LMFDB - Embedded newform 735.2.y.f.557.5

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			557.5
Character	$\chi$	$=$	735.557
Dual form			735.2.y.f.128.5

$q$-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} +(-1.40294 + 1.01575i) 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} +(0.936492 - 2.85008i) q^{9} +(0.911602 - 1.14436i) q^{10} +(0.139773 + 0.0806980i) q^{11} +(2.70814 - 0.280105i) q^{12} +(-4.65555 + 4.65555i) q^{13} +(0.829304 + 3.78315i) q^{15} +(0.807294 + 1.39827i) q^{16} +(1.18329 + 4.41610i) q^{17} +(1.07453 - 1.64269i) 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} +(3.99709 + 0.639861i) q^{24} +(-3.40476 - 3.66164i) q^{25} +(-3.73076 + 2.15395i) q^{26} +(1.58114 + 4.94975i) q^{27} -2.00000 q^{29} +(-0.116536 + 2.53143i) q^{30} +(-3.73115 + 6.46254i) q^{31} +(1.48320 + 5.53538i) q^{32} +(-0.278063 + 0.0287603i) q^{33} +2.99141i q^{34} +(-3.51484 + 3.14377i) q^{36} +(-0.513548 + 1.91659i) q^{37} +(-2.27325 + 0.609116i) q^{38} +(1.80258 - 11.2603i) q^{39} +(-4.86366 + 1.91183i) q^{40} -12.0388i q^{41} +(-5.56631 + 5.56631i) q^{43} +(-0.126848 - 0.219707i) q^{44} +(-5.00622 - 4.46518i) q^{45} +(0.783154 - 1.35646i) q^{46} +(-5.87394 - 1.57392i) q^{47} +(-2.55289 - 1.14169i) q^{48} +(-1.53176 - 2.89078i) q^{50} +(-6.14576 - 4.99360i) q^{51} +(9.99654 - 2.67857i) q^{52} +(-3.80695 + 1.02007i) q^{53} +(0.161073 + 3.39605i) q^{54} +(0.290259 - 0.214460i) q^{55} +(2.54336 - 5.68713i) q^{57} +(-1.26402 - 0.338694i) q^{58} +(-1.24335 + 2.15354i) q^{59} +(1.84442 - 5.80176i) q^{60} +(0.997366 + 1.72749i) q^{61} +(-3.45254 + 3.45254i) q^{62} +0.520416i q^{64} +(5.38589 + 13.7016i) q^{65} +(-0.180609 - 0.0289122i) q^{66} +(-2.52804 + 0.677387i) q^{67} +(1.86000 - 6.94160i) q^{68} +(1.47948 + 3.87333i) q^{69} +9.39746i q^{71} +(-6.25763 + 3.16237i) q^{72} +(1.00634 + 3.75571i) q^{73} +(-0.649136 + 1.12434i) q^{74} +(8.49600 + 1.67867i) q^{75} +5.65384 q^{76} +(3.04615 - 6.81140i) q^{78} +(4.68478 - 2.70476i) q^{79} +(3.58741 - 0.406138i) q^{80} +(-7.24597 - 5.33816i) 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} +(2.80588 - 2.03151i) q^{87} +(-0.0976263 - 0.364346i) q^{88} +(-5.43562 - 9.41477i) q^{89} +(-2.40782 - 3.66983i) q^{90} +(-2.66074 + 2.66074i) q^{92} +(-1.32976 - 12.8565i) q^{93} +(-3.44585 - 1.98946i) q^{94} +(0.904763 + 7.99176i) q^{95} +(-7.70342 - 6.25925i) 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} - 56 q^{15} + 48 q^{16} - 12 q^{18} + 16 q^{22} - 16 q^{23} - 8 q^{25} - 64 q^{29} - 8 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 - 56 * q^15 + 48 * q^16 - 12 * q^18 + 16 * q^22 - 16 * q^23 - 8 * q^25 - 64 * q^29 - 8 * 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 + 32 * q^57 - 8 * q^58 + 116 * q^60 + 112 * q^65 - 16 * q^67 - 116 * q^72 + 8 * q^74 + 128 * q^78 + 16 * q^81 + 48 * q^85 + 80 * q^88 - 160 * q^92 - 80 * q^93 - 72 * q^95 + 80 * q^99

Character values

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

$n$	$346$	$442$	$491$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{4}\right)$	$-1$

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	$-0.342358\pi$
$2$	0.632011	+	0.169347i	0.446899	+	0.119746i	−0.0283490	+	0.999598i	$0.509025\pi$
$3$	−1.40294	+	1.01575i	−0.809989	+	0.586445i
$3$	−1.40294	+	1.01575i	−0.809989	+	0.586445i
$4$	−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
$9$	0.936492	−	2.85008i	0.312164	−	0.950028i
$10$	0.911602	−	1.14436i	0.288274	−	0.361879i
$11$	0.139773	+	0.0806980i	0.0421431	+	0.0243313i	0.520924	−	0.853603i	$-0.325588\pi$
$11$	0.139773	+	0.0806980i	0.0421431	+	0.0243313i	−0.478780	+	0.877935i	$0.658921\pi$
$12$	2.70814	−	0.280105i	0.781772	−	0.0808593i
$13$	−4.65555	+	4.65555i	−1.29122	+	1.29122i	−0.357181	+	0.934035i	$0.616262\pi$
$13$	−4.65555	+	4.65555i	−1.29122	+	1.29122i	−0.934035	+	0.357181i	$0.883738\pi$
$14$		0			0
$15$	0.829304	+	3.78315i	0.214125	+	0.976806i
$16$	0.807294	+	1.39827i	0.201823	+	0.349569i
$17$	1.18329	+	4.41610i	0.286990	+	1.07106i	0.947373	+	0.320133i	$0.103727\pi$
$17$	1.18329	+	4.41610i	0.286990	+	1.07106i	−0.660383	+	0.750929i	$0.729606\pi$
$18$	1.07453	−	1.64269i	0.253268	−	0.387186i
$19$	−3.11497	+	1.79843i	−0.714623	+	0.412588i	−0.812770	−	0.582584i	$-0.802042\pi$
$19$	−3.11497	+	1.79843i	−0.714623	+	0.412588i	0.0981474	+	0.995172i	$0.468708\pi$
$20$	−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	$-0.836375\pi$
$23$	0.619573	−	2.31228i	0.129190	−	0.482144i	0.999954	+	0.00955698i	$0.00304213\pi$
$24$	3.99709	+	0.639861i	0.815903	+	0.130611i
$25$	−3.40476	−	3.66164i	−0.680953	−	0.732328i
$26$	−3.73076	+	2.15395i	−0.731662	+	0.422425i
$27$	1.58114	+	4.94975i	0.304290	+	0.952579i
$28$		0			0
$29$	−2.00000			−0.371391			−0.185695	−	0.982607i	$-0.559454\pi$
$29$	−2.00000			−0.371391			−0.185695	+	0.982607i	$0.559454\pi$
$30$	−0.116536	+	2.53143i	−0.0212764	+	0.462174i
$31$	−3.73115	+	6.46254i	−0.670134	+	1.16071i	0.307732	+	0.951473i	$0.400430\pi$
$31$	−3.73115	+	6.46254i	−0.670134	+	1.16071i	−0.977866	+	0.209233i	$0.932903\pi$
$32$	1.48320	+	5.53538i	0.262195	+	0.978525i
$33$	−0.278063	+	0.0287603i	−0.0484045	+	0.00500652i
$34$			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	−0.995205	−	0.0978108i	$-0.968816\pi$
$37$	−0.513548	+	1.91659i	−0.0844268	+	0.315085i	0.910778	+	0.412896i	$0.135483\pi$
$38$	−2.27325	+	0.609116i	−0.368770	+	0.0988117i
$39$	1.80258	−	11.2603i	0.288643	−	1.80310i
$40$	−4.86366	+	1.91183i	−0.769012	+	0.302287i
$41$		−	12.0388i		−	1.88014i	−0.340977	−	0.940072i	$-0.610758\pi$
$41$		−	12.0388i		−	1.88014i	0.340977	−	0.940072i	$-0.389242\pi$
$42$		0			0
$43$	−5.56631	+	5.56631i	−0.848854	+	0.848854i	−0.989990	−	0.141136i	$-0.954924\pi$
$43$	−5.56631	+	5.56631i	−0.848854	+	0.848854i	0.141136	+	0.989990i	$0.454924\pi$
$44$	−0.126848	−	0.219707i	−0.0191230	−	0.0331221i
$45$	−5.00622	−	4.46518i	−0.746283	−	0.665629i
$46$	0.783154	−	1.35646i	0.115470	−	0.200000i
$47$	−5.87394	−	1.57392i	−0.856802	−	0.229579i	−0.196430	−	0.980518i	$-0.562935\pi$
$47$	−5.87394	−	1.57392i	−0.856802	−	0.229579i	−0.660372	+	0.750939i	$0.729601\pi$
$48$	−2.55289	−	1.14169i	−0.368478	−	0.164788i
$49$		0			0
$50$	−1.53176	−	2.89078i	−0.216624	−	0.408818i
$51$	−6.14576	−	4.99360i	−0.860578	−	0.699244i
$52$	9.99654	−	2.67857i	1.38627	−	0.371450i
$53$	−3.80695	+	1.02007i	−0.522924	+	0.140117i	−0.510619	−	0.859807i	$-0.670584\pi$
$53$	−3.80695	+	1.02007i	−0.522924	+	0.140117i	−0.0123054	+	0.999924i	$0.503917\pi$
$54$	0.161073	+	3.39605i	0.0219193	+	0.462144i
$55$	0.290259	−	0.214460i	0.0391385	−	0.0289177i
$56$		0			0
$57$	2.54336	−	5.68713i	0.336877	−	0.753279i
$58$	−1.26402	−	0.338694i	−0.165974	−	0.0444726i
$59$	−1.24335	+	2.15354i	−0.161870	+	0.280367i	−0.935539	−	0.353223i	$-0.885086\pi$
$59$	−1.24335	+	2.15354i	−0.161870	+	0.280367i	0.773669	+	0.633589i	$0.218419\pi$
$60$	1.84442	−	5.80176i	0.238113	−	0.749004i
$61$	0.997366	+	1.72749i	0.127700	+	0.221182i	0.922785	−	0.385315i	$-0.125907\pi$
$61$	0.997366	+	1.72749i	0.127700	+	0.221182i	−0.795085	+	0.606498i	$0.792574\pi$
$62$	−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
$66$	−0.180609	−	0.0289122i	−0.0222314	−	0.00355884i
$67$	−2.52804	+	0.677387i	−0.308850	+	0.0827560i	−0.409915	−	0.912124i	$-0.634442\pi$
$67$	−2.52804	+	0.677387i	−0.308850	+	0.0827560i	0.101065	+	0.994880i	$0.467775\pi$
$68$	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	$0.811708\pi$
$72$	−6.25763	+	3.16237i	−0.737469	+	0.372689i
