LMFDB - Embedded newform 513.2.g.c.505.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [513,2,Mod(64,513)] 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("513.64"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(513, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 513 = 3^{3} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	513.g (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [32,-1,0,-17,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$4.09632562369$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 171)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			505.5
Character	$\chi$	$=$	513.505
Dual form			513.2.g.c.64.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.847114 - 1.46725i) q^{2} +(-0.435206 + 0.753799i) q^{4} -0.0882176 q^{5} +(1.84695 - 3.19901i) q^{7} -1.91378 q^{8} +(0.0747304 + 0.129437i) q^{10} +(1.97689 - 3.42408i) q^{11} +(-2.03012 + 3.51627i) q^{13} -6.25832 q^{14} +(2.49160 + 4.31558i) q^{16} +(0.586674 - 1.01615i) q^{17} +(3.26283 - 2.89032i) q^{19} +(0.0383928 - 0.0664983i) q^{20} -6.69862 q^{22} +(1.91604 - 3.31868i) q^{23} -4.99222 q^{25} +6.87897 q^{26} +(1.60761 + 2.78446i) q^{28} -6.56701 q^{29} +(-4.14650 - 7.18194i) q^{31} +(2.30757 - 3.99682i) q^{32} -1.98792 q^{34} +(-0.162934 + 0.282209i) q^{35} -6.88356 q^{37} +(-7.00480 - 2.33893i) q^{38} +0.168829 q^{40} +4.66112 q^{41} +(4.12481 + 7.14438i) q^{43} +(1.72071 + 2.98036i) q^{44} -6.49243 q^{46} -4.43759 q^{47} +(-3.32246 - 5.75467i) q^{49} +(4.22898 + 7.32481i) q^{50} +(-1.76704 - 3.06060i) q^{52} +(3.62409 + 6.27711i) q^{53} +(-0.174397 + 0.302064i) q^{55} +(-3.53466 + 6.12221i) q^{56} +(5.56301 + 9.63542i) q^{58} -1.01191 q^{59} +3.22038 q^{61} +(-7.02511 + 12.1679i) q^{62} +2.14732 q^{64} +(0.179092 - 0.310197i) q^{65} +(1.45149 - 2.51405i) q^{67} +(0.510648 + 0.884469i) q^{68} +0.552094 q^{70} +(4.36630 - 7.56265i) q^{71} +(3.43748 - 5.95390i) q^{73} +(5.83116 + 10.0999i) q^{74} +(0.758720 + 3.71740i) q^{76} +(-7.30245 - 12.6482i) q^{77} +(2.65505 + 4.59868i) q^{79} +(-0.219803 - 0.380711i) q^{80} +(-3.94850 - 6.83901i) q^{82} +(-3.34887 + 5.80042i) q^{83} +(-0.0517550 + 0.0896423i) q^{85} +(6.98837 - 12.1042i) q^{86} +(-3.78334 + 6.55294i) q^{88} +(-4.41568 - 7.64818i) q^{89} +(7.49906 + 12.9888i) q^{91} +(1.66775 + 2.88862i) q^{92} +(3.75915 + 6.51104i) q^{94} +(-0.287839 + 0.254977i) q^{95} +(-0.894933 - 1.55007i) q^{97} +(-5.62901 + 9.74973i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - q^{2} - 17 q^{4} + 6 q^{5} + q^{7} + 36 q^{8} - 8 q^{10} - 7 q^{11} - 4 q^{13} + 2 q^{14} - 11 q^{16} + 7 q^{17} + 7 q^{19} + 3 q^{20} + 16 q^{22} - 5 q^{23} + 18 q^{25} + 4 q^{26} - 10 q^{28}+ \cdots - 18 q^{98}+O(q^{100}) $ 32 * q - q^2 - 17 * q^4 + 6 * q^5 + q^7 + 36 * q^8 - 8 * q^10 - 7 * q^11 - 4 * q^13 + 2 * q^14 - 11 * q^16 + 7 * q^17 + 7 * q^19 + 3 * q^20 + 16 * q^22 - 5 * q^23 + 18 * q^25 + 4 * q^26 - 10 * q^28 + 20 * q^29 - 10 * q^31 - 17 * q^32 + 26 * q^34 + 3 * q^35 + 2 * q^37 - 38 * q^38 - 24 * q^40 + 12 * q^41 + 7 * q^43 - 20 * q^44 - 18 * q^47 - 13 * q^49 - q^50 + 19 * q^52 - 16 * q^53 + 15 * q^55 + 6 * q^56 + 74 * q^59 + 24 * q^61 - 54 * q^62 - 64 * q^64 - 54 * q^65 - 11 * q^67 + 2 * q^68 - 48 * q^70 - 9 * q^71 - 10 * q^73 - 6 * q^74 + 29 * q^76 - 46 * q^77 - 8 * q^79 + 24 * q^80 + 7 * q^82 - 3 * q^83 - 27 * q^85 - 17 * q^86 + 9 * q^88 - 30 * q^89 - q^91 + 17 * q^92 - 18 * q^94 + 6 * q^95 - 18 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/513\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.847114	−	1.46725i	−0.599000	−	1.03750i	−0.992969	−	0.118375i	$-0.962231\pi$
$2$	−0.847114	−	1.46725i	−0.599000	−	1.03750i	0.393969	−	0.919124i	$-0.371102\pi$
$3$		0			0
$3$		0			0
$4$	−0.435206	+	0.753799i	−0.217603	+	0.376899i
$5$	−0.0882176			−0.0394521			−0.0197261	−	0.999805i	$-0.506279\pi$
$5$	−0.0882176			−0.0394521			−0.0197261	+	0.999805i	$0.506279\pi$
$6$		0			0
$7$	1.84695	−	3.19901i	0.698082	−	1.20911i	−0.271049	−	0.962566i	$-0.587370\pi$
$7$	1.84695	−	3.19901i	0.698082	−	1.20911i	0.969131	−	0.246548i	$-0.0792963\pi$
$8$	−1.91378			−0.676624
$9$		0			0
$10$	0.0747304	+	0.129437i	0.0236318	+	0.0409315i
$11$	1.97689	−	3.42408i	0.596056	−	1.03240i	−0.397341	−	0.917671i	$-0.630067\pi$
$11$	1.97689	−	3.42408i	0.596056	−	1.03240i	0.993397	−	0.114728i	$-0.0365996\pi$
$12$		0			0
$13$	−2.03012	+	3.51627i	−0.563054	+	0.975238i	0.434174	+	0.900829i	$0.357040\pi$
$13$	−2.03012	+	3.51627i	−0.563054	+	0.975238i	−0.997228	+	0.0744086i	$0.976293\pi$
$14$	−6.25832			−1.67261
$15$		0			0
$16$	2.49160	+	4.31558i	0.622901	+	1.07890i
$17$	0.586674	−	1.01615i	0.142289	−	0.246452i	−0.786069	−	0.618139i	$-0.787887\pi$
$17$	0.586674	−	1.01615i	0.142289	−	0.246452i	0.928358	+	0.371686i	$0.121220\pi$
$18$		0			0
$19$	3.26283	−	2.89032i	0.748544	−	0.663085i
$19$	3.26283	−	2.89032i	0.748544	−	0.663085i
$20$	0.0383928	−	0.0664983i	0.00858490	−	0.0148695i
$21$		0			0
$22$	−6.69862			−1.42815
$23$	1.91604	−	3.31868i	0.399523	−	0.691994i	−0.594144	−	0.804358i	$-0.702509\pi$
$23$	1.91604	−	3.31868i	0.399523	−	0.691994i	0.993667	+	0.112365i	$0.0358425\pi$
$24$		0			0
$25$	−4.99222			−0.998444
$26$	6.87897			1.34908
$27$		0			0
$28$	1.60761	+	2.78446i	0.303809	+	0.526213i
$29$	−6.56701			−1.21946			−0.609732	−	0.792608i	$-0.708723\pi$
$29$	−6.56701			−1.21946			−0.609732	+	0.792608i	$0.708723\pi$
$30$		0			0
$31$	−4.14650	−	7.18194i	−0.744733	−	1.28991i	−0.950320	−	0.311276i	$-0.899244\pi$
$31$	−4.14650	−	7.18194i	−0.744733	−	1.28991i	0.205587	−	0.978639i	$-0.434090\pi$
$32$	2.30757	−	3.99682i	0.407924	−	0.706545i
$33$		0			0
$34$	−1.98792			−0.340926
$35$	−0.162934	+	0.282209i	−0.0275408	+	0.0477021i
$36$		0			0
$37$	−6.88356			−1.13165			−0.565825	−	0.824525i	$-0.691442\pi$
$37$	−6.88356			−1.13165			−0.565825	+	0.824525i	$0.691442\pi$
$38$	−7.00480	−	2.33893i	−1.13633	−	0.379425i
$39$		0			0
$40$	0.168829			0.0266942
$41$	4.66112			0.727945			0.363972	−	0.931410i	$-0.381420\pi$
$41$	4.66112			0.727945			0.363972	+	0.931410i	$0.381420\pi$
$42$		0			0
$43$	4.12481	+	7.14438i	0.629028	+	1.08951i	0.987747	+	0.156062i	$0.0498801\pi$
$43$	4.12481	+	7.14438i	0.629028	+	1.08951i	−0.358720	+	0.933445i	$0.616787\pi$
$44$	1.72071	+	2.98036i	0.259407	+	0.449306i
$45$		0			0
$46$	−6.49243			−0.957257
$47$	−4.43759			−0.647290			−0.323645	−	0.946179i	$-0.604908\pi$
$47$	−4.43759			−0.647290			−0.323645	+	0.946179i	$0.604908\pi$
$48$		0			0
$49$	−3.32246	−	5.75467i	−0.474637	−	0.822095i
$50$	4.22898	+	7.32481i	0.598068	+	1.03588i
$51$		0			0
$52$	−1.76704	−	3.06060i	−0.245044	−	0.424429i
$53$	3.62409	+	6.27711i	0.497807	+	0.862227i	0.999997	−	0.00253016i	$-0.000805377\pi$
$53$	3.62409	+	6.27711i	0.497807	+	0.862227i	−0.502190	+	0.864758i	$0.667472\pi$
$54$		0			0
$55$	−0.174397	+	0.302064i	−0.0235157	+	0.0407303i
$56$	−3.53466	+	6.12221i	−0.472339	+	0.818115i
$57$		0			0
$58$	5.56301	+	9.63542i	0.730459	+	1.26519i
$59$	−1.01191			−0.131740			−0.0658700	−	0.997828i	$-0.520982\pi$
$59$	−1.01191			−0.131740			−0.0658700	+	0.997828i	$0.520982\pi$
$60$		0			0
$61$	3.22038			0.412327			0.206164	−	0.978518i	$-0.433902\pi$
$61$	3.22038			0.412327			0.206164	+	0.978518i	$0.433902\pi$
$62$	−7.02511	+	12.1679i	−0.892190	+	1.54532i
$63$		0			0
$64$	2.14732			0.268415
