LMFDB - Embedded newform 605.2.g.a.511.1

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			511.1
Root			$-0.309017 + 0.951057i$ of defining polynomial
Character	$\chi$	$=$	605.511
Dual form			605.2.g.a.251.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 + 0.951057i) q^{2} +(0.809017 - 0.587785i) q^{4} +(0.309017 - 0.951057i) q^{5} +(2.42705 + 1.76336i) q^{8} +(-0.927051 - 2.85317i) q^{9} +O(q^{10})$	\(q+(0.309017 + 0.951057i) q^{2} +(0.809017 - 0.587785i) q^{4} +(0.309017 - 0.951057i) q^{5} +(2.42705 + 1.76336i) q^{8} +(-0.927051 - 2.85317i) q^{9} +1.00000 q^{10} +(0.618034 + 1.90211i) q^{13} +(-0.309017 + 0.951057i) q^{16} +(1.85410 - 5.70634i) q^{17} +(2.42705 - 1.76336i) q^{18} +(3.23607 + 2.35114i) q^{19} +(-0.309017 - 0.951057i) q^{20} +4.00000 q^{23} +(-0.809017 - 0.587785i) q^{25} +(-1.61803 + 1.17557i) q^{26} +(-4.85410 + 3.52671i) q^{29} +(-2.47214 - 7.60845i) q^{31} +5.00000 q^{32} +6.00000 q^{34} +(-2.42705 - 1.76336i) q^{36} +(1.61803 - 1.17557i) q^{37} +(-1.23607 + 3.80423i) q^{38} +(2.42705 - 1.76336i) q^{40} +(-1.61803 - 1.17557i) q^{41} +4.00000 q^{43} -3.00000 q^{45} +(1.23607 + 3.80423i) q^{46} +(9.70820 + 7.05342i) q^{47} +(-2.16312 + 6.65740i) q^{49} +(0.309017 - 0.951057i) q^{50} +(1.61803 + 1.17557i) q^{52} +(-0.618034 - 1.90211i) q^{53} +(-4.85410 - 3.52671i) q^{58} +(-3.23607 + 2.35114i) q^{59} +(-3.09017 + 9.51057i) q^{61} +(6.47214 - 4.70228i) q^{62} +(2.16312 + 6.65740i) q^{64} +2.00000 q^{65} -16.0000 q^{67} +(-1.85410 - 5.70634i) q^{68} +(2.47214 - 7.60845i) q^{71} +(2.78115 - 8.55951i) q^{72} +(-11.3262 + 8.22899i) q^{73} +(1.61803 + 1.17557i) q^{74} +4.00000 q^{76} +(2.47214 + 7.60845i) q^{79} +(0.809017 + 0.587785i) q^{80} +(-7.28115 + 5.29007i) q^{81} +(0.618034 - 1.90211i) q^{82} +(-1.23607 + 3.80423i) q^{83} +(-4.85410 - 3.52671i) q^{85} +(1.23607 + 3.80423i) q^{86} +10.0000 q^{89} +(-0.927051 - 2.85317i) q^{90} +(3.23607 - 2.35114i) q^{92} +(-3.70820 + 11.4127i) q^{94} +(3.23607 - 2.35114i) q^{95} +(3.09017 + 9.51057i) q^{97} -7.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$

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 $

$2$	0.309017	+	0.951057i	0.218508	+	0.672499i	0.998886	+	0.0471903i	$0.0150267\pi$
$2$	0.309017	+	0.951057i	0.218508	+	0.672499i	−0.780378	+	0.625308i	$0.784973\pi$
$3$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$3$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$4$	0.809017	−	0.587785i	0.404508	−	0.293893i
$5$	0.309017	−	0.951057i	0.138197	−	0.425325i
$5$	0.309017	−	0.951057i	0.138197	−	0.425325i
$6$		0			0
$7$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$7$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$8$	2.42705	+	1.76336i	0.858092	+	0.623440i
$9$	−0.927051	−	2.85317i	−0.309017	−	0.951057i
$10$	1.00000			0.316228
$11$		0			0
$11$		0			0
$12$		0			0
$13$	0.618034	+	1.90211i	0.171412	+	0.527551i	0.999451	−	0.0331183i	$-0.0105438\pi$
$13$	0.618034	+	1.90211i	0.171412	+	0.527551i	−0.828040	+	0.560670i	$0.810544\pi$
$14$		0			0
$15$		0			0
$16$	−0.309017	+	0.951057i	−0.0772542	+	0.237764i
$17$	1.85410	−	5.70634i	0.449686	−	1.38399i	−0.427576	−	0.903979i	$-0.640633\pi$
$17$	1.85410	−	5.70634i	0.449686	−	1.38399i	0.877262	−	0.480011i	$-0.159367\pi$
$18$	2.42705	−	1.76336i	0.572061	−	0.415627i
$19$	3.23607	+	2.35114i	0.742405	+	0.539389i	0.893463	−	0.449136i	$-0.148268\pi$
$19$	3.23607	+	2.35114i	0.742405	+	0.539389i	−0.151058	+	0.988525i	$0.548268\pi$
$20$	−0.309017	−	0.951057i	−0.0690983	−	0.212663i
$21$		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
$25$	−0.809017	−	0.587785i	−0.161803	−	0.117557i
$26$	−1.61803	+	1.17557i	−0.317323	+	0.230548i
$27$		0			0
$28$		0			0
$29$	−4.85410	+	3.52671i	−0.901384	+	0.654894i	−0.938821	−	0.344405i	$-0.888081\pi$
$29$	−4.85410	+	3.52671i	−0.901384	+	0.654894i	0.0374370	+	0.999299i	$0.488081\pi$
$30$		0			0
$31$	−2.47214	−	7.60845i	−0.444009	−	1.36652i	−0.883567	−	0.468304i	$-0.844865\pi$
$31$	−2.47214	−	7.60845i	−0.444009	−	1.36652i	0.439558	−	0.898214i	$-0.355135\pi$
$32$	5.00000			0.883883
$33$		0			0
$34$	6.00000			1.02899
$35$		0			0
$36$	−2.42705	−	1.76336i	−0.404508	−	0.293893i
$37$	1.61803	−	1.17557i	0.266003	−	0.193263i	−0.446786	−	0.894641i	$-0.647432\pi$
$37$	1.61803	−	1.17557i	0.266003	−	0.193263i	0.712789	+	0.701378i	$0.247432\pi$
$38$	−1.23607	+	3.80423i	−0.200517	+	0.617127i
$39$		0			0
$40$	2.42705	−	1.76336i	0.383750	−	0.278811i
$41$	−1.61803	−	1.17557i	−0.252694	−	0.183593i	0.454226	−	0.890887i	$-0.349916\pi$
$41$	−1.61803	−	1.17557i	−0.252694	−	0.183593i	−0.706920	+	0.707293i	$0.749916\pi$
$42$		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
$46$	1.23607	+	3.80423i	0.182248	+	0.560903i
$47$	9.70820	+	7.05342i	1.41609	+	1.02885i	0.992402	+	0.123038i	$0.0392637\pi$
$47$	9.70820	+	7.05342i	1.41609	+	1.02885i	0.423685	+	0.905810i	$0.360736\pi$
$48$		0			0
$49$	−2.16312	+	6.65740i	−0.309017	+	0.951057i
$50$	0.309017	−	0.951057i	0.0437016	−	0.134500i
$51$		0			0
$52$	1.61803	+	1.17557i	0.224381	+	0.163022i
$53$	−0.618034	−	1.90211i	−0.0848935	−	0.261275i	0.899595	−	0.436726i	$-0.143862\pi$
$53$	−0.618034	−	1.90211i	−0.0848935	−	0.261275i	−0.984488	+	0.175450i	$0.943862\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		0			0
$58$	−4.85410	−	3.52671i	−0.637375	−	0.463080i
$59$	−3.23607	+	2.35114i	−0.421300	+	0.306092i	−0.778161	−	0.628065i	$-0.783847\pi$
$59$	−3.23607	+	2.35114i	−0.421300	+	0.306092i	0.356861	+	0.934158i	$0.383847\pi$
$60$		0			0
$61$	−3.09017	+	9.51057i	−0.395656	+	1.21770i	0.532794	+	0.846245i	$0.321142\pi$
$61$	−3.09017	+	9.51057i	−0.395656	+	1.21770i	−0.928450	+	0.371458i	$0.878858\pi$
$62$	6.47214	−	4.70228i	0.821962	−	0.597190i
$63$		0			0
$64$	2.16312	+	6.65740i	0.270390	+	0.832174i
$65$	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	$0.932131\pi$
$68$	−1.85410	−	5.70634i	−0.224843	−	0.691995i
$69$		0			0
$70$		0			0
$71$	2.47214	−	7.60845i	0.293389	−	0.902957i	−0.690369	−	0.723457i	$-0.742552\pi$
$71$	2.47214	−	7.60845i	0.293389	−	0.902957i	0.983758	−	0.179500i	$-0.0574480\pi$
$72$	2.78115	−	8.55951i	0.327762	−	1.00875i
$73$	−11.3262	+	8.22899i	−1.32564	+	0.963131i	−0.325792	+	0.945441i	$0.605631\pi$
$73$	−11.3262	+	8.22899i	−1.32564	+	0.963131i	−0.999844	+	0.0176895i	$0.994369\pi$
$74$	1.61803	+	1.17557i	0.188093	+	0.136657i
$75$		0			0
$76$	4.00000			0.458831
$77$		0			0
$78$		0			0
$79$	2.47214	+	7.60845i	0.278137	+	0.856018i	0.988372	+	0.152053i	$0.0485886\pi$
$79$	2.47214	+	7.60845i	0.278137	+	0.856018i	−0.710235	+	0.703964i	$0.751411\pi$
$80$	0.809017	+	0.587785i	0.0904508	+	0.0657164i
$81$	−7.28115	+	5.29007i	−0.809017	+	0.587785i
