LMFDB - Embedded newform 729.2.e.s.163.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("729.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 18x^{10} + 105x^{8} + 266x^{6} + 306x^{4} + 132x^{2} + 1 $ x^12 + 18x^10 + 105x^8 + 266x^6 + 306x^4 + 132*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			163.2
Root			$-3.10658i$ of defining polynomial
Character	$\chi$	$=$	729.163
Dual form			729.2.e.s.568.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.99687 - 0.726803i) q^{2} +(1.92717 - 1.61709i) q^{4} +(-0.359615 - 2.03948i) q^{5} +(3.71430 + 3.11667i) q^{7} +(0.547989 - 0.949144i) q^{8} +(-2.20040 - 3.81121i) q^{10} +(0.720551 - 4.08645i) q^{11} +(1.14268 + 0.415902i) q^{13} +(9.68219 + 3.52403i) q^{14} +(-0.469286 + 2.66145i) q^{16} +(-1.18182 - 2.04697i) q^{17} +(0.919003 - 1.59176i) q^{19} +(-3.99106 - 3.34890i) q^{20} +(-1.53119 - 8.68382i) q^{22} +(-3.29673 + 2.76628i) q^{23} +(0.668315 - 0.243247i) q^{25} +2.58407 q^{26} +12.1980 q^{28} +(-2.80199 + 1.01984i) q^{29} +(1.12883 - 0.947203i) q^{31} +(1.37788 + 7.81432i) q^{32} +(-3.84769 - 3.22859i) q^{34} +(5.02066 - 8.69603i) q^{35} +(-4.48554 - 7.76918i) q^{37} +(0.678238 - 3.84648i) q^{38} +(-2.13282 - 0.776284i) q^{40} +(-2.12420 - 0.773145i) q^{41} +(-0.952435 + 5.40153i) q^{43} +(-5.21953 - 9.04050i) q^{44} +(-4.57260 + 7.91998i) q^{46} +(5.50260 + 4.61723i) q^{47} +(2.86687 + 16.2588i) q^{49} +(1.15775 - 0.971466i) q^{50} +(2.87470 - 1.04630i) q^{52} -6.32803 q^{53} -8.59334 q^{55} +(4.99356 - 1.81751i) q^{56} +(-4.85400 + 4.07299i) q^{58} +(0.0455404 + 0.258272i) q^{59} +(-3.41319 - 2.86401i) q^{61} +(1.56571 - 2.71188i) q^{62} +(5.72840 + 9.92188i) q^{64} +(0.437297 - 2.48004i) q^{65} +(-3.88197 - 1.41292i) q^{67} +(-5.58771 - 2.03376i) q^{68} +(3.70532 - 21.0139i) q^{70} +(-1.54276 - 2.67213i) q^{71} +(-6.38003 + 11.0505i) q^{73} +(-14.6037 - 12.2540i) q^{74} +(-0.802942 - 4.55371i) q^{76} +(15.4124 - 12.9326i) q^{77} +(-4.27786 + 1.55701i) q^{79} +5.59674 q^{80} -4.80368 q^{82} +(7.94328 - 2.89112i) q^{83} +(-3.74975 + 3.14642i) q^{85} +(2.02395 + 11.4784i) q^{86} +(-3.48378 - 2.92323i) q^{88} +(-8.48158 + 14.6905i) q^{89} +(2.94803 + 5.10614i) q^{91} +(-1.88004 + 10.6622i) q^{92} +(14.3438 + 5.22072i) q^{94} +(-3.57685 - 1.30187i) q^{95} +(-0.887302 + 5.03214i) q^{97} +(17.5417 + 30.3831i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{2} - 3 q^{4} - 12 q^{5} - 3 q^{7} + 6 q^{8} - 6 q^{10} + 3 q^{11} + 6 q^{13} + 6 q^{14} + 27 q^{16} - 9 q^{17} - 12 q^{19} - 39 q^{20} - 39 q^{22} - 21 q^{23} + 6 q^{25} - 48 q^{26} + 6 q^{28}+ \cdots + 18 q^{98}+O(q^{100}) $ 12 * q + 3 * q^2 - 3 * q^4 - 12 * q^5 - 3 * q^7 + 6 * q^8 - 6 * q^10 + 3 * q^11 + 6 * q^13 + 6 * q^14 + 27 * q^16 - 9 * q^17 - 12 * q^19 - 39 * q^20 - 39 * q^22 - 21 * q^23 + 6 * q^25 - 48 * q^26 + 6 * q^28 - 6 * q^29 + 6 * q^31 - 27 * q^32 - 18 * q^34 + 30 * q^35 - 3 * q^37 - 3 * q^38 + 33 * q^40 + 15 * q^41 - 30 * q^43 - 33 * q^44 + 3 * q^46 + 21 * q^47 - 3 * q^49 - 6 * q^50 + 18 * q^53 + 30 * q^55 - 15 * q^56 - 3 * q^58 - 30 * q^59 - 30 * q^61 - 30 * q^62 - 6 * q^64 + 12 * q^65 - 39 * q^67 - 18 * q^68 + 51 * q^70 - 12 * q^73 - 57 * q^74 + 57 * q^76 + 24 * q^77 + 15 * q^79 + 42 * q^80 - 42 * q^82 + 21 * q^83 + 54 * q^85 + 60 * q^86 + 12 * q^88 - 9 * q^89 - 18 * q^91 + 15 * q^92 + 33 * q^94 - 42 * q^95 - 12 * q^97 + 18 * q^98

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{8}{9}\right)$

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 $

$2$	1.99687	−	0.726803i	1.41200	−	0.513927i	0.480286	−	0.877112i	$-0.340533\pi$
$2$	1.99687	−	0.726803i	1.41200	−	0.513927i	0.931717	+	0.363185i	$0.118311\pi$
$3$		0			0
$3$		0			0
$4$	1.92717	−	1.61709i	0.963587	−	0.808546i
$5$	−0.359615	−	2.03948i	−0.160825	−	0.912082i	−0.953266	−	0.302134i	$-0.902301\pi$
$5$	−0.359615	−	2.03948i	−0.160825	−	0.912082i	0.792441	−	0.609949i	$-0.208810\pi$
$6$		0			0
$7$	3.71430	+	3.11667i	1.40387	+	1.17799i	0.959349	+	0.282222i	$0.0910716\pi$
$7$	3.71430	+	3.11667i	1.40387	+	1.17799i	0.444524	+	0.895767i	$0.353373\pi$
$8$	0.547989	−	0.949144i	0.193743	−	0.335573i
$9$		0			0
$10$	−2.20040	−	3.81121i	−0.695829	−	1.20521i
$11$	0.720551	−	4.08645i	0.217254	−	1.23211i	−0.659697	−	0.751532i	$-0.729315\pi$
$11$	0.720551	−	4.08645i	0.217254	−	1.23211i	0.876951	−	0.480579i	$-0.159573\pi$
$12$		0			0
$13$	1.14268	+	0.415902i	0.316923	+	0.115350i	0.495583	−	0.868560i	$-0.334954\pi$
$13$	1.14268	+	0.415902i	0.316923	+	0.115350i	−0.178661	+	0.983911i	$0.557176\pi$
$14$	9.68219	+	3.52403i	2.58767	+	0.941836i
$15$		0			0
$16$	−0.469286	+	2.66145i	−0.117322	+	0.665363i
$17$	−1.18182	−	2.04697i	−0.286633	−	0.496463i	0.686371	−	0.727252i	$-0.259203\pi$
$17$	−1.18182	−	2.04697i	−0.286633	−	0.496463i	−0.973004	+	0.230789i	$0.925869\pi$
$18$		0			0
$19$	0.919003	−	1.59176i	0.210834	−	0.365175i	−0.741142	−	0.671348i	$-0.765715\pi$
$19$	0.919003	−	1.59176i	0.210834	−	0.365175i	0.951976	+	0.306174i	$0.0990488\pi$
$20$	−3.99106	−	3.34890i	−0.892429	−	0.748837i
$21$		0			0
$22$	−1.53119	−	8.68382i	−0.326451	−	1.85140i
$23$	−3.29673	+	2.76628i	−0.687415	+	0.576809i	−0.918162	−	0.396204i	$-0.870327\pi$
$23$	−3.29673	+	2.76628i	−0.687415	+	0.576809i	0.230748	+	0.973014i	$0.425883\pi$
$24$		0			0
$25$	0.668315	−	0.243247i	0.133663	−	0.0486494i
$26$	2.58407			0.506777
$27$		0			0
$28$	12.1980			2.30521
$29$	−2.80199	+	1.01984i	−0.520317	+	0.189380i	−0.588810	−	0.808272i	$-0.700403\pi$
$29$	−2.80199	+	1.01984i	−0.520317	+	0.189380i	0.0684925	+	0.997652i	$0.478181\pi$
$30$		0			0
$31$	1.12883	−	0.947203i	0.202744	−	0.170123i	−0.535762	−	0.844369i	$-0.679976\pi$
$31$	1.12883	−	0.947203i	0.202744	−	0.170123i	0.738507	+	0.674246i	$0.235531\pi$
$32$	1.37788	+	7.81432i	0.243576	+	1.38139i
$33$		0			0
$34$	−3.84769	−	3.22859i	−0.659873	−	0.553699i
$35$	5.02066	−	8.69603i	0.848646	−	1.46990i
$36$		0			0
$37$	−4.48554	−	7.76918i	−0.737418	−	1.27725i	−0.953654	−	0.300905i	$-0.902711\pi$
$37$	−4.48554	−	7.76918i	−0.737418	−	1.27725i	0.216236	−	0.976341i	$-0.430622\pi$
$38$	0.678238	−	3.84648i	0.110025	−	0.623981i
$39$		0			0
$40$	−2.13282	−	0.776284i	−0.337229	−	0.122741i
$41$	−2.12420	−	0.773145i	−0.331744	−	0.120745i	0.170778	−	0.985310i	$-0.445372\pi$
$41$	−2.12420	−	0.773145i	−0.331744	−	0.120745i	−0.502522	+	0.864565i	$0.667594\pi$
$42$		0			0
$43$	−0.952435	+	5.40153i	−0.145245	+	0.823726i	0.821925	+	0.569596i	$0.192900\pi$
$43$	−0.952435	+	5.40153i	−0.145245	+	0.823726i	−0.967170	+	0.254130i	$0.918211\pi$
$44$	−5.21953	−	9.04050i	−0.786874	−	1.36291i
$45$		0			0
$46$	−4.57260	+	7.91998i	−0.674194	+	1.16774i
$47$	5.50260	+	4.61723i	0.802636	+	0.673492i	0.948838	−	0.315763i	$-0.102260\pi$
$47$	5.50260	+	4.61723i	0.802636	+	0.673492i	−0.146202	+	0.989255i	$0.546705\pi$
$48$		0			0
$49$	2.86687	+	16.2588i	0.409552	+	2.32269i
$50$	1.15775	−	0.971466i	0.163730	−	0.137386i
$51$		0			0
$52$	2.87470	−	1.04630i	0.398649	−	0.145096i
$53$	−6.32803			−0.869222			−0.434611	−	0.900618i	$-0.643114\pi$
$53$	−6.32803			−0.869222			−0.434611	+	0.900618i	$0.643114\pi$
$54$		0			0
$55$	−8.59334			−1.15873
$56$	4.99356	−	1.81751i	0.667293	−	0.242875i
$57$		0			0
$58$	−4.85400	+	4.07299i	−0.637362	+	0.534810i
$59$	0.0455404	+	0.258272i	0.00592886	+	0.0336242i	0.987629	−	0.156811i	$-0.0501213\pi$
$59$	0.0455404	+	0.258272i	0.00592886	+	0.0336242i	−0.981700	+	0.190435i	$0.939010\pi$
$60$		0			0
$61$	−3.41319	−	2.86401i	−0.437014	−	0.366699i	0.397576	−	0.917569i	$-0.369851\pi$
$61$	−3.41319	−	2.86401i	−0.437014	−	0.366699i	−0.834591	+	0.550870i	$0.814296\pi$
$62$	1.56571	−	2.71188i	0.198845	−	0.344410i
$63$		0			0
