LMFDB - Embedded newform 462.2.j.b.421.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(169,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("462.169");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.j (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:	$3.68908857338$
Analytic rank:	$0$
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			421.1
Root			$0.809017 + 0.587785i$ of defining polynomial
Character	$\chi$	$=$	462.421
Dual form			462.2.j.b.169.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 + 0.587785i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.309017 + 0.224514i) q^{5} +(0.809017 + 0.587785i) q^{6} +(0.309017 - 0.951057i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(-0.809017 + 0.587785i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.309017 + 0.224514i) q^{5} +(0.809017 + 0.587785i) q^{6} +(0.309017 - 0.951057i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.809017 + 0.587785i) q^{9} -0.381966 q^{10} +(3.04508 - 1.31433i) q^{11} -1.00000 q^{12} +(-1.00000 + 0.726543i) q^{13} +(0.309017 + 0.951057i) q^{14} +(0.118034 - 0.363271i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(2.11803 + 1.53884i) q^{17} +(0.309017 - 0.951057i) q^{18} +(-2.42705 - 7.46969i) q^{19} +(0.309017 - 0.224514i) q^{20} -1.00000 q^{21} +(-1.69098 + 2.85317i) q^{22} +3.38197 q^{23} +(0.809017 - 0.587785i) q^{24} +(-1.50000 - 4.61653i) q^{25} +(0.381966 - 1.17557i) q^{26} +(0.809017 + 0.587785i) q^{27} +(-0.809017 - 0.587785i) q^{28} +(-0.145898 + 0.449028i) q^{29} +(0.118034 + 0.363271i) q^{30} +(3.92705 - 2.85317i) q^{31} +1.00000 q^{32} +(-2.19098 - 2.48990i) q^{33} -2.61803 q^{34} +(0.309017 - 0.224514i) q^{35} +(0.309017 + 0.951057i) q^{36} +(1.50000 - 4.61653i) q^{37} +(6.35410 + 4.61653i) q^{38} +(1.00000 + 0.726543i) q^{39} +(-0.118034 + 0.363271i) q^{40} +(-1.35410 - 4.16750i) q^{41} +(0.809017 - 0.587785i) q^{42} +1.23607 q^{43} +(-0.309017 - 3.30220i) q^{44} -0.381966 q^{45} +(-2.73607 + 1.98787i) q^{46} +(0.145898 + 0.449028i) q^{47} +(-0.309017 + 0.951057i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(3.92705 + 2.85317i) q^{50} +(0.809017 - 2.48990i) q^{51} +(0.381966 + 1.17557i) q^{52} +(7.85410 - 5.70634i) q^{53} -1.00000 q^{54} +(1.23607 + 0.277515i) q^{55} +1.00000 q^{56} +(-6.35410 + 4.61653i) q^{57} +(-0.145898 - 0.449028i) q^{58} +(-0.854102 + 2.62866i) q^{59} +(-0.309017 - 0.224514i) q^{60} +(-1.50000 + 4.61653i) q^{62} +(0.309017 + 0.951057i) q^{63} +(-0.809017 + 0.587785i) q^{64} -0.472136 q^{65} +(3.23607 + 0.726543i) q^{66} +4.00000 q^{67} +(2.11803 - 1.53884i) q^{68} +(-1.04508 - 3.21644i) q^{69} +(-0.118034 + 0.363271i) q^{70} +(9.70820 + 7.05342i) q^{71} +(-0.809017 - 0.587785i) q^{72} +(-3.61803 + 11.1352i) q^{73} +(1.50000 + 4.61653i) q^{74} +(-3.92705 + 2.85317i) q^{75} -7.85410 q^{76} +(-0.309017 - 3.30220i) q^{77} -1.23607 q^{78} +(-6.85410 + 4.97980i) q^{79} +(-0.118034 - 0.363271i) q^{80} +(0.309017 - 0.951057i) q^{81} +(3.54508 + 2.57565i) q^{82} +(2.38197 + 1.73060i) q^{83} +(-0.309017 + 0.951057i) q^{84} +(0.309017 + 0.951057i) q^{85} +(-1.00000 + 0.726543i) q^{86} +0.472136 q^{87} +(2.19098 + 2.48990i) q^{88} -14.3262 q^{89} +(0.309017 - 0.224514i) q^{90} +(0.381966 + 1.17557i) q^{91} +(1.04508 - 3.21644i) q^{92} +(-3.92705 - 2.85317i) q^{93} +(-0.381966 - 0.277515i) q^{94} +(0.927051 - 2.85317i) q^{95} +(-0.309017 - 0.951057i) q^{96} +(-0.381966 + 0.277515i) q^{97} +1.00000 q^{98} +(-1.69098 + 2.85317i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} + q^{3} - q^{4} - q^{5} + q^{6} - q^{7} - q^{8} - q^{9}+O(q^{10}) $ 4 * q - q^2 + q^3 - q^4 - q^5 + q^6 - q^7 - q^8 - q^9	\( 4 q - q^{2} + q^{3} - q^{4} - q^{5} + q^{6} - q^{7} - q^{8} - q^{9} - 6 q^{10} + q^{11} - 4 q^{12} - 4 q^{13} - q^{14} - 4 q^{15} - q^{16} + 4 q^{17} - q^{18} - 3 q^{19} - q^{20} - 4 q^{21} - 9 q^{22} + 18 q^{23} + q^{24} - 6 q^{25} + 6 q^{26} + q^{27} - q^{28} - 14 q^{29} - 4 q^{30} + 9 q^{31} + 4 q^{32} - 11 q^{33} - 6 q^{34} - q^{35} - q^{36} + 6 q^{37} + 12 q^{38} + 4 q^{39} + 4 q^{40} + 8 q^{41} + q^{42} - 4 q^{43} + q^{44} - 6 q^{45} - 2 q^{46} + 14 q^{47} + q^{48} - q^{49} + 9 q^{50} + q^{51} + 6 q^{52} + 18 q^{53} - 4 q^{54} - 4 q^{55} + 4 q^{56} - 12 q^{57} - 14 q^{58} + 10 q^{59} + q^{60} - 6 q^{62} - q^{63} - q^{64} + 16 q^{65} + 4 q^{66} + 16 q^{67} + 4 q^{68} + 7 q^{69} + 4 q^{70} + 12 q^{71} - q^{72} - 10 q^{73} + 6 q^{74} - 9 q^{75} - 18 q^{76} + q^{77} + 4 q^{78} - 14 q^{79} + 4 q^{80} - q^{81} + 3 q^{82} + 14 q^{83} + q^{84} - q^{85} - 4 q^{86} - 16 q^{87} + 11 q^{88} - 26 q^{89} - q^{90} + 6 q^{91} - 7 q^{92} - 9 q^{93} - 6 q^{94} - 3 q^{95} + q^{96} - 6 q^{97} + 4 q^{98} - 9 q^{99}+O(q^{100}) \) 4 * q - q^2 + q^3 - q^4 - q^5 + q^6 - q^7 - q^8 - q^9 - 6 * q^10 + q^11 - 4 * q^12 - 4 * q^13 - q^14 - 4 * q^15 - q^16 + 4 * q^17 - q^18 - 3 * q^19 - q^20 - 4 * q^21 - 9 * q^22 + 18 * q^23 + q^24 - 6 * q^25 + 6 * q^26 + q^27 - q^28 - 14 * q^29 - 4 * q^30 + 9 * q^31 + 4 * q^32 - 11 * q^33 - 6 * q^34 - q^35 - q^36 + 6 * q^37 + 12 * q^38 + 4 * q^39 + 4 * q^40 + 8 * q^41 + q^42 - 4 * q^43 + q^44 - 6 * q^45 - 2 * q^46 + 14 * q^47 + q^48 - q^49 + 9 * q^50 + q^51 + 6 * q^52 + 18 * q^53 - 4 * q^54 - 4 * q^55 + 4 * q^56 - 12 * q^57 - 14 * q^58 + 10 * q^59 + q^60 - 6 * q^62 - q^63 - q^64 + 16 * q^65 + 4 * q^66 + 16 * q^67 + 4 * q^68 + 7 * q^69 + 4 * q^70 + 12 * q^71 - q^72 - 10 * q^73 + 6 * q^74 - 9 * q^75 - 18 * q^76 + q^77 + 4 * q^78 - 14 * q^79 + 4 * q^80 - q^81 + 3 * q^82 + 14 * q^83 + q^84 - q^85 - 4 * q^86 - 16 * q^87 + 11 * q^88 - 26 * q^89 - q^90 + 6 * q^91 - 7 * q^92 - 9 * q^93 - 6 * q^94 - 3 * q^95 + q^96 - 6 * q^97 + 4 * q^98 - 9 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	0.309017	+	0.224514i	0.138197	+	0.100406i	0.654736	−	0.755858i	$-0.272780\pi$
$5$	0.309017	+	0.224514i	0.138197	+	0.100406i	−0.516539	+	0.856264i	$0.672780\pi$
$6$	0.809017	+	0.587785i	0.330280	+	0.239962i
$7$	0.309017	−	0.951057i	0.116797	−	0.359466i
$7$	0.309017	−	0.951057i	0.116797	−	0.359466i
$8$	0.309017	+	0.951057i	0.109254	+	0.336249i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$	−0.381966			−0.120788
$11$	3.04508	−	1.31433i	0.918128	−	0.396285i
$11$	3.04508	−	1.31433i	0.918128	−	0.396285i
$12$	−1.00000			−0.288675
$13$	−1.00000	+	0.726543i	−0.277350	+	0.201507i	−0.717761	−	0.696290i	$-0.754833\pi$
$13$	−1.00000	+	0.726543i	−0.277350	+	0.201507i	0.440411	+	0.897796i	$0.354833\pi$
$14$	0.309017	+	0.951057i	0.0825883	+	0.254181i
$15$	0.118034	−	0.363271i	0.0304762	−	0.0937962i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	2.11803	+	1.53884i	0.513699	+	0.373224i	0.814225	−	0.580550i	$-0.197162\pi$
$17$	2.11803	+	1.53884i	0.513699	+	0.373224i	−0.300526	+	0.953774i	$0.597162\pi$
$18$	0.309017	−	0.951057i	0.0728360	−	0.224166i
$19$	−2.42705	−	7.46969i	−0.556804	−	1.71367i	−0.691132	−	0.722729i	$-0.742888\pi$
$19$	−2.42705	−	7.46969i	−0.556804	−	1.71367i	0.134328	−	0.990937i	$-0.457112\pi$
$20$	0.309017	−	0.224514i	0.0690983	−	0.0502029i
$21$	−1.00000			−0.218218
$22$	−1.69098	+	2.85317i	−0.360519	+	0.608298i
$23$	3.38197			0.705189			0.352594	−	0.935776i	$-0.385300\pi$
$23$	3.38197			0.705189			0.352594	+	0.935776i	$0.385300\pi$
$24$	0.809017	−	0.587785i	0.165140	−	0.119981i
$25$	−1.50000	−	4.61653i	−0.300000	−	0.923305i
$26$	0.381966	−	1.17557i	0.0749097	−	0.230548i
$27$	0.809017	+	0.587785i	0.155695	+	0.113119i
$28$	−0.809017	−	0.587785i	−0.152890	−	0.111081i
$29$	−0.145898	+	0.449028i	−0.0270926	+	0.0833824i	−0.963689	−	0.267029i	$-0.913958\pi$
$29$	−0.145898	+	0.449028i	−0.0270926	+	0.0833824i	0.936596	+	0.350411i	$0.113958\pi$
$30$	0.118034	+	0.363271i	0.0215500	+	0.0663240i
$31$	3.92705	−	2.85317i	0.705319	−	0.512444i	−0.176341	−	0.984329i	$-0.556426\pi$
$31$	3.92705	−	2.85317i	0.705319	−	0.512444i	0.881660	+	0.471885i	$0.156426\pi$
$32$	1.00000			0.176777
$33$	−2.19098	−	2.48990i	−0.381401	−	0.433436i
$34$	−2.61803			−0.448989
$35$	0.309017	−	0.224514i	0.0522334	−	0.0379498i
$36$	0.309017	+	0.951057i	0.0515028	+	0.158509i
$37$	1.50000	−	4.61653i	0.246598	−	0.758952i	−0.748771	−	0.662829i	$-0.769356\pi$
$37$	1.50000	−	4.61653i	0.246598	−	0.758952i	0.995369	−	0.0961233i	$-0.0306443\pi$
$38$	6.35410	+	4.61653i	1.03077	+	0.748899i
$39$	1.00000	+	0.726543i	0.160128	+	0.116340i
$40$	−0.118034	+	0.363271i	−0.0186628	+	0.0574382i
$41$	−1.35410	−	4.16750i	−0.211475	−	0.650854i	−0.999385	−	0.0350632i	$-0.988837\pi$
$41$	−1.35410	−	4.16750i	−0.211475	−	0.650854i	0.787910	−	0.615791i	$-0.211163\pi$
$42$	0.809017	−	0.587785i	0.124834	−	0.0906972i
$43$	1.23607			0.188499			0.0942493	−	0.995549i	$-0.469955\pi$
$43$	1.23607			0.188499			0.0942493	+	0.995549i	$0.469955\pi$
$44$	−0.309017	−	3.30220i	−0.0465861	−	0.497825i
$45$	−0.381966			−0.0569401
$46$	−2.73607	+	1.98787i	−0.403411	+	0.293095i
$47$	0.145898	+	0.449028i	0.0212814	+	0.0654975i	0.961133	−	0.276085i	$-0.0890371\pi$
$47$	0.145898	+	0.449028i	0.0212814	+	0.0654975i	−0.939852	+	0.341582i	$0.889037\pi$
$48$	−0.309017	+	0.951057i	−0.0446028	+	0.137273i
$49$	−0.809017	−	0.587785i	−0.115574	−	0.0839693i
$50$	3.92705	+	2.85317i	0.555369	+	0.403499i
$51$	0.809017	−	2.48990i	0.113285	−	0.348655i
$52$	0.381966	+	1.17557i	0.0529692	+	0.163022i
$53$	7.85410	−	5.70634i	1.07884	−	0.783826i	0.101363	−	0.994850i	$-0.467680\pi$
