LMFDB - Embedded newform 729.2.e.u.649.2

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			649.2
Root			$3.10658i$ of defining polynomial
Character	$\chi$	$=$	729.649
Dual form			729.2.e.u.82.2

$q$-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 $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.369007	−	2.09274i	0.260928	−	1.47979i	−0.519458	−	0.854496i	$-0.673866\pi$
$2$	0.369007	−	2.09274i	0.260928	−	1.47979i	0.780386	−	0.625298i	$-0.215023\pi$
$3$		0			0
$3$		0			0
$4$	−2.36403	−	0.860436i	−1.18201	−	0.430218i
$5$	1.58643	−	1.33117i	0.709474	−	0.595319i	−0.214977	−	0.976619i	$-0.568968\pi$
$5$	1.58643	−	1.33117i	0.709474	−	0.595319i	0.924452	+	0.381300i	$0.124523\pi$
$6$		0			0
$7$	−4.55626	+	1.65834i	−1.72211	+	0.626795i	−0.998019	−	0.0629144i	$-0.979960\pi$
$7$	−4.55626	+	1.65834i	−1.72211	+	0.626795i	−0.724086	+	0.689709i	$0.757738\pi$
$8$	−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	0.0222820	−	0.999752i	$-0.492907\pi$
$11$	−3.17869	−	2.66724i	−0.958412	−	0.804203i	−0.980694	+	0.195549i	$0.937351\pi$
$12$		0			0
$13$	−0.211159	−	1.19754i	−0.0585649	−	0.332138i	0.941422	−	0.337230i	$-0.109490\pi$
$13$	−0.211159	−	1.19754i	−0.0585649	−	0.332138i	−0.999987	+	0.00509231i	$0.998379\pi$
$14$	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	0.973004	−	0.230789i	$-0.0741306\pi$
$17$	1.18182	+	2.04697i	0.286633	+	0.496463i	−0.686371	+	0.727252i	$0.740797\pi$
$18$		0			0
$19$	0.919003	−	1.59176i	0.210834	−	0.365175i	−0.741142	−	0.671348i	$-0.765715\pi$
$19$	0.919003	−	1.59176i	0.210834	−	0.365175i	0.951976	+	0.306174i	$0.0990488\pi$
$20$	−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	−0.115958	−	0.993254i	$-0.536994\pi$
$23$	−4.04403	−	1.47191i	−0.843239	−	0.306914i	−0.727281	+	0.686340i	$0.759216\pi$
$24$		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	0.898238	+	0.439510i	$0.144848\pi$
$29$	−0.517788	+	2.93652i	−0.0961507	+	0.545298i	−0.994389	+	0.105788i	$0.966263\pi$
$30$		0			0
$31$	−1.38472	−	0.503996i	−0.248703	−	0.0905204i	0.214661	−	0.976689i	$-0.431135\pi$
$31$	−1.38472	−	0.503996i	−0.248703	−	0.0905204i	−0.463364	+	0.886168i	$0.653358\pi$
$32$	−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	−0.953654	−	0.300905i	$-0.902711\pi$
$37$	−4.48554	−	7.76918i	−0.737418	−	1.27725i	0.216236	−	0.976341i	$-0.430622\pi$
$38$	−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	−0.999996	−	0.00291413i	$-0.999072\pi$
$41$	−0.392536	−	2.22618i	−0.0613038	−	0.347671i	0.938692	−	0.344757i	$-0.112039\pi$
$42$		0			0
$43$	−4.20164	−	3.52560i	−0.640745	−	0.537649i	0.263502	−	0.964659i	$-0.415122\pi$
$43$	−4.20164	−	3.52560i	−0.640745	−	0.537649i	−0.904247	+	0.427010i	$0.859567\pi$
$44$	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	0.200960	−	0.979599i	$-0.435594\pi$
$47$	6.74994	−	2.45678i	0.984579	−	0.358358i	0.783619	+	0.621242i	$0.213372\pi$
$48$		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	−0.655771	−	0.754959i	$-0.727657\pi$
$59$	−0.200900	+	0.168575i	−0.0261550	+	0.0219466i	0.629616	+	0.776906i	$0.283212\pi$
$60$		0			0
$61$	4.18690	−	1.52391i	0.536078	−	0.195116i	−0.0597724	−	0.998212i	$-0.519037\pi$
$61$	4.18690	−	1.52391i	0.536078	−	0.195116i	0.595850	+	0.803096i	$0.296815\pi$
$62$	−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	0.996756	+	0.0804853i	$0.0256470\pi$
$67$	0.717359	+	4.06834i	0.0876393	+	0.497027i	−0.909116	+	0.416542i	$0.863242\pi$
$68$	−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	0.942932	−	0.332986i	$-0.108056\pi$
$71$	1.54276	+	2.67213i	0.183091	+	0.317124i	−0.759840	+	0.650110i	$0.774723\pi$