$64$	5.72840	+	9.92188i	0.716050	+	1.24024i
$65$	0.437297	−	2.48004i	0.0542401	−	0.307611i
$66$		0			0
$67$	−3.88197	−	1.41292i	−0.474258	−	0.172616i	0.0938223	−	0.995589i	$-0.470091\pi$
$67$	−3.88197	−	1.41292i	−0.474258	−	0.172616i	−0.568080	+	0.822973i	$0.692314\pi$
$68$	−5.58771	−	2.03376i	−0.677609	−	0.246630i
$69$		0			0
$70$	3.70532	−	21.0139i	0.442870	−	2.51164i
$71$	−1.54276	−	2.67213i	−0.183091	−	0.317124i	0.759840	−	0.650110i	$-0.225277\pi$
$71$	−1.54276	−	2.67213i	−0.183091	−	0.317124i	−0.942932	+	0.332986i	$0.891944\pi$
$72$		0			0
$73$	−6.38003	+	11.0505i	−0.746726	+	1.29337i	0.202658	+	0.979250i	$0.435042\pi$
$73$	−6.38003	+	11.0505i	−0.746726	+	1.29337i	−0.949384	+	0.314118i	$0.898291\pi$
$74$	−14.6037	−	12.2540i	−1.69765	−	1.42450i
$75$		0			0
$76$	−0.802942	−	4.55371i	−0.0921038	−	0.522346i
$77$	15.4124	−	12.9326i	1.75641	−	1.47380i
$78$		0			0
$79$	−4.27786	+	1.55701i	−0.481297	+	0.175178i	−0.571263	−	0.820767i	$-0.693546\pi$
$79$	−4.27786	+	1.55701i	−0.481297	+	0.175178i	0.0899659	+	0.995945i	$0.471324\pi$
$80$	5.59674			0.625734
$81$		0			0
$82$	−4.80368			−0.530478
$83$	7.94328	−	2.89112i	0.871888	−	0.317341i	0.132956	−	0.991122i	$-0.457553\pi$
$83$	7.94328	−	2.89112i	0.871888	−	0.317341i	0.738931	+	0.673781i	$0.235331\pi$
$84$		0			0
$85$	−3.74975	+	3.14642i	−0.406718	+	0.341277i
$86$	2.02395	+	11.4784i	0.218248	+	1.23775i
$87$		0			0
$88$	−3.48378	−	2.92323i	−0.371372	−	0.311618i
$89$	−8.48158	+	14.6905i	−0.899046	+	1.55719i	−0.0703304	+	0.997524i	$0.522405\pi$
$89$	−8.48158	+	14.6905i	−0.899046	+	1.55719i	−0.828716	+	0.559670i	$0.810928\pi$
$90$		0			0
$91$	2.94803	+	5.10614i	0.309038	+	0.535269i
$92$	−1.88004	+	10.6622i	−0.196007	+	1.11161i
$93$		0			0
$94$	14.3438	+	5.22072i	1.47945	+	0.538476i
$95$	−3.57685	−	1.30187i	−0.366977	−	0.133569i
$96$		0			0
$97$	−0.887302	+	5.03214i	−0.0900919	+	0.510937i	0.906049	+	0.423172i	$0.139083\pi$
$97$	−0.887302	+	5.03214i	−0.0900919	+	0.510937i	−0.996141	+	0.0877646i	$0.972028\pi$
$98$	17.5417	+	30.3831i	1.77198	+	3.06916i
$99$		0			0
$100$	0.894607	−	1.54951i	0.0894607	−	0.154951i
$101$	14.2330	+	11.9429i	1.41624	+	1.18836i	0.953319	+	0.301964i	$0.0976422\pi$
$101$	14.2330	+	11.9429i	1.41624	+	1.18836i	0.462918	+	0.886401i	$0.346802\pi$
$102$		0			0
$103$	1.56384	+	8.86895i	0.154089	+	0.873884i	0.959614	+	0.281321i	$0.0907726\pi$
$103$	1.56384	+	8.86895i	0.154089	+	0.873884i	−0.805524	+	0.592563i	$0.798116\pi$
$104$	1.02093	−	0.856659i	0.100110	−	0.0840024i
$105$		0			0
$106$	−12.6363	+	4.59923i	−1.22734	+	0.446717i
$107$	7.42680			0.717976			0.358988	−	0.933342i	$-0.383122\pi$
$107$	7.42680			0.717976			0.358988	+	0.933342i	$0.383122\pi$
$108$		0			0
$109$	−5.62396			−0.538678			−0.269339	−	0.963045i	$-0.586805\pi$
$109$	−5.62396			−0.538678			−0.269339	+	0.963045i	$0.586805\pi$
$110$	−17.1598	+	6.24567i	−1.63612	+	0.595501i
$111$		0			0
$112$	−10.0379	+	8.42283i	−0.948495	+	0.795882i
$113$	−0.417219	−	2.36617i	−0.0392487	−	0.222590i	0.958874	−	0.283831i	$-0.0916054\pi$
$113$	−0.417219	−	2.36617i	−0.0392487	−	0.222590i	−0.998123	+	0.0612406i	$0.980494\pi$
$114$		0			0
$115$	6.82732	+	5.72880i	0.636651	+	0.534214i
$116$	−3.75075	+	6.49649i	−0.348249	+	0.603184i
$117$		0			0
$118$	0.278652	+	0.482639i	0.0256520	+	0.0444305i
$119$	1.99010	−	11.2864i	0.182432	−	1.03462i
$120$		0			0
$121$	−5.84325	−	2.12677i	−0.531205	−	0.193343i
$122$	−8.89728	−	3.23835i	−0.805522	−	0.293186i
$123$		0			0
$124$	0.643744	−	3.65085i	0.0578099	−	0.327856i
$125$	−5.91378	−	10.2430i	−0.528945	−	0.916159i
$126$		0			0
$127$	4.61735	−	7.99748i	0.409723	−	0.709662i	−0.585135	−	0.810936i	$-0.698959\pi$
$127$	4.61735	−	7.99748i	0.409723	−	0.709662i	0.994859	+	0.101274i	$0.0322919\pi$
$128$	6.49322	+	5.44846i	0.573925	+	0.481580i
$129$		0			0
$130$	−0.929269	−	5.27015i	−0.0815023	−	0.462223i
$131$	−11.7504	+	9.85972i	−1.02663	+	0.861448i	−0.990447	−	0.137897i	$-0.955966\pi$
$131$	−11.7504	+	9.85972i	−1.02663	+	0.861448i	−0.0361871	+	0.999345i	$0.511521\pi$
$132$		0			0
$133$	8.37444	−	3.04805i	0.726156	−	0.264299i
$134$	−8.77871			−0.758365
$135$		0			0
$136$	−2.59049			−0.222133
$137$	3.42421	−	1.24631i	0.292550	−	0.106480i	−0.191576	−	0.981478i	$-0.561360\pi$
$137$	3.42421	−	1.24631i	0.292550	−	0.106480i	0.484126	+	0.874998i	$0.339138\pi$
$138$		0			0
$139$	10.1697	−	8.53335i	0.862579	−	0.723789i	−0.0999433	−	0.994993i	$-0.531866\pi$
$139$	10.1697	−	8.53335i	0.862579	−	0.723789i	0.962522	+	0.271204i	$0.0874217\pi$
$140$	−4.38660	−	24.8776i	−0.370735	−	2.10254i
$141$		0			0
$142$	−5.02280	−	4.21463i	−0.421504	−	0.353684i
$143$	2.52292	−	4.36983i	0.210977	−	0.365423i
$144$		0			0
$145$	3.08759	+	5.34786i	0.256410	+	0.444115i
$146$	−4.70856	+	26.7036i	−0.389683	+	2.21000i
$147$		0			0
$148$	−21.2079	−	7.71904i	−1.74328	−	0.634501i
$149$	−8.37359	−	3.04774i	−0.685991	−	0.249680i	−0.0245732	−	0.999698i	$-0.507823\pi$
$149$	−8.37359	−	3.04774i	−0.685991	−	0.249680i	−0.661418	+	0.750018i	$0.730045\pi$
$150$		0			0
$151$	−0.123708	+	0.701581i	−0.0100672	+	0.0570938i	−0.989428	−	0.145028i	$-0.953673\pi$
$151$	−0.123708	+	0.701581i	−0.0100672	+	0.0570938i	0.979360	+	0.202122i	$0.0647838\pi$
$152$	−1.00721	−	1.74453i	−0.0816953	−	0.141500i
$153$		0			0
$154$	21.3773	−	37.0265i	1.72263	−	2.98368i
$155$	−2.33775	−	1.96160i	−0.187772	−	0.157560i
$156$		0			0
$157$	−2.39948	−	13.6081i	−0.191499	−	1.08605i	−0.917316	−	0.398159i	$-0.869649\pi$
$157$	−2.39948	−	13.6081i	−0.191499	−	1.08605i	0.725817	−	0.687888i	$-0.241462\pi$
$158$	−7.41071	+	6.21832i	−0.589564	+	0.494703i
$159$		0			0
$160$	15.4416	−	5.62029i	1.22077	−	0.444323i
$161$	−20.8666			−1.64452
$162$		0			0
$163$	−1.19321			−0.0934597			−0.0467298	−	0.998908i	$-0.514880\pi$
$163$	−1.19321			−0.0934597			−0.0467298	+	0.998908i	$0.514880\pi$
$164$	−5.34395	+	1.94504i	−0.417292	+	0.151882i
$165$		0			0
$166$	13.7604	−	11.5464i	1.06802	−	0.896173i
$167$	−4.15650	−	23.5727i	−0.321640	−	1.82411i	−0.532308	−	0.846551i	$-0.678675\pi$
$167$	−4.15650	−	23.5727i	−0.321640	−	1.82411i	0.210669	−	0.977558i	$-0.432436\pi$
$168$		0			0
$169$	−8.82583	−	7.40575i	−0.678910	−	0.569673i
$170$	−5.20096	+	9.00832i	−0.398895	+	0.690907i
$171$		0			0
$172$	6.89926	+	11.9499i	0.526063	+	0.911169i
$173$	−1.58714	+	9.00115i	−0.120668	+	0.684344i	0.863118	+	0.505002i	$0.168508\pi$
$173$	−1.58714	+	9.00115i	−0.120668	+	0.684344i	−0.983787	+	0.179343i	$0.942603\pi$
$174$		0			0
$175$	3.24044	+	1.17942i	0.244954	+	0.0891561i
$176$	10.5377	+	3.83543i	0.794313	+	0.289106i
$177$		0			0
$178$	−6.25953	+	35.4996i	−0.469172	+	2.66081i
$179$	−5.30038	−	9.18052i	−0.396169	−	0.686184i	0.597081	−	0.802181i	$-0.296327\pi$
$179$	−5.30038	−	9.18052i	−0.396169	−	0.686184i	−0.993250	+	0.115997i	$0.962994\pi$
$180$		0			0
$181$	0.731460	−	1.26693i	0.0543690	−	0.0941699i	−0.837560	−	0.546345i	$-0.816019\pi$
$181$	0.731460	−	1.26693i	0.0543690	−	0.0941699i	0.891929	+	0.452176i	$0.149352\pi$
$182$	9.59800	+	8.05368i	0.711451	+	0.596978i
$183$		0			0
$184$	0.819031	+	4.64496i	0.0603798	+	0.342431i
$185$	−14.2320	+	11.9421i	−1.04636	+	0.877999i
$186$		0			0
$187$	−9.21640	+	3.35450i	−0.673970	+	0.245305i
$188$	18.0709			1.31796
$189$		0			0
$190$	−8.08871			−0.586817
$191$	−11.6731	+	4.24867i	−0.844637	+	0.307423i	−0.727852	−	0.685734i	$-0.759481\pi$
$191$	−11.6731	+	4.24867i	−0.844637	+	0.307423i	−0.116785	+	0.993157i	$0.537259\pi$
$192$		0			0
$193$	15.9133	−	13.3528i	1.14546	−	0.961157i	0.145859	−	0.989305i	$-0.453406\pi$
$193$	15.9133	−	13.3528i	1.14546	−	0.961157i	0.999604	+	0.0281484i	$0.00896109\pi$
$194$	1.88554	+	10.6934i	0.135374	+	0.767745i
