LMFDB - Embedded newform 187.2.g.a.69.1

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:	$1$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			69.1
Root			$0.809017 + 0.587785i$ of defining polynomial
Character	$\chi$	$=$	187.69
Dual form			187.2.g.a.103.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.363271i) q^{2} +(-0.690983 - 2.12663i) q^{3} +(-0.500000 + 1.53884i) q^{4} +(-1.80902 - 1.31433i) q^{5} +(1.11803 + 0.812299i) q^{6} +(-0.881966 + 2.71441i) q^{7} +(-0.690983 - 2.12663i) q^{8} +(-1.61803 + 1.17557i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.363271i) q^{2} +(-0.690983 - 2.12663i) q^{3} +(-0.500000 + 1.53884i) q^{4} +(-1.80902 - 1.31433i) q^{5} +(1.11803 + 0.812299i) q^{6} +(-0.881966 + 2.71441i) q^{7} +(-0.690983 - 2.12663i) q^{8} +(-1.61803 + 1.17557i) q^{9} +1.38197 q^{10} +(-3.23607 - 0.726543i) q^{11} +3.61803 q^{12} +(-4.92705 + 3.57971i) q^{13} +(-0.545085 - 1.67760i) q^{14} +(-1.54508 + 4.75528i) q^{15} +(-1.50000 - 1.08981i) q^{16} +(0.809017 + 0.587785i) q^{17} +(0.381966 - 1.17557i) q^{18} +(0.309017 + 0.951057i) q^{19} +(2.92705 - 2.12663i) q^{20} +6.38197 q^{21} +(1.88197 - 0.812299i) q^{22} -1.76393 q^{23} +(-4.04508 + 2.93893i) q^{24} +(1.16312 - 3.57971i) q^{26} +(-1.80902 - 1.31433i) q^{27} +(-3.73607 - 2.71441i) q^{28} +(0.736068 - 2.26538i) q^{29} +(-0.954915 - 2.93893i) q^{30} +(3.85410 - 2.80017i) q^{31} +5.61803 q^{32} +(0.690983 + 7.38394i) q^{33} -0.618034 q^{34} +(5.16312 - 3.75123i) q^{35} +(-1.00000 - 3.07768i) q^{36} +(2.38197 - 7.33094i) q^{37} +(-0.500000 - 0.363271i) q^{38} +(11.0172 + 8.00448i) q^{39} +(-1.54508 + 4.75528i) q^{40} +(0.236068 + 0.726543i) q^{41} +(-3.19098 + 2.31838i) q^{42} -9.00000 q^{43} +(2.73607 - 4.61653i) q^{44} +4.47214 q^{45} +(0.881966 - 0.640786i) q^{46} +(0.690983 + 2.12663i) q^{47} +(-1.28115 + 3.94298i) q^{48} +(-0.927051 - 0.673542i) q^{49} +(0.690983 - 2.12663i) q^{51} +(-3.04508 - 9.37181i) q^{52} +(0.881966 - 0.640786i) q^{53} +1.38197 q^{54} +(4.89919 + 5.56758i) q^{55} +6.38197 q^{56} +(1.80902 - 1.31433i) q^{57} +(0.454915 + 1.40008i) q^{58} +(-3.50000 + 10.7719i) q^{59} +(-6.54508 - 4.75528i) q^{60} +(10.1631 + 7.38394i) q^{61} +(-0.909830 + 2.80017i) q^{62} +(-1.76393 - 5.42882i) q^{63} +(0.190983 - 0.138757i) q^{64} +13.6180 q^{65} +(-3.02786 - 3.44095i) q^{66} -13.8541 q^{67} +(-1.30902 + 0.951057i) q^{68} +(1.21885 + 3.75123i) q^{69} +(-1.21885 + 3.75123i) q^{70} +(-6.35410 - 4.61653i) q^{71} +(3.61803 + 2.62866i) q^{72} +(0.718847 - 2.21238i) q^{73} +(1.47214 + 4.53077i) q^{74} -1.61803 q^{76} +(4.82624 - 8.14324i) q^{77} -8.41641 q^{78} +(-0.809017 + 0.587785i) q^{79} +(1.28115 + 3.94298i) q^{80} +(-3.39919 + 10.4616i) q^{81} +(-0.381966 - 0.277515i) q^{82} +(-8.16312 - 5.93085i) q^{83} +(-3.19098 + 9.82084i) q^{84} +(-0.690983 - 2.12663i) q^{85} +(4.50000 - 3.26944i) q^{86} -5.32624 q^{87} +(0.690983 + 7.38394i) q^{88} -7.09017 q^{89} +(-2.23607 + 1.62460i) q^{90} +(-5.37132 - 16.5312i) q^{91} +(0.881966 - 2.71441i) q^{92} +(-8.61803 - 6.26137i) q^{93} +(-1.11803 - 0.812299i) q^{94} +(0.690983 - 2.12663i) q^{95} +(-3.88197 - 11.9475i) q^{96} +(-12.3262 + 8.95554i) q^{97} +0.708204 q^{98} +(6.09017 - 2.62866i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 5 q^{3} - 2 q^{4} - 5 q^{5} - 8 q^{7} - 5 q^{8} - 2 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 - 5 * q^3 - 2 * q^4 - 5 * q^5 - 8 * q^7 - 5 * q^8 - 2 * q^9	\( 4 q - 2 q^{2} - 5 q^{3} - 2 q^{4} - 5 q^{5} - 8 q^{7} - 5 q^{8} - 2 q^{9} + 10 q^{10} - 4 q^{11} + 10 q^{12} - 13 q^{13} + 9 q^{14} + 5 q^{15} - 6 q^{16} + q^{17} + 6 q^{18} - q^{19} + 5 q^{20} + 30 q^{21} + 12 q^{22} - 16 q^{23} - 5 q^{24} - 11 q^{26} - 5 q^{27} - 6 q^{28} - 6 q^{29} - 15 q^{30} + 2 q^{31} + 18 q^{32} + 5 q^{33} + 2 q^{34} + 5 q^{35} - 4 q^{36} + 14 q^{37} - 2 q^{38} + 15 q^{39} + 5 q^{40} - 8 q^{41} - 15 q^{42} - 36 q^{43} + 2 q^{44} + 8 q^{46} + 5 q^{47} + 15 q^{48} + 3 q^{49} + 5 q^{51} - q^{52} + 8 q^{53} + 10 q^{54} - 5 q^{55} + 30 q^{56} + 5 q^{57} + 13 q^{58} - 14 q^{59} - 15 q^{60} + 25 q^{61} - 26 q^{62} - 16 q^{63} + 3 q^{64} + 50 q^{65} - 30 q^{66} - 42 q^{67} - 3 q^{68} + 25 q^{69} - 25 q^{70} - 12 q^{71} + 10 q^{72} + 23 q^{73} - 12 q^{74} - 2 q^{76} - 12 q^{77} + 20 q^{78} - q^{79} - 15 q^{80} + 11 q^{81} - 6 q^{82} - 17 q^{83} - 15 q^{84} - 5 q^{85} + 18 q^{86} + 10 q^{87} + 5 q^{88} - 6 q^{89} + 21 q^{91} + 8 q^{92} - 30 q^{93} + 5 q^{95} - 20 q^{96} - 18 q^{97} - 24 q^{98} + 2 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 - 5 * q^3 - 2 * q^4 - 5 * q^5 - 8 * q^7 - 5 * q^8 - 2 * q^9 + 10 * q^10 - 4 * q^11 + 10 * q^12 - 13 * q^13 + 9 * q^14 + 5 * q^15 - 6 * q^16 + q^17 + 6 * q^18 - q^19 + 5 * q^20 + 30 * q^21 + 12 * q^22 - 16 * q^23 - 5 * q^24 - 11 * q^26 - 5 * q^27 - 6 * q^28 - 6 * q^29 - 15 * q^30 + 2 * q^31 + 18 * q^32 + 5 * q^33 + 2 * q^34 + 5 * q^35 - 4 * q^36 + 14 * q^37 - 2 * q^38 + 15 * q^39 + 5 * q^40 - 8 * q^41 - 15 * q^42 - 36 * q^43 + 2 * q^44 + 8 * q^46 + 5 * q^47 + 15 * q^48 + 3 * q^49 + 5 * q^51 - q^52 + 8 * q^53 + 10 * q^54 - 5 * q^55 + 30 * q^56 + 5 * q^57 + 13 * q^58 - 14 * q^59 - 15 * q^60 + 25 * q^61 - 26 * q^62 - 16 * q^63 + 3 * q^64 + 50 * q^65 - 30 * q^66 - 42 * q^67 - 3 * q^68 + 25 * q^69 - 25 * q^70 - 12 * q^71 + 10 * q^72 + 23 * q^73 - 12 * q^74 - 2 * q^76 - 12 * q^77 + 20 * q^78 - q^79 - 15 * q^80 + 11 * q^81 - 6 * q^82 - 17 * q^83 - 15 * q^84 - 5 * q^85 + 18 * q^86 + 10 * q^87 + 5 * q^88 - 6 * q^89 + 21 * q^91 + 8 * q^92 - 30 * q^93 + 5 * q^95 - 20 * q^96 - 18 * q^97 - 24 * q^98 + 2 * 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 $

$2$	−0.500000	+	0.363271i	−0.353553	+	0.256872i	−0.750358	−	0.661031i	$-0.770119\pi$
$2$	−0.500000	+	0.363271i	−0.353553	+	0.256872i	0.396805	+	0.917903i	$0.370119\pi$
$3$	−0.690983	−	2.12663i	−0.398939	−	1.22781i	−0.925851	−	0.377889i	$-0.876650\pi$
$3$	−0.690983	−	2.12663i	−0.398939	−	1.22781i	0.526912	−	0.849920i	$-0.323350\pi$
$4$	−0.500000	+	1.53884i	−0.250000	+	0.769421i
$5$	−1.80902	−	1.31433i	−0.809017	−	0.587785i	0.104528	−	0.994522i	$-0.466667\pi$
$5$	−1.80902	−	1.31433i	−0.809017	−	0.587785i	−0.913545	+	0.406737i	$0.866667\pi$
$6$	1.11803	+	0.812299i	0.456435	+	0.331620i
$7$	−0.881966	+	2.71441i	−0.333352	+	1.02595i	0.634176	+	0.773188i	$0.281339\pi$
$7$	−0.881966	+	2.71441i	−0.333352	+	1.02595i	−0.967528	+	0.252763i	$0.918661\pi$
$8$	−0.690983	−	2.12663i	−0.244299	−	0.751876i
$9$	−1.61803	+	1.17557i	−0.539345	+	0.391857i
$10$	1.38197			0.437016
$11$	−3.23607	−	0.726543i	−0.975711	−	0.219061i
$11$	−3.23607	−	0.726543i	−0.975711	−	0.219061i
$12$	3.61803			1.04444
$13$	−4.92705	+	3.57971i	−1.36652	+	0.992833i	−0.368518	+	0.929621i	$0.620135\pi$
$13$	−4.92705	+	3.57971i	−1.36652	+	0.992833i	−0.998000	+	0.0632129i	$0.979865\pi$
$14$	−0.545085	−	1.67760i	−0.145680	−	0.448357i
$15$	−1.54508	+	4.75528i	−0.398939	+	1.22781i
$16$	−1.50000	−	1.08981i	−0.375000	−	0.272453i
$17$	0.809017	+	0.587785i	0.196215	+	0.142559i
$17$	0.809017	+	0.587785i	0.196215	+	0.142559i
$18$	0.381966	−	1.17557i	0.0900303	−	0.277085i
$19$	0.309017	+	0.951057i	0.0708934	+	0.218187i	0.980226	−	0.197884i	$-0.0634068\pi$
$19$	0.309017	+	0.951057i	0.0708934	+	0.218187i	−0.909332	+	0.416071i	$0.863407\pi$
$20$	2.92705	−	2.12663i	0.654508	−	0.475528i
$21$	6.38197			1.39266
$22$	1.88197	−	0.812299i	0.401237	−	0.173183i
$23$	−1.76393			−0.367805			−0.183903	−	0.982944i	$-0.558873\pi$
$23$	−1.76393			−0.367805			−0.183903	+	0.982944i	$0.558873\pi$
$24$	−4.04508	+	2.93893i	−0.825700	+	0.599906i
$25$		0			0
$26$	1.16312	−	3.57971i	0.228106	−	0.702039i
$27$	−1.80902	−	1.31433i	−0.348145	−	0.252942i
$28$	−3.73607	−	2.71441i	−0.706050	−	0.512976i
$29$	0.736068	−	2.26538i	0.136684	−	0.420671i	−0.859164	−	0.511701i	$-0.829016\pi$
$29$	0.736068	−	2.26538i	0.136684	−	0.420671i	0.995848	+	0.0910293i	$0.0290157\pi$
$30$	−0.954915	−	2.93893i	−0.174343	−	0.536572i
$31$	3.85410	−	2.80017i	0.692217	−	0.502925i	−0.185171	−	0.982706i	$-0.559284\pi$
$31$	3.85410	−	2.80017i	0.692217	−	0.502925i	0.877388	+	0.479781i	$0.159284\pi$
$32$	5.61803			0.993137
$33$	0.690983	+	7.38394i	0.120285	+	1.28538i
$34$	−0.618034			−0.105992
$35$	5.16312	−	3.75123i	0.872726	−	0.634073i
$36$	−1.00000	−	3.07768i	−0.166667	−	0.512947i
$37$	2.38197	−	7.33094i	0.391593	−	1.20520i	−0.539991	−	0.841671i	$-0.681572\pi$
$37$	2.38197	−	7.33094i	0.391593	−	1.20520i	0.931583	−	0.363528i	$-0.118428\pi$
$38$	−0.500000	−	0.363271i	−0.0811107	−	0.0589304i
$39$	11.0172	+	8.00448i	1.76417	+	1.28174i
$40$	−1.54508	+	4.75528i	−0.244299	+	0.751876i
$41$	0.236068	+	0.726543i	0.0368676	+	0.113467i	0.967797	−	0.251733i	$-0.0810006\pi$
$41$	0.236068	+	0.726543i	0.0368676	+	0.113467i	−0.930929	+	0.365200i	$0.881001\pi$
$42$	−3.19098	+	2.31838i	−0.492379	+	0.357735i
$43$	−9.00000			−1.37249			−0.686244	−	0.727372i	$-0.740742\pi$
$43$	−9.00000			−1.37249			−0.686244	+	0.727372i	$0.740742\pi$
$44$	2.73607	−	4.61653i	0.412478	−	0.695967i
$45$	4.47214			0.666667
$46$	0.881966	−	0.640786i	0.130039	−	0.0944787i
$47$	0.690983	+	2.12663i	0.100790	+	0.310200i	0.988719	−	0.149780i	$-0.0478565\pi$
$47$	0.690983	+	2.12663i	0.100790	+	0.310200i	−0.887929	+	0.459980i	$0.847856\pi$
$48$	−1.28115	+	3.94298i	−0.184919	+	0.569121i
