LMFDB - Embedded newform 187.2.g.f.69.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [187,2,Mod(69,187)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(187, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8, 0]))

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

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

chi := DirichletCharacter("187.69");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 187 = 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	187.g (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:	$1.49320251780$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$9$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			69.9
Character	$\chi$	$=$	187.69
Dual form			187.2.g.f.103.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.11405 - 1.53595i) q^{2} +(0.334210 + 1.02859i) q^{3} +(1.49204 - 4.59203i) q^{4} +(-0.441442 - 0.320727i) q^{5} +(2.28641 + 1.66117i) q^{6} +(-1.38827 + 4.27266i) q^{7} +(-2.28388 - 7.02906i) q^{8} +(1.48074 - 1.07582i) q^{9} +O(q^{10})$	\(q+(2.11405 - 1.53595i) q^{2} +(0.334210 + 1.02859i) q^{3} +(1.49204 - 4.59203i) q^{4} +(-0.441442 - 0.320727i) q^{5} +(2.28641 + 1.66117i) q^{6} +(-1.38827 + 4.27266i) q^{7} +(-2.28388 - 7.02906i) q^{8} +(1.48074 - 1.07582i) q^{9} -1.42585 q^{10} +(-1.73263 - 2.82807i) q^{11} +5.22199 q^{12} +(-4.88824 + 3.55151i) q^{13} +(3.62770 + 11.1649i) q^{14} +(0.182363 - 0.561255i) q^{15} +(-7.81208 - 5.67581i) q^{16} +(-0.809017 - 0.587785i) q^{17} +(1.47796 - 4.54869i) q^{18} +(0.452025 + 1.39119i) q^{19} +(-2.13144 + 1.54858i) q^{20} -4.85880 q^{21} +(-8.00664 - 3.31746i) q^{22} +6.44879 q^{23} +(6.46675 - 4.69837i) q^{24} +(-1.45308 - 4.47212i) q^{25} +(-4.87904 + 15.0162i) q^{26} +(4.22639 + 3.07065i) q^{27} +(17.5488 + 12.7500i) q^{28} +(-0.776783 + 2.39069i) q^{29} +(-0.476534 - 1.46662i) q^{30} +(-1.36977 + 0.995194i) q^{31} -10.4513 q^{32} +(2.32988 - 2.72734i) q^{33} -2.61311 q^{34} +(1.98320 - 1.44088i) q^{35} +(-2.73088 - 8.40479i) q^{36} +(-1.05939 + 3.26045i) q^{37} +(3.09240 + 2.24676i) q^{38} +(-5.28676 - 3.84106i) q^{39} +(-1.24621 + 3.83543i) q^{40} +(-1.55440 - 4.78394i) q^{41} +(-10.2718 + 7.46287i) q^{42} +6.64111 q^{43} +(-15.5718 + 3.73668i) q^{44} -0.998707 q^{45} +(13.6331 - 9.90501i) q^{46} +(-2.59458 - 7.98531i) q^{47} +(3.22722 - 9.93237i) q^{48} +(-10.6652 - 7.74871i) q^{49} +(-9.94083 - 7.22243i) q^{50} +(0.334210 - 1.02859i) q^{51} +(9.01521 + 27.7460i) q^{52} +(1.09281 - 0.793974i) q^{53} +13.6512 q^{54} +(-0.142183 + 1.80413i) q^{55} +33.2034 q^{56} +(-1.27990 + 0.929901i) q^{57} +(2.02982 + 6.24714i) q^{58} +(-2.07519 + 6.38676i) q^{59} +(-2.30521 - 1.67483i) q^{60} +(-1.64548 - 1.19551i) q^{61} +(-1.36719 + 4.20778i) q^{62} +(2.54095 + 7.82023i) q^{63} +(-6.47043 + 4.70104i) q^{64} +3.29694 q^{65} +(0.736422 - 9.34431i) q^{66} +8.07662 q^{67} +(-3.90622 + 2.83803i) q^{68} +(2.15525 + 6.63319i) q^{69} +(1.97947 - 6.09217i) q^{70} +(-6.13633 - 4.45831i) q^{71} +(-10.9439 - 7.95118i) q^{72} +(2.88034 - 8.86478i) q^{73} +(2.76829 + 8.51992i) q^{74} +(4.11436 - 2.98926i) q^{75} +7.06283 q^{76} +(14.4887 - 3.47680i) q^{77} -17.0762 q^{78} +(-4.32095 + 3.13935i) q^{79} +(1.62820 + 5.01108i) q^{80} +(-0.0491700 + 0.151330i) q^{81} +(-10.6340 - 7.72602i) q^{82} +(5.17112 + 3.75704i) q^{83} +(-7.24954 + 22.3118i) q^{84} +(0.168616 + 0.518947i) q^{85} +(14.0396 - 10.2004i) q^{86} -2.71866 q^{87} +(-15.9216 + 18.6377i) q^{88} +3.30077 q^{89} +(-2.11132 + 1.53396i) q^{90} +(-8.38820 - 25.8162i) q^{91} +(9.62187 - 29.6131i) q^{92} +(-1.48144 - 1.07633i) q^{93} +(-17.7501 - 12.8962i) q^{94} +(0.246649 - 0.759107i) q^{95} +(-3.49293 - 10.7501i) q^{96} +(-8.54301 + 6.20686i) q^{97} -34.4483 q^{98} +(-5.60808 - 2.32365i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 4 q^{2} - q^{3} - 14 q^{4} + q^{5} - 5 q^{6} + q^{7} + 17 q^{8} - 22 q^{9}+O(q^{10}) $ 36 * q - 4 * q^2 - q^3 - 14 * q^4 + q^5 - 5 * q^6 + q^7 + 17 * q^8 - 22 * q^9	\( 36 q - 4 q^{2} - q^{3} - 14 q^{4} + q^{5} - 5 q^{6} + q^{7} + 17 q^{8} - 22 q^{9} - 10 q^{10} + 3 q^{11} + 28 q^{12} - 13 q^{13} + 14 q^{14} - 24 q^{15} + 16 q^{16} - 9 q^{17} + 2 q^{18} + 10 q^{19} + 19 q^{20} - 50 q^{21} - 25 q^{22} + 38 q^{23} - 17 q^{24} - 28 q^{25} + 20 q^{26} - 16 q^{27} + 31 q^{28} - 45 q^{29} + 68 q^{30} - 13 q^{31} - 40 q^{32} - 29 q^{33} - 4 q^{34} + 13 q^{35} - 25 q^{36} + q^{37} + 65 q^{38} - 34 q^{39} - 54 q^{40} + 37 q^{41} + 28 q^{42} - 8 q^{43} - 2 q^{44} + 42 q^{45} + 22 q^{46} - 35 q^{47} + 48 q^{48} - 2 q^{49} - 49 q^{50} - q^{51} + 56 q^{52} + 58 q^{53} - 58 q^{54} - 19 q^{55} - 28 q^{56} + 9 q^{57} - 52 q^{58} + 16 q^{59} + 97 q^{60} - 14 q^{61} - 64 q^{62} + 34 q^{63} - 33 q^{64} - 42 q^{65} - 28 q^{66} + 54 q^{67} - 14 q^{68} + 19 q^{69} + 4 q^{70} + 25 q^{71} - 72 q^{72} + 8 q^{73} + 84 q^{74} + 30 q^{75} - 140 q^{76} - 31 q^{77} - 48 q^{78} + 19 q^{79} - 19 q^{80} + 56 q^{81} + 48 q^{82} + 42 q^{83} - 91 q^{84} - 9 q^{85} + 30 q^{86} - 32 q^{87} + 126 q^{88} + 12 q^{89} + 160 q^{90} - 59 q^{91} + 69 q^{92} - 40 q^{93} - 77 q^{94} - 11 q^{95} + 192 q^{96} - 49 q^{97} - 212 q^{98} + 38 q^{99}+O(q^{100}) \) 36 * q - 4 * q^2 - q^3 - 14 * q^4 + q^5 - 5 * q^6 + q^7 + 17 * q^8 - 22 * q^9 - 10 * q^10 + 3 * q^11 + 28 * q^12 - 13 * q^13 + 14 * q^14 - 24 * q^15 + 16 * q^16 - 9 * q^17 + 2 * q^18 + 10 * q^19 + 19 * q^20 - 50 * q^21 - 25 * q^22 + 38 * q^23 - 17 * q^24 - 28 * q^25 + 20 * q^26 - 16 * q^27 + 31 * q^28 - 45 * q^29 + 68 * q^30 - 13 * q^31 - 40 * q^32 - 29 * q^33 - 4 * q^34 + 13 * q^35 - 25 * q^36 + q^37 + 65 * q^38 - 34 * q^39 - 54 * q^40 + 37 * q^41 + 28 * q^42 - 8 * q^43 - 2 * q^44 + 42 * q^45 + 22 * q^46 - 35 * q^47 + 48 * q^48 - 2 * q^49 - 49 * q^50 - q^51 + 56 * q^52 + 58 * q^53 - 58 * q^54 - 19 * q^55 - 28 * q^56 + 9 * q^57 - 52 * q^58 + 16 * q^59 + 97 * q^60 - 14 * q^61 - 64 * q^62 + 34 * q^63 - 33 * q^64 - 42 * q^65 - 28 * q^66 + 54 * q^67 - 14 * q^68 + 19 * q^69 + 4 * q^70 + 25 * q^71 - 72 * q^72 + 8 * q^73 + 84 * q^74 + 30 * q^75 - 140 * q^76 - 31 * q^77 - 48 * q^78 + 19 * q^79 - 19 * q^80 + 56 * q^81 + 48 * q^82 + 42 * q^83 - 91 * q^84 - 9 * q^85 + 30 * q^86 - 32 * q^87 + 126 * q^88 + 12 * q^89 + 160 * q^90 - 59 * q^91 + 69 * q^92 - 40 * q^93 - 77 * q^94 - 11 * q^95 + 192 * q^96 - 49 * q^97 - 212 * q^98 + 38 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/187\mathbb{Z}\right)^\times$.

$n$	$35$	$122$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$

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 $

$2$	2.11405	−	1.53595i	1.49486	−	1.08608i	0.522487	−	0.852647i	$-0.325004\pi$
$2$	2.11405	−	1.53595i	1.49486	−	1.08608i	0.972373	−	0.233432i	$-0.0749957\pi$
$3$	0.334210	+	1.02859i	0.192957	+	0.593859i	0.999994	+	0.00335935i	$0.00106932\pi$
$3$	0.334210	+	1.02859i	0.192957	+	0.593859i	−0.807038	+	0.590500i	$0.798931\pi$
$4$	1.49204	−	4.59203i	0.746021	−	2.29602i
$5$	−0.441442	−	0.320727i	−0.197419	−	0.143433i	0.484684	−	0.874689i	$-0.338935\pi$
$5$	−0.441442	−	0.320727i	−0.197419	−	0.143433i	−0.682103	+	0.731256i	$0.738935\pi$
$6$	2.28641	+	1.66117i	0.933421	+	0.678170i
$7$	−1.38827	+	4.27266i	−0.524717	+	1.61491i	0.240158	+	0.970734i	$0.422801\pi$
$7$	−1.38827	+	4.27266i	−0.524717	+	1.61491i	−0.764875	+	0.644179i	$0.777199\pi$
$8$	−2.28388	−	7.02906i	−0.807474	−	2.48515i
$9$	1.48074	−	1.07582i	0.493581	−	0.358607i
$10$	−1.42585			−0.450894
$11$	−1.73263	−	2.82807i	−0.522407	−	0.852696i
$11$	−1.73263	−	2.82807i	−0.522407	−	0.852696i
$12$	5.22199			1.50746
$13$	−4.88824	+	3.55151i	−1.35575	+	0.985012i	−0.357051	+	0.934085i	$0.616218\pi$
$13$	−4.88824	+	3.55151i	−1.35575	+	0.985012i	−0.998702	+	0.0509271i	$0.983782\pi$
$14$	3.62770	+	11.1649i	0.969545	+	2.98395i
$15$	0.182363	−	0.561255i	0.0470859	−	0.144915i
$16$	−7.81208	−	5.67581i	−1.95302	−	1.41895i
$17$	−0.809017	−	0.587785i	−0.196215	−	0.142559i
$17$	−0.809017	−	0.587785i	−0.196215	−	0.142559i
$18$	1.47796	−	4.54869i	0.348358	−	1.07214i
$19$	0.452025	+	1.39119i	0.103702	+	0.319161i	0.989424	−	0.145055i	$-0.0463360\pi$
$19$	0.452025	+	1.39119i	0.103702	+	0.319161i	−0.885722	+	0.464216i	$0.846336\pi$
$20$	−2.13144	+	1.54858i	−0.476604	+	0.346273i
$21$	−4.85880			−1.06028
$22$	−8.00664	−	3.31746i	−1.70702	−	0.707286i
$23$	6.44879			1.34467			0.672333	−	0.740249i	$-0.265292\pi$
$23$	6.44879			1.34467			0.672333	+	0.740249i	$0.265292\pi$
$24$	6.46675	−	4.69837i	1.32002	−	0.959051i
$25$	−1.45308	−	4.47212i	−0.290616	−	0.894424i
$26$	−4.87904	+	15.0162i	−0.956859	+	2.94491i
$27$	4.22639	+	3.07065i	0.813368	+	0.590947i
$28$	17.5488	+	12.7500i	3.31642	+	2.40952i
$29$	−0.776783	+	2.39069i	−0.144245	+	0.443940i	−0.996913	−	0.0785125i	$-0.974983\pi$
$29$	−0.776783	+	2.39069i	−0.144245	+	0.443940i	0.852668	+	0.522453i	$0.174983\pi$
$30$	−0.476534	−	1.46662i	−0.0870029	−	0.267767i
$31$	−1.36977	+	0.995194i	−0.246017	+	0.178742i	−0.703960	−	0.710240i	$-0.748587\pi$
$31$	−1.36977	+	0.995194i	−0.246017	+	0.178742i	0.457942	+	0.888982i	$0.348587\pi$
$32$	−10.4513			−1.84755
$33$	2.32988	−	2.72734i	0.405580	−	0.474769i
$34$	−2.61311			−0.448145
$35$	1.98320	−	1.44088i	0.335221	−	0.243552i
$36$	−2.73088	−	8.40479i	−0.455147	−	1.40080i
$37$	−1.05939	+	3.26045i	−0.174162	+	0.536015i	−0.999594	−	0.0284860i	$-0.990931\pi$
$37$	−1.05939	+	3.26045i	−0.174162	+	0.536015i	0.825432	+	0.564501i	$0.190931\pi$
$38$	3.09240	+	2.24676i	0.501654	+	0.364473i
$39$	−5.28676	−	3.84106i	−0.846560	−	0.615062i
$40$	−1.24621	+	3.83543i	−0.197042	+	0.606434i
