LMFDB - Embedded newform 729.2.e.m.325.2

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:	$\Q(\zeta_{36})$
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			325.2
Root			$-0.342020 - 0.939693i$ of defining polynomial
Character	$\chi$	$=$	729.325
Dual form			729.2.e.m.406.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.984808 - 0.826352i) q^{2} +(-0.0603074 + 0.342020i) q^{4} +(-0.419550 + 0.152704i) q^{5} +(-0.613341 - 3.47843i) q^{7} +(1.50881 + 2.61334i) q^{8} +O(q^{10})$	\(q+(0.984808 - 0.826352i) q^{2} +(-0.0603074 + 0.342020i) q^{4} +(-0.419550 + 0.152704i) q^{5} +(-0.613341 - 3.47843i) q^{7} +(1.50881 + 2.61334i) q^{8} +(-0.286989 + 0.497079i) q^{10} +(2.61240 + 0.950837i) q^{11} +(2.52094 + 2.11532i) q^{13} +(-3.47843 - 2.91875i) q^{14} +(2.99273 + 1.08926i) q^{16} +(3.51968 - 6.09627i) q^{17} +(2.59240 + 4.49016i) q^{19} +(-0.0269258 - 0.152704i) q^{20} +(3.35844 - 1.22237i) q^{22} +(1.26363 - 7.16637i) q^{23} +(-3.67752 + 3.08580i) q^{25} +4.23065 q^{26} +1.22668 q^{28} +(2.77244 - 2.32635i) q^{29} +(-0.336152 + 1.90641i) q^{31} +(-1.82391 + 0.663848i) q^{32} +(-1.57145 - 8.91215i) q^{34} +(0.788496 + 1.36571i) q^{35} +(1.61334 - 2.79439i) q^{37} +(6.26347 + 2.27972i) q^{38} +(-1.03209 - 0.866025i) q^{40} +(-3.72362 - 3.12449i) q^{41} +(5.41147 + 1.96962i) q^{43} +(-0.482753 + 0.836152i) q^{44} +(-4.67752 - 8.10170i) q^{46} +(0.524005 + 2.97178i) q^{47} +(-5.14543 + 1.87278i) q^{49} +(-1.07169 + 6.07785i) q^{50} +(-0.875515 + 0.734644i) q^{52} +8.77141 q^{53} -1.24123 q^{55} +(8.16490 - 6.85117i) q^{56} +(0.807934 - 4.58202i) q^{58} +(-2.78504 + 1.01367i) q^{59} +(1.36959 + 7.76730i) q^{61} +(1.24432 + 2.15523i) q^{62} +(-4.43242 + 7.67717i) q^{64} +(-1.38068 - 0.502526i) q^{65} +(-7.23055 - 6.06715i) q^{67} +(1.87278 + 1.57145i) q^{68} +(1.90508 + 0.693392i) q^{70} +(-2.65366 + 4.59627i) q^{71} +(0.777189 + 1.34613i) q^{73} +(-0.720317 - 4.08512i) q^{74} +(-1.69207 + 0.615862i) q^{76} +(1.70513 - 9.67024i) q^{77} +(-9.11721 + 7.65025i) q^{79} -1.42193 q^{80} -6.24897 q^{82} +(-12.4538 + 10.4500i) q^{83} +(-0.545759 + 3.09516i) q^{85} +(6.95686 - 2.53209i) q^{86} +(1.45677 + 8.26173i) q^{88} +(-9.21291 - 15.9572i) q^{89} +(5.81180 - 10.0663i) q^{91} +(2.37484 + 0.864370i) q^{92} +(2.97178 + 2.49362i) q^{94} +(-1.77330 - 1.48798i) q^{95} +(-9.50387 - 3.45913i) q^{97} +(-3.51968 + 6.09627i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	−0.224372	−	0.974503i	$-0.572033\pi$
$2$	0.984808	−	0.826352i	0.696364	−	0.584319i	0.920737	+	0.390184i	$0.127589\pi$
$3$		0			0
$3$		0			0
$4$	−0.0603074	+	0.342020i	−0.0301537	+	0.171010i
$5$	−0.419550	+	0.152704i	−0.187628	+	0.0682911i	−0.434126	−	0.900852i	$-0.642943\pi$
$5$	−0.419550	+	0.152704i	−0.187628	+	0.0682911i	0.246497	+	0.969143i	$0.420720\pi$
$6$		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	0.704367	−	0.709836i	$-0.251231\pi$
$11$	2.61240	+	0.950837i	0.787669	+	0.286688i	0.0833024	+	0.996524i	$0.473453\pi$
$12$		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	$-0.507718\pi$
$17$	3.51968	−	6.09627i	0.853648	−	1.47856i	0.877894	−	0.478856i	$-0.158948\pi$
$18$		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	$-0.670293\pi$
$23$	1.26363	−	7.16637i	0.263484	−	1.49429i	0.773317	−	0.634019i	$-0.218596\pi$
$24$		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	−0.347996	−	0.937496i	$-0.613138\pi$
$29$	2.77244	−	2.32635i	0.514829	−	0.431993i	0.862825	+	0.505503i	$0.168693\pi$
$30$		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	0.303918	−	0.952698i	$-0.401705\pi$
$41$	−3.72362	−	3.12449i	−0.581531	−	0.487963i	−0.885450	+	0.464735i	$0.846149\pi$