$65$	0.179092	−	0.310197i	0.0222137	−	0.0384752i
$66$		0			0
$67$	1.45149	−	2.51405i	0.177327	−	0.307140i	−0.763637	−	0.645646i	$-0.776588\pi$
$67$	1.45149	−	2.51405i	0.177327	−	0.307140i	0.940964	+	0.338506i	$0.109922\pi$
$68$	0.510648	+	0.884469i	0.0619252	+	0.107258i
$69$		0			0
$70$	0.552094			0.0659878
$71$	4.36630	−	7.56265i	0.518184	−	0.897521i	−0.481593	−	0.876395i	$-0.659942\pi$
$71$	4.36630	−	7.56265i	0.518184	−	0.897521i	0.999777	−	0.0211261i	$-0.00672514\pi$
$72$		0			0
$73$	3.43748	−	5.95390i	0.402327	−	0.696851i	−0.591679	−	0.806173i	$-0.701535\pi$
$73$	3.43748	−	5.95390i	0.402327	−	0.696851i	0.994006	+	0.109323i	$0.0348682\pi$
$74$	5.83116	+	10.0999i	0.677859	+	1.17409i
$75$		0			0
$76$	0.758720	+	3.71740i	0.0870312	+	0.426415i
$77$	−7.30245	−	12.6482i	−0.832191	−	1.44140i
$78$		0			0
$79$	2.65505	+	4.59868i	0.298716	+	0.517392i	0.975843	−	0.218475i	$-0.0701082\pi$
$79$	2.65505	+	4.59868i	0.298716	+	0.517392i	−0.677126	+	0.735867i	$0.736775\pi$
$80$	−0.219803	−	0.380711i	−0.0245748	−	0.0425647i
$81$		0			0
$82$	−3.94850	−	6.83901i	−0.436039	−	0.755242i
$83$	−3.34887	+	5.80042i	−0.367586	+	0.636678i	−0.989188	−	0.146655i	$-0.953149\pi$
$83$	−3.34887	+	5.80042i	−0.367586	+	0.636678i	0.621601	+	0.783334i	$0.286482\pi$
$84$		0			0
$85$	−0.0517550	+	0.0896423i	−0.00561362	+	0.00972307i
$86$	6.98837	−	12.1042i	0.753576	−	1.30523i
$87$		0			0
$88$	−3.78334	+	6.55294i	−0.403305	+	0.698545i
$89$	−4.41568	−	7.64818i	−0.468061	−	0.810706i	0.531273	−	0.847201i	$-0.321714\pi$
$89$	−4.41568	−	7.64818i	−0.468061	−	0.810706i	−0.999334	+	0.0364951i	$0.988381\pi$
$90$		0			0
$91$	7.49906	+	12.9888i	0.786115	+	1.36159i
$92$	1.66775	+	2.88862i	0.173875	+	0.301160i
$93$		0			0
$94$	3.75915	+	6.51104i	0.387727	+	0.671563i
$95$	−0.287839	+	0.254977i	−0.0295316	+	0.0261601i
$96$		0			0
$97$	−0.894933	−	1.55007i	−0.0908667	−	0.157386i	0.817009	−	0.576624i	$-0.195630\pi$
$97$	−0.894933	−	1.55007i	−0.0908667	−	0.157386i	−0.907876	+	0.419239i	$0.862297\pi$
$98$	−5.62901	+	9.74973i	−0.568616	+	0.984871i
$99$		0			0
$100$	2.17264	−	3.76313i	0.217264	−	0.376313i
$101$	7.88340			0.784428			0.392214	−	0.919874i	$-0.371709\pi$
$101$	7.88340			0.784428			0.392214	+	0.919874i	$0.371709\pi$
$102$		0			0
$103$	−0.0529084	−	0.0916401i	−0.00521322	−	0.00902956i	0.863407	−	0.504508i	$-0.168326\pi$
$103$	−0.0529084	−	0.0916401i	−0.00521322	−	0.00902956i	−0.868620	+	0.495478i	$0.834993\pi$
$104$	3.88520	−	6.72937i	0.380975	−	0.659869i
$105$		0			0
$106$	6.14004	−	10.6349i	0.596373	−	1.03295i
$107$	11.4812			1.10993			0.554966	−	0.831873i	$-0.312731\pi$
$107$	11.4812			1.10993			0.554966	+	0.831873i	$0.312731\pi$
$108$		0			0
$109$	9.52628	−	16.5000i	0.912452	−	1.58041i	0.101862	−	0.994799i	$-0.467520\pi$
$109$	9.52628	−	16.5000i	0.912452	−	1.58041i	0.810590	−	0.585614i	$-0.199147\pi$
$110$	0.590936			0.0563436
$111$		0			0
$112$	18.4075			1.73934
$113$	10.4274	+	18.0607i	0.980923	+	1.69901i	0.658812	+	0.752307i	$0.271059\pi$
$113$	10.4274	+	18.0607i	0.980923	+	1.69901i	0.322111	+	0.946702i	$0.395608\pi$
$114$		0			0
$115$	−0.169029	+	0.292767i	−0.0157620	+	0.0273006i
$116$	2.85800	−	4.95021i	0.265359	−	0.459615i
$117$		0			0
$118$	0.857208	+	1.48473i	0.0789124	+	0.136680i
$119$	−2.16712	−	3.75356i	−0.198659	−	0.344088i
$120$		0			0
$121$	−2.31621	−	4.01180i	−0.210565	−	0.364709i
$122$	−2.72803	−	4.72508i	−0.246984	−	0.427789i
$123$		0			0
$124$	7.21832			0.648224
$125$	0.881490			0.0788428
$126$		0			0
$127$	−0.856344	−	1.48323i	−0.0759883	−	0.131616i	0.825527	−	0.564362i	$-0.190878\pi$
$127$	−0.856344	−	1.48323i	−0.0759883	−	0.131616i	−0.901516	+	0.432747i	$0.857544\pi$
$128$	−6.43416	−	11.1443i	−0.568705	−	0.985026i
$129$		0			0
$130$	−0.606847			−0.0532240
$131$	−12.5149			−1.09343			−0.546716	−	0.837318i	$-0.684122\pi$
$131$	−12.5149			−1.09343			−0.546716	+	0.837318i	$0.684122\pi$
$132$		0			0
$133$	−3.21990	−	15.7761i	−0.279201	−	1.36796i
$134$	−4.91830			−0.424876
$135$		0			0
$136$	−1.12277	+	1.94469i	−0.0962764	+	0.166756i
$137$	21.3990			1.82824			0.914121	−	0.405441i	$-0.132882\pi$
$137$	21.3990			1.82824			0.914121	+	0.405441i	$0.132882\pi$
$138$		0			0
$139$	8.50131	−	14.7247i	0.721072	−	1.24893i	−0.239499	−	0.970897i	$-0.576983\pi$
$139$	8.50131	−	14.7247i	0.721072	−	1.24893i	0.960571	−	0.278036i	$-0.0896836\pi$
$140$	−0.141819	−	0.245638i	−0.0119859	−	0.0207602i
$141$		0			0
$142$	−14.7950			−1.24157
$143$	8.02666	+	13.9026i	0.671223	+	1.16259i
$144$		0			0
$145$	0.579326			0.0481104
$146$	−11.6478			−0.963976
$147$		0			0
$148$	2.99576	−	5.18882i	0.246250	−	0.426518i
$149$	0.774691			0.0634652			0.0317326	−	0.999496i	$-0.489898\pi$
$149$	0.774691			0.0634652			0.0317326	+	0.999496i	$0.489898\pi$
$150$		0			0
$151$	0.798471	−	1.38299i	0.0649787	−	0.112546i	−0.831706	−	0.555217i	$-0.812635\pi$
$151$	0.798471	−	1.38299i	0.0649787	−	0.112546i	0.896685	+	0.442670i	$0.145969\pi$
$152$	−6.24433	+	5.53144i	−0.506482	+	0.448659i
$153$		0			0
$154$	−12.3720	+	21.4290i	−0.996966	+	1.72680i
$155$	0.365794	+	0.633574i	0.0293813	+	0.0508899i
$156$		0			0
$157$	15.8915			1.26828			0.634141	−	0.773218i	$-0.281354\pi$
$157$	15.8915			1.26828			0.634141	+	0.773218i	$0.281354\pi$
$158$	4.49826	−	7.79122i	0.357862	−	0.619836i
$159$		0			0
$160$	−0.203568	+	0.352590i	−0.0160935	+	0.0278747i
$161$	−7.07768	−	12.2589i	−0.557799	−	0.966137i
$162$		0			0
$163$	5.95901			0.466746			0.233373	−	0.972387i	$-0.425024\pi$
$163$	5.95901			0.466746			0.233373	+	0.972387i	$0.425024\pi$
$164$	−2.02855	+	3.51355i	−0.158403	+	0.274362i
$165$		0			0
$166$	11.3475			0.880738
$167$	−1.83762	+	3.18285i	−0.142199	+	0.246297i	−0.928325	−	0.371771i	$-0.878751\pi$
$167$	−1.83762	+	3.18285i	−0.142199	+	0.246297i	0.786125	+	0.618067i	$0.212084\pi$
$168$		0			0
$169$	−1.74276	−	3.01856i	−0.134059	−	0.232197i
$170$	0.175370			0.0134502
$171$		0			0
$172$	−7.18057			−0.547513
$173$	7.20716	+	12.4832i	0.547950	+	0.949077i	0.998415	+	0.0562832i	$0.0179250\pi$
$173$	7.20716	+	12.4832i	0.547950	+	0.949077i	−0.450465	+	0.892794i	$0.648742\pi$
$174$		0			0
$175$	−9.22038	+	15.9702i	−0.696995	+	1.20723i
$176$	19.7025			1.48513
$177$		0			0
$178$	−7.48117	+	12.9578i	−0.560738	+	0.971226i
$179$	22.3972			1.67405			0.837023	−	0.547168i	$-0.184294\pi$
$179$	22.3972			1.67405			0.837023	+	0.547168i	$0.184294\pi$
$180$		0			0
$181$	9.03198	+	15.6438i	0.671341	+	1.16280i	0.977524	+	0.210825i	$0.0676149\pi$
$181$	9.03198	+	15.6438i	0.671341	+	1.16280i	−0.306182	+	0.951973i	$0.599052\pi$
$182$	12.7051	−	22.0059i	0.941767	−	1.63119i
$183$		0			0
$184$	−3.66689	+	6.35124i	−0.270327	+	0.468219i
$185$	0.607251			0.0446460
$186$		0			0
$187$	−2.31958	−	4.01764i	−0.169625	−	0.293799i
$188$	1.93127	−	3.34505i	0.140852	−	0.243963i
$189$		0			0
$190$	0.617947	+	0.206335i	0.0448306	+	0.0149691i
$191$	−2.81287	+	4.87204i	−0.203532	+	0.352528i	−0.949664	−	0.313270i	$-0.898576\pi$
$191$	−2.81287	+	4.87204i	−0.203532	+	0.352528i	0.746132	+	0.665798i	$0.231909\pi$
$192$		0			0
$193$	−7.70392			−0.554540			−0.277270	−	0.960792i	$-0.589430\pi$
$193$	−7.70392			−0.554540			−0.277270	+	0.960792i	$0.589430\pi$
$194$	−1.51622	+	2.62617i	−0.108858	+	0.188548i
$195$		0			0
$196$	5.78382			0.413130
$197$	−14.7969			−1.05424			−0.527119	−	0.849792i	$-0.676728\pi$