$41$	−1.55440	−	4.78394i	−0.242756	−	0.747126i	−0.995997	−	0.0893818i	$-0.971511\pi$
$41$	−1.55440	−	4.78394i	−0.242756	−	0.747126i	0.753242	−	0.657744i	$-0.228489\pi$
$42$	−10.2718	+	7.46287i	−1.58497	+	1.15155i
$43$	6.64111			1.01276			0.506380	−	0.862311i	$-0.330983\pi$
$43$	6.64111			1.01276			0.506380	+	0.862311i	$0.330983\pi$
$44$	−15.5718	+	3.73668i	−2.34753	+	0.563326i
$45$	−0.998707			−0.148878
$46$	13.6331	−	9.90501i	2.01009	−	1.46041i
$47$	−2.59458	−	7.98531i	−0.378459	−	1.16478i	−0.941115	−	0.338086i	$-0.890220\pi$
$47$	−2.59458	−	7.98531i	−0.378459	−	1.16478i	0.562656	−	0.826691i	$-0.309780\pi$
$48$	3.22722	−	9.93237i	0.465810	−	1.43361i
$49$	−10.6652	−	7.74871i	−1.52360	−	1.10696i
$50$	−9.94083	−	7.22243i	−1.40585	−	1.02141i
$51$	0.334210	−	1.02859i	0.0467988	−	0.144032i
$52$	9.01521	+	27.7460i	1.25018	+	3.84767i
$53$	1.09281	−	0.793974i	0.150109	−	0.109061i	−0.510196	−	0.860058i	$-0.670427\pi$
$53$	1.09281	−	0.793974i	0.150109	−	0.109061i	0.660305	+	0.750998i	$0.270427\pi$
$54$	13.6512			1.85769
$55$	−0.142183	+	1.80413i	−0.0191719	+	0.243269i
$56$	33.2034			4.43699
$57$	−1.27990	+	0.929901i	−0.169527	+	0.123168i
$58$	2.02982	+	6.24714i	0.266528	+	0.820290i
$59$	−2.07519	+	6.38676i	−0.270166	+	0.831486i	0.720292	+	0.693671i	$0.244008\pi$
$59$	−2.07519	+	6.38676i	−0.270166	+	0.831486i	−0.990458	+	0.137815i	$0.955992\pi$
$60$	−2.30521	−	1.67483i	−0.297601	−	0.216220i
$61$	−1.64548	−	1.19551i	−0.210683	−	0.153070i	0.477440	−	0.878664i	$-0.341565\pi$
$61$	−1.64548	−	1.19551i	−0.210683	−	0.153070i	−0.688122	+	0.725595i	$0.741565\pi$
$62$	−1.36719	+	4.20778i	−0.173634	+	0.534389i
$63$	2.54095	+	7.82023i	0.320129	+	0.985257i
$64$	−6.47043	+	4.70104i	−0.808804	+	0.587630i
$65$	3.29694			0.408935
$66$	0.736422	−	9.34431i	0.0906473	−	1.15021i
$67$	8.07662			0.986716			0.493358	−	0.869826i	$-0.335769\pi$
$67$	8.07662			0.986716			0.493358	+	0.869826i	$0.335769\pi$
$68$	−3.90622	+	2.83803i	−0.473698	+	0.344162i
$69$	2.15525	+	6.63319i	0.259462	+	0.798542i
$70$	1.97947	−	6.09217i	0.236592	−	0.728154i
$71$	−6.13633	−	4.45831i	−0.728249	−	0.529104i	0.160760	−	0.986993i	$-0.448605\pi$
$71$	−6.13633	−	4.45831i	−0.728249	−	0.529104i	−0.889009	+	0.457890i	$0.848605\pi$
$72$	−10.9439	−	7.95118i	−1.28975	−	0.937055i
$73$	2.88034	−	8.86478i	0.337118	−	1.03754i	−0.628551	−	0.777769i	$-0.716352\pi$
$73$	2.88034	−	8.86478i	0.337118	−	1.03754i	0.965669	−	0.259775i	$-0.0836484\pi$
$74$	2.76829	+	8.51992i	0.321807	+	0.990421i
$75$	4.11436	−	2.98926i	0.475085	−	0.345170i
$76$	7.06283			0.810162
$77$	14.4887	−	3.47680i	1.65115	−	0.396218i
$78$	−17.0762			−1.93349
$79$	−4.32095	+	3.13935i	−0.486144	+	0.353205i	−0.803700	−	0.595035i	$-0.797138\pi$
$79$	−4.32095	+	3.13935i	−0.486144	+	0.353205i	0.317555	+	0.948240i	$0.397138\pi$
$80$	1.62820	+	5.01108i	0.182038	+	0.560256i
$81$	−0.0491700	+	0.151330i	−0.00546334	+	0.0168144i
$82$	−10.6340	−	7.72602i	−1.17432	−	0.853196i
$83$	5.17112	+	3.75704i	0.567605	+	0.412389i	0.834234	−	0.551410i	$-0.185910\pi$
$83$	5.17112	+	3.75704i	0.567605	+	0.412389i	−0.266630	+	0.963799i	$0.585910\pi$
$84$	−7.24954	+	22.3118i	−0.790990	+	2.43442i
$85$	0.168616	+	0.518947i	0.0182890	+	0.0562877i
$86$	14.0396	−	10.2004i	1.51393	−	1.09994i
$87$	−2.71866			−0.291471
$88$	−15.9216	+	18.6377i	−1.69725	+	1.98679i
$89$	3.30077			0.349881			0.174941	−	0.984579i	$-0.444027\pi$
$89$	3.30077			0.349881			0.174941	+	0.984579i	$0.444027\pi$
$90$	−2.11132	+	1.53396i	−0.222552	+	0.161694i
$91$	−8.38820	−	25.8162i	−0.879322	−	2.70627i
$92$	9.62187	−	29.6131i	1.00315	−	3.08737i
$93$	−1.48144	−	1.07633i	−0.153618	−	0.111610i
$94$	−17.7501	−	12.8962i	−1.83078	−	1.33014i
$95$	0.246649	−	0.759107i	0.0253056	−	0.0778827i
$96$	−3.49293	−	10.7501i	−0.356496	−	1.09718i
$97$	−8.54301	+	6.20686i	−0.867411	+	0.630211i	−0.929891	−	0.367835i	$-0.880099\pi$
$97$	−8.54301	+	6.20686i	−0.867411	+	0.630211i	0.0624800	+	0.998046i	$0.480099\pi$
$98$	−34.4483			−3.47981
$99$	−5.60808	−	2.32365i	−0.563633	−	0.233535i
$100$	−22.7042			−2.27042
$101$	−3.39902	+	2.46953i	−0.338215	+	0.245728i	−0.743908	−	0.668282i	$-0.767030\pi$
$101$	−3.39902	+	2.46953i	−0.338215	+	0.245728i	0.405693	+	0.914009i	$0.367030\pi$
$102$	−0.873329	−	2.68783i	−0.0864725	−	0.266135i
$103$	3.55674	−	10.9465i	0.350456	−	1.07859i	−0.608142	−	0.793828i	$-0.708085\pi$
$103$	3.55674	−	10.9465i	0.350456	−	1.07859i	0.958598	−	0.284763i	$-0.0919150\pi$
$104$	36.1279	+	26.2485i	3.54264	+	2.57388i
$105$	2.14488	+	1.55835i	0.209319	+	0.152079i
$106$	1.09076	−	3.35700i	0.105944	−	0.326061i
$107$	1.81692	+	5.59189i	0.175648	+	0.540589i	0.999662	−	0.0259799i	$-0.00827059\pi$
$107$	1.81692	+	5.59189i	0.175648	+	0.540589i	−0.824015	+	0.566569i	$0.808271\pi$
$108$	20.4065	−	14.8262i	1.96361	−	1.42665i
$109$	−7.51857			−0.720148			−0.360074	−	0.932924i	$-0.617249\pi$
$109$	−7.51857			−0.720148			−0.360074	+	0.932924i	$0.617249\pi$
$110$	2.47047	+	4.03241i	0.235550	+	0.384475i
$111$	−3.70774			−0.351923
$112$	35.0961	−	25.4988i	3.31627	−	2.40941i
$113$	2.88418	+	8.87659i	0.271321	+	0.835039i	0.990169	+	0.139873i	$0.0446694\pi$
$113$	2.88418	+	8.87659i	0.271321	+	0.835039i	−0.718849	+	0.695166i	$0.755331\pi$
$114$	−1.27749	+	3.93172i	−0.119648	+	0.368239i
$115$	−2.84677	−	2.06830i	−0.265463	−	0.192870i
$116$	9.81914	+	7.13403i	0.911685	+	0.662378i
$117$	−3.41742	+	10.5177i	−0.315941	+	0.972366i
$118$	5.42269	+	16.6893i	0.499199	+	1.53638i
$119$	3.63454	−	2.64065i	0.333178	−	0.242068i
$120$	−4.36159			−0.398157
$121$	−4.99600	+	9.80000i	−0.454182	+	0.890909i
$122$	−5.31488			−0.481187
$123$	4.40124	−	3.19768i	0.396846	−	0.288326i
$124$	2.52621	+	7.77489i	0.226861	+	0.698206i
$125$	−1.63596	+	5.03496i	−0.146324	+	0.450340i
$126$	17.3832	+	12.6296i	1.54862	+	1.12514i
$127$	−0.473796	−	0.344233i	−0.0420426	−	0.0305458i	0.566565	−	0.824017i	$-0.308272\pi$
$127$	−0.473796	−	0.344233i	−0.0420426	−	0.0305458i	−0.608608	+	0.793471i	$0.708272\pi$
$128$	0.000997965	−	0.00307142i	8.82085e−5	−	0.000271478i
$129$	2.21953	+	6.83100i	0.195418	+	0.601436i
$130$	6.96990	−	5.06393i	0.611300	−	0.444136i
$131$	4.47420			0.390913			0.195456	−	0.980712i	$-0.437381\pi$
$131$	4.47420			0.390913			0.195456	+	0.980712i	$0.437381\pi$
$132$	−9.04778	−	14.7682i	−0.787508	−	1.28541i
$133$	−6.57161			−0.569831
$134$	17.0744	−	12.4053i	1.47500	−	1.07165i
$135$	−0.880867	−	2.71103i	−0.0758129	−	0.233328i
$136$	−2.28388	+	7.02906i	−0.195841	+	0.602737i
$137$	−11.2335	−	8.16165i	−0.959747	−	0.697297i	−0.00665492	−	0.999978i	$-0.502118\pi$
$137$	−11.2335	−	8.16165i	−0.959747	−	0.697297i	−0.953092	+	0.302681i	$0.902118\pi$
$138$	14.7445	+	10.7125i	1.25514	+	0.911912i
$139$	4.68677	−	14.4244i	0.397527	−	1.22346i	−0.529450	−	0.848341i	$-0.677602\pi$
$139$	4.68677	−	14.4244i	0.397527	−	1.22346i	0.926976	−	0.375120i	$-0.122398\pi$
$140$	−3.65754	−	11.2567i	−0.309119	−	0.951369i
$141$	7.34651	−	5.33755i	0.618687	−	0.449503i
$142$	−19.8202			−1.66328
$143$	18.5134	+	7.67084i	1.54817	+	0.641468i
$144$	−17.6738			−1.47282
$145$	1.10966	−	0.806218i	0.0921525	−	0.0669527i
$146$	−7.52665	−	23.1646i	−0.622910	−	1.91712i
$147$	4.40586	−	13.5598i	0.363389	−	1.11840i
$148$	13.3915	+	9.72946i	1.10077	+	0.799757i
$149$	8.93506	+	6.49170i	0.731989	+	0.531821i	0.890192	−	0.455586i	$-0.150570\pi$
$149$	8.93506	+	6.49170i	0.731989	+	0.531821i	−0.158203	+	0.987407i	$0.550570\pi$
$150$	4.10662	−	12.6389i	0.335304	−	1.03196i
$151$	5.49277	+	16.9050i	0.446995	+	1.37571i	0.880281	+	0.474453i	$0.157354\pi$
$151$	5.49277	+	16.9050i	0.446995	+	1.37571i	−0.433286	+	0.901256i	$0.642646\pi$
$152$	8.74639	−	6.35462i	0.709426	−	0.515428i
$153$	−1.83030			−0.147971
$154$	25.2898	−	29.6041i	2.03791	−	2.38556i
$155$	0.923859			0.0742061
$156$	−25.5263	+	18.5460i	−2.04374	+	1.48487i
$157$	2.86691	+	8.82344i	0.228804	+	0.704187i	0.997883	+	0.0650331i	$0.0207153\pi$
$157$	2.86691	+	8.82344i	0.228804	+	0.704187i	−0.769079	+	0.639154i	$0.779285\pi$
$158$	−4.31282	+	13.2735i	−0.343110	+	1.05598i
$159$	1.18191	+	0.858705i	0.0937312	+	0.0680997i
$160$	4.61365	+	3.35201i	0.364741	+	0.265000i
$161$	−8.95266	+	27.5535i	−0.705569	+	2.17152i
$162$	0.128487	+	0.395442i	0.0100949	+	0.0310688i
$163$	−15.1714	+	11.0226i	−1.18831	+	0.863360i	−0.993085	−	0.117398i	$-0.962545\pi$
$163$	−15.1714	+	11.0226i	−1.18831	+	0.863360i	−0.195228	+	0.980758i	$0.562545\pi$
$164$	−24.2872			−1.89651
$165$	−1.90324	+	0.456711i	−0.148167	+	0.0355549i
$166$	16.7026			1.29638
$167$	−4.29100	+	3.11759i	−0.332048	+	0.241247i	−0.741299	−	0.671175i	$-0.765790\pi$
$167$	−4.29100	+	3.11759i	−0.332048	+	0.241247i	0.409251	+	0.912422i	$0.365790\pi$
$168$	11.0969	+	34.1528i	0.856146	+	2.63495i
$169$	7.26440	−	22.3575i	0.558800	−	1.71981i
$170$	1.15354	+	0.838094i	0.0884723	+	0.0642789i
$171$	2.16601	+	1.57370i	0.165639	+	0.120343i
$172$	9.90881	−	30.4962i	0.755540	−	2.32531i
$173$	1.09584	+	3.37265i	0.0833151	+	0.256417i	0.984033	−	0.177988i	$-0.0569587\pi$
$173$	1.09584	+	3.37265i	0.0833151	+	0.256417i	−0.900718	+	0.434405i	$0.856959\pi$
$174$	−5.74739	+	4.17572i	−0.435708	+	0.316561i
$175$	21.1251			1.59691
$176$	−2.51617	+	31.9272i	−0.189664	+	2.40660i
$177$	−7.26294			−0.545916
$178$	6.97801	−	5.06982i	0.523024	−	0.379999i
$179$	7.93596	+	24.4244i	0.593162	+	1.82556i	0.563671	+	0.825999i	$0.309389\pi$
$179$	7.93596	+	24.4244i	0.593162	+	1.82556i	0.0294907	+	0.999565i	$0.490611\pi$
$180$	−1.49011	+	4.58610i	−0.111066	+	0.341827i
