LMFDB - Embedded newform 1008.2.bf.i.31.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1008,2,Mod(31,1008)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1008, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 0, 2, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1008.31"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.bf (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,0,0,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.4
Character	$\chi$	$=$	1008.31
Dual form			1008.2.bf.i.943.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.14316 + 1.30123i) q^{3} +4.29566i q^{5} +(0.334043 - 2.62458i) q^{7} +(-0.386381 - 2.97501i) q^{9} -3.60507i q^{11} +(-4.45873 - 2.57425i) q^{13} +(-5.58963 - 4.91062i) q^{15} +(-0.886675 - 0.511922i) q^{17} +(0.662930 + 1.14823i) q^{19} +(3.03331 + 3.43497i) q^{21} -3.14466i q^{23} -13.4527 q^{25} +(4.31286 + 2.89814i) q^{27} +(-0.373020 - 0.646090i) q^{29} +(-4.64826 - 8.05102i) q^{31} +(4.69102 + 4.12117i) q^{33} +(11.2743 + 1.43494i) q^{35} +(-0.761414 - 1.31881i) q^{37} +(8.44671 - 2.85904i) q^{39} +(4.22328 + 2.43831i) q^{41} +(6.14560 - 3.54817i) q^{43} +(12.7796 - 1.65976i) q^{45} +(-3.70487 + 6.41703i) q^{47} +(-6.77683 - 1.75345i) q^{49} +(1.67974 - 0.568557i) q^{51} +(-0.0746200 + 0.129246i) q^{53} +15.4862 q^{55} +(-2.25194 - 0.449984i) q^{57} +(0.996973 + 1.72681i) q^{59} +(5.05446 + 2.91820i) q^{61} +(-7.93723 + 0.0203037i) q^{63} +(11.0581 - 19.1532i) q^{65} +(-7.86136 + 4.53876i) q^{67} +(4.09191 + 3.59484i) q^{69} -11.3710i q^{71} +(4.04560 + 2.33573i) q^{73} +(15.3785 - 17.5050i) q^{75} +(-9.46180 - 1.20425i) q^{77} +(-9.68102 - 5.58934i) q^{79} +(-8.70142 + 2.29898i) q^{81} +(-6.90574 - 11.9611i) q^{83} +(2.19904 - 3.80885i) q^{85} +(1.26713 + 0.253199i) q^{87} +(14.0722 - 8.12459i) q^{89} +(-8.24573 + 10.8424i) q^{91} +(15.7899 + 3.15515i) q^{93} +(-4.93240 + 2.84772i) q^{95} +(-6.25228 + 3.60975i) q^{97} +(-10.7251 + 1.39293i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 4 q^{9} - 6 q^{13} - 18 q^{17} - 8 q^{21} - 32 q^{25} - 12 q^{29} + 30 q^{33} + 2 q^{37} + 36 q^{41} + 30 q^{45} + 2 q^{49} - 12 q^{53} - 46 q^{57} + 42 q^{61} + 18 q^{65} - 42 q^{69} - 66 q^{77}+ \cdots - 6 q^{97}+O(q^{100}) $ 32 * q - 4 * q^9 - 6 * q^13 - 18 * q^17 - 8 * q^21 - 32 * q^25 - 12 * q^29 + 30 * q^33 + 2 * q^37 + 36 * q^41 + 30 * q^45 + 2 * q^49 - 12 * q^53 - 46 * q^57 + 42 * q^61 + 18 * q^65 - 42 * q^69 - 66 * q^77 - 16 * q^81 - 12 * q^85 - 18 * q^89 + 58 * q^93 - 6 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{1}{3}\right)$

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			0
$2$		0			0
$3$	−1.14316	+	1.30123i	−0.660002	+	0.751263i
$3$	−1.14316	+	1.30123i	−0.660002	+	0.751263i
$4$		0			0
$5$			4.29566i			1.92108i	0.278147	+	0.960539i	$0.410280\pi$
$5$			4.29566i			1.92108i	−0.278147	+	0.960539i	$0.589720\pi$
$6$		0			0
$7$	0.334043	−	2.62458i	0.126256	−	0.991998i
$7$	0.334043	−	2.62458i	0.126256	−	0.991998i
$8$		0			0
$9$	−0.386381	−	2.97501i	−0.128794	−	0.991671i
$10$		0			0
$11$		−	3.60507i		−	1.08697i	−0.839419	−	0.543485i	$-0.817104\pi$
$11$		−	3.60507i		−	1.08697i	0.839419	−	0.543485i	$-0.182896\pi$
$12$		0			0
$13$	−4.45873	−	2.57425i	−1.23663	−	0.713968i	−0.268225	−	0.963356i	$-0.586437\pi$
$13$	−4.45873	−	2.57425i	−1.23663	−	0.713968i	−0.968404	+	0.249388i	$0.919770\pi$
$14$		0			0
$15$	−5.58963	−	4.91062i	−1.44324	−	1.26792i
$16$		0			0
$17$	−0.886675	−	0.511922i	−0.215050	−	0.124159i	0.388606	−	0.921404i	$-0.372957\pi$
$17$	−0.886675	−	0.511922i	−0.215050	−	0.124159i	−0.603656	+	0.797245i	$0.706290\pi$
$18$		0			0
$19$	0.662930	+	1.14823i	0.152087	+	0.263422i	0.931994	−	0.362473i	$-0.118067\pi$
$19$	0.662930	+	1.14823i	0.152087	+	0.263422i	−0.779908	+	0.625894i	$0.784734\pi$
$20$		0			0
$21$	3.03331	+	3.43497i	0.661922	+	0.749573i
$22$		0			0
$23$		−	3.14466i		−	0.655706i	−0.944729	−	0.327853i	$-0.893675\pi$
$23$		−	3.14466i		−	0.655706i	0.944729	−	0.327853i	$-0.106325\pi$
$24$		0			0
$25$	−13.4527			−2.69054
$26$		0			0
$27$	4.31286	+	2.89814i	0.830011	+	0.557748i
$28$		0			0
$29$	−0.373020	−	0.646090i	−0.0692681	−	0.119976i	0.829311	−	0.558787i	$-0.188733\pi$
$29$	−0.373020	−	0.646090i	−0.0692681	−	0.119976i	−0.898579	+	0.438811i	$0.855400\pi$
$30$		0			0
$31$	−4.64826	−	8.05102i	−0.834851	−	1.44601i	−0.894151	−	0.447765i	$-0.852220\pi$
$31$	−4.64826	−	8.05102i	−0.834851	−	1.44601i	0.0592999	−	0.998240i	$-0.481113\pi$
$32$		0			0
$33$	4.69102	+	4.12117i	0.816601	+	0.717403i
$34$		0			0
$35$	11.2743	+	1.43494i	1.90570	+	0.242548i
$36$		0			0
$37$	−0.761414	−	1.31881i	−0.125176	−	0.216811i	0.796626	−	0.604473i	$-0.206616\pi$
$37$	−0.761414	−	1.31881i	−0.125176	−	0.216811i	−0.921802	+	0.387662i	$0.873283\pi$
$38$		0			0
$39$	8.44671	−	2.85904i	1.35256	−	0.457813i
$40$		0			0
$41$	4.22328	+	2.43831i	0.659565	+	0.380800i	0.792111	−	0.610377i	$-0.208982\pi$
$41$	4.22328	+	2.43831i	0.659565	+	0.380800i	−0.132546	+	0.991177i	$0.542315\pi$
$42$		0			0
$43$	6.14560	−	3.54817i	0.937196	−	0.541090i	0.0481156	−	0.998842i	$-0.484678\pi$
$43$	6.14560	−	3.54817i	0.937196	−	0.541090i	0.889080	+	0.457752i	$0.151345\pi$
$44$		0			0
$45$	12.7796	−	1.65976i	1.90508	−	0.247422i
$46$		0			0
$47$	−3.70487	+	6.41703i	−0.540411	+	0.936020i	0.458469	+	0.888710i	$0.348398\pi$
$47$	−3.70487	+	6.41703i	−0.540411	+	0.936020i	−0.998880	+	0.0473095i	$0.984935\pi$
$48$		0			0
$49$	−6.77683	−	1.75345i	−0.968119	−	0.250492i
$50$		0			0
$51$	1.67974	−	0.568557i	0.235210	−	0.0796139i
$52$		0			0
$53$	−0.0746200	+	0.129246i	−0.0102499	+	0.0177533i	−0.871105	−	0.491097i	$-0.836596\pi$
$53$	−0.0746200	+	0.129246i	−0.0102499	+	0.0177533i	0.860855	+	0.508850i	$0.169929\pi$
$54$		0			0
$55$	15.4862			2.08815
$56$		0			0
$57$	−2.25194	−	0.449984i	−0.298277	−	0.0596019i
$58$		0			0
$59$	0.996973	+	1.72681i	0.129795	+	0.224811i	0.923597	−	0.383365i	$-0.125235\pi$
$59$	0.996973	+	1.72681i	0.129795	+	0.224811i	−0.793802	+	0.608176i	$0.791901\pi$
$60$		0			0
$61$	5.05446	+	2.91820i	0.647158	+	0.373637i	0.787366	−	0.616485i	$-0.211444\pi$
$61$	5.05446	+	2.91820i	0.647158	+	0.373637i	−0.140209	+	0.990122i	$0.544777\pi$
$62$		0			0
$63$	−7.93723	+	0.0203037i	−0.999997	+	0.00255802i
$64$		0			0
$65$	11.0581	−	19.1532i	1.37159	−	2.37566i
$66$		0			0
$67$	−7.86136	+	4.53876i	−0.960418	+	0.554498i	−0.896302	−	0.443445i	$-0.853756\pi$
$67$	−7.86136	+	4.53876i	−0.960418	+	0.554498i	−0.0641164	+	0.997942i	$0.520423\pi$
$68$		0			0
$69$	4.09191	+	3.59484i	0.492608	+	0.432768i
$70$		0			0
$71$		−	11.3710i		−	1.34949i	−0.738052	−	0.674743i	$-0.764254\pi$
$71$		−	11.3710i		−	1.34949i	0.738052	−	0.674743i	$-0.235746\pi$
$72$		0			0
