LMFDB - Embedded newform 605.2.g.h.251.2

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:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.324000000.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 3x^{6} + 9x^{4} + 27x^{2} + 81 $ x^8 + 3x^6 + 9x^4 + 27*x^2 + 81
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			251.2
Root			$-1.40126 + 1.01807i$ of defining polynomial
Character	$\chi$	$=$	605.251
Dual form			605.2.g.h.511.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.535233 - 1.64728i) q^{2} +(-1.61803 + 1.17557i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.309017 + 0.951057i) q^{5} +(1.07047 + 3.29456i) q^{6} +(-2.80252 - 2.03615i) q^{7} +(1.40126 - 1.01807i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(0.535233 - 1.64728i) q^{2} +(-1.61803 + 1.17557i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.309017 + 0.951057i) q^{5} +(1.07047 + 3.29456i) q^{6} +(-2.80252 - 2.03615i) q^{7} +(1.40126 - 1.01807i) q^{8} +(0.309017 - 0.951057i) q^{9} +1.73205 q^{10} +2.00000 q^{12} +(-4.85410 + 3.52671i) q^{14} +(-1.61803 - 1.17557i) q^{15} +(-1.54508 - 4.75528i) q^{16} +(-2.14093 - 6.58911i) q^{17} +(-1.40126 - 1.01807i) q^{18} +(5.60503 - 4.07230i) q^{19} +(0.309017 - 0.951057i) q^{20} +6.92820 q^{21} +6.00000 q^{23} +(-1.07047 + 3.29456i) q^{24} +(-0.809017 + 0.587785i) q^{25} +(-1.23607 - 3.80423i) q^{27} +(1.07047 + 3.29456i) q^{28} +(-2.80252 + 2.03615i) q^{30} +(1.23607 - 3.80423i) q^{31} -5.19615 q^{32} -12.0000 q^{34} +(1.07047 - 3.29456i) q^{35} +(-0.809017 + 0.587785i) q^{36} +(-8.09017 - 5.87785i) q^{37} +(-3.70820 - 11.4127i) q^{38} +(1.40126 + 1.01807i) q^{40} +(-5.60503 + 4.07230i) q^{41} +(3.70820 - 11.4127i) q^{42} -3.46410 q^{43} +1.00000 q^{45} +(3.21140 - 9.88367i) q^{46} +(4.85410 - 3.52671i) q^{47} +(8.09017 + 5.87785i) q^{48} +(1.54508 + 4.75528i) q^{49} +(0.535233 + 1.64728i) q^{50} +(11.2101 + 8.14459i) q^{51} +(-1.85410 + 5.70634i) q^{53} -6.92820 q^{54} -6.00000 q^{56} +(-4.28187 + 13.1782i) q^{57} +(0.618034 + 1.90211i) q^{60} +(2.14093 + 6.58911i) q^{61} +(-5.60503 - 4.07230i) q^{62} +(-2.80252 + 2.03615i) q^{63} +(0.309017 - 0.951057i) q^{64} +10.0000 q^{67} +(-2.14093 + 6.58911i) q^{68} +(-9.70820 + 7.05342i) q^{69} +(-4.85410 - 3.52671i) q^{70} +(-0.535233 - 1.64728i) q^{72} +(5.60503 + 4.07230i) q^{73} +(-14.0126 + 10.1807i) q^{74} +(0.618034 - 1.90211i) q^{75} -6.92820 q^{76} +(-2.14093 + 6.58911i) q^{79} +(4.04508 - 2.93893i) q^{80} +(8.89919 + 6.46564i) q^{81} +(3.70820 + 11.4127i) q^{82} +(-5.35233 - 16.4728i) q^{83} +(-5.60503 - 4.07230i) q^{84} +(5.60503 - 4.07230i) q^{85} +(-1.85410 + 5.70634i) q^{86} -6.00000 q^{89} +(0.535233 - 1.64728i) q^{90} +(-4.85410 - 3.52671i) q^{92} +(2.47214 + 7.60845i) q^{93} +(-3.21140 - 9.88367i) q^{94} +(5.60503 + 4.07230i) q^{95} +(8.40755 - 6.10844i) q^{96} +(-3.09017 + 9.51057i) q^{97} +8.66025 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{9}+O(q^{10}) $ 8 * q - 4 * q^3 - 2 * q^4 - 2 * q^5 - 2 * q^9	$ 8 q - 4 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{9} + 16 q^{12} - 12 q^{14} - 4 q^{15} + 10 q^{16} - 2 q^{20} + 48 q^{23} - 2 q^{25} + 8 q^{27} - 8 q^{31} - 96 q^{34} - 2 q^{36} - 20 q^{37} + 24 q^{38} - 24 q^{42} + 8 q^{45} + 12 q^{47} + 20 q^{48} - 10 q^{49} + 12 q^{53} - 48 q^{56} - 4 q^{60} - 2 q^{64} + 80 q^{67} - 24 q^{69} - 12 q^{70} - 4 q^{75} + 10 q^{80} + 22 q^{81} - 24 q^{82} + 12 q^{86} - 48 q^{89} - 12 q^{92} - 16 q^{93} + 20 q^{97}+O(q^{100}) $ 8 * q - 4 * q^3 - 2 * q^4 - 2 * q^5 - 2 * q^9 + 16 * q^12 - 12 * q^14 - 4 * q^15 + 10 * q^16 - 2 * q^20 + 48 * q^23 - 2 * q^25 + 8 * q^27 - 8 * q^31 - 96 * q^34 - 2 * q^36 - 20 * q^37 + 24 * q^38 - 24 * q^42 + 8 * q^45 + 12 * q^47 + 20 * q^48 - 10 * q^49 + 12 * q^53 - 48 * q^56 - 4 * q^60 - 2 * q^64 + 80 * q^67 - 24 * q^69 - 12 * q^70 - 4 * q^75 + 10 * q^80 + 22 * q^81 - 24 * q^82 + 12 * q^86 - 48 * q^89 - 12 * q^92 - 16 * q^93 + 20 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$122$	$486$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	0.535233	−	1.64728i	0.378467	−	1.16480i	−0.562643	−	0.826700i	$-0.690215\pi$
$2$	0.535233	−	1.64728i	0.378467	−	1.16480i	0.941110	−	0.338101i	$-0.109785\pi$
$3$	−1.61803	+	1.17557i	−0.934172	+	0.678716i	−0.947011	−	0.321202i	$-0.895913\pi$
$3$	−1.61803	+	1.17557i	−0.934172	+	0.678716i	0.0128385	+	0.999918i	$0.495913\pi$
$4$	−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
$6$	1.07047	+	3.29456i	0.437016	+	1.34500i
$7$	−2.80252	−	2.03615i	−1.05925	−	0.769592i	−0.0853021	−	0.996355i	$-0.527186\pi$
$7$	−2.80252	−	2.03615i	−1.05925	−	0.769592i	−0.973950	+	0.226764i	$0.927186\pi$
$8$	1.40126	−	1.01807i	0.495420	−	0.359943i
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$	1.73205			0.547723
$11$		0			0
$11$		0			0
$12$	2.00000			0.577350
$13$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$13$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$14$	−4.85410	+	3.52671i	−1.29731	+	0.942553i
$15$	−1.61803	−	1.17557i	−0.417775	−	0.303531i
$16$	−1.54508	−	4.75528i	−0.386271	−	1.18882i
$17$	−2.14093	−	6.58911i	−0.519252	−	1.59809i	−0.775409	−	0.631459i	$-0.782456\pi$
$17$	−2.14093	−	6.58911i	−0.519252	−	1.59809i	0.256157	−	0.966635i	$-0.417544\pi$
$18$	−1.40126	−	1.01807i	−0.330280	−	0.239962i
$19$	5.60503	−	4.07230i	1.28588	−	0.934249i	0.286169	−	0.958179i	$-0.407618\pi$
$19$	5.60503	−	4.07230i	1.28588	−	0.934249i	0.999714	+	0.0239303i	$0.00761799\pi$
$20$	0.309017	−	0.951057i	0.0690983	−	0.212663i
$21$	6.92820			1.51186
$22$		0			0
$23$	6.00000			1.25109			0.625543	−	0.780189i	$-0.284877\pi$
$23$	6.00000			1.25109			0.625543	+	0.780189i	$0.284877\pi$
$24$	−1.07047	+	3.29456i	−0.218508	+	0.672499i
$25$	−0.809017	+	0.587785i	−0.161803	+	0.117557i
$26$		0			0
$27$	−1.23607	−	3.80423i	−0.237881	−	0.732124i
$28$	1.07047	+	3.29456i	0.202299	+	0.622613i
$29$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$29$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$30$	−2.80252	+	2.03615i	−0.511667	+	0.371748i
$31$	1.23607	−	3.80423i	0.222004	−	0.683259i	−0.776578	−	0.630022i	$-0.783046\pi$
$31$	1.23607	−	3.80423i	0.222004	−	0.683259i	0.998582	−	0.0532375i	$-0.0169540\pi$
$32$	−5.19615			−0.918559
$33$		0			0
$34$	−12.0000			−2.05798
$35$	1.07047	−	3.29456i	0.180942	−	0.556882i
$36$	−0.809017	+	0.587785i	−0.134836	+	0.0979642i
$37$	−8.09017	−	5.87785i	−1.33002	−	0.966313i	−0.999749	−	0.0224255i	$-0.992861\pi$
$37$	−8.09017	−	5.87785i	−1.33002	−	0.966313i	−0.330267	−	0.943887i	$-0.607139\pi$
$38$	−3.70820	−	11.4127i	−0.601550	−	1.85138i
$39$		0			0
$40$	1.40126	+	1.01807i	0.221558	+	0.160972i
$41$	−5.60503	+	4.07230i	−0.875359	+	0.635986i	−0.932020	−	0.362408i	$-0.881955\pi$
$41$	−5.60503	+	4.07230i	−0.875359	+	0.635986i	0.0566604	+	0.998394i	$0.481955\pi$
$42$	3.70820	−	11.4127i	0.572188	−	1.76101i
$43$	−3.46410			−0.528271			−0.264135	−	0.964486i	$-0.585087\pi$
$43$	−3.46410			−0.528271			−0.264135	+	0.964486i	$0.585087\pi$
$44$		0			0
$45$	1.00000			0.149071
$46$	3.21140	−	9.88367i	0.473495	−	1.45727i
$47$	4.85410	−	3.52671i	0.708044	−	0.514424i	−0.174498	−	0.984657i	$-0.555830\pi$
$47$	4.85410	−	3.52671i	0.708044	−	0.514424i	0.882542	+	0.470234i	$0.155830\pi$
$48$	8.09017	+	5.87785i	1.16772	+	0.848395i
$49$	1.54508	+	4.75528i	0.220726	+	0.679326i
$50$	0.535233	+	1.64728i	0.0756934	+	0.232960i
$51$	11.2101	+	8.14459i	1.56972	+	1.14047i
$52$		0			0
$53$	−1.85410	+	5.70634i	−0.254680	+	0.783826i	0.739212	+	0.673473i	$0.235198\pi$
$53$	−1.85410	+	5.70634i	−0.254680	+	0.783826i	−0.993892	+	0.110353i	$0.964802\pi$
$54$	−6.92820			−0.942809
$55$		0			0
$56$	−6.00000			−0.801784
$57$	−4.28187	+	13.1782i	−0.567147	+	1.74550i
$58$		0			0
$59$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$59$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$60$	0.618034	+	1.90211i	0.0797878	+	0.245562i
$61$	2.14093	+	6.58911i	0.274118	+	0.843649i	0.989451	+	0.144866i	$0.0462750\pi$
$61$	2.14093	+	6.58911i	0.274118	+	0.843649i	−0.715333	+	0.698784i	$0.753725\pi$
$62$	−5.60503	−	4.07230i	−0.711840	−	0.517182i
