LMFDB - Embedded newform 729.2.e.s.325.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("729.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
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			325.1
Root			$1.22778i$ of defining polynomial
Character	$\chi$	$=$	729.325
Dual form			729.2.e.s.406.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.20913 + 1.01458i) q^{2} +(0.0853237 - 0.483895i) q^{4} +(-1.57728 + 0.574083i) q^{5} +(0.482617 + 2.73706i) q^{7} +(-1.19062 - 2.06222i) q^{8} +O(q^{10})$	\(q+(-1.20913 + 1.01458i) q^{2} +(0.0853237 - 0.483895i) q^{4} +(-1.57728 + 0.574083i) q^{5} +(0.482617 + 2.73706i) q^{7} +(-1.19062 - 2.06222i) q^{8} +(1.32468 - 2.29442i) q^{10} +(3.90087 + 1.41980i) q^{11} +(5.26736 + 4.41984i) q^{13} +(-3.36051 - 2.81980i) q^{14} +(4.45535 + 1.62162i) q^{16} +(-0.488276 + 0.845718i) q^{17} +(-1.34264 - 2.32553i) q^{19} +(0.143217 + 0.812221i) q^{20} +(-6.15715 + 2.24102i) q^{22} +(0.280124 - 1.58866i) q^{23} +(-1.67198 + 1.40296i) q^{25} -10.8532 q^{26} +1.36563 q^{28} +(-6.30292 + 5.28878i) q^{29} +(0.181301 - 1.02821i) q^{31} +(-2.55707 + 0.930697i) q^{32} +(-0.267660 - 1.51798i) q^{34} +(-2.33252 - 4.04005i) q^{35} +(0.654172 - 1.13306i) q^{37} +(3.98286 + 1.44964i) q^{38} +(3.06183 + 2.56918i) q^{40} +(-3.71391 - 3.11634i) q^{41} +(-9.24679 - 3.36556i) q^{43} +(1.01987 - 1.76647i) q^{44} +(1.27312 + 2.20510i) q^{46} +(2.17020 + 12.3078i) q^{47} +(-0.680721 + 0.247762i) q^{49} +(0.598226 - 3.39271i) q^{50} +(2.58817 - 2.17173i) q^{52} +7.34280 q^{53} -6.96786 q^{55} +(5.06980 - 4.25406i) q^{56} +(2.25515 - 12.7896i) q^{58} +(-8.50598 + 3.09592i) q^{59} +(-0.223267 - 1.26621i) q^{61} +(0.823982 + 1.42718i) q^{62} +(-2.59373 + 4.49247i) q^{64} +(-10.8455 - 3.94742i) q^{65} +(-3.55927 - 2.98658i) q^{67} +(0.367577 + 0.308434i) q^{68} +(6.91926 + 2.51841i) q^{70} +(-2.81187 + 4.87030i) q^{71} +(2.28072 + 3.95033i) q^{73} +(0.358600 + 2.03372i) q^{74} +(-1.23987 + 0.451276i) q^{76} +(-2.00345 + 11.3621i) q^{77} +(3.56732 - 2.99333i) q^{79} -7.95828 q^{80} +7.65237 q^{82} +(4.41578 - 3.70528i) q^{83} +(0.284635 - 1.61425i) q^{85} +(14.5952 - 5.31221i) q^{86} +(-1.71652 - 9.73490i) q^{88} +(-2.27221 - 3.93558i) q^{89} +(-9.55523 + 16.5502i) q^{91} +(-0.744844 - 0.271101i) q^{92} +(-15.1113 - 12.6799i) q^{94} +(3.45278 + 2.89722i) q^{95} +(-8.05828 - 2.93297i) q^{97} +(0.571704 - 0.990221i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{2} - 3 q^{4} - 12 q^{5} - 3 q^{7} + 6 q^{8}+O(q^{10}) $ 12 * q + 3 * q^2 - 3 * q^4 - 12 * q^5 - 3 * q^7 + 6 * q^8	$ 12 q + 3 q^{2} - 3 q^{4} - 12 q^{5} - 3 q^{7} + 6 q^{8} - 6 q^{10} + 3 q^{11} + 6 q^{13} + 6 q^{14} + 27 q^{16} - 9 q^{17} - 12 q^{19} - 39 q^{20} - 39 q^{22} - 21 q^{23} + 6 q^{25} - 48 q^{26} + 6 q^{28} - 6 q^{29} + 6 q^{31} - 27 q^{32} - 18 q^{34} + 30 q^{35} - 3 q^{37} - 3 q^{38} + 33 q^{40} + 15 q^{41} - 30 q^{43} - 33 q^{44} + 3 q^{46} + 21 q^{47} - 3 q^{49} - 6 q^{50} + 18 q^{53} + 30 q^{55} - 15 q^{56} - 3 q^{58} - 30 q^{59} - 30 q^{61} - 30 q^{62} - 6 q^{64} + 12 q^{65} - 39 q^{67} - 18 q^{68} + 51 q^{70} - 12 q^{73} - 57 q^{74} + 57 q^{76} + 24 q^{77} + 15 q^{79} + 42 q^{80} - 42 q^{82} + 21 q^{83} + 54 q^{85} + 60 q^{86} + 12 q^{88} - 9 q^{89} - 18 q^{91} + 15 q^{92} + 33 q^{94} - 42 q^{95} - 12 q^{97} + 18 q^{98}+O(q^{100}) $ 12 * q + 3 * q^2 - 3 * q^4 - 12 * q^5 - 3 * q^7 + 6 * q^8 - 6 * q^10 + 3 * q^11 + 6 * q^13 + 6 * q^14 + 27 * q^16 - 9 * q^17 - 12 * q^19 - 39 * q^20 - 39 * q^22 - 21 * q^23 + 6 * q^25 - 48 * q^26 + 6 * q^28 - 6 * q^29 + 6 * q^31 - 27 * q^32 - 18 * q^34 + 30 * q^35 - 3 * q^37 - 3 * q^38 + 33 * q^40 + 15 * q^41 - 30 * q^43 - 33 * q^44 + 3 * q^46 + 21 * q^47 - 3 * q^49 - 6 * q^50 + 18 * q^53 + 30 * q^55 - 15 * q^56 - 3 * q^58 - 30 * q^59 - 30 * q^61 - 30 * q^62 - 6 * q^64 + 12 * q^65 - 39 * q^67 - 18 * q^68 + 51 * q^70 - 12 * q^73 - 57 * q^74 + 57 * q^76 + 24 * q^77 + 15 * q^79 + 42 * q^80 - 42 * q^82 + 21 * q^83 + 54 * q^85 + 60 * q^86 + 12 * q^88 - 9 * q^89 - 18 * q^91 + 15 * q^92 + 33 * q^94 - 42 * q^95 - 12 * q^97 + 18 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{7}{9}\right)$

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 $

$2$	−1.20913	+	1.01458i	−0.854982	+	0.717415i	−0.960881	−	0.276961i	$-0.910673\pi$
$2$	−1.20913	+	1.01458i	−0.854982	+	0.717415i	0.105899	+	0.994377i	$0.466228\pi$
$3$		0			0
$3$		0			0
$4$	0.0853237	−	0.483895i	0.0426619	−	0.241948i
$5$	−1.57728	+	0.574083i	−0.705382	+	0.256738i	−0.669707	−	0.742626i	$-0.733580\pi$
$5$	−1.57728	+	0.574083i	−0.705382	+	0.256738i	−0.0356747	+	0.999363i	$0.511358\pi$
$6$		0			0
$7$	0.482617	+	2.73706i	0.182412	+	1.03451i	0.929235	+	0.369488i	$0.120467\pi$
$7$	0.482617	+	2.73706i	0.182412	+	1.03451i	−0.746823	+	0.665023i	$0.768422\pi$
$8$	−1.19062	−	2.06222i	−0.420948	−	0.729104i
$9$		0			0
$10$	1.32468	−	2.29442i	0.418901	−	0.725558i
$11$	3.90087	+	1.41980i	1.17616	+	0.428086i	0.854843	−	0.518886i	$-0.173653\pi$
$11$	3.90087	+	1.41980i	1.17616	+	0.428086i	0.321314	+	0.946973i	$0.395875\pi$
$12$		0			0
$13$	5.26736	+	4.41984i	1.46090	+	1.22584i	0.924110	+	0.382128i	$0.124809\pi$
$13$	5.26736	+	4.41984i	1.46090	+	1.22584i	0.536792	+	0.843715i	$0.319636\pi$
$14$	−3.36051	−	2.81980i	−0.898133	−	0.753623i
$15$		0			0
$16$	4.45535	+	1.62162i	1.11384	+	0.405404i
$17$	−0.488276	+	0.845718i	−0.118424	+	0.205117i	−0.919143	−	0.393923i	$-0.871118\pi$
$17$	−0.488276	+	0.845718i	−0.118424	+	0.205117i	0.800719	+	0.599040i	$0.204451\pi$
$18$		0			0
$19$	−1.34264	−	2.32553i	−0.308024	−	0.533513i	0.669906	−	0.742446i	$-0.266334\pi$
$19$	−1.34264	−	2.32553i	−0.308024	−	0.533513i	−0.977930	+	0.208933i	$0.933001\pi$
$20$	0.143217	+	0.812221i	0.0320242	+	0.181618i
$21$		0			0
$22$	−6.15715	+	2.24102i	−1.31271	+	0.477787i
$23$	0.280124	−	1.58866i	0.0584099	−	0.331259i	−0.941575	−	0.336804i	$-0.890654\pi$
$23$	0.280124	−	1.58866i	0.0584099	−	0.331259i	0.999985	+	0.00554518i	$0.00176509\pi$
$24$		0			0
$25$	−1.67198	+	1.40296i	−0.334396	+	0.280591i
$26$	−10.8532			−2.12848
$27$		0			0
$28$	1.36563			0.258079
$29$	−6.30292	+	5.28878i	−1.17042	+	0.982101i	−0.999995	−	0.00326885i	$-0.998959\pi$
$29$	−6.30292	+	5.28878i	−1.17042	+	0.982101i	−0.170428	+	0.985370i	$0.554515\pi$