$72$		0			0
$73$	−6.38003	+	11.0505i	−0.746726	+	1.29337i	0.202658	+	0.979250i	$0.435042\pi$
$73$	−6.38003	+	11.0505i	−0.746726	+	1.29337i	−0.949384	+	0.314118i	$0.898291\pi$
$74$	−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	−0.907497	−	0.420060i	$-0.862009\pi$
$79$	0.790517	−	4.48325i	0.0889401	−	0.504404i	0.996437	−	0.0843449i	$-0.0268797\pi$
$80$	−5.59674			−0.625734
$81$		0			0
$82$	−4.80368			−0.530478
$83$	1.46786	−	8.32464i	0.161118	−	0.913748i	−0.791859	−	0.610705i	$-0.790886\pi$
$83$	1.46786	−	8.32464i	0.161118	−	0.913748i	0.952977	−	0.303043i	$-0.0980026\pi$
$84$		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	0.0703304	−	0.997524i	$-0.477595\pi$
$89$	8.48158	−	14.6905i	0.899046	−	1.55719i	0.828716	−	0.559670i	$-0.189072\pi$
$90$		0			0
$91$	2.94803	+	5.10614i	0.309038	+	0.535269i
$92$	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	0.422064	−	0.906566i	$-0.361306\pi$
$97$	−3.91431	−	3.28450i	−0.397438	−	0.333490i	−0.819502	+	0.573076i	$0.805750\pi$
$98$	−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	0.738168	−	0.674617i	$-0.235691\pi$
$101$	17.4594	−	6.35469i	1.73727	−	0.632316i	0.999105	+	0.0423013i	$0.0134689\pi$
$102$		0			0
$103$	6.89882	−	5.78880i	0.679761	−	0.570387i	−0.236176	−	0.971710i	$-0.575894\pi$
$103$	6.89882	−	5.78880i	0.679761	−	0.570387i	0.915936	+	0.401323i	$0.131450\pi$
$104$	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	−0.552097	−	0.833780i	$-0.686172\pi$
$113$	1.84055	−	1.54441i	0.173144	−	0.145285i	0.725242	+	0.688494i	$0.241728\pi$
$114$		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	−0.585135	−	0.810936i	$-0.698959\pi$
$127$	4.61735	−	7.99748i	0.409723	−	0.709662i	0.994859	+	0.101274i	$0.0322919\pi$
$128$	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	−0.375801	−	0.926700i	$-0.622632\pi$
$131$	−14.4140	−	5.24625i	−1.25935	−	0.458367i	−0.883552	+	0.468334i	$0.844855\pi$
$132$		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	−0.945773	−	0.324829i	$-0.894693\pi$
$137$	0.632769	−	3.58861i	0.0540611	−	0.306596i	0.999834	+	0.0182336i	$0.00580427\pi$
$138$		0			0
$139$	−12.4749	−	4.54050i	−1.05811	−	0.385120i	−0.246392	−	0.969170i	$-0.579245\pi$
$139$	−12.4749	−	4.54050i	−1.05811	−	0.385120i	−0.811718	+	0.584050i	$0.801467\pi$
$140$	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	−0.980243	−	0.197796i	$-0.936622\pi$
$149$	−1.54738	−	8.77561i	−0.126766	−	0.718926i	0.853477	−	0.521130i	$-0.174489\pi$
$150$		0			0
$151$	−0.545733	−	0.457924i	−0.0444111	−	0.0372653i	0.620312	−	0.784355i	$-0.287006\pi$
$151$	−0.545733	−	0.457924i	−0.0444111	−	0.0372653i	−0.664723	+	0.747090i	$0.731450\pi$
$152$	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	−0.958637	−	0.284632i	$-0.908129\pi$
$157$	−10.5852	+	8.88207i	−0.844794	+	0.708867i	0.113842	+	0.993499i	$0.463684\pi$
$158$	−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	0.466980	−	0.884268i	$-0.345342\pi$
$167$	18.3363	−	15.3860i	1.41890	−	1.19060i	0.951924	−	0.306334i	$-0.0991026\pi$
$168$		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	0.868904	−	0.494981i	$-0.164825\pi$
$173$	7.00165	+	5.87508i	0.532325	+	0.446674i	−0.336578	+	0.941656i	$0.609270\pi$
$174$		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	0.993250	−	0.115997i	$-0.0370062\pi$
$179$	5.30038	+	9.18052i	0.396169	+	0.686184i	−0.597081	+	0.802181i	$0.703673\pi$
$180$		0			0
$181$	0.731460	−	1.26693i	0.0543690	−	0.0941699i	−0.837560	−	0.546345i	$-0.816019\pi$
$181$	0.731460	−	1.26693i	0.0543690	−	0.0941699i	0.891929	+	0.452176i	$0.149352\pi$
