LMFDB - Embedded newform 729.2.g.b.28.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("729.28");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			28.2
Character	$\chi$	$=$	729.28
Dual form			729.2.g.b.703.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.76769 + 1.16263i) q^{2} +(0.980860 - 2.27389i) q^{4} +(2.67150 - 2.83162i) q^{5} +(3.31264 + 0.387192i) q^{7} +(0.175036 + 0.992677i) q^{8} +O(q^{10})$	\(q+(-1.76769 + 1.16263i) q^{2} +(0.980860 - 2.27389i) q^{4} +(2.67150 - 2.83162i) q^{5} +(3.31264 + 0.387192i) q^{7} +(0.175036 + 0.992677i) q^{8} +(-1.43025 + 8.11138i) q^{10} +(0.217034 - 0.724944i) q^{11} +(-0.144562 + 2.48203i) q^{13} +(-6.30588 + 3.16693i) q^{14} +(1.93533 + 2.05133i) q^{16} +(0.700932 - 0.255119i) q^{17} +(4.21736 + 1.53499i) q^{19} +(-3.81843 - 8.85211i) q^{20} +(0.459191 + 1.53380i) q^{22} +(-2.27126 + 0.265472i) q^{23} +(-0.590459 - 10.1378i) q^{25} +(-2.63013 - 4.55552i) q^{26} +(4.12967 - 7.15280i) q^{28} +(-0.414639 - 0.208240i) q^{29} +(-2.35407 - 3.16206i) q^{31} +(-7.76762 - 1.84096i) q^{32} +(-0.942422 + 1.26589i) q^{34} +(9.94610 - 8.34577i) q^{35} +(-3.64375 - 3.05747i) q^{37} +(-9.23961 + 2.18983i) q^{38} +(3.27849 + 2.15630i) q^{40} +(4.08763 + 2.68847i) q^{41} +(5.78094 - 1.37011i) q^{43} +(-1.43556 - 1.20458i) q^{44} +(3.70623 - 3.10990i) q^{46} +(6.42922 - 8.63594i) q^{47} +(4.01237 + 0.950949i) q^{49} +(12.8302 + 17.2340i) q^{50} +(5.50206 + 2.76324i) q^{52} +(-5.75294 + 9.96438i) q^{53} +(-1.47296 - 2.55124i) q^{55} +(0.195474 + 3.35616i) q^{56} +(0.975058 - 0.113968i) q^{58} +(-1.19000 - 3.97488i) q^{59} +(0.105839 + 0.245363i) q^{61} +(7.83755 + 2.85264i) q^{62} +(10.5709 - 3.84748i) q^{64} +(6.64196 + 7.04007i) q^{65} +(-1.71358 + 0.860594i) q^{67} +(0.107405 - 1.84408i) q^{68} +(-7.87859 + 26.3163i) q^{70} +(-1.17278 + 6.65118i) q^{71} +(1.37723 + 7.81064i) q^{73} +(9.99572 + 1.16833i) q^{74} +(7.62705 - 8.08420i) q^{76} +(0.999649 - 2.31745i) q^{77} +(-3.60662 + 2.37211i) q^{79} +10.9788 q^{80} -10.3513 q^{82} +(-2.12790 + 1.39954i) q^{83} +(1.15014 - 2.66632i) q^{85} +(-8.62597 + 9.14299i) q^{86} +(0.757624 + 0.0885535i) q^{88} +(0.935549 + 5.30576i) q^{89} +(-1.43990 + 8.16609i) q^{91} +(-1.62413 + 5.42498i) q^{92} +(-1.32448 + 22.7404i) q^{94} +(15.6132 - 7.84124i) q^{95} +(-6.51132 - 6.90160i) q^{97} +(-8.19821 + 2.98391i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8}+O(q^{10}) $ 144 * q - 9 * q^2 + 9 * q^4 - 9 * q^5 + 9 * q^7 + 18 * q^8	$ 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8} - 18 q^{10} - 9 q^{11} + 9 q^{13} - 9 q^{14} + 9 q^{16} + 18 q^{17} - 18 q^{19} + 63 q^{20} + 9 q^{22} - 36 q^{23} + 9 q^{25} - 45 q^{26} - 9 q^{28} + 45 q^{29} + 9 q^{31} - 63 q^{32} + 9 q^{34} - 9 q^{35} - 18 q^{37} + 9 q^{38} + 9 q^{40} + 27 q^{41} + 9 q^{43} - 54 q^{44} - 18 q^{46} - 63 q^{47} + 9 q^{49} + 225 q^{50} + 27 q^{52} - 45 q^{53} - 9 q^{55} - 99 q^{56} + 9 q^{58} + 117 q^{59} + 9 q^{61} - 81 q^{62} - 18 q^{64} - 81 q^{65} + 36 q^{67} + 18 q^{68} + 63 q^{70} + 90 q^{71} - 18 q^{73} - 81 q^{74} + 90 q^{76} - 81 q^{77} + 63 q^{79} + 288 q^{80} - 36 q^{82} - 45 q^{83} + 63 q^{85} - 81 q^{86} + 90 q^{88} + 81 q^{89} - 18 q^{91} + 63 q^{92} + 63 q^{94} - 153 q^{95} + 36 q^{97} - 81 q^{98}+O(q^{100}) $ 144 * q - 9 * q^2 + 9 * q^4 - 9 * q^5 + 9 * q^7 + 18 * q^8 - 18 * q^10 - 9 * q^11 + 9 * q^13 - 9 * q^14 + 9 * q^16 + 18 * q^17 - 18 * q^19 + 63 * q^20 + 9 * q^22 - 36 * q^23 + 9 * q^25 - 45 * q^26 - 9 * q^28 + 45 * q^29 + 9 * q^31 - 63 * q^32 + 9 * q^34 - 9 * q^35 - 18 * q^37 + 9 * q^38 + 9 * q^40 + 27 * q^41 + 9 * q^43 - 54 * q^44 - 18 * q^46 - 63 * q^47 + 9 * q^49 + 225 * q^50 + 27 * q^52 - 45 * q^53 - 9 * q^55 - 99 * q^56 + 9 * q^58 + 117 * q^59 + 9 * q^61 - 81 * q^62 - 18 * q^64 - 81 * q^65 + 36 * q^67 + 18 * q^68 + 63 * q^70 + 90 * q^71 - 18 * q^73 - 81 * q^74 + 90 * q^76 - 81 * q^77 + 63 * q^79 + 288 * q^80 - 36 * q^82 - 45 * q^83 + 63 * q^85 - 81 * q^86 + 90 * q^88 + 81 * q^89 - 18 * q^91 + 63 * q^92 + 63 * q^94 - 153 * q^95 + 36 * q^97 - 81 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−1.76769	+	1.16263i	−1.24994	+	0.822101i	−0.989660	−	0.143431i	$-0.954186\pi$
$2$	−1.76769	+	1.16263i	−1.24994	+	0.822101i	−0.260284	+	0.965532i	$0.583816\pi$
$3$		0			0
$3$		0			0
$4$	0.980860	−	2.27389i	0.490430	−	1.13694i
$5$	2.67150	−	2.83162i	1.19473	−	1.26634i	0.239359	−	0.970931i	$-0.423063\pi$
$5$	2.67150	−	2.83162i	1.19473	−	1.26634i	0.955371	−	0.295408i	$-0.0954557\pi$
$6$		0			0
$7$	3.31264	+	0.387192i	1.25206	+	0.146345i	0.716160	−	0.697936i	$-0.245898\pi$
$7$	3.31264	+	0.387192i	1.25206	+	0.146345i	0.535901	+	0.844281i	$0.319972\pi$
$8$	0.175036	+	0.992677i	0.0618845	+	0.350964i
$9$		0			0
$10$	−1.43025	+	8.11138i	−0.452286	+	2.56504i
$11$	0.217034	−	0.724944i	0.0654382	−	0.218579i	−0.919016	−	0.394220i	$-0.871015\pi$
$11$	0.217034	−	0.724944i	0.0654382	−	0.218579i	0.984454	+	0.175641i	$0.0561999\pi$
$12$		0			0
$13$	−0.144562	+	2.48203i	−0.0400942	+	0.688390i	0.917049	+	0.398775i	$0.130564\pi$
$13$	−0.144562	+	2.48203i	−0.0400942	+	0.688390i	−0.957143	+	0.289615i	$0.906473\pi$
$14$	−6.30588	+	3.16693i	−1.68532	+	0.846398i
$15$		0			0
$16$	1.93533	+	2.05133i	0.483831	+	0.512831i
$17$	0.700932	−	0.255119i	0.170001	−	0.0618753i	−0.255617	−	0.966778i	$-0.582279\pi$
$17$	0.700932	−	0.255119i	0.170001	−	0.0618753i	0.425619	+	0.904903i	$0.360057\pi$
$18$		0			0
$19$	4.21736	+	1.53499i	0.967530	+	0.352152i	0.776980	−	0.629526i	$-0.216751\pi$
$19$	4.21736	+	1.53499i	0.967530	+	0.352152i	0.190550	+	0.981678i	$0.438973\pi$
$20$	−3.81843	−	8.85211i	−0.853827	−	1.97939i
$21$		0			0
$22$	0.459191	+	1.53380i	0.0978998	+	0.327008i
$23$	−2.27126	+	0.265472i	−0.473590	+	0.0553547i	−0.349540	−	0.936921i	$-0.613662\pi$
$23$	−2.27126	+	0.265472i	−0.473590	+	0.0553547i	−0.124049	+	0.992276i	$0.539588\pi$
$24$		0			0
$25$	−0.590459	−	10.1378i	−0.118092	−	2.02756i
$26$	−2.63013	−	4.55552i	−0.515811	−	0.893410i
$27$		0			0
$28$	4.12967	−	7.15280i	0.780435	−	1.35175i
$29$	−0.414639	−	0.208240i	−0.0769966	−	0.0386691i	0.409884	−	0.912138i	$-0.365569\pi$
$29$	−0.414639	−	0.208240i	−0.0769966	−	0.0386691i	−0.486881	+	0.873468i	$0.661865\pi$
$30$		0			0
$31$	−2.35407	−	3.16206i	−0.422803	−	0.567923i	0.538777	−	0.842449i	$-0.318887\pi$
$31$	−2.35407	−	3.16206i	−0.422803	−	0.567923i	−0.961580	+	0.274526i	$0.911479\pi$
$32$	−7.76762	−	1.84096i	−1.37313	−	0.325439i
$33$		0			0
$34$	−0.942422	+	1.26589i	−0.161624	+	0.217099i
$35$	9.94610	−	8.34577i	1.68120	−	1.41069i
$36$		0			0
