LMFDB - Embedded newform 729.2.c.d.487.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(244,729)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("729.244");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.c (of order $3$, degree $2$, 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:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 18x^{10} + 105x^{8} + 266x^{6} + 306x^{4} + 132x^{2} + 1 $ x^12 + 18x^10 + 105x^8 + 266x^6 + 306x^4 + 132*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			487.4
Root			$-1.91182i$ of defining polynomial
Character	$\chi$	$=$	729.487
Dual form			729.2.c.d.244.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.789202 - 1.36694i) q^{2} +(-0.245680 - 0.425530i) q^{4} +(-0.839254 - 1.45363i) q^{5} +(-1.38964 + 2.40693i) q^{7} +2.38124 q^{8} +O(q^{10})$	\(q+(0.789202 - 1.36694i) q^{2} +(-0.245680 - 0.425530i) q^{4} +(-0.839254 - 1.45363i) q^{5} +(-1.38964 + 2.40693i) q^{7} +2.38124 q^{8} -2.64936 q^{10} +(2.07561 - 3.59506i) q^{11} +(-3.43802 - 5.95483i) q^{13} +(2.19342 + 3.79911i) q^{14} +(2.37064 - 4.10607i) q^{16} +0.976551 q^{17} +2.68529 q^{19} +(-0.412376 + 0.714256i) q^{20} +(-3.27615 - 5.67446i) q^{22} +(-0.806585 - 1.39705i) q^{23} +(1.09131 - 1.89020i) q^{25} -10.8532 q^{26} +1.36563 q^{28} +(4.11394 - 7.12555i) q^{29} +(-0.522035 - 0.904190i) q^{31} +(-1.36059 - 2.35661i) q^{32} +(0.770696 - 1.33489i) q^{34} +4.66505 q^{35} -1.30834 q^{37} +(2.11924 - 3.67062i) q^{38} +(-1.99847 - 3.46145i) q^{40} +(2.42408 + 4.19864i) q^{41} +(-4.92011 + 8.52189i) q^{43} -2.03974 q^{44} -2.54623 q^{46} +(-6.24885 + 10.8233i) q^{47} +(-0.362204 - 0.627356i) q^{49} +(-1.72252 - 2.98350i) q^{50} +(-1.68931 + 2.92596i) q^{52} +7.34280 q^{53} -6.96786 q^{55} +(-3.30907 + 5.73148i) q^{56} +(-6.49346 - 11.2470i) q^{58} +(-4.52594 - 7.83915i) q^{59} +(0.642871 - 1.11349i) q^{61} -1.64796 q^{62} +5.18745 q^{64} +(-5.77075 + 9.99523i) q^{65} +(2.32315 + 4.02381i) q^{67} +(-0.239919 - 0.415552i) q^{68} +(3.68166 - 6.37683i) q^{70} +5.62373 q^{71} -4.56144 q^{73} +(-1.03255 + 1.78843i) q^{74} +(-0.659722 - 1.14267i) q^{76} +(5.76871 + 9.99170i) q^{77} +(-2.32840 + 4.03291i) q^{79} -7.95828 q^{80} +7.65237 q^{82} +(-2.88220 + 4.99211i) q^{83} +(-0.819574 - 1.41954i) q^{85} +(7.76593 + 13.4510i) q^{86} +(4.94254 - 8.56072i) q^{88} +4.54442 q^{89} +19.1105 q^{91} +(-0.396323 + 0.686452i) q^{92} +(9.86321 + 17.0836i) q^{94} +(-2.25364 - 3.90342i) q^{95} +(-4.28772 + 7.42655i) q^{97} -1.14341 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{2} - 9 q^{4} - 3 q^{5} - 6 q^{7} - 12 q^{8}+O(q^{10}) $ 12 * q + 3 * q^2 - 9 * q^4 - 3 * q^5 - 6 * q^7 - 12 * q^8	$ 12 q + 3 q^{2} - 9 q^{4} - 3 q^{5} - 6 q^{7} - 12 q^{8} + 12 q^{10} - 6 q^{11} - 6 q^{13} + 24 q^{14} - 15 q^{16} + 18 q^{17} + 24 q^{19} - 21 q^{20} - 3 q^{22} - 12 q^{23} - 9 q^{25} - 48 q^{26} + 6 q^{28} + 21 q^{29} - 15 q^{31} - 60 q^{35} + 6 q^{37} + 15 q^{38} - 3 q^{40} - 12 q^{41} - 6 q^{43} + 66 q^{44} - 6 q^{46} - 15 q^{47} - 12 q^{49} - 24 q^{50} - 3 q^{52} + 18 q^{53} + 30 q^{55} + 12 q^{56} + 15 q^{58} + 6 q^{59} - 24 q^{61} + 60 q^{62} + 12 q^{64} - 15 q^{65} - 15 q^{67} + 36 q^{68} + 15 q^{70} + 24 q^{73} + 24 q^{74} - 9 q^{76} + 15 q^{77} - 24 q^{79} + 42 q^{80} - 42 q^{82} - 6 q^{83} + 18 q^{85} - 30 q^{86} + 21 q^{88} + 18 q^{89} + 36 q^{91} + 6 q^{92} + 6 q^{94} - 33 q^{95} + 21 q^{97} - 36 q^{98}+O(q^{100}) $ 12 * q + 3 * q^2 - 9 * q^4 - 3 * q^5 - 6 * q^7 - 12 * q^8 + 12 * q^10 - 6 * q^11 - 6 * q^13 + 24 * q^14 - 15 * q^16 + 18 * q^17 + 24 * q^19 - 21 * q^20 - 3 * q^22 - 12 * q^23 - 9 * q^25 - 48 * q^26 + 6 * q^28 + 21 * q^29 - 15 * q^31 - 60 * q^35 + 6 * q^37 + 15 * q^38 - 3 * q^40 - 12 * q^41 - 6 * q^43 + 66 * q^44 - 6 * q^46 - 15 * q^47 - 12 * q^49 - 24 * q^50 - 3 * q^52 + 18 * q^53 + 30 * q^55 + 12 * q^56 + 15 * q^58 + 6 * q^59 - 24 * q^61 + 60 * q^62 + 12 * q^64 - 15 * q^65 - 15 * q^67 + 36 * q^68 + 15 * q^70 + 24 * q^73 + 24 * q^74 - 9 * q^76 + 15 * q^77 - 24 * q^79 + 42 * q^80 - 42 * q^82 - 6 * q^83 + 18 * q^85 - 30 * q^86 + 21 * q^88 + 18 * q^89 + 36 * q^91 + 6 * q^92 + 6 * q^94 - 33 * q^95 + 21 * q^97 - 36 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.789202	−	1.36694i	0.558050	−	0.966571i	−0.439609	−	0.898189i	$-0.644883\pi$
$2$	0.789202	−	1.36694i	0.558050	−	0.966571i	0.997659	−	0.0683820i	$-0.0217837\pi$
$3$		0			0
$3$		0			0
$4$	−0.245680	−	0.425530i	−0.122840	−	0.212765i
$5$	−0.839254	−	1.45363i	−0.375326	−	0.650083i	0.615050	−	0.788488i	$-0.289136\pi$
$5$	−0.839254	−	1.45363i	−0.375326	−	0.650083i	−0.990376	+	0.138405i	$0.955802\pi$
$6$		0			0
$7$	−1.38964	+	2.40693i	−0.525235	+	0.909734i	0.474333	+	0.880345i	$0.342689\pi$
$7$	−1.38964	+	2.40693i	−0.525235	+	0.909734i	−0.999568	+	0.0293881i	$0.990644\pi$
$8$	2.38124			0.841897
$9$		0			0
$10$	−2.64936			−0.837802
$11$	2.07561	−	3.59506i	0.625820	−	1.08395i	−0.362561	−	0.931960i	$-0.618098\pi$
$11$	2.07561	−	3.59506i	0.625820	−	1.08395i	0.988382	−	0.151993i	$-0.0485690\pi$
$12$		0			0
$13$	−3.43802	−	5.95483i	−0.953536	−	1.65157i	−0.737684	−	0.675147i	$-0.764080\pi$
$13$	−3.43802	−	5.95483i	−0.953536	−	1.65157i	−0.215852	−	0.976426i	$-0.569253\pi$
$14$	2.19342	+	3.79911i	0.586215	+	1.01535i
$15$		0			0
$16$	2.37064	−	4.10607i	0.592661	−	1.02652i
$17$	0.976551			0.236848			0.118424	−	0.992963i	$-0.462216\pi$
$17$	0.976551			0.236848			0.118424	+	0.992963i	$0.462216\pi$
$18$		0			0
$19$	2.68529			0.616048			0.308024	−	0.951379i	$-0.400332\pi$
$19$	2.68529			0.616048			0.308024	+	0.951379i	$0.400332\pi$
$20$	−0.412376	+	0.714256i	−0.0922100	+	0.159712i
$21$		0			0
$22$	−3.27615	−	5.67446i	−0.698478	−	1.20980i
$23$	−0.806585	−	1.39705i	−0.168185	−	0.291304i	0.769597	−	0.638530i	$-0.220457\pi$
$23$	−0.806585	−	1.39705i	−0.168185	−	0.291304i	−0.937782	+	0.347226i	$0.887124\pi$
$24$		0			0
$25$	1.09131	−	1.89020i	0.218261	−	0.378040i
$26$	−10.8532			−2.12848
$27$		0			0
$28$	1.36563			0.258079
$29$	4.11394	−	7.12555i	0.763939	−	1.32318i	−0.176866	−	0.984235i	$-0.556596\pi$
$29$	4.11394	−	7.12555i	0.763939	−	1.32318i	0.940806	−	0.338947i	$-0.110071\pi$
$30$		0			0
$31$	−0.522035	−	0.904190i	−0.0937602	−	0.162397i	0.815330	−	0.578996i	$-0.196555\pi$
$31$	−0.522035	−	0.904190i	−0.0937602	−	0.162397i	−0.909090	+	0.416599i	$0.863222\pi$
$32$	−1.36059	−	2.35661i	−0.240520	−	0.416593i
$33$		0			0
$34$	0.770696	−	1.33489i	0.132173	−	0.228931i
$35$	4.66505			0.788537
$36$		0			0
$37$	−1.30834			−0.215091			−0.107545	−	0.994200i	$-0.534299\pi$
$37$	−1.30834			−0.215091			−0.107545	+	0.994200i	$0.534299\pi$
$38$	2.11924	−	3.67062i	0.343785	−	0.595454i
$39$		0			0
$40$	−1.99847	−	3.46145i	−0.315986	−	0.547303i
$41$	2.42408	+	4.19864i	0.378578	+	0.655717i	0.990856	−	0.134926i	$-0.0430797\pi$
$41$	2.42408	+	4.19864i	0.378578	+	0.655717i	−0.612277	+	0.790643i	$0.709746\pi$
$42$		0			0
$43$	−4.92011	+	8.52189i	−0.750310	+	1.29958i	0.197362	+	0.980331i	$0.436763\pi$
$43$	−4.92011	+	8.52189i	−0.750310	+	1.29958i	−0.947672	+	0.319245i	$0.896571\pi$
$44$	−2.03974			−0.307503
$45$		0			0
$46$	−2.54623			−0.375422
$47$	−6.24885	+	10.8233i	−0.911488	+	1.57874i	−0.0995258	+	0.995035i	$0.531733\pi$
$47$	−6.24885	+	10.8233i	−0.911488	+	1.57874i	−0.811963	+	0.583709i	$0.801601\pi$
$48$		0			0
$49$	−0.362204	−	0.627356i	−0.0517434	−	0.0896222i
$50$	−1.72252	−	2.98350i	−0.243601	−	0.421930i
$51$		0			0
$52$	−1.68931	+	2.92596i	−0.234265	+	0.405758i
$53$	7.34280			1.00861			0.504305	−	0.863525i	$-0.331749\pi$
