458	+	0.0714614i
$907$			47.7635i			1.58596i	0.609247	+	0.792980i	$0.291472\pi$
$907$			47.7635i			1.58596i	−0.609247	+	0.792980i	$0.708528\pi$
$908$	−3.43437	+	12.8172i	−0.113974	+	0.425355i
$909$	42.4416	−	24.2648i	1.40770	−	0.804812i
$910$	−0.701591	+	22.9697i	−0.0232575	+	0.761438i
$911$	−6.17593	−	3.56567i	−0.204618	−	0.118136i	0.394190	−	0.919029i	$-0.371025\pi$
$911$	−6.17593	−	3.56567i	−0.204618	−	0.118136i	−0.598807	+	0.800893i	$0.704359\pi$
$912$	6.47805	−	3.72185i	0.214510	−	0.123243i
$913$	−27.1146	+	46.9639i	−0.897363	+	1.55428i
$914$	−3.60729			−0.119318
$915$	−48.3315	−	84.1231i	−1.59779	−	2.78102i
$916$	−2.33894	+	8.72905i	−0.0772808	+	0.288416i
$917$	−3.04276	+	0.815306i	−0.100481	+	0.0269238i
$918$	5.23735	+	3.06828i	0.172858	+	0.101268i
$919$	−8.93424	+	15.4746i	−0.294713	+	0.510459i	−0.974918	−	0.222563i	$-0.928558\pi$
$919$	−8.93424	+	15.4746i	−0.294713	+	0.510459i	0.680205	+	0.733022i	$0.261891\pi$
$920$	12.9734			0.427719
$921$	0.291079	−	0.501709i	0.00959138	−	0.0165319i
$922$	−28.7402	+	16.5932i	−0.946509	+	0.546467i
$923$	−13.1264	−	0.400936i	−0.432062	−	0.0131970i
$924$	9.78670	−	9.74537i	0.321959	−	0.320599i
$925$	−33.7119	−	33.7119i	−1.10844	−	1.10844i
$926$	−3.17625	+	1.83381i	−0.104378	+	0.0602627i
$927$	3.49350	−	5.99221i	0.114742	−	0.196810i
$928$	5.30733	+	5.30733i	0.174222	+	0.174222i
$929$	8.45303	+	2.26498i	0.277335	+	0.0743116i	0.394806	−	0.918765i	$-0.370812\pi$
$929$	8.45303	+	2.26498i	0.277335	+	0.0743116i	−0.117471	+	0.993076i	$0.537479\pi$
$930$	−25.7107	−	44.7507i	−0.843088	−	1.46743i
$931$	18.4122	+	4.93355i	0.603437	+	0.161690i
$932$		−	5.07704i		−	0.166304i
$933$	−18.5121	−	18.5906i	−0.606060	−	0.608630i
$934$	4.17609	−	4.17609i	0.136646	−	0.136646i
$935$	−23.0038			−0.752306
$936$	−5.73067	+	9.17384i	−0.187313	+	0.299856i
$937$	−33.0858			−1.08087			−0.540433	−	0.841387i	$-0.681740\pi$
$937$	−33.0858			−1.08087			−0.540433	+	0.841387i	$0.681740\pi$
$938$	−3.75426	+	3.75426i	−0.122581	+	0.122581i
$939$	−5.60006	+	20.7242i	−0.182751	+	0.676308i
$940$		−	10.0126i		−	0.326575i
$941$	−52.2010	−	13.9872i	−1.70170	−	0.455970i	−0.728335	−	0.685221i	$-0.759706\pi$
$941$	−52.2010	−	13.9872i	−1.70170	−	0.455970i	−0.973367	+	0.229251i	$0.926372\pi$
$942$	−13.7251	−	0.0290434i	−0.447189	−	0.000946284i
$943$	−17.6945	−	4.74122i	−0.576211	−	0.154395i
$944$	−5.81273	−	5.81273i	−0.189188	−	0.189188i
$945$	−32.0436	+	8.36840i	−1.04238	+	0.272224i
$946$	−3.82409	+	2.20784i	−0.124332	+	0.0717831i
$947$	−7.71869	−	7.71869i	−0.250824	−	0.250824i	0.570485	−	0.821308i	$-0.306755\pi$
