LMFDB - Embedded newform 729.2.e.p.82.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(82,729)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, base_ring=CyclotomicField(18))

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("729.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.e (of order $9$, degree $6$, 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:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	12.0.101559956668416.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 8x^{6} + 64 $ x^12 - 8*x^6 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	no (minimal twist has level 243)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			82.1
Root			$0.483690 - 1.32893i$ of defining polynomial
Character	$\chi$	$=$	729.82
Dual form			729.2.e.p.649.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.425349 - 2.41228i) q^{2} +(-3.75877 + 1.36808i) q^{4} +(1.87642 + 1.57450i) q^{5} +(-1.87939 - 0.684040i) q^{7} +(2.44949 + 4.24264i) q^{8} +O(q^{10})$	\(q+(-0.425349 - 2.41228i) q^{2} +(-3.75877 + 1.36808i) q^{4} +(1.87642 + 1.57450i) q^{5} +(-1.87939 - 0.684040i) q^{7} +(2.44949 + 4.24264i) q^{8} +(3.00000 - 5.19615i) q^{10} +(-1.87642 + 1.57450i) q^{11} +(-0.173648 + 0.984808i) q^{13} +(-0.850699 + 4.82455i) q^{14} +(3.06418 - 2.57115i) q^{16} +(-3.67423 + 6.36396i) q^{17} +(0.500000 + 0.866025i) q^{19} +(-9.20707 - 3.35110i) q^{20} +(4.59627 + 3.85673i) q^{22} +(-2.30177 + 0.837775i) q^{23} +(0.173648 + 0.984808i) q^{25} +2.44949 q^{26} +8.00000 q^{28} +(0.850699 + 4.82455i) q^{29} +(0.939693 - 0.342020i) q^{31} +(16.9145 + 6.15636i) q^{34} +(-2.44949 - 4.24264i) q^{35} +(-4.00000 + 6.92820i) q^{37} +(1.87642 - 1.57450i) q^{38} +(-2.08378 + 11.8177i) q^{40} +(-0.850699 + 4.82455i) q^{41} +(8.42649 - 7.07066i) q^{43} +(4.89898 - 8.48528i) q^{44} +(3.00000 + 5.19615i) q^{46} +(9.20707 + 3.35110i) q^{47} +(-2.29813 - 1.92836i) q^{49} +(2.30177 - 0.837775i) q^{50} +(-0.694593 - 3.93923i) q^{52} -7.34847 q^{53} -6.00000 q^{55} +(-1.70140 - 9.64911i) q^{56} +(11.2763 - 4.10424i) q^{58} +(1.87642 + 1.57450i) q^{59} +(-4.69846 - 1.71010i) q^{61} +(-1.22474 - 2.12132i) q^{62} +(4.00000 - 6.92820i) q^{64} +(-1.87642 + 1.57450i) q^{65} +(-1.21554 + 6.89365i) q^{67} +(5.10419 - 28.9473i) q^{68} +(-9.19253 + 7.71345i) q^{70} +(3.67423 - 6.36396i) q^{71} +(-5.50000 - 9.52628i) q^{73} +(18.4141 + 6.70220i) q^{74} +(-3.06418 - 2.57115i) q^{76} +(4.60353 - 1.67555i) q^{77} +(-1.21554 - 6.89365i) q^{79} +9.79796 q^{80} +12.0000 q^{82} +(2.12675 + 12.0614i) q^{83} +(-16.9145 + 6.15636i) q^{85} +(-20.6406 - 17.3195i) q^{86} +(-11.2763 - 4.10424i) q^{88} +(1.00000 - 1.73205i) q^{91} +(7.50567 - 6.29801i) q^{92} +(4.16756 - 23.6354i) q^{94} +(-0.425349 + 2.41228i) q^{95} +(-5.36231 + 4.49951i) q^{97} +(-3.67423 + 6.36396i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q+O(q^{10}) $ 12 * q	$ 12 q + 36 q^{10} + 6 q^{19} + 96 q^{28} - 48 q^{37} + 36 q^{46} - 72 q^{55} + 48 q^{64} - 66 q^{73} + 144 q^{82} + 12 q^{91}+O(q^{100}) $ 12 * q + 36 * q^10 + 6 * q^19 + 96 * q^28 - 48 * q^37 + 36 * q^46 - 72 * q^55 + 48 * q^64 - 66 * q^73 + 144 * q^82 + 12 * q^91

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{4}{9}\right)$

Coefficient data

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

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

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

$2$	−0.425349	−	2.41228i	−0.300767	−	1.70574i	−0.642788	−	0.766044i	$-0.722222\pi$
$2$	−0.425349	−	2.41228i	−0.300767	−	1.70574i	0.342020	−	0.939693i	$-0.388889\pi$
$3$		0			0
$3$		0			0
$4$	−3.75877	+	1.36808i	−1.87939	+	0.684040i
$5$	1.87642	+	1.57450i	0.839160	+	0.704139i	0.957375	−	0.288849i	$-0.0932727\pi$
$5$	1.87642	+	1.57450i	0.839160	+	0.704139i	−0.118215	+	0.992988i	$0.537717\pi$
$6$		0			0
$7$	−1.87939	−	0.684040i	−0.710341	−	0.258543i	−0.0385213	−	0.999258i	$-0.512265\pi$
$7$	−1.87939	−	0.684040i	−0.710341	−	0.258543i	−0.671820	+	0.740715i	$0.734487\pi$
$8$	2.44949	+	4.24264i	0.866025	+	1.50000i
$9$		0			0
$10$	3.00000	−	5.19615i	0.948683	−	1.64317i
$11$	−1.87642	+	1.57450i	−0.565761	+	0.474730i	−0.880236	−	0.474536i	$-0.842616\pi$
$11$	−1.87642	+	1.57450i	−0.565761	+	0.474730i	0.314475	+	0.949266i	$0.398172\pi$
$12$		0			0
$13$	−0.173648	+	0.984808i	−0.0481613	+	0.273137i	−0.999373	−	0.0354021i	$-0.988729\pi$
$13$	−0.173648	+	0.984808i	−0.0481613	+	0.273137i	0.951212	+	0.308539i	$0.0998399\pi$
$14$	−0.850699	+	4.82455i	−0.227359	+	1.28942i
$15$		0			0
$16$	3.06418	−	2.57115i	0.766044	−	0.642788i
$17$	−3.67423	+	6.36396i	−0.891133	+	1.54349i	−0.0526138	+	0.998615i	$0.516755\pi$
$17$	−3.67423	+	6.36396i	−0.891133	+	1.54349i	−0.838519	+	0.544872i	$0.816578\pi$
$18$		0			0
$19$	0.500000	+	0.866025i	0.114708	+	0.198680i	0.917663	−	0.397360i	$-0.130073\pi$
$19$	0.500000	+	0.866025i	0.114708	+	0.198680i	−0.802955	+	0.596040i	$0.796740\pi$
$20$	−9.20707	−	3.35110i	−2.05876	−	0.749329i
$21$		0			0
$22$	4.59627	+	3.85673i	0.979927	+	0.822257i
$23$	−2.30177	+	0.837775i	−0.479952	+	0.174688i	−0.570655	−	0.821190i	$-0.693311\pi$
$23$	−2.30177	+	0.837775i	−0.479952	+	0.174688i	0.0907034	+	0.995878i	$0.471088\pi$
$24$		0			0
$25$	0.173648	+	0.984808i	0.0347296	+	0.196962i
$26$	2.44949			0.480384
$27$		0			0
$28$	8.00000			1.51186
$29$	0.850699	+	4.82455i	0.157971	+	0.895897i	0.956019	+	0.293304i	$0.0947547\pi$
$29$	0.850699	+	4.82455i	0.157971	+	0.895897i	−0.798048	+	0.602593i	$0.794134\pi$
$30$		0			0
$31$	0.939693	−	0.342020i	0.168774	−	0.0614286i	−0.256251	−	0.966610i	$-0.582487\pi$
$31$	0.939693	−	0.342020i	0.168774	−	0.0614286i	0.425025	+	0.905182i	$0.360265\pi$
$32$		0			0
$33$		0			0
$34$	16.9145	+	6.15636i	2.90081	+	1.05581i
$35$	−2.44949	−	4.24264i	−0.414039	−	0.717137i
$36$		0			0
$37$	−4.00000	+	6.92820i	−0.657596	+	1.13899i	0.323640	+	0.946180i	$0.395093\pi$
$37$	−4.00000	+	6.92820i	−0.657596	+	1.13899i	−0.981236	+	0.192809i	$0.938240\pi$
$38$	1.87642	−	1.57450i	0.304395	−	0.255418i
$39$		0			0
$40$	−2.08378	+	11.8177i	−0.329474	+	1.86854i
$41$	−0.850699	+	4.82455i	−0.132857	+	0.753469i	0.843471	+	0.537174i	$0.180508\pi$
$41$	−0.850699	+	4.82455i	−0.132857	+	0.753469i	−0.976328	+	0.216294i	$0.930603\pi$
$42$		0			0
$43$	8.42649	−	7.07066i	1.28503	−	1.07827i	0.292497	−	0.956266i	$-0.405514\pi$
$43$	8.42649	−	7.07066i	1.28503	−	1.07827i	0.992530	−	0.122000i	$-0.0389307\pi$
$44$	4.89898	−	8.48528i	0.738549	−	1.27920i
$45$		0			0
$46$	3.00000	+	5.19615i	0.442326	+	0.766131i
$47$	9.20707	+	3.35110i	1.34299	+	0.488808i	0.910753	−	0.412952i	$-0.135502\pi$
$47$	9.20707	+	3.35110i	1.34299	+	0.488808i	0.432236	+	0.901760i	$0.357725\pi$
$48$		0			0
$49$	−2.29813	−	1.92836i	−0.328305	−	0.275480i
$50$	2.30177	−	0.837775i	0.325519	−	0.118479i
$51$		0			0
$52$	−0.694593	−	3.93923i	−0.0963227	−	0.546273i
$53$	−7.34847			−1.00939			−0.504695	−	0.863298i	$-0.668395\pi$
$53$	−7.34847			−1.00939			−0.504695	+	0.863298i	$0.668395\pi$
$54$		0			0
$55$	−6.00000			−0.809040
$56$	−1.70140	−	9.64911i	−0.227359	−	1.28942i
$57$		0			0
$58$	11.2763	−	4.10424i	1.48065	−	0.538913i
$59$	1.87642	+	1.57450i	0.244289	+	0.204983i	0.756708	−	0.653753i	$-0.226806\pi$
$59$	1.87642	+	1.57450i	0.244289	+	0.204983i	−0.512420	+	0.858735i	$0.671251\pi$
$60$		0			0
$61$	−4.69846	−	1.71010i	−0.601577	−	0.218956i	0.0232370	−	0.999730i	$-0.492603\pi$
$61$	−4.69846	−	1.71010i	−0.601577	−	0.218956i	−0.624814	+	0.780774i	$0.714825\pi$
$62$	−1.22474	−	2.12132i	−0.155543	−	0.269408i
$63$		0			0
$64$	4.00000	−	6.92820i	0.500000	−	0.866025i
$65$	−1.87642	+	1.57450i	−0.232741	+	0.195293i
$66$		0			0
