LMFDB - Embedded newform 570.2.f.c.341.5

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			341.5
Root			$0.828750 - 1.52091i$ of defining polynomial
Character	$\chi$	$=$	570.341
Dual form			570.2.f.c.341.6

$q$-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} +(7.45730 - 1.17841i) 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} + 26 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 + 26 * 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	$-0.902509\pi$
$11$		−	2.00000i		−	0.603023i	0.953463	−	0.301511i	$-0.0974911\pi$
$12$	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	$0.00540807\pi$
$17$			0.140096i			0.0339783i	−0.999856	+	0.0169891i	$0.994592\pi$
$18$	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	$0.243251\pi$
$23$			6.63702i			1.38391i	−0.721939	+	0.691957i	$0.756749\pi$
$24$	−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	$-0.450818\pi$
$29$	1.65750			0.307790			0.153895	+	0.988087i	$0.450818\pi$
$30$	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	$-0.470581\pi$
$41$	1.18192			0.184585			0.0922924	+	0.995732i	$0.470581\pi$
$42$	−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	$-0.886932\pi$
$47$		−	4.76865i		−	0.695579i	0.937573	−	0.347789i	$-0.113068\pi$
$48$	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	$-0.696444\pi$
$53$	−8.42615			−1.15742			−0.578710	+	0.815533i	$0.696444\pi$
$54$	5.18192	−	0.384324i	0.705170	−	0.0522998i
$55$	−2.00000			−0.269680
$56$	−4.83942			−0.646695
$57$	7.45730	−	1.17841i	0.987744	−	0.156085i
$58$	−1.65750			−0.217640
$59$	−0.350965			−0.0456918			−0.0228459	−	0.999739i	$-0.507273\pi$
$59$	−0.350965			−0.0456918			−0.0228459	+	0.999739i	$0.507273\pi$
$60$	−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	$-0.254085\pi$
$71$	11.7625			1.39595			0.697975	+	0.716122i	$0.254085\pi$
$72$	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	$-0.814361\pi$
$83$		−	10.0342i		−	1.10140i	0.834704	−	0.550699i	$-0.185639\pi$
$84$	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	$-0.161298\pi$
$89$	16.4969			1.74867			0.874335	+	0.485323i	$0.161298\pi$
$90$	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	$0.174747\pi$
$101$			10.4885i			1.04364i	−0.853056	+	0.521820i	$0.825253\pi$
$102$	−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	$-0.252578\pi$
$107$	14.5098			1.40271			0.701357	+	0.712810i	$0.252578\pi$
$108$	−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	$-0.901523\pi$
$113$	−20.2509			−1.90505			−0.952524	+	0.304463i	$0.901523\pi$
$114$	−7.45730	+	1.17841i	−0.698440	+	0.110368i
$115$	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	$-0.940908\pi$
$131$		−	4.22519i		−	0.369157i	0.982818	−	0.184578i	$-0.0590920\pi$
$132$	−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	$0.435971\pi$
$137$			22.9374i			1.95967i	−0.199799	+	0.979837i	$0.564029\pi$
$138$	−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	$0.0235358\pi$
$149$			1.80346i			0.147745i	−0.997268	+	0.0738724i	$0.976464\pi$
$150$	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	$-0.560843\pi$
$167$	−4.91019			−0.379962			−0.189981	+	0.981788i	$0.560843\pi$
$168$	−4.01067	+	7.36033i	−0.309430	+	0.567862i
$169$	11.9146			0.916508
$170$	−0.140096			−0.0107449
$171$	4.38798	−	12.3185i	0.335557	−	0.942020i
$172$	−8.76865			−0.668603
$173$	16.8692			1.28254			0.641272	−	0.767314i	$-0.278407\pi$
$173$	16.8692			1.28254			0.641272	+	0.767314i	$0.278407\pi$
$174$	−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	$-0.509044\pi$
$179$	−0.760182			−0.0568187			−0.0284093	+	0.999596i	$0.509044\pi$
$180$	−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	$0.323656\pi$
$191$			23.5062i			1.70085i	−0.526095	+	0.850426i	$0.676344\pi$
$192$	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	$0.104817\pi$
$197$			9.07749i			0.646744i	−0.946272	+	0.323372i	$0.895183\pi$
