LMFDB - Embedded newform 462.2.j.e.421.2

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:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.484000000.9
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + x^{6} + 16x^{4} + 66x^{2} + 121 $ x^8 + x^6 + 16x^4 + 66x^2 + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			421.2
Root			$0.476925 + 1.46782i$ of defining polynomial
Character	$\chi$	$=$	462.421
Dual form			462.2.j.e.169.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 + 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.309017 - 0.951057i) q^{4} +(2.52029 + 1.83110i) q^{5} +(-0.809017 - 0.587785i) q^{6} +(0.309017 - 0.951057i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(-0.809017 + 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.309017 - 0.951057i) q^{4} +(2.52029 + 1.83110i) 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} -3.11525 q^{10} +(2.97414 + 1.46782i) q^{11} +1.00000 q^{12} +(1.74861 - 1.27044i) q^{13} +(0.309017 + 0.951057i) q^{14} +(-0.962664 + 2.96278i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-0.574672 - 0.417524i) q^{17} +(0.309017 - 0.951057i) q^{18} +(0.0949591 + 0.292254i) q^{19} +(2.52029 - 1.83110i) q^{20} +1.00000 q^{21} +(-3.26889 + 0.560659i) q^{22} +0.879178 q^{23} +(-0.809017 + 0.587785i) q^{24} +(1.45385 + 4.47449i) q^{25} +(-0.667908 + 2.05561i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(-0.809017 - 0.587785i) q^{28} +(2.03082 - 6.25023i) q^{29} +(-0.962664 - 2.96278i) q^{30} +(-6.21902 + 4.51838i) q^{31} +1.00000 q^{32} +(-0.476925 + 3.28216i) q^{33} +0.710334 q^{34} +(2.52029 - 1.83110i) q^{35} +(0.309017 + 0.951057i) q^{36} +(-1.19873 + 3.68932i) q^{37} +(-0.248606 - 0.180623i) q^{38} +(1.74861 + 1.27044i) q^{39} +(-0.962664 + 2.96278i) q^{40} +(1.32558 + 4.07972i) q^{41} +(-0.809017 + 0.587785i) q^{42} -8.24254 q^{43} +(2.31504 - 2.37499i) q^{44} -3.11525 q^{45} +(-0.711270 + 0.516768i) q^{46} +(3.10205 + 9.54713i) q^{47} +(0.309017 - 0.951057i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(-3.80623 - 2.76539i) q^{50} +(0.219505 - 0.675568i) q^{51} +(-0.667908 - 2.05561i) q^{52} +(5.32652 - 3.86994i) q^{53} +1.00000 q^{54} +(4.80795 + 9.14527i) q^{55} +1.00000 q^{56} +(-0.248606 + 0.180623i) q^{57} +(2.03082 + 6.25023i) q^{58} +(-1.77713 + 5.46944i) q^{59} +(2.52029 + 1.83110i) q^{60} +(-2.52759 - 1.83640i) q^{61} +(2.37545 - 7.31090i) q^{62} +(0.309017 + 0.951057i) q^{63} +(-0.809017 + 0.587785i) q^{64} +6.73328 q^{65} +(-1.54336 - 2.93565i) q^{66} -6.67624 q^{67} +(-0.574672 + 0.417524i) q^{68} +(0.271681 + 0.836148i) q^{69} +(-0.962664 + 2.96278i) q^{70} +(-8.77385 - 6.37458i) q^{71} +(-0.809017 - 0.587785i) q^{72} +(3.32049 - 10.2194i) q^{73} +(-1.19873 - 3.68932i) q^{74} +(-3.80623 + 2.76539i) q^{75} +0.307294 q^{76} +(2.31504 - 2.37499i) q^{77} -2.16140 q^{78} +(7.86013 - 5.71072i) q^{79} +(-0.962664 - 2.96278i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-3.47041 - 2.52140i) q^{82} +(-12.7701 - 9.27804i) q^{83} +(0.309017 - 0.951057i) q^{84} +(-0.683813 - 2.10456i) q^{85} +(6.66836 - 4.84485i) q^{86} +6.57188 q^{87} +(-0.476925 + 3.28216i) q^{88} +14.8726 q^{89} +(2.52029 - 1.83110i) q^{90} +(-0.667908 - 2.05561i) q^{91} +(0.271681 - 0.836148i) q^{92} +(-6.21902 - 4.51838i) q^{93} +(-8.12127 - 5.90045i) q^{94} +(-0.295821 + 0.910443i) q^{95} +(0.309017 + 0.951057i) q^{96} +(0.211270 - 0.153497i) q^{97} +1.00000 q^{98} +(-3.26889 + 0.560659i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 4 q^{5} - 2 q^{6} - 2 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) $ 8 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + 4 * q^5 - 2 * q^6 - 2 * q^7 - 2 * q^8 - 2 * q^9	$ 8 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 4 q^{5} - 2 q^{6} - 2 q^{7} - 2 q^{8} - 2 q^{9} + 4 q^{10} + 8 q^{12} + 4 q^{13} - 2 q^{14} - 6 q^{15} - 2 q^{16} - 8 q^{17} - 2 q^{18} - 12 q^{19} + 4 q^{20} + 8 q^{21} - 4 q^{23} - 2 q^{24} + 4 q^{25} - 6 q^{26} - 2 q^{27} - 2 q^{28} - 4 q^{29} - 6 q^{30} - 14 q^{31} + 8 q^{32} + 12 q^{34} + 4 q^{35} - 2 q^{36} + 10 q^{37} + 8 q^{38} + 4 q^{39} - 6 q^{40} - 12 q^{41} - 2 q^{42} + 20 q^{43} + 4 q^{45} + 6 q^{46} + 28 q^{47} - 2 q^{48} - 2 q^{49} - 6 q^{50} + 2 q^{51} - 6 q^{52} + 2 q^{53} + 8 q^{54} + 4 q^{55} + 8 q^{56} + 8 q^{57} - 4 q^{58} + 4 q^{60} - 34 q^{61} + 6 q^{62} - 2 q^{63} - 2 q^{64} + 16 q^{65} - 24 q^{67} - 8 q^{68} - 4 q^{69} - 6 q^{70} - 2 q^{72} + 10 q^{74} - 6 q^{75} + 8 q^{76} + 4 q^{78} + 22 q^{79} - 6 q^{80} - 2 q^{81} - 2 q^{82} - 30 q^{83} - 2 q^{84} - 28 q^{85} + 36 q^{87} - 4 q^{89} + 4 q^{90} - 6 q^{91} - 4 q^{92} - 14 q^{93} - 22 q^{94} - 30 q^{95} - 2 q^{96} - 10 q^{97} + 8 q^{98}+O(q^{100}) $ 8 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + 4 * q^5 - 2 * q^6 - 2 * q^7 - 2 * q^8 - 2 * q^9 + 4 * q^10 + 8 * q^12 + 4 * q^13 - 2 * q^14 - 6 * q^15 - 2 * q^16 - 8 * q^17 - 2 * q^18 - 12 * q^19 + 4 * q^20 + 8 * q^21 - 4 * q^23 - 2 * q^24 + 4 * q^25 - 6 * q^26 - 2 * q^27 - 2 * q^28 - 4 * q^29 - 6 * q^30 - 14 * q^31 + 8 * q^32 + 12 * q^34 + 4 * q^35 - 2 * q^36 + 10 * q^37 + 8 * q^38 + 4 * q^39 - 6 * q^40 - 12 * q^41 - 2 * q^42 + 20 * q^43 + 4 * q^45 + 6 * q^46 + 28 * q^47 - 2 * q^48 - 2 * q^49 - 6 * q^50 + 2 * q^51 - 6 * q^52 + 2 * q^53 + 8 * q^54 + 4 * q^55 + 8 * q^56 + 8 * q^57 - 4 * q^58 + 4 * q^60 - 34 * q^61 + 6 * q^62 - 2 * q^63 - 2 * q^64 + 16 * q^65 - 24 * q^67 - 8 * q^68 - 4 * q^69 - 6 * q^70 - 2 * q^72 + 10 * q^74 - 6 * q^75 + 8 * q^76 + 4 * q^78 + 22 * q^79 - 6 * q^80 - 2 * q^81 - 2 * q^82 - 30 * q^83 - 2 * q^84 - 28 * q^85 + 36 * q^87 - 4 * q^89 + 4 * q^90 - 6 * q^91 - 4 * q^92 - 14 * q^93 - 22 * q^94 - 30 * q^95 - 2 * q^96 - 10 * q^97 + 8 * q^98

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
$5$	2.52029	+	1.83110i	1.12711	+	0.818891i	0.985271	−	0.170999i	$-0.0546996\pi$
$5$	2.52029	+	1.83110i	1.12711	+	0.818891i	0.141835	+	0.989890i	$0.454700\pi$
$6$	−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
$10$	−3.11525			−0.985127
$11$	2.97414	+	1.46782i	0.896736	+	0.442566i
$11$	2.97414	+	1.46782i	0.896736	+	0.442566i
$12$	1.00000			0.288675
$13$	1.74861	−	1.27044i	0.484976	−	0.352356i	−0.318273	−	0.947999i	$-0.603103\pi$
$13$	1.74861	−	1.27044i	0.484976	−	0.352356i	0.803249	+	0.595643i	$0.203103\pi$
$14$	0.309017	+	0.951057i	0.0825883	+	0.254181i
$15$	−0.962664	+	2.96278i	−0.248559	+	0.764985i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	−0.574672	−	0.417524i	−0.139378	−	0.101264i	0.515911	−	0.856642i	$-0.327453\pi$
$17$	−0.574672	−	0.417524i	−0.139378	−	0.101264i	−0.655290	+	0.755378i	$0.727453\pi$
$18$	0.309017	−	0.951057i	0.0728360	−	0.224166i
$19$	0.0949591	+	0.292254i	0.0217851	+	0.0670476i	0.961358	−	0.275301i	$-0.0887776\pi$
$19$	0.0949591	+	0.292254i	0.0217851	+	0.0670476i	−0.939573	+	0.342349i	$0.888778\pi$
$20$	2.52029	−	1.83110i	0.563553	−	0.409445i
$21$	1.00000			0.218218
$22$	−3.26889	+	0.560659i	−0.696930	+	0.119533i
$23$	0.879178			0.183321			0.0916606	−	0.995790i	$-0.470782\pi$
$23$	0.879178			0.183321			0.0916606	+	0.995790i	$0.470782\pi$
$24$	−0.809017	+	0.587785i	−0.165140	+	0.119981i
$25$	1.45385	+	4.47449i	0.290770	+	0.894898i
$26$	−0.667908	+	2.05561i	−0.130988	+	0.403138i
$27$	−0.809017	−	0.587785i	−0.155695	−	0.113119i
$28$	−0.809017	−	0.587785i	−0.152890	−	0.111081i
$29$	2.03082	−	6.25023i	0.377115	−	1.16064i	−0.564926	−	0.825141i	$-0.691095\pi$
$29$	2.03082	−	6.25023i	0.377115	−	1.16064i	0.942041	−	0.335498i	$-0.108905\pi$
$30$	−0.962664	−	2.96278i	−0.175758	−	0.540926i
$31$	−6.21902	+	4.51838i	−1.11697	+	0.811525i	−0.983747	−	0.179561i	$-0.942532\pi$
$31$	−6.21902	+	4.51838i	−1.11697	+	0.811525i	−0.133222	+	0.991086i	$0.542532\pi$
$32$	1.00000			0.176777
$33$	−0.476925	+	3.28216i	−0.0830220	+	0.571350i
$34$	0.710334			0.121821
$35$	2.52029	−	1.83110i	0.426006	−	0.309512i
$36$	0.309017	+	0.951057i	0.0515028	+	0.158509i
$37$	−1.19873	+	3.68932i	−0.197070	+	0.606520i	0.802876	+	0.596146i	$0.203302\pi$
$37$	−1.19873	+	3.68932i	−0.197070	+	0.606520i	−0.999946	+	0.0103738i	$0.996698\pi$
$38$	−0.248606	−	0.180623i	−0.0403292	−	0.0293009i
$39$	1.74861	+	1.27044i	0.280001	+	0.203433i
$40$	−0.962664	+	2.96278i	−0.152211	+	0.468456i
$41$	1.32558	+	4.07972i	0.207021	+	0.637144i	0.999624	+	0.0274071i	$0.00872506\pi$
$41$	1.32558	+	4.07972i	0.207021	+	0.637144i	−0.792604	+	0.609737i	$0.791275\pi$
$42$	−0.809017	+	0.587785i	−0.124834	+	0.0906972i
$43$	−8.24254			−1.25698			−0.628488	−	0.777819i	$-0.716326\pi$
$43$	−8.24254			−1.25698			−0.628488	+	0.777819i	$0.716326\pi$
$44$	2.31504	−	2.37499i	0.349006	−	0.358043i
$45$	−3.11525			−0.464393
$46$	−0.711270	+	0.516768i	−0.104871	+	0.0761933i
$47$	3.10205	+	9.54713i	0.452480	+	1.39259i	0.874068	+	0.485804i	$0.161473\pi$
$47$	3.10205	+	9.54713i	0.452480	+	1.39259i	−0.421587	+	0.906788i	$0.638527\pi$
$48$	0.309017	−	0.951057i	0.0446028	−	0.137273i
$49$	−0.809017	−	0.587785i	−0.115574	−	0.0839693i
$50$	−3.80623	−	2.76539i	−0.538282	−	0.391085i
$51$	0.219505	−	0.675568i	0.0307369	−	0.0945984i
$52$	−0.667908	−	2.05561i	−0.0926222	−	0.285062i
$53$	5.32652	−	3.86994i	0.731653	−	0.531577i	−0.158433	−	0.987370i	$-0.550644\pi$
$53$	5.32652	−	3.86994i	0.731653	−	0.531577i	0.890086	+	0.455793i	$0.150644\pi$
$54$	1.00000			0.136083
$55$	4.80795	+	9.14527i	0.648304	+	1.23315i
$56$	1.00000			0.133631
