LMFDB - Embedded newform 729.2.g.d.676.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("729.28");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			676.6
Character	$\chi$	$=$	729.676
Dual form			729.2.g.d.55.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

$n$	$2$
$\chi(n)$	$e\left(\frac{10}{27}\right)$

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	$-0.0249011\pi$
$2$	0.361975	+	0.839152i	0.255955	+	0.593370i	−0.740987	+	0.671520i	$0.765642\pi$
$3$		0			0
$3$		0			0
$4$	0.799333	−	0.847243i	0.399666	−	0.423621i
$5$	0.221432	−	3.80183i	0.0990272	−	1.70023i	−0.473862	−	0.880599i	$-0.657141\pi$
$5$	0.221432	−	3.80183i	0.0990272	−	1.70023i	0.572889	−	0.819633i	$-0.305822\pi$
$6$		0			0
$7$	−0.706680	+	0.167486i	−0.267100	+	0.0633039i	−0.361983	−	0.932185i	$-0.617900\pi$
$7$	−0.706680	+	0.167486i	−0.267100	+	0.0633039i	0.0948834	+	0.995488i	$0.469752\pi$
$8$	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	$-0.552145\pi$
$11$	2.24948	−	1.47950i	0.678243	−	0.446087i	0.841328	+	0.540525i	$0.181774\pi$
$12$		0			0
$13$	−4.57632	+	0.534895i	−1.26924	+	0.148353i	−0.723927	−	0.689877i	$-0.757665\pi$
$13$	−4.57632	+	0.534895i	−1.26924	+	0.148353i	−0.545317	+	0.838230i	$0.683591\pi$
$14$	−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	$-0.312753\pi$
$17$	−0.692702	−	0.581246i	−0.168005	−	0.140973i	−0.722914	+	0.690938i	$0.757198\pi$
$18$		0			0
$19$	−1.12072	+	0.940396i	−0.257111	+	0.215742i	−0.762227	−	0.647310i	$-0.775894\pi$
$19$	−1.12072	+	0.940396i	−0.257111	+	0.215742i	0.505116	+	0.863051i	$0.331450\pi$
$20$	−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	$-0.292594\pi$
$23$	3.79608	+	0.899688i	0.791538	+	0.187598i	0.185090	+	0.982722i	$0.440742\pi$
$24$		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	$-0.637909\pi$
$29$	3.06986	−	4.12353i	0.570058	−	0.765721i	0.989883	+	0.141884i	$0.0453161\pi$
$30$		0			0
$31$	−2.86446	−	9.56797i	−0.514473	−	1.71846i	−0.680874	−	0.732400i	$-0.738400\pi$
$31$	−2.86446	−	9.56797i	−0.514473	−	1.71846i	0.166402	−	0.986058i	$-0.446785\pi$
$32$	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	−0.999961	−	0.00877810i	$-0.997206\pi$
$37$	−0.348559	+	1.97678i	−0.0573028	+	0.324980i	0.942659	+	0.333758i	$0.108317\pi$
$38$	−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	0.585778	+	0.810472i	$0.300789\pi$
$41$	−2.59790	+	6.02260i	−0.405723	+	0.940572i	−0.991501	+	0.130100i	$0.958470\pi$
$42$		0			0
$43$	6.51223	+	3.27057i	0.993106	+	0.498757i	0.869690	−	0.493598i	$-0.164319\pi$
$43$	6.51223	+	3.27057i	0.993106	+	0.498757i	0.123416	+	0.992355i	$0.460615\pi$
$44$	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	−0.812042	−	0.583598i	$-0.801644\pi$
$47$	1.28270	−	4.28453i	0.187102	−	0.624963i	0.999144	−	0.0413648i	$-0.0131706\pi$
$48$		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	$-0.676902\pi$
$53$	3.43548	−	5.95043i	0.471900	−	0.817355i	0.999483	+	0.0321487i	$0.0102350\pi$
$54$		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	$-0.300155\pi$
$59$	0.590929	+	0.388660i	0.0769324	+	0.0505992i	−0.510460	+	0.859901i	$0.670525\pi$
$60$		0			0
$61$	1.83608	+	1.94613i	0.235086	+	0.249177i	0.834167	−	0.551512i	$-0.185949\pi$
$61$	1.83608	+	1.94613i	0.235086	+	0.249177i	−0.599081	+	0.800688i	$0.704467\pi$
$62$	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	0.873887	+	0.486129i	$0.161591\pi$