$63$	−2.80252	+	2.03615i	−0.353084	+	0.256531i
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$		0			0
$66$		0			0
$67$	10.0000			1.22169			0.610847	−	0.791748i	$-0.290829\pi$
$67$	10.0000			1.22169			0.610847	+	0.791748i	$0.290829\pi$
$68$	−2.14093	+	6.58911i	−0.259626	+	0.799047i
$69$	−9.70820	+	7.05342i	−1.16873	+	0.849132i
$70$	−4.85410	−	3.52671i	−0.580176	−	0.421523i
$71$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$71$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$72$	−0.535233	−	1.64728i	−0.0630778	−	0.194134i
$73$	5.60503	+	4.07230i	0.656020	+	0.476626i	0.865316	−	0.501226i	$-0.167117\pi$
$73$	5.60503	+	4.07230i	0.656020	+	0.476626i	−0.209297	+	0.977852i	$0.567117\pi$
$74$	−14.0126	+	10.1807i	−1.62893	+	1.18349i
$75$	0.618034	−	1.90211i	0.0713644	−	0.219637i
$76$	−6.92820			−0.794719
$77$		0			0
$78$		0			0
$79$	−2.14093	+	6.58911i	−0.240874	+	0.741333i	0.755414	+	0.655248i	$0.227436\pi$
$79$	−2.14093	+	6.58911i	−0.240874	+	0.741333i	−0.996288	+	0.0860853i	$0.972564\pi$
$80$	4.04508	−	2.93893i	0.452254	−	0.328582i
$81$	8.89919	+	6.46564i	0.988799	+	0.718404i
$82$	3.70820	+	11.4127i	0.409503	+	1.26032i
$83$	−5.35233	−	16.4728i	−0.587495	−	1.80812i	−0.589013	−	0.808124i	$-0.700483\pi$
$83$	−5.35233	−	16.4728i	−0.587495	−	1.80812i	0.00151786	−	0.999999i	$-0.499517\pi$
$84$	−5.60503	−	4.07230i	−0.611559	−	0.444324i
$85$	5.60503	−	4.07230i	0.607951	−	0.441702i
$86$	−1.85410	+	5.70634i	−0.199933	+	0.615330i
$87$		0			0
$88$		0			0
$89$	−6.00000			−0.635999			−0.317999	−	0.948091i	$-0.603011\pi$
$89$	−6.00000			−0.635999			−0.317999	+	0.948091i	$0.603011\pi$
$90$	0.535233	−	1.64728i	0.0564185	−	0.173638i
$91$		0			0
$92$	−4.85410	−	3.52671i	−0.506075	−	0.367685i
$93$	2.47214	+	7.60845i	0.256349	+	0.788960i
$94$	−3.21140	−	9.88367i	−0.331230	−	1.01942i
$95$	5.60503	+	4.07230i	0.575064	+	0.417809i
$96$	8.40755	−	6.10844i	0.858092	−	0.623440i
$97$	−3.09017	+	9.51057i	−0.313759	+	0.965652i	0.662503	+	0.749059i	$0.269494\pi$
$97$	−3.09017	+	9.51057i	−0.313759	+	0.965652i	−0.976262	+	0.216592i	$0.930506\pi$
$98$	8.66025			0.874818
$99$		0			0
$100$	1.00000			0.100000
$101$	4.28187	−	13.1782i	0.426061	−	1.31128i	−0.475913	−	0.879493i	$-0.657882\pi$
$101$	4.28187	−	13.1782i	0.426061	−	1.31128i	0.901974	−	0.431790i	$-0.142118\pi$
$102$	19.4164	−	14.1068i	1.92251	−	1.39679i
$103$	−1.61803	−	1.17557i	−0.159430	−	0.115832i	0.505210	−	0.862996i	$-0.331415\pi$
$103$	−1.61803	−	1.17557i	−0.159430	−	0.115832i	−0.664640	+	0.747164i	$0.731415\pi$
$104$		0			0
$105$	2.14093	+	6.58911i	0.208934	+	0.643032i
$106$	8.40755	+	6.10844i	0.816614	+	0.593304i
$107$	2.80252	−	2.03615i	0.270930	−	0.196842i	−0.444022	−	0.896016i	$-0.646449\pi$
$107$	2.80252	−	2.03615i	0.270930	−	0.196842i	0.714951	+	0.699174i	$0.246449\pi$
$108$	−1.23607	+	3.80423i	−0.118941	+	0.366062i
$109$	6.92820			0.663602			0.331801	−	0.943349i	$-0.392344\pi$
$109$	6.92820			0.663602			0.331801	+	0.943349i	$0.392344\pi$
$110$		0			0
$111$	20.0000			1.89832
$112$	−5.35233	+	16.4728i	−0.505748	+	1.55653i
$113$	−4.85410	+	3.52671i	−0.456636	+	0.331765i	−0.792210	−	0.610249i	$-0.791070\pi$
$113$	−4.85410	+	3.52671i	−0.456636	+	0.331765i	0.335575	+	0.942014i	$0.391070\pi$
$114$	19.4164	+	14.1068i	1.81851	+	1.32123i
$115$	1.85410	+	5.70634i	0.172896	+	0.532119i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−7.41641	+	22.8254i	−0.679861	+	2.09240i
$120$	−3.46410			−0.316228
$121$		0			0
$122$	12.0000			1.08643
$123$	4.28187	−	13.1782i	0.386083	−	1.18824i
$124$	−3.23607	+	2.35114i	−0.290607	+	0.211139i
$125$	−0.809017	−	0.587785i	−0.0723607	−	0.0525731i
$126$	1.85410	+	5.70634i	0.165177	+	0.508361i
$127$	3.21140	+	9.88367i	0.284966	+	0.877034i	0.986409	+	0.164309i	$0.0525393\pi$
$127$	3.21140	+	9.88367i	0.284966	+	0.877034i	−0.701443	+	0.712725i	$0.747461\pi$
$128$	−9.80881	−	7.12652i	−0.866984	−	0.629901i
$129$	5.60503	−	4.07230i	0.493496	−	0.358546i
$130$		0			0
$131$	6.92820			0.605320			0.302660	−	0.953099i	$-0.402125\pi$
$131$	6.92820			0.605320			0.302660	+	0.953099i	$0.402125\pi$
$132$		0			0
$133$	−24.0000			−2.08106
$134$	5.35233	−	16.4728i	0.462371	−	1.42303i
$135$	3.23607	−	2.35114i	0.278516	−	0.202354i
$136$	−9.70820	−	7.05342i	−0.832472	−	0.604826i
$137$	1.85410	+	5.70634i	0.158407	+	0.487525i	0.998490	−	0.0549317i	$-0.0174941\pi$
$137$	1.85410	+	5.70634i	0.158407	+	0.487525i	−0.840083	+	0.542457i	$0.817494\pi$
$138$	6.42280	+	19.7673i	0.546745	+	1.68271i
$139$	−11.2101	−	8.14459i	−0.950826	−	0.690815i	0.000176405	−	1.00000i	$-0.499944\pi$
$139$	−11.2101	−	8.14459i	−0.950826	−	0.690815i	−0.951002	+	0.309185i	$0.899944\pi$
$140$	−2.80252	+	2.03615i	−0.236856	+	0.172086i
$141$	−3.70820	+	11.4127i	−0.312287	+	0.961121i
$142$		0			0
$143$		0			0
$144$	−5.00000			−0.416667
$145$		0			0
$146$	9.70820	−	7.05342i	0.803457	−	0.583745i
$147$	−8.09017	−	5.87785i	−0.667266	−	0.484797i
$148$	3.09017	+	9.51057i	0.254010	+	0.781764i
$149$	2.14093	+	6.58911i	0.175392	+	0.539801i	0.999651	−	0.0264116i	$-0.00840805\pi$
$149$	2.14093	+	6.58911i	0.175392	+	0.539801i	−0.824259	+	0.566213i	$0.808408\pi$
$150$	−2.80252	−	2.03615i	−0.228825	−	0.166251i
$151$	−5.60503	+	4.07230i	−0.456131	+	0.331399i	−0.792012	−	0.610506i	$-0.790966\pi$
$151$	−5.60503	+	4.07230i	−0.456131	+	0.331399i	0.335881	+	0.941905i	$0.390966\pi$
$152$	3.70820	−	11.4127i	0.300775	−	0.925690i
$153$	−6.92820			−0.560112
$154$		0			0
$155$	4.00000			0.321288
$156$		0			0
$157$	1.61803	−	1.17557i	0.129133	−	0.0938207i	−0.521344	−	0.853347i	$-0.674569\pi$
$157$	1.61803	−	1.17557i	0.129133	−	0.0938207i	0.650477	+	0.759526i	$0.274569\pi$
$158$	9.70820	+	7.05342i	0.772343	+	0.561140i
$159$	−3.70820	−	11.4127i	−0.294080	−	0.905084i
$160$	−1.60570	−	4.94183i	−0.126942	−	0.390686i
$161$	−16.8151	−	12.2169i	−1.32522	−	0.962826i
$162$	15.4138	−	11.1988i	1.21103	−	0.879862i
$163$	0.618034	−	1.90211i	0.0484082	−	0.148985i	−0.923931	−	0.382560i	$-0.875042\pi$
$163$	0.618034	−	1.90211i	0.0484082	−	0.148985i	0.972339	+	0.233575i	$0.0750425\pi$
$164$	6.92820			0.541002
$165$		0			0
$166$	−30.0000			−2.32845
$167$	3.21140	−	9.88367i	0.248506	−	0.764821i	−0.746535	−	0.665347i	$-0.768284\pi$
$167$	3.21140	−	9.88367i	0.248506	−	0.764821i	0.995040	−	0.0994747i	$-0.0317162\pi$
$168$	9.70820	−	7.05342i	0.749004	−	0.544183i
$169$	10.5172	+	7.64121i	0.809017	+	0.587785i
$170$	−3.70820	−	11.4127i	−0.284406	−	0.875312i
$171$	−2.14093	−	6.58911i	−0.163721	−	0.503882i
$172$	2.80252	+	2.03615i	0.213690	+	0.155255i
$173$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$173$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$174$		0			0
$175$	3.46410			0.261861
$176$		0			0
$177$		0			0
$178$	−3.21140	+	9.88367i	−0.240705	+	0.740812i
$179$	9.70820	−	7.05342i	0.725625	−	0.527198i	−0.162551	−	0.986700i	$-0.551972\pi$
$179$	9.70820	−	7.05342i	0.725625	−	0.527198i	0.888176	+	0.459503i	$0.151972\pi$
$180$	−0.809017	−	0.587785i	−0.0603006	−	0.0438109i
$181$	4.32624	+	13.3148i	0.321567	+	0.989681i	0.972967	+	0.230946i	$0.0741821\pi$
$181$	4.32624	+	13.3148i	0.321567	+	0.989681i	−0.651400	+	0.758735i	$0.725818\pi$
$182$		0			0
$183$	−11.2101	−	8.14459i	−0.828672	−	0.602066i
$184$	8.40755	−	6.10844i	0.619813	−	0.450320i
$185$	3.09017	−	9.51057i	0.227194	−	0.699231i
$186$	13.8564			1.01600
$187$		0			0
$188$	−6.00000			−0.437595
$189$	−4.28187	+	13.1782i	−0.311460	+	0.958575i
$190$	9.70820	−	7.05342i	0.704307	−	0.511709i
$191$	9.70820	+	7.05342i	0.702461	+	0.510368i	0.880733	−	0.473614i	$-0.157051\pi$
$191$	9.70820	+	7.05342i	0.702461	+	0.510368i	−0.178272	+	0.983981i	$0.557051\pi$
$192$	0.618034	+	1.90211i	0.0446028	+	0.137273i
$193$	−2.14093	−	6.58911i	−0.154108	−	0.474295i	0.843962	−	0.536403i	$-0.180217\pi$
$193$	−2.14093	−	6.58911i	−0.154108	−	0.474295i	−0.998069	+	0.0621087i	$0.980217\pi$
$194$	14.0126	+	10.1807i	1.00605	+	0.730934i
$195$		0			0
$196$	1.54508	−	4.75528i	0.110363	−	0.339663i
$197$		0			0			−	1.00000i	$-0.5\pi$
$197$		0			0				1.00000i	$0.5\pi$
$198$		0			0
