LMFDB - Embedded newform 729.2.g.a.703.6

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			703.6
Character	$\chi$	$=$	729.703
Dual form			729.2.g.a.28.6

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

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{27}\right)$

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	$-0.134326\pi$
$2$	1.26928	+	0.834819i	0.897517	+	0.590306i	−0.0147548	+	0.999891i	$0.504697\pi$
$3$		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	$-0.246407\pi$
$5$	−0.0546290	−	0.0579033i	−0.0244308	−	0.0258952i	−0.739474	+	0.673185i	$0.764926\pi$
$6$		0			0
$7$	0.848729	−	0.0992022i	0.320790	−	0.0374949i	0.0458256	−	0.998949i	$-0.485408\pi$
$7$	0.848729	−	0.0992022i	0.320790	−	0.0374949i	0.274964	+	0.961455i	$0.411334\pi$
$8$	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	0.937623	+	0.347654i	$0.113022\pi$
$11$	1.14520	+	3.82522i	0.345289	+	1.15335i	−0.592333	+	0.805693i	$0.701793\pi$
$12$		0			0
$13$	0.117949	+	2.02511i	0.0327132	+	0.561664i	0.974351	+	0.225035i	$0.0722498\pi$
$13$	0.117949	+	2.02511i	0.0327132	+	0.561664i	−0.941637	+	0.336629i	$0.890713\pi$
$14$	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	$-0.308931\pi$
$17$	1.92609	+	0.701038i	0.467144	+	0.170027i	−0.0977140	+	0.995215i	$0.531153\pi$
$18$		0			0
$19$	5.26032	−	1.91460i	1.20680	−	0.439239i	0.341207	−	0.939988i	$-0.389164\pi$
$19$	5.26032	−	1.91460i	1.20680	−	0.439239i	0.865593	+	0.500749i	$0.166942\pi$
$20$	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	$-0.176993\pi$
$23$	7.45312	+	0.871145i	1.55408	+	0.181646i	0.704732	+	0.709474i	$0.251067\pi$
$24$		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	$-0.681051\pi$
$29$	−0.993107	+	0.498757i	−0.184415	+	0.0926169i	0.354196	+	0.935171i	$0.384755\pi$
$30$		0			0
$31$	3.57847	−	4.80672i	0.642712	−	0.863313i	−0.354717	−	0.934974i	$-0.615423\pi$
$31$	3.57847	−	4.80672i	0.642712	−	0.863313i	0.997429	+	0.0716613i	$0.0228301\pi$
$32$	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	−0.704822	−	0.709385i	$-0.748973\pi$
$37$	−0.782274	+	0.656406i	−0.128605	+	0.107913i	0.576216	+	0.817297i	$0.304529\pi$
$38$	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	$-0.796230\pi$
$41$	−3.65733	+	2.40547i	−0.571180	+	0.375671i	0.230819	+	0.972997i	$0.425859\pi$
$42$		0			0
$43$	−11.6846	−	2.76930i	−1.78189	−	0.422315i	−0.798227	−	0.602357i	$-0.794228\pi$
$43$	−11.6846	−	2.76930i	−1.78189	−	0.422315i	−0.983659	+	0.180043i	$0.942376\pi$
$44$	−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	$-0.326150\pi$
$47$	−3.07256	−	4.12716i	−0.448179	−	0.602008i	−0.967593	+	0.252514i	$0.918743\pi$
$48$		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	0.965261	+	0.261288i	$0.0841473\pi$
$53$	5.16096	+	8.93905i	0.708913	+	1.22787i	−0.256348	+	0.966584i	$0.582519\pi$
$54$		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	0.467102	+	0.884203i	$0.345298\pi$
$59$	−3.14185	+	10.4945i	−0.409034	+	1.36627i	−0.876136	+	0.482064i	$0.839887\pi$
$60$		0			0
$61$	−4.21089	+	9.76194i	−0.539149	+	1.24989i	0.403155	+	0.915132i	$0.367914\pi$
$61$	−4.21089	+	9.76194i	−0.539149	+	1.24989i	−0.942304	+	0.334757i	$0.891346\pi$
$62$	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	0.179926	−	0.983680i	$-0.442414\pi$
$67$	−4.10628	−	2.06225i	−0.501662	−	0.251944i	−0.681588	+	0.731736i	$0.738710\pi$