$53$	7.85410	−	5.70634i	1.07884	−	0.783826i	0.977481	+	0.211024i	$0.0676797\pi$
$54$	−1.00000			−0.136083
$55$	1.23607	+	0.277515i	0.166671	+	0.0374201i
$56$	1.00000			0.133631
$57$	−6.35410	+	4.61653i	−0.841621	+	0.611474i
$58$	−0.145898	−	0.449028i	−0.0191574	−	0.0589603i
$59$	−0.854102	+	2.62866i	−0.111195	+	0.342222i	−0.991134	−	0.132864i	$-0.957583\pi$
$59$	−0.854102	+	2.62866i	−0.111195	+	0.342222i	0.879940	+	0.475085i	$0.157583\pi$
$60$	−0.309017	−	0.224514i	−0.0398939	−	0.0289846i
$61$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$61$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$62$	−1.50000	+	4.61653i	−0.190500	+	0.586299i
$63$	0.309017	+	0.951057i	0.0389325	+	0.119822i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	−0.472136			−0.0585613
$66$	3.23607	+	0.726543i	0.398332	+	0.0894312i
$67$	4.00000			0.488678			0.244339	−	0.969690i	$-0.421429\pi$
$67$	4.00000			0.488678			0.244339	+	0.969690i	$0.421429\pi$
$68$	2.11803	−	1.53884i	0.256849	−	0.186612i
$69$	−1.04508	−	3.21644i	−0.125813	−	0.387214i
$70$	−0.118034	+	0.363271i	−0.0141078	+	0.0434192i
$71$	9.70820	+	7.05342i	1.15215	+	0.837087i	0.988766	−	0.149475i	$-0.0477583\pi$
$71$	9.70820	+	7.05342i	1.15215	+	0.837087i	0.163386	+	0.986562i	$0.447758\pi$
$72$	−0.809017	−	0.587785i	−0.0953436	−	0.0692712i
$73$	−3.61803	+	11.1352i	−0.423459	+	1.30327i	0.481003	+	0.876719i	$0.340272\pi$
$73$	−3.61803	+	11.1352i	−0.423459	+	1.30327i	−0.904462	+	0.426554i	$0.859728\pi$
$74$	1.50000	+	4.61653i	0.174371	+	0.536660i
$75$	−3.92705	+	2.85317i	−0.453457	+	0.329456i
$76$	−7.85410			−0.900927
$77$	−0.309017	−	3.30220i	−0.0352158	−	0.376320i
$78$	−1.23607			−0.139957
$79$	−6.85410	+	4.97980i	−0.771147	+	0.560271i	−0.902309	−	0.431090i	$-0.858129\pi$
$79$	−6.85410	+	4.97980i	−0.771147	+	0.560271i	0.131162	+	0.991361i	$0.458129\pi$
$80$	−0.118034	−	0.363271i	−0.0131966	−	0.0406150i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	3.54508	+	2.57565i	0.391489	+	0.284434i
$83$	2.38197	+	1.73060i	0.261455	+	0.189958i	0.710788	−	0.703406i	$-0.248338\pi$
$83$	2.38197	+	1.73060i	0.261455	+	0.189958i	−0.449333	+	0.893364i	$0.648338\pi$
$84$	−0.309017	+	0.951057i	−0.0337165	+	0.103769i
$85$	0.309017	+	0.951057i	0.0335176	+	0.103157i
$86$	−1.00000	+	0.726543i	−0.107833	+	0.0783451i
$87$	0.472136			0.0506183
$88$	2.19098	+	2.48990i	0.233560	+	0.265424i
$89$	−14.3262			−1.51858			−0.759289	−	0.650753i	$-0.774453\pi$
$89$	−14.3262			−1.51858			−0.759289	+	0.650753i	$0.774453\pi$
$90$	0.309017	−	0.224514i	0.0325733	−	0.0236659i
$91$	0.381966	+	1.17557i	0.0400409	+	0.123233i
$92$	1.04508	−	3.21644i	0.108958	−	0.335337i
$93$	−3.92705	−	2.85317i	−0.407216	−	0.295860i
$94$	−0.381966	−	0.277515i	−0.0393968	−	0.0286234i
$95$	0.927051	−	2.85317i	0.0951134	−	0.292729i
$96$	−0.309017	−	0.951057i	−0.0315389	−	0.0970668i
$97$	−0.381966	+	0.277515i	−0.0387828	+	0.0281773i	−0.607008	−	0.794696i	$-0.707630\pi$
$97$	−0.381966	+	0.277515i	−0.0387828	+	0.0281773i	0.568225	+	0.822873i	$0.307630\pi$
$98$	1.00000			0.101015
$99$	−1.69098	+	2.85317i	−0.169950	+	0.286754i
$100$	−4.85410			−0.485410
$101$	−14.7812	+	10.7391i	−1.47078	+	1.06858i	−0.490393	+	0.871502i	$0.663147\pi$
$101$	−14.7812	+	10.7391i	−1.47078	+	1.06858i	−0.980387	+	0.197082i	$0.936853\pi$
$102$	0.809017	+	2.48990i	0.0801046	+	0.246537i
$103$	3.57295	−	10.9964i	0.352053	−	1.08351i	−0.605645	−	0.795735i	$-0.707085\pi$
$103$	3.57295	−	10.9964i	0.352053	−	1.08351i	0.957699	−	0.287773i	$-0.0929150\pi$
$104$	−1.00000	−	0.726543i	−0.0980581	−	0.0712434i
$105$	−0.309017	−	0.224514i	−0.0301570	−	0.0219103i
$106$	−3.00000	+	9.23305i	−0.291386	+	0.896793i
$107$	2.10081	+	6.46564i	0.203093	+	0.625057i	0.999786	+	0.0206726i	$0.00658077\pi$
$107$	2.10081	+	6.46564i	0.203093	+	0.625057i	−0.796693	+	0.604384i	$0.793419\pi$
$108$	0.809017	−	0.587785i	0.0778477	−	0.0565597i
$109$	−19.3262			−1.85112			−0.925559	−	0.378604i	$-0.876404\pi$
$109$	−19.3262			−1.85112			−0.925559	+	0.378604i	$0.876404\pi$
$110$	−1.16312	+	0.502029i	−0.110899	+	0.0478665i
$111$	−4.85410			−0.460731
$112$	−0.809017	+	0.587785i	−0.0764449	+	0.0555405i
$113$	4.52786	+	13.9353i	0.425946	+	1.31093i	0.902086	+	0.431556i	$0.142035\pi$
$113$	4.52786	+	13.9353i	0.425946	+	1.31093i	−0.476140	+	0.879369i	$0.657965\pi$
$114$	2.42705	−	7.46969i	0.227314	−	0.699601i
$115$	1.04508	+	0.759299i	0.0974547	+	0.0708050i
$116$	0.381966	+	0.277515i	0.0354647	+	0.0257666i
$117$	0.381966	−	1.17557i	0.0353128	−	0.108682i
$118$	−0.854102	−	2.62866i	−0.0786265	−	0.241987i
$119$	2.11803	−	1.53884i	0.194160	−	0.141065i
$120$	0.381966			0.0348686
$121$	7.54508	−	8.00448i	0.685917	−	0.727680i
$122$		0			0
$123$	−3.54508	+	2.57565i	−0.319650	+	0.232239i
$124$	−1.50000	−	4.61653i	−0.134704	−	0.414576i
$125$	1.16312	−	3.57971i	0.104033	−	0.320179i
$126$	−0.809017	−	0.587785i	−0.0720730	−	0.0523641i
$127$	17.5623	+	12.7598i	1.55840	+	1.13225i	0.937304	+	0.348514i	$0.113313\pi$
$127$	17.5623	+	12.7598i	1.55840	+	1.13225i	0.621099	+	0.783732i	$0.286687\pi$
$128$	0.309017	−	0.951057i	0.0273135	−	0.0840623i
$129$	−0.381966	−	1.17557i	−0.0336302	−	0.103503i
$130$	0.381966	−	0.277515i	0.0335006	−	0.0243396i
$131$	−8.18034			−0.714720			−0.357360	−	0.933967i	$-0.616323\pi$
$131$	−8.18034			−0.714720			−0.357360	+	0.933967i	$0.616323\pi$
$132$	−3.04508	+	1.31433i	−0.265041	+	0.114398i
$133$	−7.85410			−0.681037
$134$	−3.23607	+	2.35114i	−0.279554	+	0.203108i
$135$	0.118034	+	0.363271i	0.0101587	+	0.0312654i
$136$	−0.809017	+	2.48990i	−0.0693726	+	0.213507i
$137$	−8.23607	−	5.98385i	−0.703655	−	0.511235i	0.177466	−	0.984127i	$-0.443210\pi$
$137$	−8.23607	−	5.98385i	−0.703655	−	0.511235i	−0.881120	+	0.472892i	$0.843210\pi$
$138$	2.73607	+	1.98787i	0.232910	+	0.169219i
$139$	0.718847	−	2.21238i	0.0609718	−	0.187652i	−0.915931	−	0.401336i	$-0.868546\pi$
$139$	0.718847	−	2.21238i	0.0609718	−	0.187652i	0.976903	+	0.213684i	$0.0685461\pi$
$140$	−0.118034	−	0.363271i	−0.00997569	−	0.0307020i
$141$	0.381966	−	0.277515i	0.0321673	−	0.0233709i
$142$	−12.0000			−1.00702
$143$	−2.09017	+	3.52671i	−0.174789	+	0.294918i
$144$	1.00000			0.0833333
$145$	−0.145898	+	0.106001i	−0.0121162	+	0.00880291i
$146$	−3.61803	−	11.1352i	−0.299431	−	0.921553i
$147$	−0.309017	+	0.951057i	−0.0254873	+	0.0784418i
$148$	−3.92705	−	2.85317i	−0.322802	−	0.234529i
$149$	7.23607	+	5.25731i	0.592802	+	0.430696i	0.843317	−	0.537417i	$-0.180600\pi$
$149$	7.23607	+	5.25731i	0.592802	+	0.430696i	−0.250515	+	0.968113i	$0.580600\pi$
$150$	1.50000	−	4.61653i	0.122474	−	0.376938i
$151$	1.67376	+	5.15131i	0.136209	+	0.419208i	0.995776	−	0.0918150i	$-0.0292668\pi$
$151$	1.67376	+	5.15131i	0.136209	+	0.419208i	−0.859567	+	0.511023i	$0.829267\pi$
$152$	6.35410	−	4.61653i	0.515386	−	0.374450i
$153$	−2.61803			−0.211656
$154$	2.19098	+	2.48990i	0.176554	+	0.200642i
$155$	1.85410			0.148925
$156$	1.00000	−	0.726543i	0.0800641	−	0.0581700i
$157$	−0.0557281	−	0.171513i	−0.00444759	−	0.0136883i	0.948808	−	0.315853i	$-0.102291\pi$
$157$	−0.0557281	−	0.171513i	−0.00444759	−	0.0136883i	−0.953256	+	0.302165i	$0.902291\pi$
$158$	2.61803	−	8.05748i	0.208280	−	0.641019i
$159$	−7.85410	−	5.70634i	−0.622871	−	0.452542i
$160$	0.309017	+	0.224514i	0.0244299	+	0.0177494i
$161$	1.04508	−	3.21644i	0.0823642	−	0.253491i
$162$	0.309017	+	0.951057i	0.0242787	+	0.0747221i
$163$	0.381966	−	0.277515i	0.0299179	−	0.0217366i	−0.572726	−	0.819747i	$-0.694114\pi$
$163$	0.381966	−	0.277515i	0.0299179	−	0.0217366i	0.602644	+	0.798010i	$0.294114\pi$
$164$	−4.38197			−0.342174
$165$	−0.118034	−	1.26133i	−0.00918893	−	0.0981942i
$166$	−2.94427			−0.228520
$167$	−7.85410	+	5.70634i	−0.607769	+	0.441570i	−0.848628	−	0.528990i	$-0.822571\pi$
$167$	−7.85410	+	5.70634i	−0.607769	+	0.441570i	0.240859	+	0.970560i	$0.422571\pi$
$168$	−0.309017	−	0.951057i	−0.0238412	−	0.0733756i
$169$	−3.54508	+	10.9106i	−0.272699	+	0.839281i
$170$	−0.809017	−	0.587785i	−0.0620488	−	0.0450811i
$171$	6.35410	+	4.61653i	0.485910	+	0.353035i
$172$	0.381966	−	1.17557i	0.0291246	−	0.0896364i
$173$	−3.10081	−	9.54332i	−0.235750	−	0.725565i	−0.997021	−	0.0771309i	$-0.975424\pi$
$173$	−3.10081	−	9.54332i	−0.235750	−	0.725565i	0.761271	−	0.648434i	$-0.224576\pi$
$174$	−0.381966	+	0.277515i	−0.0289568	+	0.0210383i
$175$	−4.85410			−0.366936
$176$	−3.23607	−	0.726543i	−0.243928	−	0.0547652i
$177$	2.76393			0.207750
$178$	11.5902	−	8.42075i	0.868720	−	0.631162i
$179$	1.06231	+	3.26944i	0.0794005	+	0.244370i	0.982875	−	0.184271i	$-0.0589925\pi$
$179$	1.06231	+	3.26944i	0.0794005	+	0.244370i	−0.903475	+	0.428641i	$0.858993\pi$
$180$	−0.118034	+	0.363271i	−0.00879773	+	0.0270766i
$181$	17.3262	+	12.5882i	1.28785	+	0.935677i	0.999760	−	0.0219263i	$-0.00697992\pi$
$181$	17.3262	+	12.5882i	1.28785	+	0.935677i	0.288090	+	0.957603i	$0.406980\pi$
$182$	−1.00000	−	0.726543i	−0.0741249	−	0.0538549i
$183$		0			0
$184$	1.04508	+	3.21644i	0.0770447	+	0.237119i
$185$	1.50000	−	1.08981i	0.110282	−	0.0801247i
$186$	4.85410			0.355920
$187$	8.47214	+	1.90211i	0.619544	+	0.139096i
$188$	0.472136			0.0344341
$189$	0.809017	−	0.587785i	0.0588473	−	0.0427551i
$190$	0.927051	+	2.85317i	0.0672553	+	0.206991i
$191$	1.11803	−	3.44095i	0.0808981	−	0.248979i	−0.902425	−	0.430848i	$-0.858215\pi$
$191$	1.11803	−	3.44095i	0.0808981	−	0.248979i	0.983323	+	0.181869i	$0.0582146\pi$
$192$	0.809017	+	0.587785i	0.0583858	+	0.0424197i
