LMFDB - Embedded newform 729.2.g.a.55.3

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			55.3
Character	$\chi$	$=$	729.55
Dual form			729.2.g.a.676.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.361975 + 0.839152i) q^{2} +(0.799333 + 0.847243i) q^{4} +(-0.221432 - 3.80183i) q^{5} +(-0.706680 - 0.167486i) q^{7} +(-2.71786 + 0.989221i) q^{8} +O(q^{10})$	\(q+(-0.361975 + 0.839152i) q^{2} +(0.799333 + 0.847243i) q^{4} +(-0.221432 - 3.80183i) q^{5} +(-0.706680 - 0.167486i) q^{7} +(-2.71786 + 0.989221i) q^{8} +(3.27047 + 1.19035i) q^{10} +(-2.24948 - 1.47950i) q^{11} +(-4.57632 - 0.534895i) q^{13} +(0.396347 - 0.532387i) q^{14} +(0.0182372 - 0.313121i) q^{16} +(0.692702 - 0.581246i) q^{17} +(-1.12072 - 0.940396i) q^{19} +(3.04408 - 3.22654i) q^{20} +(2.05578 - 1.35211i) q^{22} +(-3.79608 + 0.899688i) q^{23} +(-9.43871 + 1.10323i) q^{25} +(2.10537 - 3.64661i) q^{26} +(-0.422971 - 0.732607i) q^{28} +(-3.06986 - 4.12353i) q^{29} +(-2.86446 + 9.56797i) q^{31} +(-4.91313 - 2.46747i) q^{32} +(0.237013 + 0.791679i) q^{34} +(-0.480274 + 2.72377i) q^{35} +(-0.348559 - 1.97678i) q^{37} +(1.19481 - 0.600055i) q^{38} +(4.36268 + 10.1138i) q^{40} +(2.59790 + 6.02260i) q^{41} +(6.51223 - 3.27057i) q^{43} +(-0.544580 - 3.08847i) q^{44} +(0.619111 - 3.51115i) q^{46} +(-1.28270 - 4.28453i) q^{47} +(-5.78408 - 2.90488i) q^{49} +(2.49080 - 8.31986i) q^{50} +(-3.20482 - 4.30482i) q^{52} +(-3.43548 - 5.95043i) q^{53} +(-5.12672 + 8.87974i) q^{55} +(2.08634 - 0.243858i) q^{56} +(4.57148 - 1.08346i) q^{58} +(-0.590929 + 0.388660i) q^{59} +(1.83608 - 1.94613i) q^{61} +(-6.99212 - 5.86709i) q^{62} +(4.32956 - 3.63293i) q^{64} +(-1.02024 + 17.5169i) q^{65} +(8.91352 - 11.9729i) q^{67} +(1.04616 + 0.122278i) q^{68} +(-2.11181 - 1.38896i) q^{70} +(9.19719 + 3.34750i) q^{71} +(15.0748 - 5.48678i) q^{73} +(1.78499 + 0.423050i) q^{74} +(-0.0990843 - 1.70121i) q^{76} +(1.34186 + 1.42229i) q^{77} +(1.89166 - 4.38536i) q^{79} -1.19447 q^{80} -5.99425 q^{82} +(2.86882 - 6.65067i) q^{83} +(-2.36319 - 2.50483i) q^{85} +(0.387238 + 6.64862i) q^{86} +(7.57733 + 1.79586i) q^{88} +(-7.00321 + 2.54896i) q^{89} +(3.14441 + 1.14447i) q^{91} +(-3.79659 - 2.49705i) q^{92} +(4.05968 + 0.474509i) q^{94} +(-3.32707 + 4.46903i) q^{95} +(0.258735 - 4.44232i) q^{97} +(4.53133 - 3.80223i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{17}{27}\right)$

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 $

$2$	−0.361975	+	0.839152i	−0.255955	+	0.593370i	−0.996942	−	0.0781494i	$-0.975099\pi$
$2$	−0.361975	+	0.839152i	−0.255955	+	0.593370i	0.740987	+	0.671520i	$0.234358\pi$
$3$		0			0
$3$		0			0
$4$	0.799333	+	0.847243i	0.399666	+	0.423621i
$5$	−0.221432	−	3.80183i	−0.0990272	−	1.70023i	−0.572889	−	0.819633i	$-0.694178\pi$
$5$	−0.221432	−	3.80183i	−0.0990272	−	1.70023i	0.473862	−	0.880599i	$-0.342859\pi$
$6$		0			0
$7$	−0.706680	−	0.167486i	−0.267100	−	0.0633039i	0.0948834	−	0.995488i	$-0.469752\pi$
$7$	−0.706680	−	0.167486i	−0.267100	−	0.0633039i	−0.361983	+	0.932185i	$0.617900\pi$
$8$	−2.71786	+	0.989221i	−0.960910	+	0.349743i
$9$		0			0
$10$	3.27047	+	1.19035i	1.03421	+	0.376423i
$11$	−2.24948	−	1.47950i	−0.678243	−	0.446087i	0.163086	−	0.986612i	$-0.447855\pi$
$11$	−2.24948	−	1.47950i	−0.678243	−	0.446087i	−0.841328	+	0.540525i	$0.818226\pi$
$12$		0			0
$13$	−4.57632	−	0.534895i	−1.26924	−	0.148353i	−0.545317	−	0.838230i	$-0.683591\pi$
$13$	−4.57632	−	0.534895i	−1.26924	−	0.148353i	−0.723927	+	0.689877i	$0.757665\pi$
$14$	0.396347	−	0.532387i	0.105928	−	0.142286i
$15$		0			0
$16$	0.0182372	−	0.313121i	0.00455931	−	0.0782803i
$17$	0.692702	−	0.581246i	0.168005	−	0.140973i	−0.554909	−	0.831911i	$-0.687247\pi$
$17$	0.692702	−	0.581246i	0.168005	−	0.140973i	0.722914	+	0.690938i	$0.242802\pi$
$18$		0			0
$19$	−1.12072	−	0.940396i	−0.257111	−	0.215742i	0.505116	−	0.863051i	$-0.331450\pi$
$19$	−1.12072	−	0.940396i	−0.257111	−	0.215742i	−0.762227	+	0.647310i	$0.775894\pi$
$20$	3.04408	−	3.22654i	0.680677	−	0.721475i
$21$		0			0
$22$	2.05578	−	1.35211i	0.438294	−	0.288271i
$23$	−3.79608	+	0.899688i	−0.791538	+	0.187598i	−0.606447	−	0.795124i	$-0.707406\pi$
$23$	−3.79608	+	0.899688i	−0.791538	+	0.187598i	−0.185090	+	0.982722i	$0.559258\pi$
$24$		0			0
$25$	−9.43871	+	1.10323i	−1.88774	+	0.220645i
$26$	2.10537	−	3.64661i	0.412898	−	0.715160i
$27$		0			0
$28$	−0.422971	−	0.732607i	−0.0799340	−	0.138450i
$29$	−3.06986	−	4.12353i	−0.570058	−	0.765721i	0.419825	−	0.907605i	$-0.362091\pi$
$29$	−3.06986	−	4.12353i	−0.570058	−	0.765721i	−0.989883	+	0.141884i	$0.954684\pi$
$30$		0			0
$31$	−2.86446	+	9.56797i	−0.514473	+	1.71846i	0.166402	+	0.986058i	$0.446785\pi$
$31$	−2.86446	+	9.56797i	−0.514473	+	1.71846i	−0.680874	+	0.732400i	$0.738400\pi$
$32$	−4.91313	−	2.46747i	−0.868528	−	0.436191i
$33$		0			0
$34$	0.237013	+	0.791679i	0.0406474	+	0.135772i
$35$	−0.480274	+	2.72377i	−0.0811811	+	0.460401i
$36$		0			0
$37$	−0.348559	−	1.97678i	−0.0573028	−	0.324980i	0.942659	−	0.333758i	$-0.108317\pi$
$37$	−0.348559	−	1.97678i	−0.0573028	−	0.324980i	−0.999961	+	0.00877810i	$0.997206\pi$
$38$	1.19481	−	0.600055i	0.193824	−	0.0973418i
$39$		0			0
$40$	4.36268	+	10.1138i	0.689800	+	1.59914i
$41$	2.59790	+	6.02260i	0.405723	+	0.940572i	0.991501	+	0.130100i	$0.0415299\pi$
$41$	2.59790	+	6.02260i	0.405723	+	0.940572i	−0.585778	+	0.810472i	$0.699211\pi$
$42$		0			0
$43$	6.51223	−	3.27057i	0.993106	−	0.498757i	0.123416	−	0.992355i	$-0.460615\pi$
$43$	6.51223	−	3.27057i	0.993106	−	0.498757i	0.869690	+	0.493598i	$0.164319\pi$
$44$	−0.544580	−	3.08847i	−0.0820986	−	0.465604i
$45$		0			0
$46$	0.619111	−	3.51115i	0.0912830	−	0.517692i
$47$	−1.28270	−	4.28453i	−0.187102	−	0.624963i	−0.999144	−	0.0413648i	$-0.986829\pi$
$47$	−1.28270	−	4.28453i	−0.187102	−	0.624963i	0.812042	−	0.583598i	$-0.198356\pi$
$48$		0			0
$49$	−5.78408	−	2.90488i	−0.826298	−	0.414982i
$50$	2.49080	−	8.31986i	0.352253	−	1.17661i
$51$		0			0
$52$	−3.20482	−	4.30482i	−0.444428	−	0.596971i
$53$	−3.43548	−	5.95043i	−0.471900	−	0.817355i	0.527583	−	0.849503i	$-0.323098\pi$
$53$	−3.43548	−	5.95043i	−0.471900	−	0.817355i	−0.999483	+	0.0321487i	$0.989765\pi$
$54$		0			0
$55$	−5.12672	+	8.87974i	−0.691287	+	1.19734i
$56$	2.08634	−	0.243858i	0.278799	−	0.0325870i
$57$		0			0
$58$	4.57148	−	1.08346i	0.600265	−	0.142265i
$59$	−0.590929	+	0.388660i	−0.0769324	+	0.0505992i	−0.587392	−	0.809302i	$-0.699845\pi$
$59$	−0.590929	+	0.388660i	−0.0769324	+	0.0505992i	0.510460	+	0.859901i	$0.329475\pi$
$60$		0			0
$61$	1.83608	−	1.94613i	0.235086	−	0.249177i	−0.599081	−	0.800688i	$-0.704467\pi$
$61$	1.83608	−	1.94613i	0.235086	−	0.249177i	0.834167	+	0.551512i	$0.185949\pi$
$62$	−6.99212	−	5.86709i	−0.888000	−	0.745121i
$63$		0			0
$64$	4.32956	−	3.63293i	0.541195	−	0.454116i
$65$	−1.02024	+	17.5169i	−0.126545	+	2.17270i
$66$		0			0
$67$	8.91352	−	11.9729i	1.08896	−	1.46273i	0.215073	−	0.976598i	$-0.431001\pi$
$67$	8.91352	−	11.9729i	1.08896	−	1.46273i	0.873887	−	0.486129i	$-0.161591\pi$
$68$	1.04616	+	0.122278i	0.126865	+	0.0148284i
$69$		0			0
$70$	−2.11181	−	1.38896i	−0.252409	−	0.166012i
$71$	9.19719	+	3.34750i	1.09151	+	0.397276i	0.824179	−	0.566330i	$-0.191637\pi$
$71$	9.19719	+	3.34750i	1.09151	+	0.397276i	0.267328	+	0.963606i	$0.413859\pi$
$72$		0			0
$73$	15.0748	−	5.48678i	1.76437	−	0.642179i	0.764376	−	0.644771i	$-0.223047\pi$
$73$	15.0748	−	5.48678i	1.76437	−	0.642179i	0.999997	+	0.00259223i	$0.000825133\pi$
$74$	1.78499	+	0.423050i	0.207501	+	0.0491785i
$75$		0			0
$76$	−0.0990843	−	1.70121i	−0.0113658	−	0.195142i
$77$	1.34186	+	1.42229i	0.152920	+	0.162085i
$78$		0			0
$79$	1.89166	−	4.38536i	0.212828	−	0.493391i	−0.778042	−	0.628213i	$-0.783787\pi$
$79$	1.89166	−	4.38536i	0.212828	−	0.493391i	0.990870	+	0.134821i	$0.0430461\pi$
