LMFDB - Embedded newform 810.2.s.a.143.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [810,2,Mod(17,810)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(810, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([22, 9]))

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

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

chi := DirichletCharacter("810.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 810 = 2 \cdot 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	810.s (of order $36$, degree $12$, 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:	$6.46788256372$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$18$ over $\Q(\zeta_{36})$
Twist minimal:	no (minimal twist has level 270)
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			143.17
Character	$\chi$	$=$	810.143
Dual form			810.2.s.a.17.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.906308 + 0.422618i) q^{2} +(0.642788 + 0.766044i) q^{4} +(2.00011 + 0.999773i) q^{5} +(-3.41173 + 0.298488i) q^{7} +(0.258819 + 0.965926i) q^{8} +O(q^{10})$	\(q+(0.906308 + 0.422618i) q^{2} +(0.642788 + 0.766044i) q^{4} +(2.00011 + 0.999773i) q^{5} +(-3.41173 + 0.298488i) q^{7} +(0.258819 + 0.965926i) q^{8} +(1.39020 + 1.75139i) q^{10} +(4.70038 + 0.828804i) q^{11} +(-0.816512 - 1.75102i) q^{13} +(-3.21823 - 1.17134i) q^{14} +(-0.173648 + 0.984808i) q^{16} +(-1.39278 + 5.19794i) q^{17} +(5.37612 + 3.10390i) q^{19} +(0.519777 + 2.17482i) q^{20} +(3.90972 + 2.73762i) q^{22} +(-0.0973994 + 1.11328i) q^{23} +(3.00091 + 3.99932i) q^{25} -1.93203i q^{26} +(-2.42167 - 2.42167i) q^{28} +(0.0131911 - 0.00480116i) q^{29} +(1.74674 - 1.46569i) q^{31} +(-0.573576 + 0.819152i) q^{32} +(-3.45904 + 4.12232i) q^{34} +(-7.12227 - 2.81395i) q^{35} +(-9.61180 - 2.57547i) q^{37} +(3.56065 + 5.08514i) q^{38} +(-0.448040 + 2.19072i) q^{40} +(0.132710 - 0.364617i) q^{41} +(3.98494 - 2.79028i) q^{43} +(2.38644 + 4.13344i) q^{44} +(-0.558767 + 0.967812i) q^{46} +(0.0692108 + 0.791084i) q^{47} +(4.65717 - 0.821184i) q^{49} +(1.02956 + 4.89285i) q^{50} +(0.816512 - 1.75102i) q^{52} +(-5.53811 + 5.53811i) q^{53} +(8.57267 + 6.35701i) q^{55} +(-1.17134 - 3.21823i) q^{56} +(0.0139842 + 0.00122346i) q^{58} +(-2.02310 - 11.4736i) q^{59} +(1.20616 + 1.01209i) q^{61} +(2.20251 - 0.590162i) q^{62} +(-0.866025 + 0.500000i) q^{64} +(0.117503 - 4.31856i) q^{65} +(10.2083 - 4.76023i) q^{67} +(-4.87712 + 2.27424i) q^{68} +(-5.26574 - 5.56031i) q^{70} +(2.10165 - 1.21339i) q^{71} +(8.26239 - 2.21390i) q^{73} +(-7.62281 - 6.39630i) q^{74} +(1.07797 + 6.11349i) q^{76} +(-16.2838 - 1.42465i) q^{77} +(-3.80042 - 10.4416i) q^{79} +(-1.33190 + 1.79612i) q^{80} +(0.274370 - 0.274370i) q^{82} +(5.81691 - 12.4744i) q^{83} +(-7.98249 + 9.00400i) q^{85} +(4.79081 - 0.844748i) q^{86} +(0.415985 + 4.75473i) q^{88} +(-7.52167 + 13.0279i) q^{89} +(3.30838 + 5.73028i) q^{91} +(-0.915429 + 0.640991i) q^{92} +(-0.271600 + 0.746215i) q^{94} +(7.64964 + 11.5831i) q^{95} +(-10.2282 - 14.6074i) q^{97} +(4.56787 + 1.22396i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q+O(q^{10}) $ 216 * q	$ 216 q - 24 q^{11} + 24 q^{20} - 24 q^{23} + 36 q^{25} + 108 q^{35} + 36 q^{38} + 72 q^{41} + 48 q^{47} + 48 q^{50} + 12 q^{56} + 36 q^{61} - 24 q^{65} - 72 q^{67} - 36 q^{68} + 240 q^{77} + 60 q^{83} - 72 q^{86} + 48 q^{92} + 60 q^{95} - 72 q^{97}+O(q^{100}) $ 216 * q - 24 * q^11 + 24 * q^20 - 24 * q^23 + 36 * q^25 + 108 * q^35 + 36 * q^38 + 72 * q^41 + 48 * q^47 + 48 * q^50 + 12 * q^56 + 36 * q^61 - 24 * q^65 - 72 * q^67 - 36 * q^68 + 240 * q^77 + 60 * q^83 - 72 * q^86 + 48 * q^92 + 60 * q^95 - 72 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/810\mathbb{Z}\right)^\times$.

$n$	$487$	$731$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{7}{18}\right)$

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 $

$2$	0.906308	+	0.422618i	0.640856	+	0.298836i
$2$	0.906308	+	0.422618i	0.640856	+	0.298836i
$3$		0			0
$3$		0			0
$4$	0.642788	+	0.766044i	0.321394	+	0.383022i
$5$	2.00011	+	0.999773i	0.894478	+	0.447112i
$5$	2.00011	+	0.999773i	0.894478	+	0.447112i
$6$		0			0
$7$	−3.41173	+	0.298488i	−1.28951	+	0.112818i	−0.711196	−	0.702994i	$-0.751846\pi$
$7$	−3.41173	+	0.298488i	−1.28951	+	0.112818i	−0.578318	+	0.815812i	$0.696291\pi$
$8$	0.258819	+	0.965926i	0.0915064	+	0.341506i
$9$		0			0
$10$	1.39020	+	1.75139i	0.439618	+	0.553837i
$11$	4.70038	+	0.828804i	1.41722	+	0.249894i	0.829199	−	0.558954i	$-0.188797\pi$
$11$	4.70038	+	0.828804i	1.41722	+	0.249894i	0.588019	+	0.808847i	$0.299908\pi$
$12$		0			0
$13$	−0.816512	−	1.75102i	−0.226460	−	0.485645i	0.759943	−	0.649990i	$-0.225227\pi$
$13$	−0.816512	−	1.75102i	−0.226460	−	0.485645i	−0.986403	+	0.164345i	$0.947449\pi$
$14$	−3.21823	−	1.17134i	−0.860107	−	0.313053i
$15$		0			0
$16$	−0.173648	+	0.984808i	−0.0434120	+	0.246202i
$17$	−1.39278	+	5.19794i	−0.337800	+	1.26069i	0.563002	+	0.826455i	$0.309646\pi$
$17$	−1.39278	+	5.19794i	−0.337800	+	1.26069i	−0.900802	+	0.434230i	$0.857020\pi$
$18$		0			0
$19$	5.37612	+	3.10390i	1.23337	+	0.712084i	0.967730	−	0.251989i	$-0.0810848\pi$
$19$	5.37612	+	3.10390i	1.23337	+	0.712084i	0.265636	+	0.964073i	$0.414418\pi$
$20$	0.519777	+	2.17482i	0.116226	+	0.486304i
$21$		0			0
$22$	3.90972	+	2.73762i	0.833556	+	0.583662i
$23$	−0.0973994	+	1.11328i	−0.0203092	+	0.232135i	0.979255	+	0.202630i	$0.0649488\pi$
$23$	−0.0973994	+	1.11328i	−0.0203092	+	0.232135i	−0.999565	+	0.0295054i	$0.990607\pi$
$24$		0			0
$25$	3.00091	+	3.99932i	0.600181	+	0.799864i
$26$		−	1.93203i		−	0.378903i
$27$		0			0
$28$	−2.42167	−	2.42167i	−0.457653	−	0.457653i
$29$	0.0131911	−	0.00480116i	0.00244952	−	0.000891553i	−0.340795	−	0.940138i	$-0.610696\pi$
$29$	0.0131911	−	0.00480116i	0.00244952	−	0.000891553i	0.343245	+	0.939246i	$0.388474\pi$
$30$		0			0
$31$	1.74674	−	1.46569i	0.313724	−	0.263246i	−0.472305	−	0.881435i	$-0.656578\pi$
$31$	1.74674	−	1.46569i	0.313724	−	0.263246i	0.786029	+	0.618189i	$0.212133\pi$
$32$	−0.573576	+	0.819152i	−0.101395	+	0.144807i
$33$		0			0
$34$	−3.45904	+	4.12232i	−0.593220	+	0.706972i
$35$	−7.12227	−	2.81395i	−1.20388	−	0.475644i
$36$		0			0
$37$	−9.61180	−	2.57547i	−1.58017	−	0.423405i	−0.641192	−	0.767381i	$-0.721560\pi$
$37$	−9.61180	−	2.57547i	−1.58017	−	0.423405i	−0.938979	+	0.343975i	$0.888226\pi$
$38$	3.56065	+	5.08514i	0.577614	+	0.824918i
$39$		0			0
$40$	−0.448040	+	2.19072i	−0.0708413	+	0.346383i
$41$	0.132710	−	0.364617i	0.0207258	−	0.0569436i	−0.928898	−	0.370335i	$-0.879243\pi$
$41$	0.132710	−	0.364617i	0.0207258	−	0.0569436i	0.949624	+	0.313391i	$0.101465\pi$
$42$		0			0
$43$	3.98494	−	2.79028i	0.607697	−	0.425514i	−0.228809	−	0.973471i	$-0.573483\pi$
$43$	3.98494	−	2.79028i	0.607697	−	0.425514i	0.836506	+	0.547957i	$0.184594\pi$
$44$	2.38644	+	4.13344i	0.359770	+	0.623140i
$45$		0			0
$46$	−0.558767	+	0.967812i	−0.0823856	+	0.142696i
$47$	0.0692108	+	0.791084i	0.0100954	+	0.115391i	0.999570	−	0.0293137i	$-0.00933219\pi$
$47$	0.0692108	+	0.791084i	0.0100954	+	0.115391i	−0.989475	+	0.144705i	$0.953777\pi$
$48$		0			0
$49$	4.65717	−	0.821184i	0.665310	−	0.117312i
$50$	1.02956	+	4.89285i	0.145602	+	0.691954i
$51$		0			0
$52$	0.816512	−	1.75102i	0.113230	−	0.242822i
$53$	−5.53811	+	5.53811i	−0.760717	+	0.760717i	−0.976452	−	0.215735i	$-0.930785\pi$
$53$	−5.53811	+	5.53811i	−0.760717	+	0.760717i	0.215735	+	0.976452i	$0.430785\pi$
$54$		0			0
$55$	8.57267	+	6.35701i	1.15594	+	0.857180i
$56$	−1.17134	−	3.21823i	−0.156527	−	0.430054i
$57$		0			0
$58$	0.0139842	+	0.00122346i	0.00183622	+	0.000160648i
$59$	−2.02310	−	11.4736i	−0.263385	−	1.49373i	−0.773595	−	0.633681i	$-0.781543\pi$
$59$	−2.02310	−	11.4736i	−0.263385	−	1.49373i	0.510210	−	0.860050i	$-0.329568\pi$
$60$		0			0
$61$	1.20616	+	1.01209i	0.154433	+	0.129584i	0.716730	−	0.697351i	$-0.245638\pi$
$61$	1.20616	+	1.01209i	0.154433	+	0.129584i	−0.562298	+	0.826935i	$0.690082\pi$
$62$	2.20251	−	0.590162i	0.279720	−	0.0749506i
