LMFDB - Embedded newform 729.2.e.t.649.1

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			649.1
Root			$1.22778i$ of defining polynomial
Character	$\chi$	$=$	729.649
Dual form			729.2.e.t.82.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.274087 + 1.55442i) q^{2} +(-0.461727 - 0.168055i) q^{4} +(1.28581 - 1.07892i) q^{5} +(-2.61167 + 0.950570i) q^{7} +(-1.19062 + 2.06222i) q^{8} +O(q^{10})$	\(q+(-0.274087 + 1.55442i) q^{2} +(-0.461727 - 0.168055i) q^{4} +(1.28581 - 1.07892i) q^{5} +(-2.61167 + 0.950570i) q^{7} +(-1.19062 + 2.06222i) q^{8} +(1.32468 + 2.29442i) q^{10} +(-3.18002 - 2.66835i) q^{11} +(1.19401 + 6.77158i) q^{13} +(-0.761765 - 4.32018i) q^{14} +(-3.63204 - 3.04764i) q^{16} +(-0.488276 - 0.845718i) q^{17} +(-1.34264 + 2.32553i) q^{19} +(-0.775013 + 0.282082i) q^{20} +(5.01936 - 4.21174i) q^{22} +(-1.51588 - 0.551737i) q^{23} +(-0.379007 + 2.14945i) q^{25} -10.8532 q^{26} +1.36563 q^{28} +(-1.42876 + 8.10288i) q^{29} +(-0.981104 - 0.357093i) q^{31} +(2.08454 - 1.74914i) q^{32} +(1.44844 - 0.527187i) q^{34} +(-2.33252 + 4.04005i) q^{35} +(0.654172 + 1.13306i) q^{37} +(-3.24686 - 2.72444i) q^{38} +(0.694061 + 3.93621i) q^{40} +(-0.841876 - 4.77452i) q^{41} +(7.53805 + 6.32518i) q^{43} +(1.01987 + 1.76647i) q^{44} +(1.27312 - 2.20510i) q^{46} +(-11.7440 + 4.27447i) q^{47} +(0.554929 - 0.465640i) q^{49} +(-3.23728 - 1.17827i) q^{50} +(0.586690 - 3.32728i) q^{52} +7.34280 q^{53} -6.96786 q^{55} +(1.14923 - 6.51760i) q^{56} +(-12.2037 - 4.44179i) q^{58} +(6.93414 - 5.81843i) q^{59} +(1.20820 - 0.439750i) q^{61} +(0.823982 - 1.42718i) q^{62} +(-2.59373 - 4.49247i) q^{64} +(8.84130 + 7.41873i) q^{65} +(-0.806821 - 4.57571i) q^{67} +(0.0833230 + 0.472548i) q^{68} +(-5.64064 - 4.73306i) q^{70} +(-2.81187 - 4.87030i) q^{71} +(2.28072 - 3.95033i) q^{73} +(-1.94056 + 0.706305i) q^{74} +(1.01075 - 0.848122i) q^{76} +(10.8416 + 3.94603i) q^{77} +(0.808645 - 4.58605i) q^{79} -7.95828 q^{80} +7.65237 q^{82} +(1.00098 - 5.67682i) q^{83} +(-1.54030 - 0.560622i) q^{85} +(-11.8981 + 9.98369i) q^{86} +(9.28893 - 3.38089i) q^{88} +(-2.27221 + 3.93558i) q^{89} +(-9.55523 - 16.5502i) q^{91} +(0.607203 + 0.509504i) q^{92} +(-3.42546 - 19.4267i) q^{94} +(0.782681 + 4.43880i) q^{95} +(6.56917 + 5.51219i) q^{97} +(0.571704 + 0.990221i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{2} - 3 q^{4} + 6 q^{5} + 6 q^{7} + 6 q^{8}+O(q^{10}) $ 12 * q + 3 * q^2 - 3 * q^4 + 6 * q^5 + 6 * q^7 + 6 * q^8	$ 12 q + 3 q^{2} - 3 q^{4} + 6 q^{5} + 6 q^{7} + 6 q^{8} - 6 q^{10} - 15 q^{11} - 3 q^{13} - 21 q^{14} + 9 q^{16} - 9 q^{17} - 12 q^{19} - 3 q^{20} + 33 q^{22} + 15 q^{23} - 12 q^{25} - 48 q^{26} + 6 q^{28} - 6 q^{29} - 12 q^{31} - 27 q^{32} + 27 q^{34} + 30 q^{35} - 3 q^{37} - 39 q^{38} + 24 q^{40} - 39 q^{41} + 24 q^{43} - 33 q^{44} + 3 q^{46} - 42 q^{47} - 30 q^{49} - 15 q^{50} - 45 q^{52} + 18 q^{53} + 30 q^{55} + 12 q^{56} - 30 q^{58} + 15 q^{59} - 3 q^{61} - 30 q^{62} - 6 q^{64} - 6 q^{65} - 3 q^{67} + 36 q^{68} - 75 q^{70} - 12 q^{73} + 60 q^{74} + 30 q^{76} + 33 q^{77} + 33 q^{79} + 42 q^{80} - 42 q^{82} - 33 q^{83} - 18 q^{85} - 30 q^{86} - 42 q^{88} - 9 q^{89} - 18 q^{91} + 33 q^{92} - 66 q^{94} + 12 q^{95} + 15 q^{97} + 18 q^{98}+O(q^{100}) $ 12 * q + 3 * q^2 - 3 * q^4 + 6 * q^5 + 6 * q^7 + 6 * q^8 - 6 * q^10 - 15 * q^11 - 3 * q^13 - 21 * q^14 + 9 * q^16 - 9 * q^17 - 12 * q^19 - 3 * q^20 + 33 * q^22 + 15 * q^23 - 12 * q^25 - 48 * q^26 + 6 * q^28 - 6 * q^29 - 12 * q^31 - 27 * q^32 + 27 * q^34 + 30 * q^35 - 3 * q^37 - 39 * q^38 + 24 * q^40 - 39 * q^41 + 24 * q^43 - 33 * q^44 + 3 * q^46 - 42 * q^47 - 30 * q^49 - 15 * q^50 - 45 * q^52 + 18 * q^53 + 30 * q^55 + 12 * q^56 - 30 * q^58 + 15 * q^59 - 3 * q^61 - 30 * q^62 - 6 * q^64 - 6 * q^65 - 3 * q^67 + 36 * q^68 - 75 * q^70 - 12 * q^73 + 60 * q^74 + 30 * q^76 + 33 * q^77 + 33 * q^79 + 42 * q^80 - 42 * q^82 - 33 * q^83 - 18 * q^85 - 30 * q^86 - 42 * q^88 - 9 * q^89 - 18 * q^91 + 33 * q^92 - 66 * q^94 + 12 * q^95 + 15 * q^97 + 18 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{9}\right)$

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 $

$2$	−0.274087	+	1.55442i	−0.193809	+	1.09914i	0.720296	+	0.693667i	$0.244006\pi$
$2$	−0.274087	+	1.55442i	−0.193809	+	1.09914i	−0.914105	+	0.405478i	$0.867105\pi$
$3$		0			0
$3$		0			0
$4$	−0.461727	−	0.168055i	−0.230864	−	0.0840275i
$5$	1.28581	−	1.07892i	0.575032	−	0.482509i	−0.308279	−	0.951296i	$-0.599753\pi$
$5$	1.28581	−	1.07892i	0.575032	−	0.482509i	0.883311	+	0.468787i	$0.155309\pi$
$6$		0			0
$7$	−2.61167	+	0.950570i	−0.987119	+	0.359282i	−0.784604	−	0.619997i	$-0.787134\pi$
$7$	−2.61167	+	0.950570i	−0.987119	+	0.359282i	−0.202515	+	0.979279i	$0.564911\pi$
$8$	−1.19062	+	2.06222i	−0.420948	+	0.729104i
$9$		0			0
$10$	1.32468	+	2.29442i	0.418901	+	0.725558i
$11$	−3.18002	−	2.66835i	−0.958812	−	0.804539i	0.0219472	−	0.999759i	$-0.493013\pi$
$11$	−3.18002	−	2.66835i	−0.958812	−	0.804539i	−0.980759	+	0.195220i	$0.937458\pi$
$12$		0			0
$13$	1.19401	+	6.77158i	0.331160	+	1.87810i	0.462282	+	0.886733i	$0.347031\pi$
$13$	1.19401	+	6.77158i	0.331160	+	1.87810i	−0.131123	+	0.991366i	$0.541858\pi$
$14$	−0.761765	−	4.32018i	−0.203590	−	1.15462i
$15$		0			0
$16$	−3.63204	−	3.04764i	−0.908009	−	0.761910i
$17$	−0.488276	−	0.845718i	−0.118424	−	0.205117i	0.800719	−	0.599040i	$-0.204451\pi$
$17$	−0.488276	−	0.845718i	−0.118424	−	0.205117i	−0.919143	+	0.393923i	$0.871118\pi$
$18$		0			0
$19$	−1.34264	+	2.32553i	−0.308024	+	0.533513i	−0.977930	−	0.208933i	$-0.933001\pi$
$19$	−1.34264	+	2.32553i	−0.308024	+	0.533513i	0.669906	+	0.742446i	$0.266334\pi$
$20$	−0.775013	+	0.282082i	−0.173298	+	0.0630754i
$21$		0			0
$22$	5.01936	−	4.21174i	1.07013	−	0.897946i
$23$	−1.51588	−	0.551737i	−0.316084	−	0.115045i	0.179106	−	0.983830i	$-0.442679\pi$
$23$	−1.51588	−	0.551737i	−0.316084	−	0.115045i	−0.495190	+	0.868785i	$0.664902\pi$
$24$		0			0
$25$	−0.379007	+	2.14945i	−0.0758013	+	0.429891i
$26$	−10.8532			−2.12848
$27$		0			0
$28$	1.36563			0.258079
$29$	−1.42876	+	8.10288i	−0.265313	+	1.50467i	0.502828	+	0.864386i	$0.332293\pi$
$29$	−1.42876	+	8.10288i	−0.265313	+	1.50467i	−0.768142	+	0.640280i	$0.778818\pi$
$30$		0			0
