LMFDB - Embedded newform 729.2.g.b.109.3

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			109.3
Character	$\chi$	$=$	729.109
Dual form			729.2.g.b.622.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.01387 - 1.07464i) q^{2} +(-0.0106282 + 0.182479i) q^{4} +(2.58446 - 0.302080i) q^{5} +(-0.442742 - 0.222353i) q^{7} +(-2.05667 + 1.72575i) q^{8} +O(q^{10})$	\(q+(-1.01387 - 1.07464i) q^{2} +(-0.0106282 + 0.182479i) q^{4} +(2.58446 - 0.302080i) q^{5} +(-0.442742 - 0.222353i) q^{7} +(-2.05667 + 1.72575i) q^{8} +(-2.94494 - 2.47110i) q^{10} +(2.16887 + 5.02801i) q^{11} +(5.47152 + 1.29677i) q^{13} +(0.209933 + 0.701226i) q^{14} +(4.30287 + 0.502934i) q^{16} +(-0.861719 + 4.88705i) q^{17} +(-0.156770 - 0.889086i) q^{19} +(0.0276551 + 0.474820i) q^{20} +(3.20435 - 7.42851i) q^{22} +(-0.523602 + 0.262963i) q^{23} +(1.72298 - 0.408353i) q^{25} +(-4.15385 - 7.19468i) q^{26} +(0.0452802 - 0.0784277i) q^{28} +(-1.06410 + 3.55434i) q^{29} +(1.44158 + 0.948144i) q^{31} +(-0.615586 - 0.826876i) q^{32} +(6.12550 - 4.02880i) q^{34} +(-1.21142 - 0.440920i) q^{35} +(5.72681 - 2.08439i) q^{37} +(-0.796504 + 1.06989i) q^{38} +(-4.79408 + 5.08143i) q^{40} +(-0.162140 + 0.171859i) q^{41} +(-5.38987 + 7.23985i) q^{43} +(-0.940554 + 0.342334i) q^{44} +(0.813456 + 0.296074i) q^{46} +(-1.89654 + 1.24737i) q^{47} +(-4.03353 - 5.41797i) q^{49} +(-2.18571 - 1.43756i) q^{50} +(-0.294786 + 0.984653i) q^{52} +(0.273896 - 0.474403i) q^{53} +(7.12423 + 12.3395i) q^{55} +(1.29430 - 0.306755i) q^{56} +(4.89850 - 2.46012i) q^{58} +(4.28786 - 9.94038i) q^{59} +(-0.416681 - 7.15413i) q^{61} +(-0.442665 - 2.51048i) q^{62} +(1.24008 - 7.03282i) q^{64} +(14.5327 + 1.69863i) q^{65} +(-1.76366 - 5.89102i) q^{67} +(-0.882623 - 0.209186i) q^{68} +(0.754392 + 1.74888i) q^{70} +(-1.42883 - 1.19893i) q^{71} +(7.12761 - 5.98078i) q^{73} +(-8.04622 - 4.04096i) q^{74} +(0.163905 - 0.0191578i) q^{76} +(0.157744 - 2.70836i) q^{77} +(-4.63436 - 4.91214i) q^{79} +11.2725 q^{80} +0.349076 q^{82} +(-0.212551 - 0.225290i) q^{83} +(-0.750798 + 12.8907i) q^{85} +(13.2449 - 1.54810i) q^{86} +(-13.1378 - 6.59803i) q^{88} +(11.7618 - 9.86931i) q^{89} +(-2.13413 - 1.79075i) q^{91} +(-0.0424202 - 0.0983410i) q^{92} +(3.26333 + 0.773423i) q^{94} +(-0.673742 - 2.25045i) q^{95} +(14.4555 + 1.68960i) q^{97} +(-1.73289 + 9.82772i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} + 63 q^{20} + 9 q^{22} - 36 q^{23} + 9 q^{25} - 45 q^{26} - 9 q^{28} + 45 q^{29} + 9 q^{31} - 63 q^{32} + 9 q^{34} - 9 q^{35} - 18 q^{37} + 9 q^{38} + 9 q^{40} + 27 q^{41} + 9 q^{43} - 54 q^{44} - 18 q^{46} - 63 q^{47} + 9 q^{49} + 225 q^{50} + 27 q^{52} - 45 q^{53} - 9 q^{55} - 99 q^{56} + 9 q^{58} + 117 q^{59} + 9 q^{61} - 81 q^{62} - 18 q^{64} - 81 q^{65} + 36 q^{67} + 18 q^{68} + 63 q^{70} + 90 q^{71} - 18 q^{73} - 81 q^{74} + 90 q^{76} - 81 q^{77} + 63 q^{79} + 288 q^{80} - 36 q^{82} - 45 q^{83} + 63 q^{85} - 81 q^{86} + 90 q^{88} + 81 q^{89} - 18 q^{91} + 63 q^{92} + 63 q^{94} - 153 q^{95} + 36 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 + 63 * q^20 + 9 * q^22 - 36 * q^23 + 9 * q^25 - 45 * q^26 - 9 * q^28 + 45 * q^29 + 9 * q^31 - 63 * q^32 + 9 * q^34 - 9 * q^35 - 18 * q^37 + 9 * q^38 + 9 * q^40 + 27 * q^41 + 9 * q^43 - 54 * q^44 - 18 * q^46 - 63 * q^47 + 9 * q^49 + 225 * q^50 + 27 * q^52 - 45 * q^53 - 9 * q^55 - 99 * q^56 + 9 * q^58 + 117 * q^59 + 9 * q^61 - 81 * q^62 - 18 * q^64 - 81 * q^65 + 36 * q^67 + 18 * q^68 + 63 * q^70 + 90 * q^71 - 18 * q^73 - 81 * q^74 + 90 * q^76 - 81 * q^77 + 63 * q^79 + 288 * q^80 - 36 * q^82 - 45 * q^83 + 63 * q^85 - 81 * q^86 + 90 * q^88 + 81 * q^89 - 18 * q^91 + 63 * q^92 + 63 * q^94 - 153 * q^95 + 36 * q^97 - 81 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.01387	−	1.07464i	−0.716915	−	0.759886i	0.261797	−	0.965123i	$-0.415685\pi$
$2$	−1.01387	−	1.07464i	−0.716915	−	0.759886i	−0.978712	+	0.205237i	$0.934203\pi$
$3$		0			0
$3$		0			0
$4$	−0.0106282	+	0.182479i	−0.00531408	+	0.0912393i
$5$	2.58446	−	0.302080i	1.15581	−	0.135094i	0.483485	−	0.875353i	$-0.339371\pi$
$5$	2.58446	−	0.302080i	1.15581	−	0.135094i	0.672323	+	0.740258i	$0.265297\pi$
$6$		0			0
$7$	−0.442742	−	0.222353i	−0.167341	−	0.0840417i	0.363157	−	0.931728i	$-0.381699\pi$
$7$	−0.442742	−	0.222353i	−0.167341	−	0.0840417i	−0.530498	+	0.847686i	$0.677995\pi$
$8$	−2.05667	+	1.72575i	−0.727144	+	0.610146i
$9$		0			0
$10$	−2.94494	−	2.47110i	−0.931272	−	0.781430i
$11$	2.16887	+	5.02801i	0.653939	+	1.51600i	0.845194	+	0.534460i	$0.179485\pi$
$11$	2.16887	+	5.02801i	0.653939	+	1.51600i	−0.191255	+	0.981540i	$0.561256\pi$
$12$		0			0
$13$	5.47152	+	1.29677i	1.51753	+	0.359661i	0.903141	−	0.429345i	$-0.141255\pi$
$13$	5.47152	+	1.29677i	1.51753	+	0.359661i	0.614386	+	0.789005i	$0.289404\pi$
$14$	0.209933	+	0.701226i	0.0561070	+	0.187411i
$15$		0			0
$16$	4.30287	+	0.502934i	1.07572	+	0.125733i
$17$	−0.861719	+	4.88705i	−0.208998	+	1.18528i	0.682026	+	0.731327i	$0.261099\pi$
$17$	−0.861719	+	4.88705i	−0.208998	+	1.18528i	−0.891024	+	0.453956i	$0.850012\pi$
$18$		0			0
$19$	−0.156770	−	0.889086i	−0.0359655	−	0.203970i	0.961530	−	0.274700i	$-0.0885784\pi$
$19$	−0.156770	−	0.889086i	−0.0359655	−	0.203970i	−0.997496	+	0.0707293i	$0.977467\pi$
$20$	0.0276551	+	0.474820i	0.00618387	+	0.106173i
$21$		0			0
$22$	3.20435	−	7.42851i	0.683169	−	1.58376i
$23$	−0.523602	+	0.262963i	−0.109179	+	0.0548316i	−0.502550	−	0.864548i	$-0.667605\pi$
$23$	−0.523602	+	0.262963i	−0.109179	+	0.0548316i	0.393372	+	0.919380i	$0.371309\pi$
$24$		0			0
$25$	1.72298	−	0.408353i	0.344595	−	0.0816705i
$26$	−4.15385	−	7.19468i	−0.814637	−	1.41099i
$27$		0			0
$28$	0.0452802	−	0.0784277i	0.00855716	−	0.0148214i
$29$	−1.06410	+	3.55434i	−0.197598	+	0.660024i	0.800554	+	0.599261i	$0.204539\pi$
$29$	−1.06410	+	3.55434i	−0.197598	+	0.660024i	−0.998152	+	0.0607635i	$0.980646\pi$
$30$		0			0
$31$	1.44158	+	0.948144i	0.258916	+	0.170292i	0.672330	−	0.740251i	$-0.265294\pi$
$31$	1.44158	+	0.948144i	0.258916	+	0.170292i	−0.413414	+	0.910543i	$0.635664\pi$
$32$	−0.615586	−	0.826876i	−0.108821	−	0.146172i
$33$		0			0
$34$	6.12550	−	4.02880i	1.05051	−	0.690934i
$35$	−1.21142	−	0.440920i	−0.204767	−	0.0745292i
$36$		0			0
$37$	5.72681	−	2.08439i	0.941482	−	0.342671i	0.174731	−	0.984616i	$-0.444094\pi$
$37$	5.72681	−	2.08439i	0.941482	−	0.342671i	0.766751	+	0.641945i	$0.221872\pi$
$38$	−0.796504	+	1.06989i	−0.129210	+	0.173559i
$39$		0			0
$40$	−4.79408	+	5.08143i	−0.758011	+	0.803445i
$41$	−0.162140	+	0.171859i	−0.0253221	+	0.0268398i	−0.739911	−	0.672705i	$-0.765132\pi$
$41$	−0.162140	+	0.171859i	−0.0253221	+	0.0268398i	0.714589	+	0.699545i	$0.246614\pi$
$42$		0			0
$43$	−5.38987	+	7.23985i	−0.821947	+	1.10407i	0.170972	+	0.985276i	$0.445309\pi$
$43$	−5.38987	+	7.23985i	−0.821947	+	1.10407i	−0.992919	+	0.118791i	$0.962098\pi$
$44$	−0.940554	+	0.342334i	−0.141794	+	0.0516088i
$45$		0			0
$46$	0.813456	+	0.296074i	0.119938	+	0.0436537i
$47$	−1.89654	+	1.24737i	−0.276639	+	0.181948i	−0.680245	−	0.732984i	$-0.738127\pi$
$47$	−1.89654	+	1.24737i	−0.276639	+	0.181948i	0.403607	+	0.914933i	$0.367756\pi$
$48$		0			0
$49$	−4.03353	−	5.41797i	−0.576219	−	0.773996i
$50$	−2.18571	−	1.43756i	−0.309106	−	0.203302i
$51$		0			0
$52$	−0.294786	+	0.984653i	−0.0408794	+	0.136547i
$53$	0.273896	−	0.474403i	0.0376226	−	0.0651642i	−0.846601	−	0.532228i	$-0.821355\pi$
$53$	0.273896	−	0.474403i	0.0376226	−	0.0651642i	0.884224	+	0.467064i	$0.154688\pi$
$54$		0			0
$55$	7.12423	+	12.3395i	0.960631	+	1.66386i
$56$	1.29430	−	0.306755i	0.172958	−	0.0409919i
$57$		0			0
$58$	4.89850	−	2.46012i	0.643204	−	0.323029i
$59$	4.28786	−	9.94038i	0.558232	−	1.29413i	−0.372366	−	0.928086i	$-0.621454\pi$
$59$	4.28786	−	9.94038i	0.558232	−	1.29413i	0.930599	−	0.366042i	$-0.119287\pi$
$60$		0			0
$61$	−0.416681	−	7.15413i	−0.0533505	−	0.915992i	−0.913726	−	0.406331i	$-0.866808\pi$
$61$	−0.416681	−	7.15413i	−0.0533505	−	0.915992i	0.860375	−	0.509661i	$-0.170229\pi$
$62$	−0.442665	−	2.51048i	−0.0562186	−	0.318831i
$63$		0			0
$64$	1.24008	−	7.03282i	0.155009	−	0.879102i
$65$	14.5327	+	1.69863i	1.80256	+	0.210689i
