LMFDB - Embedded newform 840.2.dd.b.313.8

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 = [48,0,0,0,0,0,4] 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			313.8
Character	$\chi$	$=$	840.313
Dual form			840.2.dd.b.577.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.965926 + 0.258819i) q^{3} +(-1.93782 - 1.11573i) q^{5} +(2.10702 + 1.60015i) q^{7} +(0.866025 + 0.500000i) q^{9} +(2.59281 + 4.49089i) q^{11} +(-0.393426 + 0.393426i) q^{13} +(-1.58302 - 1.57925i) q^{15} +(1.10099 - 4.10895i) q^{17} +(-2.32458 + 4.02629i) q^{19} +(1.62108 + 2.09096i) q^{21} +(-3.65466 + 0.979264i) q^{23} +(2.51031 + 4.32416i) q^{25} +(0.707107 + 0.707107i) q^{27} -1.14155i q^{29} +(9.03971 - 5.21908i) q^{31} +(1.34214 + 5.00893i) q^{33} +(-2.29771 - 5.45166i) q^{35} +(1.75408 + 6.54631i) q^{37} +(-0.481847 + 0.278194i) q^{39} +3.89354i q^{41} +(8.49370 + 8.49370i) q^{43} +(-1.12034 - 1.93516i) q^{45} +(8.87026 - 2.37678i) q^{47} +(1.87906 + 6.74308i) q^{49} +(2.12695 - 3.68398i) q^{51} +(1.00442 - 3.74856i) q^{53} +(-0.0138177 - 11.5954i) q^{55} +(-3.28745 + 3.28745i) q^{57} +(-1.64769 - 2.85388i) q^{59} +(3.21272 + 1.85487i) q^{61} +(1.02466 + 2.43928i) q^{63} +(1.20135 - 0.323435i) q^{65} +(8.44346 + 2.26242i) q^{67} -3.78358 q^{69} -14.9427 q^{71} +(-10.6282 - 2.84783i) q^{73} +(1.30560 + 4.82653i) q^{75} +(-1.72296 + 13.6113i) q^{77} +(-14.8470 - 8.57194i) q^{79} +(0.500000 + 0.866025i) q^{81} +(-0.465956 + 0.465956i) q^{83} +(-6.71798 + 6.73401i) q^{85} +(0.295455 - 1.10265i) q^{87} +(-1.44086 + 2.49564i) q^{89} +(-1.45850 + 0.199417i) q^{91} +(10.0825 - 2.70159i) q^{93} +(8.99686 - 5.20864i) q^{95} +(-3.58097 - 3.58097i) q^{97} +5.18563i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 4 q^{7} - 4 q^{11} - 16 q^{13} - 4 q^{15} + 4 q^{17} - 8 q^{19} + 48 q^{23} - 20 q^{25} + 24 q^{33} - 4 q^{37} + 12 q^{39} + 16 q^{43} + 4 q^{45} - 12 q^{47} + 12 q^{49} - 52 q^{53} + 56 q^{55} + 8 q^{57}+ \cdots - 44 q^{97}+O(q^{100}) $ 48 * q + 4 * q^7 - 4 * q^11 - 16 * q^13 - 4 * q^15 + 4 * q^17 - 8 * q^19 + 48 * q^23 - 20 * q^25 + 24 * q^33 - 4 * q^37 + 12 * q^39 + 16 * q^43 + 4 * q^45 - 12 * q^47 + 12 * q^49 - 52 * q^53 + 56 * q^55 + 8 * q^57 - 8 * q^59 + 12 * q^65 + 68 * q^67 + 8 * q^69 + 16 * q^71 + 52 * q^73 + 24 * q^75 + 16 * q^77 - 108 * q^79 + 24 * q^81 - 64 * q^83 + 32 * q^85 - 8 * q^87 - 64 * q^89 + 48 * q^91 + 48 * q^93 - 84 * q^95 - 44 * q^97

Character values

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

$n$	$241$	$281$	$337$	$421$	$631$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{3}{4}\right)$	$1$	$1$

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
$3$	0.965926	+	0.258819i	0.557678	+	0.149429i
$3$	0.965926	+	0.258819i	0.557678	+	0.149429i
$4$		0			0
$5$	−1.93782	−	1.11573i	−0.866621	−	0.498968i
$5$	−1.93782	−	1.11573i	−0.866621	−	0.498968i
$6$		0			0
$7$	2.10702	+	1.60015i	0.796379	+	0.604799i
$7$	2.10702	+	1.60015i	0.796379	+	0.604799i
$8$		0			0
$9$	0.866025	+	0.500000i	0.288675	+	0.166667i
$10$		0			0
$11$	2.59281	+	4.49089i	0.781763	+	1.35405i	0.930914	+	0.365238i	$0.119013\pi$
$11$	2.59281	+	4.49089i	0.781763	+	1.35405i	−0.149151	+	0.988814i	$0.547654\pi$
$12$		0			0
$13$	−0.393426	+	0.393426i	−0.109117	+	0.109117i	−0.759557	−	0.650440i	$-0.774584\pi$
$13$	−0.393426	+	0.393426i	−0.109117	+	0.109117i	0.650440	+	0.759557i	$0.274584\pi$
$14$		0			0
$15$	−1.58302	−	1.57925i	−0.408734	−	0.407762i
$16$		0			0
$17$	1.10099	−	4.10895i	0.267029	−	0.996567i	−0.693967	−	0.720007i	$-0.744139\pi$
$17$	1.10099	−	4.10895i	0.267029	−	0.996567i	0.960997	−	0.276560i	$-0.0891946\pi$
$18$		0			0
$19$	−2.32458	+	4.02629i	−0.533295	+	0.923695i	0.465948	+	0.884812i	$0.345713\pi$
$19$	−2.32458	+	4.02629i	−0.533295	+	0.923695i	−0.999244	+	0.0388828i	$0.987620\pi$
$20$		0			0
$21$	1.62108	+	2.09096i	0.353748	+	0.456285i
$22$		0			0
$23$	−3.65466	+	0.979264i	−0.762050	+	0.204191i	−0.618856	−	0.785504i	$-0.712404\pi$
$23$	−3.65466	+	0.979264i	−0.762050	+	0.204191i	−0.143193	+	0.989695i	$0.545737\pi$
$24$		0			0
$25$	2.51031	+	4.32416i	0.502063	+	0.864831i
$26$		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	0.637627	−	0.770345i	$-0.279916\pi$
$31$	9.03971	−	5.21908i	1.62358	−	0.937374i	0.985952	−	0.167029i	$-0.0534172\pi$
$32$		0			0
$33$	1.34214	+	5.00893i	0.233636	+	0.871943i
$34$		0			0
$35$	−2.29771	−	5.45166i	−0.388383	−	0.921498i
$36$		0			0
$37$	1.75408	+	6.54631i	0.288369	+	1.07621i	0.946342	+	0.323166i	$0.104747\pi$
$37$	1.75408	+	6.54631i	0.288369	+	1.07621i	−0.657974	+	0.753041i	$0.728586\pi$
$38$		0			0
$39$	−0.481847	+	0.278194i	−0.0771573	+	0.0445468i
$40$		0			0
$41$			3.89354i			0.608068i	0.952661	+	0.304034i	$0.0983337\pi$
$41$			3.89354i			0.608068i	−0.952661	+	0.304034i	$0.901666\pi$
$42$		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
$45$	−1.12034	−	1.93516i	−0.167011	−	0.288476i
$46$		0			0
$47$	8.87026	−	2.37678i	1.29386	−	0.346689i	0.454735	−	0.890627i	$-0.349734\pi$
$47$	8.87026	−	2.37678i	1.29386	−	0.346689i	0.839125	+	0.543938i	$0.183067\pi$
$48$		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
$53$	1.00442	−	3.74856i	0.137968	−	0.514904i	−0.862000	−	0.506908i	$-0.830788\pi$
$53$	1.00442	−	3.74856i	0.137968	−	0.514904i	0.999968	−	0.00799545i	$-0.00254506\pi$
$54$		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	$-0.235482\pi$
$59$	−1.64769	−	2.85388i	−0.214511	−	0.371544i	−0.953121	+	0.302589i	$0.902149\pi$
$60$		0			0
$61$	3.21272	+	1.85487i	0.411347	+	0.237491i	0.691368	−	0.722502i	$-0.257008\pi$
$61$	3.21272	+	1.85487i	0.411347	+	0.237491i	−0.280021	+	0.959994i	$0.590342\pi$
$62$		0			0