$31$	−0.981104	−	0.357093i	−0.176212	−	0.0641357i	0.252408	−	0.967621i	$-0.418778\pi$
$31$	−0.981104	−	0.357093i	−0.176212	−	0.0641357i	−0.428619	+	0.903485i	$0.641000\pi$
$32$	2.08454	−	1.74914i	0.368498	−	0.309207i
$33$		0			0
$34$	1.44844	−	0.527187i	0.248405	−	0.0904119i
$35$	−2.33252	+	4.04005i	−0.394268	+	0.682893i
$36$		0			0
$37$	0.654172	+	1.13306i	0.107545	+	0.186274i	0.914775	−	0.403963i	$-0.132368\pi$
$37$	0.654172	+	1.13306i	0.107545	+	0.186274i	−0.807230	+	0.590237i	$0.799034\pi$
$38$	−3.24686	−	2.72444i	−0.526710	−	0.441962i
$39$		0			0
$40$	0.694061	+	3.93621i	0.109741	+	0.622370i
$41$	−0.841876	−	4.77452i	−0.131479	−	0.745654i	−0.977247	−	0.212104i	$-0.931969\pi$
$41$	−0.841876	−	4.77452i	−0.131479	−	0.745654i	0.845768	−	0.533550i	$-0.179143\pi$
$42$		0			0
$43$	7.53805	+	6.32518i	1.14954	+	0.964580i	0.999709	−	0.0241308i	$-0.00768182\pi$
$43$	7.53805	+	6.32518i	1.14954	+	0.964580i	0.149833	+	0.988711i	$0.452126\pi$
$44$	1.01987	+	1.76647i	0.153751	+	0.266305i
$45$		0			0
$46$	1.27312	−	2.20510i	0.187711	−	0.325125i
$47$	−11.7440	+	4.27447i	−1.71304	+	0.623495i	−0.997201	−	0.0747722i	$-0.976177\pi$
$47$	−11.7440	+	4.27447i	−1.71304	+	0.623495i	−0.715837	+	0.698267i	$0.753955\pi$
$48$		0			0
$49$	0.554929	−	0.465640i	0.0792755	−	0.0665201i
$50$	−3.23728	−	1.17827i	−0.457821	−	0.166633i
$51$		0			0
$52$	0.586690	−	3.32728i	0.0813593	−	0.461411i
$53$	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
$56$	1.14923	−	6.51760i	0.153572	−	0.870951i
$57$		0			0
$58$	−12.2037	−	4.44179i	−1.60243	−	0.583235i
$59$	6.93414	−	5.81843i	0.902748	−	0.757496i	−0.0679775	−	0.997687i	$-0.521655\pi$
$59$	6.93414	−	5.81843i	0.902748	−	0.757496i	0.970726	+	0.240191i	$0.0772102\pi$
$60$		0			0
$61$	1.20820	−	0.439750i	0.154694	−	0.0563042i	−0.263512	−	0.964656i	$-0.584881\pi$
$61$	1.20820	−	0.439750i	0.154694	−	0.0563042i	0.418207	+	0.908352i	$0.362659\pi$
$62$	0.823982	−	1.42718i	0.104646	−	0.181252i
$63$		0			0
$64$	−2.59373	−	4.49247i	−0.324216	−	0.561558i
$65$	8.84130	+	7.41873i	1.09663	+	0.920180i
$66$		0			0
$67$	−0.806821	−	4.57571i	−0.0985689	−	0.559012i	−0.993595	−	0.112999i	$-0.963954\pi$
$67$	−0.806821	−	4.57571i	−0.0985689	−	0.559012i	0.895026	−	0.446014i	$-0.147157\pi$
$68$	0.0833230	+	0.472548i	0.0101044	+	0.0573049i
$69$		0			0
$70$	−5.64064	−	4.73306i	−0.674185	−	0.565708i
$71$	−2.81187	−	4.87030i	−0.333707	−	0.577998i	0.649528	−	0.760337i	$-0.274966\pi$
$71$	−2.81187	−	4.87030i	−0.333707	−	0.577998i	−0.983236	+	0.182339i	$0.941633\pi$
$72$		0			0
$73$	2.28072	−	3.95033i	0.266938	−	0.462351i	−0.701131	−	0.713032i	$-0.747321\pi$
$73$	2.28072	−	3.95033i	0.266938	−	0.462351i	0.968070	+	0.250681i	$0.0806547\pi$
$74$	−1.94056	+	0.706305i	−0.225585	+	0.0821062i
$75$		0			0
$76$	1.01075	−	0.848122i	0.115941	−	0.0972862i
$77$	10.8416	+	3.94603i	1.23552	+	0.449692i
$78$		0			0
$79$	0.808645	−	4.58605i	0.0909797	−	0.515971i	−0.904926	−	0.425570i	$-0.860074\pi$
$79$	0.808645	−	4.58605i	0.0909797	−	0.515971i	0.995905	−	0.0904018i	$-0.0288151\pi$
$80$	−7.95828			−0.889763
$81$		0			0
$82$	7.65237			0.845063
$83$	1.00098	−	5.67682i	0.109871	−	0.623112i	−0.879291	−	0.476285i	$-0.841983\pi$
$83$	1.00098	−	5.67682i	0.109871	−	0.623112i	0.989162	−	0.146827i	$-0.0469059\pi$
$84$		0			0
$85$	−1.54030	−	0.560622i	−0.167069	−	0.0608080i
$86$	−11.8981	+	9.98369i	−1.28300	+	1.07657i
$87$		0			0
$88$	9.28893	−	3.38089i	0.990203	−	0.360405i
$89$	−2.27221	+	3.93558i	−0.240854	+	0.417171i	−0.960958	−	0.276695i	$-0.910761\pi$
$89$	−2.27221	+	3.93558i	−0.240854	+	0.417171i	0.720104	+	0.693866i	$0.244094\pi$
$90$		0			0
$91$	−9.55523	−	16.5502i	−1.00166	−	1.73493i
$92$	0.607203	+	0.509504i	0.0633053	+	0.0531194i
$93$		0			0
$94$	−3.42546	−	19.4267i	−0.353309	−	2.00371i
$95$	0.782681	+	4.43880i	0.0803013	+	0.455411i
$96$		0			0
$97$	6.56917	+	5.51219i	0.666998	+	0.559678i	0.912175	−	0.409800i	$-0.134402\pi$
$97$	6.56917	+	5.51219i	0.666998	+	0.559678i	−0.245177	+	0.969478i	$0.578846\pi$
$98$	0.571704	+	0.990221i	0.0577508	+	0.100027i
$99$		0			0
$100$	0.536224	−	0.928767i	0.0536224	−	0.0928767i
$101$	7.33496	−	2.66971i	0.729856	−	0.265646i	0.0497521	−	0.998762i	$-0.484157\pi$
$101$	7.33496	−	2.66971i	0.729856	−	0.265646i	0.680104	+	0.733116i	$0.261935\pi$
$102$		0			0
$103$	−1.65937	+	1.39237i	−0.163502	+	0.137195i	−0.720868	−	0.693073i	$-0.756257\pi$
$103$	−1.65937	+	1.39237i	−0.163502	+	0.137195i	0.557366	+	0.830267i	$0.311812\pi$
$104$	−15.3861	−	5.60008i	−1.50873	−	0.549133i
$105$		0			0
$106$	−2.01257	+	11.4138i	−0.195478	+	1.10861i
$107$	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	$0.698884\pi$
$110$	1.90980	−	10.8310i	0.182092	−	1.03270i
$111$		0			0
$112$	12.3827	+	4.50693i	1.17005	+	0.425864i
$113$	0.345358	−	0.289790i	0.0324886	−	0.0272611i	−0.626399	−	0.779503i	$-0.715472\pi$
$113$	0.345358	−	0.289790i	0.0324886	−	0.0272611i	0.658887	+	0.752242i	$0.271027\pi$
$114$		0			0
$115$	−2.54442	+	0.926094i	−0.237269	+	0.0863587i
$116$	2.02142	−	3.50121i	0.187685	−	0.325079i
$117$		0			0
$118$	7.14376	+	12.3734i	0.657636	+	1.13906i
$119$	2.07913	+	1.74460i	0.190594	+	0.159927i
$120$		0			0
$121$	1.08229	+	6.13796i	0.0983898	+	0.557996i
$122$	0.352405	+	1.99859i	0.0319053	+	0.180944i
$123$		0			0
$124$	0.392991	+	0.329759i	0.0352917	+	0.0296132i
$125$	6.02803	+	10.4409i	0.539164	+	0.933859i
$126$		0			0
$127$	0.265534	−	0.459919i	0.0235624	−	0.0408112i	−0.854004	−	0.520267i	$-0.825833\pi$
$127$	0.265534	−	0.459919i	0.0235624	−	0.0408112i	0.877566	+	0.479456i	$0.159166\pi$
$128$	12.8082	−	4.66182i	1.13210	−	0.412051i
$129$		0			0
$130$	−13.9551	+	11.7098i	−1.22395	+	1.02701i
$131$	10.7276	+	3.90451i	0.937272	+	0.341139i	0.765088	−	0.643926i	$-0.222695\pi$
$131$	10.7276	+	3.90451i	0.937272	+	0.341139i	0.172184	+	0.985065i	$0.444918\pi$
$132$		0			0
$133$	1.29597	−	7.34979i	0.112375	−	0.637308i
$134$	7.33374			0.633539
$135$		0			0
$136$	2.32541			0.199402
$137$	−0.734400	+	4.16499i	−0.0627440	+	0.355839i	0.937231	+	0.348710i	$0.113380\pi$
$137$	−0.734400	+	4.16499i	−0.0627440	+	0.355839i	−0.999975	+	0.00712879i	$0.997731\pi$
$138$		0			0
$139$	10.4828	+	3.81542i	0.889137	+	0.323619i	0.745891	−	0.666068i	$-0.232024\pi$
$139$	10.4828	+	3.81542i	0.889137	+	0.323619i	0.143246	+	0.989687i	$0.454246\pi$
