LMFDB - Embedded newform 462.2.j.f.169.1

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:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.64000000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{6} + 4x^{4} - 8x^{2} + 16 $ x^8 - 2x^6 + 4x^4 - 8*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			169.1
Root			$-0.831254 + 1.14412i$ of defining polynomial
Character	$\chi$	$=$	462.169
Dual form			462.2.j.f.421.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 - 0.587785i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-2.65401 + 1.92825i) q^{5} +(0.809017 - 0.587785i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(q+(-0.809017 - 0.587785i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-2.65401 + 1.92825i) 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} +3.28054 q^{10} +(2.53598 + 2.13748i) q^{11} -1.00000 q^{12} +(-2.52125 - 1.83179i) q^{13} +(-0.309017 + 0.951057i) q^{14} +(-1.01374 - 3.11998i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-3.18999 + 2.31767i) q^{17} +(0.309017 + 0.951057i) q^{18} +(1.74456 - 5.36921i) q^{19} +(-2.65401 - 1.92825i) q^{20} +1.00000 q^{21} +(-0.795274 - 3.21987i) q^{22} -4.33551 q^{23} +(0.809017 + 0.587785i) q^{24} +(1.78054 - 5.47994i) q^{25} +(0.963031 + 2.96390i) q^{26} +(0.809017 - 0.587785i) q^{27} +(0.809017 - 0.587785i) q^{28} +(-3.11180 - 9.57712i) q^{29} +(-1.01374 + 3.11998i) q^{30} +(-8.56473 - 6.22264i) q^{31} +1.00000 q^{32} +(-2.81652 + 1.75134i) q^{33} +3.94305 q^{34} +(2.65401 + 1.92825i) q^{35} +(0.309017 - 0.951057i) q^{36} +(0.249811 + 0.768840i) q^{37} +(-4.56732 + 3.31835i) q^{38} +(2.52125 - 1.83179i) q^{39} +(1.01374 + 3.11998i) q^{40} +(0.864979 - 2.66213i) q^{41} +(-0.809017 - 0.587785i) q^{42} +8.17461 q^{43} +(-1.24920 + 3.07238i) q^{44} +3.28054 q^{45} +(3.50750 + 2.54835i) q^{46} +(-3.52125 + 10.8373i) q^{47} +(-0.309017 - 0.951057i) q^{48} +(-0.809017 + 0.587785i) q^{49} +(-4.66152 + 3.38679i) q^{50} +(-1.21847 - 3.75006i) q^{51} +(0.963031 - 2.96390i) q^{52} +(1.41696 + 1.02948i) q^{53} -1.00000 q^{54} +(-10.8521 - 0.782879i) q^{55} -1.00000 q^{56} +(4.56732 + 3.31835i) q^{57} +(-3.11180 + 9.57712i) q^{58} +(-2.68536 - 8.26468i) q^{59} +(2.65401 - 1.92825i) q^{60} +(-7.12714 + 5.17817i) q^{61} +(3.27144 + 10.0684i) q^{62} +(-0.309017 + 0.951057i) q^{63} +(-0.809017 - 0.587785i) q^{64} +10.2236 q^{65} +(3.30803 + 0.238643i) q^{66} -10.9875 q^{67} +(-3.18999 - 2.31767i) q^{68} +(1.33975 - 4.12332i) q^{69} +(-1.01374 - 3.11998i) q^{70} +(-2.85410 + 2.07363i) q^{71} +(-0.809017 + 0.587785i) q^{72} +(0.196232 + 0.603941i) q^{73} +(0.249811 - 0.768840i) q^{74} +(4.66152 + 3.38679i) q^{75} +5.64552 q^{76} +(1.24920 - 3.07238i) q^{77} -3.11643 q^{78} +(9.41232 + 6.83845i) q^{79} +(1.01374 - 3.11998i) q^{80} +(0.309017 + 0.951057i) q^{81} +(-2.26454 + 1.64529i) q^{82} +(-12.5071 + 9.08696i) q^{83} +(0.309017 + 0.951057i) q^{84} +(3.99724 - 12.3022i) q^{85} +(-6.61340 - 4.80491i) q^{86} +10.0700 q^{87} +(2.81652 - 1.75134i) q^{88} +7.99802 q^{89} +(-2.65401 - 1.92825i) q^{90} +(-0.963031 + 2.96390i) q^{91} +(-1.33975 - 4.12332i) q^{92} +(8.56473 - 6.22264i) q^{93} +(9.21875 - 6.69781i) q^{94} +(5.72311 + 17.6139i) q^{95} +(-0.309017 + 0.951057i) q^{96} +(11.0500 + 8.02830i) q^{97} +1.00000 q^{98} +(-0.795274 - 3.21987i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 6 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 - 6 * q^5 + 2 * q^6 + 2 * q^7 - 2 * q^8 - 2 * q^9	\( 8 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 6 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9} + 4 q^{10} + 14 q^{11} - 8 q^{12} + 8 q^{13} + 2 q^{14} - 4 q^{15} - 2 q^{16} - 4 q^{17} - 2 q^{18} - 2 q^{19} - 6 q^{20} + 8 q^{21} - 6 q^{22} + 4 q^{23} + 2 q^{24} - 8 q^{25} - 12 q^{26} + 2 q^{27} + 2 q^{28} + 4 q^{29} - 4 q^{30} - 10 q^{31} + 8 q^{32} + 6 q^{33} - 4 q^{34} + 6 q^{35} - 2 q^{36} - 20 q^{37} - 12 q^{38} - 8 q^{39} + 4 q^{40} + 12 q^{41} - 2 q^{42} + 48 q^{43} - 6 q^{44} + 4 q^{45} + 4 q^{46} + 2 q^{48} - 2 q^{49} + 2 q^{50} - 6 q^{51} - 12 q^{52} - 12 q^{53} - 8 q^{54} - 8 q^{55} - 8 q^{56} + 12 q^{57} + 4 q^{58} + 12 q^{59} + 6 q^{60} - 32 q^{61} + 20 q^{62} + 2 q^{63} - 2 q^{64} + 24 q^{65} - 4 q^{66} - 48 q^{67} - 4 q^{68} + 6 q^{69} - 4 q^{70} + 4 q^{71} - 2 q^{72} - 20 q^{74} - 2 q^{75} + 28 q^{76} + 6 q^{77} - 8 q^{78} + 40 q^{79} + 4 q^{80} - 2 q^{81} - 18 q^{82} - 32 q^{83} - 2 q^{84} - 42 q^{85} - 32 q^{86} + 16 q^{87} - 6 q^{88} + 12 q^{89} - 6 q^{90} + 12 q^{91} - 6 q^{92} + 10 q^{93} + 54 q^{95} + 2 q^{96} + 8 q^{97} + 8 q^{98} - 6 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 6 * q^5 + 2 * q^6 + 2 * q^7 - 2 * q^8 - 2 * q^9 + 4 * q^10 + 14 * q^11 - 8 * q^12 + 8 * q^13 + 2 * q^14 - 4 * q^15 - 2 * q^16 - 4 * q^17 - 2 * q^18 - 2 * q^19 - 6 * q^20 + 8 * q^21 - 6 * q^22 + 4 * q^23 + 2 * q^24 - 8 * q^25 - 12 * q^26 + 2 * q^27 + 2 * q^28 + 4 * q^29 - 4 * q^30 - 10 * q^31 + 8 * q^32 + 6 * q^33 - 4 * q^34 + 6 * q^35 - 2 * q^36 - 20 * q^37 - 12 * q^38 - 8 * q^39 + 4 * q^40 + 12 * q^41 - 2 * q^42 + 48 * q^43 - 6 * q^44 + 4 * q^45 + 4 * q^46 + 2 * q^48 - 2 * q^49 + 2 * q^50 - 6 * q^51 - 12 * q^52 - 12 * q^53 - 8 * q^54 - 8 * q^55 - 8 * q^56 + 12 * q^57 + 4 * q^58 + 12 * q^59 + 6 * q^60 - 32 * q^61 + 20 * q^62 + 2 * q^63 - 2 * q^64 + 24 * q^65 - 4 * q^66 - 48 * q^67 - 4 * q^68 + 6 * q^69 - 4 * q^70 + 4 * q^71 - 2 * q^72 - 20 * q^74 - 2 * q^75 + 28 * q^76 + 6 * q^77 - 8 * q^78 + 40 * q^79 + 4 * q^80 - 2 * q^81 - 18 * q^82 - 32 * q^83 - 2 * q^84 - 42 * q^85 - 32 * q^86 + 16 * q^87 - 6 * q^88 + 12 * q^89 - 6 * q^90 + 12 * q^91 - 6 * q^92 + 10 * q^93 + 54 * q^95 + 2 * q^96 + 8 * q^97 + 8 * q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$5$	−2.65401	+	1.92825i	−1.18691	+	0.862341i	−0.992934	−	0.118665i	$-0.962139\pi$
$5$	−2.65401	+	1.92825i	−1.18691	+	0.862341i	−0.193977	+	0.981006i	$0.562139\pi$
$6$	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
$10$	3.28054			1.03740
$11$	2.53598	+	2.13748i	0.764627	+	0.644473i
$11$	2.53598	+	2.13748i	0.764627	+	0.644473i
$12$	−1.00000			−0.288675
$13$	−2.52125	−	1.83179i	−0.699268	−	0.508048i	0.180425	−	0.983589i	$-0.442253\pi$
$13$	−2.52125	−	1.83179i	−0.699268	−	0.508048i	−0.879694	+	0.475540i	$0.842253\pi$
$14$	−0.309017	+	0.951057i	−0.0825883	+	0.254181i
$15$	−1.01374	−	3.11998i	−0.261747	−	0.805576i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−3.18999	+	2.31767i	−0.773687	+	0.562117i	−0.903078	−	0.429477i	$-0.858698\pi$
$17$	−3.18999	+	2.31767i	−0.773687	+	0.562117i	0.129391	+	0.991594i	$0.458698\pi$
$18$	0.309017	+	0.951057i	0.0728360	+	0.224166i
$19$	1.74456	−	5.36921i	0.400230	−	1.23178i	−0.524583	−	0.851359i	$-0.675779\pi$
$19$	1.74456	−	5.36921i	0.400230	−	1.23178i	0.924813	−	0.380422i	$-0.124221\pi$
$20$	−2.65401	−	1.92825i	−0.593456	−	0.431171i
$21$	1.00000			0.218218
$22$	−0.795274	−	3.21987i	−0.169553	−	0.686478i
$23$	−4.33551			−0.904017			−0.452009	−	0.892014i	$-0.649292\pi$
$23$	−4.33551			−0.904017			−0.452009	+	0.892014i	$0.649292\pi$
$24$	0.809017	+	0.587785i	0.165140	+	0.119981i
$25$	1.78054	−	5.47994i	0.356108	−	1.09599i
$26$	0.963031	+	2.96390i	0.188866	+	0.581270i
$27$	0.809017	−	0.587785i	0.155695	−	0.113119i
$28$	0.809017	−	0.587785i	0.152890	−	0.111081i
$29$	−3.11180	−	9.57712i	−0.577846	−	1.77843i	−0.626277	−	0.779600i	$-0.715422\pi$
$29$	−3.11180	−	9.57712i	−0.577846	−	1.77843i	0.0484313	−	0.998827i	$-0.484578\pi$
$30$	−1.01374	+	3.11998i	−0.185083	+	0.569628i
$31$	−8.56473	−	6.22264i	−1.53827	−	1.11762i	−0.951408	−	0.307934i	$-0.900362\pi$
$31$	−8.56473	−	6.22264i	−1.53827	−	1.11762i	−0.586864	−	0.809686i	$-0.699638\pi$
$32$	1.00000			0.176777
$33$	−2.81652	+	1.75134i	−0.490294	+	0.304870i
$34$	3.94305			0.676227
$35$	2.65401	+	1.92825i	0.448610	+	0.325934i
$36$	0.309017	−	0.951057i	0.0515028	−	0.158509i
$37$	0.249811	+	0.768840i	0.0410687	+	0.126396i	0.969489	−	0.245136i	$-0.0788325\pi$
$37$	0.249811	+	0.768840i	0.0410687	+	0.126396i	−0.928420	+	0.371532i	$0.878833\pi$
$38$	−4.56732	+	3.31835i	−0.740917	+	0.538308i
$39$	2.52125	−	1.83179i	0.403723	−	0.293322i
$40$	1.01374	+	3.11998i	0.160287	+	0.493312i
$41$	0.864979	−	2.66213i	0.135087	−	0.415755i	−0.860517	−	0.509422i	$-0.829859\pi$
$41$	0.864979	−	2.66213i	0.135087	−	0.415755i	0.995604	+	0.0936675i	$0.0298591\pi$
$42$	−0.809017	−	0.587785i	−0.124834	−	0.0906972i
$43$	8.17461			1.24662			0.623308	−	0.781976i	$-0.285788\pi$
$43$	8.17461			1.24662			0.623308	+	0.781976i	$0.285788\pi$
$44$	−1.24920	+	3.07238i	−0.188324	+	0.463178i
$45$	3.28054			0.489034
$46$	3.50750	+	2.54835i	0.517153	+	0.375734i
$47$	−3.52125	+	10.8373i	−0.513627	+	1.58078i	0.272140	+	0.962258i	$0.412269\pi$
$47$	−3.52125	+	10.8373i	−0.513627	+	1.58078i	−0.785767	+	0.618523i	$0.787731\pi$
$48$	−0.309017	−	0.951057i	−0.0446028	−	0.137273i
$49$	−0.809017	+	0.587785i	−0.115574	+	0.0839693i
$50$	−4.66152	+	3.38679i	−0.659238	+	0.478965i
$51$	−1.21847	−	3.75006i	−0.170620	−	0.525114i
$52$	0.963031	−	2.96390i	0.133548	−	0.411020i
$53$	1.41696	+	1.02948i	0.194634	+	0.141410i	0.680834	−	0.732438i	$-0.261617\pi$
$53$	1.41696	+	1.02948i	0.194634	+	0.141410i	−0.486200	+	0.873847i	$0.661617\pi$
$54$	−1.00000			−0.136083
$55$	−10.8521	−	0.782879i	−1.46330	−	0.105563i
$56$	−1.00000			−0.133631
$57$	4.56732	+	3.31835i	0.604957	+	0.439527i
