LMFDB - Embedded newform 324.3.f.r.271.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,3,Mod(55,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("324.55");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	324.f (of order $6$, degree $2$, 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:	$8.82836056527$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.119023932416481.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} - 3 x^{10} + 11 x^{9} - 5 x^{8} - 14 x^{7} + 29 x^{6} - 28 x^{5} - 20 x^{4} + \cdots + 64 $ x^12 - 2x^11 - 3x^10 + 11x^9 - 5x^8 - 14x^7 + 29x^6 - 28x^5 - 20x^4 + 88x^3 - 48x^2 - 64*x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			271.3
Root			$1.38685 - 0.276848i$ of defining polynomial
Character	$\chi$	$=$	324.271
Dual form			324.3.f.r.55.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0560770 + 1.99921i) q^{2} +(-3.99371 + 0.224220i) q^{4} +(-0.931627 + 1.61363i) q^{5} +(9.80189 - 5.65913i) q^{7} +(-0.672219 - 7.97171i) q^{8} +O(q^{10})$	\(q+(0.0560770 + 1.99921i) q^{2} +(-3.99371 + 0.224220i) q^{4} +(-0.931627 + 1.61363i) q^{5} +(9.80189 - 5.65913i) q^{7} +(-0.672219 - 7.97171i) q^{8} +(-3.27823 - 1.77203i) q^{10} +(5.08539 - 2.93605i) q^{11} +(6.96926 - 12.0711i) q^{13} +(11.8635 + 19.2787i) q^{14} +(15.8995 - 1.79094i) q^{16} -11.0753 q^{17} -9.34459i q^{19} +(3.35884 - 6.65324i) q^{20} +(6.15496 + 10.0021i) q^{22} +(26.3984 + 15.2411i) q^{23} +(10.7641 + 18.6440i) q^{25} +(24.5236 + 13.2561i) q^{26} +(-37.8770 + 24.7987i) q^{28} +(22.7710 + 39.4406i) q^{29} +(-42.9526 - 24.7987i) q^{31} +(4.47206 + 31.6860i) q^{32} +(-0.621068 - 22.1418i) q^{34} +21.0888i q^{35} +48.9848 q^{37} +(18.6818 - 0.524016i) q^{38} +(13.4896 + 6.34195i) q^{40} +(7.44787 - 12.9001i) q^{41} +(-4.34763 + 2.51011i) q^{43} +(-19.6512 + 12.8660i) q^{44} +(-28.9899 + 53.6308i) q^{46} +(71.9894 - 41.5631i) q^{47} +(39.5514 - 68.5051i) q^{49} +(-36.6698 + 22.5653i) q^{50} +(-25.1266 + 49.7712i) q^{52} -53.6036 q^{53} +10.9412i q^{55} +(-51.7019 - 74.3337i) q^{56} +(-77.5732 + 47.7359i) q^{58} +(-85.1674 - 49.1714i) q^{59} +(-10.2103 - 17.6847i) q^{61} +(47.1692 - 87.2621i) q^{62} +(-63.0962 + 10.7175i) q^{64} +(12.9855 + 22.4916i) q^{65} +(14.9296 + 8.61963i) q^{67} +(44.2314 - 2.48329i) q^{68} +(-42.1610 + 1.18260i) q^{70} +52.6439i q^{71} +98.1594 q^{73} +(2.74692 + 97.9311i) q^{74} +(2.09524 + 37.3196i) q^{76} +(33.2309 - 57.5577i) q^{77} +(2.63838 - 1.52327i) q^{79} +(-11.9225 + 27.3242i) q^{80} +(26.2077 + 14.1665i) q^{82} +(-88.2594 + 50.9566i) q^{83} +(10.3180 - 17.8713i) q^{85} +(-5.26204 - 8.55108i) q^{86} +(-26.8238 - 38.5655i) q^{88} +17.0580 q^{89} -157.760i q^{91} +(-108.845 - 54.9496i) q^{92} +(87.1305 + 141.591i) q^{94} +(15.0787 + 8.70567i) q^{95} +(26.0051 + 45.0422i) q^{97} +(139.174 + 75.2302i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + q^{2} + 3 q^{4} + 2 q^{5} - 14 q^{8}+O(q^{10}) $ 12 * q + q^2 + 3 * q^4 + 2 * q^5 - 14 * q^8	$ 12 q + q^{2} + 3 