$57$	−0.248606	+	0.180623i	−0.0329287	+	0.0239241i
$58$	2.03082	+	6.25023i	0.266660	+	0.820696i
$59$	−1.77713	+	5.46944i	−0.231362	+	0.712060i	0.766221	+	0.642577i	$0.222135\pi$
$59$	−1.77713	+	5.46944i	−0.231362	+	0.712060i	−0.997583	+	0.0694828i	$0.977865\pi$
$60$	2.52029	+	1.83110i	0.325368	+	0.236393i
$61$	−2.52759	−	1.83640i	−0.323624	−	0.235127i	0.414096	−	0.910233i	$-0.364098\pi$
$61$	−2.52759	−	1.83640i	−0.323624	−	0.235127i	−0.737720	+	0.675106i	$0.764098\pi$
$62$	2.37545	−	7.31090i	0.301683	−	0.928485i
$63$	0.309017	+	0.951057i	0.0389325	+	0.119822i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	6.73328			0.835161
$66$	−1.54336	−	2.93565i	−0.189975	−	0.361353i
$67$	−6.67624			−0.815632			−0.407816	−	0.913064i	$-0.633710\pi$
$67$	−6.67624			−0.815632			−0.407816	+	0.913064i	$0.633710\pi$
$68$	−0.574672	+	0.417524i	−0.0696892	+	0.0506322i
$69$	0.271681	+	0.836148i	0.0327065	+	0.100660i
$70$	−0.962664	+	2.96278i	−0.115060	+	0.354119i
$71$	−8.77385	−	6.37458i	−1.04126	−	0.756523i	−0.0707328	−	0.997495i	$-0.522534\pi$
$71$	−8.77385	−	6.37458i	−1.04126	−	0.756523i	−0.970532	+	0.240972i	$0.922534\pi$
$72$	−0.809017	−	0.587785i	−0.0953436	−	0.0692712i
$73$	3.32049	−	10.2194i	0.388634	−	1.19609i	−0.545176	−	0.838322i	$-0.683537\pi$
$73$	3.32049	−	10.2194i	0.388634	−	1.19609i	0.933810	−	0.357770i	$-0.116463\pi$
$74$	−1.19873	−	3.68932i	−0.139350	−	0.428874i
$75$	−3.80623	+	2.76539i	−0.439505	+	0.319319i
$76$	0.307294			0.0352490
$77$	2.31504	−	2.37499i	0.263824	−	0.270655i
$78$	−2.16140			−0.244730
$79$	7.86013	−	5.71072i	0.884333	−	0.642506i	−0.0500609	−	0.998746i	$-0.515942\pi$
$79$	7.86013	−	5.71072i	0.884333	−	0.642506i	0.934394	+	0.356240i	$0.115942\pi$
$80$	−0.962664	−	2.96278i	−0.107629	−	0.331248i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	−3.47041	−	2.52140i	−0.383243	−	0.278442i
$83$	−12.7701	−	9.27804i	−1.40170	−	1.01840i	−0.994464	−	0.105076i	$-0.966491\pi$
$83$	−12.7701	−	9.27804i	−1.40170	−	1.01840i	−0.407240	−	0.913321i	$-0.633509\pi$
$84$	0.309017	−	0.951057i	0.0337165	−	0.103769i
$85$	−0.683813	−	2.10456i	−0.0741699	−	0.228271i
$86$	6.66836	−	4.84485i	0.719068	−	0.522433i
$87$	6.57188			0.704580
$88$	−0.476925	+	3.28216i	−0.0508404	+	0.349879i
$89$	14.8726			1.57650			0.788248	−	0.615358i	$-0.210989\pi$
$89$	14.8726			1.57650			0.788248	+	0.615358i	$0.210989\pi$
$90$	2.52029	−	1.83110i	0.265662	−	0.193014i
$91$	−0.667908	−	2.05561i	−0.0700158	−	0.215486i
$92$	0.271681	−	0.836148i	0.0283247	−	0.0871745i
$93$	−6.21902	−	4.51838i	−0.644882	−	0.468534i
$94$	−8.12127	−	5.90045i	−0.837645	−	0.608585i
$95$	−0.295821	+	0.910443i	−0.0303506	+	0.0934095i
$96$	0.309017	+	0.951057i	0.0315389	+	0.0970668i
$97$	0.211270	−	0.153497i	0.0214512	−	0.0155852i	−0.577008	−	0.816739i	$-0.695780\pi$
$97$	0.211270	−	0.153497i	0.0214512	−	0.0155852i	0.598459	+	0.801153i	$0.295780\pi$
$98$	1.00000			0.101015
$99$	−3.26889	+	0.560659i	−0.328536	+	0.0563484i
$100$	4.70476			0.470476
$101$	−2.06365	+	1.49933i	−0.205341	+	0.149189i	−0.685703	−	0.727881i	$-0.740505\pi$
$101$	−2.06365	+	1.49933i	−0.205341	+	0.149189i	0.480362	+	0.877070i	$0.340505\pi$
$102$	0.219505	+	0.675568i	0.0217343	+	0.0668912i
$103$	5.82249	−	17.9198i	0.573707	−	1.76569i	−0.0668329	−	0.997764i	$-0.521289\pi$
$103$	5.82249	−	17.9198i	0.573707	−	1.76569i	0.640540	−	0.767925i	$-0.278711\pi$
$104$	1.74861	+	1.27044i	0.171465	+	0.124577i
$105$	2.52029	+	1.83110i	0.245955	+	0.178697i
$106$	−2.03455	+	6.26170i	−0.197613	+	0.608190i
$107$	−1.05094	−	3.23446i	−0.101598	−	0.312687i	0.887319	−	0.461156i	$-0.152565\pi$
$107$	−1.05094	−	3.23446i	−0.101598	−	0.312687i	−0.988917	+	0.148470i	$0.952565\pi$
$108$	−0.809017	+	0.587785i	−0.0778477	+	0.0565597i
$109$	6.96590			0.667212			0.333606	−	0.942713i	$-0.391734\pi$
$109$	6.96590			0.667212			0.333606	+	0.942713i	$0.391734\pi$
$110$	−9.26517	−	4.57263i	−0.883399	−	0.435984i
$111$	−3.87918			−0.368195
$112$	−0.809017	+	0.587785i	−0.0764449	+	0.0555405i
$113$	−0.432012	−	1.32960i	−0.0406403	−	0.125078i	0.928678	−	0.370887i	$-0.120946\pi$
$113$	−0.432012	−	1.32960i	−0.0406403	−	0.125078i	−0.969318	+	0.245809i	$0.920946\pi$
$114$	0.0949591	−	0.292254i	0.00889373	−	0.0273721i
$115$	2.21578	+	1.60986i	0.206623	+	0.150120i
$116$	−5.31677	−	3.86286i	−0.493649	−	0.358657i
$117$	−0.667908	+	2.05561i	−0.0617481	+	0.190041i
$118$	−1.77713	−	5.46944i	−0.163598	−	0.503503i
$119$	−0.574672	+	0.417524i	−0.0526801	+	0.0382743i
$120$	−3.11525			−0.284382
$121$	6.69098	+	8.73102i	0.608271	+	0.793729i
$122$	3.12427			0.282858
$123$	−3.47041	+	2.52140i	−0.312917	+	0.227347i
$124$	2.37545	+	7.31090i	0.213322	+	0.656538i
$125$	0.284219	−	0.874736i	0.0254213	−	0.0782388i
$126$	−0.809017	−	0.587785i	−0.0720730	−	0.0523641i
$127$	−12.9791	−	9.42987i	−1.15171	−	0.836765i	−0.163002	−	0.986626i	$-0.552118\pi$
$127$	−12.9791	−	9.42987i	−1.15171	−	0.836765i	−0.988707	+	0.149860i	$0.952118\pi$
$128$	0.309017	−	0.951057i	0.0273135	−	0.0840623i
$129$	−2.54709	−	7.83913i	−0.224258	−	0.690196i
$130$	−5.44734	+	3.95772i	−0.477763	+	0.347115i
$131$	19.8696			1.73601			0.868007	−	0.496551i	$-0.165400\pi$
$131$	19.8696			1.73601			0.868007	+	0.496551i	$0.165400\pi$
$132$	2.97414	+	1.46782i	0.258865	+	0.127758i
$133$	0.307294			0.0266458
$134$	5.40119	−	3.92419i	0.466592	−	0.338999i
$135$	−0.962664	−	2.96278i	−0.0828529	−	0.254995i
$136$	0.219505	−	0.675568i	0.0188224	−	0.0579294i
$137$	−1.87963	−	1.36563i	−0.160587	−	0.116674i	0.504589	−	0.863359i	$-0.331644\pi$
$137$	−1.87963	−	1.36563i	−0.160587	−	0.116674i	−0.665177	+	0.746686i	$0.731644\pi$
$138$	−0.711270	−	0.516768i	−0.0605473	−	0.0439902i
$139$	2.31208	−	7.11586i	0.196108	−	0.603559i	−0.803854	−	0.594827i	$-0.797220\pi$
$139$	2.31208	−	7.11586i	0.196108	−	0.603559i	0.999962	−	0.00873210i	$-0.00277955\pi$
$140$	−0.962664	−	2.96278i	−0.0813600	−	0.250400i
$141$	−8.12127	+	5.90045i	−0.683934	+	0.496907i
$142$	10.8451			0.910099
$143$	7.06537	−	1.21181i	0.590836	−	0.101336i
$144$	1.00000			0.0833333
$145$	16.5630	−	12.0337i	1.37549	−	0.999348i
$146$	3.32049	+	10.2194i	0.274806	+	0.845765i
$147$	0.309017	−	0.951057i	0.0254873	−	0.0784418i
$148$	3.13832	+	2.28012i	0.257968	+	0.187425i
$149$	−1.15492	−	0.839099i	−0.0946147	−	0.0687416i	0.539472	−	0.842003i	$-0.318624\pi$
$149$	−1.15492	−	0.839099i	−0.0946147	−	0.0687416i	−0.634087	+	0.773262i	$0.718624\pi$
$150$	1.45385	−	4.47449i	0.118706	−	0.365341i
$151$	−3.07840	−	9.47433i	−0.250516	−	0.771010i	−0.994680	−	0.103013i	$-0.967152\pi$
$151$	−3.07840	−	9.47433i	−0.250516	−	0.771010i	0.744164	−	0.667997i	$-0.232848\pi$
$152$	−0.248606	+	0.180623i	−0.0201646	+	0.0146504i
$153$	0.710334			0.0574271
$154$	−0.476925	+	3.28216i	−0.0384317	+	0.264484i
$155$	−23.9473			−1.92349
$156$	1.74861	−	1.27044i	0.140001	−	0.101716i
$157$	−7.61459	−	23.4353i	−0.607710	−	1.87034i	−0.476961	−	0.878924i	$-0.658262\pi$
$157$	−7.61459	−	23.4353i	−0.607710	−	1.87034i	−0.130749	−	0.991415i	$-0.541738\pi$
$158$	−3.00230	+	9.24013i	−0.238850	+	0.735106i
$159$	5.32652	+	3.86994i	0.422420	+	0.306906i
$160$	2.52029	+	1.83110i	0.199246	+	0.144761i
$161$	0.271681	−	0.836148i	0.0214115	−	0.0658977i
$162$	0.309017	+	0.951057i	0.0242787	+	0.0747221i
$163$	−11.6069	+	8.43289i	−0.909121	+	0.660515i	−0.940792	−	0.338983i	$-0.889917\pi$
$163$	−11.6069	+	8.43289i	−0.909121	+	0.660515i	0.0316713	+	0.999498i	$0.489917\pi$
$164$	4.28967			0.334967
$165$	−7.21193	+	7.39868i	−0.561448	+	0.575986i
$166$	15.7847			1.22513
$167$	−11.3518	+	8.24754i	−0.878426	+	0.638214i	−0.932835	−	0.360305i	$-0.882673\pi$
$167$	−11.3518	+	8.24754i	−0.878426	+	0.638214i	0.0544087	+	0.998519i	$0.482673\pi$
$168$	0.309017	+	0.951057i	0.0238412	+	0.0733756i
$169$	−2.57361	+	7.92075i	−0.197970	+	0.609288i
$170$	1.79024	+	1.30069i	0.137306	+	0.0997583i
$171$	−0.248606	−	0.180623i	−0.0190114	−	0.0138126i
$172$	−2.54709	+	7.83913i	−0.194213	+	0.597728i
$173$	4.38107	+	13.4836i	0.333087	+	1.02514i	0.967657	+	0.252270i	$0.0811772\pi$
$173$	4.38107	+	13.4836i	0.333087	+	1.02514i	−0.634570	+	0.772865i	$0.718823\pi$
$174$	−5.31677	+	3.86286i	−0.403063	+	0.292842i
$175$	4.70476			0.355646
$176$	−1.54336	−	2.93565i	−0.116335	−	0.221283i
$177$	−5.75091			−0.432265
$178$	−12.0322	+	8.74191i	−0.901852	+	0.655234i
$179$	−4.91066	−	15.1135i	−0.367040	−	1.12963i	−0.948694	−	0.316196i	$-0.897594\pi$
$179$	−4.91066	−	15.1135i	−0.367040	−	1.12963i	0.581654	−	0.813436i	$-0.302406\pi$
$180$	−0.962664	+	2.96278i	−0.0717527	+	0.220832i
$181$	14.3675	+	10.4386i	1.06793	+	0.775897i	0.975539	−	0.219826i	$-0.0705488\pi$
$181$	14.3675	+	10.4386i	1.06793	+	0.775897i	0.0923916	+	0.995723i	$0.470549\pi$
$182$	1.74861	+	1.27044i	0.129615	+	0.0941710i
$183$	0.965452	−	2.97136i	0.0713683	−	0.219649i
$184$	0.271681	+	0.836148i	0.0200286	+	0.0616416i
$185$	−9.77664	+	7.10315i	−0.718793	+	0.522234i
$186$	7.68713			0.563648
$187$	−1.09630	−	2.08529i	−0.0801695	−	0.152492i
$188$	10.0384			0.732129
$189$	−0.809017	+	0.587785i	−0.0588473	+	0.0427551i
$190$	−0.295821	−	0.910443i	−0.0214611	−	0.0660505i
$191$	−8.12423	+	25.0038i	−0.587849	+	1.80921i	−0.000332794		1.00000i	$0.500106\pi$
$191$	−8.12423	+	25.0038i	−0.587849	+	1.80921i	−0.587516	+	0.809213i	$0.699894\pi$
$192$	−0.809017	−	0.587785i	−0.0583858	−	0.0424197i
$193$	−4.50451	−	3.27272i	−0.324242	−	0.235575i	0.413742	−	0.910394i	$-0.364222\pi$