$37$	−3.64375	−	3.05747i	−0.599029	−	0.502645i	0.292104	−	0.956387i	$-0.405645\pi$
$37$	−3.64375	−	3.05747i	−0.599029	−	0.502645i	−0.891134	+	0.453741i	$0.850089\pi$
$38$	−9.23961	+	2.18983i	−1.49886	+	0.355237i
$39$		0			0
$40$	3.27849	+	2.15630i	0.518375	+	0.340941i
$41$	4.08763	+	2.68847i	0.638380	+	0.419869i	0.827016	−	0.562178i	$-0.190036\pi$
$41$	4.08763	+	2.68847i	0.638380	+	0.419869i	−0.188636	+	0.982047i	$0.560407\pi$
$42$		0			0
$43$	5.78094	−	1.37011i	0.881585	−	0.208939i	0.235196	−	0.971948i	$-0.424427\pi$
$43$	5.78094	−	1.37011i	0.881585	−	0.208939i	0.646388	+	0.763009i	$0.276279\pi$
$44$	−1.43556	−	1.20458i	−0.216419	−	0.181597i
$45$		0			0
$46$	3.70623	−	3.10990i	0.546454	−	0.458529i
$47$	6.42922	−	8.63594i	0.937798	−	1.25968i	−0.0277927	−	0.999614i	$-0.508848\pi$
$47$	6.42922	−	8.63594i	0.937798	−	1.25968i	0.965590	−	0.260067i	$-0.0837448\pi$
$48$		0			0
$49$	4.01237	+	0.950949i	0.573195	+	0.135850i
$50$	12.8302	+	17.2340i	1.81447	+	2.43725i
$51$		0			0
$52$	5.50206	+	2.76324i	0.762998	+	0.383192i
$53$	−5.75294	+	9.96438i	−0.790227	+	1.36871i	0.135600	+	0.990764i	$0.456704\pi$
$53$	−5.75294	+	9.96438i	−0.790227	+	1.36871i	−0.925826	+	0.377949i	$0.876629\pi$
$54$		0			0
$55$	−1.47296	−	2.55124i	−0.198614	−	0.344010i
$56$	0.195474	+	3.35616i	0.0261213	+	0.448485i
$57$		0			0
$58$	0.975058	−	0.113968i	0.128031	−	0.0149647i
$59$	−1.19000	−	3.97488i	−0.154925	−	0.517485i	0.844924	−	0.534887i	$-0.179646\pi$
$59$	−1.19000	−	3.97488i	−0.154925	−	0.517485i	−0.999849	+	0.0174017i	$0.994461\pi$
$60$		0			0
$61$	0.105839	+	0.245363i	0.0135513	+	0.0314155i	0.924857	−	0.380314i	$-0.124184\pi$
$61$	0.105839	+	0.245363i	0.0135513	+	0.0314155i	−0.911306	+	0.411730i	$0.864925\pi$
$62$	7.83755	+	2.85264i	0.995370	+	0.362285i
$63$		0			0
$64$	10.5709	−	3.84748i	1.32136	−	0.480935i
$65$	6.64196	+	7.04007i	0.823834	+	0.873213i
$66$		0			0
$67$	−1.71358	+	0.860594i	−0.209348	+	0.105138i	−0.550384	−	0.834912i	$-0.685519\pi$
$67$	−1.71358	+	0.860594i	−0.209348	+	0.105138i	0.341036	+	0.940050i	$0.389222\pi$
$68$	0.107405	−	1.84408i	0.0130248	−	0.223627i
$69$		0			0
$70$	−7.87859	+	26.3163i	−0.941671	+	3.14540i
$71$	−1.17278	+	6.65118i	−0.139184	+	0.789350i	0.832671	+	0.553768i	$0.186811\pi$
$71$	−1.17278	+	6.65118i	−0.139184	+	0.789350i	−0.971855	+	0.235582i	$0.924300\pi$
$72$		0			0
$73$	1.37723	+	7.81064i	0.161192	+	0.914167i	0.952904	+	0.303272i	$0.0980791\pi$
$73$	1.37723	+	7.81064i	0.161192	+	0.914167i	−0.791712	+	0.610895i	$0.790810\pi$
$74$	9.99572	+	1.16833i	1.16198	+	0.135816i
$75$		0			0
$76$	7.62705	−	8.08420i	0.874883	−	0.927322i
$77$	0.999649	−	2.31745i	0.113921	−	0.264098i
$78$		0			0
$79$	−3.60662	+	2.37211i	−0.405777	+	0.266884i	−0.735949	−	0.677037i	$-0.763264\pi$
$79$	−3.60662	+	2.37211i	−0.405777	+	0.266884i	0.330172	+	0.943921i	$0.392893\pi$
$80$	10.9788			1.22747
$81$		0			0
$82$	−10.3513			−1.14311
$83$	−2.12790	+	1.39954i	−0.233567	+	0.153620i	−0.660898	−	0.750476i	$-0.729824\pi$
$83$	−2.12790	+	1.39954i	−0.233567	+	0.153620i	0.427331	+	0.904095i	$0.359454\pi$
$84$		0			0
$85$	1.15014	−	2.66632i	0.124750	−	0.289203i
$86$	−8.62597	+	9.14299i	−0.930162	+	0.985914i
$87$		0			0
$88$	0.757624	+	0.0885535i	0.0807630	+	0.00943984i
$89$	0.935549	+	5.30576i	0.0991680	+	0.562410i	0.993390	+	0.114786i	$0.0366184\pi$
$89$	0.935549	+	5.30576i	0.0991680	+	0.562410i	−0.894222	+	0.447623i	$0.852271\pi$
$90$		0			0
$91$	−1.43990	+	8.16609i	−0.150943	+	0.856039i
$92$	−1.62413	+	5.42498i	−0.169327	+	0.565593i
$93$		0			0
$94$	−1.32448	+	22.7404i	−0.136610	+	2.34550i
$95$	15.6132	−	7.84124i	1.60188	−	0.804495i
$96$		0			0
$97$	−6.51132	−	6.90160i	−0.661125	−	0.700751i	0.306862	−	0.951754i	$-0.400721\pi$
$97$	−6.51132	−	6.90160i	−0.661125	−	0.700751i	−0.967986	+	0.251003i	$0.919240\pi$
$98$	−8.19821	+	2.98391i	−0.828145	+	0.301420i
$99$		0			0
$100$	−23.6314	−	8.60112i	−2.36314	−	0.860112i
$101$	4.87482	+	11.3011i	0.485063	+	1.12450i	0.968475	+	0.249109i	$0.0801377\pi$
$101$	4.87482	+	11.3011i	0.485063	+	1.12450i	−0.483413	+	0.875392i	$0.660603\pi$
$102$		0			0
$103$	−4.78109	−	15.9700i	−0.471095	−	1.57357i	−0.782096	−	0.623158i	$-0.785849\pi$
$103$	−4.78109	−	15.9700i	−0.471095	−	1.57357i	0.311001	−	0.950410i	$-0.399336\pi$
$104$	−2.48915	+	0.290940i	−0.244081	+	0.0285290i
$105$		0			0
$106$	−1.41546	−	24.3024i	−0.137481	−	2.36046i
$107$	−1.84694	−	3.19899i	−0.178550	−	0.309258i	0.762834	−	0.646595i	$-0.223807\pi$
$107$	−1.84694	−	3.19899i	−0.178550	−	0.309258i	−0.941384	+	0.337336i	$0.890474\pi$
$108$		0			0
$109$	8.66961	−	15.0162i	0.830398	−	1.43829i	−0.0673245	−	0.997731i	$-0.521446\pi$
$109$	8.66961	−	15.0162i	0.830398	−	1.43829i	0.897723	−	0.440561i	$-0.145220\pi$
$110$	5.56988	+	2.79730i	0.531067	+	0.266712i
$111$		0			0
$112$	5.61678	+	7.54465i	0.530736	+	0.712902i
$113$	10.0311	+	2.37743i	0.943651	+	0.223649i	0.673516	−	0.739173i	$-0.264783\pi$
$113$	10.0311	+	2.37743i	0.943651	+	0.223649i	0.270135	+	0.962822i	$0.412932\pi$
$114$		0			0
$115$	−5.31594	+	7.14055i	−0.495714	+	0.665859i
$116$	−0.880217	+	0.738590i	−0.0817261	+	0.0685764i
$117$		0			0
$118$	6.72485	+	5.64282i	0.619072	+	0.519464i
$119$	2.42072	−	0.573721i	0.221907	−	0.0525929i
$120$		0			0
$121$	8.71193	+	5.72992i	0.791993	+	0.520902i
$122$	−0.472356	−	0.310674i	−0.0427651	−	0.0281271i
$123$		0			0
$124$	−9.49919	+	2.25135i	−0.853052	+	0.202177i
$125$	−15.3730	−	12.8995i	−1.37500	−	1.15376i
$126$		0			0
$127$	−10.1217	+	8.49315i	−0.898159	+	0.753645i	−0.969830	−	0.243783i	$-0.921611\pi$
$127$	−10.1217	+	8.49315i	−0.898159	+	0.753645i	0.0716705	+	0.997428i	$0.477167\pi$
$128$	−4.67882	+	6.28474i	−0.413553	+	0.555498i
$129$		0			0
$130$	−19.9259	−	4.72252i	−1.74762	−	0.414192i
$131$	−6.00822	−	8.07044i	−0.524940	−	0.705117i	0.458018	−	0.888943i	$-0.348559\pi$
$131$	−6.00822	−	8.07044i	−0.524940	−	0.705117i	−0.982959	+	0.183825i	$0.941152\pi$
$132$		0			0
$133$	13.3763	+	6.71782i	1.15987	+	0.582509i
$134$	2.02853	−	3.51352i	0.175238	−	0.303522i
$135$		0			0
$136$	0.375938	+	0.651145i	0.0322365	+	0.0558352i
$137$	−0.550552	−	9.45261i	−0.0470368	−	0.807591i	−0.936518	−	0.350619i	$-0.885971\pi$
$137$	−0.550552	−	9.45261i	−0.0470368	−	0.807591i	0.889481	−	0.456972i	$-0.151066\pi$
$138$		0			0
$139$	10.4293	−	1.21902i	0.884605	−	0.103396i	0.338356	−	0.941018i	$-0.390129\pi$
$139$	10.4293	−	1.21902i	0.884605	−	0.103396i	0.546249	+	0.837623i	$0.316055\pi$
$140$	−9.22162	−	30.8024i	−0.779369	−	2.60327i
$141$		0			0
$142$	−5.65973	−	13.1207i	−0.474954	−	1.10107i
