LMFDB - Embedded newform 840.2.cp.b.521.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [840,2,Mod(521,840)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(840, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 3, 0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("840.521"); 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.cp (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,0,0,0,16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$6.70743376979$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			521.14
Character	$\chi$	$=$	840.521
Dual form			840.2.cp.b.761.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.56554 + 0.741007i) q^{3} +(0.500000 + 0.866025i) q^{5} +(2.50460 + 0.852628i) q^{7} +(1.90182 + 2.32015i) q^{9} +(-0.731508 - 0.422337i) q^{11} +0.804561i q^{13} +(0.141038 + 1.72630i) q^{15} +(0.395740 - 0.685442i) q^{17} +(1.25255 - 0.723159i) q^{19} +(3.28925 + 3.19075i) q^{21} +(-2.47256 + 1.42754i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(1.25812 + 5.04154i) q^{27} -3.55504i q^{29} +(-1.45279 - 0.838768i) q^{31} +(-0.832250 - 1.20324i) q^{33} +(0.513903 + 2.59536i) q^{35} +(-1.16085 - 2.01066i) q^{37} +(-0.596185 + 1.25957i) q^{39} -6.25730 q^{41} +5.35419 q^{43} +(-1.05840 + 2.80710i) q^{45} +(3.11317 + 5.39217i) q^{47} +(5.54605 + 4.27098i) q^{49} +(1.12746 - 0.779839i) q^{51} +(-3.57859 - 2.06610i) q^{53} -0.844673i q^{55} +(2.49678 - 0.203986i) q^{57} +(6.26531 - 10.8518i) q^{59} +(2.39276 - 1.38146i) q^{61} +(2.78507 + 7.43259i) q^{63} +(-0.696770 + 0.402280i) q^{65} +(-3.41081 + 5.90770i) q^{67} +(-4.92870 + 0.402675i) q^{69} +13.0053i q^{71} +(-6.52756 - 3.76869i) q^{73} +(-1.42450 + 0.985292i) q^{75} +(-1.47204 - 1.68149i) q^{77} +(-4.91157 - 8.50709i) q^{79} +(-1.76617 + 8.82500i) q^{81} +15.1845 q^{83} +0.791480 q^{85} +(2.63431 - 5.56555i) q^{87} +(-7.43687 - 12.8810i) q^{89} +(-0.685991 + 2.01510i) q^{91} +(-1.65286 - 2.38965i) q^{93} +(1.25255 + 0.723159i) q^{95} -13.9030i q^{97} +(-0.411313 - 2.50042i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{5} - 2 q^{7} + 8 q^{9} + 6 q^{19} - 14 q^{21} + 24 q^{23} - 16 q^{25} + 24 q^{27} + 42 q^{31} + 18 q^{33} + 2 q^{35} + 6 q^{37} + 12 q^{39} + 44 q^{41} - 20 q^{43} + 10 q^{45} + 4 q^{47} + 16 q^{49}+ \cdots - 8 q^{99}+O(q^{100}) $ 32 * q + 16 * q^5 - 2 * q^7 + 8 * q^9 + 6 * q^19 - 14 * q^21 + 24 * q^23 - 16 * q^25 + 24 * q^27 + 42 * q^31 + 18 * q^33 + 2 * q^35 + 6 * q^37 + 12 * q^39 + 44 * q^41 - 20 * q^43 + 10 * q^45 + 4 * q^47 + 16 * q^49 - 36 * q^51 + 12 * q^59 - 18 * q^61 + 34 * q^63 - 6 * q^65 - 6 * q^67 - 34 * q^69 - 6 * q^73 + 40 * q^77 - 2 * q^79 - 12 * q^81 - 88 * q^83 - 72 * q^87 - 6 * q^89 - 26 * q^91 + 50 * q^93 + 6 * q^95 - 8 * q^99

Character values

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

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

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
$3$	1.56554	+	0.741007i	0.903864	+	0.427820i
$3$	1.56554	+	0.741007i	0.903864	+	0.427820i
$4$		0			0
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$		0			0
$7$	2.50460	+	0.852628i	0.946650	+	0.322263i
$7$	2.50460	+	0.852628i	0.946650	+	0.322263i
$8$		0			0
$9$	1.90182	+	2.32015i	0.633939	+	0.773383i
$10$		0			0
$11$	−0.731508	−	0.422337i	−0.220558	−	0.127339i	0.385651	−	0.922645i	$-0.373977\pi$
$11$	−0.731508	−	0.422337i	−0.220558	−	0.127339i	−0.606209	+	0.795306i	$0.707310\pi$
$12$		0			0
$13$			0.804561i			0.223145i	0.993756	+	0.111573i	$0.0355887\pi$
$13$			0.804561i			0.223145i	−0.993756	+	0.111573i	$0.964411\pi$
$14$		0			0
$15$	0.141038	+	1.72630i	0.0364160	+	0.445728i
$16$		0			0
$17$	0.395740	−	0.685442i	0.0959810	−	0.166244i	−0.814037	−	0.580814i	$-0.802735\pi$
$17$	0.395740	−	0.685442i	0.0959810	−	0.166244i	0.910018	+	0.414570i	$0.136068\pi$
$18$		0			0
$19$	1.25255	−	0.723159i	0.287354	−	0.165904i	−0.349394	−	0.936976i	$-0.613612\pi$
$19$	1.25255	−	0.723159i	0.287354	−	0.165904i	0.636748	+	0.771072i	$0.280279\pi$
$20$		0			0
$21$	3.28925	+	3.19075i	0.717772	+	0.696278i
$22$		0			0
$23$	−2.47256	+	1.42754i	−0.515565	+	0.297662i	−0.735118	−	0.677939i	$-0.762873\pi$
$23$	−2.47256	+	1.42754i	−0.515565	+	0.297662i	0.219553	+	0.975601i	$0.429540\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$	1.25812	+	5.04154i	0.242126	+	0.970245i
$28$		0			0
$29$		−	3.55504i		−	0.660154i	−0.943954	−	0.330077i	$-0.892925\pi$
$29$		−	3.55504i		−	0.660154i	0.943954	−	0.330077i	$-0.107075\pi$
$30$		0			0
$31$	−1.45279	−	0.838768i	−0.260929	−	0.150647i	0.363830	−	0.931466i	$-0.381469\pi$
$31$	−1.45279	−	0.838768i	−0.260929	−	0.150647i	−0.624758	+	0.780818i	$0.714802\pi$
$32$		0			0
$33$	−0.832250	−	1.20324i	−0.144876	−	0.209457i
$34$		0			0
$35$	0.513903	+	2.59536i	0.0868655	+	0.438696i
$36$		0			0
$37$	−1.16085	−	2.01066i	−0.190843	−	0.330550i	0.754687	−	0.656085i	$-0.227789\pi$
$37$	−1.16085	−	2.01066i	−0.190843	−	0.330550i	−0.945530	+	0.325535i	$0.894455\pi$
$38$		0			0
$39$	−0.596185	+	1.25957i	−0.0954660	+	0.201693i
$40$		0			0
$41$	−6.25730			−0.977226			−0.488613	−	0.872501i	$-0.662497\pi$
$41$	−6.25730			−0.977226			−0.488613	+	0.872501i	$0.662497\pi$
$42$		0			0
$43$	5.35419			0.816506			0.408253	−	0.912869i	$-0.366138\pi$
$43$	5.35419			0.816506			0.408253	+	0.912869i	$0.366138\pi$
$44$		0			0
$45$	−1.05840	+	2.80710i	−0.157777	+	0.418457i
$46$		0			0
$47$	3.11317	+	5.39217i	0.454102	+	0.786528i	0.998636	−	0.0522107i	$-0.0166267\pi$
$47$	3.11317	+	5.39217i	0.454102	+	0.786528i	−0.544534	+	0.838739i	$0.683293\pi$
$48$		0			0
$49$	5.54605	+	4.27098i	0.792293	+	0.610141i
$50$		0			0
$51$	1.12746	−	0.779839i	0.157876	−	0.109199i
$52$		0			0
$53$	−3.57859	−	2.06610i	−0.491557	−	0.283801i	0.233663	−	0.972318i	$-0.424929\pi$
$53$	−3.57859	−	2.06610i	−0.491557	−	0.283801i	−0.725220	+	0.688517i	$0.758262\pi$
$54$		0			0
$55$		−	0.844673i		−	0.113896i
$56$		0			0
$57$	2.49678	−	0.203986i	0.330706	−	0.0270187i
$58$		0			0
$59$	6.26531	−	10.8518i	0.815674	−	1.41279i	−0.0931697	−	0.995650i	$-0.529700\pi$
$59$	6.26531	−	10.8518i	0.815674	−	1.41279i	0.908843	−	0.417138i	$-0.136967\pi$
$60$		0			0
$61$	2.39276	−	1.38146i	0.306362	−	0.176878i	−0.338936	−	0.940810i	$-0.610067\pi$
$61$	2.39276	−	1.38146i	0.306362	−	0.176878i	0.645297	+	0.763932i	$0.276734\pi$
$62$		0			0
$63$	2.78507	+	7.43259i	0.350886	+	0.936418i
$64$		0			0
$65$	−0.696770	+	0.402280i	−0.0864237	+	0.0498967i
$66$		0			0
$67$	−3.41081	+	5.90770i	−0.416697	+	0.721741i	−0.995605	−	0.0936522i	$-0.970146\pi$
$67$	−3.41081	+	5.90770i	−0.416697	+	0.721741i	0.578908	+	0.815393i	$0.303479\pi$
$68$		0			0
$69$	−4.92870	+	0.402675i	−0.593346	+	0.0484763i
