LMFDB - Embedded newform 603.2.g.f.37.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [603,2,Mod(37,603)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(603, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("603.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 603 = 3^{2} \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	603.g (of order $3$, degree $2$, 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:	$4.81497924188$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.3665654523963.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 8x^{8} + 21x^{6} - 5x^{5} + 26x^{4} + 4x^{3} + 13x^{2} - 3x + 1 $ x^10 - 2x^9 + 8x^8 + 21x^6 - 5x^5 + 26x^4 + 4x^3 + 13x^2 - 3x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 201)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			37.3
Root			$1.39901 - 2.42316i$ of defining polynomial
Character	$\chi$	$=$	603.37
Dual form			603.2.g.f.163.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0732181 + 0.126817i) q^{2} +(0.989278 - 1.71348i) q^{4} +1.65158 q^{5} +(1.22031 - 2.11364i) q^{7} +0.582605 q^{8} +O(q^{10})$	\(q+(0.0732181 + 0.126817i) q^{2} +(0.989278 - 1.71348i) q^{4} +1.65158 q^{5} +(1.22031 - 2.11364i) q^{7} +0.582605 q^{8} +(0.120926 + 0.209450i) q^{10} +(-0.0152111 + 0.0263464i) q^{11} +(-0.0993860 - 0.172142i) q^{13} +0.357396 q^{14} +(-1.93590 - 3.35308i) q^{16} +(-0.847470 - 1.46786i) q^{17} +(2.97511 + 5.15305i) q^{19} +(1.63388 - 2.82995i) q^{20} -0.00445491 q^{22} +(-1.79419 - 3.10762i) q^{23} -2.27227 q^{25} +(0.0145537 - 0.0252078i) q^{26} +(-2.41446 - 4.18196i) q^{28} +(-2.17615 + 3.76920i) q^{29} +(-0.519043 + 0.899009i) q^{31} +(0.866091 - 1.50011i) q^{32} +(0.124100 - 0.214948i) q^{34} +(2.01545 - 3.49085i) q^{35} +(1.72055 + 2.98007i) q^{37} +(-0.435664 + 0.754593i) q^{38} +0.962220 q^{40} +(3.49665 - 6.05638i) q^{41} -1.37165 q^{43} +(0.0300960 + 0.0521278i) q^{44} +(0.262734 - 0.455069i) q^{46} +(2.74199 - 4.74927i) q^{47} +(0.521679 + 0.903574i) q^{49} +(-0.166372 - 0.288164i) q^{50} -0.393281 q^{52} +6.67481 q^{53} +(-0.0251224 + 0.0435133i) q^{55} +(0.710959 - 1.23142i) q^{56} -0.637333 q^{58} +7.66502 q^{59} +(1.19840 + 2.07569i) q^{61} -0.152013 q^{62} -7.48994 q^{64} +(-0.164144 - 0.284306i) q^{65} +(0.201842 + 8.18286i) q^{67} -3.35353 q^{68} +0.590269 q^{70} +(-5.29802 + 9.17644i) q^{71} +(-1.00288 - 1.73705i) q^{73} +(-0.251950 + 0.436391i) q^{74} +11.7729 q^{76} +(0.0371246 + 0.0643016i) q^{77} +(5.81596 - 10.0735i) q^{79} +(-3.19730 - 5.53788i) q^{80} +1.02407 q^{82} +(3.82603 + 6.62687i) q^{83} +(-1.39967 - 2.42429i) q^{85} +(-0.100429 - 0.173949i) q^{86} +(-0.00886206 + 0.0153495i) q^{88} -18.1923 q^{89} -0.485127 q^{91} -7.09980 q^{92} +0.803053 q^{94} +(4.91365 + 8.51068i) q^{95} +(-0.0738755 - 0.127956i) q^{97} +(-0.0763926 + 0.132316i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 6 q^{4} - 6 q^{5} - q^{7}+O(q^{10}) $ 10 * q - 6 * q^4 - 6 * q^5 - q^7	$ 10 q - 6 q^{4} - 6 q^{5} - q^{7} - 12 q^{10} - 6 q^{11} - q^{13} + 6 q^{14} - 24 q^{16} - 8 q^{17} - 5 q^{19} + 8 q^{20} + 22 q^{22} + 7 q^{23} - 8 q^{25} + 17 q^{26} + 3 q^{28} + 12 q^{29} - 12 q^{31} + 5 q^{32} + 5 q^{35} - 17 q^{37} - 30 q^{38} + 34 q^{40} - 13 q^{41} - 4 q^{43} - 43 q^{44} - 26 q^{46} + 25 q^{47} + 16 q^{49} + 25 q^{50} + 64 q^{52} + 12 q^{53} - 14 q^{55} + 11 q^{56} + 4 q^{58} + 12 q^{59} + 9 q^{61} - 46 q^{62} + 64 q^{64} + 14 q^{65} + 2 q^{67} + 98 q^{68} + 2 q^{70} - 29 q^{71} + 12 q^{73} - 15 q^{74} - 6 q^{76} - 4 q^{77} - q^{79} + 13 q^{80} - 2 q^{82} + 6 q^{83} + 9 q^{85} + 21 q^{86} + 18 q^{88} + 4 q^{89} - 40 q^{91} + 30 q^{94} + 14 q^{95} + 11 q^{97} - 12 q^{98}+O(q^{100}) $ 10 * q - 6 * q^4 - 6 * q^5 - q^7 - 12 * q^10 - 6 * q^11 - q^13 + 6 * q^14 - 24 * q^16 - 8 * q^17 - 5 * q^19 + 8 * q^20 + 22 * q^22 + 7 * q^23 - 8 * q^25 + 17 * q^26 + 3 * q^28 + 12 * q^29 - 12 * q^31 + 5 * q^32 + 5 * q^35 - 17 * q^37 - 30 * q^38 + 34 * q^40 - 13 * q^41 - 4 * q^43 - 43 * q^44 - 26 * q^46 + 25 * q^47 + 16 * q^49 + 25 * q^50 + 64 * q^52 + 12 * q^53 - 14 * q^55 + 11 * q^56 + 4 * q^58 + 12 * q^59 + 9 * q^61 - 46 * q^62 + 64 * q^64 + 14 * q^65 + 2 * q^67 + 98 * q^68 + 2 * q^70 - 29 * q^71 + 12 * q^73 - 15 * q^74 - 6 * q^76 - 4 * q^77 - q^79 + 13 * q^80 - 2 * q^82 + 6 * q^83 + 9 * q^85 + 21 * q^86 + 18 * q^88 + 4 * q^89 - 40 * q^91 + 30 * q^94 + 14 * q^95 + 11 * q^97 - 12 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/603\mathbb{Z}\right)^\times$.

$n$	$136$	$470$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	0.0732181	+	0.126817i	0.0517730	+	0.0896735i	0.890750	−	0.454493i	$-0.150179\pi$
$2$	0.0732181	+	0.126817i	0.0517730	+	0.0896735i	−0.838977	+	0.544166i	$0.816846\pi$
$3$		0			0
$3$		0			0
$4$	0.989278	−	1.71348i	0.494639	−	0.856740i
$5$	1.65158			0.738610			0.369305	−	0.929308i	$-0.379596\pi$
$5$	1.65158			0.738610			0.369305	+	0.929308i	$0.379596\pi$
$6$		0			0
$7$	1.22031	−	2.11364i	0.461234	−	0.798882i	−0.537788	−	0.843080i	$-0.680740\pi$
$7$	1.22031	−	2.11364i	0.461234	−	0.798882i	0.999023	+	0.0441984i	$0.0140734\pi$
$8$	0.582605			0.205982
$9$		0			0
$10$	0.120926	+	0.209450i	0.0382401	+	0.0662338i
$11$	−0.0152111	+	0.0263464i	−0.00458632	+	0.00794374i	−0.868309	−	0.496023i	$-0.834793\pi$
$11$	−0.0152111	+	0.0263464i	−0.00458632	+	0.00794374i	0.863723	+	0.503967i	$0.168127\pi$
$12$		0			0
$13$	−0.0993860	−	0.172142i	−0.0275647	−	0.0477435i	0.851914	−	0.523682i	$-0.175442\pi$
$13$	−0.0993860	−	0.172142i	−0.0275647	−	0.0477435i	−0.879479	+	0.475938i	$0.842109\pi$
$14$	0.357396			0.0955180
$15$		0			0
$16$	−1.93590	−	3.35308i	−0.483975	−	0.838269i
$17$	−0.847470	−	1.46786i	−0.205542	−	0.356009i	0.744764	−	0.667328i	$-0.232562\pi$
$17$	−0.847470	−	1.46786i	−0.205542	−	0.356009i	−0.950305	+	0.311320i	$0.899229\pi$
$18$		0			0
$19$	2.97511	+	5.15305i	0.682538	+	1.18219i	0.974204	+	0.225670i	$0.0724570\pi$
$19$	2.97511	+	5.15305i	0.682538	+	1.18219i	−0.291666	+	0.956520i	$0.594210\pi$
$20$	1.63388	−	2.82995i	0.365346	−	0.632797i
$21$		0			0
$22$	−0.00445491			−0.000949791
$23$	−1.79419	−	3.10762i	−0.374114	−	0.647984i	0.616080	−	0.787684i	$-0.288720\pi$
$23$	−1.79419	−	3.10762i	−0.374114	−	0.647984i	−0.990194	+	0.139699i	$0.955386\pi$
$24$		0			0
$25$	−2.27227			−0.454455
$26$	0.0145537	−	0.0252078i	0.00285422	−	0.00494365i
$27$		0			0
$28$	−2.41446	−	4.18196i	−0.456289	−	0.790316i
$29$	−2.17615	+	3.76920i	−0.404100	+	0.699922i	−0.994216	−	0.107396i	$-0.965749\pi$
$29$	−2.17615	+	3.76920i	−0.404100	+	0.699922i	0.590116	+	0.807318i	$0.299082\pi$
$30$		0			0
$31$	−0.519043	+	0.899009i	−0.0932229	+	0.161467i	−0.908866	−	0.417089i	$-0.863050\pi$
$31$	−0.519043	+	0.899009i	−0.0932229	+	0.161467i	0.815643	+	0.578556i	$0.196384\pi$
$32$	0.866091	−	1.50011i	0.153105	−	0.265185i
$33$		0			0
$34$	0.124100	−	0.214948i	0.0212830	−	0.0368633i
$35$	2.01545	−	3.49085i	0.340673	−	0.590062i
$36$		0			0
$37$	1.72055	+	2.98007i	0.282856	+	0.489921i	0.972087	−	0.234621i	$-0.0753848\pi$
$37$	1.72055	+	2.98007i	0.282856	+	0.489921i	−0.689231	+	0.724542i	$0.742051\pi$
$38$	−0.435664	+	0.754593i	−0.0706741	+	0.122411i
$39$		0			0
$40$	0.962220			0.152140
$41$	3.49665	−	6.05638i	0.546085	−	0.945848i	−0.452452	−	0.891789i	$-0.649451\pi$
$41$	3.49665	−	6.05638i	0.546085	−	0.945848i	0.998538	−	0.0540590i	$-0.0172159\pi$
$42$		0			0
$43$	−1.37165			−0.209174			−0.104587	−	0.994516i	$-0.533352\pi$
$43$	−1.37165			−0.209174			−0.104587	+	0.994516i	$0.533352\pi$
$44$	0.0300960	+	0.0521278i	0.00453715	+	0.00785857i