$143$	1.76795	+	0.643483i	0.147844	+	0.0538107i
$144$		0			0
$145$	−1.69736	+	0.617790i	−0.140958	+	0.0513047i
$146$	−11.5154	−	12.2056i	−0.953019	−	1.01014i
$147$		0			0
$148$	−10.5264	+	5.28654i	−0.865262	+	0.434551i
$149$	0.722705	−	12.4084i	0.0592063	−	1.01653i	−0.829632	−	0.558311i	$-0.811449\pi$
$149$	0.722705	−	12.4084i	0.0592063	−	1.01653i	0.888838	−	0.458222i	$-0.151513\pi$
$150$		0			0
$151$	5.22757	−	17.4613i	0.425413	−	1.42098i	−0.429904	−	0.902875i	$-0.641453\pi$
$151$	5.22757	−	17.4613i	0.425413	−	1.42098i	0.855317	−	0.518105i	$-0.173362\pi$
$152$	−0.785565	+	4.45516i	−0.0637177	+	0.361361i
$153$		0			0
$154$	0.927258	+	5.25874i	0.0747206	+	0.423761i
$155$	−15.2426	−	1.78161i	−1.22432	−	0.143102i
$156$		0			0
$157$	−16.0388	+	17.0001i	−1.28003	+	1.35675i	−0.377573	+	0.925980i	$0.623241\pi$
$157$	−16.0388	+	17.0001i	−1.28003	+	1.35675i	−0.902459	+	0.430775i	$0.858240\pi$
$158$	3.61750	−	8.38631i	0.287793	−	0.667179i
$159$		0			0
$160$	−25.9641	+	17.0768i	−2.05264	+	1.35004i
$161$	−7.62665			−0.601064
$162$		0			0
$163$	11.7238			0.918278			0.459139	−	0.888364i	$-0.348158\pi$
$163$	11.7238			0.918278			0.459139	+	0.888364i	$0.348158\pi$
$164$	10.1227	−	6.65780i	0.790449	−	0.519886i
$165$		0			0
$166$	2.13432	−	4.94790i	0.165655	−	0.384032i
$167$	−16.6160	+	17.6119i	−1.28579	+	1.36285i	−0.388472	+	0.921461i	$0.626997\pi$
$167$	−16.6160	+	17.6119i	−1.28579	+	1.36285i	−0.897314	+	0.441393i	$0.854484\pi$
$168$		0			0
$169$	6.77255	+	0.791597i	0.520965	+	0.0608921i
$170$	1.06685	+	6.05041i	0.0818237	+	0.464045i
$171$		0			0
$172$	2.55482	−	14.4891i	0.194803	−	1.10478i
$173$	−4.44902	+	14.8608i	−0.338253	+	1.12984i	0.604571	+	0.796551i	$0.293345\pi$
$173$	−4.44902	+	14.8608i	−0.338253	+	1.12984i	−0.942824	+	0.333292i	$0.891841\pi$
$174$		0			0
$175$	1.96930	−	33.8115i	0.148865	−	2.55591i
$176$	1.90713	−	0.957795i	0.143755	−	0.0721965i
$177$		0			0
$178$	−7.82238	−	8.29124i	−0.586312	−	0.621455i
$179$	−6.75474	+	2.45852i	−0.504873	+	0.183759i	−0.581884	−	0.813271i	$-0.697684\pi$
$179$	−6.75474	+	2.45852i	−0.504873	+	0.183759i	0.0770114	+	0.997030i	$0.475462\pi$
$180$		0			0
$181$	7.27112	+	2.64647i	0.540458	+	0.196711i	0.597802	−	0.801644i	$-0.296041\pi$
$181$	7.27112	+	2.64647i	0.540458	+	0.196711i	−0.0573439	+	0.998354i	$0.518263\pi$
$182$	−6.94882	−	16.1092i	−0.515081	−	1.19409i
$183$		0			0
$184$	−0.661079	−	2.20816i	−0.0487354	−	0.162787i
$185$	−18.3919	+	2.14970i	−1.35220	+	0.158049i
$186$		0			0
$187$	−0.0328205	−	0.563506i	−0.00240007	−	0.0412077i
$188$	−13.3310	−	23.0900i	−0.972264	−	1.68401i
$189$		0			0
$190$	−18.4828	+	32.0132i	−1.34089	+	2.32248i
$191$	9.00617	+	4.52307i	0.651664	+	0.327278i	0.743735	−	0.668475i	$-0.233052\pi$
$191$	9.00617	+	4.52307i	0.651664	+	0.327278i	−0.0920711	+	0.995752i	$0.529349\pi$
$192$		0			0
$193$	−9.54993	−	12.8278i	−0.687419	−	0.923364i	0.312226	−	0.950008i	$-0.398925\pi$
$193$	−9.54993	−	12.8278i	−0.687419	−	0.923364i	−0.999645	+	0.0266441i	$0.991518\pi$
$194$	19.5340	+	4.62964i	1.40246	+	0.332389i
$195$		0			0
$196$	6.09793	−	8.19094i	0.435566	−	0.585067i
$197$	−8.40349	+	7.05136i	−0.598724	+	0.502389i	−0.891035	−	0.453934i	$-0.850020\pi$
$197$	−8.40349	+	7.05136i	−0.598724	+	0.502389i	0.292311	+	0.956323i	$0.405576\pi$
$198$		0			0
$199$	2.68937	+	2.25665i	0.190644	+	0.159970i	0.733114	−	0.680106i	$-0.238066\pi$
$199$	2.68937	+	2.25665i	0.190644	+	0.159970i	−0.542470	+	0.840075i	$0.682511\pi$
$200$	9.96020	−	2.36061i	0.704293	−	0.166920i
$201$		0			0
$202$	−21.7561	−	14.3092i	−1.53075	−	1.00679i
$203$	−1.29292	−	0.850369i	−0.0907454	−	0.0596842i
$204$		0			0
$205$	18.5328	−	4.39236i	1.29439	−	0.306776i
$206$	27.0186	+	22.6713i	1.88247	+	1.57958i
$207$		0			0
$208$	−5.37122	+	4.50698i	−0.372427	+	0.312503i
$209$	2.02810	−	2.72421i	0.140286	−	0.188437i
$210$		0			0
$211$	−7.47663	−	1.77199i	−0.514712	−	0.121989i	−0.0349525	−	0.999389i	$-0.511128\pi$
$211$	−7.47663	−	1.77199i	−0.514712	−	0.121989i	−0.479760	+	0.877400i	$0.659276\pi$
$212$	17.0151	+	22.8552i	1.16860	+	1.56970i
$213$		0			0
$214$	6.98404	+	3.50752i	0.477419	+	0.239769i
$215$	11.5641	−	20.0297i	0.788667	−	1.36601i
$216$		0			0
$217$	−6.57386	−	11.3863i	−0.446262	−	0.772949i
$218$	2.13308	+	36.6235i	0.144470	+	2.48046i
$219$		0			0
$220$	−7.24602	+	0.846938i	−0.488526	+	0.0571005i
$221$	0.531883	+	1.77661i	0.0357783	+	0.119508i
$222$		0			0
$223$	4.29520	+	9.95739i	0.287628	+	0.666796i	0.999364	−	0.0356504i	$-0.0113503\pi$
$223$	4.29520	+	9.95739i	0.287628	+	0.666796i	−0.711737	+	0.702447i	$0.752091\pi$
$224$	−25.0185	−	9.10600i	−1.67162	−	0.608420i
$225$		0			0
$226$	−20.4960	+	7.45993i	−1.36337	+	0.496227i
$227$	−7.45351	−	7.90026i	−0.494707	−	0.524358i	0.431126	−	0.902292i	$-0.358116\pi$
$227$	−7.45351	−	7.90026i	−0.494707	−	0.524358i	−0.925833	+	0.377933i	$0.876635\pi$
$228$		0			0
$229$	2.04594	−	1.02751i	0.135199	−	0.0678997i	−0.379914	−	0.925022i	$-0.624046\pi$
$229$	2.04594	−	1.02751i	0.135199	−	0.0678997i	0.515113	+	0.857122i	$0.327750\pi$
$230$	1.09513	−	18.8027i	0.0722110	−	1.23981i
$231$		0			0
$232$	0.134138	−	0.448052i	0.00880659	−	0.0294161i
$233$	−3.09286	+	17.5405i	−0.202620	+	1.14912i	0.698521	+	0.715590i	$0.253842\pi$
$233$	−3.09286	+	17.5405i	−0.202620	+	1.14912i	−0.901141	+	0.433526i	$0.857269\pi$
$234$		0			0
$235$	−7.27807	−	41.2760i	−0.474769	−	2.69255i
$236$	−10.2057	−	1.19287i	−0.664332	−	0.0776493i
$237$		0			0
$238$	−3.61205	+	3.82855i	−0.234135	+	0.248168i
$239$	4.85842	−	11.2631i	0.314265	−	0.728548i	−0.685735	−	0.727851i	$-0.740519\pi$
$239$	4.85842	−	11.2631i	0.314265	−	0.728548i	1.00000		0.000696435i	$-0.000221682\pi$
$240$		0			0
$241$	−14.6206	+	9.61612i	−0.941795	+	0.619429i	−0.924811	−	0.380427i	$-0.875777\pi$
$241$	−14.6206	+	9.61612i	−0.941795	+	0.619429i	−0.0169845	+	0.999856i	$0.505407\pi$
$242$	−22.0617			−1.41818
$243$		0			0
$244$	0.661742			0.0423637
$245$	13.4118	−	8.82105i	0.856846	−	0.563556i
$246$		0			0
$247$	−4.41956	+	10.2457i	−0.281210	+	0.651918i
$248$	2.72686	−	2.89030i	0.173156	−	0.183534i
$249$		0			0
$250$	42.1719	+	4.92919i	2.66719	+	0.311749i
$251$	−3.26810	−	18.5343i	−0.206281	−	1.16988i	−0.895412	−	0.445239i	$-0.853119\pi$
$251$	−3.26810	−	18.5343i	−0.206281	−	1.16988i	0.689131	−	0.724637i	$-0.257992\pi$
$252$		0			0
$253$	−0.300488	+	1.70415i	−0.0188915	+	0.107139i
$254$	8.01772	−	26.7810i	0.503076	−	1.68039i
$255$		0			0
$256$	−0.344295	+	5.91131i	−0.0215184	+	0.369457i
$257$	−15.4090	+	7.73869i	−0.961187	+	0.482726i	−0.858964	−	0.512035i	$-0.828892\pi$