$66$		0			0
$67$	−1.76366	−	5.89102i	−0.215465	−	0.719703i	−0.995567	−	0.0940512i	$-0.970018\pi$
$67$	−1.76366	−	5.89102i	−0.215465	−	0.719703i	0.780102	−	0.625652i	$-0.215167\pi$
$68$	−0.882623	−	0.209186i	−0.107034	−	0.0253675i
$69$		0			0
$70$	0.754392	+	1.74888i	0.0901671	+	0.209031i
$71$	−1.42883	−	1.19893i	−0.169571	−	0.142287i	0.554053	−	0.832482i	$-0.313081\pi$
$71$	−1.42883	−	1.19893i	−0.169571	−	0.142287i	−0.723624	+	0.690194i	$0.757525\pi$
$72$		0			0
$73$	7.12761	−	5.98078i	0.834224	−	0.699997i	−0.122033	−	0.992526i	$-0.538941\pi$
$73$	7.12761	−	5.98078i	0.834224	−	0.699997i	0.956257	+	0.292529i	$0.0944968\pi$
$74$	−8.04622	−	4.04096i	−0.935354	−	0.469752i
$75$		0			0
$76$	0.163905	−	0.0191578i	0.0188012	−	0.00219755i
$77$	0.157744	−	2.70836i	0.0179766	−	0.308647i
$78$		0			0
$79$	−4.63436	−	4.91214i	−0.521407	−	0.552659i	0.412137	−	0.911122i	$-0.364782\pi$
$79$	−4.63436	−	4.91214i	−0.521407	−	0.552659i	−0.933544	+	0.358463i	$0.883301\pi$
$80$	11.2725			1.26031
$81$		0			0
$82$	0.349076			0.0385490
$83$	−0.212551	−	0.225290i	−0.0233305	−	0.0247288i	0.715603	−	0.698507i	$-0.246152\pi$
$83$	−0.212551	−	0.225290i	−0.0233305	−	0.0247288i	−0.738934	+	0.673778i	$0.764670\pi$
$84$		0			0
$85$	−0.750798	+	12.8907i	−0.0814355	+	1.39819i
$86$	13.2449	−	1.54810i	1.42823	−	0.166936i
$87$		0			0
$88$	−13.1378	−	6.59803i	−1.40049	−	0.703352i
$89$	11.7618	−	9.86931i	1.24675	−	1.04615i	0.249782	−	0.968302i	$-0.419641\pi$
$89$	11.7618	−	9.86931i	1.24675	−	1.04615i	0.996966	−	0.0778431i	$-0.0248033\pi$
$90$		0			0
$91$	−2.13413	−	1.79075i	−0.223718	−	0.187721i
$92$	−0.0424202	−	0.0983410i	−0.00442261	−	0.0102528i
$93$		0			0
$94$	3.26333	+	0.773423i	0.336586	+	0.0797725i
$95$	−0.673742	−	2.25045i	−0.0691244	−	0.230892i
$96$		0			0
$97$	14.4555	+	1.68960i	1.46773	+	0.171553i	0.812095	−	0.583525i	$-0.198327\pi$
$97$	14.4555	+	1.68960i	1.46773	+	0.171553i	0.655635	+	0.755078i	$0.272401\pi$
$98$	−1.73289	+	9.82772i	−0.175049	+	0.992750i
$99$		0			0
$100$	0.0562035	+	0.318746i	0.00562035	+	0.0318746i
$101$	−0.393848	−	6.76210i	−0.0391893	−	0.672854i	−0.959507	−	0.281683i	$-0.909107\pi$
$101$	−0.393848	−	6.76210i	−0.0391893	−	0.672854i	0.920318	−	0.391171i	$-0.127930\pi$
$102$		0			0
$103$	−6.04868	+	14.0224i	−0.595994	+	1.38167i	0.306874	+	0.951750i	$0.400717\pi$
$103$	−6.04868	+	14.0224i	−0.595994	+	1.38167i	−0.902868	+	0.429919i	$0.858542\pi$
$104$	−13.4910	+	6.77546i	−1.32291	+	0.664388i
$105$		0			0
$106$	−0.787508	+	0.186643i	−0.0764896	+	0.0181284i
$107$	−7.68656	−	13.3135i	−0.743088	−	1.28707i	−0.951083	−	0.308936i	$-0.900027\pi$
$107$	−7.68656	−	13.3135i	−0.743088	−	1.28707i	0.207995	−	0.978130i	$-0.433306\pi$
$108$		0			0
$109$	−7.19648	+	12.4647i	−0.689298	+	1.19390i	0.282768	+	0.959188i	$0.408747\pi$
$109$	−7.19648	+	12.4647i	−0.689298	+	1.19390i	−0.972065	+	0.234710i	$0.924586\pi$
$110$	6.03751	−	20.1667i	0.575654	−	1.92282i
$111$		0			0
$112$	−1.79323	−	1.17943i	−0.169445	−	0.111445i
$113$	6.47750	+	8.70079i	0.609352	+	0.818501i	0.994542	−	0.104336i	$-0.0332717\pi$
$113$	6.47750	+	8.70079i	0.609352	+	0.818501i	−0.385191	+	0.922837i	$0.625864\pi$
$114$		0			0
$115$	−1.27380	+	0.837788i	−0.118782	+	0.0781242i
$116$	−0.637281	−	0.231951i	−0.0591701	−	0.0215361i
$117$		0			0
$118$	−15.0297	+	5.47036i	−1.38359	+	0.503587i
$119$	1.46817	−	1.97210i	0.134587	−	0.180782i
$120$		0			0
$121$	−13.0282	+	13.8091i	−1.18438	+	1.25537i
$122$	−7.26566	+	7.70115i	−0.657802	+	0.697229i
$123$		0			0
$124$	−0.188337	+	0.252981i	−0.0169132	+	0.0227184i
$125$	−7.89606	+	2.87393i	−0.706245	+	0.257052i
$126$		0			0
$127$	−2.81938	−	1.02617i	−0.250180	−	0.0910581i	0.213886	−	0.976859i	$-0.431388\pi$
$127$	−2.81938	−	1.02617i	−0.250180	−	0.0910581i	−0.464066	+	0.885801i	$0.653610\pi$
$128$	−10.5376	+	6.93067i	−0.931398	+	0.612590i
$129$		0			0
$130$	−12.9089	−	17.3396i	−1.13218	−	1.52078i
$131$	−6.78889	−	4.46513i	−0.593148	−	0.390120i	0.217149	−	0.976138i	$-0.430324\pi$
$131$	−6.78889	−	4.46513i	−0.593148	−	0.390120i	−0.810298	+	0.586019i	$0.800695\pi$
$132$		0			0
$133$	−0.128283	+	0.428494i	−0.0111235	+	0.0371551i
$134$	−4.54261	+	7.86804i	−0.392422	+	0.679695i
$135$		0			0
$136$	−6.66157	−	11.5382i	−0.571225	−	0.989391i
$137$	−5.66593	+	1.34285i	−0.484073	+	0.114727i	−0.465404	−	0.885098i	$-0.654091\pi$
$137$	−5.66593	+	1.34285i	−0.484073	+	0.114727i	−0.0186687	+	0.999826i	$0.505943\pi$
$138$		0			0
$139$	12.9453	−	6.50139i	1.09801	−	0.551441i	0.194887	−	0.980826i	$-0.437566\pi$
$139$	12.9453	−	6.50139i	1.09801	−	0.551441i	0.903122	+	0.429385i	$0.141270\pi$
$140$	0.0933337	−	0.216372i	0.00788814	−	0.0182868i
$141$		0			0
$142$	0.160230	+	2.75105i	0.0134462	+	0.230863i
$143$	5.34683	+	30.3234i	0.447124	+	2.53577i
$144$		0			0
$145$	−1.67643	+	9.50750i	−0.139220	+	0.789555i
$146$	−13.6537	−	1.59589i	−1.12999	−	0.132076i
$147$		0			0
$148$	0.319491	+	1.06717i	0.0262620	+	0.0877211i
$149$	3.02152	+	0.716114i	0.247533	+	0.0586663i	0.352509	−	0.935808i	$-0.385329\pi$
$149$	3.02152	+	0.716114i	0.247533	+	0.0586663i	−0.104976	+	0.994475i	$0.533477\pi$
$150$		0			0
$151$	3.95173	+	9.16114i	0.321587	+	0.745523i	0.999942	+	0.0107883i	$0.00343409\pi$
$151$	3.95173	+	9.16114i	0.321587	+	0.745523i	−0.678355	+	0.734735i	$0.737307\pi$
$152$	1.85677	+	1.55801i	0.150604	+	0.126372i
$153$		0			0
$154$	−3.07045	+	2.57641i	−0.247424	+	0.207613i
$155$	4.01213	+	2.01497i	0.322262	+	0.161846i
$156$		0			0
$157$	12.3804	−	1.44706i	0.988065	−	0.115488i	0.393319	−	0.919402i	$-0.371327\pi$
$157$	12.3804	−	1.44706i	0.988065	−	0.115488i	0.594746	+	0.803914i	$0.297253\pi$
$158$	−0.580136	+	9.96055i	−0.0461532	+	0.792419i
$159$		0			0
$160$	−1.84074	−	1.95107i	−0.145524	−	0.154246i
$161$	0.290291			0.0228782
$162$		0			0
$163$	−6.05763			−0.474470			−0.237235	−	0.971452i	$-0.576241\pi$
$163$	−6.05763			−0.474470			−0.237235	+	0.971452i	$0.576241\pi$
$164$	−0.0296373	−	0.0314137i	−0.00231428	−	0.00245300i
$165$		0			0
$166$	−0.0266074	+	0.456831i	−0.00206513	+	0.0354570i
$167$	−17.2871	+	2.02058i	−1.33772	+	0.156357i	−0.754683	−	0.656089i	$-0.772209\pi$
$167$	−17.2871	+	2.02058i	−1.33772	+	0.156357i	−0.583036	+	0.812446i	$0.698135\pi$
$168$		0			0
$169$	16.6387	+	8.35627i	1.27990	+	0.642790i
$170$	14.6141	−	12.2627i	1.12085	−	0.940505i
$171$		0			0
$172$	−1.26383	−	1.06048i	−0.0963664	−	0.0808610i
$173$	−0.493913	−	1.14502i	−0.0375515	−	0.0870541i	0.898408	−	0.439162i	$-0.144724\pi$
$173$	−0.493913	−	1.14502i	−0.0375515	−	0.0870541i	−0.935960	+	0.352107i	$0.885465\pi$
$174$		0			0
$175$	−0.853632	−	0.202314i	−0.0645285	−	0.0152935i
$176$	6.80362	+	22.7257i	0.512842	+	1.71301i
$177$		0			0
$178$	−22.5309	−	2.63349i	−1.68876	−	0.197388i
$179$	0.660341	−	3.74498i	0.0493562	−	0.279913i	−0.950134	−	0.311842i	$-0.899054\pi$
$179$	0.660341	−	3.74498i	0.0493562	−	0.279913i	0.999490	+	0.0319291i	$0.0101651\pi$
$180$		0			0
$181$	−1.75067	−	9.92855i	−0.130126	−	0.737983i	−0.978130	−	0.207993i	$-0.933307\pi$
$181$	−1.75067	−	9.92855i	−0.130126	−	0.737983i	0.848004	−	0.529990i	$-0.177804\pi$
$182$	0.239323	+	4.10901i	0.0177398	+	0.304580i
$183$		0			0
$184$	0.623070	−	1.44444i	0.0459333	−	0.106485i
$185$	14.1711	−	7.11699i	1.04188	−	0.523251i
$186$		0			0
$187$	−26.4411	+	6.26665i	−1.93356	+	0.458263i
$188$	−0.207462	−	0.359335i	−0.0151307	−	0.0262072i
$189$		0			0
$190$	−1.73534	+	3.00570i	−0.125895	+	0.218056i
$191$	−0.186970	+	0.624525i	−0.0135287	+	0.0451890i	−0.964487	−	0.264129i	$-0.914916\pi$
$191$	−0.186970	+	0.624525i	−0.0135287	+	0.0451890i	0.950959	+	0.309318i	$0.100101\pi$
$192$		0			0
$193$	−8.39008	−	5.51824i	−0.603931	−	0.397212i	0.210397	−	0.977616i	$-0.432524\pi$
$193$	−8.39008	−	5.51824i	−0.603931	−	0.397212i	−0.814329	+	0.580404i	$0.802895\pi$
$194$	−12.8403	−	17.2475i	−0.921878	−	1.23830i
$195$		0			0
$196$	1.03153	−	0.678450i	0.0736809	−	0.0484607i
$197$	3.58166	+	1.30362i	0.255182	+	0.0928788i	0.466444	−	0.884551i	$-0.345535\pi$
$197$	3.58166	+	1.30362i	0.255182	+	0.0928788i	−0.211262	+	0.977430i	$0.567757\pi$
$198$		0			0
$199$	−10.3868	+	3.78048i	−0.736299	+	0.267991i	−0.682829	−	0.730579i	$-0.739250\pi$
