LMFDB - Embedded newform 810.2.s.a.17.17

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			17.17
Character	$\chi$	$=$	810.17
Dual form			810.2.s.a.143.17

$q$-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 $\left(\mathbb{Z}/810\mathbb{Z}\right)^\times$.

$n$	$487$	$731$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{11}{18}\right)$

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	−0.578318	−	0.815812i	$-0.696291\pi$
$7$	−3.41173	−	0.298488i	−1.28951	−	0.112818i	−0.711196	+	0.702994i	$0.751846\pi$
$8$	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	0.588019	−	0.808847i	$-0.299908\pi$
$11$	4.70038	−	0.828804i	1.41722	−	0.249894i	0.829199	+	0.558954i	$0.188797\pi$
$12$		0			0
$13$	−0.816512	+	1.75102i	−0.226460	+	0.485645i	−0.986403	−	0.164345i	$-0.947449\pi$
$13$	−0.816512	+	1.75102i	−0.226460	+	0.485645i	0.759943	+	0.649990i	$0.225227\pi$
$14$	−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	−0.900802	−	0.434230i	$-0.857020\pi$
$17$	−1.39278	−	5.19794i	−0.337800	−	1.26069i	0.563002	−	0.826455i	$-0.309646\pi$
$18$		0			0
$19$	5.37612	−	3.10390i	1.23337	−	0.712084i	0.265636	−	0.964073i	$-0.414418\pi$
$19$	5.37612	−	3.10390i	1.23337	−	0.712084i	0.967730	+	0.251989i	$0.0810848\pi$
$20$	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	−0.999565	−	0.0295054i	$-0.990607\pi$
$23$	−0.0973994	−	1.11328i	−0.0203092	−	0.232135i	0.979255	−	0.202630i	$-0.0649488\pi$
$24$		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	0.343245	−	0.939246i	$-0.388474\pi$
$29$	0.0131911	+	0.00480116i	0.00244952	+	0.000891553i	−0.340795	+	0.940138i	$0.610696\pi$
$30$		0			0
$31$	1.74674	+	1.46569i	0.313724	+	0.263246i	0.786029	−	0.618189i	$-0.212133\pi$
$31$	1.74674	+	1.46569i	0.313724	+	0.263246i	−0.472305	+	0.881435i	$0.656578\pi$
$32$	−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	−0.938979	−	0.343975i	$-0.888226\pi$
$37$	−9.61180	+	2.57547i	−1.58017	+	0.423405i	−0.641192	+	0.767381i	$0.721560\pi$
$38$	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	0.949624	−	0.313391i	$-0.101465\pi$
$41$	0.132710	+	0.364617i	0.0207258	+	0.0569436i	−0.928898	+	0.370335i	$0.879243\pi$
$42$		0			0
$43$	3.98494	+	2.79028i	0.607697	+	0.425514i	0.836506	−	0.547957i	$-0.184594\pi$
$43$	3.98494	+	2.79028i	0.607697	+	0.425514i	−0.228809	+	0.973471i	$0.573483\pi$
$44$	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	−0.989475	−	0.144705i	$-0.953777\pi$
$47$	0.0692108	−	0.791084i	0.0100954	−	0.115391i	0.999570	+	0.0293137i	$0.00933219\pi$
$48$		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	0.215735	−	0.976452i	$-0.430785\pi$
$53$	−5.53811	−	5.53811i	−0.760717	−	0.760717i	−0.976452	+	0.215735i	$0.930785\pi$
$54$		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	0.510210	+	0.860050i	$0.329568\pi$
$59$	−2.02310	+	11.4736i	−0.263385	+	1.49373i	−0.773595	+	0.633681i	$0.781543\pi$
$60$		0			0
$61$	1.20616	−	1.01209i	0.154433	−	0.129584i	−0.562298	−	0.826935i	$-0.690082\pi$
$61$	1.20616	−	1.01209i	0.154433	−	0.129584i	0.716730	+	0.697351i	$0.245638\pi$
$62$	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	0.930257	−	0.366907i	$-0.119583\pi$
$67$	10.2083	+	4.76023i	1.24715	+	0.581555i	0.316891	+	0.948462i	$0.397361\pi$
$68$	−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	0.619499	−	0.784998i	$-0.287336\pi$
$71$	2.10165	+	1.21339i	0.249420	+	0.144003i	−0.370078	+	0.929001i	$0.620669\pi$
$72$		0			0
$73$	8.26239	+	2.21390i	0.967039	+	0.259117i	0.707577	−	0.706636i	$-0.249788\pi$
$73$	8.26239	+	2.21390i	0.967039	+	0.259117i	0.259462	+	0.965753i	$0.416455\pi$
$74$	−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	0.519696	+	0.854351i	$0.326045\pi$
$79$	−3.80042	+	10.4416i	−0.427580	+	1.17477i	−0.947277	+	0.320417i	$0.896177\pi$