$68$	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	0.987065	+	0.160323i	$0.0512535\pi$
$71$	0.963622	+	5.46497i	0.114361	+	0.648573i	−0.872704	+	0.488250i	$0.837635\pi$
$72$		0			0
$73$	0.267464	−	1.51686i	0.0313043	−	0.177536i	−0.965147	−	0.261709i	$-0.915714\pi$
$73$	0.267464	−	1.51686i	0.0313043	−	0.177536i	0.996451	+	0.0841735i	$0.0268250\pi$
$74$	−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	−0.289775	−	0.957095i	$-0.593581\pi$
$79$	−11.4068	−	7.50239i	−1.28337	−	0.844085i	−0.993594	+	0.113009i	$0.963951\pi$
$80$	−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	$-0.426884\pi$
$83$	−5.24973	−	3.45280i	−0.576232	−	0.378994i	−0.803917	+	0.594741i	$0.797255\pi$
$84$		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	−0.728676	−	0.684858i	$-0.759864\pi$
$89$	1.79520	−	10.1811i	0.190291	−	1.07919i	0.918967	−	0.394334i	$-0.129025\pi$
$90$		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	−0.0426250	−	0.999091i	$-0.513572\pi$
$97$	9.42786	−	9.99295i	0.957254	−	1.01463i	0.999879	−	0.0155391i	$-0.00494645\pi$
$98$	−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	−0.663051	−	0.748574i	$-0.730739\pi$
$101$	3.38133	−	7.83881i	0.336455	−	0.779991i	0.999506	−	0.0314167i	$-0.0100019\pi$
$102$		0			0
$103$	−2.36031	+	7.88398i	−0.232568	+	0.776832i	0.759431	+	0.650588i	$0.225477\pi$
$103$	−2.36031	+	7.88398i	−0.232568	+	0.776832i	−0.991999	+	0.126244i	$0.959708\pi$
$104$	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	$-0.924989\pi$
$107$	−2.93755	+	5.08798i	−0.283984	+	0.491874i	0.688379	+	0.725352i	$0.258323\pi$
$108$		0			0
$109$	−5.21293	−	9.02906i	−0.499308	−	0.864827i	0.500692	−	0.865626i	$-0.333079\pi$
$109$	−5.21293	−	9.02906i	−0.499308	−	0.864827i	−1.00000		0.000798944i	$0.999746\pi$
$110$	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	$-0.532432\pi$
$113$	2.69864	−	0.639589i	0.253867	−	0.0601675i	0.355579	+	0.934646i	$0.384284\pi$
$114$		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	0.180825	−	0.983515i	$-0.442123\pi$
$127$	−8.52362	−	7.15216i	−0.756349	−	0.634652i	−0.937174	+	0.348863i	$0.886568\pi$
$128$	−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	$-0.939133\pi$
$131$	−5.93022	+	7.96566i	−0.518125	+	0.695963i	0.463648	+	0.886020i	$0.346540\pi$
$132$		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	0.685601	+	0.727977i	$0.259539\pi$
$137$	−0.934938	+	16.0523i	−0.0798772	+	1.37144i	−0.765479	+	0.643461i	$0.777498\pi$
$138$		0			0
$139$	20.1578	+	2.35611i	1.70976	+	0.199843i	0.913986	−	0.405745i	$-0.132988\pi$
$139$	20.1578	+	2.35611i	1.70976	+	0.199843i	0.795778	+	0.605588i	$0.207062\pi$
$140$	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	−0.988348	−	0.152213i	$-0.951360\pi$
$149$	−0.297275	−	5.10402i	−0.0243538	−	0.418138i	0.963994	−	0.265924i	$-0.0856772\pi$
$150$		0			0
$151$	5.09479	+	17.0178i	0.414608	+	1.38489i	0.869320	+	0.494249i	$0.164557\pi$
$151$	5.09479	+	17.0178i	0.414608	+	1.38489i	−0.454712	+	0.890638i	$0.650258\pi$
$152$	−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	0.894188	−	0.447691i	$-0.147754\pi$
$157$	4.95262	+	5.24948i	0.395262	+	0.418954i	−0.498926	+	0.866645i	$0.666272\pi$
$158$	−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	−0.999951	−	0.00992510i	$-0.996841\pi$
$167$	−12.2989	−	13.0361i	−0.951717	−	1.00876i	0.0482337	−	0.998836i	$-0.484641\pi$
$168$		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	$-0.0717283\pi$
