LMFDB - Embedded newform 570.2.f.d.341.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(341,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

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

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

chi := DirichletCharacter("570.341");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.f (of order $2$, degree $1$, 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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.7278137344.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + x^{6} + 6x^{5} - 20x^{4} + 18x^{3} + 9x^{2} - 54x + 81 $ x^8 - 2x^7 + x^6 + 6x^5 - 20x^4 + 18x^3 + 9x^2 - 54x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			341.3
Root			$0.828750 + 1.52091i$ of defining polynomial
Character	$\chi$	$=$	570.341
Dual form			570.2.f.d.341.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(-0.828750 - 1.52091i) q^{3} +1.00000 q^{4} +1.00000i q^{5} +(-0.828750 - 1.52091i) q^{6} +4.83942 q^{7} +1.00000 q^{8} +(-1.62635 + 2.52091i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(-0.828750 - 1.52091i) q^{3} +1.00000 q^{4} +1.00000i q^{5} +(-0.828750 - 1.52091i) q^{6} +4.83942 q^{7} +1.00000 q^{8} +(-1.62635 + 2.52091i) q^{9} +1.00000i q^{10} +2.00000i q^{11} +(-0.828750 - 1.52091i) q^{12} -1.04182i q^{13} +4.83942 q^{14} +(1.52091 - 0.828750i) q^{15} +1.00000 q^{16} -0.140096i q^{17} +(-1.62635 + 2.52091i) q^{18} +(2.65750 + 3.45510i) q^{19} +1.00000i q^{20} +(-4.01067 - 7.36033i) q^{21} +2.00000i q^{22} -6.63702i q^{23} +(-0.828750 - 1.52091i) q^{24} -1.00000 q^{25} -1.04182i q^{26} +(5.18192 + 0.384324i) q^{27} +4.83942 q^{28} -1.65750 q^{29} +(1.52091 - 0.828750i) q^{30} -3.58673i q^{31} +1.00000 q^{32} +(3.04182 - 1.65750i) q^{33} -0.140096i q^{34} +4.83942i q^{35} +(-1.62635 + 2.52091i) q^{36} -6.36384i q^{37} +(2.65750 + 3.45510i) q^{38} +(-1.58452 + 0.863412i) q^{39} +1.00000i q^{40} -1.18192 q^{41} +(-4.01067 - 7.36033i) q^{42} -8.76865 q^{43} +2.00000i q^{44} +(-2.52091 - 1.62635i) q^{45} -6.63702i q^{46} +4.76865i q^{47} +(-0.828750 - 1.52091i) q^{48} +16.4200 q^{49} -1.00000 q^{50} +(-0.213074 + 0.116105i) q^{51} -1.04182i q^{52} +8.42615 q^{53} +(5.18192 + 0.384324i) q^{54} -2.00000 q^{55} +4.83942 q^{56} +(3.05249 - 6.90524i) q^{57} -1.65750 q^{58} +0.350965 q^{59} +(1.52091 - 0.828750i) q^{60} -10.4475 q^{61} -3.58673i q^{62} +(-7.87057 + 12.1998i) q^{63} +1.00000 q^{64} +1.04182 q^{65} +(3.04182 - 1.65750i) q^{66} +13.6309i q^{67} -0.140096i q^{68} +(-10.0943 + 5.50043i) q^{69} +4.83942i q^{70} -11.7625 q^{71} +(-1.62635 + 2.52091i) q^{72} -2.83095 q^{73} -6.36384i q^{74} +(0.828750 + 1.52091i) q^{75} +(2.65750 + 3.45510i) q^{76} +9.67884i q^{77} +(-1.58452 + 0.863412i) q^{78} -10.0921i q^{79} +1.00000i q^{80} +(-3.70999 - 8.19975i) q^{81} -1.18192 q^{82} +10.0342i q^{83} +(-4.01067 - 7.36033i) q^{84} +0.140096 q^{85} -8.76865 q^{86} +(1.37365 + 2.52091i) q^{87} +2.00000i q^{88} -16.4969 q^{89} +(-2.52091 - 1.62635i) q^{90} -5.04182i q^{91} -6.63702i q^{92} +(-5.45510 + 2.97250i) q^{93} +4.76865i q^{94} +(-3.45510 + 2.65750i) q^{95} +(-0.828750 - 1.52091i) q^{96} +7.67884i q^{97} +16.4200 q^{98} +(-5.04182 - 3.25269i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} - 2 q^{3} + 8 q^{4} - 2 q^{6} + 4 q^{7} + 8 q^{8} + 2 q^{9}+O(q^{10}) $ 8 * q + 8 * q^2 - 2 * q^3 + 8 * q^4 - 2 * q^6 + 4 * q^7 + 8 * q^8 + 2 * q^9	$ 8 q + 8 q^{2} - 2 q^{3} + 8 q^{4} - 2 q^{6} + 4 q^{7} + 8 q^{8} + 2 q^{9} - 2 q^{12} + 4 q^{14} + 8 q^{16} + 2 q^{18} + 12 q^{19} - 2 q^{21} - 2 q^{24} - 8 q^{25} + 16 q^{27} + 4 q^{28} - 4 q^{29} + 8 q^{32} + 2 q^{36} + 12 q^{38} - 22 q^{39} + 16 q^{41} - 2 q^{42} - 40 q^{43} - 8 q^{45} - 2 q^{48} + 4 q^{49} - 8 q^{50} + 18 q^{51} + 28 q^{53} + 16 q^{54} - 16 q^{55} + 4 q^{56} - 30 q^{57} - 4 q^{58} - 4 q^{59} + 16 q^{61} - 34 q^{63} + 8 q^{64} - 16 q^{65} - 2 q^{69} + 24 q^{71} + 2 q^{72} - 4 q^{73} + 2 q^{75} + 12 q^{76} - 22 q^{78} + 34 q^{81} + 16 q^{82} - 2 q^{84} - 40 q^{86} + 26 q^{87} - 88 q^{89} - 8 q^{90} - 24 q^{93} - 8 q^{95} - 2 q^{96} + 4 q^{98} - 16 q^{99}+O(q^{100}) $ 8 * q + 8 * q^2 - 2 * q^3 + 8 * q^4 - 2 * q^6 + 4 * q^7 + 8 * q^8 + 2 * q^9 - 2 * q^12 + 4 * q^14 + 8 * q^16 + 2 * q^18 + 12 * q^19 - 2 * q^21 - 2 * q^24 - 8 * q^25 + 16 * q^27 + 4 * q^28 - 4 * q^29 + 8 * q^32 + 2 * q^36 + 12 * q^38 - 22 * q^39 + 16 * q^41 - 2 * q^42 - 40 * q^43 - 8 * q^45 - 2 * q^48 + 4 * q^49 - 8 * q^50 + 18 * q^51 + 28 * q^53 + 16 * q^54 - 16 * q^55 + 4 * q^56 - 30 * q^57 - 4 * q^58 - 4 * q^59 + 16 * q^61 - 34 * q^63 + 8 * q^64 - 16 * q^65 - 2 * q^69 + 24 * q^71 + 2 * q^72 - 4 * q^73 + 2 * q^75 + 12 * q^76 - 22 * q^78 + 34 * q^81 + 16 * q^82 - 2 * q^84 - 40 * q^86 + 26 * q^87 - 88 * q^89 - 8 * q^90 - 24 * q^93 - 8 * q^95 - 2 * q^96 + 4 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	−0.828750	−	1.52091i	−0.478479	−	0.878099i
$3$	−0.828750	−	1.52091i	−0.478479	−	0.878099i
$4$	1.00000			0.500000
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$	−0.828750	−	1.52091i	−0.338336	−	0.620910i
$7$	4.83942			1.82913			0.914564	−	0.404440i	$-0.132534\pi$
$7$	4.83942			1.82913			0.914564	+	0.404440i	$0.132534\pi$
$8$	1.00000			0.353553
$9$	−1.62635	+	2.52091i	−0.542115	+	0.840304i
$10$			1.00000i			0.316228i
$11$			2.00000i			0.603023i	0.953463	+	0.301511i	$0.0974911\pi$
$11$			2.00000i			0.603023i	−0.953463	+	0.301511i	$0.902509\pi$
$12$	−0.828750	−	1.52091i	−0.239240	−	0.439049i
$13$		−	1.04182i		−	0.288950i	−0.989508	−	0.144475i	$-0.953851\pi$
$13$		−	1.04182i		−	0.288950i	0.989508	−	0.144475i	$-0.0461493\pi$
$14$	4.83942			1.29339
$15$	1.52091	−	0.828750i	0.392698	−	0.213982i
$16$	1.00000			0.250000
$17$		−	0.140096i		−	0.0339783i	−0.999856	−	0.0169891i	$-0.994592\pi$
$17$		−	0.140096i		−	0.0339783i	0.999856	−	0.0169891i	$-0.00540807\pi$
$18$	−1.62635	+	2.52091i	−0.383334	+	0.594185i
$19$	2.65750	+	3.45510i	0.609672	+	0.792654i
$19$	2.65750	+	3.45510i	0.609672	+	0.792654i
$20$			1.00000i			0.223607i
$21$	−4.01067	−	7.36033i	−0.875200	−	1.60616i
$22$			2.00000i			0.426401i
$23$		−	6.63702i		−	1.38391i	−0.721939	−	0.691957i	$-0.756749\pi$
$23$		−	6.63702i		−	1.38391i	0.721939	−	0.691957i	$-0.243251\pi$
$24$	−0.828750	−	1.52091i	−0.169168	−	0.310455i
$25$	−1.00000			−0.200000
$26$		−	1.04182i		−	0.204318i
$27$	5.18192	+	0.384324i	0.997261	+	0.0739631i
$28$	4.83942			0.914564
$29$	−1.65750			−0.307790			−0.153895	−	0.988087i	$-0.549182\pi$
$29$	−1.65750			−0.307790			−0.153895	+	0.988087i	$0.549182\pi$
$30$	1.52091	−	0.828750i	0.277679	−	0.151308i
$31$		−	3.58673i		−	0.644195i	−0.946706	−	0.322098i	$-0.895612\pi$
$31$		−	3.58673i		−	0.644195i	0.946706	−	0.322098i	$-0.104388\pi$
$32$	1.00000			0.176777
$33$	3.04182	−	1.65750i	0.529514	−	0.288534i
$34$		−	0.140096i		−	0.0240263i
$35$			4.83942i			0.818011i
$36$	−1.62635	+	2.52091i	−0.271058	+	0.420152i
$37$		−	6.36384i		−	1.04621i	−0.852269	−	0.523104i	$-0.824774\pi$
$37$		−	6.36384i		−	1.04621i	0.852269	−	0.523104i	$-0.175226\pi$
$38$	2.65750	+	3.45510i	0.431103	+	0.560491i
$39$	−1.58452	+	0.863412i	−0.253727	+	0.138257i
$40$			1.00000i			0.158114i
$41$	−1.18192			−0.184585			−0.0922924	−	0.995732i	$-0.529419\pi$
$41$	−1.18192			−0.184585			−0.0922924	+	0.995732i	$0.529419\pi$
$42$	−4.01067	−	7.36033i	−0.618860	−	1.13572i
$43$	−8.76865			−1.33721			−0.668603	−	0.743619i	$-0.733107\pi$
$43$	−8.76865			−1.33721			−0.668603	+	0.743619i	$0.733107\pi$
$44$			2.00000i			0.301511i
$45$	−2.52091	−	1.62635i	−0.375795	−	0.242441i
$46$		−	6.63702i		−	0.978575i
$47$			4.76865i			0.695579i	0.937573	+	0.347789i	$0.113068\pi$
$47$			4.76865i			0.695579i	−0.937573	+	0.347789i	$0.886932\pi$
$48$	−0.828750	−	1.52091i	−0.119620	−	0.219525i
$49$	16.4200			2.34571
