LMFDB - Embedded newform 729.2.e.b.406.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("729.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 243)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			406.1
Root			$0.939693 - 0.342020i$ of defining polynomial
Character	$\chi$	$=$	729.406
Dual form			729.2.e.b.325.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.673648 - 0.565258i) q^{2} +(-0.213011 - 1.20805i) q^{4} +(-3.64543 - 1.32683i) q^{5} +(-0.379385 + 2.15160i) q^{7} +(-1.41875 + 2.45734i) q^{8} +O(q^{10})$	\(q+(-0.673648 - 0.565258i) q^{2} +(-0.213011 - 1.20805i) q^{4} +(-3.64543 - 1.32683i) q^{5} +(-0.379385 + 2.15160i) q^{7} +(-1.41875 + 2.45734i) q^{8} +(1.70574 + 2.95442i) q^{10} +(-0.152704 + 0.0555796i) q^{11} +(1.84730 - 1.55007i) q^{13} +(1.47178 - 1.23497i) q^{14} +(0.0393628 - 0.0143269i) q^{16} +(-1.50000 - 2.59808i) q^{17} +(-1.79813 + 3.11446i) q^{19} +(-0.826352 + 4.68647i) q^{20} +(0.134285 + 0.0488759i) q^{22} +(0.492726 + 2.79439i) q^{23} +(7.69846 + 6.45978i) q^{25} -2.12061 q^{26} +2.68004 q^{28} +(5.14543 + 4.31753i) q^{29} +(-0.900330 - 5.10602i) q^{31} +(5.29813 + 1.92836i) q^{32} +(-0.458111 + 2.59808i) q^{34} +(4.23783 - 7.34013i) q^{35} +(3.31908 + 5.74881i) q^{37} +(2.97178 - 1.08164i) q^{38} +(8.43242 - 7.07564i) q^{40} +(-4.44356 + 3.72859i) q^{41} +(5.85117 - 2.12965i) q^{43} +(0.0996702 + 0.172634i) q^{44} +(1.24763 - 2.16095i) q^{46} +(1.28446 - 7.28455i) q^{47} +(2.09240 + 0.761570i) q^{49} +(-1.53462 - 8.70323i) q^{50} +(-2.26604 - 1.90144i) q^{52} +1.40373 q^{53} +0.630415 q^{55} +(-4.74897 - 3.98486i) q^{56} +(-1.02569 - 5.81699i) q^{58} +(4.81180 + 1.75135i) q^{59} +(-0.656574 + 3.72362i) q^{61} +(-2.27972 + 3.94858i) q^{62} +(-2.52094 - 4.36640i) q^{64} +(-8.79086 + 3.19961i) q^{65} +(-4.49273 + 3.76984i) q^{67} +(-2.81908 + 2.36549i) q^{68} +(-7.00387 + 2.54920i) q^{70} +(7.65910 + 13.2660i) q^{71} +(-4.34002 + 7.51714i) q^{73} +(1.01367 - 5.74881i) q^{74} +(4.14543 + 1.50881i) q^{76} +(-0.0616516 - 0.349643i) q^{77} +(-0.971782 - 0.815422i) q^{79} -0.162504 q^{80} +5.10101 q^{82} +(-6.49273 - 5.44804i) q^{83} +(2.02094 + 11.4613i) q^{85} +(-5.14543 - 1.87278i) q^{86} +(0.0800699 - 0.454099i) q^{88} +(-3.86097 + 6.68739i) q^{89} +(2.63429 + 4.56272i) q^{91} +(3.27079 - 1.19047i) q^{92} +(-4.98293 + 4.18117i) q^{94} +(10.6873 - 8.96773i) q^{95} +(3.67112 - 1.33618i) q^{97} +(-0.979055 - 1.69577i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} - 9 q^{4} - 6 q^{5} + 9 q^{7} - 6 q^{8}+O(q^{10}) $ 6 * q - 3 * q^2 - 9 * q^4 - 6 * q^5 + 9 * q^7 - 6 * q^8	$ 6 q - 3 q^{2} - 9 q^{4} - 6 q^{5} + 9 q^{7} - 6 q^{8} - 3 q^{11} + 9 q^{13} - 6 q^{14} + 9 q^{16} - 9 q^{17} + 3 q^{19} - 6 q^{20} - 9 q^{22} - 15 q^{23} + 18 q^{25} - 24 q^{26} - 24 q^{28} + 15 q^{29} + 9 q^{31} + 18 q^{32} - 9 q^{34} + 6 q^{35} + 3 q^{37} + 3 q^{38} + 27 q^{40} + 3 q^{41} + 9 q^{43} + 15 q^{44} - 9 q^{46} + 15 q^{47} + 9 q^{49} + 15 q^{50} - 9 q^{52} + 36 q^{53} + 18 q^{55} - 3 q^{56} - 36 q^{58} - 6 q^{59} + 18 q^{61} + 12 q^{62} - 12 q^{64} - 21 q^{65} - 9 q^{67} - 18 q^{70} + 9 q^{71} - 6 q^{73} - 15 q^{74} + 9 q^{76} + 3 q^{77} + 9 q^{79} - 6 q^{80} + 36 q^{82} - 21 q^{83} + 9 q^{85} - 15 q^{86} + 9 q^{88} + 6 q^{91} + 48 q^{92} - 9 q^{94} + 42 q^{95} + 36 q^{97} - 9 q^{98}+O(q^{100}) $ 6 * q - 3 * q^2 - 9 * q^4 - 6 * q^5 + 9 * q^7 - 6 * q^8 - 3 * q^11 + 9 * q^13 - 6 * q^14 + 9 * q^16 - 9 * q^17 + 3 * q^19 - 6 * q^20 - 9 * q^22 - 15 * q^23 + 18 * q^25 - 24 * q^26 - 24 * q^28 + 15 * q^29 + 9 * q^31 + 18 * q^32 - 9 * q^34 + 6 * q^35 + 3 * q^37 + 3 * q^38 + 27 * q^40 + 3 * q^41 + 9 * q^43 + 15 * q^44 - 9 * q^46 + 15 * q^47 + 9 * q^49 + 15 * q^50 - 9 * q^52 + 36 * q^53 + 18 * q^55 - 3 * q^56 - 36 * q^58 - 6 * q^59 + 18 * q^61 + 12 * q^62 - 12 * q^64 - 21 * q^65 - 9 * q^67 - 18 * q^70 + 9 * q^71 - 6 * q^73 - 15 * q^74 + 9 * q^76 + 3 * q^77 + 9 * q^79 - 6 * q^80 + 36 * q^82 - 21 * q^83 + 9 * q^85 - 15 * q^86 + 9 * q^88 + 6 * q^91 + 48 * q^92 - 9 * q^94 + 42 * q^95 + 36 * q^97 - 9 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.673648	−	0.565258i	−0.476341	−	0.399698i	0.372760	−	0.927928i	$-0.378411\pi$
$2$	−0.673648	−	0.565258i	−0.476341	−	0.399698i	−0.849101	+	0.528230i	$0.822856\pi$
$3$		0			0
$3$		0			0
$4$	−0.213011	−	1.20805i	−0.106506	−	0.604023i
$5$	−3.64543	−	1.32683i	−1.63029	−	0.593375i	−0.644984	−	0.764196i	$-0.723136\pi$
$5$	−3.64543	−	1.32683i	−1.63029	−	0.593375i	−0.985302	+	0.170821i	$0.945358\pi$
$6$		0			0
$7$	−0.379385	+	2.15160i	−0.143394	+	0.813229i	0.825248	+	0.564770i	$0.191035\pi$
$7$	−0.379385	+	2.15160i	−0.143394	+	0.813229i	−0.968643	+	0.248459i	$0.920076\pi$
$8$	−1.41875	+	2.45734i	−0.501603	+	0.868802i
$9$		0			0
$10$	1.70574	+	2.95442i	0.539401	+	0.934271i
$11$	−0.152704	+	0.0555796i	−0.0460419	+	0.0167579i	−0.364938	−	0.931032i	$-0.618910\pi$
$11$	−0.152704	+	0.0555796i	−0.0460419	+	0.0167579i	0.318897	+	0.947790i	$0.396688\pi$
$12$		0			0
$13$	1.84730	−	1.55007i	0.512348	−	0.429911i	−0.349607	−	0.936897i	$-0.613685\pi$
$13$	1.84730	−	1.55007i	0.512348	−	0.429911i	0.861954	+	0.506986i	$0.169240\pi$
$14$	1.47178	−	1.23497i	0.393350	−	0.330060i
$15$		0			0
$16$	0.0393628	−	0.0143269i	0.00984071	−	0.00358173i
$17$	−1.50000	−	2.59808i	−0.363803	−	0.630126i	0.624780	−	0.780801i	$-0.285189\pi$
$17$	−1.50000	−	2.59808i	−0.363803	−	0.630126i	−0.988583	+	0.150675i	$0.951855\pi$
$18$		0			0
$19$	−1.79813	+	3.11446i	−0.412520	+	0.714506i	−0.995165	−	0.0982214i	$-0.968685\pi$
$19$	−1.79813	+	3.11446i	−0.412520	+	0.714506i	0.582645	+	0.812727i	$0.302018\pi$
$20$	−0.826352	+	4.68647i	−0.184778	+	1.04793i
$21$		0			0
$22$	0.134285	+	0.0488759i	0.0286297	+	0.0104204i
$23$	0.492726	+	2.79439i	0.102740	+	0.582670i	0.992099	+	0.125459i	$0.0400404\pi$
$23$	0.492726	+	2.79439i	0.102740	+	0.582670i	−0.889358	+	0.457211i	$0.848848\pi$
$24$		0			0
$25$	7.69846	+	6.45978i	1.53969	+	1.29196i
$26$	−2.12061			−0.415887
$27$		0			0
$28$	2.68004			0.506481
$29$	5.14543	+	4.31753i	0.955482	+	0.801745i	0.980212	−	0.197949i	$-0.0634281\pi$
$29$	5.14543	+	4.31753i	0.955482	+	0.801745i	−0.0247300	+	0.999694i	$0.507873\pi$
$30$		0			0
$31$	−0.900330	−	5.10602i	−0.161704	−	0.917069i	−0.952398	−	0.304857i	$-0.901391\pi$
$31$	−0.900330	−	5.10602i	−0.161704	−	0.917069i	0.790694	−	0.612212i	$-0.209720\pi$
$32$	5.29813	+	1.92836i	0.936587	+	0.340890i
$33$		0			0
$34$	−0.458111	+	2.59808i	−0.0785654	+	0.445566i
$35$	4.23783	−	7.34013i	0.716323	−	1.24071i
$36$		0			0
$37$	3.31908	+	5.74881i	0.545653	+	0.945099i	0.998566	+	0.0535438i	$0.0170517\pi$
$37$	3.31908	+	5.74881i	0.545653	+	0.945099i	−0.452912	+	0.891555i	$0.649615\pi$
$38$	2.97178	−	1.08164i	0.482087	−	0.175465i
$39$		0			0
$40$	8.43242	−	7.07564i	1.33328	−	1.11876i
$41$	−4.44356	+	3.72859i	−0.693968	+	0.582308i	−0.920050	−	0.391800i	$-0.871853\pi$
$41$	−4.44356	+	3.72859i	−0.693968	+	0.582308i	0.226082	+	0.974108i	$0.427408\pi$
$42$		0			0
$43$	5.85117	−	2.12965i	0.892295	−	0.324769i	0.145134	−	0.989412i	$-0.453639\pi$
$43$	5.85117	−	2.12965i	0.892295	−	0.324769i	0.747161	+	0.664643i	$0.231417\pi$
$44$	0.0996702	+	0.172634i	0.0150259	+	0.0260255i
$45$		0			0
$46$	1.24763	−	2.16095i	0.183952	−	0.318615i
$47$	1.28446	−	7.28455i	0.187358	−	1.06256i	−0.735530	−	0.677492i	$-0.763067\pi$
$47$	1.28446	−	7.28455i	0.187358	−	1.06256i	0.922888	−	0.385069i	$-0.125822\pi$
$48$		0			0
$49$	2.09240	+	0.761570i	0.298914	+	0.108796i
$50$	−1.53462	−	8.70323i	−0.217027	−	1.23082i
$51$		0			0
$52$	−2.26604	−	1.90144i	−0.314244	−	0.263682i
$53$	1.40373			0.192818			0.0964088	−	0.995342i	$-0.469264\pi$
$53$	1.40373			0.192818			0.0964088	+	0.995342i	$0.469264\pi$
$54$		0			0
$55$	0.630415			0.0850051
$56$	−4.74897	−	3.98486i	−0.634608	−	0.532499i
$57$		0			0
$58$	−1.02569	−	5.81699i	−0.134680	−	0.763808i
$59$	4.81180	+	1.75135i	0.626444	+	0.228007i	0.635683	−	0.771951i	$-0.280719\pi$
$59$	4.81180	+	1.75135i	0.626444	+	0.228007i	−0.00923910	+	0.999957i	$0.502941\pi$
$60$		0			0