$195$		0			0
$196$	31.8169	+	26.6976i	2.27264	+	1.90697i
$197$	7.09433	−	12.2877i	0.505450	−	0.875465i	−0.494530	−	0.869161i	$-0.664660\pi$
$197$	7.09433	−	12.2877i	0.505450	−	0.875465i	0.999980	−	0.00630469i	$-0.00200686\pi$
$198$		0			0
$199$	−10.1643	−	17.6051i	−0.720529	−	1.24799i	−0.960788	−	0.277284i	$-0.910566\pi$
$199$	−10.1643	−	17.6051i	−0.720529	−	1.24799i	0.240259	−	0.970709i	$-0.422768\pi$
$200$	0.135353	−	0.767624i	0.00957089	−	0.0542792i
$201$		0			0
$202$	37.1017	+	13.5039i	2.61046	+	0.950132i
$203$	−13.5860	−	4.94488i	−0.953547	−	0.347063i
$204$		0			0
$205$	−0.812919	+	4.61029i	−0.0567767	+	0.321997i
$206$	9.56876	+	16.5736i	0.666687	+	1.15474i
$207$		0			0
$208$	−1.64315	+	2.84601i	−0.113932	+	0.197336i
$209$	−5.84246	−	4.90240i	−0.404131	−	0.339106i
$210$		0			0
$211$	−1.71275	−	9.71347i	−0.117910	−	0.668703i	−0.985268	−	0.171018i	$-0.945294\pi$
$211$	−1.71275	−	9.71347i	−0.117910	−	0.668703i	0.867358	−	0.497685i	$-0.165817\pi$
$212$	−12.1952	+	10.2330i	−0.837571	+	0.702805i
$213$		0			0
$214$	14.8304	−	5.39782i	1.01378	−	0.368987i
$215$	11.3588			0.774665
$216$		0			0
$217$	7.14494			0.485030
$218$	−11.2303	+	4.08751i	−0.760615	+	0.276841i
$219$		0			0
$220$	−16.5609	+	13.8962i	−1.11653	+	0.936883i
$221$	−0.499103	−	2.83055i	−0.0335733	−	0.190404i
$222$		0			0
$223$	11.5453	+	9.68770i	0.773134	+	0.648736i	0.941509	−	0.336987i	$-0.109408\pi$
$223$	11.5453	+	9.68770i	0.773134	+	0.648736i	−0.168376	+	0.985723i	$0.553852\pi$
$224$	−19.2368	+	33.3191i	−1.28531	+	2.22623i
$225$		0			0
$226$	−2.55287	−	4.42170i	−0.169814	−	0.294127i
$227$	−3.94052	+	22.3478i	−0.261542	+	1.48328i	0.517164	+	0.855886i	$0.326988\pi$
$227$	−3.94052	+	22.3478i	−0.261542	+	1.48328i	−0.778705	+	0.627390i	$0.784123\pi$
$228$		0			0
$229$	−8.19102	−	2.98129i	−0.541278	−	0.197009i	0.0568892	−	0.998381i	$-0.481882\pi$
$229$	−8.19102	−	2.98129i	−0.541278	−	0.197009i	−0.598167	+	0.801371i	$0.704104\pi$
$230$	17.7970	+	6.47758i	1.17350	+	0.427119i
$231$		0			0
$232$	−0.567483	+	3.21836i	−0.0372571	+	0.211296i
$233$	11.7945	+	20.4286i	0.772682	+	1.33832i	0.936088	+	0.351766i	$0.114419\pi$
$233$	11.7945	+	20.4286i	0.772682	+	1.33832i	−0.163406	+	0.986559i	$0.552248\pi$
$234$		0			0
$235$	7.43792	−	12.8829i	0.485196	−	0.840385i
$236$	0.505414	+	0.424093i	0.0328997	+	0.0276061i
$237$		0			0
$238$	−4.22901	−	23.9839i	−0.274126	−	1.55465i
$239$	7.62560	−	6.39864i	0.493259	−	0.413894i	−0.361933	−	0.932204i	$-0.617883\pi$
$239$	7.62560	−	6.39864i	0.493259	−	0.413894i	0.855193	+	0.518310i	$0.173439\pi$
$240$		0			0
$241$	−5.36889	+	1.95411i	−0.345840	+	0.125876i	−0.509100	−	0.860708i	$-0.670022\pi$
$241$	−5.36889	+	1.95411i	−0.345840	+	0.125876i	0.163259	+	0.986583i	$0.447799\pi$
$242$	−13.2140			−0.849427
$243$		0			0
$244$	−11.2092			−0.717594
$245$	32.1285	−	11.6938i	2.05262	−	0.747091i
$246$		0			0
$247$	1.71214	−	1.43666i	0.108941	−	0.0914124i
$248$	−0.280445	−	1.59048i	−0.0178083	−	0.100996i
$249$		0			0
$250$	−19.2537	−	16.1558i	−1.21771	−	1.02178i
$251$	3.64483	−	6.31303i	0.230060	−	0.398475i	−0.727766	−	0.685826i	$-0.759441\pi$
$251$	3.64483	−	6.31303i	0.230060	−	0.398475i	0.957825	+	0.287351i	$0.0927745\pi$
$252$		0			0
$253$	8.92881	+	15.4651i	0.561349	+	0.972285i
$254$	3.40767	−	19.3259i	0.213816	−	1.21261i
$255$		0			0
$256$	−4.60565	−	1.67632i	−0.287853	−	0.104770i
$257$	21.8413	+	7.94960i	1.36243	+	0.495882i	0.916803	−	0.399339i	$-0.130760\pi$
$257$	21.8413	+	7.94960i	1.36243	+	0.495882i	0.445622	+	0.895221i	$0.352982\pi$
$258$		0			0
$259$	7.55332	−	42.8370i	0.469340	−	2.66176i
$260$	−3.16770	−	5.48661i	−0.196452	−	0.340265i
$261$		0			0
$262$	−16.2979	+	28.2288i	−1.00689	+	1.74398i
$263$	−20.9893	−	17.6121i	−1.29426	−	1.08601i	−0.991107	−	0.133067i	$-0.957517\pi$
$263$	−20.9893	−	17.6121i	−1.29426	−	1.08601i	−0.303150	−	0.952943i	$-0.598038\pi$
$264$		0			0
$265$	2.27565	+	12.9059i	0.139792	+	0.792802i
$266$	14.5074	−	12.1731i	0.889504	−	0.746382i
$267$		0			0
$268$	−9.76605	+	3.55455i	−0.596556	+	0.217129i
$269$	9.41973			0.574331			0.287166	−	0.957881i	$-0.407287\pi$
$269$	9.41973			0.574331			0.287166	+	0.957881i	$0.407287\pi$
$270$		0			0
$271$	26.2797			1.59638			0.798189	−	0.602408i	$-0.205792\pi$
$271$	26.2797			1.59638			0.798189	+	0.602408i	$0.205792\pi$
$272$	6.00253	−	2.18474i	0.363957	−	0.132469i
$273$		0			0
$274$	5.93190	−	4.97745i	0.358359	−	0.300699i
$275$	−0.512460	−	2.90631i	−0.0309025	−	0.175257i
$276$		0			0
$277$	0.287123	+	0.240924i	0.0172515	+	0.0144757i	0.651373	−	0.758758i	$-0.274193\pi$
$277$	0.287123	+	0.240924i	0.0172515	+	0.0144757i	−0.634121	+	0.773234i	$0.718638\pi$
$278$	14.1054	−	24.4314i	0.845989	−	1.46530i
$279$		0			0
$280$	−5.50253	−	9.53065i	−0.328839	−	0.569566i
$281$	2.42788	−	13.7692i	0.144835	−	0.821400i	−0.822665	−	0.568527i	$-0.807513\pi$
$281$	2.42788	−	13.7692i	0.144835	−	0.821400i	0.967500	−	0.252873i	$-0.0813755\pi$
$282$		0			0
$283$	−14.6234	−	5.32248i	−0.869270	−	0.316389i	−0.131399	−	0.991330i	$-0.541947\pi$
$283$	−14.6234	−	5.32248i	−0.869270	−	0.316389i	−0.737872	+	0.674941i	$0.764169\pi$
$284$	−7.29424	−	2.65488i	−0.432833	−	0.157538i
$285$		0			0
$286$	1.86195	−	10.5597i	0.110100	−	0.624406i
$287$	−5.48027	−	9.49211i	−0.323490	−	0.560301i
$288$		0			0
$289$	5.70661	−	9.88413i	0.335683	−	0.581420i
$290$	10.0524	+	8.43493i	0.590295	+	0.495316i
$291$		0			0
$292$	5.57430	+	31.6134i	0.326211	+	1.85003i
$293$	18.8633	−	15.8281i	1.10200	−	0.924690i	0.104445	−	0.994531i	$-0.466693\pi$
$293$	18.8633	−	15.8281i	1.10200	−	0.924690i	0.997558	+	0.0698405i	$0.0222490\pi$
$294$		0			0
$295$	0.510364	−	0.185757i	0.0297145	−	0.0108152i
$296$	−9.83210			−0.571479
$297$		0			0
$298$	−18.9361			−1.09694
$299$	−4.91760	+	1.78986i	−0.284392	+	0.103510i
$300$		0			0
$301$	−20.3724	+	17.0945i	−1.17425	+	0.985309i
$302$	0.262882	+	1.49088i	0.0151272	+	0.0857904i
$303$		0			0
$304$	3.80512	+	3.19288i	0.218239	+	0.183124i
$305$	−4.61365	+	7.99107i	−0.264177	+	0.457567i
$306$		0			0
$307$	10.1956	+	17.6593i	0.581893	+	1.00787i	0.995255	+	0.0973012i	$0.0310210\pi$
$307$	10.1956	+	17.6593i	0.581893	+	1.00787i	−0.413362	+	0.910567i	$0.635646\pi$
$308$	8.78931	−	49.8466i	0.500817	−	2.84028i
$309$		0			0
$310$	−6.09388	−	2.21799i	−0.346109	−	0.125973i
$311$	−20.8415	−	7.58567i	−1.18181	−	0.430144i	−0.324970	−	0.945724i	$-0.605354\pi$
$311$	−20.8415	−	7.58567i	−1.18181	−	0.430144i	−0.856841	+	0.515580i	$0.827576\pi$
$312$		0			0
$313$	−1.94000	+	11.0023i	−0.109656	+	0.621887i	0.879603	+	0.475709i	$0.157808\pi$
$313$	−1.94000	+	11.0023i	−0.109656	+	0.621887i	−0.989258	+	0.146178i	$0.953303\pi$
$314$	−14.6819	−	25.4298i	−0.828547	−	1.43508i
$315$		0			0
$316$	−5.72635	+	9.91833i	−0.322132	+	0.557950i
$317$	19.3171	+	16.2090i	1.08496	+	0.910386i	0.996323	−	0.0856786i	$-0.0273058\pi$
$317$	19.3171	+	16.2090i	1.08496	+	0.910386i	0.0886327	+	0.996064i	$0.471750\pi$
$318$		0			0
$319$	2.14855	+	12.1851i	0.120296	+	0.682232i
$320$	18.1754	−	15.2510i	1.01604	−	0.852557i
$321$		0			0
$322$	−41.6680	+	15.1659i	−2.32206	+	0.845162i
$323$	−4.34438			−0.241728
$324$		0			0
$325$	0.864837			0.0479725
$326$	−2.38270	+	0.867231i	−0.131965	+	0.0480315i
$327$		0			0
$328$	−1.89786	+	1.59250i	−0.104792	+	0.0879309i
$329$	6.04793	+	34.2995i	0.333433	+	1.89099i
$330$		0			0
$331$	−20.0441	−	16.8190i	−1.10172	−	0.924455i	−0.104183	−	0.994558i	$-0.533223\pi$
$331$	−20.0441	−	16.8190i	−1.10172	−	0.924455i	−0.997540	+	0.0701033i	$0.977667\pi$
$332$	10.6329	−	18.4167i	0.583555	−	1.01075i
$333$		0			0
$334$	−25.4327	−	44.0507i	−1.39161	−	2.41035i
