LMFDB - Embedded newform 605.2.g.a.366.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,2,Mod(81,605)]

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

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.83094932229$
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			366.1
Root			$0.809017 + 0.587785i$ of defining polynomial
Character	$\chi$	$=$	605.366
Dual form			605.2.g.a.81.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$122$	$486$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

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	$-0.815027\pi$
$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i	0.263792	+	0.964580i	$0.415027\pi$
$3$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$3$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$4$	−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	$-0.900000\pi$
$7$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$8$	−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	$-0.789456\pi$
$13$	−1.61803	+	1.17557i	−0.448762	+	0.326045i	0.340345	+	0.940301i	$0.389456\pi$
$14$		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	$-0.559367\pi$
$17$	−4.85410	−	3.52671i	−1.17729	−	0.855353i	−0.991864	+	0.127304i	$0.959367\pi$
$18$	−0.927051	+	2.85317i	−0.218508	+	0.672499i
$19$	−1.23607	−	3.80423i	−0.283573	−	0.872749i	−0.986823	−	0.161806i	$-0.948268\pi$
$19$	−1.23607	−	3.80423i	−0.283573	−	0.872749i	0.703249	−	0.710943i	$-0.251732\pi$
$20$	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	−0.617660	−	0.786445i	$-0.711919\pi$
$29$	1.85410	−	5.70634i	0.344298	−	1.05964i	0.961958	−	0.273196i	$-0.0880806\pi$
$30$		0			0
$31$	6.47214	−	4.70228i	1.16243	−	0.844555i	0.172347	−	0.985036i	$-0.444865\pi$
$31$	6.47214	−	4.70228i	1.16243	−	0.844555i	0.990083	+	0.140482i	$0.0448651\pi$
$32$	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	−0.988918	−	0.148460i	$-0.952568\pi$
$37$	−0.618034	+	1.90211i	−0.101604	+	0.312705i	0.887314	+	0.461165i	$0.152568\pi$
$38$	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	$-0.0500840\pi$
$41$	0.618034	+	1.90211i	0.0965207	+	0.297060i	−0.891126	+	0.453755i	$0.850084\pi$
$42$		0			0
$43$	4.00000			0.609994			0.304997	−	0.952353i	$-0.401344\pi$
$43$	4.00000			0.609994			0.304997	+	0.952353i	$0.401344\pi$
$44$		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	−0.730550	−	0.682859i	$-0.760736\pi$
$47$	−3.70820	−	11.4127i	−0.540897	−	1.66471i	0.189653	−	0.981851i	$-0.439264\pi$
$48$		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	−0.471087	−	0.882087i	$-0.656138\pi$
$53$	1.61803	−	1.17557i	0.222254	−	0.161477i	0.693341	+	0.720610i	$0.256138\pi$
$54$		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	−0.837790	−	0.545992i	$-0.816153\pi$
$59$	1.23607	−	3.80423i	0.160922	−	0.495268i	0.998713	+	0.0507240i	$0.0161529\pi$
$60$		0			0
$61$	8.09017	+	5.87785i	1.03584	+	0.752582i	0.969469	−	0.245213i	$-0.0788579\pi$
$61$	8.09017	+	5.87785i	1.03584	+	0.752582i	0.0663709	+	0.997795i	$0.478858\pi$
$62$	−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	0.133283	−	0.991078i	$-0.457448\pi$
$71$	−6.47214	−	4.70228i	−0.768101	−	0.558058i	−0.901384	+	0.433020i	$0.857448\pi$
$72$	−7.28115	−	5.29007i	−0.858092	−	0.623440i
$73$	4.32624	−	13.3148i	0.506348	−	1.55838i	−0.292145	−	0.956374i	$-0.594369\pi$
$73$	4.32624	−	13.3148i	0.506348	−	1.55838i	0.798493	−	0.602004i	$-0.205631\pi$
$74$	−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	$-0.848589\pi$
$79$	−6.47214	+	4.70228i	−0.728172	+	0.529048i	0.160813	+	0.986985i	$0.448589\pi$