$58$	−3.11180	+	9.57712i	−0.408599	+	1.25754i
$59$	−2.68536	−	8.26468i	−0.349604	−	1.07597i	−0.959073	−	0.283159i	$-0.908617\pi$
$59$	−2.68536	−	8.26468i	−0.349604	−	1.07597i	0.609469	−	0.792810i	$-0.291383\pi$
$60$	2.65401	−	1.92825i	0.342632	−	0.248937i
$61$	−7.12714	+	5.17817i	−0.912537	+	0.662997i	−0.941655	−	0.336579i	$-0.890730\pi$
$61$	−7.12714	+	5.17817i	−0.912537	+	0.662997i	0.0291185	+	0.999576i	$0.490730\pi$
$62$	3.27144	+	10.0684i	0.415473	+	1.27869i
$63$	−0.309017	+	0.951057i	−0.0389325	+	0.119822i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	10.2236			1.26808
$66$	3.30803	+	0.238643i	0.407190	+	0.0293749i
$67$	−10.9875			−1.34234			−0.671170	−	0.741304i	$-0.734208\pi$
$67$	−10.9875			−1.34234			−0.671170	+	0.741304i	$0.734208\pi$
$68$	−3.18999	−	2.31767i	−0.386844	−	0.281058i
$69$	1.33975	−	4.12332i	0.161287	−	0.496389i
$70$	−1.01374	−	3.11998i	−0.121165	−	0.372909i
$71$	−2.85410	+	2.07363i	−0.338720	+	0.246094i	−0.744121	−	0.668044i	$-0.767132\pi$
$71$	−2.85410	+	2.07363i	−0.338720	+	0.246094i	0.405402	+	0.914139i	$0.367132\pi$
$72$	−0.809017	+	0.587785i	−0.0953436	+	0.0692712i
$73$	0.196232	+	0.603941i	0.0229673	+	0.0706860i	0.961883	−	0.273461i	$-0.0881683\pi$
$73$	0.196232	+	0.603941i	0.0229673	+	0.0706860i	−0.938916	+	0.344147i	$0.888168\pi$
$74$	0.249811	−	0.768840i	0.0290400	−	0.0893758i
$75$	4.66152	+	3.38679i	0.538266	+	0.391073i
$76$	5.64552			0.647586
$77$	1.24920	−	3.07238i	0.142360	−	0.350130i
$78$	−3.11643			−0.352867
$79$	9.41232	+	6.83845i	1.05897	+	0.769386i	0.973897	−	0.226989i	$-0.0728882\pi$
$79$	9.41232	+	6.83845i	1.05897	+	0.769386i	0.0850713	+	0.996375i	$0.472888\pi$
$80$	1.01374	−	3.11998i	0.113340	−	0.348824i
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$	−2.26454	+	1.64529i	−0.250077	+	0.181692i
$83$	−12.5071	+	9.08696i	−1.37284	+	0.997423i	−0.375326	+	0.926893i	$0.622469\pi$
$83$	−12.5071	+	9.08696i	−1.37284	+	0.997423i	−0.997510	+	0.0705305i	$0.977531\pi$
$84$	0.309017	+	0.951057i	0.0337165	+	0.103769i
$85$	3.99724	−	12.3022i	0.433561	−	1.33437i
$86$	−6.61340	−	4.80491i	−0.713141	−	0.518127i
$87$	10.0700			1.07962
$88$	2.81652	−	1.75134i	0.300242	−	0.186694i
$89$	7.99802			0.847789			0.423894	−	0.905712i	$-0.360663\pi$
$89$	7.99802			0.847789			0.423894	+	0.905712i	$0.360663\pi$
$90$	−2.65401	−	1.92825i	−0.279758	−	0.203256i
$91$	−0.963031	+	2.96390i	−0.100953	+	0.310702i
$92$	−1.33975	−	4.12332i	−0.139678	−	0.429886i
$93$	8.56473	−	6.22264i	0.888121	−	0.645258i
$94$	9.21875	−	6.69781i	0.950841	−	0.690827i
$95$	5.72311	+	17.6139i	0.587178	+	1.80715i
$96$	−0.309017	+	0.951057i	−0.0315389	+	0.0970668i
$97$	11.0500	+	8.02830i	1.12196	+	0.815150i	0.984505	−	0.175358i	$-0.0561084\pi$
$97$	11.0500	+	8.02830i	1.12196	+	0.815150i	0.137453	+	0.990508i	$0.456108\pi$
$98$	1.00000			0.101015
$99$	−0.795274	−	3.21987i	−0.0799280	−	0.323609i
$100$	5.76195			0.576195
$101$	−4.12295	−	2.99550i	−0.410249	−	0.298063i	0.363454	−	0.931612i	$-0.381597\pi$
$101$	−4.12295	−	2.99550i	−0.410249	−	0.298063i	−0.773703	+	0.633549i	$0.781597\pi$
$102$	−1.21847	+	3.75006i	−0.120646	+	0.371312i
$103$	0.384221	+	1.18251i	0.0378585	+	0.116516i	0.968200	−	0.250179i	$-0.0804893\pi$
$103$	0.384221	+	1.18251i	0.0378585	+	0.116516i	−0.930341	+	0.366695i	$0.880489\pi$
$104$	−2.52125	+	1.83179i	−0.247229	+	0.179622i
$105$	−2.65401	+	1.92825i	−0.259005	+	0.188178i
$106$	−0.541229	−	1.66573i	−0.0525689	−	0.161790i
$107$	0.508494	−	1.56498i	0.0491579	−	0.151293i	−0.923464	−	0.383684i	$-0.874655\pi$
$107$	0.508494	−	1.56498i	0.0491579	−	0.151293i	0.972622	+	0.232392i	$0.0746551\pi$
$108$	0.809017	+	0.587785i	0.0778477	+	0.0565597i
$109$	5.69771			0.545741			0.272871	−	0.962051i	$-0.412027\pi$
$109$	5.69771			0.545741			0.272871	+	0.962051i	$0.412027\pi$
$110$	8.31939	+	7.01208i	0.793223	+	0.668576i
$111$	−0.808406			−0.0767305
$112$	0.809017	+	0.587785i	0.0764449	+	0.0555405i
$113$	4.70336	−	14.4755i	0.442455	−	1.36174i	−0.442796	−	0.896622i	$-0.646013\pi$
$113$	4.70336	−	14.4755i	0.442455	−	1.36174i	0.885251	−	0.465114i	$-0.153987\pi$
$114$	−1.74456	−	5.36921i	−0.163393	−	0.502872i
$115$	11.5065	−	8.35997i	1.07299	−	0.779572i
$116$	8.14679	−	5.91899i	0.756410	−	0.549564i
$117$	0.963031	+	2.96390i	0.0890322	+	0.274013i
$118$	−2.68536	+	8.26468i	−0.247207	+	0.760825i
$119$	3.18999	+	2.31767i	0.292426	+	0.212460i
$120$	−3.28054			−0.299471
$121$	1.86239	+	10.8412i	0.169308	+	0.985563i
$122$	8.80963			0.797586
$123$	2.26454	+	1.64529i	0.204187	+	0.148351i
$124$	3.27144	−	10.0684i	0.293784	−	0.904173i
$125$	0.772426	+	2.37728i	0.0690879	+	0.212631i
$126$	0.809017	−	0.587785i	0.0720730	−	0.0523641i
$127$	−8.18696	+	5.94817i	−0.726475	+	0.527815i	−0.888446	−	0.458981i	$-0.848215\pi$
$127$	−8.18696	+	5.94817i	−0.726475	+	0.527815i	0.161971	+	0.986795i	$0.448215\pi$
$128$	0.309017	+	0.951057i	0.0273135	+	0.0840623i
$129$	−2.52609	+	7.77451i	−0.222410	+	0.684508i
$130$	−8.27106	−	6.00928i	−0.725420	−	0.527048i
$131$	−21.0939			−1.84298			−0.921492	−	0.388396i	$-0.873029\pi$
$131$	−21.0939			−1.84298			−0.921492	+	0.388396i	$0.873029\pi$
$132$	−2.53598	−	2.13748i	−0.220729	−	0.186043i
$133$	−5.64552			−0.489529
$134$	8.88909	+	6.45830i	0.767901	+	0.557913i
$135$	−1.01374	+	3.11998i	−0.0872491	+	0.268525i
$136$	1.21847	+	3.75006i	0.104483	+	0.321565i
$137$	−8.50447	+	6.17886i	−0.726586	+	0.527895i	−0.888481	−	0.458912i	$-0.848239\pi$
$137$	−8.50447	+	6.17886i	−0.726586	+	0.527895i	0.161896	+	0.986808i	$0.448239\pi$
$138$	−3.50750	+	2.54835i	−0.298579	+	0.216930i
$139$	1.34561	+	4.14136i	0.114133	+	0.351265i	0.991765	−	0.128069i	$-0.0408780\pi$
$139$	1.34561	+	4.14136i	0.114133	+	0.351265i	−0.877632	+	0.479335i	$0.840878\pi$
$140$	−1.01374	+	3.11998i	−0.0856769	+	0.263686i
$141$	−9.21875	−	6.69781i	−0.776359	−	0.564057i
$142$	3.52786			0.296052
$143$	−2.47842	−	10.0345i	−0.207256	−	0.839127i
$144$	1.00000			0.0833333
$145$	26.7259	+	19.4175i	2.21946	+	1.61253i
$146$	0.196232	−	0.603941i	0.0162403	−	0.0499825i
$147$	−0.309017	−	0.951057i	−0.0254873	−	0.0784418i
$148$	−0.654014	+	0.475169i	−0.0537596	+	0.0390587i
$149$	1.37999	−	1.00262i	0.113053	−	0.0821378i	−0.529822	−	0.848109i	$-0.677741\pi$
$149$	1.37999	−	1.00262i	0.113053	−	0.0821378i	0.642875	+	0.765971i	$0.277741\pi$
$150$	−1.78054	−	5.47994i	−0.145381	−	0.447436i
$151$	−0.788424	+	2.42652i	−0.0641611	+	0.197467i	−0.977998	−	0.208614i	$-0.933105\pi$
$151$	−0.788424	+	2.42652i	−0.0641611	+	0.197467i	0.913837	+	0.406081i	$0.133105\pi$
$152$	−4.56732	−	3.31835i	−0.370459	−	0.269154i
$153$	3.94305			0.318777
$154$	−2.81652	+	1.75134i	−0.226962	+	0.141127i
$155$	34.7298			2.78956
$156$	2.52125	+	1.83179i	0.201861	+	0.146661i
$157$	0.181095	−	0.557354i	0.0144530	−	0.0444817i	−0.943570	−	0.331173i	$-0.892556\pi$
$157$	0.181095	−	0.557354i	0.0144530	−	0.0444817i	0.958023	+	0.286692i	$0.0925555\pi$
$158$	−3.59519	−	11.0648i	−0.286018	−	0.880272i
$159$	−1.41696	+	1.02948i	−0.112372	+	0.0816430i
$160$	−2.65401	+	1.92825i	−0.209818	+	0.152442i
$161$	1.33975	+	4.12332i	0.105587	+	0.324963i
$162$	0.309017	−	0.951057i	0.0242787	−	0.0747221i
$163$	−10.8541	−	7.88597i	−0.850159	−	0.617677i	0.0750310	−	0.997181i	$-0.476094\pi$
$163$	−10.8541	−	7.88597i	−0.850159	−	0.617677i	−0.925190	+	0.379505i	$0.876094\pi$
$164$	2.79913			0.218575
$165$	4.09805	−	10.0791i	0.319033	−	0.784654i
$166$	15.4597			1.19990
$167$	1.74661	+	1.26899i	0.135157	+	0.0981972i	0.653309	−	0.757091i	$-0.273380\pi$
$167$	1.74661	+	1.26899i	0.135157	+	0.0981972i	−0.518153	+	0.855288i	$0.673380\pi$
$168$	0.309017	−	0.951057i	0.0238412	−	0.0733756i
$169$	−1.01600	−	3.12692i	−0.0781537	−	0.240532i
$170$	−10.4649	+	7.60320i	−0.802622	+	0.583139i
$171$	−4.56732	+	3.31835i	−0.349272	+	0.253761i
$172$	2.52609	+	7.77451i	0.192613	+	0.592801i
$173$	3.71994	−	11.4488i	0.282822	−	0.870436i	−0.704221	−	0.709981i	$-0.748704\pi$
$173$	3.71994	−	11.4488i	0.282822	−	0.870436i	0.987043	−	0.160456i	$-0.0512964\pi$
$174$	−8.14679	−	5.91899i	−0.617606	−	0.448717i
$175$	−5.76195			−0.435563
$176$	−3.30803	−	0.238643i	−0.249352	−	0.0179884i
$177$	8.68999			0.653180
$178$	−6.47054	−	4.70112i	−0.484987	−	0.352364i
$179$	−5.00502	+	15.4039i	−0.374092	+	1.15134i	0.569996	+	0.821647i	$0.306945\pi$
$179$	−5.00502	+	15.4039i	−0.374092	+	1.15134i	−0.944089	+	0.329691i	$0.893055\pi$
$180$	1.01374	+	3.11998i	0.0755600	+	0.232550i
$181$	6.44929	−	4.68568i	0.479372	−	0.348284i	−0.321711	−	0.946838i	$-0.604258\pi$
$181$	6.44929	−	4.68568i	0.479372	−	0.348284i	0.801082	+	0.598554i	$0.204258\pi$
$182$	2.52125	−	1.83179i	0.186887	−	0.135782i
$183$	−2.72232	−	8.37845i	−0.201240	−	0.619353i
$184$	−1.33975	+	4.12332i	−0.0987675	+	0.303975i
$185$	−2.14552	−	1.55881i	−0.157742	−	0.114606i
$186$	−10.5866			−0.776247
$187$	−13.0437	−	0.940981i	−0.953851	−	0.0688114i
$188$	−11.3950			−0.831066
$189$	−0.809017	−	0.587785i	−0.0588473	−	0.0427551i
$190$	5.72311	−	17.6139i	0.415198	−	1.27785i
$191$	−4.01838	−	12.3673i	−0.290760	−	0.894867i	−0.984613	−	0.174750i	$-0.944088\pi$
$191$	−4.01838	−	12.3673i	−0.290760	−	0.894867i	0.693853	−	0.720117i	$-0.255912\pi$
$192$	0.809017	−	0.587785i	0.0583858	−	0.0424197i
$193$	−18.3371	+	13.3227i	−1.31993	+	0.958986i	−0.319997	+	0.947418i	$0.603682\pi$
$193$	−18.3371	+	13.3227i	−1.31993	+	0.958986i	−0.999933	+	0.0115670i	$0.996318\pi$