$140$	1.75594	−	1.47341i	0.148404	−	0.124526i
$141$		0			0
$142$	8.34121	−	3.03595i	0.699978	−	0.254771i
$143$	14.2720	−	24.7198i	1.19348	−	2.06718i
$144$		0			0
$145$	6.90528	+	11.9603i	0.573452	+	0.993248i
$146$	5.51537	+	4.62794i	0.456455	+	0.383011i
$147$		0			0
$148$	−0.111633	−	0.633101i	−0.00917616	−	0.0520406i
$149$	3.38227	+	19.1818i	0.277086	+	1.57143i	0.732257	+	0.681029i	$0.238467\pi$
$149$	3.38227	+	19.1818i	0.277086	+	1.57143i	−0.455171	+	0.890404i	$0.650422\pi$
$150$		0			0
$151$	−0.952086	−	0.798895i	−0.0774797	−	0.0650131i	0.603225	−	0.797571i	$-0.293882\pi$
$151$	−0.952086	−	0.798895i	−0.0774797	−	0.0650131i	−0.680705	+	0.732558i	$0.738326\pi$
$152$	−3.19716	−	5.53765i	−0.259324	−	0.449163i
$153$		0			0
$154$	−9.10535	+	15.7709i	−0.733730	+	1.27086i
$155$	−1.64679	+	0.599383i	−0.132273	+	0.0481436i
$156$		0			0
$157$	−2.70654	+	2.27106i	−0.216006	+	0.181250i	−0.744370	−	0.667768i	$-0.767250\pi$
$157$	−2.70654	+	2.27106i	−0.216006	+	0.181250i	0.528364	+	0.849018i	$0.322806\pi$
$158$	6.90704	+	2.51396i	0.549494	+	0.200000i
$159$		0			0
$160$	0.793141	−	4.49812i	0.0627033	−	0.355608i
$161$	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	$0.285228\pi$
$164$	−0.413664	+	2.34601i	−0.0323017	+	0.183192i
$165$		0			0
$166$	8.54983	+	3.11188i	0.663596	+	0.241529i
$167$	−11.0959	+	9.31055i	−0.858625	+	0.720472i	−0.961671	−	0.274205i	$-0.911585\pi$
$167$	−11.0959	+	9.31055i	−0.858625	+	0.720472i	0.103046	+	0.994677i	$0.467141\pi$
$168$		0			0
$169$	−32.2127	+	11.7244i	−2.47790	+	0.901881i
$170$	1.29362	−	2.24061i	0.0992161	−	0.171847i
$171$		0			0
$172$	−2.41755	−	4.18731i	−0.184336	−	0.319280i
$173$	−9.66549	−	8.11031i	−0.734853	−	0.616615i	0.196597	−	0.980484i	$-0.437011\pi$
$173$	−9.66549	−	8.11031i	−0.734853	−	0.616615i	−0.931450	+	0.363869i	$0.881455\pi$
$174$		0			0
$175$	−1.05337	−	5.97394i	−0.0796270	−	0.451587i
$176$	3.41777	+	19.3831i	0.257624	+	1.46106i
$177$		0			0
$178$	−5.49478	−	4.61067i	−0.411851	−	0.345584i
$179$	0.147949	+	0.256256i	0.0110582	+	0.0191534i	0.871502	−	0.490393i	$-0.163147\pi$
$179$	0.147949	+	0.256256i	0.0110582	+	0.0191534i	−0.860443	+	0.509546i	$0.829813\pi$
$180$		0			0
$181$	−0.710251	+	1.23019i	−0.0527925	+	0.0914393i	−0.891214	−	0.453583i	$-0.850146\pi$
$181$	−0.710251	+	1.23019i	−0.0527925	+	0.0914393i	0.838421	+	0.545022i	$0.183479\pi$
$182$	28.3449	−	10.3167i	2.10107	−	0.764725i
$183$		0			0
$184$	2.94265	−	2.46917i	0.216935	−	0.182030i
$185$	2.06363	+	0.751099i	0.151721	+	0.0552219i
$186$		0			0
$187$	−0.703949	+	3.99229i	−0.0514779	+	0.291945i
$188$	6.14087			0.447869
$189$		0			0
$190$	−7.11431			−0.516126
$191$	−3.58133	+	20.3108i	−0.259136	+	1.46963i	0.526091	+	0.850428i	$0.323657\pi$
$191$	−3.58133	+	20.3108i	−0.259136	+	1.46963i	−0.785228	+	0.619207i	$0.787454\pi$
$192$		0			0
$193$	19.6921	+	7.16735i	1.41747	+	0.515917i	0.933313	−	0.359063i	$-0.116904\pi$
$193$	19.6921	+	7.16735i	1.41747	+	0.515917i	0.484158	+	0.874981i	$0.339126\pi$
$194$	−10.3688	+	8.70046i	−0.744437	+	0.624657i
$195$		0			0
$196$	−0.334479	+	0.121740i	−0.0238913	+	0.00869574i
$197$	−4.79810	+	8.31056i	−0.341851	+	0.592103i	−0.984776	−	0.173826i	$-0.944387\pi$
$197$	−4.79810	+	8.31056i	−0.341851	+	0.592103i	0.642926	+	0.765929i	$0.277720\pi$
$198$		0			0
$199$	5.34583	+	9.25925i	0.378956	+	0.656371i	0.990911	−	0.134522i	$-0.0429498\pi$
$199$	5.34583	+	9.25925i	0.378956	+	0.656371i	−0.611955	+	0.790893i	$0.709616\pi$
$200$	−3.98139	−	3.34078i	−0.281527	−	0.236229i
$201$		0			0
$202$	2.13944	+	12.1334i	0.150531	+	0.853701i
$203$	−3.97092	−	22.5202i	−0.278704	−	1.58061i
$204$		0			0
$205$	−6.23383	−	5.23081i	−0.435390	−	0.365335i
$206$	−1.70953	−	2.96099i	−0.119108	−	0.206302i
$207$		0			0
$208$	16.3006	−	28.2335i	1.13025	−	1.95764i
$209$	10.4750	−	3.81258i	0.724569	−	0.263722i
$210$		0			0
$211$	−11.5292	+	9.67411i	−0.793700	+	0.665993i	−0.946658	−	0.322240i	$-0.895564\pi$
$211$	−11.5292	+	9.67411i	−0.793700	+	0.665993i	0.152959	+	0.988233i	$0.451120\pi$
$212$	−3.39037	−	1.23399i	−0.232851	−	0.0847510i
$213$		0			0
$214$	−3.44937	+	19.5624i	−0.235794	+	1.33726i
$215$	16.5169			1.12644
$216$		0			0
$217$	2.90176			0.196984
$218$	3.34770	−	18.9857i	0.226735	−	1.28588i
$219$		0			0
$220$	3.21725	+	1.17098i	0.216907	+	0.0789477i
$221$	5.14384	−	4.31620i	0.346012	−	0.290339i
$222$		0			0
$223$	11.5470	−	4.20278i	0.773247	−	0.281439i	0.0748934	−	0.997192i	$-0.476138\pi$
$223$	11.5470	−	4.20278i	0.773247	−	0.281439i	0.698354	+	0.715753i	$0.253916\pi$
$224$	−3.78146	+	6.54968i	−0.252659	+	0.437619i
$225$		0			0
$226$	0.355798	+	0.616261i	0.0236674	+	0.0409931i
$227$	−2.87463	−	2.41210i	−0.190796	−	0.160097i	0.542386	−	0.840129i	$-0.317521\pi$
$227$	−2.87463	−	2.41210i	−0.190796	−	0.160097i	−0.733182	+	0.680033i	$0.761966\pi$
$228$		0			0
$229$	−3.23028	−	18.3198i	−0.213463	−	1.21061i	−0.883554	−	0.468329i	$-0.844856\pi$
$229$	−3.23028	−	18.3198i	−0.213463	−	1.21061i	0.670092	−	0.742278i	$-0.266255\pi$
$230$	−0.742150	−	4.20894i	−0.0489359	−	0.277529i
$231$		0			0
$232$	−15.0088	−	12.5939i	−0.985375	−	0.826828i
$233$	0.272892	+	0.472663i	0.0178777	+	0.0309652i	0.874826	−	0.484438i	$-0.160976\pi$
$233$	0.272892	+	0.472663i	0.0178777	+	0.0309652i	−0.856948	+	0.515403i	$0.827642\pi$
$234$		0			0
$235$	−10.4887	+	18.1670i	−0.684210	+	1.18509i
$236$	−4.17950	+	1.52121i	−0.272062	+	0.0990225i
$237$		0			0
$238$	−3.28171	+	2.75368i	−0.212721	+	0.178495i
$239$	−18.8829	−	6.87281i	−1.22143	−	0.444565i	−0.350777	−	0.936459i	$-0.614083\pi$
$239$	−18.8829	−	6.87281i	−1.22143	−	0.444565i	−0.870655	+	0.491894i	$0.836305\pi$
$240$		0			0
$241$	2.65531	−	15.0590i	0.171043	−	0.970035i	−0.771569	−	0.636146i	$-0.780528\pi$
$241$	2.65531	−	15.0590i	0.171043	−	0.970035i	0.942612	−	0.333889i	$-0.108361\pi$
$242$	−9.83763			−0.632387
$243$		0			0
$244$	−0.631762			−0.0404444
$245$	0.211143	−	1.19745i	0.0134894	−	0.0765024i
$246$		0			0
$247$	−17.3506	−	6.31512i	−1.10399	−	0.401821i
$248$	1.90453	−	1.59809i	0.120938	−	0.101479i
$249$		0			0
$250$	−17.8817	+	6.50842i	−1.13094	+	0.411629i
$251$	6.37816	−	11.0473i	0.402586	−	0.697299i	−0.591451	−	0.806341i	$-0.701445\pi$
$251$	6.37816	−	11.0473i	0.402586	−	0.697299i	0.994037	+	0.109042i	$0.0347782\pi$
