LMFDB - Embedded newform 864.2.bi.a.767.19

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [864,2,Mod(95,864)] 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("864.95"); 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([9, 0, 17])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.bi (of order $18$, degree $6$, 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:	$216$
Relative dimension:	$36$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			767.19
Character	$\chi$	$=$	864.767
Dual form			864.2.bi.a.383.19

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.000656376 - 1.73205i) q^{3} +(1.14458 - 3.14471i) q^{5} +(0.868740 + 0.153182i) q^{7} +(-3.00000 - 0.00227375i) q^{9} +(2.12626 - 0.773894i) q^{11} +(2.22748 - 1.86908i) q^{13} +(-5.44605 - 1.98454i) q^{15} +(3.66548 - 2.11626i) q^{17} +(-2.73141 - 1.57698i) q^{19} +(0.265890 - 1.50460i) q^{21} +(0.991104 + 5.62083i) q^{23} +(-4.74891 - 3.98481i) q^{25} +(-0.00590738 + 5.19615i) q^{27} +(3.68903 - 4.39642i) q^{29} +(-6.00083 + 1.05811i) q^{31} +(-1.33903 - 3.68329i) q^{33} +(1.47606 - 2.55661i) q^{35} +(1.04289 + 1.80634i) q^{37} +(-3.23587 - 3.85933i) q^{39} +(-3.86079 - 4.60111i) q^{41} +(1.42901 + 3.92618i) q^{43} +(-3.44089 + 9.43152i) q^{45} +(-1.42488 + 8.08089i) q^{47} +(-5.84660 - 2.12799i) q^{49} +(-3.66307 - 6.35018i) q^{51} +9.10008i q^{53} -7.57224i q^{55} +(-2.73321 + 4.72991i) q^{57} +(-7.34922 - 2.67490i) q^{59} +(-1.35378 + 7.67767i) q^{61} +(-2.60587 - 0.461522i) q^{63} +(-3.32817 - 9.14408i) q^{65} +(-2.03294 - 2.42277i) q^{67} +(9.73621 - 1.71295i) q^{69} +(5.53273 + 9.58297i) q^{71} +(7.03972 - 12.1932i) q^{73} +(-6.90501 + 8.22274i) q^{75} +(1.96571 - 0.346608i) q^{77} +(5.52652 - 6.58625i) q^{79} +(8.99999 + 0.0136425i) q^{81} +(-9.67557 - 8.11877i) q^{83} +(-2.45960 - 13.9491i) q^{85} +(-7.61240 - 6.39248i) q^{87} +(11.7949 + 6.80981i) q^{89} +(2.22141 - 1.28253i) q^{91} +(1.82876 + 10.3944i) q^{93} +(-8.08547 + 6.78452i) q^{95} +(-10.8609 + 3.95304i) q^{97} +(-6.38053 + 2.31685i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q - 24 q^{29} + 36 q^{33} + 36 q^{41} - 24 q^{45} + 12 q^{57} + 48 q^{65} + 48 q^{69} + 48 q^{77} + 48 q^{81} + 36 q^{89} - 144 q^{93} - 36 q^{97}+O(q^{100}) $ 216 * q - 24 * q^29 + 36 * q^33 + 36 * q^41 - 24 * q^45 + 12 * q^57 + 48 * q^65 + 48 * q^69 + 48 * q^77 + 48 * q^81 + 36 * q^89 - 144 * q^93 - 36 * q^97

Character values

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

$n$	$325$	$353$	$703$
$\chi(n)$	$1$	$e\left(\frac{13}{18}\right)$	$-1$

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
$3$	0.000656376	−	1.73205i	0.000378959	−	1.00000i
$3$	0.000656376	−	1.73205i	0.000378959	−	1.00000i
$4$		0			0
$5$	1.14458	−	3.14471i	0.511872	−	1.40636i	−0.367411	−	0.930058i	$-0.619756\pi$
$5$	1.14458	−	3.14471i	0.511872	−	1.40636i	0.879284	−	0.476299i	$-0.158022\pi$
$6$		0			0
$7$	0.868740	+	0.153182i	0.328353	+	0.0578975i	0.335395	−	0.942078i	$-0.391130\pi$
$7$	0.868740	+	0.153182i	0.328353	+	0.0578975i	−0.00704165	+	0.999975i	$0.502241\pi$
$8$		0			0
$9$	−3.00000	−	0.00227375i	−1.00000	−	0.000757918i
$10$		0			0
$11$	2.12626	−	0.773894i	0.641090	−	0.233338i	−0.000960866	−	1.00000i	$-0.500306\pi$
$11$	2.12626	−	0.773894i	0.641090	−	0.233338i	0.642051	+	0.766662i	$0.278084\pi$
$12$		0			0
$13$	2.22748	−	1.86908i	0.617791	−	0.518389i	−0.279317	−	0.960199i	$-0.590108\pi$
$13$	2.22748	−	1.86908i	0.617791	−	0.518389i	0.897108	+	0.441810i	$0.145664\pi$
$14$		0			0
$15$	−5.44605	−	1.98454i	−1.40616	−	0.512405i
$16$		0			0
$17$	3.66548	−	2.11626i	0.889008	−	0.513269i	0.0153903	−	0.999882i	$-0.495101\pi$
$17$	3.66548	−	2.11626i	0.889008	−	0.513269i	0.873618	+	0.486612i	$0.161768\pi$
$18$		0			0
$19$	−2.73141	−	1.57698i	−0.626629	−	0.361785i	0.152816	−	0.988255i	$-0.451166\pi$
$19$	−2.73141	−	1.57698i	−0.626629	−	0.361785i	−0.779445	+	0.626470i	$0.784499\pi$
$20$		0			0
$21$	0.265890	−	1.50460i	0.0580219	−	0.328331i
$22$		0			0
$23$	0.991104	+	5.62083i	0.206659	+	1.17202i	0.894807	+	0.446453i	$0.147313\pi$
$23$	0.991104	+	5.62083i	0.206659	+	1.17202i	−0.688147	+	0.725571i	$0.741576\pi$
$24$		0			0
$25$	−4.74891	−	3.98481i	−0.949783	−	0.796962i
$26$		0			0
$27$	−0.00590738	+	5.19615i	−0.00113688	+	0.999999i
$28$		0			0
$29$	3.68903	−	4.39642i	0.685036	−	0.816394i	−0.305710	−	0.952125i	$-0.598894\pi$
$29$	3.68903	−	4.39642i	0.685036	−	0.816394i	0.990746	+	0.135731i	$0.0433382\pi$
$30$		0			0
$31$	−6.00083	+	1.05811i	−1.07778	+	0.190042i	−0.684234	−	0.729262i	$-0.739863\pi$
$31$	−6.00083	+	1.05811i	−1.07778	+	0.190042i	−0.393547	+	0.919304i	$0.628752\pi$
$32$		0			0
$33$	−1.33903	−	3.68329i	−0.233095	−	0.641179i
$34$		0			0
$35$	1.47606	−	2.55661i	0.249499	−	0.432145i
$36$		0			0
$37$	1.04289	+	1.80634i	0.171450	+	0.296960i	0.938927	−	0.344116i	$-0.111821\pi$
$37$	1.04289	+	1.80634i	0.171450	+	0.296960i	−0.767477	+	0.641076i	$0.778488\pi$
$38$		0			0
$39$	−3.23587	−	3.85933i	−0.518154	−	0.617988i
$40$		0			0
$41$	−3.86079	−	4.60111i	−0.602954	−	0.718573i	0.375086	−	0.926990i	$-0.377613\pi$
$41$	−3.86079	−	4.60111i	−0.602954	−	0.718573i	−0.978040	+	0.208417i	$0.933169\pi$
$42$		0			0
$43$	1.42901	+	3.92618i	0.217922	+	0.598737i	0.999692	−	0.0248309i	$-0.00790472\pi$
$43$	1.42901	+	3.92618i	0.217922	+	0.598737i	−0.781769	+	0.623568i	$0.785683\pi$
$44$		0			0
$45$	−3.44089	+	9.43152i	−0.512938	+	1.40597i
$46$		0			0
$47$	−1.42488	+	8.08089i	−0.207840	+	1.17872i	0.685068	+	0.728479i	$0.259773\pi$
$47$	−1.42488	+	8.08089i	−0.207840	+	1.17872i	−0.892908	+	0.450240i	$0.851338\pi$
$48$		0			0
$49$	−5.84660	−	2.12799i	−0.835229	−	0.303999i
$50$		0			0
$51$	−3.66307	−	6.35018i	−0.512932	−	0.889203i
$52$		0			0
$53$			9.10008i			1.24999i	0.780628	+	0.624996i	$0.214899\pi$
$53$			9.10008i			1.24999i	−0.780628	+	0.624996i	$0.785101\pi$
$54$		0			0
$55$		−	7.57224i		−	1.02104i
$56$		0			0
$57$	−2.73321	+	4.72991i	−0.362022	+	0.626492i
$58$		0			0
$59$	−7.34922	−	2.67490i	−0.956787	−	0.348242i	−0.184014	−	0.982924i	$-0.558909\pi$
$59$	−7.34922	−	2.67490i	−0.956787	−	0.348242i	−0.772774	+	0.634682i	$0.781131\pi$
$60$		0			0
$61$	−1.35378	+	7.67767i	−0.173334	+	0.983025i	0.766716	+	0.641987i	$0.221890\pi$
$61$	−1.35378	+	7.67767i	−0.173334	+	0.983025i	−0.940049	+	0.341038i	$0.889221\pi$
$62$		0			0
$63$	−2.60587	−	0.461522i	−0.328309	−	0.0581463i
$64$		0			0
$65$	−3.32817	−	9.14408i	−0.412809	−	1.13418i
$66$		0			0
$67$	−2.03294	−	2.42277i	−0.248364	−	0.295988i	0.627431	−	0.778672i	$-0.284106\pi$
$67$	−2.03294	−	2.42277i	−0.248364	−	0.295988i	−0.875795	+	0.482684i	$0.839662\pi$
$68$		0			0
$69$	9.73621	−	1.71295i	1.17210	−	0.206215i
$70$		0			0
$71$	5.53273	+	9.58297i	0.656614	+	1.13729i	0.981486	+	0.191531i	$0.0613454\pi$
$71$	5.53273	+	9.58297i	0.656614	+	1.13729i	−0.324872	+	0.945758i	$0.605321\pi$
