LMFDB - Embedded newform 735.2.y.e.128.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [735,2,Mod(128,735)] 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("735.128"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(735, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 9, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 735 = 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	735.y (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [32,-4,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$5.86900454856$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			128.3
Character	$\chi$	$=$	735.128
Dual form			735.2.y.e.557.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.632011 + 0.169347i) q^{2} +(-1.72286 + 0.178197i) q^{3} +(-1.36129 + 0.785942i) q^{4} +(0.893095 + 2.04997i) q^{5} +(1.05869 - 0.404383i) q^{6} +(1.65258 - 1.65258i) q^{8} +(2.93649 - 0.614017i) q^{9} +(-0.911602 - 1.14436i) q^{10} +(-0.139773 + 0.0806980i) q^{11} +(2.20526 - 1.59665i) q^{12} +(4.65555 + 4.65555i) q^{13} +(-1.90398 - 3.37267i) q^{15} +(0.807294 - 1.39827i) q^{16} +(1.18329 - 4.41610i) q^{17} +(-1.75191 + 0.885351i) q^{18} +(3.11497 + 1.79843i) q^{19} +(-2.82692 - 2.08869i) q^{20} +(0.0746721 - 0.0746721i) q^{22} +(-0.619573 - 2.31228i) q^{23} +(-2.55268 + 3.14165i) q^{24} +(-3.40476 + 3.66164i) q^{25} +(-3.73076 - 2.15395i) q^{26} +(-4.94975 + 1.58114i) q^{27} +2.00000 q^{29} +(1.77448 + 1.80913i) q^{30} +(3.73115 + 6.46254i) q^{31} +(-1.48320 + 5.53538i) q^{32} +(0.226429 - 0.163938i) q^{33} +2.99141i q^{34} +(-3.51484 + 3.14377i) q^{36} +(-0.513548 - 1.91659i) q^{37} +(-2.27325 - 0.609116i) q^{38} +(-8.85046 - 7.19125i) q^{39} +(4.86366 + 1.91183i) q^{40} +12.0388i q^{41} +(-5.56631 - 5.56631i) q^{43} +(0.126848 - 0.219707i) q^{44} +(3.88128 + 5.47135i) q^{45} +(0.783154 + 1.35646i) q^{46} +(-5.87394 + 1.57392i) q^{47} +(-1.14169 + 2.55289i) q^{48} +(1.53176 - 2.89078i) q^{50} +(-1.25171 + 7.81918i) q^{51} +(-9.99654 - 2.67857i) q^{52} +(3.80695 + 1.02007i) q^{53} +(2.86053 - 1.83752i) q^{54} +(-0.290259 - 0.214460i) q^{55} +(-5.68713 - 2.54336i) q^{57} +(-1.26402 + 0.338694i) q^{58} +(-1.24335 - 2.15354i) q^{59} +(5.24259 + 3.09477i) q^{60} +(-0.997366 + 1.72749i) q^{61} +(-3.45254 - 3.45254i) q^{62} -0.520416i q^{64} +(-5.38589 + 13.7016i) q^{65} +(-0.115343 + 0.141956i) q^{66} +(-2.52804 - 0.677387i) q^{67} +(1.86000 + 6.94160i) q^{68} +(1.47948 + 3.87333i) q^{69} +9.39746i q^{71} +(3.83808 - 5.86751i) q^{72} +(-1.00634 + 3.75571i) q^{73} +(0.649136 + 1.12434i) q^{74} +(5.21344 - 6.91521i) q^{75} -5.65384 q^{76} +(6.81140 + 3.04615i) q^{78} +(4.68478 + 2.70476i) q^{79} +(3.58741 + 0.406138i) q^{80} +(8.24597 - 3.60611i) q^{81} +(-2.03873 - 7.60864i) q^{82} +(6.75913 - 6.75913i) q^{83} +(10.1097 - 1.51829i) q^{85} +(4.46060 + 2.57533i) q^{86} +(-3.44572 + 0.356394i) q^{87} +(-0.0976263 + 0.364346i) q^{88} +(-5.43562 + 9.41477i) q^{89} +(-3.37957 - 2.80067i) q^{90} +(2.66074 + 2.66074i) q^{92} +(-7.57985 - 10.4692i) q^{93} +(3.44585 - 1.98946i) q^{94} +(-0.904763 + 7.99176i) q^{95} +(1.56896 - 9.80098i) q^{96} +(9.70695 - 9.70695i) q^{97} +(-0.360892 + 0.322792i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 4 q^{2} - 56 q^{8} + 32 q^{9} + 8 q^{15} + 48 q^{16} + 28 q^{18} + 16 q^{22} + 16 q^{23} - 8 q^{25} + 64 q^{29} - 64 q^{30} + 52 q^{32} - 80 q^{36} + 24 q^{37} - 8 q^{39} + 48 q^{43} - 8 q^{44} - 88 q^{46}+ \cdots - 80 q^{99}+O(q^{100}) $ 32 * q - 4 * q^2 - 56 * q^8 + 32 * q^9 + 8 * q^15 + 48 * q^16 + 28 * q^18 + 16 * q^22 + 16 * q^23 - 8 * q^25 + 64 * q^29 - 64 * q^30 + 52 * q^32 - 80 * q^36 + 24 * q^37 - 8 * q^39 + 48 * q^43 - 8 * q^44 - 88 * q^46 - 104 * q^50 - 40 * q^51 - 8 * q^53 - 8 * q^58 - 28 * q^60 - 112 * q^65 - 16 * q^67 + 4 * q^72 - 8 * q^74 + 16 * q^81 + 48 * q^85 + 80 * q^88 + 160 * q^92 - 16 * q^93 + 72 * q^95 - 80 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/735\mathbb{Z}\right)^\times$.

$n$	$346$	$442$	$491$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	−0.632011	+	0.169347i	−0.446899	+	0.119746i	−0.475248	−	0.879852i	$-0.657642\pi$
$2$	−0.632011	+	0.169347i	−0.446899	+	0.119746i	0.0283490	+	0.999598i	$0.490975\pi$
$3$	−1.72286	+	0.178197i	−0.994694	+	0.102882i
$3$	−1.72286	+	0.178197i	−0.994694	+	0.102882i
$4$	−1.36129	+	0.785942i	−0.680646	+	0.392971i
$5$	0.893095	+	2.04997i	0.399404	+	0.916775i
$5$	0.893095	+	2.04997i	0.399404	+	0.916775i
$6$	1.05869	−	0.404383i	0.432208	−	0.165089i
$7$		0			0
$7$		0			0
$8$	1.65258	−	1.65258i	0.584276	−	0.584276i
$9$	2.93649	−	0.614017i	0.978831	−	0.204672i
$10$	−0.911602	−	1.14436i	−0.288274	−	0.361879i
$11$	−0.139773	+	0.0806980i	−0.0421431	+	0.0243313i	−0.520924	−	0.853603i	$-0.674412\pi$
$11$	−0.139773	+	0.0806980i	−0.0421431	+	0.0243313i	0.478780	+	0.877935i	$0.341079\pi$
$12$	2.20526	−	1.59665i	0.636604	−	0.460912i
$13$	4.65555	+	4.65555i	1.29122	+	1.29122i	0.934035	+	0.357181i	$0.116262\pi$
$13$	4.65555	+	4.65555i	1.29122	+	1.29122i	0.357181	+	0.934035i	$0.383738\pi$
$14$		0			0
$15$	−1.90398	−	3.37267i	−0.491605	−	0.870819i
$16$	0.807294	−	1.39827i	0.201823	−	0.349569i
$17$	1.18329	−	4.41610i	0.286990	−	1.07106i	−0.660383	−	0.750929i	$-0.729606\pi$
$17$	1.18329	−	4.41610i	0.286990	−	1.07106i	0.947373	−	0.320133i	$-0.103727\pi$
$18$	−1.75191	+	0.885351i	−0.412930	+	0.208679i
$19$	3.11497	+	1.79843i	0.714623	+	0.412588i	0.812770	−	0.582584i	$-0.197958\pi$
$19$	3.11497	+	1.79843i	0.714623	+	0.412588i	−0.0981474	+	0.995172i	$0.531292\pi$
$20$	−2.82692	−	2.08869i	−0.632119	−	0.467045i
$21$		0			0
$22$	0.0746721	−	0.0746721i	0.0159201	−	0.0159201i
$23$	−0.619573	−	2.31228i	−0.129190	−	0.482144i	0.870764	−	0.491701i	$-0.163625\pi$
$23$	−0.619573	−	2.31228i	−0.129190	−	0.482144i	−0.999954	+	0.00955698i	$0.996958\pi$
$24$	−2.55268	+	3.14165i	−0.521064	+	0.641287i
$25$	−3.40476	+	3.66164i	−0.680953	+	0.732328i
$26$	−3.73076	−	2.15395i	−0.731662	−	0.422425i
$27$	−4.94975	+	1.58114i	−0.952579	+	0.304290i
$28$		0			0
$29$	2.00000			0.371391			0.185695	−	0.982607i	$-0.440546\pi$
$29$	2.00000			0.371391			0.185695	+	0.982607i	$0.440546\pi$
$30$	1.77448	+	1.80913i	0.323975	+	0.330300i
$31$	3.73115	+	6.46254i	0.670134	+	1.16071i	0.977866	+	0.209233i	$0.0670968\pi$
$31$	3.73115	+	6.46254i	0.670134	+	1.16071i	−0.307732	+	0.951473i	$0.599570\pi$
$32$	−1.48320	+	5.53538i	−0.262195	+	0.978525i
$33$	0.226429	−	0.163938i	0.0394162	−	0.0285380i
$34$			2.99141i			0.513023i
$35$		0			0
$36$	−3.51484	+	3.14377i	−0.585807	+	0.523961i
$37$	−0.513548	−	1.91659i	−0.0844268	−	0.315085i	0.910778	−	0.412896i	$-0.135483\pi$
$37$	−0.513548	−	1.91659i	−0.0844268	−	0.315085i	−0.995205	+	0.0978108i	$0.968816\pi$
$38$	−2.27325	−	0.609116i	−0.368770	−	0.0988117i
$39$	−8.85046	−	7.19125i	−1.41721	−	1.15152i
$40$	4.86366	+	1.91183i	0.769012	+	0.302287i
$41$			12.0388i			1.88014i	0.340977	+	0.940072i	$0.389242\pi$
$41$			12.0388i			1.88014i	−0.340977	+	0.940072i	$0.610758\pi$
$42$		0			0
$43$	−5.56631	−	5.56631i	−0.848854	−	0.848854i	0.141136	−	0.989990i	$-0.454924\pi$
$43$	−5.56631	−	5.56631i	−0.848854	−	0.848854i	−0.989990	+	0.141136i	$0.954924\pi$
$44$	0.126848	−	0.219707i	0.0191230	−	0.0331221i
$45$	3.88128	+	5.47135i	0.578587	+	0.815620i
$46$	0.783154	+	1.35646i	0.115470	+	0.200000i
$47$	−5.87394	+	1.57392i	−0.856802	+	0.229579i	−0.660372	−	0.750939i	$-0.729601\pi$
$47$	−5.87394	+	1.57392i	−0.856802	+	0.229579i	−0.196430	+	0.980518i	$0.562935\pi$
$48$	−1.14169	+	2.55289i	−0.164788	+	0.368478i
$49$		0			0
$50$	1.53176	−	2.89078i	0.216624	−	0.408818i
$51$	−1.25171	+	7.81918i	−0.175274	+	1.09490i
$52$	−9.99654	−	2.67857i	−1.38627	−	0.371450i
$53$	3.80695	+	1.02007i	0.522924	+	0.140117i	0.510619	−	0.859807i	$-0.329416\pi$
$53$	3.80695	+	1.02007i	0.522924	+	0.140117i	0.0123054	+	0.999924i	$0.496083\pi$
$54$	2.86053	−	1.83752i	0.389269	−	0.250055i
$55$	−0.290259	−	0.214460i	−0.0391385	−	0.0289177i
$56$		0			0
$57$	−5.68713	−	2.54336i	−0.753279	−	0.336877i
$58$	−1.26402	+	0.338694i	−0.165974	+	0.0444726i
$59$	−1.24335	−	2.15354i	−0.161870	−	0.280367i	0.773669	−	0.633589i	$-0.218419\pi$
$59$	−1.24335	−	2.15354i	−0.161870	−	0.280367i	−0.935539	+	0.353223i	$0.885086\pi$
$60$	5.24259	+	3.09477i	0.676815	+	0.399533i
$61$	−0.997366	+	1.72749i	−0.127700	+	0.221182i	−0.922785	−	0.385315i	$-0.874093\pi$
$61$	−0.997366	+	1.72749i	−0.127700	+	0.221182i	0.795085	+	0.606498i	$0.207426\pi$
$62$	−3.45254	−	3.45254i	−0.438473	−	0.438473i
$63$		0			0
$64$		−	0.520416i		−	0.0650520i
$65$	−5.38589	+	13.7016i	−0.668037	+	1.69947i
$66$	−0.115343	+	0.141956i	−0.0141978	+	0.0174736i
$67$	−2.52804	−	0.677387i	−0.308850	−	0.0827560i	0.101065	−	0.994880i	$-0.467775\pi$
$67$	−2.52804	−	0.677387i	−0.308850	−	0.0827560i	−0.409915	+	0.912124i	$0.634442\pi$
$68$	1.86000	+	6.94160i	0.225558	+	0.841793i
