LMFDB - Embedded newform 864.2.bh.b.815.18

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [864,2,Mod(47,864)] 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("864.47"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(864, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 9, 7])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.bh (of order $18$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [192] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$32$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 216)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			815.18
Character	$\chi$	$=$	864.815
Dual form			864.2.bh.b.335.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.00307742 - 1.73205i) q^{3} +(2.47648 - 0.901367i) q^{5} +(-2.55949 + 0.451307i) q^{7} +(-2.99998 + 0.0106605i) q^{9} +(-0.556608 + 1.52927i) q^{11} +(1.88389 - 2.24514i) q^{13} +(-1.56883 - 4.28662i) q^{15} +(-3.28845 - 1.89859i) q^{17} +(-4.30904 - 7.46347i) q^{19} +(0.789562 + 4.43177i) q^{21} +(1.07009 - 6.06879i) q^{23} +(1.49029 - 1.25050i) q^{25} +(0.0276967 + 5.19608i) q^{27} +(3.88174 - 3.25716i) q^{29} +(3.57300 + 0.630016i) q^{31} +(2.65048 + 0.959365i) q^{33} +(-5.93174 + 3.42469i) q^{35} +(-6.40179 - 3.69607i) q^{37} +(-3.89448 - 3.25608i) q^{39} +(-4.43232 + 5.28224i) q^{41} +(3.77811 + 1.37512i) q^{43} +(-7.41980 + 2.73048i) q^{45} +(-0.253807 - 1.43941i) q^{47} +(-0.230541 + 0.0839100i) q^{49} +(-3.27833 + 5.70160i) q^{51} +0.180986 q^{53} +4.28892i q^{55} +(-12.9138 + 7.48643i) q^{57} +(-0.253090 - 0.695359i) q^{59} +(11.1190 - 1.96057i) q^{61} +(7.67361 - 1.38120i) q^{63} +(2.64174 - 7.25812i) q^{65} +(10.5159 + 8.82387i) q^{67} +(-10.5147 - 1.83477i) q^{69} +(-2.57253 + 4.45576i) q^{71} +(-2.62831 - 4.55236i) q^{73} +(-2.17052 - 2.57741i) q^{75} +(0.734463 - 4.16534i) q^{77} +(6.72831 + 8.01849i) q^{79} +(8.99977 - 0.0639625i) q^{81} +(-7.39656 - 8.81488i) q^{83} +(-9.85513 - 1.73773i) q^{85} +(-5.65351 - 6.71333i) q^{87} +(-0.211259 + 0.121971i) q^{89} +(-3.80856 + 6.59662i) q^{91} +(1.08022 - 6.19054i) q^{93} +(-17.3986 - 14.5992i) q^{95} +(1.95441 + 0.711348i) q^{97} +(1.65351 - 4.59371i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 12 q^{3} - 12 q^{9} + 30 q^{11} - 18 q^{17} + 6 q^{19} - 12 q^{25} - 18 q^{27} - 30 q^{33} + 18 q^{35} + 18 q^{41} + 42 q^{43} - 12 q^{49} + 18 q^{51} - 36 q^{57} + 84 q^{59} - 12 q^{65} - 30 q^{67}+ \cdots + 12 q^{99}+O(q^{100}) $ 192 * q + 12 * q^3 - 12 * q^9 + 30 * q^11 - 18 * q^17 + 6 * q^19 - 12 * q^25 - 18 * q^27 - 30 * q^33 + 18 * q^35 + 18 * q^41 + 42 * q^43 - 12 * q^49 + 18 * q^51 - 36 * q^57 + 84 * q^59 - 12 * q^65 - 30 * q^67 - 6 * q^73 + 96 * q^75 - 12 * q^81 + 72 * q^83 + 144 * q^89 + 6 * q^91 - 42 * q^97 + 12 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$-1$	$e\left(\frac{5}{18}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−0.00307742	−	1.73205i	−0.00177675	−	0.999998i
$3$	−0.00307742	−	1.73205i	−0.00177675	−	0.999998i
$4$		0			0
$5$	2.47648	−	0.901367i	1.10752	−	0.403103i	0.277435	−	0.960744i	$-0.410516\pi$
$5$	2.47648	−	0.901367i	1.10752	−	0.403103i	0.830082	+	0.557641i	$0.188293\pi$
$6$		0			0
$7$	−2.55949	+	0.451307i	−0.967396	+	0.170578i	−0.634958	−	0.772547i	$-0.718982\pi$
$7$	−2.55949	+	0.451307i	−0.967396	+	0.170578i	−0.332438	+	0.943125i	$0.607871\pi$
$8$		0			0
$9$	−2.99998	+	0.0106605i	−0.999994	+	0.00355349i
$10$		0			0
$11$	−0.556608	+	1.52927i	−0.167824	+	0.461091i	−0.994884	−	0.101021i	$-0.967789\pi$
$11$	−0.556608	+	1.52927i	−0.167824	+	0.461091i	0.827061	+	0.562113i	$0.190011\pi$
$12$		0			0
$13$	1.88389	−	2.24514i	0.522498	−	0.622689i	−0.438672	−	0.898647i	$-0.644551\pi$
$13$	1.88389	−	2.24514i	0.522498	−	0.622689i	0.961169	+	0.275959i	$0.0889953\pi$
$14$		0			0
$15$	−1.56883	−	4.28662i	−0.405071	−	1.10680i
$16$		0			0
$17$	−3.28845	−	1.89859i	−0.797567	−	0.460476i	0.0450525	−	0.998985i	$-0.485654\pi$
$17$	−3.28845	−	1.89859i	−0.797567	−	0.460476i	−0.842620	+	0.538509i	$0.818988\pi$
$18$		0			0
$19$	−4.30904	−	7.46347i	−0.988561	−	1.71224i	−0.624895	−	0.780708i	$-0.714858\pi$
$19$	−4.30904	−	7.46347i	−0.988561	−	1.71224i	−0.363666	−	0.931530i	$-0.618475\pi$
$20$		0			0
$21$	0.789562	+	4.43177i	0.172297	+	0.967091i
$22$		0			0
$23$	1.07009	−	6.06879i	0.223129	−	1.26543i	−0.643100	−	0.765783i	$-0.722352\pi$
$23$	1.07009	−	6.06879i	0.223129	−	1.26543i	0.866229	−	0.499647i	$-0.166537\pi$
$24$		0			0
$25$	1.49029	−	1.25050i	0.298059	−	0.250101i
$26$		0			0
$27$	0.0276967	+	5.19608i	0.00533022	+	0.999986i
$28$		0			0
$29$	3.88174	−	3.25716i	0.720820	−	0.604840i	−0.206792	−	0.978385i	$-0.566302\pi$
$29$	3.88174	−	3.25716i	0.720820	−	0.604840i	0.927612	+	0.373545i	$0.121858\pi$
$30$		0			0
$31$	3.57300	+	0.630016i	0.641729	+	0.113154i	0.485037	−	0.874493i	$-0.338806\pi$
$31$	3.57300	+	0.630016i	0.641729	+	0.113154i	0.156692	+	0.987648i	$0.449917\pi$
$32$		0			0
$33$	2.65048	+	0.959365i	0.461389	+	0.167004i
$34$		0			0
$35$	−5.93174	+	3.42469i	−1.00265	+	0.578879i
$36$		0			0
$37$	−6.40179	−	3.69607i	−1.05245	−	0.607631i	−0.129114	−	0.991630i	$-0.541213\pi$
$37$	−6.40179	−	3.69607i	−1.05245	−	0.607631i	−0.923333	+	0.383999i	$0.874547\pi$
$38$		0			0
$39$	−3.89448	−	3.25608i	−0.623616	−	0.521391i
$40$		0			0
$41$	−4.43232	+	5.28224i	−0.692212	+	0.824947i	−0.991621	−	0.129178i	$-0.958766\pi$
$41$	−4.43232	+	5.28224i	−0.692212	+	0.824947i	0.299409	+	0.954125i	$0.403211\pi$
$42$		0			0
$43$	3.77811	+	1.37512i	0.576156	+	0.209704i	0.613630	−	0.789594i	$-0.289709\pi$
$43$	3.77811	+	1.37512i	0.576156	+	0.209704i	−0.0374734	+	0.999298i	$0.511931\pi$
$44$		0			0
$45$	−7.41980	+	2.73048i	−1.10608	+	0.407036i
$46$		0			0
$47$	−0.253807	−	1.43941i	−0.0370215	−	0.209960i	0.960686	−	0.277639i	$-0.0895517\pi$
$47$	−0.253807	−	1.43941i	−0.0370215	−	0.209960i	−0.997707	+	0.0676790i	$0.978441\pi$
$48$		0			0
$49$	−0.230541	+	0.0839100i	−0.0329344	+	0.0119871i
$50$		0			0
$51$	−3.27833	+	5.70160i	−0.459058	+	0.798384i
$52$		0			0
$53$	0.180986			0.0248604			0.0124302	−	0.999923i	$-0.496043\pi$
$53$	0.180986			0.0248604			0.0124302	+	0.999923i	$0.496043\pi$
$54$		0			0
$55$			4.28892i			0.578317i
$56$		0			0
$57$	−12.9138	+	7.48643i	−1.71048	+	0.991602i
$58$		0			0
$59$	−0.253090	−	0.695359i	−0.0329495	−	0.0905280i	0.922127	−	0.386887i	$-0.126450\pi$
$59$	−0.253090	−	0.695359i	−0.0329495	−	0.0905280i	−0.955077	+	0.296359i	$0.904227\pi$
$60$		0			0
$61$	11.1190	−	1.96057i	1.42364	−	0.251026i	0.591817	−	0.806072i	$-0.298411\pi$
$61$	11.1190	−	1.96057i	1.42364	−	0.251026i	0.831819	+	0.555047i	$0.187300\pi$
$62$		0			0
$63$	7.67361	−	1.38120i	0.966784	−	0.174015i
$64$		0			0
$65$	2.64174	−	7.25812i	0.327668	−	0.900259i
$66$		0			0
$67$	10.5159	+	8.82387i	1.28472	+	1.07801i	0.992575	+	0.121633i	$0.0388130\pi$
$67$	10.5159	+	8.82387i	1.28472	+	1.07801i	0.292144	+	0.956374i	$0.405631\pi$
$68$		0			0
$69$	−10.5147	−	1.83477i	−1.26582	−	0.220881i
$70$		0			0