$199$	−10.3868	+	3.78048i	−0.736299	+	0.267991i	−0.0534702	+	0.998569i	$0.517028\pi$
$200$	−2.83888	+	3.81328i	−0.200739	+	0.269640i
$201$		0			0
$202$	−6.86752	+	7.27914i	−0.483197	+	0.512159i
$203$	1.26144	−	1.33705i	0.0885358	−	0.0938424i
$204$		0			0
$205$	−0.367131	+	0.493142i	−0.0256415	+	0.0344425i
$206$	21.2016	−	7.71676i	1.47719	−	0.537652i
$207$		0			0
$208$	22.8911	+	8.33167i	1.58721	+	0.577697i
$209$	4.13032	−	2.71655i	0.285700	−	0.187908i
$210$		0			0
$211$	11.5055	+	15.4546i	0.792074	+	1.06394i	0.996378	+	0.0850321i	$0.0270993\pi$
$211$	11.5055	+	15.4546i	0.792074	+	1.06394i	−0.204305	+	0.978907i	$0.565493\pi$
$212$	0.0836573	+	0.0550223i	0.00574561	+	0.00377894i
$213$		0			0
$214$	−6.51406	+	21.7585i	−0.445292	+	1.48738i
$215$	−11.7429	+	20.3393i	−0.800859	+	1.38713i
$216$		0			0
$217$	−0.427426	−	0.740324i	−0.0290156	−	0.0502565i
$218$	20.6913	−	4.90394i	1.40139	−	0.332137i
$219$		0			0
$220$	−2.32742	+	1.16887i	−0.156914	+	0.0788054i
$221$	−11.0523	+	25.6221i	−0.743459	+	1.72353i
$222$		0			0
$223$	0.191888	+	3.29459i	0.0128498	+	0.220622i	0.998620	+	0.0525223i	$0.0167261\pi$
$223$	0.191888	+	3.29459i	0.0128498	+	0.220622i	−0.985770	+	0.168100i	$0.946237\pi$
$224$	0.0886872	+	0.502970i	0.00592566	+	0.0336061i
$225$		0			0
$226$	2.78287	−	15.7825i	0.185114	−	1.04983i
$227$	−2.00235	−	0.234041i	−0.132901	−	0.0155339i	0.0493825	−	0.998780i	$-0.484275\pi$
$227$	−2.00235	−	0.234041i	−0.132901	−	0.0155339i	−0.182283	+	0.983246i	$0.558349\pi$
$228$		0			0
$229$	−6.15109	−	20.5461i	−0.406476	−	1.35772i	−0.879175	−	0.476500i	$-0.841905\pi$
$229$	−6.15109	−	20.5461i	−0.406476	−	1.35772i	0.472699	−	0.881224i	$-0.343280\pi$
$230$	2.19179	+	0.519463i	0.144522	+	0.0342524i
$231$		0			0
$232$	−3.94541	−	9.14649i	−0.259029	−	0.600496i
$233$	−7.53018	−	6.31858i	−0.493319	−	0.413944i	0.361895	−	0.932219i	$-0.382130\pi$
$233$	−7.53018	−	6.31858i	−0.493319	−	0.413944i	−0.855214	+	0.518275i	$0.826574\pi$
$234$		0			0
$235$	−4.52473	+	3.79670i	−0.295161	+	0.247669i
$236$	1.76833	+	0.888091i	0.115109	+	0.0578098i
$237$		0			0
$238$	−3.60783	+	0.421695i	−0.233861	+	0.0273344i
$239$	0.974957	−	16.7394i	0.0630647	−	1.08278i	−0.807227	−	0.590242i	$-0.799032\pi$
$239$	0.974957	−	16.7394i	0.0630647	−	1.08278i	0.870291	−	0.492537i	$-0.163931\pi$
$240$		0			0
$241$	6.51491	+	6.90540i	0.419662	+	0.444816i	0.902368	−	0.430967i	$-0.141827\pi$
$241$	6.51491	+	6.90540i	0.419662	+	0.444816i	−0.482706	+	0.875783i	$0.660346\pi$
$242$	28.0487			1.80304
$243$		0			0
$244$	1.30990			0.0838580
$245$	−12.0612	−	12.7841i	−0.770560	−	0.816746i
$246$		0			0
$247$	0.295174	−	5.06795i	0.0187815	−	0.322466i
$248$	−4.60113	+	0.537795i	−0.292172	+	0.0341500i
$249$		0			0
$250$	11.0940	+	5.57163i	0.701648	+	0.352381i
$251$	−4.66395	+	3.91352i	−0.294386	+	0.247019i	−0.778003	−	0.628260i	$-0.783767\pi$
$251$	−4.66395	+	3.91352i	−0.294386	+	0.247019i	0.483617	+	0.875280i	$0.339323\pi$
$252$		0			0
$253$	−2.45781	−	2.06234i	−0.154521	−	0.129658i
$254$	1.75573	+	4.07023i	0.110164	+	0.255389i
$255$		0			0
$256$	4.23409	+	1.00350i	0.264631	+	0.0627186i
$257$	1.23610	+	4.12885i	0.0771055	+	0.257550i	0.987848	−	0.155425i	$-0.0496747\pi$
$257$	1.23610	+	4.12885i	0.0771055	+	0.257550i	−0.910742	+	0.412975i	$0.864490\pi$
$258$		0			0
$259$	−2.99897	−	0.350529i	−0.186347	−	0.0217808i
$260$	−0.464419	+	2.63385i	−0.0288020	+	0.163344i
$261$		0			0
$262$	2.08466	+	11.8227i	0.128791	+	0.730408i
$263$	1.51474	+	26.0070i	0.0934026	+	1.60366i	0.641417	+	0.767192i	$0.278347\pi$
$263$	1.51474	+	26.0070i	0.0934026	+	1.60366i	−0.548014	+	0.836469i	$0.684616\pi$
$264$		0			0
$265$	0.564568	−	1.30882i	0.0346811	−	0.0803999i
$266$	0.590539	−	0.296580i	0.0362083	−	0.0181845i
$267$		0			0
$268$	1.09373	−	0.259219i	0.0668102	−	0.0158343i
$269$	−13.9432	−	24.1504i	−0.850135	−	1.47248i	−0.881086	−	0.472956i	$-0.843187\pi$
$269$	−13.9432	−	24.1504i	−0.850135	−	1.47248i	0.0309512	−	0.999521i	$-0.490146\pi$
$270$		0			0
$271$	12.0986	−	20.9554i	0.734937	−	1.27295i	−0.219815	−	0.975542i	$-0.570545\pi$
$271$	12.0986	−	20.9554i	0.734937	−	1.27295i	0.954751	−	0.297406i	$-0.0961214\pi$
$272$	−6.16573	+	20.5950i	−0.373852	+	1.24875i
$273$		0			0
$274$	7.18760	+	4.72736i	0.434219	+	0.285590i
$275$	5.79011	+	7.77747i	0.349157	+	0.468999i
$276$		0			0
$277$	−6.64652	+	4.37149i	−0.399351	+	0.262657i	−0.733260	−	0.679948i	$-0.762002\pi$
$277$	−6.64652	+	4.37149i	−0.399351	+	0.262657i	0.333910	+	0.942605i	$0.391632\pi$
$278$	−20.1116	−	7.32001i	−1.20621	−	0.439025i
$279$		0			0
$280$	3.25241	−	1.18378i	0.194369	−	0.0707445i
$281$	3.40294	−	4.57094i	0.203003	−	0.272680i	−0.688950	−	0.724809i	$-0.741928\pi$
$281$	3.40294	−	4.57094i	0.203003	−	0.272680i	0.891952	+	0.452129i	$0.149335\pi$
$282$		0			0
$283$	1.16813	−	1.23814i	0.0694379	−	0.0735999i	−0.691723	−	0.722163i	$-0.743148\pi$
$283$	1.16813	−	1.23814i	0.0694379	−	0.0735999i	0.761161	+	0.648563i	$0.224630\pi$
$284$	0.233965	−	0.247989i	0.0138833	−	0.0147154i
$285$		0			0
$286$	27.1657	−	36.4899i	1.60634	−	2.15769i
$287$	0.110000	−	0.0400366i	0.00649308	−	0.00236329i
$288$		0			0
$289$	−7.16593	−	2.60818i	−0.421525	−	0.153423i
$290$	11.9168	−	7.83783i	0.699781	−	0.460253i
$291$		0			0
$292$	1.01561	+	1.36420i	0.0594341	+	0.0798338i
$293$	−8.17237	−	5.37505i	−0.477435	−	0.314014i	0.287884	−	0.957665i	$-0.407048\pi$
$293$	−8.17237	−	5.37505i	−0.477435	−	0.314014i	−0.765319	+	0.643651i	$0.777419\pi$
$294$		0			0
$295$	8.07903	−	26.9858i	0.470379	−	1.57118i
$296$	−8.18104	+	14.1700i	−0.475513	+	0.823613i
$297$		0			0
$298$	−2.29387	−	3.97310i	−0.132880	−	0.230155i
$299$	−3.20591	+	0.759814i	−0.185402	+	0.0439412i
$300$		0			0
$301$	3.99613	−	2.00693i	0.230333	−	0.115678i
$302$	5.83839	−	13.5349i	0.335962	−	0.778846i
$303$		0			0
$304$	−0.227409	−	3.90447i	−0.0130428	−	0.223937i
$305$	−3.23802	−	18.3637i	−0.185408	−	1.05150i
$306$		0			0
$307$	−4.19072	+	23.7667i	−0.239177	+	1.35644i	0.594460	+	0.804125i	$0.297366\pi$
$307$	−4.19072	+	23.7667i	−0.239177	+	1.35644i	−0.833636	+	0.552314i	$0.813745\pi$
$308$	0.492542	+	0.0575699i	0.0280652	+	0.00328035i
$309$		0			0
$310$	−1.90242	−	6.35452i	−0.108050	−	0.360913i
$311$	2.04298	+	0.484195i	0.115847	+	0.0274562i	0.288130	−	0.957591i	$-0.406966\pi$
$311$	2.04298	+	0.484195i	0.115847	+	0.0274562i	−0.172284	+	0.985047i	$0.555115\pi$
$312$		0			0
$313$	2.68443	+	6.22322i	0.151733	+	0.351757i	0.977081	−	0.212867i	$-0.0682803\pi$
$313$	2.68443	+	6.22322i	0.151733	+	0.351757i	−0.825348	+	0.564624i	$0.809021\pi$
$314$	−14.1072	−	11.8374i	−0.796117	−	0.668021i
$315$		0			0
$316$	0.945615	−	0.793465i	0.0531950	−	0.0446359i
$317$	−4.57530	−	2.29780i	−0.256975	−	0.129058i	0.315649	−	0.948876i	$-0.397778\pi$
$317$	−4.57530	−	2.29780i	−0.256975	−	0.129058i	−0.572623	+	0.819819i	$0.694074\pi$
$318$		0			0
$319$	−20.1791	+	2.35860i	−1.12981	+	0.132056i
$320$	1.08045	−	18.5507i	0.0603992	−	1.03701i
$321$		0			0
$322$	−0.294318	−	0.311959i	−0.0164017	−	0.0173848i
$323$	4.48010			0.249279
$324$		0			0
$325$	9.95684			0.552306
$326$	6.14166	+	6.50977i	0.340155	+	0.360543i
$327$		0			0
$328$	0.0368839	−	0.633272i	0.00203657	−	0.0349666i
$329$	1.11704	−	0.130563i	0.0615842	−	0.00719816i
$330$		0			0
$331$	1.49743	+	0.752036i	0.0823060	+	0.0413356i	0.489476	−	0.872017i	$-0.337188\pi$
$331$	1.49743	+	0.752036i	0.0823060	+	0.0413356i	−0.407170	+	0.913352i	$0.633484\pi$
$332$	0.0433697	−	0.0363915i	0.00238022	−	0.00199724i
$333$		0			0
$334$	19.6983	+	16.5289i	1.07784	+	0.904419i
$335$	−6.33767	−	14.6924i	−0.346264	−	0.802730i
$336$		0			0
$337$	18.2176	+	4.31765i	0.992375	+	0.235197i	0.694567	−	0.719428i	$-0.255596\pi$
$337$	18.2176	+	4.31765i	0.992375	+	0.235197i	0.297809	+	0.954626i	$0.403744\pi$
$338$	−7.88951	−	26.3528i	−0.429133	−	1.43340i
$339$		0			0
$340$	−2.34430	−	0.274009i	−0.127137	−	0.0148602i
$341$	−1.64067	+	9.30469i	−0.0888471	+	0.503877i
$342$		0			0
$343$	1.18334	+	6.71103i	0.0638941	+	0.362362i
$344$	−1.40900	−	24.1916i	−0.0759682	−	1.30432i
$345$		0			0
$346$	−0.729720	+	1.69168i	−0.0392300	+	0.0909453i
