LMFDB - Embedded newform 729.2.g.b.28.1

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			28.1
Character	$\chi$	$=$	729.28
Dual form			729.2.g.b.703.1

$q$-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	$0.707682\pi$
$2$	−2.23053	+	1.46704i	−1.57722	+	1.03736i	−0.970087	+	0.242758i	$0.921948\pi$
$3$		0			0
$3$		0			0
$4$	2.03089	−	4.70814i	1.01545	−	2.35407i
$5$	−1.73981	+	1.84410i	−0.778069	+	0.824705i	−0.988232	−	0.152962i	$-0.951119\pi$
$5$	−1.73981	+	1.84410i	−0.778069	+	0.824705i	0.210163	+	0.977666i	$0.432600\pi$
$6$		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	−0.865475	−	0.500953i	$-0.832983\pi$
$11$	0.440769	−	1.47227i	0.132897	−	0.443907i	0.998372	+	0.0570461i	$0.0181682\pi$
$12$		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	−0.175548	−	0.984471i	$-0.556170\pi$
$17$	1.33086	−	0.484393i	0.322781	−	0.117483i	0.498328	+	0.866988i	$0.333947\pi$
$18$		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	−0.0890888	−	0.996024i	$-0.528395\pi$
$23$	0.258604	−	0.0302265i	0.0539227	−	0.00630266i	0.143011	+	0.989721i	$0.454321\pi$
$24$		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	0.295070	−	0.955475i	$-0.404657\pi$
$29$	−1.58935	−	0.798201i	−0.295135	−	0.148222i	−0.590205	+	0.807253i	$0.700953\pi$
$30$		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	0.0259221	−	0.999664i	$-0.491748\pi$
$41$	−5.64575	−	3.71327i	−0.881718	−	0.579915i	−0.907640	+	0.419749i	$0.862118\pi$
$42$		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	−0.996997	−	0.0774440i	$-0.975324\pi$
$47$	−4.36612	+	5.86472i	−0.636864	+	0.855457i	0.360132	+	0.932901i	$0.382732\pi$
$48$		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	$0.392608\pi$
$53$	−4.74440	+	8.21755i	−0.651694	+	1.12877i	−0.982712	+	0.185142i	$0.940725\pi$
$54$		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	$-0.988055\pi$
$59$	−1.42111	−	4.74684i	−0.185013	−	0.617986i	0.814283	−	0.580468i	$-0.197130\pi$
$60$		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	$-0.845311\pi$
$71$	0.896716	−	5.08553i	0.106421	−	0.603541i	0.990643	−	0.136476i	$-0.0435776\pi$
$72$		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	0.207397	−	0.978257i	$-0.433501\pi$
$83$	10.8213	−	7.11730i	1.18779	−	0.781225i	0.980397	+	0.197032i	$0.0631303\pi$
$84$		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	$0.119523\pi$
$89$	1.71260	+	9.71264i	0.181535	+	1.02954i	−0.748791	+	0.662806i	$0.769366\pi$
$90$		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	$-0.782590\pi$
$101$	−7.05948	−	16.3657i	−0.702444	−	1.62845i	0.0732293	−	0.997315i	$-0.476669\pi$
$102$		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	0.606192	−	0.795319i	$-0.292696\pi$
$107$	−3.98940	−	6.90985i	−0.385670	−	0.668000i	−0.991862	+	0.127318i	$0.959363\pi$
$108$		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	−0.0312133	−	0.999513i	$-0.509937\pi$
$113$	−5.39679	−	1.27906i	−0.507687	−	0.120324i	−0.476474	+	0.879189i	$0.658085\pi$
$114$		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	0.541267	−	0.840851i	$-0.317945\pi$
$131$	−4.80136	−	6.44934i	−0.419497	−	0.563482i	−0.960763	+	0.277369i	$0.910537\pi$
$132$		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	$0.100239\pi$
$137$	0.496123	+	8.51811i	0.0423867	+	0.727751i	−0.908438	+	0.418020i	$0.862724\pi$
$138$		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	$0.251485\pi$
$149$	−0.948613	+	16.2871i	−0.0777134	+	1.33429i	−0.781513	+	0.623889i	$0.785552\pi$
$150$		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	−0.874878	−	0.484343i	$-0.839059\pi$
$167$	−4.40004	+	4.66377i	−0.340486	+	0.360894i	0.534393	+	0.845236i	$0.320540\pi$
$168$		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	−0.994600	−	0.103780i	$-0.966906\pi$
$173$	−1.40205	+	4.68318i	−0.106596	+	0.356055i	0.888004	+	0.459835i	$0.152091\pi$
$174$		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	−0.359959	−	0.932968i	$-0.617209\pi$
$179$	−0.481678	+	0.175316i	−0.0360023	+	0.0131038i	0.323956	+	0.946072i	$0.394987\pi$
$180$		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	0.989618	−	0.143719i	$-0.0459063\pi$
$191$	20.2508	+	10.1703i	1.46530	+	0.735900i	0.475678	+	0.879619i	$0.342203\pi$