$73$	4.04560	+	2.33573i	0.473502	+	0.273377i	0.717705	−	0.696348i	$-0.245193\pi$
$73$	4.04560	+	2.33573i	0.473502	+	0.273377i	−0.244202	+	0.969724i	$0.578526\pi$
$74$		0			0
$75$	15.3785	−	17.5050i	1.77576	−	2.02130i
$76$		0			0
$77$	−9.46180	−	1.20425i	−1.07827	−	0.137237i
$78$		0			0
$79$	−9.68102	−	5.58934i	−1.08920	−	0.628850i	−0.155836	−	0.987783i	$-0.549807\pi$
$79$	−9.68102	−	5.58934i	−1.08920	−	0.628850i	−0.933363	+	0.358933i	$0.883141\pi$
$80$		0			0
$81$	−8.70142	+	2.29898i	−0.966824	+	0.255442i
$82$		0			0
$83$	−6.90574	−	11.9611i	−0.758003	−	1.31290i	−0.943867	−	0.330324i	$-0.892842\pi$
$83$	−6.90574	−	11.9611i	−0.758003	−	1.31290i	0.185864	−	0.982575i	$-0.440492\pi$
$84$		0			0
$85$	2.19904	−	3.80885i	0.238520	−	0.413128i
$86$		0			0
$87$	1.26713	+	0.253199i	0.135851	+	0.0271458i
$88$		0			0
$89$	14.0722	−	8.12459i	1.49165	−	0.861205i	0.491697	−	0.870767i	$-0.336377\pi$
$89$	14.0722	−	8.12459i	1.49165	−	0.861205i	0.999954	+	0.00956141i	$0.00304354\pi$
$90$		0			0
$91$	−8.24573	+	10.8424i	−0.864387	+	1.13659i
$92$		0			0
$93$	15.7899	+	3.15515i	1.63733	+	0.327173i
$94$		0			0
$95$	−4.93240	+	2.84772i	−0.506053	+	0.292170i
$96$		0			0
$97$	−6.25228	+	3.60975i	−0.634822	+	0.366515i	−0.782617	−	0.622503i	$-0.786116\pi$
$97$	−6.25228	+	3.60975i	−0.634822	+	0.366515i	0.147795	+	0.989018i	$0.452782\pi$
$98$		0			0
$99$	−10.7251	+	1.39293i	−1.07792	+	0.139995i
$100$		0			0
$101$			9.00333i			0.895865i	0.894067	+	0.447932i	$0.147839\pi$
$101$			9.00333i			0.895865i	−0.894067	+	0.447932i	$0.852161\pi$
$102$		0			0
$103$	−9.29530			−0.915893			−0.457947	−	0.888980i	$-0.651415\pi$
$103$	−9.29530			−0.915893			−0.457947	+	0.888980i	$0.651415\pi$
$104$		0			0
$105$	−14.7555	+	13.0301i	−1.43999	+	1.27160i
$106$		0			0
$107$	−4.62335	+	2.66929i	−0.446956	+	0.258050i	−0.706544	−	0.707669i	$-0.749747\pi$
$107$	−4.62335	+	2.66929i	−0.446956	+	0.258050i	0.259588	+	0.965720i	$0.416413\pi$
$108$		0			0
$109$	−2.66385	+	4.61393i	−0.255151	+	0.441934i	−0.964936	−	0.262484i	$-0.915458\pi$
$109$	−2.66385	+	4.61393i	−0.255151	+	0.441934i	0.709786	+	0.704418i	$0.248792\pi$
$110$		0			0
$111$	2.58648	+	0.516833i	0.245498	+	0.0490556i
$112$		0			0
$113$	5.83794	−	10.1116i	0.549187	−	0.951221i	−0.449143	−	0.893460i	$-0.648271\pi$
$113$	5.83794	−	10.1116i	0.549187	−	0.951221i	0.998330	−	0.0577607i	$-0.0183960\pi$
$114$		0			0
$115$	13.5084			1.25966
$116$		0			0
$117$	−5.93566	+	14.2594i	−0.548752	+	1.31828i
$118$		0			0
$119$	−1.63977	+	2.15614i	−0.150317	+	0.197653i
$120$		0			0
$121$	−1.99655			−0.181504
$122$		0			0
$123$	−8.00066	+	2.70807i	−0.721395	+	0.244178i
$124$		0			0
$125$		−	36.3099i		−	3.24765i
$126$		0			0
$127$			13.4887i			1.19693i	0.801150	+	0.598463i	$0.204222\pi$
$127$			13.4887i			1.19693i	−0.801150	+	0.598463i	$0.795778\pi$
$128$		0			0
$129$	−2.40843	+	12.0529i	−0.212050	+	1.06120i
$130$		0			0
$131$	−16.5823			−1.44880			−0.724399	−	0.689381i	$-0.757883\pi$
$131$	−16.5823			−1.44880			−0.724399	+	0.689381i	$0.757883\pi$
$132$		0			0
$133$	3.23506	−	1.35635i	0.280516	−	0.117611i
$134$		0			0
$135$	−12.4494	+	18.5266i	−1.07148	+	1.59451i
$136$		0			0
$137$	5.97903			0.510823			0.255411	−	0.966832i	$-0.417789\pi$
$137$	5.97903			0.510823			0.255411	+	0.966832i	$0.417789\pi$
$138$		0			0
$139$	8.75126	−	15.1576i	0.742272	−	1.28565i	−0.209187	−	0.977876i	$-0.567082\pi$
$139$	8.75126	−	15.1576i	0.742272	−	1.28565i	0.951459	−	0.307777i	$-0.0995850\pi$
$140$		0			0
$141$	−4.11475	−	12.1566i	−0.346525	−	1.02377i
$142$		0			0
$143$	−9.28035	+	16.0740i	−0.776062	+	1.34418i
$144$		0			0
$145$	2.77538	−	1.60237i	0.230483	−	0.133069i
$146$		0			0
$147$	10.0286	−	6.81373i	0.827146	−	0.561987i
$148$		0			0
$149$	−15.1776			−1.24339			−0.621697	−	0.783258i	$-0.713556\pi$
$149$	−15.1776			−1.24339			−0.621697	+	0.783258i	$0.713556\pi$
$150$		0			0
$151$		−	7.04117i		−	0.573003i	−0.958080	−	0.286501i	$-0.907508\pi$
$151$		−	7.04117i		−	0.573003i	0.958080	−	0.286501i	$-0.0924923\pi$
$152$		0			0
$153$	−1.18038	+	2.83567i	−0.0954281	+	0.229250i
$154$		0			0
$155$	34.5844	−	19.9673i	2.77789	−	1.60381i
$156$		0			0
$157$	−13.7064	+	7.91337i	−1.09389	+	0.631556i	−0.934609	−	0.355678i	$-0.884250\pi$
$157$	−13.7064	+	7.91337i	−1.09389	+	0.631556i	−0.159278	+	0.987234i	$0.550917\pi$
$158$		0			0
$159$	−0.0828755	−	0.244846i	−0.00657245	−	0.0194175i
$160$		0			0
$161$	−8.25340	−	1.05045i	−0.650459	−	0.0827871i
$162$		0			0
$163$	9.98202	−	5.76312i	0.781852	−	0.451403i	−0.0552341	−	0.998473i	$-0.517591\pi$
$163$	9.98202	−	5.76312i	0.781852	−	0.451403i	0.837086	+	0.547071i	$0.184257\pi$
$164$		0			0
$165$	−17.7031	+	20.1510i	−1.37819	+	1.56875i
$166$		0			0
$167$	−3.14269	+	5.44330i	−0.243189	+	0.421215i	−0.961621	−	0.274382i	$-0.911527\pi$
$167$	−3.14269	+	5.44330i	−0.243189	+	0.421215i	0.718432	+	0.695597i	$0.244860\pi$
$168$		0			0
$169$	6.75351	+	11.6974i	0.519500	+	0.899801i
$170$		0			0
$171$	3.15985	−	2.41588i	0.241640	−	0.184747i
$172$		0			0
$173$	6.21442	+	3.58789i	0.472473	+	0.272783i	0.717274	−	0.696791i	$-0.245389\pi$
$173$	6.21442	+	3.58789i	0.472473	+	0.272783i	−0.244801	+	0.969573i	$0.578723\pi$
$174$		0			0
$175$	−4.49378	+	35.3076i	−0.339698	+	2.66901i
$176$		0			0
$177$	−3.38667	−	0.676726i	−0.254557	−	0.0508659i
$178$		0			0
$179$	17.9847	+	10.3835i	1.34424	+	0.776098i	0.987427	−	0.158077i	$-0.0505293\pi$
$179$	17.9847	+	10.3835i	1.34424	+	0.776098i	0.356815	+	0.934175i	$0.383863\pi$
$180$		0			0
$181$		−	13.7498i		−	1.02201i	−0.859577	−	0.511005i	$-0.829273\pi$
$181$		−	13.7498i		−	1.02201i	0.859577	−	0.511005i	$-0.170727\pi$
$182$		0			0
$183$	−9.57529	+	3.24104i	−0.707825	+	0.239585i
$184$		0			0
$185$	5.66515	−	3.27077i	0.416510	−	0.240472i
$186$		0			0
$187$	−1.84552	+	3.19653i	−0.134957	+	0.233753i
$188$		0			0
$189$	9.04708	−	10.3513i	0.658079	−	0.752949i
$190$		0			0
$191$	5.06422	+	2.92383i	0.366434	+	0.211561i	0.671899	−	0.740642i	$-0.265479\pi$
$191$	5.06422	+	2.92383i	0.366434	+	0.211561i	−0.305466	+	0.952203i	$0.598812\pi$
$192$		0			0
$193$	1.13564	+	1.96698i	0.0817448	+	0.141586i	0.903999	−	0.427534i	$-0.140617\pi$
$193$	1.13564	+	1.96698i	0.0817448	+	0.141586i	−0.822255	+	0.569120i	$0.807284\pi$
$194$		0			0
$195$	12.2815	+	36.2842i	0.879495	+	2.59836i
$196$		0			0
$197$	−9.34192			−0.665584			−0.332792	−	0.943000i	$-0.607991\pi$
$197$	−9.34192			−0.665584			−0.332792	+	0.943000i	$0.607991\pi$
$198$		0			0
$199$	−1.05079	+	1.82002i	−0.0744883	+	0.129017i	−0.900864	−	0.434102i	$-0.857066\pi$
$199$	−1.05079	+	1.82002i	−0.0744883	+	0.129017i	0.826375	+	0.563120i	$0.190399\pi$
$200$		0			0
$201$	3.08082	−	15.4179i	0.217304	−	1.08750i
$202$		0			0
$203$	−1.82032	+	0.763199i	−0.127761	+	0.0535660i
$204$		0			0
