LMFDB - Embedded newform 729.2.e.s.568.2

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			568.2
Root			$3.10658i$ of defining polynomial
Character	$\chi$	$=$	729.568
Dual form			729.2.e.s.163.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{9}\right)$

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	0.931717	−	0.363185i	$-0.118311\pi$
$2$	1.99687	+	0.726803i	1.41200	+	0.513927i	0.480286	+	0.877112i	$0.340533\pi$
$3$		0			0
$3$		0			0
$4$	1.92717	+	1.61709i	0.963587	+	0.808546i
$5$	−0.359615	+	2.03948i	−0.160825	+	0.912082i	0.792441	+	0.609949i	$0.208810\pi$
$5$	−0.359615	+	2.03948i	−0.160825	+	0.912082i	−0.953266	+	0.302134i	$0.902301\pi$
$6$		0			0
$7$	3.71430	−	3.11667i	1.40387	−	1.17799i	0.444524	−	0.895767i	$-0.353373\pi$
$7$	3.71430	−	3.11667i	1.40387	−	1.17799i	0.959349	−	0.282222i	$-0.0910716\pi$
$8$	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	0.876951	+	0.480579i	$0.159573\pi$
$11$	0.720551	+	4.08645i	0.217254	+	1.23211i	−0.659697	+	0.751532i	$0.729315\pi$
$12$		0			0
$13$	1.14268	−	0.415902i	0.316923	−	0.115350i	−0.178661	−	0.983911i	$-0.557176\pi$
$13$	1.14268	−	0.415902i	0.316923	−	0.115350i	0.495583	+	0.868560i	$0.334954\pi$
$14$	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	−0.973004	−	0.230789i	$-0.925869\pi$
$17$	−1.18182	+	2.04697i	−0.286633	+	0.496463i	0.686371	+	0.727252i	$0.259203\pi$
$18$		0			0
$19$	0.919003	+	1.59176i	0.210834	+	0.365175i	0.951976	−	0.306174i	$-0.0990488\pi$
$19$	0.919003	+	1.59176i	0.210834	+	0.365175i	−0.741142	+	0.671348i	$0.765715\pi$
$20$	−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	0.230748	−	0.973014i	$-0.425883\pi$
$23$	−3.29673	−	2.76628i	−0.687415	−	0.576809i	−0.918162	+	0.396204i	$0.870327\pi$
$24$		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	0.0684925	−	0.997652i	$-0.478181\pi$
$29$	−2.80199	−	1.01984i	−0.520317	−	0.189380i	−0.588810	+	0.808272i	$0.700403\pi$
$30$		0			0
$31$	1.12883	+	0.947203i	0.202744	+	0.170123i	0.738507	−	0.674246i	$-0.235531\pi$
$31$	1.12883	+	0.947203i	0.202744	+	0.170123i	−0.535762	+	0.844369i	$0.679976\pi$
$32$	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	0.216236	+	0.976341i	$0.430622\pi$
$37$	−4.48554	+	7.76918i	−0.737418	+	1.27725i	−0.953654	+	0.300905i	$0.902711\pi$
$38$	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	−0.502522	−	0.864565i	$-0.667594\pi$
$41$	−2.12420	+	0.773145i	−0.331744	+	0.120745i	0.170778	+	0.985310i	$0.445372\pi$
$42$		0			0
$43$	−0.952435	−	5.40153i	−0.145245	−	0.823726i	−0.967170	−	0.254130i	$-0.918211\pi$
$43$	−0.952435	−	5.40153i	−0.145245	−	0.823726i	0.821925	−	0.569596i	$-0.192900\pi$
$44$	−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	−0.146202	−	0.989255i	$-0.546705\pi$
$47$	5.50260	−	4.61723i	0.802636	−	0.673492i	0.948838	+	0.315763i	$0.102260\pi$
$48$		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	−0.981700	−	0.190435i	$-0.939010\pi$
$59$	0.0455404	−	0.258272i	0.00592886	−	0.0336242i	0.987629	+	0.156811i	$0.0501213\pi$
$60$		0			0
$61$	−3.41319	+	2.86401i	−0.437014	+	0.366699i	−0.834591	−	0.550870i	$-0.814296\pi$
$61$	−3.41319	+	2.86401i	−0.437014	+	0.366699i	0.397576	+	0.917569i	$0.369851\pi$
$62$	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	−0.568080	−	0.822973i	$-0.692314\pi$