$347$	11.2749	−	5.66248i	0.605270	−	0.303978i	−0.119645	−	0.992817i	$-0.538176\pi$
$347$	11.2749	−	5.66248i	0.605270	−	0.303978i	0.724914	+	0.688839i	$0.241879\pi$
$348$		0			0
$349$	18.3761	−	4.35522i	0.983650	−	0.233129i	0.292837	−	0.956162i	$-0.405401\pi$
$349$	18.3761	−	4.35522i	0.983650	−	0.233129i	0.690814	+	0.723033i	$0.257253\pi$
$350$	0.648058	+	1.12247i	0.0346401	+	0.0599985i
$351$		0			0
$352$	2.82241	−	4.88856i	0.150435	−	0.260561i
$353$	2.64152	−	8.82330i	0.140594	−	0.469617i	−0.858470	−	0.512863i	$-0.828585\pi$
$353$	2.64152	−	8.82330i	0.140594	−	0.469617i	0.999064	+	0.0432463i	$0.0137700\pi$
$354$		0			0
$355$	−4.05494	−	2.66698i	−0.215214	−	0.141548i
$356$	1.67593	+	2.25117i	0.0888242	+	0.119312i
$357$		0			0
$358$	−4.69401	+	3.08730i	−0.248086	+	0.163169i
$359$	13.4793	+	4.90607i	0.711411	+	0.258932i	0.672275	−	0.740301i	$-0.265317\pi$
$359$	13.4793	+	4.90607i	0.711411	+	0.258932i	0.0391360	+	0.999234i	$0.487539\pi$
$360$		0			0
$361$	17.0883	−	6.21962i	0.899382	−	0.327348i
$362$	−8.89467	+	11.9476i	−0.467493	+	0.627953i
$363$		0			0
$364$	0.349455	−	0.370401i	0.0183164	−	0.0194143i
$365$	16.6144	−	17.6102i	0.869636	−	0.921761i
$366$		0			0
$367$	−4.26008	+	5.72228i	−0.222375	+	0.298701i	−0.899284	−	0.437366i	$-0.855912\pi$
$367$	−4.26008	+	5.72228i	−0.222375	+	0.298701i	0.676909	+	0.736067i	$0.263319\pi$
$368$	−2.38525	+	0.868159i	−0.124340	+	0.0452559i
$369$		0			0
$370$	−22.0159	−	8.01312i	−1.14455	−	0.416582i
$371$	−0.226750	+	0.149136i	−0.0117723	+	0.00774276i
$372$		0			0
$373$	20.5746	+	27.6365i	1.06531	+	1.43096i	0.895269	+	0.445526i	$0.146983\pi$
$373$	20.5746	+	27.6365i	1.06531	+	1.43096i	0.170043	+	0.985437i	$0.445609\pi$
$374$	33.5422	+	22.0611i	1.73443	+	1.14075i
$375$		0			0
$376$	1.74790	−	5.83840i	0.0901412	−	0.301093i
$377$	−10.4314	+	18.0677i	−0.537245	+	0.930536i
$378$		0			0
$379$	−3.66451	−	6.34713i	−0.188233	−	0.326030i	0.756428	−	0.654077i	$-0.226943\pi$
$379$	−3.66451	−	6.34713i	−0.188233	−	0.326030i	−0.944661	+	0.328047i	$0.893609\pi$
$380$	0.417820	−	0.0990252i	0.0214337	−	0.00507989i
$381$		0			0
$382$	0.860704	−	0.432262i	0.0440374	−	0.0221164i
$383$	8.46645	−	19.6274i	0.432616	−	1.00292i	−0.552887	−	0.833256i	$-0.686474\pi$
$383$	8.46645	−	19.6274i	0.432616	−	1.00292i	0.985503	−	0.169660i	$-0.0542668\pi$
$384$		0			0
$385$	−0.410460	−	7.04732i	−0.0209190	−	0.359165i
$386$	2.57633	+	14.6111i	0.131132	+	0.743686i
$387$		0			0
$388$	−0.461951	+	2.61986i	−0.0234520	+	0.133003i
$389$	−18.0877	−	2.11415i	−0.917085	−	0.107192i	−0.355562	−	0.934653i	$-0.615710\pi$
$389$	−18.0877	−	2.11415i	−0.917085	−	0.107192i	−0.561523	+	0.827461i	$0.689785\pi$
$390$		0			0
$391$	−0.833915	−	2.78547i	−0.0421729	−	0.140867i
$392$	17.6457	+	4.18212i	0.891245	+	0.211229i
$393$		0			0
$394$	−2.23042	−	5.17069i	−0.112367	−	0.260496i
$395$	−13.4612	−	11.2953i	−0.677307	−	0.568328i
$396$		0			0
$397$	24.5024	−	20.5600i	1.22974	−	1.03188i	0.231486	−	0.972838i	$-0.425641\pi$
$397$	24.5024	−	20.5600i	1.22974	−	1.03188i	0.998256	−	0.0590372i	$-0.0188031\pi$
$398$	14.5935	+	7.32913i	0.731506	+	0.367376i
$399$		0			0
$400$	7.61912	−	0.890547i	0.380956	−	0.0445273i
$401$	−2.32734	+	39.9588i	−0.116222	+	1.99545i	−0.0239879	+	0.999712i	$0.507636\pi$
$401$	−2.32734	+	39.9588i	−0.116222	+	1.99545i	−0.0922338	+	0.995737i	$0.529401\pi$
$402$		0			0
$403$	6.65812	+	7.05720i	0.331665	+	0.351544i
$404$	1.23812			0.0615990
$405$		0			0
$406$	−2.71579			−0.134782
$407$	22.9010	+	24.2737i	1.13516	+	1.20320i
$408$		0			0
$409$	1.29008	−	22.1499i	0.0637905	−	1.09524i	−0.802809	−	0.596236i	$-0.796662\pi$
$409$	1.29008	−	22.1499i	0.0637905	−	1.09524i	0.866599	−	0.499004i	$-0.166301\pi$
$410$	0.902174	−	0.105449i	0.0445552	−	0.00520776i
$411$		0			0
$412$	−2.49450	−	1.25279i	−0.122895	−	0.0617203i
$413$	−4.10869	+	3.44760i	−0.202176	+	0.169645i
$414$		0			0
$415$	−0.617385	−	0.518048i	−0.0303062	−	0.0254300i
$416$	−2.29592	−	5.32255i	−0.112567	−	0.260959i
$417$		0			0
$418$	−7.10693	−	1.68437i	−0.347611	−	0.0823854i
$419$	−8.05133	−	26.8933i	−0.393333	−	1.31382i	−0.893954	−	0.448158i	$-0.852080\pi$
$419$	−8.05133	−	26.8933i	−0.393333	−	1.31382i	0.500621	−	0.865667i	$-0.333105\pi$
$420$		0			0
$421$	−12.9595	−	1.51475i	−0.631609	−	0.0738245i	−0.205736	−	0.978608i	$-0.565959\pi$
$421$	−12.9595	−	1.51475i	−0.631609	−	0.0738245i	−0.425873	+	0.904783i	$0.640033\pi$
$422$	4.94303	−	28.0333i	0.240623	−	1.36464i
$423$		0			0
$424$	0.255387	+	1.44837i	0.0124027	+	0.0703390i
$425$	0.510920	+	8.77215i	0.0247832	+	0.425512i
$426$		0			0
$427$	−1.40626	+	3.26008i	−0.0680538	+	0.157767i
$428$	2.51112	−	1.26113i	0.121380	−	0.0609592i
$429$		0			0
$430$	33.7632	−	8.00203i	1.62821	−	0.385892i
$431$	−6.22218	−	10.7771i	−0.299712	−	0.519116i	0.676358	−	0.736573i	$-0.263557\pi$
$431$	−6.22218	−	10.7771i	−0.299712	−	0.519116i	−0.976070	+	0.217457i	$0.930224\pi$
$432$		0			0
$433$	0.963724	−	1.66922i	0.0463136	−	0.0802176i	−0.841939	−	0.539572i	$-0.818586\pi$
$433$	0.963724	−	1.66922i	0.0463136	−	0.0802176i	0.888253	+	0.459355i	$0.151919\pi$
$434$	−0.362227	+	1.20992i	−0.0173875	+	0.0580781i
$435$		0			0
$436$	−2.19805	−	1.44568i	−0.105267	−	0.0692355i
$437$	0.315882	+	0.424303i	0.0151107	+	0.0202972i
$438$		0			0
$439$	6.95891	−	4.57695i	0.332131	−	0.218446i	−0.372480	−	0.928040i	$-0.621492\pi$
$439$	6.95891	−	4.57695i	0.332131	−	0.218446i	0.704610	+	0.709595i	$0.251122\pi$
$440$	−35.9472	−	13.0837i	−1.71372	−	0.623741i
$441$		0			0
$442$	38.7402	−	14.1003i	1.84268	−	0.670682i
$443$	17.5850	−	23.6207i	0.835488	−	1.12225i	−0.155438	−	0.987846i	$-0.549679\pi$
$443$	17.5850	−	23.6207i	0.835488	−	1.12225i	0.990926	−	0.134409i	$-0.0429136\pi$
$444$		0			0
$445$	27.4166	−	29.0599i	1.29967	−	1.37757i
$446$	3.34595	−	3.54650i	0.158435	−	0.167932i
$447$		0			0
$448$	−2.11280	+	2.83799i	−0.0998206	+	0.134082i
$449$	30.8060	−	11.2125i	1.45383	−	0.529149i	0.510169	−	0.860074i	$-0.329583\pi$
$449$	30.8060	−	11.2125i	1.45383	−	0.529149i	0.943657	+	0.330925i	$0.107361\pi$
$450$		0			0
$451$	−1.21577	−	0.442504i	−0.0572483	−	0.0208367i
$452$	−1.65655	+	1.08953i	−0.0779176	+	0.0512472i
$453$		0			0
$454$	1.77861	+	2.38909i	0.0834745	+	0.112126i
$455$	−6.05653	−	3.98344i	−0.283935	−	0.186747i
$456$		0			0
$457$	8.96435	−	29.9430i	0.419334	−	1.40067i	−0.443993	−	0.896030i	$-0.646438\pi$
$457$	8.96435	−	29.9430i	0.419334	−	1.40067i	0.863327	−	0.504644i	$-0.168376\pi$
$458$	−15.8432	+	27.4413i	−0.740306	+	1.28225i
$459$		0			0
$460$	−0.139340	−	0.241344i	−0.00649677	−	0.0112527i
$461$	−23.3775	+	5.54057i	−1.08880	+	0.258050i	−0.735544	−	0.677477i	$-0.763073\pi$
$461$	−23.3775	+	5.54057i	−1.08880	+	0.258050i	−0.353255	+	0.935527i	$0.614925\pi$
$462$		0			0
$463$	−34.0207	+	17.0858i	−1.58107	+	0.794046i	−0.999807	−	0.0196667i	$-0.993739\pi$
$463$	−34.0207	+	17.0858i	−1.58107	+	0.794046i	−0.581268	+	0.813712i	$0.697443\pi$
$464$	−6.36628	+	14.7587i	−0.295547	+	0.685155i
$465$		0			0
$466$	0.844439	+	14.4985i	0.0391179	+	0.671628i
$467$	−1.00160	−	5.68035i	−0.0463485	−	0.262855i	0.952824	−	0.303523i	$-0.0981628\pi$
$467$	−1.00160	−	5.68035i	−0.0463485	−	0.262855i	−0.999173	+	0.0406671i	$0.987052\pi$
$468$		0			0
$469$	−0.529044	+	3.00036i	−0.0244290	+	0.138544i
$470$	8.66759	+	1.01310i	0.399806	+	0.0467306i
$471$		0			0
$472$	8.33592	+	27.8439i	0.383692	+	1.28162i
$473$	−48.0919	−	11.3980i	−2.21127	−	0.524081i
$474$		0			0
$475$	−0.633171	−	1.46786i	−0.0290519	−	0.0673499i
$476$	0.344261	+	0.288869i	0.0157792	+	0.0132403i
$477$		0			0
$478$	−18.9773	+	15.9238i	−0.868000	+	0.728339i
$479$	20.2227	+	10.1562i	0.923997	+	0.464049i	0.846167	−	0.532918i	$-0.178905\pi$
$479$	20.2227	+	10.1562i	0.923997	+	0.464049i	0.0778299	+	0.996967i	$0.475201\pi$
$480$		0			0
$481$	34.0374	−	3.97840i	1.55197	−	0.181399i
$482$	0.815546	−	14.0024i	0.0371471	−	0.637791i
$483$		0			0
$484$	−2.38139	−	2.52413i	−0.108245	−	0.114733i
$485$	37.8700			1.71959
$486$		0			0
$487$	−22.8018			−1.03325			−0.516624	−	0.856212i	$-0.672811\pi$
$487$	−22.8018			−1.03325			−0.516624	+	0.856212i	$0.672811\pi$
$488$	13.2032	+	13.9946i	0.597683	+	0.633507i
$489$		0			0