$205$	−10.4741	+	18.1418i	−0.731546	+	1.26707i
$206$		0			0
$207$	−9.35540	+	1.21503i	−0.650245	+	0.0844508i
$208$		0			0
$209$	4.13945	−	2.38991i	0.286332	−	0.165314i
$210$		0			0
$211$	8.07179	+	4.66025i	0.555685	+	0.320825i	0.751412	−	0.659834i	$-0.229373\pi$
$211$	8.07179	+	4.66025i	0.555685	+	0.320825i	−0.195727	+	0.980658i	$0.562707\pi$
$212$		0			0
$213$	14.7962	+	12.9988i	1.01382	+	0.890664i
$214$		0			0
$215$	15.2417	+	26.3994i	1.03948	+	1.80043i
$216$		0			0
$217$	−22.6832	+	9.51033i	−1.53984	+	0.645603i
$218$		0			0
$219$	−7.66408	+	2.59414i	−0.517890	+	0.175296i
$220$		0			0
$221$	2.63563	+	4.56504i	0.177292	+	0.307078i
$222$		0			0
$223$	3.87550	+	6.71256i	0.259523	+	0.449506i	0.966114	−	0.258115i	$-0.0831014\pi$
$223$	3.87550	+	6.71256i	0.259523	+	0.449506i	−0.706591	+	0.707622i	$0.749768\pi$
$224$		0			0
$225$	5.19786	+	40.0219i	0.346524	+	2.66813i
$226$		0			0
$227$	−18.3087			−1.21519			−0.607595	−	0.794247i	$-0.707866\pi$
$227$	−18.3087			−1.21519			−0.607595	+	0.794247i	$0.707866\pi$
$228$		0			0
$229$		−	22.2784i		−	1.47220i	−0.676874	−	0.736099i	$-0.736666\pi$
$229$		−	22.2784i		−	1.47220i	0.676874	−	0.736099i	$-0.263334\pi$
$230$		0			0
$231$	12.3833	−	10.9353i	0.814763	−	0.719489i
$232$		0			0
$233$	2.35026	+	4.07076i	0.153970	+	0.266684i	0.932684	−	0.360696i	$-0.117461\pi$
$233$	2.35026	+	4.07076i	0.153970	+	0.266684i	−0.778713	+	0.627380i	$0.784127\pi$
$234$		0			0
$235$	−27.5654	−	15.9149i	−1.79817	−	1.03817i
$236$		0			0
$237$	18.3399	−	6.20770i	1.19131	−	0.403233i
$238$		0			0
$239$	−9.76287	−	5.63659i	−0.631507	−	0.364601i	0.149828	−	0.988712i	$-0.452128\pi$
$239$	−9.76287	−	5.63659i	−0.631507	−	0.364601i	−0.781336	+	0.624111i	$0.785461\pi$
$240$		0			0
$241$		−	3.72908i		−	0.240211i	−0.992761	−	0.120106i	$-0.961677\pi$
$241$		−	3.72908i		−	0.240211i	0.992761	−	0.120106i	$-0.0383233\pi$
$242$		0			0
$243$	6.95561	−	13.9506i	0.446202	−	0.894932i
$244$		0			0
$245$	7.53220	−	29.1110i	0.481215	−	1.85983i
$246$		0			0
$247$		−	6.82619i		−	0.434340i
$248$		0			0
$249$	23.4584	+	4.68748i	1.48662	+	0.297057i
$250$		0			0
$251$	−12.5374			−0.791354			−0.395677	−	0.918390i	$-0.629490\pi$
$251$	−12.5374			−0.791354			−0.395677	+	0.918390i	$0.629490\pi$
$252$		0			0
$253$	−11.3367			−0.712733
$254$		0			0
$255$	2.44233	+	7.21557i	0.152944	+	0.451857i
$256$		0			0
$257$		−	15.4524i		−	0.963894i	−0.876200	−	0.481947i	$-0.839930\pi$
$257$		−	15.4524i		−	0.963894i	0.876200	−	0.481947i	$-0.160070\pi$
$258$		0			0
$259$	−3.71566	+	1.55785i	−0.230880	+	0.0968002i
$260$		0			0
$261$	−1.77800	+	1.35938i	−0.110055	+	0.0841433i
$262$		0			0
$263$		−	17.2727i		−	1.06508i	−0.846404	−	0.532541i	$-0.821237\pi$
$263$		−	17.2727i		−	1.06508i	0.846404	−	0.532541i	$-0.178763\pi$
$264$		0			0
$265$	−0.555196	−	0.320542i	−0.0341054	−	0.0196908i
$266$		0			0
$267$	−5.51482	+	27.5988i	−0.337501	+	1.68902i
$268$		0			0
$269$	8.06706	+	4.65752i	0.491857	+	0.283974i	0.725345	−	0.688386i	$-0.241680\pi$
$269$	8.06706	+	4.65752i	0.491857	+	0.283974i	−0.233487	+	0.972360i	$0.575014\pi$
$270$		0			0
$271$	−10.1759	−	17.6251i	−0.618140	−	1.07065i	−0.989825	−	0.142291i	$-0.954553\pi$
$271$	−10.1759	−	17.6251i	−0.618140	−	1.07065i	0.371685	−	0.928359i	$-0.378780\pi$
$272$		0			0
$273$	−4.68222	−	23.1241i	−0.283381	−	1.39953i
$274$		0			0
$275$			48.4979i			2.92453i
$276$		0			0
$277$	−32.6761			−1.96331			−0.981657	−	0.190654i	$-0.938939\pi$
$277$	−32.6761			−1.96331			−0.981657	+	0.190654i	$0.938939\pi$
$278$		0			0
$279$	−22.1559	+	16.9394i	−1.32644	+	1.01413i
$280$		0			0
$281$	10.8916	+	18.8647i	0.649736	+	1.12538i	0.983186	+	0.182609i	$0.0584541\pi$
$281$	10.8916	+	18.8647i	0.649736	+	1.12538i	−0.333449	+	0.942768i	$0.608213\pi$
$282$		0			0
$283$	−1.72157	−	2.98184i	−0.102336	−	0.177252i	0.810310	−	0.586001i	$-0.199298\pi$
$283$	−1.72157	−	2.98184i	−0.102336	−	0.177252i	−0.912647	+	0.408749i	$0.865965\pi$
$284$		0			0
$285$	1.93298	−	9.67356i	0.114500	−	0.573012i
$286$		0			0
$287$	7.81029	−	10.2698i	0.461027	−	0.606208i
$288$		0			0
$289$	−7.97587	−	13.8146i	−0.469169	−	0.812624i
$290$		0			0
$291$	2.45023	−	12.2621i	0.143635	−	0.718820i
$292$		0			0
$293$	17.0502	+	9.84397i	0.996086	+	0.575091i	0.907088	−	0.420941i	$-0.138300\pi$
$293$	17.0502	+	9.84397i	0.996086	+	0.575091i	0.0889983	+	0.996032i	$0.471633\pi$
$294$		0			0
$295$	−7.41778	+	4.28266i	−0.431880	+	0.249346i
$296$		0			0
$297$	10.4480	−	15.5482i	0.606255	−	0.902197i
$298$		0			0
$299$	−8.09513	+	14.0212i	−0.468153	+	0.810865i
$300$		0			0
$301$	−7.25954	−	17.3149i	−0.418433	−	0.998012i
$302$		0			0
$303$	−11.7154	−	10.2922i	−0.673030	−	0.591273i
$304$		0			0
$305$	−12.5356	+	21.7123i	−0.717785	+	1.24324i
$306$		0			0
$307$	−12.5054			−0.713719			−0.356859	−	0.934158i	$-0.616152\pi$
$307$	−12.5054			−0.713719			−0.356859	+	0.934158i	$0.616152\pi$
$308$		0			0
$309$	10.6260	−	12.0953i	0.604492	−	0.688077i
$310$		0			0
$311$	5.35524	+	9.27554i	0.303668	+	0.525968i	0.976964	−	0.213405i	$-0.0684554\pi$
$311$	5.35524	+	9.27554i	0.303668	+	0.525968i	−0.673296	+	0.739373i	$0.735122\pi$
$312$		0			0
$313$	−9.95819	−	5.74936i	−0.562870	−	0.324973i	0.191427	−	0.981507i	$-0.438689\pi$
$313$	−9.95819	−	5.74936i	−0.562870	−	0.324973i	−0.754297	+	0.656534i	$0.772022\pi$
$314$		0			0
$315$	−0.0872176	−	34.0956i	−0.00491416	−	1.92107i
$316$		0			0
$317$	−8.70784	+	15.0824i	−0.489081	+	0.847113i	−0.999921	−	0.0125628i	$-0.996001\pi$
$317$	−8.70784	+	15.0824i	−0.489081	+	0.847113i	0.510840	+	0.859676i	$0.329334\pi$
$318$		0			0
$319$	−2.32920	+	1.34476i	−0.130410	+	0.0752923i
$320$		0			0
$321$	1.81186	−	9.06745i	0.101128	−	0.506096i
$322$		0			0
$323$		−	1.35747i		−	0.0755319i
$324$		0			0
$325$	59.9819	+	34.6306i	3.32720	+	1.92096i
$326$		0			0
$327$	−2.95856	−	8.74072i	−0.163609	−	0.483363i
$328$		0			0
$329$	15.6044	+	11.8673i	0.860299	+	0.654265i
$330$		0			0
$331$	10.1816	+	5.87837i	0.559634	+	0.323105i	0.752998	−	0.658022i	$-0.228607\pi$
$331$	10.1816	+	5.87837i	0.559634	+	0.323105i	−0.193365	+	0.981127i	$0.561940\pi$
$332$		0			0
$333$	−3.62927	+	2.77478i	−0.198883	+	0.152057i
$334$		0			0
$335$	−19.4970	−	33.7697i	−1.06523	−	1.84504i
$336$		0			0
$337$	9.72282	−	16.8404i	0.529636	−	0.917356i	−0.469767	−	0.882791i	$-0.655662\pi$
$337$	9.72282	−	16.8404i	0.529636	−	0.917356i	0.999402	−	0.0345655i	$-0.0110047\pi$
$338$		0			0
$339$	6.48381	+	19.1557i	0.352152	+	1.04039i
$340$		0			0
$341$	−29.0245	+	16.7573i	−1.57176	+	0.907459i
$342$		0			0
$343$	−6.86581	+	17.2006i	−0.370719	+	0.928745i
$344$		0			0
$345$	−15.4422	+	17.5775i	−0.831380	+	0.946338i
$346$		0			0
$347$	8.58776	−	4.95814i	0.461015	−	0.266167i	−0.251456	−	0.967869i	$-0.580909\pi$