$67$	−1.21554	+	6.89365i	−0.148502	+	0.842194i	0.815987	+	0.578070i	$0.196194\pi$
$67$	−1.21554	+	6.89365i	−0.148502	+	0.842194i	−0.964489	+	0.264124i	$0.914917\pi$
$68$	5.10419	−	28.9473i	0.618974	−	3.51038i
$69$		0			0
$70$	−9.19253	+	7.71345i	−1.09872	+	0.921934i
$71$	3.67423	−	6.36396i	0.436051	−	0.755263i	−0.561329	−	0.827592i	$-0.689710\pi$
$71$	3.67423	−	6.36396i	0.436051	−	0.755263i	0.997381	+	0.0723293i	$0.0230432\pi$
$72$		0			0
$73$	−5.50000	−	9.52628i	−0.643726	−	1.11497i	−0.984594	−	0.174855i	$-0.944054\pi$
$73$	−5.50000	−	9.52628i	−0.643726	−	1.11497i	0.340868	−	0.940111i	$-0.389279\pi$
$74$	18.4141	+	6.70220i	2.14060	+	0.779115i
$75$		0			0
$76$	−3.06418	−	2.57115i	−0.351485	−	0.294931i
$77$	4.60353	−	1.67555i	0.524621	−	0.190947i
$78$		0			0
$79$	−1.21554	−	6.89365i	−0.136759	−	0.775597i	−0.973619	−	0.228180i	$-0.926722\pi$
$79$	−1.21554	−	6.89365i	−0.136759	−	0.775597i	0.836860	−	0.547417i	$-0.184389\pi$
$80$	9.79796			1.09545
$81$		0			0
$82$	12.0000			1.32518
$83$	2.12675	+	12.0614i	0.233441	+	1.32391i	0.845872	+	0.533385i	$0.179080\pi$
$83$	2.12675	+	12.0614i	0.233441	+	1.32391i	−0.612432	+	0.790524i	$0.709809\pi$
$84$		0			0
$85$	−16.9145	+	6.15636i	−1.83463	+	0.667751i
$86$	−20.6406	−	17.3195i	−2.22573	−	1.86761i
$87$		0			0
$88$	−11.2763	−	4.10424i	−1.20206	−	0.437514i
$89$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$89$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$90$		0			0
$91$	1.00000	−	1.73205i	0.104828	−	0.181568i
$92$	7.50567	−	6.29801i	0.782520	−	0.656613i
$93$		0			0
$94$	4.16756	−	23.6354i	0.429851	−	2.43780i
$95$	−0.425349	+	2.41228i	−0.0436399	+	0.247494i
$96$		0			0
$97$	−5.36231	+	4.49951i	−0.544460	+	0.456856i	−0.873060	−	0.487613i	$-0.837868\pi$
$97$	−5.36231	+	4.49951i	−0.544460	+	0.456856i	0.328600	+	0.944469i	$0.393423\pi$
$98$	−3.67423	+	6.36396i	−0.371154	+	0.642857i
$99$		0			0
$100$	−2.00000	−	3.46410i	−0.200000	−	0.346410i
$101$	−4.60353	−	1.67555i	−0.458069	−	0.166723i	0.102671	−	0.994715i	$-0.467261\pi$
$101$	−4.60353	−	1.67555i	−0.458069	−	0.166723i	−0.560740	+	0.827992i	$0.689483\pi$
$102$		0			0
$103$	−5.36231	−	4.49951i	−0.528364	−	0.443350i	0.339172	−	0.940724i	$-0.389853\pi$
$103$	−5.36231	−	4.49951i	−0.528364	−	0.443350i	−0.867536	+	0.497374i	$0.834298\pi$
$104$	−4.60353	+	1.67555i	−0.451414	+	0.164301i
$105$		0			0
$106$	3.12567	+	17.7265i	0.303592	+	1.72175i
$107$	−14.6969			−1.42081			−0.710403	−	0.703795i	$-0.751487\pi$
$107$	−14.6969			−1.42081			−0.710403	+	0.703795i	$0.751487\pi$
$108$		0			0
$109$	−1.00000			−0.0957826			−0.0478913	−	0.998853i	$-0.515250\pi$
$109$	−1.00000			−0.0957826			−0.0478913	+	0.998853i	$0.515250\pi$
$110$	2.55210	+	14.4737i	0.243333	+	1.38001i
$111$		0			0
$112$	−7.51754	+	2.73616i	−0.710341	+	0.258543i
$113$	7.50567	+	6.29801i	0.706074	+	0.592467i	0.923495	−	0.383611i	$-0.125320\pi$
$113$	7.50567	+	6.29801i	0.706074	+	0.592467i	−0.217420	+	0.976078i	$0.569764\pi$
$114$		0			0
$115$	−5.63816	−	2.05212i	−0.525761	−	0.191361i
$116$	−9.79796	−	16.9706i	−0.909718	−	1.57568i
$117$		0			0
$118$	3.00000	−	5.19615i	0.276172	−	0.478345i
$119$	11.2585	−	9.44701i	1.03207	−	0.866006i
$120$		0			0
$121$	−0.868241	+	4.92404i	−0.0789310	+	0.447640i
$122$	−2.12675	+	12.0614i	−0.192547	+	1.09199i
$123$		0			0
$124$	−3.06418	+	2.57115i	−0.275171	+	0.230896i
$125$	4.89898	−	8.48528i	0.438178	−	0.758947i
$126$		0			0
$127$	9.50000	+	16.4545i	0.842989	+	1.46010i	0.887357	+	0.461084i	$0.152539\pi$
$127$	9.50000	+	16.4545i	0.842989	+	1.46010i	−0.0443678	+	0.999015i	$0.514127\pi$
$128$	−18.4141	−	6.70220i	−1.62760	−	0.592396i
$129$		0			0
$130$	4.59627	+	3.85673i	0.403119	+	0.338257i
$131$	11.5088	−	4.18887i	1.00553	−	0.365984i	0.213816	−	0.976874i	$-0.431411\pi$
$131$	11.5088	−	4.18887i	1.00553	−	0.365984i	0.791715	+	0.610890i	$0.209188\pi$
$132$		0			0
$133$	−0.347296	−	1.96962i	−0.0301144	−	0.170787i
$134$	17.1464			1.48123
$135$		0			0
$136$	−36.0000			−3.08697
$137$	−1.70140	−	9.64911i	−0.145360	−	0.824379i	−0.967077	−	0.254483i	$-0.918095\pi$
$137$	−1.70140	−	9.64911i	−0.145360	−	0.824379i	0.821717	−	0.569896i	$-0.193016\pi$
$138$		0			0
$139$	9.39693	−	3.42020i	0.797037	−	0.290098i	0.0887789	−	0.996051i	$-0.471704\pi$
$139$	9.39693	−	3.42020i	0.797037	−	0.290098i	0.708258	+	0.705954i	$0.249481\pi$
$140$	15.0113	+	12.5960i	1.26869	+	1.06456i
$141$		0			0
$142$	−16.9145	−	6.15636i	−1.41943	−	0.516630i
$143$	−1.22474	−	2.12132i	−0.102418	−	0.177394i
$144$		0			0
$145$	−6.00000	+	10.3923i	−0.498273	+	0.863034i
$146$	−20.6406	+	17.3195i	−1.70823	+	1.43337i
$147$		0			0
$148$	5.55674	−	31.5138i	0.456761	−	2.59042i
$149$	−2.12675	+	12.0614i	−0.174230	+	0.988107i	0.764799	+	0.644269i	$0.222838\pi$
$149$	−2.12675	+	12.0614i	−0.174230	+	0.988107i	−0.939029	+	0.343838i	$0.888273\pi$
$150$		0			0
$151$	3.83022	−	3.21394i	0.311699	−	0.261547i	−0.473495	−	0.880797i	$-0.657008\pi$
$151$	3.83022	−	3.21394i	0.311699	−	0.261547i	0.785194	+	0.619250i	$0.212563\pi$
$152$	−2.44949	+	4.24264i	−0.198680	+	0.344124i
$153$		0			0
$154$	−6.00000	−	10.3923i	−0.483494	−	0.837436i
$155$	2.30177	+	0.837775i	0.184882	+	0.0672917i
$156$		0			0
$157$	13.0228	+	10.9274i	1.03933	+	0.872101i	0.991931	−	0.126775i	$-0.0404628\pi$
$157$	13.0228	+	10.9274i	1.03933	+	0.872101i	0.0473976	+	0.998876i	$0.484907\pi$
$158$	−16.1124	+	5.86442i	−1.28183	+	0.466549i
$159$		0			0
$160$		0			0
$161$	4.89898			0.386094
$162$		0			0
$163$	−10.0000			−0.783260			−0.391630	−	0.920123i	$-0.628089\pi$
$163$	−10.0000			−0.783260			−0.391630	+	0.920123i	$0.628089\pi$
$164$	−3.40280	−	19.2982i	−0.265714	−	1.50694i
$165$		0			0
$166$	28.1908	−	10.2606i	2.18803	−	0.796377i
$167$	−3.75284	−	3.14900i	−0.290403	−	0.243677i	0.485933	−	0.873996i	$-0.338480\pi$
$167$	−3.75284	−	3.14900i	−0.290403	−	0.243677i	−0.776336	+	0.630319i	$0.782924\pi$
$168$		0			0
$169$	11.2763	+	4.10424i	0.867409	+	0.315711i
$170$	22.0454	+	38.1838i	1.69081	+	2.92856i
$171$		0			0
$172$	−22.0000	+	38.1051i	−1.67748	+	2.90549i
$173$	−7.50567	+	6.29801i	−0.570646	+	0.478829i	−0.881860	−	0.471511i	$-0.843709\pi$
$173$	−7.50567	+	6.29801i	−0.570646	+	0.478829i	0.311214	+	0.950340i	$0.399264\pi$
$174$		0			0
$175$	0.347296	−	1.96962i	0.0262531	−	0.148889i
$176$	−1.70140	+	9.64911i	−0.128248	+	0.727329i
$177$		0			0
$178$		0			0
$179$	−7.34847	+	12.7279i	−0.549250	+	0.951330i	0.449076	+	0.893494i	$0.351753\pi$
$179$	−7.34847	+	12.7279i	−0.549250	+	0.951330i	−0.998326	+	0.0578359i	$0.981580\pi$
$180$		0			0
$181$	−4.00000	−	6.92820i	−0.297318	−	0.514969i	0.678204	−	0.734874i	$-0.262759\pi$
$181$	−4.00000	−	6.92820i	−0.297318	−	0.514969i	−0.975521	+	0.219905i	$0.929425\pi$
$182$	−4.60353	−	1.67555i	−0.341237	−	0.124200i
$183$		0			0
$184$	−9.19253	−	7.71345i	−0.677683	−	0.568643i
$185$	−18.4141	+	6.70220i	−1.35383	+	0.492755i
$186$		0			0
$187$	−3.12567	−	17.7265i	−0.228571	−	1.29629i
$188$	−39.1918			−2.85836
$189$		0			0
$190$	6.00000			0.435286
$191$	−1.70140	−	9.64911i	−0.123109	−	0.698185i	−0.982413	−	0.186720i	$-0.940214\pi$
$191$	−1.70140	−	9.64911i	−0.123109	−	0.698185i	0.859304	−	0.511465i	$-0.170897\pi$
$192$		0			0
$193$	−10.3366	+	3.76222i	−0.744046	+	0.270811i	−0.686098	−	0.727509i	$-0.740678\pi$
$193$	−10.3366	+	3.76222i	−0.744046	+	0.270811i	−0.0579479	+	0.998320i	$0.518456\pi$
$194$	13.1349	+	11.0215i	0.943033	+	0.791298i
$195$		0			0
$196$	11.2763	+	4.10424i	0.805451	+	0.293160i
$197$	7.34847	+	12.7279i	0.523557	+	0.906827i	0.999624	+	0.0274180i	$0.00872853\pi$
$197$	7.34847	+	12.7279i	0.523557	+	0.906827i	−0.476067	+	0.879409i	$0.657938\pi$
$198$		0			0
