LMFDB - Embedded newform 1344.2.bl.j.703.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1344,2,Mod(703,1344)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1344, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 0, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1344.703");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1344 = 2^{6} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1344.bl (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$10.7318940317$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.562828176.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + x^{6} + 2x^{5} - 6x^{4} + 4x^{3} + 4x^{2} - 16x + 16 $ x^8 - 2x^7 + x^6 + 2x^5 - 6x^4 + 4x^3 + 4x^2 - 16x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 84)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			703.4
Root			$0.856419 - 1.12541i$ of defining polynomial
Character	$\chi$	$=$	1344.703
Dual form			1344.2.bl.j.1279.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{3} +(3.33878 - 1.92764i) q^{5} +(1.59285 + 2.11254i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{3} +(3.33878 - 1.92764i) q^{5} +(1.59285 + 2.11254i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(-1.17975 - 0.681127i) q^{11} -0.369798i q^{13} -3.85529i q^{15} +(3.89853 + 2.25082i) q^{17} +(-0.0330925 - 0.0573178i) q^{19} +(2.62594 - 0.323174i) q^{21} +(2.77902 - 1.60447i) q^{23} +(4.93162 - 8.54182i) q^{25} -1.00000 q^{27} +3.11951 q^{29} +(-3.01852 + 5.22824i) q^{31} +(-1.17975 + 0.681127i) q^{33} +(9.39039 + 3.98287i) q^{35} +(-2.74593 - 4.75609i) q^{37} +(-0.320254 - 0.184899i) q^{39} -8.45017i q^{41} +6.30324i q^{43} +(-3.33878 - 1.92764i) q^{45} +(-0.712838 - 1.23467i) q^{47} +(-1.92568 + 6.72992i) q^{49} +(3.89853 - 2.25082i) q^{51} +(-1.27259 + 2.20420i) q^{53} -5.25188 q^{55} -0.0661849 q^{57} +(-1.71879 + 2.97703i) q^{59} +(-1.23998 + 0.715904i) q^{61} +(1.03309 - 2.43572i) q^{63} +(-0.712838 - 1.23467i) q^{65} +(-8.45877 - 4.88367i) q^{67} -3.20894i q^{69} +12.9518i q^{71} +(-1.56024 - 0.900803i) q^{73} +(-4.93162 - 8.54182i) q^{75} +(-0.440245 - 3.57719i) q^{77} +(10.8156 - 6.24438i) q^{79} +(-0.500000 + 0.866025i) q^{81} -12.2889 q^{83} +17.3551 q^{85} +(1.55975 - 2.70157i) q^{87} +(1.11951 - 0.646349i) q^{89} +(0.781213 - 0.589031i) q^{91} +(3.01852 + 5.22824i) q^{93} +(-0.220977 - 0.127581i) q^{95} +2.88422i q^{97} +1.36225i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{3} + 2 q^{7} - 4 q^{9}+O(q^{10}) $ 8 * q + 4 * q^3 + 2 * q^7 - 4 * q^9	$ 8 q + 4 q^{3} + 2 q^{7} - 4 q^{9} - 6 q^{11} + 6 q^{19} + 4 q^{21} + 2 q^{25} - 8 q^{27} + 16 q^{29} + 6 q^{31} - 6 q^{33} + 12 q^{35} - 6 q^{37} - 6 q^{39} + 4 q^{47} + 4 q^{49} + 4 q^{53} - 8 q^{55} + 12 q^{57} + 14 q^{59} - 12 q^{61} + 2 q^{63} + 4 q^{65} - 42 q^{67} - 18 q^{73} - 2 q^{75} - 8 q^{77} - 6 q^{79} - 4 q^{81} - 4 q^{83} + 32 q^{85} + 8 q^{87} + 34 q^{91} - 6 q^{93} - 24 q^{95}+O(q^{100}) $ 8 * q + 4 * q^3 + 2 * q^7 - 4 * q^9 - 6 * q^11 + 6 * q^19 + 4 * q^21 + 2 * q^25 - 8 * q^27 + 16 * q^29 + 6 * q^31 - 6 * q^33 + 12 * q^35 - 6 * q^37 - 6 * q^39 + 4 * q^47 + 4 * q^49 + 4 * q^53 - 8 * q^55 + 12 * q^57 + 14 * q^59 - 12 * q^61 + 2 * q^63 + 4 * q^65 - 42 * q^67 - 18 * q^73 - 2 * q^75 - 8 * q^77 - 6 * q^79 - 4 * q^81 - 4 * q^83 + 32 * q^85 + 8 * q^87 + 34 * q^91 - 6 * q^93 - 24 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times$.

$n$	$127$	$449$	$577$	$1093$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$		0			0
$5$	3.33878	−	1.92764i	1.49315	−	0.862069i	0.493178	−	0.869929i	$-0.335835\pi$
$5$	3.33878	−	1.92764i	1.49315	−	0.862069i	0.999969	+	0.00785986i	$0.00250190\pi$
$6$		0			0
$7$	1.59285	+	2.11254i	0.602040	+	0.798466i
$7$	1.59285	+	2.11254i	0.602040	+	0.798466i
$8$		0			0
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	−1.17975	−	0.681127i	−0.355707	−	0.205367i	0.311489	−	0.950250i	$-0.399172\pi$
$11$	−1.17975	−	0.681127i	−0.355707	−	0.205367i	−0.667196	+	0.744882i	$0.732506\pi$
$12$		0			0
$13$		−	0.369798i		−	0.102563i	−0.998684	−	0.0512817i	$-0.983669\pi$
$13$		−	0.369798i		−	0.102563i	0.998684	−	0.0512817i	$-0.0163306\pi$
$14$		0			0
$15$		−	3.85529i		−	0.995431i
$16$		0			0
$17$	3.89853	+	2.25082i	0.945533	+	0.545904i	0.891690	−	0.452646i	$-0.149520\pi$
$17$	3.89853	+	2.25082i	0.945533	+	0.545904i	0.0538425	+	0.998549i	$0.482853\pi$
$18$		0			0
$19$	−0.0330925	−	0.0573178i	−0.00759193	−	0.0131496i	0.862204	−	0.506560i	$-0.169083\pi$
$19$	−0.0330925	−	0.0573178i	−0.00759193	−	0.0131496i	−0.869796	+	0.493411i	$0.835750\pi$
$20$		0			0
$21$	2.62594	−	0.323174i	0.573027	−	0.0705224i
$22$		0			0
$23$	2.77902	−	1.60447i	0.579466	−	0.334555i	−0.181455	−	0.983399i	$-0.558081\pi$
$23$	2.77902	−	1.60447i	0.579466	−	0.334555i	0.760921	+	0.648844i	$0.224747\pi$
$24$		0			0
$25$	4.93162	−	8.54182i	0.986325	−	1.70836i
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	3.11951			0.579278			0.289639	−	0.957136i	$-0.406465\pi$
$29$	3.11951			0.579278			0.289639	+	0.957136i	$0.406465\pi$
$30$		0			0
$31$	−3.01852	+	5.22824i	−0.542143	+	0.939019i	0.456638	+	0.889653i	$0.349054\pi$
$31$	−3.01852	+	5.22824i	−0.542143	+	0.939019i	−0.998781	+	0.0493663i	$0.984280\pi$
$32$		0			0
$33$	−1.17975	+	0.681127i	−0.205367	+	0.118569i
$34$		0			0
$35$	9.39039	+	3.98287i	1.58727	+	0.673228i
$36$		0			0
$37$	−2.74593	−	4.75609i	−0.451428	−	0.781897i	0.547047	−	0.837102i	$-0.315752\pi$
$37$	−2.74593	−	4.75609i	−0.451428	−	0.781897i	−0.998475	+	0.0552054i	$0.982419\pi$
$38$		0			0
$39$	−0.320254	−	0.184899i	−0.0512817	−	0.0296075i
$40$		0			0
$41$		−	8.45017i		−	1.31970i	−0.751399	−	0.659848i	$-0.770621\pi$
$41$		−	8.45017i		−	1.31970i	0.751399	−	0.659848i	$-0.229379\pi$
$42$		0			0
$43$			6.30324i			0.961236i	0.876930	+	0.480618i	$0.159588\pi$
$43$			6.30324i			0.961236i	−0.876930	+	0.480618i	$0.840412\pi$
$44$		0			0
$45$	−3.33878	−	1.92764i	−0.497716	−	0.287356i
$46$		0			0
$47$	−0.712838	−	1.23467i	−0.103978	−	0.180095i	0.809342	−	0.587338i	$-0.199824\pi$
$47$	−0.712838	−	1.23467i	−0.103978	−	0.180095i	−0.913320	+	0.407242i	$0.866491\pi$
$48$		0			0
$49$	−1.92568	+	6.72992i	−0.275097	+	0.961417i
$50$		0			0
$51$	3.89853	−	2.25082i	0.545904	−	0.315178i
$52$		0			0
$53$	−1.27259	+	2.20420i	−0.174804	+	0.302770i	−0.940093	−	0.340917i	$-0.889263\pi$
$53$	−1.27259	+	2.20420i	−0.174804	+	0.302770i	0.765289	+	0.643686i	$0.222596\pi$
$54$		0			0
$55$	−5.25188			−0.708163
$56$		0			0
$57$	−0.0661849			−0.00876641
$58$		0			0
$59$	−1.71879	+	2.97703i	−0.223767	+	0.387576i	−0.955949	−	0.293533i	$-0.905169\pi$
$59$	−1.71879	+	2.97703i	−0.223767	+	0.387576i	0.732182	+	0.681109i	$0.238502\pi$
$60$		0			0
$61$	−1.23998	+	0.715904i	−0.158763	+	0.0916621i	−0.577277	−	0.816549i	$-0.695885\pi$
$61$	−1.23998	+	0.715904i	−0.158763	+	0.0916621i	0.418513	+	0.908211i	$0.362551\pi$