$173$	0.494173	+	1.65065i	0.0375713	+	0.125497i	−0.937147	+	0.348936i	$0.886543\pi$
$174$		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	$-0.541620\pi$
$179$	−11.6071	−	4.22465i	−0.867558	−	0.315765i	−0.737178	+	0.675699i	$0.763842\pi$
$180$		0			0
$181$	−0.0341083	+	0.0124144i	−0.00253525	+	0.000922757i	−0.343287	−	0.939230i	$-0.611541\pi$
$181$	−0.0341083	+	0.0124144i	−0.00253525	+	0.000922757i	0.340752	+	0.940153i	$0.389318\pi$
$182$	−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	−0.734118	+	0.679021i	$0.762404\pi$
$191$	−23.7317	+	11.9185i	−1.71716	+	0.862391i	−0.983044	+	0.183370i	$0.941299\pi$
$192$		0			0
$193$	−0.0270102	+	0.0362809i	−0.00194423	+	0.00261156i	−0.803094	−	0.595852i	$-0.796814\pi$
$193$	−0.0270102	+	0.0362809i	−0.00194423	+	0.00261156i	0.801150	+	0.598464i	$0.204222\pi$
$194$	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	$-0.420666\pi$
$197$	−9.33211	−	7.83057i	−0.664885	−	0.557905i	−0.911547	+	0.411197i	$0.865111\pi$
$198$		0			0
$199$	9.63166	−	8.08192i	0.682770	−	0.572912i	−0.234044	−	0.972226i	$-0.575196\pi$
$199$	9.63166	−	8.08192i	0.682770	−	0.572912i	0.916814	+	0.399314i	$0.130752\pi$
$200$	−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	0.256453	−	0.966557i	$-0.417446\pi$
$211$	13.3553	−	3.16527i	0.919418	−	0.217906i	0.662965	+	0.748651i	$0.269298\pi$
$212$	−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	−0.952718	−	0.303856i	$-0.901726\pi$
$223$	−1.16339	+	2.69705i	−0.0779066	+	0.180608i	0.874811	+	0.484464i	$0.160985\pi$
$224$	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	$-0.717242\pi$
$227$	2.72165	−	2.88478i	0.180642	−	0.191469i	0.811367	+	0.584537i	$0.198724\pi$
$228$		0			0
$229$	−9.13092	−	4.58572i	−0.603388	−	0.303033i	0.120755	−	0.992682i	$-0.461468\pi$
$229$	−9.13092	−	4.58572i	−0.603388	−	0.303033i	−0.724143	+	0.689649i	$0.757765\pi$
$230$	−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	$-0.0822117\pi$
$233$	−0.443423	−	2.51478i	−0.0290496	−	0.164748i	−0.995881	+	0.0906654i	$0.971101\pi$
$234$		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	$-0.0814537\pi$
$239$	1.84643	+	4.28050i	0.119435	+	0.276883i	−0.848002	+	0.529993i	$0.822194\pi$
$240$		0			0
$241$	−1.26850	−	0.834304i	−0.0817112	−	0.0537423i	0.507996	−	0.861359i	$-0.330386\pi$
$241$	−1.26850	−	0.834304i	−0.0817112	−	0.0537423i	−0.589707	+	0.807617i	$0.700757\pi$
$242$	−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	0.592293	+	0.805723i	$0.298223\pi$
$251$	−3.80000	+	21.5509i	−0.239854	+	1.36028i	−0.832146	+	0.554556i	$0.812888\pi$
$252$		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	$-0.280593\pi$
$257$	6.36081	+	3.19452i	0.396776	+	0.199269i	−0.239212	+	0.970967i	$0.576889\pi$
$258$		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	−0.580584	−	0.814200i	$-0.697176\pi$
$263$	6.65013	−	15.4167i	0.410064	−	0.950636i	0.990649	−	0.136436i	$-0.0435649\pi$
$264$		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	−0.359948	−	0.932972i	$-0.617206\pi$
$269$	10.3000	−	17.8402i	0.628003	−	1.08773i	0.987952	−	0.154762i	$-0.0494610\pi$
$270$		0			0
$271$	−1.75375	−	3.03758i	−0.106533	−	0.184520i	0.807831	−	0.589414i	$-0.200641\pi$
$271$	−1.75375	−	3.03758i	−0.106533	−	0.184520i	−0.914363	+	0.404895i	$0.867308\pi$
$272$	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	0.408725	−	0.912657i	$-0.365973\pi$
