LMFDB - Embedded newform 729.2.e.l.163.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("729.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$12$
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			163.1
Root			$3.10658i$ of defining polynomial
Character	$\chi$	$=$	729.163
Dual form			729.2.e.l.568.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.99687 + 0.726803i) q^{2} +(1.92717 - 1.61709i) q^{4} +(0.359615 + 2.03948i) q^{5} +(3.71430 + 3.11667i) q^{7} +(-0.547989 + 0.949144i) q^{8} +O(q^{10})$	\(q+(-1.99687 + 0.726803i) q^{2} +(1.92717 - 1.61709i) q^{4} +(0.359615 + 2.03948i) q^{5} +(3.71430 + 3.11667i) q^{7} +(-0.547989 + 0.949144i) q^{8} +(-2.20040 - 3.81121i) q^{10} +(-0.720551 + 4.08645i) q^{11} +(1.14268 + 0.415902i) q^{13} +(-9.68219 - 3.52403i) q^{14} +(-0.469286 + 2.66145i) q^{16} +(1.18182 + 2.04697i) q^{17} +(0.919003 - 1.59176i) q^{19} +(3.99106 + 3.34890i) q^{20} +(-1.53119 - 8.68382i) q^{22} +(3.29673 - 2.76628i) q^{23} +(0.668315 - 0.243247i) q^{25} -2.58407 q^{26} +12.1980 q^{28} +(2.80199 - 1.01984i) q^{29} +(1.12883 - 0.947203i) q^{31} +(-1.37788 - 7.81432i) q^{32} +(-3.84769 - 3.22859i) q^{34} +(-5.02066 + 8.69603i) q^{35} +(-4.48554 - 7.76918i) q^{37} +(-0.678238 + 3.84648i) q^{38} +(-2.13282 - 0.776284i) q^{40} +(2.12420 + 0.773145i) q^{41} +(-0.952435 + 5.40153i) q^{43} +(5.21953 + 9.04050i) q^{44} +(-4.57260 + 7.91998i) q^{46} +(-5.50260 - 4.61723i) q^{47} +(2.86687 + 16.2588i) q^{49} +(-1.15775 + 0.971466i) q^{50} +(2.87470 - 1.04630i) q^{52} +6.32803 q^{53} -8.59334 q^{55} +(-4.99356 + 1.81751i) q^{56} +(-4.85400 + 4.07299i) q^{58} +(-0.0455404 - 0.258272i) q^{59} +(-3.41319 - 2.86401i) q^{61} +(-1.56571 + 2.71188i) q^{62} +(5.72840 + 9.92188i) q^{64} +(-0.437297 + 2.48004i) q^{65} +(-3.88197 - 1.41292i) q^{67} +(5.58771 + 2.03376i) q^{68} +(3.70532 - 21.0139i) q^{70} +(1.54276 + 2.67213i) q^{71} +(-6.38003 + 11.0505i) q^{73} +(14.6037 + 12.2540i) q^{74} +(-0.802942 - 4.55371i) q^{76} +(-15.4124 + 12.9326i) q^{77} +(-4.27786 + 1.55701i) q^{79} -5.59674 q^{80} -4.80368 q^{82} +(-7.94328 + 2.89112i) q^{83} +(-3.74975 + 3.14642i) q^{85} +(-2.02395 - 11.4784i) q^{86} +(-3.48378 - 2.92323i) q^{88} +(8.48158 - 14.6905i) q^{89} +(2.94803 + 5.10614i) q^{91} +(1.88004 - 10.6622i) q^{92} +(14.3438 + 5.22072i) q^{94} +(3.57685 + 1.30187i) q^{95} +(-0.887302 + 5.03214i) q^{97} +(-17.5417 - 30.3831i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

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

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	−0.931717	−	0.363185i	$-0.881689\pi$
$2$	−1.99687	+	0.726803i	−1.41200	+	0.513927i	−0.480286	+	0.877112i	$0.659467\pi$
$3$		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	$0.0976989\pi$
$5$	0.359615	+	2.03948i	0.160825	+	0.912082i	−0.792441	+	0.609949i	$0.791190\pi$
$6$		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	$0.270685\pi$
$11$	−0.720551	+	4.08645i	−0.217254	+	1.23211i	−0.876951	+	0.480579i	$0.840427\pi$
$12$		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	0.973004	−	0.230789i	$-0.0741306\pi$
$17$	1.18182	+	2.04697i	0.286633	+	0.496463i	−0.686371	+	0.727252i	$0.740797\pi$
$18$		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	−0.230748	−	0.973014i	$-0.574117\pi$
$23$	3.29673	−	2.76628i	0.687415	−	0.576809i	0.918162	+	0.396204i	$0.129673\pi$
$24$		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	$-0.521819\pi$
$29$	2.80199	−	1.01984i	0.520317	−	0.189380i	0.588810	+	0.808272i	$0.299597\pi$
$30$		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	0.502522	−	0.864565i	$-0.332406\pi$