$335$	−1.48561	+	8.42530i	−0.0811674	+	0.460323i
$336$		0			0
$337$	−10.2859	−	3.74377i	−0.560310	−	0.203936i	0.0463114	−	0.998927i	$-0.485253\pi$
$337$	−10.2859	−	3.74377i	−0.560310	−	0.203936i	−0.606621	+	0.794991i	$0.707476\pi$
$338$	−23.0066	−	8.37372i	−1.25139	−	0.455470i
$339$		0			0
$340$	−2.13838	+	12.1274i	−0.115970	+	0.657700i
$341$	−3.05732	−	5.29543i	−0.165563	−	0.286763i
$342$		0			0
$343$	−23.0545	+	39.9316i	−1.24483	+	2.15611i
$344$	4.60491	+	3.86398i	0.248280	+	0.208332i
$345$		0			0
$346$	3.37273	+	19.1277i	0.181319	+	1.02831i
$347$	2.69140	−	2.25836i	0.144482	−	0.121235i	−0.567682	−	0.823248i	$-0.692160\pi$
$347$	2.69140	−	2.25836i	0.144482	−	0.121235i	0.712164	+	0.702013i	$0.247715\pi$
$348$		0			0
$349$	27.4361	−	9.98591i	1.46862	−	0.534534i	0.520894	−	0.853622i	$-0.325599\pi$
$349$	27.4361	−	9.98591i	1.46862	−	0.534534i	0.947725	+	0.319088i	$0.103377\pi$
$350$	7.32796			0.391696
$351$		0			0
$352$	32.9256			1.75494
$353$	23.5645	−	8.57677i	1.25421	−	0.456496i	0.372389	−	0.928077i	$-0.378539\pi$
$353$	23.5645	−	8.57677i	1.25421	−	0.456496i	0.881823	+	0.471581i	$0.156317\pi$
$354$		0			0
$355$	−4.89495	+	4.10735i	−0.259797	+	0.217996i
$356$	7.41044	+	42.0267i	0.392753	+	2.22741i
$357$		0			0
$358$	−17.2566	−	14.4800i	−0.912040	−	0.765293i
$359$	−2.10362	+	3.64358i	−0.111025	+	0.192301i	−0.916184	−	0.400758i	$-0.868747\pi$
$359$	−2.10362	+	3.64358i	−0.111025	+	0.192301i	0.805159	+	0.593059i	$0.202080\pi$
$360$		0			0
$361$	7.81087	+	13.5288i	0.411098	+	0.712043i
$362$	0.539828	−	3.06152i	0.0283727	−	0.160910i
$363$		0			0
$364$	13.9385	+	5.07318i	0.730574	+	0.265907i
$365$	24.8317	+	9.03799i	1.29975	+	0.473070i
$366$		0			0
$367$	3.03826	−	17.2308i	0.158596	−	0.899441i	−0.796829	−	0.604205i	$-0.793491\pi$
$367$	3.03826	−	17.2308i	0.158596	−	0.899441i	0.955424	−	0.295236i	$-0.0953983\pi$
$368$	−5.81522	−	10.0723i	−0.303139	−	0.525053i
$369$		0			0
$370$	−19.7400	+	34.1907i	−1.02623	+	1.77749i
$371$	−23.5042	−	19.7224i	−1.22028	−	1.02393i
$372$		0			0
$373$	−5.14946	−	29.2040i	−0.266629	−	1.51213i	−0.764356	−	0.644794i	$-0.776943\pi$
$373$	−5.14946	−	29.2040i	−0.266629	−	1.51213i	0.497727	−	0.867334i	$-0.334168\pi$
$374$	−15.9659	+	13.3970i	−0.825579	+	0.692743i
$375$		0			0
$376$	7.39778	−	2.69257i	0.381511	−	0.138859i
$377$	−3.62594			−0.186745
$378$		0			0
$379$	20.9523			1.07625			0.538124	−	0.842865i	$-0.319133\pi$
$379$	20.9523			1.07625			0.538124	+	0.842865i	$0.319133\pi$
$380$	−8.99844	+	3.27517i	−0.461610	+	0.168012i
$381$		0			0
$382$	−20.2218	+	16.9681i	−1.03464	+	0.868164i
$383$	1.71856	+	9.74642i	0.0878142	+	0.498019i	0.996714	+	0.0810039i	$0.0258126\pi$
$383$	1.71856	+	9.74642i	0.0878142	+	0.498019i	−0.908900	+	0.417015i	$0.863076\pi$
$384$		0			0
$385$	−31.9182	−	26.7826i	−1.62670	−	1.36497i
$386$	22.0719	−	38.2297i	1.12343	−	1.94584i
$387$		0			0
$388$	6.42745	+	11.1327i	0.326304	+	0.565175i
$389$	−3.66654	+	20.7940i	−0.185901	+	1.05430i	0.738891	+	0.673825i	$0.235350\pi$
$389$	−3.66654	+	20.7940i	−0.185901	+	1.05430i	−0.924792	+	0.380472i	$0.875761\pi$
$390$		0			0
$391$	9.55863	+	3.47906i	0.483401	+	0.175943i
$392$	17.0030	+	6.18857i	0.858779	+	0.312570i
$393$		0			0
$394$	5.23572	−	29.6932i	0.263772	−	1.49592i
$395$	4.71388	+	8.16468i	0.237181	+	0.410810i
$396$		0			0
$397$	4.88955	−	8.46894i	0.245399	−	0.425044i	−0.716845	−	0.697233i	$-0.754414\pi$
$397$	4.88955	−	8.46894i	0.245399	−	0.425044i	0.962244	+	0.272189i	$0.0877476\pi$
$398$	−33.0923	−	27.7677i	−1.65877	−	1.39187i
$399$		0			0
$400$	0.333759	+	1.89284i	0.0166880	+	0.0946421i
$401$	−14.6616	+	12.3025i	−0.732164	+	0.614359i	−0.930721	−	0.365731i	$-0.880819\pi$
$401$	−14.6616	+	12.3025i	−0.732164	+	0.614359i	0.198556	+	0.980089i	$0.436375\pi$
$402$		0			0
$403$	1.68384	−	0.612867i	0.0838780	−	0.0305291i
$404$	46.7423			2.32552
$405$		0			0
$406$	−30.7234			−1.52478
$407$	−34.9804	+	12.7318i	−1.73392	+	0.631094i
$408$		0			0
$409$	11.4873	−	9.63896i	0.568009	−	0.476616i	−0.312976	−	0.949761i	$-0.601326\pi$
$409$	11.4873	−	9.63896i	0.568009	−	0.476616i	0.880984	+	0.473145i	$0.156881\pi$
$410$	1.72748	+	9.79700i	0.0853139	+	0.483839i
$411$		0			0
$412$	17.3557	+	14.5631i	0.855053	+	0.717475i
$413$	−0.635799	+	1.10124i	−0.0312856	+	0.0541883i
$414$		0			0
$415$	−8.75289	−	15.1604i	−0.429662	−	0.744197i
$416$	−1.67552	+	9.50233i	−0.0821490	+	0.465890i
$417$		0			0
$418$	−15.2297	−	5.54317i	−0.744911	−	0.271125i
$419$	−5.46131	−	1.98775i	−0.266802	−	0.0971081i	0.205155	−	0.978729i	$-0.434230\pi$
$419$	−5.46131	−	1.98775i	−0.266802	−	0.0971081i	−0.471957	+	0.881621i	$0.656452\pi$
$420$		0			0
$421$	−2.31187	+	13.1113i	−0.112674	+	0.639003i	0.875202	+	0.483757i	$0.160728\pi$
$421$	−2.31187	+	13.1113i	−0.112674	+	0.639003i	−0.987876	+	0.155246i	$0.950383\pi$
$422$	−10.4799	−	18.1518i	−0.510154	−	0.883613i
$423$		0			0
$424$	−3.46769	+	6.00621i	−0.168406	+	0.291687i
$425$	−1.28775	−	1.08055i	−0.0624649	−	0.0524143i
$426$		0			0
$427$	−3.75146	−	21.2756i	−0.181546	−	1.02960i
$428$	14.3127	−	12.0098i	0.691833	−	0.580516i
$429$		0			0
$430$	22.6821	−	8.25561i	1.09383	−	0.398121i
$431$	−36.4166			−1.75413			−0.877064	−	0.480374i	$-0.840501\pi$
$431$	−36.4166			−1.75413			−0.877064	+	0.480374i	$0.840501\pi$
$432$		0			0
$433$	−10.8761			−0.522674			−0.261337	−	0.965248i	$-0.584163\pi$
$433$	−10.8761			−0.522674			−0.261337	+	0.965248i	$0.584163\pi$
$434$	14.2675	−	5.19296i	0.684864	−	0.249270i
$435$		0			0
$436$	−10.8384	+	9.09446i	−0.519063	+	0.435546i
$437$	1.37355	+	7.78982i	0.0657060	+	0.372637i
$438$		0			0
$439$	7.24162	+	6.07644i	0.345624	+	0.290013i	0.799030	−	0.601291i	$-0.205347\pi$
$439$	7.24162	+	6.07644i	0.345624	+	0.290013i	−0.453406	+	0.891304i	$0.649791\pi$
$440$	−4.70906	+	8.15632i	−0.224495	+	0.388837i
$441$		0			0
$442$	−3.05390	−	5.28951i	−0.145259	−	0.251596i
$443$	2.86935	−	16.2729i	0.136327	−	0.773148i	−0.837600	−	0.546284i	$-0.816042\pi$
$443$	2.86935	−	16.2729i	0.136327	−	0.773148i	0.973927	−	0.226863i	$-0.0728471\pi$
$444$		0			0
$445$	33.0111	+	12.0151i	1.56488	+	0.569569i
$446$	30.0957	+	10.9539i	1.42507	+	0.518683i
$447$		0			0
$448$	−9.64620	+	54.7063i	−0.455740	+	2.58463i
$449$	2.37181	+	4.10809i	0.111933	+	0.193873i	0.916549	−	0.399921i	$-0.130963\pi$
$449$	2.37181	+	4.10809i	0.111933	+	0.193873i	−0.804617	+	0.593794i	$0.797629\pi$
$450$		0			0
$451$	−4.69001	+	8.12334i	−0.220844	+	0.382513i
$452$	−4.63036	−	3.88533i	−0.217794	−	0.182751i
$453$		0			0
$454$	8.37372	+	47.4897i	0.392998	+	2.22880i
$455$	9.35370	−	7.84869i	0.438508	−	0.367952i
$456$		0			0
$457$	21.0571	−	7.66417i	0.985012	−	0.358515i	0.201225	−	0.979545i	$-0.435508\pi$
$457$	21.0571	−	7.66417i	0.985012	−	0.358515i	0.783787	+	0.621030i	$0.213286\pi$
$458$	−18.5232			−0.865534
$459$		0			0
$460$	22.4214			1.04540
$461$	14.0223	−	5.10371i	0.653085	−	0.237704i	0.00583713	−	0.999983i	$-0.498142\pi$
$461$	14.0223	−	5.10371i	0.653085	−	0.237704i	0.647248	+	0.762279i	$0.275920\pi$
$462$		0			0
$463$	−11.3736	+	9.54358i	−0.528576	+	0.443528i	−0.867609	−	0.497247i	$-0.834344\pi$
$463$	−11.3736	+	9.54358i	−0.528576	+	0.443528i	0.339033	+	0.940774i	$0.389900\pi$
$464$	−1.39933	−	7.93597i	−0.0649621	−	0.368418i
$465$		0			0
$466$	38.3997	+	32.2212i	1.77883	+	1.49262i
$467$	7.67571	−	13.2947i	0.355190	−	0.615206i	−0.631961	−	0.775000i	$-0.717750\pi$
$467$	7.67571	−	13.2947i	0.355190	−	0.615206i	0.987150	+	0.159794i	$0.0510830\pi$
$468$		0			0
$469$	−10.0152	−	17.3468i	−0.462458	−	0.801001i
$470$	5.48929	−	31.1313i	0.253202	−	1.43598i
$471$		0			0
$472$	0.270093	+	0.0983060i	0.0124321	+	0.00452490i
$473$	21.3868	+	7.78416i	0.983366	+	0.357916i