$67$	8.91352	+	11.9729i	1.08896	+	1.46273i	0.215073	+	0.976598i	$0.431001\pi$
$68$	−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	$-0.808363\pi$
$71$	−9.19719	+	3.34750i	−1.09151	+	0.397276i	−0.267328	+	0.963606i	$0.586141\pi$
$72$		0			0
$73$	15.0748	+	5.48678i	1.76437	+	0.642179i	0.999997	−	0.00259223i	$-0.000825133\pi$
$73$	15.0748	+	5.48678i	1.76437	+	0.642179i	0.764376	+	0.644771i	$0.223047\pi$
$74$	−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	0.990870	−	0.134821i	$-0.0430461\pi$
$79$	1.89166	+	4.38536i	0.212828	+	0.493391i	−0.778042	+	0.628213i	$0.783787\pi$
$80$	1.19447			0.133546
$81$		0			0
$82$	−5.99425			−0.661954
$83$	−2.86882	−	6.65067i	−0.314894	−	0.730006i	−0.999999	−	0.00156176i	$-0.999503\pi$
$83$	−2.86882	−	6.65067i	−0.314894	−	0.730006i	0.685105	−	0.728444i	$-0.259756\pi$
$84$		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	$-0.259637\pi$
$89$	7.00321	+	2.54896i	0.742339	+	0.270189i	0.0569608	+	0.998376i	$0.481859\pi$
$90$		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	0.985636	+	0.168883i	$0.0540159\pi$
$97$	0.258735	+	4.44232i	0.0262706	+	0.451049i	−0.959366	+	0.282166i	$0.908947\pi$
$98$	−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	$-0.0577185\pi$
$101$	7.50105	+	7.95065i	0.746383	+	0.791119i	−0.237222	+	0.971455i	$0.576237\pi$
$102$		0			0
$103$	−4.04794	−	2.66237i	−0.398856	−	0.262332i	0.334197	−	0.942503i	$-0.391535\pi$
$103$	−4.04794	−	2.66237i	−0.398856	−	0.262332i	−0.733053	+	0.680172i	$0.761905\pi$
$104$	−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	$-0.124476\pi$
$107$	1.36707	+	2.36783i	0.132159	+	0.228906i	−0.792349	+	0.610067i	$0.791142\pi$
$108$		0			0
$109$	1.70034	−	2.94507i	0.162863	−	0.282087i	−0.773031	−	0.634368i	$-0.781261\pi$
$109$	1.70034	−	2.94507i	0.162863	−	0.282087i	0.935894	+	0.352281i	$0.114594\pi$
$110$	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	$-0.502146\pi$
$113$	8.41203	−	4.22468i	0.791337	−	0.397424i	0.798079	+	0.602553i	$0.205850\pi$
$114$		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	−0.983402	−	0.181441i	$-0.941924\pi$
$127$	−1.36769	−	7.75655i	−0.121363	−	0.688283i	0.862039	−	0.506842i	$-0.169187\pi$
$128$	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	$-0.107663\pi$
$131$	−0.310717	−	1.03787i	−0.0271475	−	0.0906789i	−0.970490	+	0.241142i	$0.922478\pi$
$132$		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	$-0.452955\pi$
$137$	0.730936	+	0.0854341i	0.0624481	+	0.00729913i	−0.0848115	+	0.996397i	$0.527029\pi$
$138$		0			0
$139$	−4.09766	−	0.971163i	−0.347559	−	0.0823730i	0.0531287	−	0.998588i	$-0.483081\pi$
$139$	−4.09766	−	0.971163i	−0.347559	−	0.0823730i	−0.400688	+	0.916215i	$0.631229\pi$
$140$	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	$-0.695706\pi$
$149$	−11.5926	+	1.35499i	−0.949706	+	0.111005i	−0.372887	+	0.927877i	$0.621632\pi$
$150$		0			0
$151$	4.00498	−	2.63412i	0.325920	−	0.214361i	−0.375995	−	0.926622i	$-0.622699\pi$
$151$	4.00498	−	2.63412i	0.325920	−	0.214361i	0.701915	+	0.712261i	$0.252329\pi$
$152$	−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	0.904564	+	0.426338i	$0.140197\pi$
$157$	−0.543531	+	9.33207i	−0.0433785	+	0.744780i	−0.947942	+	0.318442i	$0.896840\pi$
$158$	−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	0.882355	+	0.470585i	$0.155957\pi$
$167$	−0.628896	+	10.7977i	−0.0486654	+	0.835553i	−0.931020	+	0.364968i	$0.881080\pi$