$490$	−1.50983	+	25.9229i	−0.0682074	+	1.17108i
$491$	−1.69776	+	0.198440i	−0.0766188	+	0.00895545i	−0.154316	−	0.988022i	$-0.549317\pi$
$491$	−1.69776	+	0.198440i	−0.0766188	+	0.00895545i	0.0776971	+	0.996977i	$0.475243\pi$
$492$		0			0
$493$	−16.4533	−	8.26315i	−0.741019	−	0.372153i
$494$	−5.74549	+	4.82104i	−0.258502	+	0.216909i
$495$		0			0
$496$	5.72609	+	4.80476i	0.257109	+	0.215740i
$497$	0.366017	+	0.848524i	0.0164181	+	0.0380615i
$498$		0			0
$499$	−17.1060	−	4.05419i	−0.765769	−	0.181491i	−0.170873	−	0.985293i	$-0.554659\pi$
$499$	−17.1060	−	4.05419i	−0.765769	−	0.181491i	−0.594896	+	0.803803i	$0.702807\pi$
$500$	−0.440510	−	1.47141i	−0.0197002	−	0.0658033i
$501$		0			0
$502$	8.93428	+	1.04427i	0.398756	+	0.0466079i
$503$	−1.61077	+	9.13515i	−0.0718208	+	0.407316i	0.927609	+	0.373553i	$0.121860\pi$
$503$	−1.61077	+	9.13515i	−0.0718208	+	0.407316i	−0.999430	+	0.0337636i	$0.989251\pi$
$504$		0			0
$505$	−3.06058	−	17.3574i	−0.136194	−	0.772396i
$506$	0.275620	+	4.73221i	0.0122528	+	0.210372i
$507$		0			0
$508$	0.217219	−	0.503571i	0.00963755	−	0.0223423i
$509$	−1.45983	+	0.733155i	−0.0647059	+	0.0324965i	−0.480858	−	0.876799i	$-0.659675\pi$
$509$	−1.45983	+	0.733155i	−0.0647059	+	0.0324965i	0.416152	+	0.909295i	$0.363378\pi$
$510$		0			0
$511$	−4.48554	+	1.06309i	−0.198429	+	0.0470284i
$512$	9.39806	+	16.2779i	0.415339	+	0.719389i
$513$		0			0
$514$	3.18378	−	5.51448i	0.140431	−	0.243233i
$515$	−11.3967	+	38.0676i	−0.502198	+	1.67746i
$516$		0			0
$517$	−10.3852	−	6.83042i	−0.456739	−	0.300402i
$518$	2.66388	+	3.57821i	0.117044	+	0.157217i
$519$		0			0
$520$	−32.8204	+	21.5863i	−1.43927	+	0.946622i
$521$	−31.0098	−	11.2866i	−1.35856	−	0.494476i	−0.442953	−	0.896545i	$-0.646069\pi$
$521$	−31.0098	−	11.2866i	−1.35856	−	0.494476i	−0.915610	+	0.402069i	$0.868291\pi$
$522$		0			0
$523$	−9.00499	+	3.27755i	−0.393761	+	0.143317i	−0.531309	−	0.847178i	$-0.678300\pi$
$523$	−9.00499	+	3.27755i	−0.393761	+	0.143317i	0.137549	+	0.990495i	$0.456078\pi$
$524$	0.886943	−	1.19137i	0.0387463	−	0.0520453i
$525$		0			0
$526$	26.4125	−	27.9956i	1.15164	−	1.22066i
$527$	−5.87587	+	6.22805i	−0.255957	+	0.271298i
$528$		0			0
$529$	−13.5296	+	18.1735i	−0.588245	+	0.790150i
$530$	−1.97890	+	0.720263i	−0.0859581	+	0.0312862i
$531$		0			0
$532$	−0.0768276	−	0.0279629i	−0.00333090	−	0.00121235i
$533$	−1.11002	+	0.730069i	−0.0480802	+	0.0316228i
$534$		0			0
$535$	−23.8874	−	32.0863i	−1.03274	−	1.38721i
$536$	13.7937	+	9.07227i	0.595798	+	0.391863i
$537$		0			0
$538$	−11.8164	+	39.4694i	−0.509440	+	1.70165i
$539$	18.4934	−	32.0315i	0.796567	−	1.37969i
$540$		0			0
$541$	7.99125	+	13.8412i	0.343571	+	0.595082i	0.985093	−	0.172023i	$-0.0550302\pi$
$541$	7.99125	+	13.8412i	0.343571	+	0.595082i	−0.641522	+	0.767104i	$0.721697\pi$
$542$	−34.7859	+	8.24441i	−1.49418	+	0.354128i
$543$		0			0
$544$	4.57145	−	2.29587i	0.195999	−	0.0984345i
$545$	−14.8337	+	34.3884i	−0.635406	+	1.47304i
$546$		0			0
$547$	1.43860	+	24.6998i	0.0615101	+	1.05609i	0.877979	+	0.478699i	$0.158891\pi$
$547$	1.43860	+	24.6998i	0.0615101	+	1.05609i	−0.816469	+	0.577389i	$0.804072\pi$
$548$	−0.184823	−	1.04818i	−0.00789524	−	0.0447761i
$549$		0			0
$550$	2.48756	−	14.1076i	0.106070	−	0.601552i
$551$	3.32693	+	0.388863i	0.141732	+	0.0165661i
$552$		0			0
$553$	0.959597	+	3.20528i	0.0408062	+	0.136302i
$554$	11.4365	+	2.71050i	0.485890	+	0.115158i
$555$		0			0
$556$	1.04878	+	2.43134i	0.0444781	+	0.103112i
$557$	23.7887	+	19.9611i	1.00796	+	0.845780i	0.988067	−	0.154022i	$-0.0492226\pi$
$557$	23.7887	+	19.9611i	1.00796	+	0.845780i	0.0198942	+	0.999802i	$0.493667\pi$
$558$		0			0
$559$	−38.8792	+	32.6236i	−1.64442	+	1.37983i
$560$	−4.99083	−	2.50649i	−0.210901	−	0.105918i
$561$		0			0
$562$	−8.36227	+	0.977409i	−0.352741	+	0.0412295i
$563$	−1.48189	+	25.4430i	−0.0624540	+	1.07229i	0.810893	+	0.585195i	$0.198982\pi$
$563$	−1.48189	+	25.4430i	−0.0624540	+	1.07229i	−0.873347	+	0.487099i	$0.838055\pi$
$564$		0			0
$565$	19.3692	+	20.5301i	0.814868	+	0.863710i
$566$	−2.51489			−0.105709
$567$		0			0
$568$	5.00771			0.210119
$569$	−11.3829	−	12.0651i	−0.477194	−	0.505796i	0.443396	−	0.896326i	$-0.353773\pi$
$569$	−11.3829	−	12.0651i	−0.477194	−	0.505796i	−0.920590	+	0.390530i	$0.872292\pi$
$570$		0			0
$571$	1.20016	−	20.6060i	0.0502253	−	0.862335i	−0.875284	−	0.483610i	$-0.839325\pi$
$571$	1.20016	−	20.6060i	0.0502253	−	0.862335i	0.925509	−	0.378725i	$-0.123638\pi$
$572$	−5.59019	+	0.653400i	−0.233738	+	0.0273200i
$573$		0			0
$574$	−0.154551	−	0.0776182i	−0.00645082	−	0.00323972i
$575$	−0.794772	+	0.666893i	−0.0331443	+	0.0278114i
$576$		0			0
$577$	−19.3961	−	16.2753i	−0.807470	−	0.677548i	0.142532	−	0.989790i	$-0.454475\pi$
$577$	−19.3961	−	16.2753i	−0.807470	−	0.677548i	−0.950003	+	0.312242i	$0.898920\pi$
$578$	4.46247	+	10.3452i	0.185614	+	0.430302i
$579$		0			0
$580$	−1.71710	−	0.406960i	−0.0712986	−	0.0168981i
$581$	0.0440110	+	0.147007i	0.00182588	+	0.00609887i
$582$		0			0
$583$	2.97934	+	0.348235i	0.123392	+	0.0144224i
$584$	−4.33782	+	24.6010i	−0.179500	+	1.01800i
$585$		0			0
$586$	2.50948	+	14.2320i	0.103666	+	0.587918i
$587$	−2.50059	−	42.9335i	−0.103210	−	1.77205i	−0.511579	−	0.859236i	$-0.670939\pi$
$587$	−2.50059	−	42.9335i	−0.103210	−	1.77205i	0.408368	−	0.912817i	$-0.366098\pi$
$588$		0			0
$589$	0.616985	−	1.43033i	0.0254224	−	0.0589358i
$590$	−37.1912	+	18.6781i	−1.53114	+	0.768965i
$591$		0			0
$592$	25.6900	−	6.08865i	1.05585	−	0.250242i
$593$	6.58096	+	11.3986i	0.270248	+	0.468083i	0.968925	−	0.247354i	$-0.0795610\pi$
$593$	6.58096	+	11.3986i	0.270248	+	0.468083i	−0.698677	+	0.715437i	$0.746228\pi$
$594$		0			0
$595$	3.19870	−	5.54032i	0.131134	−	0.227131i
$596$	−0.162789	+	0.543752i	−0.00666808	+	0.0222729i
$597$		0			0
$598$	4.06690	+	2.67484i	0.166308	+	0.109382i
$599$	1.13093	+	1.51910i	0.0462085	+	0.0620688i	0.824627	−	0.565677i	$-0.191385\pi$
$599$	1.13093	+	1.51910i	0.0462085	+	0.0620688i	−0.778418	+	0.627746i	$0.783978\pi$
$600$		0			0
$601$	9.77037	−	6.42607i	0.398542	−	0.262125i	−0.334380	−	0.942439i	$-0.608527\pi$
$601$	9.77037	−	6.42607i	0.398542	−	0.262125i	0.732921	+	0.680313i	$0.238156\pi$
$602$	−6.20829	−	2.25963i	−0.253031	−	0.0920957i
$603$		0			0
$604$	−1.71371	+	0.623740i	−0.0697299	+	0.0253796i
$605$	−29.4994	+	39.6246i	−1.19932	+	1.61097i
$606$		0			0
$607$	31.4306	−	33.3145i	1.27573	−	1.35219i	0.369597	−	0.929192i	$-0.379496\pi$
$607$	31.4306	−	33.3145i	1.27573	−	1.35219i	0.906130	−	0.423000i	$-0.139023\pi$
$608$	−0.638659	+	0.676939i	−0.0259010	+	0.0274535i
$609$		0			0
$610$	−16.4515	+	22.0982i	−0.666100	+	0.894728i
$611$	−11.9945	+	4.36565i	−0.485247	+	0.176615i
$612$		0			0
$613$	−16.9158	−	6.15684i	−0.683222	−	0.248672i	−0.0229915	−	0.999736i	$-0.507319\pi$
$613$	−16.9158	−	6.15684i	−0.683222	−	0.248672i	−0.660230	+	0.751063i	$0.729541\pi$
$614$	29.7895	−	19.5929i	1.20221	−	0.790705i
$615$		0			0
$616$	4.34954	+	5.84245i	0.175248	+	0.235399i
$617$	11.5649	+	7.60632i	0.465583	+	0.306219i	0.760539	−	0.649292i	$-0.224935\pi$
$617$	11.5649	+	7.60632i	0.465583	+	0.306219i	−0.294956	+	0.955511i	$0.595305\pi$
$618$		0			0
$619$	−0.296246	+	0.989531i	−0.0119071	+	0.0397726i	−0.963737	−	0.266855i	$-0.914015\pi$
$619$	−0.296246	+	0.989531i	−0.0119071	+	0.0397726i	0.951830	+	0.306628i	$0.0992007\pi$
$620$	−0.410330	+	0.710713i	−0.0164793	+	0.0285429i
$621$		0			0
$622$	−1.55098	−	2.68638i	−0.0621887	−	0.107714i
$623$	−7.40191	+	1.75429i	−0.296551	+	0.0702840i
$624$		0			0
$625$	−27.4507	+	13.7863i	−1.09803	+	0.551451i
$626$	3.96605	−	9.19434i	0.158515	−	0.367480i
$627$		0			0
$628$	0.132477	+	2.27454i	0.00528640	+	0.0907640i
$629$	5.25161	+	29.7834i	0.209395	+	1.18754i
$630$		0			0
$631$	3.36622	−	19.0908i	0.134007	−	0.759992i	−0.841539	−	0.540196i	$-0.818350\pi$
$631$	3.36622	−	19.0908i	0.134007	−	0.759992i	0.975546	−	0.219795i	$-0.0705389\pi$
$632$	18.0085	+	2.10489i	0.716340	+	0.0837282i
$633$		0			0
$634$	2.16946	+	7.24649i	0.0861601	+	0.287795i
$635$	−7.59658	−	1.80042i	−0.301461	−	0.0714476i
$636$		0			0
$637$	−15.0437	−	34.8751i	−0.596052	−	1.38180i
