LMFDB - Embedded newform 729.2.g.c.55.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(28,729)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([44]))

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

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

chi := DirichletCharacter("729.28");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.g (of order $27$, degree $18$, 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:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$8$ over $\Q(\zeta_{27})$
Twist minimal:	no (minimal twist has level 81)
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			55.3
Character	$\chi$	$=$	729.55
Dual form			729.2.g.c.676.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.588281 + 1.36379i) q^{2} +(-0.141360 - 0.149832i) q^{4} +(-0.0932044 - 1.60026i) q^{5} +(-1.85061 - 0.438602i) q^{7} +(-2.50387 + 0.911335i) q^{8} +O(q^{10})$	\(q+(-0.588281 + 1.36379i) q^{2} +(-0.141360 - 0.149832i) q^{4} +(-0.0932044 - 1.60026i) q^{5} +(-1.85061 - 0.438602i) q^{7} +(-2.50387 + 0.911335i) q^{8} +(2.23724 + 0.814290i) q^{10} +(-3.38752 - 2.22800i) q^{11} +(1.67851 + 0.196189i) q^{13} +(1.68684 - 2.26582i) q^{14} +(0.254067 - 4.36216i) q^{16} +(4.14727 - 3.47997i) q^{17} +(3.70167 + 3.10607i) q^{19} +(-0.226595 + 0.240177i) q^{20} +(5.03133 - 3.30916i) q^{22} +(0.651612 - 0.154435i) q^{23} +(2.41405 - 0.282162i) q^{25} +(-1.25499 + 2.17371i) q^{26} +(0.195884 + 0.339282i) q^{28} +(-2.85835 - 3.83943i) q^{29} +(1.39576 - 4.66216i) q^{31} +(1.03731 + 0.520955i) q^{32} +(2.30618 + 7.70319i) q^{34} +(-0.529392 + 3.00233i) q^{35} +(-2.07926 - 11.7921i) q^{37} +(-6.41363 + 3.22105i) q^{38} +(1.69174 + 3.92190i) q^{40} +(-4.00621 - 9.28743i) q^{41} +(7.64192 - 3.83792i) q^{43} +(0.145031 + 0.822509i) q^{44} +(-0.172714 + 0.979511i) q^{46} +(0.0578400 + 0.193199i) q^{47} +(-3.02305 - 1.51823i) q^{49} +(-1.03533 + 3.45825i) q^{50} +(-0.207877 - 0.279228i) q^{52} +(2.48138 + 4.29788i) q^{53} +(-3.24965 + 5.62856i) q^{55} +(5.03340 - 0.588321i) q^{56} +(6.91768 - 1.63952i) q^{58} +(1.58520 - 1.04260i) q^{59} +(0.124028 - 0.131462i) q^{61} +(5.53710 + 4.64618i) q^{62} +(5.37384 - 4.50919i) q^{64} +(0.157509 - 2.70433i) q^{65} +(-7.95826 + 10.6898i) q^{67} +(-1.10767 - 0.129468i) q^{68} +(-3.78311 - 2.48819i) q^{70} +(9.41216 + 3.42575i) q^{71} +(-10.9327 + 3.97917i) q^{73} +(17.3051 + 4.10138i) q^{74} +(-0.0578765 - 0.993701i) q^{76} +(5.29176 + 5.60894i) q^{77} +(-1.45390 + 3.37053i) q^{79} -7.00426 q^{80} +15.0229 q^{82} +(-2.17367 + 5.03914i) q^{83} +(-5.95539 - 6.31235i) q^{85} +(0.738510 + 12.6797i) q^{86} +(10.5124 + 2.49148i) q^{88} +(-6.65218 + 2.42120i) q^{89} +(-3.02021 - 1.09927i) q^{91} +(-0.115251 - 0.0758017i) q^{92} +(-0.297508 - 0.0347738i) q^{94} +(4.62550 - 6.21312i) q^{95} +(0.0778051 - 1.33586i) q^{97} +(3.84894 - 3.22965i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8}+O(q^{10}) $ 144 * q + 9 * q^2 + 9 * q^4 + 9 * q^5 + 9 * q^7 - 18 * q^8	$ 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8} - 18 q^{10} + 9 q^{11} + 9 q^{13} + 9 q^{14} + 9 q^{16} - 18 q^{17} - 18 q^{19} - 63 q^{20} + 9 q^{22} + 36 q^{23} + 9 q^{25} + 45 q^{26} - 9 q^{28} - 45 q^{29} + 9 q^{31} + 63 q^{32} + 9 q^{34} + 9 q^{35} - 18 q^{37} - 9 q^{38} + 9 q^{40} - 27 q^{41} + 9 q^{43} + 54 q^{44} - 18 q^{46} + 63 q^{47} + 9 q^{49} - 225 q^{50} + 27 q^{52} + 45 q^{53} - 9 q^{55} + 99 q^{56} + 9 q^{58} - 117 q^{59} + 9 q^{61} + 81 q^{62} - 18 q^{64} + 81 q^{65} + 36 q^{67} - 18 q^{68} + 63 q^{70} - 90 q^{71} - 18 q^{73} + 81 q^{74} + 90 q^{76} + 81 q^{77} + 63 q^{79} - 288 q^{80} - 36 q^{82} + 45 q^{83} + 63 q^{85} + 81 q^{86} + 90 q^{88} - 81 q^{89} - 18 q^{91} - 63 q^{92} + 63 q^{94} + 153 q^{95} + 36 q^{97} + 81 q^{98}+O(q^{100}) $ 144 * q + 9 * q^2 + 9 * q^4 + 9 * q^5 + 9 * q^7 - 18 * q^8 - 18 * q^10 + 9 * q^11 + 9 * q^13 + 9 * q^14 + 9 * q^16 - 18 * q^17 - 18 * q^19 - 63 * q^20 + 9 * q^22 + 36 * q^23 + 9 * q^25 + 45 * q^26 - 9 * q^28 - 45 * q^29 + 9 * q^31 + 63 * q^32 + 9 * q^34 + 9 * q^35 - 18 * q^37 - 9 * q^38 + 9 * q^40 - 27 * q^41 + 9 * q^43 + 54 * q^44 - 18 * q^46 + 63 * q^47 + 9 * q^49 - 225 * q^50 + 27 * q^52 + 45 * q^53 - 9 * q^55 + 99 * q^56 + 9 * q^58 - 117 * q^59 + 9 * q^61 + 81 * q^62 - 18 * q^64 + 81 * q^65 + 36 * q^67 - 18 * q^68 + 63 * q^70 - 90 * q^71 - 18 * q^73 + 81 * q^74 + 90 * q^76 + 81 * q^77 + 63 * q^79 - 288 * q^80 - 36 * q^82 + 45 * q^83 + 63 * q^85 + 81 * q^86 + 90 * q^88 - 81 * q^89 - 18 * q^91 - 63 * q^92 + 63 * q^94 + 153 * q^95 + 36 * q^97 + 81 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{17}{27}\right)$

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 $

$2$	−0.588281	+	1.36379i	−0.415977	+	0.964344i	0.573440	+	0.819247i	$0.305608\pi$
$2$	−0.588281	+	1.36379i	−0.415977	+	0.964344i	−0.989418	+	0.145096i	$0.953651\pi$
$3$		0			0
$3$		0			0
$4$	−0.141360	−	0.149832i	−0.0706798	−	0.0749162i
$5$	−0.0932044	−	1.60026i	−0.0416823	−	0.715657i	−0.952816	−	0.303547i	$-0.901829\pi$
$5$	−0.0932044	−	1.60026i	−0.0416823	−	0.715657i	0.911134	−	0.412110i	$-0.135208\pi$
$6$		0			0
$7$	−1.85061	−	0.438602i	−0.699465	−	0.165776i	−0.134527	−	0.990910i	$-0.542952\pi$
$7$	−1.85061	−	0.438602i	−0.699465	−	0.165776i	−0.564937	+	0.825134i	$0.691100\pi$
$8$	−2.50387	+	0.911335i	−0.885253	+	0.322206i
$9$		0			0
$10$	2.23724	+	0.814290i	0.707478	+	0.257501i
$11$	−3.38752	−	2.22800i	−1.02137	−	0.671769i	−0.0757828	−	0.997124i	$-0.524146\pi$
$11$	−3.38752	−	2.22800i	−1.02137	−	0.671769i	−0.945592	+	0.325356i	$0.894516\pi$
$12$		0			0
$13$	1.67851	+	0.196189i	0.465534	+	0.0544131i	0.345627	−	0.938372i	$-0.387666\pi$
$13$	1.67851	+	0.196189i	0.465534	+	0.0544131i	0.119907	+	0.992785i	$0.461740\pi$
$14$	1.68684	−	2.26582i	0.450826	−	0.605565i
$15$		0			0
$16$	0.254067	−	4.36216i	0.0635167	−	1.09054i
$17$	4.14727	−	3.47997i	1.00586	−	0.844017i	0.0180743	−	0.999837i	$-0.494246\pi$
$17$	4.14727	−	3.47997i	1.00586	−	0.844017i	0.987785	+	0.155820i	$0.0498020\pi$
$18$		0			0
$19$	3.70167	+	3.10607i	0.849220	+	0.712581i	0.959618	−	0.281307i	$-0.0907679\pi$
$19$	3.70167	+	3.10607i	0.849220	+	0.712581i	−0.110397	+	0.993888i	$0.535212\pi$
$20$	−0.226595	+	0.240177i	−0.0506682	+	0.0537052i
$21$		0			0
$22$	5.03133	−	3.30916i	1.07268	−	0.705515i
$23$	0.651612	−	0.154435i	0.135870	−	0.0322019i	−0.162118	−	0.986771i	$-0.551832\pi$
$23$	0.651612	−	0.154435i	0.135870	−	0.0322019i	0.297988	+	0.954570i	$0.403684\pi$
$24$		0			0
$25$	2.41405	−	0.282162i	0.482811	−	0.0564325i
$26$	−1.25499	+	2.17371i	−0.246124	+	0.426300i
$27$		0			0
$28$	0.195884	+	0.339282i	0.0370187	+	0.0641182i
$29$	−2.85835	−	3.83943i	−0.530782	−	0.712965i	0.453164	−	0.891427i	$-0.350295\pi$
