LMFDB - Embedded newform 729.2.g.d.676.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("729.28");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			676.8
Character	$\chi$	$=$	729.676
Dual form			729.2.g.d.55.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.900807 + 2.08831i) q^{2} +(-2.17708 + 2.30757i) q^{4} +(0.0341238 - 0.585883i) q^{5} +(3.70692 - 0.878555i) q^{7} +(-2.50575 - 0.912019i) q^{8} +O(q^{10})$	\(q+(0.900807 + 2.08831i) q^{2} +(-2.17708 + 2.30757i) q^{4} +(0.0341238 - 0.585883i) q^{5} +(3.70692 - 0.878555i) q^{7} +(-2.50575 - 0.912019i) q^{8} +(1.25424 - 0.456507i) q^{10} +(4.16873 - 2.74182i) q^{11} +(2.46908 - 0.288594i) q^{13} +(5.17391 + 6.94977i) q^{14} +(0.0163015 + 0.279887i) q^{16} +(-2.18854 - 1.83640i) q^{17} +(0.319901 - 0.268429i) q^{19} +(1.27768 + 1.35426i) q^{20} +(9.48097 + 6.23573i) q^{22} +(-7.15813 - 1.69651i) q^{23} +(4.62410 + 0.540479i) q^{25} +(2.82684 + 4.89622i) q^{26} +(-6.04293 + 10.4667i) q^{28} +(-3.15459 + 4.23736i) q^{29} +(-0.842702 - 2.81482i) q^{31} +(-5.33566 + 2.67967i) q^{32} +(1.86352 - 6.22458i) q^{34} +(-0.388237 - 2.20180i) q^{35} +(-1.09265 + 6.19675i) q^{37} +(0.848730 + 0.426248i) q^{38} +(-0.619842 + 1.43696i) q^{40} +(-1.44585 + 3.35186i) q^{41} +(-5.37705 - 2.70046i) q^{43} +(-2.74873 + 15.5888i) q^{44} +(-2.90527 - 16.4766i) q^{46} +(-1.88833 + 6.30747i) q^{47} +(6.71394 - 3.37187i) q^{49} +(3.03673 + 10.1434i) q^{50} +(-4.70944 + 6.32588i) q^{52} +(1.23882 - 2.14569i) q^{53} +(-1.46413 - 2.53595i) q^{55} +(-10.0899 - 1.17934i) q^{56} +(-11.6906 - 2.77072i) q^{58} +(-3.87162 - 2.54640i) q^{59} +(-7.81976 - 8.28846i) q^{61} +(5.11909 - 4.29543i) q^{62} +(-9.97283 - 8.36820i) q^{64} +(-0.0848280 - 1.45644i) q^{65} +(3.55143 + 4.77040i) q^{67} +(9.00226 - 1.05221i) q^{68} +(4.24831 - 2.79416i) q^{70} +(2.65492 - 0.966311i) q^{71} +(12.9084 + 4.69828i) q^{73} +(-13.9250 + 3.30028i) q^{74} +(-0.0770319 + 1.32259i) q^{76} +(13.0443 - 13.8261i) q^{77} +(4.97764 + 11.5395i) q^{79} +0.164537 q^{80} -8.30214 q^{82} +(0.831044 + 1.92658i) q^{83} +(-1.15060 + 1.21956i) q^{85} +(0.795693 - 13.6615i) q^{86} +(-12.9464 + 3.06835i) q^{88} +(-0.324629 - 0.118155i) q^{89} +(8.89913 - 3.23902i) q^{91} +(19.4987 - 12.8245i) q^{92} +(-14.8729 + 1.73840i) q^{94} +(-0.146352 - 0.196584i) q^{95} +(-0.637880 - 10.9520i) q^{97} +(13.0895 + 10.9834i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	0.900807	+	2.08831i	0.636967	+	1.47665i	0.864371	+	0.502855i	$0.167717\pi$
$2$	0.900807	+	2.08831i	0.636967	+	1.47665i	−0.227404	+	0.973800i	$0.573024\pi$
$3$		0			0
$3$		0			0
$4$	−2.17708	+	2.30757i	−1.08854	+	1.15379i
$5$	0.0341238	−	0.585883i	0.0152606	−	0.262015i	−0.982044	−	0.188650i	$-0.939589\pi$
$5$	0.0341238	−	0.585883i	0.0152606	−	0.262015i	0.997305	−	0.0733655i	$-0.0233740\pi$
$6$		0			0
$7$	3.70692	−	0.878555i	1.40108	−	0.332063i	0.540487	−	0.841352i	$-0.318240\pi$
$7$	3.70692	−	0.878555i	1.40108	−	0.332063i	0.860595	+	0.509289i	$0.170092\pi$
$8$	−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	$-0.414175\pi$
$11$	4.16873	−	2.74182i	1.25692	−	0.826689i	0.990546	+	0.137181i	$0.0438042\pi$
$12$		0			0
$13$	2.46908	−	0.288594i	0.684799	−	0.0800416i	0.233423	−	0.972375i	$-0.425007\pi$
$13$	2.46908	−	0.288594i	0.684799	−	0.0800416i	0.451376	+	0.892334i	$0.350933\pi$
$14$	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	$-0.390392\pi$
$17$	−2.18854	−	1.83640i	−0.530799	−	0.445393i	−0.868377	+	0.495904i	$0.834837\pi$
$18$		0			0
$19$	0.319901	−	0.268429i	0.0733903	−	0.0615818i	−0.605355	−	0.795956i	$-0.706969\pi$
$19$	0.319901	−	0.268429i	0.0733903	−	0.0615818i	0.678745	+	0.734374i	$0.262524\pi$
$20$	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	$-0.704157\pi$
$23$	−7.15813	−	1.69651i	−1.49257	−	0.353746i	−0.894271	+	0.447525i	$0.852306\pi$
$24$		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	$-0.959476\pi$
$29$	−3.15459	+	4.23736i	−0.585794	+	0.786857i	0.406114	+	0.913823i	$0.366884\pi$
$30$		0			0
$31$	−0.842702	−	2.81482i	−0.151354	−	0.505556i	0.848362	−	0.529417i	$-0.177589\pi$
$31$	−0.842702	−	2.81482i	−0.151354	−	0.505556i	−0.999715	+	0.0238607i	$0.992404\pi$
$32$	−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	0.753030	+	0.657986i	$0.228591\pi$
$37$	−1.09265	+	6.19675i	−0.179631	+	1.01874i	−0.932661	+	0.360753i	$0.882520\pi$
$38$	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	$-0.962380\pi$
$41$	−1.44585	+	3.35186i	−0.225804	+	0.523473i	0.767220	+	0.641384i	$0.221639\pi$
$42$		0			0
$43$	−5.37705	−	2.70046i	−0.819993	−	0.411816i	−0.0112199	−	0.999937i	$-0.503571\pi$
$43$	−5.37705	−	2.70046i	−0.819993	−	0.411816i	−0.808773	+	0.588121i	$0.799868\pi$
$44$	−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	0.702592	+	0.711592i	$0.252026\pi$
