LMFDB - Embedded newform 864.2.bi.a.767.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(95,864)]

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

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$6.89907473464$
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			767.18
Character	$\chi$	$=$	864.767
Dual form			864.2.bi.a.383.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.000656376 + 1.73205i) q^{3} +(1.14458 - 3.14471i) q^{5} +(-0.868740 - 0.153182i) q^{7} +(-3.00000 - 0.00227375i) q^{9} +O(q^{10})$	\(q+(-0.000656376 + 1.73205i) q^{3} +(1.14458 - 3.14471i) q^{5} +(-0.868740 - 0.153182i) q^{7} +(-3.00000 - 0.00227375i) q^{9} +(-2.12626 + 0.773894i) q^{11} +(2.22748 - 1.86908i) q^{13} +(5.44605 + 1.98454i) q^{15} +(3.66548 - 2.11626i) q^{17} +(2.73141 + 1.57698i) q^{19} +(0.265890 - 1.50460i) q^{21} +(-0.991104 - 5.62083i) q^{23} +(-4.74891 - 3.98481i) q^{25} +(0.00590738 - 5.19615i) q^{27} +(3.68903 - 4.39642i) q^{29} +(6.00083 - 1.05811i) q^{31} +(-1.33903 - 3.68329i) q^{33} +(-1.47606 + 2.55661i) q^{35} +(1.04289 + 1.80634i) q^{37} +(3.23587 + 3.85933i) q^{39} +(-3.86079 - 4.60111i) q^{41} +(-1.42901 - 3.92618i) q^{43} +(-3.44089 + 9.43152i) q^{45} +(1.42488 - 8.08089i) q^{47} +(-5.84660 - 2.12799i) q^{49} +(3.66307 + 6.35018i) q^{51} +9.10008i q^{53} +7.57224i q^{55} +(-2.73321 + 4.72991i) q^{57} +(7.34922 + 2.67490i) q^{59} +(-1.35378 + 7.67767i) q^{61} +(2.60587 + 0.461522i) q^{63} +(-3.32817 - 9.14408i) q^{65} +(2.03294 + 2.42277i) q^{67} +(9.73621 - 1.71295i) q^{69} +(-5.53273 - 9.58297i) q^{71} +(7.03972 - 12.1932i) q^{73} +(6.90501 - 8.22274i) q^{75} +(1.96571 - 0.346608i) q^{77} +(-5.52652 + 6.58625i) q^{79} +(8.99999 + 0.0136425i) q^{81} +(9.67557 + 8.11877i) q^{83} +(-2.45960 - 13.9491i) q^{85} +(7.61240 + 6.39248i) q^{87} +(11.7949 + 6.80981i) q^{89} +(-2.22141 + 1.28253i) q^{91} +(1.82876 + 10.3944i) q^{93} +(8.08547 - 6.78452i) q^{95} +(-10.8609 + 3.95304i) q^{97} +(6.38053 - 2.31685i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q+O(q^{10}) $ 216 * 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

Display 100 coefficients 10 coefficients

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	0.00704165	−	0.999975i	$-0.497759\pi$
$7$	−0.868740	−	0.153182i	−0.328353	−	0.0578975i	−0.335395	+	0.942078i	$0.608870\pi$
$8$		0			0
$9$	−3.00000	−	0.00227375i	−1.00000	−	0.000757918i
$10$		0			0
$11$	−2.12626	+	0.773894i	−0.641090	+	0.233338i	−0.642051	−	0.766662i	$-0.721916\pi$
$11$	−2.12626	+	0.773894i	−0.641090	+	0.233338i	0.000960866		1.00000i	$0.499694\pi$
$12$		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	0.779445	−	0.626470i	$-0.215501\pi$
$19$	2.73141	+	1.57698i	0.626629	+	0.361785i	−0.152816	+	0.988255i	$0.548834\pi$
$20$		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	$-0.852687\pi$
$23$	−0.991104	−	5.62083i	−0.206659	−	1.17202i	0.688147	−	0.725571i	$-0.258424\pi$
$24$		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	0.393547	−	0.919304i	$-0.371248\pi$
$31$	6.00083	−	1.05811i	1.07778	−	0.190042i	0.684234	+	0.729262i	$0.260137\pi$
$32$		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	0.781769	−	0.623568i	$-0.214317\pi$
$43$	−1.42901	−	3.92618i	−0.217922	−	0.598737i	−0.999692	+	0.0248309i	$0.992095\pi$
$44$		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	$-0.740227\pi$
