LMFDB - Embedded newform 729.2.e.g.82.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("729.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 243)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			82.1
Root			$-0.766044 + 0.642788i$ of defining polynomial
Character	$\chi$	$=$	729.82
Dual form			729.2.e.g.649.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.439693 - 2.49362i) q^{2} +(-4.14543 + 1.50881i) q^{4} +(-0.358441 - 0.300767i) q^{5} +(3.03209 + 1.10359i) q^{7} +(3.05303 + 5.28801i) q^{8} +(-0.592396 + 1.02606i) q^{10} +(2.37939 - 1.99654i) q^{11} +(-0.379385 + 2.15160i) q^{13} +(1.41875 - 8.04612i) q^{14} +(5.08512 - 4.26692i) q^{16} +(1.50000 - 2.59808i) q^{17} +(-0.0209445 - 0.0362770i) q^{19} +(1.93969 + 0.705990i) q^{20} +(-6.02481 - 5.05542i) q^{22} +(5.73783 - 2.08840i) q^{23} +(-0.830222 - 4.70842i) q^{25} +5.53209 q^{26} -14.2344 q^{28} +(-1.14156 - 6.47410i) q^{29} +(5.85117 - 2.12965i) q^{31} +(-3.52094 - 2.95442i) q^{32} +(-7.13816 - 2.59808i) q^{34} +(-0.754900 - 1.30753i) q^{35} +(-1.79813 + 3.11446i) q^{37} +(-0.0812519 + 0.0681784i) q^{38} +(0.496130 - 2.81369i) q^{40} +(-1.33750 + 7.58532i) q^{41} +(-0.450837 + 0.378297i) q^{43} +(-6.85117 + 11.8666i) q^{44} +(-7.73055 - 13.3897i) q^{46} +(-9.07785 - 3.30407i) q^{47} +(2.61334 + 2.19285i) q^{49} +(-11.3760 + 4.14052i) q^{50} +(-1.67365 - 9.49173i) q^{52} -4.95811 q^{53} -1.45336 q^{55} +(3.42127 + 19.4030i) q^{56} +(-15.6420 + 5.69323i) q^{58} +(6.53596 + 5.48432i) q^{59} +(1.19207 + 0.433877i) q^{61} +(-7.88326 - 13.6542i) q^{62} +(0.819078 - 1.41868i) q^{64} +(0.783119 - 0.657115i) q^{65} +(1.73783 - 9.85570i) q^{67} +(-2.29813 + 13.0334i) q^{68} +(-2.92855 + 2.45734i) q^{70} +(5.91534 - 10.2457i) q^{71} +(4.11721 + 7.13122i) q^{73} +(8.55690 + 3.11446i) q^{74} +(0.141559 + 0.118782i) q^{76} +(9.41787 - 3.42782i) q^{77} +(1.91875 + 10.8818i) q^{79} -3.10607 q^{80} +19.5030 q^{82} +(0.262174 + 1.48686i) q^{83} +(-1.31908 + 0.480105i) q^{85} +(1.14156 + 0.957882i) q^{86} +(17.8221 + 6.48670i) q^{88} +(-7.93629 - 13.7461i) q^{89} +(-3.52481 + 6.10516i) q^{91} +(-20.6348 + 17.3146i) q^{92} +(-4.24763 + 24.0895i) q^{94} +(-0.00340357 + 0.0193026i) q^{95} +(14.2836 - 11.9854i) q^{97} +(4.31908 - 7.48086i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} - 9 q^{4} + 6 q^{5} + 9 q^{7} + 6 q^{8} + 3 q^{11} + 9 q^{13} + 6 q^{14} + 9 q^{16} + 9 q^{17} + 3 q^{19} + 6 q^{20} - 9 q^{22} + 15 q^{23} + 18 q^{25} + 24 q^{26} - 24 q^{28} - 15 q^{29}+ \cdots + 9 q^{98}+O(q^{100}) $ 6 * q + 3 * q^2 - 9 * q^4 + 6 * q^5 + 9 * q^7 + 6 * q^8 + 3 * q^11 + 9 * q^13 + 6 * q^14 + 9 * q^16 + 9 * q^17 + 3 * q^19 + 6 * q^20 - 9 * q^22 + 15 * q^23 + 18 * q^25 + 24 * q^26 - 24 * q^28 - 15 * q^29 + 9 * q^31 - 18 * q^32 - 9 * q^34 - 6 * q^35 + 3 * q^37 - 3 * q^38 + 27 * q^40 - 3 * q^41 + 9 * q^43 - 15 * q^44 - 9 * q^46 - 15 * q^47 + 9 * q^49 - 15 * q^50 - 9 * q^52 - 36 * q^53 + 18 * q^55 + 3 * q^56 - 36 * q^58 + 6 * q^59 + 18 * q^61 - 12 * q^62 - 12 * q^64 + 21 * q^65 - 9 * q^67 - 18 * q^70 - 9 * q^71 - 6 * q^73 + 15 * q^74 + 9 * q^76 - 3 * q^77 + 9 * q^79 + 6 * q^80 + 36 * q^82 + 21 * q^83 + 9 * q^85 + 15 * q^86 + 9 * q^88 + 6 * q^91 - 48 * q^92 - 9 * q^94 - 42 * q^95 + 36 * q^97 + 9 * q^98

Character values

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

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

Coefficient data

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

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

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

$2$	−0.439693	−	2.49362i	−0.310910	−	1.76326i	−0.594292	−	0.804249i	$-0.702568\pi$
$2$	−0.439693	−	2.49362i	−0.310910	−	1.76326i	0.283383	−	0.959007i	$-0.408543\pi$
$3$		0			0
$3$		0			0
$4$	−4.14543	+	1.50881i	−2.07271	+	0.754407i
$5$	−0.358441	−	0.300767i	−0.160300	−	0.134507i	0.559110	−	0.829094i	$-0.311143\pi$
$5$	−0.358441	−	0.300767i	−0.160300	−	0.134507i	−0.719409	+	0.694586i	$0.755587\pi$
$6$		0			0
$7$	3.03209	+	1.10359i	1.14602	+	0.417118i	0.844085	−	0.536210i	$-0.180144\pi$
$7$	3.03209	+	1.10359i	1.14602	+	0.417118i	0.301937	+	0.953328i	$0.402367\pi$
$8$	3.05303	+	5.28801i	1.07941	+	1.86959i
$9$		0			0
$10$	−0.592396	+	1.02606i	−0.187332	+	0.324469i
$11$	2.37939	−	1.99654i	0.717412	−	0.601980i	−0.209256	−	0.977861i	$-0.567104\pi$
$11$	2.37939	−	1.99654i	0.717412	−	0.601980i	0.926668	+	0.375881i	$0.122660\pi$
$12$		0			0
$13$	−0.379385	+	2.15160i	−0.105223	+	0.596747i	0.885909	+	0.463860i	$0.153536\pi$
$13$	−0.379385	+	2.15160i	−0.105223	+	0.596747i	−0.991131	+	0.132887i	$0.957575\pi$
$14$	1.41875	−	8.04612i	0.379176	−	2.15042i
$15$		0			0
$16$	5.08512	−	4.26692i	1.27128	−	1.06673i
$17$	1.50000	−	2.59808i	0.363803	−	0.630126i	−0.624780	−	0.780801i	$-0.714811\pi$
$17$	1.50000	−	2.59808i	0.363803	−	0.630126i	0.988583	+	0.150675i	$0.0481447\pi$
$18$		0			0
$19$	−0.0209445	−	0.0362770i	−0.00480501	−	0.00832251i	0.863613	−	0.504155i	$-0.168196\pi$
$19$	−0.0209445	−	0.0362770i	−0.00480501	−	0.00832251i	−0.868418	+	0.495833i	$0.834863\pi$
$20$	1.93969	+	0.705990i	0.433728	+	0.157864i
$21$		0			0
$22$	−6.02481	−	5.05542i	−1.28449	−	1.07782i
$23$	5.73783	−	2.08840i	1.19642	−	0.435461i	0.334446	−	0.942415i	$-0.391451\pi$
$23$	5.73783	−	2.08840i	1.19642	−	0.435461i	0.861973	+	0.506954i	$0.169229\pi$
$24$		0			0
$25$	−0.830222	−	4.70842i	−0.166044	−	0.941685i
$26$	5.53209			1.08493
$27$		0			0
$28$	−14.2344			−2.69005
$29$	−1.14156	−	6.47410i	−0.211982	−	1.20221i	−0.886067	−	0.463557i	$-0.846573\pi$
$29$	−1.14156	−	6.47410i	−0.211982	−	1.20221i	0.674085	−	0.738654i	$-0.264538\pi$
$30$		0			0
$31$	5.85117	−	2.12965i	1.05090	−	0.382497i	0.241898	−	0.970302i	$-0.422230\pi$
$31$	5.85117	−	2.12965i	1.05090	−	0.382497i	0.809003	+	0.587805i	$0.200008\pi$
$32$	−3.52094	−	2.95442i	−0.622421	−	0.522273i
$33$		0			0
$34$	−7.13816	−	2.59808i	−1.22418	−	0.445566i
$35$	−0.754900	−	1.30753i	−0.127601	−	0.221012i
$36$		0			0
$37$	−1.79813	+	3.11446i	−0.295611	+	0.512014i	−0.975127	−	0.221647i	$-0.928857\pi$
$37$	−1.79813	+	3.11446i	−0.295611	+	0.512014i	0.679516	+	0.733661i	$0.262190\pi$
$38$	−0.0812519	+	0.0681784i	−0.0131808	+	0.0110600i
$39$		0			0
$40$	0.496130	−	2.81369i	0.0784450	−	0.444884i