$45$		0			0
$46$	0.262734	−	0.455069i	0.0387380	−	0.0670962i
$47$	2.74199	−	4.74927i	0.399960	−	0.692752i	−0.593760	−	0.804642i	$-0.702357\pi$
$47$	2.74199	−	4.74927i	0.399960	−	0.692752i	0.993721	+	0.111890i	$0.0356905\pi$
$48$		0			0
$49$	0.521679	+	0.903574i	0.0745255	+	0.129082i
$50$	−0.166372	−	0.288164i	−0.0235285	−	0.0407526i
$51$		0			0
$52$	−0.393281			−0.0545383
$53$	6.67481			0.916856			0.458428	−	0.888732i	$-0.348413\pi$
$53$	6.67481			0.916856			0.458428	+	0.888732i	$0.348413\pi$
$54$		0			0
$55$	−0.0251224	+	0.0435133i	−0.00338750	+	0.00586733i
$56$	0.710959	−	1.23142i	0.0950060	−	0.164555i
$57$		0			0
$58$	−0.637333			−0.0836860
$59$	7.66502			0.997900			0.498950	−	0.866631i	$-0.333719\pi$
$59$	7.66502			0.997900			0.498950	+	0.866631i	$0.333719\pi$
$60$		0			0
$61$	1.19840	+	2.07569i	0.153439	+	0.265764i	0.932490	−	0.361197i	$-0.117632\pi$
$61$	1.19840	+	2.07569i	0.153439	+	0.265764i	−0.779050	+	0.626961i	$0.784298\pi$
$62$	−0.152013			−0.0193057
$63$		0			0
$64$	−7.48994			−0.936243
$65$	−0.164144	−	0.284306i	−0.0203596	−	0.0352638i
$66$		0			0
$67$	0.201842	+	8.18286i	0.0246589	+	0.999696i
$67$	0.201842	+	8.18286i	0.0246589	+	0.999696i
$68$	−3.35353			−0.406676
$69$		0			0
$70$	0.590269			0.0705506
$71$	−5.29802	+	9.17644i	−0.628759	+	1.08904i	0.359042	+	0.933321i	$0.383104\pi$
$71$	−5.29802	+	9.17644i	−0.628759	+	1.08904i	−0.987801	+	0.155721i	$0.950230\pi$
$72$		0			0
$73$	−1.00288	−	1.73705i	−0.117379	−	0.203306i	0.801349	−	0.598197i	$-0.204116\pi$
$73$	−1.00288	−	1.73705i	−0.117379	−	0.203306i	−0.918728	+	0.394891i	$0.870782\pi$
$74$	−0.251950	+	0.436391i	−0.0292886	+	0.0507294i
$75$		0			0
$76$	11.7729			1.35044
$77$	0.0371246	+	0.0643016i	0.00423074	+	0.00732785i
$78$		0			0
$79$	5.81596	−	10.0735i	0.654347	−	1.13336i	−0.327710	−	0.944778i	$-0.606277\pi$
$79$	5.81596	−	10.0735i	0.654347	−	1.13336i	0.982057	−	0.188584i	$-0.0603897\pi$
$80$	−3.19730	−	5.53788i	−0.357469	−	0.619154i
$81$		0			0
$82$	1.02407			0.113090
$83$	3.82603	+	6.62687i	0.419961	+	0.727394i	0.995935	−	0.0900742i	$-0.0287104\pi$
$83$	3.82603	+	6.62687i	0.419961	+	0.727394i	−0.575974	+	0.817468i	$0.695377\pi$
$84$		0			0
$85$	−1.39967	−	2.42429i	−0.151815	−	0.262952i
$86$	−0.100429	−	0.173949i	−0.0108296	−	0.0187574i
$87$		0			0
$88$	−0.00886206	+	0.0153495i	−0.000944699	+	0.00163627i
$89$	−18.1923			−1.92838			−0.964188	−	0.265218i	$-0.914556\pi$
$89$	−18.1923			−1.92838			−0.964188	+	0.265218i	$0.914556\pi$
$90$		0			0
$91$	−0.485127			−0.0508552
$92$	−7.09980			−0.740205
$93$		0			0
$94$	0.803053			0.0828286
$95$	4.91365	+	8.51068i	0.504129	+	0.873178i
$96$		0			0
$97$	−0.0738755	−	0.127956i	−0.00750092	−	0.0129920i	0.862251	−	0.506482i	$-0.169054\pi$
$97$	−0.0738755	−	0.127956i	−0.00750092	−	0.0129920i	−0.869752	+	0.493490i	$0.835721\pi$
$98$	−0.0763926	+	0.132316i	−0.00771682	+	0.0133659i
$99$		0			0
$100$	−2.24791	+	3.89350i	−0.224791	+	0.389350i
$101$	−7.09746	+	12.2932i	−0.706223	+	1.22321i	0.260025	+	0.965602i	$0.416269\pi$
$101$	−7.09746	+	12.2932i	−0.706223	+	1.22321i	−0.966248	+	0.257613i	$0.917064\pi$
$102$		0			0
$103$	3.74592	−	6.48812i	0.369096	−	0.639294i	−0.620328	−	0.784342i	$-0.713001\pi$
$103$	3.74592	−	6.48812i	0.369096	−	0.639294i	0.989425	+	0.145049i	$0.0463339\pi$
$104$	−0.0579027	−	0.100290i	−0.00567783	−	0.00983429i
$105$		0			0
$106$	0.488717	+	0.846483i	0.0474684	+	0.0822177i
$107$	18.7944			1.81692			0.908459	−	0.417973i	$-0.137259\pi$
$107$	18.7944			1.81692			0.908459	+	0.417973i	$0.137259\pi$
$108$		0			0
$109$	−9.56778			−0.916427			−0.458213	−	0.888842i	$-0.651510\pi$
$109$	−9.56778			−0.916427			−0.458213	+	0.888842i	$0.651510\pi$
$110$	−0.00735766			−0.000701525
$111$		0			0
$112$	−9.44960			−0.892903
$113$	−9.54539	+	16.5331i	−0.897955	+	1.55530i	−0.0678504	+	0.997696i	$0.521614\pi$
$113$	−9.54539	+	16.5331i	−0.897955	+	1.55530i	−0.830104	+	0.557608i	$0.811719\pi$
$114$		0			0
$115$	−2.96325	−	5.13250i	−0.276324	−	0.478608i
$116$	4.30563	+	7.45757i	0.399768	+	0.692418i
$117$		0			0
$118$	0.561218	+	0.972058i	0.0516643	+	0.0894852i
$119$	−4.13671			−0.379212
$120$		0			0
$121$	5.49954	+	9.52548i	0.499958	+	0.865953i
$122$	−0.175489	+	0.303956i	−0.0158880	+	0.0275189i
$123$		0			0
$124$	1.02696	+	1.77874i	0.0922234	+	0.159736i
$125$	−12.0108			−1.07428
$126$		0			0
$127$	−5.89367	+	10.2081i	−0.522979	+	0.905826i	0.476664	+	0.879086i	$0.341846\pi$
$127$	−5.89367	+	10.2081i	−0.522979	+	0.905826i	−0.999642	+	0.0267398i	$0.991487\pi$
$128$	−2.28058	−	3.95008i	−0.201577	−	0.349141i
$129$		0			0
$130$	0.0240366	−	0.0416327i	0.00210815	−	0.00365143i
$131$	−1.46338			−0.127856			−0.0639281	−	0.997955i	$-0.520363\pi$
$131$	−1.46338			−0.127856			−0.0639281	+	0.997955i	$0.520363\pi$
$132$		0			0
$133$	14.5223			1.25924
$134$	−1.02295	+	0.624731i	−0.0883696	+	0.0539685i
$135$		0			0
$136$	−0.493740	−	0.855183i	−0.0423379	−	0.0733313i
$137$	6.71932			0.574070			0.287035	−	0.957920i	$-0.407330\pi$
$137$	6.71932			0.574070			0.287035	+	0.957920i	$0.407330\pi$
$138$		0			0
$139$	−5.83978			−0.495324			−0.247662	−	0.968846i	$-0.579662\pi$
$139$	−5.83978			−0.495324			−0.247662	+	0.968846i	$0.579662\pi$
$140$	−3.98767	−	6.90685i	−0.337020	−	0.583736i
$141$		0			0
$142$	−1.55164			−0.130211
$143$	0.00604708			0.000505682
$144$		0			0
$145$	−3.59409	+	6.22514i	−0.298473	+	0.516970i
$146$	0.146859	−	0.254367i	0.0121541	−	0.0210515i
$147$		0			0
$148$	6.80840			0.559647
$149$	−17.9179			−1.46789			−0.733946	−	0.679208i	$-0.762324\pi$
$149$	−17.9179			−1.46789			−0.733946	+	0.679208i	$0.762324\pi$
$150$		0			0
$151$	−9.24499	−	16.0128i	−0.752346	−	1.30310i	−0.946683	−	0.322167i	$-0.895589\pi$
$151$	−9.24499	−	16.0128i	−0.752346	−	1.30310i	0.194337	−	0.980935i	$-0.437745\pi$
$152$	1.73331	+	3.00219i	0.140590	+	0.243510i
$153$		0			0
$154$	−0.00543638	+	0.00941609i	−0.000438076	+	0.000758770i
$155$	−0.857243	+	1.48479i	−0.0688554	+	0.119261i
$156$		0			0
$157$	0.955212	+	1.65448i	0.0762342	+	0.132041i	0.901622	−	0.432524i	$-0.142377\pi$
$157$	0.955212	+	1.65448i	0.0762342	+	0.132041i	−0.825388	+	0.564566i	$0.809044\pi$
$158$	1.70334			0.135510
$159$		0			0
$160$	1.43042	−	2.47756i	0.113085	−	0.195868i
$161$	−8.75787			−0.690217
$162$		0			0
$163$	−8.65087	+	14.9837i	−0.677588	+	1.17362i	0.298117	+	0.954529i	$0.403642\pi$
$163$	−8.65087	+	14.9837i	−0.677588	+	1.17362i	−0.975705	+	0.219088i	$0.929692\pi$
$164$	−6.91832	−	11.9829i	−0.540230	−	0.935706i
$165$		0			0
$166$	−0.560269	+	0.970414i	−0.0434853	+	0.0753187i
$167$	1.27911	−	2.21549i	0.0989809	−	0.171440i	−0.812282	−	0.583265i	$-0.801775\pi$
$167$	1.27911	−	2.21549i	0.0989809	−	0.171440i	0.911263	+	0.411825i	$0.135108\pi$
$168$		0			0
$169$	6.48024	−	11.2241i	0.498480	−	0.863393i
$170$	0.204962	−	0.355005i	0.0157199	−	0.0272276i
$171$		0			0
$172$	−1.35694	+	2.35029i	−0.103466	+	0.179208i
$173$	1.15579	+	2.00188i	0.0878730	+	0.152200i	0.906612	−	0.421966i	$-0.138660\pi$
$173$	1.15579	+	2.00188i	0.0878730	+	0.152200i	−0.818739	+	0.574166i	$0.805326\pi$
$174$		0			0
$175$	−2.77288	+	4.80277i	−0.209610	+	0.363056i
$176$	0.117789			0.00887865
$177$		0			0
$178$	−1.33200	−	2.30710i	−0.0998379	−	0.172924i
$179$	19.9835			1.49364			0.746818	−	0.665029i	$-0.231581\pi$
$179$	19.9835			1.49364			0.746818	+	0.665029i	$0.231581\pi$
$180$		0			0
$181$	−9.57734	+	16.5884i	−0.711878	+	1.23301i	0.252273	+	0.967656i	$0.418822\pi$
$181$	−9.57734	+	16.5884i	−0.711878	+	1.23301i	−0.964151	+	0.265353i	$0.914511\pi$
$182$	−0.0355201	−	0.0615226i	−0.00263293	−	0.00456036i