$193$	21.4894	+	15.6129i	1.54684	+	1.12384i	0.945859	+	0.324579i	$0.105222\pi$
$193$	21.4894	+	15.6129i	1.54684	+	1.12384i	0.600979	+	0.799265i	$0.294778\pi$
$194$	0.145898	−	0.449028i	0.0104749	−	0.0322383i
$195$	0.145898	+	0.449028i	0.0104480	+	0.0321556i
$196$	−0.809017	+	0.587785i	−0.0577869	+	0.0419847i
$197$	17.8885			1.27451			0.637253	−	0.770655i	$-0.280071\pi$
$197$	17.8885			1.27451			0.637253	+	0.770655i	$0.280071\pi$
$198$	−0.309017	−	3.30220i	−0.0219609	−	0.234677i
$199$	11.2705			0.798945			0.399473	−	0.916745i	$-0.369193\pi$
$199$	11.2705			0.798945			0.399473	+	0.916745i	$0.369193\pi$
$200$	3.92705	−	2.85317i	0.277684	−	0.201750i
$201$	−1.23607	−	3.80423i	−0.0871855	−	0.268329i
$202$	5.64590	−	17.3763i	0.397244	−	1.22259i
$203$	0.381966	+	0.277515i	0.0268088	+	0.0194777i
$204$	−2.11803	−	1.53884i	−0.148292	−	0.107740i
$205$	0.517221	−	1.59184i	0.0361243	−	0.111179i
$206$	3.57295	+	10.9964i	0.248939	+	0.766156i
$207$	−2.73607	+	1.98787i	−0.190170	+	0.138166i
$208$	1.23607			0.0857059
$209$	−17.2082	−	19.5559i	−1.19032	−	1.35271i
$210$	0.381966			0.0263582
$211$	11.3262	−	8.22899i	0.779730	−	0.566507i	−0.125168	−	0.992136i	$-0.539947\pi$
$211$	11.3262	−	8.22899i	0.779730	−	0.566507i	0.904898	+	0.425628i	$0.139947\pi$
$212$	−3.00000	−	9.23305i	−0.206041	−	0.634129i
$213$	3.70820	−	11.4127i	0.254082	−	0.781984i
$214$	−5.50000	−	3.99598i	−0.375972	−	0.273160i
$215$	0.381966	+	0.277515i	0.0260499	+	0.0189263i
$216$	−0.309017	+	0.951057i	−0.0210259	+	0.0647112i
$217$	−1.50000	−	4.61653i	−0.101827	−	0.313390i
$218$	15.6353	−	11.3597i	1.05895	−	0.769374i
$219$	11.7082			0.791167
$220$	0.645898	−	1.08981i	0.0435464	−	0.0734752i
$221$	−3.23607			−0.217681
$222$	3.92705	−	2.85317i	0.263566	−	0.191492i
$223$	0.246711	+	0.759299i	0.0165210	+	0.0508464i	0.958977	−	0.283483i	$-0.0914901\pi$
$223$	0.246711	+	0.759299i	0.0165210	+	0.0508464i	−0.942456	+	0.334330i	$0.891490\pi$
$224$	0.309017	−	0.951057i	0.0206471	−	0.0635451i
$225$	3.92705	+	2.85317i	0.261803	+	0.190211i
$226$	−11.8541	−	8.61251i	−0.788523	−	0.572896i
$227$	−7.09017	+	21.8213i	−0.470591	+	1.44833i	0.381221	+	0.924484i	$0.375504\pi$
$227$	−7.09017	+	21.8213i	−0.470591	+	1.44833i	−0.851813	+	0.523847i	$0.824496\pi$
$228$	2.42705	+	7.46969i	0.160735	+	0.494693i
$229$	11.9443	−	8.67802i	0.789300	−	0.573460i	−0.118456	−	0.992959i	$-0.537794\pi$
$229$	11.9443	−	8.67802i	0.789300	−	0.573460i	0.907756	+	0.419500i	$0.137794\pi$
$230$	−1.29180			−0.0851785
$231$	−3.04508	+	1.31433i	−0.200352	+	0.0864764i
$232$	−0.472136			−0.0309972
$233$	1.85410	−	1.34708i	0.121466	−	0.0882504i	−0.525394	−	0.850859i	$-0.676082\pi$
$233$	1.85410	−	1.34708i	0.121466	−	0.0882504i	0.646860	+	0.762609i	$0.276082\pi$
$234$	0.381966	+	1.17557i	0.0249699	+	0.0768494i
$235$	−0.0557281	+	0.171513i	−0.00363530	+	0.0111883i
$236$	2.23607	+	1.62460i	0.145556	+	0.105752i
$237$	6.85410	+	4.97980i	0.445222	+	0.323473i
$238$	−0.809017	+	2.48990i	−0.0524408	+	0.161396i
$239$	−2.48278	−	7.64121i	−0.160598	−	0.494269i	0.838087	−	0.545536i	$-0.183674\pi$
$239$	−2.48278	−	7.64121i	−0.160598	−	0.494269i	−0.998685	+	0.0512674i	$0.983674\pi$
$240$	−0.309017	+	0.224514i	−0.0199470	+	0.0144923i
$241$	−16.9443			−1.09148			−0.545738	−	0.837956i	$-0.683751\pi$
$241$	−16.9443			−1.09148			−0.545738	+	0.837956i	$0.683751\pi$
$242$	−1.39919	+	10.9106i	−0.0899431	+	0.701363i
$243$	−1.00000			−0.0641500
$244$		0			0
$245$	−0.118034	−	0.363271i	−0.00754091	−	0.0232085i
$246$	1.35410	−	4.16750i	0.0863344	−	0.265710i
$247$	7.85410	+	5.70634i	0.499745	+	0.363086i
$248$	3.92705	+	2.85317i	0.249368	+	0.181176i
$249$	0.909830	−	2.80017i	0.0576581	−	0.177453i
$250$	1.16312	+	3.57971i	0.0735621	+	0.226401i
$251$	21.5623	−	15.6659i	1.36100	−	0.988825i	0.362620	−	0.931937i	$-0.381882\pi$
$251$	21.5623	−	15.6659i	1.36100	−	0.988825i	0.998381	−	0.0568878i	$-0.0181177\pi$
$252$	1.00000			0.0629941
$253$	10.2984	−	4.44501i	0.647453	−	0.279456i
$254$	−21.7082			−1.36209
$255$	0.809017	−	0.587785i	0.0506626	−	0.0368085i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	−5.48278	+	16.8743i	−0.342006	+	1.05259i	0.621161	+	0.783683i	$0.286661\pi$
$257$	−5.48278	+	16.8743i	−0.342006	+	1.05259i	−0.963167	+	0.268904i	$0.913339\pi$
$258$	1.00000	+	0.726543i	0.0622573	+	0.0452326i
$259$	−3.92705	−	2.85317i	−0.244015	−	0.177287i
$260$	−0.145898	+	0.449028i	−0.00904821	+	0.0278475i
$261$	−0.145898	−	0.449028i	−0.00903086	−	0.0277941i
$262$	6.61803	−	4.80828i	0.408864	−	0.297057i
$263$	−5.20163			−0.320746			−0.160373	−	0.987056i	$-0.551270\pi$
$263$	−5.20163			−0.320746			−0.160373	+	0.987056i	$0.551270\pi$
$264$	1.69098	−	2.85317i	0.104073	−	0.175600i
$265$	3.70820			0.227793
$266$	6.35410	−	4.61653i	0.389595	−	0.283057i
$267$	4.42705	+	13.6251i	0.270931	+	0.833840i
$268$	1.23607	−	3.80423i	0.0755049	−	0.232380i
$269$	−12.0902	−	8.78402i	−0.737151	−	0.535571i	0.154667	−	0.987967i	$-0.450570\pi$
$269$	−12.0902	−	8.78402i	−0.737151	−	0.535571i	−0.891817	+	0.452395i	$0.850570\pi$
$270$	−0.309017	−	0.224514i	−0.0188062	−	0.0136635i
$271$	2.31966	−	7.13918i	0.140909	−	0.433674i	−0.855553	−	0.517715i	$-0.826783\pi$
$271$	2.31966	−	7.13918i	0.140909	−	0.433674i	0.996462	+	0.0840410i	$0.0267827\pi$
$272$	−0.809017	−	2.48990i	−0.0490539	−	0.150972i
$273$	1.00000	−	0.726543i	0.0605228	−	0.0439724i
$274$	10.1803			0.615017
$275$	−10.6353	−	12.0862i	−0.641330	−	0.728826i
$276$	−3.38197			−0.203570
$277$	−9.73607	+	7.07367i	−0.584984	+	0.425015i	−0.840517	−	0.541785i	$-0.817749\pi$
$277$	−9.73607	+	7.07367i	−0.584984	+	0.425015i	0.255534	+	0.966800i	$0.417749\pi$
$278$	0.718847	+	2.21238i	0.0431136	+	0.132690i
$279$	−1.50000	+	4.61653i	−0.0898027	+	0.276384i
$280$	0.309017	+	0.224514i	0.0184673	+	0.0134173i
$281$	−12.0902	−	8.78402i	−0.721239	−	0.524011i	0.165541	−	0.986203i	$-0.447063\pi$
$281$	−12.0902	−	8.78402i	−0.721239	−	0.524011i	−0.886780	+	0.462192i	$0.847063\pi$
$282$	−0.145898	+	0.449028i	−0.00868810	+	0.0267392i
$283$	−7.15248	−	22.0131i	−0.425171	−	1.30854i	−0.902831	−	0.429996i	$-0.858515\pi$
$283$	−7.15248	−	22.0131i	−0.425171	−	1.30854i	0.477660	−	0.878545i	$-0.341485\pi$
$284$	9.70820	−	7.05342i	0.576076	−	0.418544i
$285$	−3.00000			−0.177705
$286$	−0.381966	−	4.08174i	−0.0225861	−	0.241358i
$287$	−4.38197			−0.258659
$288$	−0.809017	+	0.587785i	−0.0476718	+	0.0346356i
$289$	−3.13525	−	9.64932i	−0.184427	−	0.567607i
$290$	0.0557281	−	0.171513i	0.00327247	−	0.0100716i
$291$	0.381966	+	0.277515i	0.0223912	+	0.0162682i
$292$	9.47214	+	6.88191i	0.554315	+	0.402733i
$293$	3.82624	−	11.7759i	0.223531	−	0.687958i	−0.774906	−	0.632076i	$-0.782203\pi$
$293$	3.82624	−	11.7759i	0.223531	−	0.687958i	0.998437	−	0.0558820i	$-0.0177971\pi$
$294$	−0.309017	−	0.951057i	−0.0180222	−	0.0554667i
$295$	−0.854102	+	0.620541i	−0.0497277	+	0.0361293i
$296$	4.85410			0.282139
$297$	3.23607	+	0.726543i	0.187776	+	0.0421583i
$298$	−8.94427			−0.518128
$299$	−3.38197	+	2.45714i	−0.195584	+	0.142100i
$300$	1.50000	+	4.61653i	0.0866025	+	0.266535i
$301$	0.381966	−	1.17557i	0.0220162	−	0.0677588i
$302$	−4.38197	−	3.18368i	−0.252154	−	0.183200i
$303$	14.7812	+	10.7391i	0.849155	+	0.616947i
$304$	−2.42705	+	7.46969i	−0.139201	+	0.428416i
$305$		0			0
$306$	2.11803	−	1.53884i	0.121080	−	0.0879697i
$307$	−4.85410			−0.277038			−0.138519	−	0.990360i	$-0.544234\pi$
$307$	−4.85410			−0.277038			−0.138519	+	0.990360i	$0.544234\pi$
$308$	−3.23607	−	0.726543i	−0.184392	−	0.0413986i
$309$	−11.5623			−0.657757
$310$	−1.50000	+	1.08981i	−0.0851943	+	0.0618973i
$311$	5.00000	+	15.3884i	0.283524	+	0.872597i	0.986837	+	0.161717i	$0.0517032\pi$
$311$	5.00000	+	15.3884i	0.283524	+	0.872597i	−0.703313	+	0.710880i	$0.748297\pi$
$312$	−0.381966	+	1.17557i	−0.0216246	+	0.0665536i
$313$	−9.00000	−	6.53888i	−0.508710	−	0.369600i	0.303624	−	0.952792i	$-0.401803\pi$
$313$	−9.00000	−	6.53888i	−0.508710	−	0.369600i	−0.812334	+	0.583192i	$0.801803\pi$
$314$	0.145898	+	0.106001i	0.00823350	+	0.00598199i
$315$	−0.118034	+	0.363271i	−0.00665046	+	0.0204680i
$316$	2.61803	+	8.05748i	0.147276	+	0.453269i
$317$	−16.3262	+	11.8617i	−0.916973	+	0.666220i	−0.942769	−	0.333447i	$-0.891788\pi$
$317$	−16.3262	+	11.8617i	−0.916973	+	0.666220i	0.0257958	+	0.999667i	$0.491788\pi$
$318$	9.70820			0.544409
$319$	0.145898	+	1.55909i	0.00816872	+	0.0872921i
$320$	−0.381966			−0.0213525
$321$	5.50000	−	3.99598i	0.306980	−	0.223034i
$322$	1.04508	+	3.21644i	0.0582403	+	0.179245i
$323$	6.35410	−	19.5559i	0.353552	−	1.08812i
$324$	−0.809017	−	0.587785i	−0.0449454	−	0.0326547i
$325$	4.85410	+	3.52671i	0.269257	+	0.195627i
$326$	−0.145898	+	0.449028i	−0.00808054	+	0.0248694i
$327$	5.97214	+	18.3803i	0.330260	+	1.01644i
$328$	3.54508	−	2.57565i	0.195745	−	0.142217i
$329$	0.472136			0.0260297
$330$	0.836881	+	0.951057i	0.0460688	+	0.0523539i
$331$	6.58359			0.361867			0.180933	−	0.983495i	$-0.442088\pi$
$331$	6.58359			0.361867			0.180933	+	0.983495i	$0.442088\pi$
$332$	2.38197	−	1.73060i	0.130727	−	0.0949790i
$333$	1.50000	+	4.61653i	0.0821995	+	0.252984i
$334$	3.00000	−	9.23305i	0.164153	−	0.505210i
$335$	1.23607	+	0.898056i	0.0675336	+	0.0490660i
$336$	0.809017	+	0.587785i	0.0441355	+	0.0320663i
$337$	−9.91641	+	30.5196i	−0.540181	+	1.66251i	0.191999	+	0.981395i	$0.438503\pi$
$337$	−9.91641	+	30.5196i	−0.540181	+	1.66251i	−0.732180	+	0.681111i	$0.761497\pi$