$61$	−0.656574	+	3.72362i	−0.0840657	+	0.476760i	0.913489	+	0.406864i	$0.133378\pi$
$61$	−0.656574	+	3.72362i	−0.0840657	+	0.476760i	−0.997554	+	0.0698959i	$0.977733\pi$
$62$	−2.27972	+	3.94858i	−0.289524	+	0.501470i
$63$		0			0
$64$	−2.52094	−	4.36640i	−0.315118	−	0.545801i
$65$	−8.79086	+	3.19961i	−1.09037	+	0.396863i
$66$		0			0
$67$	−4.49273	+	3.76984i	−0.548874	+	0.460560i	−0.874559	−	0.484918i	$-0.838849\pi$
$67$	−4.49273	+	3.76984i	−0.548874	+	0.460560i	0.325686	+	0.945478i	$0.394405\pi$
$68$	−2.81908	+	2.36549i	−0.341863	+	0.286857i
$69$		0			0
$70$	−7.00387	+	2.54920i	−0.837123	+	0.304688i
$71$	7.65910	+	13.2660i	0.908968	+	1.57438i	0.815500	+	0.578756i	$0.196462\pi$
$71$	7.65910	+	13.2660i	0.908968	+	1.57438i	0.0934675	+	0.995622i	$0.470205\pi$
$72$		0			0
$73$	−4.34002	+	7.51714i	−0.507961	+	0.879815i	0.491996	+	0.870597i	$0.336267\pi$
$73$	−4.34002	+	7.51714i	−0.507961	+	0.879815i	−0.999958	+	0.00921733i	$0.997066\pi$
$74$	1.01367	−	5.74881i	0.117837	−	0.668286i
$75$		0			0
$76$	4.14543	+	1.50881i	0.475513	+	0.173073i
$77$	−0.0616516	−	0.349643i	−0.00702585	−	0.0398456i
$78$		0			0
$79$	−0.971782	−	0.815422i	−0.109334	−	0.0917421i	0.586482	−	0.809962i	$-0.300513\pi$
$79$	−0.971782	−	0.815422i	−0.109334	−	0.0917421i	−0.695816	+	0.718220i	$0.744957\pi$
$80$	−0.162504			−0.0181685
$81$		0			0
$82$	5.10101			0.563313
$83$	−6.49273	−	5.44804i	−0.712669	−	0.598001i	0.212677	−	0.977122i	$-0.431782\pi$
$83$	−6.49273	−	5.44804i	−0.712669	−	0.598001i	−0.925347	+	0.379122i	$0.876226\pi$
$84$		0			0
$85$	2.02094	+	11.4613i	0.219202	+	1.24316i
$86$	−5.14543	−	1.87278i	−0.554846	−	0.201947i
$87$		0			0
$88$	0.0800699	−	0.454099i	0.00853548	−	0.0484071i
$89$	−3.86097	+	6.68739i	−0.409262	+	0.708862i	−0.994807	−	0.101778i	$-0.967547\pi$
$89$	−3.86097	+	6.68739i	−0.409262	+	0.708862i	0.585546	+	0.810640i	$0.300880\pi$
$90$		0			0
$91$	2.63429	+	4.56272i	0.276148	+	0.478303i
$92$	3.27079	−	1.19047i	0.341004	−	0.124115i
$93$		0			0
$94$	−4.98293	+	4.18117i	−0.513950	+	0.431255i
$95$	10.6873	−	8.96773i	1.09650	−	0.920069i
$96$		0			0
$97$	3.67112	−	1.33618i	0.372746	−	0.135668i	−0.148853	−	0.988859i	$-0.547558\pi$
$97$	3.67112	−	1.33618i	0.372746	−	0.135668i	0.521599	+	0.853191i	$0.325336\pi$
$98$	−0.979055	−	1.69577i	−0.0988995	−	0.171299i
$99$		0			0
$100$	6.16385	−	10.6761i	0.616385	−	1.06761i
$101$	−1.40895	+	7.99054i	−0.140196	+	0.795089i	0.830904	+	0.556415i	$0.187824\pi$
$101$	−1.40895	+	7.99054i	−0.140196	+	0.795089i	−0.971100	+	0.238673i	$0.923288\pi$
$102$		0			0
$103$	−17.5214	−	6.37727i	−1.72644	−	0.628371i	−0.728069	−	0.685503i	$-0.759582\pi$
$103$	−17.5214	−	6.37727i	−1.72644	−	0.628371i	−0.998367	+	0.0571322i	$0.981804\pi$
$104$	1.18820	+	6.73859i	0.116512	+	0.660774i
$105$		0			0
$106$	−0.945622	−	0.793471i	−0.0918470	−	0.0770688i
$107$	7.59627			0.734359			0.367179	−	0.930150i	$-0.380324\pi$
$107$	7.59627			0.734359			0.367179	+	0.930150i	$0.380324\pi$
$108$		0			0
$109$	−15.6382			−1.49786			−0.748932	−	0.662647i	$-0.769433\pi$
$109$	−15.6382			−1.49786			−0.748932	+	0.662647i	$0.769433\pi$
$110$	−0.424678	−	0.356347i	−0.0404914	−	0.0339764i
$111$		0			0
$112$	0.0158921	+	0.0901285i	0.00150166	+	0.00851635i
$113$	2.17365	+	0.791143i	0.204480	+	0.0744245i	0.442230	−	0.896902i	$-0.354188\pi$
$113$	2.17365	+	0.791143i	0.204480	+	0.0744245i	−0.237750	+	0.971326i	$0.576410\pi$
$114$		0			0
$115$	1.91147	−	10.8405i	0.178246	−	1.01088i
$116$	4.11974	−	7.13559i	0.382508	−	0.662523i
$117$		0			0
$118$	−2.25150	−	3.89971i	−0.207267	−	0.358997i
$119$	6.15910	−	2.24173i	0.564604	−	0.205499i
$120$		0			0
$121$	−8.40626	+	7.05369i	−0.764205	+	0.641244i
$122$	2.54710	−	2.13727i	0.230604	−	0.193500i
$123$		0			0
$124$	−5.97653	+	2.17528i	−0.536708	+	0.195346i
$125$	−9.79473	−	16.9650i	−0.876067	−	1.51739i
$126$		0			0
$127$	−0.0209445	+	0.0362770i	−0.00185853	+	0.00321906i	−0.866953	−	0.498390i	$-0.833925\pi$
$127$	−0.0209445	+	0.0362770i	−0.00185853	+	0.00321906i	0.865095	+	0.501609i	$0.167258\pi$
$128$	1.18820	−	6.73859i	0.105023	−	0.595613i
$129$		0			0
$130$	7.73055	+	2.81369i	0.678014	+	0.246777i
$131$	3.18614	+	18.0695i	0.278374	+	1.57874i	0.728036	+	0.685539i	$0.240433\pi$
$131$	3.18614	+	18.0695i	0.278374	+	1.57874i	−0.449662	+	0.893199i	$0.648456\pi$
$132$		0			0
$133$	−6.01889	−	5.05044i	−0.521904	−	0.437929i
$134$	5.15745			0.445536
$135$		0			0
$136$	8.51249			0.729940
$137$	10.9645	+	9.20031i	0.936761	+	0.786036i	0.977019	−	0.213153i	$-0.0683734\pi$
$137$	10.9645	+	9.20031i	0.936761	+	0.786036i	−0.0402576	+	0.999189i	$0.512818\pi$
$138$		0			0
$139$	1.82248	+	10.3358i	0.154581	+	0.876672i	0.959168	+	0.282837i	$0.0912755\pi$
$139$	1.82248	+	10.3358i	0.154581	+	0.876672i	−0.804587	+	0.593835i	$0.797613\pi$
$140$	−9.76991	−	3.55596i	−0.825709	−	0.300533i
$141$		0			0
$142$	2.33915	−	13.2660i	0.196297	−	1.11325i
$143$	−0.195937	+	0.339373i	−0.0163851	+	0.0283798i
$144$		0			0
$145$	−13.0287	−	22.5663i	−1.08197	−	1.87403i
$146$	7.17277	−	2.61068i	0.593623	−	0.216061i
$147$		0			0
$148$	6.23783	−	5.23416i	0.512746	−	0.430245i
$149$	−0.973841	+	0.817150i	−0.0797802	+	0.0669435i	−0.681806	−	0.731533i	$-0.738805\pi$
$149$	−0.973841	+	0.817150i	−0.0797802	+	0.0669435i	0.602025	+	0.798477i	$0.294361\pi$
$150$		0			0
$151$	−7.38326	+	2.68729i	−0.600841	+	0.218688i	−0.624491	−	0.781032i	$-0.714693\pi$
$151$	−7.38326	+	2.68729i	−0.600841	+	0.218688i	0.0236500	+	0.999720i	$0.492471\pi$
$152$	−5.10220	−	8.83726i	−0.413843	−	0.716797i
$153$		0			0
$154$	−0.156107	+	0.270386i	−0.0125795	+	0.0217883i
$155$	−3.49273	+	19.8082i	−0.280543	+	1.59104i
$156$		0			0
$157$	11.6074	+	4.22475i	0.926372	+	0.337172i	0.760771	−	0.649021i	$-0.224821\pi$
$157$	11.6074	+	4.22475i	0.926372	+	0.337172i	0.165602	+	0.986193i	$0.447043\pi$
$158$	0.193715	+	1.09861i	0.0154112	+	0.0874011i
$159$		0			0
$160$	−16.7554	−	14.0594i	−1.32463	−	1.11149i
$161$	−6.19934			−0.488576
$162$		0			0
$163$	−13.7469			−1.07674			−0.538371	−	0.842708i	$-0.680960\pi$
$163$	−13.7469			−1.07674			−0.538371	+	0.842708i	$0.680960\pi$
$164$	5.45084	+	4.57380i	0.425639	+	0.357153i
$165$		0			0
$166$	1.29426	+	7.34013i	0.100454	+	0.569705i
$167$	3.49273	+	1.27125i	0.270275	+	0.0983721i	0.473603	−	0.880739i	$-0.342953\pi$
$167$	3.49273	+	1.27125i	0.270275	+	0.0983721i	−0.203327	+	0.979111i	$0.565176\pi$
$168$		0			0
$169$	−1.24763	+	7.07564i	−0.0959712	+	0.544280i
$170$	5.11721	−	8.86327i	0.392472	−	0.679782i
$171$		0			0
$172$	−3.81908	−	6.61484i	−0.291202	−	0.504377i
$173$	1.46538	−	0.533356i	0.111411	−	0.0405503i	−0.285713	−	0.958315i	$-0.592230\pi$
$173$	1.46538	−	0.533356i	0.111411	−	0.0405503i	0.397124	+	0.917765i	$0.370008\pi$
$174$		0			0
$175$	−16.8195	+	14.1133i	−1.27144	+	1.06686i
$176$	−0.00521457	+	0.00437554i	−0.000393063	+	0.000329819i
$177$		0			0
$178$	6.38103	−	2.32251i	0.478279	−	0.174079i
$179$	6.09627	+	10.5590i	0.455656	+	0.789220i	0.998726	−	0.0504679i	$-0.0160713\pi$
$179$	6.09627	+	10.5590i	0.455656	+	0.789220i	−0.543069	+	0.839688i	$0.682738\pi$
$180$		0			0
$181$	8.43629	−	14.6121i	0.627064	−	1.08611i	−0.361073	−	0.932537i	$-0.617590\pi$
$181$	8.43629	−	14.6121i	0.627064	−	1.08611i	0.988138	−	0.153570i	$-0.0490771\pi$
$182$	0.804530	−	4.56272i	0.0596357	−	0.338211i
$183$		0			0
$184$	−7.56583	−	2.75374i	−0.557760	−	0.203008i
$185$	−4.47178	−	25.3607i	−0.328772	−	1.86456i
$186$		0			0
$187$	0.373455	+	0.313366i	0.0273098	+	0.0229156i
$188$	−9.07367			−0.661766
$189$		0			0
$190$	−12.2686			−0.890056
$191$	−13.3871	−	11.2331i	−0.968658	−	0.812801i	0.0136814	−	0.999906i	$-0.495645\pi$
$191$	−13.3871	−	11.2331i	−0.968658	−	0.812801i	−0.982340	+	0.187105i	$0.940089\pi$
$192$		0			0
$193$	−0.345952	−	1.96199i	−0.0249022	−	0.141227i	0.969822	−	0.243815i	$-0.0783989\pi$
$193$	−0.345952	−	1.96199i	−0.0249022	−	0.141227i	−0.994724	+	0.102588i	$0.967288\pi$
$194$	−3.22833	−	1.17502i	−0.231781	−	0.0843612i
$195$		0			0
$196$	0.474308	−	2.68993i	0.0338791	−	0.192138i
$197$	−10.5963	+	18.3533i	−0.754953	+	1.30762i	0.190445	+	0.981698i	$0.439007\pi$
