LMFDB - Embedded newform 864.2.bf.a.241.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [864,2,Mod(49,864)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("864.49"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(864, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 9, 14])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.bf (of order $18$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 216)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			241.6
Character	$\chi$	$=$	864.241
Dual form			864.2.bf.a.337.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.40283 - 1.01591i) q^{3} +(1.55785 + 1.85658i) q^{5} +(-0.763942 + 0.278052i) q^{7} +(0.935847 + 2.85030i) q^{9} +(-2.23007 + 2.65769i) q^{11} +(-2.83964 + 0.500705i) q^{13} +(-0.299281 - 4.18710i) q^{15} +(-3.55127 - 6.15099i) q^{17} +(-5.16371 - 2.98127i) q^{19} +(1.35415 + 0.386038i) q^{21} +(6.58997 + 2.39855i) q^{23} +(-0.151733 + 0.860521i) q^{25} +(1.58282 - 4.94921i) q^{27} +(-6.59552 - 1.16297i) q^{29} +(-2.55724 - 0.930757i) q^{31} +(5.82838 - 1.46273i) q^{33} +(-1.70634 - 0.985154i) q^{35} +(-3.59434 + 2.07519i) q^{37} +(4.49220 + 2.18242i) q^{39} +(-0.742124 - 4.20880i) q^{41} +(-1.77034 + 2.10981i) q^{43} +(-3.83389 + 6.17782i) q^{45} +(-2.80028 + 1.01922i) q^{47} +(-4.85602 + 4.07468i) q^{49} +(-1.26704 + 12.2365i) q^{51} +7.38929i q^{53} -8.40834 q^{55} +(4.21509 + 9.42808i) q^{57} +(-4.72368 - 5.62947i) q^{59} +(-0.0900385 - 0.247379i) q^{61} +(-1.50746 - 1.91725i) q^{63} +(-5.35335 - 4.49199i) q^{65} +(2.20513 - 0.388825i) q^{67} +(-6.80787 - 10.0596i) q^{69} +(-2.69918 - 4.67512i) q^{71} +(-1.97245 + 3.41639i) q^{73} +(1.08707 - 1.05302i) q^{75} +(0.964666 - 2.65040i) q^{77} +(-1.76846 + 10.0295i) q^{79} +(-7.24838 + 5.33489i) q^{81} +(7.86515 + 1.38684i) q^{83} +(5.88742 - 16.1756i) q^{85} +(8.07090 + 8.33191i) q^{87} +(2.14833 - 3.72101i) q^{89} +(2.03010 - 1.17208i) q^{91} +(2.64179 + 3.90362i) q^{93} +(-2.50935 - 14.2312i) q^{95} +(4.28345 + 3.59424i) q^{97} +(-9.66221 - 3.86916i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q + 12 q^{7} - 12 q^{9} + 12 q^{15} - 6 q^{17} + 12 q^{23} - 12 q^{25} + 12 q^{31} + 12 q^{39} - 24 q^{41} + 12 q^{47} - 12 q^{49} + 24 q^{55} - 30 q^{57} + 72 q^{63} - 12 q^{65} + 90 q^{71} - 6 q^{73}+ \cdots - 12 q^{97}+O(q^{100}) $ 204 * q + 12 * q^7 - 12 * q^9 + 12 * q^15 - 6 * q^17 + 12 * q^23 - 12 * q^25 + 12 * q^31 + 12 * q^39 - 24 * q^41 + 12 * q^47 - 12 * q^49 + 24 * q^55 - 30 * q^57 + 72 * q^63 - 12 * q^65 + 90 * q^71 - 6 * q^73 + 12 * q^79 - 12 * q^81 + 48 * q^87 - 6 * q^89 + 42 * q^95 - 12 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$-1$	$e\left(\frac{5}{9}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.40283	−	1.01591i	−0.809923	−	0.586537i
$3$	−1.40283	−	1.01591i	−0.809923	−	0.586537i
$4$		0			0
$5$	1.55785	+	1.85658i	0.696694	+	0.830287i	0.992148	−	0.125070i	$-0.0399154\pi$
$5$	1.55785	+	1.85658i	0.696694	+	0.830287i	−0.295454	+	0.955357i	$0.595471\pi$
$6$		0			0
$7$	−0.763942	+	0.278052i	−0.288743	+	0.105094i	−0.482331	−	0.875989i	$-0.660210\pi$
$7$	−0.763942	+	0.278052i	−0.288743	+	0.105094i	0.193588	+	0.981083i	$0.437988\pi$
$8$		0			0
$9$	0.935847	+	2.85030i	0.311949	+	0.950099i
$10$		0			0
$11$	−2.23007	+	2.65769i	−0.672391	+	0.801324i	−0.989107	−	0.147196i	$-0.952975\pi$
$11$	−2.23007	+	2.65769i	−0.672391	+	0.801324i	0.316716	+	0.948520i	$0.397420\pi$
$12$		0			0
$13$	−2.83964	+	0.500705i	−0.787574	+	0.138871i	−0.552949	−	0.833215i	$-0.686498\pi$
$13$	−2.83964	+	0.500705i	−0.787574	+	0.138871i	−0.234626	+	0.972086i	$0.575386\pi$
$14$		0			0
$15$	−0.299281	−	4.18710i	−0.0772740	−	1.08110i
$16$		0			0
$17$	−3.55127	−	6.15099i	−0.861310	−	1.49183i	−0.870665	−	0.491877i	$-0.836311\pi$
$17$	−3.55127	−	6.15099i	−0.861310	−	1.49183i	0.00935441	−	0.999956i	$-0.497022\pi$
$18$		0			0
$19$	−5.16371	−	2.98127i	−1.18464	−	0.683950i	−0.227554	−	0.973765i	$-0.573073\pi$
$19$	−5.16371	−	2.98127i	−1.18464	−	0.683950i	−0.957083	+	0.289815i	$0.906406\pi$
$20$		0			0
$21$	1.35415	+	0.386038i	0.295501	+	0.0842405i
$22$		0			0
$23$	6.58997	+	2.39855i	1.37410	+	0.500133i	0.920386	−	0.391012i	$-0.127875\pi$
$23$	6.58997	+	2.39855i	1.37410	+	0.500133i	0.453719	+	0.891145i	$0.350097\pi$
$24$		0			0
$25$	−0.151733	+	0.860521i	−0.0303466	+	0.172104i
$26$		0			0
$27$	1.58282	−	4.94921i	0.304613	−	0.952476i
$28$		0			0
$29$	−6.59552	−	1.16297i	−1.22476	−	0.215958i	−0.476385	−	0.879237i	$-0.658053\pi$
$29$	−6.59552	−	1.16297i	−1.22476	−	0.215958i	−0.748372	+	0.663279i	$0.769164\pi$
$30$		0			0
$31$	−2.55724	−	0.930757i	−0.459293	−	0.167169i	0.102003	−	0.994784i	$-0.467475\pi$
$31$	−2.55724	−	0.930757i	−0.459293	−	0.167169i	−0.561296	+	0.827615i	$0.689697\pi$
$32$		0			0
$33$	5.82838	−	1.46273i	1.01459	−	0.254629i
$34$		0			0
$35$	−1.70634	−	0.985154i	−0.288423	−	0.166521i
$36$		0			0
$37$	−3.59434	+	2.07519i	−0.590905	+	0.341159i	−0.765455	−	0.643489i	$-0.777486\pi$
$37$	−3.59434	+	2.07519i	−0.590905	+	0.341159i	0.174550	+	0.984648i	$0.444153\pi$
$38$		0			0
$39$	4.49220	+	2.18242i	0.719327	+	0.349467i
$40$		0			0
$41$	−0.742124	−	4.20880i	−0.115900	−	0.657304i	−0.986301	−	0.164959i	$-0.947251\pi$
$41$	−0.742124	−	4.20880i	−0.115900	−	0.657304i	0.870400	−	0.492345i	$-0.163860\pi$
$42$		0			0
$43$	−1.77034	+	2.10981i	−0.269975	+	0.321743i	−0.883950	−	0.467582i	$-0.845125\pi$
$43$	−1.77034	+	2.10981i	−0.269975	+	0.321743i	0.613975	+	0.789326i	$0.289570\pi$
$44$		0			0
$45$	−3.83389	+	6.17782i	−0.571522	+	0.920935i
$46$		0			0
$47$	−2.80028	+	1.01922i	−0.408463	+	0.148668i	−0.538076	−	0.842896i	$-0.680849\pi$
$47$	−2.80028	+	1.01922i	−0.408463	+	0.148668i	0.129613	+	0.991565i	$0.458626\pi$
$48$		0			0
$49$	−4.85602	+	4.07468i	−0.693717	+	0.582097i
$50$		0			0
$51$	−1.26704	+	12.2365i	−0.177420	+	1.71346i
$52$		0			0
$53$			7.38929i			1.01500i	0.861653	+	0.507498i	$0.169430\pi$
$53$			7.38929i			1.01500i	−0.861653	+	0.507498i	$0.830570\pi$
$54$		0			0
$55$	−8.40834			−1.13378
$56$		0			0
$57$	4.21509	+	9.42808i	0.558302	+	1.24878i
$58$		0			0
$59$	−4.72368	−	5.62947i	−0.614971	−	0.732894i	0.365226	−	0.930919i	$-0.380992\pi$
$59$	−4.72368	−	5.62947i	−0.614971	−	0.732894i	−0.980197	+	0.198025i	$0.936547\pi$
$60$		0			0
$61$	−0.0900385	−	0.247379i	−0.0115283	−	0.0316736i	0.933795	−	0.357808i	$-0.116476\pi$
$61$	−0.0900385	−	0.247379i	−0.0115283	−	0.0316736i	−0.945323	+	0.326135i	$0.894254\pi$
$62$		0			0
$63$	−1.50746	−	1.91725i	−0.189923	−	0.241550i
$64$		0			0
$65$	−5.35335	−	4.49199i	−0.664001	−	0.557163i
$66$		0			0
$67$	2.20513	−	0.388825i	0.269400	−	0.0475025i	−0.0373162	−	0.999304i	$-0.511881\pi$
$67$	2.20513	−	0.388825i	0.269400	−	0.0475025i	0.306716	+	0.951801i	$0.400770\pi$
$68$		0			0
$69$	−6.80787	−	10.0596i	−0.819572	−	1.21103i
$70$		0			0
$71$	−2.69918	−	4.67512i	−0.320334	−	0.554835i	0.660223	−	0.751070i	$-0.270462\pi$
$71$	−2.69918	−	4.67512i	−0.320334	−	0.554835i	−0.980557	+	0.196235i	$0.937129\pi$