$47$	1.42488	−	8.08089i	0.207840	−	1.17872i	0.892908	−	0.450240i	$-0.148662\pi$
$48$		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	0.772774	−	0.634682i	$-0.218869\pi$
$59$	7.34922	+	2.67490i	0.956787	+	0.348242i	0.184014	+	0.982924i	$0.441091\pi$
$60$		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	0.875795	−	0.482684i	$-0.160338\pi$
$67$	2.03294	+	2.42277i	0.248364	+	0.295988i	−0.627431	+	0.778672i	$0.715894\pi$
$68$		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	$-0.938655\pi$
$71$	−5.53273	−	9.58297i	−0.656614	−	1.13729i	0.324872	−	0.945758i	$-0.394679\pi$
$72$		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	−0.981376	−	0.192098i	$-0.938471\pi$
$79$	−5.52652	+	6.58625i	−0.621782	+	0.741011i	0.359594	+	0.933109i	$0.382915\pi$
$80$		0			0
$81$	8.99999	+	0.0136425i	0.999999	+	0.00151583i
$82$		0			0
$83$	9.67557	+	8.11877i	1.06203	+	0.891151i	0.994307	−	0.106553i	$-0.0339815\pi$
$83$	9.67557	+	8.11877i	1.06203	+	0.891151i	0.0677249	+	0.997704i	$0.478426\pi$
$84$		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	$0.466371\pi$
$103$	−6.23682	+	17.1355i	−0.614533	+	1.68841i	−0.719985	+	0.693990i	$0.755851\pi$
$104$		0			0
$105$	−4.42720	−	2.55829i	−0.432051	−	0.249663i
$106$		0			0
$107$	−13.5440			−1.30935			−0.654676	−	0.755910i	$-0.727195\pi$
$107$	−13.5440			−1.30935			−0.654676	+	0.755910i	$0.727195\pi$
$108$		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	0.632624	−	0.774459i	$-0.281978\pi$
$127$	3.13554	+	1.81031i	0.278234	+	0.160639i	−0.354389	+	0.935098i	$0.615311\pi$
$128$		0			0
$129$	6.80128	−	2.47255i	0.598820	−	0.217696i
$130$		0			0
$131$	−0.684563	−	3.88235i	−0.0598106	−	0.339203i	0.940188	−	0.340655i	$-0.110649\pi$
$131$	−0.684563	−	3.88235i	−0.0598106	−	0.339203i	−0.999999	+	0.00145237i	$0.999538\pi$
$132$		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	−0.931480	−	0.363791i	$-0.881482\pi$
$139$	−19.8348	+	3.49740i	−1.68236	+	0.296646i	−0.750881	+	0.660437i	$0.770371\pi$
$140$		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	$-0.912078\pi$
$151$	−4.92003	−	13.5177i	−0.400386	−	1.10005i	0.561708	−	0.827336i	$-0.310144\pi$
$152$		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	$0.121508\pi$
$163$			9.51214i			0.745048i	−0.928023	+	0.372524i	$0.878492\pi$
$164$		0			0
$165$	−13.1155	−	0.00497024i	−1.02104	−	0.000386933i
$166$		0			0
$167$	−6.43985	−	2.34391i	−0.498331	−	0.181378i	0.0806123	−	0.996746i	$-0.474312\pi$
$167$	−6.43985	−	2.34391i	−0.498331	−	0.181378i	−0.578943	+	0.815368i	$0.696535\pi$
$168$		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	0.887283	−	0.461226i	$-0.152590\pi$
$179$	0.591468	+	1.02445i	0.0442084	+	0.0765712i	−0.843075	+	0.537797i	$0.819257\pi$
$180$		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	0.0312086	−	0.999513i	$-0.490064\pi$
$191$	−13.0975	−	10.9901i	−0.947700	−	0.795215i	−0.978909	+	0.204298i	$0.934509\pi$
$192$		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	0.266087	−	0.963949i	$-0.414269\pi$
$199$	17.4068	−	10.0498i	1.23394	−	0.712413i	0.967848	+	0.251536i	$0.0809357\pi$
$200$		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	−0.981989	−	0.188936i	$-0.939496\pi$
$211$	−1.57309	+	4.32203i	−0.108296	+	0.297541i	0.873693	+	0.486477i	$0.161718\pi$
$212$		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	0.632892	−	0.774240i	$-0.281868\pi$