$197$	−14.7969			−1.05424			−0.527119	+	0.849792i	$0.676728\pi$
$198$		0			0
$199$	7.47940	+	12.9547i	0.530201	+	0.918335i	0.999379	+	0.0352314i	$0.0112168\pi$
$199$	7.47940	+	12.9547i	0.530201	+	0.918335i	−0.469178	+	0.883103i	$0.655450\pi$
$200$	9.55401			0.675571
$201$		0			0
$202$	−6.67815	−	11.5669i	−0.469873	−	0.813843i
$203$	−12.1290	+	21.0080i	−0.851286	+	1.47447i
$204$		0			0
$205$	−0.411193			−0.0287190
$206$	−0.0896390	+	0.155259i	−0.00624544	+	0.0108174i
$207$		0			0
$208$	−20.2330			−1.40291
$209$	−3.44643	−	16.8860i	−0.238395	−	1.16803i
$210$		0			0
$211$	−5.75054			−0.395883			−0.197942	−	0.980214i	$-0.563426\pi$
$211$	−5.75054			−0.395883			−0.197942	+	0.980214i	$0.563426\pi$
$212$	−6.30890			−0.433297
$213$		0			0
$214$	−9.72592	−	16.8458i	−0.664850	−	1.15155i
$215$	−0.363881	−	0.630260i	−0.0248165	−	0.0429834i
$216$		0			0
$217$	−30.6335			−2.07954
$218$	−32.2794			−2.18624
$219$		0			0
$220$	−0.151797	−	0.262920i	−0.0102342	−	0.0177261i
$221$	2.38204	+	4.12581i	0.160233	+	0.277532i
$222$		0			0
$223$	0.710622	+	1.23083i	0.0475868	+	0.0824227i	0.888838	−	0.458222i	$-0.151514\pi$
$223$	0.710622	+	1.23083i	0.0475868	+	0.0824227i	−0.841251	+	0.540645i	$0.818180\pi$
$224$	−8.52392	−	14.7639i	−0.569529	−	0.986453i
$225$		0			0
$226$	17.6663	−	30.5990i	1.17515	−	2.03541i
$227$	−13.0339	+	22.5754i	−0.865090	+	1.49838i	0.00186784	+	0.999998i	$0.499405\pi$
$227$	−13.0339	+	22.5754i	−0.865090	+	1.49838i	−0.866958	+	0.498382i	$0.833928\pi$
$228$		0			0
$229$	−7.69901	−	13.3351i	−0.508765	−	0.881207i	−0.999948	−	0.0101508i	$-0.996769\pi$
$229$	−7.69901	−	13.3351i	−0.508765	−	0.881207i	0.491183	−	0.871056i	$-0.336564\pi$
$230$	0.572747			0.0377658
$231$		0			0
$232$	12.5678			0.825118
$233$	−2.91634	+	5.05126i	−0.191056	+	0.330919i	−0.945600	−	0.325330i	$-0.894525\pi$
$233$	−2.91634	+	5.05126i	−0.191056	+	0.330919i	0.754544	+	0.656249i	$0.227858\pi$
$234$		0			0
$235$	0.391474			0.0255370
$236$	0.440391	−	0.762780i	0.0286670	−	0.0496528i
$237$		0			0
$238$	−3.67159	+	6.35939i	−0.237994	+	0.412218i
$239$	−13.6975	−	23.7248i	−0.886020	−	1.53463i	−0.844540	−	0.535493i	$-0.820126\pi$
$239$	−13.6975	−	23.7248i	−0.886020	−	1.53463i	−0.0414809	−	0.999139i	$-0.513208\pi$
$240$		0			0
$241$	2.22615			0.143399			0.0716994	−	0.997426i	$-0.477158\pi$
$241$	2.22615			0.143399			0.0716994	+	0.997426i	$0.477158\pi$
$242$	−3.92419	+	6.79690i	−0.252257	+	0.436921i
$243$		0			0
$244$	−1.40153	+	2.42752i	−0.0897236	+	0.155406i
$245$	0.293099	+	0.507663i	0.0187254	+	0.0324334i
$246$		0			0
$247$	3.53923	+	17.3407i	0.225196	+	1.10336i
$248$	7.93548	+	13.7447i	0.503904	+	0.872787i
$249$		0			0
$250$	−0.746723	−	1.29336i	−0.0472269	−	0.0817994i
$251$	−1.28824	−	2.23129i	−0.0813128	−	0.140838i	0.822501	−	0.568763i	$-0.192578\pi$
$251$	−1.28824	−	2.23129i	−0.0813128	−	0.140838i	−0.903814	+	0.427925i	$0.859245\pi$
$252$		0			0
$253$	−7.57563	−	13.1214i	−0.476276	−	0.824933i
$254$	−1.45084	+	2.51293i	−0.0910340	+	0.157676i
$255$		0			0
$256$	−8.75362	+	15.1617i	−0.547101	+	0.947607i
$257$	5.43354	−	9.41117i	0.338935	−	0.587053i	−0.645298	−	0.763931i	$-0.723267\pi$
$257$	5.43354	−	9.41117i	0.338935	−	0.587053i	0.984233	+	0.176879i	$0.0566000\pi$
$258$		0			0
$259$	−12.7136	+	22.0206i	−0.789984	+	1.36829i
$260$	0.155884	+	0.269999i	0.00966752	+	0.0167446i
$261$		0			0
$262$	10.6016	+	18.3624i	0.654966	+	1.13443i
$263$	−9.38673	−	16.2583i	−0.578810	−	1.00253i	−0.995616	−	0.0935334i	$-0.970184\pi$
$263$	−9.38673	−	16.2583i	−0.578810	−	1.00253i	0.416806	−	0.908996i	$-0.363150\pi$
$264$		0			0
$265$	−0.319709	−	0.553752i	−0.0196396	−	0.0340167i
$266$	−20.4198	+	18.0886i	−1.25202	+	1.10908i
$267$		0			0
$268$	1.26339	+	2.18826i	0.0771738	+	0.133669i
$269$	1.78002	−	3.08308i	0.108529	−	0.187979i	−0.806645	−	0.591036i	$-0.798719\pi$
$269$	1.78002	−	3.08308i	0.108529	−	0.187979i	0.915175	+	0.403057i	$0.132052\pi$
$270$		0			0
$271$	−8.62661	+	14.9417i	−0.524029	+	0.907645i	0.475579	+	0.879673i	$0.342238\pi$
$271$	−8.62661	+	14.9417i	−0.524029	+	0.907645i	−0.999609	+	0.0279725i	$0.991095\pi$
$272$	5.84704			0.354529
$273$		0			0
$274$	−18.1274	−	31.3976i	−1.09512	−	1.89680i
$275$	−9.86908	+	17.0937i	−0.595128	+	1.03079i
$276$		0			0
$277$	−6.79331	+	11.7664i	−0.408171	+	0.706972i	−0.994685	−	0.102967i	$-0.967167\pi$
$277$	−6.79331	+	11.7664i	−0.408171	+	0.706972i	0.586514	+	0.809939i	$0.300500\pi$
$278$	−28.8063			−1.72769
$279$		0			0
$280$	0.311819	−	0.540087i	0.0186348	−	0.0322764i
$281$	18.1229			1.08112			0.540561	−	0.841305i	$-0.318212\pi$
$281$	18.1229			1.08112			0.540561	+	0.841305i	$0.318212\pi$
$282$		0			0
$283$	−4.35791			−0.259051			−0.129525	−	0.991576i	$-0.541345\pi$
$283$	−4.35791			−0.259051			−0.129525	+	0.991576i	$0.541345\pi$
$284$	3.80048	+	6.58262i	0.225517	+	0.390607i
$285$		0			0
$286$	13.5990	−	23.5541i	0.804125	−	1.39279i
$287$	8.60886	−	14.9110i	0.508165	−	0.880168i
$288$		0			0
$289$	7.81163	+	13.5301i	0.459507	+	0.795890i
$290$	−0.490756	−	0.850014i	−0.0288182	−	0.0499145i
$291$		0			0
$292$	2.99203	+	5.18234i	0.175095	+	0.303274i
$293$	−11.3314	−	19.6265i	−0.661986	−	1.14659i	−0.980093	−	0.198538i	$-0.936381\pi$
$293$	−11.3314	−	19.6265i	−0.661986	−	1.14659i	0.318108	−	0.948055i	$-0.396953\pi$
$294$		0			0
$295$	0.0892687			0.00519743
$296$	13.1736			0.765701
$297$		0			0
$298$	−0.656252	−	1.13666i	−0.0380157	−	0.0658450i
$299$	7.77959	+	13.4746i	0.449905	+	0.779259i
$300$		0			0
$301$	30.4733			1.75645
$302$	−2.70559			−0.155689
$303$		0			0
$304$	20.6031	+	6.87946i	1.18167	+	0.394564i
$305$	−0.284094			−0.0162672
$306$		0			0
$307$	−6.03741	+	10.4571i	−0.344573	+	0.596819i	−0.985276	−	0.170970i	$-0.945310\pi$
$307$	−6.03741	+	10.4571i	−0.344573	+	0.596819i	0.640703	+	0.767789i	$0.278643\pi$
$308$	12.7123			0.724349
$309$		0			0
$310$	0.619739	−	1.07342i	0.0351988	−	0.0609661i
$311$	4.12927	+	7.15210i	0.234149	+	0.405559i	0.959025	−	0.283321i	$-0.0914362\pi$
$311$	4.12927	+	7.15210i	0.234149	+	0.405559i	−0.724876	+	0.688880i	$0.758103\pi$
$312$		0			0
$313$	−24.7032			−1.39631			−0.698155	−	0.715947i	$-0.745995\pi$
$313$	−24.7032			−1.39631			−0.698155	+	0.715947i	$0.745995\pi$
$314$	−13.4619	−	23.3168i	−0.759701	−	1.31584i
$315$		0			0
$316$	−4.62197			−0.260006
$317$	19.0751			1.07136			0.535681	−	0.844420i	$-0.320055\pi$
$317$	19.0751			1.07136			0.535681	+	0.844420i	$0.320055\pi$
$318$		0			0
$319$	−12.9823	+	22.4860i	−0.726868	+	1.25897i
$320$	−0.189432			−0.0105896
$321$		0			0
$322$	−11.9912	+	20.7694i	−0.668244	+	1.15743i
$323$	−1.02278	−	5.01120i	−0.0569092	−	0.278830i
$324$		0			0
$325$	10.1348	−	17.5540i	0.562177	−	0.973720i
$326$	−5.04797	−	8.74334i	−0.279581	−	0.484249i
$327$		0			0
$328$	−8.92036			−0.492545
$329$	−8.19602	+	14.1959i	−0.451861	+	0.782647i
$330$		0			0
$331$	13.8654	−	24.0156i	0.762113	−	1.32002i	−0.179646	−	0.983731i	$-0.557495\pi$
$331$	13.8654	−	24.0156i	0.762113	−	1.32002i	0.941759	−	0.336288i	$-0.109171\pi$
$332$	−2.91490	−	5.04875i	−0.159976	−	0.277086i
$333$		0			0
$334$	6.22670			0.340710
$335$	−0.128047	+	0.221783i	−0.00699593	+	0.0121173i
$336$		0			0
$337$	−34.0121			−1.85276			−0.926379	−	0.376591i	$-0.877096\pi$
$337$	−34.0121			−1.85276			−0.926379	+	0.376591i	$0.877096\pi$
$338$	−2.95264	+	5.11413i	−0.160603	+	0.278172i
