LMFDB - Embedded newform 729.2.e.k.406.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("729.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.e (of order $9$, degree $6$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
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:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			406.2
Root			$-3.10658i$ of defining polynomial
Character	$\chi$	$=$	729.406
Dual form			729.2.e.k.325.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.62787 + 1.36594i) q^{2} +(0.436855 + 2.47753i) q^{4} +(-1.94605 - 0.708303i) q^{5} +(0.841963 - 4.77501i) q^{7} +(-0.547989 + 0.949144i) q^{8} +O(q^{10})$	\(q+(1.62787 + 1.36594i) q^{2} +(0.436855 + 2.47753i) q^{4} +(-1.94605 - 0.708303i) q^{5} +(0.841963 - 4.77501i) q^{7} +(-0.547989 + 0.949144i) q^{8} +(-2.20040 - 3.81121i) q^{10} +(3.89924 - 1.41921i) q^{11} +(-0.931522 + 0.781640i) q^{13} +(7.89299 - 6.62301i) q^{14} +(2.53953 - 0.924313i) q^{16} +(1.18182 + 2.04697i) q^{17} +(0.919003 - 1.59176i) q^{19} +(0.904700 - 5.13081i) q^{20} +(8.28601 + 3.01586i) q^{22} +(0.747307 + 4.23819i) q^{23} +(-0.544815 - 0.457154i) q^{25} -2.58407 q^{26} +12.1980 q^{28} +(-2.28421 - 1.91668i) q^{29} +(0.255886 + 1.45120i) q^{31} +(7.45634 + 2.71388i) q^{32} +(-0.872200 + 4.94649i) q^{34} +(-5.02066 + 8.69603i) q^{35} +(-4.48554 - 7.76918i) q^{37} +(3.67027 - 1.33587i) q^{38} +(1.73869 - 1.45894i) q^{40} +(-1.73166 + 1.45304i) q^{41} +(5.15408 - 1.87593i) q^{43} +(5.21953 + 9.04050i) q^{44} +(-4.57260 + 7.91998i) q^{46} +(-1.24734 + 7.07400i) q^{47} +(-15.5140 - 5.64663i) q^{49} +(-0.262440 - 1.48837i) q^{50} +(-2.34347 - 1.96641i) q^{52} +6.32803 q^{53} -8.59334 q^{55} +(4.07079 + 3.41580i) q^{56} +(-1.10031 - 6.24019i) q^{58} +(0.246441 + 0.0896971i) q^{59} +(-0.773708 + 4.38792i) q^{61} +(-1.56571 + 2.71188i) q^{62} +(5.72840 + 9.92188i) q^{64} +(2.36642 - 0.861308i) q^{65} +(3.16461 - 2.65542i) q^{67} +(-4.55514 + 3.82222i) q^{68} +(-20.0512 + 7.29805i) q^{70} +(1.54276 + 2.67213i) q^{71} +(-6.38003 + 11.0505i) q^{73} +(3.31040 - 18.7742i) q^{74} +(4.34510 + 1.58149i) q^{76} +(-3.49372 - 19.8139i) q^{77} +(3.48735 + 2.92623i) q^{79} -5.59674 q^{80} -4.80368 q^{82} +(6.47542 + 5.43352i) q^{83} +(-0.850000 - 4.82059i) q^{85} +(10.9526 + 3.98641i) q^{86} +(-0.789708 + 4.47866i) q^{88} +(8.48158 - 14.6905i) q^{89} +(2.94803 + 5.10614i) q^{91} +(-10.1738 + 3.70295i) q^{92} +(-11.6932 + 9.81174i) q^{94} +(-2.91587 + 2.44671i) q^{95} +(4.80161 - 1.74764i) q^{97} +(-17.5417 - 30.3831i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{2} - 3 q^{4} - 6 q^{5} + 6 q^{7} - 6 q^{8}+O(q^{10}) $ 12 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 + 6 * q^7 - 6 * q^8	$ 12 q - 3 q^{2} - 3 q^{4} - 6 q^{5} + 6 q^{7} - 6 q^{8} - 6 q^{10} + 15 q^{11} - 3 q^{13} + 21 q^{14} + 9 q^{16} + 9 q^{17} - 12 q^{19} + 3 q^{20} + 33 q^{22} - 15 q^{23} - 12 q^{25} + 48 q^{26} + 6 q^{28} + 6 q^{29} - 12 q^{31} + 27 q^{32} + 27 q^{34} - 30 q^{35} - 3 q^{37} + 39 q^{38} + 24 q^{40} + 39 q^{41} + 24 q^{43} + 33 q^{44} + 3 q^{46} + 42 q^{47} - 30 q^{49} + 15 q^{50} - 45 q^{52} - 18 q^{53} + 30 q^{55} - 12 q^{56} - 30 q^{58} - 15 q^{59} - 3 q^{61} + 30 q^{62} - 6 q^{64} + 6 q^{65} - 3 q^{67} - 36 q^{68} - 75 q^{70} - 12 q^{73} - 60 q^{74} + 30 q^{76} - 33 q^{77} + 33 q^{79} - 42 q^{80} - 42 q^{82} + 33 q^{83} - 18 q^{85} + 30 q^{86} - 42 q^{88} + 9 q^{89} - 18 q^{91} - 33 q^{92} - 66 q^{94} - 12 q^{95} + 15 q^{97} - 18 q^{98}+O(q^{100}) $ 12 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 + 6 * q^7 - 6 * q^8 - 6 * q^10 + 15 * q^11 - 3 * q^13 + 21 * q^14 + 9 * q^16 + 9 * q^17 - 12 * q^19 + 3 * q^20 + 33 * q^22 - 15 * q^23 - 12 * q^25 + 48 * q^26 + 6 * q^28 + 6 * q^29 - 12 * q^31 + 27 * q^32 + 27 * q^34 - 30 * q^35 - 3 * q^37 + 39 * q^38 + 24 * q^40 + 39 * q^41 + 24 * q^43 + 33 * q^44 + 3 * q^46 + 42 * q^47 - 30 * q^49 + 15 * q^50 - 45 * q^52 - 18 * q^53 + 30 * q^55 - 12 * q^56 - 30 * q^58 - 15 * q^59 - 3 * q^61 + 30 * q^62 - 6 * q^64 + 6 * q^65 - 3 * q^67 - 36 * q^68 - 75 * q^70 - 12 * q^73 - 60 * q^74 + 30 * q^76 - 33 * q^77 + 33 * q^79 - 42 * q^80 - 42 * q^82 + 33 * q^83 - 18 * q^85 + 30 * q^86 - 42 * q^88 + 9 * q^89 - 18 * q^91 - 33 * q^92 - 66 * q^94 - 12 * q^95 + 15 * q^97 - 18 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	1.62787	+	1.36594i	1.15108	+	0.965867i	0.999744	−	0.0226162i	$-0.00719956\pi$
$2$	1.62787	+	1.36594i	1.15108	+	0.965867i	0.151331	+	0.988483i	$0.451644\pi$
$3$		0			0
$3$		0			0
$4$	0.436855	+	2.47753i	0.218427	+	1.23876i
$5$	−1.94605	−	0.708303i	−0.870299	−	0.316763i	−0.132011	−	0.991248i	$-0.542143\pi$
$5$	−1.94605	−	0.708303i	−0.870299	−	0.316763i	−0.738288	+	0.674485i	$0.764366\pi$
$6$		0			0
$7$	0.841963	−	4.77501i	0.318232	−	1.80478i	−0.235263	−	0.971932i	$-0.575595\pi$
$7$	0.841963	−	4.77501i	0.318232	−	1.80478i	0.553495	−	0.832853i	$-0.313294\pi$
$8$	−0.547989	+	0.949144i	−0.193743	+	0.335573i
$9$		0			0
$10$	−2.20040	−	3.81121i	−0.695829	−	1.20521i
$11$	3.89924	−	1.41921i	1.17567	−	0.427908i	0.320997	−	0.947080i	$-0.395982\pi$
$11$	3.89924	−	1.41921i	1.17567	−	0.427908i	0.854669	+	0.519173i	$0.173760\pi$
$12$		0			0
$13$	−0.931522	+	0.781640i	−0.258358	+	0.216788i	−0.762761	−	0.646680i	$-0.776157\pi$
$13$	−0.931522	+	0.781640i	−0.258358	+	0.216788i	0.504404	+	0.863468i	$0.331712\pi$
$14$	7.89299	−	6.62301i	2.10949	−	1.77007i
$15$		0			0
$16$	2.53953	−	0.924313i	0.634882	−	0.231078i
$17$	1.18182	+	2.04697i	0.286633	+	0.496463i	0.973004	−	0.230789i	$-0.0741306\pi$
$17$	1.18182	+	2.04697i	0.286633	+	0.496463i	−0.686371	+	0.727252i	$0.740797\pi$
$18$		0			0
$19$	0.919003	−	1.59176i	0.210834	−	0.365175i	−0.741142	−	0.671348i	$-0.765715\pi$
$19$	0.919003	−	1.59176i	0.210834	−	0.365175i	0.951976	+	0.306174i	$0.0990488\pi$
$20$	0.904700	−	5.13081i	0.202297	−	1.14728i
$21$		0			0
$22$	8.28601	+	3.01586i	1.76658	+	0.642983i
$23$	0.747307	+	4.23819i	0.155824	+	0.883723i	0.958028	+	0.286673i	$0.0925495\pi$
$23$	0.747307	+	4.23819i	0.155824	+	0.883723i	−0.802204	+	0.597050i	$0.796339\pi$
$24$		0			0
$25$	−0.544815	−	0.457154i	−0.108963	−	0.0914309i
$26$	−2.58407			−0.506777
$27$		0			0
$28$	12.1980			2.30521
$29$	−2.28421	−	1.91668i	−0.424167	−	0.355918i	0.405579	−	0.914060i	$-0.367070\pi$
$29$	−2.28421	−	1.91668i	−0.424167	−	0.355918i	−0.829745	+	0.558142i	$0.811514\pi$
$30$		0			0