$182$	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	0.801707	+	0.597718i	$0.203926\pi$
$191$	−2.15711	+	12.2336i	−0.156083	+	0.885189i	−0.957789	+	0.287471i	$0.907185\pi$
$192$		0			0
$193$	−19.5205	−	7.10489i	−1.40512	−	0.511421i	−0.475425	−	0.879756i	$-0.657706\pi$
$193$	−19.5205	−	7.10489i	−1.40512	−	0.511421i	−0.929693	+	0.368335i	$0.879928\pi$
$194$	−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	0.494530	+	0.869161i	$0.335340\pi$
$197$	−7.09433	+	12.2877i	−0.505450	+	0.875465i	−0.999980	+	0.00630469i	$0.997993\pi$
$198$		0			0
$199$	−10.1643	−	17.6051i	−0.720529	−	1.24799i	−0.960788	−	0.277284i	$-0.910566\pi$
$199$	−10.1643	−	17.6051i	−0.720529	−	1.24799i	0.240259	−	0.970709i	$-0.422768\pi$
$200$	−0.597105	−	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	−0.864687	−	0.502311i	$-0.832483\pi$
$211$	−7.55574	+	6.34002i	−0.520159	+	0.436465i	0.344528	+	0.938776i	$0.388039\pi$
$212$	−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	−0.769473	−	0.638679i	$-0.779481\pi$
$223$	−14.1625	+	5.15472i	−0.948389	+	0.345185i	−0.178916	+	0.983864i	$0.557259\pi$
$224$	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	0.999801	−	0.0199338i	$-0.00634555\pi$
$227$	17.3835	+	14.5865i	1.15378	+	0.968140i	0.153983	+	0.988074i	$0.450790\pi$
$228$		0			0
$229$	1.51364	+	8.58428i	0.100024	+	0.567265i	0.993092	+	0.117342i	$0.0374374\pi$
$229$	1.51364	+	8.58428i	0.100024	+	0.567265i	−0.893067	+	0.449923i	$0.851451\pi$
$230$	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	−0.936088	−	0.351766i	$-0.885581\pi$
$233$	−11.7945	−	20.4286i	−0.772682	−	1.33832i	0.163406	−	0.986559i	$-0.447752\pi$
$234$		0			0
$235$	7.43792	−	12.8829i	0.485196	−	0.840385i
$236$	0.619983	−	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	0.626346	−	0.779545i	$-0.284550\pi$
$239$	9.35419	+	3.40465i	0.605072	+	0.220228i	−0.0212736	+	0.999774i	$0.506772\pi$
$240$		0			0
$241$	0.992130	−	5.62665i	0.0639087	−	0.362444i	−0.936036	−	0.351905i	$-0.885534\pi$
$241$	0.992130	−	5.62665i	0.0639087	−	0.362444i	0.999944	−	0.0105394i	$-0.00335485\pi$
$242$	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	−0.957825	−	0.287351i	$-0.907226\pi$
$251$	−3.64483	+	6.31303i	−0.230060	+	0.398475i	0.727766	+	0.685826i	$0.240559\pi$
$252$		0			0
$253$	8.92881	+	15.4651i	0.561349	+	0.972285i
$254$	−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	0.804239	+	0.594306i	$0.202573\pi$
$257$	4.03612	+	22.8900i	0.251766	+	1.42784i	−0.552473	+	0.833531i	$0.686316\pi$
$258$		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	−0.976848	−	0.213936i	$-0.931372\pi$
$263$	−25.7472	+	9.37122i	−1.58764	+	0.577854i	−0.610793	+	0.791790i	$0.709149\pi$
$264$		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	−0.352580	−	0.935782i	$-0.614695\pi$
$277$	−0.352208	+	0.128193i	−0.0211621	+	0.00770238i	0.331417	+	0.943484i	$0.392473\pi$
$278$	−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	0.264755	−	0.964316i	$-0.414709\pi$
$281$	−10.7105	−	8.98719i	−0.638936	−	0.536131i	−0.903691	+	0.428185i	$0.859153\pi$
$282$		0			0
$283$	2.70229	+	15.3255i	0.160635	+	0.911005i	0.953452	+	0.301545i	$0.0975024\pi$
$283$	2.70229	+	15.3255i	0.160635	+	0.911005i	−0.792817	+	0.609459i	$0.791387\pi$
$284$	−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	0.913511	−	0.406814i	$-0.133360\pi$
$293$	23.1392	+	8.42198i	1.35181	+	0.492017i	0.438295	+	0.898831i	$0.355582\pi$
$294$		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	0.995255	+	0.0973012i	$0.0310210\pi$
$307$	10.1956	+	17.6593i	0.581893	+	1.00787i	−0.413362	+	0.910567i	$0.635646\pi$
