LMFDB - Embedded newform 243.2.g.a.19.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [243,2,Mod(10,243)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(243, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([8]))

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

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

chi := DirichletCharacter("243.10");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 243 = 3^{5} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	243.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:	$1.94036476912$
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			19.2
Character	$\chi$	$=$	243.19
Dual form			243.2.g.a.64.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.69853 + 0.198530i) q^{2} +(0.899496 - 0.213184i) q^{4} +(-1.22732 - 0.616384i) q^{5} +(0.0889729 + 0.297190i) q^{7} +(1.72842 - 0.629095i) q^{8} +O(q^{10})$	\(q+(-1.69853 + 0.198530i) q^{2} +(0.899496 - 0.213184i) q^{4} +(-1.22732 - 0.616384i) q^{5} +(0.0889729 + 0.297190i) q^{7} +(1.72842 - 0.629095i) q^{8} +(2.20701 + 0.803287i) q^{10} +(-0.140180 + 2.40680i) q^{11} +(-2.75712 + 3.70345i) q^{13} +(-0.210124 - 0.487122i) q^{14} +(-4.46306 + 2.24143i) q^{16} +(-0.161307 + 0.135352i) q^{17} +(2.66964 + 2.24009i) q^{19} +(-1.23537 - 0.292789i) q^{20} +(-0.239721 - 4.11585i) q^{22} +(-2.29728 + 7.67346i) q^{23} +(-1.85940 - 2.49761i) q^{25} +(3.94780 - 6.83779i) q^{26} +(0.143387 + 0.248354i) q^{28} +(-3.29291 + 7.63382i) q^{29} +(-0.550159 - 0.583135i) q^{31} +(4.06213 - 2.67170i) q^{32} +(0.247112 - 0.261924i) q^{34} +(0.0739849 - 0.419589i) q^{35} +(1.88786 + 10.7066i) q^{37} +(-4.97918 - 3.27486i) q^{38} +(-2.50910 - 0.293272i) q^{40} +(4.66578 + 0.545352i) q^{41} +(-6.21456 - 4.08738i) q^{43} +(0.387001 + 2.19479i) q^{44} +(2.37859 - 13.4897i) q^{46} +(4.27143 - 4.52745i) q^{47} +(5.76801 - 3.79368i) q^{49} +(3.65410 + 3.87312i) q^{50} +(-1.69050 + 3.91901i) q^{52} +(-4.27003 - 7.39591i) q^{53} +(1.65556 - 2.86752i) q^{55} +(0.340744 + 0.457698i) q^{56} +(4.07756 - 13.6200i) q^{58} +(-0.410699 - 7.05143i) q^{59} +(9.74699 + 2.31008i) q^{61} +(1.05023 + 0.881248i) q^{62} +(1.28246 - 1.07611i) q^{64} +(5.66662 - 2.84588i) q^{65} +(-0.497063 - 1.15232i) q^{67} +(-0.116240 + 0.156137i) q^{68} +(-0.0423646 + 0.727373i) q^{70} +(1.68007 + 0.611494i) q^{71} +(-12.6834 + 4.61640i) q^{73} +(-5.33215 - 17.8106i) q^{74} +(2.87888 + 1.44583i) q^{76} +(-0.727750 + 0.172480i) q^{77} +(3.14586 - 0.367698i) q^{79} +6.85919 q^{80} -8.03324 q^{82} +(0.796837 - 0.0931369i) q^{83} +(0.281404 - 0.0666940i) q^{85} +(11.3671 + 5.70875i) q^{86} +(1.27182 + 4.24816i) q^{88} +(-12.2626 + 4.46322i) q^{89} +(-1.34594 - 0.489881i) q^{91} +(-0.430534 + 7.39199i) q^{92} +(-6.35631 + 8.53801i) q^{94} +(-1.89575 - 4.39484i) q^{95} +(-5.96090 + 2.99368i) q^{97} +(-9.04397 + 7.58879i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 18 q^{2} - 18 q^{4} + 18 q^{5} - 18 q^{7} + 18 q^{8}+O(q^{10}) $ 144 * q + 18 * q^2 - 18 * q^4 + 18 * q^5 - 18 * q^7 + 18 * q^8	$ 144 q + 18 q^{2} - 18 q^{4} + 18 q^{5} - 18 q^{7} + 18 q^{8} - 18 q^{10} + 18 q^{11} - 18 q^{13} + 18 q^{14} - 18 q^{16} + 18 q^{17} - 18 q^{19} - 18 q^{20} - 18 q^{22} - 9 q^{23} - 18 q^{25} - 45 q^{26} - 9 q^{28} - 9 q^{29} - 18 q^{31} - 36 q^{32} - 18 q^{34} - 9 q^{35} - 18 q^{37} + 9 q^{38} - 18 q^{40} - 18 q^{43} - 54 q^{44} - 18 q^{46} - 36 q^{47} - 18 q^{49} - 99 q^{50} - 45 q^{53} - 9 q^{55} - 126 q^{56} - 18 q^{58} - 45 q^{59} - 18 q^{61} - 81 q^{62} - 18 q^{64} + 9 q^{67} + 99 q^{68} + 36 q^{70} + 90 q^{71} - 18 q^{73} + 162 q^{74} + 63 q^{76} + 162 q^{77} + 36 q^{79} + 288 q^{80} - 36 q^{82} + 90 q^{83} + 36 q^{85} + 162 q^{86} + 63 q^{88} + 81 q^{89} - 18 q^{91} + 144 q^{92} + 36 q^{94} - 18 q^{95} + 9 q^{97} - 81 q^{98}+O(q^{100}) $ 144 * q + 18 * q^2 - 18 * q^4 + 18 * q^5 - 18 * q^7 + 18 * q^8 - 18 * q^10 + 18 * q^11 - 18 * q^13 + 18 * q^14 - 18 * q^16 + 18 * q^17 - 18 * q^19 - 18 * q^20 - 18 * q^22 - 9 * q^23 - 18 * q^25 - 45 * q^26 - 9 * q^28 - 9 * q^29 - 18 * q^31 - 36 * q^32 - 18 * q^34 - 9 * q^35 - 18 * q^37 + 9 * q^38 - 18 * q^40 - 18 * q^43 - 54 * q^44 - 18 * q^46 - 36 * q^47 - 18 * q^49 - 99 * q^50 - 45 * q^53 - 9 * q^55 - 126 * q^56 - 18 * q^58 - 45 * q^59 - 18 * q^61 - 81 * q^62 - 18 * q^64 + 9 * q^67 + 99 * q^68 + 36 * q^70 + 90 * q^71 - 18 * q^73 + 162 * q^74 + 63 * q^76 + 162 * q^77 + 36 * q^79 + 288 * q^80 - 36 * q^82 + 90 * q^83 + 36 * q^85 + 162 * q^86 + 63 * q^88 + 81 * q^89 - 18 * q^91 + 144 * q^92 + 36 * q^94 - 18 * q^95 + 9 * q^97 - 81 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/243\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{26}{27}\right)$

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 $

$2$	−1.69853	+	0.198530i	−1.20104	+	0.140382i	−0.692991	−	0.720946i	$-0.743708\pi$
$2$	−1.69853	+	0.198530i	−1.20104	+	0.140382i	−0.508050	+	0.861328i	$0.669633\pi$
$3$		0			0
$3$		0			0
$4$	0.899496	−	0.213184i	0.449748	−	0.106592i
$5$	−1.22732	−	0.616384i	−0.548875	−	0.275655i	0.152674	−	0.988277i	$-0.451212\pi$
$5$	−1.22732	−	0.616384i	−0.548875	−	0.275655i	−0.701549	+	0.712621i	$0.747508\pi$
$6$		0			0
$7$	0.0889729	+	0.297190i	0.0336286	+	0.112327i	0.973156	−	0.230146i	$-0.0739205\pi$
$7$	0.0889729	+	0.297190i	0.0336286	+	0.112327i	−0.939527	+	0.342474i	$0.888735\pi$
$8$	1.72842	−	0.629095i	0.611091	−	0.222419i
$9$		0			0
$10$	2.20701	+	0.803287i	0.697918	+	0.254022i
$11$	−0.140180	+	2.40680i	−0.0422659	+	0.725678i	0.908903	+	0.417008i	$0.136921\pi$
$11$	−0.140180	+	2.40680i	−0.0422659	+	0.725678i	−0.951169	+	0.308671i	$0.900116\pi$
$12$		0			0
$13$	−2.75712	+	3.70345i	−0.764687	+	1.02715i	0.233807	+	0.972283i	$0.424882\pi$
$13$	−2.75712	+	3.70345i	−0.764687	+	1.02715i	−0.998494	+	0.0548697i	$0.982526\pi$
$14$	−0.210124	−	0.487122i	−0.0561580	−	0.130189i
$15$		0			0
$16$	−4.46306	+	2.24143i	−1.11576	+	0.560358i
$17$	−0.161307	+	0.135352i	−0.0391226	+	0.0328277i	−0.662139	−	0.749381i	$-0.730351\pi$
$17$	−0.161307	+	0.135352i	−0.0391226	+	0.0328277i	0.623017	+	0.782209i	$0.285907\pi$
$18$		0			0
$19$	2.66964	+	2.24009i	0.612457	+	0.513913i	0.895422	−	0.445218i	$-0.146874\pi$
$19$	2.66964	+	2.24009i	0.612457	+	0.513913i	−0.282965	+	0.959130i	$0.591318\pi$
$20$	−1.23537	−	0.292789i	−0.276238	−	0.0654696i
$21$		0			0
$22$	−0.239721	−	4.11585i	−0.0511087	−	0.877503i
$23$	−2.29728	+	7.67346i	−0.479017	+	1.60003i	0.287485	+	0.957785i	$0.407181\pi$
$23$	−2.29728	+	7.67346i	−0.479017	+	1.60003i	−0.766502	+	0.642242i	$0.778004\pi$
$24$		0			0
$25$	−1.85940	−	2.49761i	−0.371881	−	0.499522i
$26$	3.94780	−	6.83779i	0.774227	−	1.34100i
$27$		0			0
$28$	0.143387	+	0.248354i	0.0270976	+	0.0469344i
$29$	−3.29291	+	7.63382i	−0.611478	+	1.41756i	0.277998	+	0.960582i	$0.410329\pi$
$29$	−3.29291	+	7.63382i	−0.611478	+	1.41756i	−0.889475	+	0.456983i	$0.848930\pi$
$30$		0			0
$31$	−0.550159	−	0.583135i	−0.0988115	−	0.104734i	0.676080	−	0.736828i	$-0.263677\pi$
$31$	−0.550159	−	0.583135i	−0.0988115	−	0.104734i	−0.774892	+	0.632094i	$0.782196\pi$
$32$	4.06213	−	2.67170i	0.718090	−	0.472295i
$33$		0			0
$34$	0.247112	−	0.261924i	0.0423794	−	0.0449196i
$35$	0.0739849	−	0.419589i	0.0125057	−	0.0709236i
$36$		0			0
$37$	1.88786	+	10.7066i	0.310362	+	1.76015i	0.597126	+	0.802148i	$0.296309\pi$
$37$	1.88786	+	10.7066i	0.310362	+	1.76015i	−0.286764	+	0.958001i	$0.592580\pi$
$38$	−4.97918	−	3.27486i	−0.807730	−	0.531252i
$39$		0			0
$40$	−2.50910	−	0.293272i	−0.396723	−	0.0463703i
$41$	4.66578	+	0.545352i	0.728673	+	0.0851697i	0.472337	−	0.881418i	$-0.343411\pi$
$41$	4.66578	+	0.545352i	0.728673	+	0.0851697i	0.256336	+	0.966588i	$0.417485\pi$
$42$		0			0
$43$	−6.21456	−	4.08738i	−0.947711	−	0.623319i	−0.0212756	−	0.999774i	$-0.506773\pi$
$43$	−6.21456	−	4.08738i	−0.947711	−	0.623319i	−0.926435	+	0.376454i	$0.877143\pi$
$44$	0.387001	+	2.19479i	0.0583426	+	0.330877i
$45$		0			0
$46$	2.37859	−	13.4897i	0.350704	−	1.98894i
$47$	4.27143	−	4.52745i	0.623052	−	0.660397i	−0.336580	−	0.941655i	$-0.609270\pi$
$47$	4.27143	−	4.52745i	0.623052	−	0.660397i	0.959632	+	0.281258i	$0.0907518\pi$
$48$		0			0
$49$	5.76801	−	3.79368i	0.824001	−	0.541954i
$50$	3.65410	+	3.87312i	0.516768	+	0.547742i
$51$		0			0
$52$	−1.69050	+	3.91901i	−0.234430	+	0.543470i