$338$	−3.54508	−	10.9106i	−0.192827	−	0.593461i
$339$	11.8541	−	8.61251i	0.643826	−	0.467767i
$340$	1.00000			0.0542326
$341$	8.20820	−	13.8496i	0.444499	−	0.749997i
$342$	−7.85410			−0.424701
$343$	−0.809017	+	0.587785i	−0.0436828	+	0.0317374i
$344$	0.381966	+	1.17557i	0.0205942	+	0.0633825i
$345$	0.399187	−	1.22857i	0.0214915	−	0.0661440i
$346$	8.11803	+	5.89810i	0.436428	+	0.317084i
$347$	14.0172	+	10.1841i	0.752484	+	0.546712i	0.896596	−	0.442850i	$-0.146033\pi$
$347$	14.0172	+	10.1841i	0.752484	+	0.546712i	−0.144112	+	0.989561i	$0.546033\pi$
$348$	0.145898	−	0.449028i	0.00782096	−	0.0240704i
$349$	−4.85410	−	14.9394i	−0.259834	−	0.799687i	−0.992839	−	0.119463i	$-0.961883\pi$
$349$	−4.85410	−	14.9394i	−0.259834	−	0.799687i	0.733004	−	0.680224i	$-0.238117\pi$
$350$	3.92705	−	2.85317i	0.209910	−	0.152508i
$351$	−1.23607			−0.0659764
$352$	3.04508	−	1.31433i	0.162304	−	0.0700539i
$353$	−18.3607			−0.977240			−0.488620	−	0.872497i	$-0.662500\pi$
$353$	−18.3607			−0.977240			−0.488620	+	0.872497i	$0.662500\pi$
$354$	−2.23607	+	1.62460i	−0.118846	+	0.0863464i
$355$	1.41641	+	4.35926i	0.0751751	+	0.231365i
$356$	−4.42705	+	13.6251i	−0.234633	+	0.722127i
$357$	−2.11803	−	1.53884i	−0.112098	−	0.0814441i
$358$	−2.78115	−	2.02063i	−0.146989	−	0.106793i
$359$	−7.64590	+	23.5317i	−0.403535	+	1.24195i	0.518577	+	0.855031i	$0.326462\pi$
$359$	−7.64590	+	23.5317i	−0.403535	+	1.24195i	−0.922112	+	0.386922i	$0.873538\pi$
$360$	−0.118034	−	0.363271i	−0.00622094	−	0.0191461i
$361$	−34.5344	+	25.0907i	−1.81760	+	1.32057i
$362$	−21.4164			−1.12562
$363$	−9.94427	−	4.70228i	−0.521939	−	0.246806i
$364$	1.23607			0.0647876
$365$	−3.61803	+	2.62866i	−0.189377	+	0.137590i
$366$		0			0
$367$	5.20820	−	16.0292i	0.271866	−	0.836718i	−0.718166	−	0.695872i	$-0.755018\pi$
$367$	5.20820	−	16.0292i	0.271866	−	0.836718i	0.990032	−	0.140845i	$-0.0449820\pi$
$368$	−2.73607	−	1.98787i	−0.142627	−	0.103625i
$369$	3.54508	+	2.57565i	0.184550	+	0.134083i
$370$	−0.572949	+	1.76336i	−0.0297862	+	0.0916725i
$371$	−3.00000	−	9.23305i	−0.155752	−	0.479356i
$372$	−3.92705	+	2.85317i	−0.203608	+	0.147930i
$373$	9.61803			0.498003			0.249001	−	0.968503i	$-0.419898\pi$
$373$	9.61803			0.498003			0.249001	+	0.968503i	$0.419898\pi$
$374$	−7.97214	+	3.44095i	−0.412229	+	0.177928i
$375$	−3.76393			−0.194369
$376$	−0.381966	+	0.277515i	−0.0196984	+	0.0143117i
$377$	−0.180340	−	0.555029i	−0.00928798	−	0.0285855i
$378$	−0.309017	+	0.951057i	−0.0158941	+	0.0489171i
$379$	−30.6525	−	22.2703i	−1.57451	−	1.14395i	−0.922667	−	0.385598i	$-0.873995\pi$
$379$	−30.6525	−	22.2703i	−1.57451	−	1.14395i	−0.651845	−	0.758352i	$-0.726005\pi$
$380$	−2.42705	−	1.76336i	−0.124505	−	0.0904582i
$381$	6.70820	−	20.6457i	0.343672	−	1.05771i
$382$	1.11803	+	3.44095i	0.0572036	+	0.176055i
$383$	−21.7984	+	15.8374i	−1.11384	+	0.809256i	−0.983265	−	0.182182i	$-0.941684\pi$
$383$	−21.7984	+	15.8374i	−1.11384	+	0.809256i	−0.130580	+	0.991438i	$0.541684\pi$
$384$	−1.00000			−0.0510310
$385$	0.645898	−	1.08981i	0.0329180	−	0.0555421i
$386$	−26.5623			−1.35199
$387$	−1.00000	+	0.726543i	−0.0508329	+	0.0369322i
$388$	0.145898	+	0.449028i	0.00740685	+	0.0227959i
$389$	3.03444	−	9.33905i	0.153852	−	0.473509i	−0.844190	−	0.536043i	$-0.819918\pi$
$389$	3.03444	−	9.33905i	0.153852	−	0.473509i	0.998043	+	0.0625346i	$0.0199184\pi$
$390$	−0.381966	−	0.277515i	−0.0193416	−	0.0140525i
$391$	7.16312	+	5.20431i	0.362254	+	0.263193i
$392$	0.309017	−	0.951057i	0.0156077	−	0.0480356i
$393$	2.52786	+	7.77997i	0.127514	+	0.392447i
$394$	−14.4721	+	10.5146i	−0.729096	+	0.529719i
$395$	−3.23607			−0.162824
$396$	2.19098	+	2.48990i	0.110101	+	0.125122i
$397$	21.7082			1.08950			0.544752	−	0.838597i	$-0.316624\pi$
$397$	21.7082			1.08950			0.544752	+	0.838597i	$0.316624\pi$
$398$	−9.11803	+	6.62464i	−0.457046	+	0.332063i
$399$	2.42705	+	7.46969i	0.121505	+	0.373952i
$400$	−1.50000	+	4.61653i	−0.0750000	+	0.230826i
$401$	6.76393	+	4.91428i	0.337775	+	0.245408i	0.743722	−	0.668489i	$-0.233058\pi$
$401$	6.76393	+	4.91428i	0.337775	+	0.245408i	−0.405948	+	0.913896i	$0.633058\pi$
$402$	3.23607	+	2.35114i	0.161400	+	0.117264i
$403$	−1.85410	+	5.70634i	−0.0923594	+	0.284253i
$404$	5.64590	+	17.3763i	0.280894	+	0.864503i
$405$	0.309017	−	0.224514i	0.0153552	−	0.0111562i
$406$	−0.472136			−0.0234317
$407$	−1.50000	−	16.0292i	−0.0743522	−	0.794538i
$408$	2.61803			0.129612
$409$	11.5623	−	8.40051i	0.571719	−	0.415378i	−0.264010	−	0.964520i	$-0.585045\pi$
$409$	11.5623	−	8.40051i	0.571719	−	0.415378i	0.835729	+	0.549142i	$0.185045\pi$
$410$	0.517221	+	1.59184i	0.0255437	+	0.0786155i
$411$	−3.14590	+	9.68208i	−0.155176	+	0.477582i
$412$	−9.35410	−	6.79615i	−0.460844	−	0.334822i
$413$	2.23607	+	1.62460i	0.110030	+	0.0799413i
$414$	1.04508	−	3.21644i	0.0513631	−	0.158079i
$415$	0.347524	+	1.06957i	0.0170593	+	0.0525031i
$416$	−1.00000	+	0.726543i	−0.0490290	+	0.0356217i
$417$	−2.32624			−0.113916
$418$	25.4164	+	5.70634i	1.24316	+	0.279106i
$419$	−5.23607			−0.255799			−0.127899	−	0.991787i	$-0.540823\pi$
$419$	−5.23607			−0.255799			−0.127899	+	0.991787i	$0.540823\pi$
$420$	−0.309017	+	0.224514i	−0.0150785	+	0.0109552i
$421$	−2.75329	−	8.47375i	−0.134187	−	0.412985i	0.861276	−	0.508138i	$-0.169666\pi$
$421$	−2.75329	−	8.47375i	−0.134187	−	0.412985i	−0.995463	+	0.0951527i	$0.969666\pi$
$422$	−4.32624	+	13.3148i	−0.210598	+	0.648154i
$423$	−0.381966	−	0.277515i	−0.0185718	−	0.0134932i
$424$	7.85410	+	5.70634i	0.381429	+	0.277124i
$425$	3.92705	−	12.0862i	0.190490	−	0.586268i
$426$	3.70820	+	11.4127i	0.179663	+	0.552946i
$427$		0			0
$428$	6.79837			0.328612
$429$	4.00000	+	0.898056i	0.193122	+	0.0433585i
$430$	−0.472136			−0.0227684
$431$	8.92705	−	6.48588i	0.430001	−	0.312414i	−0.351648	−	0.936132i	$-0.614379\pi$
$431$	8.92705	−	6.48588i	0.430001	−	0.312414i	0.781649	+	0.623718i	$0.214379\pi$
$432$	−0.309017	−	0.951057i	−0.0148676	−	0.0457577i
$433$	−11.0344	+	33.9605i	−0.530281	+	1.63204i	0.223348	+	0.974739i	$0.428301\pi$
$433$	−11.0344	+	33.9605i	−0.530281	+	1.63204i	−0.753629	+	0.657300i	$0.771699\pi$
$434$	3.92705	+	2.85317i	0.188504	+	0.136957i
$435$	0.145898	+	0.106001i	0.00699528	+	0.00508236i
$436$	−5.97214	+	18.3803i	−0.286013	+	0.880259i
$437$	−8.20820	−	25.2623i	−0.392652	−	1.20846i
$438$	−9.47214	+	6.88191i	−0.452596	+	0.328830i
$439$	−24.2705			−1.15837			−0.579184	−	0.815197i	$-0.696629\pi$
$439$	−24.2705			−1.15837			−0.579184	+	0.815197i	$0.696629\pi$
$440$	0.118034	+	1.26133i	0.00562705	+	0.0601314i
$441$	1.00000			0.0476190
$442$	2.61803	−	1.90211i	0.124527	−	0.0904743i
$443$	12.5729	+	38.6956i	0.597359	+	1.83848i	0.542616	+	0.839981i	$0.317434\pi$
$443$	12.5729	+	38.6956i	0.597359	+	1.83848i	0.0547430	+	0.998500i	$0.482566\pi$
$444$	−1.50000	+	4.61653i	−0.0711868	+	0.219091i
$445$	−4.42705	−	3.21644i	−0.209862	−	0.152474i
$446$	−0.645898	−	0.469272i	−0.0305842	−	0.0222207i
$447$	2.76393	−	8.50651i	0.130729	−	0.402344i
$448$	0.309017	+	0.951057i	0.0145997	+	0.0449332i
$449$	1.23607	−	0.898056i	0.0583337	−	0.0423819i	−0.558236	−	0.829682i	$-0.688522\pi$
$449$	1.23607	−	0.898056i	0.0583337	−	0.0423819i	0.616570	+	0.787300i	$0.288522\pi$
$450$	−4.85410			−0.228825
$451$	−9.60081	−	10.9106i	−0.452085	−	0.513762i
$452$	14.6525			0.689194
$453$	4.38197	−	3.18368i	0.205883	−	0.149583i
$454$	−7.09017	−	21.8213i	−0.332758	−	1.02412i
$455$	−0.145898	+	0.449028i	−0.00683981	+	0.0210508i
$456$	−6.35410	−	4.61653i	−0.297558	−	0.216189i
$457$	5.32624	+	3.86974i	0.249151	+	0.181019i	0.705350	−	0.708859i	$-0.250790\pi$
$457$	5.32624	+	3.86974i	0.249151	+	0.181019i	−0.456200	+	0.889878i	$0.650790\pi$
$458$	−4.56231	+	14.0413i	−0.213183	+	0.656108i
$459$	0.809017	+	2.48990i	0.0377617	+	0.116218i
$460$	1.04508	−	0.759299i	0.0487273	−	0.0354025i
$461$	37.4164			1.74266			0.871328	−	0.490701i	$-0.163259\pi$
$461$	37.4164			1.74266			0.871328	+	0.490701i	$0.163259\pi$
$462$	1.69098	−	2.85317i	0.0786716	−	0.132741i
$463$	36.0000			1.67306			0.836531	−	0.547920i	$-0.184580\pi$
$463$	36.0000			1.67306			0.836531	+	0.547920i	$0.184580\pi$
$464$	0.381966	−	0.277515i	0.0177323	−	0.0128833i
$465$	−0.572949	−	1.76336i	−0.0265699	−	0.0817737i
$466$	−0.708204	+	2.17963i	−0.0328069	+	0.100969i
$467$	−18.7984	−	13.6578i	−0.869885	−	0.632008i	0.0606711	−	0.998158i	$-0.480676\pi$
$467$	−18.7984	−	13.6578i	−0.869885	−	0.632008i	−0.930556	+	0.366149i	$0.880676\pi$
$468$	−1.00000	−	0.726543i	−0.0462250	−	0.0335844i
$469$	1.23607	−	3.80423i	0.0570763	−	0.175663i
$470$	−0.0557281	−	0.171513i	−0.00257055	−	0.00791132i
$471$	−0.145898	+	0.106001i	−0.00672263	+	0.00488427i
$472$	−2.76393			−0.127220
$473$	3.76393	−	1.62460i	0.173066	−	0.0746991i
$474$	−8.47214			−0.389138
$475$	−30.8435	+	22.4091i	−1.41519	+	1.02820i
$476$	−0.809017	−	2.48990i	−0.0370812	−	0.114124i
$477$	−3.00000	+	9.23305i	−0.137361	+	0.422752i
$478$	6.50000	+	4.72253i	0.297303	+	0.216003i
$479$	−19.4164	−	14.1068i	−0.887158	−	0.644558i	0.0479772	−	0.998848i	$-0.484723\pi$
$479$	−19.4164	−	14.1068i	−0.887158	−	0.644558i	−0.935136	+	0.354290i	$0.884723\pi$
$480$	0.118034	−	0.363271i	0.00538749	−	0.0165810i
$481$	1.85410	+	5.70634i	0.0845398	+	0.260187i
$482$	13.7082	−	9.95959i	0.624392	−	0.453647i
$483$	−3.38197			−0.153885
$484$	−5.28115	−	9.64932i	−0.240052	−	0.438606i
$485$	−0.180340			−0.00818881
