LMFDB - Embedded newform 840.2.dd.a.73.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [840,2,Mod(73,840)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(840, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 0, 0, 9, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("840.73"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	840.dd (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,0,0,0,0,0] 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:	$6.70743376979$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			73.7
Character	$\chi$	$=$	840.73
Dual form			840.2.dd.a.817.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.258819 + 0.965926i) q^{3} +(-1.93516 + 1.12034i) q^{5} +(-1.60015 - 2.10702i) q^{7} +(-0.866025 + 0.500000i) q^{9} +(2.59281 - 4.49089i) q^{11} +(0.393426 - 0.393426i) q^{13} +(-1.58302 - 1.57925i) q^{15} +(4.10895 - 1.10099i) q^{17} +(2.32458 + 4.02629i) q^{19} +(1.62108 - 2.09096i) q^{21} +(0.979264 - 3.65466i) q^{23} +(2.48967 - 4.33607i) q^{25} +(-0.707107 - 0.707107i) q^{27} -1.14155i q^{29} +(9.03971 + 5.21908i) q^{31} +(5.00893 + 1.34214i) q^{33} +(5.45712 + 2.28471i) q^{35} +(-6.54631 - 1.75408i) q^{37} +(0.481847 + 0.278194i) q^{39} -3.89354i q^{41} +(8.49370 + 8.49370i) q^{43} +(1.11573 - 1.93782i) q^{45} +(2.37678 - 8.87026i) q^{47} +(-1.87906 + 6.74308i) q^{49} +(2.12695 + 3.68398i) q^{51} +(-3.74856 + 1.00442i) q^{53} +(0.0138177 + 11.5954i) q^{55} +(-3.28745 + 3.28745i) q^{57} +(1.64769 - 2.85388i) q^{59} +(3.21272 - 1.85487i) q^{61} +(2.43928 + 1.02466i) q^{63} +(-0.320571 + 1.20211i) q^{65} +(-2.26242 - 8.44346i) q^{67} +3.78358 q^{69} -14.9427 q^{71} +(-2.84783 - 10.6282i) q^{73} +(4.83270 + 1.28258i) q^{75} +(-13.6113 + 1.72296i) q^{77} +(14.8470 - 8.57194i) q^{79} +(0.500000 - 0.866025i) q^{81} +(0.465956 - 0.465956i) q^{83} +(-6.71798 + 6.73401i) q^{85} +(1.10265 - 0.295455i) q^{87} +(1.44086 + 2.49564i) q^{89} +(-1.45850 - 0.199417i) q^{91} +(-2.70159 + 10.0825i) q^{93} +(-9.00925 - 5.18719i) q^{95} +(3.58097 + 3.58097i) q^{97} +5.18563i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{11} + 16 q^{13} - 4 q^{15} - 4 q^{17} + 8 q^{19} - 24 q^{23} + 28 q^{25} + 12 q^{33} - 4 q^{37} - 12 q^{39} + 16 q^{43} - 4 q^{45} + 12 q^{47} - 12 q^{49} + 20 q^{53} - 56 q^{55} + 8 q^{57}+ \cdots + 44 q^{97}+O(q^{100}) $ 48 * q - 4 * q^11 + 16 * q^13 - 4 * q^15 - 4 * q^17 + 8 * q^19 - 24 * q^23 + 28 * q^25 + 12 * q^33 - 4 * q^37 - 12 * q^39 + 16 * q^43 - 4 * q^45 + 12 * q^47 - 12 * q^49 + 20 * q^53 - 56 * q^55 + 8 * q^57 + 8 * q^59 + 8 * q^63 + 12 * q^65 - 52 * q^67 - 8 * q^69 + 16 * q^71 - 4 * q^73 + 24 * q^75 + 8 * q^77 + 108 * q^79 + 24 * q^81 + 64 * q^83 + 32 * q^85 + 20 * q^87 + 64 * q^89 + 48 * q^91 - 24 * q^93 + 36 * q^95 + 44 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/840\mathbb{Z}\right)^\times$.

$n$	$241$	$281$	$337$	$421$	$631$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{3}{4}\right)$	$1$	$1$

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
$3$	0.258819	+	0.965926i	0.149429	+	0.557678i
$3$	0.258819	+	0.965926i	0.149429	+	0.557678i
$4$		0			0
$5$	−1.93516	+	1.12034i	−0.865429	+	0.501032i
$5$	−1.93516	+	1.12034i	−0.865429	+	0.501032i
$6$		0			0
$7$	−1.60015	−	2.10702i	−0.604799	−	0.796379i
$7$	−1.60015	−	2.10702i	−0.604799	−	0.796379i
$8$		0			0
$9$	−0.866025	+	0.500000i	−0.288675	+	0.166667i
$10$		0			0
$11$	2.59281	−	4.49089i	0.781763	−	1.35405i	−0.149151	−	0.988814i	$-0.547654\pi$
$11$	2.59281	−	4.49089i	0.781763	−	1.35405i	0.930914	−	0.365238i	$-0.119013\pi$
$12$		0			0
$13$	0.393426	−	0.393426i	0.109117	−	0.109117i	−0.650440	−	0.759557i	$-0.725416\pi$
$13$	0.393426	−	0.393426i	0.109117	−	0.109117i	0.759557	+	0.650440i	$0.225416\pi$
$14$		0			0
$15$	−1.58302	−	1.57925i	−0.408734	−	0.407762i
$16$		0			0
$17$	4.10895	−	1.10099i	0.996567	−	0.267029i	0.276560	−	0.960997i	$-0.410805\pi$
$17$	4.10895	−	1.10099i	0.996567	−	0.267029i	0.720007	+	0.693967i	$0.244139\pi$
$18$		0			0
$19$	2.32458	+	4.02629i	0.533295	+	0.923695i	0.999244	+	0.0388828i	$0.0123799\pi$
$19$	2.32458	+	4.02629i	0.533295	+	0.923695i	−0.465948	+	0.884812i	$0.654287\pi$
$20$		0			0
$21$	1.62108	−	2.09096i	0.353748	−	0.456285i
$22$		0			0
$23$	0.979264	−	3.65466i	0.204191	−	0.762050i	−0.785504	−	0.618856i	$-0.787596\pi$
$23$	0.979264	−	3.65466i	0.204191	−	0.762050i	0.989695	−	0.143193i	$-0.0457371\pi$
$24$		0			0
$25$	2.48967	−	4.33607i	0.497935	−	0.867215i
$26$		0			0
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$		0			0
$29$		−	1.14155i		−	0.211980i	−0.994367	−	0.105990i	$-0.966199\pi$
$29$		−	1.14155i		−	0.211980i	0.994367	−	0.105990i	$-0.0338012\pi$
$30$		0			0
$31$	9.03971	+	5.21908i	1.62358	+	0.937374i	0.985952	+	0.167029i	$0.0534172\pi$
$31$	9.03971	+	5.21908i	1.62358	+	0.937374i	0.637627	+	0.770345i	$0.279916\pi$
$32$		0			0
$33$	5.00893	+	1.34214i	0.871943	+	0.233636i
$34$		0			0
$35$	5.45712	+	2.28471i	0.922421	+	0.386186i
$36$		0			0
$37$	−6.54631	−	1.75408i	−1.07621	−	0.288369i	−0.323166	−	0.946342i	$-0.604747\pi$
$37$	−6.54631	−	1.75408i	−1.07621	−	0.288369i	−0.753041	+	0.657974i	$0.771414\pi$
$38$		0			0
$39$	0.481847	+	0.278194i	0.0771573	+	0.0445468i
$40$		0			0
$41$		−	3.89354i		−	0.608068i	−0.952661	−	0.304034i	$-0.901666\pi$
$41$		−	3.89354i		−	0.608068i	0.952661	−	0.304034i	$-0.0983337\pi$
$42$		0			0
$43$	8.49370	+	8.49370i	1.29528	+	1.29528i	0.931477	+	0.363799i	$0.118521\pi$
$43$	8.49370	+	8.49370i	1.29528	+	1.29528i	0.363799	+	0.931477i	$0.381479\pi$
$44$		0			0
$45$	1.11573	−	1.93782i	0.166323	−	0.288874i
$46$		0			0
$47$	2.37678	−	8.87026i	0.346689	−	1.29386i	−0.543938	−	0.839125i	$-0.683067\pi$
$47$	2.37678	−	8.87026i	0.346689	−	1.29386i	0.890627	−	0.454735i	$-0.150266\pi$
$48$		0			0
$49$	−1.87906	+	6.74308i	−0.268438	+	0.963297i
$50$		0			0
$51$	2.12695	+	3.68398i	0.297832	+	0.515861i
$52$		0			0
$53$	−3.74856	+	1.00442i	−0.514904	+	0.137968i	−0.506908	−	0.862000i	$-0.669212\pi$
$53$	−3.74856	+	1.00442i	−0.514904	+	0.137968i	−0.00799545	+	0.999968i	$0.502545\pi$
$54$		0			0
$55$	0.0138177	+	11.5954i	0.00186317	+	1.56352i
$56$		0			0
$57$	−3.28745	+	3.28745i	−0.435434	+	0.435434i
$58$		0			0
$59$	1.64769	−	2.85388i	0.214511	−	0.371544i	−0.738610	−	0.674133i	$-0.764518\pi$
$59$	1.64769	−	2.85388i	0.214511	−	0.371544i	0.953121	+	0.302589i	$0.0978509\pi$
$60$		0			0
$61$	3.21272	−	1.85487i	0.411347	−	0.237491i	−0.280021	−	0.959994i	$-0.590342\pi$
$61$	3.21272	−	1.85487i	0.411347	−	0.237491i	0.691368	+	0.722502i	$0.257008\pi$
$62$		0			0
$63$	2.43928	+	1.02466i	0.307320	+	0.129095i
$64$		0			0
$65$	−0.320571	+	1.20211i	−0.0397619	+	0.149104i
$66$		0			0
$67$	−2.26242	−	8.44346i	−0.276398	−	1.03153i	−0.954898	−	0.296933i	$-0.904036\pi$
$67$	−2.26242	−	8.44346i	−0.276398	−	1.03153i	0.678500	−	0.734600i	$-0.262630\pi$
$68$		0			0
$69$	3.78358			0.455490