$53$	−4.27003	−	7.39591i	−0.586533	−	1.01591i	−0.994682	−	0.102990i	$-0.967159\pi$
$53$	−4.27003	−	7.39591i	−0.586533	−	1.01591i	0.408149	−	0.912915i	$-0.366174\pi$
$54$		0			0
$55$	1.65556	−	2.86752i	0.223236	−	0.386656i
$56$	0.340744	+	0.457698i	0.0455338	+	0.0611625i
$57$		0			0
$58$	4.07756	−	13.6200i	0.535410	−	1.78839i
$59$	−0.410699	−	7.05143i	−0.0534685	−	0.918018i	−0.913261	−	0.407375i	$-0.866444\pi$
$59$	−0.410699	−	7.05143i	−0.0534685	−	0.918018i	0.859793	−	0.510643i	$-0.170593\pi$
$60$		0			0
$61$	9.74699	+	2.31008i	1.24797	+	0.295775i	0.800941	−	0.598743i	$-0.204333\pi$
$61$	9.74699	+	2.31008i	1.24797	+	0.295775i	0.447032	+	0.894518i	$0.352481\pi$
$62$	1.05023	+	0.881248i	0.133379	+	0.111919i
$63$		0			0
$64$	1.28246	−	1.07611i	0.160308	−	0.134514i
$65$	5.66662	−	2.84588i	0.702858	−	0.352988i
$66$		0			0
$67$	−0.497063	−	1.15232i	−0.0607259	−	0.140778i	0.885151	−	0.465303i	$-0.154055\pi$
$67$	−0.497063	−	1.15232i	−0.0607259	−	0.140778i	−0.945877	+	0.324525i	$0.894796\pi$
$68$	−0.116240	+	0.156137i	−0.0140961	+	0.0189344i
$69$		0			0
$70$	−0.0423646	+	0.727373i	−0.00506354	+	0.0869377i
$71$	1.68007	+	0.611494i	0.199387	+	0.0725710i	0.439784	−	0.898104i	$-0.355055\pi$
$71$	1.68007	+	0.611494i	0.199387	+	0.0725710i	−0.240396	+	0.970675i	$0.577277\pi$
$72$		0			0
$73$	−12.6834	+	4.61640i	−1.48448	+	0.540308i	−0.951991	−	0.306126i	$-0.900967\pi$
$73$	−12.6834	+	4.61640i	−1.48448	+	0.540308i	−0.532494	+	0.846434i	$0.678745\pi$
$74$	−5.33215	−	17.8106i	−0.619850	−	2.07044i
$75$		0			0
$76$	2.87888	+	1.44583i	0.330230	+	0.165848i
$77$	−0.727750	+	0.172480i	−0.0829348	+	0.0196559i
$78$		0			0
$79$	3.14586	−	0.367698i	0.353937	−	0.0413693i	0.0627332	−	0.998030i	$-0.480018\pi$
$79$	3.14586	−	0.367698i	0.353937	−	0.0413693i	0.291204	+	0.956661i	$0.405944\pi$
$80$	6.85919			0.766881
$81$		0			0
$82$	−8.03324			−0.887123
$83$	0.796837	−	0.0931369i	0.0874642	−	0.0102231i	−0.0722482	−	0.997387i	$-0.523017\pi$
$83$	0.796837	−	0.0931369i	0.0874642	−	0.0102231i	0.159712	+	0.987164i	$0.448943\pi$
$84$		0			0
$85$	0.281404	−	0.0666940i	0.0305226	−	0.00723398i
$86$	11.3671	+	5.70875i	1.22574	+	0.615591i
$87$		0			0
$88$	1.27182	+	4.24816i	0.135576	+	0.452856i
$89$	−12.2626	+	4.46322i	−1.29983	+	0.473101i	−0.896942	−	0.442147i	$-0.854217\pi$
$89$	−12.2626	+	4.46322i	−1.29983	+	0.473101i	−0.402891	+	0.915248i	$0.631995\pi$
$90$		0			0
$91$	−1.34594	−	0.489881i	−0.141093	−	0.0513535i
$92$	−0.430534	+	7.39199i	−0.0448863	+	0.770668i
$93$		0			0
$94$	−6.35631	+	8.53801i	−0.655604	+	0.880628i
$95$	−1.89575	−	4.39484i	−0.194500	−	0.450901i
$96$		0			0
$97$	−5.96090	+	2.99368i	−0.605237	+	0.303962i	−0.724901	−	0.688853i	$-0.758115\pi$
$97$	−5.96090	+	2.99368i	−0.605237	+	0.303962i	0.119664	+	0.992814i	$0.461818\pi$
$98$	−9.04397	+	7.58879i	−0.913579	+	0.766584i
$99$		0			0
$100$	−2.20498	−	1.85020i	−0.220498	−	0.185020i
$101$	9.06888	+	2.14936i	0.902387	+	0.213870i	0.655518	−	0.755179i	$-0.272450\pi$
$101$	9.06888	+	2.14936i	0.902387	+	0.213870i	0.246869	+	0.969049i	$0.420598\pi$
$102$		0			0
$103$	0.0763459	+	1.31081i	0.00752258	+	0.129158i	0.999979	+	0.00655584i	$0.00208680\pi$
$103$	0.0763459	+	1.31081i	0.00752258	+	0.129158i	−0.992456	+	0.122602i	$0.960876\pi$
$104$	−2.43565	+	8.13563i	−0.238835	+	0.797764i
$105$		0			0
$106$	8.72107	+	11.7144i	0.847065	+	1.13781i
$107$	−0.386855	+	0.670052i	−0.0373987	+	0.0647764i	−0.884119	−	0.467262i	$-0.845240\pi$
$107$	−0.386855	+	0.670052i	−0.0373987	+	0.0647764i	0.846720	+	0.532038i	$0.178574\pi$
$108$		0			0
$109$	1.03104	+	1.78582i	0.0987559	+	0.171050i	0.911170	−	0.412031i	$-0.135180\pi$
$109$	1.03104	+	1.78582i	0.0987559	+	0.171050i	−0.812414	+	0.583081i	$0.801847\pi$
$110$	−2.24273	+	5.19924i	−0.213836	+	0.495728i
$111$		0			0
$112$	−1.06322	−	1.12695i	−0.100465	−	0.106487i
$113$	−4.91077	+	3.22986i	−0.461966	+	0.303840i	−0.759074	−	0.651004i	$-0.774348\pi$
$113$	−4.91077	+	3.22986i	−0.461966	+	0.303840i	0.297108	+	0.954844i	$0.403978\pi$
$114$		0			0
$115$	7.54931	−	8.00180i	0.703977	−	0.746171i
$116$	−1.33455	+	7.56859i	−0.123909	+	0.702726i
$117$		0			0
$118$	2.09750	+	11.8955i	0.193091	+	1.09507i
$119$	−0.0545773	−	0.0358960i	−0.00500309	−	0.00329058i
$120$		0			0
$121$	5.15258	+	0.602250i	0.468416	+	0.0547500i
$122$	−17.0142	−	1.98867i	−1.54039	−	0.180046i
$123$		0			0
$124$	−0.619181	−	0.407242i	−0.0556041	−	0.0365714i
$125$	1.93505	+	10.9742i	0.173076	+	0.981562i
$126$		0			0
$127$	1.81538	−	10.2955i	0.161089	−	0.913580i	−0.791917	−	0.610628i	$-0.790917\pi$
$127$	1.81538	−	10.2955i	0.161089	−	0.913580i	0.953006	−	0.302951i	$-0.0979720\pi$
$128$	−8.63765	+	9.15537i	−0.763468	+	0.809228i
$129$		0			0
$130$	−9.05993	+	5.95881i	−0.794608	+	0.522622i
$131$	−4.11030	−	4.35667i	−0.359119	−	0.380644i	0.522473	−	0.852656i	$-0.325009\pi$
$131$	−4.11030	−	4.35667i	−0.359119	−	0.380644i	−0.881592	+	0.472012i	$0.843528\pi$
$132$		0			0
$133$	−0.428208	+	0.992698i	−0.0371303	+	0.0860778i
$134$	1.07305	+	1.85857i	0.0926970	+	0.160556i
$135$		0			0
$136$	−0.193657	+	0.335423i	−0.0166059	+	0.0287623i
$137$	−0.693717	−	0.931823i	−0.0592682	−	0.0796110i	0.771501	−	0.636228i	$-0.219506\pi$
$137$	−0.693717	−	0.931823i	−0.0592682	−	0.0796110i	−0.830769	+	0.556617i	$0.812099\pi$
$138$		0			0
$139$	−4.67728	+	15.6232i	−0.396722	+	1.32514i	0.493551	+	0.869717i	$0.335699\pi$
$139$	−4.67728	+	15.6232i	−0.396722	+	1.32514i	−0.890273	+	0.455427i	$0.849487\pi$
$140$	−0.0229008	−	0.393191i	−0.00193547	−	0.0332307i
$141$		0			0
$142$	−2.97504	−	0.705098i	−0.249660	−	0.0591705i
$143$	−8.52698	−	7.15499i	−0.713062	−	0.598330i
$144$		0			0
$145$	8.74683	−	7.33946i	0.726384	−	0.609509i
$146$	20.6267	−	10.3591i	1.70708	−	0.857327i
$147$		0			0
$148$	3.98059	+	9.22805i	0.327203	+	0.758541i
$149$	5.33177	−	7.16181i	0.436796	−	0.586719i	−0.528156	−	0.849148i	$-0.677116\pi$
$149$	5.33177	−	7.16181i	0.436796	−	0.586719i	0.964951	+	0.262429i	$0.0845236\pi$
$150$		0			0
$151$	0.906740	−	15.5681i	0.0737894	−	1.26692i	−0.734695	−	0.678398i	$-0.762675\pi$
$151$	0.906740	−	15.5681i	0.0737894	−	1.26692i	0.808484	−	0.588518i	$-0.200288\pi$
$152$	6.02350	+	2.19238i	0.488571	+	0.177825i
$153$		0			0
$154$	1.20186	−	0.437442i	0.0968488	−	0.0352501i
$155$	0.315787	+	1.05480i	0.0253647	+	0.0847238i
$156$		0			0
$157$	10.9371	+	5.49283i	0.872878	+	0.438376i	0.828073	−	0.560620i	$-0.189437\pi$
$157$	10.9371	+	5.49283i	0.872878	+	0.438376i	0.0448048	+	0.998996i	$0.485733\pi$
$158$	−5.27034	+	1.24909i	−0.419285	+	0.0993725i
$159$		0			0
$160$	−6.63234	+	0.775209i	−0.524332	+	0.0612857i
$161$	−2.48487			−0.195835
$162$		0			0
$163$	−25.0816			−1.96454			−0.982271	−	0.187465i	$-0.939973\pi$
$163$	−25.0816			−1.96454			−0.982271	+	0.187465i	$0.939973\pi$
$164$	4.31311	−	0.504131i	0.336798	−	0.0393660i
$165$		0			0
$166$	−1.33496	+	0.316391i	−0.103613	+	0.0245567i
$167$	−7.19682	−	3.61438i	−0.556907	−	0.279689i	0.148002	−	0.988987i	$-0.452716\pi$
$167$	−7.19682	−	3.61438i	−0.556907	−	0.279689i	−0.704909	+	0.709298i	$0.749012\pi$
$168$		0			0
$169$	−2.38542	−	7.96785i	−0.183494	−	0.612911i
$170$	−0.464732	+	0.169149i	−0.0356433	+	0.0129731i
$171$		0			0
$172$	−6.46133	−	2.35173i	−0.492672	−	0.179318i
$173$	−1.03421	+	17.7567i	−0.0786295	+	1.35002i	0.696201	+	0.717847i	$0.254872\pi$
$173$	−1.03421	+	17.7567i	−0.0786295	+	1.35002i	−0.774830	+	0.632170i	$0.782165\pi$
$174$		0			0
$175$	0.576829	−	0.774816i	0.0436042	−	0.0585706i
$176$	−4.76905	−	11.0559i	−0.359481	−	0.833370i
$177$		0			0
$178$	19.9423	−	10.0154i	1.49474	−	0.750686i
$179$	13.5735	−	11.3896i	1.01453	−	0.851295i	0.0256035	−	0.999672i	$-0.491849\pi$
$179$	13.5735	−	11.3896i	1.01453	−	0.851295i	0.988931	+	0.148377i	$0.0474048\pi$
$180$		0			0
$181$	20.5130	+	17.2124i	1.52472	+	1.27939i	0.825340	+	0.564636i	$0.190983\pi$
$181$	20.5130	+	17.2124i	1.52472	+	1.27939i	0.699377	+	0.714753i	$0.253461\pi$
$182$	2.38337	+	0.564869i	0.176667	+	0.0418709i
$183$		0			0
$184$	0.856656	+	14.7082i	0.0631535	+	1.08430i
$185$	4.28235	−	14.3040i	0.314845	−	1.05165i
$186$		0			0
$187$	−0.303154	−	0.407207i	−0.0221688	−	0.0297779i
$188$	2.87695	−	4.98303i	0.209823	−	0.363424i
$189$		0			0
$190$	4.09249	+	7.08840i	0.296900	+	0.514246i