$80$	−1.19447			−0.133546
$81$		0			0
$82$	−5.99425			−0.661954
$83$	2.86882	−	6.65067i	0.314894	−	0.730006i	−0.685105	−	0.728444i	$-0.740244\pi$
$83$	2.86882	−	6.65067i	0.314894	−	0.730006i	0.999999	−	0.00156176i	$-0.000497123\pi$
$84$		0			0
$85$	−2.36319	−	2.50483i	−0.256324	−	0.271687i
$86$	0.387238	+	6.64862i	0.0417569	+	0.716939i
$87$		0			0
$88$	7.57733	+	1.79586i	0.807746	+	0.191439i
$89$	−7.00321	+	2.54896i	−0.742339	+	0.270189i	−0.685378	−	0.728187i	$-0.740363\pi$
$89$	−7.00321	+	2.54896i	−0.742339	+	0.270189i	−0.0569608	+	0.998376i	$0.518141\pi$
$90$		0			0
$91$	3.14441	+	1.14447i	0.329624	+	0.119973i
$92$	−3.79659	−	2.49705i	−0.395821	−	0.260336i
$93$		0			0
$94$	4.05968	+	0.474509i	0.418724	+	0.0489418i
$95$	−3.32707	+	4.46903i	−0.341350	+	0.458512i
$96$		0			0
$97$	0.258735	−	4.44232i	0.0262706	−	0.451049i	−0.959366	−	0.282166i	$-0.908947\pi$
$97$	0.258735	−	4.44232i	0.0262706	−	0.451049i	0.985636	−	0.168883i	$-0.0540159\pi$
$98$	4.53133	−	3.80223i	0.457733	−	0.384084i
$99$		0			0
$100$	−8.47937	−	7.11504i	−0.847937	−	0.711504i
$101$	−7.50105	+	7.95065i	−0.746383	+	0.791119i	−0.983605	−	0.180336i	$-0.942282\pi$
$101$	−7.50105	+	7.95065i	−0.746383	+	0.791119i	0.237222	+	0.971455i	$0.423763\pi$
$102$		0			0
$103$	−4.04794	+	2.66237i	−0.398856	+	0.262332i	−0.733053	−	0.680172i	$-0.761905\pi$
$103$	−4.04794	+	2.66237i	−0.398856	+	0.262332i	0.334197	+	0.942503i	$0.391535\pi$
$104$	12.9669	−	3.07322i	1.27151	−	0.301354i
$105$		0			0
$106$	6.23688	−	0.728986i	0.605779	−	0.0708054i
$107$	−1.36707	+	2.36783i	−0.132159	+	0.228906i	−0.924509	−	0.381161i	$-0.875524\pi$
$107$	−1.36707	+	2.36783i	−0.132159	+	0.228906i	0.792349	+	0.610067i	$0.208858\pi$
$108$		0			0
$109$	1.70034	+	2.94507i	0.162863	+	0.282087i	0.935894	−	0.352281i	$-0.114594\pi$
$109$	1.70034	+	2.94507i	0.162863	+	0.282087i	−0.773031	+	0.634368i	$0.781261\pi$
$110$	−5.59571	−	7.51635i	−0.533530	−	0.716655i
$111$		0			0
$112$	−0.0653315	+	0.218222i	−0.00617324	+	0.0206201i
$113$	−8.41203	−	4.22468i	−0.791337	−	0.397424i	0.00674204	−	0.999977i	$-0.497854\pi$
$113$	−8.41203	−	4.22468i	−0.791337	−	0.397424i	−0.798079	+	0.602553i	$0.794150\pi$
$114$		0			0
$115$	4.26104	+	14.2328i	0.397344	+	1.32722i
$116$	1.03980	−	5.89699i	0.0965428	−	0.547521i
$117$		0			0
$118$	−0.112244	−	0.636565i	−0.0103329	−	0.0586005i
$119$	−0.586870	+	0.294737i	−0.0537983	+	0.0270185i
$120$		0			0
$121$	−1.48567	−	3.44416i	−0.135061	−	0.313106i
$122$	0.968487	+	2.24520i	0.0876827	+	0.203271i
$123$		0			0
$124$	−10.3961	+	5.22109i	−0.933593	+	0.468868i
$125$	2.97782	+	16.8880i	0.266344	+	1.51051i
$126$		0			0
$127$	−1.36769	+	7.75655i	−0.121363	+	0.688283i	0.862039	+	0.506842i	$0.169187\pi$
$127$	−1.36769	+	7.75655i	−0.121363	+	0.688283i	−0.983402	+	0.181441i	$0.941924\pi$
$128$	−1.67226	−	5.58574i	−0.147808	−	0.493714i
$129$		0			0
$130$	−14.3300	−	7.19680i	−1.25683	−	0.631201i
$131$	0.310717	−	1.03787i	0.0271475	−	0.0906789i	−0.943342	−	0.331821i	$-0.892337\pi$
$131$	0.310717	−	1.03787i	0.0271475	−	0.0906789i	0.970490	+	0.241142i	$0.0775221\pi$
$132$		0			0
$133$	0.634488	+	0.852265i	0.0550171	+	0.0739008i
$134$	6.82065	+	11.8137i	0.589214	+	1.02055i
$135$		0			0
$136$	−1.30769	+	2.26498i	−0.112133	+	0.194221i
$137$	−0.730936	+	0.0854341i	−0.0624481	+	0.00729913i	−0.147260	−	0.989098i	$-0.547045\pi$
$137$	−0.730936	+	0.0854341i	−0.0624481	+	0.00729913i	0.0848115	+	0.996397i	$0.472971\pi$
$138$		0			0
$139$	−4.09766	+	0.971163i	−0.347559	+	0.0823730i	−0.400688	−	0.916215i	$-0.631229\pi$
$139$	−4.09766	+	0.971163i	−0.347559	+	0.0823730i	0.0531287	+	0.998588i	$0.483081\pi$
$140$	−2.69159	+	1.77029i	−0.227481	+	0.149617i
$141$		0			0
$142$	−6.13822	+	6.50613i	−0.515108	+	0.545983i
$143$	9.50295	+	7.97392i	0.794676	+	0.666813i
$144$		0			0
$145$	−14.9972	+	12.5842i	−1.24545	+	1.04506i
$146$	−0.852458	+	14.6361i	−0.0705499	+	1.21130i
$147$		0			0
$148$	1.39620	−	1.87542i	0.114767	−	0.154158i
$149$	11.5926	+	1.35499i	0.949706	+	0.111005i	0.576819	−	0.816872i	$-0.304294\pi$
$149$	11.5926	+	1.35499i	0.949706	+	0.111005i	0.372887	+	0.927877i	$0.378368\pi$
$150$		0			0
$151$	4.00498	+	2.63412i	0.325920	+	0.214361i	0.701915	−	0.712261i	$-0.252329\pi$
$151$	4.00498	+	2.63412i	0.325920	+	0.214361i	−0.375995	+	0.926622i	$0.622699\pi$
$152$	3.97623	+	1.44723i	0.322515	+	0.117386i
$153$		0			0
$154$	−1.67924	+	0.611194i	−0.135317	+	0.0492514i
$155$	37.0101	+	8.77156i	2.97272	+	0.704549i
$156$		0			0
$157$	−0.543531	−	9.33207i	−0.0433785	−	0.744780i	−0.947942	−	0.318442i	$-0.896840\pi$
$157$	−0.543531	−	9.33207i	−0.0433785	−	0.744780i	0.904564	−	0.426338i	$-0.140197\pi$
$158$	2.99525	+	3.17478i	0.238289	+	0.252572i
$159$		0			0
$160$	−8.29298	+	19.2253i	−0.655618	+	1.51989i
$161$	2.83330			0.223295
$162$		0			0
$163$	−7.79498			−0.610550			−0.305275	−	0.952264i	$-0.598748\pi$
$163$	−7.79498			−0.610550			−0.305275	+	0.952264i	$0.598748\pi$
$164$	−3.02602	+	7.01511i	−0.236293	+	0.547788i
$165$		0			0
$166$	4.54249	+	4.81475i	0.352565	+	0.373697i
$167$	0.628896	+	10.7977i	0.0486654	+	0.835553i	0.931020	+	0.364968i	$0.118920\pi$
$167$	0.628896	+	10.7977i	0.0486654	+	0.835553i	−0.882355	+	0.470585i	$0.844043\pi$
$168$		0			0
$169$	8.00703	+	1.89770i	0.615925	+	0.145977i
$170$	2.95735	−	1.07639i	0.226818	−	0.0825551i
$171$		0			0
$172$	7.97640	+	2.90317i	0.608195	+	0.221365i
$173$	−9.71059	−	6.38676i	−0.738282	−	0.485576i	0.123823	−	0.992304i	$-0.460484\pi$
$173$	−9.71059	−	6.38676i	−0.738282	−	0.485576i	−0.862106	+	0.506728i	$0.830855\pi$
$174$		0			0
$175$	6.85493	+	0.801226i	0.518184	+	0.0605670i
$176$	−0.504289	+	0.677377i	−0.0380122	+	0.0510592i
$177$		0			0
$178$	0.396021	−	6.79942i	0.0296831	−	0.509638i
$179$	−2.09069	+	1.75429i	−0.156265	+	0.131122i	−0.717568	−	0.696488i	$-0.754745\pi$
$179$	−2.09069	+	1.75429i	−0.156265	+	0.131122i	0.561303	+	0.827611i	$0.310300\pi$
$180$		0			0
$181$	−11.5914	−	9.72633i	−0.861581	−	0.722953i	0.100727	−	0.994914i	$-0.467883\pi$
$181$	−11.5914	−	9.72633i	−0.861581	−	0.722953i	−0.962308	+	0.271962i	$0.912328\pi$
$182$	−2.09858	+	2.22437i	−0.155557	+	0.164881i
$183$		0			0
$184$	9.42724	−	6.20039i	0.694985	−	0.457099i
$185$	−7.43820	+	1.76288i	−0.546867	+	0.129610i
$186$		0			0
$187$	−2.41817	+	0.282644i	−0.176834	+	0.0206690i
$188$	2.60473	−	4.51153i	0.189970	−	0.329037i
$189$		0			0
$190$	−2.54588	−	4.40959i	−0.184697	−	0.319905i
$191$	1.47784	+	1.98509i	0.106933	+	0.143636i	0.852368	−	0.522942i	$-0.175166\pi$
$191$	1.47784	+	1.98509i	0.106933	+	0.143636i	−0.745435	+	0.666578i	$0.767758\pi$
$192$		0			0
$193$	1.13748	−	3.79946i	0.0818778	−	0.273491i	−0.907241	−	0.420612i	$-0.861815\pi$
$193$	1.13748	−	3.79946i	0.0818778	−	0.273491i	0.989119	+	0.147121i	$0.0470006\pi$
$194$	3.63412	+	1.82513i	0.260915	+	0.131036i
$195$		0			0
$196$	−2.16227	−	7.22248i	−0.154448	−	0.515892i
$197$	−4.31848	+	24.4913i	−0.307679	+	1.74493i	0.302942	+	0.953009i	$0.402031\pi$
$197$	−4.31848	+	24.4913i	−0.307679	+	1.74493i	−0.610621	+	0.791923i	$0.709080\pi$
$198$		0			0
$199$	2.00332	+	11.3614i	0.142011	+	0.805386i	0.969718	+	0.244226i	$0.0785338\pi$
$199$	2.00332	+	11.3614i	0.142011	+	0.805386i	−0.827707	+	0.561160i	$0.810355\pi$
$200$	24.5618	−	12.3354i	1.73678	−	0.872245i
$201$		0			0
$202$	−3.95661	−	9.17246i	−0.278386	−	0.645372i
$203$	1.47877	+	3.42818i	0.103789	+	0.240611i
$204$		0			0
$205$	22.3217	−	11.2104i	1.55901	−	0.782966i
$206$	−0.768884	−	4.36056i	−0.0535707	−	0.303814i
$207$		0			0
$208$	−0.250947	+	1.42319i	−0.0174000	+	0.0986804i
$209$	1.12971	+	3.77351i	0.0781440	+	0.261019i
$210$		0			0
$211$	18.9771	+	9.53064i	1.30643	+	0.656116i	0.959483	−	0.281767i	$-0.0909205\pi$