$181$	2.91762	+	2.11978i	0.216865	+	0.157562i	0.690914	−	0.722937i	$-0.257208\pi$
$181$	2.91762	+	2.11978i	0.216865	+	0.157562i	−0.474049	+	0.880498i	$0.657208\pi$
$182$	−57.3854	−	41.6930i	−4.25369	−	3.09049i
$183$	0.679760	−	2.09209i	0.0502493	−	0.154652i
$184$	−14.7283	−	45.3289i	−1.08578	−	3.34169i
$185$	1.51337	−	1.09953i	0.111265	−	0.0808389i
$186$	−4.78503			−0.350855
$187$	−0.260574	+	3.30637i	−0.0190551	+	0.241786i
$188$	−40.5400			−2.95669
$189$	−18.9872	+	13.7950i	−1.38112	+	1.00344i
$190$	−0.644521	−	1.98363i	−0.0467584	−	0.143908i
$191$	−5.27350	+	16.2302i	−0.381577	+	1.17437i	0.557356	+	0.830274i	$0.311816\pi$
$191$	−5.27350	+	16.2302i	−0.381577	+	1.17437i	−0.938933	+	0.344100i	$0.888184\pi$
$192$	−6.99795	−	5.08431i	−0.505033	−	0.366928i
$193$	0.382363	+	0.277803i	0.0275231	+	0.0199967i	0.601462	−	0.798902i	$-0.294585\pi$
$193$	0.382363	+	0.277803i	0.0275231	+	0.0199967i	−0.573939	+	0.818898i	$0.694585\pi$
$194$	−8.52694	+	26.2432i	−0.612199	+	1.88415i
$195$	1.10187	+	3.39121i	0.0789067	+	0.242850i
$196$	−51.4952	+	37.4135i	−3.67823	+	2.67239i
$197$	−3.50289			−0.249571			−0.124785	−	0.992184i	$-0.539824\pi$
$197$	−3.50289			−0.249571			−0.124785	+	0.992184i	$0.539824\pi$
$198$	−15.4248	+	3.70141i	−1.09619	+	0.263048i
$199$	16.5555			1.17359			0.586793	−	0.809737i	$-0.300390\pi$
$199$	16.5555			1.17359			0.586793	+	0.809737i	$0.300390\pi$
$200$	−28.1161	+	20.4276i	−1.98811	+	1.44445i
$201$	2.69929	+	8.30756i	0.190393	+	0.585970i
$202$	−3.39263	+	10.4414i	−0.238704	+	0.734657i
$203$	−9.13622	−	6.63785i	−0.641237	−	0.465886i
$204$	−4.22468	−	3.06941i	−0.295787	−	0.214902i
$205$	−0.848160	+	2.61037i	−0.0592381	+	0.182316i
$206$	−9.29415	−	28.6044i	−0.647554	−	1.99297i
$207$	9.54899	−	6.93775i	0.663701	−	0.482207i
$208$	58.3450			4.04550
$209$	3.15120	−	3.68878i	0.217973	−	0.255158i
$210$	6.92793			0.478073
$211$	−6.26767	+	4.55373i	−0.431484	+	0.313491i	−0.782242	−	0.622975i	$-0.785924\pi$
$211$	−6.26767	+	4.55373i	−0.431484	+	0.313491i	0.350758	+	0.936466i	$0.385924\pi$
$212$	−2.01543	−	6.20287i	−0.138421	−	0.426015i
$213$	2.53496	−	7.80181i	0.173693	−	0.534571i
$214$	12.4299	+	9.03086i	0.849691	+	0.617337i
$215$	−2.93167	−	2.12998i	−0.199938	−	0.145263i
$216$	11.9312	−	36.7205i	0.811817	−	2.49852i
$217$	−2.35052	−	7.23414i	−0.159563	−	0.491086i
$218$	−15.8946	+	11.5481i	−1.07652	+	0.782138i
$219$	10.0809			0.681204
$220$	8.07249	+	3.34475i	0.544247	+	0.225503i
$221$	6.04219			0.406442
$222$	−7.83835	+	5.69490i	−0.526076	+	0.382216i
$223$	1.92639	+	5.92882i	0.129001	+	0.397023i	0.994609	−	0.103699i	$-0.0330679\pi$
$223$	1.92639	+	5.92882i	0.129001	+	0.397023i	−0.865608	+	0.500722i	$0.833068\pi$
$224$	14.5092	−	44.6548i	0.969439	−	2.98363i
$225$	−6.96284	−	5.05880i	−0.464189	−	0.337253i
$226$	19.7313	+	14.3356i	1.31251	+	0.953591i
$227$	4.07283	−	12.5349i	0.270323	−	0.831969i	−0.720096	−	0.693875i	$-0.755902\pi$
$227$	4.07283	−	12.5349i	0.270323	−	0.831969i	0.990419	−	0.138094i	$-0.0440978\pi$
$228$	2.36047	+	7.26479i	0.156326	+	0.481122i
$229$	10.8622	−	7.89184i	0.717793	−	0.521507i	−0.167885	−	0.985807i	$-0.553694\pi$
$229$	10.8622	−	7.89184i	0.717793	−	0.521507i	0.885678	+	0.464299i	$0.153694\pi$
$230$	−9.19501			−0.606301
$231$	8.41850	+	13.7411i	0.553897	+	0.904095i
$232$	18.5784			1.21973
$233$	15.3452	−	11.1490i	1.00530	−	0.730392i	0.0420807	−	0.999114i	$-0.486601\pi$
$233$	15.3452	−	11.1490i	1.00530	−	0.730392i	0.963218	+	0.268722i	$0.0866013\pi$
$234$	8.93010	+	27.4840i	0.583779	+	1.79669i
$235$	−1.41574	+	4.35721i	−0.0923528	+	0.284233i
$236$	26.2320	+	19.0586i	1.70756	+	1.24061i
$237$	−4.67322	−	3.39529i	−0.303558	−	0.220548i
$238$	3.62770	−	11.1649i	0.235149	−	0.723715i
$239$	−3.16422	−	9.73846i	−0.204676	−	0.629928i	−0.999727	−	0.0233850i	$-0.992556\pi$
$239$	−3.16422	−	9.73846i	−0.204676	−	0.629928i	0.795050	−	0.606543i	$-0.207444\pi$
$240$	−4.61021	+	3.34951i	−0.297588	+	0.216210i
$241$	−26.7424			−1.72263			−0.861314	−	0.508072i	$-0.830358\pi$
$241$	−26.7424			−1.72263			−0.861314	+	0.508072i	$0.830358\pi$
$242$	4.49050	+	28.3913i	0.288660	+	1.82506i
$243$	15.5002			0.994339
$244$	−7.94497	+	5.77236i	−0.508624	+	0.369537i
$245$	2.22284	+	6.84121i	0.142012	+	0.437069i
$246$	4.39296	−	13.5201i	0.280085	−	0.862013i
$247$	−7.15043	−	5.19509i	−0.454971	−	0.330556i
$248$	10.1237	+	7.35527i	0.642853	+	0.467060i
$249$	−2.13623	+	6.57463i	−0.135378	+	0.416650i
$250$	4.27494	+	13.1569i	0.270371	+	0.832115i
$251$	12.1326	−	8.81488i	0.765805	−	0.556390i	−0.134880	−	0.990862i	$-0.543065\pi$
$251$	12.1326	−	8.81488i	0.765805	−	0.556390i	0.900685	+	0.434472i	$0.143065\pi$
$252$	39.7020			2.50099
$253$	−11.1734	−	18.2376i	−0.702463	−	1.14659i
$254$	−1.53035			−0.0960230
$255$	−0.477432	+	0.346875i	−0.0298980	+	0.0217221i
$256$	−4.94558	−	15.2209i	−0.309098	−	0.951307i
$257$	−7.38027	+	22.7141i	−0.460368	+	1.41687i	0.404347	+	0.914606i	$0.367499\pi$
$257$	−7.38027	+	22.7141i	−0.460368	+	1.41687i	−0.864715	+	0.502263i	$0.832501\pi$
$258$	15.1843	+	11.0320i	0.945331	+	0.686823i
$259$	−12.4601	−	9.05278i	−0.774232	−	0.562512i
$260$	4.91917	−	15.1397i	0.305074	−	0.938921i
$261$	1.42174	+	4.37568i	0.0880037	+	0.270848i
$262$	9.45869	−	6.87214i	0.584360	−	0.424562i
$263$	13.4133			0.827102			0.413551	−	0.910481i	$-0.364288\pi$
$263$	13.4133			0.827102			0.413551	+	0.910481i	$0.364288\pi$
$264$	−24.4918	−	10.1479i	−1.50737	−	0.624561i
$265$	−0.737061			−0.0452773
$266$	−13.8927	+	10.0937i	−0.851817	+	0.618882i
$267$	1.10315	+	3.39516i	0.0675119	+	0.207780i
$268$	12.0507	−	37.0881i	0.736111	−	2.26552i
$269$	8.43939	+	6.13157i	0.514558	+	0.373849i	0.814550	−	0.580093i	$-0.196984\pi$
$269$	8.43939	+	6.13157i	0.514558	+	0.373849i	−0.299992	+	0.953942i	$0.596984\pi$
$270$	−6.02620	−	4.37829i	−0.366743	−	0.266454i
$271$	2.99154	−	9.20701i	0.181723	−	0.559286i	−0.818154	−	0.575000i	$-0.805002\pi$
$271$	2.99154	−	9.20701i	0.181723	−	0.559286i	0.999877	+	0.0157139i	$0.00500211\pi$
$272$	2.98395	+	9.18365i	0.180929	+	0.556841i
$273$	23.7510	−	17.2561i	1.43747	−	1.04439i
$274$	−36.2842			−2.19201
$275$	−10.1298	+	11.8579i	−0.610852	+	0.715060i
$276$	33.6755			2.02703
$277$	−20.3874	+	14.8123i	−1.22496	+	0.889987i	−0.996502	−	0.0835669i	$-0.973369\pi$
$277$	−20.3874	+	14.8123i	−1.22496	+	0.889987i	−0.228459	+	0.973553i	$0.573369\pi$
$278$	−12.2470	−	37.6925i	−0.734529	−	2.26065i
$279$	−0.957620	+	2.94725i	−0.0573312	+	0.176447i
$280$	−14.6574	−	10.6492i	−0.875946	−	0.636412i
$281$	−17.3508	−	12.6061i	−1.03506	−	0.752018i	−0.0657479	−	0.997836i	$-0.520943\pi$
$281$	−17.3508	−	12.6061i	−1.03506	−	0.752018i	−0.969316	+	0.245818i	$0.920943\pi$
$282$	7.33269	−	22.5677i	0.436655	−	1.34389i
$283$	2.86136	+	8.80635i	0.170090	+	0.523483i	0.999375	−	0.0353422i	$-0.0112521\pi$
$283$	2.86136	+	8.80635i	0.170090	+	0.523483i	−0.829285	+	0.558826i	$0.811252\pi$
$284$	−29.6284	+	21.5263i	−1.75812	+	1.27735i
$285$	0.863245			0.0511342
$286$	50.9204	−	12.2191i	3.01098	−	0.722532i
$287$	22.5980			1.33392
$288$	−15.4757	+	11.2437i	−0.911913	+	0.662544i
$289$	0.309017	+	0.951057i	0.0181775	+	0.0559445i
$290$	1.10758	−	3.40877i	0.0650391	−	0.200170i
$291$	−9.23950	−	6.71289i	−0.541629	−	0.393517i
$292$	−36.4098	−	26.4532i	−2.13072	−	1.54806i
$293$	6.09366	−	18.7544i	0.355995	−	1.09564i	−0.599435	−	0.800424i	$-0.704608\pi$
$293$	6.09366	−	18.7544i	0.355995	−	1.09564i	0.955430	−	0.295218i	$-0.0953921\pi$
$294$	−11.5130	−	35.4334i	−0.671452	−	2.06652i
$295$	2.96448	−	2.15382i	0.172599	−	0.125400i
$296$	25.3374			1.47271
$297$	1.36127	−	17.2728i	0.0789886	−	1.00227i
$298$	28.8601			1.67182
$299$	−31.5232	+	22.9030i	−1.82303	+	1.32451i
$300$	−7.58797	−	23.3534i	−0.438092	−	1.34831i
$301$	−9.21965	+	28.3752i	−0.531412	+	1.63552i
$302$	37.5772	+	27.3014i	2.16232	+	1.57102i
$303$	−3.67613	−	2.67087i	−0.211188	−	0.153437i
$304$	4.36487	−	13.4337i	0.250343	−	0.770475i
$305$	0.342953	+	1.05550i	0.0196374	+	0.0604378i
$306$	−3.86934	+	2.81124i	−0.221196	+	0.160708i
$307$	−18.1122			−1.03372			−0.516860	−	0.856070i	$-0.672899\pi$
$307$	−18.1122			−1.03372			−0.516860	+	0.856070i	$0.672899\pi$
$308$	5.65225	−	71.7203i	0.322067	−	4.08664i
$309$	12.4482			0.708154
$310$	1.95308	−	1.41900i	0.110928	−	0.0805937i
$311$	−8.71538	−	26.8232i	−0.494204	−	1.52100i	−0.818194	−	0.574942i	$-0.805025\pi$
$311$	−8.71538	−	26.8232i	−0.494204	−	1.52100i	0.323991	−	0.946060i	$-0.394975\pi$
$312$	−14.9247	+	45.9335i	−0.844945	+	2.60047i
$313$	−24.0428	−	17.4681i	−1.35898	−	0.987357i	−0.998509	−	0.0545871i	$-0.982616\pi$
$313$	−24.0428	−	17.4681i	−1.35898	−	0.987357i	−0.360472	−	0.932770i	$-0.617384\pi$
$314$	19.6131	+	14.2498i	1.10683	+	0.804161i
$315$	1.38647	−	4.26713i	0.0781190	−	0.240426i
$316$	7.96897	+	24.5260i	0.448290	+	1.37969i
$317$	−1.59141	+	1.15623i	−0.0893828	+	0.0649404i	−0.631579	−	0.775311i	$-0.717593\pi$
$317$	−1.59141	+	1.15623i	−0.0893828	+	0.0649404i	0.542196	+	0.840252i	$0.317593\pi$
$318$	3.81753			0.214077
$319$	8.10693	−	1.94538i	0.453901	−	0.108920i
$320$	4.36407			0.243959
$321$	−5.14456	+	3.73774i	−0.287141	+	0.208620i
$322$	23.3943	+	72.0003i	1.30371	+	4.01242i
$323$	0.452025	−	1.39119i	0.0251513	−	0.0774079i
$324$	0.621548	+	0.451581i	0.0345304	+	0.0250878i
$325$	22.9858	+	16.7001i	1.27502	+	0.926357i
$326$	−15.1428	+	46.6049i	−0.838684	+	2.58120i
$327$	−2.51278	−	7.73355i	−0.138957	−	0.427666i
$328$	−30.0765	+	21.8519i	−1.66070	+	1.20657i
$329$	37.7205			2.07960
$330$	−3.32206	+	3.88878i	−0.182873	+	0.214071i