$53$	7.34280			1.00861			0.504305	+	0.863525i	$0.331749\pi$
$54$		0			0
$55$	−6.96786			−0.939546
$56$	−3.30907	+	5.73148i	−0.442194	+	0.765902i
$57$		0			0
$58$	−6.49346	−	11.2470i	−0.852633	−	1.47680i
$59$	−4.52594	−	7.83915i	−0.589227	−	1.02057i	−0.994334	−	0.106302i	$-0.966099\pi$
$59$	−4.52594	−	7.83915i	−0.589227	−	1.02057i	0.405107	−	0.914269i	$-0.367234\pi$
$60$		0			0
$61$	0.642871	−	1.11349i	0.0823112	−	0.142567i	−0.821931	−	0.569587i	$-0.807103\pi$
$61$	0.642871	−	1.11349i	0.0823112	−	0.142567i	0.904242	+	0.427020i	$0.140437\pi$
$62$	−1.64796			−0.209292
$63$		0			0
$64$	5.18745			0.648432
$65$	−5.77075	+	9.99523i	−0.715773	+	1.23976i
$66$		0			0
$67$	2.32315	+	4.02381i	0.283818	+	0.491587i	0.972322	−	0.233646i	$-0.0750655\pi$
$67$	2.32315	+	4.02381i	0.283818	+	0.491587i	−0.688504	+	0.725233i	$0.741732\pi$
$68$	−0.239919	−	0.415552i	−0.0290945	−	0.0503931i
$69$		0			0
$70$	3.68166	−	6.37683i	0.440043	−	0.762177i
$71$	5.62373			0.667414			0.333707	−	0.942677i	$-0.391700\pi$
$71$	5.62373			0.667414			0.333707	+	0.942677i	$0.391700\pi$
$72$		0			0
$73$	−4.56144			−0.533877			−0.266938	−	0.963714i	$-0.586012\pi$
$73$	−4.56144			−0.533877			−0.266938	+	0.963714i	$0.586012\pi$
$74$	−1.03255	+	1.78843i	−0.120031	+	0.207900i
$75$		0			0
$76$	−0.659722	−	1.14267i	−0.0756753	−	0.131073i
$77$	5.76871	+	9.99170i	0.657405	+	1.13866i
$78$		0			0
$79$	−2.32840	+	4.03291i	−0.261966	+	0.453738i	−0.966764	−	0.255670i	$-0.917704\pi$
$79$	−2.32840	+	4.03291i	−0.261966	+	0.453738i	0.704799	+	0.709407i	$0.251037\pi$
$80$	−7.95828			−0.889763
$81$		0			0
$82$	7.65237			0.845063
$83$	−2.88220	+	4.99211i	−0.316362	+	0.547955i	−0.979726	−	0.200342i	$-0.935795\pi$
$83$	−2.88220	+	4.99211i	−0.316362	+	0.547955i	0.663364	+	0.748297i	$0.269128\pi$
$84$		0			0
$85$	−0.819574	−	1.41954i	−0.0888953	−	0.153971i
$86$	7.76593	+	13.4510i	0.837422	+	1.45046i
$87$		0			0
$88$	4.94254	−	8.56072i	0.526876	−	0.912576i
$89$	4.54442			0.481707			0.240854	−	0.970561i	$-0.422573\pi$
$89$	4.54442			0.481707			0.240854	+	0.970561i	$0.422573\pi$
$90$		0			0
$91$	19.1105			2.00332
$92$	−0.396323	+	0.686452i	−0.0413196	+	0.0715676i
$93$		0			0
$94$	9.86321	+	17.0836i	1.01731	+	1.76204i
$95$	−2.25364	−	3.90342i	−0.231218	−	0.400482i
$96$		0			0
$97$	−4.28772	+	7.42655i	−0.435352	+	0.754052i	−0.997324	−	0.0731042i	$-0.976709\pi$
$97$	−4.28772	+	7.42655i	−0.435352	+	0.754052i	0.561972	+	0.827156i	$0.310043\pi$
$98$	−1.14341			−0.115502
$99$		0			0
$100$	−1.07245			−0.107245
$101$	3.90285	−	6.75994i	0.388348	−	0.672639i	−0.603879	−	0.797076i	$-0.706379\pi$
$101$	3.90285	−	6.75994i	0.388348	−	0.672639i	0.992228	+	0.124437i	$0.0397124\pi$
$102$		0			0
$103$	1.08307	+	1.87594i	0.106718	+	0.184842i	0.914439	−	0.404724i	$-0.132632\pi$
$103$	1.08307	+	1.87594i	0.106718	+	0.184842i	−0.807721	+	0.589565i	$0.799299\pi$
$104$	−8.18677	−	14.1799i	−0.802779	−	1.39045i
$105$		0			0
$106$	5.79495	−	10.0371i	0.562855	−	0.974894i
$107$	12.5849			1.21663			0.608317	−	0.793695i	$-0.291845\pi$
$107$	12.5849			1.21663			0.608317	+	0.793695i	$0.291845\pi$
$108$		0			0
$109$	−12.2140			−1.16989			−0.584945	−	0.811073i	$-0.698884\pi$
$109$	−12.2140			−1.16989			−0.584945	+	0.811073i	$0.698884\pi$
$110$	−5.49905	+	9.52463i	−0.524314	+	0.908138i
$111$		0			0
$112$	6.58868	+	11.4119i	0.622572	+	1.07833i
$113$	−0.225417	−	0.390433i	−0.0212054	−	0.0367288i	0.855228	−	0.518252i	$-0.173417\pi$
$113$	−0.225417	−	0.390433i	−0.0212054	−	0.0367288i	−0.876433	+	0.481523i	$0.840084\pi$
$114$		0			0
$115$	−1.35386	+	2.34495i	−0.126248	+	0.218668i
$116$	−4.04285			−0.375369
$117$		0			0
$118$	−14.2875			−1.31527
$119$	−1.35706	+	2.35049i	−0.124401	+	0.215469i
$120$		0			0
$121$	−3.11632	−	5.39763i	−0.283302	−	0.490694i
$122$	−1.01471	−	1.75753i	−0.0918675	−	0.159119i
$123$		0			0
$124$	−0.256507	+	0.444283i	−0.0230350	+	0.0398978i
$125$	−12.0561			−1.07833
$126$		0			0
$127$	−0.531069			−0.0471247			−0.0235624	−	0.999722i	$-0.507501\pi$
$127$	−0.531069			−0.0471247			−0.0235624	+	0.999722i	$0.507501\pi$
$128$	6.81513	−	11.8041i	0.602378	−	1.04335i
$129$		0			0
$130$	9.10857	+	15.7765i	0.798875	+	1.38369i
$131$	5.70802	+	9.88658i	0.498712	+	0.863794i	0.999999	−	0.00148672i	$-0.000473237\pi$
$131$	5.70802	+	9.88658i	0.498712	+	0.863794i	−0.501287	+	0.865281i	$0.667140\pi$
$132$		0			0
$133$	−3.73159	+	6.46330i	−0.323570	+	0.560439i
$134$	7.33374			0.633539
$135$		0			0
$136$	2.32541			0.199402
$137$	2.11462	−	3.66263i	0.180664	−	0.312920i	−0.761443	−	0.648232i	$-0.775509\pi$
$137$	2.11462	−	3.66263i	0.180664	−	0.312920i	0.942107	+	0.335313i	$0.108842\pi$
$138$		0			0
$139$	5.57776	+	9.66097i	0.473100	+	0.819433i	0.999526	−	0.0307879i	$-0.00980165\pi$
$139$	5.57776	+	9.66097i	0.473100	+	0.819433i	−0.526426	+	0.850221i	$0.676468\pi$
$140$	−1.14611	−	1.98512i	−0.0968638	−	0.167773i
$141$		0			0
$142$	4.43826	−	7.68730i	0.372451	−	0.645104i
$143$	−28.5440			−2.38697
$144$		0			0
$145$	−13.8106			−1.14690
$146$	−3.59990	+	6.23521i	−0.297930	+	0.516030i
$147$		0			0
$148$	0.321434	+	0.556740i	0.0264217	+	0.0457638i
$149$	−9.73885	−	16.8682i	−0.797837	−	1.38189i	−0.921022	−	0.389511i	$-0.872644\pi$
$149$	−9.73885	−	16.8682i	−0.797837	−	1.38189i	0.123184	−	0.992384i	$-0.460689\pi$
$150$		0			0
$151$	0.621430	−	1.07635i	0.0505713	−	0.0875920i	−0.839632	−	0.543156i	$-0.817229\pi$
$151$	0.621430	−	1.07635i	0.0505713	−	0.0875920i	0.890203	+	0.455564i	$0.150562\pi$
$152$	6.39433			0.518649
$153$		0			0
$154$	18.2107			1.46746
$155$	−0.876239	+	1.51769i	−0.0703812	+	0.121904i
$156$		0			0
$157$	1.76657	+	3.05979i	0.140988	+	0.244198i	0.927869	−	0.372907i	$-0.121639\pi$
$157$	1.76657	+	3.05979i	0.140988	+	0.244198i	−0.786881	+	0.617105i	$0.788306\pi$
$158$	3.67516	+	6.36556i	0.292380	+	0.506417i
$159$		0			0
$160$	−2.28376	+	3.95558i	−0.180547	+	0.312716i
$161$	4.48345			0.353346
$162$		0			0
$163$	15.9509			1.24937			0.624685	−	0.780877i	$-0.285228\pi$
$163$	15.9509			1.24937			0.624685	+	0.780877i	$0.285228\pi$
$164$	1.19110	−	2.06304i	0.0930091	−	0.161097i
$165$		0			0
$166$	4.54927	+	7.87957i	0.353092	+	0.611573i
$167$	7.24232	+	12.5441i	0.560428	+	0.970689i	0.997459	+	0.0712430i	$0.0226966\pi$
$167$	7.24232	+	12.5441i	0.560428	+	0.970689i	−0.437031	+	0.899446i	$0.643970\pi$
$168$		0			0
$169$	−17.1400	+	29.6873i	−1.31846	+	2.28364i
$170$	−2.58724			−0.198432
$171$		0			0
$172$	4.83509			0.368672
$173$	6.30870	−	10.9270i	0.479641	−	0.830763i	−0.520086	−	0.854114i	$-0.674100\pi$
$173$	6.30870	−	10.9270i	0.479641	−	0.830763i	0.999727	+	0.0233506i	$0.00743341\pi$
$174$		0			0
$175$	3.03305	+	5.25339i	0.229277	+	0.397119i
$176$	−9.84106	−	17.0452i	−0.741798	−	1.28483i
$177$		0			0
$178$	3.58646	−	6.21194i	0.268817	−	0.465605i
$179$	−0.295899			−0.0221165			−0.0110582	−	0.999939i	$-0.503520\pi$
$179$	−0.295899			−0.0221165			−0.0110582	+	0.999939i	$0.503520\pi$
$180$		0			0
$181$	1.42050			0.105585			0.0527925	−	0.998606i	$-0.483188\pi$
$181$	1.42050			0.105585			0.0527925	+	0.998606i	$0.483188\pi$
$182$	15.0820	−	26.1228i	1.11795	−	1.93635i
$183$		0			0
$184$	−1.92068	−	3.32671i	−0.141594	−	0.245248i
$185$	1.09803	+	1.90185i	0.0807290	+	0.139827i
$186$		0			0
$187$	2.02694	−	3.51076i	0.148225	−	0.256732i
$188$	6.14087			0.447869
$189$		0			0
$190$	−7.11431			−0.516126
$191$	10.3120	−	17.8610i	0.746153	−	1.29238i	−0.203501	−	0.979075i	$-0.565232\pi$
$191$	10.3120	−	17.8610i	0.746153	−	1.29238i	0.949654	−	0.313301i	$-0.101435\pi$
