LMFDB - Embedded newform 735.2.y.e.422.6

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			422.6
Character	$\chi$	$=$	735.422
Dual form			735.2.y.e.263.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.169347 + 0.632011i) q^{2} +(1.01575 - 1.40294i) q^{3} +(1.36129 - 0.785942i) q^{4} +(-2.22187 + 0.251543i) q^{5} +(1.05869 + 0.404383i) q^{6} +(1.65258 + 1.65258i) q^{8} +(-0.936492 - 2.85008i) q^{9} +(-0.535245 - 1.36165i) q^{10} +(0.139773 - 0.0806980i) q^{11} +(0.280105 - 2.70814i) q^{12} +(4.65555 - 4.65555i) q^{13} +(-1.90398 + 3.37267i) q^{15} +(0.807294 - 1.39827i) q^{16} +(-4.41610 - 1.18329i) q^{17} +(1.64269 - 1.07453i) q^{18} +(-3.11497 - 1.79843i) q^{19} +(-2.82692 + 2.08869i) q^{20} +(0.0746721 + 0.0746721i) q^{22} +(2.31228 - 0.619573i) q^{23} +(3.99709 - 0.639861i) q^{24} +(4.87345 - 1.11779i) q^{25} +(3.73076 + 2.15395i) q^{26} +(-4.94975 - 1.58114i) q^{27} +2.00000 q^{29} +(-2.45399 - 0.632183i) q^{30} +(3.73115 + 6.46254i) q^{31} +(5.53538 + 1.48320i) q^{32} +(0.0287603 - 0.278063i) q^{33} -2.99141i q^{34} +(-3.51484 - 3.14377i) q^{36} +(1.91659 - 0.513548i) q^{37} +(0.609116 - 2.27325i) q^{38} +(-1.80258 - 11.2603i) q^{39} +(-4.08752 - 3.25614i) q^{40} -12.0388i q^{41} +(-5.56631 + 5.56631i) q^{43} +(0.126848 - 0.219707i) q^{44} +(2.79768 + 6.09696i) q^{45} +(0.783154 + 1.35646i) q^{46} +(1.57392 + 5.87394i) q^{47} +(-1.14169 - 2.55289i) q^{48} +(1.53176 + 2.89078i) q^{50} +(-6.14576 + 4.99360i) q^{51} +(2.67857 - 9.99654i) q^{52} +(-1.02007 + 3.80695i) q^{53} +(0.161073 - 3.39605i) q^{54} +(-0.290259 + 0.214460i) q^{55} +(-5.68713 + 2.54336i) q^{57} +(0.338694 + 1.26402i) q^{58} +(-1.24335 - 2.15354i) q^{59} +(0.0588534 + 6.08760i) q^{60} +(-0.997366 + 1.72749i) q^{61} +(-3.45254 + 3.45254i) q^{62} +0.520416i q^{64} +(-9.17297 + 11.5151i) q^{65} +(0.180609 - 0.0289122i) q^{66} +(0.677387 - 2.52804i) q^{67} +(-6.94160 + 1.86000i) q^{68} +(1.47948 - 3.87333i) q^{69} -9.39746i q^{71} +(3.16237 - 6.25763i) q^{72} +(3.75571 + 1.00634i) q^{73} +(0.649136 + 1.12434i) q^{74} +(3.38203 - 7.97257i) q^{75} -5.65384 q^{76} +(6.81140 - 3.04615i) q^{78} +(-4.68478 - 2.70476i) q^{79} +(-1.44198 + 3.30986i) q^{80} +(-7.24597 + 5.33816i) q^{81} +(7.60864 - 2.03873i) q^{82} +(6.75913 + 6.75913i) q^{83} +(10.1097 + 1.51829i) q^{85} +(-4.46060 - 2.57533i) q^{86} +(2.03151 - 2.80588i) q^{87} +(0.364346 + 0.0976263i) q^{88} +(-5.43562 + 9.41477i) q^{89} +(-3.37957 + 2.80067i) q^{90} +(2.66074 - 2.66074i) q^{92} +(12.8565 + 1.32976i) q^{93} +(-3.44585 + 1.98946i) q^{94} +(7.37345 + 3.21233i) 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} + 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 $\left(\mathbb{Z}/735\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.169347	+	0.632011i	0.119746	+	0.446899i	0.999598	−	0.0283490i	$-0.00902498\pi$
$2$	0.169347	+	0.632011i	0.119746	+	0.446899i	−0.879852	+	0.475248i	$0.842358\pi$
$3$	1.01575	−	1.40294i	0.586445	−	0.809989i
$3$	1.01575	−	1.40294i	0.586445	−	0.809989i
$4$	1.36129	−	0.785942i	0.680646	−	0.392971i
$5$	−2.22187	+	0.251543i	−0.993652	+	0.112493i
$5$	−2.22187	+	0.251543i	−0.993652	+	0.112493i
$6$	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
$10$	−0.535245	−	1.36165i	−0.169259	−	0.430592i
$11$	0.139773	−	0.0806980i	0.0421431	−	0.0243313i	−0.478780	−	0.877935i	$-0.658921\pi$
$11$	0.139773	−	0.0806980i	0.0421431	−	0.0243313i	0.520924	+	0.853603i	$0.325588\pi$
$12$	0.280105	−	2.70814i	0.0808593	−	0.781772i
$13$	4.65555	−	4.65555i	1.29122	−	1.29122i	0.357181	−	0.934035i	$-0.383738\pi$
$13$	4.65555	−	4.65555i	1.29122	−	1.29122i	0.934035	−	0.357181i	$-0.116262\pi$
$14$		0			0
$15$	−1.90398	+	3.37267i	−0.491605	+	0.870819i
$16$	0.807294	−	1.39827i	0.201823	−	0.349569i
$17$	−4.41610	−	1.18329i	−1.07106	−	0.286990i	−0.320133	−	0.947373i	$-0.603727\pi$
$17$	−4.41610	−	1.18329i	−1.07106	−	0.286990i	−0.750929	+	0.660383i	$0.770394\pi$
$18$	1.64269	−	1.07453i	0.387186	−	0.253268i
$19$	−3.11497	−	1.79843i	−0.714623	−	0.412588i	0.0981474	−	0.995172i	$-0.468708\pi$
$19$	−3.11497	−	1.79843i	−0.714623	−	0.412588i	−0.812770	+	0.582584i	$0.802042\pi$
$20$	−2.82692	+	2.08869i	−0.632119	+	0.467045i
$21$		0			0
$22$	0.0746721	+	0.0746721i	0.0159201	+	0.0159201i
$23$	2.31228	−	0.619573i	0.482144	−	0.129190i	−0.00955698	−	0.999954i	$-0.503042\pi$
$23$	2.31228	−	0.619573i	0.482144	−	0.129190i	0.491701	+	0.870764i	$0.336375\pi$
$24$	3.99709	−	0.639861i	0.815903	−	0.130611i
$25$	4.87345	−	1.11779i	0.974691	−	0.223558i
$26$	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	$0.440546\pi$
$30$	−2.45399	−	0.632183i	−0.448036	−	0.115420i
$31$	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	$0.599570\pi$
$32$	5.53538	+	1.48320i	0.978525	+	0.262195i
$33$	0.0287603	−	0.278063i	0.00500652	−	0.0484045i
$34$		−	2.99141i		−	0.513023i
$35$		0			0
$36$	−3.51484	−	3.14377i	−0.585807	−	0.523961i
$37$	1.91659	−	0.513548i	0.315085	−	0.0844268i	−0.0978108	−	0.995205i	$-0.531184\pi$
$37$	1.91659	−	0.513548i	0.315085	−	0.0844268i	0.412896	+	0.910778i	$0.364517\pi$
$38$	0.609116	−	2.27325i	0.0988117	−	0.368770i
$39$	−1.80258	−	11.2603i	−0.288643	−	1.80310i
$40$	−4.08752	−	3.25614i	−0.646294	−	0.514840i
$41$		−	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
$45$	2.79768	+	6.09696i	0.417054	+	0.908882i
$46$	0.783154	+	1.35646i	0.115470	+	0.200000i
$47$	1.57392	+	5.87394i	0.229579	+	0.856802i	0.980518	+	0.196430i	$0.0629348\pi$
$47$	1.57392	+	5.87394i	0.229579	+	0.856802i	−0.750939	+	0.660372i	$0.770399\pi$
$48$	−1.14169	−	2.55289i	−0.164788	−	0.368478i
$49$		0			0
$50$	1.53176	+	2.89078i	0.216624	+	0.408818i
$51$	−6.14576	+	4.99360i	−0.860578	+	0.699244i
$52$	2.67857	−	9.99654i	0.371450	−	1.38627i
$53$	−1.02007	+	3.80695i	−0.140117	+	0.522924i	0.859807	+	0.510619i	$0.170584\pi$
$53$	−1.02007	+	3.80695i	−0.140117	+	0.522924i	−0.999924	+	0.0123054i	$0.996083\pi$
$54$	0.161073	−	3.39605i	0.0219193	−	0.462144i
$55$	−0.290259	+	0.214460i	−0.0391385	+	0.0289177i
$56$		0			0
$57$	−5.68713	+	2.54336i	−0.753279	+	0.336877i
$58$	0.338694	+	1.26402i	0.0444726	+	0.165974i
$59$	−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	$0.885086\pi$
$60$	0.0588534	+	6.08760i	0.00759794	+	0.785905i
$61$	−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
$65$	−9.17297	+	11.5151i	−1.13777	+	1.42827i
$66$	0.180609	−	0.0289122i	0.0222314	−	0.00355884i
$67$	0.677387	−	2.52804i	0.0827560	−	0.308850i	−0.912124	−	0.409915i	$-0.865558\pi$
$67$	0.677387	−	2.52804i	0.0827560	−	0.308850i	0.994880	+	0.101065i	$0.0322251\pi$
$68$	−6.94160	+	1.86000i	−0.841793	+	0.225558i
$69$	1.47948	−	3.87333i	0.178108	−	0.466294i
$70$		0			0
$71$		−	9.39746i		−	1.11527i	−0.830085	−	0.557637i	$-0.811708\pi$
$71$		−	9.39746i		−	1.11527i	0.830085	−	0.557637i	$-0.188292\pi$
$72$	3.16237	−	6.25763i	0.372689	−	0.737469i
$73$	3.75571	+	1.00634i	0.439573	+	0.117783i	0.471816	−	0.881697i	$-0.343599\pi$