q^{4} + 2 q^{5} - 14 q^{8} + 18 q^{10} - 6 q^{13} + 15 q^{16} + 20 q^{17} - 67 q^{20} - 48 q^{22} + 146 q^{26} - 96 q^{28} - 22 q^{29} + 31 q^{32} - 81 q^{34} + 108 q^{37} + 168 q^{38} + 81 q^{40} + 92 q^{41} - 336 q^{44} + 240 q^{46} + 66 q^{49} - 48 q^{50} + 117 q^{52} - 232 q^{53} - 312 q^{56} - 201 q^{58} - 54 q^{61} + 624 q^{62} - 510 q^{64} + 82 q^{65} + 53 q^{68} - 264 q^{70} - 156 q^{73} + 383 q^{74} + 192 q^{76} - 168 q^{77} - 754 q^{80} + 300 q^{82} - 66 q^{85} - 144 q^{86} + 336 q^{88} + 500 q^{89} - 504 q^{92} - 216 q^{94} + 204 q^{97} + 814 q^{98}+O(q^{100}) $ 12 * q + q^2 + 3 * q^4 + 2 * q^5 - 14 * q^8 + 18 * q^10 - 6 * q^13 + 15 * q^16 + 20 * q^17 - 67 * q^20 - 48 * q^22 + 146 * q^26 - 96 * q^28 - 22 * q^29 + 31 * q^32 - 81 * q^34 + 108 * q^37 + 168 * q^38 + 81 * q^40 + 92 * q^41 - 336 * q^44 + 240 * q^46 + 66 * q^49 - 48 * q^50 + 117 * q^52 - 232 * q^53 - 312 * q^56 - 201 * q^58 - 54 * q^61 + 624 * q^62 - 510 * q^64 + 82 * q^65 + 53 * q^68 - 264 * q^70 - 156 * q^73 + 383 * q^74 + 192 * q^76 - 168 * q^77 - 754 * q^80 + 300 * q^82 - 66 * q^85 - 144 * q^86 + 336 * q^88 + 500 * q^89 - 504 * q^92 - 216 * q^94 + 204 * q^97 + 814 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.0560770	+	1.99921i	0.0280385	+	0.999607i
$2$	0.0560770	+	1.99921i	0.0280385	+	0.999607i
$3$		0			0
$3$		0			0
$4$	−3.99371	+	0.224220i	−0.998428	+	0.0560550i
$5$	−0.931627	+	1.61363i	−0.186325	+	0.322725i	−0.944022	−	0.329881i	$-0.892991\pi$
$5$	−0.931627	+	1.61363i	−0.186325	+	0.322725i	0.757697	+	0.652607i	$0.226325\pi$
$6$		0			0
$7$	9.80189	−	5.65913i	1.40027	−	0.808447i	0.405851	−	0.913939i	$-0.366975\pi$
$7$	9.80189	−	5.65913i	1.40027	−	0.808447i	0.994420	+	0.105493i	$0.0336420\pi$
$8$	−0.672219	−	7.97171i	−0.0840273	−	0.996463i
$9$		0			0
$10$	−3.27823	−	1.77203i	−0.327823	−	0.177203i
$11$	5.08539	−	2.93605i	0.462308	−	0.266914i	−0.250706	−	0.968063i	$-0.580663\pi$
$11$	5.08539	−	2.93605i	0.462308	−	0.266914i	0.713014	+	0.701150i	$0.247330\pi$
$12$		0			0
$13$	6.96926	−	12.0711i	0.536097	−	0.928547i	−0.463012	−	0.886352i	$-0.653231\pi$
$13$	6.96926	−	12.0711i	0.536097	−	0.928547i	0.999109	−	0.0421954i	$-0.0134352\pi$
$14$	11.8635	+	19.2787i	0.847390	+	1.37705i
$15$		0			0
$16$	15.8995	−	1.79094i	0.993716	−	0.111934i
$17$	−11.0753			−0.651486			−0.325743	−	0.945458i	$-0.605614\pi$
$17$	−11.0753			−0.651486			−0.325743	+	0.945458i	$0.605614\pi$
$18$		0			0
$19$		−	9.34459i		−	0.491820i	−0.969293	−	0.245910i	$-0.920913\pi$
$19$		−	9.34459i		−	0.491820i	0.969293	−	0.245910i	$-0.0790868\pi$
$20$	3.35884	−	6.65324i	0.167942	−	0.332662i
$21$		0			0
$22$	6.15496	+	10.0021i	0.279771	+	0.454642i
$23$	26.3984	+	15.2411i	1.14776	+	0.662658i	0.948340	−	0.317257i	$-0.102762\pi$
$23$	26.3984	+	15.2411i	1.14776	+	0.662658i	0.199418	+	0.979915i	$0.436095\pi$
$24$		0			0
$25$	10.7641	+	18.6440i	0.430566	+	0.745762i
$26$	24.5236	+	13.2561i	0.943213	+	0.509851i
$27$		0			0
$28$	−37.8770	+	24.7987i	−1.35275	+	0.885668i