$72$		0			0
$73$	−1.97245	+	3.41639i	−0.230858	+	0.399858i	−0.958061	−	0.286565i	$-0.907487\pi$
$73$	−1.97245	+	3.41639i	−0.230858	+	0.399858i	0.727203	+	0.686423i	$0.240820\pi$
$74$		0			0
$75$	1.08707	−	1.05302i	0.125524	−	0.121592i
$76$		0			0
$77$	0.964666	−	2.65040i	0.109934	−	0.302041i
$78$		0			0
$79$	−1.76846	+	10.0295i	−0.198968	+	1.12840i	0.707686	+	0.706527i	$0.249739\pi$
$79$	−1.76846	+	10.0295i	−0.198968	+	1.12840i	−0.906654	+	0.421875i	$0.861372\pi$
$80$		0			0
$81$	−7.24838	+	5.33489i	−0.805375	+	0.592765i
$82$		0			0
$83$	7.86515	+	1.38684i	0.863312	+	0.152225i	0.587735	−	0.809054i	$-0.300020\pi$
$83$	7.86515	+	1.38684i	0.863312	+	0.152225i	0.275577	+	0.961279i	$0.411131\pi$
$84$		0			0
$85$	5.88742	−	16.1756i	0.638581	−	1.75449i
$86$		0			0
$87$	8.07090	+	8.33191i	0.865292	+	0.893274i
$88$		0			0
$89$	2.14833	−	3.72101i	0.227722	−	0.394426i	−0.729410	−	0.684076i	$-0.760206\pi$
$89$	2.14833	−	3.72101i	0.227722	−	0.394426i	0.957133	+	0.289650i	$0.0935389\pi$
$90$		0			0
$91$	2.03010	−	1.17208i	0.212812	−	0.122867i
$92$		0			0
$93$	2.64179	+	3.90362i	0.273941	+	0.404786i
$94$		0			0
$95$	−2.50935	−	14.2312i	−0.257454	−	1.46009i
$96$		0			0
$97$	4.28345	+	3.59424i	0.434918	+	0.364940i	0.833804	−	0.552061i	$-0.186159\pi$
$97$	4.28345	+	3.59424i	0.434918	+	0.364940i	−0.398886	+	0.917001i	$0.630603\pi$
$98$		0			0
$99$	−9.66221	−	3.86916i	−0.971089	−	0.388865i
$100$		0			0
$101$	−5.64914	−	15.5209i	−0.562110	−	1.54438i	−0.816537	−	0.577293i	$-0.804109\pi$
$101$	−5.64914	−	15.5209i	−0.562110	−	1.54438i	0.254427	−	0.967092i	$-0.418113\pi$
$102$		0			0
$103$	−14.0312	+	11.7736i	−1.38254	+	1.16009i	−0.414278	+	0.910151i	$0.635966\pi$
$103$	−14.0312	+	11.7736i	−1.38254	+	1.16009i	−0.968262	+	0.249938i	$0.919590\pi$
$104$		0			0
$105$	1.39287	+	3.11549i	0.135930	+	0.304040i
$106$		0			0
$107$			17.0660i			1.64983i	0.565254	+	0.824917i	$0.308778\pi$
$107$			17.0660i			1.64983i	−0.565254	+	0.824917i	$0.691222\pi$
$108$		0			0
$109$			18.3759i			1.76009i	0.474890	+	0.880045i	$0.342488\pi$
$109$			18.3759i			1.76009i	−0.474890	+	0.880045i	$0.657512\pi$
$110$		0			0
$111$	7.15044	+	0.740394i	0.678690	+	0.0702751i
$112$		0			0
$113$	6.55711	−	5.50207i	0.616841	−	0.517591i	−0.279968	−	0.960009i	$-0.590324\pi$
$113$	6.55711	−	5.50207i	0.616841	−	0.517591i	0.896809	+	0.442418i	$0.145879\pi$
$114$		0			0
$115$	5.81311	+	15.9714i	0.542076	+	1.48934i
$116$		0			0
$117$	−4.08463	−	7.62523i	−0.377624	−	0.704953i
$118$		0			0
$119$	4.42326	+	3.71156i	0.405480	+	0.340238i
$120$		0			0
$121$	−0.179992	−	1.02079i	−0.0163629	−	0.0927987i
$122$		0			0
$123$	−3.23469	+	6.65815i	−0.291662	+	0.600345i
$124$		0			0
$125$	8.66046	−	5.00012i	0.774615	−	0.447224i
$126$		0			0
$127$	2.28240	−	3.95324i	0.202530	−	0.350793i	−0.746813	−	0.665034i	$-0.768417\pi$
$127$	2.28240	−	3.95324i	0.202530	−	0.350793i	0.949343	+	0.314242i	$0.101750\pi$
$128$		0			0
$129$	4.62687	−	1.16119i	0.407373	−	0.102237i
$130$		0			0
$131$	4.55139	−	12.5048i	0.397657	−	1.09255i	−0.565766	−	0.824566i	$-0.691419\pi$
$131$	4.55139	−	12.5048i	0.397657	−	1.09255i	0.963422	−	0.267987i	$-0.0863585\pi$
$132$		0			0
$133$	4.77372	+	0.841736i	0.413934	+	0.0729878i
$134$		0			0
$135$	11.6544	−	4.77153i	1.00305	−	0.410668i
$136$		0			0
$137$	−0.374428	+	2.12348i	−0.0319895	+	0.181422i	−0.996616	−	0.0821992i	$-0.973806\pi$
$137$	−0.374428	+	2.12348i	−0.0319895	+	0.181422i	0.964626	+	0.263621i	$0.0849167\pi$
$138$		0			0
$139$	−0.200125	+	0.549839i	−0.0169744	+	0.0466367i	−0.947890	−	0.318596i	$-0.896789\pi$
$139$	−0.200125	+	0.549839i	−0.0169744	+	0.0466367i	0.930916	+	0.365233i	$0.119011\pi$
$140$		0			0
$141$	4.96375	+	1.41505i	0.418023	+	0.119169i
$142$		0			0
$143$	5.00187	−	8.66350i	0.418278	−	0.724478i
$144$		0			0
$145$	−8.11572	−	14.0568i	−0.673974	−	1.16736i
$146$		0			0
$147$	10.9517	−	0.782791i	0.903278	−	0.0645635i
$148$		0			0
$149$	21.5708	−	3.80351i	1.76715	−	0.311596i	0.806888	−	0.590705i	$-0.201150\pi$
$149$	21.5708	−	3.80351i	1.76715	−	0.311596i	0.960259	+	0.279109i	$0.0900390\pi$
$150$		0			0
$151$	−5.91767	−	4.96552i	−0.481573	−	0.404088i	0.369422	−	0.929262i	$-0.379556\pi$
$151$	−5.91767	−	4.96552i	−0.481573	−	0.404088i	−0.850995	+	0.525174i	$0.824000\pi$
$152$		0			0
$153$	14.2087	−	15.8786i	1.14870	−	1.28371i
$154$		0			0
$155$	−2.25578	−	6.19769i	−0.181188	−	0.497811i
$156$		0			0
$157$	0.882254	+	1.05143i	0.0704116	+	0.0839132i	0.800100	−	0.599866i	$-0.204780\pi$
$157$	0.882254	+	1.05143i	0.0704116	+	0.0839132i	−0.729689	+	0.683779i	$0.760335\pi$
$158$		0			0
$159$	7.50686	−	10.3659i	0.595333	−	0.822068i
$160$		0			0
$161$	−5.70128			−0.449324
$162$		0			0
$163$		−	13.5989i		−	1.06515i	−0.846383	−	0.532574i	$-0.821225\pi$
$163$		−	13.5989i		−	1.06515i	0.846383	−	0.532574i	$-0.178775\pi$
$164$		0			0
$165$	11.7954	+	8.54213i	0.918274	+	0.665004i
$166$		0			0
$167$	−3.38292	+	2.83861i	−0.261778	+	0.219658i	−0.764224	−	0.644950i	$-0.776878\pi$
$167$	−3.38292	+	2.83861i	−0.261778	+	0.219658i	0.502446	+	0.864609i	$0.332434\pi$
$168$		0			0
$169$	−4.40315	+	1.60262i	−0.338704	+	0.123278i
$170$		0			0
$171$	3.66506	−	17.5081i	0.280274	−	1.33888i
$172$		0			0
$173$	−12.4793	+	14.8722i	−0.948781	+	1.13071i	0.0425201	+	0.999096i	$0.486461\pi$
$173$	−12.4793	+	14.8722i	−0.948781	+	1.13071i	−0.991301	+	0.131617i	$0.957983\pi$
$174$		0			0
$175$	−0.123355	−	0.699578i	−0.00932472	−	0.0528831i
$176$		0			0
$177$	0.907471	+	12.6960i	0.0682097	+	0.954291i
$178$		0			0
$179$	4.00038	−	2.30962i	0.299002	−	0.172629i	−0.342992	−	0.939338i	$-0.611441\pi$
$179$	4.00038	−	2.30962i	0.299002	−	0.172629i	0.641995	+	0.766709i	$0.278107\pi$
$180$		0			0
$181$	−5.55052	−	3.20459i	−0.412567	−	0.238195i	0.279325	−	0.960197i	$-0.409889\pi$
$181$	−5.55052	−	3.20459i	−0.412567	−	0.238195i	−0.691892	+	0.722001i	$0.743223\pi$
$182$		0			0
$183$	−0.125007	+	0.438501i	−0.00924075	+	0.0324149i
$184$		0			0
$185$	−9.45221	−	3.44032i	−0.694940	−	0.252938i
$186$		0			0
$187$	24.2670	+	4.27893i	1.77458	+	0.312906i
$188$		0			0
$189$	0.166959	+	4.22102i	0.0121444	+	0.307034i
$190$		0			0
$191$	3.51460	−	19.9323i	0.254307	−	1.44225i	−0.543537	−	0.839385i	$-0.682915\pi$
$191$	3.51460	−	19.9323i	0.254307	−	1.44225i	0.797844	−	0.602864i	$-0.205974\pi$
$192$		0			0
$193$	5.28857	+	1.92488i	0.380680	+	0.138556i	0.525270	−	0.850935i	$-0.323964\pi$
$193$	5.28857	+	1.92488i	0.380680	+	0.138556i	−0.144590	+	0.989492i	$0.546186\pi$
$194$		0			0
$195$	2.94635	+	11.7400i	0.210993	+	0.840720i
$196$		0			0
$197$	−3.79439	−	2.19069i	−0.270339	−	0.156080i	0.358703	−	0.933452i	$-0.383219\pi$
$197$	−3.79439	−	2.19069i	−0.270339	−	0.156080i	−0.629042	+	0.777371i	$0.716553\pi$
$198$		0			0
$199$	6.64564	+	11.5106i	0.471097	+	0.815963i	0.999453	−	0.0330592i	$-0.0105250\pi$
$199$	6.64564	+	11.5106i	0.471097	+	0.815963i	−0.528357	+	0.849022i	$0.677192\pi$
$200$		0			0