$223$	14.3778	+	2.53520i	0.962811	+	0.169769i	0.329918	+	0.944009i	$0.392979\pi$
$224$		0			0
$225$	14.2377	+	11.9652i	0.949178	+	0.797682i
$226$		0			0
$227$	−14.6993	+	5.35010i	−0.975625	+	0.355099i	−0.780138	−	0.625608i	$-0.784851\pi$
$227$	−14.6993	+	5.35010i	−0.975625	+	0.355099i	−0.195487	+	0.980706i	$0.562629\pi$
$228$		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	$0.0767014\pi$
$239$	2.16720	+	12.2908i	0.140185	+	0.795026i	−0.830924	+	0.556386i	$0.812187\pi$
$240$		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	−0.990812	−	0.135243i	$-0.956819\pi$
$251$	−5.99312	+	10.3804i	−0.378283	+	0.655205i	0.612530	+	0.790447i	$0.290152\pi$
$252$		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	$-0.597782\pi$
$263$	4.99124	−	28.3067i	0.307773	−	1.74547i	0.610156	−	0.792281i	$-0.291107\pi$
$264$		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	$6.80377e-5\pi$
$271$			0.00703743i			0.000427493i	−1.00000		0.000213747i	$0.999932\pi$
$272$		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	0.909253	−	0.416243i	$-0.136653\pi$
$283$	5.74398	+	6.84540i	0.341444	+	0.406917i	−0.567810	+	0.823160i	$0.692209\pi$
$284$		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	0.392172	−	0.919892i	$-0.371724\pi$
$307$	24.2655	−	14.0097i	1.38491	−	0.799577i	0.992736	+	0.120315i	$0.0383906\pi$
$308$		0			0
$309$	−29.6755	−	10.8137i	−1.68818	−	0.615172i
$310$		0			0
$311$	−5.67584	+	4.76260i	−0.321848	+	0.270062i	−0.789368	−	0.613920i	$-0.789592\pi$
$311$	−5.67584	+	4.76260i	−0.321848	+	0.270062i	0.467521	+	0.883982i	$0.345147\pi$
$312$		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	−0.0377645	−	0.999287i	$-0.512024\pi$
$331$	−7.55077	−	1.33140i	−0.415028	−	0.0731806i	−0.377263	+	0.926106i	$0.623135\pi$
$332$		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	$0.222718\pi$
$347$	4.96234	+	28.1428i	0.266392	+	1.51079i	−0.498649	+	0.866804i	$0.666170\pi$
$348$		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	$-0.645029\pi$
$359$	10.5663	−	18.3014i	0.557668	−	0.965910i	0.997691	−	0.0679229i	$-0.0216372\pi$
$360$		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	$0.136840\pi$
$367$	9.20633	+	25.2942i	0.480567	+	1.32035i	−0.428442	+	0.903569i	$0.640938\pi$
$368$		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	$-0.924031\pi$
$379$		−	9.20462i		−	0.472809i	0.971655	−	0.236405i	$-0.0759691\pi$
$380$		0			0
$381$	−3.13760	+	5.42973i	−0.160744	+	0.278173i
$382$		0			0
$383$	25.6057	+	9.31972i	1.30839	+	0.476215i	0.899720	−	0.436467i	$-0.143770\pi$
$383$	25.6057	+	9.31972i	1.30839	+	0.476215i	0.408671	+	0.912682i	$0.365992\pi$
$384$		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	−0.622812	−	0.782371i	$-0.714010\pi$
$419$	0.809018	−	0.678846i	0.0395231	−	0.0331638i	0.662335	+	0.749208i	$0.269565\pi$
$420$		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	$-0.627472\pi$
$431$	−16.1868			−0.779692			−0.389846	+	0.920880i	$0.627472\pi$
$432$		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	−0.546988	−	0.837140i	$-0.684226\pi$
$439$	−28.2292	−	4.97758i	−1.34731	−	0.237567i	−0.800320	+	0.599574i	$0.795337\pi$
$440$		0			0
$441$	17.5350	+	6.39726i	0.834998	+	0.304631i
$442$		0			0
$443$	−11.6723	+	4.24836i	−0.554566	+	0.201846i	−0.604074	−	0.796928i	$-0.706457\pi$
$443$	−11.6723	+	4.24836i	−0.554566	+	0.201846i	0.0495080	+	0.998774i	$0.484235\pi$