$70$		0			0
$71$	−14.9427			−1.77337			−0.886685	−	0.462373i	$-0.846998\pi$
$71$	−14.9427			−1.77337			−0.886685	+	0.462373i	$0.846998\pi$
$72$		0			0
$73$	−2.84783	−	10.6282i	−0.333313	−	1.24394i	−0.905687	−	0.423947i	$-0.860644\pi$
$73$	−2.84783	−	10.6282i	−0.333313	−	1.24394i	0.572374	−	0.819993i	$-0.306023\pi$
$74$		0			0
$75$	4.83270	+	1.28258i	0.558032	+	0.148100i
$76$		0			0
$77$	−13.6113	+	1.72296i	−1.55115	+	0.196350i
$78$		0			0
$79$	14.8470	−	8.57194i	1.67042	−	0.964419i	0.703021	−	0.711169i	$-0.251834\pi$
$79$	14.8470	−	8.57194i	1.67042	−	0.964419i	0.967401	−	0.253250i	$-0.0814995\pi$
$80$		0			0
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$		0			0
$83$	0.465956	−	0.465956i	0.0511453	−	0.0511453i	−0.681072	−	0.732217i	$-0.738486\pi$
$83$	0.465956	−	0.465956i	0.0511453	−	0.0511453i	0.732217	+	0.681072i	$0.238486\pi$
$84$		0			0
$85$	−6.71798	+	6.73401i	−0.728668	+	0.730406i
$86$		0			0
$87$	1.10265	−	0.295455i	0.118217	−	0.0316761i
$88$		0			0
$89$	1.44086	+	2.49564i	0.152731	+	0.264538i	0.932231	−	0.361865i	$-0.117860\pi$
$89$	1.44086	+	2.49564i	0.152731	+	0.264538i	−0.779500	+	0.626403i	$0.784527\pi$
$90$		0			0
$91$	−1.45850	−	0.199417i	−0.152892	−	0.0209046i
$92$		0			0
$93$	−2.70159	+	10.0825i	−0.280142	+	1.04550i
$94$		0			0
$95$	−9.00925	−	5.18719i	−0.924329	−	0.532194i
$96$		0			0
$97$	3.58097	+	3.58097i	0.363593	+	0.363593i	0.865134	−	0.501541i	$-0.167233\pi$
$97$	3.58097	+	3.58097i	0.363593	+	0.363593i	−0.501541	+	0.865134i	$0.667233\pi$
$98$		0			0
$99$			5.18563i			0.521175i
$100$		0			0
$101$	2.59340	+	1.49730i	0.258053	+	0.148987i	0.623446	−	0.781866i	$-0.285732\pi$
$101$	2.59340	+	1.49730i	0.258053	+	0.148987i	−0.365393	+	0.930853i	$0.619065\pi$
$102$		0			0
$103$	−9.12385	−	2.44473i	−0.899000	−	0.240886i	−0.220413	−	0.975407i	$-0.570741\pi$
$103$	−9.12385	−	2.44473i	−0.899000	−	0.240886i	−0.678587	+	0.734520i	$0.737407\pi$
$104$		0			0
$105$	−0.794451	+	5.86249i	−0.0775305	+	0.572121i
$106$		0			0
$107$	17.1428	+	4.59341i	1.65726	+	0.444062i	0.961633	−	0.274340i	$-0.0884595\pi$
$107$	17.1428	+	4.59341i	1.65726	+	0.444062i	0.695628	+	0.718402i	$0.255126\pi$
$108$		0			0
$109$	1.85248	+	1.06953i	0.177435	+	0.102442i	0.586087	−	0.810248i	$-0.300668\pi$
$109$	1.85248	+	1.06953i	0.177435	+	0.102442i	−0.408652	+	0.912690i	$0.634001\pi$
$110$		0			0
$111$		−	6.77724i		−	0.643267i
$112$		0			0
$113$	−12.5269	−	12.5269i	−1.17843	−	1.17843i	−0.980145	−	0.198284i	$-0.936463\pi$
$113$	−12.5269	−	12.5269i	−1.17843	−	1.17843i	−0.198284	−	0.980145i	$-0.563537\pi$
$114$		0			0
$115$	2.19944	+	8.16946i	0.205099	+	0.761806i
$116$		0			0
$117$	−0.144004	+	0.537430i	−0.0133132	+	0.0496855i
$118$		0			0
$119$	−8.89473	−	6.89589i	−0.815379	−	0.632146i
$120$		0			0
$121$	−7.94537	−	13.7618i	−0.722306	−	1.25107i
$122$		0			0
$123$	3.76087	−	1.00772i	0.339106	−	0.0908632i
$124$		0			0
$125$	0.0399691	+	11.1803i	0.00357494	+	0.999994i
$126$		0			0
$127$	6.02008	−	6.02008i	0.534196	−	0.534196i	−0.387622	−	0.921818i	$-0.626704\pi$
$127$	6.02008	−	6.02008i	0.534196	−	0.534196i	0.921818	+	0.387622i	$0.126704\pi$
$128$		0			0
$129$	−6.00595	+	10.4026i	−0.528794	+	0.915899i
$130$		0			0
$131$	10.5610	−	6.09739i	0.922719	−	0.532732i	0.0382172	−	0.999269i	$-0.487832\pi$
$131$	10.5610	−	6.09739i	0.922719	−	0.532732i	0.884501	+	0.466538i	$0.154499\pi$
$132$		0			0
$133$	4.76381	−	11.3406i	0.413074	−	0.983354i
$134$		0			0
$135$	2.16056	+	0.576163i	0.185952	+	0.0495882i
$136$		0			0
$137$	−3.67836	−	13.7278i	−0.314263	−	1.17285i	−0.924674	−	0.380761i	$-0.875662\pi$
$137$	−3.67836	−	13.7278i	−0.314263	−	1.17285i	0.610411	−	0.792085i	$-0.291004\pi$
$138$		0			0
$139$	4.95654			0.420408			0.210204	−	0.977658i	$-0.432587\pi$
$139$	4.95654			0.420408			0.210204	+	0.977658i	$0.432587\pi$
$140$		0			0
$141$	9.18316			0.773362
$142$		0			0
$143$	−0.746751	−	2.78691i	−0.0624465	−	0.233053i
$144$		0			0
$145$	1.27892	+	2.20908i	0.106209	+	0.183454i
$146$		0			0
$147$	−6.99965	−	0.0697977i	−0.577322	−	0.00575681i
$148$		0			0
$149$	0.210154	−	0.121333i	0.0172165	−	0.00993996i	−0.491367	−	0.870953i	$-0.663503\pi$
$149$	0.210154	−	0.121333i	0.0172165	−	0.00993996i	0.508584	+	0.861013i	$0.330169\pi$
$150$		0			0
$151$	−4.21957	+	7.30851i	−0.343384	+	0.594758i	−0.985059	−	0.172219i	$-0.944906\pi$
$151$	−4.21957	+	7.30851i	−0.343384	+	0.594758i	0.641675	+	0.766977i	$0.278240\pi$
$152$		0			0
$153$	−3.00796	+	3.00796i	−0.243179	+	0.243179i
$154$		0			0
$155$	−23.3404	+	0.0278136i	−1.87475	+	0.00223404i
$156$		0			0
$157$	−4.12461	+	1.10519i	−0.329180	+	0.0882034i	−0.419624	−	0.907698i	$-0.637838\pi$
$157$	−4.12461	+	1.10519i	−0.329180	+	0.0882034i	0.0904442	+	0.995902i	$0.471171\pi$
$158$		0			0
$159$	−1.94040	−	3.36086i	−0.153883	−	0.266534i
$160$		0			0
$161$	−9.26741	+	3.78467i	−0.730374	+	0.298274i
$162$		0			0
$163$	−3.40022	+	12.6898i	−0.266326	+	0.993941i	0.695108	+	0.718905i	$0.255356\pi$
$163$	−3.40022	+	12.6898i	−0.266326	+	0.993941i	−0.961434	+	0.275036i	$0.911310\pi$
$164$		0			0
$165$	−11.1967	+	3.01446i	−0.871664	+	0.234675i
$166$		0			0
$167$	2.07382	+	2.07382i	0.160477	+	0.160477i	0.782778	−	0.622301i	$-0.213802\pi$
$167$	2.07382	+	2.07382i	0.160477	+	0.160477i	−0.622301	+	0.782778i	$0.713802\pi$
$168$		0			0
$169$			12.6904i			0.976187i
$170$		0			0
$171$	−4.02629	−	2.32458i	−0.307898	−	0.177765i
$172$		0			0
$173$	−10.5205	−	2.81896i	−0.799860	−	0.214322i	−0.164338	−	0.986404i	$-0.552549\pi$
$173$	−10.5205	−	2.81896i	−0.799860	−	0.214322i	−0.635523	+	0.772082i	$0.719215\pi$
$174$		0			0
$175$	−13.1200	+	1.69256i	−0.991781	+	0.127946i
$176$		0			0
$177$	3.18309	+	0.852907i	0.239256	+	0.0641084i
$178$		0			0
$179$	15.7767	+	9.10869i	1.17921	+	0.680816i	0.955831	−	0.293917i	$-0.0949589\pi$
$179$	15.7767	+	9.10869i	1.17921	+	0.680816i	0.223376	+	0.974732i	$0.428292\pi$
$180$		0			0
$181$			13.2224i			0.982812i	0.870931	+	0.491406i	$0.163517\pi$
$181$			13.2224i			0.982812i	−0.870931	+	0.491406i	$0.836483\pi$
$182$		0			0
$183$	2.62318	+	2.62318i	0.193911	+	0.193911i
$184$		0			0
$185$	14.6333	−	3.93968i	1.07586	−	0.289651i
$186$		0			0
$187$	5.70932	−	21.3075i	0.417507	−	1.55816i
$188$		0			0
$189$	−0.358413	+	2.62136i	−0.0260707	+	0.190676i
$190$		0			0
$191$	−1.40402	−	2.43183i	−0.101591	−	0.175961i	0.810749	−	0.585394i	$-0.199060\pi$
$191$	−1.40402	−	2.43183i	−0.101591	−	0.175961i	−0.912340	+	0.409433i	$0.865727\pi$
$192$		0			0
$193$	−13.7001	+	3.67092i	−0.986153	+	0.264239i	−0.715634	−	0.698476i	$-0.753862\pi$
$193$	−13.7001	+	3.67092i	−0.986153	+	0.264239i	−0.270519	+	0.962715i	$0.587195\pi$
$194$		0			0
$195$	−1.24412	+	0.00148256i	−0.0890935	+	0.000106168i
$196$		0			0
$197$	−5.51870	+	5.51870i	−0.393191	+	0.393191i	−0.875823	−	0.482632i	$-0.839681\pi$
$197$	−5.51870	+	5.51870i	−0.393191	+	0.393191i	0.482632	+	0.875823i	$0.339681\pi$