$70$		0			0
$71$			13.0053i			1.54345i	0.635958	+	0.771724i	$0.280605\pi$
$71$			13.0053i			1.54345i	−0.635958	+	0.771724i	$0.719395\pi$
$72$		0			0
$73$	−6.52756	−	3.76869i	−0.763993	−	0.441091i	0.0667347	−	0.997771i	$-0.478742\pi$
$73$	−6.52756	−	3.76869i	−0.763993	−	0.441091i	−0.830727	+	0.556679i	$0.812075\pi$
$74$		0			0
$75$	−1.42450	+	0.985292i	−0.164487	+	0.113772i
$76$		0			0
$77$	−1.47204	−	1.68149i	−0.167755	−	0.191623i
$78$		0			0
$79$	−4.91157	−	8.50709i	−0.552595	−	0.957122i	−0.998086	−	0.0618363i	$-0.980304\pi$
$79$	−4.91157	−	8.50709i	−0.552595	−	0.957122i	0.445491	−	0.895286i	$-0.353029\pi$
$80$		0			0
$81$	−1.76617	+	8.82500i	−0.196241	+	0.980556i
$82$		0			0
$83$	15.1845			1.66672			0.833358	−	0.552733i	$-0.186415\pi$
$83$	15.1845			1.66672			0.833358	+	0.552733i	$0.186415\pi$
$84$		0			0
$85$	0.791480			0.0858480
$86$		0			0
$87$	2.63431	−	5.56555i	0.282427	−	0.596689i
$88$		0			0
$89$	−7.43687	−	12.8810i	−0.788306	−	1.36539i	−0.927004	−	0.375052i	$-0.877625\pi$
$89$	−7.43687	−	12.8810i	−0.788306	−	1.36539i	0.138698	−	0.990335i	$-0.455708\pi$
$90$		0			0
$91$	−0.685991	+	2.01510i	−0.0719114	+	0.211240i
$92$		0			0
$93$	−1.65286	−	2.38965i	−0.171394	−	0.247795i
$94$		0			0
$95$	1.25255	+	0.723159i	0.128509	+	0.0741945i
$96$		0			0
$97$		−	13.9030i		−	1.41164i	−0.708391	−	0.705820i	$-0.750579\pi$
$97$		−	13.9030i		−	1.41164i	0.708391	−	0.705820i	$-0.249421\pi$
$98$		0			0
$99$	−0.411313	−	2.50042i	−0.0413385	−	0.251301i
$100$		0			0
$101$	−9.16337	+	15.8714i	−0.911789	+	1.57926i	−0.100254	+	0.994962i	$0.531965\pi$
$101$	−9.16337	+	15.8714i	−0.911789	+	1.57926i	−0.811536	+	0.584303i	$0.801368\pi$
$102$		0			0
$103$	0.227036	−	0.131079i	0.0223705	−	0.0129156i	−0.488773	−	0.872411i	$-0.662555\pi$
$103$	0.227036	−	0.131079i	0.0223705	−	0.0129156i	0.511144	+	0.859495i	$0.329222\pi$
$104$		0			0
$105$	−1.11865	+	4.44394i	−0.109169	+	0.433684i
$106$		0			0
$107$	8.09189	−	4.67185i	0.782272	−	0.451645i	−0.0549626	−	0.998488i	$-0.517504\pi$
$107$	8.09189	−	4.67185i	0.782272	−	0.451645i	0.837235	+	0.546843i	$0.184171\pi$
$108$		0			0
$109$	−3.10494	+	5.37791i	−0.297399	+	0.515110i	−0.975540	−	0.219822i	$-0.929452\pi$
$109$	−3.10494	+	5.37791i	−0.297399	+	0.515110i	0.678141	+	0.734932i	$0.262786\pi$
$110$		0			0
$111$	−0.327450	−	4.00796i	−0.0310802	−	0.380418i
$112$		0			0
$113$		−	10.3445i		−	0.973128i	−0.873645	−	0.486564i	$-0.838250\pi$
$113$		−	10.3445i		−	0.973128i	0.873645	−	0.486564i	$-0.161750\pi$
$114$		0			0
$115$	−2.47256	−	1.42754i	−0.230568	−	0.133118i
$116$		0			0
$117$	−1.86670	+	1.53013i	−0.172576	+	0.141460i
$118$		0			0
$119$	1.57560	−	1.37934i	0.144435	−	0.126444i
$120$		0			0
$121$	−5.14326	−	8.90839i	−0.467569	−	0.809854i
$122$		0			0
$123$	−9.79604	−	4.63670i	−0.883279	−	0.418077i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	6.55673			0.581816			0.290908	−	0.956751i	$-0.406043\pi$
$127$	6.55673			0.581816			0.290908	+	0.956751i	$0.406043\pi$
$128$		0			0
$129$	8.38219	+	3.96749i	0.738010	+	0.349318i
$130$		0			0
$131$	9.96153	+	17.2539i	0.870343	+	1.50748i	0.861643	+	0.507515i	$0.169436\pi$
$131$	9.96153	+	17.2539i	0.870343	+	1.50748i	0.00869979	+	0.999962i	$0.497231\pi$
$132$		0			0
$133$	3.75372	−	0.743267i	0.325489	−	0.0644494i
$134$		0			0
$135$	−3.73704	+	3.61034i	−0.321633	+	0.310728i
$136$		0			0
$137$	−4.72888	−	2.73022i	−0.404015	−	0.233258i	0.284200	−	0.958765i	$-0.408272\pi$
$137$	−4.72888	−	2.73022i	−0.404015	−	0.233258i	−0.688215	+	0.725507i	$0.741605\pi$
$138$		0			0
$139$		−	17.3682i		−	1.47315i	−0.676357	−	0.736574i	$-0.736442\pi$
$139$		−	17.3682i		−	1.47315i	0.676357	−	0.736574i	$-0.263558\pi$
$140$		0			0
$141$	0.878153	+	10.7485i	0.0739538	+	0.905188i
$142$		0			0
$143$	0.339795	−	0.588543i	0.0284151	−	0.0492164i
$144$		0			0
$145$	3.07875	−	1.77752i	0.255677	−	0.147615i
$146$		0			0
$147$	5.51773	+	10.7960i	0.455094	+	0.890443i
$148$		0			0
$149$	−1.39720	+	0.806672i	−0.114463	+	0.0660852i	−0.556138	−	0.831090i	$-0.687718\pi$
$149$	−1.39720	+	0.806672i	−0.114463	+	0.0660852i	0.441676	+	0.897175i	$0.354384\pi$
$150$		0			0
$151$	−0.497773	+	0.862168i	−0.0405082	+	0.0701623i	−0.885569	−	0.464508i	$-0.846231\pi$
$151$	−0.497773	+	0.862168i	−0.0405082	+	0.0701623i	0.845060	+	0.534671i	$0.179564\pi$
$152$		0			0
$153$	2.34295	−	0.385410i	0.189416	−	0.0311586i
$154$		0			0
$155$		−	1.67754i		−	0.134743i
$156$		0			0
$157$	−11.2973	−	6.52248i	−0.901620	−	0.520550i	−0.0238944	−	0.999714i	$-0.507607\pi$
$157$	−11.2973	−	6.52248i	−0.901620	−	0.520550i	−0.877725	+	0.479164i	$0.840940\pi$
$158$		0			0
$159$	−4.07143	−	5.88632i	−0.322885	−	0.466816i
$160$		0			0
$161$	−7.40994	+	1.46723i	−0.583985	+	0.115634i
$162$		0			0
$163$	−7.00756	−	12.1375i	−0.548875	−	0.950679i	−0.998352	−	0.0573870i	$-0.981723\pi$
$163$	−7.00756	−	12.1375i	−0.548875	−	0.950679i	0.449477	−	0.893292i	$-0.351610\pi$
$164$		0			0
$165$	0.625908	−	1.32237i	0.0487269	−	0.102946i
$166$		0			0
$167$	−3.39763			−0.262917			−0.131458	−	0.991322i	$-0.541966\pi$
$167$	−3.39763			−0.262917			−0.131458	+	0.991322i	$0.541966\pi$
$168$		0			0
$169$	12.3527			0.950206
$170$		0			0
$171$	4.05995	+	1.53078i	0.310472	+	0.117062i
$172$		0			0
$173$	−2.49825	−	4.32709i	−0.189938	−	0.328983i	0.755291	−	0.655389i	$-0.227495\pi$
$173$	−2.49825	−	4.32709i	−0.189938	−	0.328983i	−0.945229	+	0.326407i	$0.894162\pi$
$174$		0			0
$175$	−1.99070	+	1.74273i	−0.150483	+	0.131738i
$176$		0			0
$177$	17.8499	−	12.3463i	1.34168	−	0.928006i
$178$		0			0
$179$	13.6504	+	7.88106i	1.02028	+	0.589058i	0.914185	−	0.405298i	$-0.132832\pi$
$179$	13.6504	+	7.88106i	1.02028	+	0.589058i	0.106094	+	0.994356i	$0.466166\pi$
$180$		0			0
$181$		−	16.3223i		−	1.21322i	−0.794998	−	0.606612i	$-0.792528\pi$
$181$		−	16.3223i		−	1.21322i	0.794998	−	0.606612i	$-0.207472\pi$
$182$		0			0
$183$	4.76963	−	0.389678i	0.352581	−	0.0288058i
$184$		0			0
$185$	1.16085	−	2.01066i	0.0853476	−	0.147826i
$186$		0			0
$187$	−0.578974	+	0.334271i	−0.0423388	+	0.0244443i
$188$		0			0
$189$	−1.14746	+	13.6998i	−0.0834653	+	0.996511i
$190$		0			0
$191$	−20.2436	+	11.6876i	−1.46478	+	0.845688i	−0.999226	−	0.0393335i	$-0.987477\pi$
$191$	−20.2436	+	11.6876i	−1.46478	+	0.845688i	−0.465549	+	0.885022i	$0.654143\pi$
$192$		0			0
$193$	−3.25242	+	5.63336i	−0.234114	+	0.405498i	−0.959015	−	0.283355i	$-0.908552\pi$
$193$	−3.25242	+	5.63336i	−0.234114	+	0.405498i	0.724900	+	0.688854i	$0.241886\pi$
$194$		0			0
$195$	−1.38891	+	0.113474i	−0.0994621	+	0.00812604i
$196$		0			0
$197$		−	11.4637i		−	0.816752i	−0.912814	−	0.408376i	$-0.866095\pi$
$197$		−	11.4637i		−	0.816752i	0.912814	−	0.408376i	$-0.133905\pi$