$50$	−1.00000			−0.141421
$51$	−0.213074	+	0.116105i	−0.0298363	+	0.0162579i
$52$		−	1.04182i		−	0.144475i
$53$	8.42615			1.15742			0.578710	−	0.815533i	$-0.303556\pi$
$53$	8.42615			1.15742			0.578710	+	0.815533i	$0.303556\pi$
$54$	5.18192	+	0.384324i	0.705170	+	0.0522998i
$55$	−2.00000			−0.269680
$56$	4.83942			0.646695
$57$	3.05249	−	6.90524i	0.404313	−	0.914621i
$58$	−1.65750			−0.217640
$59$	0.350965			0.0456918			0.0228459	−	0.999739i	$-0.492727\pi$
$59$	0.350965			0.0456918			0.0228459	+	0.999739i	$0.492727\pi$
$60$	1.52091	−	0.828750i	0.196349	−	0.106991i
$61$	−10.4475			−1.33766			−0.668832	−	0.743414i	$-0.733205\pi$
$61$	−10.4475			−1.33766			−0.668832	+	0.743414i	$0.733205\pi$
$62$		−	3.58673i		−	0.455515i
$63$	−7.87057	+	12.1998i	−0.991599	+	1.53702i
$64$	1.00000			0.125000
$65$	1.04182			0.129222
$66$	3.04182	−	1.65750i	0.374423	−	0.204024i
$67$			13.6309i			1.66527i	0.553819	+	0.832637i	$0.313170\pi$
$67$			13.6309i			1.66527i	−0.553819	+	0.832637i	$0.686830\pi$
$68$		−	0.140096i		−	0.0169891i
$69$	−10.0943	+	5.50043i	−1.21521	+	0.662174i
$70$			4.83942i			0.578421i
$71$	−11.7625			−1.39595			−0.697975	−	0.716122i	$-0.745915\pi$
$71$	−11.7625			−1.39595			−0.697975	+	0.716122i	$0.745915\pi$
$72$	−1.62635	+	2.52091i	−0.191667	+	0.297092i
$73$	−2.83095			−0.331338			−0.165669	−	0.986181i	$-0.552978\pi$
$73$	−2.83095			−0.331338			−0.165669	+	0.986181i	$0.552978\pi$
$74$		−	6.36384i		−	0.739781i
$75$	0.828750	+	1.52091i	0.0956958	+	0.175620i
$76$	2.65750	+	3.45510i	0.304836	+	0.396327i
$77$			9.67884i			1.10301i
$78$	−1.58452	+	0.863412i	−0.179412	+	0.0977621i
$79$		−	10.0921i		−	1.13545i	−0.823218	−	0.567726i	$-0.807823\pi$
$79$		−	10.0921i		−	1.13545i	0.823218	−	0.567726i	$-0.192177\pi$
$80$			1.00000i			0.111803i
$81$	−3.70999	−	8.19975i	−0.412222	−	0.911084i
$82$	−1.18192			−0.130521
$83$			10.0342i			1.10140i	0.834704	+	0.550699i	$0.185639\pi$
$83$			10.0342i			1.10140i	−0.834704	+	0.550699i	$0.814361\pi$
$84$	−4.01067	−	7.36033i	−0.437600	−	0.803078i
$85$	0.140096			0.0151956
$86$	−8.76865			−0.945548
$87$	1.37365	+	2.52091i	0.147271	+	0.270270i
$88$			2.00000i			0.213201i
$89$	−16.4969			−1.74867			−0.874335	−	0.485323i	$-0.838702\pi$
$89$	−16.4969			−1.74867			−0.874335	+	0.485323i	$0.838702\pi$
$90$	−2.52091	−	1.62635i	−0.265727	−	0.171432i
$91$		−	5.04182i		−	0.528527i
$92$		−	6.63702i		−	0.691957i
$93$	−5.45510	+	2.97250i	−0.565667	+	0.308234i
$94$			4.76865i			0.491848i
$95$	−3.45510	+	2.65750i	−0.354485	+	0.272654i
$96$	−0.828750	−	1.52091i	−0.0845840	−	0.155227i
$97$			7.67884i			0.779668i	0.920885	+	0.389834i	$0.127468\pi$
$97$			7.67884i			0.779668i	−0.920885	+	0.389834i	$0.872532\pi$
$98$	16.4200			1.65867
$99$	−5.04182	−	3.25269i	−0.506722	−	0.326908i
$100$	−1.00000			−0.100000
$101$		−	10.4885i		−	1.04364i	−0.853056	−	0.521820i	$-0.825253\pi$
$101$		−	10.4885i		−	1.04364i	0.853056	−	0.521820i	$-0.174747\pi$
$102$	−0.213074	+	0.116105i	−0.0210975	+	0.0114961i
$103$			11.5373i			1.13680i	0.822751	+	0.568402i	$0.192438\pi$
$103$			11.5373i			1.13680i	−0.822751	+	0.568402i	$0.807562\pi$
$104$		−	1.04182i		−	0.102159i
$105$	7.36033	−	4.01067i	0.718295	−	0.391401i
$106$	8.42615			0.818420
$107$	−14.5098			−1.40271			−0.701357	−	0.712810i	$-0.747422\pi$
$107$	−14.5098			−1.40271			−0.701357	+	0.712810i	$0.747422\pi$
$108$	5.18192	+	0.384324i	0.498630	+	0.0369816i
$109$			8.62855i			0.826465i	0.910625	+	0.413233i	$0.135600\pi$
$109$			8.62855i			0.826465i	−0.910625	+	0.413233i	$0.864400\pi$
$110$	−2.00000			−0.190693
$111$	−9.67884	+	5.27403i	−0.918675	+	0.500589i
$112$	4.83942			0.457282
$113$	20.2509			1.90505			0.952524	−	0.304463i	$-0.0984769\pi$
$113$	20.2509			1.90505			0.952524	+	0.304463i	$0.0984769\pi$
$114$	3.05249	−	6.90524i	0.285892	−	0.646735i
$115$	6.63702			0.618905
$116$	−1.65750			−0.153895
$117$	2.62635	+	1.69437i	0.242806	+	0.156644i
$118$	0.350965			0.0323090
$119$		−	0.677984i		−	0.0621507i
$120$	1.52091	−	0.828750i	0.138840	−	0.0756542i
$121$	7.00000			0.636364
$122$	−10.4475			−0.945871
$123$	0.979516	+	1.79760i	0.0883200	+	0.162084i
$124$		−	3.58673i		−	0.322098i
$125$		−	1.00000i		−	0.0894427i
$126$	−7.87057	+	12.1998i	−0.701166	+	1.08684i
$127$			5.31500i			0.471630i	0.971798	+	0.235815i	$0.0757759\pi$
$127$			5.31500i			0.471630i	−0.971798	+	0.235815i	$0.924224\pi$
$128$	1.00000			0.0883883
$129$	7.26702	+	13.3363i	0.639825	+	1.17420i
$130$	1.04182			0.0913740
$131$			4.22519i			0.369157i	0.982818	+	0.184578i	$0.0590920\pi$
$131$			4.22519i			0.369157i	−0.982818	+	0.184578i	$0.940908\pi$
$132$	3.04182	−	1.65750i	0.264757	−	0.144267i
$133$	12.8608	+	16.7207i	1.11517	+	1.44987i
$134$			13.6309i			1.17753i
$135$	−0.384324	+	5.18192i	−0.0330773	+	0.445989i
$136$		−	0.140096i		−	0.0120131i
$137$		−	22.9374i		−	1.95967i	−0.199799	−	0.979837i	$-0.564029\pi$
$137$		−	22.9374i		−	1.95967i	0.199799	−	0.979837i	$-0.435971\pi$
$138$	−10.0943	+	5.50043i	−0.859285	+	0.468228i
$139$	−14.1673			−1.20165			−0.600827	−	0.799379i	$-0.705162\pi$
$139$	−14.1673			−1.20165			−0.600827	+	0.799379i	$0.705162\pi$
$140$			4.83942i			0.409006i
$141$	7.25269	−	3.95202i	0.610787	−	0.332820i
$142$	−11.7625			−0.987086
$143$	2.08365			0.174243
$144$	−1.62635	+	2.52091i	−0.135529	+	0.210076i
$145$		−	1.65750i		−	0.137648i
$146$	−2.83095			−0.234292
$147$	−13.6081	−	24.9734i	−1.12237	−	2.05977i
$148$		−	6.36384i		−	0.523104i
$149$		−	1.80346i		−	0.147745i	−0.997268	−	0.0738724i	$-0.976464\pi$
$149$		−	1.80346i		−	0.147745i	0.997268	−	0.0738724i	$-0.0235358\pi$
$150$	0.828750	+	1.52091i	0.0676672	+	0.124182i
$151$			2.62154i			0.213338i	0.994295	+	0.106669i	$0.0340184\pi$
$151$			2.62154i			0.213338i	−0.994295	+	0.106669i	$0.965982\pi$
$152$	2.65750	+	3.45510i	0.215552	+	0.280245i
$153$	0.353170	+	0.227845i	0.0285521	+	0.0184202i
$154$			9.67884i			0.779943i
$155$	3.58673			0.288093
$156$	−1.58452	+	0.863412i	−0.126863	+	0.0691283i
$157$	0.271727			0.0216862			0.0108431	−	0.999941i	$-0.496548\pi$
$157$	0.271727			0.0216862			0.0108431	+	0.999941i	$0.496548\pi$
$158$		−	10.0921i		−	0.802885i
$159$	−6.98317	−	12.8154i	−0.553801	−	1.01633i
$160$			1.00000i			0.0790569i
$161$		−	32.1193i		−	2.53136i
$162$	−3.70999	−	8.19975i	−0.291485	−	0.644233i
$163$	−2.96519			−0.232252			−0.116126	−	0.993235i	$-0.537048\pi$
$163$	−2.96519			−0.232252			−0.116126	+	0.993235i	$0.537048\pi$
$164$	−1.18192			−0.0922924
$165$	1.65750	+	3.04182i	0.129036	+	0.236806i
$166$			10.0342i			0.778806i
$167$	4.91019			0.379962			0.189981	−	0.981788i	$-0.439157\pi$
$167$	4.91019			0.379962			0.189981	+	0.981788i	$0.439157\pi$
$168$	−4.01067	−	7.36033i	−0.309430	−	0.567862i
$169$	11.9146			0.916508
$170$	0.140096			0.0107449
$171$	−13.0320	+	1.08014i	−0.996583	+	0.0826004i
$172$	−8.76865			−0.668603
$173$	−16.8692			−1.28254			−0.641272	−	0.767314i	$-0.721593\pi$
$173$	−16.8692			−1.28254			−0.641272	+	0.767314i	$0.721593\pi$
$174$	1.37365	+	2.52091i	0.104136	+	0.191110i
$175$	−4.83942			−0.365826
$176$			2.00000i			0.150756i
$177$	−0.290862	−	0.533787i	−0.0218626	−	0.0401219i
$178$	−16.4969			−1.23650
$179$	0.760182			0.0568187			0.0284093	−	0.999596i	$-0.490956\pi$
$179$	0.760182			0.0568187			0.0284093	+	0.999596i	$0.490956\pi$
$180$	−2.52091	−	1.62635i	−0.187898	−	0.121221i
$181$			16.7221i			1.24294i	0.783436	+	0.621472i	$0.213465\pi$
$181$			16.7221i			1.24294i	−0.783436	+	0.621472i	$0.786535\pi$
$182$		−	5.04182i		−	0.373725i
$183$	8.65836	+	15.8897i	0.640044	+	1.17460i
$184$		−	6.63702i		−	0.489287i
$185$	6.36384			0.467879
$186$	−5.45510	+	2.97250i	−0.399987	+	0.217954i
$187$	0.280192			0.0204897
$188$			4.76865i			0.347789i
$189$	25.0775	+	1.85990i	1.82412	+	0.135288i
$190$	−3.45510	+	2.65750i	−0.250659	+	0.192795i