$486$	0.809017	−	0.587785i	0.0366978	−	0.0266625i
$487$	−1.58359	−	4.87380i	−0.0717594	−	0.220853i	0.908744	−	0.417353i	$-0.137042\pi$
$487$	−1.58359	−	4.87380i	−0.0717594	−	0.220853i	−0.980504	+	0.196501i	$0.937042\pi$
$488$		0			0
$489$	−0.381966	−	0.277515i	−0.0172731	−	0.0125496i
$490$	0.309017	+	0.224514i	0.0139600	+	0.0101425i
$491$	−2.57295	+	7.91872i	−0.116116	+	0.357367i	−0.992178	−	0.124831i	$-0.960161\pi$
$491$	−2.57295	+	7.91872i	−0.116116	+	0.357367i	0.876063	+	0.482198i	$0.160161\pi$
$492$	1.35410	+	4.16750i	0.0610476	+	0.187885i
$493$	−1.00000	+	0.726543i	−0.0450377	+	0.0327218i
$494$	−9.70820			−0.436793
$495$	−1.16312	+	0.502029i	−0.0522783	+	0.0225645i
$496$	−4.85410			−0.217956
$497$	9.70820	−	7.05342i	0.435472	−	0.316389i
$498$	0.909830	+	2.80017i	0.0407705	+	0.125479i
$499$	7.32624	−	22.5478i	0.327967	−	1.00938i	−0.642116	−	0.766608i	$-0.721943\pi$
$499$	7.32624	−	22.5478i	0.327967	−	1.00938i	0.970083	−	0.242772i	$-0.0780568\pi$
$500$	−3.04508	−	2.21238i	−0.136180	−	0.0989408i
$501$	7.85410	+	5.70634i	0.350895	+	0.254940i
$502$	−8.23607	+	25.3480i	−0.367594	+	1.13134i
$503$	10.0000	+	30.7768i	0.445878	+	1.37227i	0.881518	+	0.472150i	$0.156522\pi$
$503$	10.0000	+	30.7768i	0.445878	+	1.37227i	−0.435640	+	0.900121i	$0.643478\pi$
$504$	−0.809017	+	0.587785i	−0.0360365	+	0.0261820i
$505$	−6.97871			−0.310549
$506$	−5.71885	+	9.64932i	−0.254234	+	0.428965i
$507$	11.4721			0.509495
$508$	17.5623	−	12.7598i	0.779201	−	0.566123i
$509$	9.40983	+	28.9605i	0.417083	+	1.28365i	0.910374	+	0.413786i	$0.135794\pi$
$509$	9.40983	+	28.9605i	0.417083	+	1.28365i	−0.493291	+	0.869865i	$0.664206\pi$
$510$	−0.309017	+	0.951057i	−0.0136835	+	0.0421135i
$511$	9.47214	+	6.88191i	0.419023	+	0.304438i
$512$	−0.809017	−	0.587785i	−0.0357538	−	0.0259767i
$513$	2.42705	−	7.46969i	0.107157	−	0.329795i
$514$	−5.48278	−	16.8743i	−0.241835	−	0.744292i
$515$	3.57295	−	2.59590i	0.157443	−	0.114389i
$516$	−1.23607			−0.0544149
$517$	1.03444	+	1.17557i	0.0454947	+	0.0517015i
$518$	4.85410			0.213277
$519$	−8.11803	+	5.89810i	−0.356342	+	0.258898i
$520$	−0.145898	−	0.449028i	−0.00639805	−	0.0196912i
$521$	−12.0623	+	37.1240i	−0.528459	+	1.62643i	0.228913	+	0.973447i	$0.426483\pi$
$521$	−12.0623	+	37.1240i	−0.528459	+	1.62643i	−0.757372	+	0.652983i	$0.773517\pi$
$522$	0.381966	+	0.277515i	0.0167182	+	0.0121465i
$523$	−5.88197	−	4.27350i	−0.257200	−	0.186867i	0.451712	−	0.892164i	$-0.350814\pi$
$523$	−5.88197	−	4.27350i	−0.257200	−	0.186867i	−0.708912	+	0.705297i	$0.750814\pi$
$524$	−2.52786	+	7.77997i	−0.110430	+	0.339869i
$525$	1.50000	+	4.61653i	0.0654654	+	0.201482i
$526$	4.20820	−	3.05744i	0.183486	−	0.133311i
$527$	12.7082			0.553578
$528$	0.309017	+	3.30220i	0.0134482	+	0.143710i
$529$	−11.5623			−0.502709
$530$	−3.00000	+	2.17963i	−0.130312	+	0.0946770i
$531$	−0.854102	−	2.62866i	−0.0370649	−	0.114074i
$532$	−2.42705	+	7.46969i	−0.105226	+	0.323852i
$533$	4.38197	+	3.18368i	0.189804	+	0.137901i
$534$	−11.5902	−	8.42075i	−0.501556	−	0.364402i
$535$	−0.802439	+	2.46965i	−0.0346925	+	0.106772i
$536$	1.23607	+	3.80423i	0.0533900	+	0.164318i
$537$	2.78115	−	2.02063i	0.120016	−	0.0871964i
$538$	14.9443			0.644293
$539$	−3.23607	−	0.726543i	−0.139387	−	0.0312944i
$540$	0.381966			0.0164372
$541$	8.07295	−	5.86534i	0.347083	−	0.252171i	−0.400561	−	0.916270i	$-0.631185\pi$
$541$	8.07295	−	5.86534i	0.347083	−	0.252171i	0.747644	+	0.664099i	$0.231185\pi$
$542$	2.31966	+	7.13918i	0.0996379	+	0.306654i
$543$	6.61803	−	20.3682i	0.284007	−	0.874084i
$544$	2.11803	+	1.53884i	0.0908100	+	0.0659773i
$545$	−5.97214	−	4.33901i	−0.255818	−	0.185863i
$546$	−0.381966	+	1.17557i	−0.0163466	+	0.0503098i
$547$	−9.56231	−	29.4298i	−0.408855	−	1.25833i	−0.917633	−	0.397428i	$-0.869903\pi$
$547$	−9.56231	−	29.4298i	−0.408855	−	1.25833i	0.508779	−	0.860897i	$-0.330097\pi$
$548$	−8.23607	+	5.98385i	−0.351827	+	0.255618i
$549$		0			0
$550$	15.7082	+	3.52671i	0.669800	+	0.150379i
$551$	3.70820			0.157975
$552$	2.73607	−	1.98787i	0.116455	−	0.0846094i
$553$	2.61803	+	8.05748i	0.111330	+	0.342639i
$554$	3.71885	−	11.4454i	0.157999	−	0.486270i
$555$	−1.50000	−	1.08981i	−0.0636715	−	0.0462600i
$556$	−1.88197	−	1.36733i	−0.0798131	−	0.0579876i
$557$	12.4377	−	38.2793i	0.527002	−	1.62195i	−0.233321	−	0.972400i	$-0.574959\pi$
$557$	12.4377	−	38.2793i	0.527002	−	1.62195i	0.760323	−	0.649546i	$-0.225041\pi$
$558$	−1.50000	−	4.61653i	−0.0635001	−	0.195433i
$559$	−1.23607	+	0.898056i	−0.0522801	+	0.0379837i
$560$	−0.381966			−0.0161410
$561$	−0.809017	−	8.64527i	−0.0341567	−	0.365003i
$562$	14.9443			0.630386
$563$	5.70820	−	4.14725i	0.240572	−	0.174786i	−0.460966	−	0.887418i	$-0.652497\pi$
$563$	5.70820	−	4.14725i	0.240572	−	0.174786i	0.701538	+	0.712632i	$0.252497\pi$
$564$	−0.145898	−	0.449028i	−0.00614342	−	0.0189075i
$565$	−1.72949	+	5.32282i	−0.0727602	+	0.223933i
$566$	18.7254	+	13.6048i	0.787088	+	0.571853i
$567$	−0.809017	−	0.587785i	−0.0339755	−	0.0246847i
$568$	−3.70820	+	11.4127i	−0.155593	+	0.478865i
$569$	2.56231	+	7.88597i	0.107417	+	0.330597i	0.990290	−	0.139015i	$-0.0443937\pi$
$569$	2.56231	+	7.88597i	0.107417	+	0.330597i	−0.882873	+	0.469612i	$0.844394\pi$
$570$	2.42705	−	1.76336i	0.101658	−	0.0738588i
$571$	−17.1246			−0.716643			−0.358321	−	0.933598i	$-0.616651\pi$
$571$	−17.1246			−0.716643			−0.358321	+	0.933598i	$0.616651\pi$
$572$	2.70820	+	3.07768i	0.113236	+	0.128684i
$573$	−3.61803			−0.151146
$574$	3.54508	−	2.57565i	0.147969	−	0.107506i
$575$	−5.07295	−	15.6129i	−0.211557	−	0.651104i
$576$	0.309017	−	0.951057i	0.0128757	−	0.0396274i
$577$	19.0902	+	13.8698i	0.794734	+	0.577408i	0.909365	−	0.416000i	$-0.136568\pi$
$577$	19.0902	+	13.8698i	0.794734	+	0.577408i	−0.114630	+	0.993408i	$0.536568\pi$
$578$	8.20820	+	5.96361i	0.341416	+	0.248053i
$579$	8.20820	−	25.2623i	0.341121	−	1.04986i
$580$	0.0557281	+	0.171513i	0.00231398	+	0.00712171i
$581$	2.38197	−	1.73060i	0.0988206	−	0.0717974i
$582$	−0.472136			−0.0195707
$583$	16.4164	−	27.6992i	0.679898	−	1.14718i
$584$	−11.7082			−0.484489
$585$	0.381966	−	0.277515i	0.0157924	−	0.0114738i
$586$	3.82624	+	11.7759i	0.158060	+	0.486460i
$587$	7.09017	−	21.8213i	0.292643	−	0.900661i	−0.691360	−	0.722510i	$-0.742988\pi$
$587$	7.09017	−	21.8213i	0.292643	−	0.900661i	0.984003	−	0.178151i	$-0.0570117\pi$
$588$	0.809017	+	0.587785i	0.0333633	+	0.0242399i
$589$	−30.8435	−	22.4091i	−1.27088	−	0.923350i
$590$	0.326238	−	1.00406i	0.0134310	−	0.0413364i
$591$	−5.52786	−	17.0130i	−0.227386	−	0.699822i
$592$	−3.92705	+	2.85317i	−0.161401	+	0.117265i
$593$	9.90983			0.406948			0.203474	−	0.979080i	$-0.434777\pi$
$593$	9.90983			0.406948			0.203474	+	0.979080i	$0.434777\pi$
$594$	−3.04508	+	1.31433i	−0.124941	+	0.0539275i
$595$	1.00000			0.0409960
$596$	7.23607	−	5.25731i	0.296401	−	0.215348i
$597$	−3.48278	−	10.7189i	−0.142541	−	0.438695i
$598$	1.29180	−	3.97574i	0.0528255	−	0.162580i
$599$	−23.3885	−	16.9928i	−0.955630	−	0.694306i	−0.00349827	−	0.999994i	$-0.501114\pi$
$599$	−23.3885	−	16.9928i	−0.955630	−	0.694306i	−0.952132	+	0.305688i	$0.901114\pi$
$600$	−3.92705	−	2.85317i	−0.160321	−	0.116480i
$601$	−10.1459	+	31.2259i	−0.413860	+	1.27373i	0.499407	+	0.866368i	$0.333551\pi$
$601$	−10.1459	+	31.2259i	−0.413860	+	1.27373i	−0.913267	+	0.407362i	$0.866449\pi$
$602$	0.381966	+	1.17557i	0.0155678	+	0.0479127i
$603$	−3.23607	+	2.35114i	−0.131783	+	0.0957459i
$604$	5.41641			0.220391
$605$	4.12868	−	0.779543i	0.167855	−	0.0316929i
$606$	−18.2705			−0.742189
$607$	13.1180	−	9.53081i	0.532445	−	0.386844i	−0.288827	−	0.957381i	$-0.593265\pi$
$607$	13.1180	−	9.53081i	0.532445	−	0.386844i	0.821271	+	0.570538i	$0.193265\pi$
$608$	−2.42705	−	7.46969i	−0.0984299	−	0.302936i
$609$	0.145898	−	0.449028i	0.00591209	−	0.0181955i
$610$		0			0
$611$	−0.472136	−	0.343027i	−0.0191006	−	0.0138774i
$612$	−0.809017	+	2.48990i	−0.0327026	+	0.100648i
$613$	−2.28115	−	7.02067i	−0.0921349	−	0.283562i	0.894362	−	0.447345i	$-0.147630\pi$
$613$	−2.28115	−	7.02067i	−0.0921349	−	0.283562i	−0.986496	+	0.163783i	$0.947630\pi$
$614$	3.92705	−	2.85317i	0.158483	−	0.115145i
$615$	−1.67376			−0.0674926
$616$	3.04508	−	1.31433i	0.122690	−	0.0529558i
$617$	9.81966			0.395325			0.197662	−	0.980270i	$-0.436665\pi$
$617$	9.81966			0.395325			0.197662	+	0.980270i	$0.436665\pi$
$618$	9.35410	−	6.79615i	0.376277	−	0.273381i
$619$	−3.08359	−	9.49032i	−0.123940	−	0.381448i	0.869766	−	0.493464i	$-0.164269\pi$
$619$	−3.08359	−	9.49032i	−0.123940	−	0.381448i	−0.993706	+	0.112015i	$0.964269\pi$
$620$	0.572949	−	1.76336i	0.0230102	−	0.0708181i
$621$	2.73607	+	1.98787i	0.109795	+	0.0797705i
$622$	−13.0902	−	9.51057i	−0.524868	−	0.381339i
$623$	−4.42705	+	13.6251i	−0.177366	+	0.545877i
$624$	−0.381966	−	1.17557i	−0.0152909	−	0.0470605i
$625$	−18.4721	+	13.4208i	−0.738885	+	0.536832i
$626$	11.1246			0.444629
$627$	−13.2812	+	22.4091i	−0.530398	+	0.894933i
$628$	−0.180340			−0.00719634
$629$	10.2812	−	7.46969i	0.409936	−	0.297836i
$630$	−0.118034	−	0.363271i	−0.00470259	−	0.0144731i
$631$	8.00000	−	24.6215i	0.318475	−	0.980165i	−0.655825	−	0.754913i	$-0.727679\pi$
$631$	8.00000	−	24.6215i	0.318475	−	0.980165i	0.974300	−	0.225253i	$-0.0723207\pi$
$632$	−6.85410	−	4.97980i	−0.272642	−	0.198086i
$633$	−11.3262	−	8.22899i	−0.450178	−	0.327073i
$634$	6.23607	−	19.1926i	0.247666	−	0.762237i
$635$	2.56231	+	7.88597i	0.101682	+	0.312945i