$30$		0			0
$31$	0.181301	−	1.02821i	0.0325626	−	0.184672i	−0.964188	−	0.265219i	$-0.914556\pi$
$31$	0.181301	−	1.02821i	0.0325626	−	0.184672i	0.996751	+	0.0805475i	$0.0256669\pi$
$32$	−2.55707	+	0.930697i	−0.452030	+	0.164526i
$33$		0			0
$34$	−0.267660	−	1.51798i	−0.0459033	−	0.260331i
$35$	−2.33252	−	4.04005i	−0.394268	−	0.682893i
$36$		0			0
$37$	0.654172	−	1.13306i	0.107545	−	0.186274i	−0.807230	−	0.590237i	$-0.799034\pi$
$37$	0.654172	−	1.13306i	0.107545	−	0.186274i	0.914775	+	0.403963i	$0.132368\pi$
$38$	3.98286	+	1.44964i	0.646105	+	0.235163i
$39$		0			0
$40$	3.06183	+	2.56918i	0.484118	+	0.406223i
$41$	−3.71391	−	3.11634i	−0.580016	−	0.486691i	0.304936	−	0.952373i	$-0.401365\pi$
$41$	−3.71391	−	3.11634i	−0.580016	−	0.486691i	−0.884952	+	0.465682i	$0.845809\pi$
$42$		0			0
$43$	−9.24679	−	3.36556i	−1.41012	−	0.513243i	−0.478957	−	0.877839i	$-0.658985\pi$
$43$	−9.24679	−	3.36556i	−1.41012	−	0.513243i	−0.931166	+	0.364596i	$0.881207\pi$
$44$	1.01987	−	1.76647i	0.153751	−	0.266305i
$45$		0			0
$46$	1.27312	+	2.20510i	0.187711	+	0.325125i
$47$	2.17020	+	12.3078i	0.316557	+	1.79528i	0.563355	+	0.826215i	$0.309510\pi$
$47$	2.17020	+	12.3078i	0.316557	+	1.79528i	−0.246798	+	0.969067i	$0.579379\pi$
$48$		0			0
$49$	−0.680721	+	0.247762i	−0.0972458	+	0.0353946i
$50$	0.598226	−	3.39271i	0.0846019	−	0.479801i
$51$		0			0
$52$	2.58817	−	2.17173i	0.358914	−	0.301165i
$53$	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
$56$	5.06980	−	4.25406i	0.677480	−	0.568473i
$57$		0			0
$58$	2.25515	−	12.7896i	0.296116	−	1.67936i
$59$	−8.50598	+	3.09592i	−1.10738	+	0.403055i	−0.830033	−	0.557714i	$-0.811679\pi$
$59$	−8.50598	+	3.09592i	−1.10738	+	0.403055i	−0.277351	+	0.960769i	$0.589456\pi$
$60$		0			0
$61$	−0.223267	−	1.26621i	−0.0285864	−	0.162121i	0.967173	−	0.254120i	$-0.0817857\pi$
$61$	−0.223267	−	1.26621i	−0.0285864	−	0.162121i	−0.995759	+	0.0919982i	$0.970675\pi$
$62$	0.823982	+	1.42718i	0.104646	+	0.181252i
$63$		0			0
$64$	−2.59373	+	4.49247i	−0.324216	+	0.561558i
$65$	−10.8455	−	3.94742i	−1.34521	−	0.489618i
$66$		0			0
$67$	−3.55927	−	2.98658i	−0.434834	−	0.364869i	0.398938	−	0.916978i	$-0.369379\pi$
$67$	−3.55927	−	2.98658i	−0.434834	−	0.364869i	−0.833772	+	0.552109i	$0.813823\pi$
$68$	0.367577	+	0.308434i	0.0445753	+	0.0374031i
$69$		0			0
$70$	6.91926	+	2.51841i	0.827010	+	0.301007i
$71$	−2.81187	+	4.87030i	−0.333707	+	0.577998i	−0.983236	−	0.182339i	$-0.941633\pi$
$71$	−2.81187	+	4.87030i	−0.333707	+	0.577998i	0.649528	+	0.760337i	$0.274966\pi$
$72$		0			0
$73$	2.28072	+	3.95033i	0.266938	+	0.462351i	0.968070	−	0.250681i	$-0.0806547\pi$
$73$	2.28072	+	3.95033i	0.266938	+	0.462351i	−0.701131	+	0.713032i	$0.747321\pi$
$74$	0.358600	+	2.03372i	0.0416864	+	0.236416i
$75$		0			0
$76$	−1.23987	+	0.451276i	−0.142223	+	0.0517649i
$77$	−2.00345	+	11.3621i	−0.228314	+	1.29484i
$78$		0			0
$79$	3.56732	−	2.99333i	0.401354	−	0.336776i	−0.419662	−	0.907680i	$-0.637852\pi$
$79$	3.56732	−	2.99333i	0.401354	−	0.336776i	0.821017	+	0.570904i	$0.193407\pi$
$80$	−7.95828			−0.889763
$81$		0			0
$82$	7.65237			0.845063
$83$	4.41578	−	3.70528i	0.484695	−	0.406707i	−0.367426	−	0.930053i	$-0.619761\pi$
$83$	4.41578	−	3.70528i	0.484695	−	0.406707i	0.852121	+	0.523346i	$0.175316\pi$
$84$		0			0
$85$	0.284635	−	1.61425i	0.0308730	−	0.175090i
$86$	14.5952	−	5.31221i	1.57384	−	0.572830i
$87$		0			0
$88$	−1.71652	−	9.73490i	−0.182982	−	1.03774i
$89$	−2.27221	−	3.93558i	−0.240854	−	0.417171i	0.720104	−	0.693866i	$-0.244094\pi$
$89$	−2.27221	−	3.93558i	−0.240854	−	0.417171i	−0.960958	+	0.276695i	$0.910761\pi$
$90$		0			0
$91$	−9.55523	+	16.5502i	−1.00166	+	1.73493i
$92$	−0.744844	−	0.271101i	−0.0776554	−	0.0282643i
$93$		0			0
$94$	−15.1113	−	12.6799i	−1.55861	−	1.30783i
$95$	3.45278	+	2.89722i	0.354247	+	0.297249i
$96$		0			0
$97$	−8.05828	−	2.93297i	−0.818194	−	0.297798i	−0.101190	−	0.994867i	$-0.532265\pi$
$97$	−8.05828	−	2.93297i	−0.818194	−	0.297798i	−0.717004	+	0.697069i	$0.754487\pi$
$98$	0.571704	−	0.990221i	0.0577508	−	0.100027i
$99$		0			0
$100$	0.536224	+	0.928767i	0.0536224	+	0.0928767i
$101$	−1.35545	−	7.68712i	−0.134872	−	0.764897i	−0.974949	−	0.222429i	$-0.928601\pi$
$101$	−1.35545	−	7.68712i	−0.134872	−	0.764897i	0.840077	−	0.542467i	$-0.182510\pi$
$102$		0			0
$103$	2.03551	−	0.740866i	0.200565	−	0.0729997i	−0.239784	−	0.970826i	$-0.577077\pi$
$103$	2.03551	−	0.740866i	0.200565	−	0.0729997i	0.440349	+	0.897826i	$0.354855\pi$
$104$	2.84324	−	16.1248i	0.278802	−	1.58117i
$105$		0			0
$106$	−8.87838	+	7.44984i	−0.862344	+	0.723593i
$107$	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	$0.698884\pi$
$110$	8.42503	−	7.06944i	0.803295	−	0.674045i
$111$		0			0
$112$	−2.28823	+	12.9772i	−0.216217	+	1.22623i
$113$	−0.423644	+	0.154194i	−0.0398531	+	0.0145053i	−0.361870	−	0.932229i	$-0.617862\pi$
$113$	−0.423644	+	0.154194i	−0.0398531	+	0.0145053i	0.322017	+	0.946734i	$0.395639\pi$
$114$		0			0
$115$	0.470190	+	2.66658i	0.0438455	+	0.248660i
$116$	2.02142	+	3.50121i	0.187685	+	0.325079i
$117$		0			0
$118$	7.14376	−	12.3734i	0.657636	−	1.13906i
$119$	−2.55043	−	0.928281i	−0.233798	−	0.0850954i
$120$		0			0
$121$	4.77448	+	4.00627i	0.434044	+	0.364206i
$122$	1.55463	+	1.30449i	0.140749	+	0.118103i
$123$		0			0
$124$	−0.482075	−	0.175461i	−0.0432916	−	0.0157569i
$125$	6.02803	−	10.4409i	0.539164	−	0.933859i
$126$		0			0
$127$	0.265534	+	0.459919i	0.0235624	+	0.0408112i	0.877566	−	0.479456i	$-0.159166\pi$
$127$	0.265534	+	0.459919i	0.0235624	+	0.0408112i	−0.854004	+	0.520267i	$0.825833\pi$
$128$	−2.36687	−	13.4232i	−0.209204	−	1.18645i
$129$		0			0
$130$	17.1185	−	6.23063i	1.50139	−	0.546462i
$131$	−1.98237	+	11.2426i	−0.173201	+	0.982271i	0.766999	+	0.641648i	$0.221749\pi$
$131$	−1.98237	+	11.2426i	−0.173201	+	0.982271i	−0.940200	+	0.340623i	$0.889362\pi$
$132$		0			0
$133$	5.71712	−	4.79724i	0.495738	−	0.415973i
$134$	7.33374			0.633539
$135$		0			0
$136$	2.32541			0.199402
$137$	−3.23979	+	2.71850i	−0.276794	+	0.232257i	−0.770607	−	0.637310i	$-0.780047\pi$
$137$	−3.23979	+	2.71850i	−0.276794	+	0.232257i	0.493814	+	0.869568i	$0.335603\pi$
$138$		0			0
$139$	−1.93714	+	10.9861i	−0.164306	+	0.931825i	0.785471	+	0.618898i	$0.212421\pi$