$198$		0			0
$199$	−17.7667	−	10.2576i	−1.25945	−	0.727142i	−0.286480	−	0.958086i	$-0.592485\pi$
$199$	−17.7667	−	10.2576i	−1.25945	−	0.727142i	−0.972967	+	0.230944i	$0.925819\pi$
$200$		0			0
$201$	−9.71741	+	6.72130i	−0.685413	+	0.474084i
$202$		0			0
$203$	3.03112	−	8.90395i	0.212743	−	0.624935i
$204$		0			0
$205$	−3.12865	−	5.41898i	−0.218514	−	0.378478i
$206$		0			0
$207$	−8.01446	−	3.02180i	−0.557043	−	0.210030i
$208$		0			0
$209$	−1.22167			−0.0845044
$210$		0			0
$211$	5.90017			0.406184			0.203092	−	0.979160i	$-0.434901\pi$
$211$	5.90017			0.406184			0.203092	+	0.979160i	$0.434901\pi$
$212$		0			0
$213$	−9.63703	+	20.3603i	−0.660318	+	1.39507i
$214$		0			0
$215$	2.67709	+	4.63686i	0.182576	+	0.316232i
$216$		0			0
$217$	−2.92350	−	3.33947i	−0.198460	−	0.226698i
$218$		0			0
$219$	−7.42652	−	10.7370i	−0.501837	−	0.725538i
$220$		0			0
$221$	0.551479	+	0.318397i	0.0370965	+	0.0214177i
$222$		0			0
$223$		−	16.9239i		−	1.13331i	−0.823956	−	0.566654i	$-0.808238\pi$
$223$		−	16.9239i		−	1.13331i	0.823956	−	0.566654i	$-0.191762\pi$
$224$		0			0
$225$	−2.96022	+	0.486949i	−0.197348	+	0.0324633i
$226$		0			0
$227$	10.1061	−	17.5042i	0.670764	−	1.16180i	−0.306924	−	0.951734i	$-0.599300\pi$
$227$	10.1061	−	17.5042i	0.670764	−	1.16180i	0.977688	−	0.210063i	$-0.0673668\pi$
$228$		0			0
$229$	−14.2204	+	8.21013i	−0.939707	+	0.542540i	−0.889869	−	0.456217i	$-0.849204\pi$
$229$	−14.2204	+	8.21013i	−0.939707	+	0.542540i	−0.0498389	+	0.998757i	$0.515871\pi$
$230$		0			0
$231$	−1.05854	−	3.72323i	−0.0696469	−	0.244970i
$232$		0			0
$233$	8.74100	−	5.04662i	0.572642	−	0.330615i	−0.185562	−	0.982633i	$-0.559410\pi$
$233$	8.74100	−	5.04662i	0.572642	−	0.330615i	0.758204	+	0.652018i	$0.226077\pi$
$234$		0			0
$235$	−3.11317	+	5.39217i	−0.203081	+	0.351746i
$236$		0			0
$237$	−1.38544	−	16.9577i	−0.0899941	−	1.10152i
$238$		0			0
$239$			7.87661i			0.509496i	0.967007	+	0.254748i	$0.0819925\pi$
$239$			7.87661i			0.509496i	−0.967007	+	0.254748i	$0.918008\pi$
$240$		0			0
$241$	−21.0642	−	12.1614i	−1.35687	−	0.783388i	−0.367667	−	0.929958i	$-0.619843\pi$
$241$	−21.0642	−	12.1614i	−1.35687	−	0.783388i	−0.989200	+	0.146570i	$0.953177\pi$
$242$		0			0
$243$	−9.30439	+	12.5071i	−0.596877	+	0.802333i
$244$		0			0
$245$	−0.925755	+	6.93851i	−0.0591443	+	0.443285i
$246$		0			0
$247$	0.581825	+	1.00775i	0.0370206	+	0.0641216i
$248$		0			0
$249$	23.7719	+	11.2518i	1.50648	+	0.713055i
$250$		0			0
$251$	−6.88663			−0.434680			−0.217340	−	0.976096i	$-0.569738\pi$
$251$	−6.88663			−0.434680			−0.217340	+	0.976096i	$0.569738\pi$
$252$		0			0
$253$	2.41160			0.151616
$254$		0			0
$255$	1.23909	+	0.586492i	0.0775949	+	0.0367275i
$256$		0			0
$257$	−9.31053	−	16.1263i	−0.580775	−	1.00593i	−0.995388	−	0.0959335i	$-0.969416\pi$
$257$	−9.31053	−	16.1263i	−0.580775	−	1.00593i	0.414613	−	0.909998i	$-0.363917\pi$
$258$		0			0
$259$	−1.19313	−	6.02567i	−0.0741376	−	0.374417i
$260$		0			0
$261$	8.24822	−	6.76104i	0.510552	−	0.418498i
$262$		0			0
$263$	0.560405	+	0.323550i	0.0345561	+	0.0199510i	0.517179	−	0.855878i	$-0.326982\pi$
$263$	0.560405	+	0.323550i	0.0345561	+	0.0199510i	−0.482622	+	0.875829i	$0.660316\pi$
$264$		0			0
$265$		−	4.13220i		−	0.253839i
$266$		0			0
$267$	−2.09777	−	25.6765i	−0.128381	−	1.57138i
$268$		0			0
$269$	1.55153	−	2.68732i	0.0945982	−	0.163849i	−0.814843	−	0.579682i	$-0.803177\pi$
$269$	1.55153	−	2.68732i	0.0945982	−	0.163849i	0.909441	+	0.415833i	$0.136510\pi$
$270$		0			0
$271$	−17.2290	+	9.94715i	−1.04658	+	0.604246i	−0.921691	−	0.387924i	$-0.873192\pi$
$271$	−17.2290	+	9.94715i	−1.04658	+	0.604246i	−0.124894	+	0.992170i	$0.539859\pi$
$272$		0			0
$273$	−2.56715	+	2.64640i	−0.155371	+	0.160167i
$274$		0			0
$275$	0.731508	−	0.422337i	0.0441116	−	0.0254679i
$276$		0			0
$277$	1.21962	−	2.11245i	0.0732801	−	0.126925i	−0.827057	−	0.562118i	$-0.809987\pi$
$277$	1.21962	−	2.11245i	0.0732801	−	0.126925i	0.900337	+	0.435193i	$0.143320\pi$
$278$		0			0
$279$	−0.816875	−	4.96587i	−0.0489050	−	0.297299i
$280$		0			0
$281$			15.6270i			0.932227i	0.884725	+	0.466113i	$0.154346\pi$
$281$			15.6270i			0.932227i	−0.884725	+	0.466113i	$0.845654\pi$
$282$		0			0
$283$	−10.7860	−	6.22732i	−0.641163	−	0.370176i	0.143899	−	0.989592i	$-0.454036\pi$
$283$	−10.7860	−	6.22732i	−0.641163	−	0.370176i	−0.785062	+	0.619417i	$0.787369\pi$
$284$		0			0
$285$	1.42505	+	2.06028i	0.0844124	+	0.122040i
$286$		0			0
$287$	−15.6720	−	5.33515i	−0.925091	−	0.314924i
$288$		0			0
$289$	8.18678	+	14.1799i	0.481575	+	0.834113i
$290$		0			0
$291$	10.3022	−	21.7657i	0.603928	−	1.27593i
$292$		0			0
$293$	22.4053			1.30893			0.654464	−	0.756093i	$-0.272894\pi$
$293$	22.4053			1.30893			0.654464	+	0.756093i	$0.272894\pi$
$294$		0			0
$295$	12.5306			0.729561
$296$		0			0
$297$	1.20890	−	4.21928i	0.0701474	−	0.244827i
$298$		0			0
$299$	−1.14854	−	1.98933i	−0.0664217	−	0.115046i
$300$		0			0
$301$	13.4101	+	4.56513i	0.772946	+	0.263130i
$302$		0			0
$303$	−26.1064	+	18.0572i	−1.49977	+	1.03736i
$304$		0			0
$305$	2.39276	+	1.38146i	0.137009	+	0.0791022i
$306$		0			0
$307$			8.19542i			0.467738i	0.972268	+	0.233869i	$0.0751386\pi$
$307$			8.19542i			0.467738i	−0.972268	+	0.233869i	$0.924861\pi$
$308$		0			0
$309$	0.452564	−	0.0369744i	0.0257455	−	0.00210340i
$310$		0			0
$311$	−8.67007	+	15.0170i	−0.491635	+	0.851536i	−0.999954	−	0.00963275i	$-0.996934\pi$
$311$	−8.67007	+	15.0170i	−0.491635	+	0.851536i	0.508319	+	0.861169i	$0.330267\pi$
$312$		0			0
$313$	−1.97581	+	1.14073i	−0.111679	+	0.0644781i	−0.554799	−	0.831984i	$-0.687205\pi$
$313$	−1.97581	+	1.14073i	−0.111679	+	0.0644781i	0.443120	+	0.896462i	$0.353872\pi$
$314$		0			0
$315$	−5.04427	+	6.12824i	−0.284213	+	0.345287i
$316$		0			0
$317$	24.1048	−	13.9169i	1.35386	−	0.781651i	0.365072	−	0.930979i	$-0.381044\pi$
$317$	24.1048	−	13.9169i	1.35386	−	0.781651i	0.988788	+	0.149328i	$0.0477109\pi$
$318$		0			0
$319$	−1.50142	+	2.60054i	−0.0840635	+	0.145602i
$320$		0			0
$321$	16.1300	−	1.31782i	0.900291	−	0.0735537i
$322$		0			0
$323$		−	1.14473i		−	0.0636945i
$324$		0			0
$325$	−0.696770	−	0.402280i	−0.0386499	−	0.0223145i
$326$		0			0
$327$	−8.84596	+	6.11854i	−0.489183	+	0.338356i
$328$		0			0
$329$	3.19973	+	16.1596i	0.176407	+	0.890907i
$330$		0			0
$331$	13.0938	+	22.6792i	0.719702	+	1.24656i	0.961118	+	0.276138i	$0.0890547\pi$
$331$	13.0938	+	22.6792i	0.719702	+	1.24656i	−0.241416	+	0.970422i	$0.577612\pi$
$332$		0			0
$333$	2.45729	−	6.51725i	0.134659	−	0.357143i
$334$		0			0
$335$	−6.82163			−0.372705
$336$		0			0
$337$	28.1999			1.53614			0.768072	−	0.640363i	$-0.221216\pi$