$191$	1.24181	−	2.87885i	0.0898545	−	0.208306i	−0.867363	−	0.497677i	$-0.834187\pi$
$191$	1.24181	−	2.87885i	0.0898545	−	0.208306i	0.957217	+	0.289370i	$0.0934459\pi$
$192$		0			0
$193$	−6.78035	−	7.18675i	−0.488060	−	0.517314i	0.435800	−	0.900043i	$-0.356465\pi$
$193$	−6.78035	−	7.18675i	−0.488060	−	0.517314i	−0.923860	+	0.382730i	$0.874984\pi$
$194$	9.53042	−	6.26826i	0.684244	−	0.450035i
$195$		0			0
$196$	4.37955	−	4.64205i	0.312825	−	0.331575i
$197$	−0.354010	+	2.00769i	−0.0252221	+	0.143042i	−0.994818	−	0.101669i	$-0.967582\pi$
$197$	−0.354010	+	2.00769i	−0.0252221	+	0.143042i	0.969596	+	0.244711i	$0.0786929\pi$
$198$		0			0
$199$	−2.26949	−	12.8709i	−0.160880	−	0.912396i	−0.953211	−	0.302305i	$-0.902244\pi$
$199$	−2.26949	−	12.8709i	−0.160880	−	0.912396i	0.792331	−	0.610091i	$-0.208867\pi$
$200$	−4.78507	−	3.14719i	−0.338356	−	0.222540i
$201$		0			0
$202$	−15.8305	−	1.85032i	−1.11383	−	0.130188i
$203$	−2.56168	−	0.299417i	−0.179794	−	0.0210149i
$204$		0			0
$205$	−5.39027	−	3.54524i	−0.376473	−	0.247610i
$206$	−0.389910	−	2.21129i	−0.0271663	−	0.154068i
$207$		0			0
$208$	4.00414	−	22.7086i	0.277637	−	1.57456i
$209$	−5.76569	+	6.11128i	−0.398821	+	0.422726i
$210$		0			0
$211$	13.2622	−	8.72269i	0.913008	−	0.600495i	−0.00372605	−	0.999993i	$-0.501186\pi$
$211$	13.2622	−	8.72269i	0.913008	−	0.600495i	0.916734	+	0.399498i	$0.130816\pi$
$212$	−5.41756	−	5.74228i	−0.372080	−	0.394382i
$213$		0			0
$214$	0.524059	−	1.21491i	0.0358239	−	0.0830492i
$215$	5.10787	+	8.84708i	0.348354	+	0.603366i
$216$		0			0
$217$	0.124353	−	0.215385i	0.00844160	−	0.0146213i
$218$	−2.10579	−	2.82857i	−0.142622	−	0.191575i
$219$		0			0
$220$	0.877861	−	2.93226i	0.0591854	−	0.197693i
$221$	−0.0565295	−	0.970573i	−0.00380258	−	0.0652878i
$222$		0			0
$223$	−1.84454	−	0.437163i	−0.123519	−	0.0292746i	0.168391	−	0.985720i	$-0.446143\pi$
$223$	−1.84454	−	0.437163i	−0.123519	−	0.0292746i	−0.291910	+	0.956446i	$0.594291\pi$
$224$	1.15542	+	0.969515i	0.0772000	+	0.0647785i
$225$		0			0
$226$	7.69986	−	6.46095i	0.512187	−	0.429776i
$227$	22.8390	−	11.4702i	1.51588	−	0.761301i	0.520186	−	0.854053i	$-0.325862\pi$
$227$	22.8390	−	11.4702i	1.51588	−	0.761301i	0.995689	+	0.0927514i	$0.0295662\pi$
$228$		0			0
$229$	−1.85823	−	4.30787i	−0.122795	−	0.284672i	0.845719	−	0.533628i	$-0.179172\pi$
$229$	−1.85823	−	4.30787i	−0.122795	−	0.284672i	−0.968515	+	0.248956i	$0.919912\pi$
$230$	−11.2341	+	15.0900i	−0.740756	+	0.995008i
$231$		0			0
$232$	−0.889146	+	15.2660i	−0.0583753	+	1.00226i
$233$	10.7706	+	3.92018i	0.705605	+	0.256819i	0.669802	−	0.742540i	$-0.266379\pi$
$233$	10.7706	+	3.92018i	0.705605	+	0.256819i	0.0358031	+	0.999359i	$0.488601\pi$
$234$		0			0
$235$	−8.03307	+	2.92380i	−0.524020	+	0.190728i
$236$	−1.87268	−	6.25518i	−0.121901	−	0.407178i
$237$		0			0
$238$	0.0998275	+	0.0501352i	0.00647085	+	0.00324978i
$239$	11.4299	−	2.70892i	0.739336	−	0.175226i	0.156343	−	0.987703i	$-0.450030\pi$
$239$	11.4299	−	2.70892i	0.739336	−	0.175226i	0.582993	+	0.812477i	$0.301881\pi$
$240$		0			0
$241$	−4.38905	+	0.513006i	−0.282723	+	0.0330456i	−0.256273	−	0.966605i	$-0.582495\pi$
$241$	−4.38905	+	0.513006i	−0.282723	+	0.0330456i	−0.0264506	+	0.999650i	$0.508420\pi$
$242$	−8.87136			−0.570273
$243$		0			0
$244$	9.25985			0.592801
$245$	−9.41757	+	1.10076i	−0.601666	+	0.0703247i
$246$		0			0
$247$	−15.6566	+	3.71068i	−0.996205	+	0.236105i
$248$	−1.31776	−	0.661802i	−0.0836776	−	0.0420245i
$249$		0			0
$250$	−5.46543	−	18.2558i	−0.345664	−	1.15460i
$251$	5.90077	−	2.14770i	0.372453	−	0.135562i	−0.149010	−	0.988836i	$-0.547609\pi$
$251$	5.90077	−	2.14770i	0.372453	−	0.135562i	0.521463	+	0.853274i	$0.325386\pi$
$252$		0			0
$253$	−18.1465	−	6.60477i	−1.14086	−	0.415239i
$254$	−1.03951	+	17.8476i	−0.0652245	+	1.11986i
$255$		0			0
$256$	10.8542	−	14.5798i	0.678390	−	0.911236i
$257$	0.936302	+	2.17059i	0.0584049	+	0.135398i	0.944919	−	0.327303i	$-0.106140\pi$
$257$	0.936302	+	2.17059i	0.0584049	+	0.135398i	−0.886515	+	0.462701i	$0.846880\pi$
$258$		0			0
$259$	−3.01392	+	1.51365i	−0.187276	+	0.0940534i
$260$	4.49040	−	3.76790i	0.278483	−	0.233675i
$261$		0			0
$262$	7.84639	+	6.58390i	0.484752	+	0.406755i
$263$	13.6191	+	3.22778i	0.839787	+	0.199033i	0.627932	−	0.778268i	$-0.283902\pi$
$263$	13.6191	+	3.22778i	0.839787	+	0.199033i	0.211855	+	0.977301i	$0.432050\pi$
$264$		0			0
$265$	0.681979	+	11.7091i	0.0418937	+	0.719286i
$266$	0.530244	−	1.77114i	0.0325113	−	0.108595i
$267$		0			0
$268$	−0.692763	−	0.930542i	−0.0423172	−	0.0568419i
$269$	−12.8630	+	22.2793i	−0.784268	+	1.35839i	0.145167	+	0.989407i	$0.453628\pi$
$269$	−12.8630	+	22.2793i	−0.784268	+	1.35839i	−0.929435	+	0.368985i	$0.879705\pi$
$270$		0			0
$271$	−6.52248	−	11.2973i	−0.396212	−	0.686260i	0.597043	−	0.802209i	$-0.296342\pi$
$271$	−6.52248	−	11.2973i	−0.396212	−	0.686260i	−0.993255	+	0.115950i	$0.963009\pi$
$272$	0.416538	−	0.965643i	0.0252563	−	0.0585507i
$273$		0			0
$274$	1.36329	+	1.44501i	0.0823595	+	0.0872959i
$275$	6.27191	−	4.12510i	0.378210	−	0.248753i
$276$		0			0
$277$	−3.58097	+	3.79560i	−0.215159	+	0.228056i	−0.825960	−	0.563729i	$-0.809366\pi$
$277$	−3.58097	+	3.79560i	−0.215159	+	0.228056i	0.610800	+	0.791785i	$0.290848\pi$
$278$	4.84283	−	27.4651i	0.290454	−	1.64725i
$279$		0			0
$280$	−0.136084	−	0.771772i	−0.00813259	−	0.0461222i
$281$	−4.74552	−	3.12118i	−0.283094	−	0.186194i	0.400019	−	0.916507i	$-0.369004\pi$
$281$	−4.74552	−	3.12118i	−0.283094	−	0.186194i	−0.683112	+	0.730313i	$0.739374\pi$
$282$		0			0
$283$	11.2778	+	1.31819i	0.670396	+	0.0783580i	0.444480	−	0.895789i	$-0.353388\pi$
$283$	11.2778	+	1.31819i	0.670396	+	0.0783580i	0.225916	+	0.974147i	$0.427463\pi$
$284$	1.64157	+	0.191872i	0.0974095	+	0.0113855i
$285$		0			0
$286$	15.9038	+	10.4601i	0.940412	+	0.618518i
$287$	0.253055	+	1.43515i	0.0149374	+	0.0847140i
$288$		0			0
$289$	−2.94432	+	16.6981i	−0.173195	+	0.982239i
$290$	−13.3996	+	14.2028i	−0.786854	+	0.834016i
$291$		0			0
$292$	−10.4246	+	6.85634i	−0.610051	+	0.401237i
$293$	11.8588	+	12.5696i	0.692799	+	0.734324i	0.974304	−	0.225236i	$-0.0723153\pi$
$293$	11.8588	+	12.5696i	0.692799	+	0.734324i	−0.281506	+	0.959560i	$0.590834\pi$
$294$		0			0
$295$	−3.84233	+	8.90753i	−0.223709	+	0.518616i
$296$	9.99847	+	17.3179i	0.581149	+	1.00658i
$297$		0			0
$298$	−7.63434	+	13.2231i	−0.442245	+	0.765991i
$299$	−22.0844	−	29.6645i	−1.27717	−	1.71554i
$300$		0			0
$301$	0.661801	−	2.21057i	0.0381456	−	0.127415i
$302$	1.55061	+	26.6229i	0.0892275	+	1.53198i
$303$		0			0
$304$	−16.9358	−	4.01385i	−0.971333	−	0.230210i
$305$	−10.5388	−	8.84310i	−0.603450	−	0.506354i
$306$		0			0
$307$	−6.44460	+	5.40766i	−0.367812	+	0.308631i	−0.807895	−	0.589326i	$-0.799393\pi$
$307$	−6.44460	+	5.40766i	−0.367812	+	0.308631i	0.440083	+	0.897957i	$0.354949\pi$
$308$	−0.617838	+	0.310290i	−0.0352046	+	0.0176804i
$309$		0			0
$310$	−0.745784	−	1.72892i	−0.0423577	−	0.0981961i
$311$	−3.91461	+	5.25824i	−0.221977	+	0.298167i	−0.899136	−	0.437670i	$-0.855804\pi$
$311$	−3.91461	+	5.25824i	−0.221977	+	0.298167i	0.677158	+	0.735837i	$0.263211\pi$
$312$		0			0
$313$	−0.317011	+	5.44287i	−0.0179185	+	0.307649i	0.977427	+	0.211275i	$0.0677616\pi$
$313$	−0.317011	+	5.44287i	−0.0179185	+	0.307649i	−0.995345	+	0.0963741i	$0.969275\pi$
$314$	−19.6675	−	7.15839i	−1.10990	−	0.403971i
$315$		0			0
$316$	2.75130	−	1.00139i	0.154773	−	0.0563327i
$317$	−1.03115	−	3.44428i	−0.0579151	−	0.193450i	0.924136	−	0.382063i	$-0.124786\pi$
$317$	−1.03115	−	3.44428i	−0.0579151	−	0.193450i	−0.982052	+	0.188613i	$0.939601\pi$
$318$		0			0
$319$	−17.9115	−	8.99549i	−1.00285	−	0.503651i
$320$	−2.23729	+	0.530248i	−0.125068	+	0.0296417i
$321$		0			0
$322$	4.22063	−	0.493321i	0.235206	−	0.0274917i
$323$	−0.733832			−0.0408315
$324$		0			0
$325$	14.3764			0.797458
$326$	42.6018	−	4.97944i	2.35950	−	0.275786i
$327$		0			0
$328$	8.40754	−	1.99262i	0.464229	−	0.110024i
$329$	1.72555	+	0.866606i	0.0951329	+	0.0477775i
$330$		0			0
$331$	7.68837	+	25.6809i	0.422591	+	1.41155i	0.859079	+	0.511842i	$0.171037\pi$
$331$	7.68837	+	25.6809i	0.422591	+	1.41155i	−0.436488	+	0.899710i	$0.643778\pi$
$332$	0.696896	−	0.253649i	0.0382471	−	0.0139208i
$333$		0			0
$334$	12.9416	+	4.71034i	0.708131	+	0.257739i
$335$	−0.100216	+	1.72065i	−0.00547541	+	0.0940092i
