LMFDB - Embedded newform 729.2.e.m.325.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("729.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\Q(\zeta_{36})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{6} + 1 $ x^12 - x^6 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			325.1
Root			$0.342020 + 0.939693i$ of defining polynomial
Character	$\chi$	$=$	729.325
Dual form			729.2.e.m.406.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.984808 + 0.826352i) q^{2} +(-0.0603074 + 0.342020i) q^{4} +(0.419550 - 0.152704i) q^{5} +(-0.613341 - 3.47843i) q^{7} +(-1.50881 - 2.61334i) q^{8} +O(q^{10})$	\(q+(-0.984808 + 0.826352i) q^{2} +(-0.0603074 + 0.342020i) q^{4} +(0.419550 - 0.152704i) q^{5} +(-0.613341 - 3.47843i) q^{7} +(-1.50881 - 2.61334i) q^{8} +(-0.286989 + 0.497079i) q^{10} +(-2.61240 - 0.950837i) q^{11} +(2.52094 + 2.11532i) q^{13} +(3.47843 + 2.91875i) q^{14} +(2.99273 + 1.08926i) q^{16} +(-3.51968 + 6.09627i) q^{17} +(2.59240 + 4.49016i) q^{19} +(0.0269258 + 0.152704i) q^{20} +(3.35844 - 1.22237i) q^{22} +(-1.26363 + 7.16637i) q^{23} +(-3.67752 + 3.08580i) q^{25} -4.23065 q^{26} +1.22668 q^{28} +(-2.77244 + 2.32635i) q^{29} +(-0.336152 + 1.90641i) q^{31} +(1.82391 - 0.663848i) q^{32} +(-1.57145 - 8.91215i) q^{34} +(-0.788496 - 1.36571i) q^{35} +(1.61334 - 2.79439i) q^{37} +(-6.26347 - 2.27972i) q^{38} +(-1.03209 - 0.866025i) q^{40} +(3.72362 + 3.12449i) q^{41} +(5.41147 + 1.96962i) q^{43} +(0.482753 - 0.836152i) q^{44} +(-4.67752 - 8.10170i) q^{46} +(-0.524005 - 2.97178i) q^{47} +(-5.14543 + 1.87278i) q^{49} +(1.07169 - 6.07785i) q^{50} +(-0.875515 + 0.734644i) q^{52} -8.77141 q^{53} -1.24123 q^{55} +(-8.16490 + 6.85117i) q^{56} +(0.807934 - 4.58202i) q^{58} +(2.78504 - 1.01367i) q^{59} +(1.36959 + 7.76730i) q^{61} +(-1.24432 - 2.15523i) q^{62} +(-4.43242 + 7.67717i) q^{64} +(1.38068 + 0.502526i) q^{65} +(-7.23055 - 6.06715i) q^{67} +(-1.87278 - 1.57145i) q^{68} +(1.90508 + 0.693392i) q^{70} +(2.65366 - 4.59627i) q^{71} +(0.777189 + 1.34613i) q^{73} +(0.720317 + 4.08512i) q^{74} +(-1.69207 + 0.615862i) q^{76} +(-1.70513 + 9.67024i) q^{77} +(-9.11721 + 7.65025i) q^{79} +1.42193 q^{80} -6.24897 q^{82} +(12.4538 - 10.4500i) q^{83} +(-0.545759 + 3.09516i) q^{85} +(-6.95686 + 2.53209i) q^{86} +(1.45677 + 8.26173i) q^{88} +(9.21291 + 15.9572i) q^{89} +(5.81180 - 10.0663i) q^{91} +(-2.37484 - 0.864370i) q^{92} +(2.97178 + 2.49362i) q^{94} +(1.77330 + 1.48798i) q^{95} +(-9.50387 - 3.45913i) q^{97} +(3.51968 - 6.09627i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{4} + 6 q^{7}+O(q^{10}) $ 12 * q - 12 * q^4 + 6 * q^7	$ 12 q - 12 q^{4} + 6 q^{7} + 12 q^{10} + 24 q^{13} + 24 q^{19} + 24 q^{22} + 6 q^{25} - 12 q^{28} - 12 q^{31} - 18 q^{34} + 6 q^{37} + 6 q^{40} + 24 q^{43} - 6 q^{46} - 30 q^{49} - 36 q^{52} - 60 q^{55} - 12 q^{58} - 12 q^{61} - 6 q^{64} - 12 q^{67} + 60 q^{70} - 12 q^{73} - 42 q^{76} - 48 q^{79} - 24 q^{82} + 54 q^{85} + 48 q^{88} + 6 q^{94} - 66 q^{97}+O(q^{100}) $ 12 * q - 12 * q^4 + 6 * q^7 + 12 * q^10 + 24 * q^13 + 24 * q^19 + 24 * q^22 + 6 * q^25 - 12 * q^28 - 12 * q^31 - 18 * q^34 + 6 * q^37 + 6 * q^40 + 24 * q^43 - 6 * q^46 - 30 * q^49 - 36 * q^52 - 60 * q^55 - 12 * q^58 - 12 * q^61 - 6 * q^64 - 12 * q^67 + 60 * q^70 - 12 * q^73 - 42 * q^76 - 48 * q^79 - 24 * q^82 + 54 * q^85 + 48 * q^88 + 6 * q^94 - 66 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.984808	+	0.826352i	−0.696364	+	0.584319i	−0.920737	−	0.390184i	$-0.872411\pi$
$2$	−0.984808	+	0.826352i	−0.696364	+	0.584319i	0.224372	+	0.974503i	$0.427967\pi$
$3$		0			0
$3$		0			0
$4$	−0.0603074	+	0.342020i	−0.0301537	+	0.171010i
$5$	0.419550	−	0.152704i	0.187628	−	0.0682911i	−0.246497	−	0.969143i	$-0.579280\pi$
$5$	0.419550	−	0.152704i	0.187628	−	0.0682911i	0.434126	+	0.900852i	$0.357057\pi$
$6$		0			0
$7$	−0.613341	−	3.47843i	−0.231821	−	1.31472i	−0.849206	−	0.528061i	$-0.822919\pi$
$7$	−0.613341	−	3.47843i	−0.231821	−	1.31472i	0.617385	−	0.786661i	$-0.288192\pi$
$8$	−1.50881	−	2.61334i	−0.533446	−	0.923956i
$9$		0			0
$10$	−0.286989	+	0.497079i	−0.0907539	+	0.157190i
$11$	−2.61240	−	0.950837i	−0.787669	−	0.286688i	−0.0833024	−	0.996524i	$-0.526547\pi$
$11$	−2.61240	−	0.950837i	−0.787669	−	0.286688i	−0.704367	+	0.709836i	$0.748769\pi$
$12$		0			0
$13$	2.52094	+	2.11532i	0.699184	+	0.586685i	0.921541	−	0.388280i	$-0.126931\pi$
$13$	2.52094	+	2.11532i	0.699184	+	0.586685i	−0.222357	+	0.974965i	$0.571375\pi$
$14$	3.47843	+	2.91875i	0.929649	+	0.780068i
$15$		0			0
$16$	2.99273	+	1.08926i	0.748182	+	0.272316i
$17$	−3.51968	+	6.09627i	−0.853648	+	1.47856i	0.0242455	+	0.999706i	$0.492282\pi$
$17$	−3.51968	+	6.09627i	−0.853648	+	1.47856i	−0.877894	+	0.478856i	$0.841052\pi$
$18$		0			0
$19$	2.59240	+	4.49016i	0.594736	+	1.03011i	0.993584	+	0.113097i	$0.0360769\pi$
$19$	2.59240	+	4.49016i	0.594736	+	1.03011i	−0.398848	+	0.917017i	$0.630590\pi$
$20$	0.0269258	+	0.152704i	0.00602079	+	0.0341456i
$21$		0			0
$22$	3.35844	−	1.22237i	0.716022	−	0.260611i
$23$	−1.26363	+	7.16637i	−0.263484	+	1.49429i	0.509833	+	0.860273i	$0.329707\pi$
$23$	−1.26363	+	7.16637i	−0.263484	+	1.49429i	−0.773317	+	0.634019i	$0.781404\pi$
$24$		0			0
$25$	−3.67752	+	3.08580i	−0.735504	+	0.617161i
$26$	−4.23065			−0.829698
$27$		0			0
$28$	1.22668			0.231821
$29$	−2.77244	+	2.32635i	−0.514829	+	0.431993i	−0.862825	−	0.505503i	$-0.831307\pi$
$29$	−2.77244	+	2.32635i	−0.514829	+	0.431993i	0.347996	+	0.937496i	$0.386862\pi$
$30$		0			0
$31$	−0.336152	+	1.90641i	−0.0603747	+	0.342402i	0.939625	+	0.342205i	$0.111174\pi$
$31$	−0.336152	+	1.90641i	−0.0603747	+	0.342402i	−1.00000		0.000196783i	$0.999937\pi$
$32$	1.82391	−	0.663848i	0.322424	−	0.117353i
$33$		0			0
$34$	−1.57145	−	8.91215i	−0.269502	−	1.52842i
$35$	−0.788496	−	1.36571i	−0.133280	−	0.230848i
$36$		0			0
$37$	1.61334	−	2.79439i	0.265232	−	0.459395i	−0.702393	−	0.711790i	$-0.747885\pi$
$37$	1.61334	−	2.79439i	0.265232	−	0.459395i	0.967624	+	0.252395i	$0.0812183\pi$
$38$	−6.26347	−	2.27972i	−1.01607	−	0.369819i
$39$		0			0
$40$	−1.03209	−	0.866025i	−0.163188	−	0.136931i
$41$	3.72362	+	3.12449i	0.581531	+	0.487963i	0.885450	−	0.464735i	$-0.153851\pi$
$41$	3.72362	+	3.12449i	0.581531	+	0.487963i	−0.303918	+	0.952698i	$0.598295\pi$
$42$		0			0
$43$	5.41147	+	1.96962i	0.825242	+	0.300364i	0.719905	−	0.694073i	$-0.244186\pi$
$43$	5.41147	+	1.96962i	0.825242	+	0.300364i	0.105337	+	0.994437i	$0.466408\pi$
$44$	0.482753	−	0.836152i	0.0727777	−	0.126055i
$45$		0			0
$46$	−4.67752	−	8.10170i	−0.689662	−	1.19453i
$47$	−0.524005	−	2.97178i	−0.0764340	−	0.433479i	−0.998878	−	0.0473489i	$-0.984923\pi$
$47$	−0.524005	−	2.97178i	−0.0764340	−	0.433479i	0.922444	−	0.386130i	$-0.126188\pi$
$48$		0			0
$49$	−5.14543	+	1.87278i	−0.735061	+	0.267540i
$50$	1.07169	−	6.07785i	0.151560	−	0.859538i
$51$		0			0
$52$	−0.875515	+	0.734644i	−0.121412	+	0.101877i
$53$	−8.77141			−1.20485			−0.602423	−	0.798177i	$-0.705798\pi$
$53$	−8.77141			−1.20485			−0.602423	+	0.798177i	$0.705798\pi$
$54$		0			0
$55$	−1.24123			−0.167367
$56$	−8.16490	+	6.85117i	−1.09108	+	0.915526i
$57$		0			0
$58$	0.807934	−	4.58202i	0.106087	−	0.601649i
$59$	2.78504	−	1.01367i	0.362581	−	0.131969i	−0.154304	−	0.988023i	$-0.549314\pi$
$59$	2.78504	−	1.01367i	0.362581	−	0.131969i	0.516885	+	0.856055i	$0.327091\pi$
$60$		0			0
$61$	1.36959	+	7.76730i	0.175357	+	0.994501i	0.937731	+	0.347364i	$0.112923\pi$
$61$	1.36959	+	7.76730i	0.175357	+	0.994501i	−0.762373	+	0.647138i	$0.775966\pi$
$62$	−1.24432	−	2.15523i	−0.158029	−	0.273714i
$63$		0			0
$64$	−4.43242	+	7.67717i	−0.554052	+	0.959647i
$65$	1.38068	+	0.502526i	0.171252	+	0.0623307i