$29$	−2.85835	−	3.83943i	−0.530782	−	0.712965i	−0.983947	+	0.178462i	$0.942888\pi$
$30$		0			0
$31$	1.39576	−	4.66216i	0.250686	−	0.837349i	−0.736316	−	0.676638i	$-0.763436\pi$
$31$	1.39576	−	4.66216i	0.250686	−	0.837349i	0.987002	−	0.160711i	$-0.0513786\pi$
$32$	1.03731	+	0.520955i	0.183372	+	0.0920927i
$33$		0			0
$34$	2.30618	+	7.70319i	0.395507	+	1.32109i
$35$	−0.529392	+	3.00233i	−0.0894836	+	0.507487i
$36$		0			0
$37$	−2.07926	−	11.7921i	−0.341829	−	1.93861i	−0.344973	−	0.938613i	$-0.612112\pi$
$37$	−2.07926	−	11.7921i	−0.341829	−	1.93861i	0.00314382	−	0.999995i	$-0.498999\pi$
$38$	−6.41363	+	3.22105i	−1.04043	+	0.522523i
$39$		0			0
$40$	1.69174	+	3.92190i	0.267488	+	0.620107i
$41$	−4.00621	−	9.28743i	−0.625664	−	1.45045i	−0.876009	−	0.482296i	$-0.839803\pi$
$41$	−4.00621	−	9.28743i	−0.625664	−	1.45045i	0.250344	−	0.968157i	$-0.419456\pi$
$42$		0			0
$43$	7.64192	−	3.83792i	1.16538	−	0.585277i	0.242421	−	0.970171i	$-0.422059\pi$
$43$	7.64192	−	3.83792i	1.16538	−	0.585277i	0.922961	+	0.384895i	$0.125762\pi$
$44$	0.145031	+	0.822509i	0.0218642	+	0.123998i
$45$		0			0
$46$	−0.172714	+	0.979511i	−0.0254653	+	0.144421i
$47$	0.0578400	+	0.193199i	0.00843683	+	0.0281810i	0.962104	−	0.272682i	$-0.0879106\pi$
$47$	0.0578400	+	0.193199i	0.00843683	+	0.0281810i	−0.953667	+	0.300863i	$0.902725\pi$
$48$		0			0
$49$	−3.02305	−	1.51823i	−0.431864	−	0.216890i
$50$	−1.03533	+	3.45825i	−0.146418	+	0.489070i
$51$		0			0
$52$	−0.207877	−	0.279228i	−0.0288274	−	0.0387219i
$53$	2.48138	+	4.29788i	0.340844	+	0.590359i	0.984590	−	0.174880i	$-0.0559538\pi$
$53$	2.48138	+	4.29788i	0.340844	+	0.590359i	−0.643746	+	0.765240i	$0.722621\pi$
$54$		0			0
$55$	−3.24965	+	5.62856i	−0.438183	+	0.758955i
$56$	5.03340	−	0.588321i	0.672617	−	0.0786177i
$57$		0			0
$58$	6.91768	−	1.63952i	0.908336	−	0.215280i
$59$	1.58520	−	1.04260i	0.206375	−	0.135735i	−0.442114	−	0.896959i	$-0.645771\pi$
$59$	1.58520	−	1.04260i	0.206375	−	0.135735i	0.648489	+	0.761224i	$0.275401\pi$
$60$		0			0
$61$	0.124028	−	0.131462i	0.0158802	−	0.0168320i	−0.719385	−	0.694612i	$-0.755576\pi$
$61$	0.124028	−	0.131462i	0.0158802	−	0.0168320i	0.735265	+	0.677780i	$0.237058\pi$
$62$	5.53710	+	4.64618i	0.703212	+	0.590065i
$63$		0			0
$64$	5.37384	−	4.50919i	0.671730	−	0.563648i
$65$	0.157509	−	2.70433i	0.0195366	−	0.335431i
$66$		0			0
$67$	−7.95826	+	10.6898i	−0.972256	+	1.30597i	−0.0202796	+	0.999794i	$0.506456\pi$
$67$	−7.95826	+	10.6898i	−0.972256	+	1.30597i	−0.951976	+	0.306172i	$0.900952\pi$
$68$	−1.10767	−	0.129468i	−0.134324	−	0.0157003i
$69$		0			0
$70$	−3.78311	−	2.48819i	−0.452168	−	0.297396i
$71$	9.41216	+	3.42575i	1.11702	+	0.406561i	0.833563	−	0.552424i	$-0.186297\pi$
$71$	9.41216	+	3.42575i	1.11702	+	0.406561i	0.283455	+	0.958985i	$0.408519\pi$
$72$		0			0
$73$	−10.9327	+	3.97917i	−1.27957	+	0.465726i	−0.890291	−	0.455392i	$-0.849499\pi$
$73$	−10.9327	+	3.97917i	−1.27957	+	0.465726i	−0.389282	+	0.921119i	$0.627277\pi$
$74$	17.3051	+	4.10138i	2.01168	+	0.476776i
$75$		0			0
$76$	−0.0578765	−	0.993701i	−0.00663889	−	0.113985i
$77$	5.29176	+	5.60894i	0.603052	+	0.639198i
$78$		0			0
$79$	−1.45390	+	3.37053i	−0.163577	+	0.379214i	−0.980215	−	0.197936i	$-0.936576\pi$
$79$	−1.45390	+	3.37053i	−0.163577	+	0.379214i	0.816638	+	0.577150i	$0.195835\pi$
$80$	−7.00426			−0.783100
$81$		0			0
$82$	15.0229			1.65900
$83$	−2.17367	+	5.03914i	−0.238592	+	0.553117i	−0.994873	−	0.101129i	$-0.967755\pi$
$83$	−2.17367	+	5.03914i	−0.238592	+	0.553117i	0.756282	+	0.654246i	$0.227014\pi$
$84$		0			0
$85$	−5.95539	−	6.31235i	−0.645953	−	0.684670i
$86$	0.738510	+	12.6797i	0.0796356	+	1.36729i
$87$		0			0
$88$	10.5124	+	2.49148i	1.12062	+	0.265592i
$89$	−6.65218	+	2.42120i	−0.705130	+	0.256646i	−0.669600	−	0.742722i	$-0.733534\pi$
$89$	−6.65218	+	2.42120i	−0.705130	+	0.256646i	−0.0355305	+	0.999369i	$0.511312\pi$
$90$		0			0
$91$	−3.02021	−	1.09927i	−0.316604	−	0.115234i
$92$	−0.115251	−	0.0758017i	−0.0120157	−	0.00790287i
$93$		0			0
$94$	−0.297508	−	0.0347738i	−0.0306857	−	0.00358664i
$95$	4.62550	−	6.21312i	0.474566	−	0.637453i
$96$		0			0
$97$	0.0778051	−	1.33586i	0.00789992	−	0.135636i	−0.992052	−	0.125829i	$-0.959841\pi$
$97$	0.0778051	−	1.33586i	0.00789992	−	0.135636i	0.999952	−	0.00980765i	$-0.00312192\pi$
$98$	3.84894	−	3.22965i	0.388802	−	0.326244i
$99$		0			0
$100$	−0.383526	−	0.321817i	−0.0383526	−	0.0321817i
$101$	−3.40131	+	3.60518i	−0.338443	+	0.358729i	−0.874134	−	0.485686i	$-0.838570\pi$
$101$	−3.40131	+	3.60518i	−0.338443	+	0.358729i	0.535690	+	0.844415i	$0.320051\pi$
$102$		0			0
$103$	1.90445	−	1.25258i	0.187652	−	0.123420i	−0.452207	−	0.891913i	$-0.649363\pi$
$103$	1.90445	−	1.25258i	0.187652	−	0.123420i	0.639859	+	0.768493i	$0.278993\pi$
$104$	−4.38156	+	1.03845i	−0.429648	+	0.101828i
$105$		0			0
$106$	−7.32115	+	0.855719i	−0.711092	+	0.0831148i
$107$	2.21467	−	3.83593i	0.214101	−	0.370833i	−0.738893	−	0.673822i	$-0.764651\pi$
$107$	2.21467	−	3.83593i	0.214101	−	0.370833i	0.952994	+	0.302989i	$0.0979846\pi$
$108$		0			0
$109$	−9.21824	−	15.9665i	−0.882947	−	1.52931i	−0.848049	−	0.529918i	$-0.822223\pi$
$109$	−9.21824	−	15.9665i	−0.882947	−	1.52931i	−0.0348978	−	0.999391i	$-0.511111\pi$
$110$	−5.76445	−	7.74301i	−0.549619	−	0.738267i
$111$		0			0
$112$	−2.38343	+	7.96121i	−0.225213	+	0.752264i
$113$	8.05934	+	4.04755i	0.758159	+	0.380762i	0.785498	−	0.618865i	$-0.212407\pi$
$113$	8.05934	+	4.04755i	0.758159	+	0.380762i	−0.0273390	+	0.999626i	$0.508703\pi$
$114$		0			0
$115$	−0.307869	−	1.02835i	−0.0287089	−	0.0958944i
$116$	−0.171216	+	0.971014i	−0.0158970	+	0.0901563i
$117$		0			0
$118$	0.489346	+	2.77522i	0.0450479	+	0.255479i
$119$	−9.20129	+	4.62106i	−0.843481	+	0.423612i
$120$		0			0
$121$	2.15438	+	4.99442i	0.195853	+	0.454038i
$122$	0.106323	+	0.246485i	0.00962604	+	0.0223157i
$123$		0			0
$124$	−0.895846	+	0.449911i	−0.0804493	+	0.0404032i
$125$	−2.06830	−	11.7299i	−0.184994	−	1.04915i
$126$		0			0
$127$	−0.304561	+	1.72725i	−0.0270254	+	0.153269i	−0.995334	−	0.0964872i	$-0.969239\pi$
$127$	−0.304561	+	1.72725i	−0.0270254	+	0.153269i	0.968309	+	0.249756i	$0.0803504\pi$
$128$	3.65408	+	12.2055i	0.322978	+	1.07882i
$129$		0			0
$130$	3.59547	+	1.80571i	0.315344	+	0.158372i
$131$	−2.05452	+	6.86256i	−0.179504	+	0.599585i	0.820121	+	0.572191i	$0.193906\pi$
$131$	−2.05452	+	6.86256i	−0.179504	+	0.599585i	−0.999625	+	0.0273945i	$0.991279\pi$
$132$		0			0
$133$	−5.48801	−	7.37168i	−0.475871	−	0.639205i
$134$	−9.89692	−	17.1420i	−0.854964	−	1.48084i
$135$		0			0
$136$	−7.21281	+	12.4930i	−0.618493	+	1.07126i
$137$	17.3549	−	2.02850i	1.48273	−	0.173307i	0.664109	−	0.747636i	$-0.268811\pi$