$252$		0			0
$253$	3.34831	+	5.79945i	0.210507	+	0.364608i
$254$	0.642130	+	0.538811i	0.0402908	+	0.0338080i
$255$		0			0
$256$	1.93429	+	10.9699i	0.120893	+	0.685619i
$257$	2.27561	+	12.9056i	0.141949	+	0.805030i	0.969767	+	0.244034i	$0.0784708\pi$
$257$	2.27561	+	12.9056i	0.141949	+	0.805030i	−0.827818	+	0.560996i	$0.810418\pi$
$258$		0			0
$259$	−2.78554	−	2.33734i	−0.173085	−	0.145235i
$260$	−2.83551	−	4.91125i	−0.175851	−	0.304583i
$261$		0			0
$262$	−9.00956	+	15.6050i	−0.556613	+	0.964081i
$263$	−8.94040	+	3.25404i	−0.551289	+	0.200653i	−0.602619	−	0.798029i	$-0.705876\pi$
$263$	−8.94040	+	3.25404i	−0.551289	+	0.200653i	0.0513303	+	0.998682i	$0.483654\pi$
$264$		0			0
$265$	9.44145	−	7.92232i	0.579984	−	0.486664i
$266$	11.0695	+	4.02897i	0.678714	+	0.247032i
$267$		0			0
$268$	−0.396440	+	2.24832i	−0.0242164	+	0.137338i
$269$	−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	$0.177020\pi$
$272$	−0.804010	+	4.55977i	−0.0487503	+	0.276476i
$273$		0			0
$274$	−6.27287	−	2.28314i	−0.378958	−	0.137929i
$275$	6.94075	−	5.82398i	0.418543	−	0.351199i
$276$		0			0
$277$	17.7449	−	6.45860i	1.06618	−	0.388060i	0.251436	−	0.967874i	$-0.419097\pi$
$277$	17.7449	−	6.45860i	1.06618	−	0.388060i	0.814749	+	0.579814i	$0.196875\pi$
$278$	−8.80397	+	15.2489i	−0.528027	+	0.914569i
$279$		0			0
$280$	−5.55431	−	9.62034i	−0.331933	−	0.574925i
$281$	15.3222	+	12.8569i	0.914047	+	0.766977i	0.972885	−	0.231291i	$-0.0742949\pi$
$281$	15.3222	+	12.8569i	0.914047	+	0.766977i	−0.0588373	+	0.998268i	$0.518739\pi$
$282$		0			0
$283$	2.90775	+	16.4906i	0.172848	+	0.980267i	0.940599	+	0.339519i	$0.110264\pi$
$283$	2.90775	+	16.4906i	0.172848	+	0.980267i	−0.767752	+	0.640748i	$0.778624\pi$
$284$	0.479838	+	2.72130i	0.0284732	+	0.161479i
$285$		0			0
$286$	34.5133	+	28.9601i	2.04082	+	1.71245i
$287$	6.73722	+	11.6692i	0.397685	+	0.688811i
$288$		0			0
$289$	8.02317	−	13.8965i	0.471951	−	0.817444i
$290$	−20.4840	+	7.45557i	−1.20286	+	0.437806i
$291$		0			0
$292$	−1.71694	+	1.44069i	−0.100476	+	0.0843098i
$293$	18.3917	+	6.69402i	1.07445	+	0.391069i	0.817840	−	0.575446i	$-0.195171\pi$
$293$	18.3917	+	6.69402i	1.07445	+	0.391069i	0.256613	+	0.966514i	$0.417394\pi$
$294$		0			0
$295$	2.63835	−	14.9628i	0.153611	−	0.871169i
$296$	−3.11549			−0.181084
$297$		0			0
$298$	−30.7437			−1.78093
$299$	1.92615	−	10.9237i	0.111392	−	0.631735i
$300$		0			0
$301$	−25.6994	−	9.35383i	−1.48129	−	0.539146i
$302$	1.50278	−	1.26098i	0.0864751	−	0.0725612i
$303$		0			0
$304$	11.9639	−	4.35451i	0.686177	−	0.249748i
$305$	1.07906	−	1.86899i	0.0617870	−	0.107018i
$306$		0			0
$307$	−7.44973	−	12.9033i	−0.425179	−	0.736431i	0.571258	−	0.820770i	$-0.306455\pi$
$307$	−7.44973	−	12.9033i	−0.425179	−	0.736431i	−0.996437	+	0.0843392i	$0.973122\pi$
$308$	−4.34272	−	3.64398i	−0.247450	−	0.207635i
$309$		0			0
$310$	−0.480331	−	2.72410i	−0.0272810	−	0.154718i
$311$	−0.797455	−	4.52259i	−0.0452195	−	0.256453i	0.953814	−	0.300396i	$-0.0971189\pi$
$311$	−0.797455	−	4.52259i	−0.0452195	−	0.256453i	−0.999034	+	0.0439436i	$0.986008\pi$
$312$		0			0
$313$	9.09194	+	7.62904i	0.513907	+	0.431219i	0.862501	−	0.506055i	$-0.168897\pi$
$313$	9.09194	+	7.62904i	0.513907	+	0.431219i	−0.348595	+	0.937274i	$0.613341\pi$
$314$	−2.78836	−	4.82958i	−0.157356	−	0.272549i
$315$		0			0
$316$	−1.14408	+	1.98161i	−0.0643597	+	0.111474i
$317$	−13.6418	+	4.96522i	−0.766202	+	0.278875i	−0.695407	−	0.718616i	$-0.744776\pi$
$317$	−13.6418	+	4.96522i	−0.766202	+	0.278875i	−0.0707952	+	0.997491i	$0.522554\pi$
$318$		0			0
$319$	26.1648	−	21.9549i	1.46495	−	1.22924i
$320$	−8.18207	−	2.97803i	−0.457392	−	0.166477i
$321$		0			0
$322$	−1.22886	+	6.96919i	−0.0684815	+	0.388378i
$323$	2.62232			0.145910
$324$		0			0
$325$	−15.0077			−0.832480
$326$	−4.37193	+	24.7944i	−0.242139	+	1.37324i
$327$		0			0
$328$	10.8484	+	3.94851i	0.599005	+	0.218020i
$329$	26.6083	−	22.3270i	1.46696	−	1.23093i
$330$		0			0
$331$	7.61687	−	2.77231i	0.418661	−	0.152380i	−0.124095	−	0.992270i	$-0.539603\pi$
$331$	7.61687	−	2.77231i	0.418661	−	0.152380i	0.542756	+	0.839890i	$0.317381\pi$
$332$	−1.41620	+	2.45292i	−0.0777238	+	0.134622i
$333$		0			0
$334$	−11.4313	−	19.7996i	−0.625494	−	1.08339i
$335$	−5.97426	−	5.01300i	−0.326409	−	0.273890i
$336$		0			0
$337$	−3.26597	−	18.5222i	−0.177909	−	1.00897i	−0.934733	−	0.355351i	$-0.884361\pi$
$337$	−3.26597	−	18.5222i	−0.177909	−	1.00897i	0.756824	−	0.653618i	$-0.226750\pi$
$338$	−9.39570	−	53.2857i	−0.511059	−	2.89836i
$339$		0			0
$340$	0.616981	+	0.517709i	0.0334605	+	0.0280767i
$341$	2.16708	+	3.75350i	0.117354	+	0.203263i
$342$		0			0
$343$	8.72082	−	15.1049i	0.470880	−	0.815588i
$344$	−22.0189	+	8.01421i	−1.18718	+	0.432097i
$345$		0			0
$346$	15.2560	−	12.8013i	0.820170	−	0.688204i
$347$	−16.5552	−	6.02558i	−0.888727	−	0.323470i	−0.143001	−	0.989723i	$-0.545675\pi$
$347$	−16.5552	−	6.02558i	−0.888727	−	0.323470i	−0.745726	+	0.666252i	$0.767897\pi$
$348$		0			0
$349$	−2.95016	+	16.7312i	−0.157918	+	0.895600i	0.798151	+	0.602458i	$0.205812\pi$
$349$	−2.95016	+	16.7312i	−0.157918	+	0.895600i	−0.956069	+	0.293142i	$0.905299\pi$
$350$	9.57475			0.511792
$351$		0			0
$352$	−11.2962			−0.602090
$353$	2.63174	−	14.9254i	0.140074	−	0.794396i	−0.831118	−	0.556096i	$-0.812299\pi$
$353$	2.63174	−	14.9254i	0.140074	−	0.794396i	0.971192	−	0.238300i	$-0.0765902\pi$
$354$		0			0
$355$	−8.87021	−	3.22849i	−0.470782	−	0.171351i
$356$	1.71054	−	1.43531i	0.0906582	−	0.0760712i
$357$		0			0
$358$	−0.438881	+	0.159740i	−0.0231956	+	0.00844250i
$359$	1.22548	−	2.12259i	0.0646783	−	0.112026i	−0.831873	−	0.554966i	$-0.812731\pi$
$359$	1.22548	−	2.12259i	0.0646783	−	0.112026i	0.896551	+	0.442940i	$0.146065\pi$
$360$		0			0
$361$	5.89461	+	10.2098i	0.310243	+	0.537356i
$362$	−1.71757	−	1.44121i	−0.0902734	−	0.0757484i
$363$		0			0
$364$	1.63058	+	9.24746i	0.0854654	+	0.484699i
$365$	−1.32952	−	7.54010i	−0.0695904	−	0.394667i
$366$		0			0
$367$	−1.00622	−	0.844323i	−0.0525245	−	0.0440733i	0.616148	−	0.787631i	$-0.288693\pi$
$367$	−1.00622	−	0.844323i	−0.0525245	−	0.0440733i	−0.668672	+	0.743557i	$0.733137\pi$
$368$	3.82425	+	6.62379i	0.199353	+	0.345289i
$369$		0			0