$73$	3.75571	+	1.00634i	0.439573	+	0.117783i	−0.0322434	+	0.999480i	$0.510265\pi$
$74$	0.649136	+	1.12434i	0.0754605	+	0.130701i
$75$	3.38203	−	7.97257i	0.390523	−	0.920593i
$76$	−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	0.212747	−	0.977107i	$-0.431759\pi$
$79$	−4.68478	−	2.70476i	−0.527079	−	0.304309i	−0.739826	+	0.672798i	$0.765092\pi$
$80$	−1.44198	+	3.30986i	−0.161218	+	0.370053i
$81$	−7.24597	+	5.33816i	−0.805107	+	0.593129i
$82$	7.60864	−	2.03873i	0.840234	−	0.225140i
$83$	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
$87$	2.03151	−	2.80588i	0.217800	−	0.300822i
$88$	0.364346	+	0.0976263i	0.0388394	+	0.0104070i
$89$	−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
$93$	12.8565	+	1.32976i	1.33316	+	0.137890i
$94$	−3.44585	+	1.98946i	−0.355413	+	0.205198i
$95$	7.37345	+	3.21233i	0.756500	+	0.329579i
$96$	7.70342	−	6.25925i	0.786227	−	0.638832i
$97$	9.70695	+	9.70695i	0.985592	+	0.985592i	0.999898	−	0.0143059i	$-0.00455388\pi$
$97$	9.70695	+	9.70695i	0.985592	+	0.985592i	−0.0143059	+	0.999898i	$0.504554\pi$
$98$		0			0
$99$	−0.360892	−	0.322792i	−0.0362710	−	0.0324418i
$100$	5.75567	−	5.35189i	0.575567	−	0.535189i
$101$	4.02217	−	2.32220i	0.400221	−	0.231068i	−0.286358	−	0.958123i	$-0.592445\pi$
$101$	4.02217	−	2.32220i	0.400221	−	0.231068i	0.686579	+	0.727055i	$0.259111\pi$
$102$	−4.19677	−	3.03853i	−0.415543	−	0.300860i
$103$	2.57232	+	9.60004i	0.253459	+	0.945920i	0.968941	+	0.247290i	$0.0795401\pi$
$103$	2.57232	+	9.60004i	0.253459	+	0.945920i	−0.715483	+	0.698630i	$0.753793\pi$
$104$	15.3873			1.50885
$105$		0			0
$106$	−2.57878			−0.250473
$107$	3.75029	+	13.9963i	0.362554	+	1.35307i	0.870706	+	0.491804i	$0.163662\pi$
$107$	3.75029	+	13.9963i	0.362554	+	1.35307i	−0.508151	+	0.861268i	$0.669671\pi$
$108$	−7.98073	+	1.73782i	−0.767946	+	0.167222i
$109$	−7.99867	+	4.61803i	−0.766134	+	0.442327i	−0.831494	−	0.555534i	$-0.812514\pi$
$109$	−7.99867	+	4.61803i	−0.766134	+	0.442327i	0.0653600	+	0.997862i	$0.479180\pi$
$110$	−0.184695	−	0.147129i	−0.0176100	−	0.0140282i
$111$	1.22630	−	3.21050i	0.116395	−	0.304727i
$112$		0			0
$113$	4.87918	+	4.87918i	0.458994	+	0.458994i	0.898325	−	0.439331i	$-0.144784\pi$
$113$	4.87918	+	4.87918i	0.458994	+	0.458994i	−0.439331	+	0.898325i	$0.644784\pi$
$114$	−2.57053	−	3.16362i	−0.240752	−	0.296300i
$115$	−4.98175	+	1.95825i	−0.464550	+	0.182608i
$116$	2.72258	−	1.57188i	0.252785	−	0.145946i
$117$	−17.6286	−	8.90882i	−1.62976	−	0.823621i
$118$	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
$122$	−1.26069	−	0.337801i	−0.114138	−	0.0305831i
$123$	−16.8897	−	12.2284i	−1.52289	−	1.10260i
$124$	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	$0.753836\pi$
$128$	10.7418	−	2.87827i	0.949454	−	0.254405i
$129$	2.15521	+	13.4632i	0.189756	+	1.18537i
$130$	−8.83108	−	3.84737i	−0.774537	−	0.337437i
$131$	11.9048	+	6.87326i	1.04013	+	0.600519i	0.919870	−	0.392223i	$-0.128294\pi$
$131$	11.9048	+	6.87326i	1.04013	+	0.600519i	0.120260	+	0.992742i	$0.461627\pi$
$132$	−0.179390	−	0.401128i	−0.0156139	−	0.0349137i
$133$		0			0
$134$	1.71246			0.147934
$135$	11.3954	+	2.26802i	0.980763	+	0.195200i
$136$	−5.34248	−	9.25345i	−0.458114	−	0.793477i
$137$	7.65030	+	2.04989i	0.653609	+	0.175134i	0.570360	−	0.821395i	$-0.306804\pi$
$137$	7.65030	+	2.04989i	0.653609	+	0.175134i	0.0832489	+	0.996529i	$0.473470\pi$
$138$	2.69853	+	0.279111i	0.229714	+	0.0237595i
$139$			16.6862i			1.41531i	0.706560	+	0.707653i	$0.250246\pi$
$139$			16.6862i			1.41531i	−0.706560	+	0.707653i	$0.749754\pi$
$140$		0			0
$141$	9.83950	+	3.75836i	0.828636	+	0.316511i
$142$	5.93930	−	1.59143i	0.498415	−	0.133550i
$143$	0.275026	−	1.02641i	0.0229989	−	0.0858329i
$144$	−4.74122	−	0.991384i	−0.395102	−	0.0826153i
$145$	−4.44375	+	0.503085i	−0.369033	+	0.0417790i
$146$			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	$-0.0542550\pi$
$150$	5.61149	+	0.787348i	0.458176	+	0.0642867i
$151$	−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	$0.928992\pi$
$152$	−2.17569	−	8.11979i	−0.176472	−	0.658602i
$153$	0.763163	+	13.6944i	0.0616981	+	1.10713i
$154$		0			0
$155$	−9.91575	−	13.4204i	−0.796452	−	1.07795i
$156$	−11.3038	−	13.9119i	−0.905029	−	1.11384i
$157$	−4.09630	+	15.2876i	−0.326921	+	1.22008i	0.585447	+	0.810711i	$0.300919\pi$
$157$	−4.09630	+	15.2876i	−0.326921	+	1.22008i	−0.912367	+	0.409373i	$0.865747\pi$
$158$	0.916084	−	3.41887i	0.0728797	−	0.271991i
$159$	4.30479	+	5.29801i	0.341392	+	0.420160i
$160$	−12.6720	−	1.90310i	−1.00181	−	0.150453i
$161$		0			0
$162$	−4.60086	−	3.67553i	−0.361477	−	0.288777i
$163$	−3.74189	−	13.9649i	−0.293088	−	1.09382i	−0.942724	−	0.333573i	$-0.891746\pi$
$163$	−3.74189	−	13.9649i	−0.293088	−	1.09382i	0.649636	−	0.760245i	$-0.274921\pi$
$164$	−9.46179	−	16.3883i	−0.738842	−	1.27971i
$165$	0.00604288	+	0.625054i	0.000470437	+	0.0486604i
$166$	−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
$170$	0.752467	+	6.64654i	0.0577116	+	0.509766i
$171$	−2.20853	+	10.5621i	−0.168891	+	0.807707i
$172$	−3.20257	+	11.9522i	−0.244194	+	0.911344i
$173$	−1.96899	+	0.527588i	−0.149699	+	0.0401118i	−0.332890	−	0.942966i	$-0.608024\pi$
$173$	−1.96899	+	0.527588i	−0.149699	+	0.0401118i	0.183191	+	0.983077i	$0.441357\pi$
$174$	2.11738	+	0.808766i	0.160518	+	0.0613124i
$175$		0			0
$176$		−	0.260588i		−	0.0196426i
$177$	−4.28422	−	0.443121i	−0.322022	−	0.0333070i
$178$	−6.87074	−	1.84101i	−0.514984	−	0.137990i
$179$	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	$0.562945\pi$
$180$	8.60032	+	6.10093i	0.641030	+	0.454736i
$181$	−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
$185$	−4.12924	+	1.62314i	−0.303588	+	0.119336i
$186$	1.33678	+	8.35063i	0.0980177	+	0.612298i
$187$	−0.712741	+	0.190978i	−0.0521208	+	0.0139657i
$188$	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	−0.366298	−	0.930498i	$-0.619375\pi$
$191$	−18.7304	−	10.8140i	−1.35528	−	0.782472i	−0.988984	+	0.148026i	$0.952708\pi$
$192$	0.730113	+	0.528614i	0.0526914	+	0.0381494i
$193$	5.60798	+	1.50265i	0.403671	+	0.108163i	0.454941	−	0.890521i	$-0.349660\pi$
$193$	5.60798	+	1.50265i	0.403671	+	0.108163i	−0.0512701	+	0.998685i	$0.516327\pi$
$194$	−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	−0.952952	−	0.303121i	$-0.901972\pi$
$197$	−9.12082	+	9.12082i	−0.649832	+	0.649832i	0.303121	+	0.952952i	$0.401972\pi$
$198$	0.142892	−	0.282752i	0.0101549	−	0.0200943i
$199$	−0.552436	+	0.318949i	−0.0391612	+	0.0226097i	−0.519453	−	0.854499i	$-0.673864\pi$
$199$	−0.552436	+	0.318949i	−0.0391612	+	0.0226097i	0.480292	+	0.877109i	$0.340531\pi$
$200$	9.90102	+	6.20654i	0.700108	+	0.438868i
$201$	−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
$205$	3.02827	+	26.7487i	0.211503	+	1.86821i
$206$	−5.63172	+	3.25147i	−0.392380	+	0.226541i
$207$	−3.93127	−	6.00997i	−0.273242	−	0.417722i
$208$	−2.75134	−	10.2681i	−0.190771	−	0.711966i