$49$	−0.927051	−	0.673542i	−0.132436	−	0.0962203i
$50$		0			0
$51$	0.690983	−	2.12663i	0.0967570	−	0.297787i
$52$	−3.04508	−	9.37181i	−0.422277	−	1.29964i
$53$	0.881966	−	0.640786i	0.121147	−	0.0880187i	−0.525562	−	0.850755i	$-0.676145\pi$
$53$	0.881966	−	0.640786i	0.121147	−	0.0880187i	0.646709	+	0.762737i	$0.276145\pi$
$54$	1.38197			0.188062
$55$	4.89919	+	5.56758i	0.660606	+	0.750733i
$56$	6.38197			0.852826
$57$	1.80902	−	1.31433i	0.239610	−	0.174087i
$58$	0.454915	+	1.40008i	0.0597333	+	0.183840i
$59$	−3.50000	+	10.7719i	−0.455661	+	1.40238i	0.414696	+	0.909960i	$0.363888\pi$
$59$	−3.50000	+	10.7719i	−0.455661	+	1.40238i	−0.870357	+	0.492421i	$0.836112\pi$
$60$	−6.54508	−	4.75528i	−0.844967	−	0.613904i
$61$	10.1631	+	7.38394i	1.30125	+	0.945416i	0.999967	−	0.00811711i	$-0.00258378\pi$
$61$	10.1631	+	7.38394i	1.30125	+	0.945416i	0.301287	+	0.953534i	$0.402584\pi$
$62$	−0.909830	+	2.80017i	−0.115549	+	0.355622i
$63$	−1.76393	−	5.42882i	−0.222235	−	0.683968i
$64$	0.190983	−	0.138757i	0.0238729	−	0.0173447i
$65$	13.6180			1.68911
$66$	−3.02786	−	3.44095i	−0.372704	−	0.423552i
$67$	−13.8541			−1.69255			−0.846274	−	0.532748i	$-0.821159\pi$
$67$	−13.8541			−1.69255			−0.846274	+	0.532748i	$0.821159\pi$
$68$	−1.30902	+	0.951057i	−0.158742	+	0.115333i
$69$	1.21885	+	3.75123i	0.146732	+	0.451594i
$70$	−1.21885	+	3.75123i	−0.145680	+	0.448357i
$71$	−6.35410	−	4.61653i	−0.754093	−	0.547881i	0.143000	−	0.989723i	$-0.454325\pi$
$71$	−6.35410	−	4.61653i	−0.754093	−	0.547881i	−0.897093	+	0.441842i	$0.854325\pi$
$72$	3.61803	+	2.62866i	0.426389	+	0.309790i
$73$	0.718847	−	2.21238i	0.0841347	−	0.258940i	−0.900135	−	0.435610i	$-0.856533\pi$
$73$	0.718847	−	2.21238i	0.0841347	−	0.258940i	0.984270	+	0.176670i	$0.0565326\pi$
$74$	1.47214	+	4.53077i	0.171132	+	0.526691i
$75$		0			0
$76$	−1.61803			−0.185601
$77$	4.82624	−	8.14324i	0.550001	−	0.928008i
$78$	−8.41641			−0.952971
$79$	−0.809017	+	0.587785i	−0.0910215	+	0.0661310i	−0.632365	−	0.774670i	$-0.717916\pi$
$79$	−0.809017	+	0.587785i	−0.0910215	+	0.0661310i	0.541344	+	0.840801i	$0.317916\pi$
$80$	1.28115	+	3.94298i	0.143237	+	0.440839i
$81$	−3.39919	+	10.4616i	−0.377687	+	1.16240i
$82$	−0.381966	−	0.277515i	−0.0421811	−	0.0306464i
$83$	−8.16312	−	5.93085i	−0.896019	−	0.650996i	0.0414216	−	0.999142i	$-0.486811\pi$
$83$	−8.16312	−	5.93085i	−0.896019	−	0.650996i	−0.937440	+	0.348146i	$0.886811\pi$
$84$	−3.19098	+	9.82084i	−0.348165	+	1.07154i
$85$	−0.690983	−	2.12663i	−0.0749476	−	0.230665i
$86$	4.50000	−	3.26944i	0.485247	−	0.352553i
$87$	−5.32624			−0.571033
$88$	0.690983	+	7.38394i	0.0736590	+	0.787130i
$89$	−7.09017			−0.751557			−0.375778	−	0.926710i	$-0.622625\pi$
$89$	−7.09017			−0.751557			−0.375778	+	0.926710i	$0.622625\pi$
$90$	−2.23607	+	1.62460i	−0.235702	+	0.171248i
$91$	−5.37132	−	16.5312i	−0.563068	−	1.73294i
$92$	0.881966	−	2.71441i	0.0919513	−	0.282997i
$93$	−8.61803	−	6.26137i	−0.893648	−	0.649274i
$94$	−1.11803	−	0.812299i	−0.115316	−	0.0837823i
$95$	0.690983	−	2.12663i	0.0708934	−	0.218187i
$96$	−3.88197	−	11.9475i	−0.396201	−	1.21938i
$97$	−12.3262	+	8.95554i	−1.25154	+	0.909297i	−0.998310	−	0.0581093i	$-0.981493\pi$
$97$	−12.3262	+	8.95554i	−1.25154	+	0.909297i	−0.253230	+	0.967406i	$0.581493\pi$
$98$	0.708204			0.0715394
$99$	6.09017	−	2.62866i	0.612085	−	0.264190i
$100$		0			0
$101$	11.0172	−	8.00448i	1.09625	−	0.796475i	0.115810	−	0.993271i	$-0.463054\pi$
$101$	11.0172	−	8.00448i	1.09625	−	0.796475i	0.980444	+	0.196796i	$0.0630536\pi$
$102$	0.427051	+	1.31433i	0.0422843	+	0.130138i
$103$	−4.63525	+	14.2658i	−0.456725	+	1.40566i	0.412372	+	0.911015i	$0.364700\pi$
$103$	−4.63525	+	14.2658i	−0.456725	+	1.40566i	−0.869098	+	0.494640i	$0.835300\pi$
$104$	11.0172	+	8.00448i	1.08033	+	0.784904i
$105$	−11.5451	−	8.38800i	−1.12668	−	0.818585i
$106$	−0.208204	+	0.640786i	−0.0202226	+	0.0622386i
$107$	−0.927051	−	2.85317i	−0.0896214	−	0.275826i	0.896193	−	0.443664i	$-0.146322\pi$
$107$	−0.927051	−	2.85317i	−0.0896214	−	0.275826i	−0.985815	+	0.167838i	$0.946322\pi$
$108$	2.92705	−	2.12663i	0.281656	−	0.204635i
$109$	8.56231			0.820120			0.410060	−	0.912059i	$-0.365508\pi$
$109$	8.56231			0.820120			0.410060	+	0.912059i	$0.365508\pi$
$110$	−4.47214	−	1.00406i	−0.426401	−	0.0957331i
$111$	−17.2361			−1.63598
$112$	4.28115	−	3.11044i	0.404531	−	0.293909i
$113$	−5.54508	−	17.0660i	−0.521638	−	1.60544i	−0.770870	−	0.636992i	$-0.780178\pi$
$113$	−5.54508	−	17.0660i	−0.521638	−	1.60544i	0.249233	−	0.968444i	$-0.419822\pi$
$114$	−0.427051	+	1.31433i	−0.0399970	+	0.123098i
$115$	3.19098	+	2.31838i	0.297561	+	0.216191i
$116$	3.11803	+	2.26538i	0.289502	+	0.210336i
$117$	3.76393	−	11.5842i	0.347976	−	1.07096i
$118$	−2.16312	−	6.65740i	−0.199131	−	0.612863i
$119$	−2.30902	+	1.67760i	−0.211667	+	0.153785i
$120$	11.1803			1.02062
$121$	9.94427	+	4.70228i	0.904025	+	0.427480i
$122$	−7.76393			−0.702913
$123$	1.38197	−	1.00406i	0.124608	−	0.0905328i
$124$	2.38197	+	7.33094i	0.213907	+	0.658338i
$125$	−3.45492	+	10.6331i	−0.309017	+	0.951057i
$126$	2.85410	+	2.07363i	0.254264	+	0.184733i
$127$	3.42705	+	2.48990i	0.304102	+	0.220943i	0.729361	−	0.684129i	$-0.239817\pi$
$127$	3.42705	+	2.48990i	0.304102	+	0.220943i	−0.425260	+	0.905071i	$0.639817\pi$
$128$	−3.51722	+	10.8249i	−0.310881	+	0.956794i
$129$	6.21885	+	19.1396i	0.547539	+	1.68515i
$130$	−6.80902	+	4.94704i	−0.597190	+	0.433884i
$131$	−9.70820			−0.848210			−0.424105	−	0.905613i	$-0.639411\pi$
$131$	−9.70820			−0.848210			−0.424105	+	0.905613i	$0.639411\pi$
$132$	−11.7082	−	2.62866i	−1.01907	−	0.228795i
$133$	−2.85410			−0.247482
$134$	6.92705	−	5.03280i	0.598406	−	0.434767i
$135$	1.54508	+	4.75528i	0.132980	+	0.409270i
$136$	0.690983	−	2.12663i	0.0592513	−	0.182357i
$137$	18.0623	+	13.1230i	1.54317	+	1.12118i	0.948310	+	0.317345i	$0.102791\pi$
$137$	18.0623	+	13.1230i	1.54317	+	1.12118i	0.594857	+	0.803832i	$0.297209\pi$
$138$	−1.97214	−	1.43284i	−0.167879	−	0.121971i
$139$	0.326238	−	1.00406i	0.0276711	−	0.0851630i	−0.936267	−	0.351289i	$-0.885744\pi$
$139$	0.326238	−	1.00406i	0.0276711	−	0.0851630i	0.963938	+	0.266126i	$0.0857436\pi$
$140$	3.19098	+	9.82084i	0.269687	+	0.830012i
$141$	4.04508	−	2.93893i	0.340658	−	0.247502i
$142$	4.85410			0.407347
$143$	18.5451	−	8.00448i	1.55082	−	0.669368i
$144$	3.70820			0.309017
$145$	−4.30902	+	3.13068i	−0.357844	+	0.259989i
$146$	0.444272	+	1.36733i	0.0367682	+	0.113161i
$147$	−0.791796	+	2.43690i	−0.0653062	+	0.200992i
$148$	10.0902	+	7.33094i	0.829407	+	0.602599i
$149$	−6.35410	−	4.61653i	−0.520548	−	0.378200i	0.296262	−	0.955107i	$-0.404260\pi$
$149$	−6.35410	−	4.61653i	−0.520548	−	0.378200i	−0.816810	+	0.576906i	$0.804260\pi$
$150$		0			0
$151$	6.92705	+	21.3193i	0.563715	+	1.73494i	0.671738	+	0.740789i	$0.265548\pi$
$151$	6.92705	+	21.3193i	0.563715	+	1.73494i	−0.108022	+	0.994148i	$0.534452\pi$
$152$	1.80902	−	1.31433i	0.146731	−	0.106606i
$153$	−2.00000			−0.161690
$154$	0.545085	+	5.82485i	0.0439242	+	0.469380i
$155$	−10.6525			−0.855627
$156$	−17.8262	+	12.9515i	−1.42724	+	1.03695i
$157$	−0.500000	−	1.53884i	−0.0399043	−	0.122813i	0.929120	−	0.369779i	$-0.120566\pi$
$157$	−0.500000	−	1.53884i	−0.0399043	−	0.122813i	−0.969024	+	0.246966i	$0.920566\pi$
$158$	0.190983	−	0.587785i	0.0151938	−	0.0467617i
$159$	−1.97214	−	1.43284i	−0.156401	−	0.113632i
$160$	−10.1631	−	7.38394i	−0.803465	−	0.583752i
$161$	1.55573	−	4.78804i	0.122609	−	0.377350i
$162$	−2.10081	−	6.46564i	−0.165055	−	0.507988i
$163$	15.5172	−	11.2739i	1.21540	−	0.883042i	0.219692	−	0.975569i	$-0.429495\pi$
$163$	15.5172	−	11.2739i	1.21540	−	0.883042i	0.995710	+	0.0925276i	$0.0294946\pi$
$164$	−1.23607			−0.0965207
$165$	8.45492	−	14.2658i	0.658214	−	1.11059i
$166$	6.23607			0.484013
$167$	−9.42705	+	6.84915i	−0.729487	+	0.530003i	−0.889401	−	0.457128i	$-0.848878\pi$
$167$	−9.42705	+	6.84915i	−0.729487	+	0.530003i	0.159914	+	0.987131i	$0.448878\pi$
$168$	−4.40983	−	13.5721i	−0.340226	−	1.04711i
$169$	7.44427	−	22.9111i	0.572636	−	1.76239i
$170$	1.11803	+	0.812299i	0.0857493	+	0.0623005i
$171$	−1.61803	−	1.17557i	−0.123734	−	0.0898981i
$172$	4.50000	−	13.8496i	0.343122	−	1.05602i
$173$	−0.218847	−	0.673542i	−0.0166386	−	0.0512084i	0.942392	−	0.334509i	$-0.108571\pi$
$173$	−0.218847	−	0.673542i	−0.0166386	−	0.0512084i	−0.959031	+	0.283301i	$0.908571\pi$
$174$	2.66312	−	1.93487i	0.201891	−	0.146682i
$175$		0			0
$176$	4.06231	+	4.61653i	0.306208	+	0.347984i
$177$	25.3262			1.90364
$178$	3.54508	−	2.57565i	0.265715	−	0.193054i
$179$	−5.44427	−	16.7557i	−0.406924	−	1.25238i	−0.919278	−	0.393609i	$-0.871226\pi$
$179$	−5.44427	−	16.7557i	−0.406924	−	1.25238i	0.512354	−	0.858774i	$-0.328774\pi$
$180$	−2.23607	+	6.88191i	−0.166667	+	0.512947i
$181$	1.35410	+	0.983813i	0.100650	+	0.0731262i	0.636972	−	0.770887i	$-0.280187\pi$
$181$	1.35410	+	0.983813i	0.100650	+	0.0731262i	−0.536322	+	0.844013i	$0.680187\pi$
$182$	8.69098	+	6.31437i	0.644219	+	0.468052i
$183$	8.68034	−	26.7153i	0.641669	−	1.97485i
$184$	1.21885	+	3.75123i	0.0898546	+	0.276544i
$185$	−13.9443	+	10.1311i	−1.02520	+	0.744854i
$186$	6.58359			0.482732
$187$	−2.19098	−	2.48990i	−0.160221	−	0.182079i
$188$	−3.61803			−0.263872
$189$	5.16312	−	3.75123i	0.375562	−	0.272862i