$63$		0			0
$64$	−0.866025	+	0.500000i	−0.108253	+	0.0625000i
$65$	0.117503	−	4.31856i	0.0145744	−	0.535651i
$66$		0			0
$67$	10.2083	−	4.76023i	1.24715	−	0.581555i	0.316891	−	0.948462i	$-0.397361\pi$
$67$	10.2083	−	4.76023i	1.24715	−	0.581555i	0.930257	+	0.366907i	$0.119583\pi$
$68$	−4.87712	+	2.27424i	−0.591437	+	0.275792i
$69$		0			0
$70$	−5.26574	−	5.56031i	−0.629377	−	0.664584i
$71$	2.10165	−	1.21339i	0.249420	−	0.144003i	−0.370078	−	0.929001i	$-0.620669\pi$
$71$	2.10165	−	1.21339i	0.249420	−	0.144003i	0.619499	+	0.784998i	$0.287336\pi$
$72$		0			0
$73$	8.26239	−	2.21390i	0.967039	−	0.259117i	0.259462	−	0.965753i	$-0.416455\pi$
$73$	8.26239	−	2.21390i	0.967039	−	0.259117i	0.707577	+	0.706636i	$0.249788\pi$
$74$	−7.62281	−	6.39630i	−0.886133	−	0.743554i
$75$		0			0
$76$	1.07797	+	6.11349i	0.123652	+	0.701266i
$77$	−16.2838	−	1.42465i	−1.85571	−	0.162354i
$78$		0			0
$79$	−3.80042	−	10.4416i	−0.427580	−	1.17477i	−0.947277	−	0.320417i	$-0.896177\pi$
$79$	−3.80042	−	10.4416i	−0.427580	−	1.17477i	0.519696	−	0.854351i	$-0.326045\pi$
$80$	−1.33190	+	1.79612i	−0.148911	+	0.200812i
$81$		0			0
$82$	0.274370	−	0.274370i	0.0302990	−	0.0302990i
$83$	5.81691	−	12.4744i	0.638489	−	1.36924i	−0.274630	−	0.961550i	$-0.588555\pi$
$83$	5.81691	−	12.4744i	0.638489	−	1.36924i	0.913119	−	0.407693i	$-0.133667\pi$
$84$		0			0
$85$	−7.98249	+	9.00400i	−0.865822	+	0.976621i
$86$	4.79081	−	0.844748i	0.516606	−	0.0910915i
$87$		0			0
$88$	0.415985	+	4.75473i	0.0443441	+	0.506856i
$89$	−7.52167	+	13.0279i	−0.797296	+	1.38096i	0.124075	+	0.992273i	$0.460404\pi$
$89$	−7.52167	+	13.0279i	−0.797296	+	1.38096i	−0.921371	+	0.388684i	$0.872930\pi$
$90$		0			0
$91$	3.30838	+	5.73028i	0.346812	+	0.600697i
$92$	−0.915429	+	0.640991i	−0.0954401	+	0.0668279i
$93$		0			0
$94$	−0.271600	+	0.746215i	−0.0280134	+	0.0769662i
$95$	7.64964	+	11.5831i	0.784837	+	1.18840i
$96$		0			0
$97$	−10.2282	−	14.6074i	−1.03852	−	1.48315i	−0.867215	−	0.497935i	$-0.834092\pi$
$97$	−10.2282	−	14.6074i	−1.03852	−	1.48315i	−0.171301	−	0.985219i	$-0.554797\pi$
$98$	4.56787	+	1.22396i	0.461425	+	0.123638i
$99$		0			0
$100$	−1.13471	+	4.86954i	−0.113471	+	0.486954i
$101$	1.36748	−	1.62970i	0.136069	−	0.162161i	−0.693707	−	0.720257i	$-0.744024\pi$
$101$	1.36748	−	1.62970i	0.136069	−	0.162161i	0.829776	+	0.558097i	$0.188468\pi$
$102$		0			0
$103$	1.45888	−	2.08350i	0.143748	−	0.205293i	−0.740821	−	0.671702i	$-0.765564\pi$
$103$	1.45888	−	2.08350i	0.143748	−	0.205293i	0.884569	+	0.466409i	$0.154452\pi$
$104$	1.48002	−	1.24189i	0.145128	−	0.121777i
$105$		0			0
$106$	−7.35973	+	2.67872i	−0.714840	+	0.260181i
$107$	−4.24792	−	4.24792i	−0.410662	−	0.410662i	0.471307	−	0.881969i	$-0.343782\pi$
$107$	−4.24792	−	4.24792i	−0.410662	−	0.410662i	−0.881969	+	0.471307i	$0.843782\pi$
$108$		0			0
$109$			2.45742i			0.235378i	0.993051	+	0.117689i	$0.0375486\pi$
$109$			2.45742i			0.235378i	−0.993051	+	0.117689i	$0.962451\pi$
$110$	5.08289	+	9.38438i	0.484635	+	0.894766i
$111$		0			0
$112$	0.298488	−	3.41173i	0.0282045	−	0.322378i
$113$	11.9224	+	8.34818i	1.12157	+	0.785331i	0.978880	−	0.204437i	$-0.0655363\pi$
$113$	11.9224	+	8.34818i	1.12157	+	0.785331i	0.142689	+	0.989768i	$0.454425\pi$
$114$		0			0
$115$	−1.30784	+	2.12931i	−0.121957	+	0.198559i
$116$	0.0121570	+	0.00701882i	0.00112875	+	0.000651681i
$117$		0			0
$118$	3.01539	−	11.2536i	0.277589	−	1.03598i
$119$	3.20028	−	18.1497i	0.293369	−	1.66378i
$120$		0			0
$121$	11.0700	+	4.02916i	1.00637	+	0.366287i
$122$	0.665423	+	1.42701i	0.0602446	+	0.129195i
$123$		0			0
$124$	2.24557	+	0.395954i	0.201658	+	0.0355577i
$125$	2.00374	+	10.9993i	0.179220	+	0.983809i
$126$		0			0
$127$	4.89147	+	18.2552i	0.434048	+	1.61989i	0.743335	+	0.668919i	$0.233243\pi$
$127$	4.89147	+	18.2552i	0.434048	+	1.61989i	−0.309288	+	0.950969i	$0.600091\pi$
$128$	−0.996195	+	0.0871557i	−0.0880520	+	0.00770355i
$129$		0			0
$130$	1.93160	−	3.86428i	0.169412	−	0.338920i
$131$	−1.19590	−	1.42522i	−0.104486	−	0.124522i	0.711267	−	0.702922i	$-0.248122\pi$
$131$	−1.19590	−	1.42522i	−0.104486	−	0.124522i	−0.815753	+	0.578400i	$0.803677\pi$
$132$		0			0
$133$	−19.2683	−	8.98498i	−1.67078	−	0.779096i
$134$	11.2637			0.973032
$135$		0			0
$136$	−5.38130			−0.461443
$137$	7.40450	+	3.45278i	0.632609	+	0.294991i	0.712349	−	0.701825i	$-0.247631\pi$
$137$	7.40450	+	3.45278i	0.632609	+	0.294991i	−0.0797400	+	0.996816i	$0.525409\pi$
$138$		0			0
$139$	−10.7748	−	12.8409i	−0.913904	−	1.08915i	−0.995713	−	0.0925002i	$-0.970514\pi$
$139$	−10.7748	−	12.8409i	−0.913904	−	1.08915i	0.0818088	−	0.996648i	$-0.473930\pi$
$140$	−2.42250	−	7.26475i	−0.204738	−	0.613983i
$141$		0			0
$142$	2.41755	−	0.211508i	0.202876	−	0.0177494i
$143$	−2.38667	−	8.90717i	−0.199583	−	0.744855i
$144$		0			0
$145$	0.0311837	+	0.00358523i	0.00258967	+	0.000297737i
$146$	8.42390	+	1.48536i	0.697167	+	0.122929i
$147$		0			0
$148$	−4.20542	−	9.01855i	−0.345683	−	0.741320i
$149$	−15.3073	−	5.57142i	−1.25403	−	0.456428i	−0.372266	−	0.928126i	$-0.621419\pi$
$149$	−15.3073	−	5.57142i	−1.25403	−	0.456428i	−0.881760	+	0.471698i	$0.843641\pi$
$150$		0			0
$151$	2.09008	−	11.8534i	0.170088	−	0.964618i	−0.773574	−	0.633706i	$-0.781533\pi$
$151$	2.09008	−	11.8534i	0.170088	−	0.964618i	0.943662	−	0.330911i	$-0.107356\pi$
$152$	−1.60670	+	5.99628i	−0.130320	+	0.486362i
$153$		0			0
$154$	−14.1561	−	8.17301i	−1.14073	−	0.658600i
$155$	4.95904	−	1.18520i	0.398320	−	0.0951976i
$156$		0			0
$157$	−9.03750	−	6.32813i	−0.721271	−	0.505039i	0.154363	−	0.988014i	$-0.450667\pi$
$157$	−9.03750	−	6.32813i	−0.721271	−	0.505039i	−0.875634	+	0.482975i	$0.839556\pi$
$158$	0.968447	−	11.0694i	0.0770455	−	0.880634i
$159$		0			0
$160$	−1.96618	+	1.06495i	−0.155441	+	0.0841917i
$161$		−	3.82729i		−	0.301633i
$162$		0			0
$163$	−7.80113	−	7.80113i	−0.611032	−	0.611032i	0.332183	−	0.943215i	$-0.392215\pi$
$163$	−7.80113	−	7.80113i	−0.611032	−	0.611032i	−0.943215	+	0.332183i	$0.892215\pi$
$164$	0.364617	−	0.132710i	0.0284718	−	0.0103629i
$165$		0			0
$166$	10.5438	−	8.84731i	0.818359	−	0.686685i
$167$	11.3321	−	16.1839i	0.876903	−	1.25235i	−0.0896736	−	0.995971i	$-0.528582\pi$
$167$	11.3321	−	16.1839i	0.876903	−	1.25235i	0.966577	−	0.256377i	$-0.0825287\pi$
$168$		0			0
$169$	5.95687	−	7.09912i	0.458221	−	0.546087i
$170$	−11.0398	+	4.78685i	−0.846718	+	0.367135i
$171$		0			0
$172$	4.69895	+	1.25908i	0.358292	+	0.0960039i
$173$	−13.8009	−	19.7098i	−1.04927	−	1.49851i	−0.855736	−	0.517412i	$-0.826895\pi$
$173$	−13.8009	−	19.7098i	−1.04927	−	1.49851i	−0.193529	−	0.981095i	$-0.561993\pi$
$174$		0			0
$175$	−11.4320	−	12.7489i	−0.864181	−	0.963724i
$176$	−1.63242	+	4.48505i	−0.123049	+	0.338073i
$177$		0			0
$178$	−12.3228	+	8.62851i	−0.923632	+	0.646734i
$179$	−3.91228	−	6.77627i	−0.292418	−	0.506482i	0.681963	−	0.731386i	$-0.261126\pi$
$179$	−3.91228	−	6.77627i	−0.292418	−	0.506482i	−0.974381	+	0.224904i	$0.927793\pi$
$180$		0			0
$181$	−0.435002	+	0.753445i	−0.0323334	+	0.0560032i	−0.881739	−	0.471737i	$-0.843627\pi$
$181$	−0.435002	+	0.753445i	−0.0323334	+	0.0560032i	0.849406	+	0.527740i	$0.176961\pi$
$182$	0.576688	+	6.59158i	0.0427470	+	0.488600i
$183$		0			0
$184$	−1.10056	+	0.194058i	−0.0811340	+	0.0143061i
$185$	−16.6498	−	14.7609i	−1.22412	−	1.08524i
$186$		0			0
$187$	−10.8547	+	23.2779i	−0.793773	+	1.70225i
$188$	−0.561517	+	0.561517i	−0.0409529	+	0.0409529i
$189$		0			0
$190$	2.03772	+	13.7307i	0.147832	+	0.996129i
$191$	3.36360	+	9.24141i	0.243381	+	0.668685i	0.999892	+	0.0147032i	$0.00468034\pi$
$191$	3.36360	+	9.24141i	0.243381	+	0.668685i	−0.756511	+	0.653981i	$0.773097\pi$
$192$		0			0
$193$	8.13419	+	0.711650i	0.585512	+	0.0512257i	0.376063	−	0.926594i	$-0.377278\pi$
$193$	8.13419	+	0.711650i	0.585512	+	0.0512257i	0.209449	+	0.977820i	$0.432833\pi$
$194$	−3.09655	−	17.5614i	−0.222319	−	1.26083i
$195$		0			0
$196$	3.62263	+	3.03975i	0.258759	+	0.217125i
$197$	21.1806	−	5.67532i	1.50905	−	0.404350i	0.592933	−	0.805252i	$-0.297970\pi$