$191$		−	23.5062i		−	1.70085i	−0.526095	−	0.850426i	$-0.676344\pi$
$191$		−	23.5062i		−	1.70085i	0.526095	−	0.850426i	$-0.323656\pi$
$192$	−0.828750	−	1.52091i	−0.0598099	−	0.109762i
$193$		−	6.10058i		−	0.439129i	−0.975598	−	0.219565i	$-0.929536\pi$
$193$		−	6.10058i		−	0.439129i	0.975598	−	0.219565i	$-0.0704637\pi$
$194$			7.67884i			0.551309i
$195$	−0.863412	−	1.58452i	−0.0618302	−	0.113470i
$196$	16.4200			1.17286
$197$		−	9.07749i		−	0.646744i	−0.946272	−	0.323372i	$-0.895183\pi$
$197$		−	9.07749i		−	0.646744i	0.946272	−	0.323372i	$-0.104817\pi$
$198$	−5.04182	−	3.25269i	−0.358307	−	0.231159i
$199$	−3.87979			−0.275031			−0.137516	−	0.990500i	$-0.543912\pi$
$199$	−3.87979			−0.275031			−0.137516	+	0.990500i	$0.543912\pi$
$200$	−1.00000			−0.0707107
$201$	20.7313	−	11.2966i	1.46228	−	0.796799i
$202$		−	10.4885i		−	0.737965i
$203$	−8.02134			−0.562988
$204$	−0.213074	+	0.116105i	−0.0149182	+	0.00812895i
$205$		−	1.18192i		−	0.0825489i
$206$			11.5373i			0.803841i
$207$	16.7313	+	10.7941i	1.16291	+	0.750241i
$208$		−	1.04182i		−	0.0722375i
$209$	−6.91019	+	5.31500i	−0.477988	+	0.367646i
$210$	7.36033	−	4.01067i	0.507911	−	0.276763i
$211$		−	18.8453i		−	1.29736i	−0.761060	−	0.648681i	$-0.775321\pi$
$211$		−	18.8453i		−	1.29736i	0.761060	−	0.648681i	$-0.224679\pi$
$212$	8.42615			0.578710
$213$	9.74816	+	17.8897i	0.667933	+	1.22578i
$214$	−14.5098			−0.991869
$215$		−	8.76865i		−	0.598017i
$216$	5.18192	+	0.384324i	0.352585	+	0.0261499i
$217$		−	17.3577i		−	1.17832i
$218$			8.62855i			0.584399i
$219$	2.34615	+	4.30563i	0.158538	+	0.290948i
$220$	−2.00000			−0.134840
$221$	−0.145955			−0.00981803
$222$	−9.67884	+	5.27403i	−0.649601	+	0.353970i
$223$		−	20.3925i		−	1.36558i	−0.730614	−	0.682791i	$-0.760766\pi$
$223$		−	20.3925i		−	1.36558i	0.730614	−	0.682791i	$-0.239234\pi$
$224$	4.83942			0.323347
$225$	1.62635	−	2.52091i	0.108423	−	0.168061i
$226$	20.2509			1.34707
$227$	4.14596			0.275177			0.137588	−	0.990489i	$-0.456065\pi$
$227$	4.14596			0.275177			0.137588	+	0.990489i	$0.456065\pi$
$228$	3.05249	−	6.90524i	0.202156	−	0.457310i
$229$	−4.50539			−0.297724			−0.148862	−	0.988858i	$-0.547561\pi$
$229$	−4.50539			−0.297724			−0.148862	+	0.988858i	$0.547561\pi$
$230$	6.63702			0.437632
$231$	14.7207	−	8.02134i	0.968549	−	0.527765i
$232$	−1.65750			−0.108820
$233$		−	9.86982i		−	0.646593i	−0.946298	−	0.323297i	$-0.895209\pi$
$233$		−	9.86982i		−	0.646593i	0.946298	−	0.323297i	$-0.104791\pi$
$234$	2.62635	+	1.69437i	0.171690	+	0.110764i
$235$	−4.76865			−0.311072
$236$	0.350965			0.0228459
$237$	−15.3492	+	8.36384i	−0.997039	+	0.543290i
$238$		−	0.677984i		−	0.0439472i
$239$			25.8970i			1.67514i	0.546331	+	0.837569i	$0.316024\pi$
$239$			25.8970i			1.67514i	−0.546331	+	0.837569i	$0.683976\pi$
$240$	1.52091	−	0.828750i	0.0981744	−	0.0534956i
$241$		−	10.5311i		−	0.678370i	−0.940720	−	0.339185i	$-0.889849\pi$
$241$		−	10.5311i		−	0.678370i	0.940720	−	0.339185i	$-0.110151\pi$
$242$	7.00000			0.449977
$243$	−9.39644	+	12.4381i	−0.602782	+	0.797906i
$244$	−10.4475			−0.668832
$245$			16.4200i			1.04903i
$246$	0.979516	+	1.79760i	0.0624517	+	0.114611i
$247$	3.59960	−	2.76865i	0.229037	−	0.176165i
$248$		−	3.58673i		−	0.227757i
$249$	15.2612	−	8.31586i	0.967137	−	0.526996i
$250$		−	1.00000i		−	0.0632456i
$251$			19.9848i			1.26143i	0.776015	+	0.630714i	$0.217238\pi$
$251$			19.9848i			1.26143i	−0.776015	+	0.630714i	$0.782762\pi$
$252$	−7.87057	+	12.1998i	−0.495800	+	0.768512i
$253$	13.2740			0.834531
$254$			5.31500i			0.333493i
$255$	−0.116105	−	0.213074i	−0.00727076	−	0.0133432i
$256$	1.00000			0.0625000
$257$	−9.59519			−0.598532			−0.299266	−	0.954170i	$-0.596742\pi$
$257$	−9.59519			−0.598532			−0.299266	+	0.954170i	$0.596742\pi$
$258$	7.26702	+	13.3363i	0.452425	+	0.830284i
$259$		−	30.7973i		−	1.91365i
$260$	1.04182			0.0646112
$261$	2.69567	−	4.17841i	0.166858	−	0.258637i
$262$			4.22519i			0.261033i
$263$		−	12.3925i		−	0.764154i	−0.924131	−	0.382077i	$-0.875209\pi$
$263$		−	12.3925i		−	0.764154i	0.924131	−	0.382077i	$-0.124791\pi$
$264$	3.04182	−	1.65750i	0.187211	−	0.102012i
$265$			8.42615i			0.517614i
$266$	12.8608	+	16.7207i	0.788544	+	1.02521i
$267$	13.6718	+	25.0904i	0.836702	+	1.53551i
$268$			13.6309i			0.832637i
$269$	−13.1354			−0.800879			−0.400439	−	0.916323i	$-0.631142\pi$
$269$	−13.1354			−0.800879			−0.400439	+	0.916323i	$0.631142\pi$
$270$	−0.384324	+	5.18192i	−0.0233892	+	0.315362i
$271$	10.2179			0.620692			0.310346	−	0.950624i	$-0.399555\pi$
$271$	10.2179			0.620692			0.310346	+	0.950624i	$0.399555\pi$
$272$		−	0.140096i		−	0.00849457i
$273$	−7.66817	+	4.17841i	−0.464099	+	0.252889i
$274$		−	22.9374i		−	1.38570i
$275$		−	2.00000i		−	0.120605i
$276$	−10.0943	+	5.50043i	−0.607607	+	0.331087i
$277$	−10.2337			−0.614881			−0.307440	−	0.951567i	$-0.599472\pi$
$277$	−10.2337			−0.614881			−0.307440	+	0.951567i	$0.599472\pi$
$278$	−14.1673			−0.849698
$279$	9.04182	+	5.83326i	0.541320	+	0.349228i
$280$			4.83942i			0.289211i
$281$	−7.00231			−0.417723			−0.208861	−	0.977945i	$-0.566976\pi$
$281$	−7.00231			−0.417723			−0.208861	+	0.977945i	$0.566976\pi$
$282$	7.25269	−	3.95202i	0.431892	−	0.235339i
$283$	11.9708			0.711587			0.355794	−	0.934565i	$-0.384211\pi$
$283$	11.9708			0.711587			0.355794	+	0.934565i	$0.384211\pi$
$284$	−11.7625			−0.697975
$285$	6.90524	+	3.05249i	0.409031	+	0.180814i
$286$	2.08365			0.123209
$287$	−5.71981			−0.337630
$288$	−1.62635	+	2.52091i	−0.0958334	+	0.148546i
$289$	16.9804			0.998845
$290$		−	1.65750i		−	0.0973318i
$291$	11.6788	−	6.36384i	0.684626	−	0.373055i
$292$	−2.83095			−0.165669
$293$	21.7581			1.27112			0.635560	−	0.772051i	$-0.280769\pi$
$293$	21.7581			1.27112			0.635560	+	0.772051i	$0.280769\pi$
$294$	−13.6081	−	24.9734i	−0.793639	−	1.45648i
$295$			0.350965i			0.0204340i
$296$		−	6.36384i		−	0.369891i
$297$	−0.768647	+	10.3638i	−0.0446014	+	0.601371i
$298$		−	1.80346i		−	0.104471i
$299$	−6.91460			−0.399882
$300$	0.828750	+	1.52091i	0.0478479	+	0.0878099i
$301$	−42.4352			−2.44592
$302$			2.62154i			0.150852i
$303$	−15.9520	+	8.69231i	−0.916419	+	0.499360i
$304$	2.65750	+	3.45510i	0.152418	+	0.198163i
$305$		−	10.4475i		−	0.598221i
$306$	0.353170	+	0.227845i	0.0201894	+	0.0130250i
$307$			29.4413i			1.68031i	0.542350	+	0.840153i	$0.317535\pi$
$307$			29.4413i			1.68031i	−0.542350	+	0.840153i	$0.682465\pi$
$308$			9.67884i			0.551503i
$309$	17.5472	−	9.56153i	0.998226	−	0.543937i
$310$	3.58673			0.203712
$311$			1.50453i			0.0853140i	0.999090	+	0.0426570i	$0.0135823\pi$
$311$			1.50453i			0.0853140i	−0.999090	+	0.0426570i	$0.986418\pi$
$312$	−1.58452	+	0.863412i	−0.0897059	+	0.0488811i
$313$	−26.4975			−1.49773			−0.748863	−	0.662725i	$-0.769400\pi$
$313$	−26.4975			−1.49773			−0.748863	+	0.662725i	$0.769400\pi$
$314$	0.271727			0.0153344
$315$	−12.1998	−	7.87057i	−0.687378	−	0.443457i
$316$		−	10.0921i		−	0.567726i
$317$	9.47499			0.532168			0.266084	−	0.963950i	$-0.414270\pi$
$317$	9.47499			0.532168			0.266084	+	0.963950i	$0.414270\pi$
$318$	−6.98317	−	12.8154i	−0.391597	−	0.718654i
$319$		−	3.31500i		−	0.185604i
$320$			1.00000i			0.0559017i
$321$	12.0250	+	22.0681i	0.671170	+	1.23172i
$322$		−	32.1193i		−	1.78994i
$323$	0.484046	−	0.372305i	0.0269330	−	0.0207156i
$324$	−3.70999	−	8.19975i	−0.206111	−	0.455542i
$325$			1.04182i			0.0577900i
$326$	−2.96519			−0.164227
$327$	13.1233	−	7.15091i	0.725718	−	0.395446i
$328$	−1.18192			−0.0652606
$329$			23.0775i			1.27230i
$330$	1.65750	+	3.04182i	0.0912424	+	0.167447i
$331$			1.48931i			0.0818600i	0.999162	+	0.0409300i	$0.0130321\pi$
$331$			1.48931i			0.0818600i	−0.999162	+	0.0409300i	$0.986968\pi$
$332$			10.0342i			0.550699i
$333$	16.0427	+	10.3498i	0.879133	+	0.567166i