$67$	−3.88197	+	1.41292i	−0.474258	+	0.172616i	0.0938223	+	0.995589i	$0.470091\pi$
$68$	−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	−0.942932	−	0.332986i	$-0.891944\pi$
$71$	−1.54276	+	2.67213i	−0.183091	+	0.317124i	0.759840	+	0.650110i	$0.225277\pi$
$72$		0			0
$73$	−6.38003	−	11.0505i	−0.746726	−	1.29337i	−0.949384	−	0.314118i	$-0.898291\pi$
$73$	−6.38003	−	11.0505i	−0.746726	−	1.29337i	0.202658	−	0.979250i	$-0.435042\pi$
$74$	−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	0.0899659	−	0.995945i	$-0.471324\pi$
$79$	−4.27786	−	1.55701i	−0.481297	−	0.175178i	−0.571263	+	0.820767i	$0.693546\pi$
$80$	5.59674			0.625734
$81$		0			0
$82$	−4.80368			−0.530478
$83$	7.94328	+	2.89112i	0.871888	+	0.317341i	0.738931	−	0.673781i	$-0.235331\pi$
$83$	7.94328	+	2.89112i	0.871888	+	0.317341i	0.132956	+	0.991122i	$0.457553\pi$
$84$		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	−0.828716	−	0.559670i	$-0.810928\pi$
$89$	−8.48158	−	14.6905i	−0.899046	−	1.55719i	−0.0703304	−	0.997524i	$-0.522405\pi$
$90$		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	−0.996141	−	0.0877646i	$-0.972028\pi$
$97$	−0.887302	−	5.03214i	−0.0900919	−	0.510937i	0.906049	−	0.423172i	$-0.139083\pi$
$98$	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	0.462918	−	0.886401i	$-0.346802\pi$
$101$	14.2330	−	11.9429i	1.41624	−	1.18836i	0.953319	−	0.301964i	$-0.0976422\pi$
$102$		0			0
$103$	1.56384	−	8.86895i	0.154089	−	0.873884i	−0.805524	−	0.592563i	$-0.798116\pi$
$103$	1.56384	−	8.86895i	0.154089	−	0.873884i	0.959614	−	0.281321i	$-0.0907726\pi$
$104$	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	−0.998123	−	0.0612406i	$-0.980494\pi$
$113$	−0.417219	+	2.36617i	−0.0392487	+	0.222590i	0.958874	+	0.283831i	$0.0916054\pi$
$114$		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	0.994859	−	0.101274i	$-0.0322919\pi$
$127$	4.61735	+	7.99748i	0.409723	+	0.709662i	−0.585135	+	0.810936i	$0.698959\pi$
$128$	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	−0.0361871	−	0.999345i	$-0.511521\pi$
$131$	−11.7504	−	9.85972i	−1.02663	−	0.861448i	−0.990447	+	0.137897i	$0.955966\pi$
$132$		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	0.484126	−	0.874998i	$-0.339138\pi$
$137$	3.42421	+	1.24631i	0.292550	+	0.106480i	−0.191576	+	0.981478i	$0.561360\pi$
$138$		0			0
$139$	10.1697	+	8.53335i	0.862579	+	0.723789i	0.962522	−	0.271204i	$-0.0874217\pi$
$139$	10.1697	+	8.53335i	0.862579	+	0.723789i	−0.0999433	+	0.994993i	$0.531866\pi$
$140$	−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	−0.661418	−	0.750018i	$-0.730045\pi$
$149$	−8.37359	+	3.04774i	−0.685991	+	0.249680i	−0.0245732	+	0.999698i	$0.507823\pi$
$150$		0			0
$151$	−0.123708	−	0.701581i	−0.0100672	−	0.0570938i	0.979360	−	0.202122i	$-0.0647838\pi$
$151$	−0.123708	−	0.701581i	−0.0100672	−	0.0570938i	−0.989428	+	0.145028i	$0.953673\pi$
$152$	−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	0.725817	+	0.687888i	$0.241462\pi$
$157$	−2.39948	+	13.6081i	−0.191499	+	1.08605i	−0.917316	+	0.398159i	$0.869649\pi$
$158$	−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	0.210669	+	0.977558i	$0.432436\pi$
$167$	−4.15650	+	23.5727i	−0.321640	+	1.82411i	−0.532308	+	0.846551i	$0.678675\pi$