$474$		0			0
$475$	0.226993	−	1.28734i	0.0104152	−	0.0590673i
$476$	−14.4159	−	24.9690i	−0.660750	−	1.14445i
$477$		0			0
$478$	10.5768	−	18.3196i	0.483772	−	0.837918i
$479$	8.00410	+	6.71624i	0.365717	+	0.306873i	0.807064	−	0.590464i	$-0.201055\pi$
$479$	8.00410	+	6.71624i	0.365717	+	0.306873i	−0.441348	+	0.897336i	$0.645499\pi$
$480$		0			0
$481$	−1.89432	−	10.7432i	−0.0863737	−	0.489850i
$482$	−9.30073	+	7.80424i	−0.423637	+	0.355473i
$483$		0			0
$484$	−14.7001	+	5.35041i	−0.668188	+	0.243201i
$485$	10.5820			0.480505
$486$		0			0
$487$	−16.1649			−0.732500			−0.366250	−	0.930516i	$-0.619359\pi$
$487$	−16.1649			−0.732500			−0.366250	+	0.930516i	$0.619359\pi$
$488$	−4.58875	+	1.67017i	−0.207723	+	0.0756049i
$489$		0			0
$490$	55.6575	−	46.7022i	2.51435	−	2.10979i
$491$	−1.87147	−	10.6136i	−0.0844581	−	0.478985i	−0.997472	−	0.0710576i	$-0.977363\pi$
$491$	−1.87147	−	10.6136i	−0.0844581	−	0.478985i	0.913014	−	0.407928i	$-0.133749\pi$
$492$		0			0
$493$	5.39904	+	4.53033i	0.243160	+	0.204036i
$494$	2.37477	−	4.11322i	0.106846	−	0.185062i
$495$		0			0
$496$	1.99119	+	3.44885i	0.0894071	+	0.154858i
$497$	2.59789	−	14.7333i	0.116531	−	0.660881i
$498$		0			0
$499$	18.0301	+	6.56240i	0.807136	+	0.293774i	0.712440	−	0.701733i	$-0.247590\pi$
$499$	18.0301	+	6.56240i	0.807136	+	0.293774i	0.0946959	+	0.995506i	$0.469812\pi$
$500$	−27.9607	−	10.1769i	−1.25044	−	0.455123i
$501$		0			0
$502$	2.68994	−	15.2554i	0.120058	−	0.680882i
$503$	6.01253	+	10.4140i	0.268086	+	0.464338i	0.968367	−	0.249529i	$-0.0802757\pi$
$503$	6.01253	+	10.4140i	0.268086	+	0.464338i	−0.700282	+	0.713866i	$0.746942\pi$
$504$		0			0
$505$	19.2389	−	33.3228i	0.856120	−	1.48284i
$506$	29.0698	+	24.3925i	1.29231	+	1.08438i
$507$		0			0
$508$	−4.03422	−	22.8792i	−0.178990	−	1.01510i
$509$	−11.4547	+	9.61162i	−0.507720	+	0.426027i	−0.860326	−	0.509744i	$-0.829740\pi$
$509$	−11.4547	+	9.61162i	−0.507720	+	0.426027i	0.352606	+	0.935772i	$0.385296\pi$
$510$		0			0
$511$	−58.1382	+	21.1606i	−2.57188	+	0.936088i
$512$	−27.3678			−1.20950
$513$		0			0
$514$	49.3922			2.17860
$515$	17.5257	−	6.37882i	0.772273	−	0.281084i
$516$		0			0
$517$	22.8330	−	19.1591i	1.00419	−	0.842618i
$518$	−16.0510	−	91.0299i	−0.705241	−	3.99962i
$519$		0			0
$520$	−2.11428	−	1.77409i	−0.0927172	−	0.0777990i
$521$	−18.7094	+	32.4056i	−0.819673	+	1.41972i	0.0862502	+	0.996274i	$0.472512\pi$
$521$	−18.7094	+	32.4056i	−0.819673	+	1.41972i	−0.905923	+	0.423442i	$0.860822\pi$
$522$		0			0
$523$	4.22489	+	7.31773i	0.184742	+	0.319982i	0.943489	−	0.331403i	$-0.107522\pi$
$523$	4.22489	+	7.31773i	0.184742	+	0.319982i	−0.758748	+	0.651385i	$0.774188\pi$
$524$	−6.70092	+	38.0028i	−0.292731	+	1.66016i
$525$		0			0
$526$	−54.7136	−	19.9141i	−2.38562	−	0.868296i
$527$	−3.27297	−	1.19126i	−0.142573	−	0.0518923i
$528$		0			0
$529$	−0.777821	+	4.41124i	−0.0338183	+	0.191793i
$530$	13.9242	+	24.1175i	0.604829	+	1.04760i
$531$		0			0
$532$	11.2100	−	19.4163i	0.486017	−	0.841805i
$533$	−2.10573	−	1.76692i	−0.0912092	−	0.0765336i
$534$		0			0
$535$	−2.67079	−	15.1468i	−0.115468	−	0.654853i
$536$	−3.46834	+	2.91028i	−0.149809	+	0.125705i
$537$		0			0
$538$	18.8100	−	6.84628i	0.810957	−	0.295164i
$539$	68.5065			2.95078
$540$		0			0
$541$	12.6259			0.542828			0.271414	−	0.962463i	$-0.412509\pi$
$541$	12.6259			0.542828			0.271414	+	0.962463i	$0.412509\pi$
$542$	52.4772	−	19.1001i	2.25409	−	0.820422i
$543$		0			0
$544$	14.3673	−	12.0556i	0.615992	−	0.516879i
$545$	2.02246	+	11.4699i	0.0866327	+	0.491319i
$546$		0			0
$547$	24.0500	+	20.1804i	1.02830	+	0.862850i	0.990648	−	0.136441i	$-0.0435665\pi$
$547$	24.0500	+	20.1804i	1.02830	+	0.862850i	0.0376558	+	0.999291i	$0.488011\pi$
$548$	4.58365	−	7.93912i	0.195804	−	0.339142i
$549$		0			0
$550$	−3.13563	−	5.43107i	−0.133704	−	0.231582i
$551$	−0.951697	+	5.39734i	−0.0405437	+	0.229934i
$552$		0			0
$553$	−20.7420	−	7.54945i	−0.882038	−	0.321035i
$554$	0.748452	+	0.272414i	0.0317987	+	0.0115738i
$555$		0			0
$556$	5.79948	−	32.8905i	0.245953	−	1.39487i
$557$	7.96515	+	13.7960i	0.337494	+	0.584557i	0.983961	−	0.178385i	$-0.0570874\pi$
$557$	7.96515	+	13.7960i	0.337494	+	0.584557i	−0.646467	+	0.762942i	$0.723754\pi$
$558$		0			0
$559$	−3.33484	+	5.77610i	−0.141048	+	0.244303i
$560$	20.7880	+	17.4432i	0.878452	+	0.737108i
$561$		0			0
$562$	−5.15931	−	29.2599i	−0.217632	−	1.23425i
$563$	−19.0445	+	15.9802i	−0.802631	+	0.673487i	−0.948837	−	0.315767i	$-0.897738\pi$
$563$	−19.0445	+	15.9802i	−0.802631	+	0.673487i	0.146206	+	0.989254i	$0.453294\pi$
$564$		0			0
$565$	−4.67571	+	1.70182i	−0.196708	+	0.0715960i
$566$	−33.0695			−1.39001
$567$		0			0
$568$	−3.38165			−0.141891
$569$	−18.0327	+	6.56337i	−0.755970	+	0.275151i	−0.691116	−	0.722744i	$-0.742881\pi$
$569$	−18.0327	+	6.56337i	−0.755970	+	0.275151i	−0.0648545	+	0.997895i	$0.520658\pi$
$570$		0			0
$571$	−15.6114	+	13.0995i	−0.653317	+	0.548198i	−0.908075	−	0.418807i	$-0.862448\pi$
$571$	−15.6114	+	13.0995i	−0.653317	+	0.548198i	0.254759	+	0.967005i	$0.418004\pi$
$572$	−2.20430	−	12.5012i	−0.0921664	−	0.522702i
$573$		0			0
$574$	−17.8423	−	14.9715i	−0.744723	−	0.624897i
$575$	−1.53036	+	2.65066i	−0.0638205	+	0.110540i
$576$		0			0
$577$	−11.6495	−	20.1776i	−0.484976	−	0.840004i	0.514875	−	0.857265i	$-0.327838\pi$
$577$	−11.6495	−	20.1776i	−0.484976	−	0.840004i	−0.999851	+	0.0172619i	$0.994505\pi$
$578$	4.21156	−	23.8849i	0.175178	−	0.993483i
$579$		0			0
$580$	14.5983	+	5.31334i	0.606161	+	0.220624i
$581$	38.5143	+	14.0181i	1.59784	+	0.581568i
$582$		0			0
$583$	−4.55967	+	25.8592i	−0.188842	+	1.07098i
$584$	6.99237	+	12.1111i	0.289346	+	0.501163i
$585$		0			0
$586$	26.1636	−	45.3167i	1.08081	−	1.87201i
$587$	−28.2741	−	23.7248i	−1.16700	−	0.979228i	−0.167021	−	0.985953i	$-0.553415\pi$
$587$	−28.2741	−	23.7248i	−1.16700	−	0.979228i	−0.999977	+	0.00672500i	$0.997859\pi$
$588$		0			0
$589$	−0.470319	−	2.66731i	−0.0193792	−	0.109905i
$590$	0.884124	−	0.741868i	0.0363988	−	0.0305422i
$591$		0			0
$592$	22.7823	−	8.29209i	0.936348	−	0.340803i
$593$	4.36830			0.179385			0.0896923	−	0.995970i	$-0.471412\pi$
$593$	4.36830			0.179385			0.0896923	+	0.995970i	$0.471412\pi$
$594$		0			0
$595$	−23.7340			−0.973000
$596$	−21.0658	+	7.66733i	−0.862890	+	0.314066i
$597$		0			0
$598$	−8.51896	+	7.14826i	−0.348366	+	0.292314i
$599$	−5.41880	−	30.7315i	−0.221406	−	1.25566i	−0.869438	−	0.494043i	$-0.835519\pi$
$599$	−5.41880	−	30.7315i	−0.221406	−	1.25566i	0.648032	−	0.761613i	$-0.275592\pi$
$600$		0			0
$601$	33.6578	+	28.2422i	1.37293	+	1.15202i	0.971747	+	0.236027i	$0.0758452\pi$
$601$	33.6578	+	28.2422i	1.37293	+	1.15202i	0.401183	+	0.915998i	$0.368599\pi$
$602$	−28.2568	+	48.9422i	−1.15166	+	1.99474i
$603$		0			0
$604$	0.896114	+	1.55211i	0.0364623	+	0.0631546i
$605$	−2.23618	+	12.6820i	−0.0909136	+	0.515597i
$606$		0			0
$607$	−16.3118	−	5.93701i	−0.662075	−	0.240976i	−0.0109432	−	0.999940i	$-0.503483\pi$
$607$	−16.3118	−	5.93701i	−0.662075	−	0.240976i	−0.651132	+	0.758964i	$0.725706\pi$
$608$	13.7048	+	4.98814i	0.555803	+	0.202296i
$609$		0			0
$610$	−3.40494	+	19.3104i	−0.137862	+	0.781854i
$611$	4.36740	+	7.56456i	0.176686	+	0.306029i
$612$		0			0
$613$	0.599024	−	1.03754i	0.0241944	−	0.0419059i	−0.853675	−	0.520807i	$-0.825631\pi$
$613$	0.599024	−	1.03754i	0.0241944	−	0.0419059i	0.877869	+	0.478901i	$0.158965\pi$
$614$	33.1941	+	27.8532i	1.33961	+	1.12406i
$615$		0			0
$616$	−3.82903	−	21.7155i	−0.154276	−	0.874944i
$617$	19.9277	−	16.7213i	0.802257	−	0.673174i	−0.146489	−	0.989212i	$-0.546797\pi$
$617$	19.9277	−	16.7213i	0.802257	−	0.673174i	0.948746	+	0.316038i	$0.102353\pi$