$197$	21.1806	−	5.67532i	1.50905	−	0.404350i	0.916121	+	0.400902i	$0.131303\pi$
$198$		0			0
$199$	−4.58949	+	2.64974i	−0.325340	+	0.187835i	−0.653770	−	0.756693i	$-0.726814\pi$
$199$	−4.58949	+	2.64974i	−0.325340	+	0.187835i	0.328430	+	0.944528i	$0.393480\pi$
$200$	−3.08636	+	3.93375i	−0.218238	+	0.278158i
$201$		0			0
$202$	1.92809	−	0.899085i	0.135660	−	0.0632594i
$203$	−0.0435713	+	0.0203176i	−0.00305811	+	0.00142602i
$204$		0			0
$205$	0.629969	−	0.596595i	0.0439989	−	0.0416680i
$206$	2.20272	−	1.27174i	0.153471	−	0.0886064i
$207$		0			0
$208$	1.86620	−	0.500047i	0.129398	−	0.0346720i
$209$	22.6973	+	19.0453i	1.57000	+	1.31739i
$210$		0			0
$211$	2.85111	+	16.1695i	0.196279	+	1.11315i	0.910586	+	0.413319i	$0.135631\pi$
$211$	2.85111	+	16.1695i	0.196279	+	1.11315i	−0.714308	+	0.699832i	$0.753258\pi$
$212$	−7.80226	−	0.682609i	−0.535861	−	0.0468818i
$213$		0			0
$214$	−2.05467	−	5.64517i	−0.140455	−	0.385896i
$215$	10.7600	−	1.59685i	0.733824	−	0.108904i
$216$		0			0
$217$	−5.52193	+	5.52193i	−0.374853	+	0.374853i
$218$	−1.03855	+	2.22718i	−0.0703395	+	0.150843i
$219$		0			0
$220$	0.640653	+	10.6533i	0.0431928	+	0.718243i
$221$	10.2389	−	1.80540i	0.688743	−	0.121444i
$222$		0			0
$223$	0.866913	+	9.90886i	0.0580528	+	0.663547i	0.968351	+	0.249593i	$0.0802968\pi$
$223$	0.866913	+	9.90886i	0.0580528	+	0.663547i	−0.910298	+	0.413954i	$0.864148\pi$
$224$	1.71238	−	2.96593i	0.114413	−	0.198170i
$225$		0			0
$226$	7.27730	+	12.6047i	0.484079	+	0.838450i
$227$	−9.94373	+	6.96268i	−0.659989	+	0.462129i	−0.854970	−	0.518678i	$-0.826424\pi$
$227$	−9.94373	+	6.96268i	−0.659989	+	0.462129i	0.194981	+	0.980807i	$0.437535\pi$
$228$		0			0
$229$	3.56444	−	9.79323i	0.235545	−	0.647155i	−0.764452	−	0.644681i	$-0.776990\pi$
$229$	3.56444	−	9.79323i	0.235545	−	0.647155i	0.999997	−	0.00247388i	$-0.000787462\pi$
$230$	−2.08519	+	1.37709i	−0.137493	+	0.0908029i
$231$		0			0
$232$	0.00805166	+	0.0114990i	0.000528618	+	0.000754944i
$233$	−9.67519	−	2.59246i	−0.633843	−	0.169838i	−0.0724298	−	0.997374i	$-0.523075\pi$
$233$	−9.67519	−	2.59246i	−0.633843	−	0.169838i	−0.561413	+	0.827536i	$0.689742\pi$
$234$		0			0
$235$	−0.652475	+	1.65145i	−0.0425628	+	0.107729i
$236$	7.48884	−	8.92485i	0.487482	−	0.580958i
$237$		0			0
$238$	10.5708	−	15.0967i	0.685206	−	0.978575i
$239$	−0.520564	+	0.436805i	−0.0336725	+	0.0282546i	−0.659469	−	0.751732i	$-0.729219\pi$
$239$	−0.520564	+	0.436805i	−0.0336725	+	0.0282546i	0.625796	+	0.779987i	$0.284774\pi$
$240$		0			0
$241$	18.3051	−	6.66251i	1.17913	−	0.429170i	0.323238	−	0.946318i	$-0.395229\pi$
$241$	18.3051	−	6.66251i	1.17913	−	0.429170i	0.855896	+	0.517148i	$0.173006\pi$
$242$	8.33005	+	8.33005i	0.535476	+	0.535476i
$243$		0			0
$244$			1.57453i			0.100799i
$245$	10.1359	+	3.01365i	0.647556	+	0.192535i
$246$		0			0
$247$	1.04532	−	11.9480i	0.0665120	−	0.760236i
$248$	1.86784	+	1.30787i	0.118608	+	0.0830501i
$249$		0			0
$250$	−2.83251	+	10.8156i	−0.179144	+	0.684038i
$251$	3.84250	+	2.21847i	0.242537	+	0.140029i	0.616342	−	0.787479i	$-0.288614\pi$
$251$	3.84250	+	2.21847i	0.242537	+	0.140029i	−0.373805	+	0.927507i	$0.621947\pi$
$252$		0			0
$253$	−1.38051	+	5.15211i	−0.0867916	+	0.323911i
$254$	−3.28181	+	18.6121i	−0.205919	+	1.16782i
$255$		0			0
$256$	−0.939693	−	0.342020i	−0.0587308	−	0.0213763i
$257$	5.48091	+	11.7539i	0.341890	+	0.733185i	0.999802	−	0.0199097i	$-0.00633787\pi$
$257$	5.48091	+	11.7539i	0.341890	+	0.733185i	−0.657912	+	0.753095i	$0.728560\pi$
$258$		0			0
$259$	33.5616	+	5.91782i	2.08542	+	0.367716i
$260$	3.38374	−	2.68590i	0.209850	−	0.166573i
$261$		0			0
$262$	−0.481530	−	1.79709i	−0.0297490	−	0.111025i
$263$	−25.0764	+	2.19390i	−1.54628	+	0.135282i	−0.828100	−	0.560580i	$-0.810578\pi$
$263$	−25.0764	+	2.19390i	−1.54628	+	0.135282i	−0.718175	+	0.695862i	$0.755022\pi$
$264$		0			0
$265$	−16.6137	+	5.53999i	−1.02057	+	0.340319i
$266$	−13.6658	−	16.2863i	−0.837906	−	0.998578i
$267$		0			0
$268$	10.2083	+	4.76023i	0.623574	+	0.290777i
$269$	0.955430			0.0582536			0.0291268	−	0.999576i	$-0.490727\pi$
$269$	0.955430			0.0582536			0.0291268	+	0.999576i	$0.490727\pi$
$270$		0			0
$271$	−7.26969			−0.441602			−0.220801	−	0.975319i	$-0.570867\pi$
$271$	−7.26969			−0.441602			−0.220801	+	0.975319i	$0.570867\pi$
$272$	−4.87712	−	2.27424i	−0.295719	−	0.137896i
$273$		0			0
$274$	5.25155	+	6.25856i	0.317258	+	0.378093i
$275$	10.7907	+	21.2855i	0.650706	+	1.28356i
$276$		0			0
$277$	5.18616	−	0.453730i	0.311606	−	0.0272620i	0.0697199	−	0.997567i	$-0.477789\pi$
$277$	5.18616	−	0.453730i	0.311606	−	0.0272620i	0.241886	+	0.970305i	$0.422234\pi$
$278$	−4.33847	−	16.1914i	−0.260204	−	0.971095i
$279$		0			0
$280$	0.874687	−	7.60789i	0.0522726	−	0.454658i
$281$	−8.66284	−	1.52749i	−0.516782	−	0.0911226i	−0.0908264	−	0.995867i	$-0.528951\pi$
$281$	−8.66284	−	1.52749i	−0.516782	−	0.0911226i	−0.425955	+	0.904744i	$0.640062\pi$
$282$		0			0
$283$	4.92646	+	10.5648i	0.292848	+	0.628014i	0.996596	−	0.0824351i	$-0.0262697\pi$
$283$	4.92646	+	10.5648i	0.292848	+	0.628014i	−0.703749	+	0.710449i	$0.748492\pi$
$284$	2.28043	+	0.830008i	0.135319	+	0.0492519i
$285$		0			0
$286$	1.60128	−	9.08129i	0.0946854	−	0.536988i
$287$	−0.343936	+	1.28359i	−0.0203019	+	0.0757678i
$288$		0			0
$289$	−10.3563	−	5.97921i	−0.609194	−	0.351718i
$290$	0.0267469	+	0.0164281i	0.00157063	+	0.000964693i
$291$		0			0
$292$	7.00691	+	4.90629i	0.410048	+	0.287119i
$293$	−1.06878	+	12.2162i	−0.0624388	+	0.713679i	0.898872	+	0.438212i	$0.144388\pi$
$293$	−1.06878	+	12.2162i	−0.0624388	+	0.713679i	−0.961311	+	0.275467i	$0.911168\pi$
$294$		0			0
$295$	7.42454	−	24.9711i	0.432273	−	1.45387i
$296$		−	9.95087i		−	0.578383i
$297$		0			0
$298$	−11.5186	−	11.5186i	−0.667254	−	0.667254i
$299$	2.02890	−	0.738459i	0.117334	−	0.0427062i
$300$		0			0
$301$	−12.7627	+	10.7092i	−0.735628	+	0.617266i
$302$	6.90372	−	9.85954i	0.397265	−	0.567353i
$303$		0			0
$304$	−3.99030	+	4.75545i	−0.228859	+	0.272744i
$305$	1.40059	+	3.23017i	0.0801978	+	0.184959i
$306$		0			0
$307$	−25.1777	−	6.74634i	−1.43697	−	0.385034i	−0.545495	−	0.838114i	$-0.683658\pi$
$307$	−25.1777	−	6.74634i	−1.43697	−	0.385034i	−0.891470	+	0.453080i	$0.850325\pi$
$308$	−9.37569	−	13.3899i	−0.534230	−	0.762959i
$309$		0			0
$310$	4.99530	+	1.02162i	0.283714	+	0.0580244i
$311$	−7.56811	+	20.7932i	−0.429148	+	1.17908i	0.517182	+	0.855875i	$0.326981\pi$
$311$	−7.56811	+	20.7932i	−0.429148	+	1.17908i	−0.946331	+	0.323200i	$0.895241\pi$
$312$		0			0
$313$	−17.9286	+	12.5537i	−1.01338	+	0.709578i	−0.957374	−	0.288853i	$-0.906726\pi$
$313$	−17.9286	+	12.5537i	−1.01338	+	0.709578i	−0.0560084	+	0.998430i	$0.517837\pi$
$314$	−5.51638	−	9.55464i	−0.311307	−	0.539200i
$315$		0			0
$316$	5.55584	−	9.62300i	0.312540	−	0.541336i
$317$	−0.865153	−	9.88874i	−0.0485918	−	0.555407i	−0.981001	−	0.194003i	$-0.937853\pi$
$317$	−0.865153	−	9.88874i	−0.0485918	−	0.555407i	0.932409	−	0.361404i	$-0.117703\pi$
$318$		0			0
$319$	0.0659823	−	0.0116345i	0.00369430	−	0.000651404i
$320$	−2.23204	+	0.134227i	−0.124775	+	0.00750354i
$321$		0			0
$322$	1.61748	−	3.46870i	0.0901387	−	0.193303i
$323$	−23.6217	+	23.6217i	−1.31434	+	1.31434i
$324$		0			0
$325$	4.55260	−	8.52013i	0.252533	−	0.472612i
$326$	−3.77333	−	10.3671i	−0.208985	−	0.574182i
$327$		0			0
$328$	0.386541	+	0.0338179i	0.0213431	+	0.00186728i
$329$	−0.472258	−	2.67831i	−0.0260364	−	0.147660i
$330$		0			0
$331$	22.7451	+	19.0854i	1.25018	+	1.04903i	0.996657	+	0.0817003i	$0.0260350\pi$
$331$	22.7451	+	19.0854i	1.25018	+	1.04903i	0.253527	+	0.967328i	$0.418409\pi$
$332$	13.2950	−	3.56238i	0.729657	−	0.195511i
$333$		0			0
$334$	17.1100	−	9.87845i	0.936216	−	0.540525i
$335$	25.1770	+	0.685035i	1.37557	+	0.0374274i
$336$		0			0
$337$	−14.7628	+	6.88399i	−0.804179	+	0.374995i	−0.780839	−	0.624733i	$-0.785208\pi$
$337$	−14.7628	+	6.88399i	−0.804179	+	0.374995i	−0.0233403	+	0.999728i	$0.507430\pi$