$192$		0			0
$193$	10.4780	+	18.1484i	0.754221	+	1.30635i	0.945761	+	0.324864i	$0.105319\pi$
$193$	10.4780	+	18.1484i	0.754221	+	1.30635i	−0.191540	+	0.981485i	$0.561348\pi$
$194$	6.76776	+	11.7221i	0.485897	+	0.841598i
$195$		0			0
$196$	−0.177972	+	0.308257i	−0.0127123	+	0.0220184i
$197$	9.59621			0.683702			0.341851	−	0.939754i	$-0.388946\pi$
$197$	9.59621			0.683702			0.341851	+	0.939754i	$0.388946\pi$
$198$		0			0
$199$	−10.6917			−0.757912			−0.378956	−	0.925415i	$-0.623717\pi$
$199$	−10.6917			−0.757912			−0.378956	+	0.925415i	$0.623717\pi$
$200$	2.59867	−	4.50102i	0.183753	−	0.318270i
$201$		0			0
$202$	−6.16028	−	10.6699i	−0.433436	−	0.750732i
$203$	11.4338	+	19.8039i	0.802495	+	1.38996i
$204$		0			0
$205$	4.06885	−	7.04745i	0.284180	−	0.492215i
$206$	3.41906			0.238217
$207$		0			0
$208$	−32.6013			−2.26049
$209$	5.57362	−	9.65379i	0.385535	−	0.667766i
$210$		0			0
$211$	7.52512	+	13.0339i	0.518051	+	0.897290i	0.999780	+	0.0209700i	$0.00667546\pi$
$211$	7.52512	+	13.0339i	0.518051	+	0.897290i	−0.481729	+	0.876320i	$0.659991\pi$
$212$	−1.80398	−	3.12458i	−0.123898	−	0.214597i
$213$		0			0
$214$	9.93207	−	17.2028i	0.678942	−	1.17596i
$215$	16.5169			1.12644
$216$		0			0
$217$	2.90176			0.196984
$218$	−9.63931	+	16.6958i	−0.652857	+	1.13078i
$219$		0			0
$220$	1.71186	+	2.96503i	0.115414	+	0.199903i
$221$	−3.35741	−	5.81520i	−0.225844	−	0.391172i
$222$		0			0
$223$	6.14405	−	10.6418i	0.411436	−	0.712629i	−0.583611	−	0.812034i	$-0.698361\pi$
$223$	6.14405	−	10.6418i	0.411436	−	0.712629i	0.995047	+	0.0994049i	$0.0316939\pi$
$224$	7.56292			0.505319
$225$		0			0
$226$	−0.711597			−0.0473347
$227$	1.87628	−	3.24981i	0.124533	−	0.215698i	−0.797017	−	0.603957i	$-0.793590\pi$
$227$	1.87628	−	3.24981i	0.124533	−	0.215698i	0.921550	+	0.388259i	$0.126923\pi$
$228$		0			0
$229$	9.30121	+	16.1102i	0.614641	+	1.06459i	0.990447	+	0.137892i	$0.0440326\pi$
$229$	9.30121	+	16.1102i	0.614641	+	1.06459i	−0.375806	+	0.926698i	$0.622634\pi$
$230$	2.13694	+	3.70128i	0.140905	+	0.244055i
$231$		0			0
$232$	9.79629	−	16.9677i	0.643158	−	1.11398i
$233$	−0.545784			−0.0357555			−0.0178777	−	0.999840i	$-0.505691\pi$
$233$	−0.545784			−0.0357555			−0.0178777	+	0.999840i	$0.505691\pi$
$234$		0			0
$235$	20.9775			1.36842
$236$	−2.22386	+	3.85185i	−0.144761	+	0.250734i
$237$		0			0
$238$	2.14198	+	3.71002i	0.138844	+	0.240485i
$239$	−10.0474	−	17.4026i	−0.649911	−	1.12568i	−0.983144	−	0.182834i	$-0.941473\pi$
$239$	−10.0474	−	17.4026i	−0.649911	−	1.12568i	0.333233	−	0.942844i	$-0.391860\pi$
$240$		0			0
$241$	−7.64565	+	13.2427i	−0.492500	+	0.853034i	−0.999963	−	0.00863907i	$-0.997250\pi$
$241$	−7.64565	+	13.2427i	−0.492500	+	0.853034i	0.507463	+	0.861674i	$0.330583\pi$
$242$	−9.83763			−0.632387
$243$		0			0
$244$	−0.631762			−0.0404444
$245$	−0.607962	+	1.05302i	−0.0388413	+	0.0672751i
$246$		0			0
$247$	−9.23208	−	15.9904i	−0.587423	−	1.01745i
$248$	−1.24309	−	2.15310i	−0.0789364	−	0.136722i
$249$		0			0
$250$	−9.51468	+	16.4799i	−0.601761	+	1.04228i
$251$	−12.7563			−0.805171			−0.402586	−	0.915382i	$-0.631888\pi$
$251$	−12.7563			−0.805171			−0.402586	+	0.915382i	$0.631888\pi$
$252$		0			0
$253$	−6.69663			−0.421013
$254$	−0.419121	+	0.725938i	−0.0262980	+	0.0455494i
$255$		0			0
$256$	−5.56957	−	9.64678i	−0.348098	−	0.602924i
$257$	−6.55235	−	11.3490i	−0.408725	−	0.707932i	0.586023	−	0.810295i	$-0.300693\pi$
$257$	−6.55235	−	11.3490i	−0.408725	−	0.707932i	−0.994747	+	0.102363i	$0.967360\pi$
$258$		0			0
$259$	1.81813	−	3.14909i	0.112973	−	0.195675i
$260$	5.67103			0.351702
$261$		0			0
$262$	18.0191			1.11323
$263$	−4.75709	+	8.23952i	−0.293335	+	0.508070i	−0.974596	−	0.223970i	$-0.928098\pi$
$263$	−4.75709	+	8.23952i	−0.293335	+	0.508070i	0.681262	+	0.732040i	$0.261432\pi$
$264$		0			0
$265$	−6.16247	−	10.6737i	−0.378557	−	0.655681i
$266$	5.88995	+	10.2017i	0.361136	+	0.625506i
$267$		0			0
$268$	1.14150	−	1.97714i	0.0697284	−	0.120773i
$269$	−22.1408			−1.34995			−0.674973	−	0.737842i	$-0.735845\pi$
$269$	−22.1408			−1.34995			−0.674973	+	0.737842i	$0.735845\pi$
$270$		0			0
$271$	27.9627			1.69861			0.849307	−	0.527899i	$-0.177020\pi$
$271$	27.9627			1.69861			0.849307	+	0.527899i	$0.177020\pi$
$272$	2.31505	−	4.00979i	0.140371	−	0.243129i
$273$		0			0
$274$	−3.33773	−	5.78111i	−0.201639	−	0.349250i
$275$	−4.53025	−	7.84663i	−0.273185	−	0.473170i
$276$		0			0
$277$	9.44184	−	16.3537i	0.567305	−	0.982601i	−0.429526	−	0.903054i	$-0.641319\pi$
$277$	9.44184	−	16.3537i	0.567305	−	0.982601i	0.996831	−	0.0795468i	$-0.0253473\pi$
$278$	17.6079			1.05605
$279$		0			0
$280$	11.1086			0.663867
$281$	−10.0009	+	17.3220i	−0.596602	+	1.03335i	0.396717	+	0.917941i	$0.370150\pi$
$281$	−10.0009	+	17.3220i	−0.596602	+	1.03335i	−0.993319	+	0.115404i	$0.963184\pi$
$282$		0			0
$283$	−8.37252	−	14.5016i	−0.497695	−	0.862032i	0.502302	−	0.864692i	$-0.332487\pi$
$283$	−8.37252	−	14.5016i	−0.497695	−	0.862032i	−0.999996	+	0.00266002i	$0.999153\pi$
$284$	−1.38164	−	2.39307i	−0.0819852	−	0.142002i
$285$		0			0
$286$	−22.5270	+	39.0179i	−1.33205	+	2.30717i
$287$	−13.4744			−0.795371
$288$		0			0
$289$	−16.0463			−0.943903
$290$	−10.8993	+	18.8782i	−0.640030	+	1.10856i
$291$		0			0
$292$	1.12066	+	1.94103i	0.0655814	+	0.113590i
$293$	9.78600	+	16.9499i	0.571704	+	0.990221i	0.996391	+	0.0848806i	$0.0270509\pi$
$293$	9.78600	+	16.9499i	0.571704	+	0.990221i	−0.424687	+	0.905340i	$0.639616\pi$
$294$		0			0
$295$	−7.59682	+	13.1581i	−0.442304	+	0.766093i
$296$	−3.11549			−0.181084
$297$		0			0
$298$	−30.7437			−1.78093
$299$	−5.54611	+	9.60615i	−0.320740	+	0.555538i
$300$		0			0
$301$	−13.6744	−	23.6847i	−0.788178	−	1.36517i
$302$	−0.980868	−	1.69891i	−0.0564426	−	0.0977614i
$303$		0			0
$304$	6.36586	−	11.0260i	0.365107	−	0.632384i
$305$	−2.15813			−0.123574
$306$		0			0
$307$	14.8995			0.850357			0.425179	−	0.905109i	$-0.360211\pi$
$307$	14.8995			0.850357			0.425179	+	0.905109i	$0.360211\pi$
$308$	2.83451	−	4.90952i	0.161511	−	0.279746i
$309$		0			0
$310$	1.38306	+	2.39553i	0.0785525	+	0.136057i
$311$	2.29618	+	3.97710i	0.130204	+	0.225521i	0.923755	−	0.382983i	$-0.125103\pi$
$311$	2.29618	+	3.97710i	0.130204	+	0.225521i	−0.793551	+	0.608504i	$0.791770\pi$
$312$		0			0
$313$	−5.93434	+	10.2786i	−0.335429	+	0.580980i	−0.983567	−	0.180543i	$-0.942215\pi$
$313$	−5.93434	+	10.2786i	−0.335429	+	0.580980i	0.648138	+	0.761523i	$0.275548\pi$
$314$	5.57672			0.314713
$315$		0			0
$316$	2.28817			0.128719
$317$	−7.25867	+	12.5724i	−0.407688	+	0.706136i	−0.994630	−	0.103493i	$-0.966998\pi$
$317$	−7.25867	+	12.5724i	−0.407688	+	0.706136i	0.586943	+	0.809629i	$0.300331\pi$
$318$		0			0
$319$	−17.0779	−	29.5797i	−0.956177	−	1.65615i
$320$	−4.35359	−	7.54064i	−0.243373	−	0.421535i
$321$		0			0
$322$	3.53835	−	6.12860i	0.197185	−	0.341534i
$323$	2.62232			0.145910
$324$		0			0
$325$	−15.0077			−0.832480
$326$	12.5885	−	21.8039i	0.697211	−	1.20760i
$327$		0			0
$328$	5.77234	+	9.99798i	0.318724	+	0.552046i
$329$	−17.3673	−	30.0811i	−0.957491	−	1.65842i
$330$		0			0
$331$	4.05285	−	7.01974i	0.222765	−	0.385840i	−0.732882	−	0.680356i	$-0.761825\pi$
$331$	4.05285	−	7.01974i	0.222765	−	0.385840i	0.955647	+	0.294516i	$0.0951585\pi$
$332$	2.83239			0.155448
$333$		0			0
$334$	22.8626			1.25099
$335$	3.89942	−	6.75400i	0.213048	−	0.369010i
$336$		0			0
$337$	9.40398	+	16.2882i	0.512267	+	0.887273i	0.999899	+	0.0142235i	$0.00452764\pi$