$618$		0			0
$619$	−9.05051	+	3.29412i	−0.363771	+	0.132402i	−0.517437	−	0.855721i	$-0.673114\pi$
$619$	−9.05051	+	3.29412i	−0.363771	+	0.132402i	0.153667	+	0.988123i	$0.450892\pi$
$620$	−7.67733			−0.308329
$621$		0			0
$622$	−47.1311			−1.88978
$623$	−77.2886	+	28.1308i	−3.09650	+	1.12704i
$624$		0			0
$625$	−16.0396	+	13.4588i	−0.641582	+	0.538351i
$626$	4.12256	+	23.3802i	0.164771	+	0.934462i
$627$		0			0
$628$	−26.6298	−	22.3451i	−1.06264	−	0.891665i
$629$	−10.6022	+	18.3635i	−0.422737	+	0.732202i
$630$		0			0
$631$	7.08366	+	12.2693i	0.281996	+	0.488431i	0.971876	−	0.235492i	$-0.0756702\pi$
$631$	7.08366	+	12.2693i	0.281996	+	0.488431i	−0.689880	+	0.723924i	$0.742337\pi$
$632$	−0.866389	+	4.91354i	−0.0344631	+	0.195450i
$633$		0			0
$634$	50.3545	+	18.3275i	1.99983	+	0.727879i
$635$	−17.9712	−	6.54096i	−0.713163	−	0.259570i
$636$		0			0
$637$	−3.48615	+	19.7710i	−0.138126	+	0.783354i
$638$	13.1465	+	22.7704i	0.520476	+	0.901490i
$639$		0			0
$640$	8.77695	−	15.2021i	0.346939	−	0.600917i
$641$	17.0069	+	14.2705i	0.671732	+	0.563650i	0.913577	−	0.406665i	$-0.133308\pi$
$641$	17.0069	+	14.2705i	0.671732	+	0.563650i	−0.241846	+	0.970315i	$0.577753\pi$
$642$		0			0
$643$	3.73982	+	21.2096i	0.147484	+	0.836425i	0.965339	+	0.261000i	$0.0840522\pi$
$643$	3.73982	+	21.2096i	0.147484	+	0.836425i	−0.817855	+	0.575425i	$0.804837\pi$
$644$	−40.2136	+	33.7432i	−1.58464	+	1.32967i
$645$		0			0
$646$	−8.67518	+	3.15751i	−0.341321	+	0.124231i
$647$	13.4037			0.526952			0.263476	−	0.964666i	$-0.415131\pi$
$647$	13.4037			0.526952			0.263476	+	0.964666i	$0.415131\pi$
$648$		0			0
$649$	1.08823			0.0427168
$650$	1.72697	−	0.628566i	0.0677374	−	0.0246544i
$651$		0			0
$652$	−2.29953	+	1.92953i	−0.0900565	+	0.0755664i
$653$	−3.28384	−	18.6236i	−0.128506	−	0.728796i	−0.979163	−	0.203075i	$-0.934907\pi$
$653$	−3.28384	−	18.6236i	−0.128506	−	0.728796i	0.850657	−	0.525722i	$-0.176205\pi$
$654$		0			0
$655$	24.3343	+	20.4189i	0.950820	+	0.797832i
$656$	3.05455	−	5.29063i	0.119260	−	0.206564i
$657$		0			0
$658$	37.0059	+	64.0962i	1.44264	+	2.49873i
$659$	−0.00489366	+	0.0277533i	−0.000190630	+	0.00108112i	−0.984903	−	0.173108i	$-0.944619\pi$
$659$	−0.00489366	+	0.0277533i	−0.000190630	+	0.00108112i	0.984712	+	0.174189i	$0.0557303\pi$
$660$		0			0
$661$	42.3254	+	15.4052i	1.64627	+	0.599192i	0.988118	−	0.153696i	$-0.0491177\pi$
$661$	42.3254	+	15.4052i	1.64627	+	0.599192i	0.658148	+	0.752888i	$0.271340\pi$
$662$	−52.2496	−	19.0173i	−2.03074	−	0.739128i
$663$		0			0
$664$	1.60874	−	9.12361i	0.0624312	−	0.354065i
$665$	−9.22800	−	15.9834i	−0.357846	−	0.619808i
$666$		0			0
$667$	6.41623	−	11.1132i	0.248438	−	0.430306i
$668$	−46.1295	−	38.7072i	−1.78480	−	1.49763i
$669$		0			0
$670$	3.15696	+	17.9040i	0.121964	+	0.691692i
$671$	−14.1630	+	11.8842i	−0.546757	+	0.458783i
$672$		0			0
$673$	9.17111	−	3.33801i	0.353520	−	0.128671i	−0.159155	−	0.987254i	$-0.550877\pi$
$673$	9.17111	−	3.33801i	0.353520	−	0.128671i	0.512675	+	0.858583i	$0.328655\pi$
$674$	−23.2607			−0.895968
$675$		0			0
$676$	−28.9847			−1.11480
$677$	−38.4153	+	13.9820i	−1.47642	+	0.537374i	−0.949836	−	0.312748i	$-0.898750\pi$
$677$	−38.4153	+	13.9820i	−1.47642	+	0.537374i	−0.526586	+	0.850122i	$0.676528\pi$
$678$		0			0
$679$	−18.9792	+	15.9255i	−0.728356	+	0.611163i
$680$	0.931581	+	5.28326i	0.0357245	+	0.202604i
$681$		0			0
$682$	−9.95380	−	8.35223i	−0.381151	−	0.319823i
$683$	22.0126	−	38.1269i	0.842287	−	1.45888i	−0.0456696	−	0.998957i	$-0.514542\pi$
$683$	22.0126	−	38.1269i	0.842287	−	1.45888i	0.887957	−	0.459927i	$-0.152125\pi$
$684$		0			0
$685$	−3.77322	−	6.53541i	−0.144167	−	0.249705i
$686$	−17.0146	+	96.4945i	−0.649620	+	3.68418i
$687$		0			0
$688$	−13.9290	−	5.06973i	−0.531036	−	0.193281i
$689$	−7.23092	−	2.63184i	−0.275476	−	0.100265i
$690$		0			0
$691$	3.74240	−	21.2242i	0.142368	−	0.807406i	−0.827076	−	0.562090i	$-0.809997\pi$
$691$	3.74240	−	21.2242i	0.142368	−	0.807406i	0.969443	−	0.245316i	$-0.0788916\pi$
$692$	11.4970	+	19.9133i	0.437049	+	0.756991i
$693$		0			0
$694$	3.73302	−	6.46577i	0.141703	−	0.245437i
$695$	−21.0607	−	17.6721i	−0.798880	−	0.670340i
$696$		0			0
$697$	0.927813	+	5.26189i	0.0351434	+	0.199308i
$698$	47.5286	−	39.8812i	1.79898	−	1.50953i
$699$		0			0
$700$	8.15213	−	2.96713i	0.308122	−	0.112147i
$701$	−12.8521			−0.485419			−0.242709	−	0.970099i	$-0.578036\pi$
$701$	−12.8521			−0.485419			−0.242709	+	0.970099i	$0.578036\pi$
$702$		0			0
$703$	−16.4889			−0.621891
$704$	44.6729	−	16.2596i	1.68367	−	0.612806i
$705$		0			0
$706$	40.8217	−	34.2535i	1.53634	−	1.28915i
$707$	15.6436	+	88.7191i	0.588337	+	3.33663i
$708$		0			0
$709$	−38.0814	−	31.9541i	−1.43018	−	1.20006i	−0.945609	−	0.325306i	$-0.894533\pi$
$709$	−38.0814	−	31.9541i	−1.43018	−	1.20006i	−0.484567	−	0.874754i	$-0.661023\pi$
$710$	−6.78937	+	11.7595i	−0.254800	+	0.441327i
$711$		0			0
$712$	9.29562	+	16.1005i	0.348368	+	0.603392i
$713$	−1.10122	+	6.24534i	−0.0412411	+	0.233890i
$714$		0			0
$715$	−9.81945	−	3.57399i	−0.367227	−	0.133660i
$716$	−25.0605	−	9.12127i	−0.936554	−	0.340878i
$717$		0			0
$718$	−1.55250	+	8.80469i	−0.0579389	+	0.328588i
$719$	2.81873	+	4.88218i	0.105121	+	0.182075i	0.913788	−	0.406192i	$-0.133144\pi$
$719$	2.81873	+	4.88218i	0.105121	+	0.182075i	−0.808667	+	0.588267i	$0.799810\pi$
$720$		0			0
$721$	−21.8330	+	37.8159i	−0.813104	+	1.40834i
$722$	25.4301	+	21.3384i	0.946410	+	0.794132i
$723$		0			0
$724$	−0.639084	−	3.62442i	−0.0237514	−	0.134701i
$725$	−1.62454	+	1.36315i	−0.0603340	+	0.0506262i
$726$		0			0
$727$	42.6755	−	15.5326i	1.58275	−	0.576072i	0.606947	−	0.794743i	$-0.292394\pi$
$727$	42.6755	−	15.5326i	1.58275	−	0.576072i	0.975799	+	0.218670i	$0.0701719\pi$
$728$	6.46195			0.239496
$729$		0			0
$730$	56.1546			2.07837
$731$	12.1824	−	4.43402i	0.450582	−	0.163998i
$732$		0			0
$733$	−19.6620	+	16.4983i	−0.726231	+	0.609380i	−0.929101	−	0.369826i	$-0.879417\pi$
$733$	−19.6620	+	16.4983i	−0.726231	+	0.609380i	0.202870	+	0.979206i	$0.434973\pi$
$734$	−6.45639	−	36.6160i	−0.238310	−	1.35152i
$735$		0			0
$736$	−26.1591	−	21.9501i	−0.964236	−	0.809090i
$737$	−8.57098	+	14.8454i	−0.315716	+	0.546837i
$738$		0			0
$739$	7.22763	+	12.5186i	0.265873	+	0.460505i	0.967792	−	0.251752i	$-0.0810066\pi$
$739$	7.22763	+	12.5186i	0.265873	+	0.460505i	−0.701919	+	0.712256i	$0.747673\pi$
$740$	−8.11614	+	46.0289i	−0.298355	+	1.69206i
$741$		0			0
$742$	−61.2692	−	22.3002i	−2.24926	−	0.818664i
$743$	−32.6954	−	11.9002i	−1.19948	−	0.436574i	−0.336436	−	0.941706i	$-0.609222\pi$
$743$	−32.6954	−	11.9002i	−1.19948	−	0.436574i	−0.863042	+	0.505132i	$0.831444\pi$
$744$		0			0
$745$	−3.20452	+	18.1738i	−0.117405	+	0.665835i
$746$	−31.5084	−	54.5742i	−1.15360	−	1.99810i
$747$		0			0
$748$	−12.3371	+	21.3685i	−0.451089	+	0.781308i
$749$	27.5854	+	23.1469i	1.00795	+	0.845768i
$750$		0			0
$751$	3.14624	+	17.8432i	0.114808	+	0.651107i	0.986845	+	0.161668i	$0.0516874\pi$
$751$	3.14624	+	17.8432i	0.114808	+	0.651107i	−0.872037	+	0.489439i	$0.837202\pi$
$752$	−14.8708	+	12.4781i	−0.542283	+	0.455030i
$753$		0			0
$754$	−7.24054	+	2.63534i	−0.263685	+	0.0959735i
$755$	1.47535			0.0536933
$756$		0			0
$757$	−37.0045			−1.34495			−0.672475	−	0.740120i	$-0.734769\pi$
$757$	−37.0045			−1.34495			−0.672475	+	0.740120i	$0.734769\pi$
$758$	41.8391	−	15.2282i	1.51967	−	0.553113i
$759$		0			0
$760$	−3.19573	+	2.68154i	−0.115921	+	0.0972696i
$761$	−2.16095	−	12.2554i	−0.0783344	−	0.444256i	−0.998597	−	0.0529549i	$-0.983136\pi$
$761$	−2.16095	−	12.2554i	−0.0783344	−	0.444256i	0.920263	−	0.391302i	$-0.127975\pi$
$762$		0			0