$199$	0.500000	−	0.866025i	0.0354441	−	0.0613909i	−0.847759	−	0.530381i	$-0.822049\pi$
$199$	0.500000	−	0.866025i	0.0354441	−	0.0613909i	0.883203	+	0.468990i	$0.155382\pi$
$200$	−3.75284	+	3.14900i	−0.265366	+	0.222668i
$201$		0			0
$202$	−2.08378	+	11.8177i	−0.146614	+	0.831490i
$203$	1.70140	−	9.64911i	0.119415	−	0.677234i
$204$		0			0
$205$	−9.19253	+	7.71345i	−0.642034	+	0.538731i
$206$	−8.57321	+	14.8492i	−0.597324	+	1.03460i
$207$		0			0
$208$	2.00000	+	3.46410i	0.138675	+	0.240192i
$209$	−2.30177	−	0.837775i	−0.159217	−	0.0579501i
$210$		0			0
$211$	−0.766044	−	0.642788i	−0.0527367	−	0.0442513i	0.616038	−	0.787716i	$-0.288737\pi$
$211$	−0.766044	−	0.642788i	−0.0527367	−	0.0442513i	−0.668775	+	0.743465i	$0.733181\pi$
$212$	27.6212	−	10.0533i	1.89703	−	0.690463i
$213$		0			0
$214$	6.25133	+	35.4531i	0.427332	+	2.42352i
$215$	26.9444			1.83759
$216$		0			0
$217$	−2.00000			−0.135769
$218$	0.425349	+	2.41228i	0.0288083	+	0.163380i
$219$		0			0
$220$	22.5526	−	8.20848i	1.52050	−	0.553416i
$221$	−5.62925	−	4.72350i	−0.378665	−	0.317737i
$222$		0			0
$223$	6.57785	+	2.39414i	0.440485	+	0.160324i	0.552736	−	0.833356i	$-0.313584\pi$
$223$	6.57785	+	2.39414i	0.440485	+	0.160324i	−0.112251	+	0.993680i	$0.535806\pi$
$224$		0			0
$225$		0			0
$226$	12.0000	−	20.7846i	0.798228	−	1.38257i
$227$	−7.50567	+	6.29801i	−0.498169	+	0.418013i	−0.856943	−	0.515411i	$-0.827639\pi$
$227$	−7.50567	+	6.29801i	−0.498169	+	0.418013i	0.358774	+	0.933424i	$0.383195\pi$
$228$		0			0
$229$	−0.173648	+	0.984808i	−0.0114750	+	0.0650779i	−0.990008	−	0.141014i	$-0.954964\pi$
$229$	−0.173648	+	0.984808i	−0.0114750	+	0.0650779i	0.978533	+	0.206092i	$0.0660747\pi$
$230$	−2.55210	+	14.4737i	−0.168280	+	0.954365i
$231$		0			0
$232$	−18.3851	+	15.4269i	−1.20704	+	1.01283i
$233$	−3.67423	+	6.36396i	−0.240707	+	0.416917i	−0.960916	−	0.276840i	$-0.910713\pi$
$233$	−3.67423	+	6.36396i	−0.240707	+	0.416917i	0.720209	+	0.693757i	$0.244046\pi$
$234$		0			0
$235$	12.0000	+	20.7846i	0.782794	+	1.35584i
$236$	−9.20707	−	3.35110i	−0.599329	−	0.218138i
$237$		0			0
$238$	−27.5776	−	23.1404i	−1.78759	−	1.49997i
$239$	−2.30177	+	0.837775i	−0.148889	+	0.0541911i	−0.415390	−	0.909644i	$-0.636355\pi$
$239$	−2.30177	+	0.837775i	−0.148889	+	0.0541911i	0.266501	+	0.963835i	$0.414133\pi$
$240$		0			0
$241$	−2.77837	−	15.7569i	−0.178971	−	1.01499i	−0.933460	−	0.358681i	$-0.883227\pi$
$241$	−2.77837	−	15.7569i	−0.178971	−	1.01499i	0.754490	−	0.656312i	$-0.227884\pi$
$242$	12.2474			0.787296
$243$		0			0
$244$	20.0000			1.28037
$245$	−1.27605	−	7.23683i	−0.0815237	−	0.462344i
$246$		0			0
$247$	−0.939693	+	0.342020i	−0.0597912	+	0.0217622i
$248$	3.75284	+	3.14900i	0.238305	+	0.199962i
$249$		0			0
$250$	−22.5526	−	8.20848i	−1.42635	−	0.519150i
$251$	−3.67423	−	6.36396i	−0.231916	−	0.401690i	0.726456	−	0.687213i	$-0.241166\pi$
$251$	−3.67423	−	6.36396i	−0.231916	−	0.401690i	−0.958372	+	0.285523i	$0.907833\pi$
$252$		0			0
$253$	3.00000	−	5.19615i	0.188608	−	0.326679i
$254$	35.6519	−	29.9155i	2.23700	−	1.87707i
$255$		0			0
$256$	−5.55674	+	31.5138i	−0.347296	+	1.96962i
$257$	2.97745	−	16.8859i	0.185728	−	1.05332i	−0.739289	−	0.673389i	$-0.764838\pi$
$257$	2.97745	−	16.8859i	0.185728	−	1.05332i	0.925017	−	0.379927i	$-0.124051\pi$
$258$		0			0
$259$	12.2567	−	10.2846i	0.761595	−	0.639054i
$260$	4.89898	−	8.48528i	0.303822	−	0.526235i
$261$		0			0
$262$	−15.0000	−	25.9808i	−0.926703	−	1.60510i
$263$	−25.3194	−	9.21552i	−1.56126	−	0.568254i	−0.590238	−	0.807229i	$-0.700966\pi$
$263$	−25.3194	−	9.21552i	−1.56126	−	0.568254i	−0.971026	+	0.238976i	$0.923188\pi$
$264$		0			0
$265$	−13.7888	−	11.5702i	−0.847039	−	0.710750i
$266$	−4.60353	+	1.67555i	−0.282261	+	0.102735i
$267$		0			0
$268$	−4.86215	−	27.5746i	−0.297003	−	1.68439i
$269$	22.0454			1.34413			0.672066	−	0.740491i	$-0.265407\pi$
$269$	22.0454			1.34413			0.672066	+	0.740491i	$0.265407\pi$
$270$		0			0
$271$	−7.00000			−0.425220			−0.212610	−	0.977137i	$-0.568196\pi$
$271$	−7.00000			−0.425220			−0.212610	+	0.977137i	$0.568196\pi$
$272$	5.10419	+	28.9473i	0.309487	+	1.75519i
$273$		0			0
$274$	−22.5526	+	8.20848i	−1.36245	+	0.495893i
$275$	−1.87642	−	1.57450i	−0.113152	−	0.0949460i
$276$		0			0
$277$	−10.3366	−	3.76222i	−0.621067	−	0.226050i	0.0122715	−	0.999925i	$-0.496094\pi$
$277$	−10.3366	−	3.76222i	−0.621067	−	0.226050i	−0.633339	+	0.773875i	$0.718316\pi$
$278$	−12.2474	−	21.2132i	−0.734553	−	1.27228i
$279$		0			0
$280$	12.0000	−	20.7846i	0.717137	−	1.24212i
$281$	9.38209	−	7.87251i	0.559689	−	0.469634i	−0.318517	−	0.947917i	$-0.603185\pi$
$281$	9.38209	−	7.87251i	0.559689	−	0.469634i	0.878206	+	0.478283i	$0.158741\pi$
$282$		0			0
$283$	2.95202	−	16.7417i	0.175479	−	0.995193i	−0.762110	−	0.647448i	$-0.775836\pi$
$283$	2.95202	−	16.7417i	0.175479	−	0.995193i	0.937589	−	0.347745i	$-0.113052\pi$
$284$	−5.10419	+	28.9473i	−0.302878	+	1.71771i
$285$		0			0
$286$	−4.59627	+	3.85673i	−0.271783	+	0.228053i
$287$	4.89898	−	8.48528i	0.289178	−	0.500870i
$288$		0			0
$289$	−18.5000	−	32.0429i	−1.08824	−	1.88488i
$290$	27.6212	+	10.0533i	1.62197	+	0.590350i
$291$		0			0
$292$	33.7060	+	28.2827i	1.97249	+	1.65512i
$293$	4.60353	−	1.67555i	0.268941	−	0.0978867i	−0.204029	−	0.978965i	$-0.565404\pi$
$293$	4.60353	−	1.67555i	0.268941	−	0.0978867i	0.472971	+	0.881078i	$0.343182\pi$
$294$		0			0
$295$	1.04189	+	5.90885i	0.0606611	+	0.344026i
$296$	−39.1918			−2.27798
$297$		0			0
$298$	30.0000			1.73785
$299$	−0.425349	−	2.41228i	−0.0245986	−	0.139506i
$300$		0			0
$301$	−20.6732	+	7.52444i	−1.19159	+	0.433702i
$302$	−9.38209	−	7.87251i	−0.539879	−	0.453012i
$303$		0			0
$304$	3.75877	+	1.36808i	0.215580	+	0.0784648i
$305$	−6.12372	−	10.6066i	−0.350643	−	0.607332i
$306$		0			0
$307$	−1.00000	+	1.73205i	−0.0570730	+	0.0988534i	−0.893150	−	0.449758i	$-0.851510\pi$
$307$	−1.00000	+	1.73205i	−0.0570730	+	0.0988534i	0.836077	+	0.548612i	$0.184843\pi$
$308$	−15.0113	+	12.5960i	−0.855351	+	0.717724i
$309$		0			0
$310$	1.04189	−	5.90885i	0.0591753	−	0.335600i
$311$	4.25349	−	24.1228i	0.241194	−	1.36788i	−0.587976	−	0.808879i	$-0.700075\pi$
$311$	4.25349	−	24.1228i	0.241194	−	1.36788i	0.829169	−	0.558998i	$-0.188814\pi$
$312$		0			0
$313$	−12.2567	+	10.2846i	−0.692790	+	0.581320i	−0.919712	−	0.392593i	$-0.871578\pi$
$313$	−12.2567	+	10.2846i	−0.692790	+	0.581320i	0.226922	+	0.973913i	$0.427134\pi$
$314$	20.8207	−	36.0624i	1.17498	−	2.03512i
$315$		0			0
$316$	14.0000	+	24.2487i	0.787562	+	1.36410i
$317$	9.20707	+	3.35110i	0.517121	+	0.188216i	0.587378	−	0.809312i	$-0.300160\pi$
$317$	9.20707	+	3.35110i	0.517121	+	0.188216i	−0.0702579	+	0.997529i	$0.522382\pi$
$318$		0			0
$319$	−9.19253	−	7.71345i	−0.514683	−	0.431870i
$320$	18.4141	−	6.70220i	1.02938	−	0.374664i
$321$		0			0
$322$	−2.08378	−	11.8177i	−0.116124	−	0.658574i
$323$	−7.34847			−0.408880
$324$		0			0
$325$	−1.00000			−0.0554700
$326$	4.25349	+	24.1228i	0.235579	+	1.33604i
$327$		0			0
$328$	−22.5526	+	8.20848i	−1.24526	+	0.453238i
$329$	−15.0113	−	12.5960i	−0.827602	−	0.694441i
$330$		0			0
$331$	6.57785	+	2.39414i	0.361551	+	0.131594i	0.516407	−	0.856343i	$-0.327269\pi$
$331$	6.57785	+	2.39414i	0.361551	+	0.131594i	−0.154856	+	0.987937i	$0.549491\pi$
$332$	−24.4949	−	42.4264i	−1.34433	−	2.32845i
$333$		0			0
$334$	−6.00000	+	10.3923i	−0.328305	+	0.568642i
$335$	−13.1349	+	11.0215i	−0.717638	+	0.602170i
$336$		0			0
$337$	−4.86215	+	27.5746i	−0.264858	+	1.50209i	0.504581	+	0.863365i	$0.331647\pi$
$337$	−4.86215	+	27.5746i	−0.264858	+	1.50209i	−0.769439	+	0.638721i	$0.779464\pi$
$338$	5.10419	−	28.9473i	0.277632	−	1.57453i
$339$		0			0
$340$	55.1552	−	46.2807i	2.99121	−	2.50992i
