LMFDB - Embedded newform 729.2.g.a.460.7

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			460.7
Character	$\chi$	$=$	729.460
Dual form			729.2.g.a.271.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.38698 - 0.696568i) q^{2} +(0.244190 - 0.328004i) q^{4} +(0.888415 - 2.96751i) q^{5} +(0.422238 - 0.978857i) q^{7} +(-0.428818 + 2.43195i) q^{8} +O(q^{10})$	\(q+(1.38698 - 0.696568i) q^{2} +(0.244190 - 0.328004i) q^{4} +(0.888415 - 2.96751i) q^{5} +(0.422238 - 0.978857i) q^{7} +(-0.428818 + 2.43195i) q^{8} +(-0.834859 - 4.73472i) q^{10} +(-1.34713 - 0.319276i) q^{11} +(5.24827 - 3.45184i) q^{13} +(-0.0962048 - 1.65177i) q^{14} +(1.33381 + 4.45525i) q^{16} +(-3.04443 - 1.10808i) q^{17} +(3.32892 - 1.21163i) q^{19} +(-0.756415 - 1.01604i) q^{20} +(-2.09084 + 0.495538i) q^{22} +(-2.97660 - 6.90053i) q^{23} +(-3.83941 - 2.52522i) q^{25} +(4.87480 - 8.44340i) q^{26} +(-0.217963 - 0.377523i) q^{28} +(-0.148690 + 2.55291i) q^{29} +(-3.27217 - 0.382462i) q^{31} +(1.56405 + 1.65780i) q^{32} +(-4.99442 + 0.583764i) q^{34} +(-2.52965 - 2.12263i) q^{35} +(-1.51778 + 1.27357i) q^{37} +(3.77317 - 3.99932i) q^{38} +(6.83587 + 3.43310i) q^{40} +(9.99336 + 5.01885i) q^{41} +(-2.57467 + 2.72899i) q^{43} +(-0.433680 + 0.363900i) q^{44} +(-8.93516 - 7.49749i) q^{46} +(1.82585 - 0.213412i) q^{47} +(4.02382 + 4.26499i) q^{49} +(-7.08417 - 0.828021i) q^{50} +(0.149357 - 2.56436i) q^{52} +(-2.00231 - 3.46810i) q^{53} +(-2.14427 + 3.71398i) q^{55} +(2.19947 + 1.44661i) q^{56} +(1.57205 + 3.64441i) q^{58} +(-4.72923 + 1.12085i) q^{59} +(5.89835 + 7.92286i) q^{61} +(-4.80485 + 1.74882i) q^{62} +(-5.41623 - 1.97135i) q^{64} +(-5.58074 - 18.6410i) q^{65} +(-0.126951 - 2.17967i) q^{67} +(-1.10688 + 0.728003i) q^{68} +(-4.98712 - 1.18197i) q^{70} +(0.733100 + 4.15761i) q^{71} +(-1.93909 + 10.9972i) q^{73} +(-1.21801 + 2.82366i) q^{74} +(0.415470 - 1.38777i) q^{76} +(-0.881334 + 1.18384i) q^{77} +(13.6538 - 6.85721i) q^{79} +14.4060 q^{80} +17.3566 q^{82} +(-2.54531 + 1.27830i) q^{83} +(-5.99297 + 8.04995i) q^{85} +(-1.67009 + 5.57848i) q^{86} +(1.35414 - 3.13924i) q^{88} +(0.910318 - 5.16267i) q^{89} +(-1.16284 - 6.59480i) q^{91} +(-2.99026 - 0.708704i) q^{92} +(2.38377 - 1.56783i) q^{94} +(-0.638059 - 10.9550i) q^{95} +(3.45426 + 11.5380i) q^{97} +(8.55181 + 3.11260i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} - 45 q^{20} + 9 q^{22} + 45 q^{23} + 9 q^{25} - 45 q^{26} - 9 q^{28} - 36 q^{29} + 9 q^{31} + 99 q^{32} + 9 q^{34} - 9 q^{35} - 18 q^{37} - 18 q^{38} + 9 q^{40} - 27 q^{41} + 9 q^{43} - 54 q^{44} - 18 q^{46} + 99 q^{47} + 9 q^{49} - 126 q^{50} - 27 q^{52} - 45 q^{53} - 9 q^{55} + 225 q^{56} + 9 q^{58} - 72 q^{59} + 9 q^{61} - 81 q^{62} - 18 q^{64} + 81 q^{65} - 45 q^{67} - 117 q^{68} - 99 q^{70} + 90 q^{71} - 18 q^{73} - 81 q^{74} - 153 q^{76} - 81 q^{77} - 99 q^{79} + 288 q^{80} - 36 q^{82} - 45 q^{83} - 99 q^{85} - 81 q^{86} - 153 q^{88} + 81 q^{89} - 18 q^{91} - 207 q^{92} - 99 q^{94} + 171 q^{95} - 45 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 - 45 * q^20 + 9 * q^22 + 45 * q^23 + 9 * q^25 - 45 * q^26 - 9 * q^28 - 36 * q^29 + 9 * q^31 + 99 * q^32 + 9 * q^34 - 9 * q^35 - 18 * q^37 - 18 * q^38 + 9 * q^40 - 27 * q^41 + 9 * q^43 - 54 * q^44 - 18 * q^46 + 99 * q^47 + 9 * q^49 - 126 * q^50 - 27 * q^52 - 45 * q^53 - 9 * q^55 + 225 * q^56 + 9 * q^58 - 72 * q^59 + 9 * q^61 - 81 * q^62 - 18 * q^64 + 81 * q^65 - 45 * q^67 - 117 * q^68 - 99 * q^70 + 90 * q^71 - 18 * q^73 - 81 * q^74 - 153 * q^76 - 81 * q^77 - 99 * q^79 + 288 * q^80 - 36 * q^82 - 45 * q^83 - 99 * q^85 - 81 * q^86 - 153 * q^88 + 81 * q^89 - 18 * q^91 - 207 * q^92 - 99 * q^94 + 171 * q^95 - 45 * q^97 - 81 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{23}{27}\right)$

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 $

$2$	1.38698	−	0.696568i	0.980743	−	0.492548i	0.115178	−	0.993345i	$-0.463256\pi$
$2$	1.38698	−	0.696568i	0.980743	−	0.492548i	0.865565	+	0.500797i	$0.166960\pi$
$3$		0			0
$3$		0			0
$4$	0.244190	−	0.328004i	0.122095	−	0.164002i
$5$	0.888415	−	2.96751i	0.397311	−	1.32711i	−0.492313	−	0.870418i	$-0.663848\pi$
$5$	0.888415	−	2.96751i	0.397311	−	1.32711i	0.889624	−	0.456694i	$-0.150966\pi$
$6$		0			0
$7$	0.422238	−	0.978857i	0.159591	−	0.369973i	−0.819594	−	0.572945i	$-0.805801\pi$
$7$	0.422238	−	0.978857i	0.159591	−	0.369973i	0.979185	+	0.202972i	$0.0650600\pi$
$8$	−0.428818	+	2.43195i	−0.151610	+	0.859824i
$9$		0			0
$10$	−0.834859	−	4.73472i	−0.264006	−	1.49725i
$11$	−1.34713	−	0.319276i	−0.406175	−	0.0962652i	0.0224495	−	0.999748i	$-0.492854\pi$
$11$	−1.34713	−	0.319276i	−0.406175	−	0.0962652i	−0.428624	+	0.903483i	$0.641002\pi$
$12$		0			0
$13$	5.24827	−	3.45184i	1.45561	−	0.957368i	0.457948	−	0.888979i	$-0.348584\pi$
$13$	5.24827	−	3.45184i	1.45561	−	0.957368i	0.997659	−	0.0683890i	$-0.0217859\pi$
$14$	−0.0962048	−	1.65177i	−0.0257118	−	0.441455i
$15$		0			0
$16$	1.33381	+	4.45525i	0.333454	+	1.11381i
$17$	−3.04443	−	1.10808i	−0.738383	−	0.268749i	−0.0546740	−	0.998504i	$-0.517412\pi$
$17$	−3.04443	−	1.10808i	−0.738383	−	0.268749i	−0.683709	+	0.729755i	$0.739634\pi$
$18$		0			0
$19$	3.32892	−	1.21163i	0.763707	−	0.277967i	0.0693452	−	0.997593i	$-0.477909\pi$
$19$	3.32892	−	1.21163i	0.763707	−	0.277967i	0.694362	+	0.719626i	$0.255687\pi$
$20$	−0.756415	−	1.01604i	−0.169139	−	0.227194i
$21$		0			0
$22$	−2.09084	+	0.495538i	−0.445769	+	0.105649i
$23$	−2.97660	−	6.90053i	−0.620663	−	1.43886i	−0.880894	−	0.473313i	$-0.843058\pi$
$23$	−2.97660	−	6.90053i	−0.620663	−	1.43886i	0.260231	−	0.965546i	$-0.416201\pi$
$24$		0			0
$25$	−3.83941	−	2.52522i	−0.767882	−	0.505044i
$26$	4.87480	−	8.44340i	0.956027	−	1.65589i
$27$		0			0
$28$	−0.217963	−	0.377523i	−0.0411911	−	0.0713451i
$29$	−0.148690	+	2.55291i	−0.0276111	+	0.474064i	0.955955	+	0.293514i	$0.0948248\pi$
$29$	−0.148690	+	2.55291i	−0.0276111	+	0.474064i	−0.983566	+	0.180550i	$0.942212\pi$
$30$		0			0
$31$	−3.27217	−	0.382462i	−0.587699	−	0.0686922i	−0.182954	−	0.983122i	$-0.558566\pi$
$31$	−3.27217	−	0.382462i	−0.587699	−	0.0686922i	−0.404746	+	0.914429i	$0.632640\pi$
$32$	1.56405	+	1.65780i	0.276488	+	0.293060i
$33$		0			0
$34$	−4.99442	+	0.583764i	−0.856536	+	0.100115i
$35$	−2.52965	−	2.12263i	−0.427589	−	0.358789i
$36$		0			0
$37$	−1.51778	+	1.27357i	−0.249522	+	0.209374i	−0.758967	−	0.651130i	$-0.774295\pi$
$37$	−1.51778	+	1.27357i	−0.249522	+	0.209374i	0.509444	+	0.860504i	$0.329851\pi$
$38$	3.77317	−	3.99932i	0.612088	−	0.648776i
$39$		0			0
$40$	6.83587	+	3.43310i	1.08085	+	0.542822i
$41$	9.99336	+	5.01885i	1.56070	+	0.783813i	0.999051	−	0.0435625i	$-0.0138708\pi$
$41$	9.99336	+	5.01885i	1.56070	+	0.783813i	0.561649	+	0.827375i	$0.310167\pi$
$42$		0			0
$43$	−2.57467	+	2.72899i	−0.392633	+	0.416167i	−0.893291	−	0.449478i	$-0.851610\pi$
$43$	−2.57467	+	2.72899i	−0.392633	+	0.416167i	0.500658	+	0.865645i	$0.333091\pi$
$44$	−0.433680	+	0.363900i	−0.0653797	+	0.0548601i
$45$		0			0
$46$	−8.93516	−	7.49749i	−1.31742	−	1.10544i
$47$	1.82585	−	0.213412i	0.266328	−	0.0311293i	0.0181192	−	0.999836i	$-0.494232\pi$
$47$	1.82585	−	0.213412i	0.266328	−	0.0311293i	0.248209	+	0.968707i	$0.420158\pi$
$48$		0			0
$49$	4.02382	+	4.26499i	0.574831	+	0.609285i
$50$	−7.08417	−	0.828021i	−1.00185	−	0.117100i
$51$		0			0
$52$	0.149357	−	2.56436i	0.0207121	−	0.355613i
$53$	−2.00231	−	3.46810i	−0.275038	−	0.476380i	0.695107	−	0.718907i	$-0.255357\pi$
$53$	−2.00231	−	3.46810i	−0.275038	−	0.476380i	−0.970145	+	0.242527i	$0.922024\pi$
$54$		0			0
$55$	−2.14427	+	3.71398i	−0.289133	+	0.500792i
$56$	2.19947	+	1.44661i	0.293916	+	0.193312i
$57$		0			0
$58$	1.57205	+	3.64441i	0.206420	+	0.478535i
$59$	−4.72923	+	1.12085i	−0.615693	+	0.145922i	−0.526617	−	0.850103i	$-0.676540\pi$
$59$	−4.72923	+	1.12085i	−0.615693	+	0.145922i	−0.0890765	+	0.996025i	$0.528392\pi$
$60$		0			0
$61$	5.89835	+	7.92286i	0.755206	+	1.01442i	0.999005	+	0.0445923i	$0.0141989\pi$
$61$	5.89835	+	7.92286i	0.755206	+	1.01442i	−0.243799	+	0.969826i	$0.578394\pi$
$62$	−4.80485	+	1.74882i	−0.610216	+	0.222100i
$63$		0			0