$69$	1.47948	+	3.87333i	0.178108	+	0.466294i
$70$		0			0
$71$			9.39746i			1.11527i	0.830085	+	0.557637i	$0.188292\pi$
$71$			9.39746i			1.11527i	−0.830085	+	0.557637i	$0.811708\pi$
$72$	3.83808	−	5.86751i	0.452322	−	0.691492i
$73$	−1.00634	+	3.75571i	−0.117783	+	0.439573i	−0.999480	−	0.0322434i	$-0.989735\pi$
$73$	−1.00634	+	3.75571i	−0.117783	+	0.439573i	0.881697	+	0.471816i	$0.156401\pi$
$74$	0.649136	+	1.12434i	0.0754605	+	0.130701i
$75$	5.21344	−	6.91521i	0.601996	−	0.798499i
$76$	−5.65384			−0.648540
$77$		0			0
$78$	6.81140	+	3.04615i	0.771239	+	0.344909i
$79$	4.68478	+	2.70476i	0.527079	+	0.304309i	0.739826	−	0.672798i	$-0.234908\pi$
$79$	4.68478	+	2.70476i	0.527079	+	0.304309i	−0.212747	+	0.977107i	$0.568241\pi$
$80$	3.58741	+	0.406138i	0.401085	+	0.0454076i
$81$	8.24597	−	3.60611i	0.916219	−	0.400679i
$82$	−2.03873	−	7.60864i	−0.225140	−	0.840234i
$83$	6.75913	−	6.75913i	0.741911	−	0.741911i	−0.231034	−	0.972946i	$-0.574211\pi$
$83$	6.75913	−	6.75913i	0.741911	−	0.741911i	0.972946	+	0.231034i	$0.0742109\pi$
$84$		0			0
$85$	10.1097	−	1.51829i	1.09655	−	0.164681i
$86$	4.46060	+	2.57533i	0.480999	+	0.277705i
$87$	−3.44572	+	0.356394i	−0.369420	+	0.0382094i
$88$	−0.0976263	+	0.364346i	−0.0104070	+	0.0388394i
$89$	−5.43562	+	9.41477i	−0.576175	+	0.997964i	0.419738	+	0.907645i	$0.362122\pi$
$89$	−5.43562	+	9.41477i	−0.576175	+	0.997964i	−0.995913	+	0.0903187i	$0.971211\pi$
$90$	−3.37957	−	2.80067i	−0.356238	−	0.295216i
$91$		0			0
$92$	2.66074	+	2.66074i	0.277401	+	0.277401i
$93$	−7.57985	−	10.4692i	−0.785994	−	1.08560i
$94$	3.44585	−	1.98946i	0.355413	−	0.205198i
$95$	−0.904763	+	7.99176i	−0.0928267	+	0.819938i
$96$	1.56896	−	9.80098i	0.160131	−	1.00031i
$97$	9.70695	−	9.70695i	0.985592	−	0.985592i	−0.0143059	−	0.999898i	$-0.504554\pi$
$97$	9.70695	−	9.70695i	0.985592	−	0.985592i	0.999898	+	0.0143059i	$0.00455388\pi$
$98$		0			0
$99$	−0.360892	+	0.322792i	−0.0362710	+	0.0324418i
$100$	1.75704	−	7.66050i	0.175704	−	0.766050i
$101$	−4.02217	+	2.32220i	−0.400221	+	0.231068i	−0.686579	−	0.727055i	$-0.740889\pi$
$101$	−4.02217	+	2.32220i	−0.400221	+	0.231068i	0.286358	+	0.958123i	$0.407555\pi$
$102$	−0.533060	−	5.15378i	−0.0527808	−	0.510300i
$103$	−9.60004	+	2.57232i	−0.945920	+	0.253459i	−0.698630	−	0.715483i	$-0.746207\pi$
$103$	−9.60004	+	2.57232i	−0.945920	+	0.253459i	−0.247290	+	0.968941i	$0.579540\pi$
$104$	15.3873			1.50885
$105$		0			0
$106$	−2.57878			−0.250473
$107$	−13.9963	+	3.75029i	−1.35307	+	0.362554i	−0.861268	−	0.508151i	$-0.830329\pi$
$107$	−13.9963	+	3.75029i	−1.35307	+	0.362554i	−0.491804	+	0.870706i	$0.663662\pi$
$108$	5.49537	−	6.04261i	0.528792	−	0.581450i
$109$	7.99867	−	4.61803i	0.766134	−	0.442327i	−0.0653600	−	0.997862i	$-0.520820\pi$
$109$	7.99867	−	4.61803i	0.766134	−	0.442327i	0.831494	+	0.555534i	$0.187486\pi$
$110$	0.219765	+	0.0863863i	0.0209538	+	0.00823661i
$111$	1.22630	+	3.21050i	0.116395	+	0.304727i
$112$		0			0
$113$	4.87918	−	4.87918i	0.458994	−	0.458994i	−0.439331	−	0.898325i	$-0.644784\pi$
$113$	4.87918	−	4.87918i	0.458994	−	0.458994i	0.898325	+	0.439331i	$0.144784\pi$
$114$	4.02504	+	0.644335i	0.376979	+	0.0603475i
$115$	4.18677	−	3.33519i	0.390418	−	0.311008i
$116$	−2.72258	+	1.57188i	−0.252785	+	0.145946i
$117$	16.5296	+	10.8124i	1.52816	+	0.999606i
$118$	1.15050	+	1.15050i	0.105912	+	0.105912i
$119$		0			0
$120$	−8.72008	−	2.42713i	−0.796031	−	0.221566i
$121$	−5.48698	+	9.50372i	−0.498816	+	0.863975i
$122$	0.337801	−	1.26069i	0.0305831	−	0.114138i
$123$	−2.14528	−	20.7411i	−0.193433	−	1.87017i
$124$	−10.1584	−	5.86493i	−0.912248	−	0.526687i
$125$	−10.5470	−	3.70948i	−0.943355	−	0.331786i
$126$		0			0
$127$	−0.192048	+	0.192048i	−0.0170415	+	0.0170415i	−0.715576	−	0.698535i	$-0.753836\pi$
$127$	−0.192048	+	0.192048i	−0.0170415	+	0.0170415i	0.698535	+	0.715576i	$0.253836\pi$
$128$	−2.87827	−	10.7418i	−0.254405	−	0.949454i
$129$	10.5819	+	8.59807i	0.931682	+	0.757018i
$130$	1.08362	−	9.57163i	0.0950399	−	0.839487i
$131$	−11.9048	−	6.87326i	−1.04013	−	0.600519i	−0.120260	−	0.992742i	$-0.538373\pi$
$131$	−11.9048	−	6.87326i	−1.04013	−	0.600519i	−0.919870	+	0.392223i	$0.871706\pi$
$132$	−0.179390	+	0.401128i	−0.0156139	+	0.0349137i
$133$		0			0
$134$	1.71246			0.147934
$135$	−7.66188	−	8.73473i	−0.659430	−	0.751766i
$136$	−5.34248	−	9.25345i	−0.458114	−	0.793477i
$137$	−2.04989	+	7.65030i	−0.175134	+	0.653609i	0.821395	+	0.570360i	$0.193196\pi$
$137$	−2.04989	+	7.65030i	−0.175134	+	0.653609i	−0.996529	+	0.0832489i	$0.973470\pi$
$138$	−1.59098	−	2.19744i	−0.135433	−	0.187058i
$139$		−	16.6862i		−	1.41531i	−0.706560	−	0.707653i	$-0.749754\pi$
$139$		−	16.6862i		−	1.41531i	0.706560	−	0.707653i	$-0.250246\pi$
$140$		0			0
$141$	9.83950	−	3.75836i	0.828636	−	0.316511i
$142$	−1.59143	−	5.93930i	−0.133550	−	0.498415i
$143$	−1.02641	−	0.275026i	−0.0858329	−	0.0229989i
$144$	1.51205	−	4.60171i	0.126004	−	0.383476i
$145$	1.78619	+	4.09994i	0.148335	+	0.340482i
$146$		−	2.54407i		−	0.210549i
$147$		0			0
$148$	2.20542	+	2.20542i	0.181284	+	0.181284i
$149$	7.80795	−	13.5238i	0.639652	−	1.10791i	−0.345857	−	0.938287i	$-0.612412\pi$
$149$	7.80795	−	13.5238i	0.639652	−	1.10791i	0.985509	−	0.169623i	$-0.0542550\pi$
$150$	−2.12388	+	5.25336i	−0.173414	+	0.428935i
$151$	−3.63753	−	6.30039i	−0.296018	−	0.512719i	0.679203	−	0.733951i	$-0.262326\pi$
$151$	−3.63753	−	6.30039i	−0.296018	−	0.512719i	−0.975221	+	0.221232i	$0.928992\pi$
$152$	8.11979	−	2.17569i	0.658602	−	0.176472i
$153$	0.763163	−	13.6944i	0.0616981	−	1.10713i
$154$		0			0
$155$	−9.91575	+	13.4204i	−0.796452	+	1.07795i
$156$	17.7000	+	2.83344i	1.41713	+	0.226857i
$157$	15.2876	+	4.09630i	1.22008	+	0.326921i	0.810711	−	0.585447i	$-0.199081\pi$
$157$	15.2876	+	4.09630i	1.22008	+	0.326921i	0.409373	+	0.912367i	$0.365747\pi$
$158$	−3.41887	−	0.916084i	−0.271991	−	0.0728797i
$159$	−6.74061	−	1.07905i	−0.534565	−	0.0855741i
$160$	−12.6720	+	1.90310i	−1.00181	+	0.150453i
$161$		0			0
$162$	−4.60086	+	3.67553i	−0.361477	+	0.288777i
$163$	13.9649	−	3.74189i	1.09382	−	0.293088i	0.333573	−	0.942724i	$-0.391746\pi$
$163$	13.9649	−	3.74189i	1.09382	−	0.293088i	0.760245	+	0.649636i	$0.225079\pi$
$164$	−9.46179	−	16.3883i	−0.738842	−	1.27971i
$165$	0.538292	+	0.317761i	0.0419059	+	0.0247376i
$166$	−3.12721	+	5.41648i	−0.242718	+	0.420401i
$167$	2.52703	+	2.52703i	0.195547	+	0.195547i	0.798088	−	0.602541i	$-0.205845\pi$
$167$	2.52703	+	2.52703i	0.195547	+	0.195547i	−0.602541	+	0.798088i	$0.705845\pi$
$168$		0			0
$169$			30.3482i			2.33448i
$170$	−6.13230	+	2.67161i	−0.470326	+	0.204903i
$171$	10.2513	+	3.36843i	0.783940	+	0.257590i
$172$	11.9522	+	3.20257i	0.911344	+	0.244194i
$173$	0.527588	+	1.96899i	0.0401118	+	0.149699i	0.983077	−	0.183191i	$-0.0586427\pi$
$173$	0.527588	+	1.96899i	0.0401118	+	0.149699i	−0.942966	+	0.332890i	$0.891976\pi$
$174$	2.11738	−	0.808766i	0.160518	−	0.0613124i
$175$		0			0
$176$			0.260588i			0.0196426i
$177$	2.52586	+	3.48868i	0.189856	+	0.262225i
$178$	1.84101	−	6.87074i	0.137990	−	0.514984i
$179$	10.0466	+	17.4012i	0.750918	+	1.30063i	0.947378	+	0.320117i	$0.103722\pi$
$179$	10.0466	+	17.4012i	0.750918	+	1.30063i	−0.196460	+	0.980512i	$0.562945\pi$
$180$	−9.58372	−	4.39764i	−0.714328	−	0.327780i
$181$	−16.6805			−1.23986			−0.619928	−	0.784659i	$-0.712838\pi$
$181$	−16.6805			−1.23986			−0.619928	+	0.784659i	$0.712838\pi$
$182$		0			0
$183$	1.41049	−	3.15395i	0.104266	−	0.233147i
$184$	−4.84513	−	2.79734i	−0.357188	−	0.206222i
$185$	3.47030	−	2.76445i	0.255142	−	0.203247i
$186$	6.56347	+	5.33300i	0.481257	+	0.391035i
$187$	0.190978	+	0.712741i	0.0139657	+	0.0521208i
$188$	6.75913	−	6.75913i	0.492961	−	0.492961i
$189$		0			0
$190$	−0.781560	−	5.20410i	−0.0567003	−	0.377545i
$191$	18.7304	+	10.8140i	1.35528	+	0.782472i	0.988984	−	0.148026i	$-0.0472918\pi$
$191$	18.7304	+	10.8140i	1.35528	+	0.782472i	0.366298	+	0.930498i	$0.380625\pi$
$192$	0.0927365	+	0.896603i	0.00669268	+	0.0647068i
$193$	−1.50265	+	5.60798i	−0.108163	+	0.403671i	−0.998685	−	0.0512701i	$-0.983673\pi$
$193$	−1.50265	+	5.60798i	−0.108163	+	0.403671i	0.890521	+	0.454941i	$0.150340\pi$
$194$	−4.49106	+	7.77874i	−0.322439	+	0.558481i
$195$	6.83755	−	24.5656i	0.489647	−	1.75918i
$196$		0			0
$197$	−9.12082	−	9.12082i	−0.649832	−	0.649832i	0.303121	−	0.952952i	$-0.401972\pi$
$197$	−9.12082	−	9.12082i	−0.649832	−	0.649832i	−0.952952	+	0.303121i	$0.901972\pi$
$198$	0.173424	−	0.265124i	0.0123247	−	0.0188415i
$199$	0.552436	−	0.318949i	0.0391612	−	0.0226097i	−0.480292	−	0.877109i	$-0.659469\pi$
$199$	0.552436	−	0.318949i	0.0391612	−	0.0226097i	0.519453	+	0.854499i	$0.326136\pi$
$200$	0.424507	+	11.6778i	0.0300172	+	0.825746i
$201$	4.47617	+	0.716553i	0.315725	+	0.0505418i
$202$	2.14880	−	2.14880i	0.151189	−	0.151189i
$203$		0			0
$204$	−4.44148	−	11.6280i	−0.310966	−	0.814120i
