LMFDB - Embedded newform 729.2.g.a.55.1

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			55.1
Character	$\chi$	$=$	729.55
Dual form			729.2.g.a.676.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.900807 + 2.08831i) q^{2} +(-2.17708 - 2.30757i) q^{4} +(-0.0341238 - 0.585883i) q^{5} +(3.70692 + 0.878555i) q^{7} +(2.50575 - 0.912019i) q^{8} +O(q^{10})$	\(q+(-0.900807 + 2.08831i) q^{2} +(-2.17708 - 2.30757i) q^{4} +(-0.0341238 - 0.585883i) q^{5} +(3.70692 + 0.878555i) q^{7} +(2.50575 - 0.912019i) q^{8} +(1.25424 + 0.456507i) q^{10} +(-4.16873 - 2.74182i) q^{11} +(2.46908 + 0.288594i) q^{13} +(-5.17391 + 6.94977i) q^{14} +(0.0163015 - 0.279887i) q^{16} +(2.18854 - 1.83640i) q^{17} +(0.319901 + 0.268429i) q^{19} +(-1.27768 + 1.35426i) q^{20} +(9.48097 - 6.23573i) q^{22} +(7.15813 - 1.69651i) q^{23} +(4.62410 - 0.540479i) q^{25} +(-2.82684 + 4.89622i) q^{26} +(-6.04293 - 10.4667i) q^{28} +(3.15459 + 4.23736i) q^{29} +(-0.842702 + 2.81482i) q^{31} +(5.33566 + 2.67967i) q^{32} +(1.86352 + 6.22458i) q^{34} +(0.388237 - 2.20180i) q^{35} +(-1.09265 - 6.19675i) q^{37} +(-0.848730 + 0.426248i) q^{38} +(-0.619842 - 1.43696i) q^{40} +(1.44585 + 3.35186i) q^{41} +(-5.37705 + 2.70046i) q^{43} +(2.74873 + 15.5888i) q^{44} +(-2.90527 + 16.4766i) q^{46} +(1.88833 + 6.30747i) q^{47} +(6.71394 + 3.37187i) q^{49} +(-3.03673 + 10.1434i) q^{50} +(-4.70944 - 6.32588i) q^{52} +(-1.23882 - 2.14569i) q^{53} +(-1.46413 + 2.53595i) q^{55} +(10.0899 - 1.17934i) q^{56} +(-11.6906 + 2.77072i) q^{58} +(3.87162 - 2.54640i) q^{59} +(-7.81976 + 8.28846i) q^{61} +(-5.11909 - 4.29543i) q^{62} +(-9.97283 + 8.36820i) q^{64} +(0.0848280 - 1.45644i) q^{65} +(3.55143 - 4.77040i) q^{67} +(-9.00226 - 1.05221i) q^{68} +(4.24831 + 2.79416i) q^{70} +(-2.65492 - 0.966311i) q^{71} +(12.9084 - 4.69828i) q^{73} +(13.9250 + 3.30028i) q^{74} +(-0.0770319 - 1.32259i) q^{76} +(-13.0443 - 13.8261i) q^{77} +(4.97764 - 11.5395i) q^{79} -0.164537 q^{80} -8.30214 q^{82} +(-0.831044 + 1.92658i) q^{83} +(-1.15060 - 1.21956i) q^{85} +(-0.795693 - 13.6615i) q^{86} +(-12.9464 - 3.06835i) q^{88} +(0.324629 - 0.118155i) q^{89} +(8.89913 + 3.23902i) q^{91} +(-19.4987 - 12.8245i) q^{92} +(-14.8729 - 1.73840i) q^{94} +(0.146352 - 0.196584i) q^{95} +(-0.637880 + 10.9520i) q^{97} +(-13.0895 + 10.9834i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8}+O(q^{10}) $ 144 * q - 9 * q^2 + 9 * q^4 - 9 * q^5 + 9 * q^7 + 18 * q^8	$ 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8} - 18 q^{10} - 9 q^{11} + 9 q^{13} - 9 q^{14} + 9 q^{16} + 18 q^{17} - 18 q^{19} - 45 q^{20} + 9 q^{22} + 45 q^{23} + 9 q^{25} - 45 q^{26} - 9 q^{28} - 36 q^{29} + 9 q^{31} + 99 q^{32} + 9 q^{34} - 9 q^{35} - 18 q^{37} - 18 q^{38} + 9 q^{40} - 27 q^{41} + 9 q^{43} - 54 q^{44} - 18 q^{46} + 99 q^{47} + 9 q^{49} - 126 q^{50} - 27 q^{52} - 45 q^{53} - 9 q^{55} + 225 q^{56} + 9 q^{58} - 72 q^{59} + 9 q^{61} - 81 q^{62} - 18 q^{64} + 81 q^{65} - 45 q^{67} - 117 q^{68} - 99 q^{70} + 90 q^{71} - 18 q^{73} - 81 q^{74} - 153 q^{76} - 81 q^{77} - 99 q^{79} + 288 q^{80} - 36 q^{82} - 45 q^{83} - 99 q^{85} - 81 q^{86} - 153 q^{88} + 81 q^{89} - 18 q^{91} - 207 q^{92} - 99 q^{94} + 171 q^{95} - 45 q^{97} - 81 q^{98}+O(q^{100}) $ 144 * q - 9 * q^2 + 9 * q^4 - 9 * q^5 + 9 * q^7 + 18 * q^8 - 18 * q^10 - 9 * q^11 + 9 * q^13 - 9 * q^14 + 9 * q^16 + 18 * q^17 - 18 * q^19 - 45 * q^20 + 9 * q^22 + 45 * q^23 + 9 * q^25 - 45 * q^26 - 9 * q^28 - 36 * q^29 + 9 * q^31 + 99 * q^32 + 9 * q^34 - 9 * q^35 - 18 * q^37 - 18 * q^38 + 9 * q^40 - 27 * q^41 + 9 * q^43 - 54 * q^44 - 18 * q^46 + 99 * q^47 + 9 * q^49 - 126 * q^50 - 27 * q^52 - 45 * q^53 - 9 * q^55 + 225 * q^56 + 9 * q^58 - 72 * q^59 + 9 * q^61 - 81 * q^62 - 18 * q^64 + 81 * q^65 - 45 * q^67 - 117 * q^68 - 99 * q^70 + 90 * q^71 - 18 * q^73 - 81 * q^74 - 153 * q^76 - 81 * q^77 - 99 * q^79 + 288 * q^80 - 36 * q^82 - 45 * q^83 - 99 * q^85 - 81 * q^86 - 153 * q^88 + 81 * q^89 - 18 * q^91 - 207 * q^92 - 99 * q^94 + 171 * q^95 - 45 * q^97 - 81 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.900807	+	2.08831i	−0.636967	+	1.47665i	0.227404	+	0.973800i	$0.426976\pi$
$2$	−0.900807	+	2.08831i	−0.636967	+	1.47665i	−0.864371	+	0.502855i	$0.832283\pi$
$3$		0			0
$3$		0			0
$4$	−2.17708	−	2.30757i	−1.08854	−	1.15379i
$5$	−0.0341238	−	0.585883i	−0.0152606	−	0.262015i	−0.997305	−	0.0733655i	$-0.976626\pi$
$5$	−0.0341238	−	0.585883i	−0.0152606	−	0.262015i	0.982044	−	0.188650i	$-0.0604110\pi$
$6$		0			0
$7$	3.70692	+	0.878555i	1.40108	+	0.332063i	0.860595	−	0.509289i	$-0.170092\pi$
$7$	3.70692	+	0.878555i	1.40108	+	0.332063i	0.540487	+	0.841352i	$0.318240\pi$
$8$	2.50575	−	0.912019i	0.885917	−	0.322447i
$9$		0			0
$10$	1.25424	+	0.456507i	0.396626	+	0.144360i
$11$	−4.16873	−	2.74182i	−1.25692	−	0.826689i	−0.266373	−	0.963870i	$-0.585825\pi$
$11$	−4.16873	−	2.74182i	−1.25692	−	0.826689i	−0.990546	+	0.137181i	$0.956196\pi$
$12$		0			0
$13$	2.46908	+	0.288594i	0.684799	+	0.0800416i	0.451376	−	0.892334i	$-0.350933\pi$
$13$	2.46908	+	0.288594i	0.684799	+	0.0800416i	0.233423	+	0.972375i	$0.425007\pi$
$14$	−5.17391	+	6.94977i	−1.38279	+	1.85740i
$15$		0			0
$16$	0.0163015	−	0.279887i	0.00407538	−	0.0699716i
$17$	2.18854	−	1.83640i	0.530799	−	0.445393i	−0.337578	−	0.941297i	$-0.609608\pi$
$17$	2.18854	−	1.83640i	0.530799	−	0.445393i	0.868377	+	0.495904i	$0.165163\pi$
$18$		0			0
$19$	0.319901	+	0.268429i	0.0733903	+	0.0615818i	0.678745	−	0.734374i	$-0.262524\pi$
$19$	0.319901	+	0.268429i	0.0733903	+	0.0615818i	−0.605355	+	0.795956i	$0.706969\pi$
$20$	−1.27768	+	1.35426i	−0.285698	+	0.302822i
$21$		0			0
$22$	9.48097	−	6.23573i	2.02135	−	1.32946i
$23$	7.15813	−	1.69651i	1.49257	−	0.353746i	0.598301	−	0.801271i	$-0.295843\pi$
$23$	7.15813	−	1.69651i	1.49257	−	0.353746i	0.894271	+	0.447525i	$0.147694\pi$
$24$		0			0
$25$	4.62410	−	0.540479i	0.924819	−	0.108096i
$26$	−2.82684	+	4.89622i	−0.554388	+	0.960229i
$27$		0			0
$28$	−6.04293	−	10.4667i	−1.14201	−	1.97801i
$29$	3.15459	+	4.23736i	0.585794	+	0.786857i	0.991907	−	0.126965i	$-0.0405237\pi$
$29$	3.15459	+	4.23736i	0.585794	+	0.786857i	−0.406114	+	0.913823i	$0.633116\pi$
$30$		0			0
$31$	−0.842702	+	2.81482i	−0.151354	+	0.505556i	−0.999715	−	0.0238607i	$-0.992404\pi$
$31$	−0.842702	+	2.81482i	−0.151354	+	0.505556i	0.848362	+	0.529417i	$0.177589\pi$
$32$	5.33566	+	2.67967i	0.943221	+	0.473703i
$33$		0			0
$34$	1.86352	+	6.22458i	0.319591	+	1.06751i
$35$	0.388237	−	2.20180i	0.0656240	−	0.372172i
$36$		0			0
$37$	−1.09265	−	6.19675i	−0.179631	−	1.01874i	−0.932661	−	0.360753i	$-0.882520\pi$