$71$	−2.57253	+	4.45576i	−0.305303	+	0.528801i	−0.977329	−	0.211727i	$-0.932091\pi$
$71$	−2.57253	+	4.45576i	−0.305303	+	0.528801i	0.672025	+	0.740528i	$0.265425\pi$
$72$		0			0
$73$	−2.62831	−	4.55236i	−0.307620	−	0.532814i	0.670221	−	0.742161i	$-0.266199\pi$
$73$	−2.62831	−	4.55236i	−0.307620	−	0.532814i	−0.977841	+	0.209348i	$0.932866\pi$
$74$		0			0
$75$	−2.17052	−	2.57741i	−0.250630	−	0.297614i
$76$		0			0
$77$	0.734463	−	4.16534i	0.0836998	−	0.474685i
$78$		0			0
$79$	6.72831	+	8.01849i	0.756994	+	0.902151i	0.997654	−	0.0684588i	$-0.0218082\pi$
$79$	6.72831	+	8.01849i	0.756994	+	0.902151i	−0.240660	+	0.970610i	$0.577364\pi$
$80$		0			0
$81$	8.99977	−	0.0639625i	0.999975	−	0.00710694i
$82$		0			0
$83$	−7.39656	−	8.81488i	−0.811878	−	0.967559i	0.188015	−	0.982166i	$-0.439795\pi$
$83$	−7.39656	−	8.81488i	−0.811878	−	0.967559i	−0.999893	+	0.0146072i	$0.995350\pi$
$84$		0			0
$85$	−9.85513	−	1.73773i	−1.06894	−	0.188483i
$86$		0			0
$87$	−5.65351	−	6.71333i	−0.606120	−	0.719744i
$88$		0			0
$89$	−0.211259	+	0.121971i	−0.0223934	+	0.0129289i	−0.511155	−	0.859489i	$-0.670782\pi$
$89$	−0.211259	+	0.121971i	−0.0223934	+	0.0129289i	0.488761	+	0.872417i	$0.337449\pi$
$90$		0			0
$91$	−3.80856	+	6.59662i	−0.399245	+	0.691513i
$92$		0			0
$93$	1.08022	−	6.19054i	0.112014	−	0.641929i
$94$		0			0
$95$	−17.3986	−	14.5992i	−1.78506	−	1.49784i
$96$		0			0
$97$	1.95441	+	0.711348i	0.198441	+	0.0722264i	0.439329	−	0.898326i	$-0.355216\pi$
$97$	1.95441	+	0.711348i	0.198441	+	0.0722264i	−0.240888	+	0.970553i	$0.577439\pi$
$98$		0			0
$99$	1.65351	−	4.59371i	0.166184	−	0.461685i
$100$		0			0
$101$	−3.09813	−	17.5704i	−0.308276	−	1.74832i	−0.607670	−	0.794190i	$-0.707896\pi$
$101$	−3.09813	−	17.5704i	−0.308276	−	1.74832i	0.299394	−	0.954130i	$-0.403216\pi$
$102$		0			0
$103$	4.29301	+	11.7949i	0.423003	+	1.16219i	0.949980	+	0.312311i	$0.101103\pi$
$103$	4.29301	+	11.7949i	0.423003	+	1.16219i	−0.526977	+	0.849879i	$0.676675\pi$
$104$		0			0
$105$	5.94999	+	10.2635i	0.580659	+	1.00162i
$106$		0			0
$107$		−	10.9395i		−	1.05757i	−0.848757	−	0.528783i	$-0.822649\pi$
$107$		−	10.9395i		−	1.05757i	0.848757	−	0.528783i	$-0.177351\pi$
$108$		0			0
$109$			6.35577i			0.608772i	0.952549	+	0.304386i	$0.0984513\pi$
$109$			6.35577i			0.608772i	−0.952549	+	0.304386i	$0.901549\pi$
$110$		0			0
$111$	−6.38208	+	11.0996i	−0.605760	+	1.05353i
$112$		0			0
$113$	−1.20684	−	3.31577i	−0.113530	−	0.311921i	0.869895	−	0.493237i	$-0.164187\pi$
$113$	−1.20684	−	3.31577i	−0.113530	−	0.311921i	−0.983425	+	0.181316i	$0.941964\pi$
$114$		0			0
$115$	−2.82014	−	15.9938i	−0.262979	−	1.49143i
$116$		0			0
$117$	−5.62771	+	6.75545i	−0.520282	+	0.624541i
$118$		0			0
$119$	9.27361	+	3.37532i	0.850110	+	0.309415i
$120$		0			0
$121$	6.39764	+	5.36826i	0.581604	+	0.488024i
$122$		0			0
$123$	9.16273	+	7.66074i	0.826175	+	0.690746i
$124$		0			0
$125$	−4.02503	+	6.97155i	−0.360009	+	0.623554i
$126$		0			0
$127$	15.7942	−	9.11876i	1.40150	−	0.809159i	0.406958	−	0.913447i	$-0.366590\pi$
$127$	15.7942	−	9.11876i	1.40150	−	0.809159i	0.994547	+	0.104288i	$0.0332563\pi$
$128$		0			0
$129$	2.37015	−	6.54810i	0.208680	−	0.576528i
$130$		0			0
$131$	−4.10519	−	0.723856i	−0.358672	−	0.0632436i	−0.00859153	−	0.999963i	$-0.502735\pi$
$131$	−4.10519	−	0.723856i	−0.358672	−	0.0632436i	−0.350081	+	0.936719i	$0.613846\pi$
$132$		0			0
$133$	14.3973	+	17.1580i	1.24840	+	1.48779i
$134$		0			0
$135$	4.75216	+	12.8430i	0.409001	+	1.10535i
$136$		0			0
$137$	−10.2458	−	12.2105i	−0.875360	−	1.04321i	−0.998706	−	0.0508494i	$-0.983807\pi$
$137$	−10.2458	−	12.2105i	−0.875360	−	1.04321i	0.123347	−	0.992364i	$-0.460637\pi$
$138$		0			0
$139$	0.411616	−	2.33439i	0.0349128	−	0.198000i	−0.962363	−	0.271769i	$-0.912391\pi$
$139$	0.411616	−	2.33439i	0.0349128	−	0.198000i	0.997275	+	0.0737683i	$0.0235025\pi$
$140$		0			0
$141$	−2.49235	+	0.444035i	−0.209893	+	0.0373945i
$142$		0			0
$143$	2.38482	+	4.13064i	0.199429	+	0.345421i
$144$		0			0
$145$	6.67716	−	11.5652i	0.554508	−	0.960436i
$146$		0			0
$147$	0.146046	+	0.399050i	0.0120456	+	0.0329131i
$148$		0			0
$149$	12.2426	+	10.2728i	1.00295	+	0.841578i	0.987391	−	0.158300i	$-0.0506014\pi$
$149$	12.2426	+	10.2728i	1.00295	+	0.841578i	0.0155632	+	0.999879i	$0.495046\pi$
$150$		0			0
$151$	−0.806403	+	2.21557i	−0.0656242	+	0.180301i	−0.968170	−	0.250292i	$-0.919473\pi$
$151$	−0.806403	+	2.21557i	−0.0656242	+	0.180301i	0.902546	+	0.430593i	$0.141696\pi$
$152$		0			0
$153$	9.88554	+	5.66068i	0.799199	+	0.457639i
$154$		0			0
$155$	9.41635	−	1.66036i	0.756339	−	0.133363i
$156$		0			0
$157$	0.284046	+	0.780410i	0.0226693	+	0.0622835i	0.950511	−	0.310691i	$-0.100560\pi$
$157$	0.284046	+	0.780410i	0.0226693	+	0.0622835i	−0.927842	+	0.372974i	$0.878338\pi$
$158$		0			0
$159$	−0.000556971	−	0.313477i	−4.41706e−5	−	0.0248603i
$160$		0			0
$161$			16.0159i			1.26223i
$162$		0			0
$163$	11.2657			0.882401			0.441200	−	0.897409i	$-0.354553\pi$
$163$	11.2657			0.882401			0.441200	+	0.897409i	$0.354553\pi$
$164$		0			0
$165$	7.42861	−	0.0131988i	0.578316	−	0.00102752i
$166$		0			0
$167$	16.4192	−	5.97611i	1.27056	−	0.462445i	0.383260	−	0.923641i	$-0.374801\pi$
$167$	16.4192	−	5.97611i	1.27056	−	0.462445i	0.887299	+	0.461195i	$0.152579\pi$
$168$		0			0
$169$	0.765842	+	4.34331i	0.0589110	+	0.334101i
$170$		0			0
$171$	13.0066	+	22.3443i	0.994639	+	1.70871i
$172$		0			0
$173$	17.4791	+	6.36186i	1.32891	+	0.483683i	0.906302	−	0.422630i	$-0.138893\pi$
$173$	17.4791	+	6.36186i	1.32891	+	0.483683i	0.422606	+	0.906313i	$0.361115\pi$
$174$		0			0
$175$	−3.25003	+	3.87323i	−0.245679	+	0.292789i
$176$		0			0
$177$	−1.20362	+	0.440504i	−0.0904693	+	0.0331103i
$178$		0			0
$179$	6.13650	+	3.54291i	0.458663	+	0.264809i	0.711482	−	0.702704i	$-0.248024\pi$
$179$	6.13650	+	3.54291i	0.458663	+	0.264809i	−0.252819	+	0.967514i	$0.581358\pi$
$180$		0			0
$181$	−0.129860	+	0.0749748i	−0.00965242	+	0.00557283i	−0.504818	−	0.863226i	$-0.668441\pi$
$181$	−0.129860	+	0.0749748i	−0.00965242	+	0.00557283i	0.495166	+	0.868798i	$0.335107\pi$
$182$		0			0
$183$	−3.43002	−	19.2525i	−0.253555	−	1.42319i
$184$		0			0
$185$	−19.1854	−	3.38291i	−1.41054	−	0.248717i
$186$		0			0
$187$	4.73383	−	3.97216i	0.346172	−	0.290473i
$188$		0			0
$189$	−2.41592	−	13.2868i	−0.175732	−	0.966473i
$190$		0			0
$191$	−8.37441	+	7.02696i	−0.605951	+	0.508453i	−0.893352	−	0.449357i	$-0.851653\pi$
$191$	−8.37441	+	7.02696i	−0.605951	+	0.508453i	0.287401	+	0.957810i	$0.407209\pi$
$192$		0			0
$193$	0.508999	−	2.88668i	0.0366385	−	0.207788i	−0.960993	−	0.276573i	$-0.910801\pi$
$193$	0.508999	−	2.88668i	0.0366385	−	0.207788i	0.997631	+	0.0687854i	$0.0219124\pi$
$194$		0			0
$195$	−12.5795	−	4.55329i	−0.900840	−	0.326068i
$196$		0			0
$197$	−1.40635	−	2.43587i	−0.100198	−	0.173548i	0.811568	−	0.584258i	$-0.198614\pi$
$197$	−1.40635	−	2.43587i	−0.100198	−	0.173548i	−0.911766	+	0.410710i	$0.865281\pi$
$198$		0			0
