LMFDB - Embedded newform 729.2.g.c.28.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("729.28");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			28.8
Character	$\chi$	$=$	729.28
Dual form			729.2.g.c.703.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.23053 - 1.46704i) q^{2} +(2.03089 - 4.70814i) q^{4} +(1.73981 - 1.84410i) q^{5} +(-0.507474 - 0.0593153i) q^{7} +(-1.44988 - 8.22270i) q^{8} +O(q^{10})$	\(q+(2.23053 - 1.46704i) q^{2} +(2.03089 - 4.70814i) q^{4} +(1.73981 - 1.84410i) q^{5} +(-0.507474 - 0.0593153i) q^{7} +(-1.44988 - 8.22270i) q^{8} +(1.17534 - 6.66569i) q^{10} +(-0.440769 + 1.47227i) q^{11} +(-0.328014 + 5.63177i) q^{13} +(-1.21896 + 0.612182i) q^{14} +(-8.25967 - 8.75474i) q^{16} +(-1.33086 + 0.484393i) q^{17} +(0.986977 + 0.359230i) q^{19} +(-5.14888 - 11.9364i) q^{20} +(1.17674 + 3.93058i) q^{22} +(-0.258604 + 0.0302265i) q^{23} +(-0.0830100 - 1.42523i) q^{25} +(7.53041 + 13.0431i) q^{26} +(-1.30989 + 2.26880i) q^{28} +(1.58935 + 0.798201i) q^{29} +(3.08537 + 4.14437i) q^{31} +(-15.0181 - 3.55935i) q^{32} +(-2.25790 + 3.03288i) q^{34} +(-0.992294 + 0.832634i) q^{35} +(-5.04999 - 4.23745i) q^{37} +(2.72849 - 0.646664i) q^{38} +(-17.6860 - 11.6322i) q^{40} +(5.64575 + 3.71327i) q^{41} +(-5.94513 + 1.40902i) q^{43} +(6.03650 + 5.06523i) q^{44} +(-0.532481 + 0.446804i) q^{46} +(4.36612 - 5.86472i) q^{47} +(-6.55730 - 1.55411i) q^{49} +(-2.27603 - 3.05723i) q^{50} +(25.8490 + 12.9819i) q^{52} +(4.74440 - 8.21755i) q^{53} +(1.94815 + 3.37430i) q^{55} +(0.248047 + 4.25881i) q^{56} +(4.71609 - 0.551232i) q^{58} +(1.42111 + 4.74684i) q^{59} +(-5.10974 - 11.8457i) q^{61} +(12.9620 + 4.71777i) q^{62} +(-16.0995 + 5.85975i) q^{64} +(9.81485 + 10.4031i) q^{65} +(5.73622 - 2.88084i) q^{67} +(-0.422242 + 7.24961i) q^{68} +(-0.991833 + 3.31295i) q^{70} +(-0.896716 + 5.08553i) q^{71} +(-1.03528 - 5.87137i) q^{73} +(-17.4807 - 2.04320i) q^{74} +(3.69575 - 3.91726i) q^{76} +(0.311007 - 0.720996i) q^{77} +(-8.30647 + 5.46325i) q^{79} -30.5149 q^{80} +18.0405 q^{82} +(-10.8213 + 7.11730i) q^{83} +(-1.42218 + 3.29699i) q^{85} +(-11.1937 + 11.8646i) q^{86} +(12.7451 + 1.48969i) q^{88} +(-1.71260 - 9.71264i) q^{89} +(0.500509 - 2.83853i) q^{91} +(-0.382886 + 1.27893i) q^{92} +(1.13497 - 19.4867i) q^{94} +(2.37961 - 1.19509i) q^{95} +(2.46841 + 2.61636i) q^{97} +(-16.9062 + 6.15336i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8}+O(q^{10}) $ 144 * q + 9 * q^2 + 9 * q^4 + 9 * q^5 + 9 * q^7 - 18 * q^8	$ 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8} - 18 q^{10} + 9 q^{11} + 9 q^{13} + 9 q^{14} + 9 q^{16} - 18 q^{17} - 18 q^{19} - 63 q^{20} + 9 q^{22} + 36 q^{23} + 9 q^{25} + 45 q^{26} - 9 q^{28} - 45 q^{29} + 9 q^{31} + 63 q^{32} + 9 q^{34} + 9 q^{35} - 18 q^{37} - 9 q^{38} + 9 q^{40} - 27 q^{41} + 9 q^{43} + 54 q^{44} - 18 q^{46} + 63 q^{47} + 9 q^{49} - 225 q^{50} + 27 q^{52} + 45 q^{53} - 9 q^{55} + 99 q^{56} + 9 q^{58} - 117 q^{59} + 9 q^{61} + 81 q^{62} - 18 q^{64} + 81 q^{65} + 36 q^{67} - 18 q^{68} + 63 q^{70} - 90 q^{71} - 18 q^{73} + 81 q^{74} + 90 q^{76} + 81 q^{77} + 63 q^{79} - 288 q^{80} - 36 q^{82} + 45 q^{83} + 63 q^{85} + 81 q^{86} + 90 q^{88} - 81 q^{89} - 18 q^{91} - 63 q^{92} + 63 q^{94} + 153 q^{95} + 36 q^{97} + 81 q^{98}+O(q^{100}) $ 144 * q + 9 * q^2 + 9 * q^4 + 9 * q^5 + 9 * q^7 - 18 * q^8 - 18 * q^10 + 9 * q^11 + 9 * q^13 + 9 * q^14 + 9 * q^16 - 18 * q^17 - 18 * q^19 - 63 * q^20 + 9 * q^22 + 36 * q^23 + 9 * q^25 + 45 * q^26 - 9 * q^28 - 45 * q^29 + 9 * q^31 + 63 * q^32 + 9 * q^34 + 9 * q^35 - 18 * q^37 - 9 * q^38 + 9 * q^40 - 27 * q^41 + 9 * q^43 + 54 * q^44 - 18 * q^46 + 63 * q^47 + 9 * q^49 - 225 * q^50 + 27 * q^52 + 45 * q^53 - 9 * q^55 + 99 * q^56 + 9 * q^58 - 117 * q^59 + 9 * q^61 + 81 * q^62 - 18 * q^64 + 81 * q^65 + 36 * q^67 - 18 * q^68 + 63 * q^70 - 90 * q^71 - 18 * q^73 + 81 * q^74 + 90 * q^76 + 81 * q^77 + 63 * q^79 - 288 * q^80 - 36 * q^82 + 45 * q^83 + 63 * q^85 + 81 * q^86 + 90 * q^88 - 81 * q^89 - 18 * q^91 - 63 * q^92 + 63 * q^94 + 153 * q^95 + 36 * q^97 + 81 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	2.23053	−	1.46704i	1.57722	−	1.03736i	0.607136	−	0.794598i	$-0.292318\pi$
$2$	2.23053	−	1.46704i	1.57722	−	1.03736i	0.970087	−	0.242758i	$-0.0780522\pi$
$3$		0			0
$3$		0			0
$4$	2.03089	−	4.70814i	1.01545	−	2.35407i
$5$	1.73981	−	1.84410i	0.778069	−	0.824705i	−0.210163	−	0.977666i	$-0.567400\pi$
$5$	1.73981	−	1.84410i	0.778069	−	0.824705i	0.988232	+	0.152962i	$0.0488811\pi$
$6$		0			0
$7$	−0.507474	−	0.0593153i	−0.191807	−	0.0224191i	0.0196468	−	0.999807i	$-0.493746\pi$
$7$	−0.507474	−	0.0593153i	−0.191807	−	0.0224191i	−0.211454	+	0.977388i	$0.567820\pi$
$8$	−1.44988	−	8.22270i	−0.512611	−	2.90716i
$9$		0			0
$10$	1.17534	−	6.66569i	0.371676	−	2.10788i
$11$	−0.440769	+	1.47227i	−0.132897	+	0.443907i	−0.998372	−	0.0570461i	$-0.981832\pi$
$11$	−0.440769	+	1.47227i	−0.132897	+	0.443907i	0.865475	+	0.500953i	$0.167017\pi$
$12$		0			0
$13$	−0.328014	+	5.63177i	−0.0909746	+	1.56197i	0.576348	+	0.817204i	$0.304477\pi$
$13$	−0.328014	+	5.63177i	−0.0909746	+	1.56197i	−0.667323	+	0.744769i	$0.732560\pi$
$14$	−1.21896	+	0.612182i	−0.325779	+	0.163613i
$15$		0			0
$16$	−8.25967	−	8.75474i	−2.06492	−	2.18869i
$17$	−1.33086	+	0.484393i	−0.322781	+	0.117483i	−0.498328	−	0.866988i	$-0.666053\pi$
$17$	−1.33086	+	0.484393i	−0.322781	+	0.117483i	0.175548	+	0.984471i	$0.443830\pi$
$18$		0			0
$19$	0.986977	+	0.359230i	0.226428	+	0.0824131i	0.452743	−	0.891641i	$-0.350446\pi$
$19$	0.986977	+	0.359230i	0.226428	+	0.0824131i	−0.226315	+	0.974054i	$0.572668\pi$
$20$	−5.14888	−	11.9364i	−1.15132	−	2.66907i
$21$		0			0
$22$	1.17674	+	3.93058i	0.250881	+	0.838001i
$23$	−0.258604	+	0.0302265i	−0.0539227	+	0.00630266i	−0.143011	−	0.989721i	$-0.545679\pi$
$23$	−0.258604	+	0.0302265i	−0.0539227	+	0.00630266i	0.0890888	+	0.996024i	$0.471605\pi$
$24$		0			0
$25$	−0.0830100	−	1.42523i	−0.0166020	−	0.285045i
$26$	7.53041	+	13.0431i	1.47684	+	2.55795i
$27$		0			0
$28$	−1.30989	+	2.26880i	−0.247546	+	0.428762i
$29$	1.58935	+	0.798201i	0.295135	+	0.148222i	0.590205	−	0.807253i	$-0.299047\pi$
$29$	1.58935	+	0.798201i	0.295135	+	0.148222i	−0.295070	+	0.955475i	$0.595343\pi$
$30$		0			0
$31$	3.08537	+	4.14437i	0.554148	+	0.744350i	0.987628	−	0.156813i	$-0.0501220\pi$
$31$	3.08537	+	4.14437i	0.554148	+	0.744350i	−0.433480	+	0.901163i	$0.642715\pi$
$32$	−15.0181	−	3.55935i	−2.65485	−	0.629210i
$33$		0			0
$34$	−2.25790	+	3.03288i	−0.387226	+	0.520135i
$35$	−0.992294	+	0.832634i	−0.167728	+	0.140741i
$36$		0			0
$37$	−5.04999	−	4.23745i	−0.830214	−	0.696632i	0.125126	−	0.992141i	$-0.460066\pi$
$37$	−5.04999	−	4.23745i	−0.830214	−	0.696632i	−0.955340	+	0.295509i	$0.904511\pi$
$38$	2.72849	−	0.646664i	0.442619	−	0.104903i
$39$		0			0
$40$	−17.6860	−	11.6322i	−2.79640	−	1.83922i
$41$	5.64575	+	3.71327i	0.881718	+	0.579915i	0.907640	−	0.419749i	$-0.137882\pi$
$41$	5.64575	+	3.71327i	0.881718	+	0.579915i	−0.0259221	+	0.999664i	$0.508252\pi$
$42$		0			0
$43$	−5.94513	+	1.40902i	−0.906624	+	0.214874i	−0.657373	−	0.753565i	$-0.728333\pi$
$43$	−5.94513	+	1.40902i	−0.906624	+	0.214874i	−0.249251	+	0.968439i	$0.580184\pi$
$44$	6.03650	+	5.06523i	0.910037	+	0.763612i
$45$		0			0
$46$	−0.532481	+	0.446804i	−0.0785100	+	0.0658777i
$47$	4.36612	−	5.86472i	0.636864	−	0.855457i	−0.360132	−	0.932901i	$-0.617268\pi$
$47$	4.36612	−	5.86472i	0.636864	−	0.855457i	0.996997	+	0.0774440i	$0.0246759\pi$
$48$		0			0
$49$	−6.55730	−	1.55411i	−0.936757	−	0.222016i
$50$	−2.27603	−	3.05723i	−0.321879	−	0.432358i
$51$		0			0
$52$	25.8490	+	12.9819i	3.58461	+	1.80026i
$53$	4.74440	−	8.21755i	0.651694	−	1.12877i	−0.331018	−	0.943624i	$-0.607392\pi$
$53$	4.74440	−	8.21755i	0.651694	−	1.12877i	0.982712	−	0.185142i	$-0.0592746\pi$
$54$		0			0
$55$	1.94815	+	3.37430i	0.262689	+	0.454991i
$56$	0.248047	+	4.25881i	0.0331467	+	0.569107i
$57$		0			0
$58$	4.71609	−	0.551232i	0.619253	−	0.0723802i
$59$	1.42111	+	4.74684i	0.185013	+	0.617986i	0.999296	+	0.0375182i	$0.0119452\pi$
$59$	1.42111	+	4.74684i	0.185013	+	0.617986i	−0.814283	+	0.580468i	$0.802870\pi$