$947$	−7.71869	−	7.71869i	−0.250824	−	0.250824i	−0.821308	+	0.570485i	$0.806755\pi$
$948$	3.90938	+	1.05639i	0.126971	+	0.0343099i
$949$	−8.04526	−	14.9726i	−0.261160	−	0.486033i
$950$	40.1205	−	23.1636i	1.30168	−	0.751526i
$951$	−10.9003	−	18.9725i	−0.353466	−	0.615224i
$952$	−1.87665			−0.0608226
$953$	14.0664	−	24.3636i	0.455654	−	0.789216i	−0.543072	−	0.839686i	$-0.682739\pi$
$953$	14.0664	−	24.3636i	0.455654	−	0.789216i	0.998726	+	0.0504706i	$0.0160721\pi$
$954$	19.1087	+	5.20694i	0.618667	+	0.168581i
$955$	−46.3811	+	12.4278i	−1.50086	+	0.402154i
$956$	7.78032	−	29.0366i	0.251634	−	0.939109i
$957$	32.3819	−	55.8140i	1.04676	−	1.80421i
$958$	21.4871			0.694217
$959$	−13.5115	+	23.4026i	−0.436308	+	0.755708i
$960$	−0.0145410	+	6.87171i	−0.000469309	+	0.221783i
$961$	−22.0049	−	12.7045i	−0.709834	−	0.409823i
$962$	3.66850	+	15.5790i	0.118277	+	0.502286i
$963$	−15.5430	+	26.6600i	−0.500865	+	0.859107i
$964$	4.53340	−	16.9189i	0.146011	−	0.544920i
$965$			63.2488i			2.03605i
$966$	−2.33637	−	8.79383i	−0.0751714	−	0.282937i
$967$	8.99010	−	33.5515i	0.289102	−	1.07894i	−0.656687	−	0.754163i	$-0.728043\pi$
$967$	8.99010	−	33.5515i	0.289102	−	1.07894i	0.945789	−	0.324781i	$-0.105291\pi$
$968$	−9.64271	+	9.64271i	−0.309929	+	0.309929i
$969$	−0.0184678	+	8.72743i	−0.000593272	+	0.280365i
$970$	−6.56939	−	24.5173i	−0.210930	−	0.787202i
$971$	4.54874	+	2.62622i	0.145976	+	0.0842793i	0.571209	−	0.820805i	$-0.306475\pi$
$971$	4.54874	+	2.62622i	0.145976	+	0.0842793i	−0.425233	+	0.905084i	$0.639808\pi$
$972$	−15.0138	−	4.19367i	−0.481567	−	0.134512i
$973$	−24.9396	−	6.68255i	−0.799528	−	0.214233i
$974$	−21.2435	+	36.7947i	−0.680684	+	1.17898i
$975$	−35.4146	+	56.9607i	−1.13417	+	1.82420i
$976$	7.05927	+	12.2270i	0.225962	+	0.391377i
$977$	12.8590	+	47.9906i	0.411397	+	1.53536i	0.791944	+	0.610593i	$0.209069\pi$
$977$	12.8590	+	47.9906i	0.411397	+	1.53536i	−0.380547	+	0.924762i	$0.624264\pi$
$978$	29.6809	+	8.02034i	0.949092	+	0.256462i
$979$	29.6123	−	17.0967i	0.946413	−	0.546412i
$980$	−12.3974	+	12.3974i	−0.396019	+	0.396019i
$981$	24.2831	+	6.61691i	0.775299	+	0.211262i
$982$	5.32775	+	19.8834i	0.170015	+	0.634506i
$983$	47.6197	−	12.7597i	1.51883	−	0.406970i	0.599474	−	0.800394i	$-0.295376\pi$
$983$	47.6197	−	12.7597i	1.51883	−	0.406970i	0.919357	+	0.393424i	$0.128710\pi$
$984$	2.53115	−	9.36706i	0.0806902	−	0.298611i
$985$	43.9891	+	25.3971i	1.40161	+	0.809220i
$986$	−8.46910	+	2.26929i	−0.269711	+	0.0722689i
$987$	−6.78691	+	1.80316i	−0.216030	+	0.0573953i
$988$	−15.5451	−	0.474812i	−0.494555	−	0.0151058i
$989$			2.90906i			0.0925027i
$990$	57.1283	−	15.0486i	1.81566	−	0.478277i
