LMFDB - Embedded newform 605.2.g.c.81.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [605,2,Mod(81,605)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("605.81"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(605, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.g (of order $5$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,1,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			81.1
Root			$0.809017 - 0.587785i$ of defining polynomial
Character	$\chi$	$=$	605.81
Dual form			605.2.g.c.366.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.809017 + 0.587785i) q^{2} +(-0.309017 - 0.951057i) q^{4} +(-0.809017 + 0.587785i) q^{5} +(0.927051 - 2.85317i) q^{8} +(2.42705 + 1.76336i) q^{9} -1.00000 q^{10} +(1.61803 + 1.17557i) q^{13} +(0.809017 - 0.587785i) q^{16} +(4.85410 - 3.52671i) q^{17} +(0.927051 + 2.85317i) q^{18} +(1.23607 - 3.80423i) q^{19} +(0.809017 + 0.587785i) q^{20} +4.00000 q^{23} +(0.309017 - 0.951057i) q^{25} +(0.618034 + 1.90211i) q^{26} +(-1.85410 - 5.70634i) q^{29} +(6.47214 + 4.70228i) q^{31} -5.00000 q^{32} +6.00000 q^{34} +(0.927051 - 2.85317i) q^{36} +(-0.618034 - 1.90211i) q^{37} +(3.23607 - 2.35114i) q^{38} +(0.927051 + 2.85317i) q^{40} +(-0.618034 + 1.90211i) q^{41} -4.00000 q^{43} -3.00000 q^{45} +(3.23607 + 2.35114i) q^{46} +(-3.70820 + 11.4127i) q^{47} +(5.66312 - 4.11450i) q^{49} +(0.809017 - 0.587785i) q^{50} +(0.618034 - 1.90211i) q^{52} +(1.61803 + 1.17557i) q^{53} +(1.85410 - 5.70634i) q^{58} +(1.23607 + 3.80423i) q^{59} +(-8.09017 + 5.87785i) q^{61} +(2.47214 + 7.60845i) q^{62} +(-5.66312 - 4.11450i) q^{64} -2.00000 q^{65} -16.0000 q^{67} +(-4.85410 - 3.52671i) q^{68} +(-6.47214 + 4.70228i) q^{71} +(7.28115 - 5.29007i) q^{72} +(-4.32624 - 13.3148i) q^{73} +(0.618034 - 1.90211i) q^{74} -4.00000 q^{76} +(6.47214 + 4.70228i) q^{79} +(-0.309017 + 0.951057i) q^{80} +(2.78115 + 8.55951i) q^{81} +(-1.61803 + 1.17557i) q^{82} +(-3.23607 + 2.35114i) q^{83} +(-1.85410 + 5.70634i) q^{85} +(-3.23607 - 2.35114i) q^{86} +10.0000 q^{89} +(-2.42705 - 1.76336i) q^{90} +(-1.23607 - 3.80423i) q^{92} +(-9.70820 + 7.05342i) q^{94} +(1.23607 + 3.80423i) q^{95} +(-8.09017 - 5.87785i) q^{97} +7.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} + q^{4} - q^{5} - 3 q^{8} + 3 q^{9} - 4 q^{10} + 2 q^{13} + q^{16} + 6 q^{17} - 3 q^{18} - 4 q^{19} + q^{20} + 16 q^{23} - q^{25} - 2 q^{26} + 6 q^{29} + 8 q^{31} - 20 q^{32} + 24 q^{34}+ \cdots + 28 q^{98}+O(q^{100}) $ 4 * q + q^2 + q^4 - q^5 - 3 * q^8 + 3 * q^9 - 4 * q^10 + 2 * q^13 + q^16 + 6 * q^17 - 3 * q^18 - 4 * q^19 + q^20 + 16 * q^23 - q^25 - 2 * q^26 + 6 * q^29 + 8 * q^31 - 20 * q^32 + 24 * q^34 - 3 * q^36 + 2 * q^37 + 4 * q^38 - 3 * q^40 + 2 * q^41 - 16 * q^43 - 12 * q^45 + 4 * q^46 + 12 * q^47 + 7 * q^49 + q^50 - 2 * q^52 + 2 * q^53 - 6 * q^58 - 4 * q^59 - 10 * q^61 - 8 * q^62 - 7 * q^64 - 8 * q^65 - 64 * q^67 - 6 * q^68 - 8 * q^71 + 9 * q^72 + 14 * q^73 - 2 * q^74 - 16 * q^76 + 8 * q^79 + q^80 - 9 * q^81 - 2 * q^82 - 4 * q^83 + 6 * q^85 - 4 * q^86 + 40 * q^89 - 3 * q^90 + 4 * q^92 - 12 * q^94 - 4 * q^95 - 10 * q^97 + 28 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$

Coefficient data

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

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

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

$2$	0.809017	+	0.587785i	0.572061	+	0.415627i	0.835853	−	0.548953i	$-0.184973\pi$
$2$	0.809017	+	0.587785i	0.572061	+	0.415627i	−0.263792	+	0.964580i	$0.584973\pi$
$3$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$3$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$4$	−0.309017	−	0.951057i	−0.154508	−	0.475528i
$5$	−0.809017	+	0.587785i	−0.361803	+	0.262866i
$5$	−0.809017	+	0.587785i	−0.361803	+	0.262866i
$6$		0			0
$7$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$7$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$8$	0.927051	−	2.85317i	0.327762	−	1.00875i
$9$	2.42705	+	1.76336i	0.809017	+	0.587785i
$10$	−1.00000			−0.316228
$11$		0			0
$11$		0			0
$12$		0			0
$13$	1.61803	+	1.17557i	0.448762	+	0.326045i	0.789107	−	0.614256i	$-0.210544\pi$
$13$	1.61803	+	1.17557i	0.448762	+	0.326045i	−0.340345	+	0.940301i	$0.610544\pi$
$14$		0			0
$15$		0			0
$16$	0.809017	−	0.587785i	0.202254	−	0.146946i
$17$	4.85410	−	3.52671i	1.17729	−	0.855353i	0.185429	−	0.982658i	$-0.440633\pi$
$17$	4.85410	−	3.52671i	1.17729	−	0.855353i	0.991864	+	0.127304i	$0.0406325\pi$
$18$	0.927051	+	2.85317i	0.218508	+	0.672499i
$19$	1.23607	−	3.80423i	0.283573	−	0.872749i	−0.703249	−	0.710943i	$-0.748268\pi$
$19$	1.23607	−	3.80423i	0.283573	−	0.872749i	0.986823	−	0.161806i	$-0.0517318\pi$
$20$	0.809017	+	0.587785i	0.180902	+	0.131433i
$21$		0			0
$22$		0			0
$23$	4.00000			0.834058			0.417029	−	0.908893i	$-0.363071\pi$
$23$	4.00000			0.834058			0.417029	+	0.908893i	$0.363071\pi$
$24$		0			0
$25$	0.309017	−	0.951057i	0.0618034	−	0.190211i
$26$	0.618034	+	1.90211i	0.121206	+	0.373035i
$27$		0			0
$28$		0			0
$29$	−1.85410	−	5.70634i	−0.344298	−	1.05964i	−0.961958	−	0.273196i	$-0.911919\pi$
$29$	−1.85410	−	5.70634i	−0.344298	−	1.05964i	0.617660	−	0.786445i	$-0.288081\pi$
$30$		0			0
$31$	6.47214	+	4.70228i	1.16243	+	0.844555i	0.990083	−	0.140482i	$-0.0448651\pi$
$31$	6.47214	+	4.70228i	1.16243	+	0.844555i	0.172347	+	0.985036i	$0.444865\pi$
$32$	−5.00000			−0.883883
$33$		0			0
$34$	6.00000			1.02899
$35$		0			0
$36$	0.927051	−	2.85317i	0.154508	−	0.475528i
$37$	−0.618034	−	1.90211i	−0.101604	−	0.312705i	0.887314	−	0.461165i	$-0.152568\pi$
$37$	−0.618034	−	1.90211i	−0.101604	−	0.312705i	−0.988918	+	0.148460i	$0.952568\pi$
$38$	3.23607	−	2.35114i	0.524960	−	0.381405i
$39$		0			0
$40$	0.927051	+	2.85317i	0.146580	+	0.451126i
$41$	−0.618034	+	1.90211i	−0.0965207	+	0.297060i	−0.987647	−	0.156695i	$-0.949916\pi$
$41$	−0.618034	+	1.90211i	−0.0965207	+	0.297060i	0.891126	+	0.453755i	$0.149916\pi$
$42$		0			0
$43$	−4.00000			−0.609994			−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−4.00000			−0.609994			−0.304997	+	0.952353i	$0.598656\pi$
$44$		0			0
$45$	−3.00000			−0.447214
$46$	3.23607	+	2.35114i	0.477132	+	0.346657i
$47$	−3.70820	+	11.4127i	−0.540897	+	1.66471i	0.189653	+	0.981851i	$0.439264\pi$
$47$	−3.70820	+	11.4127i	−0.540897	+	1.66471i	−0.730550	+	0.682859i	$0.760736\pi$
$48$		0			0
$49$	5.66312	−	4.11450i	0.809017	−	0.587785i
$50$	0.809017	−	0.587785i	0.114412	−	0.0831254i
$51$		0			0
$52$	0.618034	−	1.90211i	0.0857059	−	0.263776i
$53$	1.61803	+	1.17557i	0.222254	+	0.161477i	0.693341	−	0.720610i	$-0.256138\pi$
$53$	1.61803	+	1.17557i	0.222254	+	0.161477i	−0.471087	+	0.882087i	$0.656138\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		0			0
$58$	1.85410	−	5.70634i	0.243456	−	0.749279i
$59$	1.23607	+	3.80423i	0.160922	+	0.495268i	0.998713	−	0.0507240i	$-0.0161529\pi$
$59$	1.23607	+	3.80423i	0.160922	+	0.495268i	−0.837790	+	0.545992i	$0.816153\pi$
$60$		0			0
$61$	−8.09017	+	5.87785i	−1.03584	+	0.752582i	−0.969469	−	0.245213i	$-0.921142\pi$
$61$	−8.09017	+	5.87785i	−1.03584	+	0.752582i	−0.0663709	+	0.997795i	$0.521142\pi$
$62$	2.47214	+	7.60845i	0.313962	+	0.966274i
$63$		0			0
$64$	−5.66312	−	4.11450i	−0.707890	−	0.514312i
$65$	−2.00000			−0.248069
$66$		0			0
$67$	−16.0000			−1.95471			−0.977356	−	0.211604i	$-0.932131\pi$