$60$		0			0
$61$	−5.10974	−	11.8457i	−0.654235	−	1.51669i	−0.844839	−	0.535021i	$-0.820304\pi$
$61$	−5.10974	−	11.8457i	−0.654235	−	1.51669i	0.190604	−	0.981667i	$-0.438955\pi$
$62$	12.9620	+	4.71777i	1.64617	+	0.599157i
$63$		0			0
$64$	−16.0995	+	5.85975i	−2.01244	+	0.732468i
$65$	9.81485	+	10.4031i	1.21738	+	1.29035i
$66$		0			0
$67$	5.73622	−	2.88084i	0.700791	−	0.351951i	−0.0624643	−	0.998047i	$-0.519896\pi$
$67$	5.73622	−	2.88084i	0.700791	−	0.351951i	0.763256	+	0.646097i	$0.223600\pi$
$68$	−0.422242	+	7.24961i	−0.0512044	+	0.879145i
$69$		0			0
$70$	−0.991833	+	3.31295i	−0.118547	+	0.395974i
$71$	−0.896716	+	5.08553i	−0.106421	+	0.603541i	0.884223	+	0.467065i	$0.154689\pi$
$71$	−0.896716	+	5.08553i	−0.106421	+	0.603541i	−0.990643	+	0.136476i	$0.956422\pi$
$72$		0			0
$73$	−1.03528	−	5.87137i	−0.121171	−	0.687192i	−0.983509	−	0.180860i	$-0.942112\pi$
$73$	−1.03528	−	5.87137i	−0.121171	−	0.687192i	0.862338	−	0.506332i	$-0.168999\pi$
$74$	−17.4807	−	2.04320i	−2.03209	−	0.237517i
$75$		0			0
$76$	3.69575	−	3.91726i	0.423931	−	0.449341i
$77$	0.311007	−	0.720996i	0.0354426	−	0.0821651i
$78$		0			0
$79$	−8.30647	+	5.46325i	−0.934551	+	0.614664i	−0.922805	−	0.385267i	$-0.874109\pi$
$79$	−8.30647	+	5.46325i	−0.934551	+	0.614664i	−0.0117457	+	0.999931i	$0.503739\pi$
$80$	−30.5149			−3.41167
$81$		0			0
$82$	18.0405			1.99224
$83$	−10.8213	+	7.11730i	−1.18779	+	0.781225i	−0.980397	−	0.197032i	$-0.936870\pi$
$83$	−10.8213	+	7.11730i	−1.18779	+	0.781225i	−0.207397	+	0.978257i	$0.566499\pi$
$84$		0			0
$85$	−1.42218	+	3.29699i	−0.154257	+	0.357608i
$86$	−11.1937	+	11.8646i	−1.20705	+	1.27940i
$87$		0			0
$88$	12.7451	+	1.48969i	1.35863	+	0.158801i
$89$	−1.71260	−	9.71264i	−0.181535	−	1.02954i	−0.930327	−	0.366732i	$-0.880477\pi$
$89$	−1.71260	−	9.71264i	−0.181535	−	1.02954i	0.748791	−	0.662806i	$-0.230634\pi$
$90$		0			0
$91$	0.500509	−	2.83853i	0.0524676	−	0.297558i
$92$	−0.382886	+	1.27893i	−0.0399187	+	0.133338i
$93$		0			0
$94$	1.13497	−	19.4867i	0.117063	−	2.00990i
$95$	2.37961	−	1.19509i	0.244143	−	0.122613i
$96$		0			0
$97$	2.46841	+	2.61636i	0.250629	+	0.265651i	0.840458	−	0.541877i	$-0.182286\pi$
$97$	2.46841	+	2.61636i	0.250629	+	0.265651i	−0.589829	+	0.807528i	$0.700805\pi$
$98$	−16.9062	+	6.15336i	−1.70778	+	0.621583i
$99$		0			0
$100$	−6.87874	−	2.50366i	−0.687874	−	0.250366i
$101$	7.05948	+	16.3657i	0.702444	+	1.62845i	0.775674	+	0.631134i	$0.217410\pi$
$101$	7.05948	+	16.3657i	0.702444	+	1.62845i	−0.0732293	+	0.997315i	$0.523331\pi$
$102$		0			0
$103$	−1.23827	−	4.13613i	−0.122011	−	0.407545i	0.875061	−	0.484012i	$-0.160821\pi$
$103$	−1.23827	−	4.13613i	−0.122011	−	0.407545i	−0.997072	+	0.0764677i	$0.975636\pi$
$104$	46.7839	−	5.46826i	4.58754	−	0.536207i
$105$		0			0
$106$	−1.47296	−	25.2897i	−0.143066	−	2.45636i
$107$	3.98940	+	6.90985i	0.385670	+	0.668000i	0.991862	−	0.127318i	$-0.0406369\pi$
$107$	3.98940	+	6.90985i	0.385670	+	0.668000i	−0.606192	+	0.795319i	$0.707304\pi$
$108$		0			0
$109$	0.106432	−	0.184345i	0.0101943	−	0.0176571i	−0.860883	−	0.508803i	$-0.830088\pi$
$109$	0.106432	−	0.184345i	0.0101943	−	0.0176571i	0.871078	+	0.491145i	$0.163422\pi$
$110$	9.29566	+	4.66846i	0.886306	+	0.445120i
$111$		0			0
$112$	3.67228	+	4.93273i	0.346998	+	0.466099i
$113$	5.39679	+	1.27906i	0.507687	+	0.120324i	0.476474	−	0.879189i	$-0.341915\pi$
$113$	5.39679	+	1.27906i	0.507687	+	0.120324i	0.0312133	+	0.999513i	$0.490063\pi$
$114$		0			0
$115$	−0.394182	+	0.529479i	−0.0367577	+	0.0493742i
$116$	6.98584	−	5.86181i	0.648619	−	0.544256i
$117$		0			0
$118$	10.1337	+	8.50315i	0.932878	+	0.782778i
$119$	0.704109	−	0.166877i	0.0645455	−	0.0152976i
$120$		0			0
$121$	7.21706	+	4.74673i	0.656096	+	0.431521i
$122$	−28.7756	−	18.9260i	−2.60522	−	1.71348i
$123$		0			0
$124$	25.7783	−	6.10956i	2.31496	−	0.548655i
$125$	6.93801	+	5.82168i	0.620554	+	0.520707i
$126$		0			0
$127$	−13.9870	+	11.7365i	−1.24115	+	1.04145i	−0.243713	+	0.969847i	$0.578365\pi$
$127$	−13.9870	+	11.7365i	−1.24115	+	1.04145i	−0.997434	+	0.0715979i	$0.977190\pi$
$128$	−8.88076	+	11.9289i	−0.784956	+	1.05438i
$129$		0			0
$130$	37.1542	+	8.80570i	3.25863	+	0.772311i
$131$	4.80136	+	6.44934i	0.419497	+	0.563482i	0.960763	−	0.277369i	$-0.0894625\pi$
$131$	4.80136	+	6.44934i	0.419497	+	0.563482i	−0.541267	+	0.840851i	$0.682055\pi$
$132$		0			0
$133$	−0.479558	−	0.240843i	−0.0415829	−	0.0208837i
$134$	8.56851	−	14.8411i	0.740206	−	1.28207i
$135$		0			0
$136$	5.91261	+	10.2409i	0.507002	+	0.878153i
$137$	−0.496123	−	8.51811i	−0.0423867	−	0.727751i	−0.950824	−	0.309731i	$-0.899761\pi$
$137$	−0.496123	−	8.51811i	−0.0423867	−	0.727751i	0.908438	−	0.418020i	$-0.137276\pi$
$138$		0			0
$139$	−12.9612	+	1.51494i	−1.09935	+	0.128496i	−0.646370	−	0.763024i	$-0.723714\pi$
$139$	−12.9612	+	1.51494i	−1.09935	+	0.128496i	−0.452981	+	0.891520i	$0.649640\pi$
$140$	1.90491	+	6.36285i	0.160994	+	0.537759i
$141$		0			0
$142$	5.46054	+	12.6589i	0.458238	+	1.06232i
$143$	−8.14693	−	2.96524i	−0.681280	−	0.247966i
$144$		0			0
$145$	4.23713	−	1.54219i	0.351875	−	0.128072i
$146$	−10.9228	−	11.5775i	−0.903976	−	0.958159i
$147$		0			0
$148$	−30.2065	+	15.1703i	−2.48296	+	1.24699i
$149$	0.948613	−	16.2871i	0.0777134	−	1.33429i	−0.703799	−	0.710399i	$-0.748515\pi$
$149$	0.948613	−	16.2871i	0.0777134	−	1.33429i	0.781513	−	0.623889i	$-0.214448\pi$
$150$		0			0
$151$	−6.21112	+	20.7466i	−0.505454	+	1.68833i	0.200182	+	0.979759i	$0.435847\pi$
$151$	−6.21112	+	20.7466i	−0.505454	+	1.68833i	−0.705636	+	0.708575i	$0.749339\pi$
$152$	1.52284	−	8.63645i	0.123519	−	0.700509i
$153$		0			0
$154$	−0.364021	−	2.06446i	−0.0293336	−	0.166359i
$155$	13.0106	+	1.52072i	1.04503	+	0.122147i
$156$		0			0
$157$	1.73207	−	1.83589i	0.138234	−	0.146520i	−0.654558	−	0.756012i	$-0.727145\pi$
$157$	1.73207	−	1.83589i	0.138234	−	0.146520i	0.792792	+	0.609492i	$0.208627\pi$
$158$	−10.5130	+	24.3719i	−0.836370	+	1.93892i
$159$		0			0
$160$	−32.6924	+	21.5022i	−2.58456	+	1.69989i
$161$	0.133028			0.0104841
$162$		0			0
$163$	7.30888			0.572476			0.286238	−	0.958159i	$-0.407595\pi$
$163$	7.30888			0.572476			0.286238	+	0.958159i	$0.407595\pi$
$164$	28.9485	−	19.0397i	2.26050	−	1.48675i
$165$		0			0
$166$	−13.6959	+	31.7507i	−1.06301	+	2.46433i
$167$	4.40004	−	4.66377i	0.340486	−	0.360894i	−0.534393	−	0.845236i	$-0.679460\pi$
$167$	4.40004	−	4.66377i	0.340486	−	0.360894i	0.874878	+	0.484343i	$0.160941\pi$
$168$		0			0
$169$	−18.6972	−	2.18539i	−1.43825	−	0.168107i
$170$	1.66460	+	9.44043i	0.127669	+	0.724048i
$171$		0			0
$172$	−5.44005	+	30.8521i	−0.414800	+	2.35245i
$173$	1.40205	−	4.68318i	0.106596	−	0.356055i	−0.888004	−	0.459835i	$-0.847909\pi$
$173$	1.40205	−	4.68318i	0.106596	−	0.356055i	0.994600	+	0.103780i	$0.0330937\pi$
$174$		0			0
$175$	−0.0424122	+	0.728190i	−0.00320606	+	0.0550460i
$176$	16.5300	−	8.30166i	1.24599	−	0.625762i
$177$		0			0
$178$	−18.0689	−	19.1519i	−1.35432	−	1.43549i
$179$	0.481678	−	0.175316i	0.0360023	−	0.0131038i	−0.323956	−	0.946072i	$-0.605013\pi$
$179$	0.481678	−	0.175316i	0.0360023	−	0.0131038i	0.359959	+	0.932968i	$0.382791\pi$
$180$		0			0
$181$	3.55046	+	1.29226i	0.263904	+	0.0960531i	0.470583	−	0.882356i	$-0.344044\pi$
$181$	3.55046	+	1.29226i	0.263904	+	0.0960531i	−0.206680	+	0.978409i	$0.566266\pi$
$182$	−3.04784	−	7.06568i	−0.225921	−	0.523743i
$183$		0			0
$184$	0.623489	+	2.08260i	0.0459642	+	0.153531i
$185$	−16.6003	+	1.94030i	−1.22048	+	0.142654i
$186$		0			0
$187$	−0.126557	−	2.17289i	−0.00925473	−	0.158898i
$188$	−18.7448	−	32.4669i	−1.36710	−	2.36789i
$189$		0			0
$190$	3.55455	−	6.15667i	0.257874	−	0.446652i
$191$	−20.2508	−	10.1703i	−1.46530	−	0.735900i	−0.475678	−	0.879619i	$-0.657797\pi$
$191$	−20.2508	−	10.1703i	−1.46530	−	0.735900i	−0.989618	+	0.143719i	$0.954094\pi$
$192$		0			0
$193$	−3.41785	−	4.59097i	−0.246022	−	0.330465i	0.661909	−	0.749584i	$-0.269746\pi$
$193$	−3.41785	−	4.59097i	−0.246022	−	0.330465i	−0.907931	+	0.419119i	$0.862339\pi$
$194$	9.34418	+	2.21461i	0.670873	+	0.159000i
$195$		0			0
$196$	−20.6341	+	27.7164i	−1.47387	+	1.97975i