$80$	−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	0.913119	+	0.407693i	$0.133667\pi$
$83$	5.81691	+	12.4744i	0.638489	+	1.36924i	−0.274630	+	0.961550i	$0.588555\pi$
$84$		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	−0.921371	−	0.388684i	$-0.872930\pi$
$89$	−7.52167	−	13.0279i	−0.797296	−	1.38096i	0.124075	−	0.992273i	$-0.460404\pi$
$90$		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	−0.171301	+	0.985219i	$0.554797\pi$
$97$	−10.2282	+	14.6074i	−1.03852	+	1.48315i	−0.867215	+	0.497935i	$0.834092\pi$
$98$	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	0.829776	−	0.558097i	$-0.188468\pi$
$101$	1.36748	+	1.62970i	0.136069	+	0.162161i	−0.693707	+	0.720257i	$0.744024\pi$
$102$		0			0
$103$	1.45888	+	2.08350i	0.143748	+	0.205293i	0.884569	−	0.466409i	$-0.154452\pi$
$103$	1.45888	+	2.08350i	0.143748	+	0.205293i	−0.740821	+	0.671702i	$0.765564\pi$
$104$	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	−0.881969	−	0.471307i	$-0.843782\pi$
$107$	−4.24792	+	4.24792i	−0.410662	+	0.410662i	0.471307	+	0.881969i	$0.343782\pi$
$108$		0			0
$109$		−	2.45742i		−	0.235378i	−0.993051	−	0.117689i	$-0.962451\pi$
$109$		−	2.45742i		−	0.235378i	0.993051	−	0.117689i	$-0.0375486\pi$
$110$	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	0.142689	−	0.989768i	$-0.454425\pi$
$113$	11.9224	−	8.34818i	1.12157	−	0.785331i	0.978880	+	0.204437i	$0.0655363\pi$
$114$		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	−0.309288	−	0.950969i	$-0.600091\pi$
$127$	4.89147	−	18.2552i	0.434048	−	1.61989i	0.743335	−	0.668919i	$-0.233243\pi$
$128$	−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	−0.815753	−	0.578400i	$-0.803677\pi$
$131$	−1.19590	+	1.42522i	−0.104486	+	0.124522i	0.711267	+	0.702922i	$0.248122\pi$
$132$		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	−0.0797400	−	0.996816i	$-0.525409\pi$
$137$	7.40450	−	3.45278i	0.632609	−	0.294991i	0.712349	+	0.701825i	$0.247631\pi$
$138$		0			0
$139$	−10.7748	+	12.8409i	−0.913904	+	1.08915i	0.0818088	+	0.996648i	$0.473930\pi$
$139$	−10.7748	+	12.8409i	−0.913904	+	1.08915i	−0.995713	+	0.0925002i	$0.970514\pi$
$140$	−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	−0.881760	−	0.471698i	$-0.843641\pi$
$149$	−15.3073	+	5.57142i	−1.25403	+	0.456428i	−0.372266	+	0.928126i	$0.621419\pi$
$150$		0			0
$151$	2.09008	+	11.8534i	0.170088	+	0.964618i	0.943662	+	0.330911i	$0.107356\pi$
$151$	2.09008	+	11.8534i	0.170088	+	0.964618i	−0.773574	+	0.633706i	$0.781533\pi$
$152$	−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	−0.875634	−	0.482975i	$-0.839556\pi$
$157$	−9.03750	+	6.32813i	−0.721271	+	0.505039i	0.154363	+	0.988014i	$0.450667\pi$
$158$	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	−0.943215	−	0.332183i	$-0.892215\pi$
$163$	−7.80113	+	7.80113i	−0.611032	+	0.611032i	0.332183	+	0.943215i	$0.392215\pi$
$164$	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	0.966577	+	0.256377i	$0.0825287\pi$
$167$	11.3321	+	16.1839i	0.876903	+	1.25235i	−0.0896736	+	0.995971i	$0.528582\pi$
$168$		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	−0.193529	+	0.981095i	$0.561993\pi$
$173$	−13.8009	+	19.7098i	−1.04927	+	1.49851i	−0.855736	+	0.517412i	$0.826895\pi$
$174$		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	−0.974381	−	0.224904i	$-0.927793\pi$
$179$	−3.91228	+	6.77627i	−0.292418	+	0.506482i	0.681963	+	0.731386i	$0.261126\pi$
$180$		0			0
$181$	−0.435002	−	0.753445i	−0.0323334	−	0.0560032i	0.849406	−	0.527740i	$-0.176961\pi$
$181$	−0.435002	−	0.753445i	−0.0323334	−	0.0560032i	−0.881739	+	0.471737i	$0.843627\pi$
$182$	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	−0.756511	−	0.653981i	$-0.773097\pi$
$191$	3.36360	−	9.24141i	0.243381	−	0.668685i	0.999892	−	0.0147032i	$-0.00468034\pi$