$72$		0			0
$73$	7.03972	−	12.1932i	0.823937	−	1.42710i	−0.0787918	−	0.996891i	$-0.525106\pi$
$73$	7.03972	−	12.1932i	0.823937	−	1.42710i	0.902729	−	0.430210i	$-0.141560\pi$
$74$		0			0
$75$	−6.90501	+	8.22274i	−0.797322	+	0.949481i
$76$		0			0
$77$	1.96571	−	0.346608i	0.224014	−	0.0394996i
$78$		0			0
$79$	5.52652	−	6.58625i	0.621782	−	0.741011i	−0.359594	−	0.933109i	$-0.617085\pi$
$79$	5.52652	−	6.58625i	0.621782	−	0.741011i	0.981376	+	0.192098i	$0.0615292\pi$
$80$		0			0
$81$	8.99999	+	0.0136425i	0.999999	+	0.00151583i
$82$		0			0
$83$	−9.67557	−	8.11877i	−1.06203	−	0.891151i	−0.0677249	−	0.997704i	$-0.521574\pi$
$83$	−9.67557	−	8.11877i	−1.06203	−	0.891151i	−0.994307	+	0.106553i	$0.966018\pi$
$84$		0			0
$85$	−2.45960	−	13.9491i	−0.266781	−	1.51299i
$86$		0			0
$87$	−7.61240	−	6.39248i	−0.816134	−	0.685345i
$88$		0			0
$89$	11.7949	+	6.80981i	1.25026	+	0.721839i	0.971161	−	0.238423i	$-0.0766306\pi$
$89$	11.7949	+	6.80981i	1.25026	+	0.721839i	0.279100	+	0.960262i	$0.409964\pi$
$90$		0			0
$91$	2.22141	−	1.28253i	0.232867	−	0.134446i
$92$		0			0
$93$	1.82876	+	10.3944i	0.189634	+	1.07785i
$94$		0			0
$95$	−8.08547	+	6.78452i	−0.829552	+	0.696077i
$96$		0			0
$97$	−10.8609	+	3.95304i	−1.10276	+	0.401370i	−0.828331	−	0.560239i	$-0.810709\pi$
$97$	−10.8609	+	3.95304i	−1.10276	+	0.401370i	−0.274424	+	0.961609i	$0.588487\pi$
$98$		0			0
$99$	−6.38053	+	2.31685i	−0.641267	+	0.232852i
$100$		0			0
$101$	16.2348	+	2.86263i	1.61542	+	0.284842i	0.907058	−	0.421005i	$-0.138323\pi$
$101$	16.2348	+	2.86263i	1.61542	+	0.284842i	0.708364	+	0.705848i	$0.249434\pi$
$102$		0			0
$103$	6.23682	−	17.1355i	0.614533	−	1.68841i	−0.105452	−	0.994424i	$-0.533629\pi$
$103$	6.23682	−	17.1355i	0.614533	−	1.68841i	0.719985	−	0.693990i	$-0.244149\pi$
$104$		0			0
$105$	−4.42720	−	2.55829i	−0.432051	−	0.249663i
$106$		0			0
$107$	13.5440			1.30935			0.654676	−	0.755910i	$-0.272805\pi$
$107$	13.5440			1.30935			0.654676	+	0.755910i	$0.272805\pi$
$108$		0			0
$109$	−12.9994			−1.24512			−0.622561	−	0.782572i	$-0.713908\pi$
$109$	−12.9994			−1.24512			−0.622561	+	0.782572i	$0.713908\pi$
$110$		0			0
$111$	3.12935	−	1.80515i	0.297025	−	0.171337i
$112$		0			0
$113$	4.66065	−	12.8050i	0.438437	−	1.20460i	−0.502072	−	0.864826i	$-0.667429\pi$
$113$	4.66065	−	12.8050i	0.438437	−	1.20460i	0.940509	−	0.339770i	$-0.110349\pi$
$114$		0			0
$115$	18.8103	+	3.31676i	1.75407	+	0.309289i
$116$		0			0
$117$	−6.68668	+	5.60216i	−0.618184	+	0.517920i
$118$		0			0
$119$	3.50852	−	1.27700i	0.321626	−	0.117062i
$120$		0			0
$121$	−4.50444	+	3.77967i	−0.409494	+	0.343606i
$122$		0			0
$123$	−7.97189	+	6.68406i	−0.718801	+	0.602682i
$124$		0			0
$125$	−3.47569	+	2.00669i	−0.310875	+	0.179484i
$126$		0			0
$127$	−3.13554	−	1.81031i	−0.278234	−	0.160639i	0.354389	−	0.935098i	$-0.384689\pi$
$127$	−3.13554	−	1.81031i	−0.278234	−	0.160639i	−0.632624	+	0.774459i	$0.718022\pi$
$128$		0			0
$129$	6.80128	−	2.47255i	0.598820	−	0.217696i
$130$		0			0
$131$	0.684563	+	3.88235i	0.0598106	+	0.339203i	0.999999	−	0.00145237i	$-0.000462302\pi$
$131$	0.684563	+	3.88235i	0.0598106	+	0.339203i	−0.940188	+	0.340655i	$0.889351\pi$
$132$		0			0
$133$	−2.13132	−	1.78839i	−0.184809	−	0.155073i
$134$		0			0
$135$	16.3336	+	5.96599i	1.40577	+	0.513471i
$136$		0			0
$137$	−13.8193	+	16.4692i	−1.18066	+	1.40706i	−0.287234	+	0.957861i	$0.592736\pi$
$137$	−13.8193	+	16.4692i	−1.18066	+	1.40706i	−0.893431	+	0.449201i	$0.851709\pi$
$138$		0			0
$139$	19.8348	−	3.49740i	1.68236	−	0.296646i	0.750881	−	0.660437i	$-0.229629\pi$
$139$	19.8348	−	3.49740i	1.68236	−	0.296646i	0.931480	+	0.363791i	$0.118518\pi$
$140$		0			0
$141$	13.9956	+	2.47327i	1.17864	+	0.208287i
$142$		0			0
$143$	3.28972	−	5.69797i	0.275100	−	0.476488i
$144$		0			0
$145$	−9.60306	−	16.6330i	−0.797491	−	1.38129i
$146$		0			0
$147$	−3.68962	+	10.1252i	−0.304315	+	0.835114i
$148$		0			0
$149$	5.98178	+	7.12880i	0.490046	+	0.584014i	0.953229	−	0.302248i	$-0.0977372\pi$
$149$	5.98178	+	7.12880i	0.490046	+	0.584014i	−0.463183	+	0.886263i	$0.653293\pi$
$150$		0			0
$151$	4.92003	+	13.5177i	0.400386	+	1.10005i	0.962094	+	0.272717i	$0.0879223\pi$
$151$	4.92003	+	13.5177i	0.400386	+	1.10005i	−0.561708	+	0.827336i	$0.689856\pi$
$152$		0			0
$153$	−11.0012	+	6.34045i	−0.889397	+	0.512595i
$154$		0			0
$155$	−3.54099	+	20.0820i	−0.284419	+	1.61302i
$156$		0			0
$157$	11.3646	+	4.13637i	0.906993	+	0.330118i	0.753052	−	0.657961i	$-0.228581\pi$
$157$	11.3646	+	4.13637i	0.906993	+	0.330118i	0.153941	+	0.988080i	$0.450803\pi$
$158$		0			0
$159$	15.7618	+	0.00597307i	1.24999	+	0.000473695i
$160$		0			0
$161$			5.03486i			0.396803i
$162$		0			0
$163$		−	9.51214i		−	0.745048i	−0.928023	−	0.372524i	$-0.878492\pi$
$163$		−	9.51214i		−	0.745048i	0.928023	−	0.372524i	$-0.121508\pi$
$164$		0			0
$165$	−13.1155	−	0.00497024i	−1.02104	−	0.000386933i
$166$		0			0
$167$	6.43985	+	2.34391i	0.498331	+	0.181378i	0.578943	−	0.815368i	$-0.303465\pi$
$167$	6.43985	+	2.34391i	0.498331	+	0.181378i	−0.0806123	+	0.996746i	$0.525688\pi$
$168$		0			0
$169$	−0.789212	+	4.47584i	−0.0607086	+	0.344296i
$170$		0			0
$171$	8.19065	+	4.73716i	0.626355	+	0.362259i
$172$		0			0
$173$	−2.96541	−	8.14738i	−0.225456	−	0.619434i	0.774457	−	0.632626i	$-0.218023\pi$
$173$	−2.96541	−	8.14738i	−0.225456	−	0.619434i	−0.999913	+	0.0131919i	$0.995801\pi$
$174$		0			0
$175$	−3.51517	−	4.18922i	−0.265722	−	0.316675i
$176$		0			0
$177$	−4.63788	+	12.7275i	−0.348605	+	0.956655i
$178$		0			0
$179$	−0.591468	−	1.02445i	−0.0442084	−	0.0765712i	0.843075	−	0.537797i	$-0.180743\pi$
$179$	−0.591468	−	1.02445i	−0.0442084	−	0.0765712i	−0.887283	+	0.461226i	$0.847410\pi$
$180$		0			0
$181$	3.28638	−	5.69218i	0.244275	−	0.423096i	−0.717653	−	0.696401i	$-0.754783\pi$
$181$	3.28638	−	5.69218i	0.244275	−	0.423096i	0.961927	+	0.273305i	$0.0881168\pi$
$182$		0			0
$183$	13.2972	+	2.34986i	0.982959	+	0.173706i
$184$		0			0
$185$	6.87408	−	1.21209i	0.505392	−	0.0891143i
$186$		0			0
$187$	6.15598	−	7.33641i	0.450170	−	0.536491i
$188$		0			0
$189$	−0.801090	+	4.51320i	−0.0582708	+	0.328287i
$190$		0			0
$191$	13.0975	+	10.9901i	0.947700	+	0.795215i	0.978909	−	0.204298i	$-0.0654912\pi$
$191$	13.0975	+	10.9901i	0.947700	+	0.795215i	−0.0312086	+	0.999513i	$0.509936\pi$
$192$		0			0
$193$	2.94544	+	16.7044i	0.212018	+	1.20241i	0.886007	+	0.463671i	$0.153468\pi$
$193$	2.94544	+	16.7044i	0.212018	+	1.20241i	−0.673990	+	0.738741i	$0.735421\pi$
$194$		0			0
$195$	−15.8402	+	5.75856i	−1.13434	+	0.412379i
$196$		0			0
$197$	−1.81206	−	1.04619i	−0.129104	−	0.0745382i	0.434057	−	0.900885i	$-0.357082\pi$
$197$	−1.81206	−	1.04619i	−0.129104	−	0.0745382i	−0.563161	+	0.826347i	$0.690415\pi$
$198$		0			0
$199$	−17.4068	+	10.0498i	−1.23394	+	0.712413i	−0.967848	−	0.251536i	$-0.919064\pi$