$190$	0.427051	+	1.31433i	0.0309815	+	0.0953514i
$191$	5.78115	−	17.7926i	0.418310	−	1.28742i	−0.490947	−	0.871189i	$-0.663349\pi$
$191$	5.78115	−	17.7926i	0.418310	−	1.28742i	0.909257	−	0.416235i	$-0.136651\pi$
$192$	−0.427051	−	0.310271i	−0.0308198	−	0.0223919i
$193$	6.47214	+	4.70228i	0.465875	+	0.338478i	0.795831	−	0.605518i	$-0.207034\pi$
$193$	6.47214	+	4.70228i	0.465875	+	0.338478i	−0.329957	+	0.943996i	$0.607034\pi$
$194$	2.90983	−	8.95554i	0.208914	−	0.642970i
$195$	−9.40983	−	28.9605i	−0.673852	−	2.07390i
$196$	1.50000	−	1.08981i	0.107143	−	0.0778438i
$197$	−20.3820			−1.45215			−0.726077	−	0.687613i	$-0.758659\pi$
$197$	−20.3820			−1.45215			−0.726077	+	0.687613i	$0.758659\pi$
$198$	−2.09017	+	3.52671i	−0.148542	+	0.250632i
$199$	−7.76393			−0.550371			−0.275185	−	0.961391i	$-0.588739\pi$
$199$	−7.76393			−0.550371			−0.275185	+	0.961391i	$0.588739\pi$
$200$		0			0
$201$	9.57295	+	29.4625i	0.675224	+	2.07813i
$202$	−2.60081	+	8.00448i	−0.182993	+	0.563193i
$203$	5.50000	+	3.99598i	0.386024	+	0.280463i
$204$	2.92705	+	2.12663i	0.204935	+	0.148894i
$205$	0.527864	−	1.62460i	0.0368676	−	0.113467i
$206$	−2.86475	−	8.81678i	−0.199596	−	0.614294i
$207$	2.85410	−	2.07363i	0.198374	−	0.144127i
$208$	11.2918			0.782945
$209$	−0.309017	−	3.30220i	−0.0213752	−	0.228418i
$210$	8.81966			0.608614
$211$	−17.1803	+	12.4822i	−1.18274	+	0.859313i	−0.992478	−	0.122419i	$-0.960935\pi$
$211$	−17.1803	+	12.4822i	−1.18274	+	0.859313i	−0.190265	+	0.981733i	$0.560935\pi$
$212$	0.545085	+	1.67760i	0.0374366	+	0.115218i
$213$	−5.42705	+	16.7027i	−0.371855	+	1.14445i
$214$	1.50000	+	1.08981i	0.102538	+	0.0744981i
$215$	16.2812	+	11.8290i	1.11037	+	0.806728i
$216$	−1.54508	+	4.75528i	−0.105130	+	0.323556i
$217$	4.20163	+	12.9313i	0.285225	+	0.877832i
$218$	−4.28115	+	3.11044i	−0.289956	+	0.210666i
$219$	−5.20163			−0.351493
$220$	−11.0172	+	4.75528i	−0.742781	+	0.320601i
$221$	−6.09017			−0.409669
$222$	8.61803	−	6.26137i	0.578405	−	0.420236i
$223$	−5.04508	−	15.5272i	−0.337844	−	1.03978i	−0.965304	−	0.261128i	$-0.915906\pi$
$223$	−5.04508	−	15.5272i	−0.337844	−	1.03978i	0.627460	−	0.778649i	$-0.284094\pi$
$224$	−4.95492	+	15.2497i	−0.331064	+	1.01891i
$225$		0			0
$226$	8.97214	+	6.51864i	0.596818	+	0.433613i
$227$	−0.236068	+	0.726543i	−0.0156684	+	0.0482223i	−0.958585	−	0.284807i	$-0.908071\pi$
$227$	−0.236068	+	0.726543i	−0.0156684	+	0.0482223i	0.942917	+	0.333029i	$0.108071\pi$
$228$	1.11803	+	3.44095i	0.0740436	+	0.227883i
$229$	1.04508	−	0.759299i	0.0690612	−	0.0501759i	−0.552719	−	0.833368i	$-0.686410\pi$
$229$	1.04508	−	0.759299i	0.0690612	−	0.0501759i	0.621780	+	0.783192i	$0.286410\pi$
$230$	−2.43769			−0.160737
$231$	−20.6525	−	4.63677i	−1.35883	−	0.305077i
$232$	−5.32624			−0.349685
$233$	4.19098	−	3.04493i	0.274560	−	0.199480i	−0.441981	−	0.897024i	$-0.645724\pi$
$233$	4.19098	−	3.04493i	0.274560	−	0.199480i	0.716541	+	0.697545i	$0.245724\pi$
$234$	2.32624	+	7.15942i	0.152071	+	0.468026i
$235$	1.54508	−	4.75528i	0.100790	−	0.310200i
$236$	−14.8262	−	10.7719i	−0.965106	−	0.701190i
$237$	1.80902	+	1.31433i	0.117508	+	0.0853748i
$238$	0.545085	−	1.67760i	0.0353326	−	0.108743i
$239$	2.85410	+	8.78402i	0.184617	+	0.568191i	0.999942	−	0.0108123i	$-0.00344174\pi$
$239$	2.85410	+	8.78402i	0.184617	+	0.568191i	−0.815325	+	0.579004i	$0.803442\pi$
$240$	7.50000	−	5.44907i	0.484123	−	0.351736i
$241$	−19.7082			−1.26952			−0.634759	−	0.772711i	$-0.718900\pi$
$241$	−19.7082			−1.26952			−0.634759	+	0.772711i	$0.718900\pi$
$242$	−6.68034	+	1.26133i	−0.429429	+	0.0810812i
$243$	17.8885			1.14755
$244$	−16.4443	+	11.9475i	−1.05274	+	0.764858i
$245$	0.791796	+	2.43690i	0.0505860	+	0.155688i
$246$	−0.326238	+	1.00406i	−0.0208002	+	0.0640163i
$247$	−4.92705	−	3.57971i	−0.313501	−	0.227772i
$248$	−8.61803	−	6.26137i	−0.547246	−	0.397597i
$249$	−6.97214	+	21.4580i	−0.441841	+	1.35985i
$250$	−2.13525	−	6.57164i	−0.135045	−	0.415627i
$251$	7.28115	−	5.29007i	0.459582	−	0.333906i	−0.333785	−	0.942649i	$-0.608326\pi$
$251$	7.28115	−	5.29007i	0.459582	−	0.333906i	0.793367	+	0.608743i	$0.208326\pi$
$252$	9.23607			0.581818
$253$	5.70820	+	1.28157i	0.358872	+	0.0805717i
$254$	−2.61803			−0.164270
$255$	−4.04508	+	2.93893i	−0.253313	+	0.184043i
$256$	−2.02786	−	6.24112i	−0.126742	−	0.390070i
$257$	−2.14590	+	6.60440i	−0.133857	+	0.411971i	−0.995411	−	0.0956966i	$-0.969492\pi$
$257$	−2.14590	+	6.60440i	−0.133857	+	0.411971i	0.861553	+	0.507667i	$0.169492\pi$
$258$	−10.0623	−	7.31069i	−0.626452	−	0.455144i
$259$	17.7984	+	12.9313i	1.10594	+	0.803510i
$260$	−6.80902	+	20.9560i	−0.422277	+	1.29964i
$261$	1.47214	+	4.53077i	0.0911229	+	0.280448i
$262$	4.85410	−	3.52671i	0.299887	−	0.217881i
$263$	13.3820			0.825167			0.412584	−	0.910920i	$-0.364626\pi$
$263$	13.3820			0.825167			0.412584	+	0.910920i	$0.364626\pi$
$264$	15.2254	−	6.57164i	0.937060	−	0.404456i
$265$	−2.43769			−0.149746
$266$	1.42705	−	1.03681i	0.0874981	−	0.0635711i
$267$	4.89919	+	15.0781i	0.299825	+	0.922768i
$268$	6.92705	−	21.3193i	0.423137	−	1.30228i
$269$	2.97214	+	2.15938i	0.181214	+	0.131660i	0.674694	−	0.738097i	$-0.264275\pi$
$269$	2.97214	+	2.15938i	0.181214	+	0.131660i	−0.493480	+	0.869757i	$0.664275\pi$
$270$	−2.50000	−	1.81636i	−0.152145	−	0.110540i
$271$	5.34346	−	16.4455i	0.324592	−	0.998991i	−0.647032	−	0.762462i	$-0.723990\pi$
$271$	5.34346	−	16.4455i	0.324592	−	0.998991i	0.971624	−	0.236529i	$-0.0760098\pi$
$272$	−0.572949	−	1.76336i	−0.0347401	−	0.106919i
$273$	−31.4443	+	22.8456i	−1.90309	+	1.38268i
$274$	−13.7984			−0.833590
$275$		0			0
$276$	−6.38197			−0.384149
$277$	6.73607	−	4.89404i	0.404731	−	0.294054i	−0.366734	−	0.930326i	$-0.619524\pi$
$277$	6.73607	−	4.89404i	0.404731	−	0.294054i	0.771465	+	0.636271i	$0.219524\pi$
$278$	0.201626	+	0.620541i	0.0120927	+	0.0372176i
$279$	−2.94427	+	9.06154i	−0.176269	+	0.542500i
$280$	−11.5451	−	8.38800i	−0.689951	−	0.501279i
$281$	−18.9894	−	13.7966i	−1.13281	−	0.823035i	−0.146709	−	0.989180i	$-0.546868\pi$
$281$	−18.9894	−	13.7966i	−1.13281	−	0.823035i	−0.986101	+	0.166145i	$0.946868\pi$
$282$	−0.954915	+	2.93893i	−0.0568644	+	0.175011i
$283$	−3.75329	−	11.5514i	−0.223110	−	0.686662i	−0.998478	−	0.0551520i	$-0.982436\pi$
$283$	−3.75329	−	11.5514i	−0.223110	−	0.686662i	0.775368	−	0.631510i	$-0.217564\pi$
$284$	10.2812	−	7.46969i	0.610074	−	0.443245i
$285$	−5.00000			−0.296174
$286$	−6.36475	+	10.7391i	−0.376355	+	0.635018i
$287$	−2.18034			−0.128701
$288$	−9.09017	+	6.60440i	−0.535643	+	0.389168i
$289$	0.309017	+	0.951057i	0.0181775	+	0.0559445i
$290$	1.01722	−	3.13068i	0.0597333	−	0.183840i
$291$	27.5623	+	20.0252i	1.61573	+	1.17390i
$292$	3.04508	+	2.21238i	0.178200	+	0.129470i
$293$	−3.31966	+	10.2169i	−0.193937	+	0.596876i	0.806051	+	0.591846i	$0.201601\pi$
$293$	−3.31966	+	10.2169i	−0.193937	+	0.596876i	−0.999987	+	0.00502909i	$0.998399\pi$
$294$	−0.489357	−	1.50609i	−0.0285399	−	0.0878367i
$295$	20.4894	−	14.8864i	1.19294	−	0.866719i
$296$	−17.2361			−1.00183
$297$	4.89919	+	5.56758i	0.284280	+	0.323064i
$298$	4.85410			0.281191
$299$	8.69098	−	6.31437i	0.502613	−	0.365169i
$300$		0			0
$301$	7.93769	−	24.4297i	0.457521	−	1.40811i
$302$	−11.2082	−	8.14324i	−0.644960	−	0.468591i
$303$	−24.6353	−	17.8986i	−1.41526	−	1.02825i
$304$	0.572949	−	1.76336i	0.0328609	−	0.101135i
$305$	−8.68034	−	26.7153i	−0.497035	−	1.52972i
$306$	1.00000	−	0.726543i	0.0571662	−	0.0415337i
$307$	−11.3262			−0.646423			−0.323211	−	0.946327i	$-0.604762\pi$
$307$	−11.3262			−0.646423			−0.323211	+	0.946327i	$0.604762\pi$
$308$	10.1180	+	11.4984i	0.576528	+	0.655184i
$309$	33.5410			1.90808
$310$	5.32624	−	3.86974i	0.302510	−	0.219786i
$311$	0.145898	+	0.449028i	0.00827312	+	0.0254620i	0.955108	−	0.296258i	$-0.0957389\pi$
$311$	0.145898	+	0.449028i	0.00827312	+	0.0254620i	−0.946835	+	0.321720i	$0.895739\pi$
$312$	9.40983	−	28.9605i	0.532727	−	1.63956i
$313$	−6.51722	−	4.73504i	−0.368375	−	0.267640i	0.388162	−	0.921591i	$-0.373110\pi$
$313$	−6.51722	−	4.73504i	−0.368375	−	0.267640i	−0.756537	+	0.653951i	$0.773110\pi$
$314$	0.809017	+	0.587785i	0.0456555	+	0.0331706i
$315$	−3.94427	+	12.1392i	−0.222235	+	0.683968i
$316$	−0.500000	−	1.53884i	−0.0281272	−	0.0865666i
$317$	−22.9443	+	16.6700i	−1.28868	+	0.936280i	−0.999778	−	0.0210791i	$-0.993290\pi$
$317$	−22.9443	+	16.6700i	−1.28868	+	0.936280i	−0.288901	+	0.957359i	$0.593290\pi$
$318$	1.50658			0.0844847
$319$	−4.02786	+	6.79615i	−0.225517	+	0.380512i
$320$	−0.527864			−0.0295085
$321$	−5.42705	+	3.94298i	−0.302908	+	0.220076i
$322$	0.961493	+	2.95917i	0.0535819	+	0.164908i
$323$	−0.309017	+	0.951057i	−0.0171942	+	0.0529182i
$324$	−14.3992	−	10.4616i	−0.799955	−	0.581201i
$325$		0			0
$326$	−3.66312	+	11.2739i	−0.202881	+	0.624405i
$327$	−5.91641	−	18.2088i	−0.327178	−	1.00695i
$328$	1.38197	−	1.00406i	0.0763063	−	0.0554398i
$329$	−6.38197			−0.351849
$330$	0.954915	+	10.2044i	0.0525663	+	0.561731i
$331$	−3.00000			−0.164895			−0.0824475	−	0.996595i	$-0.526274\pi$
$331$	−3.00000			−0.164895			−0.0824475	+	0.996595i	$0.526274\pi$
$332$	13.2082	−	9.59632i	0.724894	−	0.526667i
$333$	4.76393	+	14.6619i	0.261062	+	0.803466i
$334$	2.22542	−	6.84915i	0.121770	−	0.374769i
$335$	25.0623	+	18.2088i	1.36930	+	0.994855i
$336$	−9.57295	−	6.95515i	−0.522247	−	0.379435i