$199$	4.00000			0.283552			0.141776	−	0.989899i	$-0.454719\pi$
$199$	4.00000			0.283552			0.141776	+	0.989899i	$0.454719\pi$
$200$	−0.535233	+	1.64728i	−0.0378467	+	0.116480i
$201$	−16.1803	+	11.7557i	−1.14127	+	0.829184i
$202$	−19.4164	−	14.1068i	−1.36613	−	0.992554i
$203$		0			0
$204$	−4.28187	−	13.1782i	−0.299791	−	0.922660i
$205$	−5.60503	−	4.07230i	−0.391473	−	0.284421i
$206$	−2.80252	+	2.03615i	−0.195261	+	0.141865i
$207$	1.85410	−	5.70634i	0.128869	−	0.396618i
$208$		0			0
$209$		0			0
$210$	12.0000			0.828079
$211$	−6.42280	+	19.7673i	−0.442164	+	1.36084i	0.443401	+	0.896323i	$0.353772\pi$
$211$	−6.42280	+	19.7673i	−0.442164	+	1.36084i	−0.885565	+	0.464516i	$0.846228\pi$
$212$	4.85410	−	3.52671i	0.333381	−	0.242216i
$213$		0			0
$214$	−1.85410	−	5.70634i	−0.126744	−	0.390077i
$215$	−1.07047	−	3.29456i	−0.0730052	−	0.224687i
$216$	−5.60503	−	4.07230i	−0.381374	−	0.277085i
$217$	−11.2101	+	8.14459i	−0.760989	+	0.552891i
$218$	3.70820	−	11.4127i	0.251151	−	0.772964i
$219$	−13.8564			−0.936329
$220$		0			0
$221$		0			0
$222$	10.7047	−	32.9456i	0.718450	−	2.21116i
$223$	−11.3262	+	8.22899i	−0.758461	+	0.551054i	−0.898438	−	0.439101i	$-0.855297\pi$
$223$	−11.3262	+	8.22899i	−0.758461	+	0.551054i	0.139977	+	0.990155i	$0.455297\pi$
$224$	14.5623	+	10.5801i	0.972985	+	0.706915i
$225$	0.309017	+	0.951057i	0.0206011	+	0.0634038i
$226$	3.21140	+	9.88367i	0.213619	+	0.657452i
$227$	−2.80252	−	2.03615i	−0.186010	−	0.135144i	0.490883	−	0.871225i	$-0.336674\pi$
$227$	−2.80252	−	2.03615i	−0.186010	−	0.135144i	−0.676893	+	0.736081i	$0.736674\pi$
$228$	11.2101	−	8.14459i	0.742405	−	0.539389i
$229$	−0.618034	+	1.90211i	−0.0408408	+	0.125695i	−0.969398	−	0.245494i	$-0.921050\pi$
$229$	−0.618034	+	1.90211i	−0.0408408	+	0.125695i	0.928557	+	0.371189i	$0.121050\pi$
$230$	10.3923			0.685248
$231$		0			0
$232$		0			0
$233$	2.14093	−	6.58911i	0.140257	−	0.431667i	−0.856113	−	0.516788i	$-0.827128\pi$
$233$	2.14093	−	6.58911i	0.140257	−	0.431667i	0.996371	+	0.0851207i	$0.0271276\pi$
$234$		0			0
$235$	4.85410	+	3.52671i	0.316647	+	0.230057i
$236$		0			0
$237$	−4.28187	−	13.1782i	−0.278137	−	0.856018i
$238$	33.6302	+	24.4338i	2.17992	+	1.58381i
$239$	5.60503	−	4.07230i	0.362560	−	0.263415i	−0.391559	−	0.920153i	$-0.628064\pi$
$239$	5.60503	−	4.07230i	0.362560	−	0.263415i	0.754119	+	0.656738i	$0.228064\pi$
$240$	−3.09017	+	9.51057i	−0.199470	+	0.613904i
$241$	−20.7846			−1.33885			−0.669427	−	0.742878i	$-0.733460\pi$
$241$	−20.7846			−1.33885			−0.669427	+	0.742878i	$0.733460\pi$
$242$		0			0
$243$	−10.0000			−0.641500
$244$	2.14093	−	6.58911i	0.137059	−	0.421825i
$245$	−4.04508	+	2.93893i	−0.258431	+	0.187761i
$246$	−19.4164	−	14.1068i	−1.23794	−	0.899420i
$247$		0			0
$248$	−2.14093	−	6.58911i	−0.135949	−	0.418409i
$249$	28.0252	+	20.3615i	1.77602	+	1.29036i
$250$	−1.40126	+	1.01807i	−0.0886234	+	0.0643886i
$251$	3.70820	−	11.4127i	0.234060	−	0.720362i	−0.763185	−	0.646180i	$-0.776365\pi$
$251$	3.70820	−	11.4127i	0.234060	−	0.720362i	0.997245	−	0.0741818i	$-0.0236345\pi$
$252$	3.46410			0.218218
$253$		0			0
$254$	18.0000			1.12942
$255$	−4.28187	+	13.1782i	−0.268141	+	0.825253i
$256$	−15.3713	+	11.1679i	−0.960708	+	0.697995i
$257$	4.85410	+	3.52671i	0.302791	+	0.219990i	0.728797	−	0.684730i	$-0.240080\pi$
$257$	4.85410	+	3.52671i	0.302791	+	0.219990i	−0.426006	+	0.904720i	$0.640080\pi$
$258$	−3.70820	−	11.4127i	−0.230863	−	0.710522i
$259$	10.7047	+	32.9456i	0.665155	+	2.04714i
$260$		0			0
$261$		0			0
$262$	3.70820	−	11.4127i	0.229094	−	0.705078i
$263$	3.46410			0.213606			0.106803	−	0.994280i	$-0.465939\pi$
$263$	3.46410			0.213606			0.106803	+	0.994280i	$0.465939\pi$
$264$		0			0
$265$	−6.00000			−0.368577
$266$	−12.8456	+	39.5347i	−0.787614	+	2.42403i
$267$	9.70820	−	7.05342i	0.594132	−	0.431662i
$268$	−8.09017	−	5.87785i	−0.494186	−	0.359047i
$269$	−9.27051	−	28.5317i	−0.565233	−	1.73961i	−0.667258	−	0.744826i	$-0.732532\pi$
$269$	−9.27051	−	28.5317i	−0.565233	−	1.73961i	0.102025	−	0.994782i	$-0.467468\pi$
$270$	−2.14093	−	6.58911i	−0.130293	−	0.401001i
$271$	−5.60503	−	4.07230i	−0.340482	−	0.247374i	0.404383	−	0.914590i	$-0.367486\pi$
$271$	−5.60503	−	4.07230i	−0.340482	−	0.247374i	−0.744865	+	0.667215i	$0.767486\pi$
$272$	−28.0252	+	20.3615i	−1.69928	+	1.23460i
$273$		0			0
$274$	10.3923			0.627822
$275$		0			0
$276$	12.0000			0.722315
$277$	8.56373	−	26.3565i	0.514545	−	1.58361i	−0.269564	−	0.962982i	$-0.586880\pi$
$277$	8.56373	−	26.3565i	0.514545	−	1.58361i	0.784109	−	0.620623i	$-0.213120\pi$
$278$	−19.4164	+	14.1068i	−1.16452	+	0.846072i
$279$	−3.23607	−	2.35114i	−0.193738	−	0.140759i
$280$	−1.85410	−	5.70634i	−0.110804	−	0.341019i
$281$	−2.14093	−	6.58911i	−0.127717	−	0.393074i	0.866669	−	0.498884i	$-0.166256\pi$
$281$	−2.14093	−	6.58911i	−0.127717	−	0.393074i	−0.994386	+	0.105810i	$0.966256\pi$
$282$	16.8151	+	12.2169i	1.00132	+	0.727505i
$283$	−19.6176	+	14.2530i	−1.16615	+	0.847255i	−0.990543	−	0.137206i	$-0.956188\pi$
$283$	−19.6176	+	14.2530i	−1.16615	+	0.847255i	−0.175604	+	0.984461i	$0.556188\pi$
$284$		0			0
$285$	−13.8564			−0.820783
$286$		0			0
$287$	24.0000			1.41668
$288$	−1.60570	+	4.94183i	−0.0946167	+	0.291200i
$289$	−25.0795	+	18.2213i	−1.47527	+	1.07184i
$290$		0			0
$291$	−6.18034	−	19.0211i	−0.362298	−	1.11504i
$292$	−2.14093	−	6.58911i	−0.125289	−	0.385599i
$293$	−11.2101	−	8.14459i	−0.654899	−	0.475812i	0.210037	−	0.977693i	$-0.432641\pi$
$293$	−11.2101	−	8.14459i	−0.654899	−	0.475812i	−0.864937	+	0.501881i	$0.832641\pi$
$294$	−14.0126	+	10.1807i	−0.817231	+	0.593753i
$295$		0			0
$296$	−17.3205			−1.00673
$297$		0			0
$298$	12.0000			0.695141
$299$		0			0
$300$	−1.61803	+	1.17557i	−0.0934172	+	0.0678716i
$301$	9.70820	+	7.05342i	0.559572	+	0.406553i
$302$	3.70820	+	11.4127i	0.213383	+	0.656726i
$303$	8.56373	+	26.3565i	0.491973	+	1.51414i
$304$	−28.0252	−	20.3615i	−1.60735	−	1.16781i
$305$	−5.60503	+	4.07230i	−0.320943	+	0.233179i
$306$	−3.70820	+	11.4127i	−0.211984	+	0.652419i
$307$	−3.46410			−0.197707			−0.0988534	−	0.995102i	$-0.531517\pi$
$307$	−3.46410			−0.197707			−0.0988534	+	0.995102i	$0.531517\pi$
$308$		0			0
$309$	4.00000			0.227552
$310$	2.14093	−	6.58911i	0.121597	−	0.374236i
$311$	19.4164	−	14.1068i	1.10100	−	0.799926i	0.119780	−	0.992800i	$-0.461781\pi$
$311$	19.4164	−	14.1068i	1.10100	−	0.799926i	0.981223	+	0.192875i	$0.0617811\pi$
$312$		0			0
$313$	10.5066	+	32.3359i	0.593867	+	1.82773i	0.560287	+	0.828298i	$0.310691\pi$
$313$	10.5066	+	32.3359i	0.593867	+	1.82773i	0.0335795	+	0.999436i	$0.489309\pi$
$314$	−1.07047	−	3.29456i	−0.0604099	−	0.185923i
$315$	−2.80252	−	2.03615i	−0.157904	−	0.114724i
$316$	5.60503	−	4.07230i	0.315308	−	0.229085i
$317$	−5.56231	+	17.1190i	−0.312410	+	0.961500i	0.664397	+	0.747380i	$0.268688\pi$
$317$	−5.56231	+	17.1190i	−0.312410	+	0.961500i	−0.976807	+	0.214120i	$0.931312\pi$
$318$	−20.7846			−1.16554
$319$		0			0
$320$	1.00000			0.0559017
$321$	−2.14093	+	6.58911i	−0.119495	+	0.367768i
$322$	−29.1246	+	21.1603i	−1.62305	+	1.17922i
$323$	−38.8328	−	28.2137i	−2.16072	−	1.56985i
$324$	−3.39919	−	10.4616i	−0.188844	−	0.581201i
$325$		0			0
$326$	−2.80252	−	2.03615i	−0.155217	−	0.112772i
$327$	−11.2101	+	8.14459i	−0.619918	+	0.450397i
$328$	−3.70820	+	11.4127i	−0.204751	+	0.630160i
$329$	−20.7846			−1.14589
$330$		0			0
$331$	8.00000			0.439720			0.219860	−	0.975531i	$-0.429440\pi$
$331$	8.00000			0.439720			0.219860	+	0.975531i	$0.429440\pi$
$332$	−5.35233	+	16.4728i	−0.293747	+	0.904061i
$333$	−8.09017	+	5.87785i	−0.443339	+	0.322104i
$334$	−14.5623	−	10.5801i	−0.796814	−	0.578919i
$335$	3.09017	+	9.51057i	0.168834	+	0.519618i
$336$	−10.7047	−	32.9456i	−0.583987	−	1.79733i
$337$	16.8151	+	12.2169i	0.915977	+	0.665496i	0.942519	−	0.334151i	$-0.108450\pi$
$337$	16.8151	+	12.2169i	0.915977	+	0.665496i	−0.0265424	+	0.999648i	$0.508450\pi$
$338$	18.2164	−	13.2350i	0.990839	−	0.719887i
$339$	3.70820	−	11.4127i	0.201402	−	0.619852i
$340$	−6.92820			−0.375735
$341$		0			0
$342$	−12.0000			−0.648886
$343$	−2.14093	+	6.58911i	−0.115599	+	0.355779i
$344$	−4.85410	+	3.52671i	−0.261716	+	0.190148i