$137$	17.3549	−	2.02850i	1.48273	−	0.173307i	0.818624	+	0.574329i	$0.194737\pi$
$138$		0			0
$139$	−18.4877	+	4.38167i	−1.56811	+	0.371649i	−0.920630	−	0.390435i	$-0.872325\pi$
$139$	−18.4877	+	4.38167i	−1.56811	+	0.371649i	−0.647478	+	0.762084i	$0.724176\pi$
$140$	0.524681	−	0.345088i	0.0443436	−	0.0291653i
$141$		0			0
$142$	−10.2090	+	10.8209i	−0.856719	+	0.908069i
$143$	−5.24886	−	4.40431i	−0.438931	−	0.368307i
$144$		0			0
$145$	−5.87767	+	4.93195i	−0.488114	+	0.409576i
$146$	1.00474	−	17.2507i	0.0831528	−	1.42768i
$147$		0			0
$148$	−1.47291	+	1.97847i	−0.121073	+	0.162629i
$149$	−7.32320	−	0.855959i	−0.599940	−	0.0701229i	−0.189298	−	0.981920i	$-0.560621\pi$
$149$	−7.32320	−	0.855959i	−0.599940	−	0.0701229i	−0.410642	+	0.911797i	$0.634695\pi$
$150$		0			0
$151$	2.23139	+	1.46761i	0.181588	+	0.119432i	0.637048	−	0.770824i	$-0.280155\pi$
$151$	2.23139	+	1.46761i	0.181588	+	0.119432i	−0.455461	+	0.890256i	$0.650525\pi$
$152$	−12.0992	−	4.40374i	−0.981372	−	0.357190i
$153$		0			0
$154$	−10.7624	+	3.91721i	−0.867262	+	0.315658i
$155$	−7.59075	−	1.79904i	−0.609704	−	0.144502i
$156$		0			0
$157$	0.332250	+	5.70452i	0.0265165	+	0.455270i	0.985267	+	0.171022i	$0.0547069\pi$
$157$	0.332250	+	5.70452i	0.0265165	+	0.455270i	−0.958751	+	0.284248i	$0.908256\pi$
$158$	−3.74138	−	3.96563i	−0.297648	−	0.315489i
$159$		0			0
$160$	0.736981	−	1.70851i	0.0582635	−	0.135070i
$161$	−1.27361			−0.100375
$162$		0			0
$163$	16.0381			1.25620			0.628100	−	0.778132i	$-0.283833\pi$
$163$	16.0381			1.25620			0.628100	+	0.778132i	$0.283833\pi$
$164$	−0.825242	+	1.91313i	−0.0644406	+	0.149390i
$165$		0			0
$166$	−5.59359	−	5.92886i	−0.434147	−	0.460168i
$167$	−1.11336	−	19.1157i	−0.0861545	−	1.47922i	−0.713599	−	0.700554i	$-0.752936\pi$
$167$	−1.11336	−	19.1157i	−0.0861545	−	1.47922i	0.627445	−	0.778661i	$-0.284101\pi$
$168$		0			0
$169$	−9.87069	−	2.33940i	−0.759284	−	0.179954i
$170$	12.1121	−	4.40846i	0.928959	−	0.338113i
$171$		0			0
$172$	−1.65530	−	0.602480i	−0.126216	−	0.0459387i
$173$	19.7483	+	12.9886i	1.50143	+	0.987509i	0.991895	+	0.127061i	$0.0405544\pi$
$173$	19.7483	+	12.9886i	1.50143	+	0.987509i	0.509539	+	0.860448i	$0.329816\pi$
$174$		0			0
$175$	−4.59123	−	0.536637i	−0.347064	−	0.0405660i
$176$	−10.5796	+	14.2108i	−0.797464	+	1.07118i
$177$		0			0
$178$	0.611352	−	10.4965i	0.0458228	−	0.786747i
$179$	−3.43489	+	2.88222i	−0.256736	+	0.215427i	−0.762066	−	0.647499i	$-0.775815\pi$
$179$	−3.43489	+	2.88222i	−0.256736	+	0.215427i	0.505331	+	0.862926i	$0.331371\pi$
$180$		0			0
$181$	2.92076	+	2.45081i	0.217098	+	0.182167i	0.744851	−	0.667231i	$-0.232521\pi$
$181$	2.92076	+	2.45081i	0.217098	+	0.182167i	−0.527752	+	0.849398i	$0.676965\pi$
$182$	3.27590	−	3.47225i	0.242826	−	0.257380i
$183$		0			0
$184$	−1.49081	+	0.980522i	−0.109904	+	0.0722850i
$185$	−18.6766	+	4.42643i	−1.37313	+	0.325438i
$186$		0			0
$187$	−21.8023	+	2.54833i	−1.59434	+	0.186352i
$188$	0.0207712	−	0.0359768i	0.00151490	−	0.00262388i
$189$		0			0
$190$	5.75229	+	9.96325i	0.417315	+	0.722810i
$191$	−10.9862	−	14.7571i	−0.794936	−	1.06778i	−0.996100	−	0.0882265i	$-0.971880\pi$
$191$	−10.9862	−	14.7571i	−0.794936	−	1.06778i	0.201165	−	0.979557i	$-0.435527\pi$
$192$		0			0
$193$	4.71004	−	15.7326i	0.339036	−	1.13246i	−0.603223	−	0.797573i	$-0.706117\pi$
$193$	4.71004	−	15.7326i	0.339036	−	1.13246i	0.942259	−	0.334886i	$-0.108698\pi$
$194$	1.77606	+	0.891972i	0.127514	+	0.0640398i
$195$		0			0
$196$	0.199856	+	0.667566i	0.0142754	+	0.0476833i
$197$	−3.25113	+	18.4381i	−0.231633	+	1.31366i	0.617956	+	0.786213i	$0.287961\pi$
$197$	−3.25113	+	18.4381i	−0.231633	+	1.31366i	−0.849589	+	0.527445i	$0.823150\pi$
$198$		0			0
$199$	0.155470	+	0.881713i	0.0110210	+	0.0625029i	0.989822	−	0.142309i	$-0.0454527\pi$
$199$	0.155470	+	0.881713i	0.0110210	+	0.0625029i	−0.978801	+	0.204812i	$0.934342\pi$
$200$	−5.78734	+	2.90651i	−0.409227	+	0.205521i
$201$		0			0
$202$	−2.91577	−	6.75953i	−0.205153	−	0.475599i
$203$	3.60571	+	8.35897i	0.253071	+	0.586685i
$204$		0			0
$205$	−14.4889	+	7.27659i	−1.01195	+	0.508219i
$206$	0.587899	+	3.33414i	0.0409609	+	0.232301i
$207$		0			0
$208$	1.28226	−	7.27206i	0.0889088	−	0.504227i
$209$	−5.61912	−	18.7692i	−0.388683	−	1.29829i
$210$		0			0
$211$	13.3695	+	6.71439i	0.920391	+	0.462238i	0.844909	−	0.534909i	$-0.179654\pi$
$211$	13.3695	+	6.71439i	0.920391	+	0.462238i	0.0754817	+	0.997147i	$0.475951\pi$
$212$	0.293194	−	0.979338i	0.0201367	−	0.0672612i
$213$		0			0
$214$	3.92854	+	5.27695i	0.268550	+	0.360725i
$215$	−6.85392	−	11.8713i	−0.467433	−	0.809618i
$216$		0			0
$217$	−4.62784	+	8.01565i	−0.314158	+	0.544138i
$218$	27.1978	−	3.17896i	1.84206	−	0.215306i
$219$		0			0
$220$	1.30271	−	0.308748i	0.0878286	−	0.0208158i
$221$	7.64395	−	5.02750i	0.514188	−	0.338186i
$222$		0			0
$223$	4.25530	−	4.51035i	0.284956	−	0.302036i	−0.569046	−	0.822306i	$-0.692687\pi$
$223$	4.25530	−	4.51035i	0.284956	−	0.302036i	0.854002	+	0.520270i	$0.174169\pi$
$224$	−1.69116	−	1.41905i	−0.112995	−	0.0948142i
$225$		0			0
$226$	−10.2612	+	8.61013i	−0.682562	+	0.572737i
$227$	−0.830506	+	14.2592i	−0.0551226	+	0.946419i	0.851468	+	0.524407i	$0.175713\pi$
$227$	−0.830506	+	14.2592i	−0.0551226	+	0.946419i	−0.906590	+	0.422012i	$0.861324\pi$
$228$		0			0
$229$	11.6644	−	15.6680i	0.770804	−	1.03537i	−0.227300	−	0.973825i	$-0.572990\pi$
$229$	11.6644	−	15.6680i	0.770804	−	1.03537i	0.998104	−	0.0615447i	$-0.0196027\pi$
$230$	1.58357	+	0.185093i	0.104417	+	0.0122046i
$231$		0			0
$232$	10.6560	+	7.00853i	0.699598	+	0.460133i
$233$	8.91628	+	3.24526i	0.584125	+	0.212604i	0.617143	−	0.786851i	$-0.288290\pi$
$233$	8.91628	+	3.24526i	0.584125	+	0.212604i	−0.0330187	+	0.999455i	$0.510512\pi$
$234$		0			0
$235$	0.303777	−	0.110566i	0.0198162	−	0.00721252i
$236$	−0.380298	−	0.0901324i	−0.0247553	−	0.00586712i
$237$		0			0
$238$	−0.889207	−	15.2671i	−0.0576387	−	0.989619i
$239$	−7.55122	−	8.00383i	−0.488448	−	0.517725i	0.435528	−	0.900175i	$-0.356562\pi$
$239$	−7.55122	−	8.00383i	−0.488448	−	0.517725i	−0.923976	+	0.382451i	$0.875080\pi$
$240$		0			0
$241$	−0.867612	+	2.01135i	−0.0558878	+	0.129562i	−0.943872	−	0.330312i	$-0.892846\pi$
$241$	−0.867612	+	2.01135i	−0.0558878	+	0.129562i	0.887984	+	0.459874i	$0.152105\pi$
$242$	−8.07871			−0.519319
$243$		0			0
$244$	−0.0372298			−0.00238340
$245$	−2.14780	+	4.97916i	−0.137218	+	0.318107i
$246$		0			0
$247$	5.60389	+	5.93978i	0.356567	+	0.377939i
$248$	0.753987	+	12.9455i	0.0478782	+	0.822038i
$249$		0			0
$250$	17.2138	+	4.07975i	1.08870	+	0.258026i
$251$	6.59388	−	2.39998i	0.416202	−	0.151485i	−0.125427	−	0.992103i	$-0.540030\pi$