$347$	8.58776	−	4.95814i	0.461015	−	0.266167i	0.712471	+	0.701702i	$0.247576\pi$
$348$		0			0
$349$	8.22452	−	4.74843i	0.440248	−	0.254178i	−0.263455	−	0.964672i	$-0.584862\pi$
$349$	8.22452	−	4.74843i	0.440248	−	0.254178i	0.703703	+	0.710494i	$0.251529\pi$
$350$		0			0
$351$	−11.7693	−	24.0244i	−0.628201	−	1.28233i
$352$		0			0
$353$			7.38308i			0.392962i	0.980508	+	0.196481i	$0.0629514\pi$
$353$			7.38308i			0.392962i	−0.980508	+	0.196481i	$0.937049\pi$
$354$		0			0
$355$	48.8458			2.59247
$356$		0			0
$357$	−0.931119	−	4.59852i	−0.0492800	−	0.243380i
$358$		0			0
$359$	9.92939	−	5.73274i	0.524053	−	0.302562i	−0.214538	−	0.976716i	$-0.568825\pi$
$359$	9.92939	−	5.73274i	0.524053	−	0.302562i	0.738591	+	0.674153i	$0.235491\pi$
$360$		0			0
$361$	8.62105	−	14.9321i	0.453739	−	0.785900i
$362$		0			0
$363$	2.28237	−	2.59796i	0.119793	−	0.136357i
$364$		0			0
$365$	−10.0335	+	17.3785i	−0.525178	+	0.909634i
$366$		0			0
$367$	−26.7766			−1.39773			−0.698864	−	0.715254i	$-0.746311\pi$
$367$	−26.7766			−1.39773			−0.698864	+	0.715254i	$0.746311\pi$
$368$		0			0
$369$	5.62221	−	13.5064i	0.292681	−	0.703116i
$370$		0			0
$371$	0.314289	+	0.239020i	0.0163171	+	0.0124093i
$372$		0			0
$373$	−13.6607			−0.707323			−0.353662	−	0.935373i	$-0.615064\pi$
$373$	−13.6607			−0.707323			−0.353662	+	0.935373i	$0.615064\pi$
$374$		0			0
$375$	47.2474	+	41.5079i	2.43984	+	2.14346i
$376$		0			0
$377$			3.84098i			0.197821i
$378$		0			0
$379$			1.70006i			0.0873261i	0.999046	+	0.0436630i	$0.0139028\pi$
$379$			1.70006i			0.0873261i	−0.999046	+	0.0436630i	$0.986097\pi$
$380$		0			0
$381$	−17.5518	−	15.4197i	−0.899207	−	0.789974i
$382$		0			0
$383$	−20.6059			−1.05291			−0.526455	−	0.850203i	$-0.676479\pi$
$383$	−20.6059			−1.05291			−0.526455	+	0.850203i	$0.676479\pi$
$384$		0			0
$385$	5.17305	−	40.6447i	0.263643	−	2.07144i
$386$		0			0
$387$	−12.9304	−	16.9123i	−0.657289	−	0.859701i
$388$		0			0
$389$	−13.4475			−0.681814			−0.340907	−	0.940097i	$-0.610734\pi$
$389$	−13.4475			−0.681814			−0.340907	+	0.940097i	$0.610734\pi$
$390$		0			0
$391$	−1.60982	+	2.78829i	−0.0814120	+	0.141010i
$392$		0			0
$393$	18.9561	−	21.5773i	0.956211	−	1.08843i
$394$		0			0
$395$	24.0099	−	41.5863i	1.20807	−	2.09244i
$396$		0			0
$397$	−10.9040	+	6.29540i	−0.547254	+	0.315957i	−0.748014	−	0.663683i	$-0.768992\pi$
$397$	−10.9040	+	6.29540i	−0.547254	+	0.315957i	0.200760	+	0.979641i	$0.435659\pi$
$398$		0			0
$399$	−1.93326	+	5.76008i	−0.0967843	+	0.288365i
$400$		0			0
$401$	4.60899			0.230162			0.115081	−	0.993356i	$-0.463287\pi$
$401$	4.60899			0.230162			0.115081	+	0.993356i	$0.463287\pi$
$402$		0			0
$403$			47.8631i			2.38423i
$404$		0			0
$405$	−9.87562	−	37.3783i	−0.490724	−	1.85734i
$406$		0			0
$407$	−4.75439	+	2.74495i	−0.235667	+	0.136062i
$408$		0			0
$409$	−17.8209	+	10.2889i	−0.881187	+	0.508754i	−0.871050	−	0.491195i	$-0.836560\pi$
$409$	−17.8209	+	10.2889i	−0.881187	+	0.508754i	−0.0101377	+	0.999949i	$0.503227\pi$
$410$		0			0
$411$	−6.83497	+	7.78007i	−0.337144	+	0.383762i
$412$		0			0
$413$	4.86518	−	2.03981i	0.239400	−	0.100372i
$414$		0			0
$415$	51.3808	−	29.6647i	2.52218	−	1.45618i
$416$		0			0
$417$	9.71943	+	28.7149i	0.475963	+	1.40618i
$418$		0			0
$419$	−3.93303	+	6.81221i	−0.192141	+	0.332798i	−0.945960	−	0.324284i	$-0.894877\pi$
$419$	−3.93303	+	6.81221i	−0.192141	+	0.332798i	0.753818	+	0.657083i	$0.228210\pi$
$420$		0			0
$421$	10.8367	+	18.7697i	0.528149	+	0.914781i	0.999461	+	0.0328148i	$0.0104471\pi$
$421$	10.8367	+	18.7697i	0.528149	+	0.914781i	−0.471312	+	0.881966i	$0.656220\pi$
$422$		0			0
$423$	20.5222	+	8.54263i	0.997826	+	0.415357i
$424$		0			0
$425$	11.9282	+	6.88672i	0.578601	+	0.334055i
$426$		0			0
$427$	9.34745	−	12.2910i	0.452355	−	0.594805i
$428$		0			0
$429$	−10.3071	−	30.4510i	−0.497630	−	1.47019i
$430$		0			0
$431$	−0.640472	−	0.369776i	−0.0308504	−	0.0178115i	0.484495	−	0.874794i	$-0.339003\pi$
$431$	−0.640472	−	0.369776i	−0.0308504	−	0.0178115i	−0.515346	+	0.856982i	$0.672337\pi$
$432$		0			0
$433$		−	26.1089i		−	1.25471i	−0.778732	−	0.627357i	$-0.784137\pi$
$433$		−	26.1089i		−	1.25471i	0.778732	−	0.627357i	$-0.215863\pi$
$434$		0			0
$435$	−1.08766	+	5.44316i	−0.0521491	+	0.260979i
$436$		0			0
$437$	3.61078	−	2.08469i	0.172727	−	0.0997241i
$438$		0			0
$439$	−7.41381	+	12.8411i	−0.353842	+	0.612872i	−0.986919	−	0.161216i	$-0.948458\pi$
$439$	−7.41381	+	12.8411i	−0.353842	+	0.612872i	0.633077	+	0.774089i	$0.281792\pi$
$440$		0			0
$441$	−2.59809	+	20.8387i	−0.123718	+	0.992317i
$442$		0			0
$443$	−8.78723	−	5.07331i	−0.417494	−	0.241040i	0.276511	−	0.961011i	$-0.410822\pi$
$443$	−8.78723	−	5.07331i	−0.417494	−	0.241040i	−0.694005	+	0.719971i	$0.744155\pi$
$444$		0			0
$445$	34.9005	+	60.4494i	1.65444	+	2.86558i
$446$		0			0
$447$	17.3503	−	19.7494i	0.820643	−	0.934116i
$448$		0			0
$449$	25.0880			1.18397			0.591987	−	0.805948i	$-0.298344\pi$
$449$	25.0880			1.18397			0.591987	+	0.805948i	$0.298344\pi$
$450$		0			0
$451$	8.79028	−	15.2252i	0.413918	−	0.716927i
$452$		0			0
$453$	9.16216	+	8.04917i	0.430476	+	0.378183i
$454$		0			0
$455$	−46.5751	−	35.4208i	−2.18348	−	1.66055i
$456$		0			0
$457$	11.9988	−	20.7825i	0.561279	−	0.972163i	−0.436107	−	0.899895i	$-0.643643\pi$
$457$	11.9988	−	20.7825i	0.561279	−	0.972163i	0.997385	−	0.0722682i	$-0.0230237\pi$
$458$		0			0
$459$	−2.34048	−	4.77756i	−0.109244	−	0.222997i
$460$		0			0
$461$	−12.2178	+	7.05393i	−0.569038	+	0.328534i	−0.756765	−	0.653687i	$-0.773221\pi$
$461$	−12.2178	+	7.05393i	−0.569038	+	0.328534i	0.187727	+	0.982221i	$0.439888\pi$
$462$		0			0
$463$	12.0911	+	6.98080i	0.561921	+	0.324425i	0.753916	−	0.656971i	$-0.228163\pi$
$463$	12.0911	+	6.98080i	0.561921	+	0.324425i	−0.191995	+	0.981396i	$0.561496\pi$
$464$		0			0
$465$	−13.5534	+	67.8280i	−0.628526	+	3.14545i
$466$		0			0
$467$	13.2526	+	22.9542i	0.613258	+	1.06219i	0.990687	+	0.136156i	$0.0434748\pi$
$467$	13.2526	+	22.9542i	0.613258	+	1.06219i	−0.377429	+	0.926038i	$0.623192\pi$
$468$		0			0
$469$	9.28630	+	22.1489i	0.428801	+	1.02274i
$470$		0			0
$471$	5.37145	−	26.8813i	0.247503	−	1.23863i
$472$		0			0
$473$	−12.7914	−	22.1553i	−0.588149	−	1.01870i
$474$		0			0
$475$	−8.91819	−	15.4468i	−0.409195	−	0.708746i
$476$		0			0
$477$	0.413340	+	0.172058i	0.0189255	+	0.00787798i
$478$		0			0
$479$	39.0894			1.78604			0.893019	−	0.450018i	$-0.148582\pi$
$479$	39.0894			1.78604			0.893019	+	0.450018i	$0.148582\pi$
$480$		0			0
$481$			7.84027i			0.357486i
$482$		0			0
$483$	10.8018	−	9.53871i	0.491499	−	0.434026i
$484$		0			0
$485$	−15.5063	−	26.8576i	−0.704103	−	1.21954i
$486$		0			0
$487$	−6.79167	−	3.92117i	−0.307760	−	0.177685i	0.338164	−	0.941087i	$-0.390194\pi$