$63$	1.02466	+	2.43928i	0.129095	+	0.307320i
$64$		0			0
$65$	1.20135	−	0.323435i	0.149009	−	0.0401171i
$66$		0			0
$67$	8.44346	+	2.26242i	1.03153	+	0.276398i	0.734600	−	0.678500i	$-0.237370\pi$
$67$	8.44346	+	2.26242i	1.03153	+	0.276398i	0.296933	+	0.954898i	$0.404036\pi$
$68$		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
$73$	−10.6282	−	2.84783i	−1.24394	−	0.333313i	−0.423947	−	0.905687i	$-0.639356\pi$
$73$	−10.6282	−	2.84783i	−1.24394	−	0.333313i	−0.819993	+	0.572374i	$0.806023\pi$
$74$		0			0
$75$	1.30560	+	4.82653i	0.150758	+	0.557320i
$76$		0			0
$77$	−1.72296	+	13.6113i	−0.196350	+	1.55115i
$78$		0			0
$79$	−14.8470	−	8.57194i	−1.67042	−	0.964419i	−0.967401	−	0.253250i	$-0.918501\pi$
$79$	−14.8470	−	8.57194i	−1.67042	−	0.964419i	−0.703021	−	0.711169i	$-0.748166\pi$
$80$		0			0
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$		0			0
$83$	−0.465956	+	0.465956i	−0.0511453	+	0.0511453i	−0.732217	−	0.681072i	$-0.761514\pi$
$83$	−0.465956	+	0.465956i	−0.0511453	+	0.0511453i	0.681072	+	0.732217i	$0.261514\pi$
$84$		0			0
$85$	−6.71798	+	6.73401i	−0.728668	+	0.730406i
$86$		0			0
$87$	0.295455	−	1.10265i	0.0316761	−	0.118217i
$88$		0			0
$89$	−1.44086	+	2.49564i	−0.152731	+	0.264538i	−0.932231	−	0.361865i	$-0.882140\pi$
$89$	−1.44086	+	2.49564i	−0.152731	+	0.264538i	0.779500	+	0.626403i	$0.215473\pi$
$90$		0			0
$91$	−1.45850	+	0.199417i	−0.152892	+	0.0209046i
$92$		0			0
$93$	10.0825	−	2.70159i	1.04550	−	0.280142i
$94$		0			0
$95$	8.99686	−	5.20864i	0.923058	−	0.534396i
$96$		0			0
$97$	−3.58097	−	3.58097i	−0.363593	−	0.363593i	0.501541	−	0.865134i	$-0.332767\pi$
$97$	−3.58097	−	3.58097i	−0.363593	−	0.363593i	−0.865134	+	0.501541i	$0.832767\pi$
$98$		0			0
$99$			5.18563i			0.521175i
$100$		0			0
$101$	2.59340	−	1.49730i	0.258053	−	0.148987i	−0.365393	−	0.930853i	$-0.619065\pi$
$101$	2.59340	−	1.49730i	0.258053	−	0.148987i	0.623446	+	0.781866i	$0.285732\pi$
$102$		0			0
$103$	−2.44473	−	9.12385i	−0.240886	−	0.899000i	−0.975407	−	0.220413i	$-0.929259\pi$
$103$	−2.44473	−	9.12385i	−0.240886	−	0.899000i	0.734520	−	0.678587i	$-0.237407\pi$
$104$		0			0
$105$	−0.808421	−	5.86058i	−0.0788938	−	0.571935i
$106$		0			0
$107$	−4.59341	−	17.1428i	−0.444062	−	1.65726i	−0.718402	−	0.695628i	$-0.755126\pi$
$107$	−4.59341	−	17.1428i	−0.444062	−	1.65726i	0.274340	−	0.961633i	$-0.411540\pi$
$108$		0			0
$109$	−1.85248	+	1.06953i	−0.177435	+	0.102442i	−0.586087	−	0.810248i	$-0.699332\pi$
$109$	−1.85248	+	1.06953i	−0.177435	+	0.102442i	0.408652	+	0.912690i	$0.365999\pi$
$110$		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
$115$	8.17468	+	2.17996i	0.762292	+	0.203282i
$116$		0			0
$117$	−0.537430	+	0.144004i	−0.0496855	+	0.0133132i
$118$		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
$123$	−1.00772	+	3.76087i	−0.0908632	+	0.339106i
$124$		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	0.884501	−	0.466538i	$-0.154499\pi$
$131$	10.5610	+	6.09739i	0.922719	+	0.532732i	0.0382172	+	0.999269i	$0.487832\pi$
$132$		0			0
$133$	−11.3406	+	4.76381i	−0.983354	+	0.413074i
$134$		0			0
$135$	−0.581310	−	2.15918i	−0.0500312	−	0.185833i
$136$		0			0
$137$	13.7278	+	3.67836i	1.17285	+	0.314263i	0.792085	−	0.610411i	$-0.208996\pi$
$137$	13.7278	+	3.67836i	1.17285	+	0.314263i	0.380761	+	0.924674i	$0.375662\pi$
$138$		0			0
$139$	−4.95654			−0.420408			−0.210204	−	0.977658i	$-0.567413\pi$
$139$	−4.95654			−0.420408			−0.210204	+	0.977658i	$0.567413\pi$
$140$		0			0
$141$	9.18316			0.773362
$142$		0			0
$143$	−2.78691	−	0.746751i	−0.233053	−	0.0624465i
$144$		0			0
$145$	−1.27366	+	2.21212i	−0.105771	+	0.183707i
$146$		0			0
$147$	0.0697977	+	6.99965i	0.00575681	+	0.577322i
$148$		0			0
$149$	−0.210154	−	0.121333i	−0.0172165	−	0.00993996i	0.491367	−	0.870953i	$-0.336497\pi$
$149$	−0.210154	−	0.121333i	−0.0172165	−	0.00993996i	−0.508584	+	0.861013i	$0.669831\pi$
$150$		0			0
$151$	−4.21957	−	7.30851i	−0.343384	−	0.594758i	0.641675	−	0.766977i	$-0.278240\pi$
$151$	−4.21957	−	7.30851i	−0.343384	−	0.594758i	−0.985059	+	0.172219i	$0.944906\pi$
$152$		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
$157$	−1.10519	+	4.12461i	−0.0882034	+	0.329180i	−0.995902	−	0.0904442i	$-0.971171\pi$
$157$	−1.10519	+	4.12461i	−0.0882034	+	0.329180i	0.907698	+	0.419624i	$0.137838\pi$
$158$		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
$163$	12.6898	−	3.40022i	0.993941	−	0.266326i	0.275036	−	0.961434i	$-0.411310\pi$
$163$	12.6898	−	3.40022i	0.993941	−	0.266326i	0.718905	+	0.695108i	$0.244644\pi$
$164$		0			0
$165$	2.98777	−	11.2039i	0.232597	−	0.872221i
$166$		0			0
$167$	−2.07382	−	2.07382i	−0.160477	−	0.160477i	0.622301	−	0.782778i	$-0.286198\pi$
$167$	−2.07382	−	2.07382i	−0.160477	−	0.160477i	−0.782778	+	0.622301i	$0.786198\pi$
$168$		0			0
$169$			12.6904i			0.976187i
$170$		0			0
$171$	−4.02629	+	2.32458i	−0.307898	+	0.177765i
$172$		0			0
$173$	−2.81896	−	10.5205i	−0.214322	−	0.799860i	−0.986404	−	0.164338i	$-0.947451\pi$
$173$	−2.81896	−	10.5205i	−0.214322	−	0.799860i	0.772082	−	0.635523i	$-0.219215\pi$
$174$		0			0
$175$	−1.63001	+	13.1280i	−0.123217	+	0.992380i
$176$		0			0
$177$	−0.852907	−	3.18309i	−0.0641084	−	0.239256i
$178$		0			0
$179$	−15.7767	+	9.10869i	−1.17921	+	0.680816i	−0.955831	−	0.293917i	$-0.905041\pi$
$179$	−15.7767	+	9.10869i	−1.17921	+	0.680816i	−0.223376	+	0.974732i	$0.571708\pi$
$180$		0			0
$181$		−	13.2224i		−	0.982812i	−0.870931	−	0.491406i	$-0.836483\pi$
$181$		−	13.2224i		−	0.982812i	0.870931	−	0.491406i	$-0.163517\pi$
$182$		0			0
$183$	2.62318	+	2.62318i	0.193911	+	0.193911i
$184$		0			0
$185$	3.90479	−	14.6427i	0.287086	−	1.07655i