$199$	0.874354	+	0.504808i	0.0619813	+	0.0357849i	0.530670	−	0.847578i	$-0.321940\pi$
$199$	0.874354	+	0.504808i	0.0619813	+	0.0357849i	−0.468689	+	0.883363i	$0.655274\pi$
$200$		0			0
$201$	15.2510	−	18.2412i	1.07572	−	1.28663i
$202$		0			0
$203$	−8.46528	+	10.0885i	−0.594146	+	0.708076i
$204$		0			0
$205$	−6.21535	+	17.0765i	−0.434099	+	1.19268i
$206$		0			0
$207$	−3.14556	+	18.2177i	−0.218631	+	1.26621i
$208$		0			0
$209$	13.8121	−	2.43544i	0.955402	−	0.168463i
$210$		0			0
$211$	3.98399	−	1.45005i	0.274269	−	0.0998257i	−0.201224	−	0.979545i	$-0.564492\pi$
$211$	3.98399	−	1.45005i	0.274269	−	0.0998257i	0.475493	+	0.879720i	$0.342270\pi$
$212$		0			0
$213$	7.72550	+	4.44204i	0.529343	+	0.304363i
$214$		0			0
$215$	10.5959			0.722636
$216$		0			0
$217$	−9.42938			−0.640108
$218$		0			0
$219$	−7.87682	+	4.56636i	−0.532266	+	0.308566i
$220$		0			0
$221$	−10.4577	+	3.80629i	−0.703460	+	0.256039i
$222$		0			0
$223$	−15.7442	+	2.77613i	−1.05431	+	0.185903i	−0.673831	−	0.738886i	$-0.735352\pi$
$223$	−15.7442	+	2.77613i	−1.05431	+	0.185903i	−0.380480	+	0.924789i	$0.624241\pi$
$224$		0			0
$225$	−4.45752	+	3.76738i	−0.297168	+	0.251158i
$226$		0			0
$227$	−0.588042	+	1.61563i	−0.0390297	+	0.107233i	−0.957677	−	0.287846i	$-0.907061\pi$
$227$	−0.588042	+	1.61563i	−0.0390297	+	0.107233i	0.918647	+	0.395080i	$0.129283\pi$
$228$		0			0
$229$	−5.91992	+	7.05508i	−0.391199	+	0.466213i	−0.925316	−	0.379198i	$-0.876200\pi$
$229$	−5.91992	+	7.05508i	−0.391199	+	0.466213i	0.534116	+	0.845411i	$0.320644\pi$
$230$		0			0
$231$	−7.21684	−	1.25931i	−0.474833	−	0.0828563i
$232$		0			0
$233$	16.7671	+	9.68050i	1.09845	+	0.634191i	0.935814	−	0.352495i	$-0.114667\pi$
$233$	16.7671	+	9.68050i	1.09845	+	0.634191i	0.162637	+	0.986686i	$0.448000\pi$
$234$		0			0
$235$	−1.92599	−	3.33590i	−0.125637	−	0.217610i
$236$		0			0
$237$	13.8677	−	11.6784i	0.900804	−	0.758596i
$238$		0			0
$239$	−0.803749	+	4.55829i	−0.0519902	+	0.294851i	−0.999706	−	0.0242659i	$-0.992275\pi$
$239$	−0.803749	+	4.55829i	−0.0519902	+	0.294851i	0.947715	+	0.319117i	$0.103386\pi$
$240$		0			0
$241$	21.1035	−	17.7079i	1.35939	−	1.14067i	0.383226	−	0.923655i	$-0.374813\pi$
$241$	21.1035	−	17.7079i	1.35939	−	1.14067i	0.976169	−	0.217012i	$-0.0696312\pi$
$242$		0			0
$243$	−0.138482	−	15.5878i	−0.00888363	−	0.999961i
$244$		0			0
$245$	−0.495297	+	0.415604i	−0.0316434	+	0.0265519i
$246$		0			0
$247$	−24.8743	−	4.38601i	−1.58271	−	0.279075i
$248$		0			0
$249$	−15.2450	+	12.8383i	−0.966115	+	0.813596i
$250$		0			0
$251$	12.0234	−	6.94172i	0.758911	−	0.438158i	−0.0699933	−	0.997547i	$-0.522298\pi$
$251$	12.0234	−	6.94172i	0.758911	−	0.438158i	0.828905	+	0.559390i	$0.188964\pi$
$252$		0			0
$253$	8.68518	+	5.01439i	0.546033	+	0.315252i
$254$		0			0
$255$	−2.97950	+	17.0749i	−0.186583	+	1.06927i
$256$		0			0
$257$	−1.09064	+	1.29978i	−0.0680325	+	0.0810779i	−0.798987	−	0.601348i	$-0.794631\pi$
$257$	−1.09064	+	1.29978i	−0.0680325	+	0.0810779i	0.730955	+	0.682426i	$0.239075\pi$
$258$		0			0
$259$	18.0534	+	6.57089i	1.12178	+	0.408295i
$260$		0			0
$261$	−11.6104	+	9.81281i	−0.718666	+	0.607398i
$262$		0			0
$263$	0.720517	+	4.08625i	0.0444290	+	0.251969i	0.998931	−	0.0462368i	$-0.0147229\pi$
$263$	0.720517	+	4.08625i	0.0444290	+	0.251969i	−0.954502	+	0.298206i	$0.903612\pi$
$264$		0			0
$265$	0.448210	−	0.163135i	0.0275333	−	0.0100213i
$266$		0			0
$267$	0.211909	+	0.365536i	0.0129686	+	0.0223704i
$268$		0			0
$269$	−31.4461			−1.91730			−0.958650	−	0.284588i	$-0.908143\pi$
$269$	−31.4461			−1.91730			−0.958650	+	0.284588i	$0.908143\pi$
$270$		0			0
$271$		−	28.1714i		−	1.71129i	−0.517564	−	0.855644i	$-0.673161\pi$
$271$		−	28.1714i		−	1.71129i	0.517564	−	0.855644i	$-0.326839\pi$
$272$		0			0
$273$	11.4374	+	6.57631i	0.692222	+	0.398016i
$274$		0			0
$275$	1.08285	+	2.97510i	0.0652981	+	0.179405i
$276$		0			0
$277$	24.3185	−	4.28801i	1.46116	−	0.257641i	0.614136	−	0.789201i	$-0.289505\pi$
$277$	24.3185	−	4.28801i	1.46116	−	0.257641i	0.847021	+	0.531559i	$0.178394\pi$
$278$		0			0
$279$	−10.7256	−	1.85195i	−0.642127	−	0.110873i
$280$		0			0
$281$	−6.58678	+	18.0970i	−0.392935	+	1.07958i	0.572720	+	0.819751i	$0.305888\pi$
$281$	−6.58678	+	18.0970i	−0.392935	+	1.07958i	−0.965655	+	0.259828i	$0.916334\pi$
$282$		0			0
$283$	−6.85978	−	5.75604i	−0.407772	−	0.342161i	0.415717	−	0.909494i	$-0.363531\pi$
$283$	−6.85978	−	5.75604i	−0.407772	−	0.342161i	−0.823488	+	0.567333i	$0.807975\pi$
$284$		0			0
$285$	−25.2329	+	30.1801i	−1.49467	+	1.78772i
$286$		0			0
$287$	8.96057	−	15.5202i	0.528926	−	0.916126i
$288$		0			0
$289$	−1.29071	−	2.23558i	−0.0759243	−	0.131505i
$290$		0			0
$291$	1.22607	−	3.38733i	0.0718738	−	0.198569i
$292$		0			0
$293$	3.69497	−	20.9552i	0.215863	−	1.22422i	−0.663540	−	0.748140i	$-0.730947\pi$
$293$	3.69497	−	20.9552i	0.215863	−	1.22422i	0.879403	−	0.476078i	$-0.157942\pi$
$294$		0			0
$295$	−1.25355	−	1.49392i	−0.0729843	−	0.0869793i
$296$		0			0
$297$	−7.96161	−	2.84982i	−0.461979	−	0.165363i
$298$		0			0
$299$	−11.6093	−	13.8354i	−0.671384	−	0.800125i
$300$		0			0
$301$	−10.2906	−	1.81452i	−0.593142	−	0.104587i
$302$		0			0
$303$	−30.4232	+	5.42019i	−1.74777	+	0.311382i
$304$		0			0
$305$	25.7687	−	14.8776i	1.47551	−	0.851888i
$306$		0			0
$307$	−4.48896	+	7.77511i	−0.256199	+	0.443749i	−0.965220	−	0.261438i	$-0.915803\pi$
$307$	−4.48896	+	7.77511i	−0.256199	+	0.443749i	0.709022	+	0.705187i	$0.249137\pi$
$308$		0			0
$309$	20.4162	−	7.47200i	1.16144	−	0.425067i
$310$		0			0
$311$	−13.0417	−	10.9433i	−0.739525	−	0.620535i	0.193185	−	0.981162i	$-0.438118\pi$
$311$	−13.0417	−	10.9433i	−0.739525	−	0.620535i	−0.932710	+	0.360627i	$0.882563\pi$
$312$		0			0
$313$	−9.04413	−	3.29179i	−0.511204	−	0.186063i	0.0735224	−	0.997294i	$-0.476576\pi$
$313$	−9.04413	−	3.29179i	−0.511204	−	0.186063i	−0.584727	+	0.811230i	$0.698798\pi$
$314$		0			0
$315$	17.7586	−	10.3373i	1.00058	−	0.582438i
$316$		0			0
$317$	1.05306	+	5.97220i	0.0591457	+	0.335432i	0.999994	−	0.00339548i	$-0.00108082\pi$
$317$	1.05306	+	5.97220i	0.0591457	+	0.335432i	−0.940849	+	0.338827i	$0.889970\pi$
$318$		0			0
$319$	2.82047	+	7.74917i	0.157916	+	0.433870i
$320$		0			0
$321$	−18.9478	+	0.0336656i	−1.05756	+	0.00187903i
$322$		0			0
$323$			32.7244i			1.82083i
$324$		0			0
$325$		−	5.70173i		−	0.316275i
$326$		0			0
$327$	11.0085	−	0.0195594i	0.608771	−	0.00108164i
$328$		0			0
$329$	1.29923	+	3.56961i	0.0716290	+	0.196799i
$330$		0			0
$331$	−0.638218	−	3.61951i	−0.0350796	−	0.198946i	0.962231	−	0.272233i	$-0.0877622\pi$
$331$	−0.638218	−	3.61951i	−0.0350796	−	0.198946i	−0.997311	+	0.0732869i	$0.976651\pi$
$332$		0			0
$333$	19.2446	+	11.0199i	1.05460	+	0.603887i
$334$		0			0
$335$	33.9960	+	12.3735i	1.85740	+	0.676037i
$336$		0			0
$337$	14.8826	+	12.4880i	0.810707	+	0.680264i	0.950776	−	0.309878i	$-0.100288\pi$
$337$	14.8826	+	12.4880i	0.810707	+	0.680264i	−0.140070	+	0.990142i	$0.544733\pi$
$338$		0			0
$339$	−5.73936	+	2.10051i	−0.311719	+	0.114084i