$341$	−1.22474	+	2.12132i	−0.0663237	+	0.114876i
$342$		0			0
$343$	10.0000	+	17.3205i	0.539949	+	0.935220i
$344$	50.6389	+	18.4310i	2.73027	+	0.993735i
$345$		0			0
$346$	18.3851	+	15.4269i	0.988387	+	0.829355i
$347$	−23.0177	+	8.37775i	−1.23565	+	0.449741i	−0.875530	−	0.483164i	$-0.839488\pi$
$347$	−23.0177	+	8.37775i	−1.23565	+	0.449741i	−0.360123	+	0.932905i	$0.617265\pi$
$348$		0			0
$349$	3.47296	+	19.6962i	0.185903	+	1.05431i	0.924789	+	0.380480i	$0.124241\pi$
$349$	3.47296	+	19.6962i	0.185903	+	1.05431i	−0.738886	+	0.673831i	$0.764648\pi$
$350$	−4.89898			−0.261861
$351$		0			0
$352$		0			0
$353$	−0.425349	−	2.41228i	−0.0226391	−	0.128393i	0.971394	−	0.237475i	$-0.0763198\pi$
$353$	−0.425349	−	2.41228i	−0.0226391	−	0.128393i	−0.994033	+	0.109083i	$0.965209\pi$
$354$		0			0
$355$	16.9145	−	6.15636i	0.897727	−	0.326746i
$356$		0			0
$357$		0			0
$358$	33.8289	+	12.3127i	1.78791	+	0.650748i
$359$	14.6969	+	25.4558i	0.775675	+	1.34351i	0.934414	+	0.356188i	$0.115924\pi$
$359$	14.6969	+	25.4558i	0.775675	+	1.34351i	−0.158740	+	0.987320i	$0.550743\pi$
$360$		0			0
$361$	9.00000	−	15.5885i	0.473684	−	0.820445i
$362$	−15.0113	+	12.5960i	−0.788979	+	0.662032i
$363$		0			0
$364$	−1.38919	+	7.87846i	−0.0728131	+	0.412944i
$365$	4.67884	−	26.5350i	0.244902	−	1.38891i
$366$		0			0
$367$	3.83022	−	3.21394i	0.199936	−	0.167766i	−0.537323	−	0.843377i	$-0.680564\pi$
$367$	3.83022	−	3.21394i	0.199936	−	0.167766i	0.737259	+	0.675610i	$0.236120\pi$
$368$	−4.89898	+	8.48528i	−0.255377	+	0.442326i
$369$		0			0
$370$	24.0000	+	41.5692i	1.24770	+	2.16108i
$371$	13.8106	+	5.02665i	0.717011	+	0.260971i
$372$		0			0
$373$	26.8116	+	22.4976i	1.38825	+	1.16488i	0.966043	+	0.258380i	$0.0831887\pi$
$373$	26.8116	+	22.4976i	1.38825	+	1.16488i	0.422206	+	0.906500i	$0.361256\pi$
$374$	−41.4318	+	15.0799i	−2.14239	+	0.779765i
$375$		0			0
$376$	8.33511	+	47.2708i	0.429851	+	2.43780i
$377$	−4.89898			−0.252310
$378$		0			0
$379$	8.00000			0.410932			0.205466	−	0.978664i	$-0.434129\pi$
$379$	8.00000			0.410932			0.205466	+	0.978664i	$0.434129\pi$
$380$	−1.70140	−	9.64911i	−0.0872799	−	0.494989i
$381$		0			0
$382$	−22.5526	+	8.20848i	−1.15389	+	0.419983i
$383$	−26.2699	−	22.0430i	−1.34233	−	1.12635i	−0.981022	−	0.193898i	$-0.937887\pi$
$383$	−26.2699	−	22.0430i	−1.34233	−	1.12635i	−0.361305	−	0.932448i	$-0.617669\pi$
$384$		0			0
$385$	11.2763	+	4.10424i	0.574694	+	0.209172i
$386$	13.4722	+	23.3345i	0.685717	+	1.18770i
$387$		0			0
$388$	14.0000	−	24.2487i	0.710742	−	1.23104i
$389$	20.6406	−	17.3195i	1.04652	−	0.878134i	0.0537965	−	0.998552i	$-0.482868\pi$
$389$	20.6406	−	17.3195i	1.04652	−	0.878134i	0.992723	+	0.120417i	$0.0384233\pi$
$390$		0			0
$391$	3.12567	−	17.7265i	0.158072	−	0.896470i
$392$	2.55210	−	14.4737i	0.128900	−	0.731030i
$393$		0			0
$394$	27.5776	−	23.1404i	1.38934	−	1.16579i
$395$	8.57321	−	14.8492i	0.431365	−	0.747146i
$396$		0			0
$397$	0.500000	+	0.866025i	0.0250943	+	0.0434646i	0.878300	−	0.478110i	$-0.158678\pi$
$397$	0.500000	+	0.866025i	0.0250943	+	0.0434646i	−0.853206	+	0.521575i	$0.825345\pi$
$398$	−2.30177	−	0.837775i	−0.115377	−	0.0419939i
$399$		0			0
$400$	3.06418	+	2.57115i	0.153209	+	0.128558i
$401$	32.2247	−	11.7288i	1.60923	−	0.585711i	0.627940	−	0.778262i	$-0.283898\pi$
$401$	32.2247	−	11.7288i	1.60923	−	0.585711i	0.981287	+	0.192551i	$0.0616761\pi$
$402$		0			0
$403$	0.173648	+	0.984808i	0.00865003	+	0.0490568i
$404$	19.5959			0.974933
$405$		0			0
$406$	−24.0000			−1.19110
$407$	−3.40280	−	19.2982i	−0.168670	−	0.956577i
$408$		0			0
$409$	26.3114	−	9.57656i	1.30101	−	0.473531i	0.403688	−	0.914897i	$-0.367728\pi$
$409$	26.3114	−	9.57656i	1.30101	−	0.473531i	0.897327	+	0.441366i	$0.145506\pi$
$410$	22.5170	+	18.8940i	1.11204	+	0.933109i
$411$		0			0
$412$	26.3114	+	9.57656i	1.29627	+	0.471803i
$413$	−2.44949	−	4.24264i	−0.120532	−	0.208767i
$414$		0			0
$415$	−15.0000	+	25.9808i	−0.736321	+	1.27535i
$416$		0			0
$417$		0			0
$418$	−1.04189	+	5.90885i	−0.0509605	+	0.289011i
$419$	−5.95489	+	33.7719i	−0.290916	+	1.64986i	0.392440	+	0.919778i	$0.371631\pi$
$419$	−5.95489	+	33.7719i	−0.290916	+	1.64986i	−0.683355	+	0.730086i	$0.739480\pi$
$420$		0			0
$421$	1.53209	−	1.28558i	0.0746694	−	0.0626551i	−0.604689	−	0.796462i	$-0.706703\pi$
$421$	1.53209	−	1.28558i	0.0746694	−	0.0626551i	0.679358	+	0.733807i	$0.262258\pi$
$422$	−1.22474	+	2.12132i	−0.0596196	+	0.103264i
$423$		0			0
$424$	−18.0000	−	31.1769i	−0.874157	−	1.51408i
$425$	−6.90530	−	2.51332i	−0.334956	−	0.121914i
$426$		0			0
$427$	7.66044	+	6.42788i	0.370715	+	0.311067i
$428$	55.2424	−	20.1066i	2.67024	−	0.971889i
$429$		0			0
$430$	−11.4608	−	64.9973i	−0.552688	−	3.13445i
$431$	7.34847			0.353963			0.176982	−	0.984214i	$-0.443367\pi$
$431$	7.34847			0.353963			0.176982	+	0.984214i	$0.443367\pi$
$432$		0			0
$433$	17.0000			0.816968			0.408484	−	0.912766i	$-0.366058\pi$
$433$	17.0000			0.816968			0.408484	+	0.912766i	$0.366058\pi$
$434$	0.850699	+	4.82455i	0.0408349	+	0.231586i
$435$		0			0
$436$	3.75877	−	1.36808i	0.180012	−	0.0655192i
$437$	−1.87642	−	1.57450i	−0.0897612	−	0.0753186i
$438$		0			0
$439$	−13.1557	−	4.78828i	−0.627887	−	0.228532i	0.00842428	−	0.999965i	$-0.497318\pi$
$439$	−13.1557	−	4.78828i	−0.627887	−	0.228532i	−0.636311	+	0.771432i	$0.719541\pi$
$440$	−14.6969	−	25.4558i	−0.700649	−	1.21356i
$441$		0			0
$442$	−9.00000	+	15.5885i	−0.428086	+	0.741467i
$443$	9.38209	−	7.87251i	0.445757	−	0.374034i	−0.392102	−	0.919922i	$-0.628252\pi$
$443$	9.38209	−	7.87251i	0.445757	−	0.374034i	0.837858	+	0.545888i	$0.183807\pi$
$444$		0			0
$445$		0			0
$446$	2.97745	−	16.8859i	0.140986	−	0.799572i
$447$		0			0
$448$	−12.2567	+	10.2846i	−0.579075	+	0.485902i
$449$	11.0227	−	19.0919i	0.520194	−	0.901002i	−0.479531	−	0.877525i	$-0.659193\pi$
$449$	11.0227	−	19.0919i	0.520194	−	0.901002i	0.999724	−	0.0234766i	$-0.00747353\pi$
$450$		0			0
$451$	−6.00000	−	10.3923i	−0.282529	−	0.489355i
$452$	−36.8283	−	13.4044i	−1.73226	−	0.630490i
$453$		0			0
$454$	18.3851	+	15.4269i	0.862854	+	0.724020i
$455$	4.60353	−	1.67555i	0.215817	−	0.0785510i
$456$		0			0
$457$	5.03580	+	28.5594i	0.235565	+	1.33595i	0.841421	+	0.540380i	$0.181719\pi$
$457$	5.03580	+	28.5594i	0.235565	+	1.33595i	−0.605857	+	0.795574i	$0.707169\pi$
$458$	2.44949			0.114457
$459$		0			0
$460$	24.0000			1.11901
$461$	4.67884	+	26.5350i	0.217915	+	1.23586i	0.875775	+	0.482719i	$0.160351\pi$
$461$	4.67884	+	26.5350i	0.217915	+	1.23586i	−0.657860	+	0.753141i	$0.728538\pi$
$462$		0			0
$463$	17.8542	−	6.49838i	0.829753	−	0.302005i	0.107996	−	0.994151i	$-0.465557\pi$
$463$	17.8542	−	6.49838i	0.829753	−	0.302005i	0.721758	+	0.692146i	$0.243335\pi$
$464$	15.0113	+	12.5960i	0.696884	+	0.584755i
$465$		0			0
$466$	16.9145	+	6.15636i	0.783548	+	0.285188i
$467$	7.34847	+	12.7279i	0.340047	+	0.588978i	0.984441	−	0.175715i	$-0.0562238\pi$
$467$	7.34847	+	12.7279i	0.340047	+	0.588978i	−0.644394	+	0.764693i	$0.722890\pi$
$468$		0			0
$469$	7.00000	−	12.1244i	0.323230	−	0.559851i
$470$	45.0340	−	37.7880i	2.07727	−	1.74303i
$471$		0			0
$472$	−2.08378	+	11.8177i	−0.0959137	+	0.543953i
$473$	−4.67884	+	26.5350i	−0.215133	+	1.22008i
$474$		0			0
$475$	−0.766044	+	0.642788i	−0.0351485	+	0.0294931i
$476$	−29.3939	+	50.9117i	−1.34727	+	2.33353i
$477$		0			0
$478$	3.00000	+	5.19615i	0.137217	+	0.237666i
$479$	−25.3194	−	9.21552i	−1.15687	−	0.421068i	−0.308895	−	0.951096i	$-0.599959\pi$
$479$	−25.3194	−	9.21552i	−1.15687	−	0.421068i	−0.847980	+	0.530028i	$0.822181\pi$
$480$		0			0
$481$	−6.12836	−	5.14230i	−0.279429	−	0.234469i
$482$	−36.8283	+	13.4044i	−1.67748	+	0.610554i
$483$		0			0