$193$	−4.50451	−	3.27272i	−0.324242	−	0.235575i	−0.737983	+	0.674819i	$0.764222\pi$
$194$	−0.0806980	+	0.248363i	−0.00579378	+	0.0178314i
$195$	2.08070	+	6.40373i	0.149002	+	0.458581i
$196$	−0.809017	+	0.587785i	−0.0577869	+	0.0419847i
$197$	−11.8089			−0.841346			−0.420673	−	0.907212i	$-0.638206\pi$
$197$	−11.8089			−0.841346			−0.420673	+	0.907212i	$0.638206\pi$
$198$	2.31504	−	2.37499i	0.164523	−	0.168783i
$199$	9.53591			0.675983			0.337991	−	0.941149i	$-0.390252\pi$
$199$	9.53591			0.675983			0.337991	+	0.941149i	$0.390252\pi$
$200$	−3.80623	+	2.76539i	−0.269141	+	0.195542i
$201$	−2.06307	−	6.34948i	−0.145518	−	0.447858i
$202$	0.788244	−	2.42596i	0.0554606	−	0.170690i
$203$	−5.31677	−	3.86286i	−0.373164	−	0.271119i
$204$	−0.574672	−	0.417524i	−0.0402351	−	0.0292325i
$205$	−4.12951	+	12.7093i	−0.288417	+	0.887657i
$206$	5.82249	+	17.9198i	0.405672	+	1.24853i
$207$	−0.711270	+	0.516768i	−0.0494367	+	0.0359179i
$208$	−2.16140			−0.149866
$209$	−0.146556	+	1.00859i	−0.0101375	+	0.0697654i
$210$	−3.11525			−0.214972
$211$	9.67135	−	7.02665i	0.665803	−	0.483735i	−0.202814	−	0.979217i	$-0.565009\pi$
$211$	9.67135	−	7.02665i	0.665803	−	0.483735i	0.868618	+	0.495483i	$0.165009\pi$
$212$	−2.03455	−	6.26170i	−0.139733	−	0.430055i
$213$	3.35131	−	10.3143i	0.229628	−	0.706723i
$214$	2.75139	+	1.99900i	0.188081	+	0.136649i
$215$	−20.7736	−	15.0929i	−1.41675	−	1.02933i
$216$	0.309017	−	0.951057i	0.0210259	−	0.0647112i
$217$	2.37545	+	7.31090i	0.161256	+	0.496296i
$218$	−5.63553	+	4.09445i	−0.381686	+	0.277311i
$219$	10.7453			0.726102
$220$	10.1834	−	1.74659i	0.686565	−	0.117755i
$221$	−1.53531			−0.103276
$222$	3.13832	−	2.28012i	0.210630	−	0.153032i
$223$	−2.71282	−	8.34921i	−0.181664	−	0.559104i	0.818211	−	0.574918i	$-0.194966\pi$
$223$	−2.71282	−	8.34921i	−0.181664	−	0.559104i	−0.999875	+	0.0158139i	$0.994966\pi$
$224$	0.309017	−	0.951057i	0.0206471	−	0.0635451i
$225$	−3.80623	−	2.76539i	−0.253749	−	0.184359i
$226$	1.13102	+	0.821736i	0.0752345	+	0.0546610i
$227$	−6.02667	+	18.5482i	−0.400004	+	1.23109i	0.524991	+	0.851108i	$0.324069\pi$
$227$	−6.02667	+	18.5482i	−0.400004	+	1.23109i	−0.924995	+	0.379979i	$0.875931\pi$
$228$	0.0949591	+	0.292254i	0.00628882	+	0.0193550i
$229$	5.88938	−	4.27888i	0.389181	−	0.282757i	−0.375939	−	0.926645i	$-0.622680\pi$
$229$	5.88938	−	4.27888i	0.389181	−	0.282757i	0.765120	+	0.643888i	$0.222680\pi$
$230$	−2.73886			−0.180595
$231$	2.97414	+	1.46782i	0.195684	+	0.0965758i
$232$	6.57188			0.431465
$233$	2.21054	−	1.60605i	0.144817	−	0.105216i	−0.513018	−	0.858378i	$-0.671472\pi$
$233$	2.21054	−	1.60605i	0.144817	−	0.105216i	0.657835	+	0.753162i	$0.271472\pi$
$234$	−0.667908	−	2.05561i	−0.0436625	−	0.134379i
$235$	−9.66365	+	29.7417i	−0.630387	+	1.94013i
$236$	4.65258	+	3.38030i	0.302857	+	0.220039i
$237$	7.86013	+	5.71072i	0.510570	+	0.370951i
$238$	0.219505	−	0.675568i	0.0142284	−	0.0437905i
$239$	8.00283	+	24.6302i	0.517660	+	1.59319i	0.778389	+	0.627782i	$0.216037\pi$
$239$	8.00283	+	24.6302i	0.517660	+	1.59319i	−0.260729	+	0.965412i	$0.583963\pi$
$240$	2.52029	−	1.83110i	0.162684	−	0.118197i
$241$	−6.36034			−0.409705			−0.204853	−	0.978793i	$-0.565672\pi$
$241$	−6.36034			−0.409705			−0.204853	+	0.978793i	$0.565672\pi$
$242$	−10.5451	−	3.13068i	−0.677864	−	0.201248i
$243$	1.00000			0.0641500
$244$	−2.52759	+	1.83640i	−0.161812	+	0.117563i
$245$	−0.962664	−	2.96278i	−0.0615023	−	0.189285i
$246$	1.32558	−	4.07972i	0.0845159	−	0.260113i
$247$	0.537336	+	0.390397i	0.0341899	+	0.0248404i
$248$	−6.21902	−	4.51838i	−0.394908	−	0.286918i
$249$	4.87776	−	15.0122i	0.309115	−	0.951359i
$250$	0.284219	+	0.874736i	0.0179756	+	0.0553232i
$251$	10.4223	−	7.57222i	0.657847	−	0.477954i	−0.208088	−	0.978110i	$-0.566724\pi$
$251$	10.4223	−	7.57222i	0.657847	−	0.477954i	0.865935	+	0.500156i	$0.166724\pi$
$252$	1.00000			0.0629941
$253$	2.61480	+	1.29048i	0.164391	+	0.0811317i
$254$	16.0430			1.00663
$255$	1.79024	−	1.30069i	0.112109	−	0.0814523i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	1.61565	−	4.97247i	0.100782	−	0.310174i	−0.887936	−	0.459968i	$-0.847861\pi$
$257$	1.61565	−	4.97247i	0.100782	−	0.310174i	0.988717	+	0.149794i	$0.0478610\pi$
$258$	6.66836	+	4.84485i	0.415154	+	0.301627i
$259$	3.13832	+	2.28012i	0.195006	+	0.141680i
$260$	2.08070	−	6.40373i	0.129039	−	0.397142i
$261$	2.03082	+	6.25023i	0.125705	+	0.386880i
$262$	−16.0748	+	11.6791i	−0.993107	+	0.721535i
$263$	26.8248			1.65409			0.827043	−	0.562139i	$-0.190021\pi$
$263$	26.8248			1.65409			0.827043	+	0.562139i	$0.190021\pi$
$264$	−3.26889	+	0.560659i	−0.201186	+	0.0345062i
$265$	20.5106			1.25995
$266$	−0.248606	+	0.180623i	−0.0152430	+	0.0110747i
$267$	4.59590	+	14.1447i	0.281264	+	0.865642i
$268$	−2.06307	+	6.34948i	−0.126022	+	0.387856i
$269$	8.93180	+	6.48934i	0.544582	+	0.395662i	0.825784	−	0.563987i	$-0.190733\pi$
$269$	8.93180	+	6.48934i	0.544582	+	0.395662i	−0.281202	+	0.959649i	$0.590733\pi$
$270$	2.52029	+	1.83110i	0.153380	+	0.111437i
$271$	−5.59734	+	17.2268i	−0.340014	+	1.04646i	0.624185	+	0.781277i	$0.285431\pi$
$271$	−5.59734	+	17.2268i	−0.340014	+	1.04646i	−0.964199	+	0.265179i	$0.914569\pi$
$272$	0.219505	+	0.675568i	0.0133095	+	0.0409623i
$273$	1.74861	−	1.27044i	0.105830	−	0.0768903i
$274$	2.32335			0.140359
$275$	−2.24382	+	15.4417i	−0.135307	+	0.931172i
$276$	0.879178			0.0529203
$277$	−9.15906	+	6.65445i	−0.550314	+	0.399827i	−0.827901	−	0.560874i	$-0.810465\pi$
$277$	−9.15906	+	6.65445i	−0.550314	+	0.399827i	0.277587	+	0.960701i	$0.410465\pi$
$278$	2.31208	+	7.11586i	0.138670	+	0.426781i
$279$	2.37545	−	7.31090i	0.142215	−	0.437692i
$280$	2.52029	+	1.83110i	0.150616	+	0.109429i
$281$	−20.3541	−	14.7881i	−1.21422	−	0.882184i	−0.218614	−	0.975811i	$-0.570154\pi$
$281$	−20.3541	−	14.7881i	−1.21422	−	0.882184i	−0.995607	+	0.0936276i	$0.970154\pi$
$282$	3.10205	−	9.54713i	0.184724	−	0.568523i
$283$	1.73590	+	5.34254i	0.103188	+	0.317581i	0.989301	−	0.145889i	$-0.0466042\pi$
$283$	1.73590	+	5.34254i	0.103188	+	0.317581i	−0.886113	+	0.463470i	$0.846604\pi$
$284$	−8.77385	+	6.37458i	−0.520632	+	0.378262i
$285$	−0.957296			−0.0567053
$286$	−5.00372	+	5.13329i	−0.295876	+	0.303538i
$287$	4.28967			0.253211
$288$	−0.809017	+	0.587785i	−0.0476718	+	0.0346356i
$289$	−5.09737	−	15.6881i	−0.299845	−	0.922828i
$290$	−6.32652	+	19.4710i	−0.371506	+	1.14338i
$291$	0.211270	+	0.153497i	0.0123849	+	0.00899813i
$292$	−8.69316	−	6.31595i	−0.508728	−	0.369613i
$293$	2.56520	−	7.89487i	0.149861	−	0.461223i	−0.847743	−	0.530407i	$-0.822039\pi$
$293$	2.56520	−	7.89487i	0.149861	−	0.461223i	0.997604	+	0.0691831i	$0.0220393\pi$
$294$	0.309017	+	0.951057i	0.0180222	+	0.0554667i
$295$	−14.4939	+	10.5305i	−0.843870	+	0.613107i
$296$	−3.87918			−0.225473
$297$	−1.54336	−	2.93565i	−0.0895549	−	0.170344i
$298$	1.42756			0.0826963
$299$	1.53734	−	1.11694i	0.0889064	−	0.0645943i
$300$	1.45385	+	4.47449i	0.0839381	+	0.258335i
$301$	−2.54709	+	7.83913i	−0.146812	+	0.451840i
$302$	8.05935	+	5.85546i	0.463763	+	0.336944i
$303$	−2.06365	−	1.49933i	−0.118554	−	0.0861342i
$304$	0.0949591	−	0.292254i	0.00544628	−	0.0167619i
$305$	−3.00762	−	9.25650i	−0.172216	−	0.530026i
$306$	−0.574672	+	0.417524i	−0.0328518	+	0.0238682i
$307$	1.44088			0.0822355			0.0411178	−	0.999154i	$-0.486908\pi$
$307$	1.44088			0.0822355			0.0411178	+	0.999154i	$0.486908\pi$
$308$	−1.54336	−	2.93565i	−0.0879412	−	0.167274i
$309$	18.8420			1.07188
$310$	19.3738	−	14.0759i	1.10036	−	0.799456i
$311$	3.05749	+	9.41000i	0.173375	+	0.533592i	0.999556	−	0.0298128i	$-0.00949111\pi$
$311$	3.05749	+	9.41000i	0.173375	+	0.533592i	−0.826181	+	0.563405i	$0.809491\pi$
$312$	−0.667908	+	2.05561i	−0.0378128	+	0.116376i
$313$	4.49721	+	3.26742i	0.254197	+	0.184685i	0.707585	−	0.706628i	$-0.249785\pi$
$313$	4.49721	+	3.26742i	0.254197	+	0.184685i	−0.453388	+	0.891313i	$0.649785\pi$
$314$	19.9352	+	14.4838i	1.12501	+	0.817369i
$315$	−0.962664	+	2.96278i	−0.0542400	+	0.166933i
$316$	−3.00230	−	9.24013i	−0.168893	−	0.519798i
$317$	0.561684	−	0.408087i	0.0315473	−	0.0229205i	−0.571900	−	0.820323i	$-0.693793\pi$
$317$	0.561684	−	0.408087i	0.0315473	−	0.0229205i	0.603447	+	0.797403i	$0.293793\pi$
$318$	−6.58394			−0.369209
$319$	15.2142	−	15.6082i	0.851831	−	0.873889i
$320$	−3.11525			−0.174148
$321$	2.75139	−	1.99900i	0.153568	−	0.111574i
$322$	0.271681	+	0.836148i	0.0151402	+	0.0465967i
$323$	0.0674526	−	0.207598i	0.00375316	−	0.0115511i
$324$	−0.809017	−	0.587785i	−0.0449454	−	0.0326547i
$325$	8.22677	+	5.97710i	0.456339	+	0.331550i
$326$	4.43343	−	13.6447i	0.245545	−	0.755710i
$327$	2.15258	+	6.62497i	0.119038	+	0.366361i
$328$	−3.47041	+	2.52140i	−0.191621	+	0.139221i
$329$	10.0384			0.553437
$330$	1.48574	−	10.2247i	0.0817872	−	0.562852i
$331$	−31.0269			−1.70539			−0.852696	−	0.522408i	$-0.825034\pi$
$331$	−31.0269			−1.70539			−0.852696	+	0.522408i	$0.825034\pi$
$332$	−12.7701	+	9.27804i	−0.700852	+	0.509199i
$333$	−1.19873	−	3.68932i	−0.0656901	−	0.202173i
$334$	4.33599	−	13.3448i	0.237255	−	0.730195i
$335$	−16.8260	−	12.2248i	−0.919304	−	0.667914i
$336$	−0.809017	−	0.587785i	−0.0441355	−	0.0320663i
$337$	5.07933	−	15.6326i	0.276689	−	0.851561i	−0.712079	−	0.702100i	$-0.752246\pi$
$337$	5.07933	−	15.6326i	0.276689	−	0.851561i	0.988768	−	0.149461i	$-0.0477539\pi$
$338$	−2.57361	−	7.92075i	−0.139986	−	0.430832i
$339$	1.13102	−	0.821736i	0.0614287	−	0.0446306i
$340$	−2.21286			−0.120009
