LMFDB - Embedded newform 729.2.g.d.28.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("729.28");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$8$ over $\Q(\zeta_{27})$
Twist minimal:	no (minimal twist has level 81)
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			28.3
Character	$\chi$	$=$	729.28
Dual form			729.2.g.d.703.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.26928 + 0.834819i) q^{2} +(0.121992 - 0.282809i) q^{4} +(0.0546290 - 0.0579033i) q^{5} +(0.848729 + 0.0992022i) q^{7} +(-0.446364 - 2.53145i) q^{8} +O(q^{10})$	\(q+(-1.26928 + 0.834819i) q^{2} +(0.121992 - 0.282809i) q^{4} +(0.0546290 - 0.0579033i) q^{5} +(0.848729 + 0.0992022i) q^{7} +(-0.446364 - 2.53145i) q^{8} +(-0.0210007 + 0.119101i) q^{10} +(-1.14520 + 3.82522i) q^{11} +(0.117949 - 2.02511i) q^{13} +(-1.16009 + 0.582620i) q^{14} +(3.10259 + 3.28855i) q^{16} +(-1.92609 + 0.701038i) q^{17} +(5.26032 + 1.91460i) q^{19} +(-0.00971128 - 0.0225133i) q^{20} +(-1.73979 - 5.81131i) q^{22} +(-7.45312 + 0.871145i) q^{23} +(0.290356 + 4.98521i) q^{25} +(1.54089 + 2.66890i) q^{26} +(0.131593 - 0.227926i) q^{28} +(0.993107 + 0.498757i) q^{29} +(3.57847 + 4.80672i) q^{31} +(-1.68097 - 0.398397i) q^{32} +(1.85950 - 2.49775i) q^{34} +(0.0521094 - 0.0437249i) q^{35} +(-0.782274 - 0.656406i) q^{37} +(-8.27517 + 1.96125i) q^{38} +(-0.170964 - 0.112445i) q^{40} +(3.65733 + 2.40547i) q^{41} +(-11.6846 + 2.76930i) q^{43} +(0.942101 + 0.790516i) q^{44} +(8.73286 - 7.32774i) q^{46} +(3.07256 - 4.12716i) q^{47} +(-6.10081 - 1.44592i) q^{49} +(-4.53030 - 6.08524i) q^{50} +(-0.558330 - 0.280404i) q^{52} +(-5.16096 + 8.93905i) q^{53} +(0.158932 + 0.275278i) q^{55} +(-0.127716 - 2.19280i) q^{56} +(-1.67690 + 0.196002i) q^{58} +(3.14185 + 10.4945i) q^{59} +(-4.21089 - 9.76194i) q^{61} +(-8.55483 - 3.11370i) q^{62} +(-6.03074 + 2.19501i) q^{64} +(-0.110817 - 0.117459i) q^{65} +(-4.10628 + 2.06225i) q^{67} +(-0.0367070 + 0.630234i) q^{68} +(-0.0296390 + 0.0990011i) q^{70} +(-0.963622 + 5.46497i) q^{71} +(0.267464 + 1.51686i) q^{73} +(1.54091 + 0.180106i) q^{74} +(1.18318 - 1.25410i) q^{76} +(-1.35143 + 3.13297i) q^{77} +(-11.4068 + 7.50239i) q^{79} +0.359909 q^{80} -6.65031 q^{82} +(5.24973 - 3.45280i) q^{83} +(-0.0646276 + 0.149824i) q^{85} +(12.5192 - 13.2696i) q^{86} +(10.1945 + 1.19157i) q^{88} +(-1.79520 - 10.1811i) q^{89} +(0.301002 - 1.70707i) q^{91} +(-0.662852 + 2.21408i) q^{92} +(-0.454506 + 7.80356i) q^{94} +(0.398228 - 0.199997i) q^{95} +(9.42786 + 9.99295i) q^{97} +(8.95073 - 3.25780i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{22}{27}\right)$

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 $

$2$	−1.26928	+	0.834819i	−0.897517	+	0.590306i	−0.912272	−	0.409585i	$-0.865674\pi$
$2$	−1.26928	+	0.834819i	−0.897517	+	0.590306i	0.0147548	+	0.999891i	$0.495303\pi$
$3$		0			0
$3$		0			0
$4$	0.121992	−	0.282809i	0.0609959	−	0.141404i
$5$	0.0546290	−	0.0579033i	0.0244308	−	0.0258952i	−0.715043	−	0.699080i	$-0.753593\pi$
$5$	0.0546290	−	0.0579033i	0.0244308	−	0.0258952i	0.739474	+	0.673185i	$0.235074\pi$
$6$		0			0
$7$	0.848729	+	0.0992022i	0.320790	+	0.0374949i	0.274964	−	0.961455i	$-0.411334\pi$
$7$	0.848729	+	0.0992022i	0.320790	+	0.0374949i	0.0458256	+	0.998949i	$0.485408\pi$
$8$	−0.446364	−	2.53145i	−0.157813	−	0.895004i
$9$		0			0
$10$	−0.0210007	+	0.119101i	−0.00664101	+	0.0376630i
$11$	−1.14520	+	3.82522i	−0.345289	+	1.15335i	0.592333	+	0.805693i	$0.298207\pi$
$11$	−1.14520	+	3.82522i	−0.345289	+	1.15335i	−0.937623	+	0.347654i	$0.886978\pi$
$12$		0			0
$13$	0.117949	−	2.02511i	0.0327132	−	0.561664i	−0.941637	−	0.336629i	$-0.890713\pi$
$13$	0.117949	−	2.02511i	0.0327132	−	0.561664i	0.974351	−	0.225035i	$-0.0722498\pi$
$14$	−1.16009	+	0.582620i	−0.310048	+	0.155712i
$15$		0			0
$16$	3.10259	+	3.28855i	0.775647	+	0.822138i
$17$	−1.92609	+	0.701038i	−0.467144	+	0.170027i	−0.564858	−	0.825188i	$-0.691069\pi$
$17$	−1.92609	+	0.701038i	−0.467144	+	0.170027i	0.0977140	+	0.995215i	$0.468847\pi$
$18$		0			0
$19$	5.26032	+	1.91460i	1.20680	+	0.439239i	0.865593	−	0.500749i	$-0.166942\pi$
$19$	5.26032	+	1.91460i	1.20680	+	0.439239i	0.341207	+	0.939988i	$0.389164\pi$
$20$	−0.00971128	−	0.0225133i	−0.00217151	−	0.00503412i
$21$		0			0
$22$	−1.73979	−	5.81131i	−0.370925	−	1.23898i
$23$	−7.45312	+	0.871145i	−1.55408	+	0.181646i	−0.849352	−	0.527827i	$-0.823007\pi$
$23$	−7.45312	+	0.871145i	−1.55408	+	0.181646i	−0.704732	+	0.709474i	$0.748933\pi$
$24$		0			0
$25$	0.290356	+	4.98521i	0.0580711	+	0.997043i
$26$	1.54089	+	2.66890i	0.302193	+	0.523414i
$27$		0			0
$28$	0.131593	−	0.227926i	0.0248688	−	0.0430740i
$29$	0.993107	+	0.498757i	0.184415	+	0.0926169i	0.538611	−	0.842554i	$-0.318949\pi$
$29$	0.993107	+	0.498757i	0.184415	+	0.0926169i	−0.354196	+	0.935171i	$0.615245\pi$
$30$		0			0
$31$	3.57847	+	4.80672i	0.642712	+	0.863313i	0.997429	−	0.0716613i	$-0.0228301\pi$
$31$	3.57847	+	4.80672i	0.642712	+	0.863313i	−0.354717	+	0.934974i	$0.615423\pi$
$32$	−1.68097	−	0.398397i	−0.297156	−	0.0704274i
$33$		0			0
$34$	1.85950	−	2.49775i	0.318902	−	0.428360i
$35$	0.0521094	−	0.0437249i	0.00880809	−	0.00739086i
$36$		0			0
$37$	−0.782274	−	0.656406i	−0.128605	−	0.107913i	0.576216	−	0.817297i	$-0.304529\pi$
$37$	−0.782274	−	0.656406i	−0.128605	−	0.107913i	−0.704822	+	0.709385i	$0.748973\pi$
$38$	−8.27517	+	1.96125i	−1.34241	+	0.318157i
$39$		0			0
$40$	−0.170964	−	0.112445i	−0.0270318	−	0.0177791i
$41$	3.65733	+	2.40547i	0.571180	+	0.375671i	0.801999	−	0.597326i	$-0.203770\pi$
$41$	3.65733	+	2.40547i	0.571180	+	0.375671i	−0.230819	+	0.972997i	$0.574141\pi$
$42$		0			0
$43$	−11.6846	+	2.76930i	−1.78189	+	0.422315i	−0.983659	−	0.180043i	$-0.942376\pi$
$43$	−11.6846	+	2.76930i	−1.78189	+	0.422315i	−0.798227	+	0.602357i	$0.794228\pi$
$44$	0.942101	+	0.790516i	0.142027	+	0.119175i
$45$		0			0
$46$	8.73286	−	7.32774i	1.28759	−	1.08042i
$47$	3.07256	−	4.12716i	0.448179	−	0.602008i	−0.519415	−	0.854522i	$-0.673850\pi$
$47$	3.07256	−	4.12716i	0.448179	−	0.602008i	0.967593	+	0.252514i	$0.0812573\pi$
$48$		0			0
$49$	−6.10081	−	1.44592i	−0.871545	−	0.206560i
$50$	−4.53030	−	6.08524i	−0.640681	−	0.860583i
$51$		0			0
$52$	−0.558330	−	0.280404i	−0.0774264	−	0.0388850i
$53$	−5.16096	+	8.93905i	−0.708913	+	1.22787i	0.256348	+	0.966584i	$0.417481\pi$
$53$	−5.16096	+	8.93905i	−0.708913	+	1.22787i	−0.965261	+	0.261288i	$0.915853\pi$
$54$		0			0
$55$	0.158932	+	0.275278i	0.0214304	+	0.0371185i
$56$	−0.127716	−	2.19280i	−0.0170668	−	0.293025i
$57$		0			0
$58$	−1.67690	+	0.196002i	−0.220188	+	0.0257363i
$59$	3.14185	+	10.4945i	0.409034	+	1.36627i	0.876136	+	0.482064i	$0.160113\pi$
$59$	3.14185	+	10.4945i	0.409034	+	1.36627i	−0.467102	+	0.884203i	$0.654702\pi$
$60$		0			0
$61$	−4.21089	−	9.76194i	−0.539149	−	1.24989i	−0.942304	−	0.334757i	$-0.891346\pi$
$61$	−4.21089	−	9.76194i	−0.539149	−	1.24989i	0.403155	−	0.915132i	$-0.367914\pi$
$62$	−8.55483	−	3.11370i	−1.08646	−	0.395441i
$63$		0			0
$64$	−6.03074	+	2.19501i	−0.753842	+	0.274376i
$65$	−0.110817	−	0.117459i	−0.0137452	−	0.0145690i
$66$		0			0
$67$	−4.10628	+	2.06225i	−0.501662	+	0.251944i	−0.681588	−	0.731736i	$-0.738710\pi$
$67$	−4.10628	+	2.06225i	−0.501662	+	0.251944i	0.179926	+	0.983680i	$0.442414\pi$
$68$	−0.0367070	+	0.630234i	−0.00445137	+	0.0764271i
$69$		0			0
$70$	−0.0296390	+	0.0990011i	−0.00354254	+	0.0118329i
$71$	−0.963622	+	5.46497i	−0.114361	+	0.648573i	0.872704	+	0.488250i	$0.162365\pi$
$71$	−0.963622	+	5.46497i	−0.114361	+	0.648573i	−0.987065	+	0.160323i	$0.948746\pi$
$72$		0			0
$73$	0.267464	+	1.51686i	0.0313043	+	0.177536i	0.996451	−	0.0841735i	$-0.0268250\pi$
$73$	0.267464	+	1.51686i	0.0313043	+	0.177536i	−0.965147	+	0.261709i	$0.915714\pi$
$74$	1.54091	+	0.180106i	0.179127	+	0.0209369i
$75$		0			0
$76$	1.18318	−	1.25410i	0.135720	−	0.143855i
$77$	−1.35143	+	3.13297i	−0.154010	+	0.357035i
$78$		0			0
$79$	−11.4068	+	7.50239i	−1.28337	+	0.844085i	−0.993594	−	0.113009i	$-0.963951\pi$
$79$	−11.4068	+	7.50239i	−1.28337	+	0.844085i	−0.289775	+	0.957095i	$0.593581\pi$