$62$		0			0
$63$	1.03309	−	2.43572i	0.130157	−	0.306872i
$64$		0			0
$65$	−0.712838	−	1.23467i	−0.0884167	−	0.153142i
$66$		0			0
$67$	−8.45877	−	4.88367i	−1.03340	−	0.596636i	−0.115445	−	0.993314i	$-0.536830\pi$
$67$	−8.45877	−	4.88367i	−1.03340	−	0.596636i	−0.917958	+	0.396678i	$0.870163\pi$
$68$		0			0
$69$		−	3.20894i		−	0.386311i
$70$		0			0
$71$			12.9518i			1.53710i	0.639792	+	0.768549i	$0.279021\pi$
$71$			12.9518i			1.53710i	−0.639792	+	0.768549i	$0.720979\pi$
$72$		0			0
$73$	−1.56024	−	0.900803i	−0.182612	−	0.105431i	0.405907	−	0.913914i	$-0.366956\pi$
$73$	−1.56024	−	0.900803i	−0.182612	−	0.105431i	−0.588519	+	0.808483i	$0.700289\pi$
$74$		0			0
$75$	−4.93162	−	8.54182i	−0.569455	−	0.986325i
$76$		0			0
$77$	−0.440245	−	3.57719i	−0.0501706	−	0.407659i
$78$		0			0
$79$	10.8156	−	6.24438i	1.21685	−	0.702548i	0.252606	−	0.967569i	$-0.418712\pi$
$79$	10.8156	−	6.24438i	1.21685	−	0.702548i	0.964243	+	0.265021i	$0.0853790\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	−12.2889			−1.34888			−0.674442	−	0.738327i	$-0.735616\pi$
$83$	−12.2889			−1.34888			−0.674442	+	0.738327i	$0.735616\pi$
$84$		0			0
$85$	17.3551			1.88243
$86$		0			0
$87$	1.55975	−	2.70157i	0.167223	−	0.289639i
$88$		0			0
$89$	1.11951	−	0.646349i	0.118668	−	0.0685128i	−0.439491	−	0.898247i	$-0.644841\pi$
$89$	1.11951	−	0.646349i	0.118668	−	0.0685128i	0.558159	+	0.829734i	$0.311508\pi$
$90$		0			0
$91$	0.781213	−	0.589031i	0.0818934	−	0.0617472i
$92$		0			0
$93$	3.01852	+	5.22824i	0.313006	+	0.542143i
$94$		0			0
$95$	−0.220977	−	0.127581i	−0.0226717	−	0.0130895i
$96$		0			0
$97$			2.88422i			0.292848i	0.989222	+	0.146424i	$0.0467764\pi$
$97$			2.88422i			0.292848i	−0.989222	+	0.146424i	$0.953224\pi$
$98$		0			0
$99$			1.36225i			0.136912i
$100$		0			0
$101$	−5.35949	−	3.09430i	−0.533289	−	0.307895i	0.209066	−	0.977902i	$-0.432958\pi$
$101$	−5.35949	−	3.09430i	−0.533289	−	0.307895i	−0.742355	+	0.670007i	$0.766291\pi$
$102$		0			0
$103$	−8.89634	−	15.4089i	−0.876583	−	1.51829i	−0.855067	−	0.518517i	$-0.826484\pi$
$103$	−8.89634	−	15.4089i	−0.876583	−	1.51829i	−0.0215154	−	0.999769i	$-0.506849\pi$
$104$		0			0
$105$	8.14446	−	6.14088i	0.794818	−	0.599289i
$106$		0			0
$107$	5.27683	−	3.04658i	0.510131	−	0.294524i	−0.222757	−	0.974874i	$-0.571506\pi$
$107$	5.27683	−	3.04658i	0.510131	−	0.294524i	0.732887	+	0.680350i	$0.238172\pi$
$108$		0			0
$109$	3.93162	−	6.80977i	0.376581	−	0.652258i	−0.613981	−	0.789321i	$-0.710433\pi$
$109$	3.93162	−	6.80977i	0.376581	−	0.652258i	0.990562	+	0.137063i	$0.0437662\pi$
$110$		0			0
$111$	−5.49186			−0.521264
$112$		0			0
$113$	4.70669			0.442768			0.221384	−	0.975187i	$-0.428943\pi$
$113$	4.70669			0.442768			0.221384	+	0.975187i	$0.428943\pi$
$114$		0			0
$115$	6.18569	−	10.7139i	0.576819	−	0.999080i
$116$		0			0
$117$	−0.320254	+	0.184899i	−0.0296075	+	0.0170939i
$118$		0			0
$119$	1.45481	+	11.8210i	0.133363	+	1.08363i
$120$		0			0
$121$	−4.57213	−	7.91917i	−0.415648	−	0.719924i
$122$		0			0
$123$	−7.31806	−	4.22509i	−0.659848	−	0.380963i
$124$		0			0
$125$		−	18.7492i		−	1.67698i
$126$		0			0
$127$			2.70312i			0.239863i	0.992782	+	0.119931i	$0.0382675\pi$
$127$			2.70312i			0.239863i	−0.992782	+	0.119931i	$0.961733\pi$
$128$		0			0
$129$	5.45877	+	3.15162i	0.480618	+	0.277485i
$130$		0			0
$131$	3.88644	+	6.73151i	0.339560	+	0.588135i	0.984350	−	0.176225i	$-0.0563886\pi$
$131$	3.88644	+	6.73151i	0.339560	+	0.588135i	−0.644790	+	0.764360i	$0.723055\pi$
$132$		0			0
$133$	0.0683751	−	0.161208i	0.00592888	−	0.0139785i
$134$		0			0
$135$	−3.33878	+	1.92764i	−0.287356	+	0.165905i
$136$		0			0
$137$	−1.42568	+	2.46934i	−0.121804	+	0.210970i	−0.920479	−	0.390792i	$-0.872201\pi$
$137$	−1.42568	+	2.46934i	−0.121804	+	0.210970i	0.798675	+	0.601762i	$0.205535\pi$
$138$		0			0
$139$	7.15656			0.607011			0.303506	−	0.952830i	$-0.401843\pi$
$139$	7.15656			0.607011			0.303506	+	0.952830i	$0.401843\pi$
$140$		0			0
$141$	−1.42568			−0.120064
$142$		0			0
$143$	−0.251879	+	0.436267i	−0.0210632	+	0.0364825i
$144$		0			0
$145$	10.4153	−	6.01330i	0.864948	−	0.499378i
$146$		0			0
$147$	4.86544	+	5.03264i	0.401295	+	0.415085i
$148$		0			0
$149$	10.6776	+	18.4941i	0.874739	+	1.51509i	0.857040	+	0.515250i	$0.172301\pi$
$149$	10.6776	+	18.4941i	0.874739	+	1.51509i	0.0176994	+	0.999843i	$0.494366\pi$
$150$		0			0
$151$	−19.2373	−	11.1067i	−1.56551	−	0.903848i	−0.996682	−	0.0813911i	$-0.974064\pi$
$151$	−19.2373	−	11.1067i	−1.56551	−	0.903848i	−0.568828	−	0.822457i	$-0.692603\pi$
$152$		0			0
$153$		−	4.50164i		−	0.363936i
$154$		0			0
$155$			23.2746i			1.86946i
$156$		0			0
$157$	4.71898	+	2.72451i	0.376616	+	0.217439i	0.676345	−	0.736585i	$-0.263563\pi$
$157$	4.71898	+	2.72451i	0.376616	+	0.217439i	−0.299729	+	0.954024i	$0.596896\pi$
$158$		0			0
$159$	1.27259	+	2.20420i	0.100923	+	0.174804i
$160$		0			0
$161$	7.81607	+	3.31513i	0.615993	+	0.261269i
$162$		0			0
$163$	−4.11951	+	2.37840i	−0.322665	+	0.186291i	−0.652580	−	0.757720i	$-0.726313\pi$
$163$	−4.11951	+	2.37840i	−0.322665	+	0.186291i	0.329915	+	0.944011i	$0.392980\pi$
$164$		0			0
$165$	−2.62594	+	4.54826i	−0.204429	+	0.354082i
$166$		0			0
$167$	14.0618			1.08814			0.544068	−	0.839041i	$-0.316884\pi$
$167$	14.0618			1.08814			0.544068	+	0.839041i	$0.316884\pi$
$168$		0			0
$169$	12.8632			0.989481
$170$		0			0
$171$	−0.0330925	+	0.0573178i	−0.00253064	+	0.00438320i
$172$		0			0
$173$	−1.53904	+	0.888566i	−0.117011	+	0.0675564i	−0.557363	−	0.830269i	$-0.688187\pi$
$173$	−1.53904	+	0.888566i	−0.117011	+	0.0675564i	0.440352	+	0.897825i	$0.354854\pi$
$174$		0			0
$175$	25.9003	−	3.18755i	1.95788	−	0.240956i
$176$		0			0
$177$	1.71879	+	2.97703i	0.129192	+	0.223767i
$178$		0			0
$179$	2.81607	+	1.62586i	0.210483	+	0.121522i	0.601536	−	0.798846i	$-0.294556\pi$
$179$	2.81607	+	1.62586i	0.210483	+	0.121522i	−0.391053	+	0.920368i	$0.627889\pi$
$180$		0			0
$181$			23.5015i			1.74685i	0.486954	+	0.873427i	$0.338108\pi$
$181$			23.5015i			1.74685i	−0.486954	+	0.873427i	$0.661892\pi$
$182$		0			0
$183$			1.43181i			0.105842i
$184$		0			0
$185$	−18.3361	−	10.5864i	−1.34810	−	0.778324i
$186$		0			0
$187$	−3.06618	−	5.31079i	−0.224222	−	0.388363i
$188$		0			0
$189$	−1.59285	−	2.11254i	−0.115863	−	0.153665i
$190$		0			0
$191$	−20.6956	+	11.9486i	−1.49748	+	0.864571i	−0.999996	−	0.00290157i	$-0.999076\pi$
$191$	−20.6956	+	11.9486i	−1.49748	+	0.864571i	−0.497485	+	0.867473i	$0.665743\pi$
$192$		0			0
$193$	−9.93757	+	17.2124i	−0.715322	+	1.23897i	0.247513	+	0.968885i	$0.420387\pi$
$193$	−9.93757	+	17.2124i	−0.715322	+	1.23897i	−0.962835	+	0.270090i	$0.912947\pi$
$194$		0			0
$195$	−1.42568			−0.102095
$196$		0			0
$197$	−19.0198			−1.35511			−0.677553	−	0.735474i	$-0.736959\pi$
$197$	−19.0198			−1.35511			−0.677553	+	0.735474i	$0.736959\pi$