$336$		0			0
$337$	12.9090	−	17.3398i	0.703198	−	0.944559i	−0.296748	−	0.954956i	$-0.595902\pi$
$337$	12.9090	−	17.3398i	0.703198	−	0.944559i	0.999946	+	0.0103968i	$0.00330947\pi$
$338$	5.63355	+	13.0600i	0.306425	+	0.710372i
$339$		0			0
$340$	0.238904	−	0.119982i	0.0129564	−	0.00650693i
$341$	1.48061	−	1.24238i	0.0801796	−	0.0672787i
$342$		0			0
$343$	3.30415	+	2.77251i	0.178407	+	0.149702i
$344$	−13.3127	−	3.15518i	−0.717775	−	0.170116i
$345$		0			0
$346$	−1.76859	−	30.3656i	−0.0950802	−	1.63246i
$347$	4.83041	−	16.1347i	0.259310	−	0.866156i	−0.724855	−	0.688901i	$-0.758093\pi$
$347$	4.83041	−	16.1347i	0.259310	−	0.866156i	0.984165	−	0.177254i	$-0.0567215\pi$
$348$		0			0
$349$	−1.17716	−	1.58120i	−0.0630118	−	0.0846396i	0.769500	−	0.638647i	$-0.220505\pi$
$349$	−1.17716	−	1.58120i	−0.0630118	−	0.0846396i	−0.832512	+	0.554007i	$0.813098\pi$
$350$	−0.825937	+	1.43056i	−0.0441482	+	0.0764669i
$351$		0			0
$352$	5.86083	+	10.1513i	0.312384	+	0.541064i
$353$	−2.30243	+	5.33762i	−0.122546	+	0.284093i	−0.968435	−	0.249265i	$-0.919811\pi$
$353$	−2.30243	+	5.33762i	−0.122546	+	0.284093i	0.845889	+	0.533358i	$0.179070\pi$
$354$		0			0
$355$	−1.68507	−	1.78607i	−0.0894341	−	0.0947946i
$356$	−10.0787	+	6.62885i	−0.534168	+	0.351328i
$357$		0			0
$358$	−20.7939	+	22.0402i	−1.09899	+	1.16486i
$359$	−3.38611	+	19.2036i	−0.178712	+	1.01353i	0.755059	+	0.655657i	$0.227608\pi$
$359$	−3.38611	+	19.2036i	−0.178712	+	1.01353i	−0.933771	+	0.357871i	$0.883503\pi$
$360$		0			0
$361$	−1.19036	−	6.75087i	−0.0626506	−	0.355309i
$362$	−38.2590	−	25.1634i	−2.01085	−	1.32256i
$363$		0			0
$364$	−1.31510	−	0.153713i	−0.0689300	−	0.00805676i
$365$	18.4121	+	2.15207i	0.963736	+	0.112645i
$366$		0			0
$367$	15.7834	+	10.3809i	0.823885	+	0.541878i	0.890014	−	0.455933i	$-0.150694\pi$
$367$	15.7834	+	10.3809i	0.823885	+	0.541878i	−0.0661288	+	0.997811i	$0.521065\pi$
$368$	−6.94663	−	39.3963i	−0.362118	−	2.05367i
$369$		0			0
$370$	−4.43392	+	25.1460i	−0.230509	+	1.30728i
$371$	1.81807	−	1.92704i	0.0943897	−	0.100047i
$372$		0			0
$373$	18.6275	−	12.2515i	0.964495	−	0.634359i	0.0335191	−	0.999438i	$-0.489329\pi$
$373$	18.6275	−	12.2515i	0.964495	−	0.634359i	0.930976	+	0.365079i	$0.118958\pi$
$374$	0.595759	+	0.631467i	0.0308059	+	0.0326524i
$375$		0			0
$376$	4.53465	−	10.5125i	0.233857	−	0.542141i
$377$	−19.1926	−	33.2425i	−0.988467	−	1.71207i
$378$		0			0
$379$	5.97107	−	10.3422i	0.306713	−	0.531243i	−0.670928	−	0.741522i	$-0.734104\pi$
$379$	5.97107	−	10.3422i	0.306713	−	0.531243i	0.977641	+	0.210280i	$0.0674374\pi$
$380$	−2.64213	−	3.54899i	−0.135538	−	0.182060i
$381$		0			0
$382$	−1.53772	+	5.13634i	−0.0786766	+	0.262798i
$383$	1.21579	+	20.8743i	0.0621238	+	1.06662i	0.874980	+	0.484160i	$0.160875\pi$
$383$	1.21579	+	20.8743i	0.0621238	+	1.06662i	−0.812856	+	0.582465i	$0.802088\pi$
$384$		0			0
$385$	0.999498	+	0.236885i	0.0509391	+	0.0120728i
$386$	12.9434	+	10.8608i	0.658802	+	0.552800i
$387$		0			0
$388$	−4.72360	+	3.96357i	−0.239804	+	0.201220i
$389$	−8.58044	+	4.30926i	−0.435046	+	0.218488i	−0.652823	−	0.757510i	$-0.726416\pi$
$389$	−8.58044	+	4.30926i	−0.435046	+	0.218488i	0.217778	+	0.975998i	$0.430119\pi$
$390$		0			0
$391$	−0.668054	−	1.54872i	−0.0337849	−	0.0783222i
$392$	7.58299	−	10.1857i	0.382999	−	0.514456i
$393$		0			0
$394$	0.202710	−	3.48040i	0.0102124	−	0.175340i
$395$	−4.08763	−	1.48777i	−0.205671	−	0.0748581i
$396$		0			0
$397$	1.93277	−	0.703471i	0.0970030	−	0.0353062i	−0.293063	−	0.956093i	$-0.594674\pi$
$397$	1.93277	−	0.703471i	0.0970030	−	0.0353062i	0.390066	+	0.920787i	$0.372452\pi$
$398$	6.41005	+	21.4111i	0.321307	+	1.07324i
$399$		0			0
$400$	13.8969	+	6.97926i	0.694843	+	0.348963i
$401$	−0.658673	+	0.156108i	−0.0328925	+	0.00779568i	−0.247029	−	0.969008i	$-0.579454\pi$
$401$	−0.658673	+	0.156108i	−0.0328925	+	0.00779568i	0.214137	+	0.976804i	$0.431306\pi$
$402$		0			0
$403$	3.67646	−	0.429717i	0.183138	−	0.0214057i
$404$	8.61563			0.428644
$405$		0			0
$406$	4.41052			0.218891
$407$	−26.0332	+	3.04285i	−1.29042	+	0.150828i
$408$		0			0
$409$	16.6911	−	3.95585i	0.825319	−	0.195604i	0.203810	−	0.979011i	$-0.434668\pi$
$409$	16.6911	−	3.95585i	0.825319	−	0.195604i	0.621510	+	0.783406i	$0.286520\pi$
$410$	9.85937	+	4.95156i	0.486920	+	0.244540i
$411$		0			0
$412$	0.348117	+	1.16279i	0.0171505	+	0.0572866i
$413$	2.05907	−	0.749442i	0.101320	−	0.0368776i
$414$		0			0
$415$	−1.03538	−	0.376849i	−0.0508250	−	0.0184988i
$416$	−1.30524	+	22.4101i	−0.0639947	+	1.09875i
$417$		0			0
$418$	8.57992	−	11.5248i	0.419658	−	0.563698i
$419$	11.1249	+	25.7904i	0.543486	+	1.25994i	0.939768	+	0.341813i	$0.111041\pi$
$419$	11.1249	+	25.7904i	0.543486	+	1.25994i	−0.396282	+	0.918129i	$0.629700\pi$
$420$		0			0
$421$	−8.98026	+	4.51006i	−0.437671	+	0.219807i	−0.653970	−	0.756521i	$-0.726898\pi$
$421$	−8.98026	+	4.51006i	−0.437671	+	0.219807i	0.216299	+	0.976327i	$0.430601\pi$
$422$	−20.7945	+	17.4487i	−1.01226	+	0.849388i
$423$		0			0
$424$	−12.0332	−	10.0970i	−0.584382	−	0.490354i
$425$	0.637991	+	0.151207i	0.0309471	+	0.00733460i
$426$		0			0
$427$	0.180685	+	3.10224i	0.00874396	+	0.150128i
$428$	−0.205130	+	0.685181i	−0.00991532	+	0.0331195i
$429$		0			0
$430$	−10.4323	−	14.0130i	−0.503088	−	0.675765i
$431$	2.67380	−	4.63116i	0.128792	−	0.223075i	−0.794417	−	0.607373i	$-0.792223\pi$
$431$	2.67380	−	4.63116i	0.128792	−	0.223075i	0.923209	+	0.384298i	$0.125557\pi$
$432$		0			0
$433$	3.44686	+	5.97014i	0.165646	+	0.286906i	0.936884	−	0.349639i	$-0.113696\pi$
$433$	3.44686	+	5.97014i	0.165646	+	0.286906i	−0.771239	+	0.636546i	$0.780363\pi$
$434$	−0.168456	+	0.390525i	−0.00808615	+	0.0187458i
$435$		0			0
$436$	1.30813	+	1.38653i	0.0626479	+	0.0664029i
$437$	−23.3222	+	15.3392i	−1.11565	+	0.733775i
$438$		0			0
$439$	−10.6865	+	11.3270i	−0.510039	+	0.540610i	−0.930303	−	0.366792i	$-0.880456\pi$
$439$	−10.6865	+	11.3270i	−0.510039	+	0.540610i	0.420264	+	0.907402i	$0.361937\pi$
$440$	1.05757	−	5.99779i	0.0504178	−	0.285934i
$441$		0			0
$442$	0.288704	+	1.63732i	0.0137323	+	0.0778796i
$443$	−23.3555	−	15.3611i	−1.10965	−	0.729830i	−0.143977	−	0.989581i	$-0.545989\pi$
$443$	−23.3555	−	15.3611i	−1.10965	−	0.729830i	−0.965675	+	0.259751i	$0.916359\pi$
$444$		0			0
$445$	17.8012	+	2.08066i	0.843859	+	0.0986330i
$446$	3.21979	+	0.376339i	0.152461	+	0.0178202i
$447$		0			0
$448$	0.433914	+	0.285390i	0.0205005	+	0.0134834i
$449$	1.89891	+	10.7693i	0.0896152	+	0.508233i	0.996265	+	0.0863489i	$0.0275200\pi$
$449$	1.89891	+	10.7693i	0.0896152	+	0.508233i	−0.906650	+	0.421884i	$0.861369\pi$
$450$		0			0
$451$	−1.96661	+	11.1532i	−0.0926038	+	0.525182i
$452$	−3.72866	+	3.95215i	−0.175381	+	0.185893i
$453$		0			0
$454$	−36.5155	+	24.0166i	−1.71376	+	1.12716i
$455$	1.34994	+	1.43086i	0.0632864	+	0.0670796i
$456$		0			0
$457$	−6.50790	+	15.0870i	−0.304427	+	0.705740i	−0.999918	−	0.0127940i	$-0.995927\pi$
$457$	−6.50790	+	15.0870i	−0.304427	+	0.705740i	0.695492	+	0.718534i	$0.255187\pi$
$458$	4.01150	+	6.94812i	0.187445	+	0.324664i
$459$		0			0
$460$	5.08471	−	8.80698i	0.237076	−	0.410627i
$461$	14.9299	+	20.0543i	0.695355	+	0.934024i	0.999829	−	0.0184970i	$-0.00588810\pi$
$461$	14.9299	+	20.0543i	0.695355	+	0.934024i	−0.304474	+	0.952521i	$0.598481\pi$
$462$		0			0
$463$	−3.89051	+	12.9952i	−0.180807	+	0.603938i	0.818749	+	0.574151i	$0.194668\pi$
$463$	−3.89051	+	12.9952i	−0.180807	+	0.603938i	−0.999556	+	0.0297865i	$0.990517\pi$
$464$	−2.41425	−	41.4510i	−0.112079	−	1.92431i
$465$		0			0
$466$	−19.0724	−	4.52025i	−0.883514	−	0.209397i
$467$	26.2848	+	22.0556i	1.21632	+	1.02061i	0.999009	+	0.0445082i	$0.0141721\pi$
$467$	26.2848	+	22.0556i	1.21632	+	1.02061i	0.217308	+	0.976103i	$0.430272\pi$
$468$		0			0
$469$	0.298233	−	0.250247i	0.0137711	−	0.0115554i
$470$	13.0639	−	6.56096i	0.602595	−	0.302634i
$471$		0			0
$472$	−5.14589	−	11.9295i	−0.236859	−	0.549100i
$473$	10.7087	−	14.3842i	0.492385	−	0.661388i
$474$		0			0
$475$	0.630948	−	10.8330i	0.0289499	−	0.497050i
$476$	−0.0567445	−	0.0206533i	−0.00260088	−	0.000946643i
$477$		0			0
$478$	−18.8761	+	6.87035i	−0.863374	+	0.314242i
$479$	−6.21271	−	20.7519i	−0.283866	−	0.948178i	−0.974389	−	0.224868i	$-0.927805\pi$
$479$	−6.21271	−	20.7519i	−0.283866	−	0.948178i	0.690523	−	0.723310i	$-0.257380\pi$
