LMFDB - Embedded newform 729.2.g.d.109.1

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			109.1
Character	$\chi$	$=$	729.109
Dual form			729.2.g.d.622.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.31781 - 1.39680i) q^{2} +(-0.0981285 + 1.68480i) q^{4} +(-0.783127 + 0.0915344i) q^{5} +(1.06502 + 0.534872i) q^{7} +(-0.459476 + 0.385546i) q^{8} +O(q^{10})$	\(q+(-1.31781 - 1.39680i) q^{2} +(-0.0981285 + 1.68480i) q^{4} +(-0.783127 + 0.0915344i) q^{5} +(1.06502 + 0.534872i) q^{7} +(-0.459476 + 0.385546i) q^{8} +(1.15987 + 0.973243i) q^{10} +(-0.814497 - 1.88822i) q^{11} +(2.96806 + 0.703443i) q^{13} +(-0.656382 - 2.19247i) q^{14} +(4.49652 + 0.525568i) q^{16} +(-0.788777 + 4.47337i) q^{17} +(-0.838570 - 4.75577i) q^{19} +(-0.0773702 - 1.32839i) q^{20} +(-1.56410 + 3.62599i) q^{22} +(5.89280 - 2.95948i) q^{23} +(-4.26032 + 1.00971i) q^{25} +(-2.92877 - 5.07278i) q^{26} +(-1.00566 + 1.74186i) q^{28} +(2.88435 - 9.63442i) q^{29} +(7.44201 + 4.89468i) q^{31} +(-4.47508 - 6.01108i) q^{32} +(7.28784 - 4.79329i) q^{34} +(-0.883002 - 0.321387i) q^{35} +(-0.563666 + 0.205158i) q^{37} +(-5.53776 + 7.43850i) q^{38} +(0.324537 - 0.343989i) q^{40} +(0.763120 - 0.808860i) q^{41} +(4.47179 - 6.00665i) q^{43} +(3.26119 - 1.18698i) q^{44} +(-11.8994 - 4.33101i) q^{46} +(0.765373 - 0.503394i) q^{47} +(-3.33194 - 4.47557i) q^{49} +(7.02464 + 4.62018i) q^{50} +(-1.47641 + 4.93156i) q^{52} +(3.63216 - 6.29109i) q^{53} +(0.810691 + 1.40416i) q^{55} +(-0.695567 + 0.164852i) q^{56} +(-17.2583 + 8.66746i) q^{58} +(-2.06499 + 4.78719i) q^{59} +(0.00126297 + 0.0216843i) q^{61} +(-2.97027 - 16.8452i) q^{62} +(-0.926691 + 5.25553i) q^{64} +(-2.38876 - 0.279206i) q^{65} +(-4.31847 - 14.4247i) q^{67} +(-7.45934 - 1.76790i) q^{68} +(0.714717 + 1.65690i) q^{70} +(3.88852 + 3.26285i) q^{71} +(-0.586995 + 0.492548i) q^{73} +(1.02937 + 0.516967i) q^{74} +(8.09481 - 0.946147i) q^{76} +(0.142500 - 2.44663i) q^{77} +(-5.44517 - 5.77154i) q^{79} -3.56945 q^{80} -2.13546 q^{82} +(9.18487 + 9.73539i) q^{83} +(0.208244 - 3.57542i) q^{85} +(-14.2830 + 1.66945i) q^{86} +(1.10224 + 0.553563i) q^{88} +(-4.47086 + 3.75149i) q^{89} +(2.78478 + 2.33671i) q^{91} +(4.40788 + 10.2186i) q^{92} +(-1.71175 - 0.405693i) q^{94} +(1.09202 + 3.64761i) q^{95} +(-7.21661 - 0.843501i) q^{97} +(-1.86060 + 10.5520i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{7}{27}\right)$

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 $

$2$	−1.31781	−	1.39680i	−0.931831	−	0.987683i	0.0681188	−	0.997677i	$-0.478300\pi$
$2$	−1.31781	−	1.39680i	−0.931831	−	0.987683i	−0.999950	+	0.00999381i	$0.996819\pi$
$3$		0			0
$3$		0			0
$4$	−0.0981285	+	1.68480i	−0.0490642	+	0.842400i
$5$	−0.783127	+	0.0915344i	−0.350225	+	0.0409354i	−0.289387	−	0.957212i	$-0.593451\pi$
$5$	−0.783127	+	0.0915344i	−0.350225	+	0.0409354i	−0.0608381	+	0.998148i	$0.519377\pi$
$6$		0			0
$7$	1.06502	+	0.534872i	0.402539	+	0.202162i	0.638537	−	0.769591i	$-0.279540\pi$
$7$	1.06502	+	0.534872i	0.402539	+	0.202162i	−0.235999	+	0.971753i	$0.575836\pi$
$8$	−0.459476	+	0.385546i	−0.162449	+	0.136311i
$9$		0			0
$10$	1.15987	+	0.973243i	0.366782	+	0.307766i
$11$	−0.814497	−	1.88822i	−0.245580	−	0.569319i	0.750188	−	0.661225i	$-0.229963\pi$
$11$	−0.814497	−	1.88822i	−0.245580	−	0.569319i	−0.995768	+	0.0919065i	$0.970704\pi$
$12$		0			0
$13$	2.96806	+	0.703443i	0.823192	+	0.195100i	0.620564	−	0.784156i	$-0.286904\pi$
$13$	2.96806	+	0.703443i	0.823192	+	0.195100i	0.202628	+	0.979256i	$0.435052\pi$
$14$	−0.656382	−	2.19247i	−0.175425	−	0.585962i
$15$		0			0
$16$	4.49652	+	0.525568i	1.12413	+	0.131392i
$17$	−0.788777	+	4.47337i	−0.191306	+	1.08495i	0.726275	+	0.687404i	$0.241250\pi$
$17$	−0.788777	+	4.47337i	−0.191306	+	1.08495i	−0.917581	+	0.397548i	$0.869861\pi$
$18$		0			0
$19$	−0.838570	−	4.75577i	−0.192381	−	1.09105i	−0.916099	−	0.400952i	$-0.868679\pi$
$19$	−0.838570	−	4.75577i	−0.192381	−	1.09105i	0.723718	−	0.690096i	$-0.242432\pi$
$20$	−0.0773702	−	1.32839i	−0.0173005	−	0.297038i
$21$		0			0
$22$	−1.56410	+	3.62599i	−0.333467	+	0.773064i
$23$	5.89280	−	2.95948i	1.22873	−	0.617093i	0.288453	−	0.957494i	$-0.406859\pi$
$23$	5.89280	−	2.95948i	1.22873	−	0.617093i	0.940281	+	0.340401i	$0.110563\pi$
$24$		0			0
$25$	−4.26032	+	1.00971i	−0.852063	+	0.201943i
$26$	−2.92877	−	5.07278i	−0.574379	−	0.994853i
$27$		0			0
$28$	−1.00566	+	1.74186i	−0.190052	+	0.329180i
$29$	2.88435	−	9.63442i	0.535611	−	1.78907i	−0.0750566	−	0.997179i	$-0.523914\pi$
$29$	2.88435	−	9.63442i	0.535611	−	1.78907i	0.610668	−	0.791887i	$-0.290901\pi$
$30$		0			0
$31$	7.44201	+	4.89468i	1.33662	+	0.879111i	0.998086	−	0.0618416i	$-0.0196974\pi$
$31$	7.44201	+	4.89468i	1.33662	+	0.879111i	0.338538	+	0.940953i	$0.390068\pi$
$32$	−4.47508	−	6.01108i	−0.791091	−	1.06262i
$33$		0			0
$34$	7.28784	−	4.79329i	1.24985	−	0.822043i
$35$	−0.883002	−	0.321387i	−0.149255	−	0.0543242i
$36$		0			0
$37$	−0.563666	+	0.205158i	−0.0926661	+	0.0337277i	−0.387937	−	0.921686i	$-0.626812\pi$
$37$	−0.563666	+	0.205158i	−0.0926661	+	0.0337277i	0.295271	+	0.955414i	$0.404590\pi$
$38$	−5.53776	+	7.43850i	−0.898343	+	1.20668i
$39$		0			0
$40$	0.324537	−	0.343989i	0.0513138	−	0.0543894i
$41$	0.763120	−	0.808860i	0.119179	−	0.126323i	−0.665036	−	0.746811i	$-0.731584\pi$
$41$	0.763120	−	0.808860i	0.119179	−	0.126323i	0.784216	+	0.620488i	$0.213066\pi$
$42$		0			0
$43$	4.47179	−	6.00665i	0.681941	−	0.916006i	−0.317539	−	0.948245i	$-0.602857\pi$
$43$	4.47179	−	6.00665i	0.681941	−	0.916006i	0.999480	+	0.0322396i	$0.0102639\pi$
$44$	3.26119	−	1.18698i	0.491643	−	0.178944i
$45$		0			0
$46$	−11.8994	−	4.33101i	−1.75447	−	0.638573i
$47$	0.765373	−	0.503394i	0.111641	−	0.0734275i	−0.492461	−	0.870335i	$-0.663902\pi$
$47$	0.765373	−	0.503394i	0.111641	−	0.0734275i	0.604102	+	0.796907i	$0.293532\pi$
$48$		0			0
$49$	−3.33194	−	4.47557i	−0.475991	−	0.639367i
$50$	7.02464	+	4.62018i	0.993434	+	0.653392i
$51$		0			0
$52$	−1.47641	+	4.93156i	−0.204742	+	0.683885i
$53$	3.63216	−	6.29109i	0.498916	−	0.864147i	−0.501084	−	0.865399i	$-0.667065\pi$
$53$	3.63216	−	6.29109i	0.498916	−	0.864147i	0.999999	+	0.00125165i	$0.000398413\pi$
$54$		0			0
$55$	0.810691	+	1.40416i	0.109314	+	0.189337i
$56$	−0.695567	+	0.164852i	−0.0929490	+	0.0220293i
$57$		0			0
$58$	−17.2583	+	8.66746i	−2.26613	+	1.13809i
$59$	−2.06499	+	4.78719i	−0.268839	+	0.623239i	−0.998141	−	0.0609534i	$-0.980586\pi$
$59$	−2.06499	+	4.78719i	−0.268839	+	0.623239i	0.729302	+	0.684192i	$0.239845\pi$
$60$		0			0
$61$	0.00126297	+	0.0216843i	0.000161707	+	0.00277640i	0.998388	−	0.0567566i	$-0.0180759\pi$
$61$	0.00126297	+	0.0216843i	0.000161707	+	0.00277640i	−0.998226	+	0.0595330i	$0.981039\pi$
$62$	−2.97027	−	16.8452i	−0.377224	−	2.13934i
$63$		0			0
$64$	−0.926691	+	5.25553i	−0.115836	+	0.656941i
$65$	−2.38876	−	0.279206i	−0.296289	−	0.0346312i
$66$		0			0
$67$	−4.31847	−	14.4247i	−0.527586	−	1.76226i	−0.639765	−	0.768571i	$-0.720968\pi$
$67$	−4.31847	−	14.4247i	−0.527586	−	1.76226i	0.112179	−	0.993688i	$-0.464217\pi$
$68$	−7.45934	−	1.76790i	−0.904578	−	0.214389i
$69$		0			0
$70$	0.714717	+	1.65690i	0.0854250	+	0.198037i
$71$	3.88852	+	3.26285i	0.461482	+	0.387229i	0.843676	−	0.536853i	$-0.180387\pi$
$71$	3.88852	+	3.26285i	0.461482	+	0.387229i	−0.382194	+	0.924082i	$0.624831\pi$
$72$		0			0
$73$	−0.586995	+	0.492548i	−0.0687026	+	0.0576483i	−0.676492	−	0.736450i	$-0.736501\pi$
$73$	−0.586995	+	0.492548i	−0.0687026	+	0.0576483i	0.607790	+	0.794098i	$0.292056\pi$
$74$	1.02937	+	0.516967i	0.119661	+	0.0600962i
$75$		0			0
$76$	8.09481	−	0.946147i	0.928538	−	0.108531i
$77$	0.142500	−	2.44663i	0.0162394	−	0.278820i
$78$		0			0
$79$	−5.44517	−	5.77154i	−0.612630	−	0.649349i	0.344576	−	0.938758i	$-0.388023\pi$