$41$	2.12420	+	0.773145i	0.331744	+	0.120745i	−0.170778	+	0.985310i	$0.554628\pi$
$42$		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	0.146202	−	0.989255i	$-0.453295\pi$
$47$	−5.50260	−	4.61723i	−0.802636	−	0.673492i	−0.948838	+	0.315763i	$0.897740\pi$
$48$		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	$-0.356886\pi$
$53$	6.32803			0.869222			0.434611	+	0.900618i	$0.356886\pi$
$54$		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	$-0.0609898\pi$
$59$	−0.0455404	−	0.258272i	−0.00592886	−	0.0336242i	−0.987629	+	0.156811i	$0.949879\pi$
$60$		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	0.942932	−	0.332986i	$-0.108056\pi$
$71$	1.54276	+	2.67213i	0.183091	+	0.317124i	−0.759840	+	0.650110i	$0.774723\pi$
$72$		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	−0.738931	−	0.673781i	$-0.764669\pi$
$83$	−7.94328	+	2.89112i	−0.871888	+	0.317341i	−0.132956	+	0.991122i	$0.542447\pi$
$84$		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	$-0.477595\pi$
$89$	8.48158	−	14.6905i	0.899046	−	1.55719i	0.828716	−	0.559670i	$-0.189072\pi$
$90$		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	$-0.902358\pi$
$101$	−14.2330	−	11.9429i	−1.41624	−	1.18836i	−0.462918	−	0.886401i	$-0.653198\pi$
$102$		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	$-0.616878\pi$
$107$	−7.42680			−0.717976			−0.358988	+	0.933342i	$0.616878\pi$
$108$		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	$-0.0195057\pi$
$113$	0.417219	+	2.36617i	0.0392487	+	0.222590i	−0.958874	+	0.283831i	$0.908395\pi$
$114$		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	0.0361871	−	0.999345i	$-0.488479\pi$
$131$	11.7504	−	9.85972i	1.02663	−	0.861448i	0.990447	+	0.137897i	$0.0440343\pi$
$132$		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	$-0.660862\pi$
$137$	−3.42421	+	1.24631i	−0.292550	+	0.106480i	0.191576	+	0.981478i	$0.438640\pi$
$138$		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	0.661418	−	0.750018i	$-0.269955\pi$
$149$	8.37359	+	3.04774i	0.685991	+	0.249680i	0.0245732	+	0.999698i	$0.492177\pi$
$150$		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	$0.321325\pi$
$167$	4.15650	+	23.5727i	0.321640	+	1.82411i	−0.210669	+	0.977558i	$0.567564\pi$
$168$		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	$-0.831492\pi$
$173$	1.58714	−	9.00115i	0.120668	−	0.684344i	0.983787	−	0.179343i	$-0.0573971\pi$
$174$		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	$-0.0370062\pi$
$179$	5.30038	+	9.18052i	0.396169	+	0.686184i	−0.597081	+	0.802181i	$0.703673\pi$
$180$		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	0.116785	−	0.993157i	$-0.462741\pi$
$191$	11.6731	−	4.24867i	0.844637	−	0.307423i	0.727852	+	0.685734i	$0.240519\pi$
$192$		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	$0.335340\pi$
$197$	−7.09433	+	12.2877i	−0.505450	+	0.875465i	−0.999980	+	0.00630469i	$0.997993\pi$
$198$		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	$-0.673012\pi$
$227$	3.94052	−	22.3478i	0.261542	−	1.48328i	0.778705	−	0.627390i	$-0.215877\pi$
$228$		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	$-0.885581\pi$
$233$	−11.7945	−	20.4286i	−0.772682	−	1.33832i	0.163406	−	0.986559i	$-0.447752\pi$
$234$		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	$-0.826561\pi$
$239$	−7.62560	+	6.39864i	−0.493259	+	0.413894i	0.361933	+	0.932204i	$0.382117\pi$
$240$		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	−0.957825	−	0.287351i	$-0.907226\pi$
$251$	−3.64483	+	6.31303i	−0.230060	+	0.398475i	0.727766	+	0.685826i	$0.240559\pi$
