LMFDB - Embedded newform 729.2.g.a.271.7

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			271.7
Character	$\chi$	$=$	729.271
Dual form			729.2.g.a.460.7

$q$-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 $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{4}{27}\right)$

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	0.865565	−	0.500797i	$-0.166960\pi$
$2$	1.38698	+	0.696568i	0.980743	+	0.492548i	0.115178	+	0.993345i	$0.463256\pi$
$3$		0			0
$3$		0			0
$4$	0.244190	+	0.328004i	0.122095	+	0.164002i
$5$	0.888415	+	2.96751i	0.397311	+	1.32711i	0.889624	+	0.456694i	$0.150966\pi$
$5$	0.888415	+	2.96751i	0.397311	+	1.32711i	−0.492313	+	0.870418i	$0.663848\pi$
$6$		0			0
$7$	0.422238	+	0.978857i	0.159591	+	0.369973i	0.979185	−	0.202972i	$-0.0650600\pi$
$7$	0.422238	+	0.978857i	0.159591	+	0.369973i	−0.819594	+	0.572945i	$0.805801\pi$
$8$	−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	−0.428624	−	0.903483i	$-0.641002\pi$
$11$	−1.34713	+	0.319276i	−0.406175	+	0.0962652i	0.0224495	+	0.999748i	$0.492854\pi$
$12$		0			0
$13$	5.24827	+	3.45184i	1.45561	+	0.957368i	0.997659	+	0.0683890i	$0.0217859\pi$
$13$	5.24827	+	3.45184i	1.45561	+	0.957368i	0.457948	+	0.888979i	$0.348584\pi$
$14$	−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	−0.683709	−	0.729755i	$-0.739634\pi$
$17$	−3.04443	+	1.10808i	−0.738383	+	0.268749i	−0.0546740	+	0.998504i	$0.517412\pi$
$18$		0			0
$19$	3.32892	+	1.21163i	0.763707	+	0.277967i	0.694362	−	0.719626i	$-0.255687\pi$
$19$	3.32892	+	1.21163i	0.763707	+	0.277967i	0.0693452	+	0.997593i	$0.477909\pi$
$20$	−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	0.260231	+	0.965546i	$0.416201\pi$
$23$	−2.97660	+	6.90053i	−0.620663	+	1.43886i	−0.880894	+	0.473313i	$0.843058\pi$
$24$		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	−0.983566	−	0.180550i	$-0.942212\pi$
$29$	−0.148690	−	2.55291i	−0.0276111	−	0.474064i	0.955955	−	0.293514i	$-0.0948248\pi$
$30$		0			0
$31$	−3.27217	+	0.382462i	−0.587699	+	0.0686922i	−0.404746	−	0.914429i	$-0.632640\pi$
$31$	−3.27217	+	0.382462i	−0.587699	+	0.0686922i	−0.182954	+	0.983122i	$0.558566\pi$
$32$	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	0.509444	−	0.860504i	$-0.329851\pi$
$37$	−1.51778	−	1.27357i	−0.249522	−	0.209374i	−0.758967	+	0.651130i	$0.774295\pi$
$38$	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	0.561649	−	0.827375i	$-0.310167\pi$
$41$	9.99336	−	5.01885i	1.56070	−	0.783813i	0.999051	+	0.0435625i	$0.0138708\pi$
$42$		0			0
$43$	−2.57467	−	2.72899i	−0.392633	−	0.416167i	0.500658	−	0.865645i	$-0.333091\pi$
$43$	−2.57467	−	2.72899i	−0.392633	−	0.416167i	−0.893291	+	0.449478i	$0.851610\pi$
$44$	−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	0.248209	−	0.968707i	$-0.420158\pi$
$47$	1.82585	+	0.213412i	0.266328	+	0.0311293i	0.0181192	+	0.999836i	$0.494232\pi$
$48$		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	−0.970145	−	0.242527i	$-0.922024\pi$
$53$	−2.00231	+	3.46810i	−0.275038	+	0.476380i	0.695107	+	0.718907i	$0.255357\pi$
$54$		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	−0.0890765	−	0.996025i	$-0.528392\pi$
$59$	−4.72923	−	1.12085i	−0.615693	−	0.145922i	−0.526617	+	0.850103i	$0.676540\pi$
$60$		0			0
$61$	5.89835	−	7.92286i	0.755206	−	1.01442i	−0.243799	−	0.969826i	$-0.578394\pi$
$61$	5.89835	−	7.92286i	0.755206	−	1.01442i	0.999005	−	0.0445923i	$-0.0141989\pi$
$62$	−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	0.981635	+	0.190770i	$0.0610984\pi$
$67$	−0.126951	+	2.17967i	−0.0155096	+	0.266289i	−0.997144	+	0.0755191i	$0.975939\pi$
$68$	−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	−0.909903	−	0.414820i	$-0.863845\pi$
$71$	0.733100	−	4.15761i	0.0870029	−	0.493418i	0.996906	−	0.0785980i	$-0.0250443\pi$
$72$		0			0
$73$	−1.93909	−	10.9972i	−0.226954	−	1.28712i	−0.858915	−	0.512119i	$-0.828861\pi$