$444$		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	0.187867	−	0.982195i	$-0.439843\pi$
$463$	15.0694	−	2.65714i	0.700334	−	0.123488i	0.512467	+	0.858707i	$0.328732\pi$
$464$		0			0
$465$	34.7807	+	6.14636i	1.61292	+	0.285031i
$466$		0			0
$467$	−6.68919	+	11.5860i	−0.309539	+	0.536137i	−0.978262	−	0.207375i	$-0.933508\pi$
$467$	−6.68919	+	11.5860i	−0.309539	+	0.536137i	0.668723	+	0.743512i	$0.266841\pi$
$468$		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	$0.111281\pi$
$479$	−1.32388	+	7.50808i	−0.0604895	+	0.343053i	−1.00000		0.000532564i	$0.999830\pi$
$480$		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	$0.0589820\pi$
$487$			8.13160i			0.368478i	−0.982881	+	0.184239i	$0.941018\pi$
$488$		0			0
$489$	−16.4755	−	0.00624354i	−0.745048	−	0.000282343i
$490$		0			0
$491$	10.9530	+	3.98657i	0.494302	+	0.179911i	0.577129	−	0.816653i	$-0.304173\pi$
$491$	10.9530	+	3.98657i	0.494302	+	0.179911i	−0.0828274	+	0.996564i	$0.526395\pi$
$492$		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	0.999911	−	0.0133401i	$-0.00424642\pi$
$499$	18.1642	+	21.6472i	0.813141	+	0.969064i	−0.186770	+	0.982404i	$0.559802\pi$
$500$		0			0
$501$	4.06401	−	11.1526i	0.181566	−	0.498262i
$502$		0			0
$503$	8.94833	+	15.4990i	0.398987	+	0.691065i	0.993601	−	0.112946i	$-0.0360287\pi$
$503$	8.94833	+	15.4990i	0.398987	+	0.691065i	−0.594615	+	0.804011i	$0.702695\pi$
$504$		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	0.146210	−	0.989254i	$-0.453292\pi$
$523$	24.6080	−	14.2074i	1.07603	−	0.621248i	0.929824	+	0.368005i	$0.119959\pi$
$524$		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	0.542890	−	0.839804i	$-0.317330\pi$
$547$	17.9108	+	3.15816i	0.765810	+	0.135033i	0.222920	+	0.974837i	$0.428441\pi$
$548$		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	$0.154575\pi$
$563$	5.05333	+	28.6589i	0.212973	+	1.20783i	−0.671418	+	0.741079i	$0.734314\pi$
$564$		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	0.740227	−	0.672357i	$-0.234718\pi$
$571$	39.8047	−	7.01864i	1.66577	−	0.293721i	0.925546	+	0.378636i	$0.123607\pi$
$572$		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	$-0.707586\pi$
$587$	5.69919	−	32.3217i	0.235231	−	1.33406i	0.842127	−	0.539279i	$-0.181303\pi$
$588$		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	0.129957	−	0.991520i	$-0.458516\pi$
$599$	−9.98136	−	3.63292i	−0.407827	−	0.148437i	−0.537784	+	0.843083i	$0.680738\pi$
$600$		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	0.670176	−	0.742202i	$-0.266219\pi$
$607$	−4.36390	−	5.20069i	−0.177125	−	0.211090i	−0.847301	+	0.531113i	$0.821774\pi$
$608$		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	−0.687304	−	0.726370i	$-0.741206\pi$
$619$	3.66676	−	4.36988i	0.147380	−	0.175640i	0.834684	+	0.550730i	$0.185650\pi$
$620$		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	−0.582008	−	0.813183i	$-0.697733\pi$
$631$	−4.23956	+	2.44771i	−0.168774	+	0.0974419i	0.413233	+	0.910625i	$0.364399\pi$
$632$		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	$-0.667989\pi$
$643$	11.0942	−	30.4811i	0.437513	−	1.20206i	0.941105	−	0.338115i	$-0.109789\pi$
$644$		0			0
$645$	0.00917766	−	24.2181i	0.000361370	−	0.953586i
$646$		0			0
$647$	28.1784			1.10781			0.553903	−	0.832581i	$-0.313138\pi$
$647$	28.1784			1.10781			0.553903	+	0.832581i	$0.313138\pi$