$211$	18.9771	+	9.53064i	1.30643	+	0.656116i	0.346952	+	0.937883i	$0.387217\pi$
$212$	2.29537	−	7.66706i	0.157647	−	0.526576i
$213$		0			0
$214$	−1.49212	−	2.00427i	−0.101999	−	0.137009i
$215$	−13.8762	−	24.0342i	−0.946346	−	1.63912i
$216$		0			0
$217$	3.62676	−	6.28174i	0.246201	−	0.426432i
$218$	−3.08684	+	0.360800i	−0.209068	+	0.0244365i
$219$		0			0
$220$	−11.6213	+	2.75429i	−0.783505	+	0.185694i
$221$	−3.48093	+	2.28945i	−0.234153	+	0.154005i
$222$		0			0
$223$	−1.53505	+	1.62706i	−0.102795	+	0.108956i	−0.776728	−	0.629836i	$-0.783122\pi$
$223$	−1.53505	+	1.62706i	−0.102795	+	0.108956i	0.673933	+	0.738792i	$0.264604\pi$
$224$	3.05875	+	2.56659i	0.204371	+	0.171488i
$225$		0			0
$226$	6.59009	−	5.52974i	0.438366	−	0.367833i
$227$	−0.205125	+	3.52186i	−0.0136146	+	0.233754i	0.984636	+	0.174622i	$0.0558704\pi$
$227$	−0.205125	+	3.52186i	−0.0136146	+	0.233754i	−0.998250	+	0.0591321i	$0.981167\pi$
$228$		0			0
$229$	−6.30941	+	8.47500i	−0.416937	+	0.560044i	−0.960126	−	0.279566i	$-0.909809\pi$
$229$	−6.30941	+	8.47500i	−0.416937	+	0.560044i	0.543189	+	0.839610i	$0.317217\pi$
$230$	−13.4859	−	1.57628i	−0.889235	−	0.103937i
$231$		0			0
$232$	12.4225	+	8.17043i	0.815579	+	0.536415i
$233$	−16.8171	−	6.12092i	−1.10172	−	0.400995i	−0.273773	−	0.961794i	$-0.588272\pi$
$233$	−16.8171	−	6.12092i	−1.10172	−	0.400995i	−0.827952	+	0.560799i	$0.810494\pi$
$234$		0			0
$235$	−16.0050	+	5.82536i	−1.04405	+	0.380005i
$236$	−0.801638	−	0.189992i	−0.0521822	−	0.0123674i
$237$		0			0
$238$	−0.0348971	−	0.599160i	−0.00226204	−	0.0388378i
$239$	0.254893	+	0.270171i	0.0164877	+	0.0174759i	0.735565	−	0.677454i	$-0.236917\pi$
$239$	0.254893	+	0.270171i	0.0164877	+	0.0174759i	−0.719077	+	0.694930i	$0.755435\pi$
$240$		0			0
$241$	2.49079	−	5.77431i	0.160446	−	0.371956i	−0.818962	−	0.573848i	$-0.805450\pi$
$241$	2.49079	−	5.77431i	0.160446	−	0.371956i	0.979408	+	0.201892i	$0.0647091\pi$
$242$	3.42795			0.220357
$243$		0			0
$244$	3.11649			0.199513
$245$	−9.76307	+	22.6334i	−0.623740	+	1.44599i
$246$		0			0
$247$	4.62577	+	4.90302i	0.294330	+	0.311972i
$248$	−1.67962	−	28.8380i	−0.106656	−	1.83122i
$249$		0			0
$250$	−15.2495	−	3.61420i	−0.964465	−	0.228582i
$251$	4.91237	−	1.78796i	0.310066	−	0.112855i	−0.182300	−	0.983243i	$-0.558354\pi$
$251$	4.91237	−	1.78796i	0.310066	−	0.112855i	0.492366	+	0.870388i	$0.336132\pi$
$252$		0			0
$253$	9.87029	+	3.59249i	0.620540	+	0.225858i
$254$	−6.01386	−	3.95538i	−0.377343	−	0.248182i
$255$		0			0
$256$	16.5198	+	1.93089i	1.03249	+	0.120681i
$257$	1.94989	−	2.61916i	0.121631	−	0.163379i	−0.737137	−	0.675743i	$-0.763823\pi$
$257$	1.94989	−	2.61916i	0.121631	−	0.163379i	0.858768	+	0.512364i	$0.171230\pi$
$258$		0			0
$259$	−0.0847632	+	1.45533i	−0.00526693	+	0.0904297i
$260$	−15.6565	+	13.1374i	−0.970978	+	0.814747i
$261$		0			0
$262$	0.758457	+	0.636421i	0.0468576	+	0.0393182i
$263$	0.961659	−	1.01930i	0.0592984	−	0.0628527i	−0.697045	−	0.717027i	$-0.745502\pi$
$263$	0.961659	−	1.01930i	0.0592984	−	0.0628527i	0.756344	+	0.654175i	$0.226984\pi$
$264$		0			0
$265$	−21.8618	+	14.3787i	−1.34296	+	0.883280i
$266$	−0.944849	+	0.223933i	−0.0579324	+	0.0137302i
$267$		0			0
$268$	17.2689	−	2.01844i	1.05486	−	0.123296i
$269$	5.17838	−	8.96922i	0.315732	−	0.546863i	−0.663861	−	0.747856i	$-0.731083\pi$
$269$	5.17838	−	8.96922i	0.315732	−	0.546863i	0.979593	+	0.200993i	$0.0644168\pi$
$270$		0			0
$271$	−9.29809	−	16.1048i	−0.564819	−	0.978295i	−0.997067	−	0.0765398i	$-0.975613\pi$
$271$	−9.29809	−	16.1048i	−0.564819	−	0.978295i	0.432248	−	0.901755i	$-0.357721\pi$
$272$	−0.169368	−	0.227500i	−0.0102694	−	0.0137942i
$273$		0			0
$274$	0.192888	−	0.644292i	0.0116528	−	0.0389231i
$275$	22.8644	+	11.4829i	1.37877	+	0.692447i
$276$		0			0
$277$	−2.93650	−	9.80858i	−0.176437	−	0.589341i	−0.999763	−	0.0217719i	$-0.993069\pi$
$277$	−2.93650	−	9.80858i	−0.176437	−	0.589341i	0.823326	−	0.567569i	$-0.192116\pi$
$278$	0.668297	−	3.79010i	0.0400818	−	0.227315i
$279$		0			0
$280$	−1.38909	−	7.87793i	−0.0830141	−	0.470796i
$281$	16.0079	−	8.03947i	0.954951	−	0.479595i	0.0981105	−	0.995176i	$-0.468720\pi$
$281$	16.0079	−	8.03947i	0.954951	−	0.479595i	0.856841	+	0.515581i	$0.172424\pi$
$282$		0			0
$283$	−10.5546	−	24.4683i	−0.627404	−	1.45449i	−0.874271	−	0.485437i	$-0.838660\pi$
$283$	−10.5546	−	24.4683i	−0.627404	−	1.45449i	0.246867	−	0.969049i	$-0.420599\pi$
$284$	4.51547	+	10.4680i	0.267944	+	0.621163i
$285$		0			0
$286$	−10.1312	+	5.08806i	−0.599068	+	0.300863i
$287$	−0.827179	−	4.69117i	−0.0488268	−	0.276911i
$288$		0			0
$289$	−2.81003	+	15.9365i	−0.165296	+	0.937439i
$290$	−5.13141	−	17.1401i	−0.301327	−	1.00650i
$291$		0			0
$292$	16.6984	+	8.38626i	0.977201	+	0.490769i
$293$	−8.29474	+	27.7063i	−0.484584	+	1.61862i	0.270309	+	0.962774i	$0.412874\pi$
$293$	−8.29474	+	27.7063i	−0.484584	+	1.61862i	−0.754893	+	0.655848i	$0.772311\pi$
$294$		0			0
$295$	1.60847	+	2.16055i	0.0936488	+	0.125792i
$296$	2.90281	+	5.02781i	0.168722	+	0.292235i
$297$		0			0
$298$	−5.33328	+	9.23752i	−0.308949	+	0.535115i
$299$	17.8533	−	2.08675i	1.03248	−	0.120680i
$300$		0			0
$301$	−5.14984	+	1.22053i	−0.296832	+	0.0703505i
$302$	−3.66013	+	2.40730i	−0.210617	+	0.138525i
$303$		0			0
$304$	−0.314897	+	0.333771i	−0.0180606	+	0.0191431i
$305$	−7.80544	−	6.54955i	−0.446938	−	0.375026i
$306$		0			0
$307$	2.94847	−	2.47406i	0.168278	−	0.141202i	−0.554759	−	0.832011i	$-0.687190\pi$
$307$	2.94847	−	2.47406i	0.168278	−	0.141202i	0.723038	+	0.690809i	$0.242745\pi$
$308$	−0.132432	+	2.27377i	−0.00754601	+	0.129560i
$309$		0			0
$310$	−20.7574	+	27.8820i	−1.17894	+	1.58359i
$311$	−14.0725	−	1.64484i	−0.797977	−	0.0932701i	−0.292674	−	0.956212i	$-0.594545\pi$
$311$	−14.0725	−	1.64484i	−0.797977	−	0.0932701i	−0.505303	+	0.862942i	$0.668619\pi$
$312$		0			0
$313$	−17.3980	−	11.4428i	−0.983391	−	0.646786i	−0.0474241	−	0.998875i	$-0.515101\pi$
$313$	−17.3980	−	11.4428i	−0.983391	−	0.646786i	−0.935967	+	0.352089i	$0.885472\pi$
$314$	8.02777	+	2.92187i	0.453033	+	0.164891i
$315$		0			0
$316$	5.22753	−	1.90266i	0.294071	−	0.107033i
$317$	−23.7891	−	5.63811i	−1.33613	−	0.316668i	−0.500391	−	0.865800i	$-0.666810\pi$
$317$	−23.7891	−	5.63811i	−1.33613	−	0.316668i	−0.835736	+	0.549132i	$0.814959\pi$
$318$		0			0
$319$	0.804786	+	13.8176i	0.0450594	+	0.773640i
$320$	−14.7705	−	15.6558i	−0.825696	−	0.875186i
$321$		0			0
$322$	−1.02558	+	2.37757i	−0.0571536	+	0.132497i
$323$	−1.32293			−0.0736096
$324$		0			0
$325$	43.7847			2.42874
$326$	2.82159	−	6.54117i	0.156273	−	0.362282i
$327$		0			0
$328$	−13.0184	−	13.7987i	−0.718822	−	0.761906i
$329$	0.188862	+	3.24263i	0.0104123	+	0.178772i
$330$		0			0
$331$	−6.56661	−	1.55632i	−0.360934	−	0.0855429i	0.0461480	−	0.998935i	$-0.485305\pi$
$331$	−6.56661	−	1.55632i	−0.360934	−	0.0855429i	−0.407082	+	0.913392i	$0.633454\pi$
$332$	7.92788	−	2.88551i	0.435099	−	0.158363i
$333$		0			0
$334$	−9.28858	−	3.38077i	−0.508249	−	0.184987i
$335$	−47.4928	−	31.2365i	−2.59481	−	1.70663i
$336$		0			0
$337$	4.23038	+	0.494461i	0.230444	+	0.0269350i	0.230531	−	0.973065i	$-0.425954\pi$
$337$	4.23038	+	0.494461i	0.230444	+	0.0269350i	−8.72681e−5		1.00000i	$0.500028\pi$
$338$	−4.49080	+	6.03220i	−0.244268	+	0.328108i
$339$		0			0
$340$	0.233229	−	4.00439i	0.0126486	−	0.217168i
$341$	20.5994	−	17.2849i	1.11552	−	0.936032i
$342$		0			0
$343$	7.49539	+	6.28938i	0.404713	+	0.339594i
$344$	−14.4640	+	15.3310i	−0.779849	+	0.826592i
$345$		0			0
$346$	8.87445	−	5.83682i	0.477093	−	0.313789i
$347$	19.6616	−	4.65989i	1.05549	−	0.250156i	0.333996	−	0.942575i	$-0.391603\pi$
$347$	19.6616	−	4.65989i	1.05549	−	0.250156i	0.721496	+	0.692418i	$0.243455\pi$
$348$		0			0
$349$	−22.8564	+	2.67153i	−1.22348	+	0.143004i	−0.703199	−	0.710993i	$-0.748246\pi$