$31$	0.255886	+	1.45120i	0.0459584	+	0.260643i	0.999126	−	0.0417995i	$-0.0133091\pi$
$31$	0.255886	+	1.45120i	0.0459584	+	0.260643i	−0.953168	+	0.302443i	$0.902198\pi$
$32$	7.45634	+	2.71388i	1.31811	+	0.479752i
$33$		0			0
$34$	−0.872200	+	4.94649i	−0.149581	+	0.848316i
$35$	−5.02066	+	8.69603i	−0.848646	+	1.46990i
$36$		0			0
$37$	−4.48554	−	7.76918i	−0.737418	−	1.27725i	−0.953654	−	0.300905i	$-0.902711\pi$
$37$	−4.48554	−	7.76918i	−0.737418	−	1.27725i	0.216236	−	0.976341i	$-0.430622\pi$
$38$	3.67027	−	1.33587i	0.595396	−	0.216706i
$39$		0			0
$40$	1.73869	−	1.45894i	0.274912	−	0.230678i
$41$	−1.73166	+	1.45304i	−0.270440	+	0.226926i	−0.767914	−	0.640553i	$-0.778705\pi$
$41$	−1.73166	+	1.45304i	−0.270440	+	0.226926i	0.497474	+	0.867479i	$0.334261\pi$
$42$		0			0
$43$	5.15408	−	1.87593i	0.785990	−	0.286077i	0.0823218	−	0.996606i	$-0.473766\pi$
$43$	5.15408	−	1.87593i	0.785990	−	0.286077i	0.703668	+	0.710529i	$0.251544\pi$
$44$	5.21953	+	9.04050i	0.786874	+	1.36291i
$45$		0			0
$46$	−4.57260	+	7.91998i	−0.674194	+	1.16774i
$47$	−1.24734	+	7.07400i	−0.181943	+	1.03185i	0.747878	+	0.663836i	$0.231073\pi$
$47$	−1.24734	+	7.07400i	−0.181943	+	1.03185i	−0.929821	+	0.368013i	$0.880038\pi$
$48$		0			0
$49$	−15.5140	−	5.64663i	−2.21628	−	0.806661i
$50$	−0.262440	−	1.48837i	−0.0371147	−	0.210488i
$51$		0			0
$52$	−2.34347	−	1.96641i	−0.324981	−	0.272692i
$53$	6.32803			0.869222			0.434611	−	0.900618i	$-0.356886\pi$
$53$	6.32803			0.869222			0.434611	+	0.900618i	$0.356886\pi$
$54$		0			0
$55$	−8.59334			−1.15873
$56$	4.07079	+	3.41580i	0.543982	+	0.456455i
$57$		0			0
$58$	−1.10031	−	6.24019i	−0.144478	−	0.819377i
$59$	0.246441	+	0.0896971i	0.0320839	+	0.0116776i	0.358012	−	0.933717i	$-0.383455\pi$
$59$	0.246441	+	0.0896971i	0.0320839	+	0.0116776i	−0.325928	+	0.945394i	$0.605677\pi$
$60$		0			0
$61$	−0.773708	+	4.38792i	−0.0990631	+	0.561815i	0.894363	+	0.447342i	$0.147629\pi$
$61$	−0.773708	+	4.38792i	−0.0990631	+	0.561815i	−0.993426	+	0.114473i	$0.963482\pi$
$62$	−1.56571	+	2.71188i	−0.198845	+	0.344410i
$63$		0			0
$64$	5.72840	+	9.92188i	0.716050	+	1.24024i
$65$	2.36642	−	0.861308i	0.293519	−	0.106832i
$66$		0			0
$67$	3.16461	−	2.65542i	0.386619	−	0.324411i	−0.428676	−	0.903458i	$-0.641020\pi$
$67$	3.16461	−	2.65542i	0.386619	−	0.324411i	0.815294	+	0.579047i	$0.196575\pi$
$68$	−4.55514	+	3.82222i	−0.552392	+	0.463512i
$69$		0			0
$70$	−20.0512	+	7.29805i	−2.39658	+	0.872284i
$71$	1.54276	+	2.67213i	0.183091	+	0.317124i	0.942932	−	0.332986i	$-0.108056\pi$
$71$	1.54276	+	2.67213i	0.183091	+	0.317124i	−0.759840	+	0.650110i	$0.774723\pi$
$72$		0			0
$73$	−6.38003	+	11.0505i	−0.746726	+	1.29337i	0.202658	+	0.979250i	$0.435042\pi$
$73$	−6.38003	+	11.0505i	−0.746726	+	1.29337i	−0.949384	+	0.314118i	$0.898291\pi$
$74$	3.31040	−	18.7742i	0.384826	−	2.18245i
$75$		0			0
$76$	4.34510	+	1.58149i	0.498417	+	0.181409i
$77$	−3.49372	−	19.8139i	−0.398146	−	2.25800i
$78$		0			0
$79$	3.48735	+	2.92623i	0.392357	+	0.329227i	0.817531	−	0.575885i	$-0.195342\pi$
$79$	3.48735	+	2.92623i	0.392357	+	0.329227i	−0.425174	+	0.905112i	$0.639787\pi$
$80$	−5.59674			−0.625734
$81$		0			0
$82$	−4.80368			−0.530478
$83$	6.47542	+	5.43352i	0.710769	+	0.596406i	0.924815	−	0.380417i	$-0.124220\pi$
$83$	6.47542	+	5.43352i	0.710769	+	0.596406i	−0.214045	+	0.976824i	$0.568664\pi$
$84$		0			0
$85$	−0.850000	−	4.82059i	−0.0921954	−	0.522866i
$86$	10.9526	+	3.98641i	1.18105	+	0.429866i
$87$		0			0
$88$	−0.789708	+	4.47866i	−0.0841831	+	0.477426i
$89$	8.48158	−	14.6905i	0.899046	−	1.55719i	0.0703304	−	0.997524i	$-0.477595\pi$
$89$	8.48158	−	14.6905i	0.899046	−	1.55719i	0.828716	−	0.559670i	$-0.189072\pi$
$90$		0			0
$91$	2.94803	+	5.10614i	0.309038	+	0.535269i
$92$	−10.1738	+	3.70295i	−1.06069	+	0.386059i
$93$		0			0
$94$	−11.6932	+	9.81174i	−1.20606	+	1.01200i
$95$	−2.91587	+	2.44671i	−0.299162	+	0.251027i
$96$		0			0
$97$	4.80161	−	1.74764i	0.487530	−	0.177446i	−0.0865469	−	0.996248i	$-0.527583\pi$
$97$	4.80161	−	1.74764i	0.487530	−	0.177446i	0.574077	+	0.818801i	$0.305361\pi$
$98$	−17.5417	−	30.3831i	−1.77198	−	3.06916i
$99$		0			0
$100$	0.894607	−	1.54951i	0.0894607	−	0.154951i
$101$	−3.22636	+	18.2976i	−0.321035	+	1.82068i	0.215151	+	0.976581i	$0.430975\pi$
$101$	−3.22636	+	18.2976i	−0.321035	+	1.82068i	−0.536186	+	0.844100i	$0.680136\pi$
$102$		0			0
$103$	−8.46266	−	3.08015i	−0.833850	−	0.303497i	−0.110412	−	0.993886i	$-0.535217\pi$
$103$	−8.46266	−	3.08015i	−0.833850	−	0.303497i	−0.723438	+	0.690389i	$0.757439\pi$
$104$	−0.231425	−	1.31248i	−0.0226931	−	0.128699i
$105$		0			0
$106$	10.3012	+	8.64372i	1.00054	+	0.839552i
$107$	−7.42680			−0.717976			−0.358988	−	0.933342i	$-0.616878\pi$
$107$	−7.42680			−0.717976			−0.358988	+	0.933342i	$0.616878\pi$
$108$		0			0
$109$	−5.62396			−0.538678			−0.269339	−	0.963045i	$-0.586805\pi$
$109$	−5.62396			−0.538678			−0.269339	+	0.963045i	$0.586805\pi$
$110$	−13.9888	−	11.7380i	−1.33378	−	1.11918i
$111$		0			0
$112$	−2.27541	−	12.9045i	−0.215006	−	1.21936i
$113$	−2.25777	−	0.821761i	−0.212393	−	0.0773048i	0.233632	−	0.972325i	$-0.424939\pi$
$113$	−2.25777	−	0.821761i	−0.212393	−	0.0773048i	−0.446026	+	0.895020i	$0.647161\pi$
$114$		0			0
$115$	1.54763	−	8.77703i	0.144317	−	0.818463i
$116$	3.75075	−	6.49649i	0.348249	−	0.603184i
$117$		0			0
$118$	0.278652	+	0.482639i	0.0256520	+	0.0444305i
$119$	10.7694	−	3.91972i	0.987225	−	0.359321i
$120$		0			0
$121$	4.76346	−	3.99702i	0.433042	−	0.363365i
$122$	−7.25313	+	6.08610i	−0.656668	+	0.551010i
$123$		0			0
$124$	−3.48360	+	1.26793i	−0.312837	+	0.113863i
$125$	5.91378	+	10.2430i	0.528945	+	0.916159i
$126$		0			0
$127$	4.61735	−	7.99748i	0.409723	−	0.709662i	−0.585135	−	0.810936i	$-0.698959\pi$
$127$	4.61735	−	7.99748i	0.409723	−	0.709662i	0.994859	+	0.101274i	$0.0322919\pi$
$128$	−1.47189	+	8.34752i	−0.130098	+	0.737824i
$129$		0			0
$130$	5.02872	+	1.83030i	0.441048	+	0.160528i
$131$	2.66359	+	15.1060i	0.232719	+	1.31981i	0.847365	+	0.531011i	$0.178188\pi$
$131$	2.66359	+	15.1060i	0.232719	+	1.31981i	−0.614646	+	0.788803i	$0.710701\pi$
$132$		0			0
$133$	−6.82691	−	5.72845i	−0.591968	−	0.496720i
$134$	8.77871			0.758365
$135$		0			0
$136$	−2.59049			−0.222133
$137$	2.79144	+	2.34230i	0.238489	+	0.200116i	0.754197	−	0.656649i	$-0.228026\pi$
$137$	2.79144	+	2.34230i	0.238489	+	0.200116i	−0.515708	+	0.856765i	$0.672471\pi$
$138$		0			0
$139$	2.30527	+	13.0739i	0.195531	+	1.10891i	0.911661	+	0.410943i	$0.134801\pi$