$183$		0			0
$184$	−1.04530	−	1.81052i	−0.0770607	−	0.133473i
$185$	2.84163	+	4.92184i	0.208920	+	0.361861i
$186$		0			0
$187$	0.0515638			0.00377072
$188$	−5.42518	−	9.39669i	−0.395672	−	0.685324i
$189$		0			0
$190$	−0.719536	+	1.24627i	−0.0522006	+	0.0904141i
$191$	9.38531	+	16.2558i	0.679097	+	1.17623i	0.975253	+	0.221092i	$0.0709620\pi$
$191$	9.38531	+	16.2558i	0.679097	+	1.17623i	−0.296156	+	0.955140i	$0.595705\pi$
$192$		0			0
$193$	−10.4313			−0.750859			−0.375430	−	0.926851i	$-0.622505\pi$
$193$	−10.4313			−0.750859			−0.375430	+	0.926851i	$0.622505\pi$
$194$	0.0108181	−	0.0187374i	0.000776691	−	0.00134527i
$195$		0			0
$196$	2.06434			0.147453
$197$	8.74723	−	15.1507i	0.623215	−	1.07944i	−0.365669	−	0.930745i	$-0.619160\pi$
$197$	8.74723	−	15.1507i	0.623215	−	1.07944i	0.988883	−	0.148694i	$-0.0475070\pi$
$198$		0			0
$199$	0.975590	+	1.68977i	0.0691577	+	0.119785i	0.898531	−	0.438911i	$-0.144635\pi$
$199$	0.975590	+	1.68977i	0.0691577	+	0.119785i	−0.829373	+	0.558695i	$0.811302\pi$
$200$	−1.32384			−0.0936095
$201$		0			0
$202$	−2.07865			−0.146253
$203$	5.31115	+	9.19919i	0.372770	+	0.645656i
$204$		0			0
$205$	5.77501	−	10.0026i	0.403344	−	0.698613i
$206$	1.09708			0.0764369
$207$		0			0
$208$	−0.384802	+	0.666497i	−0.0266812	+	0.0462133i
$209$	−0.181019			−0.0125213
$210$		0			0
$211$	2.39263	+	4.14415i	0.164715	+	0.285295i	0.936554	−	0.350523i	$-0.113996\pi$
$211$	2.39263	+	4.14415i	0.164715	+	0.285295i	−0.771839	+	0.635818i	$0.780663\pi$
$212$	6.60325	−	11.4372i	0.453513	−	0.785507i
$213$		0			0
$214$	1.37609	+	2.38345i	0.0940674	+	0.162929i
$215$	−2.26539			−0.154498
$216$		0			0
$217$	1.26679	+	2.19414i	0.0859952	+	0.148948i
$218$	−0.700534	−	1.21336i	−0.0474462	−	0.0821792i
$219$		0			0
$220$	0.0497061	+	0.0860935i	0.00335118	+	0.00580442i
$221$	−0.168453	+	0.291770i	−0.0113314	+	0.0196265i
$222$		0			0
$223$	16.8622			1.12918			0.564589	−	0.825372i	$-0.309035\pi$
$223$	16.8622			1.12918			0.564589	+	0.825372i	$0.309035\pi$
$224$	−2.11380	−	3.66121i	−0.141234	−	0.244625i
$225$		0			0
$226$	−2.79558			−0.185959
$227$	8.72461	−	15.1115i	0.579073	−	1.00298i	−0.416513	−	0.909130i	$-0.636748\pi$
$227$	8.72461	−	15.1115i	0.579073	−	1.00298i	0.995586	−	0.0938540i	$-0.0299187\pi$
$228$		0			0
$229$	−8.19926	−	14.2015i	−0.541822	−	0.938463i	−0.998800	−	0.0489851i	$-0.984401\pi$
$229$	−8.19926	−	14.2015i	−0.541822	−	0.938463i	0.456977	−	0.889478i	$-0.348932\pi$
$230$	0.433927	−	0.751584i	0.0286123	−	0.0495580i
$231$		0			0
$232$	−1.26783	+	2.19595i	−0.0832373	+	0.144171i
$233$	−3.91692	+	6.78430i	−0.256606	+	0.444454i	−0.965330	−	0.261031i	$-0.915938\pi$
$233$	−3.91692	+	6.78430i	−0.256606	+	0.444454i	0.708725	+	0.705485i	$0.249271\pi$
$234$		0			0
$235$	4.52862	−	7.84381i	0.295415	−	0.511674i
$236$	7.58283	−	13.1339i	0.493600	−	0.854941i
$237$		0			0
$238$	−0.302882	−	0.524607i	−0.0196329	−	0.0340052i
$239$	−5.40997	+	9.37034i	−0.349942	+	0.606117i	−0.986239	−	0.165327i	$-0.947132\pi$
$239$	−5.40997	+	9.37034i	−0.349942	+	0.606117i	0.636297	+	0.771444i	$0.280465\pi$
$240$		0			0
$241$	13.3049			0.857043			0.428521	−	0.903532i	$-0.359035\pi$
$241$	13.3049			0.857043			0.428521	+	0.903532i	$0.359035\pi$
$242$	−0.805331	+	1.39488i	−0.0517687	+	0.0896660i
$243$		0			0
$244$	4.74220			0.303588
$245$	0.861595	+	1.49233i	0.0550453	+	0.0953413i
$246$		0			0
$247$	0.591369	−	1.02428i	0.0376279	−	0.0651734i
$248$	−0.302397	+	0.523767i	−0.0192022	+	0.0332592i
$249$		0			0
$250$	−0.879405	−	1.52317i	−0.0556185	−	0.0963340i
$251$	7.92646	+	13.7290i	0.500313	+	0.866568i	1.00000		0.000361976i	$0.000115221\pi$
$251$	7.92646	+	13.7290i	0.500313	+	0.866568i	−0.499686	+	0.866206i	$0.666551\pi$
$252$		0			0
$253$	0.109166			0.00686322
$254$	−1.72609			−0.108305
$255$		0			0
$256$	−7.15598	+	12.3945i	−0.447249	+	0.774658i
$257$	9.54846	−	16.5384i	0.595617	−	1.03164i	−0.397843	−	0.917454i	$-0.630241\pi$
$257$	9.54846	−	16.5384i	0.595617	−	1.03164i	0.993460	−	0.114185i	$-0.0364256\pi$
$258$		0			0
$259$	8.39841			0.521852
$260$	−0.649537			−0.0402826
$261$		0			0
$262$	−0.107146	−	0.185582i	−0.00661951	−	0.0114653i
$263$	20.2644			1.24955			0.624777	−	0.780803i	$-0.285190\pi$
$263$	20.2644			1.24955			0.624777	+	0.780803i	$0.285190\pi$
$264$		0			0
$265$	11.0240			0.677199
$266$	1.06329	+	1.84168i	0.0651946	+	0.112920i
$267$		0			0
$268$	14.2209	+	7.74928i	0.868677	+	0.473362i
$269$	−16.4143			−1.00080			−0.500398	−	0.865796i	$-0.666813\pi$
$269$	−16.4143			−1.00080			−0.500398	+	0.865796i	$0.666813\pi$
$270$		0			0
$271$	−23.5202			−1.42875			−0.714375	−	0.699763i	$-0.753289\pi$
$271$	−23.5202			−1.42875			−0.714375	+	0.699763i	$0.753289\pi$
$272$	−3.28123	+	5.68326i	−0.198954	+	0.344598i
$273$		0			0
$274$	0.491976	+	0.852127i	0.0297213	+	0.0514789i
$275$	0.0345638	−	0.0598662i	0.00208427	−	0.00361007i
$276$		0			0
$277$	0.561769			0.0337534			0.0168767	−	0.999858i	$-0.494628\pi$
$277$	0.561769			0.0337534			0.0168767	+	0.999858i	$0.494628\pi$
$278$	−0.427578	−	0.740587i	−0.0256444	−	0.0444174i
$279$		0			0
$280$	1.17421	−	2.03379i	0.0701724	−	0.121542i
$281$	−0.489429	−	0.847716i	−0.0291969	−	0.0505705i	0.851058	−	0.525072i	$-0.175962\pi$
$281$	−0.489429	−	0.847716i	−0.0291969	−	0.0505705i	−0.880255	+	0.474502i	$0.842628\pi$
$282$		0			0
$283$	−13.5348			−0.804561			−0.402281	−	0.915516i	$-0.631782\pi$
$283$	−13.5348			−0.804561			−0.402281	+	0.915516i	$0.631782\pi$
$284$	10.4824	+	18.1561i	0.622018	+	1.07737i
$285$		0			0
$286$	0.000442756	0	0.000766875i	2.61807e−5	0	4.53463e-5i
$287$	−8.53401	−	14.7813i	−0.503747	−	0.872515i
$288$		0			0
$289$	7.06359	−	12.2345i	0.415505	−	0.719676i
$290$	−1.05261			−0.0618113
$291$		0			0
$292$	−3.96853			−0.232241
$293$	4.41891			0.258155			0.129078	−	0.991634i	$-0.458798\pi$
$293$	4.41891			0.258155			0.129078	+	0.991634i	$0.458798\pi$
$294$		0			0
$295$	12.6594			0.737059
$296$	1.00240	+	1.73621i	0.0582632	+	0.100915i
$297$		0			0
$298$	−1.31192	−	2.27230i	−0.0759972	−	0.131631i
$299$	−0.356634	+	0.617708i	−0.0206247	+	0.0357230i
$300$		0			0
$301$	−1.67383	+	2.89917i	−0.0964782	+	0.167105i
$302$	1.35380	−	2.34485i	0.0779025	−	0.134931i
$303$		0			0
$304$	11.5190	−	19.9516i	0.660662	−	1.14430i
$305$	1.97925	+	3.42817i	0.113332	+	0.196296i
$306$		0			0
$307$	5.40997	+	9.37034i	0.308763	+	0.534793i	0.978092	−	0.208173i	$-0.0667516\pi$
$307$	5.40997	+	9.37034i	0.308763	+	0.534793i	−0.669329	+	0.742966i	$0.733418\pi$
$308$	0.146906			0.00837075
$309$		0			0
$310$	−0.251063			−0.0142594
$311$	−17.9596			−1.01839			−0.509197	−	0.860650i	$-0.670057\pi$
$311$	−17.9596			−1.01839			−0.509197	+	0.860650i	$0.670057\pi$
$312$		0			0
$313$	1.25678			0.0710375			0.0355188	−	0.999369i	$-0.488692\pi$
$313$	1.25678			0.0710375			0.0355188	+	0.999369i	$0.488692\pi$
$314$	−0.139878	+	0.242275i	−0.00789375	+	0.0136724i
$315$		0			0
$316$	−11.5072	−	19.9311i	−0.647331	−	1.12121i
$317$	−10.2605	−	17.7717i	−0.576286	−	0.998157i	−0.995901	−	0.0904543i	$-0.971168\pi$
$317$	−10.2605	−	17.7717i	−0.576286	−	0.998157i	0.419615	−	0.907702i	$-0.362165\pi$
$318$		0			0
$319$	−0.0662032	−	0.114667i	−0.00370667	−	0.00642013i
$320$	−12.3703			−0.691519
$321$		0			0
$322$	−0.641235	−	1.11065i	−0.0357346	−	0.0618942i
$323$	5.04264	−	8.73410i	0.280580	−	0.485979i
$324$		0			0
$325$	0.225832	+	0.391153i	0.0125269	+	0.0216972i
$326$	−2.53360			−0.140323
$327$		0			0
$328$	2.03717	−	3.52848i	0.112484	−	0.194827i
$329$	−6.69217	−	11.5912i	−0.368951	−	0.639042i
$330$		0			0