$80$	−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	$-0.229548\pi$
$83$	3.23607	+	2.35114i	0.355205	+	0.258071i	−0.395845	+	0.918318i	$0.629548\pi$
$84$		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	−0.917122	−	0.398606i	$-0.869494\pi$
$97$	−8.09017	+	5.87785i	−0.821432	+	0.596806i	0.0956901	+	0.995411i	$0.469494\pi$
$98$	−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	$-0.534245\pi$
$101$	8.09017	−	5.87785i	0.805002	−	0.584868i	0.912377	+	0.409350i	$0.134245\pi$
$102$		0			0
$103$	−1.23607	+	3.80423i	−0.121793	+	0.374842i	−0.993303	−	0.115536i	$-0.963141\pi$
$103$	−1.23607	+	3.80423i	−0.121793	+	0.374842i	0.871510	+	0.490378i	$0.163141\pi$
$104$	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	0.953961	+	0.299932i	$0.0969638\pi$
$107$	3.70820	+	11.4127i	0.358486	+	1.10331i	−0.595475	+	0.803374i	$0.703036\pi$
$108$		0			0
$109$	−18.0000			−1.72409			−0.862044	−	0.506834i	$-0.830816\pi$
$109$	−18.0000			−1.72409			−0.862044	+	0.506834i	$0.830816\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−1.85410	−	5.70634i	−0.174419	−	0.536807i	0.825187	−	0.564859i	$-0.191070\pi$
$113$	−1.85410	−	5.70634i	−0.174419	−	0.536807i	−0.999606	+	0.0280521i	$0.991070\pi$
$114$		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	$-0.551253\pi$
$127$	−12.9443	−	9.40456i	−1.14862	−	0.834520i	−0.988297	+	0.152545i	$0.951253\pi$
$128$	−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	$-0.675644\pi$
$131$	−12.0000			−1.04844			−0.524222	+	0.851581i	$0.675644\pi$
$132$		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	−0.246275	−	0.969200i	$-0.579207\pi$
$137$	−14.5623	−	10.5801i	−1.24414	−	0.903922i	−0.997867	+	0.0652782i	$0.979207\pi$
$138$		0			0
$139$	3.70820	−	11.4127i	0.314526	−	0.968011i	−0.661423	−	0.750013i	$-0.730047\pi$
$139$	3.70820	−	11.4127i	0.314526	−	0.968011i	0.975949	−	0.217998i	$-0.0699526\pi$
$140$		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	$-0.165663\pi$
$149$	8.09017	+	5.87785i	0.662773	+	0.481532i	−0.204826	+	0.978798i	$0.565663\pi$
$150$		0			0
$151$	2.47214	+	7.60845i	0.201180	+	0.619167i	0.999849	+	0.0173966i	$0.00553779\pi$
$151$	2.47214	+	7.60845i	0.201180	+	0.619167i	−0.798669	+	0.601770i	$0.794462\pi$
$152$	−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	0.923361	−	0.383934i	$-0.125431\pi$
$157$	−0.618034	−	1.90211i	−0.0493245	−	0.151805i	−0.972685	+	0.232129i	$0.925431\pi$
$158$	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	−0.965018	−	0.262184i	$-0.915557\pi$
$163$	−12.9443	+	9.40456i	−1.01387	+	0.736622i	−0.0488556	+	0.998806i	$0.515557\pi$
$164$	−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	$-0.599829\pi$
$167$	6.47214	−	4.70228i	0.500829	−	0.363874i	0.809334	+	0.587349i	$0.199829\pi$
$168$		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	$-0.173247\pi$
$173$	−1.85410	−	5.70634i	−0.140965	−	0.433845i	−0.996470	+	0.0839492i	$0.973247\pi$
$174$		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	0.986564	−	0.163374i	$-0.0522378\pi$
$179$	1.23607	+	3.80423i	0.0923881	+	0.284341i	−0.894176	+	0.447715i	$0.852238\pi$
$180$	0.927051	−	2.85317i	0.0690983	−	0.212663i
$181$	8.09017	+	5.87785i	0.601338	+	0.436897i	0.846353	−	0.532622i	$-0.178793\pi$
$181$	8.09017	+	5.87785i	0.601338	+	0.436897i	−0.245016	+	0.969519i	$0.578793\pi$
$182$		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	−0.820912	−	0.571055i	$-0.806534\pi$
$191$	2.47214	−	7.60845i	0.178877	−	0.550528i	0.999789	+	0.0205267i	$0.00653431\pi$
$192$		0			0
$193$	21.0344	+	15.2824i	1.51409	+	1.10005i	0.964321	+	0.264737i	$0.0852853\pi$