$168$		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	$-0.539516\pi$
$173$	9.71059	−	6.38676i	0.738282	−	0.485576i	0.862106	+	0.506728i	$0.169145\pi$
$174$		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	$-0.245255\pi$
$179$	2.09069	+	1.75429i	0.156265	+	0.131122i	−0.561303	+	0.827611i	$0.689700\pi$
$180$		0			0
$181$	−11.5914	+	9.72633i	−0.861581	+	0.722953i	−0.962308	−	0.271962i	$-0.912328\pi$
$181$	−11.5914	+	9.72633i	−0.861581	+	0.722953i	0.100727	+	0.994914i	$0.467883\pi$
$182$	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	$-0.824834\pi$
$191$	−1.47784	+	1.98509i	−0.106933	+	0.143636i	0.745435	+	0.666578i	$0.232242\pi$
$192$		0			0
$193$	1.13748	+	3.79946i	0.0818778	+	0.273491i	0.989119	−	0.147121i	$-0.0470006\pi$
$193$	1.13748	+	3.79946i	0.0818778	+	0.273491i	−0.907241	+	0.420612i	$0.861815\pi$
$194$	−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	0.610621	+	0.791923i	$0.290920\pi$
$197$	4.31848	+	24.4913i	0.307679	+	1.74493i	−0.302942	+	0.953009i	$0.597969\pi$
$198$		0			0
$199$	2.00332	−	11.3614i	0.142011	−	0.805386i	−0.827707	−	0.561160i	$-0.810355\pi$
$199$	2.00332	−	11.3614i	0.142011	−	0.805386i	0.969718	−	0.244226i	$-0.0785338\pi$
$200$	−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	0.346952	−	0.937883i	$-0.387217\pi$
$211$	18.9771	−	9.53064i	1.30643	−	0.656116i	0.959483	+	0.281767i	$0.0909205\pi$
$212$	−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	0.673933	−	0.738792i	$-0.264604\pi$
$223$	−1.53505	−	1.62706i	−0.102795	−	0.108956i	−0.776728	+	0.629836i	$0.783122\pi$
$224$	−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	0.998250	+	0.0591321i	$0.0188333\pi$
$227$	0.205125	+	3.52186i	0.0136146	+	0.233754i	−0.984636	+	0.174622i	$0.944130\pi$
$228$		0			0
$229$	−6.30941	−	8.47500i	−0.416937	−	0.560044i	0.543189	−	0.839610i	$-0.317217\pi$
$229$	−6.30941	−	8.47500i	−0.416937	−	0.560044i	−0.960126	+	0.279566i	$0.909809\pi$
$230$	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	$-0.411728\pi$
$233$	16.8171	−	6.12092i	1.10172	−	0.400995i	0.827952	+	0.560799i	$0.189506\pi$
$234$		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	$-0.763083\pi$
$239$	−0.254893	+	0.270171i	−0.0164877	+	0.0174759i	0.719077	+	0.694930i	$0.244565\pi$
$240$		0			0
$241$	2.49079	+	5.77431i	0.160446	+	0.371956i	0.979408	−	0.201892i	$-0.0647091\pi$
$241$	2.49079	+	5.77431i	0.160446	+	0.371956i	−0.818962	+	0.573848i	$0.805450\pi$
$242$	−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	$-0.441646\pi$
$251$	−4.91237	−	1.78796i	−0.310066	−	0.112855i	−0.492366	+	0.870388i	$0.663868\pi$
$252$		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	$-0.236177\pi$
$257$	−1.94989	−	2.61916i	−0.121631	−	0.163379i	−0.858768	+	0.512364i	$0.828770\pi$
$258$		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	$-0.254498\pi$
$263$	−0.961659	−	1.01930i	−0.0592984	−	0.0628527i	−0.756344	+	0.654175i	$0.773016\pi$
$264$		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	$-0.268917\pi$
$269$	−5.17838	−	8.96922i	−0.315732	−	0.546863i	−0.979593	+	0.200993i	$0.935583\pi$
$270$		0			0
$271$	−9.29809	+	16.1048i	−0.564819	+	0.978295i	0.432248	+	0.901755i	$0.357721\pi$
$271$	−9.29809	+	16.1048i	−0.564819	+	0.978295i	−0.997067	+	0.0765398i	$0.975613\pi$
$272$	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	0.823326	+	0.567569i	$0.192116\pi$
$277$	−2.93650	+	9.80858i	−0.176437	+	0.589341i	−0.999763	+	0.0217719i	$0.993069\pi$