$337$	7.06231	−	21.7355i	0.384708	−	1.18401i	−0.551983	−	0.833855i	$-0.686129\pi$
$337$	7.06231	−	21.7355i	0.384708	−	1.18401i	0.936692	−	0.350155i	$-0.113871\pi$
$338$	4.60081	+	14.1598i	0.250251	+	0.770194i
$339$	−32.4615	+	23.5847i	−1.76307	+	1.28094i
$340$	3.61803			0.196215
$341$	−14.5066	+	6.26137i	−0.785575	+	0.339072i
$342$	1.23607			0.0668389
$343$	−13.5172	+	9.82084i	−0.729861	+	0.530275i
$344$	6.21885	+	19.1396i	0.335298	+	1.03194i
$345$	2.72542	−	8.38800i	0.146732	−	0.451594i
$346$	0.354102	+	0.257270i	0.0190366	+	0.0138309i
$347$	−13.2812	−	9.64932i	−0.712970	−	0.518003i	0.171161	−	0.985243i	$-0.445248\pi$
$347$	−13.2812	−	9.64932i	−0.712970	−	0.518003i	−0.884130	+	0.467240i	$0.845248\pi$
$348$	2.66312	−	8.19624i	0.142758	−	0.439364i
$349$	5.38197	+	16.5640i	0.288090	+	0.886650i	0.985455	+	0.169934i	$0.0543555\pi$
$349$	5.38197	+	16.5640i	0.288090	+	0.886650i	−0.697365	+	0.716716i	$0.745644\pi$
$350$		0			0
$351$	13.6180			0.726877
$352$	−18.1803	−	4.08174i	−0.969015	−	0.217558i
$353$	−22.4164			−1.19311			−0.596553	−	0.802574i	$-0.703463\pi$
$353$	−22.4164			−1.19311			−0.596553	+	0.802574i	$0.703463\pi$
$354$	−12.6631	+	9.20029i	−0.673037	+	0.488990i
$355$	5.42705	+	16.7027i	0.288038	+	0.886490i
$356$	3.54508	−	10.9106i	0.187889	−	0.578263i
$357$	5.16312	+	3.75123i	0.273261	+	0.198536i
$358$	8.80902	+	6.40013i	0.465571	+	0.338257i
$359$	−6.84346	+	21.0620i	−0.361184	+	1.11161i	0.591152	+	0.806560i	$0.298673\pi$
$359$	−6.84346	+	21.0620i	−0.361184	+	1.11161i	−0.952336	+	0.305050i	$0.901327\pi$
$360$	−3.09017	−	9.51057i	−0.162866	−	0.501251i
$361$	14.5623	−	10.5801i	0.766437	−	0.556849i
$362$	−1.03444			−0.0543691
$363$	3.12868	−	24.3970i	0.164213	−	1.28051i
$364$	28.1246			1.47413
$365$	−4.20820	+	3.05744i	−0.220267	+	0.160034i
$366$	5.36475	+	16.5110i	0.280420	+	0.863043i
$367$	−2.56231	+	7.88597i	−0.133751	+	0.411644i	−0.995394	−	0.0958717i	$-0.969436\pi$
$367$	−2.56231	+	7.88597i	−0.133751	+	0.411644i	0.861642	+	0.507516i	$0.169436\pi$
$368$	2.64590	+	1.92236i	0.137927	+	0.100210i
$369$	−1.23607	−	0.898056i	−0.0643471	−	0.0467509i
$370$	3.29180	−	10.1311i	0.171132	−	0.526691i
$371$	0.961493	+	2.95917i	0.0499182	+	0.153632i
$372$	13.9443	−	10.1311i	0.722977	−	0.525273i
$373$	26.5623			1.37534			0.687672	−	0.726021i	$-0.258633\pi$
$373$	26.5623			1.37534			0.687672	+	0.726021i	$0.258633\pi$
$374$	2.00000	+	0.449028i	0.103418	+	0.0232187i
$375$	25.0000			1.29099
$376$	4.04508	−	2.93893i	0.208609	−	0.151564i
$377$	4.48278	+	13.7966i	0.230875	+	0.710560i
$378$	−1.21885	+	3.75123i	−0.0626907	+	0.192942i
$379$	−13.1803	−	9.57608i	−0.677029	−	0.491890i	0.195342	−	0.980735i	$-0.437418\pi$
$379$	−13.1803	−	9.57608i	−0.677029	−	0.491890i	−0.872371	+	0.488845i	$0.837418\pi$
$380$	2.92705	+	2.12663i	0.150155	+	0.109094i
$381$	2.92705	−	9.00854i	0.149957	−	0.461521i
$382$	3.57295	+	10.9964i	0.182808	+	0.562625i
$383$	21.0623	−	15.3027i	1.07623	−	0.781929i	0.0992112	−	0.995066i	$-0.468368\pi$
$383$	21.0623	−	15.3027i	1.07623	−	0.781929i	0.977022	+	0.213137i	$0.0683681\pi$
$384$	25.4508			1.29878
$385$	−19.4336	+	8.38800i	−0.990429	+	0.427492i
$386$	−4.94427			−0.251657
$387$	14.5623	−	10.5801i	0.740244	−	0.537818i
$388$	−7.61803	−	23.4459i	−0.386747	−	1.19029i
$389$	1.83688	−	5.65334i	0.0931336	−	0.286636i	−0.893629	−	0.448806i	$-0.851849\pi$
$389$	1.83688	−	5.65334i	0.0931336	−	0.286636i	0.986763	+	0.162170i	$0.0518494\pi$
$390$	15.2254	+	11.0619i	0.770969	+	0.560142i
$391$	−1.42705	−	1.03681i	−0.0721691	−	0.0524339i
$392$	−0.791796	+	2.43690i	−0.0399917	+	0.123082i
$393$	6.70820	+	20.6457i	0.338384	+	1.04144i
$394$	10.1910	−	7.40418i	0.513414	−	0.373017i
$395$	2.23607			0.112509
$396$	1.00000	+	10.6861i	0.0502519	+	0.536999i
$397$	6.41641			0.322030			0.161015	−	0.986952i	$-0.448523\pi$
$397$	6.41641			0.322030			0.161015	+	0.986952i	$0.448523\pi$
$398$	3.88197	−	2.82041i	0.194585	−	0.141375i
$399$	1.97214	+	6.06961i	0.0987303	+	0.303861i
$400$		0			0
$401$	−19.4164	−	14.1068i	−0.969609	−	0.704462i	−0.0142467	−	0.999899i	$-0.504535\pi$
$401$	−19.4164	−	14.1068i	−0.969609	−	0.704462i	−0.955362	+	0.295436i	$0.904535\pi$
$402$	−15.4894	−	11.2537i	−0.772539	−	0.561282i
$403$	−8.96556	+	27.5932i	−0.446606	+	1.37451i
$404$	6.80902	+	20.9560i	0.338761	+	1.04260i
$405$	19.8992	−	14.4576i	0.988799	−	0.718404i
$406$	−4.20163			−0.208523
$407$	−13.0344	+	21.9928i	−0.646093	+	1.09014i
$408$	−5.00000			−0.247537
$409$	15.8262	−	11.4984i	0.782557	−	0.568561i	−0.123188	−	0.992383i	$-0.539312\pi$
$409$	15.8262	−	11.4984i	0.782557	−	0.568561i	0.905745	+	0.423822i	$0.139312\pi$
$410$	0.326238	+	1.00406i	0.0161117	+	0.0495868i
$411$	15.4271	−	47.4796i	0.760960	−	2.34200i
$412$	−19.6353	−	14.2658i	−0.967360	−	0.702828i
$413$	−26.1525	−	19.0009i	−1.28688	−	0.934972i
$414$	−0.673762	+	2.07363i	−0.0331136	+	0.101913i
$415$	6.97214	+	21.4580i	0.342249	+	1.05333i
$416$	−27.6803	+	20.1109i	−1.35714	+	0.986020i
$417$	−2.36068			−0.115603
$418$	1.35410	+	1.53884i	0.0662313	+	0.0752672i
$419$	33.5410			1.63859			0.819293	−	0.573375i	$-0.194366\pi$
$419$	33.5410			1.63859			0.819293	+	0.573375i	$0.194366\pi$
$420$	18.6803	−	13.5721i	0.911507	−	0.662249i
$421$	−5.29180	−	16.2865i	−0.257906	−	0.793754i	−0.993243	−	0.116052i	$-0.962976\pi$
$421$	−5.29180	−	16.2865i	−0.257906	−	0.793754i	0.735337	−	0.677702i	$-0.237024\pi$
$422$	4.05573	−	12.4822i	0.197430	−	0.607626i
$423$	−3.61803	−	2.62866i	−0.175915	−	0.127810i
$424$	−1.97214	−	1.43284i	−0.0957754	−	0.0695849i
$425$		0			0
$426$	−3.35410	−	10.3229i	−0.162507	−	0.500144i
$427$	−29.0066	+	21.0745i	−1.40373	+	1.01987i
$428$	4.85410			0.234632
$429$	−29.8369	−	33.9075i	−1.44054	−	1.63707i
$430$	−12.4377			−0.599799
$431$	−19.4721	+	14.1473i	−0.937940	+	0.681453i	−0.947924	−	0.318497i	$-0.896822\pi$
$431$	−19.4721	+	14.1473i	−0.937940	+	0.681453i	0.00998408	+	0.999950i	$0.496822\pi$
$432$	1.28115	+	3.94298i	0.0616395	+	0.189707i
$433$	0.763932	−	2.35114i	0.0367122	−	0.112989i	−0.931021	−	0.364966i	$-0.881081\pi$
$433$	0.763932	−	2.35114i	0.0367122	−	0.112989i	0.967733	+	0.251977i	$0.0810807\pi$
$434$	−6.79837	−	4.93931i	−0.326332	−	0.237094i
$435$	9.63525	+	7.00042i	0.461975	+	0.335645i
$436$	−4.28115	+	13.1760i	−0.205030	+	0.631018i
$437$	−0.545085	−	1.67760i	−0.0260750	−	0.0802504i
$438$	2.60081	−	1.88960i	0.124272	−	0.0902886i
$439$	−5.12461			−0.244584			−0.122292	−	0.992494i	$-0.539024\pi$
$439$	−5.12461			−0.244584			−0.122292	+	0.992494i	$0.539024\pi$
$440$	8.45492	−	14.2658i	0.403072	−	0.680098i
$441$	2.29180			0.109133
$442$	3.04508	−	2.21238i	0.144840	−	0.105232i
$443$	−4.48278	−	13.7966i	−0.212983	−	0.655495i	−0.999291	−	0.0376596i	$-0.988010\pi$
$443$	−4.48278	−	13.7966i	−0.212983	−	0.655495i	0.786307	−	0.617836i	$-0.211990\pi$
$444$	8.61803	−	26.5236i	0.408994	−	1.25875i
$445$	12.8262	+	9.31881i	0.608022	+	0.441754i
$446$	8.16312	+	5.93085i	0.386535	+	0.280834i
$447$	−5.42705	+	16.7027i	−0.256691	+	0.790013i
$448$	0.208204	+	0.640786i	0.00983671	+	0.0302743i
$449$	−5.85410	+	4.25325i	−0.276272	+	0.200723i	−0.717290	−	0.696775i	$-0.754618\pi$
$449$	−5.85410	+	4.25325i	−0.276272	+	0.200723i	0.441018	+	0.897498i	$0.354618\pi$
$450$		0			0
$451$	−0.236068	−	2.52265i	−0.0111160	−	0.118787i
$452$	29.0344			1.36567
$453$	40.5517	−	29.4625i	1.90528	−	1.38427i
$454$	−0.145898	−	0.449028i	−0.00684733	−	0.0210739i
$455$	−12.0106	+	36.9650i	−0.563068	+	1.73294i
$456$	−4.04508	−	2.93893i	−0.189428	−	0.137628i
$457$	−5.54508	−	4.02874i	−0.259388	−	0.188457i	0.450489	−	0.892782i	$-0.351250\pi$
$457$	−5.54508	−	4.02874i	−0.259388	−	0.188457i	−0.709877	+	0.704325i	$0.751250\pi$
$458$	−0.246711	+	0.759299i	−0.0115281	+	0.0354797i
$459$	−0.690983	−	2.12663i	−0.0322523	−	0.0992624i
$460$	−5.16312	+	3.75123i	−0.240732	+	0.174902i
$461$	−6.09017			−0.283647			−0.141824	−	0.989892i	$-0.545297\pi$
$461$	−6.09017			−0.283647			−0.141824	+	0.989892i	$0.545297\pi$
$462$	12.0106	−	5.18407i	0.558786	−	0.241185i
$463$	−0.201626			−0.00937036			−0.00468518	−	0.999989i	$-0.501491\pi$
$463$	−0.201626			−0.00937036			−0.00468518	+	0.999989i	$0.501491\pi$
$464$	−3.57295	+	2.59590i	−0.165870	+	0.120512i
$465$	7.36068	+	22.6538i	0.341343	+	1.05055i
$466$	−0.989357	+	3.04493i	−0.0458311	+	0.141054i
$467$	29.1246	+	21.1603i	1.34773	+	0.979180i	0.999121	+	0.0419107i	$0.0133445\pi$
$467$	29.1246	+	21.1603i	1.34773	+	0.979180i	0.348605	+	0.937270i	$0.386655\pi$
$468$	15.9443	+	11.5842i	0.737024	+	0.535479i
$469$	12.2188	−	37.6057i	0.564214	−	1.73647i
$470$	0.954915	+	2.93893i	0.0440469	+	0.135563i
$471$	−2.92705	+	2.12663i	−0.134871	+	0.0979898i
$472$	25.3262			1.16573
$473$	29.1246	+	6.53888i	1.33915	+	0.300658i
$474$	−1.38197			−0.0634758
$475$		0			0
$476$	−1.42705	−	4.39201i	−0.0654088	−	0.201308i
$477$	−0.673762	+	2.07363i	−0.0308494	+	0.0949448i
$478$	−4.61803	−	3.35520i	−0.211224	−	0.153463i
$479$	5.42705	+	3.94298i	0.247968	+	0.180160i	0.704826	−	0.709380i	$-0.251025\pi$
$479$	5.42705	+	3.94298i	0.247968	+	0.180160i	−0.456858	+	0.889540i	$0.651025\pi$
$480$	−8.68034	+	26.7153i	−0.396201	+	1.21938i
$481$	14.5066	+	44.6467i	0.661443	+	2.03571i
$482$	9.85410	−	7.15942i	0.448842	−	0.326103i
$483$	−11.2574			−0.512227
$484$	−12.2082	+	12.9515i	−0.554918	+	0.588705i