$198$		0			0
$199$	−4.12786	+	7.14966i	−0.292616	+	0.506826i	−0.974428	−	0.224702i	$-0.927859\pi$
$199$	−4.12786	+	7.14966i	−0.292616	+	0.506826i	0.681811	+	0.731528i	$0.261192\pi$
$200$		0			0
$201$	7.57020	−	4.37066i	0.533961	−	0.308282i
$202$		0			0
$203$	−2.40527	+	1.82665i	−0.168817	+	0.128205i
$204$		0			0
$205$	4.36209	+	7.53461i	0.304662	+	0.526240i
$206$		0			0
$207$	0.979264	+	3.65466i	0.0680635	+	0.254017i
$208$		0			0
$209$	24.1088			1.66764
$210$		0			0
$211$	−15.1499			−1.04296			−0.521480	−	0.853263i	$-0.674620\pi$
$211$	−15.1499			−1.04296			−0.521480	+	0.853263i	$0.674620\pi$
$212$		0			0
$213$	−3.86745	−	14.4335i	−0.264993	−	0.988969i
$214$		0			0
$215$	−25.9525	−	6.92081i	−1.76994	−	0.471995i
$216$		0			0
$217$	−3.46816	−	27.3981i	−0.235434	−	1.85991i
$218$		0			0
$219$	9.52901	−	5.50158i	0.643911	−	0.371762i
$220$		0			0
$221$	1.18341	−	2.04973i	0.0796048	−	0.137880i
$222$		0			0
$223$	−19.8934	+	19.8934i	−1.33216	+	1.33216i	−0.428729	+	0.903433i	$0.641038\pi$
$223$	−19.8934	+	19.8934i	−1.33216	+	1.33216i	−0.903433	+	0.428729i	$0.858962\pi$
$224$		0			0
$225$	0.0119165	+	4.99999i	0.000794433	+	0.333332i
$226$		0			0
$227$	−11.5946	+	3.10675i	−0.769558	+	0.206202i	−0.622176	−	0.782877i	$-0.713751\pi$
$227$	−11.5946	+	3.10675i	−0.769558	+	0.206202i	−0.147382	+	0.989080i	$0.547085\pi$
$228$		0			0
$229$	9.20168	+	15.9378i	0.608064	+	1.05320i	0.991559	+	0.129655i	$0.0413871\pi$
$229$	9.20168	+	15.9378i	0.608064	+	1.05320i	−0.383495	+	0.923543i	$0.625280\pi$
$230$		0			0
$231$	−5.18711	−	12.7015i	−0.341287	−	0.835700i
$232$		0			0
$233$	−3.05959	+	11.4185i	−0.200440	+	0.748053i	0.790351	+	0.612654i	$0.209898\pi$
$233$	−3.05959	+	11.4185i	−0.200440	+	0.748053i	−0.990791	+	0.135399i	$0.956768\pi$
$234$		0			0
$235$	5.33827	+	19.8281i	0.348230	+	1.29345i
$236$		0			0
$237$	12.1226	+	12.1226i	0.787445	+	0.787445i
$238$		0			0
$239$		−	5.47505i		−	0.354151i	−0.984197	−	0.177076i	$-0.943336\pi$
$239$		−	5.47505i		−	0.354151i	0.984197	−	0.177076i	$-0.0566637\pi$
$240$		0			0
$241$	5.95534	+	3.43832i	0.383617	+	0.221481i	0.679391	−	0.733777i	$-0.262244\pi$
$241$	5.95534	+	3.43832i	0.383617	+	0.221481i	−0.295774	+	0.955258i	$0.595577\pi$
$242$		0			0
$243$	0.965926	+	0.258819i	0.0619642	+	0.0166032i
$244$		0			0
$245$	−3.91826	−	15.1541i	−0.250329	−	0.968161i
$246$		0			0
$247$	2.49860	+	0.669498i	0.158982	+	0.0425991i
$248$		0			0
$249$	0.570677	+	0.329481i	0.0361652	+	0.0208800i
$250$		0			0
$251$			1.79547i			0.113329i	0.998393	+	0.0566646i	$0.0180466\pi$
$251$			1.79547i			0.113329i	−0.998393	+	0.0566646i	$0.981953\pi$
$252$		0			0
$253$	−13.8736	−	13.8736i	−0.872227	−	0.872227i
$254$		0			0
$255$	−8.24330	−	4.74618i	−0.516216	−	0.297218i
$256$		0			0
$257$	−4.73693	+	17.6785i	−0.295481	+	1.10275i	0.645353	+	0.763885i	$0.276710\pi$
$257$	−4.73693	+	17.6785i	−0.295481	+	1.10275i	−0.940834	+	0.338867i	$0.889956\pi$
$258$		0			0
$259$	6.77918	+	16.6000i	0.421238	+	1.03147i
$260$		0			0
$261$	0.570775	+	0.988611i	0.0353301	+	0.0611935i
$262$		0			0
$263$	9.60757	−	2.57434i	0.592428	−	0.158741i	0.0498654	−	0.998756i	$-0.484121\pi$
$263$	9.60757	−	2.57434i	0.592428	−	0.158741i	0.542563	+	0.840015i	$0.317454\pi$
$264$		0			0
$265$	6.12875	−	6.14338i	0.376486	−	0.377385i
$266$		0			0
$267$	−2.03769	+	2.03769i	−0.124704	+	0.124704i
$268$		0			0
$269$	12.7900	−	22.1530i	0.779823	−	1.35069i	−0.152221	−	0.988347i	$-0.548642\pi$
$269$	12.7900	−	22.1530i	0.779823	−	1.35069i	0.932044	−	0.362346i	$-0.118024\pi$
$270$		0			0
$271$	−7.57164	+	4.37149i	−0.459945	+	0.265549i	−0.712021	−	0.702158i	$-0.752220\pi$
$271$	−7.57164	+	4.37149i	−0.459945	+	0.265549i	0.252076	+	0.967707i	$0.418887\pi$
$272$		0			0
$273$	−0.184865	−	1.46041i	−0.0111885	−	0.0883882i
$274$		0			0
$275$	−13.0175	−	22.4235i	−0.784988	−	1.35219i
$276$		0			0
$277$	1.39663	+	5.21230i	0.0839155	+	0.313177i	0.995107	−	0.0988070i	$-0.0315026\pi$
$277$	1.39663	+	5.21230i	0.0839155	+	0.313177i	−0.911191	+	0.411984i	$0.864836\pi$
$278$		0			0
$279$	−10.4382			−0.624916
$280$		0			0
$281$	0.500607			0.0298637			0.0149319	−	0.999889i	$-0.495247\pi$
$281$	0.500607			0.0298637			0.0149319	+	0.999889i	$0.495247\pi$
$282$		0			0
$283$	0.758042	+	2.82905i	0.0450609	+	0.168170i	0.984789	−	0.173752i	$-0.0555890\pi$
$283$	0.758042	+	2.82905i	0.0450609	+	0.168170i	−0.939729	+	0.341921i	$0.888922\pi$
$284$		0			0
$285$	2.67867	−	10.0448i	0.158671	−	0.595003i
$286$		0			0
$287$	−8.20376	+	6.23023i	−0.484253	+	0.367759i
$288$		0			0
$289$	0.948865	−	0.547827i	0.0558156	−	0.0322251i
$290$		0			0
$291$	−2.53213	+	4.38578i	−0.148436	+	0.257099i
$292$		0			0
$293$	−7.44336	+	7.44336i	−0.434846	+	0.434846i	−0.890273	−	0.455427i	$-0.849487\pi$
$293$	−7.44336	+	7.44336i	−0.434846	+	0.434846i	0.455427	+	0.890273i	$0.349487\pi$
$294$		0			0
$295$	0.00878090	+	7.36869i	0.000511244	+	0.429021i
$296$		0			0
$297$	−5.00893	+	1.34214i	−0.290648	+	0.0778788i
$298$		0			0
$299$	−1.05257	−	1.82311i	−0.0608718	−	0.105433i
$300$		0			0
$301$	4.30523	−	31.4875i	0.248149	−	1.81491i
$302$		0			0
$303$	−0.775060	+	2.89256i	−0.0445261	+	0.166173i
$304$		0			0
$305$	−4.13904	+	7.18880i	−0.237001	+	0.411630i
$306$		0			0
$307$	9.68865	+	9.68865i	0.552960	+	0.552960i	0.927294	−	0.374334i	$-0.122129\pi$
$307$	9.68865	+	9.68865i	0.552960	+	0.552960i	−0.374334	+	0.927294i	$0.622129\pi$
$308$		0			0
$309$		−	9.44571i		−	0.537347i
$310$		0			0
$311$	9.90068	+	5.71616i	0.561416	+	0.324134i	0.753714	−	0.657203i	$-0.228261\pi$
$311$	9.90068	+	5.71616i	0.561416	+	0.324134i	−0.192298	+	0.981337i	$0.561594\pi$
$312$		0			0
$313$	−14.7181	−	3.94369i	−0.831914	−	0.222911i	−0.182366	−	0.983231i	$-0.558375\pi$
$313$	−14.7181	−	3.94369i	−0.831914	−	0.222911i	−0.649549	+	0.760320i	$0.725042\pi$
$314$		0			0
$315$	−5.86835	+	0.749944i	−0.330644	+	0.0422546i
$316$		0			0
$317$	−9.83081	−	2.63416i	−0.552153	−	0.147949i	−0.0280544	−	0.999606i	$-0.508931\pi$
$317$	−9.83081	−	2.63416i	−0.552153	−	0.147949i	−0.524099	+	0.851657i	$0.675598\pi$
$318$		0			0
$319$	−5.12657	−	2.95983i	−0.287033	−	0.165718i
$320$		0			0
$321$			17.7476i			0.990573i
$322$		0			0
$323$	13.9845	+	13.9845i	0.778118	+	0.778118i
$324$		0			0
$325$	−0.726422	−	2.68543i	−0.0402947	−	0.148961i
$326$		0			0
$327$	−0.553630	+	2.06617i	−0.0306158	+	0.114260i
$328$		0			0
$329$	−22.4930	+	9.18579i	−1.24008	+	0.506429i
$330$		0			0
$331$	−0.188793	−	0.326998i	−0.0103770	−	0.0179735i	0.860790	−	0.508960i	$-0.169970\pi$
$331$	−0.188793	−	0.326998i	−0.0103770	−	0.0179735i	−0.871167	+	0.490986i	$0.836636\pi$
$332$		0			0
$333$	6.54631	−	1.75408i	0.358736	−	0.0961229i
$334$		0			0
$335$	13.8377	+	13.8048i	0.756034	+	0.754234i
$336$		0			0
$337$	3.98808	−	3.98808i	0.217244	−	0.217244i	−0.590092	−	0.807336i	$-0.700908\pi$
$337$	3.98808	−	3.98808i	0.217244	−	0.217244i	0.807336	+	0.590092i	$0.200908\pi$