$201$	−3.48843	−	1.69477i	−0.246055	−	0.119540i
$202$		0			0
$203$	5.36196	−	0.945458i	0.376336	−	0.0663582i
$204$		0			0
$205$	6.65784	−	7.93450i	0.465004	−	0.554170i
$206$		0			0
$207$	−0.669380	+	21.0281i	−0.0465251	+	1.46155i
$208$		0			0
$209$	19.4387	−	7.07512i	1.34460	−	0.489396i
$210$		0			0
$211$	−16.0858	−	19.1703i	−1.10739	−	1.31974i	−0.942794	−	0.333376i	$-0.891812\pi$
$211$	−16.0858	−	19.1703i	−1.10739	−	1.31974i	−0.164597	−	0.986361i	$-0.552632\pi$
$212$		0			0
$213$	−0.963024	+	9.30052i	−0.0659853	+	0.637261i
$214$		0			0
$215$	−6.67497			−0.455229
$216$		0			0
$217$	2.21238			0.150186
$218$		0			0
$219$	6.23776	−	2.78877i	0.421509	−	0.188447i
$220$		0			0
$221$	13.1642	+	15.6884i	0.885518	+	1.05532i
$222$		0			0
$223$	−1.52221	+	0.554040i	−0.101935	+	0.0371013i	−0.392484	−	0.919759i	$-0.628384\pi$
$223$	−1.52221	+	0.554040i	−0.101935	+	0.0371013i	0.290549	+	0.956860i	$0.406162\pi$
$224$		0			0
$225$	−2.59474	+	0.372832i	−0.172983	+	0.0248555i
$226$		0			0
$227$	4.47903	−	5.33790i	0.297284	−	0.354289i	−0.596639	−	0.802510i	$-0.703498\pi$
$227$	4.47903	−	5.33790i	0.297284	−	0.354289i	0.893923	+	0.448221i	$0.147942\pi$
$228$		0			0
$229$	24.7618	−	4.36618i	1.63631	−	0.288525i	0.721500	−	0.692415i	$-0.243453\pi$
$229$	24.7618	−	4.36618i	1.63631	−	0.288525i	0.914808	+	0.403890i	$0.132342\pi$
$230$		0			0
$231$	−4.04583	+	2.73803i	−0.266196	+	0.180149i
$232$		0			0
$233$	7.86096	+	13.6156i	0.514989	+	0.891987i	0.999849	+	0.0173948i	$0.00553722\pi$
$233$	7.86096	+	13.6156i	0.514989	+	0.891987i	−0.484860	+	0.874592i	$0.661129\pi$
$234$		0			0
$235$	−6.25469	−	3.61115i	−0.408011	−	0.235565i
$236$		0			0
$237$	12.6699	−	12.2730i	0.822998	−	0.797216i
$238$		0			0
$239$	−14.6050	−	5.31579i	−0.944720	−	0.343850i	−0.176692	−	0.984266i	$-0.556540\pi$
$239$	−14.6050	−	5.31579i	−0.944720	−	0.343850i	−0.768028	+	0.640416i	$0.778762\pi$
$240$		0			0
$241$	−2.19088	+	12.4251i	−0.141127	+	0.800370i	0.829269	+	0.558850i	$0.188757\pi$
$241$	−2.19088	+	12.4251i	−0.141127	+	0.800370i	−0.970396	+	0.241520i	$0.922354\pi$
$242$		0			0
$243$	15.5880	−	0.120210i	0.999970	−	0.00771147i
$244$		0			0
$245$	−15.1299	−	2.66782i	−0.966616	−	0.170441i
$246$		0			0
$247$	16.1558	+	5.88024i	1.02797	+	0.374151i
$248$		0			0
$249$	−9.62454	−	9.93579i	−0.609930	−	0.629655i
$250$		0			0
$251$	4.86765	+	2.81034i	0.307244	+	0.177387i	0.645692	−	0.763598i	$-0.276569\pi$
$251$	4.86765	+	2.81034i	0.307244	+	0.177387i	−0.338449	+	0.940985i	$0.609902\pi$
$252$		0			0
$253$	−21.0707	+	12.1652i	−1.32470	+	0.764818i
$254$		0			0
$255$	−24.6920	+	16.7104i	−1.54627	+	1.04645i
$256$		0			0
$257$	3.35726	+	19.0399i	0.209420	+	1.18768i	0.890331	+	0.455313i	$0.150473\pi$
$257$	3.35726	+	19.0399i	0.209420	+	1.18768i	−0.680911	+	0.732366i	$0.738416\pi$
$258$		0			0
$259$	2.16885	−	2.58474i	0.134766	−	0.160608i
$260$		0			0
$261$	−2.85760	−	19.8876i	−0.176881	−	1.23101i
$262$		0			0
$263$	−10.8424	+	3.94631i	−0.668571	+	0.243340i	−0.653932	−	0.756553i	$-0.726882\pi$
$263$	−10.8424	+	3.94631i	−0.668571	+	0.243340i	−0.0146383	+	0.999893i	$0.504660\pi$
$264$		0			0
$265$	−13.7188	+	11.5114i	−0.842739	+	0.707142i
$266$		0			0
$267$	−6.79395	+	3.03742i	−0.415783	+	0.185887i
$268$		0			0
$269$			13.3630i			0.814758i	0.913259	+	0.407379i	$0.133557\pi$
$269$			13.3630i			0.814758i	−0.913259	+	0.407379i	$0.866443\pi$
$270$		0			0
$271$	−3.26667			−0.198436			−0.0992182	−	0.995066i	$-0.531634\pi$
$271$	−3.26667			−0.198436			−0.0992182	+	0.995066i	$0.531634\pi$
$272$		0			0
$273$	−4.03860	−	0.418178i	−0.244427	−	0.0253093i
$274$		0			0
$275$	−1.94863	−	2.32228i	−0.117507	−	0.140039i
$276$		0			0
$277$	−0.102104	−	0.280528i	−0.00613482	−	0.0168553i	0.936587	−	0.350434i	$-0.113966\pi$
$277$	−0.102104	−	0.280528i	−0.00613482	−	0.0168553i	−0.942722	+	0.333579i	$0.891744\pi$
$278$		0			0
$279$	0.259753	−	8.15992i	0.0155510	−	0.488522i
$280$		0			0
$281$	−13.3262	−	11.1820i	−0.794976	−	0.667064i	0.151996	−	0.988381i	$-0.451430\pi$
$281$	−13.3262	−	11.1820i	−0.794976	−	0.667064i	−0.946972	+	0.321317i	$0.895874\pi$
$282$		0			0
$283$	−1.31422	+	0.231732i	−0.0781220	+	0.0137750i	−0.212573	−	0.977145i	$-0.568184\pi$
$283$	−1.31422	+	0.231732i	−0.0781220	+	0.0137750i	0.134451	+	0.990920i	$0.457073\pi$
$284$		0			0
$285$	−10.9375	+	22.5132i	−0.647880	+	1.33357i
$286$		0			0
$287$	1.73720	+	3.00893i	0.102544	+	0.177611i
$288$		0			0
$289$	−16.7231	+	28.9652i	−0.983711	+	1.70384i
$290$		0			0
$291$	−2.35751	−	9.39370i	−0.138199	−	0.550668i
$292$		0			0
$293$	2.77744	−	7.63095i	0.162260	−	0.445805i	−0.831743	−	0.555161i	$-0.812657\pi$
$293$	2.77744	−	7.63095i	0.162260	−	0.445805i	0.994003	+	0.109356i	$0.0348789\pi$
$294$		0			0
$295$	3.09274	−	17.5398i	0.180066	−	1.02121i
$296$		0			0
$297$	9.62369	+	15.2437i	0.558423	+	0.884530i
$298$		0			0
$299$	−19.9141	−	3.51140i	−1.15166	−	0.203069i
$300$		0			0
$301$	0.765801	−	2.10402i	0.0441400	−	0.121274i
$302$		0			0
$303$	−7.84307	+	27.5121i	−0.450573	+	1.58053i
$304$		0			0
$305$	0.319011	−	0.552544i	0.0182665	−	0.0316386i
$306$		0			0
$307$	−22.1985	+	12.8163i	−1.26693	+	0.731464i	−0.974406	−	0.224793i	$-0.927829\pi$
$307$	−22.1985	+	12.8163i	−1.26693	+	0.731464i	−0.292527	+	0.956257i	$0.594496\pi$
$308$		0			0
$309$	31.6444	−	2.26184i	1.80018	−	0.128671i
$310$		0			0
$311$	3.08781	+	17.5119i	0.175094	+	0.993007i	0.938035	+	0.346539i	$0.112643\pi$
$311$	3.08781	+	17.5119i	0.175094	+	0.993007i	−0.762942	+	0.646467i	$0.776246\pi$
$312$		0			0
$313$	−25.2201	−	21.1622i	−1.42553	−	1.19616i	−0.948299	−	0.317377i	$-0.897198\pi$
$313$	−25.2201	−	21.1622i	−1.42553	−	1.19616i	−0.477226	−	0.878781i	$-0.658358\pi$
$314$		0			0
$315$	1.21111	−	5.78552i	0.0682383	−	0.325977i
$316$		0			0
$317$	2.41535	+	6.63611i	0.135659	+	0.372721i	0.988857	−	0.148866i	$-0.0475624\pi$
$317$	2.41535	+	6.63611i	0.135659	+	0.372721i	−0.853198	+	0.521587i	$0.825340\pi$
$318$		0			0
$319$	17.7993	−	14.9354i	0.996568	−	0.836220i
$320$		0			0
$321$	17.3376	−	23.9407i	0.967688	−	1.33624i
$322$		0			0
$323$			42.3492i			2.35637i
$324$		0			0
$325$		−	2.51954i		−	0.139759i
$326$		0			0
$327$	18.6683	−	25.7782i	1.03236	−	1.42554i
$328$		0			0
$329$	1.85586	−	1.55725i	0.102317	−	0.0858539i
$330$		0			0
$331$	4.15163	+	11.4065i	0.228194	+	0.626958i	0.999960	−	0.00894876i	$-0.00284852\pi$
$331$	4.15163	+	11.4065i	0.228194	+	0.626958i	−0.771766	+	0.635907i	$0.780626\pi$
$332$		0			0
$333$	−9.27866	−	8.30286i	−0.508468	−	0.454994i
$334$		0			0
$335$	4.15716	+	3.48827i	0.227130	+	0.190585i
$336$		0			0
$337$	−4.48506	−	25.4361i	−0.244317	−	1.38559i	−0.822074	−	0.569381i	$-0.807183\pi$
$337$	−4.48506	−	25.4361i	−0.244317	−	1.38559i	0.577757	−	0.816209i	$-0.303928\pi$
$338$		0			0
$339$	−14.7881	+	1.05701i	−0.803180	+	0.0574088i
$340$		0			0
$341$	8.17648	−	4.72069i	0.442781	−	0.255640i
$342$		0			0
$343$	5.42214	−	9.39142i	0.292768	−	0.507089i
$344$		0			0