$79$	−5.44517	−	5.77154i	−0.612630	−	0.649349i	−0.957206	+	0.289409i	$0.906541\pi$
$80$	−3.56945			−0.399077
$81$		0			0
$82$	−2.13546			−0.235822
$83$	9.18487	+	9.73539i	1.00817	+	1.06860i	0.997641	+	0.0686535i	$0.0218703\pi$
$83$	9.18487	+	9.73539i	1.00817	+	1.06860i	0.0105297	+	0.999945i	$0.496648\pi$
$84$		0			0
$85$	0.208244	−	3.57542i	0.0225873	−	0.387809i
$86$	−14.2830	+	1.66945i	−1.54018	+	0.180021i
$87$		0			0
$88$	1.10224	+	0.553563i	0.117499	+	0.0590101i
$89$	−4.47086	+	3.75149i	−0.473910	+	0.397658i	−0.848218	−	0.529647i	$-0.822325\pi$
$89$	−4.47086	+	3.75149i	−0.473910	+	0.397658i	0.374309	+	0.927304i	$0.377880\pi$
$90$		0			0
$91$	2.78478	+	2.33671i	0.291925	+	0.244954i
$92$	4.40788	+	10.2186i	0.459553	+	1.06536i
$93$		0			0
$94$	−1.71175	−	0.405693i	−0.176554	−	0.0418440i
$95$	1.09202	+	3.64761i	0.112039	+	0.374237i
$96$		0			0
$97$	−7.21661	−	0.843501i	−0.732736	−	0.0856445i	−0.258461	−	0.966022i	$-0.583215\pi$
$97$	−7.21661	−	0.843501i	−0.732736	−	0.0856445i	−0.474274	+	0.880377i	$0.657290\pi$
$98$	−1.86060	+	10.5520i	−0.187949	+	1.06591i
$99$		0			0
$100$	−1.28311	−	7.27686i	−0.128311	−	0.727686i
$101$	−0.419625	−	7.20469i	−0.0417543	−	0.716893i	−0.952615	−	0.304179i	$-0.901618\pi$
$101$	−0.419625	−	7.20469i	−0.0417543	−	0.716893i	0.910861	−	0.412714i	$-0.135419\pi$
$102$		0			0
$103$	−0.596404	+	1.38262i	−0.0587654	+	0.136234i	−0.945069	−	0.326872i	$-0.894006\pi$
$103$	−0.596404	+	1.38262i	−0.0587654	+	0.136234i	0.886303	+	0.463105i	$0.153265\pi$
$104$	−1.63496	+	0.821108i	−0.160321	+	0.0805163i
$105$		0			0
$106$	−13.5739	+	3.21706i	−1.31841	+	0.312469i
$107$	−1.73493	−	3.00499i	−0.167722	−	0.290503i	0.769897	−	0.638169i	$-0.220308\pi$
$107$	−1.73493	−	3.00499i	−0.167722	−	0.290503i	−0.937619	+	0.347666i	$0.886974\pi$
$108$		0			0
$109$	3.95947	−	6.85801i	0.379249	−	0.656878i	−0.611705	−	0.791086i	$-0.709516\pi$
$109$	3.95947	−	6.85801i	0.379249	−	0.656878i	0.990953	+	0.134209i	$0.0428492\pi$
$110$	0.892986	−	2.98278i	0.0851429	−	0.284397i
$111$		0			0
$112$	4.50776	+	2.96480i	0.425943	+	0.280147i
$113$	3.20052	+	4.29904i	0.301080	+	0.404420i	0.926757	−	0.375662i	$-0.122585\pi$
$113$	3.20052	+	4.29904i	0.301080	+	0.404420i	−0.625677	+	0.780082i	$0.715177\pi$
$114$		0			0
$115$	−4.34392	+	2.85704i	−0.405072	+	0.266420i
$116$	15.9490	+	5.80497i	1.48083	+	0.538978i
$117$		0			0
$118$	9.40799	−	3.42423i	0.866076	−	0.315226i
$119$	−3.23274	+	4.34232i	−0.296345	+	0.398060i
$120$		0			0
$121$	4.64670	−	4.92522i	0.422428	−	0.447747i
$122$	0.0286242	−	0.0303399i	0.00259152	−	0.00274685i
$123$		0			0
$124$	−8.97684	+	12.0580i	−0.806144	+	1.08284i
$125$	6.94848	−	2.52904i	0.621491	−	0.226204i
$126$		0			0
$127$	5.22612	+	1.90215i	0.463743	+	0.168789i	0.563316	−	0.826242i	$-0.309525\pi$
$127$	5.22612	+	1.90215i	0.463743	+	0.168789i	−0.0995729	+	0.995030i	$0.531748\pi$
$128$	−3.96013	+	2.60462i	−0.350030	+	0.230218i
$129$		0			0
$130$	2.75793	+	3.70454i	0.241887	+	0.324910i
$131$	−2.04212	−	1.34312i	−0.178421	−	0.117349i	0.457157	−	0.889386i	$-0.348868\pi$
$131$	−2.04212	−	1.34312i	−0.178421	−	0.117349i	−0.635578	+	0.772037i	$0.719238\pi$
$132$		0			0
$133$	1.65063	−	5.51350i	0.143128	−	0.478081i
$134$	−14.4574	+	25.0410i	−1.24893	+	2.16322i
$135$		0			0
$136$	−1.36227	−	2.35952i	−0.116813	−	0.202327i
$137$	10.6941	−	2.53455i	0.913658	−	0.216541i	0.253209	−	0.967412i	$-0.418514\pi$
$137$	10.6941	−	2.53455i	0.913658	−	0.216541i	0.660449	+	0.750871i	$0.270366\pi$
$138$		0			0
$139$	−12.7658	+	6.41125i	−1.08278	+	0.543795i	−0.898453	−	0.439069i	$-0.855308\pi$
$139$	−12.7658	+	6.41125i	−1.08278	+	0.543795i	−0.184331	+	0.982864i	$0.559012\pi$
$140$	0.628120	−	1.45615i	0.0530858	−	0.123067i
$141$		0			0
$142$	−0.566782	−	9.73127i	−0.0475633	−	0.816630i
$143$	−1.08922	−	6.17729i	−0.0910854	−	0.516571i
$144$		0			0
$145$	−1.37694	+	7.80899i	−0.114348	+	0.648501i
$146$	1.46154	+	0.170829i	0.120958	+	0.0141379i
$147$		0			0
$148$	−0.290338	−	0.969796i	−0.0238656	−	0.0797167i
$149$	10.0150	+	2.37361i	0.820464	+	0.194454i	0.619351	−	0.785114i	$-0.287396\pi$
$149$	10.0150	+	2.37361i	0.820464	+	0.194454i	0.201113	+	0.979568i	$0.435544\pi$
$150$		0			0
$151$	4.03089	+	9.34466i	0.328030	+	0.760458i	0.999806	+	0.0197039i	$0.00627235\pi$
$151$	4.03089	+	9.34466i	0.328030	+	0.760458i	−0.671776	+	0.740754i	$0.734468\pi$
$152$	2.21887	+	1.86185i	0.179974	+	0.151016i
$153$		0			0
$154$	−3.60523	+	3.02515i	−0.290518	+	0.243774i
$155$	−6.27607	−	3.15196i	−0.504106	−	0.253171i
$156$		0			0
$157$	20.4692	−	2.39250i	1.63362	−	0.190942i	0.750757	−	0.660579i	$-0.229689\pi$
$157$	20.4692	−	2.39250i	1.63362	−	0.190942i	0.882860	+	0.469636i	$0.155615\pi$
$158$	−0.885974	+	15.2116i	−0.0704843	+	1.21017i
$159$		0			0
$160$	4.05478	+	4.29781i	0.320558	+	0.339772i
$161$	7.85887			0.619366
$162$		0			0
$163$	18.6813			1.46324			0.731618	−	0.681715i	$-0.238766\pi$
$163$	18.6813			1.46324			0.731618	+	0.681715i	$0.238766\pi$
$164$	1.28788	+	1.36508i	0.100567	+	0.106595i
$165$		0			0
$166$	1.49445	−	25.6588i	0.115992	−	1.99151i
$167$	16.7625	−	1.95926i	1.29712	−	0.151612i	0.560634	−	0.828063i	$-0.310557\pi$
$167$	16.7625	−	1.95926i	1.29712	−	0.151612i	0.736487	+	0.676452i	$0.236483\pi$
$168$		0			0
$169$	−3.30268	−	1.65867i	−0.254052	−	0.127590i
$170$	−5.26856	+	4.42084i	−0.404080	+	0.339063i
$171$		0			0
$172$	9.68120	+	8.12349i	0.738184	+	0.619410i
$173$	−0.496104	−	1.15010i	−0.0377181	−	0.0874404i	0.898316	−	0.439351i	$-0.144791\pi$
$173$	−0.496104	−	1.15010i	−0.0377181	−	0.0874404i	−0.936034	+	0.351910i	$0.885532\pi$
$174$		0			0
$175$	−5.07737	−	1.20336i	−0.383813	−	0.0909655i
$176$	−2.67002	−	8.91847i	−0.201260	−	0.672255i
$177$		0			0
$178$	11.1318	+	1.30112i	0.834364	+	0.0975231i
$179$	−1.77871	+	10.0875i	−0.132947	+	0.753978i	0.843321	+	0.537410i	$0.180597\pi$
$179$	−1.77871	+	10.0875i	−0.132947	+	0.753978i	−0.976268	+	0.216568i	$0.930514\pi$
$180$		0			0
$181$	3.12183	+	17.7048i	0.232044	+	1.31599i	0.848751	+	0.528793i	$0.177355\pi$
$181$	3.12183	+	17.7048i	0.232044	+	1.31599i	−0.616707	+	0.787193i	$0.711534\pi$
$182$	−0.405904	−	6.96911i	−0.0300876	−	0.516585i
$183$		0			0
$184$	−1.56658	+	3.63175i	−0.115490	+	0.267736i
$185$	0.422643	−	0.212259i	0.0310733	−	0.0156056i
$186$		0			0
$187$	9.08915	−	2.15417i	0.664665	−	0.157528i
$188$	0.773013	+	1.33890i	0.0563778	+	0.0976492i
$189$		0			0
$190$	3.65589	−	6.33218i	0.265226	−	0.459385i
$191$	−2.38919	+	7.98046i	−0.172876	+	0.577446i	0.827008	+	0.562190i	$0.190041\pi$
$191$	−2.38919	+	7.98046i	−0.172876	+	0.577446i	−0.999884	+	0.0152551i	$0.995144\pi$
$192$		0			0
$193$	18.7290	+	12.3183i	1.34815	+	0.886689i	0.998735	−	0.0502808i	$-0.0160116\pi$
$193$	18.7290	+	12.3183i	1.34815	+	0.886689i	0.349410	+	0.936970i	$0.386382\pi$
$194$	8.33191	+	11.1917i	0.598196	+	0.803517i
$195$		0			0
$196$	7.86740	−	5.17447i	0.561957	−	0.369605i
$197$	19.3055	+	7.02662i	1.37546	+	0.500626i	0.920798	−	0.390039i	$-0.127538\pi$
$197$	19.3055	+	7.02662i	1.37546	+	0.500626i	0.454661	+	0.890665i	$0.349761\pi$
$198$		0			0
$199$	−23.4867	+	8.54846i	−1.66493	+	0.605984i	−0.991126	−	0.132928i	$-0.957562\pi$
$199$	−23.4867	+	8.54846i	−1.66493	+	0.605984i	−0.673802	+	0.738912i	$0.735340\pi$
$200$	1.56822	−	2.10649i	0.110890	−	0.148951i
$201$		0			0
$202$	−9.51049	+	10.0805i	−0.669155	+	0.709263i
$203$	8.22506	−	8.71806i	0.577286	−	0.611888i
$204$		0			0
$205$	−0.523581	+	0.703292i	−0.0365685	+	0.0491200i
$206$	2.71718	−	0.988973i	0.189315	−	0.0689050i
$207$		0			0
$208$	12.9762	+	4.72296i	0.899740	+	0.327478i
$209$	−8.29690	+	5.45696i	−0.573909	+	0.377466i
$210$		0			0
$211$	−5.35225	−	7.18932i	−0.368464	−	0.494933i	0.578763	−	0.815496i	$-0.303536\pi$
$211$	−5.35225	−	7.18932i	−0.368464	−	0.494933i	−0.947227	+	0.320562i	$0.896128\pi$