$337$	28.1999			1.53614			0.768072	+	0.640363i	$0.221216\pi$
$338$		0			0
$339$	7.66534	−	16.1947i	0.416324	−	0.879575i
$340$		0			0
$341$	0.708485	+	1.22713i	0.0383666	+	0.0664529i
$342$		0			0
$343$	10.2491	+	15.4258i	0.553399	+	0.832917i
$344$		0			0
$345$	−2.81308	−	4.06705i	−0.151451	−	0.218962i
$346$		0			0
$347$	−23.2148	−	13.4031i	−1.24624	−	0.719514i	−0.275879	−	0.961192i	$-0.588969\pi$
$347$	−23.2148	−	13.4031i	−1.24624	−	0.719514i	−0.970356	+	0.241678i	$0.922302\pi$
$348$		0			0
$349$			9.13263i			0.488859i	0.969667	+	0.244429i	$0.0786006\pi$
$349$			9.13263i			0.488859i	−0.969667	+	0.244429i	$0.921399\pi$
$350$		0			0
$351$	−4.05623	+	1.01224i	−0.216505	+	0.0540292i
$352$		0			0
$353$	−6.16778	+	10.6829i	−0.328278	+	0.568594i	−0.982170	−	0.187994i	$-0.939802\pi$
$353$	−6.16778	+	10.6829i	−0.328278	+	0.568594i	0.653892	+	0.756588i	$0.273135\pi$
$354$		0			0
$355$	−11.2629	+	6.50266i	−0.597775	+	0.345125i
$356$		0			0
$357$	3.48876	−	0.991880i	0.184645	−	0.0524958i
$358$		0			0
$359$	−30.5654	+	17.6469i	−1.61318	+	0.931370i	−0.624553	+	0.780982i	$0.714719\pi$
$359$	−30.5654	+	17.6469i	−1.61318	+	0.931370i	−0.988627	+	0.150388i	$0.951948\pi$
$360$		0			0
$361$	−8.45408	+	14.6429i	−0.444952	+	0.770679i
$362$		0			0
$363$	−1.45080	−	17.7576i	−0.0761470	−	0.932033i
$364$		0			0
$365$		−	7.53737i		−	0.394524i
$366$		0			0
$367$	12.9825	+	7.49544i	0.677681	+	0.391259i	0.798981	−	0.601357i	$-0.205373\pi$
$367$	12.9825	+	7.49544i	0.677681	+	0.391259i	−0.121300	+	0.992616i	$0.538706\pi$
$368$		0			0
$369$	−11.9002	−	14.5179i	−0.619502	−	0.755770i
$370$		0			0
$371$	−7.20133	−	8.22597i	−0.373874	−	0.427071i
$372$		0			0
$373$	13.9629	+	24.1845i	0.722973	+	1.25223i	0.959803	+	0.280675i	$0.0905584\pi$
$373$	13.9629	+	24.1845i	0.722973	+	1.25223i	−0.236829	+	0.971551i	$0.576108\pi$
$374$		0			0
$375$	−1.56554	−	0.741007i	−0.0808440	−	0.0382654i
$376$		0			0
$377$	2.86024			0.147310
$378$		0			0
$379$	24.2621			1.24626			0.623130	−	0.782118i	$-0.285861\pi$
$379$	24.2621			1.24626			0.623130	+	0.782118i	$0.285861\pi$
$380$		0			0
$381$	10.2648	+	4.85858i	0.525882	+	0.248913i
$382$		0			0
$383$	1.03247	+	1.78829i	0.0527568	+	0.0913774i	0.891198	−	0.453615i	$-0.149866\pi$
$383$	1.03247	+	1.78829i	0.0527568	+	0.0913774i	−0.838441	+	0.544992i	$0.816533\pi$
$384$		0			0
$385$	0.720192	−	2.11557i	0.0367044	−	0.107819i
$386$		0			0
$387$	10.1827	+	12.4225i	0.517616	+	0.631472i
$388$		0			0
$389$	19.4560	+	11.2329i	0.986460	+	0.569533i	0.904214	−	0.427079i	$-0.140457\pi$
$389$	19.4560	+	11.2329i	0.986460	+	0.569533i	0.0822460	+	0.996612i	$0.473791\pi$
$390$		0			0
$391$			2.25973i			0.114279i
$392$		0			0
$393$	2.80992	+	34.3931i	0.141742	+	1.73490i
$394$		0			0
$395$	4.91157	−	8.50709i	0.247128	−	0.428038i
$396$		0			0
$397$	−21.2728	+	12.2818i	−1.06765	+	0.616408i	−0.927538	−	0.373728i	$-0.878079\pi$
$397$	−21.2728	+	12.2818i	−1.06765	+	0.616408i	−0.140112	+	0.990136i	$0.544746\pi$
$398$		0			0
$399$	6.42735	+	1.61792i	0.321770	+	0.0809971i
$400$		0			0
$401$	−2.17015	+	1.25294i	−0.108372	+	0.0625686i	−0.553206	−	0.833044i	$-0.686596\pi$
$401$	−2.17015	+	1.25294i	−0.108372	+	0.0625686i	0.444834	+	0.895613i	$0.353263\pi$
$402$		0			0
$403$	0.674840	−	1.16886i	0.0336162	−	0.0582249i
$404$		0			0
$405$	−8.52576	+	2.88295i	−0.423648	+	0.143255i
$406$		0			0
$407$			1.96108i			0.0972072i
$408$		0			0
$409$	13.7159	+	7.91885i	0.678205	+	0.391562i	0.799178	−	0.601094i	$-0.205268\pi$
$409$	13.7159	+	7.91885i	0.678205	+	0.391562i	−0.120973	+	0.992656i	$0.538602\pi$
$410$		0			0
$411$	−5.38013	−	7.77839i	−0.265382	−	0.383680i
$412$		0			0
$413$	24.9447	−	21.8375i	1.22745	−	1.07455i
$414$		0			0
$415$	7.59225	+	13.1502i	0.372689	+	0.645516i
$416$		0			0
$417$	12.8699	−	27.1905i	0.630243	−	1.33153i
$418$		0			0
$419$	−15.0218			−0.733864			−0.366932	−	0.930248i	$-0.619592\pi$
$419$	−15.0218			−0.733864			−0.366932	+	0.930248i	$0.619592\pi$
$420$		0			0
$421$	39.9642			1.94774			0.973868	−	0.227117i	$-0.0729299\pi$
$421$	39.9642			1.94774			0.973868	+	0.227117i	$0.0729299\pi$
$422$		0			0
$423$	−6.58994	+	17.4779i	−0.320414	+	0.849806i
$424$		0			0
$425$	0.395740	+	0.685442i	0.0191962	+	0.0332488i
$426$		0			0
$427$	7.17078	−	1.41987i	0.347018	−	0.0687125i
$428$		0			0
$429$	0.968077	−	0.669596i	0.0467392	−	0.0323284i
$430$		0			0
$431$	4.22505	+	2.43933i	0.203513	+	0.117499i	0.598293	−	0.801277i	$-0.295846\pi$
$431$	4.22505	+	2.43933i	0.203513	+	0.117499i	−0.394780	+	0.918776i	$0.629179\pi$
$432$		0			0
$433$			26.9452i			1.29490i	0.762106	+	0.647452i	$0.224165\pi$
$433$			26.9452i			1.29490i	−0.762106	+	0.647452i	$0.775835\pi$
$434$		0			0
$435$	6.13706	−	0.501397i	0.294249	−	0.0240402i
$436$		0			0
$437$	−2.06467	+	3.57611i	−0.0987665	+	0.171069i
$438$		0			0
$439$	8.94245	−	5.16293i	0.426800	−	0.246413i	−0.271182	−	0.962528i	$-0.587415\pi$
$439$	8.94245	−	5.16293i	0.426800	−	0.246413i	0.697982	+	0.716115i	$0.254081\pi$
$440$		0			0
$441$	0.638267	+	20.9903i	0.0303937	+	0.999538i
$442$		0			0
$443$	18.5261	−	10.6961i	0.880203	−	0.508186i	0.00947789	−	0.999955i	$-0.496983\pi$
$443$	18.5261	−	10.6961i	0.880203	−	0.508186i	0.870725	+	0.491769i	$0.163650\pi$
$444$		0			0
$445$	7.43687	−	12.8810i	0.352541	−	0.610619i
$446$		0			0
$447$	−2.78512	+	0.227544i	−0.131731	+	0.0107624i
$448$		0			0
$449$			10.0887i			0.476116i	0.971251	+	0.238058i	$0.0765109\pi$
$449$			10.0887i			0.476116i	−0.971251	+	0.238058i	$0.923489\pi$
$450$		0			0
$451$	4.57727	+	2.64269i	0.215535	+	0.124439i
$452$		0			0
$453$	−1.41816	+	0.980904i	−0.0666308	+	0.0460869i
$454$		0			0
$455$	−2.08813	+	0.413466i	−0.0978929	+	0.0193836i
$456$		0			0
$457$	5.33179	+	9.23494i	0.249411	+	0.431992i	0.963362	−	0.268203i	$-0.0864297\pi$
$457$	5.33179	+	9.23494i	0.249411	+	0.431992i	−0.713952	+	0.700195i	$0.753096\pi$
$458$		0			0
$459$	3.95357	+	1.13277i	0.184537	+	0.0528731i
$460$		0			0
$461$	−10.8662			−0.506091			−0.253045	−	0.967454i	$-0.581432\pi$
$461$	−10.8662			−0.506091			−0.253045	+	0.967454i	$0.581432\pi$
$462$		0			0
$463$	26.9175			1.25096			0.625481	−	0.780240i	$-0.284903\pi$
$463$	26.9175			1.25096			0.625481	+	0.780240i	$0.284903\pi$
$464$		0			0
$465$	1.24307	−	2.62625i	0.0576458	−	0.121789i
$466$		0			0
$467$	19.3269	+	33.4752i	0.894343	+	1.54905i	0.834616	+	0.550833i	$0.185690\pi$
$467$	19.3269	+	33.4752i	0.894343	+	1.54905i	0.0597271	+	0.998215i	$0.480977\pi$
$468$		0			0
$469$	−13.5798	+	11.8883i	−0.627057	+	0.548950i
$470$		0			0
$471$	−12.8531	−	18.5825i	−0.592239	−	0.856238i
$472$		0			0
$473$	−3.91663	−	2.26127i	−0.180087	−	0.103973i
$474$		0			0
$475$			1.44632i			0.0663616i
$476$		0			0
