LMFDB - Embedded newform 729.2.e.m.406.2

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			406.2
Root			$-0.342020 + 0.939693i$ of defining polynomial
Character	$\chi$	$=$	729.406
Dual form			729.2.e.m.325.2

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

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

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	$-0.127589\pi$
$2$	0.984808	+	0.826352i	0.696364	+	0.584319i	−0.224372	+	0.974503i	$0.572033\pi$
$3$		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	$-0.420720\pi$
$5$	−0.419550	−	0.152704i	−0.187628	−	0.0682911i	−0.434126	+	0.900852i	$0.642943\pi$
$6$		0			0
$7$	−0.613341	+	3.47843i	−0.231821	+	1.31472i	0.617385	+	0.786661i	$0.288192\pi$
$7$	−0.613341	+	3.47843i	−0.231821	+	1.31472i	−0.849206	+	0.528061i	$0.822919\pi$
$8$	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	$-0.473453\pi$
$11$	2.61240	−	0.950837i	0.787669	−	0.286688i	0.704367	+	0.709836i	$0.251231\pi$
$12$		0			0
$13$	2.52094	−	2.11532i	0.699184	−	0.586685i	−0.222357	−	0.974965i	$-0.571375\pi$
$13$	2.52094	−	2.11532i	0.699184	−	0.586685i	0.921541	+	0.388280i	$0.126931\pi$
$14$	−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	0.877894	+	0.478856i	$0.158948\pi$
$17$	3.51968	+	6.09627i	0.853648	+	1.47856i	−0.0242455	+	0.999706i	$0.507718\pi$
$18$		0			0
$19$	2.59240	−	4.49016i	0.594736	−	1.03011i	−0.398848	−	0.917017i	$-0.630590\pi$
$19$	2.59240	−	4.49016i	0.594736	−	1.03011i	0.993584	−	0.113097i	$-0.0360769\pi$
$20$	−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	0.773317	+	0.634019i	$0.218596\pi$
$23$	1.26363	+	7.16637i	0.263484	+	1.49429i	−0.509833	+	0.860273i	$0.670293\pi$
$24$		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	$-0.168693\pi$
$29$	2.77244	+	2.32635i	0.514829	+	0.431993i	−0.347996	+	0.937496i	$0.613138\pi$
$30$		0			0
$31$	−0.336152	−	1.90641i	−0.0603747	−	0.342402i	−1.00000		0.000196783i	$-0.999937\pi$
$31$	−0.336152	−	1.90641i	−0.0603747	−	0.342402i	0.939625	−	0.342205i	$-0.111174\pi$
$32$	−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	0.967624	−	0.252395i	$-0.0812183\pi$
$37$	1.61334	+	2.79439i	0.265232	+	0.459395i	−0.702393	+	0.711790i	$0.747885\pi$
$38$	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	$-0.846149\pi$
$41$	−3.72362	+	3.12449i	−0.581531	+	0.487963i	0.303918	+	0.952698i	$0.401705\pi$
$42$		0			0
$43$	5.41147	−	1.96962i	0.825242	−	0.300364i	0.105337	−	0.994437i	$-0.466408\pi$
$43$	5.41147	−	1.96962i	0.825242	−	0.300364i	0.719905	+	0.694073i	$0.244186\pi$
$44$	−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	−0.922444	−	0.386130i	$-0.873812\pi$
$47$	0.524005	−	2.97178i	0.0764340	−	0.433479i	0.998878	−	0.0473489i	$-0.0150773\pi$
$48$		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	0.154304	−	0.988023i	$-0.450686\pi$
$59$	−2.78504	−	1.01367i	−0.362581	−	0.131969i	−0.516885	+	0.856055i	$0.672909\pi$
$60$		0			0
$61$	1.36959	−	7.76730i	0.175357	−	0.994501i	−0.762373	−	0.647138i	$-0.775966\pi$
$61$	1.36959	−	7.76730i	0.175357	−	0.994501i	0.937731	−	0.347364i	$-0.112923\pi$
