LMFDB - Embedded newform 946.2.f.e.861.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [946,2,Mod(345,946)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(946, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("946.345");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 946 = 2 \cdot 11 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	946.f (of order $5$, 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:	$7.55384803121$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			861.2
Character	$\chi$	$=$	946.861
Dual form			946.2.f.e.345.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 - 0.587785i) q^{2} +(-0.758361 - 2.33399i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.984942 - 0.715602i) q^{5} +(-1.98541 - 1.44249i) q^{6} +(-1.47181 + 4.52976i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-2.44536 + 1.77666i) q^{9} +O(q^{10})$	\(q+(0.809017 - 0.587785i) q^{2} +(-0.758361 - 2.33399i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.984942 - 0.715602i) q^{5} +(-1.98541 - 1.44249i) q^{6} +(-1.47181 + 4.52976i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-2.44536 + 1.77666i) q^{9} -1.21746 q^{10} +(1.85513 + 2.74927i) q^{11} -2.45411 q^{12} +(-4.37246 + 3.17678i) q^{13} +(1.47181 + 4.52976i) q^{14} +(-0.923270 + 2.84153i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(3.48965 + 2.53538i) q^{17} +(-0.934046 + 2.87470i) q^{18} +(0.504999 + 1.55423i) q^{19} +(-0.984942 + 0.715602i) q^{20} +11.6886 q^{21} +(3.11681 + 1.13379i) q^{22} -8.69451 q^{23} +(-1.98541 + 1.44249i) q^{24} +(-1.08706 - 3.34563i) q^{25} +(-1.67013 + 5.14013i) q^{26} +(0.0449442 + 0.0326539i) q^{27} +(3.85325 + 2.79955i) q^{28} +(-1.96497 + 6.04757i) q^{29} +(0.923270 + 2.84153i) q^{30} +(0.432025 - 0.313885i) q^{31} -1.00000 q^{32} +(5.00993 - 6.41479i) q^{33} +4.31344 q^{34} +(4.69115 - 3.40832i) q^{35} +(0.934046 + 2.87470i) q^{36} +(-0.120009 + 0.369349i) q^{37} +(1.32211 + 0.960566i) q^{38} +(10.7305 + 7.79615i) q^{39} +(-0.376214 + 1.15787i) q^{40} +(0.746817 + 2.29847i) q^{41} +(9.45628 - 6.87039i) q^{42} +1.00000 q^{43} +(3.18798 - 0.914757i) q^{44} +3.67992 q^{45} +(-7.03401 + 5.11050i) q^{46} +(-3.16532 - 9.74185i) q^{47} +(-0.758361 + 2.33399i) q^{48} +(-12.6894 - 9.21940i) q^{49} +(-2.84596 - 2.06771i) q^{50} +(3.27114 - 10.0675i) q^{51} +(1.67013 + 5.14013i) q^{52} +(2.45499 - 1.78366i) q^{53} +0.0555541 q^{54} +(0.140195 - 4.03541i) q^{55} +4.76288 q^{56} +(3.24459 - 2.35733i) q^{57} +(1.96497 + 6.04757i) q^{58} +(-4.36775 + 13.4426i) q^{59} +(2.41715 + 1.75616i) q^{60} +(-7.95125 - 5.77692i) q^{61} +(0.165019 - 0.507876i) q^{62} +(-4.44875 - 13.6918i) q^{63} +(-0.809017 + 0.587785i) q^{64} +6.57992 q^{65} +(0.282600 - 8.13444i) q^{66} +8.50278 q^{67} +(3.48965 - 2.53538i) q^{68} +(6.59357 + 20.2929i) q^{69} +(1.79186 - 5.51478i) q^{70} +(8.26599 + 6.00559i) q^{71} +(2.44536 + 1.77666i) q^{72} +(2.66142 - 8.19102i) q^{73} +(0.120009 + 0.369349i) q^{74} +(-6.98429 + 5.07439i) q^{75} +1.63421 q^{76} +(-15.1840 + 4.35688i) q^{77} +13.2636 q^{78} +(-7.66177 + 5.56661i) q^{79} +(0.376214 + 1.15787i) q^{80} +(-2.76001 + 8.49443i) q^{81} +(1.95519 + 1.42053i) q^{82} +(2.28453 + 1.65981i) q^{83} +(3.61198 - 11.1165i) q^{84} +(-1.62278 - 4.99440i) q^{85} +(0.809017 - 0.587785i) q^{86} +15.6052 q^{87} +(2.04145 - 2.61390i) q^{88} +4.77898 q^{89} +(2.97712 - 2.16301i) q^{90} +(-7.95462 - 24.4818i) q^{91} +(-2.68675 + 8.26897i) q^{92} +(-1.06024 - 0.770307i) q^{93} +(-8.28692 - 6.02080i) q^{94} +(0.614814 - 1.89220i) q^{95} +(0.758361 + 2.33399i) q^{96} +(4.47922 - 3.25434i) q^{97} -15.6850 q^{98} +(-9.42099 - 3.42705i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{2} - q^{3} - 6 q^{4} - 11 q^{5} - 9 q^{6} + 3 q^{7} + 6 q^{8} - 7 q^{9}+O(q^{10}) $ 24 * q + 6 * q^2 - q^3 - 6 * q^4 - 11 * q^5 - 9 * q^6 + 3 * q^7 + 6 * q^8 - 7 * q^9	\( 24 q + 6 q^{2} - q^{3} - 6 q^{4} - 11 q^{5} - 9 q^{6} + 3 q^{7} + 6 q^{8} - 7 q^{9} - 4 q^{10} - 7 q^{11} - 16 q^{12} - 12 q^{13} - 3 q^{14} - 21 q^{15} - 6 q^{16} + 15 q^{17} - 3 q^{18} - 4 q^{19} - 11 q^{20} - 14 q^{21} - 3 q^{22} - 62 q^{23} - 9 q^{24} + 23 q^{25} - 3 q^{26} + 20 q^{27} - 7 q^{28} + 13 q^{29} + 21 q^{30} + 27 q^{31} - 24 q^{32} + 17 q^{33} - 20 q^{34} + 22 q^{35} + 3 q^{36} + 29 q^{37} + 24 q^{38} + 43 q^{39} - 9 q^{40} + 5 q^{41} - 11 q^{42} + 24 q^{43} + 8 q^{44} + 34 q^{45} - 13 q^{46} + 4 q^{47} - q^{48} - 19 q^{49} + 27 q^{50} + 22 q^{51} + 3 q^{52} - 32 q^{53} + 10 q^{54} - 83 q^{55} - 8 q^{56} - 7 q^{57} - 13 q^{58} - 36 q^{59} + 19 q^{60} - 3 q^{61} + 38 q^{62} - 56 q^{63} - 6 q^{64} + 58 q^{65} - 37 q^{66} + 26 q^{67} + 15 q^{68} - 20 q^{69} + 8 q^{70} - 4 q^{71} + 7 q^{72} + 29 q^{73} - 29 q^{74} + 33 q^{75} + 56 q^{76} - 63 q^{77} + 2 q^{78} - 10 q^{79} + 9 q^{80} + 36 q^{81} + 5 q^{82} - 51 q^{83} - 4 q^{84} + 21 q^{85} + 6 q^{86} + 104 q^{87} - 8 q^{88} - 8 q^{89} + 46 q^{90} - 4 q^{91} + 18 q^{92} - 27 q^{93} - 19 q^{94} + 59 q^{95} + q^{96} + 31 q^{97} - 56 q^{98} - 87 q^{99}+O(q^{100}) \) 24 * q + 6 * q^2 - q^3 - 6 * q^4 - 11 * q^5 - 9 * q^6 + 3 * q^7 + 6 * q^8 - 7 * q^9 - 4 * q^10 - 7 * q^11 - 16 * q^12 - 12 * q^13 - 3 * q^14 - 21 * q^15 - 6 * q^16 + 15 * q^17 - 3 * q^18 - 4 * q^19 - 11 * q^20 - 14 * q^21 - 3 * q^22 - 62 * q^23 - 9 * q^24 + 23 * q^25 - 3 * q^26 + 20 * q^27 - 7 * q^28 + 13 * q^29 + 21 * q^30 + 27 * q^31 - 24 * q^32 + 17 * q^33 - 20 * q^34 + 22 * q^35 + 3 * q^36 + 29 * q^37 + 24 * q^38 + 43 * q^39 - 9 * q^40 + 5 * q^41 - 11 * q^42 + 24 * q^43 + 8 * q^44 + 34 * q^45 - 13 * q^46 + 4 * q^47 - q^48 - 19 * q^49 + 27 * q^50 + 22 * q^51 + 3 * q^52 - 32 * q^53 + 10 * q^54 - 83 * q^55 - 8 * q^56 - 7 * q^57 - 13 * q^58 - 36 * q^59 + 19 * q^60 - 3 * q^61 + 38 * q^62 - 56 * q^63 - 6 * q^64 + 58 * q^65 - 37 * q^66 + 26 * q^67 + 15 * q^68 - 20 * q^69 + 8 * q^70 - 4 * q^71 + 7 * q^72 + 29 * q^73 - 29 * q^74 + 33 * q^75 + 56 * q^76 - 63 * q^77 + 2 * q^78 - 10 * q^79 + 9 * q^80 + 36 * q^81 + 5 * q^82 - 51 * q^83 - 4 * q^84 + 21 * q^85 + 6 * q^86 + 104 * q^87 - 8 * q^88 - 8 * q^89 + 46 * q^90 - 4 * q^91 + 18 * q^92 - 27 * q^93 - 19 * q^94 + 59 * q^95 + q^96 + 31 * q^97 - 56 * q^98 - 87 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/946\mathbb{Z}\right)^\times$.

$n$	$89$	$431$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	0.809017	−	0.587785i	0.572061	−	0.415627i
$2$	0.809017	−	0.587785i	0.572061	−	0.415627i
$3$	−0.758361	−	2.33399i	−0.437840	−	1.34753i	−0.890149	−	0.455671i	$-0.849400\pi$
$3$	−0.758361	−	2.33399i	−0.437840	−	1.34753i	0.452309	−	0.891861i	$-0.350600\pi$
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	−0.984942	−	0.715602i	−0.440479	−	0.320027i	0.345346	−	0.938475i	$-0.387762\pi$
$5$	−0.984942	−	0.715602i	−0.440479	−	0.320027i	−0.785825	+	0.618448i	$0.787762\pi$
$6$	−1.98541	−	1.44249i	−0.810542	−	0.588893i
$7$	−1.47181	+	4.52976i	−0.556292	+	1.71209i	0.136216	+	0.990679i	$0.456506\pi$
$7$	−1.47181	+	4.52976i	−0.556292	+	1.71209i	−0.692508	+	0.721410i	$0.743494\pi$
$8$	−0.309017	−	0.951057i	−0.109254	−	0.336249i
$9$	−2.44536	+	1.77666i	−0.815122	+	0.592221i
$10$	−1.21746			−0.384993
$11$	1.85513	+	2.74927i	0.559342	+	0.828937i
$11$	1.85513	+	2.74927i	0.559342	+	0.828937i
$12$	−2.45411			−0.708439
$13$	−4.37246	+	3.17678i	−1.21270	+	0.881079i	−0.995473	−	0.0950418i	$-0.969702\pi$
$13$	−4.37246	+	3.17678i	−1.21270	+	0.881079i	−0.217228	+	0.976121i	$0.569702\pi$
$14$	1.47181	+	4.52976i	0.393358	+	1.21063i
$15$	−0.923270	+	2.84153i	−0.238387	+	0.733681i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	3.48965	+	2.53538i	0.846364	+	0.614919i	0.924141	−	0.382051i	$-0.124782\pi$
$17$	3.48965	+	2.53538i	0.846364	+	0.614919i	−0.0777771	+	0.996971i	$0.524782\pi$
$18$	−0.934046	+	2.87470i	−0.220157	+	0.677573i
$19$	0.504999	+	1.55423i	0.115855	+	0.356564i	0.992124	−	0.125257i	$-0.0399755\pi$
$19$	0.504999	+	1.55423i	0.115855	+	0.356564i	−0.876270	+	0.481821i	$0.839975\pi$
$20$	−0.984942	+	0.715602i	−0.220240	+	0.160013i
$21$	11.6886			2.55066
$22$	3.11681	+	1.13379i	0.664506	+	0.241726i
$23$	−8.69451			−1.81293			−0.906465	−	0.422280i	$-0.861230\pi$
$23$	−8.69451			−1.81293			−0.906465	+	0.422280i	$0.861230\pi$
$24$	−1.98541	+	1.44249i	−0.405271	+	0.294447i
$25$	−1.08706	−	3.34563i	−0.217412	−	0.669126i
$26$	−1.67013	+	5.14013i	−0.327539	+	1.00806i
$27$	0.0449442	+	0.0326539i	0.00864952	+	0.00628425i
$28$	3.85325	+	2.79955i	0.728195	+	0.529065i
$29$	−1.96497	+	6.04757i	−0.364887	+	1.12301i	0.585165	+	0.810914i	$0.301030\pi$
$29$	−1.96497	+	6.04757i	−0.364887	+	1.12301i	−0.950052	+	0.312092i	$0.898970\pi$
$30$	0.923270	+	2.84153i	0.168565	+	0.518790i
$31$	0.432025	−	0.313885i	0.0775941	−	0.0563754i	−0.548312	−	0.836274i	$-0.684729\pi$
$31$	0.432025	−	0.313885i	0.0775941	−	0.0563754i	0.625906	+	0.779898i	$0.284729\pi$
$32$	−1.00000			−0.176777
$33$	5.00993	−	6.41479i	0.872117	−	1.11667i
$34$	4.31344			0.739749
$35$	4.69115	−	3.40832i	0.792950	−	0.576112i
$36$	0.934046	+	2.87470i	0.155674	+	0.479116i
$37$	−0.120009	+	0.369349i	−0.0197293	+	0.0607207i	−0.960436	−	0.278499i	$-0.910163\pi$
$37$	−0.120009	+	0.369349i	−0.0197293	+	0.0607207i	0.940707	+	0.339220i	$0.110163\pi$
$38$	1.32211	+	0.960566i	0.214474	+	0.155824i
$39$	10.7305	+	7.79615i	1.71825	+	1.24838i
$40$	−0.376214	+	1.15787i	−0.0594847	+	0.183075i
$41$	0.746817	+	2.29847i	0.116633	+	0.358960i	0.992284	−	0.123984i	$-0.0395673\pi$
$41$	0.746817	+	2.29847i	0.116633	+	0.358960i	−0.875651	+	0.482945i	$0.839567\pi$