$139$	2.30527	+	13.0739i	0.195531	+	1.10891i	−0.716130	+	0.697967i	$0.754088\pi$
$140$	−23.7380	−	8.63991i	−2.00622	−	0.730206i
$141$		0			0
$142$	−1.13858	+	6.45719i	−0.0955472	+	0.541875i
$143$	−2.52292	+	4.36983i	−0.210977	+	0.365423i
$144$		0			0
$145$	3.08759	+	5.34786i	0.256410	+	0.444115i
$146$	−25.4802	+	9.27405i	−2.10876	+	0.767526i
$147$		0			0
$148$	17.2888	−	14.5071i	1.42113	−	1.19247i
$149$	−6.82621	+	5.72787i	−0.559225	+	0.469245i	−0.878051	−	0.478568i	$-0.841156\pi$
$149$	−6.82621	+	5.72787i	−0.559225	+	0.469245i	0.318826	+	0.947813i	$0.396712\pi$
$150$		0			0
$151$	0.669440	−	0.243656i	0.0544783	−	0.0198285i	−0.314637	−	0.949212i	$-0.601883\pi$
$151$	0.669440	−	0.243656i	0.0544783	−	0.0198285i	0.369116	+	0.929384i	$0.379661\pi$
$152$	1.00721	+	1.74453i	0.0816953	+	0.141500i
$153$		0			0
$154$	21.3773	−	37.0265i	1.72263	−	2.98368i
$155$	0.529924	−	3.00535i	0.0425645	−	0.241395i
$156$		0			0
$157$	12.9847	+	4.72605i	1.03629	+	0.377180i	0.803474	−	0.595340i	$-0.202983\pi$
$157$	12.9847	+	4.72605i	1.03629	+	0.377180i	0.232820	+	0.972520i	$0.425205\pi$
$158$	1.67987	+	9.52702i	0.133643	+	0.757929i
$159$		0			0
$160$	−12.5881	−	10.5627i	−0.995179	−	0.835054i
$161$	20.8666			1.64452
$162$		0			0
$163$	−1.19321			−0.0934597			−0.0467298	−	0.998908i	$-0.514880\pi$
$163$	−1.19321			−0.0934597			−0.0467298	+	0.998908i	$0.514880\pi$
$164$	−4.35642	−	3.65547i	−0.340180	−	0.285445i
$165$		0			0
$166$	3.11924	+	17.6901i	0.242100	+	1.37302i
$167$	−22.4928	−	8.18670i	−1.74054	−	0.633506i	−0.741255	−	0.671223i	$-0.765769\pi$
$167$	−22.4928	−	8.18670i	−1.74054	−	0.633506i	−0.999288	+	0.0377169i	$0.987991\pi$
$168$		0			0
$169$	−2.00065	+	11.3463i	−0.153896	+	0.872790i
$170$	5.20096	−	9.00832i	0.398895	−	0.690907i
$171$		0			0
$172$	6.89926	+	11.9499i	0.526063	+	0.911169i
$173$	−8.58879	+	3.12607i	−0.652994	+	0.237670i	−0.647209	−	0.762313i	$-0.724064\pi$
$173$	−8.58879	+	3.12607i	−0.652994	+	0.237670i	−0.00578525	+	0.999983i	$0.501842\pi$
$174$		0			0
$175$	−2.64163	+	2.21659i	−0.199689	+	0.167559i
$176$	8.59045	−	7.20824i	0.647530	−	0.543342i
$177$		0			0
$178$	33.8733	−	12.3289i	2.53891	−	0.924088i
$179$	5.30038	+	9.18052i	0.396169	+	0.686184i	0.993250	−	0.115997i	$-0.0370062\pi$
$179$	5.30038	+	9.18052i	0.396169	+	0.686184i	−0.597081	+	0.802181i	$0.703673\pi$
$180$		0			0
$181$	0.731460	−	1.26693i	0.0543690	−	0.0941699i	−0.837560	−	0.546345i	$-0.816019\pi$
$181$	0.731460	−	1.26693i	0.0543690	−	0.0941699i	0.891929	+	0.452176i	$0.149352\pi$
$182$	−2.17569	+	12.3389i	−0.161273	+	0.914624i
$183$		0			0
$184$	−4.43217	−	1.61318i	−0.326744	−	0.118925i
$185$	3.22614	+	18.2963i	0.237190	+	1.34517i
$186$		0			0
$187$	7.51328	+	6.30439i	0.549425	+	0.461023i
$188$	−18.0709			−1.31796
$189$		0			0
$190$	−8.08871			−0.586817
$191$	−9.51601	−	7.98488i	−0.688555	−	0.577766i	0.229937	−	0.973205i	$-0.426148\pi$
$191$	−9.51601	−	7.98488i	−0.688555	−	0.577766i	−0.918492	+	0.395439i	$0.870592\pi$
$192$		0			0
$193$	3.60725	+	20.4577i	0.259655	+	1.47258i	0.783834	+	0.620970i	$0.213261\pi$
$193$	3.60725	+	20.4577i	0.259655	+	1.47258i	−0.524179	+	0.851608i	$0.675628\pi$
$194$	10.2036	+	3.71380i	0.732574	+	0.266635i
$195$		0			0
$196$	7.21231	−	40.9031i	0.515165	−	2.92165i
$197$	−7.09433	+	12.2877i	−0.505450	+	0.875465i	0.494530	+	0.869161i	$0.335340\pi$
$197$	−7.09433	+	12.2877i	−0.505450	+	0.875465i	−0.999980	+	0.00630469i	$0.997993\pi$
$198$		0			0
$199$	−10.1643	−	17.6051i	−0.720529	−	1.24799i	−0.960788	−	0.277284i	$-0.910566\pi$
$199$	−10.1643	−	17.6051i	−0.720529	−	1.24799i	0.240259	−	0.970709i	$-0.422768\pi$
$200$	0.732458	−	0.266593i	0.0517926	−	0.0188510i
$201$		0			0
$202$	−30.2456	+	25.3790i	−2.12807	+	1.78566i
$203$	−11.0754	+	9.29334i	−0.777339	+	0.652265i
$204$		0			0
$205$	4.39909	−	1.60114i	0.307246	−	0.111828i
$206$	−9.56876	−	16.5736i	−0.666687	−	1.15474i
$207$		0			0
$208$	−1.64315	+	2.84601i	−0.113932	+	0.197336i
$209$	1.32438	−	7.51092i	0.0916091	−	0.519541i
$210$		0			0
$211$	9.26849	+	3.37345i	0.638069	+	0.232238i	0.640740	−	0.767758i	$-0.278628\pi$
$211$	9.26849	+	3.37345i	0.638069	+	0.232238i	−0.00267052	+	0.999996i	$0.500850\pi$
$212$	2.76443	+	15.6779i	0.189862	+	1.07676i
$213$		0			0
$214$	−12.0898	−	10.1446i	−0.826445	−	0.693470i
$215$	−11.3588			−0.774665
$216$		0			0
$217$	7.14494			0.485030
$218$	−9.15506	−	7.68201i	−0.620059	−	0.520291i
$219$		0			0
$220$	−3.75404	−	21.2902i	−0.253098	−	1.43539i
$221$	−2.70088	−	0.983041i	−0.181681	−	0.0661265i
$222$		0			0
$223$	2.61712	−	14.8424i	0.175255	−	0.993922i	−0.762594	−	0.646878i	$-0.776074\pi$
$223$	2.61712	−	14.8424i	0.175255	−	0.993922i	0.937849	−	0.347044i	$-0.112815\pi$
$224$	19.2368	−	33.3191i	1.28531	−	2.22623i
$225$		0			0
$226$	−2.55287	−	4.42170i	−0.169814	−	0.294127i
$227$	−21.3240	+	7.76131i	−1.41533	+	0.515136i	−0.932688	−	0.360684i	$-0.882543\pi$
$227$	−21.3240	+	7.76131i	−1.41533	+	0.515136i	−0.482637	+	0.875820i	$0.660321\pi$
$228$		0			0
$229$	6.67738	−	5.60299i	0.441254	−	0.370256i	−0.394925	−	0.918714i	$-0.629229\pi$
$229$	6.67738	−	5.60299i	0.441254	−	0.370256i	0.836178	+	0.548458i	$0.184785\pi$
$230$	14.5083	−	12.1739i	0.956646	−	0.802721i
$231$		0			0
$232$	3.07092	−	1.11772i	0.201616	−	0.0733822i
$233$	−11.7945	−	20.4286i	−0.772682	−	1.33832i	−0.936088	−	0.351766i	$-0.885581\pi$
$233$	−11.7945	−	20.4286i	−0.772682	−	1.33832i	0.163406	−	0.986559i	$-0.447752\pi$
$234$		0			0
$235$	7.43792	−	12.8829i	0.485196	−	0.840385i
$236$	−0.114568	+	0.649748i	−0.00745775	+	0.0422950i
$237$		0			0
$238$	22.8852	+	8.32953i	1.48343	+	0.539923i
$239$	−1.72858	−	9.80329i	−0.111813	−	0.634122i	−0.988279	−	0.152658i	$-0.951217\pi$
$239$	−1.72858	−	9.80329i	−0.111813	−	0.634122i	0.876466	−	0.481463i	$-0.159895\pi$
$240$		0			0
$241$	4.37676	+	3.67253i	0.281932	+	0.236569i	0.772776	−	0.634678i	$-0.218867\pi$
$241$	4.37676	+	3.67253i	0.281932	+	0.236569i	−0.490845	+	0.871247i	$0.663312\pi$
$242$	13.2140			0.849427
$243$		0			0
$244$	−11.2092			−0.717594
$245$	26.1914	+	21.9772i	1.67331	+	1.40407i
$246$		0			0
$247$	0.388111	+	2.20109i	0.0246949	+	0.140052i
$248$	−1.51762	−	0.552369i	−0.0963690	−	0.0350754i
$249$		0			0
$250$	−4.36446	+	24.7521i	−0.276033	+	1.56546i
$251$	−3.64483	+	6.31303i	−0.230060	+	0.398475i	−0.957825	−	0.287351i	$-0.907226\pi$
$251$	−3.64483	+	6.31303i	−0.230060	+	0.398475i	0.727766	+	0.685826i	$0.240559\pi$
