LMFDB - Embedded newform 847.2.f.f.729.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [847,2,Mod(148,847)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(847, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("847.148");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 847 = 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	847.f (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:	$6.76332905120$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			729.1
Root			$0.809017 + 0.587785i$ of defining polynomial
Character	$\chi$	$=$	847.729
Dual form			847.2.f.f.323.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 + 0.951057i) q^{3} +(-0.618034 + 1.90211i) q^{4} +(-2.42705 - 1.76336i) q^{5} +(0.309017 - 0.951057i) q^{7} +(1.61803 - 1.17557i) q^{9} +O(q^{10})$	\(q+(0.309017 + 0.951057i) q^{3} +(-0.618034 + 1.90211i) q^{4} +(-2.42705 - 1.76336i) q^{5} +(0.309017 - 0.951057i) q^{7} +(1.61803 - 1.17557i) q^{9} -2.00000 q^{12} +(3.23607 - 2.35114i) q^{13} +(0.927051 - 2.85317i) q^{15} +(-3.23607 - 2.35114i) q^{16} +(4.85410 + 3.52671i) q^{17} +(0.618034 + 1.90211i) q^{19} +(4.85410 - 3.52671i) q^{20} +1.00000 q^{21} +3.00000 q^{23} +(1.23607 + 3.80423i) q^{25} +(4.04508 + 2.93893i) q^{27} +(1.61803 + 1.17557i) q^{28} +(-1.85410 + 5.70634i) q^{29} +(-4.04508 + 2.93893i) q^{31} +(-2.42705 + 1.76336i) q^{35} +(1.23607 + 3.80423i) q^{36} +(3.39919 - 10.4616i) q^{37} +(3.23607 + 2.35114i) q^{39} +(1.85410 + 5.70634i) q^{41} +8.00000 q^{43} -6.00000 q^{45} +(1.23607 - 3.80423i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(-1.85410 + 5.70634i) q^{51} +(2.47214 + 7.60845i) q^{52} +(4.85410 - 3.52671i) q^{53} +(-1.61803 + 1.17557i) q^{57} +(-2.78115 + 8.55951i) q^{59} +(4.85410 + 3.52671i) q^{60} +(8.09017 + 5.87785i) q^{61} +(-0.618034 - 1.90211i) q^{63} +(6.47214 - 4.70228i) q^{64} -12.0000 q^{65} +5.00000 q^{67} +(-9.70820 + 7.05342i) q^{68} +(0.927051 + 2.85317i) q^{69} +(-7.28115 - 5.29007i) q^{71} +(0.618034 - 1.90211i) q^{73} +(-3.23607 + 2.35114i) q^{75} -4.00000 q^{76} +(8.09017 - 5.87785i) q^{79} +(3.70820 + 11.4127i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-9.70820 - 7.05342i) q^{83} +(-0.618034 + 1.90211i) q^{84} +(-5.56231 - 17.1190i) q^{85} -6.00000 q^{87} -3.00000 q^{89} +(-1.23607 - 3.80423i) q^{91} +(-1.85410 + 5.70634i) q^{92} +(-4.04508 - 2.93893i) q^{93} +(1.85410 - 5.70634i) q^{95} +(0.809017 - 0.587785i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{3} + 2 q^{4} - 3 q^{5} - q^{7} + 2 q^{9}+O(q^{10}) $ 4 * q - q^3 + 2 * q^4 - 3 * q^5 - q^7 + 2 * q^9	$ 4 q - q^{3} + 2 q^{4} - 3 q^{5} - q^{7} + 2 q^{9} - 8 q^{12} + 4 q^{13} - 3 q^{15} - 4 q^{16} + 6 q^{17} - 2 q^{19} + 6 q^{20} + 4 q^{21} + 12 q^{23} - 4 q^{25} + 5 q^{27} + 2 q^{28} + 6 q^{29} - 5 q^{31} - 3 q^{35} - 4 q^{36} - 11 q^{37} + 4 q^{39} - 6 q^{41} + 32 q^{43} - 24 q^{45} - 4 q^{48} - q^{49} + 6 q^{51} - 8 q^{52} + 6 q^{53} - 2 q^{57} + 9 q^{59} + 6 q^{60} + 10 q^{61} + 2 q^{63} + 8 q^{64} - 48 q^{65} + 20 q^{67} - 12 q^{68} - 3 q^{69} - 9 q^{71} - 2 q^{73} - 4 q^{75} - 16 q^{76} + 10 q^{79} - 12 q^{80} - q^{81} - 12 q^{83} + 2 q^{84} + 18 q^{85} - 24 q^{87} - 12 q^{89} + 4 q^{91} + 6 q^{92} - 5 q^{93} - 6 q^{95} + q^{97}+O(q^{100}) $ 4 * q - q^3 + 2 * q^4 - 3 * q^5 - q^7 + 2 * q^9 - 8 * q^12 + 4 * q^13 - 3 * q^15 - 4 * q^16 + 6 * q^17 - 2 * q^19 + 6 * q^20 + 4 * q^21 + 12 * q^23 - 4 * q^25 + 5 * q^27 + 2 * q^28 + 6 * q^29 - 5 * q^31 - 3 * q^35 - 4 * q^36 - 11 * q^37 + 4 * q^39 - 6 * q^41 + 32 * q^43 - 24 * q^45 - 4 * q^48 - q^49 + 6 * q^51 - 8 * q^52 + 6 * q^53 - 2 * q^57 + 9 * q^59 + 6 * q^60 + 10 * q^61 + 2 * q^63 + 8 * q^64 - 48 * q^65 + 20 * q^67 - 12 * q^68 - 3 * q^69 - 9 * q^71 - 2 * q^73 - 4 * q^75 - 16 * q^76 + 10 * q^79 - 12 * q^80 - q^81 - 12 * q^83 + 2 * q^84 + 18 * q^85 - 24 * q^87 - 12 * q^89 + 4 * q^91 + 6 * q^92 - 5 * q^93 - 6 * q^95 + q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/847\mathbb{Z}\right)^\times$.

$n$	$122$	$365$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$2$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i	0.999773	−	0.0213149i	$-0.00678525\pi$
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i	−0.821362	+	0.570408i	$0.806785\pi$
$4$	−0.618034	+	1.90211i	−0.309017	+	0.951057i
$5$	−2.42705	−	1.76336i	−1.08541	−	0.788597i	−0.106792	−	0.994281i	$-0.534058\pi$
$5$	−2.42705	−	1.76336i	−1.08541	−	0.788597i	−0.978618	+	0.205685i	$0.934058\pi$
$6$		0			0
$7$	0.309017	−	0.951057i	0.116797	−	0.359466i
$7$	0.309017	−	0.951057i	0.116797	−	0.359466i
$8$		0			0
$9$	1.61803	−	1.17557i	0.539345	−	0.391857i
$10$		0			0
$11$		0			0
$11$		0			0
$12$	−2.00000			−0.577350
$13$	3.23607	−	2.35114i	0.897524	−	0.652089i	−0.0403050	−	0.999187i	$-0.512833\pi$
$13$	3.23607	−	2.35114i	0.897524	−	0.652089i	0.937829	+	0.347098i	$0.112833\pi$
$14$		0			0
$15$	0.927051	−	2.85317i	0.239364	−	0.736685i
$16$	−3.23607	−	2.35114i	−0.809017	−	0.587785i
$17$	4.85410	+	3.52671i	1.17729	+	0.855353i	0.991864	−	0.127304i	$-0.0406325\pi$
$17$	4.85410	+	3.52671i	1.17729	+	0.855353i	0.185429	+	0.982658i	$0.440633\pi$
$18$		0			0
$19$	0.618034	+	1.90211i	0.141787	+	0.436375i	0.996584	−	0.0825877i	$-0.0263185\pi$
$19$	0.618034	+	1.90211i	0.141787	+	0.436375i	−0.854797	+	0.518962i	$0.826318\pi$
$20$	4.85410	−	3.52671i	1.08541	−	0.788597i
$21$	1.00000			0.218218
$22$		0			0
$23$	3.00000			0.625543			0.312772	−	0.949828i	$-0.398743\pi$
$23$	3.00000			0.625543			0.312772	+	0.949828i	$0.398743\pi$
$24$		0			0
$25$	1.23607	+	3.80423i	0.247214	+	0.760845i
$26$		0			0
$27$	4.04508	+	2.93893i	0.778477	+	0.565597i
$28$	1.61803	+	1.17557i	0.305780	+	0.222162i
$29$	−1.85410	+	5.70634i	−0.344298	+	1.05964i	0.617660	+	0.786445i	$0.288081\pi$
$29$	−1.85410	+	5.70634i	−0.344298	+	1.05964i	−0.961958	+	0.273196i	$0.911919\pi$
$30$		0			0
$31$	−4.04508	+	2.93893i	−0.726519	+	0.527847i	−0.888460	−	0.458954i	$-0.848224\pi$
$31$	−4.04508	+	2.93893i	−0.726519	+	0.527847i	0.161942	+	0.986800i	$0.448224\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−2.42705	+	1.76336i	−0.410246	+	0.298062i
$36$	1.23607	+	3.80423i	0.206011	+	0.634038i
$37$	3.39919	−	10.4616i	0.558823	−	1.71988i	−0.126805	−	0.991928i	$-0.540472\pi$
$37$	3.39919	−	10.4616i	0.558823	−	1.71988i	0.685628	−	0.727952i	$-0.259528\pi$
$38$		0			0
$39$	3.23607	+	2.35114i	0.518186	+	0.376484i
$40$		0			0
$41$	1.85410	+	5.70634i	0.289562	+	0.891180i	0.984994	+	0.172588i	$0.0552131\pi$
$41$	1.85410	+	5.70634i	0.289562	+	0.891180i	−0.695432	+	0.718592i	$0.744787\pi$
$42$		0			0
$43$	8.00000			1.21999			0.609994	−	0.792406i	$-0.291172\pi$
$43$	8.00000			1.21999			0.609994	+	0.792406i	$0.291172\pi$
$44$		0			0
$45$	−6.00000			−0.894427
$46$		0			0
$47$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$47$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$48$	1.23607	−	3.80423i	0.178411	−	0.549093i
$49$	−0.809017	−	0.587785i	−0.115574	−	0.0839693i
$50$		0			0
$51$	−1.85410	+	5.70634i	−0.259626	+	0.799047i
$52$	2.47214	+	7.60845i	0.342824	+	1.05510i
$53$	4.85410	−	3.52671i	0.666762	−	0.484431i	−0.202178	−	0.979349i	$-0.564802\pi$
$53$	4.85410	−	3.52671i	0.666762	−	0.484431i	0.868940	+	0.494918i	$0.164802\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−1.61803	+	1.17557i	−0.214314	+	0.155708i
$58$		0			0
$59$	−2.78115	+	8.55951i	−0.362075	+	1.11435i	0.589717	+	0.807610i	$0.299239\pi$