$991$	−18.2173	−	31.5533i	−0.578692	−	1.00232i	−0.995630	−	0.0933883i	$-0.970230\pi$
$991$	−18.2173	−	31.5533i	−0.578692	−	1.00232i	0.416938	−	0.908935i	$-0.363103\pi$
$992$	3.75530	+	6.50436i	0.119231	+	0.206514i
$993$	−0.00526969	+	2.49032i	−0.000167229	+	0.0790280i
$994$	4.13756	+	4.13756i	0.131235	+	0.131235i
$995$	35.6957	+	35.6957i	1.13163	+	1.13163i
$996$	−16.4082	+	9.42705i	−0.519914	+	0.298707i
$997$	9.99849	+	17.3179i	0.316655	+	0.548463i	0.979788	−	0.200039i	$-0.0641068\pi$
$997$	9.99849	+	17.3179i	0.316655	+	0.548463i	−0.663133	+	0.748502i	$0.730773\pi$
$998$	10.0275	+	17.3681i	0.317414	+	0.549777i
$999$	−20.0484	+	11.4058i	−0.634302	+	0.360865i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	234.2.y.a.11.7	✓	56
3.2	odd	2		702.2.bb.a.89.8		56
9.4	even	3		702.2.bc.a.557.1		56
9.5	odd	6		234.2.z.a.167.10	yes	56
13.6	odd	12		234.2.z.a.227.10	yes	56
39.32	even	12		702.2.bc.a.305.1		56
117.32	even	12	inner	234.2.y.a.149.7	yes	56
117.58	odd	12		702.2.bb.a.71.8		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
234.2.y.a.11.7	✓	56	1.1	even	1	trivial
234.2.y.a.149.7	yes	56	117.32	even	12	inner
234.2.z.a.167.10	yes	56	9.5	odd	6
234.2.z.a.227.10	yes	56	13.6	odd	12
702.2.bb.a.71.8		56	117.58	odd	12
702.2.bb.a.89.8		56	3.2	odd	2
702.2.bc.a.305.1		56	39.32	even	12
702.2.bc.a.557.1		56	9.4	even	3

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:	\( N \)	\(=\)	\( 234 = 2 \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	234.y (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(1.67398 - 0.444746i) q^{3} -1.00000i q^{4} +(3.83221 + 1.02684i) q^{5} +(-0.869198 + 1.49816i) q^{6} +(-1.55176 - 0.415793i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.60440 - 1.48899i) q^{9} +(-3.43586 + 1.98370i) q^{10} +(-3.50976 - 3.50976i) q^{11} +(-0.444746 - 1.67398i) q^{12} +(-1.03908 + 3.45258i) q^{13} +(1.39127 - 0.803251i) q^{14} +(6.87171 + 0.0145410i) q^{15} -1.00000 q^{16} +(0.584080 - 1.01166i) q^{17} +(-0.788714 + 2.89447i) q^{18} +(-4.16646 + 1.11640i) q^{19} +(1.02684 - 3.83221i) q^{20} +(-2.78254 - 0.00588804i) q^{21} +4.96355 q^{22} +(1.63500 - 2.83190i) q^{23} +(1.49816 + 0.869198i) q^{24} +(9.30128 + 5.37010i) q^{25} +(-1.70661 - 3.17608i) q^{26} +(3.69749 - 3.65084i) q^{27} +(-0.415793 + 1.55176i) q^{28} +7.50570i q^{29} +(-4.86931 + 4.84875i) q^{30} +(-1.94388 + 7.25468i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-7.43622 - 4.31431i) q^{33} +(0.302342 + 1.12836i) q^{34} +(-5.51972 - 3.18681i) q^{35} +(-1.48899 - 2.60440i) q^{36} +(-4.28775 - 1.14890i) q^{37} +(2.15672 - 3.73555i) q^{38} +(-0.203868 + 