$168$		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	−0.983787	−	0.179343i	$-0.942603\pi$
$173$	−1.58714	−	9.00115i	−0.120668	−	0.684344i	0.863118	−	0.505002i	$-0.168508\pi$
$174$		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	−0.993250	−	0.115997i	$-0.962994\pi$
$179$	−5.30038	+	9.18052i	−0.396169	+	0.686184i	0.597081	+	0.802181i	$0.296327\pi$
$180$		0			0
$181$	0.731460	+	1.26693i	0.0543690	+	0.0941699i	0.891929	−	0.452176i	$-0.149352\pi$
$181$	0.731460	+	1.26693i	0.0543690	+	0.0941699i	−0.837560	+	0.546345i	$0.816019\pi$
$182$	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	−0.116785	−	0.993157i	$-0.537259\pi$
$191$	−11.6731	−	4.24867i	−0.844637	−	0.307423i	−0.727852	+	0.685734i	$0.759481\pi$
$192$		0			0
$193$	15.9133	+	13.3528i	1.14546	+	0.961157i	0.999604	−	0.0281484i	$-0.00896109\pi$
$193$	15.9133	+	13.3528i	1.14546	+	0.961157i	0.145859	+	0.989305i	$0.453406\pi$
$194$	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	0.999980	+	0.00630469i	$0.00200686\pi$
$197$	7.09433	+	12.2877i	0.505450	+	0.875465i	−0.494530	+	0.869161i	$0.664660\pi$
$198$		0			0
$199$	−10.1643	+	17.6051i	−0.720529	+	1.24799i	0.240259	+	0.970709i	$0.422768\pi$
$199$	−10.1643	+	17.6051i	−0.720529	+	1.24799i	−0.960788	+	0.277284i	$0.910566\pi$
$200$	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	0.867358	+	0.497685i	$0.165817\pi$
$211$	−1.71275	+	9.71347i	−0.117910	+	0.668703i	−0.985268	+	0.171018i	$0.945294\pi$
$212$	−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	−0.168376	−	0.985723i	$-0.553852\pi$
$223$	11.5453	−	9.68770i	0.773134	−	0.648736i	0.941509	+	0.336987i	$0.109408\pi$
$224$	−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	−0.778705	−	0.627390i	$-0.784123\pi$
$227$	−3.94052	−	22.3478i	−0.261542	−	1.48328i	0.517164	−	0.855886i	$-0.326988\pi$
$228$		0			0
$229$	−8.19102	+	2.98129i	−0.541278	+	0.197009i	−0.598167	−	0.801371i	$-0.704104\pi$
$229$	−8.19102	+	2.98129i	−0.541278	+	0.197009i	0.0568892	+	0.998381i	$0.481882\pi$
$230$	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	−0.163406	−	0.986559i	$-0.552248\pi$
$233$	11.7945	−	20.4286i	0.772682	−	1.33832i	0.936088	−	0.351766i	$-0.114419\pi$
$234$		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	0.855193	−	0.518310i	$-0.173439\pi$
$239$	7.62560	+	6.39864i	0.493259	+	0.413894i	−0.361933	+	0.932204i	$0.617883\pi$
$240$		0			0
$241$	−5.36889	−	1.95411i	−0.345840	−	0.125876i	0.163259	−	0.986583i	$-0.447799\pi$
$241$	−5.36889	−	1.95411i	−0.345840	−	0.125876i	−0.509100	+	0.860708i	$0.670022\pi$
$242$	−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	0.957825	−	0.287351i	$-0.0927745\pi$
$251$	3.64483	+	6.31303i	0.230060	+	0.398475i	−0.727766	+	0.685826i	$0.759441\pi$
$252$		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	0.445622	−	0.895221i	$-0.352982\pi$
$257$	21.8413	−	7.94960i	1.36243	−	0.495882i	0.916803	+	0.399339i	$0.130760\pi$
$258$		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	−0.303150	+	0.952943i	$0.598038\pi$
$263$	−20.9893	+	17.6121i	−1.29426	+	1.08601i	−0.991107	+	0.133067i	$0.957517\pi$
$264$		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	−0.634121	−	0.773234i	$-0.718638\pi$