$338$	8.39898	−	3.91651i	0.456844	−	0.213030i
$339$		0			0
$340$	−12.0285	−	0.327281i	−0.652337	−	0.0177493i
$341$	9.42512	−	5.44160i	0.510399	−	0.294679i
$342$		0			0
$343$	7.51259	−	2.01299i	0.405642	−	0.108691i
$344$	3.72658	+	3.12698i	0.200924	+	0.168595i
$345$		0			0
$346$	−4.17818	−	23.6957i	−0.224620	−	1.27389i
$347$	0.00836757		0.000732067i	0.000449195		3.92994e-5i	0.0873803	−	0.996175i	$-0.472150\pi$
$347$	0.00836757		0.000732067i	0.000449195		3.92994e-5i	−0.0869311	+	0.996214i	$0.527706\pi$
$348$		0			0
$349$	4.18645	+	11.5022i	0.224096	+	0.615697i	0.999883	−	0.0152969i	$-0.00486935\pi$
$349$	4.18645	+	11.5022i	0.224096	+	0.615697i	−0.775787	+	0.630994i	$0.782647\pi$
$350$	−4.97304	−	16.3858i	−0.265820	−	0.875857i
$351$		0			0
$352$	−3.37494	+	3.37494i	−0.179885	+	0.179885i
$353$	−8.17015	+	17.5209i	−0.434853	+	0.932545i	0.559737	+	0.828670i	$0.310902\pi$
$353$	−8.17015	+	17.5209i	−0.434853	+	0.932545i	−0.994590	+	0.103875i	$0.966876\pi$
$354$		0			0
$355$	5.41666	−	0.325741i	0.287487	−	0.0172885i
$356$	−14.8148	+	2.61225i	−0.785183	+	0.138449i
$357$		0			0
$358$	−0.681955	−	7.79479i	−0.0360425	−	0.411967i
$359$	−4.88715	+	8.46479i	−0.257934	+	0.446754i	−0.965688	−	0.259704i	$-0.916375\pi$
$359$	−4.88715	+	8.46479i	−0.257934	+	0.446754i	0.707754	+	0.706459i	$0.249708\pi$
$360$		0			0
$361$	9.76842	+	16.9194i	0.514127	+	0.890495i
$362$	−0.712665	+	0.499014i	−0.0374569	+	0.0262276i
$363$		0			0
$364$	−2.26306	+	6.21772i	−0.118617	+	0.325897i
$365$	18.7391	+	3.83247i	0.980850	+	0.200600i
$366$		0			0
$367$	12.8485	+	18.3496i	0.670688	+	0.957842i	0.999908	+	0.0135884i	$0.00432544\pi$
$367$	12.8485	+	18.3496i	0.670688	+	0.957842i	−0.329220	+	0.944253i	$0.606786\pi$
$368$	−1.07945	−	0.289239i	−0.0562704	−	0.0150776i
$369$		0			0
$370$	−8.85163	−	20.4144i	−0.460174	−	1.06129i
$371$	17.2415	−	20.5476i	0.895133	−	1.06678i
$372$		0			0
$373$	2.19410	−	3.13349i	0.113606	−	0.162246i	−0.758322	−	0.651880i	$-0.773981\pi$
$373$	2.19410	−	3.13349i	0.113606	−	0.162246i	0.871928	+	0.489634i	$0.162870\pi$
$374$	−19.6754	+	16.5096i	−1.01739	+	0.853691i
$375$		0			0
$376$	−0.746215	+	0.271600i	−0.0384831	+	0.0140067i
$377$	−0.0191776	−	0.0191776i	−0.000987696	−	0.000987696i
$378$		0			0
$379$			14.9557i			0.768225i	0.923286	+	0.384112i	$0.125493\pi$
$379$			14.9557i			0.768225i	−0.923286	+	0.384112i	$0.874507\pi$
$380$	−3.95604	+	13.3054i	−0.202941	+	0.682553i
$381$		0			0
$382$	−0.857133	+	9.79707i	−0.0438547	+	0.501262i
$383$	−0.914955	−	0.640659i	−0.0467520	−	0.0327361i	0.549967	−	0.835187i	$-0.314640\pi$
$383$	−0.914955	−	0.640659i	−0.0467520	−	0.0327361i	−0.596719	+	0.802450i	$0.703529\pi$
$384$		0			0
$385$	−31.1452	−	19.1296i	−1.58730	−	0.974934i
$386$	7.07133	+	4.08263i	0.359921	+	0.207800i
$387$		0			0
$388$	4.61534	−	17.2247i	0.234308	−	0.874451i
$389$	−5.28039	+	29.9466i	−0.267726	+	1.51835i	0.493432	+	0.869784i	$0.335742\pi$
$389$	−5.28039	+	29.9466i	−0.267726	+	1.51835i	−0.761158	+	0.648566i	$0.775369\pi$
$390$		0			0
$391$	−5.65111	−	2.05684i	−0.285789	−	0.104019i
$392$	1.99857	+	4.28594i	0.100943	+	0.216473i
$393$		0			0
$394$	21.5946	+	3.80772i	1.08792	+	0.191830i
$395$	2.83793	−	24.6839i	0.142792	−	1.24198i
$396$		0			0
$397$	2.92694	+	10.9235i	0.146899	+	0.548234i	0.999664	+	0.0259385i	$0.00825740\pi$
$397$	2.92694	+	10.9235i	0.146899	+	0.548234i	−0.852765	+	0.522295i	$0.825076\pi$
$398$	−5.27932	+	0.461881i	−0.264628	+	0.0231520i
$399$		0			0
$400$	−4.45966	+	2.26084i	−0.222983	+	0.113042i
$401$	−8.78262	−	10.4667i	−0.438583	−	0.522683i	0.500795	−	0.865566i	$-0.333041\pi$
$401$	−8.78262	−	10.4667i	−0.438583	−	0.522683i	−0.939378	+	0.342883i	$0.888597\pi$
$402$		0			0
$403$	−3.99269	−	1.86182i	−0.198890	−	0.0927438i
$404$	2.12742			0.105843
$405$		0			0
$406$	−0.0480756			−0.00238595
$407$	−43.0445	−	20.0720i	−2.13364	−	0.994932i
$408$		0			0
$409$	−13.3918	−	15.9597i	−0.662183	−	0.789159i	0.325515	−	0.945537i	$-0.394462\pi$
$409$	−13.3918	−	15.9597i	−0.662183	−	0.789159i	−0.987697	+	0.156378i	$0.950018\pi$
$410$	0.823078	−	0.274463i	0.0406489	−	0.0135548i
$411$		0			0
$412$	2.53380	−	0.221679i	0.124831	−	0.0109213i
$413$	10.3270	+	38.5408i	0.508158	+	1.89647i
$414$		0			0
$415$	24.1060	−	19.1346i	1.18332	−	0.939282i
$416$	1.90268	+	0.335494i	0.0932866	+	0.0164489i
$417$		0			0
$418$	12.5218	+	26.8531i	0.612463	+	1.31343i
$419$	6.74264	+	2.45412i	0.329399	+	0.119892i	0.501426	−	0.865201i	$-0.332809\pi$
$419$	6.74264	+	2.45412i	0.329399	+	0.119892i	−0.172026	+	0.985092i	$0.555031\pi$
$420$		0			0
$421$	3.74087	−	21.2156i	0.182319	−	1.03398i	−0.747033	−	0.664787i	$-0.768522\pi$
$421$	3.74087	−	21.2156i	0.182319	−	1.03398i	0.929352	−	0.369195i	$-0.120367\pi$
$422$	−4.24952	+	15.8594i	−0.206863	+	0.772025i
$423$		0			0
$424$	−6.78277	−	3.91603i	−0.329400	−	0.190179i
$425$	−24.9678	+	10.0283i	−1.21112	+	0.486446i
$426$		0			0
$427$	−4.41718	−	3.09294i	−0.213762	−	0.149678i
$428$	0.523585	−	5.98460i	0.0253084	−	0.289277i
$429$		0			0
$430$	10.4267	+	3.10013i	0.502821	+	0.149501i
$431$			21.6869i			1.04462i	0.852756	+	0.522310i	$0.174930\pi$
$431$			21.6869i			1.04462i	−0.852756	+	0.522310i	$0.825070\pi$
$432$		0			0
$433$	9.64432	+	9.64432i	0.463476	+	0.463476i	0.899793	−	0.436317i	$-0.143717\pi$
$433$	9.64432	+	9.64432i	0.463476	+	0.463476i	−0.436317	+	0.899793i	$0.643717\pi$
$434$	−7.33823	+	2.67090i	−0.352246	+	0.128207i
$435$		0			0
$436$	−1.88249	+	1.57960i	−0.0901550	+	0.0756490i
$437$	−3.97914	+	5.68281i	−0.190348	+	0.271846i
$438$		0			0
$439$	18.8665	−	22.4842i	0.900449	−	1.07311i	−0.0965218	−	0.995331i	$-0.530772\pi$
$439$	18.8665	−	22.4842i	0.900449	−	1.07311i	0.996970	−	0.0777820i	$-0.0247838\pi$
$440$	−3.92163	+	9.92588i	−0.186957	+	0.473198i
$441$		0			0
$442$	10.0426	+	2.69090i	0.477677	+	0.127993i
$443$	10.1169	+	14.4484i	0.480669	+	0.686466i	0.984109	−	0.177564i	$-0.0568215\pi$
$443$	10.1169	+	14.4484i	0.480669	+	0.686466i	−0.503440	+	0.864030i	$0.667933\pi$
$444$		0			0
$445$	−28.0692	+	18.5373i	−1.33061	+	0.878755i
$446$	−3.40198	+	9.34685i	−0.161088	+	0.442586i
$447$		0			0
$448$	2.80540	−	1.96436i	0.132543	−	0.0928075i
$449$	−3.52178	−	6.09990i	−0.166203	−	0.287872i	0.770879	−	0.636982i	$-0.219817\pi$
$449$	−3.52178	−	6.09990i	−0.166203	−	0.287872i	−0.937082	+	0.349110i	$0.886484\pi$
$450$		0			0
$451$	0.925982	−	1.60385i	0.0436028	−	0.0755222i
$452$	1.26852	+	14.4992i	0.0596661	+	0.681986i
$453$		0			0
$454$	−11.9546	+	2.10792i	−0.561059	+	0.0989298i
$455$	0.888150	+	14.7688i	0.0416371	+	0.692374i
$456$		0			0
$457$	−2.14412	+	4.59808i	−0.100298	+	0.215089i	−0.950053	−	0.312088i	$-0.898972\pi$
$457$	−2.14412	+	4.59808i	−0.100298	+	0.215089i	0.849756	+	0.527177i	$0.176749\pi$
$458$	7.36928	−	7.36928i	0.344344	−	0.344344i
$459$		0			0
$460$	−2.47181	+	0.366832i	−0.115249	+	0.0171036i
$461$	0.701773	+	1.92811i	0.0326848	+	0.0898009i	0.954962	−	0.296729i	$-0.0958958\pi$
$461$	0.701773	+	1.92811i	0.0326848	+	0.0898009i	−0.922277	+	0.386530i	$0.873674\pi$
$462$		0			0
$463$	13.8800	+	1.21434i	0.645058	+	0.0564353i	0.404990	−	0.914321i	$-0.367275\pi$
$463$	13.8800	+	1.21434i	0.645058	+	0.0564353i	0.240068	+	0.970756i	$0.422830\pi$
$464$	0.00243761	+	0.0138244i	0.000113163	+	0.000641781i
$465$		0			0
$466$	−7.67308	−	6.43848i	−0.355448	−	0.298257i
$467$	−1.32327	+	0.354570i	−0.0612338	+	0.0164076i	−0.289306	−	0.957237i	$-0.593424\pi$
$467$	−1.32327	+	0.354570i	−0.0612338	+	0.0164076i	0.228072	+	0.973644i	$0.426758\pi$
$468$		0			0
$469$	−33.4073	+	19.2877i	−1.54260	+	0.890623i
$470$	−1.28928	+	1.22098i	−0.0594699	+	0.0563194i
$471$		0			0
$472$	10.5590	−	4.92374i	0.486017	−	0.226633i
$473$	21.0433	−	9.81266i	0.967573	−	0.451187i
$474$		0			0
$475$	3.71972	+	30.8153i	0.170673	+	1.41390i
$476$	15.9606	−	9.21485i	0.731552	−	0.422362i
$477$		0			0
$478$	−0.656393	+	0.175880i	−0.0300227	+	0.00804456i
$479$	−5.32223	−	4.46588i	−0.243179	−	0.204051i	0.513050	−	0.858359i	$-0.328516\pi$