$340$		0			0
$341$	−2.95222	+	5.11340i	−0.159872	+	0.276906i
$342$		0			0
$343$	16.3076	−	9.41522i	0.880530	−	0.508374i
$344$		0			0
$345$	−27.6934	+	4.93384i	−1.49096	+	0.265629i
$346$		0			0
$347$	−14.8923	−	2.62591i	−0.799458	−	0.140966i	−0.241029	−	0.970518i	$-0.577485\pi$
$347$	−14.8923	−	2.62591i	−0.799458	−	0.140966i	−0.558430	+	0.829552i	$0.688596\pi$
$348$		0			0
$349$	−14.4505	−	17.2214i	−0.773518	−	0.921843i	0.225104	−	0.974335i	$-0.427728\pi$
$349$	−14.4505	−	17.2214i	−0.773518	−	0.921843i	−0.998621	+	0.0524923i	$0.983284\pi$
$350$		0			0
$351$	11.7181	+	9.72667i	0.625465	+	0.519171i
$352$		0			0
$353$	−13.4020	−	15.9719i	−0.713316	−	0.850096i	0.280648	−	0.959811i	$-0.409451\pi$
$353$	−13.4020	−	15.9719i	−0.713316	−	0.850096i	−0.993963	+	0.109715i	$0.965006\pi$
$354$		0			0
$355$	−2.35457	+	13.3534i	−0.124967	+	0.708725i
$356$		0			0
$357$	5.81767	−	16.0727i	0.307904	−	0.850659i
$358$		0			0
$359$	5.43854	+	9.41983i	0.287035	+	0.497159i	0.973101	−	0.230380i	$-0.0739970\pi$
$359$	5.43854	+	9.41983i	0.287035	+	0.497159i	−0.686066	+	0.727540i	$0.740664\pi$
$360$		0			0
$361$	−27.6356	+	47.8663i	−1.45451	+	2.51928i
$362$		0			0
$363$	9.27839	−	11.0975i	0.486989	−	0.582470i
$364$		0			0
$365$	−10.6123	−	8.90479i	−0.555474	−	0.466098i
$366$		0			0
$367$	3.96735	−	10.9002i	0.207094	−	0.568985i	−0.792046	−	0.610462i	$-0.790984\pi$
$367$	3.96735	−	10.9002i	0.207094	−	0.568985i	0.999139	+	0.0414764i	$0.0132061\pi$
$368$		0			0
$369$	13.2406	−	15.8939i	0.689277	−	0.827401i
$370$		0			0
$371$	−0.463232	+	0.0816804i	−0.0240498	+	0.00424063i
$372$		0			0
$373$	−1.65913	−	4.55843i	−0.0859066	−	0.236027i	0.889299	−	0.457326i	$-0.151193\pi$
$373$	−1.65913	−	4.55843i	−0.0859066	−	0.236027i	−0.975206	+	0.221299i	$0.928970\pi$
$374$		0			0
$375$	12.0874	+	6.95008i	0.624193	+	0.358901i
$376$		0			0
$377$		−	14.8512i		−	0.764874i
$378$		0			0
$379$	−31.5863			−1.62248			−0.811238	−	0.584715i	$-0.801206\pi$
$379$	−31.5863			−1.62248			−0.811238	+	0.584715i	$0.801206\pi$
$380$		0			0
$381$	−15.8427	−	27.3282i	−0.811648	−	1.40006i
$382$		0			0
$383$	−5.33286	+	1.94100i	−0.272496	+	0.0991805i	−0.474654	−	0.880172i	$-0.657427\pi$
$383$	−5.33286	+	1.94100i	−0.272496	+	0.0991805i	0.202158	+	0.979353i	$0.435205\pi$
$384$		0			0
$385$	−1.93562	−	10.9774i	−0.0986482	−	0.559462i
$386$		0			0
$387$	−11.3489	−	4.08506i	−0.576898	−	0.207655i
$388$		0			0
$389$	7.70166	+	2.80317i	0.390490	+	0.142127i	0.529801	−	0.848122i	$-0.322267\pi$
$389$	7.70166	+	2.80317i	0.390490	+	0.142127i	−0.139311	+	0.990249i	$0.544489\pi$
$390$		0			0
$391$	−15.0411	+	17.9253i	−0.760660	+	0.906520i
$392$		0			0
$393$	−1.24112	+	7.11262i	−0.0626063	+	0.358784i
$394$		0			0
$395$	23.8902	+	13.7930i	1.20204	+	0.694001i
$396$		0			0
$397$	25.2112	−	14.5557i	1.26532	−	0.730531i	0.291218	−	0.956657i	$-0.405939\pi$
$397$	25.2112	−	14.5557i	1.26532	−	0.730531i	0.974098	+	0.226126i	$0.0726061\pi$
$398$		0			0
$399$	29.6741	−	24.9895i	1.48556	−	1.25104i
$400$		0			0
$401$	13.6729	+	2.41090i	0.682792	+	0.120395i	0.504276	−	0.863542i	$-0.331759\pi$
$401$	13.6729	+	2.41090i	0.682792	+	0.120395i	0.178516	+	0.983937i	$0.442870\pi$
$402$		0			0
$403$	8.14562	−	6.83498i	0.405762	−	0.340475i
$404$		0			0
$405$	22.2301	−	8.27050i	1.10462	−	0.410964i
$406$		0			0
$407$	9.21557	−	7.73278i	0.456799	−	0.383300i
$408$		0			0
$409$	−2.85854	+	16.2116i	−0.141346	+	0.801613i	0.828883	+	0.559422i	$0.188977\pi$
$409$	−2.85854	+	16.2116i	−0.141346	+	0.801613i	−0.970229	+	0.242190i	$0.922134\pi$
$410$		0			0
$411$	−21.1176	+	17.7838i	−1.04166	+	0.877212i
$412$		0			0
$413$	0.961601	+	1.66554i	0.0473173	+	0.0819559i
$414$		0			0
$415$	−26.2629	−	15.1629i	−1.28920	−	0.744318i
$416$		0			0
$417$	−4.04454	−	0.705755i	−0.198062	−	0.0345610i
$418$		0			0
$419$	−10.4296	+	12.4295i	−0.509520	+	0.607223i	−0.958070	−	0.286535i	$-0.907496\pi$
$419$	−10.4296	+	12.4295i	−0.509520	+	0.607223i	0.448549	+	0.893758i	$0.351941\pi$
$420$		0			0
$421$	−0.181389	+	0.498362i	−0.00884036	+	0.0242887i	−0.944034	−	0.329847i	$-0.893003\pi$
$421$	−0.181389	+	0.498362i	−0.00884036	+	0.0242887i	0.935194	+	0.354136i	$0.115225\pi$
$422$		0			0
$423$	0.776761	+	4.31550i	0.0377674	+	0.209827i
$424$		0			0
$425$	−7.27495	+	1.28277i	−0.352887	+	0.0622235i
$426$		0			0
$427$	−27.5740	+	10.0361i	−1.33440	+	0.485682i
$428$		0			0
$429$	7.14712	−	4.14334i	0.345066	−	0.200042i
$430$		0			0
$431$	−12.2920			−0.592084			−0.296042	−	0.955175i	$-0.595667\pi$
$431$	−12.2920			−0.592084			−0.296042	+	0.955175i	$0.595667\pi$
$432$		0			0
$433$	14.6907			0.705991			0.352996	−	0.935625i	$-0.385163\pi$
$433$	14.6907			0.705991			0.352996	+	0.935625i	$0.385163\pi$
$434$		0			0
$435$	−20.0520	−	11.5296i	−0.961420	−	0.552801i
$436$		0			0
$437$	−49.9053	+	18.1640i	−2.38729	+	0.868904i
$438$		0			0
$439$	28.8488	−	5.08682i	1.37688	−	0.242781i	0.564270	−	0.825591i	$-0.309158\pi$
$439$	28.8488	−	5.08682i	1.37688	−	0.242781i	0.812609	+	0.582810i	$0.198047\pi$
$440$		0			0
$441$	0.690724	−	0.254186i	0.0328916	−	0.0121041i
$442$		0			0
$443$	11.6096	−	31.8970i	0.551588	−	1.51547i	−0.279955	−	0.960013i	$-0.590320\pi$
$443$	11.6096	−	31.8970i	0.551588	−	1.51547i	0.831543	−	0.555461i	$-0.187458\pi$
$444$		0			0
$445$	−0.413240	+	0.492480i	−0.0195895	+	0.0233458i
$446$		0			0
$447$	17.7553	−	21.2364i	0.839795	−	1.00445i
$448$		0			0
$449$	−15.4011	−	8.89184i	−0.726823	−	0.419632i	0.0904355	−	0.995902i	$-0.471174\pi$
$449$	−15.4011	−	8.89184i	−0.726823	−	0.419632i	−0.817259	+	0.576271i	$0.804507\pi$
$450$		0			0
$451$	−5.61089	−	9.71834i	−0.264206	−	0.457619i
$452$		0			0
$453$	3.83996	+	1.38991i	0.180417	+	0.0653037i
$454$		0			0
$455$	−3.48587	+	19.7693i	−0.163420	+	0.926800i
$456$		0			0
$457$	9.21939	−	7.73598i	0.431265	−	0.361874i	−0.401164	−	0.916006i	$-0.631394\pi$
$457$	9.21939	−	7.73598i	0.431265	−	0.361874i	0.832429	+	0.554132i	$0.186950\pi$
$458$		0			0
$459$	9.77414	−	17.1397i	0.456218	−	0.800010i
$460$		0			0
$461$	12.6139	−	10.5843i	0.587487	−	0.492960i	−0.299909	−	0.953968i	$-0.596956\pi$
$461$	12.6139	−	10.5843i	0.587487	−	0.492960i	0.887396	+	0.461008i	$0.152512\pi$
$462$		0			0
$463$	3.83957	+	0.677019i	0.178440	+	0.0314638i	0.262154	−	0.965026i	$-0.415567\pi$
$463$	3.83957	+	0.677019i	0.178440	+	0.0314638i	−0.0837142	+	0.996490i	$0.526678\pi$
$464$		0			0
$465$	−2.90480	−	16.3045i	−0.134707	−	0.756101i
$466$		0			0
$467$	8.38005	−	4.83822i	0.387782	−	0.223886i	−0.293416	−	0.955985i	$-0.594792\pi$
$467$	8.38005	−	4.83822i	0.387782	−	0.223886i	0.681199	+	0.732098i	$0.261459\pi$
$468$		0			0
$469$	−30.8975	−	17.8387i	−1.42672	−	0.823715i
$470$		0			0
$471$	1.35083	−	0.494383i	0.0622431	−	0.0227800i
$472$		0			0
$473$	−4.20585	+	5.01234i	−0.193385	+	0.230468i
$474$		0			0
$475$	−15.7548	−	5.73429i	−0.722881	−	0.263107i
$476$		0			0
$477$	−0.542955	+	0.00192940i	−0.0248602	+	8.83411e-5i
$478$		0			0
$479$	0.352574	+	1.99955i	0.0161095	+	0.0913616i	0.991802	−	0.127780i	$-0.0407853\pi$