$763$	−20.8891	−	17.5280i	−0.756235	−	0.634557i
$764$	−15.6257	+	27.0644i	−0.565316	+	0.979156i
$765$		0			0
$766$	10.5155	+	18.2133i	0.379939	+	0.658074i
$767$	−0.0553778	+	0.314063i	−0.00199958	+	0.0113402i
$768$		0			0
$769$	38.4199	+	13.9837i	1.38546	+	0.504265i	0.923828	−	0.382809i	$-0.125043\pi$
$769$	38.4199	+	13.9837i	1.38546	+	0.504265i	0.461628	+	0.887074i	$0.347265\pi$
$770$	−83.2024	−	30.2832i	−2.99841	−	1.09133i
$771$		0			0
$772$	9.07492	−	51.4664i	0.326613	−	1.85232i
$773$	18.2081	+	31.5374i	0.654900	+	1.13432i	0.981919	+	0.189302i	$0.0606226\pi$
$773$	18.2081	+	31.5374i	0.654900	+	1.13432i	−0.327019	+	0.945018i	$0.606044\pi$
$774$		0			0
$775$	0.524012	−	0.907615i	0.0188231	−	0.0326025i
$776$	4.29000	+	3.59974i	0.154002	+	0.129223i
$777$		0			0
$778$	7.79150	+	44.1878i	0.279339	+	1.58421i
$779$	−3.18281	+	2.67069i	−0.114036	+	0.0956875i
$780$		0			0
$781$	−12.0312	+	4.37898i	−0.430509	+	0.156692i
$782$	21.6160			0.772985
$783$		0			0
$784$	−44.6174			−1.59348
$785$	−26.8906	+	9.78737i	−0.959766	+	0.349326i
$786$		0			0
$787$	14.0547	−	11.7933i	0.500997	−	0.420387i	−0.356951	−	0.934123i	$-0.616184\pi$
$787$	14.0547	−	11.7933i	0.500997	−	0.420387i	0.857948	+	0.513737i	$0.171739\pi$
$788$	−6.19839	−	35.1528i	−0.220808	−	1.25227i
$789$		0			0
$790$	15.3471	+	12.8778i	0.546027	+	0.458171i
$791$	5.82488	−	10.0890i	0.207109	−	0.358723i
$792$		0			0
$793$	−2.70904	−	4.69220i	−0.0962009	−	0.166625i
$794$	3.60856	−	20.4651i	0.128063	−	0.726281i
$795$		0			0
$796$	−48.0575	−	17.4915i	−1.70335	−	0.619969i
$797$	−3.25596	−	1.18507i	−0.115332	−	0.0419775i	0.283709	−	0.958910i	$-0.408435\pi$
$797$	−3.25596	−	1.18507i	−0.115332	−	0.0419775i	−0.399042	+	0.916933i	$0.630657\pi$
$798$		0			0
$799$	2.94825	−	16.7204i	0.104302	−	0.591525i
$800$	2.82166	+	4.88726i	0.0997608	+	0.172791i
$801$		0			0
$802$	−20.3358	+	35.2227i	−0.718083	+	1.24376i
$803$	40.5603	+	34.0341i	1.43134	+	1.20104i
$804$		0			0
$805$	7.50394	+	42.5570i	0.264479	+	1.49994i
$806$	2.91698	−	2.44764i	0.102746	−	0.0862143i
$807$		0			0
$808$	19.1351	−	6.96460i	0.673170	−	0.245014i
$809$	−24.8406			−0.873348			−0.436674	−	0.899620i	$-0.643844\pi$
$809$	−24.8406			−0.873348			−0.436674	+	0.899620i	$0.643844\pi$
$810$		0			0
$811$	−40.3286			−1.41613			−0.708063	−	0.706149i	$-0.750431\pi$
$811$	−40.3286			−1.41613			−0.708063	+	0.706149i	$0.750431\pi$
$812$	−34.1788	+	12.4401i	−1.19944	+	0.436561i
$813$		0			0
$814$	−60.5980	+	50.8477i	−2.12396	+	1.78221i
$815$	0.429097	+	2.43353i	0.0150306	+	0.0852429i
$816$		0			0
$817$	7.72265	+	6.48007i	0.270181	+	0.226709i
$818$	15.9330	−	27.5968i	0.557084	−	0.964898i
$819$		0			0
$820$	5.88862	+	10.1994i	0.205640	+	0.356178i
$821$	6.97747	−	39.5712i	0.243515	−	1.38104i	−0.580400	−	0.814331i	$-0.697104\pi$
$821$	6.97747	−	39.5712i	0.243515	−	1.38104i	0.823916	−	0.566713i	$-0.191785\pi$
$822$		0			0
$823$	45.0633	+	16.4017i	1.57081	+	0.571727i	0.973180	−	0.230046i	$-0.0738876\pi$
$823$	45.0633	+	16.4017i	1.57081	+	0.571727i	0.597628	+	0.801773i	$0.296110\pi$
$824$	9.27488	+	3.37578i	0.323106	+	0.117601i
$825$		0			0
$826$	−0.469229	+	2.66113i	−0.0163266	+	0.0925925i
$827$	2.50024	+	4.33054i	0.0869419	+	0.150588i	0.906217	−	0.422813i	$-0.138957\pi$
$827$	2.50024	+	4.33054i	0.0869419	+	0.150588i	−0.819275	+	0.573401i	$0.805624\pi$
$828$		0			0
$829$	−14.8519	+	25.7242i	−0.515826	+	0.893438i	0.484005	+	0.875065i	$0.339182\pi$
$829$	−14.8519	+	25.7242i	−0.515826	+	0.893438i	−0.999831	+	0.0183722i	$0.994152\pi$
$830$	−28.4971	−	23.9119i	−0.989148	−	0.829993i
$831$		0			0
$832$	2.41920	+	13.7200i	0.0838708	+	0.475655i
$833$	29.8932	−	25.0834i	1.03574	−	0.869087i
$834$		0			0
$835$	−46.5812	+	16.9542i	−1.61201	+	0.586723i
$836$	−19.1871			−0.663599
$837$		0			0
$838$	−12.3502			−0.426632
$839$	24.3423	−	8.85987i	0.840389	−	0.305877i	0.114274	−	0.993449i	$-0.463546\pi$
$839$	24.3423	−	8.85987i	0.840389	−	0.305877i	0.726116	+	0.687573i	$0.241324\pi$
$840$		0			0
$841$	−15.4042	+	12.9257i	−0.531179	+	0.445712i
$842$	4.91279	+	27.8618i	0.169306	+	0.960181i
$843$		0			0
$844$	−19.0083	−	15.9499i	−0.654294	−	0.549018i
$845$	−11.9300	+	20.6633i	−0.410403	+	0.710840i
$846$		0			0
$847$	−15.0751	−	26.1109i	−0.517988	−	0.897182i
$848$	2.96966	−	16.8418i	0.101978	−	0.578348i
$849$		0			0
$850$	−3.35681	−	1.22178i	−0.115138	−	0.0419067i
$851$	36.2793	+	13.2046i	1.24364	+	0.452648i
$852$		0			0
$853$	−0.866793	+	4.91583i	−0.0296784	+	0.168315i	−0.996045	−	0.0888556i	$-0.971679\pi$
$853$	−0.866793	+	4.91583i	−0.0296784	+	0.168315i	0.966366	+	0.257170i	$0.0827901\pi$
$854$	−22.9543	−	39.7580i	−0.785481	−	1.36049i
$855$		0			0
$856$	4.06980	−	7.04911i	0.139103	−	0.240934i
$857$	−11.2478	−	9.43806i	−0.384219	−	0.322398i	0.430137	−	0.902764i	$-0.358465\pi$
$857$	−11.2478	−	9.43806i	−0.384219	−	0.322398i	−0.814356	+	0.580366i	$0.802910\pi$
$858$		0			0
$859$	−3.03621	−	17.2192i	−0.103594	−	0.587512i	−0.991772	−	0.128013i	$-0.959140\pi$
$859$	−3.03621	−	17.2192i	−0.103594	−	0.587512i	0.888178	−	0.459499i	$-0.151971\pi$
$860$	21.8904	−	18.3682i	0.746457	−	0.626352i
$861$		0			0
$862$	−72.7194	+	26.4677i	−2.47683	+	0.901493i
$863$	6.33263			0.215565			0.107783	−	0.994174i	$-0.465625\pi$
$863$	6.33263			0.215565			0.107783	+	0.994174i	$0.465625\pi$
$864$		0			0
$865$	18.9284			0.643585
$866$	−21.7183	+	7.90480i	−0.738017	+	0.268616i
$867$		0			0
$868$	13.7695	−	11.5540i	0.467369	−	0.392169i
$869$	3.28024	+	18.6032i	0.111275	+	0.631070i
$870$		0			0
$871$	−3.84821	−	3.22903i	−0.130392	−	0.109412i
$872$	−3.08187	+	5.33795i	−0.104365	+	0.180766i
$873$		0			0
$874$	8.40448	+	14.5570i	0.284286	+	0.492397i
$875$	9.95838	−	56.4768i	0.336655	−	1.90926i
$876$		0			0
$877$	−30.5691	−	11.1263i	−1.03225	−	0.375707i	−0.230310	−	0.973117i	$-0.573974\pi$
$877$	−30.5691	−	11.1263i	−1.03225	−	0.375707i	−0.801936	+	0.597410i	$0.796196\pi$
$878$	18.8770	+	6.87066i	0.637067	+	0.231873i
$879$		0			0
$880$	4.03274	−	22.8708i	0.135944	−	0.770974i
$881$	16.6800	+	28.8906i	0.561963	+	0.973348i	0.997325	+	0.0730926i	$0.0232869\pi$
$881$	16.6800	+	28.8906i	0.561963	+	0.973348i	−0.435363	+	0.900255i	$0.643380\pi$
$882$		0			0
$883$	27.4256	−	47.5025i	0.922944	−	1.59859i	0.128109	−	0.991760i	$-0.459109\pi$
$883$	27.4256	−	47.5025i	0.922944	−	1.59859i	0.794835	−	0.606826i	$-0.207557\pi$
$884$	−5.53912	−	4.64788i	−0.186301	−	0.156325i
$885$		0			0
$886$	−6.09745	−	34.5803i	−0.204848	−	1.16175i
$887$	16.1235	−	13.5292i	0.541374	−	0.454267i	−0.330633	−	0.943759i	$-0.607262\pi$
$887$	16.1235	−	13.5292i	0.541374	−	0.454267i	0.872008	+	0.489492i	$0.162818\pi$
$888$		0			0
$889$	42.0757	−	15.3143i	1.41117	−	0.513625i
$890$	74.6516			2.50233
$891$		0			0
$892$	37.9158			1.26951
$893$	12.4064	−	4.51557i	0.415165	−	0.151108i
$894$		0			0
$895$	−16.8174	+	14.1115i	−0.562143	+	0.471694i
$896$	7.13673	+	40.4744i	0.238421	+	1.35215i
$897$		0			0
$898$	7.72198	+	6.47951i	0.257686	+	0.216224i
$899$	−2.19698	+	3.80529i	−0.0732735	+	0.126914i
$900$		0			0
$901$	7.47859	+	12.9533i	0.249148	+	0.431537i
$902$	−3.46130	+	19.6300i	−0.115249	+	0.653607i
$903$		0			0
$904$	−2.47446	−	0.900631i	−0.0822995	−	0.0299546i
$905$	−2.84691	−	1.03619i	−0.0946346	−	0.0344442i
$906$		0			0
$907$	2.57660	−	14.6126i	0.0855545	−	0.485204i	−0.911681	−	0.410899i	$-0.865215\pi$
$907$	2.57660	−	14.6126i	0.0855545	−	0.485204i	0.997236	−	0.0743051i	$-0.0236739\pi$
$908$	28.5444	+	49.4403i	0.947278	+	1.64073i
$909$		0			0
$910$	12.9737	−	22.4711i	0.430074	−	0.744911i
$911$	13.8114	+	11.5892i	0.457593	+	0.383966i	0.842244	−	0.539096i	$-0.181234\pi$
$911$	13.8114	+	11.5892i	0.457593	+	0.383966i	−0.384652	+	0.923062i	$0.625678\pi$
