LMFDB - Embedded newform 729.2.e.u.82.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("729.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 18x^{10} + 105x^{8} + 266x^{6} + 306x^{4} + 132x^{2} + 1 $ x^12 + 18x^10 + 105x^8 + 266x^6 + 306x^4 + 132*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			82.2
Root			$-3.10658i$ of defining polynomial
Character	$\chi$	$=$	729.82
Dual form			729.2.e.u.649.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.369007 + 2.09274i) q^{2} +(-2.36403 + 0.860436i) q^{4} +(1.58643 + 1.33117i) q^{5} +(-4.55626 - 1.65834i) q^{7} +(-0.547989 - 0.949144i) q^{8} +O(q^{10})$	\(q+(0.369007 + 2.09274i) q^{2} +(-2.36403 + 0.860436i) q^{4} +(1.58643 + 1.33117i) q^{5} +(-4.55626 - 1.65834i) q^{7} +(-0.547989 - 0.949144i) q^{8} +(-2.20040 + 3.81121i) q^{10} +(-3.17869 + 2.66724i) q^{11} +(-0.211159 + 1.19754i) q^{13} +(1.78920 - 10.1470i) q^{14} +(-2.07024 + 1.73714i) q^{16} +(1.18182 - 2.04697i) q^{17} +(0.919003 + 1.59176i) q^{19} +(-4.89576 - 1.78191i) q^{20} +(-6.75481 - 5.66796i) q^{22} +(-4.04403 + 1.47191i) q^{23} +(-0.123500 - 0.700401i) q^{25} -2.58407 q^{26} +12.1980 q^{28} +(-0.517788 - 2.93652i) q^{29} +(-1.38472 + 0.503996i) q^{31} +(-6.07846 - 5.10043i) q^{32} +(4.71989 + 1.71790i) q^{34} +(-5.02066 - 8.69603i) q^{35} +(-4.48554 + 7.76918i) q^{37} +(-2.99203 + 2.51061i) q^{38} +(0.394130 - 2.23522i) q^{40} +(-0.392536 + 2.22618i) q^{41} +(-4.20164 + 3.52560i) q^{43} +(5.21953 - 9.04050i) q^{44} +(-4.57260 - 7.91998i) q^{46} +(6.74994 + 2.45678i) q^{47} +(12.6471 + 10.6122i) q^{49} +(1.42019 - 0.516906i) q^{50} +(-0.531222 - 3.01271i) q^{52} +6.32803 q^{53} -8.59334 q^{55} +(0.922773 + 5.23330i) q^{56} +(5.95432 - 2.16719i) q^{58} +(-0.200900 - 0.168575i) q^{59} +(4.18690 + 1.52391i) q^{61} +(-1.56571 - 2.71188i) q^{62} +(5.72840 - 9.92188i) q^{64} +(-1.92913 + 1.61873i) q^{65} +(0.717359 - 4.06834i) q^{67} +(-1.03257 + 5.85598i) q^{68} +(16.3459 - 13.7159i) q^{70} +(1.54276 - 2.67213i) q^{71} +(-6.38003 - 11.0505i) q^{73} +(-17.9141 - 6.52021i) q^{74} +(-3.54216 - 2.97222i) q^{76} +(18.9062 - 6.88128i) q^{77} +(0.790517 + 4.48325i) q^{79} -5.59674 q^{80} -4.80368 q^{82} +(1.46786 + 8.32464i) q^{83} +(4.59975 - 1.67417i) q^{85} +(-8.92862 - 7.49200i) q^{86} +(4.27348 + 1.55542i) q^{88} +(8.48158 + 14.6905i) q^{89} +(2.94803 - 5.10614i) q^{91} +(8.29373 - 6.95926i) q^{92} +(-2.65063 + 15.0325i) q^{94} +(-0.660975 + 3.74857i) q^{95} +(-3.91431 + 3.28450i) q^{97} +(-17.5417 + 30.3831i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{2} + 6 q^{4} - 6 q^{5} - 3 q^{7} - 6 q^{8}+O(q^{10}) $ 12 * q + 6 * q^2 + 6 * q^4 - 6 * q^5 - 3 * q^7 - 6 * q^8	$ 12 q + 6 q^{2} + 6 q^{4} - 6 q^{5} - 3 q^{7} - 6 q^{8} - 6 q^{10} - 12 q^{11} - 3 q^{13} - 15 q^{14} - 36 q^{16} + 9 q^{17} - 12 q^{19} - 42 q^{20} + 6 q^{22} - 6 q^{23} + 6 q^{25} + 48 q^{26} + 6 q^{28} - 12 q^{29} + 6 q^{31} - 54 q^{32} - 9 q^{34} - 30 q^{35} - 3 q^{37} - 42 q^{38} - 57 q^{40} - 24 q^{41} + 6 q^{43} + 33 q^{44} + 3 q^{46} - 21 q^{47} + 33 q^{49} - 21 q^{50} + 45 q^{52} - 18 q^{53} + 30 q^{55} - 3 q^{56} + 33 q^{58} - 15 q^{59} + 33 q^{61} + 30 q^{62} - 6 q^{64} + 6 q^{65} + 42 q^{67} + 18 q^{68} + 24 q^{70} - 12 q^{73} + 3 q^{74} - 87 q^{76} + 57 q^{77} - 48 q^{79} - 42 q^{80} - 42 q^{82} - 12 q^{83} - 36 q^{85} + 30 q^{86} + 30 q^{88} + 9 q^{89} - 18 q^{91} + 48 q^{92} + 33 q^{94} - 30 q^{95} - 3 q^{97} - 18 q^{98}+O(q^{100}) $ 12 * q + 6 * q^2 + 6 * q^4 - 6 * q^5 - 3 * q^7 - 6 * q^8 - 6 * q^10 - 12 * q^11 - 3 * q^13 - 15 * q^14 - 36 * q^16 + 9 * q^17 - 12 * q^19 - 42 * q^20 + 6 * q^22 - 6 * q^23 + 6 * q^25 + 48 * q^26 + 6 * q^28 - 12 * q^29 + 6 * q^31 - 54 * q^32 - 9 * q^34 - 30 * q^35 - 3 * q^37 - 42 * q^38 - 57 * q^40 - 24 * q^41 + 6 * q^43 + 33 * q^44 + 3 * q^46 - 21 * q^47 + 33 * q^49 - 21 * q^50 + 45 * q^52 - 18 * q^53 + 30 * q^55 - 3 * q^56 + 33 * q^58 - 15 * q^59 + 33 * q^61 + 30 * q^62 - 6 * q^64 + 6 * q^65 + 42 * q^67 + 18 * q^68 + 24 * q^70 - 12 * q^73 + 3 * q^74 - 87 * q^76 + 57 * q^77 - 48 * q^79 - 42 * q^80 - 42 * q^82 - 12 * q^83 - 36 * q^85 + 30 * q^86 + 30 * q^88 + 9 * q^89 - 18 * q^91 + 48 * q^92 + 33 * q^94 - 30 * q^95 - 3 * q^97 - 18 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	0.369007	+	2.09274i	0.260928	+	1.47979i	0.780386	+	0.625298i	$0.215023\pi$
$2$	0.369007	+	2.09274i	0.260928	+	1.47979i	−0.519458	+	0.854496i	$0.673866\pi$
$3$		0			0
$3$		0			0
$4$	−2.36403	+	0.860436i	−1.18201	+	0.430218i
$5$	1.58643	+	1.33117i	0.709474	+	0.595319i	0.924452	−	0.381300i	$-0.124523\pi$
$5$	1.58643	+	1.33117i	0.709474	+	0.595319i	−0.214977	+	0.976619i	$0.568968\pi$
$6$		0			0
$7$	−4.55626	−	1.65834i	−1.72211	−	0.626795i	−0.724086	−	0.689709i	$-0.757738\pi$
$7$	−4.55626	−	1.65834i	−1.72211	−	0.626795i	−0.998019	+	0.0629144i	$0.979960\pi$
$8$	−0.547989	−	0.949144i	−0.193743	−	0.335573i
$9$		0			0
$10$	−2.20040	+	3.81121i	−0.695829	+	1.20521i
$11$	−3.17869	+	2.66724i	−0.958412	+	0.804203i	−0.980694	−	0.195549i	$-0.937351\pi$
$11$	−3.17869	+	2.66724i	−0.958412	+	0.804203i	0.0222820	+	0.999752i	$0.492907\pi$
$12$		0			0
$13$	−0.211159	+	1.19754i	−0.0585649	+	0.332138i	−0.999987	−	0.00509231i	$-0.998379\pi$
$13$	−0.211159	+	1.19754i	−0.0585649	+	0.332138i	0.941422	+	0.337230i	$0.109490\pi$
$14$	1.78920	−	10.1470i	0.478183	−	2.71191i
$15$		0			0
$16$	−2.07024	+	1.73714i	−0.517561	+	0.434285i
$17$	1.18182	−	2.04697i	0.286633	−	0.496463i	−0.686371	−	0.727252i	$-0.740797\pi$
$17$	1.18182	−	2.04697i	0.286633	−	0.496463i	0.973004	+	0.230789i	$0.0741306\pi$
$18$		0			0
$19$	0.919003	+	1.59176i	0.210834	+	0.365175i	0.951976	−	0.306174i	$-0.0990488\pi$
$19$	0.919003	+	1.59176i	0.210834	+	0.365175i	−0.741142	+	0.671348i	$0.765715\pi$
$20$	−4.89576	−	1.78191i	−1.09473	−	0.398448i
$21$		0			0
$22$	−6.75481	−	5.66796i	−1.44013	−	1.20841i
$23$	−4.04403	+	1.47191i	−0.843239	+	0.306914i	−0.727281	−	0.686340i	$-0.759216\pi$
$23$	−4.04403	+	1.47191i	−0.843239	+	0.306914i	−0.115958	+	0.993254i	$0.536994\pi$
$24$		0			0
$25$	−0.123500	−	0.700401i	−0.0246999	−	0.140080i
$26$	−2.58407			−0.506777
$27$		0			0
$28$	12.1980			2.30521
$29$	−0.517788	−	2.93652i	−0.0961507	−	0.545298i	−0.994389	−	0.105788i	$-0.966263\pi$
$29$	−0.517788	−	2.93652i	−0.0961507	−	0.545298i	0.898238	−	0.439510i	$-0.144848\pi$
$30$		0			0
$31$	−1.38472	+	0.503996i	−0.248703	+	0.0905204i	−0.463364	−	0.886168i	$-0.653358\pi$
$31$	−1.38472	+	0.503996i	−0.248703	+	0.0905204i	0.214661	+	0.976689i	$0.431135\pi$
$32$	−6.07846	−	5.10043i	−1.07453	−	0.901638i
$33$		0			0
$34$	4.71989	+	1.71790i	0.809454	+	0.294617i
$35$	−5.02066	−	8.69603i	−0.848646	−	1.46990i
$36$		0			0
$37$	−4.48554	+	7.76918i	−0.737418	+	1.27725i	0.216236	+	0.976341i	$0.430622\pi$
$37$	−4.48554	+	7.76918i	−0.737418	+	1.27725i	−0.953654	+	0.300905i	$0.902711\pi$
$38$	−2.99203	+	2.51061i	−0.485371	+	0.407275i
$39$		0			0
$40$	0.394130	−	2.23522i	0.0623174	−	0.353420i
$41$	−0.392536	+	2.22618i	−0.0613038	+	0.347671i	0.938692	+	0.344757i	$0.112039\pi$
$41$	−0.392536	+	2.22618i	−0.0613038	+	0.347671i	−0.999996	+	0.00291413i	$0.999072\pi$
$42$		0			0
$43$	−4.20164	+	3.52560i	−0.640745	+	0.537649i	−0.904247	−	0.427010i	$-0.859567\pi$
$43$	−4.20164	+	3.52560i	−0.640745	+	0.537649i	0.263502	+	0.964659i	$0.415122\pi$
$44$	5.21953	−	9.04050i	0.786874	−	1.36291i
$45$		0			0
$46$	−4.57260	−	7.91998i	−0.674194	−	1.16774i
$47$	6.74994	+	2.45678i	0.984579	+	0.358358i	0.783619	−	0.621242i	$-0.213372\pi$
$47$	6.74994	+	2.45678i	0.984579	+	0.358358i	0.200960	+	0.979599i	$0.435594\pi$
$48$		0			0
$49$	12.6471	+	10.6122i	1.80673	+	1.51603i
$50$	1.42019	−	0.516906i	0.200845	−	0.0731016i
$51$		0			0
$52$	−0.531222	−	3.01271i	−0.0736673	−	0.417788i
$53$	6.32803			0.869222			0.434611	−	0.900618i	$-0.356886\pi$
$53$	6.32803			0.869222			0.434611	+	0.900618i	$0.356886\pi$
$54$		0			0
$55$	−8.59334			−1.15873
$56$	0.922773	+	5.23330i	0.123311	+	0.699330i
$57$		0			0
$58$	5.95432	−	2.16719i	0.781840	−	0.284567i