$29$	22.7710	+	39.4406i	0.785208	+	1.36002i	0.928875	+	0.370394i	$0.120777\pi$
$29$	22.7710	+	39.4406i	0.785208	+	1.36002i	−0.143667	+	0.989626i	$0.545889\pi$
$30$		0			0
$31$	−42.9526	−	24.7987i	−1.38557	−	0.799958i	−0.392756	−	0.919643i	$-0.628478\pi$
$31$	−42.9526	−	24.7987i	−1.38557	−	0.799958i	−0.992812	+	0.119685i	$0.961812\pi$
$32$	4.47206	+	31.6860i	0.139752	+	0.990187i
$33$		0			0
$34$	−0.621068	−	22.1418i	−0.0182667	−	0.651230i
$35$			21.0888i			0.602537i
$36$		0			0
$37$	48.9848			1.32391			0.661957	−	0.749542i	$-0.269726\pi$
$37$	48.9848			1.32391			0.661957	+	0.749542i	$0.269726\pi$
$38$	18.6818	−	0.524016i	0.491627	−	0.0137899i
$39$		0			0
$40$	13.4896	+	6.34195i	0.337240	+	0.158549i
$41$	7.44787	−	12.9001i	0.181655	−	0.314636i	−0.760789	−	0.648999i	$-0.775188\pi$
$41$	7.44787	−	12.9001i	0.181655	−	0.314636i	0.942444	+	0.334363i	$0.108521\pi$
$42$		0			0
$43$	−4.34763	+	2.51011i	−0.101108	+	0.0583745i	−0.549701	−	0.835361i	$-0.685258\pi$
$43$	−4.34763	+	2.51011i	−0.101108	+	0.0583745i	0.448594	+	0.893736i	$0.351925\pi$
$44$	−19.6512	+	12.8660i	−0.446619	+	0.292409i
$45$		0			0
$46$	−28.9899	+	53.6308i	−0.630216	+	1.16589i
$47$	71.9894	−	41.5631i	1.53169	−	0.884321i	0.532405	−	0.846490i	$-0.321288\pi$
$47$	71.9894	−	41.5631i	1.53169	−	0.884321i	0.999284	−	0.0378317i	$-0.0120451\pi$
$48$		0			0
$49$	39.5514	−	68.5051i	0.807172	−	1.39806i
$50$	−36.6698	+	22.5653i	−0.733396	+	0.451306i
$51$		0			0
$52$	−25.1266	+	49.7712i	−0.483204	+	0.957138i
$53$	−53.6036			−1.01139			−0.505694	−	0.862713i	$-0.668763\pi$
$53$	−53.6036			−1.01139			−0.505694	+	0.862713i	$0.668763\pi$
$54$		0			0
$55$			10.9412i			0.198931i
$56$	−51.7019	−	74.3337i	−0.923249	−	1.32739i
$57$		0			0
$58$	−77.5732	+	47.7359i	−1.33747	+	0.823032i
$59$	−85.1674	−	49.1714i	−1.44352	−	0.833414i	−0.445434	−	0.895315i	$-0.646950\pi$
$59$	−85.1674	−	49.1714i	−1.44352	−	0.833414i	−0.998082	+	0.0619007i	$0.980284\pi$
$60$		0			0
$61$	−10.2103	−	17.6847i	−0.167381	−	0.289913i	0.770117	−	0.637903i	$-0.220198\pi$
$61$	−10.2103	−	17.6847i	−0.167381	−	0.289913i	−0.937498	+	0.347990i	$0.886864\pi$
$62$	47.1692	−	87.2621i	0.760794	−	1.40745i
$63$		0			0
$64$	−63.0962	+	10.7175i	−0.985879	+	0.167460i
$65$	12.9855	+	22.4916i	0.199777	+	0.346024i
$66$		0			0
$67$	14.9296	+	8.61963i	0.222830	+	0.128651i	0.607260	−	0.794503i	$-0.292269\pi$
$67$	14.9296	+	8.61963i	0.222830	+	0.128651i	−0.384430	+	0.923154i	$0.625602\pi$
$68$	44.2314	−	2.48329i	0.650462	−	0.0365190i
$69$		0			0
$70$	−42.1610	+	1.18260i	−0.602300	+	0.0168942i
$71$			52.6439i			0.741464i	0.928740	+	0.370732i	$0.120893\pi$
$71$			52.6439i			0.741464i	−0.928740	+	0.370732i	$0.879107\pi$
$72$		0			0
$73$	98.1594			1.34465			0.672325	−	0.740256i	$-0.265296\pi$
$73$	98.1594			1.34465			0.672325	+	0.740256i	$0.265296\pi$
$74$	2.74692	+	97.9311i	0.0371206	+	1.32339i
$75$		0			0
$76$	2.09524	+	37.3196i	0.0275690	+	0.491047i
$77$	33.2309	−	57.5577i	0.431571	−	0.747502i
$78$		0			0