$198$		0			0
$199$	7.42568	−	12.8616i	0.526392	−	0.911738i	−0.473135	−	0.880990i	$-0.656878\pi$
$199$	7.42568	−	12.8616i	0.526392	−	0.911738i	0.999527	−	0.0307481i	$-0.00978898\pi$
$200$		0			0
$201$	−8.45877	+	4.88367i	−0.596636	+	0.344468i
$202$		0			0
$203$	4.96890	+	6.59010i	0.348748	+	0.462534i
$204$		0			0
$205$	−16.2889	−	28.2132i	−1.13767	−	1.97050i
$206$		0			0
$207$	−2.77902	−	1.60447i	−0.193155	−	0.111518i
$208$		0			0
$209$			0.0901606i			0.00623654i
$210$		0			0
$211$		−	19.6676i		−	1.35398i	−0.735994	−	0.676988i	$-0.763285\pi$
$211$		−	19.6676i		−	1.35398i	0.735994	−	0.676988i	$-0.236715\pi$
$212$		0			0
$213$	11.2166	+	6.47590i	0.768549	+	0.443722i
$214$		0			0
$215$	12.1504	+	21.0451i	0.828651	+	1.43527i
$216$		0			0
$217$	−15.8529	+	1.95102i	−1.07617	+	0.132444i
$218$		0			0
$219$	−1.56024	+	0.900803i	−0.105431	+	0.0608706i
$220$		0			0
$221$	0.832347	−	1.44167i	0.0559897	−	0.0969771i
$222$		0			0
$223$	−8.10323			−0.542633			−0.271316	−	0.962490i	$-0.587459\pi$
$223$	−8.10323			−0.542633			−0.271316	+	0.962490i	$0.587459\pi$
$224$		0			0
$225$	−9.86325			−0.657550
$226$		0			0
$227$	−6.04300	+	10.4668i	−0.401088	+	0.694704i	−0.993857	−	0.110668i	$-0.964701\pi$
$227$	−6.04300	+	10.4668i	−0.401088	+	0.694704i	0.592770	+	0.805372i	$0.298034\pi$
$228$		0			0
$229$	−20.5963	+	11.8913i	−1.36104	+	0.785799i	−0.989763	−	0.142722i	$-0.954414\pi$
$229$	−20.5963	+	11.8913i	−1.36104	+	0.785799i	−0.371280	+	0.928521i	$0.621081\pi$
$230$		0			0
$231$	−3.31806	−	1.40733i	−0.218313	−	0.0925957i
$232$		0			0
$233$	9.96472	+	17.2594i	0.652810	+	1.13070i	0.982438	+	0.186590i	$0.0597435\pi$
$233$	9.96472	+	17.2594i	0.652810	+	1.13070i	−0.329628	+	0.944111i	$0.606923\pi$
$234$		0			0
$235$	−4.76002	−	2.74820i	−0.310509	−	0.179273i
$236$		0			0
$237$		−	12.4888i		−	0.811233i
$238$		0			0
$239$			9.60993i			0.621615i	0.950473	+	0.310807i	$0.100599\pi$
$239$			9.60993i			0.621615i	−0.950473	+	0.310807i	$0.899401\pi$
$240$		0			0
$241$	−9.01386	−	5.20415i	−0.580634	−	0.335229i	0.180752	−	0.983529i	$-0.442147\pi$
$241$	−9.01386	−	5.20415i	−0.580634	−	0.335229i	−0.761385	+	0.648300i	$0.775480\pi$
$242$		0			0
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$		0			0
$245$	6.54348	+	26.1817i	0.418047	+	1.67269i
$246$		0			0
$247$	−0.0211960	+	0.0122375i	−0.00134867	+	0.000778654i
$248$		0			0
$249$	−6.14446	+	10.6425i	−0.389390	+	0.674442i
$250$		0			0
$251$	20.6860			1.30569			0.652846	−	0.757491i	$-0.273575\pi$
$251$	20.6860			1.30569			0.652846	+	0.757491i	$0.273575\pi$
$252$		0			0
$253$	−4.37139			−0.274827
$254$		0			0
$255$	8.67756	−	15.0300i	0.543410	−	0.941213i
$256$		0			0
$257$	−15.3732	+	8.87569i	−0.958951	+	0.553651i	−0.895850	−	0.444357i	$-0.853432\pi$
$257$	−15.3732	+	8.87569i	−0.958951	+	0.553651i	−0.0631009	+	0.998007i	$0.520099\pi$
$258$		0			0
$259$	5.67360	−	13.3766i	0.352540	−	0.831183i
$260$		0			0
$261$	−1.55975	−	2.70157i	−0.0965464	−	0.167223i
$262$		0			0
$263$	−1.80241	−	1.04062i	−0.111141	−	0.0641675i	0.443399	−	0.896324i	$-0.353773\pi$
$263$	−1.80241	−	1.04062i	−0.111141	−	0.0641675i	−0.554540	+	0.832157i	$0.687106\pi$
$264$		0			0
$265$			9.81243i			0.602773i
$266$		0			0
$267$		−	1.29270i		−	0.0791118i
$268$		0			0
$269$	−3.08075	−	1.77867i	−0.187837	−	0.108448i	0.403133	−	0.915142i	$-0.367921\pi$
$269$	−3.08075	−	1.77867i	−0.187837	−	0.108448i	−0.590970	+	0.806694i	$0.701255\pi$
$270$		0			0
$271$	6.18399	+	10.7110i	0.375650	+	0.650646i	0.990424	−	0.138058i	$-0.0440860\pi$
$271$	6.18399	+	10.7110i	0.375650	+	0.650646i	−0.614774	+	0.788704i	$0.710753\pi$
$272$		0			0
$273$	−0.119509	−	0.971066i	−0.00723302	−	0.0587716i
$274$		0			0
$275$	−11.6361	+	6.71812i	−0.701685	+	0.405118i
$276$		0			0
$277$	−5.93162	+	10.2739i	−0.356397	+	0.617297i	−0.987356	−	0.158519i	$-0.949328\pi$
$277$	−5.93162	+	10.2739i	−0.356397	+	0.617297i	0.630959	+	0.775816i	$0.282662\pi$
$278$		0			0
$279$	6.03705			0.361429
$280$		0			0
$281$	−19.3428			−1.15390			−0.576948	−	0.816781i	$-0.695756\pi$
$281$	−19.3428			−1.15390			−0.576948	+	0.816781i	$0.695756\pi$
$282$		0			0
$283$	12.4707	−	21.5998i	0.741304	−	1.28398i	−0.210598	−	0.977573i	$-0.567541\pi$
$283$	12.4707	−	21.5998i	0.741304	−	1.28398i	0.951902	−	0.306404i	$-0.0991257\pi$
$284$		0			0
$285$	−0.220977	+	0.127581i	−0.0130895	+	0.00755725i
$286$		0			0
$287$	17.8514	−	13.4598i	1.05373	−	0.794509i
$288$		0			0
$289$	1.63237	+	2.82735i	0.0960218	+	0.166315i
$290$		0			0
$291$	2.49781	+	1.44211i	0.146424	+	0.0845381i
$292$		0			0
$293$			6.88234i			0.402071i	0.979584	+	0.201035i	$0.0644306\pi$
$293$			6.88234i			0.402071i	−0.979584	+	0.201035i	$0.935569\pi$
$294$		0			0
$295$			13.2528i			0.771610i
$296$		0			0
$297$	1.17975	+	0.681127i	0.0684558	+	0.0395230i
$298$		0			0
$299$	−0.593329	−	1.02768i	−0.0343131	−	0.0594321i
$300$		0			0
$301$	−13.3159	+	10.0401i	−0.767514	+	0.578702i
$302$		0			0
$303$	−5.35949	+	3.09430i	−0.307895	+	0.177763i
$304$		0			0
$305$	−2.76002	+	4.78049i	−0.158038	+	0.273730i
$306$		0			0
$307$	−17.4213			−0.994286			−0.497143	−	0.867669i	$-0.665618\pi$
$307$	−17.4213			−0.994286			−0.497143	+	0.867669i	$0.665618\pi$
$308$		0			0
$309$	−17.7927			−1.01219
$310$		0			0
$311$	12.5580	−	21.7512i	0.712101	−	1.23340i	−0.251965	−	0.967736i	$-0.581077\pi$
$311$	12.5580	−	21.7512i	0.712101	−	1.23340i	0.964067	−	0.265660i	$-0.0855898\pi$
$312$		0			0
$313$	−19.1361	+	11.0482i	−1.08164	+	0.624484i	−0.931338	−	0.364156i	$-0.881357\pi$
$313$	−19.1361	+	11.0482i	−1.08164	+	0.624484i	−0.150300	+	0.988640i	$0.548024\pi$
$314$		0			0
$315$	−1.24593	−	10.1238i	−0.0702002	−	0.570409i
$316$		0			0
$317$	−0.811634	−	1.40579i	−0.0455859	−	0.0789571i	0.842332	−	0.538959i	$-0.181182\pi$
$317$	−0.811634	−	1.40579i	−0.0455859	−	0.0789571i	−0.887918	+	0.460002i	$0.847849\pi$
$318$		0			0
$319$	−3.68023	−	2.12478i	−0.206053	−	0.118965i
$320$		0			0
$321$		−	6.09316i		−	0.340087i
$322$		0			0
$323$		−	0.297941i		−	0.0165779i
$324$		0			0
$325$	−3.15875	−	1.82370i	−0.175216	−	0.101161i
$326$		0			0
$327$	−3.93162	−	6.80977i	−0.217419	−	0.376581i
$328$		0			0
$329$	1.47286	−	3.47255i	0.0812012	−	0.191448i
$330$		0			0
$331$	−23.0949	+	13.3338i	−1.26941	+	0.732894i	−0.974876	−	0.222747i	$-0.928498\pi$
$331$	−23.0949	+	13.3338i	−1.26941	+	0.732894i	−0.294534	+	0.955641i	$0.595164\pi$
$332$		0			0
$333$	−2.74593	+	4.75609i	−0.150476	+	0.260632i
$334$		0			0
$335$	−37.6559			−2.05736
$336$		0			0
$337$	29.8426			1.62563			0.812815	−	0.582522i	$-0.197934\pi$
$337$	29.8426			1.62563			0.812815	+	0.582522i	$0.197934\pi$
$338$		0			0
$339$	2.35335	−	4.07612i	0.127816	−	0.221384i
$340$		0			0
$341$	7.12218	−	4.11199i	0.385688	−	0.222677i
$342$		0			0
$343$	−17.2845	+	6.65165i	−0.933278	+	0.359155i
$344$		0			0
$345$	−6.18569	−	10.7139i	−0.333027	−	0.576819i