$199$	−17.4068	+	10.0498i	−1.23394	+	0.712413i	−0.266087	+	0.963949i	$0.585731\pi$
$200$		0			0
$201$	−4.19769	+	3.51957i	−0.296082	+	0.248252i
$202$		0			0
$203$	3.87826	−	3.25425i	0.272201	−	0.228404i
$204$		0			0
$205$	−18.8881	+	6.87472i	−1.31920	+	0.480151i
$206$		0			0
$207$	−2.96053	−	16.8647i	−0.205771	−	1.17218i
$208$		0			0
$209$	−7.02810	−	1.23924i	−0.486144	−	0.0857203i
$210$		0			0
$211$	1.57309	−	4.32203i	0.108296	−	0.297541i	−0.873693	−	0.486477i	$-0.838282\pi$
$211$	1.57309	−	4.32203i	0.108296	−	0.297541i	0.981989	+	0.188936i	$0.0605039\pi$
$212$		0			0
$213$	16.6018	−	9.57668i	1.13754	−	0.656183i
$214$		0			0
$215$	13.9823			0.953586
$216$		0			0
$217$	−5.37525			−0.364896
$218$		0			0
$219$	−21.1145	−	12.2012i	−1.42679	−	0.824478i
$220$		0			0
$221$	4.20931	−	11.5650i	0.283149	−	0.777945i
$222$		0			0
$223$	−14.3778	−	2.53520i	−0.962811	−	0.169769i	−0.329918	−	0.944009i	$-0.607021\pi$
$223$	−14.3778	−	2.53520i	−0.962811	−	0.169769i	−0.632892	+	0.774240i	$0.718132\pi$
$224$		0			0
$225$	14.2377	+	11.9652i	0.949178	+	0.797682i
$226$		0			0
$227$	14.6993	−	5.35010i	0.975625	−	0.355099i	0.195487	−	0.980706i	$-0.437371\pi$
$227$	14.6993	−	5.35010i	0.975625	−	0.355099i	0.780138	+	0.625608i	$0.215149\pi$
$228$		0			0
$229$	8.18118	−	6.86482i	0.540627	−	0.453640i	−0.331125	−	0.943587i	$-0.607428\pi$
$229$	8.18118	−	6.86482i	0.540627	−	0.453640i	0.871752	+	0.489947i	$0.162984\pi$
$230$		0			0
$231$	−0.599052	−	3.40494i	−0.0394148	−	0.224029i
$232$		0			0
$233$	13.8643	−	8.00458i	0.908283	−	0.524397i	0.0284048	−	0.999597i	$-0.490957\pi$
$233$	13.8643	−	8.00458i	0.908283	−	0.524397i	0.879878	+	0.475199i	$0.157624\pi$
$234$		0			0
$235$	23.7812	+	13.7301i	1.55131	+	0.895651i
$236$		0			0
$237$	−11.4041	−	9.57653i	−0.740775	−	0.622063i
$238$		0			0
$239$	−2.16720	−	12.2908i	−0.140185	−	0.795026i	−0.971108	−	0.238640i	$-0.923299\pi$
$239$	−2.16720	−	12.2908i	−0.140185	−	0.795026i	0.830924	−	0.556386i	$-0.187813\pi$
$240$		0			0
$241$	2.44749	+	2.05369i	0.157657	+	0.132290i	0.718204	−	0.695833i	$-0.244965\pi$
$241$	2.44749	+	2.05369i	0.157657	+	0.132290i	−0.560547	+	0.828123i	$0.689409\pi$
$242$		0			0
$243$	0.0295369	−	15.5884i	0.00189479	−	0.999998i
$244$		0			0
$245$	−13.3838	+	15.9502i	−0.855061	+	1.01902i
$246$		0			0
$247$	−9.03167	+	1.59253i	−0.574671	+	0.101330i
$248$		0			0
$249$	−14.0685	+	16.7533i	−0.891553	+	1.06169i
$250$		0			0
$251$	5.99312	−	10.3804i	0.378283	−	0.655205i	−0.612530	−	0.790447i	$-0.709848\pi$
$251$	5.99312	−	10.3804i	0.378283	−	0.655205i	0.990812	+	0.135243i	$0.0431814\pi$
$252$		0			0
$253$	6.45727	+	11.1843i	0.405965	+	0.703152i
$254$		0			0
$255$	−24.1621	+	4.25100i	−1.51309	+	0.266208i
$256$		0			0
$257$	8.79072	+	10.4764i	0.548350	+	0.653498i	0.967038	−	0.254632i	$-0.0819544\pi$
$257$	8.79072	+	10.4764i	0.548350	+	0.653498i	−0.418688	+	0.908130i	$0.637510\pi$
$258$		0			0
$259$	0.629301	+	1.72899i	0.0391029	+	0.107434i
$260$		0			0
$261$	−11.0771	+	13.1809i	−0.685655	+	0.815875i
$262$		0			0
$263$	−4.99124	+	28.3067i	−0.307773	+	1.74547i	0.302383	+	0.953187i	$0.402218\pi$
$263$	−4.99124	+	28.3067i	−0.307773	+	1.74547i	−0.610156	+	0.792281i	$0.708893\pi$
$264$		0			0
$265$	28.6171	+	10.4158i	1.75793	+	0.639836i
$266$		0			0
$267$	11.8027	−	20.4250i	0.722312	−	1.24999i
$268$		0			0
$269$		−	6.73747i		−	0.410791i	−0.978679	−	0.205395i	$-0.934152\pi$
$269$		−	6.73747i		−	0.410791i	0.978679	−	0.205395i	$-0.0658481\pi$
$270$		0			0
$271$		−	0.00703743i		−	0.000427493i	−1.00000		0.000213747i	$-0.999932\pi$
$271$		−	0.00703743i		−	0.000427493i	1.00000		0.000213747i	$-6.80377e-5\pi$
$272$		0			0
$273$	−2.21995	−	3.84844i	−0.134358	−	0.232918i
$274$		0			0
$275$	−13.1812	−	4.79758i	−0.794858	−	0.289305i
$276$		0			0
$277$	−1.12942	+	6.40528i	−0.0678605	+	0.384856i	0.931895	+	0.362729i	$0.118155\pi$
$277$	−1.12942	+	6.40528i	−0.0678605	+	0.384856i	−0.999755	+	0.0221271i	$0.992956\pi$
$278$		0			0
$279$	18.0049	−	3.16068i	1.07793	−	0.189225i
$280$		0			0
$281$	−6.33675	−	17.4101i	−0.378019	−	1.03860i	−0.972176	−	0.234250i	$-0.924737\pi$
$281$	−6.33675	−	17.4101i	−0.378019	−	1.03860i	0.594157	−	0.804349i	$-0.297486\pi$
$282$		0			0
$283$	−5.74398	−	6.84540i	−0.341444	−	0.406917i	0.567810	−	0.823160i	$-0.307791\pi$
$283$	−5.74398	−	6.84540i	−0.341444	−	0.406917i	−0.909253	+	0.416243i	$0.863347\pi$
$284$		0			0
$285$	11.7458	+	14.0089i	0.695763	+	0.829816i
$286$		0			0
$287$	−2.64921	−	4.58857i	−0.156378	−	0.270855i
$288$		0			0
$289$	0.457139	−	0.791789i	0.0268906	−	0.0465758i
$290$		0			0
$291$	6.83973	+	18.8142i	0.400952	+	1.10291i
$292$		0			0
$293$	16.5602	−	2.92001i	0.967458	−	0.170589i	0.332473	−	0.943113i	$-0.392117\pi$
$293$	16.5602	−	2.92001i	0.967458	−	0.170589i	0.634986	+	0.772524i	$0.281006\pi$
$294$		0			0
$295$	−16.8236	+	20.0495i	−0.979506	+	1.16733i
$296$		0			0
$297$	4.00871	+	11.0529i	0.232609	+	0.641355i
$298$		0			0
$299$	12.7134	+	10.6678i	0.735236	+	0.616937i
$300$		0			0
$301$	0.640020	+	3.62973i	0.0368901	+	0.209214i
$302$		0			0
$303$	4.96888	−	28.1176i	0.285455	−	1.61531i
$304$		0			0
$305$	22.5945	+	13.0450i	1.29376	+	0.746953i
$306$		0			0
$307$	−24.2655	+	14.0097i	−1.38491	+	0.799577i	−0.992736	−	0.120315i	$-0.961609\pi$
$307$	−24.2655	+	14.0097i	−1.38491	+	0.799577i	−0.392172	+	0.919892i	$0.628276\pi$
$308$		0			0
$309$	−29.6755	−	10.8137i	−1.68818	−	0.615172i
$310$		0			0
$311$	5.67584	−	4.76260i	0.321848	−	0.270062i	−0.467521	−	0.883982i	$-0.654853\pi$
$311$	5.67584	−	4.76260i	0.321848	−	0.270062i	0.789368	+	0.613920i	$0.210408\pi$
$312$		0			0
$313$	23.0099	−	8.37492i	1.30060	−	0.473378i	0.403405	−	0.915021i	$-0.367826\pi$
$313$	23.0099	−	8.37492i	1.30060	−	0.473378i	0.897191	+	0.441643i	$0.145604\pi$
$314$		0			0
$315$	−4.43399	+	7.66646i	−0.249827	+	0.431956i
$316$		0			0
$317$	−4.17866	−	0.736810i	−0.234697	−	0.0413834i	0.0550626	−	0.998483i	$-0.482464\pi$
$317$	−4.17866	−	0.736810i	−0.234697	−	0.0413834i	−0.289759	+	0.957100i	$0.593575\pi$
$318$		0			0
$319$	4.44147	−	12.2028i	0.248674	−	0.683227i
$320$		0			0
$321$	0.00888998	−	23.4590i	0.000496191	−	1.30935i
$322$		0			0
$323$	−13.3492			−0.742771
$324$		0			0
$325$	−18.0260			−0.999904
$326$		0			0
$327$	−0.00853252	+	22.5157i	−0.000471850	+	1.24512i
$328$		0			0
$329$	−2.47570	+	6.80193i	−0.136490	+	0.375003i
$330$		0			0
$331$	7.55077	+	1.33140i	0.415028	+	0.0731806i	0.377263	−	0.926106i	$-0.376865\pi$
$331$	7.55077	+	1.33140i	0.415028	+	0.0731806i	0.0377645	+	0.999287i	$0.487976\pi$
$332$		0			0
$333$	−3.12456	−	5.42138i	−0.171225	−	0.297090i
$334$		0			0
$335$	−9.94577	+	3.61997i	−0.543396	+	0.197780i
$336$		0			0
$337$	−12.2141	+	10.2488i	−0.665344	+	0.558290i	−0.911683	−	0.410894i	$-0.865217\pi$
$337$	−12.2141	+	10.2488i	−0.665344	+	0.558290i	0.246339	+	0.969184i	$0.420772\pi$