$341$	−25.1284	+	4.30986i	−1.36078	+	0.233392i
$342$	0.307294			0.0166166
$343$	−0.809017	+	0.587785i	−0.0436828	+	0.0317374i
$344$	−2.54709	−	7.83913i	−0.137330	−	0.422657i
$345$	−0.846353	+	2.60481i	−0.0455661	+	0.140238i
$346$	−11.4698	−	8.33330i	−0.616620	−	0.448001i
$347$	−28.3634	−	20.6072i	−1.52263	−	1.10625i	−0.960166	−	0.279430i	$-0.909854\pi$
$347$	−28.3634	−	20.6072i	−1.52263	−	1.10625i	−0.562462	−	0.826823i	$-0.690146\pi$
$348$	2.03082	−	6.25023i	0.108864	−	0.335048i
$349$	2.66588	+	8.20475i	0.142702	+	0.439190i	0.996708	−	0.0810718i	$-0.0258343\pi$
$349$	2.66588	+	8.20475i	0.142702	+	0.439190i	−0.854007	+	0.520262i	$0.825834\pi$
$350$	−3.80623	+	2.76539i	−0.203451	+	0.147816i
$351$	−2.16140			−0.115367
$352$	2.97414	+	1.46782i	0.158522	+	0.0782353i
$353$	−28.0551			−1.49322			−0.746611	−	0.665261i	$-0.768320\pi$
$353$	−28.0551			−1.49322			−0.746611	+	0.665261i	$0.768320\pi$
$354$	4.65258	−	3.38030i	0.247282	−	0.179661i
$355$	−10.4402	−	32.1315i	−0.554107	−	1.70536i
$356$	4.59590	−	14.1447i	0.243582	−	0.749668i
$357$	−0.574672	−	0.417524i	−0.0304149	−	0.0220977i
$358$	12.8563	+	9.34063i	0.679475	+	0.493668i
$359$	−5.76547	+	17.7443i	−0.304290	+	0.936508i	0.675651	+	0.737221i	$0.263862\pi$
$359$	−5.76547	+	17.7443i	−0.304290	+	0.936508i	−0.979941	+	0.199287i	$0.936138\pi$
$360$	−0.962664	−	2.96278i	−0.0507368	−	0.156152i
$361$	15.2949	−	11.1124i	0.804996	−	0.584864i
$362$	−17.7593			−0.933406
$363$	−6.23607	+	9.06154i	−0.327309	+	0.475607i
$364$	−2.16140			−0.113288
$365$	27.0813	−	19.6757i	1.41750	−	1.02987i
$366$	0.965452	+	2.97136i	0.0504650	+	0.155315i
$367$	−0.465624	+	1.43304i	−0.0243054	+	0.0748042i	−0.962473	−	0.271376i	$-0.912521\pi$
$367$	−0.465624	+	1.43304i	−0.0243054	+	0.0748042i	0.938168	+	0.346180i	$0.112521\pi$
$368$	−0.711270	−	0.516768i	−0.0370775	−	0.0269384i
$369$	−3.47041	−	2.52140i	−0.180662	−	0.131259i
$370$	3.73434	−	11.4931i	0.194139	−	0.597499i
$371$	−2.03455	−	6.26170i	−0.105628	−	0.325091i
$372$	−6.21902	+	4.51838i	−0.322441	+	0.234267i
$373$	−34.9467			−1.80947			−0.904737	−	0.425971i	$-0.859933\pi$
$373$	−34.9467			−1.80947			−0.904737	+	0.425971i	$0.859933\pi$
$374$	2.11263	+	1.04265i	0.109241	+	0.0539139i
$375$	0.919752			0.0474958
$376$	−8.12127	+	5.90045i	−0.418823	+	0.304292i
$377$	−4.38941	−	13.5092i	−0.226066	−	0.695761i
$378$	0.309017	−	0.951057i	0.0158941	−	0.0489171i
$379$	−9.65258	−	7.01301i	−0.495820	−	0.360234i	0.311598	−	0.950214i	$-0.399136\pi$
$379$	−9.65258	−	7.01301i	−0.495820	−	0.360234i	−0.807418	+	0.589980i	$0.799136\pi$
$380$	0.774469	+	0.562685i	0.0397294	+	0.0288651i
$381$	4.95757	−	15.2578i	0.253984	−	0.781683i
$382$	−8.12423	−	25.0038i	−0.415672	−	1.27931i
$383$	−14.6245	+	10.6253i	−0.747278	+	0.542929i	−0.894982	−	0.446103i	$-0.852812\pi$
$383$	−14.6245	+	10.6253i	−0.747278	+	0.542929i	0.147704	+	0.989032i	$0.452812\pi$
$384$	1.00000			0.0510310
$385$	10.1834	−	1.74659i	0.518994	−	0.0890145i
$386$	5.56788			0.283398
$387$	6.66836	−	4.84485i	0.338972	−	0.246277i
$388$	−0.0806980	−	0.248363i	−0.00409682	−	0.0126087i
$389$	−0.468412	+	1.44162i	−0.0237494	+	0.0730932i	−0.962229	−	0.272242i	$-0.912235\pi$
$389$	−0.468412	+	1.44162i	−0.0237494	+	0.0730932i	0.938479	+	0.345335i	$0.112235\pi$
$390$	−5.44734	−	3.95772i	−0.275837	−	0.200407i
$391$	−0.505239	−	0.367078i	−0.0255510	−	0.0185639i
$392$	0.309017	−	0.951057i	0.0156077	−	0.0480356i
$393$	6.14004	+	18.8971i	0.309724	+	0.953233i
$394$	9.55356	−	6.94107i	0.481301	−	0.349686i
$395$	30.2666			1.52288
$396$	−0.476925	+	3.28216i	−0.0239664	+	0.164935i
$397$	32.2351			1.61783			0.808917	−	0.587924i	$-0.200054\pi$
$397$	32.2351			1.61783			0.808917	+	0.587924i	$0.200054\pi$
$398$	−7.71472	+	5.60507i	−0.386704	+	0.280957i
$399$	0.0949591	+	0.292254i	0.00475390	+	0.0146310i
$400$	1.45385	−	4.47449i	0.0726925	−	0.223725i
$401$	−7.22677	−	5.25055i	−0.360888	−	0.262200i	0.392535	−	0.919737i	$-0.371598\pi$
$401$	−7.22677	−	5.25055i	−0.360888	−	0.262200i	−0.753422	+	0.657537i	$0.771598\pi$
$402$	5.40119	+	3.92419i	0.269387	+	0.195721i
$403$	−5.13430	+	15.8017i	−0.255758	+	0.787141i
$404$	0.788244	+	2.42596i	0.0392166	+	0.120696i
$405$	2.52029	−	1.83110i	0.125234	−	0.0909879i
$406$	6.57188			0.326157
$407$	−8.98046	+	9.21301i	−0.445145	+	0.456672i
$408$	0.710334			0.0351668
$409$	17.3829	−	12.6294i	0.859527	−	0.624483i	−0.0682290	−	0.997670i	$-0.521735\pi$
$409$	17.3829	−	12.6294i	0.859527	−	0.624483i	0.927756	+	0.373186i	$0.121735\pi$
$410$	−4.12951	−	12.7093i	−0.203942	−	0.627668i
$411$	0.717954	−	2.20964i	0.0354141	−	0.108993i
$412$	−15.2435	−	11.0750i	−0.750992	−	0.545628i
$413$	4.65258	+	3.38030i	0.228939	+	0.166334i
$414$	0.271681	−	0.836148i	0.0133524	−	0.0410944i
$415$	−15.1954	−	46.7667i	−0.745913	−	2.29568i
$416$	1.74861	−	1.27044i	0.0857325	−	0.0622883i
$417$	7.48206			0.366398
$418$	−0.474266	−	0.902107i	−0.0231971	−	0.0441235i
$419$	22.3380			1.09128			0.545642	−	0.838018i	$-0.316286\pi$
$419$	22.3380			1.09128			0.545642	+	0.838018i	$0.316286\pi$
$420$	2.52029	−	1.83110i	0.122977	−	0.0893483i
$421$	3.05944	+	9.41598i	0.149108	+	0.458907i	0.997516	−	0.0704352i	$-0.0224388\pi$
$421$	3.05944	+	9.41598i	0.149108	+	0.458907i	−0.848408	+	0.529342i	$0.822439\pi$
$422$	−3.69413	+	11.3694i	−0.179827	+	0.553452i
$423$	−8.12127	−	5.90045i	−0.394870	−	0.286890i
$424$	5.32652	+	3.86994i	0.258678	+	0.187941i
$425$	1.03272	−	3.17838i	0.0500942	−	0.154174i
$426$	3.35131	+	10.3143i	0.162372	+	0.499729i
$427$	−2.52759	+	1.83640i	−0.122318	+	0.0888696i
$428$	−3.40091			−0.164389
$429$	3.33582	+	6.34510i	0.161055	+	0.306344i
$430$	25.6776			1.23828
$431$	−1.31574	+	0.955939i	−0.0633768	+	0.0460460i	−0.619023	−	0.785373i	$-0.712471\pi$
$431$	−1.31574	+	0.955939i	−0.0633768	+	0.0460460i	0.555646	+	0.831419i	$0.312471\pi$
$432$	0.309017	+	0.951057i	0.0148676	+	0.0457577i
$433$	−5.08416	+	15.6474i	−0.244329	+	0.751967i	0.751417	+	0.659828i	$0.229371\pi$
$433$	−5.08416	+	15.6474i	−0.244329	+	0.751967i	−0.995746	+	0.0921398i	$0.970629\pi$
$434$	−6.21902	−	4.51838i	−0.298522	−	0.216889i
$435$	16.5630	+	12.0337i	0.794137	+	0.576974i
$436$	2.15258	−	6.62497i	0.103090	−	0.317278i
$437$	0.0834859	+	0.256943i	0.00399367	+	0.0122913i
$438$	−8.69316	+	6.31595i	−0.415375	+	0.301788i
$439$	−6.45481			−0.308071			−0.154036	−	0.988065i	$-0.549227\pi$
$439$	−6.45481			−0.308071			−0.154036	+	0.988065i	$0.549227\pi$
$440$	−7.21193	+	7.39868i	−0.343815	+	0.352718i
$441$	1.00000			0.0476190
$442$	1.24209	−	0.902434i	0.0590804	−	0.0429244i
$443$	10.7204	+	32.9941i	0.509344	+	1.56760i	0.793344	+	0.608774i	$0.208338\pi$
$443$	10.7204	+	32.9941i	0.509344	+	1.56760i	−0.284000	+	0.958824i	$0.591662\pi$
$444$	−1.19873	+	3.68932i	−0.0568893	+	0.175087i
$445$	37.4833	+	27.2332i	1.77688	+	1.29098i
$446$	7.10226	+	5.16009i	0.336302	+	0.244337i
$447$	0.441140	−	1.35769i	0.0208652	−	0.0642165i
$448$	0.309017	+	0.951057i	0.0145997	+	0.0449332i
$449$	29.3647	−	21.3347i	1.38581	−	1.00685i	0.389496	−	0.921028i	$-0.372649\pi$
$449$	29.3647	−	21.3347i	1.38581	−	1.00685i	0.996311	−	0.0858192i	$-0.0273508\pi$
$450$	4.70476			0.221784
$451$	−2.04585	+	14.0794i	−0.0963353	+	0.662971i
$452$	−1.39802			−0.0657573
$453$	8.05935	−	5.85546i	0.378661	−	0.275113i
$454$	−6.02667	−	18.5482i	−0.282846	−	0.870509i
$455$	2.08070	−	6.40373i	0.0975446	−	0.300211i
$456$	−0.248606	−	0.180623i	−0.0116420	−	0.00845844i
$457$	−17.2230	−	12.5133i	−0.805660	−	0.585346i	0.106909	−	0.994269i	$-0.465905\pi$
$457$	−17.2230	−	12.5133i	−0.805660	−	0.585346i	−0.912569	+	0.408923i	$0.865905\pi$
$458$	−2.24954	+	6.92338i	−0.105114	+	0.323508i
$459$	0.219505	+	0.675568i	0.0102456	+	0.0315328i
$460$	2.21578	−	1.60986i	0.103311	−	0.0750601i
$461$	−34.3997			−1.60215			−0.801076	−	0.598562i	$-0.795739\pi$
$461$	−34.3997			−1.60215			−0.801076	+	0.598562i	$0.795739\pi$
$462$	−3.26889	+	0.560659i	−0.152083	+	0.0260842i
$463$	33.4916			1.55648			0.778242	−	0.627964i	$-0.216111\pi$
$463$	33.4916			1.55648			0.778242	+	0.627964i	$0.216111\pi$
$464$	−5.31677	+	3.86286i	−0.246825	+	0.179329i
$465$	−7.40012	−	22.7752i	−0.343172	−	1.05618i
$466$	−0.844352	+	2.59865i	−0.0391138	+	0.120380i
$467$	20.1500	+	14.6398i	0.932429	+	0.677449i	0.946586	−	0.322450i	$-0.104507\pi$
$467$	20.1500	+	14.6398i	0.932429	+	0.677449i	−0.0141572	+	0.999900i	$0.504507\pi$
$468$	1.74861	+	1.27044i	0.0808293	+	0.0587260i
$469$	−2.06307	+	6.34948i	−0.0952637	+	0.293192i
$470$	−9.66365	−	29.7417i	−0.445751	−	1.37188i
$471$	19.9352	−	14.4838i	0.918568	−	0.667379i
$472$	−5.75091			−0.264707
$473$	−24.5145	−	12.0986i	−1.12718	−	0.556295i
$474$	−9.71565			−0.446255
$475$	−1.16963	+	0.849787i	−0.0536664	+	0.0389909i
$476$	0.219505	+	0.675568i	0.0100610	+	0.0309646i
$477$	−2.03455	+	6.26170i	−0.0931556	+	0.286703i
$478$	−20.9517	−	15.2223i	−0.958308	−	0.696251i
$479$	21.0876	+	15.3211i	0.963518	+	0.700037i	0.953965	−	0.299917i	$-0.0969591\pi$
$479$	21.0876	+	15.3211i	0.963518	+	0.700037i	0.00955297	+	0.999954i	$0.496959\pi$
$480$	−0.962664	+	2.96278i	−0.0439394	+	0.135232i
$481$	2.59093	+	7.97408i	0.118136	+	0.363587i
$482$	5.14562	−	3.73851i	0.234377	−	0.170285i
$483$	0.879178			0.0400040
$484$	10.3713	−	3.66547i	0.471424	−	0.166612i
$485$	0.813528			0.0369404
$486$	−0.809017	+	0.587785i	−0.0366978	+	0.0266625i
$487$	−3.41038	−	10.4961i	−0.154539	−	0.475623i	0.843575	−	0.537012i	$-0.180447\pi$