$479$	−5.32223	−	4.46588i	−0.243179	−	0.204051i	−0.756228	+	0.654308i	$0.772960\pi$
$480$		0			0
$481$	3.33846	+	18.9333i	0.152221	+	0.863285i
$482$	19.4057	+	1.69778i	0.883907	+	0.0773319i
$483$		0			0
$484$	4.02916	+	11.0700i	0.183144	+	0.503183i
$485$	−5.85348	−	39.4423i	−0.265793	−	1.79098i
$486$		0			0
$487$	14.1069	−	14.1069i	0.639243	−	0.639243i	−0.311126	−	0.950369i	$-0.600706\pi$
$487$	14.1069	−	14.1069i	0.639243	−	0.639243i	0.950369	+	0.311126i	$0.100706\pi$
$488$	−0.665423	+	1.42701i	−0.0301223	+	0.0645975i
$489$		0			0
$490$	7.91258	+	7.01489i	0.357454	+	0.316901i
$491$	41.1519	−	7.25619i	1.85716	−	0.327467i	0.870743	−	0.491738i	$-0.163638\pi$
$491$	41.1519	−	7.25619i	1.85716	−	0.327467i	0.986415	+	0.164271i	$0.0525271\pi$
$492$		0			0
$493$	0.00658382	+	0.0752534i	0.000296520	+	0.00338924i
$494$	5.99684	−	10.3868i	0.269811	−	0.467326i
$495$		0			0
$496$	1.14010	+	1.97472i	0.0511922	+	0.0886675i
$497$	−6.80810	+	4.76708i	−0.305385	+	0.213833i
$498$		0			0
$499$	−1.84540	+	5.07021i	−0.0826116	+	0.226974i	−0.974120	−	0.226030i	$-0.927425\pi$
$499$	−1.84540	+	5.07021i	−0.0826116	+	0.226974i	0.891509	+	0.453004i	$0.149648\pi$
$500$	−7.13799	+	8.60518i	−0.319221	+	0.384835i
$501$		0			0
$502$	2.54492	+	3.63453i	0.113585	+	0.162217i
$503$	−17.3675	−	4.65361i	−0.774379	−	0.207494i	−0.150074	−	0.988675i	$-0.547951\pi$
$503$	−17.3675	−	4.65361i	−0.774379	−	0.207494i	−0.624305	+	0.781181i	$0.714618\pi$
$504$		0			0
$505$	4.36443	−	1.89241i	0.194215	−	0.0842111i
$506$	−3.42854	+	4.08598i	−0.152417	+	0.181644i
$507$		0			0
$508$	−10.8401	+	15.4813i	−0.480953	+	0.686872i
$509$	7.61493	−	6.38969i	0.337526	−	0.283218i	−0.458232	−	0.888833i	$-0.651517\pi$
$509$	7.61493	−	6.38969i	0.337526	−	0.283218i	0.795758	+	0.605615i	$0.207073\pi$
$510$		0			0
$511$	−27.5282	+	10.0195i	−1.21778	+	0.443235i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$		0			0
$514$			12.9689i			0.572036i
$515$	5.00095	−	2.70868i	0.220368	−	0.119359i
$516$		0			0
$517$	−0.330336	+	3.77575i	−0.0145281	+	0.166058i
$518$	27.9162	+	19.5471i	1.22657	+	0.858852i
$519$		0			0
$520$	4.20182	−	1.00423i	0.184262	−	0.0440382i
$521$	−28.8597	−	16.6622i	−1.26437	−	0.729983i	−0.290451	−	0.956890i	$-0.593805\pi$
$521$	−28.8597	−	16.6622i	−1.26437	−	0.729983i	−0.973917	+	0.226907i	$0.927139\pi$
$522$		0			0
$523$	0.128833	−	0.480813i	0.00563349	−	0.0210245i	−0.963052	−	0.269316i	$-0.913202\pi$
$523$	0.128833	−	0.480813i	0.00563349	−	0.0210245i	0.968685	+	0.248291i	$0.0798691\pi$
$524$	0.323070	−	1.83222i	0.0141134	−	0.0800410i
$525$		0			0
$526$	−23.6541	−	8.60939i	−1.03137	−	0.375387i
$527$	5.18574	+	11.1209i	0.225894	+	0.484432i
$528$		0			0
$529$	21.4207	+	3.77704i	0.931334	+	0.164219i
$530$	−17.3984	−	2.00031i	−0.755739	−	0.0868881i
$531$		0			0
$532$	−5.50256	−	20.5358i	−0.238566	−	0.890342i
$533$	−0.746809	+	0.0653373i	−0.0323479	+	0.00283007i
$534$		0			0
$535$	−4.24936	−	12.7433i	−0.183716	−	0.550940i
$536$	7.24014	+	8.62847i	0.312727	+	0.372693i
$537$		0			0
$538$	0.865913	+	0.403782i	0.0373322	+	0.0174083i
$539$	22.5710			0.972204
$540$		0			0
$541$	39.4681			1.69687			0.848433	−	0.529303i	$-0.177546\pi$
$541$	39.4681			1.69687			0.848433	+	0.529303i	$0.177546\pi$
$542$	−6.58857	−	3.07230i	−0.283004	−	0.131967i
$543$		0			0
$544$	−3.45904	−	4.12232i	−0.148305	−	0.176743i
$545$	−2.45686	+	4.91511i	−0.105240	+	0.210540i
$546$		0			0
$547$	19.7841	−	1.73088i	0.845906	−	0.0740072i	0.344043	−	0.938954i	$-0.388204\pi$
$547$	19.7841	−	1.73088i	0.845906	−	0.0740072i	0.501863	+	0.864947i	$0.332648\pi$
$548$	2.11454	+	7.89158i	0.0903288	+	0.337112i
$549$		0			0
$550$	0.784102	+	23.8516i	0.0334342	+	1.01703i
$551$	0.0858191	+	0.0151322i	0.00365602	+	0.000644654i
$552$		0			0
$553$	16.0827	+	34.4894i	0.683906	+	1.46664i
$554$	4.89201	+	1.78055i	0.207842	+	0.0756482i
$555$		0			0
$556$	2.91079	−	16.5079i	0.123445	−	0.700091i
$557$	−1.00253	+	3.74149i	−0.0424786	+	0.158532i	−0.983907	−	0.178680i	$-0.942817\pi$
$557$	−1.00253	+	3.74149i	−0.0424786	+	0.158532i	0.941429	+	0.337212i	$0.109484\pi$
$558$		0			0
$559$	−8.13958	−	4.69939i	−0.344268	−	0.198763i
$560$	4.00797	−	6.52543i	0.169368	−	0.275750i
$561$		0			0
$562$	−7.20565	−	5.04545i	−0.303952	−	0.212830i
$563$	2.77303	−	31.6959i	0.116869	−	1.33582i	−0.680685	−	0.732576i	$-0.738318\pi$
$563$	2.77303	−	31.6959i	0.116869	−	1.33582i	0.797554	−	0.603247i	$-0.206127\pi$
$564$		0			0
$565$	15.4999	+	28.6170i	0.652087	+	1.20393i
$566$			11.6570i			0.489980i
$567$		0			0
$568$	1.71599	+	1.71599i	0.0720015	+	0.0720015i
$569$	0.625558	−	0.227685i	0.0262248	−	0.00954503i	−0.328874	−	0.944374i	$-0.606669\pi$
$569$	0.625558	−	0.227685i	0.0262248	−	0.00954503i	0.355099	+	0.934829i	$0.384447\pi$
$570$		0			0
$571$	15.8737	−	13.3196i	0.664295	−	0.557410i	−0.247076	−	0.968996i	$-0.579470\pi$
$571$	15.8737	−	13.3196i	0.664295	−	0.557410i	0.911371	+	0.411586i	$0.135025\pi$
$572$	5.28917	−	7.55371i	0.221151	−	0.315837i
$573$		0			0
$574$	−0.854179	+	1.01797i	−0.0356528	+	0.0424893i
$575$	−4.74465	+	2.95132i	−0.197866	+	0.123078i
$576$		0			0
$577$	5.39239	+	1.44489i	0.224488	+	0.0601514i	0.369310	−	0.929306i	$-0.379594\pi$
$577$	5.39239	+	1.44489i	0.224488	+	0.0601514i	−0.144822	+	0.989458i	$0.546261\pi$
$578$	−6.85907	−	9.79577i	−0.285300	−	0.407450i
$579$		0			0
$580$	0.0172981	+	0.0261926i	0.000718263	+	0.00108759i
$581$	−16.1223	+	44.2956i	−0.668865	+	1.83769i
$582$		0			0
$583$	−30.6212	+	21.4412i	−1.26820	+	0.888003i
$584$	4.27693	+	7.40785i	0.176980	+	0.306539i
$585$		0			0
$586$	−6.13144	+	10.6200i	−0.253287	+	0.438707i
$587$	−0.721578	−	8.24768i	−0.0297827	−	0.340418i	−0.996437	−	0.0843348i	$-0.973123\pi$
$587$	−0.721578	−	8.24768i	−0.0297827	−	0.340418i	0.966655	−	0.256083i	$-0.0824321\pi$
$588$		0			0
$589$	13.9401	−	2.45801i	0.574390	−	0.101280i
$590$	17.2821	−	19.4937i	0.711495	−	0.802544i
$591$		0			0
$592$	4.20542	−	9.01855i	0.172842	−	0.370660i
$593$	−11.2101	+	11.2101i	−0.460343	+	0.460343i	−0.898768	−	0.438425i	$-0.855536\pi$
$593$	−11.2101	+	11.2101i	−0.460343	+	0.460343i	0.438425	+	0.898768i	$0.355536\pi$
$594$		0			0
$595$	24.5465	−	33.1019i	1.00631	−	1.35705i
$596$	−5.57142	−	15.3073i	−0.228214	−	0.627013i
$597$		0			0
$598$	2.15089	+	0.188179i	0.0879566	+	0.00769521i
$599$	−1.64551	−	9.33216i	−0.0672338	−	0.381302i	−0.999794	−	0.0202877i	$-0.993542\pi$
$599$	−1.64551	−	9.33216i	−0.0672338	−	0.381302i	0.932560	−	0.361014i	$-0.117569\pi$
$600$		0			0
$601$	−20.5855	−	17.2733i	−0.839699	−	0.704591i	0.117797	−	0.993038i	$-0.462417\pi$
$601$	−20.5855	−	17.2733i	−0.839699	−	0.704591i	−0.957496	+	0.288447i	$0.906861\pi$
$602$	−16.0928	+	4.31205i	−0.655893	+	0.175746i
$603$		0			0
$604$	10.4237	−	6.01814i	0.424135	−	0.244875i
$605$	18.1131	+	19.1263i	0.736401	+	0.777594i
$606$		0			0
$607$	4.57123	−	2.13160i	0.185541	−	0.0865190i	−0.327628	−	0.944807i	$-0.606249\pi$
$607$	4.57123	−	2.13160i	0.185541	−	0.0865190i	0.513169	+	0.858288i	$0.328472\pi$
$608$	−5.62618	+	2.62353i	−0.228172	+	0.106398i
$609$		0			0
$610$	−0.0957597	+	3.51944i	−0.00387720	+	0.142498i
$611$	1.32869	−	0.767119i	0.0537530	−	0.0310343i
$612$		0			0
$613$	5.24282	−	1.40481i	0.211756	−	0.0567397i	−0.151382	−	0.988475i	$-0.548372\pi$
$613$	5.24282	−	1.40481i	0.211756	−	0.0567397i	0.363137	+	0.931736i	$0.381706\pi$
$614$	−19.9676	−	16.7548i	−0.805826	−	0.676169i
$615$		0			0
$616$	−2.83846	−	16.0977i	−0.114365	−	0.648594i
$617$	−27.0727	−	2.36856i	−1.08991	−	0.0953545i	−0.471995	−	0.881601i	$-0.656466\pi$
$617$	−27.0727	−	2.36856i	−1.08991	−	0.0953545i	−0.617913	+	0.786247i	$0.712021\pi$
$618$		0			0
$619$	−3.84505	−	10.5642i	−0.154546	−	0.424611i	0.838122	−	0.545482i	$-0.183653\pi$
$619$	−3.84505	−	10.5642i	−0.154546	−	0.424611i	−0.992668	+	0.120871i	$0.961431\pi$
$620$	4.09553	+	3.03701i	0.164480	+	0.121969i
$621$		0			0
$622$	−15.6466	+	15.6466i	−0.627373	+	0.627373i
$623$	21.7733	−	46.6929i	0.872327	−	1.87071i
