LMFDB - Embedded newform 1638.2.dm.e.1117.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1638,2,Mod(415,1638)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1638, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 3]))

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

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

chi := DirichletCharacter("1638.415");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1638.dm (of order $6$, degree $2$, 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:	$13.0794958511$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 26 x^{18} + 431 x^{16} - 4370 x^{14} + 32381 x^{12} - 160412 x^{10} + 573820 x^{8} + \cdots + 810000 $ x^20 - 26x^18 + 431x^16 - 4370x^14 + 32381x^12 - 160412x^10 + 573820x^8 - 1203000x^6 + 1802736x^4 - 1479600*x^2 + 810000
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 546)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1117.9
Root			$-2.18313 + 1.26043i$ of defining polynomial
Character	$\chi$	$=$	1638.1117
Dual form			1638.2.dm.e.415.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(2.18313 - 1.26043i) q^{5} +(1.47350 + 2.19745i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(2.18313 - 1.26043i) q^{5} +(1.47350 + 2.19745i) q^{7} -1.00000i q^{8} +(1.26043 - 2.18313i) q^{10} +(4.88772 + 2.82193i) q^{11} +(-3.13524 - 1.78052i) q^{13} +(2.37482 + 1.16630i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-0.123703 + 0.214260i) q^{17} +(2.70459 - 1.56150i) q^{19} -2.52086i q^{20} +5.64385 q^{22} +(1.80107 + 3.11954i) q^{23} +(0.677364 - 1.17323i) q^{25} +(-3.60546 + 0.0256500i) q^{26} +(2.63980 - 0.177364i) q^{28} +4.24895 q^{29} +(-5.30267 - 3.06150i) q^{31} +(-0.866025 - 0.500000i) q^{32} +0.247406i q^{34} +(5.98657 + 2.94007i) q^{35} +(-7.01858 + 4.05218i) q^{37} +(1.56150 - 2.70459i) q^{38} +(-1.26043 - 2.18313i) q^{40} +8.59917i q^{41} +5.56103 q^{43} +(4.88772 - 2.82193i) q^{44} +(3.11954 + 1.80107i) q^{46} +(5.78854 - 3.34201i) q^{47} +(-2.65759 + 6.47590i) q^{49} -1.35473i q^{50} +(-3.10959 + 1.82494i) q^{52} +(3.28052 - 5.68202i) q^{53} +14.2274 q^{55} +(2.19745 - 1.47350i) q^{56} +(3.67970 - 2.12447i) q^{58} +(-6.89004 - 3.97797i) q^{59} +(-6.39419 - 11.0751i) q^{61} -6.12299 q^{62} -1.00000 q^{64} +(-9.08886 + 0.0646601i) q^{65} +(-10.5562 - 6.09461i) q^{67} +(0.123703 + 0.214260i) q^{68} +(6.65456 - 0.447110i) q^{70} -4.06419i q^{71} +(6.81789 + 3.93631i) q^{73} +(-4.05218 + 7.01858i) q^{74} -3.12299i q^{76} +(1.00102 + 14.8986i) q^{77} +(3.22763 + 5.59041i) q^{79} +(-2.18313 - 1.26043i) q^{80} +(4.29959 + 7.44710i) q^{82} -0.662485i q^{83} +0.623675i q^{85} +(4.81600 - 2.78052i) q^{86} +(2.82193 - 4.88772i) q^{88} +(-4.86906 + 2.81116i) q^{89} +(-0.707191 - 9.51314i) q^{91} +3.60213 q^{92} +(3.34201 - 5.78854i) q^{94} +(3.93631 - 6.81789i) q^{95} -16.8748i q^{97} +(0.936412 + 6.93708i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 10 q^{4}+O(q^{10}) $ 20 * q + 10 * q^4	$ 20 q + 10 q^{4} + 4 q^{10} + 4 q^{13} + 2 q^{14} - 10 q^{16} + 6 q^{17} - 12 q^{22} + 16 q^{23} + 2 q^{25} + 4 q^{26} + 28 q^{29} - 16 q^{35} - 10 q^{38} - 4 q^{40} + 24 q^{43} + 2 q^{49} + 2 q^{52} + 22 q^{53} + 88 q^{55} + 10 q^{56} + 14 q^{61} - 40 q^{62} - 20 q^{64} - 20 q^{65} - 6 q^{68} - 24 q^{74} + 28 q^{77} + 4 q^{79} + 12 q^{82} - 6 q^{88} + 68 q^{91} + 32 q^{92} - 18 q^{94} - 8 q^{95}+O(q^{100}) $ 20 * q + 10 * q^4 + 4 * q^10 + 4 * q^13 + 2 * q^14 - 10 * q^16 + 6 * q^17 - 12 * q^22 + 16 * q^23 + 2 * q^25 + 4 * q^26 + 28 * q^29 - 16 * q^35 - 10 * q^38 - 4 * q^40 + 24 * q^43 + 2 * q^49 + 2 * q^52 + 22 * q^53 + 88 * q^55 + 10 * q^56 + 14 * q^61 - 40 * q^62 - 20 * q^64 - 20 * q^65 - 6 * q^68 - 24 * q^74 + 28 * q^77 + 4 * q^79 + 12 * q^82 - 6 * q^88 + 68 * q^91 + 32 * q^92 - 18 * q^94 - 8 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times$.

$n$	$379$	$703$	$911$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	2.18313	−	1.26043i	0.976324	−	0.563681i	0.0751659	−	0.997171i	$-0.476051\pi$
$5$	2.18313	−	1.26043i	0.976324	−	0.563681i	0.901158	+	0.433490i	$0.142718\pi$
$6$		0			0
$7$	1.47350	+	2.19745i	0.556931	+	0.830559i
$7$	1.47350	+	2.19745i	0.556931	+	0.830559i
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	1.26043	−	2.18313i	0.398583	−	0.690366i
$11$	4.88772	+	2.82193i	1.47370	+	0.850843i	0.999562	−	0.0296062i	$-0.00942532\pi$
$11$	4.88772	+	2.82193i	1.47370	+	0.850843i	0.474141	+	0.880449i	$0.342759\pi$
$12$		0			0
$13$	−3.13524	−	1.78052i	−0.869561	−	0.493826i
$13$	−3.13524	−	1.78052i	−0.869561	−	0.493826i
$14$	2.37482	+	1.16630i	0.634696	+	0.311706i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−0.123703	+	0.214260i	−0.0300024	+	0.0519656i	−0.880637	−	0.473792i	$-0.842885\pi$
$17$	−0.123703	+	0.214260i	−0.0300024	+	0.0519656i	0.850634	+	0.525758i	$0.176218\pi$
$18$		0			0
$19$	2.70459	−	1.56150i	0.620476	−	0.358232i	−0.156578	−	0.987666i	$-0.550046\pi$
$19$	2.70459	−	1.56150i	0.620476	−	0.358232i	0.777054	+	0.629434i	$0.216713\pi$
$20$		−	2.52086i		−	0.563681i
$21$		0			0
$22$	5.64385			1.20327
$23$	1.80107	+	3.11954i	0.375548	+	0.650469i	0.990409	−	0.138167i	$-0.0441210\pi$
$23$	1.80107	+	3.11954i	0.375548	+	0.650469i	−0.614860	+	0.788636i	$0.710788\pi$
$24$		0			0
$25$	0.677364	−	1.17323i	0.135473	−	0.234646i
$26$	−3.60546	+	0.0256500i	−0.707089	+	0.00503038i
$27$		0			0
$28$	2.63980	−	0.177364i	0.498875	−	0.0335187i
$29$	4.24895			0.789010			0.394505	−	0.918894i	$-0.370916\pi$
$29$	4.24895			0.789010			0.394505	+	0.918894i	$0.370916\pi$
$30$		0			0
$31$	−5.30267	−	3.06150i	−0.952387	−	0.549861i	−0.0585655	−	0.998284i	$-0.518653\pi$
$31$	−5.30267	−	3.06150i	−0.952387	−	0.549861i	−0.893822	+	0.448423i	$0.851986\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$		0			0
$34$			0.247406i			0.0424298i
$35$	5.98657	+	2.94007i	1.01192	+	0.496963i
$36$		0			0
$37$	−7.01858	+	4.05218i	−1.15385	+	0.666174i	−0.949822	−	0.312791i	$-0.898736\pi$
$37$	−7.01858	+	4.05218i	−1.15385	+	0.666174i	−0.204026	+	0.978966i	$0.565403\pi$
$38$	1.56150	−	2.70459i	0.253308	−	0.438743i
$39$		0			0
$40$	−1.26043	−	2.18313i	−0.199291	−	0.345183i
$41$			8.59917i			1.34296i	0.741020	+	0.671482i	$0.234342\pi$
$41$			8.59917i			1.34296i	−0.741020	+	0.671482i	$0.765658\pi$
$42$		0			0
$43$	5.56103			0.848050			0.424025	−	0.905651i	$-0.360617\pi$
$43$	5.56103			0.848050			0.424025	+	0.905651i	$0.360617\pi$
$44$	4.88772	−	2.82193i	0.736851	−	0.425421i
$45$		0			0
$46$	3.11954	+	1.80107i	0.459951	+	0.265553i
$47$	5.78854	−	3.34201i	0.844345	−	0.487483i	−0.0143939	−	0.999896i	$-0.504582\pi$
$47$	5.78854	−	3.34201i	0.844345	−	0.487483i	0.858739	+	0.512414i	$0.171249\pi$
$48$		0			0
$49$	−2.65759	+	6.47590i	−0.379655	+	0.925128i
$50$		−	1.35473i		−	0.191588i
$51$		0			0
$52$	−3.10959	+	1.82494i	−0.431223	+	0.253074i
$53$	3.28052	−	5.68202i	0.450614	−	0.780486i	−0.547811	−	0.836602i	$-0.684539\pi$
$53$	3.28052	−	5.68202i	0.450614	−	0.780486i	0.998424	+	0.0561167i	$0.0178719\pi$
$54$		0			0
$55$	14.2274			1.91842
$56$	2.19745	−	1.47350i	0.293647	−	0.196905i
$57$		0			0
$58$	3.67970	−	2.12447i	0.483168	−	0.278957i
$59$	−6.89004	−	3.97797i	−0.897007	−	0.517887i	−0.0207791	−	0.999784i	$-0.506615\pi$
$59$	−6.89004	−	3.97797i	−0.897007	−	0.517887i	−0.876228	+	0.481897i	$0.839948\pi$
$60$		0			0
$61$	−6.39419	−	11.0751i	−0.818693	−	1.41802i	−0.906646	−	0.421892i	$-0.861366\pi$