$251$	6.59388	−	2.39998i	0.416202	−	0.151485i	0.541629	+	0.840618i	$0.317808\pi$
$252$		0			0
$253$	−2.55143	−	0.928643i	−0.160407	−	0.0583833i
$254$	−2.17644	−	1.43147i	−0.136562	−	0.0898181i
$255$		0			0
$256$	−4.86005	−	0.568059i	−0.303753	−	0.0355037i
$257$	−0.279271	+	0.375126i	−0.0174205	+	0.0233997i	−0.810748	−	0.585395i	$-0.800939\pi$
$257$	−0.279271	+	0.375126i	−0.0174205	+	0.0233997i	0.793328	+	0.608795i	$0.208347\pi$
$258$		0			0
$259$	−1.32414	+	22.7345i	−0.0822778	+	1.41265i
$260$	−0.427461	+	0.358683i	−0.0265100	+	0.0222446i
$261$		0			0
$262$	−8.15045	−	6.83904i	−0.503536	−	0.422517i
$263$	−13.0974	+	13.8824i	−0.807621	+	0.856028i	−0.991923	−	0.126842i	$-0.959516\pi$
$263$	−13.0974	+	13.8824i	−0.807621	+	0.856028i	0.184302	+	0.982870i	$0.440997\pi$
$264$		0			0
$265$	6.64644	−	4.37143i	0.408288	−	0.268535i
$266$	13.2819	−	3.14787i	0.814365	−	0.193008i
$267$		0			0
$268$	2.72665	−	0.318700i	0.166557	−	0.0194677i
$269$	−2.12061	+	3.67300i	−0.129296	+	0.223947i	−0.923404	−	0.383830i	$-0.874605\pi$
$269$	−2.12061	+	3.67300i	−0.129296	+	0.223947i	0.794108	+	0.607776i	$0.207938\pi$
$270$		0			0
$271$	−3.83162	−	6.63656i	−0.232754	−	0.403142i	0.725863	−	0.687839i	$-0.241440\pi$
$271$	−3.83162	−	6.63656i	−0.232754	−	0.403142i	−0.958618	+	0.284697i	$0.908107\pi$
$272$	−14.1265	−	18.9752i	−0.856544	−	1.15054i
$273$		0			0
$274$	−7.44313	+	24.8618i	−0.449656	+	1.50196i
$275$	−8.80630	−	4.42269i	−0.531040	−	0.266698i
$276$		0			0
$277$	−4.25476	−	14.2119i	−0.255644	−	0.853909i	−0.985408	−	0.170210i	$-0.945555\pi$
$277$	−4.25476	−	14.2119i	−0.255644	−	0.853909i	0.729764	−	0.683699i	$-0.239630\pi$
$278$	4.90030	−	27.7910i	0.293901	−	1.66679i
$279$		0			0
$280$	−1.41060	−	7.99991i	−0.0842995	−	0.478086i
$281$	0.994631	−	0.499522i	0.0593347	−	0.0297990i	−0.418884	−	0.908040i	$-0.637579\pi$
$281$	0.994631	−	0.499522i	0.0593347	−	0.0297990i	0.478219	+	0.878241i	$0.341282\pi$
$282$		0			0
$283$	−2.61783	−	6.06882i	−0.155614	−	0.360754i	0.822518	−	0.568739i	$-0.192569\pi$
$283$	−2.61783	−	6.06882i	−0.155614	−	0.360754i	−0.978132	+	0.207985i	$0.933309\pi$
$284$	−0.817211	−	1.89451i	−0.0484926	−	0.112418i
$285$		0			0
$286$	9.09435	−	4.56735i	0.537760	−	0.270073i
$287$	3.34043	+	18.9445i	0.197179	+	1.11826i
$288$		0			0
$289$	2.13761	−	12.1230i	0.125742	−	0.713117i
$290$	−3.26841	−	10.9173i	−0.191928	−	0.641084i
$291$		0			0
$292$	2.14165	+	1.07557i	0.125330	+	0.0629432i
$293$	−0.892759	+	2.98202i	−0.0521555	+	0.174212i	−0.980099	−	0.198509i	$-0.936390\pi$
$293$	−0.892759	+	2.98202i	−0.0521555	+	0.174212i	0.927943	+	0.372721i	$0.121575\pi$
$294$		0			0
$295$	−1.81618	−	2.43955i	−0.105742	−	0.142036i
$296$	15.9528	+	27.6310i	0.927235	+	1.60602i
$297$		0			0
$298$	5.47544	−	9.48374i	0.317184	−	0.549379i
$299$	1.12403	−	0.131381i	0.0650045	−	0.00759794i
$300$		0			0
$301$	−15.8255	+	3.75072i	−0.912168	+	0.216188i
$302$	−3.31418	+	2.17977i	−0.190710	+	0.125432i
$303$		0			0
$304$	14.4896	−	15.3581i	0.831037	−	0.880848i
$305$	−0.221933	−	0.186224i	−0.0127079	−	0.0106632i
$306$		0			0
$307$	−5.76257	+	4.83537i	−0.328887	+	0.275969i	−0.792246	−	0.610202i	$-0.791088\pi$
$307$	−5.76257	+	4.83537i	−0.328887	+	0.275969i	0.463359	+	0.886171i	$0.346644\pi$
$308$	0.0923596	−	1.58575i	0.00526268	−	0.0903567i
$309$		0			0
$310$	6.91900	−	9.29383i	0.392973	−	0.527854i
$311$	15.2831	+	1.78634i	0.866628	+	0.101294i	0.537777	−	0.843087i	$-0.319264\pi$
$311$	15.2831	+	1.78634i	0.866628	+	0.101294i	0.328851	+	0.944382i	$0.393338\pi$
$312$		0			0
$313$	3.31693	+	2.18158i	0.187484	+	0.123310i	0.639781	−	0.768557i	$-0.279025\pi$
$313$	3.31693	+	2.18158i	0.187484	+	0.123310i	−0.452297	+	0.891867i	$0.649395\pi$
$314$	−7.97521	−	2.90274i	−0.450067	−	0.163811i
$315$		0			0
$316$	0.710537	−	0.258614i	0.0399708	−	0.0145482i
$317$	8.34397	+	1.97756i	0.468644	+	0.111071i	0.458151	−	0.888874i	$-0.348512\pi$
$317$	8.34397	+	1.97756i	0.468644	+	0.111071i	0.0104930	+	0.999945i	$0.496660\pi$
$318$		0			0
$319$	1.12844	+	19.3746i	0.0631805	+	1.08477i
$320$	−7.71673	−	8.17925i	−0.431378	−	0.457234i
$321$		0			0
$322$	0.749242	−	1.73694i	0.0417536	−	0.0967958i
$323$	26.1608			1.45563
$324$		0			0
$325$	4.10736			0.227835
$326$	−9.43490	+	21.8726i	−0.522551	+	1.21141i
$327$		0			0
$328$	18.4950	+	19.6035i	1.02121	+	1.08242i
$329$	−0.0223016	−	0.382905i	−0.00122953	−	0.0211102i
$330$		0			0
$331$	−9.07927	−	2.15183i	−0.499042	−	0.118275i	−0.0266164	−	0.999646i	$-0.508473\pi$
$331$	−9.07927	−	2.15183i	−0.499042	−	0.118275i	−0.472425	+	0.881371i	$0.656621\pi$
$332$	1.06230	−	0.386644i	0.0583010	−	0.0212198i
$333$		0			0
$334$	26.7247	+	9.72699i	1.46231	+	0.532237i
$335$	17.8482	+	11.7389i	0.975150	+	0.641366i
$336$		0			0
$337$	−4.37776	−	0.511687i	−0.238472	−	0.0278734i	−0.00398267	−	0.999992i	$-0.501268\pi$
$337$	−4.37776	−	0.511687i	−0.238472	−	0.0278734i	−0.234489	+	0.972119i	$0.575342\pi$
$338$	8.99717	−	12.0853i	0.489382	−	0.657354i
$339$		0			0
$340$	−0.103942	+	1.78462i	−0.00563706	+	0.0967847i
$341$	−15.1155	+	12.6834i	−0.818548	+	0.686844i
$342$		0			0
$343$	15.1270	+	12.6931i	0.816782	+	0.685362i
$344$	−15.6368	+	16.5740i	−0.843078	+	0.893610i
$345$		0			0
$346$	−29.3313	+	19.2915i	−1.57686	+	1.03712i
$347$	19.4982	−	4.62117i	1.04672	−	0.248077i	0.328943	−	0.944350i	$-0.393308\pi$
$347$	19.4982	−	4.62117i	1.04672	−	0.248077i	0.717777	+	0.696273i	$0.245160\pi$
$348$		0			0
$349$	33.4202	−	3.90626i	1.78894	−	0.209097i	0.844001	−	0.536342i	$-0.180194\pi$
$349$	33.4202	−	3.90626i	1.78894	−	0.209097i	0.944939	+	0.327245i	$0.106120\pi$
$350$	3.43279	−	5.94576i	0.183490	−	0.317814i
$351$		0			0
$352$	−2.35320	−	4.07587i	−0.125426	−	0.217244i
$353$	4.81620	+	6.46927i	0.256340	+	0.344325i	0.911600	−	0.411079i	$-0.134848\pi$
$353$	4.81620	+	6.46927i	0.256340	+	0.344325i	−0.655259	+	0.755404i	$0.727441\pi$
$354$		0			0
$355$	4.60483	−	15.3812i	0.244399	−	0.816349i
$356$	1.30312	+	0.654453i	0.0690654	+	0.0346859i
$357$		0			0
$358$	−1.91005	−	6.38002i	−0.100949	−	0.337194i
$359$	−2.83469	+	16.0764i	−0.149609	+	0.848477i	0.813940	+	0.580948i	$0.197318\pi$
$359$	−2.83469	+	16.0764i	−0.149609	+	0.848477i	−0.963550	+	0.267529i	$0.913793\pi$
$360$		0			0
$361$	0.755367	+	4.28390i	0.0397562	+	0.225468i
$362$	−5.06061	+	2.54153i	−0.265980	+	0.133580i
$363$		0			0
$364$	0.262230	+	0.607917i	0.0137446	+	0.0318635i
$365$	7.38667	+	17.1242i	0.386636	+	0.896323i
$366$		0			0
$367$	11.7615	−	5.90686i	0.613947	−	0.308336i	−0.114516	−	0.993421i	$-0.536532\pi$
$367$	11.7615	−	5.90686i	0.613947	−	0.308336i	0.728462	+	0.685086i	$0.240235\pi$
$368$	−0.508116	−	2.88167i	−0.0264874	−	0.150217i
$369$		0			0