$194$	−4.22072	−	12.9901i	−0.303030	−	0.932632i
$195$	−3.15926	+	9.72321i	−0.226240	+	0.696294i
$196$	−0.809017	−	0.587785i	−0.0577869	−	0.0419847i
$197$	−0.153197			−0.0109148			−0.00545740	−	0.999985i	$-0.501737\pi$
$197$	−0.153197			−0.0109148			−0.00545740	+	0.999985i	$0.501737\pi$
$198$	−1.24920	+	3.07238i	−0.0887768	+	0.218344i
$199$	−18.2216			−1.29170			−0.645848	−	0.763466i	$-0.723496\pi$
$199$	−18.2216			−1.29170			−0.645848	+	0.763466i	$0.723496\pi$
$200$	−4.66152	−	3.38679i	−0.329619	−	0.239482i
$201$	3.39533	−	10.4498i	0.239488	−	0.737069i
$202$	1.57483	+	4.84682i	0.110804	+	0.341021i
$203$	−8.14679	+	5.91899i	−0.571792	+	0.415431i
$204$	3.18999	−	2.31767i	0.223344	−	0.162269i
$205$	2.83760	+	8.73323i	0.198186	+	0.609955i
$206$	0.384221	−	1.18251i	0.0267700	−	0.0823895i
$207$	3.50750	+	2.54835i	0.243788	+	0.177123i
$208$	3.11643			0.216086
$209$	15.9007	−	9.88725i	1.09988	−	0.683915i
$210$	3.28054			0.226379
$211$	−8.38749	−	6.09387i	−0.577419	−	0.419519i	0.260374	−	0.965508i	$-0.416154\pi$
$211$	−8.38749	−	6.09387i	−0.577419	−	0.419519i	−0.837793	+	0.545989i	$0.816154\pi$
$212$	−0.541229	+	1.66573i	−0.0371718	+	0.114403i
$213$	−1.09017	−	3.35520i	−0.0746972	−	0.229894i
$214$	−1.33125	+	0.967213i	−0.0910026	+	0.0661173i
$215$	−21.6955	+	15.7627i	−1.47962	+	1.07501i
$216$	−0.309017	−	0.951057i	−0.0210259	−	0.0647112i
$217$	−3.27144	+	10.0684i	−0.222080	+	0.683491i
$218$	−4.60954	−	3.34903i	−0.312197	−	0.226825i
$219$	−0.635021			−0.0429108
$220$	−2.60893	−	10.5629i	−0.175894	−	0.712151i
$221$	12.2883			0.826597
$222$	0.654014	+	0.475169i	0.0438945	+	0.0318913i
$223$	0.142420	−	0.438324i	0.00953717	−	0.0293524i	−0.946175	−	0.323656i	$-0.895088\pi$
$223$	0.142420	−	0.438324i	0.00953717	−	0.0293524i	0.955712	+	0.294304i	$0.0950878\pi$
$224$	−0.309017	−	0.951057i	−0.0206471	−	0.0635451i
$225$	−4.66152	+	3.38679i	−0.310768	+	0.225786i
$226$	−12.3136	+	8.94632i	−0.819085	+	0.595100i
$227$	−5.76495	−	17.7427i	−0.382633	−	1.17762i	−0.938183	−	0.346140i	$-0.887492\pi$
$227$	−5.76495	−	17.7427i	−0.382633	−	1.17762i	0.555550	−	0.831483i	$-0.312508\pi$
$228$	−1.74456	+	5.36921i	−0.115536	+	0.355585i
$229$	−10.9611	−	7.96367i	−0.724327	−	0.526254i	0.163437	−	0.986554i	$-0.447742\pi$
$229$	−10.9611	−	7.96367i	−0.724327	−	0.526254i	−0.887764	+	0.460300i	$0.847742\pi$
$230$	−14.2228			−0.937826
$231$	2.53598	+	2.13748i	0.166855	+	0.140636i
$232$	−10.0700			−0.661127
$233$	2.20572	+	1.60255i	0.144501	+	0.104986i	0.657687	−	0.753291i	$-0.271535\pi$
$233$	2.20572	+	1.60255i	0.144501	+	0.104986i	−0.513186	+	0.858277i	$0.671535\pi$
$234$	0.963031	−	2.96390i	0.0629553	−	0.193757i
$235$	−11.5516	−	35.5522i	−0.753543	−	2.31917i
$236$	7.03035	−	5.10785i	0.457637	−	0.332493i
$237$	−9.41232	+	6.83845i	−0.611396	+	0.444205i
$238$	−1.21847	−	3.75006i	−0.0789816	−	0.243080i
$239$	−0.160630	+	0.494369i	−0.0103903	+	0.0319781i	−0.956117	−	0.292984i	$-0.905352\pi$
$239$	−0.160630	+	0.494369i	−0.0103903	+	0.0319781i	0.945727	+	0.324962i	$0.105352\pi$
$240$	2.65401	+	1.92825i	0.171316	+	0.124468i
$241$	7.06349			0.455000			0.227500	−	0.973778i	$-0.426945\pi$
$241$	7.06349			0.455000			0.227500	+	0.973778i	$0.426945\pi$
$242$	4.86559	−	9.86540i	0.312772	−	0.634172i
$243$	−1.00000			−0.0641500
$244$	−7.12714	−	5.17817i	−0.456268	−	0.331498i
$245$	1.01374	−	3.11998i	0.0647657	−	0.199328i
$246$	−0.864979	−	2.66213i	−0.0551490	−	0.169731i
$247$	−14.2338	+	10.3414i	−0.905672	+	0.658009i
$248$	−8.56473	+	6.22264i	−0.543861	+	0.395138i
$249$	−4.77730	−	14.7030i	−0.302749	−	0.931765i
$250$	0.772426	−	2.37728i	0.0488525	−	0.150353i
$251$	16.4947	+	11.9841i	1.04113	+	0.756427i	0.970506	−	0.241075i	$-0.0775001\pi$
$251$	16.4947	+	11.9841i	1.04113	+	0.756427i	0.0706267	+	0.997503i	$0.477500\pi$
$252$	−1.00000			−0.0629941
$253$	−10.9948	−	9.26706i	−0.691236	−	0.582615i
$254$	10.1196			0.634962
$255$	10.4649	+	7.60320i	0.655338	+	0.476131i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	4.85349	+	14.9375i	0.302752	+	0.931776i	0.980506	+	0.196487i	$0.0629535\pi$
$257$	4.85349	+	14.9375i	0.302752	+	0.931776i	−0.677754	+	0.735289i	$0.737047\pi$
$258$	6.61340	−	4.80491i	0.411732	−	0.299141i
$259$	0.654014	−	0.475169i	0.0406385	−	0.0295256i
$260$	3.15926	+	9.72321i	0.195929	+	0.603008i
$261$	−3.11180	+	9.57712i	−0.192615	+	0.592809i
$262$	17.0653	+	12.3987i	1.05430	+	0.765994i
$263$	3.62411			0.223472			0.111736	−	0.993738i	$-0.464359\pi$
$263$	3.62411			0.223472			0.111736	+	0.993738i	$0.464359\pi$
$264$	0.795274	+	3.21987i	0.0489457	+	0.198169i
$265$	−5.74572			−0.352957
$266$	4.56732	+	3.31835i	0.280040	+	0.203461i
$267$	−2.47152	+	7.60657i	−0.151255	+	0.465515i
$268$	−3.39533	−	10.4498i	−0.207403	−	0.638320i
$269$	1.66571	−	1.21021i	0.101560	−	0.0737877i	−0.535846	−	0.844316i	$-0.680007\pi$
$269$	1.66571	−	1.21021i	0.101560	−	0.0737877i	0.637406	+	0.770528i	$0.280007\pi$
$270$	2.65401	−	1.92825i	0.161518	−	0.117350i
$271$	7.41733	+	22.8282i	0.450571	+	1.38671i	0.876257	+	0.481844i	$0.160033\pi$
$271$	7.41733	+	22.8282i	0.450571	+	1.38671i	−0.425686	+	0.904871i	$0.639967\pi$
$272$	1.21847	−	3.75006i	0.0738806	−	0.227381i
$273$	−2.52125	−	1.83179i	−0.152593	−	0.110865i
$274$	10.5121			0.635059
$275$	16.2287	−	10.0912i	0.978626	−	0.608520i
$276$	4.33551			0.260967
$277$	−7.76642	−	5.64264i	−0.466639	−	0.339033i	0.329491	−	0.944159i	$-0.393123\pi$
$277$	−7.76642	−	5.64264i	−0.466639	−	0.339033i	−0.796130	+	0.605126i	$0.793123\pi$
$278$	1.34561	−	4.14136i	0.0807042	−	0.248382i
$279$	3.27144	+	10.0684i	0.195856	+	0.602782i
$280$	2.65401	−	1.92825i	0.158608	−	0.115235i
$281$	10.8564	−	7.88766i	0.647640	−	0.470538i	−0.214826	−	0.976652i	$-0.568919\pi$
$281$	10.8564	−	7.88766i	0.647640	−	0.470538i	0.862467	+	0.506114i	$0.168919\pi$
$282$	3.52125	+	10.8373i	0.209687	+	0.645351i
$283$	−8.46468	+	26.0516i	−0.503173	+	1.54861i	0.300648	+	0.953735i	$0.402797\pi$
$283$	−8.46468	+	26.0516i	−0.503173	+	1.54861i	−0.803821	+	0.594871i	$0.797203\pi$
$284$	−2.85410	−	2.07363i	−0.169360	−	0.123047i
$285$	−18.5204			−1.09705
$286$	−3.89305	+	9.57486i	−0.230201	+	0.566173i
$287$	−2.79913			−0.165227
$288$	−0.809017	−	0.587785i	−0.0476718	−	0.0346356i
$289$	−0.448804	+	1.38128i	−0.0264002	+	0.0812516i
$290$	−10.2084	−	31.4181i	−0.599456	−	1.84494i
$291$	−11.0500	+	8.02830i	−0.647763	+	0.470627i
$292$	−0.513743	+	0.373256i	−0.0300645	+	0.0218432i
$293$	2.03195	+	6.25371i	0.118708	+	0.365346i	0.992702	−	0.120590i	$-0.0384788\pi$
$293$	2.03195	+	6.25371i	0.118708	+	0.365346i	−0.873994	+	0.485936i	$0.838479\pi$
$294$	−0.309017	+	0.951057i	−0.0180222	+	0.0554667i
$295$	23.0634	+	16.7565i	1.34280	+	0.975602i
$296$	0.808406			0.0469876
$297$	3.30803	+	0.238643i	0.191951	+	0.0138475i
$298$	−1.70576			−0.0988120
$299$	10.9309	+	7.94177i	0.632151	+	0.459284i
$300$	−1.78054	+	5.47994i	−0.102800	+	0.316385i
$301$	−2.52609	−	7.77451i	−0.145602	−	0.448115i
$302$	2.06412	−	1.49967i	0.118777	−	0.0862964i
$303$	4.12295	−	2.99550i	0.236857	−	0.172087i
$304$	1.74456	+	5.36921i	0.100057	+	0.307945i
$305$	8.93070	−	27.4859i	0.511370	−	1.57384i
$306$	−3.18999	−	2.31767i	−0.182360	−	0.132492i
$307$	3.91024			0.223169			0.111585	−	0.993755i	$-0.464407\pi$
$307$	3.91024			0.223169			0.111585	+	0.993755i	$0.464407\pi$
$308$	3.30803	+	0.238643i	0.188492	+	0.0135980i
$309$	−1.24337			−0.0707326
$310$	−28.0970	−	20.4136i	−1.59580	−	1.15942i
$311$	−3.76107	+	11.5754i	−0.213270	+	0.656379i	0.786001	+	0.618225i	$0.212148\pi$
$311$	−3.76107	+	11.5754i	−0.213270	+	0.656379i	−0.999272	+	0.0381543i	$0.987852\pi$
$312$	−0.963031	−	2.96390i	−0.0545209	−	0.167798i
$313$	−3.57676	+	2.59867i	−0.202170	+	0.146885i	−0.684264	−	0.729234i	$-0.739876\pi$
$313$	−3.57676	+	2.59867i	−0.202170	+	0.146885i	0.482094	+	0.876120i	$0.339876\pi$
$314$	−0.474114	+	0.344464i	−0.0267558	+	0.0194392i
$315$	−1.01374	−	3.11998i	−0.0571180	−	0.175791i
$316$	−3.59519	+	11.0648i	−0.202245	+	0.622446i
$317$	−25.4927	−	18.5215i	−1.43181	−	1.04027i	−0.989676	−	0.143323i	$-0.954221\pi$
$317$	−25.4927	−	18.5215i	−1.43181	−	1.04027i	−0.442135	−	0.896948i	$-0.645779\pi$
$318$	1.75146			0.0982167
$319$	12.5794	−	30.9388i	0.704312	−	1.73224i
$320$	3.28054			0.183388
$321$	1.33125	+	0.967213i	0.0743033	+	0.0539845i
$322$	1.33975	−	4.12332i	0.0746612	−	0.229784i
$323$	6.87889	+	21.1711i	0.382752	+	1.17799i
$324$	−0.809017	+	0.587785i	−0.0449454	+	0.0326547i
$325$	−14.5273	+	10.5547i	−0.805830	+	0.585470i
$326$	4.14590	+	12.7598i	0.229620	+	0.706698i
$327$	−1.76069	+	5.41884i	−0.0973663	+	0.299663i
$328$	−2.26454	−	1.64529i	−0.125038	−	0.0908458i
$329$	11.3950			0.628227
$330$	−9.23972	+	5.74536i	−0.508630	+	0.316271i
$331$	−5.90178			−0.324391			−0.162195	−	0.986759i	$-0.551858\pi$
$331$	−5.90178			−0.324391			−0.162195	+	0.986759i	$0.551858\pi$
$332$	−12.5071	−	9.08696i	−0.686418	−	0.498712i
$333$	0.249811	−	0.768840i	0.0136896	−	0.0421321i
$334$	−0.667146	−	2.05326i	−0.0365046	−	0.112350i
$335$	29.1610	−	21.1867i	1.59324	−	1.15756i
$336$	−0.809017	+	0.587785i	−0.0441355	+	0.0320663i
$337$	−2.89895	−	8.92206i	−0.157916	−	0.486016i	0.840529	−	0.541767i	$-0.182245\pi$
$337$	−2.89895	−	8.92206i	−0.157916	−	0.486016i	−0.998445	+	0.0557515i	$0.982245\pi$
$338$	−1.01600	+	3.12692i	−0.0552630	+	0.170082i
$339$	12.3136	+	8.94632i	0.668781	+	0.485897i