$349$	−22.8564	+	2.67153i	−1.22348	+	0.143004i	−0.520278	+	0.853997i	$0.674172\pi$
$350$	−3.15366	+	5.46231i	−0.168570	+	0.291973i
$351$		0			0
$352$	7.40135	+	12.8195i	0.394493	+	0.683282i
$353$	−12.9522	−	17.3979i	−0.689378	−	0.925995i	0.310319	−	0.950633i	$-0.399564\pi$
$353$	−12.9522	−	17.3979i	−0.689378	−	0.925995i	−0.999696	+	0.0246374i	$0.992157\pi$
$354$		0			0
$355$	10.6901	−	35.7074i	0.567372	−	1.89515i
$356$	−7.75749	−	3.89596i	−0.411146	−	0.206485i
$357$		0			0
$358$	−0.715344	−	2.38942i	−0.0378071	−	0.126285i
$359$	5.76399	−	32.6892i	0.304212	−	1.72527i	−0.322981	−	0.946405i	$-0.604685\pi$
$359$	5.76399	−	32.6892i	0.304212	−	1.72527i	0.627193	−	0.778864i	$-0.284204\pi$
$360$		0			0
$361$	−2.92765	−	16.6035i	−0.154087	−	0.873869i
$362$	12.3577	−	6.20625i	0.649505	−	0.326193i
$363$		0			0
$364$	1.54378	+	3.57889i	0.0809162	+	0.187585i
$365$	−24.1979	−	56.0969i	−1.26657	−	2.93625i
$366$		0			0
$367$	−18.5041	+	9.29311i	−0.965906	+	0.485096i	−0.860565	−	0.509340i	$-0.829890\pi$
$367$	−18.5041	+	9.29311i	−0.965906	+	0.485096i	−0.105341	+	0.994436i	$0.533593\pi$
$368$	0.212481	+	1.20504i	0.0110764	+	0.0628172i
$369$		0			0
$370$	1.21311	−	6.87990i	0.0630667	−	0.357669i
$371$	1.43117	+	4.78045i	0.0743028	+	0.248189i
$372$		0			0
$373$	−3.59966	−	1.80782i	−0.186383	−	0.0936052i	0.353161	−	0.935563i	$-0.385107\pi$
$373$	−3.59966	−	1.80782i	−0.186383	−	0.0936052i	−0.539544	+	0.841958i	$0.681403\pi$
$374$	0.638137	−	2.13152i	0.0329973	−	0.110219i
$375$		0			0
$376$	7.72457	+	10.3759i	0.398364	+	0.535096i
$377$	11.8430	+	20.5127i	0.609945	+	1.05646i
$378$		0			0
$379$	17.2610	−	29.8970i	0.886640	−	1.53570i	0.0428169	−	0.999083i	$-0.486367\pi$
$379$	17.2610	−	29.8970i	0.886640	−	1.53570i	0.843823	−	0.536622i	$-0.180300\pi$
$380$	−6.44578	+	0.753404i	−0.330662	+	0.0386488i
$381$		0			0
$382$	−2.20073	+	0.521583i	−0.112599	+	0.0266865i
$383$	11.9143	−	7.83617i	0.608793	−	0.400410i	−0.207344	−	0.978268i	$-0.566482\pi$
$383$	11.9143	−	7.83617i	0.608793	−	0.400410i	0.816137	+	0.577859i	$0.196111\pi$
$384$		0			0
$385$	5.11019	−	5.41648i	0.260439	−	0.276050i
$386$	2.77658	+	2.32983i	0.141324	+	0.118585i
$387$		0			0
$388$	3.97054	−	3.33168i	0.201573	−	0.169140i
$389$	−1.20812	+	20.7426i	−0.0612541	+	1.05169i	0.817963	+	0.575271i	$0.195103\pi$
$389$	−1.20812	+	20.7426i	−0.0612541	+	1.05169i	−0.879217	+	0.476421i	$0.841934\pi$
$390$		0			0
$391$	−2.10661	+	2.82967i	−0.106536	+	0.143103i
$392$	18.5939	+	2.17332i	0.939134	+	0.109769i
$393$		0			0
$394$	−18.9887	−	12.4891i	−0.956639	−	0.629191i
$395$	−17.0913	−	6.22071i	−0.859955	−	0.312998i
$396$		0			0
$397$	21.4426	−	7.80446i	1.07617	−	0.391695i	0.257691	−	0.966227i	$-0.417038\pi$
$397$	21.4426	−	7.80446i	1.07617	−	0.391695i	0.818482	+	0.574533i	$0.194816\pi$
$398$	−10.2591	−	2.43144i	−0.514241	−	0.121877i
$399$		0			0
$400$	0.173308	+	2.97558i	0.00866540	+	0.148779i
$401$	5.89097	+	6.24406i	0.294181	+	0.311814i	0.857559	−	0.514386i	$-0.171980\pi$
$401$	5.89097	+	6.24406i	0.294181	+	0.311814i	−0.563378	+	0.826199i	$0.690499\pi$
$402$		0			0
$403$	18.2266	−	42.2539i	0.907930	−	2.10482i
$404$	−12.7320			−0.633439
$405$		0			0
$406$	−3.41204			−0.169337
$407$	−2.14057	+	4.96241i	−0.106104	+	0.245977i
$408$		0			0
$409$	19.3500	+	20.5098i	0.956798	+	1.01415i	0.999886	+	0.0150751i	$0.00479872\pi$
$409$	19.3500	+	20.5098i	0.956798	+	1.01415i	−0.0430887	+	0.999071i	$0.513720\pi$
$410$	1.32732	+	22.7891i	0.0655515	+	1.12548i
$411$		0			0
$412$	−5.49133	−	1.30147i	−0.270538	−	0.0641188i
$413$	0.482693	−	0.175686i	0.0237518	−	0.00864494i
$414$		0			0
$415$	−25.9200	−	9.43411i	−1.27236	−	0.463102i
$416$	21.1642	+	13.9199i	1.03766	+	0.682481i
$417$		0			0
$418$	−3.57548	−	0.417913i	−0.174882	−	0.0204408i
$419$	19.0798	−	25.6286i	0.932108	−	1.25204i	−0.0354460	−	0.999372i	$-0.511285\pi$
$419$	19.0798	−	25.6286i	0.932108	−	1.25204i	0.967554	−	0.252666i	$-0.0813074\pi$
$420$		0			0
$421$	−1.62148	+	27.8397i	−0.0790260	+	1.35682i	0.692865	+	0.721068i	$0.256348\pi$
$421$	−1.62148	+	27.8397i	−0.0790260	+	1.35682i	−0.771891	+	0.635755i	$0.780689\pi$
$422$	−14.8669	+	12.4748i	−0.723708	+	0.607263i
$423$		0			0
$424$	15.2235	+	12.7740i	0.739317	+	0.620361i
$425$	−5.89697	+	6.25042i	−0.286045	+	0.303190i
$426$		0			0
$427$	−1.62347	+	1.06778i	−0.0785654	+	0.0516733i
$428$	−3.09886	+	0.734444i	−0.149789	+	0.0355007i
$429$		0			0
$430$	25.1912	−	2.94443i	1.21483	−	0.141993i
$431$	−16.9276	+	29.3195i	−0.815375	+	1.41227i	0.0936837	+	0.995602i	$0.470136\pi$
$431$	−16.9276	+	29.3195i	−0.815375	+	1.41227i	−0.909058	+	0.416669i	$0.863198\pi$
$432$		0			0
$433$	4.23939	+	7.34284i	0.203732	+	0.352874i	0.949728	−	0.313076i	$-0.101360\pi$
$433$	4.23939	+	7.34284i	0.203732	+	0.352874i	−0.745996	+	0.665950i	$0.768026\pi$
$434$	3.95854	+	5.31724i	0.190016	+	0.255236i
$435$		0			0
$436$	−1.13606	+	3.79469i	−0.0544072	+	0.181733i
$437$	5.10041	+	2.56152i	0.243986	+	0.122534i
$438$		0			0
$439$	6.37737	+	21.3019i	0.304375	+	1.01668i	0.964180	+	0.265247i	$0.0854535\pi$
$439$	6.37737	+	21.3019i	0.304375	+	1.01668i	−0.659805	+	0.751437i	$0.729361\pi$
$440$	5.14970	−	29.2054i	0.245502	−	1.39231i
$441$		0			0
$442$	−0.661183	−	3.74976i	−0.0314493	−	0.178358i
$443$	20.1340	−	10.1117i	0.956596	−	0.480420i	0.0991939	−	0.995068i	$-0.468374\pi$
$443$	20.1340	−	10.1117i	0.956596	−	0.480420i	0.857402	+	0.514648i	$0.172077\pi$
$444$		0			0
$445$	11.2415	+	26.0606i	0.532896	+	1.23539i
$446$	−0.809702	−	1.87710i	−0.0383405	−	0.0888832i
$447$		0			0
$448$	−3.66808	+	1.84218i	−0.173300	+	0.0870348i
$449$	−3.85889	−	21.8849i	−0.182112	−	1.03281i	−0.929610	−	0.368546i	$-0.879856\pi$
$449$	−3.85889	−	21.8849i	−0.182112	−	1.03281i	0.747497	−	0.664265i	$-0.231255\pi$
$450$		0			0
$451$	3.06655	−	17.3913i	0.144398	−	0.818924i
$452$	−3.14468	−	10.5040i	−0.147913	−	0.494064i
$453$		0			0
$454$	−2.88113	−	1.44696i	−0.135218	−	0.0679091i
$455$	3.65482	−	12.2079i	0.171341	−	0.572317i
$456$		0			0
$457$	−1.38320	−	1.85796i	−0.0647032	−	0.0869115i	0.768594	−	0.639737i	$-0.220957\pi$
$457$	−1.38320	−	1.85796i	−0.0647032	−	0.0869115i	−0.833297	+	0.552826i	$0.813549\pi$
$458$	−4.82797	−	8.36229i	−0.225596	−	0.390744i
$459$		0			0
$460$	−8.65270	+	14.9869i	−0.403434	+	0.698768i
$461$	24.3727	−	2.84876i	1.13515	−	0.132680i	0.472305	−	0.881435i	$-0.343422\pi$
$461$	24.3727	−	2.84876i	1.13515	−	0.132680i	0.662846	+	0.748755i	$0.269348\pi$
$462$		0			0
$463$	26.5407	−	6.29025i	1.23345	−	0.292333i	0.438345	−	0.898807i	$-0.355565\pi$
$463$	26.5407	−	6.29025i	1.23345	−	0.292333i	0.795103	+	0.606474i	$0.207417\pi$
$464$	−1.34715	+	0.886036i	−0.0625399	+	0.0411332i
$465$		0			0
$466$	11.2238	−	11.8965i	0.519931	−	0.551094i
$467$	−2.81518	−	2.36222i	−0.130271	−	0.109310i	0.575324	−	0.817925i	$-0.304876\pi$
$467$	−2.81518	−	2.36222i	−0.130271	−	0.109310i	−0.705595	+	0.708615i	$0.749320\pi$
$468$		0			0
$469$	−8.30431	+	6.96815i	−0.383458	+	0.321759i
$470$	0.905062	−	15.5393i	0.0417474	−	0.716775i
$471$		0			0
$472$	1.22159	−	1.64088i	0.0562284	−	0.0755278i
$473$	−19.4879	−	2.27781i	−0.896056	−	0.104734i
$474$		0			0
$475$	11.6156	+	7.63972i	0.532962	+	0.350535i
$476$	−0.718818	−	0.261628i	−0.0329470	−	0.0119917i
$477$		0			0
$478$	−0.318980	+	0.116099i	−0.0145898	+	0.00531025i
$479$	2.89958	+	0.687214i	0.132485	+	0.0313996i	0.296324	−	0.955088i	$-0.404239\pi$
$479$	2.89958	+	0.687214i	0.132485	+	0.0313996i	−0.163838	+	0.986487i	$0.552387\pi$
$480$		0			0
$481$	0.537750	+	9.23281i	0.0245193	+	0.420980i
$482$	3.94392	+	4.18031i	0.179641	+	0.190408i
$483$		0			0
$484$	1.73050	−	4.01175i	0.0786591	−	0.182352i
$485$	−16.9462			−0.769489
$486$		0			0
$487$	−19.3605			−0.877310			−0.438655	−	0.898656i	$-0.644545\pi$