$257$	−15.4090	+	7.73869i	−0.961187	+	0.482726i	−0.102222	+	0.994762i	$0.532595\pi$
$258$		0			0
$259$	−10.8866	−	11.5391i	−0.676462	−	0.717008i
$260$	22.5232	−	8.19776i	1.39683	−	0.508404i
$261$		0			0
$262$	20.0036	+	7.28070i	1.23582	+	0.449803i
$263$	9.74813	+	22.5987i	0.601095	+	1.39350i	0.898597	+	0.438774i	$0.144587\pi$
$263$	9.74813	+	22.5987i	0.601095	+	1.39350i	−0.297502	+	0.954721i	$0.596154\pi$
$264$		0			0
$265$	12.8464	+	42.9100i	0.789148	+	2.63594i
$266$	−31.4554	+	3.67661i	−1.92865	+	0.225427i
$267$		0			0
$268$	0.276110	+	4.74062i	0.0168661	+	0.289580i
$269$	5.32448	+	9.22227i	0.324639	+	0.562292i	0.981439	−	0.191773i	$-0.0614238\pi$
$269$	5.32448	+	9.22227i	0.324639	+	0.562292i	−0.656800	+	0.754065i	$0.728090\pi$
$270$		0			0
$271$	2.35817	−	4.08447i	0.143249	−	0.248114i	−0.785469	−	0.618900i	$-0.787578\pi$
$271$	2.35817	−	4.08447i	0.143249	−	0.248114i	0.928718	+	0.370786i	$0.120912\pi$
$272$	1.87986	+	0.944103i	0.113983	+	0.0572447i
$273$		0			0
$274$	11.9631	+	16.0692i	0.722715	+	0.970775i
$275$	−7.47748	−	1.77220i	−0.450909	−	0.106867i
$276$		0			0
$277$	−3.94818	+	5.30333i	−0.237223	+	0.318646i	−0.904753	−	0.425937i	$-0.859944\pi$
$277$	−3.94818	+	5.30333i	−0.237223	+	0.318646i	0.667529	+	0.744583i	$0.267352\pi$
$278$	−17.0186	+	14.2803i	−1.02071	+	0.856474i
$279$		0			0
$280$	10.0256	+	8.41245i	0.599142	+	0.502740i
$281$	2.40945	−	0.571049i	0.143736	−	0.0340659i	−0.158118	−	0.987420i	$-0.550543\pi$
$281$	2.40945	−	0.571049i	0.143736	−	0.0340659i	0.301854	+	0.953354i	$0.402395\pi$
$282$		0			0
$283$	−0.774627	−	0.509480i	−0.0460468	−	0.0302855i	0.526277	−	0.850313i	$-0.323588\pi$
$283$	−0.774627	−	0.509480i	−0.0460468	−	0.0302855i	−0.572324	+	0.820028i	$0.693958\pi$
$284$	13.9737	+	9.19066i	0.829188	+	0.545365i
$285$		0			0
$286$	−3.87332	+	0.917994i	−0.229034	+	0.0542821i
$287$	12.4999	+	10.4887i	0.737845	+	0.619126i
$288$		0			0
$289$	−12.5965	+	10.5697i	−0.740973	+	0.621750i
$290$	2.28215	−	3.06546i	0.134012	−	0.180010i
$291$		0			0
$292$	19.1114	+	4.52949i	1.11841	+	0.265068i
$293$	−1.40037	−	1.88103i	−0.0818106	−	0.109891i	0.759334	−	0.650701i	$-0.225525\pi$
$293$	−1.40037	−	1.88103i	−0.0818106	−	0.109891i	−0.841144	+	0.540811i	$0.818118\pi$
$294$		0			0
$295$	−14.4344	−	7.24925i	−0.840405	−	0.422067i
$296$	2.39729	−	4.15224i	0.139340	−	0.241344i
$297$		0			0
$298$	13.1488	+	22.7744i	0.761688	+	1.31928i
$299$	−0.330572	−	5.67569i	−0.0191174	−	0.328234i
$300$		0			0
$301$	19.6807	−	2.30034i	1.13438	−	0.132589i
$302$	11.0603	+	36.9438i	0.636446	+	2.12588i
$303$		0			0
$304$	5.01320	+	11.6219i	0.287527	+	0.666562i
$305$	0.977524	+	0.355790i	0.0559729	+	0.0203725i
$306$		0			0
$307$	14.3376	−	5.21846i	0.818289	−	0.297833i	0.101246	−	0.994861i	$-0.467717\pi$
$307$	14.3376	−	5.21846i	0.818289	−	0.297833i	0.717043	+	0.697028i	$0.245495\pi$
$308$	−4.28910	−	4.54618i	−0.244394	−	0.259043i
$309$		0			0
$310$	29.0156	−	14.5722i	1.64797	−	0.827644i
$311$	−0.973556	+	16.7153i	−0.0552053	+	0.947838i	0.851044	+	0.525094i	$0.175970\pi$
$311$	−0.973556	+	16.7153i	−0.0552053	+	0.947838i	−0.906249	+	0.422744i	$0.861067\pi$
$312$		0			0
$313$	−9.34214	+	31.2049i	−0.528049	+	1.76381i	0.110129	+	0.993917i	$0.464873\pi$
$313$	−9.34214	+	31.2049i	−0.528049	+	1.76381i	−0.638178	+	0.769889i	$0.720312\pi$
$314$	8.58676	−	48.6979i	0.484579	−	2.74818i
$315$		0			0
$316$	1.85633	+	10.5278i	0.104427	+	0.592234i
$317$	21.5243	+	2.51583i	1.20893	+	0.141303i	0.696582	−	0.717477i	$-0.254703\pi$
$317$	21.5243	+	2.51583i	1.20893	+	0.141303i	0.512344	+	0.858780i	$0.328777\pi$
$318$		0			0
$319$	−0.240953	+	0.255395i	−0.0134908	+	0.0142994i
$320$	17.3454	−	40.2112i	0.969639	−	2.24788i
$321$		0			0
$322$	13.4815	−	8.86695i	0.751297	−	0.494136i
$323$	3.34769			0.186271
$324$		0			0
$325$	25.2476			1.40049
$326$	−20.7240	+	13.6304i	−1.14780	+	0.754917i
$327$		0			0
$328$	−1.95331	+	4.52827i	−0.107853	+	0.250032i
$329$	24.6415	−	26.1184i	1.35853	−	1.43996i
$330$		0			0
$331$	−23.6512	−	2.76443i	−1.29999	−	0.151947i	−0.562212	−	0.826993i	$-0.690050\pi$
$331$	−23.6512	−	2.76443i	−1.29999	−	0.151947i	−0.737775	+	0.675046i	$0.764124\pi$
$332$	1.09523	+	6.21136i	0.0601086	+	0.340893i
$333$		0			0
$334$	8.89581	−	50.4507i	0.486757	−	2.76054i
$335$	−2.14096	+	7.15130i	−0.116973	+	0.390717i
$336$		0			0
$337$	1.06959	−	18.3641i	0.0582643	−	1.00036i	−0.834835	−	0.550500i	$-0.814437\pi$
$337$	1.06959	−	18.3641i	0.0582643	−	1.00036i	0.893100	−	0.449859i	$-0.148526\pi$
$338$	−12.8921	+	6.47465i	−0.701237	+	0.352174i
$339$		0			0
$340$	−4.93480	−	5.23058i	−0.267627	−	0.283668i
$341$	−2.80323	+	1.02029i	−0.151803	+	0.0552519i
$342$		0			0
$343$	−9.01506	−	3.28121i	−0.486767	−	0.177169i
$344$	2.37194	+	5.49878i	0.127887	+	0.296475i
$345$		0			0
$346$	−9.41304	−	31.4417i	−0.506048	−	1.69032i
$347$	−16.7968	+	1.96326i	−0.901698	+	0.105393i	−0.554293	−	0.832322i	$-0.687011\pi$
$347$	−16.7968	+	1.96326i	−0.901698	+	0.105393i	−0.347405	+	0.937715i	$0.612937\pi$
$348$		0			0
$349$	−0.474881	−	8.15340i	−0.0254198	−	0.436441i	−0.986876	−	0.161482i	$-0.948373\pi$
$349$	−0.474881	−	8.15340i	−0.0254198	−	0.436441i	0.961456	−	0.274959i	$-0.0886644\pi$
$350$	35.8291	+	62.0578i	1.91514	+	3.31713i
$351$		0			0
$352$	−3.02043	+	5.23154i	−0.160989	+	0.278842i
$353$	−21.9963	−	11.0469i	−1.17074	−	0.587969i	−0.246264	−	0.969203i	$-0.579203\pi$
$353$	−21.9963	−	11.0469i	−1.17074	−	0.587969i	−0.924479	+	0.381234i	$0.875499\pi$
$354$		0			0
$355$	15.7005	+	21.0895i	0.833298	+	1.11931i
$356$	12.9824	+	3.07688i	0.688064	+	0.163074i
$357$		0			0
$358$	9.08193	−	12.1991i	0.479995	−	0.644745i
$359$	9.68682	−	8.12821i	0.511251	−	0.428990i	−0.350318	−	0.936631i	$-0.613927\pi$
$359$	9.68682	−	8.12821i	0.511251	−	0.428990i	0.861569	+	0.507640i	$0.169482\pi$
$360$		0			0
$361$	0.875105	+	0.734300i	0.0460582	+	0.0386474i
$362$	−15.9299	+	3.77546i	−0.837258	+	0.198434i
$363$		0			0
$364$	17.1564	+	11.2840i	0.899242	+	0.591441i
$365$	25.7960	+	16.9663i	1.35023	+	0.888058i
$366$		0			0
$367$	−10.2113	+	2.42012i	−0.533025	+	0.126329i	−0.488309	−	0.872671i	$-0.662386\pi$
$367$	−10.2113	+	2.42012i	−0.533025	+	0.126329i	−0.0447153	+	0.999000i	$0.514238\pi$
$368$	−4.94019	−	4.14531i	−0.257525	−	0.216089i
$369$		0			0
$370$	30.0118	−	25.1829i	1.56024	−	1.30920i
$371$	−22.9156	+	30.7809i	−1.18972	+	1.59807i
$372$		0			0
$373$	11.4784	+	2.72044i	0.594330	+	0.140859i	0.516763	−	0.856128i	$-0.327137\pi$
$373$	11.4784	+	2.72044i	0.594330	+	0.140859i	0.0775669	+	0.996987i	$0.475285\pi$
$374$	0.713164	+	0.957945i	0.0368768	+	0.0495342i