$197$	−1.85381	+	1.55553i	−0.132078	+	0.110827i	−0.706434	−	0.707779i	$-0.749697\pi$
$197$	−1.85381	+	1.55553i	−0.132078	+	0.110827i	0.574356	+	0.818606i	$0.305253\pi$
$198$		0			0
$199$	−7.49610	−	6.28997i	−0.531384	−	0.445884i	0.337195	−	0.941435i	$-0.390522\pi$
$199$	−7.49610	−	6.28997i	−0.531384	−	0.445884i	−0.868579	+	0.495550i	$0.834966\pi$
$200$	−11.5988	+	2.74898i	−0.820163	+	0.194382i
$201$		0			0
$202$	39.7556	+	26.1477i	2.79719	+	1.83974i
$203$	−0.759209	−	0.499339i	−0.0532860	−	0.0350467i
$204$		0			0
$205$	16.6702	−	3.95091i	1.16430	−	0.275943i
$206$	−8.82988	−	7.40915i	−0.615207	−	0.516220i
$207$		0			0
$208$	52.0140	−	43.6449i	3.60652	−	3.02623i
$209$	−0.963914	+	1.29476i	−0.0666753	+	0.0895605i
$210$		0			0
$211$	−19.0832	−	4.52280i	−1.31374	−	0.311362i	−0.486732	−	0.873551i	$-0.661811\pi$
$211$	−19.0832	−	4.52280i	−1.31374	−	0.311362i	−0.827009	+	0.562189i	$0.809959\pi$
$212$	−29.0540	−	39.0262i	−1.99543	−	2.68033i
$213$		0			0
$214$	19.0355	+	9.56000i	1.30124	+	0.653508i
$215$	−7.74505	+	13.4148i	−0.528208	+	0.914884i
$216$		0			0
$217$	−1.31992	−	2.28617i	−0.0896020	−	0.155195i
$218$	−0.0330431	−	0.567328i	−0.00223796	−	0.0384243i
$219$		0			0
$220$	19.8432	−	2.31933i	1.33783	−	0.156369i
$221$	−2.29145	−	7.65399i	−0.154140	−	0.514863i
$222$		0			0
$223$	1.03775	+	2.40578i	0.0694930	+	0.161103i	0.949423	−	0.314001i	$-0.101670\pi$
$223$	1.03775	+	2.40578i	0.0694930	+	0.161103i	−0.879930	+	0.475104i	$0.842410\pi$
$224$	7.41017	+	2.69708i	0.495113	+	0.180206i
$225$		0			0
$226$	13.9141	−	5.06433i	0.925555	−	0.336874i
$227$	−0.847597	−	0.898400i	−0.0562570	−	0.0596289i	0.698634	−	0.715479i	$-0.253792\pi$
$227$	−0.847597	−	0.898400i	−0.0562570	−	0.0596289i	−0.754891	+	0.655850i	$0.772310\pi$
$228$		0			0
$229$	4.37803	−	2.19873i	0.289308	−	0.145296i	−0.298226	−	0.954495i	$-0.596395\pi$
$229$	4.37803	−	2.19873i	0.289308	−	0.145296i	0.587534	+	0.809199i	$0.300099\pi$
$230$	−0.102468	+	1.75930i	−0.00675652	+	0.116005i
$231$		0			0
$232$	4.25899	−	14.2260i	0.279617	−	0.933985i
$233$	−0.664049	+	3.76601i	−0.0435033	+	0.246719i	−0.998803	−	0.0489208i	$-0.984422\pi$
$233$	−0.664049	+	3.76601i	−0.0435033	+	0.246719i	0.955299	+	0.295640i	$0.0955329\pi$
$234$		0			0
$235$	−3.21886	−	18.2551i	−0.209975	−	1.19083i
$236$	25.2349	+	2.94954i	1.64265	+	0.191999i
$237$		0			0
$238$	1.32572	−	1.40518i	0.0859337	−	0.0910844i
$239$	−3.58337	+	8.30719i	−0.231789	+	0.537348i	−0.993924	−	0.110071i	$-0.964892\pi$
$239$	−3.58337	+	8.30719i	−0.231789	+	0.537348i	0.762135	+	0.647419i	$0.224151\pi$
$240$		0			0
$241$	19.5722	−	12.8728i	1.26075	−	0.829211i	0.269735	−	0.962935i	$-0.413064\pi$
$241$	19.5722	−	12.8728i	1.26075	−	0.829211i	0.991019	+	0.133724i	$0.0426936\pi$
$242$	23.0615			1.48245
$243$		0			0
$244$	−66.1485			−4.23473
$245$	−14.2744	+	9.38843i	−0.911959	+	0.599805i
$246$		0			0
$247$	−2.34685	+	5.44060i	−0.149326	+	0.346177i
$248$	29.6044	−	31.3789i	1.87988	−	1.99256i
$249$		0			0
$250$	24.0161	+	2.80708i	1.51891	+	0.177535i
$251$	−2.14133	−	12.1441i	−0.135160	−	0.766530i	−0.974748	−	0.223307i	$-0.928315\pi$
$251$	−2.14133	−	12.1441i	−0.135160	−	0.766530i	0.839588	−	0.543223i	$-0.182796\pi$
$252$		0			0
$253$	0.0694831	−	0.394058i	0.00436837	−	0.0247742i
$254$	−13.9805	+	46.6981i	−0.877215	+	2.93010i
$255$		0			0
$256$	−0.316189	+	5.42876i	−0.0197618	+	0.339298i
$257$	26.3443	−	13.2306i	1.64331	−	0.825302i	0.645192	−	0.764021i	$-0.276778\pi$
$257$	26.3443	−	13.2306i	1.64331	−	0.825302i	0.998121	−	0.0612816i	$-0.0195188\pi$
$258$		0			0
$259$	2.31140	+	2.44994i	0.143623	+	0.152232i
$260$	68.9122	−	25.0820i	4.27376	−	1.55552i
$261$		0			0
$262$	20.1710	+	7.34166i	1.24617	+	0.453569i
$263$	−8.15499	−	18.9054i	−0.502858	−	1.16576i	−0.960918	−	0.276834i	$-0.910715\pi$
$263$	−8.15499	−	18.9054i	−0.502858	−	1.16576i	0.458060	−	0.888922i	$-0.348545\pi$
$264$		0			0
$265$	−6.89956	−	23.0461i	−0.423837	−	1.41571i
$266$	−1.42300	+	0.166324i	−0.0872494	+	0.0101980i
$267$		0			0
$268$	−1.91374	−	32.8576i	−0.116900	−	2.00710i
$269$	−6.08593	−	10.5411i	−0.371066	−	0.642705i	0.618664	−	0.785656i	$-0.287674\pi$
$269$	−6.08593	−	10.5411i	−0.371066	−	0.642705i	−0.989730	+	0.142951i	$0.954341\pi$
$270$		0			0
$271$	−11.5577	+	20.0185i	−0.702078	+	1.21603i	0.265658	+	0.964067i	$0.414411\pi$
$271$	−11.5577	+	20.0185i	−0.702078	+	1.21603i	−0.967736	+	0.251967i	$0.918922\pi$
$272$	15.2332	+	7.65040i	0.923648	+	0.463874i
$273$		0			0
$274$	−13.6030	−	18.2721i	−0.821790	−	1.10386i
$275$	2.13491	+	0.505983i	0.128740	+	0.0305119i
$276$		0			0
$277$	0.817359	−	1.09790i	0.0491104	−	0.0659667i	−0.776890	−	0.629637i	$-0.783204\pi$
$277$	0.817359	−	1.09790i	0.0491104	−	0.0659667i	0.826000	+	0.563670i	$0.190611\pi$
$278$	−26.6878	+	22.3937i	−1.60063	+	1.34308i
$279$		0			0
$280$	8.28520	+	6.95211i	0.495136	+	0.415468i
$281$	−17.4219	+	4.12908i	−1.03931	+	0.246320i	−0.714628	−	0.699505i	$-0.753404\pi$
$281$	−17.4219	+	4.12908i	−1.03931	+	0.246320i	−0.324678	+	0.945825i	$0.605256\pi$
$282$		0			0
$283$	−8.15153	−	5.36135i	−0.484558	−	0.318699i	0.283618	−	0.958937i	$-0.408465\pi$
$283$	−8.15153	−	5.36135i	−0.484558	−	0.318699i	−0.768176	+	0.640238i	$0.778836\pi$
$284$	22.1222	+	14.5500i	1.31271	+	0.863385i
$285$		0			0
$286$	−22.5221	+	5.33784i	−1.33176	+	0.315633i
$287$	−2.64482	−	2.21927i	−0.156119	−	0.130999i
$288$		0			0
$289$	−11.4862	+	9.63807i	−0.675659	+	0.566945i
$290$	7.18859	−	9.65596i	0.422129	−	0.567017i
$291$		0			0
$292$	−29.7458	−	7.04988i	−1.74074	−	0.412563i
$293$	1.83443	+	2.46406i	0.107168	+	0.143952i	0.852472	−	0.522774i	$-0.175103\pi$
$293$	1.83443	+	2.46406i	0.107168	+	0.143952i	−0.745303	+	0.666726i	$0.767695\pi$
$294$		0			0
$295$	11.2261	+	5.63796i	0.653609	+	0.328255i
$296$	−27.5213	+	47.6684i	−1.59965	+	2.77067i
$297$		0			0
$298$	−21.7779	−	37.7204i	−1.26156	−	2.18509i
$299$	−0.0854031	−	1.46631i	−0.00493899	−	0.0847991i
$300$		0			0
$301$	3.10058	−	0.362406i	0.178714	−	0.0208887i
$302$	16.5820	+	55.3879i	0.954189	+	3.18721i
$303$		0			0
$304$	−5.00714	−	11.6079i	−0.287179	−	0.665756i
$305$	−30.7346	−	11.1865i	−1.75986	−	0.640536i
$306$		0			0
$307$	5.34825	−	1.94660i	0.305241	−	0.111099i	−0.184859	−	0.982765i	$-0.559183\pi$
$307$	5.34825	−	1.94660i	0.305241	−	0.111099i	0.490099	+	0.871667i	$0.336960\pi$
$308$	−2.76293	−	2.92853i	−0.157432	−	0.166868i
$309$		0			0
$310$	31.2514	−	15.6951i	1.77496	−	0.891419i
$311$	0.189058	−	3.24600i	0.0107205	−	0.184064i	−0.988697	−	0.149929i	$-0.952095\pi$
$311$	0.189058	−	3.24600i	0.0107205	−	0.184064i	0.999417	−	0.0341346i	$-0.0108675\pi$
$312$		0			0
$313$	2.71298	−	9.06199i	0.153347	−	0.512214i	−0.846448	−	0.532471i	$-0.821263\pi$
$313$	2.71298	−	9.06199i	0.153347	−	0.512214i	0.999795	+	0.0202573i	$0.00644855\pi$
$314$	1.17011	−	6.63603i	0.0660332	−	0.374493i
$315$		0			0
$316$	8.85219	+	50.2032i	0.497974	+	2.82415i
$317$	−20.3710	−	2.38103i	−1.14415	−	0.133732i	−0.477172	−	0.878810i	$-0.658338\pi$
$317$	−20.3710	−	2.38103i	−1.14415	−	0.133732i	−0.666977	+	0.745078i	$0.732412\pi$
$318$		0			0
$319$	−1.87571	+	1.98813i	−0.105019	+	0.111314i
$320$	−17.2042	+	39.8839i	−0.961747	+	2.22958i
$321$		0			0
$322$	0.296723	−	0.195158i	0.0165357	−	0.0108757i
$323$	−1.48754			−0.0827687
$324$		0			0
$325$	8.05378			0.446744
$326$	16.3027	−	10.7224i	0.902922	−	0.593861i
$327$		0			0
$328$	22.3474	−	51.8071i	1.23393	−	2.86057i
$329$	−2.56356	+	2.71722i	−0.141334	+	0.149805i
$330$		0			0
$331$	6.85491	+	0.801224i	0.376780	+	0.0440393i	0.302376	−	0.953189i	$-0.402220\pi$
$331$	6.85491	+	0.801224i	0.376780	+	0.0440393i	0.0744045	+	0.997228i	$0.476294\pi$
$332$	11.5323	+	65.4027i	0.632915	+	3.58944i
$333$		0			0
$334$	2.97247	−	16.8577i	0.162647	−	0.922415i
$335$	4.66742	−	15.5903i	0.255008	−	0.851788i
$336$		0			0
$337$	−1.57688	+	27.0740i	−0.0858981	+	1.47481i	0.629993	+	0.776601i	$0.283058\pi$
$337$	−1.57688	+	27.0740i	−0.0858981	+	1.47481i	−0.715891	+	0.698212i	$0.753979\pi$
$338$	−44.9107	+	22.5550i	−2.44282	+	1.22683i
$339$		0			0
$340$	12.6344	+	13.3916i	0.685194	+	0.726264i
$341$	−7.46157	+	2.71579i	−0.404067	+	0.147068i