$345$	−9.70820	−	7.05342i	−0.522672	−	0.379744i
$346$		0			0
$347$	7.49326	+	23.0619i	0.402259	+	1.23803i	0.923162	+	0.384411i	$0.125596\pi$
$347$	7.49326	+	23.0619i	0.402259	+	1.23803i	−0.520902	+	0.853616i	$0.674404\pi$
$348$		0			0
$349$	11.2101	−	8.14459i	0.600061	−	0.435970i	−0.245839	−	0.969311i	$-0.579064\pi$
$349$	11.2101	−	8.14459i	0.600061	−	0.435970i	0.845901	+	0.533341i	$0.179064\pi$
$350$	1.85410	−	5.70634i	0.0991059	−	0.305017i
$351$		0			0
$352$		0			0
$353$	−6.00000			−0.319348			−0.159674	−	0.987170i	$-0.551044\pi$
$353$	−6.00000			−0.319348			−0.159674	+	0.987170i	$0.551044\pi$
$354$		0			0
$355$		0			0
$356$	4.85410	+	3.52671i	0.257267	+	0.186915i
$357$	−14.8328	−	45.6507i	−0.785036	−	2.41609i
$358$	−6.42280	−	19.7673i	−0.339455	−	1.04474i
$359$	28.0252	+	20.3615i	1.47911	+	1.07464i	0.977841	+	0.209347i	$0.0671339\pi$
$359$	28.0252	+	20.3615i	1.47911	+	1.07464i	0.501271	+	0.865291i	$0.332866\pi$
$360$	1.40126	−	1.01807i	0.0738528	−	0.0536572i
$361$	8.96149	−	27.5806i	0.471658	−	1.45161i
$362$	24.2487			1.27448
$363$		0			0
$364$		0			0
$365$	−2.14093	+	6.58911i	−0.112062	+	0.344890i
$366$	−19.4164	+	14.1068i	−1.01491	+	0.737377i
$367$	−1.61803	−	1.17557i	−0.0844607	−	0.0613643i	0.544754	−	0.838596i	$-0.316623\pi$
$367$	−1.61803	−	1.17557i	−0.0844607	−	0.0613643i	−0.629214	+	0.777232i	$0.716623\pi$
$368$	−9.27051	−	28.5317i	−0.483259	−	1.48732i
$369$	2.14093	+	6.58911i	0.111452	+	0.343016i
$370$	−14.0126	−	10.1807i	−0.728480	−	0.529271i
$371$	16.8151	−	12.2169i	0.872997	−	0.634269i
$372$	2.47214	−	7.60845i	0.128174	−	0.394480i
$373$	27.7128			1.43492			0.717458	−	0.696602i	$-0.245306\pi$
$373$	27.7128			1.43492			0.717458	+	0.696602i	$0.245306\pi$
$374$		0			0
$375$	2.00000			0.103280
$376$	3.21140	−	9.88367i	0.165615	−	0.509711i
$377$		0			0
$378$	19.4164	+	14.1068i	0.998672	+	0.725578i
$379$	9.88854	+	30.4338i	0.507940	+	1.56328i	0.795771	+	0.605598i	$0.207066\pi$
$379$	9.88854	+	30.4338i	0.507940	+	1.56328i	−0.287830	+	0.957681i	$0.592934\pi$
$380$	−2.14093	−	6.58911i	−0.109828	−	0.338014i
$381$	−16.8151	−	12.2169i	−0.861464	−	0.625890i
$382$	16.8151	−	12.2169i	0.860335	−	0.625070i
$383$	5.56231	−	17.1190i	0.284221	−	0.874741i	−0.702411	−	0.711772i	$-0.747893\pi$
$383$	5.56231	−	17.1190i	0.284221	−	0.874741i	0.986631	−	0.162969i	$-0.0521070\pi$
$384$	24.2487			1.23744
$385$		0			0
$386$	−12.0000			−0.610784
$387$	−1.07047	+	3.29456i	−0.0544149	+	0.167472i
$388$	8.09017	−	5.87785i	0.410716	−	0.298403i
$389$	−4.85410	−	3.52671i	−0.246113	−	0.178811i	0.457890	−	0.889009i	$-0.348606\pi$
$389$	−4.85410	−	3.52671i	−0.246113	−	0.178811i	−0.704002	+	0.710198i	$0.748606\pi$
$390$		0			0
$391$	−12.8456	−	39.5347i	−0.649630	−	1.99935i
$392$	7.00629	+	5.09037i	0.353871	+	0.257102i
$393$	−11.2101	+	8.14459i	−0.565473	+	0.410840i
$394$		0			0
$395$	−6.92820			−0.348596
$396$		0			0
$397$	−34.0000			−1.70641			−0.853206	−	0.521575i	$-0.825345\pi$
$397$	−34.0000			−1.70641			−0.853206	+	0.521575i	$0.825345\pi$
$398$	2.14093	−	6.58911i	0.107315	−	0.330282i
$399$	38.8328	−	28.2137i	1.94407	−	1.41245i
$400$	4.04508	+	2.93893i	0.202254	+	0.146946i
$401$	−5.56231	−	17.1190i	−0.277768	−	0.854883i	−0.988474	−	0.151393i	$-0.951624\pi$
$401$	−5.56231	−	17.1190i	−0.277768	−	0.854883i	0.710705	−	0.703490i	$-0.248376\pi$
$402$	10.7047	+	32.9456i	0.533900	+	1.64318i
$403$		0			0
$404$	−11.2101	+	8.14459i	−0.557722	+	0.405209i
$405$	−3.39919	+	10.4616i	−0.168907	+	0.519842i
$406$		0			0
$407$		0			0
$408$	24.0000			1.18818
$409$	6.42280	−	19.7673i	0.317587	−	0.977432i	−0.657090	−	0.753812i	$-0.728213\pi$
$409$	6.42280	−	19.7673i	0.317587	−	0.977432i	0.974677	−	0.223620i	$-0.0717873\pi$
$410$	−9.70820	+	7.05342i	−0.479454	+	0.348344i
$411$	−9.70820	−	7.05342i	−0.478870	−	0.347920i
$412$	0.618034	+	1.90211i	0.0304483	+	0.0937104i
$413$		0			0
$414$	−8.40755	−	6.10844i	−0.413209	−	0.300214i
$415$	14.0126	−	10.1807i	0.687851	−	0.499753i
$416$		0			0
$417$	27.7128			1.35710
$418$		0			0
$419$	−12.0000			−0.586238			−0.293119	−	0.956076i	$-0.594693\pi$
$419$	−12.0000			−0.586238			−0.293119	+	0.956076i	$0.594693\pi$
$420$	2.14093	−	6.58911i	0.104467	−	0.321516i
$421$	21.0344	−	15.2824i	1.02516	−	0.744819i	0.0578225	−	0.998327i	$-0.481584\pi$
$421$	21.0344	−	15.2824i	1.02516	−	0.744819i	0.967333	+	0.253507i	$0.0815842\pi$
$422$	29.1246	+	21.1603i	1.41776	+	1.03007i
$423$	−1.85410	−	5.70634i	−0.0901495	−	0.277452i
$424$	3.21140	+	9.88367i	0.155959	+	0.479993i
$425$	5.60503	+	4.07230i	0.271884	+	0.197535i
$426$		0			0
$427$	7.41641	−	22.8254i	0.358905	−	1.10460i
$428$	−3.46410			−0.167444
$429$		0			0
$430$	−6.00000			−0.289346
$431$	8.56373	−	26.3565i	0.412500	−	1.26955i	−0.501967	−	0.864887i	$-0.667390\pi$
$431$	8.56373	−	26.3565i	0.412500	−	1.26955i	0.914468	−	0.404659i	$-0.132610\pi$
$432$	−16.1803	+	11.7557i	−0.778477	+	0.565597i
$433$	27.5066	+	19.9847i	1.32188	+	0.960403i	0.999907	+	0.0136552i	$0.00434671\pi$
$433$	27.5066	+	19.9847i	1.32188	+	0.960403i	0.321975	+	0.946748i	$0.395653\pi$
$434$	7.41641	+	22.8254i	0.355999	+	1.09565i
$435$		0			0
$436$	−5.60503	−	4.07230i	−0.268432	−	0.195028i
$437$	33.6302	−	24.4338i	1.60875	−	1.16883i
$438$	−7.41641	+	22.8254i	−0.354370	+	1.09064i
$439$	13.8564			0.661330			0.330665	−	0.943748i	$-0.392727\pi$
$439$	13.8564			0.661330			0.330665	+	0.943748i	$0.392727\pi$
$440$		0			0
$441$	5.00000			0.238095
$442$		0			0
$443$	4.85410	−	3.52671i	0.230625	−	0.167559i	−0.466471	−	0.884536i	$-0.654475\pi$
$443$	4.85410	−	3.52671i	0.230625	−	0.167559i	0.697097	+	0.716977i	$0.254475\pi$
$444$	−16.1803	−	11.7557i	−0.767885	−	0.557901i
$445$	−1.85410	−	5.70634i	−0.0878929	−	0.270506i
$446$	7.49326	+	23.0619i	0.354816	+	1.09201i
$447$	−11.2101	−	8.14459i	−0.530218	−	0.385226i
$448$	−2.80252	+	2.03615i	−0.132406	+	0.0961989i
$449$	9.27051	−	28.5317i	0.437502	−	1.34649i	−0.452998	−	0.891512i	$-0.649646\pi$
$449$	9.27051	−	28.5317i	0.437502	−	1.34649i	0.890500	−	0.454982i	$-0.150354\pi$
$450$	1.73205			0.0816497
$451$		0			0
$452$	6.00000			0.282216
$453$	4.28187	−	13.1782i	0.201180	−	0.619167i
$454$	−4.85410	+	3.52671i	−0.227814	+	0.165517i
$455$		0			0
$456$	7.41641	+	22.8254i	0.347305	+	1.06890i
$457$	6.42280	+	19.7673i	0.300446	+	0.924677i	0.981338	+	0.192293i	$0.0615924\pi$
$457$	6.42280	+	19.7673i	0.300446	+	0.924677i	−0.680892	+	0.732384i	$0.738408\pi$
$458$	2.80252	+	2.03615i	0.130953	+	0.0951429i
$459$	−22.4201	+	16.2892i	−1.04648	+	0.760314i
$460$	1.85410	−	5.70634i	0.0864479	−	0.266059i
$461$	−27.7128			−1.29071			−0.645357	−	0.763881i	$-0.723291\pi$
$461$	−27.7128			−1.29071			−0.645357	+	0.763881i	$0.723291\pi$
$462$		0			0
$463$	14.0000			0.650635			0.325318	−	0.945605i	$-0.394529\pi$
$463$	14.0000			0.650635			0.325318	+	0.945605i	$0.394529\pi$
$464$		0			0
$465$	−6.47214	+	4.70228i	−0.300138	+	0.218063i
$466$	−9.70820	−	7.05342i	−0.449724	−	0.326744i
$467$	5.56231	+	17.1190i	0.257393	+	0.792174i	0.993349	+	0.115144i	$0.0367330\pi$
$467$	5.56231	+	17.1190i	0.257393	+	0.792174i	−0.735956	+	0.677029i	$0.763267\pi$
$468$		0			0
$469$	−28.0252	−	20.3615i	−1.29408	−	0.940206i
$470$	8.40755	−	6.10844i	0.387811	−	0.281761i
$471$	−1.23607	+	3.80423i	−0.0569550	+	0.175289i
$472$		0			0
$473$		0			0
$474$	−24.0000			−1.10236
$475$	−2.14093	+	6.58911i	−0.0982327	+	0.302329i
$476$	19.4164	−	14.1068i	0.889950	−	0.646586i
$477$	4.85410	+	3.52671i	0.222254	+	0.161477i
$478$	−3.70820	−	11.4127i	−0.169609	−	0.522004i
$479$	−6.42280	−	19.7673i	−0.293465	−	0.903193i	−0.983733	−	0.179639i	$-0.942507\pi$
$479$	−6.42280	−	19.7673i	−0.293465	−	0.903193i	0.690268	−	0.723554i	$-0.257493\pi$
$480$	8.40755	+	6.10844i	0.383750	+	0.278811i
$481$		0			0
$482$	−11.1246	+	34.2380i	−0.506712	+	1.55950i
$483$	41.5692			1.89146
$484$		0			0
$485$	−10.0000			−0.454077
$486$	−5.35233	+	16.4728i	−0.242787	+	0.747221i
$487$	11.3262	−	8.22899i	0.513241	−	0.372891i	−0.300811	−	0.953684i	$-0.597257\pi$
$487$	11.3262	−	8.22899i	0.513241	−	0.372891i	0.814052	+	0.580793i	$0.197257\pi$
$488$	9.70820	+	7.05342i	0.439470	+	0.319293i