$479$	0.352574	+	1.99955i	0.0161095	+	0.0913616i	−0.975693	+	0.219142i	$0.929674\pi$
$480$		0			0
$481$	−20.3585	+	7.40988i	−0.928266	+	0.337861i
$482$		0			0
$483$	27.7404	−	0.0492878i	1.26223	−	0.00224267i
$484$		0			0
$485$	5.48126			0.248891
$486$		0			0
$487$			7.67766i			0.347908i	0.984754	+	0.173954i	$0.0556544\pi$
$487$			7.67766i			0.347908i	−0.984754	+	0.173954i	$0.944346\pi$
$488$		0			0
$489$	−0.0346694	−	19.5128i	−0.00156780	−	0.882399i
$490$		0			0
$491$	−6.23136	−	17.1205i	−0.281217	−	0.772638i	−0.997218	−	0.0745389i	$-0.976251\pi$
$491$	−6.23136	−	17.1205i	−0.281217	−	0.772638i	0.716001	−	0.698100i	$-0.245971\pi$
$492$		0			0
$493$	−18.9489	+	3.34121i	−0.853417	+	0.150480i
$494$		0			0
$495$	−0.0457219	−	12.8667i	−0.00205505	−	0.578314i
$496$		0			0
$497$	4.57346	−	12.5655i	0.205148	−	0.563638i
$498$		0			0
$499$	0.594620	+	0.498945i	0.0266189	+	0.0223359i	0.656000	−	0.754761i	$-0.272247\pi$
$499$	0.594620	+	0.498945i	0.0266189	+	0.0223359i	−0.629381	+	0.777097i	$0.716692\pi$
$500$		0			0
$501$	−10.4014	−	28.4205i	−0.464702	−	1.26973i
$502$		0			0
$503$	−16.6264	+	28.7978i	−0.741335	+	1.28403i	0.210552	+	0.977583i	$0.432474\pi$
$503$	−16.6264	+	28.7978i	−0.741335	+	1.28403i	−0.951887	+	0.306448i	$0.900859\pi$
$504$		0			0
$505$	−23.5098	−	40.7203i	−1.04617	−	1.81203i
$506$		0			0
$507$	7.52046	−	1.33984i	0.333995	−	0.0595045i
$508$		0			0
$509$	5.59821	−	31.7490i	0.248136	−	1.40725i	−0.564958	−	0.825119i	$-0.691108\pi$
$509$	5.59821	−	31.7490i	0.248136	−	1.40725i	0.813095	−	0.582132i	$-0.197781\pi$
$510$		0			0
$511$	8.78164	+	10.4655i	0.388477	+	0.462969i
$512$		0			0
$513$	38.6614	−	22.5968i	1.70694	−	0.997674i
$514$		0			0
$515$	21.2631	+	25.3404i	0.936966	+	1.11663i
$516$		0			0
$517$	2.34251	+	0.413048i	0.103024	+	0.0181658i
$518$		0			0
$519$	10.9653	−	30.2942i	0.481321	−	1.32977i
$520$		0			0
$521$	−27.9816	+	16.1552i	−1.22590	+	0.707773i	−0.966169	−	0.257909i	$-0.916966\pi$
$521$	−27.9816	+	16.1552i	−1.22590	+	0.707773i	−0.259729	+	0.965682i	$0.583633\pi$
$522$		0			0
$523$	1.25831	−	2.17946i	0.0550222	−	0.0953012i	−0.837202	−	0.546893i	$-0.815810\pi$
$523$	1.25831	−	2.17946i	0.0550222	−	0.0953012i	0.892225	+	0.451592i	$0.149144\pi$
$524$		0			0
$525$	6.71862	+	5.61728i	0.293225	+	0.245158i
$526$		0			0
$527$	−10.5535	−	8.85544i	−0.459718	−	0.385749i
$528$		0			0
$529$	−14.0722	−	5.12185i	−0.611833	−	0.222689i
$530$		0			0
$531$	0.766678	+	2.08336i	0.0332710	+	0.0904103i
$532$		0			0
$533$	3.50932	+	19.9023i	0.152005	+	0.862066i
$534$		0			0
$535$	−9.86054	−	27.0916i	−0.426308	−	1.17127i
$536$		0			0
$537$	6.11760	−	10.6396i	0.263994	−	0.459133i
$538$		0			0
$539$		−	0.399264i		−	0.0171975i
$540$		0			0
$541$			20.7984i			0.894192i	0.894486	+	0.447096i	$0.147542\pi$
$541$			20.7984i			0.894192i	−0.894486	+	0.447096i	$0.852458\pi$
$542$		0			0
$543$	0.130260	+	0.224693i	0.00558997	+	0.00964251i
$544$		0			0
$545$	5.72888	+	15.7400i	0.245398	+	0.674226i
$546$		0			0
$547$	3.11764	+	17.6810i	0.133301	+	0.755985i	0.976028	+	0.217645i	$0.0698375\pi$
$547$	3.11764	+	17.6810i	0.133301	+	0.755985i	−0.842727	+	0.538341i	$0.819051\pi$
$548$		0			0
$549$	−33.3358	+	6.00021i	−1.42274	+	0.256083i
$550$		0			0
$551$	−41.0363	−	14.9360i	−1.74820	−	0.636294i
$552$		0			0
$553$	−20.8398	−	17.4867i	−0.886200	−	0.743610i
$554$		0			0
$555$	−5.80032	+	33.2405i	−0.246210	+	1.41098i
$556$		0			0
$557$	−15.8779	+	27.5013i	−0.672766	+	1.16527i	0.304350	+	0.952560i	$0.401561\pi$
$557$	−15.8779	+	27.5013i	−0.672766	+	1.16527i	−0.977116	+	0.212705i	$0.931773\pi$
$558$		0			0
$559$	10.2049	−	5.89179i	0.431621	−	0.249196i
$560$		0			0
$561$	−6.89453	−	8.18700i	−0.291087	−	0.345655i
$562$		0			0
$563$	−21.2510	−	3.74712i	−0.895621	−	0.157922i	−0.293153	−	0.956065i	$-0.594705\pi$
$563$	−21.2510	−	3.74712i	−0.895621	−	0.157922i	−0.602468	+	0.798143i	$0.705816\pi$
$564$		0			0
$565$	−5.97745	−	7.12365i	−0.251473	−	0.299694i
$566$		0			0
$567$	−23.0060	+	4.22537i	−0.966159	+	0.177449i
$568$		0			0
$569$	28.0024	+	33.3720i	1.17392	+	1.39903i	0.899221	+	0.437495i	$0.144134\pi$
$569$	28.0024	+	33.3720i	1.17392	+	1.39903i	0.274701	+	0.961530i	$0.411421\pi$
$570$		0			0
$571$	−5.33260	+	30.2427i	−0.223162	+	1.26562i	0.643005	+	0.765862i	$0.277687\pi$
$571$	−5.33260	+	30.2427i	−0.223162	+	1.26562i	−0.866167	+	0.499754i	$0.833424\pi$
$572$		0			0
$573$	12.1968	+	14.4833i	0.509529	+	0.605046i
$574$		0			0
$575$	−5.99429	−	10.3824i	−0.249979	−	0.432977i
$576$		0			0
$577$	−18.5251	+	32.0864i	−0.771210	+	1.33578i	0.165690	+	0.986178i	$0.447015\pi$
$577$	−18.5251	+	32.0864i	−0.771210	+	1.33578i	−0.936900	+	0.349597i	$0.886318\pi$
$578$		0			0
$579$	−5.00143	−	0.872727i	−0.207852	−	0.0362693i
$580$		0			0
$581$	22.9096	+	19.2235i	0.950452	+	0.797524i
$582$		0			0
$583$	−0.100738	+	0.276776i	−0.00417216	+	0.0114629i
$584$		0			0
$585$	−7.84780	+	21.8024i	−0.324467	+	0.901418i
$586$		0			0
$587$	−2.18563	+	0.385385i	−0.0902104	+	0.0159065i	−0.218571	−	0.975821i	$-0.570140\pi$
$587$	−2.18563	+	0.385385i	−0.0902104	+	0.0159065i	0.128361	+	0.991728i	$0.459028\pi$
$588$		0			0
$589$	−10.6941	−	29.3817i	−0.440642	−	1.21065i
$590$		0			0
$591$	−4.21471	+	2.44336i	−0.173370	+	0.100506i
$592$		0			0
$593$			7.72015i			0.317028i	0.987357	+	0.158514i	$0.0506704\pi$
$593$			7.72015i			0.317028i	−0.987357	+	0.158514i	$0.949330\pi$
$594$		0			0
$595$	26.0084			1.06624
$596$		0			0
$597$	0.871661	−	1.51598i	0.0356747	−	0.0620448i
$598$		0			0
$599$	5.13051	−	1.86735i	0.209627	−	0.0762980i	−0.235072	−	0.971978i	$-0.575533\pi$
$599$	5.13051	−	1.86735i	0.209627	−	0.0762980i	0.444699	+	0.895680i	$0.353311\pi$
$600$		0			0
$601$	2.68385	+	15.2209i	0.109477	+	0.620872i	0.989337	+	0.145641i	$0.0465245\pi$
$601$	2.68385	+	15.2209i	0.109477	+	0.620872i	−0.879861	+	0.475231i	$0.842364\pi$
$602$		0			0
$603$	−31.6415	−	26.3593i	−1.28854	−	1.07344i
$604$		0			0
$605$	20.6824	+	7.52779i	0.840860	+	0.306048i
$606$		0			0
$607$	0.0926471	−	0.110413i	0.00376043	−	0.00448151i	−0.764161	−	0.645026i	$-0.776847\pi$
$607$	0.0926471	−	0.110413i	0.00376043	−	0.00448151i	0.767921	+	0.640544i	$0.221291\pi$
$608$		0			0
$609$	17.4999	+	14.6312i	0.709130	+	0.592887i
$610$		0			0
$611$	−3.70982	−	2.14186i	−0.150083	−	0.0866505i
$612$		0			0
$613$	30.3578	−	17.5271i	1.22614	−	0.707913i	0.259921	−	0.965630i	$-0.416304\pi$
$613$	30.3578	−	17.5271i	1.22614	−	0.707913i	0.966220	+	0.257717i	$0.0829702\pi$
$614$		0			0
$615$	29.5965	+	10.7127i	1.19345	+	0.431979i
$616$		0			0
$617$	1.95314	+	0.344391i	0.0786304	+	0.0138647i	0.212825	−	0.977090i	$-0.431734\pi$
$617$	1.95314	+	0.344391i	0.0786304	+	0.0138647i	−0.134195	+	0.990955i	$0.542845\pi$
$618$		0			0
$619$	−30.9839	+	25.9986i	−1.24535	+	1.04497i	−0.248262	+	0.968693i	$0.579859\pi$
$619$	−30.9839	+	25.9986i	−1.24535	+	1.04497i	−0.997087	+	0.0762782i	$0.975696\pi$
$620$		0			0
$621$	31.5635	+	5.39219i	1.26660	+	0.216381i