$82$	0.618034	−	1.90211i	0.0682504	−	0.210053i
$83$	−1.23607	+	3.80423i	−0.135676	+	0.417568i	−0.995695	−	0.0926948i	$-0.970452\pi$
$83$	−1.23607	+	3.80423i	−0.135676	+	0.417568i	0.860018	+	0.510263i	$0.170452\pi$
$84$		0			0
$85$	−4.85410	−	3.52671i	−0.526501	−	0.382526i
$86$	1.23607	+	3.80423i	0.133289	+	0.410220i
$87$		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	$0.322192\pi$
$90$	−0.927051	−	2.85317i	−0.0977198	−	0.300750i
$91$		0			0
$92$	3.23607	−	2.35114i	0.337383	−	0.245123i
$93$		0			0
$94$	−3.70820	+	11.4127i	−0.382472	+	1.17713i
$95$	3.23607	−	2.35114i	0.332014	−	0.241222i
$96$		0			0
$97$	3.09017	+	9.51057i	0.313759	+	0.965652i	0.976262	+	0.216592i	$0.0694942\pi$
$97$	3.09017	+	9.51057i	0.313759	+	0.965652i	−0.662503	+	0.749059i	$0.730506\pi$
$98$	−7.00000			−0.707107
$99$		0			0
$100$	−1.00000			−0.100000
$101$	−3.09017	−	9.51057i	−0.307483	−	0.946337i	−0.978739	−	0.205110i	$-0.934245\pi$
$101$	−3.09017	−	9.51057i	−0.307483	−	0.946337i	0.671255	−	0.741226i	$-0.265755\pi$
$102$		0			0
$103$	3.23607	−	2.35114i	0.318859	−	0.231665i	−0.416829	−	0.908985i	$-0.636859\pi$
$103$	3.23607	−	2.35114i	0.318859	−	0.231665i	0.735689	+	0.677320i	$0.236859\pi$
$104$	−1.85410	+	5.70634i	−0.181810	+	0.559553i
$105$		0			0
$106$	1.61803	−	1.17557i	0.157157	−	0.114182i
$107$	−9.70820	−	7.05342i	−0.938527	−	0.681880i	0.00953827	−	0.999955i	$-0.496964\pi$
$107$	−9.70820	−	7.05342i	−0.938527	−	0.681880i	−0.948066	+	0.318074i	$0.896964\pi$
$108$		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
$113$	4.85410	+	3.52671i	0.456636	+	0.331765i	0.792210	−	0.610249i	$-0.208930\pi$
$113$	4.85410	+	3.52671i	0.456636	+	0.331765i	−0.335575	+	0.942014i	$0.608930\pi$
$114$		0			0
$115$	1.23607	−	3.80423i	0.115264	−	0.354746i
$116$	−1.85410	+	5.70634i	−0.172149	+	0.529820i
$117$	4.85410	−	3.52671i	0.448762	−	0.326045i
$118$	−3.23607	−	2.35114i	−0.297904	−	0.216440i
$119$		0			0
$120$		0			0
$121$		0			0
$122$	−10.0000			−0.905357
$123$		0			0
$124$	−6.47214	−	4.70228i	−0.581215	−	0.422277i
$125$	−0.809017	+	0.587785i	−0.0723607	+	0.0525731i
$126$		0			0
$127$	4.94427	−	15.2169i	0.438733	−	1.35028i	−0.450479	−	0.892787i	$-0.648747\pi$
$127$	4.94427	−	15.2169i	0.438733	−	1.35028i	0.889212	−	0.457495i	$-0.151253\pi$
$128$	2.42705	−	1.76336i	0.214523	−	0.155860i
$129$		0			0
$130$	0.618034	+	1.90211i	0.0542052	+	0.166826i
$131$	−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
$134$	−4.94427	−	15.2169i	−0.427120	−	1.31454i
$135$		0			0
$136$	14.5623	−	10.5801i	1.24871	−	0.907239i
$137$	5.56231	−	17.1190i	0.475220	−	1.46258i	−0.370441	−	0.928856i	$-0.620793\pi$
$137$	5.56231	−	17.1190i	0.475220	−	1.46258i	0.845661	−	0.533720i	$-0.179207\pi$
$138$		0			0
$139$	−9.70820	+	7.05342i	−0.823439	+	0.598264i	−0.917696	−	0.397284i	$-0.869953\pi$
$139$	−9.70820	+	7.05342i	−0.823439	+	0.598264i	0.0942564	+	0.995548i	$0.469953\pi$
$140$		0			0
$141$		0			0
$142$	8.00000			0.671345
$143$		0			0
$144$	3.00000			0.250000
$145$	1.85410	+	5.70634i	0.153975	+	0.473886i
$146$	−11.3262	−	8.22899i	−0.937366	−	0.681036i
$147$		0			0
$148$	0.618034	−	1.90211i	0.0508021	−	0.156353i
$149$	−3.09017	+	9.51057i	−0.253157	+	0.779136i	0.741031	+	0.671471i	$0.234337\pi$
$149$	−3.09017	+	9.51057i	−0.253157	+	0.779136i	−0.994187	+	0.107665i	$0.965663\pi$
$150$		0			0
$151$	−6.47214	−	4.70228i	−0.526695	−	0.382666i	0.292425	−	0.956288i	$-0.405538\pi$
$151$	−6.47214	−	4.70228i	−0.526695	−	0.382666i	−0.819120	+	0.573622i	$0.805538\pi$
$152$	3.70820	+	11.4127i	0.300775	+	0.925690i
$153$	−18.0000			−1.45521
$154$		0			0
$155$	−8.00000			−0.642575
$156$		0			0
$157$	1.61803	+	1.17557i	0.129133	+	0.0938207i	0.650477	−	0.759526i	$-0.274569\pi$
$157$	1.61803	+	1.17557i	0.129133	+	0.0938207i	−0.521344	+	0.853347i	$0.674569\pi$
$158$	−6.47214	+	4.70228i	−0.514895	+	0.374093i
$159$		0			0
$160$	1.54508	−	4.75528i	0.122150	−	0.375938i
$161$		0			0
$162$	−7.28115	−	5.29007i	−0.572061	−	0.415627i
$163$	4.94427	+	15.2169i	0.387265	+	1.19188i	0.934824	+	0.355112i	$0.115557\pi$
$163$	4.94427	+	15.2169i	0.387265	+	1.19188i	−0.547558	+	0.836768i	$0.684443\pi$
$164$	−2.00000			−0.156174
$165$		0			0
$166$	−4.00000			−0.310460
$167$	−2.47214	−	7.60845i	−0.191300	−	0.588760i	−1.00000		0.000538710i	$-0.999829\pi$
$167$	−2.47214	−	7.60845i	−0.191300	−	0.588760i	0.808700	−	0.588221i	$-0.200171\pi$
$168$		0			0
$169$	7.28115	−	5.29007i	0.560089	−	0.406928i
$170$	1.85410	−	5.70634i	0.142203	−	0.437656i
$171$	3.70820	−	11.4127i	0.283573	−	0.872749i
$172$	3.23607	−	2.35114i	0.246748	−	0.179273i
$173$	4.85410	+	3.52671i	0.369051	+	0.268131i	0.756817	−	0.653627i	$-0.226753\pi$
$173$	4.85410	+	3.52671i	0.369051	+	0.268131i	−0.387767	+	0.921758i	$0.626753\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$	3.09017	+	9.51057i	0.231618	+	0.712847i
$179$	−3.23607	−	2.35114i	−0.241875	−	0.175733i	0.460243	−	0.887793i	$-0.347762\pi$
$179$	−3.23607	−	2.35114i	−0.241875	−	0.175733i	−0.702118	+	0.712060i	$0.747762\pi$
$180$	−2.42705	+	1.76336i	−0.180902	+	0.131433i
$181$	−3.09017	+	9.51057i	−0.229691	+	0.706915i	0.768091	+	0.640341i	$0.221207\pi$
$181$	−3.09017	+	9.51057i	−0.229691	+	0.706915i	−0.997781	+	0.0665740i	$0.978793\pi$
$182$		0			0
$183$		0			0
$184$	9.70820	+	7.05342i	0.715698	+	0.519985i
$185$	−0.618034	−	1.90211i	−0.0454388	−	0.139846i
$186$		0			0
$187$		0			0
$188$	12.0000			0.875190
$189$		0			0
$190$	3.23607	+	2.35114i	0.234769	+	0.170570i
$191$	−6.47214	+	4.70228i	−0.468307	+	0.340245i	−0.796781	−	0.604268i	$-0.793466\pi$
$191$	−6.47214	+	4.70228i	−0.468307	+	0.340245i	0.328474	+	0.944513i	$0.393466\pi$
$192$		0			0
$193$	−8.03444	+	24.7275i	−0.578332	+	1.77992i	0.0462111	+	0.998932i	$0.485285\pi$
$193$	−8.03444	+	24.7275i	−0.578332	+	1.77992i	−0.624543	+	0.780991i	$0.714715\pi$
$194$	−8.09017	+	5.87785i	−0.580840	+	0.422005i
$195$		0			0
$196$	2.16312	+	6.65740i	0.154508	+	0.475528i
$197$	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	$0.5\pi$
$200$	−0.927051	−	2.85317i	−0.0655524	−	0.201750i
$201$		0			0
$202$	8.09017	−	5.87785i	0.569222	−	0.413564i
$203$		0			0
$204$		0			0
$205$	−1.61803	+	1.17557i	−0.113008	+	0.0821054i
$206$	3.23607	+	2.35114i	0.225468	+	0.163812i
$207$	−3.70820	−	11.4127i	−0.257738	−	0.793236i
$208$	−2.00000			−0.138675
$209$		0			0
$210$		0			0
$211$	1.23607	+	3.80423i	0.0850944	+	0.261894i	0.984546	−	0.175127i	$-0.0560336\pi$
$211$	1.23607	+	3.80423i	0.0850944	+	0.261894i	−0.899451	+	0.437021i	$0.856034\pi$
$212$	−1.61803	−	1.17557i	−0.111127	−	0.0807385i
$213$		0			0
$214$	3.70820	−	11.4127i	0.253488	−	0.780155i
$215$	1.23607	−	3.80423i	0.0842991	−	0.259446i