$59$	−0.200900	−	0.168575i	−0.0261550	−	0.0219466i	0.629616	−	0.776906i	$-0.283212\pi$
$59$	−0.200900	−	0.168575i	−0.0261550	−	0.0219466i	−0.655771	+	0.754959i	$0.727657\pi$
$60$		0			0
$61$	4.18690	+	1.52391i	0.536078	+	0.195116i	0.595850	−	0.803096i	$-0.296815\pi$
$61$	4.18690	+	1.52391i	0.536078	+	0.195116i	−0.0597724	+	0.998212i	$0.519037\pi$
$62$	−1.56571	−	2.71188i	−0.198845	−	0.344410i
$63$		0			0
$64$	5.72840	−	9.92188i	0.716050	−	1.24024i
$65$	−1.92913	+	1.61873i	−0.239279	+	0.200779i
$66$		0			0
$67$	0.717359	−	4.06834i	0.0876393	−	0.497027i	−0.909116	−	0.416542i	$-0.863242\pi$
$67$	0.717359	−	4.06834i	0.0876393	−	0.497027i	0.996756	−	0.0804853i	$-0.0256470\pi$
$68$	−1.03257	+	5.85598i	−0.125217	+	0.710142i
$69$		0			0
$70$	16.3459	−	13.7159i	1.95371	−	1.63936i
$71$	1.54276	−	2.67213i	0.183091	−	0.317124i	−0.759840	−	0.650110i	$-0.774723\pi$
$71$	1.54276	−	2.67213i	0.183091	−	0.317124i	0.942932	+	0.332986i	$0.108056\pi$
$72$		0			0
$73$	−6.38003	−	11.0505i	−0.746726	−	1.29337i	−0.949384	−	0.314118i	$-0.898291\pi$
$73$	−6.38003	−	11.0505i	−0.746726	−	1.29337i	0.202658	−	0.979250i	$-0.435042\pi$
$74$	−17.9141	−	6.52021i	−2.08247	−	0.757958i
$75$		0			0
$76$	−3.54216	−	2.97222i	−0.406313	−	0.340937i
$77$	18.9062	−	6.88128i	2.15456	−	0.784195i
$78$		0			0
$79$	0.790517	+	4.48325i	0.0889401	+	0.504404i	0.996437	+	0.0843449i	$0.0268797\pi$
$79$	0.790517	+	4.48325i	0.0889401	+	0.504404i	−0.907497	+	0.420060i	$0.862009\pi$
$80$	−5.59674			−0.625734
$81$		0			0
$82$	−4.80368			−0.530478
$83$	1.46786	+	8.32464i	0.161118	+	0.913748i	0.952977	+	0.303043i	$0.0980026\pi$
$83$	1.46786	+	8.32464i	0.161118	+	0.913748i	−0.791859	+	0.610705i	$0.790886\pi$
$84$		0			0
$85$	4.59975	−	1.67417i	0.498913	−	0.181590i
$86$	−8.92862	−	7.49200i	−0.962797	−	0.807883i
$87$		0			0
$88$	4.27348	+	1.55542i	0.455555	+	0.165808i
$89$	8.48158	+	14.6905i	0.899046	+	1.55719i	0.828716	+	0.559670i	$0.189072\pi$
$89$	8.48158	+	14.6905i	0.899046	+	1.55719i	0.0703304	+	0.997524i	$0.477595\pi$
$90$		0			0
$91$	2.94803	−	5.10614i	0.309038	−	0.535269i
$92$	8.29373	−	6.95926i	0.864681	−	0.725553i
$93$		0			0
$94$	−2.65063	+	15.0325i	−0.273391	+	1.55048i
$95$	−0.660975	+	3.74857i	−0.0678146	+	0.384596i
$96$		0			0
$97$	−3.91431	+	3.28450i	−0.397438	+	0.333490i	−0.819502	−	0.573076i	$-0.805750\pi$
$97$	−3.91431	+	3.28450i	−0.397438	+	0.333490i	0.422064	+	0.906566i	$0.361306\pi$
$98$	−17.5417	+	30.3831i	−1.77198	+	3.06916i
$99$		0			0
$100$	0.894607	+	1.54951i	0.0894607	+	0.154951i
$101$	17.4594	+	6.35469i	1.73727	+	0.632316i	0.999105	−	0.0423013i	$-0.0134689\pi$
$101$	17.4594	+	6.35469i	1.73727	+	0.632316i	0.738168	+	0.674617i	$0.235691\pi$
$102$		0			0
$103$	6.89882	+	5.78880i	0.679761	+	0.570387i	0.915936	−	0.401323i	$-0.131450\pi$
$103$	6.89882	+	5.78880i	0.679761	+	0.570387i	−0.236176	+	0.971710i	$0.575894\pi$
$104$	1.25235	−	0.455819i	0.122803	−	0.0446967i
$105$		0			0
$106$	2.33509	+	13.2429i	0.226804	+	1.28627i
$107$	−7.42680			−0.717976			−0.358988	−	0.933342i	$-0.616878\pi$
$107$	−7.42680			−0.717976			−0.358988	+	0.933342i	$0.616878\pi$
$108$		0			0
$109$	−5.62396			−0.538678			−0.269339	−	0.963045i	$-0.586805\pi$
$109$	−5.62396			−0.538678			−0.269339	+	0.963045i	$0.586805\pi$
$110$	−3.17101	−	17.9837i	−0.302344	−	1.71468i
$111$		0			0
$112$	12.3133	−	4.48169i	1.16350	−	0.423480i
$113$	1.84055	+	1.54441i	0.173144	+	0.145285i	0.725242	−	0.688494i	$-0.241728\pi$
$113$	1.84055	+	1.54441i	0.173144	+	0.145285i	−0.552097	+	0.833780i	$0.686172\pi$
$114$		0			0
$115$	−8.37495	−	3.04823i	−0.780968	−	0.284249i
$116$	3.75075	+	6.49649i	0.348249	+	0.603184i
$117$		0			0
$118$	0.278652	−	0.482639i	0.0256520	−	0.0444305i
$119$	−8.77926	+	7.36667i	−0.804793	+	0.675302i
$120$		0			0
$121$	1.07979	−	6.12379i	0.0981626	−	0.556708i
$122$	−1.64415	+	9.32445i	−0.148854	+	0.844196i
$123$		0			0
$124$	2.83986	−	2.38292i	0.255027	−	0.213993i
$125$	5.91378	−	10.2430i	0.528945	−	0.916159i
$126$		0			0
$127$	4.61735	+	7.99748i	0.409723	+	0.709662i	0.994859	−	0.101274i	$-0.0322919\pi$
$127$	4.61735	+	7.99748i	0.409723	+	0.709662i	−0.585135	+	0.810936i	$0.698959\pi$
$128$	7.96511	+	2.89906i	0.704023	+	0.256243i
$129$		0			0
$130$	−4.09945	−	3.43985i	−0.359545	−	0.301694i
$131$	−14.4140	+	5.24625i	−1.25935	+	0.458367i	−0.883552	−	0.468334i	$-0.844855\pi$
$131$	−14.4140	+	5.24625i	−1.25935	+	0.458367i	−0.375801	+	0.926700i	$0.622632\pi$
$132$		0			0
$133$	−1.54753	−	8.77650i	−0.134188	−	0.761019i
$134$	8.77871			0.758365
$135$		0			0
$136$	−2.59049			−0.222133
$137$	0.632769	+	3.58861i	0.0540611	+	0.306596i	0.999834	−	0.0182336i	$-0.00580427\pi$
$137$	0.632769	+	3.58861i	0.0540611	+	0.306596i	−0.945773	+	0.324829i	$0.894693\pi$
$138$		0			0
$139$	−12.4749	+	4.54050i	−1.05811	+	0.385120i	−0.811718	−	0.584050i	$-0.801467\pi$
$139$	−12.4749	+	4.54050i	−1.05811	+	0.385120i	−0.246392	+	0.969170i	$0.579245\pi$
$140$	19.3514	+	16.2377i	1.63549	+	1.37234i
$141$		0			0
$142$	6.16138	+	2.24256i	0.517051	+	0.188191i
$143$	−2.52292	−	4.36983i	−0.210977	−	0.365423i
$144$		0			0
$145$	3.08759	−	5.34786i	0.256410	−	0.444115i
$146$	20.7717	−	17.4295i	1.71908	−	1.44248i
$147$		0			0
$148$	3.91906	−	22.2261i	0.322145	−	1.82697i
$149$	−1.54738	+	8.77561i	−0.126766	+	0.718926i	0.853477	+	0.521130i	$0.174489\pi$
$149$	−1.54738	+	8.77561i	−0.126766	+	0.718926i	−0.980243	+	0.197796i	$0.936622\pi$
$150$		0			0
$151$	−0.545733	+	0.457924i	−0.0444111	+	0.0372653i	−0.664723	−	0.747090i	$-0.731450\pi$
$151$	−0.545733	+	0.457924i	−0.0444111	+	0.0372653i	0.620312	+	0.784355i	$0.287006\pi$
$152$	1.00721	−	1.74453i	0.0816953	−	0.141500i
$153$		0			0
$154$	21.3773	+	37.0265i	1.72263	+	2.98368i
$155$	−2.86767	−	1.04375i	−0.230337	−	0.0838357i
$156$		0			0
$157$	−10.5852	−	8.88207i	−0.844794	−	0.708867i	0.113842	−	0.993499i	$-0.463684\pi$
$157$	−10.5852	−	8.88207i	−0.844794	−	0.708867i	−0.958637	+	0.284632i	$0.908129\pi$
$158$	−9.09058	+	3.30870i	−0.723208	+	0.263226i
$159$		0			0
$160$	−2.85350	−	16.1830i	−0.225589	−	1.27938i
$161$	20.8666			1.64452
$162$		0			0
$163$	−1.19321			−0.0934597			−0.0467298	−	0.998908i	$-0.514880\pi$
$163$	−1.19321			−0.0934597			−0.0467298	+	0.998908i	$0.514880\pi$
$164$	−0.987521	−	5.60051i	−0.0771124	−	0.437326i
$165$		0			0
$166$	−16.8797	+	6.14370i	−1.31012	+	0.476844i
$167$	18.3363	+	15.3860i	1.41890	+	1.19060i	0.951924	+	0.306334i	$0.0991026\pi$
$167$	18.3363	+	15.3860i	1.41890	+	1.19060i	0.466980	+	0.884268i	$0.345342\pi$
$168$		0			0
$169$	10.8265	+	3.94052i	0.832807	+	0.303117i
$170$	5.20096	+	9.00832i	0.398895	+	0.690907i
$171$		0			0
$172$	6.89926	−	11.9499i	0.526063	−	0.911169i
$173$	7.00165	−	5.87508i	0.532325	−	0.446674i	−0.336578	−	0.941656i	$-0.609270\pi$
$173$	7.00165	−	5.87508i	0.532325	−	0.446674i	0.868904	+	0.494981i	$0.164825\pi$
$174$		0			0
$175$	−0.598809	+	3.39602i	−0.0452657	+	0.256715i
$176$	1.94730	−	11.0437i	0.146783	−	0.832448i
$177$		0			0
$178$	−27.6138	+	23.1707i	−2.06974	+	1.73672i
$179$	5.30038	−	9.18052i	0.396169	−	0.686184i	−0.597081	−	0.802181i	$-0.703673\pi$
$179$	5.30038	−	9.18052i	0.396169	−	0.686184i	0.993250	+	0.115997i	$0.0370062\pi$
$180$		0			0
$181$	0.731460	+	1.26693i	0.0543690	+	0.0941699i	0.891929	−	0.452176i	$-0.149352\pi$
$181$	0.731460	+	1.26693i	0.0543690	+	0.0941699i	−0.837560	+	0.546345i	$0.816019\pi$
$182$	11.7737	+	4.28527i	0.872724	+	0.317645i
$183$		0			0
$184$	3.61314	+	3.03178i	0.266364	+	0.223506i
$185$	−17.4581	+	6.35425i	−1.28355	+	0.467174i
$186$		0			0
$187$	1.70312	+	9.65889i	0.124545	+	0.706328i
$188$	−18.0709			−1.31796
$189$		0			0
$190$	−8.08871			−0.586817
$191$	−2.15711	−	12.2336i	−0.156083	−	0.885189i	−0.957789	−	0.287471i	$-0.907185\pi$
$191$	−2.15711	−	12.2336i	−0.156083	−	0.885189i	0.801707	−	0.597718i	$-0.203926\pi$
$192$		0			0
$193$	−19.5205	+	7.10489i	−1.40512	+	0.511421i	−0.929693	−	0.368335i	$-0.879928\pi$
$193$	−19.5205	+	7.10489i	−1.40512	+	0.511421i	−0.475425	+	0.879756i	$0.657706\pi$