$338$		0			0
$339$	8.85783	−	15.3422i	0.481091	−	0.833275i
$340$		0			0
$341$	46.8765	−	27.0642i	2.53851	−	1.46561i
$342$		0			0
$343$	17.2146	−	6.83069i	0.929500	−	0.368823i
$344$		0			0
$345$	−7.32183	+	4.23890i	−0.394194	+	0.228215i
$346$		0			0
$347$	−6.16581	−	23.0111i	−0.330998	−	1.23530i	−0.908143	−	0.418660i	$-0.862500\pi$
$347$	−6.16581	−	23.0111i	−0.330998	−	1.23530i	0.577145	−	0.816641i	$-0.304167\pi$
$348$		0			0
$349$	19.6652			1.05265			0.526326	−	0.850283i	$-0.323569\pi$
$349$	19.6652			1.05265			0.526326	+	0.850283i	$0.323569\pi$
$350$		0			0
$351$	−0.556389			−0.0296978
$352$		0			0
$353$	8.69371	+	32.4454i	0.462720	+	1.72689i	0.664341	+	0.747430i	$0.268712\pi$
$353$	8.69371	+	32.4454i	0.462720	+	1.72689i	−0.201621	+	0.979464i	$0.564621\pi$
$354$		0			0
$355$	28.9165	−	16.7409i	1.53473	−	0.888515i
$356$		0			0
$357$	4.35880	−	10.3764i	0.230692	−	0.549179i
$358$		0			0
$359$	0.716930	−	0.413919i	0.0378381	−	0.0218458i	−0.480962	−	0.876742i	$-0.659712\pi$
$359$	0.716930	−	0.413919i	0.0378381	−	0.0218458i	0.518800	+	0.854896i	$0.326379\pi$
$360$		0			0
$361$	−1.30735	+	2.26440i	−0.0688078	+	0.119179i
$362$		0			0
$363$	11.2364	−	11.2364i	0.589760	−	0.589760i
$364$		0			0
$365$	17.4182	+	17.3768i	0.911712	+	0.909542i
$366$		0			0
$367$	9.06608	−	2.42925i	0.473246	−	0.126806i	−0.0143102	−	0.999898i	$-0.504555\pi$
$367$	9.06608	−	2.42925i	0.473246	−	0.126806i	0.487556	+	0.873092i	$0.337889\pi$
$368$		0			0
$369$	1.94677	+	3.37190i	0.101345	+	0.175534i
$370$		0			0
$371$	8.11458	+	6.29106i	0.421288	+	0.326615i
$372$		0			0
$373$	−5.45608	+	20.3624i	−0.282505	+	1.05432i	0.668138	+	0.744037i	$0.267091\pi$
$373$	−5.45608	+	20.3624i	−0.282505	+	1.05432i	−0.950643	+	0.310286i	$0.899575\pi$
$374$		0			0
$375$	−10.7890	+	2.93227i	−0.557140	+	0.151422i
$376$		0			0
$377$	−0.449116	−	0.449116i	−0.0231306	−	0.0231306i
$378$		0			0
$379$			17.2469i			0.885915i	0.896543	+	0.442958i	$0.146071\pi$
$379$			17.2469i			0.885915i	−0.896543	+	0.442958i	$0.853929\pi$
$380$		0			0
$381$	7.37306	+	4.25684i	0.377734	+	0.218085i
$382$		0			0
$383$	1.15701	+	0.310019i	0.0591204	+	0.0158413i	0.288258	−	0.957553i	$-0.406924\pi$
$383$	1.15701	+	0.310019i	0.0591204	+	0.0158413i	−0.229138	+	0.973394i	$0.573591\pi$
$384$		0			0
$385$	24.4096	−	18.5835i	1.24403	−	0.947101i
$386$		0			0
$387$	−11.6026	−	3.10891i	−0.589794	−	0.158035i
$388$		0			0
$389$	16.3871	+	9.46111i	0.830860	+	0.479697i	0.854147	−	0.520031i	$-0.174080\pi$
$389$	16.3871	+	9.46111i	0.830860	+	0.479697i	−0.0232869	+	0.999729i	$0.507413\pi$
$390$		0			0
$391$		−	16.0950i		−	0.813958i
$392$		0			0
$393$	8.62302	+	8.62302i	0.434974	+	0.434974i
$394$		0			0
$395$	−19.1279	+	33.2218i	−0.962427	+	1.67157i
$396$		0			0
$397$	2.28999	−	8.54635i	0.114931	−	0.428929i	−0.884351	−	0.466823i	$-0.845398\pi$
$397$	2.28999	−	8.54635i	0.114931	−	0.428929i	0.999282	+	0.0378944i	$0.0120651\pi$
$398$		0			0
$399$	12.1871	+	1.66632i	0.610120	+	0.0834204i
$400$		0			0
$401$	−1.29046	−	2.23514i	−0.0644426	−	0.111618i	0.832004	−	0.554770i	$-0.187194\pi$
$401$	−1.29046	−	2.23514i	−0.0644426	−	0.111618i	−0.896447	+	0.443152i	$0.853860\pi$
$402$		0			0
$403$	5.60978	−	1.50314i	0.279443	−	0.0748766i
$404$		0			0
$405$	0.00266461	+	2.23607i	0.000132406	+	0.111111i
$406$		0			0
$407$	−24.8507	+	24.8507i	−1.23180	+	1.23180i
$408$		0			0
$409$	13.9599	−	24.1793i	0.690273	−	1.19559i	−0.281476	−	0.959568i	$-0.590824\pi$
$409$	13.9599	−	24.1793i	0.690273	−	1.19559i	0.971748	−	0.236019i	$-0.0758428\pi$
$410$		0			0
$411$	12.3080	−	7.10604i	0.607110	−	0.350515i
$412$		0			0
$413$	−8.64973	+	1.09492i	−0.425625	+	0.0538772i
$414$		0			0
$415$	−0.379669	+	1.42373i	−0.0186372	+	0.0698881i
$416$		0			0
$417$	1.28285	+	4.78765i	0.0628213	+	0.234452i
$418$		0			0
$419$	−13.4480			−0.656980			−0.328490	−	0.944508i	$-0.606540\pi$
$419$	−13.4480			−0.656980			−0.328490	+	0.944508i	$0.606540\pi$
$420$		0			0
$421$	−15.1153			−0.736676			−0.368338	−	0.929692i	$-0.620073\pi$
$421$	−15.1153			−0.736676			−0.368338	+	0.929692i	$0.620073\pi$
$422$		0			0
$423$	2.37678	+	8.87026i	0.115563	+	0.431287i
$424$		0			0
$425$	5.45597	−	20.5578i	0.264653	−	0.997201i
$426$		0			0
$427$	−9.04907	−	3.80121i	−0.437915	−	0.183954i
$428$		0			0
$429$	2.49868	−	1.44261i	0.120637	−	0.0696500i
$430$		0			0
$431$	17.9055	−	31.0133i	0.862479	−	1.49386i	−0.00705073	−	0.999975i	$-0.502244\pi$
$431$	17.9055	−	31.0133i	0.862479	−	1.49386i	0.869529	−	0.493881i	$-0.164422\pi$
$432$		0			0
$433$	11.7831	−	11.7831i	0.566261	−	0.566261i	−0.364818	−	0.931079i	$-0.618869\pi$
$433$	11.7831	−	11.7831i	0.566261	−	0.566261i	0.931079	+	0.364818i	$0.118869\pi$
$434$		0			0
$435$	−1.80280	+	1.80710i	−0.0864375	+	0.0866437i
$436$		0			0
$437$	16.9911	−	4.55275i	0.812795	−	0.217788i
$438$		0			0
$439$	−19.3867	−	33.5788i	−0.925279	−	1.60263i	−0.791112	−	0.611671i	$-0.790498\pi$
$439$	−19.3867	−	33.5788i	−0.925279	−	1.60263i	−0.134167	−	0.990959i	$-0.542836\pi$
$440$		0			0
$441$	−1.74422	−	6.77921i	−0.0830583	−	0.322820i
$442$		0			0
$443$	3.04474	−	11.3631i	0.144660	−	0.539878i	−0.855111	−	0.518446i	$-0.826511\pi$
$443$	3.04474	−	11.3631i	0.144660	−	0.539878i	0.999770	−	0.0214319i	$-0.00682251\pi$
$444$		0			0
$445$	−5.58427	−	3.21521i	−0.264720	−	0.152416i
$446$		0			0
$447$	0.171590	+	0.171590i	0.00811595	+	0.00811595i
$448$		0			0
$449$		−	8.88927i		−	0.419511i	−0.977754	−	0.209755i	$-0.932733\pi$
$449$		−	8.88927i		−	0.419511i	0.977754	−	0.209755i	$-0.0672668\pi$
$450$		0			0
$451$	−17.4854	−	10.0952i	−0.823357	−	0.475365i
$452$		0			0
$453$	−8.15158	−	2.18421i	−0.382995	−	0.102623i
$454$		0			0
$455$	3.04584	−	1.24811i	0.142791	−	0.0585123i
$456$		0			0
$457$	17.0656	+	4.57271i	0.798295	+	0.213902i	0.634835	−	0.772648i	$-0.281068\pi$
$457$	17.0656	+	4.57271i	0.798295	+	0.213902i	0.163460	+	0.986550i	$0.447735\pi$
$458$		0			0
$459$	−3.68398	−	2.12695i	−0.171954	−	0.0992775i
$460$		0			0
$461$			17.7227i			0.825427i	0.910861	+	0.412713i	$0.135419\pi$
$461$			17.7227i			0.825427i	−0.910861	+	0.412713i	$0.864581\pi$
$462$		0			0
$463$	−6.25998	−	6.25998i	−0.290926	−	0.290926i	0.546520	−	0.837446i	$-0.315952\pi$
$463$	−6.25998	−	6.25998i	−0.290926	−	0.290926i	−0.837446	+	0.546520i	$0.815952\pi$
$464$		0			0
$465$	−6.06781	−	22.5379i	−0.281388	−	1.04517i
$466$		0			0
$467$	5.17117	−	19.2991i	0.239293	−	0.893054i	−0.736873	−	0.676031i	$-0.763699\pi$
$467$	5.17117	−	19.2991i	0.239293	−	0.893054i	0.976166	−	0.217023i	$-0.0696347\pi$
$468$		0			0
$469$	−14.1703	+	18.2777i	−0.654325	+	0.843987i
$470$		0			0
$471$	−2.13505	−	3.69802i	−0.0983781	−	0.170396i
$472$		0			0
$473$	60.1668	−	16.1216i	2.76647	−	0.741274i
$474$		0			0
$475$	23.2457	−	0.0554017i	1.06659	−	0.00254200i
$476$		0			0
$477$	2.74413	−	2.74413i	0.125645	−	0.125645i
$478$		0			0