$64$	−5.41623	−	1.97135i	−0.677029	−	0.246418i
$65$	−5.58074	−	18.6410i	−0.692205	−	2.31213i
$66$		0			0
$67$	−0.126951	−	2.17967i	−0.0155096	−	0.266289i	−0.997144	−	0.0755191i	$-0.975939\pi$
$67$	−0.126951	−	2.17967i	−0.0155096	−	0.266289i	0.981635	−	0.190770i	$-0.0610984\pi$
$68$	−1.10688	+	0.728003i	−0.134228	+	0.0882834i
$69$		0			0
$70$	−4.98712	−	1.18197i	−0.596075	−	0.141272i
$71$	0.733100	+	4.15761i	0.0870029	+	0.493418i	0.996906	+	0.0785980i	$0.0250443\pi$
$71$	0.733100	+	4.15761i	0.0870029	+	0.493418i	−0.909903	+	0.414820i	$0.863845\pi$
$72$		0			0
$73$	−1.93909	+	10.9972i	−0.226954	+	1.28712i	0.631961	+	0.775000i	$0.282250\pi$
$73$	−1.93909	+	10.9972i	−0.226954	+	1.28712i	−0.858915	+	0.512119i	$0.828861\pi$
$74$	−1.21801	+	2.82366i	−0.141590	+	0.328244i
$75$		0			0
$76$	0.415470	−	1.38777i	0.0476577	−	0.159188i
$77$	−0.881334	+	1.18384i	−0.100437	+	0.134911i
$78$		0			0
$79$	13.6538	−	6.85721i	1.53618	−	0.771496i	0.538699	−	0.842498i	$-0.318916\pi$
$79$	13.6538	−	6.85721i	1.53618	−	0.771496i	0.997476	+	0.0710022i	$0.0226198\pi$
$80$	14.4060			1.61064
$81$		0			0
$82$	17.3566			1.91671
$83$	−2.54531	+	1.27830i	−0.279384	+	0.140312i	−0.582974	−	0.812491i	$-0.698111\pi$
$83$	−2.54531	+	1.27830i	−0.279384	+	0.140312i	0.303590	+	0.952803i	$0.401815\pi$
$84$		0			0
$85$	−5.99297	+	8.04995i	−0.650028	+	0.873140i
$86$	−1.67009	+	5.57848i	−0.180090	+	0.601543i
$87$		0			0
$88$	1.35414	−	3.13924i	0.144351	−	0.334644i
$89$	0.910318	−	5.16267i	0.0964935	−	0.547242i	−0.897786	−	0.440432i	$-0.854825\pi$
$89$	0.910318	−	5.16267i	0.0964935	−	0.547242i	0.994279	−	0.106810i	$-0.0340636\pi$
$90$		0			0
$91$	−1.16284	−	6.59480i	−0.121899	−	0.691323i
$92$	−2.99026	−	0.708704i	−0.311756	−	0.0738875i
$93$		0			0
$94$	2.38377	−	1.56783i	0.245867	−	0.161709i
$95$	−0.638059	−	10.9550i	−0.0654634	−	1.12396i
$96$		0			0
$97$	3.45426	+	11.5380i	0.350727	+	1.17151i	0.933411	+	0.358810i	$0.116817\pi$
$97$	3.45426	+	11.5380i	0.350727	+	1.17151i	−0.582684	+	0.812699i	$0.697997\pi$
$98$	8.55181	+	3.11260i	0.863863	+	0.314420i
$99$		0			0
$100$	−1.76583	+	0.642709i	−0.176583	+	0.0642709i
$101$	5.06506	+	6.80356i	0.503993	+	0.676980i	0.979201	−	0.202894i	$-0.0650346\pi$
$101$	5.06506	+	6.80356i	0.503993	+	0.676980i	−0.475208	+	0.879873i	$0.657627\pi$
$102$		0			0
$103$	−9.27652	+	2.19857i	−0.914042	+	0.216632i	−0.660617	−	0.750723i	$-0.729705\pi$
$103$	−9.27652	+	2.19857i	−0.914042	+	0.216632i	−0.253425	+	0.967355i	$0.581557\pi$
$104$	6.14415	+	14.2437i	0.602483	+	1.39671i
$105$		0			0
$106$	−5.19292	−	3.41544i	−0.504381	−	0.331737i
$107$	−5.04592	+	8.73979i	−0.487807	+	0.844907i	−0.999902	−	0.0140222i	$-0.995536\pi$
$107$	−5.04592	+	8.73979i	−0.487807	+	0.844907i	0.512094	+	0.858929i	$0.328870\pi$
$108$		0			0
$109$	9.05373	+	15.6815i	0.867190	+	1.50202i	0.864856	+	0.502020i	$0.167409\pi$
$109$	9.05373	+	15.6815i	0.867190	+	1.50202i	0.00233359	+	0.999997i	$0.499257\pi$
$110$	−0.387018	+	6.64484i	−0.0369007	+	0.633560i
$111$		0			0
$112$	4.92424	+	0.575561i	0.465297	+	0.0543854i
$113$	0.438007	+	0.464260i	0.0412042	+	0.0436739i	0.747648	−	0.664095i	$-0.231183\pi$
$113$	0.438007	+	0.464260i	0.0412042	+	0.0436739i	−0.706444	+	0.707769i	$0.749702\pi$
$114$		0			0
$115$	−23.1219	+	2.70256i	−2.15612	+	0.252015i
$116$	0.801058	+	0.672167i	0.0743764	+	0.0624092i
$117$		0			0
$118$	−5.77860	+	4.84882i	−0.531963	+	0.446370i
$119$	−2.37013	+	2.51219i	−0.217269	+	0.230292i
$120$		0			0
$121$	−8.11714	−	4.07658i	−0.737922	−	0.370598i
$122$	13.6997	+	6.88025i	1.24031	+	0.622908i
$123$		0			0
$124$	−0.924481	+	0.979892i	−0.0830208	+	0.0879969i
$125$	0.960062	−	0.805588i	0.0858705	−	0.0720539i
$126$		0			0
$127$	1.02140	+	0.857057i	0.0906346	+	0.0760515i	0.686979	−	0.726677i	$-0.258936\pi$
$127$	1.02140	+	0.857057i	0.0906346	+	0.0760515i	−0.596345	+	0.802729i	$0.703381\pi$
$128$	−13.4129	+	1.56774i	−1.18554	+	0.138570i
$129$		0			0
$130$	−20.7251	−	21.9673i	−1.81771	−	1.92666i
$131$	−18.2682	−	2.13524i	−1.59610	−	0.186557i	−0.728935	−	0.684583i	$-0.759984\pi$
$131$	−18.2682	−	2.13524i	−1.59610	−	0.186557i	−0.867162	+	0.498026i	$0.834058\pi$
$132$		0			0
$133$	0.219585	−	3.77013i	0.0190405	−	0.326912i
$134$	−1.69437	−	2.93473i	−0.146371	−	0.253522i
$135$		0			0
$136$	4.00031	−	6.92874i	0.343024	−	0.594134i
$137$	3.89470	+	2.56158i	0.332747	+	0.218851i	0.704877	−	0.709330i	$-0.251002\pi$
$137$	3.89470	+	2.56158i	0.332747	+	0.218851i	−0.372130	+	0.928180i	$0.621373\pi$
$138$		0			0
$139$	0.403437	+	0.935272i	0.0342191	+	0.0793287i	0.934469	−	0.356046i	$-0.115875\pi$
$139$	0.403437	+	0.935272i	0.0342191	+	0.0793287i	−0.900249	+	0.435374i	$0.856616\pi$
$140$	−1.31395	+	0.311411i	−0.111049	+	0.0263190i
$141$		0			0
$142$	3.91285	+	5.25587i	0.328359	+	0.441063i
$143$	−8.17218	+	2.97443i	−0.683392	+	0.248735i
$144$		0			0
$145$	7.44371	+	2.70929i	0.618166	+	0.224994i
$146$	4.97077	+	16.6035i	0.411384	+	1.37412i
$147$		0			0
$148$	0.0471092	+	0.808833i	0.00387235	+	0.0664857i
$149$	−0.969230	+	0.637473i	−0.0794025	+	0.0522238i	−0.588589	−	0.808432i	$-0.700317\pi$
$149$	−0.969230	+	0.637473i	−0.0794025	+	0.0522238i	0.509187	+	0.860656i	$0.329946\pi$
$150$		0			0
$151$	12.5987	+	2.98595i	1.02527	+	0.242993i	0.708651	−	0.705560i	$-0.249304\pi$
$151$	12.5987	+	2.98595i	1.02527	+	0.242993i	0.316619	+	0.948553i	$0.397452\pi$
$152$	1.51912	+	8.61534i	0.123217	+	0.698796i
$153$		0			0
$154$	−0.397770	+	2.25587i	−0.0320532	+	0.181783i
$155$	−4.04201	+	9.37042i	−0.324662	+	0.752650i
$156$		0			0
$157$	0.624250	−	2.08514i	0.0498206	−	0.166412i	−0.929459	−	0.368926i	$-0.879726\pi$
$157$	0.624250	−	2.08514i	0.0498206	−	0.166412i	0.979280	+	0.202513i	$0.0649109\pi$
$158$	14.1611	−	19.0216i	1.12659	−	1.51328i
$159$		0			0
$160$	6.30907	−	3.16854i	0.498776	−	0.250495i
$161$	−8.01146			−0.631392
$162$		0			0
$163$	−15.2864			−1.19732			−0.598660	−	0.801003i	$-0.704300\pi$
$163$	−15.2864			−1.19732			−0.598660	+	0.801003i	$0.704300\pi$
$164$	4.08648	−	2.05231i	0.319101	−	0.160258i
$165$		0			0
$166$	−2.63987	+	3.54596i	−0.204894	+	0.275220i
$167$	−2.25412	+	7.52930i	−0.174429	+	0.582635i	0.825407	+	0.564538i	$0.190946\pi$
$167$	−2.25412	+	7.52930i	−0.174429	+	0.582635i	−0.999836	+	0.0180964i	$0.994239\pi$
$168$		0			0
$169$	10.4801	−	24.2955i	0.806159	−	1.86889i
$170$	−2.70479	+	15.3396i	−0.207448	+	1.17650i
$171$		0			0
$172$	0.266411	+	1.51089i	0.0203137	+	0.115205i
$173$	4.40674	+	1.04442i	0.335038	+	0.0794055i	0.394692	−	0.918814i	$-0.370851\pi$
$173$	4.40674	+	1.04442i	0.335038	+	0.0794055i	−0.0596535	+	0.998219i	$0.519000\pi$
$174$		0			0
$175$	−4.09297	+	2.69199i	−0.309400	+	0.203495i
$176$	−0.374368	−	6.42765i	−0.0282191	−	0.484503i
$177$		0			0
$178$	−2.33355	−	7.79461i	−0.174907	−	0.584231i
$179$	4.33186	+	1.57667i	0.323778	+	0.117846i	0.498795	−	0.866720i	$-0.333776\pi$
$179$	4.33186	+	1.57667i	0.323778	+	0.117846i	−0.175017	+	0.984565i	$0.555998\pi$
$180$		0			0
$181$	−7.67715	+	2.79425i	−0.570638	+	0.207695i	−0.611192	−	0.791482i	$-0.709310\pi$
$181$	−7.67715	+	2.79425i	−0.570638	+	0.207695i	0.0405545	+	0.999177i	$0.487088\pi$
$182$	−6.20656	−	8.33686i	−0.460061	−	0.617969i
$183$		0			0
$184$	18.0582	−	4.27986i	1.33126	−	0.315516i
$185$	2.43092	+	5.63550i	0.178725	+	0.414330i
$186$		0			0
$187$	3.74746	+	2.46474i	0.274041	+	0.180240i
$188$	0.375855	−	0.651001i	0.0274121	−	0.0474791i
$189$		0			0
$190$	−8.51590	−	14.7500i	−0.617809	−	1.07008i
$191$	0.229311	−	3.93712i	0.0165924	−	0.284880i	−0.979798	−	0.199990i	$-0.935909\pi$
$191$	0.229311	−	3.93712i	0.0165924	−	0.284880i	0.996390	−	0.0848901i	$-0.0270539\pi$
$192$		0			0
$193$	−7.15252	−	0.836009i	−0.514850	−	0.0601773i	−0.145299	−	0.989388i	$-0.546414\pi$
$193$	−7.15252	−	0.836009i	−0.514850	−	0.0601773i	−0.369551	+	0.929211i	$0.620488\pi$
$194$	12.8280	+	13.5969i	0.920997	+	0.976199i
$195$		0			0
$196$	2.38151	−	0.278359i	0.170108	−	0.0198828i
$197$	−7.85452	−	6.59072i	−0.559611	−	0.469570i	0.318569	−	0.947900i	$-0.396798\pi$
$197$	−7.85452	−	6.59072i	−0.559611	−	0.469570i	−0.878180	+	0.478330i	$0.841242\pi$
$198$		0			0