$489$	1.23607	+	3.80423i	0.0558969	+	0.172033i
$490$	2.67617	+	8.23639i	0.120897	+	0.372082i
$491$	−11.2101	−	8.14459i	−0.505903	−	0.367560i	0.305364	−	0.952236i	$-0.401222\pi$
$491$	−11.2101	−	8.14459i	−0.505903	−	0.367560i	−0.811267	+	0.584675i	$0.801222\pi$
$492$	−11.2101	+	8.14459i	−0.505389	+	0.367187i
$493$		0			0
$494$		0			0
$495$		0			0
$496$	−20.0000			−0.898027
$497$		0			0
$498$	48.5410	−	35.2671i	2.17518	−	1.58036i
$499$	−12.9443	−	9.40456i	−0.579465	−	0.421006i	0.259066	−	0.965860i	$-0.416585\pi$
$499$	−12.9443	−	9.40456i	−0.579465	−	0.421006i	−0.838531	+	0.544853i	$0.816585\pi$
$500$	0.309017	+	0.951057i	0.0138197	+	0.0425325i
$501$	6.42280	+	19.7673i	0.286949	+	0.883140i
$502$	−16.8151	−	12.2169i	−0.750495	−	0.545266i
$503$	14.0126	−	10.1807i	0.624790	−	0.453937i	−0.229801	−	0.973238i	$-0.573808\pi$
$503$	14.0126	−	10.1807i	0.624790	−	0.453937i	0.854591	+	0.519301i	$0.173808\pi$
$504$	−1.85410	+	5.70634i	−0.0825883	+	0.254181i
$505$	13.8564			0.616602
$506$		0			0
$507$	−26.0000			−1.15470
$508$	3.21140	−	9.88367i	0.142483	−	0.438517i
$509$	−4.85410	+	3.52671i	−0.215154	+	0.156319i	−0.690143	−	0.723673i	$-0.742452\pi$
$509$	−4.85410	+	3.52671i	−0.215154	+	0.156319i	0.474988	+	0.879992i	$0.342452\pi$
$510$	19.4164	+	14.1068i	0.859773	+	0.624662i
$511$	−7.41641	−	22.8254i	−0.328083	−	1.00973i
$512$	2.67617	+	8.23639i	0.118271	+	0.364000i
$513$	−22.4201	−	16.2892i	−0.989873	−	0.719185i
$514$	8.40755	−	6.10844i	0.370841	−	0.269432i
$515$	0.618034	−	1.90211i	0.0272338	−	0.0838171i
$516$	−6.92820			−0.304997
$517$		0			0
$518$	60.0000			2.63625
$519$		0			0
$520$		0			0
$521$	33.9787	+	24.6870i	1.48863	+	1.08156i	0.974644	+	0.223760i	$0.0718333\pi$
$521$	33.9787	+	24.6870i	1.48863	+	1.08156i	0.513990	+	0.857796i	$0.328167\pi$
$522$		0			0
$523$	−7.49326	−	23.0619i	−0.327658	−	1.00843i	−0.970227	−	0.242199i	$-0.922131\pi$
$523$	−7.49326	−	23.0619i	−0.327658	−	1.00843i	0.642569	−	0.766228i	$-0.277869\pi$
$524$	−5.60503	−	4.07230i	−0.244857	−	0.177899i
$525$	−5.60503	+	4.07230i	−0.244624	+	0.177730i
$526$	1.85410	−	5.70634i	0.0808427	−	0.248808i
$527$	−27.7128			−1.20719
$528$		0			0
$529$	13.0000			0.565217
$530$	−3.21140	+	9.88367i	−0.139494	+	0.429319i
$531$		0			0
$532$	19.4164	+	14.1068i	0.841808	+	0.611609i
$533$		0			0
$534$	−6.42280	−	19.7673i	−0.277942	−	0.855416i
$535$	2.80252	+	2.03615i	0.121163	+	0.0880303i
$536$	14.0126	−	10.1807i	0.605252	−	0.439741i
$537$	−7.41641	+	22.8254i	−0.320042	+	0.984987i
$538$	−51.9615			−2.24022
$539$		0			0
$540$	−4.00000			−0.172133
$541$	−4.28187	+	13.1782i	−0.184092	+	0.566576i	−0.999932	−	0.0117018i	$-0.996275\pi$
$541$	−4.28187	+	13.1782i	−0.184092	+	0.566576i	0.815840	+	0.578278i	$0.196275\pi$
$542$	−9.70820	+	7.05342i	−0.417003	+	0.302970i
$543$	−22.6525	−	16.4580i	−0.972111	−	0.706280i
$544$	11.1246	+	34.2380i	0.476964	+	1.46794i
$545$	2.14093	+	6.58911i	0.0917075	+	0.282247i
$546$		0			0
$547$	−14.0126	+	10.1807i	−0.599135	+	0.435297i	−0.845572	−	0.533862i	$-0.820740\pi$
$547$	−14.0126	+	10.1807i	−0.599135	+	0.435297i	0.246437	+	0.969159i	$0.420740\pi$
$548$	1.85410	−	5.70634i	0.0792033	−	0.243763i
$549$	6.92820			0.295689
$550$		0			0
$551$		0			0
$552$	−6.42280	+	19.7673i	−0.273372	+	0.841354i
$553$	19.4164	−	14.1068i	0.825670	−	0.599884i
$554$	−38.8328	−	28.2137i	−1.64985	−	1.19868i
$555$	6.18034	+	19.0211i	0.262341	+	0.807402i
$556$	4.28187	+	13.1782i	0.181592	+	0.558881i
$557$	22.4201	+	16.2892i	0.949972	+	0.690195i	0.950800	−	0.309805i	$-0.100264\pi$
$557$	22.4201	+	16.2892i	0.949972	+	0.690195i	−0.000828494		1.00000i	$0.500264\pi$
$558$	−5.60503	+	4.07230i	−0.237280	+	0.172394i
$559$		0			0
$560$	−17.3205			−0.731925
$561$		0			0
$562$	−12.0000			−0.506189
$563$	−3.21140	+	9.88367i	−0.135344	+	0.416547i	−0.995643	−	0.0932426i	$-0.970277\pi$
$563$	−3.21140	+	9.88367i	−0.135344	+	0.416547i	0.860299	+	0.509790i	$0.170277\pi$
$564$	9.70820	−	7.05342i	0.408789	−	0.297003i
$565$	−4.85410	−	3.52671i	−0.204214	−	0.148370i
$566$	12.9787	+	39.9444i	0.545536	+	1.67899i
$567$	−11.7751	−	36.2401i	−0.494509	−	1.52194i
$568$		0			0
$569$	5.60503	−	4.07230i	0.234975	−	0.170720i	−0.464067	−	0.885800i	$-0.653610\pi$
$569$	5.60503	−	4.07230i	0.234975	−	0.170720i	0.699042	+	0.715081i	$0.253610\pi$
$570$	−7.41641	+	22.8254i	−0.310639	+	0.956049i
$571$	27.7128			1.15975			0.579873	−	0.814707i	$-0.303102\pi$
$571$	27.7128			1.15975			0.579873	+	0.814707i	$0.303102\pi$
$572$		0			0
$573$	−24.0000			−1.00261
$574$	12.8456	−	39.5347i	0.536165	−	1.65015i
$575$	−4.85410	+	3.52671i	−0.202430	+	0.147074i
$576$	−0.809017	−	0.587785i	−0.0337090	−	0.0244911i
$577$	−0.618034	−	1.90211i	−0.0257291	−	0.0791860i	0.937367	−	0.348342i	$-0.113255\pi$
$577$	−0.618034	−	1.90211i	−0.0257291	−	0.0791860i	−0.963097	+	0.269156i	$0.913255\pi$
$578$	16.5922	+	51.0656i	0.690146	+	2.12405i
$579$	11.2101	+	8.14459i	0.465875	+	0.338478i
$580$		0			0
$581$	−18.5410	+	57.0634i	−0.769211	+	2.36739i
$582$	−34.6410			−1.43592
$583$		0			0
$584$	12.0000			0.496564
$585$		0			0
$586$	−19.4164	+	14.1068i	−0.802084	+	0.582748i
$587$	24.2705	+	17.6336i	1.00175	+	0.727815i	0.962463	−	0.271413i	$-0.0874910\pi$
$587$	24.2705	+	17.6336i	1.00175	+	0.727815i	0.0392882	+	0.999228i	$0.487491\pi$
$588$	3.09017	+	9.51057i	0.127436	+	0.392209i
$589$	−8.56373	−	26.3565i	−0.352862	−	1.08600i
$590$		0			0
$591$		0			0
$592$	−15.4508	+	47.5528i	−0.635026	+	1.95441i
$593$	−6.92820			−0.284507			−0.142254	−	0.989830i	$-0.545435\pi$
$593$	−6.92820			−0.284507			−0.142254	+	0.989830i	$0.545435\pi$
$594$		0			0
$595$	−24.0000			−0.983904
$596$	2.14093	−	6.58911i	0.0876960	−	0.269901i
$597$	−6.47214	+	4.70228i	−0.264887	+	0.192452i
$598$		0			0
$599$	7.41641	+	22.8254i	0.303026	+	0.932619i	0.980406	+	0.196986i	$0.0631152\pi$
$599$	7.41641	+	22.8254i	0.303026	+	0.932619i	−0.677380	+	0.735633i	$0.736885\pi$
$600$	−1.07047	−	3.29456i	−0.0437016	−	0.134500i
$601$	39.2352	+	28.5061i	1.60044	+	1.16279i	0.886667	+	0.462408i	$0.153015\pi$
$601$	39.2352	+	28.5061i	1.60044	+	1.16279i	0.713772	+	0.700378i	$0.246985\pi$
$602$	16.8151	−	12.2169i	0.685332	−	0.497923i
$603$	3.09017	−	9.51057i	0.125841	−	0.387300i
$604$	6.92820			0.281905
$605$		0			0
$606$	48.0000			1.94987
$607$	−1.07047	+	3.29456i	−0.0434489	+	0.133722i	−0.970428	−	0.241391i	$-0.922396\pi$
$607$	−1.07047	+	3.29456i	−0.0434489	+	0.133722i	0.926979	+	0.375113i	$0.122396\pi$
$608$	−29.1246	+	21.1603i	−1.18116	+	0.858162i
$609$		0			0
$610$	3.70820	+	11.4127i	0.150141	+	0.462086i
$611$		0			0
$612$	5.60503	+	4.07230i	0.226570	+	0.164613i
$613$	−22.4201	+	16.2892i	−0.905541	+	0.657914i	−0.939883	−	0.341496i	$-0.889066\pi$
$613$	−22.4201	+	16.2892i	−0.905541	+	0.657914i	0.0343424	+	0.999410i	$0.489066\pi$
$614$	−1.85410	+	5.70634i	−0.0748255	+	0.230289i
$615$	13.8564			0.558744
$616$		0			0
$617$	6.00000			0.241551			0.120775	−	0.992680i	$-0.461462\pi$
$617$	6.00000			0.241551			0.120775	+	0.992680i	$0.461462\pi$
$618$	2.14093	−	6.58911i	0.0861209	−	0.265053i
$619$	22.6525	−	16.4580i	0.910480	−	0.661502i	−0.0306563	−	0.999530i	$-0.509760\pi$
$619$	22.6525	−	16.4580i	0.910480	−	0.661502i	0.941136	+	0.338028i	$0.109760\pi$
$620$	−3.23607	−	2.35114i	−0.129964	−	0.0944241i
$621$	−7.41641	−	22.8254i	−0.297610	−	0.915950i
$622$	−12.8456	−	39.5347i	−0.515061	−	1.58520i
$623$	16.8151	+	12.2169i	0.673683	+	0.489459i
$624$		0			0
$625$	0.309017	−	0.951057i	0.0123607	−	0.0380423i
$626$	58.8897			2.35371
$627$		0			0
$628$	−2.00000			−0.0798087
$629$	−21.4093	+	65.8911i	−0.853646	+	2.62725i
$630$	−4.85410	+	3.52671i	−0.193392	+	0.140508i
$631$	−12.9443	−	9.40456i	−0.515303	−	0.374390i	0.299528	−	0.954087i	$-0.403171\pi$
$631$	−12.9443	−	9.40456i	−0.515303	−	0.374390i	−0.814832	+	0.579698i	$0.803171\pi$
$632$	3.70820	+	11.4127i	0.147504	+	0.453972i
$633$	−12.8456	−	39.5347i	−0.510567	−	1.57136i
$634$	25.2227	+	18.3253i	1.00172	+	0.727792i
$635$	−8.40755	+	6.10844i	−0.333643	+	0.242406i
$636$	−3.70820	+	11.4127i	−0.147040	+	0.452542i
$637$		0			0
$638$		0			0
$639$		0			0