$186$		0			0
$187$	21.3075	−	5.70932i	1.55816	−	0.417507i
$188$		0			0
$189$	0.358413	+	2.62136i	0.0260707	+	0.190676i
$190$		0			0
$191$	−1.40402	+	2.43183i	−0.101591	+	0.175961i	−0.912340	−	0.409433i	$-0.865727\pi$
$191$	−1.40402	+	2.43183i	−0.101591	+	0.175961i	0.810749	+	0.585394i	$0.199060\pi$
$192$		0			0
$193$	3.67092	−	13.7001i	0.264239	−	0.986153i	−0.698476	−	0.715634i	$-0.746138\pi$
$193$	3.67092	−	13.7001i	0.264239	−	0.986153i	0.962715	−	0.270519i	$-0.0871953\pi$
$194$		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	$-0.0721408\pi$
$199$	4.12786	+	7.14966i	0.292616	+	0.506826i	−0.681811	+	0.731528i	$0.738808\pi$
$200$		0			0
$201$	7.57020	+	4.37066i	0.533961	+	0.308282i
$202$		0			0
$203$	1.82665	−	2.40527i	0.128205	−	0.168817i
$204$		0			0
$205$	4.34412	−	7.54499i	0.303406	−	0.526965i
$206$		0			0
$207$	−3.65466	−	0.979264i	−0.254017	−	0.0680635i
$208$		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
$213$	−14.4335	−	3.86745i	−0.988969	−	0.264993i
$214$		0			0
$215$	−6.98264	−	25.9359i	−0.476212	−	1.76881i
$216$		0			0
$217$	27.3981	+	3.46816i	1.85991	+	0.235434i
$218$		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	$-0.358962\pi$
$223$	19.8934	−	19.8934i	1.33216	−	1.33216i	0.903433	−	0.428729i	$-0.141038\pi$
$224$		0			0
$225$	0.0119165	+	4.99999i	0.000794433	+	0.333332i
$226$		0			0
$227$	−3.10675	+	11.5946i	−0.206202	+	0.769558i	0.782877	+	0.622176i	$0.213751\pi$
$227$	−3.10675	+	11.5946i	−0.206202	+	0.769558i	−0.989080	+	0.147382i	$0.952915\pi$
$228$		0			0
$229$	−9.20168	+	15.9378i	−0.608064	+	1.05320i	0.383495	+	0.923543i	$0.374720\pi$
$229$	−9.20168	+	15.9378i	−0.608064	+	1.05320i	−0.991559	+	0.129655i	$0.958613\pi$
$230$		0			0
$231$	−5.18711	+	12.7015i	−0.341287	+	0.835700i
$232$		0			0
$233$	11.4185	−	3.05959i	0.748053	−	0.200440i	0.135399	−	0.990791i	$-0.456768\pi$
$233$	11.4185	−	3.05959i	0.748053	−	0.200440i	0.612654	+	0.790351i	$0.290102\pi$
$234$		0			0
$235$	−19.8408	−	5.29100i	−1.29427	−	0.345147i
$236$		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	−0.295774	−	0.955258i	$-0.595577\pi$
$241$	5.95534	−	3.43832i	0.383617	−	0.221481i	0.679391	+	0.733777i	$0.262244\pi$
$242$		0			0
$243$	0.258819	+	0.965926i	0.0166032	+	0.0619642i
$244$		0			0
$245$	3.88214	−	15.1634i	0.248021	−	0.968755i
$246$		0			0
$247$	−0.669498	−	2.49860i	−0.0425991	−	0.158982i
$248$		0			0
$249$	−0.570677	+	0.329481i	−0.0361652	+	0.0208800i
$250$		0			0
$251$		−	1.79547i		−	0.113329i	−0.998393	−	0.0566646i	$-0.981953\pi$
$251$		−	1.79547i		−	0.113329i	0.998393	−	0.0566646i	$-0.0180466\pi$
$252$		0			0
$253$	−13.8736	−	13.8736i	−0.872227	−	0.872227i
$254$		0			0
$255$	−8.23197	+	4.76582i	−0.515506	+	0.298447i
$256$		0			0
$257$	−17.6785	+	4.73693i	−1.10275	+	0.295481i	−0.763885	−	0.645353i	$-0.776710\pi$
$257$	−17.6785	+	4.73693i	−1.10275	+	0.295481i	−0.338867	+	0.940834i	$0.610044\pi$
$258$		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
$263$	−2.57434	+	9.60757i	−0.158741	+	0.592428i	0.840015	+	0.542563i	$0.182546\pi$
$263$	−2.57434	+	9.60757i	−0.158741	+	0.592428i	−0.998756	+	0.0498654i	$0.984121\pi$
$264$		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	−0.932044	−	0.362346i	$-0.881976\pi$
$269$	−12.7900	−	22.1530i	−0.779823	−	1.35069i	0.152221	−	0.988347i	$-0.451358\pi$
$270$		0			0
$271$	−7.57164	−	4.37149i	−0.459945	−	0.265549i	0.252076	−	0.967707i	$-0.418887\pi$
$271$	−7.57164	−	4.37149i	−0.459945	−	0.265549i	−0.712021	+	0.702158i	$0.752220\pi$
$272$		0			0
$273$	−1.46041	−	0.184865i	−0.0883882	−	0.0111885i
$274$		0			0
$275$	−12.9105	+	22.4853i	−0.778533	+	1.35591i
$276$		0			0
$277$	−5.21230	−	1.39663i	−0.313177	−	0.0839155i	0.0988070	−	0.995107i	$-0.468497\pi$
$277$	−5.21230	−	1.39663i	−0.313177	−	0.0839155i	−0.411984	+	0.911191i	$0.635164\pi$
$278$		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
$283$	2.82905	+	0.758042i	0.168170	+	0.0450609i	0.341921	−	0.939729i	$-0.388922\pi$
$283$	2.82905	+	0.758042i	0.168170	+	0.0450609i	−0.173752	+	0.984789i	$0.555589\pi$
$284$		0			0
$285$	10.0384	−	2.70261i	0.594623	−	0.160089i
$286$		0			0
$287$	−6.23023	+	8.20376i	−0.367759	+	0.484253i
$288$		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	−0.455427	−	0.890273i	$-0.650513\pi$
$293$	7.44336	−	7.44336i	0.434846	−	0.434846i	0.890273	+	0.455427i	$0.150513\pi$
$294$		0			0
$295$	0.00878090	+	7.36869i	0.000511244	+	0.429021i
$296$		0			0
$297$	−1.34214	+	5.00893i	−0.0778788	+	0.290648i
$298$		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
$303$	2.89256	−	0.775060i	0.166173	−	0.0445261i
$304$		0			0
$305$	−4.15616	−	7.17892i	−0.237981	−	0.411064i
$306$		0			0
$307$	−9.68865	−	9.68865i	−0.552960	−	0.552960i	0.374334	−	0.927294i	$-0.377871\pi$
$307$	−9.68865	−	9.68865i	−0.552960	−	0.552960i	−0.927294	+	0.374334i	$0.877871\pi$
$308$		0			0
$309$		−	9.44571i		−	0.537347i
$310$		0			0
$311$	9.90068	−	5.71616i	0.561416	−	0.324134i	−0.192298	−	0.981337i	$-0.561594\pi$
$311$	9.90068	−	5.71616i	0.561416	−	0.324134i	0.753714	+	0.657203i	$0.228261\pi$
$312$		0			0
$313$	−3.94369	−	14.7181i	−0.222911	−	0.831914i	−0.983231	−	0.182366i	$-0.941625\pi$
$313$	−3.94369	−	14.7181i	−0.222911	−	0.831914i	0.760320	−	0.649549i	$-0.225042\pi$
$314$		0			0
$315$	0.735956	−	5.87013i	0.0414664	−	0.330744i
$316$		0			0
$317$	2.63416	+	9.83081i	0.147949	+	0.552153i	0.999606	+	0.0280544i	$0.00893118\pi$
$317$	2.63416	+	9.83081i	0.147949	+	0.552153i	−0.851657	+	0.524099i	$0.824402\pi$
$318$		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
$325$	−2.68886	−	0.713614i	−0.149151	−	0.0395842i
$326$		0			0