$487$	−19.3605			−0.877310			−0.438655	+	0.898656i	$0.644545\pi$
$488$	−3.06506	+	7.10562i	−0.138749	+	0.321656i
$489$		0			0
$490$	−15.4588	−	16.3854i	−0.698359	−	0.740218i
$491$	−0.624138	−	10.7160i	−0.0281669	−	0.483608i	−0.982665	−	0.185390i	$-0.940645\pi$
$491$	−0.624138	−	10.7160i	−0.0281669	−	0.483608i	0.954498	−	0.298217i	$-0.0963920\pi$
$492$		0			0
$493$	−4.52328	−	1.07204i	−0.203718	−	0.0482821i
$494$	−5.78880	+	2.10695i	−0.260450	+	0.0947961i
$495$		0			0
$496$	2.94370	+	1.07142i	0.132176	+	0.0481081i
$497$	−5.93882	−	3.90602i	−0.266392	−	0.175209i
$498$		0			0
$499$	−30.4517	−	3.55929i	−1.36320	−	0.159336i	−0.597159	−	0.802123i	$-0.703704\pi$
$499$	−30.4517	−	3.55929i	−1.36320	−	0.159336i	−0.766045	+	0.642787i	$0.777778\pi$
$500$	−11.9280	+	16.0221i	−0.533436	+	0.716529i
$501$		0			0
$502$	−0.277787	+	4.76942i	−0.0123982	+	0.212870i
$503$	21.3536	−	17.9178i	0.952111	−	0.798916i	−0.0275408	−	0.999621i	$-0.508768\pi$
$503$	21.3536	−	17.9178i	0.952111	−	0.798916i	0.979652	+	0.200705i	$0.0643232\pi$
$504$		0			0
$505$	31.8880	+	26.7572i	1.41900	+	1.19068i
$506$	−6.58744	+	6.98228i	−0.292848	+	0.310400i
$507$		0			0
$508$	−7.66492	+	5.04130i	−0.340076	+	0.223671i
$509$	−36.4747	+	8.64466i	−1.61671	+	0.383168i	−0.936728	−	0.350059i	$-0.886161\pi$
$509$	−36.4747	+	8.64466i	−1.61671	+	0.383168i	−0.679984	+	0.733227i	$0.738013\pi$
$510$		0			0
$511$	−11.5720	+	1.35258i	−0.511916	+	0.0598345i
$512$	−1.76939	+	3.06468i	−0.0781968	+	0.135441i
$513$		0			0
$514$	1.49206	+	2.58432i	0.0658120	+	0.113990i
$515$	11.0182	+	14.8001i	0.485522	+	0.652169i
$516$		0			0
$517$	−3.45357	+	11.5357i	−0.151888	+	0.507340i
$518$	−1.19056	−	0.597922i	−0.0523102	−	0.0262712i
$519$		0			0
$520$	−14.5552	−	48.6177i	−0.638287	−	2.13203i
$521$	−6.93526	+	39.3318i	−0.303839	+	1.72316i	0.325079	+	0.945687i	$0.394609\pi$
$521$	−6.93526	+	39.3318i	−0.303839	+	1.72316i	−0.628918	+	0.777472i	$0.716502\pi$
$522$		0			0
$523$	1.17678	+	6.67383i	0.0514568	+	0.291826i	0.999667	−	0.0258185i	$-0.00821918\pi$
$523$	1.17678	+	6.67383i	0.0514568	+	0.291826i	−0.948210	+	0.317645i	$0.897108\pi$
$524$	1.12769	−	0.566348i	0.0492634	−	0.0247410i
$525$		0			0
$526$	0.507251	+	1.17594i	0.0221172	+	0.0512734i
$527$	3.57713	+	8.29271i	0.155822	+	0.361236i
$528$		0			0
$529$	−6.95276	+	3.49181i	−0.302294	+	0.151818i
$530$	−4.15253	−	23.5502i	−0.180374	−	1.02295i
$531$		0			0
$532$	−0.214909	+	1.21881i	−0.00931748	+	0.0528421i
$533$	−8.66735	−	28.9510i	−0.375425	−	1.25401i
$534$		0			0
$535$	9.30479	+	4.67304i	0.402281	+	0.202033i
$536$	−12.3818	+	41.3583i	−0.534814	+	1.78640i
$537$		0			0
$538$	5.65210	+	7.59209i	0.243679	+	0.327318i
$539$	8.71338	+	15.0920i	0.375312	+	0.650059i
$540$		0			0
$541$	10.2033	−	17.6727i	0.438676	−	0.759809i	−0.558912	−	0.829227i	$-0.688781\pi$
$541$	10.2033	−	17.6727i	0.438676	−	0.759809i	0.997588	+	0.0694179i	$0.0221142\pi$
$542$	16.8800	−	1.97299i	0.725059	−	0.0847473i
$543$		0			0
$544$	−4.83754	+	1.14652i	−0.207408	+	0.0491566i
$545$	10.8202	−	7.11654i	0.463485	−	0.304839i
$546$		0			0
$547$	−2.46158	+	2.60912i	−0.105249	+	0.111558i	−0.777856	−	0.628442i	$-0.783693\pi$
$547$	−2.46158	+	2.60912i	−0.105249	+	0.111558i	0.672607	+	0.740000i	$0.265174\pi$
$548$	−0.656644	−	0.550990i	−0.0280505	−	0.0235371i
$549$		0			0
$550$	−17.9123	+	15.0302i	−0.763782	+	0.640889i
$551$	−0.437303	+	7.50821i	−0.0186297	+	0.319860i
$552$		0			0
$553$	−2.07129	+	2.78222i	−0.0880800	+	0.118312i
$554$	9.29384	+	1.08629i	0.394857	+	0.0461522i
$555$		0			0
$556$	−4.09820	−	2.69543i	−0.173803	−	0.114312i
$557$	2.23552	+	0.813664i	0.0947221	+	0.0344760i	0.388947	−	0.921260i	$-0.372839\pi$
$557$	2.23552	+	0.813664i	0.0947221	+	0.0344760i	−0.294224	+	0.955736i	$0.595061\pi$
$558$		0			0
$559$	−31.5515	+	11.4838i	−1.33449	+	0.485713i
$560$	0.844111	+	0.200058i	0.0356702	+	0.00845399i
$561$		0			0
$562$	0.951880	+	16.3432i	0.0401527	+	0.689394i
$563$	−24.2686	−	25.7232i	−1.02280	−	1.08410i	−0.996428	−	0.0844510i	$-0.973086\pi$
$563$	−24.2686	−	25.7232i	−1.02280	−	1.08410i	−0.0263710	−	0.999652i	$-0.508395\pi$
$564$		0			0
$565$	−14.1988	+	32.9166i	−0.597349	+	1.38481i
$566$	24.3531			1.02364
$567$		0			0
$568$	−28.3081			−1.18778
$569$	12.7694	−	29.6028i	0.535322	−	1.24102i	−0.409163	−	0.912461i	$-0.634179\pi$
$569$	12.7694	−	29.6028i	0.535322	−	1.24102i	0.944485	−	0.328554i	$-0.106561\pi$
$570$		0			0
$571$	−2.04866	−	2.17145i	−0.0857336	−	0.0908723i	0.683086	−	0.730338i	$-0.260637\pi$
$571$	−2.04866	−	2.17145i	−0.0857336	−	0.0908723i	−0.768820	+	0.639465i	$0.779156\pi$
$572$	0.840167	+	14.4251i	0.0351292	+	0.603145i
$573$		0			0
$574$	4.23602	+	1.00396i	0.176808	+	0.0419043i
$575$	34.8376	−	12.6798i	1.45283	−	0.528786i
$576$		0			0
$577$	−31.1151	−	11.3250i	−1.29534	−	0.471464i	−0.399862	−	0.916575i	$-0.630942\pi$
$577$	−31.1151	−	11.3250i	−1.29534	−	0.471464i	−0.895475	+	0.445111i	$0.853164\pi$
$578$	−12.3560	−	8.12665i	−0.513940	−	0.338024i
$579$		0			0
$580$	−22.6496	−	2.64736i	−0.940474	−	0.109926i
$581$	−3.14124	+	4.21941i	−0.130320	+	0.175051i
$582$		0			0
$583$	−1.07565	+	18.4682i	−0.0445488	+	0.764873i
$584$	−35.5436	+	29.8246i	−1.47081	+	1.23415i
$585$		0			0
$586$	−20.2474	−	16.9896i	−0.836411	−	0.701832i
$587$	−5.80543	+	6.15339i	−0.239616	+	0.253978i	−0.836010	−	0.548714i	$-0.815118\pi$
$587$	−5.80543	+	6.15339i	−0.239616	+	0.253978i	0.596395	+	0.802691i	$0.296599\pi$
$588$		0			0
$589$	12.2079	−	8.02929i	0.503020	−	0.330841i
$590$	−2.39526	+	0.567687i	−0.0986112	+	0.0233713i
$591$		0			0
$592$	−0.625328	+	0.0730904i	−0.0257008	+	0.00300400i
$593$	1.61604	−	2.79907i	0.0663629	−	0.114944i	−0.830935	−	0.556370i	$-0.812194\pi$
$593$	1.61604	−	2.79907i	0.0663629	−	0.114944i	0.897298	+	0.441426i	$0.145527\pi$
$594$		0			0
$595$	1.25049	+	2.16592i	0.0512652	+	0.0887939i
$596$	8.11837	+	10.9049i	0.332541	+	0.446681i
$597$		0			0
$598$	−4.71135	+	15.7370i	−0.192662	+	0.643534i
$599$	−0.552166	−	0.277308i	−0.0225609	−	0.0113305i	0.437483	−	0.899227i	$-0.355870\pi$
$599$	−0.552166	−	0.277308i	−0.0225609	−	0.0113305i	−0.460044	+	0.887896i	$0.652166\pi$
$600$		0			0
$601$	−5.21882	−	17.4321i	−0.212880	−	0.711068i	−0.996013	−	0.0892137i	$-0.971565\pi$
$601$	−5.21882	−	17.4321i	−0.212880	−	0.711068i	0.783133	−	0.621855i	$-0.213621\pi$
$602$	0.839899	−	4.76331i	0.0342317	−	0.194138i
$603$		0			0
$604$	0.969573	+	5.49872i	0.0394514	+	0.223740i
$605$	−12.7652	+	6.41090i	−0.518977	+	0.260640i
$606$		0			0
$607$	−2.86882	−	6.65067i	−0.116442	−	0.269942i	0.850021	−	0.526748i	$-0.176589\pi$
$607$	−2.86882	−	6.65067i	−0.116442	−	0.269942i	−0.966463	+	0.256806i	$0.917330\pi$
$608$	3.18585	+	7.38564i	0.129203	+	0.299527i
$609$		0			0
$610$	8.32144	−	4.17919i	0.336925	−	0.169210i
$611$	3.57829	+	20.2935i	0.144762	+	0.820988i
$612$		0			0
$613$	−6.98532	+	39.6157i	−0.282134	+	1.60006i	0.433211	+	0.901293i	$0.357381\pi$
$613$	−6.98532	+	39.6157i	−0.282134	+	1.60006i	−0.715345	+	0.698771i	$0.753731\pi$
$614$	1.00884	+	3.36977i	0.0407136	+	0.135993i
$615$		0			0
$616$	−5.05397	−	2.53820i	−0.203630	−	0.102267i
$617$	−5.02262	+	16.7767i	−0.202203	+	0.675405i	0.795392	+	0.606095i	$0.207265\pi$
$617$	−5.02262	+	16.7767i	−0.202203	+	0.675405i	−0.997595	+	0.0693101i	$0.977920\pi$
$618$		0			0
$619$	6.13883	+	8.24588i	0.246740	+	0.331430i	0.908189	−	0.418561i	$-0.137465\pi$
$619$	6.13883	+	8.24588i	0.246740	+	0.331430i	−0.661448	+	0.749991i	$0.730058\pi$
$620$	22.1517	+	38.3680i	0.889636	+	1.54089i
$621$		0			0
$622$	6.47415	−	11.2136i	0.259590	−	0.449623i
$623$	5.37595	−	0.628359i	0.215383	−	0.0251747i
$624$		0			0
$625$	17.3120	−	4.10302i	0.692481	−	0.164121i
$626$	15.8999	−	10.4575i	0.635488	−	0.417967i
$627$		0			0
$628$	7.47207	−	7.91993i	0.298168	−	0.316039i