$331$	10.2864	−	17.8167i	0.565394	−	0.979292i	−0.431619	−	0.902056i	$-0.642057\pi$
$331$	10.2864	−	17.8167i	0.565394	−	0.979292i	0.997013	−	0.0772355i	$-0.0246093\pi$
$332$	15.1400			0.830916
$333$		0			0
$334$	0.374617			0.0204982
$335$	0.333359	+	13.5147i	0.0182134	+	0.738386i
$336$		0			0
$337$	−17.6237	−	30.5252i	−0.960025	−	1.66281i	−0.722425	−	0.691449i	$-0.756973\pi$
$337$	−17.6237	−	30.5252i	−0.960025	−	1.66281i	−0.237600	−	0.971363i	$-0.576361\pi$
$338$	1.89789			0.103231
$339$		0			0
$340$	−5.53864			−0.300375
$341$	−0.0157904	−	0.0273498i	−0.000855100	−	0.00148108i
$342$		0			0
$343$	19.6308			1.05996
$344$	−0.799127			−0.0430860
$345$		0			0
$346$	−0.169249	+	0.293148i	−0.00909890	+	0.0157598i
$347$	9.85067	−	17.0619i	0.528812	−	0.915929i	−0.470624	−	0.882334i	$-0.655971\pi$
$347$	9.85067	−	17.0619i	0.528812	−	0.915929i	0.999436	−	0.0335949i	$-0.0106956\pi$
$348$		0			0
$349$	3.80443			0.203647			0.101823	−	0.994802i	$-0.467532\pi$
$349$	3.80443			0.203647			0.101823	+	0.994802i	$0.467532\pi$
$350$	−0.812101			−0.0434086
$351$		0			0
$352$	0.0263484	+	0.0456367i	0.00140437	+	0.00243245i
$353$	−17.8119	−	30.8511i	−0.948033	−	1.64204i	−0.749562	−	0.661934i	$-0.769736\pi$
$353$	−17.8119	−	30.8511i	−0.948033	−	1.64204i	−0.198470	−	0.980107i	$-0.563597\pi$
$354$		0			0
$355$	−8.75012	+	15.1556i	−0.464408	+	0.804378i
$356$	−17.9972	+	31.1721i	−0.953851	+	1.65212i
$357$		0			0
$358$	1.46315	+	2.53425i	0.0773300	+	0.133940i
$359$	1.78421			0.0941672			0.0470836	−	0.998891i	$-0.485007\pi$
$359$	1.78421			0.0941672			0.0470836	+	0.998891i	$0.485007\pi$
$360$		0			0
$361$	−8.20259	+	14.2073i	−0.431715	+	0.747753i
$362$	−2.80494			−0.147424
$363$		0			0
$364$	−0.479926	+	0.831256i	−0.0251550	+	0.0435697i
$365$	−1.65635	−	2.86888i	−0.0866972	−	0.150164i
$366$		0			0
$367$	4.09088	−	7.08561i	0.213542	−	0.369866i	−0.739279	−	0.673400i	$-0.764833\pi$
$367$	4.09088	−	7.08561i	0.213542	−	0.369866i	0.952821	+	0.303534i	$0.0981666\pi$
$368$	−6.94673	+	12.0321i	−0.362123	+	0.627216i
$369$		0			0
$370$	−0.416117	+	0.720736i	−0.0216329	+	0.0374693i
$371$	8.14535	−	14.1082i	0.422886	−	0.732459i
$372$		0			0
$373$	13.5388	−	23.4499i	0.701012	−	1.21419i	−0.267100	−	0.963669i	$-0.586065\pi$
$373$	13.5388	−	23.4499i	0.701012	−	1.21419i	0.968112	−	0.250519i	$-0.0806013\pi$
$374$	0.00377541	+	0.00653919i	0.000195222	+	0.000338134i
$375$		0			0
$376$	1.59750	−	2.76695i	0.0823846	−	0.142694i
$377$	0.865113			0.0445556
$378$		0			0
$379$	12.1410	+	21.0288i	0.623640	+	1.08018i	0.988802	+	0.149232i	$0.0476802\pi$
$379$	12.1410	+	21.0288i	0.623640	+	1.08018i	−0.365162	+	0.930944i	$0.618987\pi$
$380$	19.4438			0.997448
$381$		0			0
$382$	−1.37435	+	2.38044i	−0.0703179	+	0.121794i
$383$	5.58177	+	9.66792i	0.285215	+	0.494007i	0.972661	−	0.232228i	$-0.0746015\pi$
$383$	5.58177	+	9.66792i	0.285215	+	0.494007i	−0.687446	+	0.726235i	$0.741268\pi$
$384$		0			0
$385$	0.0613143	+	0.106200i	0.00312487	+	0.00541243i
$386$	−0.763758	−	1.32287i	−0.0388743	−	0.0673322i
$387$		0			0
$388$	−0.292334			−0.0148410
$389$	1.29069	+	2.23555i	0.0654408	+	0.113347i	0.896889	−	0.442255i	$-0.145821\pi$
$389$	1.29069	+	2.23555i	0.0654408	+	0.113347i	−0.831449	+	0.555602i	$0.812488\pi$
$390$		0			0
$391$	−3.04104	+	5.26724i	−0.153792	+	0.266376i
$392$	0.303932	+	0.526426i	0.0153509	+	0.0265885i
$393$		0			0
$394$	2.56182			0.129063
$395$	9.60554	−	16.6373i	0.483307	−	0.837113i
$396$		0			0
$397$	5.96514			0.299382			0.149691	−	0.988733i	$-0.452172\pi$
$397$	5.96514			0.299382			0.149691	+	0.988733i	$0.452172\pi$
$398$	−0.142862	+	0.247444i	−0.00716101	+	0.0124032i
$399$		0			0
$400$	4.39889	+	7.61911i	0.219945	+	0.380955i
$401$	18.7249			0.935078			0.467539	−	0.883972i	$-0.345141\pi$
$401$	18.7249			0.935078			0.467539	+	0.883972i	$0.345141\pi$
$402$		0			0
$403$	0.206342			0.0102786
$404$	14.0427	+	24.3227i	0.698651	+	1.21010i
$405$		0			0
$406$	−0.777745	+	1.34709i	−0.0385989	+	0.0668552i
$407$	−0.104686			−0.00518907
$408$		0			0
$409$	−13.0164	+	22.5451i	−0.643620	+	1.11478i	0.340999	+	0.940064i	$0.389235\pi$
$409$	−13.0164	+	22.5451i	−0.643620	+	1.11478i	−0.984618	+	0.174718i	$0.944099\pi$
$410$	1.69134			0.0835294
$411$		0			0
$412$	−7.41151	−	12.8371i	−0.365139	−	0.632439i
$413$	9.35371	−	16.2011i	0.460266	−	0.797204i
$414$		0			0
$415$	6.31900	+	10.9448i	0.310188	+	0.537261i
$416$	−0.344309			−0.0168811
$417$		0			0
$418$	−0.0132539	−	0.0229564i	−0.000648268	−	0.00112283i
$419$	−6.45477	−	11.1800i	−0.315336	−	0.546178i	0.664173	−	0.747579i	$-0.268784\pi$
$419$	−6.45477	−	11.1800i	−0.315336	−	0.546178i	−0.979509	+	0.201401i	$0.935451\pi$
$420$		0			0
$421$	0.763046	+	1.32163i	0.0371886	+	0.0644125i	0.884021	−	0.467448i	$-0.154826\pi$
$421$	0.763046	+	1.32163i	0.0371886	+	0.0644125i	−0.846832	+	0.531860i	$0.821493\pi$
$422$	−0.350367	+	0.606854i	−0.0170556	+	0.0295412i
$423$		0			0
$424$	3.88878			0.188856
$425$	1.92568	+	3.33538i	0.0934094	+	0.161790i
$426$		0			0
$427$	5.84968			0.283086
$428$	18.5928	−	32.2038i	0.898719	−	1.55663i
$429$		0			0
$430$	−0.165867	−	0.287291i	−0.00799883	−	0.0138544i
$431$	9.84170	−	17.0463i	0.474058	−	0.821093i	−0.525501	−	0.850793i	$-0.676122\pi$
$431$	9.84170	−	17.0463i	0.474058	−	0.821093i	0.999559	+	0.0297004i	$0.00945534\pi$
$432$		0			0
$433$	−9.00241	+	15.5926i	−0.432628	+	0.749334i	−0.997099	−	0.0761193i	$-0.975747\pi$
$433$	−9.00241	+	15.5926i	−0.432628	+	0.749334i	0.564471	+	0.825453i	$0.309080\pi$
$434$	−0.185504	+	0.321302i	−0.00890446	+	0.0154230i
$435$		0			0
$436$	−9.46519	+	16.3942i	−0.453300	+	0.785139i
$437$	10.6758	−	18.4911i	0.510694	−	0.884547i
$438$		0			0
$439$	−18.5838	−	32.1882i	−0.886959	−	1.53626i	−0.843452	−	0.537204i	$-0.819481\pi$
$439$	−18.5838	−	32.1882i	−0.886959	−	1.53626i	−0.0435062	−	0.999053i	$-0.513853\pi$
$440$	−0.0146364	+	0.0253510i	−0.000697764	+	0.00120856i
$441$		0			0
$442$	−0.0493353			−0.00234664
$443$	−3.57980	+	6.20039i	−0.170081	+	0.294590i	−0.938448	−	0.345420i	$-0.887736\pi$
$443$	−3.57980	+	6.20039i	−0.170081	+	0.294590i	0.768367	+	0.640010i	$0.221070\pi$
$444$		0			0
$445$	−30.0460			−1.42432
$446$	1.23462	+	2.13843i	0.0584610	+	0.101257i
$447$		0			0
$448$	−9.14007	+	15.8311i	−0.431827	+	0.747947i
$449$	−2.73256	+	4.73294i	−0.128958	+	0.223361i	−0.923273	−	0.384144i	$-0.874496\pi$
$449$	−2.73256	+	4.73294i	−0.128958	+	0.223361i	0.794315	+	0.607506i	$0.207830\pi$
$450$		0			0
$451$	0.106376	+	0.184248i	0.00500904	+	0.00867592i
$452$	18.8861	+	32.7117i	0.888327	+	1.53863i
$453$		0			0
$454$	2.55520			0.119921
$455$	−0.801228			−0.0375622
$456$		0			0
$457$	−8.92557	+	15.4595i	−0.417520	+	0.723166i	−0.995689	−	0.0927506i	$-0.970434\pi$
$457$	−8.92557	+	15.4595i	−0.417520	+	0.723166i	0.578169	+	0.815917i	$0.303767\pi$
$458$	1.20067	−	2.07962i	0.0561035	−	0.0971742i
$459$		0			0
$460$	−11.7259			−0.546723
$461$	−26.1831			−1.21947			−0.609735	−	0.792606i	$-0.708724\pi$
$461$	−26.1831			−1.21947			−0.609735	+	0.792606i	$0.708724\pi$
$462$		0			0
$463$	−4.14876	−	7.18587i	−0.192809	−	0.333956i	0.753371	−	0.657596i	$-0.228427\pi$
$463$	−4.14876	−	7.18587i	−0.192809	−	0.333956i	−0.946180	+	0.323640i	$0.895093\pi$
$464$	16.8512			0.782297
$465$		0			0
$466$	−1.14716			−0.0531410
$467$	−0.0463441	−	0.0802703i	−0.00214455	−	0.00371447i	0.864951	−	0.501856i	$-0.167349\pi$
$467$	−0.0463441	−	0.0802703i	−0.00214455	−	0.00371447i	−0.867096	+	0.498142i	$0.834016\pi$
$468$		0			0
$469$	17.5420	+	9.55902i	0.810012	+	0.441395i
$470$	1.32631			0.0611781