$197$	−10.5963	+	18.3533i	−0.754953	+	1.30762i	−0.945398	+	0.325919i	$0.894326\pi$
$198$		0			0
$199$	1.54189	+	2.67063i	0.109302	+	0.189316i	0.915488	−	0.402346i	$-0.131805\pi$
$199$	1.54189	+	2.67063i	0.109302	+	0.189316i	−0.806186	+	0.591662i	$0.798472\pi$
$200$	−26.7961	+	9.75297i	−1.89477	+	0.689639i
$201$		0			0
$202$	5.46585	−	4.58639i	0.384576	−	0.322698i
$203$	−11.2417	+	9.43290i	−0.789012	+	0.662060i
$204$		0			0
$205$	21.1459	−	7.69648i	1.47689	−	0.537545i
$206$	8.19846	+	14.2002i	0.571214	+	0.989372i
$207$		0			0
$208$	0.0505072	−	0.0874810i	0.00350204	−	0.00606572i
$209$	0.101481	−	0.575529i	0.00701960	−	0.0398101i
$210$		0			0
$211$	−0.946967	−	0.344668i	−0.0651919	−	0.0237279i	0.309218	−	0.950991i	$-0.399933\pi$
$211$	−0.946967	−	0.344668i	−0.0651919	−	0.0237279i	−0.374410	+	0.927263i	$0.622155\pi$
$212$	−0.299011	−	1.69577i	−0.0205361	−	0.116466i
$213$		0			0
$214$	−5.11721	−	4.29385i	−0.349805	−	0.293522i
$215$	−24.1557			−1.64740
$216$		0			0
$217$	11.3277			0.768974
$218$	10.5346	+	8.83959i	0.713494	+	0.598693i
$219$		0			0
$220$	−0.134285	−	0.761570i	−0.00905352	−	0.0513450i
$221$	−6.79813	−	2.47432i	−0.457292	−	0.166441i
$222$		0			0
$223$	3.17499	−	18.0063i	0.212613	−	1.20579i	−0.672387	−	0.740199i	$-0.734731\pi$
$223$	3.17499	−	18.0063i	0.212613	−	1.20579i	0.885001	−	0.465590i	$-0.154158\pi$
$224$	−6.15910	+	10.6679i	−0.411522	+	0.712777i
$225$		0			0
$226$	−1.01707	−	1.76162i	−0.0676548	−	0.117181i
$227$	2.48545	−	0.904631i	0.164965	−	0.0600424i	−0.258217	−	0.966087i	$-0.583135\pi$
$227$	2.48545	−	0.904631i	0.164965	−	0.0600424i	0.423183	+	0.906044i	$0.360913\pi$
$228$		0			0
$229$	−2.65270	+	2.22588i	−0.175296	+	0.147090i	−0.726214	−	0.687469i	$-0.758722\pi$
$229$	−2.65270	+	2.22588i	−0.175296	+	0.147090i	0.550919	+	0.834559i	$0.314277\pi$
$230$	−7.41534	+	6.22221i	−0.488953	+	0.410281i
$231$		0			0
$232$	−17.9097	+	6.51860i	−1.17583	+	0.427967i
$233$	−3.06283	−	5.30498i	−0.200653	−	0.347541i	0.748086	−	0.663602i	$-0.230973\pi$
$233$	−3.06283	−	5.30498i	−0.200653	−	0.347541i	−0.948739	+	0.316061i	$0.897640\pi$
$234$		0			0
$235$	−14.3478	+	24.8511i	−0.935945	+	1.62110i
$236$	1.09075	−	6.18594i	0.0710016	−	0.402670i
$237$		0			0
$238$	−5.41622	−	1.97134i	−0.351082	−	0.127783i
$239$	−5.02734	−	28.5115i	−0.325192	−	1.84425i	−0.508325	−	0.861165i	$-0.669735\pi$
$239$	−5.02734	−	28.5115i	−0.325192	−	1.84425i	0.183133	−	0.983088i	$-0.441376\pi$
$240$		0			0
$241$	17.1027	+	14.3508i	1.10168	+	0.924419i	0.997537	−	0.0701436i	$-0.0223458\pi$
$241$	17.1027	+	14.3508i	1.10168	+	0.924419i	0.104142	+	0.994562i	$0.466790\pi$
$242$	9.65002			0.620326
$243$		0			0
$244$	4.63816			0.296927
$245$	−6.61721	−	5.55250i	−0.422758	−	0.354736i
$246$		0			0
$247$	1.50593	+	8.54055i	0.0958200	+	0.543422i
$248$	13.8246	+	5.03174i	0.877863	+	0.319516i
$249$		0			0
$250$	−2.99138	+	16.9650i	−0.189192	+	1.07296i
$251$	11.3610	−	19.6778i	0.717098	−	1.24205i	−0.245047	−	0.969511i	$-0.578803\pi$
$251$	11.3610	−	19.6778i	0.717098	−	1.24205i	0.962145	−	0.272539i	$-0.0878633\pi$
$252$		0			0
$253$	−0.230552	−	0.399328i	−0.0144947	−	0.0251055i
$254$	0.0346151	−	0.0125989i	0.00217194	−	0.000790523i
$255$		0			0
$256$	−12.3341	+	10.3495i	−0.770881	+	0.646846i
$257$	−15.0064	+	12.5919i	−0.936073	+	0.785459i	−0.976898	−	0.213708i	$-0.931446\pi$
$257$	−15.0064	+	12.5919i	−0.936073	+	0.785459i	0.0408244	+	0.999166i	$0.487002\pi$
$258$		0			0
$259$	−13.6284	+	4.96032i	−0.846825	+	0.308219i
$260$	5.73783	+	9.93821i	0.355845	+	0.616341i
$261$		0			0
$262$	8.06758	−	13.9735i	0.498417	−	0.863283i
$263$	3.09105	−	17.5302i	0.190602	−	1.08096i	−0.727941	−	0.685640i	$-0.759523\pi$
$263$	3.09105	−	17.5302i	0.190602	−	1.08096i	0.918543	−	0.395320i	$-0.129366\pi$
$264$		0			0
$265$	−5.11721	−	1.86251i	−0.314348	−	0.114413i
$266$	1.19981	+	6.80445i	0.0735649	+	0.417207i
$267$		0			0
$268$	5.51114	+	4.62440i	0.336647	+	0.282480i
$269$	22.7888			1.38946			0.694729	−	0.719272i	$-0.255524\pi$
$269$	22.7888			1.38946			0.694729	+	0.719272i	$0.255524\pi$
$270$		0			0
$271$	−3.44562			−0.209307			−0.104653	−	0.994509i	$-0.533373\pi$
$271$	−3.44562			−0.209307			−0.104653	+	0.994509i	$0.533373\pi$
$272$	−0.0962667	−	0.0807773i	−0.00583702	−	0.00489784i
$273$		0			0
$274$	−2.18567	−	12.3955i	−0.132041	−	0.748843i
$275$	−1.53462	−	0.558554i	−0.0925408	−	0.0336821i
$276$		0			0
$277$	−0.453830	+	2.57380i	−0.0272680	+	0.154645i	−0.995402	−	0.0957898i	$-0.969462\pi$
$277$	−0.453830	+	2.57380i	−0.0272680	+	0.154645i	0.968134	+	0.250434i	$0.0805734\pi$
$278$	4.61468	−	7.99287i	0.276770	−	0.479380i
$279$		0			0
$280$	12.0248	+	20.8276i	0.718620	+	1.24469i
$281$	12.8598	−	4.68058i	0.767150	−	0.279220i	0.0713464	−	0.997452i	$-0.477270\pi$
$281$	12.8598	−	4.68058i	0.767150	−	0.279220i	0.695804	+	0.718232i	$0.255048\pi$
$282$		0			0
$283$	17.5273	−	14.7072i	1.04189	−	0.874251i	0.0496744	−	0.998765i	$-0.484182\pi$
$283$	17.5273	−	14.7072i	1.04189	−	0.874251i	0.992218	+	0.124514i	$0.0397372\pi$
$284$	14.3944	−	12.0783i	0.854150	−	0.716717i
$285$		0			0
$286$	0.323826	−	0.117863i	0.0191482	−	0.00696938i
$287$	−6.33662	−	10.9753i	−0.374039	−	0.647854i
$288$		0			0
$289$	4.00000	−	6.92820i	0.235294	−	0.407541i
$290$	−3.97906	+	22.5663i	−0.233658	+	1.32514i
$291$		0			0
$292$	10.0055	+	3.64171i	0.585529	+	0.213115i
$293$	4.21641	+	23.9125i	0.246326	+	1.39698i	0.817394	+	0.576079i	$0.195418\pi$
$293$	4.21641	+	23.9125i	0.246326	+	1.39698i	−0.571068	+	0.820903i	$0.693471\pi$
$294$		0			0
$295$	−15.2173	−	12.7689i	−0.885988	−	0.743432i
$296$	−18.8357			−1.09481
$297$		0			0
$298$	1.11793			0.0647597
$299$	5.24170	+	4.39831i	0.303135	+	0.254361i
$300$		0			0
$301$	2.36231	+	13.3973i	0.136161	+	0.772209i
$302$	6.49273	+	2.36316i	0.373614	+	0.135985i
$303$		0			0
$304$	−0.0261591	+	0.148356i	−0.00150033	+	0.00850878i
$305$	7.33409	−	12.7030i	0.419949	−	0.727373i
$306$		0			0
$307$	8.07444	+	13.9853i	0.460833	+	0.798186i	0.999003	−	0.0446505i	$-0.0142174\pi$
$307$	8.07444	+	13.9853i	0.460833	+	0.798186i	−0.538170	+	0.842836i	$0.680884\pi$
$308$	−0.409253	+	0.148956i	−0.0233193	+	0.00848754i
$309$		0			0
$310$	13.5496	−	11.3695i	0.769567	−	0.645744i
$311$	14.3327	−	12.0266i	0.812736	−	0.681966i	−0.138523	−	0.990359i	$-0.544236\pi$
$311$	14.3327	−	12.0266i	0.812736	−	0.681966i	0.951259	+	0.308393i	$0.0997912\pi$
$312$		0			0
$313$	−2.60607	+	0.948531i	−0.147304	+	0.0536141i	−0.414620	−	0.909995i	$-0.636085\pi$
$313$	−2.60607	+	0.948531i	−0.147304	+	0.0536141i	0.267316	+	0.963609i	$0.413863\pi$
$314$	−5.43124	−	9.40718i	−0.306502	−	0.530878i
$315$		0			0
$316$	−0.778066	+	1.34765i	−0.0437696	+	0.0758112i
$317$	3.03580	−	17.2169i	0.170507	−	0.966995i	−0.772695	−	0.634777i	$-0.781092\pi$
$317$	3.03580	−	17.2169i	0.170507	−	0.966995i	0.943203	−	0.332218i	$-0.107797\pi$
$318$		0			0
$319$	−1.02569	−	0.373321i	−0.0574277	−	0.0209020i
$320$	3.39646	+	19.2623i	0.189868	+	1.07679i
$321$		0			0
$322$	4.17617	+	3.50423i	0.232729	+	0.195283i
$323$	10.7888			0.600305
$324$		0			0
$325$	24.2344			1.34428
$326$	9.26058	+	7.77055i	0.512896	+	0.430371i
$327$		0			0
$328$	−2.85814	−	16.2093i	−0.157814	−	0.895009i
$329$	15.1861	+	5.52730i	0.837239	+	0.304730i
$330$		0			0
$331$	−5.63651	+	31.9662i	−0.309810	+	1.75702i	0.290139	+	0.956984i	$0.406298\pi$
$331$	−5.63651	+	31.9662i	−0.309810	+	1.75702i	−0.599950	+	0.800038i	$0.704813\pi$
$332$	−5.19846	+	9.00400i	−0.285303	+	0.494159i
$333$		0			0
$334$	−1.63429	−	2.83067i	−0.0894241	−	0.154887i
$335$	21.3799	−	7.78163i	1.16811	−	0.425156i
$336$		0			0
$337$	6.34730	−	5.32601i	0.345759	−	0.290126i	−0.453325	−	0.891345i	$-0.649762\pi$
$337$	6.34730	−	5.32601i	0.345759	−	0.290126i	0.799085	+	0.601219i	$0.205318\pi$
$338$	4.84002	−	4.06126i	0.263263	−	0.220903i
$339$		0			0
$340$	13.4153	−	4.88279i	0.727549	−	0.264806i
$341$	0.421274	+	0.729669i	0.0228133	+	0.0395138i
$342$		0			0
$343$	−10.0792	+	17.4577i	−0.544225	+	0.942626i
$344$	−3.06805	+	17.3998i	−0.165418	+	0.938132i
$345$		0			0