$212$	10.2428	+	6.73680i	0.703479	+	0.462685i
$213$		0			0
$214$	−1.91105	+	6.38334i	−0.130636	+	0.436356i
$215$	−2.95216	+	5.11329i	−0.201336	+	0.348724i
$216$		0			0
$217$	5.30783	+	9.19344i	0.360319	+	0.624091i
$218$	−14.7971	+	3.50697i	−1.00218	+	0.237522i
$219$		0			0
$220$	−2.44528	+	1.22806i	−0.164861	+	0.0827961i
$221$	−5.48790	+	12.7224i	−0.369156	+	0.855800i
$222$		0			0
$223$	0.437201	+	7.50645i	0.0292772	+	0.502669i	0.980791	+	0.195063i	$0.0624910\pi$
$223$	0.437201	+	7.50645i	0.0292772	+	0.502669i	−0.951514	+	0.307607i	$0.900472\pi$
$224$	−1.55088	−	8.79550i	−0.103623	−	0.587674i
$225$		0			0
$226$	1.78721	−	10.1358i	0.118884	−	0.674222i
$227$	9.60064	+	1.12215i	0.637217	+	0.0744800i	0.428566	−	0.903510i	$-0.359019\pi$
$227$	9.60064	+	1.12215i	0.637217	+	0.0744800i	0.208651	+	0.977990i	$0.433093\pi$
$228$		0			0
$229$	−2.29389	−	7.66212i	−0.151584	−	0.506327i	0.848141	−	0.529771i	$-0.177722\pi$
$229$	−2.29389	−	7.66212i	−0.151584	−	0.506327i	−0.999725	+	0.0234439i	$0.992537\pi$
$230$	9.71515	+	2.30253i	0.640598	+	0.151824i
$231$		0			0
$232$	2.38922	+	5.53883i	0.156860	+	0.363642i
$233$	−17.1136	−	14.3600i	−1.12115	−	0.940754i	−0.122485	−	0.992470i	$-0.539086\pi$
$233$	−17.1136	−	14.3600i	−1.12115	−	0.940754i	−0.998662	+	0.0517161i	$0.983531\pi$
$234$		0			0
$235$	−0.553306	+	0.464279i	−0.0360937	+	0.0302862i
$236$	−7.86283	−	3.94886i	−0.511826	−	0.257049i
$237$		0			0
$238$	10.3255	−	1.20687i	0.669301	−	0.0782301i
$239$	0.376574	−	6.46553i	0.0243586	−	0.418220i	−0.963983	−	0.265965i	$-0.914309\pi$
$239$	0.376574	−	6.46553i	0.0243586	−	0.418220i	0.988341	−	0.152255i	$-0.0486536\pi$
$240$		0			0
$241$	1.91577	+	2.03059i	0.123405	+	0.130802i	0.786130	−	0.618061i	$-0.212082\pi$
$241$	1.91577	+	2.03059i	0.123405	+	0.130802i	−0.662725	+	0.748863i	$0.730600\pi$
$242$	−13.0030			−0.835864
$243$		0			0
$244$	−0.0366577			−0.00234677
$245$	3.01900	+	3.19995i	0.192877	+	0.204437i
$246$		0			0
$247$	0.856485	−	14.7053i	0.0544969	−	0.935675i
$248$	−5.30655	+	0.620246i	−0.336966	+	0.0393857i
$249$		0			0
$250$	−12.6893	−	6.37282i	−0.802543	−	0.403052i
$251$	−8.90582	+	7.47287i	−0.562131	+	0.471684i	−0.879024	−	0.476778i	$-0.841805\pi$
$251$	−8.90582	+	7.47287i	−0.562131	+	0.471684i	0.316893	+	0.948461i	$0.397360\pi$
$252$		0			0
$253$	−10.3878	−	8.71640i	−0.653075	−	0.547995i
$254$	−4.23011	−	9.80649i	−0.265420	−	0.615314i
$255$		0			0
$256$	19.2423	+	4.56051i	1.20265	+	0.285032i
$257$	−5.98437	−	19.9892i	−0.373295	−	1.24689i	−0.914012	−	0.405687i	$-0.867032\pi$
$257$	−5.98437	−	19.9892i	−0.373295	−	1.24689i	0.540718	−	0.841204i	$-0.318153\pi$
$258$		0			0
$259$	−0.710046	−	0.0829925i	−0.0441201	−	0.00515690i
$260$	0.704811	−	3.99718i	0.0437105	−	0.247895i
$261$		0			0
$262$	0.815054	+	4.62240i	0.0503542	+	0.285573i
$263$	1.20185	+	20.6350i	0.0741095	+	1.27241i	0.806380	+	0.591398i	$0.201424\pi$
$263$	1.20185	+	20.6350i	0.0741095	+	1.27241i	−0.732271	+	0.681014i	$0.761539\pi$
$264$		0			0
$265$	−2.26859	+	5.25919i	−0.139358	+	0.323069i
$266$	−9.87645	+	4.96014i	−0.605564	+	0.304126i
$267$		0			0
$268$	24.7265	−	5.86029i	1.51041	−	0.357974i
$269$	−6.13247	−	10.6218i	−0.373903	−	0.647620i	0.616259	−	0.787544i	$-0.288648\pi$
$269$	−6.13247	−	10.6218i	−0.373903	−	0.647620i	−0.990162	+	0.139924i	$0.955314\pi$
$270$		0			0
$271$	3.52249	−	6.10113i	0.213976	−	0.370617i	−0.738979	−	0.673728i	$-0.764692\pi$
$271$	3.52249	−	6.10113i	0.213976	−	0.370617i	0.952955	+	0.303111i	$0.0980253\pi$
$272$	−5.89781	+	19.7001i	−0.357607	+	1.19449i
$273$		0			0
$274$	−17.6330	−	11.5974i	−1.06525	−	0.700625i
$275$	5.37657	+	7.22199i	0.324219	+	0.435502i
$276$		0			0
$277$	−25.5545	+	16.8075i	−1.53542	+	1.00986i	−0.550908	+	0.834566i	$0.685719\pi$
$277$	−25.5545	+	16.8075i	−1.53542	+	1.00986i	−0.984515	+	0.175298i	$0.943911\pi$
$278$	25.7781	+	9.38247i	1.54607	+	0.562723i
$279$		0			0
$280$	0.529627	−	0.192769i	0.0316513	−	0.0115201i
$281$	10.0305	−	13.4733i	0.598371	−	0.803752i	−0.395003	−	0.918680i	$-0.629256\pi$
$281$	10.0305	−	13.4733i	0.598371	−	0.803752i	0.993374	+	0.114928i	$0.0366638\pi$
$282$		0			0
$283$	−14.0046	+	14.8441i	−0.832490	+	0.882387i	−0.994536	−	0.104396i	$-0.966709\pi$
$283$	−14.0046	+	14.8441i	−0.832490	+	0.882387i	0.162046	+	0.986783i	$0.448191\pi$
$284$	−5.87883	+	6.23119i	−0.348844	+	0.369753i
$285$		0			0
$286$	−7.19302	+	9.66191i	−0.425332	+	0.571321i
$287$	1.24537	−	0.453278i	0.0735120	−	0.0267562i
$288$		0			0
$289$	−3.41413	−	1.24264i	−0.200831	−	0.0730967i
$290$	12.7221	−	8.36745i	0.747067	−	0.491354i
$291$		0			0
$292$	−0.772244	−	1.03730i	−0.0451921	−	0.0607036i
$293$	−17.9293	−	11.7923i	−1.04744	−	0.688912i	−0.0955731	−	0.995422i	$-0.530468\pi$
$293$	−17.9293	−	11.7923i	−1.04744	−	0.688912i	−0.951867	+	0.306510i	$0.900839\pi$
$294$		0			0
$295$	1.17896	−	3.93799i	0.0686416	−	0.229279i
$296$	0.179893	−	0.311584i	0.0104561	−	0.0181104i
$297$		0			0
$298$	−9.88246	−	17.1169i	−0.572476	−	0.991557i
$299$	19.5720	−	4.63865i	1.13188	−	0.268260i
$300$		0			0
$301$	7.97531	−	4.00535i	0.459689	−	0.230865i
$302$	7.74064	−	17.9448i	0.445424	−	1.03261i
$303$		0			0
$304$	−1.27117	−	21.8251i	−0.0729065	−	1.25176i
$305$	−0.00297393	−	0.0168660i	−0.000170287	−	0.000965744i
$306$		0			0
$307$	−1.40936	+	7.99290i	−0.0804366	+	0.456179i	0.917812	+	0.397016i	$0.129954\pi$
$307$	−1.40936	+	7.99290i	−0.0804366	+	0.456179i	−0.998248	+	0.0591628i	$0.981157\pi$
$308$	4.10811	+	0.480169i	0.234081	+	0.0273602i
$309$		0			0
$310$	3.86801	+	12.9201i	0.219688	+	0.733810i
$311$	−22.7672	−	5.39594i	−1.29101	−	0.305976i	−0.472942	−	0.881094i	$-0.656808\pi$
$311$	−22.7672	−	5.39594i	−1.29101	−	0.305976i	−0.818070	+	0.575118i	$0.804956\pi$
$312$		0			0
$313$	−1.40659	−	3.26084i	−0.0795052	−	0.184314i	0.873827	−	0.486237i	$-0.161631\pi$
$313$	−1.40659	−	3.26084i	−0.0795052	−	0.184314i	−0.953332	+	0.301923i	$0.902371\pi$
$314$	−30.3163	−	25.4384i	−1.71085	−	1.43557i
$315$		0			0
$316$	10.2582	−	8.60767i	0.577070	−	0.484220i
$317$	−16.7208	−	8.39751i	−0.939135	−	0.471651i	−0.0877207	−	0.996145i	$-0.527958\pi$
$317$	−16.7208	−	8.39751i	−0.939135	−	0.471651i	−0.851414	+	0.524494i	$0.824255\pi$
$318$		0			0
$319$	−20.5412	+	2.40092i	−1.15008	+	0.134426i
$320$	0.244655	−	4.20057i	0.0136766	−	0.234819i
$321$		0			0
$322$	−10.3565	−	10.9772i	−0.577144	−	0.611737i
$323$	21.9358			1.22054
$324$		0			0
$325$	−13.3551			−0.740810
$326$	−24.6184	−	26.0940i	−1.36349	−	1.44521i
$327$		0			0
$328$	−0.0387825	+	0.665869i	−0.00214140	+	0.0367665i
$329$	1.08439	−	0.126747i	0.0597841	−	0.00698776i
$330$		0			0
$331$	6.45255	+	3.24059i	0.354664	+	0.178119i	0.617206	−	0.786801i	$-0.288264\pi$
$331$	6.45255	+	3.24059i	0.354664	+	0.178119i	−0.262542	+	0.964921i	$0.584561\pi$
$332$	−17.3035	+	14.5194i	−0.949652	+	0.796853i
$333$		0			0
$334$	−24.8264	−	20.8319i	−1.35844	−	1.13987i
$335$	4.70227	+	10.9011i	0.256912	+	0.595590i
$336$		0			0
$337$	−19.9946	−	4.73881i	−1.08918	−	0.258140i	−0.353474	−	0.935444i	$-0.615000\pi$
$337$	−19.9946	−	4.73881i	−1.08918	−	0.258140i	−0.735703	+	0.677305i	$0.763148\pi$
$338$	2.03548	+	6.79896i	0.110715	+	0.369815i
$339$		0			0
$340$	6.00343	+	0.701701i	0.325582	+	0.0380551i
$341$	3.18073	−	18.0388i	0.172246	−	0.976857i
$342$		0			0
$343$	−2.60337	−	14.7645i	−0.140569	−	0.797206i
$344$	0.261163	+	4.48399i	0.0140809	+	0.241760i
$345$		0			0
$346$	−0.952682	+	2.20856i	−0.0512165	+	0.118733i
$347$	−11.6485	+	5.85011i	−0.625326	+	0.314050i	−0.733096	−	0.680126i	$-0.761925\pi$
$347$	−11.6485	+	5.85011i	−0.625326	+	0.314050i	0.107770	+	0.994176i	$0.465629\pi$
$348$		0			0
$349$	−7.68114	+	1.82046i	−0.411162	+	0.0974472i	−0.430991	−	0.902356i	$-0.641836\pi$
$349$	−7.68114	+	1.82046i	−0.411162	+	0.0974472i	0.0198291	+	0.999803i	$0.493688\pi$