$47$	−1.88833	+	6.30747i	−0.275441	+	0.920038i	−0.978034	+	0.208446i	$0.933159\pi$
$48$		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	$-0.778903\pi$
$53$	1.23882	−	2.14569i	0.170165	−	0.294734i	0.938477	+	0.345341i	$0.112237\pi$
$54$		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	$-0.412351\pi$
$59$	−3.87162	−	2.54640i	−0.504042	−	0.331513i	−0.775934	+	0.630814i	$0.782721\pi$
$60$		0			0
$61$	−7.81976	−	8.28846i	−1.00122	−	1.06123i	−0.998123	−	0.0612331i	$-0.980497\pi$
$61$	−7.81976	−	8.28846i	−1.00122	−	1.06123i	−0.00309376	−	0.999995i	$-0.500985\pi$
$62$	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	0.964259	−	0.264961i	$-0.0853592\pi$
$67$	3.55143	+	4.77040i	0.433876	+	0.582797i	−0.530383	+	0.847758i	$0.677952\pi$
$68$	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	$-0.557493\pi$
$71$	2.65492	−	0.966311i	0.315081	−	0.114680i	0.494720	+	0.869053i	$0.335271\pi$
$72$		0			0
$73$	12.9084	+	4.69828i	1.51082	+	0.549892i	0.958835	−	0.283965i	$-0.0916499\pi$
$73$	12.9084	+	4.69828i	1.51082	+	0.549892i	0.551981	+	0.833857i	$0.313872\pi$
$74$	−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	0.929422	+	0.369018i	$0.120306\pi$
$79$	4.97764	+	11.5395i	0.560028	+	1.29829i	−0.369394	+	0.929273i	$0.620435\pi$
$80$	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	$-0.0928940\pi$
$83$	0.831044	+	1.92658i	0.0912190	+	0.211469i	−0.866499	+	0.499180i	$0.833635\pi$
$84$		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	$-0.394717\pi$
$89$	−0.324629	−	0.118155i	−0.0344106	−	0.0125244i	−0.359168	+	0.933273i	$0.616940\pi$
$90$		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	−0.861528	−	0.507710i	$-0.830492\pi$
$97$	−0.637880	−	10.9520i	−0.0647669	−	1.11200i	0.796761	−	0.604294i	$-0.206545\pi$
$98$	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	$-0.212615\pi$
$101$	1.21720	+	1.29016i	0.121116	+	0.128375i	−0.663978	+	0.747752i	$0.731133\pi$
$102$		0			0
$103$	−14.7026	−	9.67007i	−1.44869	−	0.952820i	−0.998196	−	0.0600415i	$-0.980877\pi$
$103$	−14.7026	−	9.67007i	−1.44869	−	0.952820i	−0.450496	−	0.892778i	$-0.648753\pi$
$104$	−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	$-0.237089\pi$
$107$	−2.26990	−	3.93158i	−0.219439	−	0.380080i	−0.954637	+	0.297773i	$0.903756\pi$
$108$		0			0
$109$	−1.95094	+	3.37913i	−0.186866	+	0.323662i	−0.944204	−	0.329362i	$-0.893166\pi$
$109$	−1.95094	+	3.37913i	−0.186866	+	0.323662i	0.757337	+	0.653024i	$0.226500\pi$
$110$	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	$-0.858280\pi$
$113$	−11.6508	+	5.85125i	−1.09601	+	0.550439i	−0.193500	+	0.981100i	$0.561984\pi$
$114$		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	−0.980557	−	0.196236i	$-0.937128\pi$
$127$	−1.42278	−	8.06900i	−0.126252	−	0.716008i	0.854305	−	0.519772i	$-0.173983\pi$
$128$	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	$-0.0684339\pi$
$131$	0.497800	+	1.66277i	0.0434930	+	0.145277i	−0.933485	+	0.358616i	$0.883249\pi$
$132$		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	$-0.425510\pi$
$137$	2.72944	+	0.319026i	0.233192	+	0.0272562i	0.00130578	+	0.999999i	$0.499584\pi$
$138$		0			0
$139$	8.42078	+	1.99576i	0.714241	+	0.169278i	0.571643	−	0.820502i	$-0.306306\pi$
$139$	8.42078	+	1.99576i	0.714241	+	0.169278i	0.142598	+	0.989781i	$0.454454\pi$
$140$	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	$-0.612494\pi$
$149$	−5.69447	+	0.665588i	−0.466509	+	0.0545271i	−0.120408	+	0.992724i	$0.538420\pi$
$150$		0			0
$151$	−1.48268	+	0.975171i	−0.120658	+	0.0793583i	−0.608404	−	0.793628i	$-0.708190\pi$
$151$	−1.48268	+	0.975171i	−0.120658	+	0.0793583i	0.487745	+	0.872986i	$0.337819\pi$
$152$	−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	0.901582	+	0.432607i	$0.142406\pi$
$157$	−0.552903	+	9.49298i	−0.0441265	+	0.757623i	−0.945709	+	0.325015i	$0.894631\pi$
$158$	−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	−0.972450	−	0.233113i	$-0.925109\pi$
$167$	0.264756	−	4.54569i	0.0204875	−	0.351756i	0.992937	−	0.118643i	$-0.0378543\pi$
$168$		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	$-0.741802\pi$
$173$	−3.88862	+	2.55759i	−0.295647	+	0.194450i	0.393016	+	0.919532i	$0.371432\pi$
$174$		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	$-0.319206\pi$
$179$	−2.66027	−	2.23223i	−0.198838	−	0.166845i	−0.736770	+	0.676143i	$0.763650\pi$
$180$		0			0
$181$	−11.7147	+	9.82983i	−0.870749	+	0.730645i	−0.964256	−	0.264973i	$-0.914637\pi$
$181$	−11.7147	+	9.82983i	−0.870749	+	0.730645i	0.0935067	+	0.995619i	$0.470192\pi$
$182$	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	0.0132150	−	0.999913i	$-0.495793\pi$
$191$	13.3688	−	17.9574i	0.967331	−	1.29935i	0.954116	−	0.299438i	$-0.0967992\pi$
$192$		0			0
$193$	1.85645	+	6.20097i	0.133630	+	0.446356i	0.998446	−	0.0557339i	$-0.0177499\pi$