$487$	−3.41038	−	10.4961i	−0.154539	−	0.475623i	−0.998114	+	0.0613891i	$0.980447\pi$
$488$	0.965452	−	2.97136i	0.0437040	−	0.134507i
$489$	−11.6069	−	8.43289i	−0.524881	−	0.381349i
$490$	2.52029	+	1.83110i	0.113855	+	0.0827205i
$491$	0.0565149	−	0.173935i	0.00255048	−	0.00784958i	−0.949773	−	0.312939i	$-0.898686\pi$
$491$	0.0565149	−	0.173935i	0.00255048	−	0.00784958i	0.952324	+	0.305090i	$0.0986864\pi$
$492$	1.32558	+	4.07972i	0.0597618	+	0.183928i
$493$	−3.77668	+	2.74392i	−0.170093	+	0.123580i
$494$	−0.664184			−0.0298830
$495$	−9.26517	−	4.57263i	−0.416438	−	0.205525i
$496$	7.68713			0.345162
$497$	−8.77385	+	6.37458i	−0.393561	+	0.285939i
$498$	4.87776	+	15.0122i	0.218577	+	0.672712i
$499$	5.21872	−	16.0616i	0.233622	−	0.719014i	−0.763679	−	0.645596i	$-0.776609\pi$
$499$	5.21872	−	16.0616i	0.233622	−	0.719014i	0.997301	−	0.0734185i	$-0.0233909\pi$
$500$	−0.744095	−	0.540617i	−0.0332769	−	0.0241771i
$501$	−11.3518	−	8.24754i	−0.507159	−	0.368473i
$502$	−3.98095	+	12.2521i	−0.177678	+	0.546838i
$503$	1.26201	+	3.88407i	0.0562703	+	0.173182i	0.975242	−	0.221142i	$-0.0709786\pi$
$503$	1.26201	+	3.88407i	0.0562703	+	0.173182i	−0.918971	+	0.394325i	$0.870979\pi$
$504$	−0.809017	+	0.587785i	−0.0360365	+	0.0261820i
$505$	−7.94640			−0.353610
$506$	−2.87394	+	0.492919i	−0.127762	+	0.0219129i
$507$	−8.32837			−0.369876
$508$	−12.9791	+	9.42987i	−0.575854	+	0.418383i
$509$	11.5255	+	35.4719i	0.510860	+	1.57227i	0.790691	+	0.612216i	$0.209722\pi$
$509$	11.5255	+	35.4719i	0.510860	+	1.57227i	−0.279831	+	0.960049i	$0.590278\pi$
$510$	−0.683813	+	2.10456i	−0.0302797	+	0.0931914i
$511$	−8.69316	−	6.31595i	−0.384563	−	0.279401i
$512$	−0.809017	−	0.587785i	−0.0357538	−	0.0259767i
$513$	0.0949591	−	0.292254i	0.00419254	−	0.0129033i
$514$	1.61565	+	4.97247i	0.0712634	+	0.219326i
$515$	47.4872	−	34.5015i	2.09254	−	1.52032i
$516$	−8.24254			−0.362858
$517$	−4.78759	+	32.9477i	−0.210558	+	1.44904i
$518$	−3.87918			−0.170441
$519$	−11.4698	+	8.33330i	−0.503468	+	0.365791i
$520$	2.08070	+	6.40373i	0.0912446	+	0.280822i
$521$	−0.291138	+	0.896030i	−0.0127550	+	0.0392558i	−0.957231	−	0.289323i	$-0.906570\pi$
$521$	−0.291138	+	0.896030i	−0.0127550	+	0.0392558i	0.944476	+	0.328579i	$0.106570\pi$
$522$	−5.31677	−	3.86286i	−0.232709	−	0.169073i
$523$	−18.6008	−	13.5143i	−0.813357	−	0.590938i	0.101445	−	0.994841i	$-0.467653\pi$
$523$	−18.6008	−	13.5143i	−0.813357	−	0.590938i	−0.914802	+	0.403903i	$0.867653\pi$
$524$	6.14004	−	18.8971i	0.268229	−	0.825524i
$525$	1.45385	+	4.47449i	0.0634512	+	0.195283i
$526$	−21.7017	+	15.7672i	−0.946239	+	0.687483i
$527$	5.46043			0.237860
$528$	2.31504	−	2.37499i	0.100749	−	0.103358i
$529$	−22.2270			−0.966393
$530$	−16.5934	+	12.0558i	−0.720772	+	0.523671i
$531$	−1.77713	−	5.46944i	−0.0771208	−	0.237353i
$532$	0.0949591	−	0.292254i	0.00411700	−	0.0126708i
$533$	7.50094	+	5.44975i	0.324902	+	0.236055i
$534$	−12.0322	−	8.74191i	−0.520685	−	0.378300i
$535$	3.27393	−	10.0761i	0.141544	−	0.435629i
$536$	−2.06307	−	6.34948i	−0.0891111	−	0.274256i
$537$	12.8563	−	9.34063i	0.554789	−	0.403078i
$538$	−11.0403			−0.475982
$539$	−1.54336	−	2.93565i	−0.0664773	−	0.126447i
$540$	−3.11525			−0.134059
$541$	−15.1643	+	11.0175i	−0.651964	+	0.473680i	−0.863940	−	0.503595i	$-0.832010\pi$
$541$	−15.1643	+	11.0175i	−0.651964	+	0.473680i	0.211976	+	0.977275i	$0.432010\pi$
$542$	−5.59734	−	17.2268i	−0.240426	−	0.739956i
$543$	−5.48791	+	16.8901i	−0.235509	+	0.724822i
$544$	−0.574672	−	0.417524i	−0.0246389	−	0.0179012i
$545$	17.5561	+	12.7552i	0.752019	+	0.546374i
$546$	−0.667908	+	2.05561i	−0.0285838	+	0.0879720i
$547$	8.12818	+	25.0160i	0.347536	+	1.06961i	0.960212	+	0.279271i	$0.0900929\pi$
$547$	8.12818	+	25.0160i	0.347536	+	1.06961i	−0.612676	+	0.790334i	$0.709907\pi$
$548$	−1.87963	+	1.36563i	−0.0802937	+	0.0583368i
$549$	3.12427			0.133341
$550$	−7.26114	−	13.8115i	−0.309616	−	0.588925i
$551$	2.01950			0.0860336
$552$	−0.711270	+	0.516768i	−0.0302737	+	0.0219951i
$553$	−3.00230	−	9.24013i	−0.127671	−	0.392930i
$554$	3.49845	−	10.7671i	0.148635	−	0.457451i
$555$	−9.77664	−	7.10315i	−0.414995	−	0.301512i
$556$	−6.05311	−	4.39784i	−0.256709	−	0.186510i
$557$	−2.36860	+	7.28979i	−0.100361	+	0.308879i	−0.988614	−	0.150476i	$-0.951919\pi$
$557$	−2.36860	+	7.28979i	−0.100361	+	0.308879i	0.888253	+	0.459355i	$0.151919\pi$
$558$	2.37545	+	7.31090i	0.100561	+	0.309495i
$559$	−14.4130	+	10.4716i	−0.609603	+	0.442903i
$560$	−3.11525			−0.131643
$561$	1.64445	−	1.68704i	0.0694289	−	0.0712267i
$562$	25.1590			1.06127
$563$	32.5519	−	23.6503i	1.37190	−	0.996742i	0.374312	−	0.927303i	$-0.377879\pi$
$563$	32.5519	−	23.6503i	1.37190	−	0.996742i	0.997586	−	0.0694397i	$-0.0221211\pi$
$564$	3.10205	+	9.54713i	0.130620	+	0.402007i
$565$	1.34582	−	4.14202i	0.0566192	−	0.174256i
$566$	−4.54464	−	3.30187i	−0.191025	−	0.138788i
$567$	−0.809017	−	0.587785i	−0.0339755	−	0.0246847i
$568$	3.35131	−	10.3143i	0.140618	−	0.432778i
$569$	−9.29055	−	28.5934i	−0.389480	−	1.19870i	−0.933178	−	0.359415i	$-0.882976\pi$
$569$	−9.29055	−	28.5934i	−0.389480	−	1.19870i	0.543698	−	0.839281i	$-0.317024\pi$
$570$	0.774469	−	0.562685i	0.0324389	−	0.0235683i
$571$	−21.9318			−0.917817			−0.458909	−	0.888483i	$-0.651760\pi$
$571$	−21.9318			−0.917817			−0.458909	+	0.888483i	$0.651760\pi$
$572$	1.03082	−	7.09404i	0.0431009	−	0.296617i
$573$	−26.2906			−1.09830
$574$	−3.47041	+	2.52140i	−0.144852	+	0.105241i
$575$	1.27819	+	3.93387i	0.0533043	+	0.164054i
$576$	0.309017	−	0.951057i	0.0128757	−	0.0396274i
$577$	29.3684	+	21.3374i	1.22262	+	0.888287i	0.996315	−	0.0857685i	$-0.0273345\pi$
$577$	29.3684	+	21.3374i	1.22262	+	0.888287i	0.226308	+	0.974056i	$0.427335\pi$
$578$	13.3451	+	9.69577i	0.555082	+	0.403291i
$579$	1.72057	−	5.29537i	0.0715045	−	0.220068i
$580$	−6.32652	−	19.4710i	−0.262694	−	0.808490i
$581$	−12.7701	+	9.27804i	−0.529794	+	0.384918i
$582$	−0.261144			−0.0108248
$583$	21.5222	−	3.69134i	0.891358	−	0.152880i
$584$	10.7453			0.444645
$585$	−5.44734	+	3.95772i	−0.225220	+	0.163632i
$586$	2.56520	+	7.89487i	0.105967	+	0.326134i
$587$	−1.81885	+	5.59783i	−0.0750718	+	0.231047i	−0.981550	−	0.191205i	$-0.938760\pi$
$587$	−1.81885	+	5.59783i	−0.0750718	+	0.231047i	0.906478	+	0.422252i	$0.138760\pi$
$588$	−0.809017	−	0.587785i	−0.0333633	−	0.0242399i
$589$	−1.91107	−	1.38847i	−0.0787441	−	0.0572110i
$590$	5.53619	−	17.0386i	0.227921	−	0.701470i
$591$	−3.64914	−	11.2309i	−0.150105	−	0.461977i
$592$	3.13832	−	2.28012i	0.128984	−	0.0937125i
$593$	−10.5795			−0.434449			−0.217224	−	0.976122i	$-0.569700\pi$
$593$	−10.5795			−0.434449			−0.217224	+	0.976122i	$0.569700\pi$
$594$	2.97414	+	1.46782i	0.122030	+	0.0602256i
$595$	−2.21286			−0.0907186
$596$	−1.15492	+	0.839099i	−0.0473074	+	0.0343708i
$597$	2.94676	+	9.06919i	0.120603	+	0.371177i
$598$	−0.587210	+	1.80725i	−0.0240128	+	0.0739038i
$599$	9.76734	+	7.09639i	0.399083	+	0.289951i	0.769167	−	0.639047i	$-0.220671\pi$
$599$	9.76734	+	7.09639i	0.399083	+	0.289951i	−0.370085	+	0.928998i	$0.620671\pi$
$600$	−3.80623	−	2.76539i	−0.155389	−	0.112896i
$601$	−13.3021	+	40.9395i	−0.542602	+	1.66996i	0.184021	+	0.982922i	$0.441089\pi$
$601$	−13.3021	+	40.9395i	−0.542602	+	1.66996i	−0.726623	+	0.687036i	$0.758911\pi$
$602$	−2.54709	−	7.83913i	−0.103811	−	0.319499i
$603$	5.40119	−	3.92419i	0.219953	−	0.159805i
$604$	−9.96190			−0.405344
$605$	0.875861	+	34.2565i	0.0356088	+	1.39273i
$606$	2.55081			0.103620
$607$	−9.57439	+	6.95620i	−0.388613	+	0.282344i	−0.764887	−	0.644165i	$-0.777205\pi$
$607$	−9.57439	+	6.95620i	−0.388613	+	0.282344i	0.376274	+	0.926508i	$0.377205\pi$
$608$	0.0949591	+	0.292254i	0.00385110	+	0.0118525i
$609$	2.03082	−	6.25023i	0.0822931	−	0.253272i
$610$	7.87405	+	5.72083i	0.318811	+	0.231630i
$611$	17.5533	+	12.7532i	0.710130	+	0.515940i
$612$	0.219505	−	0.675568i	0.00887297	−	0.0273082i
$613$	11.6416	+	35.8292i	0.470200	+	1.44713i	0.852323	+	0.523016i	$0.175193\pi$
$613$	11.6416	+	35.8292i	0.470200	+	1.44713i	−0.382122	+	0.924112i	$0.624807\pi$
$614$	−1.16570	+	0.846930i	−0.0470438	+	0.0341793i
$615$	−13.3634			−0.538863
$616$	2.97414	+	1.46782i	0.119831	+	0.0591403i
$617$	−40.5797			−1.63368			−0.816838	−	0.576867i	$-0.804275\pi$
$617$	−40.5797			−1.63368			−0.816838	+	0.576867i	$0.804275\pi$
$618$	−15.2435	+	11.0750i	−0.613183	+	0.445503i
$619$	−7.14425	−	21.9878i	−0.287152	−	0.883762i	−0.985745	−	0.168244i	$-0.946190\pi$
$619$	−7.14425	−	21.9878i	−0.287152	−	0.883762i	0.698594	−	0.715519i	$-0.253810\pi$
$620$	−7.40012	+	22.7752i	−0.297196	+	0.914676i
$621$	−0.711270	−	0.516768i	−0.0285423	−	0.0207372i
$622$	−8.00462	−	5.81570i	−0.320956	−	0.233188i
$623$	4.59590	−	14.1447i	0.184131	−	0.566696i
$624$	−0.667908	−	2.05561i	−0.0267377	−	0.0822902i
$625$	21.3492	−	15.5111i	0.853967	−	0.620444i
$626$	−5.55886			−0.222177
$627$	−1.00451	+	0.172287i	−0.0401163	+	0.00688048i
$628$	−24.6413			−0.983296
$629$	2.22926	−	1.61965i	0.0888862	−	0.0645796i
$630$	−0.962664	−	2.96278i	−0.0383535	−	0.118040i
$631$	−5.69945	+	17.5411i	−0.226891	+	0.698300i	0.771203	+	0.636590i	$0.219655\pi$
$631$	−5.69945	+	17.5411i	−0.226891	+	0.698300i	−0.998094	+	0.0617103i	$0.980345\pi$
$632$	7.86013	+	5.71072i	0.312659	+	0.227160i
$633$	9.67135	+	7.02665i	0.384402	+	0.279284i
$634$	−0.214544	+	0.660299i	−0.00852064	+	0.0262238i
$635$	−15.4441	−	47.5319i	−0.612879	−	1.88625i