$484$	−3.47296	−	19.6962i	−0.157862	−	0.895280i
$485$	−17.1464			−0.778579
$486$		0			0
$487$	35.0000			1.58600			0.793001	−	0.609221i	$-0.208518\pi$
$487$	35.0000			1.58600			0.793001	+	0.609221i	$0.208518\pi$
$488$	−4.25349	−	24.1228i	−0.192547	−	1.09199i
$489$		0			0
$490$	−16.9145	+	6.15636i	−0.764118	+	0.278116i
$491$	30.0227	+	25.1920i	1.35490	+	1.13690i	0.977520	+	0.210844i	$0.0676212\pi$
$491$	30.0227	+	25.1920i	1.35490	+	1.13690i	0.377385	+	0.926056i	$0.376823\pi$
$492$		0			0
$493$	−33.8289	−	12.3127i	−1.52358	−	0.554537i
$494$	1.22474	+	2.12132i	0.0551039	+	0.0954427i
$495$		0			0
$496$	2.00000	−	3.46410i	0.0898027	−	0.155543i
$497$	−11.2585	+	9.44701i	−0.505013	+	0.423756i
$498$		0			0
$499$	0.347296	−	1.96962i	0.0155471	−	0.0881721i	−0.976047	−	0.217560i	$-0.930190\pi$
$499$	0.347296	−	1.96962i	0.0155471	−	0.0881721i	0.991594	+	0.129388i	$0.0413013\pi$
$500$	−6.80559	+	38.5964i	−0.304355	+	1.72608i
$501$		0			0
$502$	−13.7888	+	11.5702i	−0.615424	+	0.516402i
$503$	−7.34847	+	12.7279i	−0.327652	+	0.567510i	−0.982045	−	0.188644i	$-0.939591\pi$
$503$	−7.34847	+	12.7279i	−0.327652	+	0.567510i	0.654393	+	0.756154i	$0.272924\pi$
$504$		0			0
$505$	−6.00000	−	10.3923i	−0.266996	−	0.462451i
$506$	−13.8106	−	5.02665i	−0.613956	−	0.223462i
$507$		0			0
$508$	−58.2194	−	48.8519i	−2.58307	−	2.16745i
$509$	−9.20707	+	3.35110i	−0.408096	+	0.148535i	−0.537908	−	0.843004i	$-0.680785\pi$
$509$	−9.20707	+	3.35110i	−0.408096	+	0.148535i	0.129811	+	0.991539i	$0.458563\pi$
$510$		0			0
$511$	3.82026	+	21.6658i	0.168998	+	0.958437i
$512$	39.1918			1.73205
$513$		0			0
$514$	−42.0000			−1.85254
$515$	−2.97745	−	16.8859i	−0.131202	−	0.744083i
$516$		0			0
$517$	−22.5526	+	8.20848i	−0.991863	+	0.361009i
$518$	−30.0227	−	25.1920i	−1.31912	−	1.10687i
$519$		0			0
$520$	−11.2763	−	4.10424i	−0.494499	−	0.179983i
$521$	11.0227	+	19.0919i	0.482913	+	0.836431i	0.999808	−	0.0196188i	$-0.00624525\pi$
$521$	11.0227	+	19.0919i	0.482913	+	0.836431i	−0.516894	+	0.856049i	$0.672912\pi$
$522$		0			0
$523$	12.5000	−	21.6506i	0.546587	−	0.946716i	−0.451918	−	0.892059i	$-0.649260\pi$
$523$	12.5000	−	21.6506i	0.546587	−	0.946716i	0.998505	−	0.0546569i	$-0.0174065\pi$
$524$	−37.5284	+	31.4900i	−1.63943	+	1.37565i
$525$		0			0
$526$	−11.4608	+	64.9973i	−0.499714	+	2.83402i
$527$	−1.27605	+	7.23683i	−0.0555855	+	0.315241i
$528$		0			0
$529$	−13.0228	+	10.9274i	−0.566207	+	0.475104i
$530$	−22.0454	+	38.1838i	−0.957591	+	1.65860i
$531$		0			0
$532$	4.00000	+	6.92820i	0.173422	+	0.300376i
$533$	−4.60353	−	1.67555i	−0.199401	−	0.0725761i
$534$		0			0
$535$	−27.5776	−	23.1404i	−1.19228	−	1.00044i
$536$	−32.2247	+	11.7288i	−1.39190	+	0.506609i
$537$		0			0
$538$	−9.37700	−	53.1796i	−0.404271	−	2.29274i
$539$	7.34847			0.316521
$540$		0			0
$541$	−28.0000			−1.20381			−0.601907	−	0.798566i	$-0.705592\pi$
$541$	−28.0000			−1.20381			−0.601907	+	0.798566i	$0.705592\pi$
$542$	2.97745	+	16.8859i	0.127892	+	0.725313i
$543$		0			0
$544$		0			0
$545$	−1.87642	−	1.57450i	−0.0803769	−	0.0674442i
$546$		0			0
$547$	12.2160	+	4.44626i	0.522319	+	0.190108i	0.589705	−	0.807619i	$-0.299244\pi$
$547$	12.2160	+	4.44626i	0.522319	+	0.190108i	−0.0673867	+	0.997727i	$0.521466\pi$
$548$	19.5959	+	33.9411i	0.837096	+	1.44989i
$549$		0			0
$550$	−3.00000	+	5.19615i	−0.127920	+	0.221565i
$551$	−3.75284	+	3.14900i	−0.159876	+	0.134152i
$552$		0			0
$553$	−2.43107	+	13.7873i	−0.103380	+	0.586296i
$554$	−4.67884	+	26.5350i	−0.198785	+	1.12737i
$555$		0			0
$556$	−30.6418	+	25.7115i	−1.29950	+	1.09041i
$557$	3.67423	−	6.36396i	0.155682	−	0.269650i	−0.777625	−	0.628728i	$-0.783576\pi$
$557$	3.67423	−	6.36396i	0.155682	−	0.269650i	0.933307	+	0.359079i	$0.116909\pi$
$558$		0			0
$559$	5.50000	+	9.52628i	0.232625	+	0.402919i
$560$	−18.4141	−	6.70220i	−0.778139	−	0.283220i
$561$		0			0
$562$	−22.9813	−	19.2836i	−0.969409	−	0.813431i
$563$	11.5088	−	4.18887i	0.485040	−	0.176540i	−0.0879135	−	0.996128i	$-0.528020\pi$
$563$	11.5088	−	4.18887i	0.485040	−	0.176540i	0.572953	+	0.819588i	$0.305798\pi$
$564$		0			0
$565$	4.16756	+	23.6354i	0.175330	+	0.994348i
$566$	−41.6413			−1.75032
$567$		0			0
$568$	36.0000			1.51053
$569$	2.12675	+	12.0614i	0.0891579	+	0.505639i	0.996382	+	0.0849912i	$0.0270862\pi$
$569$	2.12675	+	12.0614i	0.0891579	+	0.505639i	−0.907224	+	0.420648i	$0.861803\pi$
$570$		0			0
$571$	9.39693	−	3.42020i	0.393249	−	0.143131i	−0.137824	−	0.990457i	$-0.544011\pi$
$571$	9.39693	−	3.42020i	0.393249	−	0.143131i	0.531074	+	0.847326i	$0.321789\pi$
$572$	7.50567	+	6.29801i	0.313828	+	0.263333i
$573$		0			0
$574$	−22.5526	−	8.20848i	−0.941328	−	0.342615i
$575$	−1.22474	−	2.12132i	−0.0510754	−	0.0884652i
$576$		0			0
$577$	12.5000	−	21.6506i	0.520382	−	0.901328i	−0.479337	−	0.877631i	$-0.659123\pi$
$577$	12.5000	−	21.6506i	0.520382	−	0.901328i	0.999719	−	0.0236970i	$-0.00754370\pi$
$578$	−69.4275	+	58.2566i	−2.88780	+	2.42315i
$579$		0			0
$580$	8.33511	−	47.2708i	0.346097	−	1.96281i
$581$	4.25349	−	24.1228i	0.176465	−	1.00078i
$582$		0			0
$583$	13.7888	−	11.5702i	0.571074	−	0.479188i
$584$	26.9444	−	46.6690i	1.11497	−	1.93118i
$585$		0			0
$586$	−6.00000	−	10.3923i	−0.247858	−	0.429302i
$587$	2.30177	+	0.837775i	0.0950041	+	0.0345787i	0.389085	−	0.921202i	$-0.372791\pi$
$587$	2.30177	+	0.837775i	0.0950041	+	0.0345787i	−0.294081	+	0.955781i	$0.595013\pi$
$588$		0			0
$589$	0.766044	+	0.642788i	0.0315643	+	0.0264856i
$590$	13.8106	−	5.02665i	0.568574	−	0.206944i
$591$		0			0
$592$	5.55674	+	31.5138i	0.228381	+	1.29521i
$593$	−7.34847			−0.301765			−0.150883	−	0.988552i	$-0.548212\pi$
$593$	−7.34847			−0.301765			−0.150883	+	0.988552i	$0.548212\pi$
$594$		0			0
$595$	36.0000			1.47586
$596$	−8.50699	−	48.2455i	−0.348460	−	1.97621i
$597$		0			0
$598$	−5.63816	+	2.05212i	−0.230561	+	0.0839175i
$599$	30.0227	+	25.1920i	1.22669	+	1.02932i	0.998447	+	0.0557151i	$0.0177438\pi$
$599$	30.0227	+	25.1920i	1.22669	+	1.02932i	0.228247	+	0.973603i	$0.426701\pi$
$600$		0			0
$601$	6.57785	+	2.39414i	0.268316	+	0.0976590i	0.472675	−	0.881237i	$-0.343289\pi$
$601$	6.57785	+	2.39414i	0.268316	+	0.0976590i	−0.204359	+	0.978896i	$0.565511\pi$
$602$	26.9444	+	46.6690i	1.09817	+	1.90209i
$603$		0			0
$604$	−10.0000	+	17.3205i	−0.406894	+	0.704761i
$605$	−9.38209	+	7.87251i	−0.381436	+	0.320063i
$606$		0			0
$607$	7.64052	−	43.3315i	0.310119	−	1.75877i	−0.288253	−	0.957554i	$-0.593074\pi$
$607$	7.64052	−	43.3315i	0.310119	−	1.75877i	0.598372	−	0.801219i	$-0.295815\pi$
$608$		0			0
$609$		0			0
$610$	−22.9813	+	19.2836i	−0.930487	+	0.780771i
$611$	−4.89898	+	8.48528i	−0.198191	+	0.343278i
$612$		0			0
$613$	−5.50000	−	9.52628i	−0.222143	−	0.384763i	0.733316	−	0.679888i	$-0.237972\pi$
$613$	−5.50000	−	9.52628i	−0.222143	−	0.384763i	−0.955458	+	0.295126i	$0.904638\pi$
$614$	4.60353	+	1.67555i	0.185784	+	0.0676197i
$615$		0			0
$616$	18.3851	+	15.4269i	0.740755	+	0.621568i
$617$	−23.0177	+	8.37775i	−0.926657	+	0.337275i	−0.760884	−	0.648888i	$-0.775234\pi$
$617$	−23.0177	+	8.37775i	−0.926657	+	0.337275i	−0.165773	+	0.986164i	$0.553012\pi$
$618$		0			0
$619$	−8.50876	−	48.2556i	−0.341996	−	1.93956i	−0.342396	−	0.939556i	$-0.611239\pi$
$619$	−8.50876	−	48.2556i	−0.341996	−	1.93956i	0.000400419	−	1.00000i	$-0.499873\pi$
$620$	−9.79796			−0.393496
$621$		0			0
$622$	−60.0000			−2.40578
$623$		0			0
$624$		0			0
$625$	27.2511	−	9.91858i	1.09004	−	0.396743i
$626$	30.0227	+	25.1920i	1.19995	+	1.00688i
$627$		0			0
$628$	−63.8991	−	23.2574i	−2.54985	−	0.928070i
$629$	−29.3939	−	50.9117i	−1.17201	−	2.02998i
$630$		0			0
$631$	−22.0000	+	38.1051i	−0.875806	+	1.51694i	−0.0199047	+	0.999802i	$0.506336\pi$