$67$	−16.0000			−1.95471			−0.977356	+	0.211604i	$0.932131\pi$
$68$	−4.85410	−	3.52671i	−0.588646	−	0.427677i
$69$		0			0
$70$		0			0
$71$	−6.47214	+	4.70228i	−0.768101	+	0.558058i	−0.901384	−	0.433020i	$-0.857448\pi$
$71$	−6.47214	+	4.70228i	−0.768101	+	0.558058i	0.133283	+	0.991078i	$0.457448\pi$
$72$	7.28115	−	5.29007i	0.858092	−	0.623440i
$73$	−4.32624	−	13.3148i	−0.506348	−	1.55838i	−0.798493	−	0.602004i	$-0.794369\pi$
$73$	−4.32624	−	13.3148i	−0.506348	−	1.55838i	0.292145	−	0.956374i	$-0.405631\pi$
$74$	0.618034	−	1.90211i	0.0718450	−	0.221116i
$75$		0			0
$76$	−4.00000			−0.458831
$77$		0			0
$78$		0			0
$79$	6.47214	+	4.70228i	0.728172	+	0.529048i	0.888985	−	0.457937i	$-0.151411\pi$
$79$	6.47214	+	4.70228i	0.728172	+	0.529048i	−0.160813	+	0.986985i	$0.551411\pi$
$80$	−0.309017	+	0.951057i	−0.0345492	+	0.106331i
$81$	2.78115	+	8.55951i	0.309017	+	0.951057i
$82$	−1.61803	+	1.17557i	−0.178682	+	0.129820i
$83$	−3.23607	+	2.35114i	−0.355205	+	0.258071i	−0.751049	−	0.660246i	$-0.770452\pi$
$83$	−3.23607	+	2.35114i	−0.355205	+	0.258071i	0.395845	+	0.918318i	$0.370452\pi$
$84$		0			0
$85$	−1.85410	+	5.70634i	−0.201106	+	0.618939i
$86$	−3.23607	−	2.35114i	−0.348954	−	0.253530i
$87$		0			0
$88$		0			0
$89$	10.0000			1.06000			0.529999	−	0.847998i	$-0.322192\pi$
$89$	10.0000			1.06000			0.529999	+	0.847998i	$0.322192\pi$
$90$	−2.42705	−	1.76336i	−0.255834	−	0.185874i
$91$		0			0
$92$	−1.23607	−	3.80423i	−0.128869	−	0.396618i
$93$		0			0
$94$	−9.70820	+	7.05342i	−1.00132	+	0.727505i
$95$	1.23607	+	3.80423i	0.126818	+	0.390305i
$96$		0			0
$97$	−8.09017	−	5.87785i	−0.821432	−	0.596806i	0.0956901	−	0.995411i	$-0.469494\pi$
$97$	−8.09017	−	5.87785i	−0.821432	−	0.596806i	−0.917122	+	0.398606i	$0.869494\pi$
$98$	7.00000			0.707107
$99$		0			0
$100$	−1.00000			−0.100000
$101$	−8.09017	−	5.87785i	−0.805002	−	0.584868i	0.107375	−	0.994219i	$-0.465755\pi$
$101$	−8.09017	−	5.87785i	−0.805002	−	0.584868i	−0.912377	+	0.409350i	$0.865755\pi$
$102$		0			0
$103$	−1.23607	−	3.80423i	−0.121793	−	0.374842i	0.871510	−	0.490378i	$-0.163141\pi$
$103$	−1.23607	−	3.80423i	−0.121793	−	0.374842i	−0.993303	+	0.115536i	$0.963141\pi$
$104$	4.85410	−	3.52671i	0.475984	−	0.345823i
$105$		0			0
$106$	0.618034	+	1.90211i	0.0600288	+	0.184750i
$107$	−3.70820	+	11.4127i	−0.358486	+	1.10331i	0.595475	+	0.803374i	$0.296964\pi$
$107$	−3.70820	+	11.4127i	−0.358486	+	1.10331i	−0.953961	+	0.299932i	$0.903036\pi$
$108$		0			0
$109$	18.0000			1.72409			0.862044	−	0.506834i	$-0.169184\pi$
$109$	18.0000			1.72409			0.862044	+	0.506834i	$0.169184\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−1.85410	+	5.70634i	−0.174419	+	0.536807i	−0.999606	−	0.0280521i	$-0.991070\pi$
$113$	−1.85410	+	5.70634i	−0.174419	+	0.536807i	0.825187	+	0.564859i	$0.191070\pi$
$114$		0			0
$115$	−3.23607	+	2.35114i	−0.301765	+	0.219245i
$116$	−4.85410	+	3.52671i	−0.450692	+	0.327447i
$117$	1.85410	+	5.70634i	0.171412	+	0.527551i
$118$	−1.23607	+	3.80423i	−0.113789	+	0.350207i
$119$		0			0
$120$		0			0
$121$		0			0
$122$	−10.0000			−0.905357
$123$		0			0
$124$	2.47214	−	7.60845i	0.222004	−	0.683259i
$125$	0.309017	+	0.951057i	0.0276393	+	0.0850651i
$126$		0			0
$127$	12.9443	−	9.40456i	1.14862	−	0.834520i	0.160322	−	0.987065i	$-0.448747\pi$
$127$	12.9443	−	9.40456i	1.14862	−	0.834520i	0.988297	+	0.152545i	$0.0487468\pi$
$128$	0.927051	+	2.85317i	0.0819405	+	0.252187i
$129$		0			0
$130$	−1.61803	−	1.17557i	−0.141911	−	0.103104i
$131$	12.0000			1.04844			0.524222	−	0.851581i	$-0.324356\pi$
$131$	12.0000			1.04844			0.524222	+	0.851581i	$0.324356\pi$
$132$		0			0
$133$		0			0
$134$	−12.9443	−	9.40456i	−1.11821	−	0.812431i
$135$		0			0
$136$	−5.56231	−	17.1190i	−0.476964	−	1.46794i
$137$	−14.5623	+	10.5801i	−1.24414	+	0.903922i	−0.997867	−	0.0652782i	$-0.979207\pi$
$137$	−14.5623	+	10.5801i	−1.24414	+	0.903922i	−0.246275	+	0.969200i	$0.579207\pi$
$138$		0			0
$139$	−3.70820	−	11.4127i	−0.314526	−	0.968011i	−0.975949	−	0.217998i	$-0.930047\pi$
$139$	−3.70820	−	11.4127i	−0.314526	−	0.968011i	0.661423	−	0.750013i	$-0.269953\pi$
$140$		0			0
$141$		0			0
$142$	−8.00000			−0.671345
$143$		0			0
$144$	3.00000			0.250000
$145$	4.85410	+	3.52671i	0.403111	+	0.292877i
$146$	4.32624	−	13.3148i	0.358042	−	1.10194i
$147$		0			0
$148$	−1.61803	+	1.17557i	−0.133002	+	0.0966313i
$149$	−8.09017	+	5.87785i	−0.662773	+	0.481532i	−0.867598	−	0.497266i	$-0.834337\pi$
$149$	−8.09017	+	5.87785i	−0.662773	+	0.481532i	0.204826	+	0.978798i	$0.434337\pi$
$150$		0			0
$151$	−2.47214	+	7.60845i	−0.201180	+	0.619167i	0.798669	+	0.601770i	$0.205538\pi$
$151$	−2.47214	+	7.60845i	−0.201180	+	0.619167i	−0.999849	+	0.0173966i	$0.994462\pi$
$152$	−9.70820	−	7.05342i	−0.787439	−	0.572108i
$153$	18.0000			1.45521
$154$		0			0
$155$	−8.00000			−0.642575
$156$		0			0
$157$	−0.618034	+	1.90211i	−0.0493245	+	0.151805i	−0.972685	−	0.232129i	$-0.925431\pi$
$157$	−0.618034	+	1.90211i	−0.0493245	+	0.151805i	0.923361	+	0.383934i	$0.125431\pi$
$158$	2.47214	+	7.60845i	0.196673	+	0.605296i
$159$		0			0
$160$	4.04508	−	2.93893i	0.319792	−	0.232343i
$161$		0			0
$162$	−2.78115	+	8.55951i	−0.218508	+	0.672499i
$163$	−12.9443	−	9.40456i	−1.01387	−	0.736622i	−0.0488556	−	0.998806i	$-0.515557\pi$
$163$	−12.9443	−	9.40456i	−1.01387	−	0.736622i	−0.965018	+	0.262184i	$0.915557\pi$
$164$	2.00000			0.156174
$165$		0			0
$166$	−4.00000			−0.310460
$167$	−6.47214	−	4.70228i	−0.500829	−	0.363874i	0.308505	−	0.951223i	$-0.400171\pi$
$167$	−6.47214	−	4.70228i	−0.500829	−	0.363874i	−0.809334	+	0.587349i	$0.800171\pi$
$168$		0			0
$169$	−2.78115	−	8.55951i	−0.213935	−	0.658424i
$170$	−4.85410	+	3.52671i	−0.372293	+	0.270486i
$171$	9.70820	−	7.05342i	0.742405	−	0.539389i
$172$	1.23607	+	3.80423i	0.0942493	+	0.290070i
$173$	1.85410	−	5.70634i	0.140965	−	0.433845i	−0.855505	−	0.517794i	$-0.826753\pi$
$173$	1.85410	−	5.70634i	0.140965	−	0.433845i	0.996470	+	0.0839492i	$0.0267533\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$	8.09017	+	5.87785i	0.606384	+	0.440564i
$179$	1.23607	−	3.80423i	0.0923881	−	0.284341i	−0.894176	−	0.447715i	$-0.852238\pi$
$179$	1.23607	−	3.80423i	0.0923881	−	0.284341i	0.986564	+	0.163374i	$0.0522378\pi$
$180$	0.927051	+	2.85317i	0.0690983	+	0.212663i
$181$	8.09017	−	5.87785i	0.601338	−	0.436897i	−0.245016	−	0.969519i	$-0.578793\pi$
$181$	8.09017	−	5.87785i	0.601338	−	0.436897i	0.846353	+	0.532622i	$0.178793\pi$
$182$		0			0
$183$		0			0
$184$	3.70820	−	11.4127i	0.273372	−	0.841354i
$185$	1.61803	+	1.17557i	0.118960	+	0.0864297i
$186$		0			0
$187$		0			0
$188$	12.0000			0.875190
$189$		0			0
$190$	−1.23607	+	3.80423i	−0.0896738	+	0.275988i
$191$	2.47214	+	7.60845i	0.178877	+	0.550528i	0.999789	−	0.0205267i	$-0.00653431\pi$
$191$	2.47214	+	7.60845i	0.178877	+	0.550528i	−0.820912	+	0.571055i	$0.806534\pi$
$192$		0			0
$193$	−21.0344	+	15.2824i	−1.51409	+	1.10005i	−0.549772	+	0.835315i	$0.685285\pi$
$193$	−21.0344	+	15.2824i	−1.51409	+	1.10005i	−0.964321	+	0.264737i	$0.914715\pi$
$194$	−3.09017	−	9.51057i	−0.221861	−	0.682819i
$195$		0			0
$196$	−5.66312	−	4.11450i	−0.404508	−	0.293893i
$197$	−2.00000			−0.142494			−0.0712470	−	0.997459i	$-0.522698\pi$
$197$	−2.00000			−0.142494			−0.0712470	+	0.997459i	$0.522698\pi$
$198$		0			0
$199$		0			0			−	1.00000i	$-0.5\pi$