$342$		0			0
$343$	6.59630	+	2.40086i	0.356166	+	0.129634i
$344$	20.2057	+	46.8421i	1.08942	+	2.52556i
$345$		0			0
$346$	−3.74310	−	12.5028i	−0.201231	−	0.672157i
$347$	−23.0562	+	2.69489i	−1.23772	+	0.144669i	−0.709665	−	0.704539i	$-0.751154\pi$
$347$	−23.0562	+	2.69489i	−1.23772	+	0.144669i	−0.528058	+	0.849209i	$0.677080\pi$
$348$		0			0
$349$	−0.178494	−	3.06463i	−0.00955458	−	0.164046i	−0.999710	−	0.0240746i	$-0.992336\pi$
$349$	−0.178494	−	3.06463i	−0.00955458	−	0.164046i	0.990156	−	0.139971i	$-0.0447010\pi$
$350$	0.973684	+	1.68647i	0.0520456	+	0.0901456i
$351$		0			0
$352$	11.8598	−	20.5418i	0.632131	−	1.09488i
$353$	9.38433	+	4.71299i	0.499477	+	0.250847i	0.680656	−	0.732603i	$-0.261695\pi$
$353$	9.38433	+	4.71299i	0.499477	+	0.250847i	−0.181179	+	0.983450i	$0.557991\pi$
$354$		0			0
$355$	7.81808	+	10.5015i	0.414941	+	0.557362i
$356$	−49.2065	−	11.6622i	−2.60794	−	0.618093i
$357$		0			0
$358$	0.817201	−	1.09769i	0.0431904	−	0.0580148i
$359$	23.6540	−	19.8481i	1.24841	−	1.04754i	0.251594	−	0.967833i	$-0.419045\pi$
$359$	23.6540	−	19.8481i	1.24841	−	1.04754i	0.996818	−	0.0797090i	$-0.0253991\pi$
$360$		0			0
$361$	−13.7098	−	11.5039i	−0.721567	−	0.605466i
$362$	9.81522	−	2.32625i	0.515876	−	0.122265i
$363$		0			0
$364$	−12.3477	−	8.12120i	−0.647194	−	0.425667i
$365$	−12.6286	−	8.30594i	−0.661010	−	0.434753i
$366$		0			0
$367$	14.8135	−	3.51087i	0.773260	−	0.183266i	0.175000	−	0.984568i	$-0.444007\pi$
$367$	14.8135	−	3.51087i	0.773260	−	0.183266i	0.598259	+	0.801302i	$0.295859\pi$
$368$	2.40061	+	2.01435i	0.125140	+	0.105005i
$369$		0			0
$370$	−34.1810	+	28.6813i	−1.77699	+	1.49107i
$371$	−2.89509	+	3.88878i	−0.150306	+	0.201895i
$372$		0			0
$373$	−0.908175	−	0.215242i	−0.0470235	−	0.0111448i	0.207037	−	0.978333i	$-0.433618\pi$
$373$	−0.908175	−	0.215242i	−0.0470235	−	0.0111448i	−0.254060	+	0.967188i	$0.581766\pi$
$374$	−3.47001	−	4.66104i	−0.179430	−	0.241017i
$375$		0			0
$376$	−54.5542	−	27.3981i	−2.81342	−	1.41295i
$377$	−5.01662	+	8.68904i	−0.258369	+	0.447508i
$378$		0			0
$379$	19.2328	+	33.3122i	0.987924	+	1.71113i	0.628143	+	0.778098i	$0.283815\pi$
$379$	19.2328	+	33.3122i	0.987924	+	1.71113i	0.359781	+	0.933037i	$0.382851\pi$
$380$	−0.793893	−	13.6306i	−0.0407259	−	0.699236i
$381$		0			0
$382$	−60.0904	+	7.02356i	−3.07449	+	0.359356i
$383$	−4.23110	−	14.1329i	−0.216199	−	0.722156i	−0.995436	−	0.0954267i	$-0.969578\pi$
$383$	−4.23110	−	14.1329i	−0.216199	−	0.722156i	0.779237	−	0.626729i	$-0.215607\pi$
$384$		0			0
$385$	−0.788491	−	1.82793i	−0.0401852	−	0.0931598i
$386$	−14.3588	−	5.22616i	−0.730841	−	0.266005i
$387$		0			0
$388$	17.3313	−	6.30806i	0.879862	−	0.320243i
$389$	11.7270	+	12.4299i	0.594583	+	0.630221i	0.952866	−	0.303392i	$-0.0981191\pi$
$389$	11.7270	+	12.4299i	0.594583	+	0.630221i	−0.358283	+	0.933613i	$0.616638\pi$
$390$		0			0
$391$	0.329524	−	0.165493i	0.0166647	−	0.00836935i
$392$	−3.27164	+	56.1720i	−0.165243	+	2.83711i
$393$		0			0
$394$	−1.85294	+	6.18926i	−0.0933500	+	0.311811i
$395$	−4.37696	+	24.8230i	−0.220229	+	1.24898i
$396$		0			0
$397$	−4.37414	−	24.8070i	−0.219532	−	1.24503i	−0.872867	−	0.487958i	$-0.837742\pi$
$397$	−4.37414	−	24.8070i	−0.219532	−	1.24503i	0.653335	−	0.757069i	$-0.273369\pi$
$398$	−25.9479	−	3.03288i	−1.30065	−	0.152024i
$399$		0			0
$400$	−11.7919	+	12.4986i	−0.589593	+	0.624932i
$401$	−8.17128	+	18.9432i	−0.408054	+	0.945976i	0.582995	+	0.812476i	$0.301881\pi$
$401$	−8.17128	+	18.9432i	−0.408054	+	0.945976i	−0.991049	+	0.133500i	$0.957378\pi$
$402$		0			0
$403$	−24.3522	+	16.0167i	−1.21307	+	0.797847i
$404$	91.3890			4.54677
$405$		0			0
$406$	−2.42599			−0.120400
$407$	8.46456	−	5.56723i	0.419573	−	0.275957i
$408$		0			0
$409$	13.9343	−	32.3033i	0.689006	−	1.59729i	−0.108579	−	0.994088i	$-0.534630\pi$
$409$	13.9343	−	32.3033i	0.689006	−	1.59729i	0.797585	−	0.603207i	$-0.206111\pi$
$410$	31.3872	−	33.2685i	1.55010	−	1.64301i
$411$		0			0
$412$	−21.9882	−	2.57006i	−1.08328	−	0.126618i
$413$	−0.439618	−	2.49319i	−0.0216322	−	0.122682i
$414$		0			0
$415$	−5.70212	+	32.3383i	−0.279906	+	1.58743i
$416$	24.9716	−	83.4109i	1.22433	−	4.08956i
$417$		0			0
$418$	−0.250569	+	4.30211i	−0.0122557	+	0.210423i
$419$	−24.2225	+	12.1650i	−1.18335	+	0.594299i	−0.928011	−	0.372553i	$-0.878482\pi$
$419$	−24.2225	+	12.1650i	−1.18335	+	0.594299i	−0.255336	+	0.966852i	$0.582186\pi$
$420$		0			0
$421$	20.8880	+	22.1400i	1.01802	+	1.07904i	0.996854	+	0.0792630i	$0.0252567\pi$
$421$	20.8880	+	22.1400i	1.01802	+	1.07904i	0.0211670	+	0.999776i	$0.493262\pi$
$422$	−49.2008	+	17.9076i	−2.39506	+	0.871729i
$423$		0			0
$424$	−74.4492	−	27.0973i	−3.61557	−	1.31596i
$425$	0.800844	+	1.85657i	0.0388467	+	0.0900567i
$426$		0			0
$427$	1.89043	+	6.31448i	0.0914844	+	0.305579i
$428$	40.6346	−	4.74950i	1.96415	−	0.229576i
$429$		0			0
$430$	2.40455	+	41.2845i	0.115958	+	1.99092i
$431$	−4.50933	−	7.81039i	−0.217207	−	0.376213i	0.736746	−	0.676170i	$-0.236361\pi$
$431$	−4.50933	−	7.81039i	−0.217207	−	0.376213i	−0.953953	+	0.299956i	$0.903028\pi$
$432$		0			0
$433$	−11.8523	+	20.5287i	−0.569584	+	0.986548i	0.427023	+	0.904241i	$0.359562\pi$
$433$	−11.8523	+	20.5287i	−0.569584	+	0.986548i	−0.996607	+	0.0823075i	$0.973771\pi$
$434$	−6.29803	−	3.16299i	−0.302315	−	0.151828i
$435$		0			0
$436$	−0.651772	−	0.875481i	−0.0312142	−	0.0419279i
$437$	−0.266094	−	0.0630655i	−0.0127290	−	0.00301683i
$438$		0			0
$439$	2.40340	−	3.22832i	0.114708	−	0.154080i	−0.741061	−	0.671438i	$-0.765677\pi$
$439$	2.40340	−	3.22832i	0.114708	−	0.154080i	0.855769	+	0.517358i	$0.173084\pi$
$440$	24.9213	−	20.9114i	1.18807	−	0.996913i
$441$		0			0
$442$	−16.3399	−	13.7108i	−0.777209	−	0.652156i
$443$	7.74314	−	1.83516i	0.367888	−	0.0871909i	−0.0425140	−	0.999096i	$-0.513537\pi$
$443$	7.74314	−	1.83516i	0.367888	−	0.0871909i	0.410402	+	0.911905i	$0.365389\pi$
$444$		0			0
$445$	−20.8906	−	13.7400i	−0.990311	−	0.651338i
$446$	5.84412	+	3.84374i	0.276727	+	0.182006i
$447$		0			0
$448$	8.51767	−	2.01872i	0.402422	−	0.0953758i
$449$	−11.2889	−	9.47253i	−0.532757	−	0.447037i	0.336295	−	0.941757i	$-0.390826\pi$
$449$	−11.2889	−	9.47253i	−0.532757	−	0.447037i	−0.869052	+	0.494720i	$0.835271\pi$
$450$		0			0
$451$	−7.95542	+	6.67539i	−0.374606	+	0.314332i
$452$	16.9823	−	22.8112i	0.798780	−	1.07295i
$453$		0			0
$454$	−3.20858	−	0.760448i	−0.150586	−	0.0356896i
$455$	−4.36372	−	5.86149i	−0.204574	−	0.274791i
$456$		0			0
$457$	−7.02454	−	3.52786i	−0.328594	−	0.165026i	0.276852	−	0.960913i	$-0.410709\pi$
$457$	−7.02454	−	3.52786i	−0.328594	−	0.165026i	−0.605446	+	0.795886i	$0.707005\pi$
$458$	6.53970	−	11.3271i	0.305580	−	0.529280i
$459$		0			0
$460$	1.69232	+	2.93118i	0.0789047	+	0.136667i
$461$	−0.192100	−	3.29823i	−0.00894699	−	0.153614i	−0.999823	−	0.0188344i	$-0.994004\pi$
$461$	−0.192100	−	3.29823i	−0.00894699	−	0.153614i	0.990876	−	0.134779i	$-0.0430326\pi$
$462$		0			0
$463$	17.5818	−	2.05502i	0.817095	−	0.0955047i	0.302730	−	0.953076i	$-0.402102\pi$
$463$	17.5818	−	2.05502i	0.817095	−	0.0955047i	0.514365	+	0.857572i	$0.328028\pi$
$464$	−6.13946	−	20.5072i	−0.285017	−	0.952024i
$465$		0			0
$466$	4.04371	+	9.37438i	0.187321	+	0.434260i
$467$	37.4545	+	13.6323i	1.73319	+	0.630829i	0.998849	−	0.0479555i	$-0.0152706\pi$
$467$	37.4545	+	13.6323i	1.73319	+	0.630829i	0.734338	+	0.678784i	$0.237493\pi$
$468$		0			0
$469$	−3.08187	+	1.12171i	−0.142307	+	0.0517956i
$470$	−33.9607	−	35.9963i	−1.56649	−	1.66038i
$471$		0			0
$472$	36.9714	−	18.5677i	1.70175	−	0.854649i
$473$	0.545968	−	9.37391i	0.0251036	−	0.431013i
$474$		0			0
$475$	0.430056	−	1.43649i	0.0197323	−	0.0659105i
$476$	0.644290	−	3.65395i	0.0295310	−	0.167478i
$477$		0			0
$478$	4.19419	+	23.7864i	0.191838	+	1.08797i
$479$	38.9258	+	4.54978i	1.77857	+	0.207885i	0.940990	−	0.338435i	$-0.109898\pi$
$479$	38.9258	+	4.54978i	1.77857	+	0.207885i	0.837577	+	0.546320i	$0.183972\pi$
$480$		0			0
$481$	25.5208	−	27.0505i	1.16365	−	1.23340i
$482$	24.7713	−	57.4264i	1.12830	−	2.61570i
$483$		0			0
$484$	37.0053	−	24.3388i	1.68206	−	1.10631i
$485$	9.11940			0.414091
$486$		0			0