$277$	−9.69997	−	13.0293i	−0.582815	−	0.782856i	−0.991540	+	0.129802i	$0.958566\pi$
$278$	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	$-0.422061\pi$
$281$	0.396059	+	0.0938677i	0.0236269	+	0.00559968i	−0.218785	+	0.975773i	$0.570209\pi$
$282$		0			0
$283$	−15.6157	+	10.2706i	−0.928258	+	0.610525i	−0.921048	−	0.389449i	$-0.872665\pi$
$283$	−15.6157	+	10.2706i	−0.928258	+	0.610525i	−0.00721029	+	0.999974i	$0.502295\pi$
$284$	−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	$-0.919055\pi$
$293$	−7.69020	+	10.3297i	−0.449266	+	0.603469i	0.518575	+	0.855032i	$0.326463\pi$
$294$		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	0.565497	−	0.824751i	$-0.308685\pi$
$307$	8.20971	+	2.98809i	0.468553	+	0.170539i	−0.0969439	+	0.995290i	$0.530907\pi$
$308$	−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	−0.879047	−	0.476735i	$-0.841820\pi$
$311$	−1.08085	−	18.5575i	−0.0612894	−	1.05230i	0.817758	−	0.575563i	$-0.195217\pi$
$312$		0			0
$313$	6.03398	+	20.1549i	0.341061	+	1.13922i	0.940782	+	0.339013i	$0.110093\pi$
$313$	6.03398	+	20.1549i	0.341061	+	1.13922i	−0.599721	+	0.800209i	$0.704722\pi$
$314$	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	$-0.386684\pi$
$317$	16.0918	−	1.88086i	0.903805	−	0.105640i	0.555283	+	0.831661i	$0.312610\pi$
$318$		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	−0.619020	−	0.785375i	$-0.712470\pi$
$331$	−18.9254	+	2.21206i	−1.04023	+	0.121586i	−0.421214	+	0.906961i	$0.638396\pi$
$332$	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	0.970347	+	0.241717i	$0.0777106\pi$
$337$	0.635590	+	10.9127i	0.0346228	+	0.594450i	−0.935724	+	0.352733i	$0.885252\pi$
$338$	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	$-0.667404\pi$
$347$	−22.1659	−	2.59082i	−1.18993	−	0.139083i	−0.687924	+	0.725783i	$0.741478\pi$
$348$		0			0
$349$	1.35928	−	23.3379i	0.0727606	−	1.24925i	−0.742377	−	0.669983i	$-0.766301\pi$
$349$	1.35928	−	23.3379i	0.0727606	−	1.24925i	0.815137	−	0.579268i	$-0.196662\pi$
$350$	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	$-0.325685\pi$
$353$	28.4906	−	14.3085i	1.51640	−	0.761566i	0.995741	+	0.0921962i	$0.0293887\pi$
$354$		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	$-0.374292\pi$
$359$	−8.66761	−	7.27299i	−0.457459	−	0.383854i	−0.842195	+	0.539173i	$0.818737\pi$
$360$		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	0.213351	−	0.976976i	$-0.431562\pi$
$367$	−0.660094	−	0.156445i	−0.0344566	−	0.00816637i	−0.247808	+	0.968809i	$0.579710\pi$
$368$	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	−0.501762	−	0.865006i	$-0.667315\pi$
$373$	−10.8528	+	2.57217i	−0.561939	+	0.133182i	−0.0601770	+	0.998188i	$0.519167\pi$
$374$	−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	0.486673	+	0.873584i	$0.338210\pi$
$379$	−9.99112	+	17.3051i	−0.513209	+	0.888905i	−0.999883	+	0.0153206i	$0.995123\pi$
$380$	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	0.592724	+	0.805405i	$0.298052\pi$
$383$	−6.75310	+	22.5569i	−0.345067	+	1.15260i	−0.937791	+	0.347199i	$0.887133\pi$
$384$		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	$-0.809867\pi$
$389$	−4.28568	+	4.54255i	−0.217292	+	0.230317i	0.609554	+	0.792745i	$0.291349\pi$
$390$		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	−0.989307	−	0.145851i	$-0.953408\pi$
$397$	−0.194836	+	1.10497i	−0.00977853	+	0.0554568i	0.979528	+	0.201308i	$0.0645191\pi$