$346$		0			0
$347$	−0.820451	−	0.473688i	−0.0440441	−	0.0254289i	0.477816	−	0.878460i	$-0.341428\pi$
$347$	−0.820451	−	0.473688i	−0.0440441	−	0.0254289i	−0.521860	+	0.853031i	$0.674762\pi$
$348$		0			0
$349$			6.41788i			0.343541i	0.985137	+	0.171771i	$0.0549488\pi$
$349$			6.41788i			0.343541i	−0.985137	+	0.171771i	$0.945051\pi$
$350$		0			0
$351$			0.369798i			0.0197383i
$352$		0			0
$353$	12.0146	+	6.93665i	0.639474	+	0.369200i	0.784412	−	0.620240i	$-0.212965\pi$
$353$	12.0146	+	6.93665i	0.639474	+	0.369200i	−0.144938	+	0.989441i	$0.546298\pi$
$354$		0			0
$355$	24.9665	+	43.2432i	1.32508	+	2.29511i
$356$		0			0
$357$	10.9647	+	4.65061i	0.580314	+	0.246136i
$358$		0			0
$359$	6.00000	−	3.46410i	0.316668	−	0.182828i	−0.333238	−	0.942843i	$-0.608141\pi$
$359$	6.00000	−	3.46410i	0.316668	−	0.182828i	0.649906	+	0.760014i	$0.274808\pi$
$360$		0			0
$361$	9.49781	−	16.4507i	0.499885	−	0.865826i
$362$		0			0
$363$	−9.14427			−0.479950
$364$		0			0
$365$	−6.94571			−0.363555
$366$		0			0
$367$	9.65903	−	16.7299i	0.504197	−	0.873295i	−0.495791	−	0.868442i	$-0.665122\pi$
$367$	9.65903	−	16.7299i	0.504197	−	0.873295i	0.999988	−	0.00485350i	$-0.00154492\pi$
$368$		0			0
$369$	−7.31806	+	4.22509i	−0.380963	+	0.219949i
$370$		0			0
$371$	−6.68350	+	0.822539i	−0.346990	+	0.0427041i
$372$		0			0
$373$	5.63832	+	9.76585i	0.291941	+	0.505657i	0.974269	−	0.225390i	$-0.0723656\pi$
$373$	5.63832	+	9.76585i	0.291941	+	0.505657i	−0.682328	+	0.731047i	$0.739032\pi$
$374$		0			0
$375$	−16.2373	−	9.37462i	−0.838491	−	0.484103i
$376$		0			0
$377$		−	1.15359i		−	0.0594128i
$378$		0			0
$379$			25.1457i			1.29165i	0.763486	+	0.645824i	$0.223486\pi$
$379$			25.1457i			1.29165i	−0.763486	+	0.645824i	$0.776514\pi$
$380$		0			0
$381$	2.34097	+	1.35156i	0.119931	+	0.0692424i
$382$		0			0
$383$	8.88226	+	15.3845i	0.453862	+	0.786112i	0.998622	−	0.0524799i	$-0.0167126\pi$
$383$	8.88226	+	15.3845i	0.453862	+	0.786112i	−0.544760	+	0.838592i	$0.683379\pi$
$384$		0			0
$385$	−8.36544	−	11.0948i	−0.426342	−	0.565444i
$386$		0			0
$387$	5.45877	−	3.15162i	0.277485	−	0.160206i
$388$		0			0
$389$	7.07233	−	12.2496i	0.358581	−	0.621081i	−0.629143	−	0.777290i	$-0.716594\pi$
$389$	7.07233	−	12.2496i	0.358581	−	0.621081i	0.987724	+	0.156209i	$0.0499272\pi$
$390$		0			0
$391$	14.4455			0.730539
$392$		0			0
$393$	7.77288			0.392090
$394$		0			0
$395$	24.0739	−	41.6972i	1.21129	−	2.09801i
$396$		0			0
$397$	10.9558	−	6.32534i	0.549856	−	0.317460i	−0.199208	−	0.979957i	$-0.563837\pi$
$397$	10.9558	−	6.32534i	0.549856	−	0.317460i	0.749064	+	0.662498i	$0.230503\pi$
$398$		0			0
$399$	−0.105422	−	0.139819i	−0.00527772	−	0.00699968i
$400$		0			0
$401$	12.3904	+	21.4608i	0.618747	+	1.07170i	0.989715	+	0.143055i	$0.0456926\pi$
$401$	12.3904	+	21.4608i	0.618747	+	1.07170i	−0.370968	+	0.928646i	$0.620974\pi$
$402$		0			0
$403$	1.93339	+	1.11624i	0.0963090	+	0.0556040i
$404$		0			0
$405$			3.85529i			0.191571i
$406$		0			0
$407$			7.48131i			0.370835i
$408$		0			0
$409$	−5.02003	−	2.89832i	−0.248225	−	0.143313i	0.370726	−	0.928742i	$-0.379109\pi$
$409$	−5.02003	−	2.89832i	−0.248225	−	0.143313i	−0.618951	+	0.785430i	$0.712442\pi$
$410$		0			0
$411$	1.42568	+	2.46934i	0.0703234	+	0.121804i
$412$		0			0
$413$	−9.02686	+	1.11094i	−0.444183	+	0.0546656i
$414$		0			0
$415$	−41.0300	+	23.6887i	−2.01408	+	1.16283i
$416$		0			0
$417$	3.57828	−	6.19776i	0.175229	−	0.303506i
$418$		0			0
$419$	−2.42966			−0.118697			−0.0593484	−	0.998237i	$-0.518902\pi$
$419$	−2.42966			−0.118697			−0.0593484	+	0.998237i	$0.518902\pi$
$420$		0			0
$421$	25.9373			1.26411			0.632054	−	0.774924i	$-0.282212\pi$
$421$	25.9373			1.26411			0.632054	+	0.774924i	$0.282212\pi$
$422$		0			0
$423$	−0.712838	+	1.23467i	−0.0346594	+	0.0600318i
$424$		0			0
$425$	38.4522	−	22.2004i	1.86521	−	1.07688i
$426$		0			0
$427$	−3.48748	−	1.47919i	−0.168771	−	0.0715830i
$428$		0			0
$429$	0.251879	+	0.436267i	0.0121608	+	0.0210632i
$430$		0			0
$431$	−12.7781	−	7.37742i	−0.615497	−	0.355358i	0.159616	−	0.987179i	$-0.448974\pi$
$431$	−12.7781	−	7.37742i	−0.615497	−	0.355358i	−0.775114	+	0.631821i	$0.782308\pi$
$432$		0			0
$433$			35.7396i			1.71754i	0.512364	+	0.858769i	$0.328770\pi$
$433$			35.7396i			1.71754i	−0.512364	+	0.858769i	$0.671230\pi$
$434$		0			0
$435$		−	12.0266i		−	0.576632i
$436$		0			0
$437$	−0.183929	−	0.106192i	−0.00879854	−	0.00507984i
$438$		0			0
$439$	9.91925	+	17.1806i	0.473420	+	0.819987i	0.999537	−	0.0304249i	$-0.00968604\pi$
$439$	9.91925	+	17.1806i	0.473420	+	0.819987i	−0.526117	+	0.850412i	$0.676353\pi$
$440$		0			0
$441$	6.79112	−	1.69727i	0.323387	−	0.0808225i
$442$		0			0
$443$	−16.4378	+	9.49035i	−0.780982	+	0.450900i	−0.836778	−	0.547542i	$-0.815564\pi$
$443$	−16.4378	+	9.49035i	−0.780982	+	0.450900i	0.0557962	+	0.998442i	$0.482230\pi$
$444$		0			0
$445$	2.49186	−	4.31603i	0.118126	−	0.204599i
$446$		0			0
$447$	21.3551			1.01006
$448$		0			0
$449$	−25.2845			−1.19325			−0.596626	−	0.802520i	$-0.703492\pi$
$449$	−25.2845			−1.19325			−0.596626	+	0.802520i	$0.703492\pi$
$450$		0			0
$451$	−5.75564	+	9.96906i	−0.271022	+	0.469425i
$452$		0			0
$453$	−19.2373	+	11.1067i	−0.903848	+	0.521837i
$454$		0			0
$455$	1.47286	−	3.47255i	0.0690485	−	0.162795i
$456$		0			0
$457$	−11.4837	−	19.8904i	−0.537186	−	0.930433i	−0.999054	−	0.0434847i	$-0.986154\pi$
$457$	−11.4837	−	19.8904i	−0.537186	−	0.930433i	0.461868	−	0.886949i	$-0.347179\pi$
$458$		0			0
$459$	−3.89853	−	2.25082i	−0.181968	−	0.105059i
$460$		0			0
$461$		−	2.95838i		−	0.137786i	−0.997624	−	0.0688928i	$-0.978053\pi$
$461$		−	2.95838i		−	0.137786i	0.997624	−	0.0688928i	$-0.0219466\pi$
$462$		0			0
$463$			3.30669i			0.153675i	0.997044	+	0.0768374i	$0.0244822\pi$
$463$			3.30669i			0.153675i	−0.997044	+	0.0768374i	$0.975518\pi$
$464$		0			0
$465$	20.1564	+	11.6373i	0.934729	+	0.539666i
$466$		0			0
$467$	5.95282	+	10.3106i	0.275464	+	0.477117i	0.970252	−	0.242097i	$-0.0778353\pi$
$467$	5.95282	+	10.3106i	0.275464	+	0.477117i	−0.694788	+	0.719214i	$0.744502\pi$
$468$		0			0
$469$	−3.15656	−	25.6485i	−0.145756	−	1.18434i
$470$		0			0
$471$	4.71898	−	2.72451i	0.217439	−	0.125539i
$472$		0			0
$473$	4.29331	−	7.43623i	0.197406	−	0.341918i
$474$		0			0
$475$	−0.652798			−0.0299524
$476$		0			0
$477$	2.54519			0.116536
$478$		0			0
$479$	5.95186	−	10.3089i	0.271947	−	0.471026i	−0.697413	−	0.716669i	$-0.745666\pi$
$479$	5.95186	−	10.3089i	0.271947	−	0.471026i	0.969360	+	0.245643i	$0.0789990\pi$
$480$		0			0
$481$	−1.75879	+	1.01544i	−0.0801940	+	0.0463000i
$482$		0			0
$483$	6.77902	−	5.11135i	0.308456	−	0.232574i
$484$		0			0
$485$	5.55975	+	9.62978i	0.252455	+	0.437266i
$486$		0			0
$487$	−6.50151	−	3.75365i	−0.294612	−	0.170094i	0.345408	−	0.938453i	$-0.387740\pi$