$42$	9.45628	−	6.87039i	1.45914	−	1.06012i
$43$	1.00000			0.152499
$43$	1.00000			0.152499
$44$	3.18798	−	0.914757i	0.480606	−	0.137905i
$45$	3.67992			0.548571
$46$	−7.03401	+	5.11050i	−1.03711	+	0.753503i
$47$	−3.16532	−	9.74185i	−0.461709	−	1.42100i	−0.863074	−	0.505077i	$-0.831464\pi$
$47$	−3.16532	−	9.74185i	−0.461709	−	1.42100i	0.401365	−	0.915918i	$-0.368536\pi$
$48$	−0.758361	+	2.33399i	−0.109460	+	0.336883i
$49$	−12.6894	−	9.21940i	−1.81277	−	1.31706i
$50$	−2.84596	−	2.06771i	−0.402480	−	0.292419i
$51$	3.27114	−	10.0675i	0.458052	−	1.40974i
$52$	1.67013	+	5.14013i	0.231605	+	0.712808i
$53$	2.45499	−	1.78366i	0.337219	−	0.245004i	−0.406268	−	0.913754i	$-0.633170\pi$
$53$	2.45499	−	1.78366i	0.337219	−	0.245004i	0.743488	+	0.668750i	$0.233170\pi$
$54$	0.0555541			0.00755996
$55$	0.140195	−	4.03541i	0.0189039	−	0.544134i
$56$	4.76288			0.636466
$57$	3.24459	−	2.35733i	0.429756	−	0.312236i
$58$	1.96497	+	6.04757i	0.258014	+	0.794085i
$59$	−4.36775	+	13.4426i	−0.568633	+	1.75007i	0.0882702	+	0.996097i	$0.471866\pi$
$59$	−4.36775	+	13.4426i	−0.568633	+	1.75007i	−0.656903	+	0.753975i	$0.728134\pi$
$60$	2.41715	+	1.75616i	0.312053	+	0.226720i
$61$	−7.95125	−	5.77692i	−1.01805	−	0.739659i	−0.0521708	−	0.998638i	$-0.516614\pi$
$61$	−7.95125	−	5.77692i	−1.01805	−	0.739659i	−0.965883	+	0.258979i	$0.916614\pi$
$62$	0.165019	−	0.507876i	0.0209574	−	0.0645004i
$63$	−4.44875	−	13.6918i	−0.560489	−	1.72501i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	6.57992			0.816139
$66$	0.282600	−	8.13444i	0.0347857	−	1.00128i
$67$	8.50278			1.03878			0.519390	−	0.854538i	$-0.326159\pi$
$67$	8.50278			1.03878			0.519390	+	0.854538i	$0.326159\pi$
$68$	3.48965	−	2.53538i	0.423182	−	0.307460i
$69$	6.59357	+	20.2929i	0.793773	+	2.44298i
$70$	1.79186	−	5.51478i	0.214168	−	0.659143i
$71$	8.26599	+	6.00559i	0.980993	+	0.712733i	0.957930	−	0.287001i	$-0.0926584\pi$
$71$	8.26599	+	6.00559i	0.980993	+	0.712733i	0.0230624	+	0.999734i	$0.492658\pi$
$72$	2.44536	+	1.77666i	0.288189	+	0.209382i
$73$	2.66142	−	8.19102i	0.311496	−	0.958686i	−0.665677	−	0.746240i	$-0.731857\pi$
$73$	2.66142	−	8.19102i	0.311496	−	0.958686i	0.977173	−	0.212446i	$-0.0681429\pi$
$74$	0.120009	+	0.369349i	0.0139508	+	0.0429360i
$75$	−6.98429	+	5.07439i	−0.806477	+	0.585940i
$76$	1.63421			0.187457
$77$	−15.1840	+	4.35688i	−1.73037	+	0.496512i
$78$	13.2636			1.50181
$79$	−7.66177	+	5.56661i	−0.862017	+	0.626292i	−0.928433	−	0.371500i	$-0.878844\pi$
$79$	−7.66177	+	5.56661i	−0.862017	+	0.626292i	0.0664160	+	0.997792i	$0.478844\pi$
$80$	0.376214	+	1.15787i	0.0420620	+	0.129454i
$81$	−2.76001	+	8.49443i	−0.306668	+	0.943826i
$82$	1.95519	+	1.42053i	0.215915	+	0.156871i
$83$	2.28453	+	1.65981i	0.250760	+	0.182187i	0.706063	−	0.708149i	$-0.250469\pi$
$83$	2.28453	+	1.65981i	0.250760	+	0.182187i	−0.455304	+	0.890336i	$0.650469\pi$
$84$	3.61198	−	11.1165i	0.394099	−	1.21291i
$85$	−1.62278	−	4.99440i	−0.176015	−	0.541719i
$86$	0.809017	−	0.587785i	0.0872385	−	0.0633825i
$87$	15.6052			1.67305
$88$	2.04145	−	2.61390i	0.217619	−	0.278643i
$89$	4.77898			0.506570			0.253285	−	0.967392i	$-0.418489\pi$
$89$	4.77898			0.506570			0.253285	+	0.967392i	$0.418489\pi$
$90$	2.97712	−	2.16301i	0.313816	−	0.228001i
$91$	−7.95462	−	24.4818i	−0.833871	−	2.56639i
$92$	−2.68675	+	8.26897i	−0.280113	+	0.862100i
$93$	−1.06024	−	0.770307i	−0.109941	−	0.0798771i
$94$	−8.28692	−	6.02080i	−0.854730	−	0.620998i
$95$	0.614814	−	1.89220i	0.0630786	−	0.194136i
$96$	0.758361	+	2.33399i	0.0773998	+	0.238212i
$97$	4.47922	−	3.25434i	0.454796	−	0.330429i	−0.336690	−	0.941615i	$-0.609308\pi$
$97$	4.47922	−	3.25434i	0.454796	−	0.330429i	0.791486	+	0.611187i	$0.209308\pi$
$98$	−15.6850			−1.58442
$99$	−9.42099	−	3.42705i	−0.946845	−	0.344431i
$100$	−3.51780			−0.351780
$101$	−5.84013	+	4.24310i	−0.581114	+	0.422204i	−0.839126	−	0.543938i	$-0.816933\pi$
$101$	−5.84013	+	4.24310i	−0.581114	+	0.422204i	0.258011	+	0.966142i	$0.416933\pi$
$102$	−3.27114	−	10.0675i	−0.323892	−	0.996836i
$103$	−2.60698	+	8.02347i	−0.256874	+	0.790576i	0.736581	+	0.676349i	$0.236439\pi$
$103$	−2.60698	+	8.02347i	−0.256874	+	0.790576i	−0.993455	+	0.114227i	$0.963561\pi$
$104$	4.37246	+	3.17678i	0.428755	+	0.311509i
$105$	−11.5126	−	8.36439i	−1.12351	−	0.816281i
$106$	0.937724	−	2.88602i	0.0910798	−	0.280315i
$107$	2.22215	+	6.83909i	0.214824	+	0.661160i	0.999166	+	0.0408314i	$0.0130007\pi$
$107$	2.22215	+	6.83909i	0.214824	+	0.661160i	−0.784342	+	0.620328i	$0.786999\pi$
$108$	0.0449442	−	0.0326539i	0.00432476	−	0.00314212i
$109$	8.82165			0.844961			0.422480	−	0.906372i	$-0.361160\pi$
$109$	8.82165			0.844961			0.422480	+	0.906372i	$0.361160\pi$
$110$	−2.25853	−	3.34712i	−0.215343	−	0.319135i
$111$	0.953069			0.0904613
$112$	3.85325	−	2.79955i	0.364098	−	0.264532i
$113$	−3.98128	−	12.2531i	−0.374528	−	1.15268i	−0.943797	−	0.330526i	$-0.892774\pi$
$113$	−3.98128	−	12.2531i	−0.374528	−	1.15268i	0.569269	−	0.822151i	$-0.307226\pi$
$114$	1.23932	−	3.81424i	0.116073	−	0.357236i
$115$	8.56359	+	6.22181i	0.798559	+	0.580187i
$116$	5.14437	+	3.73760i	0.477643	+	0.347028i
$117$	5.04820	−	15.5368i	0.466706	−	1.43637i
$118$	4.36775	+	13.4426i	0.402084	+	1.23749i
$119$	−16.6208	+	12.0757i	−1.52362	+	1.10698i
$120$	2.98776			0.272744
$121$	−4.11701	+	10.2005i	−0.374274	+	0.927318i
$122$	−9.82829			−0.889812
$123$	4.79825	−	3.48613i	0.432644	−	0.314334i
$124$	−0.165019	−	0.507876i	−0.0148191	−	0.0456086i
$125$	−3.20452	+	9.86250i	−0.286621	+	0.882129i
$126$	−11.6470	−	8.46202i	−1.03759	−	0.753856i
$127$	10.8916	+	7.91319i	0.966470	+	0.702182i	0.954644	−	0.297748i	$-0.0962357\pi$
$127$	10.8916	+	7.91319i	0.966470	+	0.702182i	0.0118258	+	0.999930i	$0.496236\pi$
$128$	−0.309017	+	0.951057i	−0.0273135	+	0.0840623i
$129$	−0.758361	−	2.33399i	−0.0667699	−	0.205497i
$130$	5.32327	−	3.86758i	0.466882	−	0.339209i
$131$	−19.5131			−1.70487			−0.852433	−	0.522837i	$-0.824874\pi$
$131$	−19.5131			−1.70487			−0.852433	+	0.522837i	$0.824874\pi$
$132$	−4.55268	−	6.74701i	−0.396260	−	0.587252i
$133$	−7.78355			−0.674919
$134$	6.87889	−	4.99781i	0.594246	−	0.431745i
$135$	−0.0209003	−	0.0643244i	−0.00179881	−	0.00553616i
$136$	1.33293	−	4.10233i	0.114298	−	0.351772i
$137$	−5.15040	−	3.74198i	−0.440028	−	0.319699i	0.345618	−	0.938375i	$-0.387669\pi$
$137$	−5.15040	−	3.74198i	−0.440028	−	0.319699i	−0.785646	+	0.618676i	$0.787669\pi$
$138$	17.2622	+	12.5417i	1.46946	+	1.06762i
$139$	−5.31332	+	16.3527i	−0.450670	+	1.38702i	0.425475	+	0.904970i	$0.360107\pi$
$139$	−5.31332	+	16.3527i	−0.450670	+	1.38702i	−0.876144	+	0.482049i	$0.839893\pi$
$140$	−1.79186	−	5.51478i	−0.151440	−	0.466084i
$141$	−20.3370	+	14.7757i	−1.71268	+	1.24434i
$142$	10.2173			0.857419
$143$	−16.8453	−	6.12776i	−1.40867	−	0.512429i
$144$	3.02264			0.251886
$145$	6.26304	−	4.55036i	0.520117	−	0.377887i
$146$	−2.66142	−	8.19102i	−0.220261	−	0.677893i
$147$	−11.8949	+	36.6086i	−0.981072	+	3.01943i
$148$	0.314187	+	0.228270i	0.0258260	+	0.0187637i
$149$	14.4577	+	10.5041i	1.18442	+	0.860530i	0.992663	−	0.120913i	$-0.0385823\pi$
$149$	14.4577	+	10.5041i	1.18442	+	0.860530i	0.191754	+	0.981443i	$0.438582\pi$
$150$	−2.66776	+	8.21053i	−0.217822	+	0.670387i
$151$	1.32106	+	4.06581i	0.107507	+	0.330871i	0.990311	−	0.138870i	$-0.0443471\pi$
$151$	1.32106	+	4.06581i	0.107507	+	0.330871i	−0.882804	+	0.469741i	$0.844347\pi$
$152$	1.32211	−	0.960566i	0.107237	−	0.0779122i
$153$	−13.0380			−1.05406
$154$	−9.72317	+	12.4497i	−0.783515	+	1.00322i
$155$	−0.650137			−0.0522202
$156$	10.7305	−	7.79615i	0.859125	−	0.624191i
$157$	−5.20017	−	16.0045i	−0.415019	−	1.27730i	−0.912234	−	0.409670i	$-0.865644\pi$
$157$	−5.20017	−	16.0045i	−0.415019	−	1.27730i	0.497215	−	0.867627i	$-0.334356\pi$
$158$	−2.92654	+	9.00696i	−0.232823	+	0.716555i
$159$	−6.02481	−	4.37728i	−0.477799	−	0.347141i
$160$	0.984942	+	0.715602i	0.0778665	+	0.0565733i
$161$	12.7967	−	39.3841i	1.00852	−	3.10390i
$162$	2.76001	+	8.49443i	0.216847	+	0.667386i
$163$	−2.79059	+	2.02749i	−0.218576	+	0.158805i	−0.691686	−	0.722199i	$-0.743132\pi$
$163$	−2.79059	+	2.02749i	−0.218576	+	0.158805i	0.473109	+	0.881004i	$0.343132\pi$
$164$	2.41675			0.188717
$165$	−9.52493	+	2.73308i	−0.741515	+	0.212770i
$166$	2.82383			0.219172
$167$	−1.02085	+	0.741693i	−0.0789959	+	0.0573939i	−0.626582	−	0.779355i	$-0.715547\pi$
$167$	−1.02085	+	0.741693i	−0.0789959	+	0.0573939i	0.547586	+	0.836749i	$0.315547\pi$
$168$	−3.61198	−	11.1165i	−0.278670	−	0.857658i
$169$	5.00925	−	15.4169i	0.385327	−	1.18592i
$170$	−4.24849	−	3.08671i	−0.325844	−	0.236740i
$171$	−3.99624	−	2.90344i	−0.305600	−	0.222032i
$172$	0.309017	−	0.951057i	0.0235623	−	0.0725174i
$173$	−5.71391	−	17.5856i	−0.434420	−	1.33701i	−0.893680	−	0.448706i	$-0.851885\pi$
$173$	−5.71391	−	17.5856i	−0.434420	−	1.33701i	0.459259	−	0.888302i	$-0.348115\pi$
$174$	12.6248	−	9.17248i	0.957086	−	0.695364i
$175$	16.7549			1.26655
$176$	0.115154	−	3.31463i	0.00868006	−	0.249849i
$177$	34.6872			2.60725
$178$	3.86627	−	2.80901i	0.289789	−	0.210544i
$179$	1.68612	+	5.18935i	0.126027	+	0.387870i	0.994087	−	0.108589i	$-0.0346333\pi$
$179$	1.68612	+	5.18935i	0.126027	+	0.387870i	−0.868060	+	0.496459i	$0.834633\pi$
$180$	1.13716	−	3.49982i	0.0847589	−	0.260861i
$181$	−7.83559	−	5.69289i	−0.582415	−	0.423149i	0.257179	−	0.966364i	$-0.417207\pi$
$181$	−7.83559	−	5.69289i	−0.582415	−	0.423149i	−0.839594	+	0.543215i	$0.817207\pi$
$182$	−20.8255	−	15.1306i	−1.54369	−	1.12155i