$331$	−33.3980			−1.83572			−0.917861	−	0.396901i	$-0.870085\pi$
$331$	−33.3980			−1.83572			−0.917861	+	0.396901i	$0.870085\pi$
$332$	24.9680	−	18.1403i	1.37030	−	0.995579i
$333$	1.93899	+	5.96760i	0.106256	+	0.327022i
$334$	−4.28293	+	13.1815i	−0.234352	+	0.721260i
$335$	−3.56536	−	2.59039i	−0.194796	−	0.141528i
$336$	37.9574	+	27.5776i	2.07074	+	1.50448i
$337$	−3.59162	+	11.0539i	−0.195648	+	0.602143i	0.804320	+	0.594196i	$0.202530\pi$
$337$	−3.59162	+	11.0539i	−0.195648	+	0.602143i	−0.999968	+	0.00794714i	$0.997470\pi$
$338$	−18.9827	−	58.4227i	−1.03252	−	3.17778i
$339$	−8.16648	+	5.93330i	−0.443543	+	0.322253i
$340$	2.63460			0.142881
$341$	5.18778	+	2.14950i	0.280934	+	0.116402i
$342$	6.99616			0.378309
$343$	22.4719	−	16.3268i	1.21337	−	0.881565i
$344$	−15.1675	−	46.6807i	−0.817776	−	2.51686i
$345$	1.17602	−	3.61942i	0.0633148	−	0.194863i
$346$	7.49687	+	5.44679i	0.403034	+	0.292821i
$347$	−8.25441	−	5.99718i	−0.443120	−	0.321946i	0.343753	−	0.939060i	$-0.388302\pi$
$347$	−8.25441	−	5.99718i	−0.443120	−	0.321946i	−0.786873	+	0.617114i	$0.788302\pi$
$348$	−4.05636	+	12.4842i	−0.217443	+	0.669222i
$349$	−6.83853	−	21.0468i	−0.366058	−	1.12661i	−0.949316	−	0.314324i	$-0.898222\pi$
$349$	−6.83853	−	21.0468i	−0.366058	−	1.12661i	0.583257	−	0.812287i	$-0.301778\pi$
$350$	44.6595	−	32.4470i	2.38715	−	1.73437i
$351$	−31.5650			−1.68482
$352$	18.1082	+	29.5571i	0.965172	+	1.57540i
$353$	−7.23587			−0.385126			−0.192563	−	0.981285i	$-0.561680\pi$
$353$	−7.23587			−0.385126			−0.192563	+	0.981285i	$0.561680\pi$
$354$	−15.3542	+	11.1555i	−0.816068	+	0.592908i
$355$	1.27894	+	3.93617i	0.0678790	+	0.208910i
$356$	4.92489	−	15.1573i	0.261019	−	0.803333i
$357$	3.93085	+	2.85593i	0.208043	+	0.151152i
$358$	54.2916	+	39.4452i	2.86940	+	2.08474i
$359$	−2.36559	+	7.28053i	−0.124851	+	0.384252i	−0.993874	−	0.110520i	$-0.964748\pi$
$359$	−2.36559	+	7.28053i	−0.124851	+	0.384252i	0.869023	+	0.494772i	$0.164748\pi$
$360$	2.28093	+	7.01997i	0.120215	+	0.369985i
$361$	13.6402	−	9.91021i	0.717907	−	0.521590i
$362$	9.42387			0.495308
$363$	−11.7499	−	1.86359i	−0.616712	−	0.0978132i
$364$	−131.064			−6.86964
$365$	−4.11467	+	2.98949i	−0.215372	+	0.156477i
$366$	−1.77629	−	5.46686i	−0.0928481	−	0.285757i
$367$	6.02057	−	18.5294i	0.314271	−	0.967227i	−0.661782	−	0.749696i	$-0.730200\pi$
$367$	6.02057	−	18.5294i	0.314271	−	0.967227i	0.976053	−	0.217531i	$-0.0698003\pi$
$368$	−50.3785	−	36.6021i	−2.62616	−	1.90802i
$369$	−7.44833	−	5.41153i	−0.387744	−	0.281713i
$370$	1.51053	−	4.64892i	0.0785285	−	0.241686i
$371$	1.87526	+	5.77146i	0.0973586	+	0.299639i
$372$	−7.15292	+	5.19690i	−0.370862	+	0.269447i
$373$	16.6416			0.861671			0.430836	−	0.902430i	$-0.358219\pi$
$373$	16.6416			0.861671			0.430836	+	0.902430i	$0.358219\pi$
$374$	4.52755	+	7.39007i	0.234114	+	0.382131i
$375$	−5.72568			−0.295673
$376$	−50.2035	+	36.4750i	−2.58905	+	1.88105i
$377$	−4.69347	−	14.4450i	−0.241726	−	0.743956i
$378$	−18.9515	+	58.3267i	−0.974760	+	3.00000i
$379$	−11.1171	−	8.07708i	−0.571049	−	0.414892i	0.264437	−	0.964403i	$-0.414814\pi$
$379$	−11.1171	−	8.07708i	−0.571049	−	0.414892i	−0.835486	+	0.549511i	$0.814814\pi$
$380$	−3.11783	−	2.26524i	−0.159941	−	0.116204i
$381$	0.195729	−	0.602390i	0.0100275	−	0.0308614i
$382$	13.7802	+	42.4112i	0.705059	+	2.16995i
$383$	−4.41877	+	3.21043i	−0.225789	+	0.164045i	−0.694929	−	0.719079i	$-0.744564\pi$
$383$	−4.41877	+	3.21043i	−0.225789	+	0.164045i	0.469140	+	0.883124i	$0.344564\pi$
$384$	0.00349277			0.000178240
$385$	−7.51104	−	3.11212i	−0.382798	−	0.158608i
$386$	1.23503			0.0628612
$387$	9.83377	−	7.14465i	0.499878	−	0.363183i
$388$	15.7556	+	48.4907i	0.799868	+	2.46174i
$389$	11.9768	−	36.8608i	0.607248	−	1.86892i	0.126715	−	0.991939i	$-0.459557\pi$
$389$	11.9768	−	36.8608i	0.607248	−	1.86892i	0.480532	−	0.876977i	$-0.340443\pi$
$390$	7.53814	+	5.47678i	0.381708	+	0.277327i
$391$	−5.21718	−	3.79050i	−0.263844	−	0.191694i
$392$	−30.1081	+	92.6633i	−1.52069	+	4.68020i
$393$	1.49532	+	4.60213i	0.0754291	+	0.232147i
$394$	−7.40530	+	5.38026i	−0.373073	+	0.271054i
$395$	2.91432			0.146635
$396$	−19.0378	+	22.2855i	−0.956683	+	1.11989i
$397$	−1.63130			−0.0818728			−0.0409364	−	0.999162i	$-0.513034\pi$
$397$	−1.63130			−0.0818728			−0.0409364	+	0.999162i	$0.513034\pi$
$398$	34.9991	−	25.4283i	1.75435	−	1.27461i
$399$	−2.19630	−	6.75952i	−0.109953	−	0.338399i
$400$	−14.0313	+	43.1839i	−0.701566	+	2.15920i
$401$	8.08481	+	5.87396i	0.403736	+	0.293332i	0.771061	−	0.636761i	$-0.219726\pi$
$401$	8.08481	+	5.87396i	0.403736	+	0.293332i	−0.367325	+	0.930093i	$0.619726\pi$
$402$	18.4664	+	13.4166i	0.921021	+	0.669161i
$403$	3.16130	−	9.72949i	0.157476	−	0.484660i
$404$	6.26869	+	19.2931i	0.311879	+	0.959865i
$405$	0.0702412	−	0.0510332i	0.00349031	−	0.00253586i
$406$	−29.5098			−1.46455
$407$	11.0563	−	2.65313i	0.548041	−	0.131511i
$408$	−7.99335			−0.395730
$409$	23.2905	−	16.9216i	1.15164	−	0.836717i	0.162944	−	0.986635i	$-0.447901\pi$
$409$	23.2905	−	16.9216i	1.15164	−	0.836717i	0.988698	+	0.149918i	$0.0479009\pi$
$410$	2.21634	+	6.82118i	0.109457	+	0.336874i
$411$	4.64066	−	14.2825i	0.228907	−	0.704502i
$412$	−44.9599	−	32.6653i	−2.21502	−	1.60930i
$413$	−24.4075	−	17.7331i	−1.20102	−	0.872589i
$414$	9.53104	−	29.3335i	0.468425	−	1.44166i
$415$	−1.07777	−	3.31703i	−0.0529056	−	0.162827i
$416$	51.0884	−	37.1179i	2.50482	−	1.81986i
$417$	16.4032			0.803269
$418$	0.996023	−	12.6383i	0.0487171	−	0.618161i
$419$	0.0109356			0.000534237			0.000267119	−	1.00000i	$-0.499915\pi$
$419$	0.0109356			0.000534237			0.000267119		1.00000i	$0.499915\pi$
$420$	10.3562	−	7.52425i	0.505333	−	0.367146i
$421$	8.13040	+	25.0228i	0.396252	+	1.21954i	0.927982	+	0.372624i	$0.121542\pi$
$421$	8.13040	+	25.0228i	0.396252	+	1.21954i	−0.531731	+	0.846913i	$0.678458\pi$
$422$	−6.25588	+	19.2536i	−0.304531	+	0.937251i
$423$	−12.4327	−	9.03287i	−0.604498	−	0.439193i
$424$	−8.07674	−	5.86809i	−0.392241	−	0.284980i
$425$	−1.45308	+	4.47212i	−0.0704847	+	0.216930i
$426$	−6.62413	−	20.3870i	−0.320940	−	0.987753i
$427$	7.39239	−	5.37089i	0.357743	−	0.259915i
$428$	28.3891			1.37224
$429$	−1.70280	+	21.6065i	−0.0822119	+	1.04317i
$430$	−9.46923			−0.456647
$431$	0.0677529	−	0.0492254i	0.00326354	−	0.00237110i	−0.586152	−	0.810201i	$-0.699358\pi$
$431$	0.0677529	−	0.0492254i	0.00326354	−	0.00237110i	0.589416	+	0.807830i	$0.299358\pi$
$432$	−15.5885	−	47.9763i	−0.750000	−	2.30826i
$433$	−6.41678	+	19.7488i	−0.308371	+	0.949067i	0.670027	+	0.742336i	$0.266282\pi$
$433$	−6.41678	+	19.7488i	−0.308371	+	0.949067i	−0.978398	+	0.206731i	$0.933718\pi$
$434$	−16.0804	−	11.6831i	−0.771883	−	0.560806i
$435$	1.20013	+	0.871947i	0.0575419	+	0.0418066i
$436$	−11.2180	+	34.5255i	−0.537246	+	1.65347i
$437$	2.91501	+	8.97149i	0.139444	+	0.429165i
$438$	21.3115	−	15.4837i	1.01830	−	0.739841i
$439$	−21.4420			−1.02337			−0.511686	−	0.859173i	$-0.670979\pi$
$439$	−21.4420			−1.02337			−0.511686	+	0.859173i	$0.670979\pi$
$440$	13.0061	−	3.12101i	0.620040	−	0.148788i
$441$	−24.1286			−1.14898
$442$	12.7735	−	9.28049i	0.607574	−	0.441428i
$443$	−1.66394	−	5.12109i	−0.0790562	−	0.243310i	0.903716	−	0.428133i	$-0.140829\pi$
$443$	−1.66394	−	5.12109i	−0.0790562	−	0.243310i	−0.982772	+	0.184823i	$0.940829\pi$
$444$	−5.53210	+	17.0261i	−0.262542	+	0.808021i
$445$	−1.45710	−	1.05865i	−0.0690732	−	0.0501846i
$446$	13.1788	+	9.57499i	0.624037	+	0.453389i
$447$	−3.69114	+	11.3601i	−0.174585	+	0.537316i
$448$	−11.1032	−	34.1722i	−0.524578	−	1.61449i
$449$	31.9702	−	23.2277i	1.50877	−	1.09618i	0.542046	−	0.840349i	$-0.317650\pi$
$449$	31.9702	−	23.2277i	1.50877	−	1.09618i	0.966721	−	0.255835i	$-0.0823502\pi$
$450$	−22.4898			−1.06018
$451$	−10.8361	+	12.6847i	−0.510254	+	0.597301i
$452$	45.0649			2.11968
$453$	−15.5526	+	11.2997i	−0.730727	+	0.530904i
$454$	−10.6428	−	32.7550i	−0.499489	−	1.53727i
$455$	−4.57704	+	14.0867i	−0.214575	+	0.660394i
$456$	9.45946	+	6.87270i	0.442980	+	0.321844i
$457$	2.61127	+	1.89720i	0.122150	+	0.0887472i	0.647183	−	0.762335i	$-0.275947\pi$
$457$	2.61127	+	1.89720i	0.122150	+	0.0887472i	−0.525033	+	0.851082i	$0.675947\pi$
$458$	10.8418	−	33.3675i	0.506602	−	1.55916i
$459$	−1.61434	−	4.96842i	−0.0753508	−	0.231906i
$460$	−13.7452	+	9.98647i	−0.640873	+	0.465621i
$461$	1.94548			0.0906099			0.0453050	−	0.998973i	$-0.485574\pi$
$461$	1.94548			0.0906099			0.0453050	+	0.998973i	$0.485574\pi$
$462$	38.9027	+	16.1189i	1.80992	+	0.749920i
$463$	20.3799			0.947136			0.473568	−	0.880757i	$-0.342966\pi$
$463$	20.3799			0.947136			0.473568	+	0.880757i	$0.342966\pi$
$464$	19.6374	−	14.2674i	0.911643	−	0.662348i
$465$	0.308763	+	0.950275i	0.0143186	+	0.0440680i
$466$	15.3164	−	47.1389i	0.709517	−	2.18367i
$467$	−10.3017	−	7.48464i	−0.476707	−	0.346348i	0.323342	−	0.946282i	$-0.395193\pi$
$467$	−10.3017	−	7.48464i	−0.476707	−	0.346348i	−0.800049	+	0.599934i	$0.795193\pi$
$468$	43.1989	+	31.3858i	1.99687	+	1.45081i
$469$	−11.2125	+	34.5086i	−0.517746	+	1.59346i
$470$	3.69949	+	11.3859i	0.170645	+	0.525191i
$471$	−8.11758	+	5.89777i	−0.374039	+	0.271755i
$472$	49.6324			2.28452
$473$	−11.5066	−	18.7815i	−0.529073	−	0.863576i
$474$	−15.0944			−0.693310
$475$	5.56474	−	4.04302i	0.255328	−	0.185506i
$476$	−6.70305	−	20.6299i	−0.307234	−	0.945569i
$477$	0.763997	−	2.35134i	0.0349810	−	0.107660i
$478$	−21.6471	−	15.7275i	−0.990114	−	0.719360i
$479$	10.8109	+	7.85460i	0.493964	+	0.358886i	0.806707	−	0.590952i	$-0.201248\pi$