$487$	−6.50151	−	3.75365i	−0.294612	−	0.170094i	−0.640020	+	0.768358i	$0.721074\pi$
$488$		0			0
$489$			4.75680i			0.215110i
$490$		0			0
$491$			22.0031i			0.992988i	0.868040	+	0.496494i	$0.165380\pi$
$491$			22.0031i			0.992988i	−0.868040	+	0.496494i	$0.834620\pi$
$492$		0			0
$493$	12.1615	+	7.02145i	0.547727	+	0.316230i
$494$		0			0
$495$	2.62594	+	4.54826i	0.118027	+	0.204429i
$496$		0			0
$497$	−27.3613	+	20.6303i	−1.22732	+	0.925393i
$498$		0			0
$499$	1.22277	−	0.705968i	0.0547389	−	0.0316035i	−0.472381	−	0.881395i	$-0.656605\pi$
$499$	1.22277	−	0.705968i	0.0547389	−	0.0316035i	0.527120	+	0.849791i	$0.323272\pi$
$500$		0			0
$501$	7.03090	−	12.1779i	0.314118	−	0.544068i
$502$		0			0
$503$	26.2303			1.16955			0.584775	−	0.811196i	$-0.301183\pi$
$503$	26.2303			1.16955			0.584775	+	0.811196i	$0.301183\pi$
$504$		0			0
$505$	−23.8589			−1.06171
$506$		0			0
$507$	6.43162	−	11.1399i	0.285638	−	0.494740i
$508$		0			0
$509$	4.38419	−	2.53121i	0.194326	−	0.112194i	−0.399680	−	0.916655i	$-0.630879\pi$
$509$	4.38419	−	2.53121i	0.194326	−	0.112194i	0.594006	+	0.804461i	$0.297545\pi$
$510$		0			0
$511$	−0.582233	−	4.73091i	−0.0257565	−	0.209283i
$512$		0			0
$513$	0.0330925	+	0.0573178i	0.00146107	+	0.00253064i
$514$		0			0
$515$	−59.4058	−	34.2980i	−2.61773	−	1.51135i
$516$		0			0
$517$			1.94213i			0.0854149i
$518$		0			0
$519$			1.77713i			0.0780074i
$520$		0			0
$521$	−8.60044	−	4.96547i	−0.376792	−	0.217541i	0.299630	−	0.954056i	$-0.403137\pi$
$521$	−8.60044	−	4.96547i	−0.376792	−	0.217541i	−0.676422	+	0.736515i	$0.736470\pi$
$522$		0			0
$523$	−15.6686	−	27.1389i	−0.685142	−	1.18670i	−0.973392	−	0.229146i	$-0.926407\pi$
$523$	−15.6686	−	27.1389i	−0.685142	−	1.18670i	0.288250	−	0.957555i	$-0.406927\pi$
$524$		0			0
$525$	10.1896	−	24.0241i	0.444713	−	1.04850i
$526$		0			0
$527$	−23.5356	+	13.5883i	−1.02523	+	0.591916i
$528$		0			0
$529$	−6.35135	+	11.0009i	−0.276146	+	0.478299i
$530$		0			0
$531$	3.43757			0.149178
$532$		0			0
$533$	−3.12485			−0.135352
$534$		0			0
$535$	11.7454	−	20.3437i	0.507800	−	0.879535i
$536$		0			0
$537$	2.81607	−	1.62586i	0.121522	−	0.0701610i
$538$		0			0
$539$	6.85573	−	6.62796i	0.295297	−	0.285486i
$540$		0			0
$541$	−2.09313	−	3.62541i	−0.0899908	−	0.155869i	0.817516	−	0.575906i	$-0.195350\pi$
$541$	−2.09313	−	3.62541i	−0.0899908	−	0.155869i	−0.907507	+	0.420037i	$0.862017\pi$
$542$		0			0
$543$	20.3529	+	11.7508i	0.873427	+	0.504274i
$544$		0			0
$545$		−	30.3151i		−	1.29856i
$546$		0			0
$547$			12.4674i			0.533067i	0.963826	+	0.266533i	$0.0858782\pi$
$547$			12.4674i			0.533067i	−0.963826	+	0.266533i	$0.914122\pi$
$548$		0			0
$549$	1.23998	+	0.715904i	0.0529212	+	0.0305540i
$550$		0			0
$551$	−0.103232	−	0.178803i	−0.00439784	−	0.00761728i
$552$		0			0
$553$	30.4191	+	12.9020i	1.29355	+	0.548651i
$554$		0			0
$555$	−18.3361	+	10.5864i	−0.778324	+	0.449366i
$556$		0			0
$557$	−18.2744	+	31.6521i	−0.774309	+	1.34114i	0.160872	+	0.986975i	$0.448569\pi$
$557$	−18.2744	+	31.6521i	−0.774309	+	1.34114i	−0.935182	+	0.354168i	$0.884764\pi$
$558$		0			0
$559$	2.33092			0.0985876
$560$		0			0
$561$	−6.13237			−0.258909
$562$		0			0
$563$	21.3672	−	37.0091i	0.900520	−	1.55975i	0.0737002	−	0.997280i	$-0.476519\pi$
$563$	21.3672	−	37.0091i	0.900520	−	1.55975i	0.826820	−	0.562466i	$-0.190147\pi$
$564$		0			0
$565$	15.7146	−	9.07283i	0.661118	−	0.381697i
$566$		0			0
$567$	−2.62594	+	0.323174i	−0.110279	+	0.0135721i
$568$		0			0
$569$	−10.7265	−	18.5788i	−0.449678	−	0.778866i	0.548687	−	0.836028i	$-0.315128\pi$
$569$	−10.7265	−	18.5788i	−0.449678	−	0.778866i	−0.998365	+	0.0571625i	$0.981795\pi$
$570$		0			0
$571$	−18.3349	−	10.5856i	−0.767291	−	0.442996i	0.0646165	−	0.997910i	$-0.479418\pi$
$571$	−18.3349	−	10.5856i	−0.767291	−	0.442996i	−0.831907	+	0.554915i	$0.812751\pi$
$572$		0			0
$573$			23.8972i			0.998321i
$574$		0			0
$575$		−	31.6506i		−	1.31992i
$576$		0			0
$577$	4.10289	+	2.36880i	0.170806	+	0.0986146i	0.582966	−	0.812497i	$-0.301892\pi$
$577$	4.10289	+	2.36880i	0.170806	+	0.0986146i	−0.412160	+	0.911111i	$0.635226\pi$
$578$		0			0
$579$	9.93757	+	17.2124i	0.412991	+	0.715322i
$580$		0			0
$581$	−19.5744	−	25.9609i	−0.812082	−	1.07704i
$582$		0			0
$583$	3.00267	−	1.73359i	0.124358	−	0.0717981i
$584$		0			0
$585$	−0.712838	+	1.23467i	−0.0294722	+	0.0510474i
$586$		0			0
$587$	29.8450			1.23184			0.615918	−	0.787810i	$-0.288785\pi$
$587$	29.8450			1.23184			0.615918	+	0.787810i	$0.288785\pi$
$588$		0			0
$589$	0.399562			0.0164636
$590$		0			0
$591$	−9.50990	+	16.4716i	−0.391185	+	0.677553i
$592$		0			0
$593$	22.9586	−	13.2551i	0.942796	−	0.544323i	0.0519600	−	0.998649i	$-0.483453\pi$
$593$	22.9586	−	13.2551i	0.942796	−	0.544323i	0.890836	+	0.454326i	$0.150120\pi$
$594$		0			0
$595$	27.6440	+	36.6634i	1.13330	+	1.50305i
$596$		0			0
$597$	−7.42568	−	12.8616i	−0.303913	−	0.526392i
$598$		0			0
$599$	−18.0000	−	10.3923i	−0.735460	−	0.424618i	0.0849563	−	0.996385i	$-0.472925\pi$
$599$	−18.0000	−	10.3923i	−0.735460	−	0.424618i	−0.820416	+	0.571767i	$0.806258\pi$
$600$		0			0
$601$		−	10.8255i		−	0.441581i	−0.975321	−	0.220790i	$-0.929136\pi$
$601$		−	10.8255i		−	0.441581i	0.975321	−	0.220790i	$-0.0708637\pi$
$602$		0			0
$603$			9.76735i			0.397757i
$604$		0			0
$605$	−30.5307	−	17.6269i	−1.24125	−	0.716635i
$606$		0			0
$607$	−6.95330	−	12.0435i	−0.282226	−	0.488830i	0.689707	−	0.724089i	$-0.257739\pi$
$607$	−6.95330	−	12.0435i	−0.282226	−	0.488830i	−0.971933	+	0.235259i	$0.924406\pi$
$608$		0			0
$609$	8.19164	−	1.00815i	0.331942	−	0.0408521i
$610$		0			0
$611$	−0.456579	+	0.263606i	−0.0184712	+	0.0106644i
$612$		0			0
$613$	0.322444	−	0.558490i	0.0130234	−	0.0225572i	−0.859440	−	0.511236i	$-0.829188\pi$
$613$	0.322444	−	0.558490i	0.0130234	−	0.0225572i	0.872464	+	0.488679i	$0.162521\pi$
$614$		0			0
$615$	−32.5779			−1.31367
$616$		0			0
$617$	12.3626			0.497701			0.248850	−	0.968542i	$-0.419947\pi$
$617$	12.3626			0.497701			0.248850	+	0.968542i	$0.419947\pi$
$618$		0			0
$619$	5.69875	−	9.87053i	0.229052	−	0.396730i	−0.728475	−	0.685072i	$-0.759771\pi$
$619$	5.69875	−	9.87053i	0.229052	−	0.396730i	0.957527	+	0.288342i	$0.0931040\pi$
$620$		0			0
$621$	−2.77902	+	1.60447i	−0.111518	+	0.0643852i
$622$		0			0
$623$	3.14865	+	1.33548i	0.126148	+	0.0535047i
$624$		0			0
$625$	−11.4837	−	19.8904i	−0.459349	−	0.795616i
$626$		0			0
$627$	0.0780814	+	0.0450803i	0.00311827	+	0.00180033i
$628$		0			0
$629$		−	24.7224i		−	0.985745i
$630$		0			0
$631$			10.8050i			0.430140i	0.976599	+	0.215070i	$0.0689979\pi$
$631$			10.8050i			0.430140i	−0.976599	+	0.215070i	$0.931002\pi$
$632$		0			0
$633$	−17.0327	−	9.83381i	−0.676988	−	0.390859i
$634$		0			0
$635$	5.21065	+	9.02511i	0.206778	+	0.358150i
$636$		0			0
$637$	2.48871	+	0.712111i	0.0986062	+	0.0282149i
$638$		0			0
$639$	11.2166	−	6.47590i	0.443722	−	0.256183i