$73$	−1.93909	−	10.9972i	−0.226954	−	1.28712i	0.631961	−	0.775000i	$-0.282250\pi$
$74$	−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	0.997476	−	0.0710022i	$-0.0226198\pi$
$79$	13.6538	+	6.85721i	1.53618	+	0.771496i	0.538699	+	0.842498i	$0.318916\pi$
$80$	14.4060			1.61064
$81$		0			0
$82$	17.3566			1.91671
$83$	−2.54531	−	1.27830i	−0.279384	−	0.140312i	0.303590	−	0.952803i	$-0.401815\pi$
$83$	−2.54531	−	1.27830i	−0.279384	−	0.140312i	−0.582974	+	0.812491i	$0.698111\pi$
$84$		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	0.994279	+	0.106810i	$0.0340636\pi$
$89$	0.910318	+	5.16267i	0.0964935	+	0.547242i	−0.897786	+	0.440432i	$0.854825\pi$
$90$		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	−0.582684	−	0.812699i	$-0.697997\pi$
$97$	3.45426	−	11.5380i	0.350727	−	1.17151i	0.933411	−	0.358810i	$-0.116817\pi$
$98$	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	−0.475208	−	0.879873i	$-0.657627\pi$
$101$	5.06506	−	6.80356i	0.503993	−	0.676980i	0.979201	+	0.202894i	$0.0650346\pi$
$102$		0			0
$103$	−9.27652	−	2.19857i	−0.914042	−	0.216632i	−0.253425	−	0.967355i	$-0.581557\pi$
$103$	−9.27652	−	2.19857i	−0.914042	−	0.216632i	−0.660617	+	0.750723i	$0.729705\pi$
$104$	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	0.512094	−	0.858929i	$-0.328870\pi$
$107$	−5.04592	−	8.73979i	−0.487807	−	0.844907i	−0.999902	+	0.0140222i	$0.995536\pi$
$108$		0			0
$109$	9.05373	−	15.6815i	0.867190	−	1.50202i	0.00233359	−	0.999997i	$-0.499257\pi$
$109$	9.05373	−	15.6815i	0.867190	−	1.50202i	0.864856	−	0.502020i	$-0.167409\pi$
$110$	−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	−0.706444	−	0.707769i	$-0.749702\pi$
$113$	0.438007	−	0.464260i	0.0412042	−	0.0436739i	0.747648	+	0.664095i	$0.231183\pi$
$114$		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	−0.596345	−	0.802729i	$-0.703381\pi$
$127$	1.02140	−	0.857057i	0.0906346	−	0.0760515i	0.686979	+	0.726677i	$0.258936\pi$
$128$	−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	−0.867162	−	0.498026i	$-0.834058\pi$
$131$	−18.2682	+	2.13524i	−1.59610	+	0.186557i	−0.728935	+	0.684583i	$0.759984\pi$
$132$		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	−0.372130	−	0.928180i	$-0.621373\pi$
$137$	3.89470	−	2.56158i	0.332747	−	0.218851i	0.704877	+	0.709330i	$0.251002\pi$
$138$		0			0
$139$	0.403437	−	0.935272i	0.0342191	−	0.0793287i	−0.900249	−	0.435374i	$-0.856616\pi$
$139$	0.403437	−	0.935272i	0.0342191	−	0.0793287i	0.934469	+	0.356046i	$0.115875\pi$
$140$	−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	0.509187	−	0.860656i	$-0.329946\pi$
$149$	−0.969230	−	0.637473i	−0.0794025	−	0.0522238i	−0.588589	+	0.808432i	$0.700317\pi$
$150$		0			0
$151$	12.5987	−	2.98595i	1.02527	−	0.242993i	0.316619	−	0.948553i	$-0.397452\pi$
$151$	12.5987	−	2.98595i	1.02527	−	0.242993i	0.708651	+	0.705560i	$0.249304\pi$
$152$	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	0.979280	−	0.202513i	$-0.0649109\pi$
$157$	0.624250	+	2.08514i	0.0498206	+	0.166412i	−0.929459	+	0.368926i	$0.879726\pi$
$158$	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	−0.999836	−	0.0180964i	$-0.994239\pi$
$167$	−2.25412	−	7.52930i	−0.174429	−	0.582635i	0.825407	−	0.564538i	$-0.190946\pi$
$168$		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	−0.0596535	−	0.998219i	$-0.519000\pi$
$173$	4.40674	−	1.04442i	0.335038	−	0.0794055i	0.394692	+	0.918814i	$0.370851\pi$
$174$		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	−0.175017	−	0.984565i	$-0.555998\pi$
$179$	4.33186	−	1.57667i	0.323778	−	0.117846i	0.498795	+	0.866720i	$0.333776\pi$
$180$		0			0
$181$	−7.67715	−	2.79425i	−0.570638	−	0.207695i	0.0405545	−	0.999177i	$-0.487088\pi$
$181$	−7.67715	−	2.79425i	−0.570638	−	0.207695i	−0.611192	+	0.791482i	$0.709310\pi$
$182$	−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	0.996390	+	0.0848901i	$0.0270539\pi$