$480$		0			0
$481$	−44.8563	−	22.5277i	−2.04527	−	1.02717i
$482$	7.35307	−	1.74271i	0.334923	−	0.0793783i
$483$		0			0
$484$	4.76311	−	0.556728i	0.216505	−	0.0253058i
$485$	9.16119			0.415988
$486$		0			0
$487$	38.8502			1.76047			0.880235	−	0.474538i	$-0.157385\pi$
$487$	38.8502			1.76047			0.880235	+	0.474538i	$0.157385\pi$
$488$	18.3002	−	2.13899i	0.828411	−	0.0968273i
$489$		0			0
$490$	15.7775	−	3.73933i	0.712754	−	0.168926i
$491$	−26.1680	−	13.1421i	−1.18095	−	0.593093i	−0.253604	−	0.967308i	$-0.581616\pi$
$491$	−26.1680	−	13.1421i	−1.18095	−	0.593093i	−0.927342	+	0.374215i	$0.877912\pi$
$492$		0			0
$493$	−0.502087	−	1.67709i	−0.0226129	−	0.0755322i
$494$	25.8565	−	9.41099i	1.16334	−	0.423420i
$495$		0			0
$496$	3.76245	+	1.36942i	0.168939	+	0.0614887i
$497$	−0.0322497	+	0.553706i	−0.00144660	+	0.0248371i
$498$		0			0
$499$	−16.4063	+	22.0374i	−0.734445	+	0.986531i	0.265304	+	0.964165i	$0.414528\pi$
$499$	−16.4063	+	22.0374i	−0.734445	+	0.986531i	−0.999750	+	0.0223667i	$0.992880\pi$
$500$	4.08009	+	9.45872i	0.182467	+	0.423007i
$501$		0			0
$502$	−9.59624	+	4.81941i	−0.428301	+	0.215101i
$503$	25.2177	−	21.1601i	1.12440	−	0.943484i	0.125583	−	0.992083i	$-0.459920\pi$
$503$	25.2177	−	21.1601i	1.12440	−	0.943484i	0.998818	+	0.0485988i	$0.0154756\pi$
$504$		0			0
$505$	−9.80560	−	8.22788i	−0.436343	−	0.366136i
$506$	32.1335	+	7.61579i	1.42851	+	0.338563i
$507$		0			0
$508$	−0.561920	−	9.64779i	−0.0249312	−	0.428051i
$509$	1.47242	−	4.91823i	0.0652639	−	0.217997i	−0.919137	−	0.393939i	$-0.871112\pi$
$509$	1.47242	−	4.91823i	0.0652639	−	0.217997i	0.984400	+	0.175942i	$0.0562973\pi$
$510$		0			0
$511$	−2.50043	−	3.35866i	−0.110612	−	0.148578i
$512$	−2.95483	+	5.11791i	−0.130586	+	0.226182i
$513$		0			0
$514$	−2.02126	−	3.50093i	−0.0891541	−	0.154419i
$515$	0.714261	−	1.65584i	0.0314741	−	0.0729651i
$516$		0			0
$517$	10.2979	+	10.9151i	0.452902	+	0.480048i
$518$	4.81872	−	3.16932i	0.211722	−	0.139252i
$519$		0			0
$520$	8.00400	−	8.48374i	0.350999	−	0.372037i
$521$	1.32353	−	7.50611i	0.0579849	−	0.328849i	−0.941992	−	0.335635i	$-0.891049\pi$
$521$	1.32353	−	7.50611i	0.0579849	−	0.328849i	0.999977	+	0.00678637i	$0.00216018\pi$
$522$		0			0
$523$	−1.93766	−	10.9890i	−0.0847279	−	0.480516i	−0.997415	−	0.0718566i	$-0.977108\pi$
$523$	−1.93766	−	10.9890i	−0.0847279	−	0.480516i	0.912687	−	0.408659i	$-0.134004\pi$
$524$	−4.62597	−	3.04255i	−0.202087	−	0.132914i
$525$		0			0
$526$	−23.7732	−	2.77868i	−1.03656	−	0.121156i
$527$	0.167673	+	0.0195981i	0.00730395	+	0.000853709i
$528$		0			0
$529$	−34.3883	−	22.6175i	−1.49514	−	0.983370i
$530$	−3.48297	−	19.7529i	−0.151291	−	0.858012i
$531$		0			0
$532$	−0.173544	+	0.984215i	−0.00752407	+	0.0426711i
$533$	−14.8838	+	15.7759i	−0.644689	+	0.683331i
$534$		0			0
$535$	0.887805	−	0.583919i	0.0383832	−	0.0252450i
$536$	−1.58406	−	1.67900i	−0.0684208	−	0.0725218i
$537$		0			0
$538$	17.4250	−	40.3957i	0.751245	−	1.74158i
$539$	8.32207	+	14.4143i	0.358457	+	0.620866i
$540$		0			0
$541$	12.8996	−	22.3428i	0.554598	−	0.960592i	−0.443337	−	0.896355i	$-0.646205\pi$
$541$	12.8996	−	22.3428i	0.554598	−	0.960592i	0.997935	−	0.0642366i	$-0.0204612\pi$
$542$	13.3215	+	17.8938i	0.572206	+	0.768605i
$543$		0			0
$544$	−0.293627	+	0.980782i	−0.0125891	+	0.0420507i
$545$	−0.164671	−	2.82729i	−0.00705373	−	0.121108i
$546$		0			0
$547$	35.1748	+	8.33659i	1.50397	+	0.356447i	0.898340	−	0.439301i	$-0.144774\pi$
$547$	35.1748	+	8.33659i	1.50397	+	0.356447i	0.605628	+	0.795748i	$0.292922\pi$
$548$	−0.822645	−	0.690281i	−0.0351417	−	0.0294874i
$549$		0			0
$550$	−9.83406	+	8.25176i	−0.419326	+	0.351856i
$551$	−25.8913	+	13.0031i	−1.10301	+	0.553952i
$552$		0			0
$553$	0.389173	+	0.902203i	0.0165493	+	0.0383656i
$554$	5.32884	−	7.15787i	0.226401	−	0.304109i
$555$		0			0
$556$	−0.876571	+	15.0501i	−0.0371749	+	0.638268i
$557$	−31.3174	−	11.3986i	−1.32696	−	0.482974i	−0.421278	−	0.906931i	$-0.638418\pi$
$557$	−31.3174	−	11.3986i	−1.32696	−	0.482974i	−0.905682	+	0.423957i	$0.860641\pi$
$558$		0			0
$559$	32.2717	−	11.7459i	1.36495	−	0.496800i
$560$	0.610282	+	2.03848i	0.0257891	+	0.0861417i
$561$		0			0
$562$	8.68004	+	4.35928i	0.366145	+	0.183885i
$563$	−33.7166	+	7.99099i	−1.42099	+	0.336780i	−0.868064	−	0.496453i	$-0.834636\pi$
$563$	−33.7166	+	7.99099i	−1.42099	+	0.336780i	−0.552923	+	0.833233i	$0.686488\pi$
$564$		0			0
$565$	8.01793	−	0.937162i	0.337317	−	0.0394267i
$566$	−19.4174			−0.816173
$567$		0			0
$568$	3.28856			0.137985
$569$	32.6401	−	3.81508i	1.36834	−	0.159936i	0.600013	−	0.799990i	$-0.295162\pi$
$569$	32.6401	−	3.81508i	1.36834	−	0.159936i	0.768330	+	0.640054i	$0.221088\pi$
$570$		0			0
$571$	−14.8522	+	3.52004i	−0.621545	+	0.147309i	−0.529310	−	0.848428i	$-0.677549\pi$
$571$	−14.8522	+	3.52004i	−0.621545	+	0.147309i	−0.0922351	+	0.995737i	$0.529401\pi$
$572$	−9.19532	−	4.61806i	−0.384476	−	0.193091i
$573$		0			0
$574$	−0.714740	−	2.38740i	−0.0298327	−	0.0996481i
$575$	23.4369	−	8.53034i	0.977386	−	0.355740i
$576$		0			0
$577$	9.00255	+	3.27666i	0.374781	+	0.136409i	0.522541	−	0.852614i	$-0.324984\pi$
$577$	9.00255	+	3.27666i	0.374781	+	0.136409i	−0.147760	+	0.989023i	$0.547206\pi$
$578$	1.68595	−	28.9467i	0.0701264	−	1.20402i
$579$		0			0
$580$	6.30308	−	8.46650i	0.261721	−	0.351552i
$581$	0.0985762	+	0.228525i	0.00408963	+	0.00948083i
$582$		0			0
$583$	18.3991	−	9.24035i	0.762011	−	0.382696i
$584$	−19.0182	+	15.9582i	−0.786980	+	0.660355i
$585$		0			0
$586$	−22.6380	−	18.9955i	−0.935165	−	0.784697i
$587$	27.7523	+	6.57742i	1.14546	+	0.271479i	0.759166	−	0.650897i	$-0.225607\pi$
$587$	27.7523	+	6.57742i	1.14546	+	0.271479i	0.386294	+	0.922376i	$0.373755\pi$
$588$		0			0
$589$	−0.162450	−	2.78917i	−0.00669365	−	0.114926i
$590$	4.75790	−	15.8925i	0.195880	−	0.654284i
$591$		0			0
$592$	−32.4237	−	43.5525i	−1.33260	−	1.79000i
$593$	21.1230	−	36.5862i	0.867419	−	1.50241i	0.00279478	−	0.999996i	$-0.499110\pi$
$593$	21.1230	−	36.5862i	0.867419	−	1.50241i	0.864625	−	0.502418i	$-0.167556\pi$
$594$		0			0
$595$	0.0448581	+	0.0776966i	0.00183900	+	0.00318525i
$596$	3.26912	−	7.57867i	0.133908	−	0.310434i
$597$		0			0
$598$	43.4003	+	46.0016i	1.77477	+	1.88115i
$599$	−14.9593	+	9.83888i	−0.611220	+	0.402006i	−0.817037	−	0.576585i	$-0.804385\pi$
$599$	−14.9593	+	9.83888i	−0.611220	+	0.402006i	0.205818	+	0.978590i	$0.434015\pi$
$600$		0			0
$601$	6.88063	−	7.29305i	0.280667	−	0.297490i	−0.571669	−	0.820484i	$-0.693704\pi$
$601$	6.88063	−	7.29305i	0.280667	−	0.297490i	0.852336	+	0.522995i	$0.175185\pi$
$602$	−0.685225	+	3.88610i	−0.0279277	+	0.158386i
$603$		0			0
$604$	−2.50327	−	14.1968i	−0.101857	−	0.577658i
$605$	−5.95265	−	3.91512i	−0.242010	−	0.159172i
$606$		0			0
$607$	11.8705	+	1.38747i	0.481811	+	0.0563156i	0.353532	−	0.935423i	$-0.384981\pi$
$607$	11.8705	+	1.38747i	0.481811	+	0.0563156i	0.128279	+	0.991738i	$0.459055\pi$
$608$	16.8293	+	1.96706i	0.682518	+	0.0797749i
$609$		0			0
$610$	19.6561	+	12.9280i	0.795851	+	0.523439i
$611$	4.99036	+	28.3018i	0.201888	+	1.14497i
$612$		0			0
$613$	−6.82305	+	38.6954i	−0.275580	+	1.56289i	0.461532	+	0.887124i	$0.347300\pi$
$613$	−6.82305	+	38.6954i	−0.275580	+	1.56289i	−0.737112	+	0.675771i	$0.763811\pi$
$614$	9.87275	−	10.4645i	0.398432	−	0.422313i
$615$		0			0
$616$	−1.14936	+	0.755943i	−0.0463088	+	0.0304578i
$617$	−28.0503	−	29.7316i	−1.12926	−	1.19695i	−0.978033	−	0.208450i	$-0.933158\pi$
$617$	−28.0503	−	29.7316i	−1.12926	−	1.19695i	−0.151230	−	0.988499i	$-0.548323\pi$
$618$		0			0
$619$	10.1196	−	23.4598i	0.406740	−	0.942928i	−0.584566	−	0.811346i	$-0.698735\pi$
$619$	10.1196	−	23.4598i	0.406740	−	0.942928i	0.991305	−	0.131582i	$-0.0420057\pi$
$620$	0.508917	+	0.881470i	0.0204386	+	0.0354007i
$621$		0			0
$622$	5.60517	−	9.70843i	0.224747	−	0.389273i
$623$	−2.41746	−	3.24722i	−0.0968537	−	0.130097i
$624$		0			0
$625$	−0.0757739	+	0.253102i	−0.00303095	+	0.0101241i
$626$	−0.542118	−	9.30781i	−0.0216674	−	0.372015i
$627$		0			0
$628$	11.0089	+	2.60915i	0.439303	+	0.104117i
$629$	−1.75368	−	1.47151i	−0.0699239	−	0.0586731i
$630$		0			0
$631$	−3.09592	+	2.59779i	−0.123247	+	0.103416i	−0.702328	−	0.711854i	$-0.747856\pi$
$631$	−3.09592	+	2.59779i	−0.123247	+	0.103416i	0.579081	+	0.815270i	$0.303411\pi$