$308$	−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	−0.874926	−	0.484256i	$-0.839090\pi$
$311$	−3.85135	−	21.8421i	−0.218390	−	1.23855i	0.656536	−	0.754294i	$-0.272021\pi$
$312$		0			0
$313$	−8.55828	−	7.18125i	−0.483742	−	0.405908i	0.368035	−	0.929812i	$-0.380031\pi$
$313$	−8.55828	−	7.18125i	−0.483742	−	0.405908i	−0.851777	+	0.523904i	$0.824475\pi$
$314$	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	0.423962	−	0.905680i	$-0.360639\pi$
$317$	23.6959	−	8.62461i	1.33089	−	0.484406i	0.906933	+	0.421274i	$0.138417\pi$
$318$		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	0.438059	−	0.898946i	$-0.355666\pi$
$331$	24.5877	−	8.94919i	1.35146	−	0.491892i	0.913404	+	0.407054i	$0.133444\pi$
$332$	−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	0.991793	+	0.127854i	$0.0408089\pi$
$337$	1.90076	+	10.7798i	0.103541	+	0.587211i	−0.888252	+	0.459357i	$0.848080\pi$
$338$	−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	0.429113	−	0.903251i	$-0.358826\pi$
$347$	3.30150	+	1.20165i	0.177234	+	0.0645078i	−0.251879	+	0.967759i	$0.581049\pi$
$348$		0			0
$349$	−5.06998	+	28.7533i	−0.271390	+	1.53913i	0.478811	+	0.877918i	$0.341068\pi$
$349$	−5.06998	+	28.7533i	−0.271390	+	1.53913i	−0.750201	+	0.661210i	$0.770043\pi$
$350$	−7.32796			−0.391696
$351$		0			0
$352$	32.9256			1.75494
$353$	4.35454	−	24.6958i	0.231769	−	1.31443i	−0.617544	−	0.786537i	$-0.711872\pi$
$353$	4.35454	−	24.6958i	0.231769	−	1.31443i	0.849313	−	0.527890i	$-0.177017\pi$
$354$		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	−0.805159	−	0.593059i	$-0.797920\pi$
$359$	2.10362	−	3.64358i	0.111025	−	0.192301i	0.916184	+	0.400758i	$0.131253\pi$
$360$		0			0
$361$	7.81087	+	13.5288i	0.411098	+	0.712043i
$362$	−2.38144	−	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	0.921672	−	0.387971i	$-0.126824\pi$
$367$	13.4032	+	11.2466i	0.699641	+	0.587069i	−0.222030	+	0.975040i	$0.571268\pi$
$368$	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	−0.176230	+	0.984349i	$0.556390\pi$
$373$	−22.7167	+	19.0616i	−1.17623	+	0.986972i	−0.999997	+	0.00262266i	$0.999165\pi$
$374$	−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	−0.815595	−	0.578623i	$-0.803590\pi$
$383$	−7.58137	+	6.36152i	−0.387390	+	0.325059i	0.428205	+	0.903681i	$0.359146\pi$
$384$		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	0.952995	−	0.302986i	$-0.0979837\pi$
$389$	16.1748	+	13.5723i	0.820097	+	0.688143i	−0.132898	+	0.991130i	$0.542428\pi$
$390$		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	−0.716845	−	0.697233i	$-0.754414\pi$
$397$	4.88955	−	8.46894i	0.245399	−	0.425044i	0.962244	+	0.272189i	$0.0877476\pi$
$398$	−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	−0.148628	−	0.988893i	$-0.547486\pi$
$401$	−17.9851	−	6.54604i	−0.898133	−	0.326894i	−0.749504	+	0.662000i	$0.769708\pi$
$402$		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	−0.0307364	−	0.999528i	$-0.509785\pi$
$409$	−14.0912	−	5.12878i	−0.696766	−	0.253602i	−0.666029	+	0.745926i	$0.732007\pi$
$410$	−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	0.950182	−	0.311695i	$-0.100897\pi$
$419$	−1.00921	−	5.72351i	−0.0493031	−	0.279612i	−0.999485	+	0.0320837i	$0.989786\pi$
$420$		0			0
$421$	−10.1987	−	8.55776i	−0.497056	−	0.417080i	0.359491	−	0.933149i	$-0.382950\pi$
$421$	−10.1987	−	8.55776i	−0.497056	−	0.417080i	−0.856547	+	0.516069i	$0.827395\pi$
$422$	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	−0.545189	−	0.838313i	$-0.683542\pi$
$439$	−8.88316	+	3.23321i	−0.423970	+	0.154313i	0.121219	+	0.992626i	$0.461320\pi$
$440$	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	0.290494	−	0.956877i	$-0.406180\pi$