$648$		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	−0.333501	−	0.942750i	$-0.608230\pi$
$659$	0.436653	−	0.158929i	0.0170096	−	0.00619098i	0.350511	+	0.936559i	$0.386008\pi$
$660$		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	−0.998446	−	0.0557301i	$-0.982251\pi$
$683$	−11.7855	+	20.4131i	−0.450959	+	0.781084i	0.547487	+	0.836814i	$0.315585\pi$
$684$		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	$-0.913001\pi$
$691$	−10.4826	−	28.8007i	−0.398776	−	1.09563i	0.564105	−	0.825703i	$-0.309221\pi$
$692$		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	$-0.983784\pi$
$719$	−14.5722	−	25.2397i	−0.543450	−	0.941284i	0.455252	−	0.890362i	$-0.349549\pi$
$720$		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	−0.347827	−	0.937559i	$-0.613080\pi$
$727$	17.1454	−	20.4331i	0.635888	−	0.757822i	0.983715	+	0.179737i	$0.0575246\pi$
$728$		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	0.0548959	−	0.998492i	$-0.482517\pi$
$739$	25.7455	−	14.8642i	0.947063	−	0.546787i	0.892167	+	0.451705i	$0.149184\pi$
$740$		0			0
$741$	2.75241	+	15.6443i	0.101112	+	0.574709i
$742$		0			0
$743$	−25.0772	+	21.0423i	−0.919993	+	0.771966i	−0.973994	−	0.226575i	$-0.927247\pi$
$743$	−25.0772	+	21.0423i	−0.919993	+	0.771966i	0.0540008	+	0.998541i	$0.482803\pi$
$744$		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	$-0.630504\pi$
$751$	13.5997	−	37.3649i	0.496261	−	1.36347i	0.894862	−	0.446342i	$-0.147274\pi$
$752$		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	−0.980784	−	0.195096i	$-0.937498\pi$
$787$	−51.4976	+	9.08042i	−1.83569	+	0.323682i	−0.854909	+	0.518778i	$0.826387\pi$
$788$		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	$0.203345\pi$
$811$			33.9604i			1.19251i	−0.802795	+	0.596255i	$0.796655\pi$
$812$		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	0.953258	−	0.302157i	$-0.0977067\pi$
$823$	14.0617	+	16.7581i	0.490160	+	0.584150i	−0.463098	+	0.886307i	$0.653262\pi$
$824$		0			0
$825$	−8.31830	+	22.8274i	−0.289606	+	0.794748i
$826$		0			0
$827$	−5.37603	−	9.31155i	−0.186943	−	0.323794i	0.757287	−	0.653083i	$-0.226525\pi$
$827$	−5.37603	−	9.31155i	−0.186943	−	0.323794i	−0.944229	+	0.329288i	$0.893191\pi$
$828$		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	−0.0862514	−	0.996273i	$-0.527489\pi$
$839$	−31.3513	−	26.3069i	−1.08237	−	0.908213i	−0.996115	+	0.0880600i	$0.971933\pi$
$840$		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	−0.820007	−	0.572354i	$-0.806030\pi$
$859$	5.15999	−	14.1770i	0.176057	−	0.483712i	0.996064	+	0.0886420i	$0.0282527\pi$
$860$		0			0
$861$	−7.94938	+	4.58556i	−0.270914	+	0.156276i
$862$		0			0
$863$	−23.7324			−0.807860			−0.403930	−	0.914790i	$-0.632356\pi$
$863$	−23.7324			−0.807860			−0.403930	+	0.914790i	$0.632356\pi$
$864$		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	0.967871	−	0.251449i	$-0.0809070\pi$
$883$	36.6700	+	21.1715i	1.23404	+	0.712476i	0.266174	+	0.963925i	$0.414240\pi$
$884$		0			0
$885$	34.7158	+	29.1524i	1.16696	+	0.979948i
$886$		0			0
$887$	−0.607035	−	3.44267i	−0.0203822	−	0.115593i	0.972919	−	0.231146i	$-0.0742474\pi$
$887$	−0.607035	−	3.44267i	−0.0203822	−	0.115593i	−0.993301	+	0.115552i	$0.963136\pi$
$888$		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	0.994943	−	0.100443i	$-0.0320261\pi$