$194$	−8.31803	−	6.97965i	−0.597199	−	0.501110i
$195$		0			0
$196$	−39.0292	−	14.2055i	−2.78780	−	1.01468i
$197$	−7.09433	−	12.2877i	−0.505450	−	0.875465i	−0.999980	−	0.00630469i	$-0.997993\pi$
$197$	−7.09433	−	12.2877i	−0.505450	−	0.875465i	0.494530	−	0.869161i	$-0.335340\pi$
$198$		0			0
$199$	−10.1643	+	17.6051i	−0.720529	+	1.24799i	0.240259	+	0.970709i	$0.422768\pi$
$199$	−10.1643	+	17.6051i	−0.720529	+	1.24799i	−0.960788	+	0.277284i	$0.910566\pi$
$200$	−0.597105	+	0.501031i	−0.0422217	+	0.0354282i
$201$		0			0
$202$	−6.85611	+	38.8829i	−0.482394	+	2.73579i
$203$	−2.51058	+	14.2382i	−0.176208	+	0.999327i
$204$		0			0
$205$	−3.58617	+	3.00915i	−0.250469	+	0.210168i
$206$	−9.56876	+	16.5736i	−0.666687	+	1.15474i
$207$		0			0
$208$	−1.64315	−	2.84601i	−0.113932	−	0.197336i
$209$	−7.16684	−	2.60851i	−0.495740	−	0.180435i
$210$		0			0
$211$	−7.55574	−	6.34002i	−0.520159	−	0.436465i	0.344528	−	0.938776i	$-0.388039\pi$
$211$	−7.55574	−	6.34002i	−0.520159	−	0.436465i	−0.864687	+	0.502311i	$0.832483\pi$
$212$	−14.9596	+	5.44487i	−1.02743	+	0.373955i
$213$		0			0
$214$	−2.74055	−	15.5424i	−0.187340	−	1.06246i
$215$	−11.3588			−0.774665
$216$		0			0
$217$	7.14494			0.485030
$218$	−2.07528	−	11.7695i	−0.140556	−	0.797132i
$219$		0			0
$220$	20.3149	−	7.39402i	1.36963	−	0.498505i
$221$	2.20178	+	1.84751i	0.148108	+	0.124277i
$222$		0			0
$223$	−14.1625	−	5.15472i	−0.948389	−	0.345185i	−0.178916	−	0.983864i	$-0.557259\pi$
$223$	−14.1625	−	5.15472i	−0.948389	−	0.345185i	−0.769473	+	0.638679i	$0.779481\pi$
$224$	19.2368	+	33.3191i	1.28531	+	2.22623i
$225$		0			0
$226$	−2.55287	+	4.42170i	−0.169814	+	0.294127i
$227$	17.3835	−	14.5865i	1.15378	−	0.968140i	0.153983	−	0.988074i	$-0.450790\pi$
$227$	17.3835	−	14.5865i	1.15378	−	0.968140i	0.999801	+	0.0199338i	$0.00634555\pi$
$228$		0			0
$229$	1.51364	−	8.58428i	0.100024	−	0.567265i	−0.893067	−	0.449923i	$-0.851451\pi$
$229$	1.51364	−	8.58428i	0.100024	−	0.567265i	0.993092	−	0.117342i	$-0.0374374\pi$
$230$	3.28875	−	18.6515i	0.216854	−	1.22984i
$231$		0			0
$232$	−2.50344	+	2.10063i	−0.164359	+	0.137913i
$233$	−11.7945	+	20.4286i	−0.772682	+	1.33832i	0.163406	+	0.986559i	$0.447752\pi$
$233$	−11.7945	+	20.4286i	−0.772682	+	1.33832i	−0.936088	+	0.351766i	$0.885581\pi$
$234$		0			0
$235$	7.43792	+	12.8829i	0.485196	+	0.840385i
$236$	0.619983	+	0.225655i	0.0403574	+	0.0146889i
$237$		0			0
$238$	−18.6562	−	15.6544i	−1.20930	−	1.01472i
$239$	9.35419	−	3.40465i	0.605072	−	0.220228i	−0.0212736	−	0.999774i	$-0.506772\pi$
$239$	9.35419	−	3.40465i	0.605072	−	0.220228i	0.626346	+	0.779545i	$0.284550\pi$
$240$		0			0
$241$	0.992130	+	5.62665i	0.0639087	+	0.362444i	0.999944	+	0.0105394i	$0.00335485\pi$
$241$	0.992130	+	5.62665i	0.0639087	+	0.362444i	−0.936036	+	0.351905i	$0.885534\pi$
$242$	13.2140			0.849427
$243$		0			0
$244$	−11.2092			−0.717594
$245$	5.93711	+	33.6710i	0.379308	+	2.15116i
$246$		0			0
$247$	−2.10025	+	0.764430i	−0.133636	+	0.0486395i
$248$	1.23718	+	1.03811i	0.0785607	+	0.0659203i
$249$		0			0
$250$	23.6182	+	8.59631i	1.49374	+	0.543678i
$251$	−3.64483	−	6.31303i	−0.230060	−	0.398475i	0.727766	−	0.685826i	$-0.240559\pi$
$251$	−3.64483	−	6.31303i	−0.230060	−	0.398475i	−0.957825	+	0.287351i	$0.907226\pi$
$252$		0			0
$253$	8.92881	−	15.4651i	0.561349	−	0.972285i
$254$	−15.0328	+	12.6141i	−0.943245	+	0.791476i
$255$		0			0
$256$	0.851090	−	4.82677i	0.0531931	−	0.301673i
$257$	4.03612	−	22.8900i	0.251766	−	1.42784i	−0.552473	−	0.833531i	$-0.686316\pi$
$257$	4.03612	−	22.8900i	0.251766	−	1.42784i	0.804239	−	0.594306i	$-0.202573\pi$
$258$		0			0
$259$	33.3213	−	27.9599i	2.07048	−	1.73734i
$260$	3.16770	−	5.48661i	0.196452	−	0.340265i
$261$		0			0
$262$	−16.2979	−	28.2288i	−1.00689	−	1.74398i
$263$	−25.7472	−	9.37122i	−1.58764	−	0.577854i	−0.610793	−	0.791790i	$-0.709149\pi$
$263$	−25.7472	−	9.37122i	−1.58764	−	0.577854i	−0.976848	+	0.213936i	$0.931372\pi$
$264$		0			0
$265$	10.0390	+	8.42371i	0.616690	+	0.517465i
$266$	17.7959	−	6.47719i	1.09114	−	0.397142i
$267$		0			0
$268$	1.80469	+	10.2349i	0.110239	+	0.625197i
$269$	−9.41973			−0.574331			−0.287166	−	0.957881i	$-0.592713\pi$
$269$	−9.41973			−0.574331			−0.287166	+	0.957881i	$0.592713\pi$
$270$		0			0
$271$	26.2797			1.59638			0.798189	−	0.602408i	$-0.205792\pi$
$271$	26.2797			1.59638			0.798189	+	0.602408i	$0.205792\pi$
$272$	1.10922	+	6.29071i	0.0672565	+	0.381430i
$273$		0			0
$274$	−7.27655	+	2.64845i	−0.439592	+	0.159999i
$275$	2.26071	+	1.89696i	0.136326	+	0.114391i
$276$		0			0
$277$	−0.352208	−	0.128193i	−0.0211621	−	0.00770238i	0.331417	−	0.943484i	$-0.392473\pi$
$277$	−0.352208	−	0.128193i	−0.0211621	−	0.00770238i	−0.352580	+	0.935782i	$0.614695\pi$
$278$	−14.1054	−	24.4314i	−0.845989	−	1.46530i
$279$		0			0
$280$	−5.50253	+	9.53065i	−0.328839	+	0.569566i
$281$	−10.7105	+	8.98719i	−0.638936	+	0.536131i	−0.903691	−	0.428185i	$-0.859153\pi$
$281$	−10.7105	+	8.98719i	−0.638936	+	0.536131i	0.264755	+	0.964316i	$0.414709\pi$
$282$		0			0
$283$	2.70229	−	15.3255i	0.160635	−	0.911005i	−0.792817	−	0.609459i	$-0.791387\pi$
$283$	2.70229	−	15.3255i	0.160635	−	0.911005i	0.953452	−	0.301545i	$-0.0975024\pi$
$284$	−1.34792	+	7.64444i	−0.0799844	+	0.453614i
$285$		0			0
$286$	8.21396	−	6.89233i	0.485701	−	0.407552i
$287$	5.48027	−	9.49211i	0.323490	−	0.560301i
$288$		0			0
$289$	5.70661	+	9.88413i	0.335683	+	0.581420i
$290$	12.3310	+	4.48813i	0.724103	+	0.263552i
$291$		0			0
$292$	24.5909	+	20.6342i	1.43907	+	1.20752i
$293$	23.1392	−	8.42198i	1.35181	−	0.492017i	0.438295	−	0.898831i	$-0.355582\pi$
$293$	23.1392	−	8.42198i	1.35181	−	0.492017i	0.913511	+	0.406814i	$0.133360\pi$
$294$		0			0
$295$	−0.0943115	−	0.534867i	−0.00549103	−	0.0311412i
$296$	9.83210			0.571479
$297$		0			0
$298$	−18.9361			−1.09694
$299$	−0.908737	−	5.15370i	−0.0525536	−	0.298046i
$300$		0			0
$301$	24.9904	−	9.09578i	1.44043	−	0.524272i
$302$	−1.15970	−	0.973102i	−0.0667331	−	0.0559957i
$303$		0			0
$304$	−4.66767	−	1.69889i	−0.267709	−	0.0974382i
$305$	4.61365	+	7.99107i	0.264177	+	0.457567i
$306$		0			0
$307$	10.1956	−	17.6593i	0.581893	−	1.00787i	−0.413362	−	0.910567i	$-0.635646\pi$
$307$	10.1956	−	17.6593i	0.581893	−	1.00787i	0.995255	−	0.0973012i	$-0.0310210\pi$
$308$	−38.7738	+	32.5351i	−2.20934	+	1.85386i
$309$		0			0
$310$	1.12610	−	6.38645i	0.0639584	−	0.362726i
$311$	−3.85135	+	21.8421i	−0.218390	+	1.23855i	0.656536	+	0.754294i	$0.272021\pi$
$311$	−3.85135	+	21.8421i	−0.218390	+	1.23855i	−0.874926	+	0.484256i	$0.839090\pi$
$312$		0			0
$313$	−8.55828	+	7.18125i	−0.483742	+	0.405908i	−0.851777	−	0.523904i	$-0.824475\pi$
$313$	−8.55828	+	7.18125i	−0.483742	+	0.405908i	0.368035	+	0.929812i	$0.380031\pi$
$314$	14.6819	−	25.4298i	0.828547	−	1.43508i
$315$		0			0
$316$	−5.72635	−	9.91833i	−0.322132	−	0.557950i
$317$	23.6959	+	8.62461i	1.33089	+	0.484406i	0.906933	−	0.421274i	$-0.138417\pi$
$317$	23.6959	+	8.62461i	1.33089	+	0.484406i	0.423962	+	0.905680i	$0.360639\pi$
$318$		0			0
$319$	9.47829	+	7.95323i	0.530682	+	0.445295i
$320$	22.2955	−	8.11489i	1.24636	−	0.453636i
$321$		0			0
$322$	7.69993	+	43.6685i	0.429100	+	2.43355i
$323$	4.34438			0.241728
$324$		0			0
$325$	0.864837			0.0479725
$326$	−0.440305	−	2.49709i	−0.0243862	−	0.138301i
$327$		0			0
$328$	2.32807	−	0.847349i	0.128546	−	0.0467870i
$329$	−26.6803	−	22.3874i	−1.47093	−	1.23426i
$330$		0			0
$331$	24.5877	+	8.94919i	1.35146	+	0.491892i	0.913404	−	0.407054i	$-0.133444\pi$
$331$	24.5877	+	8.94919i	1.35146	+	0.491892i	0.438059	+	0.898946i	$0.355666\pi$
$332$	−10.6329	−	18.4167i	−0.583555	−	1.01075i
$333$		0			0
$334$	−25.4327	+	44.0507i	−1.39161	+	2.41035i
$335$	6.55372	−	5.49922i	0.358068	−	0.300455i
$336$		0			0
$337$	1.90076	−	10.7798i	0.103541	−	0.587211i	−0.888252	−	0.459357i	$-0.848080\pi$
$337$	1.90076	−	10.7798i	0.103541	−	0.587211i	0.991793	−	0.127854i	$-0.0408089\pi$
$338$	−4.25145	+	24.1112i	−0.231248	+	1.31147i
$339$		0			0