$193$	1.85645	+	6.20097i	0.133630	+	0.446356i	−0.864815	+	0.502090i	$0.832565\pi$
$194$	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	0.999713	+	0.0239741i	$0.00763191\pi$
$197$	0.961298	+	5.45179i	0.0684897	+	0.388424i	−0.931223	+	0.364450i	$0.881257\pi$
$198$		0			0
$199$	−2.91762	+	16.5467i	−0.206825	+	1.17296i	0.687717	+	0.725979i	$0.258613\pi$
$199$	−2.91762	+	16.5467i	−0.206825	+	1.17296i	−0.894542	+	0.446984i	$0.852498\pi$
$200$	−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	−0.668278	−	0.743912i	$-0.732968\pi$
$211$	−6.83640	+	3.43337i	−0.470637	+	0.236363i	0.197641	+	0.980275i	$0.436672\pi$
$212$	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	0.891931	−	0.452171i	$-0.149350\pi$
$223$	5.80400	+	6.15188i	0.388664	+	0.411960i	−0.503267	+	0.864131i	$0.667869\pi$
$224$	−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	−0.511869	−	0.859064i	$-0.671047\pi$
$227$	−1.55475	−	26.6940i	−0.103192	−	1.77174i	0.408676	−	0.912679i	$-0.365991\pi$
$228$		0			0
$229$	−1.83844	−	2.46946i	−0.121488	−	0.163187i	0.737219	−	0.675654i	$-0.236139\pi$
$229$	−1.83844	−	2.46946i	−0.121488	−	0.163187i	−0.858706	+	0.512468i	$0.828731\pi$
$230$	−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	$-0.536346\pi$
$233$	6.67642	−	2.43002i	0.437387	−	0.159196i	0.551322	+	0.834292i	$0.314124\pi$
$234$		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	$-0.806647\pi$
$239$	−3.14712	+	3.33575i	−0.203570	+	0.215772i	0.617543	+	0.786537i	$0.288128\pi$
$240$		0			0
$241$	2.43878	+	5.65373i	0.157096	+	0.364188i	0.978527	−	0.206119i	$-0.0660834\pi$
$241$	2.43878	+	5.65373i	0.157096	+	0.364188i	−0.821431	+	0.570307i	$0.806824\pi$
$242$	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	$-0.0111339\pi$
$251$	27.6062	+	10.0478i	1.74249	+	0.634213i	0.743097	+	0.669184i	$0.233356\pi$
$252$		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	$-0.404454\pi$
$257$	−11.2905	−	15.1657i	−0.704279	−	0.946011i	−0.999957	+	0.00927680i	$0.997047\pi$
$258$		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	$-0.0915653\pi$
$263$	10.0535	+	10.6561i	0.619924	+	0.657081i	−0.338986	+	0.940792i	$0.610084\pi$
$264$		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	$-0.224138\pi$
$269$	−2.94518	−	5.10121i	−0.179571	−	0.311026i	−0.941734	+	0.336360i	$0.890804\pi$
$270$		0			0
$271$	11.5965	−	20.0857i	0.704435	−	1.22012i	−0.262460	−	0.964943i	$-0.584534\pi$
$271$	11.5965	−	20.0857i	0.704435	−	1.22012i	0.966895	−	0.255175i	$-0.0821330\pi$
$272$	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	−0.665741	−	0.746183i	$-0.731884\pi$
$277$	5.00151	−	16.7062i	0.300512	−	1.00378i	0.966253	−	0.257596i	$-0.0829304\pi$
$278$	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	$-0.676863\pi$
$281$	−25.5457	−	12.8295i	−1.52393	−	0.765346i	−0.996447	+	0.0842212i	$0.973160\pi$
$282$		0			0
$283$	7.05408	−	16.3532i	0.419321	−	0.972096i	−0.569363	−	0.822086i	$-0.692810\pi$
$283$	7.05408	−	16.3532i	0.419321	−	0.972096i	0.988684	−	0.150010i	$-0.0479306\pi$
$284$	−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	−0.976649	−	0.214842i	$-0.931076\pi$
$293$	−4.77106	−	15.9365i	−0.278728	−	0.931018i	0.697920	−	0.716175i	$-0.254109\pi$
$294$		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	0.279912	−	0.960026i	$-0.409695\pi$
$307$	−10.8094	−	9.07013i	−0.616923	−	0.517660i	−0.896835	+	0.442366i	$0.854139\pi$
$308$	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	$-0.303125\pi$
$311$	23.4882	−	2.74537i	1.33189	−	0.155676i	0.752079	+	0.659073i	$0.229051\pi$
$312$		0			0
$313$	−6.83757	+	4.49714i	−0.386482	+	0.254193i	−0.727850	−	0.685736i	$-0.759480\pi$
$313$	−6.83757	+	4.49714i	−0.386482	+	0.254193i	0.341368	+	0.939930i	$0.389110\pi$
$314$	−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	$-0.610792\pi$
$317$	−3.98806	+	0.945186i	−0.223991	+	0.0530870i	0.117087	+	0.993122i	$0.462644\pi$
$318$		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	−0.831867	−	0.554975i	$-0.812728\pi$
$331$	−24.1277	+	5.71837i	−1.32618	+	0.314310i	−0.494312	+	0.869285i	$0.664580\pi$
$332$	−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	−0.515885	−	0.856658i	$-0.672537\pi$
$337$	−15.0588	+	1.76012i	−0.820306	+	0.0958800i	−0.304421	+	0.952538i	$0.598463\pi$
$338$	−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	$-0.190365\pi$
$347$	24.4451	+	5.79358i	1.31228	+	0.311016i	0.485843	+	0.874046i	$0.338513\pi$
$348$		0			0
$349$	17.2284	+	2.01371i	0.922214	+	0.107791i	0.563931	−	0.825822i	$-0.309288\pi$
$349$	17.2284	+	2.01371i	0.922214	+	0.107791i	0.358283	+	0.933613i	$0.383362\pi$
$350$	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	$-0.992496\pi$
$353$	−12.9718	+	17.4241i	−0.690418	+	0.927392i	0.309305	+	0.950963i	$0.399904\pi$