$193$	21.0344	+	15.2824i	1.51409	+	1.10005i	0.549772	+	0.835315i	$0.314715\pi$
$194$	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	$-0.477302\pi$
$197$	2.00000			0.142494			0.0712470	+	0.997459i	$0.477302\pi$
$198$		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	$-0.743966\pi$
$211$	−3.23607	+	2.35114i	−0.222780	+	0.161859i	0.470797	+	0.882242i	$0.343966\pi$
$212$	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	0.901102	−	0.433608i	$-0.142760\pi$
$223$	−1.23607	−	3.80423i	−0.0827732	−	0.254750i	−0.983875	+	0.178858i	$0.942760\pi$
$224$		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	0.506268	+	0.862376i	$0.331025\pi$
$227$	−6.18034	+	19.0211i	−0.410204	+	1.26248i	−0.916471	+	0.400100i	$0.868975\pi$
$228$		0			0
$229$	8.09017	−	5.87785i	0.534613	−	0.388419i	−0.287467	−	0.957790i	$-0.592813\pi$
$229$	8.09017	−	5.87785i	0.534613	−	0.388419i	0.822081	+	0.569371i	$0.192813\pi$
$230$	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	$-0.762969\pi$
$233$	−4.85410	+	3.52671i	−0.318003	+	0.231043i	0.417320	+	0.908760i	$0.362969\pi$
$234$	−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	$-0.0166932\pi$
$239$	2.47214	+	7.60845i	0.159909	+	0.492150i	−0.838716	+	0.544569i	$0.816693\pi$
$240$		0			0
$241$	10.0000			0.644157			0.322078	−	0.946713i	$-0.395619\pi$
$241$	10.0000			0.644157			0.322078	+	0.946713i	$0.395619\pi$
$242$		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	−0.850391	−	0.526151i	$-0.823635\pi$
$251$	−9.70820	+	7.05342i	−0.612776	+	0.445208i	0.237614	+	0.971360i	$0.423635\pi$
$252$		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	−0.613555	−	0.789652i	$-0.710261\pi$
$257$	5.56231	−	17.1190i	0.346967	−	1.06785i	0.960522	−	0.278203i	$-0.0897388\pi$
$258$		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	$-0.234848\pi$
$263$	24.0000			1.47990			0.739952	+	0.672660i	$0.234848\pi$
$264$		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	0.935324	−	0.353792i	$-0.115108\pi$
$269$	14.5623	+	10.5801i	0.887879	+	0.645082i	−0.0474448	+	0.998874i	$0.515108\pi$
$270$		0			0
$271$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$271$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$272$	−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	$-0.797127\pi$
$277$	−8.09017	+	5.87785i	−0.486091	+	0.353166i	0.317588	+	0.948229i	$0.397127\pi$
$278$	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	$-0.480403\pi$
$281$	−14.5623	−	10.5801i	−0.868714	−	0.631158i	−0.930242	+	0.366947i	$0.880403\pi$
$282$		0			0
$283$	1.23607	+	3.80423i	0.0734766	+	0.226138i	0.981050	−	0.193756i	$-0.0620672\pi$
$283$	1.23607	+	3.80423i	0.0734766	+	0.226138i	−0.907573	+	0.419894i	$0.862067\pi$
$284$	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	$-0.805645\pi$
$293$	3.09017	−	9.51057i	0.180530	−	0.555613i	0.999843	+	0.0177332i	$0.00564495\pi$
$294$		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	$-0.306660\pi$
$307$	20.0000			1.14146			0.570730	+	0.821138i	$0.306660\pi$
$308$		0			0
$309$		0			0
$310$	6.47214	−	4.70228i	0.367593	−	0.267072i
$311$	−7.41641	−	22.8254i	−0.420546	−	1.29431i	−0.907195	−	0.420710i	$-0.861781\pi$
$311$	−7.41641	−	22.8254i	−0.420546	−	1.29431i	0.486649	−	0.873597i	$-0.338219\pi$
$312$		0			0
$313$	17.7984	+	12.9313i	1.00602	+	0.730919i	0.963371	−	0.268171i	$-0.0864192\pi$
$313$	17.7984	+	12.9313i	1.00602	+	0.730919i	0.0426523	+	0.999090i	$0.486419\pi$
$314$	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	−0.0982098	−	0.995166i	$-0.531312\pi$