$471$		0			0
$472$	4.46568			0.205549
$473$	0.0208642	−	0.0361379i	0.000959339	−	0.00166162i
$474$		0			0
$475$	−6.76027	−	11.7091i	−0.310182	−	0.537252i
$476$	−4.09236	+	7.08817i	−0.187573	+	0.324886i
$477$		0			0
$478$	−1.58443			−0.0724701
$479$	3.93176	+	6.81000i	0.179646	+	0.311157i	0.941759	−	0.336287i	$-0.109171\pi$
$479$	3.93176	+	6.81000i	0.179646	+	0.311157i	−0.762113	+	0.647444i	$0.775838\pi$
$480$		0			0
$481$	0.341996	−	0.592355i	0.0155937	−	0.0270091i
$482$	0.974158	+	1.68729i	0.0443717	+	0.0768540i
$483$		0			0
$484$	21.7623			0.989195
$485$	−0.122012	−	0.211330i	−0.00554026	−	0.00959601i
$486$		0			0
$487$	18.1895	+	31.5052i	0.824246	+	1.42764i	0.902494	+	0.430702i	$0.141734\pi$
$487$	18.1895	+	31.5052i	0.824246	+	1.42764i	−0.0782482	+	0.996934i	$0.524933\pi$
$488$	0.698193	+	1.20931i	0.0316057	+	0.0547427i
$489$		0			0
$490$	−0.126169	+	0.218531i	−0.00569972	+	0.00987221i
$491$	−36.6931			−1.65594			−0.827968	−	0.560775i	$-0.810503\pi$
$491$	−36.6931			−1.65594			−0.827968	+	0.560775i	$0.810503\pi$
$492$		0			0
$493$	7.37687			0.332238
$494$	0.173196			0.00779244
$495$		0			0
$496$	4.01926			0.180470
$497$	12.9305	+	22.3962i	0.580011	+	1.00461i
$498$		0			0
$499$	−10.5028	−	18.1914i	−0.470169	−	0.814357i	0.529249	−	0.848467i	$-0.322474\pi$
$499$	−10.5028	−	18.1914i	−0.470169	−	0.814357i	−0.999418	+	0.0341094i	$0.989141\pi$
$500$	−11.8820	+	20.5802i	−0.531379	+	0.920375i
$501$		0			0
$502$	−1.16072	+	2.01043i	−0.0518055	+	0.0897297i
$503$	−17.8269	+	30.8771i	−0.794861	+	1.37674i	0.128066	+	0.991766i	$0.459123\pi$
$503$	−17.8269	+	30.8771i	−0.794861	+	1.37674i	−0.922927	+	0.384975i	$0.874210\pi$
$504$		0			0
$505$	−11.7220	+	20.3032i	−0.521624	+	0.903479i
$506$	0.00799295	+	0.0138442i	0.000355330	+	0.000615449i
$507$		0			0
$508$	11.6610	+	20.1974i	0.517371	+	0.896113i
$509$	−8.71489			−0.386281			−0.193140	−	0.981171i	$-0.561867\pi$
$509$	−8.71489			−0.386281			−0.193140	+	0.981171i	$0.561867\pi$
$510$		0			0
$511$	−4.89533			−0.216557
$512$	−11.2181			−0.495775
$513$		0			0
$514$	2.79648			0.123348
$515$	6.18670	−	10.7157i	0.272618	−	0.472189i
$516$		0			0
$517$	0.0834174	+	0.144483i	0.00366869	+	0.00635436i
$518$	0.614916	+	1.06507i	0.0270179	+	0.0467963i
$519$		0			0
$520$	−0.0956312	−	0.165638i	−0.00419370	−	0.00726371i
$521$	−41.7619			−1.82962			−0.914812	−	0.403881i	$-0.867661\pi$
$521$	−41.7619			−1.82962			−0.914812	+	0.403881i	$0.867661\pi$
$522$		0			0
$523$	−14.7669	−	25.5770i	−0.645711	−	1.11840i	−0.984137	−	0.177411i	$-0.943228\pi$
$523$	−14.7669	−	25.5770i	−0.645711	−	1.11840i	0.338426	−	0.940993i	$-0.390106\pi$
$524$	−1.44769	+	2.50748i	−0.0632427	+	0.109540i
$525$		0			0
$526$	1.48372	+	2.56988i	0.0646932	+	0.112052i
$527$	1.75949			0.0766447
$528$		0			0
$529$	5.06178	−	8.76727i	0.220078	−	0.381186i
$530$	0.807157	+	1.39804i	0.0350607	+	0.0607268i
$531$		0			0
$532$	14.3666	−	24.8836i	0.622869	−	1.07884i
$533$	−1.39007			−0.0602107
$534$		0			0
$535$	31.0404			1.34200
$536$	0.117594	+	4.76738i	0.00507930	+	0.205919i
$537$		0			0
$538$	−1.20182	−	2.08162i	−0.0518142	−	0.0897449i
$539$	−0.0317412			−0.00136719
$540$		0			0
$541$	−21.5090			−0.924744			−0.462372	−	0.886686i	$-0.653001\pi$
$541$	−21.5090			−0.924744			−0.462372	+	0.886686i	$0.653001\pi$
$542$	−1.72210	−	2.98277i	−0.0739707	−	0.128121i
$543$		0			0
$544$	−2.93594			−0.125878
$545$	−15.8020			−0.676882
$546$		0			0
$547$	−12.8310	+	22.2239i	−0.548612	+	0.950224i	0.449758	+	0.893151i	$0.351510\pi$
$547$	−12.8310	+	22.2239i	−0.548612	+	0.950224i	−0.998370	+	0.0570737i	$0.981823\pi$
$548$	6.64727	−	11.5134i	0.283957	−	0.491829i
$549$		0			0
$550$	0.0101228			0.000431637
$551$	−25.8971			−1.10325
$552$		0			0
$553$	−14.1946	−	24.5857i	−0.603615	−	1.04549i
$554$	0.0411317	+	0.0712422i	0.00174752	+	0.00302679i
$555$		0			0
$556$	−5.77717	+	10.0064i	−0.245007	+	0.424364i
$557$	−9.13519	+	15.8226i	−0.387070	+	0.670426i	−0.992054	−	0.125812i	$-0.959846\pi$
$557$	−9.13519	+	15.8226i	−0.387070	+	0.670426i	0.604984	+	0.796238i	$0.293180\pi$
$558$		0			0
$559$	0.136322	+	0.236117i	0.00576582	+	0.00998669i
$560$	−15.6068			−0.659508
$561$		0			0
$562$	0.0716702	−	0.124136i	0.00302322	−	0.00523638i
$563$	5.25520			0.221480			0.110740	−	0.993849i	$-0.464678\pi$
$563$	5.25520			0.221480			0.110740	+	0.993849i	$0.464678\pi$
$564$		0			0
$565$	−15.7650	+	27.3058i	−0.663239	+	1.14876i
$566$	−0.990993	−	1.71645i	−0.0416546	−	0.0721478i
$567$		0			0
$568$	−3.08665	+	5.34624i	−0.129513	+	0.224323i
$569$	−7.88277	+	13.6534i	−0.330463	+	0.572378i	−0.982603	−	0.185720i	$-0.940538\pi$
$569$	−7.88277	+	13.6534i	−0.330463	+	0.572378i	0.652140	+	0.758099i	$0.273871\pi$
$570$		0			0
$571$	3.99307	−	6.91620i	0.167105	−	0.289434i	−0.770296	−	0.637687i	$-0.779892\pi$
$571$	3.99307	−	6.91620i	0.167105	−	0.289434i	0.937401	+	0.348253i	$0.113225\pi$
$572$	0.00598224	−	0.0103616i	0.000250130	−	0.000433238i
$573$		0			0
$574$	1.24969	−	2.16452i	0.0521610	−	0.0903455i
$575$	4.07688	+	7.06137i	0.170018	+	0.294480i
$576$		0			0
$577$	17.3163	−	29.9926i	0.720885	−	1.24861i	−0.239760	−	0.970832i	$-0.577069\pi$
$577$	17.3163	−	29.9926i	0.720885	−	1.24861i	0.960645	−	0.277778i	$-0.0895978\pi$
$578$	2.06873			0.0860479
$579$		0			0
$580$	7.11110	+	12.3168i	0.295272	+	0.511427i
$581$	18.6758			0.774802
$582$		0			0
$583$	−0.101531	+	0.175857i	−0.00420499	+	0.00728326i
$584$	−0.584286	−	1.01201i	−0.0241779	−	0.0418774i
$585$		0			0
$586$	0.323544	+	0.560395i	0.0133655	+	0.0231497i
$587$	−15.7784	−	27.3289i	−0.651243	−	1.12799i	−0.982822	−	0.184559i	$-0.940914\pi$
$587$	−15.7784	−	27.3289i	−0.651243	−	1.12799i	0.331578	−	0.943428i	$-0.392419\pi$
$588$		0			0
$589$	−6.17685			−0.254512
$590$	0.926898	+	1.60543i	0.0381598	+	0.0660947i
$591$		0			0
$592$	6.66161	−	11.5382i	0.273790	−	0.474219i
$593$	10.4375	+	18.0783i	0.428618	+	0.742388i	0.996751	−	0.0805488i	$-0.0256673\pi$
$593$	10.4375	+	18.0783i	0.428618	+	0.742388i	−0.568133	+	0.822937i	$0.692334\pi$
$594$		0			0
$595$	−6.83212			−0.280090
$596$	−17.7258	+	30.7020i	−0.726077	+	1.25760i
$597$		0			0
$598$	−0.104448			−0.00427121
$599$	20.2989	−	35.1587i	0.829391	−	1.43655i	−0.0691265	−	0.997608i	$-0.522021\pi$
$599$	20.2989	−	35.1587i	0.829391	−	1.43655i	0.898517	−	0.438939i	$-0.144645\pi$
$600$		0			0
$601$	4.22736	+	7.32200i	0.172438	+	0.298671i	0.939272	−	0.343175i	$-0.111502\pi$
$601$	4.22736	+	7.32200i	0.172438	+	0.298671i	−0.766834	+	0.641846i	$0.778169\pi$
$602$	−0.490220			−0.0199799
$603$		0			0
$604$	−36.5835			−1.48856
$605$	9.08294	+	15.7321i	0.369274	+	0.639602i
$606$		0			0
$607$	16.3489	−	28.3172i	0.663582	−	1.14936i	−0.316086	−	0.948731i	$-0.602369\pi$
$607$	16.3489	−	28.3172i	0.663582	−	1.14936i	0.979668	−	0.200627i	$-0.0642979\pi$
$608$	10.3069			0.417999
$609$		0			0
$610$	−0.289835	+	0.502008i	−0.0117351	+	0.0203257i
$611$	−1.09006			−0.0440992
$612$		0			0
$613$	−15.5715	−	26.9706i	−0.628926	−	1.08933i	−0.987768	−	0.155934i	$-0.950161\pi$
$613$	−15.5715	−	26.9706i	−0.628926	−	1.08933i	0.358841	−	0.933399i	$-0.383172\pi$
$614$	−0.792215	+	1.37216i	−0.0319712	+	0.0553757i
$615$		0			0
$616$	0.0216290	+	0.0374624i	0.000871455	+	0.00150941i
$617$	−22.8060			−0.918136			−0.459068	−	0.888401i	$-0.651817\pi$
$617$	−22.8060			−0.918136			−0.459068	+	0.888401i	$0.651817\pi$
$618$		0			0
$619$	6.18993	+	10.7213i	0.248794	+	0.430924i	0.963192	−	0.268816i	$-0.0866324\pi$
$619$	6.18993	+	10.7213i	0.248794	+	0.430924i	−0.714397	+	0.699740i	$0.753299\pi$
$620$	1.69610	+	2.93774i	0.0681171	+	0.117982i