$62$	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	−0.966866	−	0.255286i	$-0.917830\pi$
$67$	−7.23055	+	6.06715i	−0.883353	+	0.741221i	0.0835131	+	0.996507i	$0.473386\pi$
$68$	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	$-0.268648\pi$
$71$	−2.65366	−	4.59627i	−0.314931	−	0.545476i	−0.979423	+	0.201819i	$0.935315\pi$
$72$		0			0
$73$	0.777189	−	1.34613i	0.0909631	−	0.157553i	−0.816954	−	0.576703i	$-0.804339\pi$
$73$	0.777189	−	1.34613i	0.0909631	−	0.157553i	0.907917	+	0.419151i	$0.137672\pi$
$74$	−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	−0.0354253	−	0.999372i	$-0.511279\pi$
$79$	−9.11721	−	7.65025i	−1.02577	−	0.860720i	−0.990341	+	0.138652i	$0.955723\pi$
$80$	−1.42193			−0.158977
$81$		0			0
$82$	−6.24897			−0.690083
$83$	−12.4538	−	10.4500i	−1.36698	−	1.14703i	−0.973757	−	0.227589i	$-0.926916\pi$
$83$	−12.4538	−	10.4500i	−1.36698	−	1.14703i	−0.393222	−	0.919443i	$-0.628640\pi$
$84$		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	−0.301902	+	0.953339i	$0.597622\pi$
$89$	−9.21291	+	15.9572i	−0.976567	+	1.69146i	−0.674665	+	0.738125i	$0.735712\pi$
$90$		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	−0.775980	−	0.630758i	$-0.782744\pi$
$97$	−9.50387	+	3.45913i	−0.964972	+	0.351221i	−0.188992	+	0.981979i	$0.560522\pi$
$98$	−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	$-0.977456\pi$
$101$	−0.361323	+	2.04916i	−0.0359530	+	0.203899i	0.961540	+	0.274665i	$0.0885669\pi$
$102$		0			0
$103$	1.36097	+	0.495351i	0.134100	+	0.0488084i	0.408198	−	0.912893i	$-0.366157\pi$
$103$	1.36097	+	0.495351i	0.134100	+	0.0488084i	−0.274098	+	0.961702i	$0.588379\pi$
$104$	−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	0.266325	−	0.963883i	$-0.414191\pi$
$113$	−1.58634	−	0.577382i	−0.149231	−	0.0543155i	−0.415556	+	0.909568i	$0.636413\pi$
$114$		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	−0.800635	−	0.599153i	$-0.795504\pi$
$127$	1.33615	−	2.31428i	0.118564	−	0.205359i	0.919199	+	0.393793i	$0.128837\pi$
$128$	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	$-0.0962686\pi$
$131$	−0.507031	−	2.87551i	−0.0442995	−	0.251235i	−0.998913	+	0.0466123i	$0.985157\pi$
$132$		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	$-0.341530\pi$
$137$	−3.56764	−	2.99360i	−0.304804	−	0.255761i	−0.782340	+	0.622851i	$0.785974\pi$
$138$		0			0
$139$	−1.38965	−	7.88111i	−0.117869	−	0.668467i	−0.985290	−	0.170892i	$-0.945335\pi$
$139$	−1.38965	−	7.88111i	−0.117869	−	0.668467i	0.867421	−	0.497575i	$-0.165776\pi$
$140$	−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	0.273692	−	0.961817i	$-0.411755\pi$
$149$	15.4831	−	12.9918i	1.26842	−	1.06433i	0.994731	−	0.102516i	$-0.0326894\pi$
$150$		0			0
$151$	−6.29813	+	2.29233i	−0.512535	+	0.186547i	−0.585323	−	0.810800i	$-0.699032\pi$
$151$	−6.29813	+	2.29233i	−0.512535	+	0.186547i	0.0727885	+	0.997347i	$0.476810\pi$
$152$	−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	0.134533	−	0.990909i	$-0.457046\pi$
$157$	−5.00387	−	1.82126i	−0.399352	−	0.145352i	−0.533886	+	0.845557i	$0.679269\pi$
$158$	−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	$-0.273894\pi$