$631$	−22.0000	+	38.1051i	−0.875806	+	1.51694i	−0.855901	+	0.517139i	$0.826997\pi$
$632$	26.2699	−	22.0430i	1.04496	−	0.876824i
$633$		0			0
$634$	4.16756	−	23.6354i	0.165515	−	0.938681i
$635$	−8.08164	+	45.8333i	−0.320710	+	1.81884i
$636$		0			0
$637$	2.29813	−	1.92836i	0.0910554	−	0.0764045i
$638$	−14.6969	+	25.4558i	−0.581857	+	1.00781i
$639$		0			0
$640$	−24.0000	−	41.5692i	−0.948683	−	1.64317i
$641$	16.1124	+	5.86442i	0.636400	+	0.231631i	0.640015	−	0.768363i	$-0.278928\pi$
$641$	16.1124	+	5.86442i	0.636400	+	0.231631i	−0.00361428	+	0.999993i	$0.501150\pi$
$642$		0			0
$643$	29.1097	+	24.4259i	1.14797	+	0.963265i	0.999670	−	0.0256772i	$-0.00817422\pi$
$643$	29.1097	+	24.4259i	1.14797	+	0.963265i	0.148304	+	0.988942i	$0.452619\pi$
$644$	−18.4141	+	6.70220i	−0.725619	+	0.264104i
$645$		0			0
$646$	3.12567	+	17.7265i	0.122978	+	0.697441i
$647$	−36.7423			−1.44449			−0.722245	−	0.691637i	$-0.756890\pi$
$647$	−36.7423			−1.44449			−0.722245	+	0.691637i	$0.756890\pi$
$648$		0			0
$649$	−6.00000			−0.235521
$650$	0.425349	+	2.41228i	0.0166836	+	0.0946173i
$651$		0			0
$652$	37.5877	−	13.6808i	1.47205	−	0.535782i
$653$	7.50567	+	6.29801i	0.293720	+	0.246460i	0.777725	−	0.628605i	$-0.216374\pi$
$653$	7.50567	+	6.29801i	0.293720	+	0.246460i	−0.484005	+	0.875065i	$0.660818\pi$
$654$		0			0
$655$	28.1908	+	10.2606i	1.10150	+	0.400915i
$656$	9.79796	+	16.9706i	0.382546	+	0.662589i
$657$		0			0
$658$	−24.0000	+	41.5692i	−0.935617	+	1.62054i
$659$	15.0113	−	12.5960i	0.584759	−	0.490671i	−0.301747	−	0.953388i	$-0.597570\pi$
$659$	15.0113	−	12.5960i	0.584759	−	0.490671i	0.886506	+	0.462717i	$0.153125\pi$
$660$		0			0
$661$	1.91013	−	10.8329i	0.0742954	−	0.421350i	−0.924862	−	0.380303i	$-0.875820\pi$
$661$	1.91013	−	10.8329i	0.0742954	−	0.421350i	0.999157	−	0.0410470i	$-0.0130693\pi$
$662$	2.97745	−	16.8859i	0.115722	−	0.656291i
$663$		0			0
$664$	−45.9627	+	38.5673i	−1.78370	+	1.49670i
$665$	2.44949	−	4.24264i	0.0949871	−	0.164523i
$666$		0			0
$667$	−6.00000	−	10.3923i	−0.232321	−	0.402392i
$668$	18.4141	+	6.70220i	0.712464	+	0.259316i
$669$		0			0
$670$	32.1739	+	26.9971i	1.24298	+	1.04299i
$671$	11.5088	−	4.18887i	0.444294	−	0.161710i
$672$		0			0
$673$	5.03580	+	28.5594i	0.194116	+	1.10088i	0.913672	+	0.406451i	$0.133234\pi$
$673$	5.03580	+	28.5594i	0.194116	+	1.10088i	−0.719557	+	0.694434i	$0.755655\pi$
$674$	68.5857			2.64182
$675$		0			0
$676$	−48.0000			−1.84615
$677$	−8.08164	−	45.8333i	−0.310603	−	1.76152i	−0.595883	−	0.803071i	$-0.703198\pi$
$677$	−8.08164	−	45.8333i	−0.310603	−	1.76152i	0.285281	−	0.958444i	$-0.407913\pi$
$678$		0			0
$679$	13.1557	−	4.78828i	0.504869	−	0.183757i
$680$	−67.5510	−	56.6821i	−2.59046	−	2.17366i
$681$		0			0
$682$	5.63816	+	2.05212i	0.215896	+	0.0785798i
$683$	−11.0227	−	19.0919i	−0.421772	−	0.730531i	0.574341	−	0.818616i	$-0.305258\pi$
$683$	−11.0227	−	19.0919i	−0.421772	−	0.730531i	−0.996113	+	0.0880857i	$0.971925\pi$
$684$		0			0
$685$	12.0000	−	20.7846i	0.458496	−	0.794139i
$686$	37.5284	−	31.4900i	1.43284	−	1.20230i
$687$		0			0
$688$	7.64052	−	43.3315i	0.291292	−	1.65200i
$689$	1.27605	−	7.23683i	0.0486136	−	0.275701i
$690$		0			0
$691$	36.0041	−	30.2110i	1.36966	−	1.14928i	0.396795	−	0.917907i	$-0.370122\pi$
$691$	36.0041	−	30.2110i	1.36966	−	1.14928i	0.972865	−	0.231374i	$-0.0743221\pi$
$692$	19.5959	−	33.9411i	0.744925	−	1.29025i
$693$		0			0
$694$	30.0000	+	51.9615i	1.13878	+	1.97243i
$695$	23.0177	+	8.37775i	0.873110	+	0.317786i
$696$		0			0
$697$	−27.5776	−	23.1404i	−1.04458	−	0.876503i
$698$	46.0353	−	16.7555i	1.74246	−	0.634205i
$699$		0			0
$700$	1.38919	+	7.87846i	0.0525063	+	0.297778i
$701$	14.6969			0.555096			0.277548	−	0.960712i	$-0.410478\pi$
$701$	14.6969			0.555096			0.277548	+	0.960712i	$0.410478\pi$
$702$		0			0
$703$	−8.00000			−0.301726
$704$	3.40280	+	19.2982i	0.128248	+	0.727329i
$705$		0			0
$706$	−5.63816	+	2.05212i	−0.212195	+	0.0772326i
$707$	7.50567	+	6.29801i	0.282280	+	0.236861i
$708$		0			0
$709$	6.57785	+	2.39414i	0.247036	+	0.0899139i	0.462571	−	0.886582i	$-0.346927\pi$
$709$	6.57785	+	2.39414i	0.247036	+	0.0899139i	−0.215534	+	0.976496i	$0.569149\pi$
$710$	−22.0454	−	38.1838i	−0.827349	−	1.43301i
$711$		0			0
$712$		0			0
$713$	−1.87642	+	1.57450i	−0.0702724	+	0.0589656i
$714$		0			0
$715$	1.04189	−	5.90885i	0.0389644	−	0.220978i
$716$	10.2084	−	57.8946i	0.381505	−	2.16362i
$717$		0			0
$718$	55.1552	−	46.2807i	2.05837	−	1.72718i
$719$	−18.3712	+	31.8198i	−0.685129	+	1.18668i	0.288267	+	0.957550i	$0.406921\pi$
$719$	−18.3712	+	31.8198i	−0.685129	+	1.18668i	−0.973396	+	0.229128i	$0.926412\pi$
$720$		0			0
$721$	7.00000	+	12.1244i	0.260694	+	0.451535i
$722$	−41.4318	−	15.0799i	−1.54193	−	0.561218i
$723$		0			0
$724$	24.5134	+	20.5692i	0.911034	+	0.764448i
$725$	−4.60353	+	1.67555i	−0.170971	+	0.0622284i
$726$		0			0
$727$	2.43107	+	13.7873i	0.0901636	+	0.511343i	0.996122	+	0.0879774i	$0.0280403\pi$
$727$	2.43107	+	13.7873i	0.0901636	+	0.511343i	−0.905959	+	0.423366i	$0.860849\pi$
$728$	9.79796			0.363137
$729$		0			0
$730$	−66.0000			−2.44277
$731$	14.0365	+	79.6051i	0.519160	+	2.94430i
$732$		0			0
$733$	−15.9748	+	5.81434i	−0.590042	+	0.214758i	−0.619748	−	0.784801i	$-0.712765\pi$
$733$	−15.9748	+	5.81434i	−0.590042	+	0.214758i	0.0297060	+	0.999559i	$0.490543\pi$
$734$	−9.38209	−	7.87251i	−0.346299	−	0.290580i
$735$		0			0
$736$		0			0
$737$	−8.57321	−	14.8492i	−0.315798	−	0.546979i
$738$		0			0
$739$	0.500000	−	0.866025i	0.0183928	−	0.0318573i	−0.856683	−	0.515844i	$-0.827478\pi$
$739$	0.500000	−	0.866025i	0.0183928	−	0.0318573i	0.875075	+	0.483987i	$0.160812\pi$
$740$	60.0454	−	50.3841i	2.20731	−	1.85215i
$741$		0			0
$742$	6.25133	−	35.4531i	0.229494	−	1.30152i
$743$	5.52954	−	31.3596i	0.202859	−	1.15047i	−0.697914	−	0.716182i	$-0.745888\pi$
$743$	5.52954	−	31.3596i	0.202859	−	1.15047i	0.900773	−	0.434290i	$-0.143001\pi$
$744$		0			0
$745$	−22.9813	+	19.2836i	−0.841971	+	0.706497i
$746$	42.8661	−	74.2462i	1.56944	−	2.71835i
$747$		0			0
$748$	36.0000	+	62.3538i	1.31629	+	2.27988i
$749$	27.6212	+	10.0533i	1.00926	+	0.367340i
$750$		0			0
$751$	19.9172	+	16.7125i	0.726787	+	0.609847i	0.929254	−	0.369442i	$-0.120451\pi$
$751$	19.9172	+	16.7125i	0.726787	+	0.609847i	−0.202466	+	0.979289i	$0.564896\pi$
$752$	36.8283	−	13.4044i	1.34299	−	0.488808i
$753$		0			0
$754$	2.08378	+	11.8177i	0.0758867	+	0.430375i
$755$	12.2474			0.445730
$756$		0			0
$757$	−7.00000			−0.254419			−0.127210	−	0.991876i	$-0.540602\pi$
$757$	−7.00000			−0.254419			−0.127210	+	0.991876i	$0.540602\pi$
$758$	−3.40280	−	19.2982i	−0.123595	−	0.700943i
$759$		0			0
$760$	−11.2763	+	4.10424i	−0.409035	+	0.148876i
$761$	1.87642	+	1.57450i	0.0680201	+	0.0570756i	0.676164	−	0.736751i	$-0.263641\pi$
$761$	1.87642	+	1.57450i	0.0680201	+	0.0570756i	−0.608144	+	0.793827i	$0.708086\pi$
$762$		0			0
$763$	1.87939	+	0.684040i	0.0680383	+	0.0247639i
$764$	19.5959	+	33.9411i	0.708955	+	1.22795i
$765$		0			0
$766$	−42.0000	+	72.7461i	−1.51752	+	2.62842i
$767$	−1.87642	+	1.57450i	−0.0677535	+	0.0568520i
$768$		0			0
$769$	−6.42498	+	36.4379i	−0.231691	+	1.31398i	0.617781	+	0.786350i	$0.288032\pi$
$769$	−6.42498	+	36.4379i	−0.231691	+	1.31398i	−0.849472	+	0.527634i	$0.823079\pi$
$770$	5.10419	−	28.9473i	0.183942	−	1.04319i
$771$		0			0
$772$	33.7060	−	28.2827i	1.21310	−	1.01792i
$773$	−22.0454	+	38.1838i	−0.792918	+	1.37337i	0.131235	+	0.991351i	$0.458106\pi$
$773$	−22.0454	+	38.1838i	−0.792918	+	1.37337i	−0.924153	+	0.382023i	$0.875227\pi$
$774$		0			0
$775$	0.500000	+	0.866025i	0.0179605	+	0.0311086i
$776$	−32.2247	−	11.7288i	−1.15680	−	0.421041i
$777$		0			0