$338$		0			0
$339$	−22.1759	−	8.08089i	−1.20443	−	0.438893i
$340$		0			0
$341$	−11.9404	+	6.89382i	−0.646611	+	0.373321i
$342$		0			0
$343$	−10.1009	−	5.83176i	−0.545398	−	0.314886i
$344$		0			0
$345$	5.75714	−	32.5782i	0.309954	−	1.75395i
$346$		0			0
$347$	−4.96234	−	28.1428i	−0.266392	−	1.51079i	−0.765041	−	0.643981i	$-0.777282\pi$
$347$	−4.96234	−	28.1428i	−0.266392	−	1.51079i	0.498649	−	0.866804i	$-0.333830\pi$
$348$		0			0
$349$	−3.05383	−	2.56247i	−0.163468	−	0.137166i	0.557384	−	0.830255i	$-0.311805\pi$
$349$	−3.05383	−	2.56247i	−0.163468	−	0.137166i	−0.720852	+	0.693089i	$0.756249\pi$
$350$		0			0
$351$	9.69884	+	11.5854i	0.517686	+	0.618380i
$352$		0			0
$353$	−13.6462	+	16.2630i	−0.726316	+	0.865590i	−0.995228	−	0.0975746i	$-0.968892\pi$
$353$	−13.6462	+	16.2630i	−0.726316	+	0.865590i	0.268912	+	0.963165i	$0.413336\pi$
$354$		0			0
$355$	36.4683	−	6.43035i	1.93554	−	0.341288i
$356$		0			0
$357$	−2.20952	−	6.07777i	−0.116940	−	0.321670i
$358$		0			0
$359$	−10.5663	+	18.3014i	−0.557668	+	0.965910i	0.440022	+	0.897987i	$0.354971\pi$
$359$	−10.5663	+	18.3014i	−0.557668	+	0.965910i	−0.997691	+	0.0679229i	$0.978363\pi$
$360$		0			0
$361$	−4.52625	−	7.83970i	−0.238224	−	0.412616i
$362$		0			0
$363$	6.54362	+	7.80439i	0.343451	+	0.409624i
$364$		0			0
$365$	−30.2864	−	36.0939i	−1.58526	−	1.88924i
$366$		0			0
$367$	−9.20633	−	25.2942i	−0.480567	−	1.32035i	−0.909009	−	0.416777i	$-0.863160\pi$
$367$	−9.20633	−	25.2942i	−0.480567	−	1.32035i	0.428442	−	0.903569i	$-0.359062\pi$
$368$		0			0
$369$	11.5719	+	13.8121i	0.602409	+	0.719029i
$370$		0			0
$371$	−1.39397	+	7.90560i	−0.0723714	+	0.410439i
$372$		0			0
$373$	2.95311	+	1.07484i	0.152906	+	0.0556534i	0.417339	−	0.908751i	$-0.362963\pi$
$373$	2.95311	+	1.07484i	0.152906	+	0.0556534i	−0.264433	+	0.964404i	$0.585185\pi$
$374$		0			0
$375$	3.47341	+	6.02139i	0.179366	+	0.310943i
$376$		0			0
$377$		−	16.6880i		−	0.859476i
$378$		0			0
$379$			9.20462i			0.472809i	0.971655	+	0.236405i	$0.0759691\pi$
$379$			9.20462i			0.472809i	−0.971655	+	0.236405i	$0.924031\pi$
$380$		0			0
$381$	−3.13760	+	5.42973i	−0.160744	+	0.278173i
$382$		0			0
$383$	−25.6057	−	9.31972i	−1.30839	−	0.476215i	−0.408671	−	0.912682i	$-0.634008\pi$
$383$	−25.6057	−	9.31972i	−1.30839	−	0.476215i	−0.899720	+	0.436467i	$0.856230\pi$
$384$		0			0
$385$	1.15993	−	6.57831i	0.0591157	−	0.335262i
$386$		0			0
$387$	−4.27811	−	11.7818i	−0.217469	−	0.598902i
$388$		0			0
$389$	−0.311859	−	0.856826i	−0.0158119	−	0.0434428i	0.931536	−	0.363650i	$-0.118470\pi$
$389$	−0.311859	−	0.856826i	−0.0158119	−	0.0434428i	−0.947347	+	0.320207i	$0.896247\pi$
$390$		0			0
$391$	15.5280	+	18.5056i	0.785286	+	0.935867i
$392$		0			0
$393$	6.72488	−	1.18315i	0.339225	−	0.0596820i
$394$		0			0
$395$	−14.3863	−	24.9178i	−0.723853	−	1.25375i
$396$		0			0
$397$	9.85670	−	17.0723i	0.494694	−	0.856834i	−0.505288	−	0.862951i	$-0.668614\pi$
$397$	9.85670	−	17.0723i	0.494694	−	0.856834i	0.999981	+	0.00611653i	$0.00194696\pi$
$398$		0			0
$399$	−3.09899	+	3.69039i	−0.155143	+	0.184750i
$400$		0			0
$401$	4.06928	−	0.717523i	0.203210	−	0.0358314i	−0.0711165	−	0.997468i	$-0.522656\pi$
$401$	4.06928	−	0.717523i	0.203210	−	0.0358314i	0.274327	+	0.961637i	$0.411545\pi$
$402$		0			0
$403$	−11.3890	+	13.5729i	−0.567329	+	0.676116i
$404$		0			0
$405$	10.3441	−	28.2867i	0.514003	−	1.40558i
$406$		0			0
$407$	3.61536	+	3.03365i	0.179207	+	0.150372i
$408$		0			0
$409$	3.74092	+	21.2158i	0.184977	+	1.04906i	0.925985	+	0.377560i	$0.123237\pi$
$409$	3.74092	+	21.2158i	0.184977	+	1.04906i	−0.741008	+	0.671496i	$0.765652\pi$
$410$		0			0
$411$	28.5165	+	23.9466i	1.40661	+	1.18120i
$412$		0			0
$413$	−5.97482	−	3.44956i	−0.294002	−	0.169742i
$414$		0			0
$415$	−36.6056	+	21.1343i	−1.79690	+	1.03744i
$416$		0			0
$417$	−6.04466	−	34.3571i	−0.296008	−	1.68247i
$418$		0			0
$419$	−0.809018	+	0.678846i	−0.0395231	+	0.0331638i	−0.662335	−	0.749208i	$-0.730435\pi$
$419$	−0.809018	+	0.678846i	−0.0395231	+	0.0331638i	0.622812	+	0.782371i	$0.285990\pi$
$420$		0			0
$421$	−15.3502	+	5.58703i	−0.748125	+	0.272295i	−0.687817	−	0.725884i	$-0.741431\pi$
$421$	−15.3502	+	5.58703i	−0.748125	+	0.272295i	−0.0603086	+	0.998180i	$0.519208\pi$
$422$		0			0
$423$	4.29301	−	24.2394i	0.208733	−	1.17856i
$424$		0			0
$425$	−25.8399	−	4.55628i	−1.25342	−	0.221012i
$426$		0			0
$427$	−2.35217	+	6.46253i	−0.113829	+	0.312744i
$428$		0			0
$429$	−9.86701	−	5.70171i	−0.476384	−	0.275281i
$430$		0			0
$431$	16.1868			0.779692			0.389846	−	0.920880i	$-0.372528\pi$
$431$	16.1868			0.779692			0.389846	+	0.920880i	$0.372528\pi$
$432$		0			0
$433$	−33.5111			−1.61044			−0.805220	−	0.592977i	$-0.797953\pi$
$433$	−33.5111			−1.61044			−0.805220	+	0.592977i	$0.797953\pi$
$434$		0			0
$435$	−28.8155	+	16.6221i	−1.38160	+	0.796967i
$436$		0			0
$437$	6.15683	−	16.9158i	0.294521	−	0.809191i
$438$		0			0
$439$	28.2292	+	4.97758i	1.34731	+	0.237567i	0.800320	−	0.599574i	$-0.204663\pi$
$439$	28.2292	+	4.97758i	1.34731	+	0.237567i	0.546988	+	0.837140i	$0.315774\pi$
$440$		0			0
$441$	17.5350	+	6.39726i	0.834998	+	0.304631i
$442$		0			0
$443$	11.6723	−	4.24836i	0.554566	−	0.201846i	−0.0495080	−	0.998774i	$-0.515765\pi$
$443$	11.6723	−	4.24836i	0.554566	−	0.201846i	0.604074	+	0.796928i	$0.293543\pi$
$444$		0			0
$445$	34.9152	−	29.2973i	1.65514	−	1.38882i
$446$		0			0
$447$	12.3514	−	10.3561i	0.584200	−	0.489825i
$448$		0			0
$449$	−1.38564	+	0.800002i	−0.0653926	+	0.0377544i	−0.532340	−	0.846531i	$-0.678687\pi$
$449$	−1.38564	+	0.800002i	−0.0653926	+	0.0377544i	0.466947	+	0.884285i	$0.345354\pi$
$450$		0			0
$451$	−11.7698	−	6.79530i	−0.554218	−	0.319978i
$452$		0			0
$453$	23.4165	−	8.51287i	1.10020	−	0.399969i
$454$		0			0
$455$	−1.49061	−	8.45365i	−0.0698807	−	0.396313i
$456$		0			0
$457$	24.3663	+	20.4458i	1.13981	+	0.956413i	0.999432	−	0.0336858i	$-0.0107246\pi$
$457$	24.3663	+	20.4458i	1.13981	+	0.956413i	0.140376	+	0.990098i	$0.455169\pi$
$458$		0			0
$459$	10.9748	+	19.0589i	0.512258	+	0.889591i
$460$		0			0
$461$	−7.54795	+	8.99529i	−0.351543	+	0.418953i	−0.912619	−	0.408812i	$-0.865943\pi$
$461$	−7.54795	+	8.99529i	−0.351543	+	0.418953i	0.561076	+	0.827764i	$0.310388\pi$
$462$		0			0
$463$	−15.0694	+	2.65714i	−0.700334	+	0.123488i	−0.512467	−	0.858707i	$-0.671268\pi$
$463$	−15.0694	+	2.65714i	−0.700334	+	0.123488i	−0.187867	+	0.982195i	$0.560157\pi$
$464$		0			0
$465$	34.7807	+	6.14636i	1.61292	+	0.285031i
$466$		0			0
$467$	6.68919	−	11.5860i	0.309539	−	0.536137i	−0.668723	−	0.743512i	$-0.733159\pi$
$467$	6.68919	−	11.5860i	0.309539	−	0.536137i	0.978262	+	0.207375i	$0.0664919\pi$
$468$		0			0
$469$	−1.39498	−	2.41617i	−0.0644140	−	0.111568i
$470$		0			0
$471$	7.17187	−	19.6813i	0.330462	−	0.906868i
$472$		0			0
$473$	6.07690	+	7.24216i	0.279416	+	0.332995i
$474$		0			0