$632$	5.20607	−	2.61459i	0.207086	−	0.104003i
$633$		0			0
$634$	2.43523	+	5.64549i	0.0967152	+	0.224211i
$635$	−8.57405	+	11.5170i	−0.340251	+	0.457036i
$636$		0			0
$637$	−1.85337	+	31.8212i	−0.0734333	+	1.26080i
$638$	32.2091	+	11.7231i	1.27517	+	0.464123i
$639$		0			0
$640$	16.2444	−	5.91248i	0.642116	−	0.233711i
$641$	3.39146	+	11.3283i	0.133955	+	0.447440i	0.998478	−	0.0551528i	$-0.0175646\pi$
$641$	3.39146	+	11.3283i	0.133955	+	0.447440i	−0.864523	+	0.502593i	$0.832379\pi$
$642$		0			0
$643$	−18.1003	−	9.09029i	−0.713804	−	0.358486i	0.0545496	−	0.998511i	$-0.482628\pi$
$643$	−18.1003	−	9.09029i	−0.713804	−	0.358486i	−0.768354	+	0.640025i	$0.778924\pi$
$644$	−2.23513	+	0.529736i	−0.0880766	+	0.0208745i
$645$		0			0
$646$	1.24643	−	0.145687i	0.0490403	−	0.00573199i
$647$	−25.4173			−0.999257			−0.499629	−	0.866240i	$-0.666530\pi$
$647$	−25.4173			−0.999257			−0.499629	+	0.866240i	$0.666530\pi$
$648$		0			0
$649$	17.0290			0.668446
$650$	−24.4187	+	2.85414i	−0.957780	+	0.111948i
$651$		0			0
$652$	−22.5608	+	5.34701i	−0.883549	+	0.209405i
$653$	−5.84284	−	2.93439i	−0.228648	−	0.114831i	0.330787	−	0.943705i	$-0.392686\pi$
$653$	−5.84284	−	2.93439i	−0.228648	−	0.114831i	−0.559435	+	0.828874i	$0.688982\pi$
$654$		0			0
$655$	2.35928	+	7.88056i	0.0921848	+	0.307919i
$656$	−22.0460	+	8.02410i	−0.860753	+	0.313289i
$657$		0			0
$658$	−3.10295	−	1.12938i	−0.120966	−	0.0440279i
$659$	−1.45025	+	24.8998i	−0.0564936	+	0.969958i	0.844344	+	0.535802i	$0.179990\pi$
$659$	−1.45025	+	24.8998i	−0.0564936	+	0.969958i	−0.900838	+	0.434156i	$0.857047\pi$
$660$		0			0
$661$	−26.8875	+	36.1162i	−1.04580	+	1.40476i	−0.135518	+	0.990775i	$0.543270\pi$
$661$	−26.8875	+	36.1162i	−1.04580	+	1.40476i	−0.910285	+	0.413982i	$0.864138\pi$
$662$	−18.1573	−	42.0934i	−0.705705	−	1.63601i
$663$		0			0
$664$	1.31868	−	0.662266i	0.0511747	−	0.0257009i
$665$	1.13743	−	0.954419i	0.0441077	−	0.0370108i
$666$		0			0
$667$	−51.0131	−	42.8051i	−1.97523	−	1.65742i
$668$	−7.24404	−	1.71687i	−0.280280	−	0.0664276i
$669$		0			0
$670$	−0.171379	−	2.94247i	−0.00662096	−	0.113678i
$671$	−6.92624	+	23.1352i	−0.267384	+	0.893126i
$672$		0			0
$673$	7.24462	+	9.73122i	0.279260	+	0.375111i	0.919517	−	0.393049i	$-0.128580\pi$
$673$	7.24462	+	9.73122i	0.279260	+	0.375111i	−0.640258	+	0.768160i	$0.721172\pi$
$674$	−18.4838	+	32.0150i	−0.711971	+	1.23317i
$675$		0			0
$676$	−3.84429	−	6.65851i	−0.147857	−	0.256097i
$677$	2.36922	−	5.49247i	0.0910566	−	0.211093i	−0.866602	−	0.499001i	$-0.833700\pi$
$677$	2.36922	−	5.49247i	0.0910566	−	0.211093i	0.957658	+	0.287908i	$0.0929597\pi$
$678$		0			0
$679$	−1.42005	−	1.50516i	−0.0544965	−	0.0577629i
$680$	0.444429	−	0.292306i	0.0170431	−	0.0112094i
$681$		0			0
$682$	−2.26821	+	2.40416i	−0.0868543	+	0.0920602i
$683$	−4.79324	+	27.1838i	−0.183408	+	1.04016i	0.744575	+	0.667538i	$0.232652\pi$
$683$	−4.79324	+	27.1838i	−0.183408	+	1.04016i	−0.927984	+	0.372621i	$0.878459\pi$
$684$		0			0
$685$	0.277053	+	1.57124i	0.0105856	+	0.0600341i
$686$	−6.16262	−	4.05322i	−0.235290	−	0.154753i
$687$		0			0
$688$	36.8975	+	4.31270i	1.40670	+	0.164420i
$689$	39.1634	+	4.57754i	1.49200	+	0.174390i
$690$		0			0
$691$	24.5061	+	16.1179i	0.932254	+	0.613153i	0.922165	−	0.386796i	$-0.126418\pi$
$691$	24.5061	+	16.1179i	0.932254	+	0.613153i	0.0100889	+	0.999949i	$0.496789\pi$
$692$	2.85518	+	16.1926i	0.108538	+	0.615549i
$693$		0			0
$694$	−5.00138	+	28.3642i	−0.189850	+	1.07669i
$695$	15.3704	−	16.2917i	0.583034	−	0.617980i
$696$		0			0
$697$	−0.826436	+	0.543556i	−0.0313035	+	0.0205886i
$698$	2.31335	+	2.45201i	0.0875617	+	0.0928099i
$699$		0			0
$700$	0.353677	−	0.819915i	0.0133677	−	0.0309899i
$701$	1.45226	+	2.51539i	0.0548512	+	0.0950051i	0.892147	−	0.451745i	$-0.149198\pi$
$701$	1.45226	+	2.51539i	0.0548512	+	0.0950051i	−0.837296	+	0.546750i	$0.815865\pi$
$702$		0			0
$703$	−18.9438	+	32.8116i	−0.714479	+	1.23751i
$704$	2.41021	+	3.23748i	0.0908383	+	0.122017i
$705$		0			0
$706$	2.85106	−	9.52321i	0.107301	−	0.358411i
$707$	0.168115	+	2.88642i	0.00632260	+	0.108555i
$708$		0			0
$709$	−24.0474	−	5.69934i	−0.903119	−	0.214043i	−0.247280	−	0.968944i	$-0.579537\pi$
$709$	−24.0474	−	5.69934i	−0.903119	−	0.214043i	−0.655839	+	0.754901i	$0.727685\pi$
$710$	3.21672	+	2.69915i	0.120721	+	0.101297i
$711$		0			0
$712$	−18.3872	+	15.4287i	−0.689089	+	0.578215i
$713$	5.73853	−	2.88200i	0.214910	−	0.107932i
$714$		0			0
$715$	6.05513	+	14.0374i	0.226449	+	0.524968i
$716$	9.78127	−	13.1385i	0.365543	−	0.491010i
$717$		0			0
$718$	1.93893	−	33.2901i	0.0723602	−	1.24238i
$719$	−23.8425	−	8.67796i	−0.889175	−	0.323633i	−0.143269	−	0.989684i	$-0.545761\pi$
$719$	−23.8425	−	8.67796i	−0.889175	−	0.323633i	−0.745907	+	0.666051i	$0.767983\pi$
$720$		0			0
$721$	−0.382767	+	0.139316i	−0.0142550	+	0.00518838i
$722$	3.36211	+	11.2302i	0.125125	+	0.417946i
$723$		0			0
$724$	22.1207	+	11.1095i	0.822111	+	0.412880i
$725$	25.1892	−	5.96994i	0.935502	−	0.221718i
$726$		0			0
$727$	−17.6415	+	2.06200i	−0.654288	+	0.0764754i	−0.436759	−	0.899578i	$-0.643874\pi$
$727$	−17.6415	+	2.06200i	−0.654288	+	0.0764754i	−0.217529	+	0.976054i	$0.569800\pi$
$728$	−2.63453			−0.0976424
$729$		0			0
$730$	−31.7008			−1.17330
$731$	1.55568	−	0.181833i	0.0575391	−	0.00672535i
$732$		0			0
$733$	9.01202	−	2.13589i	0.332866	−	0.0788908i	−0.0607842	−	0.998151i	$-0.519360\pi$
$733$	9.01202	−	2.13589i	0.332866	−	0.0788908i	0.393651	+	0.919260i	$0.371212\pi$
$734$	−28.8694	−	14.4988i	−1.06559	−	0.535159i
$735$		0			0
$736$	11.1694	+	37.3083i	0.411708	+	1.37520i
$737$	2.84309	−	1.03480i	0.104726	−	0.0381173i
$738$		0			0
$739$	5.02496	+	1.82894i	0.184846	+	0.0672785i	0.432785	−	0.901497i	$-0.357531\pi$
$739$	5.02496	+	1.82894i	0.184846	+	0.0672785i	−0.247939	+	0.968776i	$0.579753\pi$
$740$	0.802557	−	13.7794i	0.0295026	−	0.506540i
$741$		0			0
$742$	−2.70547	+	3.63408i	−0.0993211	+	0.133411i
$743$	10.3074	+	23.8952i	0.378141	+	0.876629i	0.995917	+	0.0902752i	$0.0287747\pi$
$743$	10.3074	+	23.8952i	0.378141	+	0.876629i	−0.617776	+	0.786354i	$0.711966\pi$
$744$		0			0
$745$	−10.9582	+	5.50343i	−0.401478	+	0.201630i
$746$	−29.2071	+	24.5076i	−1.06935	+	0.897288i
$747$		0			0
$748$	−0.359496	−	0.301653i	−0.0131445	−	0.0110295i
$749$	−0.233553	−	0.0553530i	−0.00853382	−	0.00202255i
$750$		0			0
$751$	0.211970	+	3.63939i	0.00773490	+	0.132803i	0.999965	+	0.00838551i	$0.00266922\pi$
$751$	0.211970	+	3.63939i	0.00773490	+	0.132803i	−0.992230	+	0.124418i	$0.960294\pi$
$752$	−8.91566	+	29.7804i	−0.325121	+	1.08598i
$753$		0			0
$754$	39.1987	+	52.6530i	1.42753	+	1.91751i
$755$	−10.7088	+	18.5482i	−0.389733	+	0.675038i
$756$		0			0
$757$	−5.44196	−	9.42576i	−0.197792	−	0.342585i	0.750021	−	0.661415i	$-0.230044\pi$
$757$	−5.44196	−	9.42576i	−0.197792	−	0.342585i	−0.947812	+	0.318830i	$0.896710\pi$
$758$	−8.08880	+	18.7519i	−0.293798	+	0.681101i
$759$		0			0
$760$	−6.04143	−	6.40354i	−0.219146	−	0.232281i
$761$	20.6250	−	13.5653i	0.747655	−	0.491740i	−0.117607	−	0.993060i	$-0.537522\pi$
$761$	20.6250	−	13.5653i	0.747655	−	0.491740i	0.865262	+	0.501320i	$0.167152\pi$
$762$		0			0
$763$	−0.438992	+	0.465305i	−0.0158926	+	0.0168452i
$764$	0.503281	−	2.85425i	0.0182081	−	0.103263i
$765$		0			0
$766$	−6.20921	−	35.2142i	−0.224348	−	1.27234i
$767$	27.2470	+	17.9206i	0.983832	+	0.647076i
$768$		0			0
$769$	−31.0819	−	3.63295i	−1.12084	−	0.131008i	−0.464573	−	0.885535i	$-0.653792\pi$
$769$	−31.0819	−	3.63295i	−1.12084	−	0.131008i	−0.656269	+	0.754527i	$0.727866\pi$
$770$	−1.74470	−	0.203927i	−0.0628748	−	0.00734901i
$771$		0			0
$772$	−7.63100	−	5.01899i	−0.274646	−	0.180637i
$773$	−2.32846	−	13.2054i	−0.0837490	−	0.474964i	−0.997620	−	0.0689585i	$-0.978032\pi$
$773$	−2.32846	−	13.2054i	−0.0837490	−	0.474964i	0.913871	−	0.406006i	$-0.133079\pi$
$774$		0			0
$775$	−0.433476	+	2.45837i	−0.0155709	+	0.0883071i
$776$	−8.41966	+	8.92431i	−0.302248	+	0.320364i
$777$		0			0
$778$	13.7186	−	9.02287i	0.491836	−	0.323486i
$779$	11.2343	+	11.9077i	0.402511	+	0.426637i
$780$		0			0
$781$	−1.70726	+	3.95787i	−0.0610905	+	0.141624i
$782$	1.44218	+	2.49792i	0.0515721	+	0.0893255i
$783$		0			0
$784$	−17.2397	+	29.8600i	−0.615703	+	1.06643i
$785$	−10.0377	−	13.4830i	−0.358260	−	0.481227i
$786$		0			0