$66$		0			0
$67$	−7.23055	−	6.06715i	−0.883353	−	0.741221i	0.0835131	−	0.996507i	$-0.473386\pi$
$67$	−7.23055	−	6.06715i	−0.883353	−	0.741221i	−0.966866	+	0.255286i	$0.917830\pi$
$68$	−1.87278	−	1.57145i	−0.227108	−	0.190567i
$69$		0			0
$70$	1.90508	+	0.693392i	0.227700	+	0.0828761i
$71$	2.65366	−	4.59627i	0.314931	−	0.545476i	−0.664492	−	0.747296i	$-0.731352\pi$
$71$	2.65366	−	4.59627i	0.314931	−	0.545476i	0.979423	+	0.201819i	$0.0646853\pi$
$72$		0			0
$73$	0.777189	+	1.34613i	0.0909631	+	0.157553i	0.907917	−	0.419151i	$-0.137672\pi$
$73$	0.777189	+	1.34613i	0.0909631	+	0.157553i	−0.816954	+	0.576703i	$0.804339\pi$
$74$	0.720317	+	4.08512i	0.0837352	+	0.474886i
$75$		0			0
$76$	−1.69207	+	0.615862i	−0.194093	+	0.0706442i
$77$	−1.70513	+	9.67024i	−0.194317	+	1.10203i
$78$		0			0
$79$	−9.11721	+	7.65025i	−1.02577	+	0.860720i	−0.990341	−	0.138652i	$-0.955723\pi$
$79$	−9.11721	+	7.65025i	−1.02577	+	0.860720i	−0.0354253	+	0.999372i	$0.511279\pi$
$80$	1.42193			0.158977
$81$		0			0
$82$	−6.24897			−0.690083
$83$	12.4538	−	10.4500i	1.36698	−	1.14703i	0.393222	−	0.919443i	$-0.371360\pi$
$83$	12.4538	−	10.4500i	1.36698	−	1.14703i	0.973757	−	0.227589i	$-0.0730841\pi$
$84$		0			0
$85$	−0.545759	+	3.09516i	−0.0591959	+	0.335717i
$86$	−6.95686	+	2.53209i	−0.750177	+	0.273042i
$87$		0			0
$88$	1.45677	+	8.26173i	0.155292	+	0.880704i
$89$	9.21291	+	15.9572i	0.976567	+	1.69146i	0.674665	+	0.738125i	$0.264288\pi$
$89$	9.21291	+	15.9572i	0.976567	+	1.69146i	0.301902	+	0.953339i	$0.402378\pi$
$90$		0			0
$91$	5.81180	−	10.0663i	0.609243	−	1.05524i
$92$	−2.37484	−	0.864370i	−0.247594	−	0.0901169i
$93$		0			0
$94$	2.97178	+	2.49362i	0.306516	+	0.257197i
$95$	1.77330	+	1.48798i	0.181937	+	0.152663i
$96$		0			0
$97$	−9.50387	−	3.45913i	−0.964972	−	0.351221i	−0.188992	−	0.981979i	$-0.560522\pi$
$97$	−9.50387	−	3.45913i	−0.964972	−	0.351221i	−0.775980	+	0.630758i	$0.782744\pi$
$98$	3.51968	−	6.09627i	0.355541	−	0.615816i
$99$		0			0
$100$	−0.833626	−	1.44388i	−0.0833626	−	0.144388i
$101$	0.361323	+	2.04916i	0.0359530	+	0.203899i	0.997493	−	0.0707655i	$-0.0225442\pi$
$101$	0.361323	+	2.04916i	0.0359530	+	0.203899i	−0.961540	+	0.274665i	$0.911433\pi$
$102$		0			0
$103$	1.36097	−	0.495351i	0.134100	−	0.0488084i	−0.274098	−	0.961702i	$-0.588379\pi$
$103$	1.36097	−	0.495351i	0.134100	−	0.0488084i	0.408198	+	0.912893i	$0.366157\pi$
$104$	1.72443	−	9.77972i	0.169094	−	0.958980i
$105$		0			0
$106$	8.63816	−	7.24827i	0.839012	−	0.704015i
$107$	2.23583			0.216146			0.108073	−	0.994143i	$-0.465532\pi$
$107$	2.23583			0.216146			0.108073	+	0.994143i	$0.465532\pi$
$108$		0			0
$109$	−11.5030			−1.10179			−0.550893	−	0.834576i	$-0.685713\pi$
$109$	−11.5030			−1.10179			−0.550893	+	0.834576i	$0.685713\pi$
$110$	1.22237	−	1.02569i	0.116549	−	0.0977959i
$111$		0			0
$112$	1.95336	−	11.0781i	0.184575	−	1.04678i
$113$	1.58634	−	0.577382i	0.149231	−	0.0543155i	−0.266325	−	0.963883i	$-0.585809\pi$
$113$	1.58634	−	0.577382i	0.149231	−	0.0543155i	0.415556	+	0.909568i	$0.363587\pi$
$114$		0			0
$115$	0.564178	+	3.19961i	0.0526098	+	0.298365i
$116$	−0.628461	−	1.08853i	−0.0583511	−	0.101067i
$117$		0			0
$118$	−1.90508	+	3.29969i	−0.175377	+	0.303761i
$119$	23.3642	+	8.50387i	2.14179	+	0.779549i
$120$		0			0
$121$	−2.50593	−	2.10272i	−0.227812	−	0.191157i
$122$	−7.76730	−	6.51754i	−0.703219	−	0.590070i
$123$		0			0
$124$	−0.631759	−	0.229942i	−0.0567336	−	0.0206494i
$125$	−2.18788	+	3.78952i	−0.195690	+	0.338945i
$126$		0			0
$127$	1.33615	+	2.31428i	0.118564	+	0.205359i	0.919199	−	0.393793i	$-0.128837\pi$
$127$	1.33615	+	2.31428i	0.118564	+	0.205359i	−0.800635	+	0.599153i	$0.795504\pi$
$128$	−1.30488	−	7.40033i	−0.115336	−	0.654103i
$129$		0			0
$130$	−1.77497	+	0.646035i	−0.155675	+	0.0566610i
$131$	0.507031	−	2.87551i	0.0442995	−	0.251235i	−0.954614	−	0.297847i	$-0.903731\pi$
$131$	0.507031	−	2.87551i	0.0442995	−	0.251235i	0.998913	+	0.0466123i	$0.0148425\pi$
$132$		0			0
$133$	14.0287	−	11.7715i	1.21644	−	1.02072i
$134$	12.1343			1.04824
$135$		0			0
$136$	21.2422			1.82150
$137$	3.56764	−	2.99360i	0.304804	−	0.255761i	−0.477537	−	0.878612i	$-0.658470\pi$
$137$	3.56764	−	2.99360i	0.304804	−	0.255761i	0.782340	+	0.622851i	$0.214026\pi$
$138$		0			0
$139$	−1.38965	+	7.88111i	−0.117869	+	0.668467i	0.867421	+	0.497575i	$0.165776\pi$
$139$	−1.38965	+	7.88111i	−0.117869	+	0.668467i	−0.985290	+	0.170892i	$0.945335\pi$
$140$	0.514654	−	0.187319i	0.0434962	−	0.0158313i
$141$		0			0
$142$	1.18479	+	6.71929i	0.0994256	+	0.563870i
$143$	−4.57440	−	7.92309i	−0.382530	−	0.662562i
$144$		0			0
$145$	−0.807934	+	1.39938i	−0.0670952	+	0.116212i
$146$	−1.87776	−	0.683448i	−0.155404	−	0.0565626i
$147$		0			0
$148$	0.858441	+	0.720317i	0.0705634	+	0.0592097i
$149$	−15.4831	−	12.9918i	−1.26842	−	1.06433i	−0.994731	−	0.102516i	$-0.967311\pi$
$149$	−15.4831	−	12.9918i	−1.26842	−	1.06433i	−0.273692	−	0.961817i	$-0.588245\pi$
$150$		0			0
$151$	−6.29813	−	2.29233i	−0.512535	−	0.186547i	0.0727885	−	0.997347i	$-0.476810\pi$
$151$	−6.29813	−	2.29233i	−0.512535	−	0.186547i	−0.585323	+	0.810800i	$0.699032\pi$
$152$	7.82288	−	13.5496i	0.634520	−	1.09902i
$153$		0			0
$154$	−6.31180	−	10.9324i	−0.508620	−	0.880955i
$155$	0.150084	+	0.851167i	0.0120550	+	0.0683674i
$156$		0			0
$157$	−5.00387	+	1.82126i	−0.399352	+	0.145352i	−0.533886	−	0.845557i	$-0.679269\pi$
$157$	−5.00387	+	1.82126i	−0.399352	+	0.145352i	0.134533	+	0.990909i	$0.457046\pi$
$158$	2.65690	−	15.0680i	0.211372	−	1.19875i
$159$		0			0
$160$	0.663848	−	0.557035i	0.0524818	−	0.0440375i
$161$	25.7028			2.02566
$162$		0			0
$163$	3.81521			0.298830			0.149415	−	0.988775i	$-0.452261\pi$
$163$	3.81521			0.298830			0.149415	+	0.988775i	$0.452261\pi$
$164$	−1.29320	+	1.08512i	−0.100982	+	0.0847338i
$165$		0			0
$166$	−3.62923	+	20.5824i	−0.281683	+	1.59750i
$167$	−8.58445	+	3.12449i	−0.664285	+	0.241780i	−0.652085	−	0.758146i	$-0.726106\pi$
$167$	−8.58445	+	3.12449i	−0.664285	+	0.241780i	−0.0121996	+	0.999926i	$0.503883\pi$
$168$		0			0
$169$	−0.376859	−	2.13727i	−0.0289892	−	0.164406i
$170$	−2.02022	−	3.49912i	−0.154944	−	0.268370i
$171$		0			0
$172$	−1.00000	+	1.73205i	−0.0762493	+	0.132068i
$173$	−5.70756	−	2.07738i	−0.433938	−	0.157940i	0.115810	−	0.993271i	$-0.463054\pi$
$173$	−5.70756	−	2.07738i	−0.433938	−	0.157940i	−0.549747	+	0.835331i	$0.685276\pi$
$174$		0			0
$175$	12.9893	+	10.8993i	0.981900	+	0.823912i
$176$	−6.78250	−	5.69119i	−0.511250	−	0.428990i
$177$		0			0
$178$	−22.2592	−	8.10170i	−1.66840	−	0.607248i
$179$	−5.14057	+	8.90373i	−0.384224	+	0.665496i	−0.991661	−	0.128872i	$-0.958864\pi$
$179$	−5.14057	+	8.90373i	−0.384224	+	0.665496i	0.607437	+	0.794368i	$0.292198\pi$
$180$		0			0
$181$	11.5706	+	20.0408i	0.860034	+	1.48962i	0.871895	+	0.489693i	$0.162891\pi$
$181$	11.5706	+	20.0408i	0.860034	+	1.48962i	−0.0118609	+	0.999930i	$0.503776\pi$
$182$	2.59483	+	14.7160i	0.192341	+	1.09082i
$183$		0			0
$184$	20.6348	−	7.51044i	1.52121	−	0.553677i
$185$	0.250164	−	1.41875i	0.0183924	−	0.104308i
$186$		0			0
$187$	14.9914	−	12.5793i	1.09628	−	0.919887i
$188$	1.04801			0.0764340
$189$		0			0
$190$	−2.97596			−0.215899
$191$	11.2381	−	9.42989i	0.813161	−	0.682323i	−0.138199	−	0.990404i	$-0.544131\pi$
$191$	11.2381	−	9.42989i	0.813161	−	0.682323i	0.951360	+	0.308081i	$0.0996869\pi$
$192$		0			0
$193$	4.07057	−	23.0854i	0.293006	−	1.66172i	−0.382190	−	0.924084i	$-0.624830\pi$
$193$	4.07057	−	23.0854i	0.293006	−	1.66172i	0.675196	−	0.737638i	$-0.264059\pi$
$194$	12.2179	−	4.44697i	0.877197	−	0.319274i
$195$		0			0
$196$	−0.330222	−	1.87278i	−0.0235873	−	0.133770i