$183$	−7.45339	+	22.9392i	−0.550970	+	1.69571i
$184$	2.68675	+	8.26897i	0.198070	+	0.609597i
$185$	0.382509	−	0.277909i	0.0281226	−	0.0204323i
$186$	−1.31052			−0.0960923
$187$	−0.496710	+	14.2974i	−0.0363231	+	1.04553i
$188$	−10.2432			−0.747061
$189$	−0.214064	+	0.155526i	−0.0155708	+	0.0113129i
$190$	−0.614814	−	1.89220i	−0.0446033	−	0.137275i
$191$	−4.90131	+	15.0847i	−0.354646	+	1.09149i	0.601568	+	0.798821i	$0.294543\pi$
$191$	−4.90131	+	15.0847i	−0.354646	+	1.09149i	−0.956214	+	0.292667i	$0.905457\pi$
$192$	1.98541	+	1.44249i	0.143285	+	0.104103i
$193$	6.69847	+	4.86672i	0.482166	+	0.350314i	0.802164	−	0.597104i	$-0.203682\pi$
$193$	6.69847	+	4.86672i	0.482166	+	0.350314i	−0.319997	+	0.947418i	$0.603682\pi$
$194$	1.71091	−	5.26564i	0.122836	−	0.378051i
$195$	−4.98995	−	15.3575i	−0.357338	−	1.09977i
$196$	−12.6894	+	9.21940i	−0.906387	+	0.658529i
$197$	−16.6331			−1.18506			−0.592528	−	0.805550i	$-0.701870\pi$
$197$	−16.6331			−1.18506			−0.592528	+	0.805550i	$0.701870\pi$
$198$	−9.63611	+	2.76498i	−0.684808	+	0.196499i
$199$	15.2592			1.08169			0.540847	−	0.841121i	$-0.318104\pi$
$199$	15.2592			1.08169			0.540847	+	0.841121i	$0.318104\pi$
$200$	−2.84596	+	2.06771i	−0.201240	+	0.146209i
$201$	−6.44817	−	19.8454i	−0.454819	−	1.39979i
$202$	−2.23073	+	6.86548i	−0.156954	+	0.483054i
$203$	−24.5020	−	17.8017i	−1.71970	−	1.24944i
$204$	−8.56397	−	6.22209i	−0.599598	−	0.435633i
$205$	0.909216	−	2.79828i	0.0635024	−	0.195440i
$206$	2.60698	+	8.02347i	0.181637	+	0.559022i
$207$	21.2612	−	15.4472i	1.47776	−	1.07365i
$208$	5.40465			0.374745
$209$	−3.33616	+	4.27167i	−0.230767	+	0.295478i
$210$	−14.2303			−0.981987
$211$	−5.34680	+	3.88468i	−0.368089	+	0.267432i	−0.756418	−	0.654088i	$-0.773052\pi$
$211$	−5.34680	+	3.88468i	−0.368089	+	0.267432i	0.388329	+	0.921521i	$0.373052\pi$
$212$	−0.937724	−	2.88602i	−0.0644031	−	0.198212i
$213$	7.74842	−	23.8472i	0.530913	−	1.63398i
$214$	5.81768	+	4.22679i	0.397688	+	0.288937i
$215$	−0.984942	−	0.715602i	−0.0671725	−	0.0488037i
$216$	0.0171672	−	0.0528351i	0.00116808	−	0.00359497i
$217$	0.785965	+	2.41895i	0.0533548	+	0.164209i
$218$	7.13687	−	5.18524i	0.483370	−	0.351189i
$219$	−21.1361			−1.42825
$220$	−3.79458	−	1.38034i	−0.255830	−	0.0930627i
$221$	−23.3127			−1.56818
$222$	0.771049	−	0.560200i	0.0517494	−	0.0375982i
$223$	−1.95379	−	6.01316i	−0.130836	−	0.402671i	0.864083	−	0.503349i	$-0.167899\pi$
$223$	−1.95379	−	6.01316i	−0.130836	−	0.402671i	−0.994919	+	0.100678i	$0.967899\pi$
$224$	1.47181	−	4.52976i	0.0983394	−	0.302658i
$225$	8.60231	+	6.24995i	0.573487	+	0.416663i
$226$	−10.4231	−	7.57285i	−0.693337	−	0.503739i
$227$	−0.706746	+	2.17514i	−0.0469084	+	0.144369i	−0.971767	−	0.235941i	$-0.924183\pi$
$227$	−0.706746	+	2.17514i	−0.0469084	+	0.144369i	0.924859	+	0.380310i	$0.124183\pi$
$228$	−1.23932	−	3.81424i	−0.0820761	−	0.252604i
$229$	22.3673	−	16.2508i	1.47807	−	1.07388i	0.499903	−	0.866082i	$-0.333369\pi$
$229$	22.3673	−	16.2508i	1.47807	−	1.07388i	0.978171	−	0.207802i	$-0.0666309\pi$
$230$	10.5852			0.697966
$231$	21.6838	+	32.1352i	1.42669	+	2.11434i
$232$	6.35879			0.417475
$233$	6.76952	−	4.91834i	0.443486	−	0.322211i	−0.343533	−	0.939141i	$-0.611624\pi$
$233$	6.76952	−	4.91834i	0.443486	−	0.322211i	0.787018	+	0.616929i	$0.211624\pi$
$234$	−5.04820	−	15.5368i	−0.330011	−	1.01567i
$235$	−3.85363	+	11.8603i	−0.251383	+	0.773679i
$236$	11.4349	+	8.30796i	0.744350	+	0.540802i
$237$	18.8028	+	13.6610i	1.22137	+	0.887380i
$238$	−6.34856	+	19.5389i	−0.411516	+	1.26652i
$239$	1.77206	+	5.45385i	0.114625	+	0.352780i	0.991869	−	0.127266i	$-0.0406201\pi$
$239$	1.77206	+	5.45385i	0.114625	+	0.352780i	−0.877243	+	0.480046i	$0.840620\pi$
$240$	2.41715	−	1.75616i	0.156026	−	0.113360i
$241$	6.56707			0.423022			0.211511	−	0.977376i	$-0.432162\pi$
$241$	6.56707			0.423022			0.211511	+	0.977376i	$0.432162\pi$
$242$	2.66497	+	10.6723i	0.171311	+	0.686041i
$243$	22.0857			1.41680
$244$	−7.95125	+	5.77692i	−0.509027	+	0.369830i
$245$	5.90091	+	18.1611i	0.376996	+	1.16027i
$246$	1.83277	−	5.64068i	0.116853	−	0.359637i
$247$	−7.14552	−	5.19152i	−0.454659	−	0.330329i
$248$	−0.432025	−	0.313885i	−0.0274336	−	0.0199317i
$249$	2.14148	−	6.59081i	0.135711	−	0.417675i
$250$	3.20452	+	9.86250i	0.202672	+	0.623759i
$251$	13.4304	−	9.75774i	0.847718	−	0.615903i	−0.0767977	−	0.997047i	$-0.524470\pi$
$251$	13.4304	−	9.75774i	0.847718	−	0.615903i	0.924516	+	0.381143i	$0.124470\pi$
$252$	−14.3964			−0.906891
$253$	−16.1294	−	23.9036i	−1.01405	−	1.50281i
$254$	13.4627			0.844726
$255$	−10.4262	+	7.57511i	−0.652917	+	0.474372i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	6.36597	−	19.5925i	0.397099	−	1.22214i	−0.530217	−	0.847862i	$-0.677889\pi$
$257$	6.36597	−	19.5925i	0.397099	−	1.22214i	0.927315	−	0.374282i	$-0.122111\pi$
$258$	−1.98541	−	1.44249i	−0.123606	−	0.0898053i
$259$	−1.49644	−	1.08722i	−0.0929840	−	0.0675568i
$260$	2.03331	−	6.25788i	0.126100	−	0.388097i
$261$	−5.93941	−	18.2796i	−0.367640	−	1.13148i
$262$	−15.7864	+	11.4695i	−0.975288	+	0.708588i
$263$	18.7259			1.15469			0.577345	−	0.816500i	$-0.304089\pi$
$263$	18.7259			1.15469			0.577345	+	0.816500i	$0.304089\pi$
$264$	−7.64899	−	2.78245i	−0.470763	−	0.171248i
$265$	−3.69441			−0.226946
$266$	−6.29702	+	4.57505i	−0.386095	+	0.280515i
$267$	−3.62419	−	11.1541i	−0.221797	−	0.682620i
$268$	2.62750	−	8.08662i	0.160500	−	0.493969i
$269$	−8.59280	−	6.24303i	−0.523912	−	0.380644i	0.294163	−	0.955755i	$-0.404959\pi$
$269$	−8.59280	−	6.24303i	−0.523912	−	0.380644i	−0.818076	+	0.575111i	$0.804959\pi$
$270$	−0.0547176	−	0.0397547i	−0.00333001	−	0.00241939i
$271$	4.50882	−	13.8767i	0.273891	−	0.842950i	−0.715620	−	0.698490i	$-0.753856\pi$
$271$	4.50882	−	13.8767i	0.273891	−	0.842950i	0.989511	−	0.144460i	$-0.0461444\pi$
$272$	−1.33293	−	4.10233i	−0.0808206	−	0.248740i
$273$	−51.1079	+	37.1321i	−3.09319	+	2.24733i
$274$	−6.36624			−0.384599
$275$	7.18142	−	9.19519i	0.433056	−	0.554491i
$276$	21.3372			1.28435
$277$	−11.7184	+	8.51393i	−0.704091	+	0.511552i	−0.881262	−	0.472628i	$-0.843306\pi$
$277$	−11.7184	+	8.51393i	−0.704091	+	0.511552i	0.177171	+	0.984180i	$0.443306\pi$
$278$	5.31332	+	16.3527i	0.318672	+	0.980771i
$279$	−0.498793	+	1.53513i	−0.0298619	+	0.0919056i
$280$	−4.69115	−	3.40832i	−0.280350	−	0.203686i
$281$	−10.2097	−	7.41781i	−0.609062	−	0.442509i	0.240022	−	0.970767i	$-0.422845\pi$
$281$	−10.2097	−	7.41781i	−0.609062	−	0.442509i	−0.849084	+	0.528258i	$0.822845\pi$
$282$	−7.76803	+	23.9075i	−0.462580	+	1.42367i
$283$	−3.97004	−	12.2185i	−0.235994	−	0.726315i	−0.996988	−	0.0775562i	$-0.975288\pi$
$283$	−3.97004	−	12.2185i	−0.235994	−	0.726315i	0.760994	−	0.648759i	$-0.224712\pi$
$284$	8.26599	−	6.00559i	0.490496	−	0.356366i
$285$	−4.88264			−0.289223
$286$	−17.2299	+	4.94395i	−1.01883	+	0.292342i
$287$	−11.5107			−0.679454
$288$	2.44536	−	1.77666i	0.144095	−	0.104691i
$289$	0.496215	+	1.52719i	0.0291891	+	0.0898348i
$290$	2.39227	−	7.36264i	0.140479	−	0.432349i
$291$	−10.9925	−	7.98651i	−0.644391	−	0.468177i
$292$	−6.96769	−	5.06233i	−0.407753	−	0.296250i
$293$	0.290545	−	0.894206i	0.0169738	−	0.0522401i	−0.942211	−	0.335020i	$-0.891257\pi$
$293$	0.290545	−	0.894206i	0.0169738	−	0.0522401i	0.959185	+	0.282780i	$0.0912568\pi$
$294$	11.8949	+	36.6086i	0.693723	+	2.13506i
$295$	13.9215	−	10.1146i	0.810541	−	0.588893i
$296$	0.388357			0.0225728
$297$	−0.00639728	+	0.184141i	−0.000371208	+	0.0106850i
$298$	17.8706			1.03522
$299$	38.0164	−	27.6205i	2.19854	−	1.59734i
$300$	2.66776	+	8.21053i	0.154023	+	0.474035i
$301$	−1.47181	+	4.52976i	−0.0848337	+	0.261091i
$302$	3.45859	+	2.51281i	0.199019	+	0.144596i
$303$	14.3323	+	10.4130i	0.823369	+	0.598212i
$304$	0.504999	−	1.55423i	0.0289637	−	0.0891411i
$305$	3.69754	+	11.3799i	0.211721	+	0.651609i
$306$	−10.5479	+	7.66353i	−0.602986	+	0.438095i
$307$	−10.1217			−0.577676			−0.288838	−	0.957378i	$-0.593269\pi$
$307$	−10.1217			−0.577676			−0.288838	+	0.957378i	$0.593269\pi$
$308$	−0.548464	+	15.7871i	−0.0312517	+	0.899556i
$309$	20.7038			1.17780
$310$	−0.525972	+	0.382141i	−0.0298732	+	0.0217041i
$311$	6.57636	+	20.2400i	0.372911	+	1.14770i	0.944877	+	0.327426i	$0.106181\pi$
$311$	6.57636	+	20.2400i	0.372911	+	1.14770i	−0.571965	+	0.820278i	$0.693819\pi$
$312$	4.09868	−	12.6144i	0.232042	−	0.714151i
$313$	15.1510	+	11.0079i	0.856387	+	0.622202i	0.926900	−	0.375309i	$-0.122463\pi$
$313$	15.1510	+	11.0079i	0.856387	+	0.622202i	−0.0705124	+	0.997511i	$0.522463\pi$
$314$	−13.6142	−	9.89132i	−0.768295	−	0.558199i
$315$	−5.41615	+	16.6692i	−0.305165	+	0.939202i
$316$	2.92654	+	9.00696i	0.164631	+	0.506681i
$317$	−20.9189	+	15.1984i	−1.17492	+	0.853630i	−0.991590	−	0.129421i	$-0.958688\pi$
$317$	−20.9189	+	15.1984i	−1.17492	+	0.853630i	−0.183331	+	0.983051i	$0.558688\pi$
$318$	−7.44708			−0.417611
$319$	−20.2717	+	5.81675i	−1.13500	+	0.325676i
$320$	1.21746			0.0680578
$321$	14.2772	−	10.3730i	0.796875	−	0.578964i
$322$	−12.7967	−	39.3841i	−0.713130	−	2.19479i
$323$	−2.17828	+	6.70407i	−0.121203	+	0.373025i
$324$	7.22580	+	5.24985i	0.401433	+	0.291658i
$325$	15.3814	+	11.1753i	0.853209	+	0.619893i
$326$	−1.06591	+	3.28054i	−0.0590354	+	0.181692i
$327$	−6.68999	−	20.5897i	−0.369957	−	1.13861i
$328$	1.95519	−	1.42053i	0.107957	−	0.0784357i
$329$	48.7870			2.68972
$330$	−6.09937	+	7.80972i	−0.335759	+	0.429911i
$331$	23.4386			1.28830			0.644152	−	0.764897i	$-0.277210\pi$
$331$	23.4386			1.28830			0.644152	+	0.764897i	$0.277210\pi$