$167$	8.58445	+	3.12449i	0.664285	+	0.241780i	0.0121996	+	0.999926i	$0.496117\pi$
$168$		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	$-0.536946\pi$
$173$	5.70756	−	2.07738i	0.433938	−	0.157940i	0.549747	+	0.835331i	$0.314724\pi$
$174$		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	$-0.0411355\pi$
$179$	5.14057	+	8.90373i	0.384224	+	0.665496i	−0.607437	+	0.794368i	$0.707802\pi$
$180$		0			0
$181$	11.5706	−	20.0408i	0.860034	−	1.48962i	−0.0118609	−	0.999930i	$-0.503776\pi$
$181$	11.5706	−	20.0408i	0.860034	−	1.48962i	0.871895	−	0.489693i	$-0.162891\pi$
$182$	−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	$-0.455869\pi$
$191$	−11.2381	−	9.42989i	−0.813161	−	0.682323i	−0.951360	+	0.308081i	$0.900313\pi$
$192$		0			0
$193$	4.07057	+	23.0854i	0.293006	+	1.66172i	0.675196	+	0.737638i	$0.264059\pi$
$193$	4.07057	+	23.0854i	0.293006	+	1.66172i	−0.382190	+	0.924084i	$0.624830\pi$
$194$	−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	$-0.937553\pi$
$197$	−4.51384	+	7.81820i	−0.321598	+	0.557024i	0.659220	+	0.751950i	$0.270887\pi$
$198$		0			0
$199$	−1.30200	−	2.25514i	−0.0922966	−	0.159862i	0.816181	−	0.577797i	$-0.196087\pi$
$199$	−1.30200	−	2.25514i	−0.0922966	−	0.159862i	−0.908477	+	0.417935i	$0.862754\pi$
$200$	−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	0.811686	−	0.584094i	$-0.198550\pi$
$211$	15.3687	+	5.59375i	1.05803	+	0.385090i	0.246339	+	0.969184i	$0.420772\pi$
$212$	−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	−0.955686	−	0.294389i	$-0.904884\pi$
$223$	0.642903	−	3.64609i	0.0430520	−	0.244160i	0.998738	+	0.0502288i	$0.0159950\pi$
$224$	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	$-0.725090\pi$
$227$	−9.92388	+	3.61200i	−0.658671	+	0.239737i	−0.00900853	+	0.999959i	$0.502868\pi$
$228$		0			0
$229$	10.3610	−	8.69388i	0.684672	−	0.574508i	−0.232695	−	0.972550i	$-0.574755\pi$
$229$	10.3610	−	8.69388i	0.684672	−	0.574508i	0.917367	+	0.398042i	$0.130310\pi$
$230$	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	$-0.0300895\pi$
$233$	6.35035	+	10.9991i	0.416025	+	0.720576i	−0.579510	+	0.814965i	$0.696756\pi$
$234$		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	0.999874	+	0.0158670i	$0.00505085\pi$
$239$	1.01611	+	5.76264i	0.0657266	+	0.372754i	−0.934147	+	0.356887i	$0.883838\pi$
$240$		0			0
$241$	−6.54189	−	5.48930i	−0.421400	−	0.353597i	0.407295	−	0.913297i	$-0.366472\pi$
$241$	−6.54189	−	5.48930i	−0.421400	−	0.353597i	−0.828695	+	0.559700i	$0.810916\pi$
$242$	−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	$-0.901747\pi$
$251$	−3.37895	+	5.85251i	−0.213277	+	0.369407i	0.739461	+	0.673199i	$0.235080\pi$
$252$		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	$-0.758867\pi$
$257$	−2.82131	+	2.36736i	−0.175989	+	0.147672i	0.550538	+	0.834810i	$0.314422\pi$
$258$		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	$-0.980221\pi$
$263$	−0.631708	+	3.58260i	−0.0389528	+	0.220912i	0.959117	+	0.283009i	$0.0913325\pi$
$264$		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	0.822468	+	0.568812i	$0.192597\pi$