$197$	4.51384	+	7.81820i	0.321598	+	0.557024i	0.980818	−	0.194926i	$-0.0624468\pi$
$197$	4.51384	+	7.81820i	0.321598	+	0.557024i	−0.659220	+	0.751950i	$0.729113\pi$
$198$		0			0
$199$	−1.30200	+	2.25514i	−0.0922966	+	0.159862i	−0.908477	−	0.417935i	$-0.862754\pi$
$199$	−1.30200	+	2.25514i	−0.0922966	+	0.159862i	0.816181	+	0.577797i	$0.196087\pi$
$200$	13.6129	+	4.95471i	0.962581	+	0.350351i
$201$		0			0
$202$	−2.04916	−	1.71945i	−0.144179	−	0.120980i
$203$	9.79250	+	8.21688i	0.687299	+	0.576712i
$204$		0			0
$205$	2.03936	+	0.742267i	0.142435	+	0.0518422i
$206$	−0.930956	+	1.61246i	−0.0648628	+	0.112346i
$207$		0			0
$208$	5.24035	+	9.07656i	0.363353	+	0.629346i
$209$	−2.50297	−	14.1951i	−0.173134	−	0.981893i
$210$		0			0
$211$	15.3687	−	5.59375i	1.05803	−	0.385090i	0.246339	−	0.969184i	$-0.420772\pi$
$211$	15.3687	−	5.59375i	1.05803	−	0.385090i	0.811686	+	0.584094i	$0.198550\pi$
$212$	0.528981	−	3.00000i	0.0363306	−	0.206041i
$213$		0			0
$214$	−2.20187	+	1.84759i	−0.150517	+	0.126298i
$215$	2.57115			0.175351
$216$		0			0
$217$	6.83750			0.464159
$218$	11.3282	−	9.50552i	0.767245	−	0.643795i
$219$		0			0
$220$	0.0748553	−	0.424525i	0.00504674	−	0.0286215i
$221$	−21.7685	+	7.92309i	−1.46431	+	0.532964i
$222$		0			0
$223$	0.642903	+	3.64609i	0.0430520	+	0.244160i	0.998738	−	0.0502288i	$-0.0159950\pi$
$223$	0.642903	+	3.64609i	0.0430520	+	0.244160i	−0.955686	+	0.294389i	$0.904884\pi$
$224$	−3.42782	−	5.93717i	−0.229031	−	0.396694i
$225$		0			0
$226$	−1.08512	+	1.87949i	−0.0721813	+	0.125022i
$227$	9.92388	+	3.61200i	0.658671	+	0.239737i	0.649662	−	0.760223i	$-0.274910\pi$
$227$	9.92388	+	3.61200i	0.658671	+	0.239737i	0.00900853	+	0.999959i	$0.497132\pi$
$228$		0			0
$229$	10.3610	+	8.69388i	0.684672	+	0.574508i	0.917367	−	0.398042i	$-0.130310\pi$
$229$	10.3610	+	8.69388i	0.684672	+	0.574508i	−0.232695	+	0.972550i	$0.574755\pi$
$230$	−3.19961	−	2.68479i	−0.210976	−	0.177030i
$231$		0			0
$232$	10.2626	+	3.73530i	0.673775	+	0.245234i
$233$	−6.35035	+	10.9991i	−0.416025	+	0.720576i	−0.995535	−	0.0943883i	$-0.969910\pi$
$233$	−6.35035	+	10.9991i	−0.416025	+	0.720576i	0.579510	+	0.814965i	$0.303244\pi$
$234$		0			0
$235$	−0.673648	−	1.16679i	−0.0439440	−	0.0761132i
$236$	0.178737	+	1.01367i	0.0116348	+	0.0659843i
$237$		0			0
$238$	−30.0364	+	10.9324i	−1.94697	+	0.708640i
$239$	−1.01611	+	5.76264i	−0.0657266	+	0.372754i	0.934147	+	0.356887i	$0.116162\pi$
$239$	−1.01611	+	5.76264i	−0.0657266	+	0.372754i	−0.999874	+	0.0158670i	$0.994949\pi$
$240$		0			0
$241$	−6.54189	+	5.48930i	−0.421400	+	0.353597i	−0.828695	−	0.559700i	$-0.810916\pi$
$241$	−6.54189	+	5.48930i	−0.421400	+	0.353597i	0.407295	+	0.913297i	$0.366472\pi$
$242$	4.20545			0.270337
$243$		0			0
$244$	−2.73917			−0.175357
$245$	−1.87278	+	1.57145i	−0.119648	+	0.100396i
$246$		0			0
$247$	−2.96286	+	16.8032i	−0.188522	+	1.06916i
$248$	5.48930	−	1.99794i	0.348571	−	0.126869i
$249$		0			0
$250$	−0.976834	−	5.53990i	−0.0617804	−	0.350374i
$251$	3.37895	+	5.85251i	0.213277	+	0.369407i	0.952738	−	0.303792i	$-0.0982529\pi$
$251$	3.37895	+	5.85251i	0.213277	+	0.369407i	−0.739461	+	0.673199i	$0.764920\pi$
$252$		0			0
$253$	10.1152	−	17.5200i	0.635934	−	1.10147i
$254$	−3.22826	−	1.17499i	−0.202559	−	0.0737256i
$255$		0			0
$256$	−6.18139	−	5.18680i	−0.386337	−	0.324175i
$257$	2.82131	+	2.36736i	0.175989	+	0.147672i	0.726527	−	0.687138i	$-0.241133\pi$
$257$	2.82131	+	2.36736i	0.175989	+	0.147672i	−0.550538	+	0.834810i	$0.685578\pi$
$258$		0			0
$259$	−10.7096	−	3.89798i	−0.665463	−	0.242209i
$260$	−0.255139	+	0.441914i	−0.0158231	+	0.0274064i
$261$		0			0
$262$	1.87686	+	3.25082i	0.115953	+	0.200836i
$263$	0.631708	+	3.58260i	0.0389528	+	0.220912i	0.998070	−	0.0620963i	$-0.0197786\pi$
$263$	0.631708	+	3.58260i	0.0389528	+	0.220912i	−0.959117	+	0.283009i	$0.908667\pi$
$264$		0			0
$265$	−3.68004	+	1.33943i	−0.226063	+	0.0822803i
$266$	−4.08819	+	23.1853i	−0.250663	+	1.42158i
$267$		0			0
$268$	2.51114	−	2.10710i	0.153393	−	0.128712i
$269$	−7.08672			−0.432085			−0.216042	−	0.976384i	$-0.569315\pi$
$269$	−7.08672			−0.432085			−0.216042	+	0.976384i	$0.569315\pi$
$270$		0			0
$271$	−19.0000			−1.15417			−0.577084	−	0.816685i	$-0.695809\pi$
$271$	−19.0000			−1.15417			−0.577084	+	0.816685i	$0.695809\pi$
$272$	−17.1739	+	14.4106i	−1.04132	+	0.873771i
$273$		0			0
$274$	−1.03967	+	5.89625i	−0.0628086	+	0.356205i
$275$	12.5413	−	4.56464i	0.756266	−	0.275258i
$276$		0			0
$277$	−2.41235	−	13.6811i	−0.144944	−	0.822019i	−0.967412	−	0.253208i	$-0.918514\pi$
$277$	−2.41235	−	13.6811i	−0.144944	−	0.822019i	0.822468	−	0.568812i	$-0.192597\pi$
$278$	−5.14403	−	8.90972i	−0.308518	−	0.534369i
$279$		0			0
$280$	−2.37939	+	4.12122i	−0.142195	+	0.246290i
$281$	−20.7930	−	7.56805i	−1.24041	−	0.451472i	−0.363259	−	0.931688i	$-0.618336\pi$
$281$	−20.7930	−	7.56805i	−1.24041	−	0.451472i	−0.877150	+	0.480216i	$0.840558\pi$
$282$		0			0
$283$	−18.1800	−	15.2549i	−1.08069	−	0.906808i	−0.0847134	−	0.996405i	$-0.526997\pi$
$283$	−18.1800	−	15.2549i	−1.08069	−	0.906808i	−0.995978	+	0.0895975i	$0.971442\pi$
$284$	1.41198	+	1.18479i	0.0837856	+	0.0703045i
$285$		0			0
$286$	11.0522	+	4.02266i	0.653528	+	0.237865i
$287$	8.58445	−	14.8687i	0.506724	−	0.877672i
$288$		0			0
$289$	−16.2763	−	28.1914i	−0.957430	−	1.65832i
$290$	−0.360723	−	2.04576i	−0.0211824	−	0.120131i
$291$		0			0
$292$	−0.507274	+	0.184633i	−0.0296860	+	0.0108048i
$293$	3.23091	−	18.3234i	0.188752	−	1.07047i	−0.732287	−	0.680996i	$-0.761547\pi$
$293$	3.23091	−	18.3234i	0.188752	−	1.07047i	0.921039	−	0.389470i	$-0.127342\pi$
$294$		0			0
$295$	1.01367	−	0.850571i	0.0590182	−	0.0495221i
$296$	−9.73692			−0.565947
$297$		0			0
$298$	25.9837			1.50520
$299$	−18.3447	+	15.3931i	−1.06090	+	0.890203i
$300$		0			0
$301$	3.53209	−	20.0315i	0.203586	−	1.15459i
$302$	8.09672	−	2.94697i	0.465914	−	0.169579i
$303$		0			0
$304$	2.86736	+	16.2616i	0.164455	+	0.932668i
$305$	1.76070	+	3.04963i	0.100818	+	0.174621i
$306$		0			0
$307$	−10.3735	+	17.9674i	−0.592044	+	1.02545i	0.401912	+	0.915678i	$0.368346\pi$
$307$	−10.3735	+	17.9674i	−0.592044	+	1.02545i	−0.993957	+	0.109773i	$0.964988\pi$
$308$	−3.20459	−	1.16637i	−0.182598	−	0.0664603i
$309$		0			0
$310$	−0.851167	−	0.714214i	−0.0483430	−	0.0405646i
$311$	15.6162	+	13.1035i	0.885513	+	0.743034i	0.967305	−	0.253616i	$-0.0816199\pi$
$311$	15.6162	+	13.1035i	0.885513	+	0.743034i	−0.0817920	+	0.996649i	$0.526064\pi$
$312$		0			0
$313$	28.0412	+	10.2062i	1.58498	+	0.576886i	0.976280	−	0.216514i	$-0.0694686\pi$
$313$	28.0412	+	10.2062i	1.58498	+	0.576886i	0.608701	+	0.793400i	$0.291691\pi$
$314$	3.42285	−	5.92855i	0.193163	−	0.334567i
$315$		0			0
$316$	−2.06670	−	3.57964i	−0.116261	−	0.201370i
$317$	0.749571	+	4.25103i	0.0421001	+	0.238762i	0.998595	−	0.0529868i	$-0.0168741\pi$
$317$	0.749571	+	4.25103i	0.0421001	+	0.238762i	−0.956495	+	0.291748i	$0.905763\pi$
$318$		0			0
$319$	9.45471	−	3.44123i	0.529362	−	0.192672i
$320$	−0.687288	+	3.89780i	−0.0384206	+	0.217894i
$321$		0			0
$322$	−25.3123	+	21.2395i	−1.41060	+	1.18363i
$323$	−36.4976			−2.03078
$324$		0			0
$325$	−15.7983			−0.876332
$326$	−3.75725	+	3.15270i	−0.208095	+	0.174612i
$327$		0			0
$328$	2.54710	−	14.4453i	0.140640	−	0.797611i
$329$	−10.0157	+	3.64543i	−0.552185	+	0.200979i
$330$		0			0
$331$	−0.506863	−	2.87457i	−0.0278597	−	0.158000i	0.967704	−	0.252089i	$-0.0811175\pi$
$331$	−0.506863	−	2.87457i	−0.0278597	−	0.158000i	−0.995564	+	0.0940884i	$0.970006\pi$
$332$	2.82304	+	4.88965i	0.154935	+	0.268355i
$333$		0			0
$334$	5.87211	−	10.1708i	0.321308	−	0.556521i
$335$	−3.96005	−	1.44134i	−0.216361	−	0.0787489i
$336$		0			0