$41$	−1.33750	+	7.58532i	−0.208882	+	1.18463i	0.682331	+	0.731043i	$0.260966\pi$
$41$	−1.33750	+	7.58532i	−0.208882	+	1.18463i	−0.891213	+	0.453585i	$0.850145\pi$
$42$		0			0
$43$	−0.450837	+	0.378297i	−0.0687520	+	0.0576898i	−0.676516	−	0.736428i	$-0.736511\pi$
$43$	−0.450837	+	0.378297i	−0.0687520	+	0.0576898i	0.607764	+	0.794118i	$0.292067\pi$
$44$	−6.85117	+	11.8666i	−1.03285	+	1.78895i
$45$		0			0
$46$	−7.73055	−	13.3897i	−1.13981	−	1.97420i
$47$	−9.07785	−	3.30407i	−1.32414	−	0.481948i	−0.419358	−	0.907821i	$-0.637745\pi$
$47$	−9.07785	−	3.30407i	−1.32414	−	0.481948i	−0.904783	+	0.425874i	$0.859967\pi$
$48$		0			0
$49$	2.61334	+	2.19285i	0.373334	+	0.313265i
$50$	−11.3760	+	4.14052i	−1.60881	+	0.585558i
$51$		0			0
$52$	−1.67365	−	9.49173i	−0.232093	−	1.31627i
$53$	−4.95811			−0.681049			−0.340524	−	0.940236i	$-0.610605\pi$
$53$	−4.95811			−0.681049			−0.340524	+	0.940236i	$0.610605\pi$
$54$		0			0
$55$	−1.45336			−0.195971
$56$	3.42127	+	19.4030i	0.457187	+	2.59284i
$57$		0			0
$58$	−15.6420	+	5.69323i	−2.05390	+	0.747558i
$59$	6.53596	+	5.48432i	0.850909	+	0.713998i	0.959990	−	0.280035i	$-0.0903461\pi$
$59$	6.53596	+	5.48432i	0.850909	+	0.713998i	−0.109080	+	0.994033i	$0.534791\pi$
$60$		0			0
$61$	1.19207	+	0.433877i	0.152628	+	0.0555522i	0.417205	−	0.908813i	$-0.363010\pi$
$61$	1.19207	+	0.433877i	0.152628	+	0.0555522i	−0.264576	+	0.964365i	$0.585232\pi$
$62$	−7.88326	−	13.6542i	−1.00117	−	1.73409i
$63$		0			0
$64$	0.819078	−	1.41868i	0.102385	−	0.177336i
$65$	0.783119	−	0.657115i	0.0971339	−	0.0815050i
$66$		0			0
$67$	1.73783	−	9.85570i	0.212309	−	1.20407i	−0.673206	−	0.739455i	$-0.735083\pi$
$67$	1.73783	−	9.85570i	0.212309	−	1.20407i	0.885515	−	0.464610i	$-0.153806\pi$
$68$	−2.29813	+	13.0334i	−0.278690	+	1.58053i
$69$		0			0
$70$	−2.92855	+	2.45734i	−0.350028	+	0.293709i
$71$	5.91534	−	10.2457i	0.702022	−	1.21594i	−0.265733	−	0.964047i	$-0.585614\pi$
$71$	5.91534	−	10.2457i	0.702022	−	1.21594i	0.967755	−	0.251892i	$-0.0810526\pi$
$72$		0			0
$73$	4.11721	+	7.13122i	0.481883	+	0.834646i	0.999784	−	0.0207947i	$-0.00661964\pi$
$73$	4.11721	+	7.13122i	0.481883	+	0.834646i	−0.517901	+	0.855441i	$0.673286\pi$
$74$	8.55690	+	3.11446i	0.994720	+	0.362048i
$75$		0			0
$76$	0.141559	+	0.118782i	0.0162380	+	0.0136253i
$77$	9.41787	−	3.42782i	1.07327	−	0.390637i
$78$		0			0
$79$	1.91875	+	10.8818i	0.215876	+	1.22429i	0.879380	+	0.476121i	$0.157958\pi$
$79$	1.91875	+	10.8818i	0.215876	+	1.22429i	−0.663504	+	0.748173i	$0.730931\pi$
$80$	−3.10607			−0.347269
$81$		0			0
$82$	19.5030			2.15375
$83$	0.262174	+	1.48686i	0.0287773	+	0.163204i	0.995810	−	0.0914488i	$-0.0291498\pi$
$83$	0.262174	+	1.48686i	0.0287773	+	0.163204i	−0.967032	+	0.254653i	$0.918039\pi$
$84$		0			0
$85$	−1.31908	+	0.480105i	−0.143074	+	0.0520747i
$86$	1.14156	+	0.957882i	0.123098	+	0.103291i
$87$		0			0
$88$	17.8221	+	6.48670i	1.89984	+	0.691485i
$89$	−7.93629	−	13.7461i	−0.841245	−	1.45708i	−0.888843	−	0.458212i	$-0.848490\pi$
$89$	−7.93629	−	13.7461i	−0.841245	−	1.45708i	0.0475978	−	0.998867i	$-0.484843\pi$
$90$		0			0
$91$	−3.52481	+	6.10516i	−0.369501	+	0.639995i
$92$	−20.6348	+	17.3146i	−2.15132	+	1.80517i
$93$		0			0
$94$	−4.24763	+	24.0895i	−0.438109	+	2.48464i
$95$	−0.00340357	+	0.0193026i	−0.000349199	+	0.00198040i
$96$		0			0
$97$	14.2836	−	11.9854i	1.45028	−	1.21693i	0.517902	−	0.855440i	$-0.326713\pi$
$97$	14.2836	−	11.9854i	1.45028	−	1.21693i	0.932377	−	0.361488i	$-0.117731\pi$
$98$	4.31908	−	7.48086i	0.436293	−	0.755681i
$99$		0			0
$100$	10.5458	+	18.2658i	1.05458	+	1.82658i
$101$	8.53849	+	3.10775i	0.849611	+	0.309233i	0.729882	−	0.683573i	$-0.239575\pi$
$101$	8.53849	+	3.10775i	0.849611	+	0.309233i	0.119729	+	0.992807i	$0.461797\pi$
$102$		0			0
$103$	0.199807	+	0.167658i	0.0196876	+	0.0165199i	0.652578	−	0.757721i	$-0.273687\pi$
$103$	0.199807	+	0.167658i	0.0196876	+	0.0165199i	−0.632891	+	0.774241i	$0.718132\pi$
$104$	−12.5360	+	4.56272i	−1.22925	+	0.447411i
$105$		0			0
$106$	2.18004	+	12.3636i	0.211745	+	1.20086i
$107$	−4.04189			−0.390744			−0.195372	−	0.980729i	$-0.562591\pi$
$107$	−4.04189			−0.390744			−0.195372	+	0.980729i	$0.562591\pi$
$108$		0			0
$109$	−5.40373			−0.517584			−0.258792	−	0.965933i	$-0.583324\pi$
$109$	−5.40373			−0.517584			−0.258792	+	0.965933i	$0.583324\pi$
$110$	0.639033	+	3.62414i	0.0609294	+	0.345548i
$111$		0			0
$112$	20.1275	−	7.32580i	1.90187	−	0.692223i
$113$	−1.06031	−	0.889704i	−0.0997453	−	0.0836963i	0.591551	−	0.806267i	$-0.298516\pi$
$113$	−1.06031	−	0.889704i	−0.0997453	−	0.0836963i	−0.691297	+	0.722571i	$0.742960\pi$
$114$		0			0
$115$	−2.68479	−	0.977185i	−0.250358	−	0.0911229i
$116$	14.5005	+	25.1155i	1.34633	+	2.33192i
$117$		0			0
$118$	10.8020	−	18.7096i	0.994405	−	1.72236i
$119$	7.41534	−	6.22221i	0.679764	−	0.570389i
$120$		0			0
$121$	−0.234833	+	1.33180i	−0.0213484	+	0.121073i
$122$	0.557781	−	3.16333i	0.0504991	−	0.286395i
$123$		0			0
$124$	−21.0424	+	17.6566i	−1.88966	+	1.58561i
$125$	−2.28833	+	3.96351i	−0.204675	+	0.354507i
$126$		0			0
$127$	3.31908	+	5.74881i	0.294521	+	0.510125i	0.974873	−	0.222760i	$-0.0715067\pi$
$127$	3.31908	+	5.74881i	0.294521	+	0.510125i	−0.680353	+	0.732885i	$0.738173\pi$
$128$	−12.5360	−	4.56272i	−1.10803	−	0.403291i
$129$		0			0
$130$	−1.98293	−	1.66387i	−0.173914	−	0.145931i
$131$	−11.8785	+	4.32342i	−1.03783	+	0.377739i	−0.804057	−	0.594552i	$-0.797329\pi$
$131$	−11.8785	+	4.32342i	−1.03783	+	0.377739i	−0.233773	+	0.972291i	$0.575107\pi$
$132$		0			0
$133$	−0.0234708	−	0.133109i	−0.00203517	−	0.0115420i
$134$	−25.3405			−2.18908
$135$		0			0
$136$	18.3182			1.57077
$137$	−1.84343	−	10.4546i	−0.157495	−	0.893196i	−0.956470	−	0.291832i	$-0.905735\pi$
$137$	−1.84343	−	10.4546i	−0.157495	−	0.893196i	0.798975	−	0.601364i	$-0.205376\pi$
$138$		0			0
$139$	7.01114	−	2.55185i	0.594678	−	0.216445i	−0.0271080	−	0.999633i	$-0.508630\pi$
$139$	7.01114	−	2.55185i	0.594678	−	0.216445i	0.621785	+	0.783188i	$0.286408\pi$
$140$	5.10220	+	4.28125i	0.431214	+	0.361832i
$141$		0			0
$142$	−28.1498	−	10.2457i	−2.36228	−	0.859798i
$143$	3.39306	+	5.87695i	0.283742	+	0.491455i
$144$		0			0
$145$	−1.53802	+	2.66393i	−0.127725	+	0.221227i
$146$	15.9722	−	13.4023i	1.32187	−	1.10918i