$61$	−6.39419	−	11.0751i	−0.818693	−	1.41802i	0.0879534	−	0.996125i	$-0.471967\pi$
$62$	−6.12299			−0.777621
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−9.08886	+	0.0646601i	−1.12733	+	0.00802010i
$66$		0			0
$67$	−10.5562	−	6.09461i	−1.28964	−	0.744575i	−0.311051	−	0.950393i	$-0.600681\pi$
$67$	−10.5562	−	6.09461i	−1.28964	−	0.744575i	−0.978590	+	0.205818i	$0.934014\pi$
$68$	0.123703	+	0.214260i	0.0150012	+	0.0259828i
$69$		0			0
$70$	6.65456	−	0.447110i	0.795372	−	0.0534399i
$71$		−	4.06419i		−	0.482330i	−0.970484	−	0.241165i	$-0.922470\pi$
$71$		−	4.06419i		−	0.482330i	0.970484	−	0.241165i	$-0.0775295\pi$
$72$		0			0
$73$	6.81789	+	3.93631i	0.797974	+	0.460710i	0.842762	−	0.538286i	$-0.180928\pi$
$73$	6.81789	+	3.93631i	0.797974	+	0.460710i	−0.0447882	+	0.998997i	$0.514261\pi$
$74$	−4.05218	+	7.01858i	−0.471056	+	0.815894i
$75$		0			0
$76$		−	3.12299i		−	0.358232i
$77$	1.00102	+	14.8986i	0.114077	+	1.69786i
$78$		0			0
$79$	3.22763	+	5.59041i	0.363136	+	0.628971i	0.988475	−	0.151383i	$-0.0483726\pi$
$79$	3.22763	+	5.59041i	0.363136	+	0.628971i	−0.625339	+	0.780353i	$0.715039\pi$
$80$	−2.18313	−	1.26043i	−0.244081	−	0.140920i
$81$		0			0
$82$	4.29959	+	7.44710i	0.474810	+	0.822395i
$83$		−	0.662485i		−	0.0727172i	−0.999339	−	0.0363586i	$-0.988424\pi$
$83$		−	0.662485i		−	0.0727172i	0.999339	−	0.0363586i	$-0.0115759\pi$
$84$		0			0
$85$			0.623675i			0.0676471i
$86$	4.81600	−	2.78052i	0.519322	−	0.299831i
$87$		0			0
$88$	2.82193	−	4.88772i	0.300818	−	0.521033i
$89$	−4.86906	+	2.81116i	−0.516120	+	0.297982i	−0.735346	−	0.677692i	$-0.762980\pi$
$89$	−4.86906	+	2.81116i	−0.516120	+	0.297982i	0.219226	+	0.975674i	$0.429647\pi$
$90$		0			0
$91$	−0.707191	−	9.51314i	−0.0741337	−	0.997248i
$92$	3.60213			0.375548
$93$		0			0
$94$	3.34201	−	5.78854i	0.344702	−	0.597042i
$95$	3.93631	−	6.81789i	0.403857	−	0.699501i
$96$		0			0
$97$		−	16.8748i		−	1.71337i	−0.515836	−	0.856687i	$-0.672519\pi$
$97$		−	16.8748i		−	1.71337i	0.515836	−	0.856687i	$-0.327481\pi$
$98$	0.936412	+	6.93708i	0.0945919	+	0.700751i
$99$		0			0
$100$	−0.677364	−	1.17323i	−0.0677364	−	0.117323i
$101$	5.75972	−	9.97613i	0.573114	−	0.992662i	−0.423130	−	0.906069i	$-0.639069\pi$
$101$	5.75972	−	9.97613i	0.573114	−	0.992662i	0.996244	−	0.0865929i	$-0.0275979\pi$
$102$		0			0
$103$	2.89422	+	5.01294i	0.285176	+	0.493939i	0.972652	−	0.232268i	$-0.0746146\pi$
$103$	2.89422	+	5.01294i	0.285176	+	0.493939i	−0.687476	+	0.726207i	$0.741281\pi$
$104$	−1.78052	+	3.13524i	−0.174594	+	0.307436i
$105$		0			0
$106$		−	6.56103i		−	0.637264i
$107$	−7.96501	−	13.7958i	−0.770006	−	1.33369i	−0.937559	−	0.347827i	$-0.886920\pi$
$107$	−7.96501	−	13.7958i	−0.770006	−	1.33369i	0.167553	−	0.985863i	$-0.446414\pi$
$108$		0			0
$109$	1.28231	+	0.740342i	0.122823	+	0.0709119i	0.560153	−	0.828389i	$-0.310742\pi$
$109$	1.28231	+	0.740342i	0.122823	+	0.0709119i	−0.437330	+	0.899301i	$0.644076\pi$
$110$	12.3212	−	7.11368i	1.17479	−	0.678262i
$111$		0			0
$112$	1.16630	−	2.37482i	0.110205	−	0.224399i
$113$	−10.0373			−0.944233			−0.472117	−	0.881536i	$-0.656510\pi$
$113$	−10.0373			−0.944233			−0.472117	+	0.881536i	$0.656510\pi$
$114$		0			0
$115$	7.86392	+	4.54024i	0.733314	+	0.423379i
$116$	2.12447	−	3.67970i	0.197253	−	0.341651i
$117$		0			0
$118$	−7.95594			−0.732403
$119$	−0.653102	+	0.0438810i	−0.0598698	+	0.00402256i
$120$		0			0
$121$	10.4265	+	18.0593i	0.947867	+	1.64175i
$122$	−11.0751	−	6.39419i	−1.00269	−	0.578903i
$123$		0			0
$124$	−5.30267	+	3.06150i	−0.476194	+	0.274931i
$125$			9.18921i			0.821908i
$126$		0			0
$127$	10.3136			0.915186			0.457593	−	0.889162i	$-0.348712\pi$
$127$	10.3136			0.915186			0.457593	+	0.889162i	$0.348712\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$		0			0
$130$	−7.83885	+	4.60042i	−0.687513	+	0.403484i
$131$	9.24892	+	16.0196i	0.808082	+	1.39964i	0.914191	+	0.405285i	$0.132828\pi$
$131$	9.24892	+	16.0196i	0.808082	+	1.39964i	−0.106109	+	0.994355i	$0.533839\pi$
$132$		0			0
$133$	7.41653	+	3.64234i	0.643095	+	0.315831i
$134$	−12.1892			−1.05299
$135$		0			0
$136$	0.214260	+	0.123703i	0.0183726	+	0.0106074i
$137$	−11.8669	−	6.85133i	−1.01385	−	0.585349i	−0.101536	−	0.994832i	$-0.532376\pi$
$137$	−11.8669	−	6.85133i	−1.01385	−	0.585349i	−0.912318	+	0.409483i	$0.865709\pi$
$138$		0			0
$139$	−8.01474			−0.679802			−0.339901	−	0.940461i	$-0.610394\pi$
$139$	−8.01474			−0.679802			−0.339901	+	0.940461i	$0.610394\pi$
$140$	5.53946	−	3.71449i	0.468170	−	0.313932i
$141$		0			0
$142$	−2.03209	−	3.51969i	−0.170529	−	0.295366i
$143$	−10.2997	−	17.5501i	−0.861305	−	1.46761i
$144$		0			0
$145$	9.27600	−	5.35550i	0.770330	−	0.444750i
$146$	7.87262			0.651543
$147$		0			0
$148$			8.10436i			0.666174i
$149$	−1.62420	+	0.937732i	−0.133060	+	0.0768220i	−0.565052	−	0.825055i	$-0.691144\pi$
$149$	−1.62420	+	0.937732i	−0.133060	+	0.0768220i	0.431993	+	0.901877i	$0.357811\pi$
$150$		0			0
$151$	2.34699	+	1.35504i	0.190995	+	0.110271i	0.592449	−	0.805608i	$-0.298161\pi$
$151$	2.34699	+	1.35504i	0.190995	+	0.110271i	−0.401453	+	0.915880i	$0.631495\pi$
$152$	−1.56150	−	2.70459i	−0.126654	−	0.219371i
$153$		0			0
$154$	8.31623	+	12.4021i	0.670141	+	0.999389i
$155$	−15.4352			−1.23979
$156$		0			0
$157$	8.55178	−	14.8121i	0.682506	−	1.18214i	−0.291707	−	0.956508i	$-0.594223\pi$
$157$	8.55178	−	14.8121i	0.682506	−	1.18214i	0.974214	−	0.225628i	$-0.0724433\pi$
$158$	5.59041	+	3.22763i	0.444749	+	0.256776i
$159$		0			0
$160$	−2.52086			−0.199291
$161$	−4.20116	+	8.55441i	−0.331098	+	0.674182i
$162$		0			0
$163$	−16.1125	+	9.30258i	−1.26203	+	0.728635i	−0.973467	−	0.228826i	$-0.926511\pi$
$163$	−16.1125	+	9.30258i	−1.26203	+	0.728635i	−0.288565	+	0.957460i	$0.593178\pi$
$164$	7.44710	+	4.29959i	0.581521	+	0.335741i
$165$		0			0
$166$	−0.331243	−	0.573729i	−0.0257094	−	0.0445300i
$167$		−	14.5835i		−	1.12851i	−0.825602	−	0.564253i	$-0.809164\pi$
$167$		−	14.5835i		−	1.12851i	0.825602	−	0.564253i	$-0.190836\pi$
$168$		0			0
$169$	6.65952	+	11.1647i	0.512271	+	0.858824i
$170$	0.311838	+	0.540119i	0.0239169	+	0.0414252i
$171$		0			0
$172$	2.78052	−	4.81600i	0.212012	−	0.367216i
$173$	1.96945	+	3.41119i	0.149735	+	0.259348i	0.931129	−	0.364689i	$-0.118825\pi$
$173$	1.96945	+	3.41119i	0.149735	+	0.259348i	−0.781395	+	0.624037i	$0.785491\pi$
$174$		0			0
$175$	3.57621	−	0.240280i	0.270336	−	0.0181635i
$176$		−	5.64385i		−	0.425421i
$177$		0			0
$178$	−2.81116	+	4.86906i	−0.210705	+	0.364952i
$179$	2.35319	−	4.07584i	0.175885	−	0.304642i	−0.764582	−	0.644526i	$-0.777055\pi$
$179$	2.35319	−	4.07584i	0.175885	−	0.304642i	0.940467	+	0.339884i	$0.110388\pi$
$180$		0			0
$181$	−15.6400			−1.16251			−0.581255	−	0.813722i	$-0.697438\pi$
$181$	−15.6400			−1.16251			−0.581255	+	0.813722i	$0.697438\pi$
$182$	−5.36902	−	7.88503i	−0.397978	−	0.584477i
$183$		0			0
$184$	3.11954	−	1.80107i	0.229976	−	0.132776i
$185$	−10.2150	+	17.6929i	−0.751020	+	1.30080i
$186$		0			0
$187$	−1.20925	+	0.698161i	−0.0884292	+	0.0510546i
$188$		−	6.68403i		−	0.487483i
$189$		0			0
$190$		−	7.87262i		−	0.571140i
$191$	4.48843	+	7.77419i	0.324771	+	0.562521i	0.981466	−	0.191636i	$-0.0613793\pi$
$191$	4.48843	+	7.77419i	0.324771	+	0.562521i	−0.656695	+	0.754157i	$0.728046\pi$
$192$		0			0
$193$	6.09697	+	3.52009i	0.438869	+	0.253381i	0.703118	−	0.711073i	$-0.251791\pi$
$193$	6.09697	+	3.52009i	0.438869	+	0.253381i	−0.264248	+	0.964455i	$0.585124\pi$
$194$	−8.43739	−	14.6140i	−0.605769	−	1.04922i
$195$		0			0