$37$	−1.09265	−	6.19675i	−0.179631	−	1.01874i	0.753030	−	0.657986i	$-0.228591\pi$
$38$	−0.848730	+	0.426248i	−0.137682	+	0.0691466i
$39$		0			0
$40$	−0.619842	−	1.43696i	−0.0980057	−	0.227203i
$41$	1.44585	+	3.35186i	0.225804	+	0.523473i	0.993024	−	0.117911i	$-0.0376199\pi$
$41$	1.44585	+	3.35186i	0.225804	+	0.523473i	−0.767220	+	0.641384i	$0.778361\pi$
$42$		0			0
$43$	−5.37705	+	2.70046i	−0.819993	+	0.411816i	−0.808773	−	0.588121i	$-0.799868\pi$
$43$	−5.37705	+	2.70046i	−0.819993	+	0.411816i	−0.0112199	+	0.999937i	$0.503571\pi$
$44$	2.74873	+	15.5888i	0.414386	+	2.35010i
$45$		0			0
$46$	−2.90527	+	16.4766i	−0.428358	+	2.42934i
$47$	1.88833	+	6.30747i	0.275441	+	0.920038i	0.978034	+	0.208446i	$0.0668405\pi$
$47$	1.88833	+	6.30747i	0.275441	+	0.920038i	−0.702592	+	0.711592i	$0.747974\pi$
$48$		0			0
$49$	6.71394	+	3.37187i	0.959135	+	0.481696i
$50$	−3.03673	+	10.1434i	−0.429459	+	1.43449i
$51$		0			0
$52$	−4.70944	−	6.32588i	−0.653082	−	0.877241i
$53$	−1.23882	−	2.14569i	−0.170165	−	0.294734i	0.768313	−	0.640075i	$-0.221097\pi$
$53$	−1.23882	−	2.14569i	−0.170165	−	0.294734i	−0.938477	+	0.345341i	$0.887763\pi$
$54$		0			0
$55$	−1.46413	+	2.53595i	−0.197424	+	0.341948i
$56$	10.0899	−	1.17934i	1.34832	−	0.157595i
$57$		0			0
$58$	−11.6906	+	2.77072i	−1.53505	+	0.363813i
$59$	3.87162	−	2.54640i	0.504042	−	0.331513i	−0.271892	−	0.962328i	$-0.587649\pi$
$59$	3.87162	−	2.54640i	0.504042	−	0.331513i	0.775934	+	0.630814i	$0.217279\pi$
$60$		0			0
$61$	−7.81976	+	8.28846i	−1.00122	+	1.06123i	−0.00309376	+	0.999995i	$0.500985\pi$
$61$	−7.81976	+	8.28846i	−1.00122	+	1.06123i	−0.998123	+	0.0612331i	$0.980497\pi$
$62$	−5.11909	−	4.29543i	−0.650125	−	0.545520i
$63$		0			0
$64$	−9.97283	+	8.36820i	−1.24660	+	1.04602i
$65$	0.0848280	−	1.45644i	0.0105216	−	0.180649i
$66$		0			0
$67$	3.55143	−	4.77040i	0.433876	−	0.582797i	−0.530383	−	0.847758i	$-0.677952\pi$
$67$	3.55143	−	4.77040i	0.433876	−	0.582797i	0.964259	+	0.264961i	$0.0853592\pi$
$68$	−9.00226	−	1.05221i	−1.09168	−	0.127600i
$69$		0			0
$70$	4.24831	+	2.79416i	0.507770	+	0.333965i
$71$	−2.65492	−	0.966311i	−0.315081	−	0.114680i	0.179639	−	0.983733i	$-0.442507\pi$
$71$	−2.65492	−	0.966311i	−0.315081	−	0.114680i	−0.494720	+	0.869053i	$0.664729\pi$
$72$		0			0
$73$	12.9084	−	4.69828i	1.51082	−	0.549892i	0.551981	−	0.833857i	$-0.313872\pi$
$73$	12.9084	−	4.69828i	1.51082	−	0.549892i	0.958835	+	0.283965i	$0.0916499\pi$
$74$	13.9250	+	3.30028i	1.61874	+	0.383650i
$75$		0			0
$76$	−0.0770319	−	1.32259i	−0.00883616	−	0.151711i
$77$	−13.0443	−	13.8261i	−1.48654	−	1.57564i
$78$		0			0
$79$	4.97764	−	11.5395i	0.560028	−	1.29829i	−0.369394	−	0.929273i	$-0.620435\pi$
$79$	4.97764	−	11.5395i	0.560028	−	1.29829i	0.929422	−	0.369018i	$-0.120306\pi$
$80$	−0.164537			−0.0183958
$81$		0			0
$82$	−8.30214			−0.916818
$83$	−0.831044	+	1.92658i	−0.0912190	+	0.211469i	−0.957717	−	0.287710i	$-0.907106\pi$
$83$	−0.831044	+	1.92658i	−0.0912190	+	0.211469i	0.866499	+	0.499180i	$0.166365\pi$
$84$		0			0
$85$	−1.15060	−	1.21956i	−0.124800	−	0.132280i
$86$	−0.795693	−	13.6615i	−0.0858017	−	1.47316i
$87$		0			0
$88$	−12.9464	−	3.06835i	−1.38009	−	0.327087i
$89$	0.324629	−	0.118155i	0.0344106	−	0.0125244i	−0.324758	−	0.945797i	$-0.605283\pi$
$89$	0.324629	−	0.118155i	0.0344106	−	0.0125244i	0.359168	+	0.933273i	$0.383060\pi$
$90$		0			0
$91$	8.89913	+	3.23902i	0.932882	+	0.339541i
$92$	−19.4987	−	12.8245i	−2.03288	−	1.33704i
$93$		0			0
$94$	−14.8729	−	1.73840i	−1.53403	−	0.179302i
$95$	0.146352	−	0.196584i	0.0150154	−	0.0201691i
$96$		0			0
$97$	−0.637880	+	10.9520i	−0.0647669	+	1.11200i	0.796761	+	0.604294i	$0.206545\pi$
$97$	−0.637880	+	10.9520i	−0.0647669	+	1.11200i	−0.861528	+	0.507710i	$0.830492\pi$
$98$	−13.0895	+	10.9834i	−1.32224	+	1.10949i
$99$		0			0
$100$	−11.3142	−	9.49377i	−1.13142	−	0.949377i
$101$	−1.21720	+	1.29016i	−0.121116	+	0.128375i	−0.785094	−	0.619377i	$-0.787385\pi$
$101$	−1.21720	+	1.29016i	−0.121116	+	0.128375i	0.663978	+	0.747752i	$0.268867\pi$
$102$		0			0
$103$	−14.7026	+	9.67007i	−1.44869	+	0.952820i	−0.450496	+	0.892778i	$0.648753\pi$
$103$	−14.7026	+	9.67007i	−1.44869	+	0.952820i	−0.998196	+	0.0600415i	$0.980877\pi$
$104$	6.45010	−	1.52870i	0.632484	−	0.149902i
$105$		0			0
$106$	5.59680	−	0.654172i	0.543609	−	0.0635388i
$107$	2.26990	−	3.93158i	0.219439	−	0.380080i	−0.735197	−	0.677853i	$-0.762911\pi$
$107$	2.26990	−	3.93158i	0.219439	−	0.380080i	0.954637	+	0.297773i	$0.0962439\pi$
$108$		0			0
$109$	−1.95094	−	3.37913i	−0.186866	−	0.323662i	0.757337	−	0.653024i	$-0.226500\pi$
$109$	−1.95094	−	3.37913i	−0.186866	−	0.323662i	−0.944204	+	0.329362i	$0.893166\pi$
$110$	−3.97694	−	5.34196i	−0.379186	−	0.509336i
$111$		0			0
$112$	0.306324	−	1.02319i	0.0289449	−	0.0966828i
$113$	11.6508	+	5.85125i	1.09601	+	0.550439i	0.902514	−	0.430661i	$-0.141720\pi$
$113$	11.6508	+	5.85125i	1.09601	+	0.550439i	0.193500	+	0.981100i	$0.438016\pi$
$114$		0			0
$115$	−1.23822	−	4.13594i	−0.115464	−	0.385678i
$116$	2.91019	−	16.5045i	0.270205	−	1.53241i
$117$		0			0
$118$	1.83009	+	10.3789i	0.168473	+	0.955459i
$119$	9.72611	−	4.88464i	0.891591	−	0.447774i
$120$		0			0
$121$	5.50387	+	12.7594i	0.500352	+	1.15995i
$122$	−10.2647	−	23.7963i	−0.929326	−	2.15442i
$123$		0			0
$124$	8.33003	−	4.18350i	0.748059	−	0.375689i
$125$	−0.984000	−	5.58054i	−0.0880116	−	0.499139i
$126$		0			0
$127$	−1.42278	+	8.06900i	−0.126252	+	0.716008i	0.854305	+	0.519772i	$0.173983\pi$
$127$	−1.42278	+	8.06900i	−0.126252	+	0.716008i	−0.980557	+	0.196236i	$0.937128\pi$
$128$	−5.06690	−	16.9246i	−0.447855	−	1.49594i
$129$		0			0
$130$	2.96508	+	1.48912i	0.260055	+	0.130604i
$131$	−0.497800	+	1.66277i	−0.0434930	+	0.145277i	−0.976978	−	0.213339i	$-0.931566\pi$
$131$	−0.497800	+	1.66277i	−0.0434930	+	0.145277i	0.933485	+	0.358616i	$0.116751\pi$
$132$		0			0
$133$	0.950017	+	1.27609i	0.0823769	+	0.110651i
$134$	6.76289	+	11.7137i	0.584225	+	1.01191i
$135$		0			0
$136$	3.80910	−	6.59755i	0.326628	−	0.565736i
$137$	−2.72944	+	0.319026i	−0.233192	+	0.0272562i	−0.231886	−	0.972743i	$-0.574490\pi$
$137$	−2.72944	+	0.319026i	−0.233192	+	0.0272562i	−0.00130578	+	0.999999i	$0.500416\pi$
$138$		0			0
$139$	8.42078	−	1.99576i	0.714241	−	0.169278i	0.142598	−	0.989781i	$-0.454454\pi$
$139$	8.42078	−	1.99576i	0.714241	−	0.169278i	0.571643	+	0.820502i	$0.306306\pi$
$140$	−5.92604	+	3.89762i	−0.500842	+	0.329409i
$141$		0			0
$142$	4.40952	−	4.67382i	0.370039	−	0.392218i
$143$	−9.50165	−	7.97283i	−0.794568	−	0.666722i
$144$		0			0