$147$		0			0
$148$	2.75490	−	15.6238i	0.226451	−	1.28427i
$149$	0.738703	−	4.18939i	0.0605169	−	0.343209i	−0.939483	−	0.342596i	$-0.888694\pi$
$149$	0.738703	−	4.18939i	0.0605169	−	0.343209i	1.00000		0.000612725i	$-0.000195036\pi$
$150$		0			0
$151$	0.103541	−	0.0868809i	0.00842602	−	0.00707027i	−0.638565	−	0.769568i	$-0.720472\pi$
$151$	0.103541	−	0.0868809i	0.00842602	−	0.00707027i	0.646991	+	0.762498i	$0.276027\pi$
$152$	0.127889	−	0.221510i	0.0103731	−	0.0179668i
$153$		0			0
$154$	−12.6887	−	21.9774i	−1.02248	−	1.77099i
$155$	−2.73783	−	0.996487i	−0.219907	−	0.0800398i
$156$		0			0
$157$	10.2083	+	8.56575i	0.814708	+	0.683621i	0.951727	−	0.306947i	$-0.0993075\pi$
$157$	10.2083	+	8.56575i	0.814708	+	0.683621i	−0.137018	+	0.990568i	$0.543752\pi$
$158$	26.2913	−	9.56926i	2.09163	−	0.761289i
$159$		0			0
$160$	0.373455	+	2.11797i	0.0295242	+	0.167440i
$161$	19.7023			1.55276
$162$		0			0
$163$	−9.76382			−0.764762			−0.382381	−	0.924005i	$-0.624896\pi$
$163$	−9.76382			−0.764762			−0.382381	+	0.924005i	$0.624896\pi$
$164$	−5.90033	−	33.4624i	−0.460738	−	2.61298i
$165$		0			0
$166$	3.59240	−	1.30753i	0.278824	−	0.101484i
$167$	2.73783	+	2.29731i	0.211859	+	0.177771i	0.742542	−	0.669799i	$-0.233620\pi$
$167$	2.73783	+	2.29731i	0.211859	+	0.177771i	−0.530683	+	0.847571i	$0.678064\pi$
$168$		0			0
$169$	7.73055	+	2.81369i	0.594658	+	0.216438i
$170$	1.77719	+	3.07818i	0.136304	+	0.236086i
$171$		0			0
$172$	1.29813	−	2.24843i	0.0989817	−	0.171441i
$173$	−14.3760	+	12.0629i	−1.09299	+	0.917124i	−0.996934	−	0.0782525i	$-0.975066\pi$
$173$	−14.3760	+	12.0629i	−1.09299	+	0.917124i	−0.0960521	+	0.995376i	$0.530622\pi$
$174$		0			0
$175$	2.67886	−	15.1926i	0.202503	−	1.14845i
$176$	3.58037	−	20.3053i	0.269881	−	1.53057i
$177$		0			0
$178$	−30.7879	+	25.8341i	−2.30765	+	1.93635i
$179$	−2.54189	+	4.40268i	−0.189990	+	0.329072i	−0.945247	−	0.326357i	$-0.894179\pi$
$179$	−2.54189	+	4.40268i	−0.189990	+	0.329072i	0.755257	+	0.655429i	$0.227512\pi$
$180$		0			0
$181$	−3.57532	−	6.19264i	−0.265752	−	0.460295i	0.702009	−	0.712168i	$-0.252287\pi$
$181$	−3.57532	−	6.19264i	−0.265752	−	0.460295i	−0.967760	+	0.251873i	$0.918953\pi$
$182$	16.7738	+	6.10516i	1.24336	+	0.452544i
$183$		0			0
$184$	28.5612	+	23.9657i	2.10556	+	1.76678i
$185$	1.58125	−	0.575529i	0.116256	−	0.0423137i
$186$		0			0
$187$	−1.61809	−	9.17664i	−0.118326	−	0.671062i
$188$	42.6168			3.10815
$189$		0			0
$190$	0.0496299			0.00360053
$191$	1.82501	+	10.3501i	0.132053	+	0.748909i	0.976867	+	0.213849i	$0.0686000\pi$
$191$	1.82501	+	10.3501i	0.132053	+	0.748909i	−0.844814	+	0.535060i	$0.820289\pi$
$192$		0			0
$193$	9.53121	−	3.46908i	0.686072	−	0.249710i	0.0246193	−	0.999697i	$-0.492163\pi$
$193$	9.53121	−	3.46908i	0.686072	−	0.249710i	0.661452	+	0.749987i	$0.269940\pi$
$194$	−36.1673	−	30.3480i	−2.59666	−	2.17886i
$195$		0			0
$196$	−14.1420	−	5.14728i	−1.01014	−	0.367663i
$197$	7.04189	+	12.1969i	0.501714	+	0.868994i	0.999998	+	0.00198008i	$0.000630281\pi$
$197$	7.04189	+	12.1969i	0.501714	+	0.868994i	−0.498284	+	0.867014i	$0.666036\pi$
$198$		0			0
$199$	−5.13816	+	8.89955i	−0.364234	+	0.630872i	−0.988653	−	0.150218i	$-0.952003\pi$
$199$	−5.13816	+	8.89955i	−0.364234	+	0.630872i	0.624419	+	0.781090i	$0.285336\pi$
$200$	22.3635	−	18.7652i	1.58134	−	1.32690i
$201$		0			0
$202$	3.99525	−	22.6582i	0.281105	−	1.59423i
$203$	3.68345	−	20.8899i	0.258527	−	1.46618i
$204$		0			0
$205$	2.76083	−	2.31661i	0.192825	−	0.161799i
$206$	0.330222	−	0.571962i	0.0230077	−	0.0398505i
$207$		0			0
$208$	7.25150	+	12.5600i	0.502801	+	0.870877i
$209$	−0.122264	−	0.0445003i	−0.00845715	−	0.00307815i
$210$		0			0
$211$	−5.47178	−	4.59137i	−0.376693	−	0.316083i	0.434710	−	0.900571i	$-0.356851\pi$
$211$	−5.47178	−	4.59137i	−0.376693	−	0.316083i	−0.811403	+	0.584488i	$0.801295\pi$
$212$	20.5535	−	7.48086i	1.41162	−	0.513788i
$213$		0			0
$214$	1.77719	+	10.0789i	0.121486	+	0.688982i
$215$	0.275378			0.0187806
$216$		0			0
$217$	20.0915			1.36390
$218$	2.37598	+	13.4749i	0.160922	+	0.912633i
$219$		0			0
$220$	6.02481	−	2.19285i	0.406193	−	0.147842i
$221$	5.02094	+	4.21307i	0.337745	+	0.283402i
$222$		0			0
$223$	9.71213	+	3.53493i	0.650373	+	0.236716i	0.646074	−	0.763275i	$-0.276410\pi$
$223$	9.71213	+	3.53493i	0.650373	+	0.236716i	0.00429825	+	0.999991i	$0.498632\pi$
$224$	−7.41534	−	12.8438i	−0.495459	−	0.858159i
$225$		0			0
$226$	−1.75237	+	3.03520i	−0.116566	+	0.201899i
$227$	9.97565	−	8.37057i	0.662107	−	0.555574i	−0.248610	−	0.968604i	$-0.579974\pi$
$227$	9.97565	−	8.37057i	0.662107	−	0.555574i	0.910718	+	0.413030i	$0.135529\pi$
$228$		0			0
$229$	−4.87939	+	27.6724i	−0.322439	+	1.82864i	0.204655	+	0.978834i	$0.434393\pi$
$229$	−4.87939	+	27.6724i	−0.322439	+	1.82864i	−0.527093	+	0.849807i	$0.676718\pi$
$230$	−1.25624	+	7.12452i	−0.0828343	+	0.469777i
$231$		0			0
$232$	30.7499	−	25.8022i	2.01883	−	1.69400i
$233$	−6.95723	+	12.0503i	−0.455784	+	0.789440i	−0.998733	−	0.0503252i	$-0.983974\pi$
$233$	−6.95723	+	12.0503i	−0.455784	+	0.789440i	0.542949	+	0.839765i	$0.317308\pi$
$234$		0			0
$235$	2.26011	+	3.91463i	0.147434	+	0.255363i
$236$	−35.3692	−	12.8733i	−2.30234	−	0.837982i
$237$		0			0
$238$	−18.7763	−	15.7552i	−1.21709	−	1.02126i
$239$	−14.1138	+	5.13701i	−0.912946	+	0.332285i	−0.755429	−	0.655231i	$-0.772571\pi$
$239$	−14.1138	+	5.13701i	−0.912946	+	0.332285i	−0.157518	+	0.987516i	$0.550349\pi$
$240$		0			0
$241$	−2.25284	−	12.7765i	−0.145118	−	0.823006i	−0.967272	−	0.253741i	$-0.918339\pi$
$241$	−2.25284	−	12.7765i	−0.145118	−	0.823006i	0.822154	−	0.569265i	$-0.192772\pi$
$242$	3.42427			0.220120
$243$		0			0
$244$	−5.59627			−0.358264
$245$	−0.277189	−	1.57202i	−0.0177089	−	0.100432i
$246$		0			0
$247$	0.0859997	−	0.0313013i	0.00547203	−	0.00199165i
$248$	29.1254	+	24.4391i	1.84947	+	1.55189i
$249$		0			0
$250$	10.8897	+	3.96351i	0.688722	+	0.250674i
$251$	0.436289	+	0.755675i	0.0275383	+	0.0476978i	0.879466	−	0.475961i	$-0.157900\pi$
$251$	0.436289	+	0.755675i	0.0275383	+	0.0476978i	−0.851928	+	0.523659i	$0.824567\pi$
$252$		0			0
$253$	9.48293	−	16.4249i	0.596186	−	1.03263i
$254$	12.8760	−	10.8042i	0.807911	−	0.677918i
$255$		0			0
$256$	−5.29679	+	30.0396i	−0.331049	+	1.87747i