$340$	12.9353			0.701517
$341$	−8.41924	−	34.0874i	−0.455927	−	1.84594i
$342$	5.64552			0.305275
$343$	0.809017	+	0.587785i	0.0436828	+	0.0317374i
$344$	2.52609	−	7.77451i	0.136198	−	0.419174i
$345$	4.39510	+	13.5267i	0.236624	+	0.728254i
$346$	−9.73893	+	7.07575i	−0.523568	+	0.380395i
$347$	22.5904	−	16.4129i	1.21272	−	0.881092i	0.217244	−	0.976117i	$-0.430293\pi$
$347$	22.5904	−	16.4129i	1.21272	−	0.881092i	0.995475	+	0.0950256i	$0.0302933\pi$
$348$	3.11180	+	9.57712i	0.166810	+	0.513388i
$349$	8.67288	−	26.6924i	0.464249	−	1.42881i	−0.395677	−	0.918390i	$-0.629490\pi$
$349$	8.67288	−	26.6924i	0.464249	−	1.42881i	0.859925	−	0.510420i	$-0.170510\pi$
$350$	4.66152	+	3.38679i	0.249169	+	0.181032i
$351$	−3.11643			−0.166343
$352$	2.53598	+	2.13748i	0.135168	+	0.113928i
$353$	−6.63461			−0.353125			−0.176562	−	0.984289i	$-0.556498\pi$
$353$	−6.63461			−0.353125			−0.176562	+	0.984289i	$0.556498\pi$
$354$	−7.03035	−	5.10785i	−0.373659	−	0.271479i
$355$	3.57635	−	11.0069i	0.189813	−	0.584184i
$356$	2.47152	+	7.60657i	0.130991	+	0.403147i
$357$	−3.18999	+	2.31767i	−0.168832	+	0.122664i
$358$	13.1033	−	9.52011i	0.692531	−	0.503153i
$359$	−2.87248	−	8.84059i	−0.151604	−	0.466589i	0.846197	−	0.532870i	$-0.178887\pi$
$359$	−2.87248	−	8.84059i	−0.151604	−	0.466589i	−0.997801	+	0.0662813i	$0.978887\pi$
$360$	1.01374	−	3.11998i	0.0534290	−	0.164437i
$361$	−10.4136	−	7.56591i	−0.548083	−	0.398206i
$362$	−7.97176			−0.418986
$363$	−10.8861	−	1.57888i	−0.571372	−	0.0828695i
$364$	−3.11643			−0.163346
$365$	−1.68536	−	1.22448i	−0.0882156	−	0.0640924i
$366$	−2.72232	+	8.37845i	−0.142298	+	0.437949i
$367$	6.60771	+	20.3364i	0.344919	+	1.06155i	0.961627	+	0.274361i	$0.0884662\pi$
$367$	6.60771	+	20.3364i	0.344919	+	1.06155i	−0.616707	+	0.787192i	$0.711534\pi$
$368$	3.50750	−	2.54835i	0.182841	−	0.132842i
$369$	−2.26454	+	1.64529i	−0.117887	+	0.0856502i
$370$	0.819516	+	2.52221i	0.0426046	+	0.131123i
$371$	0.541229	−	1.66573i	0.0280992	−	0.0864805i
$372$	8.56473	+	6.22264i	0.444061	+	0.322629i
$373$	26.2248			1.35787			0.678935	−	0.734199i	$-0.262442\pi$
$373$	26.2248			1.35787			0.678935	+	0.734199i	$0.262442\pi$
$374$	9.99949	+	8.42818i	0.517062	+	0.435811i
$375$	−2.49962			−0.129080
$376$	9.21875	+	6.69781i	0.475421	+	0.345413i
$377$	−9.69771	+	29.8465i	−0.499457	+	1.53717i
$378$	0.309017	+	0.951057i	0.0158941	+	0.0489171i
$379$	14.8793	−	10.8104i	0.764297	−	0.555294i	−0.135928	−	0.990719i	$-0.543402\pi$
$379$	14.8793	−	10.8104i	0.764297	−	0.555294i	0.900225	+	0.435424i	$0.143402\pi$
$380$	−14.9833	+	10.8860i	−0.768627	+	0.558440i
$381$	−3.12714	−	9.62434i	−0.160208	−	0.493070i
$382$	−4.01838	+	12.3673i	−0.205598	+	0.632766i
$383$	−13.0627	−	9.49060i	−0.667472	−	0.484947i	0.201706	−	0.979446i	$-0.435351\pi$
$383$	−13.0627	−	9.49060i	−0.667472	−	0.484947i	−0.869178	+	0.494499i	$0.835351\pi$
$384$	−1.00000			−0.0510310
$385$	2.60893	+	10.5629i	0.132963	+	0.538336i
$386$	22.6659			1.15366
$387$	−6.61340	−	4.80491i	−0.336178	−	0.244247i
$388$	−4.22072	+	12.9901i	−0.214275	+	0.659470i
$389$	8.32801	+	25.6310i	0.422247	+	1.29954i	0.905606	+	0.424120i	$0.139417\pi$
$389$	8.32801	+	25.6310i	0.422247	+	1.29954i	−0.483359	+	0.875422i	$0.660583\pi$
$390$	8.27106	−	6.00928i	0.418821	−	0.304292i
$391$	13.8303	−	10.0483i	0.699427	−	0.508163i
$392$	0.309017	+	0.951057i	0.0156077	+	0.0480356i
$393$	6.51838	−	20.0615i	0.328809	−	1.01197i
$394$	0.123939	+	0.0900467i	0.00624394	+	0.00453649i
$395$	−38.1667			−1.92037
$396$	2.81652	−	1.75134i	0.141536	−	0.0880083i
$397$	16.4435			0.825275			0.412637	−	0.910895i	$-0.364608\pi$
$397$	16.4435			0.825275			0.412637	+	0.910895i	$0.364608\pi$
$398$	14.7416	+	10.7104i	0.738929	+	0.536864i
$399$	1.74456	−	5.36921i	0.0873373	−	0.268797i
$400$	1.78054	+	5.47994i	0.0890271	+	0.273997i
$401$	4.17161	−	3.03085i	0.208320	−	0.151354i	−0.478733	−	0.877961i	$-0.658904\pi$
$401$	4.17161	−	3.03085i	0.208320	−	0.151354i	0.687053	+	0.726607i	$0.258904\pi$
$402$	−8.88909	+	6.45830i	−0.443348	+	0.322111i
$403$	10.1952	+	31.3776i	0.507860	+	1.56303i
$404$	1.57483	−	4.84682i	0.0783506	−	0.241138i
$405$	−2.65401	−	1.92825i	−0.131879	−	0.0958157i
$406$	10.0700			0.499765
$407$	−1.00986	+	2.48373i	−0.0500569	+	0.123114i
$408$	−3.94305			−0.195210
$409$	22.2916	+	16.1958i	1.10225	+	0.800830i	0.981425	−	0.191844i	$-0.0614467\pi$
$409$	22.2916	+	16.1958i	1.10225	+	0.800830i	0.120823	+	0.992674i	$0.461447\pi$
$410$	2.83760	−	8.73323i	0.140139	−	0.431303i
$411$	−3.24842	−	9.99760i	−0.160233	−	0.493145i
$412$	−1.00590	+	0.730832i	−0.0495574	+	0.0360055i
$413$	−7.03035	+	5.10785i	−0.345941	+	0.251341i
$414$	−1.33975	−	4.12332i	−0.0658450	−	0.202650i
$415$	15.6721	−	48.2338i	0.769314	−	2.36771i
$416$	−2.52125	−	1.83179i	−0.123614	−	0.0898111i
$417$	−4.35448			−0.213240
$418$	−18.6755	−	1.34726i	−0.913450	−	0.0658968i
$419$	21.3078			1.04096			0.520478	−	0.853875i	$-0.325754\pi$
$419$	21.3078			1.04096			0.520478	+	0.853875i	$0.325754\pi$
$420$	−2.65401	−	1.92825i	−0.129503	−	0.0940892i
$421$	−2.76720	+	8.51658i	−0.134865	+	0.415073i	−0.995569	−	0.0940335i	$-0.970024\pi$
$421$	−2.76720	+	8.51658i	−0.134865	+	0.415073i	0.860704	+	0.509106i	$0.170024\pi$
$422$	3.20374	+	9.86009i	0.155955	+	0.479982i
$423$	9.21875	−	6.69781i	0.448231	−	0.325659i
$424$	1.41696	−	1.02948i	0.0688135	−	0.0499959i
$425$	7.02076	+	21.6077i	0.340557	+	1.04813i
$426$	−1.09017	+	3.35520i	−0.0528189	+	0.162560i
$427$	7.12714	+	5.17817i	0.344906	+	0.250589i
$428$	1.64552			0.0795392
$429$	10.3093	+	0.743715i	0.497735	+	0.0359069i
$430$	26.8171			1.29324
$431$	−14.8190	−	10.7666i	−0.713807	−	0.518611i	0.170593	−	0.985342i	$-0.445432\pi$
$431$	−14.8190	−	10.7666i	−0.713807	−	0.518611i	−0.884399	+	0.466731i	$0.845432\pi$
$432$	−0.309017	+	0.951057i	−0.0148676	+	0.0457577i
$433$	−5.97926	−	18.4023i	−0.287345	−	0.884357i	−0.985686	−	0.168592i	$-0.946078\pi$
$433$	−5.97926	−	18.4023i	−0.287345	−	0.884357i	0.698341	−	0.715765i	$-0.253922\pi$
$434$	8.56473	−	6.22264i	0.411120	−	0.298696i
$435$	−26.7259	+	19.4175i	−1.28141	+	0.930997i
$436$	1.76069	+	5.41884i	0.0843216	+	0.259515i
$437$	−7.56357	+	23.2783i	−0.361815	+	1.11355i
$438$	0.513743	+	0.373256i	0.0245476	+	0.0178349i
$439$	13.6238			0.650227			0.325113	−	0.945675i	$-0.394598\pi$
$439$	13.6238			0.650227			0.325113	+	0.945675i	$0.394598\pi$
$440$	−4.09805	+	10.0791i	−0.195367	+	0.480500i
$441$	1.00000			0.0476190
$442$	−9.94141	−	7.22285i	−0.472864	−	0.343556i
$443$	−8.16574	+	25.1315i	−0.387966	+	1.19404i	0.546340	+	0.837563i	$0.316021\pi$
$443$	−8.16574	+	25.1315i	−0.387966	+	1.19404i	−0.934306	+	0.356472i	$0.883979\pi$
$444$	−0.249811	−	0.768840i	−0.0118555	−	0.0364875i
$445$	−21.2269	+	15.4222i	−1.00625	+	0.731083i
$446$	−0.372861	+	0.270899i	−0.0176555	+	0.0128275i
$447$	0.527109	+	1.62227i	0.0249314	+	0.0767309i
$448$	−0.309017	+	0.951057i	−0.0145997	+	0.0449332i
$449$	−28.5280	−	20.7268i	−1.34632	−	0.978158i	−0.999186	−	0.0403426i	$-0.987155\pi$
$449$	−28.5280	−	20.7268i	−1.34632	−	0.978158i	−0.347134	−	0.937816i	$-0.612845\pi$
$450$	5.76195			0.271621
$451$	7.88381	−	4.90224i	0.371234	−	0.230837i
$452$	15.2204			0.715907
$453$	−2.06412	−	1.49967i	−0.0969809	−	0.0704607i
$454$	−5.76495	+	17.7427i	−0.270562	+	0.832706i
$455$	−3.15926	−	9.72321i	−0.148109	−	0.455831i
$456$	4.56732	−	3.31835i	0.213884	−	0.155396i
$457$	11.7293	−	8.52183i	0.548673	−	0.398634i	−0.278623	−	0.960401i	$-0.589878\pi$
$457$	11.7293	−	8.52183i	0.548673	−	0.398634i	0.827296	+	0.561766i	$0.189878\pi$
$458$	4.18675	+	12.8855i	0.195634	+	0.602099i
$459$	−1.21847	+	3.75006i	−0.0568733	+	0.175038i
$460$	11.5065	+	8.35997i	0.536494	+	0.389786i
$461$	8.01704			0.373391			0.186695	−	0.982418i	$-0.440222\pi$
$461$	8.01704			0.373391			0.186695	+	0.982418i	$0.440222\pi$
$462$	−0.795274	−	3.21987i	−0.0369995	−	0.149802i
$463$	−23.6800			−1.10050			−0.550251	−	0.835000i	$-0.685468\pi$
$463$	−23.6800			−1.10050			−0.550251	+	0.835000i	$0.685468\pi$
$464$	8.14679	+	5.91899i	0.378205	+	0.274782i
$465$	−10.7321	+	33.0300i	−0.497689	+	1.53173i
$466$	−0.842508	−	2.59297i	−0.0390284	−	0.120117i
$467$	25.0714	−	18.2154i	1.16017	−	0.842910i	0.170367	−	0.985381i	$-0.445505\pi$
$467$	25.0714	−	18.2154i	1.16017	−	0.842910i	0.989799	+	0.142470i	$0.0455045\pi$
$468$	−2.52125	+	1.83179i	−0.116545	+	0.0846747i
$469$	3.39533	+	10.4498i	0.156782	+	0.482525i
$470$	−11.5516	+	35.5522i	−0.532836	+	1.63990i
$471$	0.474114	+	0.344464i	0.0218460	+	0.0158721i
$472$	−8.68999			−0.399989
$473$	20.7306	+	17.4730i	0.953196	+	0.803411i
$474$	11.6343			0.534380
$475$	−26.3167	−	19.1202i	−1.20749	−	0.877295i
$476$	−1.21847	+	3.75006i	−0.0558484	+	0.171884i
$477$	−0.541229	−	1.66573i	−0.0247812	−	0.0762687i
$478$	0.420535	−	0.305537i	0.0192348	−	0.0139749i
$479$	19.3517	−	14.0599i	0.884204	−	0.642412i	−0.0501564	−	0.998741i	$-0.515972\pi$
$479$	19.3517	−	14.0599i	0.884204	−	0.642412i	0.934360	+	0.356330i	$0.115972\pi$
$480$	−1.01374	−	3.11998i	−0.0462708	−	0.142407i
$481$	0.778520	−	2.39604i	0.0354974	−	0.109250i
$482$	−5.71449	−	4.15182i	−0.260288	−	0.189110i
$483$	−4.33551			−0.197273
$484$	−9.73508	+	5.12135i	−0.442504	+	0.232789i
$485$	−44.8074			−2.03460
$486$	0.809017	+	0.587785i	0.0366978	+	0.0266625i
$487$	−8.85499	+	27.2529i	−0.401258	+	1.23494i	0.522722	+	0.852503i	$0.324917\pi$