$350$	5.01016	+	8.67785i	0.267804	+	0.463851i
$351$		0			0
$352$	−7.70528	+	13.3459i	−0.410693	+	0.711341i
$353$	−4.04363	+	13.5067i	−0.215221	+	0.718888i	0.780390	+	0.625294i	$0.215021\pi$
$353$	−4.04363	+	13.5067i	−0.215221	+	0.718888i	−0.995610	+	0.0935941i	$0.970164\pi$
$354$		0			0
$355$	−3.34386	−	2.19929i	−0.177474	−	0.116726i
$356$	−5.88180	−	7.90063i	−0.311735	−	0.418732i
$357$		0			0
$358$	16.4342	−	10.8090i	0.868575	−	0.571271i
$359$	−2.55305	−	0.929234i	−0.134745	−	0.0490431i	0.273768	−	0.961796i	$-0.411730\pi$
$359$	−2.55305	−	0.929234i	−0.134745	−	0.0490431i	−0.408512	+	0.912753i	$0.633952\pi$
$360$		0			0
$361$	−4.05995	+	1.47770i	−0.213682	+	0.0777738i
$362$	20.6160	−	27.6921i	1.08355	−	1.45546i
$363$		0			0
$364$	−4.21016	+	4.46251i	−0.220672	+	0.233899i
$365$	0.414607	−	0.439457i	0.0217015	−	0.0230023i
$366$		0			0
$367$	16.6172	−	22.3208i	0.867411	−	1.16514i	−0.117672	−	0.993053i	$-0.537543\pi$
$367$	16.6172	−	22.3208i	0.867411	−	1.16514i	0.985083	−	0.172083i	$-0.0550496\pi$
$368$	28.0525	−	10.2103i	1.46234	−	0.532247i
$369$		0			0
$370$	−0.853445	−	0.310628i	−0.0443685	−	0.0161488i
$371$	7.23324	−	4.75737i	0.375531	−	0.246991i
$372$		0			0
$373$	6.47060	+	8.69152i	0.335035	+	0.450030i	0.937433	−	0.348166i	$-0.113195\pi$
$373$	6.47060	+	8.69152i	0.335035	+	0.450030i	−0.602398	+	0.798196i	$0.705788\pi$
$374$	−14.9867	−	9.85690i	−0.774944	−	0.509688i
$375$		0			0
$376$	−0.157589	+	0.526383i	−0.00812703	+	0.0271462i
$377$	15.3382	−	26.5665i	0.789958	−	1.36825i
$378$		0			0
$379$	2.86635	+	4.96467i	0.147235	+	0.255018i	0.930204	−	0.367042i	$-0.119629\pi$
$379$	2.86635	+	4.96467i	0.147235	+	0.255018i	−0.782970	+	0.622060i	$0.786296\pi$
$380$	−6.25265	+	1.48191i	−0.320754	+	0.0760202i
$381$		0			0
$382$	14.2956	−	7.17950i	0.731424	−	0.367335i
$383$	−5.42592	+	12.5787i	−0.277252	+	0.642741i	−0.998766	−	0.0496578i	$-0.984187\pi$
$383$	−5.42592	+	12.5787i	−0.277252	+	0.642741i	0.721515	+	0.692399i	$0.243446\pi$
$384$		0			0
$385$	0.112355	+	1.92907i	0.00572616	+	0.0983144i
$386$	−7.47516	−	42.3938i	−0.380476	−	2.15779i
$387$		0			0
$388$	2.12928	−	12.0758i	0.108098	−	0.613055i
$389$	−14.0779	−	1.64547i	−0.713776	−	0.0834285i	−0.248549	−	0.968619i	$-0.579954\pi$
$389$	−14.0779	−	1.64547i	−0.713776	−	0.0834285i	−0.465228	+	0.885191i	$0.654028\pi$
$390$		0			0
$391$	8.59074	+	28.6951i	0.434452	+	1.45117i
$392$	3.25648	+	0.771800i	0.164477	+	0.0389818i
$393$		0			0
$394$	−15.6262	−	36.2256i	−0.787236	−	1.82502i
$395$	4.79255	+	4.02143i	0.241140	+	0.202340i
$396$		0			0
$397$	−3.48565	+	2.92481i	−0.174940	+	0.146792i	−0.726053	−	0.687638i	$-0.758647\pi$
$397$	−3.48565	+	2.92481i	−0.174940	+	0.146792i	0.551114	+	0.834430i	$0.314203\pi$
$398$	42.8914	+	21.5409i	2.14995	+	1.07975i
$399$		0			0
$400$	−19.6873	+	2.30111i	−0.984363	+	0.115056i
$401$	0.618000	−	10.6106i	0.0308614	−	0.529870i	−0.947081	−	0.320995i	$-0.895983\pi$
$401$	0.618000	−	10.6106i	0.0308614	−	0.529870i	0.977942	−	0.208875i	$-0.0669803\pi$
$402$		0			0
$403$	18.6452	+	19.7627i	0.928783	+	0.984452i
$404$	12.1796			0.605960
$405$		0			0
$406$	−23.0164			−1.14228
$407$	0.846486	+	0.897222i	0.0419587	+	0.0444737i
$408$		0			0
$409$	−1.68065	+	28.8557i	−0.0831030	+	1.42682i	0.656777	+	0.754085i	$0.271919\pi$
$409$	−1.68065	+	28.8557i	−0.0831030	+	1.42682i	−0.739880	+	0.672738i	$0.765118\pi$
$410$	1.67233	−	0.195468i	0.0825907	−	0.00965347i
$411$		0			0
$412$	−2.27091	−	1.14050i	−0.111880	−	0.0561882i
$413$	−4.75978	+	3.99393i	−0.234214	+	0.196529i
$414$		0			0
$415$	−8.08404	−	6.78331i	−0.396830	−	0.332980i
$416$	−9.05387	−	20.9892i	−0.443902	−	1.02908i
$417$		0			0
$418$	18.5560	+	4.39785i	0.907603	+	0.215106i
$419$	11.3748	+	37.9943i	0.555693	+	1.85614i	0.515388	+	0.856957i	$0.327648\pi$
$419$	11.3748	+	37.9943i	0.555693	+	1.85614i	0.0403048	+	0.999187i	$0.487167\pi$
$420$		0			0
$421$	−37.2678	−	4.35598i	−1.81632	−	0.212297i	−0.861149	−	0.508353i	$-0.830254\pi$
$421$	−37.2678	−	4.35598i	−1.81632	−	0.212297i	−0.955171	+	0.296056i	$0.904328\pi$
$422$	−2.98877	+	16.9502i	−0.145491	+	0.825121i
$423$		0			0
$424$	0.756613	+	4.29097i	0.0367444	+	0.208388i
$425$	−1.15639	−	19.8544i	−0.0560931	−	0.963081i
$426$		0			0
$427$	−0.0102533	+	0.0237697i	−0.000496190	+	0.00115030i
$428$	5.23305	−	2.62814i	0.252949	−	0.127036i
$429$		0			0
$430$	11.0326	−	2.61477i	0.532039	−	0.126096i
$431$	0.730348	+	1.26500i	0.0351796	+	0.0609329i	0.883079	−	0.469224i	$-0.155466\pi$
$431$	0.730348	+	1.26500i	0.0351796	+	0.0609329i	−0.847900	+	0.530157i	$0.822133\pi$
$432$		0			0
$433$	−3.07185	+	5.32060i	−0.147624	+	0.255692i	−0.930349	−	0.366676i	$-0.880496\pi$
$433$	−3.07185	+	5.32060i	−0.147624	+	0.255692i	0.782725	+	0.622368i	$0.213829\pi$
$434$	5.84664	−	19.5291i	0.280648	−	0.937429i
$435$		0			0
$436$	11.1658	+	7.34389i	0.534747	+	0.351708i
$437$	−19.0161	−	25.5431i	−0.909663	−	1.22189i
$438$		0			0
$439$	−13.1947	+	8.67829i	−0.629749	+	0.414192i	−0.823865	−	0.566786i	$-0.808187\pi$
$439$	−13.1947	+	8.67829i	−0.629749	+	0.414192i	0.194116	+	0.980979i	$0.437816\pi$
$440$	−0.913860	−	0.332618i	−0.0435666	−	0.0158569i
$441$		0			0
$442$	25.0026	−	9.10019i	1.18925	−	0.432852i
$443$	−11.3597	+	15.2588i	−0.539718	+	0.724967i	−0.985406	−	0.170221i	$-0.945552\pi$
$443$	−11.3597	+	15.2588i	−0.539718	+	0.724967i	0.445688	+	0.895188i	$0.352959\pi$
$444$		0			0
$445$	3.15786	−	3.34713i	0.149697	−	0.158669i
$446$	9.90883	−	10.5027i	0.469197	−	0.497320i
$447$		0			0
$448$	−3.79797	+	5.10156i	−0.179437	+	0.241026i
$449$	−17.8139	+	6.48373i	−0.840690	+	0.305986i	−0.726239	−	0.687443i	$-0.758733\pi$
$449$	−17.8139	+	6.48373i	−0.840690	+	0.305986i	−0.114452	+	0.993429i	$0.536511\pi$
$450$		0			0
$451$	−2.14886	−	0.782122i	−0.101186	−	0.0368287i
$452$	−7.55709	+	4.97038i	−0.355456	+	0.233787i
$453$		0			0
$454$	−11.0844	−	14.8889i	−0.520216	−	0.698771i
$455$	−2.39473	−	1.57504i	−0.112267	−	0.0738389i
$456$		0			0
$457$	10.9564	−	36.5970i	0.512520	−	1.71193i	−0.173931	−	0.984758i	$-0.555647\pi$
$457$	10.9564	−	36.5970i	0.512520	−	1.71193i	0.686450	−	0.727177i	$-0.259168\pi$
$458$	−7.67951	+	13.3013i	−0.358840	+	0.621529i
$459$		0			0
$460$	−4.38728	−	7.59899i	−0.204558	−	0.354305i
$461$	−7.03505	+	1.66734i	−0.327655	+	0.0776556i	−0.391151	−	0.920326i	$-0.627923\pi$
$461$	−7.03505	+	1.66734i	−0.327655	+	0.0776556i	0.0634963	+	0.997982i	$0.479775\pi$
$462$		0			0
$463$	1.22851	−	0.616980i	0.0570936	−	0.0286735i	−0.420023	−	0.907513i	$-0.637978\pi$
$463$	1.22851	−	0.616980i	0.0570936	−	0.0286735i	0.477117	+	0.878840i	$0.341682\pi$
$464$	18.0331	−	41.8054i	0.837165	−	1.94077i
$465$		0			0
$466$	2.49444	+	42.8279i	0.115553	+	1.98396i
$467$	1.50717	+	8.54757i	0.0697434	+	0.395534i	0.999617	+	0.0276564i	$0.00880442\pi$
$467$	1.50717	+	8.54757i	0.0697434	+	0.395534i	−0.929874	+	0.367878i	$0.880084\pi$
$468$		0			0
$469$	3.11612	−	17.6724i	0.143889	−	0.816035i
$470$	1.37765	+	0.161025i	0.0635465	+	0.00742752i
$471$		0			0
$472$	−0.896868	−	2.99575i	−0.0412817	−	0.137890i
$473$	−14.9841	−	3.55130i	−0.688970	−	0.163289i
$474$		0			0
$475$	8.37453	+	19.4143i	0.384250	+	0.890791i
$476$	−6.99873	−	5.87263i	−0.320786	−	0.269172i
$477$		0			0
$478$	−9.52727	+	7.99433i	−0.435767	+	0.365652i
$479$	−1.89904	−	0.953732i	−0.0867692	−	0.0435771i	0.404885	−	0.914367i	$-0.367311\pi$
$479$	−1.89904	−	0.953732i	−0.0867692	−	0.0435771i	−0.491655	+	0.870790i	$0.663608\pi$
$480$		0			0
$481$	−1.81731	+	0.212413i	−0.0828622	+	0.00968520i
$482$	0.311711	−	5.35186i	0.0141980	−	0.243771i
$483$		0			0
$484$	7.84204	+	8.31207i	0.356456	+	0.377821i
$485$	5.72873			0.260128
$486$		0			0
$487$	−7.22045			−0.327190			−0.163595	−	0.986528i	$-0.552309\pi$