$479$	−8.60064	+	14.8967i	−0.392973	+	0.680650i	−0.992840	−	0.119450i	$-0.961887\pi$
$479$	−8.60064	+	14.8967i	−0.392973	+	0.680650i	0.599867	+	0.800100i	$0.295220\pi$
$480$		0			0
$481$	−3.26559	+	1.88539i	−0.148898	+	0.0859664i
$482$		0			0
$483$	−6.05429	−	7.97209i	−0.275480	−	0.362742i
$484$		0			0
$485$	−10.9417	−	2.91784i	−0.496835	−	0.132492i
$486$		0			0
$487$	−9.37082	−	34.9724i	−0.424632	−	1.58475i	−0.764725	−	0.644357i	$-0.777125\pi$
$487$	−9.37082	−	34.9724i	−0.424632	−	1.58475i	0.340092	−	0.940392i	$-0.389542\pi$
$488$		0			0
$489$	−13.1374			−0.594095
$490$		0			0
$491$	−17.4962			−0.789592			−0.394796	−	0.918769i	$-0.629185\pi$
$491$	−17.4962			−0.789592			−0.394796	+	0.918769i	$0.629185\pi$
$492$		0			0
$493$	−1.25683	−	4.69057i	−0.0566050	−	0.211253i
$494$		0			0
$495$	−5.80967	−	10.0350i	−0.261125	−	0.451040i
$496$		0			0
$497$	23.9105	+	31.4845i	1.07253	+	1.41227i
$498$		0			0
$499$	1.03820	−	0.599404i	0.0464761	−	0.0268330i	−0.476582	−	0.879130i	$-0.658124\pi$
$499$	1.03820	−	0.599404i	0.0464761	−	0.0268330i	0.523058	+	0.852297i	$0.324791\pi$
$500$		0			0
$501$	−1.46641	+	2.53990i	−0.0655146	+	0.113475i
$502$		0			0
$503$	11.2555	−	11.2555i	0.501856	−	0.501856i	−0.410158	−	0.912014i	$-0.634527\pi$
$503$	11.2555	−	11.2555i	0.501856	−	0.501856i	0.912014	+	0.410158i	$0.134527\pi$
$504$		0			0
$505$	−6.69613	+	0.00797945i	−0.297974	+	0.000355081i
$506$		0			0
$507$	−12.2580	+	3.28453i	−0.544398	+	0.145871i
$508$		0			0
$509$	15.8833	+	27.5106i	0.704013	+	1.21939i	0.967047	+	0.254600i	$0.0819437\pi$
$509$	15.8833	+	27.5106i	0.704013	+	1.21939i	−0.263034	+	0.964787i	$0.584723\pi$
$510$		0			0
$511$	−17.8369	+	23.0071i	−0.789060	+	1.01778i
$512$		0			0
$513$	1.20329	−	4.49074i	0.0531266	−	0.198271i
$514$		0			0
$515$	20.3950	−	5.49089i	0.898712	−	0.241957i
$516$		0			0
$517$	−33.6728	−	33.6728i	−1.48093	−	1.48093i
$518$		0			0
$519$		−	10.8916i		−	0.478090i
$520$		0			0
$521$	19.9889	+	11.5406i	0.875729	+	0.505602i	0.869248	−	0.494377i	$-0.164604\pi$
$521$	19.9889	+	11.5406i	0.875729	+	0.505602i	0.00648104	+	0.999979i	$0.497937\pi$
$522$		0			0
$523$	−7.82579	−	2.09691i	−0.342198	−	0.0916917i	0.0836272	−	0.996497i	$-0.473349\pi$
$523$	−7.82579	−	2.09691i	−0.342198	−	0.0916917i	−0.425825	+	0.904805i	$0.640016\pi$
$524$		0			0
$525$	−5.03060	−	12.2349i	−0.219554	−	0.533975i
$526$		0			0
$527$	42.8899	+	11.4923i	1.86831	+	0.500613i
$528$		0			0
$529$	7.52099	+	4.34224i	0.326999	+	0.188793i
$530$		0			0
$531$			3.29538i			0.143007i
$532$		0			0
$533$	−1.53182	−	1.53182i	−0.0663505	−	0.0663505i
$534$		0			0
$535$	−38.3203	+	10.3168i	−1.65673	+	0.446036i
$536$		0			0
$537$	−4.71501	+	17.5966i	−0.203468	+	0.759351i
$538$		0			0
$539$	25.4103	+	25.9222i	1.09450	+	1.11655i
$540$		0			0
$541$	12.5563	+	21.7482i	0.539838	+	0.935026i	0.998912	+	0.0466286i	$0.0148477\pi$
$541$	12.5563	+	21.7482i	0.539838	+	0.935026i	−0.459075	+	0.888398i	$0.651819\pi$
$542$		0			0
$543$	−12.7718	+	3.42220i	−0.548092	+	0.146861i
$544$		0			0
$545$	−4.78308	+	0.00569976i	−0.204885	+	0.000244151i
$546$		0			0
$547$	22.2969	−	22.2969i	0.953346	−	0.953346i	−0.0456133	−	0.998959i	$-0.514524\pi$
$547$	22.2969	−	22.2969i	0.953346	−	0.953346i	0.998959	+	0.0456133i	$0.0145242\pi$
$548$		0			0
$549$	−1.85487	+	3.21272i	−0.0791638	+	0.137116i
$550$		0			0
$551$	4.59621	−	2.65362i	0.195805	−	0.113048i
$552$		0			0
$553$	−41.8187	−	17.5666i	−1.77831	−	0.747009i
$554$		0			0
$555$	7.59282	+	13.1150i	0.322297	+	0.556702i
$556$		0			0
$557$	−2.25465	−	8.41446i	−0.0955325	−	0.356532i	0.901567	−	0.432639i	$-0.142418\pi$
$557$	−2.25465	−	8.41446i	−0.0955325	−	0.356532i	−0.997100	+	0.0761070i	$0.975751\pi$
$558$		0			0
$559$	6.68329			0.282673
$560$		0			0
$561$	22.0591			0.931337
$562$		0			0
$563$	11.6121	+	43.3368i	0.489390	+	1.82643i	0.559422	+	0.828883i	$0.311023\pi$
$563$	11.6121	+	43.3368i	0.489390	+	1.82643i	−0.0700327	+	0.997545i	$0.522310\pi$
$564$		0			0
$565$	38.2758	+	10.2071i	1.61028	+	0.429416i
$566$		0			0
$567$	−2.62481	+	0.332258i	−0.110231	+	0.0139535i
$568$		0			0
$569$	−27.3249	+	15.7761i	−1.14552	+	0.661367i	−0.947792	−	0.318890i	$-0.896690\pi$
$569$	−27.3249	+	15.7761i	−1.14552	+	0.661367i	−0.197730	+	0.980257i	$0.563357\pi$
$570$		0			0
$571$	−15.5660	+	26.9610i	−0.651415	+	1.12828i	0.331365	+	0.943503i	$0.392491\pi$
$571$	−15.5660	+	26.9610i	−0.651415	+	1.12828i	−0.982780	+	0.184781i	$0.940842\pi$
$572$		0			0
$573$	1.98558	−	1.98558i	0.0829489	−	0.0829489i
$574$		0			0
$575$	−13.4088	−	13.3451i	−0.559187	−	0.556528i
$576$		0			0
$577$	35.8443	−	9.60444i	1.49222	−	0.399838i	0.581731	−	0.813381i	$-0.302376\pi$
$577$	35.8443	−	9.60444i	1.49222	−	0.399838i	0.910485	+	0.413543i	$0.135709\pi$
$578$		0			0
$579$	−7.09168	−	12.2831i	−0.294720	−	0.510470i
$580$		0			0
$581$	−1.72738	−	0.236181i	−0.0716636	−	0.00979842i
$582$		0			0
$583$	−5.20856	+	19.4386i	−0.215717	+	0.805065i
$584$		0			0
$585$	−0.323435	−	1.20135i	−0.0133724	−	0.0496696i
$586$		0			0
$587$	0.794072	+	0.794072i	0.0327749	+	0.0327749i	0.723304	−	0.690529i	$-0.242622\pi$
$587$	0.794072	+	0.794072i	0.0327749	+	0.0327749i	−0.690529	+	0.723304i	$0.742622\pi$
$588$		0			0
$589$			48.5287i			1.99959i
$590$		0			0
$591$	−6.75901	−	3.90231i	−0.278028	−	0.160520i
$592$		0			0
$593$	−21.4022	−	5.73471i	−0.878884	−	0.235496i	−0.208958	−	0.977925i	$-0.567007\pi$
$593$	−21.4022	−	5.73471i	−0.878884	−	0.235496i	−0.669926	+	0.742428i	$0.733674\pi$
$594$		0			0
$595$	24.9385	+	3.37952i	1.02238	+	0.138547i
$596$		0			0
$597$	−7.97441	−	2.13674i	−0.326371	−	0.0874508i
$598$		0			0
$599$	−39.6891	−	22.9145i	−1.62165	−	0.936261i	−0.986479	−	0.163891i	$-0.947596\pi$
$599$	−39.6891	−	22.9145i	−1.62165	−	0.936261i	−0.635173	−	0.772370i	$-0.719071\pi$
$600$		0			0
$601$		−	0.0299652i		−	0.00122231i	−1.00000		0.000611153i	$-0.999805\pi$
$601$		−	0.0299652i		−	0.00122231i	1.00000		0.000611153i	$-0.000194536\pi$
$602$		0			0
$603$	6.18104	+	6.18104i	0.251712	+	0.251712i
$604$		0			0
$605$	30.7934	+	17.7297i	1.25193	+	0.720815i
$606$		0			0
$607$	−3.26225	+	12.1749i	−0.132410	+	0.494163i	−0.999995	−	0.00312691i	$-0.999005\pi$
$607$	−3.26225	+	12.1749i	−0.132410	+	0.494163i	0.867585	+	0.497290i	$0.165671\pi$
$608$		0			0
$609$	−2.38693	−	1.85054i	−0.0967235	−	0.0749876i
$610$		0			0
$611$	−2.55471	−	4.42488i	−0.103352	−	0.179011i
$612$		0			0
$613$	20.2561	−	5.42761i	0.818137	−	0.219219i	0.174605	−	0.984639i	$-0.444135\pi$
$613$	20.2561	−	5.42761i	0.818137	−	0.219219i	0.643532	+	0.765420i	$0.277468\pi$
$614$		0			0
$615$	−6.14888	+	6.16356i	−0.247947	+	0.248539i
$616$		0			0
$617$	−25.1514	+	25.1514i	−1.01256	+	1.01256i	−0.0126383	+	0.999920i	$0.504023\pi$
$617$	−25.1514	+	25.1514i	−1.01256	+	1.01256i	−0.999920	+	0.0126383i	$0.995977\pi$
$618$		0			0
$619$	13.7908	−	23.8864i	0.554299	−	0.960074i	−0.443659	−	0.896196i	$-0.646320\pi$