$485$	34.0689			1.54699
$486$	−8.94427	+	6.49839i	−0.405720	+	0.294773i
$487$	−9.42705	−	29.0135i	−0.427180	−	1.31473i	−0.900891	−	0.434046i	$-0.857086\pi$
$487$	−9.42705	−	29.0135i	−0.427180	−	1.31473i	0.473710	−	0.880681i	$-0.342914\pi$
$488$	8.68034	−	26.7153i	0.392941	−	1.20935i
$489$	−34.6976	−	25.2093i	−1.56908	−	1.14000i
$490$	−1.28115	−	0.930812i	−0.0578766	−	0.0420498i
$491$	−3.76393	+	11.5842i	−0.169864	+	0.522787i	−0.999362	−	0.0357226i	$-0.988627\pi$
$491$	−3.76393	+	11.5842i	−0.169864	+	0.522787i	0.829498	+	0.558510i	$0.188627\pi$
$492$	0.854102	+	2.62866i	0.0385059	+	0.118509i
$493$	1.92705	−	1.40008i	0.0867900	−	0.0630566i
$494$	3.76393			0.169347
$495$	−14.4721	−	3.24920i	−0.650474	−	0.146041i
$496$	−8.83282			−0.396605
$497$	18.1353	−	13.1760i	0.813477	−	0.591026i
$498$	−4.30902	−	13.2618i	−0.193092	−	0.594275i
$499$	−10.7705	+	33.1482i	−0.482154	+	1.48392i	0.353906	+	0.935281i	$0.384853\pi$
$499$	−10.7705	+	33.1482i	−0.482154	+	1.48392i	−0.836060	+	0.548637i	$0.815147\pi$
$500$	−14.6353	−	10.6331i	−0.654508	−	0.475528i
$501$	21.0795	+	15.3152i	0.941764	+	0.684231i
$502$	−1.71885	+	5.29007i	−0.0767159	+	0.236107i
$503$	−2.79180	−	8.59226i	−0.124480	−	0.383110i	0.869326	−	0.494239i	$-0.164553\pi$
$503$	−2.79180	−	8.59226i	−0.124480	−	0.383110i	−0.993806	+	0.111129i	$0.964553\pi$
$504$	−10.3262	+	7.50245i	−0.459967	+	0.334186i
$505$	−30.4508			−1.35505
$506$	−3.31966	+	1.43284i	−0.147577	+	0.0636975i
$507$	−53.8673			−2.39233
$508$	−5.54508	+	4.02874i	−0.246023	+	0.178746i
$509$	9.27051	+	28.5317i	0.410908	+	1.26465i	0.915860	+	0.401498i	$0.131510\pi$
$509$	9.27051	+	28.5317i	0.410908	+	1.26465i	−0.504952	+	0.863147i	$0.668490\pi$
$510$	0.954915	−	2.93893i	0.0422843	−	0.130138i
$511$	5.37132	+	3.90249i	0.237613	+	0.172636i
$512$	−15.1353	−	10.9964i	−0.668890	−	0.485977i
$513$	0.690983	−	2.12663i	0.0305076	−	0.0938929i
$514$	−1.32624	−	4.08174i	−0.0584978	−	0.180038i
$515$	27.1353	−	19.7149i	1.19572	−	0.868743i
$516$	−32.5623			−1.43348
$517$	−0.690983	−	7.38394i	−0.0303894	−	0.324745i
$518$	−13.5967			−0.597407
$519$	−1.28115	+	0.930812i	−0.0562364	+	0.0408581i
$520$	−9.40983	−	28.9605i	−0.412648	−	1.27000i
$521$	6.13525	−	18.8824i	0.268790	−	0.827252i	−0.722005	−	0.691887i	$-0.756779\pi$
$521$	6.13525	−	18.8824i	0.268790	−	0.827252i	0.990796	−	0.135364i	$-0.0432205\pi$
$522$	−2.38197	−	1.73060i	−0.104256	−	0.0757463i
$523$	19.7533	+	14.3516i	0.863751	+	0.627552i	0.928903	−	0.370324i	$-0.120753\pi$
$523$	19.7533	+	14.3516i	0.863751	+	0.627552i	−0.0651518	+	0.997875i	$0.520753\pi$
$524$	4.85410	−	14.9394i	0.212052	−	0.652630i
$525$		0			0
$526$	−6.69098	+	4.86128i	−0.291741	+	0.211962i
$527$	4.76393			0.207520
$528$	7.01064	−	11.8290i	0.305099	−	0.514789i
$529$	−19.8885			−0.864719
$530$	1.21885	−	0.885544i	0.0529433	−	0.0384656i
$531$	−7.00000	−	21.5438i	−0.303774	−	0.934921i
$532$	1.42705	−	4.39201i	0.0618705	−	0.190418i
$533$	−3.76393	−	2.73466i	−0.163034	−	0.118451i
$534$	−7.92705	−	5.75934i	−0.343037	−	0.249231i
$535$	−2.07295	+	6.37988i	−0.0896214	+	0.275826i
$536$	9.57295	+	29.4625i	0.413488	+	1.27259i
$537$	−31.8713	+	23.1559i	−1.37535	+	0.999250i
$538$	−2.27051			−0.0978886
$539$	2.51064	+	2.85317i	0.108141	+	0.122895i
$540$	−8.09017			−0.348145
$541$	8.88197	−	6.45313i	0.381866	−	0.277442i	−0.380249	−	0.924884i	$-0.624162\pi$
$541$	8.88197	−	6.45313i	0.381866	−	0.277442i	0.762114	+	0.647443i	$0.224162\pi$
$542$	3.30244	+	10.1639i	0.141852	+	0.436575i
$543$	1.15654	−	3.55947i	0.0496319	−	0.152751i
$544$	4.54508	+	3.30220i	0.194869	+	0.141581i
$545$	−15.4894	−	11.2537i	−0.663491	−	0.482055i
$546$	7.42299	−	22.8456i	0.317674	−	0.977701i
$547$	10.5902	+	32.5932i	0.452803	+	1.39358i	0.873695	+	0.486474i	$0.161717\pi$
$547$	10.5902	+	32.5932i	0.452803	+	1.39358i	−0.420892	+	0.907111i	$0.638283\pi$
$548$	−29.2254	+	21.2335i	−1.24845	+	0.907051i
$549$	−25.1246			−1.07229
$550$		0			0
$551$	2.38197			0.101475
$552$	7.13525	−	5.18407i	0.303697	−	0.220649i
$553$	−0.881966	−	2.71441i	−0.0375050	−	0.115429i
$554$	−1.59017	+	4.89404i	−0.0675598	+	0.207928i
$555$	31.1803	+	22.6538i	1.32353	+	0.961602i
$556$	1.38197	+	1.00406i	0.0586084	+	0.0425815i
$557$	−6.24671	+	19.2254i	−0.264682	+	0.814606i	0.727085	+	0.686548i	$0.240875\pi$
$557$	−6.24671	+	19.2254i	−0.264682	+	0.814606i	−0.991767	+	0.128059i	$0.959125\pi$
$558$	−1.81966	−	5.60034i	−0.0770324	−	0.237081i
$559$	44.3435	−	32.2174i	1.87553	−	1.36265i
$560$	−11.8328			−0.500028
$561$	−3.78115	+	6.37988i	−0.159640	+	0.269359i
$562$	14.5066			0.611923
$563$	−0.190983	+	0.138757i	−0.00804897	+	0.00584792i	−0.591802	−	0.806083i	$-0.701583\pi$
$563$	−0.190983	+	0.138757i	−0.00804897	+	0.00584792i	0.583753	+	0.811931i	$0.301583\pi$
$564$	2.50000	+	7.69421i	0.105269	+	0.323985i
$565$	−12.3992	+	38.1608i	−0.521638	+	1.60544i
$566$	6.07295	+	4.41226i	0.255265	+	0.185461i
$567$	−25.3992	−	18.4536i	−1.06667	−	0.774978i
$568$	−5.42705	+	16.7027i	−0.227714	+	0.700832i
$569$	−2.63525	−	8.11048i	−0.110476	−	0.340009i	0.880501	−	0.474044i	$-0.157206\pi$
$569$	−2.63525	−	8.11048i	−0.110476	−	0.340009i	−0.990977	+	0.134035i	$0.957206\pi$
$570$	2.50000	−	1.81636i	0.104713	−	0.0760788i
$571$	−12.5623			−0.525716			−0.262858	−	0.964835i	$-0.584665\pi$
$571$	−12.5623			−0.525716			−0.262858	+	0.964835i	$0.584665\pi$
$572$	3.04508	+	32.5402i	0.127321	+	1.36057i
$573$	−41.8328			−1.74759
$574$	1.09017	−	0.792055i	0.0455028	−	0.0330597i
$575$		0			0
$576$	−0.145898	+	0.449028i	−0.00607908	+	0.0187095i
$577$	25.6976	+	18.6704i	1.06980	+	0.777258i	0.975877	−	0.218321i	$-0.0700581\pi$
$577$	25.6976	+	18.6704i	1.06980	+	0.777258i	0.0939265	+	0.995579i	$0.470058\pi$
$578$	−0.500000	−	0.363271i	−0.0207973	−	0.0151101i
$579$	5.52786	−	17.0130i	0.229730	−	0.707037i
$580$	−2.66312	−	8.19624i	−0.110580	−	0.340330i
$581$	23.2984	−	16.9273i	0.966579	−	0.702261i
$582$	−21.0557			−0.872788
$583$	−3.31966	+	1.43284i	−0.137486	+	0.0593422i
$584$	−5.20163			−0.215245
$585$	−22.0344	+	16.0090i	−0.911012	+	0.661889i
$586$	−2.05166	−	6.31437i	−0.0847534	−	0.260844i
$587$	−1.71885	+	5.29007i	−0.0709444	+	0.218344i	−0.980242	−	0.197802i	$-0.936620\pi$
$587$	−1.71885	+	5.29007i	−0.0709444	+	0.218344i	0.909298	+	0.416147i	$0.136620\pi$
$588$	−3.35410	−	2.43690i	−0.138321	−	0.100496i
$589$	3.85410	+	2.80017i	0.158806	+	0.115379i
$590$	−4.83688	+	14.8864i	−0.199131	+	0.612863i
$591$	14.0836	+	43.3448i	0.579322	+	1.78297i
$592$	−11.5623	+	8.40051i	−0.475208	+	0.345259i
$593$	−27.3050			−1.12128			−0.560640	−	0.828060i	$-0.689445\pi$
$593$	−27.3050			−1.12128			−0.560640	+	0.828060i	$0.689445\pi$
$594$	−4.47214	−	1.00406i	−0.183494	−	0.0411970i
$595$	6.38197			0.261635
$596$	10.2812	−	7.46969i	0.421132	−	0.305971i
$597$	5.36475	+	16.5110i	0.219564	+	0.675750i
$598$	−2.05166	+	6.31437i	−0.0838987	+	0.258214i
$599$	−24.6525	−	17.9111i	−1.00727	−	0.731827i	−0.0436375	−	0.999047i	$-0.513895\pi$
$599$	−24.6525	−	17.9111i	−1.00727	−	0.731827i	−0.963635	+	0.267221i	$0.913895\pi$
$600$		0			0
$601$	3.17376	−	9.76784i	0.129460	−	0.398438i	−0.865227	−	0.501381i	$-0.832826\pi$
$601$	3.17376	−	9.76784i	0.129460	−	0.398438i	0.994687	+	0.102942i	$0.0328257\pi$
$602$	4.90576	+	15.0984i	0.199944	+	0.615364i
$603$	22.4164	−	16.2865i	0.912867	−	0.663236i
$604$	−36.2705			−1.47583
$605$	−11.8090	−	21.5765i	−0.480105	−	0.877211i
$606$	18.8197			0.764496
$607$	−38.6976	+	28.1154i	−1.57069	+	1.14117i	−0.644189	+	0.764866i	$0.722805\pi$
$607$	−38.6976	+	28.1154i	−1.57069	+	1.14117i	−0.926496	+	0.376304i	$0.877195\pi$
$608$	1.73607	+	5.34307i	0.0704069	+	0.216690i
$609$	4.69756	−	14.4576i	0.190355	−	0.585852i
$610$	14.0451	+	10.2044i	0.568669	+	0.413162i
$611$	−11.0172	−	8.00448i	−0.445709	−	0.323827i
$612$	1.00000	−	3.07768i	0.0404226	−	0.124408i
$613$	−12.3262	−	37.9363i	−0.497852	−	1.53223i	−0.812464	−	0.583011i	$-0.801875\pi$
$613$	−12.3262	−	37.9363i	−0.497852	−	1.53223i	0.314612	−	0.949220i	$-0.398125\pi$
$614$	5.66312	−	4.11450i	0.228545	−	0.166048i
$615$	−3.81966			−0.154024
$616$	−20.6525	−	4.63677i	−0.832112	−	0.186821i
$617$	−49.0132			−1.97320			−0.986598	−	0.163172i	$-0.947828\pi$
$617$	−49.0132			−1.97320			−0.986598	+	0.163172i	$0.947828\pi$
$618$	−16.7705	+	12.1845i	−0.674609	+	0.490132i
$619$	−1.43769	−	4.42477i	−0.0577858	−	0.177846i	0.917997	−	0.396587i	$-0.129805\pi$
$619$	−1.43769	−	4.42477i	−0.0577858	−	0.177846i	−0.975783	+	0.218740i	$0.929805\pi$
$620$	5.32624	−	16.3925i	0.213907	−	0.658338i
$621$	3.19098	+	2.31838i	0.128050	+	0.0930336i
$622$	−0.236068	−	0.171513i	−0.00946546	−	0.00687706i
$623$	6.25329	−	19.2456i	0.250533	−	0.771060i
$624$	−7.80244	−	24.0134i	−0.312348	−	0.961307i
$625$	20.2254	−	14.6946i	0.809017	−	0.587785i
$626$	4.97871			0.198989
$627$	−6.80902	+	2.93893i	−0.271926	+	0.117369i
$628$	2.61803			0.104471
$629$	6.23607	−	4.53077i	0.248648	−	0.180654i
$630$	−2.43769	−	7.50245i	−0.0971201	−	0.298905i
$631$	1.32624	−	4.08174i	0.0527967	−	0.162492i	−0.921182	−	0.389133i	$-0.872775\pi$
$631$	1.32624	−	4.08174i	0.0527967	−	0.162492i	0.973978	+	0.226642i	$0.0727746\pi$
$632$	1.80902	+	1.31433i	0.0719588	+	0.0522812i
$633$	38.4164	+	27.9112i	1.52692	+	1.10937i
$634$	5.41641	−	16.6700i	0.215113	−	0.662050i