$636$	5.32652	−	3.86994i	0.211210	−	0.153453i
$637$	−2.16140			−0.0856376
$638$	−3.13430	+	21.5699i	−0.124088	+	0.853962i
$639$	10.8451			0.429025
$640$	2.52029	−	1.83110i	0.0996231	−	0.0723804i
$641$	−2.37656	−	7.31431i	−0.0938686	−	0.288898i	0.893089	−	0.449881i	$-0.148534\pi$
$641$	−2.37656	−	7.31431i	−0.0938686	−	0.288898i	−0.986957	+	0.160983i	$0.948534\pi$
$642$	−1.05094	+	3.23446i	−0.0414773	+	0.127654i
$643$	−13.1343	−	9.54260i	−0.517965	−	0.376323i	0.297872	−	0.954606i	$-0.403723\pi$
$643$	−13.1343	−	9.54260i	−0.517965	−	0.376323i	−0.815837	+	0.578282i	$0.803723\pi$
$644$	−0.711270	−	0.516768i	−0.0280280	−	0.0203635i
$645$	7.93480	−	24.4208i	0.312432	−	0.961568i
$646$	0.0674526	+	0.207598i	0.00265389	+	0.00816783i
$647$	11.8174	−	8.58586i	0.464591	−	0.337545i	−0.330739	−	0.943722i	$-0.607298\pi$
$647$	11.8174	−	8.58586i	0.464591	−	0.337545i	0.795329	+	0.606177i	$0.207298\pi$
$648$	1.00000			0.0392837
$649$	−13.3136	+	13.6583i	−0.522604	+	0.536137i
$650$	−10.1688			−0.398855
$651$	−6.21902	+	4.51838i	−0.243743	+	0.177089i
$652$	4.43343	+	13.6447i	0.173627	+	0.534368i
$653$	−4.36249	+	13.4264i	−0.170717	+	0.525414i	−0.999412	−	0.0342870i	$-0.989084\pi$
$653$	−4.36249	+	13.4264i	−0.170717	+	0.525414i	0.828695	+	0.559701i	$0.189084\pi$
$654$	−5.63553	−	4.09445i	−0.220367	−	0.160106i
$655$	50.0771	+	36.3831i	1.95667	+	1.42161i
$656$	1.32558	−	4.07972i	0.0517552	−	0.159286i
$657$	3.32049	+	10.2194i	0.129545	+	0.398697i
$658$	−8.12127	+	5.90045i	−0.316600	+	0.230023i
$659$	33.9283			1.32166			0.660829	−	0.750536i	$-0.270205\pi$
$659$	33.9283			1.32166			0.660829	+	0.750536i	$0.270205\pi$
$660$	4.80795	+	9.14527i	0.187149	+	0.355979i
$661$	18.7723			0.730157			0.365079	−	0.930977i	$-0.381042\pi$
$661$	18.7723			0.730157			0.365079	+	0.930977i	$0.381042\pi$
$662$	25.1013	−	18.2371i	0.975589	−	0.708807i
$663$	−0.474438	−	1.46017i	−0.0184256	−	0.0567083i
$664$	4.87776	−	15.0122i	0.189294	−	0.582586i
$665$	0.774469	+	0.562685i	0.0300326	+	0.0218200i
$666$	3.13832	+	2.28012i	0.121607	+	0.0883530i
$667$	1.78546	−	5.49507i	0.0691331	−	0.212770i
$668$	4.33599	+	13.3448i	0.167764	+	0.516326i
$669$	7.10226	−	5.16009i	0.274589	−	0.199501i
$670$	20.7981			0.803501
$671$	−4.82188	−	9.17175i	−0.186146	−	0.354072i
$672$	1.00000			0.0385758
$673$	−21.4093	+	15.5547i	−0.825266	+	0.599591i	−0.918216	−	0.396080i	$-0.870370\pi$
$673$	−21.4093	+	15.5547i	−0.825266	+	0.599591i	0.0929499	+	0.995671i	$0.470370\pi$
$674$	5.07933	+	15.6326i	0.195649	+	0.602144i
$675$	1.45385	−	4.47449i	0.0559587	−	0.172223i
$676$	6.73779	+	4.89529i	0.259146	+	0.188280i
$677$	−9.60943	−	6.98166i	−0.369320	−	0.268327i	0.387609	−	0.921824i	$-0.373301\pi$
$677$	−9.60943	−	6.98166i	−0.369320	−	0.268327i	−0.756929	+	0.653497i	$0.773301\pi$
$678$	−0.432012	+	1.32960i	−0.0165913	+	0.0510628i
$679$	−0.0806980	−	0.248363i	−0.00309690	−	0.00953129i
$680$	1.79024	−	1.30069i	0.0686528	−	0.0498791i
$681$	−19.5027			−0.747346
$682$	17.7960	−	18.2569i	0.681445	−	0.699091i
$683$	−35.6132			−1.36270			−0.681351	−	0.731957i	$-0.738607\pi$
$683$	−35.6132			−1.36270			−0.681351	+	0.731957i	$0.738607\pi$
$684$	−0.248606	+	0.180623i	−0.00950569	+	0.00690629i
$685$	−2.23660	−	6.88356i	−0.0854562	−	0.263007i
$686$	0.309017	−	0.951057i	0.0117983	−	0.0363115i
$687$	5.88938	+	4.27888i	0.224694	+	0.163250i
$688$	6.66836	+	4.84485i	0.254229	+	0.184708i
$689$	4.39746	−	13.5340i	0.167530	−	0.515604i
$690$	−0.846353	−	2.60481i	−0.0322201	−	0.0991633i
$691$	−3.14171	+	2.28258i	−0.119516	+	0.0868336i	−0.645938	−	0.763390i	$-0.723533\pi$
$691$	−3.14171	+	2.28258i	−0.119516	+	0.0868336i	0.526421	+	0.850224i	$0.323533\pi$
$692$	14.1774			0.538946
$693$	−0.476925	+	3.28216i	−0.0181169	+	0.124679i
$694$	35.0591			1.33083
$695$	18.8569	−	13.7004i	0.715284	−	0.519684i
$696$	2.03082	+	6.25023i	0.0769782	+	0.236914i
$697$	0.941604	−	2.89796i	0.0356658	−	0.109768i
$698$	−6.97938	−	5.07081i	−0.264173	−	0.191933i
$699$	2.21054	+	1.60605i	0.0836104	+	0.0607465i
$700$	1.45385	−	4.47449i	0.0549504	−	0.169120i
$701$	10.5574	+	32.4925i	0.398749	+	1.22722i	0.926003	+	0.377515i	$0.123221\pi$
$701$	10.5574	+	32.4925i	0.398749	+	1.22722i	−0.527254	+	0.849707i	$0.676779\pi$
$702$	1.74861	−	1.27044i	0.0659969	−	0.0479495i
$703$	−1.19205			−0.0449589
$704$	−3.26889	+	0.560659i	−0.123201	+	0.0211306i
$705$	−31.2722			−1.17778
$706$	22.6971	−	16.4904i	0.854215	−	0.620623i
$707$	0.788244	+	2.42596i	0.0296450	+	0.0912378i
$708$	−1.77713	+	5.46944i	−0.0667886	+	0.205554i
$709$	38.6479	+	28.0794i	1.45145	+	1.05454i	0.985489	+	0.169739i	$0.0542925\pi$
$709$	38.6479	+	28.0794i	1.45145	+	1.05454i	0.465964	+	0.884803i	$0.345707\pi$
$710$	27.3327	+	19.8584i	1.02578	+	0.745272i
$711$	−3.00230	+	9.24013i	−0.112595	+	0.346532i
$712$	4.59590	+	14.1447i	0.172238	+	0.530095i
$713$	−5.46762	+	3.97246i	−0.204764	+	0.148770i
$714$	0.710334			0.0265836
$715$	20.0257	+	9.88327i	0.748919	+	0.369613i
$716$	−15.8912			−0.593883
$717$	−20.9517	+	15.2223i	−0.782455	+	0.568487i
$718$	−5.76547	−	17.7443i	−0.215165	−	0.662211i
$719$	1.01560	−	3.12571i	0.0378756	−	0.116569i	−0.930331	−	0.366721i	$-0.880480\pi$
$719$	1.01560	−	3.12571i	0.0378756	−	0.116569i	0.968207	+	0.250152i	$0.0804804\pi$
$720$	2.52029	+	1.83110i	0.0939256	+	0.0682409i
$721$	−15.2435	−	11.0750i	−0.567697	−	0.412456i
$722$	−5.84214	+	17.9803i	−0.217422	+	0.669156i
$723$	−1.96545	−	6.04904i	−0.0730959	−	0.224966i
$724$	14.3675	−	10.4386i	0.533965	−	0.387949i
$725$	30.9191			1.14831
$726$	−0.281153	−	10.9964i	−0.0104346	−	0.408115i
$727$	−6.49508			−0.240889			−0.120445	−	0.992720i	$-0.538432\pi$
$727$	−6.49508			−0.240889			−0.120445	+	0.992720i	$0.538432\pi$
$728$	1.74861	−	1.27044i	0.0648077	−	0.0470855i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	−10.3441	+	31.8360i	−0.382854	+	1.17830i
$731$	4.73676	+	3.44146i	0.175195	+	0.127287i
$732$	−2.52759	−	1.83640i	−0.0934223	−	0.0678752i
$733$	−15.4915	+	47.6778i	−0.572190	+	1.76102i	0.0733629	+	0.997305i	$0.476627\pi$
$733$	−15.4915	+	47.6778i	−0.572190	+	1.76102i	−0.645553	+	0.763715i	$0.723373\pi$
$734$	−0.465624	−	1.43304i	−0.0171865	−	0.0528946i
$735$	2.52029	−	1.83110i	0.0929622	−	0.0675410i
$736$	0.879178			0.0324069
$737$	−19.8560	−	9.79954i	−0.731407	−	0.360971i
$738$	4.28967			0.157905
$739$	−12.3163	+	8.94833i	−0.453063	+	0.329170i	−0.790804	−	0.612070i	$-0.790337\pi$
$739$	−12.3163	+	8.94833i	−0.453063	+	0.329170i	0.337741	+	0.941239i	$0.390337\pi$
$740$	3.73434	+	11.4931i	0.137277	+	0.422496i
$741$	−0.205244	+	0.631676i	−0.00753983	+	0.0232052i
$742$	5.32652	+	3.86994i	0.195543	+	0.142070i
$743$	19.0139	+	13.8144i	0.697554	+	0.506803i	0.879135	−	0.476573i	$-0.158121\pi$
$743$	19.0139	+	13.8144i	0.697554	+	0.506803i	−0.181581	+	0.983376i	$0.558121\pi$
$744$	2.37545	−	7.31090i	0.0870884	−	0.268030i
$745$	−1.37426	−	4.22954i	−0.0503490	−	0.154958i
$746$	28.2725	−	20.5412i	1.03513	−	0.752066i
$747$	15.7847			0.577534
$748$	−2.32201	+	0.398255i	−0.0849009	+	0.0145616i
$749$	−3.40091			−0.124267
$750$	−0.744095	+	0.540617i	−0.0271705	+	0.0197405i
$751$	5.12915	+	15.7859i	0.187165	+	0.576036i	0.999979	−	0.00648819i	$-0.00206527\pi$
$751$	5.12915	+	15.7859i	0.187165	+	0.576036i	−0.812814	+	0.582524i	$0.802065\pi$
$752$	3.10205	−	9.54713i	0.113120	−	0.348148i
$753$	10.4223	+	7.57222i	0.379808	+	0.275947i
$754$	11.4916	+	8.34916i	0.418501	+	0.304059i
$755$	9.58996	−	29.5149i	0.349014	−	1.07416i
$756$	0.309017	+	0.951057i	0.0112388	+	0.0345896i
$757$	1.29103	−	0.937989i	0.0469233	−	0.0340918i	−0.564076	−	0.825723i	$-0.690768\pi$
$757$	1.29103	−	0.937989i	0.0469233	−	0.0340918i	0.611000	+	0.791631i	$0.290768\pi$
$758$	11.9312			0.433362
$759$	−0.419302	+	2.88560i	−0.0152197	+	0.104741i
$760$	−0.957296			−0.0347248
$761$	−2.91975	+	2.12132i	−0.105841	+	0.0768979i	−0.639447	−	0.768835i	$-0.720837\pi$
$761$	−2.91975	+	2.12132i	−0.105841	+	0.0768979i	0.533606	+	0.845733i	$0.320837\pi$
$762$	4.95757	+	15.2578i	0.179594	+	0.552733i
$763$	2.15258	−	6.62497i	0.0779287	−	0.239840i
$764$	21.2695	+	15.4532i	0.769504	+	0.559077i
$765$	1.79024	+	1.30069i	0.0647264	+	0.0470265i
$766$	5.58607	−	17.1921i	0.201833	−	0.621177i
$767$	3.84108	+	11.8216i	0.138693	+	0.426854i
$768$	−0.809017	+	0.587785i	−0.0291929	+	0.0212099i
$769$	−38.6906			−1.39522			−0.697609	−	0.716479i	$-0.745753\pi$
$769$	−38.6906			−1.39522			−0.697609	+	0.716479i	$0.745753\pi$
$770$	−7.21193	+	7.39868i	−0.259900	+	0.266630i
$771$	5.22836			0.188295
$772$	−4.50451	+	3.27272i	−0.162121	+	0.117788i
$773$	0.534756	+	1.64581i	0.0192338	+	0.0591957i	0.960213	−	0.279269i	$-0.0900923\pi$
$773$	0.534756	+	1.64581i	0.0192338	+	0.0591957i	−0.940979	+	0.338465i	$0.890092\pi$
$774$	−2.54709	+	7.83913i	−0.0915531	+	0.281772i
$775$	−29.2590	−	21.2579i	−1.05101	−	0.763606i
$776$	0.211270	+	0.153497i	0.00758415	+	0.00551021i
$777$	−1.19873	+	3.68932i	−0.0430043	+	0.132354i
$778$	−0.468412	−	1.44162i	−0.0167934	−	0.0516847i
$779$	−1.06644	+	0.774812i	−0.0382091	+	0.0277605i
$780$	6.73328			0.241090
$781$	−16.7379	−	31.8373i	−0.598929	−	1.13923i
$782$	0.624510			0.0223324
$783$	−5.31677	+	3.86286i	−0.190006	+	0.138047i
$784$	0.309017	+	0.951057i	0.0110363	+	0.0339663i
$785$	23.7213	−	73.0067i	0.846650	−	2.60572i
$786$	−16.0748	−	11.6791i	−0.573371	−	0.416578i
$787$	−2.10005	−	1.52577i	−0.0748587	−	0.0543880i	0.549727	−	0.835345i	$-0.314732\pi$