$340$	−9.43343	+	7.91559i	−0.511599	+	0.429283i
$341$	3.05732	−	5.29543i	0.165563	−	0.286763i
$342$		0			0
$343$	−23.0545	−	39.9316i	−1.24483	−	2.15611i
$344$	5.64876	+	2.05598i	0.304560	+	0.110851i
$345$		0			0
$346$	14.8787	+	12.4847i	0.799884	+	0.671182i
$347$	3.30150	−	1.20165i	0.177234	−	0.0645078i	−0.251879	−	0.967759i	$-0.581049\pi$
$347$	3.30150	−	1.20165i	0.177234	−	0.0645078i	0.429113	+	0.903251i	$0.358826\pi$
$348$		0			0
$349$	−5.06998	−	28.7533i	−0.271390	−	1.53913i	−0.750201	−	0.661210i	$-0.770043\pi$
$349$	−5.06998	−	28.7533i	−0.271390	−	1.53913i	0.478811	−	0.877918i	$-0.341068\pi$
$350$	−7.32796			−0.391696
$351$		0			0
$352$	32.9256			1.75494
$353$	4.35454	+	24.6958i	0.231769	+	1.31443i	0.849313	+	0.527890i	$0.177017\pi$
$353$	4.35454	+	24.6958i	0.231769	+	1.31443i	−0.617544	+	0.786537i	$0.711872\pi$
$354$		0			0
$355$	6.00455	−	2.18548i	0.318688	−	0.115993i
$356$	−32.6910	−	27.4310i	−1.73262	−	1.45384i
$357$		0			0
$358$	21.1684	+	7.70466i	1.11878	+	0.407204i
$359$	2.10362	+	3.64358i	0.111025	+	0.192301i	0.916184	−	0.400758i	$-0.131253\pi$
$359$	2.10362	+	3.64358i	0.111025	+	0.192301i	−0.805159	+	0.593059i	$0.797920\pi$
$360$		0			0
$361$	7.81087	−	13.5288i	0.411098	−	0.712043i
$362$	−2.38144	+	1.99826i	−0.125166	+	0.105026i
$363$		0			0
$364$	−2.57572	+	14.6076i	−0.135005	+	0.765649i
$365$	4.58871	−	26.0239i	0.240184	−	1.36215i
$366$		0			0
$367$	13.4032	−	11.2466i	0.699641	−	0.587069i	−0.222030	−	0.975040i	$-0.571268\pi$
$367$	13.4032	−	11.2466i	0.699641	−	0.587069i	0.921672	+	0.387971i	$0.126824\pi$
$368$	5.81522	−	10.0723i	0.303139	−	0.525053i
$369$		0			0
$370$	−19.7400	−	34.1907i	−1.02623	−	1.77749i
$371$	−28.8322	−	10.4940i	−1.49689	−	0.544824i
$372$		0			0
$373$	−22.7167	−	19.0616i	−1.17623	−	0.986972i	−0.999997	−	0.00262266i	$-0.999165\pi$
$373$	−22.7167	−	19.0616i	−1.17623	−	0.986972i	−0.176230	−	0.984349i	$-0.556390\pi$
$374$	−19.5851	+	7.12840i	−1.01272	+	0.368601i
$375$		0			0
$376$	−1.36705	−	7.75295i	−0.0705004	−	0.399828i
$377$	3.62594			0.186745
$378$		0			0
$379$	20.9523			1.07625			0.538124	−	0.842865i	$-0.319133\pi$
$379$	20.9523			1.07625			0.538124	+	0.842865i	$0.319133\pi$
$380$	−1.66285	−	9.43046i	−0.0853022	−	0.483773i
$381$		0			0
$382$	24.8057	−	9.02854i	1.26917	−	0.461940i
$383$	−7.58137	−	6.36152i	−0.387390	−	0.325059i	0.428205	−	0.903681i	$-0.359146\pi$
$383$	−7.58137	−	6.36152i	−0.387390	−	0.325059i	−0.815595	+	0.578623i	$0.803590\pi$
$384$		0			0
$385$	39.1535	+	14.2507i	1.99545	+	0.726284i
$386$	−22.0719	−	38.2297i	−1.12343	−	1.94584i
$387$		0			0
$388$	6.42745	−	11.1327i	0.326304	−	0.565175i
$389$	16.1748	−	13.5723i	0.820097	−	0.688143i	−0.132898	−	0.991130i	$-0.542428\pi$
$389$	16.1748	−	13.5723i	0.820097	−	0.688143i	0.952995	+	0.302986i	$0.0979837\pi$
$390$		0			0
$391$	−1.76636	+	10.0175i	−0.0893288	+	0.506609i
$392$	3.14202	−	17.8193i	0.158696	−	0.900010i
$393$		0			0
$394$	23.0972	−	19.3809i	1.16362	−	0.976395i
$395$	−4.71388	+	8.16468i	−0.237181	+	0.410810i
$396$		0			0
$397$	4.88955	+	8.46894i	0.245399	+	0.425044i	0.962244	−	0.272189i	$-0.0877476\pi$
$397$	4.88955	+	8.46894i	0.245399	+	0.425044i	−0.716845	+	0.697233i	$0.754414\pi$
$398$	−40.5937	−	14.7749i	−2.03478	−	0.740599i
$399$		0			0
$400$	1.47237	+	1.23546i	0.0736185	+	0.0617732i
$401$	−17.9851	+	6.54604i	−0.898133	+	0.326894i	−0.749504	−	0.662000i	$-0.769708\pi$
$401$	−17.9851	+	6.54604i	−0.898133	+	0.326894i	−0.148628	+	0.988893i	$0.547486\pi$
$402$		0			0
$403$	−0.311161	−	1.76468i	−0.0155000	−	0.0879050i
$404$	−46.7423			−2.32552
$405$		0			0
$406$	−30.7234			−1.52478
$407$	−6.46412	−	36.6599i	−0.320415	−	1.81716i
$408$		0			0
$409$	−14.0912	+	5.12878i	−0.696766	+	0.253602i	−0.666029	−	0.745926i	$-0.732007\pi$
$409$	−14.0912	+	5.12878i	−0.696766	+	0.253602i	−0.0307364	+	0.999528i	$0.509785\pi$
$410$	−7.62071	−	6.39454i	−0.376360	−	0.315804i
$411$		0			0
$412$	−21.2899	−	7.74889i	−1.04888	−	0.381760i
$413$	0.635799	+	1.10124i	0.0312856	+	0.0541883i
$414$		0			0
$415$	−8.75289	+	15.1604i	−0.429662	+	0.744197i
$416$	7.39150	−	6.20221i	0.362398	−	0.304088i
$417$		0			0
$418$	2.81434	−	15.9609i	0.137654	−	0.780674i
$419$	−1.00921	+	5.72351i	−0.0493031	+	0.279612i	−0.999485	−	0.0320837i	$-0.989786\pi$
$419$	−1.00921	+	5.72351i	−0.0493031	+	0.279612i	0.950182	+	0.311695i	$0.100897\pi$
$420$		0			0
$421$	−10.1987	+	8.55776i	−0.497056	+	0.417080i	−0.856547	−	0.516069i	$-0.827395\pi$
$421$	−10.1987	+	8.55776i	−0.497056	+	0.417080i	0.359491	+	0.933149i	$0.382950\pi$
$422$	10.4799	−	18.1518i	0.510154	−	0.883613i
$423$		0			0
$424$	−3.46769	−	6.00621i	−0.168406	−	0.291687i
$425$	−1.57965	−	0.574947i	−0.0766245	−	0.0278890i
$426$		0			0
$427$	−16.5495	−	13.8866i	−0.800884	−	0.672022i
$428$	17.5572	−	6.39029i	0.848658	−	0.308886i
$429$		0			0
$430$	−4.19149	−	23.7711i	−0.202131	−	1.14634i
$431$	36.4166			1.75413			0.877064	−	0.480374i	$-0.159499\pi$
$431$	36.4166			1.75413			0.877064	+	0.480374i	$0.159499\pi$
$432$		0			0
$433$	−10.8761			−0.522674			−0.261337	−	0.965248i	$-0.584163\pi$
$433$	−10.8761			−0.522674			−0.261337	+	0.965248i	$0.584163\pi$
$434$	2.63654	+	14.9525i	0.126558	+	0.717745i
$435$		0			0
$436$	13.2952	−	4.83906i	0.636725	−	0.231749i
$437$	−6.05940	−	5.08444i	−0.289860	−	0.243222i
$438$		0			0
$439$	−8.88316	−	3.23321i	−0.423970	−	0.154313i	0.121219	−	0.992626i	$-0.461320\pi$
$439$	−8.88316	−	3.23321i	−0.423970	−	0.154313i	−0.545189	+	0.838313i	$0.683542\pi$
$440$	4.70906	+	8.15632i	0.224495	+	0.388837i
$441$		0			0
$442$	−3.05390	+	5.28951i	−0.145259	+	0.251596i
$443$	−12.6581	+	10.6214i	−0.601402	+	0.504636i	−0.891896	−	0.452241i	$-0.850625\pi$
$443$	−12.6581	+	10.6214i	−0.601402	+	0.504636i	0.290494	+	0.956877i	$0.406180\pi$
$444$		0			0
$445$	−6.10021	+	34.5960i	−0.289178	+	1.64001i
$446$	5.56145	−	31.5406i	0.263342	−	1.49349i
$447$		0			0
$448$	−42.5540	+	35.7070i	−2.01049	+	1.68700i
$449$	−2.37181	+	4.10809i	−0.111933	+	0.193873i	−0.916549	−	0.399921i	$-0.869037\pi$
$449$	−2.37181	+	4.10809i	−0.111933	+	0.193873i	0.804617	+	0.593794i	$0.202371\pi$
$450$		0			0
$451$	−4.69001	−	8.12334i	−0.220844	−	0.382513i
$452$	−5.67998	−	2.06734i	−0.267164	−	0.0972396i
$453$		0			0
$454$	36.9405	+	30.9967i	1.73370	+	1.45475i
$455$	11.4740	−	4.17620i	0.537910	−	0.195783i
$456$		0			0
$457$	−3.89120	−	22.0681i	−0.182023	−	1.03230i	−0.929721	−	0.368264i	$-0.879952\pi$
$457$	−3.89120	−	22.0681i	−0.182023	−	1.03230i	0.747698	−	0.664039i	$-0.231159\pi$
$458$	18.5232			0.865534
$459$		0			0
$460$	22.4214			1.04540
$461$	2.59122	+	14.6956i	0.120685	+	0.684440i	0.983777	+	0.179394i	$0.0574136\pi$
$461$	2.59122	+	14.6956i	0.120685	+	0.684440i	−0.863092	+	0.505047i	$0.831475\pi$
$462$		0			0
$463$	13.9518	−	5.07803i	0.648394	−	0.235996i	0.00317653	−	0.999995i	$-0.498989\pi$
$463$	13.9518	−	5.07803i	0.648394	−	0.235996i	0.645218	+	0.763999i	$0.276767\pi$
$464$	6.17309	+	5.17984i	0.286579	+	0.240468i
$465$		0			0
$466$	−47.1042	−	17.1445i	−2.18206	−	0.794204i
$467$	−7.67571	−	13.2947i	−0.355190	−	0.615206i	0.631961	−	0.775000i	$-0.282250\pi$
$467$	−7.67571	−	13.2947i	−0.355190	−	0.615206i	−0.987150	+	0.159794i	$0.948917\pi$
$468$		0			0
$469$	−10.0152	+	17.3468i	−0.462458	+	0.801001i
$470$	−24.2159	+	20.3195i	−1.11700	+	0.937270i
$471$		0			0
$472$	−0.0499113	+	0.283061i	−0.00229735	+	0.0130289i
$473$	3.95212	−	22.4136i	0.181719	−	1.03058i
$474$		0			0
$475$	1.00137	−	0.840253i	0.0459462	−	0.0385534i
$476$	14.4159	−	24.9690i	0.660750	−	1.14445i
$477$		0			0
$478$	10.5768	+	18.3196i	0.483772	+	0.837918i
$479$	9.81848	+	3.57363i	0.448618	+	0.163284i	0.556442	−	0.830886i	$-0.312166\pi$
$479$	9.81848	+	3.57363i	0.448618	+	0.163284i	−0.107824	+	0.994170i	$0.534388\pi$
$480$		0			0
$481$	−8.35676	−	7.01215i	−0.381035	−	0.319727i
$482$	−11.4090	+	4.15255i	−0.519667	+	0.189143i
$483$		0			0
$484$	2.71648	+	15.4059i	0.123476	+	0.700268i
$485$	−10.5820			−0.480505
$486$		0			0
$487$	−16.1649			−0.732500			−0.366250	−	0.930516i	$-0.619359\pi$