$59$	−2.78115	+	8.55951i	−0.362075	+	1.11435i	−0.951792	+	0.306743i	$0.900761\pi$
$60$	4.85410	+	3.52671i	0.626662	+	0.455296i
$61$	8.09017	+	5.87785i	1.03584	+	0.752582i	0.969469	−	0.245213i	$-0.0788579\pi$
$61$	8.09017	+	5.87785i	1.03584	+	0.752582i	0.0663709	+	0.997795i	$0.478858\pi$
$62$		0			0
$63$	−0.618034	−	1.90211i	−0.0778650	−	0.239644i
$64$	6.47214	−	4.70228i	0.809017	−	0.587785i
$65$	−12.0000			−1.48842
$66$		0			0
$67$	5.00000			0.610847			0.305424	−	0.952217i	$-0.401202\pi$
$67$	5.00000			0.610847			0.305424	+	0.952217i	$0.401202\pi$
$68$	−9.70820	+	7.05342i	−1.17729	+	0.855353i
$69$	0.927051	+	2.85317i	0.111604	+	0.343481i
$70$		0			0
$71$	−7.28115	−	5.29007i	−0.864114	−	0.627815i	0.0648872	−	0.997893i	$-0.479331\pi$
$71$	−7.28115	−	5.29007i	−0.864114	−	0.627815i	−0.929001	+	0.370077i	$0.879331\pi$
$72$		0			0
$73$	0.618034	−	1.90211i	0.0723354	−	0.222625i	−0.908352	−	0.418206i	$-0.862659\pi$
$73$	0.618034	−	1.90211i	0.0723354	−	0.222625i	0.980688	+	0.195580i	$0.0626591\pi$
$74$		0			0
$75$	−3.23607	+	2.35114i	−0.373669	+	0.271486i
$76$	−4.00000			−0.458831
$77$		0			0
$78$		0			0
$79$	8.09017	−	5.87785i	0.910215	−	0.661310i	−0.0308541	−	0.999524i	$-0.509823\pi$
$79$	8.09017	−	5.87785i	0.910215	−	0.661310i	0.941069	+	0.338214i	$0.109823\pi$
$80$	3.70820	+	11.4127i	0.414590	+	1.27598i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$		0			0
$83$	−9.70820	−	7.05342i	−1.06561	−	0.774214i	−0.0904951	−	0.995897i	$-0.528845\pi$
$83$	−9.70820	−	7.05342i	−1.06561	−	0.774214i	−0.975119	+	0.221683i	$0.928845\pi$
$84$	−0.618034	+	1.90211i	−0.0674330	+	0.207538i
$85$	−5.56231	−	17.1190i	−0.603317	−	1.85682i
$86$		0			0
$87$	−6.00000			−0.643268
$88$		0			0
$89$	−3.00000			−0.317999			−0.159000	−	0.987279i	$-0.550827\pi$
$89$	−3.00000			−0.317999			−0.159000	+	0.987279i	$0.550827\pi$
$90$		0			0
$91$	−1.23607	−	3.80423i	−0.129575	−	0.398791i
$92$	−1.85410	+	5.70634i	−0.193303	+	0.594927i
$93$	−4.04508	−	2.93893i	−0.419456	−	0.304752i
$94$		0			0
$95$	1.85410	−	5.70634i	0.190227	−	0.585458i
$96$		0			0
$97$	0.809017	−	0.587785i	0.0821432	−	0.0596806i	−0.545956	−	0.837814i	$-0.683833\pi$
$97$	0.809017	−	0.587785i	0.0821432	−	0.0596806i	0.628099	+	0.778133i	$0.283833\pi$
$98$		0			0
$99$		0			0
$100$	−8.00000			−0.800000
$101$	9.70820	−	7.05342i	0.966002	−	0.701842i	0.0114654	−	0.999934i	$-0.496350\pi$
$101$	9.70820	−	7.05342i	0.966002	−	0.701842i	0.954537	+	0.298092i	$0.0963504\pi$
$102$		0			0
$103$	−1.23607	+	3.80423i	−0.121793	+	0.374842i	−0.993303	−	0.115536i	$-0.963141\pi$
$103$	−1.23607	+	3.80423i	−0.121793	+	0.374842i	0.871510	+	0.490378i	$0.163141\pi$
$104$		0			0
$105$	−2.42705	−	1.76336i	−0.236856	−	0.172086i
$106$		0			0
$107$	1.85410	+	5.70634i	0.179243	+	0.551653i	0.999802	−	0.0199092i	$-0.00633772\pi$
$107$	1.85410	+	5.70634i	0.179243	+	0.551653i	−0.820559	+	0.571562i	$0.806338\pi$
$108$	−8.09017	+	5.87785i	−0.778477	+	0.565597i
$109$	20.0000			1.91565			0.957826	−	0.287348i	$-0.0927736\pi$
$109$	20.0000			1.91565			0.957826	+	0.287348i	$0.0927736\pi$
$110$		0			0
$111$	11.0000			1.04407
$112$	−3.23607	+	2.35114i	−0.305780	+	0.222162i
$113$	−0.927051	−	2.85317i	−0.0872096	−	0.268404i	0.897936	−	0.440127i	$-0.145067\pi$
$113$	−0.927051	−	2.85317i	−0.0872096	−	0.268404i	−0.985145	+	0.171723i	$0.945067\pi$
$114$		0			0
$115$	−7.28115	−	5.29007i	−0.678971	−	0.493301i
$116$	−9.70820	−	7.05342i	−0.901384	−	0.654894i
$117$	2.47214	−	7.60845i	0.228549	−	0.703402i
$118$		0			0
$119$	4.85410	−	3.52671i	0.444975	−	0.323293i
$120$		0			0
$121$		0			0
$122$		0			0
$123$	−4.85410	+	3.52671i	−0.437680	+	0.317993i
$124$	−3.09017	−	9.51057i	−0.277505	−	0.854074i
$125$	−0.927051	+	2.85317i	−0.0829180	+	0.255195i
$126$		0			0
$127$	−1.61803	−	1.17557i	−0.143577	−	0.104315i	0.513678	−	0.857983i	$-0.328283\pi$
$127$	−1.61803	−	1.17557i	−0.143577	−	0.104315i	−0.657255	+	0.753668i	$0.728283\pi$
$128$		0			0
$129$	2.47214	+	7.60845i	0.217659	+	0.669887i
$130$		0			0
$131$	−6.00000			−0.524222			−0.262111	−	0.965038i	$-0.584419\pi$
$131$	−6.00000			−0.524222			−0.262111	+	0.965038i	$0.584419\pi$
$132$		0			0
$133$	2.00000			0.173422
$134$		0			0
$135$	−4.63525	−	14.2658i	−0.398939	−	1.22781i
$136$		0			0
$137$	2.42705	+	1.76336i	0.207357	+	0.150654i	0.686617	−	0.727019i	$-0.259095\pi$
$137$	2.42705	+	1.76336i	0.207357	+	0.150654i	−0.479260	+	0.877673i	$0.659095\pi$
$138$		0			0
$139$	4.32624	−	13.3148i	0.366947	−	1.12935i	−0.581806	−	0.813327i	$-0.697654\pi$
$139$	4.32624	−	13.3148i	0.366947	−	1.12935i	0.948753	−	0.316018i	$-0.102346\pi$
$140$	−1.85410	−	5.70634i	−0.156700	−	0.482274i
$141$		0			0
$142$		0			0
$143$		0			0
$144$	−8.00000			−0.666667
$145$	14.5623	−	10.5801i	1.20933	−	0.878632i
$146$		0			0
$147$	0.309017	−	0.951057i	0.0254873	−	0.0784418i
$148$	17.7984	+	12.9313i	1.46302	+	1.06294i
$149$	4.85410	+	3.52671i	0.397664	+	0.288919i	0.768589	−	0.639743i	$-0.220959\pi$
$149$	4.85410	+	3.52671i	0.397664	+	0.288919i	−0.370925	+	0.928663i	$0.620959\pi$
$150$		0			0
$151$	−3.09017	−	9.51057i	−0.251474	−	0.773959i	−0.994504	−	0.104700i	$-0.966612\pi$
$151$	−3.09017	−	9.51057i	−0.251474	−	0.773959i	0.743029	−	0.669259i	$-0.233388\pi$
$152$		0			0
$153$	12.0000			0.970143
$154$		0			0
$155$	15.0000			1.20483
$156$	−6.47214	+	4.70228i	−0.518186	+	0.376484i
$157$	−4.01722	−	12.3637i	−0.320609	−	0.986733i	−0.973384	−	0.229181i	$-0.926395\pi$
$157$	−4.01722	−	12.3637i	−0.320609	−	0.986733i	0.652775	−	0.757552i	$-0.273605\pi$
$158$		0			0
$159$	4.85410	+	3.52671i	0.384955	+	0.279686i
$160$		0			0
$161$	0.927051	−	2.85317i	0.0730619	−	0.224861i
$162$		0			0
$163$	−16.1803	+	11.7557i	−1.26734	+	0.920778i	−0.999093	−	0.0425718i	$-0.986445\pi$
$163$	−16.1803	+	11.7557i	−1.26734	+	0.920778i	−0.268249	+	0.963350i	$0.586445\pi$
$164$	−12.0000			−0.937043
$165$		0			0
$166$		0			0
$167$	−4.85410	+	3.52671i	−0.375622	+	0.272905i	−0.759538	−	0.650463i	$-0.774575\pi$
$167$	−4.85410	+	3.52671i	−0.375622	+	0.272905i	0.383917	+	0.923368i	$0.374575\pi$
$168$		0			0
$169$	0.927051	−	2.85317i	0.0713116	−	0.219475i
$170$		0			0
$171$	3.23607	+	2.35114i	0.247468	+	0.179796i
$172$	−4.94427	+	15.2169i	−0.376997	+	1.16028i
$173$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$173$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$174$		0			0
$175$	4.00000			0.302372
$176$		0			0
$177$	−9.00000			−0.676481
$178$		0			0
$179$	−4.63525	−	14.2658i	−0.346455	−	1.06628i	−0.960800	−	0.277242i	$-0.910580\pi$
$179$	−4.63525	−	14.2658i	−0.346455	−	1.06628i	0.614345	−	0.789038i	$-0.289420\pi$
$180$	3.70820	−	11.4127i	0.276393	−	0.850651i
$181$	5.66312	+	4.11450i	0.420936	+	0.305828i	0.778014	−	0.628246i	$-0.216227\pi$
$181$	5.66312	+	4.11450i	0.420936	+	0.305828i	−0.357078	+	0.934075i	$0.616227\pi$
$182$		0			0
$183$	−3.09017	+	9.51057i	−0.228432	+	0.703041i
$184$		0			0
$185$	−26.6976	+	19.3969i	−1.96284	+	1.42609i
$186$		0			0
$187$		0			0
$188$		0			0
$189$	4.04508	−	2.93893i	0.294237	−	0.213775i
$190$		0			0
$191$	−8.34346	+	25.6785i	−0.603711	+	1.85803i	−0.0982952	+	0.995157i	$0.531339\pi$
$191$	−8.34346	+	25.6785i	−0.603711	+	1.85803i	−0.505416	+	0.862876i	$0.668661\pi$
$192$	6.47214	+	4.70228i	0.467086	+	0.339358i
$193$	−11.3262	−	8.22899i	−0.815280	−	0.592336i	0.100076	−	0.994980i	$-0.468091\pi$
$193$	−11.3262	−	8.22899i	−0.815280	−	0.592336i	−0.915357	+	0.402644i	$0.868091\pi$
$194$		0			0
$195$	−3.70820	−	11.4127i	−0.265550	−	0.817279i