$332$	2.28453	−	1.65981i	0.125380	−	0.0910937i
$333$	−0.362743	−	1.11641i	−0.0198782	−	0.0611789i
$334$	−0.389931	+	1.20008i	−0.0213361	+	0.0656657i
$335$	−8.37474	−	6.08460i	−0.457561	−	0.332437i
$336$	−9.45628	−	6.87039i	−0.515882	−	0.374810i
$337$	−8.43928	+	25.9734i	−0.459717	+	1.41486i	0.405790	+	0.913966i	$0.366997\pi$
$337$	−8.43928	+	25.9734i	−0.459717	+	1.41486i	−0.865507	+	0.500897i	$0.833003\pi$
$338$	−5.00925	−	15.4169i	−0.272467	−	0.838569i
$339$	−25.5795	+	18.5846i	−1.38929	+	1.00938i
$340$	−5.25142			−0.284798
$341$	1.66442	+	0.605460i	0.0901333	+	0.0327875i
$342$	−4.93963			−0.267105
$343$	33.4654	−	24.3140i	1.80696	−	1.31283i
$344$	−0.309017	−	0.951057i	−0.0166611	−	0.0512775i
$345$	8.02738	−	24.7057i	0.432180	−	1.33011i
$346$	−14.9592	−	10.8685i	−0.804212	−	0.584294i
$347$	−3.89698	−	2.83132i	−0.209201	−	0.151993i	0.478251	−	0.878223i	$-0.341271\pi$
$347$	−3.89698	−	2.83132i	−0.209201	−	0.151993i	−0.687452	+	0.726230i	$0.741271\pi$
$348$	4.82226	−	14.8414i	0.258500	−	0.795581i
$349$	6.14679	+	18.9179i	0.329030	+	1.01265i	0.969588	+	0.244741i	$0.0787029\pi$
$349$	6.14679	+	18.9179i	0.329030	+	1.01265i	−0.640558	+	0.767909i	$0.721297\pi$
$350$	13.5550	−	9.84826i	0.724543	−	0.526412i
$351$	−0.300251			−0.0160262
$352$	−1.85513	−	2.74927i	−0.0988786	−	0.146537i
$353$	−28.9293			−1.53975			−0.769876	−	0.638193i	$-0.779682\pi$
$353$	−28.9293			−1.53975			−0.769876	+	0.638193i	$0.779682\pi$
$354$	28.0625	−	20.3886i	1.49151	−	1.08364i
$355$	−3.84390	−	11.8303i	−0.204013	−	0.627888i
$356$	1.47678	−	4.54508i	0.0782694	−	0.240889i
$357$	40.7891	+	29.6350i	2.15879	+	1.56845i
$358$	4.41432	+	3.20719i	0.233304	+	0.169505i
$359$	1.29742	−	3.99304i	0.0684751	−	0.210745i	−0.910964	−	0.412487i	$-0.864660\pi$
$359$	1.29742	−	3.99304i	0.0684751	−	0.210745i	0.979439	+	0.201742i	$0.0646603\pi$
$360$	−1.13716	−	3.49982i	−0.0599336	−	0.184457i
$361$	13.2107	−	9.59815i	0.695301	−	0.505166i
$362$	−9.68532			−0.509049
$363$	26.9301	+	1.87343i	1.41346	+	0.0983295i
$364$	−25.7417			−1.34923
$365$	−8.48285	+	6.16315i	−0.444013	+	0.322594i
$366$	7.45339	+	22.9392i	0.389595	+	1.19905i
$367$	0.858093	−	2.64094i	0.0447921	−	0.137856i	−0.926159	−	0.377132i	$-0.876910\pi$
$367$	0.858093	−	2.64094i	0.0447921	−	0.137856i	0.970951	+	0.239276i	$0.0769102\pi$
$368$	7.03401	+	5.11050i	0.366673	+	0.266403i
$369$	−5.90984	−	4.29375i	−0.307654	−	0.223524i
$370$	0.146105	−	0.449666i	0.00759566	−	0.0233770i
$371$	4.46626	+	13.7457i	0.231877	+	0.713643i
$372$	−1.06024	+	0.770307i	−0.0549707	+	0.0399386i
$373$	−9.15696			−0.474129			−0.237065	−	0.971494i	$-0.576185\pi$
$373$	−9.15696			−0.474129			−0.237065	+	0.971494i	$0.576185\pi$
$374$	8.00198	+	11.8588i	0.413773	+	0.613206i
$375$	25.4492			1.31419
$376$	−8.28692	+	6.02080i	−0.427365	+	0.310499i
$377$	−10.6200	−	32.6850i	−0.546958	−	1.68336i
$378$	−0.0817651	+	0.251647i	−0.00420554	+	0.0129433i
$379$	11.6097	+	8.43493i	0.596350	+	0.433273i	0.844581	−	0.535427i	$-0.179849\pi$
$379$	11.6097	+	8.43493i	0.596350	+	0.433273i	−0.248232	+	0.968701i	$0.579849\pi$
$380$	−1.60960	−	1.16945i	−0.0825709	−	0.0599913i
$381$	10.2096	−	31.4219i	0.523053	−	1.60979i
$382$	4.90131	+	15.0847i	0.250773	+	0.771799i
$383$	1.44618	−	1.05071i	0.0738964	−	0.0536889i	−0.550224	−	0.835017i	$-0.685458\pi$
$383$	1.44618	−	1.05071i	0.0738964	−	0.0536889i	0.624120	+	0.781328i	$0.285458\pi$
$384$	2.45411			0.125236
$385$	18.0731	+	6.57440i	0.921090	+	0.335062i
$386$	8.27976			0.421429
$387$	−2.44536	+	1.77666i	−0.124305	+	0.0903128i
$388$	−1.71091	−	5.26564i	−0.0868583	−	0.267322i
$389$	−0.398589	+	1.22673i	−0.0202093	+	0.0621978i	−0.960653	−	0.277753i	$-0.910410\pi$
$389$	−0.398589	+	1.22673i	−0.0202093	+	0.0621978i	0.940443	+	0.339951i	$0.110410\pi$
$390$	−13.0639	−	9.49146i	−0.661515	−	0.480619i
$391$	−30.3408	−	22.0439i	−1.53440	−	1.11481i
$392$	−4.84693	+	14.9173i	−0.244807	+	0.753437i
$393$	14.7979	+	45.5434i	0.746458	+	2.29736i
$394$	−13.4564	+	9.77667i	−0.677925	+	0.492541i
$395$	11.5299			0.580131
$396$	−6.17056	+	7.90088i	−0.310082	+	0.397034i
$397$	−35.1209			−1.76267			−0.881334	−	0.472494i	$-0.843354\pi$
$397$	−35.1209			−1.76267			−0.881334	+	0.472494i	$0.843354\pi$
$398$	12.3449	−	8.96912i	0.618795	−	0.449581i
$399$	5.90273	+	18.1667i	0.295506	+	0.909475i
$400$	−1.08706	+	3.34563i	−0.0543530	+	0.167281i
$401$	6.46896	+	4.69997i	0.323044	+	0.234705i	0.737473	−	0.675376i	$-0.236019\pi$
$401$	6.46896	+	4.69997i	0.323044	+	0.234705i	−0.414429	+	0.910082i	$0.636019\pi$
$402$	−16.8815	−	12.2651i	−0.841974	−	0.611730i
$403$	−0.891871	+	2.74490i	−0.0444273	+	0.136733i
$404$	2.23073	+	6.86548i	0.110983	+	0.341571i
$405$	8.79708	−	6.39145i	0.437131	−	0.317594i
$406$	−30.2861			−1.50308
$407$	−1.23807	+	0.355252i	−0.0613691	+	0.0176092i
$408$	−10.5856			−0.524068
$409$	−3.16851	+	2.30206i	−0.156673	+	0.113829i	−0.663360	−	0.748301i	$-0.730870\pi$
$409$	−3.16851	+	2.30206i	−0.156673	+	0.113829i	0.506687	+	0.862130i	$0.330870\pi$
$410$	−0.909216	−	2.79828i	−0.0449030	−	0.138197i
$411$	−4.82791	+	14.8588i	−0.238143	+	0.732929i
$412$	6.82517	+	4.95878i	0.336252	+	0.244302i
$413$	−54.4631	−	39.5698i	−2.67995	−	1.94710i
$414$	8.12107	−	24.9941i	0.399129	−	1.22839i
$415$	−1.06237	−	3.26963i	−0.0521495	−	0.160500i
$416$	4.37246	−	3.17678i	0.214377	−	0.155754i
$417$	42.1965			2.06637
$418$	−0.188186	+	5.41680i	−0.00920448	+	0.264944i
$419$	−31.6051			−1.54401			−0.772005	−	0.635617i	$-0.780746\pi$
$419$	−31.6051			−1.54401			−0.772005	+	0.635617i	$0.780746\pi$
$420$	−11.5126	+	8.36439i	−0.561757	+	0.408140i
$421$	8.81219	+	27.1211i	0.429480	+	1.32180i	0.898639	+	0.438690i	$0.144557\pi$
$421$	8.81219	+	27.1211i	0.429480	+	1.32180i	−0.469159	+	0.883114i	$0.655443\pi$
$422$	−2.04230	+	6.28555i	−0.0994175	+	0.305976i
$423$	25.0483	+	18.1987i	1.21789	+	0.884850i
$424$	−2.45499	−	1.78366i	−0.119225	−	0.0866220i
$425$	4.68897	−	14.4312i	0.227449	−	0.700015i
$426$	−7.74842	−	23.8472i	−0.375412	−	1.15540i
$427$	37.8708	−	27.5148i	1.83270	−	1.33153i
$428$	7.19104			0.347592
$429$	−1.52736	+	43.9638i	−0.0737415	+	2.12259i
$430$	−1.21746			−0.0587109
$431$	−17.1514	+	12.4612i	−0.826152	+	0.600235i	−0.918468	−	0.395495i	$-0.870573\pi$
$431$	−17.1514	+	12.4612i	−0.826152	+	0.600235i	0.0923161	+	0.995730i	$0.470573\pi$
$432$	−0.0171672	−	0.0528351i	−0.000825956	−	0.00254203i
$433$	6.12641	−	18.8552i	0.294416	−	0.906121i	−0.689000	−	0.724761i	$-0.741950\pi$
$433$	6.12641	−	18.8552i	0.294416	−	0.906121i	0.983417	−	0.181360i	$-0.0580498\pi$
$434$	2.05768	+	1.49499i	0.0987720	+	0.0717620i
$435$	−15.3702	−	11.1671i	−0.736943	−	0.535420i
$436$	2.72604	−	8.38989i	0.130554	−	0.401803i
$437$	−4.39072	−	13.5132i	−0.210037	−	0.646426i
$438$	−17.0995	+	12.4235i	−0.817044	+	0.593617i
$439$	−12.1035			−0.577668			−0.288834	−	0.957379i	$-0.593268\pi$
$439$	−12.1035			−0.577668			−0.288834	+	0.957379i	$0.593268\pi$
$440$	−3.88122	+	1.11368i	−0.185030	+	0.0530924i
$441$	47.4100			2.25762
$442$	−18.8603	+	13.7028i	−0.897095	+	0.651778i
$443$	7.30616	+	22.4861i	0.347126	+	1.06835i	0.960436	+	0.278502i	$0.0898379\pi$
$443$	7.30616	+	22.4861i	0.347126	+	1.06835i	−0.613309	+	0.789843i	$0.710162\pi$
$444$	0.294515	−	0.906423i	0.0139770	−	0.0430169i
$445$	−4.70701	−	3.41984i	−0.223134	−	0.162116i
$446$	−5.11510	−	3.71634i	−0.242207	−	0.175974i
$447$	13.5524	−	41.7100i	0.641006	−	1.97281i
$448$	−1.47181	−	4.52976i	−0.0695365	−	0.214011i
$449$	26.9710	−	19.5956i	1.27284	−	0.924773i	0.273529	−	0.961864i	$-0.411809\pi$
$449$	26.9710	−	19.5956i	1.27284	−	0.924773i	0.999312	+	0.0370904i	$0.0118089\pi$
$450$	10.6330			0.501246
$451$	−4.93367	+	6.31715i	−0.232318	+	0.297463i
$452$	−12.8837			−0.605998
$453$	8.48774	−	6.16670i	0.398789	−	0.289737i
$454$	0.706746	+	2.17514i	0.0331692	+	0.102084i
$455$	−9.68439	+	29.8055i	−0.454011	+	1.39730i
$456$	−3.24459	−	2.35733i	−0.151942	−	0.110392i
$457$	29.1196	+	21.1566i	1.36216	+	0.989666i	0.998304	+	0.0582101i	$0.0185393\pi$
$457$	29.1196	+	21.1566i	1.36216	+	0.989666i	0.363854	+	0.931456i	$0.381461\pi$
$458$	8.54355	−	26.2944i	0.399214	−	1.22865i
$459$	0.0740496	+	0.227901i	0.00345634	+	0.0106375i
$460$	8.56359	−	6.22181i	0.399279	−	0.290093i
$461$	−21.2509			−0.989751			−0.494876	−	0.868964i	$-0.664786\pi$
$461$	−21.2509			−0.989751			−0.494876	+	0.868964i	$0.664786\pi$
$462$	36.4312	+	13.2525i	1.69493	+	0.616560i
$463$	11.1285			0.517186			0.258593	−	0.965986i	$-0.416741\pi$
$463$	11.1285			0.517186			0.258593	+	0.965986i	$0.416741\pi$
$464$	5.14437	−	3.73760i	0.238821	−	0.173514i
$465$	0.493038	+	1.51741i	0.0228641	+	0.0703684i
$466$	2.58573	−	7.95805i	0.119781	−	0.368649i
$467$	28.2616	+	20.5333i	1.30779	+	0.950166i	0.999999	−	0.00128731i	$-0.000409765\pi$
$467$	28.2616	+	20.5333i	1.30779	+	0.950166i	0.307792	+	0.951454i	$0.400410\pi$
$468$	−13.2164	−	9.60224i	−0.610926	−	0.443864i
$469$	−12.5145	+	38.5156i	−0.577864	+	1.77848i
$470$	3.85363	+	11.8603i	0.177755	+	0.547073i
$471$	−33.4108	+	24.2743i	−1.53949	+	1.11850i
$472$	14.1343			0.650586
$473$	1.85513	+	2.74927i	0.0852988	+	0.126412i
$474$	23.2415			1.06752
$475$	4.65091	−	3.37908i	0.213398	−	0.155043i
$476$	6.34856	+	19.5389i	0.290986	+	0.895563i
$477$	−2.83440	+	8.72338i	−0.129778	+	0.399416i
$478$	4.63932	+	3.37066i	0.212198	+	0.154171i
$479$	−11.8957	−	8.64270i	−0.543526	−	0.394895i	0.281867	−	0.959454i	$-0.409046\pi$
$479$	−11.8957	−	8.64270i	−0.543526	−	0.394895i	−0.825393	+	0.564559i	$0.809046\pi$
$480$	0.923270	−	2.84153i	0.0421413	−	0.129698i