$257$	−0.794730	+	4.50714i	−0.0495739	+	0.281147i	−0.999510	−	0.0312963i	$-0.990036\pi$
$257$	−0.794730	+	4.50714i	−0.0495739	+	0.281147i	0.949936	+	0.312444i	$0.101148\pi$
$258$		0			0
$259$	−8.88919	+	7.45891i	−0.552347	+	0.463474i
$260$	−2.25490	+	3.90560i	−0.139843	+	0.242215i
$261$		0			0
$262$	16.0039	+	27.7195i	0.988722	+	1.71252i
$263$	4.03849	+	1.46989i	0.249024	+	0.0906372i	0.463516	−	0.886088i	$-0.346588\pi$
$263$	4.03849	+	1.46989i	0.249024	+	0.0906372i	−0.214493	+	0.976726i	$0.568810\pi$
$264$		0			0
$265$	1.77719	+	1.49124i	0.109172	+	0.0916061i
$266$	−0.321604	+	0.117054i	−0.0197188	+	0.00717706i
$267$		0			0
$268$	7.66637	+	43.4782i	0.468298	+	2.65585i
$269$	−12.1257			−0.739315			−0.369657	−	0.929168i	$-0.620525\pi$
$269$	−12.1257			−0.739315			−0.369657	+	0.929168i	$0.620525\pi$
$270$		0			0
$271$	−0.319955			−0.0194359			−0.00971795	−	0.999953i	$-0.503093\pi$
$271$	−0.319955			−0.0194359			−0.00971795	+	0.999953i	$0.503093\pi$
$272$	−3.45811	−	19.6119i	−0.209679	−	1.18915i
$273$		0			0
$274$	−25.2592	+	9.19361i	−1.52597	+	0.555406i
$275$	−11.3760	−	9.54558i	−0.685998	−	0.575620i
$276$		0			0
$277$	25.2037	+	9.17339i	1.51434	+	0.551175i	0.959728	−	0.280932i	$-0.0906435\pi$
$277$	25.2037	+	9.17339i	1.51434	+	0.551175i	0.554615	+	0.832107i	$0.312866\pi$
$278$	−9.44609	−	16.3611i	−0.566539	−	0.981274i
$279$		0			0
$280$	4.60947	−	7.98384i	0.275469	−	0.477126i
$281$	−20.4388	+	17.1502i	−1.21928	+	1.02310i	−0.220415	+	0.975406i	$0.570741\pi$
$281$	−20.4388	+	17.1502i	−1.21928	+	1.02310i	−0.998862	+	0.0476892i	$0.984814\pi$
$282$		0			0
$283$	−1.61381	+	9.15236i	−0.0959309	+	0.544051i	0.898527	+	0.438918i	$0.144638\pi$
$283$	−1.61381	+	9.15236i	−0.0959309	+	0.544051i	−0.994458	+	0.105133i	$0.966473\pi$
$284$	−9.06283	+	51.3979i	−0.537780	+	3.04990i
$285$		0			0
$286$	13.1630	−	11.0450i	0.778343	−	0.653107i
$287$	−12.4265	+	21.5233i	−0.733512	+	1.27048i
$288$		0			0
$289$	4.00000	+	6.92820i	0.235294	+	0.407541i
$290$	7.31908	+	2.66393i	0.429791	+	0.156431i
$291$		0			0
$292$	−27.8273	−	23.3499i	−1.62847	−	1.36645i
$293$	−18.4547	+	6.71696i	−1.07814	+	0.392409i	−0.819213	−	0.573489i	$-0.805590\pi$
$293$	−18.4547	+	6.71696i	−1.07814	+	0.392409i	−0.258922	+	0.965898i	$0.583367\pi$
$294$		0			0
$295$	−0.693249	−	3.93161i	−0.0403625	−	0.228907i
$296$	−21.9590			−1.27634
$297$		0			0
$298$	−10.7716			−0.623980
$299$	2.31655	+	13.1378i	0.133970	+	0.759780i
$300$		0			0
$301$	−1.78446	+	0.649491i	−0.102855	+	0.0374361i
$302$	−0.262174	−	0.219990i	−0.0150864	−	0.0126590i
$303$		0			0
$304$	−0.261297	−	0.0951042i	−0.0149864	−	0.00545460i
$305$	−0.296789	−	0.514054i	−0.0169941	−	0.0294346i
$306$		0			0
$307$	−14.1716	+	24.5459i	−0.808815	+	1.40091i	0.104870	+	0.994486i	$0.466557\pi$
$307$	−14.1716	+	24.5459i	−0.808815	+	1.40091i	−0.913685	+	0.406423i	$0.866776\pi$
$308$	−33.8692	+	28.4196i	−1.92988	+	1.61936i
$309$		0			0
$310$	−1.28106	+	7.26525i	−0.0727593	+	0.412638i
$311$	0.355037	−	2.01352i	0.0201323	−	0.114176i	−0.973086	−	0.230444i	$-0.925982\pi$
$311$	0.355037	−	2.01352i	0.0201323	−	0.114176i	0.993218	+	0.116268i	$0.0370932\pi$
$312$		0			0
$313$	6.44356	−	5.40679i	0.364212	−	0.305610i	−0.442255	−	0.896889i	$-0.645821\pi$
$313$	6.44356	−	5.40679i	0.364212	−	0.305610i	0.806467	+	0.591279i	$0.201377\pi$
$314$	16.8712	−	29.2218i	0.952099	−	1.64908i
$315$		0			0
$316$	−24.3726	−	42.2145i	−1.37106	−	2.37475i
$317$	29.2511	+	10.6465i	1.64290	+	0.597968i	0.987543	−	0.157347i	$-0.0502942\pi$
$317$	29.2511	+	10.6465i	1.64290	+	0.597968i	0.655361	+	0.755316i	$0.272516\pi$
$318$		0			0
$319$	−15.6420	−	13.1252i	−0.875785	−	0.734871i
$320$	−0.720285	+	0.262162i	−0.0402652	+	0.0146553i
$321$		0			0
$322$	−8.66297	−	49.1301i	−0.482768	−	2.73792i
$323$	−0.125667			−0.00699231
$324$		0			0
$325$	10.4456			0.579419
$326$	4.29308	+	24.3473i	0.237772	+	1.34847i
$327$		0			0
$328$	−44.1946	+	16.0855i	−2.44024	+	0.888175i
$329$	−23.8785	−	20.0364i	−1.31646	−	1.10465i
$330$		0			0
$331$	−29.1596	−	10.6132i	−1.60275	−	0.583355i	−0.622766	−	0.782408i	$-0.713991\pi$
$331$	−29.1596	−	10.6132i	−1.60275	−	0.583355i	−0.979989	+	0.199053i	$0.936213\pi$
$332$	−3.33022	−	5.76811i	−0.182770	−	0.316566i
$333$		0			0
$334$	4.52481	−	7.83721i	0.247587	−	0.428833i
$335$	−3.58718	+	3.01000i	−0.195989	+	0.164454i
$336$		0			0
$337$	4.12061	−	23.3692i	0.224464	−	1.27300i	−0.639243	−	0.769005i	$-0.720752\pi$
$337$	4.12061	−	23.3692i	0.224464	−	1.27300i	0.863707	−	0.503995i	$-0.168137\pi$
$338$	3.61721	−	20.5142i	0.196750	−	1.11583i
$339$		0			0
$340$	4.74376	−	3.98048i	0.257266	−	0.215872i
$341$	9.67024	−	16.7494i	0.523673	−	0.907028i
$342$		0			0
$343$	−5.78952	−	10.0277i	−0.312604	−	0.541447i
$344$	−3.37686	−	1.22908i	−0.182068	−	0.0662673i
$345$		0			0
$346$	36.4013	+	30.5443i	1.95694	+	1.64207i
$347$	−1.69934	+	0.618509i	−0.0912254	+	0.0332033i	−0.387230	−	0.921983i	$-0.626568\pi$
$347$	−1.69934	+	0.618509i	−0.0912254	+	0.0332033i	0.296004	+	0.955187i	$0.404346\pi$
$348$		0			0
$349$	2.65002	+	15.0290i	0.141852	+	0.804483i	0.969841	+	0.243739i	$0.0783739\pi$
$349$	2.65002	+	15.0290i	0.141852	+	0.804483i	−0.827989	+	0.560744i	$0.810515\pi$
$350$	−39.0624			−2.08797
$351$		0			0
$352$	−14.2763			−0.760930
$353$	5.62314	+	31.8904i	0.299290	+	1.69736i	0.649237	+	0.760586i	$0.275088\pi$
$353$	5.62314	+	31.8904i	0.299290	+	1.69736i	−0.349947	+	0.936769i	$0.613801\pi$
$354$		0			0
$355$	−5.20187	+	1.89332i	−0.276086	+	0.100487i
$356$	53.6396	+	45.0089i	2.84289	+	2.38547i
$357$		0			0
$358$	12.0963	+	4.40268i	0.639308	+	0.232689i
$359$	−0.957234	−	1.65798i	−0.0505209	−	0.0875047i	0.839659	−	0.543114i	$-0.182755\pi$
$359$	−0.957234	−	1.65798i	−0.0505209	−	0.0875047i	−0.890180	+	0.455609i	$0.849421\pi$
$360$		0			0
$361$	9.49912	−	16.4530i	0.499954	−	0.865945i
$362$	−13.8701	+	11.6384i	−0.728994	+	0.611698i
$363$		0			0
$364$	5.40033	−	30.6268i	0.283054	−	1.60528i
$365$	0.669063	−	3.79444i	0.0350203	−	0.198610i
$366$		0			0
$367$	−20.5797	+	17.2684i	−1.07425	+	0.901402i	−0.995431	−	0.0954866i	$-0.969559\pi$
$367$	−20.5797	+	17.2684i	−1.07425	+	0.901402i	−0.0788188	+	0.996889i	$0.525115\pi$
$368$	20.2665	−	35.1026i	1.05646	−	1.82985i
$369$		0			0