$339$		0			0
$340$	−0.0450482	−	0.0780257i	−0.00244308	−	0.00423154i
$341$	−32.7887			−1.77561
$342$		0			0
$343$	1.31164			0.0708217
$344$	−7.89398	−	13.6728i	−0.425615	−	0.737187i
$345$		0			0
$346$	12.2106	−	21.1493i	0.656445	−	1.13700i
$347$	8.51227			0.456962			0.228481	−	0.973548i	$-0.426624\pi$
$347$	8.51227			0.456962			0.228481	+	0.973548i	$0.426624\pi$
$348$		0			0
$349$	−9.42349	+	16.3220i	−0.504428	+	0.873695i	0.495559	+	0.868574i	$0.334963\pi$
$349$	−9.42349	+	16.3220i	−0.504428	+	0.873695i	−0.999987	+	0.00512042i	$0.998370\pi$
$350$	31.2429			1.67000
$351$		0			0
$352$	−9.12362	−	15.8026i	−0.486291	−	0.842280i
$353$	8.62239	−	14.9344i	0.458923	−	0.794878i	−0.539981	−	0.841677i	$-0.681569\pi$
$353$	8.62239	−	14.9344i	0.458923	−	0.794878i	0.998904	+	0.0467987i	$0.0149019\pi$
$354$		0			0
$355$	−0.385184	+	0.667159i	−0.0204435	+	0.0354091i
$356$	7.68692			0.407406
$357$		0			0
$358$	−18.9730	−	32.8622i	−1.00275	−	1.73682i
$359$	−0.140779	+	0.243836i	−0.00743003	+	0.0128692i	−0.869717	−	0.493552i	$-0.835698\pi$
$359$	−0.140779	+	0.243836i	−0.00743003	+	0.0128692i	0.862286	+	0.506421i	$0.169032\pi$
$360$		0			0
$361$	2.29207	−	18.8612i	0.120635	−	0.992697i
$362$	15.3022	−	26.5042i	0.804268	−	1.39303i
$363$		0			0
$364$	−13.0545			−0.684244
$365$	−0.303247	+	0.525239i	−0.0158727	+	0.0274922i
$366$		0			0
$367$	17.3938			0.907947			0.453974	−	0.891015i	$-0.350006\pi$
$367$	17.3938			0.907947			0.453974	+	0.891015i	$0.350006\pi$
$368$	19.0961			0.995452
$369$		0			0
$370$	−0.514411	−	0.890986i	−0.0267430	−	0.0463202i
$371$	26.7741			1.39004
$372$		0			0
$373$	10.7006	+	18.5340i	0.554056	+	0.959654i	0.997976	+	0.0635874i	$0.0202542\pi$
$373$	10.7006	+	18.5340i	0.554056	+	0.959654i	−0.443920	+	0.896066i	$0.646413\pi$
$374$	−3.92991	+	6.80680i	−0.203211	+	0.351971i
$375$		0			0
$376$	8.49258			0.437972
$377$	13.3318	−	23.0914i	0.686624	−	1.18927i
$378$		0			0
$379$	21.3755			1.09798			0.548992	−	0.835827i	$-0.315012\pi$
$379$	21.3755			1.09798			0.548992	+	0.835827i	$0.315012\pi$
$380$	−0.0669325	−	0.327940i	−0.00343357	−	0.0168230i
$381$		0			0
$382$	9.53130			0.487664
$383$	−22.0748			−1.12797			−0.563986	−	0.825785i	$-0.690733\pi$
$383$	−22.0748			−1.12797			−0.563986	+	0.825785i	$0.690733\pi$
$384$		0			0
$385$	0.644205	+	1.11580i	0.0328317	+	0.0568662i
$386$	6.52610	+	11.3035i	0.332170	+	0.575335i
$387$		0			0
$388$	1.55792			0.0790914
$389$	−31.4101			−1.59256			−0.796278	−	0.604931i	$-0.793201\pi$
$389$	−31.4101			−1.59256			−0.796278	+	0.604931i	$0.793201\pi$
$390$		0			0
$391$	−2.24819	−	3.89397i	−0.113696	−	0.196927i
$392$	6.35846	+	11.0132i	0.321151	+	0.556249i
$393$		0			0
$394$	12.5347	+	21.7107i	0.631489	+	1.09377i
$395$	−0.234222	−	0.405685i	−0.0117850	−	0.0204122i
$396$		0			0
$397$	−6.11785	+	10.5964i	−0.307046	+	0.531819i	−0.977715	−	0.209938i	$-0.932674\pi$
$397$	−6.11785	+	10.5964i	−0.307046	+	0.531819i	0.670669	+	0.741757i	$0.266007\pi$
$398$	12.6718	−	21.9482i	0.635181	−	1.10017i
$399$		0			0
$400$	−12.4386	−	21.5443i	−0.621931	−	1.07722i
$401$	10.8610			0.542373			0.271187	−	0.962527i	$-0.412584\pi$
$401$	10.8610			0.542373			0.271187	+	0.962527i	$0.412584\pi$
$402$		0			0
$403$	33.6715			1.67730
$404$	−3.43090	+	5.94250i	−0.170694	+	0.295650i
$405$		0			0
$406$	41.0985			2.03968
$407$	−13.6081	+	23.5698i	−0.674526	+	1.16831i
$408$		0			0
$409$	−1.09166	+	1.89081i	−0.0539791	+	0.0934946i	−0.891752	−	0.452524i	$-0.850524\pi$
$409$	−1.09166	+	1.89081i	−0.0539791	+	0.0934946i	0.837773	+	0.546018i	$0.183857\pi$
$410$	0.348328	+	0.603321i	0.0172027	+	0.0297959i
$411$		0			0
$412$	0.0921042			0.00453765
$413$	−1.86896	+	3.23713i	−0.0919654	+	0.159289i
$414$		0			0
$415$	0.295430	−	0.511699i	0.0145021	−	0.0251183i
$416$	9.36927	+	16.2280i	0.459366	+	0.795645i
$417$		0			0
$418$	−21.8564	+	19.3612i	−1.06903	+	0.946986i
$419$	−2.47165	−	4.28102i	−0.120748	−	0.209142i	0.799315	−	0.600912i	$-0.205196\pi$
$419$	−2.47165	−	4.28102i	−0.120748	−	0.209142i	−0.920063	+	0.391771i	$0.871863\pi$
$420$		0			0
$421$	9.30392	+	16.1149i	0.453445	+	0.785390i	0.998597	−	0.0529469i	$-0.0168614\pi$
$421$	9.30392	+	16.1149i	0.453445	+	0.785390i	−0.545152	+	0.838337i	$0.683528\pi$
$422$	4.87136	+	8.43745i	0.237134	+	0.410729i
$423$		0			0
$424$	−6.93572	−	12.0130i	−0.336828	−	0.583404i
$425$	−2.92881	+	5.07284i	−0.142068	+	0.246069i
$426$		0			0
$427$	5.94788	−	10.3020i	0.287838	−	0.498550i
$428$	−4.99670	+	8.65454i	−0.241525	+	0.418333i
$429$		0			0
$430$	−0.616498	+	1.06781i	−0.0297302	+	0.0514941i
$431$	−1.66939	−	2.89147i	−0.0804119	−	0.139277i	0.823015	−	0.568020i	$-0.192290\pi$
$431$	−1.66939	−	2.89147i	−0.0804119	−	0.139277i	−0.903427	+	0.428742i	$0.858957\pi$
$432$		0			0
$433$	−13.5412	−	23.4541i	−0.650751	−	1.12713i	−0.982941	−	0.183921i	$-0.941121\pi$
$433$	−13.5412	−	23.4541i	−0.650751	−	1.12713i	0.332190	−	0.943212i	$-0.392212\pi$
$434$	25.9501	+	44.9469i	1.24564	+	2.15752i
$435$		0			0
$436$	8.29178	+	14.3618i	0.397104	+	0.687805i
$437$	−3.34035	−	16.3663i	−0.159791	−	0.782905i
$438$		0			0
$439$	1.20427	+	2.08586i	0.0574768	+	0.0995528i	0.893332	−	0.449397i	$-0.148361\pi$
$439$	1.20427	+	2.08586i	0.0574768	+	0.0995528i	−0.835855	+	0.548950i	$0.815028\pi$
$440$	0.333757	−	0.578085i	0.0159113	−	0.0275591i
$441$		0			0
$442$	4.03572	−	6.99006i	0.191959	−	0.332483i
$443$	18.5968			0.883561			0.441780	−	0.897123i	$-0.354347\pi$
$443$	18.5968			0.883561			0.441780	+	0.897123i	$0.354347\pi$
$444$		0			0
$445$	0.389541	+	0.674705i	0.0184660	+	0.0319841i
$446$	1.20396	−	2.08531i	0.0570090	−	0.0987425i
$447$		0			0
$448$	3.96600	−	6.86932i	0.187376	−	0.324545i
$449$	−6.17146			−0.291249			−0.145625	−	0.989340i	$-0.546519\pi$
$449$	−6.17146			−0.291249			−0.145625	+	0.989340i	$0.546519\pi$
$450$		0			0
$451$	9.21453	−	15.9600i	0.433895	−	0.751529i
$452$	−18.1522			−0.853807
$453$		0			0
$454$	44.1648			2.07276
$455$	−0.661549	−	1.14584i	−0.0310139	−	0.0537177i
$456$		0			0
$457$	−7.28965	+	12.6260i	−0.340995	+	0.590621i	−0.984618	−	0.174722i	$-0.944097\pi$
$457$	−7.28965	+	12.6260i	−0.340995	+	0.590621i	0.643622	+	0.765343i	$0.277431\pi$
$458$	−13.0439	+	22.5927i	−0.609501	+	1.05569i
$459$		0			0
$460$	−0.147125	−	0.254827i	−0.00685972	−	0.0118814i
$461$	8.15747	+	14.1292i	0.379931	+	0.658060i	0.991052	−	0.133477i	$-0.0426143\pi$
$461$	8.15747	+	14.1292i	0.379931	+	0.658060i	−0.611121	+	0.791538i	$0.709281\pi$
$462$		0			0
$463$	−4.34688	−	7.52901i	−0.202017	−	0.349903i	0.747162	−	0.664643i	$-0.231416\pi$
$463$	−4.34688	−	7.52901i	−0.202017	−	0.349903i	−0.949178	+	0.314740i	$0.898083\pi$
$464$	−16.3624	−	28.3405i	−0.759605	−	1.31567i
$465$		0			0
$466$	9.88191			0.457771
$467$	−34.0672			−1.57644			−0.788221	−	0.615392i	$-0.788998\pi$
$467$	−34.0672			−1.57644			−0.788221	+	0.615392i	$0.788998\pi$
$468$		0			0
$469$	−5.36165	−	9.28664i	−0.247578	−	0.428817i
$470$	−0.331623	−	0.574389i	−0.0152966	−	0.0264946i
$471$		0			0
$472$	1.93658			0.0891385
$473$	32.6172			1.49974
$474$		0			0
$475$	−16.2887	+	14.4291i	−0.747379	+	0.662053i
$476$	3.77257			0.172915
$477$		0			0
$478$	−23.2068	+	40.1953i	−1.06145	+	1.83849i
$479$	0.0213142			0.000973871			0.000486935	−	1.00000i	$-0.499845\pi$
$479$	0.0213142			0.000973871			0.000486935		1.00000i	$0.499845\pi$