$636$	−7.85410	+	5.70634i	−0.311435	+	0.226271i
$637$	1.23607			0.0489748
$638$	−1.03444	−	1.17557i	−0.0409539	−	0.0465413i
$639$	−12.0000			−0.474713
$640$	0.309017	−	0.224514i	0.0122150	−	0.00887469i
$641$	1.61803	+	4.97980i	0.0639085	+	0.196690i	0.977912	−	0.209015i	$-0.0670259\pi$
$641$	1.61803	+	4.97980i	0.0639085	+	0.196690i	−0.914004	+	0.405705i	$0.867026\pi$
$642$	−2.10081	+	6.46564i	−0.0829125	+	0.255178i
$643$	22.0623	+	16.0292i	0.870052	+	0.632130i	0.930601	−	0.366035i	$-0.119285\pi$
$643$	22.0623	+	16.0292i	0.870052	+	0.632130i	−0.0605486	+	0.998165i	$0.519285\pi$
$644$	−2.73607	−	1.98787i	−0.107816	−	0.0783330i
$645$	0.145898	−	0.449028i	0.00574473	−	0.0176805i
$646$	6.35410	+	19.5559i	0.249999	+	0.769417i
$647$	25.7984	−	18.7436i	1.01424	−	0.736888i	0.0491448	−	0.998792i	$-0.484350\pi$
$647$	25.7984	−	18.7436i	1.01424	−	0.736888i	0.965094	+	0.261904i	$0.0843504\pi$
$648$	1.00000			0.0392837
$649$	0.854102	+	9.12705i	0.0335264	+	0.358268i
$650$	−6.00000			−0.235339
$651$	−3.92705	+	2.85317i	−0.153913	+	0.111825i
$652$	−0.145898	−	0.449028i	−0.00571381	−	0.0175853i
$653$	5.12461	−	15.7719i	0.200542	−	0.617203i	−0.799326	−	0.600898i	$-0.794810\pi$
$653$	5.12461	−	15.7719i	0.200542	−	0.617203i	0.999867	−	0.0163052i	$-0.00519033\pi$
$654$	−15.6353	−	11.3597i	−0.611387	−	0.444199i
$655$	−2.52786	−	1.83660i	−0.0987718	−	0.0717619i
$656$	−1.35410	+	4.16750i	−0.0528688	+	0.162713i
$657$	−3.61803	−	11.1352i	−0.141153	−	0.434424i
$658$	−0.381966	+	0.277515i	−0.0148906	+	0.0108186i
$659$	13.6869			0.533167			0.266583	−	0.963812i	$-0.414105\pi$
$659$	13.6869			0.533167			0.266583	+	0.963812i	$0.414105\pi$
$660$	−1.23607	−	0.277515i	−0.0481139	−	0.0108022i
$661$	35.1246			1.36619			0.683095	−	0.730330i	$-0.260634\pi$
$661$	35.1246			1.36619			0.683095	+	0.730330i	$0.260634\pi$
$662$	−5.32624	+	3.86974i	−0.207010	+	0.150402i
$663$	1.00000	+	3.07768i	0.0388368	+	0.119527i
$664$	−0.909830	+	2.80017i	−0.0353083	+	0.108668i
$665$	−2.42705	−	1.76336i	−0.0941170	−	0.0683800i
$666$	−3.92705	−	2.85317i	−0.152170	−	0.110558i
$667$	−0.493422	+	1.51860i	−0.0191054	+	0.0588003i
$668$	3.00000	+	9.23305i	0.116073	+	0.357237i
$669$	0.645898	−	0.469272i	0.0249719	−	0.0181431i
$670$	−1.52786			−0.0590265
$671$		0			0
$672$	−1.00000			−0.0385758
$673$	−37.0344	+	26.9071i	−1.42757	+	1.03719i	−0.437111	+	0.899408i	$0.643998\pi$
$673$	−37.0344	+	26.9071i	−1.42757	+	1.03719i	−0.990462	+	0.137785i	$0.956002\pi$
$674$	−9.91641	−	30.5196i	−0.381966	−	1.17557i
$675$	1.50000	−	4.61653i	0.0577350	−	0.177690i
$676$	9.28115	+	6.74315i	0.356967	+	0.259352i
$677$	6.56231	+	4.76779i	0.252210	+	0.183241i	0.706706	−	0.707508i	$-0.250181\pi$
$677$	6.56231	+	4.76779i	0.252210	+	0.183241i	−0.454496	+	0.890749i	$0.650181\pi$
$678$	−4.52786	+	13.9353i	−0.173892	+	0.535183i
$679$	0.145898	+	0.449028i	0.00559905	+	0.0172321i
$680$	−0.809017	+	0.587785i	−0.0310244	+	0.0225405i
$681$	22.9443			0.879226
$682$	1.50000	+	16.0292i	0.0574380	+	0.613790i
$683$	31.0344			1.18750			0.593750	−	0.804650i	$-0.297647\pi$
$683$	31.0344			1.18750			0.593750	+	0.804650i	$0.297647\pi$
$684$	6.35410	−	4.61653i	0.242955	−	0.176517i
$685$	−1.20163	−	3.69822i	−0.0459118	−	0.141302i
$686$	0.309017	−	0.951057i	0.0117983	−	0.0363115i
$687$	−11.9443	−	8.67802i	−0.455702	−	0.331087i
$688$	−1.00000	−	0.726543i	−0.0381246	−	0.0276992i
$689$	−3.70820	+	11.4127i	−0.141271	+	0.434788i
$690$	0.399187	+	1.22857i	0.0151968	+	0.0467709i
$691$	−41.7148	+	30.3076i	−1.58691	+	1.15295i	−0.678710	+	0.734406i	$0.737461\pi$
$691$	−41.7148	+	30.3076i	−1.58691	+	1.15295i	−0.908195	+	0.418548i	$0.862539\pi$
$692$	−10.0344			−0.381452
$693$	2.19098	+	2.48990i	0.0832286	+	0.0945834i
$694$	−17.3262			−0.657695
$695$	0.718847	−	0.522273i	0.0272674	−	0.0198109i
$696$	0.145898	+	0.449028i	0.00553025	+	0.0170204i
$697$	3.54508	−	10.9106i	0.134280	−	0.413270i
$698$	12.7082	+	9.23305i	0.481013	+	0.349476i
$699$	−1.85410	−	1.34708i	−0.0701286	−	0.0509514i
$700$	−1.50000	+	4.61653i	−0.0566947	+	0.174488i
$701$	−8.85410	−	27.2501i	−0.334415	−	1.02922i	−0.967010	−	0.254740i	$-0.918010\pi$
$701$	−8.85410	−	27.2501i	−0.334415	−	1.02922i	0.632595	−	0.774483i	$-0.281990\pi$
$702$	1.00000	−	0.726543i	0.0377426	−	0.0274216i
$703$	−38.1246			−1.43790
$704$	−1.69098	+	2.85317i	−0.0637313	+	0.107533i
$705$	0.180340			0.00679199
$706$	14.8541	−	10.7921i	0.559042	−	0.406167i
$707$	5.64590	+	17.3763i	0.212336	+	0.653503i
$708$	0.854102	−	2.62866i	0.0320991	−	0.0987909i
$709$	9.63525	+	7.00042i	0.361860	+	0.262906i	0.753827	−	0.657073i	$-0.228206\pi$
$709$	9.63525	+	7.00042i	0.361860	+	0.262906i	−0.391968	+	0.919979i	$0.628206\pi$
$710$	−3.70820	−	2.69417i	−0.139166	−	0.101110i
$711$	2.61803	−	8.05748i	0.0981839	−	0.302179i
$712$	−4.42705	−	13.6251i	−0.165911	−	0.510621i
$713$	13.2812	−	9.64932i	0.497383	−	0.361370i
$714$	2.61803			0.0979775
$715$	−1.43769	+	0.620541i	−0.0537667	+	0.0232069i
$716$	3.43769			0.128473
$717$	−6.50000	+	4.72253i	−0.242747	+	0.176366i
$718$	−7.64590	−	23.5317i	−0.285342	−	0.878194i
$719$	−5.61803	+	17.2905i	−0.209517	+	0.644828i	0.789980	+	0.613132i	$0.210091\pi$
$719$	−5.61803	+	17.2905i	−0.209517	+	0.644828i	−0.999498	+	0.0316957i	$0.989909\pi$
$720$	0.309017	+	0.224514i	0.0115164	+	0.00836714i
$721$	−9.35410	−	6.79615i	−0.348365	−	0.253102i
$722$	13.1910	−	40.5977i	0.490918	−	1.51089i
$723$	5.23607	+	16.1150i	0.194731	+	0.599322i
$724$	17.3262	−	12.5882i	0.643925	−	0.467839i
$725$	2.29180			0.0851152
$726$	10.8090	−	2.04087i	0.401160	−	0.0757438i
$727$	3.85410			0.142941			0.0714704	−	0.997443i	$-0.477231\pi$
$727$	3.85410			0.142941			0.0714704	+	0.997443i	$0.477231\pi$
$728$	−1.00000	+	0.726543i	−0.0370625	+	0.0269275i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	1.38197	−	4.25325i	0.0511489	−	0.157420i
$731$	2.61803	+	1.90211i	0.0968315	+	0.0703522i
$732$		0			0
$733$	−1.90983	+	5.87785i	−0.0705412	+	0.217103i	−0.980112	−	0.198446i	$-0.936411\pi$
$733$	−1.90983	+	5.87785i	−0.0705412	+	0.217103i	0.909571	+	0.415549i	$0.136411\pi$
$734$	5.20820	+	16.0292i	0.192238	+	0.591649i
$735$	−0.309017	+	0.224514i	−0.0113983	+	0.00828132i
$736$	3.38197			0.124661
$737$	12.1803	−	5.25731i	0.448669	−	0.193656i
$738$	−4.38197			−0.161302
$739$	6.23607	−	4.53077i	0.229397	−	0.166667i	−0.467149	−	0.884178i	$-0.654719\pi$
$739$	6.23607	−	4.53077i	0.229397	−	0.166667i	0.696547	+	0.717511i	$0.254719\pi$
$740$	−0.572949	−	1.76336i	−0.0210620	−	0.0648222i
$741$	3.00000	−	9.23305i	0.110208	−	0.339185i
$742$	7.85410	+	5.70634i	0.288333	+	0.209486i
$743$	−22.7812	−	16.5515i	−0.835759	−	0.607215i	0.0854234	−	0.996345i	$-0.472776\pi$
$743$	−22.7812	−	16.5515i	−0.835759	−	0.607215i	−0.921183	+	0.389130i	$0.872776\pi$
$744$	1.50000	−	4.61653i	0.0549927	−	0.169250i
$745$	1.05573	+	3.24920i	0.0386789	+	0.119041i
$746$	−7.78115	+	5.65334i	−0.284888	+	0.206983i
$747$	−2.94427			−0.107725
$748$	4.42705	−	7.46969i	0.161869	−	0.273119i
$749$	6.79837			0.248407
$750$	3.04508	−	2.21238i	0.111191	−	0.0807848i
$751$	−4.58359	−	14.1068i	−0.167258	−	0.514766i	0.831938	−	0.554869i	$-0.187232\pi$
$751$	−4.58359	−	14.1068i	−0.167258	−	0.514766i	−0.999196	+	0.0401026i	$0.987232\pi$
$752$	0.145898	−	0.449028i	0.00532035	−	0.0163744i
$753$	−21.5623	−	15.6659i	−0.785774	−	0.570898i
$754$	0.472136	+	0.343027i	0.0171942	+	0.0124923i
$755$	−0.639320	+	1.96763i	−0.0232672	+	0.0716092i
$756$	−0.309017	−	0.951057i	−0.0112388	−	0.0345896i
$757$	−14.4443	+	10.4944i	−0.524986	+	0.381425i	−0.818479	−	0.574537i	$-0.805182\pi$
$757$	−14.4443	+	10.4944i	−0.524986	+	0.381425i	0.293493	+	0.955961i	$0.405182\pi$
$758$	37.8885			1.37617
$759$	−7.40983	−	8.42075i	−0.268960	−	0.305654i
$760$	3.00000			0.108821
$761$	19.3262	−	14.0413i	0.700576	−	0.508998i	−0.179544	−	0.983750i	$-0.557462\pi$
$761$	19.3262	−	14.0413i	0.700576	−	0.508998i	0.880120	+	0.474752i	$0.157462\pi$
$762$	6.70820	+	20.6457i	0.243013	+	0.747916i
$763$	−5.97214	+	18.3803i	−0.216206	+	0.665413i
$764$	−2.92705	−	2.12663i	−0.105897	−	0.0769387i
$765$	−0.809017	−	0.587785i	−0.0292501	−	0.0212514i
$766$	8.32624	−	25.6255i	0.300839	−	0.925888i
$767$	−1.05573	−	3.24920i	−0.0381201	−	0.117322i
$768$	0.809017	−	0.587785i	0.0291929	−	0.0212099i
$769$	15.8885			0.572956			0.286478	−	0.958087i	$-0.407516\pi$
$769$	15.8885			0.572956			0.286478	+	0.958087i	$0.407516\pi$
$770$	0.118034	+	1.26133i	0.00425365	+	0.0454551i
$771$	17.7426			0.638986
$772$	21.4894	−	15.6129i	0.773419	−	0.561922i
$773$	7.38197	+	22.7194i	0.265511	+	0.817158i	0.991575	+	0.129532i	$0.0413474\pi$
$773$	7.38197	+	22.7194i	0.265511	+	0.817158i	−0.726064	+	0.687627i	$0.758653\pi$
$774$	0.381966	−	1.17557i	0.0137295	−	0.0422550i
$775$	−19.0623	−	13.8496i	−0.684738	−	0.497491i
$776$	−0.381966	−	0.277515i	−0.0137118	−	0.00996219i
$777$	−1.50000	+	4.61653i	−0.0538122	+	0.165617i
$778$	3.03444	+	9.33905i	0.108790	+	0.334821i
$779$	−27.8435	+	20.2295i	−0.997595	+	0.724796i
$780$	0.472136			0.0169052
$781$	38.8328	+	8.71851i	1.38955	+	0.311973i
$782$	−8.85410			−0.316622
$783$	−0.381966	+	0.277515i	−0.0136504	+	0.00991756i
$784$	0.309017	+	0.951057i	0.0110363	+	0.0339663i
$785$	0.0212862	−	0.0655123i	0.000759738	−	0.00233823i
$786$	−6.61803	−	4.80828i	−0.236057	−	0.171506i
$787$	−33.0517	−	24.0134i	−1.17816	−	0.855987i	−0.186201	−	0.982512i	$-0.559618\pi$