$475$	6.68727	+	18.3731i	0.306833	+	0.843017i
$476$		0			0
$477$	0.0206913	−	27.3002i	0.000947391	−	1.24999i
$478$		0			0
$479$	1.32388	−	7.50808i	0.0604895	−	0.343053i	−0.939510	−	0.342521i	$-0.888719\pi$
$479$	1.32388	−	7.50808i	0.0604895	−	0.343053i	1.00000		0.000532564i	$-0.000169520\pi$
$480$		0			0
$481$	5.69920	+	2.07434i	0.259861	+	0.0945817i
$482$		0			0
$483$	8.72064	+	0.00330476i	0.396803	+	0.000150372i
$484$		0			0
$485$			38.6789i			1.75632i
$486$		0			0
$487$		−	8.13160i		−	0.368478i	−0.982881	−	0.184239i	$-0.941018\pi$
$487$		−	8.13160i		−	0.368478i	0.982881	−	0.184239i	$-0.0589820\pi$
$488$		0			0
$489$	−16.4755	−	0.00624354i	−0.745048	−	0.000282343i
$490$		0			0
$491$	−10.9530	−	3.98657i	−0.494302	−	0.179911i	0.0828274	−	0.996564i	$-0.473605\pi$
$491$	−10.9530	−	3.98657i	−0.494302	−	0.179911i	−0.577129	+	0.816653i	$0.695827\pi$
$492$		0			0
$493$	4.21808	−	23.9219i	0.189973	−	1.07739i
$494$		0			0
$495$	−0.0172174	+	22.7167i	−0.000773865	+	1.02104i
$496$		0			0
$497$	3.33856	+	9.17263i	0.149755	+	0.411449i
$498$		0			0
$499$	−18.1642	−	21.6472i	−0.813141	−	0.969064i	0.186770	−	0.982404i	$-0.440198\pi$
$499$	−18.1642	−	21.6472i	−0.813141	−	0.969064i	−0.999911	+	0.0133401i	$0.995754\pi$
$500$		0			0
$501$	4.06401	−	11.1526i	0.181566	−	0.498262i
$502$		0			0
$503$	−8.94833	−	15.4990i	−0.398987	−	0.691065i	0.594615	−	0.804011i	$-0.297305\pi$
$503$	−8.94833	−	15.4990i	−0.398987	−	0.691065i	−0.993601	+	0.112946i	$0.963971\pi$
$504$		0			0
$505$	27.5842	−	47.7772i	1.22748	−	2.12606i
$506$		0			0
$507$	7.75187	+	1.36989i	0.344273	+	0.0608391i
$508$		0			0
$509$	9.00462	−	1.58776i	0.399123	−	0.0703761i	0.0295159	−	0.999564i	$-0.490603\pi$
$509$	9.00462	−	1.58776i	0.399123	−	0.0703761i	0.369607	+	0.929188i	$0.379492\pi$
$510$		0			0
$511$	7.98347	−	9.51433i	0.353168	−	0.420889i
$512$		0			0
$513$	8.21037	−	14.1835i	0.362497	−	0.626217i
$514$		0			0
$515$	−46.7477	−	39.2260i	−2.05995	−	1.72850i
$516$		0			0
$517$	3.22410	+	18.2848i	0.141796	+	0.804163i
$518$		0			0
$519$	−14.1136	+	5.13088i	−0.619520	+	0.225221i
$520$		0			0
$521$	−11.5026	−	6.64103i	−0.503938	−	0.290949i	0.226400	−	0.974034i	$-0.427304\pi$
$521$	−11.5026	−	6.64103i	−0.503938	−	0.290949i	−0.730338	+	0.683086i	$0.760638\pi$
$522$		0			0
$523$	−24.6080	+	14.2074i	−1.07603	+	0.621248i	−0.929824	−	0.368005i	$-0.880041\pi$
$523$	−24.6080	+	14.2074i	−1.07603	+	0.621248i	−0.146210	+	0.989254i	$0.546708\pi$
$524$		0			0
$525$	−7.25824	+	6.08570i	−0.316776	+	0.265602i
$526$		0			0
$527$	−19.7567	+	16.5778i	−0.860614	+	0.722141i
$528$		0			0
$529$	−8.99852	+	3.27519i	−0.391240	+	0.142400i
$530$		0			0
$531$	22.0416	+	8.04140i	0.956523	+	0.348967i
$532$		0			0
$533$	−17.1997	−	3.03276i	−0.745000	−	0.131364i
$534$		0			0
$535$	15.5023	−	42.5921i	0.670221	−	1.84142i
$536$		0			0
$537$	−1.77479	+	1.02378i	−0.0765879	+	0.0441794i
$538$		0			0
$539$	−14.0782			−0.606392
$540$		0			0
$541$	17.2566			0.741920			0.370960	−	0.928649i	$-0.379029\pi$
$541$	17.2566			0.741920			0.370960	+	0.928649i	$0.379029\pi$
$542$		0			0
$543$	−9.85699	−	5.69592i	−0.423004	−	0.244435i
$544$		0			0
$545$	−14.8789	+	40.8795i	−0.637343	+	1.75108i
$546$		0			0
$547$	−17.9108	−	3.15816i	−0.765810	−	0.135033i	−0.222920	−	0.974837i	$-0.571559\pi$
$547$	−17.9108	−	3.15816i	−0.765810	−	0.135033i	−0.542890	+	0.839804i	$0.682670\pi$
$548$		0			0
$549$	4.07880	−	23.0299i	0.174079	−	0.982894i
$550$		0			0
$551$	−17.0093	+	6.19089i	−0.724622	+	0.263741i
$552$		0			0
$553$	5.81001	−	4.87517i	0.247067	−	0.207314i
$554$		0			0
$555$	−2.09488	−	11.9070i	−0.0889228	−	0.505426i
$556$		0			0
$557$	−10.9083	+	6.29788i	−0.462198	+	0.266850i	−0.712968	−	0.701197i	$-0.752649\pi$
$557$	−10.9083	+	6.29788i	−0.462198	+	0.266850i	0.250770	+	0.968047i	$0.419316\pi$
$558$		0			0
$559$	10.5214	+	6.07455i	0.445009	+	0.256926i
$560$		0			0
$561$	−12.7030	−	10.6673i	−0.536321	−	0.450373i
$562$		0			0
$563$	−5.05333	−	28.6589i	−0.212973	−	1.20783i	−0.884390	−	0.466748i	$-0.845425\pi$
$563$	−5.05333	−	28.6589i	−0.212973	−	1.20783i	0.671418	−	0.741079i	$-0.265686\pi$
$564$		0			0
$565$	−34.9336	−	29.3128i	−1.46967	−	1.23320i
$566$		0			0
$567$	7.81657	+	1.39049i	0.328265	+	0.0583952i
$568$		0			0
$569$	11.4069	−	13.5943i	0.478203	−	0.569901i	−0.471973	−	0.881613i	$-0.656458\pi$
$569$	11.4069	−	13.5943i	0.478203	−	0.569901i	0.950177	+	0.311712i	$0.100903\pi$
$570$		0			0
$571$	−39.8047	+	7.01864i	−1.66577	+	0.293721i	−0.925546	−	0.378636i	$-0.876393\pi$
$571$	−39.8047	+	7.01864i	−1.66577	+	0.293721i	−0.740227	+	0.672357i	$0.765282\pi$
$572$		0			0
$573$	19.0440	−	22.6783i	0.795574	−	0.947399i
$574$		0			0
$575$	17.6913	−	30.6422i	0.737778	−	1.27787i
$576$		0			0
$577$	8.96624	+	15.5300i	0.373270	+	0.646522i	0.990066	−	0.140601i	$-0.0449033\pi$
$577$	8.96624	+	15.5300i	0.373270	+	0.646522i	−0.616797	+	0.787122i	$0.711570\pi$
$578$		0			0
$579$	28.9349	−	5.09069i	1.20249	−	0.211562i
$580$		0			0
$581$	−7.16191	−	8.53523i	−0.297126	−	0.354101i
$582$		0			0
$583$	7.04249	+	19.3491i	0.291670	+	0.801358i
$584$		0			0
$585$	9.96373	+	27.4398i	0.411949	+	1.13450i
$586$		0			0
$587$	−5.69919	+	32.3217i	−0.235231	+	1.33406i	0.606896	+	0.794781i	$0.292414\pi$
$587$	−5.69919	+	32.3217i	−0.235231	+	1.33406i	−0.842127	+	0.539279i	$0.818697\pi$
$588$		0			0
$589$	18.0594	+	6.57308i	0.744124	+	0.270839i
$590$		0			0
$591$	−1.81325	+	3.13789i	−0.0745871	+	0.129076i
$592$		0			0
$593$			12.4217i			0.510099i	0.966928	+	0.255049i	$0.0820917\pi$
$593$			12.4217i			0.510099i	−0.966928	+	0.255049i	$0.917908\pi$
$594$		0			0
$595$		−	12.4949i		−	0.512241i
$596$		0			0
$597$	17.3954	+	30.1561i	0.711945	+	1.23421i
$598$		0			0
$599$	9.98136	+	3.63292i	0.407827	+	0.148437i	0.537784	−	0.843083i	$-0.319262\pi$
$599$	9.98136	+	3.63292i	0.407827	+	0.148437i	−0.129957	+	0.991520i	$0.541484\pi$
$600$		0			0
$601$	−6.80729	+	38.6061i	−0.277675	+	1.57477i	0.452659	+	0.891684i	$0.350476\pi$
$601$	−6.80729	+	38.6061i	−0.277675	+	1.57477i	−0.730334	+	0.683090i	$0.760635\pi$
$602$		0			0
$603$	6.09332	+	7.27293i	0.248139	+	0.296176i
$604$		0			0
$605$	6.73028	+	18.4913i	0.273625	+	0.751777i
$606$		0			0
$607$	4.36390	+	5.20069i	0.177125	+	0.211090i	0.847301	−	0.531113i	$-0.178226\pi$
$607$	4.36390	+	5.20069i	0.177125	+	0.211090i	−0.670176	+	0.742202i	$0.733781\pi$
$608$		0			0
$609$	−5.63398	−	6.71949i	−0.228300	−	0.272287i
$610$		0			0
$611$	11.9299	+	20.6632i	0.482633	+	0.835945i
$612$		0			0
$613$	−3.62521	+	6.27905i	−0.146421	+	0.253608i	−0.929902	−	0.367807i	$-0.880109\pi$
$613$	−3.62521	+	6.27905i	−0.146421	+	0.253608i	0.783481	+	0.621415i	$0.213442\pi$
$614$		0			0
$615$	11.8950	+	32.7197i	0.479651	+	1.31939i
$616$		0			0
$617$	4.29605	−	0.757510i	0.172952	−	0.0304962i	−0.0865012	−	0.996252i	$-0.527569\pi$