$252$		0			0
$253$	8.92881	+	15.4651i	0.561349	+	0.972285i
$254$	18.4405	−	6.71180i	1.15706	−	0.421136i
$255$		0			0
$256$	3.75456	−	3.15045i	0.234660	−	0.196903i
$257$	17.8052	−	14.9404i	1.11066	−	0.931954i	0.112564	−	0.993644i	$-0.464094\pi$
$257$	17.8052	−	14.9404i	1.11066	−	0.931954i	0.998095	+	0.0616904i	$0.0196492\pi$
$258$		0			0
$259$	−40.8746	+	14.8771i	−2.53982	+	0.924420i
$260$	3.16770	+	5.48661i	0.196452	+	0.340265i
$261$		0			0
$262$	−16.2979	+	28.2288i	−1.00689	+	1.74398i
$263$	4.75789	−	26.9833i	0.293384	−	1.66386i	−0.380314	−	0.924858i	$-0.624184\pi$
$263$	4.75789	−	26.9833i	0.293384	−	1.66386i	0.673698	−	0.739007i	$-0.264705\pi$
$264$		0			0
$265$	−12.3146	−	4.48216i	−0.756483	−	0.275337i
$266$	−3.28855	−	18.6503i	−0.201634	−	1.14352i
$267$		0			0
$268$	7.96136	+	6.68037i	0.486317	+	0.408069i
$269$	−9.41973			−0.574331			−0.287166	−	0.957881i	$-0.592713\pi$
$269$	−9.41973			−0.574331			−0.287166	+	0.957881i	$0.592713\pi$
$270$		0			0
$271$	26.2797			1.59638			0.798189	−	0.602408i	$-0.205792\pi$
$271$	26.2797			1.59638			0.798189	+	0.602408i	$0.205792\pi$
$272$	4.89331	+	4.10597i	0.296700	+	0.248961i
$273$		0			0
$274$	1.34465	+	7.62590i	0.0812334	+	0.460697i
$275$	−2.77317	−	1.00935i	−0.167228	−	0.0608661i
$276$		0			0
$277$	0.0650854	−	0.369118i	0.00391060	−	0.0221781i	−0.982790	−	0.184726i	$-0.940860\pi$
$277$	0.0650854	−	0.369118i	0.00391060	−	0.0221781i	0.986701	+	0.162548i	$0.0519713\pi$
$278$	−14.1054	+	24.4314i	−0.845989	+	1.46530i
$279$		0			0
$280$	−5.50253	−	9.53065i	−0.328839	−	0.569566i
$281$	13.1384	−	4.78198i	0.783771	−	0.285269i	0.0810267	−	0.996712i	$-0.474180\pi$
$281$	13.1384	−	4.78198i	0.783771	−	0.285269i	0.702744	+	0.711443i	$0.251958\pi$
$282$		0			0
$283$	11.9211	−	10.0030i	0.708636	−	0.594616i	−0.215580	−	0.976486i	$-0.569164\pi$
$283$	11.9211	−	10.0030i	0.708636	−	0.594616i	0.924216	+	0.381870i	$0.124720\pi$
$284$	−5.94632	+	4.98955i	−0.352849	+	0.296075i
$285$		0			0
$286$	−10.0759	+	3.66733i	−0.595801	+	0.216854i
$287$	5.48027	+	9.49211i	0.323490	+	0.560301i
$288$		0			0
$289$	5.70661	−	9.88413i	0.335683	−	0.581420i
$290$	−2.27868	+	12.9231i	−0.133809	+	0.758868i
$291$		0			0
$292$	−30.1652	−	10.9792i	−1.76528	−	0.642510i
$293$	−4.27595	−	24.2501i	−0.249804	−	1.41671i	−0.809066	−	0.587717i	$-0.800027\pi$
$293$	−4.27595	−	24.2501i	−0.249804	−	1.41671i	0.559263	−	0.828990i	$-0.311084\pi$
$294$		0			0
$295$	−0.416053	−	0.349110i	−0.0242235	−	0.0203259i
$296$	9.83210			0.571479
$297$		0			0
$298$	−18.9361			−1.09694
$299$	−4.00887	−	3.36384i	−0.231839	−	0.194536i
$300$		0			0
$301$	−4.61805	−	26.1903i	−0.266180	−	1.50958i
$302$	1.42258	+	0.517777i	0.0818603	+	0.0297947i
$303$		0			0
$304$	0.862551	−	4.89177i	0.0494707	−	0.280562i
$305$	4.61365	−	7.99107i	0.264177	−	0.457567i
$306$		0			0
$307$	10.1956	+	17.6593i	0.581893	+	1.00787i	0.995255	+	0.0973012i	$0.0310210\pi$
$307$	10.1956	+	17.6593i	0.581893	+	1.00787i	−0.413362	+	0.910567i	$0.635646\pi$
$308$	47.5631	−	17.3116i	2.71016	−	0.986418i
$309$		0			0
$310$	4.96778	−	4.16846i	0.282151	−	0.236753i
$311$	−16.9901	+	14.2564i	−0.963421	+	0.808406i	−0.981506	−	0.191430i	$-0.938687\pi$
$311$	−16.9901	+	14.2564i	−0.963421	+	0.808406i	0.0180851	+	0.999836i	$0.494243\pi$
$312$		0			0
$313$	10.4983	−	3.82106i	0.593398	−	0.215979i	−0.0278253	−	0.999613i	$-0.508858\pi$
$313$	10.4983	−	3.82106i	0.593398	−	0.215979i	0.621223	+	0.783634i	$0.286636\pi$
$314$	14.6819	+	25.4298i	0.828547	+	1.43508i
$315$		0			0
$316$	−5.72635	+	9.91833i	−0.322132	+	0.557950i
$317$	−4.37883	+	24.8336i	−0.245939	+	1.39479i	0.572361	+	0.820002i	$0.306027\pi$
$317$	−4.37883	+	24.8336i	−0.245939	+	1.39479i	−0.818301	+	0.574790i	$0.805084\pi$
$318$		0			0
$319$	−11.6268	−	4.23182i	−0.650978	−	0.236937i
$320$	−4.12004	−	23.3659i	−0.230317	−	1.30619i
$321$		0			0
$322$	33.9680	+	28.5026i	1.89296	+	1.58839i
$323$	4.34438			0.241728
$324$		0			0
$325$	0.864837			0.0479725
$326$	−1.94239	−	1.62986i	−0.107579	−	0.0902696i
$327$		0			0
$328$	−0.430211	−	2.43985i	−0.0237544	−	0.134718i
$329$	32.7282	+	11.9121i	1.80437	+	0.656735i
$330$		0			0
$331$	−4.54362	+	25.7682i	−0.249740	+	1.41635i	0.559481	+	0.828843i	$0.311000\pi$
$331$	−4.54362	+	25.7682i	−0.249740	+	1.41635i	−0.809221	+	0.587504i	$0.800111\pi$
$332$	−10.6329	+	18.4167i	−0.583555	+	1.01075i
$333$		0			0
$334$	−25.4327	−	44.0507i	−1.39161	−	2.41035i
$335$	−8.03932	+	2.92607i	−0.439235	+	0.159869i
$336$		0			0
$337$	8.38516	−	7.03599i	0.456769	−	0.383275i	−0.385172	−	0.922845i	$-0.625858\pi$
$337$	8.38516	−	7.03599i	0.456769	−	0.383275i	0.841940	+	0.539570i	$0.181413\pi$
$338$	−18.7551	+	15.7374i	−1.02015	+	0.856004i
$339$		0			0
$340$	11.5718	−	4.21180i	0.627570	−	0.228417i
$341$	3.05732	+	5.29543i	0.165563	+	0.286763i
$342$		0			0
$343$	−23.0545	+	39.9316i	−1.24483	+	2.15611i
$344$	−1.04385	+	5.91996i	−0.0562805	+	0.319183i
$345$		0			0
$346$	−18.2514	−	6.64298i	−0.981203	−	0.357129i
$347$	−0.610092	−	3.46000i	−0.0327514	−	0.185743i	0.964043	−	0.265746i	$-0.0856181\pi$
$347$	−0.610092	−	3.46000i	−0.0327514	−	0.185743i	−0.996795	+	0.0800030i	$0.974507\pi$
$348$		0			0
$349$	−22.3661	−	18.7674i	−1.19723	−	1.00459i	−0.999705	−	0.0242965i	$-0.992265\pi$
$349$	−22.3661	−	18.7674i	−1.19723	−	1.00459i	−0.197524	−	0.980298i	$-0.563290\pi$
$350$	−7.32796			−0.391696
$351$		0			0
$352$	32.9256			1.75494
$353$	19.2100	+	16.1191i	1.02244	+	0.857931i	0.989932	−	0.141540i	$-0.0452055\pi$
$353$	19.2100	+	16.1191i	1.02244	+	0.857931i	0.0325100	+	0.999471i	$0.489650\pi$
$354$		0			0
$355$	−1.10960	−	6.29283i	−0.0588912	−	0.333989i
$356$	40.1014	+	14.5957i	2.12537	+	0.773572i
$357$		0			0
$358$	−3.91176	+	22.1847i	−0.206743	+	1.17250i
$359$	2.10362	−	3.64358i	0.111025	−	0.192301i	−0.805159	−	0.593059i	$-0.797920\pi$
$359$	2.10362	−	3.64358i	0.111025	−	0.192301i	0.916184	+	0.400758i	$0.131253\pi$
$360$		0			0
$361$	7.81087	+	13.5288i	0.411098	+	0.712043i
$362$	2.92127	−	1.06325i	0.153538	−	0.0558834i
$363$		0			0
$364$	−11.3627	+	9.53447i	−0.595569	+	0.499742i
$365$	20.2430	−	16.9859i	1.05957	−	0.889081i
$366$		0			0
$367$	−16.4415	+	5.98420i	−0.858237	+	0.312373i	−0.733394	−	0.679804i	$-0.762065\pi$
$367$	−16.4415	+	5.98420i	−0.858237	+	0.312373i	−0.124843	+	0.992177i	$0.539843\pi$
$368$	5.81522	+	10.0723i	0.303139	+	0.525053i
$369$		0			0
$370$	−19.7400	+	34.1907i	−1.02623	+	1.77749i
$371$	5.32797	−	30.2164i	0.276614	−	1.56876i