$787$	−33.0517	−	24.0134i	−1.17816	−	0.855987i	−0.991963	+	0.126525i	$0.959618\pi$
$788$	5.52786	−	17.0130i	0.196922	−	0.606064i
$789$	1.60739	+	4.94704i	0.0572246	+	0.176119i
$790$	2.61803	−	1.90211i	0.0931455	−	0.0676741i
$791$	14.6525			0.520982
$792$	−3.23607	−	0.726543i	−0.114989	−	0.0258166i
$793$		0			0
$794$	−17.5623	+	12.7598i	−0.623263	+	0.452827i
$795$	−1.14590	−	3.52671i	−0.0406408	−	0.125080i
$796$	3.48278	−	10.7189i	0.123444	−	0.379921i
$797$	18.6353	+	13.5393i	0.660095	+	0.479587i	0.866695	−	0.498839i	$-0.166240\pi$
$797$	18.6353	+	13.5393i	0.660095	+	0.479587i	−0.206600	+	0.978425i	$0.566240\pi$
$798$	−6.35410	−	4.61653i	−0.224933	−	0.163423i
$799$	−0.381966	+	1.17557i	−0.0135130	+	0.0415887i
$800$	−1.50000	−	4.61653i	−0.0530330	−	0.163219i
$801$	11.5902	−	8.42075i	0.409519	−	0.297533i
$802$	−8.36068			−0.295226
$803$	3.61803	+	38.6628i	0.127678	+	1.36438i
$804$	−4.00000			−0.141069
$805$	1.04508	−	0.759299i	0.0368344	−	0.0267618i
$806$	−1.85410	−	5.70634i	−0.0653080	−	0.200997i
$807$	−4.61803	+	14.2128i	−0.162562	+	0.500316i
$808$	−14.7812	−	10.7391i	−0.519999	−	0.377801i
$809$	14.7082	+	10.6861i	0.517113	+	0.375705i	0.815515	−	0.578736i	$-0.196454\pi$
$809$	14.7082	+	10.6861i	0.517113	+	0.375705i	−0.298402	+	0.954440i	$0.596454\pi$
$810$	−0.118034	+	0.363271i	−0.00414729	+	0.0127641i
$811$	3.88854	+	11.9677i	0.136545	+	0.420243i	0.995827	−	0.0912592i	$-0.0290892\pi$
$811$	3.88854	+	11.9677i	0.136545	+	0.420243i	−0.859282	+	0.511502i	$0.829089\pi$
$812$	0.381966	−	0.277515i	0.0134044	−	0.00973885i
$813$	−7.50658			−0.263267
$814$	10.6353	+	12.0862i	0.372765	+	0.423622i
$815$	0.180340			0.00631703
$816$	−2.11803	+	1.53884i	−0.0741460	+	0.0538702i
$817$	−3.00000	−	9.23305i	−0.104957	−	0.323024i
$818$	−4.41641	+	13.5923i	−0.154416	+	0.475244i
$819$	−1.00000	−	0.726543i	−0.0349428	−	0.0253875i
$820$	−1.35410	−	0.983813i	−0.0472873	−	0.0343562i
$821$	6.43769	−	19.8132i	0.224677	−	0.691485i	−0.773647	−	0.633617i	$-0.781570\pi$
$821$	6.43769	−	19.8132i	0.224677	−	0.691485i	0.998324	−	0.0578683i	$-0.0184303\pi$
$822$	−3.14590	−	9.68208i	−0.109726	−	0.337701i
$823$	−11.3262	+	8.22899i	−0.394808	+	0.286845i	−0.767423	−	0.641141i	$-0.778461\pi$
$823$	−11.3262	+	8.22899i	−0.394808	+	0.286845i	0.372615	+	0.927986i	$0.378461\pi$
$824$	11.5623			0.402792
$825$	−8.20820	+	13.8496i	−0.285773	+	0.482180i
$826$	−2.76393			−0.0961695
$827$	37.3885	−	27.1644i	1.30013	−	0.944598i	0.300170	−	0.953886i	$-0.402957\pi$
$827$	37.3885	−	27.1644i	1.30013	−	0.944598i	0.999957	+	0.00928806i	$0.00295653\pi$
$828$	1.04508	+	3.21644i	0.0363192	+	0.111779i
$829$	−6.36068	+	19.5762i	−0.220916	+	0.679908i	0.777765	+	0.628555i	$0.216353\pi$
$829$	−6.36068	+	19.5762i	−0.220916	+	0.679908i	−0.998681	+	0.0513530i	$0.983647\pi$
$830$	−0.909830	−	0.661030i	−0.0315807	−	0.0229447i
$831$	9.73607	+	7.07367i	0.337740	+	0.245383i
$832$	0.381966	−	1.17557i	0.0132423	−	0.0407556i
$833$	−0.809017	−	2.48990i	−0.0280308	−	0.0862699i
$834$	1.88197	−	1.36733i	0.0651672	−	0.0473467i
$835$	−3.70820			−0.128328
$836$	−23.9164	+	10.3229i	−0.827166	+	0.357024i
$837$	4.85410			0.167782
$838$	4.23607	−	3.07768i	0.146333	−	0.106317i
$839$	10.1459	+	31.2259i	0.350275	+	1.07804i	0.958699	+	0.284424i	$0.0918023\pi$
$839$	10.1459	+	31.2259i	0.350275	+	1.07804i	−0.608423	+	0.793613i	$0.708198\pi$
$840$	0.118034	−	0.363271i	0.00407256	−	0.0125340i
$841$	23.2812	+	16.9147i	0.802798	+	0.583267i
$842$	7.20820	+	5.23707i	0.248411	+	0.180481i
$843$	−4.61803	+	14.2128i	−0.159054	+	0.489516i
$844$	−4.32624	−	13.3148i	−0.148915	−	0.458314i
$845$	−3.54508	+	2.57565i	−0.121955	+	0.0886052i
$846$	0.472136			0.0162324
$847$	−5.28115	−	9.64932i	−0.181463	−	0.331555i
$848$	−9.70820			−0.333381
$849$	−18.7254	+	13.6048i	−0.642655	+	0.466916i
$850$	3.92705	+	12.0862i	0.134697	+	0.414554i
$851$	5.07295	−	15.6129i	0.173898	−	0.535204i
$852$	−9.70820	−	7.05342i	−0.332598	−	0.241646i
$853$	6.23607	+	4.53077i	0.213519	+	0.155131i	0.689404	−	0.724377i	$-0.257872\pi$
$853$	6.23607	+	4.53077i	0.213519	+	0.155131i	−0.475885	+	0.879507i	$0.657872\pi$
$854$		0			0
$855$	0.927051	+	2.85317i	0.0317045	+	0.0975763i
$856$	−5.50000	+	3.99598i	−0.187986	+	0.136580i
$857$	−25.7771			−0.880529			−0.440264	−	0.897868i	$-0.645115\pi$
$857$	−25.7771			−0.880529			−0.440264	+	0.897868i	$0.645115\pi$
$858$	−3.76393	+	1.62460i	−0.128499	+	0.0554629i
$859$	26.8328			0.915524			0.457762	−	0.889075i	$-0.348651\pi$
$859$	26.8328			0.915524			0.457762	+	0.889075i	$0.348651\pi$
$860$	0.381966	−	0.277515i	0.0130249	−	0.00946317i
$861$	1.35410	+	4.16750i	0.0461477	+	0.142028i
$862$	−3.40983	+	10.4944i	−0.116139	+	0.357440i
$863$	−4.78115	−	3.47371i	−0.162752	−	0.118246i	0.503428	−	0.864037i	$-0.332072\pi$
$863$	−4.78115	−	3.47371i	−0.162752	−	0.118246i	−0.666180	+	0.745791i	$0.732072\pi$
$864$	0.809017	+	0.587785i	0.0275233	+	0.0199969i
$865$	1.18441	−	3.64522i	0.0402710	−	0.123941i
$866$	−11.0344	−	33.9605i	−0.374966	−	1.15403i
$867$	−8.20820	+	5.96361i	−0.278765	+	0.202535i
$868$	−4.85410			−0.164759
$869$	−14.3262	+	24.1724i	−0.485984	+	0.819994i
$870$	−0.180340			−0.00611409
$871$	−4.00000	+	2.90617i	−0.135535	+	0.0984718i
$872$	−5.97214	−	18.3803i	−0.202242	−	0.622437i
$873$	0.145898	−	0.449028i	0.00493790	−	0.0151973i
$874$	21.4894	+	15.6129i	0.726888	+	0.528115i
$875$	−3.04508	−	2.21238i	−0.102943	−	0.0747922i
$876$	3.61803	−	11.1352i	0.122242	−	0.376222i
$877$	14.0344	+	43.1936i	0.473909	+	1.45854i	0.847423	+	0.530918i	$0.178153\pi$
$877$	14.0344	+	43.1936i	0.473909	+	1.45854i	−0.373513	+	0.927625i	$0.621847\pi$
$878$	19.6353	−	14.2658i	0.662658	−	0.481449i
$879$	−12.3820			−0.417633
$880$	−0.836881	−	0.951057i	−0.0282113	−	0.0320601i
$881$	40.5755			1.36702			0.683511	−	0.729940i	$-0.260452\pi$
$881$	40.5755			1.36702			0.683511	+	0.729940i	$0.260452\pi$
$882$	−0.809017	+	0.587785i	−0.0272410	+	0.0197918i
$883$	−13.9098	−	42.8101i	−0.468103	−	1.44067i	−0.855038	−	0.518566i	$-0.826466\pi$
$883$	−13.9098	−	42.8101i	−0.468103	−	1.44067i	0.386935	−	0.922107i	$-0.373534\pi$
$884$	−1.00000	+	3.07768i	−0.0336336	+	0.103514i
$885$	0.854102	+	0.620541i	0.0287103	+	0.0208593i
$886$	−32.9164	−	23.9152i	−1.10585	−	0.803446i
$887$	16.2016	−	49.8635i	0.543997	−	1.67425i	−0.179365	−	0.983783i	$-0.557404\pi$
$887$	16.2016	−	49.8635i	0.543997	−	1.67425i	0.723362	−	0.690469i	$-0.242596\pi$
$888$	−1.50000	−	4.61653i	−0.0503367	−	0.154920i
$889$	17.5623	−	12.7598i	0.589021	−	0.427949i
$890$	5.47214			0.183426
$891$	−0.309017	−	3.30220i	−0.0103525	−	0.110628i
$892$	0.798374			0.0267315
$893$	3.00000	−	2.17963i	0.100391	−	0.0729385i
$894$	2.76393	+	8.50651i	0.0924397	+	0.284500i
$895$	−0.405765	+	1.24882i	−0.0135632	+	0.0417433i
$896$	−0.809017	−	0.587785i	−0.0270274	−	0.0196365i
$897$	3.38197	+	2.45714i	0.112921	+	0.0820416i
$898$	−0.472136	+	1.45309i	−0.0157554	+	0.0484901i
$899$	0.708204	+	2.17963i	0.0236199	+	0.0726946i
$900$	3.92705	−	2.85317i	0.130902	−	0.0951057i
$901$	25.4164			0.846743
$902$	14.1803	+	3.18368i	0.472154	+	0.106005i
$903$	−1.23607			−0.0411338
$904$	−11.8541	+	8.61251i	−0.394262	+	0.286448i
$905$	2.52786	+	7.77997i	0.0840290	+	0.258615i
$906$	−1.67376	+	5.15131i	−0.0556070	+	0.171141i
$907$	12.3262	+	8.95554i	0.409286	+	0.297364i	0.773313	−	0.634025i	$-0.218598\pi$
$907$	12.3262	+	8.95554i	0.409286	+	0.297364i	−0.364027	+	0.931389i	$0.618598\pi$
$908$	18.5623	+	13.4863i	0.616012	+	0.447559i
$909$	5.64590	−	17.3763i	0.187263	−	0.576335i
$910$	−0.145898	−	0.449028i	−0.00483647	−	0.0148851i
$911$	−1.52786	+	1.11006i	−0.0506204	+	0.0367779i	−0.612808	−	0.790232i	$-0.709960\pi$
$911$	−1.52786	+	1.11006i	−0.0506204	+	0.0367779i	0.562187	+	0.827010i	$0.309960\pi$
$912$	7.85410			0.260075
$913$	9.52786	+	2.13914i	0.315326	+	0.0707952i
$914$	−6.58359			−0.217766
$915$		0			0
$916$	−4.56231	−	14.0413i	−0.150743	−	0.463939i
$917$	−2.52786	+	7.77997i	−0.0834774	+	0.256917i
$918$	−2.11803	−	1.53884i	−0.0699055	−	0.0507893i
$919$	−28.6525	−	20.8172i	−0.945158	−	0.686697i	0.00449874	−	0.999990i	$-0.498568\pi$
$919$	−28.6525	−	20.8172i	−0.945158	−	0.686697i	−0.949657	+	0.313292i	$0.898568\pi$
$920$	−0.399187	+	1.22857i	−0.0131608	+	0.0405048i
$921$	1.50000	+	4.61653i	0.0494267	+	0.152120i
$922$	−30.2705	+	21.9928i	−0.996906	+	0.724295i
$923$	−14.8328			−0.488228
$924$	0.309017	+	3.30220i	0.0101659	+	0.108634i
$925$	−23.5623			−0.774724
$926$	−29.1246	+	21.1603i	−0.957094	+	0.695370i
$927$	3.57295	+	10.9964i	0.117351	+	0.361169i
$928$	−0.145898	+	0.449028i	−0.00478934	+	0.0147401i
$929$	39.7705	+	28.8950i	1.30483	+	0.948013i	0.999990	−	0.00439119i	$-0.00139776\pi$
$929$	39.7705	+	28.8950i	1.30483	+	0.948013i	0.304838	+	0.952404i	$0.401398\pi$
$930$	1.50000	+	1.08981i	0.0491869	+	0.0357364i
$931$	−2.42705	+	7.46969i	−0.0795434	+	0.244809i
$932$	−0.708204	−	2.17963i	−0.0231980	−	0.0713961i
$933$	13.0902	−	9.51057i	0.428553	−	0.311362i
$934$	23.2361			0.760307
$935$	2.19098	+	2.48990i	0.0716528	+	0.0814284i
$936$	1.23607			0.0404021
$937$	−18.7082	+	13.5923i	−0.611170	+	0.444041i	−0.849826	−	0.527063i	$-0.823293\pi$
$937$	−18.7082	+	13.5923i	−0.611170	+	0.444041i	0.238656	+	0.971104i	$0.423293\pi$
$938$	1.23607	+	3.80423i	0.0403591	+	0.124212i
$939$	−3.43769	+	10.5801i	−0.112185	+	0.345270i
$940$	0.145898	+	0.106001i	0.00475867	+	0.00345738i