$199$		0			0				1.00000i	$0.5\pi$
$200$	−2.42705	−	1.76336i	−0.171618	−	0.124688i
$201$		0			0
$202$	−3.09017	−	9.51057i	−0.217424	−	0.669161i
$203$		0			0
$204$		0			0
$205$	−0.618034	−	1.90211i	−0.0431654	−	0.132849i
$206$	1.23607	−	3.80423i	0.0861209	−	0.265053i
$207$	9.70820	+	7.05342i	0.674767	+	0.490247i
$208$	2.00000			0.138675
$209$		0			0
$210$		0			0
$211$	3.23607	+	2.35114i	0.222780	+	0.161859i	0.693577	−	0.720382i	$-0.256034\pi$
$211$	3.23607	+	2.35114i	0.222780	+	0.161859i	−0.470797	+	0.882242i	$0.656034\pi$
$212$	0.618034	−	1.90211i	0.0424467	−	0.130638i
$213$		0			0
$214$	−9.70820	+	7.05342i	−0.663639	+	0.482162i
$215$	3.23607	−	2.35114i	0.220698	−	0.160346i
$216$		0			0
$217$		0			0
$218$	14.5623	+	10.5801i	0.986284	+	0.716577i
$219$		0			0
$220$		0			0
$221$	12.0000			0.807207
$222$		0			0
$223$	−1.23607	+	3.80423i	−0.0827732	+	0.254750i	−0.983875	−	0.178858i	$-0.942760\pi$
$223$	−1.23607	+	3.80423i	−0.0827732	+	0.254750i	0.901102	+	0.433608i	$0.142760\pi$
$224$		0			0
$225$	2.42705	−	1.76336i	0.161803	−	0.117557i
$226$	−4.85410	+	3.52671i	−0.322890	+	0.234593i
$227$	6.18034	+	19.0211i	0.410204	+	1.26248i	0.916471	+	0.400100i	$0.131025\pi$
$227$	6.18034	+	19.0211i	0.410204	+	1.26248i	−0.506268	+	0.862376i	$0.668975\pi$
$228$		0			0
$229$	8.09017	+	5.87785i	0.534613	+	0.388419i	0.822081	−	0.569371i	$-0.192813\pi$
$229$	8.09017	+	5.87785i	0.534613	+	0.388419i	−0.287467	+	0.957790i	$0.592813\pi$
$230$	−4.00000			−0.263752
$231$		0			0
$232$	−18.0000			−1.18176
$233$	4.85410	+	3.52671i	0.318003	+	0.231043i	0.735323	−	0.677717i	$-0.237031\pi$
$233$	4.85410	+	3.52671i	0.318003	+	0.231043i	−0.417320	+	0.908760i	$0.637031\pi$
$234$	−1.85410	+	5.70634i	−0.121206	+	0.373035i
$235$	−3.70820	−	11.4127i	−0.241897	−	0.744481i
$236$	3.23607	−	2.35114i	0.210650	−	0.153046i
$237$		0			0
$238$		0			0
$239$	−2.47214	+	7.60845i	−0.159909	+	0.492150i	−0.998625	−	0.0524192i	$-0.983307\pi$
$239$	−2.47214	+	7.60845i	−0.159909	+	0.492150i	0.838716	+	0.544569i	$0.183307\pi$
$240$		0			0
$241$	−10.0000			−0.644157			−0.322078	−	0.946713i	$-0.604381\pi$
$241$	−10.0000			−0.644157			−0.322078	+	0.946713i	$0.604381\pi$
$242$		0			0
$243$		0			0
$244$	8.09017	+	5.87785i	0.517920	+	0.376291i
$245$	−2.16312	+	6.65740i	−0.138197	+	0.425325i
$246$		0			0
$247$	6.47214	−	4.70228i	0.411812	−	0.299199i
$248$	19.4164	−	14.1068i	1.23294	−	0.895786i
$249$		0			0
$250$	−0.309017	+	0.951057i	−0.0195440	+	0.0601501i
$251$	−9.70820	−	7.05342i	−0.612776	−	0.445208i	0.237614	−	0.971360i	$-0.423635\pi$
$251$	−9.70820	−	7.05342i	−0.612776	−	0.445208i	−0.850391	+	0.526151i	$0.823635\pi$
$252$		0			0
$253$		0			0
$254$	16.0000			1.00393
$255$		0			0
$256$	−5.25329	+	16.1680i	−0.328331	+	1.01050i
$257$	5.56231	+	17.1190i	0.346967	+	1.06785i	0.960522	+	0.278203i	$0.0897388\pi$
$257$	5.56231	+	17.1190i	0.346967	+	1.06785i	−0.613555	+	0.789652i	$0.710261\pi$
$258$		0			0
$259$		0			0
$260$	0.618034	+	1.90211i	0.0383288	+	0.117964i
$261$	5.56231	−	17.1190i	0.344298	−	1.05964i
$262$	9.70820	+	7.05342i	0.599775	+	0.435762i
$263$	−24.0000			−1.47990			−0.739952	−	0.672660i	$-0.765152\pi$
$263$	−24.0000			−1.47990			−0.739952	+	0.672660i	$0.765152\pi$
$264$		0			0
$265$	−2.00000			−0.122859
$266$		0			0
$267$		0			0
$268$	4.94427	+	15.2169i	0.302019	+	0.929520i
$269$	14.5623	−	10.5801i	0.887879	−	0.645082i	−0.0474448	−	0.998874i	$-0.515108\pi$
$269$	14.5623	−	10.5801i	0.887879	−	0.645082i	0.935324	+	0.353792i	$0.115108\pi$
$270$		0			0
$271$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$271$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$272$	1.85410	−	5.70634i	0.112421	−	0.345998i
$273$		0			0
$274$	−18.0000			−1.08742
$275$		0			0
$276$		0			0
$277$	8.09017	+	5.87785i	0.486091	+	0.353166i	0.803679	−	0.595063i	$-0.202873\pi$
$277$	8.09017	+	5.87785i	0.486091	+	0.353166i	−0.317588	+	0.948229i	$0.602873\pi$
$278$	3.70820	−	11.4127i	0.222403	−	0.684487i
$279$	7.41641	+	22.8254i	0.444009	+	1.36652i
$280$		0			0
$281$	14.5623	−	10.5801i	0.868714	−	0.631158i	−0.0615273	−	0.998105i	$-0.519597\pi$
$281$	14.5623	−	10.5801i	0.868714	−	0.631158i	0.930242	+	0.366947i	$0.119597\pi$
$282$		0			0
$283$	−1.23607	+	3.80423i	−0.0734766	+	0.226138i	−0.981050	−	0.193756i	$-0.937933\pi$
$283$	−1.23607	+	3.80423i	−0.0734766	+	0.226138i	0.907573	+	0.419894i	$0.137933\pi$
$284$	6.47214	+	4.70228i	0.384051	+	0.279029i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−12.1353	−	8.81678i	−0.715077	−	0.519534i
$289$	5.87132	−	18.0701i	0.345372	−	1.06295i
$290$	1.85410	+	5.70634i	0.108877	+	0.335088i
$291$		0			0
$292$	−11.3262	+	8.22899i	−0.662818	+	0.481565i
$293$	−3.09017	−	9.51057i	−0.180530	−	0.555613i	0.819313	−	0.573346i	$-0.194355\pi$
$293$	−3.09017	−	9.51057i	−0.180530	−	0.555613i	−0.999843	+	0.0177332i	$0.994355\pi$
$294$		0			0
$295$	−3.23607	−	2.35114i	−0.188411	−	0.136889i
$296$	−6.00000			−0.348743
$297$		0			0
$298$	−10.0000			−0.579284
$299$	6.47214	+	4.70228i	0.374293	+	0.271940i
$300$		0			0
$301$		0			0
$302$	−6.47214	+	4.70228i	−0.372430	+	0.270586i
$303$		0			0
$304$	−1.23607	−	3.80423i	−0.0708934	−	0.218187i
$305$	3.09017	−	9.51057i	0.176943	−	0.544573i
$306$	14.5623	+	10.5801i	0.832472	+	0.604826i
$307$	−20.0000			−1.14146			−0.570730	−	0.821138i	$-0.693340\pi$
$307$	−20.0000			−1.14146			−0.570730	+	0.821138i	$0.693340\pi$
$308$		0			0
$309$		0			0
$310$	−6.47214	−	4.70228i	−0.367593	−	0.267072i
$311$	−7.41641	+	22.8254i	−0.420546	+	1.29431i	0.486649	+	0.873597i	$0.338219\pi$
$311$	−7.41641	+	22.8254i	−0.420546	+	1.29431i	−0.907195	+	0.420710i	$0.861781\pi$
$312$		0			0
$313$	17.7984	−	12.9313i	1.00602	−	0.730919i	0.0426523	−	0.999090i	$-0.486419\pi$
$313$	17.7984	−	12.9313i	1.00602	−	0.730919i	0.963371	+	0.268171i	$0.0864192\pi$
$314$	−1.61803	+	1.17557i	−0.0913109	+	0.0663413i
$315$		0			0
$316$	2.47214	−	7.60845i	0.139069	−	0.428009i
$317$	14.5623	+	10.5801i	0.817901	+	0.594240i	0.916110	−	0.400926i	$-0.131312\pi$
$317$	14.5623	+	10.5801i	0.817901	+	0.594240i	−0.0982098	+	0.995166i	$0.531312\pi$
$318$		0			0
$319$		0			0
$320$	7.00000			0.391312
$321$		0			0
$322$		0			0
$323$	−7.41641	−	22.8254i	−0.412660	−	1.27004i
$324$	7.28115	−	5.29007i	0.404508	−	0.293893i
$325$	1.61803	−	1.17557i	0.0897524	−	0.0652089i
$326$	−4.94427	−	15.2169i	−0.273838	−	0.842786i
$327$		0			0
$328$	4.85410	+	3.52671i	0.268023	+	0.194730i
$329$		0			0
$330$		0			0
$331$	4.00000			0.219860			0.109930	−	0.993939i	$-0.464937\pi$
$331$	4.00000			0.219860			0.109930	+	0.993939i	$0.464937\pi$
$332$	3.23607	+	2.35114i	0.177602	+	0.129036i
$333$	1.85410	−	5.70634i	0.101604	−	0.312705i
$334$	−2.47214	−	7.60845i	−0.135269	−	0.416316i
$335$	12.9443	−	9.40456i	0.707221	−	0.513826i
$336$		0			0
$337$	−1.85410	−	5.70634i	−0.100999	−	0.310844i	0.887771	−	0.460285i	$-0.152253\pi$
$337$	−1.85410	−	5.70634i	−0.100999	−	0.310844i	−0.988771	+	0.149441i	$0.952253\pi$
$338$	2.78115	−	8.55951i	0.151275	−	0.465576i
$339$		0			0
$340$	6.00000			0.325396
$341$		0			0
$342$	12.0000			0.648886
$343$		0			0
$344$	−3.70820	+	11.4127i	−0.199933	+	0.615330i
$345$		0			0
$346$	4.85410	−	3.52671i	0.260958	−	0.189597i
$347$	−3.23607	+	2.35114i	−0.173721	+	0.126216i	−0.671248	−	0.741233i	$-0.734242\pi$