$481$	−0.648607	−	1.99621i	−0.0295739	−	0.0910192i
$482$	5.31287	−	3.86002i	0.241995	−	0.175819i
$483$	−101.627			−4.62417
$484$	8.42902	+	7.06764i	0.383137	+	0.321256i
$485$	−6.74059			−0.306074
$486$	17.8677	−	12.9816i	0.810496	−	0.588859i
$487$	−4.72046	−	14.5281i	−0.213904	−	0.658330i	−0.999230	−	0.0392464i	$-0.987504\pi$
$487$	−4.72046	−	14.5281i	−0.213904	−	0.658330i	0.785325	−	0.619083i	$-0.212496\pi$
$488$	−3.03711	+	9.34726i	−0.137483	+	0.423131i
$489$	6.84841	+	4.97566i	0.309696	+	0.225007i
$490$	15.4488	+	11.2242i	0.697905	+	0.507058i
$491$	11.0197	−	33.9151i	0.497312	−	1.53057i	−0.316012	−	0.948755i	$-0.602344\pi$
$491$	11.0197	−	33.9151i	0.497312	−	1.53057i	0.813323	−	0.581812i	$-0.197656\pi$
$492$	−1.83277	−	5.64068i	−0.0826276	−	0.254302i
$493$	−22.1899	+	16.1219i	−0.999385	+	0.726096i
$494$	−8.83235			−0.397386
$495$	6.82673	+	10.1171i	0.306838	+	0.454731i
$496$	−0.534013			−0.0239779
$497$	−39.3699	+	28.6039i	−1.76598	+	1.28306i
$498$	−2.14148	−	6.59081i	−0.0959621	−	0.295341i
$499$	−11.6582	+	35.8801i	−0.521891	+	1.60622i	0.248491	+	0.968634i	$0.420065\pi$
$499$	−11.6582	+	35.8801i	−0.521891	+	1.60622i	−0.770383	+	0.637582i	$0.779935\pi$
$500$	8.38954	+	6.09536i	0.375192	+	0.272593i
$501$	2.50528	+	1.82019i	0.111928	+	0.0813202i
$502$	5.12995	−	15.7884i	0.228961	−	0.704669i
$503$	9.17313	+	28.2320i	0.409010	+	1.25880i	0.917500	+	0.397735i	$0.130204\pi$
$503$	9.17313	+	28.2320i	0.409010	+	1.25880i	−0.508491	+	0.861067i	$0.669796\pi$
$504$	−11.6470	+	8.46202i	−0.518797	+	0.376928i
$505$	8.78856			0.391086
$506$	−27.0991	−	9.85778i	−1.20470	−	0.438232i
$507$	−39.7818			−1.76677
$508$	10.8916	−	7.91319i	0.483235	−	0.351091i
$509$	10.2831	+	31.6483i	0.455792	+	1.40278i	0.870203	+	0.492694i	$0.163988\pi$
$509$	10.2831	+	31.6483i	0.455792	+	1.40278i	−0.414410	+	0.910090i	$0.636012\pi$
$510$	−3.98247	+	12.2568i	−0.176347	+	0.542740i
$511$	33.1863	+	24.1112i	1.46807	+	1.06662i
$512$	0.809017	+	0.587785i	0.0357538	+	0.0259767i
$513$	−0.0280548	+	0.0863438i	−0.00123865	+	0.00381217i
$514$	−6.36597	−	19.5925i	−0.280791	−	0.864186i
$515$	8.30934	−	6.03709i	0.366153	−	0.266026i
$516$	−2.45411			−0.108036
$517$	20.9110	−	26.7747i	0.919663	−	1.17755i
$518$	−1.84970			−0.0812710
$519$	−36.7115	+	26.6724i	−1.61145	+	1.17079i
$520$	−2.03331	−	6.25788i	−0.0891665	−	0.274426i
$521$	7.35740	−	22.6437i	0.322334	−	0.992041i	−0.650296	−	0.759681i	$-0.725355\pi$
$521$	7.35740	−	22.6437i	0.322334	−	0.992041i	0.972630	−	0.232360i	$-0.0746448\pi$
$522$	−15.5496	−	11.2974i	−0.680586	−	0.494475i
$523$	−18.1144	−	13.1609i	−0.792087	−	0.575485i	0.116495	−	0.993191i	$-0.462834\pi$
$523$	−18.1144	−	13.1609i	−0.792087	−	0.575485i	−0.908582	+	0.417706i	$0.862834\pi$
$524$	−6.02987	+	18.5580i	−0.263416	+	0.810712i
$525$	−12.7062	−	39.1057i	−0.554545	−	1.70671i
$526$	15.1496	−	11.0068i	0.660553	−	0.479920i
$527$	2.30343			0.100339
$528$	−7.82364	+	2.24491i	−0.340480	+	0.0976973i
$529$	52.5945			2.28672
$530$	−2.98884	+	2.17152i	−0.129827	+	0.0943249i
$531$	−13.2021	−	40.6320i	−0.572924	−	1.76328i
$532$	−2.40525	+	7.40259i	−0.104281	+	0.320943i
$533$	−10.5671	−	7.67748i	−0.457714	−	0.332548i
$534$	−9.48824	−	6.89361i	−0.410596	−	0.298316i
$535$	2.70537	−	8.32628i	0.116964	−	0.359977i
$536$	−2.62750	−	8.08662i	−0.113491	−	0.349289i
$537$	10.8332	−	7.87079i	0.467488	−	0.339650i
$538$	−10.6213			−0.457916
$539$	1.80619	−	51.9898i	0.0777981	−	2.23936i
$540$	−0.0676347			−0.00291053
$541$	18.8703	−	13.7101i	0.811298	−	0.589442i	−0.102909	−	0.994691i	$-0.532815\pi$
$541$	18.8703	−	13.7101i	0.811298	−	0.589442i	0.914207	+	0.405249i	$0.132815\pi$
$542$	−4.50882	−	13.8767i	−0.193670	−	0.596056i
$543$	−7.34496	+	22.6055i	−0.315203	+	0.970094i
$544$	−3.48965	−	2.53538i	−0.149617	−	0.108703i
$545$	−8.68881	−	6.31279i	−0.372188	−	0.270410i
$546$	−19.5215	+	60.0809i	−0.835442	+	2.57123i
$547$	−2.61538	−	8.04932i	−0.111826	−	0.344164i	0.879446	−	0.475999i	$-0.157913\pi$
$547$	−2.61538	−	8.04932i	−0.111826	−	0.344164i	−0.991272	+	0.131834i	$0.957913\pi$
$548$	−5.15040	+	3.74198i	−0.220014	+	0.159850i
$549$	29.7074			1.26788
$550$	0.405089	−	11.6602i	0.0172731	−	0.497193i
$551$	−10.3916			−0.442698
$552$	17.2622	−	12.5417i	0.734728	−	0.533811i
$553$	−13.9387	−	42.8990i	−0.592735	−	1.82425i
$554$	−4.47604	+	13.7758i	−0.190169	+	0.585279i
$555$	−0.938718	−	0.682018i	−0.0398463	−	0.0289501i
$556$	13.9104	+	10.1065i	0.589934	+	0.428612i
$557$	−8.75441	+	26.9433i	−0.370936	+	1.14162i	0.575243	+	0.817983i	$0.304907\pi$
$557$	−8.75441	+	26.9433i	−0.370936	+	1.14162i	−0.946179	+	0.323642i	$0.895093\pi$
$558$	0.498793	+	1.53513i	0.0211156	+	0.0649871i
$559$	−4.37246	+	3.17678i	−0.184935	+	0.134363i
$560$	−5.79859			−0.245035
$561$	33.7468	−	9.68330i	1.42479	−	0.408829i
$562$	−12.6199			−0.532339
$563$	−27.3533	+	19.8733i	−1.15280	+	0.837562i	−0.988851	−	0.148907i	$-0.952425\pi$
$563$	−27.3533	+	19.8733i	−1.15280	+	0.837562i	−0.163953	+	0.986468i	$0.552425\pi$
$564$	7.76803	+	23.9075i	0.327093	+	1.00669i
$565$	−4.84703	+	14.9176i	−0.203916	+	0.627590i
$566$	−10.3937	−	7.55146i	−0.436879	−	0.317411i
$567$	−34.4156	−	25.0044i	−1.44532	−	1.05008i
$568$	3.15733	−	9.71726i	0.132479	−	0.407727i
$569$	0.182514	+	0.561721i	0.00765140	+	0.0235486i	0.954809	−	0.297219i	$-0.0960592\pi$
$569$	0.182514	+	0.561721i	0.00765140	+	0.0235486i	−0.947158	+	0.320768i	$0.896059\pi$
$570$	−3.95014	+	2.86994i	−0.165453	+	0.120209i
$571$	17.7538			0.742973			0.371486	−	0.928438i	$-0.378848\pi$
$571$	17.7538			0.742973			0.371486	+	0.928438i	$0.378848\pi$
$572$	−11.0333	+	14.1272i	−0.461327	+	0.590689i
$573$	38.9245			1.62609
$574$	−9.31234	+	6.76581i	−0.388689	+	0.282399i
$575$	9.45146	+	29.0886i	0.394153	+	1.21308i
$576$	0.934046	−	2.87470i	0.0389186	−	0.119779i
$577$	−10.6370	−	7.72820i	−0.442822	−	0.321729i	0.343933	−	0.938994i	$-0.388241\pi$
$577$	−10.6370	−	7.72820i	−0.442822	−	0.321729i	−0.786755	+	0.617265i	$0.788241\pi$
$578$	1.29911	+	0.943856i	0.0540357	+	0.0392592i
$579$	6.27905	−	19.3249i	0.260948	−	0.803116i
$580$	−2.39227	−	7.36264i	−0.0993335	−	0.305717i
$581$	−10.8809	+	7.90545i	−0.451417	+	0.327973i
$582$	−13.5875			−0.563218
$583$	9.45808	+	3.44054i	0.391714	+	0.142493i
$584$	−8.61254			−0.356390
$585$	−16.0903	+	11.6903i	−0.665253	+	0.483334i
$586$	−0.290545	−	0.894206i	−0.0120023	−	0.0369393i
$587$	−7.63331	+	23.4929i	−0.315061	+	0.969657i	0.660669	+	0.750677i	$0.270273\pi$
$587$	−7.63331	+	23.4929i	−0.315061	+	0.969657i	−0.975730	+	0.218979i	$0.929727\pi$
$588$	31.1412	+	22.6254i	1.28424	+	0.933055i
$589$	0.706021	+	0.512954i	0.0290911	+	0.0211359i
$590$	5.31754	−	16.3657i	0.218920	−	0.673766i
$591$	12.6139	+	38.8215i	0.518865	+	1.59690i
$592$	0.314187	−	0.228270i	0.0129130	−	0.00938186i
$593$	25.4755			1.04615			0.523077	−	0.852286i	$-0.324784\pi$
$593$	25.4755			1.04615			0.523077	+	0.852286i	$0.324784\pi$
$594$	0.103060	+	0.152734i	0.00422860	+	0.00626673i
$595$	25.0119			1.02539
$596$	14.4577	−	10.5041i	0.592209	−	0.430265i
$597$	−11.5720	−	35.6148i	−0.473608	−	1.45762i
$598$	14.5210	−	44.6909i	0.593806	−	1.82755i
$599$	−12.9527	−	9.41069i	−0.529233	−	0.384510i	0.290838	−	0.956772i	$-0.406066\pi$
$599$	−12.9527	−	9.41069i	−0.529233	−	0.384510i	−0.820071	+	0.572262i	$0.806066\pi$
$600$	6.98429	+	5.07439i	0.285133	+	0.207161i
$601$	4.43508	−	13.6498i	0.180911	−	0.556786i	−0.818943	−	0.573874i	$-0.805440\pi$
$601$	4.43508	−	13.6498i	0.180911	−	0.556786i	0.999854	+	0.0170887i	$0.00543978\pi$
$602$	1.47181	+	4.52976i	0.0599865	+	0.184619i
$603$	−20.7924	+	15.1066i	−0.846731	+	0.615186i
$604$	4.27505			0.173949
$605$	11.3545	−	7.10076i	0.461627	−	0.288687i
$606$	17.7157			0.719651
$607$	−1.72055	+	1.25005i	−0.0698349	+	0.0507380i	−0.622155	−	0.782894i	$-0.713743\pi$
$607$	−1.72055	+	1.25005i	−0.0698349	+	0.0507380i	0.552320	+	0.833632i	$0.313743\pi$
$608$	−0.504999	−	1.55423i	−0.0204804	−	0.0630323i
$609$	−22.9678	+	70.6876i	−0.930702	+	2.86441i
$610$	9.68030	+	7.03315i	0.391944	+	0.284764i
$611$	44.7879	+	32.5403i	1.81192	+	1.31644i
$612$	−4.02895	+	12.3998i	−0.162861	+	0.501234i
$613$	7.18054	+	22.0994i	0.290019	+	0.892587i	0.984849	+	0.173413i	$0.0554796\pi$
$613$	7.18054	+	22.0994i	0.290019	+	0.892587i	−0.694830	+	0.719174i	$0.744520\pi$
$614$	−8.18863	+	5.94939i	−0.330466	+	0.240098i
$615$	−7.22068			−0.291166
$616$	8.83573	+	13.0944i	0.356002	+	0.527590i
$617$	26.2633			1.05732			0.528660	−	0.848834i	$-0.322695\pi$
$617$	26.2633			1.05732			0.528660	+	0.848834i	$0.322695\pi$
$618$	16.7497	−	12.1694i	0.673772	−	0.489524i
$619$	7.34410	+	22.6028i	0.295184	+	0.908483i	0.983160	+	0.182749i	$0.0584997\pi$
$619$	7.34410	+	22.6028i	0.295184	+	0.908483i	−0.687975	+	0.725734i	$0.741500\pi$
$620$	−0.200903	+	0.618317i	−0.00806847	+	0.0248322i
$621$	−0.390768	−	0.283910i	−0.0156810	−	0.0113929i
$622$	17.2171	+	12.5090i	0.690345	+	0.501565i
$623$	−7.03374	+	21.6476i	−0.281801	+	0.867294i
$624$	−4.09868	−	12.6144i	−0.164078	−	0.504981i
$625$	−4.01592	+	2.91774i	−0.160637	+	0.116710i
$626$	18.7277			0.748510
$627$	12.5001	+	4.54711i	0.499204	+	0.181594i
$628$	−16.8281			−0.671515
$629$	−1.35523	+	0.984632i	−0.0540365	+	0.0392598i
$630$	5.41615	+	16.6692i	0.215784	+	0.664116i
$631$	10.6972	−	32.9225i	0.425847	−	1.31062i	−0.476334	−	0.879264i	$-0.658035\pi$
$631$	10.6972	−	32.9225i	0.425847	−	1.31062i	0.902181	−	0.431358i	$-0.141965\pi$
$632$	7.66177	+	5.56661i	0.304769	+	0.221428i
$633$	13.1216	+	9.53342i	0.521538	+	0.378919i