$327$	−2.06617	+	0.553630i	−0.114260	+	0.0306158i
$328$		0			0
$329$	22.4930	+	9.18579i	1.24008	+	0.506429i
$330$		0			0
$331$	−0.188793	+	0.326998i	−0.0103770	+	0.0179735i	−0.871167	−	0.490986i	$-0.836636\pi$
$331$	−0.188793	+	0.326998i	−0.0103770	+	0.0179735i	0.860790	+	0.508960i	$0.169970\pi$
$332$		0			0
$333$	−1.75408	+	6.54631i	−0.0961229	+	0.358736i
$334$		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
$343$	−6.83069	+	17.2146i	−0.368823	+	0.929500i
$344$		0			0
$345$	7.33192	+	4.22144i	0.394737	+	0.227275i
$346$		0			0
$347$	23.0111	+	6.16581i	1.23530	+	0.330998i	0.816641	−	0.577145i	$-0.195833\pi$
$347$	23.0111	+	6.16581i	1.23530	+	0.330998i	0.418660	+	0.908143i	$0.362500\pi$
$348$		0			0
$349$	−19.6652			−1.05265			−0.526326	−	0.850283i	$-0.676431\pi$
$349$	−19.6652			−1.05265			−0.526326	+	0.850283i	$0.676431\pi$
$350$		0			0
$351$	−0.556389			−0.0296978
$352$		0			0
$353$	32.4454	+	8.69371i	1.72689	+	0.462720i	0.979464	−	0.201621i	$-0.0646210\pi$
$353$	32.4454	+	8.69371i	1.72689	+	0.462720i	0.747430	+	0.664341i	$0.231288\pi$
$354$		0			0
$355$	28.9563	+	16.6719i	1.53684	+	0.884855i
$356$		0			0
$357$	10.3764	−	4.35880i	0.549179	−	0.230692i
$358$		0			0
$359$	−0.716930	−	0.413919i	−0.0378381	−	0.0218458i	0.480962	−	0.876742i	$-0.340288\pi$
$359$	−0.716930	−	0.413919i	−0.0378381	−	0.0218458i	−0.518800	+	0.854896i	$0.673621\pi$
$360$		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
$367$	2.42925	−	9.06608i	0.126806	−	0.473246i	−0.873092	−	0.487556i	$-0.837889\pi$
$367$	2.42925	−	9.06608i	0.126806	−	0.473246i	0.999898	+	0.0143102i	$0.00455523\pi$
$368$		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
$373$	20.3624	−	5.45608i	1.05432	−	0.282505i	0.310286	−	0.950643i	$-0.399575\pi$
$373$	20.3624	−	5.45608i	1.05432	−	0.282505i	0.744037	+	0.668138i	$0.232909\pi$
$374$		0			0
$375$	2.85506	−	10.8097i	0.147435	−	0.558208i
$376$		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
$383$	0.310019	+	1.15701i	0.0158413	+	0.0591204i	0.973394	−	0.229138i	$-0.0735906\pi$
$383$	0.310019	+	1.15701i	0.0158413	+	0.0591204i	−0.957553	+	0.288258i	$0.906924\pi$
$384$		0			0
$385$	18.5252	−	24.4539i	0.944133	−	1.24628i
$386$		0			0
$387$	3.10891	+	11.6026i	0.158035	+	0.589794i
$388$		0			0
$389$	−16.3871	+	9.46111i	−0.830860	+	0.479697i	−0.854147	−	0.520031i	$-0.825920\pi$
$389$	−16.3871	+	9.46111i	−0.830860	+	0.479697i	0.0232869	+	0.999729i	$0.492587\pi$
$390$		0			0
$391$			16.0950i			0.813958i
$392$		0			0
$393$	8.62302	+	8.62302i	0.434974	+	0.434974i
$394$		0			0
$395$	19.2070	+	33.1761i	0.966409	+	1.66927i
$396$		0			0
$397$	8.54635	−	2.28999i	0.428929	−	0.114931i	−0.0378944	−	0.999282i	$-0.512065\pi$
$397$	8.54635	−	2.28999i	0.428929	−	0.114931i	0.466823	+	0.884351i	$0.345398\pi$
$398$		0			0
$399$	−12.1871	+	1.66632i	−0.610120	+	0.0834204i
$400$		0			0
$401$	−1.29046	+	2.23514i	−0.0644426	+	0.111618i	−0.896447	−	0.443152i	$-0.853860\pi$
$401$	−1.29046	+	2.23514i	−0.0644426	+	0.111618i	0.832004	+	0.554770i	$0.187194\pi$
$402$		0			0
$403$	−1.50314	+	5.60978i	−0.0748766	+	0.279443i
$404$		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	−0.971748	−	0.236019i	$-0.924157\pi$
$409$	−13.9599	−	24.1793i	−0.690273	−	1.19559i	0.281476	−	0.959568i	$-0.409176\pi$
$410$		0			0
$411$	12.3080	+	7.10604i	0.607110	+	0.350515i
$412$		0			0
$413$	1.09492	−	8.64973i	0.0538772	−	0.425625i
$414$		0			0
$415$	1.42282	−	0.383061i	0.0698434	−	0.0188037i
$416$		0			0
$417$	−4.78765	−	1.28285i	−0.234452	−	0.0628213i
$418$		0			0
$419$	13.4480			0.656980			0.328490	−	0.944508i	$-0.393460\pi$
$419$	13.4480			0.656980			0.328490	+	0.944508i	$0.393460\pi$
$420$		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
$423$	8.87026	+	2.37678i	0.431287	+	0.115563i
$424$		0			0
$425$	20.5316	−	5.55390i	0.995928	−	0.269404i
$426$		0			0
$427$	3.80121	+	9.04907i	0.183954	+	0.437915i
$428$		0			0
$429$	−2.49868	−	1.44261i	−0.120637	−	0.0696500i
$430$		0			0
$431$	17.9055	+	31.0133i	0.862479	+	1.49386i	0.869529	+	0.493881i	$0.164422\pi$
$431$	17.9055	+	31.0133i	0.862479	+	1.49386i	−0.00705073	+	0.999975i	$0.502244\pi$
$432$		0			0
$433$	−11.7831	+	11.7831i	−0.566261	+	0.566261i	−0.931079	−	0.364818i	$-0.881131\pi$
$433$	−11.7831	+	11.7831i	−0.566261	+	0.566261i	0.364818	+	0.931079i	$0.381131\pi$
$434$		0			0
$435$	−1.80280	+	1.80710i	−0.0864375	+	0.0866437i
$436$		0			0
$437$	4.55275	−	16.9911i	0.217788	−	0.812795i
$438$		0			0
$439$	19.3867	−	33.5788i	0.925279	−	1.60263i	0.134167	−	0.990959i	$-0.457164\pi$
$439$	19.3867	−	33.5788i	0.925279	−	1.60263i	0.791112	−	0.611671i	$-0.209502\pi$
$440$		0			0
$441$	−1.74422	+	6.77921i	−0.0830583	+	0.322820i
$442$		0			0
$443$	−11.3631	+	3.04474i	−0.539878	+	0.144660i	−0.518446	−	0.855111i	$-0.673489\pi$
$443$	−11.3631	+	3.04474i	−0.539878	+	0.144660i	−0.0214319	+	0.999770i	$0.506823\pi$
$444$		0			0
$445$	5.57659	−	3.22851i	0.264356	−	0.153046i
$446$		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
$453$	−2.18421	−	8.15158i	−0.102623	−	0.382995i
$454$		0			0
$455$	3.04880	+	1.24085i	0.142930	+	0.0581718i
$456$		0			0
$457$	−4.57271	−	17.0656i	−0.213902	−	0.798295i	−0.986550	−	0.163460i	$-0.947735\pi$
$457$	−4.57271	−	17.0656i	−0.213902	−	0.798295i	0.772648	−	0.634835i	$-0.218932\pi$
$458$		0			0
$459$	3.68398	−	2.12695i	0.171954	−	0.0992775i
$460$		0			0
$461$		−	17.7227i		−	0.825427i	−0.910861	−	0.412713i	$-0.864581\pi$
$461$		−	17.7227i		−	0.825427i	0.910861	−	0.412713i	$-0.135419\pi$
$462$		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
$465$	−22.5523	−	6.01408i	−1.04584	−	0.278896i
$466$		0			0