$209$	−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	$0.574029\pi$
$212$	1.60343	+	5.98408i	0.110124	+	0.410988i
$213$	−13.1841	−	9.54550i	−0.903359	−	0.654047i
$214$	−8.21070	+	4.74045i	−0.561272	+	0.324051i
$215$	10.9675	−	13.7678i	0.747976	−	0.938956i
$216$	−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
$220$	−0.226574	+	0.520069i	−0.0152756	+	0.0350630i
$221$	−26.0682	+	15.0505i	−1.75354	+	1.01241i
$222$	2.23674	+	0.231348i	0.150120	+	0.0155271i
$223$	0.382073	−	0.382073i	0.0255855	−	0.0255855i	−0.694198	−	0.719784i	$-0.744241\pi$
$223$	0.382073	−	0.382073i	0.0255855	−	0.0255855i	0.719784	+	0.694198i	$0.244241\pi$
$224$		0			0
$225$	−7.74975	−	12.8430i	−0.516650	−	0.856197i
$226$	−2.25742	+	3.90997i	−0.150161	+	0.260087i
$227$	17.0874	+	4.57855i	1.13413	+	0.303889i	0.776588	−	0.630008i	$-0.216949\pi$
$227$	17.0874	+	4.57855i	1.13413	+	0.303889i	0.357541	+	0.933897i	$0.383615\pi$
$228$	−5.74291	+	7.93201i	−0.380333	+	0.525310i
$229$	−2.00978	−	1.16035i	−0.132810	−	0.0766780i	0.432123	−	0.901815i	$-0.357765\pi$
$229$	−2.00978	−	1.16035i	−0.132810	−	0.0766780i	−0.564933	+	0.825137i	$0.691098\pi$
$230$	−2.08128	−	2.81689i	−0.137235	−	0.185740i
$231$		0			0
$232$	3.30516	+	3.30516i	0.216995	+	0.216995i
$233$	−8.28583	+	2.22018i	−0.542823	+	0.145449i	−0.519803	−	0.854286i	$-0.673995\pi$
$233$	−8.28583	+	2.22018i	−0.542823	+	0.145449i	−0.0230197	+	0.999735i	$0.507328\pi$
$234$	2.64513	−	12.6501i	0.172917	−	0.826965i
$235$	−4.97459	−	12.6552i	−0.324507	−	0.825537i
$236$	−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	$0.254289\pi$
$240$	3.17884	+	5.38501i	0.205193	+	0.347601i
$241$	−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	$0.900369\pi$
$242$	−6.93566	−	1.85840i	−0.445841	−	0.119463i
$243$	0.129018	+	15.5879i	0.00827648	+	0.999966i
$244$			3.13549i			0.200729i
$245$		0			0
$246$	4.86828	−	12.7453i	0.310390	−	0.812613i
$247$	−22.8745	+	6.12922i	−1.45547	+	0.389993i
$248$	−4.51385	+	16.8459i	−0.286630	+	1.06972i
$249$	16.3483	−	2.61706i	1.03603	−	0.165850i
$250$	−4.13053	−	6.03765i	−0.261238	−	0.381854i
$251$		−	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
$255$	12.3990	−	12.6411i	0.776455	−	0.791615i
$256$	4.15861	+	7.20292i	0.259913	+	0.450183i
$257$	2.98446	+	11.1381i	0.186165	+	0.694778i	0.994378	+	0.105888i	$0.0337684\pi$
$257$	2.98446	+	11.1381i	0.186165	+	0.694778i	−0.808213	+	0.588890i	$0.799565\pi$
$258$	−8.14391	+	3.64207i	−0.507018	+	0.226745i
$259$		0			0
$260$	−3.43688	+	22.8848i	−0.213146	+	1.41926i
$261$	−1.87298	−	5.70017i	−0.115935	−	0.352832i
$262$	−2.32793	+	8.68795i	−0.143820	+	0.536743i
$263$	5.10066	−	19.0359i	0.314520	−	1.17380i	−0.609916	−	0.792466i	$-0.708797\pi$
$263$	5.10066	−	19.0359i	0.314520	−	1.17380i	0.924436	−	0.381338i	$-0.124537\pi$
$264$	0.507050	−	0.411992i	0.0312068	−	0.0253564i
$265$	1.30885	−	8.71515i	0.0804023	−	0.535367i
$266$		0			0
$267$	7.68713	+	17.1889i	0.470445	+	1.05195i
$268$	−1.06477	−	3.97379i	−0.0650414	−	0.242738i
$269$	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	$0.800492\pi$
$270$	0.496368	+	7.58612i	0.0302080	+	0.461677i
$271$	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
$275$	0.590973	−	0.549515i	0.0356370	−	0.0331370i
$276$	−1.03021	−	6.43551i	−0.0620112	−	0.387372i
$277$	−1.72605	+	6.44170i	−0.103708	+	0.387044i	−0.998195	−	0.0600492i	$-0.980874\pi$
$277$	−1.72605	+	6.44170i	−0.103708	+	0.387044i	0.894487	+	0.447094i	$0.147541\pi$
$278$	−10.5459	+	2.82576i	−0.632499	+	0.169478i
$279$	14.9246	−	16.6862i	0.893512	−	0.998977i
$280$		0			0
$281$		−	12.5965i		−	0.751447i	−0.926732	−	0.375723i	$-0.877394\pi$
$281$		−	12.5965i		−	0.751447i	0.926732	−	0.375723i	$-0.122606\pi$
$282$	−0.709033	+	6.85514i	−0.0422223	+	0.408218i
$283$	17.6470	+	4.72849i	1.04900	+	0.281080i	0.741840	−	0.670577i	$-0.233953\pi$
$283$	17.6470	+	4.72849i	1.04900	+	0.281080i	0.307164	+	0.951657i	$0.400620\pi$
$284$	−7.38586	−	12.7927i	−0.438270	−	0.759106i
$285$	11.9963	−	7.08159i	0.710601	−	0.419477i
$286$	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
$290$	−1.07049	−	2.72330i	−0.0628613	−	0.159918i
$291$	23.4782	−	3.75842i	1.37631	−	0.220323i
$292$	5.90355	−	1.58185i	0.345479	−	0.0925708i
$293$	−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
$297$	−0.819436	+	0.178434i	−0.0475485	+	0.0103538i
$298$	9.86942	+	2.64450i	0.571720	+	0.153192i
$299$	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
$303$	0.827619	−	8.00166i	0.0475455	−	0.459683i
$304$	−5.02939	+	2.90372i	−0.288455	+	0.166540i
$305$	1.78148	−	4.08914i	0.102008	−	0.234144i
$306$	−8.52577	+	2.80143i	−0.487386	+	0.160147i
$307$	0.640910	+	0.640910i	0.0365787	+	0.0365787i	0.725160	−	0.688581i	$-0.241766\pi$
$307$	0.640910	+	0.640910i	0.0365787	+	0.0365787i	−0.688581	+	0.725160i	$0.741766\pi$
$308$		0			0
$309$	16.0811	+	6.14245i	0.914825	+	0.349432i
$310$	6.80264	−	8.53956i	0.386364	−	0.485015i
$311$	−18.0536	+	10.4233i	−1.02373	+	0.591049i	−0.915181	−	0.403042i	$-0.867953\pi$
$311$	−18.0536	+	10.4233i	−1.02373	+	0.591049i	−0.108546	+	0.994091i	$0.534619\pi$
$312$	15.6297	−	21.5875i	0.884860	−	1.22215i
$313$	−4.53760	−	16.9346i	−0.256481	−	0.957198i	−0.967261	−	0.253784i	$-0.918325\pi$
$313$	−4.53760	−	16.9346i	−0.256481	−	0.957198i	0.710780	−	0.703414i	$-0.248342\pi$
$314$	−10.3556			−0.584402
$315$		0			0
$316$	−8.50313			−0.478339
$317$	1.06928	+	3.99061i	0.0600567	+	0.224135i	0.989431	−	0.145004i	$-0.0463195\pi$
$317$	1.06928	+	3.99061i	0.0600567	+	0.224135i	−0.929374	+	0.369139i	$0.879653\pi$
$318$	−2.61940	+	3.61787i	−0.146889	+	0.202880i
$319$	0.279546	−	0.161396i	0.0156516	−	0.00903644i
$320$	−0.130907	−	1.15630i	−0.00731791	−	0.0646390i
$321$	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
$325$	17.4846	−	27.8925i	0.969874	−	1.54720i
$326$	8.19231	−	4.72983i	0.453730	−	0.261961i
$327$	−1.64584	+	15.9125i	−0.0910151	+	0.879961i
$328$	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	$0.00705403\pi$
$332$	14.5134	+	3.88886i	0.796529	+	0.213429i
$333$	−3.25852	−	4.98150i	−0.178566	−	0.272985i
$334$	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	$0.770270\pi$
$338$	19.1804	−	5.13937i	1.04328	−	0.279545i
$339$	11.8012	−	1.88916i	0.640956	−	0.102605i
$340$	14.9555	−	5.87879i	0.811076	−	0.318822i
$341$	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
$345$	−2.31291	+	8.97820i	−0.124523	+	0.483370i
$346$	−0.666883	−	1.15507i	−0.0358518	−	0.0620972i
$347$	−25.1026	−	6.72623i	−1.34758	−	0.361083i	−0.488338	−	0.872654i	$-0.662397\pi$
$347$	−25.1026	−	6.72623i	−1.34758	−	0.361083i	−0.859241	+	0.511572i	$0.829063\pi$
$348$	0.560210	−	5.41627i	0.0300304	−	0.290343i
$349$		−	28.1366i		−	1.50612i	−0.657953	−	0.753059i	$-0.728578\pi$
$349$		−	28.1366i		−	1.50612i	0.657953	−	0.753059i	$-0.271422\pi$
$350$		0			0
$351$	−30.4048	+	15.6827i	−1.62289	+	0.837081i
$352$	0.893387	−	0.239382i	0.0476177	−	0.0127591i