$370$	4.95036	−	28.0749i	0.257357	−	1.45954i
$371$	−2.70701	−	9.04204i	−0.140541	−	0.469439i
$372$		0			0
$373$	0.194504	+	0.0976835i	0.0100710	+	0.00505786i	0.453828	−	0.891090i	$-0.350058\pi$
$373$	0.194504	+	0.0976835i	0.0100710	+	0.00505786i	−0.443757	+	0.896147i	$0.646354\pi$
$374$	9.35050	−	31.2329i	0.483503	−	1.61501i
$375$		0			0
$376$	−0.320893	−	0.431034i	−0.0165488	−	0.0222289i
$377$	−4.04451	−	7.00529i	−0.208303	−	0.360791i
$378$		0			0
$379$	12.0931	−	20.9458i	0.621180	−	1.07592i	−0.368086	−	0.929792i	$-0.619987\pi$
$379$	12.0931	−	20.9458i	0.621180	−	1.07592i	0.989266	−	0.146124i	$-0.0466797\pi$
$380$	−1.58478	+	0.185235i	−0.0812977	+	0.00950234i
$381$		0			0
$382$	26.5885	−	6.30159i	1.36039	−	0.322417i
$383$	7.06738	−	4.64829i	0.361126	−	0.237516i	−0.355960	−	0.934501i	$-0.615846\pi$
$383$	7.06738	−	4.64829i	0.361126	−	0.237516i	0.717086	+	0.696985i	$0.245476\pi$
$384$		0			0
$385$	8.48253	−	8.99096i	0.432310	−	0.458222i
$386$	18.6851	+	15.6787i	0.951048	+	0.798024i
$387$		0			0
$388$	−0.211154	+	0.177179i	−0.0107197	+	0.00899491i
$389$	1.46030	−	25.0723i	0.0740400	−	1.27122i	−0.732799	−	0.680446i	$-0.761786\pi$
$389$	1.46030	−	25.0723i	0.0740400	−	1.27122i	0.806839	−	0.590772i	$-0.201177\pi$
$390$		0			0
$391$	2.16498	−	2.90807i	0.109488	−	0.147067i
$392$	8.95294	+	1.04645i	0.452192	+	0.0528536i
$393$		0			0
$394$	−23.2330	−	15.2806i	−1.17046	−	0.769826i
$395$	5.52922	+	2.01247i	0.278205	+	0.101258i
$396$		0			0
$397$	23.8173	−	8.66880i	1.19536	−	0.435074i	0.333756	−	0.942660i	$-0.391684\pi$
$397$	23.8173	−	8.66880i	1.19536	−	0.435074i	0.861602	+	0.507585i	$0.169462\pi$
$398$	−1.29393	−	0.306667i	−0.0648588	−	0.0153718i
$399$		0			0
$400$	−0.617506	−	10.6022i	−0.0308753	−	0.530108i
$401$	16.2900	+	17.2664i	0.813483	+	0.862242i	0.992580	−	0.121589i	$-0.0387991\pi$
$401$	16.2900	+	17.2664i	0.813483	+	0.862242i	−0.179097	+	0.983831i	$0.557318\pi$
$402$		0			0
$403$	3.25746	−	7.55163i	0.162265	−	0.376174i
$404$	1.02098			0.0507957
$405$		0			0
$406$	−13.5210			−0.671037
$407$	−19.2293	+	44.5785i	−0.953160	+	2.20967i
$408$		0			0
$409$	−6.44213	−	6.82826i	−0.318543	−	0.337636i	0.548240	−	0.836321i	$-0.315298\pi$
$409$	−6.44213	−	6.82826i	−0.318543	−	0.337636i	−0.866783	+	0.498685i	$0.833816\pi$
$410$	−1.40020	−	24.0404i	−0.0691508	−	1.18727i
$411$		0			0
$412$	−0.456890	−	0.108285i	−0.0225093	−	0.00533481i
$413$	−3.39087	+	1.23418i	−0.166854	+	0.0607298i
$414$		0			0
$415$	8.26652	+	3.00877i	0.405787	+	0.147695i
$416$	1.63892	+	1.07794i	0.0803547	+	0.0528501i
$417$		0			0
$418$	28.9028	+	3.37825i	1.41368	+	0.165236i
$419$	−7.01065	+	9.41694i	−0.342493	+	0.460048i	−0.939680	−	0.342054i	$-0.888877\pi$
$419$	−7.01065	+	9.41694i	−0.342493	+	0.460048i	0.597187	+	0.802102i	$0.296285\pi$
$420$		0			0
$421$	−0.393410	+	6.75459i	−0.0191736	+	0.329199i	0.975058	+	0.221948i	$0.0712416\pi$
$421$	−0.393410	+	6.75459i	−0.0191736	+	0.329199i	−0.994232	+	0.107250i	$0.965795\pi$
$422$	−17.0220	+	14.2831i	−0.828618	+	0.695293i
$423$		0			0
$424$	−10.1299	−	8.49998i	−0.491950	−	0.412795i
$425$	9.02980	−	9.57103i	0.438010	−	0.464263i
$426$		0			0
$427$	−0.287187	+	0.188886i	−0.0138980	+	0.00914083i
$428$	−0.887812	+	0.210415i	−0.0429140	+	0.0101708i
$429$		0			0
$430$	20.2220	−	2.36361i	0.975191	−	0.113984i
$431$	3.90563	−	6.76475i	0.188128	−	0.325846i	−0.756498	−	0.653996i	$-0.773092\pi$
$431$	3.90563	−	6.76475i	0.188128	−	0.325846i	0.944626	+	0.328149i	$0.106425\pi$
$432$		0			0
$433$	−2.20878	−	3.82573i	−0.106147	−	0.183853i	0.808059	−	0.589102i	$-0.200518\pi$
$433$	−2.20878	−	3.82573i	−0.106147	−	0.183853i	−0.914206	+	0.405249i	$0.867185\pi$
$434$	−8.20918	−	11.0268i	−0.394053	−	0.529305i
$435$		0			0
$436$	−1.08921	+	3.63820i	−0.0521635	+	0.174238i
$437$	2.89173	+	1.45228i	0.138330	+	0.0694721i
$438$		0			0
$439$	4.31161	+	14.4018i	0.205782	+	0.687360i	0.997110	+	0.0759684i	$0.0242048\pi$
$439$	4.31161	+	14.4018i	0.205782	+	0.687360i	−0.791328	+	0.611392i	$0.790610\pi$
$440$	3.00721	−	17.0547i	0.143363	−	0.813052i
$441$		0			0
$442$	2.35966	+	13.3823i	0.112238	+	0.636531i
$443$	10.1485	−	5.09675i	0.482168	−	0.242154i	−0.191075	−	0.981576i	$-0.561197\pi$
$443$	10.1485	−	5.09675i	0.482168	−	0.242154i	0.673243	+	0.739422i	$0.264901\pi$
$444$		0			0
$445$	4.49455	+	10.4195i	0.213062	+	0.493934i
$446$	3.64786	+	8.45668i	0.172731	+	0.400435i
$447$		0			0
$448$	−11.9226	+	5.98776i	−0.563291	+	0.282895i
$449$	−1.16004	−	6.57891i	−0.0547457	−	0.310478i	0.945122	−	0.326716i	$-0.105942\pi$
$449$	−1.16004	−	6.57891i	−0.0547457	−	0.310478i	−0.999868	+	0.0162381i	$0.994831\pi$
$450$		0			0
$451$	−7.12134	+	40.3871i	−0.335331	+	1.90176i
$452$	−0.532810	−	1.77971i	−0.0250613	−	0.0837105i
$453$		0			0
$454$	−18.9580	−	9.52106i	−0.889743	−	0.446846i
$455$	−1.47761	+	4.93557i	−0.0692716	+	0.231383i
$456$		0			0
$457$	7.17351	+	9.63570i	0.335563	+	0.450739i	0.937593	−	0.347734i	$-0.113049\pi$
$457$	7.17351	+	9.63570i	0.335563	+	0.450739i	−0.602030	+	0.798473i	$0.705641\pi$
$458$	14.5059	+	25.1249i	0.677815	+	1.17401i
$459$		0			0
$460$	−0.110560	+	0.191496i	−0.00515490	+	0.00892855i
$461$	−6.95142	+	0.812504i	−0.323760	+	0.0378421i	−0.276421	−	0.961037i	$-0.589148\pi$
$461$	−6.95142	+	0.812504i	−0.323760	+	0.0378421i	−0.0473393	+	0.998879i	$0.515074\pi$
$462$		0			0
$463$	27.2778	−	6.46495i	1.26771	−	0.300452i	0.458879	−	0.888499i	$-0.348251\pi$
$463$	27.2778	−	6.46495i	1.26771	−	0.300452i	0.808827	+	0.588047i	$0.200103\pi$
$464$	−17.4744	+	11.4931i	−0.811229	+	0.533554i
$465$		0			0
$466$	−9.67112	+	10.2508i	−0.448006	+	0.474858i
$467$	−10.9662	−	9.20178i	−0.507458	−	0.425807i	0.352776	−	0.935708i	$-0.385238\pi$
$467$	−10.9662	−	9.20178i	−0.507458	−	0.425807i	−0.860233	+	0.509900i	$0.829682\pi$
$468$		0			0
$469$	19.4162	−	16.2921i	0.896557	−	0.752300i
$470$	−0.0279179	+	0.479331i	−0.00128776	+	0.0221099i
$471$		0			0
$472$	−3.01898	+	4.05519i	−0.138960	+	0.186655i
$473$	−34.4380	−	4.02523i	−1.58346	−	0.185080i
$474$		0			0
$475$	9.81243	+	6.45374i	0.450225	+	0.296118i
$476$	1.99307	+	0.725420i	0.0913524	+	0.0332496i
$477$		0			0
$478$	15.3578	−	5.58977i	0.702448	−	0.255670i
$479$	−21.8904	−	5.18813i	−1.00020	−	0.237052i	−0.302273	−	0.953221i	$-0.597745\pi$
$479$	−21.8904	−	5.18813i	−1.00020	−	0.237052i	−0.697926	+	0.716170i	$0.745894\pi$
$480$		0			0
$481$	−1.17658	−	20.2010i	−0.0536473	−	0.921088i
$482$	−2.23266	−	2.36648i	−0.101695	−	0.107790i
$483$		0			0
$484$	0.443783	−	1.02881i	0.0201720	−	0.0467639i
$485$	−2.14498			−0.0973984
$486$		0			0
$487$	−41.7203			−1.89053			−0.945264	−	0.326307i	$-0.894196\pi$
$487$	−41.7203			−1.89053			−0.945264	+	0.326307i	$0.894196\pi$