$80$	0.359909			0.0402391
$81$		0			0
$82$	−6.65031			−0.734404
$83$	5.24973	−	3.45280i	0.576232	−	0.378994i	−0.227685	−	0.973735i	$-0.573116\pi$
$83$	5.24973	−	3.45280i	0.576232	−	0.378994i	0.803917	+	0.594741i	$0.202745\pi$
$84$		0			0
$85$	−0.0646276	+	0.149824i	−0.00700985	+	0.0162507i
$86$	12.5192	−	13.2696i	1.34998	−	1.43089i
$87$		0			0
$88$	10.1945	+	1.19157i	1.08674	+	0.127022i
$89$	−1.79520	−	10.1811i	−0.190291	−	1.07919i	−0.918967	−	0.394334i	$-0.870975\pi$
$89$	−1.79520	−	10.1811i	−0.190291	−	1.07919i	0.728676	−	0.684858i	$-0.240136\pi$
$90$		0			0
$91$	0.301002	−	1.70707i	0.0315536	−	0.178950i
$92$	−0.662852	+	2.21408i	−0.0691071	+	0.230834i
$93$		0			0
$94$	−0.454506	+	7.80356i	−0.0468787	+	0.804876i
$95$	0.398228	−	0.199997i	0.0408573	−	0.0205193i
$96$		0			0
$97$	9.42786	+	9.99295i	0.957254	+	1.01463i	0.999879	+	0.0155391i	$0.00494645\pi$
$97$	9.42786	+	9.99295i	0.957254	+	1.01463i	−0.0426250	+	0.999091i	$0.513572\pi$
$98$	8.95073	−	3.25780i	0.904160	−	0.329087i
$99$		0			0
$100$	1.44528	+	0.526040i	0.144528	+	0.0526040i
$101$	−3.38133	−	7.83881i	−0.336455	−	0.779991i	−0.999506	−	0.0314167i	$-0.989998\pi$
$101$	−3.38133	−	7.83881i	−0.336455	−	0.779991i	0.663051	−	0.748574i	$-0.269261\pi$
$102$		0			0
$103$	−2.36031	−	7.88398i	−0.232568	−	0.776832i	−0.991999	−	0.126244i	$-0.959708\pi$
$103$	−2.36031	−	7.88398i	−0.232568	−	0.776832i	0.759431	−	0.650588i	$-0.225477\pi$
$104$	−5.17912	+	0.605352i	−0.507855	+	0.0593597i
$105$		0			0
$106$	−0.911779	−	15.6546i	−0.0885598	−	1.52051i
$107$	2.93755	+	5.08798i	0.283984	+	0.491874i	0.972362	−	0.233478i	$-0.0750106\pi$
$107$	2.93755	+	5.08798i	0.283984	+	0.491874i	−0.688379	+	0.725352i	$0.741677\pi$
$108$		0			0
$109$	−5.21293	+	9.02906i	−0.499308	+	0.864827i	−1.00000		0.000798944i	$-0.999746\pi$
$109$	−5.21293	+	9.02906i	−0.499308	+	0.864827i	0.500692	+	0.865626i	$0.333079\pi$
$110$	−0.431537	−	0.216726i	−0.0411455	−	0.0206640i
$111$		0			0
$112$	2.30703	+	3.09888i	0.217994	+	0.292816i
$113$	−2.69864	−	0.639589i	−0.253867	−	0.0601675i	0.101712	−	0.994814i	$-0.467568\pi$
$113$	−2.69864	−	0.639589i	−0.253867	−	0.0601675i	−0.355579	+	0.934646i	$0.615716\pi$
$114$		0			0
$115$	−0.356714	+	0.479150i	−0.0332638	+	0.0446810i
$116$	0.262204	−	0.220015i	0.0243450	−	0.0204279i
$117$		0			0
$118$	−12.7489	−	10.6976i	−1.17363	−	0.984793i
$119$	−1.70427	+	0.403919i	−0.156230	+	0.0370272i
$120$		0			0
$121$	−4.13047	−	2.71665i	−0.375497	−	0.246968i
$122$	13.4943	+	8.87532i	1.22171	+	0.803534i
$123$		0			0
$124$	1.79593	−	0.425642i	0.161279	−	0.0382238i
$125$	0.609431	+	0.511373i	0.0545092	+	0.0457386i
$126$		0			0
$127$	−8.52362	+	7.15216i	−0.756349	+	0.634652i	−0.937174	−	0.348863i	$-0.886568\pi$
$127$	−8.52362	+	7.15216i	−0.756349	+	0.634652i	0.180825	+	0.983515i	$0.442123\pi$
$128$	7.88549	−	10.5921i	0.696986	−	0.936214i
$129$		0			0
$130$	0.238715	+	0.0565766i	0.0209367	+	0.00496210i
$131$	5.93022	+	7.96566i	0.518125	+	0.695963i	0.981773	−	0.190056i	$-0.0608671\pi$
$131$	5.93022	+	7.96566i	0.518125	+	0.695963i	−0.463648	+	0.886020i	$0.653460\pi$
$132$		0			0
$133$	4.27466	+	2.14681i	0.370660	+	0.186152i
$134$	3.49042	−	6.04558i	0.301526	−	0.522259i
$135$		0			0
$136$	2.63438	+	4.56288i	0.225896	+	0.391264i
$137$	0.934938	+	16.0523i	0.0798772	+	1.37144i	0.765479	+	0.643461i	$0.222502\pi$
$137$	0.934938	+	16.0523i	0.0798772	+	1.37144i	−0.685601	+	0.727977i	$0.740461\pi$
$138$		0			0
$139$	20.1578	−	2.35611i	1.70976	−	0.199843i	0.795778	−	0.605588i	$-0.207062\pi$
$139$	20.1578	−	2.35611i	1.70976	−	0.199843i	0.913986	+	0.405745i	$0.132988\pi$
$140$	−0.00600888	−	0.0200711i	−0.000507843	−	0.00169631i
$141$		0			0
$142$	−3.33916	−	7.74104i	−0.280216	−	0.649613i
$143$	7.61142	+	2.77033i	0.636499	+	0.231667i
$144$		0			0
$145$	0.0831321	−	0.0302576i	0.00690375	−	0.00251276i
$146$	−1.60580	−	1.70204i	−0.132897	−	0.140862i
$147$		0			0
$148$	−0.281068	+	0.141158i	−0.0231037	+	0.0116031i
$149$	0.297275	−	5.10402i	0.0243538	−	0.418138i	−0.963994	−	0.265924i	$-0.914323\pi$
$149$	0.297275	−	5.10402i	0.0243538	−	0.418138i	0.988348	−	0.152213i	$-0.0486401\pi$
$150$		0			0
$151$	5.09479	−	17.0178i	0.414608	−	1.38489i	−0.454712	−	0.890638i	$-0.650258\pi$
$151$	5.09479	−	17.0178i	0.414608	−	1.38489i	0.869320	−	0.494249i	$-0.164557\pi$
$152$	2.49871	−	14.1709i	0.202672	−	1.14941i
$153$		0			0
$154$	−0.900118	−	5.10482i	−0.0725336	−	0.411358i
$155$	0.473813	+	0.0553808i	0.0380576	+	0.00444830i
$156$		0			0
$157$	4.95262	−	5.24948i	0.395262	−	0.418954i	−0.498926	−	0.866645i	$-0.666272\pi$
$157$	4.95262	−	5.24948i	0.395262	−	0.418954i	0.894188	+	0.447691i	$0.147754\pi$
$158$	8.21534	−	19.0453i	0.653577	−	1.51516i
$159$		0			0
$160$	−0.114898	+	0.0755698i	−0.00908350	+	0.00597431i
$161$	−6.41210			−0.505345
$162$		0			0
$163$	4.94597			0.387398			0.193699	−	0.981061i	$-0.437951\pi$
$163$	4.94597			0.387398			0.193699	+	0.981061i	$0.437951\pi$
$164$	1.12645	−	0.740878i	0.0879610	−	0.0578529i
$165$		0			0
$166$	−3.78091	+	8.76515i	−0.293456	+	0.680307i
$167$	12.2989	−	13.0361i	0.951717	−	1.00876i	−0.0482337	−	0.998836i	$-0.515359\pi$
$167$	12.2989	−	13.0361i	0.951717	−	1.00876i	0.999951	−	0.00992510i	$-0.00315931\pi$
$168$		0			0
$169$	8.82494	+	1.03149i	0.678842	+	0.0793452i
$170$	−0.0430451	−	0.244121i	−0.00330141	−	0.0187232i
$171$		0			0
$172$	−0.642242	+	3.64234i	−0.0489705	+	0.277726i
$173$	−0.494173	+	1.65065i	−0.0375713	+	0.125497i	−0.974718	−	0.223439i	$-0.928272\pi$
$173$	−0.494173	+	1.65065i	−0.0375713	+	0.125497i	0.937147	+	0.348936i	$0.113457\pi$
$174$		0			0
$175$	−0.248111	+	4.25990i	−0.0187554	+	0.322018i
$176$	−16.1325	+	8.10205i	−1.21603	+	0.610715i
$177$		0			0
$178$	10.7780	+	11.4240i	0.807843	+	0.856264i
$179$	11.6071	−	4.22465i	0.867558	−	0.315765i	0.130380	−	0.991464i	$-0.458380\pi$
$179$	11.6071	−	4.22465i	0.867558	−	0.315765i	0.737178	+	0.675699i	$0.236158\pi$
$180$		0			0
$181$	−0.0341083	−	0.0124144i	−0.00253525	−	0.000922757i	0.340752	−	0.940153i	$-0.389318\pi$
$181$	−0.0341083	−	0.0124144i	−0.00253525	−	0.000922757i	−0.343287	+	0.939230i	$0.611541\pi$
$182$	1.04304	+	2.41803i	0.0773151	+	0.179237i
$183$		0			0
$184$	5.53207	+	18.4784i	0.407829	+	1.36225i
$185$	−0.0807430	+	0.00943750i	−0.00593634	+	0.000693859i
$186$		0			0
$187$	−0.475879	−	8.17052i	−0.0347997	−	0.597488i
$188$	−0.792370	−	1.37243i	−0.0577895	−	0.100094i
$189$		0			0
$190$	−0.338501	+	0.586301i	−0.0245574	+	0.0425347i
$191$	23.7317	+	11.9185i	1.71716	+	0.862391i	0.983044	+	0.183370i	$0.0587006\pi$
$191$	23.7317	+	11.9185i	1.71716	+	0.862391i	0.734118	+	0.679021i	$0.237596\pi$
$192$		0			0
$193$	−0.0270102	−	0.0362809i	−0.00194423	−	0.00261156i	0.801150	−	0.598464i	$-0.204222\pi$
$193$	−0.0270102	−	0.0362809i	−0.00194423	−	0.00261156i	−0.803094	+	0.595852i	$0.796814\pi$
$194$	−20.3089	−	4.81330i	−1.45809	−	0.345575i
$195$		0			0
$196$	−1.15317	+	1.54897i	−0.0823691	+	0.110641i
$197$	9.33211	−	7.83057i	0.664885	−	0.557905i	−0.246661	−	0.969102i	$-0.579334\pi$
$197$	9.33211	−	7.83057i	0.664885	−	0.557905i	0.911547	+	0.411197i	$0.134889\pi$
$198$		0			0
$199$	9.63166	+	8.08192i	0.682770	+	0.572912i	0.916814	−	0.399314i	$-0.130752\pi$
$199$	9.63166	+	8.08192i	0.682770	+	0.572912i	−0.234044	+	0.972226i	$0.575196\pi$
$200$	12.4902	−	2.96024i	0.883193	−	0.209321i
$201$		0			0
$202$	10.8359	+	7.12685i	0.762408	+	0.501443i
$203$	0.793401	+	0.521828i	0.0556859	+	0.0366252i
$204$		0			0
$205$	0.339081	−	0.0803636i	0.0236824	−	0.00561284i
$206$	9.57760	+	8.03656i	0.667303	+	0.559934i
$207$		0			0
$208$	7.02563	−	5.89520i	0.487140	−	0.408759i
$209$	−13.3479	+	17.9293i	−0.923291	+	1.24019i
$210$		0			0
$211$	13.3553	+	3.16527i	0.919418	+	0.217906i	0.662965	−	0.748651i	$-0.269298\pi$
$211$	13.3553	+	3.16527i	0.919418	+	0.217906i	0.256453	+	0.966557i	$0.417446\pi$
$212$	1.89844	+	2.55005i	0.130386	+	0.175138i
$213$		0			0
$214$	−7.97612	−	4.00576i	−0.545236	−	0.273828i
$215$	−0.477966	+	0.827862i	−0.0325970	+	0.0564597i
$216$		0			0
$217$	2.56032	+	4.43460i	0.173806	+	0.301040i