$398$	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	$-0.163380\pi$
$401$	−1.67881	−	3.89191i	−0.0838356	−	0.194353i	−0.954977	+	0.296679i	$0.904121\pi$
$402$		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	0.898478	−	0.439019i	$-0.144674\pi$
$409$	−0.756884	−	1.75465i	−0.0374255	−	0.0867621i	−0.935904	+	0.352256i	$0.885414\pi$
$410$	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	$-0.371161\pi$
$419$	−2.21787	−	1.11386i	−0.108350	−	0.0544156i	−0.502149	+	0.864781i	$0.667457\pi$
$420$		0			0
$421$	−11.9853	+	12.7037i	−0.584128	+	0.619140i	−0.950273	−	0.311418i	$-0.899196\pi$
$421$	−11.9853	+	12.7037i	−0.584128	+	0.619140i	0.366145	+	0.930558i	$0.380678\pi$
$422$	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	0.434401	+	0.900719i	$0.356960\pi$
$431$	−11.6850	+	20.2390i	−0.562845	+	0.974877i	−0.997247	+	0.0741572i	$0.976373\pi$
$432$		0			0
$433$	15.2874	+	26.4785i	0.734664	+	1.27247i	0.954871	+	0.297021i	$0.0959933\pi$
$433$	15.2874	+	26.4785i	0.734664	+	1.27247i	−0.220207	+	0.975453i	$0.570673\pi$
$434$	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	0.942974	−	0.332866i	$-0.108016\pi$
$439$	7.40966	+	9.95290i	0.353644	+	0.475026i	−0.589330	+	0.807892i	$0.700608\pi$
$440$	−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	$-0.452183\pi$
$443$	−3.37497	−	0.799883i	−0.160350	−	0.0380036i	−0.310007	+	0.950734i	$0.600331\pi$
$444$		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	$-0.745555\pi$
$449$	−2.37761	+	1.99505i	−0.112206	+	0.0941523i	0.584958	+	0.811063i	$0.301111\pi$
$450$		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	0.491116	−	0.871094i	$-0.336589\pi$
$457$	31.7054	−	15.9230i	1.48312	−	0.744848i	0.991999	+	0.126246i	$0.0402928\pi$
$458$	−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	−0.768937	−	0.639324i	$-0.779214\pi$
$461$	1.48196	−	25.4443i	0.0690217	−	1.18506i	0.837959	−	0.545733i	$-0.183749\pi$
$462$		0			0
$463$	9.25377	+	1.08161i	0.430059	+	0.0502667i	0.328369	−	0.944549i	$-0.393501\pi$
$463$	9.25377	+	1.08161i	0.430059	+	0.0502667i	0.101690	+	0.994816i	$0.467575\pi$
$464$	−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	$-0.703810\pi$
$467$	−11.6612	+	4.24434i	−0.539617	+	0.196404i	0.0578105	+	0.998328i	$0.481588\pi$
$468$		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	$-0.829156\pi$
$479$	−34.5296	+	4.03593i	−1.57770	+	0.184406i	−0.718306	+	0.695727i	$0.755082\pi$
$480$		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	$-0.00450023\pi$
$491$	20.5553	+	21.7873i	0.927648	+	0.983249i	−0.0722525	+	0.997386i	$0.523019\pi$
$492$		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	−0.995474	−	0.0950342i	$-0.969704\pi$
$499$	−0.396814	−	6.81303i	−0.0177638	−	0.304993i	0.977710	−	0.209959i	$-0.0673331\pi$
$500$	−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	$-0.350937\pi$
$503$	5.01364	+	1.82482i	0.223547	+	0.0813646i	−0.227818	+	0.973704i	$0.573159\pi$
$504$		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	$-0.00600410\pi$
$509$	44.4079	+	5.19054i	1.96834	+	0.230066i	0.968522	+	0.248928i	$0.0800782\pi$
$510$		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	$-0.347185\pi$
$521$	−7.56500	−	6.34779i	−0.331429	−	0.278102i	−0.793282	+	0.608855i	$0.791629\pi$
$522$		0			0
$523$	29.0347	−	24.3630i	1.26960	−	1.06532i	0.275010	−	0.961441i	$-0.411319\pi$
$523$	29.0347	−	24.3630i	1.26960	−	1.06532i	0.994590	−	0.103880i	$-0.0331258\pi$