$139$	−1.93714	+	10.9861i	−0.164306	+	0.931825i	−0.949777	+	0.312927i	$0.898691\pi$
$140$	−2.15398	+	0.783984i	−0.182044	+	0.0662588i
$141$		0			0
$142$	−1.54139	−	8.74167i	−0.129351	−	0.733585i
$143$	14.2720	+	24.7198i	1.19348	+	2.06718i
$144$		0			0
$145$	6.90528	−	11.9603i	0.573452	−	0.993248i
$146$	−6.76560	−	2.46248i	−0.559925	−	0.203796i
$147$		0			0
$148$	−0.492465	−	0.413228i	−0.0404804	−	0.0339671i
$149$	14.9208	+	12.5200i	1.22236	+	1.02568i	0.998698	+	0.0510127i	$0.0162449\pi$
$149$	14.9208	+	12.5200i	1.22236	+	1.02568i	0.223660	+	0.974667i	$0.428200\pi$
$150$		0			0
$151$	1.16791	+	0.425083i	0.0950429	+	0.0345928i	0.389104	−	0.921194i	$-0.372785\pi$
$151$	1.16791	+	0.425083i	0.0950429	+	0.0345928i	−0.294061	+	0.955787i	$0.595007\pi$
$152$	−3.19716	+	5.53765i	−0.259324	+	0.449163i
$153$		0			0
$154$	−9.10535	−	15.7709i	−0.733730	−	1.27086i
$155$	0.304315	+	1.72585i	0.0244431	+	0.138624i
$156$		0			0
$157$	3.32007	−	1.20840i	0.264970	−	0.0964412i	−0.206119	−	0.978527i	$-0.566083\pi$
$157$	3.32007	−	1.20840i	0.264970	−	0.0964412i	0.471089	+	0.882086i	$0.343861\pi$
$158$	−1.27637	+	7.23865i	−0.101542	+	0.575876i
$159$		0			0
$160$	3.49892	−	2.93594i	0.276614	−	0.232107i
$161$	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	$0.285228\pi$
$164$	−1.82487	+	1.53125i	−0.142498	+	0.119570i
$165$		0			0
$166$	−1.57994	+	8.96031i	−0.122628	+	0.695455i
$167$	13.6111	−	4.95404i	1.05326	−	0.383355i	0.243368	−	0.969934i	$-0.421748\pi$
$167$	13.6111	−	4.95404i	1.05326	−	0.383355i	0.809892	+	0.586579i	$0.199526\pi$
$168$		0			0
$169$	5.95266	+	33.7592i	0.457897	+	2.59686i
$170$	1.29362	+	2.24061i	0.0992161	+	0.171847i
$171$		0			0
$172$	−2.41755	+	4.18731i	−0.184336	+	0.319280i
$173$	11.8565	+	4.31540i	0.901431	+	0.328094i	0.750826	−	0.660500i	$-0.229656\pi$
$173$	11.8565	+	4.31540i	0.901431	+	0.328094i	0.150605	+	0.988594i	$0.451878\pi$
$174$		0			0
$175$	−4.64690	−	3.89921i	−0.351272	−	0.294753i
$176$	15.0774	+	12.6514i	1.13650	+	0.953637i
$177$		0			0
$178$	6.74035	+	2.45329i	0.505211	+	0.183882i
$179$	0.147949	−	0.256256i	0.0110582	−	0.0191534i	−0.860443	−	0.509546i	$-0.829813\pi$
$179$	0.147949	−	0.256256i	0.0110582	−	0.0191534i	0.871502	+	0.490393i	$0.163147\pi$
$180$		0			0
$181$	−0.710251	−	1.23019i	−0.0527925	−	0.0914393i	0.838421	−	0.545022i	$-0.183479\pi$
$181$	−0.710251	−	1.23019i	−0.0527925	−	0.0914393i	−0.891214	+	0.453583i	$0.850146\pi$
$182$	−5.23793	−	29.7058i	−0.388261	−	2.20194i
$183$		0			0
$184$	−3.60969	+	1.31382i	−0.266110	+	0.0968560i
$185$	−0.381343	+	2.16270i	−0.0280369	+	0.159005i
$186$		0			0
$187$	−3.10545	+	2.60578i	−0.227093	+	0.190554i
$188$	6.14087			0.447869
$189$		0			0
$190$	−7.11431			−0.516126
$191$	−15.7990	+	13.2569i	−1.14317	+	0.959236i	−0.999538	−	0.0303946i	$-0.990324\pi$
$191$	−15.7990	+	13.2569i	−1.14317	+	0.959236i	−0.143635	+	0.989631i	$0.545879\pi$
$192$		0			0
$193$	−3.63896	+	20.6376i	−0.261938	+	1.48552i	0.515676	+	0.856784i	$0.327541\pi$
$193$	−3.63896	+	20.6376i	−0.261938	+	1.48552i	−0.777614	+	0.628741i	$0.783570\pi$
$194$	12.7192	−	4.62942i	0.913187	−	0.332373i
$195$		0			0
$196$	0.0618092	+	0.350537i	0.00441494	+	0.0250384i
$197$	−4.79810	−	8.31056i	−0.341851	−	0.592103i	0.642926	−	0.765929i	$-0.277720\pi$
$197$	−4.79810	−	8.31056i	−0.341851	−	0.592103i	−0.984776	+	0.173826i	$0.944387\pi$
$198$		0			0
$199$	5.34583	−	9.25925i	0.378956	−	0.656371i	−0.611955	−	0.790893i	$-0.709616\pi$
$199$	5.34583	−	9.25925i	0.378956	−	0.656371i	0.990911	+	0.134522i	$0.0429498\pi$
$200$	4.88389	+	1.77759i	0.345344	+	0.125695i
$201$		0			0
$202$	9.43809	+	7.91950i	0.664062	+	0.557214i
$203$	−17.5176	−	14.6990i	−1.22949	−	1.03167i
$204$		0			0
$205$	7.64693	+	2.78325i	0.534085	+	0.194391i
$206$	−1.70953	+	2.96099i	−0.119108	+	0.206302i
$207$		0			0
$208$	16.3006	+	28.2335i	1.13025	+	1.95764i
$209$	−1.93570	−	10.9779i	−0.133895	−	0.759356i
$210$		0			0
$211$	14.1426	−	5.14749i	0.973617	−	0.354367i	0.194261	−	0.980950i	$-0.437769\pi$
$211$	14.1426	−	5.14749i	0.973617	−	0.354367i	0.779355	+	0.626582i	$0.215547\pi$
$212$	0.626515	−	3.55314i	0.0430292	−	0.244031i
$213$		0			0
$214$	−15.2168	+	12.7684i	−1.04020	+	0.872831i
$215$	16.5169			1.12644
$216$		0			0
$217$	2.90176			0.196984
$218$	14.7683	−	12.3921i	1.00023	−	0.839296i
$219$		0			0
$220$	−0.594524	+	3.37171i	−0.0400828	+	0.227321i
$221$	−6.30986	+	2.29660i	−0.424447	+	0.154486i
$222$		0			0
$223$	−2.13381	−	12.1014i	−0.142890	−	0.810371i	−0.969037	−	0.246916i	$-0.920583\pi$
$223$	−2.13381	−	12.1014i	−0.142890	−	0.810371i	0.826147	−	0.563455i	$-0.190528\pi$
$224$	−3.78146	−	6.54968i	−0.252659	−	0.437619i
$225$		0			0
$226$	0.355798	−	0.616261i	0.0236674	−	0.0409931i
$227$	3.52625	+	1.28345i	0.234046	+	0.0851856i	0.456380	−	0.889785i	$-0.349146\pi$
$227$	3.52625	+	1.28345i	0.234046	+	0.0851856i	−0.222335	+	0.974970i	$0.571368\pi$
$228$		0			0
$229$	−14.2503	−	11.9574i	−0.941685	−	0.790168i	0.0361925	−	0.999345i	$-0.488477\pi$
$229$	−14.2503	−	11.9574i	−0.941685	−	0.790168i	−0.977878	+	0.209177i	$0.932921\pi$
$230$	−3.27398	−	2.74719i	−0.215880	−	0.181145i
$231$		0			0
$232$	18.4110	+	6.70106i	1.20874	+	0.439946i
$233$	0.272892	−	0.472663i	0.0178777	−	0.0309652i	−0.856948	−	0.515403i	$-0.827642\pi$
$233$	0.272892	−	0.472663i	0.0178777	−	0.0309652i	0.874826	+	0.484438i	$0.160976\pi$
$234$		0			0
$235$	−10.4887	−	18.1670i	−0.684210	−	1.18509i
$236$	0.772340	+	4.38016i	0.0502750	+	0.285124i
$237$		0			0
$238$	4.02561	−	1.46520i	0.260942	−	0.0949750i
$239$	3.48942	−	19.7895i	0.225712	−	1.28007i	−0.635609	−	0.772011i	$-0.719251\pi$
$239$	3.48942	−	19.7895i	0.225712	−	1.28007i	0.861320	−	0.508062i	$-0.169638\pi$
$240$		0			0
$241$	11.7138	−	9.82906i	0.754553	−	0.633145i	−0.182150	−	0.983271i	$-0.558305\pi$
$241$	11.7138	−	9.82906i	0.754553	−	0.633145i	0.936703	+	0.350125i	$0.113861\pi$
$242$	−9.83763			−0.632387
$243$		0			0
$244$	−0.631762			−0.0404444
$245$	0.931452	−	0.781581i	0.0595083	−	0.0499334i
$246$		0			0
$247$	3.20627	−	18.1837i	0.204010	−	1.15700i
$248$	−2.33625	+	0.850325i	−0.148352	+	0.0539957i
$249$		0			0
$250$	3.30441	+	18.7403i	0.208989	+	1.18524i
$251$	6.37816	+	11.0473i	0.402586	+	0.697299i	0.994037	−	0.109042i	$-0.0347782\pi$