$487$	−6.79167	−	3.92117i	−0.307760	−	0.177685i	−0.645924	+	0.763402i	$0.723528\pi$
$488$		0			0
$489$	−3.91190	+	19.5770i	−0.176902	+	0.885304i
$490$		0			0
$491$	17.8659	+	10.3149i	0.806278	+	0.465505i	0.845662	−	0.533720i	$-0.179206\pi$
$491$	17.8659	+	10.3149i	0.806278	+	0.465505i	−0.0393839	+	0.999224i	$0.512540\pi$
$492$		0			0
$493$			0.763828i			0.0344011i
$494$		0			0
$495$	−5.98356	−	46.0716i	−0.268941	−	2.07076i
$496$		0			0
$497$	−29.8440	−	3.79840i	−1.33869	−	0.170381i
$498$		0			0
$499$		−	34.4187i		−	1.54079i	−0.637565	−	0.770397i	$-0.720058\pi$
$499$		−	34.4187i		−	1.54079i	0.637565	−	0.770397i	$-0.279942\pi$
$500$		0			0
$501$	−3.49038	−	10.3119i	−0.155939	−	0.460702i
$502$		0			0
$503$	25.7268			1.14710			0.573552	−	0.819169i	$-0.305565\pi$
$503$	25.7268			1.14710			0.573552	+	0.819169i	$0.305565\pi$
$504$		0			0
$505$	−38.6752			−1.72103
$506$		0			0
$507$	−22.9413	−	4.58415i	−1.01886	−	0.203589i
$508$		0			0
$509$		−	24.1729i		−	1.07144i	−0.844395	−	0.535722i	$-0.820040\pi$
$509$		−	24.1729i		−	1.07144i	0.844395	−	0.535722i	$-0.179960\pi$
$510$		0			0
$511$	7.48172	−	9.83777i	0.330972	−	0.435198i
$512$		0			0
$513$	−0.468603	+	6.87342i	−0.0206893	+	0.303469i
$514$		0			0
$515$		−	39.9294i		−	1.75950i
$516$		0			0
$517$	23.1339	+	13.3563i	1.01743	+	0.587411i
$518$		0			0
$519$	−11.7727	+	3.98483i	−0.516765	+	0.174915i
$520$		0			0
$521$	31.1079	+	17.9602i	1.36286	+	0.786849i	0.990004	−	0.141040i	$-0.0450445\pi$
$521$	31.1079	+	17.9602i	1.36286	+	0.786849i	0.372858	+	0.927888i	$0.378378\pi$
$522$		0			0
$523$	7.02897	+	12.1745i	0.307355	+	0.532355i	0.977783	−	0.209620i	$-0.0672226\pi$
$523$	7.02897	+	12.1745i	0.307355	+	0.532355i	−0.670428	+	0.741975i	$0.733889\pi$
$524$		0			0
$525$	−40.8061	−	46.2096i	−1.78093	−	2.01675i
$526$		0			0
$527$			9.51817i			0.414618i
$528$		0			0
$529$	13.1111			0.570049
$530$		0			0
$531$	4.75207	−	3.63322i	0.206222	−	0.157668i
$532$		0			0
$533$	−12.5536	−	21.7435i	−0.543758	−	0.941816i
$534$		0			0
$535$	−11.4664	−	19.8603i	−0.495735	−	0.858638i
$536$		0			0
$537$	−34.0707	+	11.5322i	−1.47026	+	0.497653i
$538$		0			0
$539$	−6.32130	+	24.4310i	−0.272278	+	1.05232i
$540$		0			0
$541$	−2.60496	−	4.51193i	−0.111996	−	0.193983i	0.804579	−	0.593846i	$-0.202391\pi$
$541$	−2.60496	−	4.51193i	−0.111996	−	0.193983i	−0.916575	+	0.399863i	$0.869058\pi$
$542$		0			0
$543$	17.8915	+	15.7181i	0.767800	+	0.674530i
$544$		0			0
$545$	−19.8199	−	11.4430i	−0.848989	−	0.490164i
$546$		0			0
$547$	−11.1833	+	6.45666i	−0.478162	+	0.276067i	−0.719650	−	0.694337i	$-0.755698\pi$
$547$	−11.1833	+	6.45666i	−0.478162	+	0.276067i	0.241488	+	0.970404i	$0.422365\pi$
$548$		0			0
$549$	6.72873	−	16.1646i	0.287175	−	0.689890i
$550$		0			0
$551$	0.494572	−	0.856625i	0.0210695	−	0.0364934i
$552$		0			0
$553$	−17.9035	+	23.5415i	−0.761336	+	1.00109i
$554$		0			0
$555$	−2.22014	+	11.1106i	−0.0942396	+	0.471621i
$556$		0			0
$557$	−12.6086	+	21.8388i	−0.534245	+	0.925339i	0.464955	+	0.885334i	$0.346071\pi$
$557$	−12.6086	+	21.8388i	−0.534245	+	0.925339i	−0.999199	+	0.0400045i	$0.987263\pi$
$558$		0			0
$559$	−36.5354			−1.54528
$560$		0			0
$561$	−2.04969	−	6.05557i	−0.0865380	−	0.255666i
$562$		0			0
$563$	−16.9925	−	29.4318i	−0.716148	−	1.24040i	−0.962515	−	0.271228i	$-0.912570\pi$
$563$	−16.9925	−	29.4318i	−0.716148	−	1.24040i	0.246367	−	0.969176i	$-0.420763\pi$
$564$		0			0
$565$	43.4360	+	25.0778i	1.82737	+	1.05503i
$566$		0			0
$567$	3.12720	+	23.6055i	0.131330	+	0.991339i
$568$		0			0
$569$	−13.3518	+	23.1260i	−0.559736	+	0.969490i	0.437783	+	0.899081i	$0.355764\pi$
$569$	−13.3518	+	23.1260i	−0.559736	+	0.969490i	−0.997518	+	0.0704095i	$0.977569\pi$
$570$		0			0
$571$	−24.4861	+	14.1371i	−1.02471	+	0.591618i	−0.915465	−	0.402397i	$-0.868177\pi$
$571$	−24.4861	+	14.1371i	−1.02471	+	0.591618i	−0.109247	+	0.994015i	$0.534844\pi$
$572$		0			0
$573$	−9.59376	+	3.24730i	−0.400785	+	0.135658i
$574$		0			0
$575$			42.3041i			1.76420i
$576$		0			0
$577$	−8.61528	−	4.97403i	−0.358659	−	0.207072i	0.309833	−	0.950791i	$-0.399727\pi$
$577$	−8.61528	−	4.97403i	−0.358659	−	0.207072i	−0.668492	+	0.743719i	$0.733060\pi$
$578$		0			0
$579$	−3.85770	−	0.770848i	−0.160320	−	0.0320353i
$580$		0			0
$581$	−33.6996	+	14.1291i	−1.39810	+	0.586175i
$582$		0			0
$583$	0.465940	+	0.269011i	0.0192973	+	0.0111413i
$584$		0			0
$585$	−61.2536	−	25.4976i	−2.53253	−	1.05419i
$586$		0			0
$587$	0.00256306	+	0.00443935i	0.000105789	+	0.000183231i	0.866078	−	0.499908i	$-0.166633\pi$
$587$	0.00256306	+	0.00443935i	0.000105789	+	0.000183231i	−0.865973	+	0.500092i	$0.833300\pi$
$588$		0			0
$589$	6.16294	−	10.6745i	0.253939	−	0.439836i
$590$		0			0
$591$	10.6793	−	12.1559i	0.439287	−	0.500029i
$592$		0			0
$593$	9.34883	−	5.39755i	0.383910	−	0.221651i	−0.295608	−	0.955309i	$-0.595522\pi$
$593$	9.34883	−	5.39755i	0.383910	−	0.221651i	0.679518	+	0.733659i	$0.262189\pi$
$594$		0			0
$595$	−9.26206	−	7.04388i	−0.379707	−	0.288771i
$596$		0			0
$597$	−1.16704	−	3.44788i	−0.0477637	−	0.141112i
$598$		0			0
$599$	16.2237	−	9.36674i	0.662881	−	0.382714i	−0.130493	−	0.991449i	$-0.541656\pi$
$599$	16.2237	−	9.36674i	0.662881	−	0.382714i	0.793374	+	0.608735i	$0.208323\pi$
$600$		0			0
$601$	37.3269	−	21.5507i	1.52260	−	0.879072i	0.522954	−	0.852361i	$-0.324830\pi$
$601$	37.3269	−	21.5507i	1.52260	−	0.879072i	0.999643	−	0.0267107i	$-0.00850329\pi$
$602$		0			0
$603$	16.5404	+	21.6340i	0.673575	+	0.881003i
$604$		0			0
$605$		−	8.57648i		−	0.348684i
$606$		0			0
$607$	30.9609			1.25666			0.628331	−	0.777946i	$-0.283738\pi$
$607$	30.9609			1.25666			0.628331	+	0.777946i	$0.283738\pi$
$608$		0			0
$609$	1.08782	−	3.24110i	0.0440805	−	0.131336i
$610$		0			0
$611$	33.0380	−	19.0745i	1.33658	−	0.771673i
$612$		0			0
$613$	15.9145	−	27.5646i	0.642779	−	1.11333i	−0.342031	−	0.939689i	$-0.611115\pi$
$613$	15.9145	−	27.5646i	0.642779	−	1.11333i	0.984810	−	0.173637i	$-0.0555519\pi$
$614$		0			0
$615$	−11.6329	−	34.3681i	−0.469085	−	1.38586i
$616$		0			0
$617$	−8.34757	+	14.4584i	−0.336060	+	0.582074i	−0.983688	−	0.179883i	$-0.942428\pi$
$617$	−8.34757	+	14.4584i	−0.336060	+	0.582074i	0.647627	+	0.761957i	$0.275761\pi$
$618$		0			0
$619$	8.08787			0.325079			0.162539	−	0.986702i	$-0.448032\pi$
$619$	8.08787			0.325079			0.162539	+	0.986702i	$0.448032\pi$
$620$		0			0
$621$	9.11366	−	13.5625i	0.365719	−	0.544243i
$622$		0			0
$623$	−16.6229	−	39.6476i	−0.665983	−	1.58845i
$624$		0			0
$625$	88.7114			3.54846
$626$		0			0
$627$	−1.62223	+	8.11840i	−0.0647855	+	0.324218i
$628$		0			0
$629$			1.55914i			0.0621669i
$630$		0			0
$631$		−	46.7312i		−	1.86034i	−0.367130	−	0.930170i	$-0.619660\pi$
$631$		−	46.7312i		−	1.86034i	0.367130	−	0.930170i	$-0.380340\pi$