$354$		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	0.802911	+	0.596100i	$0.203284\pi$
$359$	4.78039	+	27.1110i	0.252299	+	1.43086i	−0.550611	+	0.834762i	$0.685605\pi$
$360$		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	−0.221582	−	0.975142i	$-0.571122\pi$
$367$	−21.7643	−	10.9304i	−1.13609	−	0.570564i	−0.914504	+	0.404578i	$0.867418\pi$
$368$	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	−0.0191124	−	0.999817i	$-0.506084\pi$
$373$	14.8992	−	7.48266i	0.771451	−	0.387437i	0.790564	+	0.612380i	$0.209788\pi$
$374$	−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	0.891329	−	0.453357i	$-0.149774\pi$
$379$	1.03268	+	1.78866i	0.0530454	+	0.0918773i	−0.838283	+	0.545235i	$0.816441\pi$
$380$	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	$-0.194799\pi$
$383$	12.0397	+	7.91867i	0.615202	+	0.404625i	−0.203310	+	0.979115i	$0.565170\pi$
$384$		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	0.966376	+	0.257135i	$0.0827785\pi$
$389$	0.717641	+	12.3214i	0.0363858	+	0.624720i	−0.929990	+	0.367586i	$0.880184\pi$
$390$		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	−0.152152	−	0.988357i	$-0.548620\pi$
$397$	−18.0123	−	6.55594i	−0.904011	−	0.329033i	−0.751859	+	0.659324i	$0.770843\pi$
$398$	−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	$-0.840277\pi$
$401$	−6.92003	+	7.33480i	−0.345570	+	0.366283i	0.531155	+	0.847275i	$0.321758\pi$
$402$		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	−0.665998	−	0.745954i	$-0.731994\pi$
$409$	2.37463	−	2.51696i	0.117418	−	0.124456i	0.783416	+	0.621498i	$0.213476\pi$
$410$	−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	$-0.158220\pi$
$419$	3.48138	+	4.67630i	0.170076	+	0.228452i	−0.708910	+	0.705299i	$0.750813\pi$
$420$		0			0
$421$	−2.24181	−	38.4903i	−0.109259	−	1.87590i	−0.396486	−	0.918041i	$-0.629771\pi$
$421$	−2.24181	−	38.4903i	−0.109259	−	1.87590i	0.287227	−	0.957862i	$-0.407266\pi$
$422$	−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	$-0.168217\pi$
$431$	−0.101111	−	0.175130i	−0.00487036	−	0.00843570i	−0.868450	+	0.495776i	$0.834884\pi$
$432$		0			0
$433$	4.03061	−	6.98122i	0.193699	−	0.335496i	−0.752774	−	0.658279i	$-0.771285\pi$
$433$	4.03061	−	6.98122i	0.193699	−	0.335496i	0.946473	+	0.322782i	$0.104618\pi$
$434$	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	−0.941724	−	0.336386i	$-0.890795\pi$
$439$	0.626933	−	2.09410i	0.0299219	−	0.0999461i	0.971646	+	0.236440i	$0.0759806\pi$
$440$	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	$-0.0727584\pi$
$443$	28.9164	+	14.5224i	1.37386	+	0.689979i	0.399872	+	0.916571i	$0.369055\pi$
$444$		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	0.233505	+	0.972356i	$0.424980\pi$
$449$	−6.74854	+	38.2728i	−0.318483	+	1.80621i	−0.551988	+	0.833852i	$0.686131\pi$
$450$		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	0.167767	+	0.985827i	$0.446344\pi$
$457$	−17.6314	+	23.6830i	−0.824760	+	1.10785i	−0.992528	+	0.122019i	$0.961063\pi$
$458$	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	$-0.295839\pi$
$461$	21.3788	+	2.49882i	0.995709	+	0.116382i	0.397398	+	0.917646i	$0.369913\pi$
$462$		0			0
$463$	−33.9982	−	8.05773i	−1.58003	−	0.374474i	−0.655384	−	0.755296i	$-0.727493\pi$
$463$	−33.9982	−	8.05773i	−1.58003	−	0.374474i	−0.924648	+	0.380822i	$0.875641\pi$
$464$	−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	$-0.524880\pi$
$467$	19.2365	−	16.1414i	0.890161	−	0.746933i	0.968242	+	0.250014i	$0.0804351\pi$
$468$		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	$-0.502111\pi$
$479$	9.54744	−	2.26279i	0.436234	−	0.103389i	0.442864	+	0.896589i	$0.353962\pi$
$480$		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	0.969137	+	0.246522i	$0.0792879\pi$
$491$	−0.488962	+	8.39515i	−0.0220665	+	0.378868i	−0.991204	+	0.132345i	$0.957749\pi$
$492$		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	−0.634830	−	0.772652i	$-0.718930\pi$
$499$	−23.9994	+	2.80513i	−1.07436	+	0.125575i	−0.439533	+	0.898227i	$0.644856\pi$
$500$	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	$-0.251667\pi$
$503$	2.81544	+	2.36243i	0.125534	+	0.105336i	−0.577859	+	0.816136i	$0.696112\pi$
$504$		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	$-0.200301\pi$
$509$	28.5800	+	6.77359i	1.26679	+	0.300234i	0.458326	+	0.888784i	$0.348449\pi$
$510$		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	−0.772026	−	0.635591i	$-0.780757\pi$
$521$	−6.02463	−	34.1674i	−0.263944	−	1.49690i	0.508083	−	0.861308i	$-0.330354\pi$
$522$		0			0
$523$	5.01556	−	28.4447i	0.219315	−	1.24380i	−0.653944	−	0.756543i	$-0.726887\pi$
$523$	5.01556	−	28.4447i	0.219315	−	1.24380i	0.873259	−	0.487256i	$-0.162002\pi$
$524$	−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	0.943355	−	0.331784i	$-0.107650\pi$