$372$		0			0
$373$	27.8662	+	10.1425i	1.44286	+	0.525157i	0.940586	−	0.339554i	$-0.110276\pi$
$373$	27.8662	+	10.1425i	1.44286	+	0.525157i	0.502270	+	0.864711i	$0.332499\pi$
$374$	3.61918	+	20.5254i	0.187144	+	1.06134i
$375$		0			0
$376$	−6.03072	−	5.06038i	−0.311011	−	0.260969i
$377$	3.62594			0.186745
$378$		0			0
$379$	20.9523			1.07625			0.538124	−	0.842865i	$-0.319133\pi$
$379$	20.9523			1.07625			0.538124	+	0.842865i	$0.319133\pi$
$380$	−7.33560	−	6.15530i	−0.376308	−	0.315760i
$381$		0			0
$382$	−4.58391	−	25.9966i	−0.234533	−	1.33010i
$383$	9.29993	+	3.38490i	0.475204	+	0.172960i	0.568508	−	0.822678i	$-0.307521\pi$
$383$	9.29993	+	3.38490i	0.475204	+	0.172960i	−0.0933043	+	0.995638i	$0.529743\pi$
$384$		0			0
$385$	−7.23528	+	41.0333i	−0.368744	+	2.09125i
$386$	−22.0719	+	38.2297i	−1.12343	+	1.94584i
$387$		0			0
$388$	6.42745	+	11.1327i	0.326304	+	0.565175i
$389$	−19.8414	+	7.22167i	−1.00600	+	0.366153i	−0.791895	−	0.610658i	$-0.790905\pi$
$389$	−19.8414	+	7.22167i	−1.00600	+	0.366153i	−0.214104	+	0.976811i	$0.568683\pi$
$390$		0			0
$391$	−7.79227	+	6.53849i	−0.394072	+	0.330665i
$392$	13.8609	−	11.6307i	0.700083	−	0.587440i
$393$		0			0
$394$	−28.3330	+	10.3124i	−1.42739	+	0.519529i
$395$	−4.71388	−	8.16468i	−0.237181	−	0.410810i
$396$		0			0
$397$	4.88955	−	8.46894i	0.245399	−	0.425044i	−0.716845	−	0.697233i	$-0.754414\pi$
$397$	4.88955	−	8.46894i	0.245399	−	0.425044i	0.962244	+	0.272189i	$0.0877476\pi$
$398$	7.50142	−	42.5426i	0.376012	−	2.13247i
$399$		0			0
$400$	−1.80613	−	0.657377i	−0.0903064	−	0.0328688i
$401$	3.32351	+	18.8486i	0.165968	+	0.941252i	0.948061	+	0.318090i	$0.103041\pi$
$401$	3.32351	+	18.8486i	0.165968	+	0.941252i	−0.782092	+	0.623163i	$0.785847\pi$
$402$		0			0
$403$	−1.37268	−	1.15181i	−0.0683780	−	0.0573759i
$404$	−46.7423			−2.32552
$405$		0			0
$406$	−30.7234			−1.52478
$407$	−28.5163	−	23.9280i	−1.41350	−	1.18607i
$408$		0			0
$409$	2.60395	+	14.7677i	0.128757	+	0.730218i	0.979005	+	0.203836i	$0.0653408\pi$
$409$	2.60395	+	14.7677i	0.128757	+	0.730218i	−0.850248	+	0.526382i	$0.823548\pi$
$410$	9.34819	+	3.40246i	0.461674	+	0.168036i
$411$		0			0
$412$	3.93421	−	22.3120i	0.193825	−	1.09924i
$413$	0.635799	−	1.10124i	0.0312856	−	0.0541883i
$414$		0			0
$415$	−8.75289	−	15.1604i	−0.429662	−	0.744197i
$416$	−9.06702	+	3.30013i	−0.444547	+	0.161802i
$417$		0			0
$418$	12.4154	−	10.4177i	0.607257	−	0.509549i
$419$	−4.45210	+	3.73575i	−0.217499	+	0.182504i	−0.745027	−	0.667034i	$-0.767563\pi$
$419$	−4.45210	+	3.73575i	−0.217499	+	0.182504i	0.527528	+	0.849538i	$0.323119\pi$
$420$		0			0
$421$	12.5106	−	4.55349i	0.609730	−	0.221924i	−0.0186551	−	0.999826i	$-0.505938\pi$
$421$	12.5106	−	4.55349i	0.609730	−	0.221924i	0.628385	+	0.777902i	$0.283716\pi$
$422$	10.4799	+	18.1518i	0.510154	+	0.883613i
$423$		0			0
$424$	−3.46769	+	6.00621i	−0.168406	+	0.291687i
$425$	0.291908	−	1.65549i	0.0141596	−	0.0803033i
$426$		0			0
$427$	20.3009	+	7.38893i	0.982430	+	0.357575i
$428$	−3.24444	−	18.4001i	−0.156826	−	0.889403i
$429$		0			0
$430$	−18.4906	−	15.5155i	−0.891697	−	0.748223i
$431$	36.4166			1.75413			0.877064	−	0.480374i	$-0.159499\pi$
$431$	36.4166			1.75413			0.877064	+	0.480374i	$0.159499\pi$
$432$		0			0
$433$	−10.8761			−0.522674			−0.261337	−	0.965248i	$-0.584163\pi$
$433$	−10.8761			−0.522674			−0.261337	+	0.965248i	$0.584163\pi$
$434$	11.6310	+	9.75957i	0.558306	+	0.468475i
$435$		0			0
$436$	−2.45686	−	13.9335i	−0.117662	−	0.667295i
$437$	7.43296	+	2.70537i	0.355567	+	0.129416i
$438$		0			0
$439$	1.64154	−	9.30965i	0.0783465	−	0.444325i	−0.920248	−	0.391335i	$-0.872014\pi$
$439$	1.64154	−	9.30965i	0.0783465	−	0.444325i	0.998595	−	0.0529907i	$-0.0168754\pi$
$440$	4.70906	−	8.15632i	0.224495	−	0.388837i
$441$		0			0
$442$	−3.05390	−	5.28951i	−0.145259	−	0.251596i
$443$	15.5274	−	5.65151i	0.737729	−	0.268511i	0.0542962	−	0.998525i	$-0.482708\pi$
$443$	15.5274	−	5.65151i	0.737729	−	0.268511i	0.683433	+	0.730013i	$0.260486\pi$
$444$		0			0
$445$	−26.9109	+	22.5809i	−1.27570	+	1.07044i
$446$	24.5342	−	20.5866i	1.16173	−	0.974806i
$447$		0			0
$448$	52.2002	−	18.9993i	2.46623	−	0.897633i
$449$	−2.37181	−	4.10809i	−0.111933	−	0.193873i	0.804617	−	0.593794i	$-0.202371\pi$
$449$	−2.37181	−	4.10809i	−0.111933	−	0.193873i	−0.916549	+	0.399921i	$0.869037\pi$
$450$		0			0
$451$	−4.69001	+	8.12334i	−0.220844	+	0.382513i
$452$	1.04962	−	5.95268i	0.0493699	−	0.279990i
$453$		0			0
$454$	−45.3142	−	16.4930i	−2.12670	−	0.774055i
$455$	−2.12031	−	12.0249i	−0.0994017	−	0.563735i
$456$		0			0
$457$	−17.1659	−	14.4039i	−0.802989	−	0.673788i	0.145934	−	0.989294i	$-0.453381\pi$
$457$	−17.1659	−	14.4039i	−0.802989	−	0.673788i	−0.948923	+	0.315506i	$0.897826\pi$
$458$	18.5232			0.865534
$459$		0			0
$460$	22.4214			1.04540
$461$	11.4311	+	9.59184i	0.532400	+	0.446737i	0.868929	−	0.494936i	$-0.164809\pi$
$461$	11.4311	+	9.59184i	0.532400	+	0.446737i	−0.336529	+	0.941673i	$0.609253\pi$
$462$		0			0
$463$	−2.57818	−	14.6216i	−0.119818	−	0.679524i	−0.984251	−	0.176776i	$-0.943433\pi$
$463$	−2.57818	−	14.6216i	−0.119818	−	0.679524i	0.864433	−	0.502748i	$-0.167678\pi$
$464$	−7.57242	−	2.75614i	−0.351541	−	0.127950i
$465$		0			0
$466$	8.70450	−	49.3657i	0.403228	−	2.28682i
$467$	−7.67571	+	13.2947i	−0.355190	+	0.615206i	−0.987150	−	0.159794i	$-0.948917\pi$
$467$	−7.67571	+	13.2947i	−0.355190	+	0.615206i	0.631961	+	0.775000i	$0.282250\pi$
$468$		0			0
$469$	−10.0152	−	17.3468i	−0.462458	−	0.801001i
$470$	29.7052	−	10.8118i	1.37020	−	0.498711i
$471$		0			0
$472$	−0.220182	+	0.184755i	−0.0101347	+	0.00850403i
$473$	17.4347	−	14.6294i	0.801647	−	0.672662i
$474$		0			0
$475$	−1.22837	+	0.447089i	−0.0563614	+	0.0205139i
$476$	14.4159	+	24.9690i	0.660750	+	1.14445i
$477$		0			0
$478$	10.5768	−	18.3196i	0.483772	−	0.837918i
$479$	−1.81438	+	10.2899i	−0.0829012	+	0.470156i	0.914889	+	0.403706i	$0.132278\pi$
$479$	−1.81438	+	10.2899i	−0.0829012	+	0.470156i	−0.997790	+	0.0664497i	$0.978833\pi$
$480$		0			0
$481$	10.2511	+	3.73109i	0.467409	+	0.170123i
$482$	2.10830	+	11.9568i	0.0960306	+	0.544617i
$483$		0			0
$484$	11.9837	+	10.0555i	0.544712	+	0.457068i
$485$	−10.5820			−0.480505
$486$		0			0
$487$	−16.1649			−0.732500			−0.366250	−	0.930516i	$-0.619359\pi$
$487$	−16.1649			−0.732500			−0.366250	+	0.930516i	$0.619359\pi$
$488$	−3.74078	−	3.13889i	−0.169337	−	0.142091i
$489$		0			0