$634$	−7.99030	+	24.5916i	−0.317335	+	0.976657i
$635$	−5.06487	−	15.5881i	−0.200993	−	0.618593i
$636$	−6.02481	+	4.37728i	−0.238899	+	0.173571i
$637$	84.7719			3.35878
$638$	−12.9812	+	16.6213i	−0.513929	+	0.658042i
$639$	−30.8833			−1.22172
$640$	0.984942	−	0.715602i	0.0389332	−	0.0282867i
$641$	2.36441	+	7.27689i	0.0933884	+	0.287420i	0.986830	−	0.161759i	$-0.0517166\pi$
$641$	2.36441	+	7.27689i	0.0933884	+	0.287420i	−0.893442	+	0.449179i	$0.851717\pi$
$642$	5.45340	−	16.7839i	0.215229	−	0.662406i
$643$	−7.37024	−	5.35479i	−0.290654	−	0.211172i	0.432897	−	0.901443i	$-0.357491\pi$
$643$	−7.37024	−	5.35479i	−0.290654	−	0.211172i	−0.723551	+	0.690271i	$0.757491\pi$
$644$	−33.5021	−	24.3407i	−1.32017	−	0.959158i
$645$	−0.923270	+	2.84153i	−0.0363537	+	0.111885i
$646$	2.17828	+	6.70407i	0.0857035	+	0.263768i
$647$	2.61001	−	1.89628i	0.102610	−	0.0745505i	−0.535297	−	0.844664i	$-0.679800\pi$
$647$	2.61001	−	1.89628i	0.102610	−	0.0745505i	0.637907	+	0.770113i	$0.279800\pi$
$648$	8.93158			0.350865
$649$	−45.0600	+	12.9295i	−1.76876	+	0.507527i
$650$	19.0125			0.745732
$651$	5.04977	−	3.66888i	0.197916	−	0.143795i
$652$	1.06591	+	3.28054i	0.0417443	+	0.128476i
$653$	8.62146	−	26.5341i	0.337384	−	1.03836i	−0.628152	−	0.778091i	$-0.716188\pi$
$653$	8.62146	−	26.5341i	0.337384	−	1.03836i	0.965536	−	0.260270i	$-0.0838116\pi$
$654$	−17.5146	−	12.7251i	−0.684876	−	0.497592i
$655$	19.2192	+	13.9636i	0.750958	+	0.545603i
$656$	0.746817	−	2.29847i	0.0291583	−	0.0897401i
$657$	8.04451	+	24.7585i	0.313846	+	0.965920i
$658$	39.4695	−	28.6763i	1.53868	−	1.11792i
$659$	−35.4459			−1.38078			−0.690389	−	0.723439i	$-0.742560\pi$
$659$	−35.4459			−1.38078			−0.690389	+	0.723439i	$0.742560\pi$
$660$	−0.344053	+	9.90332i	−0.0133922	+	0.385486i
$661$	38.0534			1.48011			0.740053	−	0.672549i	$-0.234800\pi$
$661$	38.0534			1.48011			0.740053	+	0.672549i	$0.234800\pi$
$662$	18.9623	−	13.7769i	0.736989	−	0.535454i
$663$	17.6794	+	54.4116i	0.686611	+	2.11317i
$664$	0.872612	−	2.68562i	0.0338639	−	0.104222i
$665$	7.66634	+	5.56992i	0.297288	+	0.215992i
$666$	−0.949674	−	0.689979i	−0.0367991	−	0.0267361i
$667$	17.0845	−	52.5807i	0.661514	−	2.03593i
$668$	0.389931	+	1.20008i	0.0150869	+	0.0464326i
$669$	−12.5530	+	9.12029i	−0.485327	+	0.352611i
$670$	−10.3517			−0.399923
$671$	1.13177	−	32.5771i	0.0436914	−	1.25763i
$672$	−11.6886			−0.450898
$673$	−11.0999	+	8.06453i	−0.427869	+	0.310865i	−0.780796	−	0.624786i	$-0.785186\pi$
$673$	−11.0999	+	8.06453i	−0.427869	+	0.310865i	0.352927	+	0.935651i	$0.385186\pi$
$674$	8.43928	+	25.9734i	0.325069	+	1.00046i
$675$	0.0603907	−	0.185864i	0.00232444	−	0.00715389i
$676$	−13.1144	−	9.52817i	−0.504400	−	0.366468i
$677$	11.0573	+	8.03359i	0.424966	+	0.308756i	0.779633	−	0.626237i	$-0.215406\pi$
$677$	11.0573	+	8.03359i	0.424966	+	0.308756i	−0.354667	+	0.934993i	$0.615406\pi$
$678$	−9.77049	+	30.0705i	−0.375233	+	1.15485i
$679$	8.14885	+	25.0796i	0.312724	+	0.962466i
$680$	−4.24849	+	3.08671i	−0.162922	+	0.118370i
$681$	5.61273			0.215080
$682$	1.70242	−	0.488492i	0.0651891	−	0.0187053i
$683$	7.11140			0.272110			0.136055	−	0.990701i	$-0.456558\pi$
$683$	7.11140			0.272110			0.136055	+	0.990701i	$0.456558\pi$
$684$	−3.99624	+	2.90344i	−0.152800	+	0.111016i
$685$	2.39507	+	7.37127i	0.0915110	+	0.281642i
$686$	12.7826	−	39.3409i	0.488043	−	1.50204i
$687$	−54.8918	−	39.8812i	−2.09425	−	1.52156i
$688$	−0.809017	−	0.587785i	−0.0308435	−	0.0224091i
$689$	−5.06807	+	15.5979i	−0.193078	+	0.594234i
$690$	−8.02738	−	24.7057i	−0.305597	−	0.940531i
$691$	34.9672	−	25.4052i	1.33022	−	0.966459i	0.330473	−	0.943815i	$-0.392792\pi$
$691$	34.9672	−	25.4052i	1.33022	−	0.966459i	0.999744	−	0.0226436i	$-0.00720828\pi$
$692$	−18.4906			−0.702907
$693$	29.3896	−	37.6309i	1.11642	−	1.42948i
$694$	−4.81694			−0.182848
$695$	16.9353	−	12.3043i	0.642394	−	0.466727i
$696$	−4.82226	−	14.8414i	−0.182787	−	0.562561i
$697$	−3.22135	+	9.91430i	−0.122017	+	0.375531i
$698$	16.0925	+	11.6919i	0.609110	+	0.442544i
$699$	−16.6131	−	12.0701i	−0.628366	−	0.456534i
$700$	5.17754	−	15.9348i	0.195692	−	0.602279i
$701$	1.58015	+	4.86321i	0.0596816	+	0.183681i	0.976453	−	0.215732i	$-0.0692139\pi$
$701$	1.58015	+	4.86321i	0.0596816	+	0.183681i	−0.916771	+	0.399413i	$0.869214\pi$
$702$	−0.242908	+	0.176483i	−0.00916797	+	0.00666092i
$703$	−0.634658			−0.0239366
$704$	−3.11681	−	1.13379i	−0.117469	−	0.0427314i
$705$	30.6042			1.15262
$706$	−23.4043	+	17.0042i	−0.880833	+	0.639963i
$707$	−10.6247	−	32.6994i	−0.399583	−	1.22979i
$708$	10.7189	−	32.9895i	0.402842	−	1.23982i
$709$	−18.5261	−	13.4600i	−0.695762	−	0.505501i	0.182787	−	0.983152i	$-0.441488\pi$
$709$	−18.5261	−	13.4600i	−0.695762	−	0.505501i	−0.878549	+	0.477652i	$0.841488\pi$
$710$	−10.0635	−	7.31154i	−0.377675	−	0.274397i
$711$	8.84586	−	27.2248i	0.331746	−	1.02101i
$712$	−1.47678	−	4.54508i	−0.0553448	−	0.170334i
$713$	−3.75625	+	2.72908i	−0.140673	+	0.102205i
$714$	50.4181			1.88685
$715$	12.2066	+	18.0900i	0.456501	+	0.676528i
$716$	5.45640			0.203915
$717$	11.3854	−	8.27196i	0.425195	−	0.308922i
$718$	−1.29742	−	3.99304i	−0.0484192	−	0.149019i
$719$	−10.7176	+	32.9853i	−0.399699	+	1.23015i	0.525543	+	0.850767i	$0.323862\pi$
$719$	−10.7176	+	32.9853i	−0.399699	+	1.23015i	−0.925241	+	0.379379i	$0.876138\pi$
$720$	−2.97712	−	2.16301i	−0.110951	−	0.0806105i
$721$	−32.5075	−	23.6180i	−1.21064	−	0.879582i
$722$	5.04605	−	15.5301i	0.187794	−	0.577972i
$723$	−4.98020	−	15.3275i	−0.185216	−	0.570036i
$724$	−7.83559	+	5.69289i	−0.291207	+	0.211574i
$725$	22.3690			0.830763
$726$	22.8881	−	14.3135i	0.849456	−	0.531223i
$727$	4.66195			0.172902			0.0864511	−	0.996256i	$-0.472447\pi$
$727$	4.66195			0.172902			0.0864511	+	0.996256i	$0.472447\pi$
$728$	−20.8255	+	15.1306i	−0.771843	+	0.560777i
$729$	−8.46890	−	26.0646i	−0.313663	−	0.965355i
$730$	−3.24016	+	9.97219i	−0.119924	+	0.369087i
$731$	3.48965	+	2.53538i	0.129069	+	0.0937743i
$732$	19.5132	+	14.1772i	0.721229	+	0.524004i
$733$	−3.26302	+	10.0425i	−0.120522	+	0.370929i	−0.993059	−	0.117620i	$-0.962474\pi$
$733$	−3.26302	+	10.0425i	−0.120522	+	0.370929i	0.872536	+	0.488549i	$0.162474\pi$
$734$	−0.858093	−	2.64094i	−0.0316728	−	0.0974788i
$735$	37.9130	−	27.5454i	1.39844	−	1.01603i
$736$	8.69451			0.320484
$737$	15.7737	+	23.3765i	0.581032	+	0.861083i
$738$	−7.30496			−0.268899
$739$	−13.3783	+	9.71988i	−0.492127	+	0.357552i	−0.806002	−	0.591913i	$-0.798373\pi$
$739$	−13.3783	+	9.71988i	−0.492127	+	0.357552i	0.313874	+	0.949465i	$0.398373\pi$
$740$	−0.146105	−	0.449666i	−0.00537094	−	0.0165301i
$741$	−6.69810	+	20.6146i	−0.246061	+	0.757298i
$742$	11.6928	+	8.49533i	0.429257	+	0.311874i
$743$	7.39949	+	5.37604i	0.271461	+	0.197228i	0.715184	−	0.698936i	$-0.246343\pi$
$743$	7.39949	+	5.37604i	0.271461	+	0.197228i	−0.443723	+	0.896164i	$0.646343\pi$
$744$	−0.404974	+	1.24638i	−0.0148471	+	0.0456946i
$745$	−6.72319	−	20.6919i	−0.246319	−	0.758091i
$746$	−7.40813	+	5.38232i	−0.271231	+	0.197061i
$747$	−8.53542			−0.312295
$748$	13.4442	+	4.89055i	0.491568	+	0.178816i
$749$	−34.2500			−1.25147
$750$	20.5888	−	14.9587i	0.751798	−	0.546213i
$751$	−3.15731	−	9.71721i	−0.115212	−	0.354586i	0.876779	−	0.480893i	$-0.159688\pi$
$751$	−3.15731	−	9.71721i	−0.115212	−	0.354586i	−0.991991	+	0.126307i	$0.959688\pi$
$752$	−3.16532	+	9.74185i	−0.115427	+	0.355249i
$753$	−32.9596	−	23.9465i	−1.20111	−	0.872660i
$754$	−27.8035	−	20.2005i	−1.01255	−	0.735657i
$755$	1.60833	−	4.94994i	0.0585333	−	0.180147i
$756$	0.0817651	+	0.251647i	0.00297377	+	0.00915231i
$757$	−13.5040	+	9.81120i	−0.490810	+	0.356594i	−0.805496	−	0.592602i	$-0.798101\pi$
$757$	−13.5040	+	9.81120i	−0.490810	+	0.356594i	0.314686	+	0.949196i	$0.398101\pi$
$758$	14.3504			0.521229
$759$	−43.5589	+	55.7735i	−1.58109	+	2.02445i
$760$	−1.98958			−0.0721696
$761$	−33.1480	+	24.0834i	−1.20161	+	0.873023i	−0.994442	−	0.105282i	$-0.966425\pi$
$761$	−33.1480	+	24.0834i	−1.20161	+	0.873023i	−0.207170	+	0.978305i	$0.566425\pi$
$762$	−10.2096	−	31.4219i	−0.369854	−	1.13830i
$763$	−12.9838	+	39.9600i	−0.470045	+	1.44665i
$764$	12.8318	+	9.32284i	0.464238	+	0.337288i
$765$	12.8416	+	9.33000i	0.464291	+	0.337327i
$766$	0.552392	−	1.70009i	0.0199587	−	0.0614267i
$767$	−23.6062	−	72.6524i	−0.852370	−	2.62332i
$768$	1.98541	−	1.44249i	0.0716424	−	0.0520513i
$769$	−14.6278			−0.527493			−0.263747	−	0.964592i	$-0.584958\pi$
$769$	−14.6278			−0.527493			−0.263747	+	0.964592i	$0.584958\pi$
$770$	18.4858	−	5.30430i	0.666181	−	0.191154i
$771$	−50.5564			−1.82074
$772$	6.69847	−	4.86672i	0.241083	−	0.175157i
$773$	7.98011	+	24.5602i	0.287025	+	0.883371i	0.985785	+	0.168015i	$0.0537356\pi$
$773$	7.98011	+	24.5602i	0.287025	+	0.883371i	−0.698760	+	0.715356i	$0.746264\pi$
$774$	−0.934046	+	2.87470i	−0.0335736	+	0.103329i
$775$	−1.51978	−	1.10419i	−0.0545921	−	0.0396635i
$776$	−4.47922	−	3.25434i	−0.160795	−	0.116824i
$777$	−1.40274	+	4.31718i	−0.0503229	+	0.154878i
$778$	0.398589	+	1.22673i	0.0142901	+	0.0439805i
$779$	−3.19520	+	2.32145i	−0.114480	+	0.0831745i
$780$	−16.1478			−0.578185
$781$	−1.17657	+	33.8666i	−0.0421009	+	1.21184i
$782$	−37.5033			−1.34111
$783$	−0.285791	+	0.207639i	−0.0102133	+	0.00742042i
$784$	4.84693	+	14.9173i	0.173104	+	0.532761i
$785$	−6.33098	+	19.4847i	−0.225962	+	0.695440i
$786$	38.7415	+	28.1474i	1.38186	+	1.00398i
$787$	−9.68102	−	7.03367i	−0.345091	−	0.250723i	0.401716	−	0.915764i	$-0.368414\pi$
$787$	−9.68102	−	7.03367i	−0.345091	−	0.250723i	−0.746807	+	0.665041i	$0.768414\pi$