$541$	4.28774	+	7.42658i	0.184344	+	0.319294i	−0.759011	+	0.651078i	$0.774317\pi$
$542$	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	0.982413	−	0.186723i	$-0.0597867\pi$
$547$	17.2810	+	18.3168i	0.738883	+	0.783170i	−0.243529	+	0.969894i	$0.578305\pi$
$548$	−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	$-0.723357\pi$
$557$	−15.3188	+	5.57558i	−0.649077	+	0.236245i	−0.00356379	+	0.999994i	$0.501134\pi$
$558$		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	0.350802	−	0.936450i	$-0.385909\pi$
$563$	30.0218	−	31.8213i	1.26527	−	1.34111i	0.914468	−	0.404658i	$-0.132609\pi$
$564$		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	−0.923760	−	0.382971i	$-0.874901\pi$
$569$	−13.5585	−	31.4321i	−0.568401	−	1.31770i	0.355359	−	0.934730i	$-0.384359\pi$
$570$		0			0
$571$	22.2208	−	23.5527i	0.929912	−	0.985649i	−0.0700176	−	0.997546i	$-0.522306\pi$
$571$	22.2208	−	23.5527i	0.929912	−	0.985649i	0.999929	+	0.0118970i	$0.00378701\pi$
$572$	−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	0.793069	−	0.609132i	$-0.208482\pi$
$577$	43.0486	−	15.6684i	1.79214	−	0.652285i	0.999068	−	0.0431527i	$-0.0137402\pi$
$578$	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	0.943688	+	0.330837i	$0.107331\pi$
$587$	29.5363	+	31.3067i	1.21909	+	1.29216i	0.275406	+	0.961328i	$0.411188\pi$
$588$		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	0.997830	+	0.0658415i	$0.0209732\pi$
$593$	13.5379	+	23.4484i	0.555935	+	0.962909i	−0.441895	+	0.897067i	$0.645693\pi$
$594$		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	$-0.661343\pi$
$599$	−1.81269	+	0.910367i	−0.0740645	+	0.0371966i	0.411381	+	0.911463i	$0.365046\pi$
$600$		0			0
$601$	−2.25001	+	7.51554i	−0.0917797	+	0.306565i	−0.991537	−	0.129825i	$-0.958558\pi$
$601$	−2.25001	+	7.51554i	−0.0917797	+	0.306565i	0.899757	+	0.436391i	$0.143743\pi$
$602$	−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	0.668710	+	0.743523i	$0.266847\pi$
$607$	−8.15511	+	18.9057i	−0.331006	+	0.767357i	−0.999716	+	0.0238342i	$0.992413\pi$
$608$	−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	0.979332	−	0.202258i	$-0.0648280\pi$
$613$	−0.250445	−	1.42034i	−0.0101154	−	0.0573671i	−0.989448	+	0.144891i	$0.953717\pi$
$614$	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	$-0.114354\pi$
$617$	−0.973306	−	3.25107i	−0.0391838	−	0.130883i	−0.975344	+	0.220692i	$0.929169\pi$
$618$		0			0
$619$	18.4750	−	24.8162i	0.742573	−	0.997448i	−0.256946	−	0.966426i	$-0.582716\pi$
$619$	18.4750	−	24.8162i	0.742573	−	0.997448i	0.999519	−	0.0310226i	$-0.00987637\pi$
$620$	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	0.990122	−	0.140210i	$-0.0447778\pi$
$631$	25.7219	+	21.5833i	1.02397	+	0.859217i	0.0338527	+	0.999427i	$0.489222\pi$
$632$	−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	$-0.677201\pi$
$641$	−15.6851	+	3.71744i	−0.619525	+	0.146830i	−0.0911441	+	0.995838i	$0.529052\pi$
$642$		0			0
$643$	−0.436643	+	7.49687i	−0.0172195	+	0.295648i	0.978693	+	0.205328i	$0.0658260\pi$
$643$	−0.436643	+	7.49687i	−0.0172195	+	0.295648i	−0.995913	+	0.0903200i	$0.971211\pi$
$644$	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	$-0.383223\pi$
$647$	18.2475			0.717384			0.358692	+	0.933456i	$0.383223\pi$
$648$		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	−0.974688	−	0.223571i	$-0.928229\pi$
$653$	0.494837	−	8.49602i	0.0193645	−	0.332475i	0.994052	−	0.108904i	$-0.0347343\pi$
$654$		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	$-0.602673\pi$
$659$	10.9953	−	7.23170i	0.428315	−	0.281707i	0.745308	+	0.666721i	$0.232303\pi$
$660$		0			0
$661$	11.5306	−	1.34774i	0.448489	−	0.0524209i	0.111149	−	0.993804i	$-0.464547\pi$
$661$	11.5306	−	1.34774i	0.448489	−	0.0524209i	0.337340	+	0.941383i	$0.390473\pi$
$662$	−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	−0.695636	−	0.718394i	$-0.744877\pi$
$673$	−39.9042	−	4.66413i	−1.53819	−	0.179789i	−0.842558	+	0.538605i	$0.818951\pi$
$674$	−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	$-0.881089\pi$
$677$	−8.18041	+	10.9882i	−0.314399	+	0.422311i	0.616632	+	0.787251i	$0.288497\pi$
$678$		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	0.977230	+	0.212181i	$0.0680566\pi$
$683$	3.43677	+	19.4909i	0.131504	+	0.745798i	−0.845726	+	0.533617i	$0.820832\pi$
$684$		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	0.601339	−	0.798994i	$-0.294634\pi$
$691$	8.39976	+	4.21852i	0.319542	+	0.160480i	−0.281797	+	0.959474i	$0.590930\pi$
$692$	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	$-0.714569\pi$
$701$	9.65096	−	16.7160i	0.364512	−	0.631353i	0.988698	+	0.149923i	$0.0479026\pi$
$702$		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	0.586457	−	0.809980i	$-0.300522\pi$
$709$	−6.82324	−	7.23221i	−0.256252	−	0.271611i	−0.842709	+	0.538369i	$0.819041\pi$