$370$	−2.13041	−	3.68999i	−0.110755	−	0.191833i
$371$	−15.0334	−	5.47172i	−0.780497	−	0.284078i
$372$		0			0
$373$	11.3682	+	9.53909i	0.588625	+	0.493915i	0.887767	−	0.460294i	$-0.152256\pi$
$373$	11.3682	+	9.53909i	0.588625	+	0.493915i	−0.299142	+	0.954209i	$0.596700\pi$
$374$	−22.1716	+	8.06980i	−1.14647	+	0.417279i
$375$		0			0
$376$	−10.2430	−	58.0912i	−0.528244	−	2.99582i
$377$	14.3628			0.739721
$378$		0			0
$379$	−33.7870			−1.73552			−0.867762	−	0.496980i	$-0.834442\pi$
$379$	−33.7870			−1.73552			−0.867762	+	0.496980i	$0.834442\pi$
$380$	−0.0150147	−	0.0851529i	−0.000770240	−	0.00436825i
$381$		0			0
$382$	25.0069	−	9.10175i	1.27946	−	0.465686i
$383$	7.10813	+	5.96443i	0.363208	+	0.304768i	0.806068	−	0.591823i	$-0.201592\pi$
$383$	7.10813	+	5.96443i	0.363208	+	0.304768i	−0.442860	+	0.896591i	$0.646036\pi$
$384$		0			0
$385$	−4.40673	−	1.60392i	−0.224588	−	0.0817432i
$386$	−12.8414	−	22.2419i	−0.653608	−	1.13208i
$387$		0			0
$388$	−41.1279	+	71.2357i	−2.08796	+	3.61644i
$389$	12.2404	−	10.2709i	0.620610	−	0.520754i	−0.277385	−	0.960759i	$-0.589468\pi$
$389$	12.2404	−	10.2709i	0.620610	−	0.520754i	0.897995	+	0.440005i	$0.145023\pi$
$390$		0			0
$391$	3.18092	−	18.0399i	0.160866	−	0.912317i
$392$	−3.61721	+	20.5142i	−0.182697	+	1.03612i
$393$		0			0
$394$	27.3182	−	22.9227i	1.37627	−	1.15483i
$395$	2.58512	−	4.47756i	0.130072	−	0.225291i
$396$		0			0
$397$	−9.85251	−	17.0650i	−0.494483	−	0.856470i	0.505496	−	0.862829i	$-0.331309\pi$
$397$	−9.85251	−	17.0650i	−0.494483	−	0.856470i	−0.999980	+	0.00635841i	$0.997976\pi$
$398$	24.4513	+	8.89955i	1.22563	+	0.446094i
$399$		0			0
$400$	−24.3123	−	20.4004i	−1.21561	−	1.02002i
$401$	1.07873	−	0.392624i	0.0538690	−	0.0196067i	−0.314945	−	0.949110i	$-0.601986\pi$
$401$	1.07873	−	0.392624i	0.0538690	−	0.0196067i	0.368814	+	0.929503i	$0.379764\pi$
$402$		0			0
$403$	2.36231	+	13.3973i	0.117675	+	0.667369i
$404$	−40.0847			−1.99429
$405$		0			0
$406$	−53.7110			−2.66563
$407$	1.93969	+	11.0005i	0.0961470	+	0.545277i
$408$		0			0
$409$	2.91400	−	1.06061i	0.144088	−	0.0524438i	−0.268969	−	0.963149i	$-0.586683\pi$
$409$	2.91400	−	1.06061i	0.144088	−	0.0524438i	0.413057	+	0.910705i	$0.364461\pi$
$410$	−6.99067	−	5.86587i	−0.345244	−	0.289694i
$411$		0			0
$412$	−1.08125	−	0.393544i	−0.0532695	−	0.0193885i
$413$	13.7652	+	23.8420i	0.677340	+	1.17319i
$414$		0			0
$415$	0.353226	−	0.611806i	0.0173392	−	0.0300324i
$416$	7.69253	−	6.45480i	0.377157	−	0.316473i
$417$		0			0
$418$	−0.0572085	+	0.324446i	−0.00279816	+	0.0158692i
$419$	−6.15570	+	34.9107i	−0.300725	+	1.70550i	0.342247	+	0.939610i	$0.388812\pi$
$419$	−6.15570	+	34.9107i	−0.300725	+	1.70550i	−0.642973	+	0.765889i	$0.722299\pi$
$420$		0			0
$421$	7.06077	−	5.92469i	0.344121	−	0.288752i	−0.454303	−	0.890847i	$-0.650112\pi$
$421$	7.06077	−	5.92469i	0.344121	−	0.288752i	0.798424	+	0.602095i	$0.205667\pi$
$422$	−9.04323	+	15.6633i	−0.440218	+	0.762479i
$423$		0			0
$424$	−15.1373	−	26.2185i	−0.735131	−	1.27328i
$425$	−13.4782	−	4.90566i	−0.653788	−	0.237959i
$426$		0			0
$427$	3.13563	+	2.63111i	0.151744	+	0.127328i
$428$	16.7554	−	6.09845i	0.809901	−	0.294780i
$429$		0			0
$430$	−0.121082	−	0.686688i	−0.00583907	−	0.0331150i
$431$	−11.5794			−0.557758			−0.278879	−	0.960326i	$-0.589963\pi$
$431$	−11.5794			−0.557758			−0.278879	+	0.960326i	$0.589963\pi$
$432$		0			0
$433$	6.06511			0.291471			0.145735	−	0.989324i	$-0.453445\pi$
$433$	6.06511			0.291471			0.145735	+	0.989324i	$0.453445\pi$
$434$	−8.83409	−	50.1006i	−0.424050	−	2.40491i
$435$		0			0
$436$	22.4008	−	8.15322i	1.07280	−	0.390469i
$437$	−0.195937	−	0.164411i	−0.00937293	−	0.00786482i
$438$		0			0
$439$	−27.2567	−	9.92063i	−1.30089	−	0.473486i	−0.403605	−	0.914933i	$-0.632243\pi$
$439$	−27.2567	−	9.92063i	−1.30089	−	0.473486i	−0.897287	+	0.441448i	$0.854465\pi$
$440$	−4.43717	−	7.68540i	−0.211534	−	0.366387i
$441$		0			0
$442$	8.29813	−	14.3728i	0.394702	−	0.683644i
$443$	−23.6648	+	19.8571i	−1.12435	+	0.943440i	−0.998816	−	0.0486498i	$-0.984508\pi$
$443$	−23.6648	+	19.8571i	−1.12435	+	0.943440i	−0.125532	+	0.992090i	$0.540064\pi$
$444$		0			0
$445$	−1.28968	+	7.31412i	−0.0611366	+	0.346723i
$446$	4.54442	−	25.7727i	0.215184	−	1.22037i
$447$		0			0
$448$	4.04916	−	3.39765i	0.191305	−	0.160524i
$449$	−19.5410	+	33.8460i	−0.922197	+	1.59729i	−0.126190	+	0.992006i	$0.540275\pi$
$449$	−19.5410	+	33.8460i	−0.922197	+	1.59729i	−0.796008	+	0.605287i	$0.793059\pi$
$450$		0			0
$451$	11.9620	+	20.7188i	0.563268	+	0.975608i
$452$	5.73783	+	2.08840i	0.269885	+	0.0982300i
$453$		0			0
$454$	−25.2592	−	21.1950i	−1.18547	−	0.994731i
$455$	3.09967	−	1.12819i	0.145315	−	0.0528903i
$456$		0			0
$457$	−0.261297	−	1.48189i	−0.0122229	−	0.0693198i	0.978086	−	0.208200i	$-0.0667606\pi$
$457$	−0.261297	−	1.48189i	−0.0122229	−	0.0693198i	−0.990309	+	0.138881i	$0.955650\pi$
$458$	71.1498			3.32461
$459$		0			0
$460$	12.6040			0.587665
$461$	−4.55603	−	25.8385i	−0.212195	−	1.20342i	−0.885708	−	0.464243i	$-0.846326\pi$
$461$	−4.55603	−	25.8385i	−0.212195	−	1.20342i	0.673512	−	0.739176i	$-0.264785\pi$
$462$		0			0
$463$	−6.34895	+	2.31083i	−0.295061	+	0.107393i	−0.485309	−	0.874343i	$-0.661293\pi$
$463$	−6.34895	+	2.31083i	−0.295061	+	0.107393i	0.190248	+	0.981736i	$0.439071\pi$
$464$	−33.4295	−	28.0507i	−1.55192	−	1.30222i
$465$		0			0
$466$	33.1079	+	12.0503i	1.53369	+	0.558219i
$467$	16.8735	+	29.2257i	0.780810	+	1.35240i	0.931470	+	0.363818i	$0.118527\pi$
$467$	16.8735	+	29.2257i	0.780810	+	1.35240i	−0.150660	+	0.988586i	$0.548140\pi$
$468$		0			0
$469$	16.1459	−	27.9655i	0.745548	−	1.29133i
$470$	8.76786	−	7.35710i	0.404431	−	0.339358i
$471$		0			0
$472$	−9.04664	+	51.3060i	−0.416405	+	2.36155i
$473$	−0.317429	+	1.80023i	−0.0145954	+	0.0827746i
$474$		0			0
$475$	−0.153419	+	0.128734i	−0.00703934	+	0.00590671i
$476$	−21.3516	+	36.9821i	−0.978651	+	1.69507i
$477$		0			0
$478$	19.0155	+	32.9358i	0.869748	+	1.50645i
$479$	10.4556	+	3.80552i	0.477728	+	0.173879i	0.569650	−	0.821887i	$-0.307079\pi$
$479$	10.4556	+	3.80552i	0.477728	+	0.173879i	−0.0919220	+	0.995766i	$0.529301\pi$
$480$		0			0
$481$	−6.01889	−	5.05044i	−0.274438	−	0.230280i
$482$	−30.8692	+	11.2355i	−1.40605	+	0.511761i
$483$		0			0