$640$		0			0
$641$	−1.12662	+	1.95136i	−0.0444988	+	0.0770741i	−0.887417	−	0.460968i	$-0.847502\pi$
$641$	−1.12662	+	1.95136i	−0.0444988	+	0.0770741i	0.842918	+	0.538042i	$0.180836\pi$
$642$		0			0
$643$	22.0574			0.869860			0.434930	−	0.900464i	$-0.356773\pi$
$643$	22.0574			0.869860			0.434930	+	0.900464i	$0.356773\pi$
$644$		0			0
$645$	24.3008			0.956844
$646$		0			0
$647$	−2.26417	+	3.92166i	−0.0890137	+	0.154176i	−0.907094	−	0.420927i	$-0.861705\pi$
$647$	−2.26417	+	3.92166i	−0.0890137	+	0.154176i	0.818081	+	0.575103i	$0.195038\pi$
$648$		0			0
$649$	4.05546	−	2.34142i	0.159191	−	0.0919089i
$650$		0			0
$651$	−6.23683	+	14.7045i	−0.244441	+	0.576316i
$652$		0			0
$653$	20.6749	+	35.8099i	0.809071	+	1.40135i	0.913508	+	0.406820i	$0.133362\pi$
$653$	20.6749	+	35.8099i	0.809071	+	1.40135i	−0.104438	+	0.994531i	$0.533304\pi$
$654$		0			0
$655$	25.9519	+	14.9833i	1.01403	+	0.585448i
$656$		0			0
$657$			1.80161i			0.0702874i
$658$		0			0
$659$		−	10.6413i		−	0.414526i	−0.978285	−	0.207263i	$-0.933544\pi$
$659$		−	10.6413i		−	0.414526i	0.978285	−	0.207263i	$-0.0664556\pi$
$660$		0			0
$661$	−41.7871	−	24.1258i	−1.62533	−	0.938384i	−0.985462	−	0.169899i	$-0.945656\pi$
$661$	−41.7871	−	24.1258i	−1.62533	−	0.938384i	−0.639867	−	0.768485i	$-0.721011\pi$
$662$		0			0
$663$	−0.832347	−	1.44167i	−0.0323257	−	0.0559897i
$664$		0			0
$665$	−0.0824618	−	0.670040i	−0.00319773	−	0.0259830i
$666$		0			0
$667$	8.66919	−	5.00516i	0.335672	−	0.193801i
$668$		0			0
$669$	−4.05162	+	7.01760i	−0.156645	+	0.271316i
$670$		0			0
$671$	1.95049			0.0752977
$672$		0			0
$673$	−0.148647			−0.00572991			−0.00286496	−	0.999996i	$-0.500912\pi$
$673$	−0.148647			−0.00572991			−0.00286496	+	0.999996i	$0.500912\pi$
$674$		0			0
$675$	−4.93162	+	8.54182i	−0.189818	+	0.328775i
$676$		0			0
$677$	34.3935	−	19.8571i	1.32185	−	0.763170i	0.337825	−	0.941209i	$-0.390309\pi$
$677$	34.3935	−	19.8571i	1.32185	−	0.763170i	0.984023	+	0.178039i	$0.0569754\pi$
$678$		0			0
$679$	−6.09304	+	4.59412i	−0.233830	+	0.176306i
$680$		0			0
$681$	6.04300	+	10.4668i	0.231568	+	0.401088i
$682$		0			0
$683$	36.9070	+	21.3083i	1.41221	+	0.815339i	0.995596	−	0.0937450i	$-0.0298838\pi$
$683$	36.9070	+	21.3083i	1.41221	+	0.815339i	0.416613	+	0.909084i	$0.363217\pi$
$684$		0			0
$685$			10.9928i			0.420013i
$686$		0			0
$687$			23.7826i			0.907362i
$688$		0			0
$689$	0.815106	+	0.470602i	0.0310531	+	0.0179285i
$690$		0			0
$691$	2.22317	+	3.85064i	0.0845733	+	0.146485i	0.905209	−	0.424966i	$-0.139714\pi$
$691$	2.22317	+	3.85064i	0.0845733	+	0.146485i	−0.820636	+	0.571451i	$0.806381\pi$
$692$		0			0
$693$	−2.87782	+	2.16986i	−0.109319	+	0.0824262i
$694$		0			0
$695$	23.8942	−	13.7953i	0.906357	−	0.523285i
$696$		0			0
$697$	19.0198	−	32.9433i	0.720427	−	1.24782i
$698$		0			0
$699$	19.9294			0.753800
$700$		0			0
$701$	24.9907			0.943885			0.471942	−	0.881629i	$-0.343553\pi$
$701$	24.9907			0.943885			0.471942	+	0.881629i	$0.343553\pi$
$702$		0			0
$703$	−0.181739	+	0.314782i	−0.00685442	+	0.0118722i
$704$		0			0
$705$	−4.76002	+	2.74820i	−0.179273	+	0.103503i
$706$		0			0
$707$	−2.00000	−	16.2509i	−0.0752177	−	0.611178i
$708$		0			0
$709$	9.07409	+	15.7168i	0.340785	+	0.590257i	0.984579	−	0.174942i	$-0.0559739\pi$
$709$	9.07409	+	15.7168i	0.340785	+	0.590257i	−0.643794	+	0.765199i	$0.722641\pi$
$710$		0			0
$711$	−10.8156	−	6.24438i	−0.405616	−	0.234183i
$712$		0			0
$713$			19.3725i			0.725507i
$714$		0			0
$715$			1.94213i			0.0726316i
$716$		0			0
$717$	8.32244	+	4.80497i	0.310807	+	0.179445i
$718$		0			0
$719$	−20.5818	−	35.6488i	−0.767573	−	1.32948i	−0.938875	−	0.344257i	$-0.888131\pi$
$719$	−20.5818	−	35.6488i	−0.767573	−	1.32948i	0.171302	−	0.985219i	$-0.445203\pi$
$720$		0			0
$721$	18.3815	−	43.3380i	0.684562	−	1.61399i
$722$		0			0
$723$	−9.01386	+	5.20415i	−0.335229	+	0.193545i
$724$		0			0
$725$	15.3842	−	26.6463i	0.571357	−	0.989619i
$726$		0			0
$727$	−5.77231			−0.214083			−0.107042	−	0.994255i	$-0.534138\pi$
$727$	−5.77231			−0.214083			−0.107042	+	0.994255i	$0.534138\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−14.1875	+	24.5734i	−0.524742	+	0.908880i
$732$		0			0
$733$	6.63928	−	3.83319i	0.245227	−	0.141582i	−0.372350	−	0.928093i	$-0.621448\pi$
$733$	6.63928	−	3.83319i	0.245227	−	0.141582i	0.617577	+	0.786510i	$0.288114\pi$
$734$		0			0
$735$	25.9458	+	7.42404i	0.957024	+	0.273840i
$736$		0			0
$737$	6.65280	+	11.5230i	0.245059	+	0.424455i
$738$		0			0
$739$	−17.3753	−	10.0317i	−0.639162	−	0.369021i	0.145129	−	0.989413i	$-0.453640\pi$
$739$	−17.3753	−	10.0317i	−0.639162	−	0.369021i	−0.784292	+	0.620392i	$0.786973\pi$
$740$		0			0
$741$			0.0244750i			0.000899113i
$742$		0			0
$743$			8.26368i			0.303165i	0.988445	+	0.151583i	$0.0484369\pi$
$743$			8.26368i			0.303165i	−0.988445	+	0.151583i	$0.951563\pi$
$744$		0			0
$745$	71.3000	+	41.1651i	2.61223	+	1.50817i
$746$		0			0
$747$	6.14446	+	10.6425i	0.224814	+	0.389390i
$748$		0			0
$749$	14.8412	+	6.29480i	0.542286	+	0.230007i
$750$		0			0
$751$	23.4113	−	13.5165i	0.854289	−	0.493224i	−0.00780684	−	0.999970i	$-0.502485\pi$
$751$	23.4113	−	13.5165i	0.854289	−	0.493224i	0.862096	+	0.506746i	$0.169152\pi$
$752$		0			0
$753$	10.3430	−	17.9146i	0.376921	−	0.652846i
$754$		0			0
$755$	−85.6388			−3.11672
$756$		0			0
$757$	−21.9417			−0.797486			−0.398743	−	0.917063i	$-0.630553\pi$
$757$	−21.9417			−0.797486			−0.398743	+	0.917063i	$0.630553\pi$
$758$		0			0
$759$	−2.18569	+	3.78573i	−0.0793357	+	0.137413i
$760$		0			0
$761$	1.02680	−	0.592825i	0.0372216	−	0.0214899i	−0.481274	−	0.876570i	$-0.659826\pi$
$761$	1.02680	−	0.592825i	0.0372216	−	0.0214899i	0.518495	+	0.855080i	$0.326492\pi$
$762$		0			0
$763$	20.6484	−	2.54120i	0.747523	−	0.0919977i
$764$		0			0
$765$	−8.67756	−	15.0300i	−0.313738	−	0.543410i
$766$		0			0
$767$	1.10090	+	0.635603i	0.0397511	+	0.0229503i
$768$		0			0
$769$		−	19.0892i		−	0.688373i	−0.938901	−	0.344186i	$-0.888155\pi$
$769$		−	19.0892i		−	0.688373i	0.938901	−	0.344186i	$-0.111845\pi$
$770$		0			0
$771$			17.7514i			0.639301i
$772$		0			0
$773$	30.7887	+	17.7759i	1.10739	+	0.639353i	0.938153	−	0.346222i	$-0.112535\pi$
$773$	30.7887	+	17.7759i	1.10739	+	0.639353i	0.169240	+	0.985575i	$0.445869\pi$
$774$		0			0
$775$	29.7725	+	51.5674i	1.06946	+	1.85236i
$776$		0			0
$777$	−8.74770	−	11.6018i	−0.313822	−	0.416212i
$778$		0			0
$779$	−0.484346	+	0.279637i	−0.0173535	+	0.0100190i
$780$		0			0
$781$	8.82182	−	15.2798i	0.315670	−	0.546756i
$782$		0			0
$783$	−3.11951			−0.111482
$784$		0			0
$785$	21.0075			0.749790
$786$		0			0
$787$	21.3018	−	36.8958i	0.759327	−	1.31519i	−0.183868	−	0.982951i	$-0.558862\pi$
$787$	21.3018	−	36.8958i	0.759327	−	1.31519i	0.943194	−	0.332241i	$-0.107805\pi$
$788$		0			0
$789$	−1.80241	+	1.04062i	−0.0641675	+	0.0370471i
$790$		0			0