$79$	2.63838	−	1.52327i	0.0333973	−	0.0192819i	−0.483208	−	0.875505i	$-0.660529\pi$
$79$	2.63838	−	1.52327i	0.0333973	−	0.0192819i	0.516606	+	0.856223i	$0.327195\pi$
$80$	−11.9225	+	27.3242i	−0.149031	+	0.341553i
$81$		0			0
$82$	26.2077	+	14.1665i	0.319606	+	0.172762i
$83$	−88.2594	+	50.9566i	−1.06337	+	0.613935i	−0.926362	−	0.376636i	$-0.877081\pi$
$83$	−88.2594	+	50.9566i	−1.06337	+	0.613935i	−0.137005	+	0.990570i	$0.543748\pi$
$84$		0			0
$85$	10.3180	−	17.8713i	0.121388	−	0.210251i
$86$	−5.26204	−	8.55108i	−0.0611865	−	0.0994312i
$87$		0			0
$88$	−26.8238	−	38.5655i	−0.304816	−	0.438245i
$89$	17.0580			0.191663			0.0958314	−	0.995398i	$-0.469449\pi$
$89$	17.0580			0.191663			0.0958314	+	0.995398i	$0.469449\pi$
$90$		0			0
$91$		−	157.760i		−	1.73362i
$92$	−108.845	−	54.9496i	−1.18310	−	0.597279i
$93$		0			0
$94$	87.1305	+	141.591i	0.926920	+	1.50629i
$95$	15.0787	+	8.70567i	0.158723	+	0.0916386i
$96$		0			0
$97$	26.0051	+	45.0422i	0.268094	+	0.464353i	0.968370	−	0.249520i	$-0.0802728\pi$
$97$	26.0051	+	45.0422i	0.268094	+	0.464353i	−0.700275	+	0.713873i	$0.746939\pi$
$98$	139.174	+	75.2302i	1.42014	+	0.767655i
$99$		0			0
$100$	−47.1692	−	72.0454i	−0.471692	−	0.720454i
$101$	−34.7779	−	60.2371i	−0.344336	−	0.596407i	0.640897	−	0.767627i	$-0.278563\pi$
$101$	−34.7779	−	60.2371i	−0.344336	−	0.596407i	−0.985233	+	0.171220i	$0.945229\pi$
$102$		0			0
$103$	−12.4403	−	7.18240i	−0.120779	−	0.0697320i	0.438393	−	0.898783i	$-0.355548\pi$
$103$	−12.4403	−	7.18240i	−0.120779	−	0.0697320i	−0.559173	+	0.829051i	$0.688881\pi$
$104$	−100.912	−	47.4425i	−0.970310	−	0.456178i
$105$		0			0
$106$	−3.00593	−	107.165i	−0.0283578	−	1.01099i
$107$		−	94.8704i		−	0.886639i	−0.896364	−	0.443320i	$-0.853801\pi$
$107$		−	94.8704i		−	0.886639i	0.896364	−	0.443320i	$-0.146199\pi$
$108$		0			0
$109$	12.5332			0.114983			0.0574917	−	0.998346i	$-0.481690\pi$
$109$	12.5332			0.114983			0.0574917	+	0.998346i	$0.481690\pi$
$110$	−21.8738	+	0.613550i	−0.198853	+	0.00557773i
$111$		0			0
$112$	145.710	−	107.532i	1.30098	−	0.960103i
$113$	66.1788	−	114.625i	0.585653	−	1.01438i	−0.409140	−	0.912471i	$-0.634171\pi$
$113$	66.1788	−	114.625i	0.585653	−	1.01438i	0.994794	−	0.101910i	$-0.0324953\pi$
$114$		0			0
$115$	−49.1870	+	28.3981i	−0.427713	+	0.246940i
$116$	−99.7843	−	152.409i	−0.860209	−	1.31387i
$117$		0			0
$118$	93.5283	−	173.025i	0.792613	−	1.46632i
$119$	−108.559	+	62.6763i	−0.912257	+	0.526692i
$120$		0			0
$121$	−43.2592	+	74.9272i	−0.357514	+	0.619233i
$122$	34.7829	−	21.4042i	0.285106	−	0.175444i
$123$		0			0
$124$	177.101	+	89.4080i	1.42823	+	0.721032i
$125$	−86.6940			−0.693552
$126$		0			0
$127$		−	56.2142i		−	0.442632i	−0.975202	−	0.221316i	$-0.928965\pi$
$127$		−	56.2142i		−	0.442632i	0.975202	−	0.221316i	$-0.0710352\pi$
$128$	−24.9647	−	125.542i	−0.195037	−	0.980796i
$129$		0			0
$130$	−44.2372	+	27.2221i	−0.340286	+	0.209400i
$131$	−44.7042	−	25.8100i	−0.341253	−	0.197023i	0.319573	−	0.947562i	$-0.396461\pi$