$621$		0			0
$622$	−1.31497	−	2.27759i	−0.0527253	−	0.0913229i
$623$	−22.2002	+	38.4519i	−0.889434	+	1.54054i
$624$		0			0
$625$	−8.47540			−0.339016
$626$	0.0920192	+	0.159382i	0.00367783	+	0.00637019i
$627$		0			0
$628$	3.77988			0.150834
$629$	2.91622	−	5.05105i	0.116277	−	0.201398i
$630$		0			0
$631$	7.67063	+	13.2859i	0.305363	+	0.528904i	0.977342	−	0.211666i	$-0.0678888\pi$
$631$	7.67063	+	13.2859i	0.305363	+	0.528904i	−0.671979	+	0.740570i	$0.734556\pi$
$632$	3.38841	−	5.86889i	0.134784	−	0.233452i
$633$		0			0
$634$	1.50251	−	2.60242i	0.0596721	−	0.103355i
$635$	−9.73388	+	16.8596i	−0.386277	+	0.669052i
$636$		0			0
$637$	0.103695	−	0.179605i	0.00410855	−	0.00711621i
$638$	0.00969454	−	0.0167914i	0.000383811	−	0.000664779i
$639$		0			0
$640$	−3.76657	−	6.52389i	−0.148887	−	0.257879i
$641$	−15.1017	+	26.1569i	−0.596481	+	1.03314i	0.396855	+	0.917881i	$0.370102\pi$
$641$	−15.1017	+	26.1569i	−0.596481	+	1.03314i	−0.993336	+	0.115255i	$0.963232\pi$
$642$		0			0
$643$	38.4337			1.51568			0.757838	−	0.652443i	$-0.226256\pi$
$643$	38.4337			1.51568			0.757838	+	0.652443i	$0.226256\pi$
$644$	−8.66397	+	15.0064i	−0.341408	+	0.591336i
$645$		0			0
$646$	1.47685			0.0581059
$647$	−1.38108	−	2.39210i	−0.0542958	−	0.0940431i	0.837600	−	0.546284i	$-0.183958\pi$
$647$	−1.38108	−	2.39210i	−0.0542958	−	0.0940431i	−0.891896	+	0.452241i	$0.850625\pi$
$648$		0			0
$649$	−0.116593	+	0.201946i	−0.00457669	+	0.00792706i
$650$	−0.0330700	+	0.0572789i	−0.00129711	+	0.00224666i
$651$		0			0
$652$	17.1162	+	29.6462i	0.670324	+	1.16103i
$653$	11.6981	+	20.2617i	0.457781	+	0.792900i	0.998843	−	0.0480827i	$-0.0153111\pi$
$653$	11.6981	+	20.2617i	0.457781	+	0.792900i	−0.541063	+	0.840982i	$0.681978\pi$
$654$		0			0
$655$	−2.41690			−0.0944360
$656$	−27.0767			−1.05717
$657$		0			0
$658$	0.979976	−	1.69737i	0.0382034	−	0.0661703i
$659$	8.97174	−	15.5395i	0.349490	−	0.605334i	−0.636669	−	0.771137i	$-0.719688\pi$
$659$	8.97174	−	15.5395i	0.349490	−	0.605334i	0.986159	+	0.165803i	$0.0530217\pi$
$660$		0			0
$661$	32.4980			1.26402			0.632012	−	0.774958i	$-0.282229\pi$
$661$	32.4980			1.26402			0.632012	+	0.774958i	$0.282229\pi$
$662$	3.01262			0.117089
$663$		0			0
$664$	2.22906	+	3.86085i	0.0865044	+	0.149830i
$665$	23.9847			0.930087
$666$		0			0
$667$	15.6177			0.604718
$668$	−2.53080	−	4.38348i	−0.0979196	−	0.169602i
$669$		0			0
$670$	−1.68949	+	1.03180i	−0.0652707	+	0.0398617i
$671$	−0.0729158			−0.00281488
$672$		0			0
$673$	−25.3935			−0.978847			−0.489424	−	0.872046i	$-0.662793\pi$
$673$	−25.3935			−0.978847			−0.489424	+	0.872046i	$0.662793\pi$
$674$	2.58075	−	4.46999i	0.0994068	−	0.172178i
$675$		0			0
$676$	−12.8215	−	22.2075i	−0.493136	−	0.854136i
$677$	21.5141	−	37.2634i	0.826852	−	1.43215i	−0.0736434	−	0.997285i	$-0.523463\pi$
$677$	21.5141	−	37.2634i	0.826852	−	1.43215i	0.900496	−	0.434865i	$-0.143204\pi$
$678$		0			0
$679$	−0.360605			−0.0138387
$680$	−0.815453	−	1.41241i	−0.0312712	−	0.0541633i
$681$		0			0
$682$	0.00231229	−	0.00400501i	8.85422e−5	−	0.000153360i
$683$	4.84470	+	8.39127i	0.185377	+	0.321083i	0.943704	−	0.330792i	$-0.107316\pi$
$683$	4.84470	+	8.39127i	0.185377	+	0.321083i	−0.758326	+	0.651875i	$0.773983\pi$
$684$		0			0
$685$	11.0975			0.424014
$686$	1.43733	+	2.48953i	0.0548775	+	0.0950507i
$687$		0			0
$688$	2.65537	+	4.59923i	0.101235	+	0.175344i
$689$	−0.663382	−	1.14901i	−0.0252729	−	0.0437739i
$690$		0			0
$691$	−13.1298	+	22.7415i	−0.499482	+	0.865128i	−1.00000		0.000598103i	$-0.999810\pi$
$691$	−13.1298	+	22.7415i	−0.499482	+	0.865128i	0.500518	+	0.865726i	$0.333143\pi$
$692$	4.57359			0.173862
$693$		0			0
$694$	2.88499			0.109513
$695$	−9.64489			−0.365851
$696$		0			0
$697$	−11.8532			−0.448973
$698$	0.278553	+	0.482469i	0.0105434	+	0.0182617i
$699$		0			0
$700$	5.48630	+	9.50256i	0.207363	+	0.359163i
$701$	−16.7467	+	29.0061i	−0.632513	+	1.09554i	0.354523	+	0.935047i	$0.384643\pi$
$701$	−16.7467	+	29.0061i	−0.632513	+	1.09554i	−0.987036	+	0.160497i	$0.948690\pi$
$702$		0			0
$703$	−10.2376	+	17.7321i	−0.386120	+	0.668779i
$704$	0.113930	−	0.197333i	0.00429391	−	0.00743727i
$705$		0			0
$706$	2.60831	−	4.51773i	0.0981650	−	0.170027i
$707$	17.3222	+	30.0030i	0.651469	+	1.12838i
$708$		0			0
$709$	−3.95521	−	6.85063i	−0.148541	−	0.257281i	0.782147	−	0.623093i	$-0.214124\pi$
$709$	−3.95521	−	6.85063i	−0.148541	−	0.257281i	−0.930688	+	0.365813i	$0.880791\pi$
$710$	−2.56267			−0.0961752
$711$		0			0
$712$	−10.5989			−0.397211
$713$	3.72504			0.139504
$714$		0			0
$715$	0.00998725			0.000373502
$716$	19.7692	−	34.2413i	0.738811	−	1.27966i
$717$		0			0
$718$	0.130637	+	0.226269i	0.00487532	+	0.00844430i
$719$	−11.6790	−	20.2286i	−0.435554	−	0.754401i	0.561787	−	0.827282i	$-0.310114\pi$
$719$	−11.6790	−	20.2286i	−0.435554	−	0.754401i	−0.997341	+	0.0728809i	$0.976781\pi$
$720$		0			0
$721$	−9.14238	−	15.8351i	−0.340480	−	0.589728i
$722$	−2.40231			−0.0894048
$723$		0			0
$724$	18.9493	+	32.8212i	0.704246	+	1.21979i
$725$	4.94480	−	8.56465i	0.183645	−	0.318083i
$726$		0			0
$727$	−20.2932	−	35.1488i	−0.752633	−	1.30360i	−0.946543	−	0.322579i	$-0.895450\pi$
$727$	−20.2932	−	35.1488i	−0.752633	−	1.30360i	0.193910	−	0.981019i	$-0.437883\pi$
$728$	−0.282638			−0.0104752
$729$		0			0
$730$	0.242549	−	0.420108i	0.00897715	−	0.0155489i
$731$	1.16243	+	2.01338i	0.0429940	+	0.0744677i
$732$		0			0
$733$	−15.5448	+	26.9243i	−0.574160	+	0.994473i	0.421973	+	0.906608i	$0.361338\pi$
$733$	−15.5448	+	26.9243i	−0.574160	+	0.994473i	−0.996132	+	0.0878650i	$0.971996\pi$
$734$	1.19811			0.0442229
$735$		0			0
$736$	−6.21571			−0.229114
$737$	−0.218659	−	0.119153i	−0.00805442	−	0.00438904i
$738$		0			0
$739$	6.33759	+	10.9770i	0.233132	+	0.403796i	0.958728	−	0.284324i	$-0.0917693\pi$
$739$	6.33759	+	10.9770i	0.233132	+	0.403796i	−0.725596	+	0.688121i	$0.758436\pi$
$740$	11.2446			0.413361
$741$		0			0
$742$	2.38555			0.0875763
$743$	−8.72760	−	15.1167i	−0.320185	−	0.554576i	0.660341	−	0.750966i	$-0.270412\pi$
$743$	−8.72760	−	15.1167i	−0.320185	−	0.554576i	−0.980526	+	0.196390i	$0.937078\pi$
$744$		0			0
$745$	−29.5929			−1.08420
$746$	3.96514			0.145174
$747$		0			0
$748$	0.0510110	−	0.0883536i	0.00186515	−	0.00323053i
$749$	22.9350	−	39.7245i	0.838026	−	1.45150i
$750$		0			0
$751$	49.9160			1.82146			0.910731	−	0.413001i	$-0.135519\pi$
$751$	49.9160			1.82146			0.910731	+	0.413001i	$0.135519\pi$
$752$	−21.2329			−0.774283
$753$		0			0
$754$	0.0633420	+	0.109712i	0.00230678	+	0.00399546i
$755$	−15.2689	−	26.4464i	−0.555691	−	0.962485i
$756$		0			0
$757$	0.900026	−	1.55889i	0.0327120	−	0.0566589i	−0.849206	−	0.528062i	$-0.822919\pi$
$757$	0.900026	−	1.55889i	0.0327120	−	0.0566589i	0.881918	+	0.471403i	$0.156252\pi$
$758$	−1.77788	+	3.07938i	−0.0645754	+	0.111848i
$759$		0			0
$760$	2.86271	+	4.95836i	0.103842	+	0.179859i
$761$	−19.1844			−0.695433			−0.347717	−	0.937600i	$-0.613043\pi$
$761$	−19.1844			−0.695433			−0.347717	+	0.937600i	$0.613043\pi$
$762$		0			0
$763$	−11.6757	+	20.2229i	−0.422688	+	0.732116i
$764$	37.1387			1.34363
$765$		0			0
$766$	−0.817374	+	1.41573i	−0.0295329	+	0.0511525i
$767$	−0.761795	−	1.31947i	−0.0275068	−	0.0476432i
$768$		0			0
$769$	9.05362	−	15.6813i	0.326482	−	0.565483i	−0.655329	−	0.755343i	$-0.727470\pi$
$769$	9.05362	−	15.6813i	0.326482	−	0.565483i	0.981811	+	0.189860i	$0.0608034\pi$
$770$	−0.00897864	+	0.0155515i	−0.000323568	+	0.000560436i
$771$		0			0
$772$	−10.3194	+	17.8738i	−0.371404	+	0.643291i