$443$	−12.6581	−	10.6214i	−0.601402	−	0.504636i	−0.891896	+	0.452241i	$0.850625\pi$
$444$		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	0.804617	−	0.593794i	$-0.202371\pi$
$449$	−2.37181	−	4.10809i	−0.111933	−	0.193873i	−0.916549	+	0.399921i	$0.869037\pi$
$450$		0			0
$451$	−4.69001	+	8.12334i	−0.220844	+	0.382513i
$452$	−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	0.747698	+	0.664039i	$0.231159\pi$
$457$	−3.89120	+	22.0681i	−0.182023	+	1.03230i	−0.929721	+	0.368264i	$0.879952\pi$
$458$	18.5232			0.865534
$459$		0			0
$460$	22.4214			1.04540
$461$	2.59122	−	14.6956i	0.120685	−	0.684440i	−0.863092	−	0.505047i	$-0.831475\pi$
$461$	2.59122	−	14.6956i	0.120685	−	0.684440i	0.983777	−	0.179394i	$-0.0574136\pi$
$462$		0			0
$463$	13.9518	+	5.07803i	0.648394	+	0.235996i	0.645218	−	0.763999i	$-0.276767\pi$
$463$	13.9518	+	5.07803i	0.648394	+	0.235996i	0.00317653	+	0.999995i	$0.498989\pi$
$464$	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	−0.987150	−	0.159794i	$-0.948917\pi$
$467$	−7.67571	+	13.2947i	−0.355190	+	0.615206i	0.631961	+	0.775000i	$0.282250\pi$
$468$		0			0
$469$	−10.0152	−	17.3468i	−0.462458	−	0.801001i
$470$	−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	−0.107824	−	0.994170i	$-0.534388\pi$
$479$	9.81848	−	3.57363i	0.448618	−	0.163284i	0.556442	+	0.830886i	$0.312166\pi$
$480$		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	−0.437198	−	0.899365i	$-0.644029\pi$
$491$	8.25592	−	6.92754i	0.372585	−	0.312636i	0.809783	+	0.586730i	$0.199585\pi$
$492$		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	−0.963938	−	0.266125i	$-0.914257\pi$
$499$	−3.33182	−	18.8957i	−0.149153	−	0.845887i	0.814786	−	0.579762i	$-0.196855\pi$
$500$	−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	0.700282	−	0.713866i	$-0.253058\pi$
$503$	−6.01253	−	10.4140i	−0.268086	−	0.464338i	−0.968367	+	0.249529i	$0.919724\pi$
$504$		0			0
$505$	19.2389	−	33.3228i	0.856120	−	1.48284i
$506$	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	0.0112886	−	0.999936i	$-0.496407\pi$
$509$	−14.0512	−	5.11423i	−0.622810	−	0.226684i	−0.634099	+	0.773252i	$0.718629\pi$
$510$		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	−0.0862502	−	0.996274i	$-0.527488\pi$
$521$	18.7094	−	32.4056i	0.819673	−	1.41972i	0.905923	−	0.423442i	$-0.139178\pi$
$522$		0			0
$523$	4.22489	+	7.31773i	0.184742	+	0.319982i	0.943489	−	0.331403i	$-0.107522\pi$
$523$	4.22489	+	7.31773i	0.184742	+	0.319982i	−0.758748	+	0.651385i	$0.774188\pi$
$524$	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	−0.884239	−	0.467034i	$-0.845322\pi$
$547$	−29.5017	+	10.7377i	−1.26140	+	0.459113i	−0.377162	+	0.926147i	$0.623100\pi$
$548$	−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	0.646467	−	0.762942i	$-0.276246\pi$
$557$	−7.96515	−	13.7960i	−0.337494	−	0.584557i	−0.983961	+	0.178385i	$0.942913\pi$
$558$		0			0
$559$	−3.33484	+	5.77610i	−0.141048	+	0.244303i
$560$	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	−0.200956	−	0.979600i	$-0.564405\pi$
$563$	−23.3616	−	8.50291i	−0.984572	−	0.358355i	−0.783616	+	0.621245i	$0.786627\pi$
$564$		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	0.831775	+	0.555113i	$0.187325\pi$
$569$	−3.33231	+	18.8985i	−0.139698	+	0.792265i	−0.971473	+	0.237152i	$0.923786\pi$
$570$		0			0
$571$	19.1502	+	6.97011i	0.801412	+	0.291690i	0.710071	−	0.704130i	$-0.248663\pi$
$571$	19.1502	+	6.97011i	0.801412	+	0.291690i	0.0913403	+	0.995820i	$0.470885\pi$
$572$	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	0.514875	−	0.857265i	$-0.327838\pi$