$317$	14.5623	−	10.5801i	0.817901	−	0.594240i	0.916110	+	0.400926i	$0.131312\pi$
$318$		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	$-0.847747\pi$
$337$	1.85410	−	5.70634i	0.100999	−	0.310844i	0.988771	+	0.149441i	$0.0477473\pi$
$338$	−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	$-0.265758\pi$
$347$	3.23607	+	2.35114i	0.173721	+	0.126216i	−0.497527	+	0.867448i	$0.665758\pi$
$348$		0			0
$349$	−3.09017	−	9.51057i	−0.165413	−	0.509089i	0.833653	−	0.552288i	$-0.186245\pi$
$349$	−3.09017	−	9.51057i	−0.165413	−	0.509089i	−0.999066	+	0.0431990i	$0.986245\pi$
$350$		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	0.248473	+	0.968639i	$0.420071\pi$
$359$	−9.88854	+	30.4338i	−0.521897	+	1.60623i	−0.770371	+	0.637596i	$0.779929\pi$
$360$	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	−0.913598	−	0.406618i	$-0.866708\pi$
$367$	1.23607	−	3.80423i	0.0645222	−	0.198579i	0.978121	+	0.208039i	$0.0667081\pi$
$368$	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	$-0.345694\pi$
$373$	18.0000			0.932005			0.466002	+	0.884783i	$0.345694\pi$
$374$		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	0.0887501	−	0.996054i	$-0.471713\pi$
$379$	−16.1803	−	11.7557i	−0.831128	−	0.603850i	−0.919878	+	0.392204i	$0.871713\pi$
$380$	−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	−0.311446	−	0.950264i	$-0.600813\pi$
$383$	9.70820	−	7.05342i	0.496066	−	0.360413i	0.807512	+	0.589851i	$0.200813\pi$
$384$		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	−0.892987	−	0.450083i	$-0.851394\pi$
$389$	1.85410	−	5.70634i	0.0940067	−	0.289323i	0.986994	+	0.160760i	$0.0513945\pi$
$390$		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	0.546652	−	0.837360i	$-0.315902\pi$
$401$	−1.61803	−	1.17557i	−0.0808008	−	0.0587052i	−0.627452	+	0.778655i	$0.715902\pi$
$402$		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	$-0.652607\pi$
$409$	4.85410	−	3.52671i	0.240020	−	0.174385i	0.701292	+	0.712874i	$0.252607\pi$
$410$	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	0.986018	−	0.166641i	$-0.0532921\pi$
$421$	1.85410	+	5.70634i	0.0903634	+	0.278110i	−0.895654	+	0.444751i	$0.853292\pi$
$422$	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	$-0.503826\pi$
$431$	19.4164	−	14.1068i	0.935255	−	0.679503i	0.947274	+	0.320425i	$0.103826\pi$
$432$		0			0
$433$	−6.79837	+	20.9232i	−0.326709	+	1.00551i	0.643954	+	0.765064i	$0.277293\pi$
$433$	−6.79837	+	20.9232i	−0.326709	+	1.00551i	−0.970663	+	0.240443i	$0.922707\pi$
$434$		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	$-0.561144\pi$
$439$	−8.00000			−0.381819			−0.190910	+	0.981608i	$0.561144\pi$
$440$		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	0.992451	−	0.122641i	$-0.0391364\pi$
$443$	2.47214	+	7.60845i	0.117455	+	0.361488i	−0.874996	+	0.484129i	$0.839136\pi$
$444$		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	−0.625310	−	0.780376i	$-0.715028\pi$
$449$	−1.61803	+	1.17557i	−0.0763597	+	0.0554786i	0.548950	+	0.835855i	$0.315028\pi$
$450$	−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	$-0.0919262\pi$
$457$	21.0344	+	15.2824i	0.983950	+	0.714881i	0.0253618	+	0.999678i	$0.491926\pi$
$458$	−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	$-0.790840\pi$
$461$	−34.0000			−1.58354			−0.791769	+	0.610821i	$0.790840\pi$
$462$		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	$-0.300000\pi$
$467$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$468$	−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	$-0.484723\pi$
$479$	−19.4164	−	14.1068i	−0.887158	−	0.644558i	−0.935136	+	0.354290i	$0.884723\pi$