$353$	3.97434	−	14.8324i	0.211533	−	0.789451i	−0.775826	−	0.630947i	$-0.782666\pi$
$353$	3.97434	−	14.8324i	0.211533	−	0.789451i	0.987358	−	0.158503i	$-0.0506669\pi$
$354$	−0.445462	−	2.78271i	−0.0236760	−	0.147900i
$355$	2.36386	+	20.8800i	0.125461	+	1.10819i
$356$			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	$0.0510138\pi$
$360$	−5.45233	+	14.6991i	−0.287363	+	0.774712i
$361$	−3.03131	−	5.25038i	−0.159543	−	0.276336i
$362$	−2.82480	−	10.5423i	−0.148468	−	0.554090i
$363$	7.75976	+	17.3513i	0.407282	+	0.910709i
$364$		0			0
$365$	−8.59786	−	1.29124i	−0.450033	−	0.0675866i
$366$	−1.75447	+	1.42555i	−0.0917075	+	0.0745149i
$367$	−1.02051	+	3.80860i	−0.0532703	+	0.198807i	−0.987433	−	0.158041i	$-0.949482\pi$
$367$	−1.02051	+	3.80860i	−0.0532703	+	0.198807i	0.934162	+	0.356849i	$0.116149\pi$
$368$	1.00036	−	3.73338i	0.0521471	−	0.194616i
$369$	−34.3116	+	11.2742i	−1.78619	+	0.586913i
$370$	−1.72512	−	2.33485i	−0.0896846	−	0.121383i
$371$		0			0
$372$	18.5466	−	8.29427i	0.961594	−	0.430038i
$373$	−1.55051	−	5.78658i	−0.0802823	−	0.299618i	0.914097	−	0.405496i	$-0.132901\pi$
$373$	−1.55051	−	5.78658i	−0.0802823	−	0.299618i	−0.994379	+	0.105878i	$0.966235\pi$
$374$	−0.241401	−	0.418118i	−0.0124825	−	0.0216204i
$375$	−5.50900	+	18.5648i	−0.284483	+	0.958681i
$376$	−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	$0.776470\pi$
$380$	12.5621	−	1.42218i	0.644424	−	0.0729564i
$381$	−0.464505	+	0.0743588i	−0.0237973	+	0.00380952i
$382$	3.66262	−	13.6691i	0.187396	−	0.699372i
$383$	6.01154	−	1.61079i	0.307175	−	0.0823073i	−0.101939	−	0.994791i	$-0.532505\pi$
$383$	6.01154	−	1.61079i	0.307175	−	0.0823073i	0.409114	+	0.912483i	$0.365838\pi$
$384$	6.87302	−	17.9938i	0.350737	−	0.918242i
$385$		0			0
$386$			3.79877i			0.193352i
$387$	21.0773	+	10.6516i	1.07142	+	0.541454i
$388$	20.8431	+	5.58489i	1.05815	+	0.283530i
$389$	−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	$-0.396492\pi$
$390$	−14.3678	+	8.48152i	−0.727544	+	0.429478i
$391$	−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
$395$	11.0894	+	4.83121i	0.557966	+	0.243085i
$396$	−0.744975	−	0.155773i	−0.0374364	−	0.00782791i
$397$	−20.4972	+	5.49222i	−1.02873	+	0.275647i	−0.733435	−	0.679760i	$-0.762084\pi$
$397$	−20.4972	+	5.49222i	−1.02873	+	0.275647i	−0.295293	+	0.955407i	$0.595417\pi$
$398$	−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	0.576728	−	0.816936i	$-0.304329\pi$
$401$	3.15603	+	1.82213i	0.157605	+	0.0909930i	−0.419124	+	0.907929i	$0.637663\pi$
$402$	1.73944	−	2.40249i	0.0867554	−	0.119825i
$403$	47.4572	+	12.7161i	2.36401	+	0.633435i
$404$	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
$408$	−18.4087	−	1.90403i	−0.911367	−	0.0942635i
$409$	−7.47293	+	4.31450i	−0.369513	+	0.213338i	−0.673245	−	0.739419i	$-0.735100\pi$
$409$	−7.47293	+	4.31450i	−0.369513	+	0.213338i	0.303733	+	0.952757i	$0.401767\pi$
$410$	−16.3926	+	6.44370i	−0.809574	+	0.318232i
$411$	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
$415$	−16.7182	−	13.3177i	−0.820662	−	0.653742i
$416$	32.6753	−	18.8651i	1.60204	−	0.924937i
$417$	23.4098	+	16.9491i	1.14638	+	0.829999i
$418$	−0.0983088	−	0.366894i	−0.00480844	−	0.0179454i
$419$	−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	$0.317422\pi$
$422$	−1.13390	−	4.23178i	−0.0551974	−	0.206000i
$423$	15.2673	−	9.98669i	0.742320	−	0.485570i
$424$	−7.97704	+	4.60555i	−0.387399	+	0.223665i
$425$	−22.8443	−	0.830428i	−1.10811	−	0.0402817i
$426$	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
$430$	10.5587	+	4.60003i	0.509186	+	0.221833i
$431$	1.70274	−	0.983080i	0.0820183	−	0.0473533i	−0.458430	−	0.888731i	$-0.651588\pi$
$431$	1.70274	−	0.983080i	0.0820183	−	0.0473533i	0.540448	+	0.841377i	$0.318255\pi$
$432$	−6.20677	+	5.64466i	−0.298623	+	0.271579i
$433$	18.7649	−	18.7649i	0.901782	−	0.901782i	−0.0938083	−	0.995590i	$-0.529904\pi$
$433$	18.7649	−	18.7649i	0.901782	−	0.901782i	0.995590	+	0.0938083i	$0.0299041\pi$
$434$		0			0
$435$	−3.80795	+	6.74533i	−0.182577	+	0.323414i
$436$	−7.25901	+	12.5730i	−0.347644	+	0.602137i
$437$	−8.31694	−	2.22852i	−0.397853	−	0.106604i
$438$	3.56918	+	2.58415i	0.170542	+	0.123475i
$439$	22.4711	+	12.9737i	1.07249	+	0.619202i	0.928860	−	0.370430i	$-0.120790\pi$
$439$	22.4711	+	12.9737i	1.07249	+	0.619202i	0.143629	+	0.989632i	$0.454123\pi$
$440$	−0.834089	−	0.125265i	−0.0397636	−	0.00597176i
$441$		0			0
$442$	−13.9266	−	13.9266i	−0.662423	−	0.662423i
$443$	−34.2230	+	9.17002i	−1.62598	+	0.435681i	−0.952752	−	0.303751i	$-0.901761\pi$
$443$	−34.2230	+	9.17002i	−1.62598	+	0.435681i	−0.673232	+	0.739431i	$0.735094\pi$
$444$	−0.853912	−	5.33423i	−0.0405249	−	0.253151i
$445$	9.70905	−	22.2857i	0.460253	−	1.05645i
$446$	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	$0.635038\pi$
$450$	6.80449	−	7.07284i	0.320767	−	0.333417i
$451$	−0.971506	−	1.68270i	−0.0457464	−	0.0792351i
$452$	10.4767	+	2.80723i	0.492784	+	0.132041i
$453$	−12.5339	−	1.29640i	−0.588895	−	0.0609100i
$454$			11.5748i			0.543231i
$455$		0			0
$456$	−13.6016	−	5.19533i	−0.636952	−	0.243294i
$457$	33.9737	−	9.10323i	1.58922	−	0.425831i	0.647458	−	0.762101i	$-0.275832\pi$
$457$	33.9737	−	9.10323i	1.58922	−	0.425831i	0.941766	+	0.336269i	$0.109165\pi$
$458$	0.393002	−	1.46671i	0.0183638	−	0.0685346i
$459$	19.9876	+	12.8395i	0.932943	+	0.599295i
$460$	−5.24254	+	6.58111i	−0.244435	+	0.306846i
$461$			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
$465$	−28.9000	+	0.279398i	−1.34021	+	0.0129568i
$466$	−2.80636	−	4.86075i	−0.130002	−	0.225170i
$467$	−2.82346	−	10.5373i	−0.130654	−	0.487608i	0.869324	−	0.494243i	$-0.164555\pi$
$467$	−2.82346	−	10.5373i	−0.130654	−	0.487608i	−0.999978	+	0.00663489i	$0.997888\pi$
$468$	−30.9995	+	1.72754i	−1.43295	+	0.0798556i
$469$		0			0
$470$	7.15582	−	5.28712i	0.330073	−	0.243877i
$471$	17.2868	+	21.2753i	0.796533	+	0.980314i
$472$	1.50417	−	5.61363i	0.0692349	−	0.258388i
$473$	−0.328830	+	1.22721i	−0.0151196	+	0.0564271i
$474$	−3.86596	−	4.75794i	−0.177570	−	0.218540i
$475$	−17.1909	−	5.28267i	−0.788774	−	0.242385i
$476$		0			0
$477$	11.8054	−	0.657893i	0.540532	−	0.0301228i
$478$	3.65224	+	13.6304i	0.167050	+	0.623438i
$479$	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	$0.705271\pi$
$480$	−15.5416	+	15.8450i	−0.709372	+	0.723222i
$481$	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
$485$	−24.0093	−	19.1259i	−1.09021	−	0.868463i
$486$	−9.82989	+	2.72130i	−0.445893	+	0.123441i
$487$	−5.18649	+	19.3562i	−0.235022	+	0.877115i	0.743117	+	0.669162i	$0.233347\pi$
$487$	−5.18649	+	19.3562i	−0.235022	+	0.877115i	−0.978139	+	0.207953i	$0.933320\pi$
$488$	−4.50304	+	1.20659i	−0.203843	+	0.0546196i
$489$	−23.3928	−	8.93527i	−1.05786	−	0.404067i
$490$		0			0
$491$			25.4502i			1.14855i	0.818661	+	0.574277i	$0.194717\pi$
$491$			25.4502i			1.14855i	−0.818661	+	0.574277i	$0.805283\pi$