$577$	−11.6495	−	20.1776i	−0.484976	−	0.840004i	−0.999851	+	0.0172619i	$0.994505\pi$
$578$	−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	−0.937371	−	0.348332i	$-0.886748\pi$
$587$	−34.6834	+	12.6237i	−1.43154	+	0.521036i	−0.494165	+	0.869368i	$0.664526\pi$
$588$		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	−0.00686530	−	0.999976i	$-0.502185\pi$
$599$	23.9049	−	20.0586i	0.976727	−	0.819571i	0.983592	+	0.180405i	$0.0577409\pi$
$600$		0			0
$601$	−41.2874	+	15.0274i	−1.68415	+	0.612979i	−0.993869	−	0.110565i	$-0.964734\pi$
$601$	−41.2874	+	15.0274i	−1.68415	+	0.612979i	−0.690278	+	0.723544i	$0.742512\pi$
$602$	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	0.982849	+	0.184415i	$0.0590390\pi$
$607$	3.01430	+	17.0949i	0.122347	+	0.693862i	−0.860502	+	0.509447i	$0.829850\pi$
$608$	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	−0.853675	−	0.520807i	$-0.825631\pi$
$613$	0.599024	−	1.03754i	0.0241944	−	0.0419059i	0.877869	+	0.478901i	$0.158965\pi$
$614$	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	0.783439	−	0.621469i	$-0.213464\pi$
$617$	24.4449	+	8.89721i	0.984114	+	0.358188i	0.200676	+	0.979658i	$0.435686\pi$
$618$		0			0
$619$	1.67247	−	9.48503i	0.0672221	−	0.381235i	−0.932573	−	0.360982i	$-0.882442\pi$
$619$	1.67247	−	9.48503i	0.0672221	−	0.381235i	0.999795	−	0.0202534i	$-0.00644731\pi$
$620$	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	0.971876	−	0.235492i	$-0.0756702\pi$
$631$	7.08366	+	12.2693i	0.281996	+	0.488431i	−0.689880	+	0.723924i	$0.742337\pi$
$632$	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	0.104606	−	0.994514i	$-0.466642\pi$
$641$	20.8620	−	7.59316i	0.824001	−	0.299912i	0.719394	+	0.694602i	$0.244419\pi$
$642$		0			0
$643$	16.4981	−	13.8436i	0.650623	−	0.545938i	−0.256637	−	0.966508i	$-0.582614\pi$
$643$	16.4981	−	13.8436i	0.650623	−	0.545938i	0.907260	+	0.420570i	$0.138170\pi$
$644$	−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	−0.313714	−	0.949518i	$-0.601573\pi$
$653$	14.4866	−	12.1557i	0.566903	−	0.475688i	0.880617	+	0.473830i	$0.157129\pi$
$654$		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	0.643208	−	0.765692i	$-0.277603\pi$
$659$	0.0215882	+	0.0181147i	0.000840958	+	0.000705648i	−0.642367	+	0.766397i	$0.722048\pi$
$660$		0			0
$661$	−7.82141	−	44.3574i	−0.304218	−	1.72530i	−0.627164	−	0.778887i	$-0.715784\pi$
$661$	−7.82141	−	44.3574i	−0.304218	−	1.72530i	0.322946	−	0.946417i	$-0.395327\pi$
$662$	−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	0.934564	+	0.355795i	$0.115790\pi$
$673$	−1.69475	+	9.61142i	−0.0653279	+	0.370493i	−0.999892	+	0.0146980i	$0.995321\pi$
$674$	23.2607			0.895968
$675$		0			0
$676$	−28.9847			−1.11480
$677$	−7.09887	+	40.2597i	−0.272832	+	1.54731i	0.472934	+	0.881098i	$0.343195\pi$
$677$	−7.09887	+	40.2597i	−0.272832	+	1.54731i	−0.745766	+	0.666208i	$0.767916\pi$
$678$		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	0.0456696	+	0.998957i	$0.485458\pi$
$683$	−22.0126	+	38.1269i	−0.842287	+	1.45888i	−0.887957	+	0.459927i	$0.847875\pi$
$684$		0			0
$685$	−3.77322	−	6.53541i	−0.144167	−	0.249705i
$686$	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	0.900323	−	0.435223i	$-0.143331\pi$
$691$	16.5095	+	13.8531i	0.628051	+	0.526997i	−0.272272	+	0.962220i	$0.587775\pi$
$692$	−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	0.754528	−	0.656268i	$-0.227866\pi$
$709$	46.7137	−	17.0024i	1.75437	−	0.638539i	0.999843	+	0.0177295i	$0.00564379\pi$
$710$	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	0.808667	−	0.588267i	$-0.200190\pi$