$277$	−2.41235	+	13.6811i	−0.144944	+	0.822019i	−0.967412	+	0.253208i	$0.918514\pi$
$278$	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	$-0.381664\pi$
$281$	20.7930	−	7.56805i	1.24041	−	0.451472i	0.877150	+	0.480216i	$0.159442\pi$
$282$		0			0
$283$	−18.1800	+	15.2549i	−1.08069	+	0.906808i	−0.995978	−	0.0895975i	$-0.971442\pi$
$283$	−18.1800	+	15.2549i	−1.08069	+	0.906808i	−0.0847134	+	0.996405i	$0.526997\pi$
$284$	−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	−0.921039	−	0.389470i	$-0.872658\pi$
$293$	−3.23091	−	18.3234i	−0.188752	−	1.07047i	0.732287	−	0.680996i	$-0.238453\pi$
$294$		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	−0.993957	−	0.109773i	$-0.964988\pi$
$307$	−10.3735	−	17.9674i	−0.592044	−	1.02545i	0.401912	−	0.915678i	$-0.368346\pi$
$308$	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	$-0.918380\pi$
$311$	−15.6162	+	13.1035i	−0.885513	+	0.743034i	0.0817920	+	0.996649i	$0.473936\pi$
$312$		0			0
$313$	28.0412	−	10.2062i	1.58498	−	0.576886i	0.608701	−	0.793400i	$-0.291691\pi$
$313$	28.0412	−	10.2062i	1.58498	−	0.576886i	0.976280	+	0.216514i	$0.0694686\pi$
$314$	−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	$-0.983126\pi$
$317$	−0.749571	+	4.25103i	−0.0421001	+	0.238762i	0.956495	+	0.291748i	$0.0942370\pi$
$318$		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	−0.995564	−	0.0940884i	$-0.970006\pi$
$331$	−0.506863	+	2.87457i	−0.0278597	+	0.158000i	0.967704	+	0.252089i	$0.0811175\pi$
$332$	−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	−0.289659	−	0.957130i	$-0.593542\pi$
$337$	11.0628	−	9.28282i	0.602631	−	0.505667i	0.892290	+	0.451462i	$0.149098\pi$
$338$	−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	$-0.0431292\pi$
$347$	0.252492	+	1.43195i	0.0135545	+	0.0768712i	−0.977280	+	0.211951i	$0.932018\pi$
$348$		0			0
$349$	−21.1288	−	17.7292i	−1.13100	−	0.949022i	−0.131893	−	0.991264i	$-0.542105\pi$
$349$	−21.1288	−	17.7292i	−1.13100	−	0.949022i	−0.999107	+	0.0422424i	$0.986550\pi$
$350$	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	$-0.368206\pi$
$353$	−8.06807	−	6.76991i	−0.429420	−	0.360326i	−0.831733	+	0.555176i	$0.812651\pi$
$354$		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	$-0.706478\pi$
$359$	7.35273	−	12.7353i	0.388062	−	0.672143i	0.992189	+	0.124745i	$0.0398112\pi$
$360$		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	0.240016	−	0.970769i	$-0.422847\pi$
$367$	20.0744	−	7.30650i	1.04788	−	0.381396i	0.807861	+	0.589373i	$0.200625\pi$
$368$	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	−0.273193	−	0.961959i	$-0.588080\pi$
$373$	−21.2601	−	7.73805i	−1.10081	−	0.400661i	−0.827614	+	0.561298i	$0.810302\pi$
$374$	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	−0.965945	−	0.258747i	$-0.916690\pi$
$383$	−36.6401	−	13.3359i	−1.87222	−	0.681433i	−0.906276	−	0.422686i	$-0.861087\pi$
$384$		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	$-0.527756\pi$
$389$	9.59619	−	3.49273i	0.486546	−	0.177088i	0.573633	+	0.819112i	$0.305534\pi$
$390$		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	−0.851329	−	0.524632i	$-0.824203\pi$