$778$	−50.5589	−	42.4240i	−1.81263	−	1.52097i
$779$	−4.60353	+	1.67555i	−0.164939	+	0.0600328i
$780$		0			0
$781$	3.12567	+	17.7265i	0.111845	+	0.634305i
$782$	−44.0908			−1.57668
$783$		0			0
$784$	−12.0000			−0.428571
$785$	7.23094	+	41.0087i	0.258083	+	1.46366i
$786$		0			0
$787$	23.4923	−	8.55050i	0.837411	−	0.304793i	0.112514	−	0.993650i	$-0.464110\pi$
$787$	23.4923	−	8.55050i	0.837411	−	0.304793i	0.724897	+	0.688858i	$0.241887\pi$
$788$	−45.0340	−	37.7880i	−1.60427	−	1.34614i
$789$		0			0
$790$	−39.4671	−	14.3648i	−1.40418	−	0.511078i
$791$	−9.79796	−	16.9706i	−0.348375	−	0.603404i
$792$		0			0
$793$	2.50000	−	4.33013i	0.0887776	−	0.153767i
$794$	1.87642	−	1.57450i	0.0665916	−	0.0558770i
$795$		0			0
$796$	−0.694593	+	3.93923i	−0.0246192	+	0.139622i
$797$	−7.23094	+	41.0087i	−0.256133	+	1.45260i	0.537014	+	0.843573i	$0.319552\pi$
$797$	−7.23094	+	41.0087i	−0.256133	+	1.45260i	−0.793147	+	0.609030i	$0.791559\pi$
$798$		0			0
$799$	−55.1552	+	46.2807i	−1.95125	+	1.63729i
$800$		0			0
$801$		0			0
$802$	−42.0000	−	72.7461i	−1.48307	−	2.56876i
$803$	25.3194	+	9.21552i	0.893504	+	0.325209i
$804$		0			0
$805$	9.19253	+	7.71345i	0.323994	+	0.271863i
$806$	2.30177	−	0.837775i	0.0810763	−	0.0295094i
$807$		0			0
$808$	−4.16756	−	23.6354i	−0.146614	−	0.831490i
$809$	−22.0454			−0.775075			−0.387538	−	0.921854i	$-0.626674\pi$
$809$	−22.0454			−0.775075			−0.387538	+	0.921854i	$0.626674\pi$
$810$		0			0
$811$	35.0000			1.22902			0.614508	−	0.788911i	$-0.289355\pi$
$811$	35.0000			1.22902			0.614508	+	0.788911i	$0.289355\pi$
$812$	6.80559	+	38.5964i	0.238829	+	1.35447i
$813$		0			0
$814$	−45.1052	+	16.4170i	−1.58094	+	0.575414i
$815$	−18.7642	−	15.7450i	−0.657281	−	0.551524i
$816$		0			0
$817$	10.3366	+	3.76222i	0.361633	+	0.131623i
$818$	−34.2929	−	59.3970i	−1.19902	−	2.07677i
$819$		0			0
$820$	24.0000	−	41.5692i	0.838116	−	1.45166i
$821$	−30.0227	+	25.1920i	−1.04780	+	0.879208i	−0.992860	−	0.119282i	$-0.961941\pi$
$821$	−30.0227	+	25.1920i	−1.04780	+	0.879208i	−0.0549386	+	0.998490i	$0.517496\pi$
$822$		0			0
$823$	6.07769	−	34.4683i	0.211855	−	1.20149i	−0.674427	−	0.738342i	$-0.735609\pi$
$823$	6.07769	−	34.4683i	0.211855	−	1.20149i	0.886282	−	0.463147i	$-0.153280\pi$
$824$	5.95489	−	33.7719i	0.207448	−	1.17650i
$825$		0			0
$826$	−9.19253	+	7.71345i	−0.319849	+	0.268385i
$827$	−11.0227	+	19.0919i	−0.383297	+	0.663890i	−0.991531	−	0.129868i	$-0.958545\pi$
$827$	−11.0227	+	19.0919i	−0.383297	+	0.663890i	0.608234	+	0.793757i	$0.291878\pi$
$828$		0			0
$829$	18.5000	+	32.0429i	0.642532	+	1.11290i	0.984866	+	0.173319i	$0.0554492\pi$
$829$	18.5000	+	32.0429i	0.642532	+	1.11290i	−0.342334	+	0.939578i	$0.611217\pi$
$830$	69.0530	+	25.1332i	2.39687	+	0.872388i
$831$		0			0
$832$	6.12836	+	5.14230i	0.212463	+	0.178277i
$833$	20.7159	−	7.53997i	0.717764	−	0.261245i
$834$		0			0
$835$	−2.08378	−	11.8177i	−0.0721121	−	0.408968i
$836$	9.79796			0.338869
$837$		0			0
$838$	84.0000			2.90173
$839$	0.850699	+	4.82455i	0.0293694	+	0.166562i	0.995965	−	0.0897451i	$-0.0286052\pi$
$839$	0.850699	+	4.82455i	0.0293694	+	0.166562i	−0.966595	+	0.256307i	$0.917494\pi$
$840$		0			0
$841$	4.69846	−	1.71010i	0.162016	−	0.0589690i
$842$	−3.75284	−	3.14900i	−0.129331	−	0.108522i
$843$		0			0
$844$	3.75877	+	1.36808i	0.129382	+	0.0470913i
$845$	14.6969	+	25.4558i	0.505590	+	0.875708i
$846$		0			0
$847$	5.00000	−	8.66025i	0.171802	−	0.297570i
$848$	−22.5170	+	18.8940i	−0.773238	+	0.648823i
$849$		0			0
$850$	−3.12567	+	17.7265i	−0.107210	+	0.608015i
$851$	3.40280	−	19.2982i	0.116646	−	0.661534i
$852$		0			0
$853$	−9.95858	+	8.35624i	−0.340975	+	0.286112i	−0.797154	−	0.603776i	$-0.793662\pi$
$853$	−9.95858	+	8.35624i	−0.340975	+	0.286112i	0.456179	+	0.889888i	$0.349218\pi$
$854$	12.2474	−	21.2132i	0.419099	−	0.725901i
$855$		0			0
$856$	−36.0000	−	62.3538i	−1.23045	−	2.13121i
$857$	23.0177	+	8.37775i	0.786269	+	0.286178i	0.703784	−	0.710414i	$-0.251492\pi$
$857$	23.0177	+	8.37775i	0.786269	+	0.286178i	0.0824847	+	0.996592i	$0.473714\pi$
$858$		0			0
$859$	19.9172	+	16.7125i	0.679565	+	0.570222i	0.915879	−	0.401454i	$-0.131495\pi$
$859$	19.9172	+	16.7125i	0.679565	+	0.570222i	−0.236315	+	0.971677i	$0.575940\pi$
$860$	−101.278	+	36.8621i	−3.45354	+	1.25699i
$861$		0			0
$862$	−3.12567	−	17.7265i	−0.106461	−	0.603768i
$863$	7.34847			0.250145			0.125072	−	0.992148i	$-0.460084\pi$
$863$	7.34847			0.250145			0.125072	+	0.992148i	$0.460084\pi$
$864$		0			0
$865$	−24.0000			−0.816024
$866$	−7.23094	−	41.0087i	−0.245717	−	1.39353i
$867$		0			0
$868$	7.51754	−	2.73616i	0.255162	−	0.0928714i
$869$	13.1349	+	11.0215i	0.445572	+	0.373879i
$870$		0			0
$871$	−6.57785	−	2.39414i	−0.222882	−	0.0811224i
$872$	−2.44949	−	4.24264i	−0.0829502	−	0.143674i
$873$		0			0
$874$	−3.00000	+	5.19615i	−0.101477	+	0.175762i
$875$	−15.0113	+	12.5960i	−0.507476	+	0.425823i
$876$		0			0
$877$	1.38919	−	7.87846i	0.0469095	−	0.266037i	−0.952328	−	0.305075i	$-0.901318\pi$
$877$	1.38919	−	7.87846i	0.0469095	−	0.266037i	0.999238	+	0.0390385i	$0.0124295\pi$
$878$	−5.95489	+	33.7719i	−0.200968	+	1.13975i
$879$		0			0
$880$	−18.3851	+	15.4269i	−0.619760	+	0.520041i
$881$	18.3712	−	31.8198i	0.618941	−	1.07204i	−0.370739	−	0.928737i	$-0.620896\pi$
$881$	18.3712	−	31.8198i	0.618941	−	1.07204i	0.989679	−	0.143299i	$-0.0457712\pi$
$882$		0			0
$883$	−8.50000	−	14.7224i	−0.286048	−	0.495449i	0.686815	−	0.726832i	$-0.259008\pi$
$883$	−8.50000	−	14.7224i	−0.286048	−	0.495449i	−0.972863	+	0.231383i	$0.925675\pi$
$884$	27.6212	+	10.0533i	0.929002	+	0.338129i
$885$		0			0
$886$	−22.9813	−	19.2836i	−0.772073	−	0.647846i
$887$	−16.1124	+	5.86442i	−0.541001	+	0.196908i	−0.598044	−	0.801464i	$-0.704055\pi$
$887$	−16.1124	+	5.86442i	−0.541001	+	0.196908i	0.0570430	+	0.998372i	$0.481833\pi$
$888$		0			0
$889$	−6.59863	−	37.4227i	−0.221311	−	1.25512i
$890$		0			0
$891$		0			0
$892$	−28.0000			−0.937509
$893$	1.70140	+	9.64911i	0.0569351	+	0.322895i
$894$		0			0
$895$	−33.8289	+	12.3127i	−1.13078	+	0.411569i
$896$	30.0227	+	25.1920i	1.00299	+	0.841607i
$897$		0			0
$898$	−50.7434	−	18.4691i	−1.69333	−	0.616321i
$899$	2.44949	+	4.24264i	0.0816951	+	0.141500i
$900$		0			0
$901$	27.0000	−	46.7654i	0.899500	−	1.55798i
$902$	−22.5170	+	18.8940i	−0.749735	+	0.629102i
$903$		0			0
$904$	−8.33511	+	47.2708i	−0.277222	+	1.57220i
$905$	3.40280	−	19.2982i	0.113113	−	0.641494i
$906$		0			0
$907$	−5.36231	+	4.49951i	−0.178053	+	0.149404i	−0.727458	−	0.686152i	$-0.759299\pi$
$907$	−5.36231	+	4.49951i	−0.178053	+	0.149404i	0.549406	+	0.835556i	$0.314854\pi$
$908$	19.5959	−	33.9411i	0.650313	−	1.12638i
$909$		0			0
$910$	−6.00000	−	10.3923i	−0.198898	−	0.344502i
$911$	−11.5088	−	4.18887i	−0.381305	−	0.138784i	0.144254	−	0.989541i	$-0.453922\pi$
$911$	−11.5088	−	4.18887i	−0.381305	−	0.138784i	−0.525559	+	0.850757i	$0.676144\pi$
$912$		0			0
$913$	−22.9813	−	19.2836i	−0.760571	−	0.638195i
$914$	66.7513	−	24.2955i	2.20794	−	0.803623i
$915$		0			0
$916$	−0.694593	−	3.93923i	−0.0229500	−	0.130156i
$917$	−24.4949			−0.808893
$918$		0			0
$919$	20.0000			0.659739			0.329870	−	0.944027i	$-0.392995\pi$
$919$	20.0000			0.659739			0.329870	+	0.944027i	$0.392995\pi$
$920$	−5.10419	−	28.9473i	−0.168280	−	0.954365i
$921$		0			0
$922$	62.0197	−	22.5733i	2.04251	−	0.743413i
$923$	5.62925	+	4.72350i	0.185289	+	0.155476i
$924$		0			0
$925$	−7.51754	−	2.73616i	−0.247175	−	0.0899644i
$926$	−23.2702	−	40.3051i	−0.764705	−	1.32451i
$927$		0			0
$928$		0			0
$929$	20.6406	−	17.3195i	0.677196	−	0.568235i	−0.237989	−	0.971268i	$-0.576488\pi$
$929$	20.6406	−	17.3195i	0.677196	−	0.568235i	0.915186	+	0.403033i	$0.132044\pi$