$719$	−2.81873	−	4.88218i	−0.105121	−	0.182075i	−0.913788	+	0.406192i	$0.866856\pi$
$720$		0			0
$721$	−21.8330	+	37.8159i	−0.813104	+	1.40834i
$722$	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	0.384794	+	0.923002i	$0.374272\pi$
$727$	−7.88611	+	44.7243i	−0.292480	+	1.65873i	−0.677273	+	0.735731i	$0.736839\pi$
$728$	−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	0.746582	−	0.665294i	$-0.231694\pi$
$733$	24.1190	+	8.77858i	0.890854	+	0.324244i	0.144272	+	0.989538i	$0.453916\pi$
$734$	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	0.967792	−	0.251752i	$-0.0810066\pi$
$739$	7.22763	+	12.5186i	0.265873	+	0.460505i	−0.701919	+	0.712256i	$0.747673\pi$
$740$	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	−0.868978	−	0.494851i	$-0.835223\pi$
$743$	−6.04187	−	34.2651i	−0.221655	−	1.25707i	0.647323	−	0.762215i	$-0.275888\pi$
$744$		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	−0.353414	−	0.935467i	$-0.614979\pi$
$751$	13.8795	−	11.6463i	0.506471	−	0.424980i	0.859885	+	0.510487i	$0.170535\pi$
$752$	−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	−0.453438	−	0.891288i	$-0.649803\pi$
$761$	9.53298	−	7.99912i	0.345570	−	0.289968i	0.799008	+	0.601320i	$0.205358\pi$
$762$		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	−0.793436	−	0.608654i	$-0.791710\pi$
$769$	−7.09970	−	40.2644i	−0.256022	−	1.45197i	0.537414	−	0.843318i	$-0.319401\pi$
$770$	−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	−0.981919	−	0.189302i	$-0.939377\pi$
$773$	−18.2081	−	31.5374i	−0.654900	−	1.13432i	0.327019	−	0.945018i	$-0.393956\pi$
$774$		0			0
$775$	0.524012	−	0.907615i	0.0188231	−	0.0326025i
$776$	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	0.0159350	−	0.999873i	$-0.494928\pi$
$787$	−17.2407	−	6.27510i	−0.614564	−	0.223683i	−0.630499	+	0.776190i	$0.717150\pi$
$788$	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	0.972295	−	0.233756i	$-0.0751015\pi$
$797$	−0.601678	−	3.41228i	−0.0213125	−	0.120869i	−0.993608	+	0.112886i	$0.963990\pi$
$798$		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	−0.0788296	−	0.996888i	$-0.525118\pi$
$821$	−30.7809	−	25.8283i	−1.07426	−	0.901412i	−0.995432	+	0.0954758i	$0.969563\pi$
$822$		0			0
$823$	−8.32736	−	47.2268i	−0.290274	−	1.64622i	−0.685815	−	0.727776i	$-0.740554\pi$
$823$	−8.32736	−	47.2268i	−0.290274	−	1.64622i	0.395542	−	0.918448i	$-0.370557\pi$
$824$	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	0.819275	−	0.573401i	$-0.194376\pi$
$827$	−2.50024	−	4.33054i	−0.0869419	−	0.150588i	−0.906217	+	0.422813i	$0.861043\pi$
$828$		0			0
$829$	−14.8519	+	25.7242i	−0.515826	+	0.893438i	0.484005	+	0.875065i	$0.339182\pi$
$829$	−14.8519	+	25.7242i	−0.515826	+	0.893438i	−0.999831	+	0.0183722i	$0.994152\pi$
$830$	−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	−0.803216	−	0.595689i	$-0.796879\pi$
$839$	4.49827	−	25.5110i	0.155298	−	0.880737i	0.958513	−	0.285048i	$-0.0920096\pi$
$840$		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	0.574973	−	0.818172i	$-0.305012\pi$
$853$	−3.82383	−	3.20858i	−0.130926	−	0.109860i	−0.705899	+	0.708312i	$0.749457\pi$
$854$	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	−0.566748	−	0.823891i	$-0.691799\pi$
$857$	−13.7975	+	5.02189i	−0.471314	+	0.171544i	0.0954333	+	0.995436i	$0.469576\pi$
$858$		0			0
$859$	−13.3942	+	11.2390i	−0.457003	+	0.383471i	−0.842027	−	0.539435i	$-0.818638\pi$
$859$	−13.3942	+	11.2390i	−0.457003	+	0.383471i	0.385024	+	0.922907i	$0.374193\pi$
$860$	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	0.918340	+	0.395792i	$0.129530\pi$