$334$	4.91019			0.268674
$335$	−13.6309			−0.744733
$336$	−4.01067	−	7.36033i	−0.218800	−	0.401539i
$337$			22.2392i			1.21145i	0.795675	+	0.605724i	$0.207116\pi$
$337$			22.2392i			1.21145i	−0.795675	+	0.605724i	$0.792884\pi$
$338$	11.9146			0.648069
$339$	−16.7830	−	30.7999i	−0.911526	−	1.67282i
$340$	0.140096			0.00759778
$341$	7.17345			0.388464
$342$	−13.0320	+	1.08014i	−0.704690	+	0.0584073i
$343$	45.5873			2.46148
$344$	−8.76865			−0.472774
$345$	−5.50043	−	10.0943i	−0.296133	−	0.543460i
$346$	−16.8692			−0.906895
$347$		−	1.04327i		−	0.0560059i	−0.999608	−	0.0280029i	$-0.991085\pi$
$347$		−	1.04327i		−	0.0560059i	0.999608	−	0.0280029i	$-0.00891478\pi$
$348$	1.37365	+	2.52091i	0.0736356	+	0.135135i
$349$	−6.14155			−0.328749			−0.164375	−	0.986398i	$-0.552561\pi$
$349$	−6.14155			−0.328749			−0.164375	+	0.986398i	$0.552561\pi$
$350$	−4.83942			−0.258678
$351$	0.400398	−	5.39865i	0.0213716	−	0.288159i
$352$			2.00000i			0.106600i
$353$		−	2.22374i		−	0.118358i	−0.998247	−	0.0591790i	$-0.981152\pi$
$353$		−	2.22374i		−	0.118358i	0.998247	−	0.0591790i	$-0.0188483\pi$
$354$	−0.290862	−	0.533787i	−0.0154592	−	0.0283705i
$355$		−	11.7625i		−	0.624288i
$356$	−16.4969			−0.874335
$357$	−1.03115	+	0.561879i	−0.0545744	+	0.0297378i
$358$	0.760182			0.0401769
$359$			2.83646i			0.149703i	0.997195	+	0.0748513i	$0.0238482\pi$
$359$			2.83646i			0.149703i	−0.997195	+	0.0748513i	$0.976152\pi$
$360$	−2.52091	−	1.62635i	−0.132864	−	0.0857160i
$361$	−4.87538	+	18.3638i	−0.256599	+	0.966518i
$362$			16.7221i			0.878895i
$363$	−5.80125	−	10.6464i	−0.304487	−	0.558790i
$364$		−	5.04182i		−	0.264263i
$365$		−	2.83095i		−	0.148179i
$366$	8.65836	+	15.8897i	0.452580	+	0.830568i
$367$	7.87864			0.411262			0.205631	−	0.978630i	$-0.434075\pi$
$367$	7.87864			0.411262			0.205631	+	0.978630i	$0.434075\pi$
$368$		−	6.63702i		−	0.345978i
$369$	1.92221	−	2.97952i	0.100066	−	0.155107i
$370$	6.36384			0.330840
$371$	40.7777			2.11707
$372$	−5.45510	+	2.97250i	−0.282834	+	0.154117i
$373$		−	13.8684i		−	0.718077i	−0.933323	−	0.359038i	$-0.883105\pi$
$373$		−	13.8684i		−	0.718077i	0.933323	−	0.359038i	$-0.116895\pi$
$374$	0.280192			0.0144884
$375$	−1.52091	+	0.828750i	−0.0785396	+	0.0427965i
$376$			4.76865i			0.245924i
$377$			1.72682i			0.0889359i
$378$	25.0775	+	1.85990i	1.28985	+	0.0956631i
$379$		−	20.9430i		−	1.07577i	−0.843019	−	0.537884i	$-0.819224\pi$
$379$		−	20.9430i		−	1.07577i	0.843019	−	0.537884i	$-0.180776\pi$
$380$	−3.45510	+	2.65750i	−0.177243	+	0.136327i
$381$	8.08365	−	4.40481i	0.414138	−	0.225665i
$382$		−	23.5062i		−	1.20268i
$383$	22.2848			1.13870			0.569350	−	0.822095i	$-0.307195\pi$
$383$	22.2848			1.13870			0.569350	+	0.822095i	$0.307195\pi$
$384$	−0.828750	−	1.52091i	−0.0422920	−	0.0776137i
$385$	−9.67884			−0.493279
$386$		−	6.10058i		−	0.310511i
$387$	14.2609	−	22.1050i	0.724920	−	1.12366i
$388$			7.67884i			0.389834i
$389$		−	1.92807i		−	0.0977571i	−0.998805	−	0.0488785i	$-0.984435\pi$
$389$		−	1.92807i		−	0.0977571i	0.998805	−	0.0488785i	$-0.0155647\pi$
$390$	−0.863412	−	1.58452i	−0.0437206	−	0.0802354i
$391$	−0.929820			−0.0470230
$392$	16.4200			0.829335
$393$	6.42615	−	3.50163i	0.324156	−	0.176634i
$394$		−	9.07749i		−	0.457317i
$395$	10.0921			0.507789
$396$	−5.04182	−	3.25269i	−0.253361	−	0.163454i
$397$	28.4986			1.43031			0.715153	−	0.698968i	$-0.246357\pi$
$397$	28.4986			1.43031			0.715153	+	0.698968i	$0.246357\pi$
$398$	−3.87979			−0.194477
$399$	14.7723	−	33.4173i	0.739540	−	1.67296i
$400$	−1.00000			−0.0500000
$401$	2.25770			0.112744			0.0563720	−	0.998410i	$-0.482047\pi$
$401$	2.25770			0.112744			0.0563720	+	0.998410i	$0.482047\pi$
$402$	20.7313	−	11.2966i	1.03398	−	0.563422i
$403$	−3.73674			−0.186140
$404$		−	10.4885i		−	0.521820i
$405$	8.19975	−	3.70999i	0.407449	−	0.184351i
$406$	−8.02134			−0.398092
$407$	12.7277			0.630888
$408$	−0.213074	+	0.116105i	−0.0105487	+	0.00574804i
$409$		−	15.8754i		−	0.784987i	−0.919755	−	0.392494i	$-0.871613\pi$
$409$		−	15.8754i		−	0.784987i	0.919755	−	0.392494i	$-0.128387\pi$
$410$		−	1.18192i		−	0.0583709i
$411$	−34.8858	+	19.0094i	−1.72079	+	0.937663i
$412$			11.5373i			0.568402i
$413$	1.69847			0.0835761
$414$	16.7313	+	10.7941i	0.822300	+	0.530501i
$415$	−10.0342			−0.492560
$416$		−	1.04182i		−	0.0510796i
$417$	11.7411	+	21.5472i	0.574966	+	1.05517i
$418$	−6.91019	+	5.31500i	−0.337989	+	0.259965i
$419$		−	2.56038i		−	0.125083i	−0.998042	−	0.0625415i	$-0.980079\pi$
$419$		−	2.56038i		−	0.125083i	0.998042	−	0.0625415i	$-0.0199206\pi$
$420$	7.36033	−	4.01067i	0.359147	−	0.195701i
$421$		−	9.06201i		−	0.441655i	−0.975313	−	0.220828i	$-0.929124\pi$
$421$		−	9.06201i		−	0.441655i	0.975313	−	0.220828i	$-0.0708758\pi$
$422$		−	18.8453i		−	0.917374i
$423$	−12.0213	−	7.75547i	−0.584498	−	0.377084i
$424$	8.42615			0.409210
$425$			0.140096i			0.00679566i
$426$	9.74816	+	17.8897i	0.472300	+	0.866759i
$427$	−50.5598			−2.44676
$428$	−14.5098			−0.701357
$429$	−1.72682	−	3.16905i	−0.0833718	−	0.153003i
$430$		−	8.76865i		−	0.422862i
$431$	30.8259			1.48483			0.742417	−	0.669938i	$-0.233679\pi$
$431$	30.8259			1.48483			0.742417	+	0.669938i	$0.233679\pi$
$432$	5.18192	+	0.384324i	0.249315	+	0.0184908i
$433$		−	36.8692i		−	1.77182i	−0.463855	−	0.885911i	$-0.653534\pi$
$433$		−	36.8692i		−	1.77182i	0.463855	−	0.885911i	$-0.346466\pi$
$434$		−	17.3577i		−	0.833195i
$435$	−2.52091	+	1.37365i	−0.120868	+	0.0658616i
$436$			8.62855i			0.413233i
$437$	22.9315	−	17.6379i	1.09696	−	0.843734i
$438$	2.34615	+	4.30563i	0.112104	+	0.205731i
$439$			25.5715i			1.22046i	0.792224	+	0.610231i	$0.208923\pi$
$439$			25.5715i			1.22046i	−0.792224	+	0.610231i	$0.791077\pi$
$440$	−2.00000			−0.0953463
$441$	−26.7046	+	41.3933i	−1.27165	+	1.97111i
$442$	−0.145955			−0.00694239
$443$			32.4267i			1.54064i	0.637658	+	0.770320i	$0.279903\pi$
$443$			32.4267i			1.54064i	−0.637658	+	0.770320i	$0.720097\pi$
$444$	−9.67884	+	5.27403i	−0.459337	+	0.250295i
$445$		−	16.4969i		−	0.782029i
$446$		−	20.3925i		−	0.965612i
$447$	−2.74290	+	1.49461i	−0.129735	+	0.0706928i
$448$	4.83942			0.228641
$449$	−21.3521			−1.00767			−0.503834	−	0.863800i	$-0.668078\pi$
$449$	−21.3521			−1.00767			−0.503834	+	0.863800i	$0.668078\pi$
$450$	1.62635	−	2.52091i	0.0766667	−	0.118837i
$451$		−	2.36384i		−	0.111309i
$452$	20.2509			0.952524
$453$	3.98712	−	2.17260i	0.187331	−	0.102078i
$454$	4.14596			0.194579
$455$	5.04182			0.236364
$456$	3.05249	−	6.90524i	0.142946	−	0.323367i
$457$	−3.22404			−0.150814			−0.0754072	−	0.997153i	$-0.524026\pi$
$457$	−3.22404			−0.150814			−0.0754072	+	0.997153i	$0.524026\pi$
$458$	−4.50539			−0.210523
$459$	0.0538422	−	0.725967i	0.00251314	−	0.0338852i
$460$	6.63702			0.309452
$461$		−	32.5340i		−	1.51526i	−0.652684	−	0.757631i	$-0.726357\pi$
$461$		−	32.5340i		−	1.51526i	0.652684	−	0.757631i	$-0.273643\pi$
$462$	14.7207	−	8.02134i	0.684867	−	0.373187i
$463$	−24.0798			−1.11908			−0.559541	−	0.828802i	$-0.689023\pi$
$463$	−24.0798			−1.11908			−0.559541	+	0.828802i	$0.689023\pi$
$464$	−1.65750			−0.0769475
$465$	−2.97250	−	5.45510i	−0.137846	−	0.252974i
$466$		−	9.86982i		−	0.457211i
$467$			33.7996i			1.56406i	0.623241	+	0.782030i	$0.285815\pi$
$467$			33.7996i			1.56406i	−0.623241	+	0.782030i	$0.714185\pi$
$468$	2.62635	+	1.69437i	0.121403	+	0.0783221i
$469$			65.9654i			3.04600i
$470$	−4.76865			−0.219961
$471$	−0.225194	−	0.413273i	−0.0103764	−	0.0190426i
$472$	0.350965			0.0161545
$473$		−	17.5373i		−	0.806366i
$474$	−15.3492	+	8.36384i	−0.705013	+	0.384164i
$475$	−2.65750	−	3.45510i	−0.121934	−	0.158531i
$476$		−	0.677984i		−	0.0310753i
$477$	−13.7038	+	21.2416i	−0.627456	+	0.972585i
$478$			25.8970i			1.18450i
$479$		−	0.601352i		−	0.0274765i	−0.999906	−	0.0137382i	$-0.995627\pi$