$490$	12.6165	+	71.5519i	0.569957	+	3.23239i
$491$	−10.1274	−	3.68607i	−0.457043	−	0.166350i	0.103231	−	0.994657i	$-0.467082\pi$
$491$	−10.1274	−	3.68607i	−0.457043	−	0.166350i	−0.560274	+	0.828307i	$0.689304\pi$
$492$		0			0
$493$	1.22386	−	6.94087i	0.0551200	−	0.312601i
$494$	−2.37477	+	4.11322i	−0.106846	+	0.185062i
$495$		0			0
$496$	1.99119	+	3.44885i	0.0894071	+	0.154858i
$497$	14.0584	−	5.11684i	0.630605	−	0.229522i
$498$		0			0
$499$	−14.6982	+	12.3333i	−0.657983	+	0.552114i	−0.909482	−	0.415744i	$-0.863521\pi$
$499$	−14.6982	+	12.3333i	−0.657983	+	0.552114i	0.251498	+	0.967858i	$0.419077\pi$
$500$	−22.7938	+	19.1263i	−1.01937	+	0.855352i
$501$		0			0
$502$	−14.5565	+	5.29815i	−0.649690	+	0.236468i
$503$	−6.01253	−	10.4140i	−0.268086	−	0.464338i	0.700282	−	0.713866i	$-0.253058\pi$
$503$	−6.01253	−	10.4140i	−0.268086	−	0.464338i	−0.968367	+	0.249529i	$0.919724\pi$
$504$		0			0
$505$	19.2389	−	33.3228i	0.856120	−	1.48284i
$506$	−6.58959	+	37.3714i	−0.292943	+	1.66136i
$507$		0			0
$508$	21.8311	+	7.94586i	0.968598	+	0.352541i
$509$	2.59657	+	14.7259i	0.115091	+	0.652712i	0.986705	+	0.162520i	$0.0519622\pi$
$509$	2.59657	+	14.7259i	0.115091	+	0.652712i	−0.871615	+	0.490192i	$0.836927\pi$
$510$		0			0
$511$	47.3947	+	39.7689i	2.09662	+	1.75927i
$512$	27.3678			1.20950
$513$		0			0
$514$	49.3922			2.17860
$515$	14.2870	+	11.9883i	0.629562	+	0.528266i
$516$		0			0
$517$	5.17581	+	29.3535i	0.227632	+	1.29097i
$518$	−86.8597	−	31.6143i	−3.81640	−	1.38905i
$519$		0			0
$520$	−0.479268	+	2.71806i	−0.0210173	+	0.119195i
$521$	18.7094	−	32.4056i	0.819673	−	1.41972i	−0.0862502	−	0.996274i	$-0.527488\pi$
$521$	18.7094	−	32.4056i	0.819673	−	1.41972i	0.905923	−	0.423442i	$-0.139178\pi$
$522$		0			0
$523$	4.22489	+	7.31773i	0.184742	+	0.319982i	0.943489	−	0.331403i	$-0.107522\pi$
$523$	4.22489	+	7.31773i	0.184742	+	0.319982i	−0.758748	+	0.651385i	$0.774188\pi$
$524$	−36.2619	+	13.1982i	−1.58411	+	0.576568i
$525$		0			0
$526$	44.6029	−	37.4263i	1.94478	−	1.63186i
$527$	−2.66815	+	2.23885i	−0.116227	+	0.0975256i
$528$		0			0
$529$	4.20916	−	1.53201i	0.183007	−	0.0666091i
$530$	−13.9242	−	24.1175i	−0.604829	−	1.04760i
$531$		0			0
$532$	11.2100	−	19.4163i	0.486017	−	0.841805i
$533$	0.477330	−	2.70707i	0.0206754	−	0.117256i
$534$		0			0
$535$	14.4529	+	5.26043i	0.624854	+	0.227428i
$536$	0.786209	+	4.45881i	0.0339591	+	0.192591i
$537$		0			0
$538$	−15.3341	−	12.8668i	−0.661098	−	0.554727i
$539$	−68.5065			−2.95078
$540$		0			0
$541$	12.6259			0.542828			0.271414	−	0.962463i	$-0.412509\pi$
$541$	12.6259			0.542828			0.271414	+	0.962463i	$0.412509\pi$
$542$	42.7798	+	35.8965i	1.83755	+	1.54189i
$543$		0			0
$544$	3.25680	+	18.4702i	0.139634	+	0.791904i
$545$	10.9445	+	3.98347i	0.468811	+	0.170633i
$546$		0			0
$547$	5.45169	−	30.9181i	0.233098	−	1.32196i	−0.613486	−	0.789706i	$-0.710233\pi$
$547$	5.45169	−	30.9181i	0.233098	−	1.32196i	0.846583	−	0.532256i	$-0.178656\pi$
$548$	−4.58365	+	7.93912i	−0.195804	+	0.339142i
$549$		0			0
$550$	−3.13563	−	5.43107i	−0.133704	−	0.231582i
$551$	−5.15008	+	1.87448i	−0.219401	+	0.0798554i
$552$		0			0
$553$	16.9090	−	14.1883i	0.719044	−	0.603349i
$554$	0.610144	−	0.511971i	0.0259225	−	0.0217516i
$555$		0			0
$556$	−31.3838	+	11.4228i	−1.33097	+	0.484433i
$557$	−7.96515	−	13.7960i	−0.337494	−	0.584557i	0.646467	−	0.762942i	$-0.276246\pi$
$557$	−7.96515	−	13.7960i	−0.337494	−	0.584557i	−0.983961	+	0.178385i	$0.942913\pi$
$558$		0			0
$559$	−3.33484	+	5.77610i	−0.141048	+	0.244303i
$560$	−4.71225	+	26.7245i	−0.199129	+	1.12932i
$561$		0			0
$562$	27.9195	+	10.1619i	1.17771	+	0.428652i
$563$	4.31704	+	24.4832i	0.181942	+	1.03184i	0.929822	+	0.368009i	$0.119960\pi$
$563$	4.31704	+	24.4832i	0.181942	+	1.03184i	−0.747881	+	0.663833i	$0.768928\pi$
$564$		0			0
$565$	3.81167	+	3.19837i	0.160358	+	0.134557i
$566$	33.0695			1.39001
$567$		0			0
$568$	−3.38165			−0.141891
$569$	−14.7004	−	12.3351i	−0.616273	−	0.517114i	0.280357	−	0.959896i	$-0.409547\pi$
$569$	−14.7004	−	12.3351i	−0.616273	−	0.517114i	−0.896629	+	0.442782i	$0.853992\pi$
$570$		0			0
$571$	−3.53882	−	20.0696i	−0.148095	−	0.839888i	−0.964830	−	0.262875i	$-0.915329\pi$
$571$	−3.53882	−	20.0696i	−0.148095	−	0.839888i	0.816735	−	0.577013i	$-0.195782\pi$
$572$	−11.9285	−	4.34162i	−0.498756	−	0.181532i
$573$		0			0
$574$	−4.04452	+	22.9376i	−0.168815	+	0.957398i
$575$	1.53036	−	2.65066i	0.0638205	−	0.110540i
$576$		0			0
$577$	−11.6495	−	20.1776i	−0.484976	−	0.840004i	0.514875	−	0.857265i	$-0.327838\pi$
$577$	−11.6495	−	20.1776i	−0.484976	−	0.840004i	−0.999851	+	0.0172619i	$0.994505\pi$
$578$	22.7907	−	8.29515i	0.947970	−	0.345033i
$579$		0			0
$580$	−11.9006	+	9.98581i	−0.494147	+	0.414638i
$581$	31.3972	−	26.3454i	1.30257	−	1.09299i
$582$		0			0
$583$	24.6745	−	8.98079i	1.02191	−	0.371946i
$584$	−6.99237	−	12.1111i	−0.289346	−	0.501163i
$585$		0			0
$586$	26.1636	−	45.3167i	1.08081	−	1.87201i
$587$	6.40923	−	36.3485i	0.264537	−	1.50026i	−0.505813	−	0.862643i	$-0.668807\pi$
$587$	6.40923	−	36.3485i	0.264537	−	1.50026i	0.770350	−	0.637621i	$-0.220082\pi$
$588$		0			0
$589$	2.54512	+	0.926348i	0.104870	+	0.0381695i
$590$	−0.200415	−	1.13661i	−0.00825094	−	0.0467934i
$591$		0			0
$592$	−18.5723	−	15.5840i	−0.763318	−	0.640500i
$593$	−4.36830			−0.179385			−0.0896923	−	0.995970i	$-0.528588\pi$
$593$	−4.36830			−0.179385			−0.0896923	+	0.995970i	$0.528588\pi$
$594$		0			0
$595$	−23.7340			−0.973000
$596$	−17.1730	−	14.4099i	−0.703434	−	0.590251i
$597$		0			0
$598$	−1.93109	−	10.9518i	−0.0789682	−	0.447851i
$599$	−29.3237	−	10.6729i	−1.19813	−	0.436085i	−0.335561	−	0.942019i	$-0.608926\pi$
$599$	−29.3237	−	10.6729i	−1.19813	−	0.436085i	−0.862572	+	0.505934i	$0.831148\pi$
$600$		0			0
$601$	7.62960	−	43.2696i	0.311218	−	1.76500i	−0.281468	−	0.959571i	$-0.590821\pi$
$601$	7.62960	−	43.2696i	0.311218	−	1.76500i	0.592686	−	0.805433i	$-0.298067\pi$
$602$	28.2568	−	48.9422i	1.15166	−	1.99474i
$603$		0			0
$604$	0.896114	+	1.55211i	0.0364623	+	0.0631546i
$605$	−12.1010	+	4.40441i	−0.491977	+	0.179065i
$606$		0			0
$607$	13.2975	−	11.1579i	0.539729	−	0.452886i	−0.331716	−	0.943379i	$-0.607628\pi$
$607$	13.2975	−	11.1579i	0.539729	−	0.452886i	0.871445	+	0.490493i	$0.163183\pi$
$608$	11.1723	−	9.37463i	0.453095	−	0.380192i
$609$		0			0
$610$	18.4257	−	6.70642i	0.746036	−	0.271535i
$611$	−4.36740	−	7.56456i	−0.176686	−	0.306029i
$612$		0			0