$635$	−2.92705	−	9.00854i	−0.116156	−	0.357493i
$636$	3.19098	−	2.31838i	0.126531	−	0.0919299i
$637$	6.97871			0.276507
$638$	−0.454915	−	4.86128i	−0.0180103	−	0.192460i
$639$	15.7082			0.621407
$640$	20.5902	−	14.9596i	0.813898	−	0.591331i
$641$	−0.274575	−	0.845055i	−0.0108451	−	0.0333777i	0.945488	−	0.325658i	$-0.105586\pi$
$641$	−0.274575	−	0.845055i	−0.0108451	−	0.0333777i	−0.956333	+	0.292281i	$0.905586\pi$
$642$	1.28115	−	3.94298i	0.0505631	−	0.155617i
$643$	35.3713	+	25.6988i	1.39491	+	1.01346i	0.995307	+	0.0967719i	$0.0308517\pi$
$643$	35.3713	+	25.6988i	1.39491	+	1.01346i	0.399602	+	0.916689i	$0.369148\pi$
$644$	6.59017	+	4.78804i	0.259689	+	0.188675i
$645$	13.9058	−	42.7975i	0.547539	−	1.68515i
$646$	−0.190983	−	0.587785i	−0.00751413	−	0.0231261i
$647$	−4.76393	+	3.46120i	−0.187289	+	0.136074i	−0.677479	−	0.735542i	$-0.736928\pi$
$647$	−4.76393	+	3.46120i	−0.187289	+	0.136074i	0.490190	+	0.871616i	$0.336928\pi$
$648$	24.5967			0.966252
$649$	19.1525	−	32.3157i	0.751800	−	1.26850i
$650$		0			0
$651$	24.5967	−	17.8706i	0.964023	−	0.700403i
$652$	9.59017	+	29.5155i	0.375580	+	1.15592i
$653$	−3.46149	+	10.6534i	−0.135459	+	0.416899i	−0.995661	−	0.0930538i	$-0.970337\pi$
$653$	−3.46149	+	10.6534i	−0.135459	+	0.416899i	0.860202	+	0.509953i	$0.170337\pi$
$654$	9.57295	+	6.95515i	0.374332	+	0.271968i
$655$	17.5623	+	12.7598i	0.686216	+	0.498565i
$656$	0.437694	−	1.34708i	0.0170891	−	0.0525948i
$657$	1.43769	+	4.42477i	0.0560898	+	0.172627i
$658$	3.19098	−	2.31838i	0.124397	−	0.0903801i
$659$	−14.1246			−0.550217			−0.275108	−	0.961413i	$-0.588714\pi$
$659$	−14.1246			−0.550217			−0.275108	+	0.961413i	$0.588714\pi$
$660$	17.7254	+	20.1437i	0.689961	+	0.784092i
$661$	43.8328			1.70490			0.852449	−	0.522810i	$-0.175116\pi$
$661$	43.8328			1.70490			0.852449	+	0.522810i	$0.175116\pi$
$662$	1.50000	−	1.08981i	0.0582992	−	0.0423568i
$663$	4.20820	+	12.9515i	0.163433	+	0.502995i
$664$	−6.97214	+	21.4580i	−0.270571	+	0.832733i
$665$	5.16312	+	3.75123i	0.200217	+	0.145466i
$666$	−7.70820	−	5.60034i	−0.298687	−	0.217009i
$667$	−1.29837	+	3.99598i	−0.0502732	+	0.154725i
$668$	−5.82624	−	17.9313i	−0.225424	−	0.693783i
$669$	−29.5344	+	21.4580i	−1.14187	+	0.829615i
$670$	−19.1459			−0.739671
$671$	−27.5238	−	31.2789i	−1.06254	−	1.20751i
$672$	35.8541			1.38310
$673$	9.35410	−	6.79615i	0.360574	−	0.261972i	−0.392717	−	0.919659i	$-0.628465\pi$
$673$	9.35410	−	6.79615i	0.360574	−	0.261972i	0.753292	+	0.657687i	$0.228465\pi$
$674$	4.36475	+	13.4333i	0.168124	+	0.517432i
$675$		0			0
$676$	31.5344	+	22.9111i	1.21286	+	0.881197i
$677$	−34.0623	−	24.7477i	−1.30912	−	0.951132i	−1.00000		0.000109116i	$-0.999965\pi$
$677$	−34.0623	−	24.7477i	−1.30912	−	0.951132i	−0.309121	−	0.951023i	$-0.600035\pi$
$678$	7.66312	−	23.5847i	0.294300	−	0.905763i
$679$	−13.4377	−	41.3570i	−0.515691	−	1.58713i
$680$	−4.04508	+	2.93893i	−0.155122	+	0.112703i
$681$	1.70820			0.0654585
$682$	4.97871	−	8.40051i	0.190645	−	0.321672i
$683$	19.1459			0.732597			0.366299	−	0.930497i	$-0.380625\pi$
$683$	19.1459			0.732597			0.366299	+	0.930497i	$0.380625\pi$
$684$	2.61803	−	1.90211i	0.100103	−	0.0727291i
$685$	−15.4271	−	47.4796i	−0.589437	−	1.81410i
$686$	3.19098	−	9.82084i	0.121832	−	0.374961i
$687$	−2.33688	−	1.69784i	−0.0891576	−	0.0647768i
$688$	13.5000	+	9.80832i	0.514683	+	0.373939i
$689$	−2.05166	+	6.31437i	−0.0781621	+	0.240558i
$690$	1.68441	+	5.18407i	0.0641242	+	0.197354i
$691$	3.40983	−	2.47739i	0.129716	−	0.0942442i	−0.521035	−	0.853535i	$-0.674454\pi$
$691$	3.40983	−	2.47739i	0.129716	−	0.0942442i	0.650751	+	0.759291i	$0.274454\pi$
$692$	1.14590			0.0435605
$693$	1.76393	+	18.8496i	0.0670062	+	0.716038i
$694$	10.1459			0.385133
$695$	−1.90983	+	1.38757i	−0.0724440	+	0.0526336i
$696$	3.68034	+	11.3269i	0.139503	+	0.429346i
$697$	−0.236068	+	0.726543i	−0.00894171	+	0.0275198i
$698$	−8.70820	−	6.32688i	−0.329610	−	0.239476i
$699$	−9.37132	−	6.80866i	−0.354456	−	0.257527i
$700$		0			0
$701$	−3.45492	−	10.6331i	−0.130490	−	0.401608i	0.864371	−	0.502855i	$-0.167717\pi$
$701$	−3.45492	−	10.6331i	−0.130490	−	0.401608i	−0.994861	+	0.101247i	$0.967717\pi$
$702$	−6.80902	+	4.94704i	−0.256990	+	0.186714i
$703$	7.70820			0.290720
$704$	−0.718847	+	0.310271i	−0.0270926	+	0.0116938i
$705$	−11.1803			−0.421076
$706$	11.2082	−	8.14324i	0.421826	−	0.306475i
$707$	12.0106	+	36.9650i	0.451707	+	1.39021i
$708$	−12.6631	+	38.9731i	−0.475909	+	1.46470i
$709$	15.1353	+	10.9964i	0.568416	+	0.412979i	0.834530	−	0.550963i	$-0.185739\pi$
$709$	15.1353	+	10.9964i	0.568416	+	0.412979i	−0.266113	+	0.963942i	$0.585739\pi$
$710$	−8.78115	−	6.37988i	−0.329551	−	0.239433i
$711$	0.618034	−	1.90211i	0.0231781	−	0.0713348i
$712$	4.89919	+	15.0781i	0.183605	+	0.565077i
$713$	−6.79837	+	4.93931i	−0.254601	+	0.184979i
$714$	−3.94427			−0.147611
$715$	−44.0689	−	9.89408i	−1.64808	−	0.370018i
$716$	28.5066			1.06534
$717$	16.7082	−	12.1392i	0.623979	−	0.453348i
$718$	−4.22949	−	13.0170i	−0.157843	−	0.485791i
$719$	2.36068	−	7.26543i	0.0880385	−	0.270955i	−0.897338	−	0.441343i	$-0.854502\pi$
$719$	2.36068	−	7.26543i	0.0880385	−	0.270955i	0.985377	+	0.170388i	$0.0545022\pi$
$720$	−6.70820	−	4.87380i	−0.250000	−	0.181636i
$721$	−34.6353	−	25.1640i	−1.28988	−	0.937156i
$722$	−3.43769	+	10.5801i	−0.127938	+	0.393752i
$723$	13.6180	+	41.9120i	0.506460	+	1.55872i
$724$	−2.19098	+	1.59184i	−0.0814272	+	0.0591604i
$725$		0			0
$726$	7.29837	+	13.3350i	0.270868	+	0.494910i
$727$	24.0000			0.890111			0.445055	−	0.895503i	$-0.353184\pi$
$727$	24.0000			0.890111			0.445055	+	0.895503i	$0.353184\pi$
$728$	−31.4443	+	22.8456i	−1.16540	+	0.846714i
$729$	−2.16312	−	6.65740i	−0.0801155	−	0.246570i
$730$	0.993422	−	3.05744i	0.0367682	−	0.113161i
$731$	−7.28115	−	5.29007i	−0.269303	−	0.195660i
$732$	36.7705	+	26.7153i	1.35908	+	0.987427i
$733$	−11.9271	+	36.7077i	−0.440536	+	1.35583i	0.446771	+	0.894649i	$0.352574\pi$
$733$	−11.9271	+	36.7077i	−0.440536	+	1.35583i	−0.887306	+	0.461181i	$0.847426\pi$
$734$	−1.58359	−	4.87380i	−0.0584515	−	0.179895i
$735$	4.63525	−	3.36771i	0.170974	−	0.124220i
$736$	−9.90983			−0.365281
$737$	44.8328	+	10.0656i	1.65144	+	0.370771i
$738$	0.944272			0.0347591
$739$	9.78115	−	7.10642i	0.359806	−	0.261414i	−0.393165	−	0.919468i	$-0.628620\pi$
$739$	9.78115	−	7.10642i	0.359806	−	0.261414i	0.752971	+	0.658054i	$0.228620\pi$
$740$	−8.61803	−	26.5236i	−0.316805	−	0.975026i
$741$	−4.20820	+	12.9515i	−0.154592	+	0.475786i
$742$	−1.55573	−	1.13030i	−0.0571126	−	0.0414947i
$743$	39.7148	+	28.8545i	1.45699	+	1.05857i	0.984133	+	0.177431i	$0.0567787\pi$
$743$	39.7148	+	28.8545i	1.45699	+	1.05857i	0.472861	+	0.881137i	$0.343221\pi$
$744$	−7.36068	+	22.6538i	−0.269856	+	0.830530i
$745$	5.42705	+	16.7027i	0.198832	+	0.611941i
$746$	−13.2812	+	9.64932i	−0.486258	+	0.353287i
$747$	20.1803			0.738360
$748$	4.92705	−	2.12663i	0.180151	−	0.0777572i
$749$	8.56231			0.312860
$750$	−12.5000	+	9.08178i	−0.456435	+	0.331620i
$751$	−0.579527	−	1.78360i	−0.0211472	−	0.0650845i	0.939926	−	0.341378i	$-0.110894\pi$
$751$	−0.579527	−	1.78360i	−0.0211472	−	0.0650845i	−0.961073	+	0.276294i	$0.910894\pi$
$752$	1.28115	−	3.94298i	0.0467188	−	0.143786i
$753$	−16.2812	−	11.8290i	−0.593318	−	0.431071i
$754$	−7.25329	−	5.26982i	−0.264149	−	0.191916i
$755$	15.4894	−	47.6713i	0.563715	−	1.73494i
$756$	3.19098	+	9.82084i	0.116055	+	0.357180i
$757$	−3.32624	+	2.41665i	−0.120894	+	0.0878348i	−0.646589	−	0.762838i	$-0.723805\pi$
$757$	−3.32624	+	2.41665i	−0.120894	+	0.0878348i	0.525695	+	0.850673i	$0.323805\pi$
$758$	10.0689			0.365718
$759$	−1.21885	−	13.0248i	−0.0442413	−	0.472769i
$760$	−5.00000			−0.181369
$761$	28.9894	−	21.0620i	1.05086	−	0.763497i	0.0784869	−	0.996915i	$-0.474991\pi$
$761$	28.9894	−	21.0620i	1.05086	−	0.763497i	0.972376	+	0.233418i	$0.0749911\pi$
$762$	1.80902	+	5.56758i	0.0655338	+	0.201692i
$763$	−7.55166	+	23.2416i	−0.273389	+	0.841403i
$764$	24.4894	+	17.7926i	0.885994	+	0.643712i
$765$	3.61803	+	2.62866i	0.130810	+	0.0950392i
$766$	−4.97214	+	15.3027i	−0.179651	+	0.552908i
$767$	−21.3156	−	65.6027i	−0.769662	−	2.36877i
$768$	−11.8713	+	8.62502i	−0.428369	+	0.311229i
$769$	−25.1459			−0.906784			−0.453392	−	0.891311i	$-0.649786\pi$
$769$	−25.1459			−0.906784			−0.453392	+	0.891311i	$0.649786\pi$
$770$	6.66970	−	11.2537i	0.240359	−	0.405554i
$771$	15.5279			0.559222
$772$	−10.4721	+	7.60845i	−0.376900	+	0.273834i
$773$	5.66970	+	17.4495i	0.203925	+	0.627616i	0.999756	+	0.0220973i	$0.00703435\pi$
$773$	5.66970	+	17.4495i	0.203925	+	0.627616i	−0.795831	+	0.605519i	$0.792966\pi$
$774$	−3.43769	+	10.5801i	−0.123565	+	0.380295i
$775$		0			0
$776$	27.5623	+	20.0252i	0.989429	+	0.718862i
$777$	15.2016	−	46.7858i	0.545355	−	1.67843i
$778$	1.13525	+	3.49396i	0.0407009	+	0.125264i
$779$	−0.618034	+	0.449028i	−0.0221434	+	0.0160881i
$780$	49.2705			1.76417
$781$	17.2082	+	19.5559i	0.615758	+	0.699766i
$782$	1.09017			0.0389844
$783$	−4.30902	+	3.13068i	−0.153992	+	0.111882i
$784$	0.656541	+	2.02063i	0.0234479	+	0.0721652i
$785$	−1.11803	+	3.44095i	−0.0399043	+	0.122813i
$786$	−10.8541	−	7.88597i	−0.387153	−	0.281283i
$787$	−25.3885	−	18.4459i	−0.905004	−	0.657524i	0.0347425	−	0.999396i	$-0.488939\pi$
$787$	−25.3885	−	18.4459i	−0.905004	−	0.657524i	−0.939746	+	0.341873i	$0.888939\pi$