$145$	2.37495	−	1.99282i	0.197229	−	0.165495i
$146$	−1.81655	+	31.1890i	−0.150339	+	2.58122i
$147$		0			0
$148$	−11.9206	+	16.0122i	−0.979871	+	1.31620i
$149$	5.69447	+	0.665588i	0.466509	+	0.0545271i	0.346101	−	0.938197i	$-0.387506\pi$
$149$	5.69447	+	0.665588i	0.466509	+	0.0545271i	0.120408	+	0.992724i	$0.461580\pi$
$150$		0			0
$151$	−1.48268	−	0.975171i	−0.120658	−	0.0793583i	0.487745	−	0.872986i	$-0.337819\pi$
$151$	−1.48268	−	0.975171i	−0.120658	−	0.0793583i	−0.608404	+	0.793628i	$0.708190\pi$
$152$	1.04640	+	0.380860i	0.0848746	+	0.0308918i
$153$		0			0
$154$	40.6236	−	14.7858i	3.27354	−	1.19147i
$155$	1.67791	+	0.397673i	0.134773	+	0.0319418i
$156$		0			0
$157$	−0.552903	−	9.49298i	−0.0441265	−	0.757623i	−0.945709	−	0.325015i	$-0.894631\pi$
$157$	−0.552903	−	9.49298i	−0.0441265	−	0.757623i	0.901582	−	0.432607i	$-0.142406\pi$
$158$	19.6140	+	20.7897i	1.56041	+	1.65394i
$159$		0			0
$160$	1.38790	−	3.21752i	0.109723	−	0.254367i
$161$	28.0251			2.20868
$162$		0			0
$163$	7.38623			0.578534			0.289267	−	0.957248i	$-0.406588\pi$
$163$	7.38623			0.578534			0.289267	+	0.957248i	$0.406588\pi$
$164$	4.58692	−	10.6337i	0.358179	−	0.830351i
$165$		0			0
$166$	−3.27467	−	3.47095i	−0.254164	−	0.269398i
$167$	−0.264756	−	4.54569i	−0.0204875	−	0.351756i	−0.992937	−	0.118643i	$-0.962146\pi$
$167$	−0.264756	−	4.54569i	−0.0204875	−	0.351756i	0.972450	−	0.233113i	$-0.0748913\pi$
$168$		0			0
$169$	−6.63652	−	1.57288i	−0.510501	−	0.120991i
$170$	3.58329	−	1.30421i	0.274826	−	0.100028i
$171$		0			0
$172$	17.9378	+	6.52882i	1.36774	+	0.497818i
$173$	3.88862	+	2.55759i	0.295647	+	0.194450i	0.688663	−	0.725082i	$-0.258198\pi$
$173$	3.88862	+	2.55759i	0.295647	+	0.194450i	−0.393016	+	0.919532i	$0.628568\pi$
$174$		0			0
$175$	17.6160	+	2.05901i	1.33164	+	0.155647i
$176$	−0.835354	+	1.12208i	−0.0629672	+	0.0845796i
$177$		0			0
$178$	−0.0456837	+	0.784359i	−0.00342414	+	0.0587902i
$179$	2.66027	−	2.23223i	0.198838	−	0.166845i	−0.537932	−	0.842988i	$-0.680794\pi$
$179$	2.66027	−	2.23223i	0.198838	−	0.166845i	0.736770	+	0.676143i	$0.236350\pi$
$180$		0			0
$181$	−11.7147	−	9.82983i	−0.870749	−	0.730645i	0.0935067	−	0.995619i	$-0.470192\pi$
$181$	−11.7147	−	9.82983i	−0.870749	−	0.730645i	−0.964256	+	0.264973i	$0.914637\pi$
$182$	−14.7805	+	15.6664i	−1.09560	+	1.16127i
$183$		0			0
$184$	16.3892	−	10.7794i	1.20823	−	0.794666i
$185$	−3.59329	+	0.851624i	−0.264184	+	0.0626127i
$186$		0			0
$187$	−14.1585	+	1.65489i	−1.03537	+	0.121018i
$188$	10.4439	−	18.0893i	0.761699	−	1.31930i
$189$		0			0
$190$	0.278694	+	0.482712i	0.0202186	+	0.0350196i
$191$	−13.3688	−	17.9574i	−0.967331	−	1.29935i	−0.954116	−	0.299438i	$-0.903201\pi$
$191$	−13.3688	−	17.9574i	−0.967331	−	1.29935i	−0.0132150	−	0.999913i	$-0.504207\pi$
$192$		0			0
$193$	1.85645	−	6.20097i	0.133630	−	0.446356i	−0.864815	−	0.502090i	$-0.832565\pi$
$193$	1.85645	−	6.20097i	0.133630	−	0.446356i	0.998446	+	0.0557339i	$0.0177499\pi$
$194$	−22.2965	−	11.1977i	−1.60079	−	0.803948i
$195$		0			0
$196$	−6.83598	−	22.8338i	−0.488284	−	1.63098i
$197$	−0.961298	+	5.45179i	−0.0684897	+	0.388424i	0.931223	+	0.364450i	$0.118743\pi$
$197$	−0.961298	+	5.45179i	−0.0684897	+	0.388424i	−0.999713	+	0.0239741i	$0.992368\pi$
$198$		0			0
$199$	−2.91762	−	16.5467i	−0.206825	−	1.17296i	−0.894542	−	0.446984i	$-0.852498\pi$
$199$	−2.91762	−	16.5467i	−0.206825	−	1.17296i	0.687717	−	0.725979i	$-0.258613\pi$
$200$	11.0939	−	5.57157i	0.784458	−	0.393969i
$201$		0			0
$202$	−1.59778	−	3.70407i	−0.112419	−	0.260617i
$203$	7.97107	+	18.4790i	0.559459	+	1.29697i
$204$		0			0
$205$	1.91446	−	0.961479i	0.133712	−	0.0671526i
$206$	−6.94983	−	39.4144i	−0.484217	−	2.74613i
$207$		0			0
$208$	0.121023	−	0.686358i	0.00839146	−	0.0475903i
$209$	−0.597598	−	1.99612i	−0.0413367	−	0.138074i
$210$		0			0
$211$	−6.83640	−	3.43337i	−0.470637	−	0.236363i	0.197641	−	0.980275i	$-0.436672\pi$
$211$	−6.83640	−	3.43337i	−0.470637	−	0.236363i	−0.668278	+	0.743912i	$0.732968\pi$
$212$	−2.25434	+	7.53001i	−0.154829	+	0.517163i
$213$		0			0
$214$	6.16560	+	8.28184i	0.421472	+	0.566135i
$215$	1.76564	+	3.05818i	0.120416	+	0.208566i
$216$		0			0
$217$	−5.59680	+	9.69394i	−0.379935	+	0.658068i
$218$	8.81408	−	1.03022i	0.596965	−	0.0697752i
$219$		0			0
$220$	9.03943	−	2.14238i	0.609438	−	0.144440i
$221$	5.93365	−	3.90262i	0.399141	−	0.262519i
$222$		0			0
$223$	5.80400	−	6.15188i	0.388664	−	0.411960i	−0.503267	−	0.864131i	$-0.667869\pi$
$223$	5.80400	−	6.15188i	0.388664	−	0.411960i	0.891931	+	0.452171i	$0.149350\pi$
$224$	17.4246	+	14.6210i	1.16423	+	0.976906i
$225$		0			0
$226$	−22.7143	+	19.0596i	−1.51093	+	1.26782i
$227$	1.55475	−	26.6940i	0.103192	−	1.77174i	−0.408676	−	0.912679i	$-0.634009\pi$
$227$	1.55475	−	26.6940i	0.103192	−	1.77174i	0.511869	−	0.859064i	$-0.328953\pi$
$228$		0			0
$229$	−1.83844	+	2.46946i	−0.121488	+	0.163187i	−0.858706	−	0.512468i	$-0.828731\pi$
$229$	−1.83844	+	2.46946i	−0.121488	+	0.163187i	0.737219	+	0.675654i	$0.236139\pi$
$230$	9.75250	+	1.13990i	0.643061	+	0.0751630i
$231$		0			0
$232$	11.7692	+	7.74071i	0.772684	+	0.508202i
$233$	−6.67642	−	2.43002i	−0.437387	−	0.159196i	0.113936	−	0.993488i	$-0.463654\pi$
$233$	−6.67642	−	2.43002i	−0.437387	−	0.159196i	−0.551322	+	0.834292i	$0.685876\pi$
$234$		0			0
$235$	3.63100	−	1.32158i	0.236860	−	0.0862102i
$236$	−14.3048	−	3.39031i	−0.931166	−	0.220690i
$237$		0			0
$238$	1.43926	+	24.7112i	0.0932936	+	1.60179i
$239$	3.14712	+	3.33575i	0.203570	+	0.215772i	0.821113	−	0.570765i	$-0.193353\pi$
$239$	3.14712	+	3.33575i	0.203570	+	0.215772i	−0.617543	+	0.786537i	$0.711872\pi$
$240$		0			0
$241$	2.43878	−	5.65373i	0.157096	−	0.364188i	−0.821431	−	0.570307i	$-0.806824\pi$
$241$	2.43878	−	5.65373i	0.157096	−	0.364188i	0.978527	+	0.206119i	$0.0660834\pi$
$242$	−31.6035			−2.03155
$243$		0			0
$244$	36.1505			2.31430
$245$	1.74642	−	4.04865i	0.111574	−	0.258659i
$246$		0			0
$247$	0.712394	+	0.755093i	0.0453285	+	0.0480454i
$248$	0.455568	+	7.82179i	0.0289286	+	0.496684i
$249$		0			0
$250$	12.5403	+	2.97210i	0.793116	+	0.187972i
$251$	−27.6062	+	10.0478i	−1.74249	+	0.634213i	−0.999388	−	0.0349710i	$-0.988866\pi$
$251$	−27.6062	+	10.0478i	−1.74249	+	0.634213i	−0.743097	+	0.669184i	$0.766644\pi$
$252$		0			0
$253$	−34.4918	−	12.5540i	−2.16848	−	0.789263i
$254$	−15.5689	−	10.2398i	−0.976879	−	0.642503i
$255$		0			0
$256$	14.0469	+	1.64185i	0.877931	+	0.102615i
$257$	11.2905	−	15.1657i	0.704279	−	0.946011i	−0.295678	−	0.955288i	$-0.595546\pi$
$257$	11.2905	−	15.1657i	0.704279	−	0.946011i	0.999957	+	0.00927680i	$0.00295294\pi$