$787$	−5.98854	+	20.0031i	−0.213468	+	0.713034i	0.782445	+	0.622720i	$0.213972\pi$
$787$	−5.98854	+	20.0031i	−0.213468	+	0.713034i	−0.995913	+	0.0903142i	$0.971213\pi$
$788$	0.109578	+	1.88138i	0.00390354	+	0.0670213i
$789$		0			0
$790$	7.23832	+	1.71551i	0.257528	+	0.0610352i
$791$	−1.39681	−	1.17206i	−0.0496648	−	0.0416737i
$792$		0			0
$793$	−35.4289	+	29.7283i	−1.25812	+	1.05568i
$794$	−3.14321	+	1.57858i	−0.111548	+	0.0560216i
$795$		0			0
$796$	−4.78528	−	11.0935i	−0.169610	−	0.393199i
$797$	−31.0967	+	41.7701i	−1.10150	+	1.47957i	−0.240724	+	0.970594i	$0.577385\pi$
$797$	−31.0967	+	41.7701i	−1.10150	+	1.47957i	−0.860778	+	0.508980i	$0.830023\pi$
$798$		0			0
$799$	−0.0762088	+	1.30846i	−0.00269608	+	0.0462898i
$800$	−14.2260	−	5.17785i	−0.502966	−	0.183065i
$801$		0			0
$802$	1.08778	−	0.395920i	0.0384109	−	0.0139804i
$803$	−9.33278	−	31.1737i	−0.329347	−	1.10009i
$804$		0			0
$805$	3.04974	+	1.53164i	0.107489	+	0.0539831i
$806$	−6.15927	+	1.45977i	−0.216951	+	0.0514183i
$807$		0			0
$808$	17.0270	−	1.99017i	0.599009	−	0.0700141i
$809$	41.7858			1.46911			0.734554	−	0.678550i	$-0.237391\pi$
$809$	41.7858			1.46911			0.734554	+	0.678550i	$0.237391\pi$
$810$		0			0
$811$	5.44750			0.191287			0.0956437	−	0.995416i	$-0.469509\pi$
$811$	5.44750			0.191287			0.0956437	+	0.995416i	$0.469509\pi$
$812$	−2.36805	+	0.276785i	−0.0831022	+	0.00971325i
$813$		0			0
$814$	43.6141	−	10.3367i	1.52867	−	0.362302i
$815$	30.7832	+	15.4599i	1.07829	+	0.541537i
$816$		0			0
$817$	−7.43451	−	24.8330i	−0.260101	−	0.868797i
$818$	−27.5649	+	10.0328i	−0.963783	+	0.350788i
$819$		0			0
$820$	−5.60432	−	2.03981i	−0.195711	−	0.0712331i
$821$	1.78967	−	30.7275i	0.0624600	−	1.07240i	−0.810857	−	0.585244i	$-0.800999\pi$
$821$	1.78967	−	30.7275i	0.0624600	−	1.07240i	0.873317	−	0.487152i	$-0.161964\pi$
$822$		0			0
$823$	11.1564	−	14.9856i	0.388886	−	0.522365i	−0.563967	−	0.825798i	$-0.690725\pi$
$823$	11.1564	−	14.9856i	0.388886	−	0.522365i	0.952853	+	0.303433i	$0.0981327\pi$
$824$	0.956581	+	2.21760i	0.0333241	+	0.0772539i
$825$		0			0
$826$	−3.34861	+	1.68174i	−0.116513	+	0.0585151i
$827$	1.28456	−	1.07787i	0.0446686	−	0.0374814i	−0.620180	−	0.784459i	$-0.712940\pi$
$827$	1.28456	−	1.07787i	0.0446686	−	0.0374814i	0.664849	+	0.746978i	$0.268496\pi$
$828$		0			0
$829$	23.5451	+	19.7567i	0.817755	+	0.686178i	0.952445	−	0.304710i	$-0.0985595\pi$
$829$	23.5451	+	19.7567i	0.817755	+	0.686178i	−0.134690	+	0.990888i	$0.543004\pi$
$830$	1.83344	+	0.434534i	0.0636398	+	0.0150829i
$831$		0			0
$832$	0.449435	+	7.71650i	0.0155813	+	0.267521i
$833$	−0.416935	+	1.39266i	−0.0144459	+	0.0482528i
$834$		0			0
$835$	6.60497	+	8.87201i	0.228574	+	0.307029i
$836$	−3.88339	+	6.72622i	−0.134310	+	0.232631i
$837$		0			0
$838$	−24.0161	−	41.5971i	−0.829622	−	1.43695i
$839$	4.82744	−	11.1913i	0.166662	−	0.386366i	−0.814333	−	0.580397i	$-0.802897\pi$
$839$	4.82744	−	11.1913i	0.166662	−	0.386366i	0.980995	+	0.194032i	$0.0621565\pi$
$840$		0			0
$841$	−27.5310	−	29.1811i	−0.949343	−	1.00625i
$842$	14.3579	−	9.44331i	0.494804	−	0.325438i
$843$		0			0
$844$	10.0698	−	10.6733i	0.346615	−	0.367391i
$845$	−1.98358	+	11.2494i	−0.0682373	+	0.386993i
$846$		0			0
$847$	0.279457	+	1.58488i	0.00960225	+	0.0544571i
$848$	35.6348	+	23.4374i	1.22370	+	0.804843i
$849$		0			0
$850$	−1.11367	−	0.130169i	−0.0381984	−	0.00446475i
$851$	−86.4934	−	10.1096i	−2.96495	−	0.346553i
$852$		0			0
$853$	7.58261	+	4.98716i	0.259624	+	0.170757i	0.672647	−	0.739963i	$-0.265157\pi$
$853$	7.58261	+	4.98716i	0.259624	+	0.170757i	−0.413024	+	0.910720i	$0.635527\pi$
$854$	−0.922785	−	5.23338i	−0.0315771	−	0.179082i
$855$		0			0
$856$	−0.247123	+	1.40150i	−0.00844649	+	0.0479024i
$857$	17.4250	−	18.4695i	0.595228	−	0.630905i	−0.357796	−	0.933800i	$-0.616472\pi$
$857$	17.4250	−	18.4695i	0.595228	−	0.630905i	0.953024	+	0.302895i	$0.0979532\pi$
$858$		0			0
$859$	0.357616	−	0.235208i	0.0122017	−	0.00802519i	−0.543393	−	0.839478i	$-0.682861\pi$
$859$	0.357616	−	0.235208i	0.0122017	−	0.00802519i	0.555595	+	0.831453i	$0.312490\pi$
$860$	6.48056	+	6.86900i	0.220985	+	0.234231i
$861$		0			0
$862$	−3.62210	+	8.39698i	−0.123369	+	0.286002i
$863$	−20.6116	−	35.7004i	−0.701628	−	1.21526i	−0.967895	−	0.251356i	$-0.919124\pi$
$863$	−20.6116	−	35.7004i	−0.701628	−	1.21526i	0.266267	−	0.963899i	$-0.414210\pi$
$864$		0			0
$865$	12.2143	−	21.1557i	0.415297	−	0.719316i
$866$	−7.03984	−	9.45614i	−0.239223	−	0.321333i
$867$		0			0
$868$	0.0659379	−	0.220248i	0.00223808	−	0.00747570i
$869$	0.443990	+	7.62301i	0.0150613	+	0.258593i
$870$		0			0
$871$	5.63803	+	1.33624i	0.191037	+	0.0452767i
$872$	2.90553	+	2.43803i	0.0983936	+	0.0825620i
$873$		0			0
$874$	36.5681	−	30.6843i	1.23693	−	1.03791i
$875$	−3.08926	+	1.55148i	−0.104436	+	0.0524497i
$876$		0			0
$877$	−14.9215	−	34.5918i	−0.503862	−	1.16808i	−0.960462	−	0.278411i	$-0.910192\pi$
$877$	−14.9215	−	34.5918i	−0.503862	−	1.16808i	0.456600	−	0.889672i	$-0.349067\pi$
$878$	15.9026	−	21.3609i	0.536686	−	0.720894i
$879$		0			0
$880$	−0.961523	+	16.5087i	−0.0324129	+	0.556509i
$881$	−2.94091	−	1.07040i	−0.0990817	−	0.0360628i	0.292004	−	0.956417i	$-0.405678\pi$
$881$	−2.94091	−	1.07040i	−0.0990817	−	0.0360628i	−0.391085	+	0.920354i	$0.627900\pi$
$882$		0			0
$883$	46.2681	−	16.8402i	1.55705	−	0.566719i	0.586989	−	0.809595i	$-0.300313\pi$
$883$	46.2681	−	16.8402i	1.55705	−	0.566719i	0.970057	+	0.242876i	$0.0780909\pi$
$884$	−0.257759	−	0.860976i	−0.00866938	−	0.0289577i
$885$		0			0
$886$	42.7196	+	21.4546i	1.43519	+	0.720781i
$887$	52.8516	−	12.5261i	1.77458	−	0.420584i	0.792629	−	0.609704i	$-0.208712\pi$
$887$	52.8516	−	12.5261i	1.77458	−	0.420584i	0.981954	+	0.189121i	$0.0605637\pi$
$888$		0			0
$889$	3.22125	−	0.376510i	0.108037	−	0.0126277i
$890$	−30.6490			−1.02736
$891$		0			0
$892$	−1.75235			−0.0586730
$893$	21.5451	−	2.51826i	0.720979	−	0.0842703i
$894$		0			0
$895$	−23.6795	+	5.61213i	−0.791517	+	0.187593i
$896$	−3.48940	−	1.75244i	−0.116573	−	0.0585450i
$897$		0			0
$898$	−5.36337	−	17.9149i	−0.178978	−	0.597828i
$899$	6.26317	−	2.27961i	0.208888	−	0.0760291i
$900$		0			0
$901$	1.68984	+	0.615050i	0.0562966	+	0.0204903i
$902$	1.12610	−	19.3344i	0.0374951	−	0.643766i
$903$		0			0
$904$	−6.45600	+	8.67192i	−0.214723	+	0.288424i
$905$	−14.5665	−	33.7691i	−0.484208	−	1.12252i
$906$		0			0
$907$	42.0616	−	21.1241i	1.39663	−	0.701415i	0.418271	−	0.908322i	$-0.362636\pi$
$907$	42.0616	−	21.1241i	1.39663	−	0.701415i	0.978360	+	0.206908i	$0.0663400\pi$
$908$	18.0983	−	15.1863i	0.600613	−	0.503974i
$909$		0			0
$910$	−2.57699	−	2.16235i	−0.0854263	−	0.0716811i
$911$	−50.3668	−	11.9372i	−1.66873	−	0.395496i	−0.715707	−	0.698400i	$-0.753895\pi$
$911$	−50.3668	−	11.9372i	−1.66873	−	0.395496i	−0.953021	+	0.302905i	$0.902044\pi$
$912$		0			0
$913$	0.112461	+	1.93088i	0.00372192	+	0.0639029i
$914$	8.05864	−	26.9177i	0.266556	−	0.890359i
$915$		0			0
$916$	−2.58984	−	3.47876i	−0.0855708	−	0.114942i
$917$	0.929052	−	1.60917i	0.0306800	−	0.0531393i
$918$		0			0
$919$	−6.58049	−	11.3977i	−0.217070	−	0.375977i	0.736841	−	0.676066i	$-0.236317\pi$
$919$	−6.58049	−	11.3977i	−0.217070	−	0.375977i	−0.953911	+	0.300090i	$0.902983\pi$
$920$	8.01452	−	18.5797i	0.264231	−	0.612556i
$921$		0			0
$922$	−29.3402	−	31.0988i	−0.966270	−	1.02419i
$923$	−6.89678	+	4.53608i	−0.227010	+	0.149307i
$924$		0			0
$925$	23.2306	−	24.6230i	0.763816	−	0.809598i
$926$	4.02821	−	22.8451i	0.132375	−	0.750736i
$927$		0			0
$928$	7.01909	+	39.8072i	0.230413	+	1.30674i
$929$	14.3922	+	9.46587i	0.472191	+	0.310565i	0.763208	−	0.646153i	$-0.223623\pi$
$929$	14.3922	+	9.46587i	0.472191	+	0.310565i	−0.291017	+	0.956718i	$0.593994\pi$
$930$		0			0
$931$	23.8967	+	2.79312i	0.783182	+	0.0915409i
$932$	10.5238	+	1.23006i	0.344719	+	0.0402919i
$933$		0			0
$934$	−49.0242	−	32.2437i	−1.60412	−	1.05505i
$935$	0.121072	+	0.686633i	0.00395948	+	0.0224553i
$936$		0			0
$937$	6.62799	−	37.5892i	0.216527	−	1.22799i	−0.661710	−	0.749760i	$-0.730169\pi$
$937$	6.62799	−	37.5892i	0.216527	−	1.22799i	0.878237	−	0.478226i	$-0.158720\pi$
$938$	−0.456876	+	0.484261i	−0.0149175	+	0.0158117i
$939$		0			0
$940$	−6.60240	+	4.34247i	−0.215347	+	0.141636i
$941$	−14.6033	−	15.4786i	−0.476053	−	0.504586i	0.444191	−	0.895932i	$-0.353491\pi$