$199$	20.3096	−	17.0417i	1.43971	−	1.20806i	0.500023	−	0.866012i	$-0.333325\pi$
$199$	20.3096	−	17.0417i	1.43971	−	1.20806i	0.939683	−	0.342045i	$-0.111120\pi$
$200$	7.78762	−	8.25439i	0.550668	−	0.583674i
$201$		0			0
$202$	11.7643	+	5.90825i	0.827732	+	0.415703i
$203$	2.43615	+	1.22348i	0.170985	+	0.0858717i
$204$		0			0
$205$	23.7718	−	25.1966i	1.66029	−	1.75981i
$206$	−11.3349	+	9.51110i	−0.789739	+	0.662670i
$207$		0			0
$208$	22.3790	+	18.7782i	1.55171	+	1.30204i
$209$	−4.87133	+	0.569377i	−0.336957	+	0.0393846i
$210$		0			0
$211$	6.31051	+	6.68875i	0.434433	+	0.460472i	0.907190	−	0.420720i	$-0.138223\pi$
$211$	6.31051	+	6.68875i	0.434433	+	0.460472i	−0.472757	+	0.881193i	$0.656741\pi$
$212$	−1.62649	−	0.190110i	−0.111708	−	0.0130568i
$213$		0			0
$214$	−0.910736	+	15.6367i	−0.0622566	+	1.06890i
$215$	5.81093	+	10.0648i	0.396302	+	0.686415i
$216$		0			0
$217$	−1.75601	+	3.04150i	−0.119206	+	0.206470i
$218$	23.4806	+	15.4434i	1.59031	+	1.04596i
$219$		0			0
$220$	0.694592	+	1.61024i	0.0468294	+	0.108563i
$221$	−19.8029	+	4.69337i	−1.33209	+	0.315711i
$222$		0			0
$223$	−7.83078	−	10.5186i	−0.524388	−	0.704375i	0.458476	−	0.888707i	$-0.348395\pi$
$223$	−7.83078	−	10.5186i	−0.524388	−	0.704375i	−0.982864	+	0.184332i	$0.940988\pi$
$224$	2.28315	−	0.830999i	0.152550	−	0.0555235i
$225$		0			0
$226$	0.930895	+	0.338818i	0.0619222	+	0.0225379i
$227$	4.05728	+	13.5523i	0.269291	+	0.899496i	0.980501	+	0.196516i	$0.0629626\pi$
$227$	4.05728	+	13.5523i	0.269291	+	0.899496i	−0.711209	+	0.702980i	$0.751852\pi$
$228$		0			0
$229$	−0.743449	−	12.7645i	−0.0491285	−	0.843503i	−0.929409	−	0.369050i	$-0.879683\pi$
$229$	−0.743449	−	12.7645i	−0.0491285	−	0.843503i	0.880281	−	0.474453i	$-0.157354\pi$
$230$	−30.1870	+	19.8543i	−1.99047	+	1.30916i
$231$		0			0
$232$	−6.14480	−	1.45634i	−0.403426	−	0.0956137i
$233$	1.19331	+	6.76757i	0.0781760	+	0.443358i	0.998622	+	0.0524875i	$0.0167150\pi$
$233$	1.19331	+	6.76757i	0.0781760	+	0.443358i	−0.920446	+	0.390871i	$0.872174\pi$
$234$		0			0
$235$	0.988813	−	5.60784i	0.0645031	−	0.365815i
$236$	−0.787188	+	1.82491i	−0.0512416	+	0.118791i
$237$		0			0
$238$	−1.53741	+	5.13531i	−0.0996555	+	0.332873i
$239$	8.04933	−	10.8121i	0.520668	−	0.699379i	−0.461552	−	0.887113i	$-0.652707\pi$
$239$	8.04933	−	10.8121i	0.520668	−	0.699379i	0.982220	+	0.187735i	$0.0601145\pi$
$240$		0			0
$241$	−0.315013	+	0.158205i	−0.0202918	+	0.0101909i	−0.458916	−	0.888480i	$-0.651762\pi$
$241$	−0.315013	+	0.158205i	−0.0202918	+	0.0101909i	0.438624	+	0.898670i	$0.355466\pi$
$242$	−14.0979			−0.906249
$243$		0			0
$244$	4.03905			0.258574
$245$	16.2312	−	8.15164i	1.03698	−	0.520789i
$246$		0			0
$247$	13.2887	−	17.8498i	0.845541	−	1.13576i
$248$	2.33330	−	7.79375i	0.148164	−	0.494904i
$249$		0			0
$250$	0.770441	−	1.78608i	0.0487269	−	0.112962i
$251$	3.88072	−	22.0087i	0.244949	−	1.38917i	−0.575662	−	0.817688i	$-0.695256\pi$
$251$	3.88072	−	22.0087i	0.244949	−	1.38917i	0.820611	−	0.571487i	$-0.193633\pi$
$252$		0			0
$253$	1.80669	+	10.2463i	0.113586	+	0.644177i
$254$	2.01366	+	0.477246i	0.126348	+	0.0299451i
$255$		0			0
$256$	−7.88013	+	5.18285i	−0.492508	+	0.323928i
$257$	−1.07007	−	18.3725i	−0.0667494	−	1.14604i	−0.850850	−	0.525409i	$-0.823912\pi$
$257$	−1.07007	−	18.3725i	−0.0667494	−	1.14604i	0.784101	−	0.620634i	$-0.213125\pi$
$258$		0			0
$259$	0.605779	+	2.02344i	0.0376413	+	0.125731i
$260$	−7.47707	−	2.72143i	−0.463709	−	0.168776i
$261$		0			0
$262$	−26.8249	+	9.76347i	−1.65725	+	0.603189i
$263$	−1.39668	−	1.87606i	−0.0861228	−	0.115683i	0.756974	−	0.653445i	$-0.226677\pi$
$263$	−1.39668	−	1.87606i	−0.0861228	−	0.115683i	−0.843096	+	0.537763i	$0.819270\pi$
$264$		0			0
$265$	−12.0705	+	2.86076i	−0.741485	+	0.175735i
$266$	−2.32159	−	5.38206i	−0.142346	−	0.329995i
$267$		0			0
$268$	−0.745941	−	0.490613i	−0.0455656	−	0.0299690i
$269$	7.61488	−	13.1894i	0.464287	−	0.804169i	−0.534882	−	0.844927i	$-0.679644\pi$
$269$	7.61488	−	13.1894i	0.464287	−	0.804169i	0.999169	+	0.0407576i	$0.0129771\pi$
$270$		0			0
$271$	−2.75183	−	4.76631i	−0.167162	−	0.289533i	0.770259	−	0.637731i	$-0.220127\pi$
$271$	−2.75183	−	4.76631i	−0.167162	−	0.289533i	−0.937421	+	0.348198i	$0.886794\pi$
$272$	0.876078	−	15.0417i	0.0531200	−	0.912035i
$273$		0			0
$274$	7.18619	+	0.839945i	0.434133	+	0.0507429i
$275$	4.36594	+	4.62763i	0.263276	+	0.279057i
$276$		0			0
$277$	−18.5929	+	2.17320i	−1.11714	+	0.130575i	−0.654564	−	0.756006i	$-0.727148\pi$
$277$	−18.5929	+	2.17320i	−1.11714	+	0.130575i	−0.462573	+	0.886581i	$0.653074\pi$
$278$	1.21104	+	1.01618i	0.0726333	+	0.0609466i
$279$		0			0
$280$	6.24688	−	5.24176i	0.373323	−	0.313255i
$281$	−12.6610	+	13.4199i	−0.755292	+	0.800563i	−0.984974	−	0.172703i	$-0.944750\pi$
$281$	−12.6610	+	13.4199i	−0.755292	+	0.800563i	0.229682	+	0.973266i	$0.426232\pi$
$282$		0			0
$283$	−10.8300	−	5.43905i	−0.643779	−	0.323318i	0.0967834	−	0.995305i	$-0.469145\pi$
$283$	−10.8300	−	5.43905i	−0.643779	−	0.323318i	−0.740563	+	0.671987i	$0.765441\pi$
$284$	1.54273	+	0.774788i	0.0915442	+	0.0459752i
$285$		0			0
$286$	−9.26276	+	9.81796i	−0.547719	+	0.580548i
$287$	9.13231	−	7.66292i	0.539063	−	0.452328i
$288$		0			0
$289$	−4.98204	−	4.18043i	−0.293061	−	0.245908i
$290$	12.2115	−	1.42732i	0.717082	−	0.0838149i
$291$		0			0
$292$	3.13361	+	3.32143i	0.183380	+	0.194372i
$293$	19.0923	+	2.23157i	1.11538	+	0.130370i	0.653757	−	0.756705i	$-0.273192\pi$
$293$	19.0923	+	2.23157i	1.11538	+	0.130370i	0.461627	+	0.887074i	$0.347266\pi$
$294$		0			0
$295$	−0.875388	+	15.0298i	−0.0509670	+	0.875070i
$296$	−2.44641	−	4.23731i	−0.142195	−	0.246288i
$297$		0			0
$298$	−0.900260	+	1.55930i	−0.0521507	+	0.0903276i
$299$	−39.4415	−	25.9411i	−2.28096	−	1.50021i
$300$		0			0
$301$	1.58417	+	3.67251i	0.0913098	+	0.211680i
$302$	19.5541	−	4.63440i	1.12521	−	0.266680i
$303$		0			0
$304$	9.83827	+	13.2151i	0.564263	+	0.757937i
$305$	28.7514	−	10.4646i	1.64630	−	0.599204i
$306$		0			0
$307$	−10.3868	−	3.78049i	−0.592806	−	0.215764i	0.0281572	−	0.999604i	$-0.491036\pi$
$307$	−10.3868	−	3.78049i	−0.592806	−	0.215764i	−0.620963	+	0.783840i	$0.713258\pi$
$308$	0.173091	+	0.578163i	0.00986275	+	0.0329439i
$309$		0			0
$310$	0.920951	+	15.8121i	0.0523065	+	0.898068i
$311$	−11.7864	+	7.75205i	−0.668346	+	0.439578i	−0.837813	−	0.545958i	$-0.816166\pi$
$311$	−11.7864	+	7.75205i	−0.668346	+	0.439578i	0.169467	+	0.985536i	$0.445796\pi$
$312$		0			0
$313$	−1.55801	−	0.369255i	−0.0880639	−	0.0208715i	0.186348	−	0.982484i	$-0.440335\pi$
$313$	−1.55801	−	0.369255i	−0.0880639	−	0.0208715i	−0.274412	+	0.961612i	$0.588483\pi$
$314$	−0.586619	−	3.32688i	−0.0331048	−	0.187747i
$315$		0			0
$316$	1.08494	−	6.15297i	0.0610324	−	0.346132i
$317$	4.25471	−	9.86353i	0.238968	−	0.553991i	−0.755955	−	0.654623i	$-0.772827\pi$
$317$	4.25471	−	9.86353i	0.238968	−	0.553991i	0.994924	+	0.100632i	$0.0320865\pi$
$318$		0			0
$319$	1.01539	−	3.39163i	0.0568508	−	0.189895i
$320$	−10.6619	+	14.3214i	−0.596016	+	0.800589i
$321$		0			0
$322$	−11.1117	+	5.58052i	−0.619233	+	0.310990i
$323$	−11.4773			−0.638611
$324$		0			0
$325$	−28.8669			−1.60125
$326$	−21.2019	+	10.6480i	−1.17426	+	0.589737i
$327$		0			0
$328$	−16.4909	+	22.1512i	−0.910559	+	1.22309i
$329$	0.562044	−	1.87736i	0.0309865	−	0.103502i
$330$		0			0
$331$	−11.2874	+	26.1672i	−0.620412	+	1.43828i	0.260724	+	0.965413i	$0.416039\pi$
$331$	−11.2874	+	26.1672i	−0.620412	+	1.43828i	−0.881136	+	0.472863i	$0.843220\pi$
$332$	−0.202251	+	1.14702i	−0.0111000	+	0.0629510i
$333$		0			0
$334$	2.11824	+	12.0131i	0.115905	+	0.657330i
$335$	−6.58098	−	1.55972i	−0.359557	−	0.0852166i
$336$		0			0
$337$	1.05866	−	0.696292i	0.0576689	−	0.0379294i	−0.520347	−	0.853955i	$-0.674197\pi$
$337$	1.05866	−	0.696292i	0.0576689	−	0.0379294i	0.578016	+	0.816025i	$0.303827\pi$
$338$	−2.38783	−	40.9975i	−0.129881	−	2.22997i
$339$		0			0
$340$	1.17699	+	3.93144i	0.0638315	+	0.213212i
$341$	4.28593	+	1.55995i	0.232096	+	0.0844760i
$342$		0			0
$343$	12.8861	−	4.69015i	0.695783	−	0.253244i
$344$	−5.53270	−	7.43170i	−0.298303	−	0.400690i
$345$		0			0
$346$	6.83957	−	1.62101i	0.367697	−	0.0871459i