$479$	10.8109	+	7.85460i	0.493964	+	0.358886i	−0.312743	+	0.949838i	$0.601248\pi$
$480$	−1.90593	+	5.86585i	−0.0869934	+	0.267738i
$481$	−6.40101	−	19.7003i	−0.291861	−	0.898255i
$482$	−56.5348	+	41.0749i	−2.57509	+	1.87091i
$483$	−31.3334			−1.42572
$484$	37.5477	+	37.5638i	1.70671	+	1.70745i
$485$	5.76195			0.261637
$486$	32.7682	−	23.8075i	1.48640	−	1.07993i
$487$	1.88191	+	5.79193i	0.0852776	+	0.262457i	0.984598	−	0.174832i	$-0.0559384\pi$
$487$	1.88191	+	5.79193i	0.0852776	+	0.262457i	−0.899321	+	0.437290i	$0.855938\pi$
$488$	−4.64525	+	14.2966i	−0.210281	+	0.647177i
$489$	−16.4083	−	11.9213i	−0.742007	−	0.539099i
$490$	15.2070	+	11.0485i	0.686980	+	0.499120i
$491$	−5.18344	+	15.9530i	−0.233925	+	0.719948i	0.763337	+	0.646001i	$0.223560\pi$
$491$	−5.18344	+	15.9530i	−0.233925	+	0.719948i	−0.997262	+	0.0739475i	$0.976440\pi$
$492$	−8.11705	−	24.9817i	−0.365945	−	1.12626i
$493$	2.03364	−	1.47753i	0.0915907	−	0.0665445i
$494$	−23.0958			−1.03913
$495$	1.73039	+	2.82442i	0.0777751	+	0.126948i
$496$	16.3493			0.734104
$497$	27.5677	−	20.0291i	1.23658	−	0.898428i
$498$	5.58220	+	17.1802i	0.250144	+	0.769865i
$499$	10.5119	−	32.3522i	0.470576	−	1.44828i	−0.381257	−	0.924469i	$-0.624509\pi$
$499$	10.5119	−	32.3522i	0.470576	−	1.44828i	0.851833	−	0.523814i	$-0.175491\pi$
$500$	20.6798	+	15.0247i	0.924827	+	0.671926i
$501$	−4.64084	−	3.37176i	−0.207337	−	0.150639i
$502$	12.1098	−	37.2702i	0.540488	−	1.66345i
$503$	9.94096	+	30.5951i	0.443246	+	1.36417i	0.884396	+	0.466737i	$0.154571\pi$
$503$	9.94096	+	30.5951i	0.443246	+	1.36417i	−0.441150	+	0.897433i	$0.645429\pi$
$504$	49.1657	−	35.7210i	2.19001	−	1.59114i
$505$	2.29251			0.102016
$506$	−51.6331	−	21.3936i	−2.29537	−	0.951063i
$507$	25.4247			1.12915
$508$	−2.28765	+	1.66208i	−0.101498	+	0.0737428i
$509$	−9.54636	−	29.3807i	−0.423135	−	1.30228i	−0.904769	−	0.425903i	$-0.859956\pi$
$509$	−9.54636	−	29.3807i	−0.423135	−	1.30228i	0.481634	−	0.876373i	$-0.340044\pi$
$510$	−0.476534	+	1.46662i	−0.0211013	+	0.0649431i
$511$	33.8775	+	24.6134i	1.49865	+	1.08883i
$512$	−33.8285	−	24.5779i	−1.49502	−	1.08620i
$513$	−2.36142	+	7.26772i	−0.104259	+	0.320878i
$514$	19.2855	+	59.3545i	0.850645	+	2.61802i
$515$	−5.08093	+	3.69151i	−0.223893	+	0.162667i
$516$	34.6798			1.52669
$517$	−18.0876	+	21.1732i	−0.795491	+	0.931198i
$518$	−40.2458			−1.76830
$519$	−3.10284	+	2.25435i	−0.136200	+	0.0989548i
$520$	−7.52981	−	23.1744i	−0.330204	−	1.01626i
$521$	7.14466	−	21.9890i	0.313013	−	0.963356i	−0.663551	−	0.748131i	$-0.730951\pi$
$521$	7.14466	−	21.9890i	0.313013	−	0.963356i	0.976564	−	0.215225i	$-0.0690485\pi$
$522$	9.72645	+	7.06668i	0.425715	+	0.309300i
$523$	24.7087	+	17.9520i	1.08044	+	0.784984i	0.977759	−	0.209730i	$-0.0672587\pi$
$523$	24.7087	+	17.9520i	1.08044	+	0.784984i	0.102679	+	0.994715i	$0.467259\pi$
$524$	6.67569	−	20.5457i	0.291629	−	0.897542i
$525$	7.06023	+	21.7291i	0.308134	+	0.948337i
$526$	28.3565	−	20.6022i	1.23640	−	0.898298i
$527$	1.69313			0.0737537
$528$	−33.6811	+	8.08229i	−1.46578	+	0.351736i
$529$	18.5869			0.808125
$530$	−1.55819	+	1.13209i	−0.0676833	+	0.0491748i
$531$	3.79821	+	11.6897i	0.164828	+	0.507289i
$532$	−9.80512	+	30.1771i	−0.425106	+	1.30834i
$533$	24.5885	+	17.8646i	1.06504	+	0.773800i
$534$	7.54691	+	5.48315i	0.326587	+	0.237279i
$535$	0.991405	−	3.05123i	0.0428622	−	0.131916i
$536$	−18.4460	−	56.7710i	−0.796747	−	2.45213i
$537$	−22.4705	+	16.3258i	−0.969674	+	0.704509i
$538$	27.2591			1.17522
$539$	−3.43512	+	43.5875i	−0.147961	+	1.87745i
$540$	−13.7634			−0.592284
$541$	−3.12068	+	2.26731i	−0.134169	+	0.0974792i	−0.652845	−	0.757491i	$-0.726425\pi$
$541$	−3.12068	+	2.26731i	−0.134169	+	0.0974792i	0.518677	+	0.854970i	$0.326425\pi$
$542$	−7.81722	−	24.0589i	−0.335778	−	1.03342i
$543$	−1.20529	+	3.70950i	−0.0517239	+	0.159190i
$544$	8.45528	+	6.14312i	0.362517	+	0.263384i
$545$	3.31901	+	2.41140i	0.142171	+	0.103293i
$546$	23.7063	−	72.9605i	1.01454	−	3.12242i
$547$	−1.76597	−	5.43509i	−0.0755074	−	0.232388i	0.906178	−	0.422896i	$-0.138986\pi$
$547$	−1.76597	−	5.43509i	−0.0755074	−	0.232388i	−0.981686	+	0.190508i	$0.938986\pi$
$548$	−54.2395	+	39.4073i	−2.31700	+	1.68340i
$549$	−3.72270			−0.158881
$550$	−3.20181	+	40.6272i	−0.136526	+	1.73235i
$551$	−3.67703			−0.156647
$552$	41.7027	−	30.2988i	1.77499	−	1.28960i
$553$	−7.41473	−	22.8202i	−0.315306	−	0.970413i
$554$	−20.3491	+	62.6280i	−0.864550	+	2.66081i
$555$	1.63675	+	1.18917i	0.0694763	+	0.0504775i
$556$	−59.2444	−	43.0436i	−2.51252	−	1.82546i
$557$	1.37919	−	4.24472i	0.0584383	−	0.179855i	−0.917576	−	0.397560i	$-0.869857\pi$
$557$	1.37919	−	4.24472i	0.0584383	−	0.179855i	0.976015	+	0.217705i	$0.0698571\pi$
$558$	2.50237	+	7.70150i	0.105934	+	0.326030i
$559$	−32.4633	+	23.5860i	−1.37305	+	0.997580i
$560$	−23.6710			−1.00028
$561$	−3.48800	+	0.836999i	−0.147264	+	0.0353381i
$562$	−56.0429			−2.36403
$563$	−6.50204	+	4.72401i	−0.274028	+	0.199093i	−0.716309	−	0.697784i	$-0.754170\pi$
$563$	−6.50204	+	4.72401i	−0.274028	+	0.199093i	0.442280	+	0.896877i	$0.354170\pi$
$564$	−13.5489	−	41.6992i	−0.570512	−	1.75585i
$565$	1.57376	−	4.84353i	0.0662086	−	0.203769i
$566$	19.5752	+	14.2222i	0.822805	+	0.597803i
$567$	−0.578319	−	0.420173i	−0.0242871	−	0.0176456i
$568$	−17.3231	+	53.3149i	−0.726859	+	2.23704i
$569$	−3.09421	−	9.52300i	−0.129716	−	0.399225i	0.865015	−	0.501746i	$-0.167309\pi$
$569$	−3.09421	−	9.52300i	−0.129716	−	0.399225i	−0.994731	+	0.102522i	$0.967309\pi$
$570$	1.82494	−	1.32590i	0.0764385	−	0.0555358i
$571$	18.0279			0.754445			0.377222	−	0.926123i	$-0.376879\pi$
$571$	18.0279			0.754445			0.377222	+	0.926123i	$0.376879\pi$
$572$	62.8476	−	73.5691i	2.62779	−	3.07608i
$573$	−18.4567			−0.771040
$574$	47.7734	−	34.7094i	1.99402	−	1.44874i
$575$	−9.37060	−	28.8397i	−0.390781	−	1.20270i
$576$	−4.52355	+	13.9221i	−0.188481	+	0.580086i
$577$	−7.41593	−	5.38799i	−0.308729	−	0.224305i	0.422622	−	0.906306i	$-0.361110\pi$
$577$	−7.41593	−	5.38799i	−0.308729	−	0.224305i	−0.731351	+	0.682001i	$0.761110\pi$
$578$	2.11405	+	1.53595i	0.0879329	+	0.0638870i
$579$	−0.157957	+	0.486141i	−0.00656446	+	0.0202033i
$580$	−2.04651	−	6.29852i	−0.0849769	−	0.261532i
$581$	−23.2315	+	16.8786i	−0.963804	+	0.700244i
$582$	−29.8434			−1.23705
$583$	−4.13885	−	1.71489i	−0.171414	−	0.0710234i
$584$	−68.8894			−2.85066
$585$	4.88192	−	3.54692i	0.201842	−	0.146647i
$586$	−15.9234	−	49.0072i	−0.657790	−	2.02447i
$587$	−13.6646	+	42.0552i	−0.563997	+	1.73580i	0.106917	+	0.994268i	$0.465902\pi$
$587$	−13.6646	+	42.0552i	−0.563997	+	1.73580i	−0.670914	+	0.741536i	$0.734098\pi$
$588$	−55.6935	−	40.4637i	−2.29676	−	1.66869i
$589$	−2.00367	−	1.45575i	−0.0825599	−	0.0599833i
$590$	2.95891	−	9.10658i	0.121816	−	0.374912i
$591$	−1.17070	−	3.60305i	−0.0481563	−	0.148210i
$592$	26.7817	−	19.4580i	1.10072	−	0.799721i
$593$	8.61665			0.353844			0.176922	−	0.984225i	$-0.443386\pi$
$593$	8.61665			0.353844			0.176922	+	0.984225i	$0.443386\pi$
$594$	−23.6524	−	38.6065i	−0.970469	−	1.58404i
$595$	−2.45136			−0.100496
$596$	43.1416	−	31.3442i	1.76715	−	1.28391i
$597$	5.53301	+	17.0288i	0.226451	+	0.696944i
$598$	−31.4639	+	96.8360i	−1.28666	+	3.95992i
$599$	−30.4388	−	22.1151i	−1.24369	−	0.903597i	−0.245856	−	0.969306i	$-0.579069\pi$
$599$	−30.4388	−	22.1151i	−1.24369	−	0.903597i	−0.997839	+	0.0657095i	$0.979069\pi$
$600$	−30.4084	−	22.0930i	−1.24142	−	0.901942i
$601$	−1.12028	+	3.44788i	−0.0456973	+	0.140642i	−0.971302	−	0.237850i	$-0.923557\pi$
$601$	−1.12028	+	3.44788i	−0.0456973	+	0.140642i	0.925605	+	0.378492i	$0.123557\pi$
$602$	24.0920	+	74.1475i	0.981915	+	3.02203i
$603$	11.9594	−	8.68900i	0.487024	−	0.353843i
$604$	85.8237			3.49212
$605$	5.34857	−	2.72378i	0.217450	−	0.110738i
$606$	−11.8738			−0.482342
$607$	−12.0960	+	8.78823i	−0.490960	+	0.356703i	−0.805553	−	0.592523i	$-0.798132\pi$
$607$	−12.0960	+	8.78823i	−0.490960	+	0.356703i	0.314593	+	0.949227i	$0.398132\pi$
$608$	−4.72425	−	14.5398i	−0.191594	−	0.589665i
$609$	3.77423	−	11.6159i	0.152940	−	0.470700i
$610$	2.34621	+	1.70462i	0.0949954	+	0.0690182i
$611$	41.0429	+	29.8194i	1.66042	+	1.20636i
$612$	−2.73088	+	8.40479i	−0.110389	+	0.339743i
$613$	−2.22238	−	6.83979i	−0.0897612	−	0.276257i	0.896092	−	0.443869i	$-0.146394\pi$
$613$	−2.22238	−	6.83979i	−0.0897612	−	0.276257i	−0.985853	+	0.167612i	$0.946394\pi$
$614$	−38.2902	+	27.8195i	−1.54527	+	1.12270i
$615$	−2.96847			−0.119700
$616$	−57.5292	−	93.9017i	−2.31792	−	3.78341i
$617$	43.9345			1.76874			0.884368	−	0.466791i	$-0.154590\pi$
$617$	43.9345			1.76874			0.884368	+	0.466791i	$0.154590\pi$
$618$	26.3162	−	19.1198i	1.05859	−	0.769111i
$619$	4.57229	+	14.0721i	0.183776	+	0.565604i	0.999925	−	0.0122372i	$-0.00389531\pi$
$619$	4.57229	+	14.0721i	0.183776	+	0.565604i	−0.816149	+	0.577841i	$0.803895\pi$
$620$	1.37844	−	4.24239i	0.0553593	−	0.170378i
$621$	27.2551	+	19.8020i	1.09371	+	0.794626i
$622$	−59.6237	−	43.3192i	−2.39069	−	1.73694i
$623$	−4.58237	+	14.1031i	−0.183589	+	0.565028i
$624$	19.4995	+	60.0133i	0.780605	+	2.40246i
$625$	−16.6840	+	12.1217i	−0.667361	+	0.484866i
$626$	−77.6579			−3.10383
$627$	4.84742	+	2.00847i	0.193587	+	0.0802107i
$628$	44.7951			1.78752
$629$	2.77351	−	2.01507i	0.110587	−	0.0803461i
$630$	−3.62301	−	11.1505i	−0.144344	−	0.444246i
$631$	−6.97698	+	21.4729i	−0.277749	+	0.854824i	0.710730	+	0.703465i	$0.248365\pi$
$631$	−6.97698	+	21.4729i	−0.277749	+	0.854824i	−0.988479	+	0.151359i	$0.951635\pi$
$632$	31.9352	+	23.2023i	1.27031	+	0.922938i