$710$	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	$-0.357956\pi$
$719$	35.9855	−	13.0976i	1.34203	−	0.488459i	0.910452	+	0.413615i	$0.135734\pi$
$720$		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	0.999070	+	0.0431127i	$0.0137274\pi$
$727$	9.29751	+	21.5541i	0.344826	+	0.799396i	−0.654245	+	0.756283i	$0.727013\pi$
$728$	−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	−0.409242	−	0.912426i	$-0.634207\pi$
$733$	14.2256	−	15.0783i	0.525435	−	0.556928i	0.934677	+	0.355497i	$0.115688\pi$
$734$	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	−0.645616	−	0.763663i	$-0.723399\pi$
$739$	−17.6513	+	6.42454i	−0.649313	+	0.236331i	−0.00369738	+	0.999993i	$0.501177\pi$
$740$	−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	$-0.0106204\pi$
$743$	18.5584	+	24.9283i	0.680842	+	0.914530i	−0.318601	+	0.947889i	$0.603213\pi$
$744$		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	0.861479	−	0.507794i	$-0.169539\pi$
$751$	20.1814	+	13.2735i	0.736428	+	0.484357i	−0.125050	+	0.992150i	$0.539909\pi$
$752$	−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	−0.857589	−	0.514335i	$-0.828039\pi$
$757$	0.457633	−	0.792644i	0.0166330	−	0.0288091i	0.874222	+	0.485526i	$0.161372\pi$
$758$	−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	$-0.768610\pi$
$761$	−18.2165	+	9.14866i	−0.660347	+	0.331639i	0.0868695	+	0.996220i	$0.472314\pi$
$762$		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	−0.677283	−	0.735723i	$-0.736843\pi$
$769$	8.94714	−	20.7418i	0.322642	−	0.747969i	0.999925	−	0.0122459i	$-0.00389809\pi$
$770$	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	$-0.954040\pi$
$773$	−0.291023	+	1.65048i	−0.0104674	+	0.0593635i	0.979127	+	0.203251i	$0.0651508\pi$
$774$		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
$784$	1.05319	+	1.82418i	0.0376139	+	0.0651491i
$785$	5.54291	+	0.647874i	0.197835	+	0.0231236i
$786$		0			0
$787$	−30.5244	−	7.23441i	−1.08808	−	0.257879i	−0.352836	−	0.935685i	$-0.614783\pi$
$787$	−30.5244	−	7.23441i	−1.08808	−	0.257879i	−0.735241	+	0.677806i	$0.762931\pi$
$788$	−14.6732	−	9.65074i	−0.522712	−	0.343793i
$789$		0			0
$790$	11.5110	+	12.2010i	0.409543	+	0.434091i
$791$	−38.0479	+	31.9259i	−1.35283	+	1.13516i
$792$		0			0
$793$	−21.6996	−	18.2081i	−0.770575	−	0.646590i
$794$	−2.53480	−	43.5208i	−0.0899566	−	1.54450i
$795$		0			0
$796$	−31.8307	−	42.7561i	−1.12821	−	1.51545i
$797$	−46.9017	+	5.48202i	−1.66134	+	0.194183i	−0.894317	−	0.447433i	$-0.852338\pi$
$797$	−46.9017	+	5.48202i	−1.66134	+	0.194183i	−0.767026	+	0.641616i	$0.778264\pi$
$798$		0			0
$799$	15.7157	−	10.3364i	0.555983	−	0.365675i
$800$	−26.1209	+	9.50724i	−0.923514	+	0.336132i
$801$		0			0
$802$	−21.5509	−	7.84389i	−0.760990	−	0.276978i
$803$	66.6935	−	15.8067i	2.35356	−	0.557805i
$804$		0			0
$805$	−0.956322	+	16.4194i	−0.0337059	+	0.578708i
$806$	11.3998	−	12.0831i	0.401541	−	0.425609i
$807$		0			0
$808$	−1.87335	−	4.34292i	−0.0659043	−	0.152783i
$809$	15.1675			0.533260			0.266630	−	0.963799i	$-0.414090\pi$
$809$	15.1675			0.533260			0.266630	+	0.963799i	$0.414090\pi$
$810$		0			0
$811$	35.5509			1.24836			0.624181	−	0.781280i	$-0.285433\pi$
$811$	35.5509			1.24836			0.624181	+	0.781280i	$0.285433\pi$
$812$	−25.2880	−	58.6242i	−0.887435	−	2.05731i
$813$		0			0
$814$	−49.0007	+	51.9377i	−1.71747	+	1.82041i
$815$	0.252046	−	4.32747i	0.00882880	−	0.151585i
$816$		0			0
$817$	−2.44500	+	0.579477i	−0.0855399	+	0.0202733i
$818$	7.39526	+	2.69166i	0.258569	+	0.0941115i
$819$		0			0
$820$	−6.38662	+	2.32454i	−0.223031	+	0.0811765i
$821$	10.0693	−	6.62266i	0.351420	−	0.231132i	−0.361510	−	0.932368i	$-0.617738\pi$
$821$	10.0693	−	6.62266i	0.351420	−	0.231132i	0.712929	+	0.701236i	$0.247368\pi$
$822$		0			0
$823$	−36.4248	+	4.25745i	−1.26969	+	0.148406i	−0.724128	−	0.689665i	$-0.757758\pi$
$823$	−36.4248	+	4.25745i	−1.26969	+	0.148406i	−0.545562	+	0.838071i	$0.683684\pi$
$824$	28.0218	+	37.6398i	0.976186	+	1.31125i
$825$		0			0
$826$	−2.33449	−	40.0817i	−0.0812274	−	1.39462i
$827$	−35.8302	−	30.0651i	−1.24594	−	1.04547i	−0.997036	−	0.0769360i	$-0.975486\pi$
$827$	−35.8302	−	30.0651i	−1.24594	−	1.04547i	−0.248901	−	0.968529i	$-0.580069\pi$
$828$		0			0
$829$	0.460070	−	0.386045i	0.0159789	−	0.0134079i	−0.634763	−	0.772707i	$-0.718902\pi$
$829$	0.460070	−	0.386045i	0.0159789	−	0.0134079i	0.650742	+	0.759299i	$0.274458\pi$
$830$	1.92183	+	2.03702i	0.0667076	+	0.0707059i
$831$		0			0
$832$	−27.0387	−	17.7837i	−0.937399	−	0.616537i
$833$	−20.8858	−	4.95003i	−0.723651	−	0.171509i
$834$		0			0
$835$	−2.65421	−	0.310233i	−0.0918527	−	0.0107360i
$836$	3.30516	+	5.72471i	0.114312	+	0.197993i
$837$		0			0
$838$	−6.62950	+	11.4826i	−0.229012	+	0.396661i
$839$	−25.8762	+	34.7578i	−0.893347	+	1.19997i	0.0856961	+	0.996321i	$0.472689\pi$