$788$	−5.13990	+	15.8190i	−0.183101	+	0.563528i
$789$	−14.2010	−	43.7062i	−0.505569	−	1.55598i
$790$	9.32787	−	6.77709i	0.331871	−	0.241118i
$791$	61.3635			2.18183
$792$	−0.348069	+	10.0189i	−0.0123681	+	0.356006i
$793$	53.1185			1.88629
$794$	−28.4134	+	20.6435i	−1.00835	+	0.732612i
$795$	2.80170	+	8.62274i	0.0993660	+	0.305817i
$796$	4.71534	−	14.5123i	0.167131	−	0.514376i
$797$	−20.0760	−	14.5860i	−0.711127	−	0.516664i	0.172410	−	0.985025i	$-0.444845\pi$
$797$	−20.0760	−	14.5860i	−0.711127	−	0.516664i	−0.883537	+	0.468361i	$0.844845\pi$
$798$	15.4536	+	11.2277i	0.547050	+	0.397455i
$799$	13.6534	−	42.0209i	0.483023	−	1.48659i
$800$	1.08706	+	3.34563i	0.0384334	+	0.118286i
$801$	−11.6863	+	8.49062i	−0.412916	+	0.300001i
$802$	7.99607			0.282351
$803$	27.4566	−	7.87839i	0.968923	−	0.278022i
$804$	−20.8667			−0.735912
$805$	−40.7873	+	29.6337i	−1.43756	+	1.04445i
$806$	0.891871	+	2.74490i	0.0314148	+	0.0966849i
$807$	−8.05476	+	24.7900i	−0.283541	+	0.872650i
$808$	5.84013	+	4.24310i	0.205455	+	0.149272i
$809$	−25.0292	−	18.1848i	−0.879981	−	0.639344i	0.0532652	−	0.998580i	$-0.483037\pi$
$809$	−25.0292	−	18.1848i	−0.879981	−	0.639344i	−0.933247	+	0.359237i	$0.883037\pi$
$810$	3.36019	−	10.3416i	0.118065	−	0.363366i
$811$	−9.43261	−	29.0306i	−0.331224	−	1.01940i	−0.968552	−	0.248809i	$-0.919961\pi$
$811$	−9.43261	−	29.0306i	−0.331224	−	1.01940i	0.637329	−	0.770592i	$-0.280039\pi$
$812$	−24.5020	+	17.8017i	−0.859851	+	0.624719i
$813$	−35.8075			−1.25582
$814$	−0.792811	+	1.01513i	−0.0277880	+	0.0355802i
$815$	4.19945			0.147100
$816$	−8.56397	+	6.22209i	−0.299799	+	0.217817i
$817$	0.504999	+	1.55423i	0.0176677	+	0.0543755i
$818$	−1.21026	+	3.72481i	−0.0423158	+	0.130235i
$819$	62.9478	+	45.7343i	2.19958	+	1.59808i
$820$	−2.38036	−	1.72943i	−0.0831257	−	0.0603944i
$821$	−1.65855	+	5.10448i	−0.0578836	+	0.178148i	−0.975818	−	0.218585i	$-0.929856\pi$
$821$	−1.65855	+	5.10448i	−0.0578836	+	0.178148i	0.917934	+	0.396732i	$0.129856\pi$
$822$	4.82791	+	14.8588i	0.168393	+	0.518259i
$823$	29.0613	−	21.1143i	1.01301	−	0.735998i	0.0481748	−	0.998839i	$-0.484660\pi$
$823$	29.0613	−	21.1143i	1.01301	−	0.735998i	0.964839	+	0.262841i	$0.0846596\pi$
$824$	8.43638			0.293895
$825$	−26.9076	−	9.78811i	−0.936803	−	0.340778i
$826$	−67.3201			−2.34237
$827$	−31.0760	+	22.5781i	−1.08062	+	0.785116i	−0.977791	−	0.209583i	$-0.932789\pi$
$827$	−31.0760	+	22.5781i	−1.08062	+	0.785116i	−0.102828	+	0.994699i	$0.532789\pi$
$828$	−8.12107	−	24.9941i	−0.282227	−	0.868605i
$829$	7.72227	−	23.7667i	0.268206	−	0.825452i	−0.722732	−	0.691129i	$-0.757114\pi$
$829$	7.72227	−	23.7667i	0.268206	−	0.825452i	0.990938	−	0.134324i	$-0.0428862\pi$
$830$	−2.78131	−	2.02074i	−0.0965407	−	0.0701409i
$831$	28.7582	+	20.8941i	0.997612	+	0.724808i
$832$	1.67013	−	5.14013i	0.0579013	−	0.178202i
$833$	−20.9069	−	64.3449i	−0.724382	−	2.22942i
$834$	34.1377	−	24.8025i	1.18209	−	0.858841i
$835$	1.53624			0.0531637
$836$	3.03167	+	4.49290i	0.104852	+	0.155390i
$837$	0.0296666			0.00102543
$838$	−25.5691	+	18.5770i	−0.883268	+	0.641732i
$839$	−0.437285	−	1.34582i	−0.0150967	−	0.0464630i	0.943224	−	0.332156i	$-0.107776\pi$
$839$	−0.437285	−	1.34582i	−0.0150967	−	0.0464630i	−0.958321	+	0.285693i	$0.907776\pi$
$840$	−4.39742	+	13.5339i	−0.151725	+	0.466963i
$841$	−9.25049	−	6.72087i	−0.318982	−	0.231754i
$842$	23.0706	+	16.7618i	0.795066	+	0.577649i
$843$	−9.57045	+	29.4548i	−0.329624	+	1.01448i
$844$	2.04230	+	6.28555i	0.0702988	+	0.216357i
$845$	−15.9662	+	11.6001i	−0.549254	+	0.399056i
$846$	30.9614			1.06448
$847$	−40.1464	−	33.6623i	−1.37945	−	1.15665i
$848$	−3.03454			−0.104206
$849$	−25.5072	+	18.5321i	−0.875406	+	0.636019i
$850$	−4.68897	−	14.4312i	−0.160831	−	0.494985i
$851$	1.04342	−	3.21131i	0.0357679	−	0.110082i
$852$	−20.2856	−	14.7384i	−0.694974	−	0.504928i
$853$	−14.4595	−	10.5054i	−0.495083	−	0.359699i	0.312053	−	0.950065i	$-0.398983\pi$
$853$	−14.4595	−	10.5054i	−0.495083	−	0.359699i	−0.807136	+	0.590366i	$0.798983\pi$
$854$	14.4654	−	44.5198i	0.494995	−	1.52344i
$855$	1.85836	+	5.71944i	0.0635545	+	0.195601i
$856$	5.81768	−	4.22679i	0.198844	−	0.144469i
$857$	−12.1025			−0.413413			−0.206707	−	0.978403i	$-0.566275\pi$
$857$	−12.1025			−0.413413			−0.206707	+	0.978403i	$0.566275\pi$
$858$	24.6056	+	36.4653i	0.840023	+	1.24490i
$859$	26.5476			0.905794			0.452897	−	0.891563i	$-0.350391\pi$
$859$	26.5476			0.905794			0.452897	+	0.891563i	$0.350391\pi$
$860$	−0.984942	+	0.715602i	−0.0335862	+	0.0244018i
$861$	8.72925	+	26.8659i	0.297492	+	0.915586i
$862$	−6.55124	+	20.1626i	−0.223136	+	0.686742i
$863$	−27.8842	−	20.2590i	−0.949188	−	0.689625i	0.00142682	−	0.999999i	$-0.499546\pi$
$863$	−27.8842	−	20.2590i	−0.949188	−	0.689625i	−0.950615	+	0.310374i	$0.899546\pi$
$864$	−0.0449442	−	0.0326539i	−0.00152903	−	0.00111091i
$865$	−6.95642	+	21.4097i	−0.236526	+	0.727951i
$866$	−6.12641	−	18.8552i	−0.208184	−	0.640724i
$867$	3.18815	−	2.31632i	0.108275	−	0.0786665i
$868$	2.54344			0.0863299
$869$	−29.5177	−	10.7376i	−1.00132	−	0.364247i
$870$	−18.9986			−0.644112
$871$	−37.1780	+	27.0114i	−1.25973	+	0.915247i
$872$	−2.72604	−	8.38989i	−0.0923154	−	0.284117i
$873$	−5.17146	+	15.9161i	−0.175027	+	0.538679i
$874$	−11.4951	−	8.35165i	−0.388826	−	0.282499i
$875$	−39.9583	−	29.0314i	−1.35084	−	0.981441i
$876$	−6.53141	+	20.1016i	−0.220676	+	0.679171i
$877$	14.0301	+	43.1803i	0.473764	+	1.45810i	0.847617	+	0.530608i	$0.178037\pi$
$877$	14.0301	+	43.1803i	0.473764	+	1.45810i	−0.373853	+	0.927488i	$0.621963\pi$
$878$	−9.79192	+	7.11425i	−0.330461	+	0.240094i
$879$	−2.30741			−0.0778270
$880$	−2.48537	+	3.18231i	−0.0837819	+	0.107276i
$881$	35.0135			1.17964			0.589818	−	0.807536i	$-0.299200\pi$
$881$	35.0135			1.17964			0.589818	+	0.807536i	$0.299200\pi$
$882$	38.3555	−	27.8669i	1.29150	−	0.938327i
$883$	−6.65698	−	20.4881i	−0.224025	−	0.689479i	−0.998389	−	0.0567381i	$-0.981930\pi$
$883$	−6.65698	−	20.4881i	−0.224025	−	0.689479i	0.774364	−	0.632741i	$-0.218070\pi$
$884$	−7.20401	+	22.1717i	−0.242297	+	0.745714i
$885$	−34.1648	−	24.8222i	−1.14844	−	0.834390i
$886$	19.1278	+	13.8972i	0.642611	+	0.466884i
$887$	−0.323819	+	0.996612i	−0.0108728	+	0.0334629i	−0.956346	−	0.292238i	$-0.905600\pi$
$887$	−0.323819	+	0.996612i	−0.0108728	+	0.0334629i	0.945473	+	0.325701i	$0.105600\pi$
$888$	−0.294515	−	0.906423i	−0.00988326	−	0.0304176i
$889$	−51.8752	+	37.6895i	−1.73984	+	1.26407i
$890$	−5.81819			−0.195026
$891$	−28.4737	+	8.17023i	−0.953904	+	0.273713i
$892$	−6.32261			−0.211697
$893$	13.5426	−	9.83926i	0.453185	−	0.329258i
$894$	−13.5524	−	41.7100i	−0.453260	−	1.39499i
$895$	2.05278	−	6.31780i	0.0686167	−	0.211181i
$896$	−3.85325	−	2.79955i	−0.128728	−	0.0935263i
$897$	−93.2962	−	67.7837i	−3.11507	−	2.26323i
$898$	10.3020	−	31.7063i	0.343783	−	1.05805i
$899$	1.04932	+	3.22948i	0.0349968	+	0.107709i
$900$	8.60231	−	6.24995i	0.286744	−	0.208332i
$901$	13.0893			0.436068
$902$	−0.278299	+	8.01062i	−0.00926633	+	0.266725i
$903$	11.6886			0.388972
$904$	−10.4231	+	7.57285i	−0.346668	+	0.251869i
$905$	3.64376	+	11.2143i	0.121123	+	0.372777i
$906$	3.24203	−	9.97793i	0.107709	−	0.331495i
$907$	39.4407	+	28.6553i	1.30961	+	0.951485i	1.00000		0.000620025i	$0.000197360\pi$
$907$	39.4407	+	28.6553i	1.30961	+	0.951485i	0.309607	+	0.950865i	$0.399803\pi$
$908$	1.85028	+	1.34431i	0.0614038	+	0.0446125i
$909$	6.74269	−	20.7519i	0.223641	−	0.688296i
$910$	9.68439	+	29.8055i	0.321034	+	0.988043i
$911$	−32.4347	+	23.5652i	−1.07461	+	0.780749i	−0.976735	−	0.214449i	$-0.931204\pi$
$911$	−32.4347	+	23.5652i	−1.07461	+	0.780749i	−0.0978743	+	0.995199i	$0.531204\pi$
$912$	−4.01053			−0.132802
$913$	−0.325176	+	9.35994i	−0.0107617	+	0.309769i
$914$	35.9938			1.19057
$915$	23.7565	−	17.2601i	0.785365	−	0.570601i
$916$	−8.54355	−	26.2944i	−0.282287	−	0.868790i
$917$	28.7195	−	88.3896i	0.948402	−	2.91888i
$918$	0.193864	+	0.140851i	0.00639848	+	0.00464877i
$919$	−27.0099	−	19.6239i	−0.890975	−	0.647331i	0.0451572	−	0.998980i	$-0.485621\pi$
$919$	−27.0099	−	19.6239i	−0.890975	−	0.647331i	−0.936132	+	0.351649i	$0.885621\pi$
$920$	3.27100	−	10.0671i	0.107842	−	0.331902i
$921$	7.67590	+	23.6240i	0.252929	+	0.778437i
$922$	−17.1923	+	12.4909i	−0.566198	+	0.411367i
$923$	−55.2211			−1.81763
$924$	37.2630	−	10.6922i	1.22586	−	0.351749i
$925$	1.36616			0.0449192
$926$	9.00315	−	6.54117i	0.295862	−	0.214956i
$927$	−7.87997	−	24.2520i	−0.258812	−	0.796542i
$928$	1.96497	−	6.04757i	0.0645035	−	0.198521i
$929$	28.5246	+	20.7243i	0.935862	+	0.679943i	0.947421	−	0.319990i	$-0.103680\pi$
$929$	28.5246	+	20.7243i	0.935862	+	0.679943i	−0.0115593	+	0.999933i	$0.503680\pi$
$930$	1.29079	+	0.937814i	0.0423267	+	0.0307521i
$931$	7.92090	−	24.3780i	0.259597	−	0.798958i
$932$	−2.58573	−	7.95805i	−0.0846983	−	0.260674i
$933$	42.2527	−	30.6984i	1.38329	−	1.00502i
$934$	34.9333			1.14305
$935$	10.7205	−	13.7267i	0.350598	−	0.448911i
$936$	−16.3363			−0.533969
$937$	−11.2122	+	8.14611i	−0.366285	+	0.266122i	−0.755669	−	0.654954i	$-0.772688\pi$
$937$	−11.2122	+	8.14611i	−0.366285	+	0.266122i	0.389383	+	0.921076i	$0.372688\pi$
$938$	12.5145	+	38.5156i	0.408612	+	1.25758i
$939$	14.2024	−	43.7104i	0.463476	−	1.42643i
$940$	10.0889	+	7.33005i	0.329065	+	0.239080i
$941$	18.8977	+	13.7300i	0.616048	+	0.447585i	0.851539	−	0.524292i	$-0.175670\pi$
$941$	18.8977	+	13.7300i	0.616048	+	0.447585i	−0.235491	+	0.971877i	$0.575670\pi$
$942$	−12.7618	+	39.2767i	−0.415801	+	1.27970i