$278$	−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	$-0.531280\pi$
$281$	−16.0079	−	8.03947i	−0.954951	−	0.479595i	−0.856841	+	0.515581i	$0.827576\pi$
$282$		0			0
$283$	−10.5546	+	24.4683i	−0.627404	+	1.45449i	0.246867	+	0.969049i	$0.420599\pi$
$283$	−10.5546	+	24.4683i	−0.627404	+	1.45449i	−0.874271	+	0.485437i	$0.838660\pi$
$284$	−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	0.754893	+	0.655848i	$0.227689\pi$
$293$	8.29474	+	27.7063i	0.484584	+	1.61862i	−0.270309	+	0.962774i	$0.587126\pi$
$294$		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	0.723038	−	0.690809i	$-0.242745\pi$
$307$	2.94847	+	2.47406i	0.168278	+	0.141202i	−0.554759	+	0.832011i	$0.687190\pi$
$308$	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	$-0.405455\pi$
$311$	14.0725	−	1.64484i	0.797977	−	0.0932701i	0.505303	+	0.862942i	$0.331381\pi$
$312$		0			0
$313$	−17.3980	+	11.4428i	−0.983391	+	0.646786i	−0.935967	−	0.352089i	$-0.885472\pi$
$313$	−17.3980	+	11.4428i	−0.983391	+	0.646786i	−0.0474241	+	0.998875i	$0.515101\pi$
$314$	−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	$-0.333190\pi$
$317$	23.7891	−	5.63811i	1.33613	−	0.316668i	0.835736	+	0.549132i	$0.185041\pi$
$318$		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	−0.407082	−	0.913392i	$-0.633454\pi$
$331$	−6.56661	+	1.55632i	−0.360934	+	0.0855429i	0.0461480	+	0.998935i	$0.485305\pi$
$332$	−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	−8.72681e−5	−	1.00000i	$-0.500028\pi$
$337$	4.23038	−	0.494461i	0.230444	−	0.0269350i	0.230531	+	0.973065i	$0.425954\pi$
$338$	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	$-0.608397\pi$
$347$	−19.6616	−	4.65989i	−1.05549	−	0.250156i	−0.721496	+	0.692418i	$0.756545\pi$
$348$		0			0
$349$	−22.8564	−	2.67153i	−1.22348	−	0.143004i	−0.520278	−	0.853997i	$-0.674172\pi$
$349$	−22.8564	−	2.67153i	−1.22348	−	0.143004i	−0.703199	+	0.710993i	$0.748246\pi$
$350$	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	$-0.600436\pi$
$353$	12.9522	−	17.3979i	0.689378	−	0.925995i	0.999696	+	0.0246374i	$0.00784313\pi$
$354$		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	−0.627193	−	0.778864i	$-0.715796\pi$
$359$	−5.76399	−	32.6892i	−0.304212	−	1.72527i	0.322981	−	0.946405i	$-0.395315\pi$
$360$		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	−0.105341	−	0.994436i	$-0.533593\pi$
$367$	−18.5041	−	9.29311i	−0.965906	−	0.485096i	−0.860565	+	0.509340i	$0.829890\pi$
$368$	−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	−0.539544	−	0.841958i	$-0.681403\pi$
$373$	−3.59966	+	1.80782i	−0.186383	+	0.0936052i	0.353161	+	0.935563i	$0.385107\pi$
$374$	−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	0.843823	+	0.536622i	$0.180300\pi$
$379$	17.2610	+	29.8970i	0.886640	+	1.53570i	0.0428169	+	0.999083i	$0.486367\pi$
$380$	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	$-0.433518\pi$
$383$	−11.9143	−	7.83617i	−0.608793	−	0.400410i	−0.816137	+	0.577859i	$0.803889\pi$
$384$		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	0.879217	+	0.476421i	$0.158066\pi$
$389$	1.20812	+	20.7426i	0.0612541	+	1.05169i	−0.817963	+	0.575271i	$0.804897\pi$
$390$		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	0.818482	−	0.574533i	$-0.194816\pi$
$397$	21.4426	+	7.80446i	1.07617	+	0.391695i	0.257691	+	0.966227i	$0.417038\pi$
$398$	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	$-0.828020\pi$