$370$	−1.73314	+	3.00189i	−0.0901017	+	0.156061i
$371$	−19.1770	+	6.97984i	−0.995618	+	0.362375i
$372$		0			0
$373$	−7.37407	+	6.18758i	−0.381815	+	0.320381i	−0.813415	−	0.581684i	$-0.802394\pi$
$373$	−7.37407	+	6.18758i	−0.381815	+	0.320381i	0.431599	+	0.902065i	$0.357949\pi$
$374$	−6.01278	−	2.18847i	−0.310913	−	0.113163i
$375$		0			0
$376$	5.16778	−	29.3080i	0.266508	−	1.51144i
$377$	−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	$0.570582\pi$
$380$	0.384578	−	2.18105i	0.0197284	−	0.111885i
$381$		0			0
$382$	−30.5899	−	11.1338i	−1.56512	−	0.569656i
$383$	−25.7656	+	21.6199i	−1.31656	+	1.10473i	−0.329539	+	0.944142i	$0.606893\pi$
$383$	−25.7656	+	21.6199i	−1.31656	+	1.10473i	−0.987022	+	0.160584i	$0.948662\pi$
$384$		0			0
$385$	18.1977	−	6.62344i	0.927443	−	0.337562i
$386$	−16.5385	+	28.6455i	−0.841786	+	1.45802i
$387$		0			0
$388$	−2.10681	−	3.64911i	−0.106957	−	0.185255i
$389$	11.4554	+	9.61223i	0.580813	+	0.487360i	0.885214	−	0.465184i	$-0.154012\pi$
$389$	11.4554	+	9.61223i	0.580813	+	0.487360i	−0.304401	+	0.952544i	$0.598456\pi$
$390$		0			0
$391$	0.273555	+	1.55141i	0.0138343	+	0.0784582i
$392$	0.299542	+	1.69879i	0.0151291	+	0.0858016i
$393$		0			0
$394$	−11.6030	−	9.73611i	−0.584553	−	0.490498i
$395$	−3.90824	−	6.76927i	−0.196645	−	0.340599i
$396$		0			0
$397$	8.38938	−	14.5308i	0.421051	−	0.729282i	−0.574991	−	0.818159i	$-0.694995\pi$
$397$	8.38938	−	14.5308i	0.421051	−	0.729282i	0.996043	+	0.0888774i	$0.0283279\pi$
$398$	−15.8580	+	5.77185i	−0.794891	+	0.289317i
$399$		0			0
$400$	7.92732	−	6.65182i	0.396366	−	0.332591i
$401$	12.3347	+	4.48946i	0.615965	+	0.224193i	0.631111	−	0.775693i	$-0.282599\pi$
$401$	12.3347	+	4.48946i	0.615965	+	0.224193i	−0.0151464	+	0.999885i	$0.504821\pi$
$402$		0			0
$403$	1.24663	−	7.07000i	0.0620992	−	0.352182i
$404$	−3.83541			−0.190819
$405$		0			0
$406$	36.0943			1.79133
$407$	0.943123	−	5.34872i	0.0467489	−	0.265126i
$408$		0			0
$409$	−23.9157	−	8.70459i	−1.18255	−	0.430414i	−0.325450	−	0.945559i	$-0.605516\pi$
$409$	−23.9157	−	8.70459i	−1.18255	−	0.430414i	−0.857103	+	0.515145i	$0.827738\pi$
$410$	9.83951	−	8.25633i	0.485939	−	0.407751i
$411$		0			0
$412$	1.00017	−	0.364032i	0.0492748	−	0.0179346i
$413$	−12.5789	+	21.7872i	−0.618965	+	1.07208i
$414$		0			0
$415$	−4.83779	−	8.37929i	−0.237478	−	0.411323i
$416$	14.3334	+	12.0272i	0.702753	+	0.589680i
$417$		0			0
$418$	3.05531	+	17.3275i	0.149440	+	0.847517i
$419$	2.20013	+	12.4776i	0.107483	+	0.609569i	0.990199	+	0.139662i	$0.0446015\pi$
$419$	2.20013	+	12.4776i	0.107483	+	0.609569i	−0.882716	+	0.469907i	$0.844287\pi$
$420$		0			0
$421$	−13.5416	−	11.3627i	−0.659975	−	0.553785i	0.250104	−	0.968219i	$-0.419535\pi$
$421$	−13.5416	−	11.3627i	−0.659975	−	0.553785i	−0.910079	+	0.414434i	$0.863980\pi$
$422$	−11.8777	−	20.5727i	−0.578196	−	1.00147i
$423$		0			0
$424$	−8.74249	+	15.1424i	−0.424573	+	0.735382i
$425$	2.00289	−	0.728993i	0.0971545	−	0.0353614i
$426$		0			0
$427$	−2.73741	+	2.29696i	−0.132473	+	0.111158i
$428$	−5.81081	−	2.11496i	−0.280876	−	0.102231i
$429$		0			0
$430$	−4.52707	+	25.6743i	−0.218315	+	1.23812i
$431$	−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	$0.598115\pi$
$434$	−0.795335	+	4.51057i	−0.0381773	+	0.216514i
$435$		0			0
$436$	5.63954	+	2.05262i	0.270085	+	0.0983028i
$437$	3.31837	−	2.78444i	0.158739	−	0.133198i
$438$		0			0
$439$	−25.3124	+	9.21297i	−1.20810	+	0.439711i	−0.866043	−	0.499970i	$-0.833344\pi$
$439$	−25.3124	+	9.21297i	−1.20810	+	0.439711i	−0.342053	+	0.939681i	$0.611122\pi$
$440$	8.29608	−	14.3692i	0.395500	−	0.685027i
$441$		0			0
$442$	5.29934	+	9.17873i	0.252064	+	0.436588i
$443$	−26.6031	−	22.3227i	−1.26395	−	1.06058i	−0.995249	−	0.0973585i	$-0.968961\pi$
$443$	−26.6031	−	22.3227i	−1.26395	−	1.06058i	−0.268703	−	0.963223i	$-0.586595\pi$
$444$		0			0
$445$	1.32456	+	7.51196i	0.0627902	+	0.356101i
$446$	3.36801	+	19.1009i	0.159480	+	0.904456i
$447$		0			0
$448$	11.0444	+	9.26732i	0.521797	+	0.437840i
$449$	−10.3731	−	17.9667i	−0.489535	−	0.847900i	0.510392	−	0.859942i	$-0.329500\pi$
$449$	−10.3731	−	17.9667i	−0.489535	−	0.847900i	−0.999927	+	0.0120419i	$0.996167\pi$
$450$		0			0
$451$	−10.0629	+	17.4295i	−0.473844	+	0.820722i
$452$	−0.208162	+	0.0757647i	−0.00979111	+	0.00356367i
$453$		0			0
$454$	4.53732	−	3.80727i	0.212947	−	0.178684i
$455$	−30.1426	−	10.9710i	−1.41311	−	0.514329i
$456$		0			0
$457$	−1.25161	+	7.09823i	−0.0585478	+	0.332041i	−0.999987	−	0.00514224i	$-0.998363\pi$
$457$	−1.25161	+	7.09823i	−0.0585478	+	0.332041i	0.941439	+	0.337183i	$0.109474\pi$
$458$	29.3621			1.37200
$459$		0			0
$460$	1.33046			0.0620332
$461$	−4.01593	+	22.7755i	−0.187041	+	1.06076i	0.736265	+	0.676694i	$0.236588\pi$
$461$	−4.01593	+	22.7755i	−0.187041	+	1.06076i	−0.923305	+	0.384067i	$0.874523\pi$
$462$		0			0
$463$	−4.67576	−	1.70184i	−0.217301	−	0.0790911i	0.231076	−	0.972936i	$-0.425775\pi$
$463$	−4.67576	−	1.70184i	−0.217301	−	0.0790911i	−0.448377	+	0.893845i	$0.647998\pi$
$464$	29.8839	−	25.0756i	1.38733	−	1.16411i
$465$		0			0
$466$	−0.809515	+	0.294639i	−0.0375000	+	0.0136489i
$467$	−6.24068	+	10.8092i	−0.288784	+	0.500189i	−0.973520	−	0.228602i	$-0.926584\pi$
$467$	−6.24068	+	10.8092i	−0.288784	+	0.500189i	0.684735	+	0.728792i	$0.259918\pi$
$468$		0			0
$469$	6.45669	+	11.1833i	0.298142	+	0.516397i
$470$	−25.3645	−	21.2833i	−1.16998	−	0.981726i
$471$		0			0
$472$	3.74294	+	21.2273i	0.172283	+	0.977064i
$473$	−7.09335	−	40.2284i	−0.326153	−	1.84970i
$474$		0			0
$475$	−4.48974	−	3.76734i	−0.206004	−	0.172858i
$476$	−0.666803	−	1.15494i	−0.0305628	−	0.0529364i
$477$		0			0
$478$	15.8588	−	27.4683i	0.725365	−	1.25637i
$479$	26.7542	−	9.73775i	1.22243	−	0.444929i	0.351433	−	0.936213i	$-0.385694\pi$
$479$	26.7542	−	9.73775i	1.22243	−	0.444929i	0.870999	+	0.491284i	$0.163472\pi$
$480$		0			0
$481$	−6.89152	+	5.78267i	−0.314226	+	0.263667i
$482$	22.6803	+	8.25495i	1.03306	+	0.376003i
$483$		0			0
$484$	0.531793	−	3.01595i	0.0241724	−	0.137088i
$485$	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	$0.265196\pi$
$488$	−0.531653	+	3.01515i	−0.0240668	+	0.136489i
$489$		0			0
$490$	1.80348	+	0.656412i	0.0814728	+	0.0296537i
$491$	−9.50275	+	7.97375i	−0.428853	+	0.359850i	−0.831519	−	0.555497i	$-0.812528\pi$