$73$	1.00634	+	3.75571i	0.117783	+	0.439573i	0.999480	−	0.0322434i	$-0.0102652\pi$
$73$	1.00634	+	3.75571i	0.117783	+	0.439573i	−0.881697	+	0.471816i	$0.843599\pi$
$74$	−0.649136	+	1.12434i	−0.0754605	+	0.130701i
$75$	8.49600	+	1.67867i	0.981034	+	0.193836i
$76$	5.65384			0.648540
$77$		0			0
$78$	3.04615	−	6.81140i	0.344909	−	0.771239i
$79$	4.68478	−	2.70476i	0.527079	−	0.304309i	−0.212747	−	0.977107i	$-0.568241\pi$
$79$	4.68478	−	2.70476i	0.527079	−	0.304309i	0.739826	+	0.672798i	$0.234908\pi$
$80$	3.58741	−	0.406138i	0.401085	−	0.0454076i
$81$	−7.24597	−	5.33816i	−0.805107	−	0.593129i
$82$	2.03873	−	7.60864i	0.225140	−	0.840234i
$83$	6.75913	+	6.75913i	0.741911	+	0.741911i	0.972946	−	0.231034i	$-0.0742109\pi$
$83$	6.75913	+	6.75913i	0.741911	+	0.741911i	−0.231034	+	0.972946i	$0.574211\pi$
$84$		0			0
$85$	10.1097	+	1.51829i	1.09655	+	0.164681i
$86$	−4.46060	+	2.57533i	−0.480999	+	0.277705i
$87$	2.80588	−	2.03151i	0.300822	−	0.217800i
$88$	−0.0976263	−	0.364346i	−0.0104070	−	0.0388394i
$89$	−5.43562	−	9.41477i	−0.576175	−	0.997964i	−0.995913	−	0.0903187i	$-0.971211\pi$
$89$	−5.43562	−	9.41477i	−0.576175	−	0.997964i	0.419738	−	0.907645i	$-0.362122\pi$
$90$	−2.40782	−	3.66983i	−0.253806	−	0.386834i
$91$		0			0
$92$	−2.66074	+	2.66074i	−0.277401	+	0.277401i
$93$	−1.32976	−	12.8565i	−0.137890	−	1.33316i
$94$	−3.44585	−	1.98946i	−0.355413	−	0.205198i
$95$	0.904763	+	7.99176i	0.0928267	+	0.819938i
$96$	−7.70342	−	6.25925i	−0.786227	−	0.638832i
$97$	−9.70695	−	9.70695i	−0.985592	−	0.985592i	0.0143059	−	0.999898i	$-0.495446\pi$
$97$	−9.70695	−	9.70695i	−0.985592	−	0.985592i	−0.999898	+	0.0143059i	$0.995446\pi$
$98$		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	0.286358	−	0.958123i	$-0.407555\pi$
$101$	−4.02217	−	2.32220i	−0.400221	−	0.231068i	−0.686579	+	0.727055i	$0.740889\pi$
$102$	−3.03853	−	4.19677i	−0.300860	−	0.415543i
$103$	9.60004	+	2.57232i	0.945920	+	0.253459i	0.698630	−	0.715483i	$-0.253793\pi$
$103$	9.60004	+	2.57232i	0.945920	+	0.253459i	0.247290	+	0.968941i	$0.420460\pi$
$104$	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	$-0.169671\pi$
$107$	13.9963	+	3.75029i	1.35307	+	0.362554i	0.491804	+	0.870706i	$0.336338\pi$
$108$	1.73782	−	7.98073i	0.167222	−	0.767946i
$109$	7.99867	+	4.61803i	0.766134	+	0.442327i	0.831494	−	0.555534i	$-0.187486\pi$
$109$	7.99867	+	4.61803i	0.766134	+	0.442327i	−0.0653600	+	0.997862i	$0.520820\pi$
$110$	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	$-0.355216\pi$
$113$	−4.87918	−	4.87918i	−0.458994	−	0.458994i	−0.898325	+	0.439331i	$0.855216\pi$
$114$	2.57053	−	3.16362i	0.240752	−	0.296300i
$115$	−4.18677	−	3.33519i	−0.390418	−	0.311008i
$116$	2.72258	+	1.57188i	0.252785	+	0.145946i
$117$	8.90882	+	17.6286i	0.823621	+	1.62976i
$118$	−1.15050	+	1.15050i	−0.105912	+	0.105912i
$119$		0			0
$120$	4.88148	−	7.62247i	0.445616	−	0.695833i
$121$	−5.48698	−	9.50372i	−0.498816	−	0.863975i
$122$	0.337801	+	1.26069i	0.0305831	+	0.114138i
$123$	12.2284	+	16.8897i	1.10260	+	1.52289i
$124$	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	0.698535	−	0.715576i	$-0.253836\pi$
$127$	−0.192048	−	0.192048i	−0.0170415	−	0.0170415i	−0.715576	+	0.698535i	$0.753836\pi$
$128$	2.87827	−	10.7418i	0.254405	−	0.949454i
$129$	2.15521	−	13.4632i	0.189756	−	1.18537i
$130$	1.08362	+	9.57163i	0.0950399	+	0.839487i
$131$	−11.9048	+	6.87326i	−1.04013	+	0.600519i	−0.919870	−	0.392223i	$-0.871706\pi$
$131$	−11.9048	+	6.87326i	−1.04013	+	0.600519i	−0.120260	+	0.992742i	$0.538373\pi$
$132$	0.401128	+	0.179390i	0.0349137	+	0.0156139i
$133$		0			0
$134$	−1.71246			−0.147934
$135$	11.5589	+	1.17931i	0.994836	+	0.101498i
$136$	5.34248	−	9.25345i	0.458114	−	0.793477i
$137$	2.04989	+	7.65030i	0.175134	+	0.653609i	0.996529	+	0.0832489i	$0.0265297\pi$
$137$	2.04989	+	7.65030i	0.175134	+	0.653609i	−0.821395	+	0.570360i	$0.806804\pi$
$138$	0.279111	+	2.69853i	0.0237595	+	0.229714i
$139$		−	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
$144$	4.74122	−	0.991384i	0.395102	−	0.0826153i
$145$	−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	−0.985509	−	0.169623i	$-0.945745\pi$
$149$	−7.80795	−	13.5238i	−0.639652	−	1.10791i	0.345857	−	0.938287i	$-0.387588\pi$
$150$	5.08529	+	2.49971i	0.415212	+	0.204100i
$151$	−3.63753	+	6.30039i	−0.296018	+	0.512719i	−0.975221	−	0.221232i	$-0.928992\pi$
$151$	−3.63753	+	6.30039i	−0.296018	+	0.512719i	0.679203	+	0.733951i	$0.262326\pi$
$152$	8.11979	+	2.17569i	0.658602	+	0.176472i
$153$	13.6944	+	0.763163i	1.10713	+	0.0616981i
$154$		0			0
$155$	9.91575	+	13.4204i	0.796452	+	1.07795i
$156$	−11.3038	+	13.9119i	−0.905029	+	1.11384i
$157$	−15.2876	+	4.09630i	−1.22008	+	0.326921i	−0.810711	−	0.585447i	$-0.800919\pi$
$157$	−15.2876	+	4.09630i	−1.22008	+	0.326921i	−0.409373	+	0.912367i	$0.634253\pi$
$158$	3.41887	−	0.916084i	0.271991	−	0.0728797i
$159$	4.30479	−	5.29801i	0.341392	−	0.420160i
$160$	12.6720	+	1.90310i	1.00181	+	0.150453i
$161$		0			0
$162$	−3.67553	−	4.60086i	−0.288777	−	0.361477i
$163$	13.9649	+	3.74189i	1.09382	+	0.293088i	0.760245	−	0.649636i	$-0.225079\pi$
$163$	13.9649	+	3.74189i	1.09382	+	0.293088i	0.333573	+	0.942724i	$0.391746\pi$
$164$	−9.46179	+	16.3883i	−0.738842	+	1.27971i
$165$	−0.189379	+	0.595706i	−0.0147431	+	0.0463756i
$166$	3.12721	+	5.41648i	0.242718	+	0.420401i
$167$	2.52703	−	2.52703i	0.195547	−	0.195547i	−0.602541	−	0.798088i	$-0.705845\pi$
$167$	2.52703	−	2.52703i	0.195547	−	0.195547i	0.798088	+	0.602541i	$0.205845\pi$
$168$		0			0
$169$		−	30.3482i		−	2.33448i
$170$	6.13230	+	2.67161i	0.470326	+	0.204903i
$171$	2.20853	+	10.5621i	0.168891	+	0.807707i
$172$	11.9522	−	3.20257i	0.911344	−	0.244194i
$173$	0.527588	−	1.96899i	0.0401118	−	0.149699i	−0.942966	−	0.332890i	$-0.891976\pi$
$173$	0.527588	−	1.96899i	0.0401118	−	0.149699i	0.983077	+	0.183191i	$0.0586427\pi$
$174$	2.11738	−	0.808766i	0.160518	−	0.0613124i
$175$		0			0
$176$			0.260588i			0.0196426i
$177$	−0.443121	−	4.28422i	−0.0333070	−	0.322022i
$178$	−1.84101	−	6.87074i	−0.137990	−	0.514984i
$179$	−10.0466	+	17.4012i	−0.750918	+	1.30063i	0.196460	+	0.980512i	$0.437055\pi$
$179$	−10.0466	+	17.4012i	−0.750918	+	1.30063i	−0.947378	+	0.320117i	$0.896278\pi$
$180$	3.30555	+	10.0130i	0.246381	+	0.746325i
$181$	16.6805			1.23986			0.619928	−	0.784659i	$-0.287162\pi$
$181$	16.6805			1.23986			0.619928	+	0.784659i	$0.287162\pi$
$182$		0			0
$183$	−3.15395	−	1.41049i	−0.233147	−	0.104266i
$184$	−4.84513	+	2.79734i	−0.357188	+	0.206222i
$185$	3.47030	+	2.76445i	0.255142	+	0.203247i
$186$	1.33678	−	8.35063i	0.0980177	−	0.612298i
$187$	−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	$-0.952708\pi$
$191$	−18.7304	+	10.8140i	−1.35528	+	0.782472i	−0.366298	+	0.930498i	$0.619375\pi$
$192$	−0.528614	−	0.730113i	−0.0381494	−	0.0526914i
$193$	−1.50265	−	5.60798i	−0.108163	−	0.403671i	0.890521	−	0.454941i	$-0.150340\pi$
$193$	−1.50265	−	5.60798i	−0.108163	−	0.403671i	−0.998685	+	0.0512701i	$0.983673\pi$
$194$	−4.49106	−	7.77874i	−0.322439	−	0.558481i
$195$	−21.4735	−	13.7518i	−1.53775	−	0.984786i
$196$		0			0
$197$	9.12082	−	9.12082i	0.649832	−	0.649832i	−0.303121	−	0.952952i	$-0.598028\pi$
$197$	9.12082	−	9.12082i	0.649832	−	0.649832i	0.952952	+	0.303121i	$0.0980285\pi$
$198$	0.282752	−	0.142892i	0.0200943	−	0.0101549i
$199$	−0.552436	−	0.318949i	−0.0391612	−	0.0226097i	0.480292	−	0.877109i	$-0.340531\pi$
$199$	−0.552436	−	0.318949i	−0.0391612	−	0.0226097i	−0.519453	+	0.854499i	$0.673864\pi$