$524$	−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	−0.217737	+	0.976007i	$0.569868\pi$
$541$	−22.1922	+	38.4380i	−0.954116	+	1.65258i	−0.736378	+	0.676570i	$0.763466\pi$
$542$	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	−0.889056	−	0.457798i	$-0.848638\pi$
$547$	1.26392	−	2.93009i	0.0540413	−	0.125282i	0.943098	+	0.332516i	$0.107898\pi$
$548$	−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	0.921513	+	0.388348i	$0.126954\pi$
$557$	4.44633	+	25.2164i	0.188397	+	1.06845i	−0.733116	+	0.680104i	$0.761935\pi$
$558$		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	$-0.233957\pi$
$563$	−6.05077	−	14.0273i	−0.255010	−	0.591179i	−0.996842	+	0.0794062i	$0.974698\pi$
$564$		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	$-0.424294\pi$
$569$	−13.4404	−	8.83989i	−0.563451	−	0.370587i	−0.799052	+	0.601262i	$0.794665\pi$
$570$		0			0
$571$	−7.24317	−	16.7916i	−0.303117	−	0.702705i	0.696776	−	0.717288i	$-0.254617\pi$
$571$	−7.24317	−	16.7916i	−0.303117	−	0.702705i	−0.999894	+	0.0145837i	$0.995358\pi$
$572$	−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	0.998443	+	0.0557894i	$0.0177675\pi$
$577$	1.90472	+	10.8022i	0.0792945	+	0.449702i	−0.919148	+	0.393912i	$0.871121\pi$
$578$	−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	$-0.765444\pi$
$587$	6.21258	−	14.4024i	0.256421	−	0.594450i	0.996990	+	0.0775302i	$0.0247034\pi$
$588$		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	−0.0509346	−	0.998702i	$-0.516220\pi$
$593$	20.4416	−	35.4058i	0.839434	−	1.45394i	0.890369	−	0.455240i	$-0.150447\pi$
$594$		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	$-0.760430\pi$
$599$	−26.3190	+	6.23772i	−1.07537	+	0.254867i	−0.345474	+	0.938428i	$0.612282\pi$
$600$		0			0
$601$	9.97163	+	13.3942i	0.406751	+	0.546362i	0.957547	−	0.288279i	$-0.0930829\pi$
$601$	9.97163	+	13.3942i	0.406751	+	0.546362i	−0.550795	+	0.834640i	$0.685675\pi$
$602$	−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	0.566993	−	0.823723i	$-0.308107\pi$
$607$	38.1367	−	25.0829i	1.54792	−	1.01808i	0.980930	−	0.194362i	$-0.0622635\pi$
$608$	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	0.999047	+	0.0436562i	$0.0139006\pi$
$613$	30.0949	+	25.2526i	1.21552	+	1.01994i	0.216476	+	0.976288i	$0.430544\pi$
$614$	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	$-0.780030\pi$
$617$	1.51537	−	2.03549i	0.0610065	−	0.0819459i	0.831579	+	0.555406i	$0.187437\pi$
$618$		0			0
$619$	−10.9596	+	5.50411i	−0.440503	+	0.221229i	−0.655206	−	0.755451i	$-0.727418\pi$
$619$	−10.9596	+	5.50411i	−0.440503	+	0.221229i	0.214703	+	0.976679i	$0.431122\pi$
$620$	−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	−0.556419	−	0.830902i	$-0.687825\pi$
$631$	−38.1004	−	13.8674i	−1.51675	−	0.552053i	−0.960335	+	0.278848i	$0.910047\pi$
$632$	−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	$-0.740390\pi$
$641$	−29.9887	+	3.50518i	−1.18448	+	0.138446i	−0.499045	+	0.866576i	$0.666316\pi$
$642$		0			0
$643$	0.305055	+	0.323340i	0.0120302	+	0.0127513i	0.733361	−	0.679840i	$-0.237951\pi$
$643$	0.305055	+	0.323340i	0.0120302	+	0.0127513i	−0.721331	+	0.692591i	$0.756469\pi$
$644$	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	$-0.768592\pi$
$647$	−38.0107			−1.49436			−0.747178	+	0.664624i	$0.768592\pi$
$648$		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	$-0.325951\pi$