$346$	−1.28864	−	0.469026i	−0.0692776	−	0.0252150i
$347$	2.59833	+	14.7358i	0.139485	+	0.791061i	0.971631	+	0.236503i	$0.0760015\pi$
$347$	2.59833	+	14.7358i	0.139485	+	0.791061i	−0.832145	+	0.554558i	$0.812887\pi$
$348$		0			0
$349$	25.7743	+	21.6272i	1.37966	+	1.15768i	0.969336	+	0.245737i	$0.0790301\pi$
$349$	25.7743	+	21.6272i	1.37966	+	1.15768i	0.410328	+	0.911938i	$0.365414\pi$
$350$	19.3081			1.03206
$351$		0			0
$352$	−0.916222			−0.0488348
$353$	−12.0680	−	10.1263i	−0.642317	−	0.538968i	0.262412	−	0.964956i	$-0.415482\pi$
$353$	−12.0680	−	10.1263i	−0.642317	−	0.538968i	−0.904729	+	0.425988i	$0.859927\pi$
$354$		0			0
$355$	−10.3191	−	58.5224i	−0.547680	−	3.10605i
$356$	8.90110	+	3.23974i	0.471757	+	0.171706i
$357$		0			0
$358$	1.86184	−	10.5590i	0.0984015	−	0.558063i
$359$	−9.06283	+	15.6973i	−0.478318	+	0.828471i	−0.999691	−	0.0248577i	$-0.992087\pi$
$359$	−9.06283	+	15.6973i	−0.478318	+	0.828471i	0.521373	+	0.853329i	$0.325420\pi$
$360$		0			0
$361$	3.03343	+	5.25406i	0.159654	+	0.276529i
$362$	−13.9427	+	5.07472i	−0.732811	+	0.266721i
$363$		0			0
$364$	4.95084	−	4.15425i	0.259494	−	0.217742i
$365$	25.7952	−	21.6447i	1.35018	−	1.13294i
$366$		0			0
$367$	17.9884	−	6.54726i	0.938989	−	0.341764i	0.173223	−	0.984883i	$-0.444582\pi$
$367$	17.9884	−	6.54726i	0.938989	−	0.341764i	0.765767	+	0.643119i	$0.222360\pi$
$368$	0.0594300	+	0.102936i	0.00309800	+	0.00536590i
$369$		0			0
$370$	−11.3229	+	19.6119i	−0.588652	+	1.01958i
$371$	−0.532556	+	3.02027i	−0.0276489	+	0.156805i
$372$		0			0
$373$	14.3302	+	5.21577i	0.741991	+	0.270063i	0.685231	−	0.728325i	$-0.259701\pi$
$373$	14.3302	+	5.21577i	0.741991	+	0.270063i	0.0567593	+	0.998388i	$0.481923\pi$
$374$	−0.0744448	−	0.422197i	−0.00384945	−	0.0218313i
$375$		0			0
$376$	16.0783	+	13.4913i	0.829176	+	0.695761i
$377$	16.1976			0.834218
$378$		0			0
$379$	9.84760			0.505837			0.252919	−	0.967488i	$-0.418610\pi$
$379$	9.84760			0.505837			0.252919	+	0.967488i	$0.418610\pi$
$380$	−13.1099	−	11.0005i	−0.672526	−	0.564316i
$381$		0			0
$382$	2.66860	+	15.1344i	0.136537	+	0.774341i
$383$	−26.6780	−	9.70999i	−1.36318	−	0.496157i	−0.446145	−	0.894961i	$-0.647203\pi$
$383$	−26.6780	−	9.70999i	−1.36318	−	0.496157i	−0.917036	+	0.398803i	$0.869426\pi$
$384$		0			0
$385$	−0.239170	+	1.35640i	−0.0121892	+	0.0691286i
$386$	−0.875982	+	1.51724i	−0.0445863	+	0.0772257i
$387$		0			0
$388$	−2.39615	−	4.15026i	−0.121646	−	0.210698i
$389$	−10.2280	+	3.72270i	−0.518581	+	0.188748i	−0.588033	−	0.808837i	$-0.700097\pi$
$389$	−10.2280	+	3.72270i	−0.518581	+	0.188748i	0.0694513	+	0.997585i	$0.477875\pi$
$390$		0			0
$391$	6.52094	−	5.47172i	0.329778	−	0.276717i
$392$	−4.84002	+	4.06126i	−0.244458	+	0.205125i
$393$		0			0
$394$	17.5125	−	6.37402i	0.882266	−	0.321119i
$395$	2.46064	+	4.26195i	0.123808	+	0.214442i
$396$		0			0
$397$	9.05350	−	15.6811i	0.454382	−	0.787013i	−0.544270	−	0.838910i	$-0.683193\pi$
$397$	9.05350	−	15.6811i	0.454382	−	0.787013i	0.998652	+	0.0518969i	$0.0165267\pi$
$398$	0.470904	−	2.67063i	0.0236043	−	0.133867i
$399$		0			0
$400$	0.395582	+	0.143980i	0.0197791	+	0.00719900i
$401$	0.248970	+	1.41198i	0.0124330	+	0.0705110i	0.990393	−	0.138281i	$-0.0441578\pi$
$401$	0.248970	+	1.41198i	0.0124330	+	0.0705110i	−0.977960	+	0.208792i	$0.933047\pi$
$402$		0			0
$403$	−9.57785	−	8.03677i	−0.477107	−	0.400340i
$404$	9.95306			0.495183
$405$		0			0
$406$	12.9050			0.640463
$407$	−0.826352	−	0.693392i	−0.0409607	−	0.0343701i
$408$		0			0
$409$	1.49407	+	8.47329i	0.0738770	+	0.418977i	0.999207	+	0.0398148i	$0.0126768\pi$
$409$	1.49407	+	8.47329i	0.0738770	+	0.418977i	−0.925330	+	0.379163i	$0.876212\pi$
$410$	−18.5954	−	6.76817i	−0.918361	−	0.334256i
$411$		0			0
$412$	−3.97178	+	22.5251i	−0.195676	+	1.10973i
$413$	−5.59374	+	9.68864i	−0.275250	+	0.476747i
$414$		0			0
$415$	16.4402	+	28.4752i	0.807016	+	1.39779i
$416$	12.7763	−	4.65020i	0.626410	−	0.227995i
$417$		0			0
$418$	−0.393685	+	0.330341i	−0.0192558	+	0.0161575i
$419$	−9.43107	+	7.91361i	−0.460738	+	0.386605i	−0.843403	−	0.537282i	$-0.819451\pi$
$419$	−9.43107	+	7.91361i	−0.460738	+	0.386605i	0.382664	+	0.923887i	$0.375007\pi$
$420$		0			0
$421$	−10.4461	+	3.80207i	−0.509111	+	0.185301i	−0.583788	−	0.811906i	$-0.698430\pi$
$421$	−10.4461	+	3.80207i	−0.509111	+	0.185301i	0.0746763	+	0.997208i	$0.476208\pi$
$422$	0.443096	+	0.767465i	0.0215696	+	0.0373596i
$423$		0			0
$424$	−1.99154	+	3.44946i	−0.0967179	+	0.167520i
$425$	5.23530	−	29.6909i	0.253949	−	1.44022i
$426$		0			0
$427$	−7.76264	−	2.82537i	−0.375661	−	0.136729i
$428$	−1.61809	−	9.17664i	−0.0782133	−	0.443569i
$429$		0			0
$430$	16.2724	+	13.6542i	0.784727	+	0.658464i
$431$	−36.8958			−1.77721			−0.888604	−	0.458675i	$-0.848324\pi$
$431$	−36.8958			−1.77721			−0.888604	+	0.458675i	$0.848324\pi$
$432$		0			0
$433$	−37.9982			−1.82608			−0.913040	−	0.407871i	$-0.866271\pi$
$433$	−37.9982			−1.82608			−0.913040	+	0.407871i	$0.866271\pi$
$434$	−7.63088	−	6.40307i	−0.366294	−	0.307357i
$435$		0			0
$436$	3.33110	+	18.8916i	0.159531	+	0.904744i
$437$	−9.58899	−	3.49011i	−0.458704	−	0.166955i
$438$		0			0
$439$	0.0350819	−	0.198960i	0.00167437	−	0.00949582i	−0.983959	−	0.178394i	$-0.942910\pi$
$439$	0.0350819	−	0.198960i	0.00167437	−	0.00949582i	0.985633	+	0.168898i	$0.0540209\pi$
$440$	−0.894400	+	1.54915i	−0.0426388	+	0.0738526i
$441$		0			0
$442$	3.18092	+	5.50952i	0.151301	+	0.262061i
$443$	−19.9491	+	7.26087i	−0.947810	+	0.344974i	−0.769245	−	0.638954i	$-0.779368\pi$
$443$	−19.9491	+	7.26087i	−0.947810	+	0.344974i	−0.178564	+	0.983928i	$0.557145\pi$
$444$		0			0
$445$	22.9479	−	19.2556i	1.08783	−	0.912802i
$446$	−12.3170	+	10.3352i	−0.583228	+	0.489386i
$447$		0			0
$448$	10.3512	−	3.76752i	0.489047	−	0.177998i
$449$	16.6297	+	28.8035i	0.784804	+	1.35932i	0.929116	+	0.369788i	$0.120570\pi$
$449$	16.6297	+	28.8035i	0.784804	+	1.35932i	−0.144312	+	0.989532i	$0.546097\pi$
$450$		0			0
$451$	0.471315	−	0.816341i	0.0221933	−	0.0384400i
$452$	0.492726	−	2.79439i	0.0231759	−	0.131437i
$453$		0			0
$454$	−2.18567	−	0.795519i	−0.102579	−	0.0373355i
$455$	−3.54916	−	20.1283i	−0.166387	−	0.943629i
$456$		0			0
$457$	−0.0261591	−	0.0219501i	−0.00122367	−	0.00102678i	0.642176	−	0.766558i	$-0.278032\pi$
$457$	−0.0261591	−	0.0219501i	−0.00122367	−	0.00102678i	−0.643399	+	0.765531i	$0.722476\pi$
$458$	3.04519			0.142292
$459$		0			0
$460$	−13.5030			−0.629580
$461$	−11.4802	−	9.63306i	−0.534688	−	0.448656i	0.335029	−	0.942208i	$-0.391254\pi$
$461$	−11.4802	−	9.63306i	−0.534688	−	0.448656i	−0.869717	+	0.493551i	$0.835698\pi$
$462$		0			0
$463$	−5.28627	−	29.9799i	−0.245674	−	1.39329i	−0.818922	−	0.573905i	$-0.805428\pi$
$463$	−5.28627	−	29.9799i	−0.245674	−	1.39329i	0.573248	−	0.819382i	$-0.305683\pi$
$464$	0.264396	+	0.0962321i	0.0122743	+	0.00446746i
$465$		0			0
$466$	−0.935412	+	5.30498i	−0.0433321	+	0.245749i
$467$	0.255367	−	0.442308i	0.0118170	−	0.0204676i	−0.860056	−	0.510199i	$-0.829572\pi$
$467$	0.255367	−	0.442308i	0.0118170	−	0.0204676i	0.871873	+	0.489731i	$0.162905\pi$
$468$		0			0
$469$	−6.40673	−	11.0968i	−0.295835	−	0.512401i
$470$	23.7126	−	8.63068i	1.09378	−	0.398104i
$471$		0			0
$472$	−11.1304	+	9.33953i	−0.512319	+	0.429887i
$473$	−0.775129	+	0.650411i	−0.0356405	+	0.0299059i
$474$		0			0
$475$	−33.9616	+	12.3610i	−1.55826	+	0.567162i
$476$	−4.02007	−	6.96296i	−0.184259	−	0.319147i
$477$		0			0
$478$	−12.7297	+	22.0484i	−0.582242	+	1.00847i
$479$	−2.68298	+	15.2159i	−0.122589	+	0.695234i	0.860122	+	0.510088i	$0.170387\pi$
$479$	−2.68298	+	15.2159i	−0.122589	+	0.695234i	−0.982711	+	0.185147i	$0.940724\pi$
$480$		0			0
$481$	15.0424	+	5.47497i	0.685872	+	0.249637i
$482$	−3.40925	−	19.3348i	−0.155287	−	0.880677i
$483$		0			0
$484$	10.3118	+	8.65263i	0.468718	+	0.393301i
$485$	−15.1557			−0.688185
$486$		0			0
$487$	29.5107			1.33726			0.668629	−	0.743596i	$-0.266881\pi$
$487$	29.5107			1.33726			0.668629	+	0.743596i	$0.266881\pi$
$488$	−8.21869	−	6.89630i	−0.372043	−	0.312181i
$489$		0			0
$490$	1.31908	+	7.48086i	0.0595899	+	0.337951i