$619$	13.7908	−	23.8864i	0.554299	−	0.960074i	0.997958	−	0.0638784i	$-0.0203470\pi$
$620$		0			0
$621$	−3.27668	+	1.89179i	−0.131489	+	0.0759150i
$622$		0			0
$623$	2.95278	−	7.02932i	0.118301	−	0.281624i
$624$		0			0
$625$	−12.6031	−	21.5908i	−0.504122	−	0.863632i
$626$		0			0
$627$	6.23982	+	23.2873i	0.249194	+	0.930006i
$628$		0			0
$629$	−28.8297			−1.14951
$630$		0			0
$631$	21.2866			0.847405			0.423702	−	0.905801i	$-0.360730\pi$
$631$	21.2866			0.847405			0.423702	+	0.905801i	$0.360730\pi$
$632$		0			0
$633$	−3.92108	−	14.6337i	−0.155849	−	0.581636i
$634$		0			0
$635$	−4.90527	+	18.3944i	−0.194660	+	0.729958i
$636$		0			0
$637$	1.91363	+	3.39218i	0.0758209	+	0.134403i
$638$		0			0
$639$	12.9407	−	7.47134i	0.511928	−	0.295562i
$640$		0			0
$641$	−9.64037	+	16.6976i	−0.380772	+	0.659516i	−0.991173	−	0.132577i	$-0.957675\pi$
$641$	−9.64037	+	16.6976i	−0.380772	+	0.659516i	0.610401	+	0.792093i	$0.291008\pi$
$642$		0			0
$643$	−12.7834	+	12.7834i	−0.504128	+	0.504128i	−0.912718	−	0.408590i	$-0.866021\pi$
$643$	−12.7834	+	12.7834i	−0.504128	+	0.504128i	0.408590	+	0.912718i	$0.366021\pi$
$644$		0			0
$645$	−0.0320070	−	26.8594i	−0.00126028	−	1.05759i
$646$		0			0
$647$	31.2927	−	8.38484i	1.23024	−	0.329642i	0.415568	−	0.909562i	$-0.363583\pi$
$647$	31.2927	−	8.38484i	1.23024	−	0.329642i	0.814673	+	0.579920i	$0.196916\pi$
$648$		0			0
$649$	−8.54430	−	14.7992i	−0.335393	−	0.580918i
$650$		0			0
$651$	25.5669	−	10.4411i	1.00205	−	0.409220i
$652$		0			0
$653$	3.56499	−	13.3047i	0.139509	−	0.520653i	−0.860430	−	0.509569i	$-0.829805\pi$
$653$	3.56499	−	13.3047i	0.139509	−	0.520653i	0.999939	−	0.0110846i	$-0.00352841\pi$
$654$		0			0
$655$	−13.6060	+	23.6313i	−0.531632	+	0.923353i
$656$		0			0
$657$	7.78040	+	7.78040i	0.303542	+	0.303542i
$658$		0			0
$659$			15.7465i			0.613398i	0.951807	+	0.306699i	$0.0992245\pi$
$659$			15.7465i			0.613398i	−0.951807	+	0.306699i	$0.900775\pi$
$660$		0			0
$661$	−40.3367	−	23.2884i	−1.56892	−	0.905814i	−0.996296	−	0.0859933i	$-0.972594\pi$
$661$	−40.3367	−	23.2884i	−1.56892	−	0.905814i	−0.572620	−	0.819821i	$-0.694073\pi$
$662$		0			0
$663$	2.28617	+	0.612579i	0.0887877	+	0.0237906i
$664$		0			0
$665$	3.48661	+	27.2829i	0.135205	+	1.05799i
$666$		0			0
$667$	−4.17198	−	1.11788i	−0.161540	−	0.0432844i
$668$		0			0
$669$	−24.3644	−	14.0668i	−0.941981	−	0.543853i
$670$		0			0
$671$		−	19.2373i		−	0.742647i
$672$		0			0
$673$	−8.53678	−	8.53678i	−0.329069	−	0.329069i	0.523164	−	0.852232i	$-0.324752\pi$
$673$	−8.53678	−	8.53678i	−0.329069	−	0.329069i	−0.852232	+	0.523164i	$0.824752\pi$
$674$		0			0
$675$	−4.82653	+	1.30560i	−0.185773	+	0.0502526i
$676$		0			0
$677$	−8.61686	+	32.1586i	−0.331173	+	1.23595i	0.576786	+	0.816895i	$0.304307\pi$
$677$	−8.61686	+	32.1586i	−0.331173	+	1.23595i	−0.907959	+	0.419059i	$0.862360\pi$
$678$		0			0
$679$	1.81510	−	13.2753i	0.0696571	−	0.509458i
$680$		0			0
$681$	−6.00178	−	10.3954i	−0.229989	−	0.398352i
$682$		0			0
$683$	29.8223	−	7.99086i	1.14112	−	0.305762i	0.361718	−	0.932288i	$-0.382190\pi$
$683$	29.8223	−	7.99086i	1.14112	−	0.305762i	0.779401	+	0.626526i	$0.215524\pi$
$684$		0			0
$685$	22.4980	+	22.4445i	0.859605	+	0.857559i
$686$		0			0
$687$	−13.0131	+	13.0131i	−0.496483	+	0.496483i
$688$		0			0
$689$	−1.07961	+	1.86995i	−0.0411300	+	0.0712393i
$690$		0			0
$691$	−1.74803	+	1.00923i	−0.0664984	+	0.0383929i	−0.532881	−	0.846190i	$-0.678890\pi$
$691$	−1.74803	+	1.00923i	−0.0664984	+	0.0383929i	0.466382	+	0.884583i	$0.345557\pi$
$692$		0			0
$693$	10.9262	−	8.29776i	0.415053	−	0.315206i
$694$		0			0
$695$	−9.59169	+	5.55302i	−0.363834	+	0.210638i
$696$		0			0
$697$	−4.28675	−	15.9984i	−0.162372	−	0.605981i
$698$		0			0
$699$	−11.8213			−0.447124
$700$		0			0
$701$	−40.9294			−1.54588			−0.772942	−	0.634477i	$-0.781216\pi$
$701$	−40.9294			−1.54588			−0.772942	+	0.634477i	$0.781216\pi$
$702$		0			0
$703$	−8.15499	−	30.4349i	−0.307571	−	1.14787i
$704$		0			0
$705$	−17.7709	+	10.2883i	−0.669290	+	0.387479i
$706$		0			0
$707$	−0.994980	−	7.86025i	−0.0374201	−	0.295615i
$708$		0			0
$709$	−4.41817	+	2.55083i	−0.165928	+	0.0957985i	−0.580664	−	0.814143i	$-0.697207\pi$
$709$	−4.41817	+	2.55083i	−0.165928	+	0.0957985i	0.414736	+	0.909942i	$0.363874\pi$
$710$		0			0
$711$	−8.57194	+	14.8470i	−0.321473	+	0.556807i
$712$		0			0
$713$	27.9262	−	27.9262i	1.04585	−	1.04585i
$714$		0			0
$715$	4.56738	+	4.55650i	0.170810	+	0.170404i
$716$		0			0
$717$	5.28849	−	1.41705i	0.197502	−	0.0529206i
$718$		0			0
$719$	13.6654	+	23.6692i	0.509633	+	0.882710i	0.999938	+	0.0111593i	$0.00355218\pi$
$719$	13.6654	+	23.6692i	0.509633	+	0.882710i	−0.490305	+	0.871551i	$0.663114\pi$
$720$		0			0
$721$	9.44841	+	23.1361i	0.351877	+	0.861632i
$722$		0			0
$723$	−1.77980	+	6.64232i	−0.0661916	+	0.247030i
$724$		0			0
$725$	−4.94984	−	2.84209i	−0.183833	−	0.105552i
$726$		0			0
$727$	20.4882	+	20.4882i	0.759865	+	0.759865i	0.976298	−	0.216433i	$-0.0694422\pi$
$727$	20.4882	+	20.4882i	0.759865	+	0.759865i	−0.216433	+	0.976298i	$0.569442\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$		0			0
$731$	44.2517	+	25.5487i	1.63671	+	0.944953i
$732$		0			0
$733$	−0.996813	−	0.267095i	−0.0368181	−	0.00986538i	0.240363	−	0.970683i	$-0.422734\pi$
$733$	−0.996813	−	0.267095i	−0.0368181	−	0.00986538i	−0.277181	+	0.960818i	$0.589400\pi$
$734$		0			0
$735$	13.6236	−	7.70693i	0.502515	−	0.284274i
$736$		0			0
$737$	−43.7846	−	11.7321i	−1.61283	−	0.432156i
$738$		0			0
$739$	−39.9751	−	23.0797i	−1.47051	−	0.848999i	−0.471057	−	0.882103i	$-0.656127\pi$
$739$	−39.9751	−	23.0797i	−1.47051	−	0.848999i	−0.999452	+	0.0331038i	$0.989461\pi$
$740$		0			0
$741$			2.58674i			0.0950263i
$742$		0			0
$743$	3.40540	+	3.40540i	0.124932	+	0.124932i	0.766808	−	0.641876i	$-0.221844\pi$
$743$	3.40540	+	3.40540i	0.124932	+	0.124932i	−0.641876	+	0.766808i	$0.721844\pi$
$744$		0			0
$745$	−0.270748	+	0.470243i	−0.00991944	+	0.0172284i
$746$		0			0
$747$	−0.170552	+	0.636508i	−0.00624016	+	0.0232886i
$748$		0			0
$749$	−17.7526	−	43.4704i	−0.648668	−	1.58837i
$750$		0			0
$751$	−22.2521	−	38.5417i	−0.811990	−	1.40641i	−0.911469	−	0.411368i	$-0.865051\pi$
$751$	−22.2521	−	38.5417i	−0.811990	−	1.40641i	0.0994790	−	0.995040i	$-0.468282\pi$
$752$		0			0
$753$	−1.73429	+	0.464703i	−0.0632012	+	0.0169347i
$754$		0			0
$755$	−0.0224870	−	18.8705i	−0.000818386	−	0.686767i
$756$		0			0
$757$	5.48138	−	5.48138i	0.199224	−	0.199224i	−0.600443	−	0.799667i	$-0.705009\pi$
$757$	5.48138	−	5.48138i	0.199224	−	0.199224i	0.799667	+	0.600443i	$0.205009\pi$
$758$		0			0
$759$	9.81013	−	16.9916i	0.356085	−	0.616758i
$760$		0			0
$761$	−34.6531	+	20.0070i	−1.25617	+	0.725253i	−0.972329	−	0.233617i	$-0.924944\pi$
$761$	−34.6531	+	20.0070i	−1.25617	+	0.725253i	−0.283846	+	0.958870i	$0.591610\pi$
$762$		0			0