$487$	−8.85499	+	27.2529i	−0.401258	+	1.23494i	−0.923980	+	0.382442i	$0.875083\pi$
$488$	2.72232	+	8.37845i	0.123234	+	0.379275i
$489$	10.8541	−	7.88597i	0.490839	−	0.356616i
$490$	−2.65401	+	1.92825i	−0.119896	+	0.0871096i
$491$	9.77935	+	30.0977i	0.441336	+	1.35829i	0.886453	+	0.462819i	$0.153162\pi$
$491$	9.77935	+	30.0977i	0.441336	+	1.35829i	−0.445117	+	0.895472i	$0.646838\pi$
$492$	−0.864979	+	2.66213i	−0.0389962	+	0.120018i
$493$	32.1232	+	23.3389i	1.44676	+	1.05113i
$494$	17.5939			0.791587
$495$	8.31939	+	7.01208i	0.373929	+	0.315170i
$496$	10.5866			0.475352
$497$	2.85410	+	2.07363i	0.128024	+	0.0930149i
$498$	−4.77730	+	14.7030i	−0.214076	+	0.658858i
$499$	−10.2868	−	31.6596i	−0.460501	−	1.41728i	−0.864553	−	0.502542i	$-0.832398\pi$
$499$	−10.2868	−	31.6596i	−0.460501	−	1.41728i	0.404052	−	0.914736i	$-0.367602\pi$
$500$	−2.02224	+	1.46924i	−0.0904372	+	0.0657065i
$501$	−1.74661	+	1.26899i	−0.0780328	+	0.0566942i
$502$	−6.30040	−	19.3906i	−0.281200	−	0.865446i
$503$	1.25790	−	3.87142i	0.0560870	−	0.172618i	−0.919089	−	0.394051i	$-0.871073\pi$
$503$	1.25790	−	3.87142i	0.0560870	−	0.172618i	0.975176	+	0.221433i	$0.0710734\pi$
$504$	0.809017	+	0.587785i	0.0360365	+	0.0261820i
$505$	16.7184			0.743961
$506$	3.44792	+	13.9598i	0.153279	+	0.620588i
$507$	3.28784			0.146018
$508$	−8.18696	−	5.94817i	−0.363237	−	0.263907i
$509$	4.71997	−	14.5266i	0.209209	−	0.643879i	−0.790305	−	0.612713i	$-0.790078\pi$
$509$	4.71997	−	14.5266i	0.209209	−	0.643879i	0.999514	−	0.0311657i	$-0.00992195\pi$
$510$	−3.99724	−	12.3022i	−0.177001	−	0.544752i
$511$	0.513743	−	0.373256i	0.0227267	−	0.0165119i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$	−1.74456	−	5.36921i	−0.0770243	−	0.237056i
$514$	4.85349	−	14.9375i	0.214078	−	0.658865i
$515$	−3.29991	−	2.39753i	−0.145411	−	0.105648i
$516$	−8.17461			−0.359867
$517$	−32.0943	+	19.9566i	−1.41150	+	0.877688i
$518$	−0.808406			−0.0355193
$519$	9.73893	+	7.07575i	0.427492	+	0.310591i
$520$	3.15926	−	9.72321i	0.138543	−	0.426391i
$521$	−4.96088	−	15.2680i	−0.217340	−	0.668904i	−0.998979	−	0.0451732i	$-0.985616\pi$
$521$	−4.96088	−	15.2680i	−0.217340	−	0.668904i	0.781639	−	0.623731i	$-0.214384\pi$
$522$	8.14679	−	5.91899i	0.356575	−	0.259067i
$523$	11.8753	−	8.62795i	0.519273	−	0.377274i	−0.297057	−	0.954860i	$-0.596005\pi$
$523$	11.8753	−	8.62795i	0.519273	−	0.377274i	0.816330	+	0.577586i	$0.196005\pi$
$524$	−6.51838	−	20.0615i	−0.284757	−	0.876391i
$525$	1.78054	−	5.47994i	0.0777092	−	0.239164i
$526$	−2.93197	−	2.13020i	−0.127840	−	0.0928811i
$527$	41.7435			1.81837
$528$	1.24920	−	3.07238i	0.0543644	−	0.133708i
$529$	−4.20332			−0.182753
$530$	4.64839	+	3.37725i	0.201913	+	0.146698i
$531$	−2.68536	+	8.26468i	−0.116535	+	0.358656i
$532$	−1.74456	−	5.36921i	−0.0756363	−	0.232785i
$533$	−7.05730	+	5.12743i	−0.305686	+	0.222094i
$534$	6.47054	−	4.70112i	0.280007	−	0.203437i
$535$	1.66813	+	5.13399i	0.0721198	+	0.221962i
$536$	−3.39533	+	10.4498i	−0.146656	+	0.451361i
$537$	−13.1033	−	9.52011i	−0.565449	−	0.410823i
$538$	−2.05893			−0.0887667
$539$	−3.30803	−	0.238643i	−0.142487	−	0.0102791i
$540$	−3.28054			−0.141172
$541$	10.6415	+	7.73153i	0.457515	+	0.332404i	0.792556	−	0.609799i	$-0.208750\pi$
$541$	10.6415	+	7.73153i	0.457515	+	0.332404i	−0.335040	+	0.942204i	$0.608750\pi$
$542$	7.41733	−	22.8282i	0.318602	−	0.980556i
$543$	2.46341	+	7.58159i	0.105715	+	0.325357i
$544$	−3.18999	+	2.31767i	−0.136770	+	0.0993691i
$545$	−15.1218	+	10.9866i	−0.647746	+	0.470615i
$546$	0.963031	+	2.96390i	0.0412139	+	0.126843i
$547$	6.17612	−	19.0082i	0.264072	−	0.812730i	−0.727834	−	0.685754i	$-0.759473\pi$
$547$	6.17612	−	19.0082i	0.264072	−	0.812730i	0.991906	−	0.126976i	$-0.0405272\pi$
$548$	−8.50447	−	6.17886i	−0.363293	−	0.263948i
$549$	8.80963			0.375986
$550$	−19.0607	−	1.37505i	−0.812751	−	0.0586323i
$551$	−56.8503			−2.42190
$552$	−3.50750	−	2.54835i	−0.149289	−	0.108465i
$553$	3.59519	−	11.0648i	0.152883	−	0.470525i
$554$	2.96651	+	9.12998i	0.126035	+	0.387895i
$555$	2.14552	−	1.55881i	0.0910723	−	0.0661679i
$556$	−3.52285	+	2.55950i	−0.149402	+	0.108547i
$557$	−11.4976	−	35.3861i	−0.487171	−	1.49936i	−0.828812	−	0.559527i	$-0.810983\pi$
$557$	−11.4976	−	35.3861i	−0.487171	−	1.49936i	0.341641	−	0.939830i	$-0.389017\pi$
$558$	3.27144	−	10.0684i	0.138491	−	0.426231i
$559$	−20.6102	−	14.9742i	−0.871719	−	0.633341i
$560$	−3.28054			−0.138628
$561$	4.92566	−	12.1145i	0.207961	−	0.511476i
$562$	−13.4193			−0.566058
$563$	−9.26089	−	6.72843i	−0.390300	−	0.283570i	0.375278	−	0.926912i	$-0.377547\pi$
$563$	−9.26089	−	6.72843i	−0.390300	−	0.283570i	−0.765578	+	0.643343i	$0.777547\pi$
$564$	3.52125	−	10.8373i	0.148271	−	0.456332i
$565$	15.4296	+	47.4873i	0.649127	+	1.99781i
$566$	22.1608	−	16.1008i	0.931488	−	0.676766i
$567$	0.809017	−	0.587785i	0.0339755	−	0.0246847i
$568$	1.09017	+	3.35520i	0.0457425	+	0.140781i
$569$	−0.851108	+	2.61944i	−0.0356803	+	0.109813i	−0.967310	−	0.253595i	$-0.918387\pi$
$569$	−0.851108	+	2.61944i	−0.0356803	+	0.109813i	0.931630	+	0.363408i	$0.118387\pi$
$570$	14.9833	+	10.8860i	0.627581	+	0.455964i
$571$	−17.1432			−0.717419			−0.358710	−	0.933449i	$-0.616783\pi$
$571$	−17.1432			−0.717419			−0.358710	+	0.933449i	$0.616783\pi$
$572$	8.77750	−	5.45795i	0.367006	−	0.228208i
$573$	13.0038			0.543240
$574$	2.26454	+	1.64529i	0.0945202	+	0.0686730i
$575$	−7.71956	+	23.7584i	−0.321928	+	0.990793i
$576$	0.309017	+	0.951057i	0.0128757	+	0.0396274i
$577$	14.1696	−	10.2948i	0.589890	−	0.428580i	−0.252386	−	0.967627i	$-0.581215\pi$
$577$	14.1696	−	10.2948i	0.589890	−	0.428580i	0.842276	+	0.539047i	$0.181215\pi$
$578$	1.17498	−	0.853676i	0.0488729	−	0.0355082i
$579$	−7.00413	−	21.5565i	−0.291082	−	0.895858i
$580$	−10.2084	+	31.4181i	−0.423880	+	1.30457i
$581$	12.5071	+	9.08696i	0.518883	+	0.376991i
$582$	13.6586			0.566165
$583$	1.39289	+	5.63945i	0.0576875	+	0.233562i
$584$	0.635021			0.0262774
$585$	−8.27106	−	6.00928i	−0.341966	−	0.248453i
$586$	2.03195	−	6.25371i	0.0839392	−	0.258338i
$587$	−7.61728	−	23.4436i	−0.314399	−	0.967620i	−0.976001	−	0.217765i	$-0.930123\pi$
$587$	−7.61728	−	23.4436i	−0.314399	−	0.967620i	0.661602	−	0.749855i	$-0.269877\pi$
$588$	0.809017	−	0.587785i	0.0333633	−	0.0242399i
$589$	−48.3524	+	35.1301i	−1.99232	+	1.44751i
$590$	−8.80942	−	27.1126i	−0.362678	−	1.11621i
$591$	0.0473403	−	0.145699i	0.00194732	−	0.00599324i
$592$	−0.654014	−	0.475169i	−0.0268798	−	0.0195293i
$593$	−30.2795			−1.24343			−0.621716	−	0.783243i	$-0.713564\pi$
$593$	−30.2795			−1.24343			−0.621716	+	0.783243i	$0.713564\pi$
$594$	−2.53598	−	2.13748i	−0.104053	−	0.0877017i
$595$	−12.9353			−0.530297
$596$	1.37999	+	1.00262i	0.0565265	+	0.0410689i
$597$	5.63079	−	17.3298i	0.230453	−	0.709261i
$598$	−4.17523	−	12.8501i	−0.170738	−	0.525478i
$599$	−17.3943	+	12.6377i	−0.710711	+	0.516362i	−0.883403	−	0.468614i	$-0.844753\pi$
$599$	−17.3943	+	12.6377i	−0.710711	+	0.516362i	0.172692	+	0.984976i	$0.444753\pi$
$600$	4.66152	−	3.38679i	0.190306	−	0.138265i
$601$	−2.54410	−	7.82992i	−0.103776	−	0.319389i	0.885665	−	0.464324i	$-0.153703\pi$
$601$	−2.54410	−	7.82992i	−0.103776	−	0.319389i	−0.989441	+	0.144935i	$0.953703\pi$
$602$	−2.52609	+	7.77451i	−0.102956	+	0.316865i
$603$	8.88909	+	6.45830i	0.361992	+	0.263002i
$604$	−2.55139			−0.103815
$605$	−25.8474	−	25.1815i	−1.05085	−	1.02377i
$606$	−5.09625			−0.207021
$607$	−29.1471	−	21.1766i	−1.18304	−	0.859532i	−0.190532	−	0.981681i	$-0.561021\pi$
$607$	−29.1471	−	21.1766i	−1.18304	−	0.859532i	−0.992512	+	0.122149i	$0.961021\pi$
$608$	1.74456	−	5.36921i	0.0707513	−	0.217750i
$609$	−3.11180	−	9.57712i	−0.126096	−	0.388085i
$610$	−23.3809	+	16.9872i	−0.946664	+	0.687792i
$611$	28.7296	−	20.8733i	1.16228	−	0.844443i
$612$	1.21847	+	3.75006i	0.0492537	+	0.151587i
$613$	4.37023	−	13.4502i	0.176512	−	0.543248i	−0.823187	−	0.567770i	$-0.807806\pi$
$613$	4.37023	−	13.4502i	0.176512	−	0.543248i	0.999699	+	0.0245221i	$0.00780641\pi$
$614$	−3.16345	−	2.29838i	−0.127667	−	0.0927552i
$615$	−9.18266			−0.370281
$616$	−2.53598	−	2.13748i	−0.102178	−	0.0861214i
$617$	−2.09671			−0.0844105			−0.0422052	−	0.999109i	$-0.513438\pi$
$617$	−2.09671			−0.0844105			−0.0422052	+	0.999109i	$0.513438\pi$
$618$	1.00590	+	0.730832i	0.0404634	+	0.0293984i
$619$	12.8834	−	39.6510i	0.517828	−	1.59371i	−0.260250	−	0.965541i	$-0.583805\pi$
$619$	12.8834	−	39.6510i	0.517828	−	1.59371i	0.778077	−	0.628168i	$-0.216195\pi$
$620$	10.7321	+	33.0300i	0.431011	+	1.32652i
$621$	−3.50750	+	2.54835i	−0.140751	+	0.102262i
$622$	9.84660	−	7.15397i	0.394813	−	0.286848i
$623$	−2.47152	−	7.60657i	−0.0990195	−	0.304751i
$624$	−0.963031	+	2.96390i	−0.0385521	+	0.118651i
$625$	16.6736	+	12.1141i	0.666942	+	0.484562i
$626$	4.42112			0.176703
$627$	4.48973	+	18.1778i	0.179303	+	0.725952i
$628$	0.586037			0.0233854
$629$	−2.57881	−	1.87361i	−0.102824	−	0.0747059i
$630$	−1.01374	+	3.11998i	−0.0403885	+	0.124303i
$631$	9.97791	+	30.7089i	0.397214	+	1.22250i	0.927224	+	0.374508i	$0.122189\pi$
$631$	9.97791	+	30.7089i	0.397214	+	1.22250i	−0.530009	+	0.847992i	$0.677811\pi$
$632$	9.41232	−	6.83845i	0.374402	−	0.272019i
$633$	8.38749	−	6.09387i	0.333373	−	0.242210i
$634$	9.73733	+	29.9684i	0.386719	+	1.19020i
$635$	10.2587	−	31.5731i	0.407104	−	1.25294i
$636$	−1.41696	−	1.02948i	−0.0561860	−	0.0408215i
$637$	3.11643			0.123478