$787$	−2.10005	−	1.52577i	−0.0748587	−	0.0543880i	−0.624585	+	0.780957i	$0.714732\pi$
$788$	−3.64914	+	11.2309i	−0.129995	+	0.400084i
$789$	8.28931	+	25.5119i	0.295107	+	0.908247i
$790$	−24.4862	+	17.7903i	−0.871181	+	0.632950i
$791$	−1.39802			−0.0497079
$792$	−1.54336	−	2.93565i	−0.0548410	−	0.104314i
$793$	−6.75278			−0.239798
$794$	−26.0787	+	18.9473i	−0.925500	+	0.672415i
$795$	6.33812	+	19.5067i	0.224790	+	0.691832i
$796$	2.94676	−	9.06919i	0.104445	−	0.321449i
$797$	−24.3171	−	17.6674i	−0.861355	−	0.625811i	0.0668980	−	0.997760i	$-0.478690\pi$
$797$	−24.3171	−	17.6674i	−0.861355	−	0.625811i	−0.928253	+	0.371948i	$0.878690\pi$
$798$	−0.248606	−	0.180623i	−0.00880056	−	0.00639398i
$799$	2.20349	−	6.78165i	0.0779539	−	0.239917i
$800$	1.45385	+	4.47449i	0.0514014	+	0.158197i
$801$	−12.0322	+	8.74191i	−0.425137	+	0.308880i
$802$	8.93278			0.315427
$803$	24.8759	−	25.5201i	0.877852	−	0.900583i
$804$	−6.67624			−0.235453
$805$	2.21578	−	1.60986i	0.0780960	−	0.0567401i
$806$	−5.13430	−	15.8017i	−0.180848	−	0.556593i
$807$	−3.41165	+	10.5000i	−0.120096	+	0.369616i
$808$	−2.06365	−	1.49933i	−0.0725989	−	0.0527462i
$809$	−25.0367	−	18.1903i	−0.880245	−	0.639535i	0.0530713	−	0.998591i	$-0.483099\pi$
$809$	−25.0367	−	18.1903i	−0.880245	−	0.639535i	−0.933316	+	0.359055i	$0.883099\pi$
$810$	−0.962664	+	2.96278i	−0.0338246	+	0.104101i
$811$	3.91631	+	12.0532i	0.137520	+	0.423243i	0.995973	−	0.0896482i	$-0.0285743\pi$
$811$	3.91631	+	12.0532i	0.137520	+	0.423243i	−0.858453	+	0.512892i	$0.828574\pi$
$812$	−5.31677	+	3.86286i	−0.186582	+	0.135560i
$813$	−18.1134			−0.635264
$814$	1.85008	−	12.7321i	0.0648452	−	0.446259i
$815$	−44.6941			−1.56557
$816$	−0.574672	+	0.417524i	−0.0201175	+	0.0146163i
$817$	−0.782704	−	2.40892i	−0.0273834	−	0.0842773i
$818$	−6.63966	+	20.4348i	−0.232150	+	0.714485i
$819$	1.74861	+	1.27044i	0.0611012	+	0.0443926i
$820$	10.8112	+	7.85479i	0.377543	+	0.274301i
$821$	−1.18204	+	3.63795i	−0.0412535	+	0.126965i	−0.969562	−	0.244845i	$-0.921263\pi$
$821$	−1.18204	+	3.63795i	−0.0412535	+	0.126965i	0.928309	+	0.371810i	$0.121263\pi$
$822$	0.717954	+	2.20964i	0.0250415	+	0.0770699i
$823$	38.8927	−	28.2572i	1.35571	−	0.984985i	0.357010	−	0.934100i	$-0.383796\pi$
$823$	38.8927	−	28.2572i	1.35571	−	0.984985i	0.998705	−	0.0508841i	$-0.0162039\pi$
$824$	18.8420			0.656391
$825$	−15.3793	+	2.63776i	−0.535440	+	0.0918352i
$826$	−5.75091			−0.200100
$827$	35.4298	−	25.7413i	1.23202	−	0.895112i	0.234977	−	0.972001i	$-0.424499\pi$
$827$	35.4298	−	25.7413i	1.23202	−	0.895112i	0.997040	+	0.0768886i	$0.0244986\pi$
$828$	0.271681	+	0.836148i	0.00944157	+	0.0290582i
$829$	15.3747	−	47.3184i	0.533985	−	1.64344i	−0.211847	−	0.977303i	$-0.567948\pi$
$829$	15.3747	−	47.3184i	0.533985	−	1.64344i	0.745832	−	0.666134i	$-0.232052\pi$
$830$	39.7821	+	28.9034i	1.38086	+	1.00325i
$831$	−9.15906	−	6.65445i	−0.317724	−	0.230840i
$832$	−0.667908	+	2.05561i	−0.0231555	+	0.0712654i
$833$	0.219505	+	0.675568i	0.00760540	+	0.0234070i
$834$	−6.05311	+	4.39784i	−0.209602	+	0.152285i
$835$	−43.7117			−1.51271
$836$	0.913934	+	0.451054i	0.0316091	+	0.0156000i
$837$	7.68713			0.265706
$838$	−18.0718	+	13.1300i	−0.624282	+	0.453567i
$839$	−5.92774	−	18.2437i	−0.204648	−	0.629842i	−0.999728	−	0.0233371i	$-0.992571\pi$
$839$	−5.92774	−	18.2437i	−0.204648	−	0.629842i	0.795079	−	0.606505i	$-0.207429\pi$
$840$	−0.962664	+	2.96278i	−0.0332151	+	0.102225i
$841$	−11.4797	−	8.34047i	−0.395851	−	0.287603i
$842$	−8.00971	−	5.81940i	−0.276033	−	0.200550i
$843$	7.77456	−	23.9276i	0.267770	−	0.824112i
$844$	−3.69413	−	11.3694i	−0.127157	−	0.391349i
$845$	−20.9899	+	15.2500i	−0.722074	+	0.524617i
$846$	10.0384			0.345129
$847$	10.3713	−	3.66547i	0.356363	−	0.125947i
$848$	−6.58394			−0.226093
$849$	−4.54464	+	3.30187i	−0.155971	+	0.113320i
$850$	1.03272	+	3.17838i	0.0354220	+	0.109018i
$851$	−1.05390	+	3.24357i	−0.0361272	+	0.111188i
$852$	−8.77385	−	6.37458i	−0.300587	−	0.218389i
$853$	27.9632	+	20.3165i	0.957442	+	0.695623i	0.952555	−	0.304366i	$-0.0984444\pi$
$853$	27.9632	+	20.3165i	0.957442	+	0.695623i	0.00488696	+	0.999988i	$0.498444\pi$
$854$	0.965452	−	2.97136i	0.0330371	−	0.101678i
$855$	−0.295821	−	0.910443i	−0.0101169	−	0.0311365i
$856$	2.75139	−	1.99900i	0.0940407	−	0.0683246i
$857$	−1.15867			−0.0395792			−0.0197896	−	0.999804i	$-0.506300\pi$
$857$	−1.15867			−0.0395792			−0.0197896	+	0.999804i	$0.506300\pi$
$858$	−6.42829	−	3.17255i	−0.219458	−	0.108309i
$859$	−13.5036			−0.460737			−0.230369	−	0.973103i	$-0.573993\pi$
$859$	−13.5036			−0.460737			−0.230369	+	0.973103i	$0.573993\pi$
$860$	−20.7736	+	15.0929i	−0.708373	+	0.514663i
$861$	1.32558	+	4.07972i	0.0451756	+	0.139036i
$862$	0.502567	−	1.54674i	0.0171175	−	0.0526822i
$863$	−25.2030	−	18.3110i	−0.857919	−	0.623315i	0.0693991	−	0.997589i	$-0.477892\pi$
$863$	−25.2030	−	18.3110i	−0.857919	−	0.623315i	−0.927318	+	0.374274i	$0.877892\pi$
$864$	−0.809017	−	0.587785i	−0.0275233	−	0.0199969i
$865$	−13.6481	+	42.0046i	−0.464050	+	1.42820i
$866$	−5.08416	−	15.6474i	−0.172767	−	0.531721i
$867$	13.3451	−	9.69577i	0.453223	−	0.329286i
$868$	7.68713			0.260918
$869$	31.7594	−	5.44717i	1.07736	−	0.184783i
$870$	−20.4730			−0.694101
$871$	−11.6741	+	8.48173i	−0.395562	+	0.287393i
$872$	2.15258	+	6.62497i	0.0728956	+	0.224350i
$873$	−0.0806980	+	0.248363i	−0.00273121	+	0.00840581i
$874$	−0.218569	−	0.158800i	−0.00739321	−	0.00537148i
$875$	−0.744095	−	0.540617i	−0.0251550	−	0.0182762i
$876$	3.32049	−	10.2194i	0.112189	−	0.345282i
$877$	9.55294	+	29.4009i	0.322580	+	0.992799i	0.972521	+	0.232814i	$0.0747935\pi$
$877$	9.55294	+	29.4009i	0.322580	+	0.992799i	−0.649941	+	0.759984i	$0.725207\pi$
$878$	5.22205	−	3.79404i	0.176236	−	0.128043i
$879$	8.30116			0.279991
$880$	1.48574	−	10.2247i	0.0500842	−	0.344675i
$881$	23.1676			0.780535			0.390268	−	0.920701i	$-0.372382\pi$
$881$	23.1676			0.780535			0.390268	+	0.920701i	$0.372382\pi$
$882$	−0.809017	+	0.587785i	−0.0272410	+	0.0197918i
$883$	−4.67092	−	14.3756i	−0.157189	−	0.483778i	0.841187	−	0.540744i	$-0.181857\pi$
$883$	−4.67092	−	14.3756i	−0.157189	−	0.483778i	−0.998376	+	0.0569659i	$0.981857\pi$
$884$	−0.474438	+	1.46017i	−0.0159571	+	0.0491108i
$885$	−14.4939	−	10.5305i	−0.487208	−	0.353978i
$886$	−28.0665	−	20.3915i	−0.942912	−	0.685066i
$887$	−2.97262	+	9.14879i	−0.0998109	+	0.307186i	−0.988478	−	0.151367i	$-0.951632\pi$
$887$	−2.97262	+	9.14879i	−0.0998109	+	0.307186i	0.888667	+	0.458554i	$0.151632\pi$
$888$	−1.19873	−	3.68932i	−0.0402268	−	0.123805i
$889$	−12.9791	+	9.42987i	−0.435305	+	0.316268i
$890$	−46.3319			−1.55305
$891$	2.31504	−	2.37499i	0.0775569	−	0.0795652i
$892$	−8.77887			−0.293938
$893$	−2.49562	+	1.81317i	−0.0835127	+	0.0606755i
$894$	0.441140	+	1.35769i	0.0147539	+	0.0454079i
$895$	15.2979	−	47.0821i	0.511353	−	1.57378i
$896$	−0.809017	−	0.587785i	−0.0270274	−	0.0196365i
$897$	1.53734	+	1.11694i	0.0513302	+	0.0372935i
$898$	−11.2163	+	34.5203i	−0.374294	+	1.15196i
$899$	15.6112	+	48.0464i	0.520663	+	1.60244i
$900$	−3.80623	+	2.76539i	−0.126874	+	0.0921796i
$901$	−4.67679			−0.155807
$902$	−6.62051	−	12.5930i	−0.220439	−	0.419299i
$903$	−8.24254			−0.274295
$904$	1.13102	−	0.821736i	0.0376172	−	0.0273305i
$905$	17.0962	+	52.6167i	0.568297	+	1.74904i
$906$	−3.07840	+	9.47433i	−0.102273	+	0.314764i
$907$	18.5057	+	13.4452i	0.614471	+	0.446439i	0.850986	−	0.525189i	$-0.176005\pi$
$907$	18.5057	+	13.4452i	0.614471	+	0.446439i	−0.236515	+	0.971628i	$0.576005\pi$
$908$	15.7780	+	11.4634i	0.523612	+	0.380427i
$909$	0.788244	−	2.42596i	0.0261444	−	0.0804642i
$910$	2.08070	+	6.40373i	0.0689745	+	0.212282i
$911$	−19.0630	+	13.8501i	−0.631584	+	0.458873i	−0.856949	−	0.515402i	$-0.827643\pi$
$911$	−19.0630	+	13.8501i	−0.631584	+	0.458873i	0.225364	+	0.974275i	$0.427643\pi$
$912$	0.307294			0.0101755
$913$	−24.3616	−	46.3385i	−0.806251	−	1.53358i
$914$	21.2889			0.704173
$915$	7.87405	−	5.72083i	0.260308	−	0.189125i
$916$	−2.24954	−	6.92338i	−0.0743270	−	0.228755i
$917$	6.14004	−	18.8971i	0.202762	−	0.624038i
$918$	−0.574672	−	0.417524i	−0.0189670	−	0.0137803i
$919$	−24.9845	−	18.1523i	−0.824161	−	0.598788i	0.0937404	−	0.995597i	$-0.470118\pi$
$919$	−24.9845	−	18.1523i	−0.824161	−	0.598788i	−0.917901	+	0.396809i	$0.870118\pi$
$920$	−0.846353	+	2.60481i	−0.0279034	+	0.0858779i
$921$	0.445257	+	1.37036i	0.0146717	+	0.0451549i
$922$	27.8299	−	20.2196i	0.916530	−	0.665898i
$923$	−23.4405			−0.771554
$924$	2.31504	−	2.37499i	0.0761593	−	0.0781314i
$925$	−18.2506			−0.600076
$926$	−27.0952	+	19.6858i	−0.890405	+	0.646917i
$927$	5.82249	+	17.9198i	0.191236	+	0.588563i
$928$	2.03082	−	6.25023i	0.0666651	−	0.205174i
$929$	33.1831	+	24.1090i	1.08870	+	0.790989i	0.979180	−	0.202995i	$-0.0650676\pi$
$929$	33.1831	+	24.1090i	1.08870	+	0.790989i	0.109523	+	0.993984i	$0.465068\pi$
$930$	19.3738	+	14.0759i	0.635291	+	0.461566i
$931$	0.0949591	−	0.292254i	0.00311216	−	0.00957823i
$932$	−0.844352	−	2.59865i	−0.0276577	−	0.0851215i
$933$	−8.00462	+	5.81570i	−0.262060	+	0.190397i
$934$	−24.9067			−0.814973
$935$	1.05537	−	7.26296i	0.0345143	−	0.237524i
$936$	−2.16140			−0.0706474
$937$	2.92275	−	2.12350i	0.0954820	−	0.0693717i	−0.539020	−	0.842293i	$-0.681205\pi$
$937$	2.92275	−	2.12350i	0.0954820	−	0.0693717i	0.634502	+	0.772921i	$0.281205\pi$
$938$	−2.06307	−	6.34948i	−0.0673616	−	0.207318i
$939$	−1.71778	+	5.28679i	−0.0560577	+	0.172528i