$196$	1.61803	−	1.17557i	0.115574	−	0.0839693i
$197$	18.0000			1.28245			0.641223	−	0.767354i	$-0.278427\pi$
$197$	18.0000			1.28245			0.641223	+	0.767354i	$0.278427\pi$
$198$		0			0
$199$	−16.0000			−1.13421			−0.567105	−	0.823646i	$-0.691937\pi$
$199$	−16.0000			−1.13421			−0.567105	+	0.823646i	$0.691937\pi$
$200$		0			0
$201$	1.54508	+	4.75528i	0.108982	+	0.335412i
$202$		0			0
$203$	4.85410	+	3.52671i	0.340691	+	0.247527i
$204$	−9.70820	−	7.05342i	−0.679710	−	0.493838i
$205$	5.56231	−	17.1190i	0.388488	−	1.19564i
$206$		0			0
$207$	4.85410	−	3.52671i	0.337383	−	0.245123i
$208$	−16.0000			−1.10940
$209$		0			0
$210$		0			0
$211$	−11.3262	+	8.22899i	−0.779730	+	0.566507i	−0.904898	−	0.425628i	$-0.860053\pi$
$211$	−11.3262	+	8.22899i	−0.779730	+	0.566507i	0.125168	+	0.992136i	$0.460053\pi$
$212$	3.70820	+	11.4127i	0.254680	+	0.783826i
$213$	2.78115	−	8.55951i	0.190561	−	0.586488i
$214$		0			0
$215$	−19.4164	−	14.1068i	−1.32419	−	0.962079i
$216$		0			0
$217$	1.54508	+	4.75528i	0.104887	+	0.322810i
$218$		0			0
$219$	2.00000			0.135147
$220$		0			0
$221$	24.0000			1.61441
$222$		0			0
$223$	−5.87132	−	18.0701i	−0.393173	−	1.21006i	−0.930375	−	0.366608i	$-0.880519\pi$
$223$	−5.87132	−	18.0701i	−0.393173	−	1.21006i	0.537203	−	0.843453i	$-0.319481\pi$
$224$		0			0
$225$	6.47214	+	4.70228i	0.431476	+	0.313485i
$226$		0			0
$227$	−3.70820	+	11.4127i	−0.246122	+	0.757486i	0.749328	+	0.662199i	$0.230377\pi$
$227$	−3.70820	+	11.4127i	−0.246122	+	0.757486i	−0.995450	+	0.0952867i	$0.969623\pi$
$228$	−1.23607	−	3.80423i	−0.0818606	−	0.251941i
$229$	−4.04508	+	2.93893i	−0.267307	+	0.194210i	−0.713362	−	0.700796i	$-0.752828\pi$
$229$	−4.04508	+	2.93893i	−0.267307	+	0.194210i	0.446055	+	0.895005i	$0.352828\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−4.85410	+	3.52671i	−0.318003	+	0.231043i	−0.735323	−	0.677717i	$-0.762969\pi$
$233$	−4.85410	+	3.52671i	−0.318003	+	0.231043i	0.417320	+	0.908760i	$0.362969\pi$
$234$		0			0
$235$		0			0
$236$	−14.5623	−	10.5801i	−0.947925	−	0.688708i
$237$	8.09017	+	5.87785i	0.525513	+	0.381808i
$238$		0			0
$239$	−3.70820	−	11.4127i	−0.239864	−	0.738225i	−0.996439	−	0.0843180i	$-0.973129\pi$
$239$	−3.70820	−	11.4127i	−0.239864	−	0.738225i	0.756575	−	0.653907i	$-0.226871\pi$
$240$	−9.70820	+	7.05342i	−0.626662	+	0.455296i
$241$	−28.0000			−1.80364			−0.901819	−	0.432113i	$-0.857768\pi$
$241$	−28.0000			−1.80364			−0.901819	+	0.432113i	$0.857768\pi$
$242$		0			0
$243$	16.0000			1.02640
$244$	−16.1803	+	11.7557i	−1.03584	+	0.752582i
$245$	0.927051	+	2.85317i	0.0592271	+	0.182282i
$246$		0			0
$247$	6.47214	+	4.70228i	0.411812	+	0.299199i
$248$		0			0
$249$	3.70820	−	11.4127i	0.234998	−	0.723249i
$250$		0			0
$251$	7.28115	−	5.29007i	0.459582	−	0.333906i	−0.333785	−	0.942649i	$-0.608326\pi$
$251$	7.28115	−	5.29007i	0.459582	−	0.333906i	0.793367	+	0.608743i	$0.208326\pi$
$252$	4.00000			0.251976
$253$		0			0
$254$		0			0
$255$	14.5623	−	10.5801i	0.911927	−	0.662554i
$256$	4.94427	+	15.2169i	0.309017	+	0.951057i
$257$	−1.85410	+	5.70634i	−0.115656	+	0.355952i	−0.992083	−	0.125582i	$-0.959920\pi$
$257$	−1.85410	+	5.70634i	−0.115656	+	0.355952i	0.876428	+	0.481534i	$0.159920\pi$
$258$		0			0
$259$	−8.89919	−	6.46564i	−0.552969	−	0.401755i
$260$	7.41641	−	22.8254i	0.459946	−	1.41557i
$261$	3.70820	+	11.4127i	0.229532	+	0.706427i
$262$		0			0
$263$	−30.0000			−1.84988			−0.924940	−	0.380114i	$-0.875885\pi$
$263$	−30.0000			−1.84988			−0.924940	+	0.380114i	$0.875885\pi$
$264$		0			0
$265$	−18.0000			−1.10573
$266$		0			0
$267$	−0.927051	−	2.85317i	−0.0567346	−	0.174611i
$268$	−3.09017	+	9.51057i	−0.188762	+	0.580950i
$269$	−24.2705	−	17.6336i	−1.47980	−	1.07514i	−0.977621	−	0.210373i	$-0.932532\pi$
$269$	−24.2705	−	17.6336i	−1.47980	−	1.07514i	−0.502178	−	0.864764i	$-0.667468\pi$
$270$		0			0
$271$	−4.94427	+	15.2169i	−0.300343	+	0.924361i	0.681031	+	0.732255i	$0.261532\pi$
$271$	−4.94427	+	15.2169i	−0.300343	+	0.924361i	−0.981374	+	0.192106i	$0.938468\pi$
$272$	−7.41641	−	22.8254i	−0.449686	−	1.38399i
$273$	3.23607	−	2.35114i	0.195856	−	0.142298i
$274$		0			0
$275$		0			0
$276$	−6.00000			−0.361158
$277$	−6.47214	+	4.70228i	−0.388873	+	0.282533i	−0.764994	−	0.644038i	$-0.777258\pi$
$277$	−6.47214	+	4.70228i	−0.388873	+	0.282533i	0.376121	+	0.926571i	$0.377258\pi$
$278$		0			0
$279$	−3.09017	+	9.51057i	−0.185004	+	0.569383i
$280$		0			0
$281$	−9.70820	−	7.05342i	−0.579143	−	0.420772i	0.259272	−	0.965804i	$-0.416517\pi$
$281$	−9.70820	−	7.05342i	−0.579143	−	0.420772i	−0.838415	+	0.545032i	$0.816517\pi$
$282$		0			0
$283$	9.88854	+	30.4338i	0.587813	+	1.80910i	0.587668	+	0.809102i	$0.300046\pi$
$283$	9.88854	+	30.4338i	0.587813	+	1.80910i	0.000144882		1.00000i	$0.499954\pi$
$284$	14.5623	−	10.5801i	0.864114	−	0.627815i
$285$	6.00000			0.355409
$286$		0			0
$287$	6.00000			0.354169
$288$		0			0
$289$	5.87132	+	18.0701i	0.345372	+	1.06295i
$290$		0			0
$291$	0.809017	+	0.587785i	0.0474254	+	0.0344566i
$292$	3.23607	+	2.35114i	0.189377	+	0.137590i
$293$	−9.27051	+	28.5317i	−0.541589	+	1.66684i	0.187376	+	0.982288i	$0.440002\pi$
$293$	−9.27051	+	28.5317i	−0.541589	+	1.66684i	−0.728965	+	0.684551i	$0.759998\pi$
$294$		0			0
$295$	21.8435	−	15.8702i	1.27178	−	0.923999i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	9.70820	−	7.05342i	0.561440	−	0.407910i
$300$	−2.47214	−	7.60845i	−0.142729	−	0.439274i
$301$	2.47214	−	7.60845i	0.142492	−	0.438544i
$302$		0			0
$303$	9.70820	+	7.05342i	0.557722	+	0.405209i
$304$	2.47214	−	7.60845i	0.141787	−	0.436375i
$305$	−9.27051	−	28.5317i	−0.530828	−	1.63372i
$306$		0			0
$307$	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
$309$	−4.00000			−0.227552
$310$		0			0
$311$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$311$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$312$		0			0
$313$	15.3713	+	11.1679i	0.868839	+	0.631248i	0.930275	−	0.366863i	$-0.119568\pi$
$313$	15.3713	+	11.1679i	0.868839	+	0.631248i	−0.0614365	+	0.998111i	$0.519568\pi$
$314$		0			0
$315$	−1.85410	+	5.70634i	−0.104467	+	0.321516i
$316$	6.18034	+	19.0211i	0.347671	+	1.07002i
$317$	−7.28115	+	5.29007i	−0.408950	+	0.297120i	−0.773177	−	0.634191i	$-0.781333\pi$
$317$	−7.28115	+	5.29007i	−0.408950	+	0.297120i	0.364226	+	0.931310i	$0.381333\pi$
$318$		0			0
$319$		0			0
$320$	−24.0000			−1.34164
$321$	−4.85410	+	3.52671i	−0.270930	+	0.196842i
$322$		0			0
$323$	−3.70820	+	11.4127i	−0.206330	+	0.635018i
$324$	1.61803	+	1.17557i	0.0898908	+	0.0653095i
$325$	12.9443	+	9.40456i	0.718019	+	0.521671i
$326$		0			0
$327$	6.18034	+	19.0211i	0.341774	+	1.05187i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−1.00000			−0.0549650			−0.0274825	−	0.999622i	$-0.508749\pi$
$331$	−1.00000			−0.0549650			−0.0274825	+	0.999622i	$0.508749\pi$
$332$	19.4164	−	14.1068i	1.06561	−	0.774214i
$333$	−6.79837	−	20.9232i	−0.372549	−	1.14659i
$334$		0			0
$335$	−12.1353	−	8.81678i	−0.663020	−	0.481712i
$336$	−3.23607	−	2.35114i	−0.176542	−	0.128265i
$337$	4.32624	−	13.3148i	0.235665	−	0.725303i	−0.761367	−	0.648321i	$-0.775472\pi$
$337$	4.32624	−	13.3148i	0.235665	−	0.725303i	0.997032	−	0.0769821i	$-0.0245284\pi$
$338$		0			0
$339$	2.42705	−	1.76336i	0.131819	−	0.0957723i
$340$	36.0000			1.95237
$341$		0			0
$342$		0			0
$343$	−0.809017	+	0.587785i	−0.0436828	+	0.0317374i
$344$		0			0
$345$	2.78115	−	8.55951i	0.149732	−	0.460828i
$346$		0			0