$218$	−0.920959	−	15.8123i	−0.0623752	−	1.07094i
$219$		0			0
$220$	0.0972395	−	0.0113657i	0.00655589	−	0.000766273i
$221$	1.19250	+	3.98322i	0.0802161	+	0.267940i
$222$		0			0
$223$	−1.16339	−	2.69705i	−0.0779066	−	0.180608i	0.874811	−	0.484464i	$-0.160985\pi$
$223$	−1.16339	−	2.69705i	−0.0779066	−	0.180608i	−0.952718	+	0.303856i	$0.901726\pi$
$224$	−1.38717	−	0.504888i	−0.0926840	−	0.0337342i
$225$		0			0
$226$	3.95927	−	1.44106i	0.263367	−	0.0958578i
$227$	−2.72165	−	2.88478i	−0.180642	−	0.191469i	0.630725	−	0.776006i	$-0.282758\pi$
$227$	−2.72165	−	2.88478i	−0.180642	−	0.191469i	−0.811367	+	0.584537i	$0.801276\pi$
$228$		0			0
$229$	−9.13092	+	4.58572i	−0.603388	+	0.303033i	−0.724143	−	0.689649i	$-0.757765\pi$
$229$	−9.13092	+	4.58572i	−0.603388	+	0.303033i	0.120755	+	0.992682i	$0.461468\pi$
$230$	0.0527667	−	0.905969i	0.00347933	−	0.0597378i
$231$		0			0
$232$	0.819294	−	2.73663i	0.0537893	−	0.179669i
$233$	0.443423	−	2.51478i	0.0290496	−	0.164748i	−0.966832	−	0.255414i	$-0.917788\pi$
$233$	0.443423	−	2.51478i	0.0290496	−	0.164748i	0.995881	+	0.0906654i	$0.0288994\pi$
$234$		0			0
$235$	−0.0711257	−	0.403374i	−0.00463973	−	0.0263132i
$236$	3.35121	+	0.391701i	0.218145	+	0.0254975i
$237$		0			0
$238$	1.82600	−	1.93544i	0.118362	−	0.125456i
$239$	−1.84643	+	4.28050i	−0.119435	+	0.276883i	−0.967437	−	0.253111i	$-0.918546\pi$
$239$	−1.84643	+	4.28050i	−0.119435	+	0.276883i	0.848002	+	0.529993i	$0.177806\pi$
$240$		0			0
$241$	−1.26850	+	0.834304i	−0.0817112	+	0.0537423i	−0.589707	−	0.807617i	$-0.700757\pi$
$241$	−1.26850	+	0.834304i	−0.0817112	+	0.0537423i	0.507996	+	0.861359i	$0.330386\pi$
$242$	7.51064			0.482802
$243$		0			0
$244$	−3.27446			−0.209626
$245$	−0.417005	+	0.274268i	−0.0266415	+	0.0175224i
$246$		0			0
$247$	4.49773	−	10.4269i	0.286183	−	0.663448i
$248$	10.5707	−	11.2043i	0.671240	−	0.711473i
$249$		0			0
$250$	−1.20044	−	0.140312i	−0.0759227	−	0.00887410i
$251$	3.80000	+	21.5509i	0.239854	+	1.36028i	0.832146	+	0.554556i	$0.187112\pi$
$251$	3.80000	+	21.5509i	0.239854	+	1.36028i	−0.592293	+	0.805723i	$0.701777\pi$
$252$		0			0
$253$	5.20296	−	29.5075i	0.327107	−	1.85512i
$254$	4.84810	−	16.1938i	0.304197	−	1.01609i
$255$		0			0
$256$	−0.420134	+	7.21342i	−0.0262584	+	0.450839i
$257$	−6.36081	+	3.19452i	−0.396776	+	0.199269i	−0.635988	−	0.771699i	$-0.719407\pi$
$257$	−6.36081	+	3.19452i	−0.396776	+	0.199269i	0.239212	+	0.970967i	$0.423111\pi$
$258$		0			0
$259$	−0.598822	−	0.634715i	−0.0372090	−	0.0394392i
$260$	−0.0467373	+	0.0170110i	−0.00289852	+	0.00105498i
$261$		0			0
$262$	−14.1770	−	5.16001i	−0.875858	−	0.318786i
$263$	−6.65013	−	15.4167i	−0.410064	−	0.950636i	−0.990649	−	0.136436i	$-0.956435\pi$
$263$	−6.65013	−	15.4167i	−0.410064	−	0.950636i	0.580584	−	0.814200i	$-0.302824\pi$
$264$		0			0
$265$	0.235663	+	0.787168i	0.0144766	+	0.0483553i
$266$	−7.21794	+	0.843656i	−0.442560	+	0.0517279i
$267$		0			0
$268$	0.0822903	+	1.41287i	0.00502668	+	0.0863047i
$269$	−10.3000	−	17.8402i	−0.628003	−	1.08773i	−0.987952	−	0.154762i	$-0.950539\pi$
$269$	−10.3000	−	17.8402i	−0.628003	−	1.08773i	0.359948	−	0.932972i	$-0.382794\pi$
$270$		0			0
$271$	−1.75375	+	3.03758i	−0.106533	+	0.184520i	−0.914363	−	0.404895i	$-0.867308\pi$
$271$	−1.75375	+	3.03758i	−0.106533	+	0.184520i	0.807831	+	0.589414i	$0.200641\pi$
$272$	−8.28125	−	4.15900i	−0.502125	−	0.252176i
$273$		0			0
$274$	−14.5874	−	19.5943i	−0.881260	−	1.18374i
$275$	−19.4021	−	4.59837i	−1.16999	−	0.277292i
$276$		0			0
$277$	−9.69997	+	13.0293i	−0.582815	+	0.782856i	−0.991540	−	0.129802i	$-0.958566\pi$
$277$	−9.69997	+	13.0293i	−0.582815	+	0.782856i	0.408725	+	0.912657i	$0.365973\pi$
$278$	−23.6190	+	19.8187i	−1.41657	+	1.18865i
$279$		0			0
$280$	−0.133947	−	0.112395i	−0.00800489	−	0.00671690i
$281$	−0.396059	+	0.0938677i	−0.0236269	+	0.00559968i	−0.242412	−	0.970173i	$-0.577939\pi$
$281$	−0.396059	+	0.0938677i	−0.0236269	+	0.00559968i	0.218785	+	0.975773i	$0.429791\pi$
$282$		0			0
$283$	−15.6157	−	10.2706i	−0.928258	−	0.610525i	−0.00721029	−	0.999974i	$-0.502295\pi$
$283$	−15.6157	−	10.2706i	−0.928258	−	0.610525i	−0.921048	+	0.389449i	$0.872665\pi$
$284$	1.42799	+	0.939202i	0.0847354	+	0.0557314i
$285$		0			0
$286$	−11.9738	+	2.83783i	−0.708023	+	0.167804i
$287$	2.86546	+	2.40441i	0.169143	+	0.141928i
$288$		0			0
$289$	−9.80441	+	8.22687i	−0.576730	+	0.483934i
$290$	−0.0802584	+	0.107806i	−0.00471293	+	0.00633057i
$291$		0			0
$292$	0.461611	+	0.109404i	0.0270137	+	0.00640237i
$293$	7.69020	+	10.3297i	0.449266	+	0.603469i	0.967841	−	0.251563i	$-0.0809446\pi$
$293$	7.69020	+	10.3297i	0.449266	+	0.603469i	−0.518575	+	0.855032i	$0.673537\pi$
$294$		0			0
$295$	0.779302	+	0.391380i	0.0453727	+	0.0227870i
$296$	−1.31248	+	2.27329i	−0.0762865	+	0.132132i
$297$		0			0
$298$	3.88361	+	6.72661i	0.224972	+	0.389662i
$299$	0.885075	+	15.1961i	0.0511852	+	0.878816i
$300$		0			0
$301$	−10.1918	+	1.19125i	−0.587445	+	0.0686625i
$302$	7.74005	+	25.8536i	0.445390	+	1.48771i
$303$		0			0
$304$	10.0243	+	23.2391i	0.574936	+	1.33285i
$305$	−0.795286	−	0.289460i	−0.0455379	−	0.0165745i
$306$		0			0
$307$	8.20971	−	2.98809i	0.468553	−	0.170539i	−0.0969439	−	0.995290i	$-0.530907\pi$
$307$	8.20971	−	2.98809i	0.468553	−	0.170539i	0.565497	+	0.824751i	$0.308685\pi$
$308$	0.721168	+	0.764393i	0.0410923	+	0.0435553i
$309$		0			0
$310$	−0.647635	+	0.325255i	−0.0367832	+	0.0184732i
$311$	1.08085	−	18.5575i	0.0612894	−	1.05230i	−0.817758	−	0.575563i	$-0.804783\pi$
$311$	1.08085	−	18.5575i	0.0612894	−	1.05230i	0.879047	−	0.476735i	$-0.158180\pi$
$312$		0			0
$313$	6.03398	−	20.1549i	0.341061	−	1.13922i	−0.599721	−	0.800209i	$-0.704722\pi$
$313$	6.03398	−	20.1549i	0.341061	−	1.13922i	0.940782	−	0.339013i	$-0.110093\pi$
$314$	−1.90391	+	10.7976i	−0.107444	+	0.609344i
$315$		0			0
$316$	0.730202	+	4.14118i	0.0410771	+	0.232960i
$317$	−16.0918	−	1.88086i	−0.903805	−	0.105640i	−0.348521	−	0.937301i	$-0.613316\pi$
$317$	−16.0918	−	1.88086i	−0.903805	−	0.105640i	−0.555283	+	0.831661i	$0.687390\pi$
$318$		0			0
$319$	−3.04516	+	3.22768i	−0.170496	+	0.180715i
$320$	−0.202355	+	0.469111i	−0.0113120	+	0.0262241i
$321$		0			0
$322$	8.13876	−	5.35295i	0.453556	−	0.298308i
$323$	−11.4740			−0.638432
$324$		0			0
$325$	10.1299			0.561903
$326$	−6.27783	+	4.12899i	−0.347697	+	0.228684i
$327$		0			0
$328$	4.45683	−	10.3321i	0.246087	−	0.570494i
$329$	3.01719	−	3.19804i	0.166343	−	0.176314i
$330$		0			0
$331$	−18.9254	−	2.21206i	−1.04023	−	0.121586i	−0.421214	−	0.906961i	$-0.638396\pi$
$331$	−18.9254	−	2.21206i	−1.04023	−	0.121586i	−0.619020	+	0.785375i	$0.712470\pi$
$332$	−0.336058	−	1.90588i	−0.0184436	−	0.104599i
$333$		0			0
$334$	−4.72799	+	26.8138i	−0.258704	+	1.46719i
$335$	−0.104911	+	0.350426i	−0.00573188	+	0.0191458i
$336$		0			0
$337$	0.635590	−	10.9127i	0.0346228	−	0.594450i	−0.935724	−	0.352733i	$-0.885252\pi$
$337$	0.635590	−	10.9127i	0.0346228	−	0.594450i	0.970347	−	0.241717i	$-0.0777106\pi$
$338$	−12.0624	+	6.05798i	−0.656110	+	0.329511i
$339$		0			0
$340$	0.0344874	+	0.0365545i	0.00187034	+	0.00198245i
$341$	−22.4848	+	8.18380i	−1.21762	+	0.443178i
$342$		0			0
$343$	−10.6553	−	3.87822i	−0.575333	−	0.209404i
$344$	12.2259	+	28.3429i	0.659179	+	1.52815i
$345$		0			0
$346$	−0.750753	−	2.50769i	−0.0403607	−	0.134814i
$347$	22.1659	−	2.59082i	1.18993	−	0.139083i	0.502004	−	0.864865i	$-0.332596\pi$
$347$	22.1659	−	2.59082i	1.18993	−	0.139083i	0.687924	+	0.725783i	$0.258522\pi$
$348$		0			0
$349$	1.35928	+	23.3379i	0.0727606	+	1.24925i	0.815137	+	0.579268i	$0.196662\pi$
$349$	1.35928	+	23.3379i	0.0727606	+	1.24925i	−0.742377	+	0.669983i	$0.766301\pi$
$350$	−3.24133	−	5.61414i	−0.173256	−	0.300088i
$351$		0			0
$352$	3.44900	−	5.97384i	0.183832	−	0.318407i
$353$	−28.4906	−	14.3085i	−1.51640	−	0.761566i	−0.520663	−	0.853763i	$-0.674315\pi$
$353$	−28.4906	−	14.3085i	−1.51640	−	0.761566i	−0.995741	+	0.0921962i	$0.970611\pi$
$354$		0			0
$355$	0.263798	+	0.354343i	0.0140010	+	0.0188066i
$356$	−3.09830	−	0.734310i	−0.164209	−	0.0389183i
$357$		0			0