$480$		0			0
$481$	13.9744	−	24.2044i	0.637179	−	1.10363i
$482$	−1.88580	−	3.26631i	−0.0858960	−	0.148776i
$483$		0			0
$484$	4.03212			0.183278
$485$	0.0789489	+	0.136743i	0.00358488	+	0.00620920i
$486$		0			0
$487$	26.2262			1.18842			0.594212	−	0.804309i	$-0.297464\pi$
$487$	26.2262			1.18842			0.594212	+	0.804309i	$0.297464\pi$
$488$	−6.16310			−0.278990
$489$		0			0
$490$	0.496578	−	0.860098i	0.0224331	−	0.0388553i
$491$	21.7791			0.982877			0.491439	−	0.870912i	$-0.336471\pi$
$491$	21.7791			0.982877			0.491439	+	0.870912i	$0.336471\pi$
$492$		0			0
$493$	−3.85270	+	6.67307i	−0.173517	+	0.300540i
$494$	22.4449	−	19.8824i	1.00984	−	0.894554i
$495$		0			0
$496$	20.6628	−	35.7891i	0.927789	−	1.60698i
$497$	−16.1287	−	27.9357i	−0.723470	−	1.25309i
$498$		0			0
$499$	25.3550			1.13505			0.567523	−	0.823358i	$-0.307902\pi$
$499$	25.3550			1.13505			0.567523	+	0.823358i	$0.307902\pi$
$500$	−0.383630	+	0.664466i	−0.0171564	+	0.0297158i
$501$		0			0
$502$	−2.18257	+	3.78032i	−0.0974129	+	0.168724i
$503$	16.2481	+	28.1425i	0.724465	+	1.25481i	0.959194	+	0.282749i	$0.0912465\pi$
$503$	16.2481	+	28.1425i	0.724465	+	1.25481i	−0.234729	+	0.972061i	$0.575420\pi$
$504$		0			0
$505$	−0.695455			−0.0309474
$506$	−12.8348	+	22.2306i	−0.570578	+	0.988271i
$507$		0			0
$508$	1.49074			0.0661411
$509$	2.23483	−	3.87085i	0.0990573	−	0.171572i	−0.812237	−	0.583327i	$-0.801751\pi$
$509$	2.23483	−	3.87085i	0.0990573	−	0.171572i	0.911295	+	0.411755i	$0.135084\pi$
$510$		0			0
$511$	−12.6977	−	21.9931i	−0.561715	−	0.972918i
$512$	3.92462			0.173446
$513$		0			0
$514$	−18.4113			−0.812089
$515$	0.00466746	+	0.00808427i	0.000205673	+	0.000356236i
$516$		0			0
$517$	−8.77265	+	15.1947i	−0.385821	+	0.668261i
$518$	43.0795			1.89280
$519$		0			0
$520$	−0.342743	+	0.593649i	−0.0150303	+	0.0260332i
$521$	−5.89784			−0.258389			−0.129195	−	0.991619i	$-0.541239\pi$
$521$	−5.89784			−0.258389			−0.129195	+	0.991619i	$0.541239\pi$
$522$		0			0
$523$	−15.8110	−	27.3855i	−0.691367	−	1.19748i	−0.971390	−	0.237490i	$-0.923675\pi$
$523$	−15.8110	−	27.3855i	−0.691367	−	1.19748i	0.280023	−	0.959993i	$-0.409658\pi$
$524$	5.44656	−	9.43371i	0.237934	−	0.412114i
$525$		0			0
$526$	−15.9033	+	27.5453i	−0.693415	+	1.20103i
$527$	−9.73057			−0.423870
$528$		0			0
$529$	4.15755	+	7.20110i	0.180763	+	0.313091i
$530$	−0.541660	+	0.938182i	−0.0235282	+	0.0407520i
$531$		0			0
$532$	13.2933	+	4.43870i	0.576339	+	0.192442i
$533$	−9.46263	+	16.3898i	−0.409872	+	0.709919i
$534$		0			0
$535$	−1.01285			−0.0437892
$536$	−2.77783	+	4.81133i	−0.119984	+	0.207818i
$537$		0			0
$538$	−6.03151			−0.260037
$539$	−26.2726			−1.13164
$540$		0			0
$541$	11.5933	+	20.0802i	0.498435	+	0.863314i	0.999998	−	0.00180639i	$-0.000574993\pi$
$541$	11.5933	+	20.0802i	0.498435	+	0.863314i	−0.501564	+	0.865121i	$0.667242\pi$
$542$	29.2309			1.25557
$543$		0			0
$544$	−2.70758	−	4.68966i	−0.116086	−	0.201068i
$545$	−0.840386	+	1.45559i	−0.0359982	+	0.0623507i
$546$		0			0
$547$	−18.8998			−0.808095			−0.404048	−	0.914738i	$-0.632397\pi$
$547$	−18.8998			−0.808095			−0.404048	+	0.914738i	$0.632397\pi$
$548$	−9.31299	+	16.1306i	−0.397831	+	0.689064i
$549$		0			0
$550$	33.4410			1.42593
$551$	−21.4270	+	18.9808i	−0.912822	+	0.808609i
$552$		0			0
$553$	19.6150			0.834114
$554$	23.0189			0.977978
$555$		0			0
$556$	7.39964	+	12.8166i	0.313815	+	0.543543i
$557$	−14.5839	−	25.2601i	−0.617941	−	1.07031i	−0.989861	−	0.142041i	$-0.954634\pi$
$557$	−14.5839	−	25.2601i	−0.617941	−	1.07031i	0.371920	−	0.928265i	$-0.378700\pi$
$558$		0			0
$559$	−33.4954			−1.41671
$560$	−1.62386			−0.0686208
$561$		0			0
$562$	−15.3522	−	26.5907i	−0.647592	−	1.12166i
$563$	−7.67754	−	13.2979i	−0.323570	−	0.560440i	0.657652	−	0.753322i	$-0.271550\pi$
$563$	−7.67754	−	13.2979i	−0.323570	−	0.560440i	−0.981222	+	0.192882i	$0.938216\pi$
$564$		0			0
$565$	−0.919877	−	1.59327i	−0.0386995	−	0.0670295i
$566$	3.69165	+	6.39412i	0.155172	+	0.268765i
$567$		0			0
$568$	−8.35614	+	14.4733i	−0.350616	+	0.607284i
$569$	−5.99243	+	10.3792i	−0.251216	+	0.435119i	−0.963861	−	0.266406i	$-0.914164\pi$
$569$	−5.99243	+	10.3792i	−0.251216	+	0.435119i	0.712645	+	0.701525i	$0.247497\pi$
$570$		0			0
$571$	19.3857	+	33.5770i	0.811266	+	1.40515i	0.911979	+	0.410238i	$0.134554\pi$
$571$	19.3857	+	33.5770i	0.811266	+	1.40515i	−0.100713	+	0.994916i	$0.532112\pi$
$572$	−13.9730			−0.584240
$573$		0			0
$574$	−29.1708			−1.21756
$575$	−9.56531	+	16.5676i	−0.398901	+	0.690917i
$576$		0			0
$577$	−31.4108			−1.30765			−0.653824	−	0.756646i	$-0.726836\pi$
$577$	−31.4108			−1.30765			−0.653824	+	0.756646i	$0.726836\pi$
$578$	13.2347	−	22.9231i	0.550490	−	0.953477i
$579$		0			0
$580$	−0.252126	+	0.436696i	−0.0104690	+	0.0181328i
$581$	12.3704	+	21.4262i	0.513211	+	0.888908i
$582$		0			0
$583$	28.6578			1.18688
$584$	−6.57859	+	11.3945i	−0.272224	+	0.471506i
$585$		0			0
$586$	−19.1979	+	33.2518i	−0.793059	+	1.37362i
$587$	22.8980	+	39.6604i	0.945100	+	1.63696i	0.755551	+	0.655089i	$0.227369\pi$
$587$	22.8980	+	39.6604i	0.945100	+	1.63696i	0.189548	+	0.981871i	$0.439298\pi$
$588$		0			0
$589$	−34.2874	−	11.4487i	−1.41279	−	0.471736i
$590$	−0.0756208	−	0.130979i	−0.00311326	−	0.00539232i
$591$		0			0
$592$	−17.1511	−	29.7066i	−0.704906	−	1.22093i
$593$	1.17751	+	2.03951i	0.0483547	+	0.0837528i	0.889190	−	0.457539i	$-0.151269\pi$
$593$	1.17751	+	2.03951i	0.0483547	+	0.0837528i	−0.840835	+	0.541292i	$0.817936\pi$
$594$		0			0
$595$	0.191178	+	0.331130i	0.00783753	+	0.0135750i
$596$	−0.337150	+	0.583961i	−0.0138102	+	0.0239200i
$597$		0			0
$598$	13.1804	−	22.8291i	0.538987	−	0.933553i
$599$	−17.5448	+	30.3884i	−0.716859	+	1.24164i	0.245378	+	0.969427i	$0.421088\pi$
$599$	−17.5448	+	30.3884i	−0.716859	+	1.24164i	−0.962238	+	0.272210i	$0.912246\pi$
$600$		0			0
$601$	1.65448	−	2.86564i	0.0674875	−	0.116892i	−0.830307	−	0.557306i	$-0.811835\pi$
$601$	1.65448	−	2.86564i	0.0674875	−	0.116892i	0.897795	+	0.440414i	$0.145168\pi$
$602$	−25.8144	−	44.7118i	−1.05212	−	1.82232i
$603$		0			0
$604$	0.694999	+	1.20377i	0.0282791	+	0.0489809i
$605$	0.204331	+	0.353911i	0.00830722	+	0.0143885i
$606$		0			0
$607$	−12.1685	−	21.0764i	−0.493904	−	0.855466i	0.506072	−	0.862491i	$-0.331097\pi$
$607$	−12.1685	−	21.0764i	−0.493904	−	0.855466i	−0.999975	+	0.00702538i	$0.997764\pi$
$608$	−4.02292	−	19.7105i	−0.163151	−	0.799368i
$609$		0			0
$610$	0.240660	+	0.416836i	0.00974405	+	0.0168772i
$611$	9.00884	−	15.6038i	0.364459	−	0.631261i
$612$		0			0
$613$	−11.9472	+	20.6931i	−0.482542	+	0.835786i	−0.999799	−	0.0200433i	$-0.993620\pi$
$613$	−11.9472	+	20.6931i	−0.482542	+	0.835786i	0.517258	+	0.855830i	$0.326953\pi$
$614$	20.4575			0.825598
$615$		0			0
$616$	13.9753	+	24.2059i	0.563080	+	0.975284i
$617$	−7.62820	+	13.2124i	−0.307100	+	0.531912i	−0.977727	−	0.209883i	$-0.932692\pi$
$617$	−7.62820	+	13.2124i	−0.307100	+	0.531912i	0.670627	+	0.741795i	$0.266025\pi$
$618$		0			0
$619$	0.911408	−	1.57860i	0.0366326	−	0.0634495i	−0.847128	−	0.531389i	$-0.821670\pi$
$619$	0.911408	−	1.57860i	0.0366326	−	0.0634495i	0.883760	+	0.467940i	$0.155004\pi$
$620$	−0.636783			−0.0255738
$621$		0			0
$622$	6.99593	−	12.1173i	0.280511	−	0.485860i
$623$	−32.6222			−1.30698
$624$		0			0
$625$	24.8833			0.995333