$347$	14.5623	+	10.5801i	0.781746	+	0.567971i	0.905502	−	0.424341i	$-0.139494\pi$
$347$	14.5623	+	10.5801i	0.781746	+	0.567971i	−0.123757	+	0.992313i	$0.539494\pi$
$348$	3.70820	−	11.4127i	0.198781	−	0.611784i
$349$	−3.09017	−	9.51057i	−0.165413	−	0.509089i	0.833653	−	0.552288i	$-0.186245\pi$
$349$	−3.09017	−	9.51057i	−0.165413	−	0.509089i	−0.999066	+	0.0431990i	$0.986245\pi$
$350$		0			0
$351$	20.0000			1.06752
$352$		0			0
$353$	−3.00000			−0.159674			−0.0798369	−	0.996808i	$-0.525440\pi$
$353$	−3.00000			−0.159674			−0.0798369	+	0.996808i	$0.525440\pi$
$354$		0			0
$355$	8.34346	+	25.6785i	0.442825	+	1.36287i
$356$	1.85410	−	5.70634i	0.0982672	−	0.302435i
$357$	4.85410	+	3.52671i	0.256906	+	0.186653i
$358$		0			0
$359$	7.41641	−	22.8254i	0.391423	−	1.20468i	−0.540289	−	0.841479i	$-0.681685\pi$
$359$	7.41641	−	22.8254i	0.391423	−	1.20468i	0.931712	−	0.363197i	$-0.118315\pi$
$360$		0			0
$361$	12.1353	−	8.81678i	0.638698	−	0.464041i
$362$		0			0
$363$		0			0
$364$	8.00000			0.419314
$365$	−4.85410	+	3.52671i	−0.254075	+	0.184597i
$366$		0			0
$367$	5.25329	−	16.1680i	0.274219	−	0.843961i	−0.715205	−	0.698914i	$-0.753667\pi$
$367$	5.25329	−	16.1680i	0.274219	−	0.843961i	0.989425	−	0.145046i	$-0.0463331\pi$
$368$	−9.70820	−	7.05342i	−0.506075	−	0.367685i
$369$	9.70820	+	7.05342i	0.505389	+	0.367187i
$370$		0			0
$371$	−1.85410	−	5.70634i	−0.0962602	−	0.296258i
$372$	8.09017	−	5.87785i	0.419456	−	0.304752i
$373$	−4.00000			−0.207112			−0.103556	−	0.994624i	$-0.533022\pi$
$373$	−4.00000			−0.207112			−0.103556	+	0.994624i	$0.533022\pi$
$374$		0			0
$375$	−3.00000			−0.154919
$376$		0			0
$377$	7.41641	+	22.8254i	0.381964	+	1.17557i
$378$		0			0
$379$	−8.89919	−	6.46564i	−0.457121	−	0.332118i	0.335280	−	0.942118i	$-0.391169\pi$
$379$	−8.89919	−	6.46564i	−0.457121	−	0.332118i	−0.792401	+	0.610001i	$0.791169\pi$
$380$	9.70820	+	7.05342i	0.498020	+	0.361833i
$381$	0.618034	−	1.90211i	0.0316628	−	0.0974482i
$382$		0			0
$383$	−16.9894	+	12.3435i	−0.868116	+	0.630723i	−0.930081	−	0.367355i	$-0.880263\pi$
$383$	−16.9894	+	12.3435i	−0.868116	+	0.630723i	0.0619651	+	0.998078i	$0.480263\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	12.9443	−	9.40456i	0.657994	−	0.478061i
$388$	0.618034	+	1.90211i	0.0313759	+	0.0965652i
$389$	10.1976	−	31.3849i	0.517037	−	1.59128i	−0.262508	−	0.964930i	$-0.584550\pi$
$389$	10.1976	−	31.3849i	0.517037	−	1.59128i	0.779545	−	0.626346i	$-0.215450\pi$
$390$		0			0
$391$	14.5623	+	10.5801i	0.736447	+	0.535060i
$392$		0			0
$393$	−1.85410	−	5.70634i	−0.0935271	−	0.287847i
$394$		0			0
$395$	−30.0000			−1.50946
$396$		0			0
$397$	2.00000			0.100377			0.0501886	−	0.998740i	$-0.484018\pi$
$397$	2.00000			0.100377			0.0501886	+	0.998740i	$0.484018\pi$
$398$		0			0
$399$	0.618034	+	1.90211i	0.0309404	+	0.0952248i
$400$	4.94427	−	15.2169i	0.247214	−	0.760845i
$401$	4.85410	+	3.52671i	0.242402	+	0.176116i	0.702353	−	0.711829i	$-0.252133\pi$
$401$	4.85410	+	3.52671i	0.242402	+	0.176116i	−0.459951	+	0.887945i	$0.652133\pi$
$402$		0			0
$403$	−6.18034	+	19.0211i	−0.307865	+	0.947510i
$404$	7.41641	+	22.8254i	0.368980	+	1.13560i
$405$	−2.42705	+	1.76336i	−0.120601	+	0.0876219i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	−11.3262	+	8.22899i	−0.560046	+	0.406898i	−0.831476	−	0.555561i	$-0.812504\pi$
$409$	−11.3262	+	8.22899i	−0.560046	+	0.406898i	0.271430	+	0.962458i	$0.412504\pi$
$410$		0			0
$411$	−0.927051	+	2.85317i	−0.0457281	+	0.140736i
$412$	−6.47214	−	4.70228i	−0.318859	−	0.231665i
$413$	7.28115	+	5.29007i	0.358282	+	0.260307i
$414$		0			0
$415$	11.1246	+	34.2380i	0.546086	+	1.68068i
$416$		0			0
$417$	14.0000			0.685583
$418$		0			0
$419$	24.0000			1.17248			0.586238	−	0.810139i	$-0.300608\pi$
$419$	24.0000			1.17248			0.586238	+	0.810139i	$0.300608\pi$
$420$	4.85410	−	3.52671i	0.236856	−	0.172086i
$421$	−3.09017	−	9.51057i	−0.150606	−	0.463517i	0.847084	−	0.531460i	$-0.178356\pi$
$421$	−3.09017	−	9.51057i	−0.150606	−	0.463517i	−0.997689	+	0.0679432i	$0.978356\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−7.41641	+	22.8254i	−0.359749	+	1.10719i
$426$		0			0
$427$	8.09017	−	5.87785i	0.391511	−	0.284449i
$428$	−12.0000			−0.580042
$429$		0			0
$430$		0			0
$431$	−9.70820	+	7.05342i	−0.467628	+	0.339751i	−0.796516	−	0.604617i	$-0.793326\pi$
$431$	−9.70820	+	7.05342i	−0.467628	+	0.339751i	0.328888	+	0.944369i	$0.393326\pi$
$432$	−6.18034	−	19.0211i	−0.297352	−	0.915155i
$433$	3.39919	−	10.4616i	0.163354	−	0.502753i	−0.835557	−	0.549404i	$-0.814855\pi$
$433$	3.39919	−	10.4616i	0.163354	−	0.502753i	0.998911	+	0.0466507i	$0.0148548\pi$
$434$		0			0
$435$	14.5623	+	10.5801i	0.698209	+	0.507279i
$436$	−12.3607	+	38.0423i	−0.591969	+	1.82189i
$437$	1.85410	+	5.70634i	0.0886937	+	0.272971i
$438$		0			0
$439$	26.0000			1.24091			0.620456	−	0.784241i	$-0.286947\pi$
$439$	26.0000			1.24091			0.620456	+	0.784241i	$0.286947\pi$
$440$		0			0
$441$	−2.00000			−0.0952381
$442$		0			0
$443$	2.78115	+	8.55951i	0.132137	+	0.406675i	0.995134	−	0.0985344i	$-0.0314154\pi$
$443$	2.78115	+	8.55951i	0.132137	+	0.406675i	−0.862997	+	0.505209i	$0.831415\pi$
$444$	−6.79837	+	20.9232i	−0.322637	+	0.992973i
$445$	7.28115	+	5.29007i	0.345160	+	0.250773i
$446$		0			0
$447$	−1.85410	+	5.70634i	−0.0876960	+	0.269901i
$448$	−2.47214	−	7.60845i	−0.116797	−	0.359466i
$449$	7.28115	−	5.29007i	0.343619	−	0.249654i	−0.402568	−	0.915390i	$-0.631882\pi$
$449$	7.28115	−	5.29007i	0.343619	−	0.249654i	0.746187	+	0.665736i	$0.231882\pi$
$450$		0			0
$451$		0			0
$452$	6.00000			0.282216
$453$	8.09017	−	5.87785i	0.380109	−	0.276166i
$454$		0			0
$455$	−3.70820	+	11.4127i	−0.173843	+	0.535035i
$456$		0			0
$457$	−6.47214	−	4.70228i	−0.302754	−	0.219963i	0.426027	−	0.904710i	$-0.359913\pi$
$457$	−6.47214	−	4.70228i	−0.302754	−	0.219963i	−0.728781	+	0.684747i	$0.759913\pi$
$458$		0			0
$459$	9.27051	+	28.5317i	0.432710	+	1.33175i
$460$	14.5623	−	10.5801i	0.678971	−	0.493301i
$461$	−6.00000			−0.279448			−0.139724	−	0.990190i	$-0.544622\pi$
$461$	−6.00000			−0.279448			−0.139724	+	0.990190i	$0.544622\pi$
$462$		0			0
$463$	5.00000			0.232370			0.116185	−	0.993228i	$-0.462933\pi$
$463$	5.00000			0.232370			0.116185	+	0.993228i	$0.462933\pi$
$464$	19.4164	−	14.1068i	0.901384	−	0.654894i
$465$	4.63525	+	14.2658i	0.214955	+	0.661563i
$466$		0			0
$467$	−12.1353	−	8.81678i	−0.561553	−	0.407992i	0.270474	−	0.962727i	$-0.412820\pi$
$467$	−12.1353	−	8.81678i	−0.561553	−	0.407992i	−0.832027	+	0.554735i	$0.812820\pi$
$468$	12.9443	+	9.40456i	0.598349	+	0.434726i
$469$	1.54508	−	4.75528i	0.0713454	−	0.219579i
$470$		0			0
$471$	10.5172	−	7.64121i	0.484608	−	0.352088i
$472$		0			0
$473$		0			0
$474$		0			0
$475$	−6.47214	+	4.70228i	−0.296962	+	0.215755i
$476$	3.70820	+	11.4127i	0.169965	+	0.523099i
$477$	3.70820	−	11.4127i	0.169787	−	0.522551i
$478$		0			0
$479$	9.70820	+	7.05342i	0.443579	+	0.322279i	0.787055	−	0.616882i	$-0.211605\pi$
$479$	9.70820	+	7.05342i	0.443579	+	0.322279i	−0.343476	+	0.939161i	$0.611605\pi$
$480$		0			0
$481$	−13.5967	−	41.8465i	−0.619958	−	1.90804i
$482$		0			0
$483$	3.00000			0.136505
$484$		0			0
$485$	−3.00000			−0.136223
$486$		0			0
$487$	3.39919	+	10.4616i	0.154032	+	0.474061i	0.998062	−	0.0622352i	$-0.0198229\pi$
$487$	3.39919	+	10.4616i	0.154032	+	0.474061i	−0.844030	+	0.536297i	$0.819823\pi$
$488$		0			0
$489$	−16.1803	−	11.7557i	−0.731700	−	0.531611i
$490$		0			0