$487$	35.0579			1.58863			0.794313	−	0.607509i	$-0.207831\pi$
$487$	35.0579			1.58863			0.794313	+	0.607509i	$0.207831\pi$
$488$	−89.9951	+	59.1907i	−4.07389	+	2.67944i
$489$		0			0
$490$	−18.0663	+	41.8824i	−0.816152	+	1.89205i
$491$	−14.1243	+	14.9709i	−0.637421	+	0.675627i	−0.962880	−	0.269929i	$-0.913000\pi$
$491$	−14.1243	+	14.9709i	−0.637421	+	0.675627i	0.325459	+	0.945556i	$0.394481\pi$
$492$		0			0
$493$	−2.50184	−	0.292423i	−0.112677	−	0.0131701i
$494$	2.74688	+	15.5783i	0.123588	+	0.700903i
$495$		0			0
$496$	10.7987	−	61.2427i	0.484878	−	2.74988i
$497$	0.756710	−	2.52759i	0.0339431	−	0.113378i
$498$		0			0
$499$	−0.479420	+	8.23132i	−0.0214618	+	0.368484i	0.970429	+	0.241388i	$0.0776027\pi$
$499$	−0.479420	+	8.23132i	−0.0214618	+	0.368484i	−0.991890	+	0.127096i	$0.959434\pi$
$500$	41.4996	−	20.8419i	1.85592	−	0.932077i
$501$		0			0
$502$	−22.5922	−	23.9464i	−1.00834	−	1.06878i
$503$	15.9904	−	5.82003i	0.712977	−	0.259503i	0.0400358	−	0.999198i	$-0.487253\pi$
$503$	15.9904	−	5.82003i	0.712977	−	0.259503i	0.672941	+	0.739696i	$0.265031\pi$
$504$		0			0
$505$	42.4621	+	15.4549i	1.88954	+	0.687736i
$506$	−0.423116	−	0.980894i	−0.0188098	−	0.0436061i
$507$		0			0
$508$	26.8509	+	89.6883i	1.19132	+	3.97927i
$509$	16.2943	−	1.90453i	0.722232	−	0.0844168i	0.252968	−	0.967475i	$-0.418593\pi$
$509$	16.2943	−	1.90453i	0.722232	−	0.0844168i	0.469264	+	0.883058i	$0.344519\pi$
$510$		0			0
$511$	0.177117	+	3.04098i	0.00783519	+	0.134525i
$512$	−7.61274	−	13.1856i	−0.336439	−	0.582729i
$513$		0			0
$514$	39.3519	−	68.1595i	1.73574	−	3.00639i
$515$	−9.78178	−	4.91259i	−0.431037	−	0.216475i
$516$		0			0
$517$	6.71001	+	9.01311i	0.295106	+	0.396396i
$518$	8.74981	+	2.07374i	0.384444	+	0.0911150i
$519$		0			0
$520$	71.3114	−	95.7878i	3.12721	−	4.20057i
$521$	−9.25237	+	7.76366i	−0.405354	+	0.340132i	−0.822559	−	0.568680i	$-0.807454\pi$
$521$	−9.25237	+	7.76366i	−0.405354	+	0.340132i	0.417205	+	0.908812i	$0.363010\pi$
$522$		0			0
$523$	−5.53110	−	4.64114i	−0.241858	−	0.202943i	0.513799	−	0.857911i	$-0.328238\pi$
$523$	−5.53110	−	4.64114i	−0.241858	−	0.202943i	−0.755657	+	0.654968i	$0.772682\pi$
$524$	40.1154	−	9.50753i	1.75245	−	0.415338i
$525$		0			0
$526$	−45.9250	−	30.2053i	−2.00242	−	1.31701i
$527$	−6.11369	−	4.02104i	−0.266316	−	0.175159i
$528$		0			0
$529$	−22.3141	+	5.28853i	−0.970177	+	0.229936i
$530$	−49.1993	−	41.2832i	−2.13708	−	1.79323i
$531$		0			0
$532$	−2.10785	+	1.76870i	−0.0913869	+	0.0766827i
$533$	−22.7642	+	30.5776i	−0.986026	+	1.32446i
$534$		0			0
$535$	19.6832	+	4.66501i	0.850981	+	0.201686i
$536$	−32.0051	−	42.9903i	−1.38241	−	1.85690i
$537$		0			0
$538$	−29.0392	−	14.5840i	−1.25197	−	0.628762i
$539$	5.17833	−	8.96913i	0.223046	−	0.386328i
$540$		0			0
$541$	−19.0806	−	33.0486i	−0.820339	−	1.42087i	−0.905430	−	0.424496i	$-0.860451\pi$
$541$	−19.0806	−	33.0486i	−0.820339	−	1.42087i	0.0850910	−	0.996373i	$-0.472882\pi$
$542$	3.58822	+	61.6074i	0.154127	+	2.64626i
$543$		0			0
$544$	21.7111	−	2.53766i	0.930854	−	0.108801i
$545$	−0.154779	−	0.516997i	−0.00663000	−	0.0221457i
$546$		0			0
$547$	−14.7275	−	34.1421i	−0.629702	−	1.45981i	−0.871949	−	0.489598i	$-0.837144\pi$
$547$	−14.7275	−	34.1421i	−0.629702	−	1.45981i	0.242247	−	0.970215i	$-0.422116\pi$
$548$	−41.1120	−	14.9635i	−1.75622	−	0.639211i
$549$		0			0
$550$	5.50428	−	2.00339i	0.234703	−	0.0854250i
$551$	1.28191	+	1.35875i	0.0546113	+	0.0578846i
$552$		0			0
$553$	4.53937	−	2.27976i	0.193034	−	0.0969452i
$554$	0.212472	−	3.64801i	0.00902709	−	0.154989i
$555$		0			0
$556$	−19.1901	+	64.0996i	−0.813844	+	2.71843i
$557$	4.26215	−	24.1719i	0.180593	−	1.02420i	−0.750894	−	0.660422i	$-0.770377\pi$
$557$	4.26215	−	24.1719i	0.180593	−	1.02420i	0.931488	−	0.363773i	$-0.118512\pi$
$558$		0			0
$559$	−5.98521	−	33.9438i	−0.253147	−	1.43567i
$560$	15.4855	+	1.81000i	0.654383	+	0.0764864i
$561$		0			0
$562$	−32.8026	+	34.7688i	−1.38370	+	1.46663i
$563$	2.79634	−	6.48265i	0.117852	−	0.273211i	−0.849072	−	0.528278i	$-0.822838\pi$
$563$	2.79634	−	6.48265i	0.117852	−	0.273211i	0.966924	+	0.255066i	$0.0820973\pi$
$564$		0			0
$565$	11.7481	−	7.72686i	0.494247	−	0.325071i
$566$	−26.0476			−1.09486
$567$		0			0
$568$	43.1169			1.80914
$569$	7.06923	−	4.64950i	0.296357	−	0.194917i	−0.392619	−	0.919701i	$-0.628431\pi$
$569$	7.06923	−	4.64950i	0.296357	−	0.194917i	0.688976	+	0.724784i	$0.258060\pi$
$570$		0			0
$571$	−0.175018	+	0.405738i	−0.00732428	+	0.0169796i	−0.921839	−	0.387573i	$-0.873313\pi$
$571$	−0.175018	+	0.405738i	−0.00732428	+	0.0169796i	0.914515	+	0.404553i	$0.132573\pi$
$572$	−30.5063	+	32.3348i	−1.27553	+	1.35198i
$573$		0			0
$574$	−9.15512	−	1.07008i	−0.382127	−	0.0446643i
$575$	0.0645463	+	0.366060i	0.00269177	+	0.0152658i
$576$		0			0
$577$	1.80812	−	10.2544i	0.0752730	−	0.426894i	−0.923762	−	0.382968i	$-0.874902\pi$
$577$	1.80812	−	10.2544i	0.0752730	−	0.426894i	0.999035	−	0.0439266i	$-0.0139868\pi$
$578$	−11.4809	+	38.3488i	−0.477541	+	1.59510i
$579$		0			0
$580$	1.34432	−	23.0810i	0.0558197	−	0.958387i
$581$	5.91371	−	2.96998i	0.245342	−	0.123215i
$582$		0			0
$583$	10.0073	+	10.6071i	0.414459	+	0.439301i
$584$	−46.7775	+	17.0256i	−1.93567	+	0.704525i
$585$		0			0
$586$	7.70663	+	2.80498i	0.318358	+	0.115873i
$587$	−14.6266	−	33.9083i	−0.603705	−	1.39955i	−0.896360	−	0.443327i	$-0.853798\pi$
$587$	−14.6266	−	33.9083i	−0.603705	−	1.39955i	0.292655	−	0.956218i	$-0.405461\pi$
$588$		0			0
$589$	1.55640	+	5.19875i	0.0641305	+	0.214211i
$590$	33.3113	−	3.89353i	1.37140	−	0.160294i
$591$		0			0
$592$	4.61353	+	79.2113i	0.189615	+	3.25557i
$593$	1.15692	+	2.00385i	0.0475091	+	0.0822881i	0.888802	−	0.458291i	$-0.151538\pi$
$593$	1.15692	+	2.00385i	0.0475091	+	0.0822881i	−0.841293	+	0.540579i	$0.818205\pi$
$594$		0			0
$595$	0.917282	−	1.58878i	0.0376049	−	0.0651336i
$596$	−74.7552	−	37.5435i	−3.06209	−	1.53784i
$597$		0			0
$598$	−2.34164	−	3.14537i	−0.0957568	−	0.128624i
$599$	7.85260	+	1.86110i	0.320848	+	0.0760425i	0.387884	−	0.921708i	$-0.373206\pi$
$599$	7.85260	+	1.86110i	0.320848	+	0.0760425i	−0.0670358	+	0.997751i	$0.521354\pi$
$600$		0			0
$601$	9.09918	−	12.2223i	0.371163	−	0.498559i	−0.576823	−	0.816869i	$-0.695708\pi$
$601$	9.09918	−	12.2223i	0.371163	−	0.498559i	0.947987	+	0.318310i	$0.103115\pi$
$602$	6.38427	−	5.35704i	0.260203	−	0.218337i
$603$		0			0
$604$	85.0636	+	71.3769i	3.46119	+	2.90428i
$605$	21.3098	−	5.05051i	0.866365	−	0.205332i
$606$		0			0
$607$	24.4698	+	16.0940i	0.993198	+	0.653237i	0.938505	−	0.345267i	$-0.112212\pi$
$607$	24.4698	+	16.0940i	0.993198	+	0.653237i	0.0546933	+	0.998503i	$0.482582\pi$
$608$	−13.5439	−	8.90794i	−0.549276	−	0.361265i
$609$		0			0
$610$	−84.9656	+	20.1372i	−3.44015	+	0.815332i
$611$	31.5966	+	26.5127i	1.27826	+	1.07259i
$612$		0			0
$613$	5.16392	−	4.33305i	0.208569	−	0.175010i	−0.532519	−	0.846418i	$-0.678755\pi$
$613$	5.16392	−	4.33305i	0.208569	−	0.175010i	0.741088	+	0.671408i	$0.234310\pi$
$614$	9.07368	−	12.1881i	0.366184	−	0.491871i
$615$		0			0
$616$	−6.37946	−	1.51196i	−0.257036	−	0.0609186i
$617$	7.19212	+	9.66070i	0.289544	+	0.388925i	0.922966	−	0.384881i	$-0.125758\pi$
$617$	7.19212	+	9.66070i	0.289544	+	0.388925i	−0.633422	+	0.773807i	$0.718350\pi$
$618$		0			0
$619$	−12.0062	−	6.02974i	−0.482570	−	0.242356i	0.190845	−	0.981620i	$-0.438877\pi$
$619$	−12.0062	−	6.02974i	−0.482570	−	0.242356i	−0.673415	+	0.739264i	$0.735173\pi$
$620$	33.5828	−	58.1671i	1.34872	−	2.33605i
$621$		0			0
$622$	−4.34032	−	7.51765i	−0.174031	−	0.301430i
$623$	0.292993	+	5.03050i	0.0117385	+	0.201543i
$624$		0			0
$625$	29.8965	−	3.49440i	1.19586	−	0.139776i
$626$	−7.24294	−	24.1931i	−0.289486	−	0.966951i
$627$		0			0
$628$	−5.12597	−	11.8833i	−0.204548	−	0.474196i
$629$	8.77342	+	3.19326i	0.349819	+	0.127324i
$630$		0			0
$631$	−0.571023	+	0.207835i	−0.0227321	+	0.00827379i	−0.353361	−	0.935487i	$-0.614961\pi$
$631$	−0.571023	+	0.207835i	−0.0227321	+	0.00827379i	0.330629	+	0.943761i	$0.392739\pi$
$632$	56.9660	+	60.3805i	2.26599	+	2.40181i
$633$		0			0
$634$	−48.9312	+	24.5742i	−1.94331	+	0.975965i
$635$	−2.69158	+	46.2127i	−0.106812	+	1.83390i