$484$	−1.03596	−	5.87522i	−0.0470891	−	0.267055i
$485$	−8.72462			−0.396165
$486$		0			0
$487$	−4.74691			−0.215103			−0.107552	−	0.994200i	$-0.534301\pi$
$487$	−4.74691			−0.215103			−0.107552	+	0.994200i	$0.534301\pi$
$488$	1.34507	+	7.62830i	0.0608887	+	0.345317i
$489$		0			0
$490$	−3.79813	+	1.38241i	−0.171582	+	0.0624508i
$491$	−17.1138	−	14.3602i	−0.772335	−	0.648066i	0.168971	−	0.985621i	$-0.445956\pi$
$491$	−17.1138	−	14.3602i	−0.772335	−	0.648066i	−0.941306	+	0.337555i	$0.890400\pi$
$492$		0			0
$493$	−18.5326	−	6.74530i	−0.834664	−	0.303793i
$494$	−0.115867	−	0.200688i	−0.00521310	−	0.00902936i
$495$		0			0
$496$	20.6668	−	35.7960i	0.927969	−	1.60729i
$497$	29.2429	−	24.5377i	1.31172	−	1.10067i
$498$		0			0
$499$	−1.81655	+	10.3022i	−0.0813200	+	0.461189i	0.916770	+	0.399415i	$0.130787\pi$
$499$	−1.81655	+	10.3022i	−0.0813200	+	0.461189i	−0.998090	+	0.0617736i	$0.980324\pi$
$500$	3.50593	−	19.8831i	0.156790	−	0.889200i
$501$		0			0
$502$	1.69253	−	1.42020i	0.0755415	−	0.0633868i
$503$	12.5209	−	21.6869i	0.558281	−	0.966972i	−0.439359	−	0.898312i	$-0.644794\pi$
$503$	12.5209	−	21.6869i	0.558281	−	0.966972i	0.997640	−	0.0686600i	$-0.0218723\pi$
$504$		0			0
$505$	−2.12583	−	3.68204i	−0.0945982	−	0.163849i
$506$	−45.1271	−	16.4249i	−2.00614	−	0.730176i
$507$		0			0
$508$	−22.4329	−	18.8234i	−0.995298	−	0.835154i
$509$	16.9731	−	6.17771i	0.752321	−	0.273822i	0.0627387	−	0.998030i	$-0.480017\pi$
$509$	16.9731	−	6.17771i	0.752321	−	0.273822i	0.689582	+	0.724208i	$0.257794\pi$
$510$		0			0
$511$	4.61381	+	26.1662i	0.204103	+	1.15752i
$512$	50.5553			2.23425
$513$		0			0
$514$	11.5885			0.511148
$515$	−0.0211929	−	0.120191i	−0.000933872	−	0.00529625i
$516$		0			0
$517$	−28.1964	+	10.2627i	−1.24008	+	0.451351i
$518$	22.5082	+	18.8866i	0.988954	+	0.829831i
$519$		0			0
$520$	5.86571	+	2.13495i	0.257229	+	0.0936236i
$521$	−12.9791	−	22.4804i	−0.568623	−	0.984883i	−0.996703	−	0.0811425i	$-0.974143\pi$
$521$	−12.9791	−	22.4804i	−0.568623	−	0.984883i	0.428080	−	0.903741i	$-0.359190\pi$
$522$		0			0
$523$	−12.7973	+	22.1655i	−0.559585	+	0.969230i	0.437946	+	0.899001i	$0.355706\pi$
$523$	−12.7973	+	22.1655i	−0.559585	+	0.969230i	−0.997531	+	0.0702283i	$0.977627\pi$
$524$	42.7183	−	35.8449i	1.86616	−	1.56589i
$525$		0			0
$526$	1.88965	−	10.7168i	0.0823928	−	0.467273i
$527$	3.24376	−	18.3963i	0.141300	−	0.801353i
$528$		0			0
$529$	10.9422	−	9.18161i	0.475749	−	0.399201i
$530$	2.93717	−	5.08732i	0.127582	−	0.220979i
$531$		0			0
$532$	0.298133	+	0.516382i	0.0129257	+	0.0223880i
$533$	−15.8131	−	5.75552i	−0.684943	−	0.249299i
$534$		0			0
$535$	1.44878	+	1.21567i	0.0626361	+	0.0525579i
$536$	57.4227	−	20.9001i	2.48028	−	0.902749i
$537$		0			0
$538$	5.33157	+	30.2368i	0.229860	+	1.30360i
$539$	10.5963			0.456414
$540$		0			0
$541$	27.8476			1.19726			0.598631	−	0.801025i	$-0.295712\pi$
$541$	27.8476			1.19726			0.598631	+	0.801025i	$0.295712\pi$
$542$	0.140682	+	0.797847i	0.00604281	+	0.0342705i
$543$		0			0
$544$	−12.9572	+	4.71605i	−0.555537	+	0.202199i
$545$	1.93692	+	1.62527i	0.0829685	+	0.0696188i
$546$		0			0
$547$	5.55216	+	2.02082i	0.237393	+	0.0864040i	0.457977	−	0.888964i	$-0.348574\pi$
$547$	5.55216	+	2.02082i	0.237393	+	0.0864040i	−0.220584	+	0.975368i	$0.570796\pi$
$548$	23.4158	+	40.5574i	1.00027	+	1.73253i
$549$		0			0
$550$	−18.8011	+	32.5645i	−0.801683	+	1.38856i
$551$	−0.210952	+	0.177009i	−0.00898684	+	0.00754086i
$552$		0			0
$553$	−6.19119	+	35.1120i	−0.263276	+	1.49311i
$554$	11.7931	−	66.8819i	0.501040	−	2.84154i
$555$		0			0
$556$	−25.2139	+	21.1570i	−1.06931	+	0.897257i
$557$	13.3525	−	23.1272i	0.565764	−	0.979932i	−0.431214	−	0.902250i	$-0.641915\pi$
$557$	13.3525	−	23.1272i	0.565764	−	0.979932i	0.996978	−	0.0776824i	$-0.0247520\pi$
$558$		0			0
$559$	−0.642903	−	1.11354i	−0.0271919	−	0.0470978i
$560$	−9.41787	−	3.42782i	−0.397978	−	0.144852i
$561$		0			0
$562$	51.7529	+	43.4258i	2.18306	+	1.83181i
$563$	33.8876	−	12.3341i	1.42819	−	0.519819i	0.491779	−	0.870720i	$-0.336347\pi$
$563$	33.8876	−	12.3341i	1.42819	−	0.519819i	0.936413	+	0.350901i	$0.114125\pi$
$564$		0			0
$565$	0.112463	+	0.637812i	0.00473137	+	0.0268329i
$566$	23.5321			0.989127
$567$		0			0
$568$	72.2390			3.03108
$569$	1.57104	+	8.90982i	0.0658615	+	0.373519i	0.999868	+	0.0162624i	$0.00517671\pi$
$569$	1.57104	+	8.90982i	0.0658615	+	0.373519i	−0.934006	+	0.357257i	$0.883712\pi$
$570$		0			0
$571$	−28.7349	+	10.4586i	−1.20252	+	0.437681i	−0.864102	−	0.503316i	$-0.832113\pi$
$571$	−28.7349	+	10.4586i	−1.20252	+	0.437681i	−0.338415	+	0.940997i	$0.609891\pi$
$572$	−22.9329	−	19.2430i	−0.958872	−	0.804589i
$573$		0			0
$574$	59.1348	+	21.5233i	2.46824	+	0.898366i
$575$	−14.5967	−	25.2823i	−0.608726	−	1.05434i
$576$		0			0
$577$	12.5744	−	21.7796i	0.523481	−	0.906696i	−0.476146	−	0.879367i	$-0.657966\pi$
$577$	12.5744	−	21.7796i	0.523481	−	0.906696i	0.999626	−	0.0273292i	$-0.00870022\pi$
$578$	15.5175	−	13.0208i	0.645445	−	0.541592i
$579$		0			0
$580$	2.35638	−	13.3637i	0.0978434	−	0.554898i
$581$	−0.845952	+	4.79763i	−0.0350960	+	0.199039i
$582$		0			0
$583$	−11.7973	+	9.89907i	−0.488592	+	0.409978i
$584$	−25.1400	+	43.5437i	−1.04030	+	1.80185i
$585$		0			0
$586$	24.8640	+	43.0656i	1.02712	+	1.77903i
$587$	19.6147	+	7.13916i	0.809585	+	0.294665i	0.713452	−	0.700704i	$-0.247131\pi$
$587$	19.6147	+	7.13916i	0.809585	+	0.294665i	0.0961324	+	0.995369i	$0.469353\pi$
$588$		0			0
$589$	−0.199807	−	0.167658i	−0.00823292	−	0.00690824i
$590$	−9.49912	+	3.45740i	−0.391073	+	0.142339i
$591$		0			0
$592$	4.14543	+	23.5099i	0.170376	+	0.966251i
$593$	−15.6212			−0.641488			−0.320744	−	0.947166i	$-0.603933\pi$
$593$	−15.6212			−0.641488			−0.320744	+	0.947166i	$0.603933\pi$
$594$		0			0
$595$	−4.52940			−0.185687
$596$	3.25877	+	18.4814i	0.133484	+	0.757028i
$597$		0			0
$598$	31.7422	−	11.5532i	1.29803	−	0.472446i
$599$	0.343426	+	0.288169i	0.0140320	+	0.0117742i	0.649777	−	0.760125i	$-0.274862\pi$
$599$	0.343426	+	0.288169i	0.0140320	+	0.0117742i	−0.635745	+	0.771899i	$0.719307\pi$
$600$		0			0
$601$	16.6065	+	6.04428i	0.677395	+	0.246551i	0.657728	−	0.753255i	$-0.271517\pi$
$601$	16.6065	+	6.04428i	0.677395	+	0.246551i	0.0196662	+	0.999807i	$0.493740\pi$