$251$	6.37816	+	11.0473i	0.402586	+	0.697299i	−0.591451	+	0.806341i	$0.701445\pi$
$252$		0			0
$253$	3.34831	−	5.79945i	0.210507	−	0.364608i
$254$	−0.787689	−	0.286695i	−0.0494240	−	0.0179889i
$255$		0			0
$256$	8.53308	+	7.16010i	0.533317	+	0.447506i
$257$	10.0388	+	8.42354i	0.626202	+	0.525446i	0.899746	−	0.436413i	$-0.143751\pi$
$257$	10.0388	+	8.42354i	0.626202	+	0.525446i	−0.273544	+	0.961860i	$0.588196\pi$
$258$		0			0
$259$	3.41697	+	1.24367i	0.212320	+	0.0772781i
$260$	−2.83551	+	4.91125i	−0.175851	+	0.304583i
$261$		0			0
$262$	−9.00956	−	15.6050i	−0.556613	−	0.964081i
$263$	1.65212	+	9.36963i	0.101874	+	0.577756i	0.992423	+	0.122869i	$0.0392094\pi$
$263$	1.65212	+	9.36963i	0.101874	+	0.577756i	−0.890549	+	0.454888i	$0.849679\pi$
$264$		0			0
$265$	−11.5817	+	4.21538i	−0.711455	+	0.258949i
$266$	−2.04556	+	11.6009i	−0.125421	+	0.711299i
$267$		0			0
$268$	−1.74888	+	1.46749i	−0.106830	+	0.0896411i
$269$	−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	$0.177020\pi$
$272$	−3.54687	+	2.97618i	−0.215060	+	0.180457i
$273$		0			0
$274$	1.15918	−	6.57404i	0.0700286	−	0.397152i
$275$	−8.51409	+	3.09888i	−0.513419	+	0.186869i
$276$		0			0
$277$	−3.27912	−	18.5968i	−0.197023	−	1.11737i	−0.909508	−	0.415686i	$-0.863542\pi$
$277$	−3.27912	−	18.5968i	−0.197023	−	1.11737i	0.712485	−	0.701687i	$-0.247570\pi$
$278$	−8.80397	−	15.2489i	−0.528027	−	0.914569i
$279$		0			0
$280$	−5.55431	+	9.62034i	−0.331933	+	0.574925i
$281$	−18.7955	−	6.84100i	−1.12125	−	0.408100i	−0.286139	−	0.958188i	$-0.592372\pi$
$281$	−18.7955	−	6.84100i	−1.12125	−	0.408100i	−0.835106	+	0.550088i	$0.814594\pi$
$282$		0			0
$283$	12.8274	+	10.7635i	0.762512	+	0.639824i	0.938780	−	0.344519i	$-0.111958\pi$
$283$	12.8274	+	10.7635i	0.762512	+	0.639824i	−0.176267	+	0.984342i	$0.556402\pi$
$284$	2.11679	+	1.77620i	0.125609	+	0.105398i
$285$		0			0
$286$	−42.3369	−	15.4094i	−2.50343	−	0.911175i
$287$	6.73722	−	11.6692i	0.397685	−	0.688811i
$288$		0			0
$289$	8.02317	+	13.8965i	0.471951	+	0.817444i
$290$	3.78529	+	21.4675i	0.222280	+	1.26061i
$291$		0			0
$292$	2.10614	−	0.766573i	0.123253	−	0.0448603i
$293$	−3.39864	+	19.2747i	−0.198551	+	1.12604i	0.708720	+	0.705490i	$0.249273\pi$
$293$	−3.39864	+	19.2747i	−0.198551	+	1.12604i	−0.907271	+	0.420548i	$0.861838\pi$
$294$		0			0
$295$	11.6390	−	9.76628i	0.677649	−	0.568615i
$296$	−3.11549			−0.181084
$297$		0			0
$298$	−30.7437			−1.78093
$299$	8.49714	−	7.12995i	0.491402	−	0.412335i
$300$		0			0
$301$	4.74906	−	26.9333i	0.273731	−	1.55241i
$302$	−1.84343	+	0.670953i	−0.106077	+	0.0386090i
$303$		0			0
$304$	−2.21084	−	12.5383i	−0.126800	−	0.719121i
$305$	1.07906	+	1.86899i	0.0617870	+	0.107018i
$306$		0			0
$307$	−7.44973	+	12.9033i	−0.425179	+	0.736431i	−0.996437	−	0.0843392i	$-0.973122\pi$
$307$	−7.44973	+	12.9033i	−0.425179	+	0.736431i	0.571258	+	0.820770i	$0.306455\pi$
$308$	5.32714	+	1.93892i	0.303542	+	0.110480i
$309$		0			0
$310$	−2.11897	−	1.77803i	−0.120349	−	0.100985i
$311$	−3.51795	−	2.95191i	−0.199485	−	0.167388i	0.537573	−	0.843217i	$-0.319341\pi$
$311$	−3.51795	−	2.95191i	−0.199485	−	0.167388i	−0.737058	+	0.675829i	$0.763786\pi$
$312$		0			0
$313$	−11.1529	−	4.05933i	−0.630400	−	0.229447i	0.00700533	−	0.999975i	$-0.497770\pi$
$313$	−11.1529	−	4.05933i	−0.630400	−	0.229447i	−0.637405	+	0.770529i	$0.719992\pi$
$314$	−2.78836	+	4.82958i	−0.157356	+	0.272549i
$315$		0			0
$316$	−1.14408	−	1.98161i	−0.0643597	−	0.111474i
$317$	2.52091	+	14.2968i	0.141588	+	0.802988i	0.970043	+	0.242932i	$0.0781092\pi$
$317$	2.52091	+	14.2968i	0.141588	+	0.802988i	−0.828455	+	0.560056i	$0.810780\pi$
$318$		0			0
$319$	−32.0959	+	11.6820i	−1.79703	+	0.654064i
$320$	1.51199	−	8.57490i	0.0845226	−	0.479351i
$321$		0			0
$322$	−5.42107	+	4.54882i	−0.302104	+	0.253496i
$323$	2.62232			0.145910
$324$		0			0
$325$	−15.0077			−0.832480
$326$	−19.2867	+	16.1834i	−1.06819	+	0.896317i
$327$		0			0
$328$	−2.00471	+	11.3693i	−0.110692	+	0.627764i
$329$	−32.6399	+	11.8799i	−1.79949	+	0.654963i
$330$		0			0
$331$	−1.40754	−	7.98256i	−0.0773654	−	0.438761i	−0.998744	−	0.0500957i	$-0.984047\pi$
$331$	−1.40754	−	7.98256i	−0.0773654	−	0.438761i	0.921379	−	0.388665i	$-0.127064\pi$
$332$	−1.41620	−	2.45292i	−0.0777238	−	0.134622i
$333$		0			0
$334$	−11.4313	+	19.7996i	−0.625494	+	1.08339i
$335$	7.32852	+	2.66736i	0.400400	+	0.145734i
$336$		0			0
$337$	−14.4077	−	12.0895i	−0.784839	−	0.658558i	0.159623	−	0.987178i	$-0.448972\pi$
$337$	−14.4077	−	12.0895i	−0.784839	−	0.658558i	−0.944462	+	0.328620i	$0.893417\pi$
$338$	−41.4489	−	34.7798i	−2.25452	−	1.89177i
$339$		0			0
$340$	−0.756840	−	0.275467i	−0.0410454	−	0.0149393i
$341$	2.16708	−	3.75350i	0.117354	−	0.203263i
$342$		0			0
$343$	8.72082	+	15.1049i	0.470880	+	0.815588i
$344$	4.06892	+	23.0760i	0.219382	+	1.24417i
$345$		0			0
$346$	−18.7143	+	6.81145i	−1.00609	+	0.366186i
$347$	3.05927	−	17.3500i	0.164230	−	0.931396i	−0.785624	−	0.618704i	$-0.787658\pi$
$347$	3.05927	−	17.3500i	0.164230	−	0.931396i	0.949855	−	0.312692i	$-0.101231\pi$
$348$		0			0
$349$	−13.0146	+	10.9205i	−0.696653	+	0.584561i	−0.920819	−	0.389990i	$-0.872479\pi$
$349$	−13.0146	+	10.9205i	−0.696653	+	0.584561i	0.224166	+	0.974551i	$0.428034\pi$
$350$	9.57475			0.511792
$351$		0			0
$352$	−11.2962			−0.602090
$353$	11.6099	−	9.74183i	0.617931	−	0.518505i	−0.279222	−	0.960227i	$-0.590076\pi$
$353$	11.6099	−	9.74183i	0.617931	−	0.518505i	0.897152	+	0.441721i	$0.145632\pi$
$354$		0			0
$355$	1.63915	−	9.29607i	0.0869970	−	0.493384i
$356$	−2.09828	+	0.763712i	−0.111209	+	0.0404767i
$357$		0			0
$358$	0.0811020	+	0.459952i	0.00428637	+	0.0243092i
$359$	1.22548	+	2.12259i	0.0646783	+	0.112026i	0.896551	−	0.442940i	$-0.146065\pi$
$359$	1.22548	+	2.12259i	0.0646783	+	0.112026i	−0.831873	+	0.554966i	$0.812731\pi$
$360$		0			0
$361$	5.89461	−	10.2098i	0.310243	−	0.537356i
$362$	2.10691	+	0.766852i	0.110737	+	0.0403049i
$363$		0			0
$364$	7.19325	+	6.03585i	0.377029	+	0.316365i
$365$	−5.86516	−	4.92145i	−0.306996	−	0.257600i
$366$		0			0
$367$	1.23432	+	0.449255i	0.0644309	+	0.0234509i	0.374035	−	0.927415i	$-0.377974\pi$
$367$	1.23432	+	0.449255i	0.0644309	+	0.0234509i	−0.309604	+	0.950866i	$0.600196\pi$