$638$	−28.3623	+	17.6360i	−1.12288	+	0.698216i
$639$	3.52786			0.139560
$640$	−2.65401	−	1.92825i	−0.104909	−	0.0762209i
$641$	−14.6319	+	45.0325i	−0.577927	+	1.77868i	0.0480608	+	0.998844i	$0.484696\pi$
$641$	−14.6319	+	45.0325i	−0.577927	+	1.77868i	−0.625988	+	0.779833i	$0.715304\pi$
$642$	−0.508494	−	1.56498i	−0.0200686	−	0.0617649i
$643$	5.42462	−	3.94122i	0.213926	−	0.155427i	−0.475662	−	0.879628i	$-0.657791\pi$
$643$	5.42462	−	3.94122i	0.213926	−	0.155427i	0.689588	+	0.724202i	$0.257791\pi$
$644$	−3.50750	+	2.54835i	−0.138215	+	0.100419i
$645$	−8.28695	−	25.5046i	−0.326298	−	1.00424i
$646$	6.87889	−	21.1711i	0.270646	−	0.832964i
$647$	−0.479101	−	0.348087i	−0.0188354	−	0.0136847i	0.578328	−	0.815805i	$-0.303706\pi$
$647$	−0.479101	−	0.348087i	−0.0188354	−	0.0136847i	−0.597163	+	0.802120i	$0.703706\pi$
$648$	1.00000			0.0392837
$649$	10.8555	−	26.6989i	0.426117	−	1.04802i
$650$	17.9567			0.704322
$651$	−8.56473	−	6.22264i	−0.335678	−	0.243885i
$652$	4.14590	−	12.7598i	0.162366	−	0.499711i
$653$	9.55358	+	29.4029i	0.373860	+	1.15062i	0.944244	+	0.329246i	$0.106794\pi$
$653$	9.55358	+	29.4029i	0.373860	+	1.15062i	−0.570384	+	0.821378i	$0.693206\pi$
$654$	4.60954	−	3.34903i	0.180247	−	0.130957i
$655$	55.9836	−	40.6744i	2.18746	−	1.58928i
$656$	0.864979	+	2.66213i	0.0337717	+	0.103939i
$657$	0.196232	−	0.603941i	0.00765576	−	0.0235620i
$658$	−9.21875	−	6.69781i	−0.359384	−	0.261108i
$659$	22.1288			0.862016			0.431008	−	0.902348i	$-0.358158\pi$
$659$	22.1288			0.862016			0.431008	+	0.902348i	$0.358158\pi$
$660$	10.8521	+	0.782879i	0.422418	+	0.0304735i
$661$	−30.6593			−1.19251			−0.596254	−	0.802796i	$-0.703345\pi$
$661$	−30.6593			−1.19251			−0.596254	+	0.802796i	$0.703345\pi$
$662$	4.77464	+	3.46898i	0.185572	+	0.134826i
$663$	−3.79728	+	11.6868i	−0.147474	+	0.453879i
$664$	4.77730	+	14.7030i	0.185395	+	0.570587i
$665$	14.9833	−	10.8860i	0.581027	−	0.422141i
$666$	−0.654014	+	0.475169i	−0.0253425	+	0.0184124i
$667$	13.4912	+	41.5218i	0.522383	+	1.60773i
$668$	−0.667146	+	2.05326i	−0.0258127	+	0.0794432i
$669$	0.372861	+	0.270899i	0.0144156	+	0.0104736i
$670$	−36.0450			−1.39254
$671$	−29.1425	−	2.10236i	−1.12503	−	0.0811606i
$672$	1.00000			0.0385758
$673$	11.1387	+	8.09277i	0.429367	+	0.311953i	0.781396	−	0.624036i	$-0.214508\pi$
$673$	11.1387	+	8.09277i	0.429367	+	0.311953i	−0.352029	+	0.935989i	$0.614508\pi$
$674$	−2.89895	+	8.92206i	−0.111664	+	0.343665i
$675$	−1.78054	−	5.47994i	−0.0685331	−	0.210923i
$676$	2.65992	−	1.93254i	0.102305	−	0.0743286i
$677$	18.0732	−	13.1309i	0.694609	−	0.504663i	−0.183563	−	0.983008i	$-0.558763\pi$
$677$	18.0732	−	13.1309i	0.694609	−	0.504663i	0.878172	+	0.478345i	$0.158763\pi$
$678$	−4.70336	−	14.4755i	−0.180631	−	0.555926i
$679$	4.22072	−	12.9901i	0.161977	−	0.498513i
$680$	−10.4649	−	7.60320i	−0.401311	−	0.291569i
$681$	18.6558			0.714890
$682$	−13.2248	+	32.5260i	−0.506403	+	1.24548i
$683$	11.0001			0.420905			0.210453	−	0.977604i	$-0.432506\pi$
$683$	11.0001			0.420905			0.210453	+	0.977604i	$0.432506\pi$
$684$	−4.56732	−	3.31835i	−0.174636	−	0.126880i
$685$	10.6566	−	32.7975i	0.407167	−	1.25313i
$686$	−0.309017	−	0.951057i	−0.0117983	−	0.0363115i
$687$	10.9611	−	7.96367i	0.418190	−	0.303833i
$688$	−6.61340	+	4.80491i	−0.252133	+	0.183186i
$689$	−1.68671	−	5.19115i	−0.0642584	−	0.197767i
$690$	4.39510	−	13.5267i	0.167319	−	0.514953i
$691$	−5.50068	−	3.99648i	−0.209256	−	0.152033i	0.478221	−	0.878239i	$-0.341282\pi$
$691$	−5.50068	−	3.99648i	−0.209256	−	0.152033i	−0.687477	+	0.726206i	$0.741282\pi$
$692$	12.0380			0.457616
$693$	−2.81652	+	1.75134i	−0.106991	+	0.0665280i
$694$	−27.9233			−1.05996
$695$	−11.5569	−	8.39654i	−0.438376	−	0.318499i
$696$	3.11180	−	9.57712i	0.117952	−	0.363020i
$697$	3.41065	+	10.4969i	0.129188	+	0.397599i
$698$	−22.7059	+	16.4968i	−0.859431	+	0.624413i
$699$	−2.20572	+	1.60255i	−0.0834278	+	0.0606139i
$700$	−1.78054	−	5.47994i	−0.0672982	−	0.207122i
$701$	−11.4835	+	35.3427i	−0.433727	+	1.33487i	0.460659	+	0.887577i	$0.347613\pi$
$701$	−11.4835	+	35.3427i	−0.433727	+	1.33487i	−0.894386	+	0.447296i	$0.852387\pi$
$702$	2.52125	+	1.83179i	0.0951584	+	0.0691366i
$703$	4.56387			0.172130
$704$	−0.795274	−	3.21987i	−0.0299730	−	0.121353i
$705$	37.3818			1.40788
$706$	5.36751	+	3.89973i	0.202009	+	0.146768i
$707$	−1.57483	+	4.84682i	−0.0592275	+	0.182283i
$708$	2.68536	+	8.26468i	0.100922	+	0.310606i
$709$	24.8260	−	18.0371i	0.932359	−	0.677399i	−0.0142102	−	0.999899i	$-0.504523\pi$
$709$	24.8260	−	18.0371i	0.932359	−	0.677399i	0.946569	+	0.322501i	$0.104523\pi$
$710$	−9.36300	+	6.80262i	−0.351387	+	0.255298i
$711$	−3.59519	−	11.0648i	−0.134830	−	0.414964i
$712$	2.47152	−	7.60657i	0.0926243	−	0.285068i
$713$	37.1325	+	26.9784i	1.39062	+	1.01035i
$714$	3.94305			0.147565
$715$	25.9268	+	21.8527i	0.969608	+	0.817244i
$716$	−16.1966			−0.605294
$717$	−0.420535	−	0.305537i	−0.0157052	−	0.0114105i
$718$	−2.87248	+	8.84059i	−0.107200	+	0.329928i
$719$	−1.32691	−	4.08382i	−0.0494856	−	0.152301i	0.923260	−	0.384175i	$-0.125514\pi$
$719$	−1.32691	−	4.08382i	−0.0494856	−	0.152301i	−0.972746	+	0.231874i	$0.925514\pi$
$720$	−2.65401	+	1.92825i	−0.0989093	+	0.0718618i
$721$	1.00590	−	0.730832i	0.0374618	−	0.0272176i
$722$	3.97764	+	12.2419i	0.148032	+	0.455596i
$723$	−2.18274	+	6.71778i	−0.0811770	+	0.249837i
$724$	6.44929	+	4.68568i	0.239686	+	0.174142i
$725$	−58.0228			−2.15491
$726$	7.87900	+	7.67603i	0.292417	+	0.284884i
$727$	−23.5376			−0.872962			−0.436481	−	0.899714i	$-0.643775\pi$
$727$	−23.5376			−0.872962			−0.436481	+	0.899714i	$0.643775\pi$
$728$	2.52125	+	1.83179i	0.0934437	+	0.0678908i
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$	0.643749	+	1.98125i	0.0238262	+	0.0733295i
$731$	−26.0769	+	18.9460i	−0.964491	+	0.700744i
$732$	7.12714	−	5.17817i	0.263427	−	0.191391i
$733$	7.07858	+	21.7856i	0.261453	+	0.804670i	0.992489	+	0.122331i	$0.0390371\pi$
$733$	7.07858	+	21.7856i	0.261453	+	0.804670i	−0.731036	+	0.682339i	$0.760963\pi$
$734$	6.60771	−	20.3364i	0.243895	−	0.750631i
$735$	2.65401	+	1.92825i	0.0978948	+	0.0711247i
$736$	−4.33551			−0.159809
$737$	−27.8641	−	23.4856i	−1.02639	−	0.865102i
$738$	2.79913			0.103037
$739$	6.83179	+	4.96359i	0.251312	+	0.182589i	0.706308	−	0.707905i	$-0.250359\pi$
$739$	6.83179	+	4.96359i	0.251312	+	0.182589i	−0.454996	+	0.890493i	$0.650359\pi$
$740$	0.819516	−	2.52221i	0.0301260	−	0.0927183i
$741$	−5.43681	−	16.7328i	−0.199726	−	0.614694i
$742$	−1.41696	+	1.02948i	−0.0520181	+	0.0377934i
$743$	−15.6379	+	11.3616i	−0.573699	+	0.416817i	−0.836447	−	0.548048i	$-0.815371\pi$
$743$	−15.6379	+	11.3616i	−0.573699	+	0.416817i	0.262748	+	0.964865i	$0.415371\pi$
$744$	−3.27144	−	10.0684i	−0.119937	−	0.369127i
$745$	−1.72920	+	5.32194i	−0.0633530	+	0.194981i
$746$	−21.2163	−	15.4146i	−0.776785	−	0.564367i
$747$	15.4597			0.565639
$748$	−3.13580	−	12.6961i	−0.114656	−	0.464215i
$749$	−1.64552			−0.0601260
$750$	2.02224	+	1.46924i	0.0738417	+	0.0536491i
$751$	−0.688222	+	2.11813i	−0.0251136	+	0.0772917i	−0.962828	−	0.270116i	$-0.912938\pi$
$751$	−0.688222	+	2.11813i	−0.0251136	+	0.0772917i	0.937714	+	0.347408i	$0.112938\pi$
$752$	−3.52125	−	10.8373i	−0.128407	−	0.395195i
$753$	−16.4947	+	11.9841i	−0.601098	+	0.436724i
$754$	25.3889	−	18.4461i	0.924610	−	0.671768i
$755$	−2.58646	−	7.96030i	−0.0941309	−	0.289705i
$756$	0.309017	−	0.951057i	0.0112388	−	0.0345896i
$757$	25.2555	+	18.3492i	0.917928	+	0.666914i	0.943008	−	0.332771i	$-0.107984\pi$
$757$	25.2555	+	18.3492i	0.917928	+	0.666914i	−0.0250791	+	0.999685i	$0.507984\pi$
$758$	−18.3918			−0.668020
$759$	12.2111	−	7.59298i	0.443234	−	0.275608i
$760$	18.5204			0.671804
$761$	28.1582	+	20.4581i	1.02073	+	0.741606i	0.966433	−	0.256919i	$-0.0827073\pi$
$761$	28.1582	+	20.4581i	1.02073	+	0.741606i	0.0543000	+	0.998525i	$0.482707\pi$
$762$	−3.12714	+	9.62434i	−0.113284	+	0.348653i
$763$	−1.76069	−	5.41884i	−0.0637412	−	0.196175i
$764$	10.5203	−	7.64342i	0.380610	−	0.276529i
$765$	−10.4649	+	7.60320i	−0.378360	+	0.274894i
$766$	4.98950	+	15.3561i	0.180278	+	0.554839i
$767$	−8.36873	+	25.7563i	−0.302177	+	0.930007i
$768$	0.809017	+	0.587785i	0.0291929	+	0.0212099i
$769$	12.5238			0.451621			0.225810	−	0.974171i	$-0.427497\pi$
$769$	12.5238			0.451621			0.225810	+	0.974171i	$0.427497\pi$
$770$	4.09805	−	10.0791i	0.147684	−	0.363224i
$771$	−15.7062			−0.565646
$772$	−18.3371	−	13.3227i	−0.659965	−	0.479493i
$773$	−1.77524	+	5.46363i	−0.0638510	+	0.196513i	−0.977893	−	0.209107i	$-0.932944\pi$
$773$	−1.77524	+	5.46363i	−0.0638510	+	0.196513i	0.914042	+	0.405620i	$0.132944\pi$
$774$	2.52609	+	7.77451i	0.0907985	+	0.279449i
$775$	−49.3496	+	35.8546i	−1.77269	+	1.28793i
$776$	11.0500	−	8.02830i	0.396672	−	0.288199i
$777$	0.249811	+	0.768840i	0.00896192	+	0.0275820i
$778$	8.32801	−	25.6310i	0.298574	−	0.918915i
$779$	−12.7845	−	9.28850i	−0.458053	−	0.332795i
$780$	−10.2236			−0.366063
$781$	−11.6703	−	0.841900i	−0.417595	−	0.0301256i
$782$	−17.0951			−0.611321
$783$	−8.14679	−	5.91899i	−0.291142	−	0.211527i
$784$	0.309017	−	0.951057i	0.0110363	−	0.0339663i
$785$	0.594091	+	1.82842i	0.0212040	+	0.0652593i
$786$	−17.0653	+	12.3987i	−0.608701	+	0.442247i
$787$	3.56241	−	2.58824i	0.126986	−	0.0922608i	−0.522479	−	0.852652i	$-0.674993\pi$
$787$	3.56241	−	2.58824i	0.126986	−	0.0922608i	0.649465	+	0.760391i	$0.274993\pi$