$487$	−7.22045			−0.327190			−0.163595	+	0.986528i	$0.552309\pi$
$488$	−0.00894061	−	0.00947650i	−0.000404723	−	0.000428981i
$489$		0			0
$490$	0.491215	−	8.43384i	0.0221908	−	0.381002i
$491$	21.4296	−	2.50477i	0.967106	−	0.113039i	0.382147	−	0.924101i	$-0.375185\pi$
$491$	21.4296	−	2.50477i	0.967106	−	0.113039i	0.584959	+	0.811063i	$0.301111\pi$
$492$		0			0
$493$	40.8232	+	20.5022i	1.83859	+	0.923373i
$494$	−21.6690	+	18.1824i	−0.974933	+	0.818066i
$495$		0			0
$496$	30.8906	+	25.9203i	1.38703	+	1.16386i
$497$	2.39613	+	5.55485i	0.107481	+	0.249169i
$498$		0			0
$499$	7.51219	+	1.78042i	0.336292	+	0.0797026i	0.395292	−	0.918555i	$-0.370643\pi$
$499$	7.51219	+	1.78042i	0.336292	+	0.0797026i	−0.0590007	+	0.998258i	$0.518791\pi$
$500$	3.57909	+	11.9550i	0.160062	+	0.534643i
$501$		0			0
$502$	22.1742	+	2.59180i	0.989685	+	0.115678i
$503$	−1.71945	+	9.75150i	−0.0766666	+	0.434798i	0.922179	+	0.386763i	$0.126407\pi$
$503$	−1.71945	+	9.75150i	−0.0766666	+	0.434798i	−0.998846	+	0.0480347i	$0.984704\pi$
$504$		0			0
$505$	0.988096	+	5.60377i	0.0439697	+	0.249365i
$506$	1.51410	+	25.9962i	0.0673101	+	1.15567i
$507$		0			0
$508$	−3.71758	+	8.61831i	−0.164941	+	0.382376i
$509$	18.7721	−	9.42770i	0.832059	−	0.417876i	0.0188320	−	0.999823i	$-0.494005\pi$
$509$	18.7721	−	9.42770i	0.832059	−	0.417876i	0.813227	+	0.581947i	$0.197709\pi$
$510$		0			0
$511$	−0.888610	+	0.210604i	−0.0393098	+	0.00931659i
$512$	−14.2477	−	24.6777i	−0.629665	−	1.09061i
$513$		0			0
$514$	−20.0345	+	34.7008i	−0.883686	+	1.53059i
$515$	0.340503	−	1.13736i	0.0150043	−	0.0501180i
$516$		0			0
$517$	−1.57391	−	1.03518i	−0.0692205	−	0.0455270i
$518$	0.819781	+	1.10116i	0.0360191	+	0.0483821i
$519$		0			0
$520$	1.20522	−	0.792687i	0.0528525	−	0.0347616i
$521$	−20.5557	−	7.48165i	−0.900560	−	0.327777i	−0.150083	−	0.988673i	$-0.547954\pi$
$521$	−20.5557	−	7.48165i	−0.900560	−	0.327777i	−0.750477	+	0.660896i	$0.770176\pi$
$522$		0			0
$523$	28.4317	−	10.3483i	1.24323	−	0.452499i	0.365121	−	0.930960i	$-0.381028\pi$
$523$	28.4317	−	10.3483i	1.24323	−	0.452499i	0.878109	+	0.478461i	$0.158805\pi$
$524$	2.46329	−	3.30877i	0.107609	−	0.144544i
$525$		0			0
$526$	27.2391	−	28.8718i	1.18768	−	1.25887i
$527$	−27.7658	+	29.4301i	−1.20950	+	1.28199i
$528$		0			0
$529$	12.2320	−	16.4304i	0.531824	−	0.714364i
$530$	10.3356	−	3.76184i	0.448949	−	0.163404i
$531$		0			0
$532$	9.12717	+	3.32202i	0.395713	+	0.144028i
$533$	2.83397	−	1.86393i	0.122753	−	0.0807359i
$534$		0			0
$535$	1.63373	+	2.19448i	0.0706323	+	0.0948756i
$536$	7.54562	+	4.96283i	0.325921	+	0.214362i
$537$		0			0
$538$	−6.75499	+	22.5632i	−0.291228	+	0.972770i
$539$	−5.73699	+	9.93675i	−0.247110	+	0.428006i
$540$		0			0
$541$	−2.75454	−	4.77101i	−0.118427	−	0.205122i	0.800717	−	0.599042i	$-0.204452\pi$
$541$	−2.75454	−	4.77101i	−0.118427	−	0.205122i	−0.919144	+	0.393921i	$0.871119\pi$
$542$	−13.1640	+	3.11992i	−0.565442	+	0.134012i
$543$		0			0
$544$	30.4197	−	15.2773i	1.30423	−	0.655010i
$545$	−2.47302	+	5.73312i	−0.105933	+	0.245580i
$546$		0			0
$547$	0.232144	+	3.98575i	0.00992575	+	0.170419i	0.999628	+	0.0272766i	$0.00868350\pi$
$547$	0.232144	+	3.98575i	0.00992575	+	0.170419i	−0.989702	+	0.143142i	$0.954279\pi$
$548$	3.22081	+	18.2661i	0.137586	+	0.780290i
$549$		0			0
$550$	3.00235	−	17.0272i	0.128021	−	0.726041i
$551$	−48.2378	−	5.63819i	−2.05500	−	0.240195i
$552$		0			0
$553$	−2.71216	−	9.05926i	−0.115333	−	0.385239i
$554$	57.1526	+	13.5454i	2.42818	+	0.575490i
$555$		0			0
$556$	−9.54898	−	22.1370i	−0.404967	−	0.938819i
$557$	4.09443	+	3.43564i	0.173487	+	0.145573i	0.725397	−	0.688331i	$-0.241656\pi$
$557$	4.09443	+	3.43564i	0.173487	+	0.145573i	−0.551910	+	0.833904i	$0.686101\pi$
$558$		0			0
$559$	17.4979	−	14.6825i	0.740081	−	0.621002i
$560$	−3.80153	−	1.90920i	−0.160644	−	0.0806784i
$561$		0			0
$562$	−32.0378	+	3.74468i	−1.35143	+	0.157960i
$563$	0.673539	−	11.5642i	0.0283863	−	0.487374i	−0.953916	−	0.300073i	$-0.902989\pi$
$563$	0.673539	−	11.5642i	0.0283863	−	0.487374i	0.982303	−	0.187301i	$-0.0599739\pi$
$564$		0			0
$565$	−2.89992	−	3.07374i	−0.122001	−	0.129313i
$566$	39.1895			1.64726
$567$		0			0
$568$	−3.04466			−0.127751
$569$	−29.3906	−	31.1523i	−1.23212	−	1.30597i	−0.936501	−	0.350665i	$-0.885956\pi$
$569$	−29.3906	−	31.1523i	−1.23212	−	1.30597i	−0.295619	−	0.955306i	$-0.595526\pi$
$570$		0			0
$571$	−1.84172	+	31.6212i	−0.0770737	+	1.32330i	0.709016	+	0.705192i	$0.249139\pi$
$571$	−1.84172	+	31.6212i	−0.0770737	+	1.32330i	−0.786090	+	0.618112i	$0.787898\pi$
$572$	10.5144	−	1.22896i	0.439629	−	0.0513852i
$573$		0			0
$574$	−2.27430	−	1.14220i	−0.0949274	−	0.0476743i
$575$	−22.1170	+	18.5583i	−0.922341	+	0.773936i
$576$		0			0
$577$	17.4676	+	14.6571i	0.727188	+	0.610183i	0.929363	−	0.369166i	$-0.120357\pi$
$577$	17.4676	+	14.6571i	0.727188	+	0.610183i	−0.202176	+	0.979349i	$0.564801\pi$
$578$	2.76346	+	6.40641i	0.114945	+	0.266472i
$579$		0			0
$580$	−13.0215	−	3.08614i	−0.540687	−	0.128145i
$581$	4.57486	+	15.2811i	0.189797	+	0.633966i
$582$		0			0
$583$	−14.8373	−	1.73423i	−0.614499	−	0.0718246i
$584$	0.0798104	−	0.452627i	0.00330258	−	0.0187298i
$585$		0			0
$586$	7.15597	+	40.5835i	0.295610	+	1.67649i
$587$	−0.152598	−	2.62001i	−0.00629841	−	0.108139i	0.993694	−	0.112129i	$-0.0357671\pi$
$587$	−0.152598	−	2.62001i	−0.00629841	−	0.108139i	−0.999992	+	0.00398975i	$0.998730\pi$
$588$		0			0
$589$	17.0373	−	39.4970i	0.702011	−	1.62744i
$590$	−7.05421	+	3.54276i	−0.290417	+	0.145853i
$591$		0			0
$592$	−2.64236	+	0.626250i	−0.108600	+	0.0257387i
$593$	5.12692	+	8.88008i	0.210537	+	0.364661i	0.951883	−	0.306462i	$-0.0991454\pi$
$593$	5.12692	+	8.88008i	0.210537	+	0.364661i	−0.741346	+	0.671124i	$0.765812\pi$
$594$		0			0
$595$	2.13417	−	3.69650i	0.0874926	−	0.151542i
$596$	−4.98182	+	16.6404i	−0.204063	+	0.681619i
$597$		0			0
$598$	−32.2714	−	21.2252i	−1.31968	−	0.867965i
$599$	4.30284	+	5.77972i	0.175809	+	0.236153i	0.881290	−	0.472577i	$-0.156676\pi$
$599$	4.30284	+	5.77972i	0.175809	+	0.236153i	−0.705480	+	0.708730i	$0.749269\pi$
$600$		0			0
$601$	14.1176	−	9.28526i	0.575867	−	0.378754i	−0.227912	−	0.973682i	$-0.573190\pi$
$601$	14.1176	−	9.28526i	0.575867	−	0.378754i	0.803779	+	0.594928i	$0.202819\pi$
$602$	−16.1046	−	5.86159i	−0.656374	−	0.238901i
$603$		0			0
$604$	−16.1394	+	5.87428i	−0.656705	+	0.239021i
$605$	−3.18813	+	4.28240i	−0.129616	+	0.174104i
$606$		0			0
$607$	7.49458	−	7.94379i	0.304196	−	0.322429i	−0.557185	−	0.830388i	$-0.688119\pi$
$607$	7.49458	−	7.94379i	0.304196	−	0.322429i	0.861381	+	0.507960i	$0.169600\pi$
$608$	−24.8346	+	26.3232i	−1.00718	+	1.06755i
$609$		0			0
$610$	−0.0196393	+	0.0263801i	−0.000795171	+	0.00106810i
$611$	2.62578	−	0.955706i	0.106228	−	0.0386637i
$612$		0			0
$613$	7.35009	+	2.67521i	0.296867	+	0.108051i	0.486160	−	0.873870i	$-0.338397\pi$
$613$	7.35009	+	2.67521i	0.296867	+	0.108051i	−0.189293	+	0.981921i	$0.560619\pi$
$614$	13.0217	−	8.56451i	0.525513	−	0.345636i
$615$		0			0
$616$	0.877814	+	1.17911i	0.0353681	+	0.0475076i
$617$	−2.01117	−	1.32277i	−0.0809668	−	0.0532527i	0.508380	−	0.861133i	$-0.330244\pi$
$617$	−2.01117	−	1.32277i	−0.0809668	−	0.0532527i	−0.589347	+	0.807880i	$0.700615\pi$
$618$		0			0
$619$	−9.09854	+	30.3912i	−0.365701	+	1.22153i	0.555195	+	0.831720i	$0.312643\pi$
$619$	−9.09854	+	30.3912i	−0.365701	+	1.22153i	−0.920897	+	0.389807i	$0.872542\pi$
$620$	5.92628	−	10.2646i	0.238005	−	0.412237i
$621$		0			0
$622$	22.4659	+	38.9120i	0.900799	+	1.56023i
$623$	−6.76810	+	1.60407i	−0.271158	+	0.0642657i
$624$		0			0
$625$	14.3531	−	7.20838i	0.574122	−	0.288335i
$626$	−2.70111	+	6.26188i	−0.107958	+	0.250275i
$627$		0			0
$628$	2.02228	+	34.7212i	0.0806978	+	1.38553i
$629$	−0.473140	−	2.68331i	−0.0188653	−	0.106991i
$630$		0			0