$653$	−9.27699	−	9.83304i	−0.363037	−	0.384796i	−0.882985	+	0.469401i	$0.844470\pi$
$654$		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	0.971067	+	0.238809i	$0.0767569\pi$
$659$	7.46974	+	24.9507i	0.290980	+	0.971940i	−0.680087	+	0.733132i	$0.738058\pi$
$660$		0			0
$661$	−0.139876	−	2.40158i	−0.00544055	−	0.0934106i	0.994495	−	0.104786i	$-0.0334159\pi$
$661$	−0.139876	−	2.40158i	−0.00544055	−	0.0934106i	−0.999935	+	0.0113759i	$0.996379\pi$
$662$	−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	−0.950752	−	0.309954i	$-0.899686\pi$
$673$	0.766718	−	13.1640i	0.0295548	−	0.507437i	0.980306	−	0.197483i	$-0.0632766\pi$
$674$	−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	$-0.576966\pi$
$677$	10.3129	−	5.17933i	0.396357	−	0.199058i	0.635802	+	0.771852i	$0.280669\pi$
$678$		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	$-0.220498\pi$
$683$	7.16633	+	6.01327i	0.274212	+	0.230091i	−0.495302	+	0.868721i	$0.664943\pi$
$684$		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	0.499051	−	0.866572i	$-0.333682\pi$
$691$	14.6182	+	3.46458i	0.556103	+	0.131799i	0.0570515	+	0.998371i	$0.481830\pi$
$692$	−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	$-0.0637343\pi$
$701$	8.41328	+	14.5722i	0.317765	+	0.550385i	−0.662256	+	0.749277i	$0.730401\pi$
$702$		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	−0.831581	−	0.555403i	$-0.812564\pi$
$709$	3.80953	−	8.83147i	0.143070	−	0.331673i	0.974651	+	0.223730i	$0.0718233\pi$
$710$	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	−0.967638	−	0.252344i	$-0.918798\pi$
$719$	−3.87901	−	21.9989i	−0.144663	−	0.820422i	0.822975	−	0.568078i	$-0.192313\pi$
$720$		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	0.991642	−	0.129021i	$-0.0411835\pi$
$727$	34.1335	+	22.4500i	1.26594	+	0.832623i	0.274300	+	0.961644i	$0.411554\pi$
$728$	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	−0.992547	−	0.121860i	$-0.961114\pi$
$733$	−10.8312	−	25.1094i	−0.400058	−	0.927439i	0.592489	−	0.805578i	$-0.298145\pi$
$734$	−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	0.942965	−	0.332891i	$-0.108024\pi$
$739$	−1.54918	−	8.78585i	−0.0569876	−	0.323193i	−0.999953	+	0.00969806i	$0.996913\pi$
$740$	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	$-0.443169\pi$
$743$	−13.7851	−	6.92316i	−0.505728	−	0.253986i	−0.683321	+	0.730118i	$0.739465\pi$
$744$		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	0.656536	+	0.754295i	$0.272021\pi$
$751$	−8.39900	+	28.0546i	−0.306484	+	1.02373i	−0.963019	+	0.269432i	$0.913164\pi$
$752$	−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	−0.992125	−	0.125254i	$-0.960025\pi$
$757$	−16.6330	−	28.8091i	−0.604536	−	1.04709i	0.387589	−	0.921832i	$-0.373308\pi$
$758$	−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	$-0.575920\pi$
$761$	−0.311406	+	0.0738046i	−0.0112885	+	0.00267542i	0.224968	+	0.974366i	$0.427772\pi$
$762$		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	−0.580432	−	0.814309i	$-0.697116\pi$
$769$	−1.73643	+	1.14207i	−0.0626173	+	0.0411841i	0.517814	+	0.855493i	$0.326746\pi$
$770$	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	$-0.760138\pi$
$773$	−5.06191	+	4.24745i	−0.182064	+	0.152770i	0.547201	+	0.837001i	$0.315693\pi$
$774$		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

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

Related objects

Downloads

Learn more