$200$	−0.424507	+	11.6778i	−0.0300172	+	0.825746i
$201$	2.85864	−	3.51820i	0.201633	−	0.248155i
$202$	−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
$207$	−6.00997	−	3.93127i	−0.417722	−	0.273242i
$208$	−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
$213$	−9.54550	−	13.1841i	−0.654047	−	0.903359i
$214$	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
$219$	−5.22671	−	4.24685i	−0.353189	−	0.286976i
$220$	−0.563680	+	0.0638153i	−0.0380033	+	0.00430242i
$221$	−26.0682	−	15.0505i	−1.75354	−	1.01241i
$222$	−0.231348	−	2.23674i	−0.0155271	−	0.150120i
$223$	−0.382073	+	0.382073i	−0.0255855	+	0.0255855i	−0.719784	−	0.694198i	$-0.755759\pi$
$223$	−0.382073	+	0.382073i	−0.0255855	+	0.0255855i	0.694198	+	0.719784i	$0.255759\pi$
$224$		0			0
$225$	−13.6245	+	6.27477i	−0.908301	+	0.418318i
$226$	−2.25742	−	3.90997i	−0.150161	−	0.260087i
$227$	−4.57855	−	17.0874i	−0.303889	−	1.13413i	−0.933897	−	0.357541i	$-0.883615\pi$
$227$	−4.57855	−	17.0874i	−0.303889	−	1.13413i	0.630008	−	0.776588i	$-0.283051\pi$
$228$	−7.93201	+	5.74291i	−0.525310	+	0.380333i
$229$	−2.00978	+	1.16035i	−0.132810	+	0.0766780i	−0.564933	−	0.825137i	$-0.691098\pi$
$229$	−2.00978	+	1.16035i	−0.132810	+	0.0766780i	0.432123	+	0.901815i	$0.357765\pi$
$230$	−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	0.854286	+	0.519803i	$0.173995\pi$
$233$	−2.22018	+	8.28583i	−0.145449	+	0.542823i	−0.999735	+	0.0230197i	$0.992672\pi$
$234$	2.64513	+	12.6501i	0.172917	+	0.826965i
$235$	−8.47247	+	10.6357i	−0.552683	+	0.693800i
$236$	3.38511	−	1.95440i	0.220352	−	0.127220i
$237$	−3.82511	+	8.55320i	−0.248467	+	0.555590i
$238$		0			0
$239$	−21.5667			−1.39503			−0.697515	−	0.716570i	$-0.745711\pi$
$239$	−21.5667			−1.39503			−0.697515	+	0.716570i	$0.745711\pi$
$240$	−4.62039	+	4.21371i	−0.298245	+	0.271994i
$241$	3.24527	−	5.62098i	0.209047	−	0.362079i	−0.742368	−	0.669992i	$-0.766297\pi$
$241$	3.24527	−	5.62098i	0.209047	−	0.362079i	0.951414	+	0.307913i	$0.0996307\pi$
$242$	−1.85840	−	6.93566i	−0.119463	−	0.445841i
$243$	15.5879	+	0.129018i	0.999966	+	0.00827648i
$244$		−	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
$249$	−16.3483	−	2.61706i	−1.03603	−	0.165850i
$250$	−7.29402	+	0.558323i	−0.461314	+	0.0353114i
$251$		−	25.3594i		−	1.60067i	−0.599552	−	0.800336i	$-0.704655\pi$
$251$		−	25.3594i		−	1.60067i	0.599552	−	0.800336i	$-0.295345\pi$
$252$		0			0
$253$	0.273196	−	0.273196i	0.0171757	−	0.0171757i
$254$	−0.0888536	−	0.153899i	−0.00557517	−	0.00965648i
$255$	−15.7255	+	8.13886i	−0.984768	+	0.509675i
$256$	4.15861	−	7.20292i	0.259913	−	0.450183i
$257$	−11.1381	−	2.98446i	−0.694778	−	0.186165i	−0.105888	−	0.994378i	$-0.533768\pi$
$257$	−11.1381	−	2.98446i	−0.694778	−	0.186165i	−0.588890	+	0.808213i	$0.700435\pi$
$258$	3.64207	−	8.14391i	0.226745	−	0.507018i
$259$		0			0
$260$	3.43688	−	22.8848i	0.213146	−	1.41926i
$261$	−1.87298	+	5.70017i	−0.115935	+	0.352832i
$262$	−8.68795	+	2.32793i	−0.536743	+	0.143820i
$263$	19.0359	−	5.10066i	1.17380	−	0.314520i	0.381338	−	0.924436i	$-0.375463\pi$
$263$	19.0359	−	5.10066i	1.17380	−	0.314520i	0.792466	+	0.609916i	$0.208797\pi$
$264$	0.507050	+	0.411992i	0.0312068	+	0.0253564i
$265$	−1.30885	+	8.71515i	−0.0804023	+	0.535367i
$266$		0			0
$267$	17.1889	+	7.68713i	1.05195	+	0.470445i
$268$	3.97379	+	1.06477i	0.242738	+	0.0650414i
$269$	1.68918	−	2.92574i	0.102991	−	0.178386i	−0.809925	−	0.586534i	$-0.800492\pi$
$269$	1.68918	−	2.92574i	0.102991	−	0.178386i	0.912916	+	0.408148i	$0.133825\pi$
$270$	7.10567	+	2.70280i	0.432437	+	0.164487i
$271$	−8.04393	−	13.9325i	−0.488634	−	0.846339i	0.511281	−	0.859414i	$-0.329171\pi$
$271$	−8.04393	−	13.9325i	−0.488634	−	0.846339i	−0.999915	+	0.0130751i	$0.995838\pi$
$272$	−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
$276$	1.03021	−	6.43551i	0.0620112	−	0.387372i
$277$	6.44170	−	1.72605i	0.387044	−	0.103708i	−0.0600492	−	0.998195i	$-0.519126\pi$
$277$	6.44170	−	1.72605i	0.387044	−	0.103708i	0.447094	+	0.894487i	$0.352459\pi$
$278$	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	$0.877394\pi$
$282$	6.85514	−	0.709033i	0.408218	−	0.0422223i
$283$	4.72849	+	17.6470i	0.281080	+	1.04900i	0.951657	+	0.307164i	$0.0993799\pi$
$283$	4.72849	+	17.6470i	0.281080	+	1.04900i	−0.670577	+	0.741840i	$0.733953\pi$
$284$	7.38586	−	12.7927i	0.438270	−	0.759106i
$285$	−9.38699	−	10.2930i	−0.556037	−	0.609703i
$286$	−0.695278			−0.0411127
$287$		0			0
$288$	17.1653	+	0.956589i	1.01147	+	0.0563675i
$289$	−3.37934	+	1.95106i	−0.198785	+	0.114768i
$290$	−1.82320	+	2.28872i	−0.107062	+	0.134398i
$291$	23.4782	+	3.75842i	1.37631	+	0.220323i
$292$	1.58185	−	5.90355i	0.0925708	−	0.345479i
$293$	−2.06389	−	2.06389i	−0.120574	−	0.120574i	0.644245	−	0.764819i	$-0.277172\pi$
$293$	−2.06389	−	2.06389i	−0.120574	−	0.120574i	−0.764819	+	0.644245i	$0.777172\pi$
$294$		0			0
$295$	3.30426	+	4.47214i	0.192382	+	0.260378i
$296$	4.01600	−	2.31864i	0.233425	−	0.134768i
$297$	−0.178434	+	0.819436i	−0.0103538	+	0.0475485i
$298$	−2.64450	−	9.86942i	−0.153192	−	0.571720i
$299$	7.88047	+	13.6494i	0.455739	+	0.789364i
$300$	−10.2462	−	8.96252i	−0.591565	−	0.517451i
$301$		0			0
$302$	−3.36591	+	3.36591i	−0.193686	+	0.193686i
$303$	8.00166	−	0.827619i	0.459683	−	0.0475455i
$304$	−5.02939	−	2.90372i	−0.288455	−	0.166540i
$305$	4.43204	−	0.501760i	0.253778	−	0.0287307i
$306$	8.52577	+	2.80143i	0.487386	+	0.160147i
$307$	−0.640910	−	0.640910i	−0.0365787	−	0.0365787i	0.688581	−	0.725160i	$-0.258234\pi$
$307$	−0.640910	−	0.640910i	−0.0365787	−	0.0365787i	−0.725160	+	0.688581i	$0.758234\pi$
$308$		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	0.915181	−	0.403042i	$-0.132047\pi$
$311$	18.0536	+	10.4233i	1.02373	+	0.591049i	0.108546	+	0.994091i	$0.465381\pi$
$312$	−21.5875	+	15.6297i	−1.22215	+	0.884860i
$313$	−16.9346	−	4.53760i	−0.957198	−	0.256481i	−0.253784	−	0.967261i	$-0.581675\pi$
$313$	−16.9346	−	4.53760i	−0.957198	−	0.256481i	−0.703414	+	0.710780i	$0.748342\pi$
$314$	−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	$-0.379653\pi$
$317$	3.99061	+	1.06928i	0.224135	+	0.0600567i	−0.145004	+	0.989431i	$0.546319\pi$
$318$	3.61787	−	2.61940i	0.202880	−	0.146889i
$319$	−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
$324$	5.66839	+	12.9617i	0.314910	+	0.720095i
$325$	32.8980	+	1.19589i	1.82485	+	0.0663362i
$326$	8.19231	+	4.72983i	0.453730	+	0.261961i
$327$	−15.9125	+	1.64584i	−0.879961	+	0.0910151i
$328$	−19.8951	+	19.8951i	−1.09852	+	1.09852i
$329$		0			0
$330$	−0.220570	+	0.344422i	−0.0121420	+	0.0189598i
$331$	8.74533	+	15.1474i	0.480687	+	0.832574i	0.999754	−	0.0221591i	$-0.00705403\pi$
$331$	8.74533	+	15.1474i	0.480687	+	0.832574i	−0.519068	+	0.854733i	$0.673721\pi$
$332$	−3.88886	−	14.5134i	−0.213429	−	0.796529i
$333$	4.98150	+	3.25852i	0.272985	+	0.178566i
$334$	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	0.660675	−	0.750672i	$-0.270270\pi$
$337$	−1.65213	−	1.65213i	−0.0899974	−	0.0899974i	−0.750672	+	0.660675i	$0.770270\pi$
$338$	5.13937	−	19.1804i	0.279545	−	1.04328i
$339$	11.8012	+	1.88916i	0.640956	+	0.102605i
$340$	−12.5689	−	10.0124i	−0.681646	−	0.543001i
$341$	−1.04303	+	0.602192i	−0.0564831	+	0.0326105i
$342$	−0.392849	+	7.04939i	−0.0212429	+	0.381188i
$343$		0			0
$344$	18.3976			0.991930
$345$	9.26152	+	0.426359i	0.498624	+	0.0229544i
$346$	0.666883	−	1.15507i	0.0358518	−	0.0620972i
$347$	−6.72623	−	25.1026i	−0.361083	−	1.34758i	−0.872654	−	0.488338i	$-0.837603\pi$