$337$	11.0628	+	9.28282i	0.602631	+	0.505667i	0.892290	−	0.451462i	$-0.149098\pi$
$337$	11.0628	+	9.28282i	0.602631	+	0.505667i	−0.289659	+	0.957130i	$0.593542\pi$
$338$	2.13727	+	1.79339i	0.116252	+	0.0975473i
$339$		0			0
$340$	−1.02569	−	0.373321i	−0.0556260	−	0.0202462i
$341$	2.69085	−	4.66069i	0.145718	−	0.252391i
$342$		0			0
$343$	−2.69207	−	4.66280i	−0.145358	−	0.251767i
$344$	−3.01763	−	17.1138i	−0.162699	−	0.922715i
$345$		0			0
$346$	7.33750	−	2.67063i	0.394466	−	0.143574i
$347$	−0.252492	+	1.43195i	−0.0135545	+	0.0768712i	−0.990835	−	0.135080i	$-0.956871\pi$
$347$	−0.252492	+	1.43195i	−0.0135545	+	0.0768712i	0.977280	+	0.211951i	$0.0679819\pi$
$348$		0			0
$349$	−21.1288	+	17.7292i	−1.13100	+	0.949022i	−0.999107	−	0.0422424i	$-0.986550\pi$
$349$	−21.1288	+	17.7292i	−1.13100	+	0.949022i	−0.131893	+	0.991264i	$0.542105\pi$
$350$	−21.7987			−1.16519
$351$		0			0
$352$	−5.39599			−0.287607
$353$	8.06807	−	6.76991i	0.429420	−	0.360326i	−0.402313	−	0.915502i	$-0.631794\pi$
$353$	8.06807	−	6.76991i	0.429420	−	0.360326i	0.831733	+	0.555176i	$0.187349\pi$
$354$		0			0
$355$	0.411474	−	2.33359i	0.0218388	−	0.123854i
$356$	−6.01330	+	2.18866i	−0.318704	+	0.115999i
$357$		0			0
$358$	−2.29514	−	13.0164i	−0.121302	−	0.687937i
$359$	−7.35273	−	12.7353i	−0.388062	−	0.672143i	0.604127	−	0.796888i	$-0.293522\pi$
$359$	−7.35273	−	12.7353i	−0.388062	−	0.672143i	−0.992189	+	0.124745i	$0.960189\pi$
$360$		0			0
$361$	−3.94104	+	6.82608i	−0.207423	+	0.359267i
$362$	−27.9556	−	10.1750i	−1.46931	−	0.534786i
$363$		0			0
$364$	3.09240	+	2.59483i	0.162086	+	0.136006i
$365$	0.531628	+	0.446089i	0.0278267	+	0.0233494i
$366$		0			0
$367$	20.0744	+	7.30650i	1.04788	+	0.381396i	0.807861	−	0.589373i	$-0.200625\pi$
$367$	20.0744	+	7.30650i	1.04788	+	0.381396i	0.240016	+	0.970769i	$0.422847\pi$
$368$	−11.5878	+	20.0706i	−0.604053	+	1.04625i
$369$		0			0
$370$	0.926022	+	1.60392i	0.0481416	+	0.0833837i
$371$	5.37987	+	30.5107i	0.279309	+	1.58404i
$372$		0			0
$373$	−21.2601	+	7.73805i	−1.10081	+	0.400661i	−0.827614	−	0.561298i	$-0.810302\pi$
$373$	−21.2601	+	7.73805i	−1.10081	+	0.400661i	−0.273193	+	0.961959i	$0.588080\pi$
$374$	−4.36873	+	24.7763i	−0.225902	+	1.28115i
$375$		0			0
$376$	−6.97565	+	5.85327i	−0.359742	+	0.301859i
$377$	−11.9101			−0.613404
$378$		0			0
$379$	−17.0743			−0.877047			−0.438523	−	0.898720i	$-0.644498\pi$
$379$	−17.0743			−0.877047			−0.438523	+	0.898720i	$0.644498\pi$
$380$	−0.615862	+	0.516769i	−0.0315930	+	0.0265097i
$381$		0			0
$382$	−3.27497	+	18.5733i	−0.167562	+	0.950291i
$383$	36.6401	−	13.3359i	1.87222	−	0.681433i	0.906276	−	0.422686i	$-0.138913\pi$
$383$	36.6401	−	13.3359i	1.87222	−	0.681433i	0.965945	−	0.258747i	$-0.0833095\pi$
$384$		0			0
$385$	0.761297	+	4.31753i	0.0387993	+	0.220042i
$386$	15.0679	+	26.0984i	0.766936	+	1.32837i
$387$		0			0
$388$	1.75624	−	3.04190i	0.0891598	−	0.154429i
$389$	−9.59619	−	3.49273i	−0.486546	−	0.177088i	0.0870870	−	0.996201i	$-0.472244\pi$
$389$	−9.59619	−	3.49273i	−0.486546	−	0.177088i	−0.573633	+	0.819112i	$0.694466\pi$
$390$		0			0
$391$	−39.2406	−	32.9267i	−1.98448	−	1.66518i
$392$	12.6577	+	10.6211i	0.639311	+	0.536446i
$393$		0			0
$394$	−10.9058	−	3.96940i	−0.549429	−	0.199976i
$395$	−2.65690	+	4.60189i	−0.133683	+	0.231546i
$396$		0			0
$397$	0.571452	+	0.989783i	0.0286803	+	0.0496758i	0.880009	−	0.474956i	$-0.157536\pi$
$397$	0.571452	+	0.989783i	0.0286803	+	0.0496758i	−0.851329	+	0.524632i	$0.824203\pi$
$398$	−0.581313	−	3.29679i	−0.0291386	−	0.165253i
$399$		0			0
$400$	−14.3671	+	5.22918i	−0.718353	+	0.261459i
$401$	−3.56916	+	20.2417i	−0.178235	+	1.01082i	0.756108	+	0.654447i	$0.227099\pi$
$401$	−3.56916	+	20.2417i	−0.178235	+	1.01082i	−0.934343	+	0.356375i	$0.884013\pi$
$402$		0			0
$403$	−4.88010	+	4.09489i	−0.243095	+	0.203981i
$404$	−0.722645			−0.0359530
$405$		0			0
$406$	−16.4338			−0.815594
$407$	−6.87170	+	5.76604i	−0.340618	+	0.285812i
$408$		0			0
$409$	−1.41147	+	8.00487i	−0.0697929	+	0.395815i	0.929821	+	0.368013i	$0.119962\pi$
$409$	−1.41147	+	8.00487i	−0.0697929	+	0.395815i	−0.999613	+	0.0278020i	$0.991149\pi$
$410$	−2.62175	+	0.954241i	−0.129479	+	0.0471266i
$411$		0			0
$412$	0.0873438	+	0.495351i	0.00430312	+	0.0244042i
$413$	−5.23416	−	9.06583i	−0.257556	−	0.446100i
$414$		0			0
$415$	3.62923	−	6.28602i	0.178152	−	0.308568i
$416$	6.00222	+	2.18463i	0.294283	+	0.107110i
$417$		0			0
$418$	14.1951	+	11.9111i	0.694303	+	0.582589i
$419$	27.4079	+	22.9979i	1.33896	+	1.12352i	0.981891	+	0.189446i	$0.0606691\pi$
$419$	27.4079	+	22.9979i	1.33896	+	1.12352i	0.357071	+	0.934077i	$0.383775\pi$
$420$		0			0
$421$	12.3277	+	4.48691i	0.600815	+	0.218679i	0.624480	−	0.781041i	$-0.285311\pi$
$421$	12.3277	+	4.48691i	0.600815	+	0.218679i	−0.0236644	+	0.999720i	$0.507533\pi$
$422$	−10.5128	+	18.2087i	−0.511756	+	0.886387i
$423$		0			0
$424$	13.2344	+	22.9227i	0.642720	+	1.11322i
$425$	−5.86819	−	33.2802i	−0.284649	−	1.61433i
$426$		0			0
$427$	26.1780	−	9.52801i	1.26684	−	0.461093i
$428$	−0.134837	+	0.764700i	−0.00651761	+	0.0369632i
$429$		0			0
$430$	−2.53209	+	2.12467i	−0.122108	+	0.102461i
$431$	9.48411			0.456833			0.228417	−	0.973563i	$-0.426645\pi$
$431$	9.48411			0.456833			0.228417	+	0.973563i	$0.426645\pi$
$432$		0			0
$433$	17.6628			0.848820			0.424410	−	0.905470i	$-0.360481\pi$
$433$	17.6628			0.848820			0.424410	+	0.905470i	$0.360481\pi$
$434$	−6.73362	+	5.65018i	−0.323224	+	0.271217i
$435$		0			0
$436$	0.693715	−	3.93426i	0.0332229	−	0.188417i
$437$	−35.4540	+	12.9042i	−1.69599	+	0.617292i
$438$		0			0
$439$	−3.06758	−	17.3971i	−0.146408	−	0.830319i	−0.966226	−	0.257696i	$-0.917037\pi$
$439$	−3.06758	−	17.3971i	−0.146408	−	0.830319i	0.819818	−	0.572624i	$-0.194074\pi$
$440$	1.87278	+	3.24376i	0.0892814	+	0.154640i
$441$		0			0
$442$	14.8905	−	25.7912i	0.708270	−	1.22676i
$443$	12.2086	+	4.44356i	0.580048	+	0.211120i	0.615346	−	0.788257i	$-0.289016\pi$
$443$	12.2086	+	4.44356i	0.580048	+	0.211120i	−0.0352989	+	0.999377i	$0.511238\pi$
$444$		0			0
$445$	6.30200	+	5.28801i	0.298744	+	0.250676i
$446$	−3.64609	−	3.05943i	−0.172647	−	0.144868i
$447$		0			0
$448$	29.4231	+	10.7091i	1.39011	+	0.505959i
$449$	2.31428	−	4.00846i	0.109218	−	0.189171i	−0.806236	−	0.591594i	$-0.798499\pi$
$449$	2.31428	−	4.00846i	0.109218	−	0.189171i	0.915454	+	0.402424i	$0.131832\pi$
$450$		0			0
$451$	−6.75671	−	11.7030i	−0.318161	−	0.551071i
$452$	0.101808	+	0.577382i	0.00478864	+	0.0271577i
$453$		0			0
$454$	−12.7579	+	4.64349i	−0.598758	+	0.217930i
$455$	0.901175	−	5.11081i	0.0422477	−	0.239599i
$456$		0			0
$457$	15.7554	−	13.2203i	0.737005	−	0.618421i	−0.195026	−	0.980798i	$-0.562479\pi$
$457$	15.7554	−	13.2203i	0.737005	−	0.618421i	0.932031	+	0.362377i	$0.118035\pi$
$458$	−17.3878			−0.812477
$459$		0			0
$460$	−1.12836			−0.0526098
$461$	−25.7180	+	21.5800i	−1.19781	+	1.00508i	−0.198117	+	0.980178i	$0.563483\pi$
$461$	−25.7180	+	21.5800i	−1.19781	+	1.00508i	−0.999690	+	0.0249007i	$0.992073\pi$
$462$		0			0
$463$	2.28018	−	12.9316i	0.105969	−	0.600980i	−0.884860	−	0.465857i	$-0.845746\pi$
$463$	2.28018	−	12.9316i	0.105969	−	0.600980i	0.990829	−	0.135123i	$-0.0431429\pi$
$464$	−10.8312	+	3.94222i	−0.502824	+	0.183013i
$465$		0			0
$466$	−2.83527	−	16.0796i	−0.131342	−	0.744875i
$467$	−11.8154	−	20.4648i	−0.546750	−	0.946999i	−0.998495	−	0.0548513i	$-0.982532\pi$
$467$	−11.8154	−	20.4648i	−0.546750	−	0.946999i	0.451745	−	0.892147i	$-0.350802\pi$
$468$		0			0
$469$	−16.6694	+	28.8722i	−0.769720	+	1.33319i
$470$	1.62760	+	0.592396i	0.0750754	+	0.0273252i
$471$		0			0
$472$	−6.85117	−	5.74881i	−0.315351	−	0.264610i
$473$	−12.2642	−	10.2909i	−0.563907	−	0.473174i