$375$		0			0
$376$	9.69804	+	4.87054i	0.500138	+	0.251179i
$377$	0.576797	−	0.999042i	0.0297066	−	0.0514533i
$378$		0			0
$379$	−9.06853	−	15.7072i	−0.465819	−	0.806823i	0.533419	−	0.845851i	$-0.320907\pi$
$379$	−9.06853	−	15.7072i	−0.465819	−	0.806823i	−0.999238	+	0.0390286i	$0.987574\pi$
$380$	−2.51576	−	43.1939i	−0.129056	−	2.21580i
$381$		0			0
$382$	−21.1787	+	2.47544i	−1.08360	+	0.126655i
$383$	4.45051	+	14.8657i	0.227410	+	0.759603i	0.993191	+	0.116501i	$0.0371678\pi$
$383$	4.45051	+	14.8657i	0.227410	+	0.759603i	−0.765780	+	0.643102i	$0.777647\pi$
$384$		0			0
$385$	−3.89157	−	9.02168i	−0.198333	−	0.459787i
$386$	31.7952	+	11.5725i	1.61833	+	0.589025i
$387$		0			0
$388$	−22.0802	+	8.03653i	−1.12095	+	0.407993i
$389$	−10.5917	−	11.2265i	−0.537019	−	0.569207i	0.400873	−	0.916133i	$-0.368707\pi$
$389$	−10.5917	−	11.2265i	−0.537019	−	0.569207i	−0.937892	+	0.346927i	$0.887225\pi$
$390$		0			0
$391$	−1.52427	+	0.765518i	−0.0770857	+	0.0387139i
$392$	−0.241677	+	4.14943i	−0.0122065	+	0.209578i
$393$		0			0
$394$	6.65664	−	22.2347i	0.335357	−	1.12017i
$395$	−2.91816	+	16.5497i	−0.146828	+	0.832705i
$396$		0			0
$397$	0.354695	+	2.01157i	0.0178016	+	0.100958i	0.992414	−	0.122941i	$-0.0392326\pi$
$397$	0.354695	+	2.01157i	0.0178016	+	0.100958i	−0.974612	+	0.223899i	$0.928121\pi$
$398$	−7.37761	−	0.862319i	−0.369806	−	0.0432241i
$399$		0			0
$400$	19.6532	−	20.8312i	0.982659	−	1.04156i
$401$	−5.92303	+	13.7311i	−0.295782	+	0.685700i	−0.999698	−	0.0245834i	$-0.992174\pi$
$401$	−5.92303	+	13.7311i	−0.295782	+	0.685700i	0.703916	+	0.710284i	$0.251433\pi$
$402$		0			0
$403$	8.18862	−	5.38574i	0.407904	−	0.268283i
$404$	30.4790			1.51639
$405$		0			0
$406$	3.27415			0.162493
$407$	−3.00731	+	1.97794i	−0.149067	+	0.0980429i
$408$		0			0
$409$	4.11470	−	9.53894i	0.203459	−	0.471670i	−0.785684	−	0.618628i	$-0.787689\pi$
$409$	4.11470	−	9.53894i	0.203459	−	0.471670i	0.989143	+	0.146958i	$0.0469481\pi$
$410$	−27.6536	+	29.3111i	−1.36571	+	1.44757i
$411$		0			0
$412$	−41.0035	−	4.79262i	−2.02010	−	0.236116i
$413$	−2.40300	−	13.6281i	−0.118244	−	0.670595i
$414$		0			0
$415$	−1.72170	+	9.76427i	−0.0845151	+	0.479309i
$416$	5.69221	−	19.0133i	0.279083	−	0.932203i
$417$		0			0
$418$	−0.417807	+	7.17347i	−0.0204356	+	0.350866i
$419$	−0.473719	+	0.237911i	−0.0231427	+	0.0116227i	−0.460333	−	0.887746i	$-0.652270\pi$
$419$	−0.473719	+	0.237911i	−0.0231427	+	0.0116227i	0.437190	+	0.899369i	$0.355974\pi$
$420$		0			0
$421$	22.0048	+	23.3237i	1.07245	+	1.13673i	0.990134	+	0.140123i	$0.0447497\pi$
$421$	22.0048	+	23.3237i	1.07245	+	1.13673i	0.0823146	+	0.996606i	$0.473769\pi$
$422$	15.2765	−	5.56019i	0.743649	−	0.270666i
$423$		0			0
$424$	−10.8984	−	3.96668i	−0.529272	−	0.192639i
$425$	−3.00021	−	6.95527i	−0.145532	−	0.337380i
$426$		0			0
$427$	0.255605	+	0.853780i	0.0123696	+	0.0413173i
$428$	−9.08574	+	1.06197i	−0.439176	+	0.0513323i
$429$		0			0
$430$	2.84524	+	48.8510i	0.137210	+	2.35580i
$431$	2.69146	+	4.66175i	0.129643	+	0.224549i	0.923538	−	0.383506i	$-0.125283\pi$
$431$	2.69146	+	4.66175i	0.129643	+	0.224549i	−0.793895	+	0.608055i	$0.791950\pi$
$432$		0			0
$433$	−16.6465	+	28.8325i	−0.799978	+	1.38560i	0.119652	+	0.992816i	$0.461822\pi$
$433$	−16.6465	+	28.8325i	−0.799978	+	1.38560i	−0.919630	+	0.392787i	$0.871511\pi$
$434$	24.8585	+	12.4844i	1.19325	+	0.599270i
$435$		0			0
$436$	−25.6415	−	34.4425i	−1.22801	−	1.64950i
$437$	−9.98622	−	2.36678i	−0.477705	−	0.113218i
$438$		0			0
$439$	−11.1561	+	14.9852i	−0.532451	+	0.715206i	−0.984224	−	0.176927i	$-0.943384\pi$
$439$	−11.1561	+	14.9852i	−0.532451	+	0.715206i	0.451773	+	0.892133i	$0.350792\pi$
$440$	2.27474	−	1.90873i	0.108444	−	0.0909953i
$441$		0			0
$442$	−3.00574	−	2.52212i	−0.142968	−	0.119965i
$443$	18.3619	−	4.35184i	0.872398	−	0.206762i	0.230053	−	0.973178i	$-0.426110\pi$
$443$	18.3619	−	4.35184i	0.872398	−	0.206762i	0.642345	+	0.766416i	$0.277962\pi$
$444$		0			0
$445$	17.5232	+	11.5252i	0.830681	+	0.546348i
$446$	−19.1693	−	12.6078i	−0.907693	−	0.596999i
$447$		0			0
$448$	36.5072	−	8.65237i	1.72480	−	0.408786i
$449$	5.33643	+	4.47780i	0.251842	+	0.211320i	0.759965	−	0.649964i	$-0.225216\pi$
$449$	5.33643	+	4.47780i	0.251842	+	0.211320i	−0.508123	+	0.861284i	$0.669661\pi$
$450$		0			0
$451$	2.83615	−	2.37981i	0.133549	−	0.112061i
$452$	15.2452	−	20.4778i	0.717072	−	0.963195i
$453$		0			0
$454$	22.3605	+	5.29954i	1.04943	+	0.248720i
$455$	19.2766	+	25.8929i	0.903700	+	1.21388i
$456$		0			0
$457$	33.5985	+	16.8738i	1.57167	+	0.789324i	0.999525	−	0.0308265i	$-0.00981393\pi$
$457$	33.5985	+	16.8738i	1.57167	+	0.789324i	0.572148	+	0.820150i	$0.306110\pi$
$458$	−2.42197	+	4.19498i	−0.113171	+	0.196018i
$459$		0			0
$460$	11.0226	+	19.0917i	0.513932	+	0.890157i
$461$	−1.60695	−	27.5903i	−0.0748432	−	1.28501i	−0.801495	−	0.598002i	$-0.795962\pi$
$461$	−1.60695	−	27.5903i	−0.0748432	−	1.28501i	0.726652	−	0.687006i	$-0.241075\pi$
$462$		0			0
$463$	−24.4012	+	2.85209i	−1.13402	+	0.132548i	−0.662327	−	0.749215i	$-0.730431\pi$
$463$	−24.4012	+	2.85209i	−1.13402	+	0.132548i	−0.471694	+	0.881763i	$0.656357\pi$
$464$	−0.375295	−	1.25357i	−0.0174226	−	0.0581956i
$465$		0			0
$466$	−14.9258	−	34.6020i	−0.691426	−	1.60291i
$467$	7.38677	+	2.68856i	0.341819	+	0.124412i	0.507225	−	0.861814i	$-0.330671\pi$
$467$	7.38677	+	2.68856i	0.341819	+	0.124412i	−0.165406	+	0.986226i	$0.552893\pi$
$468$		0			0
$469$	−6.00971	+	2.18735i	−0.277503	+	0.101003i
$470$	60.8539	+	64.5014i	2.80698	+	2.97523i
$471$		0			0
$472$	3.73748	−	1.87703i	0.172031	−	0.0863974i
$473$	0.261409	−	4.48821i	0.0120196	−	0.206368i
$474$		0			0
$475$	13.0713	−	43.6611i	0.599752	−	2.00331i
$476$	1.06981	−	6.06719i	0.0490346	−	0.278089i
$477$		0			0
$478$	4.50659	+	25.5581i	0.206127	+	1.16900i
$479$	−17.5918	−	2.05619i	−0.803791	−	0.0939497i	−0.295731	−	0.955271i	$-0.595563\pi$
$479$	−17.5918	−	2.05619i	−0.803791	−	0.0939497i	−0.508060	+	0.861322i	$0.669637\pi$
$480$		0			0
$481$	8.11547	−	8.60190i	0.370034	−	0.392213i
$482$	14.6647	−	33.9966i	0.667959	−	1.54850i
$483$		0			0
$484$	21.5744	−	14.1897i	0.980654	−	0.644987i
$485$	−36.9377			−1.67725
$486$		0			0
$487$	−42.1146			−1.90840			−0.954198	−	0.299175i	$-0.903289\pi$
$487$	−42.1146			−1.90840			−0.954198	+	0.299175i	$0.903289\pi$
$488$	−0.225040	+	0.148011i	−0.0101871	+	0.00670016i
$489$		0			0
$490$	−13.4522	+	31.1857i	−0.607709	+	1.40883i
$491$	−4.99416	+	5.29350i	−0.225383	+	0.238892i	−0.830191	−	0.557479i	$-0.811769\pi$
$491$	−4.99416	+	5.29350i	−0.225383	+	0.238892i	0.604808	+	0.796372i	$0.293250\pi$