$602$	2.40420	+	4.16420i	0.0979879	+	0.169720i
$603$		0			0
$604$	−0.298133	+	0.516382i	−0.0121309	+	0.0210113i
$605$	0.484737	−	0.406743i	0.0197074	−	0.0165364i
$606$		0			0
$607$	4.54933	−	25.8005i	0.184651	−	1.04721i	−0.741751	−	0.670675i	$-0.766004\pi$
$607$	4.54933	−	25.8005i	0.184651	−	1.04721i	0.926402	−	0.376535i	$-0.122884\pi$
$608$	−0.0334331	+	0.189608i	−0.00135589	+	0.00768963i
$609$		0			0
$610$	−1.15136	+	0.966105i	−0.0466172	+	0.0391165i
$611$	10.5530	−	18.2784i	0.426930	−	0.739465i
$612$		0			0
$613$	−7.27719	−	12.6045i	−0.293923	−	0.509089i	0.680811	−	0.732459i	$-0.261628\pi$
$613$	−7.27719	−	12.6045i	−0.293923	−	0.509089i	−0.974734	+	0.223370i	$0.928294\pi$
$614$	67.4393	+	24.5459i	2.72163	+	0.990592i
$615$		0			0
$616$	46.8794	+	39.3365i	1.88883	+	1.58491i
$617$	13.1750	−	4.79531i	0.530405	−	0.193052i	−0.0629140	−	0.998019i	$-0.520039\pi$
$617$	13.1750	−	4.79531i	0.530405	−	0.193052i	0.593319	+	0.804967i	$0.297817\pi$
$618$		0			0
$619$	−5.50681	−	31.2307i	−0.221337	−	1.25527i	−0.869565	−	0.493819i	$-0.835600\pi$
$619$	−5.50681	−	31.2307i	−0.221337	−	1.25527i	0.648227	−	0.761447i	$-0.275511\pi$
$620$	12.8530			0.516188
$621$		0			0
$622$	−5.17705			−0.207581
$623$	−8.89352	−	50.4377i	−0.356311	−	2.02074i
$624$		0			0
$625$	−20.4513	+	7.44367i	−0.818052	+	0.297747i
$626$	−16.3157	−	13.6905i	−0.652105	−	0.547181i
$627$		0			0
$628$	−55.2418	−	20.1064i	−2.20439	−	0.802331i
$629$	5.39440	+	9.34337i	0.215089	+	0.372545i
$630$		0			0
$631$	19.2879	−	33.4077i	0.767840	−	1.32994i	−0.170892	−	0.985290i	$-0.554665\pi$
$631$	19.2879	−	33.4077i	0.767840	−	1.32994i	0.938732	−	0.344648i	$-0.112002\pi$
$632$	−51.6848	+	43.3687i	−2.05591	+	1.72512i
$633$		0			0
$634$	13.6869	−	77.6223i	0.543577	−	3.08278i
$635$	0.539363	−	3.05888i	0.0214040	−	0.121388i
$636$		0			0
$637$	−5.70961	+	4.79093i	−0.226223	+	0.189824i
$638$	−25.8516	+	44.7763i	−1.02348	+	1.77271i
$639$		0			0
$640$	3.12108	+	5.40587i	0.123372	+	0.213686i
$641$	−28.7704	−	10.4716i	−1.13636	−	0.413602i	−0.295764	−	0.955261i	$-0.595574\pi$
$641$	−28.7704	−	10.4716i	−1.13636	−	0.413602i	−0.840598	+	0.541659i	$0.817796\pi$
$642$		0			0
$643$	−26.2178	−	21.9994i	−1.03393	−	0.867570i	−0.0426164	−	0.999092i	$-0.513569\pi$
$643$	−26.2178	−	21.9994i	−1.03393	−	0.867570i	−0.991313	+	0.131521i	$0.958014\pi$
$644$	−81.6746	+	29.7271i	−3.21843	+	1.17141i
$645$		0			0
$646$	0.0552549	+	0.313366i	0.00217398	+	0.0123292i
$647$	12.8726			0.506073			0.253037	−	0.967457i	$-0.418571\pi$
$647$	12.8726			0.506073			0.253037	+	0.967457i	$0.418571\pi$
$648$		0			0
$649$	26.5012			1.04026
$650$	−4.59286	−	26.0474i	−0.180147	−	1.02166i
$651$		0			0
$652$	40.4752	−	14.7318i	1.58513	−	0.576941i
$653$	8.67096	+	7.27580i	0.339321	+	0.284724i	0.796485	−	0.604658i	$-0.206690\pi$
$653$	8.67096	+	7.27580i	0.339321	+	0.284724i	−0.457164	+	0.889382i	$0.651135\pi$
$654$		0			0
$655$	5.55809	+	2.02298i	0.217172	+	0.0790443i
$656$	25.5646	+	44.2793i	0.998132	+	1.72881i
$657$		0			0
$658$	−39.4641	+	68.3538i	−1.53847	+	2.66471i
$659$	10.5478	−	8.85067i	0.410885	−	0.344773i	−0.413798	−	0.910369i	$-0.635798\pi$
$659$	10.5478	−	8.85067i	0.410885	−	0.344773i	0.824683	+	0.565595i	$0.191354\pi$
$660$		0			0
$661$	−3.51930	+	19.9589i	−0.136885	+	0.776312i	0.836644	+	0.547747i	$0.184514\pi$
$661$	−3.51930	+	19.9589i	−0.136885	+	0.776312i	−0.973529	+	0.228565i	$0.926597\pi$
$662$	−13.6441	+	77.3795i	−0.530292	+	3.00744i
$663$		0			0
$664$	−7.06212	+	5.92582i	−0.274063	+	0.229966i
$665$	−0.0316221	+	0.0547710i	−0.00122625	+	0.00212393i
$666$		0			0
$667$	−20.0706	−	34.7633i	−0.777136	−	1.34604i
$668$	−14.8157	−	5.39246i	−0.573236	−	0.208641i
$669$		0			0
$670$	9.08306	+	7.62159i	0.350909	+	0.294448i
$671$	3.70264	−	1.34765i	0.142939	−	0.0520255i
$672$		0			0
$673$	−5.30406	−	30.0808i	−0.204457	−	1.15953i	−0.898293	−	0.439398i	$-0.855192\pi$
$673$	−5.30406	−	30.0808i	−0.204457	−	1.15953i	0.693836	−	0.720133i	$-0.255919\pi$
$674$	−60.0856			−2.31441
$675$		0			0
$676$	−36.2918			−1.39584
$677$	0.645840	+	3.66274i	0.0248217	+	0.140771i	0.994700	−	0.102819i	$-0.0327862\pi$
$677$	0.645840	+	3.66274i	0.0248217	+	0.140771i	−0.969878	+	0.243589i	$0.921675\pi$
$678$		0			0
$679$	56.5360	−	20.5774i	2.16965	−	0.789689i
$680$	−6.56599	−	5.50952i	−0.251794	−	0.211280i
$681$		0			0
$682$	−46.0185	−	16.7494i	−1.76214	−	0.641366i
$683$	−10.8735	−	18.8334i	−0.416061	−	0.720639i	0.579478	−	0.814988i	$-0.303256\pi$
$683$	−10.8735	−	18.8334i	−0.416061	−	0.720639i	−0.995539	+	0.0943487i	$0.969923\pi$
$684$		0			0
$685$	−2.48364	+	4.30179i	−0.0948950	+	0.164363i
$686$	−22.4598	+	18.8460i	−0.857518	+	0.719543i
$687$		0			0
$688$	−0.678396	+	3.84737i	−0.0258636	+	0.146680i
$689$	1.88103	−	10.6679i	0.0716617	−	0.406414i
$690$		0			0
$691$	−28.7993	+	24.1655i	−1.09558	+	0.919299i	−0.997120	−	0.0758425i	$-0.975835\pi$
$691$	−28.7993	+	24.1655i	−1.09558	+	0.919299i	−0.0984578	+	0.995141i	$0.531391\pi$
$692$	41.3940	−	71.6965i	1.57356	−	2.72549i
$693$		0			0
$694$	2.28952	+	3.96556i	0.0869088	+	0.150530i
$695$	−3.28059	−	1.19404i	−0.124440	−	0.0452924i
$696$		0			0
$697$	17.7010	+	14.8529i	0.670473	+	0.562593i
$698$	36.3114	−	13.2163i	1.37441	−	0.500243i
$699$		0			0
$700$	11.8177	+	67.0217i	0.446668	+	2.53318i
$701$	−23.3351			−0.881355			−0.440678	−	0.897665i	$-0.645262\pi$
$701$	−23.3351			−0.881355			−0.440678	+	0.897665i	$0.645262\pi$
$702$		0			0
$703$	0.150644			0.00568166
$704$	−0.883560	−	5.01092i	−0.0333004	−	0.188856i
$705$		0			0
$706$	77.0502	−	28.0440i	2.89982	−	1.05545i
$707$	22.4598	+	18.8460i	0.844686	+	0.708776i
$708$		0			0
$709$	−6.18227	−	2.25016i	−0.232180	−	0.0845066i	0.223310	−	0.974747i	$-0.428314\pi$
$709$	−6.18227	−	2.25016i	−0.232180	−	0.0845066i	−0.455490	+	0.890241i	$0.650536\pi$
$710$	7.00846	+	12.1390i	0.263023	+	0.455569i
$711$		0			0
$712$	48.4595	−	83.9343i	1.81610	−	3.14557i
$713$	29.1254	−	24.4391i	1.09076	−	0.915253i
$714$		0			0
$715$	0.551385	−	3.12706i	0.0206206	−	0.116945i
$716$	3.89440	−	22.0862i	0.145541	−	0.825402i
$717$		0			0
$718$	−3.71348	+	3.11598i	−0.138586	+	0.116287i
$719$	−8.41622	+	14.5773i	−0.313872	+	0.543642i	−0.979197	−	0.202911i	$-0.934960\pi$
$719$	−8.41622	+	14.5773i	−0.313872	+	0.543642i	0.665325	+	0.746554i	$0.268293\pi$