$474$		0			0
$475$	−23.3893	−	8.51303i	−1.07318	−	0.390604i
$476$	−4.31753	+	7.47818i	−0.197894	+	0.342762i
$477$		0			0
$478$	−3.76130	−	6.51476i	−0.172038	−	0.297978i
$479$	−1.02108	−	5.79086i	−0.0466546	−	0.264591i	0.952554	−	0.304370i	$-0.0984458\pi$
$479$	−1.02108	−	5.79086i	−0.0466546	−	0.264591i	−0.999209	+	0.0397786i	$0.987335\pi$
$480$		0			0
$481$	9.97818	−	3.63176i	0.454966	−	0.165594i
$482$	1.90641	−	10.8118i	0.0868347	−	0.492464i
$483$		0			0
$484$	0.870300	−	0.730269i	0.0395591	−	0.0331940i
$485$	−4.51557			−0.205041
$486$		0			0
$487$	38.7965			1.75804			0.879020	−	0.476786i	$-0.158198\pi$
$487$	38.7965			1.75804			0.879020	+	0.476786i	$0.158198\pi$
$488$	18.2322	−	15.2986i	0.825331	−	0.692535i
$489$		0			0
$490$	0.545759	−	3.09516i	0.0246549	−	0.139825i
$491$	35.3176	−	12.8546i	1.59386	−	0.580119i	0.615704	−	0.787978i	$-0.288872\pi$
$491$	35.3176	−	12.8546i	1.59386	−	0.580119i	0.978159	+	0.207859i	$0.0666495\pi$
$492$		0			0
$493$	−4.42396	−	25.0895i	−0.199245	−	1.12998i
$494$	−10.9675	−	18.9963i	−0.493452	−	0.854684i
$495$		0			0
$496$	−3.08260	+	5.33921i	−0.138413	+	0.239738i
$497$	−17.6154	−	6.41147i	−0.790158	−	0.287594i
$498$		0			0
$499$	25.8555	+	21.6953i	1.15745	+	0.971217i	0.999867	−	0.0162886i	$-0.00518506\pi$
$499$	25.8555	+	21.6953i	1.15745	+	0.971217i	0.157584	+	0.987506i	$0.449630\pi$
$500$	−1.16415	−	0.976834i	−0.0520622	−	0.0436853i
$501$		0			0
$502$	−8.16385	−	2.97140i	−0.364370	−	0.132620i
$503$	9.35597	−	16.2050i	0.417162	−	0.722546i	−0.578491	−	0.815689i	$-0.696358\pi$
$503$	9.35597	−	16.2050i	0.417162	−	0.722546i	0.995653	+	0.0931429i	$0.0296913\pi$
$504$		0			0
$505$	0.464508	+	0.804551i	0.0206703	+	0.0358020i
$506$	4.51617	+	25.6125i	0.200768	+	1.13861i
$507$		0			0
$508$	−0.872111	+	0.317423i	−0.0386937	+	0.0140833i
$509$	3.78000	−	21.4375i	0.167546	−	0.950199i	−0.778855	−	0.627204i	$-0.784199\pi$
$509$	3.78000	−	21.4375i	0.167546	−	0.950199i	0.946401	−	0.322995i	$-0.104690\pi$
$510$		0			0
$511$	4.20574	−	3.52903i	0.186051	−	0.156115i
$512$	25.4026			1.12265
$513$		0			0
$514$	−4.73473			−0.208840
$515$	0.495351	−	0.415649i	0.0218278	−	0.0183157i
$516$		0			0
$517$	−1.45677	+	8.26173i	−0.0640685	+	0.363351i
$518$	13.7680	−	5.01114i	0.604931	−	0.220177i
$519$		0			0
$520$	−0.769915	−	4.36640i	−0.0337630	−	0.191479i
$521$	3.23822	+	5.60876i	0.141869	+	0.245724i	0.928200	−	0.372081i	$-0.121356\pi$
$521$	3.23822	+	5.60876i	0.141869	+	0.245724i	−0.786332	+	0.617805i	$0.788022\pi$
$522$		0			0
$523$	5.43629	−	9.41593i	0.237712	−	0.411730i	−0.722345	−	0.691533i	$-0.756936\pi$
$523$	5.43629	−	9.41593i	0.237712	−	0.411730i	0.960057	+	0.279803i	$0.0902691\pi$
$524$	0.952906	+	0.346830i	0.0416279	+	0.0151513i
$525$		0			0
$526$	−3.58260	−	3.00616i	−0.156209	−	0.131075i
$527$	−10.4389	−	8.75924i	−0.454724	−	0.381558i
$528$		0			0
$529$	−28.1472	−	10.2448i	−1.22379	−	0.445424i
$530$	2.51730	−	4.36009i	0.109344	−	0.189390i
$531$		0			0
$532$	3.18004	+	5.50800i	0.137872	+	0.238802i
$533$	2.77773	+	15.7533i	0.120317	+	0.682351i
$534$		0			0
$535$	0.938044	−	0.341420i	0.0405552	−	0.0147609i
$536$	−4.94599	+	28.0501i	−0.213634	+	1.21158i
$537$		0			0
$538$	6.97906	−	5.85612i	0.300888	−	0.252475i
$539$	15.2226			0.655686
$540$		0			0
$541$	24.6459			1.05961			0.529805	−	0.848120i	$-0.322265\pi$
$541$	24.6459			1.05961			0.529805	+	0.848120i	$0.322265\pi$
$542$	18.7113	−	15.7007i	0.803721	−	0.674402i
$543$		0			0
$544$	−2.37258	+	13.4556i	−0.101723	+	0.576902i
$545$	−4.82608	+	1.75655i	−0.206726	+	0.0752423i
$546$		0			0
$547$	5.37046	+	30.4574i	0.229624	+	1.30226i	0.853644	+	0.520856i	$0.174387\pi$
$547$	5.37046	+	30.4574i	0.229624	+	1.30226i	−0.624020	+	0.781408i	$0.714502\pi$
$548$	0.808718	+	1.40074i	0.0345467	+	0.0598367i
$549$		0			0
$550$	−8.57873	+	14.8588i	−0.365798	+	0.633581i
$551$	−17.6330	−	6.41787i	−0.751189	−	0.273410i
$552$		0			0
$553$	32.2028	+	27.0214i	1.36940	+	1.14907i
$554$	13.6811	+	11.4798i	0.581255	+	0.487731i
$555$		0			0
$556$	−2.61169	−	0.950578i	−0.110760	−	0.0403135i
$557$	−11.6813	+	20.2327i	−0.494954	+	0.857286i	−0.999983	−	0.00581674i	$-0.998148\pi$
$557$	−11.6813	+	20.2327i	−0.494954	+	0.857286i	0.505029	+	0.863102i	$0.331482\pi$
$558$		0			0
$559$	9.47565	+	16.4123i	0.400777	+	0.694167i
$560$	−0.872129	−	4.94609i	−0.0368542	−	0.209010i
$561$		0			0
$562$	26.7310	−	9.72930i	1.12758	−	0.410406i
$563$	5.84981	−	33.1759i	0.246540	−	1.39820i	−0.570348	−	0.821403i	$-0.693192\pi$
$563$	5.84981	−	33.1759i	0.246540	−	1.39820i	0.816888	−	0.576796i	$-0.195697\pi$
$564$		0			0
$565$	0.577382	−	0.484481i	0.0242906	−	0.0203823i
$566$	30.5097			1.28242
$567$		0			0
$568$	−16.0155			−0.671995
$569$	−23.5910	+	19.7952i	−0.988986	+	0.829858i	−0.985421	−	0.170136i	$-0.945579\pi$
$569$	−23.5910	+	19.7952i	−0.988986	+	0.829858i	−0.00356541	+	0.999994i	$0.501135\pi$
$570$		0			0
$571$	−5.18779	+	29.4214i	−0.217102	+	1.23125i	0.660119	+	0.751161i	$0.270506\pi$
$571$	−5.18779	+	29.4214i	−0.217102	+	1.23125i	−0.877221	+	0.480086i	$0.840605\pi$
$572$	2.98572	−	1.08671i	0.124839	−	0.0454378i
$573$		0			0
$574$	3.83275	+	21.7366i	0.159976	+	0.907268i
$575$	−17.4670	−	30.2538i	−0.728425	−	1.26167i
$576$		0			0
$577$	−2.40373	+	4.16339i	−0.100069	+	0.173324i	−0.911713	−	0.410828i	$-0.865240\pi$
$577$	−2.40373	+	4.16339i	−0.100069	+	0.173324i	0.811644	+	0.584152i	$0.198573\pi$
$578$	39.3251	+	14.3131i	1.63571	+	0.595348i
$579$		0			0
$580$	−0.429892	−	0.360723i	−0.0178503	−	0.0149782i
$581$	−43.9878	−	36.9102i	−1.82492	−	1.53129i
$582$		0			0
$583$	22.9145	+	8.34018i	0.949020	+	0.345415i
$584$	2.34527	−	4.06212i	0.0970478	−	0.168092i
$585$		0			0
$586$	11.9598	+	20.7149i	0.494053	+	0.855725i
$587$	1.37835	+	7.81702i	0.0568906	+	0.322643i	0.999950	−	0.00998108i	$-0.00317713\pi$
$587$	1.37835	+	7.81702i	0.0568906	+	0.322643i	−0.943060	+	0.332624i	$0.892066\pi$
$588$		0			0
$589$	−9.43154	+	3.43280i	−0.388620	+	0.141446i
$590$	−0.295400	+	1.67530i	−0.0121614	+	0.0689709i
$591$		0			0
$592$	7.87211	−	6.60549i	0.323542	−	0.271484i
$593$	36.2753			1.48965			0.744824	−	0.667261i	$-0.232533\pi$
$593$	36.2753			1.48965			0.744824	+	0.667261i	$0.232533\pi$
$594$		0			0
$595$	11.1010			0.455097
$596$	5.37722	−	4.51202i	0.220259	−	0.184820i
$597$		0			0
$598$	5.34595	−	30.3184i	0.218612	−	1.23981i
$599$	−31.6160	+	11.5073i	−1.29179	+	0.470174i	−0.894315	−	0.447437i	$-0.852337\pi$
$599$	−31.6160	+	11.5073i	−1.29179	+	0.470174i	−0.397478	+	0.917612i	$0.630115\pi$
$600$		0			0
$601$	−0.517074	−	2.93247i	−0.0210919	−	0.119618i	0.972444	−	0.233137i	$-0.0748990\pi$
$601$	−0.517074	−	2.93247i	−0.0210919	−	0.119618i	−0.993536	+	0.113519i	$0.963788\pi$
$602$	13.0746	+	22.6459i	0.532882	+	0.922978i
$603$		0			0
$604$	1.16385	−	2.01584i	0.0473563	−	0.0820235i
$605$	−1.37246	−	0.499533i	−0.0557983	−	0.0203089i
$606$		0			0
$607$	−11.9875	−	10.0587i	−0.486558	−	0.408271i	0.366233	−	0.930523i	$-0.380647\pi$
$607$	−11.9875	−	10.0587i	−0.486558	−	0.408271i	−0.852791	+	0.522253i	$0.825092\pi$
$608$	7.70908	+	6.46868i	0.312644	+	0.262340i
$609$		0			0
$610$	−4.25402	−	1.54834i	−0.172240	−	0.0626904i
$611$	4.96529	−	8.60014i	0.200874	−	0.347924i
$612$		0			0
$613$	0.533433	+	0.923933i	0.0215452	+	0.0373173i	0.876597	−	0.481225i	$-0.159808\pi$
$613$	0.533433	+	0.923933i	0.0215452	+	0.0373173i	−0.855052	+	0.518543i	$0.826475\pi$
$614$	−4.63149	−	26.2665i	−0.186912	−	1.06003i
$615$		0			0
$616$	27.8444	−	10.1345i	1.12188	−	0.408331i
$617$	−2.26957	+	12.8714i	−0.0913696	+	0.518183i	0.904430	+	0.426622i	$0.140297\pi$
$617$	−2.26957	+	12.8714i	−0.0913696	+	0.518183i	−0.995800	+	0.0915606i	$0.970814\pi$