$617$	4.29605	−	0.757510i	0.172952	−	0.0304962i	0.259454	+	0.965756i	$0.416458\pi$
$618$		0			0
$619$	−3.66676	+	4.36988i	−0.147380	+	0.175640i	−0.834684	−	0.550730i	$-0.814350\pi$
$619$	−3.66676	+	4.36988i	−0.147380	+	0.175640i	0.687304	+	0.726370i	$0.258794\pi$
$620$		0			0
$621$	−29.2125	+	5.11672i	−1.17226	+	0.205327i
$622$		0			0
$623$	9.20360	+	7.72274i	0.368734	+	0.309405i
$624$		0			0
$625$	−3.05020	−	17.2986i	−0.122008	−	0.691943i
$626$		0			0
$627$	−2.15105	+	12.1722i	−0.0859045	+	0.486111i
$628$		0			0
$629$	7.64537	+	4.41406i	0.304841	+	0.176000i
$630$		0			0
$631$	4.23956	−	2.44771i	0.168774	−	0.0974419i	−0.413233	−	0.910625i	$-0.635601\pi$
$631$	4.23956	−	2.44771i	0.168774	−	0.0974419i	0.582008	+	0.813183i	$0.302267\pi$
$632$		0			0
$633$	−7.48495	−	2.72751i	−0.297500	−	0.108409i
$634$		0			0
$635$	−9.28177	+	7.78833i	−0.368336	+	0.309070i
$636$		0			0
$637$	−17.0006	+	6.18770i	−0.673587	+	0.245166i
$638$		0			0
$639$	−16.5764	−	28.7615i	−0.655752	−	1.13779i
$640$		0			0
$641$	−37.4250	−	6.59903i	−1.47820	−	0.260646i	−0.624339	−	0.781153i	$-0.714632\pi$
$641$	−37.4250	−	6.59903i	−1.47820	−	0.260646i	−0.853857	+	0.520507i	$0.825743\pi$
$642$		0			0
$643$	−11.0942	+	30.4811i	−0.437513	+	1.20206i	0.503592	+	0.863941i	$0.332011\pi$
$643$	−11.0942	+	30.4811i	−0.437513	+	1.20206i	−0.941105	+	0.338115i	$0.890211\pi$
$644$		0			0
$645$	0.00917766	−	24.2181i	0.000361370	−	0.953586i
$646$		0			0
$647$	−28.1784			−1.10781			−0.553903	−	0.832581i	$-0.686862\pi$
$647$	−28.1784			−1.10781			−0.553903	+	0.832581i	$0.686862\pi$
$648$		0			0
$649$	−17.6964			−0.694645
$650$		0			0
$651$	−0.00352819	+	9.31021i	−0.000138281	+	0.364896i
$652$		0			0
$653$	13.0513	−	35.8583i	0.510738	−	1.40324i	−0.369731	−	0.929139i	$-0.620550\pi$
$653$	13.0513	−	35.8583i	0.510738	−	1.40324i	0.880469	−	0.474103i	$-0.157228\pi$
$654$		0			0
$655$	12.9924	+	2.29091i	0.507655	+	0.0895133i
$656$		0			0
$657$	−21.1469	+	36.5634i	−0.825018	+	1.42648i
$658$		0			0
$659$	−0.436653	+	0.158929i	−0.0170096	+	0.00619098i	−0.350511	−	0.936559i	$-0.613992\pi$
$659$	−0.436653	+	0.158929i	−0.0170096	+	0.00619098i	0.333501	+	0.942750i	$0.391770\pi$
$660$		0			0
$661$	−12.1628	+	10.2058i	−0.473076	+	0.396958i	−0.847915	−	0.530132i	$-0.822142\pi$
$661$	−12.1628	+	10.2058i	−0.473076	+	0.396958i	0.374839	+	0.927090i	$0.377698\pi$
$662$		0			0
$663$	−20.0284	−	7.29833i	−0.777838	−	0.283444i
$664$		0			0
$665$	−8.06345	+	4.65543i	−0.312687	+	0.180530i
$666$		0			0
$667$	28.3677	+	16.3781i	1.09840	+	0.634163i
$668$		0			0
$669$	−4.40053	+	24.9015i	−0.170134	+	0.962746i
$670$		0			0
$671$	3.06322	+	17.3724i	0.118254	+	0.670653i
$672$		0			0
$673$	36.5572	+	30.6751i	1.40917	+	1.18244i	0.956849	+	0.290585i	$0.0938499\pi$
$673$	36.5572	+	30.6751i	1.40917	+	1.18244i	0.452326	+	0.891853i	$0.350595\pi$
$674$		0			0
$675$	20.7337	−	24.6525i	0.798042	−	0.948876i
$676$		0			0
$677$	−6.73383	+	8.02506i	−0.258802	+	0.308428i	−0.879762	−	0.475414i	$-0.842298\pi$
$677$	−6.73383	+	8.02506i	−0.258802	+	0.308428i	0.620960	+	0.783842i	$0.286743\pi$
$678$		0			0
$679$	−10.0408	+	1.77047i	−0.385331	+	0.0679443i
$680$		0			0
$681$	−9.25699	−	25.4634i	−0.354729	−	0.975760i
$682$		0			0
$683$	11.7855	−	20.4131i	0.450959	−	0.781084i	−0.547487	−	0.836814i	$-0.684415\pi$
$683$	11.7855	−	20.4131i	0.450959	−	0.781084i	0.998446	+	0.0557301i	$0.0177486\pi$
$684$		0			0
$685$	35.9736	+	62.3081i	1.37448	+	2.38067i
$686$		0			0
$687$	−11.8849	−	14.1747i	−0.453435	−	0.540799i
$688$		0			0
$689$	17.0087	+	20.2702i	0.647981	+	0.772234i
$690$		0			0
$691$	10.4826	+	28.8007i	0.398776	+	1.09563i	0.962881	+	0.269925i	$0.0869991\pi$
$691$	10.4826	+	28.8007i	0.398776	+	1.09563i	−0.564105	+	0.825703i	$0.690779\pi$
$692$		0			0
$693$	−5.89792	+	1.03535i	−0.224044	+	0.0393299i
$694$		0			0
$695$	11.7042	−	66.3776i	0.443964	−	2.51785i
$696$		0			0
$697$	−23.8888	−	8.69481i	−0.904852	−	0.329339i
$698$		0			0
$699$	−13.8552	−	24.0190i	−0.524053	−	0.908482i
$700$		0			0
$701$			33.0955i			1.25000i	0.780624	+	0.625001i	$0.214901\pi$
$701$			33.0955i			1.25000i	−0.780624	+	0.625001i	$0.785099\pi$
$702$		0			0
$703$		−	6.57847i		−	0.248112i
$704$		0			0
$705$	23.7968	−	41.1812i	0.896239	−	1.55097i
$706$		0			0
$707$	13.6653	+	4.97377i	0.513937	+	0.187058i
$708$		0			0
$709$	−8.80140	+	49.9152i	−0.330543	+	1.87460i	0.136905	+	0.990584i	$0.456284\pi$
$709$	−8.80140	+	49.9152i	−0.330543	+	1.87460i	−0.467448	+	0.884020i	$0.654827\pi$
$710$		0			0
$711$	−16.5945	+	19.7462i	−0.622343	+	0.740539i
$712$		0			0
$713$	−11.8949	−	32.6810i	−0.445468	−	1.22391i
$714$		0			0
$715$	−14.1531	−	16.8670i	−0.529296	−	0.630790i
$716$		0			0
$717$	−21.2897	+	3.74563i	−0.795079	+	0.139883i
$718$		0			0
$719$	14.5722	+	25.2397i	0.543450	+	0.941284i	0.998703	+	0.0509211i	$0.0162157\pi$
$719$	14.5722	+	25.2397i	0.543450	+	0.941284i	−0.455252	+	0.890362i	$0.650451\pi$
$720$		0			0
$721$	8.04304	−	13.9310i	0.299539	−	0.518816i
$722$		0			0
$723$	3.55870	−	4.23783i	0.132349	−	0.157606i
$724$		0			0
$725$	−35.0378	+	6.17811i	−1.30127	+	0.229449i
$726$		0			0
$727$	−17.1454	+	20.4331i	−0.635888	+	0.757822i	−0.983715	−	0.179737i	$-0.942475\pi$
$727$	−17.1454	+	20.4331i	−0.635888	+	0.757822i	0.347827	+	0.937559i	$0.386920\pi$
$728$		0			0
$729$	−26.9999	−	0.0613913i	−0.999997	−	0.00227375i
$730$		0			0
$731$	13.5468	+	11.3672i	0.501048	+	0.420429i
$732$		0			0
$733$	2.43317	+	13.7992i	0.0898711	+	0.509684i	0.996199	+	0.0871087i	$0.0277627\pi$
$733$	2.43317	+	13.7992i	0.0898711	+	0.509684i	−0.906328	+	0.422575i	$0.861126\pi$
$734$		0			0
$735$	27.6178	+	23.1919i	1.01870	+	0.855447i
$736$		0			0
$737$	−6.19753	−	3.57814i	−0.228289	−	0.131803i
$738$		0			0
$739$	−25.7455	+	14.8642i	−0.947063	+	0.546787i	−0.892167	−	0.451705i	$-0.850816\pi$
$739$	−25.7455	+	14.8642i	−0.947063	+	0.546787i	−0.0548959	+	0.998492i	$0.517483\pi$
$740$		0			0
$741$	2.75241	+	15.6443i	0.101112	+	0.574709i
$742$		0			0
$743$	25.0772	−	21.0423i	0.919993	−	0.771966i	−0.0540008	−	0.998541i	$-0.517197\pi$
$743$	25.0772	−	21.0423i	0.919993	−	0.771966i	0.973994	+	0.226575i	$0.0727529\pi$
$744$		0			0
$745$	29.2646	−	10.6515i	1.07217	−	0.390239i
$746$		0			0
$747$	29.0082	+	24.3783i	1.06136	+	0.891955i
$748$		0			0
$749$	11.7663	+	2.07471i	0.429930	+	0.0758082i
$750$		0			0
$751$	−13.5997	+	37.3649i	−0.496261	+	1.36347i	0.398601	+	0.917124i	$0.369496\pi$
$751$	−13.5997	+	37.3649i	−0.496261	+	1.36347i	−0.894862	+	0.446342i	$0.852726\pi$
$752$		0			0
$753$	−17.9754	−	10.3872i	−0.655061	−	0.378531i
$754$		0			0
$755$	48.1405			1.75201
$756$		0			0
$757$	15.8575			0.576352			0.288176	−	0.957577i	$-0.406951\pi$
$757$	15.8575			0.576352			0.288176	+	0.957577i	$0.406951\pi$
$758$		0			0
$759$	19.3760	−	11.1770i	0.703306	−	0.405698i
$760$		0			0