$491$	−9.27051	+	28.5317i	−0.418372	+	1.28762i	0.490827	+	0.871257i	$0.336695\pi$
$491$	−9.27051	+	28.5317i	−0.418372	+	1.28762i	−0.909200	+	0.416361i	$0.863305\pi$
$492$	−3.70820	−	11.4127i	−0.167179	−	0.514523i
$493$	−29.1246	+	21.1603i	−1.31171	+	0.953011i
$494$		0			0
$495$		0			0
$496$	20.0000			0.898027
$497$	−7.28115	+	5.29007i	−0.326604	+	0.237292i
$498$		0			0
$499$	−1.23607	+	3.80423i	−0.0553340	+	0.170301i	−0.974904	−	0.222626i	$-0.928537\pi$
$499$	−1.23607	+	3.80423i	−0.0553340	+	0.170301i	0.919570	+	0.392926i	$0.128537\pi$
$500$	−4.85410	−	3.52671i	−0.217082	−	0.157719i
$501$	−4.85410	−	3.52671i	−0.216865	−	0.157562i
$502$		0			0
$503$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$503$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$504$		0			0
$505$	−36.0000			−1.60198
$506$		0			0
$507$	3.00000			0.133235
$508$	3.23607	−	2.35114i	0.143577	−	0.104315i
$509$	6.48936	+	19.9722i	0.287636	+	0.885252i	0.985596	+	0.169115i	$0.0540911\pi$
$509$	6.48936	+	19.9722i	0.287636	+	0.885252i	−0.697961	+	0.716136i	$0.745909\pi$
$510$		0			0
$511$	−1.61803	−	1.17557i	−0.0715776	−	0.0520042i
$512$		0			0
$513$	−3.09017	+	9.51057i	−0.136434	+	0.419902i
$514$		0			0
$515$	9.70820	−	7.05342i	0.427795	−	0.310811i
$516$	−16.0000			−0.704361
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	0.927051	−	2.85317i	0.0406148	−	0.125000i	−0.928693	−	0.370849i	$-0.879067\pi$
$521$	0.927051	−	2.85317i	0.0406148	−	0.125000i	0.969308	+	0.245849i	$0.0790668\pi$
$522$		0			0
$523$	12.9443	+	9.40456i	0.566013	+	0.411233i	0.833655	−	0.552286i	$-0.186244\pi$
$523$	12.9443	+	9.40456i	0.566013	+	0.411233i	−0.267641	+	0.963519i	$0.586244\pi$
$524$	3.70820	−	11.4127i	0.161994	−	0.498565i
$525$	1.23607	+	3.80423i	0.0539464	+	0.166030i
$526$		0			0
$527$	−30.0000			−1.30682
$528$		0			0
$529$	−14.0000			−0.608696
$530$		0			0
$531$	5.56231	+	17.1190i	0.241384	+	0.742902i
$532$	−1.23607	+	3.80423i	−0.0535903	+	0.164934i
$533$	19.4164	+	14.1068i	0.841018	+	0.611035i
$534$		0			0
$535$	5.56231	−	17.1190i	0.240479	−	0.740120i
$536$		0			0
$537$	12.1353	−	8.81678i	0.523675	−	0.380472i
$538$		0			0
$539$		0			0
$540$	30.0000			1.29099
$541$	12.9443	−	9.40456i	0.556518	−	0.404334i	−0.273665	−	0.961825i	$-0.588236\pi$
$541$	12.9443	−	9.40456i	0.556518	−	0.404334i	0.830183	+	0.557491i	$0.188236\pi$
$542$		0			0
$543$	−2.16312	+	6.65740i	−0.0928283	+	0.285696i
$544$		0			0
$545$	−48.5410	−	35.2671i	−2.07927	−	1.51068i
$546$		0			0
$547$	2.47214	+	7.60845i	0.105701	+	0.325314i	0.989894	−	0.141807i	$-0.0452913\pi$
$547$	2.47214	+	7.60845i	0.105701	+	0.325314i	−0.884193	+	0.467121i	$0.845291\pi$
$548$	−4.85410	+	3.52671i	−0.207357	+	0.150654i
$549$	20.0000			0.853579
$550$		0			0
$551$	−12.0000			−0.511217
$552$		0			0
$553$	−3.09017	−	9.51057i	−0.131407	−	0.404430i
$554$		0			0
$555$	−26.6976	−	19.3969i	−1.13325	−	0.823353i
$556$	22.6525	+	16.4580i	0.960679	+	0.697974i
$557$	9.27051	−	28.5317i	0.392804	−	1.20893i	−0.537854	−	0.843038i	$-0.680765\pi$
$557$	9.27051	−	28.5317i	0.392804	−	1.20893i	0.930659	−	0.365889i	$-0.119235\pi$
$558$		0			0
$559$	25.8885	−	18.8091i	1.09497	−	0.795541i
$560$	12.0000			0.507093
$561$		0			0
$562$		0			0
$563$	−29.1246	+	21.1603i	−1.22746	+	0.891799i	−0.996697	−	0.0812119i	$-0.974121\pi$
$563$	−29.1246	+	21.1603i	−1.22746	+	0.891799i	−0.230759	+	0.973011i	$0.574121\pi$
$564$		0			0
$565$	−2.78115	+	8.55951i	−0.117004	+	0.360101i
$566$		0			0
$567$	−0.809017	−	0.587785i	−0.0339755	−	0.0246847i
$568$		0			0
$569$	−5.56231	−	17.1190i	−0.233184	−	0.717667i	−0.997357	−	0.0726553i	$-0.976853\pi$
$569$	−5.56231	−	17.1190i	−0.233184	−	0.717667i	0.764173	−	0.645011i	$-0.223147\pi$
$570$		0			0
$571$	−4.00000			−0.167395			−0.0836974	−	0.996491i	$-0.526673\pi$
$571$	−4.00000			−0.167395			−0.0836974	+	0.996491i	$0.526673\pi$
$572$		0			0
$573$	−27.0000			−1.12794
$574$		0			0
$575$	3.70820	+	11.4127i	0.154643	+	0.475942i
$576$	4.94427	−	15.2169i	0.206011	−	0.634038i
$577$	−8.89919	−	6.46564i	−0.370478	−	0.269168i	0.386931	−	0.922109i	$-0.373535\pi$
$577$	−8.89919	−	6.46564i	−0.370478	−	0.269168i	−0.757409	+	0.652941i	$0.773535\pi$
$578$		0			0
$579$	4.32624	−	13.3148i	0.179792	−	0.553344i
$580$	11.1246	+	34.2380i	0.461924	+	1.42166i
$581$	−9.70820	+	7.05342i	−0.402764	+	0.292625i
$582$		0			0
$583$		0			0
$584$		0			0
$585$	−19.4164	+	14.1068i	−0.802770	+	0.583246i
$586$		0			0
$587$	3.70820	−	11.4127i	0.153054	−	0.471052i	−0.844905	−	0.534917i	$-0.820343\pi$
$587$	3.70820	−	11.4127i	0.153054	−	0.471052i	0.997959	+	0.0638654i	$0.0203428\pi$
$588$	1.61803	+	1.17557i	0.0667266	+	0.0484797i
$589$	−8.09017	−	5.87785i	−0.333350	−	0.242193i
$590$		0			0
$591$	5.56231	+	17.1190i	0.228803	+	0.704182i
$592$	−35.5967	+	25.8626i	−1.46302	+	1.06294i
$593$	6.00000			0.246390			0.123195	−	0.992382i	$-0.460686\pi$
$593$	6.00000			0.246390			0.123195	+	0.992382i	$0.460686\pi$
$594$		0			0
$595$	−18.0000			−0.737928
$596$	−9.70820	+	7.05342i	−0.397664	+	0.288919i
$597$	−4.94427	−	15.2169i	−0.202356	−	0.622786i
$598$		0			0
$599$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$599$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$600$		0			0
$601$	2.47214	−	7.60845i	0.100841	−	0.310355i	−0.887891	−	0.460053i	$-0.847830\pi$
$601$	2.47214	−	7.60845i	0.100841	−	0.310355i	0.988732	+	0.149698i	$0.0478302\pi$
$602$		0			0
$603$	8.09017	−	5.87785i	0.329457	−	0.239365i
$604$	20.0000			0.813788
$605$		0			0
$606$		0			0
$607$	−11.3262	+	8.22899i	−0.459718	+	0.334005i	−0.793421	−	0.608674i	$-0.791702\pi$
$607$	−11.3262	+	8.22899i	−0.459718	+	0.334005i	0.333703	+	0.942678i	$0.391702\pi$
$608$		0			0
$609$	−1.85410	+	5.70634i	−0.0751320	+	0.231233i
$610$		0			0
$611$		0			0
$612$	−7.41641	+	22.8254i	−0.299791	+	0.922660i
$613$	−4.94427	−	15.2169i	−0.199697	−	0.614605i	−0.999890	−	0.0148615i	$-0.995269\pi$
$613$	−4.94427	−	15.2169i	−0.199697	−	0.614605i	0.800192	−	0.599744i	$-0.204731\pi$
$614$		0			0
$615$	18.0000			0.725830
$616$		0			0
$617$	−30.0000			−1.20775			−0.603877	−	0.797077i	$-0.706378\pi$
$617$	−30.0000			−1.20775			−0.603877	+	0.797077i	$0.706378\pi$
$618$		0			0
$619$	−5.87132	−	18.0701i	−0.235988	−	0.726298i	−0.996989	−	0.0775461i	$-0.975291\pi$
$619$	−5.87132	−	18.0701i	−0.235988	−	0.726298i	0.761000	−	0.648751i	$-0.224709\pi$
$620$	−9.27051	+	28.5317i	−0.372313	+	1.14586i
$621$	12.1353	+	8.81678i	0.486971	+	0.353805i
$622$		0			0
$623$	−0.927051	+	2.85317i	−0.0371415	+	0.114310i
$624$	−4.94427	−	15.2169i	−0.197929	−	0.609164i
$625$	23.4615	−	17.0458i	0.938460	−	0.681831i
$626$		0			0
$627$		0			0
$628$	26.0000			1.03751
$629$	53.3951	−	38.7938i	2.12900	−	1.54681i
$630$		0			0
$631$	3.39919	−	10.4616i	0.135319	−	0.416471i	−0.860320	−	0.509754i	$-0.829736\pi$
$631$	3.39919	−	10.4616i	0.135319	−	0.416471i	0.995640	+	0.0932836i	$0.0297363\pi$
$632$		0			0
$633$	−11.3262	−	8.22899i	−0.450178	−	0.327073i
$634$		0			0
$635$	1.85410	+	5.70634i	0.0735778	+	0.226449i
$636$	−9.70820	+	7.05342i	−0.384955	+	0.279686i
$637$	−4.00000			−0.158486
$638$		0			0
$639$	−18.0000			−0.712069
$640$		0			0
$641$	4.63525	+	14.2658i	0.183082	+	0.563467i	0.999910	−	0.0134135i	$-0.00426978\pi$
$641$	4.63525	+	14.2658i	0.183082	+	0.563467i	−0.816828	+	0.576881i	$0.804270\pi$
$642$		0			0
$643$	39.6418	+	28.8015i	1.56332	+	1.13582i	0.933219	+	0.359307i	$0.116987\pi$
$643$	39.6418	+	28.8015i	1.56332	+	1.13582i	0.630102	+	0.776513i	$0.283013\pi$