$397$	0.571452	−	0.989783i	0.0286803	−	0.0496758i	0.880009	+	0.474956i	$0.157536\pi$
$398$	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	0.934343	+	0.356375i	$0.115987\pi$
$401$	3.56916	+	20.2417i	0.178235	+	1.01082i	−0.756108	+	0.654447i	$0.772901\pi$
$402$		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	−0.999613	−	0.0278020i	$-0.991149\pi$
$409$	−1.41147	−	8.00487i	−0.0697929	−	0.395815i	0.929821	−	0.368013i	$-0.119962\pi$
$410$	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	−0.357071	+	0.934077i	$0.616225\pi$
$419$	−27.4079	+	22.9979i	−1.33896	+	1.12352i	−0.981891	+	0.189446i	$0.939331\pi$
$420$		0			0
$421$	12.3277	−	4.48691i	0.600815	−	0.218679i	−0.0236644	−	0.999720i	$-0.507533\pi$
$421$	12.3277	−	4.48691i	0.600815	−	0.218679i	0.624480	+	0.781041i	$0.285311\pi$
$422$	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	0.819818	+	0.572624i	$0.194074\pi$
$439$	−3.06758	+	17.3971i	−0.146408	+	0.830319i	−0.966226	+	0.257696i	$0.917037\pi$
$440$	−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	$-0.710984\pi$
$443$	−12.2086	+	4.44356i	−0.580048	+	0.211120i	0.0352989	+	0.999377i	$0.488762\pi$
$444$		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	$-0.201501\pi$
$449$	−2.31428	−	4.00846i	−0.109218	−	0.189171i	−0.915454	+	0.402424i	$0.868168\pi$
$450$		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	0.932031	−	0.362377i	$-0.118035\pi$
$457$	15.7554	+	13.2203i	0.737005	+	0.618421i	−0.195026	+	0.980798i	$0.562479\pi$
$458$	17.3878			0.812477
$459$		0			0
$460$	−1.12836			−0.0526098
$461$	25.7180	+	21.5800i	1.19781	+	1.00508i	0.999690	+	0.0249007i	$0.00792696\pi$
$461$	25.7180	+	21.5800i	1.19781	+	1.00508i	0.198117	+	0.980178i	$0.436517\pi$
$462$		0			0
$463$	2.28018	+	12.9316i	0.105969	+	0.600980i	0.990829	+	0.135123i	$0.0431429\pi$
$463$	2.28018	+	12.9316i	0.105969	+	0.600980i	−0.884860	+	0.465857i	$0.845746\pi$
$464$	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	−0.451745	−	0.892147i	$-0.649198\pi$
$467$	11.8154	−	20.4648i	0.546750	−	0.946999i	0.998495	−	0.0548513i	$-0.0174685\pi$
$468$		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	$-0.901554\pi$
$479$	1.02108	−	5.79086i	0.0466546	−	0.264591i	0.999209	+	0.0397786i	$0.0126653\pi$
$480$		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	$-0.711128\pi$
$491$	−35.3176	−	12.8546i	−1.59386	−	0.580119i	−0.978159	+	0.207859i	$0.933351\pi$
$492$		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	0.157584	−	0.987506i	$-0.449630\pi$
$499$	25.8555	−	21.6953i	1.15745	−	0.971217i	0.999867	+	0.0162886i	$0.00518506\pi$
$500$	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	$-0.303642\pi$
$503$	−9.35597	−	16.2050i	−0.417162	−	0.722546i	−0.995653	+	0.0931429i	$0.970309\pi$
$504$		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	−0.946401	−	0.322995i	$-0.895310\pi$
$509$	−3.78000	−	21.4375i	−0.167546	−	0.950199i	0.778855	−	0.627204i	$-0.215801\pi$
$510$		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	$-0.878644\pi$
$521$	−3.23822	+	5.60876i	−0.141869	+	0.245724i	0.786332	+	0.617805i	$0.211978\pi$