$491$	−2.02734	−	0.737892i	−0.0914926	−	0.0333006i	0.295868	−	0.955229i	$-0.404391\pi$
$491$	−2.02734	−	0.737892i	−0.0914926	−	0.0333006i	−0.387361	+	0.921928i	$0.626613\pi$
$492$		0			0
$493$	3.49912	−	19.8445i	0.157593	−	0.893752i
$494$	3.81315	−	6.60457i	0.171562	−	0.297153i
$495$		0			0
$496$	−0.108593	−	0.188089i	−0.00487597	−	0.00844543i
$497$	−31.4488	+	11.4464i	−1.41067	+	0.513442i
$498$		0			0
$499$	5.74170	−	4.81786i	0.257034	−	0.215677i	−0.505160	−	0.863025i	$-0.668567\pi$
$499$	5.74170	−	4.81786i	0.257034	−	0.215677i	0.762194	+	0.647349i	$0.224122\pi$
$500$	−18.4081	+	15.4462i	−0.823234	+	0.690775i
$501$		0			0
$502$	−18.7763	+	6.83402i	−0.838028	+	0.305017i
$503$	−14.2981	−	24.7651i	−0.637522	−	1.10422i	−0.985975	−	0.166894i	$-0.946626\pi$
$503$	−14.2981	−	24.7651i	−0.637522	−	1.10422i	0.348453	−	0.937326i	$-0.386707\pi$
$504$		0			0
$505$	15.7383	−	27.2595i	0.700345	−	1.21303i
$506$	−0.0704123	+	0.399328i	−0.00313021	+	0.0177523i
$507$		0			0
$508$	0.0482857	+	0.0175745i	0.00214233	+	0.000779745i
$509$	−0.293796	−	1.66620i	−0.0130223	−	0.0738530i	0.977604	−	0.210453i	$-0.0674938\pi$
$509$	−0.293796	−	1.66620i	−0.0130223	−	0.0738530i	−0.990626	+	0.136600i	$0.956383\pi$
$510$		0			0
$511$	−14.5273	−	12.1899i	−0.642652	−	0.539249i
$512$	0.473897			0.0209435
$513$		0			0
$514$	17.2267			0.759836
$515$	55.4115	+	46.4958i	2.44172	+	2.04885i
$516$		0			0
$517$	0.208730	+	1.18377i	0.00917994	+	0.0520620i
$518$	11.9846	+	4.36203i	0.526572	+	0.191657i
$519$		0			0
$520$	4.60947	−	26.1416i	0.202139	−	1.14639i
$521$	11.2019	−	19.4022i	0.490763	−	0.850026i	−0.509181	−	0.860660i	$-0.670052\pi$
$521$	11.2019	−	19.4022i	0.490763	−	0.850026i	0.999943	+	0.0106337i	$0.00338487\pi$
$522$		0			0
$523$	−1.21436	−	2.10332i	−0.0531000	−	0.0919720i	0.838254	−	0.545281i	$-0.183577\pi$
$523$	−1.21436	−	2.10332i	−0.0531000	−	0.0919720i	−0.891354	+	0.453309i	$0.850244\pi$
$524$	21.1501	−	7.69800i	0.923945	−	0.336289i
$525$		0			0
$526$	−11.9914	+	10.0620i	−0.522849	+	0.438722i
$527$	−11.9153	+	9.99816i	−0.519041	+	0.435527i
$528$		0			0
$529$	14.0471	−	5.11273i	0.610744	−	0.222293i
$530$	2.39440	+	4.14722i	0.104006	+	0.180144i
$531$		0			0
$532$	−4.81908	+	8.34689i	−0.208934	+	0.361883i
$533$	−2.42902	+	13.7756i	−0.105212	+	0.596689i
$534$		0			0
$535$	−27.6917	−	10.0789i	−1.19721	−	0.435751i
$536$	−2.88976	−	16.3886i	−0.124819	−	0.707881i
$537$		0			0
$538$	−15.3516	−	12.8816i	−0.661856	−	0.555363i
$539$	−0.361844			−0.0155857
$540$		0			0
$541$	38.9394			1.67414			0.837069	−	0.547098i	$-0.184267\pi$
$541$	38.9394			1.67414			0.837069	+	0.547098i	$0.184267\pi$
$542$	2.32114	+	1.94767i	0.0997014	+	0.0836594i
$543$		0			0
$544$	−2.93717	−	16.6575i	−0.125930	−	0.714184i
$545$	57.0078	+	20.7491i	2.44195	+	0.888796i
$546$		0			0
$547$	−2.54782	+	14.4494i	−0.108937	+	0.617812i	0.880638	+	0.473790i	$0.157115\pi$
$547$	−2.54782	+	14.4494i	−0.108937	+	0.617812i	−0.989575	+	0.144021i	$0.953997\pi$
$548$	8.77884	−	15.2054i	0.375013	−	0.649542i
$549$		0			0
$550$	0.718063	+	1.24372i	0.0306183	+	0.0530325i
$551$	−22.6989	+	8.26173i	−0.967007	+	0.351962i
$552$		0			0
$553$	2.12314	−	1.78153i	0.0902851	−	0.0757582i
$554$	1.76058	−	1.47730i	0.0747999	−	0.0627646i
$555$		0			0
$556$	12.0979	−	4.40328i	0.513066	−	0.186741i
$557$	5.55350	+	9.61894i	0.235309	+	0.407568i	0.959363	−	0.282176i	$-0.0910563\pi$
$557$	5.55350	+	9.61894i	0.235309	+	0.407568i	−0.724053	+	0.689744i	$0.757723\pi$
$558$		0			0
$559$	7.50774	−	13.0038i	0.317544	−	0.550002i
$560$	0.0616516	−	0.349643i	0.00260525	−	0.0147751i
$561$		0			0
$562$	−11.3087	−	4.11603i	−0.477029	−	0.173624i
$563$	2.83187	+	16.0603i	0.119349	+	0.676863i	0.984505	+	0.175359i	$0.0561086\pi$
$563$	2.83187	+	16.0603i	0.119349	+	0.676863i	−0.865155	+	0.501504i	$0.832780\pi$
$564$		0			0
$565$	−6.87417	−	5.76811i	−0.289199	−	0.242666i
$566$	−20.1206			−0.845733
$567$		0			0
$568$	−43.4653			−1.82376
$569$	27.5902	+	23.1509i	1.15664	+	0.970536i	0.999854	−	0.0170961i	$-0.00544212\pi$
$569$	27.5902	+	23.1509i	1.15664	+	0.970536i	0.156786	+	0.987633i	$0.449887\pi$
$570$		0			0
$571$	6.79978	+	38.5635i	0.284562	+	1.61383i	0.706846	+	0.707368i	$0.250117\pi$
$571$	6.79978	+	38.5635i	0.284562	+	1.61383i	−0.422284	+	0.906464i	$0.638771\pi$
$572$	0.451714	+	0.164411i	0.0188871	+	0.00687435i
$573$		0			0
$574$	−1.93525	+	10.9753i	−0.0807758	+	0.458102i
$575$	−14.2579	+	24.6954i	−0.594595	+	1.02987i
$576$		0			0
$577$	−5.90286	−	10.2240i	−0.245739	−	0.425633i	0.716600	−	0.697484i	$-0.245697\pi$
$577$	−5.90286	−	10.2240i	−0.245739	−	0.425633i	−0.962339	+	0.271852i	$0.912364\pi$
$578$	−6.61081	+	2.40614i	−0.274974	+	0.100082i
$579$		0			0
$580$	−24.4859	+	20.5461i	−1.01672	+	0.853131i
$581$	14.1853	−	11.9028i	0.588504	−	0.493813i
$582$		0			0
$583$	−0.214355	+	0.0780189i	−0.00887769	+	0.00323121i
$584$	−12.3148	−	21.3299i	−0.509590	−	0.882636i
$585$		0			0
$586$	10.6763	−	18.4920i	0.441035	−	0.763896i
$587$	−6.93923	+	39.3543i	−0.286413	+	1.62433i	0.413783	+	0.910375i	$0.364207\pi$
$587$	−6.93923	+	39.3543i	−0.286413	+	1.62433i	−0.700196	+	0.713951i	$0.746904\pi$
$588$		0			0
$589$	17.5214	+	6.37727i	0.721957	+	0.262771i
$590$	3.03343	+	17.2035i	0.124884	+	0.708255i
$591$		0			0
$592$	0.213011	+	0.178737i	0.00875470	+	0.00734606i
$593$	−29.2995			−1.20319			−0.601594	−	0.798802i	$-0.705467\pi$
$593$	−29.2995			−1.20319			−0.601594	+	0.798802i	$0.705467\pi$
$594$		0			0
$595$	−25.4270			−1.04240
$596$	1.19459	+	1.00238i	0.0489324	+	0.0410592i
$597$		0			0
$598$	−1.04488	−	5.92582i	−0.0427284	−	0.242325i
$599$	−9.46451	−	3.44480i	−0.386709	−	0.140751i	0.141347	−	0.989960i	$-0.454857\pi$
$599$	−9.46451	−	3.44480i	−0.386709	−	0.140751i	−0.528056	+	0.849209i	$0.677079\pi$
$600$		0			0
$601$	−5.28224	+	29.9571i	−0.215467	+	1.22197i	0.664627	+	0.747175i	$0.268590\pi$
$601$	−5.28224	+	29.9571i	−0.215467	+	1.22197i	−0.880094	+	0.474799i	$0.842521\pi$
$602$	5.98158	−	10.3604i	0.243791	−	0.422259i
$603$		0			0
$604$	4.81908	+	8.34689i	0.196085	+	0.339630i
$605$	40.0035	−	14.5601i	1.62637	−	0.591951i
$606$		0			0
$607$	−17.6759	+	14.8319i	−0.717444	+	0.602007i	−0.926677	−	0.375859i	$-0.877348\pi$
$607$	−17.6759	+	14.8319i	−0.717444	+	0.602007i	0.209233	+	0.977866i	$0.432903\pi$
$608$	−15.5326	+	13.0334i	−0.629928	+	0.528573i
$609$		0			0
$610$	−12.1211	+	4.41171i	−0.490768	+	0.178625i
$611$	−8.91875	−	15.4477i	−0.360814	−	0.624948i
$612$		0			0
$613$	−0.382789	+	0.663010i	−0.0154607	+	0.0267787i	−0.873652	−	0.486551i	$-0.838255\pi$
$613$	−0.382789	+	0.663010i	−0.0154607	+	0.0267787i	0.858192	+	0.513330i	$0.171588\pi$
$614$	2.46599	−	13.9853i	0.0995194	−	0.564403i
$615$		0			0
$616$	0.946662	+	0.344557i	0.0381421	+	0.0138826i
$617$	−1.61287	−	9.14706i	−0.0649319	−	0.368247i	−0.999908	−	0.0135372i	$-0.995691\pi$
$617$	−1.61287	−	9.14706i	−0.0649319	−	0.368247i	0.934977	−	0.354710i	$-0.115420\pi$
$618$		0			0
$619$	−26.8746	−	22.5505i	−1.08018	−	0.906381i	−0.0842469	−	0.996445i	$-0.526848\pi$
$619$	−26.8746	−	22.5505i	−1.08018	−	0.906381i	−0.995936	+	0.0900639i	$0.971293\pi$
$620$	24.6732			0.990901
$621$		0			0
$622$	−16.4534			−0.659720
$623$	−12.9238	−	10.8444i	−0.517781	−	0.434470i
$624$		0			0
$625$	4.47090	+	25.3558i	0.178836	+	1.01423i
$626$	2.29174	+	0.834124i	0.0915962	+	0.0333383i
$627$		0			0
$628$	2.63119	−	14.9222i	0.104996	−	0.595461i
$629$	9.95723	−	17.2464i	0.397021	−	0.687660i
$630$		0			0
$631$	−17.8810	−	30.9709i	−0.711833	−	1.23293i	−0.964168	−	0.265291i	$-0.914532\pi$
$631$	−17.8810	−	30.9709i	−0.711833	−	1.23293i	0.252336	−	0.967640i	$-0.418801\pi$
$632$	3.38248	−	1.23112i	0.134548	−	0.0489715i
$633$		0			0
$634$	−11.7770	+	9.88210i	−0.467725	+	0.392468i
$635$	0.124485	−	0.104455i	0.00494004	−	0.00414519i
$636$		0			0
$637$	5.04576	−	1.83651i	0.199920	−	0.0727650i
$638$	0.479933	+	0.831268i	0.0190007	+	0.0329102i
$639$		0			0
$640$	−13.2724	+	22.9885i	−0.524639	+	0.908702i
$641$	0.508151	−	2.88187i	0.0200708	−	0.113827i	−0.973126	−	0.230271i	$-0.926039\pi$