$943$	−6.49321	−	19.9840i	−0.211448	−	0.650770i
$944$	11.4349	−	8.30796i	0.372175	−	0.270401i
$945$	0.322135			0.0104791
$946$	3.11681	+	1.13379i	0.101336	+	0.0368628i
$947$	5.37177			0.174559			0.0872795	−	0.996184i	$-0.472183\pi$
$947$	5.37177			0.174559			0.0872795	+	0.996184i	$0.472183\pi$
$948$	18.8028	−	13.6610i	0.610687	−	0.443690i
$949$	14.3841	+	44.2696i	0.466927	+	1.43705i
$950$	1.77649	−	5.46747i	0.0576369	−	0.177388i
$951$	51.3371	+	37.2986i	1.66472	+	1.20949i
$952$	16.6208	+	12.0757i	0.538682	+	0.391375i
$953$	14.4490	−	44.4694i	0.468049	−	1.44051i	−0.387058	−	0.922055i	$-0.626509\pi$
$953$	14.4490	−	44.4694i	0.468049	−	1.44051i	0.855107	−	0.518451i	$-0.173491\pi$
$954$	2.83440	+	8.72338i	0.0917671	+	0.282430i
$955$	15.6221	−	11.3501i	0.505520	−	0.367282i
$956$	5.73451			0.185467
$957$	28.9495	+	42.9028i	0.935805	+	1.38685i
$958$	−14.7038			−0.475060
$959$	24.5307	−	17.8226i	0.792138	−	0.575522i
$960$	−0.923270	−	2.84153i	−0.0297984	−	0.0917101i
$961$	−9.49140	+	29.2115i	−0.306174	+	0.942308i
$962$	−1.69807	−	1.23372i	−0.0547481	−	0.0397768i
$963$	−17.5847	−	12.7761i	−0.566660	−	0.411703i
$964$	2.02934	−	6.24565i	0.0653605	−	0.201159i
$965$	−3.11497	−	9.58688i	−0.100274	−	0.308613i
$966$	−82.2177	+	59.7346i	−2.64531	+	1.92193i
$967$	−48.4977			−1.55958			−0.779790	−	0.626041i	$-0.784674\pi$
$967$	−48.4977			−1.55958			−0.779790	+	0.626041i	$0.784674\pi$
$968$	10.9735	+	0.763385i	0.352701	+	0.0245361i
$969$	17.2992			0.555730
$970$	−5.45325	+	3.96202i	−0.175093	+	0.127213i
$971$	−6.66894	−	20.5249i	−0.214017	−	0.658675i	−0.999222	−	0.0394398i	$-0.987443\pi$
$971$	−6.66894	−	20.5249i	−0.214017	−	0.658675i	0.785205	−	0.619235i	$-0.212557\pi$
$972$	6.82486	−	21.0047i	0.218907	−	0.673728i
$973$	−66.2537	−	48.1362i	−2.12400	−	1.54317i
$974$	−12.3583	−	8.97884i	−0.395986	−	0.287701i
$975$	14.4183	−	44.3751i	0.461756	−	1.42114i
$976$	3.03711	+	9.34726i	0.0972155	+	0.299199i
$977$	−11.4862	+	8.34522i	−0.367477	+	0.266987i	−0.756164	−	0.654382i	$-0.772929\pi$
$977$	−11.4862	+	8.34522i	−0.367477	+	0.266987i	0.388687	+	0.921370i	$0.372929\pi$
$978$	8.46510			0.270684
$979$	8.86560	+	13.1387i	0.283346	+	0.419915i
$980$	19.0958			0.609992
$981$	−21.5722	+	15.6731i	−0.688746	+	0.500403i
$982$	−11.0197	−	33.9151i	−0.351652	−	1.08227i
$983$	−10.6145	+	32.6680i	−0.338550	+	1.04195i	0.626397	+	0.779504i	$0.284529\pi$
$983$	−10.6145	+	32.6680i	−0.338550	+	1.04195i	−0.964947	+	0.262445i	$0.915471\pi$
$984$	−4.79825	−	3.48613i	−0.152963	−	0.111134i
$985$	16.3826	+	11.9027i	0.521993	+	0.379250i
$986$	−8.47580	+	26.0858i	−0.269925	+	0.830743i
$987$	−36.9982	−	113.869i	−1.17766	−	3.62448i
$988$	−7.14552	+	5.19152i	−0.227329	+	0.165164i
$989$	−8.69451			−0.276469
$990$	11.4696	+	4.17227i	0.364529	+	0.132604i
$991$	28.4692			0.904354			0.452177	−	0.891928i	$-0.350648\pi$
$991$	28.4692			0.904354			0.452177	+	0.891928i	$0.350648\pi$
$992$	−0.432025	+	0.313885i	−0.0137168	+	0.00996586i
$993$	−17.7749	−	54.7056i	−0.564071	−	1.73603i
$994$	−15.0380	+	46.2821i	−0.476975	+	1.46798i
$995$	−15.0294	−	10.9195i	−0.476464	−	0.346171i
$996$	−5.60647	−	4.07334i	−0.177648	−	0.129069i
$997$	0.514371	−	1.58307i	0.0162903	−	0.0501364i	−0.942581	−	0.333978i	$-0.891609\pi$
$997$	0.514371	−	1.58307i	0.0162903	−	0.0501364i	0.958871	+	0.283841i	$0.0916089\pi$
$998$	11.6582	+	35.8801i	0.369033	+	1.13577i
$999$	−0.0174544	+	0.0126814i	−0.000552233	+	0.000401221i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	946.2.f.e.861.2	yes	24
11.4	even	5	inner	946.2.f.e.345.2	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
946.2.f.e.345.2	✓	24	11.4	even	5	inner
946.2.f.e.861.2	yes	24	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 946 = 2 \cdot 11 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	946.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 - 0.587785i) q^{2} +(-0.758361 - 2.33399i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.984942 - 0.715602i) q^{5} +(-1.98541 - 1.44249i) q^{6} +(-1.47181 + 4.52976i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-2.44536 + 1.77666i) q^{9} +O(q^{10})\)	\(q+(0.809017 - 0.587785i) q^{2} +(-0.758361 - 2.33399i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.984942 - 0.715602i) q^{5} +(-1.98541 - 1.44249i) q^{6} +(-1.47181 + 4.52976i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-2.44536 + 1.77666i) q^{9} -1.21746 q^{10} +(1.85513 + 2.74927i) q^{11} -2.45411 q^{12} +(-4.37246 + 3.17678i) q^{13} +(1.47181 + 4.52976i) q^{14} +(-0.923270 + 2.84153i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(3.48965 + 2.53538i) q^{17} +(-0.934046 + 2.87470i) q^{18} +(0.504999 + 1.55423i) q^{19} +(-0.984942 + 0.715602i) q^{20} +11.6886 q^{21} +(3.11681 + 1.13379i) q^{22} -8.69451 q^{23} +(-1.98541 + 1.44249i) q^{24} +(-1.08706 - 3.34563i) q^{25} +(-1.67013 + 5.14013i) q^{26} +(0.0449442 + 0.0326539i) q^{27} +(3.85325 + 2.79955i) q^{28} +(-1.96497 + 6.04757i) q^{29} +(0.923270 + 2.84153i) q^{30} +(0.432025 - 0.313885i) q^{31} -1.00000 q^{32} +(5.00993 - 6.41479i) q^{33} +4.31344 q^{34} +(4.69115 - 3.40832i) q^{35} +(0.934046 + 2.87470i) q^{36} +(-0.120009 + 0.369349i) q^{37} +(1.32211 + 0.960566i) q^{38} +(10.7305 + 7.79615i) q^{39} +(-0.376214 + 1.15787i) q^{40} +(0.746817 + 2.29847i) q^{41} +(9.45628 - 6.87039i) q^{42} +1.00000 q^{43} +(3.18798 - 0.914757i) q^{44} +3.67992 q^{45} +(-7.03401 + 5.11050i) q^{46} +(-3.16532 - 9.74185i) q^{47} +(-0.758361 + 2.33399i) q^{48} +(-12.6894 - 9.21940i) q^{49} +(-2.84596 - 2.06771i) q^{50} +(3.27114 - 10.0675i) q^{51} +(1.67013 + 5.14013i) q^{52} +(2.45499 - 1.78366i) q^{53} +0.0555541 q^{54} +(0.140195 - 4.03541i) q^{55} +4.76288 q^{56} +(3.24459 - 2.35733i) q^{57} +(1.96497 + 6.04757i) q^{58} +(-4.36775 + 13.4426i) q^{59} +(2.41715 + 1.75616i) q^{60} +(-7.95125 - 5.77692i) q^{61} +(0.165019 - 0.507876i) q^{62} +(-4.44875 - 13.6918i) q^{63} +(-0.809017 + 0.587785i) q^{64} +6.57992 q^{65} +(0.282600 - 8.13444i) q^{66} +8.50278 q^{67} +(3.48965 - 2.53538i) q^{68} +(6.59357 + 20.2929i) q^{69} +(1.79186 - 5.51478i) q^{70} +(8.26599 + 6.00559i) q^{71} +(2.44536 + 1.77666i) q^{72} +(2.66142 - 8.19102i) q^{73} +(0.120009 + 0.369349i) q^{74} +(-6.98429 + 5.07439i) q^{75} +1.63421 q^{76} +(-15.1840 + 4.35688i) q^{77} +13.2636 q^{78} +(-7.66177 + 5.56661i) q^{79} +(0.376214 + 1.15787i) q^{80} +(-2.76001 + 8.49443i) q^{81} +(1.95519 + 1.42053i) q^{82} +(2.28453 + 1.65981i) q^{83} +(3.61198 - 11.1165i) q^{84} +(-1.62278 - 4.99440i) q^{85} +(0.809017 - 0.587785i) q^{86} +15.6052 q^{87} +(2.04145 - 2.61390i) q^{88} +4.77898 q^{89} +(2.97712 - 2.16301i) q^{90} +(-7.95462 - 24.4818i) q^{91} +(-2.68675 + 8.26897i) q^{92} +(-1.06024 - 0.770307i) q^{93} +(-8.28692 - 6.02080i) q^{94} +(0.614814 - 1.89220i) q^{95} +(0.758361 + 2.33399i) q^{96} +(4.47922 - 3.25434i) q^{97} -15.6850 q^{98} +(-9.42099 - 3.42705i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{2} - q^{3} - 6 q^{4} - 11 q^{5} - 9 q^{6} + 3 q^{7} + 6 q^{8} - 7 q^{9}+O(q^{10}) \) 24 * q + 6 * q^2 - q^3 - 6 * q^4 - 11 * q^5 - 9 * q^6 + 3 * q^7 + 6 * q^8 - 7 * q^9	\( 24 q + 6 q^{2} - q^{3} - 6 q^{4} - 11 q^{5} - 9 q^{6} + 3 q^{7} + 6 q^{8} - 7 q^{9} - 4 q^{10} - 7 q^{11} - 16 q^{12} - 12 q^{13} - 3 q^{14} - 21 q^{15} - 6 q^{16} + 15 q^{17} - 3 q^{18} - 4 q^{19} - 11 q^{20} - 14 q^{21} - 3 q^{22} - 62 q^{23} - 9 q^{24} + 23 q^{25} - 3 q^{26} + 20 q^{27} - 7 q^{28} + 13 q^{29} + 21 q^{30} + 27 q^{31} - 24 q^{32} + 17 q^{33} - 20 q^{34} + 22 q^{35} + 3 q^{36} + 29 q^{37} + 24 q^{38} + 43 q^{39} - 9 q^{40} + 5 q^{41} - 11 q^{42} + 24 q^{43} + 8 q^{44} + 34 q^{45} - 13 q^{46} + 4 q^{47} - q^{48} - 19 q^{49} + 27 q^{50} + 22 q^{51} + 3 q^{52} - 32 q^{53} + 10 q^{54} - 83 q^{55} - 8 q^{56} - 7 q^{57} - 13 q^{58} - 36 q^{59} + 19 q^{60} - 3 q^{61} + 38 q^{62} - 56 q^{63} - 6 q^{64} + 58 q^{65} - 37 q^{66} + 26 q^{67} + 15 q^{68} - 20 q^{69} + 8 q^{70} - 4 q^{71} + 7 q^{72} + 29 q^{73} - 29 q^{74} + 33 q^{75} + 56 q^{76} - 63 q^{77} + 2 q^{78} - 10 q^{79} + 9 q^{80} + 36 q^{81} + 5 q^{82} - 51 q^{83} - 4 q^{84} + 21 q^{85} + 6 q^{86} + 104 q^{87} - 8 q^{88} - 8 q^{89} + 46 q^{90} - 4 q^{91} + 18 q^{92} - 27 q^{93} - 19 q^{94} + 59 q^{95} + q^{96} + 31 q^{97} - 56 q^{98} - 87 q^{99}+O(q^{100}) \) 24 * q + 6 * q^2 - q^3 - 6 * q^4 - 11 * q^5 - 9 * q^6 + 3 * q^7 + 6 * q^8 - 7 * q^9 - 4 * q^10 - 7 * q^11 - 16 * q^12 - 12 * q^13 - 3 * q^14 - 21 * q^15 - 6 * q^16 + 15 * q^17 - 3 * q^18 - 4 * q^19 - 11 * q^20 - 14 * q^21 - 3 * q^22 - 62 * q^23 - 9 * q^24 + 23 * q^25 - 3 * q^26 + 20 * q^27 - 7 * q^28 + 13 * q^29 + 21 * q^30 + 27 * q^31 - 24 * q^32 + 17 * q^33 - 20 * q^34 + 22 * q^35 + 3 * q^36 + 29 * q^37 + 24 * q^38 + 43 * q^39 - 9 * q^40 + 5 * q^41 - 11 * q^42 + 24 * q^43 + 8 * q^44 + 34 * q^45 - 13 * q^46 + 4 * q^47 - q^48 - 19 * q^49 + 27 * q^50 + 22 * q^51 + 3 * q^52 - 32 * q^53 + 10 * q^54 - 83 * q^55 - 8 * q^56 - 7 * q^57 - 13 * q^58 - 36 * q^59 + 19 * q^60 - 3 * q^61 + 38 * q^62 - 56 * q^63 - 6 * q^64 + 58 * q^65 - 37 * q^66 + 26 * q^67 + 15 * q^68 - 20 * q^69 + 8 * q^70 - 4 * q^71 + 7 * q^72 + 29 * q^73 - 29 * q^74 + 33 * q^75 + 56 * q^76 - 63 * q^77 + 2 * q^78 - 10 * q^79 + 9 * q^80 + 36 * q^81 + 5 * q^82 - 51 * q^83 - 4 * q^84 + 21 * q^85 + 6 * q^86 + 104 * q^87 - 8 * q^88 - 8 * q^89 + 46 * q^90 - 4 * q^91 + 18 * q^92 - 27 * q^93 - 19 * q^94 + 59 * q^95 + q^96 + 31 * q^97 - 56 * q^98 - 87 * q^99

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