$492$		0			0
$493$	−0.343760	−	0.0401798i	−0.0154822	−	0.00180961i
$494$	−4.09952	−	23.2495i	−0.184446	−	1.04604i
$495$		0			0
$496$	1.93053	−	10.9486i	0.0866833	−	0.491606i
$497$	−6.46030	+	21.5789i	−0.289784	+	0.967946i
$498$		0			0
$499$	−0.937877	+	16.1027i	−0.0419851	+	0.720857i	0.909980	+	0.414651i	$0.136096\pi$
$499$	−0.937877	+	16.1027i	−0.0419851	+	0.720857i	−0.951965	+	0.306205i	$0.900941\pi$
$500$	−44.4107	+	22.3039i	−1.98611	+	0.997461i
$501$		0			0
$502$	27.3255	+	28.9633i	1.21960	+	1.29270i
$503$	−34.7114	+	12.6339i	−1.54771	+	0.563319i	−0.967878	−	0.251421i	$-0.919102\pi$
$503$	−34.7114	+	12.6339i	−1.54771	+	0.563319i	−0.579827	+	0.814739i	$0.696880\pi$
$504$		0			0
$505$	45.0235	+	16.3872i	2.00352	+	0.729221i
$506$	−1.45012	−	3.36176i	−0.0644658	−	0.149449i
$507$		0			0
$508$	9.38447	+	31.3463i	0.416369	+	1.39077i
$509$	11.6029	−	1.35619i	0.514291	−	0.0601120i	0.145011	−	0.989430i	$-0.453678\pi$
$509$	11.6029	−	1.35619i	0.514291	−	0.0601120i	0.369280	+	0.929318i	$0.379604\pi$
$510$		0			0
$511$	1.53804	+	26.4071i	0.0680389	+	1.16818i
$512$	−14.0992	−	24.4205i	−0.623101	−	1.07924i
$513$		0			0
$514$	18.2411	−	31.5945i	0.804580	−	1.39357i
$515$	−57.9936	−	29.1255i	−2.55550	−	1.28342i
$516$		0			0
$517$	−4.86521	−	6.53511i	−0.213972	−	0.287414i
$518$	32.6599	+	7.74053i	1.43499	+	0.340099i
$519$		0			0
$520$	−5.82593	+	7.82558i	−0.255484	+	0.343175i
$521$	0.659940	−	0.553755i	0.0289125	−	0.0242605i	−0.628217	−	0.778038i	$-0.716215\pi$
$521$	0.659940	−	0.553755i	0.0289125	−	0.0242605i	0.657129	+	0.753778i	$0.271771\pi$
$522$		0			0
$523$	−6.06895	−	5.09246i	−0.265377	−	0.222678i	0.500383	−	0.865804i	$-0.333192\pi$
$523$	−6.06895	−	5.09246i	−0.265377	−	0.222678i	−0.765760	+	0.643126i	$0.777637\pi$
$524$	−24.2445	+	5.74605i	−1.05913	+	0.251018i
$525$		0			0
$526$	−43.5055	−	28.6140i	−1.89693	−	1.24763i
$527$	−2.45674	−	1.61582i	−0.107017	−	0.0703864i
$528$		0			0
$529$	−17.2919	+	4.09826i	−0.751822	+	0.178185i
$530$	−72.5967	−	60.9158i	−3.15340	−	2.64601i
$531$		0			0
$532$	28.3958	−	23.8269i	1.23112	−	1.03303i
$533$	−7.26378	+	9.75694i	−0.314629	+	0.422620i
$534$		0			0
$535$	−13.9924	−	3.31627i	−0.604945	−	0.143375i
$536$	−1.15423	−	1.55040i	−0.0498552	−	0.0669671i
$537$		0			0
$538$	−20.1341	−	10.1117i	−0.868042	−	0.435947i
$539$	1.56020	−	2.70235i	0.0672028	−	0.116399i
$540$		0			0
$541$	6.01461	+	10.4176i	0.258588	+	0.447888i	0.965864	−	0.259050i	$-0.0834094\pi$
$541$	6.01461	+	10.4176i	0.258588	+	0.447888i	−0.707276	+	0.706938i	$0.750076\pi$
$542$	0.580206	+	9.96175i	0.0249220	+	0.427894i
$543$		0			0
$544$	−5.91424	+	0.691275i	−0.253571	+	0.0296382i
$545$	−19.3594	−	64.6648i	−0.829265	−	2.76994i
$546$		0			0
$547$	−2.52741	−	5.85920i	−0.108064	−	0.250521i	0.855600	−	0.517638i	$-0.173188\pi$
$547$	−2.52741	−	5.85920i	−0.108064	−	0.250521i	−0.963664	+	0.267116i	$0.913929\pi$
$548$	−22.0342	−	8.01980i	−0.941255	−	0.342589i
$549$		0			0
$550$	15.2783	−	5.56083i	0.651467	−	0.237115i
$551$	−1.42904	−	1.51469i	−0.0608791	−	0.0645280i
$552$		0			0
$553$	−12.8659	+	6.46151i	−0.547115	+	0.274771i
$554$	0.813362	−	13.9649i	0.0345565	−	0.593311i
$555$		0			0
$556$	7.45782	−	24.9109i	0.316282	−	1.05646i
$557$	6.99671	−	39.6803i	0.296460	−	1.68131i	−0.364747	−	0.931107i	$-0.618844\pi$
$557$	6.99671	−	39.6803i	0.296460	−	1.68131i	0.661207	−	0.750203i	$-0.270044\pi$
$558$		0			0
$559$	2.56494	+	14.5465i	0.108485	+	0.615251i
$560$	36.3688	+	4.25091i	1.53686	+	0.179634i
$561$		0			0
$562$	−3.59523	+	3.81072i	−0.151656	+	0.160746i
$563$	0.628050	−	1.45598i	0.0264692	−	0.0613624i	−0.904469	−	0.426540i	$-0.859732\pi$
$563$	0.628050	−	1.45598i	0.0264692	−	0.0613624i	0.930938	+	0.365177i	$0.118992\pi$
$564$		0			0
$565$	33.5302	−	22.0531i	1.41062	−	0.927782i
$566$	1.96163			0.0824536
$567$		0			0
$568$	−6.80775			−0.285647
$569$	9.22728	−	6.06888i	0.386828	−	0.254421i	−0.341168	−	0.940002i	$-0.610822\pi$
$569$	9.22728	−	6.06888i	0.386828	−	0.254421i	0.727996	+	0.685582i	$0.240452\pi$
$570$		0			0
$571$	3.13218	−	7.26120i	0.131078	−	0.303872i	−0.840020	−	0.542556i	$-0.817457\pi$
$571$	3.13218	−	7.26120i	0.131078	−	0.303872i	0.971097	+	0.238684i	$0.0767160\pi$
$572$	3.19733	−	3.38897i	0.133687	−	0.141700i
$573$		0			0
$574$	−34.2903	−	4.00796i	−1.43125	−	0.167289i
$575$	4.03238	+	22.8688i	0.168162	+	0.953695i
$576$		0			0
$577$	−8.01656	+	45.4642i	−0.333734	+	1.89270i	0.105658	+	0.994402i	$0.466305\pi$
$577$	−8.01656	+	45.4642i	−0.333734	+	1.89270i	−0.439392	+	0.898295i	$0.644806\pi$
$578$	9.97807	−	33.3291i	0.415033	−	1.38631i
$579$		0			0
$580$	−0.260091	+	4.46558i	−0.0107997	+	0.185423i
$581$	−7.59086	+	3.81227i	−0.314922	+	0.158160i
$582$		0			0
$583$	5.97503	+	6.33317i	0.247461	+	0.262293i
$584$	−7.51238	+	2.73428i	−0.310865	+	0.113145i
$585$		0			0
$586$	4.66235	+	1.69696i	0.192600	+	0.0701007i
$587$	−14.5601	−	33.7540i	−0.600959	−	1.39318i	−0.898713	−	0.438536i	$-0.855497\pi$
$587$	−14.5601	−	33.7540i	−0.600959	−	1.39318i	0.297755	−	0.954642i	$-0.403762\pi$
$588$		0			0
$589$	−5.07421	−	16.9490i	−0.209079	−	0.698373i
$590$	33.9437	−	3.96745i	1.39744	−	0.163337i
$591$		0			0
$592$	−0.779979	−	13.3917i	−0.0320570	−	0.550397i
$593$	7.17407	+	12.4258i	0.294604	+	0.510268i	0.974893	−	0.222676i	$-0.0714791\pi$
$593$	7.17407	+	12.4258i	0.294604	+	0.510268i	−0.680289	+	0.732944i	$0.738146\pi$
$594$		0			0
$595$	4.84238	−	8.38725i	0.198518	−	0.343844i
$596$	−27.5064	−	13.8142i	−1.12671	−	0.565853i
$597$		0			0
$598$	7.18306	+	9.64853i	0.293737	+	0.394558i
$599$	12.6650	+	3.00166i	0.517479	+	0.122645i	0.481053	−	0.876692i	$-0.340255\pi$
$599$	12.6650	+	3.00166i	0.517479	+	0.122645i	0.0364259	+	0.999336i	$0.488403\pi$
$600$		0			0
$601$	−3.76081	+	5.05165i	−0.153407	+	0.206061i	−0.872182	−	0.489181i	$-0.837296\pi$
$601$	−3.76081	+	5.05165i	−0.153407	+	0.206061i	0.718775	+	0.695242i	$0.244703\pi$
$602$	−32.1148	+	26.9476i	−1.30890	+	1.09830i
$603$		0			0
$604$	−34.5775	−	29.0140i	−1.40694	−	1.18056i
$605$	39.4989	−	9.36140i	1.60586	−	0.380595i
$606$		0			0
$607$	−10.9863	−	7.22582i	−0.445921	−	0.293287i	0.306620	−	0.951832i	$-0.400802\pi$
$607$	−10.9863	−	7.22582i	−0.445921	−	0.293287i	−0.752542	+	0.658545i	$0.771172\pi$
$608$	−29.9330	−	19.6872i	−1.21394	−	0.798423i
$609$		0			0
$610$	−2.14161	+	0.507571i	−0.0867112	+	0.0205509i
$611$	20.5052	+	17.2059i	0.829552	+	0.696076i
$612$		0			0
$613$	−28.3321	+	23.7734i	−1.14432	+	0.960200i	−0.999572	−	0.0292684i	$-0.990682\pi$