$791$	7.49704	+	9.94309i	0.266564	+	0.353536i
$792$		0			0
$793$	0.264740	+	0.458543i	0.00940118	+	0.0162833i
$794$		0			0
$795$	8.49781	+	4.90621i	0.301386	+	0.174005i
$796$		0			0
$797$		−	23.1179i		−	0.818879i	−0.912337	−	0.409440i	$-0.865724\pi$
$797$		−	23.1179i		−	0.818879i	0.912337	−	0.409440i	$-0.134276\pi$
$798$		0			0
$799$		−	6.41788i		−	0.227048i
$800$		0			0
$801$	−1.11951	−	0.646349i	−0.0395559	−	0.0228376i
$802$		0			0
$803$	1.22712	+	2.12544i	0.0433042	+	0.0750051i
$804$		0			0
$805$	32.4865	−	3.99812i	1.14500	−	0.140915i
$806$		0			0
$807$	−3.08075	+	1.77867i	−0.108448	+	0.0626123i
$808$		0			0
$809$	16.0852	−	27.8604i	0.565525	−	0.979518i	−0.431475	−	0.902125i	$-0.642007\pi$
$809$	16.0852	−	27.8604i	0.565525	−	0.979518i	0.997001	−	0.0773937i	$-0.0246598\pi$
$810$		0			0
$811$	−41.0797			−1.44250			−0.721251	−	0.692673i	$-0.756433\pi$
$811$	−41.0797			−1.44250			−0.721251	+	0.692673i	$0.756433\pi$
$812$		0			0
$813$	12.3680			0.433764
$814$		0			0
$815$	−9.16942	+	15.8819i	−0.321191	+	0.556319i
$816$		0			0
$817$	0.361288	−	0.208590i	0.0126399	−	0.00729764i
$818$		0			0
$819$	−0.900723	−	0.382035i	−0.0314738	−	0.0133494i
$820$		0			0
$821$	−14.6233	−	25.3283i	−0.510358	−	0.883965i	−0.999928	−	0.0120014i	$-0.996180\pi$
$821$	−14.6233	−	25.3283i	−0.510358	−	0.883965i	0.489570	−	0.871964i	$-0.337154\pi$
$822$		0			0
$823$	−17.0790	−	9.86059i	−0.595338	−	0.343719i	0.171867	−	0.985120i	$-0.445020\pi$
$823$	−17.0790	−	9.86059i	−0.595338	−	0.343719i	−0.767205	+	0.641401i	$0.778353\pi$
$824$		0			0
$825$			13.4362i			0.467790i
$826$		0			0
$827$		−	16.1125i		−	0.560286i	−0.959958	−	0.280143i	$-0.909618\pi$
$827$		−	16.1125i		−	0.560286i	0.959958	−	0.280143i	$-0.0903819\pi$
$828$		0			0
$829$	40.9056	+	23.6169i	1.42071	+	0.820248i	0.996360	−	0.0852497i	$-0.0271688\pi$
$829$	40.9056	+	23.6169i	1.42071	+	0.820248i	0.424351	+	0.905498i	$0.360502\pi$
$830$		0			0
$831$	5.93162	+	10.2739i	0.205766	+	0.356397i
$832$		0			0
$833$	−22.6551	+	21.9024i	−0.784954	+	0.758875i
$834$		0			0
$835$	46.9492	−	27.1062i	1.62475	−	0.938047i
$836$		0			0
$837$	3.01852	−	5.22824i	0.104335	−	0.180714i
$838$		0			0
$839$	−25.3551			−0.875356			−0.437678	−	0.899132i	$-0.644199\pi$
$839$	−25.3551			−0.875356			−0.437678	+	0.899132i	$0.644199\pi$
$840$		0			0
$841$	−19.2687			−0.664437
$842$		0			0
$843$	−9.67141	+	16.7514i	−0.333101	+	0.576948i
$844$		0			0
$845$	42.9475	−	24.7958i	1.47744	−	0.853000i
$846$		0			0
$847$	9.44687	−	22.2728i	0.324598	−	0.765304i
$848$		0			0
$849$	−12.4707	−	21.5998i	−0.427992	−	0.741304i
$850$		0			0
$851$	−15.2620	−	8.81153i	−0.523175	−	0.302055i
$852$		0			0
$853$		−	24.3802i		−	0.834763i	−0.908731	−	0.417382i	$-0.862948\pi$
$853$		−	24.3802i		−	0.834763i	0.908731	−	0.417382i	$-0.137052\pi$
$854$		0			0
$855$			0.255162i			0.00872636i
$856$		0			0
$857$	−22.4742	−	12.9755i	−0.767705	−	0.443235i	0.0643503	−	0.997927i	$-0.479502\pi$
$857$	−22.4742	−	12.9755i	−0.767705	−	0.443235i	−0.832055	+	0.554693i	$0.812836\pi$
$858$		0			0
$859$	−28.4213	−	49.2271i	−0.969722	−	1.67961i	−0.696354	−	0.717698i	$-0.745196\pi$
$859$	−28.4213	−	49.2271i	−0.969722	−	1.67961i	−0.273368	−	0.961909i	$-0.588138\pi$
$860$		0			0
$861$	−2.73088	−	22.1896i	−0.0930681	−	0.756221i
$862$		0			0
$863$	15.3044	−	8.83597i	0.520966	−	0.300780i	−0.216364	−	0.976313i	$-0.569420\pi$
$863$	15.3044	−	8.83597i	0.520966	−	0.300780i	0.737330	+	0.675533i	$0.236086\pi$
$864$		0			0
$865$	−3.42568	+	5.93345i	−0.116476	+	0.201743i
$866$		0			0
$867$	3.26474			0.110876
$868$		0			0
$869$	−17.0129			−0.577122
$870$		0			0
$871$	−1.80597	+	3.12803i	−0.0611930	+	0.105989i
$872$		0			0
$873$	2.49781	−	1.44211i	0.0845381	−	0.0488081i
$874$		0			0
$875$	39.6086	−	29.8647i	1.33901	−	1.00961i
$876$		0			0
$877$	−6.17283	−	10.6917i	−0.208442	−	0.361032i	0.742782	−	0.669533i	$-0.233506\pi$
$877$	−6.17283	−	10.6917i	−0.208442	−	0.361032i	−0.951224	+	0.308502i	$0.900173\pi$
$878$		0			0
$879$	5.96028	+	3.44117i	0.201035	+	0.116068i
$880$		0			0
$881$		−	33.0442i		−	1.11329i	−0.830751	−	0.556644i	$-0.812089\pi$
$881$		−	33.0442i		−	1.11329i	0.830751	−	0.556644i	$-0.187911\pi$
$882$		0			0
$883$			39.2680i			1.32147i	0.750618	+	0.660737i	$0.229756\pi$
$883$			39.2680i			1.32147i	−0.750618	+	0.660737i	$0.770244\pi$
$884$		0			0
$885$	11.4773	+	6.62642i	0.385805	+	0.222745i
$886$		0			0
$887$	−19.7517	−	34.2109i	−0.663196	−	1.14869i	−0.979771	−	0.200121i	$-0.935866\pi$
$887$	−19.7517	−	34.2109i	−0.663196	−	1.14869i	0.316576	−	0.948567i	$-0.397467\pi$
$888$		0			0
$889$	−5.71045	+	4.30565i	−0.191522	+	0.144407i
$890$		0			0
$891$	1.17975	−	0.681127i	0.0395230	−	0.0228186i
$892$		0			0
$893$	−0.0471792	+	0.0817167i	−0.00157879	+	0.00273454i
$894$		0			0
$895$	12.5363			0.419043
$896$		0			0
$897$	−1.18666			−0.0396214
$898$		0			0
$899$	−9.41631	+	16.3095i	−0.314052	+	0.543953i
$900$		0			0
$901$	−9.92249	+	5.72875i	−0.330566	+	0.190852i
$902$		0			0
$903$	2.03705	+	16.5519i	0.0677887	+	0.550814i
$904$		0			0
$905$	45.3026	+	78.4664i	1.50591	+	2.60831i
$906$		0			0
$907$	4.46372	+	2.57713i	0.148215	+	0.0855722i	0.572274	−	0.820063i	$-0.306062\pi$
$907$	4.46372	+	2.57713i	0.148215	+	0.0855722i	−0.424058	+	0.905635i	$0.639395\pi$
$908$		0			0
$909$			6.18861i			0.205263i
$910$		0			0
$911$			25.8365i			0.856002i	0.903778	+	0.428001i	$0.140782\pi$
$911$			25.8365i			0.856002i	−0.903778	+	0.428001i	$0.859218\pi$
$912$		0			0
$913$	14.4978	+	8.37031i	0.479807	+	0.277017i
$914$		0			0
$915$	2.76002	+	4.78049i	0.0912434	+	0.158038i
$916$		0			0
$917$	−8.03010	+	18.9325i	−0.265177	+	0.625207i
$918$		0			0
$919$	−30.6881	+	17.7178i	−1.01231	+	0.584455i	−0.911866	−	0.410488i	$-0.865358\pi$
$919$	−30.6881	+	17.7178i	−1.01231	+	0.584455i	−0.100440	+	0.994943i	$0.532025\pi$
$920$		0			0
$921$	−8.71065	+	15.0873i	−0.287026	+	0.497143i
$922$		0			0
$923$	4.78955			0.157650
$924$		0			0
$925$	−54.1676			−1.78102
$926$		0			0
$927$	−8.89634	+	15.4089i	−0.292194	+	0.506095i
$928$		0			0
$929$	47.6452	−	27.5080i	1.56319	−	0.902508i	0.566258	−	0.824228i	$-0.308391\pi$
$929$	47.6452	−	27.5080i	1.56319	−	0.902508i	0.996931	−	0.0782797i	$-0.0249427\pi$
$930$		0			0
$931$	0.449470	−	0.112334i	0.0147308	−	0.00368159i
$932$		0			0
$933$	−12.5580	−	21.7512i	−0.411132	−	0.712101i
$934$		0			0
$935$	−20.4746	−	11.8210i	−0.669592	−	0.386589i
$936$		0			0
$937$		−	6.90001i		−	0.225414i	−0.993628	−	0.112707i	$-0.964048\pi$
$937$		−	6.90001i		−	0.225414i	0.993628	−	0.112707i	$-0.0359521\pi$
$938$		0			0
$939$			22.0965i			0.721092i
$940$		0			0
$941$	−16.2597	−	9.38756i	−0.530052	−	0.306026i	0.210986	−	0.977489i	$-0.432333\pi$
$941$	−16.2597	−	9.38756i	−0.530052	−	0.306026i	−0.741038	+	0.671463i	$0.765666\pi$
$942$		0			0
$943$	−13.5580	−	23.4832i	−0.441511	−	0.764719i