$629$	−1.39044	−	1.16672i	−0.0554405	−	0.0465201i
$630$		0			0
$631$	22.0848	−	18.5313i	0.879182	−	0.737721i	−0.0868288	−	0.996223i	$-0.527673\pi$
$631$	22.0848	−	18.5313i	0.879182	−	0.737721i	0.966011	+	0.258502i	$0.0832289\pi$
$632$	−0.803180	+	13.7901i	−0.0319488	+	0.548540i
$633$		0			0
$634$	13.3423	−	17.9218i	0.529890	−	0.711765i
$635$	29.7920	+	3.48218i	1.18226	+	0.138186i
$636$		0			0
$637$	24.9160	+	16.3875i	0.987209	+	0.649297i
$638$	−11.8864	−	4.32630i	−0.470588	−	0.171280i
$639$		0			0
$640$	−20.8658	+	7.59452i	−0.824792	+	0.300200i
$641$	27.9023	+	6.61297i	1.10207	+	0.261197i	0.741111	−	0.671383i	$-0.234299\pi$
$641$	27.9023	+	6.61297i	1.10207	+	0.261197i	0.360964	+	0.932580i	$0.382448\pi$
$642$		0			0
$643$	−1.12427	−	19.3030i	−0.0443369	−	0.761235i	−0.945071	−	0.326864i	$-0.894008\pi$
$643$	−1.12427	−	19.3030i	−0.0443369	−	0.761235i	0.900734	−	0.434370i	$-0.143029\pi$
$644$	2.26475	+	2.40049i	0.0892437	+	0.0945928i
$645$		0			0
$646$	0.478866	−	1.11014i	0.0188407	−	0.0436778i
$647$	29.8266			1.17261			0.586303	−	0.810092i	$-0.300583\pi$
$647$	29.8266			1.17261			0.586303	+	0.810092i	$0.300583\pi$
$648$		0			0
$649$	1.90430			0.0747505
$650$	−15.8490	+	36.7420i	−0.621648	+	1.44114i
$651$		0			0
$652$	−6.23078	−	6.60424i	−0.244016	−	0.258642i
$653$	−1.44269	−	24.7701i	−0.0564569	−	0.969328i	−0.900994	−	0.433831i	$-0.857162\pi$
$653$	−1.44269	−	24.7701i	−0.0564569	−	0.969328i	0.844537	−	0.535497i	$-0.179876\pi$
$654$		0			0
$655$	−4.01460	−	0.951478i	−0.156863	−	0.0371773i
$656$	1.93318	−	0.703621i	0.0754781	−	0.0274718i
$657$		0			0
$658$	−2.78942	−	1.01527i	−0.108743	−	0.0395792i
$659$	14.6079	+	9.60779i	0.569044	+	0.374266i	0.801186	−	0.598416i	$-0.204203\pi$
$659$	14.6079	+	9.60779i	0.569044	+	0.374266i	−0.232142	+	0.972682i	$0.574573\pi$
$660$		0			0
$661$	−37.3153	−	4.36154i	−1.45140	−	0.169644i	−0.646435	−	0.762969i	$-0.723741\pi$
$661$	−37.3153	−	4.36154i	−1.45140	−	0.169644i	−0.804963	+	0.593324i	$0.797815\pi$
$662$	3.68294	−	4.94704i	0.143141	−	0.192272i
$663$		0			0
$664$	−1.21807	+	20.9135i	−0.0472704	+	0.811602i
$665$	3.09967	−	2.60094i	0.120200	−	0.100860i
$666$		0			0
$667$	15.3633	+	12.8913i	0.594870	+	0.499155i
$668$	−8.64560	+	9.16380i	−0.334508	+	0.354558i
$669$		0			0
$670$	43.4034	−	28.5469i	1.67682	−	1.10286i
$671$	−7.00954	+	1.66129i	−0.270600	+	0.0641334i
$672$		0			0
$673$	26.3408	−	3.07880i	1.01536	−	0.118679i	0.407900	−	0.913027i	$-0.366261\pi$
$673$	26.3408	−	3.07880i	1.01536	−	0.118679i	0.607464	+	0.794348i	$0.292187\pi$
$674$	−1.94622	+	3.37095i	−0.0749656	+	0.129844i
$675$		0			0
$676$	4.79246	+	8.30079i	0.184326	+	0.319261i
$677$	12.2841	+	16.5004i	0.472116	+	0.634162i	0.972849	−	0.231439i	$-0.0743435\pi$
$677$	12.2841	+	16.5004i	0.472116	+	0.634162i	−0.500733	+	0.865602i	$0.666936\pi$
$678$		0			0
$679$	−0.926871	+	3.09596i	−0.0355700	+	0.118812i
$680$	8.90065	+	4.47007i	0.341324	+	0.171420i
$681$		0			0
$682$	7.04823	+	23.5427i	0.269891	+	0.901498i
$683$	−2.39856	+	13.6029i	−0.0917785	+	0.520502i	0.903908	+	0.427726i	$0.140685\pi$
$683$	−2.39856	+	13.6029i	−0.0917785	+	0.520502i	−0.995687	+	0.0927760i	$0.970426\pi$
$684$		0			0
$685$	0.486659	+	2.75998i	0.0185943	+	0.105453i
$686$	−7.99089	+	4.01317i	−0.305093	+	0.153224i
$687$		0			0
$688$	−0.905319	−	2.09877i	−0.0345150	−	0.0800147i
$689$	12.5390	+	29.0687i	0.477699	+	1.10743i
$690$		0			0
$691$	−5.67005	+	2.84760i	−0.215699	+	0.108328i	−0.553368	−	0.832937i	$-0.686658\pi$
$691$	−5.67005	+	2.84760i	−0.215699	+	0.108328i	0.337669	+	0.941265i	$0.390361\pi$
$692$	−2.35086	−	13.3324i	−0.0893662	−	0.506821i
$693$		0			0
$694$	−3.20666	+	18.1859i	−0.121723	+	0.690326i
$695$	4.59955	+	15.3636i	0.174471	+	0.582774i
$696$		0			0
$697$	5.30018	+	2.66185i	0.200759	+	0.100825i
$698$	6.03163	−	20.1471i	0.228301	−	0.762577i
$699$		0			0
$700$	4.80054	+	6.44824i	0.181443	+	0.243720i
$701$	−11.8662	−	20.5529i	−0.448180	−	0.776271i	0.550087	−	0.835107i	$-0.314594\pi$
$701$	−11.8662	−	20.5529i	−0.448180	−	0.776271i	−0.998268	+	0.0588360i	$0.981261\pi$
$702$		0			0
$703$	−1.46832	+	2.54320i	−0.0553786	+	0.0959186i
$704$	−15.1142	+	1.76659i	−0.569637	+	0.0665810i
$705$		0			0
$706$	19.2878	−	4.57130i	0.725908	−	0.172043i
$707$	6.63247	−	4.36225i	0.249440	−	0.164059i
$708$		0			0
$709$	0.00970556	−	0.0102873i	0.000364500	−	0.000386348i	−0.727191	−	0.686435i	$-0.759175\pi$
$709$	0.00970556	−	0.0102873i	0.000364500	−	0.000386348i	0.727556	+	0.686048i	$0.240656\pi$
$710$	26.0944	+	21.8958i	0.979307	+	0.821736i
$711$		0			0
$712$	16.5123	−	13.8555i	0.618824	−	0.519255i
$713$	2.26555	−	38.8979i	0.0848454	−	1.45674i
$714$		0			0
$715$	28.2113	−	37.8943i	1.05504	−	1.41717i
$716$	−3.15747	−	0.369055i	−0.118000	−	0.0137922i
$717$		0			0
$718$	25.3448	+	16.6695i	0.945859	+	0.622101i
$719$	−23.2140	−	8.44919i	−0.865735	−	0.315102i	−0.129296	−	0.991606i	$-0.541272\pi$
$719$	−23.2140	−	8.44919i	−0.865735	−	0.315102i	−0.736439	+	0.676504i	$0.763494\pi$
$720$		0			0
$721$	3.30651	−	1.20347i	0.123141	−	0.0448197i
$722$	14.9926	+	3.55331i	0.557967	+	0.132241i
$723$		0			0
$724$	−1.02481	−	17.5953i	−0.0380867	−	0.653924i
$725$	33.5247	+	35.5341i	1.24508	+	1.31970i
$726$		0			0
$727$	−16.2048	+	37.5669i	−0.601003	+	1.39328i	0.297674	+	0.954668i	$0.403789\pi$
$727$	−16.2048	+	37.5669i	−0.601003	+	1.39328i	−0.898676	+	0.438613i	$0.855470\pi$
$728$	−9.67821			−0.358698
$729$		0			0
$730$	55.8329			2.06647
$731$	2.61003	−	6.05074i	0.0965355	−	0.223795i
$732$		0			0
$733$	−10.2665	−	10.8819i	−0.379203	−	0.401932i	0.509458	−	0.860495i	$-0.329846\pi$
$733$	−10.2665	−	10.8819i	−0.379203	−	0.401932i	−0.888662	+	0.458563i	$0.848364\pi$
$734$	−1.10031	−	18.8916i	−0.0406133	−	0.697303i
$735$		0			0
$736$	20.8706	+	4.94642i	0.769301	+	0.182328i
$737$	−37.7648	+	13.7452i	−1.39108	+	0.506313i
$738$		0			0
$739$	−12.3654	−	4.50063i	−0.454868	−	0.165558i	0.104418	−	0.994534i	$-0.466702\pi$
$739$	−12.3654	−	4.50063i	−0.454868	−	0.165558i	−0.559285	+	0.828975i	$0.688924\pi$
$740$	−7.43918	−	4.89283i	−0.273470	−	0.179864i
$741$		0			0
$742$	−4.52958	−	0.529431i	−0.166286	−	0.0194360i
$743$	16.7221	−	22.4616i	0.613473	−	0.824037i	−0.381481	−	0.924377i	$-0.624586\pi$
$743$	16.7221	−	22.4616i	0.613473	−	0.824037i	0.994953	+	0.100340i	$0.0319931\pi$
$744$		0			0
$745$	2.58445	−	44.3733i	0.0946870	−	1.62571i
$746$	2.82002	−	2.36628i	0.103248	−	0.0866355i
$747$		0			0
$748$	−2.17239	−	1.82285i	−0.0794305	−	0.0666501i
$749$	1.36266	−	1.44433i	0.0497904	−	0.0527747i
$750$		0			0
$751$	6.38696	−	4.20077i	0.233063	−	0.153288i	−0.427606	−	0.903965i	$-0.640643\pi$
$751$	6.38696	−	4.20077i	0.233063	−	0.153288i	0.660669	+	0.750677i	$0.270273\pi$
$752$	−1.36497	+	0.323504i	−0.0497754	+	0.0117970i
$753$		0			0
$754$	−21.5001	+	2.51300i	−0.782988	+	0.0915182i
$755$	9.12764	−	15.8095i	0.332189	−	0.575368i
$756$		0			0
$757$	−16.9101	−	29.2892i	−0.614608	−	1.06453i	−0.990453	−	0.137850i	$-0.955981\pi$
$757$	−16.9101	−	29.2892i	−0.614608	−	1.06453i	0.375845	−	0.926683i	$-0.377353\pi$
$758$	18.8401	+	25.3066i	0.684302	+	0.919177i
$759$		0			0
$760$	4.62166	−	15.4374i	0.167645	−	0.559974i
$761$	33.1292	+	16.6381i	1.20093	+	0.603131i	0.932850	−	0.360265i	$-0.117314\pi$
$761$	33.1292	+	16.6381i	1.20093	+	0.603131i	0.268083	+	0.963396i	$0.413610\pi$
$762$		0			0
$763$	−0.708337	−	2.36601i	−0.0256435	−	0.0856553i
$764$	−0.500564	+	2.83884i	−0.0181098	+	0.102706i
$765$		0			0
$766$	2.26306	+	12.8344i	0.0817675	+	0.463727i
$767$	2.91217	−	1.46255i	0.105152	−	0.0528096i
$768$		0			0
$769$	18.4305	+	42.7267i	0.664622	+	1.54077i	0.831942	+	0.554863i	$0.187229\pi$
$769$	18.4305	+	42.7267i	0.664622	+	1.54077i	−0.167320	+	0.985903i	$0.553511\pi$
$770$	2.69549	+	6.24886i	0.0971389	+	0.225193i
$771$		0			0