$358$	−11.2059	+	15.0521i	−0.592250	+	0.795530i
$359$	8.66761	−	7.27299i	0.457459	−	0.383854i	−0.384736	−	0.923027i	$-0.625708\pi$
$359$	8.66761	−	7.27299i	0.457459	−	0.383854i	0.842195	+	0.539173i	$0.181263\pi$
$360$		0			0
$361$	9.45042	+	7.92984i	0.497391	+	0.417360i
$362$	0.0536569	−	0.0127169i	0.00282014	−	0.000668386i
$363$		0			0
$364$	−0.446054	−	0.293374i	−0.0233796	−	0.0153770i
$365$	0.102443	+	0.0673777i	0.00536210	+	0.00352671i
$366$		0			0
$367$	−0.660094	+	0.156445i	−0.0344566	+	0.00816637i	−0.247808	−	0.968809i	$-0.579710\pi$
$367$	−0.660094	+	0.156445i	−0.0344566	+	0.00816637i	0.213351	+	0.976976i	$0.431562\pi$
$368$	−25.9888	−	21.8072i	−1.35476	−	1.13678i
$369$		0			0
$370$	0.0946069	−	0.0793846i	0.00491838	−	0.00412701i
$371$	−5.26703	+	7.07485i	−0.273451	+	0.367308i
$372$		0			0
$373$	−10.8528	−	2.57217i	−0.561939	−	0.133182i	−0.0601770	−	0.998188i	$-0.519167\pi$
$373$	−10.8528	−	2.57217i	−0.561939	−	0.133182i	−0.501762	+	0.865006i	$0.667315\pi$
$374$	7.42494	+	9.97342i	0.383934	+	0.515713i
$375$		0			0
$376$	−11.8192	−	5.93583i	−0.609529	−	0.306117i
$377$	1.12717	−	1.95232i	0.0580524	−	0.100550i
$378$		0			0
$379$	−9.99112	−	17.3051i	−0.513209	−	0.888905i	−0.999883	−	0.0153206i	$-0.995123\pi$
$379$	−9.99112	−	17.3051i	−0.513209	−	0.888905i	0.486673	−	0.873584i	$-0.338210\pi$
$380$	−0.00798052	−	0.137020i	−0.000409392	−	0.00702899i
$381$		0			0
$382$	−40.0719	+	4.68374i	−2.05026	+	0.239641i
$383$	6.75310	+	22.5569i	0.345067	+	1.15260i	0.937791	+	0.347199i	$0.112867\pi$
$383$	6.75310	+	22.5569i	0.345067	+	1.15260i	−0.592724	+	0.805405i	$0.701948\pi$
$384$		0			0
$385$	0.107582	+	0.249403i	0.00548289	+	0.0127108i
$386$	0.0645715	+	0.0235021i	0.00328660	+	0.00119623i
$387$		0			0
$388$	3.97621	−	1.44722i	0.201862	−	0.0734716i
$389$	4.28568	+	4.54255i	0.217292	+	0.230317i	0.826846	−	0.562428i	$-0.190133\pi$
$389$	4.28568	+	4.54255i	0.217292	+	0.230317i	−0.609554	+	0.792745i	$0.708651\pi$
$390$		0			0
$391$	13.7446	−	6.90282i	0.695097	−	0.349091i
$392$	−0.937097	+	16.0893i	−0.0473306	+	0.812634i
$393$		0			0
$394$	−5.30796	+	17.7298i	−0.267411	+	0.893215i
$395$	−0.188730	+	1.07034i	−0.00949604	+	0.0538547i
$396$		0			0
$397$	−0.194836	−	1.10497i	−0.00977853	−	0.0554568i	0.979528	−	0.201308i	$-0.0645191\pi$
$397$	−0.194836	−	1.10497i	−0.00977853	−	0.0554568i	−0.989307	+	0.145851i	$0.953408\pi$
$398$	−18.9722	−	2.21754i	−0.950992	−	0.111155i
$399$		0			0
$400$	−15.4933	+	16.4219i	−0.774664	+	0.821096i
$401$	1.67881	−	3.89191i	0.0838356	−	0.194353i	−0.871142	−	0.491032i	$-0.836620\pi$
$401$	1.67881	−	3.89191i	0.0838356	−	0.194353i	0.954977	+	0.296679i	$0.0958791\pi$
$402$		0			0
$403$	10.1562	−	6.67985i	0.505917	−	0.332747i
$404$	−2.62938			−0.130816
$405$		0			0
$406$	−1.44268			−0.0715991
$407$	3.40676	−	2.24066i	0.168867	−	0.111065i
$408$		0			0
$409$	−0.756884	+	1.75465i	−0.0374255	+	0.0867621i	−0.935904	−	0.352256i	$-0.885414\pi$
$409$	−0.756884	+	1.75465i	−0.0374255	+	0.0867621i	0.898478	+	0.439019i	$0.144674\pi$
$410$	−0.363300	+	0.385075i	−0.0179421	+	0.0190175i
$411$		0			0
$412$	−2.51760	−	0.294265i	−0.124033	−	0.0144974i
$413$	1.62550	+	9.21867i	0.0799856	+	0.453621i
$414$		0			0
$415$	0.0868586	−	0.492600i	0.00426372	−	0.0241808i
$416$	−1.00507	+	3.35716i	−0.0492775	+	0.164598i
$417$		0			0
$418$	1.97447	−	33.9004i	0.0965745	−	1.65812i
$419$	2.21787	−	1.11386i	0.108350	−	0.0544156i	−0.393799	−	0.919197i	$-0.628839\pi$
$419$	2.21787	−	1.11386i	0.108350	−	0.0544156i	0.502149	+	0.864781i	$0.332543\pi$
$420$		0			0
$421$	−11.9853	−	12.7037i	−0.584128	−	0.619140i	0.366145	−	0.930558i	$-0.380678\pi$
$421$	−11.9853	−	12.7037i	−0.584128	−	0.619140i	−0.950273	+	0.311418i	$0.899196\pi$
$422$	−19.5941	+	7.13166i	−0.953825	+	0.347164i
$423$		0			0
$424$	24.9325	+	9.07467i	1.21083	+	0.440705i
$425$	−4.05407	−	9.39840i	−0.196651	−	0.455889i
$426$		0			0
$427$	−2.60550	−	8.70298i	−0.126089	−	0.421167i
$428$	1.79728	−	0.210072i	0.0868749	−	0.0101542i
$429$		0			0
$430$	−0.0844415	−	1.44980i	−0.00407213	−	0.0699158i
$431$	11.6850	+	20.2390i	0.562845	+	0.974877i	0.997247	+	0.0741572i	$0.0236267\pi$
$431$	11.6850	+	20.2390i	0.562845	+	0.974877i	−0.434401	+	0.900719i	$0.643040\pi$
$432$		0			0
$433$	15.2874	−	26.4785i	0.734664	−	1.27247i	−0.220207	−	0.975453i	$-0.570673\pi$
$433$	15.2874	−	26.4785i	0.734664	−	1.27247i	0.954871	−	0.297021i	$-0.0959933\pi$
$434$	−6.95185	−	3.49135i	−0.333699	−	0.167590i
$435$		0			0
$436$	1.91756	+	2.57573i	0.0918345	+	0.123355i
$437$	−40.8737	−	9.68724i	−1.95525	−	0.463404i
$438$		0			0
$439$	7.40966	−	9.95290i	0.353644	−	0.475026i	−0.589330	−	0.807892i	$-0.700608\pi$
$439$	7.40966	−	9.95290i	0.353644	−	0.475026i	0.942974	+	0.332866i	$0.108016\pi$
$440$	0.625913	−	0.525204i	0.0298392	−	0.0250381i
$441$		0			0
$442$	−4.83889	−	4.06031i	−0.230162	−	0.193129i
$443$	3.37497	−	0.799883i	0.160350	−	0.0380036i	−0.149657	−	0.988738i	$-0.547817\pi$
$443$	3.37497	−	0.799883i	0.160350	−	0.0380036i	0.310007	+	0.950734i	$0.399669\pi$
$444$		0			0
$445$	−0.687588	−	0.452234i	−0.0325948	−	0.0214379i
$446$	3.72822	+	2.45209i	0.176537	+	0.116110i
$447$		0			0
$448$	−5.33621	+	1.26471i	−0.252112	+	0.0597517i
$449$	2.37761	+	1.99505i	0.112206	+	0.0941523i	0.697165	−	0.716911i	$-0.254445\pi$
$449$	2.37761	+	1.99505i	0.112206	+	0.0941523i	−0.584958	+	0.811063i	$0.698889\pi$
$450$		0			0
$451$	−13.3898	+	11.2354i	−0.630501	+	0.529053i
$452$	−0.510093	+	0.685174i	−0.0239928	+	0.0322279i
$453$		0			0
$454$	5.86280	+	1.38951i	0.275155	+	0.0652129i
$455$	−0.0824016	−	0.110685i	−0.00386305	−	0.00518897i
$456$		0			0
$457$	31.7054	+	15.9230i	1.48312	+	0.744848i	0.991999	−	0.126246i	$-0.0402928\pi$
$457$	31.7054	+	15.9230i	1.48312	+	0.744848i	0.491116	+	0.871094i	$0.336589\pi$
$458$	7.76145	−	13.4432i	0.362669	−	0.628161i
$459$		0			0
$460$	0.0919917	+	0.159334i	0.00428913	+	0.00742900i
$461$	−1.48196	−	25.4443i	−0.0690217	−	1.18506i	−0.837959	−	0.545733i	$-0.816251\pi$
$461$	−1.48196	−	25.4443i	−0.0690217	−	1.18506i	0.768937	−	0.639324i	$-0.220786\pi$
$462$		0			0
$463$	9.25377	−	1.08161i	0.430059	−	0.0502667i	0.101690	−	0.994816i	$-0.467575\pi$
$463$	9.25377	−	1.08161i	0.430059	−	0.0502667i	0.328369	+	0.944549i	$0.393501\pi$
$464$	1.44101	+	4.81332i	0.0668974	+	0.223453i
$465$		0			0
$466$	1.53656	+	3.56214i	0.0711795	+	0.165013i
$467$	11.6612	+	4.24434i	0.539617	+	0.196404i	0.597427	−	0.801923i	$-0.296190\pi$
$467$	11.6612	+	4.24434i	0.539617	+	0.196404i	−0.0578105	+	0.998328i	$0.518412\pi$
$468$		0			0
$469$	−3.68970	+	1.34294i	−0.170375	+	0.0620113i
$470$	0.427023	+	0.452618i	0.0196971	+	0.0208777i
$471$		0			0
$472$	25.1639	−	12.6378i	1.15826	−	0.581702i
$473$	2.78797	−	47.8676i	0.128191	−	2.20095i
$474$		0			0
$475$	−8.01733	+	26.7797i	−0.367860	+	1.22874i
$476$	−0.0936749	+	0.531257i	−0.00429358	+	0.0243501i
$477$		0			0
$478$	−1.22981	−	6.97459i	−0.0562501	−	0.319010i
$479$	34.5296	+	4.03593i	1.57770	+	0.184406i	0.859390	−	0.511321i	$-0.170844\pi$
$479$	34.5296	+	4.03593i	1.57770	+	0.184406i	0.718306	+	0.695727i	$0.244918\pi$
$480$		0			0
$481$	−1.42156	+	1.50677i	−0.0648177	+	0.0687028i
$482$	0.913587	−	2.11793i	0.0416128	−	0.0964692i
$483$		0			0
$484$	−1.27217	+	0.836723i	−0.0578261	+	0.0380328i
$485$	1.09366			0.0496605
$486$		0			0
$487$	4.53564			0.205529			0.102765	−	0.994706i	$-0.467231\pi$
$487$	4.53564			0.205529			0.102765	+	0.994706i	$0.467231\pi$
$488$	−22.8323	+	15.0171i	−1.03357	+	0.679790i
$489$		0			0
$490$	0.300332	−	0.696247i	0.0135676	−	0.0314532i
$491$	−20.5553	+	21.7873i	−0.927648	+	0.983249i	−0.999900	−	0.0141374i	$-0.995500\pi$
$491$	−20.5553	+	21.7873i	−0.927648	+	0.983249i	0.0722525	+	0.997386i	$0.476981\pi$
$492$		0			0
$493$	−2.26246	−	0.264443i	−0.101896	−	0.0119099i
$494$	2.99570	+	16.9895i	0.134783	+	0.764392i
$495$		0			0
$496$	−4.70463	+	26.6813i	−0.211244	+	1.19802i
$497$	−1.35999	+	4.54269i	−0.0610040	+	0.203767i
$498$		0			0
$499$	−0.396814	+	6.81303i	−0.0177638	+	0.304993i	0.977710	+	0.209959i	$0.0673331\pi$