$192$		0			0
$193$	8.13419	−	0.711650i	0.585512	−	0.0512257i	0.209449	−	0.977820i	$-0.432833\pi$
$193$	8.13419	−	0.711650i	0.585512	−	0.0512257i	0.376063	+	0.926594i	$0.377278\pi$
$194$	−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	0.916121	−	0.400902i	$-0.131303\pi$
$197$	21.1806	+	5.67532i	1.50905	+	0.404350i	0.592933	+	0.805252i	$0.297970\pi$
$198$		0			0
$199$	−4.58949	−	2.64974i	−0.325340	−	0.187835i	0.328430	−	0.944528i	$-0.393480\pi$
$199$	−4.58949	−	2.64974i	−0.325340	−	0.187835i	−0.653770	+	0.756693i	$0.726814\pi$
$200$	−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	−0.714308	−	0.699832i	$-0.753258\pi$
$211$	2.85111	−	16.1695i	0.196279	−	1.11315i	0.910586	−	0.413319i	$-0.135631\pi$
$212$	−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	−0.910298	−	0.413954i	$-0.864148\pi$
$223$	0.866913	−	9.90886i	0.0580528	−	0.663547i	0.968351	−	0.249593i	$-0.0802968\pi$
$224$	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	0.194981	−	0.980807i	$-0.437535\pi$
$227$	−9.94373	−	6.96268i	−0.659989	−	0.462129i	−0.854970	+	0.518678i	$0.826424\pi$
$228$		0			0
$229$	3.56444	+	9.79323i	0.235545	+	0.647155i	0.999997	+	0.00247388i	$0.000787462\pi$
$229$	3.56444	+	9.79323i	0.235545	+	0.647155i	−0.764452	+	0.644681i	$0.776990\pi$
$230$	−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	−0.561413	−	0.827536i	$-0.689742\pi$
$233$	−9.67519	+	2.59246i	−0.633843	+	0.169838i	−0.0724298	+	0.997374i	$0.523075\pi$
$234$		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	0.625796	−	0.779987i	$-0.284774\pi$
$239$	−0.520564	−	0.436805i	−0.0336725	−	0.0282546i	−0.659469	+	0.751732i	$0.729219\pi$
$240$		0			0
$241$	18.3051	+	6.66251i	1.17913	+	0.429170i	0.855896	−	0.517148i	$-0.173006\pi$
$241$	18.3051	+	6.66251i	1.17913	+	0.429170i	0.323238	+	0.946318i	$0.395229\pi$
$242$	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	−0.373805	−	0.927507i	$-0.621947\pi$
$251$	3.84250	−	2.21847i	0.242537	−	0.140029i	0.616342	+	0.787479i	$0.288614\pi$
$252$		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	−0.657912	−	0.753095i	$-0.728560\pi$
$257$	5.48091	−	11.7539i	0.341890	−	0.733185i	0.999802	+	0.0199097i	$0.00633787\pi$
$258$		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	−0.718175	−	0.695862i	$-0.755022\pi$
$263$	−25.0764	−	2.19390i	−1.54628	−	0.135282i	−0.828100	+	0.560580i	$0.810578\pi$
$264$		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	0.241886	−	0.970305i	$-0.422234\pi$
$277$	5.18616	+	0.453730i	0.311606	+	0.0272620i	0.0697199	+	0.997567i	$0.477789\pi$
$278$	−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	−0.425955	−	0.904744i	$-0.640062\pi$
$281$	−8.66284	+	1.52749i	−0.516782	+	0.0911226i	−0.0908264	+	0.995867i	$0.528951\pi$
$282$		0			0
$283$	4.92646	−	10.5648i	0.292848	−	0.628014i	−0.703749	−	0.710449i	$-0.748492\pi$
$283$	4.92646	−	10.5648i	0.292848	−	0.628014i	0.996596	+	0.0824351i	$0.0262697\pi$
$284$	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	−0.961311	−	0.275467i	$-0.911168\pi$
$293$	−1.06878	−	12.2162i	−0.0624388	−	0.713679i	0.898872	−	0.438212i	$-0.144388\pi$
$294$		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	−0.891470	−	0.453080i	$-0.850325\pi$
$307$	−25.1777	+	6.74634i	−1.43697	+	0.385034i	−0.545495	+	0.838114i	$0.683658\pi$
$308$	−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	−0.946331	−	0.323200i	$-0.895241\pi$
$311$	−7.56811	−	20.7932i	−0.429148	−	1.17908i	0.517182	−	0.855875i	$-0.326981\pi$
$312$		0			0
$313$	−17.9286	−	12.5537i	−1.01338	−	0.709578i	−0.0560084	−	0.998430i	$-0.517837\pi$
$313$	−17.9286	−	12.5537i	−1.01338	−	0.709578i	−0.957374	+	0.288853i	$0.906726\pi$
$314$	−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	0.932409	+	0.361404i	$0.117703\pi$