$788$	−0.0473403	−	0.145699i	−0.00168643	−	0.00519030i
$789$	−1.11991	+	3.44673i	−0.0398699	+	0.122707i
$790$	30.8775	+	22.4338i	1.09857	+	0.798160i
$791$	−15.2204			−0.541175
$792$	−3.30803	−	0.238643i	−0.117546	−	0.00847981i
$793$	27.4546			0.974942
$794$	−13.3031	−	9.66524i	−0.472108	−	0.343006i
$795$	1.77553	−	5.46451i	0.0629714	−	0.193806i
$796$	−5.63079	−	17.3298i	−0.199578	−	0.614238i
$797$	−17.3570	+	12.6106i	−0.614818	+	0.446691i	−0.851108	−	0.524991i	$-0.824069\pi$
$797$	−17.3570	+	12.6106i	−0.614818	+	0.446691i	0.236290	+	0.971683i	$0.424069\pi$
$798$	−4.56732	+	3.31835i	−0.161681	+	0.117468i
$799$	−13.8845	−	42.7320i	−0.491197	−	1.51175i
$800$	1.78054	−	5.47994i	0.0629517	−	0.193745i
$801$	−6.47054	−	4.70112i	−0.228625	−	0.166106i
$802$	−5.15640			−0.182079
$803$	−0.793269	+	1.95103i	−0.0279938	+	0.0688502i
$804$	10.9875			0.387500
$805$	−11.5065	−	8.35997i	−0.405551	−	0.294650i
$806$	10.1952	−	31.3776i	0.359111	−	1.10523i
$807$	0.636244	+	1.95816i	0.0223968	+	0.0689304i
$808$	−4.12295	+	2.99550i	−0.145045	+	0.105381i
$809$	38.9264	−	28.2817i	1.36858	−	0.994331i	0.370733	−	0.928740i	$-0.379107\pi$
$809$	38.9264	−	28.2817i	1.36858	−	0.994331i	0.997847	−	0.0655916i	$-0.0208934\pi$
$810$	1.01374	+	3.11998i	0.0356193	+	0.109625i
$811$	7.86911	−	24.2186i	0.276322	−	0.850431i	−0.712545	−	0.701627i	$-0.752457\pi$
$811$	7.86911	−	24.2186i	0.276322	−	0.850431i	0.988867	−	0.148805i	$-0.0475425\pi$
$812$	−8.14679	−	5.91899i	−0.285896	−	0.207716i
$813$	−24.0030			−0.841822
$814$	2.27689	−	1.41580i	0.0798050	−	0.0496236i
$815$	44.0131			1.54171
$816$	3.18999	+	2.31767i	0.111672	+	0.0811346i
$817$	14.2611	−	43.8912i	0.498933	−	1.53556i
$818$	−8.51463	−	26.2053i	−0.297707	−	0.916248i
$819$	2.52125	−	1.83179i	0.0880995	−	0.0640081i
$820$	−7.42893	+	5.39743i	−0.259429	+	0.188487i
$821$	−12.1757	−	37.4730i	−0.424935	−	1.30782i	−0.903057	−	0.429522i	$-0.858682\pi$
$821$	−12.1757	−	37.4730i	−0.424935	−	1.30782i	0.478122	−	0.878294i	$-0.341318\pi$
$822$	−3.24842	+	9.99760i	−0.113302	+	0.348706i
$823$	4.31200	+	3.13285i	0.150307	+	0.109204i	0.660397	−	0.750917i	$-0.270388\pi$
$823$	4.31200	+	3.13285i	0.150307	+	0.109204i	−0.510090	+	0.860121i	$0.670388\pi$
$824$	1.24337			0.0433147
$825$	4.58233	+	18.5527i	0.159536	+	0.645923i
$826$	8.68999			0.302364
$827$	−32.6156	−	23.6966i	−1.13415	−	0.824011i	−0.147860	−	0.989008i	$-0.547238\pi$
$827$	−32.6156	−	23.6966i	−1.13415	−	0.824011i	−0.986294	+	0.164997i	$0.947238\pi$
$828$	−1.33975	+	4.12332i	−0.0465594	+	0.143295i
$829$	−6.78759	−	20.8901i	−0.235743	−	0.725542i	−0.997022	−	0.0771174i	$-0.975428\pi$
$829$	−6.78759	−	20.8901i	−0.235743	−	0.725542i	0.761279	−	0.648424i	$-0.224572\pi$
$830$	−41.0302	+	29.8102i	−1.42418	+	1.03473i
$831$	7.76642	−	5.64264i	0.269414	−	0.195741i
$832$	0.963031	+	2.96390i	0.0333871	+	0.102755i
$833$	1.21847	−	3.75006i	0.0422175	−	0.129932i
$834$	3.52285	+	2.55950i	0.121986	+	0.0886282i
$835$	−7.08246			−0.245099
$836$	14.3169	+	12.0672i	0.495161	+	0.417352i
$837$	−10.5866			−0.365926
$838$	−17.2384	−	12.5244i	−0.595490	−	0.432649i
$839$	−15.4444	+	47.5331i	−0.533201	+	1.64103i	0.214302	+	0.976767i	$0.431252\pi$
$839$	−15.4444	+	47.5331i	−0.533201	+	1.64103i	−0.747504	+	0.664258i	$0.768748\pi$
$840$	1.01374	+	3.11998i	0.0349775	+	0.107650i
$841$	−58.5765	+	42.5583i	−2.01988	+	1.46753i
$842$	7.24463	−	5.26353i	0.249667	−	0.181393i
$843$	4.14679	+	12.7625i	0.142823	+	0.439564i
$844$	3.20374	−	9.86009i	0.110277	−	0.339398i
$845$	8.72597	+	6.33979i	0.300183	+	0.218095i
$846$	−11.3950			−0.391768
$847$	9.73508	−	5.12135i	0.334501	−	0.175972i
$848$	−1.75146			−0.0601452
$849$	−22.1608	−	16.1008i	−0.760557	−	0.552577i
$850$	7.02076	−	21.6077i	0.240810	−	0.741138i
$851$	−1.08306	−	3.33332i	−0.0371268	−	0.114265i
$852$	2.85410	−	2.07363i	0.0977799	−	0.0710413i
$853$	16.6775	−	12.1169i	0.571027	−	0.414876i	−0.264451	−	0.964399i	$-0.585191\pi$
$853$	16.6775	−	12.1169i	0.571027	−	0.414876i	0.835478	+	0.549524i	$0.185191\pi$
$854$	−2.72232	−	8.37845i	−0.0931560	−	0.286705i
$855$	5.72311	−	17.6139i	0.195726	−	0.602383i
$856$	−1.33125	−	0.967213i	−0.0455013	−	0.0330586i
$857$	−25.5579			−0.873041			−0.436520	−	0.899694i	$-0.643789\pi$
$857$	−25.5579			−0.873041			−0.436520	+	0.899694i	$0.643789\pi$
$858$	−7.90321	−	6.66130i	−0.269811	−	0.227413i
$859$	26.4772			0.903390			0.451695	−	0.892172i	$-0.350819\pi$
$859$	26.4772			0.903390			0.451695	+	0.892172i	$0.350819\pi$
$860$	−21.6955	−	15.7627i	−0.739811	−	0.537504i
$861$	0.864979	−	2.66213i	0.0294784	−	0.0907252i
$862$	5.66036	+	17.4208i	0.192793	+	0.593355i
$863$	27.9852	−	20.3325i	0.952629	−	0.692125i	0.00120149	−	0.999999i	$-0.499618\pi$
$863$	27.9852	−	20.3325i	0.952629	−	0.692125i	0.951427	+	0.307874i	$0.0996176\pi$
$864$	0.809017	−	0.587785i	0.0275233	−	0.0199969i
$865$	12.2034	+	37.5583i	0.414929	+	1.27702i
$866$	−5.97926	+	18.4023i	−0.203184	+	0.625335i
$867$	−1.17498	−	0.853676i	−0.0399046	−	0.0289924i
$868$	−10.5866			−0.359332
$869$	9.25243	+	37.4608i	0.313867	+	1.27077i
$870$	33.0350			1.11999
$871$	27.7023	+	20.1269i	0.938656	+	0.681973i
$872$	1.76069	−	5.41884i	0.0596244	−	0.183505i
$873$	−4.22072	−	12.9901i	−0.142850	−	0.439647i
$874$	19.8017	−	14.3868i	0.669802	−	0.486640i
$875$	2.02224	−	1.46924i	0.0683641	−	0.0496694i
$876$	−0.196232	−	0.603941i	−0.00663008	−	0.0204053i
$877$	−5.41675	+	16.6710i	−0.182911	+	0.562941i	−0.999906	−	0.0137030i	$-0.995638\pi$
$877$	−5.41675	+	16.6710i	−0.182911	+	0.562941i	0.816995	+	0.576644i	$0.195638\pi$
$878$	−11.0219	−	8.00785i	−0.371970	−	0.270252i
$879$	−6.57554			−0.221787
$880$	9.23972	−	5.74536i	0.311471	−	0.193676i
$881$	−23.5713			−0.794138			−0.397069	−	0.917789i	$-0.629973\pi$
$881$	−23.5713			−0.794138			−0.397069	+	0.917789i	$0.629973\pi$
$882$	−0.809017	−	0.587785i	−0.0272410	−	0.0197918i
$883$	−5.80200	+	17.8567i	−0.195253	+	0.600926i	0.804721	+	0.593653i	$0.202315\pi$
$883$	−5.80200	+	17.8567i	−0.195253	+	0.600926i	−0.999974	+	0.00727265i	$0.997685\pi$
$884$	3.79728	+	11.6868i	0.127716	+	0.393070i
$885$	−23.0634	+	16.7565i	−0.775267	+	0.563264i
$886$	21.3782	−	15.5322i	0.718214	−	0.521813i
$887$	−2.83977	−	8.73993i	−0.0953503	−	0.293458i	0.891995	−	0.452046i	$-0.149306\pi$
$887$	−2.83977	−	8.73993i	−0.0953503	−	0.293458i	−0.987345	+	0.158588i	$0.949306\pi$
$888$	−0.249811	+	0.768840i	−0.00838311	+	0.0258006i
$889$	8.18696	+	5.94817i	0.274582	+	0.199495i
$890$	26.2378			0.879495
$891$	−1.24920	+	3.07238i	−0.0418498	+	0.102928i
$892$	0.460882			0.0154315
$893$	52.0446	+	37.8126i	1.74161	+	1.26535i
$894$	0.527109	−	1.62227i	0.0176291	−	0.0542569i
$895$	−16.4192	−	50.5330i	−0.548832	−	1.68913i
$896$	0.809017	−	0.587785i	0.0270274	−	0.0196365i
$897$	−10.9309	+	7.94177i	−0.364972	+	0.265168i
$898$	10.8967	+	33.5367i	0.363628	+	1.11913i
$899$	−32.9433	+	101.389i	−1.09872	+	3.38152i
$900$	−4.66152	−	3.38679i	−0.155384	−	0.112893i
$901$	−6.90607			−0.230075
$902$	−9.25960	−	0.667993i	−0.308311	−	0.0222417i
$903$	8.17461			0.272034
$904$	−12.3136	−	8.94632i	−0.409543	−	0.297550i
$905$	−8.08132	+	24.8717i	−0.268632	+	0.826764i
$906$	0.788424	+	2.42652i	0.0261936	+	0.0806157i
$907$	3.11446	−	2.26278i	0.103414	−	0.0751345i	−0.534877	−	0.844930i	$-0.679642\pi$
$907$	3.11446	−	2.26278i	0.103414	−	0.0751345i	0.638290	+	0.769796i	$0.279642\pi$
$908$	15.0928	−	10.9656i	0.500873	−	0.363906i
$909$	1.57483	+	4.84682i	0.0522337	+	0.160759i
$910$	−3.15926	+	9.72321i	−0.104729	+	0.322321i
$911$	38.7768	+	28.1730i	1.28473	+	0.933412i	0.999685	−	0.0251016i	$-0.00799093\pi$
$911$	38.7768	+	28.1730i	1.28473	+	0.933412i	0.285047	+	0.958514i	$0.407991\pi$
$912$	−5.64552			−0.186942
$913$	−51.1410	−	3.68934i	−1.69252	−	0.122099i
$914$	−14.4982			−0.479558
$915$	23.3809	+	16.9872i	0.772948	+	0.561580i
$916$	4.18675	−	12.8855i	0.138334	−	0.425749i
$917$	6.51838	+	20.0615i	0.215256	+	0.662490i
$918$	3.18999	−	2.31767i	0.105285	−	0.0764944i
$919$	−24.1965	+	17.5798i	−0.798167	+	0.579903i	−0.910376	−	0.413782i	$-0.864208\pi$
$919$	−24.1965	+	17.5798i	−0.798167	+	0.579903i	0.112209	+	0.993685i	$0.464208\pi$
$920$	−4.39510	−	13.5267i	−0.144902	−	0.445963i
$921$	−1.20833	+	3.71886i	−0.0398159	+	0.122541i
$922$	−6.48592	−	4.71230i	−0.213603	−	0.155191i
$923$	10.9944			0.361884
$924$	−1.24920	+	3.07238i	−0.0410957	+	0.101074i
$925$	4.65800			0.153154
$926$	19.1575	+	13.9187i	0.629554	+	0.457398i
$927$	0.384221	−	1.18251i	0.0126195	−	0.0388388i
$928$	−3.11180	−	9.57712i	−0.102150	−	0.314384i
$929$	0.566782	−	0.411791i	0.0185955	−	0.0135104i	−0.578449	−	0.815719i	$-0.696342\pi$
$929$	0.566782	−	0.411791i	0.0185955	−	0.0135104i	0.597044	+	0.802208i	$0.296342\pi$
$930$	28.0970	−	20.4136i	0.921336	−	0.669390i
$931$	1.74456	+	5.36921i	0.0571757	+	0.175969i
$932$	−0.842508	+	2.59297i	−0.0275973	+	0.0849357i
$933$	−9.84660	−	7.15397i	−0.322363	−	0.234211i
$934$	−30.9900			−1.01402
$935$	36.4327	−	22.6542i	1.19148	−	0.740872i
$936$	3.11643			0.101864
$937$	25.3344	+	18.4065i	0.827640	+	0.601315i	0.918891	−	0.394513i	$-0.129087\pi$
$937$	25.3344	+	18.4065i	0.827640	+	0.601315i	−0.0912510	+	0.995828i	$0.529087\pi$
$938$	3.39533	−	10.4498i	0.110862	−	0.341197i
$939$	−1.36620	−	4.20473i	−0.0445843	−	0.137216i
$940$	30.2425	−	21.9725i	0.986401	−	0.716662i
$941$	−9.14641	+	6.64526i	−0.298164	+	0.216629i	−0.726801	−	0.686848i	$-0.758994\pi$