$618$		0			0
$619$	15.7173	−	13.1884i	0.631734	−	0.530087i	−0.269734	−	0.962935i	$-0.586936\pi$
$619$	15.7173	−	13.1884i	0.631734	−	0.530087i	0.901467	+	0.432848i	$0.142491\pi$
$620$	−0.300167			−0.0120550
$621$		0			0
$622$	−26.2071			−1.05081
$623$	49.8554	−	41.8337i	1.99742	−	1.67603i
$624$		0			0
$625$	3.82888	−	21.7146i	0.153155	−	0.868586i
$626$	−36.0490	+	13.1208i	−1.44081	+	0.524412i
$627$		0			0
$628$	−0.321137	−	1.82126i	−0.0128148	−	0.0726762i
$629$	11.3569	+	19.6707i	0.452829	+	0.784323i
$630$		0			0
$631$	5.15611	−	8.93064i	0.205261	−	0.355523i	−0.744955	−	0.667115i	$-0.767529\pi$
$631$	5.15611	−	8.93064i	0.205261	−	0.355523i	0.950216	+	0.311592i	$0.100862\pi$
$632$	33.7489	+	12.2836i	1.34246	+	0.488615i
$633$		0			0
$634$	−4.25103	−	3.56704i	−0.168830	−	0.141665i
$635$	0.913982	+	0.766922i	0.0362703	+	0.0304344i
$636$		0			0
$637$	−16.9329	−	6.16307i	−0.670905	−	0.244190i
$638$	−6.46740	+	11.2019i	−0.256047	+	0.443486i
$639$		0			0
$640$	−1.67752	−	2.90555i	−0.0663097	−	0.114852i
$641$	0.608839	+	3.45290i	0.0240477	+	0.136381i	0.994468	−	0.105041i	$-0.0334973\pi$
$641$	0.608839	+	3.45290i	0.0240477	+	0.136381i	−0.970420	+	0.241422i	$0.922386\pi$
$642$		0			0
$643$	−29.6489	+	10.7913i	−1.16924	+	0.425568i	−0.852389	−	0.522908i	$-0.824847\pi$
$643$	−29.6489	+	10.7913i	−1.16924	+	0.425568i	−0.316849	+	0.948476i	$0.602625\pi$
$644$	−1.55007	+	8.79086i	−0.0610811	+	0.346408i
$645$		0			0
$646$	35.9432	−	30.1599i	1.41416	−	1.18662i
$647$	−3.04628			−0.119762			−0.0598808	−	0.998206i	$-0.519072\pi$
$647$	−3.04628			−0.119762			−0.0598808	+	0.998206i	$0.519072\pi$
$648$		0			0
$649$	−8.23947			−0.323428
$650$	15.5583	−	13.0550i	0.610246	−	0.512057i
$651$		0			0
$652$	−0.230085	+	1.30488i	−0.00901083	+	0.0511030i
$653$	28.8837	−	10.5128i	1.13031	−	0.411397i	0.291902	−	0.956448i	$-0.405712\pi$
$653$	28.8837	−	10.5128i	1.13031	−	0.411397i	0.838403	+	0.545051i	$0.183490\pi$
$654$		0			0
$655$	−0.226377	−	1.28385i	−0.00884528	−	0.0501641i
$656$	7.74038	+	13.4067i	0.302211	+	0.523445i
$657$		0			0
$658$	6.85117	−	11.8666i	0.267086	−	0.462607i
$659$	31.1827	+	11.3496i	1.21471	+	0.442117i	0.868334	−	0.495981i	$-0.165191\pi$
$659$	31.1827	+	11.3496i	1.21471	+	0.442117i	0.346372	+	0.938097i	$0.387414\pi$
$660$		0			0
$661$	−11.4199	−	9.58246i	−0.444184	−	0.372714i	0.393088	−	0.919501i	$-0.371407\pi$
$661$	−11.4199	−	9.58246i	−0.444184	−	0.372714i	−0.837272	+	0.546786i	$0.815851\pi$
$662$	2.87457	+	2.41205i	0.111723	+	0.0937469i
$663$		0			0
$664$	−46.0997	−	16.7789i	−1.78902	−	0.651149i
$665$	4.08819	−	7.08095i	0.158533	−	0.274587i
$666$		0			0
$667$	−13.1682	−	22.8080i	−0.509874	−	0.883128i
$668$	−0.550931	−	3.12449i	−0.0213162	−	0.120890i
$669$		0			0
$670$	5.09095	−	1.85295i	0.196680	−	0.0715858i
$671$	3.80753	−	21.5936i	0.146988	−	0.833611i
$672$		0			0
$673$	5.27719	−	4.42809i	0.203421	−	0.170690i	−0.535386	−	0.844607i	$-0.679834\pi$
$673$	5.27719	−	4.42809i	0.203421	−	0.170690i	0.738807	+	0.673917i	$0.235390\pi$
$674$	−18.5656			−0.715122
$675$		0			0
$676$	0.753718			0.0289892
$677$	−10.1035	+	8.47787i	−0.388310	+	0.325831i	−0.815955	−	0.578116i	$-0.803788\pi$
$677$	−10.1035	+	8.47787i	−0.388310	+	0.325831i	0.427644	+	0.903947i	$0.359344\pi$
$678$		0			0
$679$	−6.20321	+	35.1802i	−0.238057	+	1.35009i
$680$	8.91215	−	3.24376i	0.341765	−	0.124392i
$681$		0			0
$682$	1.20140	+	6.81348i	0.0460040	+	0.260902i
$683$	1.68907	+	2.92556i	0.0646305	+	0.111943i	0.896530	−	0.442983i	$-0.146080\pi$
$683$	1.68907	+	2.92556i	0.0646305	+	0.111943i	−0.831900	+	0.554926i	$0.812746\pi$
$684$		0			0
$685$	1.03967	−	1.80076i	0.0397237	−	0.0688034i
$686$	6.50428	+	2.36736i	0.248334	+	0.0903864i
$687$		0			0
$688$	14.0496	+	11.7890i	0.535637	+	0.449453i
$689$	−22.1122	−	18.5544i	−0.842409	−	0.706865i
$690$		0			0
$691$	−22.0030	−	8.00843i	−0.837033	−	0.304655i	−0.112291	−	0.993675i	$-0.535819\pi$
$691$	−22.0030	−	8.00843i	−0.837033	−	0.304655i	−0.724742	+	0.689020i	$0.758041\pi$
$692$	1.05471	−	1.82682i	0.0400942	−	0.0694452i
$693$		0			0
$694$	−0.934640	−	1.61884i	−0.0354785	−	0.0614505i
$695$	0.620446	+	3.51872i	0.0235349	+	0.133473i
$696$		0			0
$697$	−32.1536	+	11.7030i	−1.21791	+	0.443281i
$698$	6.15728	−	34.9197i	0.233057	−	1.32173i
$699$		0			0
$700$	−4.51114	+	3.78530i	−0.170505	+	0.143071i
$701$	45.5001			1.71852			0.859258	−	0.511543i	$-0.170926\pi$
$701$	45.5001			1.71852			0.859258	+	0.511543i	$0.170926\pi$
$702$		0			0
$703$	16.7297			0.630972
$704$	18.8790	−	15.8414i	0.711529	−	0.597044i
$705$		0			0
$706$	−2.35117	+	13.3341i	−0.0884873	+	0.501837i
$707$	6.90625	−	2.51367i	0.259736	−	0.0945363i
$708$		0			0
$709$	6.70574	+	38.0301i	0.251839	+	1.42825i	0.804057	+	0.594552i	$0.202670\pi$
$709$	6.70574	+	38.0301i	0.251839	+	1.42825i	−0.552218	+	0.833700i	$0.686218\pi$
$710$	1.52314	+	2.63816i	0.0571624	+	0.0990082i
$711$		0			0
$712$	27.8011	−	48.1530i	1.04189	−	1.80461i
$713$	−13.2373	−	4.81798i	−0.495741	−	0.180435i
$714$		0			0
$715$	−3.12907	−	2.62560i	−0.117021	−	0.0981920i
$716$	−2.73524	−	2.29514i	−0.102221	−	0.0857734i
$717$		0			0
$718$	17.7649	+	6.46588i	0.662979	+	0.241305i
$719$	24.6591	−	42.7108i	0.919630	−	1.59285i	0.119652	−	0.992816i	$-0.461822\pi$
$719$	24.6591	−	42.7108i	0.919630	−	1.59285i	0.799978	−	0.600030i	$-0.204845\pi$
$720$		0			0
$721$	−2.55778	−	4.43021i	−0.0952567	−	0.164990i
$722$	−1.75958	−	9.97906i	−0.0654847	−	0.371382i
$723$		0			0
$724$	−7.55216	+	2.74876i	−0.280674	+	0.102157i
$725$	3.01703	−	17.1104i	0.112050	−	0.635464i
$726$		0			0
$727$	−24.7390	+	20.7585i	−0.917519	+	0.769890i	−0.973535	−	0.228540i	$-0.926605\pi$
$727$	−24.7390	+	20.7585i	−0.917519	+	0.769890i	0.0560155	+	0.998430i	$0.482160\pi$
$728$	−35.0757			−1.29999
$729$		0			0
$730$	−0.892178			−0.0330210
$731$	−31.0540	+	26.0574i	−1.14857	+	0.963767i
$732$		0			0
$733$	6.85323	−	38.8666i	0.253130	−	1.43557i	−0.547699	−	0.836676i	$-0.684496\pi$
$733$	6.85323	−	38.8666i	0.253130	−	1.43557i	0.800828	−	0.598894i	$-0.204393\pi$
$734$	−25.8072	+	9.39306i	−0.952561	+	0.346704i
$735$		0			0
$736$	2.45265	+	13.9097i	0.0904058	+	0.512717i
$737$	13.1202	+	22.7249i	0.483290	+	0.837083i
$738$		0			0
$739$	−17.6545	+	30.5785i	−0.649432	+	1.12485i	0.333827	+	0.942634i	$0.391660\pi$
$739$	−17.6545	+	30.5785i	−0.649432	+	1.12485i	−0.983259	+	0.182215i	$0.941673\pi$
$740$	0.470154	+	0.171122i	0.0172832	+	0.00629057i
$741$		0			0
$742$	−30.5107	−	25.6015i	−1.12008	−	0.939862i
$743$	−36.3186	−	30.4749i	−1.33240	−	1.11802i	−0.983510	−	0.180854i	$-0.942114\pi$
$743$	−36.3186	−	30.4749i	−1.33240	−	1.11802i	−0.348891	−	0.937163i	$-0.613442\pi$
$744$		0			0
$745$	−8.47983	−	3.08640i	−0.310677	−	0.113077i
$746$	14.5428	−	25.1888i	0.532449	−	0.922228i
$747$		0			0
$748$	3.39827	+	5.88598i	0.124253	+	0.215213i
$749$	−1.37133	−	7.77719i	−0.0501072	−	0.284172i
$750$		0			0
$751$	8.38965	−	3.05358i	0.306143	−	0.111427i	−0.184381	−	0.982855i	$-0.559028\pi$
$751$	8.38965	−	3.05358i	0.306143	−	0.111427i	0.490523	+	0.871428i	$0.336806\pi$
$752$	1.66885	−	9.46451i	0.0608566	−	0.345135i
$753$		0			0
$754$	11.7292	−	9.84197i	0.427153	−	0.358424i
$755$	−2.99243			−0.108906
$756$		0			0
$757$	−3.63816			−0.132231			−0.0661155	−	0.997812i	$-0.521061\pi$
$757$	−3.63816			−0.132231			−0.0661155	+	0.997812i	$0.521061\pi$
$758$	16.8149	−	14.1094i	0.610744	−	0.512475i
$759$		0			0
$760$	1.21301	−	6.87933i	0.0440005	−	0.249539i
$761$	6.28542	−	2.28770i	0.227846	−	0.0829292i	−0.225574	−	0.974226i	$-0.572426\pi$
$761$	6.28542	−	2.28770i	0.227846	−	0.0829292i	0.453420	+	0.891297i	$0.350204\pi$
$762$		0			0
$763$	7.05525	+	40.0123i	0.255417	+	1.44854i