$347$	6.09406	+	14.1276i	0.327146	+	0.758410i	0.999829	+	0.0184793i	$0.00588249\pi$
$347$	6.09406	+	14.1276i	0.327146	+	0.758410i	−0.672683	+	0.739931i	$0.734858\pi$
$348$		0			0
$349$	−9.90805	−	6.51663i	−0.530366	−	0.348827i	0.255912	−	0.966700i	$-0.417624\pi$
$349$	−9.90805	−	6.51663i	−0.530366	−	0.348827i	−0.786278	+	0.617873i	$0.787995\pi$
$350$	−3.80172	+	6.58477i	−0.203210	+	0.351971i
$351$		0			0
$352$	−1.57769	−	2.73264i	−0.0840911	−	0.145650i
$353$	0.719486	−	12.3531i	0.0382944	−	0.657489i	−0.923480	−	0.383646i	$-0.874668\pi$
$353$	0.719486	−	12.3531i	0.0382944	−	0.657489i	0.961774	−	0.273843i	$-0.0882948\pi$
$354$		0			0
$355$	12.9891	+	1.51820i	0.689388	+	0.0805779i
$356$	−1.47109	−	1.55926i	−0.0779674	−	0.0826406i
$357$		0			0
$358$	7.10645	−	0.830625i	0.375588	−	0.0438999i
$359$	9.97729	+	8.37194i	0.526581	+	0.441854i	0.866919	−	0.498449i	$-0.166097\pi$
$359$	9.97729	+	8.37194i	0.526581	+	0.441854i	−0.340338	+	0.940303i	$0.610541\pi$
$360$		0			0
$361$	−4.94117	+	4.14613i	−0.260062	+	0.218218i
$362$	−8.70166	+	9.22322i	−0.457349	+	0.484762i
$363$		0			0
$364$	−2.44708	−	1.22897i	−0.128262	−	0.0644154i
$365$	30.9115	+	15.5243i	1.61798	+	0.812580i
$366$		0			0
$367$	−4.89728	+	5.19081i	−0.255636	+	0.270958i	−0.842463	−	0.538754i	$-0.818895\pi$
$367$	−4.89728	+	5.19081i	−0.255636	+	0.270958i	0.586827	+	0.809712i	$0.300377\pi$
$368$	26.7733	−	22.4655i	1.39566	−	1.17110i
$369$		0			0
$370$	7.29714	+	6.12303i	0.379360	+	0.318321i
$371$	−4.24022	+	0.495611i	−0.220141	+	0.0257308i
$372$		0			0
$373$	8.67171	+	9.19147i	0.449004	+	0.475916i	0.911851	−	0.410522i	$-0.134653\pi$
$373$	8.67171	+	9.19147i	0.449004	+	0.475916i	−0.462847	+	0.886438i	$0.653172\pi$
$374$	6.91451	+	0.808191i	0.357541	+	0.0417905i
$375$		0			0
$376$	−0.263953	+	4.53190i	−0.0136123	+	0.233715i
$377$	8.03188	+	13.9116i	0.413663	+	0.716485i
$378$		0			0
$379$	12.0972	−	20.9529i	0.621391	−	1.07628i	−0.367836	−	0.929891i	$-0.619901\pi$
$379$	12.0972	−	20.9529i	0.621391	−	1.07628i	0.989227	−	0.146390i	$-0.0467653\pi$
$380$	−3.74911	−	2.46583i	−0.192325	−	0.126494i
$381$		0			0
$382$	−2.42442	−	5.62044i	−0.124044	−	0.287567i
$383$	−25.1288	+	5.95563i	−1.28402	+	0.304318i	−0.815305	−	0.579031i	$-0.803431\pi$
$383$	−25.1288	+	5.95563i	−1.28402	+	0.304318i	−0.468715	+	0.883350i	$0.655283\pi$
$384$		0			0
$385$	2.73006	+	3.66711i	0.139137	+	0.186893i
$386$	−10.5027	+	3.82268i	−0.534575	+	0.194569i
$387$		0			0
$388$	4.62802	+	1.68446i	0.234952	+	0.0855155i
$389$	−4.70662	−	15.7212i	−0.238635	−	0.797096i	−0.990468	−	0.137743i	$-0.956015\pi$
$389$	−4.70662	−	15.7212i	−0.238635	−	0.797096i	0.751833	−	0.659354i	$-0.229170\pi$
$390$		0			0
$391$	1.41569	+	24.3065i	0.0715946	+	1.22923i
$392$	−12.0977	+	7.95681i	−0.611028	+	0.401880i
$393$		0			0
$394$	−15.4849	−	3.67000i	−0.780120	−	0.184892i
$395$	−8.21859	−	46.6099i	−0.413522	−	2.34520i
$396$		0			0
$397$	6.21875	−	35.2683i	0.312110	−	1.77006i	−0.275877	−	0.961193i	$-0.588968\pi$
$397$	6.21875	−	35.2683i	0.312110	−	1.77006i	0.587987	−	0.808871i	$-0.299921\pi$
$398$	16.2982	−	37.7835i	0.816956	−	1.89392i
$399$		0			0
$400$	6.12942	−	20.4737i	0.306471	−	1.02369i
$401$	3.58004	−	4.80883i	0.178779	−	0.240142i	−0.703696	−	0.710501i	$-0.748468\pi$
$401$	3.58004	−	4.80883i	0.178779	−	0.240142i	0.882475	+	0.470360i	$0.155876\pi$
$402$		0			0
$403$	−18.4934	+	9.28774i	−0.921223	+	0.462655i
$404$	3.46844			0.172561
$405$		0			0
$406$	4.23114			0.209988
$407$	2.45127	−	1.23108i	0.121505	−	0.0610221i
$408$		0			0
$409$	14.9077	−	20.0245i	0.737138	−	0.990148i	−0.262544	−	0.964920i	$-0.584562\pi$
$409$	14.9077	−	20.0245i	0.737138	−	0.990148i	0.999682	−	0.0252277i	$-0.00803107\pi$
$410$	15.4198	−	51.5058i	0.761531	−	2.54369i
$411$		0			0
$412$	−1.54409	+	3.57961i	−0.0760719	+	0.176355i
$413$	−0.899709	+	5.10250i	−0.0442718	+	0.251078i
$414$		0			0
$415$	1.53209	+	8.68891i	0.0752073	+	0.426522i
$416$	13.9310	+	3.30171i	0.683025	+	0.161880i
$417$		0			0
$418$	−6.35983	+	4.18293i	−0.311070	+	0.204594i
$419$	0.561267	+	9.63658i	0.0274197	+	0.470778i	0.983870	+	0.178883i	$0.0572485\pi$
$419$	0.561267	+	9.63658i	0.0274197	+	0.470778i	−0.956451	+	0.291894i	$0.905714\pi$
$420$		0			0
$421$	−3.44297	−	11.5003i	−0.167800	−	0.560491i	−0.999982	−	0.00598851i	$-0.998094\pi$
$421$	−3.44297	−	11.5003i	−0.167800	−	0.560491i	0.832182	−	0.554502i	$-0.187091\pi$
$422$	13.4117	+	4.88146i	0.652872	+	0.237626i
$423$		0			0
$424$	9.29287	−	3.38233i	0.451301	−	0.164260i
$425$	8.89067	+	11.9422i	0.431261	+	0.579284i
$426$		0			0
$427$	10.2459	−	2.42831i	0.495831	−	0.117514i
$428$	1.63452	+	3.78925i	0.0790077	+	0.183160i
$429$		0			0
$430$	15.0705	+	9.91201i	0.726763	+	0.477999i
$431$	−19.7100	+	34.1388i	−0.949399	+	1.64441i	−0.202704	+	0.979240i	$0.564973\pi$
$431$	−19.7100	+	34.1388i	−0.949399	+	1.64441i	−0.746695	+	0.665167i	$0.768360\pi$
$432$		0			0
$433$	8.08024	+	13.9954i	0.388312	+	0.672575i	0.992223	−	0.124476i	$-0.0397251\pi$
$433$	8.08024	+	13.9954i	0.388312	+	0.672575i	−0.603911	+	0.797052i	$0.706392\pi$
$434$	−0.316941	+	5.44167i	−0.0152137	+	0.261209i
$435$		0			0
$436$	7.35443	+	0.859610i	0.352214	+	0.0411679i
$437$	−18.2697	−	19.3648i	−0.873960	−	0.926343i
$438$		0			0
$439$	31.5031	−	3.68219i	1.50356	−	0.175741i	0.675911	−	0.736984i	$-0.263751\pi$
$439$	31.5031	−	3.68219i	1.50356	−	0.175741i	0.827651	+	0.561242i	$0.189676\pi$
$440$	−8.11270	−	6.80737i	−0.386758	−	0.324528i
$441$		0			0
$442$	−24.1970	+	20.3037i	−1.15093	+	0.965747i
$443$	18.0850	−	19.1689i	0.859243	−	0.910744i	−0.137572	−	0.990492i	$-0.543930\pi$
$443$	18.0850	−	19.1689i	0.859243	−	0.910744i	0.996815	+	0.0797476i	$0.0254114\pi$
$444$		0			0
$445$	−14.5115	−	7.28797i	−0.687913	−	0.345483i
$446$	−18.1880	−	9.13437i	−0.861228	−	0.432525i
$447$		0			0
$448$	−4.21661	+	4.46934i	−0.199216	+	0.211156i
$449$	−24.0265	+	20.1606i	−1.13388	+	0.951439i	−0.999221	−	0.0394529i	$-0.987438\pi$
$449$	−24.0265	+	20.1606i	−1.13388	+	0.951439i	−0.134659	+	0.990892i	$0.542994\pi$
$450$		0			0
$451$	−11.8600	−	9.95168i	−0.558463	−	0.468606i
$452$	0.259236	−	0.0303004i	0.0121934	−	0.00142521i
$453$		0			0
$454$	15.0674	+	15.9706i	0.707150	+	0.749535i
$455$	−20.6032	−	2.40817i	−0.965894	−	0.112897i
$456$		0			0
$457$	−0.0105280	+	0.180759i	−0.000492479	+	0.00845553i	−0.998545	−	0.0539165i	$-0.982830\pi$
$457$	−0.0105280	+	0.180759i	−0.000492479	+	0.00845553i	0.998053	+	0.0623721i	$0.0198665\pi$
$458$	−9.92250	−	17.1863i	−0.463648	−	0.803062i
$459$		0			0
$460$	−4.75968	+	8.24400i	−0.221921	+	0.384379i
$461$	0.543423	+	0.357415i	0.0253097	+	0.0166465i	0.562101	−	0.827069i	$-0.309993\pi$
$461$	0.543423	+	0.357415i	0.0253097	+	0.0166465i	−0.536791	+	0.843715i	$0.680364\pi$
$462$		0			0
$463$	−3.16038	−	7.32658i	−0.146875	−	0.340495i	0.828858	−	0.559460i	$-0.188991\pi$
$463$	−3.16038	−	7.32658i	−0.146875	−	0.340495i	−0.975733	+	0.218965i	$0.929732\pi$
$464$	−11.5722	+	2.74266i	−0.537226	+	0.127325i
$465$		0			0
$466$	6.36916	+	8.55527i	0.295046	+	0.396315i
$467$	−4.53030	+	1.64889i	−0.209637	+	0.0763017i	−0.444704	−	0.895677i	$-0.646691\pi$
$467$	−4.53030	+	1.64889i	−0.209637	+	0.0763017i	0.235067	+	0.971979i	$0.424469\pi$
$468$		0			0
$469$	−2.18719	−	0.796071i	−0.100995	−	0.0367591i
$470$	−2.53477	−	8.46674i	−0.116920	−	0.390541i
$471$		0			0
$472$	−0.697866	−	11.9819i	−0.0321219	−	0.551511i
$473$	4.33971	−	2.85427i	0.199540	−	0.131240i
$474$		0			0
$475$	−15.8407	−	3.75432i	−0.726822	−	0.172260i
$476$	0.245247	+	1.39086i	0.0112409	+	0.0637501i
$477$		0			0
$478$	3.63289	−	20.6031i	0.166164	−	0.942365i
$479$	−12.4531	+	28.8695i	−0.568996	+	1.31908i	0.354350	+	0.935113i	$0.384702\pi$
$479$	−12.4531	+	28.8695i	−0.568996	+	1.31908i	−0.923346	+	0.383968i	$0.874557\pi$
$480$		0			0
$481$	−3.56957	+	11.9232i	−0.162758	+	0.543651i
$482$	−0.326716	+	0.438856i	−0.0148815	+	0.0199893i
$483$		0			0
$484$	−3.31926	+	1.66699i	−0.150875	+	0.0757725i
$485$	37.3080			1.69407
$486$		0			0
$487$	4.28326			0.194093			0.0970465	−	0.995280i	$-0.469060\pi$
$487$	4.28326			0.194093			0.0970465	+	0.995280i	$0.469060\pi$