$522$		0			0
$523$	5.43629	+	9.41593i	0.237712	+	0.411730i	0.960057	−	0.279803i	$-0.0902691\pi$
$523$	5.43629	+	9.41593i	0.237712	+	0.411730i	−0.722345	+	0.691533i	$0.756936\pi$
$524$	−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	−0.624020	−	0.781408i	$-0.714502\pi$
$547$	5.37046	−	30.4574i	0.229624	−	1.30226i	0.853644	−	0.520856i	$-0.174387\pi$
$548$	−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	$-0.00185154\pi$
$557$	11.6813	+	20.2327i	0.494954	+	0.857286i	−0.505029	+	0.863102i	$0.668518\pi$
$558$		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	−0.816888	−	0.576796i	$-0.804303\pi$
$563$	−5.84981	−	33.1759i	−0.246540	−	1.39820i	0.570348	−	0.821403i	$-0.306808\pi$
$564$		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	$-0.0544206\pi$
$569$	23.5910	+	19.7952i	0.988986	+	0.829858i	0.00356541	+	0.999994i	$0.498865\pi$
$570$		0			0
$571$	−5.18779	−	29.4214i	−0.217102	−	1.23125i	−0.877221	−	0.480086i	$-0.840605\pi$
$571$	−5.18779	−	29.4214i	−0.217102	−	1.23125i	0.660119	−	0.751161i	$-0.270506\pi$
$572$	−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	0.811644	−	0.584152i	$-0.198573\pi$
$577$	−2.40373	−	4.16339i	−0.100069	−	0.173324i	−0.911713	+	0.410828i	$0.865240\pi$
$578$	−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	$-0.996823\pi$
$587$	−1.37835	+	7.81702i	−0.0568906	+	0.322643i	0.943060	+	0.332624i	$0.107934\pi$
$588$		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	0.894315	−	0.447437i	$-0.147663\pi$
$599$	31.6160	+	11.5073i	1.29179	+	0.470174i	0.397478	+	0.917612i	$0.369885\pi$
$600$		0			0
$601$	−0.517074	+	2.93247i	−0.0210919	+	0.119618i	−0.993536	−	0.113519i	$-0.963788\pi$
$601$	−0.517074	+	2.93247i	−0.0210919	+	0.119618i	0.972444	+	0.233137i	$0.0748990\pi$
$602$	−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	−0.852791	−	0.522253i	$-0.825092\pi$
$607$	−11.9875	+	10.0587i	−0.486558	+	0.408271i	0.366233	+	0.930523i	$0.380647\pi$
$608$	−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	−0.855052	−	0.518543i	$-0.826475\pi$
$613$	0.533433	−	0.923933i	0.0215452	−	0.0373173i	0.876597	+	0.481225i	$0.159808\pi$
$614$	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	0.995800	+	0.0915606i	$0.0291855\pi$
$617$	2.26957	+	12.8714i	0.0913696	+	0.518183i	−0.904430	+	0.426622i	$0.859703\pi$
$618$		0			0
$619$	15.7173	+	13.1884i	0.631734	+	0.530087i	0.901467	−	0.432848i	$-0.142491\pi$
$619$	15.7173	+	13.1884i	0.631734	+	0.530087i	−0.269734	+	0.962935i	$0.586936\pi$
$620$	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	0.950216	−	0.311592i	$-0.100862\pi$
$631$	5.15611	+	8.93064i	0.205261	+	0.355523i	−0.744955	+	0.667115i	$0.767529\pi$
$632$	−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	$-0.966503\pi$
$641$	−0.608839	+	3.45290i	−0.0240477	+	0.136381i	0.970420	+	0.241422i	$0.0776138\pi$
$642$		0			0
$643$	−29.6489	−	10.7913i	−1.16924	−	0.425568i	−0.316849	−	0.948476i	$-0.602625\pi$
$643$	−29.6489	−	10.7913i	−1.16924	−	0.425568i	−0.852389	+	0.522908i	$0.824847\pi$
$644$	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	−0.291902	−	0.956448i	$-0.594288\pi$