$480$		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	0.931212	+	0.364479i	$0.118753\pi$
$487$	8.65248	+	26.6296i	0.392081	+	1.20670i	−0.539130	+	0.842222i	$0.681247\pi$
$488$	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	0.541945	+	0.840414i	$0.317688\pi$
$491$	−8.65248	+	26.6296i	−0.390481	+	1.20178i	−0.932426	+	0.361362i	$0.882312\pi$
$492$		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	0.314213	+	0.949352i	$0.398259\pi$
$499$	−11.1246	+	34.2380i	−0.498006	+	1.53270i	−0.812219	+	0.583352i	$0.801741\pi$
$500$	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	−0.998721	−	0.0505549i	$-0.983901\pi$
$503$	−4.94427	−	15.2169i	−0.220454	−	0.678488i	0.778267	−	0.627933i	$-0.216099\pi$
$504$		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	0.999999	+	0.00131729i	$0.000419307\pi$
$509$	4.32624	+	13.3148i	0.191757	+	0.590168i	−0.808242	+	0.588850i	$0.799581\pi$
$510$		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	−0.983421	−	0.181337i	$-0.941958\pi$
$521$	−1.85410	+	5.70634i	−0.0812297	+	0.249999i	0.902191	+	0.431336i	$0.141958\pi$
$522$	14.5623	+	10.5801i	0.637375	+	0.463080i
$523$	16.1803	+	11.7557i	0.707517	+	0.514041i	0.882372	−	0.470553i	$-0.155946\pi$
$523$	16.1803	+	11.7557i	0.707517	+	0.514041i	−0.174855	+	0.984594i	$0.555946\pi$
$524$	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	$-0.439107\pi$
$541$	27.5066	−	19.9847i	1.18260	−	0.859209i	0.992463	+	0.122548i	$0.0391066\pi$
$542$		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	$-0.0174170\pi$
$547$	3.70820	+	11.4127i	0.158551	+	0.487971i	−0.839952	+	0.542661i	$0.817417\pi$
$548$	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	$-0.832049\pi$
$557$	3.09017	−	9.51057i	0.130935	−	0.402976i	0.994936	+	0.100515i	$0.0320490\pi$
$558$	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	$-0.974121\pi$
$563$	−29.1246	+	21.1603i	−1.22746	+	0.891799i	−0.230759	+	0.973011i	$0.574121\pi$
$564$		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	0.965818	+	0.259221i	$0.0834659\pi$
$569$	8.03444	+	24.7275i	0.336821	+	1.03663i	−0.628997	+	0.777408i	$0.716534\pi$
$570$		0			0
$571$	36.0000			1.50655			0.753277	−	0.657704i	$-0.228472\pi$
$571$	36.0000			1.50655			0.753277	+	0.657704i	$0.228472\pi$
$572$		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	0.893010	−	0.450036i	$-0.148589\pi$
$577$	17.7984	+	12.9313i	0.740956	+	0.538336i	−0.152054	+	0.988372i	$0.548589\pi$
$578$	−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	0.673154	+	0.739503i	$0.264939\pi$
$587$	−7.41641	+	22.8254i	−0.306108	+	0.942103i	−0.979261	+	0.202601i	$0.935061\pi$
$588$		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	$-0.350812\pi$
$593$	22.0000			0.903432			0.451716	+	0.892162i	$0.350812\pi$
$594$		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	0.115618	−	0.993294i	$-0.463115\pi$
$599$	−19.4164	−	14.1068i	−0.793333	−	0.576390i	−0.908951	+	0.416904i	$0.863115\pi$
$600$		0			0
$601$	0.618034	−	1.90211i	0.0252101	−	0.0775888i	−0.937660	−	0.347554i	$-0.887012\pi$
$601$	0.618034	−	1.90211i	0.0252101	−	0.0775888i	0.962870	+	0.269965i	$0.0870123\pi$
$602$		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	$-0.475012\pi$
$607$	25.8885	−	18.8091i	1.05078	−	0.763439i	0.972361	+	0.233481i	$0.0750118\pi$
$608$	−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	0.903609	+	0.428358i	$0.140908\pi$
$613$	10.5066	+	32.3359i	0.424357	+	1.30604i	−0.479252	+	0.877677i	$0.659092\pi$
$614$	−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	−0.995057	−	0.0993047i	$-0.968338\pi$