$368$	3.82425	−	6.62379i	0.199353	−	0.345289i
$369$		0			0
$370$	−1.73314	−	3.00189i	−0.0901017	−	0.156061i
$371$	3.54376	+	20.0977i	0.183983	+	1.04342i
$372$		0			0
$373$	9.04564	−	3.29234i	0.468366	−	0.170471i	−0.0970463	−	0.995280i	$-0.530939\pi$
$373$	9.04564	−	3.29234i	0.468366	−	0.170471i	0.565412	+	0.824809i	$0.308717\pi$
$374$	1.11112	−	6.30145i	0.0574544	−	0.325840i
$375$		0			0
$376$	22.7975	−	19.1294i	1.17569	−	0.986524i
$377$	−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	$0.570582\pi$
$380$	1.69656	−	1.42358i	0.0870314	−	0.0730281i
$381$		0			0
$382$	5.65279	−	32.0586i	0.289222	−	1.64026i
$383$	31.6062	−	11.5037i	1.61500	−	0.587813i	0.632581	−	0.774494i	$-0.281995\pi$
$383$	31.6062	−	11.5037i	1.61500	−	0.587813i	0.982420	+	0.186681i	$0.0597732\pi$
$384$		0			0
$385$	−3.36281	−	19.0714i	−0.171385	−	0.971970i
$386$	−16.5385	−	28.6455i	−0.841786	−	1.45802i
$387$		0			0
$388$	−2.10681	+	3.64911i	−0.106957	+	0.185255i
$389$	−14.0521	−	5.11456i	−0.712472	−	0.259319i	−0.0397455	−	0.999210i	$-0.512655\pi$
$389$	−14.0521	−	5.11456i	−0.712472	−	0.259319i	−0.672727	+	0.739891i	$0.734877\pi$
$390$		0			0
$391$	1.20678	+	1.01261i	0.0610296	+	0.0512099i
$392$	1.32142	+	1.10880i	0.0667418	+	0.0560030i
$393$		0			0
$394$	14.2332	+	5.18048i	0.717060	+	0.260989i
$395$	−3.90824	+	6.76927i	−0.196645	+	0.340599i
$396$		0			0
$397$	8.38938	+	14.5308i	0.421051	+	0.729282i	0.996043	−	0.0888774i	$-0.0283279\pi$
$397$	8.38938	+	14.5308i	0.421051	+	0.729282i	−0.574991	+	0.818159i	$0.694995\pi$
$398$	2.93045	+	16.6194i	0.146890	+	0.833055i
$399$		0			0
$400$	−9.72430	+	3.53936i	−0.486215	+	0.176968i
$401$	−2.27936	+	12.9269i	−0.113826	+	0.645537i	0.873499	+	0.486825i	$0.161845\pi$
$401$	−2.27936	+	12.9269i	−0.113826	+	0.645537i	−0.987325	+	0.158712i	$0.949266\pi$
$402$		0			0
$403$	5.49948	−	4.61462i	0.273949	−	0.229870i
$404$	−3.83541			−0.190819
$405$		0			0
$406$	36.0943			1.79133
$407$	4.16056	−	3.49113i	0.206231	−	0.173049i
$408$		0			0
$409$	4.41943	−	25.0639i	0.218527	−	1.23933i	−0.656153	−	0.754628i	$-0.727818\pi$
$409$	4.41943	−	25.0639i	0.218527	−	1.23933i	0.874680	−	0.484700i	$-0.161071\pi$
$410$	−12.0699	+	4.39310i	−0.596092	+	0.216960i
$411$		0			0
$412$	−0.184824	−	1.04819i	−0.00910561	−	0.0516405i
$413$	−12.5789	−	21.7872i	−0.618965	−	1.07208i
$414$		0			0
$415$	−4.83779	+	8.37929i	−0.237478	+	0.411323i
$416$	−17.5825	−	6.39952i	−0.862054	−	0.313762i
$417$		0			0
$418$	13.4784	+	11.3097i	0.659251	+	0.553178i
$419$	9.70582	+	8.14415i	0.474160	+	0.397868i	0.848309	−	0.529501i	$-0.177621\pi$
$419$	9.70582	+	8.14415i	0.474160	+	0.397868i	−0.374149	+	0.927369i	$0.622065\pi$
$420$		0			0
$421$	16.6112	+	6.04597i	0.809579	+	0.294663i	0.713450	−	0.700706i	$-0.247132\pi$
$421$	16.6112	+	6.04597i	0.809579	+	0.294663i	0.0961292	+	0.995369i	$0.469354\pi$
$422$	−11.8777	+	20.5727i	−0.578196	+	1.00147i
$423$		0			0
$424$	−8.74249	−	15.1424i	−0.424573	−	0.735382i
$425$	−0.370119	−	2.09905i	−0.0179534	−	0.101819i
$426$		0			0
$427$	3.35793	−	1.22219i	0.162502	−	0.0591458i
$428$	1.07380	−	6.08979i	0.0519038	−	0.294361i
$429$		0			0
$430$	−19.9710	+	16.7577i	−0.963089	+	0.808128i
$431$	−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	$0.598115\pi$
$434$	−3.50860	+	2.94407i	−0.168418	+	0.141320i
$435$		0			0
$436$	−1.04214	+	5.91029i	−0.0499097	+	0.283052i
$437$	−4.07059	+	1.48157i	−0.194723	+	0.0708732i
$438$		0			0
$439$	4.67755	+	26.5277i	0.223247	+	1.26610i	0.866008	+	0.500030i	$0.166678\pi$
$439$	4.67755	+	26.5277i	0.223247	+	1.26610i	−0.642761	+	0.766067i	$0.722211\pi$
$440$	8.29608	+	14.3692i	0.395500	+	0.685027i
$441$		0			0
$442$	5.29934	−	9.17873i	0.252064	−	0.436588i
$443$	32.6335	+	11.8776i	1.55047	+	0.564324i	0.968527	−	0.248908i	$-0.0800718\pi$
$443$	32.6335	+	11.8776i	1.55047	+	0.564324i	0.581940	+	0.813232i	$0.302294\pi$
$444$		0			0
$445$	5.84327	+	4.90308i	0.276997	+	0.232428i
$446$	14.8579	+	12.4673i	0.703542	+	0.590342i
$447$		0			0
$448$	−13.5479	−	4.93104i	−0.640079	−	0.232970i
$449$	−10.3731	+	17.9667i	−0.489535	+	0.847900i	−0.999927	−	0.0120419i	$-0.996167\pi$
$449$	−10.3731	+	17.9667i	−0.489535	+	0.847900i	0.510392	+	0.859942i	$0.329500\pi$
$450$		0			0
$451$	−10.0629	−	17.4295i	−0.473844	−	0.820722i
$452$	0.0384668	+	0.218156i	0.00180932	+	0.0102612i
$453$		0			0
$454$	−5.56585	+	2.02580i	−0.261218	+	0.0950757i
$455$	5.57012	−	31.5897i	0.261131	−	1.48095i
$456$		0			0
$457$	−5.52144	+	4.63304i	−0.258282	+	0.216725i	−0.762729	−	0.646718i	$-0.776141\pi$
$457$	−5.52144	+	4.63304i	−0.258282	+	0.216725i	0.504447	+	0.863443i	$0.331697\pi$
$458$	29.3621			1.37200
$459$		0			0
$460$	1.33046			0.0620332
$461$	−17.7162	+	14.8656i	−0.825125	+	0.692362i	−0.954166	−	0.299277i	$-0.903254\pi$
$461$	−17.7162	+	14.8656i	−0.825125	+	0.692362i	0.129041	+	0.991639i	$0.458810\pi$
$462$		0			0
$463$	0.864046	−	4.90025i	0.0401556	−	0.227734i	−0.958125	−	0.286350i	$-0.907558\pi$
$463$	0.864046	−	4.90025i	0.0401556	−	0.227734i	0.998281	+	0.0586166i	$0.0186690\pi$
$464$	−36.6581	+	13.3424i	−1.70181	+	0.619408i
$465$		0			0
$466$	0.149592	+	0.848380i	0.00692973	+	0.0393004i
$467$	−6.24068	−	10.8092i	−0.288784	−	0.500189i	0.684735	−	0.728792i	$-0.259918\pi$
$467$	−6.24068	−	10.8092i	−0.288784	−	0.500189i	−0.973520	+	0.228602i	$0.926584\pi$
$468$		0			0
$469$	6.45669	−	11.1833i	0.298142	−	0.516397i
$470$	31.1141	+	11.3246i	1.43519	+	0.522365i
$471$		0			0
$472$	16.5119	+	13.8551i	0.760021	+	0.637733i
$473$	−31.2921	−	26.2572i	−1.43881	−	1.20731i
$474$		0			0
$475$	5.50749	+	2.00456i	0.252701	+	0.0919756i
$476$	−0.666803	+	1.15494i	−0.0305628	+	0.0529364i
$477$		0			0
$478$	15.8588	+	27.4683i	0.725365	+	1.25637i
$479$	−4.94398	−	28.0387i	−0.225896	−	1.28112i	−0.860964	−	0.508666i	$-0.830139\pi$
$479$	−4.94398	−	28.0387i	−0.225896	−	1.28112i	0.635068	−	0.772456i	$-0.280972\pi$
$480$		0			0
$481$	8.45370	−	3.07689i	0.385455	−	0.140294i
$482$	−4.19115	+	23.7692i	−0.190902	+	1.08266i
$483$		0			0
$484$	2.34599	−	1.96852i	0.106636	−	0.0894781i
$485$	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	$0.265196\pi$
$488$	−2.34537	+	1.96800i	−0.106170	+	0.0890872i
$489$		0			0
$490$	−0.333269	+	1.89006i	−0.0150556	+	0.0853843i