$347$	−3.23607	+	2.35114i	−0.173721	+	0.126216i	0.497527	+	0.867448i	$0.334242\pi$
$348$		0			0
$349$	3.09017	−	9.51057i	0.165413	−	0.509089i	−0.833653	−	0.552288i	$-0.813755\pi$
$349$	3.09017	−	9.51057i	0.165413	−	0.509089i	0.999066	+	0.0431990i	$0.0137549\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	18.0000			0.958043			0.479022	−	0.877803i	$-0.340992\pi$
$353$	18.0000			0.958043			0.479022	+	0.877803i	$0.340992\pi$
$354$		0			0
$355$	2.47214	−	7.60845i	0.131207	−	0.403815i
$356$	−3.09017	−	9.51057i	−0.163779	−	0.504059i
$357$		0			0
$358$	3.23607	−	2.35114i	0.171032	−	0.124262i
$359$	9.88854	+	30.4338i	0.521897	+	1.60623i	0.770371	+	0.637596i	$0.220071\pi$
$359$	9.88854	+	30.4338i	0.521897	+	1.60623i	−0.248473	+	0.968639i	$0.579929\pi$
$360$	−2.78115	+	8.55951i	−0.146580	+	0.451126i
$361$	2.42705	+	1.76336i	0.127740	+	0.0928082i
$362$	10.0000			0.525588
$363$		0			0
$364$		0			0
$365$	11.3262	+	8.22899i	0.592842	+	0.430725i
$366$		0			0
$367$	1.23607	+	3.80423i	0.0645222	+	0.198579i	0.978121	−	0.208039i	$-0.0667081\pi$
$367$	1.23607	+	3.80423i	0.0645222	+	0.198579i	−0.913598	+	0.406618i	$0.866708\pi$
$368$	3.23607	−	2.35114i	0.168692	−	0.122562i
$369$	−4.85410	+	3.52671i	−0.252694	+	0.183593i
$370$	0.618034	+	1.90211i	0.0321301	+	0.0988861i
$371$		0			0
$372$		0			0
$373$	−18.0000			−0.932005			−0.466002	−	0.884783i	$-0.654306\pi$
$373$	−18.0000			−0.932005			−0.466002	+	0.884783i	$0.654306\pi$
$374$		0			0
$375$		0			0
$376$	29.1246	+	21.1603i	1.50199	+	1.09126i
$377$	3.70820	−	11.4127i	0.190982	−	0.587783i
$378$		0			0
$379$	−16.1803	+	11.7557i	−0.831128	+	0.603850i	−0.919878	−	0.392204i	$-0.871713\pi$
$379$	−16.1803	+	11.7557i	−0.831128	+	0.603850i	0.0887501	+	0.996054i	$0.471713\pi$
$380$	3.23607	−	2.35114i	0.166007	−	0.120611i
$381$		0			0
$382$	−2.47214	+	7.60845i	−0.126485	+	0.389282i
$383$	9.70820	+	7.05342i	0.496066	+	0.360413i	0.807512	−	0.589851i	$-0.200813\pi$
$383$	9.70820	+	7.05342i	0.496066	+	0.360413i	−0.311446	+	0.950264i	$0.600813\pi$
$384$		0			0
$385$		0			0
$386$	−26.0000			−1.32337
$387$	−9.70820	−	7.05342i	−0.493496	−	0.358546i
$388$	−3.09017	+	9.51057i	−0.156880	+	0.482826i
$389$	1.85410	+	5.70634i	0.0940067	+	0.289323i	0.986994	−	0.160760i	$-0.0513945\pi$
$389$	1.85410	+	5.70634i	0.0940067	+	0.289323i	−0.892987	+	0.450083i	$0.851394\pi$
$390$		0			0
$391$	19.4164	−	14.1068i	0.981930	−	0.713414i
$392$	−6.48936	−	19.9722i	−0.327762	−	1.00875i
$393$		0			0
$394$	−1.61803	−	1.17557i	−0.0815154	−	0.0592244i
$395$	−8.00000			−0.402524
$396$		0			0
$397$	30.0000			1.50566			0.752828	−	0.658217i	$-0.228689\pi$
$397$	30.0000			1.50566			0.752828	+	0.658217i	$0.228689\pi$
$398$		0			0
$399$		0			0
$400$	−0.309017	−	0.951057i	−0.0154508	−	0.0475528i
$401$	−1.61803	+	1.17557i	−0.0808008	+	0.0587052i	−0.627452	−	0.778655i	$-0.715902\pi$
$401$	−1.61803	+	1.17557i	−0.0808008	+	0.0587052i	0.546652	+	0.837360i	$0.315902\pi$
$402$		0			0
$403$	4.94427	+	15.2169i	0.246292	+	0.758008i
$404$	−3.09017	+	9.51057i	−0.153742	+	0.473168i
$405$	−7.28115	−	5.29007i	−0.361803	−	0.262866i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	−4.85410	−	3.52671i	−0.240020	−	0.174385i	0.461272	−	0.887259i	$-0.347393\pi$
$409$	−4.85410	−	3.52671i	−0.240020	−	0.174385i	−0.701292	+	0.712874i	$0.747393\pi$
$410$	0.618034	−	1.90211i	0.0305225	−	0.0939387i
$411$		0			0
$412$	−3.23607	+	2.35114i	−0.159430	+	0.115832i
$413$		0			0
$414$	3.70820	+	11.4127i	0.182248	+	0.560903i
$415$	1.23607	−	3.80423i	0.0606762	−	0.186742i
$416$	−8.09017	−	5.87785i	−0.396653	−	0.288185i
$417$		0			0
$418$		0			0
$419$	−28.0000			−1.36789			−0.683945	−	0.729534i	$-0.739737\pi$
$419$	−28.0000			−1.36789			−0.683945	+	0.729534i	$0.739737\pi$
$420$		0			0
$421$	1.85410	−	5.70634i	0.0903634	−	0.278110i	−0.895654	−	0.444751i	$-0.853292\pi$
$421$	1.85410	−	5.70634i	0.0903634	−	0.278110i	0.986018	+	0.166641i	$0.0532921\pi$
$422$	1.23607	+	3.80423i	0.0601708	+	0.185187i
$423$	−29.1246	+	21.1603i	−1.41609	+	1.02885i
$424$	4.85410	−	3.52671i	0.235736	−	0.171272i
$425$	−1.85410	−	5.70634i	−0.0899372	−	0.276798i
$426$		0			0
$427$		0			0
$428$	12.0000			0.580042
$429$		0			0
$430$	4.00000			0.192897
$431$	−19.4164	−	14.1068i	−0.935255	−	0.679503i	0.0120185	−	0.999928i	$-0.496174\pi$
$431$	−19.4164	−	14.1068i	−0.935255	−	0.679503i	−0.947274	+	0.320425i	$0.896174\pi$
$432$		0			0
$433$	−6.79837	−	20.9232i	−0.326709	−	1.00551i	−0.970663	−	0.240443i	$-0.922707\pi$
$433$	−6.79837	−	20.9232i	−0.326709	−	1.00551i	0.643954	−	0.765064i	$-0.277293\pi$
$434$		0			0
$435$		0			0
$436$	−5.56231	−	17.1190i	−0.266386	−	0.819852i
$437$	4.94427	−	15.2169i	0.236517	−	0.727923i
$438$		0			0
$439$	8.00000			0.381819			0.190910	−	0.981608i	$-0.438856\pi$
$439$	8.00000			0.381819			0.190910	+	0.981608i	$0.438856\pi$
$440$		0			0
$441$	21.0000			1.00000
$442$	9.70820	+	7.05342i	0.461772	+	0.335497i
$443$	2.47214	−	7.60845i	0.117455	−	0.361488i	−0.874996	−	0.484129i	$-0.839136\pi$
$443$	2.47214	−	7.60845i	0.117455	−	0.361488i	0.992451	+	0.122641i	$0.0391364\pi$
$444$		0			0
$445$	−8.09017	+	5.87785i	−0.383511	+	0.278637i
$446$	−3.23607	+	2.35114i	−0.153232	+	0.111330i
$447$		0			0
$448$		0			0
$449$	−1.61803	−	1.17557i	−0.0763597	−	0.0554786i	0.548950	−	0.835855i	$-0.315028\pi$
$449$	−1.61803	−	1.17557i	−0.0763597	−	0.0554786i	−0.625310	+	0.780376i	$0.715028\pi$
$450$	3.00000			0.141421
$451$		0			0
$452$	6.00000			0.282216
$453$		0			0
$454$	−6.18034	+	19.0211i	−0.290058	+	0.892706i
$455$		0			0
$456$		0			0
$457$	−21.0344	+	15.2824i	−0.983950	+	0.714881i	−0.958588	−	0.284797i	$-0.908074\pi$
$457$	−21.0344	+	15.2824i	−0.983950	+	0.714881i	−0.0253618	+	0.999678i	$0.508074\pi$
$458$	3.09017	+	9.51057i	0.144394	+	0.444400i
$459$		0			0
$460$	3.23607	+	2.35114i	0.150882	+	0.109623i
$461$	34.0000			1.58354			0.791769	−	0.610821i	$-0.209160\pi$
$461$	34.0000			1.58354			0.791769	+	0.610821i	$0.209160\pi$
$462$		0			0
$463$	−36.0000			−1.67306			−0.836531	−	0.547920i	$-0.815420\pi$
$463$	−36.0000			−1.67306			−0.836531	+	0.547920i	$0.815420\pi$
$464$	−4.85410	−	3.52671i	−0.225346	−	0.163723i
$465$		0			0
$466$	1.85410	+	5.70634i	0.0858896	+	0.264341i
$467$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$467$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$468$	4.85410	−	3.52671i	0.224381	−	0.163022i
$469$		0			0
$470$	3.70820	−	11.4127i	0.171047	−	0.526428i
$471$		0			0
$472$	12.0000			0.552345
$473$		0			0
$474$		0			0
$475$	−3.23607	−	2.35114i	−0.148481	−	0.107878i
$476$		0			0
$477$	1.85410	+	5.70634i	0.0848935	+	0.261275i
$478$	−6.47214	+	4.70228i	−0.296029	+	0.215077i
$479$	19.4164	−	14.1068i	0.887158	−	0.644558i	−0.0479772	−	0.998848i	$-0.515277\pi$
$479$	19.4164	−	14.1068i	0.887158	−	0.644558i	0.935136	+	0.354290i	$0.115277\pi$
$480$		0			0
$481$	1.23607	−	3.80423i	0.0563598	−	0.173458i
$482$	−8.09017	−	5.87785i	−0.368497	−	0.267729i
$483$		0			0
$484$		0			0
$485$	10.0000			0.454077
$486$		0			0
$487$	8.65248	−	26.6296i	0.392081	−	1.20670i	−0.539130	−	0.842222i	$-0.681247\pi$
$487$	8.65248	−	26.6296i	0.392081	−	1.20670i	0.931212	−	0.364479i	$-0.118753\pi$
$488$	9.27051	+	28.5317i	0.419656	+	1.29157i
$489$		0			0
$490$	−5.66312	+	4.11450i	−0.255834	+	0.185874i
$491$	8.65248	+	26.6296i	0.390481	+	1.20178i	0.932426	+	0.361362i	$0.117688\pi$