$479$		−	0.601352i		−	0.0274765i	0.999906	−	0.0137382i	$-0.00437315\pi$
$480$	1.52091	−	0.828750i	0.0694198	−	0.0378271i
$481$	−6.63000			−0.302302
$482$		−	10.5311i		−	0.479680i
$483$	−48.8506	+	26.6189i	−2.22278	+	1.21120i
$484$	7.00000			0.318182
$485$	−7.67884			−0.348678
$486$	−9.39644	+	12.4381i	−0.426231	+	0.564205i
$487$			6.40481i			0.290230i	0.989415	+	0.145115i	$0.0463551\pi$
$487$			6.40481i			0.290230i	−0.989415	+	0.145115i	$0.953645\pi$
$488$	−10.4475			−0.472936
$489$	2.45740	+	4.50980i	0.111128	+	0.203940i
$490$			16.4200i			0.741779i
$491$			38.6148i			1.74266i	0.490697	+	0.871330i	$0.336742\pi$
$491$			38.6148i			1.74266i	−0.490697	+	0.871330i	$0.663258\pi$
$492$	0.979516	+	1.79760i	0.0441600	+	0.0810419i
$493$			0.232209i			0.0104582i
$494$	3.59960	−	2.76865i	0.161954	−	0.124567i
$495$	3.25269	−	5.04182i	0.146198	−	0.226613i
$496$		−	3.58673i		−	0.161049i
$497$	−56.9236			−2.55337
$498$	15.2612	−	8.31586i	0.683869	−	0.372642i
$499$	−32.2936			−1.44566			−0.722831	−	0.691025i	$-0.757159\pi$
$499$	−32.2936			−1.44566			−0.722831	+	0.691025i	$0.757159\pi$
$500$		−	1.00000i		−	0.0447214i
$501$	−4.06932	−	7.46797i	−0.181804	−	0.333644i
$502$			19.9848i			0.891965i
$503$		−	32.0643i		−	1.42968i	−0.699290	−	0.714839i	$-0.746500\pi$
$503$		−	32.0643i		−	1.42968i	0.699290	−	0.714839i	$-0.253500\pi$
$504$	−7.87057	+	12.1998i	−0.350583	+	0.543420i
$505$	10.4885			0.466730
$506$	13.2740			0.590103
$507$	−9.87423	−	18.1211i	−0.438530	−	0.804785i
$508$			5.31500i			0.235815i
$509$	9.15232			0.405669			0.202835	−	0.979213i	$-0.434985\pi$
$509$	9.15232			0.405669			0.202835	+	0.979213i	$0.434985\pi$
$510$	−0.116105	−	0.213074i	−0.00514120	−	0.00943507i
$511$	−13.7002			−0.606060
$512$	1.00000			0.0441942
$513$	12.4431	+	18.9254i	0.549375	+	0.835576i
$514$	−9.59519			−0.423226
$515$	−11.5373			−0.508394
$516$	7.26702	+	13.3363i	0.319913	+	0.587100i
$517$	−9.53729			−0.419450
$518$		−	30.7973i		−	1.35316i
$519$	13.9804	+	25.6566i	0.613670	+	1.12620i
$520$	1.04182			0.0456870
$521$	−37.6721			−1.65044			−0.825222	−	0.564808i	$-0.808950\pi$
$521$	−37.6721			−1.65044			−0.825222	+	0.564808i	$0.808950\pi$
$522$	2.69567	−	4.17841i	0.117986	−	0.182884i
$523$			6.44047i			0.281622i	0.990036	+	0.140811i	$0.0449710\pi$
$523$			6.44047i			0.281622i	−0.990036	+	0.140811i	$0.955029\pi$
$524$			4.22519i			0.184578i
$525$	4.01067	+	7.36033i	0.175040	+	0.321231i
$526$		−	12.3925i		−	0.540338i
$527$	−0.502486			−0.0218887
$528$	3.04182	−	1.65750i	0.132378	−	0.0721334i
$529$	−21.0500			−0.915217
$530$			8.42615i			0.366008i
$531$	−0.570791	+	0.884752i	−0.0247702	+	0.0383950i
$532$	12.8608	+	16.7207i	0.557585	+	0.724933i
$533$			1.23135i			0.0533358i
$534$	13.6718	+	25.0904i	0.591638	+	1.08577i
$535$		−	14.5098i		−	0.627313i
$536$			13.6309i			0.588763i
$537$	−0.630001	−	1.15617i	−0.0271865	−	0.0498924i
$538$	−13.1354			−0.566307
$539$			32.8400i			1.41452i
$540$	−0.384324	+	5.18192i	−0.0165387	+	0.222994i
$541$	−32.9190			−1.41530			−0.707649	−	0.706564i	$-0.750244\pi$
$541$	−32.9190			−1.41530			−0.707649	+	0.706564i	$0.750244\pi$
$542$	10.2179			0.438896
$543$	25.4329	−	13.8585i	1.09143	−	0.594723i
$544$		−	0.140096i		−	0.00600657i
$545$	−8.62855			−0.369607
$546$	−7.66817	+	4.17841i	−0.328167	+	0.178820i
$547$		−	31.3436i		−	1.34016i	−0.742290	−	0.670079i	$-0.766260\pi$
$547$		−	31.3436i		−	1.34016i	0.742290	−	0.670079i	$-0.233740\pi$
$548$		−	22.9374i		−	0.979837i
$549$	16.9912	−	26.3372i	0.725168	−	1.12404i
$550$		−	2.00000i		−	0.0852803i
$551$	−4.40481	−	5.72682i	−0.187651	−	0.243971i
$552$	−10.0943	+	5.50043i	−0.429643	+	0.234114i
$553$		−	48.8400i		−	2.07689i
$554$	−10.2337			−0.434787
$555$	−5.27403	−	9.67884i	−0.223870	−	0.410844i
$556$	−14.1673			−0.600827
$557$		−	4.58442i		−	0.194248i	−0.995272	−	0.0971241i	$-0.969036\pi$
$557$		−	4.58442i		−	0.194248i	0.995272	−	0.0971241i	$-0.0309644\pi$
$558$	9.04182	+	5.83326i	0.382771	+	0.246942i
$559$			9.13539i			0.386386i
$560$			4.83942i			0.204503i
$561$	−0.232209	−	0.426148i	−0.00980388	−	0.0179920i
$562$	−7.00231			−0.295374
$563$	−6.08075			−0.256273			−0.128136	−	0.991757i	$-0.540900\pi$
$563$	−6.08075			−0.256273			−0.128136	+	0.991757i	$0.540900\pi$
$564$	7.25269	−	3.95202i	0.305393	−	0.166410i
$565$			20.2509i			0.851964i
$566$	11.9708			0.503168
$567$	−17.9542	−	39.6820i	−0.754006	−	1.66649i
$568$	−11.7625			−0.493543
$569$	32.4694			1.36119			0.680594	−	0.732661i	$-0.261722\pi$
$569$	32.4694			1.36119			0.680594	+	0.732661i	$0.261722\pi$
$570$	6.90524	+	3.05249i	0.289228	+	0.127855i
$571$	15.6636			0.655502			0.327751	−	0.944764i	$-0.393709\pi$
$571$	15.6636			0.655502			0.327751	+	0.944764i	$0.393709\pi$
$572$	2.08365			0.0871217
$573$	−35.7509	+	19.4808i	−1.49352	+	0.813822i
$574$	−5.71981			−0.238740
$575$			6.63702i			0.276783i
$576$	−1.62635	+	2.52091i	−0.0677644	+	0.105038i
$577$	42.7379			1.77920			0.889601	−	0.456739i	$-0.150983\pi$
$577$	42.7379			1.77920			0.889601	+	0.456739i	$0.150983\pi$
$578$	16.9804			0.706290
$579$	−9.27844	+	5.05586i	−0.385599	+	0.210114i
$580$		−	1.65750i		−	0.0688240i
$581$			48.5598i			2.01460i
$582$	11.6788	−	6.36384i	0.484104	−	0.263790i
$583$			16.8523i			0.697951i
$584$	−2.83095			−0.117146
$585$	−1.69437	+	2.62635i	−0.0700534	+	0.108586i
$586$	21.7581			0.898818
$587$			31.5042i			1.30032i	0.759799	+	0.650159i	$0.225298\pi$
$587$			31.5042i			1.30032i	−0.759799	+	0.650159i	$0.774702\pi$
$588$	−13.6081	−	24.9734i	−0.561187	−	1.02988i
$589$	12.3925	−	9.53173i	0.510624	−	0.392748i
$590$			0.350965i			0.0144490i
$591$	−13.8061	+	7.52297i	−0.567905	+	0.309454i
$592$		−	6.36384i		−	0.261552i
$593$		−	44.9444i		−	1.84565i	−0.385225	−	0.922823i	$-0.625876\pi$
$593$		−	44.9444i		−	1.84565i	0.385225	−	0.922823i	$-0.374124\pi$
$594$	−0.768647	+	10.3638i	−0.0315380	+	0.425234i
$595$	0.677984			0.0277946
$596$		−	1.80346i		−	0.0738724i
$597$	3.21538	+	5.90083i	0.131597	+	0.241505i
$598$	−6.91460			−0.282759
$599$	10.2083			0.417098			0.208549	−	0.978012i	$-0.433126\pi$
$599$	10.2083			0.417098			0.208549	+	0.978012i	$0.433126\pi$
$600$	0.828750	+	1.52091i	0.0338336	+	0.0620910i
$601$			12.7534i			0.520223i	0.965579	+	0.260112i	$0.0837594\pi$
$601$			12.7534i			0.520223i	−0.965579	+	0.260112i	$0.916241\pi$
$602$	−42.4352			−1.72953
$603$	−34.3622	−	22.1685i	−1.39934	−	0.902771i
$604$			2.62154i			0.106669i
$605$			7.00000i			0.284590i
$606$	−15.9520	+	8.69231i	−0.648006	+	0.353101i
$607$			41.6665i			1.69119i	0.533823	+	0.845596i	$0.320755\pi$
$607$			41.6665i			1.69119i	−0.533823	+	0.845596i	$0.679245\pi$
$608$	2.65750	+	3.45510i	0.107776	+	0.140123i
$609$	6.64769	+	12.1998i	0.269378	+	0.494359i
$610$		−	10.4475i		−	0.423006i
$611$	4.96809			0.200987
$612$	0.353170	+	0.227845i	0.0142760	+	0.00921008i
$613$	9.10117			0.367593			0.183796	−	0.982964i	$-0.441161\pi$
$613$	9.10117			0.367593			0.183796	+	0.982964i	$0.441161\pi$
$614$			29.4413i			1.18816i
$615$	−1.79760	+	0.979516i	−0.0724861	+	0.0394979i
$616$			9.67884i			0.389972i
$617$			45.0128i			1.81215i	0.423119	+	0.906074i	$0.360935\pi$
$617$			45.0128i			1.81215i	−0.423119	+	0.906074i	$0.639065\pi$
$618$	17.5472	−	9.56153i	0.705852	−	0.384621i
$619$	8.58903			0.345222			0.172611	−	0.984990i	$-0.444780\pi$
$619$	8.58903			0.345222			0.172611	+	0.984990i	$0.444780\pi$
$620$	3.58673			0.144046
$621$	2.55076	−	34.3925i	0.102359	−	1.38012i
$622$			1.50453i			0.0603261i
$623$	−79.8355			−3.19854
$624$	−1.58452	+	0.863412i	−0.0634317	+	0.0345641i
$625$	1.00000			0.0400000
$626$	−26.4975			−1.05905
$627$	13.8105	+	6.10499i	0.551537	+	0.243810i
$628$	0.271727			0.0108431
$629$	−0.891549			−0.0355484
$630$	−12.1998	−	7.87057i	−0.486050	−	0.313571i