$488$	−21.7973	+	10.9470i	−0.986718	+	0.495549i
$489$		0			0
$490$	16.8342	−	22.6123i	0.760494	−	1.02152i
$491$	1.79294	−	5.98883i	0.0809142	−	0.270272i	−0.907953	−	0.419072i	$-0.862356\pi$
$491$	1.79294	−	5.98883i	0.0809142	−	0.270272i	0.988867	+	0.148799i	$0.0475408\pi$
$492$		0			0
$493$	3.28152	−	7.60741i	0.147792	−	0.342620i
$494$	5.99756	−	34.0139i	0.269843	−	1.53036i
$495$		0			0
$496$	−2.66050	−	15.0885i	−0.119460	−	0.677492i
$497$	4.37925	+	1.03790i	0.196436	+	0.0465563i
$498$		0			0
$499$	−2.77134	+	1.82274i	−0.124062	+	0.0815969i	−0.610023	−	0.792383i	$-0.708840\pi$
$499$	−2.77134	+	1.82274i	−0.124062	+	0.0815969i	0.485961	+	0.873980i	$0.338470\pi$
$500$	−0.0297985	−	0.511621i	−0.00133263	−	0.0228804i
$501$		0			0
$502$	−9.94804	−	33.2288i	−0.444003	−	1.48307i
$503$	−31.0387	−	11.2972i	−1.38395	−	0.503716i	−0.460576	−	0.887620i	$-0.652357\pi$
$503$	−31.0387	−	11.2972i	−1.38395	−	0.503716i	−0.923373	+	0.383904i	$0.874579\pi$
$504$		0			0
$505$	24.6895	−	8.98626i	1.09867	−	0.399883i
$506$	9.64306	+	12.9529i	0.428686	+	0.575826i
$507$		0			0
$508$	0.530534	−	0.125739i	0.0235386	−	0.00557876i
$509$	9.65014	+	22.3715i	0.427735	+	0.991601i	0.986721	+	0.162424i	$0.0519313\pi$
$509$	9.65014	+	22.3715i	0.427735	+	0.991601i	−0.558986	+	0.829177i	$0.688809\pi$
$510$		0			0
$511$	9.94588	+	6.54151i	0.439980	+	0.289379i
$512$	6.18481	−	10.7124i	0.273332	−	0.473426i
$513$		0			0
$514$	−14.2818	−	24.7369i	−0.629945	−	1.09110i
$515$	−1.71710	+	29.4814i	−0.0756643	+	1.29911i
$516$		0			0
$517$	−2.52780	−	0.295457i	−0.111172	−	0.0129942i
$518$	2.24967	+	2.38451i	0.0988448	+	0.104769i
$519$		0			0
$520$	47.7270	−	5.57849i	2.09297	−	0.244633i
$521$	26.0017	+	21.8180i	1.13916	+	0.955865i	0.999411	−	0.0343222i	$-0.0109273\pi$
$521$	26.0017	+	21.8180i	1.13916	+	0.955865i	0.139745	+	0.990188i	$0.455372\pi$
$522$		0			0
$523$	−8.90608	+	7.47308i	−0.389435	+	0.326775i	−0.816393	−	0.577496i	$-0.804030\pi$
$523$	−8.90608	+	7.47308i	−0.389435	+	0.326775i	0.426958	+	0.904272i	$0.359585\pi$
$524$	−5.16127	+	5.47063i	−0.225471	+	0.238986i
$525$		0			0
$526$	−3.24397	−	1.62918i	−0.141444	−	0.0710357i
$527$	9.53810	+	4.79021i	0.415486	+	0.208665i
$528$		0			0
$529$	−22.9736	+	24.3506i	−0.998852	+	1.05872i
$530$	−14.7488	+	12.3757i	−0.640648	+	0.537568i
$531$		0			0
$532$	−1.18300	−	0.992654i	−0.0512895	−	0.0430370i
$533$	69.7721	−	8.15518i	3.02216	−	0.353240i
$534$		0			0
$535$	21.4526	+	22.7384i	0.927475	+	0.983066i
$536$	5.35528	+	0.625943i	0.231313	+	0.0270366i
$537$		0			0
$538$	1.37441	−	23.5977i	0.0592549	−	1.01737i
$539$	−4.05889	−	7.03021i	−0.174829	−	0.302813i
$540$		0			0
$541$	−4.94751	+	8.56934i	−0.212710	+	0.368425i	−0.952562	−	0.304345i	$-0.901562\pi$
$541$	−4.94751	+	8.56934i	−0.212710	+	0.368425i	0.739852	+	0.672770i	$0.234896\pi$
$542$	−7.13680	−	4.69395i	−0.306552	−	0.201622i
$543$		0			0
$544$	−2.92467	−	6.78016i	−0.125394	−	0.290697i
$545$	54.5786	−	12.9354i	2.33789	−	0.554090i
$546$		0			0
$547$	−23.1671	−	31.1188i	−0.990553	−	1.33054i	−0.943401	−	0.331656i	$-0.892393\pi$
$547$	−23.1671	−	31.1188i	−0.990553	−	1.33054i	−0.0471523	−	0.998888i	$-0.515015\pi$
$548$	1.79126	−	0.651964i	0.0765187	−	0.0278505i
$549$		0			0
$550$	9.27893	+	3.37726i	0.395655	+	0.144007i
$551$	2.59820	+	8.67861i	0.110687	+	0.369721i
$552$		0			0
$553$	−0.947067	−	16.2605i	−0.0402734	−	0.691467i
$554$	−24.2742	+	15.9654i	−1.03131	+	0.678304i
$555$		0			0
$556$	0.405289	+	0.0960551i	0.0171881	+	0.00407365i
$557$	−2.03984	−	11.5685i	−0.0864307	−	0.490173i	−0.997039	−	0.0769017i	$-0.975497\pi$
$557$	−2.03984	−	11.5685i	−0.0864307	−	0.490173i	0.910608	−	0.413271i	$-0.135614\pi$
$558$		0			0
$559$	−4.09251	+	23.2098i	−0.173095	+	0.981669i
$560$	6.08275	−	14.1014i	0.257043	−	0.595893i
$561$		0			0
$562$	−8.21271	+	27.4324i	−0.346432	+	1.15716i
$563$	8.74799	−	11.7506i	0.368684	−	0.495229i	−0.578605	−	0.815608i	$-0.696403\pi$
$563$	8.74799	−	11.7506i	0.368684	−	0.495229i	0.947289	+	0.320379i	$0.103810\pi$
$564$		0			0
$565$	1.76683	−	0.887335i	0.0743311	−	0.0373305i
$566$	−18.8097			−0.790631
$567$		0			0
$568$	−10.4255			−0.437443
$569$	28.9461	−	14.5373i	1.21348	−	0.609435i	0.277246	−	0.960799i	$-0.410578\pi$
$569$	28.9461	−	14.5373i	1.21348	−	0.609435i	0.936239	+	0.351364i	$0.114282\pi$
$570$		0			0
$571$	4.74082	−	6.36802i	0.198397	−	0.266494i	−0.691780	−	0.722108i	$-0.743173\pi$
$571$	4.74082	−	6.36802i	0.198397	−	0.266494i	0.890177	+	0.455615i	$0.150581\pi$
$572$	−1.01994	+	3.40684i	−0.0426459	+	0.142447i
$573$		0			0
$574$	7.32859	−	16.9896i	0.305889	−	0.709132i
$575$	−5.99697	+	34.0105i	−0.250091	+	1.41834i
$576$		0			0
$577$	3.55054	+	20.1361i	0.147811	+	0.838277i	0.965067	+	0.262003i	$0.0843830\pi$
$577$	3.55054	+	20.1361i	0.147811	+	0.838277i	−0.817256	+	0.576274i	$0.804506\pi$
$578$	−9.82195	−	2.32784i	−0.408539	−	0.0968256i
$579$		0			0
$580$	2.70634	−	1.77999i	0.112375	−	0.0739099i
$581$	0.176550	+	3.03125i	0.00732453	+	0.125757i
$582$		0			0
$583$	1.59009	+	5.31127i	0.0658547	+	0.219970i
$584$	−25.9130	−	9.43156i	−1.07229	−	0.390281i
$585$		0			0
$586$	28.0351	−	10.2039i	1.15812	−	0.421520i
$587$	−10.2027	−	13.7046i	−0.421110	−	0.565649i	0.540053	−	0.841631i	$-0.318404\pi$
$587$	−10.2027	−	13.7046i	−0.421110	−	0.565649i	−0.961163	+	0.275982i	$0.910997\pi$
$588$		0			0
$589$	−11.3562	+	2.69147i	−0.467924	+	0.110900i
$590$	9.25515	+	21.4558i	0.381028	+	0.883323i
$591$		0			0
$592$	−7.69852	−	5.06340i	−0.316407	−	0.208104i
$593$	−2.55973	+	4.43358i	−0.105115	+	0.182065i	−0.913785	−	0.406197i	$-0.866855\pi$
$593$	−2.55973	+	4.43358i	−0.105115	+	0.182065i	0.808670	+	0.588263i	$0.200188\pi$
$594$		0			0
$595$	5.34929	+	9.26525i	0.219300	+	0.379838i
$596$	−0.0275827	+	0.473576i	−0.00112983	+	0.0193984i
$597$		0			0
$598$	−72.7743	−	8.50609i	−2.97596	−	0.347840i
$599$	11.9893	+	12.7079i	0.489868	+	0.519230i	0.924399	−	0.381427i	$-0.124567\pi$
$599$	11.9893	+	12.7079i	0.489868	+	0.519230i	−0.434531	+	0.900657i	$0.643086\pi$
$600$		0			0
$601$	16.5538	−	1.93486i	0.675243	−	0.0789246i	0.228442	−	0.973558i	$-0.426637\pi$
$601$	16.5538	−	1.93486i	0.675243	−	0.0789246i	0.446802	+	0.894633i	$0.352563\pi$
$602$	4.75536	+	3.99022i	0.193814	+	0.162629i
$603$		0			0
$604$	4.05589	−	3.40329i	0.165032	−	0.138478i
$605$	−19.3087	+	20.4660i	−0.785010	+	0.832062i
$606$		0			0
$607$	34.0785	+	17.1149i	1.38320	+	0.694671i	0.975818	−	0.218585i	$-0.0701440\pi$
$607$	34.0785	+	17.1149i	1.38320	+	0.694671i	0.407386	+	0.913256i	$0.366440\pi$
$608$	7.21525	+	3.62364i	0.292617	+	0.146958i
$609$		0			0
$610$	32.5882	−	34.5415i	1.31946	−	1.39855i
$611$	8.84590	−	7.42259i	0.357867	−	0.300286i
$612$		0			0
$613$	−27.7479	−	23.2833i	−1.12073	−	0.940402i	−0.122087	−	0.992519i	$-0.538959\pi$
$613$	−27.7479	−	23.2833i	−1.12073	−	0.940402i	−0.998641	+	0.0521174i	$0.983403\pi$
$614$	−17.0396	+	1.99165i	−0.687664	+	0.0803764i
$615$		0			0
$616$	−2.50110	−	2.65101i	−0.100772	−	0.106812i
$617$	−37.1472	−	4.34189i	−1.49549	−	0.174798i	−0.671332	−	0.741157i	$-0.734277\pi$
$617$	−37.1472	−	4.34189i	−1.49549	−	0.174798i	−0.824158	+	0.566359i	$0.808351\pi$
$618$		0			0
$619$	1.74216	−	29.9117i	0.0700233	−	1.20225i	−0.762024	−	0.647549i	$-0.775794\pi$
$619$	1.74216	−	29.9117i	0.0700233	−	1.20225i	0.832047	−	0.554705i	$-0.187169\pi$
$620$	2.08652	+	3.61396i	0.0837967	+	0.145140i
$621$		0			0
$622$	−10.9477	+	18.9620i	−0.438963	+	0.760306i
$623$	−4.66914	−	3.07094i	−0.187065	−	0.123035i
$624$		0			0
$625$	−10.6384	−	24.6626i	−0.425536	−	0.986504i
$626$	−2.41814	+	0.573109i	−0.0966482	+	0.0229061i
$627$		0			0
$628$	−0.531500	−	0.713928i	−0.0212091	−	0.0284888i
$629$	6.03201	−	2.19547i	0.240512	−	0.0875392i
$630$		0			0
$631$	−11.4941	−	4.18350i	−0.457572	−	0.166543i	0.102942	−	0.994687i	$-0.467174\pi$
$631$	−11.4941	−	4.18350i	−0.457572	−	0.166543i	−0.560514	+	0.828145i	$0.689396\pi$
$632$	10.8214	+	36.1459i	0.430451	+	1.43781i
$633$		0			0
$634$	−0.969415	−	16.6442i	−0.0385004	−	0.661026i
$635$	3.45075	−	2.26960i	0.136939	−	0.0900662i
$636$		0			0
$637$	35.8401	+	8.49427i	1.42004	+	0.336555i