$467$	19.2991	−	5.17117i	0.893054	−	0.239293i	0.217023	−	0.976166i	$-0.430365\pi$
$467$	19.2991	−	5.17117i	0.893054	−	0.239293i	0.676031	+	0.736873i	$0.263699\pi$
$468$		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
$473$	−16.1216	+	60.1668i	−0.741274	+	2.76647i
$474$		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	$-0.0381131\pi$
$479$	8.60064	+	14.8967i	0.392973	+	0.680650i	−0.599867	+	0.800100i	$0.704780\pi$
$480$		0			0
$481$	−3.26559	−	1.88539i	−0.148898	−	0.0859664i
$482$		0			0
$483$	−7.97209	−	6.05429i	−0.362742	−	0.275480i
$484$		0			0
$485$	2.94391	+	10.9347i	0.133676	+	0.496518i
$486$		0			0
$487$	34.9724	+	9.37082i	1.58475	+	0.424632i	0.940392	−	0.340092i	$-0.110458\pi$
$487$	34.9724	+	9.37082i	1.58475	+	0.424632i	0.644357	+	0.764725i	$0.277125\pi$
$488$		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
$493$	−4.69057	−	1.25683i	−0.211253	−	0.0566050i
$494$		0			0
$495$	5.78574	−	10.0488i	0.260050	−	0.451661i
$496$		0			0
$497$	−31.4845	−	23.9105i	−1.41227	−	1.07253i
$498$		0			0
$499$	−1.03820	−	0.599404i	−0.0464761	−	0.0268330i	0.476582	−	0.879130i	$-0.341876\pi$
$499$	−1.03820	−	0.599404i	−0.0464761	−	0.0268330i	−0.523058	+	0.852297i	$0.675209\pi$
$500$		0			0
$501$	−1.46641	−	2.53990i	−0.0655146	−	0.113475i
$502$		0			0
$503$	−11.2555	+	11.2555i	−0.501856	+	0.501856i	−0.912014	−	0.410158i	$-0.865473\pi$
$503$	−11.2555	+	11.2555i	−0.501856	+	0.501856i	0.410158	+	0.912014i	$0.365473\pi$
$504$		0			0
$505$	−6.69613	+	0.00797945i	−0.297974	+	0.000355081i
$506$		0			0
$507$	−3.28453	+	12.2580i	−0.145871	+	0.544398i
$508$		0			0
$509$	−15.8833	+	27.5106i	−0.704013	+	1.21939i	0.263034	+	0.964787i	$0.415277\pi$
$509$	−15.8833	+	27.5106i	−0.704013	+	1.21939i	−0.967047	+	0.254600i	$0.918056\pi$
$510$		0			0
$511$	−17.8369	−	23.0071i	−0.789060	−	1.01778i
$512$		0			0
$513$	−4.49074	+	1.20329i	−0.198271	+	0.0531266i
$514$		0			0
$515$	−5.44226	+	20.4081i	−0.239815	+	0.899286i
$516$		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	0.00648104	−	0.999979i	$-0.497937\pi$
$521$	19.9889	−	11.5406i	0.875729	−	0.505602i	0.869248	+	0.494377i	$0.164604\pi$
$522$		0			0
$523$	−2.09691	−	7.82579i	−0.0916917	−	0.342198i	0.904805	−	0.425825i	$-0.140016\pi$
$523$	−2.09691	−	7.82579i	−0.0916917	−	0.342198i	−0.996497	+	0.0836272i	$0.973349\pi$
$524$		0			0
$525$	−4.97223	+	12.2587i	−0.217006	+	0.535016i
$526$		0			0
$527$	−11.4923	−	42.8899i	−0.500613	−	1.86831i
$528$		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
$535$	−10.2255	+	38.3448i	−0.442086	+	1.65779i
$536$		0			0
$537$	−17.5966	+	4.71501i	−0.759351	+	0.203468i
$538$		0			0
$539$	−25.4103	+	25.9222i	−1.09450	+	1.11655i
$540$		0			0
$541$	12.5563	−	21.7482i	0.539838	−	0.935026i	−0.459075	−	0.888398i	$-0.651819\pi$
$541$	12.5563	−	21.7482i	0.539838	−	0.935026i	0.998912	−	0.0466286i	$-0.0148477\pi$
$542$		0			0
$543$	3.42220	−	12.7718i	0.146861	−	0.548092i
$544$		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
$553$	−17.5666	−	41.8187i	−0.747009	−	1.77831i
$554$		0			0
$555$	7.56154	−	13.1331i	0.320969	−	0.557468i
$556$		0			0
$557$	8.41446	+	2.25465i	0.356532	+	0.0955325i	0.432639	−	0.901567i	$-0.357582\pi$
$557$	8.41446	+	2.25465i	0.356532	+	0.0955325i	−0.0761070	+	0.997100i	$0.524249\pi$
$558$		0			0
$559$	−6.68329			−0.282673
$560$		0			0
$561$	22.0591			0.931337
$562$		0			0
$563$	43.3368	+	11.6121i	1.82643	+	0.489390i	0.997545	−	0.0700327i	$-0.0223104\pi$
$563$	43.3368	+	11.6121i	1.82643	+	0.489390i	0.828883	+	0.559422i	$0.188977\pi$
$564$		0			0
$565$	10.2983	+	38.2514i	0.433253	+	1.60925i
$566$		0			0
$567$	−0.332258	+	2.62481i	−0.0139535	+	0.110231i
$568$		0			0
$569$	27.3249	+	15.7761i	1.14552	+	0.661367i	0.947792	−	0.318890i	$-0.103310\pi$
$569$	27.3249	+	15.7761i	1.14552	+	0.661367i	0.197730	+	0.980257i	$0.436643\pi$
$570$		0			0
$571$	−15.5660	−	26.9610i	−0.651415	−	1.12828i	−0.982780	−	0.184781i	$-0.940842\pi$
$571$	−15.5660	−	26.9610i	−0.651415	−	1.12828i	0.331365	−	0.943503i	$-0.392491\pi$
$572$		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
$577$	9.60444	−	35.8443i	0.399838	−	1.49222i	−0.413543	−	0.910485i	$-0.635709\pi$
$577$	9.60444	−	35.8443i	0.399838	−	1.49222i	0.813381	−	0.581731i	$-0.197624\pi$
$578$		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
$583$	19.4386	−	5.20856i	0.805065	−	0.215717i
$584$		0			0
$585$	1.20211	+	0.320571i	0.0497013	+	0.0132540i
$586$		0			0
$587$	−0.794072	−	0.794072i	−0.0327749	−	0.0327749i	0.690529	−	0.723304i	$-0.257378\pi$
$587$	−0.794072	−	0.794072i	−0.0327749	−	0.0327749i	−0.723304	+	0.690529i	$0.757378\pi$
$588$		0			0
$589$			48.5287i			1.99959i
$590$		0			0
$591$	−6.75901	+	3.90231i	−0.278028	+	0.160520i
$592$		0			0
$593$	−5.73471	−	21.4022i	−0.235496	−	0.878884i	−0.977925	−	0.208958i	$-0.932993\pi$
$593$	−5.73471	−	21.4022i	−0.235496	−	0.878884i	0.742428	−	0.669926i	$-0.233674\pi$
$594$		0			0
$595$	−24.9303	+	3.43894i	−1.02204	+	0.140983i
$596$		0			0
$597$	2.13674	+	7.97441i	0.0874508	+	0.326371i
$598$		0			0
$599$	39.6891	−	22.9145i	1.62165	−	0.936261i	0.635173	−	0.772370i	$-0.280929\pi$
$599$	39.6891	−	22.9145i	1.62165	−	0.936261i	0.986479	−	0.163891i	$-0.0524044\pi$
$600$		0			0
$601$			0.0299652i			0.00122231i	1.00000		0.000611153i	$0.000194536\pi$
$601$			0.0299652i			0.00122231i	−1.00000		0.000611153i	$0.999805\pi$
$602$		0			0
$603$	6.18104	+	6.18104i	0.251712	+	0.251712i
$604$		0			0
$605$	30.7511	−	17.8030i	1.25021	−	0.723796i
$606$		0			0
$607$	−12.1749	+	3.26225i	−0.494163	+	0.132410i	−0.497290	−	0.867585i	$-0.665671\pi$
$607$	−12.1749	+	3.26225i	−0.494163	+	0.132410i	0.00312691	+	0.999995i	$0.499005\pi$