$491$	8.65248	+	26.6296i	0.390481	+	1.20178i	−0.541945	+	0.840414i	$0.682312\pi$
$492$		0			0
$493$	−29.1246	−	21.1603i	−1.31171	−	0.953011i
$494$	8.00000			0.359937
$495$		0			0
$496$	8.00000			0.359211
$497$		0			0
$498$		0			0
$499$	−11.1246	−	34.2380i	−0.498006	−	1.53270i	−0.812219	−	0.583352i	$-0.801741\pi$
$499$	−11.1246	−	34.2380i	−0.498006	−	1.53270i	0.314213	−	0.949352i	$-0.398259\pi$
$500$	0.809017	−	0.587785i	0.0361803	−	0.0262866i
$501$		0			0
$502$	−3.70820	−	11.4127i	−0.165505	−	0.509373i
$503$	4.94427	−	15.2169i	0.220454	−	0.678488i	−0.778267	−	0.627933i	$-0.783901\pi$
$503$	4.94427	−	15.2169i	0.220454	−	0.678488i	0.998721	−	0.0505549i	$-0.0160990\pi$
$504$		0			0
$505$	10.0000			0.444994
$506$		0			0
$507$		0			0
$508$	−12.9443	−	9.40456i	−0.574309	−	0.417260i
$509$	4.32624	−	13.3148i	0.191757	−	0.590168i	−0.808242	−	0.588850i	$-0.799581\pi$
$509$	4.32624	−	13.3148i	0.191757	−	0.590168i	0.999999	−	0.00131729i	$-0.000419307\pi$
$510$		0			0
$511$		0			0
$512$	−8.89919	+	6.46564i	−0.393292	+	0.285744i
$513$		0			0
$514$	−5.56231	+	17.1190i	−0.245343	+	0.755087i
$515$	3.23607	+	2.35114i	0.142598	+	0.103604i
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$	−1.85410	+	5.70634i	−0.0813077	+	0.250240i
$521$	−1.85410	−	5.70634i	−0.0812297	−	0.249999i	0.902191	−	0.431336i	$-0.141958\pi$
$521$	−1.85410	−	5.70634i	−0.0812297	−	0.249999i	−0.983421	+	0.181337i	$0.941958\pi$
$522$	14.5623	−	10.5801i	0.637375	−	0.463080i
$523$	−16.1803	+	11.7557i	−0.707517	+	0.514041i	−0.882372	−	0.470553i	$-0.844054\pi$
$523$	−16.1803	+	11.7557i	−0.707517	+	0.514041i	0.174855	+	0.984594i	$0.444054\pi$
$524$	−3.70820	−	11.4127i	−0.161994	−	0.498565i
$525$		0			0
$526$	−19.4164	−	14.1068i	−0.846596	−	0.615088i
$527$	48.0000			2.09091
$528$		0			0
$529$	−7.00000			−0.304348
$530$	−1.61803	−	1.17557i	−0.0702829	−	0.0510635i
$531$	−3.70820	+	11.4127i	−0.160922	+	0.495268i
$532$		0			0
$533$	−3.23607	+	2.35114i	−0.140170	+	0.101839i
$534$		0			0
$535$	−3.70820	−	11.4127i	−0.160320	−	0.493413i
$536$	−14.8328	+	45.6507i	−0.640680	+	1.97181i
$537$		0			0
$538$	18.0000			0.776035
$539$		0			0
$540$		0			0
$541$	−27.5066	−	19.9847i	−1.18260	−	0.859209i	−0.190138	−	0.981757i	$-0.560893\pi$
$541$	−27.5066	−	19.9847i	−1.18260	−	0.859209i	−0.992463	+	0.122548i	$0.960893\pi$
$542$		0			0
$543$		0			0
$544$	−24.2705	+	17.6336i	−1.04059	+	0.756033i
$545$	−14.5623	+	10.5801i	−0.623781	+	0.453203i
$546$		0			0
$547$	−3.70820	+	11.4127i	−0.158551	+	0.487971i	−0.998503	−	0.0546898i	$-0.982583\pi$
$547$	−3.70820	+	11.4127i	−0.158551	+	0.487971i	0.839952	+	0.542661i	$0.182583\pi$
$548$	14.5623	+	10.5801i	0.622071	+	0.451961i
$549$	−30.0000			−1.28037
$550$		0			0
$551$	−24.0000			−1.02243
$552$		0			0
$553$		0			0
$554$	3.09017	+	9.51057i	0.131289	+	0.404065i
$555$		0			0
$556$	−9.70820	+	7.05342i	−0.411720	+	0.299132i
$557$	−3.09017	−	9.51057i	−0.130935	−	0.402976i	0.864001	−	0.503490i	$-0.167951\pi$
$557$	−3.09017	−	9.51057i	−0.130935	−	0.402976i	−0.994936	+	0.100515i	$0.967951\pi$
$558$	−7.41641	+	22.8254i	−0.313962	+	0.966274i
$559$	−6.47214	−	4.70228i	−0.273742	−	0.198885i
$560$		0			0
$561$		0			0
$562$	18.0000			0.759284
$563$	29.1246	+	21.1603i	1.22746	+	0.891799i	0.996697	−	0.0812119i	$-0.0258790\pi$
$563$	29.1246	+	21.1603i	1.22746	+	0.891799i	0.230759	+	0.973011i	$0.425879\pi$
$564$		0			0
$565$	−1.85410	−	5.70634i	−0.0780027	−	0.240067i
$566$	−3.23607	+	2.35114i	−0.136022	+	0.0988258i
$567$		0			0
$568$	7.41641	+	22.8254i	0.311186	+	0.957731i
$569$	−8.03444	+	24.7275i	−0.336821	+	1.03663i	0.628997	+	0.777408i	$0.283466\pi$
$569$	−8.03444	+	24.7275i	−0.336821	+	1.03663i	−0.965818	+	0.259221i	$0.916534\pi$
$570$		0			0
$571$	−36.0000			−1.50655			−0.753277	−	0.657704i	$-0.771528\pi$
$571$	−36.0000			−1.50655			−0.753277	+	0.657704i	$0.771528\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	1.23607	−	3.80423i	0.0515476	−	0.158647i
$576$	−6.48936	−	19.9722i	−0.270390	−	0.832174i
$577$	17.7984	−	12.9313i	0.740956	−	0.538336i	−0.152054	−	0.988372i	$-0.548589\pi$
$577$	17.7984	−	12.9313i	0.740956	−	0.538336i	0.893010	+	0.450036i	$0.148589\pi$
$578$	15.3713	−	11.1679i	0.639363	−	0.464524i
$579$		0			0
$580$	1.85410	−	5.70634i	0.0769874	−	0.236943i
$581$		0			0
$582$		0			0
$583$		0			0
$584$	−42.0000			−1.73797
$585$	−4.85410	−	3.52671i	−0.200692	−	0.145812i
$586$	3.09017	−	9.51057i	0.127654	−	0.392878i
$587$	−7.41641	−	22.8254i	−0.306108	−	0.942103i	−0.979261	−	0.202601i	$-0.935061\pi$
$587$	−7.41641	−	22.8254i	−0.306108	−	0.942103i	0.673154	−	0.739503i	$-0.264939\pi$
$588$		0			0
$589$	25.8885	−	18.8091i	1.06672	−	0.775017i
$590$	−1.23607	−	3.80423i	−0.0508881	−	0.156618i
$591$		0			0
$592$	−1.61803	−	1.17557i	−0.0665008	−	0.0483157i
$593$	−22.0000			−0.903432			−0.451716	−	0.892162i	$-0.649188\pi$
$593$	−22.0000			−0.903432			−0.451716	+	0.892162i	$0.649188\pi$
$594$		0			0
$595$		0			0
$596$	8.09017	+	5.87785i	0.331386	+	0.240766i
$597$		0			0
$598$	2.47214	+	7.60845i	0.101093	+	0.311133i
$599$	−19.4164	+	14.1068i	−0.793333	+	0.576390i	−0.908951	−	0.416904i	$-0.863115\pi$
$599$	−19.4164	+	14.1068i	−0.793333	+	0.576390i	0.115618	+	0.993294i	$0.463115\pi$
$600$		0			0
$601$	−0.618034	−	1.90211i	−0.0252101	−	0.0775888i	0.937660	−	0.347554i	$-0.112988\pi$
$601$	−0.618034	−	1.90211i	−0.0252101	−	0.0775888i	−0.962870	+	0.269965i	$0.912988\pi$
$602$		0			0
$603$	−38.8328	−	28.2137i	−1.58139	−	1.14895i
$604$	8.00000			0.325515
$605$		0			0
$606$		0			0
$607$	−25.8885	−	18.8091i	−1.05078	−	0.763439i	−0.0784223	−	0.996920i	$-0.524988\pi$
$607$	−25.8885	−	18.8091i	−1.05078	−	0.763439i	−0.972361	+	0.233481i	$0.924988\pi$
$608$	−6.18034	+	19.0211i	−0.250646	+	0.771409i
$609$		0			0
$610$	8.09017	−	5.87785i	0.327561	−	0.237987i
$611$	−19.4164	+	14.1068i	−0.785504	+	0.570702i
$612$	−5.56231	−	17.1190i	−0.224843	−	0.691995i
$613$	−10.5066	+	32.3359i	−0.424357	+	1.30604i	0.479252	+	0.877677i	$0.340908\pi$
$613$	−10.5066	+	32.3359i	−0.424357	+	1.30604i	−0.903609	+	0.428358i	$0.859092\pi$
$614$	−16.1803	−	11.7557i	−0.652985	−	0.474422i
$615$		0			0
$616$		0			0
$617$	2.00000			0.0805170			0.0402585	−	0.999189i	$-0.487182\pi$
$617$	2.00000			0.0805170			0.0402585	+	0.999189i	$0.487182\pi$
$618$		0			0
$619$	−6.18034	+	19.0211i	−0.248409	+	0.764524i	0.746648	+	0.665219i	$0.231662\pi$
$619$	−6.18034	+	19.0211i	−0.248409	+	0.764524i	−0.995057	+	0.0993047i	$0.968338\pi$
$620$	2.47214	+	7.60845i	0.0992834	+	0.305563i
$621$		0			0
$622$	−19.4164	+	14.1068i	−0.778527	+	0.565633i
$623$		0			0
$624$		0			0
$625$	−0.809017	−	0.587785i	−0.0323607	−	0.0235114i
$626$	22.0000			0.879297
$627$		0			0
$628$	2.00000			0.0798087
$629$	−9.70820	−	7.05342i	−0.387091	−	0.281238i
$630$		0			0
$631$	12.3607	+	38.0423i	0.492071	+	1.51444i	0.821472	+	0.570248i	$0.193153\pi$
$631$	12.3607	+	38.0423i	0.492071	+	1.51444i	−0.329401	+	0.944190i	$0.606847\pi$
$632$	19.4164	−	14.1068i	0.772343	−	0.561140i
$633$		0			0
$634$	5.56231	+	17.1190i	0.220907	+	0.679883i
$635$	−4.94427	+	15.2169i	−0.196207	+	0.603864i
$636$		0			0
$637$	14.0000			0.554700
$638$		0			0
$639$	−24.0000			−0.949425
$640$	−2.42705	−	1.76336i	−0.0959376	−	0.0697028i
$641$	10.5066	−	32.3359i	0.414985	−	1.27719i	−0.497280	−	0.867590i	$-0.665668\pi$