$640$	3.74663	−	11.5309i	0.148099	−	0.455801i
$641$	33.9787	−	24.6870i	1.34208	−	0.975077i	0.342714	−	0.939440i	$-0.388654\pi$
$641$	33.9787	−	24.6870i	1.34208	−	0.975077i	0.999365	−	0.0356372i	$-0.0113461\pi$
$642$	9.70820	+	7.05342i	0.383152	+	0.278376i
$643$	8.03444	+	24.7275i	0.316847	+	0.975156i	0.974987	+	0.222261i	$0.0713435\pi$
$643$	8.03444	+	24.7275i	0.316847	+	0.975156i	−0.658140	+	0.752896i	$0.728656\pi$
$644$	6.42280	+	19.7673i	0.253094	+	0.778942i
$645$	5.60503	+	4.07230i	0.220698	+	0.160346i
$646$	−67.2604	+	48.8675i	−2.64633	+	1.92267i
$647$	1.85410	−	5.70634i	0.0728923	−	0.224339i	−0.907972	−	0.419030i	$-0.862370\pi$
$647$	1.85410	−	5.70634i	0.0728923	−	0.224339i	0.980865	+	0.194691i	$0.0623703\pi$
$648$	19.0526			0.748455
$649$		0			0
$650$		0			0
$651$	8.56373	−	26.3565i	0.335639	−	1.03299i
$652$	−1.61803	+	1.17557i	−0.0633671	+	0.0460389i
$653$	4.85410	+	3.52671i	0.189956	+	0.138011i	0.678698	−	0.734417i	$-0.262544\pi$
$653$	4.85410	+	3.52671i	0.189956	+	0.138011i	−0.488743	+	0.872428i	$0.662544\pi$
$654$	7.41641	+	22.8254i	0.290004	+	0.892542i
$655$	2.14093	+	6.58911i	0.0836532	+	0.257458i
$656$	28.0252	+	20.3615i	1.09420	+	0.794982i
$657$	5.60503	−	4.07230i	0.218673	−	0.158875i
$658$	−11.1246	+	34.2380i	−0.433683	+	1.33474i
$659$	−27.7128			−1.07954			−0.539769	−	0.841813i	$-0.681488\pi$
$659$	−27.7128			−1.07954			−0.539769	+	0.841813i	$0.681488\pi$
$660$		0			0
$661$	22.0000			0.855701			0.427850	−	0.903850i	$-0.359271\pi$
$661$	22.0000			0.855701			0.427850	+	0.903850i	$0.359271\pi$
$662$	4.28187	−	13.1782i	0.166419	−	0.512186i
$663$		0			0
$664$	−24.2705	−	17.6336i	−0.941878	−	0.684315i
$665$	−7.41641	−	22.8254i	−0.287596	−	0.885129i
$666$	5.35233	+	16.4728i	0.207399	+	0.638307i
$667$		0			0
$668$	−8.40755	+	6.10844i	−0.325298	+	0.236343i
$669$	8.65248	−	26.6296i	0.334524	−	1.02956i
$670$	17.3205			0.669150
$671$		0			0
$672$	−36.0000			−1.38873
$673$	−10.7047	+	32.9456i	−0.412634	+	1.26996i	0.501715	+	0.865033i	$0.332703\pi$
$673$	−10.7047	+	32.9456i	−0.412634	+	1.26996i	−0.914350	+	0.404925i	$0.867297\pi$
$674$	29.1246	−	21.1603i	1.12184	−	0.815063i
$675$	3.23607	+	2.35114i	0.124556	+	0.0904955i
$676$	−4.01722	−	12.3637i	−0.154508	−	0.475528i
$677$	−4.28187	−	13.1782i	−0.164565	−	0.506480i	0.834439	−	0.551101i	$-0.185792\pi$
$677$	−4.28187	−	13.1782i	−0.164565	−	0.506480i	−0.999004	+	0.0446206i	$0.985792\pi$
$678$	−16.8151	−	12.2169i	−0.645780	−	0.469187i
$679$	28.0252	−	20.3615i	1.07551	−	0.781402i
$680$	3.70820	−	11.4127i	0.142203	−	0.437656i
$681$	6.92820			0.265489
$682$		0			0
$683$	−42.0000			−1.60709			−0.803543	−	0.595247i	$-0.797054\pi$
$683$	−42.0000			−1.60709			−0.803543	+	0.595247i	$0.797054\pi$
$684$	−2.14093	+	6.58911i	−0.0818606	+	0.251941i
$685$	−4.85410	+	3.52671i	−0.185466	+	0.134749i
$686$	9.70820	+	7.05342i	0.370661	+	0.269301i
$687$	−1.23607	−	3.80423i	−0.0471589	−	0.145140i
$688$	5.35233	+	16.4728i	0.204056	+	0.628019i
$689$		0			0
$690$	−16.8151	+	12.2169i	−0.640140	+	0.465089i
$691$	6.18034	−	19.0211i	0.235111	−	0.723598i	−0.761995	−	0.647582i	$-0.775780\pi$
$691$	6.18034	−	19.0211i	0.235111	−	0.723598i	0.997107	−	0.0760155i	$-0.0242198\pi$
$692$		0			0
$693$		0			0
$694$	42.0000			1.59430
$695$	4.28187	−	13.1782i	0.162420	−	0.499879i
$696$		0			0
$697$	38.8328	+	28.2137i	1.47090	+	1.06867i
$698$	−7.41641	−	22.8254i	−0.280715	−	0.863952i
$699$	4.28187	+	13.1782i	0.161955	+	0.498446i
$700$	−2.80252	−	2.03615i	−0.105925	−	0.0769592i
$701$	−16.8151	+	12.2169i	−0.635098	+	0.461425i	−0.858162	−	0.513378i	$-0.828394\pi$
$701$	−16.8151	+	12.2169i	−0.635098	+	0.461425i	0.223065	+	0.974804i	$0.428394\pi$
$702$		0			0
$703$	−69.2820			−2.61302
$704$		0			0
$705$	−12.0000			−0.451946
$706$	−3.21140	+	9.88367i	−0.120863	+	0.371977i
$707$	−38.8328	+	28.2137i	−1.46046	+	1.06109i
$708$		0			0
$709$	−8.03444	−	24.7275i	−0.301740	−	0.928660i	−0.980874	−	0.194645i	$-0.937644\pi$
$709$	−8.03444	−	24.7275i	−0.301740	−	0.928660i	0.679134	−	0.734014i	$-0.262356\pi$
$710$		0			0
$711$	5.60503	+	4.07230i	0.210205	+	0.152723i
$712$	−8.40755	+	6.10844i	−0.315086	+	0.228924i
$713$	7.41641	−	22.8254i	0.277747	−	0.854816i
$714$	−83.1384			−3.11138
$715$		0			0
$716$	−12.0000			−0.448461
$717$	−4.28187	+	13.1782i	−0.159909	+	0.492150i
$718$	48.5410	−	35.2671i	1.81153	−	1.31616i
$719$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$719$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$720$	−1.54508	−	4.75528i	−0.0575819	−	0.177219i
$721$	2.14093	+	6.58911i	0.0797325	+	0.245391i
$722$	−40.6365	−	29.5241i	−1.51233	−	1.09877i
$723$	33.6302	−	24.4338i	1.25072	−	0.908702i
$724$	4.32624	−	13.3148i	0.160783	−	0.494840i
$725$		0			0
$726$		0			0
$727$	46.0000			1.70605			0.853023	−	0.521874i	$-0.174767\pi$
$727$	46.0000			1.70605			0.853023	+	0.521874i	$0.174767\pi$
$728$		0			0
$729$	−10.5172	+	7.64121i	−0.389527	+	0.283008i
$730$	9.70820	+	7.05342i	0.359317	+	0.261059i
$731$	7.41641	+	22.8254i	0.274306	+	0.844226i
$732$	4.28187	+	13.1782i	0.158262	+	0.487081i
$733$	33.6302	+	24.4338i	1.24216	+	0.902482i	0.997740	−	0.0671875i	$-0.0214026\pi$
$733$	33.6302	+	24.4338i	1.24216	+	0.902482i	0.244420	+	0.969670i	$0.421403\pi$
$734$	−2.80252	+	2.03615i	−0.103443	+	0.0751556i
$735$	3.09017	−	9.51057i	0.113983	−	0.350802i
$736$	−31.1769			−1.14920
$737$		0			0
$738$	12.0000			0.441726
$739$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$739$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$740$	−8.09017	+	5.87785i	−0.297401	+	0.216074i
$741$		0			0
$742$	−11.1246	−	34.2380i	−0.408397	−	1.25692i
$743$	9.63420	+	29.6510i	0.353444	+	1.08779i	0.956906	+	0.290398i	$0.0937877\pi$
$743$	9.63420	+	29.6510i	0.353444	+	1.08779i	−0.603462	+	0.797392i	$0.706212\pi$
$744$	11.2101	+	8.14459i	0.410981	+	0.298595i
$745$	−5.60503	+	4.07230i	−0.205353	+	0.149197i
$746$	14.8328	−	45.6507i	0.543068	−	1.67139i
$747$	−17.3205			−0.633724
$748$		0			0
$749$	−12.0000			−0.438470
$750$	1.07047	−	3.29456i	0.0390879	−	0.120300i
$751$	−12.9443	+	9.40456i	−0.472343	+	0.343177i	−0.798354	−	0.602189i	$-0.794295\pi$
$751$	−12.9443	+	9.40456i	−0.472343	+	0.343177i	0.326011	+	0.945366i	$0.394295\pi$
$752$	−24.2705	−	17.6336i	−0.885054	−	0.643030i
$753$	7.41641	+	22.8254i	0.270269	+	0.831802i
$754$		0			0
$755$	−5.60503	−	4.07230i	−0.203988	−	0.148206i
$756$	11.2101	−	8.14459i	0.407706	−	0.296216i
$757$	−0.618034	+	1.90211i	−0.0224628	+	0.0691335i	−0.961660	−	0.274246i	$-0.911572\pi$
$757$	−0.618034	+	1.90211i	−0.0224628	+	0.0691335i	0.939197	+	0.343380i	$0.111572\pi$
$758$	55.4256			2.01315
$759$		0			0
$760$	12.0000			0.435286
$761$	4.28187	−	13.1782i	0.155217	−	0.477710i	−0.842965	−	0.537968i	$-0.819192\pi$
$761$	4.28187	−	13.1782i	0.155217	−	0.477710i	0.998183	+	0.0602575i	$0.0191922\pi$
$762$	−29.1246	+	21.1603i	−1.05507	+	0.766556i
$763$	−19.4164	−	14.1068i	−0.702921	−	0.510702i
$764$	−3.70820	−	11.4127i	−0.134158	−	0.412896i
$765$	−2.14093	−	6.58911i	−0.0774056	−	0.238230i
$766$	−25.2227	−	18.3253i	−0.911332	−	0.662121i
$767$		0			0
$768$	11.7426	−	36.1401i	0.423726	−	1.30410i
$769$	41.5692			1.49902			0.749512	−	0.661991i	$-0.230288\pi$
$769$	41.5692			1.49902			0.749512	+	0.661991i	$0.230288\pi$
$770$		0			0
$771$	−12.0000			−0.432169
$772$	−2.14093	+	6.58911i	−0.0770538	+	0.237147i
$773$	4.85410	−	3.52671i	0.174590	−	0.126847i	−0.497059	−	0.867717i	$-0.665587\pi$
$773$	4.85410	−	3.52671i	0.174590	−	0.126847i	0.671648	+	0.740870i	$0.265587\pi$
$774$	4.85410	+	3.52671i	0.174477	+	0.126765i
$775$	1.23607	+	3.80423i	0.0444009	+	0.136652i
$776$	5.35233	+	16.4728i	0.192137	+	0.591338i
$777$	−56.0503	−	40.7230i	−2.01079	−	1.46093i
$778$	−8.40755	+	6.10844i	−0.301425	+	0.218998i
$779$	−14.8328	+	45.6507i	−0.531441	+	1.63561i
$780$		0			0
$781$		0			0
$782$	−72.0000			−2.57471
$783$		0			0
$784$	20.2254	−	14.6946i	0.722337	−	0.524808i
$785$	1.61803	+	1.17557i	0.0577501	+	0.0419579i
$786$	7.41641	+	22.8254i	0.264535	+	0.814154i
$787$	−13.9161	−	42.8292i	−0.496054	−	1.52670i	−0.815308	−	0.579028i	$-0.803432\pi$