$613$	0.599024	−	1.03754i	0.0241944	−	0.0419059i	−0.853675	−	0.520807i	$-0.825631\pi$
$613$	0.599024	−	1.03754i	0.0241944	−	0.0419059i	0.877869	+	0.478901i	$0.158965\pi$
$614$	−7.52449	+	42.6735i	−0.303664	+	1.72216i
$615$		0			0
$616$	20.7207	+	7.54173i	0.834862	+	0.303865i
$617$	−4.51723	−	25.6185i	−0.181857	−	1.03136i	−0.929927	−	0.367743i	$-0.880131\pi$
$617$	−4.51723	−	25.6185i	−0.181857	−	1.03136i	0.748070	−	0.663619i	$-0.230980\pi$
$618$		0			0
$619$	7.37804	+	6.19091i	0.296549	+	0.248834i	0.778906	−	0.627141i	$-0.215775\pi$
$619$	7.37804	+	6.19091i	0.296549	+	0.248834i	−0.482357	+	0.875974i	$0.660219\pi$
$620$	7.67733			0.308329
$621$		0			0
$622$	−47.1311			−1.88978
$623$	−63.0063	−	52.8685i	−2.52429	−	2.11813i
$624$		0			0
$625$	−3.63587	−	20.6201i	−0.145435	−	0.824802i
$626$	22.3092	+	8.11987i	0.891653	+	0.324535i
$627$		0			0
$628$	−6.03648	+	34.2346i	−0.240882	+	1.36611i
$629$	10.6022	−	18.3635i	0.422737	−	0.732202i
$630$		0			0
$631$	7.08366	+	12.2693i	0.281996	+	0.488431i	0.971876	−	0.235492i	$-0.0756702\pi$
$631$	7.08366	+	12.2693i	0.281996	+	0.488431i	−0.689880	+	0.723924i	$0.742337\pi$
$632$	−4.68844	+	1.70645i	−0.186496	+	0.0678791i
$633$		0			0
$634$	−41.0494	+	34.4445i	−1.63028	+	1.36797i
$635$	−14.6502	+	12.2930i	−0.581376	+	0.487833i
$636$		0			0
$637$	18.8652	−	6.86638i	0.747468	−	0.272056i
$638$	−13.1465	−	22.7704i	−0.520476	−	0.901490i
$639$		0			0
$640$	8.77695	−	15.2021i	0.346939	−	0.600917i
$641$	−3.85515	+	21.8636i	−0.152269	+	0.863561i	0.808971	+	0.587849i	$0.200025\pi$
$641$	−3.85515	+	21.8636i	−0.152269	+	0.863561i	−0.961240	+	0.275713i	$0.911086\pi$
$642$		0			0
$643$	−20.2380	−	7.36602i	−0.798107	−	0.290487i	−0.0894054	−	0.995995i	$-0.528497\pi$
$643$	−20.2380	−	7.36602i	−0.798107	−	0.290487i	−0.708702	+	0.705508i	$0.750719\pi$
$644$	9.11568	+	51.6976i	0.359208	+	2.03717i
$645$		0			0
$646$	7.07207	+	5.93417i	0.278247	+	0.233477i
$647$	−13.4037			−0.526952			−0.263476	−	0.964666i	$-0.584869\pi$
$647$	−13.4037			−0.526952			−0.263476	+	0.964666i	$0.584869\pi$
$648$		0			0
$649$	1.08823			0.0427168
$650$	1.40784	+	1.18132i	0.0552200	+	0.0463351i
$651$		0			0
$652$	−0.521261	−	2.95622i	−0.0204142	−	0.115774i
$653$	−17.7704	−	6.46790i	−0.695409	−	0.253108i	−0.0299599	−	0.999551i	$-0.509538\pi$
$653$	−17.7704	−	6.46790i	−0.695409	−	0.253108i	−0.665450	+	0.746443i	$0.731760\pi$
$654$		0			0
$655$	5.51614	−	31.2836i	0.215533	−	1.22235i
$656$	−3.05455	+	5.29063i	−0.119260	+	0.206564i
$657$		0			0
$658$	37.0059	+	64.0962i	1.44264	+	2.49873i
$659$	−0.0264819	+	0.00963862i	−0.00103159	+	0.000375467i	−0.342536	−	0.939505i	$-0.611286\pi$
$659$	−0.0264819	+	0.00963862i	−0.00103159	+	0.000375467i	0.341504	+	0.939880i	$0.389064\pi$
$660$		0			0
$661$	−34.5040	+	28.9523i	−1.34205	+	1.12611i	−0.360954	+	0.932583i	$0.617549\pi$
$661$	−34.5040	+	28.9523i	−1.34205	+	1.12611i	−0.981095	+	0.193529i	$0.938007\pi$
$662$	−42.5943	+	35.7408i	−1.65547	+	1.38911i
$663$		0			0
$664$	−8.70565	+	3.16860i	−0.337845	+	0.122965i
$665$	9.22800	+	15.9834i	0.357846	+	0.619808i
$666$		0			0
$667$	6.41623	−	11.1132i	0.248438	−	0.430306i
$668$	10.4567	−	59.3029i	0.404582	−	2.29450i
$669$		0			0
$670$	−17.0838	−	6.21799i	−0.660005	−	0.240222i
$671$	3.21049	+	18.2076i	0.123940	+	0.702897i
$672$		0			0
$673$	−7.47636	−	6.27341i	−0.288192	−	0.241822i	0.487217	−	0.873281i	$-0.338012\pi$
$673$	−7.47636	−	6.27341i	−0.288192	−	0.241822i	−0.775409	+	0.631459i	$0.782456\pi$
$674$	23.2607			0.895968
$675$		0			0
$676$	−28.9847			−1.11480
$677$	−31.3165	−	26.2776i	−1.20359	−	1.00993i	−0.999520	−	0.0309756i	$-0.990139\pi$
$677$	−31.3165	−	26.2776i	−1.20359	−	1.00993i	−0.204070	−	0.978956i	$-0.565417\pi$
$678$		0			0
$679$	−4.30224	−	24.3992i	−0.165105	−	0.936356i
$680$	5.04122	+	1.83486i	0.193322	+	0.0703635i
$681$		0			0
$682$	−2.25634	+	12.7964i	−0.0863999	+	0.489998i
$683$	−22.0126	+	38.1269i	−0.842287	+	1.45888i	0.0456696	+	0.998957i	$0.485458\pi$
$683$	−22.0126	+	38.1269i	−0.842287	+	1.45888i	−0.887957	+	0.459927i	$0.847875\pi$
$684$		0			0
$685$	−3.77322	−	6.53541i	−0.144167	−	0.249705i
$686$	−92.0740	+	33.5122i	−3.51540	+	1.27950i
$687$		0			0
$688$	11.3550	−	9.52797i	0.432905	−	0.363250i
$689$	−5.89470	+	4.94624i	−0.224570	+	0.188437i
$690$		0			0
$691$	−20.2519	+	7.37108i	−0.770418	+	0.280409i	−0.697171	−	0.716905i	$-0.745558\pi$
$691$	−20.2519	+	7.37108i	−0.770418	+	0.280409i	−0.0732468	+	0.997314i	$0.523336\pi$
$692$	−11.4970	−	19.9133i	−0.437049	−	0.756991i
$693$		0			0
$694$	3.73302	−	6.46577i	0.141703	−	0.245437i
$695$	4.77408	−	27.0752i	0.181091	−	1.02702i
$696$		0			0
$697$	−5.02084	−	1.82743i	−0.190178	−	0.0692190i
$698$	−10.7739	−	61.1016i	−0.407796	−	2.31273i
$699$		0			0
$700$	−6.64568	−	5.57639i	−0.251183	−	0.210768i
$701$	12.8521			0.485419			0.242709	−	0.970099i	$-0.421964\pi$
$701$	12.8521			0.485419			0.242709	+	0.970099i	$0.421964\pi$
$702$		0			0
$703$	−16.4889			−0.621891
$704$	36.4177	+	30.5580i	1.37254	+	1.15170i
$705$		0			0
$706$	9.25353	+	52.4794i	0.348261	+	1.97509i
$707$	84.6548	+	30.8118i	3.18377	+	1.15880i
$708$		0			0
$709$	−8.63235	+	48.9565i	−0.324195	+	1.83860i	0.191081	+	0.981574i	$0.438801\pi$
$709$	−8.63235	+	48.9565i	−0.324195	+	1.83860i	−0.515276	+	0.857025i	$0.672310\pi$
$710$	6.78937	−	11.7595i	0.254800	−	0.441327i
$711$		0			0
$712$	9.29562	+	16.1005i	0.348368	+	0.603392i
$713$	−5.95923	+	2.16898i	−0.223175	+	0.0812290i
$714$		0			0
$715$	8.00489	−	6.71690i	0.299366	−	0.251198i
$716$	−20.4295	+	17.1424i	−0.763486	+	0.640641i
$717$		0			0
$718$	8.40133	−	3.05784i	0.313535	−	0.114117i
$719$	−2.81873	−	4.88218i	−0.105121	−	0.182075i	0.808667	−	0.588267i	$-0.200190\pi$
$719$	−2.81873	−	4.88218i	−0.105121	−	0.182075i	−0.913788	+	0.406192i	$0.866856\pi$
$720$		0			0
$721$	−21.8330	+	37.8159i	−0.813104	+	1.40834i
$722$	−5.76453	+	32.6923i	−0.214534	+	1.21668i
$723$		0			0
$724$	3.45839	+	1.25875i	0.128530	+	0.0467811i
$725$	0.368254	+	2.08847i	0.0136766	+	0.0775638i
$726$		0			0
$727$	−34.7894	−	29.1917i	−1.29027	−	1.08266i	−0.991741	−	0.128260i	$-0.959061\pi$
$727$	−34.7894	−	29.1917i	−1.29027	−	1.08266i	−0.298525	−	0.954402i	$-0.596495\pi$
$728$	−6.46195			−0.239496
$729$		0			0
$730$	56.1546			2.07837
$731$	9.93117	+	8.33324i	0.367317	+	0.308216i
$732$		0			0
$733$	−4.45700	−	25.2769i	−0.164623	−	0.933624i	−0.949452	−	0.313912i	$-0.898360\pi$
$733$	−4.45700	−	25.2769i	−0.164623	−	0.933624i	0.784829	−	0.619712i	$-0.212751\pi$