$622$		0			0
$623$	0.485670	−	0.407525i	0.0194579	−	0.0163272i
$624$		0			0
$625$	−5.37310	+	30.4724i	−0.214924	+	1.21890i
$626$		0			0
$627$	−4.26081	−	23.9157i	−0.170160	−	0.955101i
$628$		0			0
$629$	14.0347	+	24.3087i	0.559598	+	0.969253i
$630$		0			0
$631$	−28.0718	−	16.2073i	−1.11752	−	0.645202i	−0.176755	−	0.984255i	$-0.556560\pi$
$631$	−28.0718	−	16.2073i	−1.11752	−	0.645202i	−0.940767	+	0.339053i	$0.889893\pi$
$632$		0			0
$633$	−2.52382	−	6.89599i	−0.100313	−	0.274091i
$634$		0			0
$635$	30.8946	−	36.8188i	1.22602	−	1.46111i
$636$		0			0
$637$	−0.245925	+	0.675673i	−0.00974390	+	0.0267711i
$638$		0			0
$639$	7.67005	−	13.3946i	0.303422	−	0.529883i
$640$		0			0
$641$	16.3026	−	2.87458i	0.643912	−	0.113539i	0.157850	−	0.987463i	$-0.449544\pi$
$641$	16.3026	−	2.87458i	0.643912	−	0.113539i	0.486063	+	0.873924i	$0.338433\pi$
$642$		0			0
$643$	25.2314	−	9.18349i	0.995030	−	0.362161i	0.207364	−	0.978264i	$-0.433511\pi$
$643$	25.2314	−	9.18349i	0.995030	−	0.362161i	0.787666	+	0.616102i	$0.211289\pi$
$644$		0			0
$645$	−0.0326081	−	18.3526i	−0.00128394	−	0.722635i
$646$		0			0
$647$	−29.0527			−1.14218			−0.571090	−	0.820887i	$-0.693479\pi$
$647$	−29.0527			−1.14218			−0.571090	+	0.820887i	$0.693479\pi$
$648$		0			0
$649$	1.20426			0.0472714
$650$		0			0
$651$	0.0290182	+	16.3321i	0.00113731	+	0.640107i
$652$		0			0
$653$	32.5052	−	11.8309i	1.27203	−	0.462980i	0.384240	−	0.923233i	$-0.374463\pi$
$653$	32.5052	−	11.8309i	1.27203	−	0.462980i	0.887788	+	0.460253i	$0.152241\pi$
$654$		0			0
$655$	−10.8189	+	1.90767i	−0.422730	+	0.0745387i
$656$		0			0
$657$	7.93340	+	13.6290i	0.309512	+	0.531717i
$658$		0			0
$659$	−7.44079	+	20.4434i	−0.289852	+	0.796362i	0.706234	+	0.707978i	$0.250393\pi$
$659$	−7.44079	+	20.4434i	−0.289852	+	0.796362i	−0.996086	+	0.0883842i	$0.971830\pi$
$660$		0			0
$661$	−16.3906	+	19.5335i	−0.637519	+	0.759766i	−0.983976	−	0.178300i	$-0.942940\pi$
$661$	−16.3906	+	19.5335i	−0.637519	+	0.759766i	0.346457	+	0.938066i	$0.387385\pi$
$662$		0			0
$663$	6.62486	+	18.1015i	0.257288	+	0.703004i
$664$		0			0
$665$	51.1202	+	29.5143i	1.98236	+	1.14451i
$666$		0			0
$667$	−15.6132	−	27.0429i	−0.604546	−	1.04710i
$668$		0			0
$669$	4.85684	+	27.2612i	0.187776	+	1.05398i
$670$		0			0
$671$	−3.19066	+	18.0951i	−0.123174	+	0.698555i
$672$		0			0
$673$	−6.18349	+	5.18857i	−0.238356	+	0.200005i	−0.754139	−	0.656715i	$-0.771946\pi$
$673$	−6.18349	+	5.18857i	−0.238356	+	0.200005i	0.515783	+	0.856719i	$0.327501\pi$
$674$		0			0
$675$	6.53899	+	7.70904i	0.251686	+	0.296721i
$676$		0			0
$677$	−11.8370	+	9.93243i	−0.454933	+	0.381734i	−0.841263	−	0.540627i	$-0.818187\pi$
$677$	−11.8370	+	9.93243i	−0.454933	+	0.381734i	0.386330	+	0.922361i	$0.373743\pi$
$678$		0			0
$679$	−5.32333	−	0.938647i	−0.204291	−	0.0360220i
$680$		0			0
$681$	2.80016	+	1.01354i	0.107302	+	0.0388391i
$682$		0			0
$683$	1.82111	−	1.05142i	0.0696830	−	0.0402315i	−0.464754	−	0.885440i	$-0.653857\pi$
$683$	1.82111	−	1.05142i	0.0696830	−	0.0402315i	0.534437	+	0.845209i	$0.320524\pi$
$684$		0			0
$685$	−36.3798	−	21.0039i	−1.39000	−	0.802516i
$686$		0			0
$687$	12.2380	+	10.2319i	0.466907	+	0.390370i
$688$		0			0
$689$	0.340959	−	0.406339i	0.0129895	−	0.0154803i
$690$		0			0
$691$	21.9905	+	8.00388i	0.836557	+	0.304482i	0.724547	−	0.689225i	$-0.242049\pi$
$691$	21.9905	+	8.00388i	0.836557	+	0.304482i	0.112010	+	0.993707i	$0.464271\pi$
$692$		0			0
$693$	−2.15897	+	12.5038i	−0.0820125	+	0.474980i
$694$		0			0
$695$	−1.08478	−	6.15210i	−0.0411481	−	0.233362i
$696$		0			0
$697$	24.6043	−	8.95523i	0.931954	−	0.339203i
$698$		0			0
$699$	16.7155	−	29.0713i	0.632238	−	1.09958i
$700$		0			0
$701$	40.5028			1.52977			0.764884	−	0.644168i	$-0.222796\pi$
$701$	40.5028			1.52977			0.764884	+	0.644168i	$0.222796\pi$
$702$		0			0
$703$			63.7061i			2.40272i
$704$		0			0
$705$	−5.77202	+	3.34617i	−0.217387	+	0.126024i
$706$		0			0
$707$	15.8593	+	43.5730i	0.596450	+	1.63873i
$708$		0			0
$709$	−12.4782	+	2.20024i	−0.468628	+	0.0826317i	−0.402975	−	0.915211i	$-0.632024\pi$
$709$	−12.4782	+	2.20024i	−0.468628	+	0.0826317i	−0.0656523	+	0.997843i	$0.520913\pi$
$710$		0			0
$711$	−20.2703	−	23.9836i	−0.760195	−	0.899455i
$712$		0			0
$713$	7.64687	−	21.0096i	0.286377	−	0.786815i
$714$		0			0
$715$	9.62920	+	8.07986i	0.360112	+	0.302170i
$716$		0			0
$717$	7.89765	+	1.37810i	0.294943	+	0.0514662i
$718$		0			0
$719$	−23.2178	+	40.2145i	−0.865879	+	1.49975i	0.000291815		1.00000i	$0.499907\pi$
$719$	−23.2178	+	40.2145i	−0.865879	+	1.49975i	−0.866171	+	0.499747i	$0.833426\pi$
$720$		0			0
$721$	−16.3111	−	28.2516i	−0.607455	−	1.05214i
$722$		0			0
$723$	−30.7359	−	36.4977i	−1.14308	−	1.35737i
$724$		0			0
$725$	1.71183	−	9.70825i	0.0635756	−	0.360555i
$726$		0			0
$727$	7.82850	+	9.32964i	0.290343	+	0.346017i	0.891424	−	0.453171i	$-0.149707\pi$
$727$	7.82850	+	9.32964i	0.290343	+	0.346017i	−0.601081	+	0.799188i	$0.705263\pi$
$728$		0			0
$729$	−26.9985	+	0.287828i	−0.999943	+	0.0106603i
$730$		0			0
$731$	−9.81335	−	11.6951i	−0.362960	−	0.432559i
$732$		0			0
$733$	9.85329	+	1.73740i	0.363939	+	0.0641723i	0.352628	−	0.935764i	$-0.385288\pi$
$733$	9.85329	+	1.73740i	0.363939	+	0.0641723i	0.0113117	+	0.999936i	$0.496399\pi$
$734$		0			0
$735$	0.721370	+	0.856600i	0.0266081	+	0.0315962i
$736$		0			0
$737$	−19.3473	+	11.1702i	−0.712666	+	0.411458i
$738$		0			0
$739$	−22.0318	+	38.1602i	−0.810454	+	1.40375i	0.102093	+	0.994775i	$0.467446\pi$
$739$	−22.0318	+	38.1602i	−0.810454	+	1.40375i	−0.912547	+	0.408972i	$0.865887\pi$
$740$		0			0
$741$	−7.52023	+	43.0969i	−0.276262	+	1.58321i
$742$		0			0
$743$	−6.42946	−	5.39496i	−0.235874	−	0.197922i	0.517187	−	0.855872i	$-0.326979\pi$
$743$	−6.42946	−	5.39496i	−0.235874	−	0.197922i	−0.753061	+	0.657950i	$0.771424\pi$
$744$		0			0
$745$	39.5782	+	14.4053i	1.45003	+	0.527769i
$746$		0			0
$747$	22.2835	+	26.3656i	0.815311	+	0.964668i
$748$		0			0
$749$	4.93709	+	27.9996i	0.180397	+	1.02308i
$750$		0			0
$751$	−7.74342	−	21.2749i	−0.282561	−	0.776331i	−0.997055	−	0.0766890i	$-0.975565\pi$
$751$	−7.74342	−	21.2749i	−0.282561	−	0.776331i	0.714494	−	0.699642i	$-0.246657\pi$
$752$		0			0
$753$	−12.0604	−	20.8038i	−0.439505	−	0.758132i
$754$		0			0
$755$			6.21370i			0.226140i
$756$		0			0
$757$		−	19.5088i		−	0.709058i	−0.935045	−	0.354529i	$-0.884641\pi$
$757$		−	19.5088i		−	0.709058i	0.935045	−	0.354529i	$-0.115359\pi$
$758$		0			0
$759$	8.65844	−	15.0586i	0.314281	−	0.546592i
$760$		0			0
$761$	−9.62500	−	26.4445i	−0.348906	−	0.958612i	−0.982715	−	0.185122i	$-0.940732\pi$
$761$	−9.62500	−	26.4445i	−0.348906	−	0.958612i	0.633809	−	0.773489i	$-0.281490\pi$
$762$		0			0
$763$	−2.86840	−	16.2675i	−0.103843	−	0.588924i
$764$		0			0
$765$	29.5837	+	5.10808i	1.06960	+	0.184683i
$766$		0			0
$767$	−2.03797	−	0.741760i	−0.0735868	−	0.0267834i
$768$		0			0
$769$	12.3157	+	10.3341i	0.444117	+	0.372658i	0.837247	−	0.546824i	$-0.184163\pi$