$191$	0.229311	+	3.93712i	0.0165924	+	0.284880i	−0.979798	+	0.199990i	$0.935909\pi$
$192$		0			0
$193$	−7.15252	+	0.836009i	−0.514850	+	0.0601773i	−0.369551	−	0.929211i	$-0.620488\pi$
$193$	−7.15252	+	0.836009i	−0.514850	+	0.0601773i	−0.145299	+	0.989388i	$0.546414\pi$
$194$	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	−0.878180	−	0.478330i	$-0.841242\pi$
$197$	−7.85452	+	6.59072i	−0.559611	+	0.469570i	0.318569	+	0.947900i	$0.396798\pi$
$198$		0			0
$199$	20.3096	+	17.0417i	1.43971	+	1.20806i	0.939683	+	0.342045i	$0.111120\pi$
$199$	20.3096	+	17.0417i	1.43971	+	1.20806i	0.500023	+	0.866012i	$0.333325\pi$
$200$	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	−0.472757	−	0.881193i	$-0.656741\pi$
$211$	6.31051	−	6.68875i	0.434433	−	0.460472i	0.907190	+	0.420720i	$0.138223\pi$
$212$	−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	−0.982864	−	0.184332i	$-0.940988\pi$
$223$	−7.83078	+	10.5186i	−0.524388	+	0.704375i	0.458476	+	0.888707i	$0.348395\pi$
$224$	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	−0.711209	−	0.702980i	$-0.751852\pi$
$227$	4.05728	−	13.5523i	0.269291	−	0.899496i	0.980501	−	0.196516i	$-0.0629626\pi$
$228$		0			0
$229$	−0.743449	+	12.7645i	−0.0491285	+	0.843503i	0.880281	+	0.474453i	$0.157354\pi$
$229$	−0.743449	+	12.7645i	−0.0491285	+	0.843503i	−0.929409	+	0.369050i	$0.879683\pi$
$230$	−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	−0.920446	−	0.390871i	$-0.872174\pi$
$233$	1.19331	−	6.76757i	0.0781760	−	0.443358i	0.998622	−	0.0524875i	$-0.0167150\pi$
$234$		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	0.982220	−	0.187735i	$-0.0601145\pi$
$239$	8.04933	+	10.8121i	0.520668	+	0.699379i	−0.461552	+	0.887113i	$0.652707\pi$
$240$		0			0
$241$	−0.315013	−	0.158205i	−0.0202918	−	0.0101909i	0.438624	−	0.898670i	$-0.355466\pi$
$241$	−0.315013	−	0.158205i	−0.0202918	−	0.0101909i	−0.458916	+	0.888480i	$0.651762\pi$
$242$	−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	0.820611	+	0.571487i	$0.193633\pi$
$251$	3.88072	+	22.0087i	0.244949	+	1.38917i	−0.575662	+	0.817688i	$0.695256\pi$
$252$		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	0.784101	+	0.620634i	$0.213125\pi$
$257$	−1.07007	+	18.3725i	−0.0667494	+	1.14604i	−0.850850	+	0.525409i	$0.823912\pi$
$258$		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	−0.843096	−	0.537763i	$-0.819270\pi$
$263$	−1.39668	+	1.87606i	−0.0861228	+	0.115683i	0.756974	+	0.653445i	$0.226677\pi$
$264$		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	0.999169	−	0.0407576i	$-0.0129771\pi$
$269$	7.61488	+	13.1894i	0.464287	+	0.804169i	−0.534882	+	0.844927i	$0.679644\pi$
$270$		0			0
$271$	−2.75183	+	4.76631i	−0.167162	+	0.289533i	−0.937421	−	0.348198i	$-0.886794\pi$
$271$	−2.75183	+	4.76631i	−0.167162	+	0.289533i	0.770259	+	0.637731i	$0.220127\pi$
$272$	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	−0.462573	−	0.886581i	$-0.653074\pi$
$277$	−18.5929	−	2.17320i	−1.11714	−	0.130575i	−0.654564	+	0.756006i	$0.727148\pi$
$278$	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	0.229682	−	0.973266i	$-0.426232\pi$
$281$	−12.6610	−	13.4199i	−0.755292	−	0.800563i	−0.984974	+	0.172703i	$0.944750\pi$
$282$		0			0
$283$	−10.8300	+	5.43905i	−0.643779	+	0.323318i	−0.740563	−	0.671987i	$-0.765441\pi$
$283$	−10.8300	+	5.43905i	−0.643779	+	0.323318i	0.0967834	+	0.995305i	$0.469145\pi$
$284$	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	0.461627	−	0.887074i	$-0.347266\pi$
$293$	19.0923	−	2.23157i	1.11538	−	0.130370i	0.653757	+	0.756705i	$0.273192\pi$
$294$		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	−0.620963	−	0.783840i	$-0.713258\pi$
$307$	−10.3868	+	3.78049i	−0.592806	+	0.215764i	0.0281572	+	0.999604i	$0.491036\pi$
$308$	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	0.169467	−	0.985536i	$-0.445796\pi$