$761$	0.663263	−	1.82230i	0.0240433	−	0.0660583i	−0.927090	−	0.374838i	$-0.877698\pi$
$761$	0.663263	−	1.82230i	0.0240433	−	0.0660583i	0.951134	+	0.308780i	$0.0999206\pi$
$762$		0			0
$763$	−11.2931	−	1.99129i	−0.408839	−	0.0720894i
$764$		0			0
$765$	7.34708	+	41.8529i	0.265634	+	1.51319i
$766$		0			0
$767$	−21.3698	+	7.77798i	−0.771620	+	0.280847i
$768$		0			0
$769$	−0.871712	+	0.731453i	−0.0314347	+	0.0263769i	−0.658370	−	0.752695i	$-0.728754\pi$
$769$	−0.871712	+	0.731453i	−0.0314347	+	0.0263769i	0.626935	+	0.779072i	$0.284309\pi$
$770$		0			0
$771$	18.1514	−	15.2191i	0.653706	−	0.548102i
$772$		0			0
$773$	−2.25340	+	1.30100i	−0.0810490	+	0.0467937i	−0.539977	−	0.841680i	$-0.681567\pi$
$773$	−2.25340	+	1.30100i	−0.0810490	+	0.0467937i	0.458928	+	0.888474i	$0.348234\pi$
$774$		0			0
$775$	32.7138	+	18.8873i	1.17511	+	0.678453i
$776$		0			0
$777$	2.99511	−	1.08885i	0.107449	−	0.0390622i
$778$		0			0
$779$	3.28954	+	18.6559i	0.117860	+	0.668418i
$780$		0			0
$781$	19.1802	+	16.0941i	0.686322	+	0.575892i
$782$		0			0
$783$	22.8226	+	19.1947i	0.815615	+	0.685964i
$784$		0			0
$785$	26.0154	−	31.0039i	0.928529	−	1.10658i
$786$		0			0
$787$	51.4976	−	9.08042i	1.83569	−	0.323682i	0.854909	−	0.518778i	$-0.173613\pi$
$787$	51.4976	−	9.08042i	1.83569	−	0.323682i	0.980784	+	0.195096i	$0.0625019\pi$
$788$		0			0
$789$	49.0254	+	8.66366i	1.74535	+	0.308435i
$790$		0			0
$791$	6.01040	−	10.4103i	0.213705	−	0.370148i
$792$		0			0
$793$	11.3346	+	19.6322i	0.402505	+	0.697159i
$794$		0			0
$795$	18.0594	−	49.5594i	0.640502	−	1.75769i
$796$		0			0
$797$	−14.0502	−	16.7444i	−0.497685	−	0.593118i	0.457470	−	0.889225i	$-0.348756\pi$
$797$	−14.0502	−	16.7444i	−0.497685	−	0.593118i	−0.955155	+	0.296107i	$0.904311\pi$
$798$		0			0
$799$	11.8784	+	32.6357i	0.420229	+	1.15457i
$800$		0			0
$801$	−35.3693	−	20.4563i	−1.24971	−	0.722786i
$802$		0			0
$803$	5.53204	−	31.3738i	0.195222	−	1.10716i
$804$		0			0
$805$	15.8332	+	5.76281i	0.558046	+	0.203112i
$806$		0			0
$807$	−11.6696	−	0.00442231i	−0.410791	−	0.000155673i
$808$		0			0
$809$		−	22.4503i		−	0.789310i	−0.918829	−	0.394655i	$-0.870864\pi$
$809$		−	22.4503i		−	0.789310i	0.918829	−	0.394655i	$-0.129136\pi$
$810$		0			0
$811$		−	33.9604i		−	1.19251i	−0.802795	−	0.596255i	$-0.796655\pi$
$811$		−	33.9604i		−	1.19251i	0.802795	−	0.596255i	$-0.203345\pi$
$812$		0			0
$813$	−0.0121892		4.61920e-6i	−0.000427493		1.62002e-7i
$814$		0			0
$815$	−29.9129	−	10.8874i	−1.04780	−	0.381369i
$816$		0			0
$817$	2.28829	−	12.9776i	0.0800572	−	0.454027i
$818$		0			0
$819$	−6.66715	+	3.84254i	−0.232969	+	0.134269i
$820$		0			0
$821$	15.5932	+	42.8420i	0.544207	+	1.49520i	0.841418	+	0.540385i	$0.181721\pi$
$821$	15.5932	+	42.8420i	0.544207	+	1.49520i	−0.297211	+	0.954812i	$0.596057\pi$
$822$		0			0
$823$	−14.0617	−	16.7581i	−0.490160	−	0.584150i	0.463098	−	0.886307i	$-0.346738\pi$
$823$	−14.0617	−	16.7581i	−0.490160	−	0.584150i	−0.953258	+	0.302157i	$0.902293\pi$
$824$		0			0
$825$	−8.31830	+	22.8274i	−0.289606	+	0.794748i
$826$		0			0
$827$	5.37603	+	9.31155i	0.186943	+	0.323794i	0.944229	−	0.329288i	$-0.106809\pi$
$827$	5.37603	+	9.31155i	0.186943	+	0.323794i	−0.757287	+	0.653083i	$0.773475\pi$
$828$		0			0
$829$	24.1231	−	41.7824i	0.837830	−	1.45116i	−0.0538750	−	0.998548i	$-0.517157\pi$
$829$	24.1231	−	41.7824i	0.837830	−	1.45116i	0.891705	−	0.452617i	$-0.149509\pi$
$830$		0			0
$831$	11.0935	+	1.96042i	0.384831	+	0.0680064i
$832$		0			0
$833$	−25.9340	+	4.57286i	−0.898559	+	0.158440i
$834$		0			0
$835$	14.7419	−	17.5687i	0.510163	−	0.607989i
$836$		0			0
$837$	−5.46264	−	31.1875i	−0.188817	−	1.07800i
$838$		0			0
$839$	31.3513	+	26.3069i	1.08237	+	0.908213i	0.996115	−	0.0880600i	$-0.0280667\pi$
$839$	31.3513	+	26.3069i	1.08237	+	0.908213i	0.0862514	+	0.996273i	$0.472511\pi$
$840$		0			0
$841$	−0.683728	−	3.87762i	−0.0235768	−	0.133711i
$842$		0			0
$843$	−30.1593	+	10.9641i	−1.03874	+	0.377625i
$844$		0			0
$845$	13.1719	+	7.60481i	0.453128	+	0.261613i
$846$		0			0
$847$	−4.49216	+	2.59355i	−0.154353	+	0.0891155i
$848$		0			0
$849$	−11.8604	+	9.94436i	−0.407046	+	0.341290i
$850$		0			0
$851$	−9.11950	+	7.65217i	−0.312613	+	0.262313i
$852$		0			0
$853$	−25.7169	+	9.36017i	−0.880528	+	0.320486i	−0.742423	−	0.669931i	$-0.766323\pi$
$853$	−25.7169	+	9.36017i	−0.880528	+	0.320486i	−0.138105	+	0.990418i	$0.544101\pi$
$854$		0			0
$855$	24.2718	−	20.3352i	0.830080	−	0.695448i
$856$		0			0
$857$	−13.4637	−	2.37402i	−0.459912	−	0.0810949i	−0.0611083	−	0.998131i	$-0.519464\pi$
$857$	−13.4637	−	2.37402i	−0.459912	−	0.0810949i	−0.398804	+	0.917036i	$0.630575\pi$
$858$		0			0
$859$	−5.15999	+	14.1770i	−0.176057	+	0.483712i	−0.996064	−	0.0886420i	$-0.971747\pi$
$859$	−5.15999	+	14.1770i	−0.176057	+	0.483712i	0.820007	+	0.572354i	$0.193970\pi$
$860$		0			0
$861$	−7.94938	+	4.58556i	−0.270914	+	0.156276i
$862$		0			0
$863$	23.7324			0.807860			0.403930	−	0.914790i	$-0.367644\pi$
$863$	23.7324			0.807860			0.403930	+	0.914790i	$0.367644\pi$
$864$		0			0
$865$	−29.0153			−0.986550
$866$		0			0
$867$	−1.37112	−	0.792308i	−0.0465656	−	0.0269082i
$868$		0			0
$869$	6.65374	−	18.2810i	0.225713	−	0.620140i
$870$		0			0
$871$	−9.05668	−	1.59694i	−0.306874	−	0.0541102i
$872$		0			0
$873$	32.5916	−	11.8344i	1.10306	−	0.400534i
$874$		0			0
$875$	−3.32686	+	1.21088i	−0.112469	+	0.0409352i
$876$		0			0
$877$	−1.78967	+	1.50171i	−0.0604328	+	0.0507091i	−0.672504	−	0.740094i	$-0.734781\pi$
$877$	−1.78967	+	1.50171i	−0.0604328	+	0.0507091i	0.612071	+	0.790803i	$0.290337\pi$
$878$		0			0
$879$	−5.04674	−	28.6851i	−0.170222	−	0.967523i
$880$		0			0
$881$	33.6777	−	19.4438i	1.13463	−	0.655080i	0.189536	−	0.981874i	$-0.439302\pi$
$881$	33.6777	−	19.4438i	1.13463	−	0.655080i	0.945095	+	0.326794i	$0.105968\pi$
$882$		0			0
$883$	−36.6700	−	21.1715i	−1.23404	−	0.712476i	−0.266174	−	0.963925i	$-0.585760\pi$
$883$	−36.6700	−	21.1715i	−1.23404	−	0.712476i	−0.967871	+	0.251449i	$0.919093\pi$
$884$		0			0
$885$	34.7158	+	29.1524i	1.16696	+	0.979948i
$886$		0			0
$887$	0.607035	+	3.44267i	0.0203822	+	0.115593i	0.993301	−	0.115552i	$-0.0368637\pi$
$887$	0.607035	+	3.44267i	0.0203822	+	0.115593i	−0.972919	+	0.231146i	$0.925753\pi$
$888$		0			0
$889$	−2.44666	−	2.05300i	−0.0820585	−	0.0688553i
$890$		0			0
$891$	19.1468	−	6.93603i	0.641443	−	0.232366i
$892$		0			0
$893$	16.6354	−	19.8252i	0.556681	−	0.663427i
$894$		0			0
$895$	−3.89859	+	0.687427i	−0.130315	+	0.0229781i
$896$		0			0
$897$	18.4856	−	22.0133i	0.617215	−	0.735003i
$898$		0			0
$899$	−17.4854	+	30.2856i	−0.583170	+	1.01008i
$900$		0			0
$901$	19.2582	+	33.3561i	0.641582	+	1.11125i
$902$		0			0
$903$	6.28730	−	1.10616i	0.209228	−	0.0368108i
$904$		0			0
$905$	−14.1387	−	16.8499i	−0.469987	−	0.560109i
$906$		0			0
$907$	−5.06585	−	13.9183i	−0.168209	−	0.462150i	0.826734	−	0.562593i	$-0.190196\pi$