$258$		0			0
$259$	1.39381	−	23.9308i	0.0866071	−	1.48699i
$260$	−3.54552	+	2.97505i	−0.219884	+	0.184505i
$261$		0			0
$262$	−3.02395	−	2.53739i	−0.186820	−	0.156761i
$263$	−10.0535	+	10.6561i	−0.619924	+	0.657081i	−0.958910	−	0.283710i	$-0.908435\pi$
$263$	−10.0535	+	10.6561i	−0.619924	+	0.657081i	0.338986	+	0.940792i	$0.389916\pi$
$264$		0			0
$265$	−1.21485	+	0.799021i	−0.0746278	+	0.0490835i
$266$	−3.52066	+	0.834411i	−0.215865	+	0.0511610i
$267$		0			0
$268$	−18.7398	+	2.19037i	−1.14472	+	0.133798i
$269$	2.94518	−	5.10121i	0.179571	−	0.311026i	−0.762163	−	0.647386i	$-0.775862\pi$
$269$	2.94518	−	5.10121i	0.179571	−	0.311026i	0.941734	+	0.336360i	$0.109196\pi$
$270$		0			0
$271$	11.5965	+	20.0857i	0.704435	+	1.22012i	0.966895	+	0.255175i	$0.0821330\pi$
$271$	11.5965	+	20.0857i	0.704435	+	1.22012i	−0.262460	+	0.964943i	$0.584534\pi$
$272$	−0.478308	−	0.642479i	−0.0290017	−	0.0389560i
$273$		0			0
$274$	1.79248	−	5.98729i	0.108288	−	0.361706i
$275$	−20.7585	−	10.4253i	−1.25178	−	0.628670i
$276$		0			0
$277$	5.00151	+	16.7062i	0.300512	+	1.00378i	0.966253	+	0.257596i	$0.0829304\pi$
$277$	5.00151	+	16.7062i	0.300512	+	1.00378i	−0.665741	+	0.746183i	$0.731884\pi$
$278$	−3.41774	+	19.3829i	−0.204982	+	1.16251i
$279$		0			0
$280$	−1.03526	−	5.87124i	−0.0618685	−	0.350874i
$281$	25.5457	−	12.8295i	1.52393	−	0.765346i	0.527481	−	0.849567i	$-0.323137\pi$
$281$	25.5457	−	12.8295i	1.52393	−	0.765346i	0.996447	+	0.0842212i	$0.0268402\pi$
$282$		0			0
$283$	7.05408	+	16.3532i	0.419321	+	0.972096i	0.988684	+	0.150010i	$0.0479306\pi$
$283$	7.05408	+	16.3532i	0.419321	+	0.972096i	−0.569363	+	0.822086i	$0.692810\pi$
$284$	3.55014	+	8.23016i	0.210662	+	0.488370i
$285$		0			0
$286$	25.2089	−	12.6604i	1.49063	−	0.748623i
$287$	2.41486	+	13.6953i	0.142544	+	0.808410i
$288$		0			0
$289$	−1.53469	+	8.70366i	−0.0902758	+	0.511980i
$290$	2.02224	+	6.75477i	0.118750	+	0.396654i
$291$		0			0
$292$	−38.9443	−	19.5586i	−2.27904	−	1.14458i
$293$	4.77106	−	15.9365i	0.278728	−	0.931018i	−0.697920	−	0.716175i	$-0.745891\pi$
$293$	4.77106	−	15.9365i	0.278728	−	0.931018i	0.976649	−	0.214842i	$-0.0689238\pi$
$294$		0			0
$295$	−1.62401	−	2.18142i	−0.0945535	−	0.127007i
$296$	−8.38946	−	14.5310i	−0.487628	−	0.844596i
$297$		0			0
$298$	−6.51957	+	11.2922i	−0.377668	+	0.654141i
$299$	18.1636	−	2.12302i	1.05043	−	0.122777i
$300$		0			0
$301$	−22.3048	+	5.28633i	−1.28563	+	0.304699i
$302$	3.37206	−	2.21784i	0.194040	−	0.127622i
$303$		0			0
$304$	0.0803445	−	0.0851602i	0.00460807	−	0.00488427i
$305$	5.12291	+	4.29863i	0.293337	+	0.246139i
$306$		0			0
$307$	−10.8094	+	9.07013i	−0.616923	+	0.517660i	−0.896835	−	0.442366i	$-0.854139\pi$
$307$	−10.8094	+	9.07013i	−0.616923	+	0.517660i	0.279912	+	0.960026i	$0.409695\pi$
$308$	−3.50633	+	60.2013i	−0.199792	+	3.43029i
$309$		0			0
$310$	−2.34194	+	3.14577i	−0.133013	+	0.178668i
$311$	−23.4882	−	2.74537i	−1.33189	−	0.155676i	−0.579813	−	0.814749i	$-0.696875\pi$
$311$	−23.4882	−	2.74537i	−1.33189	−	0.155676i	−0.752079	+	0.659073i	$0.770949\pi$
$312$		0			0
$313$	−6.83757	−	4.49714i	−0.386482	−	0.254193i	0.341368	−	0.939930i	$-0.389110\pi$
$313$	−6.83757	−	4.49714i	−0.386482	−	0.254193i	−0.727850	+	0.685736i	$0.759480\pi$
$314$	20.3223	+	7.39671i	1.14685	+	0.417421i
$315$		0			0
$316$	−37.4649	+	13.6361i	−2.10756	+	0.767091i
$317$	3.98806	+	0.945186i	0.223991	+	0.0530870i	0.341079	−	0.940035i	$-0.389208\pi$
$317$	3.98806	+	0.945186i	0.223991	+	0.0530870i	−0.117087	+	0.993122i	$0.537356\pi$
$318$		0			0
$319$	−1.53260	−	26.3137i	−0.0858091	−	1.47329i
$320$	5.24310	+	5.55736i	0.293098	+	0.310666i
$321$		0			0
$322$	−25.2452	+	58.5249i	−1.40686	+	3.26146i
$323$	1.19306			0.0663836
$324$		0			0
$325$	11.5732			0.641968
$326$	−6.65356	+	15.4247i	−0.368507	+	0.854295i
$327$		0			0
$328$	6.67990	+	7.08028i	0.368836	+	0.390943i
$329$	1.45843	+	25.0403i	0.0804058	+	1.38051i
$330$		0			0
$331$	−24.1277	−	5.71837i	−1.32618	−	0.314310i	−0.494312	−	0.869285i	$-0.664580\pi$
$331$	−24.1277	−	5.71837i	−1.32618	−	0.314310i	−0.831867	+	0.554975i	$0.812728\pi$
$332$	6.25497	−	2.27662i	0.343286	−	0.124946i
$333$		0			0
$334$	9.73128	+	3.54190i	0.532472	+	0.193804i
$335$	−2.91609	−	1.91794i	−0.159323	−	0.104788i
$336$		0			0
$337$	−15.0588	−	1.76012i	−0.820306	−	0.0958800i	−0.304421	−	0.952538i	$-0.598463\pi$
$337$	−15.0588	−	1.76012i	−0.820306	−	0.0958800i	−0.515885	+	0.856658i	$0.672537\pi$
$338$	9.26288	−	12.4422i	0.503834	−	0.676767i
$339$		0			0
$340$	−0.309283	+	5.31018i	−0.0167732	+	0.287985i
$341$	11.2307	−	9.42369i	0.608177	−	0.510321i
$342$		0			0
$343$	1.49737	+	1.25644i	0.0808503	+	0.0678415i
$344$	−11.0107	+	11.6706i	−0.593656	+	0.629239i
$345$		0			0
$346$	−8.84393	+	5.81674i	−0.475452	+	0.312710i
$347$	−24.4451	+	5.79358i	−1.31228	+	0.311016i	−0.826436	−	0.563030i	$-0.809635\pi$
$347$	−24.4451	+	5.79358i	−1.31228	+	0.311016i	−0.485843	+	0.874046i	$0.661487\pi$
$348$		0			0
$349$	17.2284	−	2.01371i	0.922214	−	0.107791i	0.358283	−	0.933613i	$-0.383362\pi$
$349$	17.2284	−	2.01371i	0.922214	−	0.107791i	0.563931	+	0.825822i	$0.309288\pi$
$350$	−20.1684	+	34.9328i	−1.07805	+	1.86724i
$351$		0			0
$352$	−14.8958	−	25.8002i	−0.793947	−	1.37516i
$353$	12.9718	+	17.4241i	0.690418	+	0.927392i	0.999722	−	0.0235712i	$-0.00750364\pi$
$353$	12.9718	+	17.4241i	0.690418	+	0.927392i	−0.309305	+	0.950963i	$0.600096\pi$
$354$		0			0
$355$	−0.475550	+	1.58845i	−0.0252396	+	0.0843060i
$356$	−0.979395	−	0.491871i	−0.0519079	−	0.0260691i
$357$		0			0
$358$	2.26519	+	7.56627i	0.119719	+	0.399890i
$359$	−4.78039	+	27.1110i	−0.252299	+	1.43086i	0.550611	+	0.834762i	$0.314395\pi$
$359$	−4.78039	+	27.1110i	−0.252299	+	1.43086i	−0.802911	+	0.596100i	$0.796716\pi$
$360$		0			0
$361$	−3.26903	−	18.5396i	−0.172054	−	0.975769i
$362$	31.0804	−	15.6092i	1.63355	−	0.820399i
$363$		0			0
$364$	−11.8999	−	27.5870i	−0.623723	−	1.44595i
$365$	−3.19313	−	7.40250i	−0.167136	−	0.387465i
$366$		0			0
$367$	−21.7643	+	10.9304i	−1.13609	+	0.570564i	−0.914504	−	0.404578i	$-0.867418\pi$
$367$	−21.7643	+	10.9304i	−1.13609	+	0.570564i	−0.221582	+	0.975142i	$0.571122\pi$
$368$	−0.358141	−	2.03112i	−0.0186694	−	0.105879i
$369$		0			0
$370$	1.45841	−	8.27103i	0.0758189	−	0.429990i
$371$	−2.70708	−	9.04227i	−0.140545	−	0.469451i
$372$		0			0
$373$	14.8992	+	7.48266i	0.771451	+	0.387437i	0.790564	−	0.612380i	$-0.209788\pi$
$373$	14.8992	+	7.48266i	0.771451	+	0.387437i	−0.0191124	+	0.999817i	$0.506084\pi$
$374$	9.29816	−	31.0580i	0.480796	−	1.60597i
$375$		0			0
$376$	10.4842	+	14.0827i	0.540682	+	0.726262i