$626$	20.9265	+	36.2457i	0.836390	+	1.44867i
$627$		0			0
$628$	−6.91608	+	11.9790i	−0.275982	+	0.478015i
$629$	−4.03840	+	6.99472i	−0.161022	+	0.278898i
$630$		0			0
$631$	−15.3499	−	26.5868i	−0.611069	−	1.05840i	−0.991061	−	0.133413i	$-0.957406\pi$
$631$	−15.3499	−	26.5868i	−0.611069	−	1.05840i	0.379992	−	0.924990i	$-0.375927\pi$
$632$	−5.08118	−	8.80086i	−0.202119	−	0.350080i
$633$		0			0
$634$	−16.1588	−	27.9878i	−0.641747	−	1.11154i
$635$	0.0755447	+	0.130847i	0.00299790	+	0.00519251i
$636$		0			0
$637$	26.9799			1.06898
$638$	43.9899			1.74158
$639$		0			0
$640$	0.567606	+	0.983123i	0.0224366	+	0.0388614i
$641$	−17.9910	−	31.1613i	−0.710601	−	1.23080i	−0.964632	−	0.263601i	$-0.915090\pi$
$641$	−17.9910	−	31.1613i	−0.710601	−	1.23080i	0.254030	−	0.967196i	$-0.418244\pi$
$642$		0			0
$643$	34.8272			1.37345			0.686725	−	0.726917i	$-0.259047\pi$
$643$	34.8272			1.37345			0.686725	+	0.726917i	$0.259047\pi$
$644$	12.3210			0.485515
$645$		0			0
$646$	−6.48624	+	5.74573i	−0.255198	+	0.226063i
$647$	34.1239			1.34155			0.670775	−	0.741661i	$-0.265962\pi$
$647$	34.1239			1.34155			0.670775	+	0.741661i	$0.265962\pi$
$648$		0			0
$649$	−2.00045	+	3.46488i	−0.0785244	+	0.136008i
$650$	−34.3413			−1.34698
$651$		0			0
$652$	−2.59340	+	4.49190i	−0.101565	+	0.175916i
$653$	−6.66481	−	11.5438i	−0.260814	−	0.451743i	0.705644	−	0.708566i	$-0.250658\pi$
$653$	−6.66481	−	11.5438i	−0.260814	−	0.451743i	−0.966458	+	0.256823i	$0.917324\pi$
$654$		0			0
$655$	1.10403			0.0431382
$656$	11.6137	+	20.1155i	0.453437	+	0.785376i
$657$		0			0
$658$	27.7719			1.08266
$659$	12.0624			0.469883			0.234941	−	0.972010i	$-0.424510\pi$
$659$	12.0624			0.469883			0.234941	+	0.972010i	$0.424510\pi$
$660$		0			0
$661$	0.422835	−	0.732372i	0.0164464	−	0.0284860i	−0.857685	−	0.514175i	$-0.828098\pi$
$661$	0.422835	−	0.732372i	0.0164464	−	0.0284860i	0.874131	+	0.485689i	$0.161431\pi$
$662$	−46.9824			−1.82602
$663$		0			0
$664$	6.40901	−	11.1007i	0.248718	−	0.430792i
$665$	0.284052	+	1.39173i	0.0110151	+	0.0539690i
$666$		0			0
$667$	−12.5827	+	21.7938i	−0.487203	+	0.843861i
$668$	−1.59949	−	2.77039i	−0.0618860	−	0.107190i
$669$		0			0
$670$	0.433881			0.0167623
$671$	6.36634	−	11.0268i	0.245770	−	0.425686i
$672$		0			0
$673$	9.27675	−	16.0678i	0.357592	−	0.619368i	−0.629966	−	0.776623i	$-0.716931\pi$
$673$	9.27675	−	16.0678i	0.357592	−	0.619368i	0.987558	+	0.157255i	$0.0502644\pi$
$674$	28.8122	+	49.9041i	1.10980	+	1.92224i
$675$		0			0
$676$	3.03385			0.116686
$677$	16.1238	−	27.9273i	0.619689	−	1.07333i	−0.369854	−	0.929090i	$-0.620592\pi$
$677$	16.1238	−	27.9273i	0.619689	−	1.07333i	0.989542	−	0.144242i	$-0.0460745\pi$
$678$		0			0
$679$	−6.61159			−0.253730
$680$	0.0990477	−	0.171556i	0.00379831	−	0.00657886i
$681$		0			0
$682$	27.7758	+	48.1091i	1.06359	+	1.84219i
$683$	−3.72149			−0.142399			−0.0711994	−	0.997462i	$-0.522683\pi$
$683$	−3.72149			−0.142399			−0.0711994	+	0.997462i	$0.522683\pi$
$684$		0			0
$685$	−1.88777			−0.0721281
$686$	−1.11111	−	1.92449i	−0.0424223	−	0.0734775i
$687$		0			0
$688$	−20.5548	+	35.6019i	−0.783644	+	1.35731i
$689$	−29.4293			−1.12117
$690$		0			0
$691$	3.49161	−	6.04764i	0.132827	−	0.230063i	−0.791938	−	0.610601i	$-0.790928\pi$
$691$	3.49161	−	6.04764i	0.132827	−	0.230063i	0.924765	+	0.380538i	$0.124261\pi$
$692$	−12.5464			−0.476942
$693$		0			0
$694$	−7.21086	−	12.4896i	−0.273721	−	0.474098i
$695$	−0.749966	+	1.29898i	−0.0284478	+	0.0492731i
$696$		0			0
$697$	2.73456	−	4.73639i	0.103579	−	0.179404i
$698$	31.9311			1.20861
$699$		0			0
$700$	−8.02553	−	13.9006i	−0.303337	−	0.525394i
$701$	9.86590	−	17.0882i	0.372630	−	0.645414i	−0.617339	−	0.786697i	$-0.711789\pi$
$701$	9.86590	−	17.0882i	0.372630	−	0.645414i	0.989969	+	0.141283i	$0.0451228\pi$
$702$		0			0
$703$	−22.4598	+	19.8957i	−0.847089	+	0.750380i
$704$	4.24503	−	7.35261i	0.159991	−	0.277112i
$705$		0			0
$706$	−29.2166			−1.09958
$707$	14.5603	−	25.2191i	0.547595	−	0.948463i
$708$		0			0
$709$	−1.40237			−0.0526672			−0.0263336	−	0.999653i	$-0.508383\pi$
$709$	−1.40237			−0.0526672			−0.0263336	+	0.999653i	$0.508383\pi$
$710$	1.30518			0.0489826
$711$		0			0
$712$	8.45065	+	14.6369i	0.316701	+	0.548543i
$713$	−31.7795			−1.19015
$714$		0			0
$715$	−0.708093	−	1.22645i	−0.0264812	−	0.0458667i
$716$	−9.74739	+	16.8830i	−0.364277	+	0.630947i
$717$		0			0
$718$	0.477024			0.0178024
$719$	−11.9553	+	20.7072i	−0.445858	+	0.772248i	−0.998112	−	0.0614280i	$-0.980435\pi$
$719$	−11.9553	+	20.7072i	−0.445858	+	0.772248i	0.552254	+	0.833676i	$0.313768\pi$
$720$		0			0
$721$	−0.390877			−0.0145570
$722$	−29.6157	+	12.6146i	−1.10218	+	0.469467i
$723$		0			0
$724$	−15.7231			−0.584344
$725$	32.7840			1.21757
$726$		0			0
$727$	−14.5442	−	25.1913i	−0.539415	−	0.934294i	−0.998936	−	0.0461269i	$-0.985312\pi$
$727$	−14.5442	−	25.1913i	−0.539415	−	0.934294i	0.459521	−	0.888167i	$-0.348021\pi$
$728$	−14.3516	−	24.8576i	−0.531904	−	0.921285i
$729$		0			0
$730$	1.02754			0.0380309
$731$	9.67968			0.358016
$732$		0			0
$733$	0.435207	+	0.753801i	0.0160747	+	0.0278423i	0.873951	−	0.486014i	$-0.161550\pi$
$733$	0.435207	+	0.753801i	0.0160747	+	0.0278423i	−0.857876	+	0.513857i	$0.828216\pi$
$734$	−14.7345	−	25.5209i	−0.543861	−	0.941995i
$735$		0			0
$736$	−8.84279	−	15.3162i	−0.325950	−	0.564561i
$737$	−5.73886	−	9.94000i	−0.211394	−	0.366145i
$738$		0			0
$739$	−0.170501	+	0.295316i	−0.00627197	+	0.0108634i	−0.869144	−	0.494558i	$-0.835330\pi$
$739$	−0.170501	+	0.295316i	−0.00627197	+	0.0108634i	0.862872	+	0.505422i	$0.168663\pi$
$740$	−0.264279	+	0.457745i	−0.00971510	+	0.0168270i
$741$		0			0
$742$	−22.6807	−	39.2841i	−0.832635	−	1.44217i
$743$	−17.1491			−0.629138			−0.314569	−	0.949235i	$-0.601860\pi$
$743$	−17.1491			−0.629138			−0.314569	+	0.949235i	$0.601860\pi$
$744$		0			0
$745$	−0.0683414			−0.00250384
$746$	18.1293	−	31.4008i	0.663760	−	1.14967i
$747$		0			0
$748$	4.03799			0.147643
$749$	21.2053	−	36.7286i	0.774824	−	1.34203i
$750$		0			0
$751$	0.808980	−	1.40119i	0.0295201	−	0.0511303i	−0.850888	−	0.525347i	$-0.823935\pi$
$751$	0.808980	−	1.40119i	0.0295201	−	0.0511303i	0.880408	+	0.474217i	$0.157269\pi$
$752$	−11.0567	−	19.1508i	−0.403197	−	0.698358i
$753$		0			0
$754$	−45.1743			−1.64515
$755$	−0.0704393	+	0.122004i	−0.00256355	+	0.00444019i
$756$		0			0
$757$	−4.42323	+	7.66127i	−0.160765	+	0.278453i	−0.935143	−	0.354270i	$-0.884730\pi$
$757$	−4.42323	+	7.66127i	−0.160765	+	0.278453i	0.774378	+	0.632723i	$0.218063\pi$
$758$	−18.1075	−	31.3631i	−0.657693	−	1.13916i
$759$		0			0
$760$	0.550860	−	0.487971i	0.0199818	−	0.0177006i
$761$	−12.9237	−	22.3844i	−0.468483	−	0.811436i	0.530869	−	0.847454i	$-0.321866\pi$
$761$	−12.9237	−	22.3844i	−0.468483	−	0.811436i	−0.999351	+	0.0360185i	$0.988532\pi$
$762$		0			0
$763$	−35.1891	−	60.9494i	−1.27393	−	2.20652i
$764$	−2.44836	−	4.24068i	−0.0885785	−	0.153422i
$765$		0			0
$766$	18.6999	+	32.3892i	0.675655	+	1.17027i
$767$	2.05431	−	3.55816i	0.0741767	−	0.128478i
$768$		0			0
$769$	−8.80940	+	15.2583i	−0.317675	+	0.550229i	−0.980003	−	0.198985i	$-0.936235\pi$
$769$	−8.80940	+	15.2583i	−0.317675	+	0.550229i	0.662327	+	0.749215i	$0.269569\pi$
$770$	1.09143	−	1.89041i	0.0393324	−	0.0681258i
$771$		0			0
$772$	3.35279	−	5.80721i	0.120670	−	0.209006i