$788$	10.1910	−	31.3646i	0.363039	−	1.11732i
$789$	−9.24671	−	28.4585i	−0.329192	−	1.01315i
$790$	−1.11803	+	0.812299i	−0.0397779	+	0.0289003i
$791$	51.2148			1.82099
$792$	−9.79837	−	11.1352i	−0.348170	−	0.395671i
$793$	−76.5066			−2.71683
$794$	−3.20820	+	2.33090i	−0.113855	+	0.0827204i
$795$	1.68441	+	5.18407i	0.0597397	+	0.183860i
$796$	3.88197	−	11.9475i	0.137593	−	0.423467i
$797$	−16.0623	−	11.6699i	−0.568956	−	0.413371i	0.265770	−	0.964037i	$-0.414374\pi$
$797$	−16.0623	−	11.6699i	−0.568956	−	0.413371i	−0.834726	+	0.550666i	$0.814374\pi$
$798$	−3.19098	−	2.31838i	−0.112960	−	0.0820699i
$799$	−0.690983	+	2.12663i	−0.0244452	+	0.0752347i
$800$		0			0
$801$	11.4721	−	8.33499i	0.405348	−	0.294503i
$802$	14.8328			0.523765
$803$	−3.93363	+	6.63715i	−0.138815	+	0.234220i
$804$	−50.1246			−1.76776
$805$	−9.10739	+	6.61691i	−0.320993	+	0.233215i
$806$	−5.54102	−	17.0535i	−0.195174	−	0.600684i
$807$	2.53851	−	7.81272i	0.0893597	−	0.275021i
$808$	−24.6353	−	17.8986i	−0.866665	−	0.629669i
$809$	20.9164	+	15.1967i	0.735382	+	0.534286i	0.891261	−	0.453490i	$-0.149821\pi$
$809$	20.9164	+	15.1967i	0.735382	+	0.534286i	−0.155880	+	0.987776i	$0.549821\pi$
$810$	−4.69756	+	14.4576i	−0.165055	+	0.507988i
$811$	−5.11803	−	15.7517i	−0.179718	−	0.553117i	0.820099	−	0.572222i	$-0.193918\pi$
$811$	−5.11803	−	15.7517i	−0.179718	−	0.553117i	−0.999817	+	0.0191051i	$0.993918\pi$
$812$	−8.89919	+	6.46564i	−0.312300	+	0.226899i
$813$	−38.6656			−1.35606
$814$	−1.47214	−	15.7314i	−0.0515983	−	0.551387i
$815$	−42.8885			−1.50232
$816$	−3.35410	+	2.43690i	−0.117417	+	0.0853085i
$817$	−2.78115	−	8.55951i	−0.0973002	−	0.299459i
$818$	−3.73607	+	11.4984i	−0.130629	+	0.402033i
$819$	28.1246	+	20.4337i	0.982753	+	0.714012i
$820$	2.23607	+	1.62460i	0.0780869	+	0.0567334i
$821$	−5.00000	+	15.3884i	−0.174501	+	0.537059i	−0.999610	−	0.0279139i	$-0.991114\pi$
$821$	−5.00000	+	15.3884i	−0.174501	+	0.537059i	0.825109	+	0.564973i	$0.191114\pi$
$822$	9.53444	+	29.3440i	0.332552	+	1.02349i
$823$	16.1803	−	11.7557i	0.564011	−	0.409778i	−0.268914	−	0.963164i	$-0.586665\pi$
$823$	16.1803	−	11.7557i	0.564011	−	0.409778i	0.832925	+	0.553386i	$0.186665\pi$
$824$	33.5410			1.16846
$825$		0			0
$826$	19.9787			0.695148
$827$	40.6246	−	29.5155i	1.41266	−	1.02635i	0.419726	−	0.907651i	$-0.362126\pi$
$827$	40.6246	−	29.5155i	1.41266	−	1.02635i	0.992930	−	0.118704i	$-0.0378740\pi$
$828$	1.76393	+	5.42882i	0.0613009	+	0.188665i
$829$	4.05573	−	12.4822i	0.140861	−	0.433526i	−0.855594	−	0.517647i	$-0.826808\pi$
$829$	4.05573	−	12.4822i	0.140861	−	0.433526i	0.996456	+	0.0841206i	$0.0268081\pi$
$830$	−11.2812	−	8.19624i	−0.391575	−	0.284496i
$831$	−15.0623	−	10.9434i	−0.522506	−	0.379623i
$832$	−0.444272	+	1.36733i	−0.0154024	+	0.0474036i
$833$	−0.354102	−	1.08981i	−0.0122689	−	0.0377598i
$834$	1.18034	−	0.857567i	0.0408718	−	0.0296951i
$835$	26.0557			0.901696
$836$	5.23607	+	1.17557i	0.181093	+	0.0406580i
$837$	−10.6525			−0.368203
$838$	−16.7705	+	12.1845i	−0.579328	+	0.420906i
$839$	−0.145898	−	0.449028i	−0.00503696	−	0.0155022i	0.948506	−	0.316758i	$-0.102594\pi$
$839$	−0.145898	−	0.449028i	−0.00503696	−	0.0155022i	−0.953543	+	0.301256i	$0.902594\pi$
$840$	−9.86068	+	30.3481i	−0.340226	+	1.04711i
$841$	18.8713	+	13.7108i	0.650735	+	0.472787i
$842$	8.56231	+	6.22088i	0.295077	+	0.214386i
$843$	−16.2188	+	49.9165i	−0.558607	+	1.71921i
$844$	−10.6180	−	32.6789i	−0.365488	−	1.12486i
$845$	−43.5795	+	31.6624i	−1.49918	+	1.08922i
$846$	2.76393			0.0950259
$847$	−21.5344	+	22.8456i	−0.739932	+	0.784984i
$848$	−2.02129			−0.0694113
$849$	−21.9721	+	15.9637i	−0.754082	+	0.547872i
$850$		0			0
$851$	−4.20163	+	12.9313i	−0.144030	+	0.443278i
$852$	−22.9894	−	16.7027i	−0.787602	−	0.572227i
$853$	13.6353	+	9.90659i	0.466862	+	0.339195i	0.796217	−	0.605011i	$-0.206831\pi$
$853$	13.6353	+	9.90659i	0.466862	+	0.339195i	−0.329355	+	0.944206i	$0.606831\pi$
$854$	6.84752	−	21.0745i	0.234317	−	0.721155i
$855$	1.38197	+	4.25325i	0.0472622	+	0.145458i
$856$	−5.42705	+	3.94298i	−0.185493	+	0.134768i
$857$	51.3394			1.75372			0.876860	−	0.480746i	$-0.159634\pi$
$857$	51.3394			1.75372			0.876860	+	0.480746i	$0.159634\pi$
$858$	27.2361	+	6.11488i	0.929824	+	0.208759i
$859$	−0.416408			−0.0142077			−0.00710383	−	0.999975i	$-0.502261\pi$
$859$	−0.416408			−0.0142077			−0.00710383	+	0.999975i	$0.502261\pi$
$860$	−26.3435	+	19.1396i	−0.898304	+	0.652656i
$861$	1.50658	+	4.63677i	0.0513440	+	0.158021i
$862$	4.59675	−	14.1473i	0.156566	−	0.481860i
$863$	3.76393	+	2.73466i	0.128126	+	0.0930888i	0.650002	−	0.759932i	$-0.274768\pi$
$863$	3.76393	+	2.73466i	0.128126	+	0.0930888i	−0.521877	+	0.853021i	$0.674768\pi$
$864$	−10.1631	−	7.38394i	−0.345756	−	0.251207i
$865$	−0.489357	+	1.50609i	−0.0166386	+	0.0512084i
$866$	0.472136	+	1.45309i	0.0160438	+	0.0493778i
$867$	1.80902	−	1.31433i	0.0614374	−	0.0446369i
$868$	−22.0000			−0.746729
$869$	3.04508	−	1.31433i	0.103297	−	0.0445855i
$870$	−7.36068			−0.249550
$871$	68.2599	−	49.5937i	2.31290	−	1.68042i
$872$	−5.91641	−	18.2088i	−0.200355	−	0.616629i
$873$	9.41641	−	28.9807i	0.318697	−	0.980849i
$874$	0.881966	+	0.640786i	0.0298329	+	0.0216749i
$875$	−25.8156	−	18.7561i	−0.872726	−	0.634073i
$876$	2.60081	−	8.00448i	0.0878733	−	0.270446i
$877$	−2.60081	−	8.00448i	−0.0878232	−	0.270292i	0.897494	−	0.441027i	$-0.145386\pi$
$877$	−2.60081	−	8.00448i	−0.0878232	−	0.270292i	−0.985317	+	0.170735i	$0.945386\pi$
$878$	2.56231	−	1.86162i	0.0864736	−	0.0628268i
$879$	24.0213			0.810218
$880$	−1.28115	−	13.6906i	−0.0431877	−	0.461509i
$881$	10.2148			0.344145			0.172072	−	0.985084i	$-0.444954\pi$
$881$	10.2148			0.344145			0.172072	+	0.985084i	$0.444954\pi$
$882$	−1.14590	+	0.832544i	−0.0385844	+	0.0280332i
$883$	1.61146	+	4.95955i	0.0542298	+	0.166902i	0.974503	−	0.224374i	$-0.0720337\pi$
$883$	1.61146	+	4.95955i	0.0542298	+	0.166902i	−0.920273	+	0.391276i	$0.872034\pi$
$884$	3.04508	−	9.37181i	0.102417	−	0.315208i
$885$	−45.8156	−	33.2870i	−1.54007	−	1.11893i
$886$	7.25329	+	5.26982i	0.243679	+	0.177043i
$887$	5.17376	−	15.9232i	0.173718	−	0.534649i	−0.825855	−	0.563883i	$-0.809307\pi$
$887$	5.17376	−	15.9232i	0.173718	−	0.534649i	0.999573	+	0.0292342i	$0.00930687\pi$
$888$	11.9098	+	36.6547i	0.399668	+	1.23005i
$889$	−9.78115	+	7.10642i	−0.328049	+	0.238342i
$890$	−9.79837			−0.328442
$891$	18.6008	−	31.3849i	0.623151	−	1.05143i
$892$	26.4164			0.884487
$893$	−1.80902	+	1.31433i	−0.0605364	+	0.0439823i
$894$	−3.35410	−	10.3229i	−0.112178	−	0.345248i
$895$	−12.1738	+	37.4670i	−0.406924	+	1.25238i
$896$	−26.2812	−	19.0944i	−0.877992	−	0.637898i
$897$	−19.4336	−	14.1194i	−0.648870	−	0.471432i
$898$	1.38197	−	4.25325i	0.0461168	−	0.141933i
$899$	−3.50658	−	10.7921i	−0.116951	−	0.359938i
$900$		0			0
$901$	1.09017			0.0363188
$902$	1.03444	+	1.17557i	0.0344431	+	0.0391422i
$903$	−57.4377			−1.91141
$904$	−32.4615	+	23.5847i	−1.07965	+	0.784414i
$905$	−1.15654	−	3.55947i	−0.0384447	−	0.118321i
$906$	−9.57295	+	29.4625i	−0.318040	+	0.978826i
$907$	−14.6631	−	10.6534i	−0.486881	−	0.353740i	0.317103	−	0.948391i	$-0.397290\pi$
$907$	−14.6631	−	10.6534i	−0.486881	−	0.353740i	−0.803984	+	0.594652i	$0.797290\pi$
$908$	−1.00000	−	0.726543i	−0.0331862	−	0.0241112i
$909$	−8.41641	+	25.9030i	−0.279155	+	0.859150i
$910$	−7.42299	−	22.8456i	−0.246070	−	0.757324i
$911$	6.48936	−	4.71479i	0.215002	−	0.156208i	−0.475072	−	0.879947i	$-0.657578\pi$
$911$	6.48936	−	4.71479i	0.215002	−	0.156208i	0.690074	+	0.723739i	$0.257578\pi$
$912$	−4.14590			−0.137284
$913$	22.1074	+	25.1235i	0.731648	+	0.831466i
$914$	4.23607			0.140117
$915$	−50.8156	+	36.9197i	−1.67991	+	1.22053i
$916$	0.645898	+	1.98787i	0.0213411	+	0.0656811i
$917$	8.56231	−	26.3521i	0.282752	−	0.870222i
$918$	1.11803	+	0.812299i	0.0369006	+	0.0268099i
$919$	−14.1910	−	10.3104i	−0.468117	−	0.340107i	0.328590	−	0.944473i	$-0.393427\pi$
$919$	−14.1910	−	10.3104i	−0.468117	−	0.340107i	−0.796707	+	0.604366i	$0.793427\pi$
$920$	2.72542	−	8.38800i	0.0898546	−	0.276544i
$921$	7.82624	+	24.0867i	0.257883	+	0.793683i
$922$	3.04508	−	2.21238i	0.100285	−	0.0728610i
$923$	47.8328			1.57444
$924$	17.4615	−	29.4625i	0.574441	−	0.969245i
$925$		0			0
$926$	0.100813	−	0.0732450i	0.00331292	−	0.00240698i
$927$	−9.27051	−	28.5317i	−0.304483	−	0.937104i
$928$	4.13525	−	12.7270i	0.135746	−	0.417784i
$929$	−40.0066	−	29.0665i	−1.31257	−	0.953640i	−0.999993	−	0.00374893i	$-0.998807\pi$
$929$	−40.0066	−	29.0665i	−1.31257	−	0.953640i	−0.312580	−	0.949891i	$-0.601193\pi$
$930$	−11.9098	−	8.65300i	−0.390539	−	0.283743i
$931$	0.354102	−	1.08981i	0.0116052	−	0.0357172i
$932$	2.59017	+	7.97172i	0.0848438	+	0.261122i
$933$	0.854102	−	0.620541i	0.0279620	−	0.0203156i
$934$	−22.2492			−0.728017
$935$	0.690983	+	7.38394i	0.0225976	+	0.241481i
$936$	−27.2361			−0.890239
$937$	−47.6246	+	34.6013i	−1.55583	+	1.13038i	−0.616500	+	0.787355i	$0.711450\pi$
$937$	−47.6246	+	34.6013i	−1.55583	+	1.13038i	−0.939328	+	0.343021i	$0.888550\pi$
$938$	7.55166	+	23.2416i	0.246571	+	0.758866i
$939$	−5.56637	+	17.1315i	−0.181652	+	0.559066i
$940$	6.54508	+	4.75528i	0.213477	+	0.155100i
$941$	4.23607	+	3.07768i	0.138092	+	0.100330i	0.654687	−	0.755900i	$-0.272801\pi$