$491$	11.6568	−	4.24274i	0.526066	−	0.191472i	−0.0653150	−	0.997865i	$-0.520805\pi$
$491$	11.6568	−	4.24274i	0.526066	−	0.191472i	0.591381	+	0.806392i	$0.298583\pi$
$492$		0			0
$493$	−1.39525	−	7.91287i	−0.0628390	−	0.356378i
$494$	14.5720	+	25.2394i	0.655623	+	1.13557i
$495$		0			0
$496$	2.47512	−	4.28702i	0.111136	−	0.192493i
$497$	−14.6873	−	5.34576i	−0.658817	−	0.239790i
$498$		0			0
$499$	−1.74645	−	1.46544i	−0.0781816	−	0.0656022i	0.602859	−	0.797847i	$-0.294028\pi$
$499$	−1.74645	−	1.46544i	−0.0781816	−	0.0656022i	−0.681041	+	0.732245i	$0.738472\pi$
$500$	−4.53795	−	3.80779i	−0.202943	−	0.170290i
$501$		0			0
$502$	−18.9204	−	6.88645i	−0.844457	−	0.307357i
$503$	20.6406	−	35.7506i	0.920320	−	1.59404i	0.121399	−	0.992604i	$-0.461262\pi$
$503$	20.6406	−	35.7506i	0.920320	−	1.59404i	0.798920	−	0.601437i	$-0.205405\pi$
$504$		0			0
$505$	6.55097	+	11.3466i	0.291514	+	0.504917i
$506$	1.83546	+	10.4094i	0.0815961	+	0.462754i
$507$		0			0
$508$	0.245209	−	0.0892487i	0.0108794	−	0.00395977i
$509$	−2.85202	+	16.1746i	−0.126414	+	0.716928i	0.854044	+	0.520200i	$0.174143\pi$
$509$	−2.85202	+	16.1746i	−0.126414	+	0.716928i	−0.980458	+	0.196728i	$0.936968\pi$
$510$		0			0
$511$	−9.71156	+	8.14896i	−0.429614	+	0.360489i
$512$	9.67844			0.427731
$513$		0			0
$514$	−20.6845			−0.912355
$515$	−2.78526	+	2.33711i	−0.122733	+	0.102985i
$516$		0			0
$517$	−9.00899	+	51.0925i	−0.396215	+	2.24705i
$518$	−5.39335	+	1.96302i	−0.236970	+	0.0862501i
$519$		0			0
$520$	4.77239	+	27.0656i	0.209283	+	1.18690i
$521$	−4.64836	−	8.05119i	−0.203648	−	0.352729i	0.746053	−	0.665887i	$-0.231947\pi$
$521$	−4.64836	−	8.05119i	−0.203648	−	0.352729i	−0.949701	+	0.313157i	$0.898613\pi$
$522$		0			0
$523$	11.3736	−	19.6996i	0.497331	−	0.861402i	−0.502664	−	0.864482i	$-0.667647\pi$
$523$	11.3736	−	19.6996i	0.497331	−	0.861402i	0.999995	+	0.00307938i	$0.000980199\pi$
$524$	5.27110	+	1.91852i	0.230269	+	0.0838110i
$525$		0			0
$526$	−11.5039	−	9.65288i	−0.501592	−	0.420886i
$527$	0.781049	+	0.655378i	0.0340230	+	0.0285487i
$528$		0			0
$529$	19.1676	+	6.97642i	0.833372	+	0.303323i
$530$	9.72687	−	16.8474i	0.422508	−	0.731806i
$531$		0			0
$532$	−1.83355	−	3.17581i	−0.0794946	−	0.137689i
$533$	−5.78878	−	32.8298i	−0.250740	−	1.42202i
$534$		0			0
$535$	−19.8500	+	7.22481i	−0.858191	+	0.312356i
$536$	−1.92124	+	10.8959i	−0.0829849	+	0.470631i
$537$		0			0
$538$	26.7710	−	22.4636i	1.15418	−	0.968473i
$539$	−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	$0.483642\pi$
$542$	−33.8105	+	28.3704i	−1.45229	+	1.21861i
$543$		0			0
$544$	0.461447	−	2.61700i	0.0197844	−	0.112203i
$545$	19.2649	−	7.01185i	0.825218	−	0.300355i
$546$		0			0
$547$	5.15158	+	29.2161i	0.220266	+	1.24919i	0.871531	+	0.490340i	$0.163127\pi$
$547$	5.15158	+	29.2161i	0.220266	+	1.24919i	−0.651266	+	0.758850i	$0.725762\pi$
$548$	1.03904	+	1.79967i	0.0443856	+	0.0768781i
$549$		0			0
$550$	7.15057	−	12.3852i	0.304901	−	0.528105i
$551$	20.7618	+	7.55667i	0.884482	+	0.321925i
$552$		0			0
$553$	9.91458	+	8.31932i	0.421611	+	0.353773i
$554$	22.8328	+	19.1590i	0.970072	+	0.813987i
$555$		0			0
$556$	5.15081	+	1.87474i	0.218443	+	0.0795068i
$557$	4.20706	−	7.28685i	0.178259	−	0.308754i	−0.763025	−	0.646369i	$-0.776287\pi$
$557$	4.20706	−	7.28685i	0.178259	−	0.308754i	0.941284	+	0.337615i	$0.109620\pi$
$558$		0			0
$559$	−33.8309	−	58.5969i	−1.43090	−	2.47838i
$560$	−3.84080	−	21.7823i	−0.162304	−	0.920470i
$561$		0			0
$562$	29.6669	−	10.7979i	1.25142	−	0.455480i
$563$	4.72783	−	26.8129i	0.199254	−	1.13003i	−0.706974	−	0.707240i	$-0.749940\pi$
$563$	4.72783	−	26.8129i	0.199254	−	1.13003i	0.906228	−	0.422788i	$-0.138949\pi$
$564$		0			0
$565$	0.579686	−	0.486415i	0.0243876	−	0.0204636i
$566$	−26.4304			−1.11095
$567$		0			0
$568$	13.3915			0.561894
$569$	16.8141	−	14.1087i	0.704886	−	0.591469i	−0.218273	−	0.975888i	$-0.570042\pi$
$569$	16.8141	−	14.1087i	0.704886	−	0.591469i	0.923159	+	0.384418i	$0.125598\pi$
$570$		0			0
$571$	−7.78872	+	44.1720i	−0.325948	+	1.84854i	0.176981	+	0.984214i	$0.443367\pi$
$571$	−7.78872	+	44.1720i	−0.325948	+	1.84854i	−0.502929	+	0.864328i	$0.667744\pi$
$572$	13.1795	−	4.79696i	0.551064	−	0.200571i
$573$		0			0
$574$	3.69317	+	20.9450i	0.154150	+	0.874227i
$575$	1.76046	+	3.04921i	0.0734163	+	0.127161i
$576$		0			0
$577$	−6.00955	+	10.4088i	−0.250181	+	0.433326i	−0.963575	−	0.267437i	$-0.913823\pi$
$577$	−6.00955	+	10.4088i	−0.250181	+	0.433326i	0.713395	+	0.700762i	$0.247157\pi$
$578$	−23.8002	−	8.66256i	−0.989957	−	0.360315i
$579$		0			0
$580$	−5.19834	−	4.36193i	−0.215849	−	0.181119i
$581$	12.2727	+	10.2980i	0.509157	+	0.427234i
$582$		0			0
$583$	28.6433	+	10.4253i	1.18628	+	0.431772i
$584$	5.43095	−	9.40669i	0.224734	−	0.389252i
$585$		0			0
$586$	−15.4463	−	26.7537i	−0.638079	−	1.10519i
$587$	2.95721	+	16.7711i	0.122057	+	0.692219i	0.983012	+	0.183539i	$0.0587554\pi$
$587$	2.95721	+	16.7711i	0.122057	+	0.692219i	−0.860956	+	0.508680i	$0.830134\pi$
$588$		0			0
$589$	−2.63455	+	0.958897i	−0.108555	+	0.0395107i
$590$	−4.16438	+	23.6174i	−0.171445	+	0.972312i
$591$		0			0
$592$	4.75195	−	3.98736i	0.195304	−	0.163880i
$593$	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
$596$	7.33147	−	6.15184i	0.300309	−	0.251989i
$597$		0			0
$598$	−3.04024	+	17.2420i	−0.124324	+	0.705079i
$599$	12.7186	−	4.62917i	0.519666	−	0.189143i	−0.0688523	−	0.997627i	$-0.521934\pi$
$599$	12.7186	−	4.62917i	0.519666	−	0.189143i	0.588518	+	0.808484i	$0.299712\pi$
$600$		0			0
$601$	−7.86926	−	44.6288i	−0.320994	−	1.82045i	−0.536449	−	0.843933i	$-0.680235\pi$
$601$	−7.86926	−	44.6288i	−0.320994	−	1.82045i	0.215456	−	0.976514i	$-0.430876\pi$
$602$	21.5837	+	37.3841i	0.879686	+	1.52366i
$603$		0			0
$604$	0.305346	−	0.528874i	0.0124243	−	0.0215196i
$605$	−9.83063	−	3.57806i	−0.399672	−	0.145469i
$606$		0			0
$607$	18.7197	+	15.7077i	0.759808	+	0.637554i	0.938077	−	0.346427i	$-0.112605\pi$
$607$	18.7197	+	15.7077i	0.759808	+	0.637554i	−0.178269	+	0.983982i	$0.557050\pi$
$608$	5.59760	+	4.69694i	0.227013	+	0.190486i
$609$		0			0
$610$	−3.20097	−	1.16506i	−0.129603	−	0.0471718i
$611$	−42.9674	+	74.4217i	−1.73827	+	3.01078i
$612$		0			0
$613$	12.5998	+	21.8235i	0.508901	+	0.881443i	0.999947	+	0.0103088i	$0.00328145\pi$