$633$	−6.77865	−	4.92498i	−0.269427	−	0.195750i
$634$	−1.58842	+	4.88866i	−0.0630843	+	0.194154i
$635$	0.0987490	+	0.303918i	0.00391873	+	0.0120606i
$636$	5.70665	−	4.14613i	0.226284	−	0.164405i
$637$	79.6535			3.15599
$638$	14.1505	−	16.5645i	0.560222	−	0.655793i
$639$	−13.8827			−0.549190
$640$	−0.00142563	+	0.00103578i	−5.63530e−5	+	4.09428e-5i
$641$	−6.35776	−	19.5672i	−0.251117	−	0.772857i	−0.994570	−	0.104070i	$-0.966814\pi$
$641$	−6.35776	−	19.5672i	−0.251117	−	0.772857i	0.743453	−	0.668788i	$-0.233186\pi$
$642$	−5.13488	+	15.8035i	−0.202658	+	0.623716i
$643$	27.5126	+	19.9891i	1.08499	+	0.788292i	0.978546	−	0.206026i	$-0.0660533\pi$
$643$	27.5126	+	19.9891i	1.08499	+	0.788292i	0.106445	+	0.994319i	$0.466053\pi$
$644$	113.169	+	82.2218i	4.45947	+	3.23999i
$645$	1.21109	−	3.72736i	0.0476867	−	0.146764i
$646$	−1.18119	−	3.63533i	−0.0464734	−	0.143030i
$647$	−16.5211	+	12.0033i	−0.649513	+	0.471899i	−0.863105	−	0.505024i	$-0.831484\pi$
$647$	−16.5211	+	12.0033i	−0.649513	+	0.471899i	0.213592	+	0.976923i	$0.431484\pi$
$648$	1.17601			0.0461978
$649$	21.6578	−	5.19711i	0.850142	−	0.204004i
$650$	74.2437			2.91208
$651$	6.65543	−	4.83545i	0.260847	−	0.189516i
$652$	27.9800	+	86.1137i	1.09578	+	3.37247i
$653$	0.0750780	−	0.231066i	0.00293803	−	0.00904233i	−0.949577	−	0.313535i	$-0.898487\pi$
$653$	0.0750780	−	0.231066i	0.00293803	−	0.00904233i	0.952515	+	0.304492i	$0.0984868\pi$
$654$	−17.1905	−	12.4896i	−0.672201	−	0.488383i
$655$	−1.97510	−	1.43499i	−0.0771736	−	0.0560699i
$656$	−15.0097	+	46.1950i	−0.586029	+	1.80361i
$657$	−5.27188	−	16.2252i	−0.205676	−	0.633005i
$658$	79.7430	−	57.9367i	3.10871	−	2.25861i
$659$	−21.2824			−0.829046			−0.414523	−	0.910039i	$-0.636052\pi$
$659$	−21.2824			−0.829046			−0.414523	+	0.910039i	$0.636052\pi$
$660$	−0.742479	+	9.42116i	−0.0289009	+	0.366718i
$661$	6.30652			0.245295			0.122648	−	0.992450i	$-0.460862\pi$
$661$	6.30652			0.245295			0.122648	+	0.992450i	$0.460862\pi$
$662$	−70.6052	+	51.2977i	−2.74415	+	1.99374i
$663$	2.01936	+	6.21496i	0.0784256	+	0.241369i
$664$	14.5982	−	44.9288i	0.566522	−	1.74357i
$665$	2.90099	+	2.10769i	0.112495	+	0.0817327i
$666$	13.2650	+	9.63762i	0.514010	+	0.373450i
$667$	−5.00931	+	15.4171i	−0.193961	+	0.596951i
$668$	7.91374	+	24.3560i	0.306192	+	0.942362i
$669$	−5.45453	+	3.96295i	−0.210884	+	0.153216i
$670$	−11.5161			−0.444904
$671$	−0.529989	+	6.72493i	−0.0204600	+	0.259613i
$672$	50.7808			1.95891
$673$	24.3637	−	17.7013i	0.939152	−	0.682334i	−0.00906406	−	0.999959i	$-0.502885\pi$
$673$	24.3637	−	17.7013i	0.939152	−	0.682334i	0.948217	+	0.317625i	$0.102885\pi$
$674$	9.38531	+	28.8850i	0.361509	+	1.11261i
$675$	7.59103	−	23.3628i	0.292179	−	0.899234i
$676$	−91.8277	−	66.7167i	−3.53184	−	2.56603i
$677$	−19.8762	−	14.4409i	−0.763903	−	0.555008i	0.136202	−	0.990681i	$-0.456510\pi$
$677$	−19.8762	−	14.4409i	−0.763903	−	0.555008i	−0.900105	+	0.435673i	$0.856510\pi$
$678$	−8.15113	+	25.0866i	−0.313042	+	0.963445i
$679$	−14.6598	−	45.1181i	−0.562590	−	1.73148i
$680$	3.26261	−	2.37042i	0.125115	−	0.0909016i
$681$	14.2545			0.546233
$682$	14.2688	−	3.42401i	0.546379	−	0.131112i
$683$	0.0972209			0.00372006			0.00186003	−	0.999998i	$-0.499408\pi$
$683$	0.0972209			0.00372006			0.00186003	+	0.999998i	$0.499408\pi$
$684$	10.4582	−	7.59835i	0.399881	−	0.290530i
$685$	2.34131	+	7.20580i	0.0894567	+	0.275319i
$686$	22.4297	−	69.0315i	0.856369	−	2.63563i
$687$	11.7478	+	8.53524i	0.448205	+	0.325640i
$688$	−51.8809	−	37.6937i	−1.97794	−	1.43706i
$689$	−2.52211	+	7.76226i	−0.0960848	+	0.295719i
$690$	−3.07307	−	9.45794i	−0.116990	−	0.360057i
$691$	3.98217	−	2.89322i	0.151489	−	0.110063i	−0.509459	−	0.860495i	$-0.670154\pi$
$691$	3.98217	−	2.89322i	0.151489	−	0.110063i	0.660948	+	0.750432i	$0.270154\pi$
$692$	17.1223			0.650894
$693$	17.7137	−	20.7355i	0.672887	−	0.787678i
$694$	−26.6616			−1.01206
$695$	−6.69523	+	4.86437i	−0.253964	+	0.184516i
$696$	6.20910	+	19.1096i	0.235355	+	0.724349i
$697$	−1.55440	+	4.78394i	−0.0588769	+	0.181205i
$698$	−46.7839	−	33.9905i	−1.77080	−	1.28656i
$699$	16.5963	+	12.0579i	0.627729	+	0.456072i
$700$	31.5195	−	97.0071i	1.19133	−	3.66652i
$701$	−12.0810	−	37.1816i	−0.456295	−	1.40433i	−0.869608	−	0.493742i	$-0.835629\pi$
$701$	−12.0810	−	37.1816i	−0.456295	−	1.40433i	0.413314	−	0.910589i	$-0.364371\pi$
$702$	−66.7301	+	48.4822i	−2.51856	+	1.82984i
$703$	−5.01478			−0.189136
$704$	24.5057	+	10.1537i	0.923595	+	0.382682i
$705$	−4.95495			−0.186614
$706$	−15.2970	+	11.1139i	−0.575710	+	0.418278i
$707$	−5.83270	−	17.9512i	−0.219361	−	0.675125i
$708$	−10.8366	+	33.3517i	−0.407265	+	1.25343i
$709$	−7.06966	−	5.13641i	−0.265507	−	0.192902i	0.447064	−	0.894502i	$-0.352469\pi$
$709$	−7.06966	−	5.13641i	−0.265507	−	0.192902i	−0.712571	+	0.701600i	$0.752469\pi$
$710$	8.74950	+	6.35688i	0.328363	+	0.238569i
$711$	−3.02082	+	9.29714i	−0.113290	+	0.348670i
$712$	−7.53857	−	23.2013i	−0.282520	−	0.869507i
$713$	−8.83334	+	6.41780i	−0.330811	+	0.240348i
$714$	12.6966			0.475158
$715$	−5.71237	−	9.32398i	−0.213630	−	0.348697i
$716$	123.998			4.63404
$717$	8.95940	−	6.50939i	0.334595	−	0.243098i
$718$	6.18154	+	19.0248i	0.230693	+	0.710001i
$719$	6.62331	−	20.3844i	0.247008	−	0.760211i	−0.748292	−	0.663369i	$-0.769126\pi$
$719$	6.62331	−	20.3844i	0.247008	−	0.760211i	0.995300	−	0.0968420i	$-0.0308742\pi$
$720$	7.80198	+	5.66847i	0.290763	+	0.211251i
$721$	41.8330	+	30.3934i	1.55794	+	1.13191i
$722$	13.6146	−	41.9014i	0.506683	−	1.55941i
$723$	−8.93759	−	27.5071i	−0.332392	−	1.02300i
$724$	14.0873	−	10.2350i	0.523551	−	0.380382i
$725$	11.8202			0.438991
$726$	−27.7023	+	14.1076i	−1.02813	+	0.523581i
$727$	−20.0733			−0.744477			−0.372238	−	0.928137i	$-0.621410\pi$
$727$	−20.0733			−0.744477			−0.372238	+	0.928137i	$0.621410\pi$
$728$	−162.306	+	117.922i	−6.01546	+	4.37049i
$729$	5.32784	+	16.3974i	0.197328	+	0.607312i
$730$	−4.10694	+	12.6399i	−0.152005	+	0.467822i
$731$	−5.37277	−	3.90354i	−0.198719	−	0.144378i
$732$	−8.59270	−	6.24296i	−0.317595	−	0.230747i
$733$	−16.1571	+	49.7265i	−0.596777	+	1.83669i	−0.0511015	+	0.998693i	$0.516273\pi$
$733$	−16.1571	+	49.7265i	−0.596777	+	1.83669i	−0.545675	+	0.837997i	$0.683727\pi$
$734$	−15.7324	−	48.4194i	−0.580694	−	1.78719i
$735$	−6.29393	+	4.57281i	−0.232155	+	0.168671i
$736$	−67.3982			−2.48433
$737$	−13.9938	−	22.8413i	−0.515467	−	0.841369i
$738$	−24.0580			−0.885586
$739$	−37.1338	+	26.9793i	−1.36599	+	0.992449i	−0.367950	+	0.929846i	$0.619940\pi$
$739$	−37.1338	+	26.9793i	−1.36599	+	0.992449i	−0.998039	+	0.0626029i	$0.980060\pi$
$740$	−2.79106	−	8.58999i	−0.102601	−	0.315774i
$741$	2.95389	−	9.09115i	0.108514	−	0.333972i
$742$	12.8291	+	9.32085i	0.470969	+	0.342179i
$743$	18.0595	+	13.1210i	0.662537	+	0.481361i	0.867519	−	0.497404i	$-0.165713\pi$
$743$	18.0595	+	13.1210i	0.662537	+	0.481361i	−0.204982	+	0.978766i	$0.565713\pi$
$744$	−4.18216	+	12.8714i	−0.153325	+	0.471887i
$745$	−1.86225	−	5.73142i	−0.0682277	−	0.209983i
$746$	35.1813	−	25.5607i	1.28808	−	0.935843i
$747$	11.6990			0.428044
$748$	14.7942	+	6.12981i	0.540929	+	0.224128i
$749$	−26.4146			−0.965169
$750$	−12.1044	+	8.79435i	−0.441989	+	0.321124i
$751$	7.96203	+	24.5046i	0.290538	+	0.894185i	0.984684	+	0.174350i	$0.0557825\pi$
$751$	7.96203	+	24.5046i	0.290538	+	0.894185i	−0.694145	+	0.719835i	$0.744217\pi$
$752$	−25.0540	+	77.1083i	−0.913625	+	2.81185i
$753$	13.1218	+	9.53353i	0.478184	+	0.347421i
$754$	−32.1090	−	23.3286i	−1.16934	−	0.849577i
$755$	2.99714	−	9.22426i	0.109077	−	0.335705i
$756$	35.0174	+	107.773i	1.27357	+	3.91965i
$757$	4.19847	−	3.05037i	0.152596	−	0.110868i	−0.508867	−	0.860845i	$-0.669936\pi$
$757$	4.19847	−	3.05037i	0.152596	−	0.110868i	0.661464	+	0.749977i	$0.269936\pi$
$758$	−35.9082			−1.30424
$759$	15.0249	−	17.5881i	0.545369	−	0.638406i
$760$	−5.89912			−0.213984
$761$	−12.6805	+	9.21293i	−0.459668	+	0.333968i	−0.793401	−	0.608699i	$-0.791692\pi$
$761$	−12.6805	+	9.21293i	−0.459668	+	0.333968i	0.333733	+	0.942668i	$0.391692\pi$
$762$	−0.511460	−	1.57411i	−0.0185283	−	0.0570241i
$763$	10.4378	−	32.1242i	0.377874	−	1.16298i
$764$	66.6612	+	48.4322i	2.41172	+	1.75222i
$765$	0.807971	+	0.587025i	0.0292122	+	0.0212239i
$766$	−4.41046	+	13.5740i	−0.159357	+	0.490449i
$767$	−12.5387	−	38.5901i	−0.452745	−	1.39341i
$768$	14.0033	−	10.1740i	0.505300	−	0.367122i
$769$	−20.8196			−0.750774			−0.375387	−	0.926868i	$-0.622490\pi$
$769$	−20.8196			−0.750774			−0.375387	+	0.926868i	$0.622490\pi$
$770$	−20.6588	+	4.95739i	−0.744491	+	0.178652i
$771$	−25.8302			−0.930251
$772$	1.84618	−	1.34133i	0.0664456	−	0.0482756i
$773$	−2.71455	−	8.35452i	−0.0976355	−	0.300491i	0.890296	−	0.455382i	$-0.150497\pi$
$773$	−2.71455	−	8.35452i	−0.0976355	−	0.300491i	−0.987932	+	0.154891i	$0.950497\pi$
$774$	9.81527	−	30.2083i	0.352803	−	1.08582i
$775$	6.44101	+	4.67967i	0.231368	+	0.168099i
$776$	63.1396	+	45.8736i	2.26658	+	1.64677i
$777$	5.14734	−	15.8419i	0.184660	−	0.568325i
$778$	−31.2967	−	96.3213i	−1.12204	−	3.45329i
$779$	5.95274	−	4.32492i	0.213279	−	0.154956i
$780$	17.2166			0.616453
$781$	−1.97643	+	25.0786i	−0.0707224	+	0.897382i
$782$	−16.8514			−0.602605
$783$	−10.6240	+	7.71876i	−0.379669	+	0.275846i
$784$	39.3371	+	121.067i	1.40490	+	4.32382i
$785$	1.56434	−	4.81453i	0.0558336	−	0.171838i
$786$	10.2298	+	7.43241i	0.364886	+	0.265105i
$787$	22.7649	+	16.5397i	0.811481	+	0.589575i	0.914260	−	0.405129i	$-0.132773\pi$
$787$	22.7649	+	16.5397i	0.811481	+	0.589575i	−0.102779	+	0.994704i	$0.532773\pi$