$941$	−1.64590	−	1.19581i	−0.0536547	−	0.0389825i	0.560635	−	0.828063i	$-0.310557\pi$
$941$	−1.64590	−	1.19581i	−0.0536547	−	0.0389825i	−0.614289	+	0.789081i	$0.710557\pi$
$942$	0.0557281	−	0.171513i	0.00181572	−	0.00558821i
$943$	−4.57953	−	14.0943i	−0.149130	−	0.458975i
$944$	2.23607	−	1.62460i	0.0727778	−	0.0528762i
$945$	0.381966			0.0124254
$946$	−2.09017	+	3.52671i	−0.0679573	+	0.114663i
$947$	−27.2148			−0.884362			−0.442181	−	0.896926i	$-0.645795\pi$
$947$	−27.2148			−0.884362			−0.442181	+	0.896926i	$0.645795\pi$
$948$	6.85410	−	4.97980i	0.222611	−	0.161736i
$949$	−4.47214	−	13.7638i	−0.145172	−	0.446792i
$950$	11.7812	−	36.2587i	0.382231	−	1.17639i
$951$	16.3262	+	11.8617i	0.529415	+	0.384642i
$952$	2.11803	+	1.53884i	0.0686459	+	0.0498741i
$953$	−13.0902	+	40.2874i	−0.424032	+	1.30504i	0.479886	+	0.877331i	$0.340678\pi$
$953$	−13.0902	+	40.2874i	−0.424032	+	1.30504i	−0.903918	+	0.427706i	$0.859322\pi$
$954$	−3.00000	−	9.23305i	−0.0971286	−	0.298931i
$955$	1.11803	−	0.812299i	0.0361787	−	0.0262854i
$956$	−8.03444			−0.259852
$957$	1.43769	−	0.620541i	0.0464741	−	0.0200593i
$958$	24.0000			0.775405
$959$	−8.23607	+	5.98385i	−0.265957	+	0.193229i
$960$	0.118034	+	0.363271i	0.00380953	+	0.0117245i
$961$	−2.29837	+	7.07367i	−0.0741411	+	0.228183i
$962$	−4.85410	−	3.52671i	−0.156503	−	0.113706i
$963$	−5.50000	−	3.99598i	−0.177235	−	0.128769i
$964$	−5.23607	+	16.1150i	−0.168642	+	0.519028i
$965$	3.13525	+	9.64932i	0.100927	+	0.310623i
$966$	2.73607	−	1.98787i	0.0880315	−	0.0639587i
$967$	16.9443			0.544891			0.272446	−	0.962171i	$-0.412168\pi$
$967$	16.9443			0.544891			0.272446	+	0.962171i	$0.412168\pi$
$968$	9.94427	+	4.70228i	0.319621	+	0.151137i
$969$	−20.5623			−0.660556
$970$	0.145898	−	0.106001i	0.00468450	−	0.00340349i
$971$	11.3607	+	34.9646i	0.364582	+	1.12207i	0.950243	+	0.311511i	$0.100835\pi$
$971$	11.3607	+	34.9646i	0.364582	+	1.12207i	−0.585661	+	0.810556i	$0.699165\pi$
$972$	−0.309017	+	0.951057i	−0.00991172	+	0.0305052i
$973$	−1.88197	−	1.36733i	−0.0603331	−	0.0438345i
$974$	4.14590	+	3.01217i	0.132843	+	0.0965162i
$975$	1.85410	−	5.70634i	0.0593788	−	0.182749i
$976$		0			0
$977$	−48.4508	+	35.2016i	−1.55008	+	1.12620i	−0.606486	+	0.795094i	$0.707421\pi$
$977$	−48.4508	+	35.2016i	−1.55008	+	1.12620i	−0.943594	+	0.331105i	$0.892579\pi$
$978$	0.472136			0.0150972
$979$	−43.6246	+	18.8294i	−1.39425	+	0.601789i
$980$	−0.381966			−0.0122015
$981$	15.6353	−	11.3597i	0.499195	−	0.362687i
$982$	−2.57295	−	7.91872i	−0.0821061	−	0.252697i
$983$	−14.6869	+	45.2017i	−0.468440	+	1.44171i	0.386164	+	0.922430i	$0.373800\pi$
$983$	−14.6869	+	45.2017i	−0.468440	+	1.44171i	−0.854604	+	0.519280i	$0.826200\pi$
$984$	−3.54508	−	2.57565i	−0.113013	−	0.0821089i
$985$	5.52786	+	4.01623i	0.176132	+	0.127968i
$986$	0.381966	−	1.17557i	0.0121643	−	0.0374378i
$987$	−0.145898	−	0.449028i	−0.00464399	−	0.0142927i
$988$	7.85410	−	5.70634i	0.249872	−	0.181543i
$989$	4.18034			0.132927
$990$	0.645898	−	1.08981i	0.0205280	−	0.0346366i
$991$	29.7082			0.943712			0.471856	−	0.881676i	$-0.343584\pi$
$991$	29.7082			0.943712			0.471856	+	0.881676i	$0.343584\pi$
$992$	3.92705	−	2.85317i	0.124684	−	0.0905882i
$993$	−2.03444	−	6.26137i	−0.0645611	−	0.198699i
$994$	−3.70820	+	11.4127i	−0.117617	+	0.361988i
$995$	3.48278	+	2.53039i	0.110412	+	0.0802187i
$996$	−2.38197	−	1.73060i	−0.0754755	−	0.0548361i
$997$	1.76393	−	5.42882i	0.0558643	−	0.171933i	−0.919231	−	0.393718i	$-0.871189\pi$
$997$	1.76393	−	5.42882i	0.0558643	−	0.171933i	0.975095	+	0.221786i	$0.0711885\pi$
$998$	7.32624	+	22.5478i	0.231908	+	0.713739i
$999$	3.92705	−	2.85317i	0.124246	−	0.0902703i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.j.b.421.1	yes	4
11.2	odd	10		5082.2.a.bd.1.2		2
11.4	even	5	inner	462.2.j.b.169.1	✓	4
11.9	even	5		5082.2.a.bn.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.j.b.169.1	✓	4	11.4	even	5	inner
462.2.j.b.421.1	yes	4	1.1	even	1	trivial
5082.2.a.bd.1.2		2	11.2	odd	10
5082.2.a.bn.1.2		2	11.9	even	5

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:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.j (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 + 0.587785i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.309017 + 0.224514i) q^{5} +(0.809017 + 0.587785i) q^{6} +(0.309017 - 0.951057i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(-0.809017 + 0.587785i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.309017 + 0.224514i) q^{5} +(0.809017 + 0.587785i) q^{6} +(0.309017 - 0.951057i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.809017 + 0.587785i) q^{9} -0.381966 q^{10} +(3.04508 - 1.31433i) q^{11} -1.00000 q^{12} +(-1.00000 + 0.726543i) q^{13} +(0.309017 + 0.951057i) q^{14} +(0.118034 - 0.363271i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(2.11803 + 1.53884i) q^{17} +(0.309017 - 0.951057i) q^{18} +(-2.42705 - 7.46969i) q^{19} +(0.309017 - 0.224514i) q^{20} -1.00000 q^{21} +(-1.69098 + 2.85317i) q^{22} +3.38197 q^{23} +(0.809017 - 0.587785i) q^{24} +(-1.50000 - 4.61653i) q^{25} +(0.381966 - 1.17557i) q^{26} +(0.809017 + 0.587785i) q^{27} +(-0.809017 - 0.587785i) q^{28} +(-0.145898 + 0.449028i) q^{29} +(0.118034 + 0.363271i) q^{30} +(3.92705 - 2.85317i) q^{31} +1.00000 q^{32} +(-2.19098 - 2.48990i) q^{33} -2.61803 q^{34} +(0.309017 - 0.224514i) q^{35} +(0.309017 + 0.951057i) q^{36} +(1.50000 - 4.61653i) q^{37} +(6.35410 + 4.61653i) q^{38} +(1.00000 + 0.726543i) q^{39} +(-0.118034 + 0.363271i) q^{40} +(-1.35410 - 4.16750i) q^{41} +(0.809017 - 0.587785i) q^{42} +1.23607 q^{43} +(-0.309017 - 3.30220i) q^{44} -0.381966 q^{45} +(-2.73607 + 1.98787i) q^{46} +(0.145898 + 0.449028i) q^{47} +(-0.309017 + 0.951057i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(3.92705 + 2.85317i) q^{50} +(0.809017 - 2.48990i) q^{51} +(0.381966 + 1.17557i) q^{52} +(7.85410 - 5.70634i) q^{53} -1.00000 q^{54} +(1.23607 + 0.277515i) q^{55} +1.00000 q^{56} +(-6.35410 + 4.61653i) q^{57} +(-0.145898 - 0.449028i) q^{58} +(-0.854102 + 2.62866i) q^{59} +(-0.309017 - 0.224514i) q^{60} +(-1.50000 + 4.61653i) q^{62} +(0.309017 + 0.951057i) q^{63} +(-0.809017 + 0.587785i) q^{64} -0.472136 q^{65} +(3.23607 + 0.726543i) q^{66} +4.00000 q^{67} +(2.11803 - 1.53884i) q^{68} +(-1.04508 - 3.21644i) q^{69} +(-0.118034 + 0.363271i) q^{70} +(9.70820 + 7.05342i) q^{71} +(-0.809017 - 0.587785i) q^{72} +(-3.61803 + 11.1352i) q^{73} +(1.50000 + 4.61653i) q^{74} +(-3.92705 + 2.85317i) q^{75} -7.85410 q^{76} +(-0.309017 - 3.30220i) q^{77} -1.23607 q^{78} +(-6.85410 + 4.97980i) q^{79} +(-0.118034 - 0.363271i) q^{80} +(0.309017 - 0.951057i) q^{81} +(3.54508 + 2.57565i) q^{82} +(2.38197 + 1.73060i) q^{83} +(-0.309017 + 0.951057i) q^{84} +(0.309017 + 0.951057i) q^{85} +(-1.00000 + 0.726543i) q^{86} +0.472136 q^{87} +(2.19098 + 2.48990i) q^{88} -14.3262 q^{89} +(0.309017 - 0.224514i) q^{90} +(0.381966 + 1.17557i) q^{91} +(1.04508 - 3.21644i) q^{92} +(-3.92705 - 2.85317i) q^{93} +(-0.381966 - 0.277515i) q^{94} +(0.927051 - 2.85317i) q^{95} +(-0.309017 - 0.951057i) q^{96} +(-0.381966 + 0.277515i) q^{97} +1.00000 q^{98} +(-1.69098 + 2.85317i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} + q^{3} - q^{4} - q^{5} + q^{6} - q^{7} - q^{8} - q^{9}+O(q^{10}) \) 4 * q - q^2 + q^3 - q^4 - q^5 + q^6 - q^7 - q^8 - q^9	\( 4 q - q^{2} + q^{3} - q^{4} - q^{5} + q^{6} - q^{7} - q^{8} - q^{9} - 6 q^{10} + q^{11} - 4 q^{12} - 4 q^{13} - q^{14} - 4 q^{15} - q^{16} + 4 q^{17} - q^{18} - 3 q^{19} - q^{20} - 4 q^{21} - 9 q^{22} + 18 q^{23} + q^{24} - 6 q^{25} + 6 q^{26} + q^{27} - q^{28} - 14 q^{29} - 4 q^{30} + 9 q^{31} + 4 q^{32} - 11 q^{33} - 6 q^{34} - q^{35} - q^{36} + 6 q^{37} + 12 q^{38} + 4 q^{39} + 4 q^{40} + 8 q^{41} + q^{42} - 4 q^{43} + q^{44} - 6 q^{45} - 2 q^{46} + 14 q^{47} + q^{48} - q^{49} + 9 q^{50} + q^{51} + 6 q^{52} + 18 q^{53} - 4 q^{54} - 4 q^{55} + 4 q^{56} - 12 q^{57} - 14 q^{58} + 10 q^{59} + q^{60} - 6 q^{62} - q^{63} - q^{64} + 16 q^{65} + 4 q^{66} + 16 q^{67} + 4 q^{68} + 7 q^{69} + 4 q^{70} + 12 q^{71} - q^{72} - 10 q^{73} + 6 q^{74} - 9 q^{75} - 18 q^{76} + q^{77} + 4 q^{78} - 14 q^{79} + 4 q^{80} - q^{81} + 3 q^{82} + 14 q^{83} + q^{84} - q^{85} - 4 q^{86} - 16 q^{87} + 11 q^{88} - 26 q^{89} - q^{90} + 6 q^{91} - 7 q^{92} - 9 q^{93} - 6 q^{94} - 3 q^{95} + q^{96} - 6 q^{97} + 4 q^{98} - 9 q^{99}+O(q^{100}) \) 4 * q - q^2 + q^3 - q^4 - q^5 + q^6 - q^7 - q^8 - q^9 - 6 * q^10 + q^11 - 4 * q^12 - 4 * q^13 - q^14 - 4 * q^15 - q^16 + 4 * q^17 - q^18 - 3 * q^19 - q^20 - 4 * q^21 - 9 * q^22 + 18 * q^23 + q^24 - 6 * q^25 + 6 * q^26 + q^27 - q^28 - 14 * q^29 - 4 * q^30 + 9 * q^31 + 4 * q^32 - 11 * q^33 - 6 * q^34 - q^35 - q^36 + 6 * q^37 + 12 * q^38 + 4 * q^39 + 4 * q^40 + 8 * q^41 + q^42 - 4 * q^43 + q^44 - 6 * q^45 - 2 * q^46 + 14 * q^47 + q^48 - q^49 + 9 * q^50 + q^51 + 6 * q^52 + 18 * q^53 - 4 * q^54 - 4 * q^55 + 4 * q^56 - 12 * q^57 - 14 * q^58 + 10 * q^59 + q^60 - 6 * q^62 - q^63 - q^64 + 16 * q^65 + 4 * q^66 + 16 * q^67 + 4 * q^68 + 7 * q^69 + 4 * q^70 + 12 * q^71 - q^72 - 10 * q^73 + 6 * q^74 - 9 * q^75 - 18 * q^76 + q^77 + 4 * q^78 - 14 * q^79 + 4 * q^80 - q^81 + 3 * q^82 + 14 * q^83 + q^84 - q^85 - 4 * q^86 - 16 * q^87 + 11 * q^88 - 26 * q^89 - q^90 + 6 * q^91 - 7 * q^92 - 9 * q^93 - 6 * q^94 - 3 * q^95 + q^96 - 6 * q^97 + 4 * q^98 - 9 * q^99

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