$763$	−0.710719	−	5.61462i	−0.0257298	−	0.203263i
$764$		0			0
$765$	2.45094	−	9.19082i	0.0886139	−	0.332295i
$766$		0			0
$767$	−0.474548	−	1.77104i	−0.0171349	−	0.0639484i
$768$		0			0
$769$	−36.9229			−1.33147			−0.665737	−	0.746187i	$-0.731883\pi$
$769$	−36.9229			−1.33147			−0.665737	+	0.746187i	$0.731883\pi$
$770$		0			0
$771$	−18.3021			−0.659133
$772$		0			0
$773$	0.797882	+	2.97774i	0.0286978	+	0.107102i	0.978789	−	0.204870i	$-0.0656772\pi$
$773$	0.797882	+	2.97774i	0.0286978	+	0.107102i	−0.950091	+	0.311972i	$0.899011\pi$
$774$		0			0
$775$	45.1362	−	26.2030i	1.62134	−	0.941241i
$776$		0			0
$777$	−14.2798	+	10.8446i	−0.512284	+	0.389047i
$778$		0			0
$779$	15.6765	−	9.05084i	0.561670	−	0.324280i
$780$		0			0
$781$	−38.7436	+	67.1059i	−1.38636	+	2.40124i
$782$		0			0
$783$	−0.807198	+	0.807198i	−0.0288469	+	0.0288469i
$784$		0			0
$785$	6.74358	−	6.75967i	0.240689	−	0.241263i
$786$		0			0
$787$	−31.2222	+	8.36596i	−1.11295	+	0.298214i	−0.768028	−	0.640416i	$-0.778762\pi$
$787$	−31.2222	+	8.36596i	−1.11295	+	0.298214i	−0.344923	+	0.938631i	$0.612095\pi$
$788$		0			0
$789$	4.97324	+	8.61391i	0.177052	+	0.306663i
$790$		0			0
$791$	−6.34953	+	46.4392i	−0.225763	+	1.65119i
$792$		0			0
$793$	0.534216	−	1.99372i	0.0189706	−	0.0707992i
$794$		0			0
$795$	7.52028	+	4.32990i	0.266717	+	0.153566i
$796$		0			0
$797$	28.9968	+	28.9968i	1.02712	+	1.02712i	0.999622	+	0.0274969i	$0.00875365\pi$
$797$	28.9968	+	28.9968i	1.02712	+	1.02712i	0.0274969	+	0.999622i	$0.491246\pi$
$798$		0			0
$799$		−	39.0643i		−	1.38199i
$800$		0			0
$801$	−2.49564	−	1.44086i	−0.0881793	−	0.0509103i
$802$		0			0
$803$	−55.1140	−	14.7678i	−1.94493	−	0.521143i
$804$		0			0
$805$	13.6938	−	17.7066i	0.482643	−	0.624075i
$806$		0			0
$807$	24.7085	+	6.62061i	0.869779	+	0.233057i
$808$		0			0
$809$	−12.2910	−	7.09622i	−0.432129	−	0.249490i	0.268124	−	0.963384i	$-0.413596\pi$
$809$	−12.2910	−	7.09622i	−0.432129	−	0.249490i	−0.700253	+	0.713894i	$0.746930\pi$
$810$		0			0
$811$			33.7867i			1.18641i	0.805051	+	0.593206i	$0.202138\pi$
$811$			33.7867i			1.18641i	−0.805051	+	0.593206i	$0.797862\pi$
$812$		0			0
$813$	−6.18222	−	6.18222i	−0.216820	−	0.216820i
$814$		0			0
$815$	−7.63692	−	28.3661i	−0.267510	−	0.993622i
$816$		0			0
$817$	−14.4538	+	53.9424i	−0.505675	+	1.88720i
$818$		0			0
$819$	1.36280	−	0.556548i	0.0476202	−	0.0194474i
$820$		0			0
$821$	−22.8091	−	39.5065i	−0.796043	−	1.37879i	−0.922175	−	0.386773i	$-0.873590\pi$
$821$	−22.8091	−	39.5065i	−0.796043	−	1.37879i	0.126132	−	0.992013i	$-0.459744\pi$
$822$		0			0
$823$	36.3271	−	9.73381i	1.26628	−	0.339299i	0.437677	−	0.899132i	$-0.355801\pi$
$823$	36.3271	−	9.73381i	1.26628	−	0.339299i	0.828606	+	0.559833i	$0.189135\pi$
$824$		0			0
$825$	18.2902	−	18.3776i	0.636784	−	0.639826i
$826$		0			0
$827$	2.49357	−	2.49357i	0.0867099	−	0.0867099i	−0.662421	−	0.749131i	$-0.730471\pi$
$827$	2.49357	−	2.49357i	0.0867099	−	0.0867099i	0.749131	+	0.662421i	$0.230471\pi$
$828$		0			0
$829$	−13.0725	+	22.6422i	−0.454026	+	0.786397i	−0.998632	−	0.0522958i	$-0.983346\pi$
$829$	−13.0725	+	22.6422i	−0.454026	+	0.786397i	0.544605	+	0.838692i	$0.316679\pi$
$830$		0			0
$831$	−4.67322	+	2.69809i	−0.162112	+	0.0935956i
$832$		0			0
$833$	−0.296912	+	29.7758i	−0.0102874	+	1.03167i
$834$		0			0
$835$	−6.33657	−	1.68979i	−0.219286	−	0.0584775i
$836$		0			0
$837$	−2.70159	−	10.0825i	−0.0933807	−	0.348502i
$838$		0			0
$839$	−45.3900			−1.56704			−0.783518	−	0.621369i	$-0.786577\pi$
$839$	−45.3900			−1.56704			−0.783518	+	0.621369i	$0.786577\pi$
$840$		0			0
$841$	27.6969			0.955064
$842$		0			0
$843$	0.129567	+	0.483550i	0.00446251	+	0.0166543i
$844$		0			0
$845$	−14.2176	−	24.5580i	−0.489101	−	0.844821i
$846$		0			0
$847$	−16.2826	+	38.7619i	−0.559476	+	1.33187i
$848$		0			0
$849$	−2.53646	+	1.46442i	−0.0870510	+	0.0502589i
$850$		0			0
$851$	−12.8211	+	22.2068i	−0.439503	+	0.761241i
$852$		0			0
$853$	−13.3034	+	13.3034i	−0.455499	+	0.455499i	−0.897175	−	0.441676i	$-0.854384\pi$
$853$	−13.3034	+	13.3034i	−0.455499	+	0.455499i	0.441676	+	0.897175i	$0.354384\pi$
$854$		0			0
$855$	10.3958	−	0.0123882i	0.355530	−	0.000423667i
$856$		0			0
$857$	−48.3905	+	12.9662i	−1.65299	+	0.442917i	−0.960447	−	0.278463i	$-0.910175\pi$
$857$	−48.3905	+	12.9662i	−1.65299	+	0.442917i	−0.692540	+	0.721379i	$0.743508\pi$
$858$		0			0
$859$	7.52733	+	13.0377i	0.256829	+	0.444841i	0.965391	−	0.260808i	$-0.0839889\pi$
$859$	7.52733	+	13.0377i	0.256829	+	0.444841i	−0.708561	+	0.705649i	$0.750656\pi$
$860$		0			0
$861$	−8.14123	−	6.31172i	−0.277452	−	0.215103i
$862$		0			0
$863$	−10.0843	+	37.6350i	−0.343272	+	1.28111i	0.551345	+	0.834277i	$0.314115\pi$
$863$	−10.0843	+	37.6350i	−0.343272	+	1.28111i	−0.894618	+	0.446833i	$0.852552\pi$
$864$		0			0
$865$	23.5171	−	6.33143i	0.799604	−	0.215275i
$866$		0			0
$867$	0.774745	+	0.774745i	0.0263117	+	0.0263117i
$868$		0			0
$869$		−	88.9018i		−	3.01579i
$870$		0			0
$871$	−4.21198	−	2.43179i	−0.142717	−	0.0823979i
$872$		0			0
$873$	−4.89170	−	1.31073i	−0.165559	−	0.0443614i
$874$		0			0
$875$	23.4931	−	17.9743i	0.794211	−	0.607642i
$876$		0			0
$877$	19.2465	+	5.15707i	0.649907	+	0.174142i	0.568687	−	0.822554i	$-0.307452\pi$
$877$	19.2465	+	5.15707i	0.649907	+	0.174142i	0.0812200	+	0.996696i	$0.474118\pi$
$878$		0			0
$879$	−9.11622	−	5.26325i	−0.307482	−	0.177525i
$880$		0			0
$881$		−	44.5448i		−	1.50075i	−0.661011	−	0.750376i	$-0.729872\pi$
$881$		−	44.5448i		−	1.50075i	0.661011	−	0.750376i	$-0.270128\pi$
$882$		0			0
$883$	13.8261	+	13.8261i	0.465285	+	0.465285i	0.900383	−	0.435098i	$-0.143286\pi$
$883$	13.8261	+	13.8261i	0.465285	+	0.465285i	−0.435098	+	0.900383i	$0.643286\pi$
$884$		0			0
$885$	−7.11533	+	1.91564i	−0.239179	+	0.0643935i
$886$		0			0
$887$	−10.7246	+	40.0248i	−0.360097	+	1.34390i	0.513850	+	0.857880i	$0.328219\pi$
$887$	−10.7246	+	40.0248i	−0.360097	+	1.34390i	−0.873947	+	0.486021i	$0.838448\pi$
$888$		0			0
$889$	−22.3174	−	3.05142i	−0.748503	−	0.102341i
$890$		0			0
$891$	−2.59281	−	4.49089i	−0.0868625	−	0.150450i
$892$		0			0
$893$	41.2392	−	11.0500i	1.38002	−	0.369775i
$894$		0			0
$895$	−40.7353	+	0.0485422i	−1.36163	+	0.00162259i
$896$		0			0
$897$	1.48856	−	1.48856i	0.0497016	−	0.0497016i
$898$		0			0
$899$	5.95784	−	10.3193i	0.198705	−	0.344167i
$900$		0			0
$901$	−14.2968	+	8.25425i	−0.476295	+	0.274989i
$902$		0			0
$903$	31.5289	−	3.99105i	1.04922	−	0.132814i
$904$		0			0
$905$	−14.8136	−	25.5874i	−0.492420	−	0.850554i
$906$		0			0
$907$	−2.95871	−	11.0421i	−0.0982424	−	0.366646i	0.899249	−	0.437438i	$-0.144114\pi$
$907$	−2.95871	−	11.0421i	−0.0982424	−	0.366646i	−0.997491	+	0.0707922i	$0.977447\pi$
$908$		0			0
$909$	−2.99460			−0.0993247
$910$		0			0
$911$	27.9017			0.924425			0.462213	−	0.886769i	$-0.347056\pi$
$911$	27.9017			0.924425			0.462213	+	0.886769i	$0.347056\pi$
$912$		0			0