$638$	22.9937	+	19.2940i	0.910329	+	0.763857i
$639$		0			0
$640$	−25.1403	+	21.0953i	−0.993759	+	0.833863i
$641$	−25.2736	−	12.6929i	−0.998247	−	0.501338i	−0.126853	−	0.991922i	$-0.540488\pi$
$641$	−25.2736	−	12.6929i	−0.998247	−	0.501338i	−0.871394	+	0.490583i	$0.836784\pi$
$642$		0			0
$643$	−30.3500	+	3.54741i	−1.19689	+	0.139896i	−0.691098	−	0.722761i	$-0.742873\pi$
$643$	−30.3500	+	3.54741i	−1.19689	+	0.139896i	−0.505789	+	0.862657i	$0.668799\pi$
$644$	−0.00308527	+	0.0529720i	−0.000121576	+	0.00208739i
$645$		0			0
$646$	−4.54225	−	4.81450i	−0.178712	−	0.189424i
$647$	4.92528			0.193633			0.0968163	−	0.995302i	$-0.469134\pi$
$647$	4.92528			0.193633			0.0968163	+	0.995302i	$0.469134\pi$
$648$		0			0
$649$	59.2801			2.32695
$650$	−10.0950	−	10.7000i	−0.395957	−	0.419689i
$651$		0			0
$652$	0.0643815	−	1.10539i	0.00252137	−	0.0432903i
$653$	−1.40936	+	0.164731i	−0.0551526	+	0.00644641i	−0.143624	−	0.989632i	$-0.545876\pi$
$653$	−1.40936	+	0.164731i	−0.0551526	+	0.00644641i	0.0884719	+	0.996079i	$0.471802\pi$
$654$		0			0
$655$	−18.8945	−	9.48916i	−0.738268	−	0.370772i
$656$	−0.784103	+	0.657940i	−0.0306141	+	0.0256883i
$657$		0			0
$658$	−1.27284	−	1.06804i	−0.0496204	−	0.0416365i
$659$	−8.54453	−	19.8084i	−0.332848	−	0.771628i	−0.999652	−	0.0263944i	$-0.991597\pi$
$659$	−8.54453	−	19.8084i	−0.332848	−	0.771628i	0.666804	−	0.745233i	$-0.267662\pi$
$660$		0			0
$661$	−11.0865	−	2.62755i	−0.431215	−	0.102200i	0.00927571	−	0.999957i	$-0.497047\pi$
$661$	−11.0865	−	2.62755i	−0.431215	−	0.102200i	−0.440491	+	0.897757i	$0.645196\pi$
$662$	−0.710029	−	2.37166i	−0.0275961	−	0.0921773i
$663$		0			0
$664$	0.825943	+	0.0965389i	0.0320528	+	0.00374644i
$665$	−0.202102	+	1.14618i	−0.00783719	+	0.0444469i
$666$		0			0
$667$	−0.377495	−	2.14088i	−0.0146167	−	0.0828952i
$668$	−0.184981	−	3.17601i	−0.00715715	−	0.122883i
$669$		0			0
$670$	−9.36344	+	21.7069i	−0.361741	+	0.838610i
$671$	35.0673	−	17.6115i	1.35376	−	0.679883i
$672$		0			0
$673$	−32.2583	+	7.64537i	−1.24347	+	0.294707i	−0.799133	−	0.601154i	$-0.794708\pi$
$673$	−32.2583	+	7.64537i	−1.24347	+	0.294707i	−0.444334	+	0.895861i	$0.646560\pi$
$674$	−13.8304	−	23.9549i	−0.532726	−	0.922708i
$675$		0			0
$676$	−1.70168	+	2.94739i	−0.0654492	+	0.113361i
$677$	3.44496	−	11.5070i	0.132401	−	0.442249i	−0.865920	−	0.500183i	$-0.833266\pi$
$677$	3.44496	−	11.5070i	0.132401	−	0.442249i	0.998320	+	0.0579342i	$0.0184513\pi$
$678$		0			0
$679$	−6.02435	−	3.96228i	−0.231194	−	0.152058i
$680$	−20.7021	−	27.8077i	−0.793887	−	1.06638i
$681$		0			0
$682$	11.6626	−	7.67063i	0.446585	−	0.293724i
$683$	1.09663	+	0.399140i	0.0419613	+	0.0152727i	0.362916	−	0.931822i	$-0.381781\pi$
$683$	1.09663	+	0.399140i	0.0419613	+	0.0152727i	−0.320954	+	0.947095i	$0.604004\pi$
$684$		0			0
$685$	−14.2377	+	5.18211i	−0.543996	+	0.197998i
$686$	6.01220	−	8.07578i	0.229547	−	0.308335i
$687$		0			0
$688$	−26.8331	+	28.4414i	−1.02300	+	1.08432i
$689$	2.11382	−	2.24052i	0.0805303	−	0.0853571i
$690$		0			0
$691$	−7.62254	+	10.2389i	−0.289975	+	0.389504i	−0.923109	−	0.384538i	$-0.874361\pi$
$691$	−7.62254	+	10.2389i	−0.289975	+	0.389504i	0.633134	+	0.774042i	$0.281768\pi$
$692$	0.214191	−	0.0779590i	0.00814231	−	0.00296356i
$693$		0			0
$694$	−17.5165	−	6.37547i	−0.664916	−	0.242009i
$695$	31.4928	−	20.7131i	1.19459	−	0.785694i
$696$		0			0
$697$	−0.700163	−	0.940482i	−0.0265206	−	0.0356233i
$698$	−23.3113	−	15.3321i	−0.882346	−	0.580328i
$699$		0			0
$700$	0.0459906	−	0.153619i	0.00173828	−	0.00580626i
$701$	15.3355	−	26.5618i	0.579213	−	1.00323i	−0.416357	−	0.909201i	$-0.636693\pi$
$701$	15.3355	−	26.5618i	0.579213	−	1.00323i	0.995570	−	0.0940253i	$-0.0299734\pi$
$702$		0			0
$703$	−2.75099	−	4.76486i	−0.103756	−	0.179710i
$704$	38.0506	−	9.01816i	1.43409	−	0.339885i
$705$		0			0
$706$	−12.1600	+	6.10700i	−0.457649	+	0.229840i
$707$	−1.32920	+	3.08144i	−0.0499898	+	0.115889i
$708$		0			0
$709$	−0.924594	−	15.8747i	−0.0347239	−	0.596186i	−0.970126	−	0.242601i	$-0.922000\pi$
$709$	−0.924594	−	15.8747i	−0.0347239	−	0.596186i	0.935402	−	0.353585i	$-0.115038\pi$
$710$	1.24515	+	7.06157i	0.0467295	+	0.265016i
$711$		0			0
$712$	−7.15816	+	40.5959i	−0.268263	+	1.52140i
$713$	−1.00414	−	0.117367i	−0.0376055	−	0.00439545i
$714$		0			0
$715$	22.9788	+	76.7545i	0.859358	+	2.87046i
$716$	0.676361	+	0.160300i	0.0252768	+	0.00599071i
$717$		0			0
$718$	−8.39403	−	19.4595i	−0.313262	−	0.726224i
$719$	−1.87986	−	1.57739i	−0.0701068	−	0.0588266i	0.607061	−	0.794655i	$-0.292348\pi$
$719$	−1.87986	−	1.57739i	−0.0701068	−	0.0588266i	−0.677168	+	0.735829i	$0.736793\pi$
$720$		0			0
$721$	5.79593	−	4.86337i	0.215852	−	0.181121i
$722$	−24.0092	−	12.0579i	−0.893528	−	0.448747i
$723$		0			0
$724$	1.83035	−	0.213938i	0.0680246	−	0.00795093i
$725$	−0.381993	+	6.55857i	−0.0141869	+	0.243579i
$726$		0			0
$727$	−27.7698	−	29.4343i	−1.02993	−	1.09166i	−0.995737	−	0.0922431i	$-0.970596\pi$
$727$	−27.7698	−	29.4343i	−1.02993	−	1.09166i	−0.0341901	−	0.999415i	$-0.510885\pi$
$728$	7.47960			0.277212
$729$		0			0
$730$	−35.7695			−1.32389
$731$	−30.7370	−	32.5793i	−1.13685	−	1.20499i
$732$		0			0
$733$	−2.11131	+	36.2498i	−0.0779831	+	1.33892i	0.701579	+	0.712592i	$0.252479\pi$
$733$	−2.11131	+	36.2498i	−0.0779831	+	1.33892i	−0.779562	+	0.626325i	$0.784558\pi$
$734$	10.4686	−	1.22360i	0.386402	−	0.0451639i
$735$		0			0
$736$	0.539760	+	0.271078i	0.0198958	+	0.00999206i
$737$	25.7950	−	21.6445i	0.950169	−	0.797287i
$738$		0			0
$739$	28.2240	+	23.6828i	1.03824	+	0.871185i	0.991808	−	0.127736i	$-0.0407711\pi$
$739$	28.2240	+	23.6828i	1.03824	+	0.871185i	0.0464300	+	0.998922i	$0.485216\pi$
$740$	1.14808	+	2.66156i	0.0422044	+	0.0978409i
$741$		0			0
$742$	0.390164	+	0.0924705i	0.0143234	+	0.00339470i
$743$	14.3291	+	47.8625i	0.525683	+	1.75590i	0.646175	+	0.763190i	$0.276368\pi$
$743$	14.3291	+	47.8625i	0.525683	+	1.75590i	−0.120492	+	0.992714i	$0.538447\pi$
$744$		0			0
$745$	8.02534	+	0.938027i	0.294026	+	0.0343667i
$746$	8.83929	−	50.1301i	0.323629	−	1.83539i
$747$		0			0
$748$	−0.862509	−	4.89153i	−0.0315365	−	0.178852i
$749$	0.442858	+	7.60358i	0.0161817	+	0.277829i
$750$		0			0
$751$	9.63029	−	22.3255i	0.351414	−	0.814670i	−0.647214	−	0.762309i	$-0.724066\pi$
$751$	9.63029	−	22.3255i	0.351414	−	0.814670i	0.998628	−	0.0523616i	$-0.0166748\pi$
$752$	−8.78792	+	4.41346i	−0.320462	+	0.160942i
$753$		0			0
$754$	29.9925	−	7.10834i	1.09226	−	0.258871i
$755$	12.9805	+	22.4829i	0.472409	+	0.818236i
$756$		0			0
$757$	−12.1062	+	20.9685i	−0.440007	+	0.762114i	−0.997689	−	0.0679403i	$-0.978357\pi$
$757$	−12.1062	+	20.9685i	−0.440007	+	0.762114i	0.557683	+	0.830054i	$0.311691\pi$
$758$	−3.10553	+	10.3732i	−0.112798	+	0.376772i
$759$		0			0
$760$	5.26940	+	3.46574i	0.191141	+	0.125715i
$761$	16.5980	+	22.2949i	0.601676	+	0.808191i	0.993737	−	0.111748i	$-0.0356450\pi$
$761$	16.5980	+	22.2949i	0.601676	+	0.808191i	−0.392060	+	0.919939i	$0.628238\pi$
$762$		0			0
$763$	5.95774	−	3.91847i	0.215685	−	0.141858i
$764$	−0.111975	−	0.0407556i	−0.00405112	−	0.00147449i
$765$		0			0
$766$	−29.6764	+	10.8013i	−1.07225	+	0.390267i
$767$	36.3516	−	48.8286i	1.31258	−	1.76310i
$768$		0			0
$769$	−8.27267	+	8.76852i	−0.298320	+	0.316201i	−0.859144	−	0.511735i	$-0.829003\pi$
$769$	−8.27267	+	8.76852i	−0.298320	+	0.316201i	0.560824	+	0.827935i	$0.310485\pi$
$770$	−7.15719	+	7.58617i	−0.257927	+	0.273387i
$771$		0			0
$772$	1.09613	−	1.47236i	0.0394507	−	0.0529914i
$773$	31.4818	−	11.4584i	1.13232	−	0.412131i	0.293186	−	0.956055i	$-0.405284\pi$
$773$	31.4818	−	11.4584i	1.13232	−	0.412131i	0.839134	+	0.543924i	$0.183062\pi$
$774$		0			0
$775$	2.87099	+	1.04495i	0.103129	+	0.0375359i
$776$	−32.6460	+	21.4716i	−1.17192	+	0.770787i
$777$		0			0
$778$	16.0667	+	21.5813i	0.576019	+	0.773727i
$779$	0.178216	+	0.117215i	0.00638525	+	0.00419965i
$780$		0			0
$781$	2.92929	−	9.78451i	0.104818	−	0.350117i
$782$	−2.14790	+	3.72027i	−0.0768087	+	0.133037i
$783$		0			0
$784$	−14.6309	−	25.3414i	−0.522532	−	0.905051i
$785$	31.5596	−	7.47976i	1.12641	−	0.266964i
$786$		0			0
$787$	−29.9267	+	15.0298i	−1.06677	+	0.535753i	−0.893473	−	0.449116i	$-0.851739\pi$