$311$	−11.7864	−	7.75205i	−0.668346	−	0.439578i	−0.837813	+	0.545958i	$0.816166\pi$
$312$		0			0
$313$	−1.55801	+	0.369255i	−0.0880639	+	0.0208715i	−0.274412	−	0.961612i	$-0.588483\pi$
$313$	−1.55801	+	0.369255i	−0.0880639	+	0.0208715i	0.186348	+	0.982484i	$0.440335\pi$
$314$	−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	0.994924	−	0.100632i	$-0.0320865\pi$
$317$	4.25471	+	9.86353i	0.238968	+	0.553991i	−0.755955	+	0.654623i	$0.772827\pi$
$318$		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	−0.881136	−	0.472863i	$-0.843220\pi$
$331$	−11.2874	−	26.1672i	−0.620412	−	1.43828i	0.260724	−	0.965413i	$-0.416039\pi$
$332$	−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	0.578016	−	0.816025i	$-0.303827\pi$
$337$	1.05866	+	0.696292i	0.0576689	+	0.0379294i	−0.520347	+	0.853955i	$0.674197\pi$
$338$	−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	−0.672683	−	0.739931i	$-0.734858\pi$
$347$	6.09406	−	14.1276i	0.327146	−	0.758410i	0.999829	−	0.0184793i	$-0.00588249\pi$
$348$		0			0
$349$	−9.90805	+	6.51663i	−0.530366	+	0.348827i	−0.786278	−	0.617873i	$-0.787995\pi$
$349$	−9.90805	+	6.51663i	−0.530366	+	0.348827i	0.255912	+	0.966700i	$0.417624\pi$
$350$	−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	0.961774	+	0.273843i	$0.0882948\pi$
$353$	0.719486	+	12.3531i	0.0382944	+	0.657489i	−0.923480	+	0.383646i	$0.874668\pi$
$354$		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	−0.340338	−	0.940303i	$-0.610541\pi$
$359$	9.97729	−	8.37194i	0.526581	−	0.441854i	0.866919	+	0.498449i	$0.166097\pi$
$360$		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	0.586827	−	0.809712i	$-0.300377\pi$
$367$	−4.89728	−	5.19081i	−0.255636	−	0.270958i	−0.842463	+	0.538754i	$0.818895\pi$
$368$	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	−0.462847	−	0.886438i	$-0.653172\pi$
$373$	8.67171	−	9.19147i	0.449004	−	0.475916i	0.911851	+	0.410522i	$0.134653\pi$
$374$	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	0.989227	+	0.146390i	$0.0467653\pi$
$379$	12.0972	+	20.9529i	0.621391	+	1.07628i	−0.367836	+	0.929891i	$0.619901\pi$
$380$	−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	−0.468715	−	0.883350i	$-0.655283\pi$
$383$	−25.1288	−	5.95563i	−1.28402	−	0.304318i	−0.815305	+	0.579031i	$0.803431\pi$
$384$		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	0.751833	+	0.659354i	$0.229170\pi$
$389$	−4.70662	+	15.7212i	−0.238635	+	0.797096i	−0.990468	+	0.137743i	$0.956015\pi$
$390$		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	0.587987	+	0.808871i	$0.299921\pi$
$397$	6.21875	+	35.2683i	0.312110	+	1.77006i	−0.275877	+	0.961193i	$0.588968\pi$
$398$	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	0.882475	−	0.470360i	$-0.155876\pi$
$401$	3.58004	+	4.80883i	0.178779	+	0.240142i	−0.703696	+	0.710501i	$0.748468\pi$
$402$		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	0.999682	+	0.0252277i	$0.00803107\pi$
$409$	14.9077	+	20.0245i	0.737138	+	0.990148i	−0.262544	+	0.964920i	$0.584562\pi$
$410$	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	−0.956451	−	0.291894i	$-0.905714\pi$
$419$	0.561267	−	9.63658i	0.0274197	−	0.470778i	0.983870	−	0.178883i	$-0.0572485\pi$
$420$		0			0
$421$	−3.44297	+	11.5003i	−0.167800	+	0.560491i	0.832182	+	0.554502i	$0.187091\pi$
$421$	−3.44297	+	11.5003i	−0.167800	+	0.560491i	−0.999982	+	0.00598851i	$0.998094\pi$
$422$	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	−0.746695	−	0.665167i	$-0.768360\pi$
$431$	−19.7100	−	34.1388i	−0.949399	−	1.64441i	−0.202704	−	0.979240i	$-0.564973\pi$
$432$		0			0
$433$	8.08024	−	13.9954i	0.388312	−	0.672575i	−0.603911	−	0.797052i	$-0.706392\pi$
$433$	8.08024	−	13.9954i	0.388312	−	0.672575i	0.992223	+	0.124476i	$0.0397251\pi$
$434$	−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	0.827651	−	0.561242i	$-0.189676\pi$