$619$	−6.18034	−	19.0211i	−0.248409	−	0.764524i	0.746648	−	0.665219i	$-0.231662\pi$
$620$	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	−0.329401	−	0.944190i	$-0.606847\pi$
$631$	12.3607	−	38.0423i	0.492071	−	1.51444i	0.821472	−	0.570248i	$-0.193153\pi$
$632$	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	0.912264	+	0.409602i	$0.134332\pi$
$641$	10.5066	+	32.3359i	0.414985	+	1.27719i	−0.497280	+	0.867590i	$0.665668\pi$
$642$		0			0
$643$	12.9443	+	9.40456i	0.510472	+	0.370880i	0.813003	−	0.582260i	$-0.197831\pi$
$643$	12.9443	+	9.40456i	0.510472	+	0.370880i	−0.302530	+	0.953140i	$0.597831\pi$
$644$		0			0
$645$		0			0
$646$	−7.41641	−	22.8254i	−0.291795	−	0.898052i
$647$	−16.1803	+	11.7557i	−0.636115	+	0.462164i	−0.858513	−	0.512791i	$-0.828611\pi$
$647$	−16.1803	+	11.7557i	−0.636115	+	0.462164i	0.222398	+	0.974956i	$0.428611\pi$
$648$	−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	−0.993137	−	0.116955i	$-0.962687\pi$
$653$	−3.09017	+	9.51057i	−0.120928	+	0.372177i	0.872209	+	0.489133i	$0.162687\pi$
$654$		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	$-0.252657\pi$
$659$	36.0000			1.40236			0.701180	+	0.712984i	$0.252657\pi$
$660$		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	$-0.532924\pi$
$673$	21.0344	−	15.2824i	0.810818	−	0.589094i	0.914068	+	0.405562i	$0.132924\pi$
$674$	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	$-0.0394132\pi$
$677$	30.7426	+	22.3358i	1.18154	+	0.858436i	0.189192	+	0.981940i	$0.439413\pi$
$678$		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	−0.0666172	−	0.997779i	$-0.521221\pi$
$691$	22.6525	−	16.4580i	0.861741	−	0.626091i	0.928358	+	0.371687i	$0.121221\pi$
$692$	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	0.993476	+	0.114045i	$0.0363809\pi$
$701$	6.79837	+	20.9232i	0.256771	+	0.790260i	−0.736705	+	0.676215i	$0.763619\pi$
$702$		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	0.729246	−	0.684252i	$-0.239871\pi$
$709$	8.09017	+	5.87785i	0.303833	+	0.220747i	−0.425413	+	0.904999i	$0.639871\pi$
$710$	−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	$-0.900000\pi$
$719$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$720$	−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	−0.360579	−	0.932729i	$-0.617421\pi$
$733$	12.9787	−	39.9444i	0.479380	−	1.47538i	0.839959	−	0.542650i	$-0.182579\pi$
$734$	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	$-0.723440\pi$
$739$	−3.23607	+	2.35114i	−0.119041	+	0.0864881i	0.526672	+	0.850069i	$0.323440\pi$
$740$	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	$-0.562222\pi$
$743$	−32.3607	−	23.5114i	−1.18720	−	0.862550i	−0.992965	+	0.118405i	$0.962222\pi$
$744$		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	0.999839	−	0.0179203i	$-0.00570452\pi$
$751$	4.94427	+	15.2169i	0.180419	+	0.555273i	−0.819420	+	0.573193i	$0.805705\pi$
$752$	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	−0.672493	−	0.740103i	$-0.734777\pi$
$757$	−4.85410	+	3.52671i	−0.176425	+	0.128181i	0.496068	+	0.868284i	$0.334777\pi$
$758$	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	$-0.758014\pi$
$761$	−8.09017	+	5.87785i	−0.293268	+	0.213072i	0.431416	+	0.902153i	$0.358014\pi$
$762$		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	$-0.629834\pi$
$769$	−22.0000			−0.793340			−0.396670	+	0.917961i	$0.629834\pi$
$770$		0			0
$771$		0			0
$772$	−21.0344	+	15.2824i	−0.757046	+	0.550026i
$773$	4.32624	+	13.3148i	0.155604	+	0.478900i	0.998222	−	0.0596126i	$-0.0189865\pi$