$636$		0			0
$637$	10.9033	−	36.4195i	0.432004	−	1.44299i
$638$	−1.26714	+	7.18633i	−0.0501667	+	0.284510i
$639$		0			0
$640$	6.54721	+	37.1311i	0.258801	+	1.46774i
$641$	22.5001	+	2.62988i	0.888700	+	0.103874i	0.548177	−	0.836362i	$-0.315322\pi$
$641$	22.5001	+	2.62988i	0.888700	+	0.103874i	0.340523	+	0.940236i	$0.389396\pi$
$642$		0			0
$643$	−33.4459	+	35.4506i	−1.31898	+	1.39803i	−0.458374	+	0.888759i	$0.651568\pi$
$643$	−33.4459	+	35.4506i	−1.31898	+	1.39803i	−0.860604	+	0.509275i	$0.829913\pi$
$644$	0.270165	−	0.626313i	0.0106460	−	0.0246802i
$645$		0			0
$646$	−3.31799	+	2.18228i	−0.130545	+	0.0858606i
$647$	−20.1953			−0.793960			−0.396980	−	0.917827i	$-0.629942\pi$
$647$	−20.1953			−0.793960			−0.396980	+	0.917827i	$0.629942\pi$
$648$		0			0
$649$	−7.61503			−0.298916
$650$	17.9642	−	11.8152i	0.704614	−	0.463432i
$651$		0			0
$652$	14.8435	−	34.4112i	0.581318	−	1.34765i
$653$	−13.1374	+	13.9248i	−0.514107	+	0.544921i	−0.931470	−	0.363819i	$-0.881473\pi$
$653$	−13.1374	+	13.9248i	−0.514107	+	0.544921i	0.417363	+	0.908740i	$0.362954\pi$
$654$		0			0
$655$	20.2467	+	2.36650i	0.791103	+	0.0924667i
$656$	−14.1233	−	80.0975i	−0.551424	−	3.12728i
$657$		0			0
$658$	−1.73183	+	9.82169i	−0.0675137	+	0.382889i
$659$	11.8035	−	39.4263i	0.459798	−	1.53583i	−0.342857	−	0.939388i	$-0.611395\pi$
$659$	11.8035	−	39.4263i	0.459798	−	1.53583i	0.802655	−	0.596444i	$-0.203420\pi$
$660$		0			0
$661$	1.65588	−	28.4304i	0.0644065	−	1.10582i	−0.799008	−	0.601321i	$-0.794641\pi$
$661$	1.65588	−	28.4304i	0.0644065	−	1.10582i	0.863414	−	0.504496i	$-0.168322\pi$
$662$	16.4655	−	8.26930i	0.639951	−	0.321395i
$663$		0			0
$664$	74.2130	+	78.6612i	2.88002	+	3.05265i
$665$	−1.27848	+	0.465328i	−0.0495773	+	0.0180447i
$666$		0			0
$667$	−0.435139	−	0.158378i	−0.0168486	−	0.00613241i
$668$	−13.0217	−	30.1876i	−0.503824	−	1.16799i
$669$		0			0
$670$	−12.4608	−	41.6219i	−0.481402	−	1.60799i
$671$	19.6923	−	2.30170i	0.760214	−	0.0888562i
$672$		0			0
$673$	2.12301	+	36.4506i	0.0818359	+	1.40507i	0.750189	+	0.661223i	$0.229962\pi$
$673$	2.12301	+	36.4506i	0.0818359	+	1.40507i	−0.668353	+	0.743844i	$0.733001\pi$
$674$	36.2014	+	62.7027i	1.39443	+	2.41522i
$675$		0			0
$676$	−48.2611	+	83.5906i	−1.85620	+	3.21502i
$677$	1.58178	+	0.794398i	0.0607926	+	0.0305312i	0.478936	−	0.877850i	$-0.341023\pi$
$677$	1.58178	+	0.794398i	0.0607926	+	0.0305312i	−0.418143	+	0.908381i	$0.637319\pi$
$678$		0			0
$679$	−1.09747	−	1.47415i	−0.0421168	−	0.0565727i
$680$	29.1721	+	6.91391i	1.11870	+	0.265137i
$681$		0			0
$682$	−12.6591	+	17.0041i	−0.484741	+	0.651120i
$683$	17.5030	−	14.6868i	0.669734	−	0.561973i	−0.243253	−	0.969963i	$-0.578214\pi$
$683$	17.5030	−	14.6868i	0.669734	−	0.561973i	0.912987	+	0.407989i	$0.133770\pi$
$684$		0			0
$685$	−16.5714	−	13.9050i	−0.633159	−	0.531284i
$686$	18.2354	−	4.32187i	0.696231	−	0.165010i
$687$		0			0
$688$	61.4405	+	40.4100i	2.34240	+	1.54062i
$689$	44.7231	+	29.4149i	1.70382	+	1.12062i
$690$		0			0
$691$	5.50438	−	1.30456i	0.209396	−	0.0496279i	−0.124579	−	0.992210i	$-0.539758\pi$
$691$	5.50438	−	1.30456i	0.209396	−	0.0496279i	0.333975	+	0.942582i	$0.391610\pi$
$692$	−19.2016	−	16.1121i	−0.729936	−	0.612489i
$693$		0			0
$694$	−47.4741	+	39.8355i	−1.80209	+	1.51213i
$695$	−19.7563	+	26.5373i	−0.749399	+	1.00662i
$696$		0			0
$697$	−9.31238	−	2.20707i	−0.352732	−	0.0835989i
$698$	−4.89408	−	6.57389i	−0.185244	−	0.248825i
$699$		0			0
$700$	3.34228	+	1.67856i	0.126326	+	0.0634435i
$701$	−12.8656	+	22.2838i	−0.485926	+	0.841648i	−0.999869	−	0.0161763i	$-0.994851\pi$
$701$	−12.8656	+	22.2838i	−0.485926	+	0.841648i	0.513944	+	0.857824i	$0.328184\pi$
$702$		0			0
$703$	−3.46201	−	5.99637i	−0.130572	−	0.226157i
$704$	−1.53097	−	26.2857i	−0.0577005	−	0.990679i
$705$		0			0
$706$	27.8462	−	3.25475i	1.04800	−	0.122494i
$707$	−2.61177	−	8.72392i	−0.0982257	−	0.328097i
$708$		0			0
$709$	13.2718	+	30.7675i	0.498433	+	1.15550i	0.962888	+	0.269901i	$0.0869908\pi$
$709$	13.2718	+	30.7675i	0.498433	+	1.15550i	−0.464455	+	0.885597i	$0.653750\pi$
$710$	32.8446	+	11.9545i	1.23264	+	0.448643i
$711$		0			0
$712$	−77.3810	+	28.1644i	−2.89997	+	1.05550i
$713$	−0.923158	−	0.978490i	−0.0345725	−	0.0366447i
$714$		0			0
$715$	−19.6423	+	9.86474i	−0.734581	+	0.368921i
$716$	0.152822	−	2.62385i	0.00571123	−	0.0980580i
$717$		0			0
$718$	23.6430	−	78.9732i	0.882350	−	2.94726i
$719$	−0.373099	+	2.11595i	−0.0139143	+	0.0789116i	−0.990974	−	0.134053i	$-0.957201\pi$
$719$	−0.373099	+	2.11595i	−0.0139143	+	0.0789116i	0.977060	+	0.212965i	$0.0683119\pi$
$720$		0			0
$721$	0.383057	+	2.17243i	0.0142658	+	0.0809054i
$722$	−47.4567	−	5.54689i	−1.76616	−	0.206434i
$723$		0			0
$724$	13.2948	−	14.0916i	0.494096	−	0.523711i
$725$	1.00569	−	2.33144i	0.0373502	−	0.0865876i
$726$		0			0
$727$	−9.24322	+	6.07936i	−0.342812	+	0.225471i	−0.709226	−	0.704981i	$-0.750956\pi$
$727$	−9.24322	+	6.07936i	−0.342812	+	0.225471i	0.366415	+	0.930452i	$0.380585\pi$
$728$	−24.0660			−0.891946
$729$		0			0
$730$	−40.3536			−1.49355
$731$	7.22961	−	4.75499i	0.267397	−	0.175870i
$732$		0			0
$733$	−6.73459	+	15.6125i	−0.248748	+	0.576662i	−0.996146	−	0.0877145i	$-0.972044\pi$
$733$	−6.73459	+	15.6125i	−0.248748	+	0.576662i	0.747398	+	0.664377i	$0.231303\pi$
$734$	27.8914	−	29.5632i	1.02949	−	1.09120i
$735$		0			0
$736$	3.99132	+	0.466519i	0.147122	+	0.0171961i
$737$	1.71303	+	9.71507i	0.0631002	+	0.357859i
$738$		0			0
$739$	−4.23694	+	24.0289i	−0.155858	+	0.883917i	0.802138	+	0.597138i	$0.203696\pi$
$739$	−4.23694	+	24.0289i	−0.155858	+	0.883917i	−0.957997	+	0.286779i	$0.907416\pi$
$740$	−24.5782	+	82.0970i	−0.903514	+	3.01795i
$741$		0			0
$742$	−0.752578	+	12.9213i	−0.0276280	+	0.474354i
$743$	−5.27562	+	2.64951i	−0.193544	+	0.0972012i	−0.542932	−	0.839777i	$-0.682686\pi$
$743$	−5.27562	+	2.64951i	−0.193544	+	0.0972012i	0.349388	+	0.936978i	$0.386389\pi$
$744$		0			0
$745$	−28.3845	−	30.0858i	−1.03993	−	1.10226i
$746$	−2.34148	+	0.852230i	−0.0857277	+	0.0312023i
$747$		0			0
$748$	−10.4873	−	3.81706i	−0.383453	−	0.139566i
$749$	−1.61466	−	3.74320i	−0.0589984	−	0.136774i
$750$		0			0
$751$	9.90970	+	33.1007i	0.361610	+	1.20786i	0.924452	+	0.381298i	$0.124523\pi$
$751$	9.90970	+	33.1007i	0.361610	+	1.20786i	−0.562842	+	0.826564i	$0.690292\pi$
$752$	−87.4068	+	10.2164i	−3.18740	+	0.372554i
$753$		0			0
$754$	1.55747	+	26.7408i	0.0567198	+	0.973841i
$755$	27.4525	+	47.5491i	0.999099	+	1.73049i
$756$		0			0
$757$	19.4091	−	33.6176i	0.705437	−	1.22185i	−0.261097	−	0.965313i	$-0.584084\pi$
$757$	19.4091	−	33.6176i	0.705437	−	1.22185i	0.966534	−	0.256540i	$-0.0825824\pi$
$758$	91.7699	+	46.0886i	3.33323	+	1.67401i
$759$		0			0
$760$	−13.2770	−	17.8341i	−0.481607	−	0.646910i
$761$	−39.7704	−	9.42575i	−1.44167	−	0.341683i	−0.565928	−	0.824455i	$-0.691482\pi$
$761$	−39.7704	−	9.42575i	−1.44167	−	0.341683i	−0.875746	+	0.482771i	$0.839630\pi$
$762$		0			0
$763$	−0.0649459	+	0.0872375i	−0.00235120	+	0.00315821i
$764$	−89.0105	+	74.6887i	−3.22029	+	2.70214i
$765$		0			0
$766$	−30.1711	−	25.3166i	−1.09013	−	0.914725i
$767$	−27.1993	+	6.44635i	−0.982109	+	0.232764i
$768$		0			0
$769$	25.8208	+	16.9826i	0.931122	+	0.612409i	0.921849	−	0.387548i	$-0.126678\pi$
$769$	25.8208	+	16.9826i	0.931122	+	0.612409i	0.00927263	+	0.999957i	$0.497048\pi$
$770$	−4.44040	−	2.92050i	−0.160021	−	0.105247i
$771$		0			0
$772$	−28.5562	+	6.76794i	−1.02776	+	0.243583i
$773$	22.5762	+	18.9437i	0.812009	+	0.681356i	0.951086	−	0.308925i	$-0.0999692\pi$
$773$	22.5762	+	18.9437i	0.812009	+	0.681356i	−0.139077	+	0.990282i	$0.544414\pi$
$774$		0			0
$775$	5.65054	−	4.74137i	0.202974	−	0.170315i
$776$	17.9346	−	24.0904i	0.643816	−	0.864795i
$777$		0			0
$778$	44.3927	+	10.5213i	1.59155	+	0.377205i
$779$	4.23831	+	5.69304i	0.151853	+	0.203974i
$780$		0			0
$781$	−7.09204	−	3.56175i	−0.253773	−	0.127450i
$782$	0.492228	−	0.852563i	0.0176020	−	0.0304876i
$783$		0			0
$784$	40.5553	+	70.2439i	1.44841	+	2.50871i
$785$	−0.372071	−	6.38821i	−0.0132798	−	0.228005i
$786$		0			0
$787$	−16.3206	+	1.90760i	−0.581765	+	0.0679986i	−0.401885	−	0.915690i	$-0.631645\pi$