$477$	−2.01217	−	12.2322i	−0.0921311	−	0.560075i
$478$		0			0
$479$	7.95661	−	13.7813i	0.363547	−	0.629682i	−0.624995	−	0.780629i	$-0.714899\pi$
$479$	7.95661	−	13.7813i	0.363547	−	0.629682i	0.988542	+	0.150947i	$0.0482323\pi$
$480$		0			0
$481$	1.61769	−	0.933977i	0.0737605	−	0.0425857i
$482$		0			0
$483$	−12.6878	−	3.19381i	−0.577314	−	0.145323i
$484$		0			0
$485$	12.0404	−	6.95152i	0.546726	−	0.315652i
$486$		0			0
$487$	−12.8179	+	22.2012i	−0.580832	+	1.00603i	0.414548	+	0.910027i	$0.363940\pi$
$487$	−12.8179	+	22.2012i	−0.580832	+	1.00603i	−0.995381	+	0.0960041i	$0.969394\pi$
$488$		0			0
$489$	−1.97667	−	24.1943i	−0.0893882	−	1.09410i
$490$		0			0
$491$		−	6.18969i		−	0.279337i	−0.990198	−	0.139668i	$-0.955396\pi$
$491$		−	6.18969i		−	0.279337i	0.990198	−	0.139668i	$-0.0446036\pi$
$492$		0			0
$493$	−2.43677	−	1.40687i	−0.109747	−	0.0633623i
$494$		0			0
$495$	1.95977	−	1.60641i	0.0880850	−	0.0722030i
$496$		0			0
$497$	−11.0887	+	32.5731i	−0.497396	+	1.46110i
$498$		0			0
$499$	7.61308	+	13.1862i	0.340808	+	0.590297i	0.984583	−	0.174918i	$-0.0559660\pi$
$499$	7.61308	+	13.1862i	0.340808	+	0.590297i	−0.643775	+	0.765215i	$0.722633\pi$
$500$		0			0
$501$	−5.31912	−	2.51767i	−0.237641	−	0.112481i
$502$		0			0
$503$	18.4999			0.824871			0.412435	−	0.910987i	$-0.364678\pi$
$503$	18.4999			0.824871			0.412435	+	0.910987i	$0.364678\pi$
$504$		0			0
$505$	−18.3267			−0.815529
$506$		0			0
$507$	19.3386	+	9.15342i	0.858857	+	0.406518i
$508$		0			0
$509$	−16.3241	−	28.2741i	−0.723551	−	1.25323i	−0.959568	−	0.281478i	$-0.909175\pi$
$509$	−16.3241	−	28.2741i	−0.723551	−	1.25323i	0.236017	−	0.971749i	$-0.424158\pi$
$510$		0			0
$511$	−13.1356	−	15.0046i	−0.581086	−	0.663766i
$512$		0			0
$513$	5.22169	+	5.40495i	0.230543	+	0.238634i
$514$		0			0
$515$	0.227036	+	0.131079i	0.0100044	+	0.00577604i
$516$		0			0
$517$		−	5.25922i		−	0.231300i
$518$		0			0
$519$	−0.704698	−	8.62545i	−0.0309328	−	0.378615i
$520$		0			0
$521$	−12.7318	+	22.0521i	−0.557789	+	0.966120i	0.439891	+	0.898051i	$0.355017\pi$
$521$	−12.7318	+	22.0521i	−0.557789	+	0.966120i	−0.997681	+	0.0680685i	$0.978316\pi$
$522$		0			0
$523$	−25.2213	+	14.5615i	−1.10285	+	0.636732i	−0.936969	−	0.349414i	$-0.886381\pi$
$523$	−25.2213	+	14.5615i	−1.10285	+	0.636732i	−0.165883	+	0.986145i	$0.553047\pi$
$524$		0			0
$525$	−4.40789	+	1.25320i	−0.192376	+	0.0546940i
$526$		0			0
$527$	−1.14985	+	0.663868i	−0.0500884	+	0.0289185i
$528$		0			0
$529$	−7.42429	+	12.8592i	−0.322795	+	0.559097i
$530$		0			0
$531$	37.0933	−	6.10177i	1.60971	−	0.264794i
$532$		0			0
$533$		−	5.03438i		−	0.218063i
$534$		0			0
$535$	8.09189	+	4.67185i	0.349843	+	0.201982i
$536$		0			0
$537$	15.5303	+	22.4531i	0.670182	+	0.968924i
$538$		0			0
$539$	−2.25319	−	5.46656i	−0.0970518	−	0.235461i
$540$		0			0
$541$	10.0754	+	17.4511i	0.433174	+	0.750279i	0.997145	−	0.0755154i	$-0.0240602\pi$
$541$	10.0754	+	17.4511i	0.433174	+	0.750279i	−0.563971	+	0.825795i	$0.690727\pi$
$542$		0			0
$543$	12.0949	−	25.5531i	0.519042	−	1.09659i
$544$		0			0
$545$	−6.20987			−0.266002
$546$		0			0
$547$	13.7371			0.587356			0.293678	−	0.955904i	$-0.405121\pi$
$547$	13.7371			0.587356			0.293678	+	0.955904i	$0.405121\pi$
$548$		0			0
$549$	7.75579	+	2.92427i	0.331009	+	0.124805i
$550$		0			0
$551$	−2.57086	−	4.45286i	−0.109522	−	0.189698i
$552$		0			0
$553$	−5.04814	−	25.4946i	−0.214669	−	1.08414i
$554$		0			0
$555$	3.30727	−	2.28756i	0.140386	−	0.0971015i
$556$		0			0
$557$	−23.6015	−	13.6263i	−1.00003	−	0.577366i	−0.0917703	−	0.995780i	$-0.529253\pi$
$557$	−23.6015	−	13.6263i	−1.00003	−	0.577366i	−0.908256	+	0.418415i	$0.862586\pi$
$558$		0			0
$559$			4.30777i			0.182199i
$560$		0			0
$561$	−1.15410	+	0.0942901i	−0.0487263	+	0.00398093i
$562$		0			0
$563$	11.1813	−	19.3666i	0.471236	−	0.816205i	−0.528222	−	0.849106i	$-0.677141\pi$
$563$	11.1813	−	19.3666i	0.471236	−	0.816205i	0.999459	+	0.0329009i	$0.0104746\pi$
$564$		0			0
$565$	8.95859	−	5.17224i	0.376891	−	0.217598i
$566$		0			0
$567$	−11.9480	+	20.5972i	−0.501769	+	0.865002i
$568$		0			0
$569$	−26.1319	+	15.0873i	−1.09551	+	0.632492i	−0.935037	−	0.354549i	$-0.884634\pi$
$569$	−26.1319	+	15.0873i	−1.09551	+	0.632492i	−0.160470	+	0.987041i	$0.551301\pi$
$570$		0			0
$571$	−5.42037	+	9.38836i	−0.226836	+	0.392891i	−0.956869	−	0.290521i	$-0.906171\pi$
$571$	−5.42037	+	9.38836i	−0.226836	+	0.392891i	0.730033	+	0.683412i	$0.239505\pi$
$572$		0			0
$573$	−40.3527	+	3.29682i	−1.68576	+	0.137726i
$574$		0			0
$575$		−	2.85507i		−	0.119065i
$576$		0			0
$577$	−19.0647	−	11.0070i	−0.793676	−	0.458229i	0.0475793	−	0.998867i	$-0.484849\pi$
$577$	−19.0647	−	11.0070i	−0.793676	−	0.458229i	−0.841255	+	0.540639i	$0.818183\pi$
$578$		0			0
$579$	−9.26615	+	6.40917i	−0.385088	+	0.266356i
$580$		0			0
$581$	38.0311	+	12.9467i	1.57780	+	0.537121i
$582$		0			0
$583$	1.74518	+	3.02274i	0.0722780	+	0.125189i
$584$		0			0
$585$	−2.25848	−	0.851545i	−0.0933767	−	0.0352071i
$586$		0			0
$587$	4.90442			0.202427			0.101213	−	0.994865i	$-0.467727\pi$
$587$	4.90442			0.202427			0.101213	+	0.994865i	$0.467727\pi$
$588$		0			0
$589$	−2.42625			−0.0999719
$590$		0			0
$591$	8.49465	−	17.9468i	0.349423	−	0.738233i
$592$		0			0
$593$	−12.6559	−	21.9207i	−0.519715	−	0.900173i	−0.999737	−	0.0229168i	$-0.992705\pi$
$593$	−12.6559	−	21.9207i	−0.519715	−	0.900173i	0.480022	−	0.877256i	$-0.340629\pi$
$594$		0			0
$595$	1.98234	+	0.674838i	0.0812681	+	0.0276656i
$596$		0			0
$597$	−20.2135	−	29.2239i	−0.827283	−	1.19605i
$598$		0			0
$599$	41.2486	+	23.8149i	1.68537	+	0.973050i	0.957983	+	0.286826i	$0.0926001\pi$
$599$	41.2486	+	23.8149i	1.68537	+	0.973050i	0.727390	+	0.686224i	$0.240733\pi$
$600$		0			0
$601$			3.74676i			0.152834i	0.997076	+	0.0764168i	$0.0243480\pi$
$601$			3.74676i			0.152834i	−0.997076	+	0.0764168i	$0.975652\pi$
$602$		0			0
$603$	−20.1935	+	3.32179i	−0.822343	+	0.135274i
$604$		0			0
$605$	5.14326	−	8.90839i	0.209103	−	0.362178i
$606$		0			0
$607$	4.50028	−	2.59824i	0.182661	−	0.105459i	−0.405881	−	0.913926i	$-0.633035\pi$
$607$	4.50028	−	2.59824i	0.182661	−	0.105459i	0.588542	+	0.808467i	$0.299702\pi$
$608$		0			0
$609$	11.3432	−	11.6934i	0.459651	−	0.473840i
$610$		0			0
$611$	−4.33833	+	2.50473i	−0.175510	+	0.101331i
$612$		0			0
$613$	−15.0561	+	26.0779i	−0.608110	+	1.05328i	0.383441	+	0.923565i	$0.374739\pi$
$613$	−15.0561	+	26.0779i	−0.608110	+	1.05328i	−0.991552	+	0.129713i	$0.958595\pi$
$614$		0			0
$615$	−0.882520	−	10.8020i	−0.0355866	−	0.435577i
$616$		0			0
$617$			26.3310i			1.06005i	0.847983	+	0.530023i	$0.177817\pi$
$617$			26.3310i			1.06005i	−0.847983	+	0.530023i	$0.822183\pi$
$618$		0			0