$941$	4.23607	+	3.07768i	0.138092	+	0.100330i	−0.516595	+	0.856230i	$0.672801\pi$
$942$	0.690983	−	2.12663i	0.0225134	−	0.0692893i
$943$	−0.416408	−	1.28157i	−0.0135601	−	0.0417337i
$944$	16.9894	−	12.3435i	0.552956	−	0.401746i
$945$	−14.2705			−0.464220
$946$	−16.9377	+	7.31069i	−0.550692	+	0.237691i
$947$	42.4853			1.38059			0.690293	−	0.723530i	$-0.257482\pi$
$947$	42.4853			1.38059			0.690293	+	0.723530i	$0.257482\pi$
$948$	−2.92705	+	2.12663i	−0.0950662	+	0.0690696i
$949$	4.37790	+	13.4738i	0.142113	+	0.437378i
$950$		0			0
$951$	51.3050	+	37.2752i	1.66368	+	1.20873i
$952$	5.16312	+	3.75123i	0.167338	+	0.121578i
$953$	−18.1008	+	55.7086i	−0.586343	+	1.80458i	0.00746673	+	0.999972i	$0.497623\pi$
$953$	−18.1008	+	55.7086i	−0.586343	+	1.80458i	−0.593810	+	0.804606i	$0.702377\pi$
$954$	−0.416408	−	1.28157i	−0.0134817	−	0.0414924i
$955$	−33.8435	+	24.5887i	−1.09515	+	0.795672i
$956$	−14.9443			−0.483332
$957$	17.2361	+	3.86974i	0.557163	+	0.125091i
$958$	−4.14590			−0.133948
$959$	−51.5517	+	37.4545i	−1.66469	+	1.20947i
$960$	0.364745	+	1.12257i	0.0117721	+	0.0362308i
$961$	−2.56637	+	7.89848i	−0.0827862	+	0.254790i
$962$	−23.4721	−	17.0535i	−0.756772	−	0.549827i
$963$	4.85410	+	3.52671i	0.156421	+	0.113647i
$964$	9.85410	−	30.3278i	0.317379	−	0.976793i
$965$	−5.52786	−	17.0130i	−0.177948	−	0.547668i
$966$	5.62868	−	4.08947i	0.181100	−	0.131577i
$967$	−1.54915			−0.0498173			−0.0249087	−	0.999690i	$-0.507929\pi$
$967$	−1.54915			−0.0498173			−0.0249087	+	0.999690i	$0.507929\pi$
$968$	3.12868	−	24.3970i	0.100559	−	0.784148i
$969$	2.23607			0.0718329
$970$	−17.0344	+	12.3762i	−0.546943	+	0.397377i
$971$	2.00000	+	6.15537i	0.0641831	+	0.197535i	0.978006	−	0.208579i	$-0.0668837\pi$
$971$	2.00000	+	6.15537i	0.0641831	+	0.197535i	−0.913823	+	0.406114i	$0.866884\pi$
$972$	−8.94427	+	27.5276i	−0.286888	+	0.882949i
$973$	2.43769	+	1.77109i	0.0781489	+	0.0567785i
$974$	15.2533	+	11.0822i	0.488747	+	0.355095i
$975$		0			0
$976$	−7.19756	−	22.1518i	−0.230388	−	0.709062i
$977$	1.47214	−	1.06957i	0.0470978	−	0.0342186i	−0.563987	−	0.825783i	$-0.690733\pi$
$977$	1.47214	−	1.06957i	0.0470978	−	0.0342186i	0.611085	+	0.791565i	$0.290733\pi$
$978$	26.5066			0.847587
$979$	22.9443	+	5.15131i	0.733302	+	0.164637i
$980$	−4.14590			−0.132436
$981$	−13.8541	+	10.0656i	−0.442327	+	0.321370i
$982$	−2.32624	−	7.15942i	−0.0742332	−	0.228466i
$983$	8.56231	−	26.3521i	0.273095	−	0.840500i	−0.716622	−	0.697462i	$-0.754313\pi$
$983$	8.56231	−	26.3521i	0.273095	−	0.840500i	0.989717	−	0.143039i	$-0.0456873\pi$
$984$	−3.09017	−	2.24514i	−0.0985110	−	0.0715724i
$985$	36.8713	+	26.7886i	1.17482	+	0.853555i
$986$	−0.454915	+	1.40008i	−0.0144874	+	0.0445878i
$987$	4.40983	+	13.5721i	0.140366	+	0.432003i
$988$	7.97214	−	5.79210i	0.253627	−	0.184271i
$989$	15.8754			0.504808
$990$	8.41641	−	3.63271i	0.267491	−	0.115455i
$991$	28.2148			0.896272			0.448136	−	0.893965i	$-0.352088\pi$
$991$	28.2148			0.896272			0.448136	+	0.893965i	$0.352088\pi$
$992$	21.6525	−	15.7314i	0.687467	−	0.499474i
$993$	2.07295	+	6.37988i	0.0657830	+	0.202459i
$994$	−4.28115	+	13.1760i	−0.135790	+	0.417918i
$995$	14.0451	+	10.2044i	0.445259	+	0.323500i
$996$	−29.5344	−	21.4580i	−0.935835	−	0.679924i
$997$	−6.00658	+	18.4863i	−0.190230	+	0.585468i	−0.999999	−	0.00128044i	$-0.999592\pi$
$997$	−6.00658	+	18.4863i	−0.190230	+	0.585468i	0.809769	+	0.586749i	$0.199592\pi$
$998$	−6.65654	−	20.4867i	−0.210709	−	0.648496i
$999$	−13.9443	+	10.1311i	−0.441177	+	0.320534i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	187.2.g.a.69.1	✓	4
11.2	odd	10		2057.2.a.l.1.1		2
11.4	even	5	inner	187.2.g.a.103.1	yes	4
11.9	even	5		2057.2.a.g.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
187.2.g.a.69.1	✓	4	1.1	even	1	trivial
187.2.g.a.103.1	yes	4	11.4	even	5	inner
2057.2.a.g.1.2		2	11.9	even	5
2057.2.a.l.1.1		2	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)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.363271i) q^{2} +(-0.690983 - 2.12663i) q^{3} +(-0.500000 + 1.53884i) q^{4} +(-1.80902 - 1.31433i) q^{5} +(1.11803 + 0.812299i) q^{6} +(-0.881966 + 2.71441i) q^{7} +(-0.690983 - 2.12663i) q^{8} +(-1.61803 + 1.17557i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.363271i) q^{2} +(-0.690983 - 2.12663i) q^{3} +(-0.500000 + 1.53884i) q^{4} +(-1.80902 - 1.31433i) q^{5} +(1.11803 + 0.812299i) q^{6} +(-0.881966 + 2.71441i) q^{7} +(-0.690983 - 2.12663i) q^{8} +(-1.61803 + 1.17557i) q^{9} +1.38197 q^{10} +(-3.23607 - 0.726543i) q^{11} +3.61803 q^{12} +(-4.92705 + 3.57971i) q^{13} +(-0.545085 - 1.67760i) q^{14} +(-1.54508 + 4.75528i) q^{15} +(-1.50000 - 1.08981i) q^{16} +(0.809017 + 0.587785i) q^{17} +(0.381966 - 1.17557i) q^{18} +(0.309017 + 0.951057i) q^{19} +(2.92705 - 2.12663i) q^{20} +6.38197 q^{21} +(1.88197 - 0.812299i) q^{22} -1.76393 q^{23} +(-4.04508 + 2.93893i) q^{24} +(1.16312 - 3.57971i) q^{26} +(-1.80902 - 1.31433i) q^{27} +(-3.73607 - 2.71441i) q^{28} +(0.736068 - 2.26538i) q^{29} +(-0.954915 - 2.93893i) q^{30} +(3.85410 - 2.80017i) q^{31} +5.61803 q^{32} +(0.690983 + 7.38394i) q^{33} -0.618034 q^{34} +(5.16312 - 3.75123i) q^{35} +(-1.00000 - 3.07768i) q^{36} +(2.38197 - 7.33094i) q^{37} +(-0.500000 - 0.363271i) q^{38} +(11.0172 + 8.00448i) q^{39} +(-1.54508 + 4.75528i) q^{40} +(0.236068 + 0.726543i) q^{41} +(-3.19098 + 2.31838i) q^{42} -9.00000 q^{43} +(2.73607 - 4.61653i) q^{44} +4.47214 q^{45} +(0.881966 - 0.640786i) q^{46} +(0.690983 + 2.12663i) q^{47} +(-1.28115 + 3.94298i) q^{48} +(-0.927051 - 0.673542i) q^{49} +(0.690983 - 2.12663i) q^{51} +(-3.04508 - 9.37181i) q^{52} +(0.881966 - 0.640786i) q^{53} +1.38197 q^{54} +(4.89919 + 5.56758i) q^{55} +6.38197 q^{56} +(1.80902 - 1.31433i) q^{57} +(0.454915 + 1.40008i) q^{58} +(-3.50000 + 10.7719i) q^{59} +(-6.54508 - 4.75528i) q^{60} +(10.1631 + 7.38394i) q^{61} +(-0.909830 + 2.80017i) q^{62} +(-1.76393 - 5.42882i) q^{63} +(0.190983 - 0.138757i) q^{64} +13.6180 q^{65} +(-3.02786 - 3.44095i) q^{66} -13.8541 q^{67} +(-1.30902 + 0.951057i) q^{68} +(1.21885 + 3.75123i) q^{69} +(-1.21885 + 3.75123i) q^{70} +(-6.35410 - 4.61653i) q^{71} +(3.61803 + 2.62866i) q^{72} +(0.718847 - 2.21238i) q^{73} +(1.47214 + 4.53077i) q^{74} -1.61803 q^{76} +(4.82624 - 8.14324i) q^{77} -8.41641 q^{78} +(-0.809017 + 0.587785i) q^{79} +(1.28115 + 3.94298i) q^{80} +(-3.39919 + 10.4616i) q^{81} +(-0.381966 - 0.277515i) q^{82} +(-8.16312 - 5.93085i) q^{83} +(-3.19098 + 9.82084i) q^{84} +(-0.690983 - 2.12663i) q^{85} +(4.50000 - 3.26944i) q^{86} -5.32624 q^{87} +(0.690983 + 7.38394i) q^{88} -7.09017 q^{89} +(-2.23607 + 1.62460i) q^{90} +(-5.37132 - 16.5312i) q^{91} +(0.881966 - 2.71441i) q^{92} +(-8.61803 - 6.26137i) q^{93} +(-1.11803 - 0.812299i) q^{94} +(0.690983 - 2.12663i) q^{95} +(-3.88197 - 11.9475i) q^{96} +(-12.3262 + 8.95554i) q^{97} +0.708204 q^{98} +(6.09017 - 2.62866i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 5 q^{3} - 2 q^{4} - 5 q^{5} - 8 q^{7} - 5 q^{8} - 2 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 - 5 * q^3 - 2 * q^4 - 5 * q^5 - 8 * q^7 - 5 * q^8 - 2 * q^9	\( 4 q - 2 q^{2} - 5 q^{3} - 2 q^{4} - 5 q^{5} - 8 q^{7} - 5 q^{8} - 2 q^{9} + 10 q^{10} - 4 q^{11} + 10 q^{12} - 13 q^{13} + 9 q^{14} + 5 q^{15} - 6 q^{16} + q^{17} + 6 q^{18} - q^{19} + 5 q^{20} + 30 q^{21} + 12 q^{22} - 16 q^{23} - 5 q^{24} - 11 q^{26} - 5 q^{27} - 6 q^{28} - 6 q^{29} - 15 q^{30} + 2 q^{31} + 18 q^{32} + 5 q^{33} + 2 q^{34} + 5 q^{35} - 4 q^{36} + 14 q^{37} - 2 q^{38} + 15 q^{39} + 5 q^{40} - 8 q^{41} - 15 q^{42} - 36 q^{43} + 2 q^{44} + 8 q^{46} + 5 q^{47} + 15 q^{48} + 3 q^{49} + 5 q^{51} - q^{52} + 8 q^{53} + 10 q^{54} - 5 q^{55} + 30 q^{56} + 5 q^{57} + 13 q^{58} - 14 q^{59} - 15 q^{60} + 25 q^{61} - 26 q^{62} - 16 q^{63} + 3 q^{64} + 50 q^{65} - 30 q^{66} - 42 q^{67} - 3 q^{68} + 25 q^{69} - 25 q^{70} - 12 q^{71} + 10 q^{72} + 23 q^{73} - 12 q^{74} - 2 q^{76} - 12 q^{77} + 20 q^{78} - q^{79} - 15 q^{80} + 11 q^{81} - 6 q^{82} - 17 q^{83} - 15 q^{84} - 5 q^{85} + 18 q^{86} + 10 q^{87} + 5 q^{88} - 6 q^{89} + 21 q^{91} + 8 q^{92} - 30 q^{93} + 5 q^{95} - 20 q^{96} - 18 q^{97} - 24 q^{98} + 2 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 - 5 * q^3 - 2 * q^4 - 5 * q^5 - 8 * q^7 - 5 * q^8 - 2 * q^9 + 10 * q^10 - 4 * q^11 + 10 * q^12 - 13 * q^13 + 9 * q^14 + 5 * q^15 - 6 * q^16 + q^17 + 6 * q^18 - q^19 + 5 * q^20 + 30 * q^21 + 12 * q^22 - 16 * q^23 - 5 * q^24 - 11 * q^26 - 5 * q^27 - 6 * q^28 - 6 * q^29 - 15 * q^30 + 2 * q^31 + 18 * q^32 + 5 * q^33 + 2 * q^34 + 5 * q^35 - 4 * q^36 + 14 * q^37 - 2 * q^38 + 15 * q^39 + 5 * q^40 - 8 * q^41 - 15 * q^42 - 36 * q^43 + 2 * q^44 + 8 * q^46 + 5 * q^47 + 15 * q^48 + 3 * q^49 + 5 * q^51 - q^52 + 8 * q^53 + 10 * q^54 - 5 * q^55 + 30 * q^56 + 5 * q^57 + 13 * q^58 - 14 * q^59 - 15 * q^60 + 25 * q^61 - 26 * q^62 - 16 * q^63 + 3 * q^64 + 50 * q^65 - 30 * q^66 - 42 * q^67 - 3 * q^68 + 25 * q^69 - 25 * q^70 - 12 * q^71 + 10 * q^72 + 23 * q^73 - 12 * q^74 - 2 * q^76 - 12 * q^77 + 20 * q^78 - q^79 - 15 * q^80 + 11 * q^81 - 6 * q^82 - 17 * q^83 - 15 * q^84 - 5 * q^85 + 18 * q^86 + 10 * q^87 + 5 * q^88 - 6 * q^89 + 21 * q^91 + 8 * q^92 - 30 * q^93 + 5 * q^95 - 20 * q^96 - 18 * q^97 - 24 * q^98 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more