$401$	−5.89097	+	6.24406i	−0.294181	+	0.311814i	0.563378	+	0.826199i	$0.309501\pi$
$402$		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	−0.0430887	−	0.999071i	$-0.513720\pi$
$409$	19.3500	−	20.5098i	0.956798	−	1.01415i	0.999886	−	0.0150751i	$-0.00479872\pi$
$410$	−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	−0.967554	−	0.252666i	$-0.918693\pi$
$419$	−19.0798	−	25.6286i	−0.932108	−	1.25204i	0.0354460	−	0.999372i	$-0.488715\pi$
$420$		0			0
$421$	−1.62148	−	27.8397i	−0.0790260	−	1.35682i	−0.771891	−	0.635755i	$-0.780689\pi$
$421$	−1.62148	−	27.8397i	−0.0790260	−	1.35682i	0.692865	−	0.721068i	$-0.256348\pi$
$422$	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	0.909058	+	0.416669i	$0.136802\pi$
$431$	16.9276	+	29.3195i	0.815375	+	1.41227i	−0.0936837	+	0.995602i	$0.529864\pi$
$432$		0			0
$433$	4.23939	−	7.34284i	0.203732	−	0.352874i	−0.745996	−	0.665950i	$-0.768026\pi$
$433$	4.23939	−	7.34284i	0.203732	−	0.352874i	0.949728	+	0.313076i	$0.101360\pi$
$434$	−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	−0.659805	−	0.751437i	$-0.729361\pi$
$439$	6.37737	−	21.3019i	0.304375	−	1.01668i	0.964180	−	0.265247i	$-0.0854535\pi$
$440$	−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	$-0.531626\pi$
$443$	−20.1340	−	10.1117i	−0.956596	−	0.480420i	−0.857402	+	0.514648i	$0.827923\pi$
$444$		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	−0.747497	−	0.664265i	$-0.768745\pi$
$449$	3.85889	−	21.8849i	0.182112	−	1.03281i	0.929610	−	0.368546i	$-0.120144\pi$
$450$		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	−0.833297	−	0.552826i	$-0.813549\pi$
$457$	−1.38320	+	1.85796i	−0.0647032	+	0.0869115i	0.768594	+	0.639737i	$0.220957\pi$
$458$	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	$-0.656578\pi$
$461$	−24.3727	−	2.84876i	−1.13515	−	0.132680i	−0.662846	+	0.748755i	$0.730652\pi$
$462$		0			0
$463$	26.5407	+	6.29025i	1.23345	+	0.292333i	0.795103	−	0.606474i	$-0.207417\pi$
$463$	26.5407	+	6.29025i	1.23345	+	0.292333i	0.438345	+	0.898807i	$0.355565\pi$
$464$	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	$-0.695124\pi$
$467$	2.81518	−	2.36222i	0.130271	−	0.109310i	0.705595	+	0.708615i	$0.250680\pi$
$468$		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	$-0.595761\pi$
$479$	−2.89958	+	0.687214i	−0.132485	+	0.0313996i	0.163838	+	0.986487i	$0.447613\pi$
$480$		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	−0.954498	−	0.298217i	$-0.903608\pi$
$491$	0.624138	−	10.7160i	0.0281669	−	0.483608i	0.982665	−	0.185390i	$-0.0593550\pi$
$492$		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	−0.766045	−	0.642787i	$-0.777778\pi$
$499$	−30.4517	+	3.55929i	−1.36320	+	0.159336i	−0.597159	+	0.802123i	$0.703704\pi$
$500$	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	$-0.491232\pi$
$503$	−21.3536	−	17.9178i	−0.952111	−	0.798916i	−0.979652	+	0.200705i	$0.935677\pi$
$504$		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	$-0.113839\pi$
$509$	36.4747	+	8.64466i	1.61671	+	0.383168i	0.679984	+	0.733227i	$0.261987\pi$
$510$		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	0.628918	+	0.777472i	$0.283498\pi$
$521$	6.93526	+	39.3318i	0.303839	+	1.72316i	−0.325079	+	0.945687i	$0.605391\pi$
$522$		0			0
$523$	1.17678	−	6.67383i	0.0514568	−	0.291826i	−0.948210	−	0.317645i	$-0.897108\pi$
$523$	1.17678	−	6.67383i	0.0514568	−	0.291826i	0.999667	+	0.0258185i	$0.00821918\pi$