$499$	−0.396814	+	6.81303i	−0.0177638	+	0.304993i	−0.995474	+	0.0950342i	$0.969704\pi$
$500$	0.218966	−	0.109969i	0.00979247	−	0.00491796i
$501$		0			0
$502$	−22.8144	−	24.1818i	−1.01825	−	1.07929i
$503$	−5.01364	+	1.82482i	−0.223547	+	0.0813646i	−0.451366	−	0.892339i	$-0.649063\pi$
$503$	−5.01364	+	1.82482i	−0.223547	+	0.0813646i	0.227818	+	0.973704i	$0.426841\pi$
$504$		0			0
$505$	−0.638612	−	0.232436i	−0.0284179	−	0.0103433i
$506$	18.0294	+	41.7968i	0.801504	+	1.85809i
$507$		0			0
$508$	0.982883	+	3.28306i	0.0436084	+	0.145662i
$509$	−44.4079	+	5.19054i	−1.96834	+	0.230066i	−0.999822	−	0.0188613i	$-0.993996\pi$
$509$	−44.4079	+	5.19054i	−1.96834	+	0.230066i	−0.968522	+	0.248928i	$0.919922\pi$
$510$		0			0
$511$	0.0765284	+	1.31394i	0.00338541	+	0.0581253i
$512$	7.71639	+	13.3652i	0.341019	+	0.590663i
$513$		0			0
$514$	5.40681	−	9.36487i	0.238484	−	0.413067i
$515$	−0.585450	−	0.294024i	−0.0257980	−	0.0129563i
$516$		0			0
$517$	12.2686	+	16.4796i	0.539573	+	0.724773i
$518$	1.28995	+	0.305723i	0.0566770	+	0.0134327i
$519$		0			0
$520$	−0.247878	+	0.332958i	−0.0108702	+	0.0146012i
$521$	7.56500	−	6.34779i	0.331429	−	0.278102i	−0.461853	−	0.886956i	$-0.652815\pi$
$521$	7.56500	−	6.34779i	0.331429	−	0.278102i	0.793282	+	0.608855i	$0.208371\pi$
$522$		0			0
$523$	29.0347	+	24.3630i	1.26960	+	1.06532i	0.994590	+	0.103880i	$0.0331258\pi$
$523$	29.0347	+	24.3630i	1.26960	+	1.06532i	0.275010	+	0.961441i	$0.411319\pi$
$524$	2.97619	−	0.705371i	0.130016	−	0.0308143i
$525$		0			0
$526$	21.3111	+	14.0165i	0.929207	+	0.611149i
$527$	−10.2621	−	6.74951i	−0.447026	−	0.294013i
$528$		0			0
$529$	32.4101	−	7.68134i	1.40914	−	0.333971i
$530$	−0.956265	−	0.802402i	−0.0415375	−	0.0348541i
$531$		0			0
$532$	1.12861	−	0.947016i	0.0489314	−	0.0410583i
$533$	5.30271	−	7.12278i	0.229686	−	0.308522i
$534$		0			0
$535$	0.455086	+	0.107857i	0.0196751	+	0.00466308i
$536$	7.05339	+	9.47435i	0.304660	+	0.409230i
$537$		0			0
$538$	27.9669	+	14.0455i	1.20574	+	0.605546i
$539$	12.5176	−	21.6811i	0.539171	−	0.933871i
$540$		0			0
$541$	−22.1922	−	38.4380i	−0.954116	−	1.65258i	−0.736378	−	0.676570i	$-0.763466\pi$
$541$	−22.1922	−	38.4380i	−0.954116	−	1.65258i	−0.217737	−	0.976007i	$-0.569868\pi$
$542$	−0.309832	−	5.31960i	−0.0133084	−	0.228496i
$543$		0			0
$544$	3.51698	−	0.411077i	0.150789	−	0.0176248i
$545$	0.238036	+	0.795094i	0.0101963	+	0.0340581i
$546$		0			0
$547$	1.26392	+	2.93009i	0.0540413	+	0.125282i	0.943098	−	0.332516i	$-0.107898\pi$
$547$	1.26392	+	2.93009i	0.0540413	+	0.125282i	−0.889056	+	0.457798i	$0.848638\pi$
$548$	4.65378	+	1.69384i	0.198799	+	0.0723571i
$549$		0			0
$550$	28.4655	−	10.3606i	1.21377	−	0.441777i
$551$	4.26914	+	4.52502i	0.181871	+	0.192772i
$552$		0			0
$553$	−10.4256	+	5.23592i	−0.443340	+	0.222654i
$554$	1.43486	−	24.6356i	0.0609613	−	1.04667i
$555$		0			0
$556$	1.79276	−	5.98823i	0.0760299	−	0.253958i
$557$	−4.44633	+	25.2164i	−0.188397	+	1.06845i	0.733116	+	0.680104i	$0.238065\pi$
$557$	−4.44633	+	25.2164i	−0.188397	+	1.06845i	−0.921513	+	0.388348i	$0.873046\pi$
$558$		0			0
$559$	4.22995	+	23.9892i	0.178908	+	1.01464i
$560$	0.305466	+	0.0357038i	0.0129083	+	0.00150876i
$561$		0			0
$562$	0.424347	−	0.449782i	0.0179000	−	0.0189729i
$563$	6.05077	−	14.0273i	0.255010	−	0.591179i	−0.741833	−	0.670585i	$-0.766043\pi$
$563$	6.05077	−	14.0273i	0.255010	−	0.591179i	0.996842	+	0.0794062i	$0.0253024\pi$
$564$		0			0
$565$	−0.184458	+	0.121320i	−0.00776022	+	0.00510398i
$566$	28.3949			1.19352
$567$		0			0
$568$	14.2645			0.598523
$569$	13.4404	−	8.83989i	0.563451	−	0.370587i	−0.235601	−	0.971850i	$-0.575706\pi$
$569$	13.4404	−	8.83989i	0.563451	−	0.370587i	0.799052	+	0.601262i	$0.205335\pi$
$570$		0			0
$571$	−7.24317	+	16.7916i	−0.303117	+	0.702705i	−0.999894	−	0.0145837i	$-0.995358\pi$
$571$	−7.24317	+	16.7916i	−0.303117	+	0.702705i	0.696776	+	0.717288i	$0.254617\pi$
$572$	1.71200	−	1.81462i	0.0715824	−	0.0758729i
$573$		0			0
$574$	−5.64432	−	0.659726i	−0.235589	−	0.0275364i
$575$	−6.50690	−	36.9025i	−0.271357	−	1.53894i
$576$		0			0
$577$	1.90472	−	10.8022i	0.0792945	−	0.449702i	−0.919148	−	0.393912i	$-0.871121\pi$
$577$	1.90472	−	10.8022i	0.0792945	−	0.449702i	0.998443	−	0.0557894i	$-0.0177675\pi$
$578$	5.57659	−	18.6271i	0.231956	−	0.774786i
$579$		0			0
$580$	0.00158432	−	0.0272017i	6.57851e−5	−	0.00112949i
$581$	4.79812	−	2.40971i	0.199060	−	0.0999715i
$582$		0			0
$583$	−28.2835	−	29.9788i	−1.17138	−	1.24159i
$584$	3.72049	−	1.35415i	0.153955	−	0.0560350i
$585$		0			0
$586$	−18.3845	−	6.69140i	−0.759456	−	0.276419i
$587$	−6.21258	−	14.4024i	−0.256421	−	0.594450i	0.740569	−	0.671980i	$-0.234556\pi$
$587$	−6.21258	−	14.4024i	−0.256421	−	0.594450i	−0.996990	+	0.0775302i	$0.975297\pi$
$588$		0			0
$589$	9.62095	+	32.1362i	0.396425	+	1.32415i
$590$	−1.31589	+	0.153805i	−0.0541742	+	0.00633205i
$591$		0			0
$592$	−0.268450	−	4.60911i	−0.0110332	−	0.189433i
$593$	−20.4416	−	35.4058i	−0.839434	−	1.45394i	−0.890369	−	0.455240i	$-0.849553\pi$
$593$	−20.4416	−	35.4058i	−0.839434	−	1.45394i	0.0509346	−	0.998702i	$-0.483780\pi$
$594$		0			0
$595$	−0.0697142	+	0.120749i	−0.00285800	+	0.00495021i
$596$	−1.40720	−	0.706721i	−0.0576410	−	0.0289484i
$597$		0			0
$598$	−13.8094	−	18.5493i	−0.564710	−	0.758537i
$599$	26.3190	+	6.23772i	1.07537	+	0.254867i	0.729893	−	0.683562i	$-0.239570\pi$
$599$	26.3190	+	6.23772i	1.07537	+	0.254867i	0.345474	+	0.938428i	$0.387718\pi$
$600$		0			0
$601$	9.97163	−	13.3942i	0.406751	−	0.546362i	−0.550795	−	0.834640i	$-0.685675\pi$
$601$	9.97163	−	13.3942i	0.406751	−	0.546362i	0.957547	+	0.288279i	$0.0930829\pi$
$602$	11.9418	−	10.0203i	0.486710	−	0.408398i
$603$		0			0
$604$	−4.19125	−	3.51688i	−0.170540	−	0.143100i
$605$	−0.382946	+	0.0907599i	−0.0155690	+	0.00368992i
$606$		0			0
$607$	38.1367	+	25.0829i	1.54792	+	1.01808i	0.980930	+	0.194362i	$0.0622635\pi$
$607$	38.1367	+	25.0829i	1.54792	+	1.01808i	0.566993	+	0.823723i	$0.308107\pi$
$608$	−8.07967	−	5.31408i	−0.327674	−	0.215515i
$609$		0			0
$610$	1.25109	−	0.296513i	0.0506551	−	0.0120055i
$611$	−7.99555	−	6.70906i	−0.323465	−	0.271420i
$612$		0			0
$613$	30.0949	−	25.2526i	1.21552	−	1.01994i	0.216476	−	0.976288i	$-0.430544\pi$
$613$	30.0949	−	25.2526i	1.21552	−	1.01994i	0.999047	−	0.0436562i	$-0.0139006\pi$
$614$	−7.92591	+	10.6463i	−0.319864	+	0.429652i
$615$		0			0
$616$	8.53420	+	2.02264i	0.343853	+	0.0814946i
$617$	−1.51537	−	2.03549i	−0.0610065	−	0.0819459i	0.770573	−	0.637352i	$-0.219970\pi$
$617$	−1.51537	−	2.03549i	−0.0610065	−	0.0819459i	−0.831579	+	0.555406i	$0.812563\pi$
$618$		0			0
$619$	−10.9596	−	5.50411i	−0.440503	−	0.221229i	0.214703	−	0.976679i	$-0.431122\pi$
$619$	−10.9596	−	5.50411i	−0.440503	−	0.221229i	−0.655206	+	0.755451i	$0.727418\pi$
$620$	0.0734635	−	0.127242i	0.00295036	−	0.00511018i
$621$		0			0
$622$	14.1202	+	24.4570i	0.566170	+	0.980635i
$623$	−0.513652	−	8.81907i	−0.0205790	−	0.353329i
$624$		0			0
$625$	−24.7366	+	2.89129i	−0.989463	+	0.115652i
$626$	9.16688	+	30.6195i	0.366382	+	1.22380i
$627$		0			0
$628$	−0.880418	−	2.04104i	−0.0351325	−	0.0814463i
$629$	1.96689	+	0.715890i	0.0784251	+	0.0285444i
$630$		0			0
$631$	−38.1004	+	13.8674i	−1.51675	+	0.552053i	−0.960335	−	0.278848i	$-0.910047\pi$
$631$	−38.1004	+	13.8674i	−1.51675	+	0.552053i	−0.556419	+	0.830902i	$0.687825\pi$
$632$	24.0836	+	25.5271i	0.957993	+	1.01541i
$633$		0			0
$634$	21.9952	−	11.0464i	0.873540	−	0.438708i
$635$	−0.0515023	+	0.884261i	−0.00204381	+	0.0350908i
$636$		0			0
$637$	−3.64773	+	12.1843i	−0.144528	+	0.482758i
$638$	1.17063	−	6.63899i	0.0463458	−	0.262840i
$639$		0			0
$640$	−0.182539	−	1.03523i	−0.00721548	−	0.0409210i
$641$	29.9887	+	3.50518i	1.18448	+	0.138446i	0.685439	−	0.728130i	$-0.259610\pi$
$641$	29.9887	+	3.50518i	1.18448	+	0.138446i	0.499045	+	0.866576i	$0.333684\pi$
$642$		0			0
$643$	0.305055	−	0.323340i	0.0120302	−	0.0127513i	−0.721331	−	0.692591i	$-0.756469\pi$
$643$	0.305055	−	0.323340i	0.0120302	−	0.0127513i	0.733361	+	0.679840i	$0.237951\pi$
$644$	−0.782224	+	1.81340i	−0.0308239	+	0.0714579i