$608$		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
$613$	−5.42761	+	20.2561i	−0.219219	+	0.818137i	0.765420	+	0.643532i	$0.222532\pi$
$613$	−5.42761	+	20.2561i	−0.219219	+	0.818137i	−0.984639	+	0.174605i	$0.944135\pi$
$614$		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	−0.997958	−	0.0638784i	$-0.979653\pi$
$619$	−13.7908	−	23.8864i	−0.554299	−	0.960074i	0.443659	−	0.896196i	$-0.353680\pi$
$620$		0			0
$621$	−3.27668	−	1.89179i	−0.131489	−	0.0759150i
$622$		0			0
$623$	−7.02932	+	2.95278i	−0.281624	+	0.118301i
$624$		0			0
$625$	−12.3967	+	21.7100i	−0.495866	+	0.868399i
$626$		0			0
$627$	−23.2873	−	6.23982i	−0.930006	−	0.249194i
$628$		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
$633$	−14.6337	−	3.92108i	−0.581636	−	0.155849i
$634$		0			0
$635$	−18.3826	+	4.94909i	−0.729492	+	0.196399i
$636$		0			0
$637$	−3.39218	−	1.91363i	−0.134403	−	0.0758209i
$638$		0			0
$639$	−12.9407	−	7.47134i	−0.511928	−	0.295562i
$640$		0			0
$641$	−9.64037	−	16.6976i	−0.380772	−	0.659516i	0.610401	−	0.792093i	$-0.291008\pi$
$641$	−9.64037	−	16.6976i	−0.380772	−	0.659516i	−0.991173	+	0.132577i	$0.957675\pi$
$642$		0			0
$643$	12.7834	−	12.7834i	0.504128	−	0.504128i	−0.408590	−	0.912718i	$-0.633979\pi$
$643$	12.7834	−	12.7834i	0.504128	−	0.504128i	0.912718	+	0.408590i	$0.133979\pi$
$644$		0			0
$645$	−0.0320070	−	26.8594i	−0.00126028	−	1.05759i
$646$		0			0
$647$	8.38484	−	31.2927i	0.329642	−	1.23024i	−0.579920	−	0.814673i	$-0.696916\pi$
$647$	8.38484	−	31.2927i	0.329642	−	1.23024i	0.909562	−	0.415568i	$-0.136417\pi$
$648$		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
$653$	−13.3047	+	3.56499i	−0.520653	+	0.139509i	−0.509569	−	0.860430i	$-0.670195\pi$
$653$	−13.3047	+	3.56499i	−0.520653	+	0.139509i	−0.0110846	+	0.999939i	$0.503528\pi$
$654$		0			0
$655$	−13.6623	−	23.5988i	−0.533831	−	0.922083i
$656$		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	−0.572620	+	0.819821i	$0.694073\pi$
$661$	−40.3367	+	23.2884i	−1.56892	+	0.905814i	−0.996296	+	0.0859933i	$0.972594\pi$
$662$		0			0
$663$	0.612579	+	2.28617i	0.0237906	+	0.0887877i
$664$		0			0
$665$	27.2912	+	3.42158i	1.05831	+	0.132683i
$666$		0			0
$667$	1.11788	+	4.17198i	0.0432844	+	0.161540i
$668$		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
$675$	−1.28258	+	4.83270i	−0.0493666	+	0.186011i
$676$		0			0
$677$	−32.1586	+	8.61686i	−1.23595	+	0.331173i	−0.816895	−	0.576786i	$-0.804307\pi$
$677$	−32.1586	+	8.61686i	−1.23595	+	0.331173i	−0.419059	+	0.907959i	$0.637640\pi$
$678$		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
$683$	−7.99086	+	29.8223i	−0.305762	+	1.14112i	0.626526	+	0.779401i	$0.284476\pi$
$683$	−7.99086	+	29.8223i	−0.305762	+	1.14112i	−0.932288	+	0.361718i	$0.882190\pi$
$684$		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	0.466382	−	0.884583i	$-0.345557\pi$
$691$	−1.74803	−	1.00923i	−0.0664984	−	0.0383929i	−0.532881	+	0.846190i	$0.678890\pi$
$692$		0			0
$693$	−8.29776	+	10.9262i	−0.315206	+	0.415053i
$694$		0			0
$695$	9.60490	+	5.53014i	0.364335	+	0.209770i
$696$		0			0
$697$	15.9984	+	4.28675i	0.605981	+	0.162372i
$698$		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
$703$	−30.4349	−	8.15499i	−1.14787	−	0.307571i
$704$		0			0
$705$	−17.7953	−	10.2459i	−0.670211	−	0.385883i
$706$		0			0
$707$	7.86025	+	0.994980i	0.295615	+	0.0374201i
$708$		0			0
$709$	4.41817	+	2.55083i	0.165928	+	0.0957985i	0.580664	−	0.814143i	$-0.302793\pi$
$709$	4.41817	+	2.55083i	0.165928	+	0.0957985i	−0.414736	+	0.909942i	$0.636126\pi$
$710$		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
$717$	1.41705	−	5.28849i	0.0529206	−	0.197502i
$718$		0			0
$719$	−13.6654	+	23.6692i	−0.509633	+	0.882710i	0.490305	+	0.871551i	$0.336886\pi$
$719$	−13.6654	+	23.6692i	−0.509633	+	0.882710i	−0.999938	+	0.0111593i	$0.996448\pi$
$720$		0			0
$721$	9.44841	−	23.1361i	0.351877	−	0.861632i
$722$		0			0
$723$	6.64232	−	1.77980i	0.247030	−	0.0661916i
$724$		0			0
$725$	4.93624	−	2.86565i	0.183327	−	0.106427i
$726$		0			0
$727$	−20.4882	−	20.4882i	−0.759865	−	0.759865i	0.216433	−	0.976298i	$-0.430558\pi$
$727$	−20.4882	−	20.4882i	−0.759865	−	0.759865i	−0.976298	+	0.216433i	$0.930558\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$		0			0
$731$	44.2517	−	25.5487i	1.63671	−	0.944953i
$732$		0			0
$733$	−0.267095	−	0.996813i	−0.00986538	−	0.0368181i	0.960818	−	0.277181i	$-0.0894002\pi$
$733$	−0.267095	−	0.996813i	−0.00986538	−	0.0368181i	−0.970683	+	0.240363i	$0.922734\pi$
$734$		0			0
$735$	7.67444	−	13.6420i	0.283076	−	0.503191i
$736$		0			0
$737$	11.7321	+	43.7846i	0.432156	+	1.61283i
$738$		0			0
$739$	39.9751	−	23.0797i	1.47051	−	0.848999i	0.471057	−	0.882103i	$-0.343873\pi$
$739$	39.9751	−	23.0797i	1.47051	−	0.848999i	0.999452	+	0.0331038i	$0.0105392\pi$
$740$		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
$745$	0.271868	+	0.469596i	0.00996047	+	0.0172047i
$746$		0			0
$747$	−0.636508	+	0.170552i	−0.0232886	+	0.00624016i
$748$		0			0
$749$	17.7526	−	43.4704i	0.648668	−	1.58837i
$750$		0			0
$751$	−22.2521	+	38.5417i	−0.811990	+	1.40641i	0.0994790	+	0.995040i	$0.468282\pi$
$751$	−22.2521	+	38.5417i	−0.811990	+	1.40641i	−0.911469	+	0.411368i	$0.865051\pi$
$752$		0			0
$753$	0.464703	−	1.73429i	0.0169347	−	0.0632012i
$754$		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	−0.283846	−	0.958870i	$-0.591610\pi$
$761$	−34.6531	−	20.0070i	−1.25617	−	0.725253i	−0.972329	+	0.233617i	$0.924944\pi$
$762$		0			0
$763$	−5.61462	−	0.710719i	−0.203263	−	0.0257298i
$764$		0			0
$765$	−9.18495	+	2.47284i	−0.332083	+	0.0894056i
$766$		0			0