$734$	−34.9386	−	12.7166i	−1.28961	−	0.469378i
$735$		0			0
$736$	−5.92978	+	33.6295i	−0.218575	+	1.23960i
$737$	8.57098	−	14.8454i	0.315716	−	0.546837i
$738$		0			0
$739$	7.22763	+	12.5186i	0.265873	+	0.460505i	0.967792	−	0.251752i	$-0.0810066\pi$
$739$	7.22763	+	12.5186i	0.265873	+	0.460505i	−0.701919	+	0.712256i	$0.747673\pi$
$740$	−43.9203	+	15.9857i	−1.61454	+	0.587645i
$741$		0			0
$742$	49.9471	−	41.9106i	1.83362	−	1.53859i
$743$	−26.6535	+	22.3650i	−0.977824	+	0.820492i	−0.983760	−	0.179491i	$-0.942555\pi$
$743$	−26.6535	+	22.3650i	−0.977824	+	0.820492i	0.00593583	+	0.999982i	$0.498111\pi$
$744$		0			0
$745$	17.3412	−	6.31168i	0.635332	−	0.231242i
$746$	31.5084	+	54.5742i	1.15360	+	1.99810i
$747$		0			0
$748$	−12.3371	+	21.3685i	−0.451089	+	0.781308i
$749$	−6.25310	+	35.4631i	−0.228483	+	1.29579i
$750$		0			0
$751$	−17.0258	−	6.19687i	−0.621279	−	0.226127i	0.0121520	−	0.999926i	$-0.496132\pi$
$751$	−17.0258	−	6.19687i	−0.621279	−	0.226127i	−0.633431	+	0.773799i	$0.718354\pi$
$752$	3.37094	+	19.1176i	0.122926	+	0.697146i
$753$		0			0
$754$	5.90254	+	4.95282i	0.214958	+	0.180371i
$755$	−1.47535			−0.0536933
$756$		0			0
$757$	−37.0045			−1.34495			−0.672475	−	0.740120i	$-0.734769\pi$
$757$	−37.0045			−1.34495			−0.672475	+	0.740120i	$0.734769\pi$
$758$	34.1076	+	28.6197i	1.23884	+	1.03951i
$759$		0			0
$760$	−0.724413	−	4.10835i	−0.0262772	−	0.149026i
$761$	−11.6939	−	4.25624i	−0.423905	−	0.154289i	0.121254	−	0.992621i	$-0.461308\pi$
$761$	−11.6939	−	4.25624i	−0.423905	−	0.154289i	−0.545159	+	0.838333i	$0.683531\pi$
$762$		0			0
$763$	−4.73517	+	26.8545i	−0.171425	+	0.972197i
$764$	15.6257	−	27.0644i	0.565316	−	0.979156i
$765$		0			0
$766$	10.5155	+	18.2133i	0.379939	+	0.658074i
$767$	−0.299676	+	0.109073i	−0.0108207	+	0.00393840i
$768$		0			0
$769$	−31.3202	+	26.2807i	−1.12943	+	0.947707i	−0.999042	−	0.0437551i	$-0.986068\pi$
$769$	−31.3202	+	26.2807i	−1.12943	+	0.947707i	−0.130391	+	0.991463i	$0.541623\pi$
$770$	−67.8272	+	56.9138i	−2.44432	+	2.05103i
$771$		0			0
$772$	−49.1087	+	17.8741i	−1.76746	+	0.643303i
$773$	−18.2081	−	31.5374i	−0.654900	−	1.13432i	−0.981919	−	0.189302i	$-0.939377\pi$
$773$	−18.2081	−	31.5374i	−0.654900	−	1.13432i	0.327019	−	0.945018i	$-0.393956\pi$
$774$		0			0
$775$	0.524012	−	0.907615i	0.0188231	−	0.0326025i
$776$	−0.972463	+	5.51511i	−0.0349094	+	0.197981i
$777$		0			0
$778$	−42.1635	−	15.3463i	−1.51164	−	0.550190i
$779$	0.721484	+	4.09174i	0.0258498	+	0.146602i
$780$		0

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.62787 + 1.36594i) q^{2} +(0.436855 + 2.47753i) q^{4} +(-1.94605 - 0.708303i) q^{5} +(0.841963 - 4.77501i) q^{7} +(-0.547989 + 0.949144i) q^{8} +O(q^{10})\)	\(q+(1.62787 + 1.36594i) q^{2} +(0.436855 + 2.47753i) q^{4} +(-1.94605 - 0.708303i) q^{5} +(0.841963 - 4.77501i) q^{7} +(-0.547989 + 0.949144i) q^{8} +(-2.20040 - 3.81121i) q^{10} +(3.89924 - 1.41921i) q^{11} +(-0.931522 + 0.781640i) q^{13} +(7.89299 - 6.62301i) q^{14} +(2.53953 - 0.924313i) q^{16} +(1.18182 + 2.04697i) q^{17} +(0.919003 - 1.59176i) q^{19} +(0.904700 - 5.13081i) q^{20} +(8.28601 + 3.01586i) q^{22} +(0.747307 + 4.23819i) q^{23} +(-0.544815 - 0.457154i) q^{25} -2.58407 q^{26} +12.1980 q^{28} +(-2.28421 - 1.91668i) q^{29} +(0.255886 + 1.45120i) q^{31} +(7.45634 + 2.71388i) q^{32} +(-0.872200 + 4.94649i) q^{34} +(-5.02066 + 8.69603i) q^{35} +(-4.48554 - 7.76918i) q^{37} +(3.67027 - 1.33587i) q^{38} +(1.73869 - 1.45894i) q^{40} +(-1.73166 + 1.45304i) q^{41} +(5.15408 - 1.87593i) q^{43} +(5.21953 + 9.04050i) q^{44} +(-4.57260 + 7.91998i) q^{46} +(-1.24734 + 7.07400i) q^{47} +(-15.5140 - 5.64663i) q^{49} +(-0.262440 - 1.48837i) q^{50} +(-2.34347 - 1.96641i) q^{52} +6.32803 q^{53} -8.59334 q^{55} +(4.07079 + 3.41580i) q^{56} +(-1.10031 - 6.24019i) q^{58} +(0.246441 + 0.0896971i) q^{59} +(-0.773708 + 4.38792i) q^{61} +(-1.56571 + 2.71188i) q^{62} +(5.72840 + 9.92188i) q^{64} +(2.36642 - 0.861308i) q^{65} +(3.16461 - 2.65542i) q^{67} +(-4.55514 + 3.82222i) q^{68} +(-20.0512 + 7.29805i) q^{70} +(1.54276 + 2.67213i) q^{71} +(-6.38003 + 11.0505i) q^{73} +(3.31040 - 18.7742i) q^{74} +(4.34510 + 1.58149i) q^{76} +(-3.49372 - 19.8139i) q^{77} +(3.48735 + 2.92623i) q^{79} -5.59674 q^{80} -4.80368 q^{82} +(6.47542 + 5.43352i) q^{83} +(-0.850000 - 4.82059i) q^{85} +(10.9526 + 3.98641i) q^{86} +(-0.789708 + 4.47866i) q^{88} +(8.48158 - 14.6905i) q^{89} +(2.94803 + 5.10614i) q^{91} +(-10.1738 + 3.70295i) q^{92} +(-11.6932 + 9.81174i) q^{94} +(-2.91587 + 2.44671i) q^{95} +(4.80161 - 1.74764i) q^{97} +(-17.5417 - 30.3831i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{2} - 3 q^{4} - 6 q^{5} + 6 q^{7} - 6 q^{8}+O(q^{10}) \) 12 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 + 6 * q^7 - 6 * q^8	\( 12 q - 3 q^{2} - 3 q^{4} - 6 q^{5} + 6 q^{7} - 6 q^{8} - 6 q^{10} + 15 q^{11} - 3 q^{13} + 21 q^{14} + 9 q^{16} + 9 q^{17} - 12 q^{19} + 3 q^{20} + 33 q^{22} - 15 q^{23} - 12 q^{25} + 48 q^{26} + 6 q^{28} + 6 q^{29} - 12 q^{31} + 27 q^{32} + 27 q^{34} - 30 q^{35} - 3 q^{37} + 39 q^{38} + 24 q^{40} + 39 q^{41} + 24 q^{43} + 33 q^{44} + 3 q^{46} + 42 q^{47} - 30 q^{49} + 15 q^{50} - 45 q^{52} - 18 q^{53} + 30 q^{55} - 12 q^{56} - 30 q^{58} - 15 q^{59} - 3 q^{61} + 30 q^{62} - 6 q^{64} + 6 q^{65} - 3 q^{67} - 36 q^{68} - 75 q^{70} - 12 q^{73} - 60 q^{74} + 30 q^{76} - 33 q^{77} + 33 q^{79} - 42 q^{80} - 42 q^{82} + 33 q^{83} - 18 q^{85} + 30 q^{86} - 42 q^{88} + 9 q^{89} - 18 q^{91} - 33 q^{92} - 66 q^{94} - 12 q^{95} + 15 q^{97} - 18 q^{98}+O(q^{100}) \) 12 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 + 6 * q^7 - 6 * q^8 - 6 * q^10 + 15 * q^11 - 3 * q^13 + 21 * q^14 + 9 * q^16 + 9 * q^17 - 12 * q^19 + 3 * q^20 + 33 * q^22 - 15 * q^23 - 12 * q^25 + 48 * q^26 + 6 * q^28 + 6 * q^29 - 12 * q^31 + 27 * q^32 + 27 * q^34 - 30 * q^35 - 3 * q^37 + 39 * q^38 + 24 * q^40 + 39 * q^41 + 24 * q^43 + 33 * q^44 + 3 * q^46 + 42 * q^47 - 30 * q^49 + 15 * q^50 - 45 * q^52 - 18 * q^53 + 30 * q^55 - 12 * q^56 - 30 * q^58 - 15 * q^59 - 3 * q^61 + 30 * q^62 - 6 * q^64 + 6 * q^65 - 3 * q^67 - 36 * q^68 - 75 * q^70 - 12 * q^73 - 60 * q^74 + 30 * q^76 - 33 * q^77 + 33 * q^79 - 42 * q^80 - 42 * q^82 + 33 * q^83 - 18 * q^85 + 30 * q^86 - 42 * q^88 + 9 * q^89 - 18 * q^91 - 33 * q^92 - 66 * q^94 - 12 * q^95 + 15 * q^97 - 18 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more