$439$	31.5031	+	3.68219i	1.50356	+	0.175741i	0.675911	+	0.736984i	$0.263751\pi$
$440$	−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	0.996815	−	0.0797476i	$-0.0254114\pi$
$443$	18.0850	+	19.1689i	0.859243	+	0.910744i	−0.137572	+	0.990492i	$0.543930\pi$
$444$		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	−0.134659	−	0.990892i	$-0.542994\pi$
$449$	−24.0265	−	20.1606i	−1.13388	−	0.951439i	−0.999221	+	0.0394529i	$0.987438\pi$
$450$		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	0.998053	−	0.0623721i	$-0.0198665\pi$
$457$	−0.0105280	−	0.180759i	−0.000492479	−	0.00845553i	−0.998545	+	0.0539165i	$0.982830\pi$
$458$	−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	−0.536791	−	0.843715i	$-0.680364\pi$
$461$	0.543423	−	0.357415i	0.0253097	−	0.0166465i	0.562101	+	0.827069i	$0.309993\pi$
$462$		0			0
$463$	−3.16038	+	7.32658i	−0.146875	+	0.340495i	−0.975733	−	0.218965i	$-0.929732\pi$
$463$	−3.16038	+	7.32658i	−0.146875	+	0.340495i	0.828858	+	0.559460i	$0.188991\pi$
$464$	−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	0.235067	−	0.971979i	$-0.424469\pi$
$467$	−4.53030	−	1.64889i	−0.209637	−	0.0763017i	−0.444704	+	0.895677i	$0.646691\pi$
$468$		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	−0.923346	−	0.383968i	$-0.874557\pi$
$479$	−12.4531	−	28.8695i	−0.568996	−	1.31908i	0.354350	−	0.935113i	$-0.384702\pi$
$480$		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	0.988867	−	0.148799i	$-0.0475408\pi$
$491$	1.79294	+	5.98883i	0.0809142	+	0.270272i	−0.907953	+	0.419072i	$0.862356\pi$
$492$		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	0.485961	−	0.873980i	$-0.338470\pi$
$499$	−2.77134	−	1.82274i	−0.124062	−	0.0815969i	−0.610023	+	0.792383i	$0.708840\pi$
$500$	−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	−0.923373	−	0.383904i	$-0.874579\pi$
$503$	−31.0387	+	11.2972i	−1.38395	+	0.503716i	−0.460576	+	0.887620i	$0.652357\pi$
$504$		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	−0.558986	−	0.829177i	$-0.688809\pi$
$509$	9.65014	−	22.3715i	0.427735	−	0.991601i	0.986721	−	0.162424i	$-0.0519313\pi$
$510$		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	0.139745	−	0.990188i	$-0.455372\pi$
$521$	26.0017	−	21.8180i	1.13916	−	0.955865i	0.999411	+	0.0343222i	$0.0109273\pi$
$522$		0			0
$523$	−8.90608	−	7.47308i	−0.389435	−	0.326775i	0.426958	−	0.904272i	$-0.359585\pi$
$523$	−8.90608	−	7.47308i	−0.389435	−	0.326775i	−0.816393	+	0.577496i	$0.804030\pi$
$524$	−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	0.739852	−	0.672770i	$-0.234896\pi$
$541$	−4.94751	−	8.56934i	−0.212710	−	0.368425i	−0.952562	+	0.304345i	$0.901562\pi$
$542$	−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	−0.0471523	+	0.998888i	$0.515015\pi$
$547$	−23.1671	+	31.1188i	−0.990553	+	1.33054i	−0.943401	+	0.331656i	$0.892393\pi$
$548$	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	0.910608	+	0.413271i	$0.135614\pi$
$557$	−2.03984	+	11.5685i	−0.0864307	+	0.490173i	−0.997039	+	0.0769017i	$0.975497\pi$
$558$		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	0.947289	−	0.320379i	$-0.103810\pi$
$563$	8.74799	+	11.7506i	0.368684	+	0.495229i	−0.578605	+	0.815608i	$0.696403\pi$
$564$		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	0.936239	−	0.351364i	$-0.114282\pi$
$569$	28.9461	+	14.5373i	1.21348	+	0.609435i	0.277246	+	0.960799i	$0.410578\pi$
$570$		0			0
$571$	4.74082	+	6.36802i	0.198397	+	0.266494i	0.890177	−	0.455615i	$-0.150581\pi$
$571$	4.74082	+	6.36802i	0.198397	+	0.266494i	−0.691780	+	0.722108i	$0.743173\pi$
$572$	−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	−0.817256	−	0.576274i	$-0.804506\pi$
$577$	3.55054	−	20.1361i	0.147811	−	0.838277i	0.965067	−	0.262003i	$-0.0843830\pi$
$578$	−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	−0.961163	−	0.275982i	$-0.910997\pi$
$587$	−10.2027	+	13.7046i	−0.421110	+	0.565649i	0.540053	+	0.841631i	$0.318404\pi$