$337$	9.40398	+	16.2882i	0.512267	+	0.887273i	−0.487631	+	0.873050i	$0.662139\pi$
$338$	27.0538	+	46.8586i	1.47154	+	2.54877i
$339$		0			0
$340$	−0.402706	+	0.697507i	−0.0218398	+	0.0378276i
$341$	−4.33416			−0.234708
$342$		0			0
$343$	−17.4416			−0.941760
$344$	−11.7160	+	20.2927i	−0.631684	+	1.09411i
$345$		0			0
$346$	−9.95768	−	17.2472i	−0.535328	−	0.927215i
$347$	−8.80881	−	15.2573i	−0.472882	−	0.819056i	0.526636	−	0.850091i	$-0.323453\pi$
$347$	−8.80881	−	15.2573i	−0.472882	−	0.819056i	−0.999518	+	0.0310351i	$0.990120\pi$
$348$		0			0
$349$	8.49465	−	14.7132i	0.454708	−	0.787577i	−0.543963	−	0.839109i	$-0.683077\pi$
$349$	8.49465	−	14.7132i	0.454708	−	0.787577i	0.998671	+	0.0515316i	$0.0164103\pi$
$350$	9.57475			0.511792
$351$		0			0
$352$	−11.2962			−0.602090
$353$	−7.57780	+	13.1251i	−0.403326	+	0.698580i	−0.994125	−	0.108238i	$-0.965479\pi$
$353$	−7.57780	+	13.1251i	−0.403326	+	0.698580i	0.590799	+	0.806818i	$0.298812\pi$
$354$		0			0
$355$	−4.71974	−	8.17483i	−0.250498	−	0.433875i
$356$	−1.11647	−	1.93379i	−0.0591729	−	0.102491i
$357$		0			0
$358$	−0.233524	+	0.404475i	−0.0123421	+	0.0213772i
$359$	−2.45096			−0.129357			−0.0646783	−	0.997906i	$-0.520602\pi$
$359$	−2.45096			−0.129357			−0.0646783	+	0.997906i	$0.520602\pi$
$360$		0			0
$361$	−11.7892			−0.620485
$362$	1.12106	−	1.94174i	0.0589218	−	0.102055i
$363$		0			0
$364$	−4.69506	−	8.13208i	−0.246088	−	0.426237i
$365$	3.82821	+	6.63065i	0.200378	+	0.347064i
$366$		0			0
$367$	0.656767	−	1.13755i	0.0342829	−	0.0593798i	−0.848375	−	0.529396i	$-0.822419\pi$
$367$	0.656767	−	1.13755i	0.0342829	−	0.0593798i	0.882658	+	0.470016i	$0.155752\pi$
$368$	−7.64850			−0.398706
$369$		0			0
$370$	3.46628			0.180203
$371$	−10.2039	+	17.6736i	−0.529758	+	0.917567i
$372$		0			0
$373$	4.81309	+	8.33651i	0.249212	+	0.431648i	0.963307	−	0.268400i	$-0.0864950\pi$
$373$	4.81309	+	8.33651i	0.249212	+	0.431648i	−0.714095	+	0.700048i	$0.753162\pi$
$374$	−3.19933	−	5.54140i	−0.165433	−	0.286539i
$375$		0			0
$376$	−14.8800	+	25.7730i	−0.767379	+	1.32914i
$377$	−56.5753			−2.91377
$378$		0			0
$379$	−8.56311			−0.439857			−0.219929	−	0.975516i	$-0.570582\pi$
$379$	−8.56311			−0.439857			−0.219929	+	0.975516i	$0.570582\pi$
$380$	−1.10735	+	1.91798i	−0.0568057	+	0.0983904i
$381$		0			0
$382$	−16.2766	−	28.1918i	−0.832782	−	1.44242i
$383$	16.8173	+	29.1284i	0.859324	+	1.48839i	0.872574	+	0.488481i	$0.162449\pi$
$383$	16.8173	+	29.1284i	0.859324	+	1.48839i	−0.0132498	+	0.999912i	$0.504218\pi$
$384$		0			0
$385$	9.68282	−	16.7711i	0.493482	−	0.854736i
$386$	33.0769			1.68357
$387$		0			0
$388$	4.21363			0.213915
$389$	−7.47699	+	12.9505i	−0.379098	+	0.656618i	−0.990931	−	0.134369i	$-0.957099\pi$
$389$	−7.47699	+	12.9505i	−0.379098	+	0.656618i	0.611833	+	0.790987i	$0.290433\pi$
$390$		0			0
$391$	−0.787671	−	1.36429i	−0.0398343	−	0.0689950i
$392$	−0.862496	−	1.49389i	−0.0435626	−	0.0754527i
$393$		0			0
$394$	7.57335	−	13.1174i	0.381540	−	0.660846i
$395$	7.81648			0.393290
$396$		0			0
$397$	−16.7788			−0.842102			−0.421051	−	0.907037i	$-0.638339\pi$
$397$	−16.7788			−0.842102			−0.421051	+	0.907037i	$0.638339\pi$
$398$	−8.43788	+	14.6148i	−0.422953	+	0.732576i
$399$		0			0
$400$	−5.17419	−	8.96197i	−0.258710	−	0.448098i
$401$	6.56315	+	11.3677i	0.327748	+	0.567676i	0.982065	−	0.188545i	$-0.0603770\pi$
$401$	6.56315	+	11.3677i	0.327748	+	0.567676i	−0.654317	+	0.756221i	$0.727044\pi$
$402$		0			0
$403$	−3.58953	+	6.21725i	−0.178807	+	0.309704i
$404$	−3.83541			−0.190819
$405$		0			0
$406$	36.0943			1.79133
$407$	−2.71561	+	4.70358i	−0.134608	+	0.233148i
$408$		0			0
$409$	−12.7253	−	22.0408i	−0.629223	−	1.08985i	−0.987708	−	0.156311i	$-0.950040\pi$
$409$	−12.7253	−	22.0408i	−0.629223	−	1.08985i	0.358485	−	0.933536i	$-0.383294\pi$
$410$	−6.42228	−	11.1237i	−0.317174	−	0.549361i
$411$		0			0
$412$	0.532179	−	0.921761i	0.0262186	−	0.0454119i
$413$	25.1577			1.23793
$414$		0			0
$415$	9.67558			0.474955
$416$	−9.35547	+	16.2041i	−0.458689	+	0.794474i
$417$		0			0
$418$	−8.79742	−	15.2376i	−0.430296	−	0.745294i
$419$	−6.33503	−	10.9726i	−0.309486	−	0.536046i	0.668764	−	0.743475i	$-0.266824\pi$
$419$	−6.33503	−	10.9726i	−0.309486	−	0.536046i	−0.978250	+	0.207429i	$0.933490\pi$
$420$		0			0
$421$	8.83862	−	15.3089i	0.430768	−	0.746112i	−0.566172	−	0.824287i	$-0.691576\pi$
$421$	8.83862	−	15.3089i	0.430768	−	0.746112i	0.996940	+	0.0781752i	$0.0249094\pi$
$422$	23.7554			1.15639
$423$		0			0
$424$	17.4850			0.849146
$425$	1.06572	−	1.84587i	0.0516948	−	0.0895381i
$426$		0			0
$427$	1.78672	+	3.09469i	0.0864654	+	0.149762i
$428$	−3.09187	−	5.35528i	−0.149451	−	0.258857i
$429$		0			0
$430$	13.0352	−	22.5776i	0.628612	−	1.08879i
$431$	−15.6974			−0.756117			−0.378059	−	0.925782i	$-0.623408\pi$
$431$	−15.6974			−0.756117			−0.378059	+	0.925782i	$0.623408\pi$
$432$		0			0
$433$	−12.6258			−0.606759			−0.303380	−	0.952870i	$-0.598115\pi$
$433$	−12.6258			−0.606759			−0.303380	+	0.952870i	$0.598115\pi$
$434$	2.29008	−	3.96653i	0.109927	−	0.190400i
$435$		0			0
$436$	3.00073	+	5.19742i	0.143709	+	0.248912i
$437$	−2.16591	−	3.75147i	−0.103610	−	0.179457i
$438$		0			0
$439$	−13.4685	+	23.3281i	−0.642814	+	1.11339i	0.341987	+	0.939705i	$0.388900\pi$
$439$	−13.4685	+	23.3281i	−0.642814	+	1.11339i	−0.984802	+	0.173683i	$0.944433\pi$
$440$	−16.5922			−0.791001
$441$		0			0
$442$	−10.5987			−0.504128
$443$	17.3639	−	30.0752i	0.824986	−	1.42892i	−0.0769438	−	0.997035i	$-0.524516\pi$
$443$	17.3639	−	30.0752i	0.824986	−	1.42892i	0.901930	−	0.431882i	$-0.142150\pi$
$444$		0			0
$445$	−3.81392	−	6.60590i	−0.180797	−	0.313150i
$446$	−9.69780	−	16.7971i	−0.459204	−	0.795365i
$447$		0			0
$448$	−7.20870	+	12.4858i	−0.340579	+	0.589900i
$449$	20.7461			0.979070			0.489535	−	0.871984i	$-0.337166\pi$
$449$	20.7461			0.979070			0.489535	+	0.871984i	$0.337166\pi$
$450$		0			0
$451$	20.1258			0.947688
$452$	−0.110761	+	0.191843i	−0.00520974	+	0.00902354i
$453$		0			0
$454$	−2.96153	−	5.12952i	−0.138991	−	0.240740i
$455$	−16.0385	−	27.7796i	−0.751898	−	1.30233i
$456$		0			0
$457$	3.60387	−	6.24208i	0.168582	−	0.291992i	−0.769340	−	0.638840i	$-0.779415\pi$
$457$	3.60387	−	6.24208i	0.168582	−	0.291992i	0.937921	+	0.346848i	$0.112748\pi$
$458$	29.3621			1.37200
$459$		0			0
$460$	1.33046			0.0620332
$461$	11.5634	−	20.0284i	0.538562	−	0.932817i	−0.460420	−	0.887701i	$-0.652301\pi$
$461$	11.5634	−	20.0284i	0.538562	−	0.932817i	0.998982	−	0.0451156i	$-0.0143656\pi$
$462$		0			0
$463$	−2.48792	−	4.30921i	−0.115623	−	0.200266i	0.802405	−	0.596779i	$-0.203553\pi$
$463$	−2.48792	−	4.30921i	−0.115623	−	0.200266i	−0.918029	+	0.396514i	$0.870220\pi$
$464$	−19.5054	−	33.7843i	−0.905513	−	1.56840i
$465$		0			0
$466$	−0.430734	+	0.746053i	−0.0199534	+	0.0345602i
$467$	12.4814			0.577569			0.288784	−	0.957394i	$-0.406749\pi$
$467$	12.4814			0.577569			0.288784	+	0.957394i	$0.406749\pi$
$468$		0			0
$469$	−12.9134			−0.596284
$470$	16.5555	−	28.6749i	0.763647	−	1.32268i
$471$		0			0
$472$	−10.7774	−	18.6669i	−0.496068	−	0.859216i
$473$	20.4245	+	35.3762i	0.939119	+	1.62660i
$474$		0			0
$475$	2.93047	−	5.07573i	0.134459	−	0.232890i
$476$	1.33361			0.0611257
$477$		0			0
$478$	−31.7176			−1.45073
$479$	14.2356	−	24.6568i	0.650443	−	1.12660i	−0.332573	−	0.943078i	$-0.607917\pi$
$479$	14.2356	−	24.6568i	0.650443	−	1.12660i	0.983016	−	0.183522i	$-0.0587499\pi$
$480$		0			0
$481$	4.49812	+	7.79097i	0.205097	+	0.355238i
$482$	12.0679	+	20.9023i	0.549679	+	0.952072i
$483$		0			0