$487$	−16.1649			−0.732500			−0.366250	+	0.930516i	$0.619359\pi$
$488$	−0.847966	−	4.80906i	−0.0383856	−	0.217696i
$489$		0			0
$490$	−68.2740	+	24.8497i	−3.08431	+	1.12260i
$491$	8.25592	+	6.92754i	0.372585	+	0.312636i	0.809783	−	0.586730i	$-0.199585\pi$
$491$	8.25592	+	6.92754i	0.372585	+	0.312636i	−0.437198	+	0.899365i	$0.644029\pi$
$492$		0			0
$493$	−6.62290	−	2.41054i	−0.298280	−	0.108565i
$494$	−2.37477	−	4.11322i	−0.106846	−	0.185062i
$495$		0			0
$496$	1.99119	−	3.44885i	0.0894071	−	0.154858i
$497$	−11.4605	+	9.61651i	−0.514074	+	0.431359i
$498$		0			0
$499$	−3.33182	+	18.8957i	−0.149153	+	0.845887i	0.814786	+	0.579762i	$0.196855\pi$
$499$	−3.33182	+	18.8957i	−0.149153	+	0.845887i	−0.963938	+	0.266125i	$0.914257\pi$
$500$	−5.16693	+	29.3031i	−0.231072	+	1.31048i
$501$		0			0
$502$	11.8666	−	9.95726i	0.529632	−	0.444414i
$503$	−6.01253	+	10.4140i	−0.268086	+	0.464338i	−0.968367	−	0.249529i	$-0.919724\pi$
$503$	−6.01253	+	10.4140i	−0.268086	+	0.464338i	0.700282	+	0.713866i	$0.253058\pi$
$504$		0			0
$505$	19.2389	+	33.3228i	0.856120	+	1.48284i
$506$	35.6594	+	12.9790i	1.58525	+	0.576985i
$507$		0			0
$508$	−17.7969	−	14.9333i	−0.789608	−	0.662560i
$509$	−14.0512	+	5.11423i	−0.622810	+	0.226684i	−0.634099	−	0.773252i	$-0.718629\pi$
$509$	−14.0512	+	5.11423i	−0.622810	+	0.226684i	0.0112886	+	0.999936i	$0.496407\pi$
$510$		0			0
$511$	10.7435	+	60.9294i	0.475265	+	2.69536i
$512$	27.3678			1.20950
$513$		0			0
$514$	49.3922			2.17860
$515$	3.23861	+	18.3671i	0.142710	+	0.809350i
$516$		0			0
$517$	−28.0088	+	10.1944i	−1.23182	+	0.448348i
$518$	70.8087	+	59.4155i	3.11115	+	2.61057i
$519$		0			0
$520$	2.59355	+	0.943974i	0.113735	+	0.0413960i
$521$	18.7094	+	32.4056i	0.819673	+	1.41972i	0.905923	+	0.423442i	$0.139178\pi$
$521$	18.7094	+	32.4056i	0.819673	+	1.41972i	−0.0862502	+	0.996274i	$0.527488\pi$
$522$		0			0
$523$	4.22489	−	7.31773i	0.184742	−	0.319982i	−0.758748	−	0.651385i	$-0.774188\pi$
$523$	4.22489	−	7.31773i	0.184742	−	0.319982i	0.943489	+	0.331403i	$0.107522\pi$
$524$	29.5609	−	24.8046i	1.29138	−	1.08359i
$525$		0			0
$526$	10.1107	−	57.3404i	0.440846	−	2.50016i
$527$	−0.604821	+	3.43011i	−0.0263464	+	0.149418i
$528$		0			0
$529$	−3.43134	+	2.87924i	−0.149189	+	0.125184i
$530$	−13.9242	+	24.1175i	−0.604829	+	1.04760i
$531$		0			0
$532$	11.2100	+	19.4163i	0.486017	+	0.841805i
$533$	−2.58306	−	0.940156i	−0.111885	−	0.0407227i
$534$		0			0
$535$	−11.7821	−	9.88637i	−0.509386	−	0.427425i
$536$	−4.25455	+	1.54853i	−0.183769	+	0.0668863i
$537$		0			0
$538$	−3.47595	−	19.7131i	−0.149859	−	0.849892i
$539$	−68.5065			−2.95078
$540$		0			0
$541$	12.6259			0.542828			0.271414	−	0.962463i	$-0.412509\pi$
$541$	12.6259			0.542828			0.271414	+	0.962463i	$0.412509\pi$
$542$	9.69740	+	54.9967i	0.416539	+	2.36231i
$543$		0			0
$544$	−17.6241	+	6.41464i	−0.755626	+	0.275025i
$545$	−8.92204	−	7.48648i	−0.382178	−	0.320685i
$546$		0			0
$547$	−29.5017	−	10.7377i	−1.26140	−	0.459113i	−0.377162	−	0.926147i	$-0.623100\pi$
$547$	−29.5017	−	10.7377i	−1.26140	−	0.459113i	−0.884239	+	0.467034i	$0.845322\pi$
$548$	−4.58365	−	7.93912i	−0.195804	−	0.339142i
$549$		0			0
$550$	−3.13563	+	5.43107i	−0.133704	+	0.231582i
$551$	4.19839	−	3.52286i	0.178857	−	0.150079i
$552$		0			0
$553$	3.83296	−	21.7378i	0.162994	−	0.924385i
$554$	0.138308	−	0.784385i	0.00587616	−	0.0333253i
$555$		0			0
$556$	25.5843	−	21.4678i	1.08501	−	0.910436i
$557$	−7.96515	+	13.7960i	−0.337494	+	0.584557i	−0.983961	−	0.178385i	$-0.942913\pi$
$557$	−7.96515	+	13.7960i	−0.337494	+	0.584557i	0.646467	+	0.762942i	$0.276246\pi$
$558$		0			0
$559$	−3.33484	−	5.77610i	−0.141048	−	0.244303i
$560$	25.5002	+	9.28132i	1.07758	+	0.392207i
$561$		0			0
$562$	−22.7602	−	19.0980i	−0.960079	−	0.805602i
$563$	−23.3616	+	8.50291i	−0.984572	+	0.358355i	−0.783616	−	0.621245i	$-0.786627\pi$
$563$	−23.3616	+	8.50291i	−0.984572	+	0.358355i	−0.200956	+	0.979600i	$0.564405\pi$
$564$		0			0
$565$	0.864036	+	4.90019i	0.0363503	+	0.206153i
$566$	33.0695			1.39001
$567$		0			0
$568$	−3.38165			−0.141891
$569$	−3.33231	−	18.8985i	−0.139698	−	0.792265i	−0.971473	−	0.237152i	$-0.923786\pi$
$569$	−3.33231	−	18.8985i	−0.139698	−	0.792265i	0.831775	−	0.555113i	$-0.187325\pi$
$570$		0			0
$571$	19.1502	−	6.97011i	0.801412	−	0.291690i	0.0913403	−	0.995820i	$-0.470885\pi$
$571$	19.1502	−	6.97011i	0.801412	−	0.291690i	0.710071	+	0.704130i	$0.248663\pi$
$572$	9.72422	+	8.15959i	0.406590	+	0.341169i
$573$		0			0
$574$	21.8868	+	7.96615i	0.913538	+	0.332501i
$575$	1.53036	+	2.65066i	0.0638205	+	0.110540i
$576$		0			0
$577$	−11.6495	+	20.1776i	−0.484976	+	0.840004i	−0.999851	−	0.0172619i	$-0.994505\pi$
$577$	−11.6495	+	20.1776i	−0.484976	+	0.840004i	0.514875	+	0.857265i	$0.327838\pi$
$578$	−18.5792	+	15.5898i	−0.772792	+	0.648450i
$579$		0			0
$580$	−2.69765	+	15.2992i	−0.112014	+	0.635263i
$581$	7.11716	−	40.3634i	0.295270	−	1.67456i
$582$		0			0
$583$	−20.1149	+	16.8784i	−0.833072	+	0.699031i
$584$	−6.99237	+	12.1111i	−0.289346	+	0.501163i
$585$		0			0
$586$	26.1636	+	45.3167i	1.08081	+	1.87201i
$587$	−34.6834	−	12.6237i	−1.43154	−	0.521036i	−0.494165	−	0.869368i	$-0.664526\pi$
$587$	−34.6834	−	12.6237i	−1.43154	−	0.521036i	−0.937371	+	0.348332i	$0.886748\pi$
$588$		0			0
$589$	−2.07480	−	1.74097i	−0.0854907	−	0.0717352i
$590$	1.08454	−	0.394740i	0.0446497	−	0.0162512i
$591$		0			0
$592$	−4.21000	−	23.8761i	−0.173030	−	0.981302i
$593$	−4.36830			−0.179385			−0.0896923	−	0.995970i	$-0.528588\pi$
$593$	−4.36830			−0.179385			−0.0896923	+	0.995970i	$0.528588\pi$
$594$		0			0
$595$	−23.7340			−0.973000
$596$	−3.89281	−	22.0772i	−0.159456	−	0.904318i
$597$		0			0
$598$	10.4501	−	3.80351i	0.427334	−	0.155537i
$599$	23.9049	+	20.0586i	0.976727	+	0.819571i	0.983592	−	0.180405i	$-0.0577409\pi$
$599$	23.9049	+	20.0586i	0.976727	+	0.819571i	−0.00686530	+	0.999976i	$0.502185\pi$
$600$		0			0
$601$	−41.2874	−	15.0274i	−1.68415	−	0.612979i	−0.690278	−	0.723544i	$-0.742512\pi$
$601$	−41.2874	−	15.0274i	−1.68415	−	0.612979i	−0.993869	+	0.110565i	$0.964734\pi$
$602$	28.2568	+	48.9422i	1.15166	+	1.99474i
$603$		0			0
$604$	0.896114	−	1.55211i	0.0364623	−	0.0631546i
$605$	9.86485	−	8.27759i	0.401063	−	0.336532i
$606$		0			0
$607$	3.01430	−	17.0949i	0.122347	−	0.693862i	−0.860502	−	0.509447i	$-0.829850\pi$
$607$	3.01430	−	17.0949i	0.122347	−	0.693862i	0.982849	−	0.184415i	$-0.0590390\pi$
$608$	2.53254	−	14.3628i	0.102708	−	0.582487i
$609$		0			0
$610$	−15.0208	+	12.6039i	−0.608174	+	0.510319i
$611$	−4.36740	+	7.56456i	−0.176686	+	0.306029i
$612$		0			0
$613$	0.599024	+	1.03754i	0.0241944	+	0.0419059i	0.877869	−	0.478901i	$-0.158965\pi$
$613$	0.599024	+	1.03754i	0.0241944	+	0.0419059i	−0.853675	+	0.520807i	$0.825631\pi$
$614$	40.7186	+	14.8204i	1.64327	+	0.598101i
$615$		0			0
$616$	−16.8917	−	14.1738i	−0.680586	−	0.571079i
$617$	24.4449	−	8.89721i	0.984114	−	0.358188i	0.200676	−	0.979658i	$-0.435686\pi$
$617$	24.4449	−	8.89721i	0.984114	−	0.358188i	0.783439	+	0.621469i	$0.213464\pi$
$618$		0			0
$619$	1.67247	+	9.48503i	0.0672221	+	0.381235i	0.999795	+	0.0202534i	$0.00644731\pi$
$619$	1.67247	+	9.48503i	0.0672221	+	0.381235i	−0.932573	+	0.360982i	$0.882442\pi$
$620$	7.67733			0.308329
$621$		0			0
$622$	−47.1311			−1.88978
$623$	−14.2824	−	80.9993i	−0.572211	−	3.24517i
$624$		0			0
$625$	19.6754	−	7.16127i	0.787017	−	0.286451i
$626$	−18.1866	−	15.2604i	−0.726882	−	0.609927i
$627$		0			0
$628$	32.6663	+	11.8896i	1.30353	+	0.474445i
$629$	10.6022	+	18.3635i	0.422737	+	0.732202i
$630$		0			0
$631$	7.08366	−	12.2693i	0.281996	−	0.488431i	−0.689880	−	0.723924i	$-0.742337\pi$
$631$	7.08366	−	12.2693i	0.281996	−	0.488431i	0.971876	+	0.235492i	$0.0756702\pi$
$632$	3.82205	−	3.20708i	0.152033	−	0.127571i
$633$		0			0
$634$	−9.30513	+	52.7720i	−0.369554	+	2.09585i
$635$	−3.32093	+	18.8340i	−0.131787	+	0.747403i
$636$		0			0
$637$	−15.3791	+	12.9046i	−0.609341	+	0.511298i
$638$	−13.1465	+	22.7704i	−0.520476	+	0.901490i