$216$		0			0
$217$		0			0
$218$	−5.56231	−	17.1190i	−0.376727	−	1.15945i
$219$		0			0
$220$		0			0
$221$	12.0000			0.807207
$222$		0			0
$223$	3.23607	+	2.35114i	0.216703	+	0.157444i	0.690841	−	0.723006i	$-0.257240\pi$
$223$	3.23607	+	2.35114i	0.216703	+	0.157444i	−0.474138	+	0.880450i	$0.657240\pi$
$224$		0			0
$225$	−0.927051	+	2.85317i	−0.0618034	+	0.190211i
$226$	−1.85410	+	5.70634i	−0.123333	+	0.379580i
$227$	16.1803	−	11.7557i	1.07393	−	0.780254i	0.0973129	−	0.995254i	$-0.468975\pi$
$227$	16.1803	−	11.7557i	1.07393	−	0.780254i	0.976614	+	0.215000i	$0.0689752\pi$
$228$		0			0
$229$	−3.09017	−	9.51057i	−0.204204	−	0.628476i	−0.999745	−	0.0225760i	$-0.992813\pi$
$229$	−3.09017	−	9.51057i	−0.204204	−	0.628476i	0.795541	−	0.605900i	$-0.207187\pi$
$230$	4.00000			0.263752
$231$		0			0
$232$	−18.0000			−1.18176
$233$	1.85410	+	5.70634i	0.121466	+	0.373835i	0.993241	−	0.116073i	$-0.0370306\pi$
$233$	1.85410	+	5.70634i	0.121466	+	0.373835i	−0.871774	+	0.489907i	$0.837031\pi$
$234$	4.85410	+	3.52671i	0.317323	+	0.230548i
$235$	9.70820	−	7.05342i	0.633293	−	0.460115i
$236$	−1.23607	+	3.80423i	−0.0804612	+	0.247634i
$237$		0			0
$238$		0			0
$239$	−6.47214	−	4.70228i	−0.418648	−	0.304165i	0.358446	−	0.933551i	$-0.383307\pi$
$239$	−6.47214	−	4.70228i	−0.418648	−	0.304165i	−0.777093	+	0.629385i	$0.783307\pi$
$240$		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
$244$	3.09017	+	9.51057i	0.197828	+	0.608852i
$245$	5.66312	+	4.11450i	0.361803	+	0.262866i
$246$		0			0
$247$	−2.47214	+	7.60845i	−0.157298	+	0.484114i
$248$	7.41641	−	22.8254i	0.470942	−	1.44941i
$249$		0			0
$250$	−0.809017	−	0.587785i	−0.0511667	−	0.0371748i
$251$	3.70820	+	11.4127i	0.234060	+	0.720362i	0.997245	+	0.0741818i	$0.0236345\pi$
$251$	3.70820	+	11.4127i	0.234060	+	0.720362i	−0.763185	+	0.646180i	$0.776365\pi$
$252$		0			0
$253$		0			0
$254$	16.0000			1.00393
$255$		0			0
$256$	13.7533	+	9.99235i	0.859581	+	0.624522i
$257$	−14.5623	+	10.5801i	−0.908372	+	0.659971i	−0.940603	−	0.339510i	$-0.889739\pi$
$257$	−14.5623	+	10.5801i	−0.908372	+	0.659971i	0.0322308	+	0.999480i	$0.489739\pi$
$258$		0			0
$259$		0			0
$260$	1.61803	−	1.17557i	0.100346	−	0.0729058i
$261$	14.5623	+	10.5801i	0.901384	+	0.654894i
$262$	−3.70820	−	11.4127i	−0.229094	−	0.705078i
$263$	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
$268$	−12.9443	+	9.40456i	−0.790697	+	0.574475i
$269$	−5.56231	+	17.1190i	−0.339140	+	1.04376i	0.625507	+	0.780219i	$0.284892\pi$
$269$	−5.56231	+	17.1190i	−0.339140	+	1.04376i	−0.964647	+	0.263546i	$0.915108\pi$
$270$		0			0
$271$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$271$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$272$	4.85410	+	3.52671i	0.294323	+	0.213838i
$273$		0			0
$274$	18.0000			1.08742
$275$		0			0
$276$		0			0
$277$	3.09017	+	9.51057i	0.185670	+	0.571434i	0.999959	−	0.00902525i	$-0.00287287\pi$
$277$	3.09017	+	9.51057i	0.185670	+	0.571434i	−0.814289	+	0.580460i	$0.802873\pi$
$278$	−9.70820	−	7.05342i	−0.582259	−	0.423036i
$279$	−19.4164	+	14.1068i	−1.16243	+	0.844555i
$280$		0			0
$281$	5.56231	−	17.1190i	0.331819	−	1.02123i	−0.636448	−	0.771319i	$-0.719597\pi$
$281$	5.56231	−	17.1190i	0.331819	−	1.02123i	0.968268	−	0.249916i	$-0.0804029\pi$
$282$		0			0
$283$	−3.23607	−	2.35114i	−0.192364	−	0.139761i	0.487434	−	0.873160i	$-0.337933\pi$
$283$	−3.23607	−	2.35114i	−0.192364	−	0.139761i	−0.679799	+	0.733399i	$0.737933\pi$
$284$	−2.47214	−	7.60845i	−0.146694	−	0.451479i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−4.63525	−	14.2658i	−0.273135	−	0.840623i
$289$	−15.3713	−	11.1679i	−0.904195	−	0.656936i
$290$	−4.85410	+	3.52671i	−0.285043	+	0.207096i
$291$		0			0
$292$	−4.32624	+	13.3148i	−0.253174	+	0.779189i
$293$	−8.09017	+	5.87785i	−0.472633	+	0.343388i	−0.798466	−	0.602039i	$-0.794355\pi$
$293$	−8.09017	+	5.87785i	−0.472633	+	0.343388i	0.325834	+	0.945427i	$0.394355\pi$
$294$		0			0
$295$	1.23607	+	3.80423i	0.0719667	+	0.221491i
$296$	6.00000			0.348743
$297$		0			0
$298$	−10.0000			−0.579284
$299$	2.47214	+	7.60845i	0.142967	+	0.440008i
$300$		0			0
$301$		0			0
$302$	2.47214	−	7.60845i	0.142255	−	0.437817i
$303$		0			0
$304$	−3.23607	+	2.35114i	−0.185601	+	0.134847i
$305$	8.09017	+	5.87785i	0.463242	+	0.336565i
$306$	−5.56231	−	17.1190i	−0.317976	−	0.978629i
$307$	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
$310$	−2.47214	−	7.60845i	−0.140408	−	0.432131i
$311$	19.4164	+	14.1068i	1.10100	+	0.799926i	0.981223	−	0.192875i	$-0.0617811\pi$
$311$	19.4164	+	14.1068i	1.10100	+	0.799926i	0.119780	+	0.992800i	$0.461781\pi$
$312$		0			0
$313$	−6.79837	+	20.9232i	−0.384267	+	1.18265i	0.552744	+	0.833351i	$0.313581\pi$
$313$	−6.79837	+	20.9232i	−0.384267	+	1.18265i	−0.937011	+	0.349300i	$0.886419\pi$
$314$	−0.618034	+	1.90211i	−0.0348777	+	0.107342i
$315$		0			0
$316$	6.47214	+	4.70228i	0.364086	+	0.264524i
$317$	−5.56231	−	17.1190i	−0.312410	−	0.961500i	−0.976807	−	0.214120i	$-0.931312\pi$
$317$	−5.56231	−	17.1190i	−0.312410	−	0.961500i	0.664397	−	0.747380i	$-0.268688\pi$
$318$		0			0
$319$		0			0
$320$	7.00000			0.391312
$321$		0			0
$322$		0			0
$323$	19.4164	−	14.1068i	1.08036	−	0.784926i
$324$	−2.78115	+	8.55951i	−0.154508	+	0.475528i
$325$	0.618034	−	1.90211i	0.0342824	−	0.105510i
$326$	−12.9443	+	9.40456i	−0.716917	+	0.520871i
$327$		0			0
$328$	−1.85410	−	5.70634i	−0.102376	−	0.315080i
$329$		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	$0.464937\pi$
$332$	1.23607	+	3.80423i	0.0678380	+	0.208784i
$333$	−4.85410	−	3.52671i	−0.266003	−	0.193263i
$334$	6.47214	−	4.70228i	0.354140	−	0.257297i
$335$	−4.94427	+	15.2169i	−0.270134	+	0.831388i
$336$		0			0
$337$	−4.85410	+	3.52671i	−0.264420	+	0.192112i	−0.712093	−	0.702085i	$-0.752253\pi$
$337$	−4.85410	+	3.52671i	−0.264420	+	0.192112i	0.447673	+	0.894197i	$0.352253\pi$
$338$	7.28115	+	5.29007i	0.396043	+	0.287742i
$339$		0			0
$340$	−6.00000			−0.325396
$341$		0			0
$342$	12.0000			0.648886
$343$		0			0
$344$	9.70820	+	7.05342i	0.523431	+	0.380295i
$345$		0			0
$346$	−1.85410	+	5.70634i	−0.0996771	+	0.306775i
$347$	−1.23607	+	3.80423i	−0.0663556	+	0.204222i	−0.978737	−	0.205120i	$-0.934242\pi$
$347$	−1.23607	+	3.80423i	−0.0663556	+	0.204222i	0.912381	+	0.409342i	$0.134242\pi$
$348$		0			0
$349$	8.09017	+	5.87785i	0.433057	+	0.314634i	0.782870	−	0.622185i	$-0.213755\pi$
$349$	8.09017	+	5.87785i	0.433057	+	0.314634i	−0.349813	+	0.936819i	$0.613755\pi$
$350$		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
$355$	−6.47214	−	4.70228i	−0.343505	−	0.249571i
$356$	8.09017	−	5.87785i	0.428778	−	0.311526i
$357$		0			0
$358$	1.23607	−	3.80423i	0.0653282	−	0.201060i