$645$		0			0
$646$	14.5638	−	9.57874i	0.573004	−	0.376871i
$647$	38.0107			1.49436			0.747178	−	0.664624i	$-0.231408\pi$
$647$	38.0107			1.49436			0.747178	+	0.664624i	$0.231408\pi$
$648$		0			0
$649$	−43.7418			−1.71702
$650$	−12.8576	+	8.45660i	−0.504318	+	0.331695i
$651$		0			0
$652$	0.603367	−	1.39876i	0.0236297	−	0.0547798i
$653$	9.27699	−	9.83304i	0.363037	−	0.384796i	−0.519948	−	0.854198i	$-0.674049\pi$
$653$	9.27699	−	9.83304i	0.363037	−	0.384796i	0.882985	+	0.469401i	$0.155530\pi$
$654$		0			0
$655$	0.785200	+	0.0917767i	0.0306803	+	0.00358601i
$656$	3.43670	+	19.4905i	0.134181	+	0.760977i
$657$		0			0
$658$	−1.15988	+	6.57802i	−0.0452169	+	0.256438i
$659$	−7.46974	+	24.9507i	−0.290980	+	0.971940i	0.680087	+	0.733132i	$0.261942\pi$
$659$	−7.46974	+	24.9507i	−0.290980	+	0.971940i	−0.971067	+	0.238809i	$0.923243\pi$
$660$		0			0
$661$	−0.139876	+	2.40158i	−0.00544055	+	0.0934106i	−0.999935	−	0.0113759i	$-0.996379\pi$
$661$	−0.139876	+	2.40158i	−0.00544055	+	0.0934106i	0.994495	+	0.104786i	$0.0334159\pi$
$662$	25.8683	−	12.9916i	1.00540	−	0.504932i
$663$		0			0
$664$	−11.0839	−	11.7482i	−0.430138	−	0.455920i
$665$	0.357828	−	0.130239i	0.0138760	−	0.00505044i
$666$		0			0
$667$	−7.83624	−	2.85216i	−0.303420	−	0.110436i
$668$	−2.18635	−	5.06853i	−0.0845924	−	0.196107i
$669$		0			0
$670$	−0.159381	−	0.532371i	−0.00615744	−	0.0205673i
$671$	42.1639	−	4.92825i	1.62772	−	0.190253i
$672$		0			0
$673$	0.766718	+	13.1640i	0.0295548	+	0.507437i	0.980306	+	0.197483i	$0.0632766\pi$
$673$	0.766718	+	13.1640i	0.0295548	+	0.507437i	−0.950752	+	0.309954i	$0.899686\pi$
$674$	8.30335	+	14.3818i	0.319833	+	0.553967i
$675$		0			0
$676$	1.36828	−	2.36994i	0.0526263	−	0.0911514i
$677$	−10.3129	−	5.17933i	−0.396357	−	0.199058i	0.239446	−	0.970910i	$-0.423034\pi$
$677$	−10.3129	−	5.17933i	−0.396357	−	0.199058i	−0.635802	+	0.771852i	$0.719331\pi$
$678$		0			0
$679$	7.01038	+	9.41658i	0.269034	+	0.361375i
$680$	0.408119	+	0.0967260i	0.0156507	+	0.00370927i
$681$		0			0
$682$	21.7076	−	29.1583i	0.831225	−	1.11653i
$683$	−7.16633	+	6.01327i	−0.274212	+	0.230091i	−0.769514	−	0.638629i	$-0.779502\pi$
$683$	−7.16633	+	6.01327i	−0.274212	+	0.230091i	0.495302	+	0.868721i	$0.335057\pi$
$684$		0			0
$685$	0.980555	+	0.822783i	0.0374651	+	0.0314369i
$686$	16.7622	−	3.97272i	0.639984	−	0.151679i
$687$		0			0
$688$	−45.3595	−	29.8334i	−1.72932	−	1.13739i
$689$	17.4938	+	11.5059i	0.666462	+	0.438339i
$690$		0			0
$691$	14.6182	−	3.46458i	0.556103	−	0.131799i	0.0570515	−	0.998371i	$-0.481830\pi$
$691$	14.6182	−	3.46458i	0.556103	−	0.131799i	0.499051	+	0.866572i	$0.333682\pi$
$692$	0.406534	+	0.341122i	0.0154541	+	0.0129675i
$693$		0			0
$694$	−25.9719	+	21.7930i	−0.985880	+	0.827251i
$695$	0.964775	−	1.29592i	0.0365960	−	0.0491569i
$696$		0			0
$697$	−8.73066	−	2.06920i	−0.330697	−	0.0783767i
$698$	−21.2083	−	28.4876i	−0.802745	−	1.07827i
$699$		0			0
$700$	1.17447	+	0.589841i	0.0443908	+	0.0222939i
$701$	−8.41328	+	14.5722i	−0.317765	+	0.550385i	−0.980021	−	0.198892i	$-0.936266\pi$
$701$	−8.41328	+	14.5722i	−0.317765	+	0.550385i	0.662256	+	0.749277i	$0.269599\pi$
$702$		0			0
$703$	−2.85826	−	4.95065i	−0.107801	−	0.186717i
$704$	−1.49002	−	25.5826i	−0.0561571	−	0.964181i
$705$		0			0
$706$	48.1077	−	5.62298i	1.81056	−	0.211624i
$707$	−2.09221	−	6.98846i	−0.0786856	−	0.262828i
$708$		0			0
$709$	3.80953	+	8.83147i	0.143070	+	0.331673i	0.974651	−	0.223730i	$-0.0718233\pi$
$709$	3.80953	+	8.83147i	0.143070	+	0.331673i	−0.831581	+	0.555403i	$0.812564\pi$
$710$	−0.630647	−	0.229537i	−0.0236677	−	0.00861435i
$711$		0			0
$712$	−24.9716	+	9.08893i	−0.935851	+	0.340622i
$713$	−30.8581	−	32.7077i	−1.15565	−	1.22491i
$714$		0			0
$715$	0.576215	−	0.289386i	0.0215492	−	0.0108224i
$716$	0.221207	−	3.79797i	0.00826688	−	0.141937i
$717$		0			0
$718$	−4.93000	+	16.4674i	−0.183986	+	0.614556i
$719$	3.87901	−	21.9989i	0.144663	−	0.820422i	−0.822975	−	0.568078i	$-0.807687\pi$
$719$	3.87901	−	21.9989i	0.144663	−	0.820422i	0.967638	−	0.252344i	$-0.0812016\pi$
$720$		0			0
$721$	−1.22116	−	6.92552i	−0.0454782	−	0.257920i
$722$	−18.6152	−	2.17581i	−0.692787	−	0.0809752i
$723$		0			0
$724$	−0.00767184	+	0.00813167i	−0.000285122	+	0.000302211i
$725$	−2.19806	+	5.09567i	−0.0816338	+	0.189248i
$726$		0			0
$727$	34.1335	−	22.4500i	1.26594	−	0.832623i	0.274300	−	0.961644i	$-0.411554\pi$
$727$	34.1335	−	22.4500i	1.26594	−	0.832623i	0.991642	+	0.129021i	$0.0411835\pi$
$728$	−4.45573			−0.165140
$729$		0			0
$730$	−0.186277			−0.00689442
$731$	20.5642	−	13.5253i	0.760593	−	0.500250i
$732$		0			0
$733$	−10.8312	+	25.1094i	−0.400058	+	0.927439i	0.592489	+	0.805578i	$0.298145\pi$
$733$	−10.8312	+	25.1094i	−0.400058	+	0.927439i	−0.992547	+	0.121860i	$0.961114\pi$
$734$	0.707241	−	0.749632i	0.0261048	−	0.0276694i
$735$		0			0
$736$	12.8755	+	1.50494i	0.474599	+	0.0554727i
$737$	−3.18607	−	18.0691i	−0.117360	−	0.665584i
$738$		0			0
$739$	−1.54918	+	8.78585i	−0.0569876	+	0.323193i	−0.999953	−	0.00969806i	$-0.996913\pi$
$739$	−1.54918	+	8.78585i	−0.0569876	+	0.323193i	0.942965	+	0.332891i	$0.108024\pi$
$740$	−0.00718097	+	0.0239861i	−0.000263978	+	0.000881746i
$741$		0			0
$742$	0.779122	−	13.3770i	0.0286025	−	0.491085i
$743$	13.7851	−	6.92316i	0.505728	−	0.253986i	−0.177593	−	0.984104i	$-0.556831\pi$
$743$	13.7851	−	6.92316i	0.505728	−	0.253986i	0.683321	+	0.730118i	$0.260535\pi$
$744$		0			0
$745$	−0.279300	−	0.296041i	−0.0102328	−	0.0108461i
$746$	15.9226	−	5.79536i	0.582968	−	0.212183i
$747$		0			0
$748$	−2.36875	−	0.862154i	−0.0866100	−	0.0315235i
$749$	1.98844	+	4.60973i	0.0726562	+	0.168436i
$750$		0			0
$751$	−8.39900	−	28.0546i	−0.306484	−	1.02373i	−0.963019	−	0.269432i	$-0.913164\pi$
$751$	−8.39900	−	28.0546i	−0.306484	−	1.02373i	0.656536	−	0.754295i	$-0.272021\pi$
$752$	23.1053	−	2.70062i	0.842563	−	0.0984815i
$753$		0			0
$754$	0.199136	+	3.41903i	0.00725211	+	0.124514i
$755$	−0.707063	−	1.22467i	−0.0257327	−	0.0445703i
$756$		0			0
$757$	−16.6330	+	28.8091i	−0.604536	+	1.04709i	0.387589	+	0.921832i	$0.373308\pi$
$757$	−16.6330	+	28.8091i	−0.604536	+	1.04709i	−0.992125	+	0.125254i	$0.960025\pi$
$758$	27.1282	+	13.6243i	0.985340	+	0.494856i
$759$		0			0
$760$	−0.684038	−	0.918823i	−0.0248127	−	0.0333292i
$761$	0.311406	+	0.0738046i	0.0112885	+	0.00267542i	0.236256	−	0.971691i	$-0.424080\pi$
$761$	0.311406	+	0.0738046i	0.0112885	+	0.00267542i	−0.224968	+	0.974366i	$0.572228\pi$
$762$		0			0
$763$	−5.32007	+	7.14609i	−0.192599	+	0.258706i
$764$	6.26572	−	5.25756i	0.226686	−	0.190212i
$765$		0			0
$766$	−27.4025	−	22.9935i	−0.990094	−	0.830787i
$767$	21.6231	−	5.12477i	0.780765	−	0.185045i
$768$		0			0
$769$	−1.73643	−	1.14207i	−0.0626173	−	0.0411841i	0.517814	−	0.855493i	$-0.326746\pi$
$769$	−1.73643	−	1.14207i	−0.0626173	−	0.0411841i	−0.580432	+	0.814309i	$0.697116\pi$
$770$	−0.344759	−	0.226751i	−0.0124242	−	0.00817155i
$771$		0			0
$772$	−0.0135556	+	0.00321273i	−0.000487876	+	0.000115629i
$773$	5.06191	+	4.24745i	0.182064	+	0.152770i	0.729265	−	0.684231i	$-0.239862\pi$
$773$	5.06191	+	4.24745i	0.182064	+	0.152770i	−0.547201	+	0.837001i	$0.684307\pi$
$774$		0			0
$775$	−22.9235	+	19.2351i	−0.823437	+	0.690945i
$776$	21.0884	−	28.3267i	0.757031	−	1.01687i
$777$		0			0
$778$	−9.23194	−	2.18801i	−0.330981	−	0.0784440i
$779$	14.6332	+	19.6558i	0.524290	+	0.704244i
$780$		0			0
$781$	−19.8012	−	9.94453i	−0.708542	−	0.355843i
$782$	−11.6832	+	20.2359i	−0.417791	+	0.723635i
$783$		0			0
$784$	−14.1733	−	24.5489i	−0.506191	−	0.876748i
$785$	−0.0334053	−	0.573547i	−0.00119229	−	0.0204708i
$786$		0			0
$787$	−3.13787	+	0.366764i	−0.111853	+	0.0130737i	−0.171835	−	0.985126i	$-0.554970\pi$
$787$	−3.13787	+	0.366764i	−0.111853	+	0.0130737i	0.0599822	+	0.998199i	$0.480896\pi$
$788$	−1.07611	−	3.59446i	−0.0383349	−	0.128047i
$789$		0			0
$790$	−0.653990	−	1.51612i	−0.0232679	−	0.0539411i
$791$	−2.22697	−	0.810550i	−0.0791818	−	0.0288198i
$792$		0			0
$793$	−20.2657	+	7.37611i	−0.719656	+	0.261933i
$794$	1.16975	+	1.23986i	0.0415129	+	0.0440011i