$131$	−44.7042	−	25.8100i	−0.341253	−	0.197023i	−0.660826	+	0.750539i	$0.729794\pi$
$132$		0			0
$133$	−52.8822	−	91.5946i	−0.397610	−	0.688681i
$134$	−16.3953	+	30.3309i	−0.122353	+	0.226350i
$135$		0			0
$136$	7.44500	+	88.2888i	0.0547427	+	0.649182i
$137$	4.70687	+	8.15253i	0.0343567	+	0.0595075i	0.882692	−	0.469951i	$-0.155728\pi$
$137$	4.70687	+	8.15253i	0.0343567	+	0.0595075i	−0.848336	+	0.529459i	$0.822395\pi$
$138$		0			0
$139$	48.2294	+	27.8452i	0.346974	+	0.200325i	0.663352	−	0.748308i	$-0.269133\pi$
$139$	48.2294	+	27.8452i	0.346974	+	0.200325i	−0.316378	+	0.948633i	$0.602467\pi$
$140$	−4.72852	−	84.2225i	−0.0337752	−	0.601589i
$141$		0			0
$142$	−105.246	+	2.95211i	−0.741172	+	0.0207895i
$143$		−	81.8484i		−	0.572366i
$144$		0			0
$145$	−84.8565			−0.585217
$146$	5.50449	+	196.242i	0.0377020	+	1.34412i
$147$		0			0
$148$	−195.631	+	10.9834i	−1.32183	+	0.0742119i
$149$	−118.270	+	204.850i	−0.793761	+	1.37483i	0.129863	+	0.991532i	$0.458546\pi$
$149$	−118.270	+	204.850i	−0.793761	+	1.37483i	−0.923623	+	0.383302i	$0.874787\pi$
$150$		0			0
$151$	84.0469	−	48.5245i	0.556602	−	0.321354i	−0.195178	−	0.980768i	$-0.562529\pi$
$151$	84.0469	−	48.5245i	0.556602	−	0.321354i	0.751781	+	0.659413i	$0.229195\pi$
$152$	−74.4923	+	6.28161i	−0.490081	+	0.0413264i
$153$		0			0
$154$	116.934	+	63.2081i	0.759309	+	0.410442i
$155$	80.0316	−	46.2063i	0.516333	−	0.298105i
$156$		0			0
$157$	−57.4873	+	99.5708i	−0.366161	+	0.634209i	−0.988962	−	0.148171i	$-0.952661\pi$
$157$	−57.4873	+	99.5708i	−0.366161	+	0.634209i	0.622801	+	0.782380i	$0.285995\pi$
$158$	3.19330	+	5.18927i	0.0202107	+	0.0328435i
$159$		0			0
$160$	−55.2956	−	22.3033i	−0.345597	−	0.139395i
$161$	345.006			2.14289
$162$		0			0
$163$			311.572i			1.91149i	0.294204	+	0.955743i	$0.404945\pi$
$163$			311.572i			1.91149i	−0.294204	+	0.955743i	$0.595055\pi$
$164$	−26.8522	+	53.1892i	−0.163733	+	0.324324i
$165$		0			0
$166$	−106.822	−	173.592i	−0.643509	−	1.04573i
$167$	−84.0608	−	48.5325i	−0.503358	−	0.290614i	0.226741	−	0.973955i	$-0.427193\pi$
$167$	−84.0608	−	48.5325i	−0.503358	−	0.290614i	−0.730099	+	0.683341i	$0.760526\pi$
$168$		0			0
$169$	−12.6412	−	21.8952i	−0.0747999	−	0.129557i
$170$	36.3072	+	19.6258i	0.213572	+	0.115446i
$171$		0			0
$172$	16.8004	−	10.9995i	0.0976765	−	0.0639503i
$173$	−53.3881	−	92.4710i	−0.308602	−	0.534514i	0.669455	−	0.742853i	$-0.266528\pi$
$173$	−53.3881	−	92.4710i	−0.308602	−	0.534514i	−0.978057	+	0.208338i	$0.933194\pi$
$174$		0			0
$175$	211.018	+	121.831i	1.20582	+	0.696179i
$176$	75.5966	−	55.7892i	0.429526	−	0.316984i
$177$		0			0
$178$	0.956561	+	34.1026i	0.00537394	+	0.191587i
$179$			176.768i			0.987529i	0.869596	+	0.493764i	$0.164379\pi$
$179$			176.768i			0.987529i	−0.869596	+	0.493764i	$0.835621\pi$
$180$		0			0
$181$	−163.621			−0.903985			−0.451993	−	0.892022i	$-0.649287\pi$
$181$	−163.621			−0.903985			−0.451993	+	0.892022i	$0.649287\pi$
$182$	315.395	−	8.84669i	1.73294	−	0.0486082i
$183$		0			0
$184$	103.752	−	220.686i	0.563872	−	1.19938i