$632$		0			0
$633$	−15.2914	+	5.17583i	−0.607778	+	0.205721i
$634$		0			0
$635$	−57.9427			−2.29939
$636$		0			0
$637$	25.7022	+	25.2634i	1.01836	+	1.00097i
$638$		0			0
$639$	−33.8288	+	4.39353i	−1.33825	+	0.173805i
$640$		0			0
$641$	−32.3555			−1.27796			−0.638982	−	0.769222i	$-0.720644\pi$
$641$	−32.3555			−1.27796			−0.638982	+	0.769222i	$0.720644\pi$
$642$		0			0
$643$	−7.92549	+	13.7273i	−0.312551	+	0.541354i	−0.978914	−	0.204274i	$-0.934517\pi$
$643$	−7.92549	+	13.7273i	−0.312551	+	0.541354i	0.666363	+	0.745627i	$0.267850\pi$
$644$		0			0
$645$	−51.7753	−	10.3458i	−2.03865	−	0.407365i
$646$		0			0
$647$	−22.9784	+	39.7997i	−0.903373	+	1.56469i	−0.0802858	+	0.996772i	$0.525583\pi$
$647$	−22.9784	+	39.7997i	−0.903373	+	1.56469i	−0.823087	+	0.567916i	$0.807750\pi$
$648$		0			0
$649$	6.22527	−	3.59416i	0.244363	−	0.141083i
$650$		0			0
$651$	13.5554	−	40.3878i	0.531279	−	1.58292i
$652$		0			0
$653$	28.4529			1.11345			0.556725	−	0.830697i	$-0.312058\pi$
$653$	28.4529			1.11345			0.556725	+	0.830697i	$0.312058\pi$
$654$		0			0
$655$		−	71.2317i		−	2.78325i
$656$		0			0
$657$	5.38569	−	12.9382i	0.210116	−	0.504768i
$658$		0			0
$659$	−24.8634	+	14.3549i	−0.968539	+	0.559186i	−0.898791	−	0.438378i	$-0.855553\pi$
$659$	−24.8634	+	14.3549i	−0.968539	+	0.559186i	−0.0697486	+	0.997565i	$0.522220\pi$
$660$		0			0
$661$	18.2524	−	10.5380i	0.709935	−	0.409881i	−0.101102	−	0.994876i	$-0.532237\pi$
$661$	18.2524	−	10.5380i	0.709935	−	0.409881i	0.811037	+	0.584995i	$0.198903\pi$
$662$		0			0
$663$	−8.95309	−	1.78901i	−0.347709	−	0.0694795i
$664$		0			0
$665$	5.82644	+	13.8967i	0.225940	+	0.538892i
$666$		0			0
$667$	−2.03173	+	1.17302i	−0.0786689	+	0.0454195i
$668$		0			0
$669$	−13.1649	−	2.63062i	−0.508983	−	0.101705i
$670$		0			0
$671$	10.5203	−	18.2217i	0.406132	−	0.703441i
$672$		0			0
$673$	−1.51490	−	2.62388i	−0.0583950	−	0.101143i	0.835350	−	0.549718i	$-0.185265\pi$
$673$	−1.51490	−	2.62388i	−0.0583950	−	0.101143i	−0.893745	+	0.448575i	$0.851932\pi$
$674$		0			0
$675$	−58.0196	−	38.9878i	−2.23317	−	1.50064i
$676$		0			0
$677$	30.8917	+	17.8353i	1.18726	+	0.685468i	0.957684	−	0.287822i	$-0.0929311\pi$
$677$	30.8917	+	17.8353i	1.18726	+	0.685468i	0.229581	+	0.973290i	$0.426264\pi$
$678$		0			0
$679$	7.38555	+	17.6154i	0.283431	+	0.676017i
$680$		0			0
$681$	20.9297	−	23.8237i	0.802028	−	0.912928i
$682$		0			0
$683$	14.7745	+	8.53004i	0.565329	+	0.326393i	0.755282	−	0.655400i	$-0.227500\pi$
$683$	14.7745	+	8.53004i	0.565329	+	0.326393i	−0.189952	+	0.981793i	$0.560833\pi$
$684$		0			0
$685$			25.6839i			0.981330i
$686$		0			0
$687$	28.9893	+	25.4677i	1.10601	+	0.971655i
$688$		0			0
$689$	0.665421	−	0.384181i	0.0253505	−	0.0146361i
$690$		0			0
$691$	2.03132	−	3.51835i	0.0772750	−	0.133844i	−0.824798	−	0.565427i	$-0.808711\pi$
$691$	2.03132	−	3.51835i	0.0772750	−	0.133844i	0.902073	+	0.431583i	$0.142045\pi$
$692$		0			0
$693$	0.0731962	+	28.6143i	0.00278049	+	1.08697i
$694$		0			0
$695$	65.1120	+	37.5924i	2.46984	+	1.42596i
$696$		0			0
$697$	−2.49645	−	4.32397i	−0.0945597	−	0.163782i
$698$		0			0
$699$	−7.98370	−	1.59531i	−0.301971	−	0.0603401i
$700$		0			0
$701$	40.4912			1.52933			0.764666	−	0.644427i	$-0.222904\pi$
$701$	40.4912			1.52933			0.764666	+	0.644427i	$0.222904\pi$
$702$		0			0
$703$	1.00953	−	1.74855i	0.0380751	−	0.0659480i
$704$		0			0
$705$	52.2204	−	17.6756i	1.96673	−	0.665701i
$706$		0			0
$707$	23.6299	+	3.00750i	0.888696	+	0.113109i
$708$		0			0
$709$	8.81206	−	15.2629i	0.330944	−	0.573212i	−0.651753	−	0.758431i	$-0.725966\pi$
$709$	8.81206	−	15.2629i	0.330944	−	0.573212i	0.982697	+	0.185219i	$0.0592996\pi$
$710$		0			0
$711$	−12.8878	+	30.9608i	−0.483330	+	1.16112i
$712$		0			0
$713$	−25.3177	+	14.6172i	−0.948155	+	0.547417i
$714$		0			0
$715$	−69.0486	−	39.8652i	−2.58227	−	1.49087i
$716$		0			0
$717$	18.4950	−	6.26019i	0.690708	−	0.233791i
$718$		0			0
$719$	−20.7748	−	35.9829i	−0.774768	−	1.34194i	−0.934925	−	0.354846i	$-0.884533\pi$
$719$	−20.7748	−	35.9829i	−0.774768	−	1.34194i	0.160157	−	0.987092i	$-0.448800\pi$
$720$		0			0
$721$	−3.10503	+	24.3963i	−0.115637	+	0.908564i
$722$		0			0
$723$	4.85238	+	4.26293i	0.180462	+	0.158540i
$724$		0			0
$725$	5.01812	+	8.69164i	0.186368	+	0.322799i
$726$		0			0
$727$	19.2047	+	33.2636i	0.712264	+	1.23368i	0.964005	+	0.265884i	$0.0856637\pi$
$727$	19.2047	+	33.2636i	0.712264	+	1.23368i	−0.251741	+	0.967795i	$0.581003\pi$
$728$		0			0
$729$	10.2016	+	24.9986i	0.377835	+	0.925873i
$730$		0			0
$731$	−7.26553			−0.268726
$732$		0			0
$733$			35.1602i			1.29867i	0.760501	+	0.649336i	$0.224953\pi$
$733$			35.1602i			1.29867i	−0.760501	+	0.649336i	$0.775047\pi$
$734$		0			0
$735$	29.2694	+	43.0795i	1.07962	+	1.58901i
$736$		0			0
$737$	16.3626	+	28.3408i	0.602722	+	1.04395i
$738$		0			0
$739$	14.6816	+	8.47640i	0.540070	+	0.311809i	0.745107	−	0.666945i	$-0.232398\pi$
$739$	14.6816	+	8.47640i	0.540070	+	0.311809i	−0.205037	+	0.978754i	$0.565732\pi$
$740$		0			0
$741$	8.88241	+	7.80341i	0.326304	+	0.286665i
$742$		0			0
$743$	23.2333	+	13.4138i	0.852349	+	0.492104i	0.861443	−	0.507855i	$-0.169561\pi$
$743$	23.2333	+	13.4138i	0.852349	+	0.492104i	−0.00909404	+	0.999959i	$0.502895\pi$
$744$		0			0
$745$		−	65.1976i		−	2.38866i
$746$		0			0
$747$	−32.9162	+	25.1662i	−1.20434	+	0.920783i
$748$		0			0
$749$	5.46137	+	13.0260i	0.199554	+	0.475960i
$750$		0			0
$751$		−	22.4872i		−	0.820569i	−0.911958	−	0.410285i	$-0.865429\pi$
$751$		−	22.4872i		−	0.820569i	0.911958	−	0.410285i	$-0.134571\pi$
$752$		0			0
$753$	14.3322	−	16.3140i	0.522295	−	0.594515i
$754$		0			0
$755$	30.2465			1.10078
$756$		0			0
$757$	27.2088			0.988921			0.494460	−	0.869200i	$-0.335366\pi$
$757$	27.2088			0.988921			0.494460	+	0.869200i	$0.335366\pi$
$758$		0			0
$759$	12.9597	−	14.7516i	0.470406	−	0.535450i
$760$		0			0
$761$			2.76386i			0.100190i	0.998744	+	0.0500949i	$0.0159524\pi$
$761$			2.76386i			0.100190i	−0.998744	+	0.0500949i	$0.984048\pi$
$762$		0			0
$763$	11.2198	+	8.53274i	0.406183	+	0.308906i
$764$		0			0
$765$	−12.1811	−	5.07051i	−0.440407	−	0.183325i
$766$		0			0
$767$		−	10.2658i		−	0.370678i
$768$		0			0
$769$	−13.4636	−	7.77321i	−0.485510	−	0.280309i	0.237200	−	0.971461i	$-0.423770\pi$
$769$	−13.4636	−	7.77321i	−0.485510	−	0.280309i	−0.722710	+	0.691152i	$0.757104\pi$
$770$		0			0
$771$	20.1071	+	17.6645i	0.724138	+	0.636172i
$772$		0			0
$773$	−2.21399	−	1.27825i	−0.0796317	−	0.0459754i	0.459655	−	0.888097i	$-0.347973\pi$
$773$	−2.21399	−	1.27825i	−0.0796317	−	0.0459754i	−0.539287	+	0.842122i	$0.681306\pi$
$774$		0			0
$775$	62.5315	+	108.308i	2.24620	+	3.89053i
$776$		0			0
$777$	2.22047	−	6.61578i	0.0796588	−	0.237340i
$778$		0			0