$773$	10.0142	+	17.3450i	0.360185	+	0.623858i	0.987991	−	0.154512i	$-0.0493804\pi$
$773$	10.0142	+	17.3450i	0.360185	+	0.623858i	−0.627806	+	0.778370i	$0.716047\pi$
$774$		0			0
$775$	20.7002	+	35.8538i	0.743573	+	1.28791i
$776$	1.71271	+	2.96649i	0.0614825	+	0.106491i
$777$		0			0
$778$	26.6080	+	46.0863i	0.953942	+	1.65228i
$779$	15.2084	−	13.4721i	0.544898	−	0.482689i
$780$		0			0
$781$	−17.2634	−	29.9011i	−0.617733	−	1.06995i
$782$	−3.80894	+	6.59728i	−0.136208	+	0.235918i
$783$		0			0
$784$	16.5565	−	28.6767i	0.591304	−	1.02417i
$785$	−1.40191			−0.0500364
$786$		0			0
$787$	6.83990	+	11.8471i	0.243816	+	0.422302i	0.961798	−	0.273760i	$-0.0882673\pi$
$787$	6.83990	+	11.8471i	0.243816	+	0.422302i	−0.717982	+	0.696062i	$0.754934\pi$
$788$	6.43971	−	11.1539i	0.229405	−	0.397342i
$789$		0			0
$790$	−0.396826	+	0.687323i	−0.0141184	+	0.0244538i
$791$	77.0353			2.73906
$792$		0			0
$793$	−6.53775	+	11.3237i	−0.232162	+	0.402117i
$794$	20.7301			0.735683
$795$		0			0
$796$	−13.0203			−0.461493
$797$	−16.5286	−	28.6283i	−0.585472	−	1.01407i	−0.994816	−	0.101687i	$-0.967576\pi$
$797$	−16.5286	−	28.6283i	−0.585472	−	1.01407i	0.409345	−	0.912380i	$-0.365757\pi$
$798$		0			0
$799$	−2.60342	+	4.50926i	−0.0921025	+	0.159526i
$800$	−11.5199	+	19.9530i	−0.407289	+	0.705445i
$801$		0			0
$802$	−9.20052	−	15.9358i	−0.324882	−	0.562712i
$803$	−13.5911	−	23.5404i	−0.479619	−	0.830724i
$804$		0			0
$805$	0.624376	+	1.08145i	0.0220064	+	0.0381161i
$806$	−28.5236	−	49.4044i	−1.00470	−	1.74019i
$807$		0			0
$808$	−15.0871			−0.530763
$809$	−18.9057			−0.664689			−0.332344	−	0.943158i	$-0.607840\pi$
$809$	−18.9057			−0.664689			−0.332344	+	0.943158i	$0.607840\pi$
$810$		0			0
$811$	13.0216	+	22.5541i	0.457250	+	0.791981i	0.998815	−	0.0486785i	$-0.0155010\pi$
$811$	13.0216	+	22.5541i	0.457250	+	0.791981i	−0.541564	+	0.840659i	$0.682168\pi$
$812$	−10.5572	−	18.2856i	−0.370485	−	0.641698i
$813$		0			0
$814$	46.1103			1.61617
$815$	−0.525690			−0.0184141
$816$		0			0
$817$	34.1081	+	11.3888i	1.19329	+	0.398445i
$818$	3.69905			0.129334
$819$		0			0
$820$	0.178954	−	0.309957i	0.00624933	−	0.0108242i
$821$	−49.7671			−1.73688			−0.868442	−	0.495791i	$-0.834878\pi$
$821$	−49.7671			−1.73688			−0.868442	+	0.495791i	$0.834878\pi$
$822$		0			0
$823$	1.97059	−	3.41317i	0.0686905	−	0.118975i	−0.829635	−	0.558307i	$-0.811451\pi$
$823$	1.97059	−	3.41317i	0.0686905	−	0.118975i	0.898325	+	0.439331i	$0.144785\pi$
$824$	0.101255	+	0.175379i	0.00352739	+	0.00610962i
$825$		0			0
$826$	6.33288			0.220349
$827$	−7.23337	−	12.5286i	−0.251529	−	0.435661i	0.712418	−	0.701755i	$-0.247600\pi$
$827$	−7.23337	−	12.5286i	−0.251529	−	0.435661i	−0.963947	+	0.266094i	$0.914267\pi$
$828$		0			0
$829$	48.5968			1.68784			0.843919	−	0.536471i	$-0.180243\pi$
$829$	48.5968			1.68784			0.843919	+	0.536471i	$0.180243\pi$
$830$	−1.00105			−0.0347470
$831$		0			0
$832$	−4.35932	+	7.55057i	−0.151132	+	0.261769i
$833$	−7.79680			−0.270143
$834$		0			0
$835$	0.162111	−	0.280784i	0.00561007	−	0.00971693i
$836$	14.2286	+	4.75098i	0.492106	+	0.164316i
$837$		0			0
$838$	−4.18754	+	7.25304i	−0.144656	+	0.250552i
$839$	−22.4248	−	38.8409i	−0.774191	−	1.34094i	−0.935248	−	0.353993i	$-0.884824\pi$
$839$	−22.4248	−	38.8409i	−0.774191	−	1.34094i	0.161057	−	0.986945i	$-0.448510\pi$
$840$		0			0
$841$	14.1257			0.487092
$842$	15.7630	−	27.3023i	0.543228	−	0.940898i
$843$		0			0
$844$	2.50267	−	4.33475i	0.0861454	−	0.149208i
$845$	0.153743	+	0.266290i	0.00528891	+	0.00916065i
$846$		0			0
$847$	−17.1117			−0.587966
$848$	−18.0596	+	31.2801i	−0.620169	+	1.07416i
$849$		0			0
$850$	9.92413			0.340395
$851$	−13.1892	+	22.8444i	−0.452120	+	0.783094i
$852$		0			0
$853$	−21.0063	−	36.3840i	−0.719243	−	1.24577i	−0.961300	−	0.275504i	$-0.911155\pi$
$853$	−21.0063	−	36.3840i	−0.719243	−	1.24577i	0.242057	−	0.970262i	$-0.422178\pi$
$854$	−20.1541			−0.689661
$855$		0			0
$856$	−21.9726			−0.751007
$857$	25.5045	+	44.1750i	0.871216	+	1.50899i	0.860740	+	0.509045i	$0.170001\pi$
$857$	25.5045	+	44.1750i	0.871216	+	1.50899i	0.0104765	+	0.999945i	$0.496665\pi$
$858$		0			0
$859$	−1.93382	+	3.34947i	−0.0659809	+	0.114282i	−0.897129	−	0.441769i	$-0.854351\pi$
$859$	−1.93382	+	3.34947i	−0.0659809	+	0.114282i	0.831148	+	0.556052i	$0.187684\pi$
$860$	0.633453			0.0216006
$861$		0			0
$862$	−2.82834	+	4.89882i	−0.0963335	+	0.166854i
$863$	−20.7446			−0.706153			−0.353077	−	0.935594i	$-0.614865\pi$
$863$	−20.7446			−0.706153			−0.353077	+	0.935594i	$0.614865\pi$
$864$		0			0
$865$	−0.635798	−	1.10124i	−0.0216178	−	0.0374431i
$866$	−22.9420	+	39.7367i	−0.779600	+	1.35031i
$867$		0			0
$868$	13.3319	−	23.0915i	0.452514	−	0.783777i
$869$	20.9950			0.712206
$870$		0			0
$871$	5.89338	+	10.2076i	0.199689	+	0.345872i
$872$	−18.2312	+	31.5774i	−0.617387	+	1.06934i
$873$		0			0
$874$	−21.1837	+	18.7652i	−0.716549	+	0.634743i
$875$	1.62807	−	2.81990i	0.0550388	−	0.0953300i
$876$		0			0
$877$	7.13060			0.240783			0.120392	−	0.992726i	$-0.461585\pi$
$877$	7.13060			0.240783			0.120392	+	0.992726i	$0.461585\pi$
$878$	2.04032	−	3.53393i	0.0688573	−	0.119264i
$879$		0			0
$880$	−1.73811			−0.0585917
$881$	52.1011			1.75533			0.877666	−	0.479273i	$-0.159099\pi$
$881$	52.1011			1.75533			0.877666	+	0.479273i	$0.159099\pi$
$882$		0			0
$883$	−5.80742	−	10.0588i	−0.195435	−	0.338504i	0.751608	−	0.659610i	$-0.229279\pi$
$883$	−5.80742	−	10.0588i	−0.195435	−	0.338504i	−0.947043	+	0.321106i	$0.895945\pi$
$884$	−4.14671			−0.139469
$885$		0			0
$886$	−15.7536	−	27.2861i	−0.529253	−	0.916694i
$887$	−18.7084	+	32.4040i	−0.628168	+	1.08802i	0.359751	+	0.933048i	$0.382862\pi$
$887$	−18.7084	+	32.4040i	−0.628168	+	1.08802i	−0.987919	+	0.154971i	$0.950472\pi$
$888$		0			0
$889$	−6.32650			−0.212184
$890$	0.659972	−	1.14310i	0.0221223	−	0.0383169i
$891$		0			0
$892$	−1.23707			−0.0414201
$893$	−14.4791	+	12.8261i	−0.484525	+	0.429208i
$894$		0			0
$895$	−1.97583			−0.0660446
$896$	−47.5343			−1.58801
$897$		0			0
$898$	5.22793	+	9.05505i	0.174458	+	0.302171i
$899$	27.2301	+	47.1639i	0.908175	+	1.57300i
$900$		0			0
$901$	8.50464			0.283331
$902$	−31.2231			−1.03961
$903$		0			0
$904$	−19.9557	−	34.5643i	−0.663716	−	1.14959i
$905$	−0.796780	−	1.38006i	−0.0264858	−	0.0458748i
$906$		0			0
$907$	29.8972	+	51.7834i	0.992719	+	1.71944i	0.600675	+	0.799493i	$0.294899\pi$
$907$	29.8972	+	51.7834i	0.992719	+	1.71944i	0.392044	+	0.919946i	$0.371768\pi$
$908$	−11.3449	−	19.6499i	−0.376492	−	0.652104i
$909$		0			0
$910$	−1.12082	+	1.94131i	−0.0371547	+	0.0643538i
$911$	10.5600	−	18.2904i	0.349868	−	0.605990i	−0.636358	−	0.771394i	$-0.719560\pi$
$911$	10.5600	−	18.2904i	0.349868	−	0.605990i	0.986226	+	0.165405i	$0.0528930\pi$
$912$		0			0
$913$	13.2407	+	22.9336i	0.438204	+	0.758992i
$914$	24.7007			0.817026
$915$		0			0
$916$	13.4026			0.442835
$917$	−23.1144	+	40.0353i	−0.763305	+	1.32208i
$918$		0			0
$919$	40.4576			1.33457			0.667286	−	0.744801i	$-0.267456\pi$
$919$	40.4576			1.33457			0.667286	+	0.744801i	$0.267456\pi$
$920$	0.323484	−	0.560291i	0.0106650	−	0.0184722i
$921$		0			0
$922$	13.8206	−	23.9380i	0.455158	−	0.788357i
$923$	17.7282	+	30.7061i	0.583531	+	1.01071i
$924$		0			0
$925$	34.3642			1.12989
$926$	−7.36461	+	12.7559i	−0.242016	+	0.419184i
$927$		0			0
$928$	−15.1538	+	26.2472i	−0.497448	+	0.861606i