$588$		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	0.808670	−	0.588263i	$-0.200188\pi$
$593$	−2.55973	−	4.43358i	−0.105115	−	0.182065i	−0.913785	+	0.406197i	$0.866855\pi$
$594$		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	−0.434531	−	0.900657i	$-0.643086\pi$
$599$	11.9893	−	12.7079i	0.489868	−	0.519230i	0.924399	+	0.381427i	$0.124567\pi$
$600$		0			0
$601$	16.5538	+	1.93486i	0.675243	+	0.0789246i	0.446802	−	0.894633i	$-0.352563\pi$
$601$	16.5538	+	1.93486i	0.675243	+	0.0789246i	0.228442	+	0.973558i	$0.426637\pi$
$602$	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	0.407386	−	0.913256i	$-0.366440\pi$
$607$	34.0785	−	17.1149i	1.38320	−	0.694671i	0.975818	+	0.218585i	$0.0701440\pi$
$608$	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	−0.998641	−	0.0521174i	$-0.983403\pi$
$613$	−27.7479	+	23.2833i	−1.12073	+	0.940402i	−0.122087	+	0.992519i	$0.538959\pi$
$614$	−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	−0.824158	−	0.566359i	$-0.808351\pi$
$617$	−37.1472	+	4.34189i	−1.49549	+	0.174798i	−0.671332	+	0.741157i	$0.734277\pi$
$618$		0			0
$619$	1.74216	+	29.9117i	0.0700233	+	1.20225i	0.832047	+	0.554705i	$0.187169\pi$
$619$	1.74216	+	29.9117i	0.0700233	+	1.20225i	−0.762024	+	0.647549i	$0.775794\pi$
$620$	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	−0.560514	−	0.828145i	$-0.689396\pi$
$631$	−11.4941	+	4.18350i	−0.457572	+	0.166543i	0.102942	+	0.994687i	$0.467174\pi$
$632$	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	0.880579	−	0.473899i	$-0.157154\pi$
$641$	−1.73208	−	4.01541i	−0.0684130	−	0.158599i	−0.948992	+	0.315300i	$0.897895\pi$
$642$		0			0
$643$	−4.00151	−	13.3660i	−0.157804	−	0.527103i	0.842121	−	0.539288i	$-0.181307\pi$
$643$	−4.00151	−	13.3660i	−0.157804	−	0.527103i	−0.999926	+	0.0121848i	$0.996121\pi$
$644$	−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	0.974016	−	0.226481i	$-0.0727221\pi$
$653$	0.914424	+	3.05439i	0.0357842	+	0.119527i	−0.938231	+	0.346008i	$0.887537\pi$
$654$		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	−0.484488	−	0.874798i	$-0.660994\pi$
$659$	−13.4730	+	3.19317i	−0.524835	+	0.124388i	−0.0403462	+	0.999186i	$0.512846\pi$
$660$		0			0
$661$	21.8213	+	14.3521i	0.848752	+	0.558233i	0.897720	−	0.440567i	$-0.145223\pi$
$661$	21.8213	+	14.3521i	0.848752	+	0.558233i	−0.0489676	+	0.998800i	$0.515593\pi$
$662$	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	−0.742387	−	0.669971i	$-0.766307\pi$
$673$	−10.9283	+	7.18764i	−0.421254	+	0.277063i	0.321133	+	0.947034i	$0.395936\pi$
$674$	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	−0.992760	−	0.120115i	$-0.961674\pi$
$677$	−0.537483	−	9.22823i	−0.0206572	−	0.354670i	0.972103	−	0.234555i	$-0.0753633\pi$
$678$		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	−0.0181400	−	0.999835i	$-0.505774\pi$
$683$	25.1766	−	21.1257i	0.963356	−	0.808351i	0.981496	+	0.191484i	$0.0613300\pi$
$684$		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	−0.996602	−	0.0823683i	$-0.973752\pi$
$691$	−26.8358	−	28.4443i	−1.02088	−	1.08207i	−0.0242817	−	0.999705i	$-0.507730\pi$
$692$	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	−0.502878	−	0.864357i	$-0.667725\pi$
$701$	13.1619	−	22.7970i	0.497117	−	0.861031i	0.999994	+	0.00332633i	$0.00105881\pi$
$702$		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	−0.484494	−	0.874795i	$-0.660996\pi$
$709$	13.1140	−	17.6151i	0.492505	−	0.661549i	0.976999	+	0.213246i	$0.0684035\pi$
$710$	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	−0.166313	−	0.986073i	$-0.553186\pi$
$719$	8.77432	−	49.7616i	0.327227	−	1.85580i	0.493540	−	0.869723i	$-0.335703\pi$
$720$		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	0.384724	−	0.923032i	$-0.374297\pi$
$727$	−3.39515	−	1.70511i	−0.125919	−	0.0632390i	−0.510644	+	0.859793i	$0.670593\pi$