$769$	12.3157	+	10.3341i	0.444117	+	0.372658i	−0.393130	+	0.919483i	$0.628608\pi$
$770$		0			0
$771$	2.25463	+	1.88505i	0.0811987	+	0.0678883i
$772$		0			0
$773$	6.27436	−	10.8675i	0.225673	−	0.390877i	−0.730848	−	0.682540i	$-0.760875\pi$
$773$	6.27436	−	10.8675i	0.225673	−	0.390877i	0.956521	+	0.291663i	$0.0942086\pi$
$774$		0			0
$775$	6.11265	−	3.52914i	0.219573	−	0.126770i
$776$		0			0
$777$	11.3255	−	31.2895i	0.406301	−	1.12251i
$778$		0			0
$779$	58.5229	+	10.3192i	2.09680	+	0.369722i
$780$		0			0
$781$	−5.38215	−	6.41420i	−0.192589	−	0.229518i
$782$		0			0
$783$	17.0320	+	20.0796i	0.608673	+	0.717586i
$784$		0			0
$785$	1.40687	+	1.67664i	0.0502134	+	0.0598420i
$786$		0			0
$787$	3.64035	−	20.6454i	0.129764	−	0.735930i	−0.848599	−	0.529037i	$-0.822553\pi$
$787$	3.64035	−	20.6454i	0.129764	−	0.735930i	0.978363	−	0.206894i	$-0.0663354\pi$
$788$		0			0
$789$	7.07537	−	1.26054i	0.251890	−	0.0448766i
$790$		0			0
$791$	4.58533	+	7.94202i	0.163036	+	0.282386i
$792$		0			0
$793$	16.5452	−	28.6571i	0.587536	−	1.01764i
$794$		0			0
$795$	−0.283937	−	0.775819i	−0.0100702	−	0.0275155i
$796$		0			0
$797$	−21.2235	−	17.8086i	−0.751775	−	0.630814i	0.184197	−	0.982889i	$-0.441032\pi$
$797$	−21.2235	−	17.8086i	−0.751775	−	0.630814i	−0.935972	+	0.352075i	$0.885476\pi$
$798$		0			0
$799$	−1.89822	+	5.21531i	−0.0671541	+	0.184504i
$800$		0			0
$801$	0.632474	−	0.368162i	0.0223474	−	0.0130084i
$802$		0			0
$803$	8.42472	−	1.48550i	0.297302	−	0.0524223i
$804$		0			0
$805$	14.4362	+	39.6632i	0.508810	+	1.39794i
$806$		0			0
$807$	0.0967727	+	54.4661i	0.00340656	+	1.91730i
$808$		0			0
$809$		−	21.9542i		−	0.771867i	−0.922527	−	0.385933i	$-0.873879\pi$
$809$		−	21.9542i		−	0.771867i	0.922527	−	0.385933i	$-0.126121\pi$
$810$		0			0
$811$	17.4685			0.613401			0.306700	−	0.951806i	$-0.400775\pi$
$811$	17.4685			0.613401			0.306700	+	0.951806i	$0.400775\pi$
$812$		0			0
$813$	−48.7942	+	0.0866951i	−1.71129	+	0.00304053i
$814$		0			0
$815$	27.8994	−	10.1546i	0.977274	−	0.355699i
$816$		0			0
$817$	−6.01685	−	34.1233i	−0.210503	−	1.19382i
$818$		0			0
$819$	11.3553	−	19.8303i	0.396786	−	0.692928i
$820$		0			0
$821$	−40.3394	−	14.6823i	−1.40786	−	0.512417i	−0.477355	−	0.878710i	$-0.658405\pi$
$821$	−40.3394	−	14.6823i	−1.40786	−	0.512417i	−0.930500	+	0.366293i	$0.880627\pi$
$822$		0			0
$823$	17.8062	−	21.2206i	0.620686	−	0.739705i	−0.360502	−	0.932758i	$-0.617395\pi$
$823$	17.8062	−	21.2206i	0.620686	−	0.739705i	0.981188	+	0.193053i	$0.0618390\pi$
$824$		0			0
$825$	5.14968	−	1.88470i	0.179289	−	0.0656168i
$826$		0			0
$827$	−23.1043	−	13.3392i	−0.803414	−	0.463851i	0.0412497	−	0.999149i	$-0.486866\pi$
$827$	−23.1043	−	13.3392i	−0.803414	−	0.463851i	−0.844663	+	0.535298i	$0.820199\pi$
$828$		0			0
$829$	−2.23315	+	1.28931i	−0.0775606	+	0.0447796i	−0.538279	−	0.842767i	$-0.680925\pi$
$829$	−2.23315	+	1.28931i	−0.0775606	+	0.0447796i	0.460718	+	0.887547i	$0.347592\pi$
$830$		0			0
$831$	−7.50187	−	42.1076i	−0.260237	−	1.46070i
$832$		0			0
$833$	0.917434	+	0.161768i	0.0317872	+	0.00560494i
$834$		0			0
$835$	35.2753	−	29.5995i	1.22075	−	1.02433i
$836$		0			0
$837$	−3.17465	+	18.5830i	−0.109732	+	0.642323i
$838$		0			0
$839$	27.0517	−	22.6991i	0.933928	−	0.783659i	−0.0425905	−	0.999093i	$-0.513561\pi$
$839$	27.0517	−	22.6991i	0.933928	−	0.783659i	0.976518	+	0.215434i	$0.0691166\pi$
$840$		0			0
$841$	−0.577037	+	3.27254i	−0.0198978	+	0.112846i
$842$		0			0
$843$	31.3652	+	11.3529i	1.08028	+	0.391016i
$844$		0			0
$845$	5.81151	+	10.0658i	0.199922	+	0.346275i
$846$		0			0
$847$	−18.7974	−	10.8527i	−0.645887	−	0.372903i
$848$		0			0
$849$	−9.94863	+	11.8992i	−0.341436	+	0.408379i
$850$		0			0
$851$	−29.2812	+	34.8959i	−1.00375	+	1.19622i
$852$		0			0
$853$	11.8972	−	32.6874i	0.407354	−	1.11919i	−0.551222	−	0.834358i	$-0.685838\pi$
$853$	11.8972	−	32.6874i	0.407354	−	1.11919i	0.958576	−	0.284837i	$-0.0919393\pi$
$854$		0			0
$855$	52.3511	+	43.6117i	1.79037	+	1.49149i
$856$		0			0
$857$	−14.7995	+	2.60955i	−0.505541	+	0.0891405i	−0.420601	−	0.907246i	$-0.638181\pi$
$857$	−14.7995	+	2.60955i	−0.505541	+	0.0891405i	−0.0849397	+	0.996386i	$0.527070\pi$
$858$		0			0
$859$	11.2421	−	4.09177i	0.383574	−	0.139610i	−0.143034	−	0.989718i	$-0.545686\pi$
$859$	11.2421	−	4.09177i	0.383574	−	0.139610i	0.526608	+	0.850108i	$0.323464\pi$
$860$		0			0
$861$	−26.9092	−	15.4724i	−0.917065	−	0.527297i
$862$		0			0
$863$	4.99128			0.169905			0.0849526	−	0.996385i	$-0.472926\pi$
$863$	4.99128			0.169905			0.0849526	+	0.996385i	$0.472926\pi$
$864$		0			0
$865$	49.0210			1.66676
$866$		0			0
$867$	−3.86816	+	2.24246i	−0.131370	+	0.0761578i
$868$		0			0
$869$	−16.0074	+	5.82624i	−0.543016	+	0.197641i
$870$		0			0
$871$	39.6216	−	6.98635i	1.34253	−	0.236724i
$872$		0			0
$873$	−5.87078	−	2.11320i	−0.198696	−	0.0715208i
$874$		0			0
$875$	7.15570	−	19.6601i	0.241907	−	0.664634i
$876$		0			0
$877$	13.3228	−	15.8774i	0.449878	−	0.536143i	−0.492670	−	0.870217i	$-0.663979\pi$
$877$	13.3228	−	15.8774i	0.449878	−	0.536143i	0.942547	+	0.334073i	$0.108423\pi$
$878$		0			0
$879$	−36.3069	−	6.33539i	−1.22460	−	0.213687i
$880$		0			0
$881$	7.33774	+	4.23645i	0.247215	+	0.142729i	0.618488	−	0.785794i	$-0.287745\pi$
$881$	7.33774	+	4.23645i	0.247215	+	0.142729i	−0.371274	+	0.928524i	$0.621079\pi$
$882$		0			0
$883$	−9.03674	−	15.6521i	−0.304111	−	0.526735i	0.672952	−	0.739686i	$-0.265026\pi$
$883$	−9.03674	−	15.6521i	−0.304111	−	0.526735i	−0.977063	+	0.212951i	$0.931693\pi$
$884$		0			0
$885$	−2.58368	+	2.17580i	−0.0868495	+	0.0731387i
$886$		0			0
$887$	−3.87890	+	21.9983i	−0.130241	+	0.738632i	0.847816	+	0.530291i	$0.177917\pi$
$887$	−3.87890	+	21.9983i	−0.130241	+	0.738632i	−0.978056	+	0.208341i	$0.933194\pi$
$888$		0			0
$889$	−36.3096	+	30.4674i	−1.21779	+	1.02184i
$890$		0			0
$891$	−4.91153	+	13.7987i	−0.164542	+	0.462273i
$892$		0			0
$893$	−9.64933	+	8.09675i	−0.322903	+	0.270948i
$894$		0			0
$895$	18.3904	+	3.24272i	0.614723	+	0.108392i
$896$		0			0
$897$	−23.9279	+	20.1505i	−0.798930	+	0.672805i
$898$		0			0
$899$	15.9215	−	9.19228i	0.531012	−	0.306580i
$900$		0			0
$901$	−0.595165	−	0.343619i	−0.0198278	−	0.0114476i
$902$		0			0
$903$	−3.11116	+	17.8295i	−0.103533	+	0.593327i
$904$		0			0
$905$	−0.254017	+	0.302725i	−0.00844380	+	0.0100629i
$906$		0			0
$907$	−37.7812	−	13.7512i	−1.25450	−	0.456602i	−0.372583	−	0.927999i	$-0.621528\pi$
$907$	−37.7812	−	13.7512i	−1.25450	−	0.456602i	−0.881921	+	0.471397i	$0.843750\pi$
$908$		0			0
$909$	9.48165	+	52.6778i	0.314487	+	1.74721i
$910$		0			0
$911$	1.26349	+	7.16560i	0.0418613	+	0.237407i	0.998558	−	0.0536786i	$-0.0170946\pi$
$911$	1.26349	+	7.16560i	0.0418613	+	0.237407i	−0.956697	+	0.291086i	$0.905984\pi$
$912$		0			0
$913$	17.5973	−	6.40489i	0.582386	−	0.211971i
$914$		0			0
$915$	−25.8480	−	44.5869i	−0.854508	−	1.47400i
$916$		0			0
$917$	10.8339			0.357766
$918$		0			0
$919$			24.9111i			0.821741i	0.911694	+	0.410870i	$0.134775\pi$
$919$			24.9111i			0.821741i	−0.911694	+	0.410870i	$0.865225\pi$