$42$		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	$0.0150773\pi$
$47$	0.524005	+	2.97178i	0.0764340	+	0.433479i	−0.922444	+	0.386130i	$0.873812\pi$
$48$		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	$-0.294202\pi$
$53$	8.77141			1.20485			0.602423	+	0.798177i	$0.294202\pi$
$54$		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	−0.516885	−	0.856055i	$-0.672909\pi$
$59$	−2.78504	+	1.01367i	−0.362581	+	0.131969i	0.154304	+	0.988023i	$0.450686\pi$
$60$		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	−0.979423	−	0.201819i	$-0.935315\pi$
$71$	−2.65366	+	4.59627i	−0.314931	+	0.545476i	0.664492	+	0.747296i	$0.268648\pi$
$72$		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	$0.628640\pi$
$83$	−12.4538	+	10.4500i	−1.36698	+	1.14703i	−0.973757	+	0.227589i	$0.926916\pi$
$84$		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	$-0.735712\pi$
$89$	−9.21291	−	15.9572i	−0.976567	−	1.69146i	−0.301902	−	0.953339i	$-0.597622\pi$
$90$		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	0.961540	−	0.274665i	$-0.0885669\pi$
$101$	−0.361323	−	2.04916i	−0.0359530	−	0.203899i	−0.997493	+	0.0707655i	$0.977456\pi$
$102$		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	$-0.534468\pi$
$107$	−2.23583			−0.216146			−0.108073	+	0.994143i	$0.534468\pi$
$108$		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	−0.415556	−	0.909568i	$-0.636413\pi$
$113$	−1.58634	+	0.577382i	−0.149231	+	0.0543155i	0.266325	+	0.963883i	$0.414191\pi$
$114$		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	−0.998913	−	0.0466123i	$-0.985157\pi$
$131$	−0.507031	+	2.87551i	−0.0442995	+	0.251235i	0.954614	+	0.297847i	$0.0962686\pi$
$132$		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	−0.782340	−	0.622851i	$-0.785974\pi$
$137$	−3.56764	+	2.99360i	−0.304804	+	0.255761i	0.477537	+	0.878612i	$0.341530\pi$
$138$		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	$0.0326894\pi$
$149$	15.4831	+	12.9918i	1.26842	+	1.06433i	0.273692	+	0.961817i	$0.411755\pi$
$150$		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	0.0121996	−	0.999926i	$-0.496117\pi$
$167$	8.58445	−	3.12449i	0.664285	−	0.241780i	0.652085	+	0.758146i	$0.273894\pi$
$168$		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	0.549747	−	0.835331i	$-0.314724\pi$
$173$	5.70756	+	2.07738i	0.433938	+	0.157940i	−0.115810	+	0.993271i	$0.536946\pi$
$174$		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	−0.607437	−	0.794368i	$-0.707802\pi$
$179$	5.14057	−	8.90373i	0.384224	−	0.665496i	0.991661	+	0.128872i	$0.0411355\pi$
$180$		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	−0.951360	−	0.308081i	$-0.900313\pi$
$191$	−11.2381	+	9.42989i	−0.813161	+	0.682323i	0.138199	+	0.990404i	$0.455869\pi$
$192$		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	0.659220	−	0.751950i	$-0.270887\pi$
$197$	−4.51384	−	7.81820i	−0.321598	−	0.557024i	−0.980818	+	0.194926i	$0.937553\pi$
$198$		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	−0.00900853	−	0.999959i	$-0.502868\pi$
$227$	−9.92388	−	3.61200i	−0.658671	−	0.239737i	−0.649662	+	0.760223i	$0.725090\pi$
$228$		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	−0.579510	−	0.814965i	$-0.696756\pi$
$233$	6.35035	−	10.9991i	0.416025	−	0.720576i	0.995535	+	0.0943883i	$0.0300895\pi$
$234$		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	$-0.883838\pi$
$239$	1.01611	−	5.76264i	0.0657266	−	0.372754i	0.999874	−	0.0158670i	$-0.00505085\pi$
$240$		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	0.739461	−	0.673199i	$-0.235080\pi$
$251$	−3.37895	−	5.85251i	−0.213277	−	0.369407i	−0.952738	+	0.303792i	$0.901747\pi$
$252$		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	0.550538	−	0.834810i	$-0.314422\pi$