$492$	−32.6027	−	3.37213i	−1.46984	−	0.152027i
$493$	−8.83220	−	2.36658i	−0.397782	−	0.106585i
$494$	−7.74746	−	13.4190i	−0.348575	−	0.603749i
$495$	0.883053	+	0.626423i	0.0396903	+	0.0281556i
$496$	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	0.765736	−	0.643155i	$-0.222375\pi$
$499$	13.2157	+	7.63009i	0.591616	+	0.341570i	−0.174120	+	0.984724i	$0.555708\pi$
$500$	−11.4421	+	13.3390i	−0.511708	+	0.596540i
$501$	−0.978437	−	6.11211i	−0.0437133	−	0.273069i
$502$	16.0274	−	4.29453i	0.715338	−	0.191674i
$503$	−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
$507$	−42.5768	−	30.8263i	−1.89090	−	1.36904i
$508$	−0.412372	−	0.110495i	−0.0182960	−	0.00490241i
$509$	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
$513$	12.5747	+	13.8270i	0.555189	+	0.610475i
$514$	−6.53402	+	3.77242i	−0.288203	+	0.166394i
$515$	−8.13020	−	20.6830i	−0.358259	−	0.911404i
$516$	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
$520$	−34.1887	+	3.87057i	−1.49928	+	0.169736i
$521$	−13.2100	+	7.62679i	−0.578740	+	0.334136i	−0.760632	−	0.649183i	$-0.775111\pi$
$521$	−13.2100	+	7.62679i	−0.578740	+	0.334136i	0.181893	+	0.983318i	$0.441778\pi$
$522$	3.28538	−	2.14905i	0.143797	−	0.0940614i
$523$	−4.81336	−	17.9637i	−0.210473	−	0.785497i	−0.987711	−	0.156290i	$-0.950046\pi$
$523$	−4.81336	−	17.9637i	−0.210473	−	0.785497i	0.777238	−	0.629207i	$-0.216620\pi$
$524$	21.6079			0.943947
$525$		0			0
$526$	12.8947			0.562235
$527$	−8.83007	−	32.9543i	−0.384644	−	1.43551i
$528$	−0.365590	−	0.264693i	−0.0159102	−	0.0115193i
$529$	−14.9558	+	8.63475i	−0.650253	+	0.375424i
$530$	5.72972	−	0.648672i	0.248883	−	0.0281765i
$531$	−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
$535$	−11.8533	−	30.1546i	−0.512465	−	1.30370i
$536$	5.29724	−	3.05836i	0.228806	−	0.132101i
$537$	34.6178	+	3.58055i	1.49387	+	0.154512i
$538$	−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	$0.153635\pi$
$542$	10.1677	+	2.72443i	0.436740	+	0.117024i
$543$	−16.9433	+	23.4018i	−0.727107	+	1.00427i
$544$	−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	$0.710449\pi$
$548$	12.0254	−	3.22219i	0.513699	−	0.137645i
$549$	5.85751	+	1.22480i	0.249993	+	0.0522731i
$550$	0.447379	+	0.280443i	0.0190763	+	0.0119581i
$551$	−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
$555$	−1.91711	+	7.44179i	−0.0813768	+	0.315887i
$556$	13.1144	+	22.7148i	0.556174	+	0.963322i
$557$	−8.90537	−	2.38619i	−0.377333	−	0.101106i	0.0651676	−	0.997874i	$-0.479242\pi$
$557$	−8.90537	−	2.38619i	−0.377333	−	0.101106i	−0.442500	+	0.896768i	$0.645908\pi$
$558$	13.0733	+	6.60675i	0.553437	+	0.279686i
$559$			51.8284i			2.19211i
$560$		0			0
$561$	−0.456037	+	1.19392i	−0.0192539	+	0.0504074i
$562$	7.96115	−	2.13318i	0.335821	−	0.0899829i
$563$	0.295060	−	1.10118i	0.0124353	−	0.0464091i	−0.959429	−	0.281949i	$-0.909019\pi$
$563$	0.295060	−	1.10118i	0.0124353	−	0.0464091i	0.971865	+	0.235540i	$0.0756858\pi$
$564$	16.3483	−	2.61706i	0.688387	−	0.110198i
$565$	−12.0682	−	9.61360i	−0.507715	−	0.404447i
$566$			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	$0.184021\pi$
$570$	6.50718	+	6.38256i	0.272556	+	0.267336i
$571$	−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	$0.851959\pi$
$572$	−0.432310	−	1.61340i	−0.0180758	−	0.0674597i
$573$	−34.1968	+	15.2933i	−1.42859	+	0.638886i
$574$		0			0
$575$	10.5762	−	5.60411i	0.441059	−	0.233708i
$576$	1.48323	−	0.487365i	0.0618012	−	0.0203069i
$577$	−4.62068	+	17.2446i	−0.192362	+	0.717903i	0.800573	+	0.599236i	$0.204529\pi$
$577$	−4.62068	+	17.2446i	−0.192362	+	0.717903i	−0.992934	+	0.118667i	$0.962138\pi$
$578$	−0.660812	+	2.46618i	−0.0274862	+	0.102580i
$579$	7.80445	−	6.34134i	0.324342	−	0.263537i
$580$	−5.65384	+	4.17737i	−0.234763	+	0.173456i
$581$		0			0
$582$	6.35131	+	14.2020i	0.263270	+	0.588691i
$583$	0.164635	+	0.614426i	0.00681848	+	0.0254469i
$584$	4.54356	+	7.86968i	0.188014	+	0.325650i
$585$	41.4094	+	15.3599i	1.71207	+	0.635055i
$586$	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
$590$	−2.26687	+	2.84567i	−0.0933256	+	0.117154i
$591$	3.53148	+	22.0605i	0.145266	+	0.907447i
$592$	0.829169	−	3.09450i	0.0340786	−	0.127183i
$593$	30.1219	−	8.07115i	1.23696	−	0.331442i	0.419674	−	0.907675i	$-0.362144\pi$
$593$	30.1219	−	8.07115i	1.23696	−	0.331442i	0.817286	+	0.576233i	$0.195478\pi$
$594$	−0.251541	−	0.487675i	−0.0103209	−	0.0200095i
$595$		0			0
$596$		−	24.5464i		−	1.00546i
$597$	−0.113672	+	1.09901i	−0.00465227	+	0.0449795i
$598$	9.96108	+	2.66906i	0.407339	+	0.109146i
$599$	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	$0.709731\pi$
$600$	18.7644	−	7.58625i	0.766054	−	0.309707i
$601$	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
$605$	9.80078	−	22.4963i	0.398458	−	0.914604i
$606$	5.19729	−	0.831991i	0.211125	−	0.0337973i
$607$	15.2070	−	4.07471i	0.617234	−	0.165387i	0.0633638	−	0.997990i	$-0.479817\pi$
$607$	15.2070	−	4.07471i	0.617234	−	0.165387i	0.553870	+	0.832603i	$0.313150\pi$
$608$	−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
$612$	11.8019	+	18.0423i	0.477063	+	0.729316i
$613$	−34.1840	−	9.15958i	−1.38068	−	0.369952i	−0.509312	−	0.860582i	$-0.670100\pi$
$613$	−34.1840	−	9.15958i	−1.38068	−	0.369952i	−0.871368	+	0.490630i	$0.836767\pi$
$614$	−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	−0.0122222	+	0.999925i	$0.503891\pi$
$617$	−25.1412	+	25.1412i	−1.01215	+	1.01215i	−0.999925	+	0.0122222i	$0.996109\pi$
$618$	−1.15881	+	11.2037i	−0.0466140	+	0.450677i
$619$	3.49101	−	2.01554i	0.140316	−	0.0810112i	−0.428199	−	0.903685i	$-0.640852\pi$
$619$	3.49101	−	2.01554i	0.140316	−	0.0810112i	0.568514	+	0.822673i	$0.307518\pi$
$620$	−24.0459	−	10.4759i	−0.965706	−	0.420722i
$621$	−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
$625$	22.5011	−	10.8950i	0.900043	−	0.435801i
$626$	9.93440	−	5.73563i	0.397058	−	0.229242i
$627$	−0.589663	+	0.814433i	−0.0235489	+	0.0325253i
$628$	6.43891	+	24.0303i	0.256941	+	0.958915i
$629$	−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	$0.329564\pi$
$632$	−3.27215	−	12.2118i	−0.130159	−	0.485760i
$633$	−6.80121	+	9.39373i	−0.270324	+	0.373367i
$634$	−2.34103	+	1.35159i	−0.0929740	+	0.0536786i
$635$	0.475015	+	0.378398i	0.0188504	+	0.0150163i
$636$	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
$640$	−23.1430	+	9.09718i	−0.914808	+	0.359598i
$641$	5.18974	−	2.99630i	0.204982	−	0.118347i	−0.393995	−	0.919113i	$-0.628907\pi$
$641$	5.18974	−	2.99630i	0.204982	−	0.118347i	0.598977	+	0.800766i	$0.295574\pi$
$642$	−1.68947	+	16.3343i	−0.0666780	+	0.644662i
$643$	−0.533933	+	0.533933i	−0.0210562	+	0.0210562i	−0.717557	−	0.696500i	$-0.754739\pi$
$643$	−0.533933	+	0.533933i	−0.0210562	+	0.0210562i	0.696500	+	0.717557i	$0.254739\pi$
$644$		0			0
$645$	−8.17518	−	29.3714i	−0.321897	−	1.15650i
$646$	−5.37984	+	9.31815i	−0.211667	+	0.366618i
$647$	−33.9314	−	9.09189i	−1.33398	−	0.357439i	−0.479783	−	0.877387i	$-0.659285\pi$