$920$		0			0
$921$	13.4807	+	7.75117i	0.444203	+	0.255410i
$922$		0			0
$923$	5.15741	+	14.1699i	0.169758	+	0.466406i
$924$		0			0
$925$	−14.1625	+	2.49723i	−0.465660	+	0.0821084i
$926$		0			0
$927$	−13.0047	−	35.3388i	−0.427130	−	1.16068i
$928$		0			0
$929$	12.8203	−	35.2236i	0.420621	−	1.15565i	−0.530730	−	0.847541i	$-0.678082\pi$
$929$	12.8203	−	35.2236i	0.420621	−	1.15565i	0.951352	−	0.308107i	$-0.0996955\pi$
$930$		0			0
$931$	1.61967	+	1.35906i	0.0530825	+	0.0445415i
$932$		0			0
$933$	−18.9141	+	22.6225i	−0.619220	+	0.740626i
$934$		0			0
$935$	8.14289	−	14.1039i	0.266301	−	0.461247i
$936$		0			0
$937$	4.91136	+	8.50673i	0.160447	+	0.277903i	0.935029	−	0.354571i	$-0.115373\pi$
$937$	4.91136	+	8.50673i	0.160447	+	0.277903i	−0.774582	+	0.632474i	$0.782040\pi$
$938$		0			0
$939$	−5.67371	+	15.6750i	−0.185155	+	0.511534i
$940$		0			0
$941$	−1.11021	+	6.29630i	−0.0361918	+	0.205254i	−0.997542	−	0.0700759i	$-0.977676\pi$
$941$	−1.11021	+	6.29630i	−0.0361918	+	0.205254i	0.961350	+	0.275330i	$0.0887870\pi$
$942$		0			0
$943$	27.3138	+	32.5513i	0.889459	+	1.06002i
$944$		0			0
$945$	−17.9593	−	30.7270i	−0.584215	−	0.999548i
$946$		0			0
$947$	−2.56959	−	3.06232i	−0.0835006	−	0.0995121i	0.722677	−	0.691186i	$-0.242912\pi$
$947$	−2.56959	−	3.06232i	−0.0835006	−	0.0995121i	−0.806177	+	0.591674i	$0.798467\pi$
$948$		0			0
$949$	−15.1721	−	2.67525i	−0.492508	−	0.0868424i
$950$		0			0
$951$	10.3409	−	1.84233i	0.335326	−	0.0597416i
$952$		0			0
$953$	38.3667	−	22.1510i	1.24282	−	0.717542i	0.273152	−	0.961971i	$-0.411934\pi$
$953$	38.3667	−	22.1510i	1.24282	−	0.717542i	0.969667	+	0.244428i	$0.0786003\pi$
$954$		0			0
$955$	−14.4052	+	24.9506i	−0.466142	+	0.807382i
$956$		0			0
$957$	13.4133	−	4.90903i	0.433589	−	0.158687i
$958$		0			0
$959$	31.7348	+	26.6286i	1.02477	+	0.859883i
$960$		0			0
$961$	−16.7611	−	6.10053i	−0.540680	−	0.196791i
$962$		0			0
$963$	0.116621	+	32.8184i	0.00375805	+	1.05756i
$964$		0			0
$965$	−1.34143	−	7.60761i	−0.0431820	−	0.244897i
$966$		0			0
$967$	−8.11445	−	22.2943i	−0.260943	−	0.716935i	−0.999104	−	0.0423110i	$-0.986528\pi$
$967$	−8.11445	−	22.2943i	−0.260943	−	0.716935i	0.738161	−	0.674624i	$-0.235694\pi$
$968$		0			0
$969$	56.6802	−	0.100707i	1.82083	−	0.00323516i
$970$		0			0
$971$		−	23.3729i		−	0.750071i	−0.927010	−	0.375036i	$-0.877631\pi$
$971$		−	23.3729i		−	0.750071i	0.927010	−	0.375036i	$-0.122369\pi$
$972$		0			0
$973$			6.16061i			0.197500i
$974$		0			0
$975$	−9.87566	+	0.0175466i	−0.316274	+	0.000561941i
$976$		0			0
$977$	17.9667	+	49.3632i	0.574807	+	1.57927i	0.796814	+	0.604224i	$0.206517\pi$
$977$	17.9667	+	49.3632i	0.574807	+	1.57927i	−0.222007	+	0.975045i	$0.571261\pi$
$978$		0			0
$979$	−0.0689371	−	0.390962i	−0.00220324	−	0.0124952i
$980$		0			0
$981$	−0.0677555	−	19.0672i	−0.00216327	−	0.608768i
$982$		0			0
$983$	10.1837	+	3.70656i	0.324809	+	0.118221i	0.499278	−	0.866442i	$-0.333599\pi$
$983$	10.1837	+	3.70656i	0.324809	+	0.118221i	−0.174469	+	0.984663i	$0.555821\pi$
$984$		0			0
$985$	−5.67841	−	4.76475i	−0.180929	−	0.151817i
$986$		0			0
$987$	6.17874	−	2.26132i	0.196671	−	0.0719785i
$988$		0			0
$989$	12.3882	−	21.4570i	0.393923	−	0.682294i
$990$		0			0
$991$	−37.1953	+	21.4747i	−1.18155	+	0.682167i	−0.956372	−	0.292152i	$-0.905629\pi$
$991$	−37.1953	+	21.4747i	−1.18155	+	0.682167i	−0.225175	+	0.974318i	$0.572295\pi$
$992$		0			0
$993$	−6.26721	+	1.11656i	−0.198884	+	0.0354330i
$994$		0			0
$995$	2.62034	+	0.462037i	0.0830704	+	0.0146475i
$996$		0			0
$997$	27.5401	+	32.8210i	0.872204	+	1.03945i	0.998871	+	0.0475071i	$0.0151277\pi$
$997$	27.5401	+	32.8210i	0.872204	+	1.03945i	−0.126667	+	0.991945i	$0.540428\pi$
$998$		0			0
$999$	19.0278	−	33.3666i	0.602012	−	1.05567i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.bh.b.815.18		192
4.3	odd	2		216.2.v.b.59.2	yes	192
8.3	odd	2	inner	864.2.bh.b.815.17		192
8.5	even	2		216.2.v.b.59.17	yes	192
12.11	even	2		648.2.v.b.611.31		192
24.5	odd	2		648.2.v.b.611.16		192
27.11	odd	18	inner	864.2.bh.b.335.17		192
108.11	even	18		216.2.v.b.11.17	yes	192
108.43	odd	18		648.2.v.b.35.16		192
216.11	even	18	inner	864.2.bh.b.335.18		192
216.173	odd	18		216.2.v.b.11.2	✓	192
216.205	even	18		648.2.v.b.35.31		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.v.b.11.2	✓	192	216.173	odd	18
216.2.v.b.11.17	yes	192	108.11	even	18
216.2.v.b.59.2	yes	192	4.3	odd	2
216.2.v.b.59.17	yes	192	8.5	even	2
648.2.v.b.35.16		192	108.43	odd	18
648.2.v.b.35.31		192	216.205	even	18
648.2.v.b.611.16		192	24.5	odd	2
648.2.v.b.611.31		192	12.11	even	2
864.2.bh.b.335.17		192	27.11	odd	18	inner
864.2.bh.b.335.18		192	216.11	even	18	inner
864.2.bh.b.815.17		192	8.3	odd	2	inner
864.2.bh.b.815.18		192	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.bh (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.00307742 - 1.73205i) q^{3} +(2.47648 - 0.901367i) q^{5} +(-2.55949 + 0.451307i) q^{7} +(-2.99998 + 0.0106605i) q^{9} +(-0.556608 + 1.52927i) q^{11} +(1.88389 - 2.24514i) q^{13} +(-1.56883 - 4.28662i) q^{15} +(-3.28845 - 1.89859i) q^{17} +(-4.30904 - 7.46347i) q^{19} +(0.789562 + 4.43177i) q^{21} +(1.07009 - 6.06879i) q^{23} +(1.49029 - 1.25050i) q^{25} +(0.0276967 + 5.19608i) q^{27} +(3.88174 - 3.25716i) q^{29} +(3.57300 + 0.630016i) q^{31} +(2.65048 + 0.959365i) q^{33} +(-5.93174 + 3.42469i) q^{35} +(-6.40179 - 3.69607i) q^{37} +(-3.89448 - 3.25608i) q^{39} +(-4.43232 + 5.28224i) q^{41} +(3.77811 + 1.37512i) q^{43} +(-7.41980 + 2.73048i) q^{45} +(-0.253807 - 1.43941i) q^{47} +(-0.230541 + 0.0839100i) q^{49} +(-3.27833 + 5.70160i) q^{51} +0.180986 q^{53} +4.28892i q^{55} +(-12.9138 + 7.48643i) q^{57} +(-0.253090 - 0.695359i) q^{59} +(11.1190 - 1.96057i) q^{61} +(7.67361 - 1.38120i) q^{63} +(2.64174 - 7.25812i) q^{65} +(10.5159 + 8.82387i) q^{67} +(-10.5147 - 1.83477i) q^{69} +(-2.57253 + 4.45576i) q^{71} +(-2.62831 - 4.55236i) q^{73} +(-2.17052 - 2.57741i) q^{75} +(0.734463 - 4.16534i) q^{77} +(6.72831 + 8.01849i) q^{79} +(8.99977 - 0.0639625i) q^{81} +(-7.39656 - 8.81488i) q^{83} +(-9.85513 - 1.73773i) q^{85} +(-5.65351 - 6.71333i) q^{87} +(-0.211259 + 0.121971i) q^{89} +(-3.80856 + 6.59662i) q^{91} +(1.08022 - 6.19054i) q^{93} +(-17.3986 - 14.5992i) q^{95} +(1.95441 + 0.711348i) q^{97} +(1.65351 - 4.59371i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 12 q^{3} - 12 q^{9} + 30 q^{11} - 18 q^{17} + 6 q^{19} - 12 q^{25} - 18 q^{27} - 30 q^{33} + 18 q^{35} + 18 q^{41} + 42 q^{43} - 12 q^{49} + 18 q^{51} - 36 q^{57} + 84 q^{59} - 12 q^{65} - 30 q^{67}+ \cdots + 12 q^{99}+O(q^{100}) \) 192 * q + 12 * q^3 - 12 * q^9 + 30 * q^11 - 18 * q^17 + 6 * q^19 - 12 * q^25 - 18 * q^27 - 30 * q^33 + 18 * q^35 + 18 * q^41 + 42 * q^43 - 12 * q^49 + 18 * q^51 - 36 * q^57 + 84 * q^59 - 12 * q^65 - 30 * q^67 - 6 * q^73 + 96 * q^75 - 12 * q^81 + 72 * q^83 + 144 * q^89 + 6 * q^91 - 42 * q^97 + 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more