$277$	0.287123	−	0.240924i	0.0172515	−	0.0144757i	0.651373	+	0.758758i	$0.274193\pi$
$278$	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	0.967500	+	0.252873i	$0.0813755\pi$
$281$	2.42788	+	13.7692i	0.144835	+	0.821400i	−0.822665	+	0.568527i	$0.807513\pi$
$282$		0			0
$283$	−14.6234	+	5.32248i	−0.869270	+	0.316389i	−0.737872	−	0.674941i	$-0.764169\pi$
$283$	−14.6234	+	5.32248i	−0.869270	+	0.316389i	−0.131399	+	0.991330i	$0.541947\pi$
$284$	−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	0.997558	−	0.0698405i	$-0.0222490\pi$
$293$	18.8633	+	15.8281i	1.10200	+	0.924690i	0.104445	+	0.994531i	$0.466693\pi$
$294$		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	−0.413362	−	0.910567i	$-0.635646\pi$
$307$	10.1956	−	17.6593i	0.581893	−	1.00787i	0.995255	−	0.0973012i	$-0.0310210\pi$
$308$	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	−0.856841	−	0.515580i	$-0.827576\pi$
$311$	−20.8415	+	7.58567i	−1.18181	+	0.430144i	−0.324970	+	0.945724i	$0.605354\pi$
$312$		0			0
$313$	−1.94000	−	11.0023i	−0.109656	−	0.621887i	−0.989258	−	0.146178i	$-0.953303\pi$
$313$	−1.94000	−	11.0023i	−0.109656	−	0.621887i	0.879603	−	0.475709i	$-0.157808\pi$
$314$	−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	0.0886327	−	0.996064i	$-0.471750\pi$
$317$	19.3171	−	16.2090i	1.08496	−	0.910386i	0.996323	+	0.0856786i	$0.0273058\pi$
$318$		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	−0.997540	−	0.0701033i	$-0.977667\pi$
$331$	−20.0441	+	16.8190i	−1.10172	+	0.924455i	−0.104183	+	0.994558i	$0.533223\pi$
$332$	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	−0.606621	−	0.794991i	$-0.707476\pi$
$337$	−10.2859	+	3.74377i	−0.560310	+	0.203936i	0.0463114	+	0.998927i	$0.485253\pi$
$338$	−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	0.712164	−	0.702013i	$-0.247715\pi$
$347$	2.69140	+	2.25836i	0.144482	+	0.121235i	−0.567682	+	0.823248i	$0.692160\pi$
$348$		0			0
$349$	27.4361	+	9.98591i	1.46862	+	0.534534i	0.947725	−	0.319088i	$-0.103377\pi$
$349$	27.4361	+	9.98591i	1.46862	+	0.534534i	0.520894	+	0.853622i	$0.325599\pi$
$350$	7.32796			0.391696
$351$		0			0
$352$	32.9256			1.75494
$353$	23.5645	+	8.57677i	1.25421	+	0.456496i	0.881823	−	0.471581i	$-0.156317\pi$
$353$	23.5645	+	8.57677i	1.25421	+	0.456496i	0.372389	+	0.928077i	$0.378539\pi$
$354$		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	0.805159	−	0.593059i	$-0.202080\pi$
$359$	−2.10362	−	3.64358i	−0.111025	−	0.192301i	−0.916184	+	0.400758i	$0.868747\pi$
$360$		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	0.955424	+	0.295236i	$0.0953983\pi$
$367$	3.03826	+	17.2308i	0.158596	+	0.899441i	−0.796829	+	0.604205i	$0.793491\pi$
$368$	−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	0.497727	+	0.867334i	$0.334168\pi$
$373$	−5.14946	+	29.2040i	−0.266629	+	1.51213i	−0.764356	+	0.644794i	$0.776943\pi$
$374$	−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	−0.908900	−	0.417015i	$-0.863076\pi$
$383$	1.71856	−	9.74642i	0.0878142	−	0.498019i	0.996714	−	0.0810039i	$-0.0258126\pi$
$384$		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	−0.924792	−	0.380472i	$-0.875761\pi$
$389$	−3.66654	−	20.7940i	−0.185901	−	1.05430i	0.738891	−	0.673825i	$-0.235350\pi$