$359$	25.8885	−	18.8091i	1.36635	−	0.992708i	0.368332	−	0.929694i	$-0.379929\pi$
$359$	25.8885	−	18.8091i	1.36635	−	0.992708i	0.998013	−	0.0630137i	$-0.0200712\pi$
$360$	−7.28115	−	5.29007i	−0.383750	−	0.278811i
$361$	−0.927051	−	2.85317i	−0.0487922	−	0.150167i
$362$	−10.0000			−0.525588
$363$		0			0
$364$		0			0
$365$	4.32624	+	13.3148i	0.226446	+	0.696928i
$366$		0			0
$367$	−3.23607	+	2.35114i	−0.168921	+	0.122729i	−0.669034	−	0.743232i	$-0.733292\pi$
$367$	−3.23607	+	2.35114i	−0.168921	+	0.122729i	0.500113	+	0.865960i	$0.333292\pi$
$368$	−1.23607	+	3.80423i	−0.0644345	+	0.198309i
$369$	−1.85410	+	5.70634i	−0.0965207	+	0.297060i
$370$	1.61803	−	1.17557i	0.0841176	−	0.0611150i
$371$		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
$376$	11.1246	+	34.2380i	0.573708	+	1.76569i
$377$	−9.70820	−	7.05342i	−0.499998	−	0.363270i
$378$		0			0
$379$	6.18034	−	19.0211i	0.317463	−	0.977050i	−0.657266	−	0.753659i	$-0.728287\pi$
$379$	6.18034	−	19.0211i	0.317463	−	0.977050i	0.974729	−	0.223391i	$-0.0717128\pi$
$380$	1.23607	−	3.80423i	0.0634089	−	0.195153i
$381$		0			0
$382$	−6.47214	−	4.70228i	−0.331143	−	0.240590i
$383$	−3.70820	−	11.4127i	−0.189480	−	0.583161i	0.810516	−	0.585716i	$-0.199187\pi$
$383$	−3.70820	−	11.4127i	−0.189480	−	0.583161i	−0.999997	+	0.00255538i	$0.999187\pi$
$384$		0			0
$385$		0			0
$386$	−26.0000			−1.32337
$387$	−3.70820	−	11.4127i	−0.188499	−	0.580139i
$388$	8.09017	+	5.87785i	0.410716	+	0.298403i
$389$	−4.85410	+	3.52671i	−0.246113	+	0.178811i	−0.704002	−	0.710198i	$-0.748606\pi$
$389$	−4.85410	+	3.52671i	−0.246113	+	0.178811i	0.457890	+	0.889009i	$0.348606\pi$
$390$		0			0
$391$	7.41641	−	22.8254i	0.375064	−	1.15433i
$392$	−16.9894	+	12.3435i	−0.858092	+	0.623440i
$393$		0			0
$394$	0.618034	+	1.90211i	0.0311361	+	0.0958271i
$395$	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
$400$	0.809017	−	0.587785i	0.0404508	−	0.0293893i
$401$	0.618034	−	1.90211i	0.0308631	−	0.0949870i	−0.934438	−	0.356125i	$-0.884098\pi$
$401$	0.618034	−	1.90211i	0.0308631	−	0.0949870i	0.965301	+	0.261138i	$0.0840977\pi$
$402$		0			0
$403$	12.9443	−	9.40456i	0.644800	−	0.468475i
$404$	−8.09017	−	5.87785i	−0.402501	−	0.292434i
$405$	2.78115	+	8.55951i	0.138197	+	0.425325i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	−1.85410	−	5.70634i	−0.0916794	−	0.282160i	0.894695	−	0.446678i	$-0.147393\pi$
$409$	−1.85410	−	5.70634i	−0.0916794	−	0.282160i	−0.986374	+	0.164518i	$0.947393\pi$
$410$	−1.61803	−	1.17557i	−0.0799090	−	0.0580573i
$411$		0			0
$412$	1.23607	−	3.80423i	0.0608967	−	0.187421i
$413$		0			0
$414$	9.70820	−	7.05342i	0.477132	−	0.346657i
$415$	3.23607	+	2.35114i	0.158852	+	0.115413i
$416$	3.09017	+	9.51057i	0.151508	+	0.466294i
$417$		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
$421$	−4.85410	−	3.52671i	−0.236574	−	0.171881i	0.463181	−	0.886264i	$-0.346708\pi$
$421$	−4.85410	−	3.52671i	−0.236574	−	0.171881i	−0.699756	+	0.714382i	$0.746708\pi$
$422$	−3.23607	+	2.35114i	−0.157529	+	0.114452i
$423$	11.1246	−	34.2380i	0.540897	−	1.66471i
$424$	1.85410	−	5.70634i	0.0900432	−	0.277124i
$425$	−4.85410	+	3.52671i	−0.235459	+	0.171071i
$426$		0			0
$427$		0			0
$428$	−12.0000			−0.580042
$429$		0			0
$430$	4.00000			0.192897
$431$	−7.41641	−	22.8254i	−0.357236	−	1.09946i	−0.954702	−	0.297564i	$-0.903826\pi$
$431$	−7.41641	−	22.8254i	−0.357236	−	1.09946i	0.597466	−	0.801894i	$-0.296174\pi$
$432$		0			0
$433$	17.7984	−	12.9313i	0.855335	−	0.621437i	−0.0712766	−	0.997457i	$-0.522707\pi$
$433$	17.7984	−	12.9313i	0.855335	−	0.621437i	0.926612	+	0.376019i	$0.122707\pi$
$434$		0			0
$435$		0			0
$436$	−14.5623	+	10.5801i	−0.697408	+	0.506697i
$437$	12.9443	+	9.40456i	0.619208	+	0.449881i
$438$		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
$442$	3.70820	+	11.4127i	0.176381	+	0.542846i
$443$	−6.47214	−	4.70228i	−0.307500	−	0.223412i	0.423323	−	0.905979i	$-0.360864\pi$
$443$	−6.47214	−	4.70228i	−0.307500	−	0.223412i	−0.730823	+	0.682567i	$0.760864\pi$
$444$		0			0
$445$	3.09017	−	9.51057i	0.146488	−	0.450844i
$446$	−1.23607	+	3.80423i	−0.0585295	+	0.180135i
$447$		0			0
$448$		0			0
$449$	0.618034	+	1.90211i	0.0291668	+	0.0897663i	0.964580	−	0.263790i	$-0.0849724\pi$
$449$	0.618034	+	1.90211i	0.0291668	+	0.0897663i	−0.935413	+	0.353556i	$0.884972\pi$
$450$	−3.00000			−0.141421
$451$		0			0
$452$	6.00000			0.282216
$453$		0			0
$454$	16.1803	+	11.7557i	0.759381	+	0.551723i
$455$		0			0
$456$		0			0
$457$	−8.03444	+	24.7275i	−0.375835	+	1.15670i	0.567078	+	0.823664i	$0.308074\pi$
$457$	−8.03444	+	24.7275i	−0.375835	+	1.15670i	−0.942913	+	0.333038i	$0.891926\pi$
$458$	8.09017	−	5.87785i	0.378029	−	0.274654i
$459$		0			0
$460$	−1.23607	−	3.80423i	−0.0576320	−	0.177373i
$461$	−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	$0.815420\pi$
$464$	−1.85410	−	5.70634i	−0.0860745	−	0.264910i
$465$		0			0
$466$	−4.85410	+	3.52671i	−0.224862	+	0.163372i
$467$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$467$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$468$	1.85410	−	5.70634i	0.0857059	−	0.263776i
$469$		0			0
$470$	9.70820	+	7.05342i	0.447806	+	0.325350i
$471$		0			0
$472$	−12.0000			−0.552345
$473$		0			0
$474$		0			0
$475$	−1.23607	−	3.80423i	−0.0567147	−	0.174550i
$476$		0			0
$477$	−4.85410	+	3.52671i	−0.222254	+	0.161477i
$478$	2.47214	−	7.60845i	0.113073	−	0.348003i
$479$	7.41641	−	22.8254i	0.338864	−	1.04292i	−0.625923	−	0.779885i	$-0.715277\pi$
$479$	7.41641	−	22.8254i	0.338864	−	1.04292i	0.964787	−	0.263032i	$-0.0847225\pi$
$480$		0			0
$481$	3.23607	+	2.35114i	0.147552	+	0.107203i
$482$	3.09017	+	9.51057i	0.140753	+	0.433194i
$483$		0			0
$484$		0			0
$485$	10.0000			0.454077
$486$		0			0
$487$	−22.6525	−	16.4580i	−1.02648	−	0.745783i	−0.0588802	−	0.998265i	$-0.518753\pi$
$487$	−22.6525	−	16.4580i	−1.02648	−	0.745783i	−0.967601	+	0.252482i	$0.918753\pi$
$488$	−24.2705	+	17.6336i	−1.09867	+	0.798234i
$489$		0			0
$490$	−2.16312	+	6.65740i	−0.0977198	+	0.300750i
$491$	22.6525	−	16.4580i	1.02229	−	0.742739i	0.0555405	−	0.998456i	$-0.482312\pi$
$491$	22.6525	−	16.4580i	1.02229	−	0.742739i	0.966751	+	0.255718i	$0.0823118\pi$
$492$		0			0
$493$	11.1246	+	34.2380i	0.501027	+	1.54200i
$494$	−8.00000			−0.359937
$495$		0			0
$496$	8.00000			0.359211
$497$		0			0
$498$		0			0
$499$	29.1246	−	21.1603i	1.30380	−	0.947264i	0.303812	−	0.952732i	$-0.401741\pi$
$499$	29.1246	−	21.1603i	1.30380	−	0.947264i	0.999985	+	0.00546838i	$0.00174065\pi$
$500$	−0.309017	+	0.951057i	−0.0138197	+	0.0425325i
$501$		0			0
$502$	−9.70820	+	7.05342i	−0.433298	+	0.314810i
$503$	12.9443	+	9.40456i	0.577157	+	0.419329i	0.837698	−	0.546134i	$-0.183901\pi$