$613$	−28.3321	+	23.7734i	−1.14432	+	0.960200i	−0.144750	+	0.989468i	$0.546238\pi$
$614$	−19.2773	+	25.8939i	−0.777967	+	1.04499i
$615$		0			0
$616$	2.47545	+	0.586692i	0.0997387	+	0.0236385i
$617$	−19.3944	−	26.0512i	−0.780789	−	1.04878i	−0.997367	−	0.0725160i	$-0.976897\pi$
$617$	−19.3944	−	26.0512i	−0.780789	−	1.04878i	0.216579	−	0.976265i	$-0.430510\pi$
$618$		0			0
$619$	−38.3557	−	19.2630i	−1.54165	−	0.774243i	−0.543760	−	0.839241i	$-0.683000\pi$
$619$	−38.3557	−	19.2630i	−1.54165	−	0.774243i	−0.997885	+	0.0649972i	$0.979296\pi$
$620$	−19.0021	+	32.9126i	−0.763142	+	1.32180i
$621$		0			0
$622$	−17.7127	−	30.6793i	−0.710215	−	1.23013i
$623$	1.04479	+	17.9383i	0.0418586	+	0.718684i
$624$		0			0
$625$	−27.1638	+	3.17499i	−1.08655	+	0.126999i
$626$	−19.7657	−	66.0220i	−0.789995	−	2.63877i
$627$		0			0
$628$	22.9245	+	53.1451i	0.914789	+	2.12072i
$629$	−3.33404	−	1.21349i	−0.132937	−	0.0483851i
$630$		0			0
$631$	13.0635	−	4.75472i	0.520049	−	0.189282i	−0.0686408	−	0.997641i	$-0.521866\pi$
$631$	13.0635	−	4.75472i	0.520049	−	0.189282i	0.588690	+	0.808359i	$0.299644\pi$
$632$	−2.98603	−	3.16501i	−0.118778	−	0.125897i
$633$		0			0
$634$	−40.9732	+	20.5775i	−1.62725	+	0.817238i
$635$	−2.99082	+	51.3504i	−0.118687	+	2.03778i
$636$		0			0
$637$	−2.94031	+	9.82133i	−0.116499	+	0.389135i
$638$	0.129000	−	0.731597i	0.00510717	−	0.0289642i
$639$		0			0
$640$	5.29656	+	30.0383i	0.209365	+	1.18737i
$641$	−2.60191	−	0.304120i	−0.102769	−	0.0120120i	0.0645528	−	0.997914i	$-0.479438\pi$
$641$	−2.60191	−	0.304120i	−0.102769	−	0.0120120i	−0.167322	+	0.985902i	$0.553512\pi$
$642$		0			0
$643$	0.0703439	−	0.0745602i	0.00277409	−	0.00294037i	−0.725985	−	0.687710i	$-0.758616\pi$
$643$	0.0703439	−	0.0745602i	0.00277409	−	0.00294037i	0.728759	+	0.684770i	$0.240097\pi$
$644$	−7.48068	+	17.3422i	−0.294780	+	0.683377i
$645$		0			0
$646$	−5.91768	+	3.89212i	−0.232828	+	0.153133i
$647$	25.1564			0.988998			0.494499	−	0.869178i	$-0.335351\pi$
$647$	25.1564			0.988998			0.494499	+	0.869178i	$0.335351\pi$
$648$		0			0
$649$	−3.13983			−0.123249
$650$	−44.6299	+	29.3536i	−1.75053	+	1.15134i
$651$		0			0
$652$	11.4994	−	26.6586i	0.450351	−	1.04403i
$653$	−5.11903	+	5.42585i	−0.200323	+	0.212330i	−0.819746	−	0.572728i	$-0.805885\pi$
$653$	−5.11903	+	5.42585i	−0.200323	+	0.212330i	0.619423	+	0.785058i	$0.287367\pi$
$654$		0			0
$655$	−38.9034	−	4.54715i	−1.52008	−	0.177672i
$656$	2.39595	+	13.5881i	0.0935463	+	0.530527i
$657$		0			0
$658$	−13.1924	+	74.8181i	−0.514295	+	2.91671i
$659$	4.66341	−	15.5769i	0.181661	−	0.606789i	−0.817848	−	0.575435i	$-0.804833\pi$
$659$	4.66341	−	15.5769i	0.181661	−	0.606789i	0.999508	−	0.0313543i	$-0.00998201\pi$
$660$		0			0
$661$	−1.09720	+	18.8381i	−0.0426760	+	0.732718i	0.907317	+	0.420447i	$0.138127\pi$
$661$	−1.09720	+	18.8381i	−0.0426760	+	0.732718i	−0.949993	+	0.312271i	$0.898910\pi$
$662$	45.0219	−	22.6109i	1.74983	−	0.878796i
$663$		0			0
$664$	−1.76175	−	1.86735i	−0.0683691	−	0.0724670i
$665$	54.7570	−	19.9299i	2.12339	−	0.772849i
$666$		0			0
$667$	0.997034	+	0.362891i	0.0386053	+	0.0140512i
$668$	23.7496	+	55.0578i	0.918901	+	2.13025i
$669$		0			0
$670$	−4.52974	−	15.1304i	−0.174999	−	0.584538i
$671$	0.200845	−	0.0234754i	0.00775354	−	0.000906259i
$672$		0			0
$673$	0.475690	+	8.16727i	0.0183365	+	0.314825i	0.994988	+	0.0999952i	$0.0318827\pi$
$673$	0.475690	+	8.16727i	0.0183365	+	0.314825i	−0.976651	+	0.214830i	$0.931080\pi$
$674$	19.4599	+	33.7056i	0.749569	+	1.29829i
$675$		0			0
$676$	8.44293	−	14.6236i	0.324728	−	0.562445i
$677$	20.6357	+	10.3637i	0.793096	+	0.398308i	0.798740	−	0.601676i	$-0.205500\pi$
$677$	20.6357	+	10.3637i	0.793096	+	0.398308i	−0.00564403	+	0.999984i	$0.501797\pi$
$678$		0			0
$679$	−18.8974	−	25.3837i	−0.725217	−	0.974136i
$680$	2.84811	+	0.675015i	0.109220	+	0.0258857i
$681$		0			0
$682$	3.76902	−	5.06267i	0.144323	−	0.193860i
$683$	14.3566	−	12.0466i	0.549340	−	0.460951i	−0.325378	−	0.945584i	$-0.605491\pi$
$683$	14.3566	−	12.0466i	0.549340	−	0.460951i	0.874717	+	0.484633i	$0.161047\pi$
$684$		0			0
$685$	−28.2370	−	23.6937i	−1.07888	−	0.905289i
$686$	19.7506	−	4.68099i	0.754083	−	0.178721i
$687$		0			0
$688$	13.9985	+	9.20698i	0.533689	+	0.351013i
$689$	−23.9002	−	15.7194i	−0.910525	−	0.598862i
$690$		0			0
$691$	−6.47006	+	1.53343i	−0.246133	+	0.0583345i	−0.351830	−	0.936064i	$-0.614441\pi$
$691$	−6.47006	+	1.53343i	−0.246133	+	0.0583345i	0.105698	+	0.994398i	$0.466292\pi$
$692$	29.4279	+	24.6929i	1.11868	+	0.938684i
$693$		0			0
$694$	27.4089	−	22.9988i	1.04043	−	0.873023i
$695$	24.4102	−	32.7885i	0.925931	−	1.24374i
$696$		0			0
$697$	3.55103	+	0.841610i	0.134505	+	0.0318782i
$698$	10.3188	+	13.8605i	0.390572	+	0.524630i
$699$		0			0
$700$	−74.9521	−	37.6423i	−2.83292	−	1.42275i
$701$	−12.1477	+	21.0405i	−0.458813	+	0.794687i	−0.998899	−	0.0469230i	$-0.985058\pi$
$701$	−12.1477	+	21.0405i	−0.458813	+	0.794687i	0.540086	+	0.841610i	$0.318392\pi$
$702$		0			0
$703$	−10.6738	−	18.4876i	−0.402571	−	0.697274i
$704$	−0.494971	−	8.49832i	−0.0186549	−	0.320292i
$705$		0			0
$706$	51.7260	−	6.04590i	1.94673	−	0.227540i
$707$	11.7728	+	39.3240i	0.442763	+	1.47893i
$708$		0			0
$709$	11.8515	+	27.4749i	0.445093	+	1.03184i	0.982117	+	0.188274i	$0.0602893\pi$
$709$	11.8515	+	27.4749i	0.445093	+	1.03184i	−0.537024	+	0.843567i	$0.680451\pi$
$710$	−52.2729	−	19.0258i	−1.96177	−	0.714024i
$711$		0			0
$712$	−5.10315	+	1.85740i	−0.191249	+	0.0696089i
$713$	6.18613	+	6.55691i	0.231672	+	0.245558i
$714$		0			0
$715$	6.54519	−	3.28712i	0.244776	−	0.122931i
$716$	−1.03504	+	17.7710i	−0.0386814	+	0.664134i
$717$		0			0
$718$	−7.67320	+	25.6303i	−0.286361	+	0.956514i
$719$	2.12889	−	12.0735i	0.0793943	−	0.450267i	−0.919032	−	0.394183i	$-0.871027\pi$
$719$	2.12889	−	12.0735i	0.0793943	−	0.450267i	0.998426	−	0.0560838i	$-0.0178614\pi$
$720$		0			0
$721$	−9.65461	−	54.7540i	−0.359556	−	2.03915i
$722$	−2.40063	−	0.280593i	−0.0893422	−	0.0104426i
$723$		0			0
$724$	13.1497	−	13.9379i	0.488706	−	0.517998i
$725$	−1.86626	+	4.32649i	−0.0693113	+	0.160682i
$726$		0			0
$727$	40.9555	−	26.9369i	1.51896	−	0.999033i	0.530473	−	0.847702i	$-0.322014\pi$
$727$	40.9555	−	26.9369i	1.51896	−	0.999033i	0.988483	−	0.151331i	$-0.0483560\pi$
$728$	−8.35832			−0.309780
$729$		0			0
$730$	−65.3249			−2.41778
$731$	3.70251	−	2.43518i	0.136942	−	0.0900683i
$732$		0			0
$733$	−8.00055	+	18.5474i	−0.295507	+	0.685063i	−0.999689	−	0.0249576i	$-0.992055\pi$
$733$	−8.00055	+	18.5474i	−0.295507	+	0.685063i	0.704181	+	0.710020i	$0.251314\pi$
$734$	15.2367	−	16.1499i	0.562396	−	0.596104i