$345$	8.07074	−	28.3107i	0.434514	−	1.52420i
$346$		0			0
$347$	4.43311	−	12.1799i	0.237982	−	0.653849i	−0.761999	−	0.647578i	$-0.775782\pi$
$347$	4.43311	−	12.1799i	0.237982	−	0.653849i	0.999980	−	0.00627055i	$-0.00199599\pi$
$348$		0			0
$349$	−1.00479	−	0.177171i	−0.0537849	−	0.00948374i	0.146691	−	0.989182i	$-0.453138\pi$
$349$	−1.00479	−	0.177171i	−0.0537849	−	0.00948374i	−0.200476	+	0.979699i	$0.564249\pi$
$350$		0			0
$351$	−2.01653	+	14.8465i	−0.107635	+	0.792448i
$352$		0			0
$353$	−2.87234	+	16.2899i	−0.152879	+	0.867022i	0.807820	+	0.589430i	$0.200648\pi$
$353$	−2.87234	+	16.2899i	−0.152879	+	0.867022i	−0.960699	+	0.277592i	$0.910464\pi$
$354$		0			0
$355$	4.47480	−	12.2944i	0.237498	−	0.652520i
$356$		0			0
$357$	−2.43446	−	9.70032i	−0.128845	−	0.513395i
$358$		0			0
$359$	−9.03871	+	15.6555i	−0.477045	+	0.826266i	−0.999654	−	0.0263063i	$-0.991625\pi$
$359$	−9.03871	+	15.6555i	−0.477045	+	0.826266i	0.522609	+	0.852573i	$0.324959\pi$
$360$		0			0
$361$	8.27594	+	14.3343i	0.435576	+	0.754439i
$362$		0			0
$363$	−0.784531	+	1.61484i	−0.0411772	+	0.0847573i
$364$		0			0
$365$	−9.41559	+	1.66022i	−0.492835	+	0.0869000i
$366$		0			0
$367$	15.6345	+	13.1189i	0.816112	+	0.684799i	0.952058	−	0.305917i	$-0.0989630\pi$
$367$	15.6345	+	13.1189i	0.816112	+	0.684799i	−0.135946	+	0.990716i	$0.543407\pi$
$368$		0			0
$369$	11.3018	−	6.05407i	0.588348	−	0.315162i
$370$		0			0
$371$	−2.05461	−	5.64499i	−0.106670	−	0.293073i
$372$		0			0
$373$	−18.6443	−	22.2194i	−0.965366	−	1.15048i	−0.988572	−	0.150748i	$-0.951832\pi$
$373$	−18.6443	−	22.2194i	−0.965366	−	1.15048i	0.0232061	−	0.999731i	$-0.492613\pi$
$374$		0			0
$375$	−17.2288	−	1.78396i	−0.889691	−	0.0921232i
$376$		0			0
$377$	19.3112			0.994578
$378$		0			0
$379$			18.7878i			0.965062i	0.875879	+	0.482531i	$0.160282\pi$
$379$			18.7878i			0.965062i	−0.875879	+	0.482531i	$0.839718\pi$
$380$		0			0
$381$	−7.21795	+	3.22699i	−0.369787	+	0.165324i
$382$		0			0
$383$	11.4097	−	9.57391i	0.583010	−	0.489204i	−0.302924	−	0.953015i	$-0.597963\pi$
$383$	11.4097	−	9.57391i	0.583010	−	0.489204i	0.885934	+	0.463811i	$0.153518\pi$
$384$		0			0
$385$	6.42348	−	2.33796i	0.327371	−	0.119153i
$386$		0			0
$387$	−7.67036	−	3.07154i	−0.389906	−	0.156135i
$388$		0			0
$389$	11.3184	−	13.4888i	0.573866	−	0.683907i	−0.398553	−	0.917145i	$-0.630488\pi$
$389$	11.3184	−	13.4888i	0.573866	−	0.683907i	0.972420	+	0.233238i	$0.0749321\pi$
$390$		0			0
$391$	−8.64932	−	49.0527i	−0.437415	−	2.48070i
$392$		0			0
$393$	−19.0886	+	12.9183i	−0.962894	+	0.651643i
$394$		0			0
$395$	−21.3755	+	12.3411i	−1.07552	+	0.620950i
$396$		0			0
$397$	−13.1290	−	7.58002i	−0.658924	−	0.380430i	0.132943	−	0.991124i	$-0.457557\pi$
$397$	−13.1290	−	7.58002i	−0.658924	−	0.380430i	−0.791867	+	0.610694i	$0.790891\pi$
$398$		0			0
$399$	−5.84158	−	6.03049i	−0.292445	−	0.301902i
$400$		0			0
$401$	0.563391	+	0.205057i	0.0281344	+	0.0102401i	0.356049	−	0.934467i	$-0.384124\pi$
$401$	0.563391	+	0.205057i	0.0281344	+	0.0102401i	−0.327915	+	0.944707i	$0.606346\pi$
$402$		0			0
$403$	7.72766	+	1.36260i	0.384942	+	0.0678757i
$404$		0			0
$405$	−21.1966	−	5.14621i	−1.05327	−	0.255717i
$406$		0			0
$407$	2.50040	−	14.1805i	0.123940	−	0.702899i
$408$		0			0
$409$	26.7235	+	9.72655i	1.32139	+	0.480947i	0.903904	−	0.427736i	$-0.140689\pi$
$409$	26.7235	+	9.72655i	1.32139	+	0.480947i	0.417487	+	0.908683i	$0.362911\pi$
$410$		0			0
$411$	2.68253	−	2.59850i	0.132319	−	0.128174i
$412$		0			0
$413$	5.17391	+	2.98716i	0.254591	+	0.146988i
$414$		0			0
$415$	9.67799	+	16.7628i	0.475074	+	0.822852i
$416$		0			0
$417$	0.839329	−	0.568020i	0.0411021	−	0.0278160i
$418$		0			0
$419$	27.5479	−	4.85743i	1.34580	−	0.237301i	0.546110	−	0.837713i	$-0.316108\pi$
$419$	27.5479	−	4.85743i	1.34580	−	0.237301i	0.799691	+	0.600412i	$0.204997\pi$
$420$		0			0
$421$	−21.0378	+	25.0719i	−1.02532	+	1.22193i	−0.0505502	+	0.998722i	$0.516097\pi$
$421$	−21.0378	+	25.0719i	−1.02532	+	1.22193i	−0.974771	+	0.223208i	$0.928347\pi$
$422$		0			0
$423$	−5.52571	−	7.02780i	−0.268669	−	0.341703i
$424$		0			0
$425$	5.83190	−	2.12264i	0.282889	−	0.102963i
$426$		0			0
$427$	0.137568	+	0.163948i	0.00665740	+	0.00793398i
$428$		0			0
$429$	−15.8181	+	7.07193i	−0.763705	+	0.341436i
$430$		0			0
$431$	9.98011			0.480725			0.240363	−	0.970683i	$-0.422734\pi$
$431$	9.98011			0.480725			0.240363	+	0.970683i	$0.422734\pi$
$432$		0			0
$433$	17.4899			0.840513			0.420257	−	0.907405i	$-0.361940\pi$
$433$	17.4899			0.840513			0.420257	+	0.907405i	$0.361940\pi$
$434$		0			0
$435$	−2.89555	+	27.9642i	−0.138831	+	1.34078i
$436$		0			0
$437$	−26.8780	−	32.0319i	−1.28575	−	1.53229i
$438$		0			0
$439$	−7.21777	+	2.62705i	−0.344485	+	0.125382i	−0.508468	−	0.861081i	$-0.669788\pi$
$439$	−7.21777	+	2.62705i	−0.344485	+	0.125382i	0.163983	+	0.986463i	$0.447566\pi$
$440$		0			0
$441$	−16.1585	−	10.0278i	−0.769454	−	0.477515i
$442$		0			0
$443$	3.13735	−	3.73895i	0.149060	−	0.177643i	−0.686348	−	0.727274i	$-0.740787\pi$
$443$	3.13735	−	3.73895i	0.149060	−	0.177643i	0.835408	+	0.549631i	$0.185232\pi$
$444$		0			0
$445$	10.2551	−	1.80826i	0.486140	−	0.0857196i
$446$		0			0
$447$	−34.1241	−	16.5783i	−1.61401	−	0.784129i
$448$		0			0
$449$	−2.49179	−	4.31590i	−0.117595	−	0.203680i	0.801219	−	0.598371i	$-0.204185\pi$
$449$	−2.49179	−	4.31590i	−0.117595	−	0.203680i	−0.918814	+	0.394691i	$0.870852\pi$
$450$		0			0
$451$	12.8407	+	7.41357i	0.604644	+	0.349091i
$452$		0			0
$453$	3.25694	+	12.9776i	0.153025	+	0.609740i
$454$		0			0
$455$	5.33865	+	1.94311i	0.250280	+	0.0910944i
$456$		0			0
$457$	3.50014	−	19.8503i	0.163729	−	0.928556i	−0.786635	−	0.617418i	$-0.788179\pi$
$457$	3.50014	−	19.8503i	0.163729	−	0.928556i	0.950365	−	0.311138i	$-0.100710\pi$
$458$		0			0
$459$	−36.0635	+	7.84012i	−1.68330	+	0.365945i
$460$		0			0
$461$	−33.4428	−	5.89687i	−1.55759	−	0.274645i	−0.672510	−	0.740088i	$-0.734784\pi$
$461$	−33.4428	−	5.89687i	−1.55759	−	0.274645i	−0.885077	+	0.465444i	$0.845895\pi$
$462$		0			0
$463$	35.9891	+	13.0990i	1.67256	+	0.608760i	0.992260	−	0.124178i	$-0.0396294\pi$
$463$	35.9891	+	13.0990i	1.67256	+	0.608760i	0.680295	+	0.732938i	$0.261852\pi$
$464$		0			0
$465$	−3.13184	+	10.9860i	−0.145236	+	0.509462i
$466$		0			0
$467$	−9.53283	−	5.50378i	−0.441127	−	0.254685i	0.262949	−	0.964810i	$-0.415305\pi$
$467$	−9.53283	−	5.50378i	−0.441127	−	0.254685i	−0.704075	+	0.710125i	$0.748638\pi$
$468$		0			0
$469$	−1.57648	+	0.910182i	−0.0727951	+	0.0420283i
$470$		0			0
$471$	−0.169491	−	2.37127i	−0.00780971	−	0.109262i
$472$		0			0
$473$	−1.65925	−	9.41005i	−0.0762922	−	0.432675i
$474$		0			0
$475$	3.34895	−	3.99113i	0.153660	−	0.183125i
$476$		0			0
$477$	−21.0617	+	6.91524i	−0.964347	+	0.316627i
$478$		0			0
$479$	−21.5794	+	7.85427i	−0.985989	+	0.358871i	−0.784166	−	0.620551i	$-0.786909\pi$
$479$	−21.5794	+	7.85427i	−0.985989	+	0.358871i	−0.201823	+	0.979422i	$0.564687\pi$
$480$		0			0