$503$	12.9443	+	9.40456i	0.577157	+	0.419329i	−0.260541	+	0.965463i	$0.583901\pi$
$504$		0			0
$505$	−10.0000			−0.444994
$506$		0			0
$507$		0			0
$508$	−4.94427	−	15.2169i	−0.219367	−	0.675141i
$509$	−11.3262	−	8.22899i	−0.502027	−	0.364744i	0.307764	−	0.951463i	$-0.400419\pi$
$509$	−11.3262	−	8.22899i	−0.502027	−	0.364744i	−0.809791	+	0.586719i	$0.800419\pi$
$510$		0			0
$511$		0			0
$512$	−3.39919	+	10.4616i	−0.150224	+	0.462343i
$513$		0			0
$514$	−14.5623	−	10.5801i	−0.642316	−	0.466670i
$515$	−1.23607	−	3.80423i	−0.0544677	−	0.167634i
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$	4.85410	+	3.52671i	0.212866	+	0.154657i
$521$	4.85410	−	3.52671i	0.212662	−	0.154508i	−0.476355	−	0.879253i	$-0.658042\pi$
$521$	4.85410	−	3.52671i	0.212662	−	0.154508i	0.689017	+	0.724745i	$0.258042\pi$
$522$	−5.56231	+	17.1190i	−0.243456	+	0.749279i
$523$	−6.18034	+	19.0211i	−0.270247	+	0.831736i	0.720190	+	0.693776i	$0.244054\pi$
$523$	−6.18034	+	19.0211i	−0.270247	+	0.831736i	−0.990438	+	0.137960i	$0.955946\pi$
$524$	−9.70820	+	7.05342i	−0.424105	+	0.308130i
$525$		0			0
$526$	7.41641	+	22.8254i	0.323371	+	0.995233i
$527$	−48.0000			−2.09091
$528$		0			0
$529$	−7.00000			−0.304348
$530$	−0.618034	−	1.90211i	−0.0268457	−	0.0826225i
$531$	9.70820	+	7.05342i	0.421300	+	0.306092i
$532$		0			0
$533$	1.23607	−	3.80423i	0.0535400	−	0.164779i
$534$		0			0
$535$	−9.70820	+	7.05342i	−0.419722	+	0.304946i
$536$	−38.8328	−	28.2137i	−1.67732	−	1.21865i
$537$		0			0
$538$	−18.0000			−0.776035
$539$		0			0
$540$		0			0
$541$	−10.5066	−	32.3359i	−0.451713	−	1.39023i	−0.874951	−	0.484211i	$-0.839107\pi$
$541$	−10.5066	−	32.3359i	−0.451713	−	1.39023i	0.423238	−	0.906019i	$-0.360893\pi$
$542$		0			0
$543$		0			0
$544$	9.27051	−	28.5317i	0.397470	−	1.22329i
$545$	−5.56231	+	17.1190i	−0.238263	+	0.733298i
$546$		0			0
$547$	−9.70820	−	7.05342i	−0.415093	−	0.301583i	0.360568	−	0.932733i	$-0.382583\pi$
$547$	−9.70820	−	7.05342i	−0.415093	−	0.301583i	−0.775660	+	0.631151i	$0.782583\pi$
$548$	−5.56231	−	17.1190i	−0.237610	−	0.731288i
$549$	30.0000			1.28037
$550$		0			0
$551$	−24.0000			−1.02243
$552$		0			0
$553$		0			0
$554$	−8.09017	+	5.87785i	−0.343718	+	0.249726i
$555$		0			0
$556$	−3.70820	+	11.4127i	−0.157263	+	0.484005i
$557$	−8.09017	+	5.87785i	−0.342792	+	0.249053i	−0.745839	−	0.666127i	$-0.767951\pi$
$557$	−8.09017	+	5.87785i	−0.342792	+	0.249053i	0.403047	+	0.915179i	$0.367951\pi$
$558$	−19.4164	−	14.1068i	−0.821962	−	0.597190i
$559$	2.47214	+	7.60845i	0.104560	+	0.321803i
$560$		0			0
$561$		0			0
$562$	18.0000			0.759284
$563$	11.1246	+	34.2380i	0.468846	+	1.44296i	0.854080	+	0.520142i	$0.174121\pi$
$563$	11.1246	+	34.2380i	0.468846	+	1.44296i	−0.385233	+	0.922819i	$0.625879\pi$
$564$		0			0
$565$	4.85410	−	3.52671i	0.204214	−	0.148370i
$566$	1.23607	−	3.80423i	0.0519558	−	0.159904i
$567$		0			0
$568$	19.4164	−	14.1068i	0.814694	−	0.591910i
$569$	−21.0344	−	15.2824i	−0.881810	−	0.640672i	0.0519200	−	0.998651i	$-0.483466\pi$
$569$	−21.0344	−	15.2824i	−0.881810	−	0.640672i	−0.933730	+	0.357979i	$0.883466\pi$
$570$		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
$575$	−3.23607	−	2.35114i	−0.134953	−	0.0980494i
$576$	16.9894	−	12.3435i	0.707890	−	0.514312i
$577$	−6.79837	+	20.9232i	−0.283020	+	0.871046i	0.703965	+	0.710235i	$0.251411\pi$
$577$	−6.79837	+	20.9232i	−0.283020	+	0.871046i	−0.986985	+	0.160811i	$0.948589\pi$
$578$	5.87132	−	18.0701i	0.244215	−	0.751616i
$579$		0			0
$580$	4.85410	+	3.52671i	0.201556	+	0.146439i
$581$		0			0
$582$		0			0
$583$		0			0
$584$	−42.0000			−1.73797
$585$	−1.85410	−	5.70634i	−0.0766577	−	0.235928i
$586$	−8.09017	−	5.87785i	−0.334202	−	0.242812i
$587$	19.4164	−	14.1068i	0.801401	−	0.582252i	−0.109924	−	0.993940i	$-0.535061\pi$
$587$	19.4164	−	14.1068i	0.801401	−	0.582252i	0.911325	+	0.411688i	$0.135061\pi$
$588$		0			0
$589$	9.88854	−	30.4338i	0.407450	−	1.25400i
$590$	−3.23607	+	2.35114i	−0.133227	+	0.0967949i
$591$		0			0
$592$	0.618034	+	1.90211i	0.0254010	+	0.0781764i
$593$	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
$596$	3.09017	+	9.51057i	0.126578	+	0.389568i
$597$		0			0
$598$	−6.47214	+	4.70228i	−0.264665	+	0.192291i
$599$	7.41641	−	22.8254i	0.303026	−	0.932619i	−0.677380	−	0.735633i	$-0.736885\pi$
$599$	7.41641	−	22.8254i	0.303026	−	0.932619i	0.980406	−	0.196986i	$-0.0631152\pi$
$600$		0			0
$601$	−1.61803	+	1.17557i	−0.0660010	+	0.0479525i	−0.620297	−	0.784367i	$-0.712988\pi$
$601$	−1.61803	+	1.17557i	−0.0660010	+	0.0479525i	0.554296	+	0.832320i	$0.312988\pi$
$602$		0			0
$603$	14.8328	+	45.6507i	0.604039	+	1.85904i
$604$	−8.00000			−0.325515
$605$		0			0
$606$		0			0
$607$	−9.88854	−	30.4338i	−0.401364	−	1.23527i	−0.923894	−	0.382649i	$-0.875012\pi$
$607$	−9.88854	−	30.4338i	−0.401364	−	1.23527i	0.522530	−	0.852621i	$-0.324988\pi$
$608$	16.1803	+	11.7557i	0.656199	+	0.476757i
$609$		0			0
$610$	−3.09017	+	9.51057i	−0.125117	+	0.385072i
$611$	−7.41641	+	22.8254i	−0.300036	+	0.923415i
$612$	−14.5623	+	10.5801i	−0.588646	+	0.427677i
$613$	−27.5066	−	19.9847i	−1.11098	−	0.807174i	−0.128162	−	0.991753i	$-0.540908\pi$
$613$	−27.5066	−	19.9847i	−1.11098	−	0.807174i	−0.982818	+	0.184579i	$0.940908\pi$
$614$	6.18034	+	19.0211i	0.249418	+	0.767630i
$615$		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
$619$	16.1803	+	11.7557i	0.650343	+	0.472502i	0.863388	−	0.504541i	$-0.168338\pi$
$619$	16.1803	+	11.7557i	0.650343	+	0.472502i	−0.213045	+	0.977042i	$0.568338\pi$
$620$	−6.47214	+	4.70228i	−0.259927	+	0.188848i
$621$		0			0
$622$	−7.41641	+	22.8254i	−0.297371	+	0.915213i
$623$		0			0
$624$		0			0
$625$	0.309017	+	0.951057i	0.0123607	+	0.0380423i
$626$	−22.0000			−0.879297
$627$		0			0
$628$	2.00000			0.0798087
$629$	−3.70820	−	11.4127i	−0.147856	−	0.455053i
$630$		0			0
$631$	−32.3607	+	23.5114i	−1.28826	+	0.935974i	−0.999769	−	0.0215086i	$-0.993153\pi$
$631$	−32.3607	+	23.5114i	−1.28826	+	0.935974i	−0.288490	+	0.957483i	$0.593153\pi$
$632$	−7.41641	+	22.8254i	−0.295009	+	0.907944i
$633$		0			0
$634$	14.5623	−	10.5801i	0.578343	−	0.420191i
$635$	−12.9443	−	9.40456i	−0.513678	−	0.373209i
$636$		0			0
$637$	−14.0000			−0.554700
$638$		0			0
$639$	−24.0000			−0.949425
$640$	−0.927051	−	2.85317i	−0.0366449	−	0.112781i
$641$	−27.5066	−	19.9847i	−1.08644	−	0.789348i	−0.107649	−	0.994189i	$-0.534332\pi$
$641$	−27.5066	−	19.9847i	−1.08644	−	0.789348i	−0.978795	+	0.204841i	$0.934332\pi$
$642$		0			0
$643$	−4.94427	+	15.2169i	−0.194983	+	0.600096i	0.804994	+	0.593283i	$0.202169\pi$
$643$	−4.94427	+	15.2169i	−0.194983	+	0.600096i	−0.999977	+	0.00681282i	$0.997831\pi$
$644$		0			0
$645$		0			0