$619$	−8.92887	−	5.15509i	−0.358882	−	0.207200i	0.309708	−	0.950832i	$-0.399769\pi$
$619$	−8.92887	−	5.15509i	−0.358882	−	0.207200i	−0.668590	+	0.743631i	$0.733102\pi$
$620$		0			0
$621$	−10.3078	−	10.6695i	−0.413636	−	0.428153i
$622$		0			0
$623$	−7.64366	−	38.6027i	−0.306237	−	1.54659i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$	−1.91256	−	0.905262i	−0.0763804	−	0.0361527i
$628$		0			0
$629$	−1.83758			−0.0732692
$630$		0			0
$631$	−32.9456			−1.31154			−0.655771	−	0.754960i	$-0.727656\pi$
$631$	−32.9456			−1.31154			−0.655771	+	0.754960i	$0.727656\pi$
$632$		0			0
$633$	9.23694	+	4.37206i	0.367135	+	0.173774i
$634$		0			0
$635$	3.27837	+	5.67830i	0.130098	+	0.225336i
$636$		0			0
$637$	−3.43627	+	4.46214i	−0.136150	+	0.176796i
$638$		0			0
$639$	−30.1743	+	24.7338i	−1.19368	+	0.978452i
$640$		0			0
$641$	−34.8388	−	20.1142i	−1.37605	−	0.794462i	−0.384368	−	0.923180i	$-0.625581\pi$
$641$	−34.8388	−	20.1142i	−1.37605	−	0.794462i	−0.991681	+	0.128718i	$0.958914\pi$
$642$		0			0
$643$		−	26.7432i		−	1.05465i	−0.849664	−	0.527324i	$-0.823196\pi$
$643$		−	26.7432i		−	1.05465i	0.849664	−	0.527324i	$-0.176804\pi$
$644$		0			0
$645$	0.755147	+	9.24293i	0.0297339	+	0.363940i
$646$		0			0
$647$	−12.9715	+	22.4672i	−0.509961	+	0.883278i	0.489972	+	0.871738i	$0.337007\pi$
$647$	−12.9715	+	22.4672i	−0.509961	+	0.883278i	−0.999933	+	0.0115404i	$0.996326\pi$
$648$		0			0
$649$	−9.16625	+	5.29214i	−0.359807	+	0.207735i
$650$		0			0
$651$	−2.10228	−	7.39439i	−0.0823949	−	0.289809i
$652$		0			0
$653$	9.06788	−	5.23534i	0.354854	−	0.204875i	−0.311967	−	0.950093i	$-0.600988\pi$
$653$	9.06788	−	5.23534i	0.354854	−	0.204875i	0.666821	+	0.745218i	$0.267655\pi$
$654$		0			0
$655$	−9.96153	+	17.2539i	−0.389229	+	0.674164i
$656$		0			0
$657$	−3.67032	−	22.3123i	−0.143193	−	0.870484i
$658$		0			0
$659$			5.02313i			0.195673i	0.995202	+	0.0978366i	$0.0311923\pi$
$659$			5.02313i			0.195673i	−0.995202	+	0.0978366i	$0.968808\pi$
$660$		0			0
$661$	−7.38331	−	4.26275i	−0.287177	−	0.165802i	0.349491	−	0.936940i	$-0.386355\pi$
$661$	−7.38331	−	4.26275i	−0.287177	−	0.165802i	−0.636668	+	0.771138i	$0.719688\pi$
$662$		0			0
$663$	0.627428	+	0.907112i	0.0243673	+	0.0352293i
$664$		0			0
$665$	2.52055	+	2.87918i	0.0977426	+	0.111650i
$666$		0			0
$667$	5.07494	+	8.79006i	0.196503	+	0.340352i
$668$		0			0
$669$	12.5407	−	26.4950i	0.484852	−	1.02436i
$670$		0			0
$671$	−2.33377			−0.0900940
$672$		0			0
$673$	21.4714			0.827661			0.413831	−	0.910354i	$-0.364191\pi$
$673$	21.4714			0.827661			0.413831	+	0.910354i	$0.364191\pi$
$674$		0			0
$675$	−4.99516	−	1.43120i	−0.192264	−	0.0550870i
$676$		0			0
$677$	22.7980	+	39.4873i	0.876199	+	1.51762i	0.855480	+	0.517836i	$0.173262\pi$
$677$	22.7980	+	39.4873i	0.876199	+	1.51762i	0.0207188	+	0.999785i	$0.493405\pi$
$678$		0			0
$679$	11.8541	−	34.8216i	0.454919	−	1.33633i
$680$		0			0
$681$	28.7922	−	19.9149i	1.10332	−	0.763140i
$682$		0			0
$683$	−3.12699	−	1.80537i	−0.119651	−	0.0690805i	0.438980	−	0.898497i	$-0.355340\pi$
$683$	−3.12699	−	1.80537i	−0.119651	−	0.0690805i	−0.558631	+	0.829416i	$0.688673\pi$
$684$		0			0
$685$		−	5.46044i		−	0.208633i
$686$		0			0
$687$	−28.3463	+	2.31589i	−1.08148	+	0.0883566i
$688$		0			0
$689$	1.66230	−	2.87920i	0.0633287	−	0.109689i
$690$		0			0
$691$	24.2995	−	14.0293i	0.924396	−	0.533700i	0.0393611	−	0.999225i	$-0.487468\pi$
$691$	24.2995	−	14.0293i	0.924396	−	0.533700i	0.885035	+	0.465525i	$0.154134\pi$
$692$		0			0
$693$	1.10175	−	6.61324i	0.0418520	−	0.251216i
$694$		0			0
$695$	15.0413	−	8.68408i	0.570548	−	0.329406i
$696$		0			0
$697$	−2.47626	+	4.28901i	−0.0937951	+	0.162458i
$698$		0			0
$699$	17.4240	−	1.42354i	0.659034	−	0.0538431i
$700$		0			0
$701$		−	37.7929i		−	1.42742i	−0.700442	−	0.713710i	$-0.747014\pi$
$701$		−	37.7929i		−	1.42742i	0.700442	−	0.713710i	$-0.252986\pi$
$702$		0			0
$703$	−2.90805	−	1.67896i	−0.109679	−	0.0633232i
$704$		0			0
$705$	−8.86941	+	6.13476i	−0.334041	+	0.231048i
$706$		0			0
$707$	−36.4830	+	31.9386i	−1.37208	+	1.20118i
$708$		0			0
$709$	−16.5765	−	28.7113i	−0.622542	−	1.07827i	−0.989011	−	0.147844i	$-0.952767\pi$
$709$	−16.5765	−	28.7113i	−0.622542	−	1.07827i	0.366469	−	0.930430i	$-0.380567\pi$
$710$		0			0
$711$	10.3968	−	27.5745i	0.389910	−	1.03413i
$712$		0			0
$713$	4.78948			0.179368
$714$		0			0
$715$	0.679591			0.0254153
$716$		0			0
$717$	−5.83662	+	12.3311i	−0.217973	+	0.460515i
$718$		0			0
$719$	−17.6439	−	30.5601i	−0.658005	−	1.13970i	−0.981131	−	0.193342i	$-0.938067\pi$
$719$	−17.6439	−	30.5601i	−0.658005	−	1.13970i	0.323127	−	0.946356i	$-0.395266\pi$
$720$		0			0
$721$	0.680396	−	0.134724i	0.0253393	−	0.00501738i
$722$		0			0
$723$	−23.9652	−	34.6479i	−0.891274	−	1.28857i
$724$		0			0
$725$	3.07875	+	1.77752i	0.114342	+	0.0660154i
$726$		0			0
$727$			9.20999i			0.341579i	0.985307	+	0.170790i	$0.0546319\pi$
$727$			9.20999i			0.341579i	−0.985307	+	0.170790i	$0.945368\pi$
$728$		0			0
$729$	−23.8342	+	12.6858i	−0.882750	+	0.469843i
$730$		0			0
$731$	2.11887	−	3.66998i	0.0783691	−	0.135739i
$732$		0			0
$733$	21.6214	−	12.4831i	0.798605	−	0.461075i	−0.0443782	−	0.999015i	$-0.514131\pi$
$733$	21.6214	−	12.4831i	0.798605	−	0.461075i	0.842983	+	0.537940i	$0.180797\pi$
$734$		0			0
$735$	−6.59079	+	10.1765i	−0.243105	+	0.375366i
$736$		0			0
$737$	4.99008	−	2.88102i	0.183812	−	0.106124i
$738$		0			0
$739$	−22.2824	+	38.5943i	−0.819671	+	1.41971i	0.0862530	+	0.996273i	$0.472511\pi$
$739$	−22.2824	+	38.5943i	−0.819671	+	1.41971i	−0.905924	+	0.423439i	$0.860823\pi$
$740$		0			0
$741$	0.164119	+	2.00881i	0.00602908	+	0.0737954i
$742$		0			0
$743$			27.1506i			0.996058i	0.867160	+	0.498029i	$0.165943\pi$
$743$			27.1506i			0.996058i	−0.867160	+	0.498029i	$0.834057\pi$
$744$		0			0
$745$	−1.39720	−	0.806672i	−0.0511894	−	0.0295542i
$746$		0			0
$747$	28.8782	+	35.2303i	1.05660	+	1.28901i
$748$		0			0
$749$	24.2503	−	4.80176i	0.886087	−	0.175453i
$750$		0			0
$751$	−8.14524	−	14.1080i	−0.297224	−	0.514807i	0.678276	−	0.734808i	$-0.262728\pi$
$751$	−8.14524	−	14.1080i	−0.297224	−	0.514807i	−0.975500	+	0.220000i	$0.929394\pi$
$752$		0			0
$753$	−10.7813	−	5.10304i	−0.392892	−	0.185965i
$754$		0			0
$755$	−0.995546			−0.0362316
$756$		0			0
$757$	−19.7700			−0.718553			−0.359276	−	0.933231i	$-0.616976\pi$
$757$	−19.7700			−0.718553			−0.359276	+	0.933231i	$0.616976\pi$
$758$		0			0
$759$	3.77545	+	1.78701i	0.137040	+	0.0648644i
$760$		0			0
$761$	−12.2130	−	21.1535i	−0.442721	−	0.766816i	0.555169	−	0.831737i	$-0.312653\pi$
$761$	−12.2130	−	21.1535i	−0.442721	−	0.766816i	−0.997890	+	0.0649219i	$0.979320\pi$
$762$		0			0