$795$		0			0
$796$	3.46062	−	1.73799i	0.122658	−	0.0616014i
$797$	−2.72242	+	46.7421i	−0.0964329	+	1.65569i	0.509720	+	0.860341i	$0.329749\pi$
$797$	−2.72242	+	46.7421i	−0.0964329	+	1.65569i	−0.606153	+	0.795348i	$0.707288\pi$
$798$		0			0
$799$	−3.02471	+	10.1032i	−0.107007	+	0.357427i
$800$	1.49802	−	8.49568i	0.0529629	−	0.300368i
$801$		0			0
$802$	1.11817	+	6.34143i	0.0394838	+	0.223924i
$803$	−6.10864	−	0.713998i	−0.215569	−	0.0251964i
$804$		0			0
$805$	−0.350287	+	0.371282i	−0.0123460	+	0.0130860i
$806$	−7.31463	+	16.9572i	−0.257647	+	0.597292i
$807$		0			0
$808$	−18.3343	+	12.0586i	−0.644998	+	0.424222i
$809$	−47.8251			−1.68144			−0.840721	−	0.541468i	$-0.817869\pi$
$809$	−47.8251			−1.68144			−0.840721	+	0.541468i	$0.817869\pi$
$810$		0			0
$811$	11.3948			0.400124			0.200062	−	0.979783i	$-0.435886\pi$
$811$	11.3948			0.400124			0.200062	+	0.979783i	$0.435886\pi$
$812$	0.244366	−	0.160722i	0.00857556	−	0.00564024i
$813$		0			0
$814$	−2.45359	+	5.68805i	−0.0859981	+	0.199366i
$815$	0.270193	−	0.286388i	0.00946446	−	0.0100317i
$816$		0			0
$817$	−66.7668	−	7.80393i	−2.33588	−	0.273025i
$818$	−0.504121	−	2.85901i	−0.0176262	−	0.0999630i
$819$		0			0
$820$	0.0186375	−	0.105699i	0.000650851	−	0.00369116i
$821$	4.57244	−	15.2730i	0.159579	−	0.533032i	−0.840380	−	0.541997i	$-0.817668\pi$
$821$	4.57244	−	15.2730i	0.159579	−	0.533032i	0.999960	+	0.00896476i	$0.00285361\pi$
$822$		0			0
$823$	−2.24527	+	38.5497i	−0.0782651	+	1.34376i	0.699242	+	0.714885i	$0.253521\pi$
$823$	−2.24527	+	38.5497i	−0.0782651	+	1.34376i	−0.777507	+	0.628874i	$0.783516\pi$
$824$	−18.9044	+	9.49414i	−0.658566	+	0.330744i
$825$		0			0
$826$	−9.75914	−	10.3441i	−0.339564	−	0.359917i
$827$	−32.7798	+	11.9309i	−1.13986	+	0.414877i	−0.841865	−	0.539689i	$-0.818542\pi$
$827$	−32.7798	+	11.9309i	−1.13986	+	0.414877i	−0.298000	+	0.954566i	$0.596320\pi$
$828$		0			0
$829$	25.8256	+	9.39976i	0.896961	+	0.326467i	0.749034	−	0.662531i	$-0.230518\pi$
$829$	25.8256	+	9.39976i	0.896961	+	0.326467i	0.147927	+	0.988998i	$0.452740\pi$
$830$	0.300984	+	0.697758i	0.0104473	+	0.0242196i
$831$		0			0
$832$	3.73381	+	12.4718i	0.129447	+	0.432382i
$833$	12.7643	−	1.49194i	0.442258	−	0.0516925i
$834$		0			0
$835$	−0.0829557	−	1.42429i	−0.00287080	−	0.0492897i
$836$	3.44223	+	5.96211i	0.119052	+	0.206204i
$837$		0			0
$838$	−1.88524	+	3.26532i	−0.0651244	+	0.112799i
$839$	−20.4441	−	10.2674i	−0.705808	−	0.354470i	0.0594167	−	0.998233i	$-0.481076\pi$
$839$	−20.4441	−	10.2674i	−0.705808	−	0.354470i	−0.765225	+	0.643763i	$0.777372\pi$
$840$		0			0
$841$	−16.5801	−	22.2709i	−0.571727	−	0.767963i
$842$	25.8180	+	6.11898i	0.889747	+	0.210874i
$843$		0			0
$844$	2.52440	−	3.39086i	0.0868935	−	0.116718i
$845$	0.541824	−	0.454644i	0.0186393	−	0.0156402i
$846$		0			0
$847$	−3.23615	−	2.71545i	−0.111195	−	0.0933041i
$848$	−45.4089	+	10.7621i	−1.55935	+	0.369572i
$849$		0			0
$850$	12.9917	+	8.54479i	0.445612	+	0.293084i
$851$	6.40221	+	4.21080i	0.219465	+	0.144344i
$852$		0			0
$853$	51.5093	−	12.2079i	1.76365	−	0.417992i	0.784333	−	0.620341i	$-0.213006\pi$
$853$	51.5093	−	12.2079i	1.76365	−	0.417992i	0.979314	+	0.202349i	$0.0648574\pi$
$854$	10.5725	+	8.87141i	0.361785	+	0.303573i
$855$		0			0
$856$	11.5688	−	9.70736i	0.395413	−	0.331791i
$857$	−9.39722	+	12.6227i	−0.321003	+	0.431182i	−0.933109	−	0.359594i	$-0.882915\pi$
$857$	−9.39722	+	12.6227i	−0.321003	+	0.431182i	0.612106	+	0.790776i	$0.290323\pi$
$858$		0			0
$859$	−17.4554	−	4.13700i	−0.595570	−	0.141153i	−0.0782339	−	0.996935i	$-0.524928\pi$
$859$	−17.4554	−	4.13700i	−0.595570	−	0.141153i	−0.517336	+	0.855782i	$0.673076\pi$
$860$	0.175818	+	0.236165i	0.00599536	+	0.00805317i
$861$		0			0
$862$	−31.7274	−	15.9341i	−1.08064	−	0.542717i
$863$	24.9816	−	43.2695i	0.850385	−	1.47291i	−0.0304761	−	0.999535i	$-0.509702\pi$
$863$	24.9816	−	43.2695i	0.850385	−	1.47291i	0.880861	−	0.473375i	$-0.156964\pi$
$864$		0			0
$865$	0.0685821	+	0.118788i	0.00233186	+	0.00403890i
$866$	2.70079	+	46.3708i	0.0917767	+	1.57574i
$867$		0			0
$868$	1.56648	−	0.183095i	0.0531698	−	0.00621466i
$869$	−15.6352	−	52.2254i	−0.530389	−	1.77162i
$870$		0			0
$871$	3.69195	+	8.55891i	0.125097	+	0.290008i
$872$	25.1835	+	9.16605i	0.852821	+	0.310401i
$873$		0			0
$874$	59.9673	−	21.8263i	2.02842	−	0.738286i
$875$	0.466513	+	0.494475i	0.0157710	+	0.0167163i
$876$		0			0
$877$	−7.31896	+	3.67572i	−0.247144	+	0.124120i	−0.568060	−	0.822987i	$-0.692306\pi$
$877$	−7.31896	+	3.67572i	−0.247144	+	0.124120i	0.320916	+	0.947108i	$0.396009\pi$
$878$	−1.09607	+	18.8187i	−0.0369905	+	0.635102i
$879$		0			0
$880$	−0.412167	+	1.37673i	−0.0138941	+	0.0464097i
$881$	−2.64591	+	15.0057i	−0.0891429	+	0.505555i	0.907243	+	0.420608i	$0.138183\pi$
$881$	−2.64591	+	15.0057i	−0.0891429	+	0.505555i	−0.996385	+	0.0849468i	$0.972928\pi$
$882$		0			0
$883$	−5.32760	−	30.2143i	−0.179288	−	1.01679i	−0.933077	−	0.359677i	$-0.882887\pi$
$883$	−5.32760	−	30.2143i	−0.179288	−	1.01679i	0.753789	−	0.657117i	$-0.228224\pi$
$884$	1.27196	+	0.148671i	0.0427808	+	0.00500036i
$885$		0			0
$886$	−3.61603	+	3.83277i	−0.121483	+	0.128764i
$887$	9.41627	−	21.8294i	0.316168	−	0.732959i	−0.683827	−	0.729644i	$-0.739686\pi$
$887$	9.41627	−	21.8294i	0.316168	−	0.732959i	0.999995	−	0.00331452i	$-0.00105505\pi$
$888$		0			0
$889$	−7.94375	+	5.22469i	−0.266425	+	0.175230i
$890$	1.25028			0.0419094
$891$		0			0
$892$	−0.904673			−0.0302907
$893$	24.0645	−	15.8275i	0.805288	−	0.529646i
$894$		0			0
$895$	0.389465	−	0.902880i	0.0130184	−	0.0301800i
$896$	7.74340	−	8.20753i	0.258689	−	0.274194i
$897$		0			0
$898$	−4.68336	−	0.547407i	−0.156286	−	0.0182672i
$899$	1.15642	+	6.55838i	0.0385687	+	0.218734i
$900$		0			0
$901$	3.67384	−	20.8354i	0.122393	−	0.694128i
$902$	7.61591	−	25.4389i	0.253582	−	0.847023i
$903$		0			0
$904$	−0.414516	+	7.11697i	−0.0137866	+	0.236707i
$905$	−0.00258214	+	0.00129680i	−8.58332e−5	+	4.31071e-5i
$906$		0			0
$907$	23.7090	+	25.1300i	0.787244	+	0.834429i	0.989444	−	0.144915i	$-0.0462908\pi$
$907$	23.7090	+	25.1300i	0.787244	+	0.834429i	−0.202201	+	0.979344i	$0.564809\pi$
$908$	−1.14786	+	0.417786i	−0.0380930	+	0.0138647i
$909$		0			0
$910$	0.196992	+	0.0716993i	0.00653023	+	0.00237681i
$911$	−19.8378	−	45.9892i	−0.657256	−	1.52369i	−0.841183	−	0.540751i	$-0.818140\pi$
$911$	−19.8378	−	45.9892i	−0.657256	−	1.52369i	0.183926	−	0.982940i	$-0.441119\pi$
$912$		0			0
$913$	7.19575	+	24.0355i	0.238145	+	0.795459i
$914$	−53.5359	+	6.25745i	−1.77081	+	0.206978i
$915$		0			0
$916$	0.182984	+	3.14172i	0.00604598	+	0.103805i
$917$	4.24294	+	7.34898i	0.140114	+	0.242685i
$918$		0			0
$919$	1.41443	−	2.44986i	0.0466577	−	0.0808136i	−0.841753	−	0.539862i	$-0.818476\pi$
$919$	1.41443	−	2.44986i	0.0466577	−	0.0808136i	0.888411	+	0.459049i	$0.151810\pi$
$920$	1.37217	+	0.689130i	0.0452392	+	0.0227200i
$921$		0			0
$922$	23.1224	+	31.0588i	0.761495	+	1.02287i
$923$	10.9535	+	2.59603i	0.360539	+	0.0854494i
$924$		0			0
$925$	3.04519	−	4.09040i	0.100125	−	0.134491i
$926$	−10.8427	+	9.09809i	−0.356313	+	0.298982i
$927$		0			0
$928$	−1.47068	−	1.23405i	−0.0482774	−	0.0405096i
$929$	12.0166	−	2.84797i	0.394250	−	0.0934390i	−0.0287088	−	0.999588i	$-0.509140\pi$
$929$	12.0166	−	2.84797i	0.394250	−	0.0934390i	0.422959	+	0.906149i	$0.360991\pi$
$930$		0			0
$931$	−29.3239	−	19.2866i	−0.961051	−	0.632093i
$932$	−0.657106	−	0.432186i	−0.0215242	−	0.0141567i
$933$		0			0
$934$	−18.3446	+	4.34775i	−0.600254	+	0.142263i
$935$	−0.499097	−	0.418792i	−0.0163222	−	0.0136960i
$936$		0			0
$937$	−4.94841	+	4.15221i	−0.161658	+	0.135647i	−0.720028	−	0.693945i	$-0.755871\pi$
$937$	−4.94841	+	4.15221i	−0.161658	+	0.135647i	0.558371	+	0.829592i	$0.311427\pi$
$938$	3.56216	−	4.78481i	0.116309	−	0.156229i
$939$		0			0
$940$	−0.122754	−	0.0290933i	−0.00400381	−	0.000948920i
$941$	−7.47147	−	10.0359i	−0.243563	−	0.327162i	0.663485	−	0.748190i	$-0.269077\pi$
$941$	−7.47147	−	10.0359i	−0.243563	−	0.327162i	−0.907048	+	0.421028i	$0.861669\pi$
$942$		0			0
$943$	−29.3541	−	14.7422i	−0.955900	−	0.480071i