$257$	−2.82131	−	2.36736i	−0.175989	−	0.147672i	−0.726527	+	0.687138i	$0.758867\pi$
$258$		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	0.959117	−	0.283009i	$-0.0913325\pi$
$263$	−0.631708	−	3.58260i	−0.0389528	−	0.220912i	−0.998070	+	0.0620963i	$0.980221\pi$
$264$		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	$-0.430685\pi$
$269$	7.08672			0.432085			0.216042	+	0.976384i	$0.430685\pi$
$270$		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	0.877150	−	0.480216i	$-0.159442\pi$
$281$	20.7930	+	7.56805i	1.24041	+	0.451472i	0.363259	+	0.931688i	$0.381664\pi$
$282$		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	$0.238453\pi$
$293$	−3.23091	+	18.3234i	−0.188752	+	1.07047i	−0.921039	+	0.389470i	$0.872658\pi$
$294$		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	0.0817920	−	0.996649i	$-0.473936\pi$
$311$	−15.6162	−	13.1035i	−0.885513	−	0.743034i	−0.967305	+	0.253616i	$0.918380\pi$
$312$		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	0.956495	−	0.291748i	$-0.0942370\pi$
$317$	−0.749571	−	4.25103i	−0.0421001	−	0.238762i	−0.998595	+	0.0529868i	$0.983126\pi$
$318$		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	−0.977280	−	0.211951i	$-0.932018\pi$
$347$	0.252492	−	1.43195i	0.0135545	−	0.0768712i	0.990835	+	0.135080i	$0.0431292\pi$
$348$		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	−0.831733	−	0.555176i	$-0.812651\pi$
$353$	−8.06807	+	6.76991i	−0.429420	+	0.360326i	0.402313	+	0.915502i	$0.368206\pi$
$354$		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	0.992189	−	0.124745i	$-0.0398112\pi$
$359$	7.35273	+	12.7353i	0.388062	+	0.672143i	−0.604127	+	0.796888i	$0.706478\pi$
$360$		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	$0.861087\pi$
$383$	−36.6401	+	13.3359i	−1.87222	+	0.681433i	−0.965945	+	0.258747i	$0.916690\pi$
$384$		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	0.573633	−	0.819112i	$-0.305534\pi$
$389$	9.59619	+	3.49273i	0.486546	+	0.177088i	−0.0870870	+	0.996201i	$0.527756\pi$
$390$		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	$-0.772901\pi$
$401$	3.56916	−	20.2417i	0.178235	−	1.01082i	0.934343	−	0.356375i	$-0.115987\pi$
$402$		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	$-0.939331\pi$
$419$	−27.4079	−	22.9979i	−1.33896	−	1.12352i	−0.357071	−	0.934077i	$-0.616225\pi$
$420$		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	$-0.573355\pi$
$431$	−9.48411			−0.456833			−0.228417	+	0.973563i	$0.573355\pi$
$432$		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	0.0352989	−	0.999377i	$-0.488762\pi$
$443$	−12.2086	−	4.44356i	−0.580048	−	0.211120i	−0.615346	+	0.788257i	$0.710984\pi$
$444$		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	−0.915454	−	0.402424i	$-0.868168\pi$
$449$	−2.31428	+	4.00846i	−0.109218	+	0.189171i	0.806236	+	0.591594i	$0.201501\pi$
$450$		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	$-0.436517\pi$
$461$	25.7180	−	21.5800i	1.19781	−	1.00508i	0.999690	−	0.0249007i	$-0.00792696\pi$
$462$		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	$0.0174685\pi$
$467$	11.8154	+	20.4648i	0.546750	+	0.946999i	−0.451745	+	0.892147i	$0.649198\pi$
$468$		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	0.999209	−	0.0397786i	$-0.0126653\pi$
$479$	1.02108	+	5.79086i	0.0466546	+	0.264591i	−0.952554	+	0.304370i	$0.901554\pi$
$480$		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	−0.978159	−	0.207859i	$-0.933351\pi$
$491$	−35.3176	+	12.8546i	−1.59386	+	0.580119i	−0.615704	+	0.787978i	$0.711128\pi$
$492$		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	−0.995653	−	0.0931429i	$-0.970309\pi$