$631$	−1.13730	+	6.44997i	−0.0452753	+	0.256769i	−0.999041	−	0.0437817i	$-0.986059\pi$
$631$	−1.13730	+	6.44997i	−0.0452753	+	0.256769i	0.953766	+	0.300551i	$0.0971705\pi$
$632$	4.72712	+	0.552521i	0.188035	+	0.0219781i
$633$		0			0
$634$	10.3052	+	34.4219i	0.409273	+	1.36707i
$635$	−4.26682	−	1.01126i	−0.169324	−	0.0401305i
$636$		0			0
$637$	−6.74108	−	15.6276i	−0.267091	−	0.619187i
$638$	30.4229	+	25.5278i	1.20445	+	1.01066i
$639$		0			0
$640$	2.86287	−	2.40224i	0.113165	−	0.0949568i
$641$	33.1107	+	16.6288i	1.30779	+	0.656798i	0.959796	−	0.280698i	$-0.0905659\pi$
$641$	33.1107	+	16.6288i	1.30779	+	0.656798i	0.347996	+	0.937496i	$0.386862\pi$
$642$		0			0
$643$	−16.0317	+	1.87384i	−0.632230	+	0.0738971i	−0.426171	−	0.904642i	$-0.640138\pi$
$643$	−16.0317	+	1.87384i	−0.632230	+	0.0738971i	−0.206059	+	0.978540i	$0.566064\pi$
$644$	−0.771179	+	13.2406i	−0.0303887	+	0.521754i
$645$		0			0
$646$	−28.9071	−	30.6398i	−1.13734	−	1.20551i
$647$	−9.95741			−0.391466			−0.195733	−	0.980657i	$-0.562709\pi$
$647$	−9.95741			−0.391466			−0.195733	+	0.980657i	$0.562709\pi$
$648$		0			0
$649$	10.7212			0.420843
$650$	17.5995	+	18.6544i	0.690310	+	0.731686i
$651$		0			0
$652$	−1.83317	+	31.4743i	−0.0717925	+	1.23263i
$653$	19.9874	−	2.33619i	0.782168	−	0.0914223i	0.284369	−	0.958715i	$-0.408216\pi$
$653$	19.9874	−	2.33619i	0.782168	−	0.0914223i	0.497799	+	0.867292i	$0.334142\pi$
$654$		0			0
$655$	1.72218	+	0.864912i	0.0672912	+	0.0337949i
$656$	3.85649	−	3.23598i	0.150571	−	0.126344i
$657$		0			0
$658$	−1.60605	−	1.34764i	−0.0626104	−	0.0525364i
$659$	−3.56046	−	8.25406i	−0.138696	−	0.321533i	0.834685	−	0.550728i	$-0.185650\pi$
$659$	−3.56046	−	8.25406i	−0.138696	−	0.321533i	−0.973380	+	0.229195i	$0.926391\pi$
$660$		0			0
$661$	−0.602072	−	0.142694i	−0.0234179	−	0.00555014i	0.218890	−	0.975749i	$-0.429756\pi$
$661$	−0.602072	−	0.142694i	−0.0234179	−	0.00555014i	−0.242308	+	0.970199i	$0.577904\pi$
$662$	−3.97678	−	13.2834i	−0.154562	−	0.516273i
$663$		0			0
$664$	−7.97366	−	0.931988i	−0.309438	−	0.0361681i
$665$	−0.787980	+	4.46886i	−0.0305566	+	0.173295i
$666$		0			0
$667$	−11.5159	−	65.3099i	−0.445897	−	2.52881i
$668$	1.65608	+	28.4337i	0.0640755	+	1.10013i
$669$		0			0
$670$	9.02990	−	20.9337i	0.348855	−	0.808737i
$671$	0.0399161	−	0.0200466i	0.00154094	−	0.000773890i
$672$		0			0
$673$	12.4696	−	2.95534i	0.480666	−	0.113920i	0.0168623	−	0.999858i	$-0.494632\pi$
$673$	12.4696	−	2.95534i	0.480666	−	0.113920i	0.463804	+	0.885938i	$0.346484\pi$
$674$	19.7299	+	34.1732i	0.759969	+	1.31630i
$675$		0			0
$676$	3.11861	−	5.40159i	0.119946	−	0.207753i
$677$	8.37100	−	27.9611i	0.321724	−	1.07463i	−0.632255	−	0.774760i	$-0.717871\pi$
$677$	8.37100	−	27.9611i	0.321724	−	1.07463i	0.953979	−	0.299872i	$-0.0969441\pi$
$678$		0			0
$679$	−7.23465	−	4.75830i	−0.277640	−	0.182607i
$680$	1.28280	+	1.72311i	0.0491933	+	0.0660781i
$681$		0			0
$682$	−29.3881	+	19.3289i	−1.12533	+	0.740141i
$683$	39.5288	+	14.3873i	1.51253	+	0.550516i	0.959269	−	0.282493i	$-0.0911614\pi$
$683$	39.5288	+	14.3873i	1.51253	+	0.550516i	0.553260	+	0.833009i	$0.313384\pi$
$684$		0			0
$685$	−8.14283	+	2.96375i	−0.311122	+	0.113239i
$686$	−17.1922	+	23.0931i	−0.656401	+	0.881699i
$687$		0			0
$688$	23.2644	−	24.6588i	0.886946	−	0.940107i
$689$	15.2059	−	16.1173i	0.579298	−	0.614020i
$690$		0			0
$691$	7.51788	−	10.0983i	0.285994	−	0.384156i	−0.635789	−	0.771863i	$-0.719325\pi$
$691$	7.51788	−	10.0983i	0.285994	−	0.384156i	0.921783	+	0.387707i	$0.126733\pi$
$692$	1.98637	−	0.722979i	0.0755104	−	0.0274835i
$693$		0			0
$694$	23.5219	+	8.56128i	0.892880	+	0.324982i
$695$	9.41042	−	6.18933i	0.356958	−	0.234775i
$696$		0			0
$697$	3.01640	+	4.05173i	0.114254	+	0.153470i
$698$	12.6651	+	8.32996i	0.479381	+	0.315294i
$699$		0			0
$700$	2.52566	−	8.43628i	0.0954608	−	0.318861i
$701$	−2.24313	+	3.88521i	−0.0847218	+	0.146742i	−0.905273	−	0.424831i	$-0.860333\pi$
$701$	−2.24313	+	3.88521i	−0.0847218	+	0.146742i	0.820551	+	0.571574i	$0.193667\pi$
$702$		0			0
$703$	1.44835	+	2.50862i	0.0546257	+	0.0946145i
$704$	10.6784	−	2.53082i	0.402456	−	0.0953838i
$705$		0			0
$706$	24.1948	−	12.1511i	0.910583	−	0.457312i
$707$	3.40667	−	7.89756i	0.128121	−	0.297018i
$708$		0			0
$709$	−0.197090	−	3.38390i	−0.00740186	−	0.127085i	−0.999985	−	0.00551558i	$-0.998244\pi$
$709$	−0.197090	−	3.38390i	−0.00740186	−	0.127085i	0.992583	−	0.121569i	$-0.0387927\pi$
$710$	1.33461	+	7.56894i	0.0500870	+	0.284057i
$711$		0			0
$712$	0.607877	−	3.44744i	0.0227811	−	0.129198i
$713$	58.3400	+	6.81896i	2.18485	+	0.255372i
$714$		0			0
$715$	1.41843	+	4.73790i	0.0530464	+	0.177187i
$716$	−16.8209	−	3.98664i	−0.628628	−	0.148988i
$717$		0			0
$718$	2.06648	+	4.79064i	0.0771203	+	0.178785i
$719$	−14.7252	−	12.3559i	−0.549159	−	0.460799i	0.325497	−	0.945543i	$-0.394468\pi$
$719$	−14.7252	−	12.3559i	−0.549159	−	0.460799i	−0.874656	+	0.484744i	$0.838913\pi$
$720$		0			0
$721$	−1.37470	+	1.15351i	−0.0511966	+	0.0429591i
$722$	7.41428	+	3.72359i	0.275931	+	0.138578i
$723$		0			0
$724$	−30.1354	+	3.52232i	−1.11997	+	0.130906i
$725$	−2.56026	+	43.9580i	−0.0950858	+	1.63256i
$726$		0			0
$727$	18.0748	+	19.1582i	0.670359	+	0.710539i	0.969889	−	0.243548i	$-0.0783113\pi$
$727$	18.0748	+	19.1582i	0.670359	+	0.710539i	−0.299530	+	0.954087i	$0.596830\pi$
$728$	−2.18045			−0.0808128
$729$		0			0
$730$	−1.16020			−0.0429411
$731$	23.3428	+	24.7419i	0.863363	+	0.915111i
$732$		0			0
$733$	−0.896233	+	15.3877i	−0.0331031	+	0.568359i	0.940455	+	0.339919i	$0.110400\pi$
$733$	−0.896233	+	15.3877i	−0.0331031	+	0.568359i	−0.973558	+	0.228440i	$0.926638\pi$
$734$	−53.0758	+	6.20368i	−1.95907	+	0.228982i
$735$		0			0
$736$	−44.1604	−	22.1782i	−1.62778	−	0.817499i
$737$	−23.7196	+	19.9031i	−0.873722	+	0.733140i
$738$		0			0
$739$	−29.4693	−	24.7277i	−1.08405	−	0.909622i	−0.0877951	−	0.996139i	$-0.527982\pi$
$739$	−29.4693	−	24.7277i	−1.08405	−	0.909622i	−0.996250	+	0.0865164i	$0.972427\pi$
$740$	0.316141	+	0.732897i	0.0116216	+	0.0269418i
$741$		0			0
$742$	−16.1771	−	3.83404i	−0.593880	−	0.140752i
$743$	2.84619	+	9.50692i	0.104416	+	0.348775i	0.994192	−	0.107624i	$-0.0343242\pi$
$743$	2.84619	+	9.50692i	0.104416	+	0.348775i	−0.889775	+	0.456399i	$0.849139\pi$
$744$		0			0
$745$	−8.06031	−	0.942116i	−0.295307	−	0.0345164i
$746$	3.61327	−	20.4919i	0.132291	−	0.750260i
$747$		0			0
$748$	2.73744	+	15.5248i	0.100091	+	0.567643i
$749$	−0.240448	−	4.12832i	−0.00878576	−	0.150846i
$750$		0			0
$751$	−0.667802	+	1.54814i	−0.0243684	+	0.0564924i	−0.929966	−	0.367646i	$-0.880164\pi$
$751$	−0.667802	+	1.54814i	−0.0243684	+	0.0564924i	0.905597	+	0.424139i	$0.139423\pi$
$752$	3.70608	−	1.86126i	0.135147	−	0.0678733i
$753$		0			0
$754$	−57.3208	+	13.5853i	−2.08750	+	0.494747i
$755$	−4.01206	−	6.94909i	−0.146014	−	0.252903i
$756$		0			0
$757$	−20.2972	+	35.1558i	−0.737716	+	1.27776i	0.215806	+	0.976436i	$0.430762\pi$
$757$	−20.2972	+	35.1558i	−0.737716	+	1.27776i	−0.953522	+	0.301325i	$0.902571\pi$
$758$	3.15732	−	10.5462i	0.114679	−	0.383055i
$759$		0			0
$760$	−1.90808	−	1.25496i	−0.0692133	−	0.0455223i
$761$	−21.2314	−	28.5187i	−0.769638	−	1.03380i	−0.998182	−	0.0602701i	$-0.980804\pi$
$761$	−21.2314	−	28.5187i	−0.769638	−	1.03380i	0.228544	−	0.973534i	$-0.426604\pi$
$762$		0			0
$763$	7.88506	−	5.18608i	0.285458	−	0.187749i
$764$	−13.2110	−	4.80842i	−0.477958	−	0.173963i
$765$		0			0
$766$	24.7202	−	8.99741i	0.893177	−	0.325090i
$767$	−9.49654	+	12.7561i	−0.342900	+	0.460595i
$768$		0			0
$769$	−4.97291	+	5.27097i	−0.179328	+	0.190076i	−0.810802	−	0.585321i	$-0.800969\pi$
$769$	−4.97291	+	5.27097i	−0.179328	+	0.190076i	0.631474	+	0.775397i	$0.282450\pi$
$770$	2.54645	−	2.69908i	0.0917677	−	0.0972681i
$771$		0			0