$317$	−0.865153	+	9.88874i	−0.0485918	+	0.555407i	−0.981001	+	0.194003i	$0.937853\pi$
$318$		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	0.253527	−	0.967328i	$-0.418409\pi$
$331$	22.7451	−	19.0854i	1.25018	−	1.04903i	0.996657	−	0.0817003i	$-0.0260350\pi$
$332$	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	−0.0233403	−	0.999728i	$-0.507430\pi$
$337$	−14.7628	−	6.88399i	−0.804179	−	0.374995i	−0.780839	+	0.624733i	$0.785208\pi$
$338$	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	−0.0869311	−	0.996214i	$-0.527706\pi$
$347$	0.00836757		0.000732067i	0.000449195		3.92994e-5i	0.0873803	+	0.996175i	$0.472150\pi$
$348$		0			0
$349$	4.18645	−	11.5022i	0.224096	−	0.615697i	−0.775787	−	0.630994i	$-0.782647\pi$
$349$	4.18645	−	11.5022i	0.224096	−	0.615697i	0.999883	+	0.0152969i	$0.00486935\pi$
$350$	−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	−0.994590	−	0.103875i	$-0.966876\pi$
$353$	−8.17015	−	17.5209i	−0.434853	−	0.932545i	0.559737	−	0.828670i	$-0.310902\pi$
$354$		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	0.707754	−	0.706459i	$-0.249708\pi$
$359$	−4.88715	−	8.46479i	−0.257934	−	0.446754i	−0.965688	+	0.259704i	$0.916375\pi$
$360$		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	−0.329220	−	0.944253i	$-0.606786\pi$
$367$	12.8485	−	18.3496i	0.670688	−	0.957842i	0.999908	−	0.0135884i	$-0.00432544\pi$
$368$	−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	0.871928	−	0.489634i	$-0.162870\pi$
$373$	2.19410	+	3.13349i	0.113606	+	0.162246i	−0.758322	+	0.651880i	$0.773981\pi$
$374$	−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	$-0.874507\pi$
$379$		−	14.9557i		−	0.768225i	0.923286	−	0.384112i	$-0.125493\pi$
$380$	−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	−0.596719	−	0.802450i	$-0.703529\pi$
$383$	−0.914955	+	0.640659i	−0.0467520	+	0.0327361i	0.549967	+	0.835187i	$0.314640\pi$
$384$		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	−0.761158	−	0.648566i	$-0.775369\pi$
$389$	−5.28039	−	29.9466i	−0.267726	−	1.51835i	0.493432	−	0.869784i	$-0.335742\pi$
$390$		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	−0.852765	−	0.522295i	$-0.825076\pi$
$397$	2.92694	−	10.9235i	0.146899	−	0.548234i	0.999664	−	0.0259385i	$-0.00825740\pi$
$398$	−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	−0.939378	−	0.342883i	$-0.888597\pi$
$401$	−8.78262	+	10.4667i	−0.438583	+	0.522683i	0.500795	+	0.865566i	$0.333041\pi$
$402$		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	−0.987697	−	0.156378i	$-0.950018\pi$
$409$	−13.3918	+	15.9597i	−0.662183	+	0.789159i	0.325515	+	0.945537i	$0.394462\pi$
$410$	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	−0.172026	−	0.985092i	$-0.555031\pi$
$419$	6.74264	−	2.45412i	0.329399	−	0.119892i	0.501426	+	0.865201i	$0.332809\pi$
$420$		0			0
$421$	3.74087	+	21.2156i	0.182319	+	1.03398i	0.929352	+	0.369195i	$0.120367\pi$
$421$	3.74087	+	21.2156i	0.182319	+	1.03398i	−0.747033	+	0.664787i	$0.768522\pi$
$422$	−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	$-0.825070\pi$
$431$		−	21.6869i		−	1.04462i	0.852756	−	0.522310i	$-0.174930\pi$
$432$		0			0
$433$	9.64432	−	9.64432i	0.463476	−	0.463476i	−0.436317	−	0.899793i	$-0.643717\pi$
$433$	9.64432	−	9.64432i	0.463476	−	0.463476i	0.899793	+	0.436317i	$0.143717\pi$
$434$	−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	0.996970	+	0.0777820i	$0.0247838\pi$
$439$	18.8665	+	22.4842i	0.900449	+	1.07311i	−0.0965218	+	0.995331i	$0.530772\pi$
$440$	−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	−0.503440	−	0.864030i	$-0.667933\pi$
$443$	10.1169	−	14.4484i	0.480669	−	0.686466i	0.984109	+	0.177564i	$0.0568215\pi$
$444$		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	−0.937082	−	0.349110i	$-0.886484\pi$