$613$	12.5998	+	21.8235i	0.508901	+	0.881443i	−0.491046	+	0.871134i	$0.663385\pi$
$614$	−4.08375	−	23.1601i	−0.164807	−	0.934665i
$615$		0			0
$616$	25.8166	−	9.39646i	1.04018	−	0.378594i
$617$	−0.701860	+	3.98045i	−0.0282558	+	0.160247i	−0.995671	−	0.0929492i	$-0.970371\pi$
$617$	−0.701860	+	3.98045i	−0.0282558	+	0.160247i	0.967415	+	0.253196i	$0.0814817\pi$
$618$		0			0
$619$	−34.2958	+	28.7776i	−1.37846	+	1.15667i	−0.408688	+	0.912674i	$0.634014\pi$
$619$	−34.2958	+	28.7776i	−1.37846	+	1.15667i	−0.969776	+	0.243995i	$0.921542\pi$
$620$	0.861097			0.0345825
$621$		0			0
$622$	7.24860			0.290642
$623$	9.67531	−	8.11855i	0.387633	−	0.325263i
$624$		0			0
$625$	−1.61895	+	9.18150i	−0.0647579	+	0.367260i
$626$	17.6038	−	6.40726i	0.703590	−	0.256086i
$627$		0			0
$628$	−0.301461	−	1.70967i	−0.0120296	−	0.0682232i
$629$	0.638833	+	1.10649i	0.0254719	+	0.0441187i
$630$		0			0
$631$	−15.7058	+	27.2033i	−0.625238	+	1.08294i	0.363256	+	0.931689i	$0.381665\pi$
$631$	−15.7058	+	27.2033i	−0.625238	+	1.08294i	−0.988495	+	0.151255i	$0.951668\pi$
$632$	−10.4202	−	3.79265i	−0.414495	−	0.150864i
$633$		0			0
$634$	−17.5533	−	14.7290i	−0.697132	−	0.584963i
$635$	−0.682854	−	0.572983i	−0.0270982	−	0.0227381i
$636$		0			0
$637$	−4.68067	−	1.70362i	−0.185455	−	0.0675000i
$638$	26.9558	−	46.6888i	1.06719	−	1.84843i
$639$		0			0
$640$	11.4392	+	19.8133i	0.452176	+	0.783191i
$641$	−8.44635	−	47.9016i	−0.333611	−	1.89200i	−0.440537	−	0.897734i	$-0.645212\pi$
$641$	−8.44635	−	47.9016i	−0.333611	−	1.89200i	0.106926	−	0.994267i	$-0.465899\pi$
$642$		0			0
$643$	26.3418	−	9.58763i	1.03882	−	0.378099i	0.234387	−	0.972143i	$-0.424692\pi$
$643$	26.3418	−	9.58763i	1.03882	−	0.378099i	0.804432	+	0.594044i	$0.202470\pi$
$644$	0.382545	−	2.16952i	0.0150744	−	0.0854911i
$645$		0			0
$646$	−3.17072	+	2.66055i	−0.124750	+	0.104678i
$647$	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
$650$	18.1463	−	15.2265i	0.711756	−	0.597234i
$651$		0			0
$652$	1.36099	−	7.71855i	0.0533004	−	0.302282i
$653$	−4.80391	+	1.74848i	−0.187992	+	0.0684234i	−0.434301	−	0.900768i	$-0.643004\pi$
$653$	−4.80391	+	1.74848i	−0.187992	+	0.0684234i	0.246309	+	0.969191i	$0.420782\pi$
$654$		0			0
$655$	−3.32743	−	18.8708i	−0.130013	−	0.737343i
$656$	−11.4933	−	19.9069i	−0.448737	−	0.777236i
$657$		0			0
$658$	27.4126	−	47.4801i	1.06866	−	1.85097i
$659$	32.8948	+	11.9727i	1.28140	+	0.466391i	0.890895	−	0.454210i	$-0.150078\pi$
$659$	32.8948	+	11.9727i	1.28140	+	0.466391i	0.390505	+	0.920601i	$0.372301\pi$
$660$		0			0
$661$	1.02149	+	0.857133i	0.0397314	+	0.0333386i	0.662437	−	0.749118i	$-0.269522\pi$
$661$	1.02149	+	0.857133i	0.0397314	+	0.0333386i	−0.622706	+	0.782456i	$0.713967\pi$
$662$	9.80083	+	8.22387i	0.380920	+	0.319630i
$663$		0			0
$664$	−12.8986	−	4.69471i	−0.500563	−	0.182190i
$665$	−6.26350	+	10.8487i	−0.242888	+	0.420694i
$666$		0			0
$667$	6.63648	+	11.4947i	0.256966	+	0.445077i
$668$	−1.23588	−	7.00905i	−0.0478178	−	0.271188i
$669$		0			0
$670$	−11.5674	+	4.21018i	−0.446886	+	0.162653i
$671$	0.926830	−	5.25631i	0.0357799	−	0.202918i
$672$		0			0
$673$	−2.74208	+	2.30088i	−0.105699	+	0.0886923i	−0.694106	−	0.719873i	$-0.744200\pi$
$673$	−2.74208	+	2.30088i	−0.105699	+	0.0886923i	0.588406	+	0.808565i	$0.299756\pi$
$674$	29.6866			1.14348
$675$		0			0
$676$	16.8438			0.647839
$677$	28.2968	−	23.7439i	1.08754	−	0.912551i	0.0910111	−	0.995850i	$-0.470990\pi$
$677$	28.2968	−	23.7439i	1.08754	−	0.912551i	0.996525	+	0.0832991i	$0.0265457\pi$
$678$		0			0
$679$	4.13866	−	23.4715i	0.158827	−	0.900753i
$680$	−3.66782	+	1.33498i	−0.140654	+	0.0511940i
$681$		0			0
$682$	1.18794	+	6.73713i	0.0454885	+	0.257978i
$683$	19.0083	+	32.9233i	0.727332	+	1.25978i	0.958007	+	0.286745i	$0.0925733\pi$
$683$	19.0083	+	32.9233i	0.727332	+	1.25978i	−0.230675	+	0.973031i	$0.574093\pi$
$684$		0			0
$685$	3.54941	−	6.14775i	0.135616	−	0.234894i
$686$	−25.8697	−	9.41580i	−0.987710	−	0.359497i
$687$		0			0
$688$	−35.7401	−	29.9895i	−1.36258	−	1.14334i
$689$	38.6771	+	32.4540i	1.47348	+	1.23640i
$690$		0			0
$691$	−0.517267	−	0.188270i	−0.0196778	−	0.00716212i	0.332163	−	0.943222i	$-0.392222\pi$
$691$	−0.517267	−	0.188270i	−0.0196778	−	0.00716212i	−0.351840	+	0.936060i	$0.614444\pi$
$692$	3.09984	−	5.36908i	0.117838	−	0.204102i
$693$		0			0
$694$	13.9039	+	24.0822i	0.527784	+	0.914148i
$695$	−3.25150	−	18.4402i	−0.123336	−	0.699476i
$696$		0			0
$697$	4.44896	−	1.61929i	0.168516	−	0.0613350i
$698$	4.65654	−	26.4086i	0.176253	−	0.999579i
$699$		0			0
$700$	−2.28330	+	1.91592i	−0.0863006	+	0.0724148i
$701$	−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
$704$	−16.4962	+	13.8420i	−0.621724	+	0.521689i
$705$		0			0
$706$	−4.15395	+	23.5582i	−0.156336	+	0.886626i
$707$	20.3859	−	7.41987i	0.766692	−	0.279053i
$708$		0			0
$709$	2.11100	+	11.9721i	0.0792804	+	0.449621i	0.998445	+	0.0557476i	$0.0177542\pi$
$709$	2.11100	+	11.9721i	0.0792804	+	0.449621i	−0.919165	+	0.393874i	$0.871135\pi$
$710$	7.44966	+	12.9032i	0.279581	+	0.484248i
$711$		0			0
$712$	−5.41068	+	9.37158i	−0.202774	+	0.351215i
$713$	−1.58269	−	0.576051i	−0.0592721	−	0.0215733i
$714$		0			0
$715$	−36.7022	−	30.7968i	−1.37258	−	1.15173i
$716$	−0.111377	−	0.0934566i	−0.00416236	−	0.00349264i
$717$		0			0
$718$	−3.63530	−	1.32314i	−0.135668	−	0.0493791i
$719$	4.88834	−	8.46685i	0.182304	−	0.315760i	−0.760361	−	0.649501i	$-0.774978\pi$
$719$	4.88834	−	8.46685i	0.182304	−	0.315760i	0.942665	+	0.333741i	$0.108311\pi$
$720$		0			0
$721$	3.01017	+	5.21376i	0.112104	+	0.194171i
$722$	3.23127	+	18.3255i	0.120256	+	0.682003i
$723$		0			0
$724$	−0.655884	+	0.238722i	−0.0243757	+	0.00887205i
$725$	3.11842	−	17.6854i	0.115815	−	0.656821i
$726$		0			0
$727$	3.32075	−	2.78644i	0.123160	−	0.103343i	−0.579128	−	0.815237i	$-0.696607\pi$
$727$	3.32075	−	2.78644i	0.123160	−	0.103343i	0.702287	+	0.711894i	$0.252162\pi$
$728$	45.5067			1.68659
$729$		0			0
$730$	12.0849			0.447283
$731$	7.36129	−	6.17686i	0.272267	−	0.228459i
$732$		0			0
$733$	5.06943	−	28.7501i	0.187244	−	1.06191i	−0.735795	−	0.677204i	$-0.763191\pi$
$733$	5.06943	−	28.7501i	0.187244	−	1.06191i	0.923039	−	0.384707i	$-0.125697\pi$
$734$	−1.94825	+	0.709106i	−0.0719113	+	0.0261736i