$481$	9.16757	−	7.69250i	0.418005	−	0.350748i
$482$		0			0
$483$	7.99791	+	5.79200i	0.363917	+	0.263545i
$484$		0			0
$485$			13.5519i			0.615358i
$486$		0			0
$487$	−8.81274			−0.399343			−0.199672	−	0.979863i	$-0.563988\pi$
$487$	−8.81274			−0.399343			−0.199672	+	0.979863i	$0.563988\pi$
$488$		0			0
$489$	−13.8153	+	19.0769i	−0.624749	+	0.862688i
$490$		0			0
$491$	7.55920	+	9.00870i	0.341142	+	0.406557i	0.909152	−	0.416465i	$-0.136731\pi$
$491$	7.55920	+	9.00870i	0.341142	+	0.406557i	−0.568010	+	0.823022i	$0.692287\pi$
$492$		0			0
$493$	16.2691	+	44.6990i	0.732723	+	2.01314i
$494$		0			0
$495$	−7.86892	−	23.9663i	−0.353682	−	1.07720i
$496$		0			0
$497$	3.36195	+	2.82101i	0.150804	+	0.126540i
$498$		0			0
$499$	−17.3768	+	3.06399i	−0.777891	+	0.137163i	−0.548477	−	0.836166i	$-0.684792\pi$
$499$	−17.3768	+	3.06399i	−0.777891	+	0.137163i	−0.229414	+	0.973329i	$0.573681\pi$
$500$		0			0
$501$	7.62943	−	0.545327i	0.340858	−	0.0243634i
$502$		0			0
$503$	10.0037	+	17.3268i	0.446041	+	0.772565i	0.998124	−	0.0612236i	$-0.0195003\pi$
$503$	10.0037	+	17.3268i	0.446041	+	0.772565i	−0.552083	+	0.833789i	$0.686167\pi$
$504$		0			0
$505$	20.0152	−	34.6673i	0.890664	−	1.54268i
$506$		0			0
$507$	7.80498	+	2.22502i	0.346631	+	0.0988166i
$508$		0			0
$509$	3.57485	−	9.82182i	0.158452	−	0.435345i	−0.834908	−	0.550390i	$-0.814479\pi$
$509$	3.57485	−	9.82182i	0.158452	−	0.435345i	0.993360	+	0.115045i	$0.0367013\pi$
$510$		0			0
$511$	0.556906	−	3.15837i	0.0246361	−	0.139718i
$512$		0			0
$513$	−22.9281	+	20.8375i	−1.01230	+	0.919998i
$514$		0			0
$515$	−43.7173	−	7.70853i	−1.92641	−	0.339679i
$516$		0			0
$517$	3.53605	−	9.71521i	0.155515	−	0.427274i
$518$		0			0
$519$	32.6151	−	8.18530i	1.43164	−	0.359295i
$520$		0			0
$521$	−10.0111	+	17.3397i	−0.438593	+	0.759665i	−0.997581	−	0.0695105i	$-0.977856\pi$
$521$	−10.0111	+	17.3397i	−0.438593	+	0.759665i	0.558988	+	0.829175i	$0.311190\pi$
$522$		0			0
$523$	−17.8863	+	10.3267i	−0.782114	+	0.451554i	−0.837179	−	0.546929i	$-0.815797\pi$
$523$	−17.8863	+	10.3267i	−0.782114	+	0.451554i	0.0550649	+	0.998483i	$0.482463\pi$
$524$		0			0
$525$	−0.537664	+	1.10670i	−0.0234656	+	0.0483005i
$526$		0			0
$527$	3.35636	+	19.0349i	0.146206	+	0.829173i
$528$		0			0
$529$	20.0556	+	16.8287i	0.871985	+	0.731682i
$530$		0			0
$531$	11.6250	−	18.7322i	0.504482	−	0.812909i
$532$		0			0
$533$	4.21473	+	11.5799i	0.182560	+	0.501580i
$534$		0			0
$535$	−31.6844	+	26.5864i	−1.36984	+	1.14943i
$536$		0			0
$537$	−7.95820	−	0.824033i	−0.343422	−	0.0355597i
$538$		0			0
$539$		−	21.9926i		−	0.947289i
$540$		0			0
$541$		−	31.7185i		−	1.36368i	−0.731499	−	0.681842i	$-0.761179\pi$
$541$		−	31.7185i		−	1.36368i	0.731499	−	0.681842i	$-0.238821\pi$
$542$		0			0
$543$	4.53083	+	10.1343i	0.194437	+	0.434905i
$544$		0			0
$545$	−34.1163	+	28.6270i	−1.46138	+	1.22624i
$546$		0			0
$547$	−2.69951	−	7.41685i	−0.115423	−	0.317122i	0.868507	−	0.495677i	$-0.165080\pi$
$547$	−2.69951	−	7.41685i	−0.115423	−	0.317122i	−0.983930	+	0.178555i	$0.942858\pi$
$548$		0			0
$549$	0.620841	−	0.488145i	0.0264968	−	0.0208335i
$550$		0			0
$551$	30.5902	+	25.6683i	1.30319	+	1.09350i
$552$		0			0
$553$	−1.43771	−	8.15365i	−0.0611376	−	0.346728i
$554$		0			0
$555$	9.76475	+	14.4288i	0.414491	+	0.612468i
$556$		0			0
$557$	−11.9380	+	6.89241i	−0.505829	+	0.292041i	−0.731118	−	0.682251i	$-0.761001\pi$
$557$	−11.9380	+	6.89241i	−0.505829	+	0.292041i	0.225288	+	0.974292i	$0.427668\pi$
$558$		0			0
$559$	3.97074	−	6.87753i	0.167944	−	0.290888i
$560$		0			0
$561$	−29.6954	−	30.6557i	−1.25374	−	1.29429i
$562$		0			0
$563$	4.49431	−	12.3480i	0.189413	−	0.520407i	−0.808242	−	0.588850i	$-0.799581\pi$
$563$	4.49431	−	12.3480i	0.189413	−	0.520407i	0.997655	+	0.0684431i	$0.0218032\pi$
$564$		0			0
$565$	20.4301	+	3.60237i	0.859499	+	0.151553i
$566$		0			0
$567$	4.05396	−	6.09097i	0.170251	−	0.255797i
$568$		0			0
$569$	−6.12718	+	34.7490i	−0.256865	+	1.45675i	0.534376	+	0.845247i	$0.320547\pi$
$569$	−6.12718	+	34.7490i	−0.256865	+	1.45675i	−0.791241	+	0.611505i	$0.790564\pi$
$570$		0			0
$571$	13.0508	−	35.8568i	0.546159	−	1.50056i	−0.292697	−	0.956205i	$-0.594553\pi$
$571$	13.0508	−	35.8568i	0.546159	−	1.50056i	0.838856	−	0.544354i	$-0.183225\pi$
$572$		0			0
$573$	−25.1798	+	24.3910i	−1.05190	+	1.01895i
$574$		0			0
$575$	−3.06392	+	5.30687i	−0.127774	+	0.221312i
$576$		0			0
$577$	−13.9536	−	24.1683i	−0.580895	−	1.00614i	−0.995374	−	0.0960807i	$-0.969369\pi$
$577$	−13.9536	−	24.1683i	−0.580895	−	1.00614i	0.414478	−	0.910059i	$-0.363964\pi$
$578$		0			0
$579$	−5.46344	−	8.07300i	−0.227053	−	0.335503i
$580$		0			0
$581$	−6.39413	+	1.12746i	−0.265273	+	0.0467748i
$582$		0			0
$583$	−19.6384	−	16.4786i	−0.813341	−	0.682474i
$584$		0			0
$585$	7.79359	−	19.4624i	0.322225	−	0.804673i
$586$		0			0
$587$	−3.04495	−	8.36592i	−0.125678	−	0.345299i	0.860857	−	0.508847i	$-0.169928\pi$
$587$	−3.04495	−	8.36592i	−0.125678	−	0.345299i	−0.986535	+	0.163549i	$0.947706\pi$
$588$		0			0
$589$	10.4300	+	12.4300i	0.429760	+	0.512168i
$590$		0			0
$591$	3.09733	+	6.92793i	0.127407	+	0.284977i
$592$		0			0
$593$	−13.6477			−0.560446			−0.280223	−	0.959935i	$-0.590408\pi$
$593$	−13.6477			−0.560446			−0.280223	+	0.959935i	$0.590408\pi$
$594$		0			0
$595$			13.9942i			0.573706i
$596$		0			0
$597$	2.37105	−	22.8987i	0.0970407	−	0.937183i
$598$		0			0
$599$	−23.2233	+	19.4867i	−0.948878	+	0.796203i	−0.979108	−	0.203340i	$-0.934820\pi$
$599$	−23.2233	+	19.4867i	−0.948878	+	0.796203i	0.0302302	+	0.999543i	$0.490376\pi$
$600$		0			0
$601$	2.85426	−	1.03887i	0.116428	−	0.0423762i	−0.283149	−	0.959076i	$-0.591379\pi$
$601$	2.85426	−	1.03887i	0.116428	−	0.0423762i	0.399577	+	0.916700i	$0.369157\pi$
$602$		0			0
$603$	3.17193	+	5.92141i	0.129171	+	0.241138i
$604$		0			0
$605$	1.61477	−	1.92441i	0.0656497	−	0.0782382i
$606$		0			0
$607$	4.34423	+	24.6374i	0.176327	+	0.999999i	0.936601	+	0.350397i	$0.113953\pi$
$607$	4.34423	+	24.6374i	0.176327	+	0.999999i	−0.760274	+	0.649602i	$0.774935\pi$
$608$		0			0
$609$	−8.48241	−	4.12096i	−0.343724	−	0.166990i
$610$		0			0
$611$	7.44146	−	4.29633i	0.301049	−	0.173811i
$612$		0			0
$613$	11.1629	+	6.44490i	0.450865	+	0.260307i	0.708195	−	0.706017i	$-0.249510\pi$
$613$	11.1629	+	6.44490i	0.450865	+	0.260307i	−0.257331	+	0.966323i	$0.582843\pi$
$614$		0			0
$615$	−17.4006	+	4.36696i	−0.701658	+	0.176093i
$616$		0			0
$617$	23.2620	+	8.46669i	0.936495	+	0.340856i	0.764781	−	0.644291i	$-0.222847\pi$
$617$	23.2620	+	8.46669i	0.936495	+	0.340856i	0.171714	+	0.985147i	$0.445070\pi$
$618$		0			0
$619$	−7.07392	−	1.24732i	−0.284325	−	0.0501341i	0.0296670	−	0.999560i	$-0.490555\pi$
$619$	−7.07392	−	1.24732i	−0.284325	−	0.0501341i	−0.313992	+	0.949426i	$0.601666\pi$
$620$		0			0
$621$	22.3017	−	28.8187i	0.894935	−	1.15645i
$622$		0			0
$623$	−0.606562	+	3.43998i	−0.0243014	+	0.137820i
$624$		0			0
$625$	26.8803	+	9.78364i	1.07521	+	0.391346i
$626$		0			0