$764$	2.54747	+	4.41235i	0.0921643	+	0.159633i
$765$		0			0
$766$	−25.0633	+	43.4109i	−0.905574	+	1.56850i
$767$	9.16517	+	3.33585i	0.330935	+	0.120450i
$768$		0			0
$769$	−16.4479	−	13.8014i	−0.593126	−	0.497692i	0.296102	−	0.955156i	$-0.404313\pi$
$769$	−16.4479	−	13.8014i	−0.593126	−	0.497692i	−0.889228	+	0.457464i	$0.848758\pi$
$770$	−4.31753	−	3.62284i	−0.155593	−	0.130558i
$771$		0			0
$772$	7.65018	+	2.78444i	0.275336	+	0.100214i
$773$	5.12208	−	8.87170i	0.184228	−	0.319093i	−0.759088	−	0.650988i	$-0.774355\pi$
$773$	5.12208	−	8.87170i	0.184228	−	0.319093i	0.943316	+	0.331895i	$0.107688\pi$
$774$		0			0
$775$	−4.64661	−	8.04817i	−0.166911	−	0.289099i
$776$	5.29969	+	30.0560i	0.190248	+	1.07895i
$777$		0			0
$778$	12.3366	−	4.49016i	0.442289	−	0.160980i
$779$	−4.37636	+	24.8195i	−0.156799	+	0.889252i
$780$		0			0
$781$	−11.3027	+	9.48411i	−0.404443	+	0.339368i
$782$	65.8535			2.35492
$783$		0			0
$784$	−17.4388			−0.622815
$785$	−1.82126	+	1.52822i	−0.0650036	+	0.0545445i
$786$		0			0
$787$	0.164563	−	0.933284i	0.00586605	−	0.0332680i	−0.981734	−	0.190257i	$-0.939068\pi$
$787$	0.164563	−	0.933284i	0.00586605	−	0.0332680i	0.987600	+	0.156989i	$0.0501789\pi$
$788$	−2.94620	+	1.07233i	−0.104954	+	0.0382001i
$789$		0			0
$790$	−1.18624	−	6.72752i	−0.0422046	−	0.239354i
$791$	−2.98135	−	5.16385i	−0.106005	−	0.183605i
$792$		0			0
$793$	−12.9777	+	22.4781i	−0.460852	+	0.798219i
$794$	−1.38068	−	0.502526i	−0.0489985	−	0.0178340i
$795$		0			0
$796$	−0.692782	−	0.581313i	−0.0245550	−	0.0206041i
$797$	5.37051	+	4.50640i	0.190233	+	0.159625i	0.732930	−	0.680304i	$-0.238152\pi$
$797$	5.37051	+	4.50640i	0.190233	+	0.159625i	−0.542697	+	0.839929i	$0.682597\pi$
$798$		0			0
$799$	19.9611	+	7.26525i	0.706173	+	0.257026i
$800$	−4.65895	+	8.06953i	−0.164719	+	0.285301i
$801$		0			0
$802$	−13.2118	−	22.8836i	−0.466526	−	0.808047i
$803$	−0.750380	−	4.25562i	−0.0264803	−	0.150177i
$804$		0			0
$805$	10.7836	−	3.92490i	0.380071	−	0.138335i
$806$	1.42214	−	8.06536i	0.0500928	−	0.284090i
$807$		0			0
$808$	4.80999	−	4.03606i	0.169215	−	0.141988i
$809$	−45.1028			−1.58573			−0.792866	−	0.609396i	$-0.791412\pi$
$809$	−45.1028			−1.58573			−0.792866	+	0.609396i	$0.791412\pi$
$810$		0			0
$811$	8.07285			0.283476			0.141738	−	0.989904i	$-0.454731\pi$
$811$	8.07285			0.283476			0.141738	+	0.989904i	$0.454731\pi$
$812$	−3.40090	+	2.85369i	−0.119348	+	0.100145i
$813$		0			0
$814$	2.00253	−	11.3569i	0.0701885	−	0.398059i
$815$	1.60067	−	0.582596i	0.0560690	−	0.0204075i
$816$		0			0
$817$	5.18479	+	29.4044i	0.181393	+	1.02873i
$818$	−5.22481	−	9.04963i	−0.182681	−	0.316413i
$819$		0			0
$820$	−0.376859	+	0.652739i	−0.0131605	+	0.0227946i
$821$	−5.89127	−	2.14425i	−0.205607	−	0.0748348i	0.237164	−	0.971470i	$-0.423782\pi$
$821$	−5.89127	−	2.14425i	−0.205607	−	0.0748348i	−0.442771	+	0.896635i	$0.646004\pi$
$822$		0			0
$823$	−15.1623	−	12.7226i	−0.528523	−	0.443483i	0.339068	−	0.940762i	$-0.389888\pi$
$823$	−15.1623	−	12.7226i	−0.528523	−	0.443483i	−0.867591	+	0.497278i	$0.834333\pi$
$824$	−3.34797	−	2.80928i	−0.116632	−	0.0978658i
$825$		0			0
$826$	12.6462	+	4.60284i	0.440018	+	0.160153i
$827$	20.9001	−	36.2001i	0.726769	−	1.25880i	−0.231472	−	0.972841i	$-0.574354\pi$
$827$	20.9001	−	36.2001i	0.726769	−	1.25880i	0.958242	−	0.285960i	$-0.0923124\pi$
$828$		0			0
$829$	−16.8640	−	29.2092i	−0.585710	−	1.01448i	−0.994787	−	0.101979i	$-0.967483\pi$
$829$	−16.8640	−	29.2092i	−0.585710	−	1.01448i	0.409077	−	0.912500i	$-0.365851\pi$
$830$	1.62036	+	9.18954i	0.0562437	+	0.318974i
$831$		0			0
$832$	−27.4136	+	9.97773i	−0.950395	+	0.345916i
$833$	6.69329	−	37.9595i	0.231909	−	1.31522i
$834$		0			0
$835$	−3.12449	+	2.62175i	−0.108127	+	0.0907296i
$836$	5.00594			0.173134
$837$		0			0
$838$	−45.9959			−1.58890
$839$	22.4350	−	18.8252i	0.774541	−	0.649917i	−0.167327	−	0.985902i	$-0.553513\pi$
$839$	22.4350	−	18.8252i	0.774541	−	0.649917i	0.941868	+	0.335984i	$0.109069\pi$
$840$		0			0
$841$	−2.76130	+	15.6601i	−0.0952171	+	0.540003i
$842$	−15.8482	+	5.76827i	−0.546164	+	0.198788i
$843$		0			0
$844$	0.986329	+	5.59375i	0.0339509	+	0.192545i
$845$	−0.484481	−	0.839145i	−0.0166666	−	0.0288675i
$846$		0			0
$847$	−5.77719	+	10.0064i	−0.198507	+	0.343823i
$848$	−26.2504	−	9.55438i	−0.901444	−	0.328099i
$849$		0			0
$850$	33.2802	+	27.9254i	1.14150	+	0.957833i
$851$	17.9870	+	15.0929i	0.616586	+	0.517377i
$852$		0			0
$853$	−35.3307	−	12.8593i	−1.20970	−	0.440295i	−0.343100	−	0.939299i	$-0.611477\pi$
$853$	−35.3307	−	12.8593i	−1.20970	−	0.440295i	−0.866600	+	0.499004i	$0.833699\pi$
$854$	−17.9068	+	31.0155i	−0.612758	+	1.06133i
$855$		0			0
$856$	−3.37346	−	5.84300i	−0.115302	−	0.199710i
$857$	5.03753	+	28.5692i	0.172079	+	0.975906i	0.941462	+	0.337119i	$0.109452\pi$
$857$	5.03753	+	28.5692i	0.172079	+	0.975906i	−0.769383	+	0.638787i	$0.779436\pi$
$858$		0			0
$859$	23.3678	−	8.50519i	0.797300	−	0.290193i	0.0889329	−	0.996038i	$-0.471654\pi$
$859$	23.3678	−	8.50519i	0.797300	−	0.290193i	0.708367	+	0.705844i	$0.249432\pi$
$860$	−0.155059	+	0.879385i	−0.00528748	+	0.0299868i
$861$		0			0
$862$	−9.34002	+	7.83721i	−0.318122	+	0.266936i
$863$	−42.4018			−1.44337			−0.721687	−	0.692219i	$-0.756633\pi$
$863$	−42.4018			−1.44337			−0.721687	+	0.692219i	$0.756633\pi$
$864$		0			0
$865$	−2.71183			−0.0922050
$866$	−17.3945	+	14.5957i	−0.591088	+	0.495982i
$867$		0			0
$868$	−0.412351	+	2.33856i	−0.0139961	+	0.0793759i
$869$	31.0920	−	11.3166i	1.05472	−	0.383888i
$870$		0			0
$871$	−5.39383	−	30.5899i	−0.182763	−	1.03650i
$872$	17.3559	+	30.0612i	0.587744	+	1.01800i
$873$		0			0
$874$	24.2520	−	42.0056i	0.820335	−	1.42086i
$875$	14.5235	+	5.28611i	0.490983	+	0.178703i
$876$		0			0
$877$	9.23442	+	7.74860i	0.311824	+	0.261652i	0.785246	−	0.619185i	$-0.212537\pi$
$877$	9.23442	+	7.74860i	0.311824	+	0.261652i	−0.473421	+	0.880836i	$0.656981\pi$
$878$	17.3971	+	14.5979i	0.587124	+	0.492656i
$879$		0			0
$880$	−3.71466	−	1.35203i	−0.125221	−	0.0455768i
$881$	−7.39133	+	12.8022i	−0.249020	+	0.431316i	−0.963254	−	0.268591i	$-0.913442\pi$
$881$	−7.39133	+	12.8022i	−0.249020	+	0.431316i	0.714234	+	0.699907i	$0.246775\pi$
$882$		0			0
$883$	12.9231	+	22.3834i	0.434896	+	0.753263i	0.997287	−	0.0736089i	$-0.0234516\pi$
$883$	12.9231	+	22.3834i	0.434896	+	0.753263i	−0.562391	+	0.826872i	$0.690118\pi$
$884$	−1.39705	−	7.92309i	−0.0469880	−	0.266482i
$885$		0			0
$886$	−15.6951	+	5.71253i	−0.527286	+	0.191916i
$887$	−7.96281	+	45.1593i	−0.267365	+	1.51630i	0.494851	+	0.868978i	$0.335223\pi$
$887$	−7.96281	+	45.1593i	−0.267365	+	1.51630i	−0.762215	+	0.647323i	$0.775888\pi$
$888$		0			0
$889$	7.23055	−	6.06715i	0.242505	−	0.203486i
$890$	−10.5760			−0.354509
$891$		0			0
$892$	−1.28581			−0.0430520
$893$	11.9854	−	10.0569i	0.401074	−	0.336541i
$894$		0			0
$895$	−0.797094	+	4.52054i	−0.0266439	+	0.151105i
$896$	−24.9412	+	9.07785i	−0.833226	+	0.303270i
$897$		0			0
$898$	1.03327	+	5.85997i	0.0344807	+	0.195550i
$899$	−3.50303	−	6.06742i	−0.116832	−	0.202360i
$900$		0			0
$901$	30.8726	−	53.4729i	1.02851	−	1.78144i
$902$	16.3248	+	5.94175i	0.543557	+	0.197839i
$903$		0			0
$904$	−3.90239	−	3.27449i	−0.129792	−	0.108908i
$905$	7.91474	+	6.64125i	0.263095	+	0.220763i
$906$		0			0
$907$	10.9944	+	4.00163i	0.365062	+	0.132872i	0.518037	−	0.855358i	$-0.326663\pi$
$907$	10.9944	+	4.00163i	0.365062	+	0.132872i	−0.152975	+	0.988230i	$0.548885\pi$
$908$	−1.83386	+	3.17634i	−0.0608587	+	0.105410i
$909$		0			0
$910$	3.33585	+	5.77786i	0.110582	+	0.191534i
$911$	−4.97941	−	28.2396i	−0.164975	−	0.935621i	−0.949090	−	0.315005i	$-0.897994\pi$