$772$	−22.5917	+	30.3459i	−0.813093	+	1.09217i
$773$	−27.7323	+	10.0937i	−0.997463	+	0.363047i	−0.788606	−	0.614899i	$-0.789197\pi$
$773$	−27.7323	+	10.0937i	−0.997463	+	0.363047i	−0.208857	+	0.977946i	$0.566974\pi$
$774$		0			0
$775$	−36.6475	−	13.3386i	−1.31642	−	0.479137i
$776$	3.64106	−	2.39477i	0.130707	−	0.0859671i
$777$		0			0
$778$	16.2536	+	21.8323i	0.582718	+	0.782726i
$779$	−4.48668	−	2.95094i	−0.160752	−	0.105728i
$780$		0			0
$781$	2.99379	−	9.99994i	0.107126	−	0.357826i
$782$	28.7602	−	49.8141i	1.02846	−	1.78135i
$783$		0			0
$784$	−12.6299	−	21.8756i	−0.451068	−	0.781273i
$785$	−15.8109	+	3.74726i	−0.564317	+	0.133746i
$786$		0			0
$787$	32.6660	−	16.4055i	1.16442	−	0.584792i	0.241730	−	0.970343i	$-0.422285\pi$
$787$	32.6660	−	16.4055i	1.16442	−	0.584792i	0.922686	+	0.385551i	$0.125989\pi$
$788$	−13.7329	+	31.8364i	−0.489213	+	1.13412i
$789$		0			0
$790$	−0.698553	−	11.9937i	−0.0248534	−	0.426716i
$791$	1.10917	+	6.29042i	0.0394376	+	0.223662i
$792$		0			0
$793$	−0.0115051	+	0.0652489i	−0.000408559	+	0.00231706i
$794$	8.67877	+	1.01440i	0.307998	+	0.0359998i
$795$		0			0
$796$	−12.0977	−	40.4092i	−0.428793	−	1.43227i
$797$	−47.0618	−	11.1538i	−1.66701	−	0.395089i	−0.714511	−	0.699624i	$-0.753351\pi$
$797$	−47.0618	−	11.1538i	−1.66701	−	0.395089i	−0.952501	+	0.304534i	$0.901499\pi$
$798$		0			0
$799$	1.64816	+	3.82086i	0.0583077	+	0.135172i
$800$	25.1347	+	21.0906i	0.888647	+	0.745664i
$801$		0			0
$802$	−15.6353	+	13.1196i	−0.552102	+	0.463269i
$803$	1.40814	+	0.707196i	0.0496923	+	0.0249564i
$804$		0			0
$805$	−6.15449	+	0.719357i	−0.216917	+	0.0253540i
$806$	3.03372	−	52.0870i	0.106858	−	1.83469i
$807$		0			0
$808$	2.97054	+	3.14859i	0.104503	+	0.110767i
$809$	−12.9603			−0.455661			−0.227831	−	0.973701i	$-0.573163\pi$
$809$	−12.9603			−0.455661			−0.227831	+	0.973701i	$0.573163\pi$
$810$		0			0
$811$	16.4612			0.578029			0.289015	−	0.957325i	$-0.406672\pi$
$811$	16.4612			0.578029			0.289015	+	0.957325i	$0.406672\pi$
$812$	13.8811	+	14.7131i	0.487130	+	0.516328i
$813$		0			0
$814$	0.137730	−	2.36473i	0.00482744	−	0.0828839i
$815$	−14.6299	+	1.70999i	−0.512462	+	0.0598982i
$816$		0			0
$817$	−32.3161	−	16.2298i	−1.13060	−	0.567808i
$818$	42.5203	−	35.6788i	1.48669	−	1.24748i
$819$		0			0
$820$	−1.13353	−	0.951143i	−0.0395845	−	0.0332154i
$821$	−3.53334	−	8.19121i	−0.123315	−	0.285875i	0.845365	−	0.534189i	$-0.179383\pi$
$821$	−3.53334	−	8.19121i	−0.123315	−	0.285875i	−0.968680	+	0.248314i	$0.920124\pi$
$822$		0			0
$823$	−4.17743	−	0.990068i	−0.145616	−	0.0345116i	0.157161	−	0.987573i	$-0.449766\pi$
$823$	−4.17743	−	0.990068i	−0.145616	−	0.0345116i	−0.302777	+	0.953061i	$0.597914\pi$
$824$	−0.259030	−	0.865221i	−0.00902374	−	0.0301414i
$825$		0			0
$826$	11.8512	+	1.38521i	0.412356	+	0.0481975i
$827$	−2.12514	+	12.0523i	−0.0738983	+	0.419098i	0.925306	+	0.379221i	$0.123808\pi$
$827$	−2.12514	+	12.0523i	−0.0738983	+	0.419098i	−0.999205	+	0.0398773i	$0.987303\pi$
$828$		0			0
$829$	−1.20691	−	6.84473i	−0.0419177	−	0.237727i	0.956649	−	0.291242i	$-0.0940686\pi$
$829$	−1.20691	−	6.84473i	−0.0419177	−	0.237727i	−0.998567	+	0.0535151i	$0.982957\pi$
$830$	1.17831	+	20.2309i	0.0408998	+	0.702223i
$831$		0			0
$832$	−6.44744	+	14.9468i	−0.223525	+	0.518189i
$833$	22.6490	−	11.3748i	0.784743	−	0.394113i
$834$		0			0
$835$	−12.9478	+	3.06869i	−0.448078	+	0.106196i
$836$	−8.37972	−	14.5141i	−0.289819	−	0.501981i
$837$		0			0
$838$	38.0805	−	65.9574i	1.31547	−	2.27846i
$839$	−1.89048	+	6.31465i	−0.0652667	+	0.218006i	−0.984401	−	0.175938i	$-0.943704\pi$
$839$	−1.89048	+	6.31465i	−0.0652667	+	0.218006i	0.919135	+	0.393944i	$0.128889\pi$
$840$		0			0
$841$	−60.2733	−	39.6424i	−2.07839	−	1.36698i
$842$	43.0273	+	57.7958i	1.48282	+	1.99177i
$843$		0			0
$844$	12.6378	−	8.31200i	0.435011	−	0.286111i
$845$	2.73824	+	0.996637i	0.0941983	+	0.0342854i
$846$		0			0
$847$	7.58318	−	2.76005i	0.260561	−	0.0948365i
$848$	19.6385	−	26.3790i	0.674388	−	0.905860i
$849$		0			0
$850$	−26.2087	+	27.7796i	−0.898950	+	0.952831i
$851$	−2.71441	+	2.87711i	−0.0930488	+	0.0986260i
$852$		0			0
$853$	−4.97050	+	6.67655i	−0.170187	+	0.228601i	−0.879031	−	0.476764i	$-0.841809\pi$
$853$	−4.97050	+	6.67655i	−0.170187	+	0.228601i	0.708844	+	0.705365i	$0.249217\pi$
$854$	0.0467133	−	0.0170022i	0.00159850	−	0.000581805i
$855$		0			0
$856$	1.95572	+	0.711823i	0.0668450	+	0.0243296i
$857$	−48.6472	+	31.9958i	−1.66176	+	1.09296i	−0.773238	+	0.634116i	$0.781364\pi$
$857$	−48.6472	+	31.9958i	−1.66176	+	1.09296i	−0.888519	+	0.458840i	$0.848265\pi$
$858$		0			0
$859$	−15.6174	−	20.9778i	−0.532858	−	0.715752i	0.451433	−	0.892305i	$-0.350913\pi$
$859$	−15.6174	−	20.9778i	−0.532858	−	0.715752i	−0.984291	+	0.176553i	$0.943505\pi$
$860$	−8.32518	−	5.47556i	−0.283886	−	0.186715i
$861$		0			0
$862$	0.804488	−	2.68718i	0.0274010	−	0.0915256i
$863$	−16.9220	+	29.3098i	−0.576032	+	0.997716i	0.419897	+	0.907572i	$0.362066\pi$
$863$	−16.9220	+	29.3098i	−0.576032	+	0.997716i	−0.995929	+	0.0901446i	$0.971267\pi$
$864$		0			0
$865$	0.493786	+	0.855262i	0.0167892	+	0.0290798i
$866$	11.4799	−	2.72079i	0.390103	−	0.0924561i
$867$		0			0
$868$	−16.0100	+	8.04050i	−0.543414	+	0.272913i
$869$	−6.46285	+	14.9826i	−0.219237	+	0.508249i
$870$		0			0
$871$	−2.67053	−	45.8512i	−0.0904874	−	1.55361i
$872$	0.824795	+	4.67764i	0.0279311	+	0.158405i
$873$		0			0
$874$	−10.6188	+	60.2224i	−0.359188	+	2.03705i
$875$	8.75297	+	1.02308i	0.295904	+	0.0345862i
$876$		0			0
$877$	0.470486	+	1.57153i	0.0158872	+	0.0530668i	0.965566	−	0.260160i	$-0.0837752\pi$
$877$	0.470486	+	1.57153i	0.0158872	+	0.0530668i	−0.949678	+	0.313227i	$0.898590\pi$
$878$	29.5099	+	6.99397i	0.995910	+	0.236035i
$879$		0			0
$880$	2.90731	+	6.73990i	0.0980053	+	0.227202i
$881$	−33.5691	−	28.1678i	−1.13097	−	0.948998i	−0.131865	−	0.991268i	$-0.542097\pi$
$881$	−33.5691	−	28.1678i	−1.13097	−	0.948998i	−0.999106	+	0.0422700i	$0.986541\pi$
$882$		0			0
$883$	10.9055	−	9.15077i	0.366998	−	0.307948i	−0.440575	−	0.897716i	$-0.645225\pi$
$883$	10.9055	−	9.15077i	0.366998	−	0.307948i	0.807573	+	0.589768i	$0.200781\pi$
$884$	−20.8962	−	10.4944i	−0.702814	−	0.352966i
$885$		0			0
$886$	36.2834	−	4.24092i	1.21896	−	0.142476i
$887$	−1.67354	+	28.7337i	−0.0561921	+	0.964782i	0.845928	+	0.533297i	$0.179047\pi$
$887$	−1.67354	+	28.7337i	−0.0561921	+	0.964782i	−0.902120	+	0.431485i	$0.857990\pi$
$888$		0			0
$889$	4.54850	+	4.82112i	0.152552	+	0.161695i
$890$	−8.83671			−0.296207
$891$		0			0
$892$	−12.6898			−0.424885
$893$	−3.03584	−	3.21780i	−0.101591	−	0.107680i
$894$		0			0
$895$	0.469595	−	8.06263i	0.0156968	−	0.269504i
$896$	−5.61075	+	0.655802i	−0.187442	+	0.0219088i
$897$		0			0
$898$	32.5318	+	16.3381i	1.08560	+	0.545208i
$899$	68.6228	−	57.5814i	2.28870	−	1.92045i
$900$		0			0
$901$	25.2774	+	21.2103i	0.842113	+	0.706617i
$902$	1.73932	+	4.03221i	0.0579132	+	0.134258i
$903$		0			0
$904$	−3.12804	−	0.741359i	−0.104037	−	0.0246572i
$905$	−4.06538	−	13.5793i	−0.135138	−	0.451392i
$906$		0			0
$907$	19.5259	+	2.28225i	0.648347	+	0.0757809i	0.433909	−	0.900957i	$-0.357134\pi$
$907$	19.5259	+	2.28225i	0.648347	+	0.0757809i	0.214438	+	0.976738i	$0.431208\pi$
$908$	−2.83270	+	16.0651i	−0.0940065	+	0.533137i
$909$		0			0
$910$	0.955787	+	5.42054i	0.0316840	+	0.179689i
$911$	−2.38173	−	40.8927i	−0.0789102	−	1.35484i	−0.772752	−	0.634708i	$-0.781120\pi$
$911$	−2.38173	−	40.8927i	−0.0789102	−	1.35484i	0.693842	−	0.720127i	$-0.255917\pi$
$912$		0			0
$913$	10.9015	−	25.2725i	0.360786	−	0.836396i
$914$	−65.5570	+	32.9239i	−2.16843	+	1.08903i
$915$		0			0
$916$	13.1342	−	3.11287i	0.433967	−	0.102852i
$917$	−1.45649	−	2.52272i	−0.0480977	−	0.0833076i
$918$		0			0
$919$	10.0461	−	17.4003i	0.331389	−	0.573983i	−0.651395	−	0.758738i	$-0.725816\pi$