$787$	−13.9161	−	42.8292i	−0.496054	−	1.52670i	0.319254	−	0.947669i	$-0.396568\pi$
$788$		0			0
$789$	−5.60503	+	4.07230i	−0.199544	+	0.144978i
$790$	−3.70820	+	11.4127i	−0.131932	+	0.406045i
$791$	20.7846			0.739016
$792$		0			0
$793$		0			0
$794$	−18.1979	+	56.0075i	−0.645820	+	1.98763i
$795$	9.70820	−	7.05342i	0.344315	−	0.250159i
$796$	−3.23607	−	2.35114i	−0.114699	−	0.0833340i
$797$	−5.56231	−	17.1190i	−0.197027	−	0.606387i	−0.999947	−	0.0102999i	$-0.996721\pi$
$797$	−5.56231	−	17.1190i	−0.197027	−	0.606387i	0.802920	−	0.596087i	$-0.203279\pi$
$798$	−25.6912	−	79.0694i	−0.909458	−	2.79902i
$799$	−33.6302	−	24.4338i	−1.18975	−	0.864405i
$800$	4.20378	−	3.05422i	0.148626	−	0.107983i
$801$	−1.85410	+	5.70634i	−0.0655115	+	0.201624i
$802$	−31.1769			−1.10090
$803$		0			0
$804$	20.0000			0.705346
$805$	6.42280	−	19.7673i	0.226374	−	0.696707i
$806$		0			0
$807$	48.5410	+	35.2671i	1.70872	+	1.24146i
$808$	−7.41641	−	22.8254i	−0.260908	−	0.802993i
$809$	4.28187	+	13.1782i	0.150542	+	0.463322i	0.997682	−	0.0680486i	$-0.0216773\pi$
$809$	4.28187	+	13.1782i	0.150542	+	0.463322i	−0.847140	+	0.531370i	$0.821677\pi$
$810$	15.4138	+	11.1988i	0.541587	+	0.393486i
$811$	11.2101	−	8.14459i	0.393639	−	0.285995i	−0.373306	−	0.927708i	$-0.621776\pi$
$811$	11.2101	−	8.14459i	0.393639	−	0.285995i	0.766945	+	0.641713i	$0.221776\pi$
$812$		0			0
$813$	13.8564			0.485965
$814$		0			0
$815$	2.00000			0.0700569
$816$	21.4093	−	65.8911i	0.749476	−	2.30665i
$817$	−19.4164	+	14.1068i	−0.679294	+	0.493536i
$818$	−29.1246	−	21.1603i	−1.01832	−	0.739851i
$819$		0			0
$820$	2.14093	+	6.58911i	0.0747646	+	0.230102i
$821$	39.2352	+	28.5061i	1.36932	+	0.994869i	0.997790	+	0.0664475i	$0.0211665\pi$
$821$	39.2352	+	28.5061i	1.36932	+	0.994869i	0.371529	+	0.928421i	$0.378834\pi$
$822$	−16.8151	+	12.2169i	−0.586494	+	0.426113i
$823$	8.03444	−	24.7275i	0.280063	−	0.861945i	−0.707772	−	0.706441i	$-0.750300\pi$
$823$	8.03444	−	24.7275i	0.280063	−	0.861945i	0.987835	−	0.155505i	$-0.0497003\pi$
$824$	−3.46410			−0.120678
$825$		0			0
$826$		0			0
$827$	−5.35233	+	16.4728i	−0.186119	+	0.572815i	−0.999966	−	0.00826439i	$-0.997369\pi$
$827$	−5.35233	+	16.4728i	−0.186119	+	0.572815i	0.813847	+	0.581079i	$0.197369\pi$
$828$	−4.85410	+	3.52671i	−0.168692	+	0.122562i
$829$	27.5066	+	19.9847i	0.955343	+	0.694097i	0.952064	−	0.305897i	$-0.0989564\pi$
$829$	27.5066	+	19.9847i	0.955343	+	0.694097i	0.00327844	+	0.999995i	$0.498956\pi$
$830$	−9.27051	−	28.5317i	−0.321784	−	0.990350i
$831$	17.1275	+	52.7129i	0.594145	+	1.82859i
$832$		0			0
$833$	28.0252	−	20.3615i	0.971015	−	0.705483i
$834$	14.8328	−	45.6507i	0.513618	−	1.58075i
$835$	10.3923			0.359641
$836$		0			0
$837$	−16.0000			−0.553041
$838$	−6.42280	+	19.7673i	−0.221872	+	0.682851i
$839$	9.70820	−	7.05342i	0.335164	−	0.243511i	−0.407454	−	0.913226i	$-0.633583\pi$
$839$	9.70820	−	7.05342i	0.335164	−	0.243511i	0.742619	+	0.669714i	$0.233583\pi$
$840$	9.70820	+	7.05342i	0.334965	+	0.243366i
$841$	−8.96149	−	27.5806i	−0.309017	−	0.951057i
$842$	−13.9161	−	42.8292i	−0.479579	−	1.47599i
$843$	11.2101	+	8.14459i	0.386095	+	0.280515i
$844$	16.8151	−	12.2169i	0.578800	−	0.420523i
$845$	−4.01722	+	12.3637i	−0.138197	+	0.425325i
$846$	−10.3923			−0.357295
$847$		0			0
$848$	30.0000			1.03020
$849$	14.9865	−	46.1238i	0.514336	−	1.58296i
$850$	9.70820	−	7.05342i	0.332989	−	0.241930i
$851$	−48.5410	−	35.2671i	−1.66396	−	1.20894i
$852$		0			0
$853$	12.8456	+	39.5347i	0.439825	+	1.35364i	0.888061	+	0.459726i	$0.152052\pi$
$853$	12.8456	+	39.5347i	0.439825	+	1.35364i	−0.448236	+	0.893915i	$0.647948\pi$
$854$	−33.6302	−	24.4338i	−1.15080	−	0.836107i
$855$	5.60503	−	4.07230i	0.191688	−	0.139270i
$856$	1.85410	−	5.70634i	0.0633719	−	0.195039i
$857$	20.7846			0.709989			0.354994	−	0.934868i	$-0.384483\pi$
$857$	20.7846			0.709989			0.354994	+	0.934868i	$0.384483\pi$
$858$		0			0
$859$	−4.00000			−0.136478			−0.0682391	−	0.997669i	$-0.521738\pi$
$859$	−4.00000			−0.136478			−0.0682391	+	0.997669i	$0.521738\pi$
$860$	−1.07047	+	3.29456i	−0.0365026	+	0.112343i
$861$	−38.8328	+	28.2137i	−1.32342	+	0.961520i
$862$	−38.8328	−	28.2137i	−1.32265	−	0.960962i
$863$	−16.6869	−	51.3571i	−0.568029	−	1.74821i	−0.658775	−	0.752340i	$-0.728925\pi$
$863$	−16.6869	−	51.3571i	−0.568029	−	1.74821i	0.0907454	−	0.995874i	$-0.471075\pi$
$864$	6.42280	+	19.7673i	0.218508	+	0.672499i
$865$		0			0
$866$	47.6428	−	34.6145i	1.61897	−	1.17625i
$867$	19.1591	−	58.9655i	0.650676	−	2.00257i
$868$	13.8564			0.470317
$869$		0			0
$870$		0			0
$871$		0			0
$872$	9.70820	−	7.05342i	0.328761	−	0.238859i
$873$	8.09017	+	5.87785i	0.273811	+	0.198935i
$874$	−22.2492	−	68.4761i	−0.752591	−	2.31624i
$875$	1.07047	+	3.29456i	0.0361884	+	0.111376i
$876$	11.2101	+	8.14459i	0.378753	+	0.275180i
$877$	−22.4201	+	16.2892i	−0.757074	+	0.550047i	−0.898012	−	0.439972i	$-0.854988\pi$
$877$	−22.4201	+	16.2892i	−0.757074	+	0.550047i	0.140937	+	0.990019i	$0.454988\pi$
$878$	7.41641	−	22.8254i	0.250292	−	0.770318i
$879$	27.7128			0.934730
$880$		0			0
$881$	−30.0000			−1.01073			−0.505363	−	0.862907i	$-0.668641\pi$
$881$	−30.0000			−1.01073			−0.505363	+	0.862907i	$0.668641\pi$
$882$	2.67617	−	8.23639i	0.0901112	−	0.277334i
$883$	−27.5066	+	19.9847i	−0.925670	+	0.672539i	−0.944929	−	0.327276i	$-0.893869\pi$
$883$	−27.5066	+	19.9847i	−0.925670	+	0.672539i	0.0192588	+	0.999815i	$0.493869\pi$
$884$		0			0
$885$		0			0
$886$	−3.21140	−	9.88367i	−0.107889	−	0.332048i
$887$	14.0126	+	10.1807i	0.470497	+	0.341836i	0.797635	−	0.603141i	$-0.206084\pi$
$887$	14.0126	+	10.1807i	0.470497	+	0.341836i	−0.327138	+	0.944977i	$0.606084\pi$
$888$	28.0252	−	20.3615i	0.940463	−	0.683286i
$889$	11.1246	−	34.2380i	0.373108	−	1.14831i
$890$	−10.3923			−0.348351
$891$		0			0
$892$	14.0000			0.468755
$893$	12.8456	−	39.5347i	0.429861	−	1.32298i
$894$	−19.4164	+	14.1068i	−0.649382	+	0.471804i
$895$	9.70820	+	7.05342i	0.324509	+	0.235770i
$896$	12.9787	+	39.9444i	0.433588	+	1.33445i
$897$		0			0
$898$	−42.0378	−	30.5422i	−1.40282	−	1.01921i
$899$		0			0
$900$	0.309017	−	0.951057i	0.0103006	−	0.0317019i
$901$	41.5692			1.38487
$902$		0			0
$903$	−24.0000			−0.798670
$904$	−3.21140	+	9.88367i	−0.106810	+	0.328726i
$905$	−11.3262	+	8.22899i	−0.376497	+	0.273541i
$906$	−19.4164	−	14.1068i	−0.645067	−	0.468669i
$907$	8.03444	+	24.7275i	0.266779	+	0.821062i	0.991278	+	0.131786i	$0.0420712\pi$
$907$	8.03444	+	24.7275i	0.266779	+	0.821062i	−0.724499	+	0.689276i	$0.757929\pi$
$908$	1.07047	+	3.29456i	0.0355247	+	0.109334i
$909$	−11.2101	−	8.14459i	−0.371814	−	0.270139i
$910$		0			0
$911$	−11.1246	+	34.2380i	−0.368575	+	1.13436i	0.579137	+	0.815230i	$0.303390\pi$
$911$	−11.1246	+	34.2380i	−0.368575	+	1.13436i	−0.947712	+	0.319127i	$0.896610\pi$
$912$	69.2820			2.29416
$913$		0			0
$914$	36.0000			1.19077
$915$	4.28187	−	13.1782i	0.141554	−	0.435659i
$916$	1.61803	−	1.17557i	0.0534613	−	0.0388419i
$917$	−19.4164	−	14.1068i	−0.641186	−	0.465849i
$918$	14.8328	+	45.6507i	0.489556	+	1.50670i
$919$	−4.28187	−	13.1782i	−0.141246	−	0.434710i	0.855263	−	0.518193i	$-0.173395\pi$
$919$	−4.28187	−	13.1782i	−0.141246	−	0.434710i	−0.996509	+	0.0834839i	$0.973395\pi$
$920$	8.40755	+	6.10844i	0.277189	+	0.201389i
$921$	5.60503	−	4.07230i	0.184692	−	0.134187i
$922$	−14.8328	+	45.6507i	−0.488493	+	1.50343i
$923$		0			0
$924$		0			0
$925$	10.0000			0.328798
$926$	7.49326	−	23.0619i	0.246244	−	0.757861i
$927$	−1.61803	+	1.17557i	−0.0531432	+	0.0386108i
$928$		0			0
$929$	−1.85410	−	5.70634i	−0.0608311	−	0.187219i	0.916023	−	0.401126i	$-0.131381\pi$
$929$	−1.85410	−	5.70634i	−0.0608311	−	0.187219i	−0.976854	+	0.213907i	$0.931381\pi$
$930$	4.28187	+	13.1782i	0.140408	+	0.432131i
$931$	28.0252	+	20.3615i	0.918488	+	0.667321i
$932$	−5.60503	+	4.07230i	−0.183599	+	0.133392i
$933$	−14.8328	+	45.6507i	−0.485605	+	1.49454i
$934$	31.1769			1.02014
$935$		0			0
$936$		0			0
$937$	−10.7047	+	32.9456i	−0.349706	+	1.07628i	0.609310	+	0.792932i	$0.291447\pi$
$937$	−10.7047	+	32.9456i	−0.349706	+	1.07628i	−0.959016	+	0.283352i	$0.908553\pi$