$631$	4.01693			0.159911			0.0799557	−	0.996798i	$-0.474522\pi$
$631$	4.01693			0.159911			0.0799557	+	0.996798i	$0.474522\pi$
$632$		−	10.0921i		−	0.401443i
$633$	−28.6620	+	15.6180i	−1.13921	+	0.620761i
$634$	9.47499			0.376300
$635$	−5.31500			−0.210919
$636$	−6.98317	−	12.8154i	−0.276901	−	0.508165i
$637$		−	17.1067i		−	0.677794i
$638$		−	3.31500i		−	0.131242i
$639$	19.1299	−	29.6522i	0.756766	−	1.17302i
$640$			1.00000i			0.0395285i
$641$	25.1088			0.991738			0.495869	−	0.868397i	$-0.334850\pi$
$641$	25.1088			0.991738			0.495869	+	0.868397i	$0.334850\pi$
$642$	12.0250	+	22.0681i	0.474589	+	0.870959i
$643$	8.77155			0.345916			0.172958	−	0.984929i	$-0.444668\pi$
$643$	8.77155			0.345916			0.172958	+	0.984929i	$0.444668\pi$
$644$		−	32.1193i		−	1.26568i
$645$	−13.3363	+	7.26702i	−0.525118	+	0.286139i
$646$	0.484046	−	0.372305i	0.0190445	−	0.0146482i
$647$			6.00530i			0.236093i	0.993008	+	0.118046i	$0.0376632\pi$
$647$			6.00530i			0.236093i	−0.993008	+	0.118046i	$0.962337\pi$
$648$	−3.70999	−	8.19975i	−0.145742	−	0.322117i
$649$			0.701930i			0.0275532i
$650$			1.04182i			0.0408637i
$651$	−26.3995	+	14.3852i	−1.03468	+	0.563800i
$652$	−2.96519			−0.116126
$653$		−	13.6121i		−	0.532684i	−0.963879	−	0.266342i	$-0.914185\pi$
$653$		−	13.6121i		−	0.532684i	0.963879	−	0.266342i	$-0.0858150\pi$
$654$	13.1233	−	7.15091i	0.513160	−	0.279623i
$655$	−4.22519			−0.165092
$656$	−1.18192			−0.0461462
$657$	4.60411	−	7.13659i	0.179624	−	0.278425i
$658$			23.0775i			0.899654i
$659$	38.7575			1.50978			0.754889	−	0.655853i	$-0.227691\pi$
$659$	38.7575			1.50978			0.754889	+	0.655853i	$0.227691\pi$
$660$	1.65750	+	3.04182i	0.0645181	+	0.118403i
$661$			0.645482i			0.0251063i	0.999921	+	0.0125532i	$0.00399590\pi$
$661$			0.645482i			0.0251063i	−0.999921	+	0.0125532i	$0.996004\pi$
$662$			1.48931i			0.0578838i
$663$	0.120961	+	0.221985i	0.00469772	+	0.00862120i
$664$			10.0342i			0.389403i
$665$	−16.7207	+	12.8608i	−0.648400	+	0.498719i
$666$	16.0427	+	10.3498i	0.621641	+	0.401047i
$667$			11.0009i			0.425955i
$668$	4.91019			0.189981
$669$	−31.0152	+	16.9003i	−1.19912	+	0.653403i
$670$	−13.6309			−0.526606
$671$		−	20.8950i		−	0.806642i
$672$	−4.01067	−	7.36033i	−0.154715	−	0.283931i
$673$		−	39.5630i		−	1.52504i	−0.646963	−	0.762522i	$-0.723961\pi$
$673$		−	39.5630i		−	1.52504i	0.646963	−	0.762522i	$-0.276039\pi$
$674$			22.2392i			0.856623i
$675$	−5.18192	−	0.384324i	−0.199452	−	0.0147926i
$676$	11.9146			0.458254
$677$	34.2173			1.31508			0.657539	−	0.753421i	$-0.271598\pi$
$677$	34.2173			1.31508			0.657539	+	0.753421i	$0.271598\pi$
$678$	−16.7830	−	30.7999i	−0.644546	−	1.18286i
$679$			37.1611i			1.42611i
$680$	0.140096			0.00537244
$681$	−3.43596	−	6.30563i	−0.131666	−	0.241632i
$682$	7.17345			0.274686
$683$	15.7508			0.602686			0.301343	−	0.953516i	$-0.402565\pi$
$683$	15.7508			0.602686			0.301343	+	0.953516i	$0.402565\pi$
$684$	−13.0320	+	1.08014i	−0.498291	+	0.0413002i
$685$	22.9374			0.876393
$686$	45.5873			1.74053
$687$	3.73384	+	6.85230i	0.142455	+	0.261431i
$688$	−8.76865			−0.334302
$689$		−	8.77856i		−	0.334437i
$690$	−5.50043	−	10.0943i	−0.209398	−	0.384284i
$691$	3.35768			0.127732			0.0638661	−	0.997958i	$-0.479657\pi$
$691$	3.35768			0.127732			0.0638661	+	0.997958i	$0.479657\pi$
$692$	−16.8692			−0.641272
$693$	−24.3995	−	15.7411i	−0.926861	−	0.597957i
$694$		−	1.04327i		−	0.0396021i
$695$		−	14.1673i		−	0.537396i
$696$	1.37365	+	2.52091i	0.0520682	+	0.0955549i
$697$			0.165582i			0.00627188i
$698$	−6.14155			−0.232461
$699$	−15.0111	+	8.17961i	−0.567773	+	0.309381i
$700$	−4.83942			−0.182913
$701$		−	9.06577i		−	0.342409i	−0.985235	−	0.171205i	$-0.945234\pi$
$701$		−	9.06577i		−	0.342409i	0.985235	−	0.171205i	$-0.0547659\pi$
$702$	0.400398	−	5.39865i	0.0151120	−	0.203759i
$703$	21.9877	−	16.9119i	0.829281	−	0.637845i
$704$			2.00000i			0.0753778i
$705$	3.95202	+	7.25269i	0.148842	+	0.273152i
$706$		−	2.22374i		−	0.0836917i
$707$		−	50.7580i		−	1.90895i
$708$	−0.290862	−	0.533787i	−0.0109313	−	0.0200609i
$709$	−8.60425			−0.323139			−0.161570	−	0.986861i	$-0.551656\pi$
$709$	−8.60425			−0.323139			−0.161570	+	0.986861i	$0.551656\pi$
$710$		−	11.7625i		−	0.441438i
$711$	25.4413	+	16.4133i	0.954124	+	0.615546i
$712$	−16.4969			−0.618248
$713$	−23.8052			−0.891511
$714$	−1.03115	+	0.561879i	−0.0385900	+	0.0210278i
$715$			2.08365i			0.0779240i
$716$	0.760182			0.0284093
$717$	39.3871	−	21.4622i	1.47094	−	0.801519i
$718$			2.83646i			0.105856i
$719$			24.3738i			0.908988i	0.890750	+	0.454494i	$0.150180\pi$
$719$			24.3738i			0.908988i	−0.890750	+	0.454494i	$0.849820\pi$
$720$	−2.52091	−	1.62635i	−0.0939488	−	0.0606104i
$721$			55.8338i			2.07936i
$722$	−4.87538	+	18.3638i	−0.181443	+	0.683431i
$723$	−16.0169	+	8.72768i	−0.595676	+	0.324586i
$724$			16.7221i			0.621472i
$725$	1.65750			0.0615580
$726$	−5.80125	−	10.6464i	−0.215305	−	0.395124i
$727$	−51.2863			−1.90210			−0.951052	−	0.309031i	$-0.899995\pi$
$727$	−51.2863			−1.90210			−0.951052	+	0.309031i	$0.899995\pi$
$728$		−	5.04182i		−	0.186862i
$729$	26.7046	+	3.98307i	0.989059	+	0.147521i
$730$		−	2.83095i		−	0.104778i
$731$			1.22845i			0.0454360i
$732$	8.65836	+	15.8897i	0.320022	+	0.587301i
$733$	23.0263			0.850497			0.425249	−	0.905077i	$-0.360187\pi$
$733$	23.0263			0.850497			0.425249	+	0.905077i	$0.360187\pi$
$734$	7.87864			0.290806
$735$	24.9734	−	13.6081i	0.921156	−	0.501941i
$736$		−	6.63702i		−	0.244644i
$737$	−27.2617			−1.00420
$738$	1.92221	−	2.97952i	0.0707576	−	0.109678i
$739$	17.8490			0.656587			0.328294	−	0.944576i	$-0.393526\pi$
$739$	17.8490			0.656587			0.328294	+	0.944576i	$0.393526\pi$
$740$	6.36384			0.233939
$741$	−7.19404	−	3.18016i	−0.264280	−	0.116826i
$742$	40.7777			1.49700
$743$	26.9652			0.989257			0.494628	−	0.869105i	$-0.335304\pi$
$743$	26.9652			0.989257			0.494628	+	0.869105i	$0.335304\pi$
$744$	−5.45510	+	2.97250i	−0.199994	+	0.108977i
$745$	1.80346			0.0660735
$746$		−	13.8684i		−	0.507757i
$747$	−25.2954	−	16.3191i	−0.925509	−	0.597085i
$748$	0.280192			0.0102448
$749$	−70.2190			−2.56575
$750$	−1.52091	+	0.828750i	−0.0555359	+	0.0302617i
$751$		−	45.1134i		−	1.64621i	−0.567888	−	0.823106i	$-0.692239\pi$
$751$		−	45.1134i		−	1.64621i	0.567888	−	0.823106i	$-0.307761\pi$
$752$			4.76865i			0.173895i
$753$	30.3951	−	16.5624i	1.10766	−	0.603567i
$754$			1.72682i			0.0628872i
$755$	−2.62154			−0.0954075
$756$	25.0775	+	1.85990i	0.912059	+	0.0676441i
$757$	19.0860			0.693691			0.346845	−	0.937922i	$-0.387253\pi$
$757$	19.0860			0.693691			0.346845	+	0.937922i	$0.387253\pi$
$758$		−	20.9430i		−	0.760683i
$759$	−11.0009	−	20.1886i	−0.399306	−	0.732801i
$760$	−3.45510	+	2.65750i	−0.125330	+	0.0963977i
$761$			33.1301i			1.20096i	0.799638	+	0.600482i	$0.205025\pi$
$761$			33.1301i			1.20096i	−0.799638	+	0.600482i	$0.794975\pi$
$762$	8.08365	−	4.40481i	0.292840	−	0.159569i
$763$			41.7572i			1.51171i
$764$		−	23.5062i		−	0.850426i
$765$	−0.227845	+	0.353170i	−0.00823775	+	0.0127689i
$766$	22.2848			0.805183
$767$		−	0.365644i		−	0.0132026i
$768$	−0.828750	−	1.52091i	−0.0299049	−	0.0548812i
$769$	12.7350			0.459235			0.229618	−	0.973281i	$-0.426252\pi$
$769$	12.7350			0.459235			0.229618	+	0.973281i	$0.426252\pi$
$770$	−9.67884			−0.348801
$771$	7.95202	+	14.5934i	0.286385	+	0.525570i
$772$		−	6.10058i		−	0.219565i
$773$	−4.46001			−0.160415			−0.0802077	−	0.996778i	$-0.525558\pi$
$773$	−4.46001			−0.160415			−0.0802077	+	0.996778i	$0.525558\pi$
$774$	14.2609	−	22.1050i	0.512596	−	0.794547i
$775$			3.58673i			0.128839i
$776$			7.67884i			0.275654i
$777$	−46.8400	+	25.5233i	−1.68037	+	0.915642i
$778$		−	1.92807i		−	0.0691247i
$779$	−3.14095	−	4.08365i	−0.112536	−	0.146312i
$780$	−0.863412	−	1.58452i	−0.0309151	−	0.0567350i