$773$	4.32624	+	13.3148i	0.155604	+	0.478900i	−0.842618	+	0.538512i	$0.818987\pi$
$774$	−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	−0.970543	−	0.240929i	$-0.922548\pi$
$787$	−42.0689	−	30.5648i	−1.49959	−	1.08952i	−0.529051	−	0.848590i	$-0.677452\pi$
$788$	−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	0.616073	−	0.787689i	$-0.288723\pi$
$797$	1.61803	+	1.17557i	0.0573137	+	0.0416408i	−0.558760	+	0.829330i	$0.688723\pi$
$798$		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	$-0.402482\pi$
$809$	−14.5623	−	10.5801i	−0.511983	−	0.371978i	−0.813575	+	0.581459i	$0.802482\pi$
$810$	2.78115	−	8.55951i	0.0977198	−	0.300750i
$811$	−3.70820	−	11.4127i	−0.130213	−	0.400753i	0.864602	−	0.502457i	$-0.167571\pi$
$811$	−3.70820	−	11.4127i	−0.130213	−	0.400753i	−0.994815	+	0.101704i	$0.967571\pi$
$812$		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	0.805860	+	0.592106i	$0.201703\pi$
$821$	−5.56231	+	17.1190i	−0.194126	+	0.597458i	−0.999986	+	0.00535152i	$0.998297\pi$
$822$		0			0
$823$	29.1246	−	21.1603i	1.01522	−	0.737601i	0.0499226	−	0.998753i	$-0.484103\pi$
$823$	29.1246	−	21.1603i	1.01522	−	0.737601i	0.965298	+	0.261152i	$0.0841025\pi$
$824$	12.0000			0.418040
$825$		0			0
$826$		0			0
$827$	−9.70820	+	7.05342i	−0.337587	+	0.245272i	−0.743643	−	0.668577i	$-0.766904\pi$
$827$	−9.70820	+	7.05342i	−0.337587	+	0.245272i	0.406056	+	0.913848i	$0.366904\pi$
$828$	3.70820	+	11.4127i	0.128869	+	0.396618i
$829$	−0.618034	+	1.90211i	−0.0214652	+	0.0660631i	−0.961215	−	0.275799i	$-0.911058\pi$
$829$	−0.618034	+	1.90211i	−0.0214652	+	0.0660631i	0.939750	+	0.341862i	$0.111058\pi$
$830$	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	−0.963488	−	0.267752i	$-0.913719\pi$
$839$	−9.88854	−	30.4338i	−0.341390	−	1.05069i	0.622097	−	0.782940i	$-0.286281\pi$
$840$		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	$-0.310901\pi$
$853$	−1.61803	−	1.17557i	−0.0554004	−	0.0402508i	−0.615141	+	0.788417i	$0.710901\pi$
$854$		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	$-0.599470\pi$
$857$	−18.0000			−0.614868			−0.307434	+	0.951569i	$0.599470\pi$
$858$		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	0.531343	−	0.847157i	$-0.321688\pi$
$863$	−3.23607	−	2.35114i	−0.110157	−	0.0800338i	−0.641500	+	0.767123i	$0.721688\pi$
$864$		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	−0.997796	−	0.0663553i	$-0.978863\pi$
$877$	−6.79837	−	20.9232i	−0.229565	−	0.706528i	0.768231	−	0.640172i	$-0.221137\pi$
$878$	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	0.832748	−	0.553652i	$-0.186766\pi$
$883$	−4.94427	−	15.2169i	−0.166388	−	0.512090i	−0.999136	+	0.0415628i	$0.986766\pi$
$884$	−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	−0.0335664	−	0.999436i	$-0.510687\pi$
$887$	17.3050	−	53.2592i	0.581043	−	1.78827i	0.614610	−	0.788831i	$-0.289313\pi$
$888$		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	0.976719	−	0.214523i	$-0.0688195\pi$
$907$	32.3607	+	23.5114i	1.07452	+	0.780684i	0.0977997	+	0.995206i	$0.468820\pi$
$908$	−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	−0.689816	−	0.723984i	$-0.742309\pi$
$911$	−6.47214	+	4.70228i	−0.214431	+	0.155794i	0.475385	+	0.879778i	$0.342309\pi$
$912$		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	$-0.429548\pi$
$919$	−19.4164	−	14.1068i	−0.640488	−	0.465342i	−0.860018	+	0.510264i	$0.829548\pi$
$920$	−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	0.757875	−	0.652400i	$-0.226238\pi$
$929$	11.3262	+	8.22899i	0.371602	+	0.269985i	−0.386273	+	0.922384i	$0.626238\pi$