$205$	−24.6792	+	10.7518i	−1.72367	+	0.750937i
$206$	5.63172	−	3.25147i	0.392380	−	0.226541i
$207$	−3.23915	−	6.40956i	−0.225137	−	0.445495i
$208$	10.2681	−	2.75134i	0.711966	−	0.190771i
$209$	−0.580518			−0.0401553
$210$		0			0
$211$	−6.69574			−0.460953			−0.230477	−	0.973078i	$-0.574029\pi$
$211$	−6.69574			−0.460953			−0.230477	+	0.973078i	$0.574029\pi$
$212$	−5.98408	+	1.60343i	−0.410988	+	0.110124i
$213$	−1.67460	−	16.1905i	−0.114742	−	1.10936i
$214$	8.21070	−	4.74045i	0.561272	−	0.324051i
$215$	6.43953	−	16.3820i	0.439172	−	1.11724i
$216$	−5.56690	+	10.7928i	−0.378780	+	0.734359i
$217$		0			0
$218$	−4.27320	+	4.27320i	−0.289417	+	0.289417i
$219$	1.06453	−	6.64989i	0.0719340	−	0.449358i
$220$	0.563680	+	0.0638153i	0.0380033	+	0.00430242i
$221$	26.0682	−	15.0505i	1.75354	−	1.01241i
$222$	−1.31872	−	1.82140i	−0.0885069	−	0.122244i
$223$	0.382073	+	0.382073i	0.0255855	+	0.0255855i	0.719784	−	0.694198i	$-0.244241\pi$
$223$	0.382073	+	0.382073i	0.0255855	+	0.0255855i	−0.694198	+	0.719784i	$0.744241\pi$
$224$		0			0
$225$	−7.74975	+	12.8430i	−0.516650	+	0.856197i
$226$	−2.25742	+	3.90997i	−0.150161	+	0.260087i
$227$	−4.57855	+	17.0874i	−0.303889	+	1.13413i	0.630008	+	0.776588i	$0.283051\pi$
$227$	−4.57855	+	17.0874i	−0.303889	+	1.13413i	−0.933897	+	0.357541i	$0.883615\pi$
$228$	9.74078	−	1.00750i	0.645099	−	0.0667232i
$229$	2.00978	+	1.16035i	0.132810	+	0.0766780i	0.564933	−	0.825137i	$-0.308902\pi$
$229$	2.00978	+	1.16035i	0.132810	+	0.0766780i	−0.432123	+	0.901815i	$0.642235\pi$
$230$	−2.08128	+	2.81689i	−0.137235	+	0.185740i
$231$		0			0
$232$	3.30516	−	3.30516i	0.216995	−	0.216995i
$233$	2.22018	+	8.28583i	0.145449	+	0.542823i	0.999735	+	0.0230197i	$0.00732805\pi$
$233$	2.22018	+	8.28583i	0.145449	+	0.542823i	−0.854286	+	0.519803i	$0.826005\pi$
$234$	−12.2779	−	4.03432i	−0.802631	−	0.263732i
$235$	−8.47247	−	10.6357i	−0.552683	−	0.693800i
$236$	3.38511	+	1.95440i	0.220352	+	0.127220i
$237$	−8.55320	−	3.82511i	−0.555590	−	0.248467i
$238$		0			0
$239$	21.5667			1.39503			0.697515	−	0.716570i	$-0.254289\pi$
$239$	21.5667			1.39503			0.697515	+	0.716570i	$0.254289\pi$
$240$	−6.25298	−	0.0604523i	−0.403628	−	0.00390218i
$241$	−3.24527	−	5.62098i	−0.209047	−	0.362079i	0.742368	−	0.669992i	$-0.233703\pi$
$241$	−3.24527	−	5.62098i	−0.209047	−	0.362079i	−0.951414	+	0.307913i	$0.900369\pi$
$242$	1.85840	−	6.93566i	0.119463	−	0.445841i
$243$	−13.5640	+	7.68223i	−0.870134	+	0.492815i
$244$		−	3.13549i		−	0.200729i
$245$		0			0
$246$	4.86828	+	12.7453i	0.310390	+	0.812613i
$247$	6.12922	+	22.8745i	0.389993	+	1.45547i
$248$	16.8459	+	4.51385i	1.06972	+	0.286630i
$249$	−10.4406	+	12.8495i	−0.661645	+	0.814304i
$250$	7.29402	+	0.558323i	0.461314	+	0.0353114i
$251$			25.3594i			1.60067i	0.599552	+	0.800336i	$0.295345\pi$
$251$			25.3594i			1.60067i	−0.599552	+	0.800336i	$0.704655\pi$
$252$		0			0
$253$	0.273196	+	0.273196i	0.0171757	+	0.0171757i
$254$	0.0888536	−	0.153899i	0.00557517	−	0.00965648i
$255$	−17.1470	+	4.41731i	−1.07379	+	0.276622i
$256$	4.15861	+	7.20292i	0.259913	+	0.450183i
$257$	−11.1381	+	2.98446i	−0.694778	+	0.186165i	−0.588890	−	0.808213i	$-0.700435\pi$
$257$	−11.1381	+	2.98446i	−0.694778	+	0.186165i	−0.105888	+	0.994378i	$0.533768\pi$
$258$	−8.14391	−	3.64207i	−0.507018	−	0.226745i
$259$		0			0
$260$	−3.43688	−	22.8848i	−0.213146	−	1.41926i
$261$	5.87298	−	1.22803i	0.363529	−	0.0760134i
$262$	8.68795	+	2.32793i	0.536743	+	0.143820i
$263$	−19.0359	−	5.10066i	−1.17380	−	0.314520i	−0.381338	−	0.924436i	$-0.624537\pi$
$263$	−19.0359	−	5.10066i	−1.17380	−	0.314520i	−0.792466	+	0.609916i	$0.791203\pi$
$264$	0.103271	−	0.645114i	0.00635589	−	0.0397040i
$265$	1.30885	+	8.71515i	0.0804023	+	0.535367i
$266$		0			0
$267$	7.68713	−	17.1889i	0.470445	−	1.05195i
$268$	3.97379	−	1.06477i	0.242738	−	0.0650414i
$269$	1.68918	+	2.92574i	0.102991	+	0.178386i	0.912916	−	0.408148i	$-0.133825\pi$
$269$	1.68918	+	2.92574i	0.102991	+	0.178386i	−0.809925	+	0.586534i	$0.800492\pi$
$270$	6.32159	+	4.22293i	0.384720	+	0.256999i
$271$	8.04393	−	13.9325i	0.488634	−	0.846339i	−0.511281	−	0.859414i	$-0.670829\pi$
$271$	8.04393	−	13.9325i	0.488634	−	0.846339i	0.999915	+	0.0130751i	$0.00416205\pi$
$272$	−5.21966	−	5.21966i	−0.316488	−	0.316488i
$273$		0			0
$274$		−	5.18221i		−	0.313069i
$275$	0.180407	−	0.786555i	0.0108790	−	0.0474311i
$276$	−5.05821	−	4.10994i	−0.304469	−	0.247389i
$277$	6.44170	+	1.72605i	0.387044	+	0.103708i	0.447094	−	0.894487i	$-0.352459\pi$
$277$	6.44170	+	1.72605i	0.387044	+	0.103708i	−0.0600492	+	0.998195i	$0.519126\pi$
$278$	2.82576	+	10.5459i	0.169478	+	0.632499i
$279$	14.9246	+	16.6862i	0.893512	+	0.998977i
$280$		0			0
$281$			12.5965i			0.751447i	0.926732	+	0.375723i	$0.122606\pi$
$281$			12.5965i			0.751447i	−0.926732	+	0.375723i	$0.877394\pi$
$282$	−5.58221	+	4.04161i	−0.332416	+	0.240674i
$283$	−4.72849	+	17.6470i	−0.281080	+	1.04900i	0.670577	+	0.741840i	$0.266047\pi$
$283$	−4.72849	+	17.6470i	−0.281080	+	1.04900i	−0.951657	+	0.307164i	$0.900620\pi$
$284$	−7.38586	−	12.7927i	−0.438270	−	0.759106i
$285$	0.134671	−	13.9299i	0.00797723	−	0.825137i
$286$	0.695278			0.0411127
$287$		0			0
$288$	−0.956589	+	17.1653i	−0.0563675	+	1.01147i
$289$	−3.37934	−	1.95106i	−0.198785	−	0.114768i
$290$	−1.82320	−	2.28872i	−0.107062	−	0.134398i
$291$	−14.9940	+	18.4535i	−0.878962	+	1.08176i
$292$	−1.58185	−	5.90355i	−0.0925708	−	0.345479i
$293$	−2.06389	+	2.06389i	−0.120574	+	0.120574i	−0.764819	−	0.644245i	$-0.777172\pi$
$293$	−2.06389	+	2.06389i	−0.120574	+	0.120574i	0.644245	+	0.764819i	$0.277172\pi$
$294$		0			0
$295$	3.30426	−	4.47214i	0.192382	−	0.260378i
$296$	−4.01600	−	2.31864i	−0.233425	−	0.134768i
$297$	0.564246	−	0.620435i	0.0327409	−	0.0360013i
$298$	−2.64450	+	9.86942i	−0.153192	+	0.571720i
$299$	7.88047	−	13.6494i	0.455739	−	0.789364i
$300$	−1.66205	+	13.5111i	−0.0959588	+	0.780062i
$301$		0			0
$302$	3.36591	+	3.36591i	0.193686	+	0.193686i
$303$	6.51583	−	4.71757i	0.374325	−	0.271017i
$304$	5.02939	−	2.90372i	0.288455	−	0.166540i
$305$	−4.43204	−	0.501760i	−0.253778	−	0.0287307i
$306$	1.83678	+	8.78425i	0.105001	+	0.502162i
$307$	0.640910	−	0.640910i	0.0365787	−	0.0365787i	−0.688581	−	0.725160i	$-0.741766\pi$
$307$	0.640910	−	0.640910i	0.0365787	−	0.0365787i	0.725160	+	0.688581i	$0.241766\pi$
$308$		0			0
$309$	16.0811	−	6.14245i	0.914825	−	0.349432i
$310$	3.99416	−	10.1610i	0.226853	−	0.577108i
$311$	18.0536	−	10.4233i	1.02373	−	0.591049i	0.108546	−	0.994091i	$-0.465381\pi$
$311$	18.0536	−	10.4233i	1.02373	−	0.591049i	0.915181	+	0.403042i	$0.132047\pi$
$312$	−26.5102	+	2.74198i	−1.50085	+	0.155234i
$313$	16.9346	−	4.53760i	0.957198	−	0.256481i	0.253784	−	0.967261i	$-0.418325\pi$
$313$	16.9346	−	4.53760i	0.957198	−	0.256481i	0.703414	+	0.710780i	$0.251658\pi$
$314$	−10.3556			−0.584402
$315$		0			0
$316$	−8.50313			−0.478339
$317$	−3.99061	+	1.06928i	−0.224135	+	0.0600567i	−0.369139	−	0.929374i	$-0.620347\pi$
$317$	−3.99061	+	1.06928i	−0.224135	+	0.0600567i	0.145004	+	0.989431i	$0.453681\pi$
$318$	4.44287	−	0.459530i	0.249144	−	0.0257692i
$319$	−0.279546	+	0.161396i	−0.0156516	+	0.00903644i
$320$	1.06684	−	0.464781i	0.0596380	−	0.0259820i
$321$	23.4453	−	8.95532i	1.30859	−	0.499837i
$322$		0			0
$323$	11.6280	−	11.6280i	0.646997	−	0.646997i
$324$	−8.39097	+	11.3898i	−0.466165	+	0.632768i
$325$	−32.8980	+	1.19589i	−1.82485	+	0.0663362i
$326$	−8.19231	+	4.72983i	−0.453730	+	0.261961i
$327$	−12.9577	+	9.38156i	−0.716561	+	0.518802i
$328$	19.8951	+	19.8951i	1.09852	+	1.09852i
$329$		0			0
$330$	−0.394018	−	0.109670i	−0.0216900	−	0.00603714i
$331$	8.74533	−	15.1474i	0.480687	−	0.832574i	−0.519068	−	0.854733i	$-0.673721\pi$
$331$	8.74533	−	15.1474i	0.480687	−	0.832574i	0.999754	+	0.0221591i	$0.00705403\pi$
$332$	−3.88886	+	14.5134i	−0.213429	+	0.796529i
$333$	−2.68485	−	5.31272i	−0.147129	−	0.291135i
$334$	−2.02505	−	1.16916i	−0.110806	−	0.0639738i
$335$	−0.869159	−	5.78739i	−0.0474872	−	0.316199i
$336$		0			0
$337$	−1.65213	+	1.65213i	−0.0899974	+	0.0899974i	−0.750672	−	0.660675i	$-0.770270\pi$
$337$	−1.65213	+	1.65213i	−0.0899974	+	0.0899974i	0.660675	+	0.750672i	$0.270270\pi$
$338$	−5.13937	−	19.1804i	−0.279545	−	1.04328i
$339$	−7.53668	+	9.27559i	−0.409337	+	0.503781i
$340$	−12.5689	+	10.0124i	−0.681646	+	0.543001i
$341$	−1.04303	−	0.602192i	−0.0564831	−	0.0326105i
$342$	−7.04939	−	0.392849i	−0.381188	−	0.0212429i
$343$		0			0
$344$	−18.3976			−0.991930
$345$	−6.61889	+	6.49214i	−0.356349	+	0.349525i
$346$	−0.666883	−	1.15507i	−0.0358518	−	0.0620972i
$347$	6.72623	−	25.1026i	0.361083	−	1.34758i	−0.511572	−	0.859241i	$-0.670937\pi$
$347$	6.72623	−	25.1026i	0.361083	−	1.34758i	0.872654	−	0.488338i	$-0.162397\pi$
$348$	4.41052	−	3.19329i	0.236429	−	0.171178i
$349$			28.1366i			1.50612i	0.657953	+	0.753059i	$0.271422\pi$