6.24167i) q^{39} +(1.98370 + 3.43586i) q^{40} +(-1.44991 - 5.41115i) q^{41} +(1.97171 - 1.96339i) q^{42} +(-0.770434 + 0.444811i) q^{43} +(-3.50976 + 3.50976i) q^{44} +(11.5096 - 3.03183i) q^{45} +(0.846338 + 3.15858i) q^{46} +(2.43773 - 0.653187i) q^{47} +(-1.67398 + 0.444746i) q^{48} +(-3.82710 - 2.20958i) q^{49} +(-10.3742 + 2.77977i) q^{50} +(0.527807 - 1.95326i) q^{51} +(3.45258 + 1.03908i) q^{52} -6.60181i q^{53} +(-0.0329860 + 5.19605i) q^{54} +(-9.84618 - 17.0541i) q^{55} +(-0.803251 - 1.39127i) q^{56} +(-6.47805 + 3.72185i) q^{57} +(-5.30733 - 5.30733i) q^{58} +(5.81273 + 5.81273i) q^{59} +(0.0145410 - 6.87171i) q^{60} +(-7.05927 - 12.2270i) q^{61} +(-3.75530 - 6.50436i) q^{62} +(-4.66052 + 1.22767i) q^{63} +1.00000i q^{64} +(-7.52719 + 12.1640i) q^{65} +(8.30888 - 2.20752i) q^{66} +(-3.19229 + 0.855370i) q^{67} +(-1.01166 - 0.584080i) q^{68} +(1.47747 - 5.46770i) q^{69} +(6.15644 - 1.64961i) q^{70} +(0.942701 + 3.51821i) q^{71} +(2.89447 + 0.788714i) q^{72} +(-3.33343 + 3.33343i) q^{73} +(3.84429 - 2.21950i) q^{74} +(17.9585 + 4.85271i) q^{75} +(1.11640 + 4.16646i) q^{76} +(3.98698 + 6.90565i) q^{77} +(-4.26937 - 4.55768i) q^{78} +(-1.16902 + 2.02480i) q^{79} +(-3.83221 - 1.02684i) q^{80} +(4.56581 - 7.75586i) q^{81} +(4.85151 + 2.80102i) q^{82} +(-2.82772 - 10.5532i) q^{83} +(-0.00588804 + 2.78254i) q^{84} +(3.27712 - 3.27712i) q^{85} +(0.230251 - 0.859308i) q^{86} +(3.33813 + 12.5644i) q^{87} -4.96355i q^{88} +(-1.78297 + 6.65415i) q^{89} +(-5.99466 + 10.2823i) q^{90} +(3.04796 - 4.92554i) q^{91} +(-2.83190 - 1.63500i) q^{92} +(-0.0275273 + 13.0087i) q^{93} +(-1.26186 + 2.18561i) q^{94} -17.1131 q^{95} +(0.869198 - 1.49816i) q^{96} +(-1.65585 + 6.17970i) q^{97} +(4.26857 - 1.14376i) q^{98} +(-14.3668 - 3.91482i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 4 q^{7} + 24 q^{15} - 56 q^{16} - 8 q^{19} + 36 q^{27} - 4 q^{28} + 8 q^{31} - 36 q^{33} + 24 q^{35} - 24 q^{36} - 4 q^{37} - 36 q^{38} - 24 q^{39} - 48 q^{41} + 36 q^{42} + 12 q^{43} - 36 q^{45}+ \cdots - 24 q^{99}+O(q^{100}) \) 56 * q + 4 * q^7 + 24 * q^15 - 56 * q^16 - 8 * q^19 + 36 * q^27 - 4 * q^28 + 8 * q^31 - 36 * q^33 + 24 * q^35 - 24 * q^36 - 4 * q^37 - 36 * q^38 - 24 * q^39 - 48 * q^41 + 36 * q^42 + 12 * q^43 - 36 * q^45 + 60 * q^47 - 24 * q^50 - 4 * q^52 + 24 * q^57 - 60 * q^63 - 120 * q^65 - 56 * q^67 - 36 * q^69 + 24 * q^71 + 28 * q^73 + 48 * q^74 + 4 * q^76 - 24 * q^77 + 36 * q^78 - 24 * q^79 - 120 * q^81 - 60 * q^83 + 24 * q^84 + 48 * q^86 + 48 * q^87 + 4 * q^91 - 24 * q^92 + 20 * q^97 - 48 * q^98 - 24 * q^99

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