$347$	−6.72623	−	25.1026i	−0.361083	−	1.34758i	0.511572	−	0.859241i	$-0.329063\pi$
$348$	−5.41627	+	0.560210i	−0.290343	+	0.0300304i
$349$			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	−0.630947	−	0.775826i	$-0.717334\pi$
$353$	−14.8324	+	3.97434i	−0.789451	+	0.211533i	−0.158503	+	0.987358i	$0.550667\pi$
$354$	0.445462	−	2.78271i	0.0236760	−	0.147900i
$355$	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	$-0.282320\pi$
$359$	−6.73373	−	11.6632i	−0.355393	−	0.615558i	−0.987185	+	0.159579i	$0.948986\pi$
$360$	0.894110	+	15.6523i	0.0471237	+	0.824946i
$361$	−3.03131	+	5.25038i	−0.159543	+	0.276336i
$362$	10.5423	+	2.82480i	0.554090	+	0.148468i
$363$	17.3513	+	7.75976i	0.910709	+	0.407282i
$364$		0			0
$365$	8.59786	+	1.29124i	0.450033	+	0.0675866i
$366$	−1.75447	−	1.42555i	−0.0917075	−	0.0745149i
$367$	−3.80860	+	1.02051i	−0.198807	+	0.0532703i	−0.356849	−	0.934162i	$-0.616149\pi$
$367$	−3.80860	+	1.02051i	−0.198807	+	0.0532703i	0.158041	+	0.987433i	$0.449482\pi$
$368$	3.73338	−	1.00036i	0.194616	−	0.0521471i
$369$	−34.3116	−	11.2742i	−1.78619	−	0.586913i
$370$	1.72512	+	2.33485i	0.0896846	+	0.121383i
$371$		0			0
$372$	−8.29427	+	18.5466i	−0.430038	+	0.961594i
$373$	5.78658	+	1.55051i	0.299618	+	0.0802823i	0.405496	−	0.914097i	$-0.367099\pi$
$373$	5.78658	+	1.55051i	0.299618	+	0.0802823i	−0.105878	+	0.994379i	$0.533765\pi$
$374$	−0.241401	+	0.418118i	−0.0124825	+	0.0216204i
$375$	11.0290	−	15.9174i	0.569533	−	0.821969i
$376$	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	$0.223530\pi$
$379$			25.1498i			1.29186i	−0.763397	+	0.645930i	$0.776470\pi$
$380$	5.04942	−	11.5902i	0.259030	−	0.594565i
$381$	0.464505	+	0.0743588i	0.0237973	+	0.00380952i
$382$	−13.6691	+	3.66262i	−0.699372	+	0.187396i
$383$	−1.61079	+	6.01154i	−0.0823073	+	0.307175i	−0.994791	−	0.101939i	$-0.967495\pi$
$383$	−1.61079	+	6.01154i	−0.0823073	+	0.307175i	0.912483	+	0.409114i	$0.134162\pi$
$384$	6.87302	+	17.9938i	0.350737	+	0.918242i
$385$		0			0
$386$		−	3.79877i		−	0.193352i
$387$	10.6516	+	21.0773i	0.541454	+	1.07142i
$388$	5.58489	+	20.8431i	0.283530	+	1.05815i
$389$	13.0350	−	22.5773i	0.660901	−	1.14471i	−0.319479	−	0.947593i	$-0.603508\pi$
$389$	13.0350	−	22.5773i	0.660901	−	1.14471i	0.980379	−	0.197120i	$-0.0631589\pi$
$390$	−11.2427	−	12.3277i	−0.569295	−	0.624240i
$391$	10.9444			0.553482
$392$		0			0
$393$	9.72026	−	21.7352i	0.490322	−	1.09639i
$394$	7.30904	−	4.21988i	0.368224	−	0.212594i
$395$	−1.36072	−	12.0193i	−0.0684654	−	0.604755i
$396$	−0.744975	+	0.155773i	−0.0374364	+	0.00782791i
$397$	−5.49222	+	20.4972i	−0.275647	+	1.02873i	0.679760	+	0.733435i	$0.262084\pi$
$397$	−5.49222	+	20.4972i	−0.275647	+	1.02873i	−0.955407	+	0.295293i	$0.904583\pi$
$398$	−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	$-0.637663\pi$
$401$	3.15603	−	1.82213i	0.157605	−	0.0909930i	0.576728	+	0.816936i	$0.304329\pi$
$402$	2.40249	−	1.73944i	0.119825	−	0.0867554i
$403$	−12.7161	−	47.4572i	−0.633435	−	2.36401i
$404$	3.65023	+	6.32239i	0.181606	+	0.314551i
$405$	−17.4144	+	10.0865i	−0.865329	+	0.501204i
$406$		0			0
$407$	−0.226445	+	0.226445i	−0.0112245	+	0.0112245i
$408$	1.90403	+	18.4087i	0.0942635	+	0.911367i
$409$	−7.47293	−	4.31450i	−0.369513	−	0.213338i	0.303733	−	0.952757i	$-0.401767\pi$
$409$	−7.47293	−	4.31450i	−0.369513	−	0.213338i	−0.673245	+	0.739419i	$0.735100\pi$
$410$	−13.7767	−	10.9746i	−0.680384	−	0.541996i
$411$	−10.6467	−	8.65074i	−0.525163	−	0.426710i
$412$	−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
$417$	16.9491	+	23.4098i	0.829999	+	1.14638i
$418$	−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
$423$	−9.98669	+	15.2673i	−0.485570	+	0.742320i
$424$	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
$429$	1.16064	−	1.42843i	0.0560361	−	0.0689651i
$430$	1.29561	+	11.4441i	0.0624799	+	0.551885i
$431$	1.70274	+	0.983080i	0.0820183	+	0.0473533i	0.540448	−	0.841377i	$-0.318255\pi$
$431$	1.70274	+	0.983080i	0.0820183	+	0.0473533i	−0.458430	+	0.888731i	$0.651588\pi$
$432$	−5.64466	+	6.20677i	−0.271579	+	0.298623i
$433$	−18.7649	+	18.7649i	−0.901782	+	0.901782i	−0.995590	−	0.0938083i	$-0.970096\pi$
$433$	−18.7649	+	18.7649i	−0.901782	+	0.901782i	0.0938083	+	0.995590i	$0.470096\pi$
$434$		0			0
$435$	−1.65861	−	7.56631i	−0.0795242	−	0.362777i
$436$	−7.25901	−	12.5730i	−0.347644	−	0.602137i
$437$	2.22852	+	8.31694i	0.106604	+	0.397853i
$438$	−2.58415	−	3.56918i	−0.123475	−	0.170542i
$439$	22.4711	−	12.9737i	1.07249	−	0.619202i	0.143629	−	0.989632i	$-0.454123\pi$
$439$	22.4711	−	12.9737i	1.07249	−	0.619202i	0.928860	+	0.370430i	$0.120790\pi$
$440$	−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	0.303751	+	0.952752i	$0.401761\pi$
$443$	−9.17002	+	34.2230i	−0.435681	+	1.62598i	−0.739431	+	0.673232i	$0.764906\pi$
$444$	−0.853912	+	5.33423i	−0.0405249	+	0.253151i
$445$	−24.1545	+	2.73458i	−1.14503	+	0.129632i
$446$	−0.306177	+	0.176771i	−0.0144979	+	0.00837036i
$447$	24.6909	+	11.0421i	1.16784	+	0.522274i
$448$		0			0
$449$	17.4443			0.823245			0.411623	−	0.911354i	$-0.364962\pi$
$449$	17.4443			0.823245			0.411623	+	0.911354i	$0.364962\pi$
$450$	−9.67345	+	1.65845i	−0.456011	+	0.0781803i
$451$	0.971506	−	1.68270i	0.0457464	−	0.0792351i
$452$	2.80723	+	10.4767i	0.132041	+	0.492784i
$453$	−1.29640	−	12.5339i	−0.0609100	−	0.588895i
$454$		−	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	0.336269	+	0.941766i	$0.390835\pi$
$457$	−9.10323	+	33.9737i	−0.425831	+	1.58922i	−0.762101	+	0.647458i	$0.775832\pi$
$458$	−1.46671	+	0.393002i	−0.0685346	+	0.0183638i
$459$	−19.9876	+	12.8395i	−0.932943	+	0.599295i
$460$	3.07814	+	7.83073i	0.143519	+	0.365110i
$461$			7.52593i			0.350517i	0.984522	+	0.175259i	$0.0560762\pi$
$461$			7.52593i			0.350517i	−0.984522	+	0.175259i	$0.943924\pi$
$462$		0			0
$463$	−16.6029	+	16.6029i	−0.771601	+	0.771601i	−0.978386	−	0.206785i	$-0.933700\pi$
$463$	−16.6029	+	16.6029i	−0.771601	+	0.771601i	0.206785	+	0.978386i	$0.433700\pi$
$464$	−1.61459	−	2.79655i	−0.0749554	−	0.129826i
$465$	−27.5430	−	8.75610i	−1.27728	−	0.406055i
$466$	−2.80636	+	4.86075i	−0.130002	+	0.225170i
$467$	10.5373	+	2.82346i	0.487608	+	0.130654i	0.494243	−	0.869324i	$-0.335445\pi$
$467$	10.5373	+	2.82346i	0.487608	+	0.130654i	−0.00663489	+	0.999978i	$0.502112\pi$
$468$	1.72754	−	30.9995i	0.0798556	−	1.43295i
$469$		0			0
$470$	−7.15582	+	5.28712i	−0.330073	+	0.243877i
$471$	17.2868	−	21.2753i	0.796533	−	0.980314i
$472$	5.61363	−	1.50417i	0.258388	−	0.0692349i
$473$	−1.22721	+	0.328830i	−0.0564271	+	0.0151196i
$474$	−3.86596	+	4.75794i	−0.177570	+	0.218540i
$475$	17.1909	+	5.28267i	0.788774	+	0.242385i
$476$		0			0
$477$	−0.657893	+	11.8054i	−0.0301228	+	0.540532i
$478$	−13.6304	−	3.65224i	−0.623438	−	0.167050i
$479$	8.56960	−	14.8430i	0.391555	−	0.678193i	−0.601100	−	0.799174i	$-0.705271\pi$
$479$	8.56960	−	14.8430i	0.391555	−	0.678193i	0.992655	+	0.120981i	$0.0386039\pi$
$480$	−19.7112	+	10.2017i	−0.899687	+	0.465641i
$481$	−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
$486$	9.82989	+	2.72130i	0.445893	+	0.123441i
$487$	19.3562	−	5.18649i	0.877115	−	0.235022i	0.207953	−	0.978139i	$-0.433320\pi$
$487$	19.3562	−	5.18649i	0.877115	−	0.235022i	0.669162	+	0.743117i	$0.266653\pi$
$488$	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	$-0.194717\pi$
$492$	−3.37213	−	32.6027i	−0.152027	−	1.46984i
$493$	−2.36658	−	8.83220i	−0.106585	−	0.397782i
$494$	7.74746	−	13.4190i	0.348575	−	0.603749i
$495$	−0.339403	−	1.02810i	−0.0152550	−	0.0462098i
$496$	−12.0485			−0.540995