$449$	−3.52178	+	6.09990i	−0.166203	+	0.287872i	0.770879	+	0.636982i	$0.219817\pi$
$450$		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	0.849756	−	0.527177i	$-0.176749\pi$
$457$	−2.14412	−	4.59808i	−0.100298	−	0.215089i	−0.950053	+	0.312088i	$0.898972\pi$
$458$	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	−0.922277	−	0.386530i	$-0.873674\pi$
$461$	0.701773	−	1.92811i	0.0326848	−	0.0898009i	0.954962	+	0.296729i	$0.0958958\pi$
$462$		0			0
$463$	13.8800	−	1.21434i	0.645058	−	0.0564353i	0.240068	−	0.970756i	$-0.422830\pi$
$463$	13.8800	−	1.21434i	0.645058	−	0.0564353i	0.404990	+	0.914321i	$0.367275\pi$
$464$	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	0.228072	−	0.973644i	$-0.426758\pi$
$467$	−1.32327	−	0.354570i	−0.0612338	−	0.0164076i	−0.289306	+	0.957237i	$0.593424\pi$
$468$		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	−0.756228	−	0.654308i	$-0.772960\pi$
$479$	−5.32223	+	4.46588i	−0.243179	+	0.204051i	0.513050	+	0.858359i	$0.328516\pi$
$480$		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	0.950369	−	0.311126i	$-0.100706\pi$
$487$	14.1069	+	14.1069i	0.639243	+	0.639243i	−0.311126	+	0.950369i	$0.600706\pi$
$488$	−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	0.986415	−	0.164271i	$-0.0525271\pi$
$491$	41.1519	+	7.25619i	1.85716	+	0.327467i	0.870743	+	0.491738i	$0.163638\pi$
$492$		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	0.891509	−	0.453004i	$-0.149648\pi$
$499$	−1.84540	−	5.07021i	−0.0826116	−	0.226974i	−0.974120	+	0.226030i	$0.927425\pi$
$500$	−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	−0.624305	−	0.781181i	$-0.714618\pi$
$503$	−17.3675	+	4.65361i	−0.774379	+	0.207494i	−0.150074	+	0.988675i	$0.547951\pi$
$504$		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	0.795758	−	0.605615i	$-0.207073\pi$
$509$	7.61493	+	6.38969i	0.337526	+	0.283218i	−0.458232	+	0.888833i	$0.651517\pi$
$510$		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	−0.973917	−	0.226907i	$-0.927139\pi$
$521$	−28.8597	+	16.6622i	−1.26437	+	0.729983i	−0.290451	+	0.956890i	$0.593805\pi$
$522$		0			0
$523$	0.128833	+	0.480813i	0.00563349	+	0.0210245i	0.968685	−	0.248291i	$-0.0798691\pi$
$523$	0.128833	+	0.480813i	0.00563349	+	0.0210245i	−0.963052	+	0.269316i	$0.913202\pi$
$524$	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	0.501863	−	0.864947i	$-0.332648\pi$
$547$	19.7841	+	1.73088i	0.845906	+	0.0740072i	0.344043	+	0.938954i	$0.388204\pi$
$548$	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	0.941429	−	0.337212i	$-0.109484\pi$
$557$	−1.00253	−	3.74149i	−0.0424786	−	0.158532i	−0.983907	+	0.178680i	$0.942817\pi$
$558$		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	0.797554	+	0.603247i	$0.206127\pi$
$563$	2.77303	+	31.6959i	0.116869	+	1.33582i	−0.680685	+	0.732576i	$0.738318\pi$
$564$		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	0.355099	−	0.934829i	$-0.384447\pi$
$569$	0.625558	+	0.227685i	0.0262248	+	0.00954503i	−0.328874	+	0.944374i	$0.606669\pi$
$570$		0			0
$571$	15.8737	+	13.3196i	0.664295	+	0.557410i	0.911371	−	0.411586i	$-0.135025\pi$
$571$	15.8737	+	13.3196i	0.664295	+	0.557410i	−0.247076	+	0.968996i	$0.579470\pi$
$572$	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	−0.144822	−	0.989458i	$-0.546261\pi$
$577$	5.39239	−	1.44489i	0.224488	−	0.0601514i	0.369310	+	0.929306i	$0.379594\pi$
$578$	−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	0.966655	+	0.256083i	$0.0824321\pi$
$587$	−0.721578	+	8.24768i	−0.0297827	+	0.340418i	−0.996437	+	0.0843348i	$0.973123\pi$
$588$		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	0.438425	−	0.898768i	$-0.355536\pi$
$593$	−11.2101	−	11.2101i	−0.460343	−	0.460343i	−0.898768	+	0.438425i	$0.855536\pi$
$594$		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	0.932560	+	0.361014i	$0.117569\pi$