$196$	4.27950	+	5.53948i	0.305678	+	0.395677i
$197$			11.7101i			0.834308i	0.908836	+	0.417154i	$0.136972\pi$
$197$			11.7101i			0.834308i	−0.908836	+	0.417154i	$0.863028\pi$
$198$		0			0
$199$	−9.05076	+	15.6764i	−0.641591	+	1.11127i	0.343486	+	0.939158i	$0.388392\pi$
$199$	−9.05076	+	15.6764i	−0.641591	+	1.11127i	−0.985078	+	0.172111i	$0.944941\pi$
$200$	−1.17323	−	0.677364i	−0.0829598	−	0.0478969i
$201$		0			0
$202$		−	11.5194i		−	0.810505i
$203$	6.26083	+	9.33686i	0.439424	+	0.655319i
$204$		0			0
$205$	10.8386	+	18.7731i	0.757004	+	1.31117i
$206$	5.01294	+	2.89422i	0.349268	+	0.201650i
$207$		0			0
$208$	0.0256500	+	3.60546i	0.00177851	+	0.249994i
$209$	17.6257			1.21920
$210$		0			0
$211$	−23.2252			−1.59889			−0.799444	−	0.600741i	$-0.794872\pi$
$211$	−23.2252			−1.59889			−0.799444	+	0.600741i	$0.794872\pi$
$212$	−3.28052	−	5.68202i	−0.225307	−	0.390243i
$213$		0			0
$214$	−13.7958	−	7.96501i	−0.943061	−	0.544477i
$215$	12.1404	−	7.00929i	0.827971	−	0.478030i
$216$		0			0
$217$	−1.08600	−	16.1635i	−0.0737225	−	1.09725i
$218$	1.48068			0.100285
$219$		0			0
$220$	7.11368	−	12.3212i	0.479604	−	0.830698i
$221$	0.769332	−	0.451502i	0.0517509	−	0.0303713i
$222$		0			0
$223$		−	7.16762i		−	0.479979i	−0.970775	−	0.239990i	$-0.922856\pi$
$223$		−	7.16762i		−	0.479979i	0.970775	−	0.239990i	$-0.0771440\pi$
$224$	−0.177364	−	2.63980i	−0.0118506	−	0.176379i
$225$		0			0
$226$	−8.69259	+	5.01867i	−0.578222	+	0.333837i
$227$	−18.6007	−	10.7391i	−1.23457	−	0.712782i	−0.266594	−	0.963809i	$-0.585898\pi$
$227$	−18.6007	−	10.7391i	−1.23457	−	0.712782i	−0.967980	+	0.251027i	$0.919232\pi$
$228$		0			0
$229$	7.15978	−	4.13370i	0.473132	−	0.273163i	−0.244418	−	0.969670i	$-0.578597\pi$
$229$	7.15978	−	4.13370i	0.473132	−	0.273163i	0.717550	+	0.696507i	$0.245264\pi$
$230$	9.08047			0.598749
$231$		0			0
$232$		−	4.24895i		−	0.278957i
$233$	13.4460	+	23.2892i	0.880877	+	1.52572i	0.850368	+	0.526189i	$0.176379\pi$
$233$	13.4460	+	23.2892i	0.880877	+	1.52572i	0.0305088	+	0.999534i	$0.490287\pi$
$234$		0			0
$235$	8.42474	−	14.5921i	0.549570	−	0.951882i
$236$	−6.89004	+	3.97797i	−0.448504	+	0.258944i
$237$		0			0
$238$	−0.543662	+	0.364553i	−0.0352404	+	0.0236305i
$239$		−	4.37478i		−	0.282981i	−0.989940	−	0.141491i	$-0.954811\pi$
$239$		−	4.37478i		−	0.282981i	0.989940	−	0.141491i	$-0.0451895\pi$
$240$		0			0
$241$	1.33779	+	0.772373i	0.0861746	+	0.0497529i	0.542468	−	0.840076i	$-0.317490\pi$
$241$	1.33779	+	0.772373i	0.0861746	+	0.0497529i	−0.456293	+	0.889829i	$0.650823\pi$
$242$	18.0593	+	10.4265i	1.16089	+	0.670243i
$243$		0			0
$244$	−12.7884			−0.818693
$245$	2.36056	+	17.4874i	0.150811	+	1.11723i
$246$		0			0
$247$	−11.2598	+	0.0801049i	−0.716446	+	0.00509695i
$248$	−3.06150	+	5.30267i	−0.194405	+	0.336720i
$249$		0			0
$250$	4.59461	+	7.95809i	0.290588	+	0.503314i
$251$	−13.4321			−0.847828			−0.423914	−	0.905703i	$-0.639344\pi$
$251$	−13.4321			−0.847828			−0.423914	+	0.905703i	$0.639344\pi$
$252$		0			0
$253$			20.3299i			1.27813i
$254$	8.93186	−	5.15681i	0.560435	−	0.323567i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	10.9173	+	18.9093i	0.681003	+	1.17953i	0.974675	+	0.223625i	$0.0717892\pi$
$257$	10.9173	+	18.9093i	0.681003	+	1.17953i	−0.293672	+	0.955906i	$0.594877\pi$
$258$		0			0
$259$	−19.2464	−	9.45210i	−1.19591	−	0.587325i
$260$	−4.48843	+	7.90351i	−0.278361	+	0.490155i
$261$		0			0
$262$	16.0196	+	9.24892i	0.989694	+	0.571400i
$263$	4.24994	−	7.36111i	0.262062	−	0.453906i	−0.704727	−	0.709478i	$-0.748931\pi$
$263$	4.24994	−	7.36111i	0.262062	−	0.453906i	0.966790	+	0.255573i	$0.0822640\pi$
$264$		0			0
$265$		−	16.5394i		−	1.01601i
$266$	8.24408	−	0.553907i	0.505477	−	0.0339622i
$267$		0			0
$268$	−10.5562	+	6.09461i	−0.644821	+	0.372287i
$269$	−10.3107	+	17.8587i	−0.628656	+	1.08886i	0.359166	+	0.933274i	$0.383061\pi$
$269$	−10.3107	+	17.8587i	−0.628656	+	1.08886i	−0.987822	+	0.155590i	$0.950272\pi$
$270$		0			0
$271$	−20.7402	+	11.9744i	−1.25988	+	0.727392i	−0.973051	−	0.230590i	$-0.925934\pi$
$271$	−20.7402	+	11.9744i	−1.25988	+	0.727392i	−0.286829	+	0.957982i	$0.592601\pi$
$272$	0.247406			0.0150012
$273$		0			0
$274$	−13.7027			−0.827808
$275$	6.62153	−	3.82294i	0.399293	−	0.230532i
$276$		0			0
$277$	2.06106	−	3.56986i	0.123837	−	0.214492i	−0.797441	−	0.603397i	$-0.793813\pi$
$277$	2.06106	−	3.56986i	0.123837	−	0.214492i	0.921278	+	0.388905i	$0.127147\pi$
$278$	−6.94097	+	4.00737i	−0.416292	+	0.240346i
$279$		0			0
$280$	2.94007	−	5.98657i	0.175703	−	0.357766i
$281$			10.3018i			0.614556i	0.951620	+	0.307278i	$0.0994181\pi$
$281$			10.3018i			0.614556i	−0.951620	+	0.307278i	$0.900582\pi$
$282$		0			0
$283$	5.43112	−	9.40698i	0.322847	−	0.559187i	−0.658227	−	0.752819i	$-0.728693\pi$
$283$	5.43112	−	9.40698i	0.322847	−	0.559187i	0.981074	+	0.193632i	$0.0620268\pi$
$284$	−3.51969	−	2.03209i	−0.208855	−	0.120583i
$285$		0			0
$286$	−17.6949	−	10.0490i	−1.04632	−	0.594208i
$287$	−18.8963	+	12.6709i	−1.11541	+	0.747939i
$288$		0			0
$289$	8.46940	+	14.6694i	0.498200	+	0.862907i
$290$	5.35550	−	9.27600i	0.314486	−	0.544705i
$291$		0			0
$292$	6.81789	−	3.93631i	0.398987	−	0.230355i
$293$			3.72513i			0.217624i	0.994062	+	0.108812i	$0.0347047\pi$
$293$			3.72513i			0.217624i	−0.994062	+	0.108812i	$0.965295\pi$
$294$		0			0
$295$	−20.0558			−1.16769
$296$	4.05218	+	7.01858i	0.235528	+	0.407947i
$297$		0			0
$298$	−0.937732	+	1.62420i	−0.0543213	+	0.0940873i
$299$	−0.0923948	−	12.9874i	−0.00534333	−	0.751078i
$300$		0			0
$301$	8.19419	+	12.2201i	0.472305	+	0.704355i
$302$	2.71007			0.155947
$303$		0			0
$304$	−2.70459	−	1.56150i	−0.155119	−	0.0895580i
$305$	−27.9187	−	16.1189i	−1.59862	−	0.922963i
$306$		0			0
$307$		−	21.0104i		−	1.19912i	−0.800328	−	0.599562i	$-0.795341\pi$
$307$		−	21.0104i		−	1.19912i	0.800328	−	0.599562i	$-0.204659\pi$
$308$	13.4031	+	6.58241i	0.763713	+	0.375068i
$309$		0			0
$310$	−13.3673	+	7.71760i	−0.759210	+	0.438330i
$311$	−3.19739	+	5.53804i	−0.181307	+	0.314034i	−0.942326	−	0.334696i	$-0.891366\pi$
$311$	−3.19739	+	5.53804i	−0.181307	+	0.314034i	0.761019	+	0.648730i	$0.224700\pi$
$312$		0			0
$313$	−7.73685	−	13.4006i	−0.437313	−	0.757448i	0.560168	−	0.828379i	$-0.310736\pi$
$313$	−7.73685	−	13.4006i	−0.437313	−	0.757448i	−0.997481	+	0.0709307i	$0.977403\pi$
$314$		−	17.1036i		−	0.965210i
$315$		0			0
$316$	6.45525			0.363136
$317$	−16.3604	+	9.44569i	−0.918893	+	0.530523i	−0.883282	−	0.468843i	$-0.844671\pi$
$317$	−16.3604	+	9.44569i	−0.918893	+	0.530523i	−0.0356109	+	0.999366i	$0.511338\pi$
$318$		0			0
$319$	20.7677	+	11.9902i	1.16277	+	0.671323i
$320$	−2.18313	+	1.26043i	−0.122041	+	0.0704601i
$321$		0			0
$322$	0.638890	+	9.50891i	0.0356039	+	0.529911i
$323$			0.772647i			0.0429912i
$324$		0			0
$325$	−4.21266	+	2.47230i	−0.233676	+	0.137139i
$326$	−9.30258	+	16.1125i	−0.515222	+	0.892391i
$327$		0			0
$328$	8.59917			0.474810
$329$	15.8733	+	7.79557i	0.875125	+	0.429783i
$330$		0			0
$331$	−22.1676	+	12.7985i	−1.21844	+	0.703468i	−0.964585	−	0.263774i	$-0.915033\pi$
$331$	−22.1676	+	12.7985i	−1.21844	+	0.703468i	−0.253857	+	0.967242i	$0.581699\pi$
$332$	−0.573729	−	0.331243i	−0.0314875	−	0.0181793i
$333$		0			0
$334$	−7.29175	−	12.6297i	−0.398987	−	0.691065i
$335$	−30.7273			−1.67881
$336$		0			0
$337$	−35.2040			−1.91769			−0.958843	−	0.283938i	$-0.908359\pi$
$337$	−35.2040			−1.91769			−0.958843	+	0.283938i	$0.908359\pi$
$338$	11.3497	+	6.33916i	0.617341	+	0.344805i