$788$	−5.22646	+	16.0854i	−0.186185	+	0.573019i
$789$	4.48288	+	13.7969i	0.159595	+	0.491182i
$790$	6.16102	−	4.47625i	0.219199	−	0.159258i
$791$	−41.9306			−1.49088
$792$	−3.52488	+	44.7265i	−0.125251	+	1.58929i
$793$	12.2894			0.436409
$794$	−3.44866	+	2.50560i	−0.122388	+	0.0889203i
$795$	−0.246334	−	0.758137i	−0.00873655	−	0.0268884i
$796$	24.7014	−	76.0232i	0.875519	−	2.69457i
$797$	23.2139	+	16.8659i	0.822279	+	0.597421i	0.917364	−	0.398048i	$-0.130312\pi$
$797$	23.2139	+	16.8659i	0.822279	+	0.597421i	−0.0950853	+	0.995469i	$0.530312\pi$
$798$	−15.0254	−	10.9166i	−0.531892	−	0.386442i
$799$	−2.59458	+	7.98531i	−0.0917898	+	0.282500i
$800$	15.1866	+	46.7395i	0.536926	+	1.65249i
$801$	4.88759	−	3.55105i	0.172695	−	0.125470i
$802$	26.1138			0.922111
$803$	−30.0608	+	7.21355i	−1.06082	+	0.254561i
$804$	42.1760			1.48743
$805$	12.7892	−	9.29191i	0.450760	−	0.327497i
$806$	−8.26084	−	25.4242i	−0.290976	−	0.895531i
$807$	−3.48637	+	10.7299i	−0.122726	+	0.377712i
$808$	25.1214	+	18.2518i	0.883769	+	0.642096i
$809$	−18.6984	−	13.5852i	−0.657399	−	0.477628i	0.208384	−	0.978047i	$-0.433179\pi$
$809$	−18.6984	−	13.5852i	−0.657399	−	0.477628i	−0.865784	+	0.500419i	$0.833179\pi$
$810$	0.0701092	−	0.215774i	0.00246338	−	0.00758152i
$811$	12.0767	+	37.1682i	0.424070	+	1.30515i	0.903882	+	0.427782i	$0.140705\pi$
$811$	12.0767	+	37.1682i	0.424070	+	1.30515i	−0.479812	+	0.877371i	$0.659295\pi$
$812$	−44.1129	+	32.0499i	−1.54806	+	1.12473i
$813$	10.4701			0.367202
$814$	19.2986	−	22.5908i	0.676414	−	0.791807i
$815$	10.2325			0.358430
$816$	−8.44898	+	6.13855i	−0.295774	+	0.214892i
$817$	3.00195	+	9.23904i	0.105025	+	0.323233i
$818$	23.2467	−	71.5461i	0.812803	−	2.50155i
$819$	−40.1944	−	29.2029i	−1.40451	−	1.02043i
$820$	10.7214	+	7.78956i	0.374408	+	0.272023i
$821$	4.63312	−	14.2593i	0.161697	−	0.497652i	−0.837081	−	0.547079i	$-0.815740\pi$
$821$	4.63312	−	14.2593i	0.161697	−	0.497652i	0.998778	+	0.0494272i	$0.0157396\pi$
$822$	−12.1266	−	37.3217i	−0.422962	−	1.30174i
$823$	12.5560	−	9.12248i	0.437675	−	0.317990i	−0.347035	−	0.937852i	$-0.612812\pi$
$823$	12.5560	−	9.12248i	0.437675	−	0.317990i	0.784710	+	0.619862i	$0.212812\pi$
$824$	−85.0668			−2.96344
$825$	−15.5825	−	6.45644i	−0.542513	−	0.224784i
$826$	−78.8359			−2.74305
$827$	36.0302	−	26.1774i	1.25289	−	0.910279i	0.254505	−	0.967071i	$-0.418087\pi$
$827$	36.0302	−	26.1774i	1.25289	−	0.910279i	0.998386	+	0.0567927i	$0.0180874\pi$
$828$	−17.6109	−	54.2007i	−0.612020	−	1.88360i
$829$	−1.94412	+	5.98340i	−0.0675222	+	0.207812i	−0.979125	−	0.203261i	$-0.934846\pi$
$829$	−1.94412	+	5.98340i	−0.0675222	+	0.207812i	0.911602	+	0.411073i	$0.134846\pi$
$830$	−7.37325	−	5.35698i	−0.255929	−	0.185944i
$831$	−22.0496	−	16.0199i	−0.764891	−	0.555726i
$832$	14.9332	−	45.9596i	0.517715	−	1.59336i
$833$	4.07374	+	12.5377i	0.141147	+	0.434404i
$834$	34.6772	−	25.1945i	1.20077	−	0.872414i
$835$	2.89412			0.100155
$836$	−12.2373	−	19.9742i	−0.423235	−	0.690822i
$837$	−8.84506			−0.305730
$838$	0.0231183	−	0.0167965i	0.000798610	−	0.000580224i
$839$	5.96465	+	18.3573i	0.205923	+	0.633765i	0.999674	+	0.0255228i	$0.00812503\pi$
$839$	5.96465	+	18.3573i	0.205923	+	0.633765i	−0.793752	+	0.608242i	$0.791875\pi$
$840$	6.05507	−	18.6356i	0.208920	−	0.642989i
$841$	18.3495	+	13.3317i	0.632741	+	0.459713i
$842$	55.6218	+	40.4116i	1.91686	+	1.39268i
$843$	7.16775	−	22.0601i	0.246870	−	0.759789i
$844$	11.5592	+	35.5757i	0.397885	+	1.22457i
$845$	−10.3775	+	7.53967i	−0.356996	+	0.259373i
$846$	−40.1574			−1.38064
$847$	−34.9362	−	34.9512i	−1.20042	−	1.20094i
$848$	−13.0436			−0.447918
$849$	−8.10187	+	5.88635i	−0.278055	+	0.202019i
$850$	3.79706	+	11.6861i	0.130238	+	0.400831i
$851$	−6.83175	+	21.0260i	−0.234189	+	0.720761i
$852$	−32.0439	−	23.2812i	−1.09781	−	0.797602i
$853$	−37.9011	−	27.5368i	−1.29771	−	0.942842i	−0.297780	−	0.954635i	$-0.596246\pi$
$853$	−37.9011	−	27.5368i	−1.29771	−	0.942842i	−0.999930	+	0.0117930i	$0.996246\pi$
$854$	7.37849	−	22.7087i	0.252487	−	0.777075i
$855$	−0.451441	−	1.38939i	−0.0154389	−	0.0475162i
$856$	35.1561	−	25.5424i	1.20161	−	0.873022i
$857$	−14.9509			−0.510711			−0.255356	−	0.966847i	$-0.582193\pi$
$857$	−14.9509			−0.510711			−0.255356	+	0.966847i	$0.582193\pi$
$858$	29.5866	+	48.2926i	1.01007	+	1.64868i
$859$	51.3587			1.75234			0.876168	−	0.482005i	$-0.160091\pi$
$859$	51.3587			1.75234			0.876168	+	0.482005i	$0.160091\pi$
$860$	−14.1551	+	10.2843i	−0.482685	+	0.350691i
$861$	7.55250	+	23.2442i	0.257389	+	0.792161i
$862$	0.0676255	−	0.208130i	0.00230333	−	0.00708894i
$863$	33.0714	+	24.0278i	1.12576	+	0.817915i	0.985073	−	0.172138i	$-0.0550676\pi$
$863$	33.0714	+	24.0278i	1.12576	+	0.817915i	0.140691	+	0.990054i	$0.455068\pi$
$864$	−44.1712	−	32.0923i	−1.50274	−	1.09180i
$865$	0.597947	−	1.84029i	0.0203308	−	0.0625718i
$866$	16.7677	+	51.6058i	0.569791	+	1.75364i
$867$	−0.874974	+	0.635706i	−0.0297157	+	0.0215897i
$868$	−36.7265			−1.24658
$869$	16.3649	+	6.78062i	0.555141	+	0.230017i
$870$	3.87640			0.131422
$871$	−39.4804	+	28.6842i	−1.33774	+	0.971927i
$872$	17.1715	+	52.8485i	0.581501	+	1.78967i
$873$	−5.97251	+	18.3815i	−0.202139	+	0.622120i
$874$	19.9422	+	14.4889i	0.674556	+	0.490094i
$875$	−19.2415	−	13.9798i	−0.650481	−	0.472602i
$876$	15.0411	−	46.2918i	0.508192	−	1.56406i
$877$	−3.23283	−	9.94963i	−0.109165	−	0.335975i	0.881520	−	0.472146i	$-0.156520\pi$
$877$	−3.23283	−	9.94963i	−0.109165	−	0.335975i	−0.990685	+	0.136171i	$0.956520\pi$
$878$	−45.3295	+	32.9338i	−1.52980	+	1.11146i
$879$	21.3272			0.719348
$880$	11.3506	−	13.2870i	0.382630	−	0.447905i
$881$	16.9774			0.571984			0.285992	−	0.958232i	$-0.407677\pi$
$881$	16.9774			0.571984			0.285992	+	0.958232i	$0.407677\pi$
$882$	−51.0091	+	37.0603i	−1.71757	+	1.24788i
$883$	−9.98430	−	30.7285i	−0.335998	−	1.03410i	−0.966228	−	0.257688i	$-0.917039\pi$
$883$	−9.98430	−	30.7285i	−0.335998	−	1.03410i	0.630230	−	0.776409i	$-0.282961\pi$
$884$	9.01521	−	27.7460i	0.303214	−	0.933197i
$885$	3.20617	+	2.32942i	0.107774	+	0.0783025i
$886$	−11.3834	−	8.27051i	−0.382432	−	0.277853i
$887$	2.94806	−	9.07321i	0.0989863	−	0.304648i	−0.889286	−	0.457352i	$-0.848798\pi$
$887$	2.94806	−	9.07321i	0.0989863	−	0.304648i	0.988272	+	0.152704i	$0.0487980\pi$
$888$	8.46803	+	26.0619i	0.284169	+	0.874581i
$889$	2.12855	−	1.54648i	0.0713892	−	0.0518673i
$890$	−4.70641			−0.157759
$891$	0.513165	−	0.123142i	0.0171917	−	0.00412541i
$892$	30.0996			1.00781
$893$	9.93627	−	7.21912i	0.332505	−	0.241579i
$894$	9.64535	+	29.6853i	0.322589	+	0.992826i
$895$	4.33028	−	13.3272i	0.144745	−	0.445480i
$896$	0.0117377	+	0.00852792i	0.000392128	+	0.000284898i
$897$	−34.0932	−	24.7702i	−1.13834	−	0.827052i
$898$	31.9101	−	98.2091i	1.06485	−	3.27728i
$899$	−1.31519	−	4.04774i	−0.0438641	−	0.135000i
$900$	−33.6190	+	24.4256i	−1.12063	+	0.814188i
$901$	−1.35079			−0.0450013
$902$	−3.42506	+	43.4599i	−0.114042	+	1.44706i
$903$	−32.2678			−1.07381
$904$	55.8070	−	40.5461i	1.85611	−	1.34854i
$905$	−0.608093	−	1.87152i	−0.0202137	−	0.0622114i
$906$	−15.5234	+	47.7761i	−0.515730	+	1.58725i
$907$	−3.92743	−	2.85345i	−0.130408	−	0.0947472i	0.520669	−	0.853759i	$-0.325683\pi$
$907$	−3.92743	−	2.85345i	−0.130408	−	0.0947472i	−0.651077	+	0.759012i	$0.725683\pi$
$908$	−51.4837	−	37.4051i	−1.70855	−	1.24133i
$909$	−2.37629	+	7.31348i	−0.0788167	+	0.242573i
$910$	11.9603	+	36.8101i	0.396481	+	1.22024i
$911$	−5.40583	+	3.92756i	−0.179103	+	0.130126i	−0.673725	−	0.738982i	$-0.735307\pi$
$911$	−5.40583	+	3.92756i	−0.179103	+	0.130126i	0.494622	+	0.869108i	$0.335307\pi$
$912$	15.2766			0.505859
$913$	1.66555	−	21.1339i	0.0551218	−	0.699429i
$914$	8.43435			0.278984
$915$	−0.971063	+	0.705519i	−0.0321024	+	0.0233237i
$916$	−20.0327	−	61.6545i	−0.661901	−	2.03712i
$917$	−6.21140	+	19.1167i	−0.205118	+	0.631290i
$918$	−11.0440	−	8.02395i	−0.364507	−	0.264830i
$919$	16.9973	+	12.3493i	0.560689	+	0.407364i	0.831711	−	0.555209i	$-0.187362\pi$
$919$	16.9973	+	12.3493i	0.560689	+	0.407364i	−0.271022	+	0.962573i	$0.587362\pi$
$920$	−8.03652	+	24.7339i	−0.264956	+	0.815451i
$921$	−6.05330	−	18.6301i	−0.199463	−	0.613884i
$922$	4.11284	−	2.98815i	0.135449	−	0.0984096i
$923$	45.8296			1.50850
$924$	75.6601	−	18.1558i	2.48904	−	0.597282i
$925$	16.1205			0.530039
$926$	43.0842	−	31.3025i	1.41584	−	1.02866i
$927$	−6.50988	−	20.0354i	−0.213813	−	0.658048i
$928$	8.11839	−	24.9858i	0.266499	−	0.820200i
$929$	−5.21647	−	3.78999i	−0.171147	−	0.124346i	0.498914	−	0.866651i	$-0.333732\pi$
$929$	−5.21647	−	3.78999i	−0.171147	−	0.124346i	−0.670061	+	0.742306i	$0.733732\pi$
$930$	2.11232	+	1.53469i	0.0692655	+	0.0503244i
$931$	5.95900	−	18.3399i	0.195298	−	0.601066i
$932$	−28.3007	−	87.1004i	−0.927019	−	2.85307i
$933$	24.6774	−	17.9292i	0.807901	−	0.586975i
$934$	−33.2744			−1.08877
$935$	1.17547	−	1.37600i	0.0384420	−	0.0450000i
$936$	81.7349			2.67159
$937$	33.8829	−	24.6174i	1.10691	−	0.804214i	0.124732	−	0.992190i	$-0.460193\pi$
$937$	33.8829	−	24.6174i	1.10691	−	0.804214i	0.982174	+	0.187977i	$0.0601929\pi$
$938$	29.2996	+	90.1748i	0.956665	+	2.94431i
$939$	9.93225	−	30.5683i	0.324127	−	0.997560i
$940$	17.8961	+	13.0023i	0.583706	+	0.424087i
$941$	−47.8342	−	34.7536i	−1.55935	−	1.13293i	−0.936540	−	0.350561i	$-0.885991\pi$
$941$	−47.8342	−	34.7536i	−1.55935	−	1.13293i	−0.622810	−	0.782373i	$-0.714009\pi$
$942$	−8.10232	+	24.9364i	−0.263988	+	0.812471i
$943$	−10.0240	−	30.8506i	−0.326425	−	1.00463i
$944$	52.4616	−	38.1156i	1.70748	−	1.24056i