$390$		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	0.962244	−	0.272189i	$-0.0877476\pi$
$397$	4.88955	+	8.46894i	0.245399	+	0.425044i	−0.716845	+	0.697233i	$0.754414\pi$
$398$	−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	0.198556	−	0.980089i	$-0.436375\pi$
$401$	−14.6616	−	12.3025i	−0.732164	−	0.614359i	−0.930721	+	0.365731i	$0.880819\pi$
$402$		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	0.880984	−	0.473145i	$-0.156881\pi$
$409$	11.4873	+	9.63896i	0.568009	+	0.476616i	−0.312976	+	0.949761i	$0.601326\pi$
$410$	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	−0.471957	−	0.881621i	$-0.656452\pi$
$419$	−5.46131	+	1.98775i	−0.266802	+	0.0971081i	0.205155	+	0.978729i	$0.434230\pi$
$420$		0			0
$421$	−2.31187	−	13.1113i	−0.112674	−	0.639003i	−0.987876	−	0.155246i	$-0.950383\pi$
$421$	−2.31187	−	13.1113i	−0.112674	−	0.639003i	0.875202	−	0.483757i	$-0.160728\pi$
$422$	−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	−0.453406	−	0.891304i	$-0.649791\pi$
$439$	7.24162	−	6.07644i	0.345624	−	0.290013i	0.799030	+	0.601291i	$0.205347\pi$
$440$	−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	0.973927	+	0.226863i	$0.0728471\pi$
$443$	2.86935	+	16.2729i	0.136327	+	0.773148i	−0.837600	+	0.546284i	$0.816042\pi$
$444$		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	−0.804617	−	0.593794i	$-0.797629\pi$
$449$	2.37181	−	4.10809i	0.111933	−	0.193873i	0.916549	+	0.399921i	$0.130963\pi$
$450$		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	0.783787	−	0.621030i	$-0.213286\pi$
$457$	21.0571	+	7.66417i	0.985012	+	0.358515i	0.201225	+	0.979545i	$0.435508\pi$
$458$	−18.5232			−0.865534
$459$		0			0
$460$	22.4214			1.04540
$461$	14.0223	+	5.10371i	0.653085	+	0.237704i	0.647248	−	0.762279i	$-0.275920\pi$
$461$	14.0223	+	5.10371i	0.653085	+	0.237704i	0.00583713	+	0.999983i	$0.498142\pi$
$462$		0			0
$463$	−11.3736	−	9.54358i	−0.528576	−	0.443528i	0.339033	−	0.940774i	$-0.389900\pi$
$463$	−11.3736	−	9.54358i	−0.528576	−	0.443528i	−0.867609	+	0.497247i	$0.834344\pi$
$464$	−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	0.987150	−	0.159794i	$-0.0510830\pi$
$467$	7.67571	+	13.2947i	0.355190	+	0.615206i	−0.631961	+	0.775000i	$0.717750\pi$
$468$		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	−0.441348	−	0.897336i	$-0.645499\pi$
$479$	8.00410	−	6.71624i	0.365717	−	0.306873i	0.807064	+	0.590464i	$0.201055\pi$
$480$		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	0.913014	+	0.407928i	$0.133749\pi$
$491$	−1.87147	+	10.6136i	−0.0844581	+	0.478985i	−0.997472	+	0.0710576i	$0.977363\pi$
$492$		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	0.0946959	−	0.995506i	$-0.469812\pi$
$499$	18.0301	−	6.56240i	0.807136	−	0.293774i	0.712440	+	0.701733i	$0.247590\pi$
$500$	−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	−0.700282	−	0.713866i	$-0.746942\pi$
$503$	6.01253	−	10.4140i	0.268086	−	0.464338i	0.968367	+	0.249529i	$0.0802757\pi$
$504$		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	0.352606	−	0.935772i	$-0.385296\pi$
$509$	−11.4547	−	9.61162i	−0.507720	−	0.426027i	−0.860326	+	0.509744i	$0.829740\pi$
$510$		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	−0.905923	−	0.423442i	$-0.860822\pi$