$911$	−4.97941	−	28.2396i	−0.164975	−	0.935621i	0.784115	−	0.620616i	$-0.213117\pi$
$912$		0			0
$913$	−42.4705	+	15.4580i	−1.40557	+	0.511585i
$914$	−4.59137	+	26.0390i	−0.151869	+	0.861292i
$915$		0			0
$916$	−3.59833	+	3.01935i	−0.118892	+	0.0997623i
$917$	−10.3133			−0.340574
$918$		0			0
$919$	4.33511			0.143002			0.0715011	−	0.997441i	$-0.477221\pi$
$919$	4.33511			0.143002			0.0715011	+	0.997441i	$0.477221\pi$
$920$	7.51044	−	6.30200i	0.247612	−	0.207771i
$921$		0			0
$922$	7.49464	−	42.5042i	0.246823	−	1.39980i
$923$	16.4123	−	5.97359i	0.540218	−	0.196623i
$924$		0			0
$925$	2.68984	+	15.2549i	0.0884416	+	0.501577i
$926$	8.44047	+	14.6193i	0.277371	+	0.480421i
$927$		0			0
$928$	−3.51233	+	6.08353i	−0.115298	+	0.199702i
$929$	−12.1135	−	4.40895i	−0.397431	−	0.144653i	0.135570	−	0.990768i	$-0.456713\pi$
$929$	−12.1135	−	4.40895i	−0.397431	−	0.144653i	−0.533001	+	0.846115i	$0.678936\pi$
$930$		0			0
$931$	−21.7481	−	18.2488i	−0.712765	−	0.598081i
$932$	−3.37895	−	2.83527i	−0.110681	−	0.0928725i
$933$		0			0
$934$	28.5470	+	10.3903i	0.934086	+	0.339980i
$935$	4.36873	−	7.56687i	0.142873	−	0.247463i
$936$		0			0
$937$	26.6040	+	46.0795i	0.869115	+	1.50535i	0.862902	+	0.505371i	$0.168644\pi$
$937$	26.6040	+	46.0795i	0.869115	+	1.50535i	0.00621270	+	0.999981i	$0.498022\pi$
$938$	−7.44247	−	42.2083i	−0.243005	−	1.37815i
$939$		0			0
$940$	0.439693	−	0.160035i	0.0143412	−	0.00521977i
$941$	−5.80114	+	32.8999i	−0.189112	+	1.07251i	0.731446	+	0.681900i	$0.238846\pi$
$941$	−5.80114	+	32.8999i	−0.189112	+	1.07251i	−0.920558	+	0.390607i	$0.872265\pi$
$942$		0			0
$943$	−27.0965	+	22.7367i	−0.882383	+	0.740407i
$944$	9.43901			0.307214
$945$		0			0
$946$	20.5817			0.669169
$947$	−11.8773	+	9.96626i	−0.385961	+	0.323860i	−0.815037	−	0.579408i	$-0.803284\pi$
$947$	−11.8773	+	9.96626i	−0.385961	+	0.323860i	0.429076	+	0.903268i	$0.358839\pi$
$948$		0			0
$949$	−0.888252	+	5.03753i	−0.0288339	+	0.163525i
$950$	30.0688	−	10.9441i	0.975560	−	0.355075i
$951$		0			0
$952$	−13.0287	−	73.8893i	−0.422262	−	2.39477i
$953$	−11.2524	−	19.4898i	−0.364502	−	0.631336i	0.624194	−	0.781269i	$-0.285427\pi$
$953$	−11.2524	−	19.4898i	−0.364502	−	0.631336i	−0.988696	+	0.149933i	$0.952094\pi$
$954$		0			0
$955$	3.27497	−	5.67241i	0.105975	−	0.183555i
$956$	−1.90966	−	0.695060i	−0.0617628	−	0.0224798i
$957$		0			0
$958$	5.79086	+	4.85911i	0.187094	+	0.156991i
$959$	−12.6012	−	10.5737i	−0.406914	−	0.341442i
$960$		0			0
$961$	25.6091	+	9.32094i	0.826099	+	0.300675i
$962$	−6.82548	+	11.8221i	−0.220062	+	0.381159i
$963$		0			0
$964$	−1.48293	−	2.56850i	−0.0477618	−	0.0827259i
$965$	−1.81741	−	10.3071i	−0.0585046	−	0.331796i
$966$		0			0
$967$	39.2870	−	14.2993i	1.26339	−	0.459835i	0.378482	−	0.925609i	$-0.376446\pi$
$967$	39.2870	−	14.2993i	1.26339	−	0.459835i	0.884904	+	0.465774i	$0.154224\pi$
$968$	−1.71416	+	9.72147i	−0.0550951	+	0.312460i
$969$		0			0
$970$	4.44697	−	3.73145i	0.142783	−	0.119810i
$971$	35.8662			1.15100			0.575501	−	0.817801i	$-0.304807\pi$
$971$	35.8662			1.15100			0.575501	+	0.817801i	$0.304807\pi$
$972$		0			0
$973$	28.2662			0.906173
$974$	−38.2071	+	32.0596i	−1.22424	+	1.02726i
$975$		0			0
$976$	−4.36184	+	24.7372i	−0.139619	+	0.791820i
$977$	−13.2027	+	4.80541i	−0.422393	+	0.153739i	−0.544467	−	0.838782i	$-0.683268\pi$
$977$	−13.2027	+	4.80541i	−0.422393	+	0.153739i	0.122073	+	0.992521i	$0.461046\pi$
$978$		0			0
$979$	−8.89512	−	50.4467i	−0.284289	−	1.61228i
$980$	−0.424525	−	0.735300i	−0.0135610	−	0.0234883i
$981$		0			0
$982$	−24.1587	+	41.8441i	−0.770935	+	1.33530i
$983$	16.6223	+	6.05004i	0.530171	+	0.192966i	0.593215	−	0.805044i	$-0.297859\pi$
$983$	16.6223	+	6.05004i	0.530171	+	0.192966i	−0.0630439	+	0.998011i	$0.520081\pi$
$984$		0			0
$985$	3.08765	+	2.59084i	0.0983807	+	0.0825512i
$986$	25.0895	+	21.0526i	0.799014	+	0.670452i
$987$		0			0
$988$	−5.56835	−	2.02671i	−0.177153	−	0.0644784i
$989$	−20.9531	+	36.2918i	−0.666269	+	1.15401i
$990$		0			0
$991$	−16.4479	−	28.4886i	−0.522485	−	0.904970i	−0.999658	−	0.0261608i	$-0.991672\pi$
$991$	−16.4479	−	28.4886i	−0.522485	−	0.904970i	0.477173	−	0.878809i	$-0.341662\pi$
$992$	0.652458	+	3.70027i	0.0207156	+	0.117484i
$993$		0			0
$994$	22.6459	−	8.24243i	0.718284	−	0.261434i
$995$	−0.201888	+	1.14496i	−0.00640027	+	0.0362978i
$996$		0			0
$997$	15.3261	−	12.8601i	0.485383	−	0.407284i	−0.366985	−	0.930227i	$-0.619610\pi$
$997$	15.3261	−	12.8601i	0.485383	−	0.407284i	0.852368	+	0.522942i	$0.175166\pi$
$998$	−43.3907			−1.37351
$999$		0			0

Twists

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

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

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)

\(f(q)\)	\(=\)	\(q+(-0.984808 + 0.826352i) q^{2} +(-0.0603074 + 0.342020i) q^{4} +(0.419550 - 0.152704i) q^{5} +(-0.613341 - 3.47843i) q^{7} +(-1.50881 - 2.61334i) q^{8} +O(q^{10})\)	\(q+(-0.984808 + 0.826352i) q^{2} +(-0.0603074 + 0.342020i) q^{4} +(0.419550 - 0.152704i) q^{5} +(-0.613341 - 3.47843i) q^{7} +(-1.50881 - 2.61334i) q^{8} +(-0.286989 + 0.497079i) q^{10} +(-2.61240 - 0.950837i) q^{11} +(2.52094 + 2.11532i) q^{13} +(3.47843 + 2.91875i) q^{14} +(2.99273 + 1.08926i) q^{16} +(-3.51968 + 6.09627i) q^{17} +(2.59240 + 4.49016i) q^{19} +(0.0269258 + 0.152704i) q^{20} +(3.35844 - 1.22237i) q^{22} +(-1.26363 + 7.16637i) q^{23} +(-3.67752 + 3.08580i) q^{25} -4.23065 q^{26} +1.22668 q^{28} +(-2.77244 + 2.32635i) q^{29} +(-0.336152 + 1.90641i) q^{31} +(1.82391 - 0.663848i) q^{32} +(-1.57145 - 8.91215i) q^{34} +(-0.788496 - 1.36571i) q^{35} +(1.61334 - 2.79439i) q^{37} +(-6.26347 - 2.27972i) q^{38} +(-1.03209 - 0.866025i) q^{40} +(3.72362 + 3.12449i) q^{41} +(5.41147 + 1.96962i) q^{43} +(0.482753 - 0.836152i) q^{44} +(-4.67752 - 8.10170i) q^{46} +(-0.524005 - 2.97178i) q^{47} +(-5.14543 + 1.87278i) q^{49} +(1.07169 - 6.07785i) q^{50} +(-0.875515 + 0.734644i) q^{52} -8.77141 q^{53} -1.24123 q^{55} +(-8.16490 + 6.85117i) q^{56} +(0.807934 - 4.58202i) q^{58} +(2.78504 - 1.01367i) q^{59} +(1.36959 + 7.76730i) q^{61} +(-1.24432 - 2.15523i) q^{62} +(-4.43242 + 7.67717i) q^{64} +(1.38068 + 0.502526i) q^{65} +(-7.23055 - 6.06715i) q^{67} +(-1.87278 - 1.57145i) q^{68} +(1.90508 + 0.693392i) q^{70} +(2.65366 - 4.59627i) q^{71} +(0.777189 + 1.34613i) q^{73} +(0.720317 + 4.08512i) q^{74} +(-1.69207 + 0.615862i) q^{76} +(-1.70513 + 9.67024i) q^{77} +(-9.11721 + 7.65025i) q^{79} +1.42193 q^{80} -6.24897 q^{82} +(12.4538 - 10.4500i) q^{83} +(-0.545759 + 3.09516i) q^{85} +(-6.95686 + 2.53209i) q^{86} +(1.45677 + 8.26173i) q^{88} +(9.21291 + 15.9572i) q^{89} +(5.81180 - 10.0663i) q^{91} +(-2.37484 - 0.864370i) q^{92} +(2.97178 + 2.49362i) q^{94} +(1.77330 + 1.48798i) q^{95} +(-9.50387 - 3.45913i) q^{97} +(3.51968 - 6.09627i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{4} + 6 q^{7}+O(q^{10}) \) 12 * q - 12 * q^4 + 6 * q^7	\( 12 q - 12 q^{4} + 6 q^{7} + 12 q^{10} + 24 q^{13} + 24 q^{19} + 24 q^{22} + 6 q^{25} - 12 q^{28} - 12 q^{31} - 18 q^{34} + 6 q^{37} + 6 q^{40} + 24 q^{43} - 6 q^{46} - 30 q^{49} - 36 q^{52} - 60 q^{55} - 12 q^{58} - 12 q^{61} - 6 q^{64} - 12 q^{67} + 60 q^{70} - 12 q^{73} - 42 q^{76} - 48 q^{79} - 24 q^{82} + 54 q^{85} + 48 q^{88} + 6 q^{94} - 66 q^{97}+O(q^{100}) \) 12 * q - 12 * q^4 + 6 * q^7 + 12 * q^10 + 24 * q^13 + 24 * q^19 + 24 * q^22 + 6 * q^25 - 12 * q^28 - 12 * q^31 - 18 * q^34 + 6 * q^37 + 6 * q^40 + 24 * q^43 - 6 * q^46 - 30 * q^49 - 36 * q^52 - 60 * q^55 - 12 * q^58 - 12 * q^61 - 6 * q^64 - 12 * q^67 + 60 * q^70 - 12 * q^73 - 42 * q^76 - 48 * q^79 - 24 * q^82 + 54 * q^85 + 48 * q^88 + 6 * q^94 - 66 * q^97

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