$624$		0			0
$625$	−6.98913	+	24.0032i	−0.279565	+	0.960127i
$626$	−21.5542	+	3.80059i	−0.861480	+	0.151902i
$627$		0			0
$628$	−0.961568	−	10.9908i	−0.0383707	−	0.438579i
$629$	26.7743	−	46.3745i	1.06756	−	1.84907i
$630$		0			0
$631$	−13.4777	−	23.3441i	−0.536539	−	0.929313i	−0.999087	−	0.0427187i	$-0.986398\pi$
$631$	−13.4777	−	23.3441i	−0.536539	−	0.929313i	0.462548	−	0.886594i	$-0.346935\pi$
$632$	9.10216	−	6.37340i	0.362064	−	0.253520i
$633$		0			0
$634$	3.39507	−	9.32788i	0.134835	−	0.370457i
$635$	−8.46758	+	41.4028i	−0.336026	+	1.64302i
$636$		0			0
$637$	−5.24054	−	7.48427i	−0.207638	−	0.296538i
$638$	0.0647172	+	0.0173409i	0.00256218	+	0.000686533i
$639$		0			0
$640$	−2.07964	−	0.821648i	−0.0822049	−	0.0324785i
$641$	−27.2802	+	32.5112i	−1.07750	+	1.28412i	−0.120917	+	0.992663i	$0.538583\pi$
$641$	−27.2802	+	32.5112i	−1.07750	+	1.28412i	−0.956585	+	0.291454i	$0.905861\pi$
$642$		0			0
$643$	−1.60171	+	2.28747i	−0.0631651	+	0.0902091i	−0.849492	−	0.527602i	$-0.823091\pi$
$643$	−1.60171	+	2.28747i	−0.0631651	+	0.0902091i	0.786327	+	0.617811i	$0.211980\pi$
$644$	2.93187	−	2.46013i	0.115532	−	0.0969428i
$645$		0			0
$646$	−31.3914	+	11.4256i	−1.23508	+	0.449532i
$647$	3.37176	+	3.37176i	0.132558	+	0.132558i	0.770273	−	0.637715i	$-0.220120\pi$
$647$	3.37176	+	3.37176i	0.132558	+	0.132558i	−0.637715	+	0.770273i	$0.720120\pi$
$648$		0			0
$649$		−	55.6068i		−	2.18276i
$650$	7.72682	−	5.79785i	0.303071	−	0.227410i
$651$		0			0
$652$	0.961543	−	10.9905i	0.0376569	−	0.430421i
$653$	−9.31500	−	6.52243i	−0.364524	−	0.255242i	0.376936	−	0.926239i	$-0.376978\pi$
$653$	−9.31500	−	6.52243i	−0.364524	−	0.255242i	−0.741460	+	0.670997i	$0.765866\pi$
$654$		0			0
$655$	−0.967039	−	4.04622i	−0.0377853	−	0.158099i
$656$	0.336033	+	0.194009i	0.0131199	+	0.00757476i
$657$		0			0
$658$	0.703890	−	2.62696i	0.0274405	−	0.102409i
$659$	−0.995226	+	5.64421i	−0.0387685	+	0.219867i	−0.998037	−	0.0626293i	$-0.980051\pi$
$659$	−0.995226	+	5.64421i	−0.0387685	+	0.219867i	0.959268	+	0.282496i	$0.0911625\pi$
$660$		0			0
$661$	−38.9403	−	14.1731i	−1.51460	−	0.551269i	−0.554807	−	0.831979i	$-0.687208\pi$
$661$	−38.9403	−	14.1731i	−1.51460	−	0.551269i	−0.959793	+	0.280709i	$0.909430\pi$
$662$	12.5482	+	26.9097i	0.487700	+	1.04588i
$663$		0			0
$664$	13.5549	+	2.39009i	0.526031	+	0.0927535i
$665$	−29.5559	−	37.2350i	−1.14613	−	1.44391i
$666$		0			0
$667$	0.00406023	+	0.0151530i	0.000157213	+	0.000586726i
$668$	19.6817	−	1.72193i	0.761508	−	0.0666233i
$669$		0			0
$670$	22.5286	+	11.2611i	0.870356	+	0.435055i
$671$	4.83057	+	5.75685i	0.186482	+	0.222241i
$672$		0			0
$673$	32.8201	+	15.3043i	1.26512	+	0.589936i	0.935216	−	0.354077i	$-0.115205\pi$
$673$	32.8201	+	15.3043i	1.26512	+	0.589936i	0.329907	+	0.944014i	$0.392983\pi$
$674$	−16.2889			−0.627425
$675$		0			0
$676$	9.26725			0.356433
$677$	−9.63788	−	4.49422i	−0.370414	−	0.172727i	0.228493	−	0.973546i	$-0.426620\pi$
$677$	−9.63788	−	4.49422i	−0.370414	−	0.172727i	−0.598907	+	0.800819i	$0.704398\pi$
$678$		0			0
$679$	39.2560	+	46.7834i	1.50651	+	1.79538i
$680$	−10.7632	−	5.38008i	−0.412751	−	0.206317i
$681$		0			0
$682$	10.8418	−	0.948533i	0.415153	−	0.0363212i
$683$	−3.39467	−	12.6691i	−0.129893	−	0.484768i	0.870074	−	0.492922i	$-0.164071\pi$
$683$	−3.39467	−	12.6691i	−0.129893	−	0.484768i	−0.999967	+	0.00815378i	$0.997405\pi$
$684$		0			0
$685$	11.3578	+	14.3088i	0.433961	+	0.546710i
$686$	7.65944	+	1.35057i	0.292439	+	0.0515649i
$687$		0			0
$688$	2.05592	+	4.40893i	0.0783811	+	0.168089i
$689$	14.2192	+	5.17538i	0.541710	+	0.197166i
$690$		0			0
$691$	3.47031	−	19.6811i	0.132017	−	0.748704i	−0.844874	−	0.534965i	$-0.820325\pi$
$691$	3.47031	−	19.6811i	0.132017	−	0.748704i	0.976891	−	0.213739i	$-0.0685642\pi$
$692$	6.22750	−	23.2413i	0.236734	−	0.883503i
$693$		0			0
$694$	0.00727421	+	0.00419977i	0.000276125	+	0.000159421i
$695$	−8.71280	−	36.4555i	−0.330495	−	1.38284i
$696$		0			0
$697$	1.71042	+	1.19765i	0.0647868	+	0.0453642i
$698$	−1.06682	+	12.1938i	−0.0403796	+	0.461541i
$699$		0			0
$700$	2.41783	−	16.9523i	0.0913855	−	0.640735i
$701$		−	20.1319i		−	0.760373i	−0.924910	−	0.380186i	$-0.875860\pi$
$701$		−	20.1319i		−	0.760373i	0.924910	−	0.380186i	$-0.124140\pi$
$702$		0			0
$703$	−43.6801	−	43.6801i	−1.64743	−	1.64743i
$704$	−4.48505	+	1.63242i	−0.169037	+	0.0615243i
$705$		0			0
$706$	−14.8093	+	12.4265i	−0.557357	+	0.467678i
$707$	−4.17902	+	5.96826i	−0.157168	+	0.224459i
$708$		0			0
$709$	−24.8113	+	29.5689i	−0.931808	+	1.11049i	0.0618554	+	0.998085i	$0.480298\pi$
$709$	−24.8113	+	29.5689i	−0.931808	+	1.11049i	−0.993663	+	0.112400i	$0.964146\pi$
$710$	5.04683	+	1.99396i	0.189404	+	0.0748320i
$711$		0			0
$712$	−14.5308	−	3.89350i	−0.544563	−	0.145915i
$713$	1.46159	+	2.08737i	0.0547371	+	0.0781727i
$714$		0			0
$715$	4.13154	−	20.2015i	0.154511	−	0.755492i
$716$	2.67616	−	7.35268i	0.100013	−	0.274783i
$717$		0			0
$718$	−8.00664	+	5.60631i	−0.298805	+	0.209225i
$719$	19.2505	+	33.3428i	0.717922	+	1.24348i	0.961822	+	0.273677i	$0.0882400\pi$
$719$	19.2505	+	33.3428i	0.717922	+	1.24348i	−0.243899	+	0.969801i	$0.578427\pi$
$720$		0			0
$721$	−4.35541	+	7.54379i	−0.162204	+	0.280946i
$722$	1.70275	+	19.4625i	0.0633697	+	0.724319i
$723$		0			0
$724$	−0.856787	+	0.151075i	−0.0318422	+	0.00561464i
$725$	0.0587865	+	0.0383475i	0.00218328	+	0.00142419i
$726$		0			0
$727$	−9.08040	+	19.4730i	−0.336773	+	0.722213i	−0.999648	−	0.0265174i	$-0.991558\pi$
$727$	−9.08040	+	19.4730i	−0.336773	+	0.722213i	0.662875	+	0.748730i	$0.269336\pi$
$728$	−4.67875	+	4.67875i	−0.173406	+	0.173406i
$729$		0			0
$730$	15.3637	+	11.3929i	0.568637	+	0.421670i
$731$	8.95357	+	24.5997i	0.331160	+	0.909854i
$732$		0			0
$733$	−27.7657	−	2.42919i	−1.02555	−	0.0897240i	−0.438052	−	0.898950i	$-0.644332\pi$
$733$	−27.7657	−	2.42919i	−1.02555	−	0.0897240i	−0.587498	+	0.809225i	$0.699887\pi$
$734$	3.88985	+	22.0604i	0.143577	+	0.814265i
$735$		0			0
$736$	−0.856080	−	0.718336i	−0.0315555	−	0.0264782i
$737$	51.9284	−	13.9142i	1.91281	−	0.512535i
$738$		0			0
$739$	−38.2159	+	22.0640i	−1.40579	+	0.811636i	−0.994979	−	0.100083i	$-0.968089\pi$
$739$	−38.2159	+	22.0640i	−1.40579	+	0.811636i	−0.410815	+	0.911719i	$0.634756\pi$
$740$	0.605193	−	22.2426i	0.0222473	−	0.817654i
$741$		0			0
$742$	24.3099	−	11.3359i	0.892443	−	0.416153i
$743$	21.7329	−	10.1342i	0.797305	−	0.371789i	0.0191139	−	0.999817i	$-0.493915\pi$
$743$	21.7329	−	10.1342i	0.797305	−	0.371789i	0.778191	+	0.628028i	$0.216138\pi$
$744$		0			0
$745$	−25.0463	−	26.4473i	−0.917624	−	0.968956i
$746$	3.31280	−	1.91264i	0.121290	−	0.0700269i
$747$		0			0
$748$	−24.8092	+	6.64760i	−0.907114	+	0.243060i
$749$	15.7607	+	13.2248i	0.575884	+	0.483224i
$750$		0			0
$751$	4.45381	+	25.2588i	0.162522	+	0.921707i	0.951583	+	0.307392i	$0.0994564\pi$
$751$	4.45381	+	25.2588i	0.162522	+	0.921707i	−0.789061	+	0.614315i	$0.789433\pi$
$752$	−0.791084	−	0.0692108i	−0.0288479	−	0.00252386i
$753$		0			0
$754$	−0.00927600	−	0.0254856i	−0.000337812	−	0.000928130i
$755$	16.0311	−	21.6186i	0.583432	−	0.786781i
$756$		0			0
$757$	21.7829	−	21.7829i	0.791712	−	0.791712i	−0.190060	−	0.981772i	$-0.560868\pi$
$757$	21.7829	−	21.7829i	0.791712	−	0.791712i	0.981772	+	0.190060i	$0.0608684\pi$
$758$	−6.32057	+	13.5545i	−0.229573	+	0.492322i
$759$		0			0
$760$	−9.20850	+	10.3869i	−0.334027	+	0.376773i
$761$	−17.2273	+	3.03764i	−0.624490	+	0.110114i	−0.476934	−	0.878939i	$-0.658252\pi$
$761$	−17.2273	+	3.03764i	−0.624490	+	0.110114i	−0.147556	+	0.989054i	$0.547141\pi$
$762$		0			0
$763$	−0.733509	−	8.38405i	−0.0265548	−	0.303523i
$764$	−4.91725	+	8.51692i	−0.177900	+	0.308132i
$765$		0			0
$766$	−0.558477	−	0.967311i	−0.0201786	−	0.0349504i
$767$	−18.4385	+	12.9108i	−0.665776	+	0.466181i
$768$		0			0
$769$	−4.82741	+	13.2632i	−0.174081	+	0.478283i	−0.995794	−	0.0916178i	$-0.970796\pi$
$769$	−4.82741	+	13.2632i	−0.174081	+	0.478283i	0.821713	+	0.569901i	$0.193018\pi$