$641$	10.5066	−	32.3359i	0.414985	−	1.27719i	0.912264	−	0.409602i	$-0.134332\pi$
$642$		0			0
$643$	12.9443	−	9.40456i	0.510472	−	0.370880i	−0.302530	−	0.953140i	$-0.597831\pi$
$643$	12.9443	−	9.40456i	0.510472	−	0.370880i	0.813003	+	0.582260i	$0.197831\pi$
$644$		0			0
$645$		0			0
$646$	7.41641	−	22.8254i	0.291795	−	0.898052i
$647$	−16.1803	−	11.7557i	−0.636115	−	0.462164i	0.222398	−	0.974956i	$-0.428611\pi$
$647$	−16.1803	−	11.7557i	−0.636115	−	0.462164i	−0.858513	+	0.512791i	$0.828611\pi$
$648$	27.0000			1.06066
$649$		0			0
$650$	2.00000			0.0784465
$651$		0			0
$652$	−4.94427	+	15.2169i	−0.193633	+	0.595940i
$653$	−3.09017	−	9.51057i	−0.120928	−	0.372177i	0.872209	−	0.489133i	$-0.162687\pi$
$653$	−3.09017	−	9.51057i	−0.120928	−	0.372177i	−0.993137	+	0.116955i	$0.962687\pi$
$654$		0			0
$655$	−9.70820	+	7.05342i	−0.379331	+	0.275600i
$656$	0.618034	+	1.90211i	0.0241302	+	0.0742650i
$657$	12.9787	−	39.9444i	0.506348	−	1.55838i
$658$		0			0
$659$	−36.0000			−1.40236			−0.701180	−	0.712984i	$-0.747343\pi$
$659$	−36.0000			−1.40236			−0.701180	+	0.712984i	$0.747343\pi$
$660$		0			0
$661$	−10.0000			−0.388955			−0.194477	−	0.980907i	$-0.562301\pi$
$661$	−10.0000			−0.388955			−0.194477	+	0.980907i	$0.562301\pi$
$662$	3.23607	+	2.35114i	0.125773	+	0.0913797i
$663$		0			0
$664$	3.70820	+	11.4127i	0.143906	+	0.442898i
$665$		0			0
$666$	4.85410	−	3.52671i	0.188093	−	0.136657i
$667$	−7.41641	−	22.8254i	−0.287164	−	0.883801i
$668$	−2.47214	+	7.60845i	−0.0956498	+	0.294380i
$669$		0			0
$670$	16.0000			0.618134
$671$		0			0
$672$		0			0
$673$	−21.0344	−	15.2824i	−0.810818	−	0.589094i	0.103250	−	0.994655i	$-0.467076\pi$
$673$	−21.0344	−	15.2824i	−0.810818	−	0.589094i	−0.914068	+	0.405562i	$0.867076\pi$
$674$	1.85410	−	5.70634i	0.0714173	−	0.219800i
$675$		0			0
$676$	−7.28115	+	5.29007i	−0.280044	+	0.203464i
$677$	−30.7426	+	22.3358i	−1.18154	+	0.858436i	−0.992344	−	0.123504i	$-0.960587\pi$
$677$	−30.7426	+	22.3358i	−1.18154	+	0.858436i	−0.189192	+	0.981940i	$0.560587\pi$
$678$		0			0
$679$		0			0
$680$	14.5623	+	10.5801i	0.558439	+	0.405730i
$681$		0			0
$682$		0			0
$683$	−16.0000			−0.612223			−0.306111	−	0.951996i	$-0.599028\pi$
$683$	−16.0000			−0.612223			−0.306111	+	0.951996i	$0.599028\pi$
$684$	−9.70820	−	7.05342i	−0.371202	−	0.269694i
$685$	5.56231	−	17.1190i	0.212525	−	0.654084i
$686$		0			0
$687$		0			0
$688$	−3.23607	+	2.35114i	−0.123374	+	0.0896364i
$689$	1.23607	+	3.80423i	0.0470904	+	0.144929i
$690$		0			0
$691$	22.6525	+	16.4580i	0.861741	+	0.626091i	0.928358	−	0.371687i	$-0.121221\pi$
$691$	22.6525	+	16.4580i	0.861741	+	0.626091i	−0.0666172	+	0.997779i	$0.521221\pi$
$692$	−6.00000			−0.228086
$693$		0			0
$694$	−4.00000			−0.151838
$695$	9.70820	+	7.05342i	0.368253	+	0.267552i
$696$		0			0
$697$	3.70820	+	11.4127i	0.140458	+	0.432286i
$698$	8.09017	−	5.87785i	0.306217	−	0.222480i
$699$		0			0
$700$		0			0
$701$	−6.79837	+	20.9232i	−0.256771	+	0.790260i	0.736705	+	0.676215i	$0.236381\pi$
$701$	−6.79837	+	20.9232i	−0.256771	+	0.790260i	−0.993476	+	0.114045i	$0.963619\pi$
$702$		0			0
$703$	−8.00000			−0.301726
$704$		0			0
$705$		0			0
$706$	14.5623	+	10.5801i	0.548060	+	0.398189i
$707$		0			0
$708$		0			0
$709$	8.09017	−	5.87785i	0.303833	−	0.220747i	−0.425413	−	0.904999i	$-0.639871\pi$
$709$	8.09017	−	5.87785i	0.303833	−	0.220747i	0.729246	+	0.684252i	$0.239871\pi$
$710$	6.47214	−	4.70228i	0.242895	−	0.176473i
$711$	7.41641	+	22.8254i	0.278137	+	0.856018i
$712$	9.27051	−	28.5317i	0.347427	−	1.06927i
$713$	25.8885	+	18.8091i	0.969534	+	0.704407i
$714$		0			0
$715$		0			0
$716$	−4.00000			−0.149487
$717$		0			0
$718$	−9.88854	+	30.4338i	−0.369037	+	1.13578i
$719$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$719$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$720$	−2.42705	+	1.76336i	−0.0904508	+	0.0657164i
$721$		0			0
$722$	0.927051	+	2.85317i	0.0345013	+	0.106184i
$723$		0			0
$724$	−8.09017	−	5.87785i	−0.300669	−	0.218449i
$725$	−6.00000			−0.222834
$726$		0			0
$727$	52.0000			1.92857			0.964287	−	0.264861i	$-0.0853260\pi$
$727$	52.0000			1.92857			0.964287	+	0.264861i	$0.0853260\pi$
$728$		0			0
$729$	−8.34346	+	25.6785i	−0.309017	+	0.951057i
$730$	4.32624	+	13.3148i	0.160121	+	0.492803i
$731$	−19.4164	+	14.1068i	−0.718142	+	0.521761i
$732$		0			0
$733$	−12.9787	−	39.9444i	−0.479380	−	1.47538i	−0.839959	−	0.542650i	$-0.817421\pi$
$733$	−12.9787	−	39.9444i	−0.479380	−	1.47538i	0.360579	−	0.932729i	$-0.382579\pi$
$734$	−1.23607	+	3.80423i	−0.0456241	+	0.140417i
$735$		0			0
$736$	−20.0000			−0.737210
$737$		0			0
$738$	−6.00000			−0.220863
$739$	3.23607	+	2.35114i	0.119041	+	0.0864881i	0.645713	−	0.763580i	$-0.276560\pi$
$739$	3.23607	+	2.35114i	0.119041	+	0.0864881i	−0.526672	+	0.850069i	$0.676560\pi$
$740$	0.618034	−	1.90211i	0.0227194	−	0.0699231i
$741$		0			0
$742$		0			0
$743$	32.3607	−	23.5114i	1.18720	−	0.862550i	0.194233	−	0.980955i	$-0.437778\pi$
$743$	32.3607	−	23.5114i	1.18720	−	0.862550i	0.992965	+	0.118405i	$0.0377783\pi$
$744$		0			0
$745$	3.09017	−	9.51057i	0.113215	−	0.348440i
$746$	−14.5623	−	10.5801i	−0.533164	−	0.387366i
$747$	−12.0000			−0.439057
$748$		0			0
$749$		0			0
$750$		0			0
$751$	4.94427	−	15.2169i	0.180419	−	0.555273i	−0.819420	−	0.573193i	$-0.805705\pi$
$751$	4.94427	−	15.2169i	0.180419	−	0.555273i	0.999839	+	0.0179203i	$0.00570452\pi$
$752$	3.70820	+	11.4127i	0.135224	+	0.416178i
$753$		0			0
$754$	9.70820	−	7.05342i	0.353552	−	0.256871i
$755$	−2.47214	−	7.60845i	−0.0899702	−	0.276900i
$756$		0			0
$757$	−4.85410	−	3.52671i	−0.176425	−	0.128181i	0.496068	−	0.868284i	$-0.334777\pi$
$757$	−4.85410	−	3.52671i	−0.176425	−	0.128181i	−0.672493	+	0.740103i	$0.734777\pi$
$758$	−20.0000			−0.726433
$759$		0			0
$760$	12.0000			0.435286
$761$	8.09017	+	5.87785i	0.293268	+	0.213072i	0.724684	−	0.689081i	$-0.241986\pi$
$761$	8.09017	+	5.87785i	0.293268	+	0.213072i	−0.431416	+	0.902153i	$0.641986\pi$
$762$		0			0
$763$		0			0
$764$	6.47214	−	4.70228i	0.234154	−	0.170123i
$765$	−14.5623	+	10.5801i	−0.526501	+	0.382526i
$766$	3.70820	+	11.4127i	0.133983	+	0.412357i
$767$	−2.47214	+	7.60845i	−0.0892637	+	0.274725i
$768$		0			0
$769$	22.0000			0.793340			0.396670	−	0.917961i	$-0.370166\pi$
$769$	22.0000			0.793340			0.396670	+	0.917961i	$0.370166\pi$
$770$		0			0
$771$		0			0
$772$	21.0344	+	15.2824i	0.757046	+	0.550026i
$773$	4.32624	−	13.3148i	0.155604	−	0.478900i	−0.842618	−	0.538512i	$-0.818987\pi$
$773$	4.32624	−	13.3148i	0.155604	−	0.478900i	0.998222	+	0.0596126i	$0.0189865\pi$
$774$	−3.70820	−	11.4127i	−0.133289	−	0.410220i
$775$	6.47214	−	4.70228i	0.232486	−	0.168911i
$776$	−24.2705	+	17.6336i	−0.871261	+	0.633008i
$777$		0			0
$778$	−1.85410	+	5.70634i	−0.0664728	+	0.204582i
$779$	6.47214	+	4.70228i	0.231888	+	0.168477i
$780$		0			0
$781$		0			0
$782$	24.0000			0.858238
$783$		0			0
$784$	2.16312	−	6.65740i	0.0772542	−	0.237764i
$785$	−0.618034	−	1.90211i	−0.0220586	−	0.0678893i
$786$		0			0
$787$	42.0689	−	30.5648i	1.49959	−	1.08952i	0.529051	−	0.848590i	$-0.322548\pi$
$787$	42.0689	−	30.5648i	1.49959	−	1.08952i	0.970543	−	0.240929i	$-0.0774519\pi$
$788$	0.618034	+	1.90211i	0.0220165	+	0.0677600i
$789$		0			0
$790$	−6.47214	−	4.70228i	−0.230268	−	0.167300i
$791$		0			0
$792$		0			0
$793$	−20.0000			−0.710221