$497$		0			0
$498$	−9.88910	−	4.42254i	−0.443141	−	0.198179i
$499$	−13.2157	+	7.63009i	−0.591616	+	0.341570i	−0.765736	−	0.643155i	$-0.777625\pi$
$499$	−13.2157	+	7.63009i	−0.591616	+	0.341570i	0.174120	+	0.984724i	$0.444292\pi$
$500$	17.2730	+	3.23968i	0.772473	+	0.144883i
$501$	−0.978437	+	6.11211i	−0.0437133	+	0.273069i
$502$	4.29453	−	16.0274i	0.191674	−	0.715338i
$503$	−7.55387	−	7.55387i	−0.336810	−	0.336810i	0.518355	−	0.855165i	$-0.326545\pi$
$503$	−7.55387	−	7.55387i	−0.336810	−	0.336810i	−0.855165	+	0.518355i	$0.826545\pi$
$504$		0			0
$505$	−8.35263	+	6.17139i	−0.371687	+	0.274623i
$506$	0.218928	−	0.126398i	0.00973252	−	0.00561907i
$507$	30.8263	+	42.5768i	1.36904	+	1.89090i
$508$	0.110495	+	0.412372i	0.00490241	+	0.0182960i
$509$	19.6787	+	34.0846i	0.872244	+	1.51077i	0.859670	+	0.510851i	$0.170669\pi$
$509$	19.6787	+	34.0846i	0.872244	+	1.51077i	0.0125748	+	0.999921i	$0.495997\pi$
$510$	−11.3170	+	2.48079i	−0.501124	+	0.109851i
$511$		0			0
$512$	−11.8791	+	11.8791i	−0.524986	+	0.524986i
$513$	−13.8270	−	12.5747i	−0.610475	−	0.555189i
$514$	−6.53402	−	3.77242i	−0.288203	−	0.166394i
$515$	13.8469	−	17.3825i	0.610169	−	0.765964i
$516$	−13.5152	+	16.6335i	−0.594972	+	0.732248i
$517$	−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	0.760632	−	0.649183i	$-0.224889\pi$
$521$	13.2100	+	7.62679i	0.578740	+	0.334136i	−0.181893	+	0.983318i	$0.558222\pi$
$522$	−2.14905	+	3.28538i	−0.0940614	+	0.143797i
$523$	−17.9637	−	4.81336i	−0.785497	−	0.210473i	−0.156290	−	0.987711i	$-0.549954\pi$
$523$	−17.9637	−	4.81336i	−0.785497	−	0.210473i	−0.629207	+	0.777238i	$0.716620\pi$
$524$	21.6079			0.943947
$525$		0			0
$526$	12.8947			0.562235
$527$	−32.9543	−	8.83007i	−1.43551	−	0.384644i
$528$	−0.264693	−	0.365590i	−0.0115193	−	0.0159102i
$529$	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
$534$	9.56181	+	7.76924i	0.413780	+	0.336208i
$535$	20.1880	−	25.3426i	0.872803	−	1.09566i
$536$	5.29724	+	3.05836i	0.228806	+	0.132101i
$537$	−3.58055	−	34.6178i	−0.154512	−	1.49387i
$538$	1.56304	−	1.56304i	0.0673876	−	0.0673876i
$539$		0			0
$540$	−14.8082	−	10.6900i	−0.637245	−	0.460026i
$541$	0.951978	+	1.64887i	0.0409287	+	0.0708906i	0.885764	−	0.464136i	$-0.153635\pi$
$541$	0.951978	+	1.64887i	0.0409287	+	0.0708906i	−0.844835	+	0.535026i	$0.820302\pi$
$542$	−2.72443	−	10.1677i	−0.117024	−	0.436740i
$543$	−23.4018	+	16.9433i	−1.00427	+	0.727107i
$544$	−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	0.789290	−	0.614021i	$-0.210449\pi$
$547$	4.09919	+	4.09919i	0.175269	+	0.175269i	−0.614021	+	0.789290i	$0.710449\pi$
$548$	3.22219	−	12.0254i	0.137645	−	0.513699i
$549$	5.85751	−	1.22480i	0.249993	−	0.0522731i
$550$	0.0191814	−	0.527663i	0.000817897	−	0.0224996i
$551$	6.22994	−	3.59686i	0.265404	−	0.153231i
$552$	3.95603	−	8.84595i	0.168380	−	0.376509i
$553$		0			0
$554$	4.36352			0.185388
$555$	−7.67664	−	0.353398i	−0.325855	−	0.0150009i
$556$	−13.1144	+	22.7148i	−0.556174	+	0.963322i
$557$	−2.38619	−	8.90537i	−0.101106	−	0.377333i	0.896768	−	0.442500i	$-0.145908\pi$
$557$	−2.38619	−	8.90537i	−0.101106	−	0.377333i	−0.997874	+	0.0651676i	$0.979242\pi$
$558$	6.60675	+	13.0733i	0.279686	+	0.553437i
$559$		−	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	−0.281949	−	0.959429i	$-0.590981\pi$
$563$	−1.10118	+	0.295060i	−0.0464091	+	0.0124353i	0.235540	+	0.971865i	$0.424314\pi$
$564$	−16.3483	−	2.61706i	−0.688387	−	0.110198i
$565$	−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	$-0.149313\pi$
$569$	1.29985	+	2.25140i	0.0544924	+	0.0943835i	−0.837492	+	0.546449i	$0.815979\pi$
$570$	−4.18960	−	8.09492i	−0.175483	−	0.339059i
$571$	−1.39746	+	2.42048i	−0.0584820	+	0.101294i	−0.893784	−	0.448497i	$-0.851959\pi$
$571$	−1.39746	+	2.42048i	−0.0584820	+	0.101294i	0.835302	+	0.549791i	$0.185293\pi$
$572$	1.61340	+	0.432310i	0.0674597	+	0.0180758i
$573$	15.2933	−	34.1968i	0.638886	−	1.42859i
$574$		0			0
$575$	−10.5762	+	5.60411i	−0.441059	+	0.233708i
$576$	1.48323	+	0.487365i	0.0618012	+	0.0203069i
$577$	−17.2446	+	4.62068i	−0.717903	+	0.192362i	−0.599236	−	0.800573i	$-0.704529\pi$
$577$	−17.2446	+	4.62068i	−0.717903	+	0.192362i	−0.118667	+	0.992934i	$0.537862\pi$
$578$	−2.46618	+	0.660812i	−0.102580	+	0.0274862i
$579$	7.80445	+	6.34134i	0.324342	+	0.263537i
$580$	5.65384	−	4.17737i	0.234763	−	0.173456i
$581$		0			0
$582$	14.2020	+	6.35131i	0.588691	+	0.263270i
$583$	−0.614426	−	0.164635i	−0.0254469	−	0.00681848i
$584$	4.54356	−	7.86968i	0.188014	−	0.325650i
$585$	44.0945	−	2.51883i	1.82308	−	0.104141i
$586$	−0.954887	−	1.65391i	−0.0394460	−	0.0683225i
$587$	−19.4664	+	19.4664i	−0.803465	+	0.803465i	−0.983635	−	0.180171i	$-0.942335\pi$
$587$	−19.4664	+	19.4664i	−0.803465	+	0.803465i	0.180171	+	0.983635i	$0.442335\pi$
$588$		0			0
$589$		−	26.8408i		−	1.10596i
$590$	1.33099	+	3.38600i	0.0547959	+	0.139400i
$591$	−3.53148	+	22.0605i	−0.145266	+	0.907447i
$592$	−3.09450	+	0.829169i	−0.127183	+	0.0340786i
$593$	−8.07115	+	30.1219i	−0.331442	+	1.23696i	0.576233	+	0.817286i	$0.304522\pi$
$593$	−8.07115	+	30.1219i	−0.331442	+	1.23696i	−0.907675	+	0.419674i	$0.862144\pi$
$594$	−0.251541	+	0.487675i	−0.0103209	+	0.0200095i
$595$		0			0
$596$			24.5464i			1.00546i
$597$	1.09901	−	0.113672i	0.0449795	−	0.00465227i
$598$	2.66906	+	9.96108i	0.109146	+	0.407339i
$599$	−9.26661	+	16.0502i	−0.378624	+	0.655795i	−0.990862	−	0.134878i	$-0.956936\pi$
$599$	−9.26661	+	16.0502i	−0.378624	+	0.655795i	0.612239	+	0.790673i	$0.290269\pi$
$600$	−11.2662	−	16.8145i	−0.459941	−	0.686448i
$601$	−5.32951			−0.217395			−0.108698	−	0.994075i	$-0.534668\pi$
$601$	−5.32951			−0.217395			−0.108698	+	0.994075i	$0.534668\pi$
$602$		0			0
$603$	−0.436881	+	7.83950i	−0.0177912	+	0.319249i
$604$	9.90349	−	5.71778i	0.402967	−	0.232653i
$605$	−24.3827	+	2.76042i	−0.991299	+	0.112227i
$606$	5.19729	+	0.831991i	0.211125	+	0.0337973i
$607$	4.07471	−	15.2070i	0.165387	−	0.617234i	−0.832603	−	0.553870i	$-0.813150\pi$
$607$	4.07471	−	15.2070i	0.165387	−	0.617234i	0.997990	−	0.0633638i	$-0.0201828\pi$
$608$	−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
$612$	−18.0423	−	11.8019i	−0.729316	−	0.477063i
$613$	9.15958	+	34.1840i	0.369952	+	1.38068i	0.860582	+	0.509312i	$0.170100\pi$
$613$	9.15958	+	34.1840i	0.369952	+	1.38068i	−0.490630	+	0.871368i	$0.663233\pi$
$614$	−0.296526	−	0.513598i	−0.0119668	−	0.0207271i
$615$	45.5446	−	9.98382i	1.83654	−	0.402586i
$616$		0			0
$617$	25.1412	−	25.1412i	1.01215	−	1.01215i	0.0122222	−	0.999925i	$-0.496109\pi$
$617$	25.1412	−	25.1412i	1.01215	−	1.01215i	0.999925	−	0.0122222i	$-0.00389054\pi$
$618$	−11.2037	+	1.15881i	−0.450677	+	0.0466140i
$619$	3.49101	+	2.01554i	0.140316	+	0.0810112i	0.568514	−	0.822673i	$-0.307518\pi$
$619$	3.49101	+	2.01554i	0.140316	+	0.0810112i	−0.428199	+	0.903685i	$0.640852\pi$
$620$	−2.95056	−	26.0623i	−0.118497	−	1.04669i
$621$	12.4248	−	0.589303i	0.498591	−	0.0236479i
$622$	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
$627$	0.814433	−	0.589663i	0.0325253	−	0.0235489i
$628$	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
$633$	9.39373	−	6.80121i	0.373367	−	0.270324i
$634$	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
$639$	26.7836	+	8.80065i	1.05954	+	0.348148i
$640$	−19.4499	−	15.4939i	−0.768825	−	0.612448i
$641$	5.18974	+	2.99630i	0.204982	+	0.118347i	0.598977	−	0.800766i	$-0.295574\pi$
$641$	5.18974	+	2.99630i	0.204982	+	0.118347i	−0.393995	+	0.919113i	$0.628907\pi$