$252$		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	$-0.647018\pi$
$257$	−21.8413	−	7.94960i	−1.36243	−	0.495882i	−0.916803	+	0.399339i	$0.869240\pi$
$258$		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	$0.0424827\pi$
$263$	20.9893	+	17.6121i	1.29426	+	1.08601i	0.303150	+	0.952943i	$0.401962\pi$
$264$		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	$-0.592713\pi$
$269$	−9.41973			−0.574331			−0.287166	+	0.957881i	$0.592713\pi$
$270$		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	$0.192487\pi$
$281$	−2.42788	+	13.7692i	−0.144835	+	0.821400i	−0.967500	+	0.252873i	$0.918625\pi$
$282$		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	−0.997558	−	0.0698405i	$-0.977751\pi$
$293$	−18.8633	+	15.8281i	−1.10200	+	0.924690i	−0.104445	+	0.994531i	$0.533307\pi$
$294$		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	0.856841	−	0.515580i	$-0.172424\pi$
$311$	20.8415	+	7.58567i	1.18181	+	0.430144i	0.324970	+	0.945724i	$0.394646\pi$
$312$		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	−0.0886327	−	0.996064i	$-0.528250\pi$
$317$	−19.3171	−	16.2090i	−1.08496	−	0.910386i	−0.996323	+	0.0856786i	$0.972694\pi$
$318$		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	−0.712164	−	0.702013i	$-0.752285\pi$
$347$	−2.69140	+	2.25836i	−0.144482	+	0.121235i	0.567682	+	0.823248i	$0.307840\pi$
$348$		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	−0.881823	−	0.471581i	$-0.843683\pi$
$353$	−23.5645	+	8.57677i	−1.25421	+	0.456496i	−0.372389	+	0.928077i	$0.621461\pi$
$354$		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	$-0.797920\pi$
$359$	2.10362	−	3.64358i	0.111025	−	0.192301i	0.916184	+	0.400758i	$0.131253\pi$
$360$		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	$-0.974187\pi$
$383$	−1.71856	−	9.74642i	−0.0878142	−	0.498019i	0.908900	−	0.417015i	$-0.136924\pi$
$384$		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	$-0.764650\pi$
$389$	3.66654	−	20.7940i	0.185901	−	1.05430i	0.924792	−	0.380472i	$-0.124239\pi$
$390$		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	−0.198556	−	0.980089i	$-0.563625\pi$
$401$	14.6616	−	12.3025i	0.732164	−	0.614359i	0.930721	+	0.365731i	$0.119181\pi$
$402$		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	0.471957	−	0.881621i	$-0.343548\pi$
$419$	5.46131	+	1.98775i	0.266802	+	0.0971081i	−0.205155	+	0.978729i	$0.565770\pi$
$420$		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	$-0.159499\pi$
$431$	36.4166			1.75413			0.877064	+	0.480374i	$0.159499\pi$
$432$		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	$0.183958\pi$
$443$	−2.86935	+	16.2729i	−0.136327	+	0.773148i	−0.973927	+	0.226863i	$0.927153\pi$
$444$		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	$-0.202371\pi$
$449$	−2.37181	−	4.10809i	−0.111933	−	0.193873i	−0.916549	+	0.399921i	$0.869037\pi$
$450$		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	−0.647248	−	0.762279i	$-0.724080\pi$
$461$	−14.0223	+	5.10371i	−0.653085	+	0.237704i	−0.00583713	+	0.999983i	$0.501858\pi$
$462$		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	−0.987150	−	0.159794i	$-0.948917\pi$
$467$	−7.67571	+	13.2947i	−0.355190	+	0.615206i	0.631961	+	0.775000i	$0.282250\pi$
$468$		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	$-0.354501\pi$
$479$	−8.00410	−	6.71624i	−0.365717	−	0.306873i	−0.807064	+	0.590464i	$0.798945\pi$
$480$		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	$0.0226374\pi$
$491$	1.87147	+	10.6136i	0.0844581	+	0.478985i	−0.913014	+	0.407928i	$0.866251\pi$
$492$		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	0.700282	−	0.713866i	$-0.253058\pi$