$198$	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	$-0.543935\pi$
$227$	−4.14596			−0.275177			−0.137588	+	0.990489i	$0.543935\pi$
$228$	7.45730	−	1.17841i	0.493872	−	0.0780423i
$229$	−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	$0.104791\pi$
$233$			9.86982i			0.646593i	−0.946298	+	0.323297i	$0.895209\pi$
$234$	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	$-0.683976\pi$
$239$		−	25.8970i		−	1.67514i	0.546331	−	0.837569i	$-0.316024\pi$
$240$	−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	$-0.782762\pi$
$251$		−	19.9848i		−	1.26143i	0.776015	−	0.630714i	$-0.217238\pi$
$252$	−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	$-0.403258\pi$
$257$	9.59519			0.598532			0.299266	+	0.954170i	$0.403258\pi$
$258$	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	$0.124791\pi$
$263$			12.3925i			0.764154i	−0.924131	+	0.382077i	$0.875209\pi$
$264$	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	$-0.368858\pi$
$269$	13.1354			0.800879			0.400439	+	0.916323i	$0.368858\pi$
$270$	−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	$-0.433024\pi$
$281$	7.00231			0.417723			0.208861	+	0.977945i	$0.433024\pi$
$282$	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
$285$	−1.17841	−	7.45730i	−0.0698031	−	0.441732i
$286$	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	$-0.719231\pi$
$293$	−21.7581			−1.27112			−0.635560	+	0.772051i	$0.719231\pi$
$294$	−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	$-0.986418\pi$
$311$		−	1.50453i		−	0.0853140i	0.999090	−	0.0426570i	$-0.0135823\pi$
$312$	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	$-0.585730\pi$
$317$	−9.47499			−0.532168			−0.266084	+	0.963950i	$0.585730\pi$
$318$	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
$342$	−4.38798	+	12.3185i	−0.237275	+	0.666109i
$343$	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	$0.00891478\pi$
$347$			1.04327i			0.0560059i	−0.999608	+	0.0280029i	$0.991085\pi$
$348$	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	$0.0188483\pi$
$353$			2.22374i			0.118358i	−0.998247	+	0.0591790i	$0.981152\pi$
$354$	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	$-0.976152\pi$
$359$		−	2.83646i		−	0.149703i	0.997195	−	0.0748513i	$-0.0238482\pi$
$360$	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	$-0.692805\pi$
$383$	−22.2848			−1.13870			−0.569350	+	0.822095i	$0.692805\pi$
$384$	−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	$0.0155647\pi$
$389$			1.92807i			0.0977571i	−0.998805	+	0.0488785i	$0.984435\pi$
$390$	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
$399$	36.0890	−	5.70283i	1.80671	−	0.285499i
$400$	−1.00000			−0.0500000
$401$	−2.25770			−0.112744			−0.0563720	−	0.998410i	$-0.517953\pi$
$401$	−2.25770			−0.112744			−0.0563720	+	0.998410i	$0.517953\pi$
$402$	−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	$0.0199206\pi$
$419$			2.56038i			0.125083i	−0.998042	+	0.0625415i	$0.980079\pi$
$420$	−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	$-0.766321\pi$
$431$	−30.8259			−1.48483			−0.742417	+	0.669938i	$0.766321\pi$
$432$	−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	$-0.720097\pi$
$443$		−	32.4267i		−	1.54064i	0.637658	−	0.770320i	$-0.279903\pi$
$444$	−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	$-0.331922\pi$
$449$	21.3521			1.00767			0.503834	+	0.863800i	$0.331922\pi$
$450$	−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
$456$	−7.45730	+	1.17841i	−0.349220	+	0.0551842i
$457$	−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	$0.273643\pi$
$461$			32.5340i			1.51526i	−0.652684	+	0.757631i	$0.726357\pi$
$462$	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	$-0.714185\pi$
$467$		−	33.7996i		−	1.56406i	0.623241	−	0.782030i	$-0.285815\pi$
$468$	−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	$0.00437315\pi$