$907$	5.06585	+	13.9183i	0.168209	+	0.462150i	−0.826734	+	0.562593i	$0.809804\pi$
$908$		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	$0.342284\pi$
$911$	−8.21622	+	46.5965i	−0.272215	+	1.54381i	−0.747670	+	0.664070i	$0.768827\pi$
$912$		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	$0.159515\pi$
$919$			29.1278i			0.960838i	−0.877039	+	0.480419i	$0.840485\pi$
$920$		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	0.0604179	−	0.998173i	$-0.480757\pi$
$947$	−28.0684	−	23.5522i	−0.912099	−	0.765342i	−0.972517	+	0.232831i	$0.925201\pi$
$948$		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	$-0.725042\pi$
$967$	10.4720	−	28.7717i	0.336758	−	0.925236i	0.986308	−	0.164916i	$-0.0527354\pi$
$968$		0			0
$969$	−0.00876212	+	23.1216i	−0.000281480	+	0.742771i
$970$		0			0
$971$	−20.2632			−0.650278			−0.325139	−	0.945666i	$-0.605411\pi$
$971$	−20.2632			−0.650278			−0.325139	+	0.945666i	$0.605411\pi$
$972$		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	0.316960	−	0.948439i	$-0.397338\pi$
$983$	36.6643	−	13.3447i	1.16941	−	0.425631i	0.852450	+	0.522808i	$0.175116\pi$
$984$		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	−0.139570	−	0.990212i	$-0.544572\pi$
$991$	−33.5863	−	19.3911i	−1.06690	−	0.615977i	−0.927334	+	0.374235i	$0.877905\pi$
$992$		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.767.18	yes	216
4.3	odd	2	inner	864.2.bi.a.767.19	yes	216
27.5	odd	18	inner	864.2.bi.a.383.19	yes	216
108.59	even	18	inner	864.2.bi.a.383.18	✓	216

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.bi (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.000656376 + 1.73205i) q^{3} +(1.14458 - 3.14471i) q^{5} +(-0.868740 - 0.153182i) q^{7} +(-3.00000 - 0.00227375i) q^{9} +O(q^{10})\)	\(q+(-0.000656376 + 1.73205i) q^{3} +(1.14458 - 3.14471i) q^{5} +(-0.868740 - 0.153182i) q^{7} +(-3.00000 - 0.00227375i) q^{9} +(-2.12626 + 0.773894i) q^{11} +(2.22748 - 1.86908i) q^{13} +(5.44605 + 1.98454i) q^{15} +(3.66548 - 2.11626i) q^{17} +(2.73141 + 1.57698i) q^{19} +(0.265890 - 1.50460i) q^{21} +(-0.991104 - 5.62083i) q^{23} +(-4.74891 - 3.98481i) q^{25} +(0.00590738 - 5.19615i) q^{27} +(3.68903 - 4.39642i) q^{29} +(6.00083 - 1.05811i) q^{31} +(-1.33903 - 3.68329i) q^{33} +(-1.47606 + 2.55661i) q^{35} +(1.04289 + 1.80634i) q^{37} +(3.23587 + 3.85933i) q^{39} +(-3.86079 - 4.60111i) q^{41} +(-1.42901 - 3.92618i) q^{43} +(-3.44089 + 9.43152i) q^{45} +(1.42488 - 8.08089i) q^{47} +(-5.84660 - 2.12799i) q^{49} +(3.66307 + 6.35018i) q^{51} +9.10008i q^{53} +7.57224i q^{55} +(-2.73321 + 4.72991i) q^{57} +(7.34922 + 2.67490i) q^{59} +(-1.35378 + 7.67767i) q^{61} +(2.60587 + 0.461522i) q^{63} +(-3.32817 - 9.14408i) q^{65} +(2.03294 + 2.42277i) q^{67} +(9.73621 - 1.71295i) q^{69} +(-5.53273 - 9.58297i) q^{71} +(7.03972 - 12.1932i) q^{73} +(6.90501 - 8.22274i) q^{75} +(1.96571 - 0.346608i) q^{77} +(-5.52652 + 6.58625i) q^{79} +(8.99999 + 0.0136425i) q^{81} +(9.67557 + 8.11877i) q^{83} +(-2.45960 - 13.9491i) q^{85} +(7.61240 + 6.39248i) q^{87} +(11.7949 + 6.80981i) q^{89} +(-2.22141 + 1.28253i) q^{91} +(1.82876 + 10.3944i) q^{93} +(8.08547 - 6.78452i) q^{95} +(-10.8609 + 3.95304i) q^{97} +(6.38053 - 2.31685i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q+O(q^{10}) \) 216 * 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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