$944$	−24.7639	+	42.8923i	−0.805995	+	1.39602i
$945$		0			0
$946$	36.4221	+	63.0849i	1.18418	+	2.05107i
$947$	2.80010	+	48.0759i	0.0909911	+	1.56226i	0.667153	+	0.744921i	$0.267513\pi$
$947$	2.80010	+	48.0759i	0.0909911	+	1.56226i	−0.576162	+	0.817336i	$0.695450\pi$
$948$		0			0
$949$	3.10337	−	0.362731i	0.100740	−	0.0117748i
$950$	−12.1800	−	40.6840i	−0.395171	−	1.31996i
$951$		0			0
$952$	1.78323	+	4.13399i	0.0577947	+	0.133983i
$953$	−23.6434	−	8.60549i	−0.765884	−	0.278759i	−0.0706105	−	0.997504i	$-0.522495\pi$
$953$	−23.6434	−	8.60549i	−0.765884	−	0.278759i	−0.695274	+	0.718745i	$0.744717\pi$
$954$		0			0
$955$	1.98656	−	0.723047i	0.0642834	−	0.0233973i
$956$	0.985313	+	1.04437i	0.0318673	+	0.0337774i
$957$		0			0
$958$	−47.1970	+	23.7032i	−1.52487	+	0.765816i
$959$	−0.798912	+	13.7168i	−0.0257982	+	0.442938i
$960$		0			0
$961$	−1.40821	+	4.70375i	−0.0454262	+	0.151734i
$962$	0.546484	−	3.09926i	0.0176193	−	0.0999242i
$963$		0			0
$964$	0.0812022	+	0.460520i	0.00261535	+	0.0148324i
$965$	−0.00357632		0.000418012i	−0.000115126		1.34563e-5i
$966$		0			0
$967$	32.3702	−	34.3105i	1.04096	−	1.10335i	0.0464244	−	0.998922i	$-0.485217\pi$
$967$	32.3702	−	34.3105i	1.04096	−	1.10335i	0.994532	−	0.104428i	$-0.0333012\pi$
$968$	−5.03339	+	11.6687i	−0.161779	+	0.375046i
$969$		0			0
$970$	−1.38816	+	0.913008i	−0.0445712	+	0.0293149i
$971$	−26.3271			−0.844876			−0.422438	−	0.906392i	$-0.638826\pi$
$971$	−26.3271			−0.844876			−0.422438	+	0.906392i	$0.638826\pi$
$972$		0			0
$973$	17.3423			0.555968
$974$	−5.75700	+	3.78644i	−0.184466	+	0.121325i
$975$		0			0
$976$	19.0380	−	44.1351i	0.609392	−	1.41273i
$977$	−11.9936	+	12.7124i	−0.383708	+	0.406707i	−0.890223	−	0.455524i	$-0.849452\pi$
$977$	−11.9936	+	12.7124i	−0.383708	+	0.406707i	0.506516	+	0.862231i	$0.330933\pi$
$978$		0			0
$979$	41.0007	+	4.79230i	1.31039	+	0.153162i
$980$	0.0266943	+	0.151391i	0.000852719	+	0.00483601i
$981$		0			0
$982$	7.90196	−	44.8142i	0.252162	−	1.43008i
$983$	−11.3960	+	38.0654i	−0.363477	+	1.21410i	0.559365	+	0.828921i	$0.311045\pi$
$983$	−11.3960	+	38.0654i	−0.363477	+	1.21410i	−0.922843	+	0.385177i	$0.874140\pi$
$984$		0			0
$985$	0.0563875	−	0.968136i	0.00179666	−	0.0308474i
$986$	3.09245	−	1.55309i	0.0984838	−	0.0494604i
$987$		0			0
$988$	−2.40013	−	2.54399i	−0.0763584	−	0.0809351i
$989$	84.6743	−	30.8189i	2.69249	−	0.979985i
$990$		0			0
$991$	−11.5059	−	4.18780i	−0.365497	−	0.133030i	0.152742	−	0.988266i	$-0.451190\pi$
$991$	−11.5059	−	4.18780i	−0.365497	−	0.133030i	−0.518238	+	0.855236i	$0.673412\pi$
$992$	−4.10032	−	9.50561i	−0.130185	−	0.301803i
$993$		0			0
$994$	−2.06611	−	6.90130i	−0.0655331	−	0.218896i
$995$	0.994138	−	0.116198i	0.0315163	−	0.00368373i
$996$		0			0
$997$	0.487030	+	8.36199i	0.0154244	+	0.264827i	0.997200	+	0.0747823i	$0.0238262\pi$
$997$	0.487030	+	8.36199i	0.0154244	+	0.264827i	−0.981775	+	0.190045i	$0.939137\pi$
$998$	−5.18398	−	8.97892i	−0.164096	−	0.284223i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.g.d.28.3		144
3.2	odd	2		729.2.g.a.28.6		144
9.2	odd	6		729.2.g.b.271.3		144
9.4	even	3		81.2.g.a.40.3	✓	144
9.5	odd	6		243.2.g.a.91.6		144
9.7	even	3		729.2.g.c.271.6		144
81.2	odd	54		729.2.g.b.460.3		144
81.25	even	27		81.2.g.a.79.3	yes	144
81.29	odd	54		729.2.g.a.703.6		144
81.32	odd	54		6561.2.a.d.1.18		72
81.49	even	27		6561.2.a.c.1.55		72
81.52	even	27	inner	729.2.g.d.703.3		144
81.56	odd	54		243.2.g.a.235.6		144
81.79	even	27		729.2.g.c.460.6		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.40.3	✓	144	9.4	even	3
81.2.g.a.79.3	yes	144	81.25	even	27
243.2.g.a.91.6		144	9.5	odd	6
243.2.g.a.235.6		144	81.56	odd	54
729.2.g.a.28.6		144	3.2	odd	2
729.2.g.a.703.6		144	81.29	odd	54
729.2.g.b.271.3		144	9.2	odd	6
729.2.g.b.460.3		144	81.2	odd	54
729.2.g.c.271.6		144	9.7	even	3
729.2.g.c.460.6		144	81.79	even	27
729.2.g.d.28.3		144	1.1	even	1	trivial
729.2.g.d.703.3		144	81.52	even	27	inner
6561.2.a.c.1.55		72	81.49	even	27
6561.2.a.d.1.18		72	81.32	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)

\(f(q)\)	\(=\)	\(q+(-1.26928 + 0.834819i) q^{2} +(0.121992 - 0.282809i) q^{4} +(0.0546290 - 0.0579033i) q^{5} +(0.848729 + 0.0992022i) q^{7} +(-0.446364 - 2.53145i) q^{8} +O(q^{10})\)	\(q+(-1.26928 + 0.834819i) q^{2} +(0.121992 - 0.282809i) q^{4} +(0.0546290 - 0.0579033i) q^{5} +(0.848729 + 0.0992022i) q^{7} +(-0.446364 - 2.53145i) q^{8} +(-0.0210007 + 0.119101i) q^{10} +(-1.14520 + 3.82522i) q^{11} +(0.117949 - 2.02511i) q^{13} +(-1.16009 + 0.582620i) q^{14} +(3.10259 + 3.28855i) q^{16} +(-1.92609 + 0.701038i) q^{17} +(5.26032 + 1.91460i) q^{19} +(-0.00971128 - 0.0225133i) q^{20} +(-1.73979 - 5.81131i) q^{22} +(-7.45312 + 0.871145i) q^{23} +(0.290356 + 4.98521i) q^{25} +(1.54089 + 2.66890i) q^{26} +(0.131593 - 0.227926i) q^{28} +(0.993107 + 0.498757i) q^{29} +(3.57847 + 4.80672i) q^{31} +(-1.68097 - 0.398397i) q^{32} +(1.85950 - 2.49775i) q^{34} +(0.0521094 - 0.0437249i) q^{35} +(-0.782274 - 0.656406i) q^{37} +(-8.27517 + 1.96125i) q^{38} +(-0.170964 - 0.112445i) q^{40} +(3.65733 + 2.40547i) q^{41} +(-11.6846 + 2.76930i) q^{43} +(0.942101 + 0.790516i) q^{44} +(8.73286 - 7.32774i) q^{46} +(3.07256 - 4.12716i) q^{47} +(-6.10081 - 1.44592i) q^{49} +(-4.53030 - 6.08524i) q^{50} +(-0.558330 - 0.280404i) q^{52} +(-5.16096 + 8.93905i) q^{53} +(0.158932 + 0.275278i) q^{55} +(-0.127716 - 2.19280i) q^{56} +(-1.67690 + 0.196002i) q^{58} +(3.14185 + 10.4945i) q^{59} +(-4.21089 - 9.76194i) q^{61} +(-8.55483 - 3.11370i) q^{62} +(-6.03074 + 2.19501i) q^{64} +(-0.110817 - 0.117459i) q^{65} +(-4.10628 + 2.06225i) q^{67} +(-0.0367070 + 0.630234i) q^{68} +(-0.0296390 + 0.0990011i) q^{70} +(-0.963622 + 5.46497i) q^{71} +(0.267464 + 1.51686i) q^{73} +(1.54091 + 0.180106i) q^{74} +(1.18318 - 1.25410i) q^{76} +(-1.35143 + 3.13297i) q^{77} +(-11.4068 + 7.50239i) q^{79} +0.359909 q^{80} -6.65031 q^{82} +(5.24973 - 3.45280i) q^{83} +(-0.0646276 + 0.149824i) q^{85} +(12.5192 - 13.2696i) q^{86} +(10.1945 + 1.19157i) q^{88} +(-1.79520 - 10.1811i) q^{89} +(0.301002 - 1.70707i) q^{91} +(-0.662852 + 2.21408i) q^{92} +(-0.454506 + 7.80356i) q^{94} +(0.398228 - 0.199997i) q^{95} +(9.42786 + 9.99295i) q^{97} +(8.95073 - 3.25780i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8}+O(q^{10}) \) 144 * q + 9 * q^2 + 9 * q^4 + 9 * q^5 + 9 * q^7 - 18 * q^8	\( 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8} - 18 q^{10} + 9 q^{11} + 9 q^{13} + 9 q^{14} + 9 q^{16} - 18 q^{17} - 18 q^{19} + 45 q^{20} + 9 q^{22} - 45 q^{23} + 9 q^{25} + 45 q^{26} - 9 q^{28} + 36 q^{29} + 9 q^{31} - 99 q^{32} + 9 q^{34} + 9 q^{35} - 18 q^{37} + 18 q^{38} + 9 q^{40} + 27 q^{41} + 9 q^{43} + 54 q^{44} - 18 q^{46} - 99 q^{47} + 9 q^{49} + 126 q^{50} - 27 q^{52} + 45 q^{53} - 9 q^{55} - 225 q^{56} + 9 q^{58} + 72 q^{59} + 9 q^{61} + 81 q^{62} - 18 q^{64} - 81 q^{65} - 45 q^{67} + 117 q^{68} - 99 q^{70} - 90 q^{71} - 18 q^{73} + 81 q^{74} - 153 q^{76} + 81 q^{77} - 99 q^{79} - 288 q^{80} - 36 q^{82} + 45 q^{83} - 99 q^{85} + 81 q^{86} - 153 q^{88} - 81 q^{89} - 18 q^{91} + 207 q^{92} - 99 q^{94} - 171 q^{95} - 45 q^{97} + 81 q^{98}+O(q^{100}) \) 144 * q + 9 * q^2 + 9 * q^4 + 9 * q^5 + 9 * q^7 - 18 * q^8 - 18 * q^10 + 9 * q^11 + 9 * q^13 + 9 * q^14 + 9 * q^16 - 18 * q^17 - 18 * q^19 + 45 * q^20 + 9 * q^22 - 45 * q^23 + 9 * q^25 + 45 * q^26 - 9 * q^28 + 36 * q^29 + 9 * q^31 - 99 * q^32 + 9 * q^34 + 9 * q^35 - 18 * q^37 + 18 * q^38 + 9 * q^40 + 27 * q^41 + 9 * q^43 + 54 * q^44 - 18 * q^46 - 99 * q^47 + 9 * q^49 + 126 * q^50 - 27 * q^52 + 45 * q^53 - 9 * q^55 - 225 * q^56 + 9 * q^58 + 72 * q^59 + 9 * q^61 + 81 * q^62 - 18 * q^64 - 81 * q^65 - 45 * q^67 + 117 * q^68 - 99 * q^70 - 90 * q^71 - 18 * q^73 + 81 * q^74 - 153 * q^76 + 81 * q^77 - 99 * q^79 - 288 * q^80 - 36 * q^82 + 45 * q^83 - 99 * q^85 + 81 * q^86 - 153 * q^88 - 81 * q^89 - 18 * q^91 + 207 * q^92 - 99 * q^94 - 171 * q^95 - 45 * q^97 + 81 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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