$770$	−20.1426	−	30.4998i	−0.725888	−	1.09914i
$771$		0			0
$772$	4.68340	+	6.68859i	0.168559	+	0.240728i
$773$	31.5871	+	8.46375i	1.13611	+	0.304420i	0.777386	−	0.629024i	$-0.216545\pi$
$773$	31.5871	+	8.46375i	1.13611	+	0.304420i	0.358724	+	0.933444i	$0.383212\pi$
$774$		0			0
$775$	11.1036	+	2.58738i	0.398852	+	0.0929415i
$776$	11.4624	−	13.6603i	0.411476	−	0.490377i
$777$		0			0
$778$	−17.4416	+	24.9092i	−0.625312	+	0.893039i
$779$	1.84520	−	1.54830i	0.0661111	−	0.0554738i
$780$		0			0
$781$	10.8842	−	3.96154i	0.389469	−	0.141755i
$782$	−4.25239	−	4.25239i	−0.152065	−	0.152065i
$783$		0			0
$784$			4.72901i			0.168893i
$785$	−11.7493	−	21.6924i	−0.419352	−	0.774236i
$786$		0			0
$787$	3.14542	−	35.9523i	0.112122	−	1.28156i	−0.706699	−	0.707514i	$-0.749817\pi$
$787$	3.14542	−	35.9523i	0.112122	−	1.28156i	0.818821	−	0.574048i	$-0.194628\pi$
$788$	17.9622	+	12.5772i	0.639876	+	0.448046i
$789$		0			0
$790$	13.0039	−	21.1718i	0.462658	−	0.753260i
$791$	−43.1680	−	24.9231i	−1.53488	−	0.886162i
$792$		0			0
$793$	0.787337	−	2.93838i	0.0279592	−	0.104345i
$794$	−1.96376	+	11.1370i	−0.0696911	+	0.395238i
$795$		0			0
$796$	−4.97989	−	1.81253i	−0.176507	−	0.0642434i
$797$	−12.9450	−	27.7606i	−0.458534	−	0.983330i	−0.990621	−	0.136640i	$-0.956370\pi$
$797$	−12.9450	−	27.7606i	−0.458534	−	0.983330i	0.532087	−	0.846690i	$-0.321408\pi$
$798$		0			0
$799$	−4.20840	−	0.742055i	−0.148883	−	0.0262520i
$800$	−4.99730	+	0.164282i	−0.176681	+	0.00580826i
$801$		0			0
$802$	−3.53633	−	13.1978i	−0.124872	−	0.466029i
$803$	40.6712	−	3.55827i	1.43526	−	0.125569i
$804$		0			0
$805$	3.82642	−	7.65501i	0.134864	−	0.269804i
$806$	−2.83176	−	3.37476i	−0.0997446	−	0.118871i
$807$		0			0
$808$	1.92809	+	0.899085i	0.0678301	+	0.0316297i
$809$	19.4742			0.684678			0.342339	−	0.939577i	$-0.388781\pi$
$809$	19.4742			0.684678			0.342339	+	0.939577i	$0.388781\pi$
$810$		0			0
$811$	−43.6309			−1.53209			−0.766044	−	0.642788i	$-0.777777\pi$
$811$	−43.6309			−1.53209			−0.766044	+	0.642788i	$0.777777\pi$
$812$	−0.0435713	−	0.0203176i	−0.00152905	−	0.000713009i
$813$		0			0
$814$	−30.5288	−	36.3828i	−1.07003	−	1.27522i
$815$	−7.80378	−	23.4025i	−0.273355	−	0.819754i
$816$		0			0
$817$	30.0843	−	2.63203i	1.05252	−	0.0920831i
$818$	−5.39223	−	20.1241i	−0.188535	−	0.703621i
$819$		0			0
$820$	0.861955	+	0.0990999i	0.0301008	+	0.00346072i
$821$	−2.91570	−	0.514117i	−0.101759	−	0.0179428i	0.122537	−	0.992464i	$-0.460897\pi$
$821$	−2.91570	−	0.514117i	−0.101759	−	0.0179428i	−0.224296	+	0.974521i	$0.572008\pi$
$822$		0			0
$823$	−15.2677	−	32.7417i	−0.532200	−	1.14131i	−0.970194	−	0.242328i	$-0.922089\pi$
$823$	−15.2677	−	32.7417i	−0.532200	−	1.14131i	0.437995	−	0.898977i	$-0.355689\pi$
$824$	2.39009	+	0.869922i	0.0832627	+	0.0303052i
$825$		0			0
$826$	−6.92864	+	39.2942i	−0.241078	+	1.36722i
$827$	−2.70802	+	10.1065i	−0.0941670	+	0.351436i	−0.996892	−	0.0787823i	$-0.974897\pi$
$827$	−2.70802	+	10.1065i	−0.0941670	+	0.351436i	0.902725	+	0.430218i	$0.141563\pi$
$828$		0			0
$829$	21.9321	+	12.6625i	0.761735	+	0.439788i	0.829918	−	0.557885i	$-0.188387\pi$
$829$	21.9321	+	12.6625i	0.761735	+	0.439788i	−0.0681835	+	0.997673i	$0.521720\pi$
$830$	29.9341	−	7.15420i	1.03903	−	0.248326i
$831$		0			0
$832$	1.58263	+	1.10817i	0.0548678	+	0.0384188i
$833$	−2.21796	+	25.3514i	−0.0768478	+	0.878374i
$834$		0			0
$835$	38.8457	−	21.0401i	1.34431	−	0.728123i
$836$			29.6292i			1.02475i
$837$		0			0
$838$	5.07375	+	5.07375i	0.175270	+	0.175270i
$839$	−36.5830	+	13.3151i	−1.26299	+	0.459689i	−0.884770	−	0.466028i	$-0.845685\pi$
$839$	−36.5830	+	13.3151i	−1.26299	+	0.459689i	−0.378216	+	0.925717i	$0.623462\pi$
$840$		0			0
$841$	−22.2151	+	18.6407i	−0.766039	+	0.642783i
$842$	12.3565	−	17.6469i	0.425832	−	0.608151i
$843$		0			0
$844$	−10.5539	+	12.5776i	−0.363279	+	0.432939i
$845$	19.0119	−	8.24353i	0.654031	−	0.283586i
$846$		0			0
$847$	−38.9706	−	10.4421i	−1.33905	−	0.358796i
$848$	−4.49229	−	6.41565i	−0.154266	−	0.220314i
$849$		0			0
$850$	−26.8667	−	1.46310i	−0.921521	−	0.0501840i
$851$	3.80341	−	10.4498i	0.130379	−	0.358214i
$852$		0			0
$853$	−10.0582	+	7.04282i	−0.344386	+	0.241142i	−0.732954	−	0.680279i	$-0.761859\pi$
$853$	−10.0582	+	7.04282i	−0.344386	+	0.241142i	0.388568	+	0.921420i	$0.372970\pi$
$854$	−2.69619	−	4.66994i	−0.0922617	−	0.159802i
$855$		0			0
$856$	3.00373	−	5.20262i	0.102665	−	0.177822i
$857$	−3.95395	−	45.1939i	−0.135065	−	1.54379i	−0.697277	−	0.716802i	$-0.745605\pi$
$857$	−3.95395	−	45.1939i	−0.135065	−	1.54379i	0.562212	−	0.826993i	$-0.309950\pi$
$858$		0			0
$859$	−26.3810	+	4.65169i	−0.900110	+	0.158714i	−0.604509	−	0.796598i	$-0.706631\pi$
$859$	−26.3810	+	4.65169i	−0.900110	+	0.158714i	−0.295600	+	0.955312i	$0.595520\pi$
$860$	8.13964	+	7.21619i	0.277559	+	0.246070i
$861$		0			0
$862$	−9.16527	+	19.6550i	−0.312170	+	0.669451i
$863$	−13.4724	+	13.4724i	−0.458608	+	0.458608i	−0.898198	−	0.439591i	$-0.855124\pi$
$863$	−13.4724	+	13.4724i	−0.458608	+	0.458608i	0.439591	+	0.898198i	$0.355124\pi$
$864$		0			0
$865$	−7.89812	−	53.2196i	−0.268544	−	1.80952i
$866$	4.66485	+	12.8166i	0.158518	+	0.435525i
$867$		0			0
$868$	−7.77947	−	0.680615i	−0.264052	−	0.0231016i
$869$	−9.20940	−	52.2291i	−0.312408	−	1.77175i
$870$		0			0
$871$	−16.6705	−	13.9882i	−0.564858	−	0.473972i
$872$	−2.37368	+	0.636027i	−0.0803831	+	0.0215386i
$873$		0			0
$874$	−6.00799	+	3.46871i	−0.203223	+	0.117331i
$875$	−10.1194	−	36.9286i	−0.342097	−	1.24842i
$876$		0			0
$877$	35.5284	−	16.5672i	1.19971	−	0.559434i	0.283051	−	0.959105i	$-0.408654\pi$
$877$	35.5284	−	16.5672i	1.19971	−	0.559434i	0.916658	+	0.399671i	$0.130876\pi$
$878$	26.6011	−	12.4043i	0.897743	−	0.418625i
$879$		0			0
$880$	−7.74907	+	7.33855i	−0.261221	+	0.247383i
$881$	22.1803	−	12.8058i	0.747272	−	0.431438i	−0.0774355	−	0.996997i	$-0.524673\pi$
$881$	22.1803	−	12.8058i	0.747272	−	0.431438i	0.824707	+	0.565560i	$0.191340\pi$
$882$		0			0
$883$	2.67694	−	0.717285i	0.0900863	−	0.0241386i	−0.213494	−	0.976944i	$-0.568484\pi$
$883$	2.67694	−	0.717285i	0.0900863	−	0.0241386i	0.303581	+	0.952806i	$0.401818\pi$
$884$	7.96445	+	6.68297i	0.267874	+	0.224773i
$885$		0			0
$886$	3.06286	+	17.3703i	0.102899	+	0.583568i
$887$	47.4566	+	4.15191i	1.59344	+	0.139408i	0.849039	−	0.528330i	$-0.177181\pi$
$887$	47.4566	+	4.15191i	1.59344	+	0.139408i	0.744397	+	0.667737i	$0.232737\pi$
$888$		0			0
$889$	−22.1373	−	60.8218i	−0.742462	−	2.03990i
$890$	−33.2735	+	4.93800i	−1.11533	+	0.165522i
$891$		0			0
$892$	−7.03339	+	7.03339i	−0.235495	+	0.235495i
$893$	−2.08336	+	4.46778i	−0.0697170	+	0.149509i
$894$		0			0
$895$	−1.05027	−	17.4647i	−0.0351067	−	0.583780i
$896$	3.37273	−	0.594704i	0.112675	−	0.0198677i
$897$		0			0
$898$	−0.613887	−	7.01676i	−0.0204857	−	0.234152i
$899$	0.0160044	−	0.0277204i	0.000533776	−	0.000924528i
$900$		0			0
$901$	−21.0734	−	36.5001i	−0.702055	−	1.21600i
$902$	1.51704	−	1.06224i	0.0505119	−	0.0353688i
$903$		0			0
$904$	−4.97797	+	13.6769i	−0.165565	+	0.454886i
$905$	−1.62333	+	1.07207i	−0.0539612	+	0.0356369i
$906$		0			0
$907$	16.4036	+	23.4268i	0.544673	+	0.777874i	0.993265	−	0.115863i	$-0.0369632\pi$
$907$	16.4036	+	23.4268i	0.544673	+	0.777874i	−0.448592	+	0.893737i	$0.648074\pi$
$908$	−11.7254	−	3.14182i	−0.389122	−	0.104265i
$909$		0			0
$910$	−5.43664	+	13.7605i	−0.180223	+	0.456155i
$911$	−22.1960	+	26.4522i	−0.735387	+	0.876400i	−0.996028	−	0.0890359i	$-0.971621\pi$
$911$	−22.1960	+	26.4522i	−0.735387	+	0.876400i	0.260642	+	0.965436i	$0.416066\pi$
$912$		0			0
$913$	37.6805	−	53.8133i	1.24704	−	1.78096i
$914$	−3.88646	+	3.26113i	−0.128553	+	0.107869i
$915$		0			0
$916$	9.79323	−	3.56444i	0.323577	−	0.117773i
$917$	4.50549	+	4.50549i	0.148785	+	0.148785i
$918$		0			0
$919$			44.2093i			1.45833i	0.684338	+	0.729165i	$0.260091\pi$
$919$			44.2093i			1.45833i	−0.684338	+	0.729165i	$0.739909\pi$
$920$	−2.39525	−	0.712169i	−0.0789690	−	0.0234795i
$921$		0			0