$639$		0			0
$640$	8.77695	+	15.2021i	0.346939	+	0.600917i
$641$	20.8620	+	7.59316i	0.824001	+	0.299912i	0.719394	−	0.694602i	$-0.244419\pi$
$641$	20.8620	+	7.59316i	0.824001	+	0.299912i	0.104606	+	0.994514i	$0.466642\pi$
$642$		0			0
$643$	16.4981	+	13.8436i	0.650623	+	0.545938i	0.907260	−	0.420570i	$-0.138170\pi$
$643$	16.4981	+	13.8436i	0.650623	+	0.545938i	−0.256637	+	0.966508i	$0.582614\pi$
$644$	−49.3292	+	17.9544i	−1.94384	+	0.707502i
$645$		0			0
$646$	1.60311	+	9.09168i	0.0630735	+	0.357707i
$647$	−13.4037			−0.526952			−0.263476	−	0.964666i	$-0.584869\pi$
$647$	−13.4037			−0.526952			−0.263476	+	0.964666i	$0.584869\pi$
$648$		0			0
$649$	1.08823			0.0427168
$650$	0.319131	+	1.80988i	0.0125174	+	0.0709895i
$651$		0			0
$652$	2.82079	−	1.02668i	0.110471	−	0.0402080i
$653$	14.4866	+	12.1557i	0.566903	+	0.475688i	0.880617	−	0.473830i	$-0.157129\pi$
$653$	14.4866	+	12.1557i	0.566903	+	0.475688i	−0.313714	+	0.949518i	$0.601573\pi$
$654$		0			0
$655$	−29.8504	−	10.8647i	−1.16635	−	0.424518i
$656$	−3.05455	−	5.29063i	−0.119260	−	0.206564i
$657$		0			0
$658$	37.0059	−	64.0962i	1.44264	−	2.49873i
$659$	0.0215882	−	0.0181147i	0.000840958	−	0.000705648i	−0.642367	−	0.766397i	$-0.722048\pi$
$659$	0.0215882	−	0.0181147i	0.000840958	−	0.000705648i	0.643208	+	0.765692i	$0.277603\pi$
$660$		0			0
$661$	−7.82141	+	44.3574i	−0.304218	+	1.72530i	0.322946	+	0.946417i	$0.395327\pi$
$661$	−7.82141	+	44.3574i	−0.304218	+	1.72530i	−0.627164	+	0.778887i	$0.715784\pi$
$662$	−9.65533	+	54.7581i	−0.375265	+	2.12823i
$663$		0			0
$664$	7.09691	−	5.95502i	0.275414	−	0.231099i
$665$	9.22800	−	15.9834i	0.357846	−	0.619808i
$666$		0			0
$667$	6.41623	+	11.1132i	0.248438	+	0.430306i
$668$	−56.5862	−	20.5957i	−2.18938	−	0.796871i
$669$		0			0
$670$	13.9268	+	11.6860i	0.538041	+	0.451470i
$671$	−17.3735	+	6.32343i	−0.670696	+	0.244113i
$672$		0			0
$673$	−1.69475	−	9.61142i	−0.0653279	−	0.370493i	−0.999892	−	0.0146980i	$-0.995321\pi$
$673$	−1.69475	−	9.61142i	−0.0653279	−	0.370493i	0.934564	−	0.355795i	$-0.115790\pi$
$674$	23.2607			0.895968
$675$		0			0
$676$	−28.9847			−1.11480
$677$	−7.09887	−	40.2597i	−0.272832	−	1.54731i	−0.745766	−	0.666208i	$-0.767916\pi$
$677$	−7.09887	−	40.2597i	−0.272832	−	1.54731i	0.472934	−	0.881098i	$-0.343195\pi$
$678$		0			0
$679$	23.2815	−	8.47376i	0.893460	−	0.325193i
$680$	−4.10964	−	3.44840i	−0.157598	−	0.132240i
$681$		0			0
$682$	12.2101	+	4.44413i	0.467551	+	0.170175i
$683$	−22.0126	−	38.1269i	−0.842287	−	1.45888i	−0.887957	−	0.459927i	$-0.847875\pi$
$683$	−22.0126	−	38.1269i	−0.842287	−	1.45888i	0.0456696	−	0.998957i	$-0.485458\pi$
$684$		0			0
$685$	−3.77322	+	6.53541i	−0.144167	+	0.249705i
$686$	75.0594	−	62.9823i	2.86578	−	2.40468i
$687$		0			0
$688$	2.57397	−	14.5977i	0.0981316	−	0.556532i
$689$	−1.33622	+	7.57808i	−0.0509059	+	0.288702i
$690$		0			0
$691$	16.5095	−	13.8531i	0.628051	−	0.526997i	−0.272272	−	0.962220i	$-0.587775\pi$
$691$	16.5095	−	13.8531i	0.628051	−	0.526997i	0.900323	+	0.435223i	$0.143331\pi$
$692$	−11.4970	+	19.9133i	−0.437049	+	0.756991i
$693$		0			0
$694$	3.73302	+	6.46577i	0.141703	+	0.245437i
$695$	−25.8348	−	9.40311i	−0.979971	−	0.356680i
$696$		0			0
$697$	4.09302	+	3.43445i	0.155034	+	0.130089i
$698$	58.3024	−	21.2203i	2.20678	−	0.803202i
$699$		0			0
$700$	−1.50645	−	8.54352i	−0.0569386	−	0.322915i
$701$	12.8521			0.485419			0.242709	−	0.970099i	$-0.421964\pi$
$701$	12.8521			0.485419			0.242709	+	0.970099i	$0.421964\pi$
$702$		0			0
$703$	−16.4889			−0.621891
$704$	8.25521	+	46.8176i	0.311130	+	1.76451i
$705$		0			0
$706$	−50.0752	+	18.2259i	−1.88461	+	0.685940i
$707$	−69.0112	−	57.9073i	−2.59543	−	2.17783i
$708$		0			0
$709$	46.7137	+	17.0024i	1.75437	+	0.638539i	0.999843	−	0.0177295i	$-0.00564379\pi$
$709$	46.7137	+	17.0024i	1.75437	+	0.638539i	0.754528	+	0.656268i	$0.227866\pi$
$710$	6.78937	+	11.7595i	0.254800	+	0.441327i
$711$		0			0
$712$	9.29562	−	16.1005i	0.348368	−	0.603392i
$713$	4.85801	−	4.07635i	0.181934	−	0.152661i
$714$		0			0
$715$	1.81456	−	10.2909i	0.0678607	−	0.384857i
$716$	−4.63099	+	26.2637i	−0.173068	+	0.981519i
$717$		0			0
$718$	−6.84883	+	5.74685i	−0.255596	+	0.214471i
$719$	−2.81873	+	4.88218i	−0.105121	+	0.182075i	−0.913788	−	0.406192i	$-0.866856\pi$
$719$	−2.81873	+	4.88218i	−0.105121	+	0.182075i	0.808667	+	0.588267i	$0.200190\pi$
$720$		0			0
$721$	−21.8330	−	37.8159i	−0.813104	−	1.40834i
$722$	31.1946	+	11.3539i	1.16094	+	0.422549i
$723$		0			0
$724$	−2.81930	−	2.36568i	−0.104779	−	0.0879196i
$725$	−1.99279	+	0.725318i	−0.0740105	+	0.0269376i
$726$		0			0
$727$	−7.88611	−	44.7243i	−0.292480	−	1.65873i	−0.677273	−	0.735731i	$-0.736839\pi$
$727$	−7.88611	−	44.7243i	−0.292480	−	1.65873i	0.384794	−	0.923002i	$-0.374272\pi$
$728$	−6.46195			−0.239496
$729$		0			0
$730$	56.1546			2.07837
$731$	2.25121	+	12.7673i	0.0832641	+	0.472214i
$732$		0			0
$733$	24.1190	−	8.77858i	0.890854	−	0.324244i	0.144272	−	0.989538i	$-0.453916\pi$
$733$	24.1190	−	8.77858i	0.890854	−	0.324244i	0.746582	+	0.665294i	$0.231694\pi$
$734$	28.4822	+	23.8994i	1.05130	+	0.882143i
$735$		0			0
$736$	32.0889	+	11.6794i	1.18281	+	0.430508i
$737$	8.57098	+	14.8454i	0.315716	+	0.546837i
$738$		0			0
$739$	7.22763	−	12.5186i	0.265873	−	0.460505i	−0.701919	−	0.712256i	$-0.747673\pi$
$739$	7.22763	−	12.5186i	0.265873	−	0.460505i	0.967792	+	0.251752i	$0.0810066\pi$
$740$	35.8041	−	30.0432i	1.31619	−	1.10441i
$741$		0			0
$742$	11.3221	−	64.2107i	0.415647	−	2.35725i
$743$	−6.04187	+	34.2651i	−0.221655	+	1.25707i	0.647323	+	0.762215i	$0.275888\pi$
$743$	−6.04187	+	34.2651i	−0.221655	+	1.25707i	−0.868978	+	0.494851i	$0.835223\pi$
$744$		0			0
$745$	−14.1367	+	11.8621i	−0.517928	+	0.434593i
$746$	31.5084	−	54.5742i	1.15360	−	1.99810i
$747$		0			0
$748$	−12.3371	−	21.3685i	−0.451089	−	0.781308i
$749$	33.8385	+	12.3162i	1.23643	+	0.450024i
$750$		0			0
$751$	13.8795	+	11.6463i	0.506471	+	0.424980i	0.859885	−	0.510487i	$-0.170535\pi$
$751$	13.8795	+	11.6463i	0.506471	+	0.424980i	−0.353414	+	0.935467i	$0.614979\pi$
$752$	−18.2418	+	6.63946i	−0.665209	+	0.242116i
$753$		0			0
$754$	1.33800	+	7.58816i	0.0487270	+	0.276345i
$755$	−1.47535			−0.0536933
$756$		0			0
$757$	−37.0045			−1.34495			−0.672475	−	0.740120i	$-0.734769\pi$
$757$	−37.0045			−1.34495			−0.672475	+	0.740120i	$0.734769\pi$
$758$	7.73156	+	43.8479i	0.280823	+	1.59263i
$759$		0			0
$760$	3.92014	−	1.42682i	0.142199	−	0.0517560i
$761$	9.53298	+	7.99912i	0.345570	+	0.289968i	0.799008	−	0.601320i	$-0.205358\pi$
$761$	9.53298	+	7.99912i	0.345570	+	0.289968i	−0.453438	+	0.891288i	$0.649803\pi$
$762$		0			0
$763$	25.6242	+	9.32646i	0.927660	+	0.337641i
$764$	15.6257	+	27.0644i	0.565316	+	0.979156i
$765$		0			0
$766$	10.5155	−	18.2133i	0.379939	−	0.658074i
$767$	0.244298	−	0.204990i	0.00882108	−	0.00740177i
$768$		0			0
$769$	−7.09970	+	40.2644i	−0.256022	+	1.45197i	0.537414	+	0.843318i	$0.319401\pi$
$769$	−7.09970	+	40.2644i	−0.256022	+	1.45197i	−0.793436	+	0.608654i	$0.791710\pi$
$770$	−15.3752	+	87.1970i	−0.554083	+	3.14236i
$771$		0			0
$772$	40.0338	−	33.5923i	1.44085	−	1.20901i
$773$	−18.2081	+	31.5374i	−0.654900	+	1.13432i	0.327019	+	0.945018i	$0.393956\pi$
$773$	−18.2081	+	31.5374i	−0.654900	+	1.13432i	−0.981919	+	0.189302i	$0.939377\pi$
$774$		0			0
$775$	0.524012	+	0.907615i	0.0188231	+	0.0326025i
$776$	5.26246	+	1.91538i	0.188911	+	0.0687581i
$777$		0			0
$778$	34.3720	+	28.8415i	1.23230	+	1.03402i
$779$	−3.90429	+	1.42105i	−0.139886	+	0.0509142i
$780$		0			0
$781$	2.22327	+	12.6088i	0.0795548	+	0.451178i
$782$	−21.6160			−0.772985
$783$		0			0
$784$	−44.6174			−1.59348
$785$	−4.96918	−	28.1816i	−0.177358	−	1.00585i
$786$		0			0
$787$	−17.2407	+	6.27510i	−0.614564	+	0.223683i	−0.630499	−	0.776190i	$-0.717150\pi$
$787$	−17.2407	+	6.27510i	−0.614564	+	0.223683i	0.0159350	+	0.999873i	$0.494928\pi$
$788$	27.3440	+	22.9444i	0.974090	+	0.817359i
$789$		0			0
$790$	−18.8261	−	6.85212i	−0.669801	−	0.243788i