$642$	−16.3343	+	1.68947i	−0.644662	+	0.0666780i
$643$	0.533933	−	0.533933i	0.0210562	−	0.0210562i	−0.696500	−	0.717557i	$-0.745261\pi$
$643$	0.533933	−	0.533933i	0.0210562	−	0.0210562i	0.717557	+	0.696500i	$0.245261\pi$
$644$		0			0
$645$	−25.6744	−	16.4420i	−1.01093	−	0.647405i
$646$	−5.37984	−	9.31815i	−0.211667	−	0.366618i
$647$	9.09189	+	33.9314i	0.357439	+	1.33398i	0.877387	+	0.479783i	$0.159285\pi$
$647$	9.09189	+	33.9314i	0.357439	+	1.33398i	−0.519948	+	0.854198i	$0.674049\pi$
$648$	3.15280	+	20.7963i	0.123854	+	0.816956i
$649$	−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	$-0.914500\pi$
$653$	0.0900386	−	0.336028i	0.00352348	−	0.0131498i	0.967665	+	0.252238i	$0.0811666\pi$
$654$	−10.3356	−	1.65453i	−0.404152	−	0.0646974i
$655$	3.45783	+	30.5430i	0.135109	+	1.19342i
$656$	16.8335	−	9.71884i	0.657239	−	0.379457i
$657$	11.6465	+	0.649039i	0.454374	+	0.0253214i
$658$		0			0
$659$	−14.9402			−0.581989			−0.290994	−	0.956725i	$-0.593986\pi$
$659$	−14.9402			−0.581989			−0.290994	+	0.956725i	$0.593986\pi$
$660$	0.725990	−	0.662089i	0.0282591	−	0.0257718i
$661$	21.4079	−	37.0797i	0.832673	−	1.44223i	−0.0632386	−	0.997998i	$-0.520143\pi$
$661$	21.4079	−	37.0797i	0.832673	−	1.44223i	0.895911	−	0.444233i	$-0.146524\pi$
$662$	2.96199	+	11.0543i	0.115121	+	0.429637i
$663$	51.8598	−	5.36391i	2.01407	−	0.208317i
$664$		−	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
$669$	0.147934	−	0.924117i	0.00571947	−	0.0357284i
$670$	−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	−0.602096	−	0.798424i	$-0.705667\pi$
$673$	5.09320	−	5.09320i	0.196328	−	0.196328i	0.798424	+	0.602096i	$0.205667\pi$
$674$	−0.764382	−	1.32395i	−0.0294429	−	0.0509966i
$675$	12.7408	−	22.6423i	0.490393	−	0.871502i
$676$	−23.8519	+	41.3128i	−0.917382	+	1.58895i
$677$	−1.68713	−	0.452066i	−0.0648418	−	0.0173743i	0.226252	−	0.974069i	$-0.427353\pi$
$677$	−1.68713	−	0.452066i	−0.0648418	−	0.0173743i	−0.291094	+	0.956694i	$0.594019\pi$
$678$	7.13859	+	3.19247i	0.274156	+	0.122606i
$679$		0			0
$680$	−14.1980	−	19.2162i	−0.544467	−	0.736906i
$681$	23.7800	+	19.3219i	0.911252	+	0.740418i
$682$	−0.761184	+	0.203959i	−0.0291472	+	0.00780998i
$683$	−34.4803	+	9.23896i	−1.31935	+	0.353519i	−0.848735	−	0.528819i	$-0.822635\pi$
$683$	−34.4803	+	9.23896i	−1.31935	+	0.353519i	−0.470616	+	0.882338i	$0.655968\pi$
$684$	5.29478	−	16.1139i	0.202451	−	0.616132i
$685$	17.5136	+	2.63022i	0.669162	+	0.100496i
$686$		0			0
$687$	1.64098	−	3.66934i	0.0626073	−	0.139994i
$688$	−12.2769	−	3.28958i	−0.468051	−	0.125414i
$689$	12.9744	−	22.4724i	0.494287	−	0.856130i
$690$	5.78118	+	1.83787i	0.220086	+	0.0699666i
$691$	22.5895	+	39.1261i	0.859344	+	1.48843i	0.872556	+	0.488514i	$0.162461\pi$
$691$	22.5895	+	39.1261i	0.859344	+	1.48843i	−0.0132121	+	0.999913i	$0.504206\pi$
$692$	−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
$696$	−7.99418	−	1.27972i	−0.303019	−	0.0485078i
$697$	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	$-0.316676\pi$
$702$	−16.5604	−	15.0606i	−0.625031	−	0.568426i
$703$	−1.84716	−	6.89369i	−0.0696669	−	0.260001i
$704$	−0.0419965	+	0.0727400i	−0.00158280	+	0.00274149i
$705$	1.08309	−	23.5273i	0.0407915	−	0.886088i
$706$	−10.0473			−0.378135
$707$		0			0
$708$	−2.76393	+	6.18034i	−0.103875	+	0.232271i
$709$	−15.7821	+	9.11180i	−0.592709	+	0.342201i	−0.766168	−	0.642640i	$-0.777839\pi$
$709$	−15.7821	+	9.11180i	−0.592709	+	0.342201i	0.173459	+	0.984841i	$0.444506\pi$
$710$	10.7541	+	8.56674i	0.403594	+	0.321504i
$711$	−3.32153	−	15.8850i	−0.124567	−	0.595734i
$712$	−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
$717$	30.2568	−	21.9064i	1.12996	−	0.818109i
$718$	−2.28067	−	8.51158i	−0.0851139	−	0.317649i
$719$	−7.20912	−	12.4866i	−0.268855	−	0.465670i	0.699712	−	0.714425i	$-0.253312\pi$
$719$	−7.20912	−	12.4866i	−0.268855	−	0.465670i	−0.968566	+	0.248755i	$0.919979\pi$
$720$	2.20205	−	10.6048i	0.0820657	−	0.395217i
$721$		0			0
$722$	−2.80496	+	2.80496i	−0.104390	+	0.104390i
$723$	1.15660	+	11.1823i	0.0430143	+	0.415874i
$724$	−22.7071	−	13.1099i	−0.843902	−	0.487227i
$725$	6.80953	+	7.32328i	0.252899	+	0.271980i
$726$	9.65214	+	7.84264i	0.358225	+	0.291068i
$727$	1.34757	+	1.34757i	0.0499787	+	0.0499787i	0.731654	−	0.681676i	$-0.238748\pi$
$727$	1.34757	+	1.34757i	0.0499787	+	0.0499787i	−0.681676	+	0.731654i	$0.738748\pi$
$728$		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
$732$	3.18488	+	4.39891i	0.117717	+	0.162588i
$733$	−18.4641	−	4.94744i	−0.681987	−	0.182738i	−0.0988384	−	0.995104i	$-0.531513\pi$
$733$	−18.4641	−	4.94744i	−0.681987	−	0.182738i	−0.583148	+	0.812366i	$0.698179\pi$
$734$	−2.57990			−0.0952258
$735$		0			0
$736$	13.7183			0.505663
$737$	−0.408016	−	0.109327i	−0.0150295	−	0.00402713i
$738$	−19.7760	−	12.9360i	−0.727966	−	0.476180i
$739$	−1.11818	−	0.645584i	−0.0411331	−	0.0237482i	0.479292	−	0.877655i	$-0.340893\pi$
$739$	−1.11818	−	0.645584i	−0.0411331	−	0.0237482i	−0.520426	+	0.853907i	$0.674227\pi$
$740$	−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	$-0.346446\pi$
$743$	−11.5021	−	11.5021i	−0.421972	−	0.421972i	−0.885882	+	0.463910i	$0.846446\pi$
$744$	−19.0489	+	23.4439i	−0.698366	+	0.859497i
$745$	−34.6966	+	3.92807i	−1.27118	+	0.143913i
$746$	3.39460	+	1.95988i	0.124285	+	0.0717562i
$747$	25.5940	−	12.9342i	0.936435	−	0.473239i
$748$	0.820150	−	0.820150i	0.0299877	−	0.0299877i
$749$		0			0
$750$	9.66597	−	8.19222i	0.352951	−	0.299138i
$751$	21.5667	+	37.3545i	0.786978	+	1.36309i	0.927810	+	0.373053i	$0.121689\pi$
$751$	21.5667	+	37.3545i	0.786978	+	1.36309i	−0.140832	+	0.990034i	$0.544978\pi$
$752$	−2.54123	−	9.48399i	−0.0926690	−	0.345845i
$753$	25.7589	+	35.5778i	0.938706	+	1.29653i
$754$	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	0.195442	−	0.980715i	$-0.437386\pi$
$757$	−21.6057	−	21.6057i	−0.785273	−	0.785273i	−0.980715	+	0.195442i	$0.937386\pi$
$758$	−4.25904	+	15.8950i	−0.154695	+	0.577331i
$759$	−0.105778	+	0.660777i	−0.00383951	+	0.0239847i
$760$	11.7119	−	14.7022i	0.424834	−	0.533306i
$761$	23.7452	−	13.7093i	0.860763	−	0.496962i	−0.00350451	−	0.999994i	$-0.501116\pi$
$761$	23.7452	−	13.7093i	0.860763	−	0.496962i	0.864268	+	0.503032i	$0.167782\pi$
$762$	0.280980	+	0.125658i	0.0101788	+	0.00455211i
$763$		0			0
$764$	33.9966			1.22996
$765$	13.7949	−	27.3916i	0.498754	−	0.990344i
$766$	−2.03607	+	3.52657i	−0.0735661	+	0.127420i
$767$	−4.23744	−	15.8143i	−0.153005	−	0.571023i
$768$	1.48210	+	14.3294i	0.0534808	+	0.517068i
$769$		−	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	0.551687	−	0.834051i	$-0.313984\pi$
$773$	40.2165	−	10.7760i	1.44649	−	0.387585i	0.894800	+	0.446466i	$0.147318\pi$
$774$	3.16259	+	15.1249i	0.113677	+	0.543652i
$775$	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
$780$	18.4236	+	35.5971i	0.659671	+	1.27458i
$781$	−0.758356	+	1.31351i	−0.0271361	+	0.0470011i
$782$	6.91698	+	1.85340i	0.247351	+	0.0662774i
$783$	−3.16228	−	9.89949i	−0.113011	−	0.353779i
$784$		0			0
$785$	−5.25598	+	34.9975i	−0.187594	+	1.24912i
$786$	9.82408	−	12.0908i	0.350413	−	0.431263i
$787$	13.2943	−	3.56220i	0.473892	−	0.126979i	−0.0139653	−	0.999902i	$-0.504445\pi$
$787$	13.2943	−	3.56220i	0.473892	−	0.126979i	0.487857	+	0.872924i	$0.337779\pi$
$788$	−19.5845	+	5.24766i	−0.697670	+	0.186940i
$789$	−21.5253	+	26.4917i	−0.766320	+	0.943130i
$790$	1.17543	−	7.82674i	0.0418200	−	0.278463i
$791$		0			0
$792$	−1.12984	−	0.0629640i	−0.0401473	−	0.00223733i
$793$	−12.6857	−	3.39912i	−0.450482	−	0.120706i