$767$	1.77104	+	0.474548i	0.0639484	+	0.0171349i
$768$		0			0
$769$	36.9229			1.33147			0.665737	−	0.746187i	$-0.268117\pi$
$769$	36.9229			1.33147			0.665737	+	0.746187i	$0.268117\pi$
$770$		0			0
$771$	−18.3021			−0.659133
$772$		0			0
$773$	2.97774	+	0.797882i	0.107102	+	0.0286978i	0.311972	−	0.950091i	$-0.399011\pi$
$773$	2.97774	+	0.797882i	0.107102	+	0.0286978i	−0.204870	+	0.978789i	$0.565677\pi$
$774$		0			0
$775$	45.2606	+	25.9876i	1.62581	+	0.933502i
$776$		0			0
$777$	−10.8446	+	14.2798i	−0.389047	+	0.512284i
$778$		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
$787$	−8.36596	+	31.2222i	−0.298214	+	1.11295i	0.640416	+	0.768028i	$0.278762\pi$
$787$	−8.36596	+	31.2222i	−0.298214	+	1.11295i	−0.938631	+	0.344923i	$0.887905\pi$
$788$		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
$793$	−1.99372	+	0.534216i	−0.0707992	+	0.0189706i
$794$		0			0
$795$	−7.50994	+	4.34781i	−0.266350	+	0.154201i
$796$		0			0
$797$	−28.9968	−	28.9968i	−1.02712	−	1.02712i	−0.999622	−	0.0274969i	$-0.991246\pi$
$797$	−28.9968	−	28.9968i	−1.02712	−	1.02712i	−0.0274969	−	0.999622i	$-0.508754\pi$
$798$		0			0
$799$		−	39.0643i		−	1.38199i
$800$		0			0
$801$	−2.49564	+	1.44086i	−0.0881793	+	0.0509103i
$802$		0			0
$803$	−14.7678	−	55.1140i	−0.521143	−	1.94493i
$804$		0			0
$805$	13.7359	+	17.6739i	0.484128	+	0.622923i
$806$		0			0
$807$	−6.62061	−	24.7085i	−0.233057	−	0.869779i
$808$		0			0
$809$	12.2910	−	7.09622i	0.432129	−	0.249490i	−0.268124	−	0.963384i	$-0.586404\pi$
$809$	12.2910	−	7.09622i	0.432129	−	0.249490i	0.700253	+	0.713894i	$0.253070\pi$
$810$		0			0
$811$		−	33.7867i		−	1.18641i	−0.805051	−	0.593206i	$-0.797862\pi$
$811$		−	33.7867i		−	1.18641i	0.805051	−	0.593206i	$-0.202138\pi$
$812$		0			0
$813$	−6.18222	−	6.18222i	−0.216820	−	0.216820i
$814$		0			0
$815$	−28.3843	−	7.56930i	−0.994257	−	0.265141i
$816$		0			0
$817$	−53.9424	+	14.4538i	−1.88720	+	0.505675i
$818$		0			0
$819$	−1.36280	−	0.556548i	−0.0476202	−	0.0194474i
$820$		0			0
$821$	−22.8091	+	39.5065i	−0.796043	+	1.37879i	0.126132	+	0.992013i	$0.459744\pi$
$821$	−22.8091	+	39.5065i	−0.796043	+	1.37879i	−0.922175	+	0.386773i	$0.873590\pi$
$822$		0			0
$823$	−9.73381	+	36.3271i	−0.339299	+	1.26628i	0.559833	+	0.828606i	$0.310865\pi$
$823$	−9.73381	+	36.3271i	−0.339299	+	1.26628i	−0.899132	+	0.437677i	$0.855801\pi$
$824$		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	$-0.0166539\pi$
$829$	13.0725	+	22.6422i	0.454026	+	0.786397i	−0.544605	+	0.838692i	$0.683321\pi$
$830$		0			0
$831$	−4.67322	−	2.69809i	−0.162112	−	0.0935956i
$832$		0			0
$833$	29.7758	−	0.296912i	1.03167	−	0.0102874i
$834$		0			0
$835$	1.70488	+	6.33252i	0.0590000	+	0.219146i
$836$		0			0
$837$	10.0825	+	2.70159i	0.348502	+	0.0933807i
$838$		0			0
$839$	45.3900			1.56704			0.783518	−	0.621369i	$-0.213423\pi$
$839$	45.3900			1.56704			0.783518	+	0.621369i	$0.213423\pi$
$840$		0			0
$841$	27.6969			0.955064
$842$		0			0
$843$	0.483550	+	0.129567i	0.0166543	+	0.00446251i
$844$		0			0
$845$	14.1590	−	24.5918i	0.487086	−	0.845984i
$846$		0			0
$847$	−38.7619	+	16.2826i	−1.33187	+	0.559476i
$848$		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	−0.441676	−	0.897175i	$-0.645616\pi$
$853$	13.3034	−	13.3034i	0.455499	−	0.455499i	0.897175	+	0.441676i	$0.145616\pi$
$854$		0			0
$855$	10.3958	−	0.0123882i	0.355530	−	0.000423667i
$856$		0			0
$857$	−12.9662	+	48.3905i	−0.442917	+	1.65299i	0.278463	+	0.960447i	$0.410175\pi$
$857$	−12.9662	+	48.3905i	−0.442917	+	1.65299i	−0.721379	+	0.692540i	$0.756492\pi$
$858$		0			0
$859$	−7.52733	+	13.0377i	−0.256829	+	0.444841i	−0.965391	−	0.260808i	$-0.916011\pi$
$859$	−7.52733	+	13.0377i	−0.256829	+	0.444841i	0.708561	+	0.705649i	$0.249344\pi$
$860$		0			0
$861$	−8.14123	+	6.31172i	−0.277452	+	0.215103i
$862$		0			0
$863$	37.6350	−	10.0843i	1.28111	−	0.343272i	0.446833	−	0.894618i	$-0.352552\pi$
$863$	37.6350	−	10.0843i	1.28111	−	0.343272i	0.834277	+	0.551345i	$0.185885\pi$
$864$		0			0
$865$	−6.27536	+	23.5321i	−0.213369	+	0.800115i
$866$		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
$873$	−1.31073	−	4.89170i	−0.0443614	−	0.165559i
$874$		0			0
$875$	17.8059	−	23.6210i	0.601948	−	0.798536i
$876$		0			0
$877$	−5.15707	−	19.2465i	−0.174142	−	0.649907i	−0.996696	−	0.0812200i	$-0.974118\pi$
$877$	−5.15707	−	19.2465i	−0.174142	−	0.649907i	0.822554	−	0.568687i	$-0.192548\pi$
$878$		0			0
$879$	9.11622	−	5.26325i	0.307482	−	0.177525i
$880$		0			0
$881$			44.5448i			1.50075i	0.661011	+	0.750376i	$0.270128\pi$
$881$			44.5448i			1.50075i	−0.661011	+	0.750376i	$0.729872\pi$
$882$		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
$885$	−1.89867	+	7.11988i	−0.0638232	+	0.239332i
$886$		0			0
$887$	−40.0248	+	10.7246i	−1.34390	+	0.360097i	−0.857880	−	0.513850i	$-0.828219\pi$
$887$	−40.0248	+	10.7246i	−1.34390	+	0.360097i	−0.486021	+	0.873947i	$0.661552\pi$
$888$		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
$893$	−11.0500	+	41.2392i	−0.369775	+	1.38002i
$894$		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
$903$	−3.99105	+	31.5289i	−0.132814	+	1.04922i
$904$		0			0
$905$	−14.7526	+	25.6226i	−0.490391	+	0.851725i
$906$		0			0
$907$	11.0421	+	2.95871i	0.366646	+	0.0982424i	0.437438	−	0.899249i	$-0.355886\pi$
$907$	11.0421	+	2.95871i	0.366646	+	0.0982424i	−0.0707922	+	0.997491i	$0.522553\pi$
$908$		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
$913$	−3.30069	−	0.884418i	−0.109237	−	0.0292700i
$914$		0			0
$915$	−2.15651	−	8.01000i	−0.0712919	−	0.264802i
$916$		0			0
$917$	12.4955	+	29.7465i	0.412638	+	0.982315i
$918$		0			0
$919$	−21.5990	−	12.4702i	−0.712485	−	0.411353i	0.0994956	−	0.995038i	$-0.468277\pi$