$877$	5.64895	+	32.0368i	0.190751	+	1.08180i	−0.727589	+	0.686013i	$0.759359\pi$
$878$	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	−0.997325	−	0.0730926i	$-0.976713\pi$
$881$	−16.6800	−	28.8906i	−0.561963	−	0.973348i	0.435363	−	0.900255i	$-0.356620\pi$
$882$		0			0
$883$	27.4256	−	47.5025i	0.922944	−	1.59859i	0.128109	−	0.991760i	$-0.459109\pi$
$883$	27.4256	−	47.5025i	0.922944	−	1.59859i	0.794835	−	0.606826i	$-0.207557\pi$
$884$	−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	0.652003	−	0.758216i	$-0.273929\pi$
$887$	19.7784	+	7.19875i	0.664094	+	0.241710i	0.0120911	+	0.999927i	$0.496151\pi$
$888$		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	0.811689	−	0.584090i	$-0.198548\pi$
$907$	11.3666	+	9.53770i	0.377422	+	0.316694i	−0.434268	+	0.900784i	$0.642993\pi$
$908$	−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	−0.0457485	−	0.998953i	$-0.514567\pi$
$911$	16.9422	−	6.16646i	0.561321	−	0.204304i	0.607069	+	0.794649i	$0.292345\pi$
$912$		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	0.978540	−	0.206056i	$-0.0660630\pi$
$929$	28.8195	+	24.1824i	0.945536	+	0.793399i	−0.0330040	+	0.999455i	$0.510507\pi$
$930$		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	−0.897888	−	0.440224i	$-0.854899\pi$
$937$	−2.07229	+	3.58931i	−0.0676988	+	0.117258i	0.830189	+	0.557482i	$0.188232\pi$
$938$	−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	0.287381	−	0.957816i	$-0.407215\pi$
$941$	−3.31742	−	1.20744i	−0.108145	−	0.0393615i	−0.395526	+	0.918455i	$0.629438\pi$
$942$		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	−0.917809	−	0.397021i	$-0.870044\pi$
$947$	2.47537	−	14.0385i	0.0804387	−	0.456190i	0.998248	−	0.0591689i	$-0.0188450\pi$
$948$		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	−0.756204	−	0.654336i	$-0.772948\pi$
$953$	5.82130	−	10.0828i	0.188570	−	0.326613i	0.944774	+	0.327723i	$0.106281\pi$
$954$		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	−0.210222	−	0.977654i	$-0.567419\pi$
$967$	22.2675	−	18.6846i	0.716074	−	0.600857i	0.926296	+	0.376796i	$0.122974\pi$
$968$	−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	−0.714653	−	0.699480i	$-0.753415\pi$
$977$	−4.68536	+	3.93148i	−0.149898	+	0.125779i	0.564755	+	0.825259i	$0.308971\pi$
$978$		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	0.503318	−	0.864101i	$-0.332113\pi$
$983$	−8.15976	−	6.84685i	−0.260256	−	0.218381i	−0.763574	+	0.645721i	$0.776557\pi$
$984$		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	−0.991200	−	0.132371i	$-0.957741\pi$
$991$	−11.9928	+	20.7721i	−0.380964	+	0.659849i	0.610236	+	0.792219i	$0.291074\pi$
$992$	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	−0.970644	−	0.240520i	$-0.922682\pi$
$997$	0.749149	−	4.24864i	0.0237258	−	0.134556i	0.994370	+	0.105965i	$0.0337930\pi$
$998$	−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.649.2		12
3.2	odd	2		729.2.e.j.649.1		12
9.2	odd	6		729.2.e.s.163.2		12
9.4	even	3		729.2.e.k.406.2		12
9.5	odd	6		729.2.e.t.406.1		12
9.7	even	3		729.2.e.l.163.1		12
27.2	odd	18		729.2.c.d.487.5		12
27.4	even	9		729.2.e.k.325.2		12
27.5	odd	18		729.2.e.s.568.2		12
27.7	even	9		729.2.c.a.244.2		12
27.11	odd	18		729.2.a.b.1.2	✓	6
27.13	even	9	inner	729.2.e.u.82.2		12
27.14	odd	18		729.2.e.j.82.1		12
27.16	even	9		729.2.a.e.1.5	yes	6
27.20	odd	18		729.2.c.d.244.5		12
27.22	even	9		729.2.e.l.568.1		12
27.23	odd	18		729.2.e.t.325.1		12
27.25	even	9		729.2.c.a.487.2		12

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

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

L-functions

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