$349$			28.1366i			1.50612i	−0.657953	+	0.753059i	$0.728578\pi$
$350$		0			0
$351$	−30.4048	−	15.6827i	−1.62289	−	0.837081i
$352$	−0.239382	−	0.893387i	−0.0127591	−	0.0476177i
$353$	−14.8324	−	3.97434i	−0.789451	−	0.211533i	−0.158503	−	0.987358i	$-0.550667\pi$
$353$	−14.8324	−	3.97434i	−0.789451	−	0.211533i	−0.630947	+	0.775826i	$0.717334\pi$
$354$	−2.18717	−	1.77714i	−0.116247	−	0.0944538i
$355$	−19.2645	+	8.39283i	−1.02246	+	0.445445i
$356$		−	17.0883i		−	0.905680i
$357$		0			0
$358$	−9.29640	−	9.29640i	−0.491330	−	0.491330i
$359$	6.73373	−	11.6632i	0.355393	−	0.615558i	−0.631792	−	0.775138i	$-0.717680\pi$
$359$	6.73373	−	11.6632i	0.355393	−	0.615558i	0.987185	+	0.159579i	$0.0510138\pi$
$360$	15.4560	+	2.62771i	0.814602	+	0.138493i
$361$	−3.03131	−	5.25038i	−0.159543	−	0.276336i
$362$	10.5423	−	2.82480i	0.554090	−	0.148468i
$363$	7.75976	−	17.3513i	0.407282	−	0.910709i
$364$		0			0
$365$	−8.59786	+	1.29124i	−0.450033	+	0.0675866i
$366$	−0.357333	+	2.23219i	−0.0186781	+	0.116678i
$367$	3.80860	+	1.02051i	0.198807	+	0.0532703i	0.356849	−	0.934162i	$-0.383851\pi$
$367$	3.80860	+	1.02051i	0.198807	+	0.0532703i	−0.158041	+	0.987433i	$0.550518\pi$
$368$	−3.73338	−	1.00036i	−0.194616	−	0.0521471i
$369$	7.39202	+	35.3518i	0.384813	+	1.84034i
$370$	−1.72512	+	2.33485i	−0.0896846	+	0.121383i
$371$		0			0
$372$	18.5466	+	8.29427i	0.961594	+	0.430038i
$373$	5.78658	−	1.55051i	0.299618	−	0.0802823i	−0.105878	−	0.994379i	$-0.533765\pi$
$373$	5.78658	−	1.55051i	0.299618	−	0.0802823i	0.405496	+	0.914097i	$0.367099\pi$
$374$	−0.241401	−	0.418118i	−0.0124825	−	0.0216204i
$375$	18.8321	+	4.51146i	0.972484	+	0.232971i
$376$	−7.10614	+	12.3082i	−0.366471	+	0.634746i
$377$	9.31109	+	9.31109i	0.479546	+	0.479546i
$378$		0			0
$379$		−	25.1498i		−	1.29186i	−0.763397	−	0.645930i	$-0.776470\pi$
$379$		−	25.1498i		−	1.29186i	0.763397	−	0.645930i	$-0.223530\pi$
$380$	−5.04942	−	11.5902i	−0.259030	−	0.594565i
$381$	0.296649	−	0.365094i	0.0151978	−	0.0187043i
$382$	−13.6691	−	3.66262i	−0.699372	−	0.187396i
$383$	−1.61079	−	6.01154i	−0.0823073	−	0.307175i	0.912483	−	0.409114i	$-0.134162\pi$
$383$	−1.61079	−	6.01154i	−0.0823073	−	0.307175i	−0.994791	+	0.101939i	$0.967495\pi$
$384$	6.87302	+	17.9938i	0.350737	+	0.918242i
$385$		0			0
$386$		−	3.79877i		−	0.193352i
$387$	−19.7632	−	12.9276i	−1.00462	−	0.657147i
$388$	−5.58489	+	20.8431i	−0.283530	+	1.05815i
$389$	−13.0350	−	22.5773i	−0.660901	−	1.14471i	−0.980379	−	0.197120i	$-0.936841\pi$
$389$	−13.0350	−	22.5773i	−0.660901	−	1.14471i	0.319479	−	0.947593i	$-0.396492\pi$
$390$	−0.161294	+	16.6837i	−0.00816743	+	0.844810i
$391$	−10.9444			−0.553482
$392$		0			0
$393$	21.7352	+	9.72026i	1.09639	+	0.490322i
$394$	7.30904	+	4.21988i	0.368224	+	0.212594i
$395$	−1.36072	+	12.0193i	−0.0684654	+	0.604755i
$396$	0.237584	−	0.723054i	0.0119390	−	0.0363348i
$397$	5.49222	+	20.4972i	0.275647	+	1.02873i	0.955407	+	0.295293i	$0.0954172\pi$
$397$	5.49222	+	20.4972i	0.275647	+	1.02873i	−0.679760	+	0.733435i	$0.737916\pi$
$398$	−0.295133	+	0.295133i	−0.0147937	+	0.0147937i
$399$		0			0
$400$	2.37133	+	7.71681i	0.118566	+	0.385840i
$401$	−3.15603	−	1.82213i	−0.157605	−	0.0909930i	0.419124	−	0.907929i	$-0.362337\pi$
$401$	−3.15603	−	1.82213i	−0.157605	−	0.0909930i	−0.576728	+	0.816936i	$0.695671\pi$
$402$	−2.95033	+	0.305156i	−0.147149	+	0.0152198i
$403$	−12.7161	+	47.4572i	−0.633435	+	2.36401i
$404$	3.65023	−	6.32239i	0.181606	−	0.314551i
$405$	14.7569	+	13.6834i	0.733274	+	0.679933i
$406$		0			0
$407$	0.226445	+	0.226445i	0.0112245	+	0.0112245i
$408$	10.8533	+	14.9904i	0.537318	+	0.742135i
$409$	7.47293	−	4.31450i	0.369513	−	0.213338i	−0.303733	−	0.952757i	$-0.598233\pi$
$409$	7.47293	−	4.31450i	0.369513	−	0.213338i	0.673245	+	0.739419i	$0.264900\pi$
$410$	13.7767	−	10.9746i	0.680384	−	0.541996i
$411$	2.16841	−	13.5457i	0.106960	−	0.668159i
$412$	11.0468	−	11.0468i	0.544235	−	0.544235i
$413$		0			0
$414$	3.13262	+	3.50237i	0.153960	+	0.172132i
$415$	19.8926	+	7.81948i	0.976488	+	0.383843i
$416$	−32.6753	+	18.8651i	−1.60204	+	0.924937i
$417$	2.97343	+	28.7480i	0.145610	+	1.40780i
$418$	0.366894	−	0.0983088i	0.0179454	−	0.00480844i
$419$	−27.9057			−1.36328			−0.681641	−	0.731687i	$-0.738733\pi$
$419$	−27.9057			−1.36328			−0.681641	+	0.731687i	$0.738733\pi$
$420$		0			0
$421$	22.2684			1.08529			0.542647	−	0.839961i	$-0.317422\pi$
$421$	22.2684			1.08529			0.542647	+	0.839961i	$0.317422\pi$
$422$	4.23178	−	1.13390i	0.206000	−	0.0551974i
$423$	−16.2824	+	8.22849i	−0.791675	+	0.400083i
$424$	7.97704	−	4.60555i	0.387399	−	0.223665i
$425$	12.1413	+	19.3686i	0.588941	+	0.939513i
$426$	3.80018	+	9.94899i	0.184119	+	0.482030i
$427$		0			0
$428$	16.1055	−	16.1055i	0.778489	−	0.778489i
$429$	1.81737	+	0.290928i	0.0877436	+	0.0140462i
$430$	−1.29561	+	11.4441i	−0.0624799	+	0.551885i
$431$	−1.70274	+	0.983080i	−0.0820183	+	0.0473533i	−0.540448	−	0.841377i	$-0.681745\pi$
$431$	−1.70274	+	0.983080i	−0.0820183	+	0.0473533i	0.458430	+	0.888731i	$0.348412\pi$
$432$	−1.78504	+	8.19755i	−0.0858826	+	0.394405i
$433$	18.7649	+	18.7649i	0.901782	+	0.901782i	0.995590	−	0.0938083i	$-0.0299041\pi$
$433$	18.7649	+	18.7649i	0.901782	+	0.901782i	−0.0938083	+	0.995590i	$0.529904\pi$
$434$		0			0
$435$	−3.80795	−	6.74533i	−0.182577	−	0.323414i
$436$	−7.25901	+	12.5730i	−0.347644	+	0.602137i
$437$	2.22852	−	8.31694i	0.106604	−	0.397853i
$438$	0.453346	+	4.38308i	0.0216617	+	0.209432i
$439$	−22.4711	−	12.9737i	−1.07249	−	0.619202i	−0.143629	−	0.989632i	$-0.545877\pi$
$439$	−22.4711	−	12.9737i	−1.07249	−	0.619202i	−0.928860	+	0.370430i	$0.879210\pi$
$440$	−0.834089	+	0.125265i	−0.0397636	+	0.00597176i
$441$		0			0
$442$	−13.9266	+	13.9266i	−0.662423	+	0.662423i
$443$	9.17002	+	34.2230i	0.435681	+	1.62598i	0.739431	+	0.673232i	$0.235094\pi$
$443$	9.17002	+	34.2230i	0.435681	+	1.62598i	−0.303751	+	0.952752i	$0.598239\pi$
$444$	−4.19262	−	3.40662i	−0.198973	−	0.161671i
$445$	−24.1545	−	2.73458i	−1.14503	−	0.129632i
$446$	−0.306177	−	0.176771i	−0.0144979	−	0.00837036i
$447$	−11.0421	+	24.6909i	−0.522274	+	1.16784i
$448$		0			0
$449$	−17.4443			−0.823245			−0.411623	−	0.911354i	$-0.635038\pi$
$449$	−17.4443			−0.823245			−0.411623	+	0.911354i	$0.635038\pi$
$450$	2.72301	−	9.42928i	0.128364	−	0.444500i
$451$	−0.971506	−	1.68270i	−0.0457464	−	0.0792351i
$452$	−2.80723	+	10.4767i	−0.132041	+	0.492784i
$453$	7.38967	+	10.2065i	0.347197	+	0.479543i
$454$		−	11.5748i		−	0.543231i
$455$		0			0
$456$	−13.6016	+	5.19533i	−0.636952	+	0.243294i
$457$	−9.10323	−	33.9737i	−0.425831	−	1.58922i	−0.762101	−	0.647458i	$-0.775832\pi$
$457$	−9.10323	−	33.9737i	−0.425831	−	1.58922i	0.336269	−	0.941766i	$-0.390835\pi$
$458$	−1.46671	−	0.393002i	−0.0685346	−	0.0183638i
$459$	1.12548	+	23.7295i	0.0525328	+	1.10760i
$460$	−3.07814	+	7.83073i	−0.143519	+	0.365110i
$461$		−	7.52593i		−	0.350517i	−0.984522	−	0.175259i	$-0.943924\pi$
$461$		−	7.52593i		−	0.350517i	0.984522	−	0.175259i	$-0.0560762\pi$
$462$		0			0
$463$	−16.6029	−	16.6029i	−0.771601	−	0.771601i	0.206785	−	0.978386i	$-0.433700\pi$
$463$	−16.6029	−	16.6029i	−0.771601	−	0.771601i	−0.978386	+	0.206785i	$0.933700\pi$
$464$	1.61459	−	2.79655i	0.0749554	−	0.129826i
$465$	14.6920	−	24.8884i	0.681324	−	1.15417i
$466$	−2.80636	−	4.86075i	−0.130002	−	0.225170i
$467$	10.5373	−	2.82346i	0.487608	−	0.130654i	−0.00663489	−	0.999978i	$-0.502112\pi$
$467$	10.5373	−	2.82346i	0.487608	−	0.130654i	0.494243	+	0.869324i	$0.335445\pi$
$468$	−30.9995	−	1.72754i	−1.43295	−	0.0798556i
$469$		0			0
$470$	7.15582	+	5.28712i	0.330073	+	0.243877i
$471$	−27.0684	−	4.33315i	−1.24724	−	0.199661i
$472$	−5.61363	−	1.50417i	−0.258388	−	0.0692349i
$473$	1.22721	+	0.328830i	0.0564271	+	0.0151196i
$474$	6.05348	+	0.969052i	0.278046	+	0.0445100i
$475$	−17.1909	+	5.28267i	−0.788774	+	0.242385i
$476$		0			0
$477$	11.8054	+	0.657893i	0.540532	+	0.0301228i
$478$	−13.6304	+	3.65224i	−0.623438	+	0.167050i
$479$	8.56960	+	14.8430i	0.391555	+	0.678193i	0.992655	−	0.120981i	$-0.0386039\pi$
$479$	8.56960	+	14.8430i	0.391555	+	0.678193i	−0.601100	+	0.799174i	$0.705271\pi$
$480$	21.4929	−	5.53689i	0.981014	−	0.252723i
$481$	6.53192	−	11.3136i	0.297830	−	0.515856i
$482$	3.00294	+	3.00294i	0.136780	+	0.136780i
$483$		0			0
$484$		−	17.2498i		−	0.784081i
$485$	28.5682	+	11.2297i	1.29722	+	0.509916i
$486$	7.27166	−	7.15228i	0.329849	−	0.324434i
$487$	19.3562	+	5.18649i	0.877115	+	0.235022i	0.669162	−	0.743117i	$-0.266653\pi$
$487$	19.3562	+	5.18649i	0.877115	+	0.235022i	0.207953	+	0.978139i	$0.433320\pi$
$488$	1.20659	+	4.50304i	0.0546196	+	0.203843i
$489$	−23.3928	+	8.93527i	−1.05786	+	0.404067i
$490$		0			0
$491$		−	25.4502i		−	1.14855i	−0.818661	−	0.574277i	$-0.805283\pi$
$491$		−	25.4502i		−	1.14855i	0.818661	−	0.574277i	$-0.194717\pi$
$492$	19.2217	+	26.5487i	0.866581	+	1.19691i