$647$	−33.9314	−	9.09189i	−1.33398	−	0.357439i	−0.854198	+	0.519948i	$0.825951\pi$
$648$	−20.7963	−	3.15280i	−0.816956	−	0.123854i
$649$	−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
$653$	0.336028	−	0.0900386i	0.0131498	−	0.00352348i	−0.252238	−	0.967665i	$-0.581167\pi$
$653$	0.336028	−	0.0900386i	0.0131498	−	0.00352348i	0.265388	+	0.964142i	$0.414500\pi$
$654$	−10.3356	+	1.65453i	−0.404152	+	0.0646974i
$655$	−28.1800	−	12.2769i	−1.10108	−	0.479700i
$656$	−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	$0.406014\pi$
$660$	0.499483	+	0.846132i	0.0194423	+	0.0329356i
$661$	−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	$-0.479857\pi$
$662$	11.0543	+	2.96199i	0.429637	+	0.115121i
$663$	−5.36391	+	51.8598i	−0.208317	+	2.01407i
$664$			22.3400i			0.866962i
$665$		0			0
$666$	2.59654	−	2.90302i	0.100614	−	0.112490i
$667$	4.62456	−	1.23915i	0.179064	−	0.0479800i
$668$	1.45392	−	5.42612i	0.0562540	−	0.209943i
$669$	−0.147934	−	0.924117i	−0.00571947	−	0.0357284i
$670$	−3.80488	+	0.430758i	−0.146995	+	0.0166416i
$671$			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
$675$	−25.8897	−	2.17282i	−0.996497	−	0.0836317i
$676$	−23.8519	−	41.3128i	−0.917382	−	1.58895i
$677$	0.452066	+	1.68713i	0.0173743	+	0.0648418i	0.974069	−	0.226252i	$-0.0726474\pi$
$677$	0.452066	+	1.68713i	0.0173743	+	0.0648418i	−0.956694	+	0.291094i	$0.905981\pi$
$678$	3.19247	+	7.13859i	0.122606	+	0.274156i
$679$		0			0
$680$	14.1980	+	19.2162i	0.544467	+	0.736906i
$681$	23.7800	−	19.3219i	0.911252	−	0.740418i
$682$	−0.203959	+	0.761184i	−0.00780998	+	0.0291472i
$683$	−9.23896	+	34.4803i	−0.353519	+	1.31935i	0.528819	+	0.848735i	$0.322635\pi$
$683$	−9.23896	+	34.4803i	−0.353519	+	1.31935i	−0.882338	+	0.470616i	$0.844032\pi$
$684$	5.29478	+	16.1139i	0.202451	+	0.616132i
$685$	−17.5136	−	2.63022i	−0.669162	−	0.100496i
$686$		0			0
$687$	−3.66934	+	1.64098i	−0.139994	+	0.0626073i
$688$	3.28958	+	12.2769i	0.125414	+	0.468051i
$689$	12.9744	+	22.4724i	0.494287	+	0.856130i
$690$	−6.06600	+	0.0586447i	−0.230929	+	0.00223256i
$691$	−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
$695$	−4.19729	−	37.0747i	−0.159212	−	1.40632i
$696$	7.99418	−	1.27972i	0.303019	−	0.0485078i
$697$	−14.2454	+	53.1645i	−0.539583	+	2.01375i
$698$	17.7826	−	4.76484i	0.673082	−	0.180352i
$699$	−5.30157	+	13.8797i	−0.200524	+	0.524978i
$700$		0			0
$701$			44.4108i			1.67737i	0.544614	+	0.838687i	$0.316676\pi$
$701$			44.4108i			1.67737i	−0.544614	+	0.838687i	$0.683324\pi$
$702$	−15.0606	−	16.5604i	−0.568426	−	0.625031i
$703$	−6.89369	−	1.84716i	−0.260001	−	0.0696669i
$704$	0.0419965	+	0.0727400i	0.00158280	+	0.00274149i
$705$	−22.8075	−	5.87554i	−0.858981	−	0.221286i
$706$	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	0.766168	−	0.642640i	$-0.222161\pi$
$709$	15.7821	+	9.11180i	0.592709	+	0.342201i	−0.173459	+	0.984841i	$0.555494\pi$
$710$	−12.7961	+	5.02994i	−0.480228	+	0.188770i
$711$	−3.32153	+	15.8850i	−0.124567	+	0.595734i
$712$	−24.5415	+	6.57587i	−0.919731	+	0.246441i
$713$	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
$717$	21.9064	−	30.2568i	0.818109	−	1.12996i
$718$	8.51158	+	2.28067i	0.317649	+	0.0851139i
$719$	−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
$723$	−11.1823	−	1.15660i	−0.415874	−	0.0430143i
$724$	−22.7071	+	13.1099i	−0.843902	+	0.487227i
$725$	9.74691	−	2.23558i	0.361991	−	0.0830275i
$726$	−9.65214	+	7.84264i	−0.358225	+	0.291068i
$727$	−1.34757	−	1.34757i	−0.0499787	−	0.0499787i	0.681676	−	0.731654i	$-0.261252\pi$
$727$	−1.34757	−	1.34757i	−0.0499787	−	0.0499787i	−0.731654	+	0.681676i	$0.761252\pi$
$728$		0			0
$729$	22.0000	+	15.6525i	0.814815	+	0.579721i
$730$	−0.639942	−	5.65261i	−0.0236853	−	0.209212i
$731$	31.1679	−	17.9948i	1.15279	−	0.665562i
$732$	4.39891	+	3.18488i	0.162588	+	0.117717i
$733$	−4.94744	−	18.4641i	−0.182738	−	0.681987i	−0.995104	−	0.0988384i	$-0.968487\pi$
$733$	−4.94744	−	18.4641i	−0.182738	−	0.681987i	0.812366	−	0.583148i	$-0.198179\pi$
$734$	−2.57990			−0.0952258
$735$		0			0
$736$	13.7183			0.505663
$737$	−0.109327	−	0.408016i	−0.00402713	−	0.0150295i
$738$	−12.9360	−	19.7760i	−0.476180	−	0.727966i
$739$	1.11818	−	0.645584i	0.0411331	−	0.0237482i	−0.479292	−	0.877655i	$-0.659107\pi$
$739$	1.11818	−	0.645584i	0.0411331	−	0.0237482i	0.520426	+	0.853907i	$0.325773\pi$
$740$	−4.34540	+	5.45491i	−0.159740	+	0.200527i
$741$	−14.6360	+	38.3174i	−0.537665	+	1.40763i
$742$		0			0
$743$	11.5021	+	11.5021i	0.421972	+	0.421972i	0.885882	−	0.463910i	$-0.153554\pi$
$743$	11.5021	+	11.5021i	0.421972	+	0.421972i	−0.463910	+	0.885882i	$0.653554\pi$
$744$	19.0489	+	23.4439i	0.698366	+	0.859497i
$745$	−13.9465	+	32.0122i	−0.510960	+	1.17283i
$746$	3.39460	−	1.95988i	0.124285	−	0.0717562i
$747$	12.9342	−	25.5940i	0.473239	−	0.936435i
$748$	−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	$-0.121689\pi$
$752$	9.48399	+	2.54123i	0.345845	+	0.0926690i
$753$	−35.5778	−	25.7589i	−1.29653	−	0.938706i
$754$	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	$0.937386\pi$
$758$	−15.8950	+	4.25904i	−0.577331	+	0.154695i
$759$	−0.105778	−	0.660777i	−0.00383951	−	0.0239847i
$760$	6.87659	+	17.4939i	0.249440	+	0.634570i
$761$	−23.7452	−	13.7093i	−0.860763	−	0.496962i	0.00350451	−	0.999994i	$-0.498884\pi$
$761$	−23.7452	−	13.7093i	−0.860763	−	0.496962i	−0.864268	+	0.503032i	$0.832218\pi$
$762$	−0.125658	−	0.280980i	−0.00455211	−	0.0101788i
$763$		0			0
$764$	−33.9966			−1.22996
$765$	−5.14038	−	30.2353i	−0.185851	−	1.09316i
$766$	2.03607	+	3.52657i	0.0735661	+	0.127420i
$767$	−15.8143	−	4.23744i	−0.571023	−	0.153005i
$768$	14.3294	+	1.48210i	0.517068	+	0.0534808i
$769$			17.1148i			0.617174i	0.951196	+	0.308587i	$0.0998561\pi$
$769$			17.1148i			0.617174i	−0.951196	+	0.308587i	$0.900144\pi$
$770$		0			0
$771$	18.6576	+	7.12658i	0.671938	+	0.256658i
$772$	8.81509	−	2.36200i	0.317262	−	0.0850101i
$773$	−10.7760	+	40.2165i	−0.387585	+	1.44649i	0.446466	+	0.894800i	$0.352682\pi$
$773$	−10.7760	+	40.2165i	−0.387585	+	1.44649i	−0.834051	+	0.551687i	$0.813984\pi$
$774$	−3.16259	+	15.1249i	−0.113677	+	0.543652i
$775$	25.4074	+	27.3242i	0.912659	+	0.981515i
$776$			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
$780$	28.6151	+	28.0671i	1.02458	+	1.00496i
$781$	−0.758356	−	1.31351i	−0.0271361	−	0.0470011i
$782$	−1.85340	−	6.91698i	−0.0662774	−	0.247351i
$783$	−9.89949	−	3.16228i	−0.353779	−	0.113011i
$784$		0			0
$785$	5.25598	−	34.9975i	0.187594	−	1.24912i
$786$	9.82408	+	12.0908i	0.350413	+	0.431263i
$787$	3.56220	−	13.2943i	0.126979	−	0.473892i	−0.872924	−	0.487857i	$-0.837779\pi$
$787$	3.56220	−	13.2943i	0.126979	−	0.473892i	0.999902	+	0.0139653i	$0.00444543\pi$
$788$	−5.24766	+	19.5845i	−0.186940	+	0.697670i
$789$	−21.5253	−	26.4917i	−0.766320	−	0.943130i
$790$	−1.17543	+	7.82674i	−0.0418200	+	0.278463i
$791$		0			0
$792$	−0.0629640	−	1.12984i	−0.00223733	−	0.0401473i