$912$		0			0
$913$	−6.09086	−	34.5430i	−0.201578	−	1.14321i
$914$	36.4781	−	30.6088i	1.20659	−	1.01245i
$915$		0			0
$916$	−20.6065	+	7.50017i	−0.680859	+	0.247812i
$917$	−74.3738			−2.45604
$918$		0			0
$919$	13.4881			0.444932			0.222466	−	0.974940i	$-0.428589\pi$
$919$	13.4881			0.444932			0.222466	+	0.974940i	$0.428589\pi$
$920$	9.17876	−	3.34079i	0.302615	−	0.110143i
$921$		0			0
$922$	24.2914	−	20.3829i	0.799996	−	0.671276i
$923$	−0.651533	−	3.69503i	−0.0214455	−	0.121623i
$924$		0			0
$925$	−4.88758	−	4.10117i	−0.160703	−	0.134846i
$926$	−15.7753	+	27.3237i	−0.518410	+	0.897912i
$927$		0			0
$928$	−11.8302	−	20.4905i	−0.388344	−	0.672632i
$929$	−6.53284	+	37.0496i	−0.214336	+	1.21556i	0.667720	+	0.744413i	$0.267270\pi$
$929$	−6.53284	+	37.0496i	−0.214336	+	1.21556i	−0.882056	+	0.471145i	$0.843841\pi$
$930$		0			0
$931$	28.5148	+	10.3785i	0.934534	+	0.340143i
$932$	55.7650	+	20.2968i	1.82664	+	0.664844i
$933$		0			0
$934$	5.66479	−	32.1266i	0.185358	−	1.05121i
$935$	10.1558	+	17.5903i	0.332129	+	0.575265i
$936$		0			0
$937$	−2.07229	+	3.58931i	−0.0676988	+	0.117258i	−0.897888	−	0.440224i	$-0.854899\pi$
$937$	−2.07229	+	3.58931i	−0.0676988	+	0.117258i	0.830189	+	0.557482i	$0.188232\pi$
$938$	−32.6068	−	27.3603i	−1.06465	−	0.893346i
$939$		0			0
$940$	−6.49858	−	36.8553i	−0.211960	−	1.20209i
$941$	−2.70439	+	2.26925i	−0.0881605	+	0.0739754i	−0.685803	−	0.727787i	$-0.740549\pi$
$941$	−2.70439	+	2.26925i	−0.0881605	+	0.0739754i	0.597642	+	0.801763i	$0.296104\pi$
$942$		0			0
$943$	9.14163	−	3.32728i	0.297693	−	0.108351i
$944$	−0.708752			−0.0230679
$945$		0			0
$946$	48.3643			1.57246
$947$	13.3954	−	4.87552i	0.435292	−	0.158433i	−0.115074	−	0.993357i	$-0.536711\pi$
$947$	13.3954	−	4.87552i	0.435292	−	0.158433i	0.550366	+	0.834924i	$0.314488\pi$
$948$		0			0
$949$	−11.8863	+	9.97377i	−0.385845	+	0.323762i
$950$	−0.482367	−	2.73564i	−0.0156500	−	0.0887558i
$951$		0			0
$952$	−9.62187	−	8.07371i	−0.311847	−	0.261670i
$953$	−5.82130	+	10.0828i	−0.188570	+	0.326613i	−0.944774	−	0.327723i	$-0.893719\pi$
$953$	−5.82130	+	10.0828i	−0.188570	+	0.326613i	0.756204	+	0.654336i	$0.227052\pi$
$954$		0			0
$955$	12.8629	+	22.2792i	0.416233	+	0.720938i
$956$	4.34868	−	24.6626i	0.140646	−	0.797645i
$957$		0			0
$958$	20.8646	+	7.59408i	0.674103	+	0.245353i
$959$	16.6029	+	6.04295i	0.536135	+	0.195137i
$960$		0			0
$961$	−5.00602	+	28.3906i	−0.161485	+	0.915825i
$962$	−11.5909	−	20.0761i	−0.373707	−	0.647279i
$963$		0			0
$964$	−7.18680	+	12.4479i	−0.231471	+	0.400920i
$965$	−32.9554	−	27.6529i	−1.06087	−	0.890178i
$966$		0			0
$967$	5.04763	+	28.6265i	0.162321	+	0.920567i	0.951784	+	0.306769i	$0.0992479\pi$
$967$	5.04763	+	28.6265i	0.162321	+	0.920567i	−0.789463	+	0.613798i	$0.789641\pi$
$968$	−5.22065	+	4.38064i	−0.167798	+	0.140799i
$969$		0			0
$970$	21.1310	−	7.69105i	0.678475	−	0.246945i
$971$	47.5792			1.52689			0.763444	−	0.645874i	$-0.223507\pi$
$971$	47.5792			1.52689			0.763444	+	0.645874i	$0.223507\pi$
$972$		0			0
$973$	64.3687			2.06357
$974$	−32.2792	+	11.7487i	−1.03429	+	0.376452i
$975$		0			0
$976$	9.22419	−	7.74001i	0.295259	−	0.247752i
$977$	1.06208	+	6.02338i	0.0339791	+	0.192705i	0.997072	−	0.0764625i	$-0.0243626\pi$
$977$	1.06208	+	6.02338i	0.0339791	+	0.192705i	−0.963093	+	0.269168i	$0.913251\pi$
$978$		0			0
$979$	53.9207	+	45.2448i	1.72331	+	1.44603i
$980$	43.0073	−	74.4908i	1.37382	−	2.37952i
$981$		0			0
$982$	−11.4511	−	19.8339i	−0.365419	−	0.632924i
$983$	1.84967	−	10.4900i	0.0589952	−	0.334579i	−0.940997	−	0.338414i	$-0.890110\pi$
$983$	1.84967	−	10.4900i	0.0589952	−	0.334579i	0.999993	+	0.00383514i	$0.00122077\pi$
$984$		0			0
$985$	−27.6118	−	10.0499i	−0.879785	−	0.320216i
$986$	14.0739	+	5.12246i	0.448203	+	0.163132i
$987$		0			0
$988$	0.976390	−	5.53738i	0.0310631	−	0.176168i
$989$	−11.8022	−	20.4421i	−0.375289	−	0.650020i
$990$		0			0
$991$	−11.9928	+	20.7721i	−0.380964	+	0.659849i	−0.991200	−	0.132371i	$-0.957741\pi$
$991$	−11.9928	+	20.7721i	−0.380964	+	0.659849i	0.610236	+	0.792219i	$0.291074\pi$
$992$	8.95714	+	7.51593i	0.284389	+	0.238631i
$993$		0			0
$994$	−5.52058	−	31.3088i	−0.175102	−	0.993054i
$995$	−32.2500	+	27.0610i	−1.02239	+	0.857890i
$996$		0			0
$997$	−4.05400	+	1.47554i	−0.128392	+	0.0467307i	−0.405417	−	0.914132i	$-0.632874\pi$
$997$	−4.05400	+	1.47554i	−0.128392	+	0.0467307i	0.277025	+	0.960863i	$0.410651\pi$
$998$	40.7733			1.29066
$999$		0			0

Twists

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

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

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)

\(f(q)\)	\(=\)	\(q+(1.99687 - 0.726803i) q^{2} +(1.92717 - 1.61709i) q^{4} +(-0.359615 - 2.03948i) q^{5} +(3.71430 + 3.11667i) q^{7} +(0.547989 - 0.949144i) q^{8} +(-2.20040 - 3.81121i) q^{10} +(0.720551 - 4.08645i) q^{11} +(1.14268 + 0.415902i) q^{13} +(9.68219 + 3.52403i) q^{14} +(-0.469286 + 2.66145i) q^{16} +(-1.18182 - 2.04697i) q^{17} +(0.919003 - 1.59176i) q^{19} +(-3.99106 - 3.34890i) q^{20} +(-1.53119 - 8.68382i) q^{22} +(-3.29673 + 2.76628i) q^{23} +(0.668315 - 0.243247i) q^{25} +2.58407 q^{26} +12.1980 q^{28} +(-2.80199 + 1.01984i) q^{29} +(1.12883 - 0.947203i) q^{31} +(1.37788 + 7.81432i) q^{32} +(-3.84769 - 3.22859i) q^{34} +(5.02066 - 8.69603i) q^{35} +(-4.48554 - 7.76918i) q^{37} +(0.678238 - 3.84648i) q^{38} +(-2.13282 - 0.776284i) q^{40} +(-2.12420 - 0.773145i) q^{41} +(-0.952435 + 5.40153i) q^{43} +(-5.21953 - 9.04050i) q^{44} +(-4.57260 + 7.91998i) q^{46} +(5.50260 + 4.61723i) q^{47} +(2.86687 + 16.2588i) q^{49} +(1.15775 - 0.971466i) q^{50} +(2.87470 - 1.04630i) q^{52} -6.32803 q^{53} -8.59334 q^{55} +(4.99356 - 1.81751i) q^{56} +(-4.85400 + 4.07299i) q^{58} +(0.0455404 + 0.258272i) q^{59} +(-3.41319 - 2.86401i) q^{61} +(1.56571 - 2.71188i) q^{62} +(5.72840 + 9.92188i) q^{64} +(0.437297 - 2.48004i) q^{65} +(-3.88197 - 1.41292i) q^{67} +(-5.58771 - 2.03376i) q^{68} +(3.70532 - 21.0139i) q^{70} +(-1.54276 - 2.67213i) q^{71} +(-6.38003 + 11.0505i) q^{73} +(-14.6037 - 12.2540i) q^{74} +(-0.802942 - 4.55371i) q^{76} +(15.4124 - 12.9326i) q^{77} +(-4.27786 + 1.55701i) q^{79} +5.59674 q^{80} -4.80368 q^{82} +(7.94328 - 2.89112i) q^{83} +(-3.74975 + 3.14642i) q^{85} +(2.02395 + 11.4784i) q^{86} +(-3.48378 - 2.92323i) q^{88} +(-8.48158 + 14.6905i) q^{89} +(2.94803 + 5.10614i) q^{91} +(-1.88004 + 10.6622i) q^{92} +(14.3438 + 5.22072i) q^{94} +(-3.57685 - 1.30187i) q^{95} +(-0.887302 + 5.03214i) q^{97} +(17.5417 + 30.3831i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{2} - 3 q^{4} - 12 q^{5} - 3 q^{7} + 6 q^{8} - 6 q^{10} + 3 q^{11} + 6 q^{13} + 6 q^{14} + 27 q^{16} - 9 q^{17} - 12 q^{19} - 39 q^{20} - 39 q^{22} - 21 q^{23} + 6 q^{25} - 48 q^{26} + 6 q^{28}+ \cdots + 18 q^{98}+O(q^{100}) \) 12 * q + 3 * q^2 - 3 * q^4 - 12 * q^5 - 3 * q^7 + 6 * q^8 - 6 * q^10 + 3 * q^11 + 6 * q^13 + 6 * q^14 + 27 * q^16 - 9 * q^17 - 12 * q^19 - 39 * q^20 - 39 * q^22 - 21 * q^23 + 6 * q^25 - 48 * q^26 + 6 * q^28 - 6 * q^29 + 6 * q^31 - 27 * q^32 - 18 * q^34 + 30 * q^35 - 3 * q^37 - 3 * q^38 + 33 * q^40 + 15 * q^41 - 30 * q^43 - 33 * q^44 + 3 * q^46 + 21 * q^47 - 3 * q^49 - 6 * q^50 + 18 * q^53 + 30 * q^55 - 15 * q^56 - 3 * q^58 - 30 * q^59 - 30 * q^61 - 30 * q^62 - 6 * q^64 + 12 * q^65 - 39 * q^67 - 18 * q^68 + 51 * q^70 - 12 * q^73 - 57 * q^74 + 57 * q^76 + 24 * q^77 + 15 * q^79 + 42 * q^80 - 42 * q^82 + 21 * q^83 + 54 * q^85 + 60 * q^86 + 12 * q^88 - 9 * q^89 - 18 * q^91 + 15 * q^92 + 33 * q^94 - 42 * q^95 - 12 * q^97 + 18 * q^98

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