$627$	−34.4569	−	9.82286i	−1.37607	−	0.392287i
$628$		0			0
$629$	25.5289	+	14.7391i	1.01791	+	0.587688i
$630$		0			0
$631$	−19.7806	−	34.2610i	−0.787453	−	1.36391i	−0.927523	−	0.373767i	$-0.878066\pi$
$631$	−19.7806	−	34.2610i	−0.787453	−	1.36391i	0.140070	−	0.990142i	$-0.455267\pi$
$632$		0			0
$633$	3.09025	+	43.2343i	0.122827	+	1.71841i
$634$		0			0
$635$	10.8951	−	1.92111i	0.432361	−	0.0762368i
$636$		0			0
$637$	11.7491	−	14.0021i	0.465517	−	0.554782i
$638$		0			0
$639$	10.7995	−	12.0687i	0.427220	−	0.477430i
$640$		0			0
$641$	20.4795	−	7.45392i	0.808891	−	0.294412i	0.0957255	−	0.995408i	$-0.469483\pi$
$641$	20.4795	−	7.45392i	0.808891	−	0.294412i	0.713166	+	0.700995i	$0.247261\pi$
$642$		0			0
$643$	24.0829	+	28.7008i	0.949735	+	1.13185i	0.991155	+	0.132709i	$0.0423675\pi$
$643$	24.0829	+	28.7008i	0.949735	+	1.13185i	−0.0414197	+	0.999142i	$0.513188\pi$
$644$		0			0
$645$	9.36383	+	6.78118i	0.368700	+	0.267009i
$646$		0			0
$647$	13.9531			0.548554			0.274277	−	0.961651i	$-0.411561\pi$
$647$	13.9531			0.548554			0.274277	+	0.961651i	$0.411561\pi$
$648$		0			0
$649$	25.4955			1.00079
$650$		0			0
$651$	−3.10358	−	2.24758i	−0.121639	−	0.0880896i
$652$		0			0
$653$	16.3129	+	19.4409i	0.638372	+	0.760782i	0.984112	−	0.177548i	$-0.0568166\pi$
$653$	16.3129	+	19.4409i	0.638372	+	0.760782i	−0.345740	+	0.938330i	$0.612372\pi$
$654$		0			0
$655$	30.3066	−	11.0307i	1.18418	−	0.431006i
$656$		0			0
$657$	−11.5836	−	2.42486i	−0.451921	−	0.0946027i
$658$		0			0
$659$	−23.0007	+	27.4112i	−0.895981	+	1.06779i	0.101355	+	0.994850i	$0.467682\pi$
$659$	−23.0007	+	27.4112i	−0.895981	+	1.06779i	−0.997336	+	0.0729384i	$0.976762\pi$
$660$		0			0
$661$	−29.1329	+	5.13692i	−1.13314	+	0.199803i	−0.708603	−	0.705608i	$-0.750674\pi$
$661$	−29.1329	+	5.13692i	−1.13314	+	0.199803i	−0.424536	+	0.905411i	$0.639563\pi$
$662$		0			0
$663$	−2.52898	−	35.3818i	−0.0982174	−	1.37412i
$664$		0			0
$665$	5.87402	+	10.1741i	0.227785	+	0.394535i
$666$		0			0
$667$	−40.6749	−	23.4836i	−1.57494	−	0.909290i
$668$		0			0
$669$	2.69826	+	0.769211i	0.104321	+	0.0297394i
$670$		0			0
$671$	0.858249	+	0.312377i	0.0331323	+	0.0120592i
$672$		0			0
$673$	3.21781	−	18.2491i	0.124038	−	0.703452i	−0.857837	−	0.513922i	$-0.828192\pi$
$673$	3.21781	−	18.2491i	0.124038	−	0.703452i	0.981875	−	0.189531i	$-0.0606967\pi$
$674$		0			0
$675$	4.01874	+	2.11301i	0.154681	+	0.0813297i
$676$		0			0
$677$	31.1495	+	5.49250i	1.19717	+	0.211094i	0.736477	−	0.676463i	$-0.236488\pi$
$677$	31.1495	+	5.49250i	1.19717	+	0.211094i	0.460698	+	0.887557i	$0.347599\pi$
$678$		0			0
$679$	−4.27169	−	1.55477i	−0.163932	−	0.0596665i
$680$		0			0
$681$	−11.7061	+	2.93785i	−0.448580	+	0.112579i
$682$		0			0
$683$	29.5187	+	17.0426i	1.12950	+	0.652117i	0.943809	−	0.330491i	$-0.107214\pi$
$683$	29.5187	+	17.0426i	1.12950	+	0.652117i	0.185691	+	0.982608i	$0.440548\pi$
$684$		0			0
$685$	−4.52572	+	2.61293i	−0.172919	+	0.0998348i
$686$		0			0
$687$	−39.1722	−	19.0308i	−1.49451	−	0.726072i
$688$		0			0
$689$	−3.69985	−	20.9829i	−0.140953	−	0.799385i
$690$		0			0
$691$	5.27112	−	6.28188i	0.200523	−	0.238974i	−0.656407	−	0.754407i	$-0.727925\pi$
$691$	5.27112	−	6.28188i	0.200523	−	0.238974i	0.856930	+	0.515433i	$0.172369\pi$
$692$		0			0
$693$	8.45720	+	0.269216i	0.321262	+	0.0102267i
$694$		0			0
$695$	−1.33259	+	0.485021i	−0.0505478	+	0.0183979i
$696$		0			0
$697$	−23.2528	+	19.5114i	−0.880761	+	0.739046i
$698$		0			0
$699$	2.80466	−	27.0864i	0.106082	−	1.02450i
$700$		0			0
$701$		−	1.97965i		−	0.0747704i	−0.999301	−	0.0373852i	$-0.988097\pi$
$701$		−	1.97965i		−	0.0747704i	0.999301	−	0.0373852i	$-0.0119029\pi$
$702$		0			0
$703$	24.7468			0.933344
$704$		0			0
$705$	5.10564	+	11.4200i	0.192290	+	0.430103i
$706$		0			0
$707$	8.63122	+	10.2863i	0.324611	+	0.386856i
$708$		0			0
$709$	−5.97488	−	16.4158i	−0.224391	−	0.616510i	0.775499	−	0.631349i	$-0.217499\pi$
$709$	−5.97488	−	16.4158i	−0.224391	−	0.616510i	−0.999890	+	0.0148394i	$0.995276\pi$
$710$		0			0
$711$	−30.2419	+	4.34540i	−1.13416	+	0.162965i
$712$		0			0
$713$	−14.6196	−	12.2673i	−0.547510	−	0.459415i
$714$		0			0
$715$	23.8767	−	4.21010i	0.892936	−	0.157449i
$716$		0			0
$717$	15.0879	+	22.2945i	0.563470	+	0.832605i
$718$		0			0
$719$	−17.2073	−	29.8038i	−0.641722	−	1.11150i	−0.985048	−	0.172279i	$-0.944887\pi$
$719$	−17.2073	−	29.8038i	−0.641722	−	1.11150i	0.343326	−	0.939216i	$-0.388446\pi$
$720$		0			0
$721$	7.44538	−	12.8958i	0.277280	−	0.480264i
$722$		0			0
$723$	15.6962	−	15.2045i	0.583748	−	0.565462i
$724$		0			0
$725$	2.00152	−	5.49913i	0.0743345	−	0.204232i
$726$		0			0
$727$	−4.21802	+	23.9216i	−0.156438	+	0.887203i	0.801022	+	0.598635i	$0.204290\pi$
$727$	−4.21802	+	23.9216i	−0.156438	+	0.887203i	−0.957460	+	0.288567i	$0.906821\pi$
$728$		0			0
$729$	−21.9894	−	15.6674i	−0.814422	−	0.580274i
$730$		0			0
$731$	19.2644	+	3.39683i	0.712519	+	0.125636i
$732$		0			0
$733$	−7.76866	+	21.3442i	−0.286942	+	0.788366i	0.709548	+	0.704657i	$0.248899\pi$
$733$	−7.76866	+	21.3442i	−0.286942	+	0.788366i	−0.996490	+	0.0837095i	$0.973323\pi$
$734$		0			0
$735$	18.5144	+	19.1132i	0.682915	+	0.705000i
$736$		0			0
$737$	−3.88422	+	6.72767i	−0.143077	+	0.247817i
$738$		0			0
$739$	0.214406	−	0.123787i	0.00788706	−	0.00455360i	−0.496051	−	0.868293i	$-0.665217\pi$
$739$	0.214406	−	0.123787i	0.00788706	−	0.00455360i	0.503938	+	0.863740i	$0.331884\pi$
$740$		0			0
$741$	−16.6900	−	24.6618i	−0.613123	−	0.905975i
$742$		0			0
$743$	−0.843956	−	4.78631i	−0.0309618	−	0.175593i	0.965406	−	0.260753i	$-0.0839709\pi$
$743$	−0.843956	−	4.78631i	−0.0309618	−	0.175593i	−0.996367	+	0.0851603i	$0.972860\pi$
$744$		0			0
$745$	40.6657	+	34.1225i	1.48987	+	1.25015i
$746$		0			0
$747$	3.40768	+	23.7159i	0.124681	+	0.867719i
$748$		0			0
$749$	−4.74524	−	13.0374i	−0.173387	−	0.476378i
$750$		0			0
$751$	−23.6852	+	19.8743i	−0.864287	+	0.725223i	−0.962887	−	0.269905i	$-0.913008\pi$
$751$	−23.6852	+	19.8743i	−0.864287	+	0.725223i	0.0986005	+	0.995127i	$0.468563\pi$
$752$		0			0
$753$	−3.97342	−	8.88753i	−0.144799	−	0.323879i
$754$		0			0
$755$		−	18.7222i		−	0.681370i
$756$		0			0
$757$			15.9221i			0.578697i	0.957224	+	0.289349i	$0.0934387\pi$
$757$			15.9221i			0.578697i	−0.957224	+	0.289349i	$0.906561\pi$
$758$		0			0
$759$	41.9173	+	4.34033i	1.52150	+	0.157544i
$760$		0			0
$761$	12.1040	−	10.1564i	0.438768	−	0.368170i	−0.396480	−	0.918043i	$-0.629768\pi$
$761$	12.1040	−	10.1564i	0.438768	−	0.368170i	0.835248	+	0.549873i	$0.185324\pi$
$762$		0			0
$763$	−5.10946	−	14.0381i	−0.184975	−	0.508214i
$764$		0			0
$765$	51.6149	+	1.64304i	1.86614	+	0.0594043i
$766$		0			0
$767$	16.2323	+	13.6205i	0.586113	+	0.491807i
$768$		0			0
$769$	−7.98567	−	45.2890i	−0.287970	−	1.63316i	−0.694478	−	0.719514i	$-0.744365\pi$
$769$	−7.98567	−	45.2890i	−0.287970	−	1.63316i	0.406507	−	0.913648i	$-0.366747\pi$
$770$		0			0
$771$	14.6332	−	30.1204i	0.527004	−	1.08476i