$493$	2.36658	−	8.83220i	0.106585	−	0.397782i
$494$	−7.74746	−	13.4190i	−0.348575	−	0.603749i
$495$	−0.984025	−	0.451535i	−0.0442286	−	0.0202950i
$496$	12.0485			0.540995
$497$		0			0
$498$	4.42254	−	9.88910i	0.198179	−	0.443141i
$499$	−13.2157	−	7.63009i	−0.591616	−	0.341570i	0.174120	−	0.984724i	$-0.444292\pi$
$499$	−13.2157	−	7.63009i	−0.591616	−	0.341570i	−0.765736	+	0.643155i	$0.777625\pi$
$500$	17.2730	−	3.23968i	0.772473	−	0.144883i
$501$	−4.80402	−	3.90341i	−0.214628	−	0.174391i
$502$	−4.29453	−	16.0274i	−0.191674	−	0.715338i
$503$	−7.55387	+	7.55387i	−0.336810	+	0.336810i	−0.855165	−	0.518355i	$-0.826545\pi$
$503$	−7.55387	+	7.55387i	−0.336810	+	0.336810i	0.518355	+	0.855165i	$0.326545\pi$
$504$		0			0
$505$	−8.35263	−	6.17139i	−0.371687	−	0.274623i
$506$	−0.218928	−	0.126398i	−0.00973252	−	0.00561907i
$507$	−5.40796	−	52.2857i	−0.240176	−	2.32209i
$508$	0.110495	−	0.412372i	0.00490241	−	0.0182960i
$509$	19.6787	−	34.0846i	0.872244	−	1.51077i	0.0125748	−	0.999921i	$-0.495997\pi$
$509$	19.6787	−	34.0846i	0.872244	−	1.51077i	0.859670	−	0.510851i	$-0.170669\pi$
$510$	10.0890	−	5.69557i	0.446750	−	0.252204i
$511$		0			0
$512$	11.8791	+	11.8791i	0.524986	+	0.524986i
$513$	−18.2619	−	3.97657i	−0.806282	−	0.175570i
$514$	6.53402	−	3.77242i	0.288203	−	0.166394i
$515$	−13.8469	−	17.3825i	−0.610169	−	0.765964i
$516$	−21.1626	−	3.38774i	−0.931631	−	0.149137i
$517$	0.694006	−	0.694006i	0.0305223	−	0.0305223i
$518$		0			0
$519$	−1.25983	−	3.29827i	−0.0553003	−	0.144778i
$520$	13.7424	+	31.5436i	0.602642	+	1.38328i
$521$	13.2100	−	7.62679i	0.578740	−	0.334136i	−0.181893	−	0.983318i	$-0.558222\pi$
$521$	13.2100	−	7.62679i	0.578740	−	0.334136i	0.760632	+	0.649183i	$0.224889\pi$
$522$	−3.50382	+	1.77070i	−0.153358	+	0.0775015i
$523$	17.9637	−	4.81336i	0.785497	−	0.210473i	0.156290	−	0.987711i	$-0.450046\pi$
$523$	17.9637	−	4.81336i	0.785497	−	0.210473i	0.629207	+	0.777238i	$0.283380\pi$
$524$	21.6079			0.943947
$525$		0			0
$526$	12.8947			0.562235
$527$	32.9543	−	8.83007i	1.43551	−	0.384644i
$528$	−0.0464360	−	0.448956i	−0.00202087	−	0.0195383i
$529$	14.9558	−	8.63475i	0.650253	−	0.375424i
$530$	−2.30309	−	5.28642i	−0.100040	−	0.229627i
$531$	−4.97338	−	5.56041i	−0.215826	−	0.241301i
$532$		0			0
$533$	−56.0471	+	56.0471i	−2.42767	+	2.42767i
$534$	−1.94746	+	12.1654i	−0.0842747	+	0.526448i
$535$	−20.1880	−	25.3426i	−0.872803	−	1.09566i
$536$	−5.29724	+	3.05836i	−0.228806	+	0.132101i
$537$	−20.4097	−	28.1896i	−0.880745	−	1.21647i
$538$	−1.56304	−	1.56304i	−0.0673876	−	0.0673876i
$539$		0			0
$540$	17.2951	+	5.86872i	0.744260	+	0.252550i
$541$	0.951978	−	1.64887i	0.0409287	−	0.0708906i	−0.844835	−	0.535026i	$-0.820302\pi$
$541$	0.951978	−	1.64887i	0.0409287	−	0.0708906i	0.885764	+	0.464136i	$0.153635\pi$
$542$	−2.72443	+	10.1677i	−0.117024	+	0.436740i
$543$	28.7382	−	2.97242i	1.23328	−	0.127559i
$544$	22.6897	+	13.0999i	0.972814	+	0.561654i
$545$	16.6104	+	12.2727i	0.711512	+	0.525705i
$546$		0			0
$547$	4.09919	−	4.09919i	0.175269	−	0.175269i	−0.614021	−	0.789290i	$-0.710449\pi$
$547$	4.09919	−	4.09919i	0.175269	−	0.175269i	0.789290	+	0.614021i	$0.210449\pi$
$548$	−3.22219	−	12.0254i	−0.137645	−	0.513699i
$549$	−1.86805	+	5.68515i	−0.0797264	+	0.242636i
$550$	0.0191814	+	0.527663i	0.000817897	+	0.0224996i
$551$	6.22994	+	3.59686i	0.265404	+	0.153231i
$552$	8.84595	+	3.95603i	0.376509	+	0.168380i
$553$		0			0
$554$	−4.36352			−0.185388
$555$	−5.48623	+	5.38116i	−0.232877	+	0.228418i
$556$	13.1144	+	22.7148i	0.556174	+	0.963322i
$557$	2.38619	−	8.90537i	0.101106	−	0.377333i	−0.896768	−	0.442500i	$-0.854092\pi$
$557$	2.38619	−	8.90537i	0.101106	−	0.377333i	0.997874	+	0.0651676i	$0.0207582\pi$
$558$	−12.2583	−	8.01843i	−0.518934	−	0.339447i
$559$		−	51.8284i		−	2.19211i
$560$		0			0
$561$	−0.456037	−	1.19392i	−0.0192539	−	0.0504074i
$562$	−2.13318	−	7.96115i	−0.0899829	−	0.335821i
$563$	−1.10118	−	0.295060i	−0.0464091	−	0.0124353i	0.235540	−	0.971865i	$-0.424314\pi$
$563$	−1.10118	−	0.295060i	−0.0464091	−	0.0124353i	−0.281949	+	0.959429i	$0.590981\pi$
$564$	−10.4406	+	12.8495i	−0.439628	+	0.541061i
$565$	14.3597	+	5.64460i	0.604119	+	0.237470i
$566$		−	11.9538i		−	0.502457i
$567$		0			0
$568$	15.5301	+	15.5301i	0.651628	+	0.651628i
$569$	−1.29985	+	2.25140i	−0.0544924	+	0.0943835i	−0.891985	−	0.452065i	$-0.850687\pi$
$569$	−1.29985	+	2.25140i	−0.0544924	+	0.0943835i	0.837492	+	0.546449i	$0.184021\pi$
$570$	2.27387	+	8.82666i	0.0952420	+	0.369708i
$571$	−1.39746	−	2.42048i	−0.0584820	−	0.101294i	0.835302	−	0.549791i	$-0.185293\pi$
$571$	−1.39746	−	2.42048i	−0.0584820	−	0.101294i	−0.893784	+	0.448497i	$0.851959\pi$
$572$	1.61340	−	0.432310i	0.0674597	−	0.0180758i
$573$	−34.1968	−	15.2933i	−1.42859	−	0.638886i
$574$		0			0
$575$	10.5762	+	5.60411i	0.441059	+	0.233708i
$576$	−0.319544	−	1.52820i	−0.0133143	−	0.0636748i
$577$	17.2446	+	4.62068i	0.717903	+	0.192362i	0.599236	−	0.800573i	$-0.295471\pi$
$577$	17.2446	+	4.62068i	0.717903	+	0.192362i	0.118667	+	0.992934i	$0.462138\pi$
$578$	2.46618	+	0.660812i	0.102580	+	0.0274862i
$579$	1.58954	−	9.92953i	0.0660588	−	0.412657i
$580$	−5.65384	−	4.17737i	−0.234763	−	0.173456i
$581$		0			0
$582$	6.35131	−	14.2020i	0.263270	−	0.588691i
$583$	−0.614426	+	0.164635i	−0.0254469	+	0.00681848i
$584$	4.54356	+	7.86968i	0.188014	+	0.325650i
$585$	−7.40262	+	43.5416i	−0.306061	+	1.80022i
$586$	0.954887	−	1.65391i	0.0394460	−	0.0683225i
$587$	−19.4664	−	19.4664i	−0.803465	−	0.803465i	0.180171	−	0.983635i	$-0.442335\pi$
$587$	−19.4664	−	19.4664i	−0.803465	−	0.803465i	−0.983635	+	0.180171i	$0.942335\pi$
$588$		0			0
$589$			26.8408i			1.10596i
$590$	−1.33099	+	3.38600i	−0.0547959	+	0.139400i
$591$	17.3392	+	14.0886i	0.713239	+	0.579527i
$592$	−3.09450	−	0.829169i	−0.127183	−	0.0340786i
$593$	−8.07115	−	30.1219i	−0.331442	−	1.23696i	−0.907675	−	0.419674i	$-0.862144\pi$
$593$	−8.07115	−	30.1219i	−0.331442	−	1.23696i	0.576233	−	0.817286i	$-0.304522\pi$
$594$	−0.251541	+	0.487675i	−0.0103209	+	0.0200095i
$595$		0			0
$596$			24.5464i			1.00546i
$597$	−0.894934	+	0.647947i	−0.0366272	+	0.0265187i
$598$	−2.66906	+	9.96108i	−0.109146	+	0.407339i
$599$	9.26661	+	16.0502i	0.378624	+	0.655795i	0.990862	−	0.134878i	$-0.0430642\pi$
$599$	9.26661	+	16.0502i	0.378624	+	0.655795i	−0.612239	+	0.790673i	$0.709731\pi$
$600$	−2.81232	−	20.0436i	−0.114812	−	0.818276i
$601$	5.32951			0.217395			0.108698	−	0.994075i	$-0.465332\pi$
$601$	5.32951			0.217395			0.108698	+	0.994075i	$0.465332\pi$
$602$		0			0
$603$	−7.83950	−	0.436881i	−0.319249	−	0.0177912i
$604$	9.90349	+	5.71778i	0.402967	+	0.232653i
$605$	−24.3827	−	2.76042i	−0.991299	−	0.112227i
$606$	−3.31917	+	4.08499i	−0.134832	+	0.165941i
$607$	−4.07471	−	15.2070i	−0.165387	−	0.617234i	−0.997990	−	0.0633638i	$-0.979817\pi$
$607$	−4.07471	−	15.2070i	−0.165387	−	0.617234i	0.832603	−	0.553870i	$-0.186850\pi$
$608$	−14.5751	+	14.5751i	−0.591098	+	0.591098i
$609$		0			0
$610$	2.88607	−	0.433434i	0.116854	−	0.0175492i
$611$	−34.6738	−	20.0189i	−1.40275	−	0.809880i
$612$	9.72412	+	19.2419i	0.393074	+	0.777807i
$613$	9.15958	−	34.1840i	0.369952	−	1.38068i	−0.490630	−	0.871368i	$-0.663233\pi$
$613$	9.15958	−	34.1840i	0.369952	−	1.38068i	0.860582	−	0.509312i	$-0.170100\pi$
$614$	−0.296526	+	0.513598i	−0.0119668	+	0.0207271i
$615$	40.6028	−	22.9216i	1.63726	−	0.924287i
$616$		0			0
$617$	−25.1412	−	25.1412i	−1.01215	−	1.01215i	−0.999925	−	0.0122222i	$-0.996109\pi$
$617$	−25.1412	−	25.1412i	−1.01215	−	1.01215i	−0.0122222	−	0.999925i	$-0.503891\pi$
$618$	−9.12325	+	6.60539i	−0.366991	+	0.265708i
$619$	−3.49101	+	2.01554i	−0.140316	+	0.0810112i	−0.568514	−	0.822673i	$-0.692482\pi$
$619$	−3.49101	+	2.01554i	−0.140316	+	0.0810112i	0.428199	+	0.903685i	$0.359148\pi$
$620$	2.95056	−	26.0623i	0.118497	−	1.04669i
$621$	6.72277	+	10.4656i	0.269775	+	0.419969i
$622$	−9.64494	+	9.64494i	−0.386727	+	0.386727i
$623$		0			0
$624$	−17.2003	+	6.56991i	−0.688561	+	0.263007i
$625$	−1.81518	−	24.9340i	−0.0726072	−	0.997361i
$626$	−9.93440	+	5.73563i	−0.397058	+	0.229242i
$627$	1.00015	−	0.103447i	0.0399422	−	0.00413126i
$628$	−24.0303	+	6.43891i	−0.958915	+	0.256941i
$629$	−9.07152			−0.361705
$630$		0			0
$631$	25.6331			1.02044			0.510219	−	0.860044i	$-0.329564\pi$
$631$	25.6331			1.02044			0.510219	+	0.860044i	$0.329564\pi$
$632$	12.2118	−	3.27215i	0.485760	−	0.130159i
$633$	11.5358	−	1.19316i	0.458507	−	0.0474238i
$634$	2.34103	−	1.35159i	0.0929740	−	0.0536786i
$635$	−0.565210	−	0.222176i	−0.0224297	−	0.00881677i
$636$	10.0240	−	3.82883i	0.397478	−	0.151823i
$637$		0			0
$638$	0.149344	−	0.149344i	0.00591259	−	0.00591259i
$639$	5.77020	+	27.5956i	0.228266	+	1.09166i
$640$	19.4499	−	15.4939i	0.768825	−	0.612448i
$641$	−5.18974	+	2.99630i	−0.204982	+	0.118347i	−0.598977	−	0.800766i	$-0.704426\pi$