$339$		0			0
$340$	0.540119	+	0.311838i	0.0292920	+	0.0169118i
$341$	−17.2786	−	29.9275i	−0.935690	−	1.62066i
$342$		0			0
$343$	−18.1464	+	3.70233i	−0.979815	+	0.199907i
$344$		−	5.56103i		−	0.299831i
$345$		0			0
$346$	3.41119	+	1.96945i	0.183387	+	0.105878i
$347$	6.34130	−	10.9835i	0.340419	−	0.589623i	−0.644092	−	0.764948i	$-0.722764\pi$
$347$	6.34130	−	10.9835i	0.340419	−	0.589623i	0.984511	+	0.175325i	$0.0560978\pi$
$348$		0			0
$349$			16.7258i			0.895311i	0.894206	+	0.447656i	$0.147741\pi$
$349$			16.7258i			0.895311i	−0.894206	+	0.447656i	$0.852259\pi$
$350$	2.97695	−	1.99619i	0.159125	−	0.106701i
$351$		0			0
$352$	−2.82193	−	4.88772i	−0.150409	−	0.260516i
$353$	−8.35129	−	4.82162i	−0.444494	−	0.256629i	0.261008	−	0.965337i	$-0.415945\pi$
$353$	−8.35129	−	4.82162i	−0.444494	−	0.256629i	−0.705502	+	0.708708i	$0.749278\pi$
$354$		0			0
$355$	−5.12262	−	8.87264i	−0.271880	−	0.470911i
$356$			5.62231i			0.297982i
$357$		0			0
$358$		−	4.70637i		−	0.248739i
$359$	−0.491107	+	0.283541i	−0.0259197	+	0.0149647i	−0.512904	−	0.858446i	$-0.671430\pi$
$359$	−0.491107	+	0.283541i	−0.0259197	+	0.0149647i	0.486984	+	0.873411i	$0.338097\pi$
$360$		0			0
$361$	−4.62346	+	8.00806i	−0.243340	+	0.421477i
$362$	−13.5446	+	7.81998i	−0.711889	+	0.411009i
$363$		0			0
$364$	−8.59222	−	4.14413i	−0.450355	−	0.217211i
$365$	19.8458			1.03878
$366$		0			0
$367$	6.62549	−	11.4757i	0.345848	−	0.599026i	−0.639660	−	0.768658i	$-0.720925\pi$
$367$	6.62549	−	11.4757i	0.345848	−	0.599026i	0.985507	+	0.169632i	$0.0542580\pi$
$368$	1.80107	−	3.11954i	0.0938871	−	0.162617i
$369$		0			0
$370$			20.4299i			1.06210i
$371$	17.3198	−	1.16369i	0.899200	−	0.0604159i
$372$		0			0
$373$	−11.9476	−	20.6939i	−0.618624	−	1.07149i	−0.989737	−	0.142900i	$-0.954357\pi$
$373$	−11.9476	−	20.6939i	−0.618624	−	1.07149i	0.371113	−	0.928588i	$-0.378976\pi$
$374$	−0.698161	+	1.20925i	−0.0361011	+	0.0625289i
$375$		0			0
$376$	−3.34201	−	5.78854i	−0.172351	−	0.298521i
$377$	−13.3215	−	7.56532i	−0.686092	−	0.389634i
$378$		0			0
$379$			1.46025i			0.0750081i	0.999296	+	0.0375040i	$0.0119407\pi$
$379$			1.46025i			0.0750081i	−0.999296	+	0.0375040i	$0.988059\pi$
$380$	−3.93631	−	6.81789i	−0.201929	−	0.349751i
$381$		0			0
$382$	7.77419	+	4.48843i	0.397762	+	0.229648i
$383$	−5.64718	+	3.26040i	−0.288557	+	0.166599i	−0.637291	−	0.770623i	$-0.719945\pi$
$383$	−5.64718	+	3.26040i	−0.288557	+	0.166599i	0.348734	+	0.937222i	$0.386612\pi$
$384$		0			0
$385$	20.9640	+	31.2639i	1.06843	+	1.59336i
$386$	7.04017			0.358335
$387$		0			0
$388$	−14.6140	−	8.43739i	−0.741913	−	0.428344i
$389$	12.8010	−	22.1719i	0.649035	−	1.12416i	−0.334319	−	0.942460i	$-0.608506\pi$
$389$	12.8010	−	22.1719i	0.649035	−	1.12416i	0.983354	−	0.181702i	$-0.0581605\pi$
$390$		0			0
$391$	−0.891189			−0.0450694
$392$	6.47590	+	2.65759i	0.327082	+	0.134228i
$393$		0			0
$394$	5.85504	+	10.1412i	0.294972	+	0.510907i
$395$	14.0926	+	8.13639i	0.709078	+	0.409386i
$396$		0			0
$397$	13.4505	−	7.76567i	0.675063	−	0.389748i	−0.122929	−	0.992415i	$-0.539229\pi$
$397$	13.4505	−	7.76567i	0.675063	−	0.389748i	0.797992	+	0.602668i	$0.205895\pi$
$398$			18.1015i			0.907347i
$399$		0			0
$400$	−1.35473			−0.0677364
$401$	30.2703	−	17.4765i	1.51163	−	0.872737i	0.511717	−	0.859154i	$-0.329009\pi$
$401$	30.2703	−	17.4765i	1.51163	−	0.872737i	0.999908	−	0.0135833i	$-0.00432384\pi$
$402$		0			0
$403$	11.1741	+	19.0400i	0.556622	+	0.948451i
$404$	−5.75972	−	9.97613i	−0.286557	−	0.496331i
$405$		0			0
$406$	10.0905	+	4.95554i	0.500782	+	0.245939i
$407$	−45.7398			−2.26724
$408$		0			0
$409$	−11.0002	−	6.35099i	−0.543927	−	0.314036i	0.202742	−	0.979232i	$-0.435015\pi$
$409$	−11.0002	−	6.35099i	−0.543927	−	0.314036i	−0.746669	+	0.665196i	$0.768348\pi$
$410$	18.7731	+	10.8386i	0.927137	+	0.535283i
$411$		0			0
$412$	5.78844			0.285176
$413$	−1.41110	−	21.0021i	−0.0694356	−	1.03344i
$414$		0			0
$415$	−0.835016	−	1.44629i	−0.0409893	−	0.0709956i
$416$	1.82494	+	3.10959i	0.0894752	+	0.152460i
$417$		0			0
$418$	15.2643	−	8.81286i	0.746602	−	0.431051i
$419$	23.7483			1.16018			0.580091	−	0.814552i	$-0.303017\pi$
$419$	23.7483			1.16018			0.580091	+	0.814552i	$0.303017\pi$
$420$		0			0
$421$			4.91285i			0.239438i	0.992808	+	0.119719i	$0.0381993\pi$
$421$			4.91285i			0.239438i	−0.992808	+	0.119719i	$0.961801\pi$
$422$	−20.1136	+	11.6126i	−0.979115	+	0.565292i
$423$		0			0
$424$	−5.68202	−	3.28052i	−0.275943	−	0.159316i
$425$	0.167584	+	0.290264i	0.00812901	+	0.0140799i
$426$		0			0
$427$	14.9151	−	30.3701i	0.721791	−	1.46971i
$428$	−15.9300			−0.770006
$429$		0			0
$430$	7.00929	−	12.1404i	0.338018	−	0.585464i
$431$	21.7888	+	12.5798i	1.04953	+	0.605947i	0.922518	−	0.385954i	$-0.126128\pi$
$431$	21.7888	+	12.5798i	1.04953	+	0.605947i	0.127013	+	0.991901i	$0.459461\pi$
$432$		0			0
$433$	6.16471			0.296257			0.148129	−	0.988968i	$-0.452675\pi$
$433$	6.16471			0.296257			0.148129	+	0.988968i	$0.452675\pi$
$434$	−9.02224	−	13.4550i	−0.433081	−	0.645860i
$435$		0			0
$436$	1.28231	−	0.740342i	0.0614115	−	0.0354560i
$437$	9.74230	+	5.62472i	0.466038	+	0.269067i
$438$		0			0
$439$	−4.44890	−	7.70572i	−0.212334	−	0.367774i	0.740110	−	0.672486i	$-0.234773\pi$
$439$	−4.44890	−	7.70572i	−0.212334	−	0.367774i	−0.952445	+	0.304712i	$0.901440\pi$
$440$		−	14.2274i		−	0.678262i
$441$		0			0
$442$	0.440510	−	0.775678i	0.0209529	−	0.0368952i
$443$	17.0804	+	29.5842i	0.811516	+	1.40559i	0.911803	+	0.410629i	$0.134691\pi$
$443$	17.0804	+	29.5842i	0.811516	+	1.40559i	−0.100286	+	0.994959i	$0.531976\pi$
$444$		0			0
$445$	−7.08653	+	12.2742i	−0.335934	+	0.581854i
$446$	−3.58381	−	6.20734i	−0.169698	−	0.293926i
$447$		0			0
$448$	−1.47350	−	2.19745i	−0.0696164	−	0.103820i
$449$			29.0848i			1.37260i	0.727320	+	0.686298i	$0.240766\pi$
$449$			29.0848i			1.37260i	−0.727320	+	0.686298i	$0.759234\pi$
$450$		0			0
$451$	−24.2662	+	42.0303i	−1.14265	+	1.97913i
$452$	−5.01867	+	8.69259i	−0.236058	+	0.408865i
$453$		0			0
$454$	−21.4783			−1.00803
$455$	−13.5345	−	19.8770i	−0.634509	−	0.931850i
$456$		0			0
$457$	−30.7370	+	17.7460i	−1.43782	+	0.830124i	−0.997698	−	0.0678157i	$-0.978397\pi$
$457$	−30.7370	+	17.7460i	−1.43782	+	0.830124i	−0.440119	+	0.897940i	$0.645064\pi$
$458$	4.13370	−	7.15978i	0.193155	−	0.334555i
$459$		0			0
$460$	7.86392	−	4.54024i	0.366657	−	0.211690i
$461$			7.57380i			0.352747i	0.984323	+	0.176373i	$0.0564366\pi$
$461$			7.57380i			0.352747i	−0.984323	+	0.176373i	$0.943563\pi$
$462$		0			0
$463$			25.0299i			1.16324i	0.813462	+	0.581618i	$0.197580\pi$
$463$			25.0299i			1.16324i	−0.813462	+	0.581618i	$0.802420\pi$
$464$	−2.12447	−	3.67970i	−0.0986263	−	0.170826i
$465$		0			0
$466$	23.2892	+	13.4460i	1.07885	+	0.622874i
$467$	−15.6334	−	27.0778i	−0.723427	−	1.25301i	−0.959618	−	0.281306i	$-0.909233\pi$
$467$	−15.6334	−	27.0778i	−0.723427	−	1.25301i	0.236191	−	0.971707i	$-0.424101\pi$
$468$		0			0
$469$	−2.16193	−	32.1771i	−0.0998287	−	1.48580i
$470$		−	16.8495i		−	0.777209i
$471$		0			0
$472$	−3.97797	+	6.89004i	−0.183101	+	0.317140i
$473$	27.1808	+	15.6928i	1.24977	+	0.721557i
$474$		0			0
$475$		−	4.23081i		−	0.194123i
$476$	−0.288549	+	0.587543i	−0.0132256	+	0.0269300i
$477$		0			0
$478$	−2.18739	−	3.78867i	−0.100049	−	0.173290i
$479$	−13.4394	−	7.75926i	−0.614063	−	0.354529i	0.160491	−	0.987037i	$-0.448692\pi$
$479$	−13.4394	−	7.75926i	−0.614063	−	0.354529i	−0.774554	+	0.632508i	$0.782026\pi$