$638$	−0.954179	−	5.41142i	−0.0377763	−	0.214240i
$639$		0			0
$640$	−7.26391	+	41.1957i	−0.287131	+	1.62840i
$641$	−1.73208	+	4.01541i	−0.0684130	+	0.158599i	−0.948992	−	0.315300i	$-0.897895\pi$
$641$	−1.73208	+	4.01541i	−0.0684130	+	0.158599i	0.880579	+	0.473899i	$0.157154\pi$
$642$		0			0
$643$	−4.00151	+	13.3660i	−0.157804	+	0.527103i	−0.999926	−	0.0121848i	$-0.996121\pi$
$643$	−4.00151	+	13.3660i	−0.157804	+	0.527103i	0.842121	+	0.539288i	$0.181307\pi$
$644$	−1.95632	+	2.62779i	−0.0770898	+	0.103550i
$645$		0			0
$646$	−15.9187	+	7.99468i	−0.626314	+	0.314547i
$647$	−32.6853			−1.28499			−0.642496	−	0.766289i	$-0.722101\pi$
$647$	−32.6853			−1.28499			−0.642496	+	0.766289i	$0.722101\pi$
$648$		0			0
$649$	6.72875			0.264126
$650$	−40.0378	+	20.1077i	−1.57041	+	0.788691i
$651$		0			0
$652$	−3.73278	+	5.01399i	−0.146187	+	0.196363i
$653$	0.914424	−	3.05439i	0.0357842	−	0.119527i	−0.938231	−	0.346008i	$-0.887537\pi$
$653$	0.914424	−	3.05439i	0.0357842	−	0.119527i	0.974016	+	0.226481i	$0.0727221\pi$
$654$		0			0
$655$	−22.5661	+	52.3140i	−0.881729	+	2.04408i
$656$	−9.03096	+	51.2171i	−0.352600	+	1.99969i
$657$		0			0
$658$	−0.528163	−	2.99536i	−0.0205899	−	0.116771i
$659$	−13.4730	−	3.19317i	−0.524835	−	0.124388i	−0.0403462	−	0.999186i	$-0.512846\pi$
$659$	−13.4730	−	3.19317i	−0.524835	−	0.124388i	−0.484488	+	0.874798i	$0.660994\pi$
$660$		0			0
$661$	21.8213	−	14.3521i	0.848752	−	0.558233i	−0.0489676	−	0.998800i	$-0.515593\pi$
$661$	21.8213	−	14.3521i	0.848752	−	0.558233i	0.897720	+	0.440567i	$0.145223\pi$
$662$	2.57178	+	44.1558i	0.0999551	+	1.71616i
$663$		0			0
$664$	−2.01729	−	6.73823i	−0.0782862	−	0.261494i
$665$	−10.9928	−	4.00106i	−0.426284	−	0.155155i
$666$		0			0
$667$	18.0590	−	6.57295i	0.699249	−	0.254506i
$668$	1.91921	+	2.57794i	0.0742564	+	0.0997436i
$669$		0			0
$670$	−10.2141	+	2.42079i	−0.394607	+	0.0935235i
$671$	−5.41627	−	12.5563i	−0.209093	−	0.484731i
$672$		0			0
$673$	−10.9283	−	7.18764i	−0.421254	−	0.277063i	0.321133	−	0.947034i	$-0.395936\pi$
$673$	−10.9283	−	7.18764i	−0.421254	−	0.277063i	−0.742387	+	0.669971i	$0.766307\pi$
$674$	0.983326	−	1.70317i	0.0378763	−	0.0656037i
$675$		0			0
$676$	−5.40991	−	9.37023i	−0.208073	−	0.360394i
$677$	−0.537483	+	9.22823i	−0.0206572	+	0.354670i	0.972103	+	0.234555i	$0.0753633\pi$
$677$	−0.537483	+	9.22823i	−0.0206572	+	0.354670i	−0.992760	+	0.120115i	$0.961674\pi$
$678$		0			0
$679$	12.7526	+	1.49056i	0.489400	+	0.0572026i
$680$	−17.0072	−	18.0266i	−0.652196	−	0.691287i
$681$		0			0
$682$	7.03111	−	0.821819i	0.269235	−	0.0314691i
$683$	25.1766	+	21.1257i	0.963356	+	0.808351i	0.981496	−	0.191484i	$-0.0613300\pi$
$683$	25.1766	+	21.1257i	0.963356	+	0.808351i	−0.0181400	+	0.999835i	$0.505774\pi$
$684$		0			0
$685$	11.0616	−	9.28182i	0.422644	−	0.354640i
$686$	14.6057	−	15.4812i	0.557650	−	0.591074i
$687$		0			0
$688$	−15.5924	−	7.83082i	−0.594456	−	0.298547i
$689$	−22.4800	−	11.2899i	−0.856418	−	0.430109i
$690$		0			0
$691$	−26.8358	+	28.4443i	−1.02088	+	1.08207i	−0.0242817	+	0.999705i	$0.507730\pi$
$691$	−26.8358	+	28.4443i	−1.02088	+	1.08207i	−0.996602	+	0.0823683i	$0.973752\pi$
$692$	1.41866	−	1.19039i	0.0539292	−	0.0452520i
$693$		0			0
$694$	18.2932	+	15.3498i	0.694399	+	0.582670i
$695$	3.13385	−	0.366295i	0.118874	−	0.0138943i
$696$		0			0
$697$	−24.8628	−	26.3530i	−0.941745	−	0.998191i
$698$	−18.2815	−	2.13681i	−0.691966	−	0.0808793i
$699$		0			0
$700$	−0.116479	+	1.99987i	−0.00440250	+	0.0755880i
$701$	13.1619	+	22.7970i	0.497117	+	0.861031i	0.999994	−	0.00332633i	$-0.00105881\pi$
$701$	13.1619	+	22.7970i	0.497117	+	0.861031i	−0.502878	+	0.864357i	$0.667725\pi$
$702$		0			0
$703$	−3.50949	+	6.07861i	−0.132363	+	0.229259i
$704$	6.66697	+	4.38493i	0.251271	+	0.165263i
$705$		0			0
$706$	−7.60685	−	17.6347i	−0.286288	−	0.663690i
$707$	8.79838	−	2.08525i	0.330897	−	0.0784240i
$708$		0			0
$709$	13.1140	+	17.6151i	0.492505	+	0.661549i	0.976999	−	0.213246i	$-0.0684035\pi$
$709$	13.1140	+	17.6151i	0.492505	+	0.661549i	−0.484494	+	0.874795i	$0.660996\pi$
$710$	19.0731	−	6.94204i	0.715801	−	0.260530i
$711$		0			0
$712$	12.1650	+	4.42769i	0.455902	+	0.165935i
$713$	7.10074	+	23.7181i	0.265925	+	0.888251i
$714$		0			0
$715$	1.56637	+	26.8936i	0.0585790	+	1.00576i
$716$	1.57495	−	1.03586i	0.0588586	−	0.0387119i
$717$		0			0
$718$	19.6699	+	4.66186i	0.734075	+	0.173979i
$719$	8.77432	+	49.7616i	0.327227	+	1.85580i	0.493540	+	0.869723i	$0.335703\pi$
$719$	8.77432	+	49.7616i	0.327227	+	1.85580i	−0.166313	+	0.986073i	$0.553186\pi$
$720$		0			0
$721$	−1.76480	+	10.0087i	−0.0657247	+	0.372744i
$722$	−3.96524	+	9.19246i	−0.147571	+	0.342108i
$723$		0			0
$724$	−0.958156	+	3.20047i	−0.0356096	+	0.118944i
$725$	7.01755	−	9.42621i	0.260625	−	0.350081i
$726$		0			0
$727$	−3.39515	+	1.70511i	−0.125919	+	0.0632390i	−0.510644	−	0.859793i	$-0.670593\pi$
$727$	−3.39515	+	1.70511i	−0.125919	+	0.0632390i	0.384724	+	0.923032i	$0.374297\pi$
$728$	16.5369			0.612897
$729$		0			0
$730$	53.6873			1.98706
$731$	10.8623	−	5.45527i	0.401758	−	0.201770i
$732$		0			0
$733$	−27.4625	+	36.8886i	−1.01435	+	1.36251i	−0.0837450	+	0.996487i	$0.526688\pi$
$733$	−27.4625	+	36.8886i	−1.01435	+	1.36251i	−0.930606	+	0.366023i	$0.880719\pi$
$734$	−3.17668	+	10.6108i	−0.117253	+	0.391653i
$735$		0			0
$736$	6.78414	−	15.7274i	0.250067	−	0.579720i
$737$	−0.524895	+	2.97683i	−0.0193348	+	0.109653i
$738$		0			0
$739$	−3.14560	−	17.8396i	−0.115713	−	0.656240i	−0.986395	−	0.164394i	$-0.947433\pi$
$739$	−3.14560	−	17.8396i	−0.115713	−	0.656240i	0.870682	−	0.491847i	$-0.163678\pi$
$740$	2.44208	+	0.578782i	0.0897725	+	0.0212765i
$741$		0			0
$742$	−5.53588	+	3.64100i	−0.203228	+	0.133665i
$743$	0.474165	+	8.14111i	0.0173954	+	0.298668i	0.995773	+	0.0918435i	$0.0292759\pi$
$743$	0.474165	+	8.14111i	0.0173954	+	0.298668i	−0.978378	+	0.206825i	$0.933687\pi$
$744$		0			0
$745$	1.03063	+	3.44254i	0.0377594	+	0.126125i
$746$	18.4300	+	6.70796i	0.674769	+	0.245596i
$747$		0			0
$748$	1.72354	−	0.627317i	0.0630188	−	0.0229370i
$749$	6.42442	+	8.62950i	0.234743	+	0.315315i
$750$		0			0
$751$	40.0164	−	9.48405i	1.46022	−	0.346078i	0.577658	−	0.816279i	$-0.303967\pi$
$751$	40.0164	−	9.48405i	1.46022	−	0.346078i	0.882559	+	0.470201i	$0.155819\pi$
$752$	3.38615	+	7.84998i	0.123480	+	0.286259i
$753$		0			0
$754$	20.8304	+	13.7004i	0.758600	+	0.498939i
$755$	20.0537	−	34.7341i	0.729830	−	1.26410i
$756$		0			0
$757$	7.55477	+	13.0853i	0.274583	+	0.475592i	0.970030	−	0.242986i	$-0.0781269\pi$
$757$	7.55477	+	13.0853i	0.274583	+	0.475592i	−0.695447	+	0.718578i	$0.744794\pi$
$758$	2.18342	−	37.4878i	0.0793053	−	1.36162i
$759$		0			0
$760$	26.9157	+	3.14600i	0.976336	+	0.114117i
$761$	11.7794	+	12.4854i	0.427003	+	0.452597i	0.904777	−	0.425886i	$-0.140037\pi$
$761$	11.7794	+	12.4854i	0.427003	+	0.452597i	−0.477773	+	0.878483i	$0.658556\pi$
$762$		0			0
$763$	19.1728	−	2.24098i	0.694101	−	0.0811288i
$764$	−1.23540	−	1.03662i	−0.0446951	−	0.0375036i
$765$		0			0
$766$	−30.7046	+	25.7642i	−1.10940	+	0.930899i
$767$	−20.9513	+	22.2071i	−0.756507	+	0.801850i
$768$		0			0
$769$	−32.7556	−	16.4505i	−1.18120	−	0.593219i	−0.253784	−	0.967261i	$-0.581675\pi$
$769$	−32.7556	−	16.4505i	−1.18120	−	0.593219i	−0.927412	+	0.374042i	$0.877972\pi$
$770$	6.34093	+	3.18454i	0.228511	+	0.114763i
$771$		0			0
$772$	−2.02079	+	2.14191i	−0.0727298	+	0.0770891i
$773$	−2.64318	+	2.21789i	−0.0950684	+	0.0797719i	−0.689083	−	0.724682i	$-0.741987\pi$
$773$	−2.64318	+	2.21789i	−0.0950684	+	0.0797719i	0.594015	+	0.804454i	$0.297542\pi$
$774$		0			0
$775$	11.5974	+	9.73138i	0.416591	+	0.349561i
$776$	−29.5411	+	3.45286i	−1.06047	+	0.123951i
$777$		0			0
$778$	−17.4789	−	18.5265i	−0.626647	−	0.664208i
$779$	39.3481	+	4.59913i	1.40979	+	0.164781i
$780$		0			0
$781$	0.339845	−	5.83491i	0.0121606	−	0.208789i
$782$	18.8946	+	32.7265i	0.675671	+	1.17030i
$783$		0			0
$784$	−13.6346	+	23.6158i	−0.486950	+	0.843422i
$785$	−5.63309	−	3.70494i	−0.201054	−	0.132235i
$786$		0			0
$787$	3.38868	+	7.85585i	0.120793	+	0.280031i	0.967875	−	0.251432i	$-0.0809016\pi$