$653$	−28.8837	−	10.5128i	−1.13031	−	0.411397i	−0.838403	+	0.545051i	$0.816510\pi$
$654$		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	$-0.834809\pi$
$659$	−31.1827	+	11.3496i	−1.21471	+	0.442117i	−0.346372	+	0.938097i	$0.612586\pi$
$660$		0			0
$661$	−11.4199	+	9.58246i	−0.444184	+	0.372714i	−0.837272	−	0.546786i	$-0.815851\pi$
$661$	−11.4199	+	9.58246i	−0.444184	+	0.372714i	0.393088	+	0.919501i	$0.371407\pi$
$662$	−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	0.738807	−	0.673917i	$-0.235390\pi$
$673$	5.27719	+	4.42809i	0.203421	+	0.170690i	−0.535386	+	0.844607i	$0.679834\pi$
$674$	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	$-0.196212\pi$
$677$	10.1035	+	8.47787i	0.388310	+	0.325831i	−0.427644	+	0.903947i	$0.640656\pi$
$678$		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	$-0.853920\pi$
$683$	−1.68907	+	2.92556i	−0.0646305	+	0.111943i	0.831900	+	0.554926i	$0.187254\pi$
$684$		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	−0.724742	−	0.689020i	$-0.758041\pi$
$691$	−22.0030	+	8.00843i	−0.837033	+	0.304655i	−0.112291	+	0.993675i	$0.535819\pi$
$692$	−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	−0.552218	−	0.833700i	$-0.686218\pi$
$709$	6.70574	−	38.0301i	0.251839	−	1.42825i	0.804057	−	0.594552i	$-0.202670\pi$
$710$	−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	−0.799978	−	0.600030i	$-0.795155\pi$
$719$	−24.6591	−	42.7108i	−0.919630	−	1.59285i	−0.119652	−	0.992816i	$-0.538178\pi$
$720$		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	0.0560155	−	0.998430i	$-0.482160\pi$
$727$	−24.7390	−	20.7585i	−0.917519	−	0.769890i	−0.973535	+	0.228540i	$0.926605\pi$
$728$	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	0.800828	+	0.598894i	$0.204393\pi$
$733$	6.85323	+	38.8666i	0.253130	+	1.43557i	−0.547699	+	0.836676i	$0.684496\pi$
$734$	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	−0.983259	−	0.182215i	$-0.941673\pi$
$739$	−17.6545	−	30.5785i	−0.649432	−	1.12485i	0.333827	−	0.942634i	$-0.391660\pi$
$740$	−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	0.348891	−	0.937163i	$-0.386558\pi$
$743$	36.3186	−	30.4749i	1.33240	−	1.11802i	0.983510	−	0.180854i	$-0.0578860\pi$
$744$		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	0.490523	−	0.871428i	$-0.336806\pi$
$751$	8.38965	+	3.05358i	0.306143	+	0.111427i	−0.184381	+	0.982855i	$0.559028\pi$
$752$	−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	$-0.427574\pi$
$761$	−6.28542	−	2.28770i	−0.227846	−	0.0829292i	−0.453420	+	0.891297i	$0.649796\pi$
$762$		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	−0.889228	−	0.457464i	$-0.848758\pi$
$769$	−16.4479	+	13.8014i	−0.593126	+	0.497692i	0.296102	+	0.955156i	$0.404313\pi$
$770$	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	$-0.225645\pi$
$773$	−5.12208	−	8.87170i	−0.184228	−	0.319093i	−0.943316	+	0.331895i	$0.892312\pi$
$774$		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
$780$

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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