$480$		0			0
$481$	29.2199	−	0.207877i	1.33231	−	0.00947838i
$482$	1.54475			0.0703613
$483$		0			0
$484$	20.8531			0.947867
$485$	−21.2695	−	36.8398i	−0.965797	−	1.67281i
$486$		0			0
$487$	28.0472	+	16.1931i	1.27094	+	0.733778i	0.975165	−	0.221479i	$-0.0710886\pi$
$487$	28.0472	+	16.1931i	1.27094	+	0.733778i	0.295776	+	0.955257i	$0.404422\pi$
$488$	−11.0751	+	6.39419i	−0.501345	+	0.289452i
$489$		0			0
$490$	10.7880	+	13.9643i	0.487353	+	0.630841i
$491$	9.22056			0.416118			0.208059	−	0.978116i	$-0.433285\pi$
$491$	9.22056			0.416118			0.208059	+	0.978116i	$0.433285\pi$
$492$		0			0
$493$	−0.525608	+	0.910379i	−0.0236722	+	0.0410014i
$494$	−9.71124	+	5.69929i	−0.436930	+	0.256423i
$495$		0			0
$496$			6.12299i			0.274931i
$497$	8.93085	−	5.98858i	0.400603	−	0.268625i
$498$		0			0
$499$	6.56445	−	3.78999i	0.293865	−	0.169663i	−0.345818	−	0.938301i	$-0.612399\pi$
$499$	6.56445	−	3.78999i	0.293865	−	0.169663i	0.639684	+	0.768638i	$0.279065\pi$
$500$	7.95809	+	4.59461i	0.355897	+	0.205477i
$501$		0			0
$502$	−11.6326	+	6.71606i	−0.519186	+	0.299752i
$503$	−1.86195			−0.0830203			−0.0415102	−	0.999138i	$-0.513217\pi$
$503$	−1.86195			−0.0830203			−0.0415102	+	0.999138i	$0.513217\pi$
$504$		0			0
$505$		−	29.0389i		−	1.29221i
$506$	10.1650	+	17.6062i	0.451887	+	0.782692i
$507$		0			0
$508$	5.15681	−	8.93186i	0.228797	−	0.396287i
$509$	6.91271	−	3.99105i	0.306400	−	0.176900i	−0.338914	−	0.940817i	$-0.610060\pi$
$509$	6.91271	−	3.99105i	0.306400	−	0.176900i	0.645315	+	0.763917i	$0.276726\pi$
$510$		0			0
$511$	1.39632	+	20.7822i	0.0617697	+	0.919348i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	18.9093	+	10.9173i	0.834055	+	0.481542i
$515$	12.6369	+	7.29592i	0.556849	+	0.321497i
$516$		0			0
$517$	37.7237			1.65908
$518$	−21.3939	+	1.43742i	−0.939993	+	0.0631568i
$519$		0			0
$520$	0.0646601	+	9.08886i	0.00283553	+	0.398573i
$521$	8.61209	−	14.9166i	0.377303	−	0.653507i	−0.613366	−	0.789799i	$-0.710185\pi$
$521$	8.61209	−	14.9166i	0.377303	−	0.653507i	0.990669	+	0.136291i	$0.0435183\pi$
$522$		0			0
$523$	12.7325	+	22.0534i	0.556755	+	0.964328i	0.997765	+	0.0668258i	$0.0212872\pi$
$523$	12.7325	+	22.0534i	0.556755	+	0.964328i	−0.441010	+	0.897502i	$0.645379\pi$
$524$	18.4978			0.808082
$525$		0			0
$526$		−	8.49988i		−	0.370612i
$527$	1.31191	−	0.757432i	0.0571478	−	0.0329943i
$528$		0			0
$529$	5.01231	−	8.68158i	0.217927	−	0.377460i
$530$	−8.26972	−	14.3236i	−0.359214	−	0.622176i
$531$		0			0
$532$	6.86263	−	4.60174i	0.297533	−	0.199511i
$533$	15.3110	−	26.9605i	0.663192	−	1.16779i
$534$		0			0
$535$	−34.7773	−	20.0787i	−1.50355	−	0.868076i
$536$	−6.09461	+	10.5562i	−0.263247	+	0.455957i
$537$		0			0
$538$			20.6215i			0.889054i
$539$	−31.2640	+	24.1529i	−1.34664	+	1.04034i
$540$		0			0
$541$	16.1619	−	9.33109i	0.694855	−	0.401175i	−0.110573	−	0.993868i	$-0.535269\pi$
$541$	16.1619	−	9.33109i	0.694855	−	0.401175i	0.805428	+	0.592693i	$0.201935\pi$
$542$	−11.9744	+	20.7402i	−0.514344	+	0.890870i
$543$		0			0
$544$	0.214260	−	0.123703i	0.00918631	−	0.00530372i
$545$	3.73260			0.159887
$546$		0			0
$547$	32.1949			1.37655			0.688277	−	0.725448i	$-0.258367\pi$
$547$	32.1949			1.37655			0.688277	+	0.725448i	$0.258367\pi$
$548$	−11.8669	+	6.85133i	−0.506927	+	0.292674i
$549$		0			0
$550$	3.82294	−	6.62153i	0.163011	−	0.282343i
$551$	11.4917	−	6.63472i	0.489562	−	0.282649i
$552$		0			0
$553$	−7.52875	+	15.3300i	−0.320155	+	0.651899i
$554$		−	4.12212i		−	0.175132i
$555$		0			0
$556$	−4.00737	+	6.94097i	−0.169950	+	0.294363i
$557$	7.52338	+	4.34362i	0.318776	+	0.184045i	0.650847	−	0.759209i	$-0.274414\pi$
$557$	7.52338	+	4.34362i	0.318776	+	0.184045i	−0.332071	+	0.943254i	$0.607747\pi$
$558$		0			0
$559$	−17.4352	−	9.90151i	−0.737430	−	0.418789i
$560$	−0.447110	−	6.65456i	−0.0188939	−	0.281207i
$561$		0			0
$562$	5.15092	+	8.92165i	0.217278	+	0.376337i
$563$	7.67650	−	13.2961i	0.323526	−	0.560363i	−0.657687	−	0.753291i	$-0.728465\pi$
$563$	7.67650	−	13.2961i	0.323526	−	0.560363i	0.981213	+	0.192928i	$0.0617984\pi$
$564$		0			0
$565$	−21.9128	+	12.6514i	−0.921878	+	0.532246i
$566$		−	10.8622i		−	0.456574i
$567$		0			0
$568$	−4.06419			−0.170529
$569$	18.4292	+	31.9204i	0.772594	+	1.33817i	0.936137	+	0.351636i	$0.114374\pi$
$569$	18.4292	+	31.9204i	0.772594	+	1.33817i	−0.163543	+	0.986536i	$0.552292\pi$
$570$		0			0
$571$	−5.61735	+	9.72953i	−0.235079	+	0.407168i	−0.959296	−	0.282404i	$-0.908868\pi$
$571$	−5.61735	+	9.72953i	−0.235079	+	0.407168i	0.724217	+	0.689572i	$0.242201\pi$
$572$	−20.3487	+	0.144765i	−0.850821	+	0.00605293i
$573$		0			0
$574$	−10.0292	+	20.4214i	−0.418611	+	0.852375i
$575$	4.87991			0.203506
$576$		0			0
$577$	−24.5422	−	14.1694i	−1.02170	−	0.589881i	−0.107107	−	0.994247i	$-0.534159\pi$
$577$	−24.5422	−	14.1694i	−1.02170	−	0.589881i	−0.914597	+	0.404366i	$0.867492\pi$
$578$	14.6694	+	8.46940i	0.610168	+	0.352280i
$579$		0			0
$580$		−	10.7110i		−	0.444750i
$581$	1.45578	−	0.976173i	0.0603959	−	0.0404985i
$582$		0			0
$583$	32.0685	−	18.5147i	1.32814	−	0.766803i
$584$	3.93631	−	6.81789i	0.162886	−	0.282126i
$585$		0			0
$586$	1.86256	+	3.22606i	0.0769418	+	0.133267i
$587$		−	0.0179623i		−	0.000741383i	−1.00000		0.000370692i	$-0.999882\pi$
$587$		−	0.0179623i		−	0.000741383i	1.00000		0.000370692i	$-0.000117995\pi$
$588$		0			0
$589$	−19.1221			−0.787911
$590$	−17.3688	+	10.0279i	−0.715063	+	0.412842i
$591$		0			0
$592$	7.01858	+	4.05218i	0.288462	+	0.166544i
$593$	−41.5164	+	23.9695i	−1.70487	+	0.984309i	−0.764209	+	0.644969i	$0.776870\pi$
$593$	−41.5164	+	23.9695i	−1.70487	+	0.984309i	−0.940664	+	0.339340i	$0.889796\pi$
$594$		0			0
$595$	−1.37050	+	0.918987i	−0.0561849	+	0.0376748i
$596$			1.87546i			0.0768220i
$597$		0			0
$598$	−6.57369	−	11.2012i	−0.268818	−	0.458050i
$599$	−7.47580	+	12.9485i	−0.305453	+	0.529060i	−0.977362	−	0.211573i	$-0.932141\pi$
$599$	−7.47580	+	12.9485i	−0.305453	+	0.529060i	0.671909	+	0.740634i	$0.265475\pi$
$600$		0			0
$601$	19.7525			0.805723			0.402861	−	0.915261i	$-0.368016\pi$
$601$	19.7525			0.805723			0.402861	+	0.915261i	$0.368016\pi$
$602$	13.2064	+	6.48582i	0.538254	+	0.264342i
$603$		0			0
$604$	2.34699	−	1.35504i	0.0954977	−	0.0551357i
$605$	45.5249	+	26.2838i	1.85085	+	1.06859i
$606$		0			0
$607$	5.09059	+	8.81716i	0.206621	+	0.357878i	0.950648	−	0.310272i	$-0.100420\pi$
$607$	5.09059	+	8.81716i	0.206621	+	0.357878i	−0.744027	+	0.668149i	$0.767087\pi$
$608$	−3.12299			−0.126654
$609$		0			0
$610$	−32.2377			−1.30527
$611$	−24.0990	+	0.171445i	−0.974941	+	0.00693594i
$612$		0			0
$613$	−26.1938	−	15.1230i	−1.05796	−	0.610812i	−0.133091	−	0.991104i	$-0.542490\pi$
$613$	−26.1938	−	15.1230i	−1.05796	−	0.610812i	−0.924867	+	0.380292i	$0.875824\pi$
$614$	−10.5052	−	18.1955i	−0.423955	−	0.734311i
$615$		0			0
$616$	14.8986	−	1.00102i	0.600283	−	0.0403322i
$617$			18.4715i			0.743636i	0.928306	+	0.371818i	$0.121265\pi$
$617$			18.4715i			0.743636i	−0.928306	+	0.371818i	$0.878735\pi$
$618$		0			0
$619$	3.42519	+	1.97754i	0.137670	+	0.0794839i	0.567253	−	0.823543i	$-0.308006\pi$
$619$	3.42519	+	1.97754i	0.137670	+	0.0794839i	−0.429583	+	0.903027i	$0.641339\pi$
$620$	−7.71760	+	13.3673i	−0.309946	+	0.536843i
$621$		0			0
$622$			6.39478i			0.256407i
$623$	−13.3520	−	6.55729i	−0.534935	−	0.262712i
$624$		0			0
$625$	14.9692	+	25.9274i	0.598767	+	1.03709i
$626$	−13.4006	−	7.73685i	−0.535597	−	0.309227i
$627$		0			0
$628$	−8.55178	−	14.8121i	−0.341253	−	0.591068i