$787$	3.38868	+	7.85585i	0.120793	+	0.280031i	−0.847081	+	0.531463i	$0.821642\pi$
$788$	−4.07978	+	0.966926i	−0.145336	+	0.0344453i
$789$		0			0
$790$	−43.8660	−	58.9222i	−1.56068	−	2.09636i
$791$	0.639387	−	0.232718i	0.0227340	−	0.00827450i
$792$		0			0
$793$	58.3045	+	21.2211i	2.07045	+	0.753584i
$794$	−15.9415	−	53.2482i	−0.565741	−	1.88971i
$795$		0			0
$796$	−0.630371	−	10.8230i	−0.0223429	−	0.383613i
$797$	−7.69741	+	5.06267i	−0.272656	+	0.179329i	−0.678472	−	0.734626i	$-0.737358\pi$
$797$	−7.69741	+	5.06267i	−0.272656	+	0.179329i	0.405816	+	0.913955i	$0.366987\pi$
$798$		0			0
$799$	−5.79516	−	1.37348i	−0.205018	−	0.0485902i
$800$	−1.81873	−	10.3146i	−0.0643020	−	0.364675i
$801$		0			0
$802$	1.61577	−	9.16349i	0.0570549	−	0.323574i
$803$	6.12334	−	14.1955i	0.216088	−	0.500948i
$804$		0			0
$805$	−7.11750	+	23.7741i	−0.250859	+	0.837927i
$806$	−19.1805	+	25.7638i	−0.675603	+	0.907492i
$807$		0			0
$808$	−18.7179	+	9.40049i	−0.658494	+	0.330708i
$809$	37.5769			1.32113			0.660567	−	0.750767i	$-0.270316\pi$
$809$	37.5769			1.32113			0.660567	+	0.750767i	$0.270316\pi$
$810$		0			0
$811$	−42.7728			−1.50196			−0.750979	−	0.660327i	$-0.770418\pi$
$811$	−42.7728			−1.50196			−0.750979	+	0.660327i	$0.770418\pi$
$812$	0.996193	−	0.500307i	0.0349595	−	0.0175573i
$813$		0			0
$814$	2.54234	−	3.41495i	0.0891089	−	0.119694i
$815$	−13.5806	+	45.3625i	−0.475709	+	1.58898i
$816$		0			0
$817$	−5.26434	+	12.2041i	−0.184176	+	0.426968i
$818$	6.72825	−	38.1578i	0.235248	−	1.33416i
$819$		0			0
$820$	−2.45976	−	13.9500i	−0.0858985	−	0.487155i
$821$	6.21560	+	1.47312i	0.216926	+	0.0514124i	0.337642	−	0.941275i	$-0.390371\pi$
$821$	6.21560	+	1.47312i	0.216926	+	0.0514124i	−0.120716	+	0.992687i	$0.538519\pi$
$822$		0			0
$823$	−38.2038	+	25.1270i	−1.33170	+	0.875873i	−0.997771	−	0.0667256i	$-0.978745\pi$
$823$	−38.2038	+	25.1270i	−1.33170	+	0.875873i	−0.333929	+	0.942598i	$0.608374\pi$
$824$	−1.36888	−	23.5028i	−0.0476873	−	0.818759i
$825$		0			0
$826$	2.30636	+	7.70378i	0.0802485	+	0.268049i
$827$	14.6029	+	5.31502i	0.507793	+	0.184821i	0.583196	−	0.812332i	$-0.301802\pi$
$827$	14.6029	+	5.31502i	0.507793	+	0.184821i	−0.0754029	+	0.997153i	$0.524024\pi$
$828$		0			0
$829$	−10.3463	+	3.76574i	−0.359341	+	0.130789i	−0.515381	−	0.856961i	$-0.672349\pi$
$829$	−10.3463	+	3.76574i	−0.359341	+	0.130789i	0.156040	+	0.987751i	$0.450127\pi$
$830$	8.17739	+	10.9841i	0.283841	+	0.381265i
$831$		0			0
$832$	−35.2306	+	8.34981i	−1.22140	+	0.289477i
$833$	−7.52426	−	17.4432i	−0.260700	−	0.604371i
$834$		0			0
$835$	20.3407	+	13.3783i	0.703919	+	0.462975i
$836$	−1.00277	+	1.73685i	−0.0346816	+	0.0600704i
$837$		0			0
$838$	7.49099	+	12.9748i	0.258772	+	0.448206i
$839$	−2.58446	+	44.3735i	−0.0892255	+	1.53194i	0.595627	+	0.803261i	$0.296904\pi$
$839$	−2.58446	+	44.3735i	−0.0892255	+	1.53194i	−0.684852	+	0.728682i	$0.740133\pi$
$840$		0			0
$841$	22.3087	+	2.60751i	0.769264	+	0.0899140i
$842$	−12.7861	−	13.5524i	−0.440637	−	0.467048i
$843$		0			0
$844$	3.73490	−	0.436547i	0.128561	−	0.0150266i
$845$	−62.7866	−	52.6842i	−2.15993	−	1.81239i
$846$		0			0
$847$	−7.41775	+	6.22423i	−0.254877	+	0.213867i
$848$	12.7805	−	13.5466i	0.438885	−	0.465191i
$849$		0			0
$850$	20.6498	+	10.3707i	0.708281	+	0.355712i
$851$	13.3061	+	6.68260i	0.456129	+	0.229077i
$852$		0			0
$853$	12.4016	−	13.1449i	0.424622	−	0.450073i	−0.479376	−	0.877610i	$-0.659137\pi$
$853$	12.4016	−	13.1449i	0.424622	−	0.450073i	0.903998	+	0.427537i	$0.140618\pi$
$854$	12.5193	−	10.5049i	0.428402	−	0.359472i
$855$		0			0
$856$	−19.0909	−	16.0192i	−0.652515	−	0.547525i
$857$	−41.8917	+	4.89643i	−1.43099	+	0.167259i	−0.796017	−	0.605274i	$-0.793064\pi$
$857$	−41.8917	+	4.89643i	−1.43099	+	0.167259i	−0.634975	+	0.772533i	$0.718990\pi$
$858$		0			0
$859$	8.13646	+	8.62414i	0.277612	+	0.294252i	0.851145	−	0.524931i	$-0.175909\pi$
$859$	8.13646	+	8.62414i	0.277612	+	0.294252i	−0.573533	+	0.819183i	$0.694427\pi$
$860$	4.72028	+	0.551721i	0.160960	+	0.0188135i
$861$		0			0
$862$	−3.55746	+	61.0792i	−0.121167	+	2.08036i
$863$	−9.42886	−	16.3313i	−0.320962	−	0.555923i	0.659725	−	0.751507i	$-0.270673\pi$
$863$	−9.42886	−	16.3313i	−0.320962	−	0.555923i	−0.980687	+	0.195585i	$0.937340\pi$
$864$		0			0
$865$	7.01433	−	12.1492i	0.238494	−	0.413085i
$866$	20.9559	+	13.7829i	0.712109	+	0.468362i
$867$		0			0
$868$	0.568824	+	1.31868i	0.0193071	+	0.0447590i
$869$	−20.5828	+	4.87822i	−0.698224	+	0.165482i
$870$		0			0
$871$	−8.19014	−	11.0013i	−0.277512	−	0.372764i
$872$	−42.0191	+	15.2937i	−1.42295	+	0.517910i
$873$		0			0
$874$	−38.8286	−	14.1325i	−1.31340	−	0.478038i
$875$	−0.383181	−	1.27991i	−0.0129539	−	0.0432689i
$876$		0			0
$877$	−0.639357	−	10.9773i	−0.0215896	−	0.370678i	−0.991748	−	0.128205i	$-0.959078\pi$
$877$	−0.639357	−	10.9773i	−0.0215896	−	0.370678i	0.970158	−	0.242473i	$-0.0779587\pi$
$878$	41.1293	−	27.0512i	1.38805	−	0.912933i
$879$		0			0
$880$	−19.4067	−	4.59948i	−0.654201	−	0.155049i
$881$	1.42184	+	8.06366i	0.0479030	+	0.271672i	0.999346	−	0.0361526i	$-0.0115102\pi$
$881$	1.42184	+	8.06366i	0.0479030	+	0.271672i	−0.951443	+	0.307824i	$0.900399\pi$
$882$		0			0
$883$	−2.52592	+	14.3252i	−0.0850039	+	0.482081i	0.912352	+	0.409407i	$0.134264\pi$
$883$	−2.52592	+	14.3252i	−0.0850039	+	0.482081i	−0.997356	+	0.0726741i	$0.976847\pi$
$884$	−3.29623	+	7.64151i	−0.110864	+	0.257012i
$885$		0			0
$886$	11.7310	−	39.1843i	0.394111	−	1.31642i
$887$	−23.4426	+	31.4888i	−0.787125	+	1.05729i	0.209708	+	0.977764i	$0.432749\pi$
$887$	−23.4426	+	31.4888i	−0.787125	+	1.05729i	−0.996833	+	0.0795279i	$0.974659\pi$
$888$		0			0
$889$	1.27021	−	0.637923i	0.0426015	−	0.0213953i
$890$	−25.2038			−0.844833
$891$		0			0
$892$	−5.36233			−0.179544
$893$	5.81955	−	2.92269i	0.194744	−	0.0978039i
$894$		0			0
$895$	8.52726	−	11.4541i	0.285035	−	0.382868i
$896$	−4.12883	+	13.7913i	−0.137935	+	0.460733i
$897$		0			0
$898$	−19.2810	+	44.6985i	−0.643417	+	1.49161i
$899$	1.46293	−	8.29670i	0.0487915	−	0.276710i
$900$		0			0
$901$	2.25295	+	12.7771i	0.0750566	+	0.425667i
$902$	−23.3815	−	5.54153i	−0.778520	−	0.184513i
$903$		0			0
$904$	−1.31688	+	0.866127i	−0.0437989	+	0.0288070i
$905$	1.47149	+	25.2645i	0.0489139	+	0.839820i
$906$		0			0
$907$	0.0803514	+	0.268392i	0.00266802	+	0.00891182i	0.959313	−	0.282344i	$-0.0911120\pi$
$907$	0.0803514	+	0.268392i	0.00266802	+	0.00891182i	−0.956645	+	0.291256i	$0.905927\pi$
$908$	5.43595	+	1.97852i	0.180398	+	0.0656596i
$909$		0			0
$910$	−30.2537	+	11.0115i	−1.00290	+	0.365026i
$911$	−14.4504	−	19.4103i	−0.478763	−	0.643091i	0.495472	−	0.868624i	$-0.334995\pi$
$911$	−14.4504	−	19.4103i	−0.478763	−	0.643091i	−0.974235	+	0.225533i	$0.927588\pi$
$912$		0			0
$913$	3.83700	−	0.909385i	0.126986	−	0.0300963i
$914$	0.111309	+	0.258042i	0.00368176	+	0.00853527i
$915$		0			0
$916$	−4.36836	−	2.87312i	−0.144335	−	0.0949304i
$917$	−9.80360	+	16.9803i	−0.323743	+	0.560740i
$918$		0			0
$919$	−8.35442	−	14.4703i	−0.275587	−	0.477331i	0.694696	−	0.719303i	$-0.255539\pi$
$919$	−8.35442	−	14.4703i	−0.275587	−	0.477331i	−0.970283	+	0.241973i	$0.922206\pi$
$920$	3.34259	−	57.3901i	0.110202	−	1.89210i
$921$		0			0
$922$	1.00268	+	0.117197i	0.0330215	+	0.00385966i
$923$	18.1989	+	19.2897i	0.599025	+	0.634929i
$924$		0			0
$925$	9.04344	−	1.05703i	0.297347	−	0.0347548i
$926$	−9.48684	−	7.96041i	−0.311757	−	0.261595i
$927$		0			0
$928$	−4.46478	+	3.74640i	−0.146564	+	0.122981i
$929$	4.20638	−	4.45850i	0.138007	−	0.146279i	−0.654684	−	0.755903i	$-0.727198\pi$
$929$	4.20638	−	4.45850i	0.138007	−	0.146279i	0.792691	+	0.609624i	$0.208680\pi$
$930$		0			0
$931$	18.5626	+	9.32246i	0.608363	+	0.305531i
$932$	2.51119	+	1.26116i	0.0822566	+	0.0413108i
$933$		0			0
$934$	−5.13487	+	5.44264i	−0.168018	+	0.178089i
$935$	10.6435	−	8.93092i	0.348078	−	0.292072i
$936$		0			0
$937$	−31.6672	−	26.5719i	−1.03452	−	0.868067i	−0.0431398	−	0.999069i	$-0.513736\pi$
$937$	−31.6672	−	26.5719i	−1.03452	−	0.868067i	−0.991382	+	0.131002i	$0.958181\pi$
$938$	−3.58810	+	0.419389i	−0.117156	+	0.0136935i
$939$		0			0