$794$	−6.94229	+	12.0244i	−0.246372	+	0.426730i
$795$	−7.01619	−	13.5563i	−0.248839	−	0.480793i
$796$	0.501351	+	0.868365i	0.0177699	+	0.0307784i
$797$	31.7624	−	31.7624i	1.12508	−	1.12508i	0.134115	−	0.990966i	$-0.457181\pi$
$797$	31.7624	−	31.7624i	1.12508	−	1.12508i	0.990966	−	0.134115i	$-0.0428192\pi$
$798$		0			0
$799$		−	27.8023i		−	0.983575i
$800$	15.2186	−	24.2776i	0.538059	−	0.858342i
$801$	−31.9233	+	6.67513i	−1.12795	+	0.235854i
$802$	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
$807$	0.602013	+	5.82043i	0.0211919	+	0.204889i
$808$	2.80934	+	10.4846i	0.0988322	+	0.368847i
$809$	−10.6115	+	18.3796i	−0.373080	+	0.646193i	−0.990038	−	0.140803i	$-0.955032\pi$
$809$	−10.6115	+	18.3796i	−0.373080	+	0.646193i	0.616958	+	0.786996i	$0.288365\pi$
$810$	−12.7142	+	3.42573i	−0.446732	+	0.120368i
$811$	−17.1374			−0.601776			−0.300888	−	0.953660i	$-0.597283\pi$
$811$	−17.1374			−0.601776			−0.300888	+	0.953660i	$0.597283\pi$
$812$		0			0
$813$	25.4371	+	11.3758i	0.892119	+	0.398968i
$814$	−0.181463	+	0.104768i	−0.00636029	+	0.00367211i
$815$	20.1428	−	25.2859i	0.705571	−	0.885725i
$816$	2.02099	−	12.6248i	0.0707489	−	0.441955i
$817$	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	$-0.647041\pi$
$821$	3.05795	−	1.76551i	0.106723	−	0.0616166i	0.552411	+	0.833572i	$0.313708\pi$
$822$	−5.26385	−	7.27034i	−0.183598	−	0.253582i
$823$	−4.73521	−	17.6720i	−0.165059	−	0.616008i	−0.998033	−	0.0626958i	$-0.980030\pi$
$823$	−4.73521	−	17.6720i	−0.165059	−	0.616008i	0.832974	−	0.553312i	$-0.186636\pi$
$824$	−11.6139	−	20.1158i	−0.404589	−	0.700768i
$825$	1.05205	+	0.920242i	0.0366276	+	0.0320387i
$826$		0			0
$827$	−28.9027	+	28.9027i	−1.00505	+	1.00505i	−0.00505903	+	0.999987i	$0.501610\pi$
$827$	−28.9027	+	28.9027i	−1.00505	+	1.00505i	−0.999987	+	0.00505903i	$0.998390\pi$
$828$	5.09157	+	10.0751i	0.176944	+	0.350133i
$829$	15.1933	+	8.77184i	0.527684	+	0.304659i	0.740073	−	0.672527i	$-0.234791\pi$
$829$	15.1933	+	8.77184i	0.527684	+	0.304659i	−0.212389	+	0.977185i	$0.568124\pi$
$830$	13.8965	−	1.57325i	0.482356	−	0.0546084i
$831$	−7.28409	+	8.96472i	−0.252682	+	0.310983i
$832$	−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
$837$	−37.8874	−	8.25007i	−1.30958	−	0.285164i
$838$	−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
$843$	−12.7950	−	17.6722i	−0.440682	−	0.608664i
$844$	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
$849$	−24.5588	−	19.9547i	−0.842855	−	0.684843i
$850$	10.9535	−	10.1850i	0.375701	−	0.349344i
$851$	4.11351	+	2.37493i	0.141009	+	0.0814117i
$852$	2.63228	+	25.4496i	0.0901803	+	0.871889i
$853$	5.62301	−	5.62301i	0.192528	−	0.192528i	−0.604259	−	0.796788i	$-0.706531\pi$
$853$	5.62301	−	5.62301i	0.192528	−	0.192528i	0.796788	+	0.604259i	$0.206531\pi$
$854$		0			0
$855$	23.6245	+	4.90557i	0.807941	+	0.167767i
$856$	−16.9323	−	29.3277i	−0.578735	−	1.00240i
$857$	5.59795	+	20.8918i	0.191222	+	0.713651i	0.993212	+	0.116314i	$0.0371079\pi$
$857$	5.59795	+	20.8918i	0.191222	+	0.713651i	−0.801990	+	0.597337i	$0.796225\pi$
$858$	0.975435	−	0.706231i	0.0333008	−	0.0241103i
$859$	39.2936	−	22.6862i	1.34068	−	0.774042i	0.353772	−	0.935332i	$-0.384899\pi$
$859$	39.2936	−	22.6862i	1.34068	−	0.774042i	0.986907	+	0.161290i	$0.0515655\pi$
$860$	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	$-0.962972\pi$
$863$	−2.20435	+	8.22674i	−0.0750369	+	0.280041i	0.918205	+	0.396106i	$0.129639\pi$
$864$	−25.0536	+	16.0937i	−0.852340	+	0.547517i
$865$	−3.56518	−	2.84003i	−0.121220	−	0.0965640i
$866$	−15.0374	+	8.68183i	−0.510991	+	0.295021i
$867$	2.75922	−	6.16980i	0.0937080	−	0.209537i
$868$		0			0
$869$	0.873074			0.0296170
$870$	0.233072	−	5.06287i	0.00790187	−	0.171647i
$871$	8.61581	−	14.9230i	0.291936	−	0.505647i
$872$	−5.58678	−	20.8501i	−0.189192	−	0.706075i
$873$	−36.7561	+	18.5752i	−1.24401	+	0.628674i
$874$			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	−0.773646	−	0.633618i	$-0.781569\pi$
$877$	6.31256	−	23.5588i	0.213160	−	0.795525i	0.986806	−	0.161906i	$-0.0517643\pi$
$878$	16.3991	−	4.39411i	0.553441	−	0.148294i
$879$	4.99192	+	0.799115i	0.168373	+	0.0269535i
$880$	0.534198	+	0.232730i	0.0180078	+	0.00784532i
$881$			0.538909i			0.0181563i	0.999959	+	0.00907815i	$0.00288970\pi$
$881$			0.538909i			0.0181563i	−0.999959	+	0.00907815i	$0.997110\pi$
$882$		0			0
$883$	−25.2230	+	25.2230i	−0.848821	+	0.848821i	−0.989986	−	0.141165i	$-0.954915\pi$
$883$	−25.2230	+	25.2230i	−0.848821	+	0.848821i	0.141165	+	0.989986i	$0.454915\pi$
$884$	23.6576	+	40.9762i	0.795692	+	1.37818i
$885$	−9.17828	−	2.91783i	−0.308524	−	0.0980818i
$886$	−11.5911	+	20.0764i	−0.389411	+	0.674479i
$887$	9.48573	+	2.54169i	0.318500	+	0.0853417i	0.414527	−	0.910037i	$-0.363947\pi$
$887$	9.48573	+	2.54169i	0.318500	+	0.0853417i	−0.0960275	+	0.995379i	$0.530614\pi$
$888$	−3.27905	+	7.33218i	−0.110038	+	0.246052i
$889$		0			0
$890$	−15.7290	−	2.36221i	−0.527238	−	0.0791814i
$891$	−0.582011	−	1.33087i	−0.0194981	−	0.0445857i
$892$	0.820399	−	0.219825i	0.0274690	−	0.00736029i
$893$	21.1277	−	5.66115i	0.707012	−	0.189443i
$894$	13.7350	+	11.1601i	0.459366	+	0.373248i
$895$	26.6994	+	36.1362i	0.892464	+	1.20790i
$896$		0			0
$897$	−24.9202	−	11.1447i	−0.832062	−	0.372110i
$898$	11.0250	+	2.95413i	0.367908	+	0.0985805i
$899$	7.46230	−	12.9251i	0.248882	−	0.431076i
$900$	23.4785	+	2.16628i	0.782618	+	0.0722095i
$901$	−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
$906$	1.30324	−	8.14111i	0.0432974	−	0.270470i
$907$	−11.8457	+	3.17404i	−0.393329	+	0.105392i	−0.450062	−	0.892997i	$-0.648598\pi$
$907$	−11.8457	+	3.17404i	−0.393329	+	0.105392i	0.0567332	+	0.998389i	$0.481932\pi$
$908$	−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	$0.852334\pi$
$912$	10.0054	−	1.03487i	0.331312	−	0.0342679i
$913$	0.399296	+	1.49019i	0.0132148	+	0.0493182i
$914$	−11.5067	+	19.9302i	−0.380607	+	0.659231i
$915$	−5.70823	+	5.20580i	−0.188708	+	0.172098i
$916$	3.64787			0.120529
$917$		0			0
$918$	−14.8067	+	4.72983i	−0.488695	+	0.156108i
$919$	10.7836	−	6.22589i	0.355717	−	0.205373i	−0.311484	−	0.950252i	$-0.600826\pi$
$919$	10.7836	−	6.22589i	0.355717	−	0.205373i	0.667200	+	0.744878i	$0.267493\pi$
$920$	1.40730	+	12.4307i	0.0463972	+	0.409827i
$921$	1.55017	+	0.248153i	0.0510797	+	0.00817693i
$922$	−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
$927$	16.3217	−	24.9520i	0.536075	−	0.819530i
$928$	−2.96640	−	11.0708i	−0.0973768	−	0.363415i
$929$	7.49824	+	12.9873i	0.246009	+	0.426100i	0.962415	−	0.271584i	$-0.0875473\pi$
$929$	7.49824	+	12.9873i	0.246009	+	0.426100i	−0.716406	+	0.697684i	$0.754214\pi$
$930$	−15.9247	−	10.1983i	−0.522191	−	0.334415i
$931$		0			0
$932$	9.53450	−	9.53450i	0.312313	−	0.312313i
$933$	−35.9157	+	3.71479i	−1.17583	+	0.121617i
$934$	6.18154	+	3.56892i	0.202266	+	0.116778i
$935$	1.29054	+	1.02804i	0.0422050	+	0.0336207i
$936$	14.4101	−	43.8552i	0.471009	−	1.43345i
$937$	−17.8137	−	17.8137i	−0.581947	−	0.581947i	0.353491	−	0.935438i	$-0.384994\pi$
$937$	−17.8137	−	17.8137i	−0.581947	−	0.581947i	−0.935438	+	0.353491i	$0.884994\pi$
$938$		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	0.998206	−	0.0598755i	$-0.0190704\pi$
$941$	44.3404	+	25.5999i	1.44546	+	0.834534i	0.447249	+	0.894409i	$0.352404\pi$
$942$	14.5283	−	10.5188i	0.473359	−	0.342720i
$943$	−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	$-0.635801\pi$
$947$	−37.7699	−	10.1204i	−1.22736	−	0.328870i	−0.813550	+	0.581495i	$0.802468\pi$