$641$	0.508151	−	2.88187i	0.0200708	−	0.113827i	0.993197	+	0.116444i	$0.0371497\pi$
$642$		0			0
$643$	19.0303	+	6.92648i	0.750483	+	0.273154i	0.688809	−	0.724943i	$-0.258134\pi$
$643$	19.0303	+	6.92648i	0.750483	+	0.273154i	0.0616741	+	0.998096i	$0.480356\pi$
$644$	1.32053	+	7.48909i	0.0520361	+	0.295111i
$645$		0			0
$646$	−7.26786	−	6.09845i	−0.285950	−	0.239940i
$647$	10.7219			0.421523			0.210761	−	0.977538i	$-0.432406\pi$
$647$	10.7219			0.421523			0.210761	+	0.977538i	$0.432406\pi$
$648$		0			0
$649$	−0.832119			−0.0326635
$650$	−16.3255	−	13.6987i	−0.640338	−	0.537307i
$651$		0			0
$652$	2.92824	+	16.6069i	0.114679	+	0.650376i
$653$	−33.5724	−	12.2193i	−1.31379	−	0.478180i	−0.412326	−	0.911036i	$-0.635284\pi$
$653$	−33.5724	−	12.2193i	−1.31379	−	0.478180i	−0.901463	+	0.432856i	$0.857506\pi$
$654$		0			0
$655$	12.3603	−	70.0985i	0.482955	−	2.73897i
$656$	−0.121492	+	0.210430i	−0.00474347	+	0.00821593i
$657$		0			0
$658$	−7.10576	−	12.3075i	−0.277011	−	0.479798i
$659$	−29.0043	+	10.5567i	−1.12985	+	0.411231i	−0.838237	−	0.545306i	$-0.816414\pi$
$659$	−29.0043	+	10.5567i	−1.12985	+	0.411231i	−0.291611	+	0.956537i	$0.594191\pi$
$660$		0			0
$661$	−7.54395	+	6.33012i	−0.293426	+	0.246213i	−0.777602	−	0.628757i	$-0.783564\pi$
$661$	−7.54395	+	6.33012i	−0.293426	+	0.246213i	0.484176	+	0.874971i	$0.339119\pi$
$662$	21.8662	−	18.3479i	0.849853	−	0.713112i
$663$		0			0
$664$	22.5993	−	8.22546i	0.877021	−	0.319210i
$665$	15.2404	+	26.3971i	0.590996	+	1.02363i
$666$		0			0
$667$	−9.52956	+	16.5057i	−0.368986	+	0.639103i
$668$	0.791737	−	4.49016i	0.0306332	−	0.173730i
$669$		0			0
$670$	−18.8011	−	6.84305i	−0.726351	−	0.264370i
$671$	−0.106696	−	0.605102i	−0.00411895	−	0.0233597i
$672$		0			0
$673$	−15.0890	−	12.6612i	−0.581638	−	0.488052i	0.303847	−	0.952721i	$-0.401729\pi$
$673$	−15.0890	−	12.6612i	−0.581638	−	0.488052i	−0.885485	+	0.464669i	$0.846173\pi$
$674$	−7.28642			−0.280662
$675$		0			0
$676$	8.81345			0.338979
$677$	−21.7993	−	18.2918i	−0.837816	−	0.703011i	0.119256	−	0.992864i	$-0.461949\pi$
$677$	−21.7993	−	18.2918i	−0.837816	−	0.703011i	−0.957071	+	0.289853i	$0.906394\pi$
$678$		0			0
$679$	1.48215	+	8.40571i	0.0568799	+	0.322582i
$680$	−31.0317	−	11.2946i	−1.19001	−	0.433128i
$681$		0			0
$682$	0.128660	−	0.729669i	0.00492666	−	0.0279405i
$683$	−6.25537	+	10.8346i	−0.239355	+	0.414575i	−0.960529	−	0.278179i	$-0.910269\pi$
$683$	−6.25537	+	10.8346i	−0.239355	+	0.414575i	0.721174	+	0.692754i	$0.243603\pi$
$684$		0			0
$685$	−27.7631	−	48.0871i	−1.06077	−	1.83731i
$686$	16.6579	−	6.06299i	0.636002	−	0.231486i
$687$		0			0
$688$	0.199807	−	0.167658i	0.00761758	−	0.00639191i
$689$	2.59311	−	2.17588i	0.0987897	−	0.0828944i
$690$		0			0
$691$	−40.0548	+	14.5788i	−1.52376	+	0.554603i	−0.962083	−	0.272756i	$-0.912065\pi$
$691$	−40.0548	+	14.5788i	−1.52376	+	0.554603i	−0.561675	+	0.827358i	$0.689843\pi$
$692$	−0.956462	−	1.65664i	−0.0363592	−	0.0629760i
$693$		0			0
$694$	6.57919	−	11.3955i	0.249743	−	0.432567i
$695$	7.07011	−	40.0966i	0.268184	−	1.52095i
$696$		0			0
$697$	16.3525	+	5.95183i	0.619396	+	0.225442i
$698$	−5.13785	−	29.1382i	−0.194471	−	1.10290i
$699$		0			0
$700$	20.6322	+	17.3125i	0.779825	+	0.654351i
$701$	51.7701			1.95533			0.977665	−	0.210167i	$-0.0674008\pi$
$701$	51.7701			1.95533			0.977665	+	0.210167i	$0.0674008\pi$
$702$		0			0
$703$	−23.8726			−0.900371
$704$	0.627640	+	0.526653i	0.0236551	+	0.0198490i
$705$		0			0
$706$	2.40565	+	13.6431i	0.0905378	+	0.513466i
$707$	−16.6579	−	6.06299i	−0.626485	−	0.228022i
$708$		0			0
$709$	2.63223	−	14.9281i	0.0988553	−	0.560636i	−0.894642	−	0.446783i	$-0.852570\pi$
$709$	2.63223	−	14.9281i	0.0988553	−	0.560636i	0.993498	−	0.113853i	$-0.0363194\pi$
$710$	−26.1288	+	45.2564i	−0.980597	+	1.69844i
$711$		0			0
$712$	−10.9555	−	18.9754i	−0.410574	−	0.711135i
$713$	13.8246	−	5.03174i	0.517735	−	0.188440i
$714$		0			0
$715$	1.16456	−	0.977185i	0.0435522	−	0.0365446i
$716$	11.4572	−	9.61376i	0.428177	−	0.359283i
$717$		0			0
$718$	14.9782	−	5.45161i	0.558981	−	0.203452i
$719$	1.30747	+	2.26460i	0.0487603	+	0.0844553i	0.889375	−	0.457178i	$-0.151140\pi$
$719$	1.30747	+	2.26460i	0.0487603	+	0.0844553i	−0.840615	+	0.541633i	$0.817806\pi$
$720$		0			0
$721$	20.3687	−	35.2796i	0.758570	−	1.31388i
$722$	0.926433	−	5.25406i	0.0344783	−	0.195536i
$723$		0			0
$724$	−19.4491	−	7.07889i	−0.722819	−	0.263085i
$725$	11.7216	+	66.4767i	0.435330	+	2.46888i
$726$		0			0
$727$	−3.14022	−	2.63495i	−0.116464	−	0.0977250i	0.582696	−	0.812690i	$-0.301998\pi$
$727$	−3.14022	−	2.63495i	−0.116464	−	0.0977250i	−0.699160	+	0.714965i	$0.746442\pi$
$728$	−14.9495			−0.554067
$729$		0			0
$730$	−29.6117			−1.09598
$731$	−14.3097	−	12.0073i	−0.529265	−	0.444106i
$732$		0			0
$733$	−6.63475	−	37.6275i	−0.245060	−	1.38981i	−0.820353	−	0.571858i	$-0.806223\pi$
$733$	−6.63475	−	37.6275i	−0.245060	−	1.38981i	0.575293	−	0.817948i	$-0.304888\pi$
$734$	−15.8188	−	5.75756i	−0.583882	−	0.212516i
$735$		0			0
$736$	−2.77807	+	15.7552i	−0.102401	+	0.580744i
$737$	0.476529	−	0.825373i	0.0175532	−	0.0304030i
$738$		0			0
$739$	12.1047	+	20.9660i	0.445279	+	0.771247i	0.998072	−	0.0620725i	$-0.0197710\pi$
$739$	12.1047	+	20.9660i	0.445279	+	0.771247i	−0.552792	+	0.833319i	$0.686438\pi$
$740$	−29.6844	+	10.8042i	−1.09122	+	0.397171i
$741$		0			0
$742$	2.06599	−	1.73357i	0.0758448	−	0.0636414i
$743$	−2.53667	+	2.12852i	−0.0930616	+	0.0780879i	−0.688131	−	0.725586i	$-0.741569\pi$
$743$	−2.53667	+	2.12852i	−0.0930616	+	0.0780879i	0.595070	+	0.803674i	$0.297124\pi$
$744$		0			0
$745$	4.63429	−	1.68674i	0.169787	−	0.0617974i
$746$	−6.70527	−	11.6139i	−0.245497	−	0.425214i
$747$		0			0
$748$	0.299011	−	0.517902i	0.0109329	−	0.0189364i
$749$	−2.88191	+	16.3441i	−0.105303	+	0.597202i
$750$		0			0
$751$	−12.8841	−	4.68944i	−0.470149	−	0.171120i	0.0960710	−	0.995374i	$-0.469372\pi$
$751$	−12.8841	−	4.68944i	−0.470149	−	0.171120i	−0.566220	+	0.824254i	$0.691595\pi$
$752$	−0.0538049	−	0.305143i	−0.00196206	−	0.0111274i
$753$		0			0
$754$	−10.9115	−	9.15581i	−0.397372	−	0.333435i
$755$	30.4807			1.10931
$756$		0			0
$757$	12.3833			0.450079			0.225040	−	0.974350i	$-0.427749\pi$
$757$	12.3833			0.450079			0.225040	+	0.974350i	$0.427749\pi$
$758$	−6.63382	−	5.56643i	−0.240951	−	0.202182i
$759$		0			0
$760$	6.87417	+	38.9854i	0.249352	+	1.41415i
$761$	−7.12536	−	2.59342i	−0.258294	−	0.0940114i	0.209628	−	0.977781i	$-0.432775\pi$
$761$	−7.12536	−	2.59342i	−0.258294	−	0.0940114i	−0.467922	+	0.883770i	$0.654997\pi$
$762$		0			0
$763$	5.93289	−	33.6471i	0.214785	−	1.21811i
$764$	−10.7185	+	18.5650i	−0.387783	+	0.671660i
$765$		0			0
$766$	12.4829	+	21.6211i	0.451026	+	0.781201i
$767$	11.6035	−	4.22334i	0.418980	−	0.152496i
$768$		0			0
$769$	2.46451	−	2.06797i	0.0888724	−	0.0745728i	−0.597269	−	0.802041i	$-0.703748\pi$
$769$	2.46451	−	2.06797i	0.0888724	−	0.0745728i	0.686141	+	0.727468i	$0.259303\pi$
$770$	0.927833	−	0.778544i	0.0334368	−	0.0280568i
$771$		0			0
$772$	−2.29648	+	0.835852i	−0.0826523	+	0.0300830i
$773$	0.0922341	+	0.159754i	0.00331743	+	0.00574596i	0.867679	−	0.497124i	$-0.165611\pi$
$773$	0.0922341	+	0.159754i	0.00331743	+	0.00574596i	−0.864362	+	0.502870i	$0.832277\pi$
$774$		0			0
$775$	26.0526	−	45.1245i	0.935838	−	1.62092i
$776$	−1.92495	+	10.9169i	−0.0691015	+	0.391894i
$777$		0			0
$778$	8.99437	+	3.27368i	0.322464	+	0.117367i
$779$	−3.62243	−	20.5438i	−0.129787	−	0.736058i
$780$		0			0
$781$	−1.90689	−	1.60007i	−0.0682338	−	0.0572550i
$782$	−7.48576			−0.267690
$783$		0			0
$784$	0.0932736			0.00333120
$785$	−36.7085	−	30.8021i	−1.31018	−	1.09937i
$786$		0			0
$787$	−0.0830066	−	0.470754i	−0.00295887	−	0.0167806i	0.983293	−	0.182032i	$-0.0582675\pi$
$787$	−0.0830066	−	0.470754i	−0.00295887	−	0.0167806i	−0.986251	+	0.165252i	$0.947156\pi$
$788$	24.4287	+	8.89132i	0.870237	+	0.316740i
$789$		0			0
$790$	0.751497	−	4.26195i	0.0267370	−	0.151633i
$791$	−2.52687	+	4.37667i	−0.0898453	+	0.155617i
$792$		0			0
$793$	4.55896	+	7.89636i	0.161894	+	0.280408i