$641$	−5.18974	+	2.99630i	−0.204982	+	0.118347i	0.393995	+	0.919113i	$0.371093\pi$
$642$	−13.3012	+	9.63025i	−0.524955	+	0.380076i
$643$	−0.533933	−	0.533933i	−0.0210562	−	0.0210562i	0.696500	−	0.717557i	$-0.254739\pi$
$643$	−0.533933	−	0.533933i	−0.0210562	−	0.0210562i	−0.717557	+	0.696500i	$0.754739\pi$
$644$		0			0
$645$	−8.17518	+	29.3714i	−0.321897	+	1.15650i
$646$	−5.37984	+	9.31815i	−0.211667	+	0.366618i
$647$	9.09189	−	33.9314i	0.357439	−	1.33398i	−0.519948	−	0.854198i	$-0.674049\pi$
$647$	9.09189	−	33.9314i	0.357439	−	1.33398i	0.877387	−	0.479783i	$-0.159285\pi$
$648$	7.66774	−	19.5865i	0.301217	−	0.769432i
$649$	0.347572	+	0.200671i	0.0136434	+	0.00787702i
$650$	20.5893	−	6.32698i	0.807580	−	0.248165i
$651$		0			0
$652$	−16.0694	+	16.0694i	−0.629328	+	0.629328i
$653$	−0.0900386	−	0.336028i	−0.00352348	−	0.0131498i	0.964142	−	0.265388i	$-0.0855000\pi$
$653$	−0.0900386	−	0.336028i	−0.00352348	−	0.0131498i	−0.967665	+	0.252238i	$0.918833\pi$
$654$	6.60065	−	8.12359i	0.258106	−	0.317657i
$655$	3.45783	−	30.5430i	0.135109	−	1.19342i
$656$	16.8335	+	9.71884i	0.657239	+	0.379457i
$657$	−0.649039	+	11.6465i	−0.0253214	+	0.454374i
$658$		0			0
$659$	14.9402			0.581989			0.290994	−	0.956725i	$-0.406014\pi$
$659$	14.9402			0.581989			0.290994	+	0.956725i	$0.406014\pi$
$660$	−0.982513	−	0.00949870i	−0.0382443	−	0.000369736i
$661$	−21.4079	−	37.0797i	−0.832673	−	1.44223i	−0.895911	−	0.444233i	$-0.853476\pi$
$661$	−21.4079	−	37.0797i	−0.832673	−	1.44223i	0.0632386	−	0.997998i	$-0.479857\pi$
$662$	−2.96199	+	11.0543i	−0.115121	+	0.429637i
$663$	−42.2299	+	30.5752i	−1.64008	+	1.18744i
$664$		−	22.3400i		−	0.866962i
$665$		0			0
$666$	2.59654	+	2.90302i	0.100614	+	0.112490i
$667$	−1.23915	−	4.62456i	−0.0479800	−	0.179064i
$668$	−5.42612	−	1.45392i	−0.209943	−	0.0562540i
$669$	−0.726342	−	0.590173i	−0.0280820	−	0.0228174i
$670$	1.52939	+	3.51050i	0.0590856	+	0.135622i
$671$		−	0.321942i		−	0.0124284i
$672$		0			0
$673$	5.09320	+	5.09320i	0.196328	+	0.196328i	0.798424	−	0.602096i	$-0.205667\pi$
$673$	5.09320	+	5.09320i	0.196328	+	0.196328i	−0.602096	+	0.798424i	$0.705667\pi$
$674$	0.764382	−	1.32395i	0.0294429	−	0.0509966i
$675$	11.0632	−	23.5076i	0.425821	−	0.904807i
$676$	−23.8519	−	41.3128i	−0.917382	−	1.58895i
$677$	−1.68713	+	0.452066i	−0.0648418	+	0.0173743i	−0.291094	−	0.956694i	$-0.594019\pi$
$677$	−1.68713	+	0.452066i	−0.0648418	+	0.0173743i	0.226252	+	0.974069i	$0.427353\pi$
$678$	3.19247	−	7.13859i	0.122606	−	0.274156i
$679$		0			0
$680$	14.1980	−	19.2162i	0.544467	−	0.736906i
$681$	4.84328	−	30.2550i	0.185595	−	1.15938i
$682$	0.761184	+	0.203959i	0.0291472	+	0.00780998i
$683$	34.4803	+	9.23896i	1.31935	+	0.353519i	0.848735	−	0.528819i	$-0.177365\pi$
$683$	34.4803	+	9.23896i	1.31935	+	0.353519i	0.470616	+	0.882338i	$0.344032\pi$
$684$	−16.6025	+	3.47155i	−0.634811	+	0.132738i
$685$	−17.5136	+	2.63022i	−0.669162	+	0.100496i
$686$		0			0
$687$	−3.66934	−	1.64098i	−0.139994	−	0.0626073i
$688$	−12.2769	+	3.28958i	−0.468051	+	0.125414i
$689$	12.9744	+	22.4724i	0.494287	+	0.856130i
$690$	3.08379	−	5.22399i	0.117398	−	0.198874i
$691$	−22.5895	+	39.1261i	−0.859344	+	1.48843i	0.0132121	+	0.999913i	$0.495794\pi$
$691$	−22.5895	+	39.1261i	−0.859344	+	1.48843i	−0.872556	+	0.488514i	$0.837539\pi$
$692$	−2.26571	−	2.26571i	−0.0861294	−	0.0861294i
$693$		0			0
$694$			17.0042i			0.645470i
$695$	34.2062	−	14.9024i	1.29752	−	0.565279i
$696$	−5.10536	+	6.28330i	−0.193518	+	0.238168i
$697$	53.1645	+	14.2454i	2.01375	+	0.539583i
$698$	−4.76484	−	17.7826i	−0.180352	−	0.673082i
$699$	−5.30157	−	13.8797i	−0.200524	−	0.524978i
$700$		0			0
$701$		−	44.4108i		−	1.67737i	−0.544614	−	0.838687i	$-0.683324\pi$
$701$		−	44.4108i		−	1.67737i	0.544614	−	0.838687i	$-0.316676\pi$
$702$	21.8720	+	4.76268i	0.825505	+	0.179756i
$703$	1.84716	−	6.89369i	0.0696669	−	0.260001i
$704$	0.0419965	+	0.0727400i	0.00158280	+	0.00274149i
$705$	16.4921	+	16.8141i	0.621130	+	0.633257i
$706$	10.0473			0.378135
$707$		0			0
$708$	−6.18034	−	2.76393i	−0.232271	−	0.103875i
$709$	−15.7821	−	9.11180i	−0.592709	−	0.342201i	0.173459	−	0.984841i	$-0.444506\pi$
$709$	−15.7821	−	9.11180i	−0.592709	−	0.342201i	−0.766168	+	0.642640i	$0.777839\pi$
$710$	10.7541	−	8.56674i	0.403594	−	0.321504i
$711$	15.4176	+	5.06597i	0.578204	+	0.189989i
$712$	6.57587	+	24.5415i	0.246441	+	0.919731i
$713$	12.6315	−	12.6315i	0.473053	−	0.473053i
$714$		0			0
$715$	−0.352888	−	2.34974i	−0.0131972	−	0.0878753i
$716$	−27.3527	−	15.7921i	−1.02222	−	0.590178i
$717$	−37.1563	+	3.84311i	−1.38763	+	0.143524i
$718$	−2.28067	+	8.51158i	−0.0851139	+	0.317649i
$719$	−7.20912	+	12.4866i	−0.268855	+	0.465670i	−0.968566	−	0.248755i	$-0.919979\pi$
$719$	−7.20912	+	12.4866i	−0.268855	+	0.465670i	0.699712	+	0.714425i	$0.253312\pi$
$720$	10.7838	−	1.01011i	0.401888	−	0.0376446i
$721$		0			0
$722$	2.80496	+	2.80496i	0.104390	+	0.104390i
$723$	6.59280	+	9.10586i	0.245189	+	0.338651i
$724$	22.7071	−	13.1099i	0.843902	−	0.487227i
$725$	−6.80953	+	7.32328i	−0.252899	+	0.271980i
$726$	−1.96586	+	12.2803i	−0.0729597	+	0.455766i
$727$	−1.34757	+	1.34757i	−0.0499787	+	0.0499787i	−0.731654	−	0.681676i	$-0.761252\pi$
$727$	−1.34757	+	1.34757i	−0.0499787	+	0.0499787i	0.681676	+	0.731654i	$0.261252\pi$
$728$		0			0
$729$	22.0000	−	15.6525i	0.814815	−	0.579721i
$730$	5.21527	−	2.27210i	0.193026	−	0.0840941i
$731$	−31.1679	+	17.9948i	−1.15279	+	0.665562i
$732$	0.558734	+	5.40200i	0.0206514	+	0.199664i
$733$	18.4641	−	4.94744i	0.681987	−	0.182738i	0.0988384	−	0.995104i	$-0.468487\pi$
$733$	18.4641	−	4.94744i	0.681987	−	0.182738i	0.583148	+	0.812366i	$0.301821\pi$
$734$	−2.57990			−0.0952258
$735$		0			0
$736$	13.7183			0.505663
$737$	0.408016	−	0.109327i	0.0150295	−	0.00402713i
$738$	−10.6585	−	21.0909i	−0.392347	−	0.776367i
$739$	−1.11818	+	0.645584i	−0.0411331	+	0.0237482i	−0.520426	−	0.853907i	$-0.674227\pi$
$739$	−1.11818	+	0.645584i	−0.0411331	+	0.0237482i	0.479292	+	0.877655i	$0.340893\pi$
$740$	−2.55139	+	6.49068i	−0.0937911	+	0.238602i
$741$	−14.6360	−	38.3174i	−0.537665	−	1.40763i
$742$		0			0
$743$	11.5021	−	11.5021i	0.421972	−	0.421972i	−0.463910	−	0.885882i	$-0.653554\pi$
$743$	11.5021	−	11.5021i	0.421972	−	0.421972i	0.885882	+	0.463910i	$0.153554\pi$
$744$	−29.8275	−	4.77484i	−1.09353	−	0.175054i
$745$	34.6966	+	3.92807i	1.27118	+	0.143913i
$746$	−3.39460	+	1.95988i	−0.124285	+	0.0717562i
$747$	15.6979	−	23.9984i	0.574357	−	0.878054i
$748$	−0.820150	−	0.820150i	−0.0299877	−	0.0299877i
$749$		0			0
$750$	−12.6661	+	0.337860i	−0.462499	+	0.0123369i
$751$	21.5667	−	37.3545i	0.786978	−	1.36309i	−0.140832	−	0.990034i	$-0.544978\pi$
$751$	21.5667	−	37.3545i	0.786978	−	1.36309i	0.927810	−	0.373053i	$-0.121689\pi$
$752$	−2.54123	+	9.48399i	−0.0926690	+	0.345845i
$753$	−4.51897	−	43.6907i	−0.164680	−	1.59218i
$754$	−7.46151	−	4.30791i	−0.271732	−	0.156885i
$755$	9.66696	−	13.0837i	0.351817	−	0.476164i
$756$		0			0
$757$	−21.6057	+	21.6057i	−0.785273	+	0.785273i	−0.980715	−	0.195442i	$-0.937386\pi$
$757$	−21.6057	+	21.6057i	−0.785273	+	0.785273i	0.195442	+	0.980715i	$0.437386\pi$
$758$	4.25904	+	15.8950i	0.154695	+	0.577331i
$759$	−0.519361	−	0.421995i	−0.0188516	−	0.0153175i
$760$	11.7119	+	14.7022i	0.424834	+	0.533306i
$761$	23.7452	+	13.7093i	0.860763	+	0.496962i	0.864268	−	0.503032i	$-0.167782\pi$
$761$	23.7452	+	13.7093i	0.860763	+	0.496962i	−0.00350451	+	0.999994i	$0.501116\pi$
$762$	−0.125658	+	0.280980i	−0.00455211	+	0.0101788i
$763$		0			0
$764$	−33.9966			−1.22996
$765$	28.7547	−	10.6659i	1.03963	−	0.385628i
$766$	2.03607	+	3.52657i	0.0735661	+	0.127420i
$767$	4.23744	−	15.8143i	0.153005	−	0.571023i
$768$	−8.44824	−	11.6686i	−0.304849	−	0.421053i
$769$		−	17.1148i		−	0.617174i	−0.951196	−	0.308587i	$-0.900144\pi$
$769$		−	17.1148i		−	0.617174i	0.951196	−	0.308587i	$-0.0998561\pi$
$770$		0			0
$771$	18.6576	−	7.12658i	0.671938	−	0.256658i
$772$	−2.36200	−	8.81509i	−0.0850101	−	0.317262i
$773$	40.2165	+	10.7760i	1.44649	+	0.387585i	0.894800	−	0.446466i	$-0.147318\pi$
$773$	40.2165	+	10.7760i	1.44649	+	0.387585i	0.551687	+	0.834051i	$0.313984\pi$
$774$	14.6798	+	4.82355i	0.527655	+	0.173379i
$775$	−36.3672	−	8.34130i	−1.30635	−	0.299628i
$776$		−	32.0831i		−	1.15172i
$777$		0			0
$778$	12.0616	+	12.0616i	0.432431	+	0.432431i
$779$	−21.6509	+	37.5005i	−0.775724	+	1.34359i
$780$	9.99927	+	38.8149i	0.358031	+	1.38980i
$781$	−0.758356	−	1.31351i	−0.0271361	−	0.0470011i
$782$	6.91698	−	1.85340i	0.247351	−	0.0662774i
$783$	−9.89949	+	3.16228i	−0.353779	+	0.113011i
$784$		0			0
$785$	5.25598	+	34.9975i	0.187594	+	1.24912i
$786$	−15.3829	−	2.46253i	−0.548691	−	0.0878355i
$787$	−13.2943	−	3.56220i	−0.473892	−	0.126979i	0.0139653	−	0.999902i	$-0.495555\pi$
$787$	−13.2943	−	3.56220i	−0.473892	−	0.126979i	−0.487857	+	0.872924i	$0.662221\pi$
$788$	19.5845	+	5.24766i	0.697670	+	0.186940i