$773$	14.6609	−	25.3935i	0.527318	−	0.913341i	−0.472175	−	0.881505i	$-0.656531\pi$
$773$	14.6609	−	25.3935i	0.527318	−	0.913341i	0.999493	−	0.0318364i	$-0.0101355\pi$
$774$		0			0
$775$	1.17941	−	2.04279i	0.0423656	−	0.0733793i
$776$	−0.0430402	−	0.0745479i	−0.00154505	−	0.00267611i
$777$		0			0
$778$	−0.189004	+	0.327365i	−0.00677613	+	0.0117366i
$779$	41.6117			1.49090
$780$		0			0
$781$	−0.161177	−	0.279167i	−0.00576738	−	0.00998940i
$782$	−0.890637			−0.0318491
$783$		0			0
$784$	2.01983	−	3.49846i	0.0721369	−	0.124945i
$785$	1.57761	+	2.73250i	0.0563074	+	0.0975272i
$786$		0			0
$787$	−9.22809	−	15.9835i	−0.328946	−	0.569751i	0.653357	−	0.757050i	$-0.273360\pi$
$787$	−9.22809	−	15.9835i	−0.328946	−	0.569751i	−0.982303	+	0.187299i	$0.940027\pi$
$788$	−17.3069	−	29.9764i	−0.616533	−	1.06787i
$789$		0			0
$790$	2.81320			0.100089
$791$	23.2967	+	40.3511i	0.828335	+	1.43472i
$792$		0			0
$793$	0.238208	−	0.412588i	0.00845901	−	0.0146514i
$794$	0.436756	+	0.756484i	0.0154999	+	0.0268466i
$795$		0			0
$796$	3.86052			0.136832
$797$	−1.52912	+	2.64851i	−0.0541641	+	0.0938149i	−0.891836	−	0.452359i	$-0.850583\pi$
$797$	−1.52912	+	2.64851i	−0.0541641	+	0.0938149i	0.837672	+	0.546173i	$0.183916\pi$
$798$		0			0
$799$	−9.29502			−0.328834
$800$	−1.96799	+	3.40867i	−0.0695791	+	0.120515i
$801$		0			0
$802$	1.37100	+	2.37465i	0.0484118	+	0.0838517i
$803$	0.0610199			0.00215335
$804$		0			0
$805$	−14.4644			−0.509801
$806$	0.0151080	+	0.0261678i	0.000532156	+	0.000921722i
$807$		0			0
$808$	−4.13501	+	7.16205i	−0.145469	+	0.251960i
$809$	46.0582			1.61932			0.809659	−	0.586900i	$-0.199652\pi$
$809$	46.0582			1.61932			0.809659	+	0.586900i	$0.199652\pi$
$810$		0			0
$811$	−16.7610	+	29.0309i	−0.588557	+	1.01941i	0.405864	+	0.913933i	$0.366971\pi$
$811$	−16.7610	+	29.0309i	−0.588557	+	1.01941i	−0.994422	+	0.105478i	$0.966363\pi$
$812$	21.0168			0.737546
$813$		0			0
$814$	−0.00766489	−	0.0132760i	−0.000268654	−	0.000465323i
$815$	−14.2876	+	24.7469i	−0.500474	+	0.866846i
$816$		0			0
$817$	−4.08080	−	7.06815i	−0.142769	−	0.247283i
$818$	−3.81215			−0.133289
$819$		0			0
$820$	−11.4262	−	19.7907i	−0.399020	−	0.691122i
$821$	−3.46700	−	6.00501i	−0.120999	−	0.209576i	0.799163	−	0.601115i	$-0.205276\pi$
$821$	−3.46700	−	6.00501i	−0.120999	−	0.209576i	−0.920162	+	0.391538i	$0.871943\pi$
$822$		0			0
$823$	−0.321614	−	0.557052i	−0.0112108	−	0.0194176i	0.860366	−	0.509677i	$-0.170235\pi$
$823$	−0.321614	−	0.557052i	−0.0112108	−	0.0194176i	−0.871576	+	0.490260i	$0.836902\pi$
$824$	2.18239	−	3.78001i	0.0760272	−	0.131683i
$825$		0			0
$826$	2.73944			0.0953174
$827$	−14.8918	−	25.7933i	−0.517838	−	0.896921i	−0.999785	−	0.0207212i	$-0.993404\pi$
$827$	−14.8918	−	25.7933i	−0.517838	−	0.896921i	0.481948	−	0.876200i	$-0.339930\pi$
$828$		0			0
$829$	−4.85711			−0.168694			−0.0843472	−	0.996436i	$-0.526880\pi$
$829$	−4.85711			−0.168694			−0.0843472	+	0.996436i	$0.526880\pi$
$830$	−0.925331	+	1.60272i	−0.0321187	+	0.0556312i
$831$		0			0
$832$	0.744395	+	1.28933i	0.0258073	+	0.0446995i
$833$	0.884214	−	1.53150i	0.0306362	−	0.0530634i
$834$		0			0
$835$	2.11256	−	3.65907i	0.0731083	−	0.126627i
$836$	−0.179078	+	0.310172i	−0.00619355	+	0.0107275i
$837$		0			0
$838$	0.945212	−	1.63716i	0.0326518	−	0.0565546i
$839$	24.3037	−	42.0952i	0.839055	−	1.45329i	−0.0516303	−	0.998666i	$-0.516442\pi$
$839$	24.3037	−	42.0952i	0.839055	−	1.45329i	0.890685	−	0.454620i	$-0.150225\pi$
$840$		0			0
$841$	5.02877	+	8.71009i	0.173406	+	0.300348i
$842$	−0.111738	+	0.193535i	−0.00385073	+	0.00666966i
$843$		0			0
$844$	9.46789			0.325898
$845$	10.7027	−	18.5376i	0.368183	−	0.637711i
$846$		0			0
$847$	26.8446			0.922391
$848$	−12.9218	−	22.3811i	−0.443735	−	0.768572i
$849$		0			0
$850$	−0.281990	+	0.488421i	−0.00967217	+	0.0167527i
$851$	6.17397	−	10.6936i	0.211641	−	0.366573i
$852$		0			0
$853$	−5.50982	−	9.54329i	−0.188653	−	0.326756i	0.756149	−	0.654400i	$-0.227079\pi$
$853$	−5.50982	−	9.54329i	−0.188653	−	0.326756i	−0.944801	+	0.327644i	$0.893745\pi$
$854$	0.428302	+	0.741841i	0.0146562	+	0.0253853i
$855$		0			0
$856$	10.9497			0.374252
$857$	24.1343			0.824414			0.412207	−	0.911090i	$-0.364758\pi$
$857$	24.1343			0.824414			0.412207	+	0.911090i	$0.364758\pi$
$858$		0			0
$859$	−1.78735	+	3.09578i	−0.0609837	+	0.105627i	−0.894905	−	0.446256i	$-0.852757\pi$
$859$	−1.78735	+	3.09578i	−0.0609837	+	0.105627i	0.833922	+	0.551883i	$0.186090\pi$
$860$	−2.24110	+	3.88169i	−0.0764208	+	0.132365i
$861$		0			0
$862$	2.88236			0.0981737
$863$	25.0414			0.852418			0.426209	−	0.904625i	$-0.359849\pi$
$863$	25.0414			0.852418			0.426209	+	0.904625i	$0.359849\pi$
$864$		0			0
$865$	1.90888	+	3.30628i	0.0649039	+	0.112417i
$866$	−2.63656			−0.0895939
$867$		0			0
$868$	5.01283			0.170146
$869$	0.176934	+	0.306459i	0.00600209	+	0.0103959i
$870$		0			0
$871$	1.38855	−	0.848007i	0.0470492	−	0.0287336i
$872$	−5.57423			−0.188767
$873$		0			0
$874$	3.12665			0.105761
$875$	−14.6569	+	25.3865i	−0.495493	+	0.858219i
$876$		0			0
$877$	−15.6556	−	27.1162i	−0.528651	−	0.915650i	−0.999442	−	0.0334055i	$-0.989365\pi$
$877$	−15.6556	−	27.1162i	−0.528651	−	0.915650i	0.470791	−	0.882245i	$-0.343969\pi$
$878$	2.72135	−	4.71351i	0.0918411	−	0.159073i
$879$		0			0
$880$	0.194538			0.00655787
$881$	1.57271	+	2.72401i	0.0529858	+	0.0917741i	0.891302	−	0.453411i	$-0.149793\pi$
$881$	1.57271	+	2.72401i	0.0529858	+	0.0917741i	−0.838316	+	0.545185i	$0.816460\pi$
$882$		0			0
$883$	24.9396	−	43.1966i	0.839283	−	1.45368i	−0.0512116	−	0.998688i	$-0.516308\pi$
$883$	24.9396	−	43.1966i	0.839283	−	1.45368i	0.890495	−	0.454993i	$-0.150358\pi$
$884$	0.333294	+	0.577283i	0.0112099	+	0.0194161i
$885$		0			0
$886$	−1.04842			−0.0352225
$887$	−24.6434	−	42.6837i	−0.827445	−	1.43318i	−0.900036	−	0.435816i	$-0.856460\pi$
$887$	−24.6434	−	42.6837i	−0.827445	−	1.43318i	0.0725907	−	0.997362i	$-0.476873\pi$
$888$		0			0
$889$	14.3842	+	24.9142i	0.482432	+	0.835596i
$890$	−2.19991	−	3.81036i	−0.0737413	−	0.127724i
$891$		0			0
$892$	16.6814	−	28.8931i	0.558536	−	0.967413i
$893$	32.6309			1.09195
$894$		0			0
$895$	33.0044			1.10321
$896$	−11.1321			−0.371897
$897$		0			0
$898$	−0.800293			−0.0267061
$899$	−2.25903	−	3.91275i	−0.0753428	−	0.130498i
$900$		0			0
$901$	−5.65670	−	9.79770i	−0.188452	−	0.326409i
$902$	−0.0155773	+	0.0269806i	−0.000518667	+	0.000898357i
$903$		0			0
$904$	−5.56119	+	9.63226i	−0.184962	+	0.320364i
$905$	−15.8178	+	27.3972i	−0.525801	+	0.910713i
$906$		0			0
$907$	5.30811	−	9.19392i	0.176253	−	0.305279i	−0.764341	−	0.644812i	$-0.776936\pi$
$907$	5.30811	−	9.19392i	0.176253	−	0.305279i	0.940594	+	0.339533i	$0.110269\pi$
$908$	−17.2621	−	29.8989i	−0.572864	−	0.992230i
$909$		0			0
$910$	−0.0586644	−	0.101610i	−0.00194471	−	0.00336833i
$911$	−8.48031			−0.280965			−0.140483	−	0.990083i	$-0.544865\pi$
$911$	−8.48031			−0.280965			−0.140483	+	0.990083i	$0.544865\pi$
$912$		0			0
$913$	−0.232792			−0.00770430
$914$	−2.61405			−0.0864652
$915$		0			0
$916$	−32.4454			−1.07203
$917$	−1.78578	+	3.09307i	−0.0589717	+	0.102142i
$918$		0			0
$919$	−25.0806	−	43.4408i	−0.827332	−	1.43298i	−0.900124	−	0.435634i	$-0.856524\pi$
$919$	−25.0806	−	43.4408i	−0.827332	−	1.43298i	0.0727916	−	0.997347i	$-0.476809\pi$
$920$	−1.72640	−	2.99022i	−0.0569178	−	0.0985846i
$921$		0			0
$922$	−1.91708	−	3.32048i	−0.0631356	−	0.109354i
$923$	2.10619			0.0693262
$924$		0			0
$925$	−3.90955	−	6.77154i	−0.128545	−	0.222647i
$926$	0.607529	−	1.05227i	0.0199646	−	0.0345798i
$927$		0			0
$928$	3.76948	+	6.52893i	0.123739	+	0.214323i