$791$	−5.82488	−	10.0890i	−0.207109	−	0.358723i
$792$		0			0
$793$	−2.70904	+	4.69220i	−0.0962009	+	0.166625i
$794$	−15.9191	+	13.3577i	−0.564946	+	0.474046i
$795$		0			0
$796$	8.88066	−	50.3647i	0.314767	−	1.78513i
$797$	−0.601678	+	3.41228i	−0.0213125	+	0.120869i	−0.993608	−	0.112886i	$-0.963990\pi$
$797$	−0.601678	+	3.41228i	−0.0213125	+	0.120869i	0.972295	+	0.233756i	$0.0751015\pi$
$798$		0			0
$799$	13.0062	−	10.9135i	0.460125	−	0.386090i
$800$	−2.82166	+	4.88726i	−0.0997608	+	0.172791i
$801$		0			0
$802$	−20.3358	−	35.2227i	−0.718083	−	1.24376i
$803$	49.7546	+	18.1092i	1.75580	+	0.639060i
$804$		0			0
$805$	33.1034	+	27.7771i	1.16674	+	0.979014i
$806$	3.57821	−	1.30236i	0.126037	−	0.0458737i
$807$		0			0
$808$	−3.53602	−	20.0538i	−0.124397	−	0.705489i
$809$	24.8406			0.873348			0.436674	−	0.899620i	$-0.356156\pi$
$809$	24.8406			0.873348			0.436674	+	0.899620i	$0.356156\pi$
$810$		0			0
$811$	−40.3286			−1.41613			−0.708063	−	0.706149i	$-0.750431\pi$
$811$	−40.3286			−1.41613			−0.708063	+	0.706149i	$0.750431\pi$
$812$	−6.31599	−	35.8198i	−0.221648	−	1.25703i
$813$		0			0
$814$	74.3344	−	27.0555i	2.60542	−	0.948295i
$815$	−1.89295	−	1.58838i	−0.0663072	−	0.0556384i
$816$		0			0
$817$	−9.47323	−	3.44797i	−0.331426	−	0.120629i
$818$	−15.9330	−	27.5968i	−0.557084	−	0.964898i
$819$		0			0
$820$	5.88862	−	10.1994i	0.205640	−	0.356178i
$821$	−30.7809	+	25.8283i	−1.07426	+	0.901412i	−0.995432	−	0.0954758i	$-0.969563\pi$
$821$	−30.7809	+	25.8283i	−1.07426	+	0.901412i	−0.0788296	+	0.996888i	$0.525118\pi$
$822$		0			0
$823$	−8.32736	+	47.2268i	−0.290274	+	1.64622i	0.395542	+	0.918448i	$0.370557\pi$
$823$	−8.32736	+	47.2268i	−0.290274	+	1.64622i	−0.685815	+	0.727776i	$0.740554\pi$
$824$	1.71393	−	9.72017i	0.0597075	−	0.338618i
$825$		0			0
$826$	−2.06999	+	1.73693i	−0.0720242	+	0.0604355i
$827$	−2.50024	+	4.33054i	−0.0869419	+	0.150588i	−0.906217	−	0.422813i	$-0.861043\pi$
$827$	−2.50024	+	4.33054i	−0.0869419	+	0.150588i	0.819275	+	0.573401i	$0.194376\pi$
$828$		0			0
$829$	−14.8519	−	25.7242i	−0.515826	−	0.893438i	−0.999831	−	0.0183722i	$-0.994152\pi$
$829$	−14.8519	−	25.7242i	−0.515826	−	0.893438i	0.484005	−	0.875065i	$-0.339182\pi$
$830$	−34.9568	−	12.7232i	−1.21337	−	0.441630i
$831$		0			0
$832$	10.6723	+	8.95509i	0.369994	+	0.310462i
$833$	36.6694	−	13.3466i	1.27052	−	0.462432i
$834$		0			0
$835$	8.60786	+	48.8176i	0.297887	+	1.68940i
$836$	19.1871			0.663599
$837$		0			0
$838$	−12.3502			−0.426632
$839$	4.49827	+	25.5110i	0.155298	+	0.880737i	0.958513	+	0.285048i	$0.0920096\pi$
$839$	4.49827	+	25.5110i	0.155298	+	0.880737i	−0.803216	+	0.595689i	$0.796879\pi$
$840$		0			0
$841$	18.8960	−	6.87760i	0.651588	−	0.237159i
$842$	−21.6726	−	18.1855i	−0.746888	−	0.626713i
$843$		0			0
$844$	23.3172	+	8.48676i	0.802610	+	0.292126i
$845$	11.9300	+	20.6633i	0.410403	+	0.710840i
$846$		0			0
$847$	−15.0751	+	26.1109i	−0.517988	+	0.897182i
$848$	−13.1006	+	10.9927i	−0.449875	+	0.377490i
$849$		0			0
$850$	0.620314	−	3.51797i	0.0212766	−	0.120666i
$851$	6.70415	−	38.0211i	0.229815	−	1.30335i
$852$		0			0
$853$	−3.82383	+	3.20858i	−0.130926	+	0.109860i	−0.705899	−	0.708312i	$-0.749457\pi$
$853$	−3.82383	+	3.20858i	−0.130926	+	0.109860i	0.574973	+	0.818172i	$0.305012\pi$
$854$	22.9543	−	39.7580i	0.785481	−	1.36049i
$855$		0			0
$856$	4.06980	+	7.04911i	0.139103	+	0.240934i
$857$	−13.7975	−	5.02189i	−0.471314	−	0.171544i	0.0954333	−	0.995436i	$-0.469576\pi$
$857$	−13.7975	−	5.02189i	−0.471314	−	0.171544i	−0.566748	+	0.823891i	$0.691799\pi$
$858$		0			0
$859$	−13.3942	−	11.2390i	−0.457003	−	0.383471i	0.385024	−	0.922907i	$-0.374193\pi$
$859$	−13.3942	−	11.2390i	−0.457003	−	0.383471i	−0.842027	+	0.539435i	$0.818638\pi$
$860$	26.8526	−	9.77353i	0.915665	−	0.333275i
$861$		0			0
$862$	13.4380	+	76.2107i	0.457700	+	2.59575i
$863$	−6.33263			−0.215565			−0.107783	−	0.994174i	$-0.534375\pi$
$863$	−6.33263			−0.215565			−0.107783	+	0.994174i	$0.534375\pi$
$864$		0			0
$865$	18.9284			0.643585
$866$	−4.01337	−	22.7610i	−0.136380	−	0.773449i
$867$		0			0
$868$	−16.8908	+	6.14776i	−0.573313	+	0.208669i
$869$	−14.4707	−	12.1424i	−0.490885	−	0.411901i
$870$		0			0
$871$	4.72053	+	1.71813i	0.159949	+	0.0582167i
$872$	3.08187	+	5.33795i	0.104365	+	0.180766i
$873$		0			0
$874$	8.40448	−	14.5570i	0.284286	−	0.492397i
$875$	−43.9311	+	36.8626i	−1.48514	+	1.24618i
$876$		0			0
$877$	5.64895	−	32.0368i	0.190751	−	1.08180i	−0.727589	−	0.686013i	$-0.759359\pi$
$877$	5.64895	−	32.0368i	0.190751	−	1.08180i	0.918340	−	0.395792i	$-0.129530\pi$
$878$	3.48832	−	19.7833i	0.117725	−	0.667653i
$879$		0			0
$880$	17.7903	−	14.9278i	0.599711	−	0.503218i
$881$	−16.6800	+	28.8906i	−0.561963	+	0.973348i	0.435363	+	0.900255i	$0.356620\pi$
$881$	−16.6800	+	28.8906i	−0.561963	+	0.973348i	−0.997325	+	0.0730926i	$0.976713\pi$
$882$		0			0
$883$	27.4256	+	47.5025i	0.922944	+	1.59859i	0.794835	+	0.606826i	$0.207557\pi$
$883$	27.4256	+	47.5025i	0.922944	+	1.59859i	0.128109	+	0.991760i	$0.459109\pi$
$884$	−6.79474	−	2.47308i	−0.228532	−	0.0831788i
$885$		0			0
$886$	−26.8987	−	22.5707i	−0.903680	−	0.758278i
$887$	19.7784	−	7.19875i	0.664094	−	0.241710i	0.0120911	−	0.999927i	$-0.496151\pi$
$887$	19.7784	−	7.19875i	0.664094	−	0.241710i	0.652003	+	0.758216i	$0.273929\pi$
$888$		0			0
$889$	−7.77527	−	44.0958i	−0.260774	−	1.47892i
$890$	−74.6516			−2.50233
$891$		0			0
$892$	37.9158			1.26951
$893$	2.29261	+	13.0021i	0.0767194	+	0.435097i
$894$		0			0
$895$	20.6296	−	7.50855i	0.689570	−	0.250983i
$896$	−31.4835	−	26.4178i	−1.05179	−	0.882556i
$897$		0			0
$898$	−9.47241	−	3.44767i	−0.316098	−	0.115050i
$899$	2.19698	+	3.80529i	0.0732735	+	0.126914i
$900$		0			0
$901$	7.47859	−	12.9533i	0.249148	−	0.431537i
$902$	15.2694	−	12.8126i	0.508416	−	0.426612i
$903$		0			0
$904$	0.457263	−	2.59326i	0.0152083	−	0.0862507i
$905$	−0.526088	+	2.98359i	−0.0174878	+	0.0991780i
$906$		0			0
$907$	11.3666	−	9.53770i	0.377422	−	0.316694i	−0.434268	−	0.900784i	$-0.642993\pi$
$907$	11.3666	−	9.53770i	0.377422	−	0.316694i	0.811689	+	0.584090i	$0.198548\pi$
$908$	−28.5444	+	49.4403i	−0.947278	+	1.64073i
$909$		0			0
$910$	12.9737	+	22.4711i	0.430074	+	0.744911i
$911$	16.9422	+	6.16646i	0.561321	+	0.204304i	0.607069	−	0.794649i	$-0.292345\pi$
$911$	16.9422	+	6.16646i	0.561321	+	0.204304i	−0.0457485	+	0.998953i	$0.514567\pi$
$912$		0			0
$913$	−26.8697	−	22.5463i	−0.889256	−	0.746175i
$914$	44.7470	−	16.2866i	1.48010	−	0.538713i
$915$		0			0
$916$	3.80793	+	21.5959i	0.125818	+	0.713547i
$917$	74.3738			2.45604
$918$		0			0
$919$	13.4881			0.444932			0.222466	−	0.974940i	$-0.428589\pi$
$919$	13.4881			0.444932			0.222466	+	0.974940i	$0.428589\pi$
$920$	1.69617	+	9.61943i	0.0559209	+	0.317143i
$921$		0			0
$922$	−29.7979	+	10.8455i	−0.981340	+	0.357179i
$923$	2.87422	+	2.41176i	0.0946061	+	0.0793839i
$924$		0			0
$925$	5.99551	+	2.18219i	0.197131	+	0.0717499i
$926$	15.7753	+	27.3237i	0.518410	+	0.897912i
$927$		0			0
$928$	−11.8302	+	20.4905i	−0.388344	+	0.672632i
$929$	28.8195	−	24.1824i	0.945536	−	0.793399i	−0.0330040	−	0.999455i	$-0.510507\pi$
$929$	28.8195	−	24.1824i	0.945536	−	0.793399i	0.978540	+	0.206056i	$0.0660630\pi$
$930$		0			0
$931$	−5.26932	+	29.8838i	−0.172695	+	0.979402i
$932$	10.3050	−	58.4423i	0.337550	−	1.91434i
$933$		0			0
$934$	24.9901	−	20.9692i	0.817700	−	0.686132i
$935$	−10.1558	+	17.5903i	−0.332129	+	0.575265i
$936$		0			0
$937$	−2.07229	−	3.58931i	−0.0676988	−	0.117258i	0.830189	−	0.557482i	$-0.188232\pi$
$937$	−2.07229	−	3.58931i	−0.0676988	−	0.117258i	−0.897888	+	0.440224i	$0.854899\pi$
$938$	−39.9981	−	14.5581i	−1.30599	−	0.475340i
$939$		0			0
$940$	−28.6683	−	24.0556i	−0.935058	−	0.784607i
$941$	−3.31742	+	1.20744i	−0.108145	+	0.0393615i	−0.395526	−	0.918455i	$-0.629438\pi$
$941$	−3.31742	+	1.20744i	−0.108145	+	0.0393615i	0.287381	+	0.957816i	$0.407215\pi$
$942$		0			0
$943$	−1.68931	−	9.58053i	−0.0550114	−	0.311985i
$944$	0.708752			0.0230679
$945$		0			0