$629$		−	2.00507i		−	0.0799472i
$630$		0			0
$631$		−	24.3547i		−	0.969546i	−0.874640	−	0.484773i	$-0.838902\pi$
$631$		−	24.3547i		−	0.969546i	0.874640	−	0.484773i	$-0.161098\pi$
$632$	5.59041	−	3.22763i	0.222375	−	0.128388i
$633$		0			0
$634$	−9.44569	+	16.3604i	−0.375136	+	0.649755i
$635$	22.5160	−	12.9996i	0.893519	−	0.515873i
$636$		0			0
$637$	19.8626	−	15.5716i	0.786986	−	0.616971i
$638$	23.9804			0.949395
$639$		0			0
$640$	−1.26043	+	2.18313i	−0.0498228	+	0.0862957i
$641$	0.398610	−	0.690412i	0.0157441	−	0.0272696i	−0.858046	−	0.513573i	$-0.828322\pi$
$641$	0.398610	−	0.690412i	0.0157441	−	0.0272696i	0.873790	+	0.486303i	$0.161655\pi$
$642$		0			0
$643$		−	36.3986i		−	1.43542i	−0.696342	−	0.717710i	$-0.745190\pi$
$643$		−	36.3986i		−	1.43542i	0.696342	−	0.717710i	$-0.254810\pi$
$644$	5.30775	+	7.91552i	0.209155	+	0.311915i
$645$		0			0
$646$	0.386323	+	0.669132i	0.0151997	+	0.0263266i
$647$	18.3127	−	31.7185i	0.719945	−	1.24698i	−0.241076	−	0.970506i	$-0.577500\pi$
$647$	18.3127	−	31.7185i	0.719945	−	1.24698i	0.961021	−	0.276475i	$-0.0891664\pi$
$648$		0			0
$649$	−22.4511	−	38.8864i	−0.881281	−	1.52642i
$650$	−2.41212	+	4.24741i	−0.0946110	+	0.166597i
$651$		0			0
$652$			18.6052i			0.728635i
$653$	18.1837	+	31.4951i	0.711583	+	1.23250i	0.964263	+	0.264948i	$0.0853547\pi$
$653$	18.1837	+	31.4951i	0.711583	+	1.23250i	−0.252680	+	0.967550i	$0.581312\pi$
$654$		0			0
$655$	40.3832	+	23.3152i	1.57790	+	0.911001i
$656$	7.44710	−	4.29959i	0.290760	−	0.167871i
$657$		0			0
$658$	17.6445	−	1.18551i	0.687854	−	0.0462159i
$659$	18.7720			0.731252			0.365626	−	0.930762i	$-0.380855\pi$
$659$	18.7720			0.731252			0.365626	+	0.930762i	$0.380855\pi$
$660$		0			0
$661$	−36.4244	−	21.0297i	−1.41675	−	0.817959i	−0.420735	−	0.907184i	$-0.638228\pi$
$661$	−36.4244	−	21.0297i	−1.41675	−	0.817959i	−0.996012	+	0.0892249i	$0.971561\pi$
$662$	−12.7985	+	22.1676i	−0.497427	+	0.861569i
$663$		0			0
$664$	−0.662485			−0.0257094
$665$	20.7822	−	1.39632i	0.805897	−	0.0541471i
$666$		0			0
$667$	7.65264	+	13.2548i	0.296312	+	0.513227i
$668$	−12.6297	−	7.29175i	−0.488657	−	0.282126i
$669$		0			0
$670$	−26.6106	+	15.3636i	−1.02806	+	0.593549i
$671$		−	72.1758i		−	2.78631i
$672$		0			0
$673$	29.6123			1.14147			0.570736	−	0.821134i	$-0.306658\pi$
$673$	29.6123			1.14147			0.570736	+	0.821134i	$0.306658\pi$
$674$	−30.4876	+	17.6020i	−1.17434	+	0.678004i
$675$		0			0
$676$	12.9987	−	0.184960i	0.499949	−	0.00711386i
$677$	6.35028	+	10.9990i	0.244061	+	0.422726i	0.961867	−	0.273517i	$-0.0881869\pi$
$677$	6.35028	+	10.9990i	0.244061	+	0.422726i	−0.717806	+	0.696243i	$0.754854\pi$
$678$		0			0
$679$	37.0815	−	24.8650i	1.42306	−	0.954232i
$680$	0.623675			0.0239169
$681$		0			0
$682$	−29.9275	−	17.2786i	−1.14598	−	0.661633i
$683$	−36.7165	−	21.1983i	−1.40492	−	0.811130i	−0.410026	−	0.912074i	$-0.634480\pi$
$683$	−36.7165	−	21.1983i	−1.40492	−	0.811130i	−0.994892	+	0.100944i	$0.967814\pi$
$684$		0			0
$685$	−34.5425			−1.31980
$686$	−13.8641	+	12.2795i	−0.529334	+	0.468834i
$687$		0			0
$688$	−2.78052	−	4.81600i	−0.106006	−	0.183608i
$689$	−20.4022	+	11.9735i	−0.777260	+	0.456155i
$690$		0			0
$691$	27.7470	−	16.0197i	1.05554	−	0.609419i	0.131348	−	0.991336i	$-0.458070\pi$
$691$	27.7470	−	16.0197i	1.05554	−	0.609419i	0.924196	+	0.381918i	$0.124736\pi$
$692$	3.93890			0.149735
$693$		0			0
$694$		−	12.6826i		−	0.481425i
$695$	−17.4972	+	10.1020i	−0.663707	+	0.383191i
$696$		0			0
$697$	−1.84246	−	1.06374i	−0.0697880	−	0.0402921i
$698$	8.36290	+	14.4850i	0.316540	+	0.548264i
$699$		0			0
$700$	1.58002	−	3.21723i	0.0597190	−	0.121600i
$701$	−50.5029			−1.90747			−0.953734	−	0.300651i	$-0.902796\pi$
$701$	−50.5029			−1.90747			−0.953734	+	0.300651i	$0.902796\pi$
$702$		0			0
$703$	−12.6549	+	21.9190i	−0.477290	+	0.826690i
$704$	−4.88772	−	2.82193i	−0.184213	−	0.106355i
$705$		0			0
$706$	−9.64324			−0.362928
$707$	30.4090	−	2.04314i	1.14365	−	0.0768401i
$708$		0			0
$709$	12.8665	−	7.42845i	0.483210	−	0.278981i	−0.238543	−	0.971132i	$-0.576670\pi$
$709$	12.8665	−	7.42845i	0.483210	−	0.278981i	0.721753	+	0.692151i	$0.243337\pi$
$710$	−8.87264	−	5.12262i	−0.332984	−	0.192248i
$711$		0			0
$712$	2.81116	+	4.86906i	0.105353	+	0.182476i
$713$		−	22.0558i		−	0.825998i
$714$		0			0
$715$	−44.6062	−	25.3320i	−1.66818	−	0.947364i
$716$	−2.35319	−	4.07584i	−0.0879427	−	0.152321i
$717$		0			0
$718$	−0.283541	+	0.491107i	−0.0105817	+	0.0183280i
$719$	8.46051	+	14.6540i	0.315524	+	0.546503i	0.979549	−	0.201207i	$-0.0644865\pi$
$719$	8.46051	+	14.6540i	0.315524	+	0.546503i	−0.664025	+	0.747710i	$0.731153\pi$
$720$		0			0
$721$	−6.75105	+	13.7465i	−0.251422	+	0.511946i
$722$			9.24691i			0.344134i
$723$		0			0
$724$	−7.81998	+	13.5446i	−0.290627	+	0.503381i
$725$	2.87809	−	4.98499i	0.106889	−	0.185138i
$726$		0			0
$727$	31.4510			1.16645			0.583227	−	0.812309i	$-0.301790\pi$
$727$	31.4510			1.16645			0.583227	+	0.812309i	$0.301790\pi$
$728$	−9.51314	+	0.707191i	−0.352581	+	0.0262102i
$729$		0			0
$730$	17.1869	−	9.92289i	0.636117	−	0.367263i
$731$	−0.687916	+	1.19151i	−0.0254435	+	0.0440694i
$732$		0			0
$733$	−13.3249	+	7.69312i	−0.492166	+	0.284152i	−0.725472	−	0.688251i	$-0.758379\pi$
$733$	−13.3249	+	7.69312i	−0.492166	+	0.284152i	0.233307	+	0.972403i	$0.425045\pi$
$734$		−	13.2510i		−	0.489103i
$735$		0			0
$736$		−	3.60213i		−	0.132776i
$737$	−34.3971	−	59.5775i	−1.26703	−	2.19456i
$738$		0			0
$739$	−9.93208	−	5.73429i	−0.365357	−	0.210939i	0.306071	−	0.952009i	$-0.400986\pi$
$739$	−9.93208	−	5.73429i	−0.365357	−	0.210939i	−0.671428	+	0.741070i	$0.734319\pi$
$740$	10.2150	+	17.6929i	0.375510	+	0.650402i
$741$		0			0
$742$	14.4176	−	9.66769i	0.529285	−	0.354912i
$743$		−	16.4784i		−	0.604534i	−0.953223	−	0.302267i	$-0.902257\pi$
$743$		−	16.4784i		−	0.604534i	0.953223	−	0.302267i	$-0.0977434\pi$
$744$		0			0
$745$	−2.36389	+	4.09438i	−0.0866062	+	0.150006i
$746$	−20.6939	−	11.9476i	−0.757656	−	0.437433i
$747$		0			0
$748$			1.39632i			0.0510546i
$749$	18.5791	−	37.8308i	0.678867	−	1.38231i
$750$		0			0
$751$	−15.2492	−	26.4123i	−0.556450	−	0.963800i	−0.997789	−	0.0664593i	$-0.978830\pi$
$751$	−15.2492	−	26.4123i	−0.556450	−	0.963800i	0.441339	−	0.897340i	$-0.354504\pi$
$752$	−5.78854	−	3.34201i	−0.211086	−	0.121871i
$753$		0			0
$754$	−15.3194	+	0.108986i	−0.557900	+	0.00396902i
$755$	6.83171			0.248631
$756$		0			0
$757$	32.1769			1.16949			0.584744	−	0.811218i	$-0.301195\pi$
$757$	32.1769			1.16949			0.584744	+	0.811218i	$0.301195\pi$
$758$	0.730126	+	1.26462i	0.0265194	+	0.0459329i
$759$		0			0
$760$	−6.81789	−	3.93631i	−0.247311	−	0.142785i
$761$	23.8111	−	13.7473i	0.863151	−	0.498341i	−0.00191497	−	0.999998i	$-0.500610\pi$
$761$	23.8111	−	13.7473i	0.863151	−	0.498341i	0.865066	+	0.501657i	$0.167276\pi$
$762$		0			0
$763$	0.262621	+	3.90871i	0.00950750	+	0.141505i
$764$	8.97686			0.324771
$765$		0			0
$766$	−3.26040	+	5.64718i	−0.117803	+	0.204041i
$767$	14.5191	+	24.7397i	0.524256	+	0.893300i
$768$		0			0
$769$			5.03709i			0.181642i	0.995867	+	0.0908210i	$0.0289491\pi$
$769$			5.03709i			0.181642i	−0.995867	+	0.0908210i	$0.971051\pi$
$770$	33.7873	+	16.5933i	1.21761	+	0.597982i
$771$		0			0
$772$	6.09697	−	3.52009i	0.219435	−	0.126691i
$773$	11.3640	+	6.56103i	0.408736	+	0.235984i	0.690247	−	0.723574i	$-0.257502\pi$
$773$	11.3640	+	6.56103i	0.408736	+	0.235984i	−0.281510	+	0.959558i	$0.590835\pi$
$774$		0			0