$929$	−20.6713			−0.678205			−0.339102	−	0.940749i	$-0.610123\pi$
$929$	−20.6713			−0.678205			−0.339102	+	0.940749i	$0.610123\pi$
$930$		0			0
$931$	−3.10410	+	5.37647i	−0.101733	+	0.176207i
$932$	7.74984	+	13.4231i	0.253855	+	0.439689i
$933$		0			0
$934$	0.00678645	−	0.0117545i	0.000222059	−	0.000384618i
$935$	0.0851619			0.00278509
$936$		0			0
$937$	55.5881			1.81598			0.907992	−	0.418987i	$-0.137615\pi$
$937$	55.5881			1.81598			0.907992	+	0.418987i	$0.137615\pi$
$938$	0.0721375	+	2.92452i	0.00235537	+	0.0954890i
$939$		0			0
$940$	−8.96014	−	15.5194i	−0.292248	−	0.506188i
$941$	39.8861			1.30025			0.650124	−	0.759828i	$-0.274717\pi$
$941$	39.8861			1.30025			0.650124	+	0.759828i	$0.274717\pi$
$942$		0			0
$943$	−25.0946			−0.817192
$944$	−14.8387	−	25.7014i	−0.482959	−	0.836509i
$945$		0			0
$946$	0.00611056			0.000198671
$947$	−14.9293			−0.485139			−0.242569	−	0.970134i	$-0.577990\pi$
$947$	−14.9293			−0.485139			−0.242569	+	0.970134i	$0.577990\pi$
$948$		0			0
$949$	−0.199345	+	0.345276i	−0.00647102	+	0.0112081i
$950$	0.989948	−	1.71464i	0.0321182	−	0.0556303i
$951$		0			0
$952$	−2.41007			−0.0781107
$953$	−55.6923			−1.80405			−0.902025	−	0.431684i	$-0.857919\pi$
$953$	−55.6923			−1.80405			−0.902025	+	0.431684i	$0.857919\pi$
$954$		0			0
$955$	15.5006	+	26.8479i	0.501588	+	0.868777i
$956$	10.7039	+	18.5397i	0.346190	+	0.599618i
$957$		0			0
$958$	−0.575751	+	0.997231i	−0.0186017	+	0.0322191i
$959$	8.19966	−	14.2022i	0.264781	−	0.458614i
$960$		0			0
$961$	14.9612	+	25.9135i	0.482619	+	0.835921i
$962$	0.100161			0.00322933
$963$		0			0
$964$	13.1622	−	22.7977i	0.423927	−	0.734263i
$965$	−17.2281			−0.554592
$966$		0			0
$967$	26.4746	−	45.8553i	0.851366	−	1.47461i	−0.0286105	−	0.999591i	$-0.509108\pi$
$967$	26.4746	−	45.8553i	0.851366	−	1.47461i	0.879976	−	0.475018i	$-0.157558\pi$
$968$	3.20406	+	5.54959i	0.102982	+	0.178371i
$969$		0			0
$970$	0.0178669	−	0.0309464i	0.000573672	−	0.000993629i
$971$	−12.2043	+	21.1385i	−0.391655	+	0.678366i	−0.992668	−	0.120873i	$-0.961431\pi$
$971$	−12.2043	+	21.1385i	−0.391655	+	0.678366i	0.601013	+	0.799239i	$0.294764\pi$
$972$		0			0
$973$	−7.12636	+	12.3432i	−0.228461	+	0.395705i
$974$	−2.66361	+	4.61350i	−0.0853474	+	0.147826i
$975$		0			0
$976$	4.63996	−	8.03664i	0.148521	−	0.257247i
$977$	11.8421	+	20.5111i	0.378863	+	0.656209i	0.990897	−	0.134622i	$-0.0429819\pi$
$977$	11.8421	+	20.5111i	0.378863	+	0.656209i	−0.612034	+	0.790831i	$0.709649\pi$
$978$		0			0
$979$	0.276724	−	0.479301i	0.00884415	−	0.0153185i
$980$	3.40943			0.108910
$981$		0			0
$982$	−2.68660	−	4.65333i	−0.0857328	−	0.148494i
$983$	19.5021			0.622019			0.311010	−	0.950407i	$-0.399333\pi$
$983$	19.5021			0.622019			0.311010	+	0.950407i	$0.399333\pi$
$984$		0			0
$985$	14.4468	−	25.0226i	0.460313	−	0.797285i
$986$	0.540121	+	0.935517i	0.0172010	+	0.0297929i
$987$		0			0
$988$	−1.17006	−	2.02660i	−0.0372245	−	0.0644747i
$989$	2.46099	+	4.26256i	0.0782549	+	0.135541i
$990$		0			0
$991$	18.2282			0.579038			0.289519	−	0.957172i	$-0.406505\pi$
$991$	18.2282			0.579038			0.289519	+	0.957172i	$0.406505\pi$
$992$	0.899077	+	1.55725i	0.0285457	+	0.0494426i
$993$		0			0
$994$	−1.89349	+	3.27962i	−0.0600578	+	0.104023i
$995$	1.61127	+	2.79080i	0.0510806	+	0.0884742i
$996$		0			0
$997$	−2.99013			−0.0946984			−0.0473492	−	0.998878i	$-0.515077\pi$
$997$	−2.99013			−0.0946984			−0.0473492	+	0.998878i	$0.515077\pi$
$998$	1.53799	−	2.66387i	0.0486842	−	0.0843235i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	603.2.g.f.37.3		10
3.2	odd	2		201.2.e.c.37.3	✓	10
67.29	even	3	inner	603.2.g.f.163.3		10
201.29	odd	6		201.2.e.c.163.3	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.2.e.c.37.3	✓	10	3.2	odd	2
201.2.e.c.163.3	yes	10	201.29	odd	6
603.2.g.f.37.3		10	1.1	even	1	trivial
603.2.g.f.163.3		10	67.29	even	3	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:	\( N \)	\(=\)	\( 603 = 3^{2} \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	603.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0732181 + 0.126817i) q^{2} +(0.989278 - 1.71348i) q^{4} +1.65158 q^{5} +(1.22031 - 2.11364i) q^{7} +0.582605 q^{8} +O(q^{10})\)	\(q+(0.0732181 + 0.126817i) q^{2} +(0.989278 - 1.71348i) q^{4} +1.65158 q^{5} +(1.22031 - 2.11364i) q^{7} +0.582605 q^{8} +(0.120926 + 0.209450i) q^{10} +(-0.0152111 + 0.0263464i) q^{11} +(-0.0993860 - 0.172142i) q^{13} +0.357396 q^{14} +(-1.93590 - 3.35308i) q^{16} +(-0.847470 - 1.46786i) q^{17} +(2.97511 + 5.15305i) q^{19} +(1.63388 - 2.82995i) q^{20} -0.00445491 q^{22} +(-1.79419 - 3.10762i) q^{23} -2.27227 q^{25} +(0.0145537 - 0.0252078i) q^{26} +(-2.41446 - 4.18196i) q^{28} +(-2.17615 + 3.76920i) q^{29} +(-0.519043 + 0.899009i) q^{31} +(0.866091 - 1.50011i) q^{32} +(0.124100 - 0.214948i) q^{34} +(2.01545 - 3.49085i) q^{35} +(1.72055 + 2.98007i) q^{37} +(-0.435664 + 0.754593i) q^{38} +0.962220 q^{40} +(3.49665 - 6.05638i) q^{41} -1.37165 q^{43} +(0.0300960 + 0.0521278i) q^{44} +(0.262734 - 0.455069i) q^{46} +(2.74199 - 4.74927i) q^{47} +(0.521679 + 0.903574i) q^{49} +(-0.166372 - 0.288164i) q^{50} -0.393281 q^{52} +6.67481 q^{53} +(-0.0251224 + 0.0435133i) q^{55} +(0.710959 - 1.23142i) q^{56} -0.637333 q^{58} +7.66502 q^{59} +(1.19840 + 2.07569i) q^{61} -0.152013 q^{62} -7.48994 q^{64} +(-0.164144 - 0.284306i) q^{65} +(0.201842 + 8.18286i) q^{67} -3.35353 q^{68} +0.590269 q^{70} +(-5.29802 + 9.17644i) q^{71} +(-1.00288 - 1.73705i) q^{73} +(-0.251950 + 0.436391i) q^{74} +11.7729 q^{76} +(0.0371246 + 0.0643016i) q^{77} +(5.81596 - 10.0735i) q^{79} +(-3.19730 - 5.53788i) q^{80} +1.02407 q^{82} +(3.82603 + 6.62687i) q^{83} +(-1.39967 - 2.42429i) q^{85} +(-0.100429 - 0.173949i) q^{86} +(-0.00886206 + 0.0153495i) q^{88} -18.1923 q^{89} -0.485127 q^{91} -7.09980 q^{92} +0.803053 q^{94} +(4.91365 + 8.51068i) q^{95} +(-0.0738755 - 0.127956i) q^{97} +(-0.0763926 + 0.132316i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 6 q^{4} - 6 q^{5} - q^{7}+O(q^{10}) \) 10 * q - 6 * q^4 - 6 * q^5 - q^7	\( 10 q - 6 q^{4} - 6 q^{5} - q^{7} - 12 q^{10} - 6 q^{11} - q^{13} + 6 q^{14} - 24 q^{16} - 8 q^{17} - 5 q^{19} + 8 q^{20} + 22 q^{22} + 7 q^{23} - 8 q^{25} + 17 q^{26} + 3 q^{28} + 12 q^{29} - 12 q^{31} + 5 q^{32} + 5 q^{35} - 17 q^{37} - 30 q^{38} + 34 q^{40} - 13 q^{41} - 4 q^{43} - 43 q^{44} - 26 q^{46} + 25 q^{47} + 16 q^{49} + 25 q^{50} + 64 q^{52} + 12 q^{53} - 14 q^{55} + 11 q^{56} + 4 q^{58} + 12 q^{59} + 9 q^{61} - 46 q^{62} + 64 q^{64} + 14 q^{65} + 2 q^{67} + 98 q^{68} + 2 q^{70} - 29 q^{71} + 12 q^{73} - 15 q^{74} - 6 q^{76} - 4 q^{77} - q^{79} + 13 q^{80} - 2 q^{82} + 6 q^{83} + 9 q^{85} + 21 q^{86} + 18 q^{88} + 4 q^{89} - 40 q^{91} + 30 q^{94} + 14 q^{95} + 11 q^{97} - 12 q^{98}+O(q^{100}) \) 10 * q - 6 * q^4 - 6 * q^5 - q^7 - 12 * q^10 - 6 * q^11 - q^13 + 6 * q^14 - 24 * q^16 - 8 * q^17 - 5 * q^19 + 8 * q^20 + 22 * q^22 + 7 * q^23 - 8 * q^25 + 17 * q^26 + 3 * q^28 + 12 * q^29 - 12 * q^31 + 5 * q^32 + 5 * q^35 - 17 * q^37 - 30 * q^38 + 34 * q^40 - 13 * q^41 - 4 * q^43 - 43 * q^44 - 26 * q^46 + 25 * q^47 + 16 * q^49 + 25 * q^50 + 64 * q^52 + 12 * q^53 - 14 * q^55 + 11 * q^56 + 4 * q^58 + 12 * q^59 + 9 * q^61 - 46 * q^62 + 64 * q^64 + 14 * q^65 + 2 * q^67 + 98 * q^68 + 2 * q^70 - 29 * q^71 + 12 * q^73 - 15 * q^74 - 6 * q^76 - 4 * q^77 - q^79 + 13 * q^80 - 2 * q^82 + 6 * q^83 + 9 * q^85 + 21 * q^86 + 18 * q^88 + 4 * q^89 - 40 * q^91 + 30 * q^94 + 14 * q^95 + 11 * q^97 - 12 * q^98

Introduction

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