$787$	−16.3206	+	1.90760i	−0.581765	+	0.0679986i	−0.179880	+	0.983689i	$0.557571\pi$
$788$	3.55876	+	11.8871i	0.126775	+	0.423460i
$789$		0			0
$790$	26.6534	+	61.7896i	0.948286	+	2.19837i
$791$	−2.66286	−	0.969203i	−0.0946805	−	0.0344609i
$792$		0			0
$793$	68.3884	−	24.8914i	2.42854	−	0.883918i
$794$	−46.1496	−	48.9157i	−1.63779	−	1.73595i
$795$		0			0
$796$	−44.8378	+	22.5184i	−1.58923	+	0.798143i
$797$	0.488972	−	8.39532i	0.0173203	−	0.297378i	−0.978513	−	0.206185i	$-0.933895\pi$
$797$	0.488972	−	8.39532i	0.0173203	−	0.297378i	0.995833	−	0.0911925i	$-0.0290679\pi$
$798$		0			0
$799$	−2.96986	+	9.92003i	−0.105066	+	0.350946i
$800$	−3.82623	+	21.6996i	−0.135278	+	0.767198i
$801$		0			0
$802$	9.56414	+	54.2409i	0.337721	+	1.91531i
$803$	9.10058	+	1.06371i	0.321152	+	0.0375373i
$804$		0			0
$805$	0.231444	−	0.245316i	0.00815732	−	0.00864625i
$806$	−30.8211	+	71.4514i	−1.08563	+	2.51677i
$807$		0			0
$808$	124.335	−	81.7763i	4.37408	−	2.87688i
$809$	−1.83823			−0.0646289			−0.0323144	−	0.999478i	$-0.510288\pi$
$809$	−1.83823			−0.0646289			−0.0323144	+	0.999478i	$0.510288\pi$
$810$		0			0
$811$	−8.25761			−0.289964			−0.144982	−	0.989434i	$-0.546312\pi$
$811$	−8.25761			−0.289964			−0.144982	+	0.989434i	$0.546312\pi$
$812$	−3.89283	+	2.56035i	−0.136611	+	0.0898508i
$813$		0			0
$814$	10.7131	−	24.8357i	0.375494	−	0.870492i
$815$	12.7161	−	13.4783i	0.445425	−	0.472123i
$816$		0			0
$817$	−6.37387	−	0.744999i	−0.222994	−	0.0260642i
$818$	−16.3095	−	92.4956i	−0.570248	−	3.23403i
$819$		0			0
$820$	15.2539	−	86.5093i	0.532690	−	3.02104i
$821$	7.32243	−	24.4586i	0.255554	−	0.853611i	−0.729883	−	0.683572i	$-0.760425\pi$
$821$	7.32243	−	24.4586i	0.255554	−	0.853611i	0.985437	−	0.170039i	$-0.0543894\pi$
$822$		0			0
$823$	0.204192	−	3.50585i	0.00711770	−	0.122206i	−0.992878	−	0.119139i	$-0.961987\pi$
$823$	0.204192	−	3.50585i	0.00711770	−	0.122206i	0.999995	−	0.00306726i	$-0.000976340\pi$
$824$	−32.2147	+	16.1789i	−1.12225	+	0.563617i
$825$		0			0
$826$	−4.63820	−	4.91621i	−0.161384	−	0.171057i
$827$	29.3726	−	10.6908i	1.02139	−	0.371754i	0.223591	−	0.974683i	$-0.428222\pi$
$827$	29.3726	−	10.6908i	1.02139	−	0.371754i	0.797795	+	0.602929i	$0.206000\pi$
$828$		0			0
$829$	44.5589	+	16.2181i	1.54759	+	0.563278i	0.967852	−	0.251521i	$-0.0809308\pi$
$829$	44.5589	+	16.2181i	1.54759	+	0.563278i	0.579743	+	0.814800i	$0.303153\pi$
$830$	34.7230	+	80.4969i	1.20525	+	2.79409i
$831$		0			0
$832$	−27.7199	−	92.5910i	−0.961015	−	3.21001i
$833$	9.47964	−	1.10801i	0.328450	−	0.0383903i
$834$		0			0
$835$	−0.945185	−	16.2282i	−0.0327095	−	0.561600i
$836$	4.13831	+	7.16776i	0.143126	+	0.247902i
$837$		0			0
$838$	−36.1825	+	62.6699i	−1.24990	+	2.16489i
$839$	26.5599	+	13.3389i	0.916950	+	0.460509i	0.843707	−	0.536805i	$-0.180369\pi$
$839$	26.5599	+	13.3389i	0.916950	+	0.460509i	0.0732431	+	0.997314i	$0.476665\pi$
$840$		0			0
$841$	−15.4287	−	20.7243i	−0.532024	−	0.714632i
$842$	79.0718	+	18.7404i	2.72499	+	0.645835i
$843$		0			0
$844$	−60.0498	+	80.6609i	−2.06700	+	2.77646i
$845$	−36.5597	+	30.6772i	−1.25769	+	1.05533i
$846$		0			0
$847$	−3.38092	−	2.83693i	−0.116170	−	0.0974780i
$848$	−111.130	+	26.3382i	−3.81621	+	0.904458i
$849$		0			0
$850$	4.50997	+	2.96625i	0.154691	+	0.101742i
$851$	1.43403	+	0.943177i	0.0491580	+	0.0323317i
$852$		0			0
$853$	10.2598	−	2.43161i	0.351287	−	0.0832566i	−0.0511840	−	0.998689i	$-0.516300\pi$
$853$	10.2598	−	2.43161i	0.351287	−	0.0832566i	0.402471	+	0.915433i	$0.368151\pi$
$854$	13.4803	+	11.3113i	0.461286	+	0.387065i
$855$		0			0
$856$	51.0334	−	42.8221i	1.74429	−	1.46363i
$857$	8.85593	−	11.8956i	0.302513	−	0.406345i	−0.624709	−	0.780858i	$-0.714782\pi$
$857$	8.85593	−	11.8956i	0.302513	−	0.406345i	0.927222	+	0.374512i	$0.122190\pi$
$858$		0			0
$859$	30.7582	+	7.28983i	1.04946	+	0.248726i	0.718938	−	0.695074i	$-0.244628\pi$
$859$	30.7582	+	7.28983i	1.04946	+	0.248726i	0.330518	+	0.943800i	$0.392777\pi$
$860$	47.4295	+	63.7088i	1.61733	+	2.17245i
$861$		0			0
$862$	−21.5164	−	10.8059i	−0.732851	−	0.368052i
$863$	1.64562	−	2.85030i	0.0560177	−	0.0970255i	−0.836657	−	0.547728i	$-0.815493\pi$
$863$	1.64562	−	2.85030i	0.0560177	−	0.0970255i	0.892674	+	0.450702i	$0.148826\pi$
$864$		0			0
$865$	−6.19692	−	10.7334i	−0.210701	−	0.364946i
$866$	3.67969	+	63.1778i	0.125041	+	2.14687i
$867$		0			0
$868$	−13.4442	+	1.57140i	−0.456326	+	0.0533369i
$869$	−4.38215	−	14.6374i	−0.148654	−	0.496540i
$870$		0			0
$871$	14.3427	+	33.2501i	0.485983	+	1.12664i
$872$	−1.67013	−	0.607878i	−0.0565577	−	0.0205853i
$873$		0			0
$874$	−0.686052	+	0.249702i	−0.0232060	+	0.00844631i
$875$	−3.17555	−	3.36588i	−0.107353	−	0.113788i
$876$		0			0
$877$	−33.0068	+	16.5766i	−1.11456	+	0.559753i	−0.908122	−	0.418706i	$-0.862484\pi$
$877$	−33.0068	+	16.5766i	−1.11456	+	0.559753i	−0.206439	+	0.978459i	$0.566187\pi$
$878$	0.624763	−	10.7268i	0.0210847	−	0.362011i
$879$		0			0
$880$	13.4500	−	44.9262i	0.453400	−	1.51446i
$881$	5.05857	−	28.6886i	0.170427	−	0.966542i	−0.772863	−	0.634573i	$-0.781176\pi$
$881$	5.05857	−	28.6886i	0.170427	−	0.966542i	0.943290	−	0.331969i	$-0.107713\pi$
$882$		0			0
$883$	−3.27904	−	18.5963i	−0.110348	−	0.625817i	−0.988949	−	0.148259i	$-0.952633\pi$
$883$	−3.27904	−	18.5963i	−0.110348	−	0.625817i	0.878600	−	0.477558i	$-0.158478\pi$
$884$	−40.6897	−	4.75594i	−1.36854	−	0.159960i
$885$		0			0
$886$	14.5790	−	15.4529i	0.489793	−	0.519150i
$887$	9.62067	−	22.3032i	0.323031	−	0.748869i	−0.676888	−	0.736086i	$-0.736672\pi$
$887$	9.62067	−	22.3032i	0.323031	−	0.748869i	0.999918	−	0.0127828i	$-0.00406901\pi$
$888$		0			0
$889$	7.79420	−	5.12633i	0.261409	−	0.171932i
$890$	−66.7543			−2.23761
$891$		0			0
$892$	13.4343			0.449814
$893$	6.41605	−	4.21990i	0.214705	−	0.141214i
$894$		0			0
$895$	0.514730	−	1.19328i	0.0172055	−	0.0398869i
$896$	5.21433	−	5.52686i	0.174198	−	0.184640i
$897$		0			0
$898$	−39.0769	−	4.56744i	−1.30401	−	0.152417i
$899$	1.59569	+	9.04959i	0.0532191	+	0.301821i
$900$		0			0
$901$	−2.33361	+	13.2346i	−0.0777438	+	0.440907i
$902$	−7.95172	+	26.5606i	−0.264763	+	0.884371i
$903$		0			0
$904$	2.69263	−	46.2306i	0.0895555	−	1.53761i
$905$	8.56020	−	4.29909i	0.284551	−	0.142907i
$906$		0			0
$907$	−27.0555	−	28.6772i	−0.898364	−	0.952211i	0.100723	−	0.994914i	$-0.467884\pi$
$907$	−27.0555	−	28.6772i	−0.898364	−	0.952211i	−0.999088	+	0.0427038i	$0.986403\pi$
$908$	−5.95117	+	2.16605i	−0.197496	+	0.0718828i
$909$		0			0
$910$	−18.3325	−	6.67247i	−0.607715	−	0.221190i
$911$	16.3902	+	37.9968i	0.543032	+	1.25889i	0.940037	+	0.341073i	$0.110790\pi$
$911$	16.3902	+	37.9968i	0.543032	+	1.25889i	−0.397004	+	0.917817i	$0.629950\pi$
$912$		0			0
$913$	−5.70889	−	19.0690i	−0.188937	−	0.631092i
$914$	−20.8440	+	2.43631i	−0.689457	+	0.0805860i
$915$		0			0
$916$	−1.46061	−	25.0777i	−0.0482600	−	0.828592i
$917$	−2.05402	−	3.55767i	−0.0678298	−	0.117485i
$918$		0			0
$919$	0.677038	−	1.17266i	0.0223334	−	0.0386826i	−0.854643	−	0.519217i	$-0.826224\pi$
$919$	0.677038	−	1.17266i	0.0223334	−	0.0386826i	0.876976	+	0.480534i	$0.159557\pi$
$920$	4.92526	+	2.47356i	0.162381	+	0.0815509i
$921$		0			0
$922$	−5.26713	−	7.07498i	−0.173464	−	0.233002i
$923$	−28.3464	−	6.71822i	−0.933034	−	0.221133i
$924$		0			0
$925$	−5.62012	+	7.54913i	−0.184788	+	0.248214i
$926$	36.2019	−	30.3770i	1.18967	−	0.998250i
$927$		0			0
$928$	−21.0279	−	17.6445i	−0.690274	−	0.579209i
$929$	−25.9999	+	6.16209i	−0.853029	+	0.202172i	−0.633796	−	0.773501i	$-0.718504\pi$
$929$	−25.9999	+	6.16209i	−0.853029	+	0.202172i	−0.219234	+	0.975672i	$0.570356\pi$
$930$		0			0
$931$	−5.91362	−	3.88945i	−0.193811	−	0.127472i
$932$	16.3823	+	10.7748i	0.536619	+	0.352940i
$933$		0			0
$934$	103.543	−	24.5400i	3.38802	−	0.802975i
$935$	−4.22721	−	3.54705i	−0.138244	−	0.116001i
$936$		0			0
$937$	−2.08507	+	1.74958i	−0.0681162	+	0.0571563i	−0.676210	−	0.736709i	$-0.736379\pi$
$937$	−2.08507	+	1.74958i	−0.0681162	+	0.0571563i	0.608094	+	0.793865i	$0.291934\pi$
$938$	−5.22860	+	7.02323i	−0.170720	+	0.229317i
$939$		0			0
$940$	−92.4845	−	21.9192i	−3.01651	−	0.714926i