$484$	−1.53124	+	2.65218i	−0.0696016	+	0.120554i
$485$	14.3939			0.653595
$486$		0			0
$487$	29.6841			1.34511			0.672557	−	0.740045i	$-0.265196\pi$
$487$	29.6841			1.34511			0.672557	+	0.740045i	$0.265196\pi$
$488$	1.53083	−	2.65148i	0.0692975	−	0.120027i
$489$		0			0
$490$	0.959610	+	1.66209i	0.0433508	+	0.0750857i
$491$	6.20248	+	10.7430i	0.279914	+	0.484825i	0.971363	−	0.237600i	$-0.0763608\pi$
$491$	6.20248	+	10.7430i	0.279914	+	0.484825i	−0.691449	+	0.722425i	$0.743027\pi$
$492$		0			0
$493$	4.01747	−	6.95846i	0.180938	−	0.313394i
$494$	−29.1439			−1.31125
$495$		0			0
$496$	−4.95023			−0.222272
$497$	−7.81497	+	13.5359i	−0.350549	+	0.607169i
$498$		0			0
$499$	1.13991	+	1.97438i	0.0510294	+	0.0883856i	0.890412	−	0.455156i	$-0.150416\pi$
$499$	1.13991	+	1.97438i	0.0510294	+	0.0883856i	−0.839382	+	0.543541i	$0.817083\pi$
$500$	2.96193	+	5.13022i	0.132462	+	0.229430i
$501$		0			0
$502$	−10.0673	+	17.4371i	−0.449326	+	0.778256i
$503$	−41.2812			−1.84064			−0.920320	−	0.391167i	$-0.872071\pi$
$503$	−41.2812			−1.84064			−0.920320	+	0.391167i	$0.872071\pi$
$504$		0			0
$505$	−13.1019			−0.583028
$506$	−5.28499	+	9.15387i	−0.234947	+	0.406939i
$507$		0			0
$508$	0.130473	+	0.225986i	0.00578880	+	0.0100265i
$509$	8.21208	+	14.2237i	0.363994	+	0.630456i	0.988614	−	0.150473i	$-0.0480796\pi$
$509$	8.21208	+	14.2237i	0.363994	+	0.630456i	−0.624620	+	0.780929i	$0.714746\pi$
$510$		0			0
$511$	6.33877	−	10.9791i	0.280411	−	0.485685i
$512$	9.67844			0.427731
$513$		0			0
$514$	−20.6845			−0.912355
$515$	1.81795	−	3.14878i	0.0801083	−	0.138752i
$516$		0			0
$517$	25.9404	+	44.9300i	1.14086	+	1.97602i
$518$	−2.86974	−	4.97054i	−0.126089	−	0.218393i
$519$		0			0
$520$	−13.7416	+	23.8011i	−0.602607	+	1.04375i
$521$	9.29672			0.407297			0.203648	−	0.979044i	$-0.434720\pi$
$521$	9.29672			0.407297			0.203648	+	0.979044i	$0.434720\pi$
$522$		0			0
$523$	−22.7471			−0.994662			−0.497331	−	0.867561i	$-0.665686\pi$
$523$	−22.7471			−0.994662			−0.497331	+	0.867561i	$0.665686\pi$
$524$	2.80469	−	4.85787i	0.122524	−	0.212217i
$525$		0			0
$526$	7.50861	+	13.0053i	0.327391	+	0.567058i
$527$	−0.509794	−	0.882988i	−0.0222070	−	0.0384636i
$528$		0			0
$529$	10.1988	−	17.6649i	0.443428	−	0.768040i
$530$	−19.4537			−0.845016
$531$		0			0
$532$	3.66710			0.158989
$533$	16.6681	−	28.8700i	0.721976	−	1.25050i
$534$		0			0
$535$	−10.5620	−	18.2939i	−0.456634	−	0.790913i
$536$	5.53199	+	9.58168i	0.238945	+	0.413866i
$537$		0			0
$538$	−17.4735	+	30.2651i	−0.753338	+	1.30482i
$539$	−3.00718			−0.129528
$540$		0			0
$541$	2.38959			0.102737			0.0513683	−	0.998680i	$-0.483642\pi$
$541$	2.38959			0.102737			0.0513683	+	0.998680i	$0.483642\pi$
$542$	22.0682	−	38.2233i	0.947912	−	1.64183i
$543$		0			0
$544$	−1.32868	−	2.30135i	−0.0569669	−	0.0986695i
$545$	10.2506	+	17.7546i	0.439089	+	0.760525i
$546$		0			0
$547$	−14.8334	+	25.6922i	−0.634230	+	1.09852i	0.352448	+	0.935832i	$0.385349\pi$
$547$	−14.8334	+	25.6922i	−0.634230	+	1.09852i	−0.986678	+	0.162687i	$0.947984\pi$
$548$	−2.07808			−0.0887712
$549$		0			0
$550$	−14.3011			−0.609803
$551$	11.0471	−	19.1342i	0.470623	−	0.815143i
$552$		0			0
$553$	−6.47128	−	11.2086i	−0.275187	−	0.476638i
$554$	−14.9030	−	25.8128i	−0.633169	−	1.09668i
$555$		0			0
$556$	2.74069	−	4.74701i	0.116231	−	0.201318i
$557$	−8.41413			−0.356518			−0.178259	−	0.983984i	$-0.557046\pi$
$557$	−8.41413			−0.356518			−0.178259	+	0.983984i	$0.557046\pi$
$558$		0			0
$559$	67.6619			2.86179
$560$	11.0592	−	19.1550i	0.467335	−	0.809447i
$561$		0			0
$562$	15.7854	+	27.3411i	0.665868	+	1.15332i
$563$	−13.6133	−	23.5788i	−0.573730	−	0.993730i	−0.996178	−	0.0873428i	$-0.972162\pi$
$563$	−13.6133	−	23.5788i	−0.573730	−	0.993730i	0.422448	−	0.906387i	$-0.361171\pi$
$564$		0			0
$565$	−0.378363	+	0.655345i	−0.0159179	+	0.0275706i
$566$	−26.4304			−1.11095
$567$		0			0
$568$	13.3915			0.561894
$569$	−10.9747	+	19.0087i	−0.460082	+	0.796885i	−0.998965	−	0.0454960i	$-0.985513\pi$
$569$	−10.9747	+	19.0087i	−0.460082	+	0.796885i	0.538883	+	0.842381i	$0.318846\pi$
$570$		0			0
$571$	22.4267	+	38.8442i	0.938530	+	1.62558i	0.768216	+	0.640191i	$0.221145\pi$
$571$	22.4267	+	38.8442i	0.938530	+	1.62558i	0.170314	+	0.985390i	$0.445522\pi$
$572$	7.01269	+	12.1463i	0.293215	+	0.507863i
$573$		0			0
$574$	−10.6340	+	18.4187i	−0.443857	+	0.768782i
$575$	−3.52092			−0.146833
$576$		0			0
$577$	12.0191			0.500361			0.250181	−	0.968199i	$-0.419510\pi$
$577$	12.0191			0.500361			0.250181	+	0.968199i	$0.419510\pi$
$578$	−12.6638	+	21.9344i	−0.526745	+	0.912349i
$579$		0			0
$580$	3.39298	+	5.87681i	0.140886	+	0.244021i
$581$	−8.01043	−	13.8745i	−0.332329	−	0.575610i
$582$		0			0
$583$	15.2408	−	26.3978i	0.631209	−	1.09329i
$584$	−10.8619			−0.449469
$585$		0			0
$586$	30.8925			1.27616
$587$	−8.51493	+	14.7483i	−0.351449	+	0.608727i	−0.986504	−	0.163740i	$-0.947644\pi$
$587$	−8.51493	+	14.7483i	−0.351449	+	0.608727i	0.635055	+	0.772467i	$0.280978\pi$
$588$		0			0
$589$	−1.40181	−	2.42801i	−0.0577607	−	0.100045i
$590$	11.9909	+	20.7688i	0.493656	+	0.855037i
$591$		0			0
$592$	−3.10162	+	5.37216i	−0.127476	+	0.220794i
$593$	14.9284			0.613037			0.306519	−	0.951865i	$-0.400836\pi$
$593$	14.9284			0.613037			0.306519	+	0.951865i	$0.400836\pi$
$594$		0			0
$595$	4.55566			0.186764
$596$	−4.78528	+	8.28835i	−0.196013	+	0.339504i
$597$		0			0
$598$	8.75401	+	15.1624i	0.357978	+	0.620036i
$599$	6.76740	+	11.7215i	0.276508	+	0.478927i	0.970515	−	0.241042i	$-0.0774893\pi$
$599$	6.76740	+	11.7215i	0.276508	+	0.478927i	−0.694006	+	0.719969i	$0.744156\pi$
$600$		0			0
$601$	22.6586	−	39.2459i	0.924265	−	1.60087i	0.131525	−	0.991313i	$-0.458013\pi$
$601$	22.6586	−	39.2459i	0.924265	−	1.60087i	0.792739	−	0.609561i	$-0.208654\pi$
$602$	−43.1674			−1.75937
$603$		0			0
$604$	−0.610691			−0.0248487
$605$	−5.23077	+	9.05996i	−0.212661	+	0.368340i
$606$		0			0
$607$	−12.2184	−	21.1629i	−0.495929	−	0.858975i	0.504060	−	0.863669i	$-0.331839\pi$
$607$	−12.2184	−	21.1629i	−0.495929	−	0.858975i	−0.999989	+	0.00469404i	$0.998506\pi$
$608$	−3.65357	−	6.32817i	−0.148172	−	0.256641i
$609$		0			0
$610$	−1.70320	+	2.95003i	−0.0689605	+	0.119443i
$611$	85.9348			3.47655
$612$		0			0
$613$	−25.1996			−1.01780			−0.508901	−	0.860825i	$-0.669948\pi$
$613$	−25.1996			−1.01780			−0.508901	+	0.860825i	$0.669948\pi$
$614$	11.7587	−	20.3666i	0.474542	−	0.821931i
$615$		0			0
$616$	13.7367	+	23.7927i	0.553467	+	0.958634i
$617$	2.02093	+	3.50034i	0.0813594	+	0.140919i	0.903834	−	0.427883i	$-0.140741\pi$
$617$	2.02093	+	3.50034i	0.0813594	+	0.140919i	−0.822475	+	0.568802i	$0.807407\pi$
$618$		0			0
$619$	22.3850	−	38.7719i	0.899729	−	1.55838i	0.0718884	−	0.997413i	$-0.477097\pi$
$619$	22.3850	−	38.7719i	0.899729	−	1.55838i	0.827841	−	0.560964i	$-0.189569\pi$
$620$	0.861097			0.0345825
$621$		0			0
$622$	7.24860			0.290642
$623$	−6.31511	+	10.9381i	−0.253010	+	0.438225i
$624$		0			0
$625$	4.66157	+	8.07408i	0.186463	+	0.322963i
$626$	9.36679	+	16.2238i	0.374372	+	0.648432i
$627$		0			0
$628$	0.868022	−	1.50346i	0.0346378	−	0.0599945i
$629$	−1.27767			−0.0509439
$630$		0			0
$631$	31.4116			1.25048			0.625238	−	0.780434i	$-0.285002\pi$
$631$	31.4116			1.25048			0.625238	+	0.780434i	$0.285002\pi$
$632$	−5.54449	+	9.60334i	−0.220548	+	0.382000i
$633$		0			0
$634$	11.4571	+	19.8443i	0.455020	+	0.788118i
$635$	0.445701	+	0.771978i	0.0176871	+	0.0306350i
$636$		0			0
$637$	−2.49053	+	4.31373i	−0.0986784	+	0.170916i
$638$	−53.9116			−2.13438