$644$	4.85410	+	3.52671i	0.191278	+	0.138972i
$645$	7.41641	−	22.8254i	0.292021	−	0.898748i
$646$		0			0
$647$	26.6976	−	19.3969i	1.04959	−	0.762571i	0.0774551	−	0.996996i	$-0.475321\pi$
$647$	26.6976	−	19.3969i	1.04959	−	0.762571i	0.972134	+	0.234424i	$0.0753206\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$	−4.04508	+	2.93893i	−0.158539	+	0.115186i
$652$	−12.3607	−	38.0423i	−0.484082	−	1.48985i
$653$	12.0517	−	37.0912i	0.471618	−	1.45149i	−0.378847	−	0.925459i	$-0.623679\pi$
$653$	12.0517	−	37.0912i	0.471618	−	1.45149i	0.850465	−	0.526032i	$-0.176321\pi$
$654$		0			0
$655$	14.5623	+	10.5801i	0.568996	+	0.413400i
$656$	7.41641	−	22.8254i	0.289562	−	0.891180i
$657$	−1.23607	−	3.80423i	−0.0482236	−	0.148417i
$658$		0			0
$659$	30.0000			1.16863			0.584317	−	0.811525i	$-0.301362\pi$
$659$	30.0000			1.16863			0.584317	+	0.811525i	$0.301362\pi$
$660$		0			0
$661$	−49.0000			−1.90588			−0.952940	−	0.303160i	$-0.901958\pi$
$661$	−49.0000			−1.90588			−0.952940	+	0.303160i	$0.901958\pi$
$662$		0			0
$663$	7.41641	+	22.8254i	0.288029	+	0.886463i
$664$		0			0
$665$	−4.85410	−	3.52671i	−0.188234	−	0.136760i
$666$		0			0
$667$	−5.56231	+	17.1190i	−0.215373	+	0.662851i
$668$	−3.70820	−	11.4127i	−0.143475	−	0.441570i
$669$	15.3713	−	11.1679i	0.594290	−	0.431777i
$670$		0			0
$671$		0			0
$672$		0			0
$673$	22.6525	−	16.4580i	0.873189	−	0.634409i	−0.0582519	−	0.998302i	$-0.518553\pi$
$673$	22.6525	−	16.4580i	0.873189	−	0.634409i	0.931441	+	0.363893i	$0.118553\pi$
$674$		0			0
$675$	−6.18034	+	19.0211i	−0.237881	+	0.732124i
$676$	4.85410	+	3.52671i	0.186696	+	0.135643i
$677$	14.5623	+	10.5801i	0.559675	+	0.406628i	0.831340	−	0.555764i	$-0.187574\pi$
$677$	14.5623	+	10.5801i	0.559675	+	0.406628i	−0.271665	+	0.962392i	$0.587574\pi$
$678$		0			0
$679$	−0.309017	−	0.951057i	−0.0118590	−	0.0364982i
$680$		0			0
$681$	−12.0000			−0.459841
$682$		0			0
$683$	12.0000			0.459167			0.229584	−	0.973289i	$-0.426264\pi$
$683$	12.0000			0.459167			0.229584	+	0.973289i	$0.426264\pi$
$684$	−6.47214	+	4.70228i	−0.247468	+	0.179796i
$685$	−2.78115	−	8.55951i	−0.106262	−	0.327042i
$686$		0			0
$687$	−4.04508	−	2.93893i	−0.154330	−	0.112127i
$688$	−25.8885	−	18.8091i	−0.986991	−	0.717091i
$689$	7.41641	−	22.8254i	0.282543	−	0.869577i
$690$		0			0
$691$	−28.3156	+	20.5725i	−1.07718	+	0.782614i	−0.977188	−	0.212375i	$-0.931880\pi$
$691$	−28.3156	+	20.5725i	−1.07718	+	0.782614i	−0.0999876	+	0.994989i	$0.531880\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−33.9787	+	24.6870i	−1.28889	+	0.936431i
$696$		0			0
$697$	−11.1246	+	34.2380i	−0.421375	+	1.29686i
$698$		0			0
$699$	−4.85410	−	3.52671i	−0.183599	−	0.133392i
$700$	−2.47214	+	7.60845i	−0.0934380	+	0.287572i
$701$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$701$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$702$		0			0
$703$	22.0000			0.829746
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−3.70820	−	11.4127i	−0.139461	−	0.429218i
$708$	5.56231	−	17.1190i	0.209044	−	0.643372i
$709$	0.809017	+	0.587785i	0.0303833	+	0.0220747i	0.602873	−	0.797837i	$-0.294022\pi$
$709$	0.809017	+	0.587785i	0.0303833	+	0.0220747i	−0.572490	+	0.819912i	$0.694022\pi$
$710$		0			0
$711$	6.18034	−	19.0211i	0.231781	−	0.713348i
$712$		0			0
$713$	−12.1353	+	8.81678i	−0.454469	+	0.330191i
$714$		0			0
$715$		0			0
$716$	30.0000			1.12115
$717$	9.70820	−	7.05342i	0.362560	−	0.263415i
$718$		0			0
$719$	−12.0517	+	37.0912i	−0.449451	+	1.38327i	0.428076	+	0.903743i	$0.359191\pi$
$719$	−12.0517	+	37.0912i	−0.449451	+	1.38327i	−0.877528	+	0.479526i	$0.840809\pi$
$720$	19.4164	+	14.1068i	0.723607	+	0.525731i
$721$	3.23607	+	2.35114i	0.120517	+	0.0875611i
$722$		0			0
$723$	−8.65248	−	26.6296i	−0.321789	−	0.990365i
$724$	−11.3262	+	8.22899i	−0.420936	+	0.305828i
$725$	−24.0000			−0.891338
$726$		0			0
$727$	17.0000			0.630495			0.315248	−	0.949009i	$-0.397912\pi$
$727$	17.0000			0.630495			0.315248	+	0.949009i	$0.397912\pi$
$728$		0			0
$729$	4.01722	+	12.3637i	0.148786	+	0.457916i
$730$		0			0
$731$	38.8328	+	28.2137i	1.43628	+	1.04352i
$732$	−16.1803	−	11.7557i	−0.598043	−	0.434503i
$733$	−1.23607	+	3.80423i	−0.0456552	+	0.140512i	−0.971286	−	0.237917i	$-0.923536\pi$
$733$	−1.23607	+	3.80423i	−0.0456552	+	0.140512i	0.925630	+	0.378429i	$0.123536\pi$
$734$		0			0
$735$	−2.42705	+	1.76336i	−0.0895231	+	0.0650424i
$736$		0			0
$737$		0			0
$738$		0			0
$739$	27.5066	−	19.9847i	1.01185	−	0.735149i	0.0472504	−	0.998883i	$-0.484954\pi$
$739$	27.5066	−	19.9847i	1.01185	−	0.735149i	0.964595	+	0.263734i	$0.0849541\pi$
$740$	−20.3951	−	62.7697i	−0.749740	−	2.30746i
$741$	−2.47214	+	7.60845i	−0.0908162	+	0.279503i
$742$		0			0
$743$	−19.4164	−	14.1068i	−0.712319	−	0.517530i	0.171602	−	0.985166i	$-0.445106\pi$
$743$	−19.4164	−	14.1068i	−0.712319	−	0.517530i	−0.883921	+	0.467636i	$0.845106\pi$
$744$		0			0
$745$	−5.56231	−	17.1190i	−0.203787	−	0.627192i
$746$		0			0
$747$	−24.0000			−0.878114
$748$		0			0
$749$	6.00000			0.219235
$750$		0			0
$751$	−9.57953	−	29.4828i	−0.349562	−	1.07584i	−0.959096	−	0.283081i	$-0.908643\pi$
$751$	−9.57953	−	29.4828i	−0.349562	−	1.07584i	0.609534	−	0.792760i	$-0.291357\pi$
$752$		0			0
$753$	7.28115	+	5.29007i	0.265340	+	0.192781i
$754$		0			0
$755$	−9.27051	+	28.5317i	−0.337388	+	1.03837i
$756$	3.09017	+	9.51057i	0.112388	+	0.345896i
$757$	−30.7426	+	22.3358i	−1.11736	+	0.811810i	−0.983807	−	0.179232i	$-0.942639\pi$
$757$	−30.7426	+	22.3358i	−1.11736	+	0.811810i	−0.133554	+	0.991042i	$0.542639\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−38.8328	+	28.2137i	−1.40769	+	1.02275i	−0.414035	+	0.910261i	$0.635881\pi$
$761$	−38.8328	+	28.2137i	−1.40769	+	1.02275i	−0.993653	+	0.112485i	$0.964119\pi$
$762$		0			0
$763$	6.18034	−	19.0211i	0.223743	−	0.688611i
$764$	−43.6869	−	31.7404i	−1.58054	−	1.14833i
$765$	−29.1246	−	21.1603i	−1.05300	−	0.765051i
$766$		0			0
$767$	11.1246	+	34.2380i	0.401686	+	1.23626i
$768$	−12.9443	+	9.40456i	−0.467086	+	0.339358i
$769$	−40.0000			−1.44244			−0.721218	−	0.692708i	$-0.756418\pi$
$769$	−40.0000			−1.44244			−0.721218	+	0.692708i	$0.756418\pi$
$770$		0			0
$771$	−6.00000			−0.216085
$772$	22.6525	−	16.4580i	0.815280	−	0.592336i
$773$	−1.85410	−	5.70634i	−0.0666874	−	0.205243i	0.912160	−	0.409834i	$-0.134413\pi$
$773$	−1.85410	−	5.70634i	−0.0666874	−	0.205243i	−0.978847	+	0.204591i	$0.934413\pi$
$774$		0			0
$775$	−16.1803	−	11.7557i	−0.581215	−	0.422277i
$776$		0			0
$777$	3.39919	−	10.4616i	0.121945	−	0.375309i
$778$		0			0
$779$	−9.70820	+	7.05342i	−0.347833	+	0.252715i
$780$	24.0000			0.859338
$781$		0			0
$782$		0			0
$783$	−24.2705	+	17.6336i	−0.867357	+	0.630172i
$784$	1.23607	+	3.80423i	0.0441453	+	0.135865i
$785$	−12.0517	+	37.0912i	−0.430142	+	1.32384i
$786$		0			0
$787$	−40.4508	−	29.3893i	−1.44192	−	1.04761i	−0.987638	−	0.156755i	$-0.949897\pi$
$787$	−40.4508	−	29.3893i	−1.44192	−	1.04761i	−0.454280	−	0.890859i	$-0.650103\pi$
$788$	−11.1246	+	34.2380i	−0.396298	+	1.21968i
$789$	−9.27051	−	28.5317i	−0.330039	−	1.01576i
$790$		0			0
$791$	−3.00000			−0.106668
$792$		0			0
$793$	40.0000			1.42044
$794$		0			0
$795$	−5.56231	−	17.1190i	−0.197275	−	0.607149i
$796$	9.88854	−	30.4338i	0.350490	−	1.07870i
$797$	16.9894	+	12.3435i	0.601794	+	0.437229i	0.846515	−	0.532365i	$-0.178696\pi$
$797$	16.9894	+	12.3435i	0.601794	+	0.437229i	−0.244721	+	0.969593i	$0.578696\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$	−4.85410	+	3.52671i	−0.171511	+	0.124610i