$491$	−9.50275	+	7.97375i	−0.428853	+	0.359850i	0.402666	+	0.915347i	$0.368084\pi$
$492$		0			0
$493$	7.55038	−	2.74811i	0.340052	−	0.123769i
$494$	14.5720	−	25.2394i	0.655623	−	1.13557i
$495$		0			0
$496$	2.47512	+	4.28702i	0.111136	+	0.192493i
$497$	11.9732	+	10.0467i	0.537073	+	0.450658i
$498$		0			0
$499$	−0.395887	−	2.24519i	−0.0177223	−	0.100508i	0.974664	−	0.223676i	$-0.0718058\pi$
$499$	−0.395887	−	2.24519i	−0.0177223	−	0.100508i	−0.992386	+	0.123168i	$0.960695\pi$
$500$	−1.02867	−	5.83387i	−0.0460035	−	0.260899i
$501$		0			0
$502$	15.4240	+	12.9423i	0.688407	+	0.577642i
$503$	20.6406	+	35.7506i	0.920320	+	1.59404i	0.798920	+	0.601437i	$0.205405\pi$
$503$	20.6406	+	35.7506i	0.920320	+	1.59404i	0.121399	+	0.992604i	$0.461262\pi$
$504$		0			0
$505$	6.55097	−	11.3466i	0.291514	−	0.504917i
$506$	−9.93253	+	3.61515i	−0.441555	+	0.160713i
$507$		0			0
$508$	−0.199896	+	0.167733i	−0.00886896	+	0.00744194i
$509$	15.4337	+	5.61739i	0.684085	+	0.248986i	0.660600	−	0.750738i	$-0.270302\pi$
$509$	15.4337	+	5.61739i	0.684085	+	0.248986i	0.0234843	+	0.999724i	$0.492524\pi$
$510$		0			0
$511$	−2.20143	+	12.4849i	−0.0973856	+	0.552301i
$512$	9.67844			0.427731
$513$		0			0
$514$	−20.6845			−0.912355
$515$	−0.631366	+	3.58066i	−0.0278213	+	0.157783i
$516$		0			0
$517$	48.7519	+	17.7443i	2.14411	+	0.780391i
$518$	4.39670	−	3.68927i	0.193180	−	0.162097i
$519$		0			0
$520$	−25.8257	+	9.39978i	−1.13253	+	0.412208i
$521$	−4.64836	+	8.05119i	−0.203648	+	0.352729i	−0.949701	−	0.313157i	$-0.898613\pi$
$521$	−4.64836	+	8.05119i	−0.203648	+	0.352729i	0.746053	+	0.665887i	$0.231947\pi$
$522$		0			0
$523$	11.3736	+	19.6996i	0.497331	+	0.861402i	0.999995	−	0.00307938i	$-0.000980199\pi$
$523$	11.3736	+	19.6996i	0.497331	+	0.861402i	−0.502664	+	0.864482i	$0.667647\pi$
$524$	−4.29704	−	3.60564i	−0.187717	−	0.157513i
$525$		0			0
$526$	−2.60771	−	14.7891i	−0.113702	−	0.644834i
$527$	0.177049	+	1.00410i	0.00771239	+	0.0437392i
$528$		0			0
$529$	−15.6255	−	13.1114i	−0.679371	−	0.570060i
$530$	9.72687	+	16.8474i	0.422508	+	0.731806i
$531$		0			0
$532$	−1.83355	+	3.17581i	−0.0794946	+	0.137689i
$533$	31.3258	−	11.4017i	1.35687	−	0.493861i
$534$		0			0
$535$	16.1819	−	13.5782i	0.699603	−	0.587037i
$536$	10.3967	+	3.78410i	0.449070	+	0.163448i
$537$		0			0
$538$	6.06850	−	34.4162i	0.261632	−	1.48379i
$539$	−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	$0.483642\pi$
$542$	−7.66422	+	43.4659i	−0.329206	+	1.86702i
$543$		0			0
$544$	−2.49711	−	0.908874i	−0.107063	−	0.0389676i
$545$	−15.7049	+	13.1780i	−0.672724	+	0.564482i
$546$		0			0
$547$	−27.8777	+	10.1466i	−1.19196	+	0.433839i	−0.860412	−	0.509599i	$-0.829794\pi$
$547$	−27.8777	+	10.1466i	−1.19196	+	0.433839i	−0.331550	+	0.943438i	$0.607572\pi$
$548$	1.03904	−	1.79967i	0.0443856	−	0.0768781i
$549$		0			0
$550$	7.15057	+	12.3852i	0.304901	+	0.528105i
$551$	−16.9252	−	14.2019i	−0.721036	−	0.605021i
$552$		0			0
$553$	2.24745	+	12.7459i	0.0955714	+	0.542012i
$554$	5.17577	+	29.3533i	0.219897	+	1.24710i
$555$		0			0
$556$	−4.19898	−	3.52336i	−0.178076	−	0.149424i
$557$	4.20706	+	7.28685i	0.178259	+	0.308754i	0.941284	−	0.337615i	$-0.109620\pi$
$557$	4.20706	+	7.28685i	0.178259	+	0.308754i	−0.763025	+	0.646369i	$0.776287\pi$
$558$		0			0
$559$	−33.8309	+	58.5969i	−1.43090	+	2.47838i
$560$	20.7844	−	7.56491i	0.878302	−	0.319676i
$561$		0			0
$562$	−24.1847	+	20.2933i	−1.02017	+	0.856023i
$563$	−25.5845	−	9.31201i	−1.07826	−	0.392455i	−0.259000	−	0.965877i	$-0.583393\pi$
$563$	−25.5845	−	9.31201i	−1.07826	−	0.392455i	−0.819260	+	0.573423i	$0.805615\pi$
$564$		0			0
$565$	0.131404	−	0.745230i	0.00552822	−	0.0313521i
$566$	−26.4304			−1.11095
$567$		0			0
$568$	13.3915			0.561894
$569$	3.81146	−	21.6159i	0.159785	−	0.906184i	−0.794495	−	0.607270i	$-0.792265\pi$
$569$	3.81146	−	21.6159i	0.159785	−	0.906184i	0.954280	−	0.298914i	$-0.0966243\pi$
$570$		0			0
$571$	42.1485	+	15.3408i	1.76386	+	0.641992i	0.999994	−	0.00338488i	$-0.00107744\pi$
$571$	42.1485	+	15.3408i	1.76386	+	0.641992i	0.763864	+	0.645377i	$0.223300\pi$
$572$	−10.7441	+	9.01533i	−0.449232	+	0.376950i
$573$		0			0
$574$	−19.9855	+	7.27412i	−0.834178	+	0.303616i
$575$	1.76046	−	3.04921i	0.0734163	−	0.127161i
$576$		0			0
$577$	−6.00955	−	10.4088i	−0.250181	−	0.433326i	0.713395	−	0.700762i	$-0.247157\pi$
$577$	−6.00955	−	10.4088i	−0.250181	−	0.433326i	−0.963575	+	0.267437i	$0.913823\pi$
$578$	19.4021	+	16.2803i	0.807020	+	0.677170i
$579$		0			0
$580$	−1.17837	−	6.68286i	−0.0489291	−	0.277491i
$581$	2.78199	+	15.7775i	0.115417	+	0.654560i
$582$		0			0
$583$	−23.3502	−	19.5932i	−0.967068	−	0.811467i
$584$	5.43095	+	9.40669i	0.224734	+	0.389252i
$585$		0			0
$586$	−15.4463	+	26.7537i	−0.638079	+	1.10519i
$587$	−16.0028	+	5.82456i	−0.660508	+	0.240405i	−0.650456	−	0.759544i	$-0.725422\pi$
$587$	−16.0028	+	5.82456i	−0.660508	+	0.240405i	−0.0100523	+	0.999949i	$0.503200\pi$
$588$		0			0
$589$	2.14770	−	1.80214i	0.0884946	−	0.0742558i
$590$	22.5354	+	8.20223i	0.927769	+	0.337680i
$591$		0			0
$592$	1.07718	−	6.10899i	0.0442718	−	0.251078i
$593$	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
$596$	1.66191	−	9.42516i	0.0680745	−	0.386070i
$597$		0			0
$598$	16.4522	+	5.98810i	0.672779	+	0.244871i
$599$	−10.3683	+	8.70000i	−0.423636	+	0.355472i	−0.829544	−	0.558441i	$-0.811400\pi$
$599$	−10.3683	+	8.70000i	−0.423636	+	0.355472i	0.405909	+	0.913914i	$0.366955\pi$
$600$		0			0
$601$	42.5843	−	15.4994i	1.73705	−	0.632234i	0.737958	−	0.674847i	$-0.235790\pi$
$601$	42.5843	−	15.4994i	1.73705	−	0.632234i	0.999092	+	0.0426125i	$0.0135681\pi$
$602$	21.5837	−	37.3841i	0.879686	−	1.52366i
$603$		0			0
$604$	0.305346	+	0.528874i	0.0124243	+	0.0215196i
$605$	8.01401	+	6.72455i	0.325816	+	0.273392i
$606$		0			0
$607$	4.24340	+	24.0655i	0.172234	+	0.976790i	0.941288	+	0.337605i	$0.109617\pi$
$607$	4.24340	+	24.0655i	0.172234	+	0.976790i	−0.769053	+	0.639185i	$0.779272\pi$
$608$	1.26887	+	7.19613i	0.0514596	+	0.291842i
$609$		0			0
$610$	2.60945	+	2.18959i	0.105654	+	0.0886539i
$611$	−42.9674	−	74.4217i	−1.73827	−	3.01078i
$612$		0			0
$613$	12.5998	−	21.8235i	0.508901	−	0.881443i	−0.491046	−	0.871134i	$-0.663385\pi$