$794$	−14.9628	+	5.44600i	−0.531008	+	0.193271i
$795$		0			0
$796$	2.89780	−	2.43155i	0.102710	−	0.0861839i
$797$	11.1068	−	9.31970i	0.393422	−	0.330121i	−0.424522	−	0.905418i	$-0.639558\pi$
$797$	11.1068	−	9.31970i	0.393422	−	0.330121i	0.817945	+	0.575297i	$0.195113\pi$
$798$		0			0
$799$	−20.8525	+	7.58969i	−0.737709	+	0.268504i
$800$	28.3307	+	49.0702i	1.00164	+	1.73489i
$801$		0			0
$802$	0.630415	−	1.09191i	0.0222607	−	0.0385567i
$803$	0.244938	−	1.38911i	0.00864367	−	0.0490207i
$804$		0			0
$805$	22.5993	+	8.22546i	0.796519	+	0.289909i
$806$	1.90925	+	10.8279i	0.0672506	+	0.381397i
$807$		0			0
$808$	−17.6366	−	14.7988i	−0.620452	−	0.520621i
$809$	−14.8743			−0.522954			−0.261477	−	0.965210i	$-0.584210\pi$
$809$	−14.8743			−0.522954			−0.261477	+	0.965210i	$0.584210\pi$
$810$		0			0
$811$	21.5963			0.758347			0.379174	−	0.925325i	$-0.376208\pi$
$811$	21.5963			0.758347			0.379174	+	0.925325i	$0.376208\pi$
$812$	13.7900	+	11.5712i	0.483933	+	0.406068i
$813$		0			0
$814$	0.164725	+	0.934204i	0.00577362	+	0.0327438i
$815$	50.1134	+	18.2398i	1.75540	+	0.638912i
$816$		0			0
$817$	−3.88847	+	22.0526i	−0.136040	+	0.771523i
$818$	3.78312	−	6.55255i	0.132274	−	0.229105i
$819$		0			0
$820$	−13.8020	−	23.9058i	−0.481987	−	0.834826i
$821$	3.08347	−	1.12229i	0.107614	−	0.0391683i	−0.287652	−	0.957735i	$-0.592875\pi$
$821$	3.08347	−	1.12229i	0.107614	−	0.0391683i	0.395266	+	0.918567i	$0.370652\pi$
$822$		0			0
$823$	10.5189	−	8.82639i	0.366665	−	0.307669i	−0.440775	−	0.897617i	$-0.645296\pi$
$823$	10.5189	−	8.82639i	0.366665	−	0.307669i	0.807441	+	0.589949i	$0.200852\pi$
$824$	40.5296	−	34.0084i	1.41192	−	1.18474i
$825$		0			0
$826$	9.24480	−	3.36483i	0.321668	−	0.117077i
$827$	−10.1163	−	17.5220i	−0.351779	−	0.609300i	0.634782	−	0.772691i	$-0.281090\pi$
$827$	−10.1163	−	17.5220i	−0.351779	−	0.609300i	−0.986561	+	0.163392i	$0.947757\pi$
$828$		0			0
$829$	−12.7638	+	22.1076i	−0.443306	+	0.767828i	−0.997932	−	0.0642710i	$-0.979528\pi$
$829$	−12.7638	+	22.1076i	−0.443306	+	0.767828i	0.554627	+	0.832099i	$0.312861\pi$
$830$	5.02094	−	28.4752i	0.174280	−	0.988388i
$831$		0			0
$832$	−11.4251	−	4.15841i	−0.396096	−	0.144167i
$833$	−1.15998	−	6.57856i	−0.0401908	−	0.227934i
$834$		0			0
$835$	−11.0458	−	9.26849i	−0.382254	−	0.320749i
$836$	−0.716881			−0.0247939
$837$		0			0
$838$	10.8265			0.373994
$839$	13.3139	+	11.1717i	0.459646	+	0.385688i	0.843001	−	0.537913i	$-0.180787\pi$
$839$	13.3139	+	11.1717i	0.459646	+	0.385688i	−0.383355	+	0.923601i	$0.625231\pi$
$840$		0			0
$841$	2.79860	+	15.8717i	0.0965035	+	0.547298i
$842$	9.18614	+	3.34348i	0.316575	+	0.115224i
$843$		0			0
$844$	−0.214660	+	1.21740i	−0.00738890	+	0.0419045i
$845$	13.9363	−	24.1384i	0.479423	−	0.830385i
$846$		0			0
$847$	−11.9875	−	20.7630i	−0.411896	−	0.713424i
$848$	0.0552549	−	0.0201112i	0.00189746	−	0.000690620i
$849$		0			0
$850$	−20.3097	+	17.0419i	−0.696618	+	0.584532i
$851$	−14.4290	+	12.1074i	−0.494620	+	0.415036i
$852$		0			0
$853$	−12.5005	+	4.54980i	−0.428008	+	0.155782i	−0.547037	−	0.837109i	$-0.684244\pi$
$853$	−12.5005	+	4.54980i	−0.428008	+	0.155782i	0.119029	+	0.992891i	$0.462022\pi$
$854$	3.63223	+	6.29120i	0.124292	+	0.215280i
$855$		0			0
$856$	−10.7772	+	18.6666i	−0.368357	+	0.638013i
$857$	−3.45929	+	19.6186i	−0.118167	+	0.670159i	0.866966	+	0.498367i	$0.166067\pi$
$857$	−3.45929	+	19.6186i	−0.118167	+	0.670159i	−0.985133	+	0.171792i	$0.945044\pi$
$858$		0			0
$859$	−24.7558	−	9.01039i	−0.844658	−	0.307430i	−0.116798	−	0.993156i	$-0.537263\pi$
$859$	−24.7558	−	9.01039i	−0.844658	−	0.307430i	−0.727860	+	0.685725i	$0.759485\pi$
$860$	5.14543	+	29.1812i	0.175458	+	0.995070i
$861$		0			0
$862$	24.8548	+	20.8556i	0.846557	+	0.710346i
$863$	38.2995			1.30373			0.651866	−	0.758334i	$-0.273987\pi$
$863$	38.2995			1.30373			0.651866	+	0.758334i	$0.273987\pi$
$864$		0			0
$865$	−6.04963			−0.205694
$866$	25.5974	+	21.4788i	0.869837	+	0.729880i
$867$		0			0
$868$	−2.41292	−	13.6844i	−0.0819000	−	0.464478i
$869$	0.193715	+	0.0705066i	0.00657134	+	0.00239177i
$870$		0			0
$871$	−2.45589	+	13.9280i	−0.0832146	+	0.471934i
$872$	22.1866	−	38.4283i	0.751333	−	1.30135i
$873$		0			0
$874$	4.48680	+	7.77136i	0.151768	+	0.262870i
$875$	40.2178	−	14.6381i	1.35961	−	0.494858i
$876$		0			0
$877$	−20.7271	+	17.3921i	−0.699906	+	0.587291i	−0.921747	−	0.387792i	$-0.873238\pi$
$877$	−20.7271	+	17.3921i	−0.699906	+	0.587291i	0.221841	+	0.975083i	$0.428793\pi$
$878$	−0.136096	+	0.114198i	−0.00459303	+	0.00385401i
$879$		0			0
$880$	0.0248149	−	0.00903189i	0.000836511	−	0.000304465i
$881$	−15.2888	−	26.4810i	−0.515093	−	0.892167i	−0.999847	−	0.0175162i	$-0.994424\pi$
$881$	−15.2888	−	26.4810i	−0.515093	−	0.892167i	0.484754	−	0.874651i	$-0.338909\pi$
$882$		0			0
$883$	−22.0526	+	38.1963i	−0.742130	+	1.28541i	0.209394	+	0.977831i	$0.432851\pi$
$883$	−22.0526	+	38.1963i	−0.742130	+	1.28541i	−0.951524	+	0.307575i	$0.900482\pi$
$884$	−1.54101	+	8.73951i	−0.0518298	+	0.293942i
$885$		0			0
$886$	17.5429	+	6.38510i	0.589366	+	0.214512i
$887$	−1.36912	−	7.76466i	−0.0459705	−	0.260712i	0.953157	−	0.302476i	$-0.0978132\pi$
$887$	−1.36912	−	7.76466i	−0.0459705	−	0.260712i	−0.999127	+	0.0417644i	$0.986702\pi$
$888$		0			0
$889$	−0.0701076	−	0.0588272i	−0.00235133	−	0.00197300i
$890$	−26.3432			−0.883025
$891$		0			0
$892$	−22.4287			−0.750969
$893$	20.3778	+	17.0990i	0.681917	+	0.572196i
$894$		0			0
$895$	−8.21348	−	46.5809i	−0.274546	−	1.55703i
$896$	14.0480	+	5.11305i	0.469310	+	0.170815i
$897$		0			0
$898$	5.07883	−	28.8035i	0.169483	−	0.961185i
$899$	17.4128	−	30.1599i	0.580750	−	1.00589i
$900$		0			0
$901$	−2.10560	−	3.64701i	−0.0701477	−	0.121499i
$902$	−0.778943	+	0.283512i	−0.0259360	+	0.00943993i
$903$		0			0
$904$	−5.02797	+	4.21897i	−0.167228	+	0.140321i
$905$	−50.1416	+	42.0738i	−1.66676	+	1.39858i
$906$		0			0
$907$	12.1284	−	4.41436i	0.402715	−	0.146576i	−0.132718	−	0.991154i	$-0.542370\pi$
$907$	12.1284	−	4.41436i	0.402715	−	0.146576i	0.535433	+	0.844577i	$0.320148\pi$
$908$	−1.62226	−	2.80984i	−0.0538367	−	0.0932479i
$909$		0			0
$910$	−8.98680	+	15.5656i	−0.297909	+	0.515994i
$911$	3.67886	−	20.8639i	0.121886	−	0.691251i	−0.861223	−	0.508228i	$-0.830301\pi$
$911$	3.67886	−	20.8639i	0.121886	−	0.691251i	0.983109	−	0.183023i	$-0.0585882\pi$
$912$		0			0
$913$	1.29426	+	0.471073i	0.0428339	+	0.0155902i
$914$	0.00521457	+	0.0295733i	0.000172483	+	0.000978197i
$915$		0			0
$916$	3.25402	+	2.73045i	0.107516	+	0.0902166i
$917$	−40.0871			−1.32379
$918$		0			0
$919$	31.4688			1.03806			0.519031	−	0.854756i	$-0.326293\pi$
$919$	31.4688			1.03806			0.519031	+	0.854756i	$0.326293\pi$
$920$	23.9270	+	20.0771i	0.788848	+	0.661922i
$921$		0			0
$922$	2.28848	+	12.9786i	0.0753669	+	0.427427i
$923$	34.7117	+	12.6340i	1.14255	+	0.415854i
$924$		0			0
$925$	−11.5842	+	65.6975i	−0.380888	+	2.16012i
$926$	−13.3853	+	23.1840i	−0.439869	+	0.761875i
$927$		0			0
$928$	18.9354	+	32.7971i	0.621585	+	1.07662i
$929$	2.18644	−	0.795800i	0.0717348	−	0.0261093i	−0.305904	−	0.952063i	$-0.598958\pi$
$929$	2.18644	−	0.795800i	0.0717348	−	0.0261093i	0.377638	+	0.925953i	$0.376736\pi$
$930$		0			0
$931$	−6.13429	+	5.14728i	−0.201043	+	0.168695i
$932$	−5.75624	+	4.83006i	−0.188552	+	0.158214i
$933$		0			0
$934$	−0.422046	+	0.153612i	−0.0138098	+	0.00502634i
$935$	−0.945622	−	1.63787i	−0.0309252	−	0.0535639i
$936$		0			0
$937$	5.49912	−	9.52476i	0.179649	−	0.311160i	−0.762112	−	0.647446i	$-0.775837\pi$
$937$	5.49912	−	9.52476i	0.179649	−	0.311160i	0.941760	+	0.336285i	$0.109171\pi$
$938$	−1.95666	+	11.0968i	−0.0638872	+	0.362323i
$939$		0			0
$940$	33.0774	+	12.0392i	1.07887	+	0.392675i
$941$	−4.18556	−	23.7375i	−0.136445	−	0.773821i	−0.973842	−	0.227225i	$-0.927035\pi$
$941$	−4.18556	−	23.7375i	−0.136445	−	0.773821i	0.837397	−	0.546596i	$-0.184076\pi$
$942$		0			0
$943$	−12.6086	−	10.5799i	−0.410592	−	0.344528i
$944$	0.214498			0.00698131
$945$		0			0
$946$	0.889814			0.0289304
$947$	−9.13088	−	7.66172i	−0.296714	−	0.248972i	0.482261	−	0.876028i	$-0.339816\pi$