$802$		0			0
$803$		0			0
$804$	−10.0000			−0.352673
$805$	−7.28115	+	5.29007i	−0.256627	+	0.186450i
$806$		0			0
$807$	9.27051	−	28.5317i	0.326337	−	1.00436i
$808$		0			0
$809$	−24.2705	−	17.6336i	−0.853306	−	0.619963i	0.0727498	−	0.997350i	$-0.476823\pi$
$809$	−24.2705	−	17.6336i	−0.853306	−	0.619963i	−0.926055	+	0.377387i	$0.876823\pi$
$810$		0			0
$811$	0.618034	+	1.90211i	0.0217021	+	0.0667922i	0.961321	−	0.275430i	$-0.0888203\pi$
$811$	0.618034	+	1.90211i	0.0217021	+	0.0667922i	−0.939619	+	0.342223i	$0.888820\pi$
$812$	−9.70820	+	7.05342i	−0.340691	+	0.247527i
$813$	−16.0000			−0.561144
$814$		0			0
$815$	60.0000			2.10171
$816$	19.4164	−	14.1068i	0.679710	−	0.493838i
$817$	4.94427	+	15.2169i	0.172978	+	0.532372i
$818$		0			0
$819$	−6.47214	−	4.70228i	−0.226155	−	0.164311i
$820$	29.1246	+	21.1603i	1.01708	+	0.738949i
$821$	5.56231	−	17.1190i	0.194126	−	0.597458i	−0.805860	−	0.592106i	$-0.798297\pi$
$821$	5.56231	−	17.1190i	0.194126	−	0.597458i	0.999986	−	0.00535152i	$-0.00170345\pi$
$822$		0			0
$823$	−18.6074	+	13.5191i	−0.648613	+	0.471245i	−0.862798	−	0.505548i	$-0.831290\pi$
$823$	−18.6074	+	13.5191i	−0.648613	+	0.471245i	0.214186	+	0.976793i	$0.431290\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−29.1246	+	21.1603i	−1.01276	+	0.735815i	−0.964787	−	0.263034i	$-0.915277\pi$
$827$	−29.1246	+	21.1603i	−1.01276	+	0.735815i	−0.0479754	+	0.998849i	$0.515277\pi$
$828$	3.70820	+	11.4127i	0.128869	+	0.396618i
$829$	−7.72542	+	23.7764i	−0.268315	+	0.825789i	0.722596	+	0.691271i	$0.242949\pi$
$829$	−7.72542	+	23.7764i	−0.268315	+	0.825789i	−0.990911	+	0.134518i	$0.957051\pi$
$830$		0			0
$831$	−6.47214	−	4.70228i	−0.224516	−	0.163120i
$832$	9.88854	−	30.4338i	0.342824	−	1.05510i
$833$	−1.85410	−	5.70634i	−0.0642408	−	0.197713i
$834$		0			0
$835$	18.0000			0.622916
$836$		0			0
$837$	−25.0000			−0.864126
$838$		0			0
$839$	−4.63525	−	14.2658i	−0.160027	−	0.492512i	0.838609	−	0.544734i	$-0.183369\pi$
$839$	−4.63525	−	14.2658i	−0.160027	−	0.492512i	−0.998635	+	0.0522225i	$0.983369\pi$
$840$		0			0
$841$	−5.66312	−	4.11450i	−0.195280	−	0.141879i
$842$		0			0
$843$	3.70820	−	11.4127i	0.127717	−	0.393074i
$844$	−8.65248	−	26.6296i	−0.297831	−	0.916628i
$845$	−7.28115	+	5.29007i	−0.250479	+	0.181984i
$846$		0			0
$847$		0			0
$848$	−24.0000			−0.824163
$849$	−25.8885	+	18.8091i	−0.888493	+	0.645528i
$850$		0			0
$851$	10.1976	−	31.3849i	0.349568	−	1.07586i
$852$	14.5623	+	10.5801i	0.498896	+	0.362469i
$853$	8.09017	+	5.87785i	0.277002	+	0.201254i	0.717609	−	0.696446i	$-0.245237\pi$
$853$	8.09017	+	5.87785i	0.277002	+	0.201254i	−0.440607	+	0.897700i	$0.645237\pi$
$854$		0			0
$855$	−3.70820	−	11.4127i	−0.126818	−	0.390305i
$856$		0			0
$857$	−12.0000			−0.409912			−0.204956	−	0.978771i	$-0.565705\pi$
$857$	−12.0000			−0.409912			−0.204956	+	0.978771i	$0.565705\pi$
$858$		0			0
$859$	−13.0000			−0.443554			−0.221777	−	0.975097i	$-0.571186\pi$
$859$	−13.0000			−0.443554			−0.221777	+	0.975097i	$0.571186\pi$
$860$	38.8328	−	28.2137i	1.32419	−	0.962079i
$861$	1.85410	+	5.70634i	0.0631876	+	0.194472i
$862$		0			0
$863$	9.70820	+	7.05342i	0.330471	+	0.240101i	0.740630	−	0.671913i	$-0.234527\pi$
$863$	9.70820	+	7.05342i	0.330471	+	0.240101i	−0.410159	+	0.912014i	$0.634527\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−15.3713	+	11.1679i	−0.522037	+	0.379282i
$868$	−10.0000			−0.339422
$869$		0			0
$870$		0			0
$871$	16.1803	−	11.7557i	0.548250	−	0.398327i
$872$		0			0
$873$	0.618034	−	1.90211i	0.0209173	−	0.0643768i
$874$		0			0
$875$	2.42705	+	1.76336i	0.0820493	+	0.0596123i
$876$	−1.23607	+	3.80423i	−0.0417629	+	0.128533i
$877$	−6.79837	−	20.9232i	−0.229565	−	0.706528i	−0.997796	−	0.0663553i	$-0.978863\pi$
$877$	−6.79837	−	20.9232i	−0.229565	−	0.706528i	0.768231	−	0.640172i	$-0.221137\pi$
$878$		0			0
$879$	−30.0000			−1.01187
$880$		0			0
$881$	−9.00000			−0.303218			−0.151609	−	0.988441i	$-0.548445\pi$
$881$	−9.00000			−0.303218			−0.151609	+	0.988441i	$0.548445\pi$
$882$		0			0
$883$	6.18034	+	19.0211i	0.207985	+	0.640112i	0.999578	+	0.0290628i	$0.00925227\pi$
$883$	6.18034	+	19.0211i	0.207985	+	0.640112i	−0.791593	+	0.611049i	$0.790748\pi$
$884$	−14.8328	+	45.6507i	−0.498882	+	1.53540i
$885$	21.8435	+	15.8702i	0.734260	+	0.533471i
$886$		0			0
$887$	−12.9787	+	39.9444i	−0.435783	+	1.34120i	0.456500	+	0.889723i	$0.349103\pi$
$887$	−12.9787	+	39.9444i	−0.435783	+	1.34120i	−0.892283	+	0.451477i	$0.850897\pi$
$888$		0			0
$889$	−1.61803	+	1.17557i	−0.0542671	+	0.0394274i
$890$		0			0
$891$		0			0
$892$	38.0000			1.27233
$893$		0			0
$894$		0			0
$895$	−13.9058	+	42.7975i	−0.464818	+	1.43056i
$896$		0			0
$897$	9.70820	+	7.05342i	0.324147	+	0.235507i
$898$		0			0
$899$	−9.27051	−	28.5317i	−0.309189	−	0.951585i
$900$	−12.9443	+	9.40456i	−0.431476	+	0.313485i
$901$	36.0000			1.19933
$902$		0			0
$903$	8.00000			0.266223
$904$		0			0
$905$	−6.48936	−	19.9722i	−0.215714	−	0.663898i
$906$		0			0
$907$	−6.47214	−	4.70228i	−0.214904	−	0.156137i	0.475126	−	0.879918i	$-0.342403\pi$
$907$	−6.47214	−	4.70228i	−0.214904	−	0.156137i	−0.690030	+	0.723781i	$0.742403\pi$
$908$	−19.4164	−	14.1068i	−0.644356	−	0.468152i
$909$	7.41641	−	22.8254i	0.245987	−	0.757069i
$910$		0			0
$911$	−38.8328	+	28.2137i	−1.28659	+	0.934761i	−0.999731	−	0.0232118i	$-0.992611\pi$
$911$	−38.8328	+	28.2137i	−1.28659	+	0.934761i	−0.286858	+	0.957973i	$0.592611\pi$
$912$	8.00000			0.264906
$913$		0			0
$914$		0			0
$915$	24.2705	−	17.6336i	0.802358	−	0.582947i
$916$	−3.09017	−	9.51057i	−0.102102	−	0.314238i
$917$	−1.85410	+	5.70634i	−0.0612278	+	0.188440i
$918$		0			0
$919$	12.9443	+	9.40456i	0.426992	+	0.310228i	0.780445	−	0.625224i	$-0.214993\pi$
$919$	12.9443	+	9.40456i	0.426992	+	0.310228i	−0.353453	+	0.935452i	$0.614993\pi$
$920$		0			0
$921$	6.18034	+	19.0211i	0.203649	+	0.626768i
$922$		0			0
$923$	−36.0000			−1.18495
$924$		0			0
$925$	44.0000			1.44671
$926$		0			0
$927$	2.47214	+	7.60845i	0.0811956	+	0.249894i
$928$		0			0
$929$	−14.5623	−	10.5801i	−0.477774	−	0.347123i	0.322689	−	0.946505i	$-0.395413\pi$
$929$	−14.5623	−	10.5801i	−0.477774	−	0.347123i	−0.800463	+	0.599382i	$0.795413\pi$
$930$		0			0
$931$	0.618034	−	1.90211i	0.0202552	−	0.0623392i
$932$	−3.70820	−	11.4127i	−0.121466	−	0.373835i
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−16.1803	+	11.7557i	−0.528589	+	0.384042i	−0.819830	−	0.572608i	$-0.805932\pi$
$937$	−16.1803	+	11.7557i	−0.528589	+	0.384042i	0.291241	+	0.956650i	$0.405932\pi$
$938$		0			0
$939$	−5.87132	+	18.0701i	−0.191603	+	0.589695i
$940$		0			0
$941$	−14.5623	−	10.5801i	−0.474718	−	0.344903i	0.324559	−	0.945865i	$-0.394784\pi$
$941$	−14.5623	−	10.5801i	−0.474718	−	0.344903i	−0.799277	+	0.600963i	$0.794784\pi$
$942$		0			0
$943$	5.56231	+	17.1190i	0.181134	+	0.557472i
$944$	29.1246	−	21.1603i	0.947925	−	0.688708i
$945$	−15.0000			−0.487950
$946$		0			0
$947$	−27.0000			−0.877382			−0.438691	−	0.898638i	$-0.644558\pi$
$947$	−27.0000			−0.877382			−0.438691	+	0.898638i	$0.644558\pi$
$948$	−16.1803	+	11.7557i	−0.525513	+	0.381808i
$949$	−2.47214	−	7.60845i	−0.0802489	−	0.246981i
$950$		0			0
$951$	−7.28115	−	5.29007i	−0.236108	−	0.171542i
$952$		0			0
$953$	−11.1246	+	34.2380i	−0.360362	+	1.10908i	0.592473	+	0.805590i	$0.298151\pi$
$953$	−11.1246	+	34.2380i	−0.360362	+	1.10908i	−0.952835	+	0.303489i	$0.901849\pi$