$377$	6.56607	+	11.3728i	0.338170	+	0.585727i
$378$		0			0
$379$	1.03268	−	1.78866i	0.0530454	−	0.0918773i	−0.838283	−	0.545235i	$-0.816441\pi$
$379$	1.03268	−	1.78866i	0.0530454	−	0.0918773i	0.891329	+	0.453357i	$0.149774\pi$
$380$	−0.772253	+	0.0902634i	−0.0396157	+	0.00463042i
$381$		0			0
$382$	49.5432	−	11.7420i	2.53485	−	0.600771i
$383$	−12.0397	+	7.91867i	−0.615202	+	0.404625i	−0.818512	−	0.574490i	$-0.805201\pi$
$383$	−12.0397	+	7.91867i	−0.615202	+	0.404625i	0.203310	+	0.979115i	$0.434830\pi$
$384$		0			0
$385$	−7.65539	+	8.11424i	−0.390155	+	0.413540i
$386$	11.2772	+	9.46272i	0.573996	+	0.481640i
$387$		0			0
$388$	26.6612	−	22.3714i	1.35352	−	1.13574i
$389$	−0.717641	+	12.3214i	−0.0363858	+	0.624720i	0.929990	+	0.367586i	$0.119816\pi$
$389$	−0.717641	+	12.3214i	−0.0363858	+	0.624720i	−0.966376	+	0.257135i	$0.917222\pi$
$390$		0			0
$391$	12.5504	−	16.8581i	0.634700	−	0.852549i
$392$	19.8987	+	2.32582i	1.00503	+	0.117472i
$393$		0			0
$394$	−10.5191	−	6.91850i	−0.529943	−	0.348549i
$395$	−6.93064	−	2.52255i	−0.348718	−	0.126923i
$396$		0			0
$397$	−18.0123	+	6.55594i	−0.904011	+	0.329033i	−0.751859	−	0.659324i	$-0.770843\pi$
$397$	−18.0123	+	6.55594i	−0.904011	+	0.329033i	−0.152152	+	0.988357i	$0.548620\pi$
$398$	37.1827	+	8.81246i	1.86380	+	0.441729i
$399$		0			0
$400$	−0.0758930	−	1.30303i	−0.00379465	−	0.0651517i
$401$	6.92003	+	7.33480i	0.345570	+	0.366283i	0.876725	−	0.480992i	$-0.159723\pi$
$401$	6.92003	+	7.33480i	0.345570	+	0.366283i	−0.531155	+	0.847275i	$0.678242\pi$
$402$		0			0
$403$	−2.89304	+	6.70681i	−0.144112	+	0.334090i
$404$	5.62708			0.279957
$405$		0			0
$406$	−45.7702			−2.27154
$407$	−12.4354	+	28.8284i	−0.616398	+	1.42897i
$408$		0			0
$409$	2.37463	+	2.51696i	0.117418	+	0.124456i	0.783416	−	0.621498i	$-0.213476\pi$
$409$	2.37463	+	2.51696i	0.117418	+	0.124456i	−0.665998	+	0.745954i	$0.731994\pi$
$410$	0.283301	+	4.86409i	0.0139912	+	0.240220i
$411$		0			0
$412$	54.3232	+	12.8748i	2.67631	+	0.634298i
$413$	16.5889	−	6.03787i	0.816287	−	0.297104i
$414$		0			0
$415$	1.15711	+	0.421153i	0.0568002	+	0.0206736i
$416$	12.4008	+	8.15616i	0.608001	+	0.399889i
$417$		0			0
$418$	4.70682	+	0.550149i	0.230218	+	0.0269086i
$419$	−3.48138	+	4.67630i	−0.170076	+	0.228452i	−0.878987	−	0.476847i	$-0.841780\pi$
$419$	−3.48138	+	4.67630i	−0.170076	+	0.228452i	0.708910	+	0.705299i	$0.249187\pi$
$420$		0			0
$421$	−2.24181	+	38.4903i	−0.109259	+	1.87590i	0.287227	+	0.957862i	$0.407266\pi$
$421$	−2.24181	+	38.4903i	−0.109259	+	1.87590i	−0.396486	+	0.918041i	$0.629771\pi$
$422$	13.3282	−	11.1837i	0.648807	−	0.544414i
$423$		0			0
$424$	−5.06108	−	4.24675i	−0.245788	−	0.206240i
$425$	9.12748	−	9.67456i	0.442748	−	0.469285i
$426$		0			0
$427$	−36.2691	+	23.8545i	−1.75518	+	1.15440i
$428$	−14.0142	+	3.32142i	−0.677400	+	0.160547i
$429$		0			0
$430$	−7.97690	+	0.932366i	−0.384680	+	0.0449627i
$431$	0.101111	−	0.175130i	0.00487036	−	0.00843570i	−0.863580	−	0.504212i	$-0.831783\pi$
$431$	0.101111	−	0.175130i	0.00487036	−	0.00843570i	0.868450	+	0.495776i	$0.165116\pi$
$432$		0			0
$433$	4.03061	+	6.98122i	0.193699	+	0.335496i	0.946473	−	0.322782i	$-0.104618\pi$
$433$	4.03061	+	6.98122i	0.193699	+	0.335496i	−0.752774	+	0.658279i	$0.771285\pi$
$434$	−15.2023	−	20.4202i	−0.729732	−	0.980201i
$435$		0			0
$436$	−3.55023	+	11.8586i	−0.170025	+	0.567924i
$437$	2.74528	+	1.37873i	0.131325	+	0.0659537i
$438$		0			0
$439$	0.626933	+	2.09410i	0.0299219	+	0.0999461i	0.971646	−	0.236440i	$-0.0759806\pi$
$439$	0.626933	+	2.09410i	0.0299219	+	0.0999461i	−0.941724	+	0.336386i	$0.890795\pi$
$440$	−1.35591	+	7.68978i	−0.0646407	+	0.366596i
$441$		0			0
$442$	2.80480	+	15.9068i	0.133411	+	0.756609i
$443$	−28.9164	+	14.5224i	−1.37386	+	0.689979i	−0.973990	−	0.226592i	$-0.927242\pi$
$443$	−28.9164	+	14.5224i	−1.37386	+	0.689979i	−0.399872	+	0.916571i	$0.630945\pi$
$444$		0			0
$445$	−0.0803027	−	0.186163i	−0.00380672	−	0.00882496i
$446$	7.61872	+	17.6622i	0.360757	+	0.836328i
$447$		0			0
$448$	−44.3204	+	22.2585i	−2.09394	+	1.05162i
$449$	6.74854	+	38.2728i	0.318483	+	1.80621i	0.551988	+	0.833852i	$0.313869\pi$
$449$	6.74854	+	38.2728i	0.318483	+	1.80621i	−0.233505	+	0.972356i	$0.575020\pi$
$450$		0			0
$451$	3.16282	−	17.9373i	0.148931	−	0.844632i
$452$	−11.8626	−	39.6237i	−0.557968	−	1.86374i
$453$		0			0
$454$	54.3447	+	27.2929i	2.55052	+	1.28092i
$455$	1.59401	−	5.32438i	0.0747285	−	0.249611i
$456$		0			0
$457$	−17.6314	−	23.6830i	−0.824760	−	1.10785i	−0.992528	−	0.122019i	$-0.961063\pi$
$457$	−17.6314	−	23.6830i	−0.824760	−	1.10785i	0.167767	−	0.985827i	$-0.446344\pi$
$458$	−3.50090	−	6.06374i	−0.163586	−	0.283340i
$459$		0			0
$460$	−6.84827	+	11.8616i	−0.319302	+	0.553048i
$461$	−21.3788	+	2.49882i	−0.995709	+	0.116382i	−0.598310	−	0.801264i	$-0.704161\pi$
$461$	−21.3788	+	2.49882i	−0.995709	+	0.116382i	−0.397398	+	0.917646i	$0.630087\pi$
$462$		0			0
$463$	−33.9982	+	8.05773i	−1.58003	+	0.374474i	−0.924648	−	0.380822i	$-0.875641\pi$
$463$	−33.9982	+	8.05773i	−1.58003	+	0.374474i	−0.655384	+	0.755296i	$0.727493\pi$
$464$	1.23740	−	0.813853i	0.0574450	−	0.0377822i
$465$		0			0
$466$	11.0888	−	11.7534i	0.513678	−	0.544467i
$467$	−19.2365	−	16.1414i	−0.890161	−	0.746933i	0.0780818	−	0.996947i	$-0.475120\pi$
$467$	−19.2365	−	16.1414i	−0.890161	−	0.746933i	−0.968242	+	0.250014i	$0.919565\pi$
$468$		0			0
$469$	17.3559	−	14.5633i	0.801422	−	0.672473i
$470$	−0.510977	+	8.77313i	−0.0235696	+	0.404674i
$471$		0			0
$472$	7.37894	−	9.91164i	0.339643	−	0.456220i
$473$	29.8196	+	3.48541i	1.37111	+	0.160260i
$474$		0			0
$475$	1.62433	+	1.06834i	0.0745295	+	0.0490188i
$476$	−32.4462	−	11.8095i	−1.48717	−	0.541286i
$477$		0			0
$478$	−9.80101	+	3.56728i	−0.448288	+	0.163163i
$479$	−9.54744	−	2.26279i	−0.436234	−	0.103389i	0.00663040	−	0.999978i	$-0.497889\pi$
$479$	−9.54744	−	2.26279i	−0.436234	−	0.103389i	−0.442864	+	0.896589i	$0.646038\pi$
$480$		0			0
$481$	−0.909505	−	15.6156i	−0.0414698	−	0.712010i
$482$	9.60984	+	10.1858i	0.437716	+	0.463952i
$483$		0			0
$484$	17.4609	−	40.4789i	0.793676	−	1.83995i
$485$	6.43835			0.292350
$486$		0			0
$487$	−17.0318			−0.771785			−0.385892	−	0.922544i	$-0.626106\pi$
$487$	−17.0318			−0.771785			−0.385892	+	0.922544i	$0.626106\pi$
$488$	−12.0351	+	27.9006i	−0.544805	+	1.26300i
$489$		0			0
$490$	6.88163	+	7.29410i	0.310880	+	0.329514i
$491$	0.488962	+	8.39515i	0.0220665	+	0.378868i	0.991204	+	0.132345i	$0.0422508\pi$
$491$	0.488962	+	8.39515i	0.0220665	+	0.378868i	−0.969137	+	0.246522i	$0.920712\pi$