$946$	48.3643			1.57246
$947$	2.47537	+	14.0385i	0.0804387	+	0.456190i	0.998248	+	0.0591689i	$0.0188450\pi$
$947$	2.47537	+	14.0385i	0.0804387	+	0.456190i	−0.917809	+	0.397021i	$0.870044\pi$
$948$		0			0
$949$	14.5807	−	5.30693i	0.473309	−	0.172270i
$950$	2.12795	+	1.78556i	0.0690398	+	0.0579313i
$951$		0			0
$952$	11.8030	+	4.29593i	0.382536	+	0.139232i
$953$	5.82130	+	10.0828i	0.188570	+	0.326613i	0.944774	−	0.327723i	$-0.106281\pi$
$953$	5.82130	+	10.0828i	0.188570	+	0.326613i	−0.756204	+	0.654336i	$0.772948\pi$
$954$		0			0
$955$	12.8629	−	22.2792i	0.416233	−	0.720938i
$956$	−19.1841	+	16.0974i	−0.620458	+	0.520626i
$957$		0			0
$958$	−3.85561	+	21.8663i	−0.124569	+	0.706467i
$959$	3.06809	−	17.4000i	0.0990737	−	0.561875i
$960$		0			0
$961$	−22.0839	+	18.5306i	−0.712385	+	0.597762i
$962$	11.5909	−	20.0761i	0.373707	−	0.647279i
$963$		0			0
$964$	−7.18680	−	12.4479i	−0.231471	−	0.400920i
$965$	−40.4258	−	14.7138i	−1.30135	−	0.473654i
$966$		0			0
$967$	22.2675	+	18.6846i	0.716074	+	0.600857i	0.926296	−	0.376796i	$-0.122974\pi$
$967$	22.2675	+	18.6846i	0.716074	+	0.600857i	−0.210222	+	0.977654i	$0.567419\pi$
$968$	−6.40407	+	2.33089i	−0.205835	+	0.0749177i
$969$		0			0
$970$	−3.90485	−	22.1455i	−0.125377	−	0.711049i
$971$	−47.5792			−1.52689			−0.763444	−	0.645874i	$-0.776493\pi$
$971$	−47.5792			−1.52689			−0.763444	+	0.645874i	$0.776493\pi$
$972$		0			0
$973$	64.3687			2.06357
$974$	−5.96496	−	33.8290i	−0.191130	−	1.08395i
$975$		0			0
$976$	−11.3151	+	4.11837i	−0.362189	+	0.131826i
$977$	−4.68536	−	3.93148i	−0.149898	−	0.125779i	0.564755	−	0.825259i	$-0.308971\pi$
$977$	−4.68536	−	3.93148i	−0.149898	−	0.125779i	−0.714653	+	0.699480i	$0.753415\pi$
$978$		0			0
$979$	−66.1435	−	24.0743i	−2.11396	−	0.769417i
$980$	−43.0073	−	74.4908i	−1.37382	−	2.37952i
$981$		0			0
$982$	−11.4511	+	19.8339i	−0.365419	+	0.632924i
$983$	−8.15976	+	6.84685i	−0.260256	+	0.218381i	−0.763574	−	0.645721i	$-0.776557\pi$
$983$	−8.15976	+	6.84685i	−0.260256	+	0.218381i	0.503318	+	0.864101i	$0.332113\pi$
$984$		0			0
$985$	5.10246	−	28.9375i	0.162578	−	0.922024i
$986$	2.60074	−	14.7495i	0.0828245	−	0.469721i
$987$		0			0
$988$	4.30732	−	3.61427i	0.137034	−	0.114985i
$989$	11.8022	−	20.4421i	0.375289	−	0.650020i
$990$		0			0
$991$	−11.9928	−	20.7721i	−0.380964	−	0.659849i	0.610236	−	0.792219i	$-0.291074\pi$
$991$	−11.9928	−	20.7721i	−0.380964	−	0.659849i	−0.991200	+	0.132371i	$0.957741\pi$
$992$	10.9876	+	3.99914i	0.348855	+	0.126973i
$993$		0			0
$994$	−24.3539	−	20.4354i	−0.772459	−	0.648170i
$995$	−39.5605	+	14.3988i	−1.25415	+	0.456474i
$996$		0			0
$997$	0.749149	+	4.24864i	0.0237258	+	0.134556i	0.994370	−	0.105965i	$-0.0337930\pi$
$997$	0.749149	+	4.24864i	0.0237258	+	0.134556i	−0.970644	+	0.240520i	$0.922682\pi$
$998$	−40.7733			−1.29066
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.e.u.82.2		12
3.2	odd	2		729.2.e.j.82.1		12
9.2	odd	6		729.2.e.t.325.1		12
9.4	even	3		729.2.e.l.568.1		12
9.5	odd	6		729.2.e.s.568.2		12
9.7	even	3		729.2.e.k.325.2		12
27.2	odd	18		729.2.e.j.649.1		12
27.4	even	9		729.2.c.a.487.2		12
27.5	odd	18		729.2.a.b.1.2	✓	6
27.7	even	9		729.2.e.k.406.2		12
27.11	odd	18		729.2.e.s.163.2		12
27.13	even	9		729.2.c.a.244.2		12
27.14	odd	18		729.2.c.d.244.5		12
27.16	even	9		729.2.e.l.163.1		12
27.20	odd	18		729.2.e.t.406.1		12
27.22	even	9		729.2.a.e.1.5	yes	6
27.23	odd	18		729.2.c.d.487.5		12
27.25	even	9	inner	729.2.e.u.649.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
729.2.a.b.1.2	✓	6	27.5	odd	18
729.2.a.e.1.5	yes	6	27.22	even	9
729.2.c.a.244.2		12	27.13	even	9
729.2.c.a.487.2		12	27.4	even	9
729.2.c.d.244.5		12	27.14	odd	18
729.2.c.d.487.5		12	27.23	odd	18
729.2.e.j.82.1		12	3.2	odd	2
729.2.e.j.649.1		12	27.2	odd	18
729.2.e.k.325.2		12	9.7	even	3
729.2.e.k.406.2		12	27.7	even	9
729.2.e.l.163.1		12	27.16	even	9
729.2.e.l.568.1		12	9.4	even	3
729.2.e.s.163.2		12	27.11	odd	18
729.2.e.s.568.2		12	9.5	odd	6
729.2.e.t.325.1		12	9.2	odd	6
729.2.e.t.406.1		12	27.20	odd	18
729.2.e.u.82.2		12	1.1	even	1	trivial
729.2.e.u.649.2		12	27.25	even	9	inner

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)

\(f(q)\)	\(=\)	\(q+(0.369007 + 2.09274i) q^{2} +(-2.36403 + 0.860436i) q^{4} +(1.58643 + 1.33117i) q^{5} +(-4.55626 - 1.65834i) q^{7} +(-0.547989 - 0.949144i) q^{8} +O(q^{10})\)	\(q+(0.369007 + 2.09274i) q^{2} +(-2.36403 + 0.860436i) q^{4} +(1.58643 + 1.33117i) q^{5} +(-4.55626 - 1.65834i) q^{7} +(-0.547989 - 0.949144i) q^{8} +(-2.20040 + 3.81121i) q^{10} +(-3.17869 + 2.66724i) q^{11} +(-0.211159 + 1.19754i) q^{13} +(1.78920 - 10.1470i) q^{14} +(-2.07024 + 1.73714i) q^{16} +(1.18182 - 2.04697i) q^{17} +(0.919003 + 1.59176i) q^{19} +(-4.89576 - 1.78191i) q^{20} +(-6.75481 - 5.66796i) q^{22} +(-4.04403 + 1.47191i) q^{23} +(-0.123500 - 0.700401i) q^{25} -2.58407 q^{26} +12.1980 q^{28} +(-0.517788 - 2.93652i) q^{29} +(-1.38472 + 0.503996i) q^{31} +(-6.07846 - 5.10043i) q^{32} +(4.71989 + 1.71790i) q^{34} +(-5.02066 - 8.69603i) q^{35} +(-4.48554 + 7.76918i) q^{37} +(-2.99203 + 2.51061i) q^{38} +(0.394130 - 2.23522i) q^{40} +(-0.392536 + 2.22618i) q^{41} +(-4.20164 + 3.52560i) q^{43} +(5.21953 - 9.04050i) q^{44} +(-4.57260 - 7.91998i) q^{46} +(6.74994 + 2.45678i) q^{47} +(12.6471 + 10.6122i) q^{49} +(1.42019 - 0.516906i) q^{50} +(-0.531222 - 3.01271i) q^{52} +6.32803 q^{53} -8.59334 q^{55} +(0.922773 + 5.23330i) q^{56} +(5.95432 - 2.16719i) q^{58} +(-0.200900 - 0.168575i) q^{59} +(4.18690 + 1.52391i) q^{61} +(-1.56571 - 2.71188i) q^{62} +(5.72840 - 9.92188i) q^{64} +(-1.92913 + 1.61873i) q^{65} +(0.717359 - 4.06834i) q^{67} +(-1.03257 + 5.85598i) q^{68} +(16.3459 - 13.7159i) q^{70} +(1.54276 - 2.67213i) q^{71} +(-6.38003 - 11.0505i) q^{73} +(-17.9141 - 6.52021i) q^{74} +(-3.54216 - 2.97222i) q^{76} +(18.9062 - 6.88128i) q^{77} +(0.790517 + 4.48325i) q^{79} -5.59674 q^{80} -4.80368 q^{82} +(1.46786 + 8.32464i) q^{83} +(4.59975 - 1.67417i) q^{85} +(-8.92862 - 7.49200i) q^{86} +(4.27348 + 1.55542i) q^{88} +(8.48158 + 14.6905i) q^{89} +(2.94803 - 5.10614i) q^{91} +(8.29373 - 6.95926i) q^{92} +(-2.65063 + 15.0325i) q^{94} +(-0.660975 + 3.74857i) q^{95} +(-3.91431 + 3.28450i) q^{97} +(-17.5417 + 30.3831i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{2} + 6 q^{4} - 6 q^{5} - 3 q^{7} - 6 q^{8}+O(q^{10}) \) 12 * q + 6 * q^2 + 6 * q^4 - 6 * q^5 - 3 * q^7 - 6 * q^8	\( 12 q + 6 q^{2} + 6 q^{4} - 6 q^{5} - 3 q^{7} - 6 q^{8} - 6 q^{10} - 12 q^{11} - 3 q^{13} - 15 q^{14} - 36 q^{16} + 9 q^{17} - 12 q^{19} - 42 q^{20} + 6 q^{22} - 6 q^{23} + 6 q^{25} + 48 q^{26} + 6 q^{28} - 12 q^{29} + 6 q^{31} - 54 q^{32} - 9 q^{34} - 30 q^{35} - 3 q^{37} - 42 q^{38} - 57 q^{40} - 24 q^{41} + 6 q^{43} + 33 q^{44} + 3 q^{46} - 21 q^{47} + 33 q^{49} - 21 q^{50} + 45 q^{52} - 18 q^{53} + 30 q^{55} - 3 q^{56} + 33 q^{58} - 15 q^{59} + 33 q^{61} + 30 q^{62} - 6 q^{64} + 6 q^{65} + 42 q^{67} + 18 q^{68} + 24 q^{70} - 12 q^{73} + 3 q^{74} - 87 q^{76} + 57 q^{77} - 48 q^{79} - 42 q^{80} - 42 q^{82} - 12 q^{83} - 36 q^{85} + 30 q^{86} + 30 q^{88} + 9 q^{89} - 18 q^{91} + 48 q^{92} + 33 q^{94} - 30 q^{95} - 3 q^{97} - 18 q^{98}+O(q^{100}) \) 12 * q + 6 * q^2 + 6 * q^4 - 6 * q^5 - 3 * q^7 - 6 * q^8 - 6 * q^10 - 12 * q^11 - 3 * q^13 - 15 * q^14 - 36 * q^16 + 9 * q^17 - 12 * q^19 - 42 * q^20 + 6 * q^22 - 6 * q^23 + 6 * q^25 + 48 * q^26 + 6 * q^28 - 12 * q^29 + 6 * q^31 - 54 * q^32 - 9 * q^34 - 30 * q^35 - 3 * q^37 - 42 * q^38 - 57 * q^40 - 24 * q^41 + 6 * q^43 + 33 * q^44 + 3 * q^46 - 21 * q^47 + 33 * q^49 - 21 * q^50 + 45 * q^52 - 18 * q^53 + 30 * q^55 - 3 * q^56 + 33 * q^58 - 15 * q^59 + 33 * q^61 + 30 * q^62 - 6 * q^64 + 6 * q^65 + 42 * q^67 + 18 * q^68 + 24 * q^70 - 12 * q^73 + 3 * q^74 - 87 * q^76 + 57 * q^77 - 48 * q^79 - 42 * q^80 - 42 * q^82 - 12 * q^83 - 36 * q^85 + 30 * q^86 + 30 * q^88 + 9 * q^89 - 18 * q^91 + 48 * q^92 + 33 * q^94 - 30 * q^95 - 3 * q^97 - 18 * q^98

Introduction

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