$646$	19.4164	+	14.1068i	0.763928	+	0.555026i
$647$	6.18034	+	19.0211i	0.242974	+	0.747798i	0.995963	+	0.0897645i	$0.0286114\pi$
$647$	6.18034	+	19.0211i	0.242974	+	0.747798i	−0.752989	+	0.658033i	$0.771389\pi$
$648$	−27.0000			−1.06066
$649$		0			0
$650$	2.00000			0.0784465
$651$		0			0
$652$	12.9443	+	9.40456i	0.506937	+	0.368311i
$653$	8.09017	−	5.87785i	0.316593	−	0.230018i	−0.418127	−	0.908388i	$-0.637313\pi$
$653$	8.09017	−	5.87785i	0.316593	−	0.230018i	0.734720	+	0.678370i	$0.237313\pi$
$654$		0			0
$655$	−3.70820	+	11.4127i	−0.144892	+	0.445930i
$656$	1.61803	−	1.17557i	0.0631736	−	0.0458983i
$657$	33.9787	+	24.6870i	1.32564	+	0.963131i
$658$		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	$0.562301\pi$
$662$	1.23607	+	3.80423i	0.0480411	+	0.147855i
$663$		0			0
$664$	−9.70820	+	7.05342i	−0.376751	+	0.273726i
$665$		0			0
$666$	1.85410	−	5.70634i	0.0718450	−	0.221116i
$667$	−19.4164	+	14.1068i	−0.751806	+	0.546219i
$668$	−6.47214	−	4.70228i	−0.250414	−	0.181937i
$669$		0			0
$670$	−16.0000			−0.618134
$671$		0			0
$672$		0			0
$673$	−8.03444	−	24.7275i	−0.309705	−	0.953174i	−0.977879	−	0.209169i	$-0.932924\pi$
$673$	−8.03444	−	24.7275i	−0.309705	−	0.953174i	0.668174	−	0.744005i	$-0.267076\pi$
$674$	−4.85410	−	3.52671i	−0.186973	−	0.135844i
$675$		0			0
$676$	2.78115	−	8.55951i	0.106967	−	0.329212i
$677$	−11.7426	+	36.1401i	−0.451307	+	1.38898i	0.424111	+	0.905610i	$0.360587\pi$
$677$	−11.7426	+	36.1401i	−0.451307	+	1.38898i	−0.875417	+	0.483368i	$0.839413\pi$
$678$		0			0
$679$		0			0
$680$	−5.56231	−	17.1190i	−0.213305	−	0.656484i
$681$		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	$0.599028\pi$
$684$	−3.70820	−	11.4127i	−0.141787	−	0.436375i
$685$	−14.5623	−	10.5801i	−0.556397	−	0.404246i
$686$		0			0
$687$		0			0
$688$	−1.23607	+	3.80423i	−0.0471246	+	0.145035i
$689$	3.23607	−	2.35114i	0.123284	−	0.0895713i
$690$		0			0
$691$	−8.65248	−	26.6296i	−0.329156	−	1.01304i	−0.969530	−	0.244974i	$-0.921221\pi$
$691$	−8.65248	−	26.6296i	−0.329156	−	1.01304i	0.640374	−	0.768063i	$-0.278779\pi$
$692$	6.00000			0.228086
$693$		0			0
$694$	−4.00000			−0.151838
$695$	3.70820	+	11.4127i	0.140660	+	0.432908i
$696$		0			0
$697$	−9.70820	+	7.05342i	−0.367724	+	0.267167i
$698$	−3.09017	+	9.51057i	−0.116965	+	0.359980i
$699$		0			0
$700$		0			0
$701$	−17.7984	−	12.9313i	−0.672235	−	0.488408i	0.198537	−	0.980093i	$-0.436381\pi$
$701$	−17.7984	−	12.9313i	−0.672235	−	0.488408i	−0.870773	+	0.491686i	$0.836381\pi$
$702$		0			0
$703$	8.00000			0.301726
$704$		0			0
$705$		0			0
$706$	5.56231	+	17.1190i	0.209340	+	0.644283i
$707$		0			0
$708$		0			0
$709$	−3.09017	+	9.51057i	−0.116054	+	0.357177i	−0.992165	−	0.124932i	$-0.960129\pi$
$709$	−3.09017	+	9.51057i	−0.116054	+	0.357177i	0.876112	+	0.482108i	$0.160129\pi$
$710$	2.47214	−	7.60845i	0.0927776	−	0.285540i
$711$	19.4164	−	14.1068i	0.728172	−	0.529048i
$712$	24.2705	+	17.6336i	0.909576	+	0.660846i
$713$	−9.88854	−	30.4338i	−0.370329	−	1.13976i
$714$		0			0
$715$		0			0
$716$	−4.00000			−0.149487
$717$		0			0
$718$	25.8885	+	18.8091i	0.966152	+	0.701950i
$719$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$719$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$720$	0.927051	−	2.85317i	0.0345492	−	0.106331i
$721$		0			0
$722$	2.42705	−	1.76336i	0.0903255	−	0.0656253i
$723$		0			0
$724$	3.09017	+	9.51057i	0.114845	+	0.353457i
$725$	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
$729$	21.8435	+	15.8702i	0.809017	+	0.587785i
$730$	−11.3262	+	8.22899i	−0.419203	+	0.304569i
$731$	7.41641	−	22.8254i	0.274306	−	0.844226i
$732$		0			0
$733$	−33.9787	+	24.6870i	−1.25503	+	0.911834i	−0.998503	−	0.0547019i	$-0.982579\pi$
$733$	−33.9787	+	24.6870i	−1.25503	+	0.911834i	−0.256530	+	0.966536i	$0.582579\pi$
$734$	−3.23607	−	2.35114i	−0.119445	−	0.0867822i
$735$		0			0
$736$	20.0000			0.737210
$737$		0			0
$738$	−6.00000			−0.220863
$739$	1.23607	+	3.80423i	0.0454695	+	0.139941i	0.971214	−	0.238209i	$-0.0765604\pi$
$739$	1.23607	+	3.80423i	0.0454695	+	0.139941i	−0.925744	+	0.378150i	$0.876560\pi$
$740$	−1.61803	−	1.17557i	−0.0594801	−	0.0432148i
$741$		0			0
$742$		0			0
$743$	12.3607	−	38.0423i	0.453469	−	1.39564i	−0.419453	−	0.907777i	$-0.637778\pi$
$743$	12.3607	−	38.0423i	0.453469	−	1.39564i	0.872923	−	0.487858i	$-0.162222\pi$
$744$		0			0
$745$	8.09017	+	5.87785i	0.296401	+	0.215348i
$746$	5.56231	+	17.1190i	0.203650	+	0.626772i
$747$	12.0000			0.439057
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−12.9443	−	9.40456i	−0.472343	−	0.343177i	0.326011	−	0.945366i	$-0.394295\pi$
$751$	−12.9443	−	9.40456i	−0.472343	−	0.343177i	−0.798354	+	0.602189i	$0.794295\pi$
$752$	−9.70820	+	7.05342i	−0.354022	+	0.257212i
$753$		0			0
$754$	3.70820	−	11.4127i	0.135045	−	0.415625i
$755$	−6.47214	+	4.70228i	−0.235545	+	0.171134i
$756$		0			0
$757$	1.85410	+	5.70634i	0.0673885	+	0.207400i	0.979080	−	0.203474i	$-0.0652233\pi$
$757$	1.85410	+	5.70634i	0.0673885	+	0.207400i	−0.911692	+	0.410875i	$0.865223\pi$
$758$	20.0000			0.726433
$759$		0			0
$760$	12.0000			0.435286
$761$	3.09017	+	9.51057i	0.112019	+	0.344758i	0.991314	−	0.131520i	$-0.0419857\pi$
$761$	3.09017	+	9.51057i	0.112019	+	0.344758i	−0.879295	+	0.476278i	$0.841986\pi$
$762$		0			0
$763$		0			0
$764$	−2.47214	+	7.60845i	−0.0894387	+	0.275264i
$765$	−5.56231	+	17.1190i	−0.201106	+	0.618939i
$766$	9.70820	−	7.05342i	0.350772	−	0.254851i
$767$	−6.47214	−	4.70228i	−0.233695	−	0.169790i
$768$		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
$772$	8.03444	+	24.7275i	0.289166	+	0.889961i
$773$	−11.3262	−	8.22899i	−0.407376	−	0.295976i	0.365162	−	0.930944i	$-0.381013\pi$
$773$	−11.3262	−	8.22899i	−0.407376	−	0.295976i	−0.772539	+	0.634968i	$0.781013\pi$
$774$	9.70820	−	7.05342i	0.348954	−	0.253530i
$775$	−2.47214	+	7.60845i	−0.0888017	+	0.273304i
$776$	−9.27051	+	28.5317i	−0.332792	+	1.02423i
$777$		0			0
$778$	−4.85410	−	3.52671i	−0.174028	−	0.126439i
$779$	−2.47214	−	7.60845i	−0.0885735	−	0.272601i
$780$		0			0
$781$		0			0
$782$	24.0000			0.858238
$783$		0			0
$784$	−5.66312	−	4.11450i	−0.202254	−	0.146946i
$785$	1.61803	−	1.17557i	0.0577501	−	0.0419579i
$786$		0			0
$787$	16.0689	−	49.4549i	0.572794	−	1.76288i	−0.0707776	−	0.997492i	$-0.522548\pi$
$787$	16.0689	−	49.4549i	0.572794	−	1.76288i	0.643571	−	0.765386i	$-0.277452\pi$
$788$	1.61803	−	1.17557i	0.0576401	−	0.0418780i
$789$		0			0
$790$	2.47214	+	7.60845i	0.0879547	+	0.270697i
$791$		0			0
$792$		0			0
$793$	−20.0000			−0.710221
$794$	9.27051	+	28.5317i	0.328998	+	1.01255i
$795$		0			0
$796$		0			0
$797$	−0.618034	+	1.90211i	−0.0218919	+	0.0673763i	−0.961406	−	0.275135i	$-0.911277\pi$