$763$	−12.3620	+	10.8222i	−0.447534	+	0.391788i
$764$		0			0
$765$	1.50525	+	1.83635i	0.0544225	+	0.0663934i
$766$		0			0
$767$	8.73096	+	5.04082i	0.315257	+	0.182013i
$768$		0			0
$769$			1.36859i			0.0493525i	0.999695	+	0.0246762i	$0.00785549\pi$
$769$			1.36859i			0.0493525i	−0.999695	+	0.0246762i	$0.992145\pi$
$770$		0			0
$771$	−2.62629	−	32.1455i	−0.0945833	−	1.15769i
$772$		0			0
$773$	−3.82678	+	6.62819i	−0.137640	+	0.238399i	−0.926603	−	0.376042i	$-0.877285\pi$
$773$	−3.82678	+	6.62819i	−0.137640	+	0.238399i	0.788963	+	0.614441i	$0.210618\pi$
$774$		0			0
$775$	1.45279	−	0.838768i	0.0521857	−	0.0301294i
$776$		0			0
$777$	2.59716	−	10.3175i	0.0931728	−	0.370139i
$778$		0			0
$779$	−7.83757	+	4.52502i	−0.280810	+	0.162126i
$780$		0			0
$781$	5.49262	−	9.51350i	0.196541	−	0.340420i
$782$		0			0
$783$	17.9229	−	4.47268i	0.640511	−	0.159841i
$784$		0			0
$785$		−	13.0450i		−	0.465594i
$786$		0			0
$787$	−19.4261	−	11.2157i	−0.692467	−	0.399796i	0.112068	−	0.993701i	$-0.464252\pi$
$787$	−19.4261	−	11.2157i	−0.692467	−	0.399796i	−0.804536	+	0.593904i	$0.797586\pi$
$788$		0			0
$789$	0.637583	+	0.921794i	0.0226986	+	0.0328167i
$790$		0			0
$791$	8.82000	−	25.9088i	0.313603	−	0.921212i
$792$		0			0
$793$	1.11147	+	1.92512i	0.0394694	+	0.0683631i
$794$		0			0
$795$	3.06199	−	6.46912i	0.108598	−	0.229436i
$796$		0			0
$797$	−24.5266			−0.868777			−0.434389	−	0.900725i	$-0.643036\pi$
$797$	−24.5266			−0.868777			−0.434389	+	0.900725i	$0.643036\pi$
$798$		0			0
$799$	4.92802			0.174341
$800$		0			0
$801$	15.7423	−	41.7520i	0.556228	−	1.47523i
$802$		0			0
$803$	3.18331	+	5.51365i	0.112337	+	0.194573i
$804$		0			0
$805$	−4.97563	−	5.68358i	−0.175368	−	0.200320i
$806$		0			0
$807$	4.42030	−	3.05741i	0.155602	−	0.107626i
$808$		0			0
$809$	−4.16717	−	2.40592i	−0.146510	−	0.0845875i	0.424953	−	0.905215i	$-0.360291\pi$
$809$	−4.16717	−	2.40592i	−0.146510	−	0.0845875i	−0.571463	+	0.820628i	$0.693624\pi$
$810$		0			0
$811$			38.9459i			1.36758i	0.729681	+	0.683788i	$0.239669\pi$
$811$			38.9459i			1.36758i	−0.729681	+	0.683788i	$0.760331\pi$
$812$		0			0
$813$	−34.3435	+	2.80586i	−1.20448	+	0.0984058i
$814$		0			0
$815$	7.00756	−	12.1375i	0.245464	−	0.425156i
$816$		0			0
$817$	6.70638	−	3.87193i	0.234626	−	0.135462i
$818$		0			0
$819$	−5.97997	+	2.24076i	−0.208957	+	0.0782985i
$820$		0			0
$821$	−18.6948	+	10.7934i	−0.652451	+	0.376693i	−0.789395	−	0.613886i	$-0.789605\pi$
$821$	−18.6948	+	10.7934i	−0.652451	+	0.376693i	0.136943	+	0.990579i	$0.456272\pi$
$822$		0			0
$823$	−0.529564	+	0.917232i	−0.0184594	+	0.0319727i	−0.875108	−	0.483928i	$-0.839209\pi$
$823$	−0.529564	+	0.917232i	−0.0184594	+	0.0319727i	0.856648	+	0.515901i	$0.172543\pi$
$824$		0			0
$825$	1.45816	−	0.119131i	0.0507666	−	0.00414762i
$826$		0			0
$827$			13.9948i			0.486648i	0.969945	+	0.243324i	$0.0782378\pi$
$827$			13.9948i			0.486648i	−0.969945	+	0.243324i	$0.921762\pi$
$828$		0			0
$829$	1.90847	+	1.10186i	0.0662840	+	0.0382691i	0.532776	−	0.846256i	$-0.321149\pi$
$829$	1.90847	+	1.10186i	0.0662840	+	0.0382691i	−0.466492	+	0.884526i	$0.654482\pi$
$830$		0			0
$831$	3.47471	−	2.40337i	0.120536	−	0.0833721i
$832$		0			0
$833$	5.12230	−	2.11130i	0.177477	−	0.0731520i
$834$		0			0
$835$	−1.69882	−	2.94243i	−0.0587899	−	0.101827i
$836$		0			0
$837$	2.40089	−	8.37957i	0.0829870	−	0.289640i
$838$		0			0
$839$	7.40205			0.255547			0.127774	−	0.991803i	$-0.459217\pi$
$839$	7.40205			0.255547			0.127774	+	0.991803i	$0.459217\pi$
$840$		0			0
$841$	16.3617			0.564197
$842$		0			0
$843$	−11.5797	+	24.4646i	−0.398826	+	0.842606i
$844$		0			0
$845$	6.17634	+	10.6977i	0.212473	+	0.368013i
$846$		0			0
$847$	−5.28628	−	26.6973i	−0.181639	−	0.917329i
$848$		0			0
$849$	−12.2715	−	17.7416i	−0.421155	−	0.608891i
$850$		0			0
$851$	5.74056	+	3.31432i	0.196784	+	0.113613i
$852$		0			0
$853$			18.3618i			0.628697i	0.949308	+	0.314349i	$0.101786\pi$
$853$			18.3618i			0.628697i	−0.949308	+	0.314349i	$0.898214\pi$
$854$		0			0
$855$	0.704283	+	4.28141i	0.0240860	+	0.146421i
$856$		0			0
$857$	−8.99197	+	15.5745i	−0.307160	+	0.532016i	−0.977740	−	0.209821i	$-0.932712\pi$
$857$	−8.99197	+	15.5745i	−0.307160	+	0.532016i	0.670580	+	0.741837i	$0.266045\pi$
$858$		0			0
$859$	40.2008	−	23.2099i	1.37163	−	0.791913i	0.380499	−	0.924781i	$-0.375752\pi$
$859$	40.2008	−	23.2099i	1.37163	−	0.791913i	0.991134	+	0.132869i	$0.0424189\pi$
$860$		0			0
$861$	−20.5818	−	19.9655i	−0.701426	−	0.680421i
$862$		0			0
$863$	1.49152	−	0.861131i	0.0507720	−	0.0293132i	−0.474399	−	0.880310i	$-0.657335\pi$
$863$	1.49152	−	0.861131i	0.0507720	−	0.0293132i	0.525171	+	0.850997i	$0.324001\pi$
$864$		0			0
$865$	2.49825	−	4.32709i	0.0849430	−	0.147126i
$866$		0			0
$867$	2.30930	+	28.2657i	0.0784280	+	0.959952i
$868$		0			0
$869$			8.29734i			0.281468i
$870$		0			0
$871$	−4.75311	−	2.74421i	−0.161053	−	0.0929839i
$872$		0			0
$873$	32.2571	−	26.4411i	1.09174	−	0.894895i
$874$		0			0
$875$	−2.50460	−	0.852628i	−0.0846710	−	0.0288241i
$876$		0			0
$877$	5.21047	+	9.02479i	0.175945	+	0.304746i	0.940488	−	0.339827i	$-0.110369\pi$
$877$	5.21047	+	9.02479i	0.175945	+	0.304746i	−0.764543	+	0.644573i	$0.777035\pi$
$878$		0			0
$879$	35.0763	+	16.6024i	1.18309	+	0.559986i
$880$		0			0
$881$	23.6170			0.795678			0.397839	−	0.917455i	$-0.369760\pi$
$881$	23.6170			0.795678			0.397839	+	0.917455i	$0.369760\pi$
$882$		0			0
$883$	−36.0969			−1.21476			−0.607379	−	0.794412i	$-0.707779\pi$
$883$	−36.0969			−1.21476			−0.607379	+	0.794412i	$0.707779\pi$
$884$		0			0
$885$	19.6172	+	9.28527i	0.659423	+	0.312121i
$886$		0			0
$887$	9.04005	+	15.6578i	0.303535	+	0.525738i	0.976934	−	0.213541i	$-0.0684997\pi$
$887$	9.04005	+	15.6578i	0.303535	+	0.525738i	−0.673399	+	0.739279i	$0.735166\pi$
$888$		0			0
$889$	16.4220	+	5.59045i	0.550776	+	0.187498i
$890$		0			0
$891$	5.01909	−	5.70964i	0.168146	−	0.191280i
$892$		0			0
$893$	7.79878	+	4.50263i	0.260976	+	0.150675i
$894$		0			0
$895$			15.7621i			0.526870i
$896$		0			0
$897$	−0.323976	−	3.96544i	−0.0108173	−	0.132402i
$898$		0			0
$899$	−2.98185	+	5.16472i	−0.0994503	+	0.172253i
$900$		0			0
$901$	−2.83238	+	1.63528i	−0.0943604	+	0.0544790i
$902$		0			0
$903$	17.6112	+	17.0839i	0.586065	+	0.568515i
$904$		0			0
$905$	14.1355	−	8.16114i	0.469880	−	0.271285i
$906$		0			0
$907$	29.2080	−	50.5897i	0.969836	−	1.67980i	0.273816	−	0.961782i	$-0.411714\pi$
$907$	29.2080	−	50.5897i	0.969836	−	1.67980i	0.696020	−	0.718023i	$-0.254953\pi$
$908$		0			0
$909$	−54.2511	+	8.92419i	−1.79940	+	0.295997i
$910$		0			0
$911$		−	45.4686i		−	1.50644i	−0.657768	−	0.753220i	$-0.728499\pi$
$911$		−	45.4686i		−	1.50644i	0.657768	−	0.753220i	$-0.271501\pi$