$479$			0.601352i			0.0274765i	−0.999906	+	0.0137382i	$0.995627\pi$
$480$	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	$-0.663258\pi$
$491$		−	38.6148i		−	1.74266i	0.490697	−	0.871330i	$-0.336742\pi$
$492$	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	$0.253500\pi$
$503$			32.0643i			1.42968i	−0.699290	+	0.714839i	$0.746500\pi$
$504$	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	$-0.565015\pi$
$509$	−9.15232			−0.405669			−0.202835	+	0.979213i	$0.565015\pi$
$510$	−0.116105	+	0.213074i	−0.00514120	+	0.00943507i
$511$	−13.7002			−0.606060
$512$	−1.00000			−0.0441942
$513$	−15.0988	−	16.8827i	−0.666630	−	0.745389i
$514$	−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	$-0.191050\pi$
$521$	37.6721			1.65044			0.825222	+	0.564808i	$0.191050\pi$
$522$	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	$0.0309644\pi$
$557$			4.58442i			0.194248i	−0.995272	+	0.0971241i	$0.969036\pi$
$558$	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	$-0.459100\pi$
$563$	6.08075			0.256273			0.128136	+	0.991757i	$0.459100\pi$
$564$	−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	$-0.738278\pi$
$569$	−32.4694			−1.36119			−0.680594	+	0.732661i	$0.738278\pi$
$570$	1.17841	+	7.45730i	0.0493583	+	0.312352i
$571$	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	$-0.774702\pi$
$587$		−	31.5042i		−	1.30032i	0.759799	−	0.650159i	$-0.225298\pi$
$588$	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	$0.374124\pi$
$593$			44.9444i			1.84565i	−0.385225	+	0.922823i	$0.625876\pi$
$594$	−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	$-0.566874\pi$
$599$	−10.2083			−0.417098			−0.208549	+	0.978012i	$0.566874\pi$
$600$	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	$-0.639065\pi$
$617$		−	45.0128i		−	1.81215i	0.423119	−	0.906074i	$-0.360935\pi$
$618$	−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
$627$	−2.35682	−	14.9146i	−0.0941225	−	0.595632i
$628$	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	$-0.665150\pi$
$641$	−25.1088			−0.991738			−0.495869	+	0.868397i	$0.665150\pi$
$642$	−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	$-0.962337\pi$
$647$		−	6.00530i		−	0.236093i	0.993008	−	0.118046i	$-0.0376632\pi$
$648$	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	$0.0858150\pi$
$653$			13.6121i			0.532684i	−0.963879	+	0.266342i	$0.914185\pi$
$654$	−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	$-0.772309\pi$
$659$	−38.7575			−1.50978			−0.754889	+	0.655853i	$0.772309\pi$
$660$	−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	$-0.728402\pi$
$677$	−34.2173			−1.31508			−0.657539	+	0.753421i	$0.728402\pi$
$678$	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	$-0.597435\pi$
$683$	−15.7508			−0.602686			−0.301343	+	0.953516i	$0.597435\pi$
$684$	4.38798	−	12.3185i	0.167779	−	0.471010i
$685$	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	$0.0547659\pi$
$701$			9.06577i			0.342409i	−0.985235	+	0.171205i	$0.945234\pi$
$702$	−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	$-0.849820\pi$
$719$		−	24.3738i		−	0.908988i	0.890750	−	0.454494i	$-0.150180\pi$
$720$	−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
$741$	−1.22770	−	7.76920i	−0.0451006	−	0.285409i
$742$	40.7777			1.49700
$743$	−26.9652			−0.989257			−0.494628	−	0.869105i	$-0.664696\pi$
$743$	−26.9652			−0.989257			−0.494628	+	0.869105i	$0.664696\pi$
$744$	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	$-0.794975\pi$
$761$		−	33.1301i		−	1.20096i	0.799638	−	0.600482i	$-0.205025\pi$
$762$	−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	$-0.474442\pi$
$773$	4.46001			0.160415			0.0802077	+	0.996778i	$0.474442\pi$
$774$	−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	$-0.480087\pi$
$797$	3.52999			0.125039			0.0625193	+	0.998044i	$0.480087\pi$