$492$		0			0
$493$	14.6854	+	3.48051i	0.661399	+	0.156754i
$494$	−2.21860	+	0.807503i	−0.0998193	+	0.0363313i
$495$		0			0
$496$	0.774093	+	0.281747i	0.0347578	+	0.0126508i
$497$	−8.99260	−	5.91453i	−0.403373	−	0.265303i
$498$		0			0
$499$	−23.9994	−	2.80513i	−1.07436	−	0.125575i	−0.439533	−	0.898227i	$-0.644856\pi$
$499$	−23.9994	−	2.80513i	−1.07436	−	0.125575i	−0.634830	+	0.772652i	$0.718930\pi$
$500$	−10.7353	+	14.4200i	−0.480095	+	0.644880i
$501$		0			0
$502$	3.88490	−	66.7012i	0.173392	−	2.97702i
$503$	−2.81544	+	2.36243i	−0.125534	+	0.105336i	−0.703393	−	0.710801i	$-0.748333\pi$
$503$	−2.81544	+	2.36243i	−0.125534	+	0.105336i	0.577859	+	0.816136i	$0.303888\pi$
$504$		0			0
$505$	0.797417	+	0.669112i	0.0354846	+	0.0297751i
$506$	57.2870	−	60.7207i	2.54672	−	2.69936i
$507$		0			0
$508$	21.7173	−	14.2837i	0.963550	−	0.633737i
$509$	−28.5800	+	6.77359i	−1.26679	+	0.300234i	−0.808461	−	0.588550i	$-0.799699\pi$
$509$	−28.5800	+	6.77359i	−1.26679	+	0.300234i	−0.458326	+	0.888784i	$0.651551\pi$
$510$		0			0
$511$	51.9781	−	6.07537i	2.29938	−	0.268759i
$512$	1.58458	−	2.74458i	0.0700293	−	0.121294i
$513$		0			0
$514$	21.5001	+	37.2393i	0.948329	+	1.64255i
$515$	6.16724	+	8.28404i	0.271761	+	0.365039i
$516$		0			0
$517$	9.42197	−	31.4716i	0.414378	−	1.38412i
$518$	48.7192	+	24.4677i	2.14060	+	1.07505i
$519$		0			0
$520$	−1.11574	−	3.72684i	−0.0489286	−	0.163433i
$521$	6.02463	−	34.1674i	0.263944	−	1.49690i	−0.508083	−	0.861308i	$-0.669646\pi$
$521$	6.02463	−	34.1674i	0.263944	−	1.49690i	0.772026	−	0.635591i	$-0.219243\pi$
$522$		0			0
$523$	5.01556	+	28.4447i	0.219315	+	1.24380i	0.873259	+	0.487256i	$0.162002\pi$
$523$	5.01556	+	28.4447i	0.219315	+	1.24380i	−0.653944	+	0.756543i	$0.726887\pi$
$524$	4.92071	−	2.47127i	0.214962	−	0.107958i
$525$		0			0
$526$	−13.1969	−	30.5938i	−0.575411	−	1.33395i
$527$	3.32486	+	7.70788i	0.144833	+	0.335761i
$528$		0			0
$529$	27.8071	−	13.9652i	1.20900	−	0.607185i
$530$	−0.574252	−	3.25675i	−0.0249439	−	0.141464i
$531$		0			0
$532$	0.876415	−	4.97039i	0.0379974	−	0.215494i
$533$	2.60259	+	8.69327i	0.112731	+	0.376547i
$534$		0			0
$535$	−2.38091	−	1.19574i	−0.102936	−	0.0516962i
$536$	4.54830	−	15.1924i	0.196457	−	0.656212i
$537$		0			0
$538$	7.99983	+	10.7456i	0.344897	+	0.463278i
$539$	−18.7436	−	32.4648i	−0.807343	−	1.39836i
$540$		0			0
$541$	4.28774	−	7.42658i	0.184344	−	0.319294i	−0.759011	−	0.651078i	$-0.774317\pi$
$541$	4.28774	−	7.42658i	0.184344	−	0.319294i	0.943355	+	0.331784i	$0.107650\pi$
$542$	−52.3912	+	6.12365i	−2.25039	+	0.263033i
$543$		0			0
$544$	16.5983	−	3.93386i	0.711644	−	0.168663i
$545$	−1.91320	+	1.25833i	−0.0819526	+	0.0539011i
$546$		0			0
$547$	17.2810	−	18.3168i	0.738883	−	0.783170i	−0.243529	−	0.969894i	$-0.578305\pi$
$547$	17.2810	−	18.3168i	0.738883	−	0.783170i	0.982413	+	0.186723i	$0.0597867\pi$
$548$	6.67840	+	5.60384i	0.285287	+	0.239384i
$549$		0			0
$550$	40.4706	−	33.9589i	1.72567	−	1.44801i
$551$	−0.128270	+	2.20232i	−0.00546450	+	0.0938219i
$552$		0			0
$553$	28.5897	−	38.4027i	1.21576	−	1.63305i
$554$	−39.3931	−	4.60439i	−1.67365	−	0.195622i
$555$		0			0
$556$	−22.9381	−	15.0866i	−0.972792	−	0.639815i
$557$	15.3188	+	5.57558i	0.649077	+	0.236245i	0.645514	−	0.763749i	$-0.276643\pi$
$557$	15.3188	+	5.57558i	0.649077	+	0.236245i	0.00356379	+	0.999994i	$0.498866\pi$
$558$		0			0
$559$	−14.0557	+	5.11586i	−0.594493	+	0.216378i
$560$	−0.609926	−	0.144555i	−0.0257741	−	0.00610856i
$561$		0			0
$562$	3.78024	+	64.9041i	0.159460	+	2.73782i
$563$	−30.0218	−	31.8213i	−1.26527	−	1.34111i	−0.914468	−	0.404658i	$-0.867391\pi$
$563$	−30.0218	−	31.8213i	−1.26527	−	1.34111i	−0.350802	−	0.936450i	$-0.614091\pi$
$564$		0			0
$565$	3.03058	−	7.02567i	0.127497	−	0.295572i
$566$	−40.5048			−1.70254
$567$		0			0
$568$	−7.53386			−0.316114
$569$	13.5585	−	31.4321i	0.568401	−	1.31770i	−0.355359	−	0.934730i	$-0.615641\pi$
$569$	13.5585	−	31.4321i	0.568401	−	1.31770i	0.923760	−	0.382971i	$-0.125099\pi$
$570$		0			0
$571$	22.2208	+	23.5527i	0.929912	+	0.985649i	0.999929	−	0.0118970i	$-0.00378701\pi$
$571$	22.2208	+	23.5527i	0.929912	+	0.985649i	−0.0700176	+	0.997546i	$0.522306\pi$
$572$	2.28799	+	39.2833i	0.0956657	+	1.64252i
$573$		0			0
$574$	−30.7753	−	7.29389i	−1.28454	−	0.304441i
$575$	32.1829	−	11.7136i	1.34212	−	0.488492i
$576$		0			0
$577$	43.0486	+	15.6684i	1.79214	+	0.652285i	0.999068	+	0.0431527i	$0.0137402\pi$
$577$	43.0486	+	15.6684i	1.79214	+	0.652285i	0.793069	+	0.609132i	$0.208482\pi$
$578$	−16.7934	−	11.0452i	−0.698515	−	0.459420i
$579$		0			0
$580$	−9.76904	−	1.14184i	−0.405637	−	0.0474122i
$581$	−4.77322	+	6.41154i	−0.198026	+	0.265996i
$582$		0			0
$583$	−0.718806	+	12.3414i	−0.0297699	+	0.511129i
$584$	28.0603	−	23.5454i	1.16115	−	0.974317i
$585$		0			0
$586$	28.9824	+	24.3191i	1.19725	+	1.00461i
$587$	−29.5363	+	31.3067i	−1.21909	+	1.29216i	−0.275406	+	0.961328i	$0.588812\pi$
$587$	−29.5363	+	31.3067i	−1.21909	+	1.29216i	−0.943688	+	0.330837i	$0.892669\pi$
$588$		0			0
$589$	−1.02516	+	0.674258i	−0.0422410	+	0.0277823i
$590$	6.01840	−	1.42639i	0.247774	−	0.0587234i
$591$		0			0
$592$	−1.75220	+	0.204803i	−0.0720149	+	0.00841733i
$593$	−13.5379	+	23.4484i	−0.555935	+	0.962909i	0.441895	+	0.897067i	$0.354307\pi$
$593$	−13.5379	+	23.4484i	−0.555935	+	0.962909i	−0.997830	+	0.0658415i	$0.979027\pi$
$594$		0			0
$595$	−3.19372	−	5.53169i	−0.130930	−	0.226777i
$596$	−10.8614	−	14.5894i	−0.444902	−	0.597607i
$597$		0			0
$598$	−11.9284	+	39.8436i	−0.487788	+	1.62932i
$599$	1.81269	+	0.910367i	0.0740645	+	0.0371966i	0.485446	−	0.874267i	$-0.338657\pi$
$599$	1.81269	+	0.910367i	0.0740645	+	0.0371966i	−0.411381	+	0.911463i	$0.634954\pi$
$600$		0			0
$601$	−2.25001	−	7.51554i	−0.0917797	−	0.306565i	0.899757	−	0.436391i	$-0.143743\pi$
$601$	−2.25001	−	7.51554i	−0.0917797	−	0.306565i	−0.991537	+	0.129825i	$0.958558\pi$
$602$	9.05283	−	51.3412i	0.368966	−	2.09251i
$603$		0			0
$604$	0.977629	+	5.54441i	0.0397792	+	0.225599i
$605$	7.28771	−	3.66003i	0.296288	−	0.148801i
$606$		0			0
$607$	−8.15511	−	18.9057i	−0.331006	−	0.767357i	−0.999716	−	0.0238342i	$-0.992413\pi$
$607$	−8.15511	−	18.9057i	−0.331006	−	0.767357i	0.668710	−	0.743523i	$-0.266847\pi$
$608$	0.987583	+	2.28947i	0.0400518	+	0.0928504i
$609$		0			0
$610$	−13.5916	+	6.82596i	−0.550308	+	0.276375i
$611$	2.84214	+	16.1186i	0.114981	+	0.652089i
$612$		0			0
$613$	−0.250445	+	1.42034i	−0.0101154	+	0.0573671i	−0.989448	−	0.144891i	$-0.953717\pi$
$613$	−0.250445	+	1.42034i	−0.0101154	+	0.0573671i	0.979332	+	0.202258i	$0.0648280\pi$