$947$	−9.13088	−	7.66172i	−0.296714	−	0.248972i	−0.778975	+	0.627055i	$0.784260\pi$
$948$		0			0
$949$	3.63475	+	20.6137i	0.117989	+	0.669149i
$950$	29.8653	+	10.8701i	0.968958	+	0.352672i
$951$		0			0
$952$	−3.22951	+	18.3155i	−0.104669	+	0.593608i
$953$	18.4145	−	31.8948i	0.596503	−	1.03317i	−0.396830	−	0.917892i	$-0.629890\pi$
$953$	18.4145	−	31.8948i	0.596503	−	1.03317i	0.993333	−	0.115281i	$-0.0367770\pi$
$954$		0			0
$955$	33.8974	+	58.7120i	1.09689	+	1.89988i
$956$	−33.3723	+	12.1465i	−1.07934	+	0.392846i
$957$		0			0
$958$	10.4083	−	8.73362i	0.336278	−	0.282170i
$959$	−23.9552	+	20.1008i	−0.773553	+	0.649088i
$960$		0			0
$961$	3.86959	−	1.40841i	0.124825	−	0.0454327i
$962$	−7.03849	−	12.1910i	−0.226930	−	0.393054i
$963$		0			0
$964$	13.6934	−	23.7177i	0.441035	−	0.763895i
$965$	−1.34208	+	7.61132i	−0.0432031	+	0.245017i
$966$		0			0
$967$	−50.3303	−	18.3187i	−1.61851	−	0.589090i	−0.635415	−	0.772171i	$-0.719171\pi$
$967$	−50.3303	−	18.3187i	−1.61851	−	0.589090i	−0.983098	+	0.183081i	$0.941393\pi$
$968$	−5.40697	−	30.6645i	−0.173787	−	0.985594i
$969$		0			0
$970$	10.2096	+	8.56688i	0.327811	+	0.275066i
$971$	53.2327			1.70832			0.854159	−	0.520012i	$-0.174073\pi$
$971$	53.2327			1.70832			0.854159	+	0.520012i	$0.174073\pi$
$972$		0			0
$973$	−22.9299			−0.735100
$974$	−19.8799	−	16.6812i	−0.636992	−	0.534499i
$975$		0			0
$976$	0.0275033	+	0.155979i	0.000880358	+	0.00499276i
$977$	−12.6454	−	4.60256i	−0.404563	−	0.147249i	0.131720	−	0.991287i	$-0.457950\pi$
$977$	−12.6454	−	4.60256i	−0.404563	−	0.147249i	−0.536283	+	0.844038i	$0.680172\pi$
$978$		0			0
$979$	0.217901	−	1.23578i	0.00696416	−	0.0394957i
$980$	−5.29813	+	9.17664i	−0.169243	+	0.293137i
$981$		0			0
$982$	0.948615	+	1.64305i	0.0302715	+	0.0524318i
$983$	9.62361	−	3.50271i	0.306945	−	0.111719i	−0.183955	−	0.982935i	$-0.558890\pi$
$983$	9.62361	−	3.50271i	0.306945	−	0.111719i	0.490900	+	0.871216i	$0.336668\pi$
$984$		0			0
$985$	62.9796	−	52.8461i	2.00670	−	1.68382i
$986$	−13.5744	+	11.3903i	−0.432298	+	0.362741i
$987$		0			0
$988$	9.99660	−	3.63846i	0.318034	−	0.115755i
$989$	8.83409	+	15.3011i	0.280908	+	0.486547i
$990$		0			0
$991$	−1.00000	+	1.73205i	−0.0317660	+	0.0550204i	−0.881471	−	0.472237i	$-0.843446\pi$
$991$	−1.00000	+	1.73205i	−0.0317660	+	0.0550204i	0.849705	+	0.527258i	$0.176780\pi$
$992$	5.07620	−	28.7886i	0.161169	−	0.914038i
$993$		0			0
$994$	27.6556	+	10.0658i	0.877182	+	0.319268i
$995$	−2.07738	−	11.7814i	−0.0658574	−	0.373496i
$996$		0			0
$997$	29.4939	+	24.7483i	0.934081	+	0.783787i	0.976546	−	0.215311i	$-0.0690764\pi$
$997$	29.4939	+	24.7483i	0.934081	+	0.783787i	−0.0424642	+	0.999098i	$0.513521\pi$
$998$	−6.59121			−0.208641
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.e.b.406.1		6
3.2	odd	2		729.2.e.g.406.1		6
9.2	odd	6		729.2.e.h.649.1		6
9.4	even	3		729.2.e.i.163.1		6
9.5	odd	6		729.2.e.a.163.1		6
9.7	even	3		729.2.e.c.649.1		6
27.2	odd	18		243.2.c.f.82.1		6
27.4	even	9		729.2.e.c.82.1		6
27.5	odd	18		729.2.e.g.325.1		6
27.7	even	9		243.2.a.f.1.1	yes	3
27.11	odd	18		243.2.c.f.163.1		6
27.13	even	9		729.2.e.i.568.1		6
27.14	odd	18		729.2.e.a.568.1		6
27.16	even	9		243.2.c.e.163.3		6
27.20	odd	18		243.2.a.e.1.3	✓	3
27.22	even	9	inner	729.2.e.b.325.1		6
27.23	odd	18		729.2.e.h.82.1		6
27.25	even	9		243.2.c.e.82.3		6
108.7	odd	18		3888.2.a.bk.1.3		3
108.47	even	18		3888.2.a.bd.1.1		3
135.34	even	18		6075.2.a.bq.1.3		3
135.74	odd	18		6075.2.a.bv.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
243.2.a.e.1.3	✓	3	27.20	odd	18
243.2.a.f.1.1	yes	3	27.7	even	9
243.2.c.e.82.3		6	27.25	even	9
243.2.c.e.163.3		6	27.16	even	9
243.2.c.f.82.1		6	27.2	odd	18
243.2.c.f.163.1		6	27.11	odd	18
729.2.e.a.163.1		6	9.5	odd	6
729.2.e.a.568.1		6	27.14	odd	18
729.2.e.b.325.1		6	27.22	even	9	inner
729.2.e.b.406.1		6	1.1	even	1	trivial
729.2.e.c.82.1		6	27.4	even	9
729.2.e.c.649.1		6	9.7	even	3
729.2.e.g.325.1		6	27.5	odd	18
729.2.e.g.406.1		6	3.2	odd	2
729.2.e.h.82.1		6	27.23	odd	18
729.2.e.h.649.1		6	9.2	odd	6
729.2.e.i.163.1		6	9.4	even	3
729.2.e.i.568.1		6	27.13	even	9
3888.2.a.bd.1.1		3	108.47	even	18
3888.2.a.bk.1.3		3	108.7	odd	18
6075.2.a.bq.1.3		3	135.34	even	18
6075.2.a.bv.1.1		3	135.74	odd	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.673648 - 0.565258i) q^{2} +(-0.213011 - 1.20805i) q^{4} +(-3.64543 - 1.32683i) q^{5} +(-0.379385 + 2.15160i) q^{7} +(-1.41875 + 2.45734i) q^{8} +O(q^{10})\)	\(q+(-0.673648 - 0.565258i) q^{2} +(-0.213011 - 1.20805i) q^{4} +(-3.64543 - 1.32683i) q^{5} +(-0.379385 + 2.15160i) q^{7} +(-1.41875 + 2.45734i) q^{8} +(1.70574 + 2.95442i) q^{10} +(-0.152704 + 0.0555796i) q^{11} +(1.84730 - 1.55007i) q^{13} +(1.47178 - 1.23497i) q^{14} +(0.0393628 - 0.0143269i) q^{16} +(-1.50000 - 2.59808i) q^{17} +(-1.79813 + 3.11446i) q^{19} +(-0.826352 + 4.68647i) q^{20} +(0.134285 + 0.0488759i) q^{22} +(0.492726 + 2.79439i) q^{23} +(7.69846 + 6.45978i) q^{25} -2.12061 q^{26} +2.68004 q^{28} +(5.14543 + 4.31753i) q^{29} +(-0.900330 - 5.10602i) q^{31} +(5.29813 + 1.92836i) q^{32} +(-0.458111 + 2.59808i) q^{34} +(4.23783 - 7.34013i) q^{35} +(3.31908 + 5.74881i) q^{37} +(2.97178 - 1.08164i) q^{38} +(8.43242 - 7.07564i) q^{40} +(-4.44356 + 3.72859i) q^{41} +(5.85117 - 2.12965i) q^{43} +(0.0996702 + 0.172634i) q^{44} +(1.24763 - 2.16095i) q^{46} +(1.28446 - 7.28455i) q^{47} +(2.09240 + 0.761570i) q^{49} +(-1.53462 - 8.70323i) q^{50} +(-2.26604 - 1.90144i) q^{52} +1.40373 q^{53} +0.630415 q^{55} +(-4.74897 - 3.98486i) q^{56} +(-1.02569 - 5.81699i) q^{58} +(4.81180 + 1.75135i) q^{59} +(-0.656574 + 3.72362i) q^{61} +(-2.27972 + 3.94858i) q^{62} +(-2.52094 - 4.36640i) q^{64} +(-8.79086 + 3.19961i) q^{65} +(-4.49273 + 3.76984i) q^{67} +(-2.81908 + 2.36549i) q^{68} +(-7.00387 + 2.54920i) q^{70} +(7.65910 + 13.2660i) q^{71} +(-4.34002 + 7.51714i) q^{73} +(1.01367 - 5.74881i) q^{74} +(4.14543 + 1.50881i) q^{76} +(-0.0616516 - 0.349643i) q^{77} +(-0.971782 - 0.815422i) q^{79} -0.162504 q^{80} +5.10101 q^{82} +(-6.49273 - 5.44804i) q^{83} +(2.02094 + 11.4613i) q^{85} +(-5.14543 - 1.87278i) q^{86} +(0.0800699 - 0.454099i) q^{88} +(-3.86097 + 6.68739i) q^{89} +(2.63429 + 4.56272i) q^{91} +(3.27079 - 1.19047i) q^{92} +(-4.98293 + 4.18117i) q^{94} +(10.6873 - 8.96773i) q^{95} +(3.67112 - 1.33618i) q^{97} +(-0.979055 - 1.69577i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} - 9 q^{4} - 6 q^{5} + 9 q^{7} - 6 q^{8}+O(q^{10}) \) 6 * q - 3 * q^2 - 9 * q^4 - 6 * q^5 + 9 * q^7 - 6 * q^8	\( 6 q - 3 q^{2} - 9 q^{4} - 6 q^{5} + 9 q^{7} - 6 q^{8} - 3 q^{11} + 9 q^{13} - 6 q^{14} + 9 q^{16} - 9 q^{17} + 3 q^{19} - 6 q^{20} - 9 q^{22} - 15 q^{23} + 18 q^{25} - 24 q^{26} - 24 q^{28} + 15 q^{29} + 9 q^{31} + 18 q^{32} - 9 q^{34} + 6 q^{35} + 3 q^{37} + 3 q^{38} + 27 q^{40} + 3 q^{41} + 9 q^{43} + 15 q^{44} - 9 q^{46} + 15 q^{47} + 9 q^{49} + 15 q^{50} - 9 q^{52} + 36 q^{53} + 18 q^{55} - 3 q^{56} - 36 q^{58} - 6 q^{59} + 18 q^{61} + 12 q^{62} - 12 q^{64} - 21 q^{65} - 9 q^{67} - 18 q^{70} + 9 q^{71} - 6 q^{73} - 15 q^{74} + 9 q^{76} + 3 q^{77} + 9 q^{79} - 6 q^{80} + 36 q^{82} - 21 q^{83} + 9 q^{85} - 15 q^{86} + 9 q^{88} + 6 q^{91} + 48 q^{92} - 9 q^{94} + 42 q^{95} + 36 q^{97} - 9 q^{98}+O(q^{100}) \) 6 * q - 3 * q^2 - 9 * q^4 - 6 * q^5 + 9 * q^7 - 6 * q^8 - 3 * q^11 + 9 * q^13 - 6 * q^14 + 9 * q^16 - 9 * q^17 + 3 * q^19 - 6 * q^20 - 9 * q^22 - 15 * q^23 + 18 * q^25 - 24 * q^26 - 24 * q^28 + 15 * q^29 + 9 * q^31 + 18 * q^32 - 9 * q^34 + 6 * q^35 + 3 * q^37 + 3 * q^38 + 27 * q^40 + 3 * q^41 + 9 * q^43 + 15 * q^44 - 9 * q^46 + 15 * q^47 + 9 * q^49 + 15 * q^50 - 9 * q^52 + 36 * q^53 + 18 * q^55 - 3 * q^56 - 36 * q^58 - 6 * q^59 + 18 * q^61 + 12 * q^62 - 12 * q^64 - 21 * q^65 - 9 * q^67 - 18 * q^70 + 9 * q^71 - 6 * q^73 - 15 * q^74 + 9 * q^76 + 3 * q^77 + 9 * q^79 - 6 * q^80 + 36 * q^82 - 21 * q^83 + 9 * q^85 - 15 * q^86 + 9 * q^88 + 6 * q^91 + 48 * q^92 - 9 * q^94 + 42 * q^95 + 36 * q^97 - 9 * q^98

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