$720$		0			0
$721$	0.420807	+	0.728860i	0.0156717	+	0.0271442i
$722$	−45.2041	−	16.4530i	−1.68232	−	0.612316i
$723$		0			0
$724$	24.1648	+	20.2767i	0.898077	+	0.753576i
$725$	−29.5351	+	10.7499i	−1.09691	+	0.399241i
$726$		0			0
$727$	4.43882	+	25.1738i	0.164627	+	0.933644i	0.949449	+	0.313922i	$0.101643\pi$
$727$	4.43882	+	25.1738i	0.164627	+	0.933644i	−0.784822	+	0.619721i	$0.787246\pi$
$728$	−43.0455			−1.59537
$729$		0			0
$730$	−9.75608			−0.361089
$731$	0.306589	+	1.73875i	0.0113396	+	0.0643102i
$732$		0			0
$733$	13.9055	−	5.06120i	0.513613	−	0.186940i	−0.0721937	−	0.997391i	$-0.523000\pi$
$733$	13.9055	−	5.06120i	0.513613	−	0.186940i	0.585807	+	0.810451i	$0.300778\pi$
$734$	52.1095	+	43.7251i	1.92340	+	1.61392i
$735$		0			0
$736$	−26.3726	−	9.59883i	−0.972106	−	0.353818i
$737$	−15.5424	−	26.9202i	−0.572510	−	0.991616i
$738$		0			0
$739$	−4.59539	+	7.95945i	−0.169044	+	0.292793i	−0.938084	−	0.346408i	$-0.887401\pi$
$739$	−4.59539	+	7.95945i	−0.169044	+	0.292793i	0.769040	+	0.639201i	$0.220735\pi$
$740$	−5.68660	+	4.77163i	−0.209044	+	0.175408i
$741$		0			0
$742$	−7.03431	+	39.8936i	−0.258238	+	1.46454i
$743$	−7.71853	+	43.7740i	−0.283165	+	1.60591i	0.428600	+	0.903494i	$0.359007\pi$
$743$	−7.71853	+	43.7740i	−0.283165	+	1.60591i	−0.711766	+	0.702417i	$0.752104\pi$
$744$		0			0
$745$	−1.52481	+	1.27947i	−0.0558649	+	0.0468762i
$746$	18.7883	−	32.5423i	0.687890	−	1.19146i
$747$		0			0
$748$	20.5535	+	35.5997i	0.751510	+	1.30165i
$749$	−12.2554	−	4.46059i	−0.447801	−	0.162986i
$750$		0			0
$751$	−27.4290	−	23.0157i	−1.00090	−	0.839854i	−0.0137902	−	0.999905i	$-0.504390\pi$
$751$	−27.4290	−	23.0157i	−1.00090	−	0.839854i	−0.987109	+	0.160051i	$0.948834\pi$
$752$	−60.2602	+	21.9329i	−2.19746	+	0.799811i
$753$		0			0
$754$	−6.31521	−	35.8153i	−0.229986	−	1.30432i
$755$	−0.0632441			−0.00230169
$756$		0			0
$757$	−45.8976			−1.66818			−0.834088	−	0.551632i	$-0.814005\pi$
$757$	−45.8976			−1.66818			−0.834088	+	0.551632i	$0.814005\pi$
$758$	14.8559	+	84.2521i	0.539591	+	3.06017i
$759$		0			0
$760$	−0.112463	+	0.0409333i	−0.00407948	+	0.00148481i
$761$	28.4932	+	23.9086i	1.03288	+	0.866687i	0.991191	−	0.132444i	$-0.0422824\pi$
$761$	28.4932	+	23.9086i	1.03288	+	0.866687i	0.0416869	+	0.999131i	$0.486727\pi$
$762$		0			0
$763$	−16.3846	−	5.96351i	−0.593162	−	0.215893i
$764$	−23.1819	−	40.1522i	−0.838690	−	1.45265i
$765$		0			0
$766$	11.7476	−	20.3475i	0.424459	−	0.735185i
$767$	−14.2797	+	11.9821i	−0.515611	+	0.432649i
$768$		0			0
$769$	−6.65657	+	37.7513i	−0.240042	+	1.36135i	0.591688	+	0.806167i	$0.298462\pi$
$769$	−6.65657	+	37.7513i	−0.240042	+	1.36135i	−0.831730	+	0.555180i	$0.812649\pi$
$770$	−2.06196	+	11.6939i	−0.0743077	+	0.421420i
$771$		0			0
$772$	−34.2768	+	28.7616i	−1.23365	+	1.03515i
$773$	26.4136	−	45.7497i	0.950031	−	1.64550i	0.204680	−	0.978829i	$-0.434385\pi$
$773$	26.4136	−	45.7497i	0.950031	−	1.64550i	0.745351	−	0.666673i	$-0.232282\pi$
$774$		0			0
$775$	−14.8851	−	25.7817i	−0.534687	−	0.926106i
$776$	106.987	+	38.9401i	3.84061	+	1.39787i
$777$		0			0
$778$	−30.9937	−	26.0068i	−1.11118	−	0.932388i
$779$	0.303186	−	0.110351i	0.0108628	−	0.00395372i
$780$		0			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)

\(f(q)\)	\(=\)	\(q+(-0.439693 - 2.49362i) q^{2} +(-4.14543 + 1.50881i) q^{4} +(-0.358441 - 0.300767i) q^{5} +(3.03209 + 1.10359i) q^{7} +(3.05303 + 5.28801i) q^{8} +(-0.592396 + 1.02606i) q^{10} +(2.37939 - 1.99654i) q^{11} +(-0.379385 + 2.15160i) q^{13} +(1.41875 - 8.04612i) q^{14} +(5.08512 - 4.26692i) q^{16} +(1.50000 - 2.59808i) q^{17} +(-0.0209445 - 0.0362770i) q^{19} +(1.93969 + 0.705990i) q^{20} +(-6.02481 - 5.05542i) q^{22} +(5.73783 - 2.08840i) q^{23} +(-0.830222 - 4.70842i) q^{25} +5.53209 q^{26} -14.2344 q^{28} +(-1.14156 - 6.47410i) q^{29} +(5.85117 - 2.12965i) q^{31} +(-3.52094 - 2.95442i) q^{32} +(-7.13816 - 2.59808i) q^{34} +(-0.754900 - 1.30753i) q^{35} +(-1.79813 + 3.11446i) q^{37} +(-0.0812519 + 0.0681784i) q^{38} +(0.496130 - 2.81369i) q^{40} +(-1.33750 + 7.58532i) q^{41} +(-0.450837 + 0.378297i) q^{43} +(-6.85117 + 11.8666i) q^{44} +(-7.73055 - 13.3897i) q^{46} +(-9.07785 - 3.30407i) q^{47} +(2.61334 + 2.19285i) q^{49} +(-11.3760 + 4.14052i) q^{50} +(-1.67365 - 9.49173i) q^{52} -4.95811 q^{53} -1.45336 q^{55} +(3.42127 + 19.4030i) q^{56} +(-15.6420 + 5.69323i) q^{58} +(6.53596 + 5.48432i) q^{59} +(1.19207 + 0.433877i) q^{61} +(-7.88326 - 13.6542i) q^{62} +(0.819078 - 1.41868i) q^{64} +(0.783119 - 0.657115i) q^{65} +(1.73783 - 9.85570i) q^{67} +(-2.29813 + 13.0334i) q^{68} +(-2.92855 + 2.45734i) q^{70} +(5.91534 - 10.2457i) q^{71} +(4.11721 + 7.13122i) q^{73} +(8.55690 + 3.11446i) q^{74} +(0.141559 + 0.118782i) q^{76} +(9.41787 - 3.42782i) q^{77} +(1.91875 + 10.8818i) q^{79} -3.10607 q^{80} +19.5030 q^{82} +(0.262174 + 1.48686i) q^{83} +(-1.31908 + 0.480105i) q^{85} +(1.14156 + 0.957882i) q^{86} +(17.8221 + 6.48670i) q^{88} +(-7.93629 - 13.7461i) q^{89} +(-3.52481 + 6.10516i) q^{91} +(-20.6348 + 17.3146i) q^{92} +(-4.24763 + 24.0895i) q^{94} +(-0.00340357 + 0.0193026i) q^{95} +(14.2836 - 11.9854i) q^{97} +(4.31908 - 7.48086i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} - 9 q^{4} + 6 q^{5} + 9 q^{7} + 6 q^{8} + 3 q^{11} + 9 q^{13} + 6 q^{14} + 9 q^{16} + 9 q^{17} + 3 q^{19} + 6 q^{20} - 9 q^{22} + 15 q^{23} + 18 q^{25} + 24 q^{26} - 24 q^{28} - 15 q^{29}+ \cdots + 9 q^{98}+O(q^{100}) \) 6 * q + 3 * q^2 - 9 * q^4 + 6 * q^5 + 9 * q^7 + 6 * q^8 + 3 * q^11 + 9 * q^13 + 6 * q^14 + 9 * q^16 + 9 * q^17 + 3 * q^19 + 6 * q^20 - 9 * q^22 + 15 * q^23 + 18 * q^25 + 24 * q^26 - 24 * q^28 - 15 * q^29 + 9 * q^31 - 18 * q^32 - 9 * q^34 - 6 * q^35 + 3 * q^37 - 3 * q^38 + 27 * q^40 - 3 * q^41 + 9 * q^43 - 15 * q^44 - 9 * q^46 - 15 * q^47 + 9 * q^49 - 15 * q^50 - 9 * q^52 - 36 * q^53 + 18 * q^55 + 3 * q^56 - 36 * q^58 + 6 * q^59 + 18 * q^61 - 12 * q^62 - 12 * q^64 + 21 * q^65 - 9 * q^67 - 18 * q^70 - 9 * q^71 - 6 * q^73 + 15 * q^74 + 9 * q^76 - 3 * q^77 + 9 * q^79 + 6 * q^80 + 36 * q^82 + 21 * q^83 + 9 * q^85 + 15 * q^86 + 9 * q^88 + 6 * q^91 - 48 * q^92 - 9 * q^94 - 42 * q^95 + 36 * q^97 + 9 * q^98

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