$797$	−0.618034	+	1.90211i	−0.0218919	+	0.0673763i	0.939514	+	0.342511i	$0.111277\pi$
$798$		0			0
$799$	58.2492	−	42.3205i	2.06071	−	1.49719i
$800$	−4.04508	−	2.93893i	−0.143015	−	0.103907i
$801$	−9.27051	−	28.5317i	−0.327557	−	1.00812i
$802$	2.00000			0.0706225
$803$		0			0
$804$		0			0
$805$		0			0
$806$	12.9443	+	9.40456i	0.455943	+	0.331262i
$807$		0			0
$808$	9.27051	−	28.5317i	0.326135	−	1.00374i
$809$	5.56231	−	17.1190i	0.195560	−	0.601873i	−0.804409	−	0.594075i	$-0.797518\pi$
$809$	5.56231	−	17.1190i	0.195560	−	0.601873i	0.999970	−	0.00779717i	$-0.00248194\pi$
$810$	−7.28115	+	5.29007i	−0.255834	+	0.185874i
$811$	9.70820	+	7.05342i	0.340901	+	0.247679i	0.745042	−	0.667018i	$-0.232429\pi$
$811$	9.70820	+	7.05342i	0.340901	+	0.247679i	−0.404141	+	0.914697i	$0.632429\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	16.0000			0.560456
$816$		0			0
$817$	12.9443	+	9.40456i	0.452863	+	0.329024i
$818$	4.85410	−	3.52671i	0.169720	−	0.123309i
$819$		0			0
$820$	−0.618034	+	1.90211i	−0.0215827	+	0.0664247i
$821$	14.5623	−	10.5801i	0.508228	−	0.369249i	−0.303923	−	0.952697i	$-0.598297\pi$
$821$	14.5623	−	10.5801i	0.508228	−	0.369249i	0.812151	+	0.583447i	$0.198297\pi$
$822$		0			0
$823$	−11.1246	−	34.2380i	−0.387780	−	1.19346i	−0.934444	−	0.356111i	$-0.884103\pi$
$823$	−11.1246	−	34.2380i	−0.387780	−	1.19346i	0.546664	−	0.837352i	$-0.315897\pi$
$824$	12.0000			0.418040
$825$		0			0
$826$		0			0
$827$	3.70820	+	11.4127i	0.128947	+	0.396858i	0.994600	−	0.103787i	$-0.0330962\pi$
$827$	3.70820	+	11.4127i	0.128947	+	0.396858i	−0.865653	+	0.500645i	$0.833096\pi$
$828$	−9.70820	−	7.05342i	−0.337383	−	0.245123i
$829$	1.61803	−	1.17557i	0.0561966	−	0.0408293i	−0.559332	−	0.828944i	$-0.688942\pi$
$829$	1.61803	−	1.17557i	0.0561966	−	0.0408293i	0.615529	+	0.788114i	$0.288942\pi$
$830$	−1.23607	+	3.80423i	−0.0429045	+	0.132047i
$831$		0			0
$832$	−11.3262	+	8.22899i	−0.392667	+	0.285289i
$833$	33.9787	+	24.6870i	1.17729	+	0.855353i
$834$		0			0
$835$	−8.00000			−0.276851
$836$		0			0
$837$		0			0
$838$	−8.65248	−	26.6296i	−0.298895	−	0.919904i
$839$	25.8885	+	18.8091i	0.893772	+	0.649363i	0.936859	−	0.349708i	$-0.113719\pi$
$839$	25.8885	+	18.8091i	0.893772	+	0.649363i	−0.0430869	+	0.999071i	$0.513719\pi$
$840$		0			0
$841$	2.16312	−	6.65740i	0.0745903	−	0.229565i
$842$	1.85410	−	5.70634i	0.0638966	−	0.196653i
$843$		0			0
$844$	3.23607	+	2.35114i	0.111390	+	0.0809296i
$845$	−2.78115	−	8.55951i	−0.0956746	−	0.294456i
$846$	36.0000			1.23771
$847$		0			0
$848$	2.00000			0.0686803
$849$		0			0
$850$	−4.85410	−	3.52671i	−0.166494	−	0.120965i
$851$	6.47214	−	4.70228i	0.221862	−	0.161192i
$852$		0			0
$853$	0.618034	−	1.90211i	0.0211611	−	0.0651271i	−0.939918	−	0.341399i	$-0.889099\pi$
$853$	0.618034	−	1.90211i	0.0211611	−	0.0651271i	0.961079	+	0.276272i	$0.0890991\pi$
$854$		0			0
$855$	−9.70820	−	7.05342i	−0.332014	−	0.241222i
$856$	−11.1246	−	34.2380i	−0.380231	−	1.17023i
$857$	−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	$0.341480\pi$
$860$	−1.23607	−	3.80423i	−0.0421496	−	0.129723i
$861$		0			0
$862$	19.4164	−	14.1068i	0.661325	−	0.480481i
$863$	1.23607	−	3.80423i	0.0420762	−	0.129497i	−0.927812	−	0.373049i	$-0.878312\pi$
$863$	1.23607	−	3.80423i	0.0420762	−	0.129497i	0.969888	+	0.243551i	$0.0783124\pi$
$864$		0			0
$865$	4.85410	−	3.52671i	0.165044	−	0.119912i
$866$	17.7984	+	12.9313i	0.604813	+	0.439423i
$867$		0			0
$868$		0			0
$869$		0			0
$870$		0			0
$871$	−9.88854	−	30.4338i	−0.335061	−	1.03121i
$872$	−43.6869	−	31.7404i	−1.47943	−	1.07487i
$873$	24.2705	−	17.6336i	0.821432	−	0.596806i
$874$	−4.94427	+	15.2169i	−0.167242	+	0.514719i
$875$		0			0
$876$		0			0
$877$	17.7984	+	12.9313i	0.601008	+	0.436658i	0.846237	−	0.532807i	$-0.178863\pi$
$877$	17.7984	+	12.9313i	0.601008	+	0.436658i	−0.245228	+	0.969465i	$0.578863\pi$
$878$	−2.47214	−	7.60845i	−0.0834305	−	0.256773i
$879$		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	$0.401939\pi$
$882$	6.48936	+	19.9722i	0.218508	+	0.672499i
$883$	12.9443	+	9.40456i	0.435609	+	0.316489i	0.783888	−	0.620902i	$-0.213234\pi$
$883$	12.9443	+	9.40456i	0.435609	+	0.316489i	−0.348279	+	0.937391i	$0.613234\pi$
$884$	9.70820	−	7.05342i	0.326522	−	0.237232i
$885$		0			0
$886$	2.47214	−	7.60845i	0.0830530	−	0.255611i
$887$	−45.3050	+	32.9160i	−1.52119	+	1.10521i	−0.560298	+	0.828291i	$0.689313\pi$
$887$	−45.3050	+	32.9160i	−1.52119	+	1.10521i	−0.960893	+	0.276919i	$0.910687\pi$
$888$		0			0
$889$		0			0
$890$	10.0000			0.335201
$891$		0			0
$892$	4.00000			0.133930
$893$	14.8328	+	45.6507i	0.496361	+	1.52764i
$894$		0			0
$895$	−3.23607	+	2.35114i	−0.108170	+	0.0785900i
$896$		0			0
$897$		0			0
$898$	−1.61803	+	1.17557i	−0.0539945	+	0.0392293i
$899$	38.8328	+	28.2137i	1.29515	+	0.940979i
$900$	0.927051	+	2.85317i	0.0309017	+	0.0951057i
$901$	−12.0000			−0.399778
$902$		0			0
$903$		0			0
$904$	5.56231	+	17.1190i	0.185000	+	0.569370i
$905$	8.09017	+	5.87785i	0.268926	+	0.195386i
$906$		0			0
$907$	−12.3607	+	38.0423i	−0.410430	+	1.26317i	0.505846	+	0.862624i	$0.331180\pi$
$907$	−12.3607	+	38.0423i	−0.410430	+	1.26317i	−0.916275	+	0.400549i	$0.868820\pi$
$908$	6.18034	−	19.0211i	0.205102	−	0.631238i
$909$	−24.2705	+	17.6336i	−0.805002	+	0.584868i
$910$		0			0
$911$	2.47214	+	7.60845i	0.0819055	+	0.252079i	0.983621	−	0.180252i	$-0.0576912\pi$
$911$	2.47214	+	7.60845i	0.0819055	+	0.252079i	−0.901715	+	0.432331i	$0.857691\pi$
$912$		0			0
$913$		0			0
$914$	−26.0000			−0.860004
$915$		0			0
$916$	−8.09017	−	5.87785i	−0.267307	−	0.194210i
$917$		0			0
$918$		0			0
$919$	7.41641	−	22.8254i	0.244645	−	0.752939i	−0.751050	−	0.660245i	$-0.770452\pi$
$919$	7.41641	−	22.8254i	0.244645	−	0.752939i	0.995695	−	0.0926936i	$-0.0295477\pi$
$920$	9.70820	−	7.05342i	0.320070	−	0.232544i
$921$		0			0
$922$	−10.5066	−	32.3359i	−0.346016	−	1.06493i
$923$	16.0000			0.526646
$924$		0			0
$925$	−2.00000			−0.0657596
$926$	−11.1246	−	34.2380i	−0.365577	−	1.12513i
$927$	−9.70820	−	7.05342i	−0.318859	−	0.231665i
$928$	−24.2705	+	17.6336i	−0.796719	+	0.578850i
$929$	−4.32624	+	13.3148i	−0.141939	+	0.436844i	−0.996605	−	0.0823350i	$-0.973762\pi$
$929$	−4.32624	+	13.3148i	−0.141939	+	0.436844i	0.854665	+	0.519179i	$0.173762\pi$
$930$		0			0
$931$	−22.6525	+	16.4580i	−0.742405	+	0.539389i
$932$	4.85410	+	3.52671i	0.159001	+	0.115521i
$933$		0			0
$934$		0			0
$935$		0			0
$936$	18.0000			0.588348
$937$	1.85410	+	5.70634i	0.0605709	+	0.186418i	0.976763	−	0.214320i	$-0.0687537\pi$
$937$	1.85410	+	5.70634i	0.0605709	+	0.186418i	−0.916193	+	0.400738i	$0.868754\pi$
$938$		0			0
$939$		0			0
$940$	3.70820	−	11.4127i	0.120948	−	0.372241i