$793$	3.39912	+	12.6857i	0.120706	+	0.450482i
$794$	−6.94229	−	12.0244i	−0.246372	−	0.426730i
$795$	−10.8974	−	10.6887i	−0.386490	−	0.379089i
$796$	−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
$800$	28.6343	+	1.04090i	1.01238	+	0.0368014i
$801$	31.9233	+	6.67513i	1.12795	+	0.235854i
$802$	−0.617145	+	2.30322i	−0.0217921	+	0.0813294i
$803$	0.606157	−	0.162419i	0.0213908	−	0.00573165i
$804$	−6.65654	−	2.54257i	−0.234758	−	0.0896697i
$805$		0			0
$806$			32.1469i			1.13233i
$807$	5.82043	+	0.602013i	0.204889	+	0.0211919i
$808$	10.4846	+	2.80934i	0.368847	+	0.0988322i
$809$	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	$0.711635\pi$
$810$	11.1471	+	7.00925i	0.391668	+	0.246280i
$811$	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
$815$	11.8268	+	30.0871i	0.414275	+	1.05390i
$816$	2.02099	+	12.6248i	0.0707489	+	0.441955i
$817$	27.3495	−	7.32827i	0.956837	−	0.256384i
$818$	−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	0.552411	−	0.833572i	$-0.313708\pi$
$821$	3.05795	+	1.76551i	0.106723	+	0.0616166i	−0.445688	+	0.895188i	$0.647041\pi$
$822$	7.27034	+	5.26385i	0.253582	+	0.183598i
$823$	17.6720	+	4.73521i	0.616008	+	0.165059i	0.553312	−	0.832974i	$-0.313364\pi$
$823$	17.6720	+	4.73521i	0.616008	+	0.165059i	0.0626958	+	0.998033i	$0.480030\pi$
$824$	−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	0.00505903	−	0.999987i	$-0.498390\pi$
$827$	28.9027	−	28.9027i	1.00505	−	1.00505i	0.999987	−	0.00505903i	$-0.00161035\pi$
$828$	−10.0751	−	5.09157i	−0.350133	−	0.176944i
$829$	15.1933	−	8.77184i	0.527684	−	0.304659i	−0.212389	−	0.977185i	$-0.568124\pi$
$829$	15.1933	−	8.77184i	0.527684	−	0.304659i	0.740073	+	0.672527i	$0.234791\pi$
$830$	5.58579	−	12.8214i	0.193886	−	0.445036i
$831$	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
$835$	−4.97908	+	6.25039i	−0.172308	+	0.216304i
$836$	−0.790254	+	0.456253i	−0.0273315	+	0.0157799i
$837$	−8.25007	−	37.8874i	−0.285164	−	1.30958i
$838$	−4.72574	−	17.6367i	−0.163248	−	0.609250i
$839$	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
$842$	3.77108	+	14.0739i	0.129960	+	0.485017i
$843$	−17.6722	−	12.7950i	−0.608664	−	0.440682i
$844$	−9.11485	+	5.26246i	−0.313746	+	0.181141i
$845$	7.63387	+	67.4299i	0.262613	+	2.31966i
$846$	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
$850$	−3.34377	−	14.5785i	−0.114691	−	0.500038i
$851$	4.11351	−	2.37493i	0.141009	−	0.0814117i
$852$	−25.4496	−	2.63228i	−0.871889	−	0.0901803i
$853$	−5.62301	+	5.62301i	−0.192528	+	0.192528i	−0.796788	−	0.604259i	$-0.793469\pi$
$853$	−5.62301	+	5.62301i	−0.192528	+	0.192528i	0.604259	+	0.796788i	$0.293469\pi$
$854$		0			0
$855$	2.25025	−	24.0233i	0.0769569	−	0.821579i
$856$	−16.9323	+	29.3277i	−0.578735	+	1.00240i
$857$	−20.8918	−	5.59795i	−0.713651	−	0.191222i	−0.116314	−	0.993212i	$-0.537108\pi$
$857$	−20.8918	−	5.59795i	−0.713651	−	0.191222i	−0.597337	+	0.801990i	$0.703775\pi$
$858$	0.706231	−	0.975435i	0.0241103	−	0.0333008i
$859$	39.2936	+	22.6862i	1.34068	+	0.774042i	0.986907	−	0.161290i	$-0.0515655\pi$
$859$	39.2936	+	22.6862i	1.34068	+	0.774042i	0.353772	+	0.935332i	$0.384899\pi$
$860$	4.10924	−	27.3618i	0.140124	−	0.933029i
$861$		0			0
$862$	0.909671	+	0.909671i	0.0309835	+	0.0309835i
$863$	−8.22674	+	2.20435i	−0.280041	+	0.0750369i	−0.396106	−	0.918205i	$-0.629639\pi$
$863$	−8.22674	+	2.20435i	−0.280041	+	0.0750369i	0.116065	+	0.993242i	$0.462972\pi$
$864$	−25.0536	−	16.0937i	−0.852340	−	0.547517i
$865$	4.24213	−	1.66752i	0.144237	−	0.0566973i
$866$	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
$870$	−4.90799	−	1.26437i	−0.166396	−	0.0428660i
$871$	−8.61581	−	14.9230i	−0.291936	−	0.505647i
$872$	−20.8501	−	5.58678i	−0.706075	−	0.189192i
$873$	18.5752	−	36.7561i	0.628674	−	1.24401i
$874$		−	5.63379i		−	0.190566i
$875$		0			0
$876$	3.77730	−	9.88910i	0.127623	−	0.334122i
$877$	−23.5588	+	6.31256i	−0.795525	+	0.213160i	−0.633618	−	0.773646i	$-0.718431\pi$
$877$	−23.5588	+	6.31256i	−0.795525	+	0.213160i	−0.161906	+	0.986806i	$0.551764\pi$
$878$	−4.39411	+	16.3991i	−0.148294	+	0.553441i
$879$	−4.99192	+	0.799115i	−0.168373	+	0.0269535i
$880$	0.0655490	+	0.578994i	0.00220965	+	0.0195179i
$881$			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
$885$	9.63046	−	0.0931050i	0.323724	−	0.00312969i
$886$	−11.5911	−	20.0764i	−0.389411	−	0.674479i
$887$	−2.54169	−	9.48573i	−0.0853417	−	0.318500i	0.910037	−	0.414527i	$-0.136053\pi$
$887$	−2.54169	−	9.48573i	−0.0853417	−	0.318500i	−0.995379	+	0.0960275i	$0.969386\pi$
$888$	7.33218	−	3.27905i	0.246052	−	0.110038i
$889$		0			0
$890$	15.7290	+	2.36221i	0.527238	+	0.0791814i
$891$	−0.582011	+	1.33087i	−0.0194981	+	0.0445857i
$892$	0.219825	−	0.820399i	0.00736029	−	0.0274690i
$893$	5.66115	−	21.1277i	0.189443	−	0.707012i
$894$	13.7350	−	11.1601i	0.459366	−	0.373248i
$895$	−26.6994	−	36.1362i	−0.892464	−	1.20790i
$896$		0			0
$897$	−11.1447	−	24.9202i	−0.372110	−	0.832062i
$898$	−2.95413	−	11.0250i	−0.0985805	−	0.367908i
$899$	7.46230	+	12.9251i	0.248882	+	0.431076i
$900$	−20.6435	−	11.3921i	−0.688116	−	0.379738i
$901$	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
$905$	37.0621	−	4.19587i	1.23199	−	0.139475i
$906$	−1.30324	−	8.14111i	−0.0432974	−	0.270470i
$907$	3.17404	−	11.8457i	0.105392	−	0.393329i	−0.892997	−	0.450062i	$-0.851402\pi$
$907$	3.17404	−	11.8457i	0.105392	−	0.393329i	0.998389	+	0.0567332i	$0.0180685\pi$
$908$	26.8594	−	7.19695i	0.891360	−	0.238839i
$909$	−10.3852	−	9.28881i	−0.344456	−	0.308090i
$910$		0			0
$911$		−	27.0102i		−	0.894889i	−0.894312	−	0.447444i	$-0.852334\pi$
$911$		−	27.0102i		−	0.894889i	0.894312	−	0.447444i	$-0.147666\pi$
$912$	−1.03487	+	10.0054i	−0.0342679	+	0.331312i
$913$	1.49019	+	0.399296i	0.0493182	+	0.0132148i
$914$	11.5067	+	19.9302i	0.380607	+	0.659231i
$915$	−3.92728	−	6.65288i	−0.129832	−	0.219937i
$916$	−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	0.311484	−	0.950252i	$-0.399174\pi$
$919$	−10.7836	−	6.22589i	−0.355717	−	0.205373i	−0.667200	+	0.744878i	$0.732507\pi$
$920$	−11.4689	−	4.99657i	−0.378119	−	0.164732i
$921$	1.55017	−	0.248153i	0.0510797	−	0.00817693i
$922$	−4.75647	+	1.27449i	−0.156646	+	0.0419731i
$923$	−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
$927$	24.9520	−	16.3217i	0.819530	−	0.536075i
$928$	11.0708	+	2.96640i	0.363415	+	0.0973768i
$929$	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
$933$	−3.71479	+	35.9157i	−0.121617	+	1.17583i
$934$	6.18154	−	3.56892i	0.202266	−	0.116778i
$935$	1.53558	−	0.603614i	0.0502189	−	0.0197403i
$936$	−14.4101	−	43.8552i	−0.471009	−	1.43345i
$937$	17.8137	+	17.8137i	0.581947	+	0.581947i	0.935438	−	0.353491i	$-0.115006\pi$
$937$	17.8137	+	17.8137i	0.581947	+	0.581947i	−0.353491	+	0.935438i	$0.615006\pi$
$938$		0			0
$939$	−28.3673	−	10.8353i	−0.925732	−	0.353598i
$940$	−16.7182	−	13.3177i	−0.545286	−	0.434377i