$779$			6.46571i			0.231658i
$780$		0			0
$781$	−40.9932			−1.46685
$782$		0			0
$783$	0.263676	−	3.86756i	0.00942299	−	0.138215i
$784$		0			0
$785$	−33.9932	−	58.8779i	−1.21327	−	2.10144i
$786$		0			0
$787$	25.4781	+	44.1294i	0.908196	+	1.57304i	0.816568	+	0.577249i	$0.195874\pi$
$787$	25.4781	+	44.1294i	0.908196	+	1.57304i	0.0916280	+	0.995793i	$0.470793\pi$
$788$		0			0
$789$	22.4757	+	19.7454i	0.800157	+	0.702956i
$790$		0			0
$791$	−24.5886	−	18.6999i	−0.874270	−	0.664890i
$792$		0			0
$793$	−15.0243	−	26.0229i	−0.533529	−	0.924100i
$794$		0			0
$795$	1.05177	−	0.356005i	0.0373026	−	0.0126262i
$796$		0			0
$797$	12.2946	+	7.09827i	0.435496	+	0.251434i	0.701685	−	0.712487i	$-0.252431\pi$
$797$	12.2946	+	7.09827i	0.435496	+	0.251434i	−0.266189	+	0.963921i	$0.585765\pi$
$798$		0			0
$799$	6.57003	−	3.79321i	0.232431	−	0.134194i
$800$		0			0
$801$	−29.6080	−	38.7258i	−1.04615	−	1.36831i
$802$		0			0
$803$	8.42048	−	14.5847i	0.297152	−	0.514683i
$804$		0			0
$805$	4.51238	−	35.4538i	0.159041	−	1.24958i
$806$		0			0
$807$	−15.2824	+	5.17279i	−0.537966	+	0.182091i
$808$		0			0
$809$	−8.76155	+	15.1755i	−0.308040	+	0.533541i	−0.977933	−	0.208916i	$-0.933006\pi$
$809$	−8.76155	+	15.1755i	−0.308040	+	0.533541i	0.669894	+	0.742457i	$0.266340\pi$
$810$		0			0
$811$	−21.5806			−0.757796			−0.378898	−	0.925438i	$-0.623697\pi$
$811$	−21.5806			−0.757796			−0.378898	+	0.925438i	$0.623697\pi$
$812$		0			0
$813$	34.5669	+	6.90718i	1.21231	+	0.242246i
$814$		0			0
$815$	24.7564	+	42.8794i	0.867179	+	1.50200i
$816$		0			0
$817$	8.14821	+	4.70437i	0.285070	+	0.164585i
$818$		0			0
$819$	35.4422	+	20.3419i	1.23845	+	0.710802i
$820$		0			0
$821$	−3.69769	+	6.40458i	−0.129050	+	0.223522i	−0.923309	−	0.384058i	$-0.874526\pi$
$821$	−3.69769	+	6.40458i	−0.129050	+	0.223522i	0.794259	+	0.607580i	$0.207860\pi$
$822$		0			0
$823$	7.58110	−	4.37695i	0.264261	−	0.152571i	−0.362016	−	0.932172i	$-0.617911\pi$
$823$	7.58110	−	4.37695i	0.264261	−	0.152571i	0.626277	+	0.779601i	$0.284578\pi$
$824$		0			0
$825$	−63.1068	−	55.4408i	−2.19710	−	1.93020i
$826$		0			0
$827$		−	10.9322i		−	0.380150i	−0.981770	−	0.190075i	$-0.939127\pi$
$827$		−	10.9322i		−	0.380150i	0.981770	−	0.190075i	$-0.0608732\pi$
$828$		0			0
$829$	2.09152	+	1.20754i	0.0726415	+	0.0419396i	0.535881	−	0.844294i	$-0.319980\pi$
$829$	2.09152	+	1.20754i	0.0726415	+	0.0419396i	−0.463239	+	0.886233i	$0.653313\pi$
$830$		0			0
$831$	37.3539	−	42.5190i	1.29579	−	1.47497i
$832$		0			0
$833$	5.11122	+	5.02394i	0.177093	+	0.174069i
$834$		0			0
$835$	−23.3826	−	13.4999i	−0.809187	−	0.467185i
$836$		0			0
$837$	3.28570	−	48.1942i	0.113570	−	1.66584i
$838$		0			0
$839$	17.1615	+	29.7246i	0.592481	+	1.02621i	0.993897	+	0.110311i	$0.0351847\pi$
$839$	17.1615	+	29.7246i	0.592481	+	1.02621i	−0.401416	+	0.915896i	$0.631482\pi$
$840$		0			0
$841$	14.2217	−	24.6327i	0.490404	−	0.849404i
$842$		0			0
$843$	−36.9981	−	7.39299i	−1.27428	−	0.254628i
$844$		0			0
$845$	−50.2481	+	29.0108i	−1.72859	+	0.998001i
$846$		0			0
$847$	−0.666933	+	5.24009i	−0.0229161	+	0.180052i
$848$		0			0
$849$	5.84807	+	1.16857i	0.200705	+	0.0401051i
$850$		0			0
$851$	−4.14720	+	2.39438i	−0.142164	+	0.0820784i
$852$		0			0
$853$	−35.5925	+	20.5493i	−1.21866	+	0.703596i	−0.964632	−	0.263600i	$-0.915090\pi$
$853$	−35.5925	+	20.5493i	−1.21866	+	0.703596i	−0.254032	+	0.967196i	$0.581757\pi$
$854$		0			0
$855$	10.3778	+	13.5737i	0.354913	+	0.464209i
$856$		0			0
$857$			20.9248i			0.714779i	0.933955	+	0.357390i	$0.116333\pi$
$857$			20.9248i			0.714779i	−0.933955	+	0.357390i	$0.883667\pi$
$858$		0			0
$859$	16.5702			0.565366			0.282683	−	0.959213i	$-0.408775\pi$
$859$	16.5702			0.565366			0.282683	+	0.959213i	$0.408775\pi$
$860$		0			0
$861$	4.43497	+	21.9030i	0.151143	+	0.746452i
$862$		0			0
$863$	−7.89280	+	4.55691i	−0.268674	+	0.155119i	−0.628285	−	0.777983i	$-0.716243\pi$
$863$	−7.89280	+	4.55691i	−0.268674	+	0.155119i	0.359611	+	0.933102i	$0.382909\pi$
$864$		0			0
$865$	−15.4124	+	26.6950i	−0.524036	+	0.907658i
$866$		0			0
$867$	27.0936	+	5.41387i	0.920148	+	0.183865i
$868$		0			0
$869$	−20.1500	+	34.9008i	−0.683541	+	1.18393i
$870$		0			0
$871$	46.7356			1.58357
$872$		0			0
$873$	13.1548	+	17.2059i	0.445223	+	0.582331i
$874$		0			0
$875$	−95.2981	−	12.1291i	−3.22166	−	0.410037i
$876$		0			0
$877$	−23.0860			−0.779558			−0.389779	−	0.920908i	$-0.627449\pi$
$877$	−23.0860			−0.779558			−0.389779	+	0.920908i	$0.627449\pi$
$878$		0			0
$879$	−32.3004	+	10.9330i	−1.08946	+	0.368762i
$880$		0			0
$881$			17.9457i			0.604606i	0.953212	+	0.302303i	$0.0977554\pi$
$881$			17.9457i			0.604606i	−0.953212	+	0.302303i	$0.902245\pi$
$882$		0			0
$883$		−	12.6165i		−	0.424580i	−0.977207	−	0.212290i	$-0.931908\pi$
$883$		−	12.6165i		−	0.424580i	0.977207	−	0.212290i	$-0.0680922\pi$
$884$		0			0
$885$	2.90699	−	14.5480i	0.0977173	−	0.489025i
$886$		0			0
$887$	−28.5632			−0.959059			−0.479530	−	0.877526i	$-0.659193\pi$
$887$	−28.5632			−0.959059			−0.479530	+	0.877526i	$0.659193\pi$
$888$		0			0
$889$	35.4021	+	4.50580i	1.18735	+	0.151120i
$890$		0			0
$891$	8.28798	+	31.3692i	0.277658	+	1.05091i
$892$		0			0
$893$	−9.82429			−0.328757
$894$		0			0
$895$	−44.6039	+	77.2563i	−1.49094	+	2.58239i
$896$		0			0
$897$	−8.99071	−	26.5620i	−0.300191	−	0.886879i
$898$		0			0
$899$	−3.46778	+	6.00638i	−0.115657	+	0.200324i
$900$		0			0
$901$	0.132327	−	0.0763993i	0.00440846	−	0.00254523i
$902$		0			0
$903$	30.8294	+	10.3473i	1.02594	+	0.344337i
$904$		0			0
$905$	59.0642			1.96336
$906$		0			0
$907$			14.8918i			0.494474i	0.968955	+	0.247237i	$0.0795226\pi$
$907$			14.8918i			0.494474i	−0.968955	+	0.247237i	$0.920477\pi$
$908$		0			0
$909$	26.7850	−	3.47871i	0.888403	−	0.115382i
$910$		0			0
$911$	16.3355	−	9.43130i	0.541219	−	0.312473i	−0.204354	−	0.978897i	$-0.565509\pi$
$911$	16.3355	−	9.43130i	0.541219	−	0.312473i	0.745573	+	0.666424i	$0.232176\pi$
$912$		0			0
$913$	−43.1206	+	24.8957i	−1.42708	+	0.823927i
$914$		0			0
$915$	−13.9224	−	41.1322i	−0.460261	−	1.35979i
$916$		0			0
$917$	−5.53919	+	43.5214i	−0.182920	+	1.43720i
$918$		0			0
$919$	−23.9314	+	13.8168i	−0.789424	+	0.455774i	−0.839760	−	0.542958i	$-0.817304\pi$
$919$	−23.9314	+	13.8168i	−0.789424	+	0.455774i	0.0503355	+	0.998732i	$0.483971\pi$
$920$		0			0
$921$	14.2956	−	16.2723i	0.471056	−	0.536191i
$922$		0			0
$923$	−29.2717	+	50.7001i	−0.963490	+	1.66881i
$924$		0			0
$925$	10.2431	+	17.7415i	0.336790	+	0.583337i
$926$		0			0
$927$	3.59153	+	27.6537i	0.117961	+	0.908265i
$928$		0			0
$929$	−15.1178	−	8.72825i	−0.495998	−	0.286365i	0.231061	−	0.972939i	$-0.425780\pi$
$929$	−15.1178	−	8.72825i	−0.495998	−	0.286365i	−0.727059	+	0.686575i	$0.759114\pi$
$930$		0			0