$599$	−1.64551	+	9.33216i	−0.0672338	+	0.381302i	−0.999794	+	0.0202877i	$0.993542\pi$
$600$		0			0
$601$	−20.5855	+	17.2733i	−0.839699	+	0.704591i	−0.957496	−	0.288447i	$-0.906861\pi$
$601$	−20.5855	+	17.2733i	−0.839699	+	0.704591i	0.117797	+	0.993038i	$0.462417\pi$
$602$	−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	0.513169	−	0.858288i	$-0.328472\pi$
$607$	4.57123	+	2.13160i	0.185541	+	0.0865190i	−0.327628	+	0.944807i	$0.606249\pi$
$608$	−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	0.363137	−	0.931736i	$-0.381706\pi$
$613$	5.24282	+	1.40481i	0.211756	+	0.0567397i	−0.151382	+	0.988475i	$0.548372\pi$
$614$	−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	−0.617913	−	0.786247i	$-0.712021\pi$
$617$	−27.0727	+	2.36856i	−1.08991	+	0.0953545i	−0.471995	+	0.881601i	$0.656466\pi$
$618$		0			0
$619$	−3.84505	+	10.5642i	−0.154546	+	0.424611i	−0.992668	−	0.120871i	$-0.961431\pi$
$619$	−3.84505	+	10.5642i	−0.154546	+	0.424611i	0.838122	+	0.545482i	$0.183653\pi$
$620$	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	0.462548	+	0.886594i	$0.346935\pi$
$631$	−13.4777	+	23.3441i	−0.536539	+	0.929313i	−0.999087	+	0.0427187i	$0.986398\pi$
$632$	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	−0.956585	−	0.291454i	$-0.905861\pi$
$641$	−27.2802	−	32.5112i	−1.07750	−	1.28412i	−0.120917	−	0.992663i	$-0.538583\pi$
$642$		0			0
$643$	−1.60171	−	2.28747i	−0.0631651	−	0.0902091i	0.786327	−	0.617811i	$-0.211980\pi$
$643$	−1.60171	−	2.28747i	−0.0631651	−	0.0902091i	−0.849492	+	0.527602i	$0.823091\pi$
$644$	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	−0.637715	−	0.770273i	$-0.720120\pi$
$647$	3.37176	−	3.37176i	0.132558	−	0.132558i	0.770273	+	0.637715i	$0.220120\pi$
$648$		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	−0.741460	−	0.670997i	$-0.765866\pi$
$653$	−9.31500	+	6.52243i	−0.364524	+	0.255242i	0.376936	+	0.926239i	$0.376978\pi$
$654$		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	0.959268	−	0.282496i	$-0.0911625\pi$
$659$	−0.995226	−	5.64421i	−0.0387685	−	0.219867i	−0.998037	+	0.0626293i	$0.980051\pi$
$660$		0			0
$661$	−38.9403	+	14.1731i	−1.51460	+	0.551269i	−0.959793	−	0.280709i	$-0.909430\pi$
$661$	−38.9403	+	14.1731i	−1.51460	+	0.551269i	−0.554807	+	0.831979i	$0.687208\pi$
$662$	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	0.329907	−	0.944014i	$-0.392983\pi$
$673$	32.8201	−	15.3043i	1.26512	−	0.589936i	0.935216	+	0.354077i	$0.115205\pi$
$674$	−16.2889			−0.627425
$675$		0			0
$676$	9.26725			0.356433
$677$	−9.63788	+	4.49422i	−0.370414	+	0.172727i	−0.598907	−	0.800819i	$-0.704398\pi$
$677$	−9.63788	+	4.49422i	−0.370414	+	0.172727i	0.228493	+	0.973546i	$0.426620\pi$
$678$		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	−0.999967	−	0.00815378i	$-0.997405\pi$
$683$	−3.39467	+	12.6691i	−0.129893	+	0.484768i	0.870074	+	0.492922i	$0.164071\pi$
$684$		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	0.976891	+	0.213739i	$0.0685642\pi$
$691$	3.47031	+	19.6811i	0.132017	+	0.748704i	−0.844874	+	0.534965i	$0.820325\pi$
$692$	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	$0.124140\pi$
$701$			20.1319i			0.760373i	−0.924910	+	0.380186i	$0.875860\pi$
$702$		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	−0.993663	−	0.112400i	$-0.964146\pi$
$709$	−24.8113	−	29.5689i	−0.931808	−	1.11049i	0.0618554	−	0.998085i	$-0.480298\pi$
$710$	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	−0.243899	−	0.969801i	$-0.578427\pi$
$719$	19.2505	−	33.3428i	0.717922	−	1.24348i	0.961822	−	0.273677i	$-0.0882400\pi$
$720$		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	0.662875	−	0.748730i	$-0.269336\pi$
$727$	−9.08040	−	19.4730i	−0.336773	−	0.722213i	−0.999648	+	0.0265174i	$0.991558\pi$