$772$	4.12829	−	2.07331i	0.148580	−	0.0746199i
$773$	7.40534	+	41.9978i	0.266352	+	1.51056i	0.765158	+	0.643842i	$0.222661\pi$
$773$	7.40534	+	41.9978i	0.266352	+	1.51056i	−0.498807	+	0.866713i	$0.666228\pi$
$774$		0			0
$775$	16.4812	−	93.4695i	0.592022	−	3.35752i
$776$	3.69123	+	12.3296i	0.132507	+	0.442605i
$777$		0			0
$778$	−16.9689	−	8.52210i	−0.608364	−	0.305532i
$779$	2.75212	−	9.19270i	0.0986048	−	0.329363i
$780$		0			0
$781$	−15.7362	−	21.1374i	−0.563086	−	0.756356i
$782$	−1.61198	−	2.79204i	−0.0576445	−	0.0998431i
$783$		0			0
$784$	−1.01506	+	1.75814i	−0.0362523	+	0.0627908i
$785$	−35.3586	+	4.13283i	−1.26200	+	0.147507i
$786$		0			0
$787$	10.0019	−	2.37049i	0.356529	−	0.0844988i	−0.0484484	−	0.998826i	$-0.515428\pi$
$787$	10.0019	−	2.37049i	0.356529	−	0.0844988i	0.404977	+	0.914327i	$0.367280\pi$
$788$	−24.2020	+	15.9179i	−0.862160	+	0.567051i
$789$		0			0
$790$	11.4067	−	12.0904i	0.405834	−	0.430158i
$791$	5.23704	+	4.39440i	0.186208	+	0.156247i
$792$		0			0
$793$	−9.44348	+	7.92402i	−0.335348	+	0.281390i
$794$	−1.21255	+	20.8186i	−0.0430317	+	0.738825i
$795$		0			0
$796$	−8.02452	+	10.7788i	−0.284422	+	0.382045i
$797$	−25.3306	−	2.96072i	−0.897254	−	0.104874i	−0.345051	−	0.938584i	$-0.612139\pi$
$797$	−25.3306	−	2.96072i	−0.897254	−	0.104874i	−0.552203	+	0.833710i	$0.686213\pi$
$798$		0			0
$799$	−3.37890	−	2.22234i	−0.119537	−	0.0786206i
$800$	49.0959	+	17.8694i	1.73580	+	0.631780i
$801$		0			0
$802$	−7.37210	+	2.68323i	−0.260318	+	0.0947480i
$803$	−42.0281	−	9.96085i	−1.48314	−	0.351511i
$804$		0			0
$805$	−0.627383	−	10.7717i	−0.0221123	−	0.379654i
$806$	28.8599	+	30.5897i	1.01655	+	1.07748i
$807$		0			0
$808$	12.5219	−	29.0290i	0.440518	−	1.02124i
$809$	−3.50823			−0.123343			−0.0616715	−	0.998097i	$-0.519643\pi$
$809$	−3.50823			−0.123343			−0.0616715	+	0.998097i	$0.519643\pi$
$810$		0			0
$811$	−51.7502			−1.81719			−0.908597	−	0.417674i	$-0.862845\pi$
$811$	−51.7502			−1.81719			−0.908597	+	0.417674i	$0.862845\pi$
$812$	−1.72247	+	3.99313i	−0.0604468	+	0.140131i
$813$		0			0
$814$	−3.38938	−	3.59253i	−0.118798	−	0.125918i
$815$	1.72605	+	29.6352i	0.0604610	+	1.03808i
$816$		0			0
$817$	−10.3740	−	2.45869i	−0.362941	−	0.0860186i
$818$	−24.2151	+	8.81358i	−0.846661	+	0.308160i
$819$		0			0
$820$	27.3403	+	9.95107i	0.954766	+	0.347506i
$821$	24.8994	+	16.3766i	0.868996	+	0.571547i	0.903852	−	0.427845i	$-0.140727\pi$
$821$	24.8994	+	16.3766i	0.868996	+	0.571547i	−0.0348565	+	0.999392i	$0.511097\pi$
$822$		0			0
$823$	−21.8315	−	2.55174i	−0.760999	−	0.0889480i	−0.273263	−	0.961939i	$-0.588103\pi$
$823$	−21.8315	−	2.55174i	−0.760999	−	0.0889480i	−0.487736	+	0.872991i	$0.662177\pi$
$824$	8.36808	−	11.2403i	0.291516	−	0.391574i
$825$		0			0
$826$	−0.0272956	+	0.468647i	−0.000949735	+	0.0163063i
$827$	42.6770	−	35.8102i	1.48402	−	1.24524i	0.582268	−	0.812997i	$-0.302166\pi$
$827$	42.6770	−	35.8102i	1.48402	−	1.24524i	0.901756	−	0.432246i	$-0.142279\pi$
$828$		0			0
$829$	−9.07696	−	7.61647i	−0.315256	−	0.264531i	0.471404	−	0.881917i	$-0.343747\pi$
$829$	−9.07696	−	7.61647i	−0.315256	−	0.264531i	−0.786660	+	0.617386i	$0.788192\pi$
$830$	17.2990	−	18.3359i	0.600459	−	0.636449i
$831$		0			0
$832$	−21.7567	+	14.3096i	−0.754277	+	0.496096i
$833$	−5.69509	+	1.34976i	−0.197323	+	0.0467665i
$834$		0			0
$835$	40.9119	−	4.78192i	1.41581	−	0.165485i
$836$	−2.29406	+	3.97343i	−0.0793418	+	0.137424i
$837$		0			0
$838$	14.5999	+	25.2877i	0.504344	+	0.873550i
$839$	−26.2002	−	35.1929i	−0.904531	−	1.21500i	−0.976048	−	0.217556i	$-0.930191\pi$
$839$	−26.2002	−	35.1929i	−0.904531	−	1.21500i	0.0715172	−	0.997439i	$-0.477216\pi$
$840$		0			0
$841$	0.737795	−	2.46441i	0.0254412	−	0.0849795i
$842$	−22.7748	−	11.4379i	−0.784872	−	0.394177i
$843$		0			0
$844$	7.09421	+	23.6963i	0.244193	+	0.815661i
$845$	5.44173	−	30.8616i	0.187201	−	1.06167i
$846$		0			0
$847$	0.473041	+	2.68275i	0.0162539	+	0.0921804i
$848$	−1.92586	+	0.967204i	−0.0661343	+	0.0332139i
$849$		0			0
$850$	−3.11050	−	7.21095i	−0.106689	−	0.247334i
$851$	3.10164	+	7.19041i	0.106323	+	0.246484i
$852$		0			0
$853$	4.50072	−	2.26035i	0.154102	−	0.0773928i	−0.370077	−	0.929001i	$-0.620669\pi$
$853$	4.50072	−	2.26035i	0.154102	−	0.0773928i	0.524179	+	0.851608i	$0.324372\pi$
$854$	−0.308370	−	1.74885i	−0.0105522	−	0.0598444i
$855$		0			0
$856$	1.37319	−	7.78776i	0.0469347	−	0.266180i
$857$	1.28851	+	4.30394i	0.0440148	+	0.147020i	0.977172	−	0.212448i	$-0.0681435\pi$
$857$	1.28851	+	4.30394i	0.0440148	+	0.147020i	−0.933158	+	0.359467i	$0.882958\pi$
$858$		0			0
$859$	−10.9535	−	5.50107i	−0.373730	−	0.187694i	0.252012	−	0.967724i	$-0.418908\pi$
$859$	−10.9535	−	5.50107i	−0.373730	−	0.187694i	−0.625742	+	0.780030i	$0.715204\pi$
$860$	9.27115	−	30.9678i	0.316144	−	1.05599i
$861$		0			0
$862$	−18.4762	−	24.8178i	−0.629300	−	0.845297i
$863$	−12.7488	−	22.0815i	−0.433974	−	0.751665i	0.563238	−	0.826295i	$-0.309556\pi$
$863$	−12.7488	−	22.0815i	−0.433974	−	0.751665i	−0.997211	+	0.0746305i	$0.976222\pi$
$864$		0			0
$865$	−22.1311	+	38.3323i	−0.752482	+	1.30334i
$866$	−7.69631	+	0.899570i	−0.261531	+	0.0305686i
$867$		0			0
$868$	8.22115	−	1.94845i	0.279044	−	0.0661347i
$869$	−10.7434	+	7.06604i	−0.364445	+	0.239699i
$870$		0			0
$871$	−47.1954	+	50.0242i	−1.59916	+	1.69501i
$872$	−7.53462	−	6.32229i	−0.255154	−	0.214100i
$873$		0			0
$874$	−3.99573	+	3.35281i	−0.135158	+	0.113411i
$875$	0.724151	−	12.4332i	0.0244808	−	0.420318i
$876$		0			0
$877$	14.8566	−	19.9559i	0.501673	−	0.673863i	−0.477091	−	0.878854i	$-0.658309\pi$
$877$	14.8566	−	19.9559i	0.501673	−	0.673863i	0.978764	+	0.204990i	$0.0657163\pi$
$878$	−20.1840	−	2.35917i	−0.681176	−	0.0796181i
$879$		0			0
$880$	2.68694	+	1.76723i	0.0905767	+	0.0595733i
$881$	15.8259	+	5.76014i	0.533187	+	0.194064i	0.594561	−	0.804051i	$-0.297326\pi$
$881$	15.8259	+	5.76014i	0.533187	+	0.194064i	−0.0613739	+	0.998115i	$0.519548\pi$
$882$		0			0
$883$	−26.9155	+	9.79645i	−0.905779	+	0.329677i	−0.752566	−	0.658516i	$-0.771184\pi$
$883$	−26.9155	+	9.79645i	−0.905779	+	0.329677i	−0.153213	+	0.988193i	$0.548962\pi$
$884$	−4.72214	−	1.11917i	−0.158823	−	0.0376417i
$885$		0			0
$886$	1.19723	+	20.5557i	0.0402218	+	0.690581i
$887$	−10.1231	−	10.7299i	−0.339902	−	0.360275i	0.534764	−	0.845001i	$-0.320401\pi$
$887$	−10.1231	−	10.7299i	−0.339902	−	0.360275i	−0.874666	+	0.484727i	$0.838919\pi$
$888$		0			0
$889$	2.26564	−	5.25233i	0.0759870	−	0.176158i
$890$	−25.9380			−0.869443
$891$		0			0
$892$	−2.60553			−0.0872398
$893$	−2.59160	+	6.00801i	−0.0867247	+	0.201051i
$894$		0			0
$895$	7.13248	+	7.55999i	0.238413	+	0.252703i
$896$	0.246219	+	4.22741i	0.00822560	+	0.141228i
$897$		0			0
$898$	19.7616	+	4.68357i	0.659452	+	0.156293i
$899$	48.2473	−	17.5606i	1.60914	−	0.585678i
$900$		0			0
$901$	−5.83843	−	2.12501i	−0.194506	−	0.0707945i
$902$	13.4839	+	8.86852i	0.448966	+	0.295289i
$903$		0			0
$904$	27.0419	+	3.16074i	0.899400	+	0.105125i
$905$	−34.4112	+	46.2223i	−1.14387	+	1.53648i
$906$		0			0
$907$	1.67313	−	28.7266i	0.0555554	−	0.953850i	−0.849241	−	0.528005i	$-0.822940\pi$
$907$	1.67313	−	28.7266i	0.0555554	−	0.953850i	0.904796	−	0.425844i	$-0.140023\pi$
$908$	−3.14784	+	2.64135i	−0.104465	+	0.0876562i
$909$		0			0
$910$	8.92137	+	7.48592i	0.295741	+	0.248156i
$911$	9.96732	−	10.5647i	0.330232	−	0.350026i	−0.540889	−	0.841094i	$-0.681912\pi$
$911$	9.96732	−	10.5647i	0.330232	−	0.350026i	0.871121	+	0.491068i	$0.163394\pi$
$912$		0			0
$913$	−16.2930	+	10.7161i	−0.539221	+	0.354651i
$914$	2.05979	−	0.488179i	0.0681318	−	0.0161475i
$915$		0			0
$916$	−12.2237	+	1.42875i	−0.403882	+	0.0472071i
$917$	−0.393406	+	0.681399i	−0.0129914	+	0.0225018i
$918$		0			0
$919$	13.7670	+	23.8452i	0.454132	+	0.786579i	0.998638	−	0.0521778i	$-0.0166163\pi$