$728$	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	−0.930606	−	0.366023i	$-0.880719\pi$
$733$	−27.4625	−	36.8886i	−1.01435	−	1.36251i	−0.0837450	−	0.996487i	$-0.526688\pi$
$734$	−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	0.870682	+	0.491847i	$0.163678\pi$
$739$	−3.14560	+	17.8396i	−0.115713	+	0.656240i	−0.986395	+	0.164394i	$0.947433\pi$
$740$	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	−0.978378	−	0.206825i	$-0.933687\pi$
$743$	0.474165	−	8.14111i	0.0173954	−	0.298668i	0.995773	−	0.0918435i	$-0.0292759\pi$
$744$		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	0.882559	−	0.470201i	$-0.155819\pi$
$751$	40.0164	+	9.48405i	1.46022	+	0.346078i	0.577658	+	0.816279i	$0.303967\pi$
$752$	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	−0.695447	−	0.718578i	$-0.744794\pi$
$757$	7.55477	−	13.0853i	0.274583	−	0.475592i	0.970030	+	0.242986i	$0.0781269\pi$
$758$	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	−0.477773	−	0.878483i	$-0.658556\pi$
$761$	11.7794	−	12.4854i	0.427003	−	0.452597i	0.904777	+	0.425886i	$0.140037\pi$
$762$		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	−0.927412	−	0.374042i	$-0.877972\pi$
$769$	−32.7556	+	16.4505i	−1.18120	+	0.593219i	−0.253784	+	0.967261i	$0.581675\pi$
$770$	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	0.594015	−	0.804454i	$-0.297542\pi$
$773$	−2.64318	−	2.21789i	−0.0950684	−	0.0797719i	−0.689083	+	0.724682i	$0.741987\pi$
$774$		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	−0.847081	−	0.531463i	$-0.821642\pi$
$787$	3.38868	−	7.85585i	0.120793	−	0.280031i	0.967875	+	0.251432i	$0.0809016\pi$
$788$	−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	0.405816	−	0.913955i	$-0.366987\pi$
$797$	−7.69741	−	5.06267i	−0.272656	−	0.179329i	−0.678472	+	0.734626i	$0.737358\pi$
$798$		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	−0.120716	−	0.992687i	$-0.538519\pi$
$821$	6.21560	−	1.47312i	0.216926	−	0.0514124i	0.337642	+	0.941275i	$0.390371\pi$
$822$		0			0
$823$	−38.2038	−	25.1270i	−1.33170	−	0.875873i	−0.333929	−	0.942598i	$-0.608374\pi$
$823$	−38.2038	−	25.1270i	−1.33170	−	0.875873i	−0.997771	+	0.0667256i	$0.978745\pi$
$824$	−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	−0.0754029	−	0.997153i	$-0.524024\pi$
$827$	14.6029	−	5.31502i	0.507793	−	0.184821i	0.583196	+	0.812332i	$0.301802\pi$
$828$		0			0
$829$	−10.3463	−	3.76574i	−0.359341	−	0.130789i	0.156040	−	0.987751i	$-0.450127\pi$
$829$	−10.3463	−	3.76574i	−0.359341	−	0.130789i	−0.515381	+	0.856961i	$0.672349\pi$
$830$	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	−0.684852	−	0.728682i	$-0.740133\pi$
$839$	−2.58446	−	44.3735i	−0.0892255	−	1.53194i	0.595627	−	0.803261i	$-0.296904\pi$
$840$		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	0.903998	−	0.427537i	$-0.140618\pi$
$853$	12.4016	+	13.1449i	0.424622	+	0.450073i	−0.479376	+	0.877610i	$0.659137\pi$
$854$	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	−0.634975	−	0.772533i	$-0.718990\pi$
$857$	−41.8917	−	4.89643i	−1.43099	−	0.167259i	−0.796017	+	0.605274i	$0.793064\pi$
$858$		0			0
$859$	8.13646	−	8.62414i	0.277612	−	0.294252i	−0.573533	−	0.819183i	$-0.694427\pi$
$859$	8.13646	−	8.62414i	0.277612	−	0.294252i	0.851145	+	0.524931i	$0.175909\pi$
$860$	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	−0.980687	−	0.195585i	$-0.937340\pi$
$863$	−9.42886	+	16.3313i	−0.320962	+	0.555923i	0.659725	+	0.751507i	$0.270673\pi$
$864$		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	0.970158	+	0.242473i	$0.0779587\pi$
$877$	−0.639357	+	10.9773i	−0.0215896	+	0.370678i	−0.991748	+	0.128205i	$0.959078\pi$
$878$	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	−0.951443	−	0.307824i	$-0.900399\pi$
$881$	1.42184	−	8.06366i	0.0479030	−	0.271672i	0.999346	+	0.0361526i	$0.0115102\pi$
$882$		0			0