$488$	−0.190745	+	0.442196i	−0.00863460	+	0.0200173i
$489$		0			0
$490$	−5.52701	−	5.85829i	−0.249685	−	0.264650i
$491$	0.643607	+	11.0503i	0.0290456	+	0.498694i	0.981190	+	0.193045i	$0.0618363\pi$
$491$	0.643607	+	11.0503i	0.0290456	+	0.498694i	−0.952144	+	0.305649i	$0.901127\pi$
$492$		0			0
$493$	−25.2154	−	5.97617i	−1.13565	−	0.269153i
$494$	−11.3973	+	4.14826i	−0.512787	+	0.186639i
$495$		0			0
$496$	−19.9825	−	7.27302i	−0.897239	−	0.326568i
$497$	−15.9157	−	10.4679i	−0.713917	−	0.469550i
$498$		0			0
$499$	−7.76171	−	0.907214i	−0.347462	−	0.0406125i	−0.0594278	−	0.998233i	$-0.518928\pi$
$499$	−7.76171	−	0.907214i	−0.347462	−	0.0406125i	−0.288034	+	0.957620i	$0.593002\pi$
$500$	−1.46514	+	1.96803i	−0.0655232	+	0.0880130i
$501$		0			0
$502$	−0.605994	+	10.4045i	−0.0270468	+	0.464376i
$503$	18.1547	−	15.2336i	0.809478	−	0.679233i	−0.141005	−	0.990009i	$-0.545033\pi$
$503$	18.1547	−	15.2336i	0.809478	−	0.679233i	0.950483	+	0.310776i	$0.100589\pi$
$504$		0			0
$505$	6.08624	+	5.10696i	0.270834	+	0.227257i
$506$	2.76743	−	2.93330i	0.123027	−	0.130401i
$507$		0			0
$508$	0.301851	−	0.198530i	0.0133925	−	0.00880836i
$509$	12.1281	−	2.87442i	0.537570	−	0.127406i	0.0471419	−	0.998888i	$-0.484989\pi$
$509$	12.1281	−	2.87442i	0.537570	−	0.127406i	0.490428	+	0.871482i	$0.336841\pi$
$510$		0			0
$511$	21.9774	−	2.56879i	0.972222	−	0.113636i
$512$	−9.10692	+	15.7736i	−0.402473	+	0.697103i
$513$		0			0
$514$	−0.347303	−	0.601546i	−0.0153189	−	0.0265331i
$515$	−2.18195	−	2.93087i	−0.0961484	−	0.129150i
$516$		0			0
$517$	0.234514	−	0.783332i	0.0103139	−	0.0344509i
$518$	−30.2261	−	15.1801i	−1.32806	−	0.666976i
$519$		0			0
$520$	2.07017	+	6.91484i	0.0907829	+	0.303236i
$521$	3.66734	−	20.7985i	0.160669	−	0.911200i	−0.792749	−	0.609548i	$-0.791351\pi$
$521$	3.66734	−	20.7985i	0.160669	−	0.911200i	0.953418	−	0.301652i	$-0.0975380\pi$
$522$		0			0
$523$	7.23247	+	41.0174i	0.316254	+	1.79356i	0.565102	+	0.825021i	$0.308837\pi$
$523$	7.23247	+	41.0174i	0.316254	+	1.79356i	−0.248848	+	0.968543i	$0.580052\pi$
$524$	1.31866	−	0.662256i	0.0576059	−	0.0289308i
$525$		0			0
$526$	−11.2277	−	26.0288i	−0.489553	−	1.13491i
$527$	−10.4356	−	24.1924i	−0.454581	−	1.05384i
$528$		0			0
$529$	−20.1528	+	10.1211i	−0.876209	+	0.440049i
$530$	2.05173	+	11.6360i	0.0891217	+	0.505434i
$531$		0			0
$532$	−0.328733	+	1.86434i	−0.0142524	+	0.0808293i
$533$	−4.90235	−	16.3750i	−0.212344	−	0.709279i
$534$		0			0
$535$	−6.34489	−	3.18653i	−0.274314	−	0.137766i
$536$	10.1845	−	34.0185i	0.439902	−	1.46938i
$537$		0			0
$538$	−3.76168	−	5.05281i	−0.162177	−	0.217842i
$539$	6.85799	+	11.8784i	0.295395	+	0.511638i
$540$		0			0
$541$	−4.87647	+	8.44629i	−0.209656	+	0.363134i	−0.951606	−	0.307320i	$-0.900568\pi$
$541$	−4.87647	+	8.44629i	−0.209656	+	0.363134i	0.741950	+	0.670455i	$0.233901\pi$
$542$	11.3049	−	1.32136i	0.485588	−	0.0567571i
$543$		0			0
$544$	6.11490	−	1.44926i	0.262174	−	0.0621364i
$545$	−24.6913	+	16.2397i	−1.05766	+	0.695632i
$546$		0			0
$547$	−0.475687	+	0.504198i	−0.0203389	+	0.0215580i	−0.737463	−	0.675387i	$-0.763976\pi$
$547$	−0.475687	+	0.504198i	−0.0203389	+	0.0215580i	0.717124	+	0.696945i	$0.245458\pi$
$548$	−2.75722	−	2.31358i	−0.117783	−	0.0988314i
$549$		0			0
$550$	11.2122	−	9.40814i	0.478089	−	0.401164i
$551$	1.34487	−	23.0905i	0.0572934	−	0.983689i
$552$		0			0
$553$	4.16893	−	5.59984i	0.177281	−	0.238130i
$554$	21.8850	+	2.55799i	0.929804	+	0.108678i
$555$		0			0
$556$	3.26993	+	2.15067i	0.138676	+	0.0912087i
$557$	−28.7125	−	10.4505i	−1.21659	−	0.442801i	−0.347602	−	0.937642i	$-0.613004\pi$
$557$	−28.7125	−	10.4505i	−1.21659	−	0.442801i	−0.868984	+	0.494841i	$0.835226\pi$
$558$		0			0
$559$	13.5800	−	4.94270i	0.574371	−	0.209054i
$560$	12.9621	+	3.07208i	0.547751	+	0.129819i
$561$		0			0
$562$	0.0961204	+	1.65032i	0.00405460	+	0.0696147i
$563$	6.68923	+	7.09017i	0.281918	+	0.298815i	0.852822	−	0.522201i	$-0.174889\pi$
$563$	6.68923	+	7.09017i	0.281918	+	0.298815i	−0.570905	+	0.821016i	$0.693407\pi$
$564$		0			0
$565$	5.72596	−	13.2743i	0.240893	−	0.558453i
$566$	9.81660			0.412622
$567$		0			0
$568$	−26.6889			−1.11984
$569$	−7.79560	+	18.0722i	−0.326808	+	0.757627i	0.673029	+	0.739616i	$0.264993\pi$
$569$	−7.79560	+	18.0722i	−0.326808	+	0.757627i	−0.999838	+	0.0180113i	$0.994267\pi$
$570$		0			0
$571$	22.6458	+	24.0031i	0.947697	+	1.00450i	0.999983	+	0.00586776i	$0.00186778\pi$
$571$	22.6458	+	24.0031i	0.947697	+	1.00450i	−0.0522860	+	0.998632i	$0.516651\pi$
$572$	0.0820673	+	1.40904i	0.00343140	+	0.0589149i
$573$		0			0
$574$	−27.8014	−	6.58906i	−1.16041	−	0.275022i
$575$	1.52945	−	0.556674i	0.0637824	−	0.0232149i
$576$		0			0
$577$	−19.1279	−	6.96197i	−0.796303	−	0.289831i	−0.0883494	−	0.996090i	$-0.528159\pi$
$577$	−19.1279	−	6.96197i	−0.796303	−	0.289831i	−0.707954	+	0.706259i	$0.750381\pi$
$578$	15.2757	+	10.0470i	0.635384	+	0.417899i
$579$		0			0
$580$	1.56983	+	0.183487i	0.0651837	+	0.00761888i
$581$	6.23280	−	8.37210i	0.258580	−	0.347333i
$582$		0			0
$583$	1.16997	−	20.0877i	0.0484553	−	0.831946i
$584$	23.7477	−	19.9267i	0.982686	−	0.824571i
$585$		0			0
$586$	−3.54165	−	2.97180i	−0.146304	−	0.122764i
$587$	24.1185	−	25.5641i	0.995477	−	1.05514i	−0.00300161	−	0.999995i	$-0.500955\pi$
$587$	24.1185	−	25.5641i	0.995477	−	1.05514i	0.998478	−	0.0551480i	$-0.0175631\pi$
$588$		0			0
$589$	19.6476	−	12.9224i	0.809566	−	0.532460i
$590$	4.39545	−	1.04174i	0.180958	−	0.0428878i
$591$		0			0
$592$	−51.9672	+	6.07410i	−2.13584	+	0.249644i
$593$	−4.46816	+	7.73909i	−0.183485	+	0.317806i	−0.943065	−	0.332608i	$-0.892071\pi$
$593$	−4.46816	+	7.73909i	−0.183485	+	0.317806i	0.759580	+	0.650414i	$0.225405\pi$
$594$		0			0
$595$	8.25249	+	14.2937i	0.338319	+	0.585986i
$596$	0.906953	+	1.21825i	0.0371503	+	0.0499015i
$597$		0			0
$598$	−0.482071	+	1.61023i	−0.0197134	+	0.0658472i
$599$	−35.4506	−	17.8040i	−1.44847	−	0.727451i	−0.461322	−	0.887233i	$-0.652625\pi$
$599$	−35.4506	−	17.8040i	−1.44847	−	0.727451i	−0.987152	+	0.159782i	$0.948921\pi$
$600$		0			0
$601$	−6.78673	−	22.6693i	−0.276837	−	0.924699i	−0.977452	−	0.211159i	$-0.932276\pi$
$601$	−6.78673	−	22.6693i	−0.276837	−	0.924699i	0.700615	−	0.713539i	$-0.252909\pi$
$602$	4.19466	−	23.7891i	0.170962	−	0.969572i
$603$		0			0
$604$	−0.0955328	−	0.541794i	−0.00388718	−	0.0220453i
$605$	7.79156	−	3.91307i	0.316772	−	0.159089i
$606$		0			0
$607$	7.03429	+	16.3073i	0.285513	+	0.661893i	0.999258	−	0.0385121i	$-0.0122618\pi$
$607$	7.03429	+	16.3073i	0.285513	+	0.661893i	−0.713745	+	0.700405i	$0.753003\pi$
$608$	2.22164	+	5.15035i	0.0900995	+	0.208874i
$609$		0			0
$610$	0.384529	−	0.193118i	0.0155691	−	0.00781911i