$524$	−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	0.997588	−	0.0694179i	$-0.0221142\pi$
$541$	10.2033	+	17.6727i	0.438676	+	0.759809i	−0.558912	+	0.829227i	$0.688781\pi$
$542$	−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	0.672607	−	0.740000i	$-0.265174\pi$
$547$	−2.46158	−	2.60912i	−0.105249	−	0.111558i	−0.777856	+	0.628442i	$0.783693\pi$
$548$	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	$-0.627161\pi$
$557$	−2.23552	+	0.813664i	−0.0947221	+	0.0344760i	0.294224	+	0.955736i	$0.404939\pi$
$558$		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	0.0263710	−	0.999652i	$-0.491605\pi$
$563$	24.2686	−	25.7232i	1.02280	−	1.08410i	0.996428	−	0.0844510i	$-0.0269137\pi$
$564$		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	−0.944485	−	0.328554i	$-0.893439\pi$
$569$	−12.7694	−	29.6028i	−0.535322	−	1.24102i	0.409163	−	0.912461i	$-0.365821\pi$
$570$		0			0
$571$	−2.04866	+	2.17145i	−0.0857336	+	0.0908723i	−0.768820	−	0.639465i	$-0.779156\pi$
$571$	−2.04866	+	2.17145i	−0.0857336	+	0.0908723i	0.683086	+	0.730338i	$0.260637\pi$
$572$	−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	−0.895475	−	0.445111i	$-0.853164\pi$
$577$	−31.1151	+	11.3250i	−1.29534	+	0.471464i	−0.399862	+	0.916575i	$0.630942\pi$
$578$	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	$-0.184882\pi$
$587$	5.80543	+	6.15339i	0.239616	+	0.253978i	−0.596395	+	0.802691i	$0.703401\pi$
$588$		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	$-0.187806\pi$
$593$	−1.61604	−	2.79907i	−0.0663629	−	0.114944i	−0.897298	+	0.441426i	$0.854473\pi$
$594$		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	$-0.644130\pi$
$599$	0.552166	−	0.277308i	0.0225609	−	0.0113305i	0.460044	+	0.887896i	$0.347834\pi$
$600$		0			0
$601$	−5.21882	+	17.4321i	−0.212880	+	0.711068i	0.783133	+	0.621855i	$0.213621\pi$
$601$	−5.21882	+	17.4321i	−0.212880	+	0.711068i	−0.996013	+	0.0892137i	$0.971565\pi$
$602$	−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	−0.966463	−	0.256806i	$-0.917330\pi$
$607$	−2.86882	+	6.65067i	−0.116442	+	0.269942i	0.850021	+	0.526748i	$0.176589\pi$
$608$	−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	−0.715345	−	0.698771i	$-0.753731\pi$
$613$	−6.98532	−	39.6157i	−0.282134	−	1.60006i	0.433211	−	0.901293i	$-0.357381\pi$
$614$	−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	0.997595	+	0.0693101i	$0.0220798\pi$
$617$	5.02262	+	16.7767i	0.202203	+	0.675405i	−0.795392	+	0.606095i	$0.792735\pi$
$618$		0			0
$619$	6.13883	−	8.24588i	0.246740	−	0.331430i	−0.661448	−	0.749991i	$-0.730058\pi$
$619$	6.13883	−	8.24588i	0.246740	−	0.331430i	0.908189	+	0.418561i	$0.137465\pi$
$620$	−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	0.966011	−	0.258502i	$-0.0832289\pi$
$631$	22.0848	+	18.5313i	0.879182	+	0.737721i	−0.0868288	+	0.996223i	$0.527673\pi$
$632$	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	$-0.765701\pi$
$641$	−27.9023	+	6.61297i	−1.10207	+	0.261197i	−0.360964	+	0.932580i	$0.617552\pi$
$642$		0			0
$643$	−1.12427	+	19.3030i	−0.0443369	+	0.761235i	0.900734	+	0.434370i	$0.143029\pi$
$643$	−1.12427	+	19.3030i	−0.0443369	+	0.761235i	−0.945071	+	0.326864i	$0.894008\pi$
$644$	−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	$-0.699417\pi$
$647$	−29.8266			−1.17261			−0.586303	+	0.810092i	$0.699417\pi$
$648$		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	−0.844537	−	0.535497i	$-0.820124\pi$