$883$	−2.52592	−	14.3252i	−0.0850039	−	0.482081i	−0.997356	−	0.0726741i	$-0.976847\pi$
$883$	−2.52592	−	14.3252i	−0.0850039	−	0.482081i	0.912352	−	0.409407i	$-0.134264\pi$
$884$	−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	−0.996833	−	0.0795279i	$-0.974659\pi$
$887$	−23.4426	−	31.4888i	−0.787125	−	1.05729i	0.209708	−	0.977764i	$-0.432749\pi$
$888$		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	−0.956645	−	0.291256i	$-0.905927\pi$
$907$	0.0803514	−	0.268392i	0.00266802	−	0.00891182i	0.959313	+	0.282344i	$0.0911120\pi$
$908$	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	−0.974235	−	0.225533i	$-0.927588\pi$
$911$	−14.4504	+	19.4103i	−0.478763	+	0.643091i	0.495472	+	0.868624i	$0.334995\pi$
$912$		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	−0.970283	−	0.241973i	$-0.922206\pi$
$919$	−8.35442	+	14.4703i	−0.275587	+	0.477331i	0.694696	+	0.719303i	$0.255539\pi$
$920$	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	0.792691	−	0.609624i	$-0.208680\pi$
$929$	4.20638	+	4.45850i	0.138007	+	0.146279i	−0.654684	+	0.755903i	$0.727198\pi$
$930$		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	−0.991382	−	0.131002i	$-0.958181\pi$
$937$	−31.6672	+	26.5719i	−1.03452	+	0.868067i	−0.0431398	+	0.999069i	$0.513736\pi$
$938$	−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	0.843187	−	0.537620i	$-0.180677\pi$
$941$	54.8368	−	6.40951i	1.78763	−	0.208944i	0.944443	+	0.328676i	$0.106603\pi$
$942$		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	−0.104913	−	0.994481i	$-0.533456\pi$
$947$	23.5934	−	15.5176i	0.766683	−	0.504255i	0.871595	+	0.490226i	$0.163086\pi$
$948$		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	0.712950	−	0.701215i	$-0.247359\pi$
$953$	24.9549	+	9.08285i	0.808369	+	0.294222i	0.0954192	+	0.995437i	$0.469581\pi$
$954$		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	0.989117	+	0.147130i	$0.0470035\pi$
$967$	7.57424	+	25.2997i	0.243571	+	0.813584i	−0.745546	+	0.666454i	$0.767811\pi$
$968$	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	0.848885	+	0.528577i	$0.177274\pi$
$977$	13.4439	+	44.9059i	0.430110	+	1.43667i	−0.418775	+	0.908090i	$0.637540\pi$
$978$		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	0.816299	−	0.577630i	$-0.196022\pi$
$983$	56.5922	−	13.4126i	1.80501	−	0.427795i	0.988711	+	0.149834i	$0.0478741\pi$
$984$		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	−0.208337	−	0.978057i	$-0.566805\pi$
$991$	−31.3736	−	11.4191i	−0.996615	−	0.362738i	−0.788278	+	0.615319i	$0.789027\pi$
$992$	−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	−0.325076	−	0.945688i	$-0.605390\pi$
$997$	13.0884	−	8.60838i	0.414514	−	0.272630i	0.739590	+	0.673058i	$0.235019\pi$
$998$	−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.271.7		144
3.2	odd	2		729.2.g.d.271.2		144
9.2	odd	6		729.2.g.c.514.7		144
9.4	even	3		243.2.g.a.172.2		144
9.5	odd	6		81.2.g.a.67.7	yes	144
9.7	even	3		729.2.g.b.514.2		144
81.2	odd	54		81.2.g.a.52.7	✓	144
81.5	odd	54		6561.2.a.c.1.19		72
81.25	even	27	inner	729.2.g.a.460.7		144
81.29	odd	54		729.2.g.c.217.7		144
81.52	even	27		729.2.g.b.217.2		144
81.56	odd	54		729.2.g.d.460.2		144
81.76	even	27		6561.2.a.d.1.54		72
81.79	even	27		243.2.g.a.154.2		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.52.7	✓	144	81.2	odd	54
81.2.g.a.67.7	yes	144	9.5	odd	6
243.2.g.a.154.2		144	81.79	even	27
243.2.g.a.172.2		144	9.4	even	3
729.2.g.a.271.7		144	1.1	even	1	trivial
729.2.g.a.460.7		144	81.25	even	27	inner
729.2.g.b.217.2		144	81.52	even	27
729.2.g.b.514.2		144	9.7	even	3
729.2.g.c.217.7		144	81.29	odd	54
729.2.g.c.514.7		144	9.2	odd	6
729.2.g.d.271.2		144	3.2	odd	2
729.2.g.d.460.2		144	81.56	odd	54
6561.2.a.c.1.19		72	81.5	odd	54
6561.2.a.d.1.54		72	81.76	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

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