$775$	−7.18368	+	4.14750i	−0.258045	+	0.148982i
$776$	−16.8748			−0.605769
$777$		0			0
$778$		−	25.6019i		−	0.917874i
$779$	13.4276	+	23.2572i	0.481093	+	0.833277i
$780$		0			0
$781$	11.4688	−	19.8646i	0.410387	−	0.710811i
$782$	−0.771793	+	0.445595i	−0.0275992	+	0.0159344i
$783$		0			0
$784$	6.93708	−	0.936412i	0.247753	−	0.0334433i
$785$		−	43.1156i		−	1.53886i
$786$		0			0
$787$	−8.11053	−	4.68261i	−0.289109	−	0.166917i	0.348431	−	0.937334i	$-0.386715\pi$
$787$	−8.11053	−	4.68261i	−0.289109	−	0.166917i	−0.637540	+	0.770417i	$0.720048\pi$
$788$	10.1412	+	5.85504i	0.361266	+	0.208577i
$789$		0			0
$790$	16.2728			0.578960
$791$	−14.7900	−	22.0566i	−0.525873	−	0.784241i
$792$		0			0
$793$	0.328022	+	46.1080i	0.0116484	+	1.63734i
$794$	7.76567	−	13.4505i	0.275593	−	0.477342i
$795$		0			0
$796$	9.05076	+	15.6764i	0.320796	+	0.555634i
$797$	23.1485			0.819963			0.409982	−	0.912094i	$-0.365535\pi$
$797$	23.1485			0.819963			0.409982	+	0.912094i	$0.365535\pi$
$798$		0			0
$799$			1.65367i			0.0585026i
$800$	−1.17323	+	0.677364i	−0.0414799	+	0.0239484i
$801$		0			0
$802$	17.4765	−	30.2703i	0.617118	−	1.06888i
$803$	22.2160	+	38.4792i	0.783984	+	1.35790i
$804$		0			0
$805$	1.61055	+	23.9706i	0.0567645	+	0.844854i
$806$	19.1971	+	10.9021i	0.676188	+	0.384010i
$807$		0			0
$808$	−9.97613	−	5.75972i	−0.350959	−	0.202626i
$809$	27.8984	−	48.3215i	0.980856	−	1.69889i	0.321784	−	0.946813i	$-0.395718\pi$
$809$	27.8984	−	48.3215i	0.980856	−	1.69889i	0.659073	−	0.752079i	$-0.270949\pi$
$810$		0			0
$811$		−	49.1611i		−	1.72628i	−0.504966	−	0.863139i	$-0.668495\pi$
$811$		−	49.1611i		−	1.72628i	0.504966	−	0.863139i	$-0.331505\pi$
$812$	11.2164	−	0.753612i	0.393618	−	0.0264466i
$813$		0			0
$814$	−39.6118	+	22.8699i	−1.38839	+	0.801590i
$815$	−23.4505	+	40.6175i	−0.821435	+	1.42277i
$816$		0			0
$817$	15.0403	−	8.68353i	0.526194	−	0.303798i
$818$	−12.7020			−0.444115
$819$		0			0
$820$	21.6773			0.757004
$821$	−28.9550	+	16.7172i	−1.01054	+	0.583433i	−0.911349	−	0.411635i	$-0.864958\pi$
$821$	−28.9550	+	16.7172i	−1.01054	+	0.583433i	−0.0991875	+	0.995069i	$0.531624\pi$
$822$		0			0
$823$	18.3644	−	31.8081i	0.640142	−	1.10876i	−0.345258	−	0.938508i	$-0.612209\pi$
$823$	18.3644	−	31.8081i	0.640142	−	1.10876i	0.985401	−	0.170251i	$-0.0544580\pi$
$824$	5.01294	−	2.89422i	0.174634	−	0.100825i
$825$		0			0
$826$	−11.7231	−	17.4828i	−0.407898	−	0.608304i
$827$		−	45.4204i		−	1.57942i	−0.613478	−	0.789712i	$-0.710230\pi$
$827$		−	45.4204i		−	1.57942i	0.613478	−	0.789712i	$-0.289770\pi$
$828$		0			0
$829$	11.4353	−	19.8065i	0.397164	−	0.687909i	−0.596211	−	0.802828i	$-0.703328\pi$
$829$	11.4353	−	19.8065i	0.397164	−	0.687909i	0.993375	+	0.114920i	$0.0366610\pi$
$830$	−1.44629	−	0.835016i	−0.0502014	−	0.0289838i
$831$		0			0
$832$	3.13524	+	1.78052i	0.108695	+	0.0617283i
$833$	−1.05877	−	1.37050i	−0.0366843	−	0.0474851i
$834$		0			0
$835$	−18.3815	−	31.8376i	−0.636117	−	1.10179i
$836$	8.81286	−	15.2643i	0.304799	−	0.527927i
$837$		0			0
$838$	20.5667	−	11.8742i	0.710464	−	0.410186i
$839$		−	7.31572i		−	0.252567i	−0.991994	−	0.126283i	$-0.959695\pi$
$839$		−	7.31572i		−	0.252567i	0.991994	−	0.126283i	$-0.0403048\pi$
$840$		0			0
$841$	−10.9464			−0.377463
$842$	2.45643	+	4.25466i	0.0846541	+	0.146625i
$843$		0			0
$844$	−11.6126	+	20.1136i	−0.399722	+	0.692339i
$845$	28.6109	+	15.9801i	0.984245	+	0.549733i
$846$		0			0
$847$	−24.3209	+	49.5222i	−0.835675	+	1.70160i
$848$	−6.56103			−0.225307
$849$		0			0
$850$	0.290264	+	0.167584i	0.00995597	+	0.00574808i
$851$	−25.2819	−	14.5965i	−0.866651	−	0.500361i
$852$		0			0
$853$			34.5603i			1.18332i	0.806187	+	0.591661i	$0.201528\pi$
$853$			34.5603i			1.18332i	−0.806187	+	0.591661i	$0.798472\pi$
$854$	−2.26820	−	33.7588i	−0.0776163	−	1.15520i
$855$		0			0
$856$	−13.7958	+	7.96501i	−0.471531	+	0.272238i
$857$	−11.9237	+	20.6525i	−0.407307	+	0.705476i	−0.994587	−	0.103908i	$-0.966865\pi$
$857$	−11.9237	+	20.6525i	−0.407307	+	0.705476i	0.587280	+	0.809384i	$0.300199\pi$
$858$		0			0
$859$	11.2768	+	19.5320i	0.384760	+	0.666424i	0.991736	−	0.128296i	$-0.0409509\pi$
$859$	11.2768	+	19.5320i	0.384760	+	0.666424i	−0.606976	+	0.794720i	$0.707618\pi$
$860$		−	14.0186i		−	0.478030i
$861$		0			0
$862$	25.1596			0.856939
$863$	31.6139	−	18.2523i	1.07615	−	0.621316i	0.146295	−	0.989241i	$-0.453265\pi$
$863$	31.6139	−	18.2523i	1.07615	−	0.621316i	0.929855	+	0.367925i	$0.119932\pi$
$864$		0			0
$865$	8.59912	+	4.96471i	0.292379	+	0.168805i
$866$	5.33880	−	3.08236i	0.181420	−	0.104743i
$867$		0			0
$868$	−14.5410	−	7.14123i	−0.493553	−	0.242389i
$869$			36.4325i			1.23589i
$870$		0			0
$871$	22.2446	+	37.9035i	0.753730	+	1.28431i
$872$	0.740342	−	1.28231i	0.0250712	−	0.0434245i
$873$		0			0
$874$	11.2494			0.380518
$875$	−20.1929	+	13.5403i	−0.682643	+	0.457746i
$876$		0			0
$877$	−5.89748	+	3.40491i	−0.199144	+	0.114976i	−0.596256	−	0.802794i	$-0.703346\pi$
$877$	−5.89748	+	3.40491i	−0.199144	+	0.114976i	0.397112	+	0.917770i	$0.370012\pi$
$878$	−7.70572	−	4.44890i	−0.260055	−	0.150143i
$879$		0			0
$880$	−7.11368	−	12.3212i	−0.239802	−	0.415349i
$881$	−10.4558			−0.352265			−0.176132	−	0.984366i	$-0.556359\pi$
$881$	−10.4558			−0.352265			−0.176132	+	0.984366i	$0.556359\pi$
$882$		0			0
$883$	−22.2786			−0.749736			−0.374868	−	0.927078i	$-0.622312\pi$
$883$	−22.2786			−0.749736			−0.374868	+	0.927078i	$0.622312\pi$
$884$	−0.00634597	−	0.892012i	−0.000213438	−	0.0300016i
$885$		0			0
$886$	29.5842	+	17.0804i	0.993901	+	0.573829i
$887$	20.8726	+	36.1524i	0.700832	+	1.21388i	0.968175	+	0.250276i	$0.0805212\pi$
$887$	20.8726	+	36.1524i	0.700832	+	1.21388i	−0.267342	+	0.963602i	$0.586145\pi$
$888$		0			0
$889$	15.1971	+	22.6637i	0.509696	+	0.760116i
$890$			14.1731i			0.475082i
$891$		0			0
$892$	−6.20734	−	3.58381i	−0.207837	−	0.119995i
$893$	10.4371	−	18.0776i	0.349264	−	0.604942i
$894$		0			0
$895$		−	11.8641i		−	0.396573i
$896$	−2.37482	−	1.16630i	−0.0793370	−	0.0389633i
$897$		0			0
$898$	14.5424	+	25.1882i	0.485286	+	0.840540i
$899$	−22.5308	−	13.0081i	−0.751443	−	0.433846i
$900$		0			0
$901$	0.811619	+	1.40577i	0.0270390	+	0.0468328i
$902$			48.5325i			1.61595i
$903$		0			0
$904$			10.0373i			0.333837i
$905$	−34.1440	+	19.7131i	−1.13499	+	0.655285i
$906$		0			0
$907$	24.6748	−	42.7379i	0.819312	−	1.41909i	−0.0868777	−	0.996219i	$-0.527689\pi$
$907$	24.6748	−	42.7379i	0.819312	−	1.41909i	0.906190	−	0.422871i	$-0.138978\pi$
$908$	−18.6007	+	10.7391i	−0.617287	+	0.356391i
$909$		0			0
$910$	−21.6598	−	10.4468i	−0.718014	−	0.346307i
$911$	−15.7093			−0.520473			−0.260237	−	0.965545i	$-0.583801\pi$
$911$	−15.7093			−0.520473			−0.260237	+	0.965545i	$0.583801\pi$
$912$		0			0
$913$	1.86948	−	3.23804i	0.0618709	−	0.107164i
$914$	−17.7460	+	30.7370i	−0.586986	+	1.01669i
$915$		0			0
$916$		−	8.26740i		−	0.273163i
$917$	−21.5740	+	43.9290i	−0.712436	+	1.45066i
$918$		0			0
$919$	−16.4337	−	28.4639i	−0.542096	−	0.938938i	−0.998783	−	0.0493110i	$-0.984297\pi$
$919$	−16.4337	−	28.4639i	−0.542096	−	0.938938i	0.456687	−	0.889627i	$-0.349036\pi$
$920$	4.54024	−	7.86392i	0.149687	−	0.259266i
$921$		0			0
$922$	3.78690	+	6.55910i	0.124715	+	0.216012i
$923$	−7.23635	+	12.7422i	−0.238187	+	0.419415i
$924$		0			0
$925$			10.9792i			0.360994i
$926$	12.5149	+	21.6765i	0.411266	+	0.712334i
$927$		0			0
$928$	−3.67970	−	2.12447i	−0.120792	−	0.0697393i
$929$	13.5536	−	7.82520i	0.444680	−	0.256736i	−0.260901	−	0.965366i	$-0.584019\pi$