$503$	−6.01253	−	10.4140i	−0.268086	−	0.464338i	−0.968367	+	0.249529i	$0.919724\pi$
$504$		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	$-0.614704\pi$
$509$	11.4547	−	9.61162i	0.507720	−	0.426027i	0.860326	+	0.509744i	$0.170260\pi$
$510$		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	$-0.527488\pi$
$521$	18.7094	−	32.4056i	0.819673	−	1.41972i	0.905923	−	0.423442i	$-0.139178\pi$
$522$		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	0.646467	−	0.762942i	$-0.276246\pi$
$557$	−7.96515	−	13.7960i	−0.337494	−	0.584557i	−0.983961	+	0.178385i	$0.942913\pi$
$558$		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	$-0.546706\pi$
$563$	19.0445	−	15.9802i	0.802631	−	0.673487i	0.948837	+	0.315767i	$0.102262\pi$
$564$		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	$-0.479342\pi$
$569$	18.0327	−	6.56337i	0.755970	−	0.275151i	0.691116	+	0.722744i	$0.257119\pi$
$570$		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	0.999977	−	0.00672500i	$-0.00214065\pi$
$587$	28.2741	+	23.7248i	1.16700	+	0.979228i	0.167021	+	0.985953i	$0.446585\pi$
$588$		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	$-0.528588\pi$
$593$	−4.36830			−0.179385			−0.0896923	+	0.995970i	$0.528588\pi$
$594$		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	$0.164481\pi$
$599$	5.41880	+	30.7315i	0.221406	+	1.25566i	−0.648032	+	0.761613i	$0.724408\pi$
$600$		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	−0.948746	−	0.316038i	$-0.897647\pi$
$617$	−19.9277	+	16.7213i	−0.802257	+	0.673174i	0.146489	+	0.989212i	$0.453203\pi$
$618$		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	0.241846	−	0.970315i	$-0.422247\pi$
$641$	−17.0069	−	14.2705i	−0.671732	−	0.563650i	−0.913577	+	0.406665i	$0.866692\pi$
$642$		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	$-0.584869\pi$
$647$	−13.4037			−0.526952			−0.263476	+	0.964666i	$0.584869\pi$
$648$		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	$0.0650935\pi$
$653$	3.28384	+	18.6236i	0.128506	+	0.728796i	−0.850657	+	0.525722i	$0.823795\pi$
$654$		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	$-0.944270\pi$
$659$	0.00489366	−	0.0277533i	0.000190630	−	0.00108112i	0.984903	+	0.173108i	$0.0553808\pi$
$660$		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	0.526586	−	0.850122i	$-0.323472\pi$
$677$	38.4153	−	13.9820i	1.47642	−	0.537374i	0.949836	+	0.312748i	$0.101250\pi$
$678$		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	$0.485458\pi$
$683$	−22.0126	+	38.1269i	−0.842287	+	1.45888i	−0.887957	+	0.459927i	$0.847875\pi$
$684$		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	$-0.421964\pi$
$701$	12.8521			0.485419			0.242709	+	0.970099i	$0.421964\pi$
$702$		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	0.808667	−	0.588267i	$-0.200190\pi$
$719$	−2.81873	−	4.88218i	−0.105121	−	0.182075i	−0.913788	+	0.406192i	$0.866856\pi$
$720$		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	0.863042	−	0.505132i	$-0.168556\pi$
$743$	32.6954	+	11.9002i	1.19948	+	0.436574i	0.336436	+	0.941706i	$0.390778\pi$
$744$		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	$0.0168640\pi$
$761$	2.16095	+	12.2554i	0.0783344	+	0.444256i	−0.920263	+	0.391302i	$0.872025\pi$
$762$		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	$-0.939377\pi$
$773$	−18.2081	−	31.5374i	−0.654900	−	1.13432i	0.327019	−	0.945018i	$-0.393956\pi$
$774$		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

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

Introduction

L-functions

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