$185$	−45.6356	+	79.0431i	−0.246679	+	0.427260i
$186$		0			0
$187$	−56.3220	+	32.5175i	−0.301187	+	0.173891i
$188$	−278.186	+	182.132i	−1.47971	+	0.968790i
$189$		0			0
$190$	−16.5589	+	30.6337i	−0.0871522	+	0.161230i
$191$	122.886	−	70.9480i	0.643380	−	0.371456i	−0.142535	−	0.989790i	$-0.545525\pi$
$191$	122.886	−	70.9480i	0.643380	−	0.371456i	0.785915	+	0.618334i	$0.212192\pi$
$192$		0			0
$193$	20.8743	−	36.1553i	0.108157	−	0.187333i	−0.806867	−	0.590733i	$-0.798838\pi$
$193$	20.8743	−	36.1553i	0.108157	−	0.187333i	0.915024	+	0.403400i	$0.132172\pi$
$194$	−88.5908	+	54.5157i	−0.456653	+	0.281009i
$195$		0			0
$196$	−142.597	+	282.458i	−0.727534	+	1.44111i
$197$	−170.486			−0.865409			−0.432704	−	0.901536i	$-0.642441\pi$
$197$	−170.486			−0.865409			−0.432704	+	0.901536i	$0.642441\pi$
$198$		0			0
$199$			169.627i			0.852397i	0.904630	+	0.426199i	$0.140148\pi$
$199$			169.627i			0.852397i	−0.904630	+	0.426199i	$0.859852\pi$
$200$	141.389	−	98.3415i	0.706945	−	0.491707i
$201$		0			0
$202$	118.477	−	72.9064i	0.586518	−	0.360923i
$203$	446.399	+	257.728i	2.19901	+	1.26960i
$204$		0			0
$205$	13.8773	+	24.0361i	0.0676940	+	0.117250i
$206$	13.6615	−	25.2735i	0.0663181	−	0.122687i
$207$		0			0
$208$	89.1888	−	204.406i	0.428792	−	0.982719i
$209$	−27.4362	−	47.5208i	−0.131274	−	0.227372i
$210$		0			0
$211$	−247.990	−	143.177i	−1.17531	−	0.678565i	−0.220385	−	0.975413i	$-0.570731\pi$
$211$	−247.990	−	143.177i	−1.17531	−	0.678565i	−0.954925	+	0.296848i	$0.904065\pi$
$212$	214.077	−	12.0190i	1.00980	−	0.0566933i
$213$		0			0
$214$	189.666	−	5.32005i	0.886291	−	0.0248600i
$215$		−	9.35393i		−	0.0435066i
$216$		0			0
$217$	−561.356			−2.58689
$218$	0.702824	+	25.0565i	0.00322396	+	0.114938i
$219$		0			0
$220$	−2.45324	−	43.6960i	−0.0111511	−	0.198618i
$221$	−77.1864	+	133.691i	−0.349260	+	0.604936i
$222$		0			0
$223$	−279.305	+	161.257i	−1.25249	+	0.723124i	−0.971603	−	0.236618i	$-0.923961\pi$
$223$	−279.305	+	161.257i	−1.25249	+	0.723124i	−0.280885	+	0.959742i	$0.590628\pi$
$224$	223.150	+	285.275i	0.996204	+	1.27355i
$225$		0			0
$226$	232.871	+	125.878i	1.03040	+	0.556981i
$227$	53.0167	−	30.6092i	0.233554	−	0.134842i	−0.378657	−	0.925537i	$-0.623614\pi$
$227$	53.0167	−	30.6092i	0.233554	−	0.134842i	0.612210	+	0.790695i	$0.290281\pi$
$228$		0			0
$229$	−180.134	+	312.001i	−0.786611	+	1.36245i	0.141422	+	0.989949i	$0.454833\pi$
$229$	−180.134	+	312.001i	−0.786611	+	1.36245i	−0.928032	+	0.372500i	$0.878501\pi$
$230$	−59.5321	−	96.7428i	−0.258835	−	0.420621i
$231$		0			0
$232$	299.102	−	208.037i	1.28923	−	0.896710i
$233$	116.935			0.501865			0.250933	−	0.968005i	$-0.419263\pi$
$233$	116.935			0.501865			0.250933	+	0.968005i	$0.419263\pi$
$234$		0			0
$235$			154.885i			0.659086i
$236$	351.159	+	177.280i	1.48796	+	0.751188i
$237$		0			0
$238$	−131.391	−	213.517i	−0.552063	−	0.897131i
$239$	15.3913	+	8.88617i	0.0643988	+	0.0371806i	0.531854	−	0.846836i	$-0.321496\pi$
$239$	15.3913	+	8.88617i	0.0643988	+	0.0371806i	−0.467455	+	0.884017i	$0.654829\pi$