$639$		0			0
$640$	−22.8785			−0.904351
$641$	24.3203	−	42.1240i	0.960594	−	1.66380i	0.239581	−	0.970876i	$-0.422990\pi$
$641$	24.3203	−	42.1240i	0.960594	−	1.66380i	0.721013	−	0.692922i	$-0.243677\pi$
$642$		0			0
$643$	14.0162	+	24.2767i	0.552744	+	0.957381i	0.998075	+	0.0620150i	$0.0197527\pi$
$643$	14.0162	+	24.2767i	0.552744	+	0.957381i	−0.445331	+	0.895366i	$0.646914\pi$
$644$	−1.10149	−	1.90784i	−0.0434050	−	0.0751796i
$645$		0			0
$646$	2.06954	−	3.58455i	0.0814251	−	0.141032i
$647$	37.5519			1.47632			0.738159	−	0.674627i	$-0.235696\pi$
$647$	37.5519			1.47632			0.738159	+	0.674627i	$0.235696\pi$
$648$		0			0
$649$	−37.5763			−1.47500
$650$	−11.8441	+	20.5147i	−0.464565	+	0.804651i
$651$		0			0
$652$	−3.91881	−	6.78758i	−0.153472	−	0.265822i
$653$	−2.55611	−	4.42731i	−0.100028	−	0.173254i	0.811668	−	0.584119i	$-0.198560\pi$
$653$	−2.55611	−	4.42731i	−0.100028	−	0.173254i	−0.911696	+	0.410865i	$0.865227\pi$
$654$		0			0
$655$	9.58095	−	16.5947i	0.374359	−	0.648408i
$656$	22.9866			0.897474
$657$		0			0
$658$	−54.8253			−2.13731
$659$	17.5030	−	30.3160i	0.681818	−	1.18094i	−0.292607	−	0.956233i	$-0.594523\pi$
$659$	17.5030	−	30.3160i	0.681818	−	1.18094i	0.974425	−	0.224711i	$-0.0721439\pi$
$660$		0			0
$661$	−0.666731	−	1.15481i	−0.0259328	−	0.0449170i	0.852768	−	0.522290i	$-0.174922\pi$
$661$	−0.666731	−	1.15481i	−0.0259328	−	0.0449170i	−0.878701	+	0.477373i	$0.841589\pi$
$662$	−6.39704	−	11.0800i	−0.248628	−	0.430636i
$663$		0			0
$664$	−6.86321	+	11.8874i	−0.266344	+	0.461322i
$665$	12.5270			0.485776
$666$		0			0
$667$	−13.2730			−0.513931
$668$	3.55859	−	6.16365i	0.137686	−	0.238479i
$669$		0			0
$670$	−6.15487	−	10.6605i	−0.237783	−	0.411853i
$671$	−2.66870	−	4.62232i	−0.103024	−	0.178443i
$672$		0			0
$673$	1.78976	−	3.09996i	0.0689904	−	0.119495i	−0.829467	−	0.558556i	$-0.811356\pi$
$673$	1.78976	−	3.09996i	0.0689904	−	0.119495i	0.898457	+	0.439061i	$0.144689\pi$
$674$	29.6866			1.14348
$675$		0			0
$676$	16.8438			0.647839
$677$	−18.4694	+	31.9900i	−0.709839	+	1.22948i	0.255078	+	0.966920i	$0.417899\pi$
$677$	−18.4694	+	31.9900i	−0.709839	+	1.22948i	−0.964917	+	0.262556i	$0.915435\pi$
$678$		0			0
$679$	−11.9168	−	20.6405i	−0.457324	−	0.792109i
$680$	−1.95161	−	3.38028i	−0.0748407	−	0.129628i
$681$		0			0
$682$	−3.42053	+	5.92453i	−0.130979	+	0.226862i
$683$	−38.0166			−1.45466			−0.727332	−	0.686286i	$-0.759240\pi$
$683$	−38.0166			−1.45466			−0.727332	+	0.686286i	$0.759240\pi$
$684$		0			0
$685$	−7.09881			−0.271232
$686$	−13.7650	+	23.8416i	−0.525549	+	0.910278i
$687$		0			0
$688$	23.3277	+	40.4047i	0.889359	+	1.54041i
$689$	−25.2447	−	43.7251i	−0.961746	−	1.66579i
$690$		0			0
$691$	−0.275232	+	0.476716i	−0.0104703	+	0.0181351i	−0.871213	−	0.490905i	$-0.836666\pi$
$691$	−0.275232	+	0.476716i	−0.0104703	+	0.0181351i	0.860743	+	0.509040i	$0.170000\pi$
$692$	−6.19968			−0.235677
$693$		0			0
$694$	−27.8077			−1.05557
$695$	9.36232	−	16.2160i	0.355133	−	0.615108i
$696$		0			0
$697$	2.36724	+	4.10019i	0.0896657	+	0.155306i
$698$	−13.4080	−	23.2233i	−0.507500	−	0.879015i
$699$		0			0
$700$	1.49032	−	2.58131i	0.0563287	−	0.0975642i
$701$	−19.0242			−0.718534			−0.359267	−	0.933235i	$-0.616973\pi$
$701$	−19.0242			−0.718534			−0.359267	+	0.933235i	$0.616973\pi$
$702$		0			0
$703$	−3.51328			−0.132506
$704$	10.7671	−	18.6492i	0.405802	−	0.702869i
$705$		0			0
$706$	11.9608	+	20.7168i	0.450152	+	0.779686i
$707$	10.8471	+	18.7878i	0.407948	+	0.706587i
$708$		0			0
$709$	−6.07839	+	10.5281i	−0.228279	+	0.395390i	−0.957298	−	0.289103i	$-0.906643\pi$
$709$	−6.07839	+	10.5281i	−0.228279	+	0.395390i	0.729019	+	0.684493i	$0.239976\pi$
$710$	−14.8993			−0.559161
$711$		0			0
$712$	10.8214			0.405548
$713$	−0.842130	+	1.45861i	−0.0315380	+	0.0546255i
$714$		0			0
$715$	23.9557	+	41.4924i	0.895891	+	1.55173i
$716$	0.0726963	+	0.125914i	0.00271679	+	0.00470562i
$717$		0			0
$718$	−1.93430	+	3.35031i	−0.0721875	+	0.125032i
$719$	−9.77667			−0.364608			−0.182304	−	0.983242i	$-0.558356\pi$
$719$	−9.77667			−0.364608			−0.182304	+	0.983242i	$0.558356\pi$
$720$		0			0
$721$	−6.02033			−0.224209
$722$	−9.30408	+	16.1151i	−0.346262	+	0.599743i
$723$		0			0
$724$	−0.348989	−	0.604466i	−0.0129701	−	0.0224648i
$725$	−8.97913	−	15.5523i	−0.333477	−	0.577598i
$726$		0			0
$727$	−2.16746	+	3.75416i	−0.0803868	+	0.139234i	−0.903416	−	0.428765i	$-0.858949\pi$
$727$	−2.16746	+	3.75416i	−0.0803868	+	0.139234i	0.823029	+	0.567999i	$0.192282\pi$
$728$	45.5067			1.68659
$729$		0			0
$730$	12.0849			0.447283
$731$	−4.80474	+	8.32206i	−0.177710	+	0.307803i
$732$		0			0
$733$	−14.5968	−	25.2824i	−0.539146	−	0.933829i	−0.998950	−	0.0458082i	$-0.985414\pi$
$733$	−14.5968	−	25.2824i	−0.539146	−	0.933829i	0.459804	−	0.888020i	$-0.347920\pi$
$734$	−1.03664	−	1.79552i	−0.0382632	−	0.0662738i
$735$		0			0
$736$	−2.19486	+	3.80161i	−0.0809036	+	0.140129i
$737$	19.2878			0.710476
$738$		0			0
$739$	41.5553			1.52864			0.764319	−	0.644838i	$-0.223075\pi$
$739$	41.5553			1.52864			0.764319	+	0.644838i	$0.223075\pi$
$740$	0.539529	−	0.934492i	0.0198335	−	0.0343526i
$741$		0			0
$742$	16.1058	+	27.8961i	0.591263	+	1.02410i
$743$	10.6887	+	18.5133i	0.392130	+	0.679188i	0.992730	−	0.120361i	$-0.0384051\pi$
$743$	10.6887	+	18.5133i	0.392130	+	0.679188i	−0.600601	+	0.799549i	$0.705072\pi$
$744$		0			0
$745$	−16.3467	+	28.3134i	−0.598898	+	1.03732i
$746$	15.1940			0.556291
$747$		0			0
$748$	−1.99191			−0.0728316
$749$	−17.4886	+	30.2911i	−0.639018	+	1.10681i
$750$		0			0
$751$	19.9838	+	34.6130i	0.729220	+	1.26305i	0.957213	+	0.289383i	$0.0934500\pi$
$751$	19.9838	+	34.6130i	0.729220	+	1.26305i	−0.227994	+	0.973663i	$0.573217\pi$
$752$	29.6276	+	51.3165i	1.08041	+	1.87132i
$753$		0			0
$754$	−44.6493	+	77.3349i	−1.62603	+	2.81637i
$755$	−2.08615			−0.0759228
$756$		0			0
$757$	6.68348			0.242915			0.121458	−	0.992597i	$-0.461243\pi$
$757$	6.68348			0.242915			0.121458	+	0.992597i	$0.461243\pi$
$758$	−6.75803	+	11.7052i	−0.245463	+	0.425154i
$759$		0			0
$760$	−5.36646	−	9.29499i	−0.194662	−	0.337165i
$761$	21.0125	+	36.3947i	0.761703	+	1.31931i	0.941972	+	0.335691i	$0.108970\pi$
$761$	21.0125	+	36.3947i	0.761703	+	1.31931i	−0.180269	+	0.983617i	$0.557697\pi$
$762$		0			0
$763$	16.9731	−	29.3982i	0.614467	−	1.06429i
$764$	−10.1338			−0.366630
$765$		0			0
$766$	53.0890			1.91818
$767$	−31.1206	+	53.9024i	−1.12370	+	1.94630i
$768$		0			0
$769$	−1.20662	−	2.08992i	−0.0435117	−	0.0753644i	0.843449	−	0.537209i	$-0.180521\pi$
$769$	−1.20662	−	2.08992i	−0.0435117	−	0.0753644i	−0.886961	+	0.461844i	$0.847188\pi$
$770$	−15.2834	−	26.4716i	−0.550776	−	0.953971i
$771$		0			0
$772$	5.14845	−	8.91738i	0.185297	−	0.320944i
$773$	−1.39780			−0.0502754			−0.0251377	−	0.999684i	$-0.508002\pi$
$773$	−1.39780			−0.0502754			−0.0251377	+	0.999684i	$0.508002\pi$
$774$		0			0
$775$	−2.27880			−0.0818569
$776$	−10.2101	+	17.6844i	−0.366522	+	0.634834i
$777$		0			0
$778$	11.8017	+	20.4412i	0.423112	+	0.732851i
$779$	6.50937	+	11.2746i	0.233222	+	0.403953i
$780$		0			0
$781$	11.6727	−	20.2177i	0.417682	−	0.723446i
$782$	−2.48653			−0.0889181
$783$		0			0
$784$	−3.43462			−0.122665
$785$	2.96520	−	5.13588i	0.105833	−	0.183307i
$786$		0			0
$787$	19.8258	+	34.3392i	0.706712	+	1.22406i	0.966070	+	0.258280i	$0.0831558\pi$
$787$	19.8258	+	34.3392i	0.706712	+	1.22406i	−0.259358	+	0.965781i	$0.583511\pi$
$788$	−2.35760	−	4.08348i	−0.0839859	−	0.145468i
$789$		0			0
$790$	6.16878	−	10.6846i	0.219475	−	0.380142i