$919$	13.7670	+	23.8452i	0.454132	+	0.786579i	−0.544506	+	0.838757i	$0.683283\pi$
$920$	−25.6604	−	34.4678i	−0.845997	−	1.13637i
$921$		0			0
$922$	−6.43177	+	21.4836i	−0.211819	+	0.707525i
$923$	−40.2988	−	20.2388i	−1.32645	−	0.666168i
$924$		0			0
$925$	5.47078	+	18.2737i	0.179878	+	0.600835i
$926$	−4.32857	+	24.5486i	−0.142246	+	0.806716i
$927$		0			0
$928$	4.90793	+	27.8342i	0.161111	+	0.913704i
$929$	−8.00130	+	4.01841i	−0.262514	+	0.131840i	−0.575189	−	0.818021i	$-0.695071\pi$
$929$	−8.00130	+	4.01841i	−0.262514	+	0.131840i	0.312675	+	0.949860i	$0.398775\pi$
$930$		0			0
$931$	3.75061	+	8.69488i	0.122921	+	0.284963i
$932$	−8.25655	−	19.1408i	−0.270452	−	0.626979i
$933$		0			0
$934$	3.00129	−	1.50730i	0.0982051	−	0.0493204i
$935$	1.61002	+	9.13090i	0.0526534	+	0.298612i
$936$		0			0
$937$	−1.85963	+	10.5465i	−0.0607515	+	0.344539i	0.939248	+	0.343240i	$0.111525\pi$
$937$	−1.85963	+	10.5465i	−0.0607515	+	0.344539i	−0.999999	+	0.00129877i	$0.999587\pi$
$938$	−2.84138	−	9.49088i	−0.0927744	−	0.309888i
$939$		0			0
$940$	−17.7289	−	8.90376i	−0.578251	−	0.290409i
$941$	5.03928	−	16.8324i	0.164276	−	0.548720i	−0.835724	−	0.549150i	$-0.814952\pi$
$941$	5.03928	−	16.8324i	0.164276	−	0.548720i	1.00000		0.000429836i	$0.000136821\pi$
$942$		0			0
$943$	−15.2803	−	20.5250i	−0.497595	−	0.668385i
$944$	0.110921	+	0.192121i	0.00361017	+	0.00625299i
$945$		0			0
$946$	8.96557	−	15.5288i	0.291496	−	0.504886i
$947$	24.0317	−	2.80891i	0.780926	−	0.0912772i	0.283717	−	0.958908i	$-0.408432\pi$
$947$	24.0317	−	2.80891i	0.780926	−	0.0912772i	0.497209	+	0.867631i	$0.334358\pi$
$948$		0			0
$949$	−71.9220	+	17.0458i	−2.33469	+	0.553331i
$950$	−10.6155	+	6.98190i	−0.344411	+	0.226523i
$951$		0			0
$952$	1.30347	−	1.38160i	0.0422458	−	0.0447779i
$953$	−42.6684	−	35.8030i	−1.38216	−	1.15977i	−0.968403	−	0.249389i	$-0.919770\pi$
$953$	−42.6684	−	35.8030i	−1.38216	−	1.15977i	−0.413761	−	0.910385i	$-0.635785\pi$
$954$		0			0
$955$	7.21973	−	6.05807i	0.233625	−	0.196035i
$956$	−0.0251561	+	0.431913i	−0.000813605	+	0.0139691i
$957$		0			0
$958$	−1.62625	+	2.18444i	−0.0525419	+	0.0705760i
$959$	0.530847	+	0.0620471i	0.0171419	+	0.00200361i
$960$		0			0
$961$	−57.4408	−	37.7794i	−1.85293	−	1.21869i
$962$	−7.94239	−	2.89079i	−0.256073	−	0.0932029i
$963$		0			0
$964$	6.88322	−	2.50529i	0.221693	−	0.0806898i
$965$	−14.6968	−	3.48320i	−0.473106	−	0.112128i
$966$		0			0
$967$	2.49855	+	42.8984i	0.0803479	+	1.37952i	0.761873	+	0.647726i	$0.224280\pi$
$967$	2.49855	+	42.8984i	0.0803479	+	1.37952i	−0.681525	+	0.731795i	$0.738683\pi$
$968$	7.44487	+	7.89111i	0.239287	+	0.253630i
$969$		0			0
$970$	6.13412	−	14.2205i	0.196955	−	0.456592i
$971$	−6.84433			−0.219645			−0.109823	−	0.993951i	$-0.535028\pi$
$971$	−6.84433			−0.219645			−0.109823	+	0.993951i	$0.535028\pi$
$972$		0			0
$973$	3.05839			0.0980476
$974$	7.00803	−	16.2464i	0.224552	−	0.520570i
$975$		0			0
$976$	−0.575891	−	0.610409i	−0.0184338	−	0.0195387i
$977$	2.13268	+	36.6167i	0.0682306	+	1.17147i	0.842528	+	0.538652i	$0.181066\pi$
$977$	2.13268	+	36.6167i	0.0682306	+	1.17147i	−0.774298	+	0.632822i	$0.781897\pi$
$978$		0			0
$979$	19.5248	+	4.62745i	0.624014	+	0.147894i
$980$	−26.9799	+	9.81988i	−0.861841	+	0.313684i
$981$		0			0
$982$	9.21831	+	3.35519i	0.294168	+	0.107068i
$983$	23.8062	+	15.6576i	0.759300	+	0.499399i	0.869150	−	0.494549i	$-0.164667\pi$
$983$	23.8062	+	15.6576i	0.759300	+	0.499399i	−0.109850	+	0.993948i	$0.535037\pi$
$984$		0			0
$985$	94.0681	+	10.9950i	2.99726	+	0.350329i
$986$	2.53692	−	3.40767i	0.0807919	−	0.108522i
$987$		0			0
$988$	−0.456529	+	7.83829i	−0.0145241	+	0.249369i
$989$	−21.7785	+	18.2743i	−0.692515	+	0.581089i
$990$		0			0
$991$	20.0475	+	16.8218i	0.636829	+	0.534363i	0.903043	−	0.429551i	$-0.141328\pi$
$991$	20.0475	+	16.8218i	0.636829	+	0.534363i	−0.266214	+	0.963914i	$0.585773\pi$
$992$	37.6822	−	39.9408i	1.19641	−	1.26812i
$993$		0			0
$994$	5.42745	−	3.56969i	0.172148	−	0.113224i
$995$	42.7504	−	10.1320i	1.35528	−	0.321207i
$996$		0			0
$997$	−20.6155	+	2.40960i	−0.652898	+	0.0763128i	−0.436092	−	0.899902i	$-0.643638\pi$
$997$	−20.6155	+	2.40960i	−0.652898	+	0.0763128i	−0.216806	+	0.976215i	$0.569564\pi$
$998$	14.0095	−	24.2652i	0.443464	−	0.768102i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.g.a.55.3		144
3.2	odd	2		729.2.g.d.55.6		144
9.2	odd	6		81.2.g.a.61.3	yes	144
9.4	even	3		729.2.g.b.541.3		144
9.5	odd	6		729.2.g.c.541.6		144
9.7	even	3		243.2.g.a.19.6		144
81.4	even	27		729.2.g.b.190.3		144
81.23	odd	54		81.2.g.a.4.3	✓	144
81.29	odd	54		6561.2.a.c.1.50		72
81.31	even	27	inner	729.2.g.a.676.3		144
81.50	odd	54		729.2.g.d.676.6		144
81.52	even	27		6561.2.a.d.1.23		72
81.58	even	27		243.2.g.a.64.6		144
81.77	odd	54		729.2.g.c.190.6		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.4.3	✓	144	81.23	odd	54
81.2.g.a.61.3	yes	144	9.2	odd	6
243.2.g.a.19.6		144	9.7	even	3
243.2.g.a.64.6		144	81.58	even	27
729.2.g.a.55.3		144	1.1	even	1	trivial
729.2.g.a.676.3		144	81.31	even	27	inner
729.2.g.b.190.3		144	81.4	even	27
729.2.g.b.541.3		144	9.4	even	3
729.2.g.c.190.6		144	81.77	odd	54
729.2.g.c.541.6		144	9.5	odd	6
729.2.g.d.55.6		144	3.2	odd	2
729.2.g.d.676.6		144	81.50	odd	54
6561.2.a.c.1.50		72	81.29	odd	54
6561.2.a.d.1.23		72	81.52	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)

\(f(q)\)	\(=\)	\(q+(-0.361975 + 0.839152i) q^{2} +(0.799333 + 0.847243i) q^{4} +(-0.221432 - 3.80183i) q^{5} +(-0.706680 - 0.167486i) q^{7} +(-2.71786 + 0.989221i) q^{8} +O(q^{10})\)	\(q+(-0.361975 + 0.839152i) q^{2} +(0.799333 + 0.847243i) q^{4} +(-0.221432 - 3.80183i) q^{5} +(-0.706680 - 0.167486i) q^{7} +(-2.71786 + 0.989221i) q^{8} +(3.27047 + 1.19035i) q^{10} +(-2.24948 - 1.47950i) q^{11} +(-4.57632 - 0.534895i) q^{13} +(0.396347 - 0.532387i) q^{14} +(0.0182372 - 0.313121i) q^{16} +(0.692702 - 0.581246i) q^{17} +(-1.12072 - 0.940396i) q^{19} +(3.04408 - 3.22654i) q^{20} +(2.05578 - 1.35211i) q^{22} +(-3.79608 + 0.899688i) q^{23} +(-9.43871 + 1.10323i) q^{25} +(2.10537 - 3.64661i) q^{26} +(-0.422971 - 0.732607i) q^{28} +(-3.06986 - 4.12353i) q^{29} +(-2.86446 + 9.56797i) q^{31} +(-4.91313 - 2.46747i) q^{32} +(0.237013 + 0.791679i) q^{34} +(-0.480274 + 2.72377i) q^{35} +(-0.348559 - 1.97678i) q^{37} +(1.19481 - 0.600055i) q^{38} +(4.36268 + 10.1138i) q^{40} +(2.59790 + 6.02260i) q^{41} +(6.51223 - 3.27057i) q^{43} +(-0.544580 - 3.08847i) q^{44} +(0.619111 - 3.51115i) q^{46} +(-1.28270 - 4.28453i) q^{47} +(-5.78408 - 2.90488i) q^{49} +(2.49080 - 8.31986i) q^{50} +(-3.20482 - 4.30482i) q^{52} +(-3.43548 - 5.95043i) q^{53} +(-5.12672 + 8.87974i) q^{55} +(2.08634 - 0.243858i) q^{56} +(4.57148 - 1.08346i) q^{58} +(-0.590929 + 0.388660i) q^{59} +(1.83608 - 1.94613i) q^{61} +(-6.99212 - 5.86709i) q^{62} +(4.32956 - 3.63293i) q^{64} +(-1.02024 + 17.5169i) q^{65} +(8.91352 - 11.9729i) q^{67} +(1.04616 + 0.122278i) q^{68} +(-2.11181 - 1.38896i) q^{70} +(9.19719 + 3.34750i) q^{71} +(15.0748 - 5.48678i) q^{73} +(1.78499 + 0.423050i) q^{74} +(-0.0990843 - 1.70121i) q^{76} +(1.34186 + 1.42229i) q^{77} +(1.89166 - 4.38536i) q^{79} -1.19447 q^{80} -5.99425 q^{82} +(2.86882 - 6.65067i) q^{83} +(-2.36319 - 2.50483i) q^{85} +(0.387238 + 6.64862i) q^{86} +(7.57733 + 1.79586i) q^{88} +(-7.00321 + 2.54896i) q^{89} +(3.14441 + 1.14447i) q^{91} +(-3.79659 - 2.49705i) q^{92} +(4.05968 + 0.474509i) q^{94} +(-3.32707 + 4.46903i) q^{95} +(0.258735 - 4.44232i) q^{97} +(4.53133 - 3.80223i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8}+O(q^{10}) \) 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

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Database

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