$913$	−0.884418	−	3.30069i	−0.0292700	−	0.109237i
$914$		0			0
$915$	−8.01511	−	2.13741i	−0.264971	−	0.0706606i
$916$		0			0
$917$	−29.7465	−	12.4955i	−0.982315	−	0.412638i
$918$		0			0
$919$	21.5990	−	12.4702i	0.712485	−	0.411353i	−0.0994956	−	0.995038i	$-0.531723\pi$
$919$	21.5990	−	12.4702i	0.712485	−	0.411353i	0.811980	+	0.583685i	$0.198390\pi$
$920$		0			0
$921$	−6.85091	+	11.8661i	−0.225745	+	0.391002i
$922$		0			0
$923$	−5.87885	+	5.87885i	−0.193505	+	0.193505i
$924$		0			0
$925$	−23.9040	+	24.0182i	−0.785958	+	0.789713i
$926$		0			0
$927$	9.12385	−	2.44473i	0.299667	−	0.0802954i
$928$		0			0
$929$	15.5688	+	26.9659i	0.510796	+	0.884724i	0.999922	+	0.0125108i	$0.00398242\pi$
$929$	15.5688	+	26.9659i	0.510796	+	0.884724i	−0.489126	+	0.872213i	$0.662684\pi$
$930$		0			0
$931$	−31.5176	+	8.10918i	−1.03295	+	0.265768i
$932$		0			0
$933$	−2.95890	+	11.0428i	−0.0968701	+	0.361524i
$934$		0			0
$935$	12.8232	+	47.6297i	0.419364	+	1.55766i
$936$		0			0
$937$	−34.9737	−	34.9737i	−1.14254	−	1.14254i	−0.987984	−	0.154558i	$-0.950605\pi$
$937$	−34.9737	−	34.9737i	−1.14254	−	1.14254i	−0.154558	−	0.987984i	$-0.549395\pi$
$938$		0			0
$939$		−	15.2373i		−	0.497249i
$940$		0			0
$941$	4.51417	+	2.60626i	0.147158	+	0.0849615i	0.571771	−	0.820413i	$-0.306257\pi$
$941$	4.51417	+	2.60626i	0.147158	+	0.0849615i	−0.424613	+	0.905375i	$0.639590\pi$
$942$		0			0
$943$	−14.2296	−	3.81280i	−0.463378	−	0.124162i
$944$		0			0
$945$	−2.24323	−	5.47430i	−0.0729724	−	0.178079i
$946$		0			0
$947$	27.0538	+	7.24905i	0.879131	+	0.235562i	0.670032	−	0.742332i	$-0.266280\pi$
$947$	27.0538	+	7.24905i	0.879131	+	0.235562i	0.209099	+	0.977895i	$0.432947\pi$
$948$		0			0
$949$	−5.30184	−	3.06102i	−0.172105	−	0.0993648i
$950$		0			0
$951$		−	10.1776i		−	0.330032i
$952$		0			0
$953$	14.6336	+	14.6336i	0.474028	+	0.474028i	0.903216	−	0.429187i	$-0.141200\pi$
$953$	14.6336	+	14.6336i	0.474028	+	0.474028i	−0.429187	+	0.903216i	$0.641200\pi$
$954$		0			0
$955$	5.44148	+	3.13300i	0.176082	+	0.101381i
$956$		0			0
$957$	1.53212	−	5.71794i	0.0495264	−	0.184835i
$958$		0			0
$959$	−23.0389	+	29.7169i	−0.743963	+	0.959608i
$960$		0			0
$961$	38.9775	+	67.5110i	1.25734	+	2.17778i
$962$		0			0
$963$	−17.1428	+	4.59341i	−0.552420	+	0.148021i
$964$		0			0
$965$	22.3991	−	22.4526i	0.721053	−	0.722774i
$966$		0			0
$967$	6.52152	−	6.52152i	0.209718	−	0.209718i	−0.594430	−	0.804148i	$-0.702622\pi$
$967$	6.52152	−	6.52152i	0.209718	−	0.209718i	0.804148	+	0.594430i	$0.202622\pi$
$968$		0			0
$969$	−9.88853	+	17.1274i	−0.317665	+	0.550213i
$970$		0			0
$971$	−29.0356	+	16.7637i	−0.931797	+	0.537973i	−0.887379	−	0.461040i	$-0.847476\pi$
$971$	−29.0356	+	16.7637i	−0.931797	+	0.537973i	−0.0444174	+	0.999013i	$0.514143\pi$
$972$		0			0
$973$	−7.93119	−	10.4435i	−0.254262	−	0.334804i
$974$		0			0
$975$	2.40591	−	1.39671i	0.0770509	−	0.0447305i
$976$		0			0
$977$	3.08347	+	11.5077i	0.0986489	+	0.368163i	0.997547	−	0.0699943i	$-0.0222981\pi$
$977$	3.08347	+	11.5077i	0.0986489	+	0.368163i	−0.898899	+	0.438157i	$0.855631\pi$
$978$		0			0
$979$	14.9435			0.477597
$980$		0			0
$981$	−2.13906			−0.0682950
$982$		0			0
$983$	−4.99506	−	18.6418i	−0.159318	−	0.594582i	−0.998697	−	0.0510354i	$-0.983748\pi$
$983$	−4.99506	−	18.6418i	−0.159318	−	0.594582i	0.839379	−	0.543546i	$-0.182919\pi$
$984$		0			0
$985$	4.49674	−	16.8624i	0.143278	−	0.537281i
$986$		0			0
$987$	−14.6944	−	19.3491i	−0.467728	−	0.615889i
$988$		0			0
$989$	39.3592	−	22.7240i	1.25155	−	0.722582i
$990$		0			0
$991$	3.68266	−	6.37856i	0.116984	−	0.202622i	−0.801587	−	0.597878i	$-0.796011\pi$
$991$	3.68266	−	6.37856i	0.116984	−	0.202622i	0.918571	+	0.395256i	$0.129344\pi$
$992$		0			0
$993$	0.266993	−	0.266993i	0.00847277	−	0.00847277i
$994$		0			0
$995$	−0.0219983	−	18.4603i	−0.000697392	−	0.585232i
$996$		0			0
$997$	8.52696	−	2.28479i	0.270051	−	0.0723601i	−0.121252	−	0.992622i	$-0.538691\pi$
$997$	8.52696	−	2.28479i	0.270051	−	0.0723601i	0.391303	+	0.920262i	$0.372024\pi$
$998$		0			0
$999$	3.38862	+	5.86926i	0.107211	+	0.185695i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	840.2.dd.a.73.7	✓	48
5.2	odd	4		840.2.dd.b.577.8	yes	48
7.5	odd	6		840.2.dd.b.313.8	yes	48
35.12	even	12	inner	840.2.dd.a.817.7	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.dd.a.73.7	✓	48	1.1	even	1	trivial
840.2.dd.a.817.7	yes	48	35.12	even	12	inner
840.2.dd.b.313.8	yes	48	7.5	odd	6
840.2.dd.b.577.8	yes	48	5.2	odd	4

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:	\( N \)	\(=\)	\( 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	840.dd (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.258819 + 0.965926i) q^{3} +(-1.93516 + 1.12034i) q^{5} +(-1.60015 - 2.10702i) q^{7} +(-0.866025 + 0.500000i) q^{9} +(2.59281 - 4.49089i) q^{11} +(0.393426 - 0.393426i) q^{13} +(-1.58302 - 1.57925i) q^{15} +(4.10895 - 1.10099i) q^{17} +(2.32458 + 4.02629i) q^{19} +(1.62108 - 2.09096i) q^{21} +(0.979264 - 3.65466i) q^{23} +(2.48967 - 4.33607i) q^{25} +(-0.707107 - 0.707107i) q^{27} -1.14155i q^{29} +(9.03971 + 5.21908i) q^{31} +(5.00893 + 1.34214i) q^{33} +(5.45712 + 2.28471i) q^{35} +(-6.54631 - 1.75408i) q^{37} +(0.481847 + 0.278194i) q^{39} -3.89354i q^{41} +(8.49370 + 8.49370i) q^{43} +(1.11573 - 1.93782i) q^{45} +(2.37678 - 8.87026i) q^{47} +(-1.87906 + 6.74308i) q^{49} +(2.12695 + 3.68398i) q^{51} +(-3.74856 + 1.00442i) q^{53} +(0.0138177 + 11.5954i) q^{55} +(-3.28745 + 3.28745i) q^{57} +(1.64769 - 2.85388i) q^{59} +(3.21272 - 1.85487i) q^{61} +(2.43928 + 1.02466i) q^{63} +(-0.320571 + 1.20211i) q^{65} +(-2.26242 - 8.44346i) q^{67} +3.78358 q^{69} -14.9427 q^{71} +(-2.84783 - 10.6282i) q^{73} +(4.83270 + 1.28258i) q^{75} +(-13.6113 + 1.72296i) q^{77} +(14.8470 - 8.57194i) q^{79} +(0.500000 - 0.866025i) q^{81} +(0.465956 - 0.465956i) q^{83} +(-6.71798 + 6.73401i) q^{85} +(1.10265 - 0.295455i) q^{87} +(1.44086 + 2.49564i) q^{89} +(-1.45850 - 0.199417i) q^{91} +(-2.70159 + 10.0825i) q^{93} +(-9.00925 - 5.18719i) q^{95} +(3.58097 + 3.58097i) q^{97} +5.18563i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{11} + 16 q^{13} - 4 q^{15} - 4 q^{17} + 8 q^{19} - 24 q^{23} + 28 q^{25} + 12 q^{33} - 4 q^{37} - 12 q^{39} + 16 q^{43} - 4 q^{45} + 12 q^{47} - 12 q^{49} + 20 q^{53} - 56 q^{55} + 8 q^{57}+ \cdots + 44 q^{97}+O(q^{100}) \) 48 * q - 4 * q^11 + 16 * q^13 - 4 * q^15 - 4 * q^17 + 8 * q^19 - 24 * q^23 + 28 * q^25 + 12 * q^33 - 4 * q^37 - 12 * q^39 + 16 * q^43 - 4 * q^45 + 12 * q^47 - 12 * q^49 + 20 * q^53 - 56 * q^55 + 8 * q^57 + 8 * q^59 + 8 * q^63 + 12 * q^65 - 52 * q^67 - 8 * q^69 + 16 * q^71 - 4 * q^73 + 24 * q^75 + 8 * q^77 + 108 * q^79 + 24 * q^81 + 64 * q^83 + 32 * q^85 + 20 * q^87 + 64 * q^89 + 48 * q^91 - 24 * q^93 + 36 * q^95 + 44 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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