$240$		0			0
$241$	113.490	+	196.570i	0.470913	+	0.815645i	0.999446	−	0.0332676i	$-0.0105914\pi$
$241$	113.490	+	196.570i	0.470913	+	0.815645i	−0.528534	+	0.848912i	$0.677258\pi$
$242$	−152.221	−	82.2828i	−0.629014	−	0.340011i
$243$		0			0
$244$	44.7421	+	68.3382i	0.183369	+	0.280075i
$245$	73.6944	+	127.642i	0.300793	+	0.520989i
$246$		0			0
$247$	−112.800	−	65.1248i	−0.456678	−	0.263663i
$248$	−168.814	+	359.076i	−0.680703	+	1.44789i
$249$		0			0
$250$	−4.86154	−	173.320i	−0.0194462	−	0.693279i
$251$		−	221.345i		−	0.881852i	−0.897543	−	0.440926i	$-0.854650\pi$
$251$		−	221.345i		−	0.881852i	0.897543	−	0.440926i	$-0.145350\pi$
$252$		0			0
$253$	178.995			0.707490
$254$	112.384	−	3.15233i	0.442458	−	0.0124107i
$255$		0			0
$256$	249.585	−	56.9499i	0.974942	−	0.222460i
$257$	−36.2012	+	62.7024i	−0.140861	+	0.243978i	−0.927821	−	0.373026i	$-0.878320\pi$
$257$	−36.2012	+	62.7024i	−0.140861	+	0.243978i	0.786960	+	0.617004i	$0.211654\pi$
$258$		0			0
$259$	480.144	−	277.211i	1.85384	−	1.07031i
$260$	−56.9034	−	86.9131i	−0.218859	−	0.334281i
$261$		0			0
$262$	49.0928	−	90.8206i	0.187377	−	0.346643i
$263$	−392.318	+	226.505i	−1.49170	+	0.861234i	−0.999955	−	0.00950362i	$-0.996975\pi$
$263$	−392.318	+	226.505i	−1.49170	+	0.861234i	−0.491747	+	0.870738i	$0.663642\pi$
$264$		0			0
$265$	49.9385	−	86.4961i	0.188447	−	0.326400i
$266$	180.152	−	110.859i	0.677262	−	0.416764i
$267$		0			0
$268$	−61.5573	−	31.0768i	−0.229692	−	0.115958i
$269$	88.5004			0.328998			0.164499	−	0.986377i	$-0.447399\pi$
$269$	88.5004			0.328998			0.164499	+	0.986377i	$0.447399\pi$
$270$		0			0
$271$		−	25.2731i		−	0.0932588i	−0.998912	−	0.0466294i	$-0.985152\pi$
$271$		−	25.2731i		−	0.0932588i	0.998912	−	0.0466294i	$-0.0148480\pi$
$272$	−176.091	+	19.8351i	−0.647392	+	0.0729232i
$273$		0			0
$274$	−16.0347	+	9.86720i	−0.0585208	+	0.0360117i
$275$	109.480	+	63.2081i	0.398108	+	0.229848i
$276$		0			0
$277$	−130.149	−	225.425i	−0.469852	−	0.813808i	0.529553	−	0.848277i	$-0.322360\pi$
$277$	−130.149	−	225.425i	−0.469852	−	0.813808i	−0.999406	+	0.0344684i	$0.989026\pi$
$278$	−52.9640	+	97.9823i	−0.190518	+	0.352454i
$279$		0			0
$280$	168.114	−	14.1763i	0.600406	−	0.0506296i
$281$	−83.1550	−	144.029i	−0.295925	−	0.512557i	0.679275	−	0.733884i	$-0.262295\pi$
$281$	−83.1550	−	144.029i	−0.295925	−	0.512557i	−0.975200	+	0.221327i	$0.928961\pi$
$282$		0			0
$283$	281.972	+	162.796i	0.996366	+	0.575252i	0.907171	−	0.420762i	$-0.138237\pi$
$283$	281.972	+	162.796i	0.996366	+	0.575252i	0.0891949	+	0.996014i	$0.471571\pi$
$284$	−11.8038	−	210.245i	−0.0415627	−	0.740298i
$285$		0			0
$286$	163.632	−	4.58981i	0.572141	−	0.0160483i
$287$		−	168.594i		−	0.587435i
$288$		0			0
$289$	−166.338			−0.575566
$290$	−4.75850	−	169.646i	−0.0164086	−	0.584987i
$291$		0			0
$292$	−392.020	+	22.0093i	−1.34254	+	0.0753743i
$293$	−228.763	+	396.228i	−0.780760	+	1.35232i	0.150740	+	0.988573i	$0.451834\pi$