$735$		0			0
$736$	18.1310	+	2.11921i	0.668317	+	0.0781150i
$737$	0.251977	+	1.42903i	0.00928168	+	0.0526390i
$738$		0			0
$739$	0.349401	−	1.98155i	0.0128529	−	0.0728925i	−0.977707	−	0.209975i	$-0.932662\pi$
$739$	0.349401	−	1.98155i	0.0128529	−	0.0728925i	0.990560	+	0.137083i	$0.0437727\pi$
$740$	−13.1517	+	43.9297i	−0.483465	+	1.61489i
$741$		0			0
$742$	4.72082	−	81.0533i	0.173307	−	2.97556i
$743$	−19.2775	+	9.68153i	−0.707223	+	0.355181i	−0.765779	−	0.643103i	$-0.777647\pi$
$743$	−19.2775	+	9.68153i	−0.707223	+	0.355181i	0.0585563	+	0.998284i	$0.481350\pi$
$744$		0			0
$745$	−33.2051	−	35.1953i	−1.21654	−	1.28946i
$746$	−23.4531	+	8.53624i	−0.858680	+	0.312534i
$747$		0			0
$748$	−1.31354	−	0.478091i	−0.0480279	−	0.0174807i
$749$	−4.87962	−	11.3122i	−0.178298	−	0.413340i
$750$		0			0
$751$	4.15221	+	13.8693i	0.151516	+	0.506099i	0.999722	−	0.0235670i	$-0.00750231\pi$
$751$	4.15221	+	13.8693i	0.151516	+	0.506099i	−0.848206	+	0.529666i	$0.822317\pi$
$752$	30.1577	−	3.52494i	1.09974	−	0.128541i
$753$		0			0
$754$	0.141915	+	2.43659i	0.00516826	+	0.0887355i
$755$	−35.4783	−	61.4503i	−1.29119	−	2.23640i
$756$		0			0
$757$	−5.26451	+	9.11840i	−0.191342	+	0.331414i	−0.945695	−	0.325055i	$-0.894617\pi$
$757$	−5.26451	+	9.11840i	−0.191342	+	0.331414i	0.754353	+	0.656469i	$0.227951\pi$
$758$	34.2919	+	17.2220i	1.24554	+	0.625533i
$759$		0			0
$760$	10.5167	+	14.1264i	0.381480	+	0.512417i
$761$	41.1358	+	9.74936i	1.49117	+	0.353414i	0.893769	−	0.448528i	$-0.148051\pi$
$761$	41.1358	+	9.74936i	1.49117	+	0.353414i	0.597402	+	0.801942i	$0.296200\pi$
$762$		0			0
$763$	34.5335	−	46.3865i	1.25020	−	1.67930i
$764$	19.1188	−	16.0425i	0.691693	−	0.580399i
$765$		0			0
$766$	−25.1504	−	21.1037i	−0.908721	−	0.762507i
$767$	10.0378	−	2.37900i	0.362443	−	0.0859006i
$768$		0			0
$769$	7.53547	+	4.95616i	0.271736	+	0.178724i	0.678062	−	0.735005i	$-0.262820\pi$
$769$	7.53547	+	4.95616i	0.271736	+	0.178724i	−0.406326	+	0.913728i	$0.633190\pi$
$770$	17.3679	+	11.4231i	0.625897	+	0.411659i
$771$		0			0
$772$	−38.5361	+	9.13322i	−1.38694	+	0.328712i
$773$	−0.551231	−	0.462537i	−0.0198264	−	0.0166363i	0.632821	−	0.774298i	$-0.281897\pi$
$773$	−0.551231	−	0.462537i	−0.0198264	−	0.0166363i	−0.652647	+	0.757662i	$0.726342\pi$
$774$		0			0
$775$	−30.6663	+	25.7321i	−1.10157	+	0.924325i
$776$	5.71134	−	7.67167i	0.205025	−	0.275397i
$777$		0			0
$778$	31.7750	+	7.53081i	1.13919	+	0.269993i
$779$	13.1122	+	17.6128i	0.469794	+	0.631043i
$780$		0			0
$781$	4.56720	+	2.29373i	0.163427	+	0.0820763i
$782$	1.80442	−	3.12535i	0.0645261	−	0.111762i
$783$		0			0

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.76769 + 1.16263i) q^{2} +(0.980860 - 2.27389i) q^{4} +(2.67150 - 2.83162i) q^{5} +(3.31264 + 0.387192i) q^{7} +(0.175036 + 0.992677i) q^{8} +O(q^{10})\)	\(q+(-1.76769 + 1.16263i) q^{2} +(0.980860 - 2.27389i) q^{4} +(2.67150 - 2.83162i) q^{5} +(3.31264 + 0.387192i) q^{7} +(0.175036 + 0.992677i) q^{8} +(-1.43025 + 8.11138i) q^{10} +(0.217034 - 0.724944i) q^{11} +(-0.144562 + 2.48203i) q^{13} +(-6.30588 + 3.16693i) q^{14} +(1.93533 + 2.05133i) q^{16} +(0.700932 - 0.255119i) q^{17} +(4.21736 + 1.53499i) q^{19} +(-3.81843 - 8.85211i) q^{20} +(0.459191 + 1.53380i) q^{22} +(-2.27126 + 0.265472i) q^{23} +(-0.590459 - 10.1378i) q^{25} +(-2.63013 - 4.55552i) q^{26} +(4.12967 - 7.15280i) q^{28} +(-0.414639 - 0.208240i) q^{29} +(-2.35407 - 3.16206i) q^{31} +(-7.76762 - 1.84096i) q^{32} +(-0.942422 + 1.26589i) q^{34} +(9.94610 - 8.34577i) q^{35} +(-3.64375 - 3.05747i) q^{37} +(-9.23961 + 2.18983i) q^{38} +(3.27849 + 2.15630i) q^{40} +(4.08763 + 2.68847i) q^{41} +(5.78094 - 1.37011i) q^{43} +(-1.43556 - 1.20458i) q^{44} +(3.70623 - 3.10990i) q^{46} +(6.42922 - 8.63594i) q^{47} +(4.01237 + 0.950949i) q^{49} +(12.8302 + 17.2340i) q^{50} +(5.50206 + 2.76324i) q^{52} +(-5.75294 + 9.96438i) q^{53} +(-1.47296 - 2.55124i) q^{55} +(0.195474 + 3.35616i) q^{56} +(0.975058 - 0.113968i) q^{58} +(-1.19000 - 3.97488i) q^{59} +(0.105839 + 0.245363i) q^{61} +(7.83755 + 2.85264i) q^{62} +(10.5709 - 3.84748i) q^{64} +(6.64196 + 7.04007i) q^{65} +(-1.71358 + 0.860594i) q^{67} +(0.107405 - 1.84408i) q^{68} +(-7.87859 + 26.3163i) q^{70} +(-1.17278 + 6.65118i) q^{71} +(1.37723 + 7.81064i) q^{73} +(9.99572 + 1.16833i) q^{74} +(7.62705 - 8.08420i) q^{76} +(0.999649 - 2.31745i) q^{77} +(-3.60662 + 2.37211i) q^{79} +10.9788 q^{80} -10.3513 q^{82} +(-2.12790 + 1.39954i) q^{83} +(1.15014 - 2.66632i) q^{85} +(-8.62597 + 9.14299i) q^{86} +(0.757624 + 0.0885535i) q^{88} +(0.935549 + 5.30576i) q^{89} +(-1.43990 + 8.16609i) q^{91} +(-1.62413 + 5.42498i) q^{92} +(-1.32448 + 22.7404i) q^{94} +(15.6132 - 7.84124i) q^{95} +(-6.51132 - 6.90160i) q^{97} +(-8.19821 + 2.98391i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8}+O(q^{10}) \) 144 * q - 9 * q^2 + 9 * q^4 - 9 * q^5 + 9 * q^7 + 18 * q^8	\( 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8} - 18 q^{10} - 9 q^{11} + 9 q^{13} - 9 q^{14} + 9 q^{16} + 18 q^{17} - 18 q^{19} + 63 q^{20} + 9 q^{22} - 36 q^{23} + 9 q^{25} - 45 q^{26} - 9 q^{28} + 45 q^{29} + 9 q^{31} - 63 q^{32} + 9 q^{34} - 9 q^{35} - 18 q^{37} + 9 q^{38} + 9 q^{40} + 27 q^{41} + 9 q^{43} - 54 q^{44} - 18 q^{46} - 63 q^{47} + 9 q^{49} + 225 q^{50} + 27 q^{52} - 45 q^{53} - 9 q^{55} - 99 q^{56} + 9 q^{58} + 117 q^{59} + 9 q^{61} - 81 q^{62} - 18 q^{64} - 81 q^{65} + 36 q^{67} + 18 q^{68} + 63 q^{70} + 90 q^{71} - 18 q^{73} - 81 q^{74} + 90 q^{76} - 81 q^{77} + 63 q^{79} + 288 q^{80} - 36 q^{82} - 45 q^{83} + 63 q^{85} - 81 q^{86} + 90 q^{88} + 81 q^{89} - 18 q^{91} + 63 q^{92} + 63 q^{94} - 153 q^{95} + 36 q^{97} - 81 q^{98}+O(q^{100}) \) 144 * q - 9 * q^2 + 9 * q^4 - 9 * q^5 + 9 * q^7 + 18 * q^8 - 18 * q^10 - 9 * q^11 + 9 * q^13 - 9 * q^14 + 9 * q^16 + 18 * q^17 - 18 * q^19 + 63 * q^20 + 9 * q^22 - 36 * q^23 + 9 * q^25 - 45 * q^26 - 9 * q^28 + 45 * q^29 + 9 * q^31 - 63 * q^32 + 9 * q^34 - 9 * q^35 - 18 * q^37 + 9 * q^38 + 9 * q^40 + 27 * q^41 + 9 * q^43 - 54 * q^44 - 18 * q^46 - 63 * q^47 + 9 * q^49 + 225 * q^50 + 27 * q^52 - 45 * q^53 - 9 * q^55 - 99 * q^56 + 9 * q^58 + 117 * q^59 + 9 * q^61 - 81 * q^62 - 18 * q^64 - 81 * q^65 + 36 * q^67 + 18 * q^68 + 63 * q^70 + 90 * q^71 - 18 * q^73 - 81 * q^74 + 90 * q^76 - 81 * q^77 + 63 * q^79 + 288 * q^80 - 36 * q^82 - 45 * q^83 + 63 * q^85 - 81 * q^86 + 90 * q^88 + 81 * q^89 - 18 * q^91 + 63 * q^92 + 63 * q^94 - 153 * q^95 + 36 * q^97 - 81 * q^98

Introduction

L-functions

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