$938$	−48.5410	+	35.2671i	−1.58492	+	1.15151i
$939$	−55.0132	−	39.9694i	−1.79529	−	1.30435i
$940$	−1.85410	−	5.70634i	−0.0604741	−	0.186120i
$941$	−4.28187	−	13.1782i	−0.139585	−	0.429598i	0.856690	−	0.515831i	$-0.172517\pi$
$941$	−4.28187	−	13.1782i	−0.139585	−	0.429598i	−0.996275	+	0.0862335i	$0.972517\pi$
$942$	5.60503	+	4.07230i	0.182622	+	0.132683i
$943$	−33.6302	+	24.4338i	−1.09515	+	0.795673i
$944$		0			0
$945$	−13.8564			−0.450749
$946$		0			0
$947$	−6.00000			−0.194974			−0.0974869	−	0.995237i	$-0.531080\pi$
$947$	−6.00000			−0.194974			−0.0974869	+	0.995237i	$0.531080\pi$
$948$	−4.28187	+	13.1782i	−0.139069	+	0.428009i
$949$		0			0
$950$	9.70820	+	7.05342i	0.314976	+	0.228843i
$951$	−11.1246	−	34.2380i	−0.360740	−	1.11024i
$952$	12.8456	+	39.5347i	0.416328	+	1.28133i
$953$	−28.0252	−	20.3615i	−0.907824	−	0.659573i	0.0326393	−	0.999467i	$-0.489609\pi$
$953$	−28.0252	−	20.3615i	−0.907824	−	0.659573i	−0.940464	+	0.339894i	$0.889609\pi$
$954$	8.40755	−	6.10844i	0.272205	−	0.197768i
$955$	−3.70820	+	11.4127i	−0.119995	+	0.369306i
$956$	−6.92820			−0.224074
$957$		0			0
$958$	−36.0000			−1.16311
$959$	6.42280	−	19.7673i	0.207403	−	0.638321i
$960$	−1.61803	+	1.17557i	−0.0522218	+	0.0379414i
$961$	12.1353	+	8.81678i	0.391460	+	0.284412i
$962$		0			0
$963$	−1.07047	−	3.29456i	−0.0344953	−	0.106166i
$964$	16.8151	+	12.2169i	0.541578	+	0.393479i
$965$	5.60503	−	4.07230i	0.180432	−	0.131092i
$966$	22.2492	−	68.4761i	0.715857	−	2.20318i
$967$	24.2487			0.779786			0.389893	−	0.920860i	$-0.372512\pi$
$967$	24.2487			0.779786			0.389893	+	0.920860i	$0.372512\pi$
$968$		0			0
$969$	96.0000			3.08396
$970$	−5.35233	+	16.4728i	−0.171853	+	0.528909i
$971$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$971$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$972$	8.09017	+	5.87785i	0.259492	+	0.188532i
$973$	14.8328	+	45.6507i	0.475518	+	1.46349i
$974$	−7.49326	−	23.0619i	−0.240100	−	0.738951i
$975$		0			0
$976$	28.0252	−	20.3615i	0.897064	−	0.651755i
$977$	−12.9787	+	39.9444i	−0.415226	+	1.27793i	0.496823	+	0.867852i	$0.334500\pi$
$977$	−12.9787	+	39.9444i	−0.415226	+	1.27793i	−0.912049	+	0.410082i	$0.865500\pi$
$978$	6.92820			0.221540
$979$		0			0
$980$	5.00000			0.159719
$981$	2.14093	−	6.58911i	0.0683547	−	0.210374i
$982$	−19.4164	+	14.1068i	−0.619602	+	0.450168i
$983$	−33.9787	−	24.6870i	−1.08375	−	0.787392i	−0.105419	−	0.994428i	$-0.533618\pi$
$983$	−33.9787	−	24.6870i	−1.08375	−	0.787392i	−0.978333	+	0.207035i	$0.933618\pi$
$984$	−7.41641	−	22.8254i	−0.236426	−	0.727646i
$985$		0			0
$986$		0			0
$987$	33.6302	−	24.4338i	1.07046	−	0.777736i
$988$		0			0
$989$	−20.7846			−0.660912
$990$		0			0
$991$	28.0000			0.889449			0.444725	−	0.895667i	$-0.353302\pi$
$991$	28.0000			0.889449			0.444725	+	0.895667i	$0.353302\pi$
$992$	−6.42280	+	19.7673i	−0.203924	+	0.627614i
$993$	−12.9443	+	9.40456i	−0.410774	+	0.298445i
$994$		0			0
$995$	1.23607	+	3.80423i	0.0391860	+	0.120602i
$996$	−10.7047	−	32.9456i	−0.339190	−	1.04392i
$997$	−33.6302	−	24.4338i	−1.06508	−	0.773825i	−0.0900579	−	0.995937i	$-0.528705\pi$
$997$	−33.6302	−	24.4338i	−1.06508	−	0.773825i	−0.975021	+	0.222111i	$0.928705\pi$
$998$	−22.4201	+	16.2892i	−0.709697	+	0.515625i
$999$	−12.3607	+	38.0423i	−0.391075	+	1.20360i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.g.h.251.2		8
11.2	odd	10	inner	605.2.g.h.366.2		8
11.3	even	5	inner	605.2.g.h.81.1		8
11.4	even	5		605.2.a.f.1.2	yes	2
11.5	even	5	inner	605.2.g.h.511.2		8
11.6	odd	10	inner	605.2.g.h.511.1		8
11.7	odd	10		605.2.a.f.1.1	✓	2
11.8	odd	10	inner	605.2.g.h.81.2		8
11.9	even	5	inner	605.2.g.h.366.1		8
11.10	odd	2	inner	605.2.g.h.251.1		8
33.26	odd	10		5445.2.a.r.1.1		2
33.29	even	10		5445.2.a.r.1.2		2
44.7	even	10		9680.2.a.bg.1.2		2
44.15	odd	10		9680.2.a.bg.1.1		2
55.4	even	10		3025.2.a.j.1.1		2
55.29	odd	10		3025.2.a.j.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
605.2.a.f.1.1	✓	2	11.7	odd	10
605.2.a.f.1.2	yes	2	11.4	even	5
605.2.g.h.81.1		8	11.3	even	5	inner
605.2.g.h.81.2		8	11.8	odd	10	inner
605.2.g.h.251.1		8	11.10	odd	2	inner
605.2.g.h.251.2		8	1.1	even	1	trivial
605.2.g.h.366.1		8	11.9	even	5	inner
605.2.g.h.366.2		8	11.2	odd	10	inner
605.2.g.h.511.1		8	11.6	odd	10	inner
605.2.g.h.511.2		8	11.5	even	5	inner
3025.2.a.j.1.1		2	55.4	even	10
3025.2.a.j.1.2		2	55.29	odd	10
5445.2.a.r.1.1		2	33.26	odd	10
5445.2.a.r.1.2		2	33.29	even	10
9680.2.a.bg.1.1		2	44.15	odd	10
9680.2.a.bg.1.2		2	44.7	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)

\(f(q)\)	\(=\)	\(q+(0.535233 - 1.64728i) q^{2} +(-1.61803 + 1.17557i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.309017 + 0.951057i) q^{5} +(1.07047 + 3.29456i) q^{6} +(-2.80252 - 2.03615i) q^{7} +(1.40126 - 1.01807i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(0.535233 - 1.64728i) q^{2} +(-1.61803 + 1.17557i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.309017 + 0.951057i) q^{5} +(1.07047 + 3.29456i) q^{6} +(-2.80252 - 2.03615i) q^{7} +(1.40126 - 1.01807i) q^{8} +(0.309017 - 0.951057i) q^{9} +1.73205 q^{10} +2.00000 q^{12} +(-4.85410 + 3.52671i) q^{14} +(-1.61803 - 1.17557i) q^{15} +(-1.54508 - 4.75528i) q^{16} +(-2.14093 - 6.58911i) q^{17} +(-1.40126 - 1.01807i) q^{18} +(5.60503 - 4.07230i) q^{19} +(0.309017 - 0.951057i) q^{20} +6.92820 q^{21} +6.00000 q^{23} +(-1.07047 + 3.29456i) q^{24} +(-0.809017 + 0.587785i) q^{25} +(-1.23607 - 3.80423i) q^{27} +(1.07047 + 3.29456i) q^{28} +(-2.80252 + 2.03615i) q^{30} +(1.23607 - 3.80423i) q^{31} -5.19615 q^{32} -12.0000 q^{34} +(1.07047 - 3.29456i) q^{35} +(-0.809017 + 0.587785i) q^{36} +(-8.09017 - 5.87785i) q^{37} +(-3.70820 - 11.4127i) q^{38} +(1.40126 + 1.01807i) q^{40} +(-5.60503 + 4.07230i) q^{41} +(3.70820 - 11.4127i) q^{42} -3.46410 q^{43} +1.00000 q^{45} +(3.21140 - 9.88367i) q^{46} +(4.85410 - 3.52671i) q^{47} +(8.09017 + 5.87785i) q^{48} +(1.54508 + 4.75528i) q^{49} +(0.535233 + 1.64728i) q^{50} +(11.2101 + 8.14459i) q^{51} +(-1.85410 + 5.70634i) q^{53} -6.92820 q^{54} -6.00000 q^{56} +(-4.28187 + 13.1782i) q^{57} +(0.618034 + 1.90211i) q^{60} +(2.14093 + 6.58911i) q^{61} +(-5.60503 - 4.07230i) q^{62} +(-2.80252 + 2.03615i) q^{63} +(0.309017 - 0.951057i) q^{64} +10.0000 q^{67} +(-2.14093 + 6.58911i) q^{68} +(-9.70820 + 7.05342i) q^{69} +(-4.85410 - 3.52671i) q^{70} +(-0.535233 - 1.64728i) q^{72} +(5.60503 + 4.07230i) q^{73} +(-14.0126 + 10.1807i) q^{74} +(0.618034 - 1.90211i) q^{75} -6.92820 q^{76} +(-2.14093 + 6.58911i) q^{79} +(4.04508 - 2.93893i) q^{80} +(8.89919 + 6.46564i) q^{81} +(3.70820 + 11.4127i) q^{82} +(-5.35233 - 16.4728i) q^{83} +(-5.60503 - 4.07230i) q^{84} +(5.60503 - 4.07230i) q^{85} +(-1.85410 + 5.70634i) q^{86} -6.00000 q^{89} +(0.535233 - 1.64728i) q^{90} +(-4.85410 - 3.52671i) q^{92} +(2.47214 + 7.60845i) q^{93} +(-3.21140 - 9.88367i) q^{94} +(5.60503 + 4.07230i) q^{95} +(8.40755 - 6.10844i) q^{96} +(-3.09017 + 9.51057i) q^{97} +8.66025 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{9}+O(q^{10}) \) 8 * q - 4 * q^3 - 2 * q^4 - 2 * q^5 - 2 * q^9	\( 8 q - 4 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{9} + 16 q^{12} - 12 q^{14} - 4 q^{15} + 10 q^{16} - 2 q^{20} + 48 q^{23} - 2 q^{25} + 8 q^{27} - 8 q^{31} - 96 q^{34} - 2 q^{36} - 20 q^{37} + 24 q^{38} - 24 q^{42} + 8 q^{45} + 12 q^{47} + 20 q^{48} - 10 q^{49} + 12 q^{53} - 48 q^{56} - 4 q^{60} - 2 q^{64} + 80 q^{67} - 24 q^{69} - 12 q^{70} - 4 q^{75} + 10 q^{80} + 22 q^{81} - 24 q^{82} + 12 q^{86} - 48 q^{89} - 12 q^{92} - 16 q^{93} + 20 q^{97}+O(q^{100}) \) 8 * q - 4 * q^3 - 2 * q^4 - 2 * q^5 - 2 * q^9 + 16 * q^12 - 12 * q^14 - 4 * q^15 + 10 * q^16 - 2 * q^20 + 48 * q^23 - 2 * q^25 + 8 * q^27 - 8 * q^31 - 96 * q^34 - 2 * q^36 - 20 * q^37 + 24 * q^38 - 24 * q^42 + 8 * q^45 + 12 * q^47 + 20 * q^48 - 10 * q^49 + 12 * q^53 - 48 * q^56 - 4 * q^60 - 2 * q^64 + 80 * q^67 - 24 * q^69 - 12 * q^70 - 4 * q^75 + 10 * q^80 + 22 * q^81 - 24 * q^82 + 12 * q^86 - 48 * q^89 - 12 * q^92 - 16 * q^93 + 20 * q^97

Introduction

L-functions

Modular forms

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