$948$	11.9294	−	8.63708i	0.387449	−	0.280519i
$949$	−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	$-0.296801\pi$
$953$	−6.39589	−	6.39589i	−0.207183	−	0.207183i	−0.803069	+	0.595886i	$0.796801\pi$
$954$	−2.41500	+	7.34973i	−0.0781886	+	0.237956i
$955$	5.44035	+	48.0546i	0.176046	+	1.55501i
$956$	29.3585	+	16.9501i	0.949522	+	0.548207i
$957$	0.556125	−	0.0575205i	0.0179770	−	0.00185937i
$958$	7.92969	−	7.92969i	0.256197	−	0.256197i
$959$		0			0
$960$	−1.96881	+	0.431583i	−0.0635432	+	0.0139293i
$961$	−12.3430	−	21.3786i	−0.398160	−	0.689633i
$962$	−2.21232	−	8.25648i	−0.0713280	−	0.266200i
$963$	23.7961	−	36.3785i	0.766817	−	1.17228i
$964$	−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	0.980670	−	0.195670i	$-0.0626882\pi$
$967$	24.4108	+	24.4108i	0.784999	+	0.784999i	−0.195670	+	0.980670i	$0.562688\pi$
$968$	−6.63800	+	24.7734i	−0.213353	+	0.796246i
$969$	28.1245	+	4.50221i	0.903488	+	0.144632i
$970$	−19.9571	+	2.25938i	−0.640785	+	0.0725445i
$971$	27.2512	−	15.7335i	0.874534	−	0.504912i	0.00568176	−	0.999984i	$-0.498191\pi$
$971$	27.2512	−	15.7335i	0.874534	−	0.504912i	0.868852	+	0.495071i	$0.164858\pi$
$972$	−21.1183	−	12.4268i	−0.677370	−	0.398591i
$973$		0			0
$974$	13.1117			0.420125
$975$	−47.3686	+	31.7384i	−1.51701	+	1.01644i
$976$	−1.61033	+	2.78918i	−0.0515456	+	0.0892795i
$977$	5.90313	+	22.0308i	0.188858	+	0.704827i	0.993772	+	0.111435i	$0.0355447\pi$
$977$	5.90313	+	22.0308i	0.188858	+	0.704827i	−0.804914	+	0.593392i	$0.797789\pi$
$978$	−16.2977	+	1.68568i	−0.521142	+	0.0539022i
$979$		−	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	−0.992724	−	0.120411i	$-0.961579\pi$
$983$	−56.1919	+	15.0566i	−1.79224	+	0.480230i	−0.799519	+	0.600641i	$0.794912\pi$
$984$	7.70316	−	48.1201i	0.245568	−	1.53401i
$985$	−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
$990$	−0.0404004	−	0.707248i	−0.00128401	−	0.0224778i
$991$	27.1762	−	47.0706i	0.863281	−	1.49525i	−0.00546280	−	0.999985i	$-0.501739\pi$
$991$	27.1762	−	47.0706i	0.863281	−	1.49525i	0.868744	−	0.495262i	$-0.164928\pi$
$992$	−41.3066	−	11.0681i	−1.31149	−	0.351412i
$993$	−27.6552	−	12.3678i	−0.877610	−	0.392479i
$994$		0			0
$995$	−1.14721	+	0.847626i	−0.0363691	+	0.0268716i
$996$	20.1979	+	16.4114i	0.639996	+	0.520015i
$997$	−8.41769	+	2.25551i	−0.266591	+	0.0714329i	−0.389638	−	0.920968i	$-0.627400\pi$
$997$	−8.41769	+	2.25551i	−0.266591	+	0.0714329i	0.123047	+	0.992401i	$0.460733\pi$
$998$	−9.64459	+	2.58426i	−0.305294	+	0.0818033i
$999$	−10.2986	+	0.488458i	−0.325834	+	0.0154541i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	735.2.y.f.557.5		32
3.2	odd	2		735.2.y.e.557.4		32
5.3	odd	4		735.2.y.e.263.5		32
7.2	even	3	inner	735.2.y.f.422.3		32
7.3	odd	6		735.2.j.c.197.3	✓	16
7.4	even	3		735.2.j.c.197.4	yes	16
7.5	odd	6	inner	735.2.y.f.422.4		32
7.6	odd	2	inner	735.2.y.f.557.6		32
15.8	even	4	inner	735.2.y.f.263.3		32
21.2	odd	6		735.2.y.e.422.5		32
21.5	even	6		735.2.y.e.422.6		32
21.11	odd	6		735.2.j.d.197.5	yes	16
21.17	even	6		735.2.j.d.197.6	yes	16
21.20	even	2		735.2.y.e.557.3		32
35.3	even	12		735.2.j.d.638.6	yes	16
35.13	even	4		735.2.y.e.263.6		32
35.18	odd	12		735.2.j.d.638.5	yes	16
35.23	odd	12		735.2.y.e.128.4		32
35.33	even	12		735.2.y.e.128.3		32
105.23	even	12	inner	735.2.y.f.128.5		32
105.38	odd	12		735.2.j.c.638.3	yes	16
105.53	even	12		735.2.j.c.638.4	yes	16
105.68	odd	12	inner	735.2.y.f.128.6		32
105.83	odd	4	inner	735.2.y.f.263.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
735.2.j.c.197.3	✓	16	7.3	odd	6
735.2.j.c.197.4	yes	16	7.4	even	3
735.2.j.c.638.3	yes	16	105.38	odd	12
735.2.j.c.638.4	yes	16	105.53	even	12
735.2.j.d.197.5	yes	16	21.11	odd	6
735.2.j.d.197.6	yes	16	21.17	even	6
735.2.j.d.638.5	yes	16	35.18	odd	12
735.2.j.d.638.6	yes	16	35.3	even	12
735.2.y.e.128.3		32	35.33	even	12
735.2.y.e.128.4		32	35.23	odd	12
735.2.y.e.263.5		32	5.3	odd	4
735.2.y.e.263.6		32	35.13	even	4
735.2.y.e.422.5		32	21.2	odd	6
735.2.y.e.422.6		32	21.5	even	6
735.2.y.e.557.3		32	21.20	even	2
735.2.y.e.557.4		32	3.2	odd	2
735.2.y.f.128.5		32	105.23	even	12	inner
735.2.y.f.128.6		32	105.68	odd	12	inner
735.2.y.f.263.3		32	15.8	even	4	inner
735.2.y.f.263.4		32	105.83	odd	4	inner
735.2.y.f.422.3		32	7.2	even	3	inner
735.2.y.f.422.4		32	7.5	odd	6	inner
735.2.y.f.557.5		32	1.1	even	1	trivial
735.2.y.f.557.6		32	7.6	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 $\F_{q}$
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} +(-1.40294 + 1.01575i) 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} +(0.936492 - 2.85008i) q^{9} +(0.911602 - 1.14436i) q^{10} +(0.139773 + 0.0806980i) q^{11} +(2.70814 - 0.280105i) q^{12} +(-4.65555 + 4.65555i) q^{13} +(0.829304 + 3.78315i) q^{15} +(0.807294 + 1.39827i) q^{16} +(1.18329 + 4.41610i) q^{17} +(1.07453 - 1.64269i) 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} +(3.99709 + 0.639861i) q^{24} +(-3.40476 - 3.66164i) q^{25} +(-3.73076 + 2.15395i) q^{26} +(1.58114 + 4.94975i) q^{27} -2.00000 q^{29} +(-0.116536 + 2.53143i) q^{30} +(-3.73115 + 6.46254i) q^{31} +(1.48320 + 5.53538i) q^{32} +(-0.278063 + 0.0287603i) q^{33} +2.99141i q^{34} +(-3.51484 + 3.14377i) q^{36} +(-0.513548 + 1.91659i) q^{37} +(-2.27325 + 0.609116i) q^{38} +(1.80258 - 11.2603i) q^{39} +(-4.86366 + 1.91183i) q^{40} -12.0388i q^{41} +(-5.56631 + 5.56631i) q^{43} +(-0.126848 - 0.219707i) q^{44} +(-5.00622 - 4.46518i) q^{45} +(0.783154 - 1.35646i) q^{46} +(-5.87394 - 1.57392i) q^{47} +(-2.55289 - 1.14169i) q^{48} +(-1.53176 - 2.89078i) q^{50} +(-6.14576 - 4.99360i) q^{51} +(9.99654 - 2.67857i) q^{52} +(-3.80695 + 1.02007i) q^{53} +(0.161073 + 3.39605i) q^{54} +(0.290259 - 0.214460i) q^{55} +(2.54336 - 5.68713i) q^{57} +(-1.26402 - 0.338694i) q^{58} +(-1.24335 + 2.15354i) q^{59} +(1.84442 - 5.80176i) q^{60} +(0.997366 + 1.72749i) q^{61} +(-3.45254 + 3.45254i) q^{62} +0.520416i q^{64} +(5.38589 + 13.7016i) q^{65} +(-0.180609 - 0.0289122i) q^{66} +(-2.52804 + 0.677387i) q^{67} +(1.86000 - 6.94160i) q^{68} +(1.47948 + 3.87333i) q^{69} +9.39746i q^{71} +(-6.25763 + 3.16237i) q^{72} +(1.00634 + 3.75571i) q^{73} +(-0.649136 + 1.12434i) q^{74} +(8.49600 + 1.67867i) q^{75} +5.65384 q^{76} +(3.04615 - 6.81140i) q^{78} +(4.68478 - 2.70476i) q^{79} +(3.58741 - 0.406138i) q^{80} +(-7.24597 - 5.33816i) 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} +(2.80588 - 2.03151i) q^{87} +(-0.0976263 - 0.364346i) q^{88} +(-5.43562 - 9.41477i) q^{89} +(-2.40782 - 3.66983i) q^{90} +(-2.66074 + 2.66074i) q^{92} +(-1.32976 - 12.8565i) q^{93} +(-3.44585 - 1.98946i) q^{94} +(0.904763 + 7.99176i) q^{95} +(-7.70342 - 6.25925i) q^{96} +(-9.70695 - 9.70695i) q^{97} +(0.360892 - 0.322792i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{2} + 56 q^{8} - 32 q^{9} - 56 q^{15} + 48 q^{16} - 12 q^{18} + 16 q^{22} - 16 q^{23} - 8 q^{25} - 64 q^{29} - 8 q^{30} - 52 q^{32} - 80 q^{36} + 24 q^{37} + 8 q^{39} + 48 q^{43} + 8 q^{44} - 88 q^{46}+ \cdots + 80 q^{99}+O(q^{100}) \) 32 * q + 4 * q^2 + 56 * q^8 - 32 * q^9 - 56 * q^15 + 48 * q^16 - 12 * q^18 + 16 * q^22 - 16 * q^23 - 8 * q^25 - 64 * q^29 - 8 * 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 + 32 * q^57 - 8 * q^58 + 116 * q^60 + 112 * q^65 - 16 * q^67 - 116 * q^72 + 8 * q^74 + 128 * q^78 + 16 * q^81 + 48 * q^85 + 80 * q^88 - 160 * q^92 - 80 * q^93 - 72 * q^95 + 80 * q^99

Introduction

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Modular forms

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