$919$	10.0461	−	17.4003i	0.331389	−	0.573983i	0.982784	+	0.184756i	$0.0591494\pi$
$920$	0.894404	−	2.98752i	0.0294876	−	0.0984956i
$921$		0			0
$922$	11.5998	+	7.62929i	0.382018	+	0.251257i
$923$	9.24612	+	12.4197i	0.304340	+	0.408799i
$924$		0			0
$925$	2.19424	−	1.44318i	0.0721463	−	0.0474513i
$926$	−2.48073	−	0.902913i	−0.0815220	−	0.0296716i
$927$		0			0
$928$	−70.8210	+	25.7767i	−2.32481	+	0.846163i
$929$	−23.3247	+	31.3305i	−0.765259	+	1.02792i	0.233200	+	0.972429i	$0.425080\pi$
$929$	−23.3247	+	31.3305i	−0.765259	+	1.02792i	−0.998459	+	0.0554927i	$0.982327\pi$
$930$		0			0
$931$	−18.4907	+	19.5990i	−0.606008	+	0.642331i
$932$	25.8730	−	27.4238i	0.847500	−	0.898297i
$933$		0			0
$934$	9.95304	−	13.3693i	0.325674	−	0.437455i
$935$	−6.92078	+	2.51896i	−0.226334	+	0.0823787i
$936$		0			0
$937$	6.55624	+	2.38628i	0.214183	+	0.0779563i	0.446883	−	0.894592i	$-0.352534\pi$
$937$	6.55624	+	2.38628i	0.214183	+	0.0779563i	−0.232700	+	0.972548i	$0.574756\pi$
$938$	−28.7912	+	18.9362i	−0.940065	+	0.618290i
$939$		0			0
$940$	−0.727923	−	0.977770i	−0.0237422	−	0.0318913i
$941$	41.8229	+	27.5073i	1.36339	+	0.896714i	0.999398	−	0.0346896i	$-0.0110443\pi$
$941$	41.8229	+	27.5073i	1.36339	+	0.896714i	0.363989	+	0.931403i	$0.381415\pi$
$942$		0			0
$943$	2.10311	−	7.02489i	0.0684868	−	0.228762i
$944$	−11.8013	+	20.4404i	−0.384099	+	0.665278i
$945$		0			0
$946$	14.7857	+	25.6097i	0.480726	+	0.832642i
$947$	−57.0504	+	13.5212i	−1.85389	+	0.439380i	−0.997088	−	0.0762644i	$-0.975701\pi$
$947$	−57.0504	+	13.5212i	−1.85389	+	0.439380i	−0.856803	+	0.515644i	$0.827553\pi$
$948$		0			0
$949$	−2.08872	+	1.04899i	−0.0678026	+	0.0340518i
$950$	16.0818	−	37.2819i	0.521764	−	1.20958i
$951$		0			0
$952$	−0.188800	−	3.24156i	−0.00611903	−	0.105060i
$953$	3.77884	+	21.4309i	0.122409	+	0.694214i	0.982813	+	0.184603i	$0.0590998\pi$
$953$	3.77884	+	21.4309i	0.122409	+	0.694214i	−0.860405	+	0.509612i	$0.829789\pi$
$954$		0			0
$955$	1.14055	−	6.46840i	0.0369075	−	0.209313i
$956$	10.8562	+	1.26890i	0.351114	+	0.0410393i
$957$		0			0
$958$	1.17040	+	3.90940i	0.0378138	+	0.126307i
$959$	12.7450	+	3.02063i	0.411559	+	0.0975413i
$960$		0			0
$961$	19.1470	+	44.3878i	0.617647	+	1.43187i
$962$	2.69156	+	2.25849i	0.0867795	+	0.0728167i
$963$		0			0
$964$	−3.60914	+	3.02842i	−0.116242	+	0.0975390i
$965$	−15.7948	−	7.93242i	−0.508451	−	0.255354i
$966$		0			0
$967$	33.0673	−	3.86502i	1.06337	−	0.124291i	0.433628	−	0.901092i	$-0.357233\pi$
$967$	33.0673	−	3.86502i	1.06337	−	0.124291i	0.629746	+	0.776801i	$0.283159\pi$
$968$	−0.236150	+	4.05453i	−0.00759014	+	0.130318i
$969$		0			0
$970$	−7.54937	−	8.00186i	−0.242396	−	0.256924i
$971$	−49.4538			−1.58705			−0.793524	−	0.608539i	$-0.791756\pi$
$971$	−49.4538			−1.58705			−0.793524	+	0.608539i	$0.791756\pi$
$972$		0			0
$973$	−17.0250			−0.545797
$974$	9.51517	+	10.0855i	0.304886	+	0.323160i
$975$		0			0
$976$	−0.00571763	+	0.0981679i	−0.000183017	+	0.00314228i
$977$	18.0842	−	2.11373i	0.578563	−	0.0676244i	0.178222	−	0.983990i	$-0.442966\pi$
$977$	18.0842	−	2.11373i	0.578563	−	0.0676244i	0.400342	+	0.916366i	$0.368891\pi$
$978$		0			0
$979$	10.7251	+	5.38636i	0.342777	+	0.172149i
$980$	−5.68753	+	4.77240i	−0.181681	+	0.152449i
$981$		0			0
$982$	−31.7388	−	26.6320i	−1.01283	−	0.849862i
$983$	0.0700904	+	0.162488i	0.00223554	+	0.00518256i	0.919330	−	0.393487i	$-0.128731\pi$
$983$	0.0700904	+	0.162488i	0.00223554	+	0.00518256i	−0.917095	+	0.398669i	$0.869472\pi$
$984$		0			0
$985$	−15.7618	−	3.73562i	−0.502213	−	0.119027i
$986$	−25.1598	−	84.0397i	−0.801252	−	2.67637i
$987$		0			0
$988$	24.6914	+	2.88601i	0.785539	+	0.0918163i
$989$	8.57480	−	48.6301i	0.272663	−	1.54635i
$990$		0			0
$991$	8.80351	+	49.9272i	0.279653	+	1.58599i	0.723783	+	0.690027i	$0.242401\pi$
$991$	8.80351	+	49.9272i	0.279653	+	1.58599i	−0.444131	+	0.895962i	$0.646487\pi$
$992$	−3.88126	−	66.6386i	−0.123230	−	2.11578i
$993$		0			0
$994$	4.60135	−	10.6671i	0.145946	−	0.338341i
$995$	17.6106	−	8.84437i	0.558293	−	0.280385i
$996$		0			0
$997$	44.2333	−	10.4835i	1.40088	−	0.332016i	0.540364	−	0.841432i	$-0.318287\pi$
$997$	44.2333	−	10.4835i	1.40088	−	0.332016i	0.860520	+	0.509416i	$0.170139\pi$
$998$	−7.41274	−	12.8392i	−0.234646	−	0.406419i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.g.d.109.1		144
3.2	odd	2		729.2.g.a.109.8		144
9.2	odd	6		729.2.g.b.352.8		144
9.4	even	3		81.2.g.a.76.8	yes	144
9.5	odd	6		243.2.g.a.118.1		144
9.7	even	3		729.2.g.c.352.1		144
81.11	odd	54		729.2.g.a.622.8		144
81.16	even	27		729.2.g.c.379.1		144
81.31	even	27		6561.2.a.c.1.60		72
81.38	odd	54		243.2.g.a.208.1		144
81.43	even	27		81.2.g.a.16.8	✓	144
81.50	odd	54		6561.2.a.d.1.13		72
81.65	odd	54		729.2.g.b.379.8		144
81.70	even	27	inner	729.2.g.d.622.1		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.16.8	✓	144	81.43	even	27
81.2.g.a.76.8	yes	144	9.4	even	3
243.2.g.a.118.1		144	9.5	odd	6
243.2.g.a.208.1		144	81.38	odd	54
729.2.g.a.109.8		144	3.2	odd	2
729.2.g.a.622.8		144	81.11	odd	54
729.2.g.b.352.8		144	9.2	odd	6
729.2.g.b.379.8		144	81.65	odd	54
729.2.g.c.352.1		144	9.7	even	3
729.2.g.c.379.1		144	81.16	even	27
729.2.g.d.109.1		144	1.1	even	1	trivial
729.2.g.d.622.1		144	81.70	even	27	inner
6561.2.a.c.1.60		72	81.31	even	27
6561.2.a.d.1.13		72	81.50	odd	54

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)

\(f(q)\)	\(=\)	\(q+(-1.31781 - 1.39680i) q^{2} +(-0.0981285 + 1.68480i) q^{4} +(-0.783127 + 0.0915344i) q^{5} +(1.06502 + 0.534872i) q^{7} +(-0.459476 + 0.385546i) q^{8} +O(q^{10})\)	\(q+(-1.31781 - 1.39680i) q^{2} +(-0.0981285 + 1.68480i) q^{4} +(-0.783127 + 0.0915344i) q^{5} +(1.06502 + 0.534872i) q^{7} +(-0.459476 + 0.385546i) q^{8} +(1.15987 + 0.973243i) q^{10} +(-0.814497 - 1.88822i) q^{11} +(2.96806 + 0.703443i) q^{13} +(-0.656382 - 2.19247i) q^{14} +(4.49652 + 0.525568i) q^{16} +(-0.788777 + 4.47337i) q^{17} +(-0.838570 - 4.75577i) q^{19} +(-0.0773702 - 1.32839i) q^{20} +(-1.56410 + 3.62599i) q^{22} +(5.89280 - 2.95948i) q^{23} +(-4.26032 + 1.00971i) q^{25} +(-2.92877 - 5.07278i) q^{26} +(-1.00566 + 1.74186i) q^{28} +(2.88435 - 9.63442i) q^{29} +(7.44201 + 4.89468i) q^{31} +(-4.47508 - 6.01108i) q^{32} +(7.28784 - 4.79329i) q^{34} +(-0.883002 - 0.321387i) q^{35} +(-0.563666 + 0.205158i) q^{37} +(-5.53776 + 7.43850i) q^{38} +(0.324537 - 0.343989i) q^{40} +(0.763120 - 0.808860i) q^{41} +(4.47179 - 6.00665i) q^{43} +(3.26119 - 1.18698i) q^{44} +(-11.8994 - 4.33101i) q^{46} +(0.765373 - 0.503394i) q^{47} +(-3.33194 - 4.47557i) q^{49} +(7.02464 + 4.62018i) q^{50} +(-1.47641 + 4.93156i) q^{52} +(3.63216 - 6.29109i) q^{53} +(0.810691 + 1.40416i) q^{55} +(-0.695567 + 0.164852i) q^{56} +(-17.2583 + 8.66746i) q^{58} +(-2.06499 + 4.78719i) q^{59} +(0.00126297 + 0.0216843i) q^{61} +(-2.97027 - 16.8452i) q^{62} +(-0.926691 + 5.25553i) q^{64} +(-2.38876 - 0.279206i) q^{65} +(-4.31847 - 14.4247i) q^{67} +(-7.45934 - 1.76790i) q^{68} +(0.714717 + 1.65690i) q^{70} +(3.88852 + 3.26285i) q^{71} +(-0.586995 + 0.492548i) q^{73} +(1.02937 + 0.516967i) q^{74} +(8.09481 - 0.946147i) q^{76} +(0.142500 - 2.44663i) q^{77} +(-5.44517 - 5.77154i) q^{79} -3.56945 q^{80} -2.13546 q^{82} +(9.18487 + 9.73539i) q^{83} +(0.208244 - 3.57542i) q^{85} +(-14.2830 + 1.66945i) q^{86} +(1.10224 + 0.553563i) q^{88} +(-4.47086 + 3.75149i) q^{89} +(2.78478 + 2.33671i) q^{91} +(4.40788 + 10.2186i) q^{92} +(-1.71175 - 0.405693i) q^{94} +(1.09202 + 3.64761i) q^{95} +(-7.21661 - 0.843501i) q^{97} +(-1.86060 + 10.5520i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8}+O(q^{10}) \) 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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Database

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