$789$	33.7051	+	5.39557i	1.19993	+	0.192087i
$790$	−1.17543	−	7.82674i	−0.0418200	−	0.278463i
$791$		0			0
$792$	−0.0629640	+	1.12984i	−0.00223733	+	0.0401473i
$793$	−12.6857	+	3.39912i	−0.450482	+	0.120706i
$794$	−6.94229	−	12.0244i	−0.246372	−	0.426730i
$795$	−3.80799	−	14.7817i	−0.135055	−	0.524254i
$796$	−0.501351	+	0.868365i	−0.0177699	+	0.0307784i
$797$	31.7624	+	31.7624i	1.12508	+	1.12508i	0.990966	+	0.134115i	$0.0428192\pi$
$797$	31.7624	+	31.7624i	1.12508	+	1.12508i	0.134115	+	0.990966i	$0.457181\pi$
$798$		0			0
$799$			27.8023i			0.983575i
$800$	−15.2186	−	24.2776i	−0.538059	−	0.858342i
$801$	−10.1808	+	30.9840i	−0.359722	+	1.09476i
$802$	2.30322	+	0.617145i	0.0813294	+	0.0217921i
$803$	−0.162419	−	0.606157i	−0.00573165	−	0.0213908i
$804$	−6.65654	+	2.54257i	−0.234758	+	0.0896697i
$805$		0			0
$806$		−	32.1469i		−	1.13233i
$807$	−3.43157	−	4.73964i	−0.120797	−	0.166843i
$808$	−2.80934	+	10.4846i	−0.0988322	+	0.368847i
$809$	10.6115	+	18.3796i	0.373080	+	0.646193i	0.990038	−	0.140803i	$-0.0449684\pi$
$809$	10.6115	+	18.3796i	0.373080	+	0.646193i	−0.616958	+	0.786996i	$0.711635\pi$
$810$	−11.6437	−	6.14903i	−0.409119	−	0.216055i
$811$	17.1374			0.601776			0.300888	−	0.953660i	$-0.402717\pi$
$811$	17.1374			0.601776			0.300888	+	0.953660i	$0.402717\pi$
$812$		0			0
$813$	−11.3758	+	25.4371i	−0.398968	+	0.892119i
$814$	−0.181463	−	0.104768i	−0.00636029	−	0.00367211i
$815$	20.1428	+	25.2859i	0.705571	+	0.885725i
$816$	9.92286	+	8.06261i	0.347370	+	0.282248i
$817$	−7.32827	−	27.3495i	−0.256384	−	0.956837i
$818$	−3.99232	+	3.99232i	−0.139588	+	0.139588i
$819$		0			0
$820$	25.1453	−	34.0327i	0.878111	−	1.18847i
$821$	−3.05795	−	1.76551i	−0.106723	−	0.0616166i	0.445688	−	0.895188i	$-0.352959\pi$
$821$	−3.05795	−	1.76551i	−0.106723	−	0.0616166i	−0.552411	+	0.833572i	$0.686292\pi$
$822$	0.923455	+	8.92823i	0.0322092	+	0.311408i
$823$	−4.73521	+	17.6720i	−0.165059	+	0.616008i	0.832974	+	0.553312i	$0.186636\pi$
$823$	−4.73521	+	17.6720i	−0.165059	+	0.616008i	−0.998033	+	0.0626958i	$0.980030\pi$
$824$	−11.6139	+	20.1158i	−0.404589	+	0.700768i
$825$	−0.170654	+	1.38727i	−0.00594142	+	0.0482986i
$826$		0			0
$827$	28.9027	+	28.9027i	1.00505	+	1.00505i	0.999987	+	0.00505903i	$0.00161035\pi$
$827$	28.9027	+	28.9027i	1.00505	+	1.00505i	0.00505903	+	0.999987i	$0.498390\pi$
$828$	9.44697	+	6.17950i	0.328305	+	0.214752i
$829$	−15.1933	+	8.77184i	−0.527684	+	0.304659i	−0.740073	−	0.672527i	$-0.765209\pi$
$829$	−15.1933	+	8.77184i	−0.527684	+	0.304659i	0.212389	+	0.977185i	$0.431876\pi$
$830$	−13.8965	−	1.57325i	−0.482356	−	0.0546084i
$831$	−11.4057	−	1.82585i	−0.395660	−	0.0633380i
$832$	2.42282	−	2.42282i	0.0839961	−	0.0839961i
$833$		0			0
$834$	−6.74762	−	17.6655i	−0.233651	−	0.611706i
$835$	−2.92346	+	7.43721i	−0.101170	+	0.257375i
$836$	0.790254	−	0.456253i	0.0273315	−	0.0157799i
$837$	−28.6864	−	26.0885i	−0.991548	−	0.901750i
$838$	17.6367	−	4.72574i	0.609250	−	0.163248i
$839$	15.4350			0.532875			0.266437	−	0.963852i	$-0.414153\pi$
$839$	15.4350			0.532875			0.266437	+	0.963852i	$0.414153\pi$
$840$		0			0
$841$	−25.0000			−0.862069
$842$	−14.0739	+	3.77108i	−0.485017	+	0.129960i
$843$	−2.24467	−	21.7021i	−0.0773104	−	0.747459i
$844$	9.11485	−	5.26246i	0.313746	−	0.181141i
$845$	−62.2130	+	27.1038i	−2.14019	+	0.932400i
$846$	8.89716	−	7.95786i	0.305891	−	0.273597i
$847$		0			0
$848$	4.49966	−	4.49966i	0.154519	−	0.154519i
$849$	5.00189	−	31.2459i	0.171664	−	1.07236i
$850$	−10.9535	−	10.1850i	−0.375701	−	0.349344i
$851$	−4.11351	+	2.37493i	−0.141009	+	0.0814117i
$852$	15.0044	+	20.7239i	0.514043	+	0.709988i
$853$	−5.62301	−	5.62301i	−0.192528	−	0.192528i	0.604259	−	0.796788i	$-0.293469\pi$
$853$	−5.62301	−	5.62301i	−0.192528	−	0.192528i	−0.796788	+	0.604259i	$0.793469\pi$
$854$		0			0
$855$	2.25025	+	24.0233i	0.0769569	+	0.821579i
$856$	−16.9323	+	29.3277i	−0.578735	+	1.00240i
$857$	5.59795	−	20.8918i	0.191222	−	0.713651i	−0.801990	−	0.597337i	$-0.796225\pi$
$857$	5.59795	−	20.8918i	0.191222	−	0.713651i	0.993212	−	0.116314i	$-0.0371079\pi$
$858$	−1.19787	+	0.123897i	−0.0408945	+	0.00422976i
$859$	−39.2936	−	22.6862i	−1.34068	−	0.774042i	−0.353772	−	0.935332i	$-0.615101\pi$
$859$	−39.2936	−	22.6862i	−1.34068	−	0.774042i	−0.986907	+	0.161290i	$0.948435\pi$
$860$	4.10924	+	27.3618i	0.140124	+	0.933029i
$861$		0			0
$862$	0.909671	−	0.909671i	0.0309835	−	0.0309835i
$863$	2.20435	+	8.22674i	0.0750369	+	0.280041i	0.993242	−	0.116065i	$-0.0370280\pi$
$863$	2.20435	+	8.22674i	0.0750369	+	0.280041i	−0.918205	+	0.396106i	$0.870361\pi$
$864$	−1.41073	−	29.7439i	−0.0479942	−	1.01191i
$865$	−3.56518	+	2.84003i	−0.121220	+	0.0965640i
$866$	−15.0374	−	8.68183i	−0.510991	−	0.295021i
$867$	6.16980	+	2.75922i	0.209537	+	0.0937080i
$868$		0			0
$869$	−0.873074			−0.0296170
$870$	3.54897	+	3.61826i	0.120321	+	0.122670i
$871$	−8.61581	−	14.9230i	−0.291936	−	0.505647i
$872$	5.58678	−	20.8501i	0.189192	−	0.706075i
$873$	22.5442	−	34.4646i	0.763004	−	1.16645i
$874$			5.63379i			0.190566i
$875$		0			0
$876$	3.77730	+	9.88910i	0.127623	+	0.334122i
$877$	6.31256	+	23.5588i	0.213160	+	0.795525i	0.986806	+	0.161906i	$0.0517643\pi$
$877$	6.31256	+	23.5588i	0.213160	+	0.795525i	−0.773646	+	0.633618i	$0.781569\pi$
$878$	16.3991	+	4.39411i	0.553441	+	0.148294i
$879$	3.18801	−	3.92357i	0.107529	−	0.132339i
$880$	−0.534198	+	0.232730i	−0.0180078	+	0.00784532i
$881$		−	0.538909i		−	0.0181563i	−0.999959	−	0.00907815i	$-0.997110\pi$
$881$		−	0.538909i		−	0.0181563i	0.999959	−	0.00907815i	$-0.00288970\pi$
$882$		0			0
$883$	−25.2230	−	25.2230i	−0.848821	−	0.848821i	0.141165	−	0.989986i	$-0.454915\pi$
$883$	−25.2230	−	25.2230i	−0.848821	−	0.848821i	−0.989986	+	0.141165i	$0.954915\pi$
$884$	−23.6576	+	40.9762i	−0.795692	+	1.37818i
$885$	−4.89586	+	8.29367i	−0.164573	+	0.278789i
$886$	−11.5911	−	20.0764i	−0.389411	−	0.674479i
$887$	9.48573	−	2.54169i	0.318500	−	0.0853417i	−0.0960275	−	0.995379i	$-0.530614\pi$
$887$	9.48573	−	2.54169i	0.318500	−	0.0853417i	0.414527	+	0.910037i	$0.363947\pi$
$888$	7.33218	+	3.27905i	0.246052	+	0.110038i
$889$		0			0
$890$	15.7290	−	2.36221i	0.527238	−	0.0791814i
$891$	−0.861557	+	1.16947i	−0.0288633	+	0.0391787i
$892$	−0.820399	−	0.219825i	−0.0274690	−	0.00736029i
$893$	−21.1277	−	5.66115i	−0.707012	−	0.189443i
$894$	2.79741	−	17.4749i	0.0935593	−	0.584447i
$895$	−26.6994	+	36.1362i	−0.892464	+	1.20790i
$896$		0			0
$897$	−11.1447	+	24.9202i	−0.372110	+	0.832062i
$898$	11.0250	−	2.95413i	0.367908	−	0.0985805i
$899$	7.46230	+	12.9251i	0.248882	+	0.431076i
$900$	0.455855	−	23.5739i	0.0151952	−	0.785795i
$901$	9.00945	−	15.6048i	0.300148	−	0.519872i
$902$	0.898961	+	0.898961i	0.0299321	+	0.0299321i
$903$		0			0
$904$		−	16.1265i		−	0.536359i
$905$	−14.8973	−	34.1946i	−0.495203	−	1.13667i
$906$	−6.39879	−	5.19920i	−0.212586	−	0.172732i
$907$	−11.8457	−	3.17404i	−0.393329	−	0.105392i	0.0567332	−	0.998389i	$-0.481932\pi$
$907$	−11.8457	−	3.17404i	−0.393329	−	0.105392i	−0.450062	+	0.892997i	$0.648598\pi$
$908$	−7.19695	−	26.8594i	−0.238839	−	0.891360i
$909$	−10.3852	+	9.28881i	−0.344456	+	0.308090i
$910$		0			0
$911$			27.0102i			0.894889i	0.894312	+	0.447444i	$0.147666\pi$
$911$			27.0102i			0.894889i	−0.894312	+	0.447444i	$0.852334\pi$
$912$	−8.14750	+	5.89893i	−0.269791	+	0.195333i
$913$	−0.399296	+	1.49019i	−0.0132148	+	0.0493182i
$914$	11.5067	+	19.9302i	0.380607	+	0.659231i
$915$	7.72520	+	0.0746854i	0.255387	+	0.00246902i
$916$	−3.64787			−0.120529
$917$		0			0
$918$	−4.72983	−	14.8067i	−0.156108	−	0.488695i
$919$	10.7836	+	6.22589i	0.355717	+	0.205373i	0.667200	−	0.744878i	$-0.267493\pi$
$919$	10.7836	+	6.22589i	0.355717	+	0.205373i	−0.311484	+	0.950252i	$0.600826\pi$
$920$	1.40730	−	12.4307i	0.0463972	−	0.409827i
$921$	−0.989990	+	1.21841i	−0.0326213	+	0.0401479i
$922$	1.27449	+	4.75647i	0.0419731	+	0.156646i
$923$	−43.7503	+	43.7503i	−1.44006	+	1.44006i
$924$		0			0
$925$	8.76636	+	4.64510i	0.288236	+	0.152730i
$926$	13.3048	+	7.68155i	0.437224	+	0.252432i
$927$	−26.6110	+	13.4482i	−0.874020	+	0.441697i
$928$	−2.96640	+	11.0708i	−0.0973768	+	0.363415i
$929$	7.49824	−	12.9873i	0.246009	−	0.426100i	−0.716406	−	0.697684i	$-0.754214\pi$
$929$	7.49824	−	12.9873i	0.246009	−	0.426100i	0.962415	+	0.271584i	$0.0875473\pi$
$930$	−5.07071	+	18.2178i	−0.166275	+	0.597385i
$931$		0			0
$932$	−9.53450	−	9.53450i	−0.312313	−	0.312313i
$933$	−29.2465	+	21.1749i	−0.957487	+	0.693236i
$934$	−6.18154	+	3.56892i	−0.202266	+	0.116778i
$935$	−1.29054	+	1.02804i	−0.0422050	+	0.0336207i
$936$	45.1848	−	9.44809i	1.47691	−	0.308820i
$937$	17.8137	−	17.8137i	0.581947	−	0.581947i	−0.353491	−	0.935438i	$-0.615006\pi$
$937$	17.8137	−	17.8137i	0.581947	−	0.581947i	0.935438	+	0.353491i	$0.115006\pi$
$938$		0			0
$939$	−28.3673	+	10.8353i	−0.925732	+	0.353598i