$941$	13.6172	+	18.2911i	0.443908	+	0.596272i	0.966613	−	0.256242i	$-0.0824844\pi$
$941$	13.6172	+	18.2911i	0.443908	+	0.596272i	−0.522705	+	0.852514i	$0.675077\pi$
$942$		0			0
$943$	−1.57225	−	0.789615i	−0.0511996	−	0.0257134i
$944$	29.8195	−	51.6488i	0.970541	−	1.68103i
$945$		0			0
$946$	−12.5341	−	21.7097i	−0.407520	−	0.705845i
$947$	−0.952785	−	16.3587i	−0.0309613	−	0.531586i	−0.977756	−	0.209747i	$-0.932736\pi$
$947$	−0.952785	−	16.3587i	−0.0309613	−	0.531586i	0.946794	−	0.321839i	$-0.104301\pi$
$948$		0			0
$949$	33.4058	−	3.90458i	1.08440	−	0.126748i
$950$	−1.14813	−	3.83503i	−0.0372504	−	0.124425i
$951$		0			0
$952$	−2.39305	−	5.54772i	−0.0775593	−	0.179803i
$953$	33.5144	+	12.1982i	1.08564	+	0.395140i	0.822003	−	0.569483i	$-0.192857\pi$
$953$	33.5144	+	12.1982i	1.08564	+	0.395140i	0.263634	+	0.964623i	$0.415079\pi$
$954$		0			0
$955$	−53.9877	+	19.6499i	−1.74700	+	0.635857i
$956$	31.8340	+	33.7420i	1.02958	+	1.09129i
$957$		0			0
$958$	93.5000	−	46.9574i	3.02085	−	1.51713i
$959$	−0.253484	+	4.35215i	−0.00818542	+	0.140538i
$960$		0			0
$961$	1.23462	−	4.12391i	0.0398263	−	0.133029i
$962$	17.2407	−	97.7770i	0.555863	−	3.15246i
$963$		0			0
$964$	−20.8580	−	118.292i	−0.671791	−	3.80992i
$965$	−14.4126	−	1.68459i	−0.463958	−	0.0542289i
$966$		0			0
$967$	5.52220	−	5.85319i	0.177582	−	0.188226i	−0.632469	−	0.774586i	$-0.717958\pi$
$967$	5.52220	−	5.85319i	0.177582	−	0.188226i	0.810050	+	0.586360i	$0.199440\pi$
$968$	28.5671	−	66.2259i	0.918180	−	2.12858i
$969$		0			0
$970$	20.3411	−	13.3785i	0.653113	−	0.429559i
$971$	−44.9410			−1.44223			−0.721113	−	0.692818i	$-0.756369\pi$
$971$	−44.9410			−1.44223			−0.721113	+	0.692818i	$0.756369\pi$
$972$		0			0
$973$	6.66731			0.213744
$974$	78.1977	−	51.4314i	2.50562	−	1.64797i
$975$		0			0
$976$	−61.5013	+	142.576i	−1.96861	+	4.56375i
$977$	19.0563	−	20.1985i	0.609664	−	0.646206i	−0.346840	−	0.937924i	$-0.612745\pi$
$977$	19.0563	−	20.1985i	0.609664	−	0.646206i	0.956504	+	0.291718i	$0.0942269\pi$
$978$		0			0
$979$	15.0545	+	1.75962i	0.481144	+	0.0562377i
$980$	15.2122	+	86.2728i	0.485936	+	2.75588i
$981$		0			0
$982$	−9.54176	+	54.1140i	−0.304490	+	1.72685i
$983$	2.00822	−	6.70794i	0.0640524	−	0.213950i	−0.919972	−	0.391984i	$-0.871789\pi$
$983$	2.00822	−	6.70794i	0.0640524	−	0.213950i	0.984024	+	0.178035i	$0.0569739\pi$
$984$		0			0
$985$	−0.356736	+	6.12492i	−0.0113666	+	0.195156i
$986$	−6.00943	+	3.01805i	−0.191379	+	0.0961143i
$987$		0			0
$988$	20.8489	+	22.0985i	0.663292	+	0.703048i
$989$	1.49485	−	0.544079i	0.0475333	−	0.0173007i
$990$		0			0
$991$	55.0238	+	20.0270i	1.74789	+	0.636179i	0.999629	−	0.0272280i	$-0.00866800\pi$
$991$	55.0238	+	20.0270i	1.74789	+	0.636179i	0.748259	+	0.663407i	$0.230890\pi$
$992$	−31.5850	−	73.2223i	−1.00283	−	2.32481i
$993$		0			0
$994$	−2.02021	−	6.74799i	−0.0640773	−	0.214033i
$995$	−24.6411	+	2.88014i	−0.781176	+	0.0913064i
$996$		0			0
$997$	2.23842	+	38.4322i	0.0708916	+	1.21716i	0.826805	+	0.562489i	$0.190156\pi$
$997$	2.23842	+	38.4322i	0.0708916	+	1.21716i	−0.755913	+	0.654672i	$0.772807\pi$
$998$	11.0063	+	19.0635i	0.348400	+	0.603446i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.g.c.28.8		144
3.2	odd	2		729.2.g.b.28.1		144
9.2	odd	6		243.2.g.a.10.8		144
9.4	even	3		729.2.g.d.514.8		144
9.5	odd	6		729.2.g.a.514.1		144
9.7	even	3		81.2.g.a.13.1	✓	144
81.2	odd	54		243.2.g.a.73.8		144
81.25	even	27		729.2.g.d.217.8		144
81.29	odd	54		729.2.g.b.703.1		144
81.32	odd	54		6561.2.a.d.1.71		72
81.49	even	27		6561.2.a.c.1.2		72
81.52	even	27	inner	729.2.g.c.703.8		144
81.56	odd	54		729.2.g.a.217.1		144
81.79	even	27		81.2.g.a.25.1	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.13.1	✓	144	9.7	even	3
81.2.g.a.25.1	yes	144	81.79	even	27
243.2.g.a.10.8		144	9.2	odd	6
243.2.g.a.73.8		144	81.2	odd	54
729.2.g.a.217.1		144	81.56	odd	54
729.2.g.a.514.1		144	9.5	odd	6
729.2.g.b.28.1		144	3.2	odd	2
729.2.g.b.703.1		144	81.29	odd	54
729.2.g.c.28.8		144	1.1	even	1	trivial
729.2.g.c.703.8		144	81.52	even	27	inner
729.2.g.d.217.8		144	81.25	even	27
729.2.g.d.514.8		144	9.4	even	3
6561.2.a.c.1.2		72	81.49	even	27
6561.2.a.d.1.71		72	81.32	odd	54

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(2.23053 - 1.46704i) q^{2} +(2.03089 - 4.70814i) q^{4} +(1.73981 - 1.84410i) q^{5} +(-0.507474 - 0.0593153i) q^{7} +(-1.44988 - 8.22270i) q^{8} +O(q^{10})\)	\(q+(2.23053 - 1.46704i) q^{2} +(2.03089 - 4.70814i) q^{4} +(1.73981 - 1.84410i) q^{5} +(-0.507474 - 0.0593153i) q^{7} +(-1.44988 - 8.22270i) q^{8} +(1.17534 - 6.66569i) q^{10} +(-0.440769 + 1.47227i) q^{11} +(-0.328014 + 5.63177i) q^{13} +(-1.21896 + 0.612182i) q^{14} +(-8.25967 - 8.75474i) q^{16} +(-1.33086 + 0.484393i) q^{17} +(0.986977 + 0.359230i) q^{19} +(-5.14888 - 11.9364i) q^{20} +(1.17674 + 3.93058i) q^{22} +(-0.258604 + 0.0302265i) q^{23} +(-0.0830100 - 1.42523i) q^{25} +(7.53041 + 13.0431i) q^{26} +(-1.30989 + 2.26880i) q^{28} +(1.58935 + 0.798201i) q^{29} +(3.08537 + 4.14437i) q^{31} +(-15.0181 - 3.55935i) q^{32} +(-2.25790 + 3.03288i) q^{34} +(-0.992294 + 0.832634i) q^{35} +(-5.04999 - 4.23745i) q^{37} +(2.72849 - 0.646664i) q^{38} +(-17.6860 - 11.6322i) q^{40} +(5.64575 + 3.71327i) q^{41} +(-5.94513 + 1.40902i) q^{43} +(6.03650 + 5.06523i) q^{44} +(-0.532481 + 0.446804i) q^{46} +(4.36612 - 5.86472i) q^{47} +(-6.55730 - 1.55411i) q^{49} +(-2.27603 - 3.05723i) q^{50} +(25.8490 + 12.9819i) q^{52} +(4.74440 - 8.21755i) q^{53} +(1.94815 + 3.37430i) q^{55} +(0.248047 + 4.25881i) q^{56} +(4.71609 - 0.551232i) q^{58} +(1.42111 + 4.74684i) q^{59} +(-5.10974 - 11.8457i) q^{61} +(12.9620 + 4.71777i) q^{62} +(-16.0995 + 5.85975i) q^{64} +(9.81485 + 10.4031i) q^{65} +(5.73622 - 2.88084i) q^{67} +(-0.422242 + 7.24961i) q^{68} +(-0.991833 + 3.31295i) q^{70} +(-0.896716 + 5.08553i) q^{71} +(-1.03528 - 5.87137i) q^{73} +(-17.4807 - 2.04320i) q^{74} +(3.69575 - 3.91726i) q^{76} +(0.311007 - 0.720996i) q^{77} +(-8.30647 + 5.46325i) q^{79} -30.5149 q^{80} +18.0405 q^{82} +(-10.8213 + 7.11730i) q^{83} +(-1.42218 + 3.29699i) q^{85} +(-11.1937 + 11.8646i) q^{86} +(12.7451 + 1.48969i) q^{88} +(-1.71260 - 9.71264i) q^{89} +(0.500509 - 2.83853i) q^{91} +(-0.382886 + 1.27893i) q^{92} +(1.13497 - 19.4867i) q^{94} +(2.37961 - 1.19509i) q^{95} +(2.46841 + 2.61636i) q^{97} +(-16.9062 + 6.15336i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8}+O(q^{10}) \) 144 * q + 9 * q^2 + 9 * q^4 + 9 * q^5 + 9 * q^7 - 18 * q^8	\( 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8} - 18 q^{10} + 9 q^{11} + 9 q^{13} + 9 q^{14} + 9 q^{16} - 18 q^{17} - 18 q^{19} - 63 q^{20} + 9 q^{22} + 36 q^{23} + 9 q^{25} + 45 q^{26} - 9 q^{28} - 45 q^{29} + 9 q^{31} + 63 q^{32} + 9 q^{34} + 9 q^{35} - 18 q^{37} - 9 q^{38} + 9 q^{40} - 27 q^{41} + 9 q^{43} + 54 q^{44} - 18 q^{46} + 63 q^{47} + 9 q^{49} - 225 q^{50} + 27 q^{52} + 45 q^{53} - 9 q^{55} + 99 q^{56} + 9 q^{58} - 117 q^{59} + 9 q^{61} + 81 q^{62} - 18 q^{64} + 81 q^{65} + 36 q^{67} - 18 q^{68} + 63 q^{70} - 90 q^{71} - 18 q^{73} + 81 q^{74} + 90 q^{76} + 81 q^{77} + 63 q^{79} - 288 q^{80} - 36 q^{82} + 45 q^{83} + 63 q^{85} + 81 q^{86} + 90 q^{88} - 81 q^{89} - 18 q^{91} - 63 q^{92} + 63 q^{94} + 153 q^{95} + 36 q^{97} + 81 q^{98}+O(q^{100}) \) 144 * q + 9 * q^2 + 9 * q^4 + 9 * q^5 + 9 * q^7 - 18 * q^8 - 18 * q^10 + 9 * q^11 + 9 * q^13 + 9 * q^14 + 9 * q^16 - 18 * q^17 - 18 * q^19 - 63 * q^20 + 9 * q^22 + 36 * q^23 + 9 * q^25 + 45 * q^26 - 9 * q^28 - 45 * q^29 + 9 * q^31 + 63 * q^32 + 9 * q^34 + 9 * q^35 - 18 * q^37 - 9 * q^38 + 9 * q^40 - 27 * q^41 + 9 * q^43 + 54 * q^44 - 18 * q^46 + 63 * q^47 + 9 * q^49 - 225 * q^50 + 27 * q^52 + 45 * q^53 - 9 * q^55 + 99 * q^56 + 9 * q^58 - 117 * q^59 + 9 * q^61 + 81 * q^62 - 18 * q^64 + 81 * q^65 + 36 * q^67 - 18 * q^68 + 63 * q^70 - 90 * q^71 - 18 * q^73 + 81 * q^74 + 90 * q^76 + 81 * q^77 + 63 * q^79 - 288 * q^80 - 36 * q^82 + 45 * q^83 + 63 * q^85 + 81 * q^86 + 90 * q^88 - 81 * q^89 - 18 * q^91 - 63 * q^92 + 63 * q^94 + 153 * q^95 + 36 * q^97 + 81 * q^98

Introduction

L-functions

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