$614$	−9.20405	−	30.7437i	−0.371445	−	1.24071i
$615$		0			0
$616$	−45.2955	−	22.7482i	−1.82501	−	0.916552i
$617$	0.973306	−	3.25107i	0.0391838	−	0.130883i	−0.936160	−	0.351575i	$-0.885646\pi$
$617$	0.973306	−	3.25107i	0.0391838	−	0.130883i	0.975344	+	0.220692i	$0.0708315\pi$
$618$		0			0
$619$	18.4750	+	24.8162i	0.742573	+	0.997448i	0.999519	+	0.0310226i	$0.00987637\pi$
$619$	18.4750	+	24.8162i	0.742573	+	0.997448i	−0.256946	+	0.966426i	$0.582716\pi$
$620$	−2.73530	−	4.73767i	−0.109852	−	0.190269i
$621$		0			0
$622$	26.8915	−	46.5774i	1.07825	−	1.86758i
$623$	1.30718	−	0.152787i	0.0523710	−	0.00612129i
$624$		0			0
$625$	19.4145	−	4.60131i	0.776578	−	0.184052i
$626$	15.5507	−	10.2279i	0.621532	−	0.408788i
$627$		0			0
$628$	−20.7020	+	21.9429i	−0.826101	+	0.875616i
$629$	−13.7710	−	11.5553i	−0.549087	−	0.460739i
$630$		0			0
$631$	25.7219	−	21.5833i	1.02397	−	0.859217i	0.0338527	−	0.999427i	$-0.489222\pi$
$631$	25.7219	−	21.5833i	1.02397	−	0.859217i	0.990122	+	0.140210i	$0.0447778\pi$
$632$	1.94852	−	33.4547i	0.0775078	−	1.33076i
$633$		0			0
$634$	−5.56631	+	7.47685i	−0.221066	+	0.296944i
$635$	4.77604	+	0.558240i	0.189532	+	0.0221531i
$636$		0			0
$637$	15.6042	+	10.2630i	0.618259	+	0.406636i
$638$	56.3316	+	20.5030i	2.23019	+	0.811723i
$639$		0			0
$640$	−9.74295	+	3.54614i	−0.385124	+	0.140174i
$641$	15.6851	+	3.71744i	0.619525	+	0.146830i	0.528381	−	0.849008i	$-0.322799\pi$
$641$	15.6851	+	3.71744i	0.619525	+	0.146830i	0.0911441	+	0.995838i	$0.470948\pi$
$642$		0			0
$643$	−0.436643	−	7.49687i	−0.0172195	−	0.295648i	−0.995913	−	0.0903200i	$-0.971211\pi$
$643$	−0.436643	−	7.49687i	−0.0172195	−	0.295648i	0.978693	−	0.205328i	$-0.0658260\pi$
$644$	−61.0129	−	64.6699i	−2.40424	−	2.54835i
$645$		0			0
$646$	−1.07472	+	2.49147i	−0.0422841	+	0.0980256i
$647$	−18.2475			−0.717384			−0.358692	−	0.933456i	$-0.616777\pi$
$647$	−18.2475			−0.717384			−0.358692	+	0.933456i	$0.616777\pi$
$648$		0			0
$649$	−23.1215			−0.907598
$650$	−10.4253	+	24.1685i	−0.408912	+	0.947965i
$651$		0			0
$652$	−16.0804	−	17.0443i	−0.629758	−	0.667505i
$653$	−0.494837	−	8.49602i	−0.0193645	−	0.332475i	−0.994052	−	0.108904i	$-0.965266\pi$
$653$	−0.494837	−	8.49602i	−0.0193645	−	0.332475i	0.974688	−	0.223571i	$-0.0717713\pi$
$654$		0			0
$655$	0.991176	+	0.234913i	0.0387284	+	0.00917881i
$656$	0.961710	−	0.350034i	0.0375485	−	0.0136665i
$657$		0			0
$658$	−53.6055	−	19.5108i	−2.08976	−	0.760610i
$659$	−10.9953	−	7.23170i	−0.428315	−	0.281707i	0.316993	−	0.948428i	$-0.397327\pi$
$659$	−10.9953	−	7.23170i	−0.428315	−	0.281707i	−0.745308	+	0.666721i	$0.767697\pi$
$660$		0			0
$661$	11.5306	+	1.34774i	0.448489	+	0.0524209i	0.337340	−	0.941383i	$-0.390473\pi$
$661$	11.5306	+	1.34774i	0.448489	+	0.0524209i	0.111149	+	0.993804i	$0.464547\pi$
$662$	33.6761	−	45.2349i	1.30886	−	1.75810i
$663$		0			0
$664$	−0.325315	+	5.58545i	−0.0126247	+	0.216758i
$665$	0.715224	−	0.600144i	0.0277352	−	0.0232726i
$666$		0			0
$667$	29.7697	+	24.9797i	1.15269	+	0.967219i
$668$	−9.91311	+	10.5073i	−0.383550	+	0.406539i
$669$		0			0
$670$	6.63207	−	4.36198i	0.256219	−	0.168518i
$671$	55.3239	−	13.1120i	2.13575	−	0.506183i
$672$		0			0
$673$	−39.9042	+	4.66413i	−1.53819	+	0.179789i	−0.842558	−	0.538605i	$-0.818951\pi$
$673$	−39.9042	+	4.66413i	−1.53819	+	0.179789i	−0.695636	+	0.718394i	$0.744877\pi$
$674$	17.2408	−	29.8619i	0.664089	−	1.15024i
$675$		0			0
$676$	10.8187	+	18.7385i	0.416104	+	0.720713i
$677$	8.18041	+	10.9882i	0.314399	+	0.422311i	0.931031	−	0.364941i	$-0.118911\pi$
$677$	8.18041	+	10.9882i	0.314399	+	0.422311i	−0.616632	+	0.787251i	$0.711503\pi$
$678$		0			0
$679$	−11.9865	+	40.0376i	−0.459999	+	1.53650i
$680$	−3.99538	−	2.00655i	−0.153216	−	0.0769479i
$681$		0			0
$682$	9.56283	+	31.9421i	0.366180	+	1.22313i
$683$	−3.43677	+	19.4909i	−0.131504	+	0.745798i	0.845726	+	0.533617i	$0.179168\pi$
$683$	−3.43677	+	19.4909i	−0.131504	+	0.745798i	−0.977230	+	0.212181i	$0.931943\pi$
$684$		0			0
$685$	0.280051	+	1.58825i	0.0107002	+	0.0606839i
$686$	−3.97267	+	1.99515i	−0.151677	+	0.0761752i
$687$		0			0
$688$	0.668167	+	1.54899i	0.0254736	+	0.0590545i
$689$	−2.43950	−	5.65540i	−0.0929376	−	0.215454i
$690$		0			0
$691$	8.39976	−	4.21852i	0.319542	−	0.160480i	−0.281797	−	0.959474i	$-0.590930\pi$
$691$	8.39976	−	4.21852i	0.319542	−	0.160480i	0.601339	+	0.798994i	$0.294634\pi$
$692$	−2.56404	−	14.5414i	−0.0974700	−	0.552780i
$693$		0			0
$694$	9.92150	−	56.2676i	0.376615	−	2.13589i
$695$	−1.45663	−	4.86549i	−0.0552532	−	0.184559i
$696$		0			0
$697$	9.31966	+	4.68051i	0.353007	+	0.177287i
$698$	−11.3142	+	37.7921i	−0.428249	+	1.43045i
$699$		0			0
$700$	−33.6001	−	45.1328i	−1.26997	−	1.70586i
$701$	−9.65096	−	16.7160i	−0.364512	−	0.631353i	0.624186	−	0.781276i	$-0.285431\pi$
$701$	−9.65096	−	16.7160i	−0.364512	−	0.631353i	−0.988698	+	0.149923i	$0.952097\pi$
$702$		0			0
$703$	1.31384	−	2.27564i	0.0495526	−	0.0858276i
$704$	64.5181	−	7.54109i	2.43162	−	0.284215i
$705$		0			0
$706$	−48.0719	+	11.3933i	−1.80921	+	0.428791i
$707$	−5.64553	+	3.71312i	−0.212322	+	0.139646i
$708$		0			0
$709$	−6.82324	+	7.23221i	−0.256252	+	0.271611i	−0.842709	−	0.538369i	$-0.819041\pi$
$709$	−6.82324	+	7.23221i	−0.256252	+	0.271611i	0.586457	+	0.809980i	$0.300522\pi$
$710$	−2.88878	−	2.42398i	−0.108414	−	0.0909703i
$711$		0			0
$712$	0.705679	−	0.592135i	0.0264464	−	0.0221912i
$713$	−1.25680	+	21.5785i	−0.0470677	+	0.808121i
$714$		0			0
$715$	−4.34692	+	5.83893i	−0.162566	+	0.218363i
$716$	−10.9427	−	1.27901i	−0.408947	−	0.0477990i
$717$		0			0
$718$	−52.3097	−	34.4047i	−1.95218	−	1.28397i
$719$	−35.9855	−	13.0976i	−1.34203	−	0.488459i	−0.431580	−	0.902075i	$-0.642044\pi$
$719$	−35.9855	−	13.0976i	−1.34203	−	0.488459i	−0.910452	+	0.413615i	$0.864266\pi$
$720$		0			0
$721$	−62.9971	+	22.9291i	−2.34613	+	0.853923i
$722$	41.6611	+	9.87387i	1.55047	+	0.367467i
$723$		0			0
$724$	2.82090	+	48.4329i	0.104838	+	1.80000i
$725$	16.8774	+	17.8890i	0.626809	+	0.664379i
$726$		0			0
$727$	9.29751	−	21.5541i	0.344826	−	0.799396i	−0.654245	−	0.756283i	$-0.727013\pi$
$727$	9.29751	−	21.5541i	0.344826	−	0.799396i	0.999070	−	0.0431127i	$-0.0137274\pi$
$728$	25.2530			0.935940
$729$		0			0
$730$	18.3351			0.678612
$731$	−6.80876	+	15.7845i	−0.251831	+	0.583810i
$732$		0			0
$733$	14.2256	+	15.0783i	0.525435	+	0.556928i	0.934677	−	0.355497i	$-0.115688\pi$
$733$	14.2256	+	15.0783i	0.525435	+	0.556928i	−0.409242	+	0.912426i	$0.634207\pi$
$734$	−3.22066	−	55.2967i	−0.118877	−	2.04104i
$735$		0			0
$736$	42.7394	+	10.1294i	1.57540	+	0.373376i