$940$	25.2998	+	18.3814i	0.825187	+	0.599534i
$941$	32.4823	+	23.5997i	1.05889	+	0.769330i	0.973883	−	0.227050i	$-0.0729082\pi$
$941$	32.4823	+	23.5997i	1.05889	+	0.769330i	0.0850086	+	0.996380i	$0.472908\pi$
$942$	−7.61459	+	23.4353i	−0.248097	+	0.763563i
$943$	1.16542	+	3.58680i	0.0379513	+	0.116802i
$944$	4.65258	−	3.38030i	0.151429	−	0.110019i
$945$	−3.11525			−0.101339
$946$	26.9440	−	4.62126i	0.876025	−	0.150250i
$947$	−33.8239			−1.09913			−0.549564	−	0.835452i	$-0.685206\pi$
$947$	−33.8239			−1.09913			−0.549564	+	0.835452i	$0.685206\pi$
$948$	7.86013	−	5.71072i	0.255285	−	0.185475i
$949$	−7.17689	−	22.0882i	−0.232972	−	0.717014i
$950$	0.446759	−	1.37498i	0.0144948	−	0.0446104i
$951$	0.561684	+	0.408087i	0.0182139	+	0.0132331i
$952$	−0.574672	−	0.417524i	−0.0186252	−	0.0135320i
$953$	10.3116	−	31.7359i	0.334026	−	1.02803i	−0.633173	−	0.774010i	$-0.718248\pi$
$953$	10.3116	−	31.7359i	0.334026	−	1.02803i	0.967200	−	0.254017i	$-0.0817520\pi$
$954$	−2.03455	−	6.26170i	−0.0658709	−	0.202730i
$955$	−66.2598	+	48.1405i	−2.14412	+	1.55779i
$956$	25.8977			0.837592
$957$	19.5457	+	9.64637i	0.631822	+	0.311823i
$958$	−26.0657			−0.842146
$959$	−1.87963	+	1.36563i	−0.0606964	+	0.0440985i
$960$	−0.962664	−	2.96278i	−0.0310698	−	0.0956232i
$961$	8.68090	−	26.7171i	0.280029	−	0.861840i
$962$	−6.78315	−	4.92825i	−0.218698	−	0.158893i
$963$	2.75139	+	1.99900i	0.0886624	+	0.0644170i
$964$	−1.96545	+	6.04904i	−0.0633029	+	0.194826i
$965$	−5.36000	−	16.4964i	−0.172544	−	0.531037i
$966$	−0.711270	+	0.516768i	−0.0228847	+	0.0166267i
$967$	48.0391			1.54483			0.772417	−	0.635116i	$-0.219048\pi$
$967$	48.0391			1.54483			0.772417	+	0.635116i	$0.219048\pi$
$968$	−6.23607	+	9.06154i	−0.200435	+	0.291249i
$969$	0.218281			0.00701220
$970$	−0.658158	+	0.478180i	−0.0211322	+	0.0153534i
$971$	−12.5807	−	38.7193i	−0.403733	−	1.24256i	−0.921949	−	0.387312i	$-0.873404\pi$
$971$	−12.5807	−	38.7193i	−0.403733	−	1.24256i	0.518216	−	0.855250i	$-0.326596\pi$
$972$	0.309017	−	0.951057i	0.00991172	−	0.0305052i
$973$	−6.05311	−	4.39784i	−0.194054	−	0.140988i
$974$	8.92850	+	6.48693i	0.286087	+	0.207855i
$975$	−3.14235	+	9.67115i	−0.100636	+	0.309725i
$976$	0.965452	+	2.97136i	0.0309034	+	0.0951108i
$977$	−2.26347	+	1.64450i	−0.0724147	+	0.0526124i	−0.623404	−	0.781900i	$-0.714251\pi$
$977$	−2.26347	+	1.64450i	−0.0724147	+	0.0526124i	0.550989	+	0.834513i	$0.314251\pi$
$978$	14.3469			0.458763
$979$	44.2332	+	21.8304i	1.41370	+	0.697703i
$980$	−3.11525			−0.0995129
$981$	−5.63553	+	4.09445i	−0.179929	+	0.130726i
$982$	0.0565149	+	0.173935i	0.00180346	+	0.00555049i
$983$	9.02142	−	27.7651i	0.287739	−	0.885568i	−0.697826	−	0.716267i	$-0.745849\pi$
$983$	9.02142	−	27.7651i	0.287739	−	0.885568i	0.985564	−	0.169301i	$-0.0541509\pi$
$984$	−3.47041	−	2.52140i	−0.110633	−	0.0803794i
$985$	−29.7617	−	21.6231i	−0.948286	−	0.688970i
$986$	1.44256	−	4.43975i	0.0459406	−	0.141390i
$987$	3.10205	+	9.54713i	0.0987393	+	0.303888i
$988$	0.537336	−	0.390397i	0.0170949	−	0.0124202i
$989$	−7.24666			−0.230430
$990$	10.1834	−	1.74659i	0.323650	−	0.0555103i
$991$	49.6877			1.57838			0.789191	−	0.614148i	$-0.210500\pi$
$991$	49.6877			1.57838			0.789191	+	0.614148i	$0.210500\pi$
$992$	−6.21902	+	4.51838i	−0.197454	+	0.143459i
$993$	−9.58783	−	29.5083i	−0.304261	−	0.936418i
$994$	3.35131	−	10.3143i	0.106297	−	0.327149i
$995$	24.0332	+	17.4612i	0.761905	+	0.553556i
$996$	−12.7701	−	9.27804i	−0.404637	−	0.293986i
$997$	−10.1095	+	31.1138i	−0.320171	+	0.985385i	0.653402	+	0.757011i	$0.273341\pi$
$997$	−10.1095	+	31.1138i	−0.320171	+	0.985385i	−0.973573	+	0.228374i	$0.926659\pi$
$998$	5.21872	+	16.0616i	0.165196	+	0.508420i
$999$	3.13832	−	2.28012i	0.0992921	−	0.0721399i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.j.e.421.2	yes	8
11.2	odd	10		5082.2.a.ca.1.1		4
11.4	even	5	inner	462.2.j.e.169.2	✓	8
11.9	even	5		5082.2.a.cf.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.j.e.169.2	✓	8	11.4	even	5	inner
462.2.j.e.421.2	yes	8	1.1	even	1	trivial
5082.2.a.ca.1.1		4	11.2	odd	10
5082.2.a.cf.1.1		4	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)

\(f(q)\)	\(=\)	\(q+(-0.809017 + 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.309017 - 0.951057i) q^{4} +(2.52029 + 1.83110i) q^{5} +(-0.809017 - 0.587785i) q^{6} +(0.309017 - 0.951057i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(-0.809017 + 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.309017 - 0.951057i) q^{4} +(2.52029 + 1.83110i) 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} -3.11525 q^{10} +(2.97414 + 1.46782i) q^{11} +1.00000 q^{12} +(1.74861 - 1.27044i) q^{13} +(0.309017 + 0.951057i) q^{14} +(-0.962664 + 2.96278i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-0.574672 - 0.417524i) q^{17} +(0.309017 - 0.951057i) q^{18} +(0.0949591 + 0.292254i) q^{19} +(2.52029 - 1.83110i) q^{20} +1.00000 q^{21} +(-3.26889 + 0.560659i) q^{22} +0.879178 q^{23} +(-0.809017 + 0.587785i) q^{24} +(1.45385 + 4.47449i) q^{25} +(-0.667908 + 2.05561i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(-0.809017 - 0.587785i) q^{28} +(2.03082 - 6.25023i) q^{29} +(-0.962664 - 2.96278i) q^{30} +(-6.21902 + 4.51838i) q^{31} +1.00000 q^{32} +(-0.476925 + 3.28216i) q^{33} +0.710334 q^{34} +(2.52029 - 1.83110i) q^{35} +(0.309017 + 0.951057i) q^{36} +(-1.19873 + 3.68932i) q^{37} +(-0.248606 - 0.180623i) q^{38} +(1.74861 + 1.27044i) q^{39} +(-0.962664 + 2.96278i) q^{40} +(1.32558 + 4.07972i) q^{41} +(-0.809017 + 0.587785i) q^{42} -8.24254 q^{43} +(2.31504 - 2.37499i) q^{44} -3.11525 q^{45} +(-0.711270 + 0.516768i) q^{46} +(3.10205 + 9.54713i) q^{47} +(0.309017 - 0.951057i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(-3.80623 - 2.76539i) q^{50} +(0.219505 - 0.675568i) q^{51} +(-0.667908 - 2.05561i) q^{52} +(5.32652 - 3.86994i) q^{53} +1.00000 q^{54} +(4.80795 + 9.14527i) q^{55} +1.00000 q^{56} +(-0.248606 + 0.180623i) q^{57} +(2.03082 + 6.25023i) q^{58} +(-1.77713 + 5.46944i) q^{59} +(2.52029 + 1.83110i) q^{60} +(-2.52759 - 1.83640i) q^{61} +(2.37545 - 7.31090i) q^{62} +(0.309017 + 0.951057i) q^{63} +(-0.809017 + 0.587785i) q^{64} +6.73328 q^{65} +(-1.54336 - 2.93565i) q^{66} -6.67624 q^{67} +(-0.574672 + 0.417524i) q^{68} +(0.271681 + 0.836148i) q^{69} +(-0.962664 + 2.96278i) q^{70} +(-8.77385 - 6.37458i) q^{71} +(-0.809017 - 0.587785i) q^{72} +(3.32049 - 10.2194i) q^{73} +(-1.19873 - 3.68932i) q^{74} +(-3.80623 + 2.76539i) q^{75} +0.307294 q^{76} +(2.31504 - 2.37499i) q^{77} -2.16140 q^{78} +(7.86013 - 5.71072i) q^{79} +(-0.962664 - 2.96278i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-3.47041 - 2.52140i) q^{82} +(-12.7701 - 9.27804i) q^{83} +(0.309017 - 0.951057i) q^{84} +(-0.683813 - 2.10456i) q^{85} +(6.66836 - 4.84485i) q^{86} +6.57188 q^{87} +(-0.476925 + 3.28216i) q^{88} +14.8726 q^{89} +(2.52029 - 1.83110i) q^{90} +(-0.667908 - 2.05561i) q^{91} +(0.271681 - 0.836148i) q^{92} +(-6.21902 - 4.51838i) q^{93} +(-8.12127 - 5.90045i) q^{94} +(-0.295821 + 0.910443i) q^{95} +(0.309017 + 0.951057i) q^{96} +(0.211270 - 0.153497i) q^{97} +1.00000 q^{98} +(-3.26889 + 0.560659i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 4 q^{5} - 2 q^{6} - 2 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + 4 * q^5 - 2 * q^6 - 2 * q^7 - 2 * q^8 - 2 * q^9	\( 8 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 4 q^{5} - 2 q^{6} - 2 q^{7} - 2 q^{8} - 2 q^{9} + 4 q^{10} + 8 q^{12} + 4 q^{13} - 2 q^{14} - 6 q^{15} - 2 q^{16} - 8 q^{17} - 2 q^{18} - 12 q^{19} + 4 q^{20} + 8 q^{21} - 4 q^{23} - 2 q^{24} + 4 q^{25} - 6 q^{26} - 2 q^{27} - 2 q^{28} - 4 q^{29} - 6 q^{30} - 14 q^{31} + 8 q^{32} + 12 q^{34} + 4 q^{35} - 2 q^{36} + 10 q^{37} + 8 q^{38} + 4 q^{39} - 6 q^{40} - 12 q^{41} - 2 q^{42} + 20 q^{43} + 4 q^{45} + 6 q^{46} + 28 q^{47} - 2 q^{48} - 2 q^{49} - 6 q^{50} + 2 q^{51} - 6 q^{52} + 2 q^{53} + 8 q^{54} + 4 q^{55} + 8 q^{56} + 8 q^{57} - 4 q^{58} + 4 q^{60} - 34 q^{61} + 6 q^{62} - 2 q^{63} - 2 q^{64} + 16 q^{65} - 24 q^{67} - 8 q^{68} - 4 q^{69} - 6 q^{70} - 2 q^{72} + 10 q^{74} - 6 q^{75} + 8 q^{76} + 4 q^{78} + 22 q^{79} - 6 q^{80} - 2 q^{81} - 2 q^{82} - 30 q^{83} - 2 q^{84} - 28 q^{85} + 36 q^{87} - 4 q^{89} + 4 q^{90} - 6 q^{91} - 4 q^{92} - 14 q^{93} - 22 q^{94} - 30 q^{95} - 2 q^{96} - 10 q^{97} + 8 q^{98}+O(q^{100}) \) 8 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + 4 * q^5 - 2 * q^6 - 2 * q^7 - 2 * q^8 - 2 * q^9 + 4 * q^10 + 8 * q^12 + 4 * q^13 - 2 * q^14 - 6 * q^15 - 2 * q^16 - 8 * q^17 - 2 * q^18 - 12 * q^19 + 4 * q^20 + 8 * q^21 - 4 * q^23 - 2 * q^24 + 4 * q^25 - 6 * q^26 - 2 * q^27 - 2 * q^28 - 4 * q^29 - 6 * q^30 - 14 * q^31 + 8 * q^32 + 12 * q^34 + 4 * q^35 - 2 * q^36 + 10 * q^37 + 8 * q^38 + 4 * q^39 - 6 * q^40 - 12 * q^41 - 2 * q^42 + 20 * q^43 + 4 * q^45 + 6 * q^46 + 28 * q^47 - 2 * q^48 - 2 * q^49 - 6 * q^50 + 2 * q^51 - 6 * q^52 + 2 * q^53 + 8 * q^54 + 4 * q^55 + 8 * q^56 + 8 * q^57 - 4 * q^58 + 4 * q^60 - 34 * q^61 + 6 * q^62 - 2 * q^63 - 2 * q^64 + 16 * q^65 - 24 * q^67 - 8 * q^68 - 4 * q^69 - 6 * q^70 - 2 * q^72 + 10 * q^74 - 6 * q^75 + 8 * q^76 + 4 * q^78 + 22 * q^79 - 6 * q^80 - 2 * q^81 - 2 * q^82 - 30 * q^83 - 2 * q^84 - 28 * q^85 + 36 * q^87 - 4 * q^89 + 4 * q^90 - 6 * q^91 - 4 * q^92 - 14 * q^93 - 22 * q^94 - 30 * q^95 - 2 * q^96 - 10 * q^97 + 8 * q^98

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