$772$		0			0
$773$	−35.6666	+	20.5921i	−1.28284	+	0.740647i	−0.977366	−	0.211554i	$-0.932147\pi$
$773$	−35.6666	+	20.5921i	−1.28284	+	0.740647i	−0.305472	+	0.952201i	$0.598814\pi$
$774$		0			0
$775$	1.18895	−	2.05933i	0.0427085	−	0.0739733i
$776$		0			0
$777$	−5.66839	+	1.42258i	−0.203352	+	0.0510347i
$778$		0			0
$779$	−8.71544	+	23.9455i	−0.312263	+	0.857936i
$780$		0			0
$781$	18.4444	+	3.25225i	0.659993	+	0.116375i
$782$		0			0
$783$	−16.1953	+	30.8019i	−0.578772	+	1.10077i
$784$		0			0
$785$	−0.577638	+	3.27595i	−0.0206168	+	0.116924i
$786$		0			0
$787$	6.23669	−	17.1352i	0.222314	−	0.610803i	−0.777523	−	0.628854i	$-0.783524\pi$
$787$	6.23669	−	17.1352i	0.222314	−	0.610803i	0.999837	+	0.0180518i	$0.00574638\pi$
$788$		0			0
$789$	19.2191	+	5.47892i	0.684218	+	0.195055i
$790$		0			0
$791$	−3.47939	+	6.02648i	−0.123713	+	0.214277i
$792$		0			0
$793$	0.379541	+	0.657384i	0.0134779	+	0.0233444i
$794$		0			0
$795$	30.9397	−	2.21147i	1.09732	−	0.0784328i
$796$		0			0
$797$	40.7976	−	7.19372i	1.44512	−	0.254814i	0.604575	−	0.796548i	$-0.293343\pi$
$797$	40.7976	−	7.19372i	1.44512	−	0.254814i	0.840550	+	0.541734i	$0.182232\pi$
$798$		0			0
$799$	16.2138	+	13.6050i	0.573602	+	0.481309i
$800$		0			0
$801$	12.6165	+	2.64107i	0.445782	+	0.0933176i
$802$		0			0
$803$	−4.68101	−	12.8610i	−0.165189	−	0.453853i
$804$		0			0
$805$	−8.88176	−	10.5849i	−0.313041	−	0.373068i
$806$		0			0
$807$	13.5757	−	18.7460i	0.477886	−	0.659891i
$808$		0			0
$809$	−19.2719			−0.677564			−0.338782	−	0.940865i	$-0.610015\pi$
$809$	−19.2719			−0.677564			−0.338782	+	0.940865i	$0.610015\pi$
$810$		0			0
$811$			15.7750i			0.553935i	0.960879	+	0.276968i	$0.0893295\pi$
$811$			15.7750i			0.553935i	−0.960879	+	0.276968i	$0.910671\pi$
$812$		0			0
$813$	4.58258	+	3.31865i	0.160718	+	0.116390i
$814$		0			0
$815$	25.2474	−	21.1851i	0.884380	−	0.742083i
$816$		0			0
$817$	15.4315	−	5.61659i	0.539878	−	0.196500i
$818$		0			0
$819$	5.24063	+	4.68950i	0.183122	+	0.163864i
$820$		0			0
$821$	6.66717	−	7.94562i	0.232686	−	0.277304i	−0.637049	−	0.770823i	$-0.719845\pi$
$821$	6.66717	−	7.94562i	0.232686	−	0.277304i	0.869735	+	0.493519i	$0.164290\pi$
$822$		0			0
$823$	−9.20557	−	52.2074i	−0.320886	−	1.81983i	−0.537135	−	0.843496i	$-0.680493\pi$
$823$	−9.20557	−	52.2074i	−0.320886	−	1.81983i	0.216249	−	0.976338i	$-0.430618\pi$
$824$		0			0
$825$	0.374352	+	5.23739i	0.0130333	+	0.182343i
$826$		0			0
$827$	23.9359	−	13.8194i	0.832332	−	0.480547i	−0.0223184	−	0.999751i	$-0.507105\pi$
$827$	23.9359	−	13.8194i	0.832332	−	0.480547i	0.854650	+	0.519204i	$0.173771\pi$
$828$		0			0
$829$	−34.2649	−	19.7829i	−1.19007	−	0.687088i	−0.231748	−	0.972776i	$-0.574445\pi$
$829$	−34.2649	−	19.7829i	−1.19007	−	0.687088i	−0.958323	+	0.285688i	$0.907778\pi$
$830$		0			0
$831$	−0.141757	+	0.497260i	−0.00491751	+	0.0172498i
$832$		0			0
$833$	42.3084	+	15.3990i	1.46590	+	0.533543i
$834$		0			0
$835$	−10.5402	−	1.85852i	−0.364759	−	0.0643168i
$836$		0			0
$837$	−8.65415	+	11.1831i	−0.299131	+	0.386544i
$838$		0			0
$839$	−4.95699	+	28.1125i	−0.171134	+	0.970551i	0.771378	+	0.636378i	$0.219568\pi$
$839$	−4.95699	+	28.1125i	−0.171134	+	0.970551i	−0.942512	+	0.334173i	$0.891543\pi$
$840$		0			0
$841$	14.8973	+	5.42218i	0.513700	+	0.186972i
$842$		0			0
$843$	7.33444	+	29.2247i	0.252611	+	1.00655i
$844$		0			0
$845$	−9.83486	−	5.67816i	−0.338329	−	0.195335i
$846$		0			0
$847$	0.421335	+	0.729774i	0.0144773	+	0.0250753i
$848$		0			0
$849$	2.07904	+	1.01005i	0.0713524	+	0.0346647i
$850$		0			0
$851$	−28.6640	+	5.05424i	−0.982591	+	0.173257i
$852$		0			0
$853$	4.41611	−	5.26292i	0.151205	−	0.180199i	−0.685125	−	0.728425i	$-0.740252\pi$
$853$	4.41611	−	5.26292i	0.151205	−	0.180199i	0.836330	+	0.548227i	$0.184697\pi$
$854$		0			0
$855$	38.2148	−	20.4706i	1.30692	−	0.700081i
$856$		0			0
$857$	−26.6254	+	9.69084i	−0.909505	+	0.331033i	−0.754055	−	0.656811i	$-0.771905\pi$
$857$	−26.6254	+	9.69084i	−0.909505	+	0.331033i	−0.155450	+	0.987844i	$0.549683\pi$
$858$		0			0
$859$	−14.7282	−	17.5524i	−0.502520	−	0.598879i	0.453836	−	0.891085i	$-0.350055\pi$
$859$	−14.7282	−	17.5524i	−0.502520	−	0.598879i	−0.956355	+	0.292206i	$0.905611\pi$
$860$		0			0
$861$	0.619806	−	5.98585i	0.0211229	−	0.203997i
$862$		0			0
$863$	−24.0297			−0.817980			−0.408990	−	0.912539i	$-0.634119\pi$
$863$	−24.0297			−0.817980			−0.408990	+	0.912539i	$0.634119\pi$
$864$		0			0
$865$	−47.0523			−1.59983
$866$		0			0
$867$	52.8857	−	23.6440i	1.79609	−	0.802994i
$868$		0			0
$869$	−22.7114	−	27.0664i	−0.770432	−	0.918165i
$870$		0			0
$871$	−6.06710	+	2.20824i	−0.205576	+	0.0748235i
$872$		0			0
$873$	−6.23599	+	15.5727i	−0.211056	+	0.527058i
$874$		0			0
$875$	−5.22579	+	6.22786i	−0.176664	+	0.210540i
$876$		0			0
$877$	−0.500115	+	0.0881838i	−0.0168877	+	0.00297776i	−0.182086	−	0.983283i	$-0.558285\pi$
$877$	−0.500115	+	0.0881838i	−0.0168877	+	0.00297776i	0.165198	+	0.986260i	$0.447174\pi$
$878$		0			0
$879$	−11.6486	+	7.88327i	−0.392899	+	0.265896i
$880$		0			0
$881$	−11.2219	−	19.4369i	−0.378076	−	0.654847i	0.612706	−	0.790311i	$-0.290081\pi$
$881$	−11.2219	−	19.4369i	−0.378076	−	0.654847i	−0.990782	+	0.135464i	$0.956747\pi$
$882$		0			0
$883$	45.9402	+	26.5236i	1.54601	+	0.892589i	0.998440	+	0.0558294i	$0.0177803\pi$
$883$	45.9402	+	26.5236i	1.54601	+	0.892589i	0.547570	+	0.836760i	$0.315553\pi$
$884$		0			0
$885$	−22.1574	+	21.4633i	−0.744814	+	0.721482i
$886$		0			0
$887$	26.2975	+	9.57151i	0.882984	+	0.321380i	0.743413	−	0.668832i	$-0.233206\pi$
$887$	26.2975	+	9.57151i	0.882984	+	0.321380i	0.139571	+	0.990212i	$0.455428\pi$
$888$		0			0
$889$	−0.644417	+	3.65467i	−0.0216130	+	0.122574i
$890$		0			0
$891$	1.98590	−	31.1611i	0.0665301	−	1.04394i
$892$		0			0
$893$	17.4984	+	3.08544i	0.585562	+	0.103250i
$894$		0			0
$895$	10.5200	+	3.82896i	0.351644	+	0.127988i
$896$		0			0
$897$	24.3688	+	25.1569i	0.813650	+	0.839963i
$898$		0			0
$899$	15.7839	+	9.11281i	0.526421	+	0.303929i
$900$		0			0
$901$	45.4514	−	26.2414i	1.51421	−	0.874227i
$902$		0			0
$903$	−3.21179	+	2.17359i	−0.106882	+	0.0723326i
$904$		0			0
$905$	−2.69732	−	15.2973i	−0.0896620	−	0.508498i
$906$		0			0
$907$	−17.3874	+	20.7215i	−0.577338	+	0.688045i	−0.973120	−	0.230300i	$-0.926029\pi$
$907$	−17.3874	+	20.7215i	−0.577338	+	0.688045i	0.395781	+	0.918345i	$0.370474\pi$
$908$		0			0
$909$	38.9524	−	30.6269i	1.29197	−	1.01583i
$910$		0			0
$911$	−9.03367	+	3.28799i	−0.299299	+	0.108936i	−0.487305	−	0.873232i	$-0.662020\pi$
$911$	−9.03367	+	3.28799i	−0.299299	+	0.108936i	0.188006	+	0.982168i	$0.439798\pi$
$912$		0			0
$913$	−21.2256	+	17.8104i	−0.702465	+	0.589438i
$914$		0			0
$915$	−1.00885	+	0.451036i	−0.0333517	+	0.0149108i
$916$		0			0
$917$			10.8185i			0.357258i
$918$		0			0
$919$	−0.257674			−0.00849989			−0.00424994	−	0.999991i	$-0.501353\pi$
$919$	−0.257674			−0.00849989			−0.00424994	+	0.999991i	$0.501353\pi$
$920$		0			0