$794$	24.2705	+	17.6336i	0.861328	+	0.625792i
$795$		0			0
$796$		0			0
$797$	1.61803	−	1.17557i	0.0573137	−	0.0416408i	−0.558760	−	0.829330i	$-0.688723\pi$
$797$	1.61803	−	1.17557i	0.0573137	−	0.0416408i	0.616073	+	0.787689i	$0.288723\pi$
$798$		0			0
$799$	22.2492	+	68.4761i	0.787121	+	2.42251i
$800$	−1.54508	+	4.75528i	−0.0546270	+	0.168125i
$801$	24.2705	+	17.6336i	0.857556	+	0.623051i
$802$	−2.00000			−0.0706225
$803$		0			0
$804$		0			0
$805$		0			0
$806$	−4.94427	+	15.2169i	−0.174155	+	0.535993i
$807$		0			0
$808$	−24.2705	+	17.6336i	−0.853834	+	0.620346i
$809$	14.5623	−	10.5801i	0.511983	−	0.371978i	−0.301592	−	0.953437i	$-0.597518\pi$
$809$	14.5623	−	10.5801i	0.511983	−	0.371978i	0.813575	+	0.581459i	$0.197518\pi$
$810$	−2.78115	−	8.55951i	−0.0977198	−	0.300750i
$811$	3.70820	−	11.4127i	0.130213	−	0.400753i	−0.864602	−	0.502457i	$-0.832429\pi$
$811$	3.70820	−	11.4127i	0.130213	−	0.400753i	0.994815	+	0.101704i	$0.0324294\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	16.0000			0.560456
$816$		0			0
$817$	−4.94427	+	15.2169i	−0.172978	+	0.532372i
$818$	−1.85410	−	5.70634i	−0.0648272	−	0.199517i
$819$		0			0
$820$	−1.61803	+	1.17557i	−0.0565042	+	0.0410527i
$821$	5.56231	+	17.1190i	0.194126	+	0.597458i	0.999986	+	0.00535152i	$0.00170345\pi$
$821$	5.56231	+	17.1190i	0.194126	+	0.597458i	−0.805860	+	0.592106i	$0.798297\pi$
$822$		0			0
$823$	29.1246	+	21.1603i	1.01522	+	0.737601i	0.965298	−	0.261152i	$-0.0841025\pi$
$823$	29.1246	+	21.1603i	1.01522	+	0.737601i	0.0499226	+	0.998753i	$0.484103\pi$
$824$	−12.0000			−0.418040
$825$		0			0
$826$		0			0
$827$	9.70820	+	7.05342i	0.337587	+	0.245272i	0.743643	−	0.668577i	$-0.233096\pi$
$827$	9.70820	+	7.05342i	0.337587	+	0.245272i	−0.406056	+	0.913848i	$0.633096\pi$
$828$	3.70820	−	11.4127i	0.128869	−	0.396618i
$829$	−0.618034	−	1.90211i	−0.0214652	−	0.0660631i	0.939750	−	0.341862i	$-0.111058\pi$
$829$	−0.618034	−	1.90211i	−0.0214652	−	0.0660631i	−0.961215	+	0.275799i	$0.911058\pi$
$830$	3.23607	−	2.35114i	0.112326	−	0.0816093i
$831$		0			0
$832$	−4.32624	−	13.3148i	−0.149985	−	0.461607i
$833$	12.9787	−	39.9444i	0.449686	−	1.38399i
$834$		0			0
$835$	8.00000			0.276851
$836$		0			0
$837$		0			0
$838$	−22.6525	−	16.4580i	−0.782517	−	0.568532i
$839$	−9.88854	+	30.4338i	−0.341390	+	1.05069i	0.622097	+	0.782940i	$0.286281\pi$
$839$	−9.88854	+	30.4338i	−0.341390	+	1.05069i	−0.963488	+	0.267752i	$0.913719\pi$
$840$		0			0
$841$	−5.66312	+	4.11450i	−0.195280	+	0.141879i
$842$	4.85410	−	3.52671i	0.167283	−	0.121539i
$843$		0			0
$844$	1.23607	−	3.80423i	0.0425472	−	0.130947i
$845$	7.28115	+	5.29007i	0.250479	+	0.181984i
$846$	−36.0000			−1.23771
$847$		0			0
$848$	2.00000			0.0686803
$849$		0			0
$850$	1.85410	−	5.70634i	0.0635952	−	0.195726i
$851$	−2.47214	−	7.60845i	−0.0847437	−	0.260814i
$852$		0			0
$853$	1.61803	−	1.17557i	0.0554004	−	0.0402508i	−0.559740	−	0.828668i	$-0.689099\pi$
$853$	1.61803	−	1.17557i	0.0554004	−	0.0402508i	0.615141	+	0.788417i	$0.289099\pi$
$854$		0			0
$855$	−3.70820	+	11.4127i	−0.126818	+	0.390305i
$856$	29.1246	+	21.1603i	0.995459	+	0.723243i
$857$	18.0000			0.614868			0.307434	−	0.951569i	$-0.400530\pi$
$857$	18.0000			0.614868			0.307434	+	0.951569i	$0.400530\pi$
$858$		0			0
$859$	28.0000			0.955348			0.477674	−	0.878537i	$-0.341480\pi$
$859$	28.0000			0.955348			0.477674	+	0.878537i	$0.341480\pi$
$860$	−3.23607	−	2.35114i	−0.110349	−	0.0801732i
$861$		0			0
$862$	−7.41641	−	22.8254i	−0.252604	−	0.777435i
$863$	−3.23607	+	2.35114i	−0.110157	+	0.0800338i	−0.641500	−	0.767123i	$-0.721688\pi$
$863$	−3.23607	+	2.35114i	−0.110157	+	0.0800338i	0.531343	+	0.847157i	$0.321688\pi$
$864$		0			0
$865$	1.85410	+	5.70634i	0.0630414	+	0.194021i
$866$	6.79837	−	20.9232i	0.231018	−	0.711001i
$867$		0			0
$868$		0			0
$869$		0			0
$870$		0			0
$871$	−25.8885	−	18.8091i	−0.877200	−	0.637323i
$872$	16.6869	−	51.3571i	0.565090	−	1.73917i
$873$	−9.27051	−	28.5317i	−0.313759	−	0.965652i
$874$	12.9443	−	9.40456i	0.437847	−	0.318114i
$875$		0			0
$876$		0			0
$877$	6.79837	−	20.9232i	0.229565	−	0.706528i	−0.768231	−	0.640172i	$-0.778863\pi$
$877$	6.79837	−	20.9232i	0.229565	−	0.706528i	0.997796	−	0.0663553i	$-0.0211371\pi$
$878$	6.47214	+	4.70228i	0.218424	+	0.158694i
$879$		0			0
$880$		0			0
$881$	18.0000			0.606435			0.303218	−	0.952921i	$-0.401939\pi$
$881$	18.0000			0.606435			0.303218	+	0.952921i	$0.401939\pi$
$882$	16.9894	+	12.3435i	0.572061	+	0.415627i
$883$	−4.94427	+	15.2169i	−0.166388	+	0.512090i	−0.999136	−	0.0415628i	$-0.986766\pi$
$883$	−4.94427	+	15.2169i	−0.166388	+	0.512090i	0.832748	+	0.553652i	$0.186766\pi$
$884$	−3.70820	−	11.4127i	−0.124720	−	0.383850i
$885$		0			0
$886$	6.47214	−	4.70228i	0.217436	−	0.157976i
$887$	−17.3050	−	53.2592i	−0.581043	−	1.78827i	−0.614610	−	0.788831i	$-0.710687\pi$
$887$	−17.3050	−	53.2592i	−0.581043	−	1.78827i	0.0335664	−	0.999436i	$-0.489313\pi$
$888$		0			0
$889$		0			0
$890$	−10.0000			−0.335201
$891$		0			0
$892$	4.00000			0.133930
$893$	38.8328	+	28.2137i	1.29949	+	0.944135i
$894$		0			0
$895$	1.23607	+	3.80423i	0.0413172	+	0.127161i
$896$		0			0
$897$		0			0
$898$	−0.618034	−	1.90211i	−0.0206241	−	0.0634743i
$899$	14.8328	−	45.6507i	0.494702	−	1.52254i
$900$	−2.42705	−	1.76336i	−0.0809017	−	0.0587785i
$901$	12.0000			0.399778
$902$		0			0
$903$		0			0
$904$	14.5623	+	10.5801i	0.484335	+	0.351890i
$905$	−3.09017	+	9.51057i	−0.102721	+	0.316142i
$906$		0			0
$907$	32.3607	−	23.5114i	1.07452	−	0.780684i	0.0977997	−	0.995206i	$-0.468820\pi$
$907$	32.3607	−	23.5114i	1.07452	−	0.780684i	0.976719	+	0.214523i	$0.0688195\pi$
$908$	16.1803	−	11.7557i	0.536963	−	0.390127i
$909$	−9.27051	−	28.5317i	−0.307483	−	0.946337i
$910$		0			0
$911$	−6.47214	−	4.70228i	−0.214431	−	0.155794i	0.475385	−	0.879778i	$-0.342309\pi$
$911$	−6.47214	−	4.70228i	−0.214431	−	0.155794i	−0.689816	+	0.723984i	$0.742309\pi$
$912$		0			0
$913$		0			0
$914$	−26.0000			−0.860004
$915$		0			0
$916$	3.09017	−	9.51057i	0.102102	−	0.314238i
$917$		0			0
$918$		0			0
$919$	19.4164	−	14.1068i	0.640488	−	0.465342i	−0.219530	−	0.975606i	$-0.570452\pi$
$919$	19.4164	−	14.1068i	0.640488	−	0.465342i	0.860018	+	0.510264i	$0.170452\pi$
$920$	3.70820	+	11.4127i	0.122256	+	0.376265i
$921$		0			0
$922$	27.5066	+	19.9847i	0.905881	+	0.658161i
$923$	−16.0000			−0.526646
$924$		0			0
$925$	−2.00000			−0.0657596
$926$	−29.1246	−	21.1603i	−0.957094	−	0.695370i
$927$	3.70820	−	11.4127i	0.121793	−	0.374842i
$928$	9.27051	+	28.5317i	0.304319	+	0.936599i
$929$	11.3262	−	8.22899i	0.371602	−	0.269985i	−0.386273	−	0.922384i	$-0.626238\pi$
$929$	11.3262	−	8.22899i	0.371602	−	0.269985i	0.757875	+	0.652400i	$0.226238\pi$
$930$		0			0
$931$	−8.65248	−	26.6296i	−0.283573	−	0.872749i
$932$	1.85410	−	5.70634i	0.0607331	−	0.186917i
$933$		0			0
$934$		0			0
$935$		0			0
$936$	18.0000			0.588348
$937$	4.85410	+	3.52671i	0.158577	+	0.115213i	0.664244	−	0.747516i	$-0.268754\pi$
$937$	4.85410	+	3.52671i	0.158577	+	0.115213i	−0.505667	+	0.862729i	$0.668754\pi$
$938$		0			0
$939$		0			0
$940$	−9.70820	+	7.05342i	−0.316647	+	0.230057i
$941$	−1.61803	+	1.17557i	−0.0527464	+	0.0383225i	−0.613846	−	0.789426i	$-0.710378\pi$
$941$	−1.61803	+	1.17557i	−0.0527464	+	0.0383225i	0.561100	+	0.827748i	$0.310378\pi$
$942$		0			0