$941$	−0.618034	+	1.90211i	−0.0201473	+	0.0620071i	−0.960625	−	0.277849i	$-0.910378\pi$
$941$	−0.618034	+	1.90211i	−0.0201473	+	0.0620071i	0.940477	+	0.339856i	$0.110378\pi$
$942$		0			0
$943$	−6.47214	−	4.70228i	−0.210762	−	0.153127i
$944$	−1.23607	−	3.80423i	−0.0402306	−	0.123817i
$945$		0			0
$946$		0			0
$947$		0			0			−	1.00000i	$-0.5\pi$
$947$		0			0				1.00000i	$0.5\pi$
$948$		0			0
$949$	−22.6525	−	16.4580i	−0.735330	−	0.534249i
$950$	3.23607	−	2.35114i	0.104992	−	0.0762811i
$951$		0			0
$952$		0			0
$953$	33.9787	−	24.6870i	1.10068	−	0.799690i	0.119508	−	0.992833i	$-0.461868\pi$
$953$	33.9787	−	24.6870i	1.10068	−	0.799690i	0.981171	+	0.193143i	$0.0618683\pi$
$954$	−4.85410	−	3.52671i	−0.157157	−	0.114182i
$955$	2.47214	+	7.60845i	0.0799964	+	0.246204i
$956$	−8.00000			−0.258738
$957$		0			0
$958$	24.0000			0.775405
$959$		0			0
$960$		0			0
$961$	−26.6976	+	19.3969i	−0.861212	+	0.625707i
$962$	−1.23607	+	3.80423i	−0.0398524	+	0.122653i
$963$	−11.1246	+	34.2380i	−0.358486	+	1.10331i
$964$	8.09017	−	5.87785i	0.260567	−	0.189313i
$965$	21.0344	+	15.2824i	0.677123	+	0.491958i
$966$		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
$970$	3.09017	+	9.51057i	0.0992194	+	0.305366i
$971$	−29.1246	−	21.1603i	−0.934653	−	0.679065i	0.0124744	−	0.999922i	$-0.496029\pi$
$971$	−29.1246	−	21.1603i	−0.934653	−	0.679065i	−0.947128	+	0.320857i	$0.896029\pi$
$972$		0			0
$973$		0			0
$974$	8.65248	−	26.6296i	0.277243	−	0.853267i
$975$		0			0
$976$	−8.09017	−	5.87785i	−0.258960	−	0.188145i
$977$	3.09017	+	9.51057i	0.0988633	+	0.304270i	0.988241	−	0.152903i	$-0.0488621\pi$
$977$	3.09017	+	9.51057i	0.0988633	+	0.304270i	−0.889378	+	0.457173i	$0.848862\pi$
$978$		0			0
$979$		0			0
$980$	7.00000			0.223607
$981$	16.6869	+	51.3571i	0.532772	+	1.63970i
$982$	22.6525	+	16.4580i	0.722870	+	0.525195i
$983$	3.23607	−	2.35114i	0.103215	−	0.0749898i	−0.534981	−	0.844864i	$-0.679681\pi$
$983$	3.23607	−	2.35114i	0.103215	−	0.0749898i	0.638195	+	0.769874i	$0.279681\pi$
$984$		0			0
$985$	0.618034	−	1.90211i	0.0196922	−	0.0606064i
$986$	−29.1246	+	21.1603i	−0.927517	+	0.673880i
$987$		0			0
$988$	2.47214	+	7.60845i	0.0786491	+	0.242057i
$989$	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	$0.459445\pi$
$992$	−12.3607	−	38.0423i	−0.392452	−	1.20784i
$993$		0			0
$994$		0			0
$995$		0			0
$996$		0			0
$997$	37.2148	−	27.0381i	1.17860	−	0.856306i	0.186590	−	0.982438i	$-0.440256\pi$
$997$	37.2148	−	27.0381i	1.17860	−	0.856306i	0.992013	+	0.126132i	$0.0402562\pi$
$998$	29.1246	+	21.1603i	0.921923	+	0.669817i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.g.a.511.1		4
11.2	odd	10		605.2.g.c.251.1		4
11.3	even	5		55.2.a.a.1.1	✓	1
11.4	even	5	inner	605.2.g.a.366.1		4
11.5	even	5	inner	605.2.g.a.81.1		4
11.6	odd	10		605.2.g.c.81.1		4
11.7	odd	10		605.2.g.c.366.1		4
11.8	odd	10		605.2.a.b.1.1		1
11.9	even	5	inner	605.2.g.a.251.1		4
11.10	odd	2		605.2.g.c.511.1		4
33.8	even	10		5445.2.a.i.1.1		1
33.14	odd	10		495.2.a.a.1.1		1
44.3	odd	10		880.2.a.h.1.1		1
44.19	even	10		9680.2.a.r.1.1		1
55.3	odd	20		275.2.b.b.199.1		2
55.14	even	10		275.2.a.a.1.1		1
55.19	odd	10		3025.2.a.f.1.1		1
55.47	odd	20		275.2.b.b.199.2		2
77.69	odd	10		2695.2.a.c.1.1		1
88.3	odd	10		3520.2.a.n.1.1		1
88.69	even	10		3520.2.a.p.1.1		1
132.47	even	10		7920.2.a.i.1.1		1
143.25	even	10		9295.2.a.b.1.1		1
165.14	odd	10		2475.2.a.i.1.1		1
165.47	even	20		2475.2.c.f.199.1		2
165.113	even	20		2475.2.c.f.199.2		2
220.3	even	20		4400.2.b.n.4049.2		2
220.47	even	20		4400.2.b.n.4049.1		2
220.179	odd	10		4400.2.a.p.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.a.a.1.1	✓	1	11.3	even	5
275.2.a.a.1.1		1	55.14	even	10
275.2.b.b.199.1		2	55.3	odd	20
275.2.b.b.199.2		2	55.47	odd	20
495.2.a.a.1.1		1	33.14	odd	10
605.2.a.b.1.1		1	11.8	odd	10
605.2.g.a.81.1		4	11.5	even	5	inner
605.2.g.a.251.1		4	11.9	even	5	inner
605.2.g.a.366.1		4	11.4	even	5	inner
605.2.g.a.511.1		4	1.1	even	1	trivial
605.2.g.c.81.1		4	11.6	odd	10
605.2.g.c.251.1		4	11.2	odd	10
605.2.g.c.366.1		4	11.7	odd	10
605.2.g.c.511.1		4	11.10	odd	2
880.2.a.h.1.1		1	44.3	odd	10
2475.2.a.i.1.1		1	165.14	odd	10
2475.2.c.f.199.1		2	165.47	even	20
2475.2.c.f.199.2		2	165.113	even	20
2695.2.a.c.1.1		1	77.69	odd	10
3025.2.a.f.1.1		1	55.19	odd	10
3520.2.a.n.1.1		1	88.3	odd	10
3520.2.a.p.1.1		1	88.69	even	10
4400.2.a.p.1.1		1	220.179	odd	10
4400.2.b.n.4049.1		2	220.47	even	20
4400.2.b.n.4049.2		2	220.3	even	20
5445.2.a.i.1.1		1	33.8	even	10
7920.2.a.i.1.1		1	132.47	even	10
9295.2.a.b.1.1		1	143.25	even	10
9680.2.a.r.1.1		1	44.19	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)

\(f(q)\)	\(=\)	\(q+(0.309017 + 0.951057i) q^{2} +(0.809017 - 0.587785i) q^{4} +(0.309017 - 0.951057i) q^{5} +(2.42705 + 1.76336i) q^{8} +(-0.927051 - 2.85317i) q^{9} +O(q^{10})\)	\(q+(0.309017 + 0.951057i) q^{2} +(0.809017 - 0.587785i) q^{4} +(0.309017 - 0.951057i) q^{5} +(2.42705 + 1.76336i) q^{8} +(-0.927051 - 2.85317i) q^{9} +1.00000 q^{10} +(0.618034 + 1.90211i) q^{13} +(-0.309017 + 0.951057i) q^{16} +(1.85410 - 5.70634i) q^{17} +(2.42705 - 1.76336i) q^{18} +(3.23607 + 2.35114i) q^{19} +(-0.309017 - 0.951057i) q^{20} +4.00000 q^{23} +(-0.809017 - 0.587785i) q^{25} +(-1.61803 + 1.17557i) q^{26} +(-4.85410 + 3.52671i) q^{29} +(-2.47214 - 7.60845i) q^{31} +5.00000 q^{32} +6.00000 q^{34} +(-2.42705 - 1.76336i) q^{36} +(1.61803 - 1.17557i) q^{37} +(-1.23607 + 3.80423i) q^{38} +(2.42705 - 1.76336i) q^{40} +(-1.61803 - 1.17557i) q^{41} +4.00000 q^{43} -3.00000 q^{45} +(1.23607 + 3.80423i) q^{46} +(9.70820 + 7.05342i) q^{47} +(-2.16312 + 6.65740i) q^{49} +(0.309017 - 0.951057i) q^{50} +(1.61803 + 1.17557i) q^{52} +(-0.618034 - 1.90211i) q^{53} +(-4.85410 - 3.52671i) q^{58} +(-3.23607 + 2.35114i) q^{59} +(-3.09017 + 9.51057i) q^{61} +(6.47214 - 4.70228i) q^{62} +(2.16312 + 6.65740i) q^{64} +2.00000 q^{65} -16.0000 q^{67} +(-1.85410 - 5.70634i) q^{68} +(2.47214 - 7.60845i) q^{71} +(2.78115 - 8.55951i) q^{72} +(-11.3262 + 8.22899i) q^{73} +(1.61803 + 1.17557i) q^{74} +4.00000 q^{76} +(2.47214 + 7.60845i) q^{79} +(0.809017 + 0.587785i) q^{80} +(-7.28115 + 5.29007i) q^{81} +(0.618034 - 1.90211i) q^{82} +(-1.23607 + 3.80423i) q^{83} +(-4.85410 - 3.52671i) q^{85} +(1.23607 + 3.80423i) q^{86} +10.0000 q^{89} +(-0.927051 - 2.85317i) q^{90} +(3.23607 - 2.35114i) q^{92} +(-3.70820 + 11.4127i) q^{94} +(3.23607 - 2.35114i) q^{95} +(3.09017 + 9.51057i) q^{97} -7.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} + q^{4} - q^{5} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 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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