$940$	19.8926	+	7.81948i	0.648824	+	0.255043i
$941$	44.3404	−	25.5999i	1.44546	−	0.834534i	0.447249	−	0.894409i	$-0.352404\pi$
$941$	44.3404	−	25.5999i	1.44546	−	0.834534i	0.998206	+	0.0598755i	$0.0190704\pi$
$942$	17.8413	−	1.84534i	0.581301	−	0.0601245i
$943$	27.8370	−	7.45891i	0.906499	−	0.242896i
$944$	−4.01498			−0.130677
$945$		0			0
$946$	−0.831296			−0.0270277
$947$	37.7699	−	10.1204i	1.22736	−	0.328870i	0.413808	−	0.910364i	$-0.364199\pi$
$947$	37.7699	−	10.1204i	1.22736	−	0.328870i	0.813550	+	0.581495i	$0.197532\pi$
$948$	14.6497	−	1.51523i	0.475800	−	0.0492125i
$949$	−22.1700	+	12.7998i	−0.719667	+	0.415500i
$950$	9.97025	−	6.24993i	0.323478	−	0.202775i
$951$	6.68471	−	2.55333i	0.216767	−	0.0827975i
$952$		0			0
$953$	6.39589	−	6.39589i	0.207183	−	0.207183i	−0.595886	−	0.803069i	$-0.703199\pi$
$953$	6.39589	−	6.39589i	0.207183	−	0.207183i	0.803069	+	0.595886i	$0.203199\pi$
$954$	−7.57256	+	1.58341i	−0.245171	+	0.0512649i
$955$	−5.44035	+	48.0546i	−0.176046	+	1.55501i
$956$	−29.3585	+	16.9501i	−0.949522	+	0.548207i
$957$	0.452858	−	0.327877i	0.0146388	−	0.0105988i
$958$	−7.92969	−	7.92969i	−0.256197	−	0.256197i
$959$		0			0
$960$	−1.75519	+	0.990859i	−0.0566485	+	0.0319798i
$961$	−12.3430	+	21.3786i	−0.398160	+	0.689633i
$962$	−2.21232	+	8.25648i	−0.0713280	+	0.266200i
$963$	−38.7972	+	19.6067i	−1.25022	+	0.631816i
$964$	8.83553	+	5.10120i	0.284573	+	0.164298i
$965$	−12.8382	+	1.92806i	−0.413276	+	0.0620665i
$966$		0			0
$967$	24.4108	−	24.4108i	0.784999	−	0.784999i	−0.195670	−	0.980670i	$-0.562688\pi$
$967$	24.4108	−	24.4108i	0.784999	−	0.784999i	0.980670	+	0.195670i	$0.0626882\pi$
$968$	6.63800	+	24.7734i	0.213353	+	0.796246i
$969$	−17.9613	+	22.1054i	−0.576999	+	0.710128i
$970$	−19.9571	−	2.25938i	−0.640785	−	0.0725445i
$971$	27.2512	+	15.7335i	0.874534	+	0.504912i	0.868852	−	0.495071i	$-0.164858\pi$
$971$	27.2512	+	15.7335i	0.874534	+	0.504912i	0.00568176	+	0.999984i	$0.498191\pi$
$972$	12.4268	−	21.1183i	0.398591	−	0.677370i
$973$		0			0
$974$	−13.1117			−0.420125
$975$	56.4655	−	7.92267i	1.80834	−	0.253729i
$976$	1.61033	+	2.78918i	0.0515456	+	0.0892795i
$977$	−5.90313	+	22.0308i	−0.188858	+	0.704827i	0.804914	+	0.593392i	$0.202211\pi$
$977$	−5.90313	+	22.0308i	−0.188858	+	0.704827i	−0.993772	+	0.111435i	$0.964455\pi$
$978$	13.2714	−	9.60869i	0.424371	−	0.307252i
$979$		−	1.75457i		−	0.0560764i
$980$		0			0
$981$	20.6525	−	18.4721i	0.659383	−	0.589770i
$982$	4.30992	+	16.0848i	0.137535	+	0.513288i
$983$	−56.1919	−	15.0566i	−1.79224	−	0.480230i	−0.799519	−	0.600641i	$-0.794912\pi$
$983$	−56.1919	−	15.0566i	−1.79224	−	0.480230i	−0.992724	+	0.120411i	$0.961579\pi$
$984$	−37.8217	−	30.7312i	−1.20571	−	0.979675i
$985$	10.5517	−	26.8432i	0.336204	−	0.855295i
$986$			5.98282i			0.190532i
$987$		0			0
$988$	−26.3217	−	26.3217i	−0.837405	−	0.837405i
$989$	−9.42212	+	16.3196i	−0.299606	+	0.518933i
$990$	0.698380	+	0.118733i	0.0221960	+	0.00377360i
$991$	27.1762	+	47.0706i	0.863281	+	1.49525i	0.868744	+	0.495262i	$0.164928\pi$
$991$	27.1762	+	47.0706i	0.863281	+	1.49525i	−0.00546280	+	0.999985i	$0.501739\pi$
$992$	−41.3066	+	11.0681i	−1.31149	+	0.351412i
$993$	−12.3678	+	27.6552i	−0.392479	+	0.877610i
$994$		0			0
$995$	1.14721	+	0.847626i	0.0363691	+	0.0268716i
$996$	4.11372	−	25.6976i	0.130348	−	0.814260i
$997$	8.41769	+	2.25551i	0.266591	+	0.0714329i	0.389638	−	0.920968i	$-0.372600\pi$
$997$	8.41769	+	2.25551i	0.266591	+	0.0714329i	−0.123047	+	0.992401i	$0.539267\pi$
$998$	9.64459	+	2.58426i	0.305294	+	0.0818033i
$999$	5.57233	+	8.67464i	0.176301	+	0.274453i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	735.2.y.e.128.3		32
3.2	odd	2		735.2.y.f.128.6		32
5.2	odd	4		735.2.y.f.422.4		32
7.2	even	3		735.2.j.d.638.6	yes	16
7.3	odd	6	inner	735.2.y.e.263.5		32
7.4	even	3	inner	735.2.y.e.263.6		32
7.5	odd	6		735.2.j.d.638.5	yes	16
7.6	odd	2	inner	735.2.y.e.128.4		32
15.2	even	4	inner	735.2.y.e.422.6		32
21.2	odd	6		735.2.j.c.638.3	yes	16
21.5	even	6		735.2.j.c.638.4	yes	16
21.11	odd	6		735.2.y.f.263.4		32
21.17	even	6		735.2.y.f.263.3		32
21.20	even	2		735.2.y.f.128.5		32
35.2	odd	12		735.2.j.c.197.3	✓	16
35.12	even	12		735.2.j.c.197.4	yes	16
35.17	even	12		735.2.y.f.557.5		32
35.27	even	4		735.2.y.f.422.3		32
35.32	odd	12		735.2.y.f.557.6		32
105.2	even	12		735.2.j.d.197.6	yes	16
105.17	odd	12	inner	735.2.y.e.557.4		32
105.32	even	12	inner	735.2.y.e.557.3		32
105.47	odd	12		735.2.j.d.197.5	yes	16
105.62	odd	4	inner	735.2.y.e.422.5		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
735.2.j.c.197.3	✓	16	35.2	odd	12
735.2.j.c.197.4	yes	16	35.12	even	12
735.2.j.c.638.3	yes	16	21.2	odd	6
735.2.j.c.638.4	yes	16	21.5	even	6
735.2.j.d.197.5	yes	16	105.47	odd	12
735.2.j.d.197.6	yes	16	105.2	even	12
735.2.j.d.638.5	yes	16	7.5	odd	6
735.2.j.d.638.6	yes	16	7.2	even	3
735.2.y.e.128.3		32	1.1	even	1	trivial
735.2.y.e.128.4		32	7.6	odd	2	inner
735.2.y.e.263.5		32	7.3	odd	6	inner
735.2.y.e.263.6		32	7.4	even	3	inner
735.2.y.e.422.5		32	105.62	odd	4	inner
735.2.y.e.422.6		32	15.2	even	4	inner
735.2.y.e.557.3		32	105.32	even	12	inner
735.2.y.e.557.4		32	105.17	odd	12	inner
735.2.y.f.128.5		32	21.20	even	2
735.2.y.f.128.6		32	3.2	odd	2
735.2.y.f.263.3		32	21.17	even	6
735.2.y.f.263.4		32	21.11	odd	6
735.2.y.f.422.3		32	35.27	even	4
735.2.y.f.422.4		32	5.2	odd	4
735.2.y.f.557.5		32	35.17	even	12
735.2.y.f.557.6		32	35.32	odd	12

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:	\( N \)	\(=\)	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	735.y (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.632011 + 0.169347i) q^{2} +(-1.72286 + 0.178197i) q^{3} +(-1.36129 + 0.785942i) q^{4} +(0.893095 + 2.04997i) q^{5} +(1.05869 - 0.404383i) q^{6} +(1.65258 - 1.65258i) q^{8} +(2.93649 - 0.614017i) q^{9} +(-0.911602 - 1.14436i) q^{10} +(-0.139773 + 0.0806980i) q^{11} +(2.20526 - 1.59665i) q^{12} +(4.65555 + 4.65555i) q^{13} +(-1.90398 - 3.37267i) q^{15} +(0.807294 - 1.39827i) q^{16} +(1.18329 - 4.41610i) q^{17} +(-1.75191 + 0.885351i) q^{18} +(3.11497 + 1.79843i) q^{19} +(-2.82692 - 2.08869i) q^{20} +(0.0746721 - 0.0746721i) q^{22} +(-0.619573 - 2.31228i) q^{23} +(-2.55268 + 3.14165i) q^{24} +(-3.40476 + 3.66164i) q^{25} +(-3.73076 - 2.15395i) q^{26} +(-4.94975 + 1.58114i) q^{27} +2.00000 q^{29} +(1.77448 + 1.80913i) q^{30} +(3.73115 + 6.46254i) q^{31} +(-1.48320 + 5.53538i) q^{32} +(0.226429 - 0.163938i) q^{33} +2.99141i q^{34} +(-3.51484 + 3.14377i) q^{36} +(-0.513548 - 1.91659i) q^{37} +(-2.27325 - 0.609116i) q^{38} +(-8.85046 - 7.19125i) q^{39} +(4.86366 + 1.91183i) q^{40} +12.0388i q^{41} +(-5.56631 - 5.56631i) q^{43} +(0.126848 - 0.219707i) q^{44} +(3.88128 + 5.47135i) q^{45} +(0.783154 + 1.35646i) q^{46} +(-5.87394 + 1.57392i) q^{47} +(-1.14169 + 2.55289i) q^{48} +(1.53176 - 2.89078i) q^{50} +(-1.25171 + 7.81918i) q^{51} +(-9.99654 - 2.67857i) q^{52} +(3.80695 + 1.02007i) q^{53} +(2.86053 - 1.83752i) q^{54} +(-0.290259 - 0.214460i) q^{55} +(-5.68713 - 2.54336i) q^{57} +(-1.26402 + 0.338694i) q^{58} +(-1.24335 - 2.15354i) q^{59} +(5.24259 + 3.09477i) q^{60} +(-0.997366 + 1.72749i) q^{61} +(-3.45254 - 3.45254i) q^{62} -0.520416i q^{64} +(-5.38589 + 13.7016i) q^{65} +(-0.115343 + 0.141956i) q^{66} +(-2.52804 - 0.677387i) q^{67} +(1.86000 + 6.94160i) q^{68} +(1.47948 + 3.87333i) q^{69} +9.39746i q^{71} +(3.83808 - 5.86751i) q^{72} +(-1.00634 + 3.75571i) q^{73} +(0.649136 + 1.12434i) q^{74} +(5.21344 - 6.91521i) q^{75} -5.65384 q^{76} +(6.81140 + 3.04615i) q^{78} +(4.68478 + 2.70476i) q^{79} +(3.58741 + 0.406138i) q^{80} +(8.24597 - 3.60611i) q^{81} +(-2.03873 - 7.60864i) q^{82} +(6.75913 - 6.75913i) q^{83} +(10.1097 - 1.51829i) q^{85} +(4.46060 + 2.57533i) q^{86} +(-3.44572 + 0.356394i) q^{87} +(-0.0976263 + 0.364346i) q^{88} +(-5.43562 + 9.41477i) q^{89} +(-3.37957 - 2.80067i) q^{90} +(2.66074 + 2.66074i) q^{92} +(-7.57985 - 10.4692i) q^{93} +(3.44585 - 1.98946i) q^{94} +(-0.904763 + 7.99176i) q^{95} +(1.56896 - 9.80098i) q^{96} +(9.70695 - 9.70695i) q^{97} +(-0.360892 + 0.322792i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{2} - 56 q^{8} + 32 q^{9} + 8 q^{15} + 48 q^{16} + 28 q^{18} + 16 q^{22} + 16 q^{23} - 8 q^{25} + 64 q^{29} - 64 q^{30} + 52 q^{32} - 80 q^{36} + 24 q^{37} - 8 q^{39} + 48 q^{43} - 8 q^{44} - 88 q^{46}+ \cdots - 80 q^{99}+O(q^{100}) \) 32 * q - 4 * q^2 - 56 * q^8 + 32 * q^9 + 8 * q^15 + 48 * q^16 + 28 * q^18 + 16 * q^22 + 16 * q^23 - 8 * q^25 + 64 * q^29 - 64 * q^30 + 52 * q^32 - 80 * q^36 + 24 * q^37 - 8 * q^39 + 48 * q^43 - 8 * q^44 - 88 * q^46 - 104 * q^50 - 40 * q^51 - 8 * q^53 - 8 * q^58 - 28 * q^60 - 112 * q^65 - 16 * q^67 + 4 * q^72 - 8 * q^74 + 16 * q^81 + 48 * q^85 + 80 * q^88 + 160 * q^92 - 16 * q^93 + 72 * q^95 - 80 * q^99

Introduction

L-functions

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