$940$	−1.59794	−	1.69371i	−0.0521190	−	0.0552429i
$941$	54.8368	+	6.40951i	1.78763	+	0.208944i	0.944443	−	0.328676i	$-0.106603\pi$
$941$	54.8368	+	6.40951i	1.78763	+	0.208944i	0.843187	+	0.537620i	$0.180677\pi$
$942$		0			0
$943$	4.88653	−	83.8985i	0.159127	−	2.73211i
$944$	−11.3016	−	19.5749i	−0.367835	−	0.637109i
$945$		0			0
$946$	4.03090	−	6.98172i	0.131056	−	0.226995i
$947$	23.5934	+	15.5176i	0.766683	+	0.504255i	0.871595	−	0.490226i	$-0.163086\pi$
$947$	23.5934	+	15.5176i	0.766683	+	0.504255i	−0.104913	+	0.994481i	$0.533456\pi$
$948$		0			0
$949$	27.7835	+	64.4094i	0.901891	+	2.09082i
$950$	−24.5859	+	5.82697i	−0.797672	+	0.189052i
$951$		0			0
$952$	−5.09316	−	6.84130i	−0.165070	−	0.221728i
$953$	24.9549	−	9.08285i	0.808369	−	0.294222i	0.0954192	−	0.995437i	$-0.469581\pi$
$953$	24.9549	−	9.08285i	0.808369	−	0.294222i	0.712950	+	0.701215i	$0.247359\pi$
$954$		0			0
$955$	−11.4797	−	4.17828i	−0.371475	−	0.135206i
$956$	−1.58086	−	5.28043i	−0.0511286	−	0.170781i
$957$		0			0
$958$	2.83737	+	48.7158i	0.0916714	+	1.57394i
$959$	4.15191	−	2.73076i	0.134072	−	0.0881807i
$960$		0			0
$961$	−19.6036	−	4.64613i	−0.632373	−	0.149875i
$962$	3.35439	+	19.0237i	0.108150	+	0.613348i
$963$		0			0
$964$	−0.0250310	+	0.141958i	−0.000806194	+	0.00457215i
$965$	−8.83527	+	20.4825i	−0.284417	+	0.659354i
$966$		0			0
$967$	7.57424	−	25.2997i	0.243571	−	0.813584i	−0.745546	−	0.666454i	$-0.767811\pi$
$967$	7.57424	−	25.2997i	0.243571	−	0.813584i	0.989117	−	0.147130i	$-0.0470035\pi$
$968$	13.3948	−	17.9924i	0.430526	−	0.578296i
$969$		0			0
$970$	51.7455	−	25.9876i	1.66145	−	0.834411i
$971$	−22.9842			−0.737600			−0.368800	−	0.929509i	$-0.620231\pi$
$971$	−22.9842			−0.737600			−0.368800	+	0.929509i	$0.620231\pi$
$972$		0			0
$973$	1.08584			0.0348106
$974$	5.94079	−	2.98358i	0.190355	−	0.0956000i
$975$		0			0
$976$	−27.4310	+	36.8462i	−0.878045	+	1.17942i
$977$	13.4439	−	44.9059i	0.430110	−	1.43667i	−0.418775	−	0.908090i	$-0.637540\pi$
$977$	13.4439	−	44.9059i	0.430110	−	1.43667i	0.848885	−	0.528577i	$-0.177274\pi$
$978$		0			0
$979$	−2.87463	+	6.66414i	−0.0918736	+	0.212987i
$980$	1.28974	−	7.31447i	0.0411992	−	0.233652i
$981$		0			0
$982$	−1.68486	−	9.55530i	−0.0537659	−	0.304922i
$983$	56.5922	+	13.4126i	1.80501	+	0.427795i	0.988711	−	0.149834i	$-0.0478741\pi$
$983$	56.5922	+	13.4126i	1.80501	+	0.427795i	0.816299	+	0.577630i	$0.196022\pi$
$984$		0			0
$985$	−26.5361	+	17.4531i	−0.845511	+	0.556101i
$986$	−0.747677	−	12.8371i	−0.0238109	−	0.408817i
$987$		0			0
$988$	−2.60985	−	8.71751i	−0.0830305	−	0.277341i
$989$	26.4952	+	9.64346i	0.842498	+	0.306644i
$990$		0			0
$991$	−31.3736	+	11.4191i	−0.996615	+	0.362738i	−0.788278	−	0.615319i	$-0.789027\pi$
$991$	−31.3736	+	11.4191i	−0.996615	+	0.362738i	−0.208337	+	0.978057i	$0.566805\pi$
$992$	−4.48381	−	6.02280i	−0.142361	−	0.191224i
$993$		0			0
$994$	6.79690	−	1.61090i	0.215585	−	0.0510945i
$995$	−32.5283	−	75.4090i	−1.03122	−	2.39063i
$996$		0			0
$997$	13.0884	+	8.60838i	0.414514	+	0.272630i	0.739590	−	0.673058i	$-0.235019\pi$
$997$	13.0884	+	8.60838i	0.414514	+	0.272630i	−0.325076	+	0.945688i	$0.605390\pi$
$998$	−2.57413	+	4.45852i	−0.0814827	+	0.141132i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.g.a.460.7		144
3.2	odd	2		729.2.g.d.460.2		144
9.2	odd	6		81.2.g.a.52.7	✓	144
9.4	even	3		729.2.g.b.217.2		144
9.5	odd	6		729.2.g.c.217.7		144
9.7	even	3		243.2.g.a.154.2		144
81.13	even	27	inner	729.2.g.a.271.7		144
81.14	odd	54		729.2.g.c.514.7		144
81.16	even	27		6561.2.a.d.1.54		72
81.40	even	27		243.2.g.a.172.2		144
81.41	odd	54		81.2.g.a.67.7	yes	144
81.65	odd	54		6561.2.a.c.1.19		72
81.67	even	27		729.2.g.b.514.2		144
81.68	odd	54		729.2.g.d.271.2		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.52.7	✓	144	9.2	odd	6
81.2.g.a.67.7	yes	144	81.41	odd	54
243.2.g.a.154.2		144	9.7	even	3
243.2.g.a.172.2		144	81.40	even	27
729.2.g.a.271.7		144	81.13	even	27	inner
729.2.g.a.460.7		144	1.1	even	1	trivial
729.2.g.b.217.2		144	9.4	even	3
729.2.g.b.514.2		144	81.67	even	27
729.2.g.c.217.7		144	9.5	odd	6
729.2.g.c.514.7		144	81.14	odd	54
729.2.g.d.271.2		144	81.68	odd	54
729.2.g.d.460.2		144	3.2	odd	2
6561.2.a.c.1.19		72	81.65	odd	54
6561.2.a.d.1.54		72	81.16	even	27

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)

\(f(q)\)	\(=\)	\(q+(1.38698 - 0.696568i) q^{2} +(0.244190 - 0.328004i) q^{4} +(0.888415 - 2.96751i) q^{5} +(0.422238 - 0.978857i) q^{7} +(-0.428818 + 2.43195i) q^{8} +O(q^{10})\)	\(q+(1.38698 - 0.696568i) q^{2} +(0.244190 - 0.328004i) q^{4} +(0.888415 - 2.96751i) q^{5} +(0.422238 - 0.978857i) q^{7} +(-0.428818 + 2.43195i) q^{8} +(-0.834859 - 4.73472i) q^{10} +(-1.34713 - 0.319276i) q^{11} +(5.24827 - 3.45184i) q^{13} +(-0.0962048 - 1.65177i) q^{14} +(1.33381 + 4.45525i) q^{16} +(-3.04443 - 1.10808i) q^{17} +(3.32892 - 1.21163i) q^{19} +(-0.756415 - 1.01604i) q^{20} +(-2.09084 + 0.495538i) q^{22} +(-2.97660 - 6.90053i) q^{23} +(-3.83941 - 2.52522i) q^{25} +(4.87480 - 8.44340i) q^{26} +(-0.217963 - 0.377523i) q^{28} +(-0.148690 + 2.55291i) q^{29} +(-3.27217 - 0.382462i) q^{31} +(1.56405 + 1.65780i) q^{32} +(-4.99442 + 0.583764i) q^{34} +(-2.52965 - 2.12263i) q^{35} +(-1.51778 + 1.27357i) q^{37} +(3.77317 - 3.99932i) q^{38} +(6.83587 + 3.43310i) q^{40} +(9.99336 + 5.01885i) q^{41} +(-2.57467 + 2.72899i) q^{43} +(-0.433680 + 0.363900i) q^{44} +(-8.93516 - 7.49749i) q^{46} +(1.82585 - 0.213412i) q^{47} +(4.02382 + 4.26499i) q^{49} +(-7.08417 - 0.828021i) q^{50} +(0.149357 - 2.56436i) q^{52} +(-2.00231 - 3.46810i) q^{53} +(-2.14427 + 3.71398i) q^{55} +(2.19947 + 1.44661i) q^{56} +(1.57205 + 3.64441i) q^{58} +(-4.72923 + 1.12085i) q^{59} +(5.89835 + 7.92286i) q^{61} +(-4.80485 + 1.74882i) q^{62} +(-5.41623 - 1.97135i) q^{64} +(-5.58074 - 18.6410i) q^{65} +(-0.126951 - 2.17967i) q^{67} +(-1.10688 + 0.728003i) q^{68} +(-4.98712 - 1.18197i) q^{70} +(0.733100 + 4.15761i) q^{71} +(-1.93909 + 10.9972i) q^{73} +(-1.21801 + 2.82366i) q^{74} +(0.415470 - 1.38777i) q^{76} +(-0.881334 + 1.18384i) q^{77} +(13.6538 - 6.85721i) q^{79} +14.4060 q^{80} +17.3566 q^{82} +(-2.54531 + 1.27830i) q^{83} +(-5.99297 + 8.04995i) q^{85} +(-1.67009 + 5.57848i) q^{86} +(1.35414 - 3.13924i) q^{88} +(0.910318 - 5.16267i) q^{89} +(-1.16284 - 6.59480i) q^{91} +(-2.99026 - 0.708704i) q^{92} +(2.38377 - 1.56783i) q^{94} +(-0.638059 - 10.9550i) q^{95} +(3.45426 + 11.5380i) q^{97} +(8.55181 + 3.11260i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8}+O(q^{10}) \) 144 * q - 9 * q^2 + 9 * q^4 - 9 * q^5 + 9 * q^7 + 18 * q^8	\( 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8} - 18 q^{10} - 9 q^{11} + 9 q^{13} - 9 q^{14} + 9 q^{16} + 18 q^{17} - 18 q^{19} - 45 q^{20} + 9 q^{22} + 45 q^{23} + 9 q^{25} - 45 q^{26} - 9 q^{28} - 36 q^{29} + 9 q^{31} + 99 q^{32} + 9 q^{34} - 9 q^{35} - 18 q^{37} - 18 q^{38} + 9 q^{40} - 27 q^{41} + 9 q^{43} - 54 q^{44} - 18 q^{46} + 99 q^{47} + 9 q^{49} - 126 q^{50} - 27 q^{52} - 45 q^{53} - 9 q^{55} + 225 q^{56} + 9 q^{58} - 72 q^{59} + 9 q^{61} - 81 q^{62} - 18 q^{64} + 81 q^{65} - 45 q^{67} - 117 q^{68} - 99 q^{70} + 90 q^{71} - 18 q^{73} - 81 q^{74} - 153 q^{76} - 81 q^{77} - 99 q^{79} + 288 q^{80} - 36 q^{82} - 45 q^{83} - 99 q^{85} - 81 q^{86} - 153 q^{88} + 81 q^{89} - 18 q^{91} - 207 q^{92} - 99 q^{94} + 171 q^{95} - 45 q^{97} - 81 q^{98}+O(q^{100}) \) 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 - 45 * q^20 + 9 * q^22 + 45 * q^23 + 9 * q^25 - 45 * q^26 - 9 * q^28 - 36 * q^29 + 9 * q^31 + 99 * q^32 + 9 * q^34 - 9 * q^35 - 18 * q^37 - 18 * q^38 + 9 * q^40 - 27 * q^41 + 9 * q^43 - 54 * q^44 - 18 * q^46 + 99 * q^47 + 9 * q^49 - 126 * q^50 - 27 * q^52 - 45 * q^53 - 9 * q^55 + 225 * q^56 + 9 * q^58 - 72 * q^59 + 9 * q^61 - 81 * q^62 - 18 * q^64 + 81 * q^65 - 45 * q^67 - 117 * q^68 - 99 * q^70 + 90 * q^71 - 18 * q^73 - 81 * q^74 - 153 * q^76 - 81 * q^77 - 99 * q^79 + 288 * q^80 - 36 * q^82 - 45 * q^83 - 99 * q^85 - 81 * q^86 - 153 * q^88 + 81 * q^89 - 18 * q^91 - 207 * q^92 - 99 * q^94 + 171 * q^95 - 45 * q^97 - 81 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more