$613$	12.5998	−	21.8235i	0.508901	−	0.881443i	0.999947	−	0.0103088i	$-0.00328145\pi$
$614$	22.0991	−	8.04342i	0.891847	−	0.324606i
$615$		0			0
$616$	−21.0458	+	17.6596i	−0.847961	+	0.711524i
$617$	3.79810	+	1.38239i	0.152906	+	0.0556531i	0.417339	−	0.908751i	$-0.362963\pi$
$617$	3.79810	+	1.38239i	0.152906	+	0.0556531i	−0.264433	+	0.964404i	$0.585185\pi$
$618$		0			0
$619$	−7.77423	+	44.0898i	−0.312473	+	1.77212i	0.273582	+	0.961849i	$0.411791\pi$
$619$	−7.77423	+	44.0898i	−0.312473	+	1.77212i	−0.586055	+	0.810271i	$0.699320\pi$
$620$	0.861097			0.0345825
$621$		0			0
$622$	7.24860			0.290642
$623$	2.19321	−	12.4383i	0.0878693	−	0.498332i
$624$		0			0
$625$	8.76089	+	3.18870i	0.350435	+	0.127548i
$626$	−14.3508	+	12.0417i	−0.573572	+	0.481284i
$627$		0			0
$628$	1.63135	−	0.593762i	0.0650978	−	0.0236937i
$629$	0.638833	−	1.10649i	0.0254719	−	0.0441187i
$630$		0			0
$631$	−15.7058	−	27.2033i	−0.625238	−	1.08294i	−0.988495	−	0.151255i	$-0.951668\pi$
$631$	−15.7058	−	27.2033i	−0.625238	−	1.08294i	0.363256	−	0.931689i	$-0.381665\pi$
$632$	8.49465	+	7.12786i	0.337899	+	0.283531i
$633$		0			0
$634$	−3.97902	−	22.5661i	−0.158027	−	0.896215i
$635$	−0.154790	−	0.877861i	−0.00614267	−	0.0348368i
$636$		0			0
$637$	3.81571	+	3.20176i	0.151184	+	0.126859i
$638$	26.9558	+	46.6888i	1.06719	+	1.84843i
$639$		0			0
$640$	11.4392	−	19.8133i	0.452176	−	0.783191i
$641$	45.7072	−	16.6361i	1.80533	−	0.657085i	0.807597	−	0.589734i	$-0.200768\pi$
$641$	45.7072	−	16.6361i	1.80533	−	0.657085i	0.997729	−	0.0673508i	$-0.0214547\pi$
$642$		0			0
$643$	−21.4740	+	18.0189i	−0.846853	+	0.710594i	−0.959094	−	0.283087i	$-0.908642\pi$
$643$	−21.4740	+	18.0189i	−0.846853	+	0.710594i	0.112241	+	0.993681i	$0.464197\pi$
$644$	−2.07013	−	0.753467i	−0.0815747	−	0.0296907i
$645$		0			0
$646$	−0.718744	+	4.07620i	−0.0282786	+	0.160376i
$647$	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
$650$	4.11343	−	23.3284i	0.161342	−	0.915015i
$651$		0			0
$652$	−7.36496	−	2.68062i	−0.288434	−	0.104981i
$653$	3.91619	−	3.28607i	0.153252	−	0.128594i	−0.562938	−	0.826499i	$-0.690329\pi$
$653$	3.91619	−	3.28607i	0.153252	−	0.128594i	0.716190	+	0.697905i	$0.245884\pi$
$654$		0			0
$655$	18.0063	−	6.55376i	0.703564	−	0.256076i
$656$	−11.4933	+	19.9069i	−0.448737	+	0.777236i
$657$		0			0
$658$	27.4126	+	47.4801i	1.06866	+	1.85097i
$659$	−26.8161	−	22.5014i	−1.04461	−	0.876529i	−0.0520901	−	0.998642i	$-0.516588\pi$
$659$	−26.8161	−	22.5014i	−1.04461	−	0.876529i	−0.992516	+	0.122114i	$0.961033\pi$
$660$		0			0
$661$	0.231553	+	1.31320i	0.00900637	+	0.0510777i	0.988980	−	0.148051i	$-0.0473000\pi$
$661$	0.231553	+	1.31320i	0.00900637	+	0.0510777i	−0.979973	+	0.199129i	$0.936189\pi$
$662$	2.22167	+	12.5997i	0.0863476	+	0.489701i
$663$		0			0
$664$	10.5151	+	8.82317i	0.408063	+	0.342406i
$665$	−6.26350	−	10.8487i	−0.242888	−	0.420694i
$666$		0			0
$667$	6.63648	−	11.4947i	0.256966	−	0.445077i
$668$	6.68795	−	2.43422i	0.258765	−	0.0941827i
$669$		0			0
$670$	9.42980	−	7.91255i	0.364305	−	0.305688i
$671$	−5.01552	−	1.82550i	−0.193622	−	0.0704726i
$672$		0			0
$673$	−0.621579	+	3.52515i	−0.0239601	+	0.135884i	−0.994441	−	0.105292i	$-0.966422\pi$
$673$	−0.621579	+	3.52515i	−0.0239601	+	0.135884i	0.970481	+	0.241177i	$0.0775333\pi$
$674$	29.6866			1.14348
$675$		0			0
$676$	16.8438			0.647839
$677$	6.41437	−	36.3777i	0.246524	−	1.39811i	−0.570401	−	0.821366i	$-0.693212\pi$
$677$	6.41437	−	36.3777i	0.246524	−	1.39811i	0.816926	−	0.576743i	$-0.195677\pi$
$678$		0			0
$679$	−22.3962	−	8.15156i	−0.859488	−	0.312828i
$680$	2.99003	−	2.50894i	0.114663	−	0.0962133i
$681$		0			0
$682$	−6.42850	+	2.33978i	−0.246160	+	0.0895948i
$683$	19.0083	−	32.9233i	0.727332	−	1.25978i	−0.230675	−	0.973031i	$-0.574093\pi$
$683$	19.0083	−	32.9233i	0.727332	−	1.25978i	0.958007	−	0.286745i	$-0.0925733\pi$
$684$		0			0
$685$	3.54941	+	6.14775i	0.135616	+	0.234894i
$686$	21.0892	+	17.6959i	0.805188	+	0.675633i
$687$		0			0
$688$	−8.10161	−	45.9465i	−0.308871	−	1.75170i
$689$	8.76739	+	49.7223i	0.334011	+	1.89427i
$690$		0			0
$691$	0.421680	+	0.353832i	0.0160415	+	0.0134604i	0.650773	−	0.759272i	$-0.274445\pi$
$691$	0.421680	+	0.353832i	0.0160415	+	0.0134604i	−0.634732	+	0.772733i	$0.718889\pi$
$692$	3.09984	+	5.36908i	0.117838	+	0.204102i
$693$		0			0
$694$	13.9039	−	24.0822i	0.527784	−	0.914148i
$695$	17.5954	−	6.40420i	0.667432	−	0.242925i
$696$		0			0
$697$	−3.62683	+	3.04327i	−0.137376	+	0.115272i
$698$	−25.1988	−	9.17160i	−0.953788	−	0.347150i
$699$		0			0
$700$	−0.517582	+	2.93535i	−0.0195628	+	0.110946i
$701$	−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
$704$	−3.73939	+	21.2071i	−0.140933	+	0.799273i
$705$		0			0
$706$	22.4790	+	8.18169i	0.846009	+	0.307922i
$707$	−16.6188	+	13.9448i	−0.625013	+	0.524448i
$708$		0			0
$709$	−11.4236	+	4.15786i	−0.429024	+	0.156152i	−0.547501	−	0.836805i	$-0.684421\pi$
$709$	−11.4236	+	4.15786i	−0.429024	+	0.156152i	0.118478	+	0.992957i	$0.462199\pi$
$710$	7.44966	−	12.9032i	0.279581	−	0.484248i
$711$		0			0
$712$	−5.41068	−	9.37158i	−0.202774	−	0.351215i
$713$	1.29022	+	1.08262i	0.0483191	+	0.0405445i
$714$		0			0
$715$	−8.31971	−	47.1834i	−0.311140	−	1.76456i
$716$	−0.0252472	−	0.143184i	−0.000943531	−	0.00535103i
$717$		0			0
$718$	2.96352	+	2.48669i	0.110598	+	0.0928024i
$719$	4.88834	+	8.46685i	0.182304	+	0.315760i	0.942665	−	0.333741i	$-0.108311\pi$
$719$	4.88834	+	8.46685i	0.182304	+	0.315760i	−0.760361	+	0.649501i	$0.774978\pi$
$720$		0			0
$721$	3.01017	−	5.21376i	0.112104	−	0.194171i
$722$	−17.4859	+	6.36437i	−0.650760	+	0.236857i
$723$		0			0
$724$	0.534682	−	0.448651i	0.0198713	−	0.0166740i
$725$	−16.8752	−	6.14209i	−0.626731	−	0.228111i
$726$		0			0
$727$	0.752752	−	4.26907i	0.0279180	−	0.158331i	−0.967662	−	0.252252i	$-0.918829\pi$
$727$	0.752752	−	4.26907i	0.0279180	−	0.158331i	0.995580	+	0.0939207i	$0.0299400\pi$
$728$	45.5067			1.68659
$729$		0			0
$730$	12.0849			0.447283
$731$	1.66867	−	9.46350i	0.0617180	−	0.350020i
$732$		0			0
$733$	−27.4331	−	9.98482i	−1.01326	−	0.368798i	−0.218578	−	0.975819i	$-0.570142\pi$
$733$	−27.4331	−	9.98482i	−1.01326	−	0.368798i	−0.794685	+	0.607022i	$0.792364\pi$
$734$	1.58823	−	1.33268i	0.0586226	−	0.0491902i
$735$		0			0
$736$	−4.12499	+	1.50137i	−0.152049	+	0.0553413i