$791$	1.25299			0.0445513
$792$		0			0
$793$	−8.84082			−0.313947
$794$	−13.2418	+	22.9355i	−0.469935	+	0.813952i
$795$		0			0
$796$	2.62673	+	4.54963i	0.0931019	+	0.161257i
$797$	−1.64693	−	2.85257i	−0.0583374	−	0.101043i	0.835382	−	0.549670i	$-0.185247\pi$
$797$	−1.64693	−	2.85257i	−0.0583374	−	0.101043i	−0.893719	+	0.448627i	$0.851913\pi$
$798$		0			0
$799$	−6.10232	+	10.5695i	−0.215885	+	0.373923i
$800$	−5.93927			−0.209985
$801$		0			0
$802$	20.7186			0.731599
$803$	−9.46778	+	16.3987i	−0.334111	+	0.578697i
$804$		0			0
$805$	−3.76276	−	6.51728i	−0.132620	−	0.229704i
$806$	5.66573	+	9.81334i	0.199567	+	0.345660i
$807$		0			0
$808$	9.29364	−	16.0971i	0.326949	−	0.566293i
$809$	6.54436			0.230087			0.115044	−	0.993360i	$-0.463299\pi$
$809$	6.54436			0.230087			0.115044	+	0.993360i	$0.463299\pi$
$810$		0			0
$811$	−44.7516			−1.57144			−0.785721	−	0.618581i	$-0.787708\pi$
$811$	−44.7516			−1.57144			−0.785721	+	0.618581i	$0.787708\pi$
$812$	5.61811	−	9.73085i	0.197157	−	0.341486i
$813$		0			0
$814$	4.28634	+	7.42415i	0.150236	+	0.260216i
$815$	−13.3868	−	23.1867i	−0.468920	−	0.812194i
$816$		0			0
$817$	−13.2119	+	22.8837i	−0.462227	+	0.800600i
$818$	−40.1712			−1.40455
$819$		0			0
$820$	−3.99853			−0.139635
$821$	−24.8420	+	43.0276i	−0.866991	+	1.50167i	−0.00193455	+	0.999998i	$0.500616\pi$
$821$	−24.8420	+	43.0276i	−0.866991	+	1.50167i	−0.865057	+	0.501674i	$0.832718\pi$
$822$		0			0
$823$	−5.31031	−	9.19772i	−0.185106	−	0.320612i	0.758506	−	0.651666i	$-0.225929\pi$
$823$	−5.31031	−	9.19772i	−0.185106	−	0.320612i	−0.943612	+	0.331053i	$0.892596\pi$
$824$	2.57906	+	4.46707i	0.0898459	+	0.155618i
$825$		0			0
$826$	19.8545	−	34.3890i	0.690827	−	1.19655i
$827$	16.4008			0.570311			0.285156	−	0.958481i	$-0.407955\pi$
$827$	16.4008			0.570311			0.285156	+	0.958481i	$0.407955\pi$
$828$		0			0
$829$	−2.95645			−0.102682			−0.0513409	−	0.998681i	$-0.516350\pi$
$829$	−2.95645			−0.102682			−0.0513409	+	0.998681i	$0.516350\pi$
$830$	7.63598	−	13.2259i	0.265049	−	0.459078i
$831$		0			0
$832$	−17.8346	−	30.8904i	−0.618303	−	1.07093i
$833$	−0.353711	−	0.612645i	−0.0122553	−	0.0212269i
$834$		0			0
$835$	12.1563	−	21.0553i	0.420686	−	0.728649i
$836$	−5.47730			−0.189436
$837$		0			0
$838$	−19.9985			−0.690835
$839$	−16.2232	+	28.0994i	−0.560088	+	0.970100i	0.437401	+	0.899267i	$0.355899\pi$
$839$	−16.2232	+	28.0994i	−0.560088	+	0.970100i	−0.997488	+	0.0708334i	$0.977434\pi$
$840$		0			0
$841$	−19.3490	−	33.5134i	−0.667206	−	1.15563i
$842$	−13.9509	−	24.1637i	−0.480780	−	0.832736i
$843$		0			0
$844$	3.69754	−	6.40433i	0.127275	−	0.220446i
$845$	57.5392			1.97941
$846$		0			0
$847$	17.3223			0.595201
$848$	17.4071	−	30.1501i	0.597764	−	1.03536i
$849$		0			0
$850$	−1.68213	−	2.91354i	−0.0576966	−	0.0999335i
$851$	1.05529	+	1.82782i	0.0361749	+	0.0626568i
$852$		0			0
$853$	−14.1665	+	24.5372i	−0.485053	+	0.840137i	−0.999853	−	0.0171737i	$-0.994533\pi$
$853$	−14.1665	+	24.5372i	−0.485053	+	0.840137i	0.514799	+	0.857311i	$0.327867\pi$
$854$	5.64033			0.193008
$855$		0			0
$856$	29.9678			1.02428
$857$	7.00173	−	12.1274i	0.239175	−	0.414262i	−0.721303	−	0.692620i	$-0.756457\pi$
$857$	7.00173	−	12.1274i	0.239175	−	0.414262i	0.960478	+	0.278357i	$0.0897899\pi$
$858$		0			0
$859$	1.07989	+	1.87042i	0.0368452	+	0.0638178i	0.883860	−	0.467752i	$-0.154936\pi$
$859$	1.07989	+	1.87042i	0.0368452	+	0.0638178i	−0.847015	+	0.531569i	$0.821602\pi$
$860$	−4.05787	−	7.02844i	−0.138372	−	0.239668i
$861$		0			0
$862$	−12.3884	+	21.4574i	−0.421951	+	0.730841i
$863$	14.9487			0.508859			0.254430	−	0.967091i	$-0.418112\pi$
$863$	14.9487			0.508859			0.254430	+	0.967091i	$0.418112\pi$
$864$		0			0
$865$	−21.1784			−0.720087
$866$	−9.96434	+	17.2588i	−0.338602	+	0.586476i
$867$		0			0
$868$	−0.712905	−	1.23479i	−0.0241976	−	0.0419114i
$869$	9.66571	+	16.7415i	0.327887	+	0.567916i
$870$		0			0
$871$	15.9741	−	27.6679i	0.541261	−	0.937492i
$872$	−29.0845			−0.984926
$873$		0			0
$874$	−6.83737			−0.231278
$875$	16.7536	−	29.0181i	0.566375	−	0.980991i
$876$		0			0
$877$	0.943539	+	1.63426i	0.0318611	+	0.0551850i	0.881516	−	0.472154i	$-0.156523\pi$
$877$	0.943539	+	1.63426i	0.0318611	+	0.0551850i	−0.849655	+	0.527339i	$0.823190\pi$
$878$	21.2587	+	36.8211i	0.717445	+	1.24265i
$879$		0			0
$880$	−16.5183	+	28.6105i	−0.556832	+	0.964461i
$881$	−46.8258			−1.57760			−0.788800	−	0.614649i	$-0.789297\pi$
$881$	−46.8258			−1.57760			−0.788800	+	0.614649i	$0.789297\pi$
$882$		0			0
$883$	−30.0635			−1.01172			−0.505858	−	0.862617i	$-0.668824\pi$
$883$	−30.0635			−1.01172			−0.505858	+	0.862617i	$0.668824\pi$
$884$	−1.64969	+	2.85735i	−0.0554852	+	0.0961032i
$885$		0			0
$886$	−27.4073	−	47.4709i	−0.920767	−	1.59482i
$887$	−14.9569	−	25.9062i	−0.502205	−	0.869844i	−0.999997	−	0.00254744i	$-0.999189\pi$
$887$	−14.9569	−	25.9062i	−0.502205	−	0.869844i	0.497792	−	0.867296i	$-0.334144\pi$
$888$		0			0
$889$	0.737995	−	1.27824i	0.0247516	−	0.0428709i
$890$	−12.0398			−0.403576
$891$		0			0
$892$	−6.03788			−0.202163
$893$	−16.7800	+	29.0638i	−0.561520	+	0.972582i
$894$		0			0
$895$	0.248334	+	0.430127i	0.00830089	+	0.0143776i
$896$	18.9412	+	32.8070i	0.632780	+	1.09601i
$897$		0			0
$898$	16.3729	−	28.3587i	0.546370	−	0.946341i
$899$	−8.59047			−0.286508
$900$		0			0
$901$	7.17062			0.238888
$902$	15.8833	−	27.5108i	0.528858	−	0.916008i
$903$		0			0
$904$	−0.536772	−	0.929716i	−0.0178528	−	0.0309219i
$905$	−1.19216	−	2.06488i	−0.0396288	−	0.0686391i
$906$		0			0
$907$	−13.3826	+	23.1794i	−0.444363	+	0.769659i	−0.998008	−	0.0630942i	$-0.979903\pi$
$907$	−13.3826	+	23.1794i	−0.444363	+	0.769659i	0.553645	+	0.832753i	$0.313236\pi$
$908$	−1.84386			−0.0611905
$909$		0			0
$910$	−50.6306			−1.67839
$911$	0.220569	−	0.382036i	0.00730776	−	0.0126574i	−0.862348	−	0.506315i	$-0.831007\pi$
$911$	0.220569	−	0.382036i	0.00730776	−	0.0126574i	0.869656	+	0.493658i	$0.164341\pi$
$912$		0			0
$913$	11.9646	+	20.7234i	0.395972	+	0.685843i
$914$	−5.68836	−	9.85253i	−0.188154	−	0.325893i
$915$		0			0
$916$	4.57024	−	7.91589i	0.151005	−	0.261548i
$917$	−31.7284			−1.04776
$918$		0			0
$919$	49.0749			1.61883			0.809416	−	0.587236i	$-0.199784\pi$
$919$	49.0749			1.61883			0.809416	+	0.587236i	$0.199784\pi$
$920$	−3.22387	+	5.58390i	−0.106288	+	0.184096i
$921$		0			0
$922$	−18.2517	−	31.6130i	−0.601089	−	1.04112i
$923$	−19.3345	−	33.4884i	−0.636404	−	1.10228i
$924$		0			0
$925$	−1.42780	+	2.47303i	−0.0469459	+	0.0813127i
$926$	−7.85389			−0.258095
$927$		0			0
$928$	−22.3895			−0.734972
$929$	16.2156	−	28.0863i	0.532017	−	0.921481i	−0.467284	−	0.884107i	$-0.654767\pi$
$929$	16.2156	−	28.0863i	0.532017	−	0.921481i	0.999301	−	0.0373737i	$-0.0118992\pi$
$930$		0			0
$931$	−0.972622	−	1.68463i	−0.0318764	−	0.0552116i
$932$	0.134088	+	0.232247i	0.00439220	+	0.00760752i
$933$		0			0
$934$	9.85032	−	17.0613i	0.322312	−	0.558261i
$935$	−6.80447			−0.222530
$936$		0			0
$937$	48.6157			1.58821			0.794103	−	0.607783i	$-0.207941\pi$
$937$	48.6157			1.58821			0.794103	+	0.607783i	$0.207941\pi$
$938$	−10.1913	+	17.6518i	−0.332757	+	0.576351i
$939$		0			0
$940$	−5.15375	−	8.92655i	−0.168097	−	0.291152i
$941$	−0.355217	−	0.615254i	−0.0115797	−	0.0200567i	0.860177	−	0.509995i	$-0.170353\pi$
$941$	−0.355217	−	0.615254i	−0.0115797	−	0.0200567i	−0.871757	+	0.489938i	$0.837019\pi$
$942$		0			0
$943$	3.91046	−	6.77312i	0.127342	−	0.220563i
$944$	−42.9175			−1.39685
$945$		0			0
$946$	64.4762			2.09630