$907$	−5.06585	−	13.9183i	−0.168209	−	0.462150i	−0.994943	+	0.100443i	$0.967974\pi$
$908$		0			0
$909$	−48.6978	−	8.62481i	−1.61521	−	0.286067i
$910$		0			0
$911$	8.21622	−	46.5965i	0.272215	−	1.54381i	−0.475454	−	0.879740i	$-0.657716\pi$
$911$	8.21622	−	46.5965i	0.272215	−	1.54381i	0.747670	−	0.664070i	$-0.231173\pi$
$912$		0			0
$913$	−26.8558	−	9.77472i	−0.888798	−	0.323496i
$914$		0			0
$915$	22.6094	−	39.1263i	0.747443	−	1.29348i
$916$		0			0
$917$			3.47762i			0.114841i
$918$		0			0
$919$		−	29.1278i		−	0.960838i	−0.877039	−	0.480419i	$-0.840485\pi$
$919$		−	29.1278i		−	0.960838i	0.877039	−	0.480419i	$-0.159515\pi$
$920$		0			0
$921$	24.2496	+	42.0383i	0.799052	+	1.38521i
$922$		0			0
$923$	30.2353	+	11.0048i	0.995209	+	0.362226i
$924$		0			0
$925$	2.24532	−	12.7339i	0.0738258	−	0.418687i
$926$		0			0
$927$	−18.7494	+	51.3924i	−0.615812	+	1.68795i
$928$		0			0
$929$	9.75399	+	26.7989i	0.320018	+	0.879243i	0.990524	+	0.137339i	$0.0438548\pi$
$929$	9.75399	+	26.7989i	0.320018	+	0.879243i	−0.670506	+	0.741904i	$0.733923\pi$
$930$		0			0
$931$	12.6137	+	15.0324i	0.413397	+	0.492667i
$932$		0			0
$933$	−8.24534	−	9.83397i	−0.269940	−	0.321950i
$934$		0			0
$935$	−16.0249	−	27.7559i	−0.524069	−	0.907714i
$936$		0			0
$937$	−12.3193	+	21.3377i	−0.402455	+	0.697073i	−0.994022	−	0.109183i	$-0.965176\pi$
$937$	−12.3193	+	21.3377i	−0.402455	+	0.697073i	0.591566	+	0.806256i	$0.298510\pi$
$938$		0			0
$939$	−14.4907	−	39.8598i	−0.472885	−	1.30078i
$940$		0			0
$941$	−15.0476	+	2.65330i	−0.490539	+	0.0864953i	−0.413446	−	0.910529i	$-0.635675\pi$
$941$	−15.0476	+	2.65330i	−0.490539	+	0.0864953i	−0.0770930	+	0.997024i	$0.524564\pi$
$942$		0			0
$943$	22.0356	−	26.2610i	0.717578	−	0.855176i
$944$		0			0
$945$	13.2758	+	7.68492i	0.431862	+	0.249990i
$946$		0			0
$947$	28.0684	+	23.5522i	0.912099	+	0.765342i	0.972517	−	0.232831i	$-0.0747989\pi$
$947$	28.0684	+	23.5522i	0.912099	+	0.765342i	−0.0604179	+	0.998173i	$0.519243\pi$
$948$		0			0
$949$	−7.10911	−	40.3178i	−0.230772	−	1.30877i
$950$		0			0
$951$	−1.27893	+	7.23716i	−0.0414723	+	0.234681i
$952$		0			0
$953$	−9.37645	−	5.41349i	−0.303733	−	0.175360i	0.340386	−	0.940286i	$-0.389442\pi$
$953$	−9.37645	−	5.41349i	−0.303733	−	0.175360i	−0.644119	+	0.764926i	$0.722776\pi$
$954$		0			0
$955$	49.5518	−	28.6087i	1.60346	−	0.925756i
$956$		0			0
$957$	−21.1330	−	7.70085i	−0.683133	−	0.248933i
$958$		0			0
$959$	−14.5282	+	12.1906i	−0.469140	+	0.393655i
$960$		0			0
$961$	5.75995	−	2.09645i	0.185805	−	0.0676274i
$962$		0			0
$963$	−40.6321	−	0.0307958i	−1.30935	−	0.000992381i
$964$		0			0
$965$	55.9019	+	9.85702i	1.79955	+	0.317309i
$966$		0			0
$967$	−10.4720	+	28.7717i	−0.336758	+	0.925236i	0.649549	+	0.760320i	$0.274958\pi$
$967$	−10.4720	+	28.7717i	−0.336758	+	0.925236i	−0.986308	+	0.164916i	$0.947265\pi$
$968$		0			0
$969$	−0.00876212	+	23.1216i	−0.000281480	+	0.742771i
$970$		0			0
$971$	20.2632			0.650278			0.325139	−	0.945666i	$-0.394589\pi$
$971$	20.2632			0.650278			0.325139	+	0.945666i	$0.394589\pi$
$972$		0			0
$973$	17.7670			0.569584
$974$		0			0
$975$	−0.0118318	+	31.2220i	−0.000378922	+	0.999904i
$976$		0			0
$977$	−12.8950	+	35.4286i	−0.412547	+	1.13346i	0.543285	+	0.839548i	$0.317180\pi$
$977$	−12.8950	+	35.4286i	−0.412547	+	1.13346i	−0.955832	+	0.293914i	$0.905042\pi$
$978$		0			0
$979$	30.3491	+	5.35137i	0.969963	+	0.171031i
$980$		0			0
$981$	38.9983	+	0.0295575i	1.24512	+	0.000943699i
$982$		0			0
$983$	−36.6643	+	13.3447i	−1.16941	+	0.425631i	−0.852450	−	0.522808i	$-0.824884\pi$
$983$	−36.6643	+	13.3447i	−1.16941	+	0.425631i	−0.316960	+	0.948439i	$0.602662\pi$
$984$		0			0
$985$	−5.36402	+	4.50095i	−0.170912	+	0.143412i
$986$		0			0
$987$	11.7797	+	4.29250i	0.374951	+	0.136632i
$988$		0			0
$989$	−20.6521	+	11.9235i	−0.656698	+	0.379145i
$990$		0			0
$991$	33.5863	+	19.3911i	1.06690	+	0.615977i	0.927334	−	0.374235i	$-0.122095\pi$
$991$	33.5863	+	19.3911i	1.06690	+	0.615977i	0.139570	+	0.990212i	$0.455428\pi$
$992$		0			0
$993$	2.31102	−	13.0774i	0.0733379	−	0.415000i
$994$		0			0
$995$	11.6803	+	66.2422i	0.370290	+	2.10002i
$996$		0			0
$997$	−47.5375	−	39.8887i	−1.50553	−	1.26329i	−0.871936	−	0.489619i	$-0.837136\pi$
$997$	−47.5375	−	39.8887i	−1.50553	−	1.26329i	−0.633591	−	0.773668i	$-0.718420\pi$
$998$		0			0
$999$	−9.39216	+	5.40834i	−0.297155	+	0.171112i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.bi.a.767.19	yes	216
4.3	odd	2	inner	864.2.bi.a.767.18	yes	216
27.5	odd	18	inner	864.2.bi.a.383.18	✓	216
108.59	even	18	inner	864.2.bi.a.383.19	yes	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.bi.a.383.18	✓	216	27.5	odd	18	inner
864.2.bi.a.383.19	yes	216	108.59	even	18	inner
864.2.bi.a.767.18	yes	216	4.3	odd	2	inner
864.2.bi.a.767.19	yes	216	1.1	even	1	trivial

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.bi (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.000656376 - 1.73205i) q^{3} +(1.14458 - 3.14471i) q^{5} +(0.868740 + 0.153182i) q^{7} +(-3.00000 - 0.00227375i) q^{9} +(2.12626 - 0.773894i) q^{11} +(2.22748 - 1.86908i) q^{13} +(-5.44605 - 1.98454i) q^{15} +(3.66548 - 2.11626i) q^{17} +(-2.73141 - 1.57698i) q^{19} +(0.265890 - 1.50460i) q^{21} +(0.991104 + 5.62083i) q^{23} +(-4.74891 - 3.98481i) q^{25} +(-0.00590738 + 5.19615i) q^{27} +(3.68903 - 4.39642i) q^{29} +(-6.00083 + 1.05811i) q^{31} +(-1.33903 - 3.68329i) q^{33} +(1.47606 - 2.55661i) q^{35} +(1.04289 + 1.80634i) q^{37} +(-3.23587 - 3.85933i) q^{39} +(-3.86079 - 4.60111i) q^{41} +(1.42901 + 3.92618i) q^{43} +(-3.44089 + 9.43152i) q^{45} +(-1.42488 + 8.08089i) q^{47} +(-5.84660 - 2.12799i) q^{49} +(-3.66307 - 6.35018i) q^{51} +9.10008i q^{53} -7.57224i q^{55} +(-2.73321 + 4.72991i) q^{57} +(-7.34922 - 2.67490i) q^{59} +(-1.35378 + 7.67767i) q^{61} +(-2.60587 - 0.461522i) q^{63} +(-3.32817 - 9.14408i) q^{65} +(-2.03294 - 2.42277i) q^{67} +(9.73621 - 1.71295i) q^{69} +(5.53273 + 9.58297i) q^{71} +(7.03972 - 12.1932i) q^{73} +(-6.90501 + 8.22274i) q^{75} +(1.96571 - 0.346608i) q^{77} +(5.52652 - 6.58625i) q^{79} +(8.99999 + 0.0136425i) q^{81} +(-9.67557 - 8.11877i) q^{83} +(-2.45960 - 13.9491i) q^{85} +(-7.61240 - 6.39248i) q^{87} +(11.7949 + 6.80981i) q^{89} +(2.22141 - 1.28253i) q^{91} +(1.82876 + 10.3944i) q^{93} +(-8.08547 + 6.78452i) q^{95} +(-10.8609 + 3.95304i) q^{97} +(-6.38053 + 2.31685i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q - 24 q^{29} + 36 q^{33} + 36 q^{41} - 24 q^{45} + 12 q^{57} + 48 q^{65} + 48 q^{69} + 48 q^{77} + 48 q^{81} + 36 q^{89} - 144 q^{93} - 36 q^{97}+O(q^{100}) \) 216 * q - 24 * q^29 + 36 * q^33 + 36 * q^41 - 24 * q^45 + 12 * q^57 + 48 * q^65 + 48 * q^69 + 48 * q^77 + 48 * q^81 + 36 * q^89 - 144 * q^93 - 36 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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