$503$	−9.35597	+	16.2050i	−0.417162	+	0.722546i	0.578491	+	0.815689i	$0.303642\pi$
$504$		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	$0.215801\pi$
$509$	−3.78000	+	21.4375i	−0.167546	+	0.950199i	−0.946401	+	0.322995i	$0.895310\pi$
$510$		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	0.786332	−	0.617805i	$-0.211978\pi$
$521$	−3.23822	−	5.60876i	−0.141869	−	0.245724i	−0.928200	+	0.372081i	$0.878644\pi$
$522$		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	−0.505029	−	0.863102i	$-0.668518\pi$
$557$	11.6813	−	20.2327i	0.494954	−	0.857286i	0.999983	+	0.00581674i	$0.00185154\pi$
$558$		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	$0.306808\pi$
$563$	−5.84981	+	33.1759i	−0.246540	+	1.39820i	−0.816888	+	0.576796i	$0.804303\pi$
$564$		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	0.00356541	−	0.999994i	$-0.498865\pi$
$569$	23.5910	−	19.7952i	0.988986	−	0.829858i	0.985421	+	0.170136i	$0.0544206\pi$
$570$		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	0.943060	−	0.332624i	$-0.107934\pi$
$587$	−1.37835	−	7.81702i	−0.0568906	−	0.322643i	−0.999950	+	0.00998108i	$0.996823\pi$
$588$		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	$-0.767467\pi$
$593$	−36.2753			−1.48965			−0.744824	+	0.667261i	$0.767467\pi$
$594$		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	0.397478	−	0.917612i	$-0.369885\pi$
$599$	31.6160	−	11.5073i	1.29179	−	0.470174i	0.894315	+	0.447437i	$0.147663\pi$
$600$		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	$-0.859703\pi$
$617$	2.26957	−	12.8714i	0.0913696	−	0.518183i	0.995800	−	0.0915606i	$-0.0291855\pi$
$618$		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	0.970420	−	0.241422i	$-0.0776138\pi$
$641$	−0.608839	−	3.45290i	−0.0240477	−	0.136381i	−0.994468	+	0.105041i	$0.966503\pi$
$642$		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	$-0.480928\pi$
$647$	3.04628			0.119762			0.0598808	+	0.998206i	$0.480928\pi$
$648$		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	−0.838403	−	0.545051i	$-0.816510\pi$
$653$	−28.8837	+	10.5128i	−1.13031	+	0.411397i	−0.291902	+	0.956448i	$0.594288\pi$
$654$		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	−0.346372	−	0.938097i	$-0.612586\pi$
$659$	−31.1827	−	11.3496i	−1.21471	−	0.442117i	−0.868334	+	0.495981i	$0.834809\pi$
$660$		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	−0.427644	−	0.903947i	$-0.640656\pi$
$677$	10.1035	−	8.47787i	0.388310	−	0.325831i	0.815955	+	0.578116i	$0.196212\pi$
$678$		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	0.831900	−	0.554926i	$-0.187254\pi$
$683$	−1.68907	−	2.92556i	−0.0646305	−	0.111943i	−0.896530	+	0.442983i	$0.853920\pi$
$684$		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	$-0.829074\pi$
$701$	−45.5001			−1.71852			−0.859258	+	0.511543i	$0.829074\pi$
$702$		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	$0.538178\pi$
$719$	−24.6591	+	42.7108i	−0.919630	+	1.59285i	−0.799978	+	0.600030i	$0.795155\pi$
$720$		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	$0.0578860\pi$
$743$	36.3186	+	30.4749i	1.33240	+	1.11802i	0.348891	+	0.937163i	$0.386558\pi$
$744$		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	−0.453420	−	0.891297i	$-0.649796\pi$
$761$	−6.28542	+	2.28770i	−0.227846	+	0.0829292i	0.225574	+	0.974226i	$0.427574\pi$
$762$		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	−0.943316	−	0.331895i	$-0.892312\pi$
$773$	−5.12208	+	8.87170i	−0.184228	+	0.319093i	0.759088	+	0.650988i	$0.225645\pi$
$774$		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

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

Introduction

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