$930$		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	$-0.731246\pi$
$937$	−4.85410	+	3.52671i	−0.158577	+	0.115213i	0.505667	+	0.862729i	$0.331246\pi$
$938$		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	$-0.289622\pi$
$941$	1.61803	+	1.17557i	0.0527464	+	0.0383225i	−0.561100	+	0.827748i	$0.689622\pi$
$942$		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	0.486889	+	0.873464i	$0.338132\pi$
$953$	−12.9787	+	39.9444i	−0.420422	+	1.29393i	−0.907311	+	0.420461i	$0.861868\pi$
$954$	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	$-0.458942\pi$
$967$	8.00000			0.257263			0.128631	+	0.991692i	$0.458942\pi$
$968$		0			0
$969$		0			0
$970$	−8.09017	+	5.87785i	−0.259760	+	0.188726i
$971$	11.1246	+	34.2380i	0.357006	+	1.09875i	0.954837	+	0.297129i	$0.0960292\pi$
$971$	11.1246	+	34.2380i	0.357006	+	1.09875i	−0.597832	+	0.801622i	$0.703971\pi$
$972$		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	−0.709630	−	0.704575i	$-0.751138\pi$
$977$	−8.09017	+	5.87785i	−0.258827	+	0.188049i	0.450803	+	0.892624i	$0.351138\pi$
$978$		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	−0.968832	−	0.247720i	$-0.920319\pi$
$983$	−1.23607	+	3.80423i	−0.0394244	+	0.121336i	0.929407	+	0.369056i	$0.120319\pi$
$984$		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	0.426508	+	0.904484i	$0.359744\pi$
$997$	−14.2148	+	43.7486i	−0.450187	+	1.38553i	−0.876694	+	0.481048i	$0.840256\pi$
$998$	−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.a.366.1		4
11.2	odd	10		605.2.a.b.1.1		1
11.3	even	5	inner	605.2.g.a.511.1		4
11.4	even	5	inner	605.2.g.a.81.1		4
11.5	even	5	inner	605.2.g.a.251.1		4
11.6	odd	10		605.2.g.c.251.1		4
11.7	odd	10		605.2.g.c.81.1		4
11.8	odd	10		605.2.g.c.511.1		4
11.9	even	5		55.2.a.a.1.1	✓	1
11.10	odd	2		605.2.g.c.366.1		4
33.2	even	10		5445.2.a.i.1.1		1
33.20	odd	10		495.2.a.a.1.1		1
44.31	odd	10		880.2.a.h.1.1		1
44.35	even	10		9680.2.a.r.1.1		1
55.9	even	10		275.2.a.a.1.1		1
55.24	odd	10		3025.2.a.f.1.1		1
55.42	odd	20		275.2.b.b.199.2		2
55.53	odd	20		275.2.b.b.199.1		2
77.20	odd	10		2695.2.a.c.1.1		1
88.53	even	10		3520.2.a.p.1.1		1
88.75	odd	10		3520.2.a.n.1.1		1
132.119	even	10		7920.2.a.i.1.1		1
143.64	even	10		9295.2.a.b.1.1		1
165.53	even	20		2475.2.c.f.199.2		2
165.119	odd	10		2475.2.a.i.1.1		1
165.152	even	20		2475.2.c.f.199.1		2
220.119	odd	10		4400.2.a.p.1.1		1
220.163	even	20		4400.2.b.n.4049.2		2
220.207	even	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	11.9	even	5
275.2.a.a.1.1		1	55.9	even	10
275.2.b.b.199.1		2	55.53	odd	20
275.2.b.b.199.2		2	55.42	odd	20
495.2.a.a.1.1		1	33.20	odd	10
605.2.a.b.1.1		1	11.2	odd	10
605.2.g.a.81.1		4	11.4	even	5	inner
605.2.g.a.251.1		4	11.5	even	5	inner
605.2.g.a.366.1		4	1.1	even	1	trivial
605.2.g.a.511.1		4	11.3	even	5	inner
605.2.g.c.81.1		4	11.7	odd	10
605.2.g.c.251.1		4	11.6	odd	10
605.2.g.c.366.1		4	11.10	odd	2
605.2.g.c.511.1		4	11.8	odd	10
880.2.a.h.1.1		1	44.31	odd	10
2475.2.a.i.1.1		1	165.119	odd	10
2475.2.c.f.199.1		2	165.152	even	20
2475.2.c.f.199.2		2	165.53	even	20
2695.2.a.c.1.1		1	77.20	odd	10
3025.2.a.f.1.1		1	55.24	odd	10
3520.2.a.n.1.1		1	88.75	odd	10
3520.2.a.p.1.1		1	88.53	even	10
4400.2.a.p.1.1		1	220.119	odd	10
4400.2.b.n.4049.1		2	220.207	even	20
4400.2.b.n.4049.2		2	220.163	even	20
5445.2.a.i.1.1		1	33.2	even	10
7920.2.a.i.1.1		1	132.119	even	10
9295.2.a.b.1.1		1	143.64	even	10
9680.2.a.r.1.1		1	44.35	even	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 $\F_{q}$

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

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