$798$	−36.0890	+	5.70283i	−1.27754	+	0.201878i
$799$	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	$-0.888618\pi$
$809$		−	19.5016i		−	0.685641i	0.939401	−	0.342820i	$-0.111382\pi$
$810$	−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	$0.160193\pi$
$821$			27.6379i			0.964568i	−0.876015	+	0.482284i	$0.839807\pi$
$822$	−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	$-0.809770\pi$
$827$	−47.5463			−1.65335			−0.826674	+	0.562682i	$0.809770\pi$
$828$	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	$-0.390626\pi$
$839$	19.5162			0.673773			0.336886	+	0.941545i	$0.390626\pi$
$840$	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
$855$	−12.3185	−	4.38798i	−0.421284	−	0.150066i
$856$	−14.5098			−0.495935
$857$	28.1292			0.960876			0.480438	−	0.877029i	$-0.340478\pi$
$857$	28.1292			0.960876			0.480438	+	0.877029i	$0.340478\pi$
$858$	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	$-0.817654\pi$
$863$	−49.3740			−1.68071			−0.840355	+	0.542036i	$0.817654\pi$
$864$	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	$-0.930394\pi$
$881$		−	12.8780i		−	0.433872i	0.976186	−	0.216936i	$-0.0696064\pi$
$882$	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	$-0.718871\pi$
$887$	−37.8052			−1.26937			−0.634687	+	0.772770i	$0.718871\pi$
$888$	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	$-0.318030\pi$
$911$	32.6604			1.08209			0.541043	+	0.840995i	$0.318030\pi$
$912$	7.45730	−	1.17841i	0.246936	−	0.0390211i
$913$	−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	$0.260127\pi$
$929$			44.4539i			1.45849i	−0.684255	+	0.729243i	$0.739873\pi$
$930$	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	$-0.681291\pi$
$941$	−33.0836			−1.07849			−0.539247	+	0.842147i	$0.681291\pi$
$942$	−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	$-0.941557\pi$
$947$		−	11.2369i		−	0.365151i	0.983192	−	0.182575i	$-0.0584434\pi$
$948$	−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	$-0.512576\pi$
$953$	−2.43867			−0.0789962			−0.0394981	+	0.999220i	$0.512576\pi$
$954$	−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
$969$	0.165091	+	1.04474i	0.00530349	+	0.0335618i
$970$	−7.67884			−0.246553
$971$	−0.708682			−0.0227427			−0.0113713	−	0.999935i	$-0.503620\pi$
$971$	−0.708682			−0.0227427			−0.0113713	+	0.999935i	$0.503620\pi$
$972$	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	$-0.685507\pi$
$977$	−34.4048			−1.10071			−0.550354	+	0.834932i	$0.685507\pi$
$978$	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	$-0.561363\pi$
$983$	−12.0134			−0.383169			−0.191584	+	0.981476i	$0.561363\pi$
$984$	−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.c.341.5	✓	8
3.2	odd	2		570.2.f.d.341.3	yes	8
19.18	odd	2		570.2.f.d.341.4	yes	8
57.56	even	2	inner	570.2.f.c.341.6	yes	8

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

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} +(7.45730 - 1.17841i) 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	\( 8 q - 8 q^{2} + 2 q^{3} + 8 q^{4} - 2 q^{6} + 4 q^{7} - 8 q^{8} + 2 q^{9} + 2 q^{12} - 4 q^{14} + 8 q^{16} - 2 q^{18} + 12 q^{19} + 2 q^{21} - 2 q^{24} - 8 q^{25} - 16 q^{27} + 4 q^{28} + 4 q^{29} - 8 q^{32} + 2 q^{36} - 12 q^{38} - 22 q^{39} - 16 q^{41} - 2 q^{42} - 40 q^{43} - 8 q^{45} + 2 q^{48} + 4 q^{49} + 8 q^{50} - 18 q^{51} - 28 q^{53} + 16 q^{54} - 16 q^{55} - 4 q^{56} + 26 q^{57} - 4 q^{58} + 4 q^{59} + 16 q^{61} - 34 q^{63} + 8 q^{64} + 16 q^{65} + 2 q^{69} - 24 q^{71} - 2 q^{72} - 4 q^{73} - 2 q^{75} + 12 q^{76} + 22 q^{78} + 34 q^{81} + 16 q^{82} + 2 q^{84} + 40 q^{86} + 26 q^{87} + 88 q^{89} + 8 q^{90} - 24 q^{93} + 8 q^{95} - 2 q^{96} - 4 q^{98} - 16 q^{99}+O(q^{100}) \) 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 + 26 * 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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