$735$		0			0
$736$	0.762267	+	4.32303i	0.0280975	+	0.159349i
$737$	−9.64391	−	16.7037i	−0.355238	−	0.615290i
$738$		0			0
$739$	−20.7777	+	35.9880i	−0.764319	+	1.32384i	0.176287	+	0.984339i	$0.443591\pi$
$739$	−20.7777	+	35.9880i	−0.764319	+	1.32384i	−0.940606	+	0.339501i	$0.889742\pi$
$740$	1.01398	+	0.369060i	0.0372748	+	0.0135669i
$741$		0			0
$742$	−24.6755	−	20.7052i	−0.905867	−	0.760112i
$743$	−16.3760	−	13.7411i	−0.600777	−	0.504112i	0.290918	−	0.956748i	$-0.406039\pi$
$743$	−16.3760	−	13.7411i	−0.600777	−	0.504112i	−0.891695	+	0.452636i	$0.850484\pi$
$744$		0			0
$745$	−30.7218	−	11.1818i	−1.12556	−	0.409670i
$746$	−7.59699	+	13.1584i	−0.278146	+	0.481763i
$747$		0			0
$748$	0.995957	+	1.72505i	0.0364158	+	0.0630740i
$749$	6.07371	+	34.4457i	0.221929	+	1.25862i
$750$		0			0
$751$	37.5573	−	13.6697i	1.37048	−	0.498816i	0.451205	−	0.892420i	$-0.350994\pi$
$751$	37.5573	−	13.6697i	1.37048	−	0.498816i	0.919280	+	0.393605i	$0.128772\pi$
$752$	−10.2896	+	58.3549i	−0.375221	+	2.12799i
$753$		0			0
$754$	68.4067	−	57.4000i	2.49123	−	2.09039i
$755$	−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	$0.461243\pi$
$758$	10.3539	−	8.68795i	0.376070	−	0.315561i
$759$		0			0
$760$	1.86375	−	10.5699i	0.0676054	−	0.383410i
$761$	39.4906	−	14.3734i	1.43153	−	0.521035i	0.494163	−	0.869369i	$-0.335475\pi$
$761$	39.4906	−	14.3734i	1.43153	−	0.521035i	0.937370	+	0.348334i	$0.113253\pi$
$762$		0			0
$763$	−5.89469	−	33.4304i	−0.213402	−	1.21026i
$764$	5.06692	+	8.77617i	0.183315	+	0.317511i
$765$		0			0
$766$	−26.5445	+	45.9764i	−0.959092	+	1.66120i
$767$	−58.4875	−	21.2877i	−2.11186	−	0.768655i
$768$		0			0
$769$	1.84864	+	1.55120i	0.0666638	+	0.0559375i	0.675511	−	0.737350i	$-0.263923\pi$
$769$	1.84864	+	1.55120i	0.0666638	+	0.0559375i	−0.608847	+	0.793288i	$0.708368\pi$
$770$	23.4155	+	19.6480i	0.843837	+	0.708064i
$771$		0			0
$772$	9.67593	+	3.52175i	0.348244	+	0.126751i
$773$	0.698900	−	1.21053i	0.0251377	−	0.0435398i	−0.853183	−	0.521612i	$-0.825331\pi$
$773$	0.698900	−	1.21053i	0.0251377	−	0.0435398i	0.878321	+	0.478072i	$0.158664\pi$
$774$		0			0
$775$	1.13940	+	1.97350i	0.0409284	+	0.0708901i
$776$	3.54593	+	20.1100i	0.127292	+	0.721907i
$777$		0			0
$778$	22.1800	−	8.07285i	0.795190	−	0.289426i
$779$	−2.26068	+	12.8210i	−0.0809973	+	0.459358i
$780$

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)

\(f(q)\)	\(=\)	\(q+(-1.20913 + 1.01458i) q^{2} +(0.0853237 - 0.483895i) q^{4} +(-1.57728 + 0.574083i) q^{5} +(0.482617 + 2.73706i) q^{7} +(-1.19062 - 2.06222i) q^{8} +O(q^{10})\)	\(q+(-1.20913 + 1.01458i) q^{2} +(0.0853237 - 0.483895i) q^{4} +(-1.57728 + 0.574083i) q^{5} +(0.482617 + 2.73706i) q^{7} +(-1.19062 - 2.06222i) q^{8} +(1.32468 - 2.29442i) q^{10} +(3.90087 + 1.41980i) q^{11} +(5.26736 + 4.41984i) q^{13} +(-3.36051 - 2.81980i) q^{14} +(4.45535 + 1.62162i) q^{16} +(-0.488276 + 0.845718i) q^{17} +(-1.34264 - 2.32553i) q^{19} +(0.143217 + 0.812221i) q^{20} +(-6.15715 + 2.24102i) q^{22} +(0.280124 - 1.58866i) q^{23} +(-1.67198 + 1.40296i) q^{25} -10.8532 q^{26} +1.36563 q^{28} +(-6.30292 + 5.28878i) q^{29} +(0.181301 - 1.02821i) q^{31} +(-2.55707 + 0.930697i) q^{32} +(-0.267660 - 1.51798i) q^{34} +(-2.33252 - 4.04005i) q^{35} +(0.654172 - 1.13306i) q^{37} +(3.98286 + 1.44964i) q^{38} +(3.06183 + 2.56918i) q^{40} +(-3.71391 - 3.11634i) q^{41} +(-9.24679 - 3.36556i) q^{43} +(1.01987 - 1.76647i) q^{44} +(1.27312 + 2.20510i) q^{46} +(2.17020 + 12.3078i) q^{47} +(-0.680721 + 0.247762i) q^{49} +(0.598226 - 3.39271i) q^{50} +(2.58817 - 2.17173i) q^{52} +7.34280 q^{53} -6.96786 q^{55} +(5.06980 - 4.25406i) q^{56} +(2.25515 - 12.7896i) q^{58} +(-8.50598 + 3.09592i) q^{59} +(-0.223267 - 1.26621i) q^{61} +(0.823982 + 1.42718i) q^{62} +(-2.59373 + 4.49247i) q^{64} +(-10.8455 - 3.94742i) q^{65} +(-3.55927 - 2.98658i) q^{67} +(0.367577 + 0.308434i) q^{68} +(6.91926 + 2.51841i) q^{70} +(-2.81187 + 4.87030i) q^{71} +(2.28072 + 3.95033i) q^{73} +(0.358600 + 2.03372i) q^{74} +(-1.23987 + 0.451276i) q^{76} +(-2.00345 + 11.3621i) q^{77} +(3.56732 - 2.99333i) q^{79} -7.95828 q^{80} +7.65237 q^{82} +(4.41578 - 3.70528i) q^{83} +(0.284635 - 1.61425i) q^{85} +(14.5952 - 5.31221i) q^{86} +(-1.71652 - 9.73490i) q^{88} +(-2.27221 - 3.93558i) q^{89} +(-9.55523 + 16.5502i) q^{91} +(-0.744844 - 0.271101i) q^{92} +(-15.1113 - 12.6799i) q^{94} +(3.45278 + 2.89722i) q^{95} +(-8.05828 - 2.93297i) q^{97} +(0.571704 - 0.990221i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{2} - 3 q^{4} - 12 q^{5} - 3 q^{7} + 6 q^{8}+O(q^{10}) \) 12 * q + 3 * q^2 - 3 * q^4 - 12 * q^5 - 3 * q^7 + 6 * q^8	\( 12 q + 3 q^{2} - 3 q^{4} - 12 q^{5} - 3 q^{7} + 6 q^{8} - 6 q^{10} + 3 q^{11} + 6 q^{13} + 6 q^{14} + 27 q^{16} - 9 q^{17} - 12 q^{19} - 39 q^{20} - 39 q^{22} - 21 q^{23} + 6 q^{25} - 48 q^{26} + 6 q^{28} - 6 q^{29} + 6 q^{31} - 27 q^{32} - 18 q^{34} + 30 q^{35} - 3 q^{37} - 3 q^{38} + 33 q^{40} + 15 q^{41} - 30 q^{43} - 33 q^{44} + 3 q^{46} + 21 q^{47} - 3 q^{49} - 6 q^{50} + 18 q^{53} + 30 q^{55} - 15 q^{56} - 3 q^{58} - 30 q^{59} - 30 q^{61} - 30 q^{62} - 6 q^{64} + 12 q^{65} - 39 q^{67} - 18 q^{68} + 51 q^{70} - 12 q^{73} - 57 q^{74} + 57 q^{76} + 24 q^{77} + 15 q^{79} + 42 q^{80} - 42 q^{82} + 21 q^{83} + 54 q^{85} + 60 q^{86} + 12 q^{88} - 9 q^{89} - 18 q^{91} + 15 q^{92} + 33 q^{94} - 42 q^{95} - 12 q^{97} + 18 q^{98}+O(q^{100}) \) 12 * q + 3 * q^2 - 3 * q^4 - 12 * q^5 - 3 * q^7 + 6 * q^8 - 6 * q^10 + 3 * q^11 + 6 * q^13 + 6 * q^14 + 27 * q^16 - 9 * q^17 - 12 * q^19 - 39 * q^20 - 39 * q^22 - 21 * q^23 + 6 * q^25 - 48 * q^26 + 6 * q^28 - 6 * q^29 + 6 * q^31 - 27 * q^32 - 18 * q^34 + 30 * q^35 - 3 * q^37 - 3 * q^38 + 33 * q^40 + 15 * q^41 - 30 * q^43 - 33 * q^44 + 3 * q^46 + 21 * q^47 - 3 * q^49 - 6 * q^50 + 18 * q^53 + 30 * q^55 - 15 * q^56 - 3 * q^58 - 30 * q^59 - 30 * q^61 - 30 * q^62 - 6 * q^64 + 12 * q^65 - 39 * q^67 - 18 * q^68 + 51 * q^70 - 12 * q^73 - 57 * q^74 + 57 * q^76 + 24 * q^77 + 15 * q^79 + 42 * q^80 - 42 * q^82 + 21 * q^83 + 54 * q^85 + 60 * q^86 + 12 * q^88 - 9 * q^89 - 18 * q^91 + 15 * q^92 + 33 * q^94 - 42 * q^95 - 12 * q^97 + 18 * q^98

Introduction

L-functions

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