$192$		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	−0.574356	−	0.818606i	$-0.694747\pi$
$197$	1.85381	−	1.55553i	0.132078	−	0.110827i	0.706434	+	0.707779i	$0.250303\pi$
$198$		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	0.754891	−	0.655850i	$-0.227690\pi$
$227$	0.847597	+	0.898400i	0.0562570	+	0.0596289i	−0.698634	+	0.715479i	$0.746208\pi$
$228$		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	−0.955299	−	0.295640i	$-0.904467\pi$
$233$	0.664049	−	3.76601i	0.0435033	−	0.246719i	0.998803	+	0.0489208i	$0.0155782\pi$
$234$		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	−0.762135	−	0.647419i	$-0.775849\pi$
$239$	3.58337	−	8.30719i	0.231789	−	0.537348i	0.993924	+	0.110071i	$0.0351078\pi$
$240$		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	$0.0716851\pi$
$251$	2.14133	+	12.1441i	0.135160	+	0.766530i	−0.839588	+	0.543223i	$0.817204\pi$
$252$		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	$0.723222\pi$
$257$	−26.3443	+	13.2306i	−1.64331	+	0.825302i	−0.998121	+	0.0612816i	$0.980481\pi$
$258$		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	$0.0892854\pi$
$263$	8.15499	+	18.9054i	0.502858	+	1.16576i	−0.458060	+	0.888922i	$0.651455\pi$
$264$		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	0.989730	−	0.142951i	$-0.0456591\pi$
$269$	6.08593	+	10.5411i	0.371066	+	0.642705i	−0.618664	+	0.785656i	$0.712326\pi$
$270$		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	0.324678	−	0.945825i	$-0.394744\pi$
$281$	17.4219	−	4.12908i	1.03931	−	0.246320i	0.714628	+	0.699505i	$0.246596\pi$
$282$		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	0.745303	−	0.666726i	$-0.232305\pi$
$293$	−1.83443	−	2.46406i	−0.107168	−	0.143952i	−0.852472	+	0.522774i	$0.824897\pi$
$294$		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	$0.0479045\pi$
$311$	−0.189058	+	3.24600i	−0.0107205	+	0.184064i	−0.999417	+	0.0341346i	$0.989133\pi$
$312$		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	0.666977	−	0.745078i	$-0.267588\pi$
$317$	20.3710	+	2.38103i	1.14415	+	0.133732i	0.477172	+	0.878810i	$0.341662\pi$
$318$		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	0.528058	−	0.849209i	$-0.322920\pi$
$347$	23.0562	−	2.69489i	1.23772	−	0.144669i	0.709665	+	0.704539i	$0.248846\pi$
$348$		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	0.181179	−	0.983450i	$-0.442009\pi$
$353$	−9.38433	−	4.71299i	−0.499477	−	0.250847i	−0.680656	+	0.732603i	$0.738305\pi$
$354$		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	$0.580955\pi$
$359$	−23.6540	+	19.8481i	−1.24841	+	1.04754i	−0.996818	+	0.0797090i	$0.974601\pi$
$360$		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	$0.0304216\pi$
$383$	4.23110	+	14.1329i	0.216199	+	0.722156i	−0.779237	+	0.626729i	$0.784393\pi$
$384$		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	0.358283	−	0.933613i	$-0.383362\pi$
$389$	−11.7270	−	12.4299i	−0.594583	−	0.630221i	−0.952866	+	0.303392i	$0.901881\pi$
$390$		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	$-0.698119\pi$
$401$	8.17128	−	18.9432i	0.408054	−	0.945976i	0.991049	−	0.133500i	$-0.0426216\pi$
$402$		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	0.255336	−	0.966852i	$-0.417814\pi$
$419$	24.2225	−	12.1650i	1.18335	−	0.594299i	0.928011	+	0.372553i	$0.121518\pi$
$420$		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	0.953953	−	0.299956i	$-0.0969720\pi$
$431$	4.50933	+	7.81039i	0.217207	+	0.376213i	−0.736746	+	0.676170i	$0.763639\pi$
$432$		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	−0.410402	−	0.911905i	$-0.634611\pi$
$443$	−7.74314	+	1.83516i	−0.367888	+	0.0871909i	0.0425140	+	0.999096i	$0.486463\pi$
$444$		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	0.869052	−	0.494720i	$-0.164729\pi$
$449$	11.2889	+	9.47253i	0.532757	+	0.447037i	−0.336295	+	0.941757i	$0.609174\pi$
$450$		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	$0.00599554\pi$
$461$	0.192100	+	3.29823i	0.00894699	+	0.153614i	−0.990876	+	0.134779i	$0.956967\pi$
$462$		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	−0.734338	−	0.678784i	$-0.762507\pi$
$467$	−37.4545	−	13.6323i	−1.73319	−	0.630829i	−0.998849	+	0.0479555i	$0.984729\pi$