$943$	−2.47214	+	7.60845i	−0.0805038	+	0.247765i
$944$	3.23607	+	2.35114i	0.105325	+	0.0765231i
$945$		0			0
$946$		0			0
$947$		0			0			−	1.00000i	$-0.5\pi$
$947$		0			0				1.00000i	$0.5\pi$
$948$		0			0
$949$	8.65248	−	26.6296i	0.280871	−	0.864433i
$950$	−1.23607	−	3.80423i	−0.0401033	−	0.123425i
$951$		0			0
$952$		0			0
$953$	12.9787	+	39.9444i	0.420422	+	1.29393i	0.907311	+	0.420461i	$0.138132\pi$
$953$	12.9787	+	39.9444i	0.420422	+	1.29393i	−0.486889	+	0.873464i	$0.661868\pi$
$954$	−1.85410	+	5.70634i	−0.0600288	+	0.184750i
$955$	−6.47214	−	4.70228i	−0.209433	−	0.152162i
$956$	8.00000			0.258738
$957$		0			0
$958$	24.0000			0.775405
$959$		0			0
$960$		0			0
$961$	10.1976	+	31.3849i	0.328954	+	1.01242i
$962$	3.23607	−	2.35114i	0.104335	−	0.0758038i
$963$	−29.1246	+	21.1603i	−0.938527	+	0.681880i
$964$	3.09017	+	9.51057i	0.0995277	+	0.306315i
$965$	8.03444	−	24.7275i	0.258638	−	0.796005i
$966$		0			0
$967$	−8.00000			−0.257263			−0.128631	−	0.991692i	$-0.541058\pi$
$967$	−8.00000			−0.257263			−0.128631	+	0.991692i	$0.541058\pi$
$968$		0			0
$969$		0			0
$970$	8.09017	+	5.87785i	0.259760	+	0.188726i
$971$	11.1246	−	34.2380i	0.357006	−	1.09875i	−0.597832	−	0.801622i	$-0.703971\pi$
$971$	11.1246	−	34.2380i	0.357006	−	1.09875i	0.954837	−	0.297129i	$-0.0960292\pi$
$972$		0			0
$973$		0			0
$974$	22.6525	−	16.4580i	0.725832	−	0.527348i
$975$		0			0
$976$	−3.09017	+	9.51057i	−0.0989139	+	0.304426i
$977$	−8.09017	−	5.87785i	−0.258827	−	0.188049i	0.450803	−	0.892624i	$-0.351138\pi$
$977$	−8.09017	−	5.87785i	−0.258827	−	0.188049i	−0.709630	+	0.704575i	$0.751138\pi$
$978$		0			0
$979$		0			0
$980$	7.00000			0.223607
$981$	43.6869	+	31.7404i	1.39482	+	1.01339i
$982$	−8.65248	+	26.6296i	−0.276112	+	0.849784i
$983$	−1.23607	−	3.80423i	−0.0394244	−	0.121336i	0.929407	−	0.369056i	$-0.120319\pi$
$983$	−1.23607	−	3.80423i	−0.0394244	−	0.121336i	−0.968832	+	0.247720i	$0.920319\pi$
$984$		0			0
$985$	1.61803	−	1.17557i	0.0515548	−	0.0374568i
$986$	−11.1246	−	34.2380i	−0.354280	−	1.09036i
$987$		0			0
$988$	−6.47214	−	4.70228i	−0.205906	−	0.149600i
$989$	−16.0000			−0.508770
$990$		0			0
$991$	8.00000			0.254128			0.127064	−	0.991894i	$-0.459445\pi$
$991$	8.00000			0.254128			0.127064	+	0.991894i	$0.459445\pi$
$992$	−32.3607	−	23.5114i	−1.02745	−	0.746488i
$993$		0			0
$994$		0			0
$995$		0			0
$996$		0			0
$997$	14.2148	+	43.7486i	0.450187	+	1.38553i	0.876694	+	0.481048i	$0.159744\pi$
$997$	14.2148	+	43.7486i	0.450187	+	1.38553i	−0.426508	+	0.904484i	$0.640256\pi$
$998$	11.1246	−	34.2380i	0.352143	−	1.08379i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.g.c.81.1		4
11.2	odd	10		605.2.g.a.511.1		4
11.3	even	5	inner	605.2.g.c.366.1		4
11.4	even	5	inner	605.2.g.c.251.1		4
11.5	even	5		605.2.a.b.1.1		1
11.6	odd	10		55.2.a.a.1.1	✓	1
11.7	odd	10		605.2.g.a.251.1		4
11.8	odd	10		605.2.g.a.366.1		4
11.9	even	5	inner	605.2.g.c.511.1		4
11.10	odd	2		605.2.g.a.81.1		4
33.5	odd	10		5445.2.a.i.1.1		1
33.17	even	10		495.2.a.a.1.1		1
44.27	odd	10		9680.2.a.r.1.1		1
44.39	even	10		880.2.a.h.1.1		1
55.17	even	20		275.2.b.b.199.2		2
55.28	even	20		275.2.b.b.199.1		2
55.39	odd	10		275.2.a.a.1.1		1
55.49	even	10		3025.2.a.f.1.1		1
77.6	even	10		2695.2.a.c.1.1		1
88.61	odd	10		3520.2.a.p.1.1		1
88.83	even	10		3520.2.a.n.1.1		1
132.83	odd	10		7920.2.a.i.1.1		1
143.116	odd	10		9295.2.a.b.1.1		1
165.17	odd	20		2475.2.c.f.199.1		2
165.83	odd	20		2475.2.c.f.199.2		2
165.149	even	10		2475.2.a.i.1.1		1
220.39	even	10		4400.2.a.p.1.1		1
220.83	odd	20		4400.2.b.n.4049.2		2
220.127	odd	20		4400.2.b.n.4049.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.a.a.1.1	✓	1	11.6	odd	10
275.2.a.a.1.1		1	55.39	odd	10
275.2.b.b.199.1		2	55.28	even	20
275.2.b.b.199.2		2	55.17	even	20
495.2.a.a.1.1		1	33.17	even	10
605.2.a.b.1.1		1	11.5	even	5
605.2.g.a.81.1		4	11.10	odd	2
605.2.g.a.251.1		4	11.7	odd	10
605.2.g.a.366.1		4	11.8	odd	10
605.2.g.a.511.1		4	11.2	odd	10
605.2.g.c.81.1		4	1.1	even	1	trivial
605.2.g.c.251.1		4	11.4	even	5	inner
605.2.g.c.366.1		4	11.3	even	5	inner
605.2.g.c.511.1		4	11.9	even	5	inner
880.2.a.h.1.1		1	44.39	even	10
2475.2.a.i.1.1		1	165.149	even	10
2475.2.c.f.199.1		2	165.17	odd	20
2475.2.c.f.199.2		2	165.83	odd	20
2695.2.a.c.1.1		1	77.6	even	10
3025.2.a.f.1.1		1	55.49	even	10
3520.2.a.n.1.1		1	88.83	even	10
3520.2.a.p.1.1		1	88.61	odd	10
4400.2.a.p.1.1		1	220.39	even	10
4400.2.b.n.4049.1		2	220.127	odd	20
4400.2.b.n.4049.2		2	220.83	odd	20
5445.2.a.i.1.1		1	33.5	odd	10
7920.2.a.i.1.1		1	132.83	odd	10
9295.2.a.b.1.1		1	143.116	odd	10
9680.2.a.r.1.1		1	44.27	odd	10

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.g (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 + 0.587785i) q^{2} +(-0.309017 - 0.951057i) q^{4} +(-0.809017 + 0.587785i) q^{5} +(0.927051 - 2.85317i) q^{8} +(2.42705 + 1.76336i) q^{9} -1.00000 q^{10} +(1.61803 + 1.17557i) q^{13} +(0.809017 - 0.587785i) q^{16} +(4.85410 - 3.52671i) q^{17} +(0.927051 + 2.85317i) q^{18} +(1.23607 - 3.80423i) q^{19} +(0.809017 + 0.587785i) q^{20} +4.00000 q^{23} +(0.309017 - 0.951057i) q^{25} +(0.618034 + 1.90211i) q^{26} +(-1.85410 - 5.70634i) q^{29} +(6.47214 + 4.70228i) q^{31} -5.00000 q^{32} +6.00000 q^{34} +(0.927051 - 2.85317i) q^{36} +(-0.618034 - 1.90211i) q^{37} +(3.23607 - 2.35114i) q^{38} +(0.927051 + 2.85317i) q^{40} +(-0.618034 + 1.90211i) q^{41} -4.00000 q^{43} -3.00000 q^{45} +(3.23607 + 2.35114i) q^{46} +(-3.70820 + 11.4127i) q^{47} +(5.66312 - 4.11450i) q^{49} +(0.809017 - 0.587785i) q^{50} +(0.618034 - 1.90211i) q^{52} +(1.61803 + 1.17557i) q^{53} +(1.85410 - 5.70634i) q^{58} +(1.23607 + 3.80423i) q^{59} +(-8.09017 + 5.87785i) q^{61} +(2.47214 + 7.60845i) q^{62} +(-5.66312 - 4.11450i) q^{64} -2.00000 q^{65} -16.0000 q^{67} +(-4.85410 - 3.52671i) q^{68} +(-6.47214 + 4.70228i) q^{71} +(7.28115 - 5.29007i) q^{72} +(-4.32624 - 13.3148i) q^{73} +(0.618034 - 1.90211i) q^{74} -4.00000 q^{76} +(6.47214 + 4.70228i) q^{79} +(-0.309017 + 0.951057i) q^{80} +(2.78115 + 8.55951i) q^{81} +(-1.61803 + 1.17557i) q^{82} +(-3.23607 + 2.35114i) q^{83} +(-1.85410 + 5.70634i) q^{85} +(-3.23607 - 2.35114i) q^{86} +10.0000 q^{89} +(-2.42705 - 1.76336i) q^{90} +(-1.23607 - 3.80423i) q^{92} +(-9.70820 + 7.05342i) q^{94} +(1.23607 + 3.80423i) q^{95} +(-8.09017 - 5.87785i) q^{97} +7.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} + q^{4} - q^{5} - 3 q^{8} + 3 q^{9} - 4 q^{10} + 2 q^{13} + q^{16} + 6 q^{17} - 3 q^{18} - 4 q^{19} + q^{20} + 16 q^{23} - q^{25} - 2 q^{26} + 6 q^{29} + 8 q^{31} - 20 q^{32} + 24 q^{34}+ \cdots + 28 q^{98}+O(q^{100}) \) 4 * q + q^2 + q^4 - q^5 - 3 * q^8 + 3 * q^9 - 4 * q^10 + 2 * q^13 + q^16 + 6 * q^17 - 3 * q^18 - 4 * q^19 + q^20 + 16 * q^23 - q^25 - 2 * q^26 + 6 * q^29 + 8 * q^31 - 20 * q^32 + 24 * q^34 - 3 * q^36 + 2 * q^37 + 4 * q^38 - 3 * q^40 + 2 * q^41 - 16 * q^43 - 12 * q^45 + 4 * q^46 + 12 * q^47 + 7 * q^49 + q^50 - 2 * q^52 + 2 * q^53 - 6 * q^58 - 4 * q^59 - 10 * q^61 - 8 * q^62 - 7 * q^64 - 8 * q^65 - 64 * q^67 - 6 * q^68 - 8 * q^71 + 9 * q^72 + 14 * q^73 - 2 * q^74 - 16 * q^76 + 8 * q^79 + q^80 - 9 * q^81 - 2 * q^82 - 4 * q^83 + 6 * q^85 - 4 * q^86 + 40 * q^89 - 3 * q^90 + 4 * q^92 - 12 * q^94 - 4 * q^95 - 10 * q^97 + 28 * q^98

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