$781$		−	23.5250i		−	0.841790i
$782$	−0.929820			−0.0332503
$783$	−8.58903	−	0.637017i	−0.306947	−	0.0227651i
$784$	16.4200			0.586428
$785$			0.271727i			0.00969835i
$786$	6.42615	−	3.50163i	0.229213	−	0.124899i
$787$		−	17.4028i		−	0.620342i	−0.950681	−	0.310171i	$-0.899614\pi$
$787$		−	17.4028i		−	0.620342i	0.950681	−	0.310171i	$-0.100386\pi$
$788$		−	9.07749i		−	0.323372i
$789$	−18.8479	+	10.2703i	−0.671002	+	0.365632i
$790$	10.0921			0.359061
$791$	98.0028			3.48458
$792$	−5.04182	−	3.25269i	−0.179153	−	0.115579i
$793$			10.8844i			0.386518i
$794$	28.4986			1.01138
$795$	12.8154	−	6.98317i	0.454516	−	0.247668i
$796$	−3.87979			−0.137516
$797$	−3.52999			−0.125039			−0.0625193	−	0.998044i	$-0.519913\pi$
$797$	−3.52999			−0.125039			−0.0625193	+	0.998044i	$0.519913\pi$
$798$	14.7723	−	33.4173i	0.522934	−	1.18296i
$799$	0.668069			0.0236346
$800$	−1.00000			−0.0353553
$801$	26.8297	−	41.5873i	0.947981	−	1.46941i
$802$	2.25770			0.0797220
$803$		−	5.66191i		−	0.199804i
$804$	20.7313	−	11.2966i	0.731138	−	0.398399i
$805$	32.1193			1.13206
$806$	−3.73674			−0.131621
$807$	10.8860	+	19.9778i	0.383204	+	0.703251i
$808$		−	10.4885i		−	0.368983i
$809$			19.5016i			0.685641i	0.939401	+	0.342820i	$0.111382\pi$
$809$			19.5016i			0.685641i	−0.939401	+	0.342820i	$0.888618\pi$
$810$	8.19975	−	3.70999i	0.288110	−	0.130356i
$811$			29.7724i			1.04545i	0.852501	+	0.522725i	$0.175085\pi$
$811$			29.7724i			1.04545i	−0.852501	+	0.522725i	$0.824915\pi$
$812$	−8.02134			−0.281494
$813$	−8.46807	−	15.5405i	−0.296988	−	0.545029i
$814$	12.7277			0.446105
$815$		−	2.96519i		−	0.103866i
$816$	−0.213074	+	0.116105i	−0.00745908	+	0.00406448i
$817$	−23.3027	−	30.2965i	−0.815258	−	1.05994i
$818$		−	15.8754i		−	0.555070i
$819$	12.7100	+	8.19975i	0.444123	+	0.286523i
$820$		−	1.18192i		−	0.0412744i
$821$		−	27.6379i		−	0.964568i	−0.876015	−	0.482284i	$-0.839807\pi$
$821$		−	27.6379i		−	0.964568i	0.876015	−	0.482284i	$-0.160193\pi$
$822$	−34.8858	+	19.0094i	−1.21678	+	0.663028i
$823$	43.3875			1.51239			0.756196	−	0.654345i	$-0.227055\pi$
$823$	43.3875			1.51239			0.756196	+	0.654345i	$0.227055\pi$
$824$			11.5373i			0.401921i
$825$	−3.04182	+	1.65750i	−0.105903	+	0.0577068i
$826$	1.69847			0.0590972
$827$	47.5463			1.65335			0.826674	−	0.562682i	$-0.190230\pi$
$827$	47.5463			1.65335			0.826674	+	0.562682i	$0.190230\pi$
$828$	16.7313	+	10.7941i	0.581454	+	0.375121i
$829$		−	31.8874i		−	1.10749i	−0.832685	−	0.553747i	$-0.813197\pi$
$829$		−	31.8874i		−	1.10749i	0.832685	−	0.553747i	$-0.186803\pi$
$830$	−10.0342			−0.348293
$831$	8.48115	+	15.5645i	0.294208	+	0.539926i
$832$		−	1.04182i		−	0.0361187i
$833$		−	2.30038i		−	0.0797033i
$834$	11.7411	+	21.5472i	0.406563	+	0.746119i
$835$			4.91019i			0.169924i
$836$	−6.91019	+	5.31500i	−0.238994	+	0.183823i
$837$	1.37846	−	18.5861i	0.0476467	−	0.642431i
$838$		−	2.56038i		−	0.0884470i
$839$	−19.5162			−0.673773			−0.336886	−	0.941545i	$-0.609374\pi$
$839$	−19.5162			−0.673773			−0.336886	+	0.941545i	$0.609374\pi$
$840$	7.36033	−	4.01067i	0.253956	−	0.138381i
$841$	−26.2527			−0.905265
$842$		−	9.06201i		−	0.312297i
$843$	5.80316	+	10.6499i	0.199872	+	0.366802i
$844$		−	18.8453i		−	0.648681i
$845$			11.9146i			0.409875i
$846$	−12.0213	−	7.75547i	−0.413302	−	0.266639i
$847$	33.8759			1.16399
$848$	8.42615			0.289355
$849$	−9.92076	−	18.2065i	−0.340480	−	0.624844i
$850$			0.140096i			0.00480526i
$851$	−42.2369			−1.44786
$852$	9.74816	+	17.8897i	0.333967	+	0.612891i
$853$	−2.77711			−0.0950865			−0.0475433	−	0.998869i	$-0.515139\pi$
$853$	−2.77711			−0.0950865			−0.0475433	+	0.998869i	$0.515139\pi$
$854$	−50.5598			−1.73012
$855$	−1.08014	−	13.0320i	−0.0369400	−	0.445685i
$856$	−14.5098			−0.495935
$857$	−28.1292			−0.960876			−0.480438	−	0.877029i	$-0.659522\pi$
$857$	−28.1292			−0.960876			−0.480438	+	0.877029i	$0.659522\pi$
$858$	−1.72682	−	3.16905i	−0.0589528	−	0.108189i
$859$	−4.88094			−0.166536			−0.0832678	−	0.996527i	$-0.526536\pi$
$859$	−4.88094			−0.166536			−0.0832678	+	0.996527i	$0.526536\pi$
$860$		−	8.76865i		−	0.299008i
$861$	4.74029	+	8.69932i	0.161549	+	0.296472i
$862$	30.8259			1.04994
$863$	49.3740			1.68071			0.840355	−	0.542036i	$-0.182346\pi$
$863$	49.3740			1.68071			0.840355	+	0.542036i	$0.182346\pi$
$864$	5.18192	+	0.384324i	0.176292	+	0.0130750i
$865$		−	16.8692i		−	0.573571i
$866$		−	36.8692i		−	1.25287i
$867$	−14.0725	−	25.8257i	−0.477927	−	0.877085i
$868$		−	17.3577i		−	0.589158i
$869$	20.1842			0.684703
$870$	−2.52091	+	1.37365i	−0.0854669	+	0.0465712i
$871$	14.2010			0.481181
$872$			8.62855i			0.292200i
$873$	−19.3577	−	12.4885i	−0.655158	−	0.422670i
$874$	22.9315	−	17.6379i	0.775671	−	0.596610i
$875$		−	4.83942i		−	0.163602i
$876$	2.34615	+	4.30563i	0.0792692	+	0.145474i
$877$		−	12.2182i		−	0.412579i	−0.978491	−	0.206289i	$-0.933861\pi$
$877$		−	12.2182i		−	0.412579i	0.978491	−	0.206289i	$-0.0661388\pi$
$878$			25.5715i			0.862997i
$879$	−18.0320	−	33.0921i	−0.608205	−	1.11617i
$880$	−2.00000			−0.0674200
$881$			12.8780i			0.433872i	0.976186	+	0.216936i	$0.0696064\pi$
$881$			12.8780i			0.433872i	−0.976186	+	0.216936i	$0.930394\pi$
$882$	−26.7046	+	41.3933i	−0.899190	+	1.39379i
$883$	27.1185			0.912609			0.456304	−	0.889824i	$-0.349173\pi$
$883$	27.1185			0.912609			0.456304	+	0.889824i	$0.349173\pi$
$884$	−0.145955			−0.00490901
$885$	0.533787	−	0.290862i	0.0179431	−	0.00977723i
$886$			32.4267i			1.08940i
$887$	37.8052			1.26937			0.634687	−	0.772770i	$-0.281129\pi$
$887$	37.8052			1.26937			0.634687	+	0.772770i	$0.281129\pi$
$888$	−9.67884	+	5.27403i	−0.324801	+	0.176985i
$889$			25.7215i			0.862672i
$890$		−	16.4969i		−	0.552978i
$891$	16.3995	−	7.41999i	0.549404	−	0.248579i
$892$		−	20.3925i		−	0.682791i
$893$	−16.4761	+	12.6727i	−0.551353	+	0.424075i
$894$	−2.74290	+	1.49461i	−0.0917362	+	0.0499874i
$895$			0.760182i			0.0254101i
$896$	4.83942			0.161674
$897$	5.73048	+	10.5165i	0.191335	+	0.351136i
$898$	−21.3521			−0.712529
$899$			5.94500i			0.198277i
$900$	1.62635	−	2.52091i	0.0542115	−	0.0840304i
$901$		−	1.18047i		−	0.0393272i
$902$		−	2.36384i		−	0.0787073i
$903$	35.1682	+	64.5402i	1.17032	+	2.14776i
$904$	20.2509			0.673536
$905$	−16.7221			−0.555862
$906$	3.98712	−	2.17260i	0.132463	−	0.0721797i
$907$		−	27.2945i		−	0.906298i	−0.891435	−	0.453149i	$-0.850300\pi$
$907$		−	27.2945i		−	0.906298i	0.891435	−	0.453149i	$-0.149700\pi$
$908$	4.14596			0.137588
$909$	26.4405	+	17.0579i	0.876975	+	0.565774i
$910$	5.04182			0.167135
$911$	−32.6604			−1.08209			−0.541043	−	0.840995i	$-0.681970\pi$
$911$	−32.6604			−1.08209			−0.541043	+	0.840995i	$0.681970\pi$
$912$	3.05249	−	6.90524i	0.101078	−	0.228655i
$913$	−20.0684			−0.664168
$914$	−3.22404			−0.106642
$915$	−15.8897	+	8.65836i	−0.525298	+	0.286236i
$916$	−4.50539			−0.148862
$917$			20.4475i			0.675236i
$918$	0.0538422	−	0.725967i	0.00177706	−	0.0239605i
$919$	−23.8944			−0.788204			−0.394102	−	0.919067i	$-0.628944\pi$
$919$	−23.8944			−0.788204			−0.394102	+	0.919067i	$0.628944\pi$
$920$	6.63702			0.218816
$921$	44.7777	−	24.3995i	1.47547	−	0.803991i
$922$		−	32.5340i		−	1.07145i
$923$			12.2544i			0.403360i
$924$	14.7207	−	8.02134i	0.484274	−	0.263883i
$925$			6.36384i			0.209242i
$926$	−24.0798			−0.791311
$927$	−29.0845	−	18.7636i	−0.955260	−	0.616279i
$928$	−1.65750			−0.0544101
$929$		−	44.4539i		−	1.45849i	−0.684255	−	0.729243i	$-0.739873\pi$
$929$		−	44.4539i		−	1.45849i	0.684255	−	0.729243i	$-0.260127\pi$
$930$	−2.97250	−	5.45510i	−0.0974721	−	0.178880i
$931$	43.6361	+	56.7326i	1.43012	+	1.85934i
$932$		−	9.86982i		−	0.323297i
$933$	2.28826	−	1.24688i	0.0749142	−	0.0408210i
$934$			33.7996i			1.10596i
$935$			0.280192i			0.00916326i
$936$	2.62635	+	1.69437i	0.0858448	+	0.0553821i