$728$	−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	−0.587498	−	0.809225i	$-0.699887\pi$
$733$	−27.7657	+	2.42919i	−1.02555	+	0.0897240i	−0.438052	+	0.898950i	$0.644332\pi$
$734$	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	−0.410815	−	0.911719i	$-0.634756\pi$
$739$	−38.2159	−	22.0640i	−1.40579	−	0.811636i	−0.994979	+	0.100083i	$0.968089\pi$
$740$	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	0.778191	−	0.628028i	$-0.216138\pi$
$743$	21.7329	+	10.1342i	0.797305	+	0.371789i	0.0191139	+	0.999817i	$0.493915\pi$
$744$		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	−0.789061	−	0.614315i	$-0.789433\pi$
$751$	4.45381	−	25.2588i	0.162522	−	0.921707i	0.951583	−	0.307392i	$-0.0994564\pi$
$752$	−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	0.981772	−	0.190060i	$-0.0608684\pi$
$757$	21.7829	+	21.7829i	0.791712	+	0.791712i	−0.190060	+	0.981772i	$0.560868\pi$
$758$	−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	−0.147556	−	0.989054i	$-0.547141\pi$
$761$	−17.2273	−	3.03764i	−0.624490	−	0.110114i	−0.476934	+	0.878939i	$0.658252\pi$
$762$		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	0.821713	−	0.569901i	$-0.193018\pi$
$769$	−4.82741	−	13.2632i	−0.174081	−	0.478283i	−0.995794	+	0.0916178i	$0.970796\pi$
$770$	−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	0.358724	−	0.933444i	$-0.383212\pi$
$773$	31.5871	−	8.46375i	1.13611	−	0.304420i	0.777386	+	0.629024i	$0.216545\pi$
$774$		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	0.818821	+	0.574048i	$0.194628\pi$
$787$	3.14542	+	35.9523i	0.112122	+	1.28156i	−0.706699	+	0.707514i	$0.749817\pi$
$788$	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	0.532087	+	0.846690i	$0.321408\pi$
$797$	−12.9450	+	27.7606i	−0.458534	+	0.983330i	−0.990621	+	0.136640i	$0.956370\pi$
$798$		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	−0.224296	−	0.974521i	$-0.572008\pi$
$821$	−2.91570	+	0.514117i	−0.101759	+	0.0179428i	0.122537	+	0.992464i	$0.460897\pi$
$822$		0			0
$823$	−15.2677	+	32.7417i	−0.532200	+	1.14131i	0.437995	+	0.898977i	$0.355689\pi$
$823$	−15.2677	+	32.7417i	−0.532200	+	1.14131i	−0.970194	+	0.242328i	$0.922089\pi$
$824$	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	0.902725	−	0.430218i	$-0.141563\pi$
$827$	−2.70802	−	10.1065i	−0.0941670	−	0.351436i	−0.996892	+	0.0787823i	$0.974897\pi$
$828$		0			0
$829$	21.9321	−	12.6625i	0.761735	−	0.439788i	−0.0681835	−	0.997673i	$-0.521720\pi$
$829$	21.9321	−	12.6625i	0.761735	−	0.439788i	0.829918	+	0.557885i	$0.188387\pi$
$830$	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	−0.378216	−	0.925717i	$-0.623462\pi$
$839$	−36.5830	−	13.3151i	−1.26299	−	0.459689i	−0.884770	+	0.466028i	$0.845685\pi$
$840$		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	0.388568	−	0.921420i	$-0.372970\pi$
$853$	−10.0582	−	7.04282i	−0.344386	−	0.241142i	−0.732954	+	0.680279i	$0.761859\pi$
$854$	−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	0.562212	+	0.826993i	$0.309950\pi$
$857$	−3.95395	+	45.1939i	−0.135065	+	1.54379i	−0.697277	+	0.716802i	$0.745605\pi$
$858$		0			0
$859$	−26.3810	−	4.65169i	−0.900110	−	0.158714i	−0.295600	−	0.955312i	$-0.595520\pi$
$859$	−26.3810	−	4.65169i	−0.900110	−	0.158714i	−0.604509	+	0.796598i	$0.706631\pi$
$860$	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	0.439591	−	0.898198i	$-0.355124\pi$
$863$	−13.4724	−	13.4724i	−0.458608	−	0.458608i	−0.898198	+	0.439591i	$0.855124\pi$
$864$		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	0.916658	−	0.399671i	$-0.130876\pi$
$877$	35.5284	+	16.5672i	1.19971	+	0.559434i	0.283051	+	0.959105i	$0.408654\pi$
$878$	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	0.824707	−	0.565560i	$-0.191340\pi$