$787$	−29.9267	+	15.0298i	−1.06677	+	0.535753i	−0.173299	+	0.984869i	$0.555443\pi$
$788$	−0.275948	+	0.639720i	−0.00983025	+	0.0227891i
$789$		0			0
$790$	1.50955	+	25.9179i	0.0537073	+	0.922119i
$791$	−0.933210	−	5.29250i	−0.0331811	−	0.188180i
$792$		0			0
$793$	6.99742	−	39.6843i	0.248486	−	1.40923i
$794$	−46.9369	−	5.48614i	−1.66573	−	0.194696i
$795$		0			0
$796$	−0.579463	−	1.93554i	−0.0205385	−	0.0686035i
$797$	11.1001	+	2.63078i	0.393187	+	0.0931869i	0.422453	−	0.906385i	$-0.361169\pi$
$797$	11.1001	+	2.63078i	0.393187	+	0.0931869i	−0.0292667	+	0.999572i	$0.509317\pi$
$798$		0			0
$799$	−4.46170	−	10.3434i	−0.157843	−	0.365922i
$800$	−1.39830	−	1.17331i	−0.0494373	−	0.0414828i
$801$		0			0
$802$	45.3010	−	38.0121i	1.59963	−	1.34225i
$803$	45.5303	+	22.8662i	1.60673	+	0.806929i
$804$		0			0
$805$	0.750248	−	0.0876914i	0.0264428	−	0.00309071i
$806$	0.833473	−	14.3102i	0.0293578	−	0.504055i
$807$		0			0
$808$	12.4797	+	13.2278i	0.439036	+	0.465351i
$809$	−20.6051			−0.724436			−0.362218	−	0.932093i	$-0.617980\pi$
$809$	−20.6051			−0.724436			−0.362218	+	0.932093i	$0.617980\pi$
$810$		0			0
$811$	−13.3672			−0.469386			−0.234693	−	0.972070i	$-0.575408\pi$
$811$	−13.3672			−0.469386			−0.234693	+	0.972070i	$0.575408\pi$
$812$	0.230576	+	0.244396i	0.00809163	+	0.00857663i
$813$		0			0
$814$	2.86678	−	49.2208i	0.100481	−	1.72519i
$815$	−15.6557	+	1.82989i	−0.548396	+	0.0640983i
$816$		0			0
$817$	7.28182	+	3.65707i	0.254759	+	0.127945i
$818$	−25.1111	+	21.0707i	−0.877990	+	0.736721i
$819$		0			0
$820$	−0.0860859	−	0.0722347i	−0.00300625	−	0.00252254i
$821$	−0.720504	−	1.67032i	−0.0251458	−	0.0582945i	0.905180	−	0.425027i	$-0.139736\pi$
$821$	−0.720504	−	1.67032i	−0.0251458	−	0.0582945i	−0.930326	+	0.366733i	$0.880476\pi$
$822$		0			0
$823$	−44.9653	−	10.6570i	−1.56739	−	0.371479i	−0.647005	−	0.762486i	$-0.723979\pi$
$823$	−44.9653	−	10.6570i	−1.56739	−	0.371479i	−0.920388	+	0.391007i	$0.872127\pi$
$824$	−11.7591	−	39.2780i	−0.409647	−	1.36832i
$825$		0			0
$826$	7.87062	+	0.919944i	0.273854	+	0.0320089i
$827$	−3.09858	+	17.5729i	−0.107748	+	0.611070i	0.882339	+	0.470614i	$0.155968\pi$
$827$	−3.09858	+	17.5729i	−0.107748	+	0.611070i	−0.990087	+	0.140455i	$0.955143\pi$
$828$		0			0
$829$	4.49900	+	25.5151i	0.156257	+	0.886175i	0.957628	+	0.288008i	$0.0929930\pi$
$829$	4.49900	+	25.5151i	0.156257	+	0.886175i	−0.801371	+	0.598167i	$0.795896\pi$
$830$	0.0692339	+	1.18870i	0.00240314	+	0.0412604i
$831$		0			0
$832$	15.9051	−	36.8721i	0.551409	−	1.27831i
$833$	29.9537	−	15.0433i	1.03783	−	0.521219i
$834$		0			0
$835$	−44.0676	+	10.4442i	−1.52502	+	0.361437i
$836$	0.451815	+	0.782566i	0.0156263	+	0.0270656i
$837$		0			0
$838$	−20.7376	+	35.9187i	−0.716370	+	1.24079i
$839$	6.95930	−	23.2457i	0.240262	−	0.802530i	−0.749772	−	0.661697i	$-0.769837\pi$
$839$	6.95930	−	23.2457i	0.240262	−	0.802530i	0.990033	−	0.140833i	$-0.0449782\pi$
$840$		0			0
$841$	12.7281	+	8.37142i	0.438901	+	0.288670i
$842$	11.5115	+	15.4626i	0.396712	+	0.532876i
$843$		0			0
$844$	−2.94242	+	1.93526i	−0.101282	+	0.0666144i
$845$	45.5264	+	16.5702i	1.56615	+	0.570034i
$846$		0			0
$847$	8.83862	−	3.21699i	0.303699	−	0.110537i
$848$	1.41713	−	1.90354i	0.0486646	−	0.0653679i
$849$		0			0
$850$	8.90891	−	9.44289i	0.305573	−	0.323888i
$851$	−2.45046	+	2.59733i	−0.0840005	+	0.0890354i
$852$		0			0
$853$	8.19208	−	11.0039i	0.280492	−	0.376766i	−0.639442	−	0.768839i	$-0.720835\pi$
$853$	8.19208	−	11.0039i	0.280492	−	0.376766i	0.919934	+	0.392074i	$0.128242\pi$
$854$	4.92919	−	1.79408i	0.168673	−	0.0613921i
$855$		0			0
$856$	38.7846	+	14.1164i	1.32563	+	0.482490i
$857$	−26.3582	+	17.3361i	−0.900380	+	0.592189i	−0.913103	−	0.407730i	$-0.866321\pi$
$857$	−26.3582	+	17.3361i	−0.900380	+	0.592189i	0.0127226	+	0.999919i	$0.495950\pi$
$858$		0			0
$859$	16.3055	+	21.9021i	0.556336	+	0.747289i	0.987951	−	0.154769i	$-0.0494634\pi$
$859$	16.3055	+	21.9021i	0.556336	+	0.747289i	−0.431615	+	0.902058i	$0.642056\pi$
$860$	−3.58668	−	2.35900i	−0.122305	−	0.0804411i
$861$		0			0
$862$	−5.27305	+	17.6132i	−0.179601	+	0.599909i
$863$	−15.4903	+	26.8301i	−0.527297	+	0.913306i	0.472196	+	0.881493i	$0.343461\pi$
$863$	−15.4903	+	26.8301i	−0.527297	+	0.913306i	−0.999494	+	0.0318126i	$0.989872\pi$
$864$		0			0
$865$	−1.62239	−	2.81006i	−0.0551628	−	0.0955448i
$866$	−2.77090	+	0.656716i	−0.0941591	+	0.0223161i
$867$		0			0
$868$	0.139636	−	0.0701278i	0.00473955	−	0.00238029i
$869$	14.6469	−	33.9554i	0.496863	−	1.15186i
$870$		0			0
$871$	−2.01056	−	34.5199i	−0.0681251	−	1.16966i
$872$	−6.71014	−	38.0551i	−0.227234	−	1.28871i
$873$		0			0
$874$	0.135710	−	0.769648i	0.00459045	−	0.0260337i
$875$	4.13495	+	0.483306i	0.139787	+	0.0163387i
$876$		0			0
$877$	−12.9072	−	43.1129i	−0.435844	−	1.45582i	−0.840731	−	0.541453i	$-0.817875\pi$
$877$	−12.9072	−	43.1129i	−0.435844	−	1.45582i	0.404888	−	0.914366i	$-0.367311\pi$
$878$	−11.9740	−	2.83789i	−0.404103	−	0.0957742i
$879$		0			0
$880$	24.4487	+	56.6784i	0.824165	+	1.91063i
$881$	−6.32139	−	5.30428i	−0.212973	−	0.178706i	0.530060	−	0.847960i	$-0.322169\pi$
$881$	−6.32139	−	5.30428i	−0.212973	−	0.178706i	−0.743033	+	0.669254i	$0.766614\pi$
$882$		0			0
$883$	12.7330	−	10.6843i	0.428501	−	0.359555i	−0.402885	−	0.915251i	$-0.631992\pi$
$883$	12.7330	−	10.6843i	0.428501	−	0.359555i	0.831386	+	0.555696i	$0.187548\pi$
$884$	−4.55803	−	2.28913i	−0.153303	−	0.0769917i
$885$		0			0
$886$	−43.2127	+	5.05084i	−1.45176	+	0.169686i
$887$	−0.428591	+	7.35862i	−0.0143907	+	0.247078i	0.983439	+	0.181237i	$0.0580101\pi$
$887$	−0.428591	+	7.35862i	−0.0143907	+	0.247078i	−0.997830	+	0.0658413i	$0.979027\pi$
$888$		0			0
$889$	1.02009	+	1.08123i	0.0342126	+	0.0362633i
$890$	−59.0258			−1.97855
$891$		0			0
$892$	−0.603232			−0.0201977
$893$	1.40634	+	1.49064i	0.0470615	+	0.0498823i
$894$		0			0
$895$	0.575342	−	9.87825i	0.0192316	−	0.330193i
$896$	6.20648	−	0.725434i	0.207344	−	0.0242350i
$897$		0			0
$898$	−43.2827	−	21.7374i	−1.44436	−	0.725386i
$899$	−4.90401	+	4.11496i	−0.163558	+	0.137241i
$900$		0			0
$901$	2.08241	+	1.74735i	0.0693751	+	0.0582126i
$902$	0.757100	+	1.75516i	0.0252087	+	0.0584403i
$903$		0			0
$904$	−28.3375	−	6.71611i	−0.942492	−	0.223375i
$905$	−7.52377	−	25.1311i	−0.250098	−	0.835387i
$906$		0			0
$907$	19.1143	+	2.23414i	0.634680	+	0.0741835i	0.427348	−	0.904087i	$-0.359448\pi$
$907$	19.1143	+	2.23414i	0.634680	+	0.0741835i	0.207332	+	0.978271i	$0.433522\pi$
$908$	0.0639888	−	0.362898i	0.00212354	−	0.0120432i
$909$		0			0
$910$	1.85977	+	10.5473i	0.0616509	+	0.349639i
$911$	1.54298	+	26.4920i	0.0511212	+	0.877718i	0.922233	+	0.386634i	$0.126362\pi$
$911$	1.54298	+	26.4920i	0.0511212	+	0.877718i	−0.871112	+	0.491084i	$0.836601\pi$
$912$		0			0
$913$	0.671767	−	1.55733i	0.0222322	−	0.0515401i
$914$	−41.2667	+	20.7249i	−1.36498	+	0.685519i
$915$		0			0
$916$	3.81459	−	0.904076i	0.126038	−	0.0298715i
$917$	2.01289	+	3.48643i	0.0664716	+	0.115132i
$918$		0			0
$919$	16.6181	−	28.7834i	0.548181	−	0.949477i	−0.450219	−	0.892918i	$-0.648654\pi$
$919$	16.6181	−	28.7834i	0.548181	−	0.949477i	0.998399	−	0.0565583i	$-0.0180127\pi$
$920$	1.17396	−	3.92131i	0.0387045	−	0.129282i
$921$		0			0
$922$	29.6559	+	19.5050i	0.976665	+	0.642363i
$923$	−6.26314	−	8.41286i	−0.206154	−	0.276913i
$924$		0			0
$925$	9.01599	−	5.92991i	0.296444	−	0.194974i
$926$	52.8537	+	19.2372i	1.73688	+	0.632173i
$927$		0			0
$928$	3.59404	−	1.30812i	0.117980	−	0.0429413i
$929$	−10.3970	+	13.9656i	−0.341114	+	0.458195i	−0.939267	−	0.343186i	$-0.888494\pi$
$929$	−10.3970	+	13.9656i	−0.341114	+	0.458195i	0.598154	+	0.801381i	$0.295901\pi$
$930$		0			0
$931$	−4.18471	+	4.43553i	−0.137148	+	0.145369i
$932$	1.23304	−	1.30694i	0.0403895	−	0.0428103i
$933$		0			0
$934$	−5.08885	+	6.83551i	−0.166512	+	0.223665i
$935$	−66.4430	+	24.1833i	−2.17292	+	0.790877i
$936$		0			0
$937$	23.8616	+	8.68490i	0.779523	+	0.283723i	0.700974	−	0.713187i	$-0.252749\pi$
$937$	23.8616	+	8.68490i	0.779523	+	0.283723i	0.0785493	+	0.996910i	$0.474971\pi$
$938$	3.76069	−	2.47344i	0.122791	−	0.0807608i
$939$		0			0