$931$	−2.47921	−	8.94376i	−0.0812528	−	0.293120i
$932$		0			0
$933$	−18.1915	−	3.63503i	−0.595562	−	0.119006i
$934$		0			0
$935$	−13.7312	−	7.92770i	−0.449058	−	0.259264i
$936$		0			0
$937$		−	6.00080i		−	0.196038i	−0.995185	−	0.0980189i	$-0.968749\pi$
$937$		−	6.00080i		−	0.196038i	0.995185	−	0.0980189i	$-0.0312505\pi$
$938$		0			0
$939$	18.8650	−	6.38543i	0.615636	−	0.208381i
$940$		0			0
$941$	−15.0847	+	8.70913i	−0.491746	+	0.283909i	−0.725298	−	0.688435i	$-0.758298\pi$
$941$	−15.0847	+	8.70913i	−0.491746	+	0.283909i	0.233553	+	0.972344i	$0.424965\pi$
$942$		0			0
$943$	7.66764	−	13.2808i	0.249693	−	0.432481i
$944$		0			0
$945$	44.4658	+	38.8632i	1.44647	+	1.26422i
$946$		0			0
$947$	11.7264	+	6.77021i	0.381055	+	0.220002i	0.678277	−	0.734806i	$-0.262727\pi$
$947$	11.7264	+	6.77021i	0.381055	+	0.220002i	−0.297222	+	0.954808i	$0.596060\pi$
$948$		0			0
$949$	−12.0255	−	20.8288i	−0.390364	−	0.676131i
$950$		0			0
$951$	−9.67121	−	28.5724i	−0.313610	−	0.926525i
$952$		0			0
$953$	−4.27802			−0.138579			−0.0692893	−	0.997597i	$-0.522073\pi$
$953$	−4.27802			−0.138579			−0.0692893	+	0.997597i	$0.522073\pi$
$954$		0			0
$955$	−12.5598	+	21.7541i	−0.406424	+	0.703948i
$956$		0			0
$957$	0.912800	−	4.56809i	0.0295066	−	0.147666i
$958$		0			0
$959$	1.99725	−	15.6924i	0.0644947	−	0.506735i
$960$		0			0
$961$	−27.7126	+	47.9996i	−0.893954	+	1.54837i
$962$		0			0
$963$	9.72756	+	12.7232i	0.313466	+	0.409999i
$964$		0			0
$965$	−8.44947	+	4.87830i	−0.271998	+	0.157038i
$966$		0			0
$967$	−40.6804	−	23.4868i	−1.30819	−	0.755285i	−0.326398	−	0.945232i	$-0.605835\pi$
$967$	−40.6804	−	23.4868i	−1.30819	−	0.755285i	−0.981794	+	0.189947i	$0.939168\pi$
$968$		0			0
$969$	1.76638	+	1.55181i	0.0567443	+	0.0498512i
$970$		0			0
$971$	−28.9103	−	50.0741i	−0.927776	−	1.60695i	−0.787035	−	0.616908i	$-0.788385\pi$
$971$	−28.9103	−	50.0741i	−0.927776	−	1.60695i	−0.140740	−	0.990047i	$-0.544948\pi$
$972$		0			0
$973$	−36.8591	−	28.0317i	−1.18165	−	0.898654i
$974$		0			0
$975$	−113.631	+	38.4618i	−3.63910	+	1.23176i
$976$		0			0
$977$	5.53978	+	9.59517i	0.177233	+	0.306977i	0.940932	−	0.338596i	$-0.109952\pi$
$977$	5.53978	+	9.59517i	0.177233	+	0.306977i	−0.763699	+	0.645573i	$0.776619\pi$
$978$		0			0
$979$	−29.2897	−	50.7313i	−0.936104	−	1.62138i
$980$		0			0
$981$	14.7558	+	6.14226i	0.471115	+	0.196107i
$982$		0			0
$983$	22.1053			0.705050			0.352525	−	0.935802i	$-0.385323\pi$
$983$	22.1053			0.705050			0.352525	+	0.935802i	$0.385323\pi$
$984$		0			0
$985$		−	40.1297i		−	1.27864i
$986$		0			0
$987$	−33.2803	+	6.73868i	−1.05933	+	0.214495i
$988$		0			0
$989$	−11.1578	−	19.3258i	−0.354796	−	0.614525i
$990$		0			0
$991$	−0.396571	−	0.228961i	−0.0125975	−	0.00727317i	0.493688	−	0.869639i	$-0.335648\pi$
$991$	−0.396571	−	0.228961i	−0.0125975	−	0.00727317i	−0.506286	+	0.862366i	$0.668982\pi$
$992$		0			0
$993$	−19.2883	+	6.52871i	−0.612096	+	0.207182i
$994$		0			0
$995$	−7.81817	−	4.51382i	−0.247853	−	0.143098i
$996$		0			0
$997$		−	34.3499i		−	1.08787i	−0.839127	−	0.543936i	$-0.816934\pi$
$997$		−	34.3499i		−	1.08787i	0.839127	−	0.543936i	$-0.183066\pi$
$998$		0			0
$999$	0.538218	−	7.89452i	0.0170285	−	0.249771i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.bf.i.31.4	✓	32
3.2	odd	2		3024.2.bf.i.1711.2		32
4.3	odd	2	inner	1008.2.bf.i.31.13	yes	32
7.5	odd	6		1008.2.cz.i.607.10	yes	32
9.2	odd	6		3024.2.cz.i.2719.15		32
9.7	even	3		1008.2.cz.i.367.7	yes	32
12.11	even	2		3024.2.bf.i.1711.1		32
21.5	even	6		3024.2.cz.i.1279.16		32
28.19	even	6		1008.2.cz.i.607.7	yes	32
36.7	odd	6		1008.2.cz.i.367.10	yes	32
36.11	even	6		3024.2.cz.i.2719.16		32
63.47	even	6		3024.2.bf.i.2287.16		32
63.61	odd	6	inner	1008.2.bf.i.943.13	yes	32
84.47	odd	6		3024.2.cz.i.1279.15		32
252.47	odd	6		3024.2.bf.i.2287.15		32
252.187	even	6	inner	1008.2.bf.i.943.4	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1008.2.bf.i.31.4	✓	32	1.1	even	1	trivial
1008.2.bf.i.31.13	yes	32	4.3	odd	2	inner
1008.2.bf.i.943.4	yes	32	252.187	even	6	inner
1008.2.bf.i.943.13	yes	32	63.61	odd	6	inner
1008.2.cz.i.367.7	yes	32	9.7	even	3
1008.2.cz.i.367.10	yes	32	36.7	odd	6
1008.2.cz.i.607.7	yes	32	28.19	even	6
1008.2.cz.i.607.10	yes	32	7.5	odd	6
3024.2.bf.i.1711.1		32	12.11	even	2
3024.2.bf.i.1711.2		32	3.2	odd	2
3024.2.bf.i.2287.15		32	252.47	odd	6
3024.2.bf.i.2287.16		32	63.47	even	6
3024.2.cz.i.1279.15		32	84.47	odd	6
3024.2.cz.i.1279.16		32	21.5	even	6
3024.2.cz.i.2719.15		32	9.2	odd	6
3024.2.cz.i.2719.16		32	36.11	even	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:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.bf (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.14316 + 1.30123i) q^{3} +4.29566i q^{5} +(0.334043 - 2.62458i) q^{7} +(-0.386381 - 2.97501i) q^{9} -3.60507i q^{11} +(-4.45873 - 2.57425i) q^{13} +(-5.58963 - 4.91062i) q^{15} +(-0.886675 - 0.511922i) q^{17} +(0.662930 + 1.14823i) q^{19} +(3.03331 + 3.43497i) q^{21} -3.14466i q^{23} -13.4527 q^{25} +(4.31286 + 2.89814i) q^{27} +(-0.373020 - 0.646090i) q^{29} +(-4.64826 - 8.05102i) q^{31} +(4.69102 + 4.12117i) q^{33} +(11.2743 + 1.43494i) q^{35} +(-0.761414 - 1.31881i) q^{37} +(8.44671 - 2.85904i) q^{39} +(4.22328 + 2.43831i) q^{41} +(6.14560 - 3.54817i) q^{43} +(12.7796 - 1.65976i) q^{45} +(-3.70487 + 6.41703i) q^{47} +(-6.77683 - 1.75345i) q^{49} +(1.67974 - 0.568557i) q^{51} +(-0.0746200 + 0.129246i) q^{53} +15.4862 q^{55} +(-2.25194 - 0.449984i) q^{57} +(0.996973 + 1.72681i) q^{59} +(5.05446 + 2.91820i) q^{61} +(-7.93723 + 0.0203037i) q^{63} +(11.0581 - 19.1532i) q^{65} +(-7.86136 + 4.53876i) q^{67} +(4.09191 + 3.59484i) q^{69} -11.3710i q^{71} +(4.04560 + 2.33573i) q^{73} +(15.3785 - 17.5050i) q^{75} +(-9.46180 - 1.20425i) q^{77} +(-9.68102 - 5.58934i) q^{79} +(-8.70142 + 2.29898i) q^{81} +(-6.90574 - 11.9611i) q^{83} +(2.19904 - 3.80885i) q^{85} +(1.26713 + 0.253199i) q^{87} +(14.0722 - 8.12459i) q^{89} +(-8.24573 + 10.8424i) q^{91} +(15.7899 + 3.15515i) q^{93} +(-4.93240 + 2.84772i) q^{95} +(-6.25228 + 3.60975i) q^{97} +(-10.7251 + 1.39293i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{9} - 6 q^{13} - 18 q^{17} - 8 q^{21} - 32 q^{25} - 12 q^{29} + 30 q^{33} + 2 q^{37} + 36 q^{41} + 30 q^{45} + 2 q^{49} - 12 q^{53} - 46 q^{57} + 42 q^{61} + 18 q^{65} - 42 q^{69} - 66 q^{77}+ \cdots - 6 q^{97}+O(q^{100}) \) 32 * q - 4 * q^9 - 6 * q^13 - 18 * q^17 - 8 * q^21 - 32 * q^25 - 12 * q^29 + 30 * q^33 + 2 * q^37 + 36 * q^41 + 30 * q^45 + 2 * q^49 - 12 * q^53 - 46 * q^57 + 42 * q^61 + 18 * q^65 - 42 * q^69 - 66 * q^77 - 16 * q^81 - 12 * q^85 - 18 * q^89 + 58 * q^93 - 6 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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