$937$	13.0333			0.425779			0.212890	−	0.977076i	$-0.431713\pi$
$937$	13.0333			0.425779			0.212890	+	0.977076i	$0.431713\pi$
$938$			65.9654i			2.15385i
$939$	21.9598	+	40.3003i	0.716631	+	1.31515i
$940$	−4.76865			−0.155536
$941$	33.0836			1.07849			0.539247	−	0.842147i	$-0.318709\pi$
$941$	33.0836			1.07849			0.539247	+	0.842147i	$0.318709\pi$
$942$	−0.225194	−	0.413273i	−0.00733721	−	0.0134652i
$943$			7.84442i			0.255450i
$944$	0.350965			0.0114229
$945$	−1.85990	+	25.0775i	−0.0605027	+	0.815771i
$946$		−	17.5373i		−	0.570187i
$947$			11.2369i			0.365151i	0.983192	+	0.182575i	$0.0584434\pi$
$947$			11.2369i			0.365151i	−0.983192	+	0.182575i	$0.941557\pi$
$948$	−15.3492	+	8.36384i	−0.498519	+	0.271645i
$949$			2.94936i			0.0957402i
$950$	−2.65750	−	3.45510i	−0.0862207	−	0.112098i
$951$	−7.85240	−	14.4106i	−0.254631	−	0.467296i
$952$		−	0.677984i		−	0.0219736i
$953$	2.43867			0.0789962			0.0394981	−	0.999220i	$-0.487424\pi$
$953$	2.43867			0.0789962			0.0394981	+	0.999220i	$0.487424\pi$
$954$	−13.7038	+	21.2416i	−0.443678	+	0.687721i
$955$	23.5062			0.760644
$956$			25.8970i			0.837569i
$957$	−5.04182	+	2.74731i	−0.162979	+	0.0888078i
$958$		−	0.601352i		−	0.0194288i
$959$		−	111.004i		−	3.58450i
$960$	1.52091	−	0.828750i	0.0490872	−	0.0267478i
$961$	18.1354			0.585012
$962$	−6.63000			−0.213760
$963$	23.5980	−	36.5779i	0.760433	−	1.17871i
$964$		−	10.5311i		−	0.339185i
$965$	6.10058			0.196385
$966$	−48.8506	+	26.6189i	−1.57174	+	0.856449i
$967$	−21.8148			−0.701517			−0.350759	−	0.936466i	$-0.614076\pi$
$967$	−21.8148			−0.701517			−0.350759	+	0.936466i	$0.614076\pi$
$968$	7.00000			0.224989
$969$	−0.967397	−	0.427642i	−0.0310773	−	0.0137379i
$970$	−7.67884			−0.246553
$971$	0.708682			0.0227427			0.0113713	−	0.999935i	$-0.496380\pi$
$971$	0.708682			0.0227427			0.0113713	+	0.999935i	$0.496380\pi$
$972$	−9.39644	+	12.4381i	−0.301391	+	0.398953i
$973$	−68.5615			−2.19798
$974$			6.40481i			0.205223i
$975$	1.58452	−	0.863412i	0.0507453	−	0.0276513i
$976$	−10.4475			−0.334416
$977$	34.4048			1.10071			0.550354	−	0.834932i	$-0.314493\pi$
$977$	34.4048			1.10071			0.550354	+	0.834932i	$0.314493\pi$
$978$	2.45740	+	4.50980i	0.0785791	+	0.144207i
$979$		−	32.9938i		−	1.05449i
$980$			16.4200i			0.524517i
$981$	−21.7518	−	14.0330i	−0.694482	−	0.448040i
$982$			38.6148i			1.23225i
$983$	12.0134			0.383169			0.191584	−	0.981476i	$-0.438637\pi$
$983$	12.0134			0.383169			0.191584	+	0.981476i	$0.438637\pi$
$984$	0.979516	+	1.79760i	0.0312258	+	0.0573053i
$985$	9.07749			0.289233
$986$			0.232209i			0.00739505i
$987$	35.0988	−	19.1255i	1.11721	−	0.608770i
$988$	3.59960	−	2.76865i	0.114519	−	0.0880824i
$989$			58.1977i			1.85058i
$990$	3.25269	−	5.04182i	0.103377	−	0.160240i
$991$			52.5975i			1.67081i	0.549631	+	0.835407i	$0.314768\pi$
$991$			52.5975i			1.67081i	−0.549631	+	0.835407i	$0.685232\pi$
$992$		−	3.58673i		−	0.113879i
$993$	2.26511	−	1.23427i	0.0718812	−	0.0391683i
$994$	−56.9236			−1.80551
$995$		−	3.87979i		−	0.122998i
$996$	15.2612	−	8.31586i	0.483568	−	0.263498i
$997$	12.3027			0.389630			0.194815	−	0.980840i	$-0.437589\pi$
$997$	12.3027			0.389630			0.194815	+	0.980840i	$0.437589\pi$
$998$	−32.2936			−1.02224
$999$	2.44577	−	32.9769i	0.0773809	−	1.04334i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.f.d.341.3	yes	8
3.2	odd	2		570.2.f.c.341.5	✓	8
19.18	odd	2		570.2.f.c.341.6	yes	8
57.56	even	2	inner	570.2.f.d.341.4	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.f.c.341.5	✓	8	3.2	odd	2
570.2.f.c.341.6	yes	8	19.18	odd	2
570.2.f.d.341.3	yes	8	1.1	even	1	trivial
570.2.f.d.341.4	yes	8	57.56	even	2	inner

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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(-0.828750 - 1.52091i) q^{3} +1.00000 q^{4} +1.00000i q^{5} +(-0.828750 - 1.52091i) q^{6} +4.83942 q^{7} +1.00000 q^{8} +(-1.62635 + 2.52091i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(-0.828750 - 1.52091i) q^{3} +1.00000 q^{4} +1.00000i q^{5} +(-0.828750 - 1.52091i) q^{6} +4.83942 q^{7} +1.00000 q^{8} +(-1.62635 + 2.52091i) q^{9} +1.00000i q^{10} +2.00000i q^{11} +(-0.828750 - 1.52091i) q^{12} -1.04182i q^{13} +4.83942 q^{14} +(1.52091 - 0.828750i) q^{15} +1.00000 q^{16} -0.140096i q^{17} +(-1.62635 + 2.52091i) q^{18} +(2.65750 + 3.45510i) q^{19} +1.00000i q^{20} +(-4.01067 - 7.36033i) q^{21} +2.00000i q^{22} -6.63702i q^{23} +(-0.828750 - 1.52091i) q^{24} -1.00000 q^{25} -1.04182i q^{26} +(5.18192 + 0.384324i) q^{27} +4.83942 q^{28} -1.65750 q^{29} +(1.52091 - 0.828750i) q^{30} -3.58673i q^{31} +1.00000 q^{32} +(3.04182 - 1.65750i) q^{33} -0.140096i q^{34} +4.83942i q^{35} +(-1.62635 + 2.52091i) q^{36} -6.36384i q^{37} +(2.65750 + 3.45510i) q^{38} +(-1.58452 + 0.863412i) q^{39} +1.00000i q^{40} -1.18192 q^{41} +(-4.01067 - 7.36033i) q^{42} -8.76865 q^{43} +2.00000i q^{44} +(-2.52091 - 1.62635i) q^{45} -6.63702i q^{46} +4.76865i q^{47} +(-0.828750 - 1.52091i) q^{48} +16.4200 q^{49} -1.00000 q^{50} +(-0.213074 + 0.116105i) q^{51} -1.04182i q^{52} +8.42615 q^{53} +(5.18192 + 0.384324i) q^{54} -2.00000 q^{55} +4.83942 q^{56} +(3.05249 - 6.90524i) q^{57} -1.65750 q^{58} +0.350965 q^{59} +(1.52091 - 0.828750i) q^{60} -10.4475 q^{61} -3.58673i q^{62} +(-7.87057 + 12.1998i) q^{63} +1.00000 q^{64} +1.04182 q^{65} +(3.04182 - 1.65750i) q^{66} +13.6309i q^{67} -0.140096i q^{68} +(-10.0943 + 5.50043i) q^{69} +4.83942i q^{70} -11.7625 q^{71} +(-1.62635 + 2.52091i) q^{72} -2.83095 q^{73} -6.36384i q^{74} +(0.828750 + 1.52091i) q^{75} +(2.65750 + 3.45510i) q^{76} +9.67884i q^{77} +(-1.58452 + 0.863412i) q^{78} -10.0921i q^{79} +1.00000i q^{80} +(-3.70999 - 8.19975i) q^{81} -1.18192 q^{82} +10.0342i q^{83} +(-4.01067 - 7.36033i) q^{84} +0.140096 q^{85} -8.76865 q^{86} +(1.37365 + 2.52091i) q^{87} +2.00000i q^{88} -16.4969 q^{89} +(-2.52091 - 1.62635i) q^{90} -5.04182i q^{91} -6.63702i q^{92} +(-5.45510 + 2.97250i) q^{93} +4.76865i q^{94} +(-3.45510 + 2.65750i) q^{95} +(-0.828750 - 1.52091i) q^{96} +7.67884i q^{97} +16.4200 q^{98} +(-5.04182 - 3.25269i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} - 2 q^{3} + 8 q^{4} - 2 q^{6} + 4 q^{7} + 8 q^{8} + 2 q^{9}+O(q^{10}) \) 8 * q + 8 * q^2 - 2 * q^3 + 8 * q^4 - 2 * q^6 + 4 * q^7 + 8 * q^8 + 2 * q^9	\( 8 q + 8 q^{2} - 2 q^{3} + 8 q^{4} - 2 q^{6} + 4 q^{7} + 8 q^{8} + 2 q^{9} - 2 q^{12} + 4 q^{14} + 8 q^{16} + 2 q^{18} + 12 q^{19} - 2 q^{21} - 2 q^{24} - 8 q^{25} + 16 q^{27} + 4 q^{28} - 4 q^{29} + 8 q^{32} + 2 q^{36} + 12 q^{38} - 22 q^{39} + 16 q^{41} - 2 q^{42} - 40 q^{43} - 8 q^{45} - 2 q^{48} + 4 q^{49} - 8 q^{50} + 18 q^{51} + 28 q^{53} + 16 q^{54} - 16 q^{55} + 4 q^{56} - 30 q^{57} - 4 q^{58} - 4 q^{59} + 16 q^{61} - 34 q^{63} + 8 q^{64} - 16 q^{65} - 2 q^{69} + 24 q^{71} + 2 q^{72} - 4 q^{73} + 2 q^{75} + 12 q^{76} - 22 q^{78} + 34 q^{81} + 16 q^{82} - 2 q^{84} - 40 q^{86} + 26 q^{87} - 88 q^{89} - 8 q^{90} - 24 q^{93} - 8 q^{95} - 2 q^{96} + 4 q^{98} - 16 q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 - 2 * q^3 + 8 * q^4 - 2 * q^6 + 4 * q^7 + 8 * q^8 + 2 * q^9 - 2 * q^12 + 4 * q^14 + 8 * q^16 + 2 * q^18 + 12 * q^19 - 2 * q^21 - 2 * q^24 - 8 * q^25 + 16 * q^27 + 4 * q^28 - 4 * q^29 + 8 * q^32 + 2 * q^36 + 12 * q^38 - 22 * q^39 + 16 * q^41 - 2 * q^42 - 40 * q^43 - 8 * q^45 - 2 * q^48 + 4 * q^49 - 8 * q^50 + 18 * q^51 + 28 * q^53 + 16 * q^54 - 16 * q^55 + 4 * q^56 - 30 * q^57 - 4 * q^58 - 4 * q^59 + 16 * q^61 - 34 * q^63 + 8 * q^64 - 16 * q^65 - 2 * q^69 + 24 * q^71 + 2 * q^72 - 4 * q^73 + 2 * q^75 + 12 * q^76 - 22 * q^78 + 34 * q^81 + 16 * q^82 - 2 * q^84 - 40 * q^86 + 26 * q^87 - 88 * q^89 - 8 * q^90 - 24 * q^93 - 8 * q^95 - 2 * q^96 + 4 * q^98 - 16 * q^99

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