$912$		0			0
$913$	−11.1076	−	6.41297i	−0.367608	−	0.212238i
$914$		0			0
$915$	2.72229	+	3.93578i	0.0899960	+	0.130113i
$916$		0			0
$917$	10.2385	+	51.7075i	0.338106	+	1.70753i
$918$		0			0
$919$	3.95167	+	6.84449i	0.130353	+	0.225779i	0.923813	−	0.382844i	$-0.125055\pi$
$919$	3.95167	+	6.84449i	0.130353	+	0.225779i	−0.793459	+	0.608623i	$0.791722\pi$
$920$		0			0
$921$	−6.07286	+	12.8302i	−0.200108	+	0.422771i
$922$		0			0
$923$	−10.4636			−0.344413
$924$		0			0
$925$	2.32171			0.0763372
$926$		0			0
$927$	0.735904	+	0.277468i	0.0241703	+	0.00911324i
$928$		0			0
$929$	−22.6921	−	39.3038i	−0.744503	−	1.28952i	−0.950427	−	0.310949i	$-0.899353\pi$
$929$	−22.6921	−	39.3038i	−0.744503	−	1.28952i	0.205924	−	0.978568i	$-0.433980\pi$
$930$		0			0
$931$	10.0353	+	1.33894i	0.328893	+	0.0438819i
$932$		0			0
$933$	−24.7010	+	17.0851i	−0.808675	+	0.559341i
$934$		0			0
$935$	−0.578974	−	0.334271i	−0.0189345	−	0.0109318i
$936$		0			0
$937$			27.2557i			0.890404i	0.895430	+	0.445202i	$0.146868\pi$
$937$			27.2557i			0.890404i	−0.895430	+	0.445202i	$0.853132\pi$
$938$		0			0
$939$	−3.93849	+	0.321775i	−0.128528	+	0.0105007i
$940$		0			0
$941$	8.14655	−	14.1102i	0.265570	−	0.459981i	−0.702143	−	0.712036i	$-0.747773\pi$
$941$	8.14655	−	14.1102i	0.265570	−	0.459981i	0.967713	+	0.252056i	$0.0811066\pi$
$942$		0			0
$943$	15.4716	−	8.93252i	0.503824	−	0.290883i
$944$		0			0
$945$	−12.4381	+	5.85615i	−0.404610	+	0.190501i
$946$		0			0
$947$	19.8661	−	11.4697i	0.645563	−	0.372716i	−0.141191	−	0.989982i	$-0.545093\pi$
$947$	19.8661	−	11.4697i	0.645563	−	0.372716i	0.786754	+	0.617266i	$0.211760\pi$
$948$		0			0
$949$	3.03214	−	5.25182i	0.0984274	−	0.170481i
$950$		0			0
$951$	48.0495	−	3.92564i	1.55811	−	0.127298i
$952$		0			0
$953$			38.6230i			1.25112i	0.780176	+	0.625560i	$0.215130\pi$
$953$			38.6230i			1.25112i	−0.780176	+	0.625560i	$0.784870\pi$
$954$		0			0
$955$	−20.2436	−	11.6876i	−0.655067	−	0.378203i
$956$		0			0
$957$	−4.27755	+	2.95868i	−0.138274	+	0.0956406i
$958$		0			0
$959$	−9.51609	−	10.8701i	−0.307291	−	0.351013i
$960$		0			0
$961$	−14.0929	−	24.4097i	−0.454611	−	0.787409i
$962$		0			0
$963$	26.2287	+	9.88936i	0.845208	+	0.318680i
$964$		0			0
$965$	−6.50484			−0.209398
$966$		0			0
$967$	−17.8716			−0.574711			−0.287355	−	0.957824i	$-0.592776\pi$
$967$	−17.8716			−0.574711			−0.287355	+	0.957824i	$0.592776\pi$
$968$		0			0
$969$	0.848253	−	1.79212i	0.0272498	−	0.0575712i
$970$		0			0
$971$	7.16636	+	12.4125i	0.229979	+	0.398336i	0.957802	−	0.287430i	$-0.0928008\pi$
$971$	7.16636	+	12.4125i	0.229979	+	0.398336i	−0.727822	+	0.685766i	$0.759467\pi$
$972$		0			0
$973$	14.8086	−	43.5003i	0.474741	−	1.39456i
$974$		0			0
$975$	−0.792728	−	1.14610i	−0.0253876	−	0.0367045i
$976$		0			0
$977$	−45.9360	−	26.5212i	−1.46962	−	0.848487i	−0.470203	−	0.882558i	$-0.655819\pi$
$977$	−45.9360	−	26.5212i	−1.46962	−	0.848487i	−0.999419	+	0.0340716i	$0.989153\pi$
$978$		0			0
$979$			12.5634i			0.401529i
$980$		0			0
$981$	−18.3826	+	3.02389i	−0.586910	+	0.0965454i
$982$		0			0
$983$	1.12377	−	1.94642i	0.0358426	−	0.0620813i	−0.847548	−	0.530719i	$-0.821922\pi$
$983$	1.12377	−	1.94642i	0.0358426	−	0.0620813i	0.883390	+	0.468638i	$0.155255\pi$
$984$		0			0
$985$	9.92782	−	5.73183i	0.316327	−	0.182631i
$986$		0			0
$987$	−6.96506	+	27.6695i	−0.221700	+	0.880729i
$988$		0			0
$989$	−13.2386	+	7.64329i	−0.420962	+	0.243043i
$990$		0			0
$991$	−11.5434	+	19.9938i	−0.366689	+	0.635125i	−0.989046	−	0.147609i	$-0.952842\pi$
$991$	−11.5434	+	19.9938i	−0.366689	+	0.635125i	0.622356	+	0.782734i	$0.286176\pi$
$992$		0			0
$993$	3.69347	+	45.2077i	0.117209	+	1.43462i
$994$		0			0
$995$		−	20.5152i		−	0.650376i
$996$		0			0
$997$	−2.56826	−	1.48279i	−0.0813377	−	0.0469603i	0.458780	−	0.888550i	$-0.348287\pi$
$997$	−2.56826	−	1.48279i	−0.0813377	−	0.0469603i	−0.540117	+	0.841590i	$0.681620\pi$
$998$		0			0
$999$	8.67630	−	8.38214i	0.274506	−	0.265199i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	840.2.cp.b.521.14	yes	32
3.2	odd	2		840.2.cp.a.521.15	✓	32
7.5	odd	6		840.2.cp.a.761.15	yes	32
21.5	even	6	inner	840.2.cp.b.761.14	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.cp.a.521.15	✓	32	3.2	odd	2
840.2.cp.a.761.15	yes	32	7.5	odd	6
840.2.cp.b.521.14	yes	32	1.1	even	1	trivial
840.2.cp.b.761.14	yes	32	21.5	even	6	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.cp (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.56554 + 0.741007i) q^{3} +(0.500000 + 0.866025i) q^{5} +(2.50460 + 0.852628i) q^{7} +(1.90182 + 2.32015i) q^{9} +(-0.731508 - 0.422337i) q^{11} +0.804561i q^{13} +(0.141038 + 1.72630i) q^{15} +(0.395740 - 0.685442i) q^{17} +(1.25255 - 0.723159i) q^{19} +(3.28925 + 3.19075i) q^{21} +(-2.47256 + 1.42754i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(1.25812 + 5.04154i) q^{27} -3.55504i q^{29} +(-1.45279 - 0.838768i) q^{31} +(-0.832250 - 1.20324i) q^{33} +(0.513903 + 2.59536i) q^{35} +(-1.16085 - 2.01066i) q^{37} +(-0.596185 + 1.25957i) q^{39} -6.25730 q^{41} +5.35419 q^{43} +(-1.05840 + 2.80710i) q^{45} +(3.11317 + 5.39217i) q^{47} +(5.54605 + 4.27098i) q^{49} +(1.12746 - 0.779839i) q^{51} +(-3.57859 - 2.06610i) q^{53} -0.844673i q^{55} +(2.49678 - 0.203986i) q^{57} +(6.26531 - 10.8518i) q^{59} +(2.39276 - 1.38146i) q^{61} +(2.78507 + 7.43259i) q^{63} +(-0.696770 + 0.402280i) q^{65} +(-3.41081 + 5.90770i) q^{67} +(-4.92870 + 0.402675i) q^{69} +13.0053i q^{71} +(-6.52756 - 3.76869i) q^{73} +(-1.42450 + 0.985292i) q^{75} +(-1.47204 - 1.68149i) q^{77} +(-4.91157 - 8.50709i) q^{79} +(-1.76617 + 8.82500i) q^{81} +15.1845 q^{83} +0.791480 q^{85} +(2.63431 - 5.56555i) q^{87} +(-7.43687 - 12.8810i) q^{89} +(-0.685991 + 2.01510i) q^{91} +(-1.65286 - 2.38965i) q^{93} +(1.25255 + 0.723159i) q^{95} -13.9030i q^{97} +(-0.411313 - 2.50042i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{5} - 2 q^{7} + 8 q^{9} + 6 q^{19} - 14 q^{21} + 24 q^{23} - 16 q^{25} + 24 q^{27} + 42 q^{31} + 18 q^{33} + 2 q^{35} + 6 q^{37} + 12 q^{39} + 44 q^{41} - 20 q^{43} + 10 q^{45} + 4 q^{47} + 16 q^{49}+ \cdots - 8 q^{99}+O(q^{100}) \) 32 * q + 16 * q^5 - 2 * q^7 + 8 * q^9 + 6 * q^19 - 14 * q^21 + 24 * q^23 - 16 * q^25 + 24 * q^27 + 42 * q^31 + 18 * q^33 + 2 * q^35 + 6 * q^37 + 12 * q^39 + 44 * q^41 - 20 * q^43 + 10 * q^45 + 4 * q^47 + 16 * q^49 - 36 * q^51 + 12 * q^59 - 18 * q^61 + 34 * q^63 - 6 * q^65 - 6 * q^67 - 34 * q^69 - 6 * q^73 + 40 * q^77 - 2 * q^79 - 12 * q^81 - 88 * q^83 - 72 * q^87 - 6 * q^89 - 26 * q^91 + 50 * q^93 + 6 * q^95 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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