$653$	1.44269	−	24.7701i	0.0564569	−	0.969328i	0.900994	−	0.433831i	$-0.142838\pi$
$654$		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	$-0.795797\pi$
$659$	−14.6079	+	9.60779i	−0.569044	+	0.374266i	0.232142	+	0.972682i	$0.425427\pi$
$660$		0			0
$661$	−37.3153	+	4.36154i	−1.45140	+	0.169644i	−0.804963	−	0.593324i	$-0.797815\pi$
$661$	−37.3153	+	4.36154i	−1.45140	+	0.169644i	−0.646435	+	0.762969i	$0.723741\pi$
$662$	−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	0.607464	−	0.794348i	$-0.292187\pi$
$673$	26.3408	+	3.07880i	1.01536	+	0.118679i	0.407900	+	0.913027i	$0.366261\pi$
$674$	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	$-0.925656\pi$
$677$	−12.2841	+	16.5004i	−0.472116	+	0.634162i	0.500733	+	0.865602i	$0.333064\pi$
$678$		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	0.995687	+	0.0927760i	$0.0295741\pi$
$683$	2.39856	+	13.6029i	0.0917785	+	0.520502i	−0.903908	+	0.427726i	$0.859315\pi$
$684$		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	0.337669	−	0.941265i	$-0.390361\pi$
$691$	−5.67005	−	2.84760i	−0.215699	−	0.108328i	−0.553368	+	0.832937i	$0.686658\pi$
$692$	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	$-0.685406\pi$
$701$	11.8662	−	20.5529i	0.448180	−	0.776271i	0.998268	+	0.0588360i	$0.0187389\pi$
$702$		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	0.727556	−	0.686048i	$-0.240656\pi$
$709$	0.00970556	+	0.0102873i	0.000364500	+	0.000386348i	−0.727191	+	0.686435i	$0.759175\pi$
$710$	−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	$-0.458728\pi$
$719$	23.2140	−	8.44919i	0.865735	−	0.315102i	0.736439	+	0.676504i	$0.236506\pi$
$720$		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	−0.898676	−	0.438613i	$-0.855470\pi$
$727$	−16.2048	−	37.5669i	−0.601003	−	1.39328i	0.297674	−	0.954668i	$-0.403789\pi$
$728$	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	−0.888662	−	0.458563i	$-0.848364\pi$
$733$	−10.2665	+	10.8819i	−0.379203	+	0.401932i	0.509458	+	0.860495i	$0.329846\pi$
$734$	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	−0.559285	−	0.828975i	$-0.688924\pi$
$739$	−12.3654	+	4.50063i	−0.454868	+	0.165558i	0.104418	+	0.994534i	$0.466702\pi$
$740$	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	$-0.375414\pi$
$743$	−16.7221	−	22.4616i	−0.613473	−	0.824037i	−0.994953	+	0.100340i	$0.968007\pi$
$744$		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	0.660669	−	0.750677i	$-0.270273\pi$
$751$	6.38696	+	4.20077i	0.233063	+	0.153288i	−0.427606	+	0.903965i	$0.640643\pi$
$752$	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	0.375845	+	0.926683i	$0.377353\pi$
$757$	−16.9101	+	29.2892i	−0.614608	+	1.06453i	−0.990453	+	0.137850i	$0.955981\pi$
$758$	−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	$-0.882686\pi$
$761$	−33.1292	+	16.6381i	−1.20093	+	0.603131i	−0.268083	+	0.963396i	$0.586390\pi$
$762$		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	−0.167320	−	0.985903i	$-0.553511\pi$
$769$	18.4305	−	42.7267i	0.664622	−	1.54077i	0.831942	−	0.554863i	$-0.187229\pi$
$770$	−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	0.498807	+	0.866713i	$0.333772\pi$
$773$	−7.40534	+	41.9978i	−0.266352	+	1.51056i	−0.765158	+	0.643842i	$0.777339\pi$
$774$		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

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

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