$919$	−21.5990	−	12.4702i	−0.712485	−	0.411353i	−0.811980	+	0.583685i	$0.801610\pi$
$920$		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
$927$	2.44473	−	9.12385i	0.0802954	−	0.299667i
$928$		0			0
$929$	−15.5688	+	26.9659i	−0.510796	+	0.884724i	0.489126	+	0.872213i	$0.337316\pi$
$929$	−15.5688	+	26.9659i	−0.510796	+	0.884724i	−0.999922	+	0.0125108i	$0.996018\pi$
$930$		0			0
$931$	−31.5176	−	8.10918i	−1.03295	−	0.265768i
$932$		0			0
$933$	11.0428	−	2.95890i	0.361524	−	0.0968701i
$934$		0			0
$935$	−47.6602	−	12.7097i	−1.55865	−	0.415650i
$936$		0			0
$937$	34.9737	+	34.9737i	1.14254	+	1.14254i	0.987984	+	0.154558i	$0.0493955\pi$
$937$	34.9737	+	34.9737i	1.14254	+	1.14254i	0.154558	+	0.987984i	$0.450605\pi$
$938$		0			0
$939$		−	15.2373i		−	0.497249i
$940$		0			0
$941$	4.51417	−	2.60626i	0.147158	−	0.0849615i	−0.424613	−	0.905375i	$-0.639590\pi$
$941$	4.51417	−	2.60626i	0.147158	−	0.0849615i	0.571771	+	0.820413i	$0.306257\pi$
$942$		0			0
$943$	−3.81280	−	14.2296i	−0.124162	−	0.463378i
$944$		0			0
$945$	2.23018	−	5.47963i	0.0725477	−	0.178252i
$946$		0			0
$947$	−7.24905	−	27.0538i	−0.235562	−	0.879131i	−0.977895	−	0.209099i	$-0.932947\pi$
$947$	−7.24905	−	27.0538i	−0.235562	−	0.879131i	0.742332	−	0.670032i	$-0.233720\pi$
$948$		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
$955$	5.43400	−	3.14596i	0.175840	−	0.101801i
$956$		0			0
$957$	5.71794	−	1.53212i	0.184835	−	0.0495264i
$958$		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
$963$	4.59341	−	17.1428i	0.148021	−	0.552420i
$964$		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	−0.0444174	−	0.999013i	$-0.514143\pi$
$971$	−29.0356	−	16.7637i	−0.931797	−	0.537973i	−0.887379	+	0.461040i	$0.847476\pi$
$972$		0			0
$973$	−10.4435	−	7.93119i	−0.334804	−	0.254262i
$974$		0			0
$975$	−2.41254	−	1.38523i	−0.0772632	−	0.0443628i
$976$		0			0
$977$	−11.5077	−	3.08347i	−0.368163	−	0.0986489i	0.0699943	−	0.997547i	$-0.477702\pi$
$977$	−11.5077	−	3.08347i	−0.368163	−	0.0986489i	−0.438157	+	0.898899i	$0.644369\pi$
$978$		0			0
$979$	−14.9435			−0.477597
$980$		0			0
$981$	−2.13906			−0.0682950
$982$		0			0
$983$	−18.6418	−	4.99506i	−0.594582	−	0.159318i	−0.0510354	−	0.998697i	$-0.516252\pi$
$983$	−18.6418	−	4.99506i	−0.594582	−	0.159318i	−0.543546	+	0.839379i	$0.682919\pi$
$984$		0			0
$985$	16.8516	−	4.53691i	0.536938	−	0.144558i
$986$		0			0
$987$	19.3491	+	14.6944i	0.615889	+	0.467728i
$988$		0			0
$989$	−39.3592	−	22.7240i	−1.25155	−	0.722582i
$990$		0			0
$991$	3.68266	+	6.37856i	0.116984	+	0.202622i	0.918571	−	0.395256i	$-0.129344\pi$
$991$	3.68266	+	6.37856i	0.116984	+	0.202622i	−0.801587	+	0.597878i	$0.796011\pi$
$992$		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
$997$	2.28479	−	8.52696i	0.0723601	−	0.270051i	−0.920262	−	0.391303i	$-0.872024\pi$
$997$	2.28479	−	8.52696i	0.0723601	−	0.270051i	0.992622	+	0.121252i	$0.0386909\pi$
$998$		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.b.313.8	yes	48
5.2	odd	4		840.2.dd.a.817.7	yes	48
7.3	odd	6		840.2.dd.a.73.7	✓	48
35.17	even	12	inner	840.2.dd.b.577.8	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.dd.a.73.7	✓	48	7.3	odd	6
840.2.dd.a.817.7	yes	48	5.2	odd	4
840.2.dd.b.313.8	yes	48	1.1	even	1	trivial
840.2.dd.b.577.8	yes	48	35.17	even	12	inner

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)

\(f(q)\)	\(=\)	\(q+(0.965926 + 0.258819i) q^{3} +(-1.93782 - 1.11573i) q^{5} +(2.10702 + 1.60015i) q^{7} +(0.866025 + 0.500000i) q^{9} +(2.59281 + 4.49089i) q^{11} +(-0.393426 + 0.393426i) q^{13} +(-1.58302 - 1.57925i) q^{15} +(1.10099 - 4.10895i) q^{17} +(-2.32458 + 4.02629i) q^{19} +(1.62108 + 2.09096i) q^{21} +(-3.65466 + 0.979264i) q^{23} +(2.51031 + 4.32416i) q^{25} +(0.707107 + 0.707107i) q^{27} -1.14155i q^{29} +(9.03971 - 5.21908i) q^{31} +(1.34214 + 5.00893i) q^{33} +(-2.29771 - 5.45166i) q^{35} +(1.75408 + 6.54631i) q^{37} +(-0.481847 + 0.278194i) q^{39} +3.89354i q^{41} +(8.49370 + 8.49370i) q^{43} +(-1.12034 - 1.93516i) q^{45} +(8.87026 - 2.37678i) q^{47} +(1.87906 + 6.74308i) q^{49} +(2.12695 - 3.68398i) q^{51} +(1.00442 - 3.74856i) q^{53} +(-0.0138177 - 11.5954i) q^{55} +(-3.28745 + 3.28745i) q^{57} +(-1.64769 - 2.85388i) q^{59} +(3.21272 + 1.85487i) q^{61} +(1.02466 + 2.43928i) q^{63} +(1.20135 - 0.323435i) q^{65} +(8.44346 + 2.26242i) q^{67} -3.78358 q^{69} -14.9427 q^{71} +(-10.6282 - 2.84783i) q^{73} +(1.30560 + 4.82653i) q^{75} +(-1.72296 + 13.6113i) q^{77} +(-14.8470 - 8.57194i) q^{79} +(0.500000 + 0.866025i) q^{81} +(-0.465956 + 0.465956i) q^{83} +(-6.71798 + 6.73401i) q^{85} +(0.295455 - 1.10265i) q^{87} +(-1.44086 + 2.49564i) q^{89} +(-1.45850 + 0.199417i) q^{91} +(10.0825 - 2.70159i) q^{93} +(8.99686 - 5.20864i) q^{95} +(-3.58097 - 3.58097i) q^{97} +5.18563i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 4 q^{7} - 4 q^{11} - 16 q^{13} - 4 q^{15} + 4 q^{17} - 8 q^{19} + 48 q^{23} - 20 q^{25} + 24 q^{33} - 4 q^{37} + 12 q^{39} + 16 q^{43} + 4 q^{45} - 12 q^{47} + 12 q^{49} - 52 q^{53} + 56 q^{55} + 8 q^{57}+ \cdots - 44 q^{97}+O(q^{100}) \) 48 * q + 4 * q^7 - 4 * q^11 - 16 * q^13 - 4 * q^15 + 4 * q^17 - 8 * q^19 + 48 * q^23 - 20 * q^25 + 24 * q^33 - 4 * q^37 + 12 * q^39 + 16 * q^43 + 4 * q^45 - 12 * q^47 + 12 * q^49 - 52 * q^53 + 56 * q^55 + 8 * q^57 - 8 * q^59 + 12 * q^65 + 68 * q^67 + 8 * q^69 + 16 * q^71 + 52 * q^73 + 24 * q^75 + 16 * q^77 - 108 * q^79 + 24 * q^81 - 64 * q^83 + 32 * q^85 - 8 * q^87 - 64 * q^89 + 48 * q^91 + 48 * q^93 - 84 * q^95 - 44 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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