$944$		0			0
$945$	−9.39039	−	3.98287i	−0.305470	−	0.129563i
$946$		0			0
$947$	25.7931	−	14.8916i	0.838162	−	0.483913i	−0.0184768	−	0.999829i	$-0.505882\pi$
$947$	25.7931	−	14.8916i	0.838162	−	0.483913i	0.856639	+	0.515916i	$0.172548\pi$
$948$		0			0
$949$	−0.333115	+	0.576972i	−0.0108134	+	0.0187293i
$950$		0			0
$951$	−1.62327			−0.0526380
$952$		0			0
$953$	−23.2676			−0.753711			−0.376856	−	0.926272i	$-0.622995\pi$
$953$	−23.2676			−0.753711			−0.376856	+	0.926272i	$0.622995\pi$
$954$		0			0
$955$	−46.0653	+	79.7875i	−1.49064	+	2.58186i
$956$		0			0
$957$	−3.68023	+	2.12478i	−0.118965	+	0.0686844i
$958$		0			0
$959$	−7.48748	+	0.921485i	−0.241783	+	0.0297563i
$960$		0			0
$961$	−2.72297	−	4.71632i	−0.0878377	−	0.152139i
$962$		0			0
$963$	−5.27683	−	3.04658i	−0.170044	−	0.0981747i
$964$		0			0
$965$			76.6244i			2.46663i
$966$		0			0
$967$		−	16.9691i		−	0.545690i	−0.962058	−	0.272845i	$-0.912035\pi$
$967$		−	16.9691i		−	0.545690i	0.962058	−	0.272845i	$-0.0879646\pi$
$968$		0			0
$969$	−0.258024	−	0.148970i	−0.00828893	−	0.00478561i
$970$		0			0
$971$	−22.8349	−	39.5512i	−0.732806	−	1.26926i	−0.955679	−	0.294410i	$-0.904877\pi$
$971$	−22.8349	−	39.5512i	−0.732806	−	1.26926i	0.222873	−	0.974847i	$-0.428456\pi$
$972$		0			0
$973$	11.3993	+	15.1185i	0.365445	+	0.484678i
$974$		0			0
$975$	−3.15875	+	1.82370i	−0.101161	+	0.0584052i
$976$		0			0
$977$	23.7102	−	41.0673i	0.758557	−	1.31386i	−0.185029	−	0.982733i	$-0.559238\pi$
$977$	23.7102	−	41.0673i	0.758557	−	1.31386i	0.943586	−	0.331127i	$-0.107429\pi$
$978$		0			0
$979$	−1.76098			−0.0562812
$980$		0			0
$981$	−7.86325			−0.251054
$982$		0			0
$983$	17.6956	−	30.6497i	0.564402	−	0.977573i	−0.432703	−	0.901536i	$-0.642440\pi$
$983$	17.6956	−	30.6497i	0.564402	−	0.977573i	0.997105	−	0.0760363i	$-0.0242265\pi$
$984$		0			0
$985$	−63.5029	+	36.6634i	−2.02337	+	1.16819i
$986$		0			0
$987$	−2.27088	−	3.01180i	−0.0722831	−	0.0958668i
$988$		0			0
$989$	10.1134	+	17.5169i	0.321586	+	0.557004i
$990$		0			0
$991$	−10.0136	−	5.78134i	−0.318092	−	0.183650i	0.332450	−	0.943121i	$-0.392125\pi$
$991$	−10.0136	−	5.78134i	−0.318092	−	0.183650i	−0.650542	+	0.759471i	$0.725458\pi$
$992$		0			0
$993$			26.6677i			0.846274i
$994$		0			0
$995$		−	57.2563i		−	1.81515i
$996$		0			0
$997$	10.6832	+	6.16793i	0.338339	+	0.195340i	0.659537	−	0.751672i	$-0.270752\pi$
$997$	10.6832	+	6.16793i	0.338339	+	0.195340i	−0.321198	+	0.947012i	$0.604086\pi$
$998$		0			0
$999$	2.74593	+	4.75609i	0.0868774	+	0.150476i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1344.2.bl.j.703.4		8
4.3	odd	2		1344.2.bl.i.703.4		8
7.5	odd	6		1344.2.bl.i.1279.4		8
8.3	odd	2		84.2.o.b.31.4	yes	8
8.5	even	2		84.2.o.a.31.2	yes	8
24.5	odd	2		252.2.bf.g.199.3		8
24.11	even	2		252.2.bf.f.199.1		8
28.19	even	6	inner	1344.2.bl.j.1279.4		8
56.3	even	6		588.2.b.b.391.4		8
56.5	odd	6		84.2.o.b.19.4	yes	8
56.11	odd	6		588.2.b.a.391.4		8
56.13	odd	2		588.2.o.d.31.2		8
56.19	even	6		84.2.o.a.19.2	✓	8
56.27	even	2		588.2.o.b.31.4		8
56.37	even	6		588.2.o.b.19.4		8
56.45	odd	6		588.2.b.a.391.3		8
56.51	odd	6		588.2.o.d.19.2		8
56.53	even	6		588.2.b.b.391.3		8
168.5	even	6		252.2.bf.f.19.1		8
168.11	even	6		1764.2.b.j.1567.5		8
168.53	odd	6		1764.2.b.i.1567.6		8
168.59	odd	6		1764.2.b.i.1567.5		8
168.101	even	6		1764.2.b.j.1567.6		8
168.131	odd	6		252.2.bf.g.19.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.2.o.a.19.2	✓	8	56.19	even	6
84.2.o.a.31.2	yes	8	8.5	even	2
84.2.o.b.19.4	yes	8	56.5	odd	6
84.2.o.b.31.4	yes	8	8.3	odd	2
252.2.bf.f.19.1		8	168.5	even	6
252.2.bf.f.199.1		8	24.11	even	2
252.2.bf.g.19.3		8	168.131	odd	6
252.2.bf.g.199.3		8	24.5	odd	2
588.2.b.a.391.3		8	56.45	odd	6
588.2.b.a.391.4		8	56.11	odd	6
588.2.b.b.391.3		8	56.53	even	6
588.2.b.b.391.4		8	56.3	even	6
588.2.o.b.19.4		8	56.37	even	6
588.2.o.b.31.4		8	56.27	even	2
588.2.o.d.19.2		8	56.51	odd	6
588.2.o.d.31.2		8	56.13	odd	2
1344.2.bl.i.703.4		8	4.3	odd	2
1344.2.bl.i.1279.4		8	7.5	odd	6
1344.2.bl.j.703.4		8	1.1	even	1	trivial
1344.2.bl.j.1279.4		8	28.19	even	6	inner
1764.2.b.i.1567.5		8	168.59	odd	6
1764.2.b.i.1567.6		8	168.53	odd	6
1764.2.b.j.1567.5		8	168.11	even	6
1764.2.b.j.1567.6		8	168.101	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1344 = 2^{6} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1344.bl (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{3} +(3.33878 - 1.92764i) q^{5} +(1.59285 + 2.11254i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{3} +(3.33878 - 1.92764i) q^{5} +(1.59285 + 2.11254i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(-1.17975 - 0.681127i) q^{11} -0.369798i q^{13} -3.85529i q^{15} +(3.89853 + 2.25082i) q^{17} +(-0.0330925 - 0.0573178i) q^{19} +(2.62594 - 0.323174i) q^{21} +(2.77902 - 1.60447i) q^{23} +(4.93162 - 8.54182i) q^{25} -1.00000 q^{27} +3.11951 q^{29} +(-3.01852 + 5.22824i) q^{31} +(-1.17975 + 0.681127i) q^{33} +(9.39039 + 3.98287i) q^{35} +(-2.74593 - 4.75609i) q^{37} +(-0.320254 - 0.184899i) q^{39} -8.45017i q^{41} +6.30324i q^{43} +(-3.33878 - 1.92764i) q^{45} +(-0.712838 - 1.23467i) q^{47} +(-1.92568 + 6.72992i) q^{49} +(3.89853 - 2.25082i) q^{51} +(-1.27259 + 2.20420i) q^{53} -5.25188 q^{55} -0.0661849 q^{57} +(-1.71879 + 2.97703i) q^{59} +(-1.23998 + 0.715904i) q^{61} +(1.03309 - 2.43572i) q^{63} +(-0.712838 - 1.23467i) q^{65} +(-8.45877 - 4.88367i) q^{67} -3.20894i q^{69} +12.9518i q^{71} +(-1.56024 - 0.900803i) q^{73} +(-4.93162 - 8.54182i) q^{75} +(-0.440245 - 3.57719i) q^{77} +(10.8156 - 6.24438i) q^{79} +(-0.500000 + 0.866025i) q^{81} -12.2889 q^{83} +17.3551 q^{85} +(1.55975 - 2.70157i) q^{87} +(1.11951 - 0.646349i) q^{89} +(0.781213 - 0.589031i) q^{91} +(3.01852 + 5.22824i) q^{93} +(-0.220977 - 0.127581i) q^{95} +2.88422i q^{97} +1.36225i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{3} + 2 q^{7} - 4 q^{9}+O(q^{10}) \) 8 * q + 4 * q^3 + 2 * q^7 - 4 * q^9	\( 8 q + 4 q^{3} + 2 q^{7} - 4 q^{9} - 6 q^{11} + 6 q^{19} + 4 q^{21} + 2 q^{25} - 8 q^{27} + 16 q^{29} + 6 q^{31} - 6 q^{33} + 12 q^{35} - 6 q^{37} - 6 q^{39} + 4 q^{47} + 4 q^{49} + 4 q^{53} - 8 q^{55} + 12 q^{57} + 14 q^{59} - 12 q^{61} + 2 q^{63} + 4 q^{65} - 42 q^{67} - 18 q^{73} - 2 q^{75} - 8 q^{77} - 6 q^{79} - 4 q^{81} - 4 q^{83} + 32 q^{85} + 8 q^{87} + 34 q^{91} - 6 q^{93} - 24 q^{95}+O(q^{100}) \) 8 * q + 4 * q^3 + 2 * q^7 - 4 * q^9 - 6 * q^11 + 6 * q^19 + 4 * q^21 + 2 * q^25 - 8 * q^27 + 16 * q^29 + 6 * q^31 - 6 * q^33 + 12 * q^35 - 6 * q^37 - 6 * q^39 + 4 * q^47 + 4 * q^49 + 4 * q^53 - 8 * q^55 + 12 * q^57 + 14 * q^59 - 12 * q^61 + 2 * q^63 + 4 * q^65 - 42 * q^67 - 18 * q^73 - 2 * q^75 - 8 * q^77 - 6 * q^79 - 4 * q^81 - 4 * q^83 + 32 * q^85 + 8 * q^87 + 34 * q^91 - 6 * q^93 - 24 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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