$941$	−14.6033	−	15.4786i	−0.476053	−	0.504586i	−0.920244	+	0.391346i	$0.872010\pi$
$942$		0			0
$943$	−14.9034	+	34.5499i	−0.485320	+	1.12510i
$944$	17.6383	+	30.5504i	0.574077	+	0.994331i
$945$		0			0
$946$	−15.3333	+	26.5580i	−0.498528	+	0.863476i
$947$	4.64962	+	6.24553i	0.151092	+	0.202952i	0.871225	−	0.490884i	$-0.163326\pi$
$947$	4.64962	+	6.24553i	0.151092	+	0.202952i	−0.720132	+	0.693837i	$0.755919\pi$
$948$		0			0
$949$	17.8731	−	59.7005i	0.580187	−	1.93796i
$950$	1.07898	+	18.5253i	0.0350067	+	0.601042i
$951$		0			0
$952$	−0.116915	−	0.0277093i	−0.00378923	−	0.000898064i
$953$	−29.0892	−	24.4088i	−0.942292	−	0.790677i	0.0356905	−	0.999363i	$-0.488637\pi$
$953$	−29.0892	−	24.4088i	−0.942292	−	0.790677i	−0.977983	+	0.208686i	$0.933081\pi$
$954$		0			0
$955$	−3.29858	+	2.76784i	−0.106740	+	0.0895652i
$956$	9.70360	−	4.87333i	0.313837	−	0.157615i
$957$		0			0
$958$	14.6723	+	34.0143i	0.474041	+	1.09895i
$959$	0.215207	−	0.289073i	0.00694939	−	0.00933464i
$960$		0			0
$961$	1.76512	−	30.3059i	0.0569393	−	0.977610i
$962$	80.6621	+	29.3586i	2.60065	+	0.946560i
$963$		0			0
$964$	−3.83856	+	1.39712i	−0.123632	+	0.0449983i
$965$	3.89187	+	12.9998i	0.125284	+	0.418477i
$966$		0			0
$967$	−4.84104	−	2.43126i	−0.155677	−	0.0781841i	0.369255	−	0.929328i	$-0.379613\pi$
$967$	−4.84104	−	2.43126i	−0.155677	−	0.0781841i	−0.524932	+	0.851144i	$0.675909\pi$
$968$	9.28471	−	2.20052i	0.298422	−	0.0707273i
$969$		0			0
$970$	−15.5606	+	1.81877i	−0.499619	+	0.0583971i
$971$	45.8419			1.47114			0.735568	−	0.677451i	$-0.236915\pi$
$971$	45.8419			1.47114			0.735568	+	0.677451i	$0.236915\pi$
$972$		0			0
$973$	−5.05922			−0.162191
$974$	−65.9882	+	7.71291i	−2.11440	+	0.247138i
$975$		0			0
$976$	−48.6792	+	11.5372i	−1.55818	+	0.369297i
$977$	45.3323	+	22.7667i	1.45031	+	0.728372i	0.987431	−	0.158050i	$-0.0505208\pi$
$977$	45.3323	+	22.7667i	1.45031	+	0.728372i	0.462877	+	0.886422i	$0.346817\pi$
$978$		0			0
$979$	−9.02312	−	30.1393i	−0.288380	−	0.963257i
$980$	−8.23640	+	2.99780i	−0.263102	+	0.0957613i
$981$		0			0
$982$	47.0562	+	17.1271i	1.50162	+	0.546546i
$983$	−2.05422	+	35.2695i	−0.0655193	+	1.12492i	0.792017	+	0.610499i	$0.209031\pi$
$983$	−2.05422	+	35.2695i	−0.0655193	+	1.12492i	−0.857536	+	0.514424i	$0.828006\pi$
$984$		0			0
$985$	1.67199	−	2.24587i	0.0532741	−	0.0715595i
$986$	1.18576	+	2.74890i	0.0377623	+	0.0875429i
$987$		0			0
$988$	−13.2920	+	6.67548i	−0.422874	+	0.212375i
$989$	45.6409	−	38.2973i	1.45130	−	1.21778i
$990$		0			0
$991$	−3.21935	−	2.70136i	−0.102266	−	0.0858114i	0.590221	−	0.807242i	$-0.299041\pi$
$991$	−3.21935	−	2.70136i	−0.102266	−	0.0858114i	−0.692487	+	0.721430i	$0.743485\pi$
$992$	−3.79278	−	0.898906i	−0.120421	−	0.0285403i
$993$		0			0
$994$	−0.0551499	−	0.946887i	−0.00174925	−	0.0300334i
$995$	−5.14804	+	17.1956i	−0.163204	+	0.545139i
$996$		0			0
$997$	4.11126	+	5.52238i	0.130205	+	0.174896i	0.862445	−	0.506151i	$-0.168932\pi$
$997$	4.11126	+	5.52238i	0.130205	+	0.174896i	−0.732240	+	0.681047i	$0.761525\pi$
$998$	23.4914	−	40.6884i	0.743608	−	1.28797i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	243.2.g.a.19.2		144
3.2	odd	2		81.2.g.a.61.7	yes	144
9.2	odd	6		729.2.g.c.541.2		144
9.4	even	3		729.2.g.a.55.7		144
9.5	odd	6		729.2.g.d.55.2		144
9.7	even	3		729.2.g.b.541.7		144
81.2	odd	54		6561.2.a.c.1.18		72
81.4	even	27	inner	243.2.g.a.64.2		144
81.23	odd	54		729.2.g.d.676.2		144
81.31	even	27		729.2.g.b.190.7		144
81.50	odd	54		729.2.g.c.190.2		144
81.58	even	27		729.2.g.a.676.7		144
81.77	odd	54		81.2.g.a.4.7	✓	144
81.79	even	27		6561.2.a.d.1.55		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.4.7	✓	144	81.77	odd	54
81.2.g.a.61.7	yes	144	3.2	odd	2
243.2.g.a.19.2		144	1.1	even	1	trivial
243.2.g.a.64.2		144	81.4	even	27	inner
729.2.g.a.55.7		144	9.4	even	3
729.2.g.a.676.7		144	81.58	even	27
729.2.g.b.190.7		144	81.31	even	27
729.2.g.b.541.7		144	9.7	even	3
729.2.g.c.190.2		144	81.50	odd	54
729.2.g.c.541.2		144	9.2	odd	6
729.2.g.d.55.2		144	9.5	odd	6
729.2.g.d.676.2		144	81.23	odd	54
6561.2.a.c.1.18		72	81.2	odd	54
6561.2.a.d.1.55		72	81.79	even	27

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:	\( N \)	\(=\)	\( 243 = 3^{5} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	243.g (of order \(27\), degree \(18\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.69853 + 0.198530i) q^{2} +(0.899496 - 0.213184i) q^{4} +(-1.22732 - 0.616384i) q^{5} +(0.0889729 + 0.297190i) q^{7} +(1.72842 - 0.629095i) q^{8} +O(q^{10})\)	\(q+(-1.69853 + 0.198530i) q^{2} +(0.899496 - 0.213184i) q^{4} +(-1.22732 - 0.616384i) q^{5} +(0.0889729 + 0.297190i) q^{7} +(1.72842 - 0.629095i) q^{8} +(2.20701 + 0.803287i) q^{10} +(-0.140180 + 2.40680i) q^{11} +(-2.75712 + 3.70345i) q^{13} +(-0.210124 - 0.487122i) q^{14} +(-4.46306 + 2.24143i) q^{16} +(-0.161307 + 0.135352i) q^{17} +(2.66964 + 2.24009i) q^{19} +(-1.23537 - 0.292789i) q^{20} +(-0.239721 - 4.11585i) q^{22} +(-2.29728 + 7.67346i) q^{23} +(-1.85940 - 2.49761i) q^{25} +(3.94780 - 6.83779i) q^{26} +(0.143387 + 0.248354i) q^{28} +(-3.29291 + 7.63382i) q^{29} +(-0.550159 - 0.583135i) q^{31} +(4.06213 - 2.67170i) q^{32} +(0.247112 - 0.261924i) q^{34} +(0.0739849 - 0.419589i) q^{35} +(1.88786 + 10.7066i) q^{37} +(-4.97918 - 3.27486i) q^{38} +(-2.50910 - 0.293272i) q^{40} +(4.66578 + 0.545352i) q^{41} +(-6.21456 - 4.08738i) q^{43} +(0.387001 + 2.19479i) q^{44} +(2.37859 - 13.4897i) q^{46} +(4.27143 - 4.52745i) q^{47} +(5.76801 - 3.79368i) q^{49} +(3.65410 + 3.87312i) q^{50} +(-1.69050 + 3.91901i) q^{52} +(-4.27003 - 7.39591i) q^{53} +(1.65556 - 2.86752i) q^{55} +(0.340744 + 0.457698i) q^{56} +(4.07756 - 13.6200i) q^{58} +(-0.410699 - 7.05143i) q^{59} +(9.74699 + 2.31008i) q^{61} +(1.05023 + 0.881248i) q^{62} +(1.28246 - 1.07611i) q^{64} +(5.66662 - 2.84588i) q^{65} +(-0.497063 - 1.15232i) q^{67} +(-0.116240 + 0.156137i) q^{68} +(-0.0423646 + 0.727373i) q^{70} +(1.68007 + 0.611494i) q^{71} +(-12.6834 + 4.61640i) q^{73} +(-5.33215 - 17.8106i) q^{74} +(2.87888 + 1.44583i) q^{76} +(-0.727750 + 0.172480i) q^{77} +(3.14586 - 0.367698i) q^{79} +6.85919 q^{80} -8.03324 q^{82} +(0.796837 - 0.0931369i) q^{83} +(0.281404 - 0.0666940i) q^{85} +(11.3671 + 5.70875i) q^{86} +(1.27182 + 4.24816i) q^{88} +(-12.2626 + 4.46322i) q^{89} +(-1.34594 - 0.489881i) q^{91} +(-0.430534 + 7.39199i) q^{92} +(-6.35631 + 8.53801i) q^{94} +(-1.89575 - 4.39484i) q^{95} +(-5.96090 + 2.99368i) q^{97} +(-9.04397 + 7.58879i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 18 q^{2} - 18 q^{4} + 18 q^{5} - 18 q^{7} + 18 q^{8}+O(q^{10}) \) 144 * q + 18 * q^2 - 18 * q^4 + 18 * q^5 - 18 * q^7 + 18 * q^8	\( 144 q + 18 q^{2} - 18 q^{4} + 18 q^{5} - 18 q^{7} + 18 q^{8} - 18 q^{10} + 18 q^{11} - 18 q^{13} + 18 q^{14} - 18 q^{16} + 18 q^{17} - 18 q^{19} - 18 q^{20} - 18 q^{22} - 9 q^{23} - 18 q^{25} - 45 q^{26} - 9 q^{28} - 9 q^{29} - 18 q^{31} - 36 q^{32} - 18 q^{34} - 9 q^{35} - 18 q^{37} + 9 q^{38} - 18 q^{40} - 18 q^{43} - 54 q^{44} - 18 q^{46} - 36 q^{47} - 18 q^{49} - 99 q^{50} - 45 q^{53} - 9 q^{55} - 126 q^{56} - 18 q^{58} - 45 q^{59} - 18 q^{61} - 81 q^{62} - 18 q^{64} + 9 q^{67} + 99 q^{68} + 36 q^{70} + 90 q^{71} - 18 q^{73} + 162 q^{74} + 63 q^{76} + 162 q^{77} + 36 q^{79} + 288 q^{80} - 36 q^{82} + 90 q^{83} + 36 q^{85} + 162 q^{86} + 63 q^{88} + 81 q^{89} - 18 q^{91} + 144 q^{92} + 36 q^{94} - 18 q^{95} + 9 q^{97} - 81 q^{98}+O(q^{100}) \) 144 * q + 18 * q^2 - 18 * q^4 + 18 * q^5 - 18 * q^7 + 18 * q^8 - 18 * q^10 + 18 * q^11 - 18 * q^13 + 18 * q^14 - 18 * q^16 + 18 * q^17 - 18 * q^19 - 18 * q^20 - 18 * q^22 - 9 * q^23 - 18 * q^25 - 45 * q^26 - 9 * q^28 - 9 * q^29 - 18 * q^31 - 36 * q^32 - 18 * q^34 - 9 * q^35 - 18 * q^37 + 9 * q^38 - 18 * q^40 - 18 * q^43 - 54 * q^44 - 18 * q^46 - 36 * q^47 - 18 * q^49 - 99 * q^50 - 45 * q^53 - 9 * q^55 - 126 * q^56 - 18 * q^58 - 45 * q^59 - 18 * q^61 - 81 * q^62 - 18 * q^64 + 9 * q^67 + 99 * q^68 + 36 * q^70 + 90 * q^71 - 18 * q^73 + 162 * q^74 + 63 * q^76 + 162 * q^77 + 36 * q^79 + 288 * q^80 - 36 * q^82 + 90 * q^83 + 36 * q^85 + 162 * q^86 + 63 * q^88 + 81 * q^89 - 18 * q^91 + 144 * q^92 + 36 * q^94 - 18 * q^95 + 9 * q^97 - 81 * q^98

Introduction

L-functions

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