$945$	12.8062			0.416585
$946$	−53.1729	−	22.0316i	−1.72880	−	0.716310i
$947$	3.20550			0.104165			0.0520824	−	0.998643i	$-0.483414\pi$
$947$	3.20550			0.104165			0.0520824	+	0.998643i	$0.483414\pi$
$948$	−22.5640	+	16.3937i	−0.732843	+	0.532442i
$949$	17.4036	+	53.5627i	0.564944	+	1.73872i
$950$	5.55427	−	17.0943i	0.180204	−	0.554612i
$951$	−1.72116	−	1.25050i	−0.0558124	−	0.0405501i
$952$	−26.8621	−	19.5165i	−0.870606	−	0.632533i
$953$	2.15266	−	6.62522i	0.0697316	−	0.214612i	−0.910118	−	0.414350i	$-0.864009\pi$
$953$	2.15266	−	6.62522i	0.0697316	−	0.214612i	0.979849	+	0.199738i	$0.0640091\pi$
$954$	−1.99641	−	6.14431i	−0.0646361	−	0.198929i
$955$	7.53339	−	5.47333i	0.243775	−	0.177113i
$956$	−49.4405			−1.59902
$957$	4.71043	+	7.68857i	0.152267	+	0.248536i
$958$	34.9191			1.12818
$959$	50.4671	−	36.6665i	1.62967	−	1.18402i
$960$	1.45852	+	4.48886i	0.0470735	+	0.144877i
$961$	−8.69368	+	26.7564i	−0.280441	+	0.863109i
$962$	−43.7907	−	31.8158i	−1.41187	−	1.02578i
$963$	8.70627	+	6.32547i	0.280556	+	0.203836i
$964$	−39.9008	+	122.802i	−1.28512	+	3.95518i
$965$	−0.0796924	−	0.245268i	−0.00256539	−	0.00789546i
$966$	−66.2404	+	48.1265i	−2.13125	+	1.54844i
$967$	−14.6682			−0.471697			−0.235848	−	0.971790i	$-0.575787\pi$
$967$	−14.6682			−0.471697			−0.235848	+	0.971790i	$0.575787\pi$
$968$	80.2951	+	12.7351i	2.58078	+	0.409323i
$969$	1.58204			0.0508225
$970$	12.1811	−	8.85006i	0.391110	−	0.284158i
$971$	10.9319	+	33.6449i	0.350821	+	1.07972i	0.958393	+	0.285452i	$0.0921436\pi$
$971$	10.9319	+	33.6449i	0.350821	+	1.07972i	−0.607572	+	0.794265i	$0.707856\pi$
$972$	23.1270	−	71.1775i	0.741798	−	2.28302i
$973$	55.1240	+	40.0499i	1.76719	+	1.28394i
$974$	12.8746	+	9.35392i	0.412528	+	0.299719i
$975$	−9.49558	+	29.2244i	−0.304102	+	0.935930i
$976$	6.06914	+	18.6789i	0.194268	+	0.597897i
$977$	29.3214	−	21.3033i	0.938076	−	0.681552i	−0.00988090	−	0.999951i	$-0.503145\pi$
$977$	29.3214	−	21.3033i	0.938076	−	0.681552i	0.947957	+	0.318399i	$0.103145\pi$
$978$	−52.9984			−1.69470
$979$	−5.71901	−	9.33483i	−0.182780	−	0.298342i
$980$	34.7317			1.10946
$981$	−11.1331	+	8.08864i	−0.355451	+	0.258250i
$982$	13.5449	+	41.6869i	0.432235	+	1.33028i
$983$	3.72488	−	11.4640i	0.118805	−	0.365645i	−0.873917	−	0.486076i	$-0.838428\pi$
$983$	3.72488	−	11.4640i	0.118805	−	0.365645i	0.992722	+	0.120431i	$0.0384278\pi$
$984$	−32.5286	−	23.6334i	−1.03697	−	0.753406i
$985$	1.54633	+	1.12347i	0.0492700	+	0.0357968i
$986$	2.02982	−	6.24714i	0.0646426	−	0.198950i
$987$	12.6066	+	38.7990i	0.401272	+	1.23499i
$988$	−34.5248	+	25.0837i	−1.09838	+	0.798020i
$989$	42.8271			1.36182
$990$	7.99629	+	3.31317i	0.254139	+	0.105300i
$991$	−51.8575			−1.64731			−0.823654	−	0.567093i	$-0.808068\pi$
$991$	−51.8575			−1.64731			−0.823654	+	0.567093i	$0.808068\pi$
$992$	14.3159	−	10.4011i	0.454529	−	0.330235i
$993$	−11.1620	−	34.3530i	−0.354215	−	1.09016i
$994$	27.5159	−	84.6851i	0.872750	−	2.68605i
$995$	−7.30828	−	5.30978i	−0.231688	−	0.168331i
$996$	27.0036	+	19.6193i	0.855641	+	0.621660i
$997$	14.7298	−	45.3336i	0.466497	−	1.43573i	−0.390594	−	0.920563i	$-0.627730\pi$
$997$	14.7298	−	45.3336i	0.466497	−	1.43573i	0.857091	−	0.515166i	$-0.172270\pi$
$998$	−27.4687	−	84.5399i	−0.869506	−	2.67606i
$999$	−14.4891	+	10.5269i	−0.458414	+	0.333057i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	187.2.g.f.69.9	✓	36
11.2	odd	10		2057.2.a.be.1.17		18
11.4	even	5	inner	187.2.g.f.103.9	yes	36
11.9	even	5		2057.2.a.bd.1.2		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
187.2.g.f.69.9	✓	36	1.1	even	1	trivial
187.2.g.f.103.9	yes	36	11.4	even	5	inner
2057.2.a.bd.1.2		18	11.9	even	5
2057.2.a.be.1.17		18	11.2	odd	10

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:	\( N \)	\(=\)	\( 187 = 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	187.g (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.11405 - 1.53595i) q^{2} +(0.334210 + 1.02859i) q^{3} +(1.49204 - 4.59203i) q^{4} +(-0.441442 - 0.320727i) q^{5} +(2.28641 + 1.66117i) q^{6} +(-1.38827 + 4.27266i) q^{7} +(-2.28388 - 7.02906i) q^{8} +(1.48074 - 1.07582i) q^{9} +O(q^{10})\)	\(q+(2.11405 - 1.53595i) q^{2} +(0.334210 + 1.02859i) q^{3} +(1.49204 - 4.59203i) q^{4} +(-0.441442 - 0.320727i) q^{5} +(2.28641 + 1.66117i) q^{6} +(-1.38827 + 4.27266i) q^{7} +(-2.28388 - 7.02906i) q^{8} +(1.48074 - 1.07582i) q^{9} -1.42585 q^{10} +(-1.73263 - 2.82807i) q^{11} +5.22199 q^{12} +(-4.88824 + 3.55151i) q^{13} +(3.62770 + 11.1649i) q^{14} +(0.182363 - 0.561255i) q^{15} +(-7.81208 - 5.67581i) q^{16} +(-0.809017 - 0.587785i) q^{17} +(1.47796 - 4.54869i) q^{18} +(0.452025 + 1.39119i) q^{19} +(-2.13144 + 1.54858i) q^{20} -4.85880 q^{21} +(-8.00664 - 3.31746i) q^{22} +6.44879 q^{23} +(6.46675 - 4.69837i) q^{24} +(-1.45308 - 4.47212i) q^{25} +(-4.87904 + 15.0162i) q^{26} +(4.22639 + 3.07065i) q^{27} +(17.5488 + 12.7500i) q^{28} +(-0.776783 + 2.39069i) q^{29} +(-0.476534 - 1.46662i) q^{30} +(-1.36977 + 0.995194i) q^{31} -10.4513 q^{32} +(2.32988 - 2.72734i) q^{33} -2.61311 q^{34} +(1.98320 - 1.44088i) q^{35} +(-2.73088 - 8.40479i) q^{36} +(-1.05939 + 3.26045i) q^{37} +(3.09240 + 2.24676i) q^{38} +(-5.28676 - 3.84106i) q^{39} +(-1.24621 + 3.83543i) q^{40} +(-1.55440 - 4.78394i) q^{41} +(-10.2718 + 7.46287i) q^{42} +6.64111 q^{43} +(-15.5718 + 3.73668i) q^{44} -0.998707 q^{45} +(13.6331 - 9.90501i) q^{46} +(-2.59458 - 7.98531i) q^{47} +(3.22722 - 9.93237i) q^{48} +(-10.6652 - 7.74871i) q^{49} +(-9.94083 - 7.22243i) q^{50} +(0.334210 - 1.02859i) q^{51} +(9.01521 + 27.7460i) q^{52} +(1.09281 - 0.793974i) q^{53} +13.6512 q^{54} +(-0.142183 + 1.80413i) q^{55} +33.2034 q^{56} +(-1.27990 + 0.929901i) q^{57} +(2.02982 + 6.24714i) q^{58} +(-2.07519 + 6.38676i) q^{59} +(-2.30521 - 1.67483i) q^{60} +(-1.64548 - 1.19551i) q^{61} +(-1.36719 + 4.20778i) q^{62} +(2.54095 + 7.82023i) q^{63} +(-6.47043 + 4.70104i) q^{64} +3.29694 q^{65} +(0.736422 - 9.34431i) q^{66} +8.07662 q^{67} +(-3.90622 + 2.83803i) q^{68} +(2.15525 + 6.63319i) q^{69} +(1.97947 - 6.09217i) q^{70} +(-6.13633 - 4.45831i) q^{71} +(-10.9439 - 7.95118i) q^{72} +(2.88034 - 8.86478i) q^{73} +(2.76829 + 8.51992i) q^{74} +(4.11436 - 2.98926i) q^{75} +7.06283 q^{76} +(14.4887 - 3.47680i) q^{77} -17.0762 q^{78} +(-4.32095 + 3.13935i) q^{79} +(1.62820 + 5.01108i) q^{80} +(-0.0491700 + 0.151330i) q^{81} +(-10.6340 - 7.72602i) q^{82} +(5.17112 + 3.75704i) q^{83} +(-7.24954 + 22.3118i) q^{84} +(0.168616 + 0.518947i) q^{85} +(14.0396 - 10.2004i) q^{86} -2.71866 q^{87} +(-15.9216 + 18.6377i) q^{88} +3.30077 q^{89} +(-2.11132 + 1.53396i) q^{90} +(-8.38820 - 25.8162i) q^{91} +(9.62187 - 29.6131i) q^{92} +(-1.48144 - 1.07633i) q^{93} +(-17.7501 - 12.8962i) q^{94} +(0.246649 - 0.759107i) q^{95} +(-3.49293 - 10.7501i) q^{96} +(-8.54301 + 6.20686i) q^{97} -34.4483 q^{98} +(-5.60808 - 2.32365i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 4 q^{2} - q^{3} - 14 q^{4} + q^{5} - 5 q^{6} + q^{7} + 17 q^{8} - 22 q^{9}+O(q^{10}) \) 36 * q - 4 * q^2 - q^3 - 14 * q^4 + q^5 - 5 * q^6 + q^7 + 17 * q^8 - 22 * q^9	\( 36 q - 4 q^{2} - q^{3} - 14 q^{4} + q^{5} - 5 q^{6} + q^{7} + 17 q^{8} - 22 q^{9} - 10 q^{10} + 3 q^{11} + 28 q^{12} - 13 q^{13} + 14 q^{14} - 24 q^{15} + 16 q^{16} - 9 q^{17} + 2 q^{18} + 10 q^{19} + 19 q^{20} - 50 q^{21} - 25 q^{22} + 38 q^{23} - 17 q^{24} - 28 q^{25} + 20 q^{26} - 16 q^{27} + 31 q^{28} - 45 q^{29} + 68 q^{30} - 13 q^{31} - 40 q^{32} - 29 q^{33} - 4 q^{34} + 13 q^{35} - 25 q^{36} + q^{37} + 65 q^{38} - 34 q^{39} - 54 q^{40} + 37 q^{41} + 28 q^{42} - 8 q^{43} - 2 q^{44} + 42 q^{45} + 22 q^{46} - 35 q^{47} + 48 q^{48} - 2 q^{49} - 49 q^{50} - q^{51} + 56 q^{52} + 58 q^{53} - 58 q^{54} - 19 q^{55} - 28 q^{56} + 9 q^{57} - 52 q^{58} + 16 q^{59} + 97 q^{60} - 14 q^{61} - 64 q^{62} + 34 q^{63} - 33 q^{64} - 42 q^{65} - 28 q^{66} + 54 q^{67} - 14 q^{68} + 19 q^{69} + 4 q^{70} + 25 q^{71} - 72 q^{72} + 8 q^{73} + 84 q^{74} + 30 q^{75} - 140 q^{76} - 31 q^{77} - 48 q^{78} + 19 q^{79} - 19 q^{80} + 56 q^{81} + 48 q^{82} + 42 q^{83} - 91 q^{84} - 9 q^{85} + 30 q^{86} - 32 q^{87} + 126 q^{88} + 12 q^{89} + 160 q^{90} - 59 q^{91} + 69 q^{92} - 40 q^{93} - 77 q^{94} - 11 q^{95} + 192 q^{96} - 49 q^{97} - 212 q^{98} + 38 q^{99}+O(q^{100}) \) 36 * q - 4 * q^2 - q^3 - 14 * q^4 + q^5 - 5 * q^6 + q^7 + 17 * q^8 - 22 * q^9 - 10 * q^10 + 3 * q^11 + 28 * q^12 - 13 * q^13 + 14 * q^14 - 24 * q^15 + 16 * q^16 - 9 * q^17 + 2 * q^18 + 10 * q^19 + 19 * q^20 - 50 * q^21 - 25 * q^22 + 38 * q^23 - 17 * q^24 - 28 * q^25 + 20 * q^26 - 16 * q^27 + 31 * q^28 - 45 * q^29 + 68 * q^30 - 13 * q^31 - 40 * q^32 - 29 * q^33 - 4 * q^34 + 13 * q^35 - 25 * q^36 + q^37 + 65 * q^38 - 34 * q^39 - 54 * q^40 + 37 * q^41 + 28 * q^42 - 8 * q^43 - 2 * q^44 + 42 * q^45 + 22 * q^46 - 35 * q^47 + 48 * q^48 - 2 * q^49 - 49 * q^50 - q^51 + 56 * q^52 + 58 * q^53 - 58 * q^54 - 19 * q^55 - 28 * q^56 + 9 * q^57 - 52 * q^58 + 16 * q^59 + 97 * q^60 - 14 * q^61 - 64 * q^62 + 34 * q^63 - 33 * q^64 - 42 * q^65 - 28 * q^66 + 54 * q^67 - 14 * q^68 + 19 * q^69 + 4 * q^70 + 25 * q^71 - 72 * q^72 + 8 * q^73 + 84 * q^74 + 30 * q^75 - 140 * q^76 - 31 * q^77 - 48 * q^78 + 19 * q^79 - 19 * q^80 + 56 * q^81 + 48 * q^82 + 42 * q^83 - 91 * q^84 - 9 * q^85 + 30 * q^86 - 32 * q^87 + 126 * q^88 + 12 * q^89 + 160 * q^90 - 59 * q^91 + 69 * q^92 - 40 * q^93 - 77 * q^94 - 11 * q^95 + 192 * q^96 - 49 * q^97 - 212 * q^98 + 38 * q^99

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