$611$	0.0591812	+	0.335633i	0.00239422	+	0.0135783i
$612$		0			0
$613$	−0.410662	+	2.32898i	−0.0165865	+	0.0940666i	−0.991977	−	0.126417i	$-0.959652\pi$
$613$	−0.410662	+	2.32898i	−0.0165865	+	0.0940666i	0.975391	+	0.220483i	$0.0707635\pi$
$614$	−3.20441	−	10.7035i	−0.129319	−	0.431957i
$615$		0			0
$616$	−18.3615	−	9.22150i	−0.739807	−	0.371545i
$617$	−9.69418	+	32.3808i	−0.390273	+	1.30360i	0.506931	+	0.861986i	$0.330780\pi$
$617$	−9.69418	+	32.3808i	−0.390273	+	1.30360i	−0.897204	+	0.441616i	$0.854405\pi$
$618$		0			0
$619$	28.3599	+	38.0940i	1.13988	+	1.53113i	0.809345	+	0.587334i	$0.199823\pi$
$619$	28.3599	+	38.0940i	1.13988	+	1.53113i	0.330537	+	0.943793i	$0.392770\pi$
$620$	0.803470	+	1.39165i	0.0322681	+	0.0558901i
$621$		0			0
$622$	−11.4270	+	19.7921i	−0.458180	+	0.793591i
$623$	13.3725	−	1.56303i	0.535759	−	0.0626213i
$624$		0			0
$625$	−6.75322	+	1.60054i	−0.270129	+	0.0640217i
$626$	−4.92649	+	3.24021i	−0.196902	+	0.129505i
$627$		0			0
$628$	0.807755	−	0.856170i	0.0322329	−	0.0341649i
$629$	−49.6594	−	41.6692i	−1.98005	−	1.66146i
$630$		0			0
$631$	−14.6874	+	12.3242i	−0.584695	+	0.490617i	−0.886485	−	0.462757i	$-0.846860\pi$
$631$	−14.6874	+	12.3242i	−0.584695	+	0.490617i	0.301790	+	0.953374i	$0.402416\pi$
$632$	0.568709	−	9.76436i	0.0226220	−	0.388406i
$633$		0			0
$634$	−7.60557	+	10.2161i	−0.302056	+	0.405731i
$635$	2.79244	+	0.326389i	0.110814	+	0.0129523i
$636$		0			0
$637$	−4.77634	−	3.14145i	−0.189246	−	0.124469i
$638$	−27.0866	−	9.85872i	−1.07237	−	0.390311i
$639$		0			0
$640$	19.1913	−	6.98507i	0.758603	−	0.276109i
$641$	2.04822	+	0.485436i	0.0808997	+	0.0191736i	0.270866	−	0.962617i	$-0.412690\pi$
$641$	2.04822	+	0.485436i	0.0808997	+	0.0191736i	−0.189967	+	0.981791i	$0.560838\pi$
$642$		0			0
$643$	2.54772	+	43.7427i	0.100472	+	1.72504i	0.552905	+	0.833244i	$0.313519\pi$
$643$	2.54772	+	43.7427i	0.100472	+	1.72504i	−0.452433	+	0.891798i	$0.649444\pi$
$644$	0.180037	+	0.190829i	0.00709447	+	0.00751970i
$645$		0			0
$646$	−15.3899	+	35.6778i	−0.605507	+	1.40372i
$647$	2.17952			0.0856859			0.0428430	−	0.999082i	$-0.486358\pi$
$647$	2.17952			0.0856859			0.0428430	+	0.999082i	$0.486358\pi$
$648$		0			0
$649$	−7.69281			−0.301969
$650$	−2.41628	+	5.60157i	−0.0947743	+	0.219712i
$651$		0			0
$652$	−2.26714	−	2.40303i	−0.0887880	−	0.0941098i
$653$	1.08815	+	18.6828i	0.0425826	+	0.731115i	0.950262	+	0.311451i	$0.100815\pi$
$653$	1.08815	+	18.6828i	0.0425826	+	0.731115i	−0.907680	+	0.419664i	$0.862148\pi$
$654$		0			0
$655$	11.1734	+	2.64814i	0.436579	+	0.103471i
$656$	−41.5311	+	15.1161i	−1.62152	+	0.590183i
$657$		0			0
$658$	0.535320	+	0.194841i	0.0208689	+	0.00759568i
$659$	11.9512	+	7.86043i	0.465553	+	0.306199i	0.760527	−	0.649306i	$-0.224941\pi$
$659$	11.9512	+	7.86043i	0.465553	+	0.306199i	−0.294974	+	0.955505i	$0.595311\pi$
$660$		0			0
$661$	−24.8243	−	2.90155i	−0.965555	−	0.112857i	−0.381321	−	0.924443i	$-0.624531\pi$
$661$	−24.8243	−	2.90155i	−0.965555	−	0.112857i	−0.584234	+	0.811586i	$0.698605\pi$
$662$	8.27579	−	11.1163i	0.321648	−	0.432048i
$663$		0			0
$664$	0.850255	−	14.5983i	0.0329963	−	0.566524i
$665$	−11.2851	+	9.46931i	−0.437617	+	0.367204i
$666$		0			0
$667$	−2.45548	−	2.06039i	−0.0950764	−	0.0797786i
$668$	−2.70676	+	2.86900i	−0.104728	+	0.111005i
$669$		0			0
$670$	−26.5091	+	17.4353i	−1.02414	+	0.673586i
$671$	−0.713045	+	0.168995i	−0.0275268	+	0.00652397i
$672$		0			0
$673$	29.4895	−	3.44683i	1.13674	−	0.132866i	0.473163	−	0.880975i	$-0.343112\pi$
$673$	29.4895	−	3.44683i	1.13674	−	0.132866i	0.663576	+	0.748109i	$0.269038\pi$
$674$	3.27319	−	5.66933i	0.126078	−	0.218374i
$675$		0			0
$676$	1.04480	+	1.80964i	0.0401846	+	0.0696017i
$677$	23.1605	+	31.1099i	0.890129	+	1.19565i	0.979860	+	0.199685i	$0.0639919\pi$
$677$	23.1605	+	31.1099i	0.890129	+	1.19565i	−0.0897310	+	0.995966i	$0.528601\pi$
$678$		0			0
$679$	−0.729900	+	2.43803i	−0.0280110	+	0.0935632i
$680$	20.6642	+	10.3780i	0.792436	+	0.397977i
$681$		0			0
$682$	−8.40530	−	28.0757i	−0.321856	−	1.07507i
$683$	−2.81006	+	15.9367i	−0.107524	+	0.609799i	0.882658	+	0.470016i	$0.155752\pi$
$683$	−2.81006	+	15.9367i	−0.107524	+	0.609799i	−0.990182	+	0.139784i	$0.955359\pi$
$684$		0			0
$685$	−4.86369	−	27.5833i	−0.185832	−	1.05391i
$686$	−26.2096	+	13.1630i	−1.00069	+	0.502564i
$687$		0			0
$688$	−14.8000	−	34.3103i	−0.564246	−	1.30807i
$689$	3.32182	+	7.70084i	0.126551	+	0.293379i
$690$		0			0
$691$	−15.7344	+	7.90210i	−0.598564	+	0.300610i	−0.722164	−	0.691722i	$-0.756852\pi$
$691$	−15.7344	+	7.90210i	−0.598564	+	0.300610i	0.123600	+	0.992332i	$0.460556\pi$
$692$	−0.845488	−	4.79500i	−0.0321406	−	0.182279i
$693$		0			0
$694$	−5.16814	+	29.3100i	−0.196180	+	1.11259i
$695$	8.73495	+	29.1768i	0.331335	+	1.10674i
$696$		0			0
$697$	−48.9348	−	24.5760i	−1.85354	−	0.930881i
$698$	−14.3331	+	47.8760i	−0.542517	+	1.81213i
$699$		0			0
$700$	0.568608	+	0.763773i	0.0214914	+	0.0288679i
$701$	−9.33660	−	16.1715i	−0.352639	−	0.610788i	0.634072	−	0.773274i	$-0.281382\pi$
$701$	−9.33660	−	16.1715i	−0.352639	−	0.610788i	−0.986711	+	0.162486i	$0.948049\pi$
$702$		0			0
$703$	28.9303	−	50.1087i	1.09113	−	1.88989i
$704$	−28.2504	+	3.30200i	−1.06473	+	0.124449i
$705$		0			0
$706$	−11.6560	+	2.76252i	−0.438679	+	0.103969i
$707$	7.87574	−	5.17996i	0.296198	−	0.194812i
$708$		0			0
$709$	−22.6076	+	23.9627i	−0.849047	+	0.899938i	−0.996013	−	0.0892040i	$-0.971568\pi$
$709$	−22.6076	+	23.9627i	−0.849047	+	0.899938i	0.146966	+	0.989142i	$0.453049\pi$
$710$	18.2677	+	15.3285i	0.685576	+	0.575267i
$711$		0			0
$712$	14.4497	−	12.1247i	0.541526	−	0.454394i
$713$	0.189493	−	3.25347i	0.00709657	−	0.121843i
$714$		0			0
$715$	−6.55882	+	8.81003i	−0.245286	+	0.329476i
$716$	0.917404	+	0.107229i	0.0342850	+	0.00400734i
$717$		0			0
$718$	−20.2571	−	13.3233i	−0.755990	−	0.497222i
$719$	43.1137	+	15.6921i	1.60787	+	0.585216i	0.981017	−	0.193922i	$-0.0621209\pi$
$719$	43.1137	+	15.6921i	1.60787	+	0.585216i	0.626852	+	0.779139i	$0.284343\pi$
$720$		0			0
$721$	−4.07379	+	1.48274i	−0.151716	+	0.0552200i
$722$	−6.28670	−	1.48997i	−0.233967	−	0.0554511i
$723$		0			0
$724$	−0.0456669	−	0.784070i	−0.00169720	−	0.0291397i
$725$	−7.98355	−	8.46207i	−0.296502	−	0.314273i
$726$		0			0
$727$	6.39466	−	14.8245i	0.237165	−	0.549810i	−0.757516	−	0.652817i	$-0.773587\pi$
$727$	6.39466	−	14.8245i	0.237165	−	0.549810i	0.994681	+	0.103007i	$0.0328464\pi$
$728$	8.56403			0.317404
$729$		0			0
$730$	−27.6992			−1.02519
$731$	18.3372	−	42.5105i	0.678227	−	1.57231i
$732$		0			0
$733$	17.6698	+	18.7289i	0.652648	+	0.691767i	0.966197	−	0.257805i	$-0.0829993\pi$
$733$	17.6698	+	18.7289i	0.652648	+	0.691767i	−0.313549	+	0.949572i	$0.601518\pi$