$929$	15.9331	+	27.5970i	0.522749	+	0.905428i	0.999650	+	0.0264707i	$0.00842688\pi$
$929$	15.9331	+	27.5970i	0.522749	+	0.905428i	−0.476900	+	0.878957i	$0.658240\pi$
$930$		0			0
$931$	−27.4735	−	9.17350i	−0.900406	−	0.300649i
$932$	−2.53842	−	4.39667i	−0.0831487	−	0.144018i
$933$		0			0
$934$	28.8588	+	49.9850i	0.944290	+	1.63556i
$935$	0.204628	+	0.354426i	0.00669206	+	0.0115910i
$936$		0			0
$937$	11.5489	+	20.0033i	0.377287	+	0.653480i	0.990666	−	0.136308i	$-0.0435238\pi$
$937$	11.5489	+	20.0033i	0.377287	+	0.653480i	−0.613380	+	0.789788i	$0.710190\pi$
$938$	−9.08386	+	15.7337i	−0.296598	+	0.513724i
$939$		0			0
$940$	−0.170372	+	0.295093i	−0.00555692	+	0.00962486i
$941$	−15.5342	+	26.9060i	−0.506401	+	0.877112i	0.493572	+	0.869705i	$0.335691\pi$
$941$	−15.5342	+	26.9060i	−0.506401	+	0.877112i	−0.999973	+	0.00740681i	$0.997642\pi$
$942$		0			0
$943$	8.93091	−	15.4688i	0.290830	−	0.503733i
$944$	−2.52129	−	4.36700i	−0.0820610	−	0.142134i
$945$		0			0
$946$	−27.6305	−	47.8575i	−0.898346	−	1.55598i
$947$	5.67769	+	9.83404i	0.184500	+	0.319563i	0.943408	−	0.331635i	$-0.107600\pi$
$947$	5.67769	+	9.83404i	0.184500	+	0.319563i	−0.758908	+	0.651198i	$0.774267\pi$
$948$		0			0
$949$	13.9570	+	24.1742i	0.453063	+	0.784729i
$950$	34.9695	+	11.6765i	1.13456	+	0.378834i
$951$		0			0
$952$	4.14739	+	7.18349i	0.134418	+	0.232818i
$953$	9.40930	−	16.2974i	0.304797	−	0.527924i	−0.672419	−	0.740171i	$-0.734745\pi$
$953$	9.40930	−	16.2974i	0.304797	−	0.527924i	0.977216	+	0.212246i	$0.0680780\pi$
$954$		0			0
$955$	0.248145	−	0.429800i	0.00802978	−	0.0139080i
$956$	23.8450			0.771203
$957$		0			0
$958$	−0.0180556	−	0.0312732i	−0.000583349	−	0.00101039i
$959$	39.5230	−	68.4558i	1.27626	−	2.21055i
$960$		0			0
$961$	−18.8869	+	32.7130i	−0.609253	+	1.05526i
$962$	−47.3518			−1.52668
$963$		0			0
$964$	−0.968833	+	1.67807i	−0.0312040	+	0.0540469i
$965$	0.679622			0.0218778
$966$		0			0
$967$	−48.7059			−1.56628			−0.783139	−	0.621847i	$-0.786382\pi$
$967$	−48.7059			−1.56628			−0.783139	+	0.621847i	$0.786382\pi$
$968$	4.43272	+	7.67770i	0.142473	+	0.246771i
$969$		0			0
$970$	0.133757	−	0.231675i	0.00429469	−	0.00743863i
$971$	5.20889	−	9.02206i	0.167161	−	0.289532i	−0.770260	−	0.637731i	$-0.779873\pi$
$971$	5.20889	−	9.02206i	0.167161	−	0.289532i	0.937421	+	0.348199i	$0.113207\pi$
$972$		0			0
$973$	−31.4030	−	54.3916i	−1.00673	−	1.74372i
$974$	−22.2166	−	38.4803i	−0.711866	−	1.23299i
$975$		0			0
$976$	8.02390	+	13.8978i	0.256839	+	0.444858i
$977$	22.5356	+	39.0327i	0.720977	+	1.24877i	0.960609	+	0.277904i	$0.0896398\pi$
$977$	22.5356	+	39.0327i	0.720977	+	1.24877i	−0.239632	+	0.970864i	$0.577027\pi$
$978$		0			0
$979$	−34.9173			−1.11596
$980$	−0.510235			−0.0162988
$981$		0			0
$982$	−18.4494	−	31.9553i	−0.588744	−	1.01973i
$983$	9.19187	+	15.9208i	0.293175	+	0.507794i	0.974559	−	0.224132i	$-0.0719547\pi$
$983$	9.19187	+	15.9208i	0.293175	+	0.507794i	−0.681383	+	0.731927i	$0.738621\pi$
$984$		0			0
$985$	1.30535			0.0415919
$986$	13.0547			0.415746
$987$		0			0
$988$	−14.6117	−	4.87890i	−0.464859	−	0.155218i
$989$	31.6133			1.00524
$990$		0			0
$991$	9.81862	−	17.0064i	0.311899	−	0.540225i	−0.666875	−	0.745170i	$-0.732368\pi$
$991$	9.81862	−	17.0064i	0.311899	−	0.540225i	0.978773	+	0.204945i	$0.0657016\pi$
$992$	−38.2733			−1.21518
$993$		0			0
$994$	−27.3257	+	47.3295i	−0.866718	+	1.50120i
$995$	−0.659815	−	1.14283i	−0.0209176	−	0.0362303i
$996$		0			0
$997$	−43.9149			−1.39080			−0.695399	−	0.718624i	$-0.744772\pi$
$997$	−43.9149			−1.39080			−0.695399	+	0.718624i	$0.744772\pi$
$998$	−21.4786	−	37.2020i	−0.679893	−	1.17761i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	513.2.g.c.505.5		32
3.2	odd	2		171.2.g.c.106.12	✓	32
9.4	even	3		513.2.h.c.334.12		32
9.5	odd	6		171.2.h.c.49.5	yes	32
19.7	even	3		513.2.h.c.235.12		32
57.26	odd	6		171.2.h.c.7.5	yes	32
171.121	even	3	inner	513.2.g.c.64.5		32
171.140	odd	6		171.2.g.c.121.12	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
171.2.g.c.106.12	✓	32	3.2	odd	2
171.2.g.c.121.12	yes	32	171.140	odd	6
171.2.h.c.7.5	yes	32	57.26	odd	6
171.2.h.c.49.5	yes	32	9.5	odd	6
513.2.g.c.64.5		32	171.121	even	3	inner
513.2.g.c.505.5		32	1.1	even	1	trivial
513.2.h.c.235.12		32	19.7	even	3
513.2.h.c.334.12		32	9.4	even	3

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:	\( N \)	\(=\)	\( 513 = 3^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	513.g (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.847114 - 1.46725i) q^{2} +(-0.435206 + 0.753799i) q^{4} -0.0882176 q^{5} +(1.84695 - 3.19901i) q^{7} -1.91378 q^{8} +(0.0747304 + 0.129437i) q^{10} +(1.97689 - 3.42408i) q^{11} +(-2.03012 + 3.51627i) q^{13} -6.25832 q^{14} +(2.49160 + 4.31558i) q^{16} +(0.586674 - 1.01615i) q^{17} +(3.26283 - 2.89032i) q^{19} +(0.0383928 - 0.0664983i) q^{20} -6.69862 q^{22} +(1.91604 - 3.31868i) q^{23} -4.99222 q^{25} +6.87897 q^{26} +(1.60761 + 2.78446i) q^{28} -6.56701 q^{29} +(-4.14650 - 7.18194i) q^{31} +(2.30757 - 3.99682i) q^{32} -1.98792 q^{34} +(-0.162934 + 0.282209i) q^{35} -6.88356 q^{37} +(-7.00480 - 2.33893i) q^{38} +0.168829 q^{40} +4.66112 q^{41} +(4.12481 + 7.14438i) q^{43} +(1.72071 + 2.98036i) q^{44} -6.49243 q^{46} -4.43759 q^{47} +(-3.32246 - 5.75467i) q^{49} +(4.22898 + 7.32481i) q^{50} +(-1.76704 - 3.06060i) q^{52} +(3.62409 + 6.27711i) q^{53} +(-0.174397 + 0.302064i) q^{55} +(-3.53466 + 6.12221i) q^{56} +(5.56301 + 9.63542i) q^{58} -1.01191 q^{59} +3.22038 q^{61} +(-7.02511 + 12.1679i) q^{62} +2.14732 q^{64} +(0.179092 - 0.310197i) q^{65} +(1.45149 - 2.51405i) q^{67} +(0.510648 + 0.884469i) q^{68} +0.552094 q^{70} +(4.36630 - 7.56265i) q^{71} +(3.43748 - 5.95390i) q^{73} +(5.83116 + 10.0999i) q^{74} +(0.758720 + 3.71740i) q^{76} +(-7.30245 - 12.6482i) q^{77} +(2.65505 + 4.59868i) q^{79} +(-0.219803 - 0.380711i) q^{80} +(-3.94850 - 6.83901i) q^{82} +(-3.34887 + 5.80042i) q^{83} +(-0.0517550 + 0.0896423i) q^{85} +(6.98837 - 12.1042i) q^{86} +(-3.78334 + 6.55294i) q^{88} +(-4.41568 - 7.64818i) q^{89} +(7.49906 + 12.9888i) q^{91} +(1.66775 + 2.88862i) q^{92} +(3.75915 + 6.51104i) q^{94} +(-0.287839 + 0.254977i) q^{95} +(-0.894933 - 1.55007i) q^{97} +(-5.62901 + 9.74973i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - q^{2} - 17 q^{4} + 6 q^{5} + q^{7} + 36 q^{8} - 8 q^{10} - 7 q^{11} - 4 q^{13} + 2 q^{14} - 11 q^{16} + 7 q^{17} + 7 q^{19} + 3 q^{20} + 16 q^{22} - 5 q^{23} + 18 q^{25} + 4 q^{26} - 10 q^{28}+ \cdots - 18 q^{98}+O(q^{100}) \) 32 * q - q^2 - 17 * q^4 + 6 * q^5 + q^7 + 36 * q^8 - 8 * q^10 - 7 * q^11 - 4 * q^13 + 2 * q^14 - 11 * q^16 + 7 * q^17 + 7 * q^19 + 3 * q^20 + 16 * q^22 - 5 * q^23 + 18 * q^25 + 4 * q^26 - 10 * q^28 + 20 * q^29 - 10 * q^31 - 17 * q^32 + 26 * q^34 + 3 * q^35 + 2 * q^37 - 38 * q^38 - 24 * q^40 + 12 * q^41 + 7 * q^43 - 20 * q^44 - 18 * q^47 - 13 * q^49 - q^50 + 19 * q^52 - 16 * q^53 + 15 * q^55 + 6 * q^56 + 74 * q^59 + 24 * q^61 - 54 * q^62 - 64 * q^64 - 54 * q^65 - 11 * q^67 + 2 * q^68 - 48 * q^70 - 9 * q^71 - 10 * q^73 - 6 * q^74 + 29 * q^76 - 46 * q^77 - 8 * q^79 + 24 * q^80 + 7 * q^82 - 3 * q^83 - 27 * q^85 - 17 * q^86 + 9 * q^88 - 30 * q^89 - q^91 + 17 * q^92 - 18 * q^94 + 6 * q^95 - 18 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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