$941$	−44.3404	+	25.5999i	−1.44546	+	0.834534i	−0.998206	−	0.0598755i	$-0.980930\pi$
$941$	−44.3404	+	25.5999i	−1.44546	+	0.834534i	−0.447249	+	0.894409i	$0.647596\pi$
$942$	−10.5188	+	14.5283i	−0.342720	+	0.473359i
$943$	−7.45891	−	27.8370i	−0.242896	−	0.906499i
$944$	−4.01498			−0.130677
$945$		0			0
$946$	−0.831296			−0.0270277
$947$	−10.1204	−	37.7699i	−0.328870	−	1.22736i	−0.910364	−	0.413808i	$-0.864199\pi$
$947$	−10.1204	−	37.7699i	−0.328870	−	1.22736i	0.581495	−	0.813550i	$-0.302468\pi$
$948$	−8.63708	+	11.9294i	−0.280519	+	0.387449i
$949$	22.1700	−	12.7998i	0.719667	−	0.415500i
$950$	0.427475	−	11.7595i	0.0138691	−	0.381527i
$951$	6.68471	+	2.55333i	0.216767	+	0.0827975i
$952$		0			0
$953$	6.39589	+	6.39589i	0.207183	+	0.207183i	0.803069	−	0.595886i	$-0.203199\pi$
$953$	6.39589	+	6.39589i	0.207183	+	0.207183i	−0.595886	+	0.803069i	$0.703199\pi$
$954$	2.41500	+	7.34973i	0.0781886	+	0.237956i
$955$	44.3367	+	19.3158i	1.43470	+	0.625045i
$956$	29.3585	−	16.9501i	0.949522	−	0.548207i
$957$	0.0575205	−	0.556125i	0.00185937	−	0.0179770i
$958$	−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
$962$	8.25648	+	2.21232i	0.266200	+	0.0713280i
$963$	36.3785	−	23.7961i	1.17228	−	0.766817i
$964$	−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	$0.562688\pi$
$968$	−24.7734	+	6.63800i	−0.796246	+	0.213353i
$969$	28.1245	−	4.50221i	0.903488	−	0.144632i
$970$	8.02188	−	18.4131i	0.257567	−	0.591208i
$971$	−27.2512	−	15.7335i	−0.874534	−	0.504912i	−0.00568176	−	0.999984i	$-0.501809\pi$
$971$	−27.2512	−	15.7335i	−0.874534	−	0.504912i	−0.868852	+	0.495071i	$0.835142\pi$
$972$	12.4268	+	21.1183i	0.398591	+	0.677370i
$973$		0			0
$974$	−13.1117			−0.420125
$975$	−21.3715	−	52.8619i	−0.684435	−	1.69293i
$976$	1.61033	+	2.78918i	0.0515456	+	0.0892795i
$977$	22.0308	+	5.90313i	0.704827	+	0.188858i	0.593392	−	0.804914i	$-0.297789\pi$
$977$	22.0308	+	5.90313i	0.704827	+	0.188858i	0.111435	+	0.993772i	$0.464455\pi$
$978$	1.68568	−	16.2977i	0.0539022	−	0.521142i
$979$			1.75457i			0.0560764i
$980$		0			0
$981$	20.6525	+	18.4721i	0.659383	+	0.589770i
$982$	−16.0848	+	4.30992i	−0.513288	+	0.137535i
$983$	15.0566	−	56.1919i	0.480230	−	1.79224i	−0.120411	−	0.992724i	$-0.538421\pi$
$983$	15.0566	−	56.1919i	0.480230	−	1.79224i	0.600641	−	0.799519i	$-0.294912\pi$
$984$	−7.70316	−	48.1201i	−0.245568	−	1.53401i
$985$	17.9710	−	22.5596i	0.572605	−	0.718809i
$986$		−	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
$990$	−0.246364	+	0.664182i	−0.00782996	+	0.0211091i
$991$	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	$0.501739\pi$
$992$	11.0681	+	41.3066i	0.351412	+	1.31149i
$993$	−12.3678	−	27.6552i	−0.392479	−	0.877610i
$994$		0			0
$995$	1.14721	−	0.847626i	0.0363691	−	0.0268716i
$996$	20.1979	−	16.4114i	0.639996	−	0.520015i
$997$	−2.25551	+	8.41769i	−0.0714329	+	0.266591i	−0.992401	−	0.123047i	$-0.960733\pi$
$997$	−2.25551	+	8.41769i	−0.0714329	+	0.266591i	0.920968	+	0.389638i	$0.127400\pi$
$998$	−2.58426	+	9.64459i	−0.0818033	+	0.305294i
$999$	−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.e.422.6		32
3.2	odd	2		735.2.y.f.422.4		32
5.3	odd	4		735.2.y.f.128.6		32
7.2	even	3		735.2.j.d.197.6	yes	16
7.3	odd	6	inner	735.2.y.e.557.4		32
7.4	even	3	inner	735.2.y.e.557.3		32
7.5	odd	6		735.2.j.d.197.5	yes	16
7.6	odd	2	inner	735.2.y.e.422.5		32
15.8	even	4	inner	735.2.y.e.128.3		32
21.2	odd	6		735.2.j.c.197.3	✓	16
21.5	even	6		735.2.j.c.197.4	yes	16
21.11	odd	6		735.2.y.f.557.6		32
21.17	even	6		735.2.y.f.557.5		32
21.20	even	2		735.2.y.f.422.3		32
35.3	even	12		735.2.y.f.263.3		32
35.13	even	4		735.2.y.f.128.5		32
35.18	odd	12		735.2.y.f.263.4		32
35.23	odd	12		735.2.j.c.638.3	yes	16
35.33	even	12		735.2.j.c.638.4	yes	16
105.23	even	12		735.2.j.d.638.6	yes	16
105.38	odd	12	inner	735.2.y.e.263.5		32
105.53	even	12	inner	735.2.y.e.263.6		32
105.68	odd	12		735.2.j.d.638.5	yes	16
105.83	odd	4	inner	735.2.y.e.128.4		32

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

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+(0.169347 + 0.632011i) q^{2} +(1.01575 - 1.40294i) q^{3} +(1.36129 - 0.785942i) q^{4} +(-2.22187 + 0.251543i) q^{5} +(1.05869 + 0.404383i) q^{6} +(1.65258 + 1.65258i) q^{8} +(-0.936492 - 2.85008i) q^{9} +(-0.535245 - 1.36165i) q^{10} +(0.139773 - 0.0806980i) q^{11} +(0.280105 - 2.70814i) q^{12} +(4.65555 - 4.65555i) q^{13} +(-1.90398 + 3.37267i) q^{15} +(0.807294 - 1.39827i) q^{16} +(-4.41610 - 1.18329i) q^{17} +(1.64269 - 1.07453i) q^{18} +(-3.11497 - 1.79843i) q^{19} +(-2.82692 + 2.08869i) q^{20} +(0.0746721 + 0.0746721i) q^{22} +(2.31228 - 0.619573i) q^{23} +(3.99709 - 0.639861i) q^{24} +(4.87345 - 1.11779i) q^{25} +(3.73076 + 2.15395i) q^{26} +(-4.94975 - 1.58114i) q^{27} +2.00000 q^{29} +(-2.45399 - 0.632183i) q^{30} +(3.73115 + 6.46254i) q^{31} +(5.53538 + 1.48320i) q^{32} +(0.0287603 - 0.278063i) q^{33} -2.99141i q^{34} +(-3.51484 - 3.14377i) q^{36} +(1.91659 - 0.513548i) q^{37} +(0.609116 - 2.27325i) q^{38} +(-1.80258 - 11.2603i) q^{39} +(-4.08752 - 3.25614i) q^{40} -12.0388i q^{41} +(-5.56631 + 5.56631i) q^{43} +(0.126848 - 0.219707i) q^{44} +(2.79768 + 6.09696i) q^{45} +(0.783154 + 1.35646i) q^{46} +(1.57392 + 5.87394i) q^{47} +(-1.14169 - 2.55289i) q^{48} +(1.53176 + 2.89078i) q^{50} +(-6.14576 + 4.99360i) q^{51} +(2.67857 - 9.99654i) q^{52} +(-1.02007 + 3.80695i) q^{53} +(0.161073 - 3.39605i) q^{54} +(-0.290259 + 0.214460i) q^{55} +(-5.68713 + 2.54336i) q^{57} +(0.338694 + 1.26402i) q^{58} +(-1.24335 - 2.15354i) q^{59} +(0.0588534 + 6.08760i) q^{60} +(-0.997366 + 1.72749i) q^{61} +(-3.45254 + 3.45254i) q^{62} +0.520416i q^{64} +(-9.17297 + 11.5151i) q^{65} +(0.180609 - 0.0289122i) q^{66} +(0.677387 - 2.52804i) q^{67} +(-6.94160 + 1.86000i) q^{68} +(1.47948 - 3.87333i) q^{69} -9.39746i q^{71} +(3.16237 - 6.25763i) q^{72} +(3.75571 + 1.00634i) q^{73} +(0.649136 + 1.12434i) q^{74} +(3.38203 - 7.97257i) q^{75} -5.65384 q^{76} +(6.81140 - 3.04615i) q^{78} +(-4.68478 - 2.70476i) q^{79} +(-1.44198 + 3.30986i) q^{80} +(-7.24597 + 5.33816i) q^{81} +(7.60864 - 2.03873i) q^{82} +(6.75913 + 6.75913i) q^{83} +(10.1097 + 1.51829i) q^{85} +(-4.46060 - 2.57533i) q^{86} +(2.03151 - 2.80588i) q^{87} +(0.364346 + 0.0976263i) q^{88} +(-5.43562 + 9.41477i) q^{89} +(-3.37957 + 2.80067i) q^{90} +(2.66074 - 2.66074i) q^{92} +(12.8565 + 1.32976i) q^{93} +(-3.44585 + 1.98946i) q^{94} +(7.37345 + 3.21233i) q^{95} +(7.70342 - 6.25925i) q^{96} +(9.70695 + 9.70695i) q^{97} +(-0.360892 - 0.322792i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{2} - 56 q^{8} + 32 q^{9} + 8 q^{15} + 48 q^{16} + 28 q^{18} + 16 q^{22} + 16 q^{23} - 8 q^{25} + 64 q^{29} - 64 q^{30} + 52 q^{32} - 80 q^{36} + 24 q^{37} - 8 q^{39} + 48 q^{43} - 8 q^{44} - 88 q^{46}+ \cdots - 80 q^{99}+O(q^{100}) \) 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

Modular forms

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