$947$	13.0539	−	22.6100i	0.424194	−	0.734725i	−0.572151	−	0.820148i	$-0.693891\pi$
$947$	13.0539	−	22.6100i	0.424194	−	0.734725i	0.996345	+	0.0854232i	$0.0272242\pi$
$948$		0			0
$949$	15.6823	+	27.1626i	0.509070	+	0.881736i
$950$	−4.62547	−	8.01155i	−0.150070	−	0.259929i
$951$		0			0
$952$	−3.23148	+	5.59709i	−0.104733	+	0.181403i
$953$	51.0054			1.65223			0.826114	−	0.563503i	$-0.190547\pi$
$953$	51.0054			1.65223			0.826114	+	0.563503i	$0.190547\pi$
$954$		0			0
$955$	−34.6177			−1.12020
$956$	−4.93688	+	8.55092i	−0.159670	+	0.276557i
$957$		0			0
$958$	−22.4696	−	38.9185i	−0.725959	−	1.25740i
$959$	5.87713	+	10.1795i	0.189782	+	0.328713i
$960$		0			0
$961$	14.9550	−	25.9028i	0.482418	−	0.835573i
$962$	14.1997			0.457817
$963$		0			0
$964$	7.51353			0.241995
$965$	17.5874	−	30.4622i	0.566157	−	0.980613i
$966$		0			0
$967$	−5.00241	−	8.66443i	−0.160867	−	0.278629i	0.774313	−	0.632803i	$-0.218096\pi$
$967$	−5.00241	−	8.66443i	−0.160867	−	0.278629i	−0.935180	+	0.354173i	$0.884762\pi$
$968$	−7.42072	−	12.8531i	−0.238511	−	0.413113i
$969$		0			0
$970$	11.3597	−	19.6756i	0.364739	−	0.631746i
$971$	−44.6269			−1.43215			−0.716073	−	0.698025i	$-0.754062\pi$
$971$	−44.6269			−1.43215			−0.716073	+	0.698025i	$0.754062\pi$
$972$		0			0
$973$	−31.0044			−0.993954
$974$	23.4267	−	40.5763i	0.750641	−	1.30015i
$975$		0			0
$976$	−3.04803	−	5.27935i	−0.0975652	−	0.168988i
$977$	−19.5428	−	33.8492i	−0.625230	−	1.08293i	−0.988496	−	0.151245i	$-0.951672\pi$
$977$	−19.5428	−	33.8492i	−0.625230	−	1.08293i	0.363266	−	0.931685i	$-0.381662\pi$
$978$		0			0
$979$	9.43245	−	16.3375i	0.301462	−	0.522148i
$980$	0.597456			0.0190850
$981$		0			0
$982$	19.5800			0.624824
$983$	3.39729	−	5.88428i	0.108357	−	0.187680i	−0.806748	−	0.590896i	$-0.798774\pi$
$983$	3.39729	−	5.88428i	0.108357	−	0.187680i	0.915105	+	0.403216i	$0.132108\pi$
$984$		0			0
$985$	−8.05365	−	13.9493i	−0.256611	−	0.444463i
$986$	−6.34119	−	10.9833i	−0.201945	−	0.349779i
$987$		0			0
$988$	−4.53628	+	7.85706i	−0.144318	+	0.249966i
$989$	15.8740			0.504763
$990$		0			0
$991$	17.2046			0.546522			0.273261	−	0.961940i	$-0.411898\pi$
$991$	17.2046			0.546522			0.273261	+	0.961940i	$0.411898\pi$
$992$	−1.42055	+	2.46046i	−0.0451025	+	0.0781197i
$993$		0			0
$994$	12.3352	+	21.3652i	0.391248	+	0.677662i
$995$	8.97302	+	15.5417i	0.284464	+	0.492706i
$996$		0			0
$997$	−3.66684	+	6.35116i	−0.116130	+	0.201143i	−0.918231	−	0.396045i	$-0.870382\pi$
$997$	−3.66684	+	6.35116i	−0.116130	+	0.201143i	0.802101	+	0.597189i	$0.203716\pi$
$998$	3.59848			0.113908
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.c.d.487.4		12
3.2	odd	2		729.2.c.a.487.3		12
9.2	odd	6		729.2.a.e.1.4	yes	6
9.4	even	3	inner	729.2.c.d.244.4		12
9.5	odd	6		729.2.c.a.244.3		12
9.7	even	3		729.2.a.b.1.3	✓	6
27.2	odd	18		729.2.e.l.325.2		12
27.4	even	9		729.2.e.j.163.2		12
27.5	odd	18		729.2.e.l.406.2		12
27.7	even	9		729.2.e.t.82.1		12
27.11	odd	18		729.2.e.u.568.1		12
27.13	even	9		729.2.e.t.649.1		12
27.14	odd	18		729.2.e.k.649.2		12
27.16	even	9		729.2.e.j.568.2		12
27.20	odd	18		729.2.e.k.82.2		12
27.22	even	9		729.2.e.s.406.1		12
27.23	odd	18		729.2.e.u.163.1		12
27.25	even	9		729.2.e.s.325.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
729.2.a.b.1.3	✓	6	9.7	even	3
729.2.a.e.1.4	yes	6	9.2	odd	6
729.2.c.a.244.3		12	9.5	odd	6
729.2.c.a.487.3		12	3.2	odd	2
729.2.c.d.244.4		12	9.4	even	3	inner
729.2.c.d.487.4		12	1.1	even	1	trivial
729.2.e.j.163.2		12	27.4	even	9
729.2.e.j.568.2		12	27.16	even	9
729.2.e.k.82.2		12	27.20	odd	18
729.2.e.k.649.2		12	27.14	odd	18
729.2.e.l.325.2		12	27.2	odd	18
729.2.e.l.406.2		12	27.5	odd	18
729.2.e.s.325.1		12	27.25	even	9
729.2.e.s.406.1		12	27.22	even	9
729.2.e.t.82.1		12	27.7	even	9
729.2.e.t.649.1		12	27.13	even	9
729.2.e.u.163.1		12	27.23	odd	18
729.2.e.u.568.1		12	27.11	odd	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.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.789202 - 1.36694i) q^{2} +(-0.245680 - 0.425530i) q^{4} +(-0.839254 - 1.45363i) q^{5} +(-1.38964 + 2.40693i) q^{7} +2.38124 q^{8} +O(q^{10})\)	\(q+(0.789202 - 1.36694i) q^{2} +(-0.245680 - 0.425530i) q^{4} +(-0.839254 - 1.45363i) q^{5} +(-1.38964 + 2.40693i) q^{7} +2.38124 q^{8} -2.64936 q^{10} +(2.07561 - 3.59506i) q^{11} +(-3.43802 - 5.95483i) q^{13} +(2.19342 + 3.79911i) q^{14} +(2.37064 - 4.10607i) q^{16} +0.976551 q^{17} +2.68529 q^{19} +(-0.412376 + 0.714256i) q^{20} +(-3.27615 - 5.67446i) q^{22} +(-0.806585 - 1.39705i) q^{23} +(1.09131 - 1.89020i) q^{25} -10.8532 q^{26} +1.36563 q^{28} +(4.11394 - 7.12555i) q^{29} +(-0.522035 - 0.904190i) q^{31} +(-1.36059 - 2.35661i) q^{32} +(0.770696 - 1.33489i) q^{34} +4.66505 q^{35} -1.30834 q^{37} +(2.11924 - 3.67062i) q^{38} +(-1.99847 - 3.46145i) q^{40} +(2.42408 + 4.19864i) q^{41} +(-4.92011 + 8.52189i) q^{43} -2.03974 q^{44} -2.54623 q^{46} +(-6.24885 + 10.8233i) q^{47} +(-0.362204 - 0.627356i) q^{49} +(-1.72252 - 2.98350i) q^{50} +(-1.68931 + 2.92596i) q^{52} +7.34280 q^{53} -6.96786 q^{55} +(-3.30907 + 5.73148i) q^{56} +(-6.49346 - 11.2470i) q^{58} +(-4.52594 - 7.83915i) q^{59} +(0.642871 - 1.11349i) q^{61} -1.64796 q^{62} +5.18745 q^{64} +(-5.77075 + 9.99523i) q^{65} +(2.32315 + 4.02381i) q^{67} +(-0.239919 - 0.415552i) q^{68} +(3.68166 - 6.37683i) q^{70} +5.62373 q^{71} -4.56144 q^{73} +(-1.03255 + 1.78843i) q^{74} +(-0.659722 - 1.14267i) q^{76} +(5.76871 + 9.99170i) q^{77} +(-2.32840 + 4.03291i) q^{79} -7.95828 q^{80} +7.65237 q^{82} +(-2.88220 + 4.99211i) q^{83} +(-0.819574 - 1.41954i) q^{85} +(7.76593 + 13.4510i) q^{86} +(4.94254 - 8.56072i) q^{88} +4.54442 q^{89} +19.1105 q^{91} +(-0.396323 + 0.686452i) q^{92} +(9.86321 + 17.0836i) q^{94} +(-2.25364 - 3.90342i) q^{95} +(-4.28772 + 7.42655i) q^{97} -1.14341 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{2} - 9 q^{4} - 3 q^{5} - 6 q^{7} - 12 q^{8}+O(q^{10}) \) 12 * q + 3 * q^2 - 9 * q^4 - 3 * q^5 - 6 * q^7 - 12 * q^8	\( 12 q + 3 q^{2} - 9 q^{4} - 3 q^{5} - 6 q^{7} - 12 q^{8} + 12 q^{10} - 6 q^{11} - 6 q^{13} + 24 q^{14} - 15 q^{16} + 18 q^{17} + 24 q^{19} - 21 q^{20} - 3 q^{22} - 12 q^{23} - 9 q^{25} - 48 q^{26} + 6 q^{28} + 21 q^{29} - 15 q^{31} - 60 q^{35} + 6 q^{37} + 15 q^{38} - 3 q^{40} - 12 q^{41} - 6 q^{43} + 66 q^{44} - 6 q^{46} - 15 q^{47} - 12 q^{49} - 24 q^{50} - 3 q^{52} + 18 q^{53} + 30 q^{55} + 12 q^{56} + 15 q^{58} + 6 q^{59} - 24 q^{61} + 60 q^{62} + 12 q^{64} - 15 q^{65} - 15 q^{67} + 36 q^{68} + 15 q^{70} + 24 q^{73} + 24 q^{74} - 9 q^{76} + 15 q^{77} - 24 q^{79} + 42 q^{80} - 42 q^{82} - 6 q^{83} + 18 q^{85} - 30 q^{86} + 21 q^{88} + 18 q^{89} + 36 q^{91} + 6 q^{92} + 6 q^{94} - 33 q^{95} + 21 q^{97} - 36 q^{98}+O(q^{100}) \) 12 * q + 3 * q^2 - 9 * q^4 - 3 * q^5 - 6 * q^7 - 12 * q^8 + 12 * q^10 - 6 * q^11 - 6 * q^13 + 24 * q^14 - 15 * q^16 + 18 * q^17 + 24 * q^19 - 21 * q^20 - 3 * q^22 - 12 * q^23 - 9 * q^25 - 48 * q^26 + 6 * q^28 + 21 * q^29 - 15 * q^31 - 60 * q^35 + 6 * q^37 + 15 * q^38 - 3 * q^40 - 12 * q^41 - 6 * q^43 + 66 * q^44 - 6 * q^46 - 15 * q^47 - 12 * q^49 - 24 * q^50 - 3 * q^52 + 18 * q^53 + 30 * q^55 + 12 * q^56 + 15 * q^58 + 6 * q^59 - 24 * q^61 + 60 * q^62 + 12 * q^64 - 15 * q^65 - 15 * q^67 + 36 * q^68 + 15 * q^70 + 24 * q^73 + 24 * q^74 - 9 * q^76 + 15 * q^77 - 24 * q^79 + 42 * q^80 - 42 * q^82 - 6 * q^83 + 18 * q^85 - 30 * q^86 + 21 * q^88 + 18 * q^89 + 36 * q^91 + 6 * q^92 + 6 * q^94 - 33 * q^95 + 21 * q^97 - 36 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more