$737$	−27.8845	+	10.1491i	−1.02714	+	0.373848i
$738$		0			0
$739$	−17.6513	−	6.42454i	−0.649313	−	0.236331i	−0.00369738	−	0.999993i	$-0.501177\pi$
$739$	−17.6513	−	6.42454i	−0.649313	−	0.236331i	−0.645616	+	0.763663i	$0.723399\pi$
$740$	9.78807	+	6.43771i	0.359817	+	0.236655i
$741$		0			0
$742$	21.3216	+	2.49214i	0.782740	+	0.0914892i
$743$	−18.5584	+	24.9283i	−0.680842	+	0.914530i	−0.999443	−	0.0333588i	$-0.989380\pi$
$743$	−18.5584	+	24.9283i	−0.680842	+	0.914530i	0.318601	+	0.947889i	$0.396787\pi$
$744$		0			0
$745$	0.195640	−	3.35901i	0.00716769	−	0.123064i
$746$	−29.0474	+	24.3736i	−1.06350	+	0.892382i
$747$		0			0
$748$	34.6430	+	29.0690i	1.26667	+	1.06287i
$749$	11.8684	−	12.5798i	0.433663	−	0.459656i
$750$		0			0
$751$	20.1814	−	13.2735i	0.736428	−	0.484357i	−0.125050	−	0.992150i	$-0.539909\pi$
$751$	20.1814	−	13.2735i	0.736428	−	0.484357i	0.861479	+	0.507794i	$0.169539\pi$
$752$	1.79616	−	0.425697i	0.0654991	−	0.0155236i
$753$		0			0
$754$	−29.6646	+	3.46729i	−1.08032	+	0.126271i
$755$	−0.520742	+	0.901951i	−0.0189517	+	0.0328254i
$756$		0			0
$757$	0.457633	+	0.792644i	0.0166330	+	0.0288091i	0.874222	−	0.485526i	$-0.161372\pi$
$757$	0.457633	+	0.792644i	0.0166330	+	0.0288091i	−0.857589	+	0.514335i	$0.828039\pi$
$758$	2.80502	+	3.76780i	0.101883	+	0.136853i
$759$		0			0
$760$	0.187432	−	0.626067i	0.00679888	−	0.0227098i
$761$	18.2165	+	9.14866i	0.660347	+	0.331639i	0.747216	−	0.664581i	$-0.231390\pi$
$761$	18.2165	+	9.14866i	0.660347	+	0.331639i	−0.0868695	+	0.996220i	$0.527686\pi$
$762$		0			0
$763$	−4.26323	−	14.2402i	−0.154339	−	0.515529i
$764$	−12.3330	+	69.9441i	−0.446194	+	2.53049i
$765$		0			0
$766$	−5.69111	−	32.2759i	−0.205628	−	1.16617i
$767$	10.2942	−	5.16995i	0.371702	−	0.186676i
$768$		0			0
$769$	8.94714	+	20.7418i	0.322642	+	0.747969i	0.999925	+	0.0122459i	$0.00389809\pi$
$769$	8.94714	+	20.7418i	0.322642	+	0.747969i	−0.677283	+	0.735723i	$0.736843\pi$
$770$	−10.0490	−	23.2962i	−0.362140	−	0.839535i
$771$		0			0
$772$	−18.3508	+	9.21614i	−0.660461	+	0.331696i
$773$	0.291023	+	1.65048i	0.0104674	+	0.0593635i	0.989594	−	0.143888i	$-0.0459604\pi$
$773$	0.291023	+	1.65048i	0.0104674	+	0.0593635i	−0.979127	+	0.203251i	$0.934849\pi$
$774$		0			0
$775$	−2.37538	+	13.4715i	−0.0853262	+	0.483909i
$776$	8.39003	+	28.0247i	0.301185	+	1.00603i
$777$		0			0
$778$	−25.0844	−	12.5979i	−0.899320	−	0.451655i
$779$	−0.437206	+	1.46037i	−0.0156645	+	0.0523232i
$780$		0			0
$781$	8.41819	+	11.3076i	0.301227	+	0.404617i
$782$	23.8993	+	41.3949i	0.854639	+	1.48028i
$783$		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)

\(f(q)\)	\(=\)	\(q+(-0.900807 + 2.08831i) q^{2} +(-2.17708 - 2.30757i) q^{4} +(-0.0341238 - 0.585883i) q^{5} +(3.70692 + 0.878555i) q^{7} +(2.50575 - 0.912019i) q^{8} +O(q^{10})\)	\(q+(-0.900807 + 2.08831i) q^{2} +(-2.17708 - 2.30757i) q^{4} +(-0.0341238 - 0.585883i) q^{5} +(3.70692 + 0.878555i) q^{7} +(2.50575 - 0.912019i) q^{8} +(1.25424 + 0.456507i) q^{10} +(-4.16873 - 2.74182i) q^{11} +(2.46908 + 0.288594i) q^{13} +(-5.17391 + 6.94977i) q^{14} +(0.0163015 - 0.279887i) q^{16} +(2.18854 - 1.83640i) q^{17} +(0.319901 + 0.268429i) q^{19} +(-1.27768 + 1.35426i) q^{20} +(9.48097 - 6.23573i) q^{22} +(7.15813 - 1.69651i) q^{23} +(4.62410 - 0.540479i) q^{25} +(-2.82684 + 4.89622i) q^{26} +(-6.04293 - 10.4667i) q^{28} +(3.15459 + 4.23736i) q^{29} +(-0.842702 + 2.81482i) q^{31} +(5.33566 + 2.67967i) q^{32} +(1.86352 + 6.22458i) q^{34} +(0.388237 - 2.20180i) q^{35} +(-1.09265 - 6.19675i) q^{37} +(-0.848730 + 0.426248i) q^{38} +(-0.619842 - 1.43696i) q^{40} +(1.44585 + 3.35186i) q^{41} +(-5.37705 + 2.70046i) q^{43} +(2.74873 + 15.5888i) q^{44} +(-2.90527 + 16.4766i) q^{46} +(1.88833 + 6.30747i) q^{47} +(6.71394 + 3.37187i) q^{49} +(-3.03673 + 10.1434i) q^{50} +(-4.70944 - 6.32588i) q^{52} +(-1.23882 - 2.14569i) q^{53} +(-1.46413 + 2.53595i) q^{55} +(10.0899 - 1.17934i) q^{56} +(-11.6906 + 2.77072i) q^{58} +(3.87162 - 2.54640i) q^{59} +(-7.81976 + 8.28846i) q^{61} +(-5.11909 - 4.29543i) q^{62} +(-9.97283 + 8.36820i) q^{64} +(0.0848280 - 1.45644i) q^{65} +(3.55143 - 4.77040i) q^{67} +(-9.00226 - 1.05221i) q^{68} +(4.24831 + 2.79416i) q^{70} +(-2.65492 - 0.966311i) q^{71} +(12.9084 - 4.69828i) q^{73} +(13.9250 + 3.30028i) q^{74} +(-0.0770319 - 1.32259i) q^{76} +(-13.0443 - 13.8261i) q^{77} +(4.97764 - 11.5395i) q^{79} -0.164537 q^{80} -8.30214 q^{82} +(-0.831044 + 1.92658i) q^{83} +(-1.15060 - 1.21956i) q^{85} +(-0.795693 - 13.6615i) q^{86} +(-12.9464 - 3.06835i) q^{88} +(0.324629 - 0.118155i) q^{89} +(8.89913 + 3.23902i) q^{91} +(-19.4987 - 12.8245i) q^{92} +(-14.8729 - 1.73840i) q^{94} +(0.146352 - 0.196584i) q^{95} +(-0.637880 + 10.9520i) q^{97} +(-13.0895 + 10.9834i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8}+O(q^{10}) \) 144 * q - 9 * q^2 + 9 * q^4 - 9 * q^5 + 9 * q^7 + 18 * q^8	\( 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8} - 18 q^{10} - 9 q^{11} + 9 q^{13} - 9 q^{14} + 9 q^{16} + 18 q^{17} - 18 q^{19} - 45 q^{20} + 9 q^{22} + 45 q^{23} + 9 q^{25} - 45 q^{26} - 9 q^{28} - 36 q^{29} + 9 q^{31} + 99 q^{32} + 9 q^{34} - 9 q^{35} - 18 q^{37} - 18 q^{38} + 9 q^{40} - 27 q^{41} + 9 q^{43} - 54 q^{44} - 18 q^{46} + 99 q^{47} + 9 q^{49} - 126 q^{50} - 27 q^{52} - 45 q^{53} - 9 q^{55} + 225 q^{56} + 9 q^{58} - 72 q^{59} + 9 q^{61} - 81 q^{62} - 18 q^{64} + 81 q^{65} - 45 q^{67} - 117 q^{68} - 99 q^{70} + 90 q^{71} - 18 q^{73} - 81 q^{74} - 153 q^{76} - 81 q^{77} - 99 q^{79} + 288 q^{80} - 36 q^{82} - 45 q^{83} - 99 q^{85} - 81 q^{86} - 153 q^{88} + 81 q^{89} - 18 q^{91} - 207 q^{92} - 99 q^{94} + 171 q^{95} - 45 q^{97} - 81 q^{98}+O(q^{100}) \) 144 * q - 9 * q^2 + 9 * q^4 - 9 * q^5 + 9 * q^7 + 18 * q^8 - 18 * q^10 - 9 * q^11 + 9 * q^13 - 9 * q^14 + 9 * q^16 + 18 * q^17 - 18 * q^19 - 45 * q^20 + 9 * q^22 + 45 * q^23 + 9 * q^25 - 45 * q^26 - 9 * q^28 - 36 * q^29 + 9 * q^31 + 99 * q^32 + 9 * q^34 - 9 * q^35 - 18 * q^37 - 18 * q^38 + 9 * q^40 - 27 * q^41 + 9 * q^43 - 54 * q^44 - 18 * q^46 + 99 * q^47 + 9 * q^49 - 126 * q^50 - 27 * q^52 - 45 * q^53 - 9 * q^55 + 225 * q^56 + 9 * q^58 - 72 * q^59 + 9 * q^61 - 81 * q^62 - 18 * q^64 + 81 * q^65 - 45 * q^67 - 117 * q^68 - 99 * q^70 + 90 * q^71 - 18 * q^73 - 81 * q^74 - 153 * q^76 - 81 * q^77 - 99 * q^79 + 288 * q^80 - 36 * q^82 - 45 * q^83 - 99 * q^85 - 81 * q^86 - 153 * q^88 + 81 * q^89 - 18 * q^91 - 207 * q^92 - 99 * q^94 + 171 * q^95 - 45 * q^97 - 81 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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