$521$	−18.7094	−	32.4056i	−0.819673	−	1.41972i	0.0862502	−	0.996274i	$-0.472512\pi$
$522$		0			0
$523$	4.22489	−	7.31773i	0.184742	−	0.319982i	−0.758748	−	0.651385i	$-0.774188\pi$
$523$	4.22489	−	7.31773i	0.184742	−	0.319982i	0.943489	+	0.331403i	$0.107522\pi$
$524$	−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	0.0376558	−	0.999291i	$-0.488011\pi$
$547$	24.0500	−	20.1804i	1.02830	−	0.862850i	0.990648	+	0.136441i	$0.0435665\pi$
$548$	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	−0.646467	−	0.762942i	$-0.723754\pi$
$557$	7.96515	−	13.7960i	0.337494	−	0.584557i	0.983961	+	0.178385i	$0.0570874\pi$
$558$		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	0.146206	−	0.989254i	$-0.453294\pi$
$563$	−19.0445	−	15.9802i	−0.802631	−	0.673487i	−0.948837	+	0.315767i	$0.897738\pi$
$564$		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	−0.0648545	−	0.997895i	$-0.520658\pi$
$569$	−18.0327	−	6.56337i	−0.755970	−	0.275151i	−0.691116	+	0.722744i	$0.742881\pi$
$570$		0			0
$571$	−15.6114	−	13.0995i	−0.653317	−	0.548198i	0.254759	−	0.967005i	$-0.418004\pi$
$571$	−15.6114	−	13.0995i	−0.653317	−	0.548198i	−0.908075	+	0.418807i	$0.862448\pi$
$572$	−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	−0.999851	−	0.0172619i	$-0.994505\pi$
$577$	−11.6495	+	20.1776i	−0.484976	+	0.840004i	0.514875	+	0.857265i	$0.327838\pi$
$578$	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	−0.999977	−	0.00672500i	$-0.997859\pi$
$587$	−28.2741	+	23.7248i	−1.16700	+	0.979228i	−0.167021	+	0.985953i	$0.553415\pi$
$588$		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	0.648032	+	0.761613i	$0.275592\pi$
$599$	−5.41880	+	30.7315i	−0.221406	+	1.25566i	−0.869438	+	0.494043i	$0.835519\pi$
$600$		0			0
$601$	33.6578	−	28.2422i	1.37293	−	1.15202i	0.401183	−	0.915998i	$-0.368599\pi$
$601$	33.6578	−	28.2422i	1.37293	−	1.15202i	0.971747	−	0.236027i	$-0.0758452\pi$
$602$	−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	−0.651132	−	0.758964i	$-0.725706\pi$
$607$	−16.3118	+	5.93701i	−0.662075	+	0.240976i	−0.0109432	+	0.999940i	$0.503483\pi$
$608$	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	0.877869	−	0.478901i	$-0.158965\pi$
$613$	0.599024	+	1.03754i	0.0241944	+	0.0419059i	−0.853675	+	0.520807i	$0.825631\pi$
$614$	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	0.948746	−	0.316038i	$-0.102353\pi$
$617$	19.9277	+	16.7213i	0.802257	+	0.673174i	−0.146489	+	0.989212i	$0.546797\pi$
$618$		0			0
$619$	−9.05051	−	3.29412i	−0.363771	−	0.132402i	0.153667	−	0.988123i	$-0.450892\pi$
$619$	−9.05051	−	3.29412i	−0.363771	−	0.132402i	−0.517437	+	0.855721i	$0.673114\pi$
$620$	−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	−0.689880	−	0.723924i	$-0.742337\pi$
$631$	7.08366	−	12.2693i	0.281996	−	0.488431i	0.971876	+	0.235492i	$0.0756702\pi$
$632$	−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	−0.241846	−	0.970315i	$-0.577753\pi$
$641$	17.0069	−	14.2705i	0.671732	−	0.563650i	0.913577	+	0.406665i	$0.133308\pi$
$642$		0			0
$643$	3.73982	−	21.2096i	0.147484	−	0.836425i	−0.817855	−	0.575425i	$-0.804837\pi$
$643$	3.73982	−	21.2096i	0.147484	−	0.836425i	0.965339	−	0.261000i	$-0.0840522\pi$
$644$	−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	0.850657	+	0.525722i	$0.176205\pi$