$941$	−9.14641	+	6.64526i	−0.298164	+	0.216629i	0.428637	+	0.903477i	$0.358994\pi$
$942$	−0.181095	−	0.557354i	−0.00590041	−	0.0181596i
$943$	−3.75013	+	11.5417i	−0.122121	+	0.375850i
$944$	7.03035	+	5.10785i	0.228818	+	0.166246i
$945$	3.28054			0.106716
$946$	−6.50105	−	26.3211i	−0.211367	−	0.855774i
$947$	−34.8426			−1.13223			−0.566117	−	0.824325i	$-0.691555\pi$
$947$	−34.8426			−1.13223			−0.566117	+	0.824325i	$0.691555\pi$
$948$	−9.41232	−	6.83845i	−0.305698	−	0.222103i
$949$	0.611545	−	1.88214i	0.0198516	−	0.0610969i
$950$	10.0521	+	30.9371i	0.326133	+	1.00373i
$951$	25.4927	−	18.5215i	0.826657	−	0.600601i
$952$	3.18999	−	2.31767i	0.103388	−	0.0751160i
$953$	−0.0833419	−	0.256500i	−0.00269971	−	0.00830885i	0.949698	−	0.313168i	$-0.101390\pi$
$953$	−0.0833419	−	0.256500i	−0.00269971	−	0.00830885i	−0.952397	+	0.304860i	$0.901390\pi$
$954$	−0.541229	+	1.66573i	−0.0175230	+	0.0539301i
$955$	34.5121	+	25.0745i	1.11679	+	0.811393i
$956$	−0.519810			−0.0168119
$957$	25.5373	+	21.5243i	0.825503	+	0.695783i
$958$	−23.9201			−0.772823
$959$	8.50447	+	6.17886i	0.274624	+	0.199526i
$960$	−1.01374	+	3.11998i	−0.0327184	+	0.100697i
$961$	25.0538	+	77.1078i	0.808188	+	2.48735i
$962$	−2.03819	+	1.48083i	−0.0657139	+	0.0477440i
$963$	−1.33125	+	0.967213i	−0.0428991	+	0.0311680i
$964$	2.18274	+	6.71778i	0.0703013	+	0.216365i
$965$	22.9774	−	70.7170i	0.739667	−	2.27646i
$966$	3.50750	+	2.54835i	0.112852	+	0.0819919i
$967$	9.53630			0.306667			0.153333	−	0.988175i	$-0.450999\pi$
$967$	9.53630			0.306667			0.153333	+	0.988175i	$0.450999\pi$
$968$	10.8861	+	1.57888i	0.349892	+	0.0507470i
$969$	−22.2606			−0.715112
$970$	36.2500	+	26.3372i	1.16392	+	0.845635i
$971$	1.79205	−	5.51535i	0.0575095	−	0.176996i	−0.918175	−	0.396174i	$-0.870338\pi$
$971$	1.79205	−	5.51535i	0.0575095	−	0.176996i	0.975685	+	0.219178i	$0.0703376\pi$
$972$	−0.309017	−	0.951057i	−0.00991172	−	0.0305052i
$973$	3.52285	−	2.55950i	0.112937	−	0.0820538i
$974$	23.1827	−	16.8432i	0.742821	−	0.539691i
$975$	−5.54894	−	17.0779i	−0.177708	−	0.546930i
$976$	2.72232	−	8.37845i	0.0871395	−	0.268188i
$977$	−12.7203	−	9.24187i	−0.406960	−	0.295674i	0.365410	−	0.930847i	$-0.380929\pi$
$977$	−12.7203	−	9.24187i	−0.406960	−	0.295674i	−0.772370	+	0.635173i	$0.780929\pi$
$978$	−13.4164			−0.429009
$979$	20.2828	+	17.0956i	0.648242	+	0.546377i
$980$	3.28054			0.104793
$981$	−4.60954	−	3.34903i	−0.147171	−	0.106926i
$982$	9.77935	−	30.0977i	0.312071	−	0.960457i
$983$	−2.13089	−	6.55820i	−0.0679648	−	0.209174i	0.911306	−	0.411730i	$-0.135075\pi$
$983$	−2.13089	−	6.55820i	−0.0679648	−	0.209174i	−0.979271	+	0.202556i	$0.935075\pi$
$984$	2.26454	−	1.64529i	0.0721910	−	0.0524498i
$985$	0.406586	−	0.295402i	0.0129549	−	0.00941228i
$986$	−12.2700	−	37.7631i	−0.390755	−	1.20262i
$987$	−3.52125	+	10.8373i	−0.112083	+	0.344955i
$988$	−14.2338	−	10.3414i	−0.452836	−	0.329005i
$989$	−35.4411			−1.12696
$990$	−2.60893	−	10.5629i	−0.0829172	−	0.335711i
$991$	−34.6639			−1.10114			−0.550568	−	0.834790i	$-0.685589\pi$
$991$	−34.6639			−1.10114			−0.550568	+	0.834790i	$0.685589\pi$
$992$	−8.56473	−	6.22264i	−0.271931	−	0.197569i
$993$	1.82375	−	5.61292i	0.0578749	−	0.178121i
$994$	−1.09017	−	3.35520i	−0.0345781	−	0.106420i
$995$	48.3604	−	35.1359i	1.53313	−	1.11388i
$996$	12.5071	−	9.08696i	0.396303	−	0.287931i
$997$	−13.7948	−	42.4561i	−0.436887	−	1.34460i	−0.891141	−	0.453727i	$-0.850094\pi$
$997$	−13.7948	−	42.4561i	−0.436887	−	1.34460i	0.454254	−	0.890872i	$-0.349906\pi$
$998$	−10.2868	+	31.6596i	−0.325624	+	1.00217i
$999$	0.654014	+	0.475169i	0.0206921	+	0.0150337i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.j.f.169.1	✓	8
11.3	even	5	inner	462.2.j.f.421.1	yes	8
11.5	even	5		5082.2.a.cc.1.4		4
11.6	odd	10		5082.2.a.bx.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.j.f.169.1	✓	8	1.1	even	1	trivial
462.2.j.f.421.1	yes	8	11.3	even	5	inner
5082.2.a.bx.1.4		4	11.6	odd	10
5082.2.a.cc.1.4		4	11.5	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)

\(f(q)\)	\(=\)	\(q+(-0.809017 - 0.587785i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-2.65401 + 1.92825i) q^{5} +(0.809017 - 0.587785i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(q+(-0.809017 - 0.587785i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-2.65401 + 1.92825i) 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} +3.28054 q^{10} +(2.53598 + 2.13748i) q^{11} -1.00000 q^{12} +(-2.52125 - 1.83179i) q^{13} +(-0.309017 + 0.951057i) q^{14} +(-1.01374 - 3.11998i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-3.18999 + 2.31767i) q^{17} +(0.309017 + 0.951057i) q^{18} +(1.74456 - 5.36921i) q^{19} +(-2.65401 - 1.92825i) q^{20} +1.00000 q^{21} +(-0.795274 - 3.21987i) q^{22} -4.33551 q^{23} +(0.809017 + 0.587785i) q^{24} +(1.78054 - 5.47994i) q^{25} +(0.963031 + 2.96390i) q^{26} +(0.809017 - 0.587785i) q^{27} +(0.809017 - 0.587785i) q^{28} +(-3.11180 - 9.57712i) q^{29} +(-1.01374 + 3.11998i) q^{30} +(-8.56473 - 6.22264i) q^{31} +1.00000 q^{32} +(-2.81652 + 1.75134i) q^{33} +3.94305 q^{34} +(2.65401 + 1.92825i) q^{35} +(0.309017 - 0.951057i) q^{36} +(0.249811 + 0.768840i) q^{37} +(-4.56732 + 3.31835i) q^{38} +(2.52125 - 1.83179i) q^{39} +(1.01374 + 3.11998i) q^{40} +(0.864979 - 2.66213i) q^{41} +(-0.809017 - 0.587785i) q^{42} +8.17461 q^{43} +(-1.24920 + 3.07238i) q^{44} +3.28054 q^{45} +(3.50750 + 2.54835i) q^{46} +(-3.52125 + 10.8373i) q^{47} +(-0.309017 - 0.951057i) q^{48} +(-0.809017 + 0.587785i) q^{49} +(-4.66152 + 3.38679i) q^{50} +(-1.21847 - 3.75006i) q^{51} +(0.963031 - 2.96390i) q^{52} +(1.41696 + 1.02948i) q^{53} -1.00000 q^{54} +(-10.8521 - 0.782879i) q^{55} -1.00000 q^{56} +(4.56732 + 3.31835i) q^{57} +(-3.11180 + 9.57712i) q^{58} +(-2.68536 - 8.26468i) q^{59} +(2.65401 - 1.92825i) q^{60} +(-7.12714 + 5.17817i) q^{61} +(3.27144 + 10.0684i) q^{62} +(-0.309017 + 0.951057i) q^{63} +(-0.809017 - 0.587785i) q^{64} +10.2236 q^{65} +(3.30803 + 0.238643i) q^{66} -10.9875 q^{67} +(-3.18999 - 2.31767i) q^{68} +(1.33975 - 4.12332i) q^{69} +(-1.01374 - 3.11998i) q^{70} +(-2.85410 + 2.07363i) q^{71} +(-0.809017 + 0.587785i) q^{72} +(0.196232 + 0.603941i) q^{73} +(0.249811 - 0.768840i) q^{74} +(4.66152 + 3.38679i) q^{75} +5.64552 q^{76} +(1.24920 - 3.07238i) q^{77} -3.11643 q^{78} +(9.41232 + 6.83845i) q^{79} +(1.01374 - 3.11998i) q^{80} +(0.309017 + 0.951057i) q^{81} +(-2.26454 + 1.64529i) q^{82} +(-12.5071 + 9.08696i) q^{83} +(0.309017 + 0.951057i) q^{84} +(3.99724 - 12.3022i) q^{85} +(-6.61340 - 4.80491i) q^{86} +10.0700 q^{87} +(2.81652 - 1.75134i) q^{88} +7.99802 q^{89} +(-2.65401 - 1.92825i) q^{90} +(-0.963031 + 2.96390i) q^{91} +(-1.33975 - 4.12332i) q^{92} +(8.56473 - 6.22264i) q^{93} +(9.21875 - 6.69781i) q^{94} +(5.72311 + 17.6139i) q^{95} +(-0.309017 + 0.951057i) q^{96} +(11.0500 + 8.02830i) q^{97} +1.00000 q^{98} +(-0.795274 - 3.21987i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 6 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 6 * q^5 + 2 * q^6 + 2 * q^7 - 2 * q^8 - 2 * q^9	\( 8 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 6 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9} + 4 q^{10} + 14 q^{11} - 8 q^{12} + 8 q^{13} + 2 q^{14} - 4 q^{15} - 2 q^{16} - 4 q^{17} - 2 q^{18} - 2 q^{19} - 6 q^{20} + 8 q^{21} - 6 q^{22} + 4 q^{23} + 2 q^{24} - 8 q^{25} - 12 q^{26} + 2 q^{27} + 2 q^{28} + 4 q^{29} - 4 q^{30} - 10 q^{31} + 8 q^{32} + 6 q^{33} - 4 q^{34} + 6 q^{35} - 2 q^{36} - 20 q^{37} - 12 q^{38} - 8 q^{39} + 4 q^{40} + 12 q^{41} - 2 q^{42} + 48 q^{43} - 6 q^{44} + 4 q^{45} + 4 q^{46} + 2 q^{48} - 2 q^{49} + 2 q^{50} - 6 q^{51} - 12 q^{52} - 12 q^{53} - 8 q^{54} - 8 q^{55} - 8 q^{56} + 12 q^{57} + 4 q^{58} + 12 q^{59} + 6 q^{60} - 32 q^{61} + 20 q^{62} + 2 q^{63} - 2 q^{64} + 24 q^{65} - 4 q^{66} - 48 q^{67} - 4 q^{68} + 6 q^{69} - 4 q^{70} + 4 q^{71} - 2 q^{72} - 20 q^{74} - 2 q^{75} + 28 q^{76} + 6 q^{77} - 8 q^{78} + 40 q^{79} + 4 q^{80} - 2 q^{81} - 18 q^{82} - 32 q^{83} - 2 q^{84} - 42 q^{85} - 32 q^{86} + 16 q^{87} - 6 q^{88} + 12 q^{89} - 6 q^{90} + 12 q^{91} - 6 q^{92} + 10 q^{93} + 54 q^{95} + 2 q^{96} + 8 q^{97} + 8 q^{98} - 6 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 6 * q^5 + 2 * q^6 + 2 * q^7 - 2 * q^8 - 2 * q^9 + 4 * q^10 + 14 * q^11 - 8 * q^12 + 8 * q^13 + 2 * q^14 - 4 * q^15 - 2 * q^16 - 4 * q^17 - 2 * q^18 - 2 * q^19 - 6 * q^20 + 8 * q^21 - 6 * q^22 + 4 * q^23 + 2 * q^24 - 8 * q^25 - 12 * q^26 + 2 * q^27 + 2 * q^28 + 4 * q^29 - 4 * q^30 - 10 * q^31 + 8 * q^32 + 6 * q^33 - 4 * q^34 + 6 * q^35 - 2 * q^36 - 20 * q^37 - 12 * q^38 - 8 * q^39 + 4 * q^40 + 12 * q^41 - 2 * q^42 + 48 * q^43 - 6 * q^44 + 4 * q^45 + 4 * q^46 + 2 * q^48 - 2 * q^49 + 2 * q^50 - 6 * q^51 - 12 * q^52 - 12 * q^53 - 8 * q^54 - 8 * q^55 - 8 * q^56 + 12 * q^57 + 4 * q^58 + 12 * q^59 + 6 * q^60 - 32 * q^61 + 20 * q^62 + 2 * q^63 - 2 * q^64 + 24 * q^65 - 4 * q^66 - 48 * q^67 - 4 * q^68 + 6 * q^69 - 4 * q^70 + 4 * q^71 - 2 * q^72 - 20 * q^74 - 2 * q^75 + 28 * q^76 + 6 * q^77 - 8 * q^78 + 40 * q^79 + 4 * q^80 - 2 * q^81 - 18 * q^82 - 32 * q^83 - 2 * q^84 - 42 * q^85 - 32 * q^86 + 16 * q^87 - 6 * q^88 + 12 * q^89 - 6 * q^90 + 12 * q^91 - 6 * q^92 + 10 * q^93 + 54 * q^95 + 2 * q^96 + 8 * q^97 + 8 * q^98 - 6 * q^99

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