$954$		0			0
$955$	65.5304	−	47.6106i	2.12051	−	1.54064i
$956$	24.0000			0.776215
$957$		0			0
$958$		0			0
$959$	2.42705	−	1.76336i	0.0783736	−	0.0569417i
$960$	−7.41641	−	22.8254i	−0.239364	−	0.736685i
$961$	−1.85410	+	5.70634i	−0.0598097	+	0.184075i
$962$		0			0
$963$	9.70820	+	7.05342i	0.312842	+	0.227293i
$964$	17.3050	−	53.2592i	0.557355	−	1.71536i
$965$	12.9787	+	39.9444i	0.417800	+	1.28585i
$966$		0			0
$967$	14.0000			0.450210			0.225105	−	0.974335i	$-0.427728\pi$
$967$	14.0000			0.450210			0.225105	+	0.974335i	$0.427728\pi$
$968$		0			0
$969$	−12.0000			−0.385496
$970$		0			0
$971$	−12.0517	−	37.0912i	−0.386756	−	1.19031i	−0.935198	−	0.354125i	$-0.884779\pi$
$971$	−12.0517	−	37.0912i	−0.386756	−	1.19031i	0.548442	−	0.836189i	$-0.315221\pi$
$972$	−9.88854	+	30.4338i	−0.317175	+	0.976165i
$973$	−11.3262	−	8.22899i	−0.363103	−	0.263809i
$974$		0			0
$975$	−4.94427	+	15.2169i	−0.158343	+	0.487331i
$976$	−12.3607	−	38.0423i	−0.395656	−	1.21770i
$977$	−7.28115	+	5.29007i	−0.232945	+	0.169244i	−0.698134	−	0.715967i	$-0.745986\pi$
$977$	−7.28115	+	5.29007i	−0.232945	+	0.169244i	0.465190	+	0.885211i	$0.345986\pi$
$978$		0			0
$979$		0			0
$980$	−6.00000			−0.191663
$981$	32.3607	−	23.5114i	1.03320	−	0.750662i
$982$		0			0
$983$	10.1976	−	31.3849i	0.325252	−	1.00102i	−0.646075	−	0.763274i	$-0.723591\pi$
$983$	10.1976	−	31.3849i	0.325252	−	1.00102i	0.971327	−	0.237748i	$-0.0764092\pi$
$984$		0			0
$985$	−43.6869	−	31.7404i	−1.39198	−	1.01133i
$986$		0			0
$987$		0			0
$988$	−12.9443	+	9.40456i	−0.411812	+	0.299199i
$989$	24.0000			0.763156
$990$		0			0
$991$	−16.0000			−0.508257			−0.254128	−	0.967170i	$-0.581789\pi$
$991$	−16.0000			−0.508257			−0.254128	+	0.967170i	$0.581789\pi$
$992$		0			0
$993$	−0.309017	−	0.951057i	−0.00980636	−	0.0301809i
$994$		0			0
$995$	38.8328	+	28.2137i	1.23108	+	0.894434i
$996$	19.4164	+	14.1068i	0.615232	+	0.446993i
$997$	−8.65248	+	26.6296i	−0.274027	+	0.843367i	0.715449	+	0.698665i	$0.246222\pi$
$997$	−8.65248	+	26.6296i	−0.274027	+	0.843367i	−0.989475	+	0.144702i	$0.953778\pi$
$998$		0			0
$999$	44.4959	−	32.3282i	1.40779	−	1.02282i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.f.f.729.1		4
11.2	odd	10		847.2.a.c.1.1		1
11.3	even	5	inner	847.2.f.f.148.1		4
11.4	even	5	inner	847.2.f.f.323.1		4
11.5	even	5	inner	847.2.f.f.372.1		4
11.6	odd	10		847.2.f.g.372.1		4
11.7	odd	10		847.2.f.g.323.1		4
11.8	odd	10		847.2.f.g.148.1		4
11.9	even	5		77.2.a.b.1.1	✓	1
11.10	odd	2		847.2.f.g.729.1		4
33.2	even	10		7623.2.a.i.1.1		1
33.20	odd	10		693.2.a.b.1.1		1
44.31	odd	10		1232.2.a.d.1.1		1
55.9	even	10		1925.2.a.f.1.1		1
55.42	odd	20		1925.2.b.g.1849.1		2
55.53	odd	20		1925.2.b.g.1849.2		2
77.9	even	15		539.2.e.d.67.1		2
77.13	even	10		5929.2.a.d.1.1		1
77.20	odd	10		539.2.a.b.1.1		1
77.31	odd	30		539.2.e.e.177.1		2
77.53	even	15		539.2.e.d.177.1		2
77.75	odd	30		539.2.e.e.67.1		2
88.53	even	10		4928.2.a.i.1.1		1
88.75	odd	10		4928.2.a.x.1.1		1
231.20	even	10		4851.2.a.k.1.1		1
308.251	even	10		8624.2.a.s.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.a.b.1.1	✓	1	11.9	even	5
539.2.a.b.1.1		1	77.20	odd	10
539.2.e.d.67.1		2	77.9	even	15
539.2.e.d.177.1		2	77.53	even	15
539.2.e.e.67.1		2	77.75	odd	30
539.2.e.e.177.1		2	77.31	odd	30
693.2.a.b.1.1		1	33.20	odd	10
847.2.a.c.1.1		1	11.2	odd	10
847.2.f.f.148.1		4	11.3	even	5	inner
847.2.f.f.323.1		4	11.4	even	5	inner
847.2.f.f.372.1		4	11.5	even	5	inner
847.2.f.f.729.1		4	1.1	even	1	trivial
847.2.f.g.148.1		4	11.8	odd	10
847.2.f.g.323.1		4	11.7	odd	10
847.2.f.g.372.1		4	11.6	odd	10
847.2.f.g.729.1		4	11.10	odd	2
1232.2.a.d.1.1		1	44.31	odd	10
1925.2.a.f.1.1		1	55.9	even	10
1925.2.b.g.1849.1		2	55.42	odd	20
1925.2.b.g.1849.2		2	55.53	odd	20
4851.2.a.k.1.1		1	231.20	even	10
4928.2.a.i.1.1		1	88.53	even	10
4928.2.a.x.1.1		1	88.75	odd	10
5929.2.a.d.1.1		1	77.13	even	10
7623.2.a.i.1.1		1	33.2	even	10
8624.2.a.s.1.1		1	308.251	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:	\( N \)	\(=\)	\( 847 = 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	847.f (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 + 0.951057i) q^{3} +(-0.618034 + 1.90211i) q^{4} +(-2.42705 - 1.76336i) q^{5} +(0.309017 - 0.951057i) q^{7} +(1.61803 - 1.17557i) q^{9} +O(q^{10})\)	\(q+(0.309017 + 0.951057i) q^{3} +(-0.618034 + 1.90211i) q^{4} +(-2.42705 - 1.76336i) q^{5} +(0.309017 - 0.951057i) q^{7} +(1.61803 - 1.17557i) q^{9} -2.00000 q^{12} +(3.23607 - 2.35114i) q^{13} +(0.927051 - 2.85317i) q^{15} +(-3.23607 - 2.35114i) q^{16} +(4.85410 + 3.52671i) q^{17} +(0.618034 + 1.90211i) q^{19} +(4.85410 - 3.52671i) q^{20} +1.00000 q^{21} +3.00000 q^{23} +(1.23607 + 3.80423i) q^{25} +(4.04508 + 2.93893i) q^{27} +(1.61803 + 1.17557i) q^{28} +(-1.85410 + 5.70634i) q^{29} +(-4.04508 + 2.93893i) q^{31} +(-2.42705 + 1.76336i) q^{35} +(1.23607 + 3.80423i) q^{36} +(3.39919 - 10.4616i) q^{37} +(3.23607 + 2.35114i) q^{39} +(1.85410 + 5.70634i) q^{41} +8.00000 q^{43} -6.00000 q^{45} +(1.23607 - 3.80423i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(-1.85410 + 5.70634i) q^{51} +(2.47214 + 7.60845i) q^{52} +(4.85410 - 3.52671i) q^{53} +(-1.61803 + 1.17557i) q^{57} +(-2.78115 + 8.55951i) q^{59} +(4.85410 + 3.52671i) q^{60} +(8.09017 + 5.87785i) q^{61} +(-0.618034 - 1.90211i) q^{63} +(6.47214 - 4.70228i) q^{64} -12.0000 q^{65} +5.00000 q^{67} +(-9.70820 + 7.05342i) q^{68} +(0.927051 + 2.85317i) q^{69} +(-7.28115 - 5.29007i) q^{71} +(0.618034 - 1.90211i) q^{73} +(-3.23607 + 2.35114i) q^{75} -4.00000 q^{76} +(8.09017 - 5.87785i) q^{79} +(3.70820 + 11.4127i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-9.70820 - 7.05342i) q^{83} +(-0.618034 + 1.90211i) q^{84} +(-5.56231 - 17.1190i) q^{85} -6.00000 q^{87} -3.00000 q^{89} +(-1.23607 - 3.80423i) q^{91} +(-1.85410 + 5.70634i) q^{92} +(-4.04508 - 2.93893i) q^{93} +(1.85410 - 5.70634i) q^{95} +(0.809017 - 0.587785i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{3} + 2 q^{4} - 3 q^{5} - q^{7} + 2 q^{9}+O(q^{10}) \) 4 * q - q^3 + 2 * q^4 - 3 * q^5 - q^7 + 2 * q^9	\( 4 q - q^{3} + 2 q^{4} - 3 q^{5} - q^{7} + 2 q^{9} - 8 q^{12} + 4 q^{13} - 3 q^{15} - 4 q^{16} + 6 q^{17} - 2 q^{19} + 6 q^{20} + 4 q^{21} + 12 q^{23} - 4 q^{25} + 5 q^{27} + 2 q^{28} + 6 q^{29} - 5 q^{31} - 3 q^{35} - 4 q^{36} - 11 q^{37} + 4 q^{39} - 6 q^{41} + 32 q^{43} - 24 q^{45} - 4 q^{48} - q^{49} + 6 q^{51} - 8 q^{52} + 6 q^{53} - 2 q^{57} + 9 q^{59} + 6 q^{60} + 10 q^{61} + 2 q^{63} + 8 q^{64} - 48 q^{65} + 20 q^{67} - 12 q^{68} - 3 q^{69} - 9 q^{71} - 2 q^{73} - 4 q^{75} - 16 q^{76} + 10 q^{79} - 12 q^{80} - q^{81} - 12 q^{83} + 2 q^{84} + 18 q^{85} - 24 q^{87} - 12 q^{89} + 4 q^{91} + 6 q^{92} - 5 q^{93} - 6 q^{95} + q^{97}+O(q^{100}) \) 4 * q - q^3 + 2 * q^4 - 3 * q^5 - q^7 + 2 * q^9 - 8 * q^12 + 4 * q^13 - 3 * q^15 - 4 * q^16 + 6 * q^17 - 2 * q^19 + 6 * q^20 + 4 * q^21 + 12 * q^23 - 4 * q^25 + 5 * q^27 + 2 * q^28 + 6 * q^29 - 5 * q^31 - 3 * q^35 - 4 * q^36 - 11 * q^37 + 4 * q^39 - 6 * q^41 + 32 * q^43 - 24 * q^45 - 4 * q^48 - q^49 + 6 * q^51 - 8 * q^52 + 6 * q^53 - 2 * q^57 + 9 * q^59 + 6 * q^60 + 10 * q^61 + 2 * q^63 + 8 * q^64 - 48 * q^65 + 20 * q^67 - 12 * q^68 - 3 * q^69 - 9 * q^71 - 2 * q^73 - 4 * q^75 - 16 * q^76 + 10 * q^79 - 12 * q^80 - q^81 - 12 * q^83 + 2 * q^84 + 18 * q^85 - 24 * q^87 - 12 * q^89 + 4 * q^91 + 6 * q^92 - 5 * q^93 - 6 * q^95 + q^97

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