$653$	−3.28384	+	18.6236i	−0.128506	+	0.728796i	−0.979163	+	0.203075i	$0.934907\pi$
$654$		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	0.984712	−	0.174189i	$-0.0557303\pi$
$659$	−0.00489366	−	0.0277533i	−0.000190630	−	0.00108112i	−0.984903	+	0.173108i	$0.944619\pi$
$660$		0			0
$661$	42.3254	−	15.4052i	1.64627	−	0.599192i	0.658148	−	0.752888i	$-0.271340\pi$
$661$	42.3254	−	15.4052i	1.64627	−	0.599192i	0.988118	+	0.153696i	$0.0491177\pi$
$662$	−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	0.512675	−	0.858583i	$-0.328655\pi$
$673$	9.17111	+	3.33801i	0.353520	+	0.128671i	−0.159155	+	0.987254i	$0.550877\pi$
$674$	−23.2607			−0.895968
$675$		0			0
$676$	−28.9847			−1.11480
$677$	−38.4153	−	13.9820i	−1.47642	−	0.537374i	−0.526586	−	0.850122i	$-0.676528\pi$
$677$	−38.4153	−	13.9820i	−1.47642	−	0.537374i	−0.949836	+	0.312748i	$0.898750\pi$
$678$		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	0.887957	+	0.459927i	$0.152125\pi$
$683$	22.0126	+	38.1269i	0.842287	+	1.45888i	−0.0456696	+	0.998957i	$0.514542\pi$
$684$		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	0.969443	+	0.245316i	$0.0788916\pi$
$691$	3.74240	+	21.2242i	0.142368	+	0.807406i	−0.827076	+	0.562090i	$0.809997\pi$
$692$	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	−0.484567	+	0.874754i	$0.661023\pi$
$709$	−38.0814	+	31.9541i	−1.43018	+	1.20006i	−0.945609	+	0.325306i	$0.894533\pi$
$710$	−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	−0.808667	−	0.588267i	$-0.799810\pi$
$719$	2.81873	−	4.88218i	0.105121	−	0.182075i	0.913788	+	0.406192i	$0.133144\pi$
$720$		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	0.975799	−	0.218670i	$-0.0701719\pi$
$727$	42.6755	+	15.5326i	1.58275	+	0.576072i	0.606947	+	0.794743i	$0.292394\pi$
$728$	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	0.202870	−	0.979206i	$-0.434973\pi$
$733$	−19.6620	−	16.4983i	−0.726231	−	0.609380i	−0.929101	+	0.369826i	$0.879417\pi$
$734$	−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	−0.701919	−	0.712256i	$-0.747673\pi$
$739$	7.22763	−	12.5186i	0.265873	−	0.460505i	0.967792	+	0.251752i	$0.0810066\pi$
$740$	−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	−0.863042	−	0.505132i	$-0.831444\pi$
$743$	−32.6954	+	11.9002i	−1.19948	+	0.436574i	−0.336436	+	0.941706i	$0.609222\pi$
$744$		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	−0.872037	−	0.489439i	$-0.837202\pi$
$751$	3.14624	−	17.8432i	0.114808	−	0.651107i	0.986845	−	0.161668i	$-0.0516874\pi$
$752$	−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	0.920263	+	0.391302i	$0.127975\pi$
$761$	−2.16095	+	12.2554i	−0.0783344	+	0.444256i	−0.998597	+	0.0529549i	$0.983136\pi$
$762$		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	0.461628	−	0.887074i	$-0.347265\pi$
$769$	38.4199	−	13.9837i	1.38546	−	0.504265i	0.923828	+	0.382809i	$0.125043\pi$
$770$	−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	−0.327019	−	0.945018i	$-0.606044\pi$
$773$	18.2081	−	31.5374i	0.654900	−	1.13432i	0.981919	−	0.189302i	$-0.0606226\pi$
$774$		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	−

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)

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