$930$		0			0
$931$	0.520945	−	2.95442i	0.0170733	−	0.0968273i
$932$	5.10419	−	28.9473i	0.167193	−	0.948201i
$933$		0			0
$934$	27.5776	−	23.1404i	0.902367	−	0.757176i
$935$	22.0454	−	38.1838i	0.720962	−	1.24874i
$936$		0			0
$937$	−4.00000	−	6.92820i	−0.130674	−	0.226335i	0.793262	−	0.608880i	$-0.208381\pi$
$937$	−4.00000	−	6.92820i	−0.130674	−	0.226335i	−0.923937	+	0.382545i	$0.875048\pi$
$938$	−32.2247	−	11.7288i	−1.05218	−	0.382960i
$939$		0			0
$940$	−73.5403	−	61.7076i	−2.39862	−	2.01268i
$941$	−9.20707	+	3.35110i	−0.300142	+	0.109243i	−0.487701	−	0.873011i	$-0.662164\pi$
$941$	−9.20707	+	3.35110i	−0.300142	+	0.109243i	0.187559	+	0.982253i	$0.439942\pi$
$942$		0			0
$943$	−2.08378	−	11.8177i	−0.0678572	−	0.384837i
$944$	9.79796			0.318896
$945$		0			0
$946$	66.0000			2.14585
$947$	−4.25349	−	24.1228i	−0.138220	−	0.783885i	−0.972563	−	0.232639i	$-0.925264\pi$
$947$	−4.25349	−	24.1228i	−0.138220	−	0.783885i	0.834343	−	0.551245i	$-0.185847\pi$
$948$		0			0
$949$	10.3366	−	3.76222i	0.335541	−	0.122127i
$950$	1.87642	+	1.57450i	0.0608790	+	0.0510836i
$951$		0			0
$952$	67.6579	+	24.6255i	2.19280	+	0.798115i
$953$	14.6969	+	25.4558i	0.476081	+	0.824596i	0.999624	−	0.0274030i	$-0.00872374\pi$
$953$	14.6969	+	25.4558i	0.476081	+	0.824596i	−0.523544	+	0.851999i	$0.675390\pi$
$954$		0			0
$955$	12.0000	−	20.7846i	0.388311	−	0.672574i
$956$	7.50567	−	6.29801i	0.242751	−	0.203692i
$957$		0			0
$958$	−11.4608	+	64.9973i	−0.370281	+	2.09997i
$959$	−3.40280	+	19.2982i	−0.109882	+	0.623172i
$960$		0			0
$961$	−22.9813	+	19.2836i	−0.741333	+	0.622053i
$962$	−9.79796	+	16.9706i	−0.315899	+	0.547153i
$963$		0			0
$964$	32.0000	+	55.4256i	1.03065	+	1.78514i
$965$	−25.3194	−	9.21552i	−0.815062	−	0.296658i
$966$		0			0
$967$	−5.36231	−	4.49951i	−0.172440	−	0.144695i	0.552483	−	0.833524i	$-0.313680\pi$
$967$	−5.36231	−	4.49951i	−0.172440	−	0.144695i	−0.724923	+	0.688830i	$0.758125\pi$
$968$	−23.0177	+	8.37775i	−0.739816	+	0.269271i
$969$		0			0
$970$	7.29322	+	41.3619i	0.234171	+	1.32805i
$971$	−29.3939			−0.943294			−0.471647	−	0.881787i	$-0.656340\pi$
$971$	−29.3939			−0.943294			−0.471647	+	0.881787i	$0.656340\pi$
$972$		0			0
$973$	−20.0000			−0.641171
$974$	−14.8872	−	84.4297i	−0.477018	−	2.70530i
$975$		0			0
$976$	−18.7939	+	6.84040i	−0.601577	+	0.218956i
$977$	18.7642	+	15.7450i	0.600319	+	0.503728i	0.891548	−	0.452926i	$-0.149620\pi$
$977$	18.7642	+	15.7450i	0.600319	+	0.503728i	−0.291229	+	0.956653i	$0.594064\pi$
$978$		0			0
$979$		0			0
$980$	14.6969	+	25.4558i	0.469476	+	0.813157i
$981$		0			0
$982$	48.0000	−	83.1384i	1.53174	−	2.65305i
$983$	3.75284	−	3.14900i	0.119697	−	0.100438i	−0.580974	−	0.813922i	$-0.697328\pi$
$983$	3.75284	−	3.14900i	0.119697	−	0.100438i	0.700671	+	0.713484i	$0.252884\pi$
$984$		0			0
$985$	−6.25133	+	35.4531i	−0.199184	+	1.12963i
$986$	−15.3126	+	86.8420i	−0.487652	+	2.76561i
$987$		0			0
$988$	3.06418	−	2.57115i	0.0974845	−	0.0817992i
$989$	−13.4722	+	23.3345i	−0.428391	+	0.741995i
$990$		0			0
$991$	3.50000	+	6.06218i	0.111181	+	0.192571i	0.916247	−	0.400614i	$-0.131203\pi$
$991$	3.50000	+	6.06218i	0.111181	+	0.192571i	−0.805066	+	0.593186i	$0.797870\pi$
$992$		0			0
$993$		0			0
$994$	27.5776	+	23.1404i	0.874708	+	0.733967i
$995$	2.30177	−	0.837775i	0.0729709	−	0.0265592i
$996$		0			0
$997$	8.68241	+	49.2404i	0.274975	+	1.55946i	0.739042	+	0.673659i	$0.235278\pi$
$997$	8.68241	+	49.2404i	0.274975	+	1.55946i	−0.464068	+	0.885800i	$0.653611\pi$
$998$	−4.89898			−0.155074
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.e.p.82.1		12
3.2	odd	2	inner	729.2.e.p.82.2		12
9.2	odd	6	inner	729.2.e.p.325.2		12
9.4	even	3	inner	729.2.e.p.568.2		12
9.5	odd	6	inner	729.2.e.p.568.1		12
9.7	even	3	inner	729.2.e.p.325.1		12
27.2	odd	18	inner	729.2.e.p.649.2		12
27.4	even	9		243.2.c.c.163.2		4
27.5	odd	18		243.2.a.d.1.2	yes	2
27.7	even	9	inner	729.2.e.p.406.1		12
27.11	odd	18	inner	729.2.e.p.163.1		12
27.13	even	9		243.2.c.c.82.2		4
27.14	odd	18		243.2.c.c.82.1		4
27.16	even	9	inner	729.2.e.p.163.2		12
27.20	odd	18	inner	729.2.e.p.406.2		12
27.22	even	9		243.2.a.d.1.1	✓	2
27.23	odd	18		243.2.c.c.163.1		4
27.25	even	9	inner	729.2.e.p.649.1		12
108.59	even	18		3888.2.a.z.1.1		2
108.103	odd	18		3888.2.a.z.1.2		2
135.49	even	18		6075.2.a.bn.1.2		2
135.59	odd	18		6075.2.a.bn.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
243.2.a.d.1.1	✓	2	27.22	even	9
243.2.a.d.1.2	yes	2	27.5	odd	18
243.2.c.c.82.1		4	27.14	odd	18
243.2.c.c.82.2		4	27.13	even	9
243.2.c.c.163.1		4	27.23	odd	18
243.2.c.c.163.2		4	27.4	even	9
729.2.e.p.82.1		12	1.1	even	1	trivial
729.2.e.p.82.2		12	3.2	odd	2	inner
729.2.e.p.163.1		12	27.11	odd	18	inner
729.2.e.p.163.2		12	27.16	even	9	inner
729.2.e.p.325.1		12	9.7	even	3	inner
729.2.e.p.325.2		12	9.2	odd	6	inner
729.2.e.p.406.1		12	27.7	even	9	inner
729.2.e.p.406.2		12	27.20	odd	18	inner
729.2.e.p.568.1		12	9.5	odd	6	inner
729.2.e.p.568.2		12	9.4	even	3	inner
729.2.e.p.649.1		12	27.25	even	9	inner
729.2.e.p.649.2		12	27.2	odd	18	inner
3888.2.a.z.1.1		2	108.59	even	18
3888.2.a.z.1.2		2	108.103	odd	18
6075.2.a.bn.1.1		2	135.59	odd	18
6075.2.a.bn.1.2		2	135.49	even	18

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.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.425349 - 2.41228i) q^{2} +(-3.75877 + 1.36808i) q^{4} +(1.87642 + 1.57450i) q^{5} +(-1.87939 - 0.684040i) q^{7} +(2.44949 + 4.24264i) q^{8} +O(q^{10})\)	\(q+(-0.425349 - 2.41228i) q^{2} +(-3.75877 + 1.36808i) q^{4} +(1.87642 + 1.57450i) q^{5} +(-1.87939 - 0.684040i) q^{7} +(2.44949 + 4.24264i) q^{8} +(3.00000 - 5.19615i) q^{10} +(-1.87642 + 1.57450i) q^{11} +(-0.173648 + 0.984808i) q^{13} +(-0.850699 + 4.82455i) q^{14} +(3.06418 - 2.57115i) q^{16} +(-3.67423 + 6.36396i) q^{17} +(0.500000 + 0.866025i) q^{19} +(-9.20707 - 3.35110i) q^{20} +(4.59627 + 3.85673i) q^{22} +(-2.30177 + 0.837775i) q^{23} +(0.173648 + 0.984808i) q^{25} +2.44949 q^{26} +8.00000 q^{28} +(0.850699 + 4.82455i) q^{29} +(0.939693 - 0.342020i) q^{31} +(16.9145 + 6.15636i) q^{34} +(-2.44949 - 4.24264i) q^{35} +(-4.00000 + 6.92820i) q^{37} +(1.87642 - 1.57450i) q^{38} +(-2.08378 + 11.8177i) q^{40} +(-0.850699 + 4.82455i) q^{41} +(8.42649 - 7.07066i) q^{43} +(4.89898 - 8.48528i) q^{44} +(3.00000 + 5.19615i) q^{46} +(9.20707 + 3.35110i) q^{47} +(-2.29813 - 1.92836i) q^{49} +(2.30177 - 0.837775i) q^{50} +(-0.694593 - 3.93923i) q^{52} -7.34847 q^{53} -6.00000 q^{55} +(-1.70140 - 9.64911i) q^{56} +(11.2763 - 4.10424i) q^{58} +(1.87642 + 1.57450i) q^{59} +(-4.69846 - 1.71010i) q^{61} +(-1.22474 - 2.12132i) q^{62} +(4.00000 - 6.92820i) q^{64} +(-1.87642 + 1.57450i) q^{65} +(-1.21554 + 6.89365i) q^{67} +(5.10419 - 28.9473i) q^{68} +(-9.19253 + 7.71345i) q^{70} +(3.67423 - 6.36396i) q^{71} +(-5.50000 - 9.52628i) q^{73} +(18.4141 + 6.70220i) q^{74} +(-3.06418 - 2.57115i) q^{76} +(4.60353 - 1.67555i) q^{77} +(-1.21554 - 6.89365i) q^{79} +9.79796 q^{80} +12.0000 q^{82} +(2.12675 + 12.0614i) q^{83} +(-16.9145 + 6.15636i) q^{85} +(-20.6406 - 17.3195i) q^{86} +(-11.2763 - 4.10424i) q^{88} +(1.00000 - 1.73205i) q^{91} +(7.50567 - 6.29801i) q^{92} +(4.16756 - 23.6354i) q^{94} +(-0.425349 + 2.41228i) q^{95} +(-5.36231 + 4.49951i) q^{97} +(-3.67423 + 6.36396i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q+O(q^{10}) \) 12 * q	\( 12 q + 36 q^{10} + 6 q^{19} + 96 q^{28} - 48 q^{37} + 36 q^{46} - 72 q^{55} + 48 q^{64} - 66 q^{73} + 144 q^{82} + 12 q^{91}+O(q^{100}) \) 12 * q + 36 * q^10 + 6 * q^19 + 96 * q^28 - 48 * q^37 + 36 * q^46 - 72 * q^55 + 48 * q^64 - 66 * q^73 + 144 * q^82 + 12 * q^91

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