$737$	−9.64391	+	16.7037i	−0.355238	+	0.615290i
$738$		0			0
$739$	−20.7777	−	35.9880i	−0.764319	−	1.32384i	−0.940606	−	0.339501i	$-0.889742\pi$
$739$	−20.7777	−	35.9880i	−0.764319	−	1.32384i	0.176287	−	0.984339i	$-0.443591\pi$
$740$	−0.826607	−	0.693606i	−0.0303867	−	0.0254975i
$741$		0			0
$742$	−5.59349	−	31.7222i	−0.205343	−	1.16456i
$743$	−3.71214	−	21.0526i	−0.136185	−	0.772345i	−0.974027	−	0.226432i	$-0.927294\pi$
$743$	−3.71214	−	21.0526i	−0.136185	−	0.772345i	0.837842	−	0.545913i	$-0.183817\pi$
$744$		0			0
$745$	25.0446	+	21.0149i	0.917565	+	0.769928i
$746$	−7.59699	−	13.1584i	−0.278146	−	0.481763i
$747$		0			0
$748$	0.995957	−	1.72505i	0.0364158	−	0.0630740i
$749$	−32.8677	+	11.9629i	−1.20096	+	0.437114i
$750$		0			0
$751$	−30.6170	+	25.6907i	−1.11723	+	0.937467i	−0.998461	−	0.0554555i	$-0.982339\pi$
$751$	−30.6170	+	25.6907i	−1.11723	+	0.937467i	−0.118768	+	0.992922i	$0.537894\pi$
$752$	55.6816	+	20.2665i	2.03050	+	0.739042i
$753$		0			0
$754$	15.5065	−	87.9420i	0.564715	−	3.20266i
$755$	−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	$0.461243\pi$
$758$	2.34704	−	13.3107i	0.0852482	−	0.483467i
$759$		0			0
$760$	−10.0857	−	3.67088i	−0.365845	−	0.133157i
$761$	−32.1930	+	27.0132i	−1.16700	+	0.979226i	−0.999977	−	0.00672735i	$-0.997859\pi$
$761$	−32.1930	+	27.0132i	−1.16700	+	0.979226i	−0.167019	+	0.985954i	$0.553414\pi$
$762$		0			0
$763$	31.8989	−	11.6103i	1.15482	−	0.420320i
$764$	5.06692	−	8.77617i	0.183315	−	0.317511i
$765$		0			0
$766$	−26.5445	−	45.9764i	−0.959092	−	1.66120i
$767$	47.6795	+	40.0078i	1.72161	+	1.44460i
$768$		0			0
$769$	0.419053	+	2.37657i	0.0151114	+	0.0857013i	0.991431	−	0.130633i	$-0.0417010\pi$
$769$	0.419053	+	2.37657i	0.0151114	+	0.0857013i	−0.976319	+	0.216334i	$0.930590\pi$
$770$	5.30787	+	30.1024i	0.191282	+	1.08482i
$771$		0			0
$772$	−7.88789	−	6.61872i	−0.283891	−	0.238213i
$773$	0.698900	+	1.21053i	0.0251377	+	0.0435398i	0.878321	−	0.478072i	$-0.158664\pi$
$773$	0.698900	+	1.21053i	0.0251377	+	0.0435398i	−0.853183	+	0.521612i	$0.825331\pi$
$774$		0			0
$775$	1.13940	−	1.97350i	0.0409284	−	0.0708901i
$776$	−19.1887	+	6.98413i	−0.688835	+	0.250715i
$777$		0			0
$778$	−18.0813	+	15.1720i	−0.648245	+	0.543942i
$779$	12.2336	+	4.45267i	0.438315	+	0.159533i
$780$		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)

\(f(q)\)	\(=\)	\(q+(-0.274087 + 1.55442i) q^{2} +(-0.461727 - 0.168055i) q^{4} +(1.28581 - 1.07892i) q^{5} +(-2.61167 + 0.950570i) q^{7} +(-1.19062 + 2.06222i) q^{8} +O(q^{10})\)	\(q+(-0.274087 + 1.55442i) q^{2} +(-0.461727 - 0.168055i) q^{4} +(1.28581 - 1.07892i) q^{5} +(-2.61167 + 0.950570i) q^{7} +(-1.19062 + 2.06222i) q^{8} +(1.32468 + 2.29442i) q^{10} +(-3.18002 - 2.66835i) q^{11} +(1.19401 + 6.77158i) q^{13} +(-0.761765 - 4.32018i) q^{14} +(-3.63204 - 3.04764i) q^{16} +(-0.488276 - 0.845718i) q^{17} +(-1.34264 + 2.32553i) q^{19} +(-0.775013 + 0.282082i) q^{20} +(5.01936 - 4.21174i) q^{22} +(-1.51588 - 0.551737i) q^{23} +(-0.379007 + 2.14945i) q^{25} -10.8532 q^{26} +1.36563 q^{28} +(-1.42876 + 8.10288i) q^{29} +(-0.981104 - 0.357093i) q^{31} +(2.08454 - 1.74914i) q^{32} +(1.44844 - 0.527187i) q^{34} +(-2.33252 + 4.04005i) q^{35} +(0.654172 + 1.13306i) q^{37} +(-3.24686 - 2.72444i) q^{38} +(0.694061 + 3.93621i) q^{40} +(-0.841876 - 4.77452i) q^{41} +(7.53805 + 6.32518i) q^{43} +(1.01987 + 1.76647i) q^{44} +(1.27312 - 2.20510i) q^{46} +(-11.7440 + 4.27447i) q^{47} +(0.554929 - 0.465640i) q^{49} +(-3.23728 - 1.17827i) q^{50} +(0.586690 - 3.32728i) q^{52} +7.34280 q^{53} -6.96786 q^{55} +(1.14923 - 6.51760i) q^{56} +(-12.2037 - 4.44179i) q^{58} +(6.93414 - 5.81843i) q^{59} +(1.20820 - 0.439750i) q^{61} +(0.823982 - 1.42718i) q^{62} +(-2.59373 - 4.49247i) q^{64} +(8.84130 + 7.41873i) q^{65} +(-0.806821 - 4.57571i) q^{67} +(0.0833230 + 0.472548i) q^{68} +(-5.64064 - 4.73306i) q^{70} +(-2.81187 - 4.87030i) q^{71} +(2.28072 - 3.95033i) q^{73} +(-1.94056 + 0.706305i) q^{74} +(1.01075 - 0.848122i) q^{76} +(10.8416 + 3.94603i) q^{77} +(0.808645 - 4.58605i) q^{79} -7.95828 q^{80} +7.65237 q^{82} +(1.00098 - 5.67682i) q^{83} +(-1.54030 - 0.560622i) q^{85} +(-11.8981 + 9.98369i) q^{86} +(9.28893 - 3.38089i) q^{88} +(-2.27221 + 3.93558i) q^{89} +(-9.55523 - 16.5502i) q^{91} +(0.607203 + 0.509504i) q^{92} +(-3.42546 - 19.4267i) q^{94} +(0.782681 + 4.43880i) q^{95} +(6.56917 + 5.51219i) q^{97} +(0.571704 + 0.990221i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{2} - 3 q^{4} + 6 q^{5} + 6 q^{7} + 6 q^{8}+O(q^{10}) \) 12 * q + 3 * q^2 - 3 * q^4 + 6 * q^5 + 6 * q^7 + 6 * q^8	\( 12 q + 3 q^{2} - 3 q^{4} + 6 q^{5} + 6 q^{7} + 6 q^{8} - 6 q^{10} - 15 q^{11} - 3 q^{13} - 21 q^{14} + 9 q^{16} - 9 q^{17} - 12 q^{19} - 3 q^{20} + 33 q^{22} + 15 q^{23} - 12 q^{25} - 48 q^{26} + 6 q^{28} - 6 q^{29} - 12 q^{31} - 27 q^{32} + 27 q^{34} + 30 q^{35} - 3 q^{37} - 39 q^{38} + 24 q^{40} - 39 q^{41} + 24 q^{43} - 33 q^{44} + 3 q^{46} - 42 q^{47} - 30 q^{49} - 15 q^{50} - 45 q^{52} + 18 q^{53} + 30 q^{55} + 12 q^{56} - 30 q^{58} + 15 q^{59} - 3 q^{61} - 30 q^{62} - 6 q^{64} - 6 q^{65} - 3 q^{67} + 36 q^{68} - 75 q^{70} - 12 q^{73} + 60 q^{74} + 30 q^{76} + 33 q^{77} + 33 q^{79} + 42 q^{80} - 42 q^{82} - 33 q^{83} - 18 q^{85} - 30 q^{86} - 42 q^{88} - 9 q^{89} - 18 q^{91} + 33 q^{92} - 66 q^{94} + 12 q^{95} + 15 q^{97} + 18 q^{98}+O(q^{100}) \) 12 * q + 3 * q^2 - 3 * q^4 + 6 * q^5 + 6 * q^7 + 6 * q^8 - 6 * q^10 - 15 * q^11 - 3 * q^13 - 21 * q^14 + 9 * q^16 - 9 * q^17 - 12 * q^19 - 3 * q^20 + 33 * q^22 + 15 * q^23 - 12 * q^25 - 48 * q^26 + 6 * q^28 - 6 * q^29 - 12 * q^31 - 27 * q^32 + 27 * q^34 + 30 * q^35 - 3 * q^37 - 39 * q^38 + 24 * q^40 - 39 * q^41 + 24 * q^43 - 33 * q^44 + 3 * q^46 - 42 * q^47 - 30 * q^49 - 15 * q^50 - 45 * q^52 + 18 * q^53 + 30 * q^55 + 12 * q^56 - 30 * q^58 + 15 * q^59 - 3 * q^61 - 30 * q^62 - 6 * q^64 - 6 * q^65 - 3 * q^67 + 36 * q^68 - 75 * q^70 - 12 * q^73 + 60 * q^74 + 30 * q^76 + 33 * q^77 + 33 * q^79 + 42 * q^80 - 42 * q^82 - 33 * q^83 - 18 * q^85 - 30 * q^86 - 42 * q^88 - 9 * q^89 - 18 * q^91 + 33 * q^92 - 66 * q^94 + 12 * q^95 + 15 * q^97 + 18 * q^98

Introduction

L-functions

Modular forms

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