$921$	44.1608	+	4.57264i	1.45515	+	0.150674i
$922$		0			0
$923$	10.0056	+	11.9242i	0.329337	+	0.392489i
$924$		0			0
$925$	−1.24037	−	3.40788i	−0.0407830	−	0.112050i
$926$		0			0
$927$	−46.6894	−	28.9749i	−1.53348	−	0.951660i
$928$		0			0
$929$	−27.9758	−	23.4745i	−0.917856	−	0.770173i	0.0557411	−	0.998445i	$-0.482248\pi$
$929$	−27.9758	−	23.4745i	−0.917856	−	0.770173i	−0.973597	+	0.228273i	$0.926692\pi$
$930$		0			0
$931$	37.2228	−	6.56338i	1.21993	−	0.215106i
$932$		0			0
$933$	13.4588	−	27.7031i	0.440622	−	0.906957i
$934$		0			0
$935$	29.8603	+	51.7196i	0.976536	+	1.69141i
$936$		0			0
$937$	−4.21635	+	7.30293i	−0.137742	+	0.238576i	−0.926642	−	0.375946i	$-0.877318\pi$
$937$	−4.21635	+	7.30293i	−0.137742	+	0.238576i	0.788899	+	0.614522i	$0.210651\pi$
$938$		0			0
$939$	13.8806	+	55.3083i	0.452975	+	1.80492i
$940$		0			0
$941$	6.23285	−	17.1246i	0.203185	−	0.558246i	−0.795688	−	0.605707i	$-0.792891\pi$
$941$	6.23285	−	17.1246i	0.203185	−	0.558246i	0.998873	+	0.0474602i	$0.0151127\pi$
$942$		0			0
$943$	5.20444	−	29.5159i	0.169480	−	0.961169i
$944$		0			0
$945$	−7.57655	+	6.88570i	−0.246465	+	0.223992i
$946$		0			0
$947$	30.4479	+	5.36879i	0.989424	+	0.174462i	0.644860	−	0.764301i	$-0.276916\pi$
$947$	30.4479	+	5.36879i	0.989424	+	0.174462i	0.344564	+	0.938763i	$0.388027\pi$
$948$		0			0
$949$	3.89045	−	10.6889i	0.126289	−	0.346977i
$950$		0			0
$951$	3.35339	−	11.7631i	0.108741	−	0.381444i
$952$		0			0
$953$	17.3439	−	30.0406i	0.561825	−	0.973109i	−0.435512	−	0.900183i	$-0.643433\pi$
$953$	17.3439	−	30.0406i	0.561825	−	0.973109i	0.997337	−	0.0729266i	$-0.0232339\pi$
$954$		0			0
$955$	42.4811	−	24.5265i	1.37466	−	0.793658i
$956$		0			0
$957$	−40.1423	+	2.86925i	−1.29762	+	0.0927495i
$958$		0			0
$959$	−0.304398	−	1.72633i	−0.00982954	−	0.0557461i
$960$		0			0
$961$	−18.0742	−	15.1661i	−0.583040	−	0.489229i
$962$		0			0
$963$	−48.6432	+	15.9712i	−1.56750	+	0.514664i
$964$		0			0
$965$	4.66513	+	12.8173i	0.150176	+	0.412605i
$966$		0			0
$967$	−23.6086	+	19.8100i	−0.759202	+	0.637046i	−0.937919	−	0.346854i	$-0.887250\pi$
$967$	−23.6086	+	19.8100i	−0.759202	+	0.637046i	0.178717	+	0.983901i	$0.442805\pi$
$968$		0			0
$969$	43.0231	−	59.4086i	1.38210	−	1.90848i
$970$		0			0
$971$		−	43.2999i		−	1.38956i	−0.719223	−	0.694779i	$-0.755502\pi$
$971$		−	43.2999i		−	1.38956i	0.719223	−	0.694779i	$-0.244498\pi$
$972$		0			0
$973$		−	0.475690i		−	0.0152499i
$974$		0			0
$975$	−2.55963	+	3.53449i	−0.0819739	+	0.113194i
$976$		0			0
$977$	4.11710	−	3.45466i	0.131718	−	0.110524i	−0.574549	−	0.818470i	$-0.694822\pi$
$977$	4.11710	−	3.45466i	0.131718	−	0.110524i	0.706267	+	0.707946i	$0.250378\pi$
$978$		0			0
$979$	5.09839	+	14.0077i	0.162945	+	0.447688i
$980$		0			0
$981$	−52.3767	+	17.1970i	−1.67226	+	0.549059i
$982$		0			0
$983$	−0.806129	−	0.676422i	−0.0257115	−	0.0215745i	0.629841	−	0.776724i	$-0.283120\pi$
$983$	−0.806129	−	0.676422i	−0.0257115	−	0.0215745i	−0.655553	+	0.755149i	$0.727564\pi$
$984$		0			0
$985$	−1.84392	−	10.4574i	−0.0587521	−	0.333200i
$986$		0			0
$987$	−4.18547	+	0.299164i	−0.133225	+	0.00952250i
$988$		0			0
$989$	−16.7270	+	9.65734i	−0.531888	+	0.307086i
$990$		0			0
$991$	−10.7235	+	18.5737i	−0.340644	+	0.590013i	−0.984553	−	0.175090i	$-0.943978\pi$
$991$	−10.7235	+	18.5737i	−0.340644	+	0.590013i	0.643908	+	0.765103i	$0.277312\pi$
$992$		0			0
$993$	5.76398	−	20.2190i	0.182914	−	0.641632i
$994$		0			0
$995$	−11.0174	+	30.2700i	−0.349274	+	0.959622i
$996$		0			0
$997$	9.02724	+	1.59175i	0.285896	+	0.0504111i	0.314757	−	0.949172i	$-0.398077\pi$
$997$	9.02724	+	1.59175i	0.285896	+	0.0504111i	−0.0288614	+	0.999583i	$0.509188\pi$
$998$		0			0
$999$	4.58138	+	21.0738i	0.144949	+	0.666745i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.bf.a.241.6		204
4.3	odd	2		216.2.t.a.133.19	yes	204
8.3	odd	2		216.2.t.a.133.20	yes	204
8.5	even	2	inner	864.2.bf.a.241.29		204
12.11	even	2		648.2.t.a.397.16		204
24.11	even	2		648.2.t.a.397.15		204
27.13	even	9	inner	864.2.bf.a.337.29		204
108.67	odd	18		216.2.t.a.13.20	yes	204
108.95	even	18		648.2.t.a.253.15		204
216.13	even	18	inner	864.2.bf.a.337.6		204
216.67	odd	18		216.2.t.a.13.19	✓	204
216.203	even	18		648.2.t.a.253.16		204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.t.a.13.19	✓	204	216.67	odd	18
216.2.t.a.13.20	yes	204	108.67	odd	18
216.2.t.a.133.19	yes	204	4.3	odd	2
216.2.t.a.133.20	yes	204	8.3	odd	2
648.2.t.a.253.15		204	108.95	even	18
648.2.t.a.253.16		204	216.203	even	18
648.2.t.a.397.15		204	24.11	even	2
648.2.t.a.397.16		204	12.11	even	2
864.2.bf.a.241.6		204	1.1	even	1	trivial
864.2.bf.a.241.29		204	8.5	even	2	inner
864.2.bf.a.337.6		204	216.13	even	18	inner
864.2.bf.a.337.29		204	27.13	even	9	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.bf (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.40283 - 1.01591i) q^{3} +(1.55785 + 1.85658i) q^{5} +(-0.763942 + 0.278052i) q^{7} +(0.935847 + 2.85030i) q^{9} +(-2.23007 + 2.65769i) q^{11} +(-2.83964 + 0.500705i) q^{13} +(-0.299281 - 4.18710i) q^{15} +(-3.55127 - 6.15099i) q^{17} +(-5.16371 - 2.98127i) q^{19} +(1.35415 + 0.386038i) q^{21} +(6.58997 + 2.39855i) q^{23} +(-0.151733 + 0.860521i) q^{25} +(1.58282 - 4.94921i) q^{27} +(-6.59552 - 1.16297i) q^{29} +(-2.55724 - 0.930757i) q^{31} +(5.82838 - 1.46273i) q^{33} +(-1.70634 - 0.985154i) q^{35} +(-3.59434 + 2.07519i) q^{37} +(4.49220 + 2.18242i) q^{39} +(-0.742124 - 4.20880i) q^{41} +(-1.77034 + 2.10981i) q^{43} +(-3.83389 + 6.17782i) q^{45} +(-2.80028 + 1.01922i) q^{47} +(-4.85602 + 4.07468i) q^{49} +(-1.26704 + 12.2365i) q^{51} +7.38929i q^{53} -8.40834 q^{55} +(4.21509 + 9.42808i) q^{57} +(-4.72368 - 5.62947i) q^{59} +(-0.0900385 - 0.247379i) q^{61} +(-1.50746 - 1.91725i) q^{63} +(-5.35335 - 4.49199i) q^{65} +(2.20513 - 0.388825i) q^{67} +(-6.80787 - 10.0596i) q^{69} +(-2.69918 - 4.67512i) q^{71} +(-1.97245 + 3.41639i) q^{73} +(1.08707 - 1.05302i) q^{75} +(0.964666 - 2.65040i) q^{77} +(-1.76846 + 10.0295i) q^{79} +(-7.24838 + 5.33489i) q^{81} +(7.86515 + 1.38684i) q^{83} +(5.88742 - 16.1756i) q^{85} +(8.07090 + 8.33191i) q^{87} +(2.14833 - 3.72101i) q^{89} +(2.03010 - 1.17208i) q^{91} +(2.64179 + 3.90362i) q^{93} +(-2.50935 - 14.2312i) q^{95} +(4.28345 + 3.59424i) q^{97} +(-9.66221 - 3.86916i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q + 12 q^{7} - 12 q^{9} + 12 q^{15} - 6 q^{17} + 12 q^{23} - 12 q^{25} + 12 q^{31} + 12 q^{39} - 24 q^{41} + 12 q^{47} - 12 q^{49} + 24 q^{55} - 30 q^{57} + 72 q^{63} - 12 q^{65} + 90 q^{71} - 6 q^{73}+ \cdots - 12 q^{97}+O(q^{100}) \) 204 * q + 12 * q^7 - 12 * q^9 + 12 * q^15 - 6 * q^17 + 12 * q^23 - 12 * q^25 + 12 * q^31 + 12 * q^39 - 24 * q^41 + 12 * q^47 - 12 * q^49 + 24 * q^55 - 30 * q^57 + 72 * q^63 - 12 * q^65 + 90 * q^71 - 6 * q^73 + 12 * q^79 - 12 * q^81 + 48 * q^87 - 6 * q^89 + 42 * q^95 - 12 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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