$940$	−0.644727	−	0.866019i	−0.0210287	−	0.0282464i
$941$	−8.24852	−	5.42514i	−0.268894	−	0.176854i	0.407900	−	0.913026i	$-0.366261\pi$
$941$	−8.24852	−	5.42514i	−0.268894	−	0.176854i	−0.676794	+	0.736172i	$0.736631\pi$
$942$		0			0
$943$	0.0397046	−	0.132623i	0.00129296	−	0.00431879i
$944$	23.4495	−	40.6157i	0.763215	−	1.32193i
$945$		0			0
$946$	36.5103	+	63.2377i	1.18705	+	2.05603i
$947$	−15.9174	+	3.77250i	−0.517247	+	0.122590i	−0.480944	−	0.876751i	$-0.659706\pi$
$947$	−15.9174	+	3.77250i	−0.517247	+	0.122590i	−0.0363025	+	0.999341i	$0.511558\pi$
$948$		0			0
$949$	46.7546	−	23.4810i	1.51772	−	0.762227i
$950$	−0.935464	+	2.16865i	−0.0303505	+	0.0703603i
$951$		0			0
$952$	0.383804	+	6.58966i	0.0124392	+	0.213572i
$953$	−7.86853	−	44.6246i	−0.254887	−	1.44553i	−0.796363	−	0.604818i	$-0.793246\pi$
$953$	−7.86853	−	44.6246i	−0.254887	−	1.44553i	0.541477	−	0.840716i	$-0.317865\pi$
$954$		0			0
$955$	−0.294561	+	1.67054i	−0.00953179	+	0.0540574i
$956$	3.04421	+	0.355817i	0.0984568	+	0.0115080i
$957$		0			0
$958$	−9.58890	−	32.0292i	−0.309803	−	1.03482i
$959$	2.80713	+	0.665302i	0.0906469	+	0.0214837i
$960$		0			0
$961$	−11.0993	−	25.7310i	−0.358042	−	0.830034i
$962$	−38.7848	−	32.5443i	−1.25047	−	1.04927i
$963$		0			0
$964$	−1.32933	+	1.11544i	−0.0428148	+	0.0359259i
$965$	−23.3508	−	11.7272i	−0.751689	−	0.377512i
$966$		0			0
$967$	−26.5333	+	3.10130i	−0.853254	+	0.0997311i	−0.531465	−	0.847080i	$-0.678358\pi$
$967$	−26.5333	+	3.10130i	−0.853254	+	0.0997311i	−0.321789	+	0.946811i	$0.604284\pi$
$968$	2.96367	−	50.8842i	0.0952559	−	1.63548i
$969$		0			0
$970$	−38.3953	−	40.6967i	−1.23280	−	1.30669i
$971$	21.0798			0.676483			0.338242	−	0.941059i	$-0.390168\pi$
$971$	21.0798			0.676483			0.338242	+	0.941059i	$0.390168\pi$
$972$		0			0
$973$	−7.17705			−0.230086
$974$	23.1181	+	24.5037i	0.740751	+	0.785150i
$975$		0			0
$976$	1.80513	−	30.9929i	0.0577808	−	0.992057i
$977$	−19.5969	+	2.29055i	−0.626961	+	0.0732813i	−0.423640	−	0.905831i	$-0.639248\pi$
$977$	−19.5969	+	2.29055i	−0.626961	+	0.0732813i	−0.203322	+	0.979112i	$0.565174\pi$
$978$		0			0
$979$	75.1328	+	37.7331i	2.40125	+	1.20595i
$980$	2.46101	−	2.06503i	0.0786142	−	0.0659651i
$981$		0			0
$982$	1.93456	+	1.62329i	0.0617343	+	0.0518012i
$983$	20.2635	+	46.9762i	0.646306	+	1.49831i	0.854086	+	0.520131i	$0.174117\pi$
$983$	20.2635	+	46.9762i	0.646306	+	1.49831i	−0.207780	+	0.978176i	$0.566624\pi$
$984$		0			0
$985$	9.65046	+	2.28720i	0.307489	+	0.0728762i
$986$	7.80159	+	26.0591i	0.248453	+	0.829892i
$987$		0			0
$988$	0.921655	+	0.107726i	0.0293217	+	0.00342722i
$989$	0.918335	−	5.20814i	0.0292014	−	0.165609i
$990$		0			0
$991$	−9.85960	−	55.9165i	−0.313200	−	1.77625i	−0.582138	−	0.813090i	$-0.697784\pi$
$991$	−9.85960	−	55.9165i	−0.313200	−	1.77625i	0.268937	−	0.963158i	$-0.413328\pi$
$992$	−0.103421	−	1.77567i	−0.00328363	−	0.0563777i
$993$		0			0
$994$	0.540764	−	1.25363i	0.0171520	−	0.0397628i
$995$	−25.7022	+	12.9081i	−0.814815	+	0.409216i
$996$		0			0
$997$	11.1432	−	2.64098i	0.352908	−	0.0836408i	−0.0503381	−	0.998732i	$-0.516030\pi$
$997$	11.1432	−	2.64098i	0.352908	−	0.0836408i	0.403246	+	0.915091i	$0.367882\pi$
$998$	12.9865	+	22.4932i	0.411079	+	0.712010i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.g.b.109.3		144
3.2	odd	2		729.2.g.c.109.6		144
9.2	odd	6		81.2.g.a.49.6	yes	144
9.4	even	3		729.2.g.a.595.6		144
9.5	odd	6		729.2.g.d.595.3		144
9.7	even	3		243.2.g.a.37.3		144
81.11	odd	54		729.2.g.c.622.6		144
81.16	even	27		243.2.g.a.46.3		144
81.31	even	27		6561.2.a.d.1.51		72
81.38	odd	54		729.2.g.d.136.3		144
81.43	even	27		729.2.g.a.136.6		144
81.50	odd	54		6561.2.a.c.1.22		72
81.65	odd	54		81.2.g.a.43.6	✓	144
81.70	even	27	inner	729.2.g.b.622.3		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.43.6	✓	144	81.65	odd	54
81.2.g.a.49.6	yes	144	9.2	odd	6
243.2.g.a.37.3		144	9.7	even	3
243.2.g.a.46.3		144	81.16	even	27
729.2.g.a.136.6		144	81.43	even	27
729.2.g.a.595.6		144	9.4	even	3
729.2.g.b.109.3		144	1.1	even	1	trivial
729.2.g.b.622.3		144	81.70	even	27	inner
729.2.g.c.109.6		144	3.2	odd	2
729.2.g.c.622.6		144	81.11	odd	54
729.2.g.d.136.3		144	81.38	odd	54
729.2.g.d.595.3		144	9.5	odd	6
6561.2.a.c.1.22		72	81.50	odd	54
6561.2.a.d.1.51		72	81.31	even	27

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-1.01387 - 1.07464i) q^{2} +(-0.0106282 + 0.182479i) q^{4} +(2.58446 - 0.302080i) q^{5} +(-0.442742 - 0.222353i) q^{7} +(-2.05667 + 1.72575i) q^{8} +O(q^{10})\)	\(q+(-1.01387 - 1.07464i) q^{2} +(-0.0106282 + 0.182479i) q^{4} +(2.58446 - 0.302080i) q^{5} +(-0.442742 - 0.222353i) q^{7} +(-2.05667 + 1.72575i) q^{8} +(-2.94494 - 2.47110i) q^{10} +(2.16887 + 5.02801i) q^{11} +(5.47152 + 1.29677i) q^{13} +(0.209933 + 0.701226i) q^{14} +(4.30287 + 0.502934i) q^{16} +(-0.861719 + 4.88705i) q^{17} +(-0.156770 - 0.889086i) q^{19} +(0.0276551 + 0.474820i) q^{20} +(3.20435 - 7.42851i) q^{22} +(-0.523602 + 0.262963i) q^{23} +(1.72298 - 0.408353i) q^{25} +(-4.15385 - 7.19468i) q^{26} +(0.0452802 - 0.0784277i) q^{28} +(-1.06410 + 3.55434i) q^{29} +(1.44158 + 0.948144i) q^{31} +(-0.615586 - 0.826876i) q^{32} +(6.12550 - 4.02880i) q^{34} +(-1.21142 - 0.440920i) q^{35} +(5.72681 - 2.08439i) q^{37} +(-0.796504 + 1.06989i) q^{38} +(-4.79408 + 5.08143i) q^{40} +(-0.162140 + 0.171859i) q^{41} +(-5.38987 + 7.23985i) q^{43} +(-0.940554 + 0.342334i) q^{44} +(0.813456 + 0.296074i) q^{46} +(-1.89654 + 1.24737i) q^{47} +(-4.03353 - 5.41797i) q^{49} +(-2.18571 - 1.43756i) q^{50} +(-0.294786 + 0.984653i) q^{52} +(0.273896 - 0.474403i) q^{53} +(7.12423 + 12.3395i) q^{55} +(1.29430 - 0.306755i) q^{56} +(4.89850 - 2.46012i) q^{58} +(4.28786 - 9.94038i) q^{59} +(-0.416681 - 7.15413i) q^{61} +(-0.442665 - 2.51048i) q^{62} +(1.24008 - 7.03282i) q^{64} +(14.5327 + 1.69863i) q^{65} +(-1.76366 - 5.89102i) q^{67} +(-0.882623 - 0.209186i) q^{68} +(0.754392 + 1.74888i) q^{70} +(-1.42883 - 1.19893i) q^{71} +(7.12761 - 5.98078i) q^{73} +(-8.04622 - 4.04096i) q^{74} +(0.163905 - 0.0191578i) q^{76} +(0.157744 - 2.70836i) q^{77} +(-4.63436 - 4.91214i) q^{79} +11.2725 q^{80} +0.349076 q^{82} +(-0.212551 - 0.225290i) q^{83} +(-0.750798 + 12.8907i) q^{85} +(13.2449 - 1.54810i) q^{86} +(-13.1378 - 6.59803i) q^{88} +(11.7618 - 9.86931i) q^{89} +(-2.13413 - 1.79075i) q^{91} +(-0.0424202 - 0.0983410i) q^{92} +(3.26333 + 0.773423i) q^{94} +(-0.673742 - 2.25045i) q^{95} +(14.4555 + 1.68960i) q^{97} +(-1.73289 + 9.82772i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8}+O(q^{10}) \) 144 * q - 9 * q^2 + 9 * q^4 - 9 * q^5 + 9 * q^7 + 18 * q^8	\( 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8} - 18 q^{10} - 9 q^{11} + 9 q^{13} - 9 q^{14} + 9 q^{16} + 18 q^{17} - 18 q^{19} + 63 q^{20} + 9 q^{22} - 36 q^{23} + 9 q^{25} - 45 q^{26} - 9 q^{28} + 45 q^{29} + 9 q^{31} - 63 q^{32} + 9 q^{34} - 9 q^{35} - 18 q^{37} + 9 q^{38} + 9 q^{40} + 27 q^{41} + 9 q^{43} - 54 q^{44} - 18 q^{46} - 63 q^{47} + 9 q^{49} + 225 q^{50} + 27 q^{52} - 45 q^{53} - 9 q^{55} - 99 q^{56} + 9 q^{58} + 117 q^{59} + 9 q^{61} - 81 q^{62} - 18 q^{64} - 81 q^{65} + 36 q^{67} + 18 q^{68} + 63 q^{70} + 90 q^{71} - 18 q^{73} - 81 q^{74} + 90 q^{76} - 81 q^{77} + 63 q^{79} + 288 q^{80} - 36 q^{82} - 45 q^{83} + 63 q^{85} - 81 q^{86} + 90 q^{88} + 81 q^{89} - 18 q^{91} + 63 q^{92} + 63 q^{94} - 153 q^{95} + 36 q^{97} - 81 q^{98}+O(q^{100}) \) 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 + 63 * q^20 + 9 * q^22 - 36 * q^23 + 9 * q^25 - 45 * q^26 - 9 * q^28 + 45 * q^29 + 9 * q^31 - 63 * q^32 + 9 * q^34 - 9 * q^35 - 18 * q^37 + 9 * q^38 + 9 * q^40 + 27 * q^41 + 9 * q^43 - 54 * q^44 - 18 * q^46 - 63 * q^47 + 9 * q^49 + 225 * q^50 + 27 * q^52 - 45 * q^53 - 9 * q^55 - 99 * q^56 + 9 * q^58 + 117 * q^59 + 9 * q^61 - 81 * q^62 - 18 * q^64 - 81 * q^65 + 36 * q^67 + 18 * q^68 + 63 * q^70 + 90 * q^71 - 18 * q^73 - 81 * q^74 + 90 * q^76 - 81 * q^77 + 63 * q^79 + 288 * q^80 - 36 * q^82 - 45 * q^83 + 63 * q^85 - 81 * q^86 + 90 * q^88 + 81 * q^89 - 18 * q^91 + 63 * q^92 + 63 * q^94 - 153 * q^95 + 36 * q^97 - 81 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more