$839$	−25.8762	+	34.7578i	−0.893347	+	1.19997i	−0.979043	+	0.203652i	$0.934719\pi$
$840$		0			0
$841$	0.313574	+	1.04741i	0.0108129	+	0.0361176i
$842$	78.3601	−	39.3539i	2.70047	−	1.35623i
$843$		0			0
$844$	6.96066	−	23.2502i	0.239596	−	0.800306i
$845$	0.695063	+	3.94190i	0.0239109	+	0.135605i
$846$		0			0
$847$	9.19255	−	52.1335i	0.315860	−	1.79133i
$848$	0.620745	+	0.311750i	0.0213165	+	0.0107055i
$849$		0			0
$850$	11.9813	−	27.7759i	0.410957	−	0.952705i
$851$	18.3342	−	42.5034i	0.628488	−	1.45700i
$852$		0			0
$853$	11.4240	+	5.73735i	0.391150	+	0.196443i	0.633494	−	0.773747i	$-0.281620\pi$
$853$	11.4240	+	5.73735i	0.391150	+	0.196443i	−0.242344	+	0.970190i	$0.577916\pi$
$854$	17.1441	−	97.2292i	0.586660	−	3.32711i
$855$		0			0
$856$	2.10213	+	11.9217i	0.0718492	+	0.407477i
$857$	−5.54688	+	18.5279i	−0.189478	+	0.632900i	0.809475	+	0.587154i	$0.199752\pi$
$857$	−5.54688	+	18.5279i	−0.189478	+	0.632900i	−0.998953	+	0.0457462i	$0.985433\pi$
$858$		0			0
$859$	23.6385	−	11.8717i	0.806535	−	0.405057i	0.00276431	−	0.999996i	$-0.499120\pi$
$859$	23.6385	−	11.8717i	0.806535	−	0.405057i	0.803771	+	0.594939i	$0.202824\pi$
$860$	−3.21302	−	10.7322i	−0.109563	−	0.365966i
$861$		0			0
$862$	0.274643	−	0.368909i	0.00935437	−	0.0125651i
$863$	−1.63147	+	2.82580i	−0.0555360	+	0.0961912i	−0.892457	−	0.451133i	$-0.851020\pi$
$863$	−1.63147	+	2.82580i	−0.0555360	+	0.0961912i	0.836921	+	0.547324i	$0.184353\pi$
$864$		0			0
$865$	1.36575	+	2.36556i	0.0464370	+	0.0804313i
$866$	18.2097	+	2.12841i	0.618792	+	0.0723264i
$867$		0			0
$868$	34.5542	+	8.18949i	1.17285	+	0.277969i
$869$	52.3895	+	34.4571i	1.77719	+	1.16888i
$870$		0			0
$871$	10.1455	+	10.7536i	0.343766	+	0.364371i
$872$	7.97041	−	6.68796i	0.269912	−	0.226483i
$873$		0			0
$874$	−5.35219	−	4.49102i	−0.181040	−	0.151911i
$875$	−1.25521	−	21.5511i	−0.0424338	−	0.728560i
$876$		0			0
$877$	−23.9734	−	32.2019i	−0.809526	−	1.08738i	−0.994510	−	0.104640i	$-0.966631\pi$
$877$	−23.9734	−	32.2019i	−0.809526	−	1.08738i	0.184984	−	0.982741i	$-0.440777\pi$
$878$	4.93787	−	0.577154i	0.166645	−	0.0194780i
$879$		0			0
$880$	0.685911	−	0.451131i	0.0231221	−	0.0152076i
$881$	42.6866	−	15.5367i	1.43815	−	0.523443i	0.498894	−	0.866663i	$-0.333740\pi$
$881$	42.6866	−	15.5367i	1.43815	−	0.523443i	0.939255	+	0.343220i	$0.111518\pi$
$882$		0			0
$883$	28.0681	+	10.2160i	0.944567	+	0.343794i	0.767968	−	0.640488i	$-0.221268\pi$
$883$	28.0681	+	10.2160i	0.944567	+	0.343794i	0.176599	+	0.984283i	$0.443490\pi$
$884$	21.9236	−	5.19600i	0.737372	−	0.174760i
$885$		0			0
$886$	−4.27904	+	73.4682i	−0.143757	+	2.46821i
$887$	−19.1243	+	20.2706i	−0.642131	+	0.680619i	−0.963920	−	0.266192i	$-0.914234\pi$
$887$	−19.1243	+	20.2706i	−0.642131	+	0.680619i	0.321789	+	0.946812i	$0.395716\pi$
$888$		0			0
$889$	−12.3632	−	28.6611i	−0.414648	−	0.961263i
$890$	−0.461102			−0.0154562
$891$		0			0
$892$	−26.8317			−0.898391
$893$	1.08903	+	2.52465i	0.0364429	+	0.0844841i
$894$		0			0
$895$	−1.39861	+	1.48244i	−0.0467502	+	0.0495524i
$896$	3.91335	−	67.1897i	0.130736	−	2.24465i
$897$		0			0
$898$	−86.0045	+	20.3834i	−2.87001	+	0.680204i
$899$	14.5858	+	5.30879i	0.486463	+	0.177058i
$900$		0			0
$901$	−6.65155	+	2.42097i	−0.221595	+	0.0806541i
$902$	−34.6094	+	22.7629i	−1.15237	+	0.757923i
$903$		0			0
$904$	34.5304	−	4.03603i	1.14846	−	0.134236i
$905$	5.35938	+	7.19890i	0.178152	+	0.239299i
$906$		0			0
$907$	1.60221	+	27.5088i	0.0532004	+	0.913415i	0.914315	+	0.405004i	$0.132730\pi$
$907$	1.60221	+	27.5088i	0.0532004	+	0.913415i	−0.861115	+	0.508411i	$0.830233\pi$
$908$	64.9832	+	54.5274i	2.15654	+	1.80955i
$909$		0			0
$910$	9.68303	−	8.12503i	0.320989	−	0.269342i
$911$	4.21950	+	4.47241i	0.139798	+	0.148177i	0.793490	−	0.608584i	$-0.208262\pi$
$911$	4.21950	+	4.47241i	0.139798	+	0.148177i	−0.653691	+	0.756761i	$0.726781\pi$
$912$		0			0
$913$	8.74672	+	5.75281i	0.289474	+	0.190390i
$914$	−65.3399	−	15.4858i	−2.16125	−	0.512226i
$915$		0			0
$916$	9.70091	+	1.13387i	0.320527	+	0.0374642i
$917$	3.30614	+	5.72640i	0.109178	+	0.189102i
$918$		0			0
$919$	−8.38084	+	14.5160i	−0.276459	+	0.478840i	−0.970502	−	0.241093i	$-0.922494\pi$
$919$	−8.38084	+	14.5160i	−0.276459	+	0.478840i	0.694044	+	0.719933i	$0.255828\pi$
$920$	6.87472	−	9.23435i	0.226653	−	0.304447i
$921$		0			0
$922$	14.0399	+	46.8964i	0.462378	+	1.54445i
$923$	6.27633	−	3.15209i	0.206588	−	0.103752i
$924$		0			0
$925$	−8.40175	+	28.0638i	−0.276248	+	0.922732i
$926$	−13.7988	−	78.2572i	−0.453458	−	2.57169i
$927$		0			0
$928$	5.47713	−	31.0624i	0.179796	−	1.01967i
$929$	49.0091	+	24.6133i	1.60794	+	0.807536i	0.999907	+	0.0136205i	$0.00433567\pi$
$929$	49.0091	+	24.6133i	1.60794	+	0.807536i	0.608029	+	0.793915i	$0.291961\pi$
$930$		0			0
$931$	1.24269	−	2.88088i	0.0407275	−	0.0944170i