$881$	22.1803	+	12.8058i	0.747272	+	0.431438i	−0.0774355	+	0.996997i	$0.524673\pi$
$882$		0			0
$883$	2.67694	+	0.717285i	0.0900863	+	0.0241386i	0.303581	−	0.952806i	$-0.401818\pi$
$883$	2.67694	+	0.717285i	0.0900863	+	0.0241386i	−0.213494	+	0.976944i	$0.568484\pi$
$884$	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	0.744397	−	0.667737i	$-0.232737\pi$
$887$	47.4566	−	4.15191i	1.59344	−	0.139408i	0.849039	+	0.528330i	$0.177181\pi$
$888$		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	−0.448592	−	0.893737i	$-0.648074\pi$
$907$	16.4036	−	23.4268i	0.544673	−	0.777874i	0.993265	+	0.115863i	$0.0369632\pi$
$908$	−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	0.260642	−	0.965436i	$-0.416066\pi$
$911$	−22.1960	−	26.4522i	−0.735387	−	0.876400i	−0.996028	+	0.0890359i	$0.971621\pi$
$912$		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	$-0.739909\pi$
$919$		−	44.2093i		−	1.45833i	0.684338	−	0.729165i	$-0.260091\pi$
$920$	−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	−0.999168	−	0.0407775i	$-0.987017\pi$
$929$	−2.26170	−	12.8267i	−0.0742039	−	0.420831i	0.924964	−	0.380054i	$-0.124095\pi$
$930$		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	0.574803	+	0.818292i	$0.305079\pi$
$937$	−10.1669	+	37.9433i	−0.332137	+	1.23955i	−0.906940	+	0.421260i	$0.861588\pi$
$938$	−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	−0.155273	+	0.987872i	$0.549626\pi$
$941$	−33.7793	+	40.2566i	−1.10117	+	1.31233i	−0.945901	+	0.324456i	$0.894819\pi$
$942$		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	0.280342	−	0.959900i	$-0.409552\pi$
$947$	36.8009	−	17.1605i	1.19587	−	0.557643i	0.915527	+	0.402258i	$0.131774\pi$
$948$		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	−0.714888	−	0.699239i	$-0.753522\pi$
$953$	7.83630	−	29.2455i	0.253843	−	0.947354i	0.968731	−	0.248115i	$-0.0798111\pi$
$954$		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	−0.967242	−	0.253855i	$-0.918301\pi$
$967$	−32.9473	+	23.0699i	−1.05951	+	0.741879i	−0.0922710	+	0.995734i	$0.529413\pi$
$968$	−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	$0.148184\pi$
$971$			27.9762i			0.897800i	−0.893582	+	0.448900i	$0.851816\pi$
$972$		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	0.720885	−	0.693054i	$-0.243735\pi$
$977$	−5.53031	−	7.89810i	−0.176930	−	0.252682i	−0.897815	+	0.440372i	$0.854847\pi$
$978$		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	0.285417	+	0.958403i	$0.407868\pi$
$983$	−22.3485	+	31.9169i	−0.712806	+	1.01799i	−0.998223	+	0.0595888i	$0.981021\pi$
$984$		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	0.596269	−	0.802785i	$-0.296649\pi$
$991$	−12.5007	−	21.6518i	−0.397097	−	0.687793i	−0.993366	+	0.114992i	$0.963316\pi$
$992$	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	0.688179	−	0.725541i	$-0.258410\pi$
$997$	−9.78742	−	20.9892i	−0.309971	−	0.664735i	−0.998150	+	0.0608066i	$0.980633\pi$
$998$	−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.17.17		216
3.2	odd	2		270.2.r.a.77.7	yes	216
5.3	odd	4	inner	810.2.s.a.503.7		216
15.8	even	4		270.2.r.a.23.11	✓	216
27.7	even	9		270.2.r.a.47.11	yes	216
27.20	odd	18	inner	810.2.s.a.467.7		216
135.88	odd	36		270.2.r.a.263.7	yes	216
135.128	even	36	inner	810.2.s.a.143.17		216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
270.2.r.a.23.11	✓	216	15.8	even	4
270.2.r.a.47.11	yes	216	27.7	even	9
270.2.r.a.77.7	yes	216	3.2	odd	2
270.2.r.a.263.7	yes	216	135.88	odd	36
810.2.s.a.17.17		216	1.1	even	1	trivial
810.2.s.a.143.17		216	135.128	even	36	inner
810.2.s.a.467.7		216	27.20	odd	18	inner
810.2.s.a.503.7		216	5.3	odd	4	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

Varieties

Fields

Representations

Groups

Database

Properties

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