$922$	−0.178830	+	2.04404i	−0.00588946	+	0.0673169i
$923$	−3.84069	−	2.68928i	−0.126418	−	0.0885188i
$924$		0			0
$925$	−18.5440	−	46.1694i	−0.609722	−	1.51804i
$926$	12.0663	+	6.96651i	0.396525	+	0.228934i
$927$		0			0
$928$	−0.00363321	+	0.0135593i	−0.000119266	+	0.000445107i
$929$	−2.26170	+	12.8267i	−0.0742039	+	0.420831i	0.924964	+	0.380054i	$0.124095\pi$
$929$	−2.26170	+	12.8267i	−0.0742039	+	0.420831i	−0.999168	+	0.0407775i	$0.987017\pi$
$930$		0			0
$931$	27.5863	+	10.0406i	0.904106	+	0.329068i
$932$	−4.23315	−	9.07802i	−0.138662	−	0.297361i
$933$		0			0
$934$	−1.34914	−	0.237890i	−0.0441453	−	0.00778400i
$935$	−44.9833	+	35.7063i	−1.47111	+	1.16772i
$936$		0			0
$937$	−10.1669	−	37.9433i	−0.332137	−	1.23955i	−0.906940	−	0.421260i	$-0.861588\pi$
$937$	−10.1669	−	37.9433i	−0.332137	−	1.23955i	0.574803	−	0.818292i	$-0.305079\pi$
$938$	−38.4286	+	3.36207i	−1.25474	+	0.109775i
$939$		0			0
$940$	−1.68449	+	0.561708i	−0.0549420	+	0.0183209i
$941$	−33.7793	−	40.2566i	−1.10117	−	1.31233i	−0.945901	−	0.324456i	$-0.894819\pi$
$941$	−33.7793	−	40.2566i	−1.10117	−	1.31233i	−0.155273	−	0.987872i	$-0.549626\pi$
$942$		0			0
$943$	0.392995	+	0.183257i	0.0127977	+	0.00596766i
$944$	11.6506			0.379193
$945$		0			0
$946$	23.2187			0.754906
$947$	36.8009	+	17.1605i	1.19587	+	0.557643i	0.915527	−	0.402258i	$-0.131774\pi$
$947$	36.8009	+	17.1605i	1.19587	+	0.557643i	0.280342	+	0.959900i	$0.409552\pi$
$948$		0			0
$949$	−10.6229	−	12.6599i	−0.344834	−	0.410958i
$950$	−9.65191	+	29.5002i	−0.313149	+	0.957113i
$951$		0			0
$952$	18.3596	−	1.60625i	0.595037	−	0.0520590i
$953$	7.83630	+	29.2455i	0.253843	+	0.947354i	0.968731	+	0.248115i	$0.0798111\pi$
$953$	7.83630	+	29.2455i	0.253843	+	0.947354i	−0.714888	+	0.699239i	$0.753522\pi$
$954$		0			0
$955$	−2.51174	+	21.8467i	−0.0812779	+	0.706942i
$956$	−0.669224	−	0.118002i	−0.0216443	−	0.00381647i
$957$		0			0
$958$	−2.93621	−	6.29673i	−0.0948648	−	0.203438i
$959$	−26.2928	−	9.56979i	−0.849038	−	0.309025i
$960$		0			0
$961$	−4.48023	+	25.4087i	−0.144524	+	0.819635i
$962$	−4.97590	+	18.5703i	−0.160429	+	0.598731i
$963$		0			0
$964$	16.8701	+	9.73993i	0.543348	+	0.313702i
$965$	15.5578	+	9.55573i	0.500824	+	0.307610i
$966$		0			0
$967$	−32.9473	−	23.0699i	−1.05951	−	0.741879i	−0.0922710	−	0.995734i	$-0.529413\pi$
$967$	−32.9473	−	23.0699i	−1.05951	−	0.741879i	−0.967242	+	0.253855i	$0.918301\pi$
$968$	−1.02674	+	11.7356i	−0.0330005	+	0.377198i
$969$		0			0
$970$	11.3640	−	38.2206i	0.364875	−	1.22719i
$971$		−	27.9762i		−	0.897800i	−0.893582	−	0.448900i	$-0.851816\pi$
$971$		−	27.9762i		−	0.897800i	0.893582	−	0.448900i	$-0.148184\pi$
$972$		0			0
$973$	40.5935	+	40.5935i	1.30137	+	1.30137i
$974$	18.7470	−	6.82334i	0.600692	−	0.218634i
$975$		0			0
$976$	−1.20616	+	1.01209i	−0.0386081	+	0.0323961i
$977$	−5.53031	+	7.89810i	−0.176930	+	0.252682i	−0.897815	−	0.440372i	$-0.854847\pi$
$977$	−5.53031	+	7.89810i	−0.176930	+	0.252682i	0.720885	+	0.693054i	$0.243735\pi$
$978$		0			0
$979$	−46.1523	+	55.0022i	−1.47503	+	1.75788i
$980$	4.20661	+	9.70166i	0.134375	+	0.309908i
$981$		0			0
$982$	40.3629	+	10.8152i	1.28803	+	0.345127i
$983$	−22.3485	−	31.9169i	−0.712806	−	1.01799i	−0.998223	−	0.0595888i	$-0.981021\pi$
$983$	−22.3485	−	31.9169i	−0.712806	−	1.01799i	0.285417	−	0.958403i	$-0.407868\pi$
$984$		0			0
$985$	48.0376	+	9.82450i	1.53061	+	0.313035i
$986$	−0.0258365	+	0.0709852i	−0.000822801	+	0.00226063i
$987$		0			0
$988$	9.82465	−	6.87929i	0.312564	−	0.218859i
$989$	2.71824	+	4.70813i	0.0864349	+	0.149710i
$990$		0			0
$991$	−12.5007	+	21.6518i	−0.397097	+	0.687793i	−0.993366	−	0.114992i	$-0.963316\pi$
$991$	−12.5007	+	21.6518i	−0.397097	+	0.687793i	0.596269	+	0.802785i	$0.296649\pi$
$992$	0.198733	+	2.27153i	0.00630979	+	0.0721212i
$993$		0			0
$994$	−8.18489	+	1.44322i	−0.259609	+	0.0457761i
$995$	−11.8286	+	0.711336i	−0.374993	+	0.0225509i
$996$		0			0
$997$	−9.78742	+	20.9892i	−0.309971	+	0.664735i	−0.998150	−	0.0608066i	$-0.980633\pi$
$997$	−9.78742	+	20.9892i	−0.309971	+	0.664735i	0.688179	+	0.725541i	$0.258410\pi$
$998$	−3.81527	+	3.81527i	−0.120770	+	0.120770i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	810.2.s.a.143.17		216
3.2	odd	2		270.2.r.a.263.7	yes	216
5.2	odd	4	inner	810.2.s.a.467.7		216
15.2	even	4		270.2.r.a.47.11	yes	216
27.4	even	9		270.2.r.a.23.11	✓	216
27.23	odd	18	inner	810.2.s.a.503.7		216
135.77	even	36	inner	810.2.s.a.17.17		216
135.112	odd	36		270.2.r.a.77.7	yes	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
270.2.r.a.23.11	✓	216	27.4	even	9
270.2.r.a.47.11	yes	216	15.2	even	4
270.2.r.a.77.7	yes	216	135.112	odd	36
270.2.r.a.263.7	yes	216	3.2	odd	2
810.2.s.a.17.17		216	135.77	even	36	inner
810.2.s.a.143.17		216	1.1	even	1	trivial
810.2.s.a.467.7		216	5.2	odd	4	inner
810.2.s.a.503.7		216	27.23	odd	18	inner

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:	\( N \)	\(=\)	\( 810 = 2 \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	810.s (of order \(36\), degree \(12\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.906308 + 0.422618i) q^{2} +(0.642788 + 0.766044i) q^{4} +(2.00011 + 0.999773i) q^{5} +(-3.41173 + 0.298488i) q^{7} +(0.258819 + 0.965926i) q^{8} +O(q^{10})\)	\(q+(0.906308 + 0.422618i) q^{2} +(0.642788 + 0.766044i) q^{4} +(2.00011 + 0.999773i) q^{5} +(-3.41173 + 0.298488i) q^{7} +(0.258819 + 0.965926i) q^{8} +(1.39020 + 1.75139i) q^{10} +(4.70038 + 0.828804i) q^{11} +(-0.816512 - 1.75102i) q^{13} +(-3.21823 - 1.17134i) q^{14} +(-0.173648 + 0.984808i) q^{16} +(-1.39278 + 5.19794i) q^{17} +(5.37612 + 3.10390i) q^{19} +(0.519777 + 2.17482i) q^{20} +(3.90972 + 2.73762i) q^{22} +(-0.0973994 + 1.11328i) q^{23} +(3.00091 + 3.99932i) q^{25} -1.93203i q^{26} +(-2.42167 - 2.42167i) q^{28} +(0.0131911 - 0.00480116i) q^{29} +(1.74674 - 1.46569i) q^{31} +(-0.573576 + 0.819152i) q^{32} +(-3.45904 + 4.12232i) q^{34} +(-7.12227 - 2.81395i) q^{35} +(-9.61180 - 2.57547i) q^{37} +(3.56065 + 5.08514i) q^{38} +(-0.448040 + 2.19072i) q^{40} +(0.132710 - 0.364617i) q^{41} +(3.98494 - 2.79028i) q^{43} +(2.38644 + 4.13344i) q^{44} +(-0.558767 + 0.967812i) q^{46} +(0.0692108 + 0.791084i) q^{47} +(4.65717 - 0.821184i) q^{49} +(1.02956 + 4.89285i) q^{50} +(0.816512 - 1.75102i) q^{52} +(-5.53811 + 5.53811i) q^{53} +(8.57267 + 6.35701i) q^{55} +(-1.17134 - 3.21823i) q^{56} +(0.0139842 + 0.00122346i) q^{58} +(-2.02310 - 11.4736i) q^{59} +(1.20616 + 1.01209i) q^{61} +(2.20251 - 0.590162i) q^{62} +(-0.866025 + 0.500000i) q^{64} +(0.117503 - 4.31856i) q^{65} +(10.2083 - 4.76023i) q^{67} +(-4.87712 + 2.27424i) q^{68} +(-5.26574 - 5.56031i) q^{70} +(2.10165 - 1.21339i) q^{71} +(8.26239 - 2.21390i) q^{73} +(-7.62281 - 6.39630i) q^{74} +(1.07797 + 6.11349i) q^{76} +(-16.2838 - 1.42465i) q^{77} +(-3.80042 - 10.4416i) q^{79} +(-1.33190 + 1.79612i) q^{80} +(0.274370 - 0.274370i) q^{82} +(5.81691 - 12.4744i) q^{83} +(-7.98249 + 9.00400i) q^{85} +(4.79081 - 0.844748i) q^{86} +(0.415985 + 4.75473i) q^{88} +(-7.52167 + 13.0279i) q^{89} +(3.30838 + 5.73028i) q^{91} +(-0.915429 + 0.640991i) q^{92} +(-0.271600 + 0.746215i) q^{94} +(7.64964 + 11.5831i) q^{95} +(-10.2282 - 14.6074i) q^{97} +(4.56787 + 1.22396i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q+O(q^{10}) \) 216 * q	\( 216 q - 24 q^{11} + 24 q^{20} - 24 q^{23} + 36 q^{25} + 108 q^{35} + 36 q^{38} + 72 q^{41} + 48 q^{47} + 48 q^{50} + 12 q^{56} + 36 q^{61} - 24 q^{65} - 72 q^{67} - 36 q^{68} + 240 q^{77} + 60 q^{83} - 72 q^{86} + 48 q^{92} + 60 q^{95} - 72 q^{97}+O(q^{100}) \) 216 * q - 24 * q^11 + 24 * q^20 - 24 * q^23 + 36 * q^25 + 108 * q^35 + 36 * q^38 + 72 * q^41 + 48 * q^47 + 48 * q^50 + 12 * q^56 + 36 * q^61 - 24 * q^65 - 72 * q^67 - 36 * q^68 + 240 * q^77 + 60 * q^83 - 72 * q^86 + 48 * q^92 + 60 * q^95 - 72 * q^97

Introduction

L-functions

Modular forms

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Database

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