$932$	−8.92767	+	20.6967i	−0.292436	+	0.677942i
$933$		0			0
$934$	51.0365	+	25.6315i	1.66997	+	0.838688i
$935$	−1.45272	+	8.23876i	−0.0475089	+	0.269436i
$936$		0			0
$937$	2.62965	+	14.9135i	0.0859070	+	0.487203i	0.997157	+	0.0753496i	$0.0240073\pi$
$937$	2.62965	+	14.9135i	0.0859070	+	0.487203i	−0.911250	+	0.411853i	$0.864882\pi$
$938$	−14.7784	+	49.3632i	−0.482531	+	1.61177i
$939$		0			0
$940$	−10.9546	+	5.50162i	−0.357301	+	0.179443i
$941$	5.98673	+	19.9971i	0.195162	+	0.651886i	0.998417	+	0.0562507i	$0.0179146\pi$
$941$	5.98673	+	19.9971i	0.195162	+	0.651886i	−0.803255	+	0.595636i	$0.796900\pi$
$942$		0			0
$943$	16.0360	−	21.5401i	0.522205	−	0.701444i
$944$	0.649591	−	1.12512i	0.0211424	−	0.0366197i
$945$		0			0
$946$	−34.1403	−	59.1328i	−1.11000	−	1.92257i
$947$	−50.2805	−	5.87694i	−1.63390	−	0.190975i	−0.750920	−	0.660394i	$-0.770389\pi$
$947$	−50.2805	−	5.87694i	−1.63390	−	0.190975i	−0.882976	+	0.469419i	$0.844463\pi$
$948$		0			0
$949$	33.2278	+	7.87513i	1.07862	+	0.255638i
$950$	3.69423	+	2.42973i	0.119857	+	0.0788310i
$951$		0			0
$952$	19.9163	+	21.1101i	0.645492	+	0.684182i
$953$	41.7445	−	35.0278i	1.35224	−	1.13466i	0.373940	−	0.927453i	$-0.378007\pi$
$953$	41.7445	−	35.0278i	1.35224	−	1.13466i	0.978297	−	0.207208i	$-0.0664377\pi$
$954$		0			0
$955$	−10.0647	−	8.44532i	−0.325687	−	0.273284i
$956$	−0.845951	−	14.5244i	−0.0273600	−	0.469753i
$957$		0			0
$958$	13.3258	+	17.8996i	0.430537	+	0.578311i
$959$	10.3981	−	1.21536i	0.335772	−	0.0392461i
$960$		0			0
$961$	18.6871	−	12.2907i	0.602808	−	0.396473i
$962$	−33.4294	+	12.1673i	−1.07781	+	0.392290i
$963$		0			0
$964$	−18.3558	−	6.68097i	−0.591201	−	0.215180i
$965$	3.69640	−	0.876062i	0.118991	−	0.0282014i
$966$		0			0
$967$	−2.39416	+	41.1061i	−0.0769910	+	1.32188i	0.709686	+	0.704519i	$0.248837\pi$
$967$	−2.39416	+	41.1061i	−0.0769910	+	1.32188i	−0.786677	+	0.617365i	$0.788200\pi$
$968$	−25.4281	+	26.9523i	−0.817291	+	0.866278i
$969$		0			0
$970$	−5.79971	−	13.4452i	−0.186217	−	0.431700i
$971$	9.59297			0.307853			0.153927	−	0.988082i	$-0.450808\pi$
$971$	9.59297			0.307853			0.153927	+	0.988082i	$0.450808\pi$
$972$		0			0
$973$	32.9685			1.05692
$974$	−15.3424	−	35.5676i	−0.491601	−	1.13966i
$975$		0			0
$976$	2.19235	−	2.32376i	0.0701755	−	0.0743817i
$977$	0.877005	−	15.0576i	0.0280579	−	0.481735i	−0.954786	−	0.297295i	$-0.903916\pi$
$977$	0.877005	−	15.0576i	0.0280579	−	0.481735i	0.982844	−	0.184440i	$-0.0590473\pi$
$978$		0			0
$979$	−1.67725	+	0.397515i	−0.0536051	+	0.0127046i
$980$	13.1447	+	4.78426i	0.419890	+	0.152828i
$981$		0			0
$982$	−17.9721	+	6.54131i	−0.573513	+	0.208741i
$983$	−46.8039	+	30.7834i	−1.49281	+	0.981838i	−0.499508	+	0.866309i	$0.666486\pi$
$983$	−46.8039	+	30.7834i	−1.49281	+	0.981838i	−0.993304	+	0.115528i	$0.963144\pi$
$984$		0			0
$985$	3.22692	−	0.377173i	0.102818	−	0.0120177i
$986$	20.4971	+	27.5324i	0.652762	+	0.876811i
$987$		0			0
$988$	0.191493	+	3.28780i	0.00609219	+	0.104599i
$989$	33.9083	+	28.4524i	1.07822	+	0.904734i
$990$		0			0
$991$	14.6989	−	12.3338i	0.466925	−	0.391796i	−0.378747	−	0.925500i	$-0.623645\pi$
$991$	14.6989	−	12.3338i	0.466925	−	0.391796i	0.845671	+	0.533704i	$0.179200\pi$
$992$	12.0392	+	12.7608i	0.382244	+	0.405155i
$993$		0			0
$994$	20.4519	+	13.4515i	0.648696	+	0.426654i
$995$	9.59486	+	2.27402i	0.304177	+	0.0720914i
$996$		0			0
$997$	−31.9385	−	3.73308i	−1.01150	−	0.118228i	−0.405836	−	0.913946i	$-0.633020\pi$
$997$	−31.9385	−	3.73308i	−1.01150	−	0.118228i	−0.605667	+	0.795718i	$0.707094\pi$
$998$	−27.4768	−	47.5913i	−0.869764	−	1.50648i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.g.d.676.8		144
3.2	odd	2		729.2.g.a.676.1		144
9.2	odd	6		729.2.g.b.190.1		144
9.4	even	3		81.2.g.a.4.1	✓	144
9.5	odd	6		243.2.g.a.64.8		144
9.7	even	3		729.2.g.c.190.8		144
81.7	even	27		81.2.g.a.61.1	yes	144
81.14	odd	54		6561.2.a.d.1.5		72
81.20	odd	54		729.2.g.b.541.1		144
81.34	even	27	inner	729.2.g.d.55.8		144
81.47	odd	54		729.2.g.a.55.1		144
81.61	even	27		729.2.g.c.541.8		144
81.67	even	27		6561.2.a.c.1.68		72
81.74	odd	54		243.2.g.a.19.8		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.4.1	✓	144	9.4	even	3
81.2.g.a.61.1	yes	144	81.7	even	27
243.2.g.a.19.8		144	81.74	odd	54
243.2.g.a.64.8		144	9.5	odd	6
729.2.g.a.55.1		144	81.47	odd	54
729.2.g.a.676.1		144	3.2	odd	2
729.2.g.b.190.1		144	9.2	odd	6
729.2.g.b.541.1		144	81.20	odd	54
729.2.g.c.190.8		144	9.7	even	3
729.2.g.c.541.8		144	81.61	even	27
729.2.g.d.55.8		144	81.34	even	27	inner
729.2.g.d.676.8		144	1.1	even	1	trivial
6561.2.a.c.1.68		72	81.67	even	27
6561.2.a.d.1.5		72	81.14	odd	54

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

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

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