$468$		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	−0.837577	−	0.546320i	$-0.816028\pi$
$479$	−38.9258	−	4.54978i	−1.77857	−	0.207885i	−0.940990	+	0.338435i	$0.890102\pi$
$480$		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	−0.325459	−	0.945556i	$-0.605519\pi$
$491$	14.1243	−	14.9709i	0.637421	−	0.675627i	0.962880	+	0.269929i	$0.0870003\pi$
$492$		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	−0.672941	−	0.739696i	$-0.734969\pi$
$503$	−15.9904	+	5.82003i	−0.712977	+	0.259503i	−0.0400358	+	0.999198i	$0.512747\pi$
$504$		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	−0.469264	−	0.883058i	$-0.655481\pi$
$509$	−16.2943	+	1.90453i	−0.722232	+	0.0844168i	−0.252968	+	0.967475i	$0.581407\pi$
$510$		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	−0.417205	−	0.908812i	$-0.636990\pi$
$521$	9.25237	−	7.76366i	0.405354	−	0.340132i	0.822559	+	0.568680i	$0.192546\pi$
$522$		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	$0.229623\pi$
$557$	−4.26215	+	24.1719i	−0.180593	+	1.02420i	−0.931488	+	0.363773i	$0.881488\pi$
$558$		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	−0.966924	−	0.255066i	$-0.917903\pi$
$563$	−2.79634	+	6.48265i	−0.117852	+	0.273211i	0.849072	+	0.528278i	$0.177162\pi$
$564$		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	−0.688976	−	0.724784i	$-0.741940\pi$
$569$	−7.06923	+	4.64950i	−0.296357	+	0.194917i	0.392619	+	0.919701i	$0.371569\pi$
$570$		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	$0.146202\pi$
$587$	14.6266	+	33.9083i	0.603705	+	1.39955i	−0.292655	+	0.956218i	$0.594539\pi$
$588$		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	0.841293	−	0.540579i	$-0.181795\pi$
$593$	−1.15692	−	2.00385i	−0.0475091	−	0.0822881i	−0.888802	+	0.458291i	$0.848462\pi$
$594$		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	0.0670358	−	0.997751i	$-0.478646\pi$
$599$	−7.85260	−	1.86110i	−0.320848	−	0.0760425i	−0.387884	+	0.921708i	$0.626794\pi$
$600$		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	0.633422	−	0.773807i	$-0.281650\pi$
$617$	−7.19212	−	9.66070i	−0.289544	−	0.388925i	−0.922966	+	0.384881i	$0.874242\pi$
$618$		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	−0.340523	−	0.940236i	$-0.610604\pi$
$641$	−22.5001	−	2.62988i	−0.888700	−	0.103874i	−0.548177	+	0.836362i	$0.684678\pi$
$642$		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	$-0.370058\pi$
$647$	20.1953			0.793960			0.396980	+	0.917827i	$0.370058\pi$
$648$		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	−0.417363	−	0.908740i	$-0.637046\pi$
$653$	13.1374	−	13.9248i	0.514107	−	0.544921i	0.931470	+	0.363819i	$0.118527\pi$
$654$		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	$0.388605\pi$
$659$	−11.8035	+	39.4263i	−0.459798	+	1.53583i	−0.802655	+	0.596444i	$0.796580\pi$
$660$		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	0.418143	−	0.908381i	$-0.362681\pi$
$677$	−1.58178	−	0.794398i	−0.0607926	−	0.0305312i	−0.478936	+	0.877850i	$0.658977\pi$
$678$		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	−0.912987	−	0.407989i	$-0.866230\pi$
$683$	−17.5030	+	14.6868i	−0.669734	+	0.561973i	0.243253	+	0.969963i	$0.421786\pi$
$684$		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	−0.513944	−	0.857824i	$-0.671816\pi$
$701$	12.8656	−	22.2838i	0.485926	−	0.841648i	0.999869	+	0.0161763i	$0.00514928\pi$
$702$		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	−0.977060	−	0.212965i	$-0.931688\pi$
$719$	0.373099	−	2.11595i	0.0139143	−	0.0789116i	0.990974	+	0.134053i	$0.0427992\pi$
$720$		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	−0.349388	−	0.936978i	$-0.613611\pi$
$743$	5.27562	−	2.64951i	0.193544	−	0.0972012i	0.542932	+	0.839777i	$0.317314\pi$
$744$		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	0.875746	−	0.482771i	$-0.160370\pi$
$761$	39.7704	+	9.42575i	1.44167	+	0.341683i	0.565928	+	0.824455i	$0.308518\pi$
$762$		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	0.139077	−	0.990282i	$-0.455586\pi$
$773$	−22.5762	−	18.9437i	−0.812009	−	0.681356i	−0.951086	+	0.308925i	$0.900031\pi$
$774$		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

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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