$734$	1.13663	+	19.5151i	0.0419536	+	0.720316i
$735$		0			0
$736$	0.756375	+	0.179264i	0.0278803	+	0.00660776i
$737$	50.7756	−	18.4808i	1.87034	−	0.680750i
$738$		0			0
$739$	−16.9934	−	6.18508i	−0.625111	−	0.227522i	0.00999089	−	0.999950i	$-0.496820\pi$
$739$	−16.9934	−	6.18508i	−0.625111	−	0.227522i	−0.635102	+	0.772428i	$0.719042\pi$
$740$	3.30334	+	2.17264i	0.121433	+	0.0798678i
$741$		0			0
$742$	13.9239	+	1.62747i	0.511162	+	0.0597463i
$743$	−26.4761	+	35.5636i	−0.971314	+	1.30470i	−0.0189230	+	0.999821i	$0.506024\pi$
$743$	−26.4761	+	35.5636i	−0.971314	+	1.30470i	−0.952391	+	0.304880i	$0.901384\pi$
$744$		0			0
$745$	−0.687201	+	11.7988i	−0.0251771	+	0.432274i
$746$	−0.247642	+	0.207797i	−0.00906683	+	0.00760798i
$747$		0			0
$748$	3.46379	+	2.90646i	0.126649	+	0.106271i
$749$	−5.78095	+	6.12744i	−0.211231	+	0.223892i
$750$		0			0
$751$	−2.09320	+	1.37672i	−0.0763819	+	0.0502372i	−0.587126	−	0.809496i	$-0.699741\pi$
$751$	−2.09320	+	1.37672i	−0.0763819	+	0.0502372i	0.510744	+	0.859733i	$0.329370\pi$
$752$	0.857459	−	0.203222i	0.0312683	−	0.00741073i
$753$		0			0
$754$	11.9330	−	1.39477i	0.434575	−	0.0507946i
$755$	2.14057	−	3.70758i	0.0779034	−	0.134933i
$756$		0			0
$757$	21.8769	+	37.8919i	0.795129	+	1.37720i	0.922757	+	0.385381i	$0.125930\pi$
$757$	21.8769	+	37.8919i	0.795129	+	1.37720i	−0.127629	+	0.991822i	$0.540737\pi$
$758$	21.4515	+	28.8144i	0.779155	+	1.04659i
$759$		0			0
$760$	−5.91942	+	19.7722i	−0.214720	+	0.717215i
$761$	41.2979	+	20.7406i	1.49705	+	0.751846i	0.993683	−	0.112227i	$-0.0357984\pi$
$761$	41.2979	+	20.7406i	1.49705	+	0.751846i	0.503366	+	0.864073i	$0.332095\pi$
$762$		0			0
$763$	10.0564	+	33.5908i	0.364067	+	1.21607i
$764$	−0.658078	+	3.73214i	−0.0238084	+	0.135024i
$765$		0			0
$766$	2.18168	+	12.3729i	0.0788272	+	0.447051i
$767$	2.86531	−	1.43901i	0.103460	−	0.0519598i
$768$		0			0
$769$	11.5490	+	26.7737i	0.416469	+	0.965483i	0.989311	+	0.145818i	$0.0465814\pi$
$769$	11.5490	+	26.7737i	0.416469	+	0.965483i	−0.572843	+	0.819665i	$0.694159\pi$
$770$	7.27165	+	16.8576i	0.262052	+	0.607505i
$771$		0			0
$772$	−3.02306	+	1.51824i	−0.108802	+	0.0546427i
$773$	−6.90323	−	39.1502i	−0.248292	−	1.40813i	−0.812721	−	0.582653i	$-0.802015\pi$
$773$	−6.90323	−	39.1502i	−0.248292	−	1.40813i	0.564429	−	0.825481i	$-0.309096\pi$
$774$		0			0
$775$	2.05395	−	11.6485i	0.0737801	−	0.418427i
$776$	1.02260	+	3.41574i	0.0367094	+	0.122618i
$777$		0			0
$778$	33.3343	+	16.7411i	1.19509	+	0.600198i
$779$	14.0177	−	46.8225i	0.502238	−	1.67759i
$780$		0			0
$781$	−24.2513	−	32.5751i	−0.867779	−	1.16563i

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:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.g (of order \(27\), degree \(18\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.588281 + 1.36379i) q^{2} +(-0.141360 - 0.149832i) q^{4} +(-0.0932044 - 1.60026i) q^{5} +(-1.85061 - 0.438602i) q^{7} +(-2.50387 + 0.911335i) q^{8} +O(q^{10})\)	\(q+(-0.588281 + 1.36379i) q^{2} +(-0.141360 - 0.149832i) q^{4} +(-0.0932044 - 1.60026i) q^{5} +(-1.85061 - 0.438602i) q^{7} +(-2.50387 + 0.911335i) q^{8} +(2.23724 + 0.814290i) q^{10} +(-3.38752 - 2.22800i) q^{11} +(1.67851 + 0.196189i) q^{13} +(1.68684 - 2.26582i) q^{14} +(0.254067 - 4.36216i) q^{16} +(4.14727 - 3.47997i) q^{17} +(3.70167 + 3.10607i) q^{19} +(-0.226595 + 0.240177i) q^{20} +(5.03133 - 3.30916i) q^{22} +(0.651612 - 0.154435i) q^{23} +(2.41405 - 0.282162i) q^{25} +(-1.25499 + 2.17371i) q^{26} +(0.195884 + 0.339282i) q^{28} +(-2.85835 - 3.83943i) q^{29} +(1.39576 - 4.66216i) q^{31} +(1.03731 + 0.520955i) q^{32} +(2.30618 + 7.70319i) q^{34} +(-0.529392 + 3.00233i) q^{35} +(-2.07926 - 11.7921i) q^{37} +(-6.41363 + 3.22105i) q^{38} +(1.69174 + 3.92190i) q^{40} +(-4.00621 - 9.28743i) q^{41} +(7.64192 - 3.83792i) q^{43} +(0.145031 + 0.822509i) q^{44} +(-0.172714 + 0.979511i) q^{46} +(0.0578400 + 0.193199i) q^{47} +(-3.02305 - 1.51823i) q^{49} +(-1.03533 + 3.45825i) q^{50} +(-0.207877 - 0.279228i) q^{52} +(2.48138 + 4.29788i) q^{53} +(-3.24965 + 5.62856i) q^{55} +(5.03340 - 0.588321i) q^{56} +(6.91768 - 1.63952i) q^{58} +(1.58520 - 1.04260i) q^{59} +(0.124028 - 0.131462i) q^{61} +(5.53710 + 4.64618i) q^{62} +(5.37384 - 4.50919i) q^{64} +(0.157509 - 2.70433i) q^{65} +(-7.95826 + 10.6898i) q^{67} +(-1.10767 - 0.129468i) q^{68} +(-3.78311 - 2.48819i) q^{70} +(9.41216 + 3.42575i) q^{71} +(-10.9327 + 3.97917i) q^{73} +(17.3051 + 4.10138i) q^{74} +(-0.0578765 - 0.993701i) q^{76} +(5.29176 + 5.60894i) q^{77} +(-1.45390 + 3.37053i) q^{79} -7.00426 q^{80} +15.0229 q^{82} +(-2.17367 + 5.03914i) q^{83} +(-5.95539 - 6.31235i) q^{85} +(0.738510 + 12.6797i) q^{86} +(10.5124 + 2.49148i) q^{88} +(-6.65218 + 2.42120i) q^{89} +(-3.02021 - 1.09927i) q^{91} +(-0.115251 - 0.0758017i) q^{92} +(-0.297508 - 0.0347738i) q^{94} +(4.62550 - 6.21312i) q^{95} +(0.0778051 - 1.33586i) q^{97} +(3.84894 - 3.22965i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8}+O(q^{10}) \) 144 * q + 9 * q^2 + 9 * q^4 + 9 * q^5 + 9 * q^7 - 18 * q^8	\( 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8} - 18 q^{10} + 9 q^{11} + 9 q^{13} + 9 q^{14} + 9 q^{16} - 18 q^{17} - 18 q^{19} - 63 q^{20} + 9 q^{22} + 36 q^{23} + 9 q^{25} + 45 q^{26} - 9 q^{28} - 45 q^{29} + 9 q^{31} + 63 q^{32} + 9 q^{34} + 9 q^{35} - 18 q^{37} - 9 q^{38} + 9 q^{40} - 27 q^{41} + 9 q^{43} + 54 q^{44} - 18 q^{46} + 63 q^{47} + 9 q^{49} - 225 q^{50} + 27 q^{52} + 45 q^{53} - 9 q^{55} + 99 q^{56} + 9 q^{58} - 117 q^{59} + 9 q^{61} + 81 q^{62} - 18 q^{64} + 81 q^{65} + 36 q^{67} - 18 q^{68} + 63 q^{70} - 90 q^{71} - 18 q^{73} + 81 q^{74} + 90 q^{76} + 81 q^{77} + 63 q^{79} - 288 q^{80} - 36 q^{82} + 45 q^{83} + 63 q^{85} + 81 q^{86} + 90 q^{88} - 81 q^{89} - 18 q^{91} - 63 q^{92} + 63 q^{94} + 153 q^{95} + 36 q^{97} + 81 q^{98}+O(q^{100}) \) 144 * q + 9 * q^2 + 9 * q^4 + 9 * q^5 + 9 * q^7 - 18 * q^8 - 18 * q^10 + 9 * q^11 + 9 * q^13 + 9 * q^14 + 9 * q^16 - 18 * q^17 - 18 * q^19 - 63 * q^20 + 9 * q^22 + 36 * q^23 + 9 * q^25 + 45 * q^26 - 9 * q^28 - 45 * q^29 + 9 * q^31 + 63 * q^32 + 9 * q^34 + 9 * q^35 - 18 * q^37 - 9 * q^38 + 9 * q^40 - 27 * q^41 + 9 * q^43 + 54 * q^44 - 18 * q^46 + 63 * q^47 + 9 * q^49 - 225 * q^50 + 27 * q^52 + 45 * q^53 - 9 * q^55 + 99 * q^56 + 9 * q^58 - 117 * q^59 + 9 * q^61 + 81 * q^62 - 18 * q^64 + 81 * q^65 + 36 * q^67 - 18 * q^68 + 63 * q^70 - 90 * q^71 - 18 * q^73 + 81 * q^74 + 90 * q^76 + 81 * q^77 + 63 * q^79 - 288 * q^80 - 36 * q^82 + 45 * q^83 + 63 * q^85 + 81 * q^86 + 90 * q^88 - 81 * q^89 - 18 * q^91 - 63 * q^92 + 63 * q^94 + 153 * q^95 + 36 * q^97 + 81 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more