$929$	13.5536	−	7.82520i	0.444680	−	0.256736i	0.705581	+	0.708629i	$0.250686\pi$
$930$		0			0
$931$	2.92441	+	21.6645i	0.0958436	+	0.710024i
$932$	26.8920			0.880877
$933$		0			0
$934$	−27.0778	−	15.6334i	−0.886013	−	0.511540i
$935$	−1.75997	+	3.04835i	−0.0575570	+	0.0996917i
$936$		0			0
$937$	3.71754			0.121447			0.0607233	−	0.998155i	$-0.480659\pi$
$937$	3.71754			0.121447			0.0607233	+	0.998155i	$0.480659\pi$
$938$	−17.9608	−	26.7852i	−0.586442	−	0.874568i
$939$		0			0
$940$	−8.42474	−	14.5921i	−0.274785	−	0.475941i
$941$	34.6486	+	20.0044i	1.12951	+	0.652124i	0.943812	−	0.330482i	$-0.107211\pi$
$941$	34.6486	+	20.0044i	1.12951	+	0.652124i	0.185700	+	0.982607i	$0.440545\pi$
$942$		0			0
$943$	−26.8255	+	15.4877i	−0.873557	+	0.504348i
$944$			7.95594i			0.258944i
$945$		0			0
$946$	31.3856			1.02044
$947$	−20.0418	+	11.5712i	−0.651272	+	0.376012i	−0.788943	−	0.614466i	$-0.789372\pi$
$947$	−20.0418	+	11.5712i	−0.651272	+	0.376012i	0.137671	+	0.990478i	$0.456038\pi$
$948$		0			0
$949$	−14.3671	−	24.4807i	−0.466376	−	0.794676i
$950$	−2.11540	−	3.66399i	−0.0686328	−	0.118875i
$951$		0			0
$952$	0.0438810	+	0.653102i	0.00142219	+	0.0211672i
$953$	9.61707			0.311527			0.155764	−	0.987794i	$-0.450216\pi$
$953$	9.61707			0.311527			0.155764	+	0.987794i	$0.450216\pi$
$954$		0			0
$955$	19.5976	+	11.3147i	0.634165	+	0.366135i
$956$	−3.78867	−	2.18739i	−0.122534	−	0.0707453i
$957$		0			0
$958$	−15.5185			−0.501380
$959$	−2.43036	−	36.1723i	−0.0784805	−	1.16806i
$960$		0			0
$961$	3.24552	+	5.62141i	0.104694	+	0.181336i
$962$	25.2013	−	14.7900i	0.812522	−	0.476849i
$963$		0			0
$964$	1.33779	−	0.772373i	0.0430873	−	0.0248765i
$965$	17.7473			0.571305
$966$		0			0
$967$		−	19.4428i		−	0.625238i	−0.949879	−	0.312619i	$-0.898794\pi$
$967$		−	19.4428i		−	0.625238i	0.949879	−	0.312619i	$-0.101206\pi$
$968$	18.0593	−	10.4265i	0.580447	−	0.335121i
$969$		0			0
$970$	−36.8398	−	21.2695i	−1.18285	−	0.682922i
$971$	18.4152	+	31.8960i	0.590971	+	1.02359i	0.994102	+	0.108450i	$0.0345886\pi$
$971$	18.4152	+	31.8960i	0.590971	+	1.02359i	−0.403131	+	0.915142i	$0.632078\pi$
$972$		0			0
$973$	−11.8097	−	17.6120i	−0.378603	−	0.564615i
$974$	32.3861			1.03772
$975$		0			0
$976$	−6.39419	+	11.0751i	−0.204673	+	0.354504i
$977$	−23.3376	−	13.4740i	−0.746635	−	0.431070i	0.0778417	−	0.996966i	$-0.475197\pi$
$977$	−23.3376	−	13.4740i	−0.746635	−	0.431070i	−0.824477	+	0.565896i	$0.808530\pi$
$978$		0			0
$979$	−31.7315			−1.01414
$980$	16.3248	+	6.69940i	0.521477	+	0.214004i
$981$		0			0
$982$	7.98524	−	4.61028i	0.254819	−	0.147120i
$983$	45.1202	+	26.0502i	1.43911	+	0.830872i	0.997788	−	0.0664765i	$-0.0211757\pi$
$983$	45.1202	+	26.0502i	1.43911	+	0.830872i	0.441324	+	0.897348i	$0.354509\pi$
$984$		0			0
$985$	14.7597	+	25.5646i	0.470284	+	0.814555i
$986$			1.05122i			0.0334775i
$987$		0			0
$988$	−5.56054	+	9.79135i	−0.176904	+	0.311504i
$989$	10.0158	+	17.3479i	0.318484	+	0.551630i
$990$		0			0
$991$	18.7490	−	32.4743i	0.595583	−	1.03158i	−0.397881	−	0.917437i	$-0.630254\pi$
$991$	18.7490	−	32.4743i	0.595583	−	1.03158i	0.993464	−	0.114143i	$-0.0364123\pi$
$992$	3.06150	+	5.30267i	0.0972026	+	0.168360i
$993$		0			0
$994$	4.74005	−	9.65169i	0.150345	−	0.306133i
$995$			45.6314i			1.44661i
$996$		0			0
$997$	−3.03388	+	5.25484i	−0.0960840	+	0.166422i	−0.910061	−	0.414475i	$-0.863965\pi$
$997$	−3.03388	+	5.25484i	−0.0960840	+	0.166422i	0.813976	+	0.580898i	$0.197298\pi$
$998$	3.78999	−	6.56445i	0.119970	−	0.207794i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1638.2.dm.e.1117.9		20
3.2	odd	2		546.2.bk.c.25.2	✓	20
7.2	even	3	inner	1638.2.dm.e.415.2		20
13.12	even	2	inner	1638.2.dm.e.1117.2		20
21.2	odd	6		546.2.bk.c.415.9	yes	20
21.11	odd	6		3822.2.c.m.883.2		10
21.17	even	6		3822.2.c.n.883.4		10
39.38	odd	2		546.2.bk.c.25.9	yes	20
91.51	even	6	inner	1638.2.dm.e.415.9		20
273.38	even	6		3822.2.c.n.883.7		10
273.116	odd	6		3822.2.c.m.883.9		10
273.233	odd	6		546.2.bk.c.415.2	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bk.c.25.2	✓	20	3.2	odd	2
546.2.bk.c.25.9	yes	20	39.38	odd	2
546.2.bk.c.415.2	yes	20	273.233	odd	6
546.2.bk.c.415.9	yes	20	21.2	odd	6
1638.2.dm.e.415.2		20	7.2	even	3	inner
1638.2.dm.e.415.9		20	91.51	even	6	inner
1638.2.dm.e.1117.2		20	13.12	even	2	inner
1638.2.dm.e.1117.9		20	1.1	even	1	trivial
3822.2.c.m.883.2		10	21.11	odd	6
3822.2.c.m.883.9		10	273.116	odd	6
3822.2.c.n.883.4		10	21.17	even	6
3822.2.c.n.883.7		10	273.38	even	6

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:	\( N \)	\(=\)	\( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1638.dm (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(2.18313 - 1.26043i) q^{5} +(1.47350 + 2.19745i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(2.18313 - 1.26043i) q^{5} +(1.47350 + 2.19745i) q^{7} -1.00000i q^{8} +(1.26043 - 2.18313i) q^{10} +(4.88772 + 2.82193i) q^{11} +(-3.13524 - 1.78052i) q^{13} +(2.37482 + 1.16630i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-0.123703 + 0.214260i) q^{17} +(2.70459 - 1.56150i) q^{19} -2.52086i q^{20} +5.64385 q^{22} +(1.80107 + 3.11954i) q^{23} +(0.677364 - 1.17323i) q^{25} +(-3.60546 + 0.0256500i) q^{26} +(2.63980 - 0.177364i) q^{28} +4.24895 q^{29} +(-5.30267 - 3.06150i) q^{31} +(-0.866025 - 0.500000i) q^{32} +0.247406i q^{34} +(5.98657 + 2.94007i) q^{35} +(-7.01858 + 4.05218i) q^{37} +(1.56150 - 2.70459i) q^{38} +(-1.26043 - 2.18313i) q^{40} +8.59917i q^{41} +5.56103 q^{43} +(4.88772 - 2.82193i) q^{44} +(3.11954 + 1.80107i) q^{46} +(5.78854 - 3.34201i) q^{47} +(-2.65759 + 6.47590i) q^{49} -1.35473i q^{50} +(-3.10959 + 1.82494i) q^{52} +(3.28052 - 5.68202i) q^{53} +14.2274 q^{55} +(2.19745 - 1.47350i) q^{56} +(3.67970 - 2.12447i) q^{58} +(-6.89004 - 3.97797i) q^{59} +(-6.39419 - 11.0751i) q^{61} -6.12299 q^{62} -1.00000 q^{64} +(-9.08886 + 0.0646601i) q^{65} +(-10.5562 - 6.09461i) q^{67} +(0.123703 + 0.214260i) q^{68} +(6.65456 - 0.447110i) q^{70} -4.06419i q^{71} +(6.81789 + 3.93631i) q^{73} +(-4.05218 + 7.01858i) q^{74} -3.12299i q^{76} +(1.00102 + 14.8986i) q^{77} +(3.22763 + 5.59041i) q^{79} +(-2.18313 - 1.26043i) q^{80} +(4.29959 + 7.44710i) q^{82} -0.662485i q^{83} +0.623675i q^{85} +(4.81600 - 2.78052i) q^{86} +(2.82193 - 4.88772i) q^{88} +(-4.86906 + 2.81116i) q^{89} +(-0.707191 - 9.51314i) q^{91} +3.60213 q^{92} +(3.34201 - 5.78854i) q^{94} +(3.93631 - 6.81789i) q^{95} -16.8748i q^{97} +(0.936412 + 6.93708i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 10 q^{4}+O(q^{10}) \) 20 * q + 10 * q^4	\( 20 q + 10 q^{4} + 4 q^{10} + 4 q^{13} + 2 q^{14} - 10 q^{16} + 6 q^{17} - 12 q^{22} + 16 q^{23} + 2 q^{25} + 4 q^{26} + 28 q^{29} - 16 q^{35} - 10 q^{38} - 4 q^{40} + 24 q^{43} + 2 q^{49} + 2 q^{52} + 22 q^{53} + 88 q^{55} + 10 q^{56} + 14 q^{61} - 40 q^{62} - 20 q^{64} - 20 q^{65} - 6 q^{68} - 24 q^{74} + 28 q^{77} + 4 q^{79} + 12 q^{82} - 6 q^{88} + 68 q^{91} + 32 q^{92} - 18 q^{94} - 8 q^{95}+O(q^{100}) \) 20 * q + 10 * q^4 + 4 * q^10 + 4 * q^13 + 2 * q^14 - 10 * q^16 + 6 * q^17 - 12 * q^22 + 16 * q^23 + 2 * q^25 + 4 * q^26 + 28 * q^29 - 16 * q^35 - 10 * q^38 - 4 * q^40 + 24 * q^43 + 2 * q^49 + 2 * q^52 + 22 * q^53 + 88 * q^55 + 10 * q^56 + 14 * q^61 - 40 * q^62 - 20 * q^64 - 20 * q^65 - 6 * q^68 - 24 * q^74 + 28 * q^77 + 4 * q^79 + 12 * q^82 - 6 * q^88 + 68 * q^91 + 32 * q^92 - 18 * q^94 - 8 * q^95

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