$293$	−228.763	+	396.228i	−0.780760	+	1.35232i	−0.931500	+	0.363742i	$0.881499\pi$
$294$		0			0
$295$	158.689	−	91.6189i	0.537927	−	0.310573i
$296$	−32.9285	−	390.492i	−0.111245	−	1.31923i
$297$		0			0
$298$	−416.172	−	224.960i	−1.39655	−	0.754900i
$299$	367.955	−	212.439i	1.23062	−	0.710498i
$300$		0			0
$301$	−28.4100	+	49.2076i	−0.0943854	+	0.163480i
$302$	101.724	+	165.307i	0.336834	+	0.547373i
$303$		0			0
$304$	−16.7356	−	148.574i	−0.0550512	−	0.488730i
$305$	38.0486			0.124750
$306$		0			0
$307$		−	193.311i		−	0.629678i	−0.949145	−	0.314839i	$-0.898050\pi$
$307$		−	193.311i		−	0.629678i	0.949145	−	0.314839i	$-0.101950\pi$
$308$	−119.809	+	237.320i	−0.388991	+	0.770519i
$309$		0			0
$310$	96.8641	+	157.409i	0.312465	+	0.507772i
$311$	−132.119	−	76.2790i	−0.424820	−	0.245270i	0.272317	−	0.962208i	$-0.412210\pi$
$311$	−132.119	−	76.2790i	−0.424820	−	0.245270i	−0.697138	+	0.716937i	$0.745543\pi$
$312$		0			0
$313$	43.7256	+	75.7349i	0.139698	+	0.241965i	0.927382	−	0.374115i	$-0.122053\pi$
$313$	43.7256	+	75.7349i	0.139698	+	0.241965i	−0.787684	+	0.616079i	$0.788720\pi$
$314$	−202.287	−	109.346i	−0.644226	−	0.348235i
$315$		0			0
$316$	−10.1954	+	6.67508i	−0.0322639	+	0.0211237i
$317$	−146.106	−	253.063i	−0.460903	−	0.798307i	0.538103	−	0.842879i	$-0.319141\pi$
$317$	−146.106	−	253.063i	−0.460903	−	0.798307i	−0.999006	+	0.0445716i	$0.985808\pi$
$318$		0			0
$319$	231.599	+	133.714i	0.726016	+	0.419165i
$320$	41.4882	−	111.798i	0.129651	−	0.349370i
$321$		0			0
$322$	19.3469	+	689.741i	0.0600836	+	2.14205i
$323$			103.494i			0.320414i
$324$		0			0
$325$	300.072			0.923300
$326$	−622.899	+	17.4720i	−1.91073	+	0.0535952i
$327$		0			0
$328$	−107.842	−	50.7006i	−0.328788	−	0.154575i
$329$	470.422	−	814.794i	1.42985	−	2.47658i
$330$		0			0
$331$	−135.318	+	78.1258i	−0.408815	+	0.236030i	−0.690281	−	0.723542i	$-0.742513\pi$
$331$	−135.318	+	78.1258i	−0.408815	+	0.236030i	0.281465	+	0.959571i	$0.409180\pi$
$332$	341.057	−	223.295i	1.02728	−	0.672576i
$333$		0			0
$334$	92.3130	−	170.777i	0.276386	−	0.511309i
$335$	−27.8177	+	16.0606i	−0.0830379	+	0.0479420i
$336$		0			0
$337$	135.646	−	234.946i	0.402511	−	0.697169i	−0.591518	−	0.806292i	$-0.701471\pi$
$337$	135.646	−	234.946i	0.402511	−	0.697169i	0.994028	+	0.109123i	$0.0348043\pi$
$338$	43.0642	−	26.5002i	0.127409	−	0.0784031i
$339$		0			0
$340$	−37.2001	+	73.6864i	−0.109412	+	0.216725i
$341$	−291.241			−0.854078
$342$		0			0
$343$		−	340.712i		−	0.993328i
$344$	22.9324	+	32.9707i	0.0666639	+	0.0958450i
$345$		0			0
$346$	181.875	−	111.920i	0.525651	−	0.323468i
$347$	−300.561	−	173.529i	−0.866171	−	0.500084i	−9.73706e−5	−	1.00000i	$-0.500031\pi$
$347$	−300.561	−	173.529i	−0.866171	−	0.500084i	−0.866074	+	0.499916i	$0.833364\pi$
$348$		0			0
$349$	−149.267	−	258.538i	−0.427699	−	0.740796i	0.568969	−	0.822359i	$-0.307342\pi$
$349$	−149.267	−	258.538i	−0.427699	−	0.740796i	−0.996668	+	0.0815625i	$0.974009\pi$
$350$	−231.733	+	428.702i	−0.662096	+	1.22486i
$351$		0			0
$352$	115.774	+	148.005i	0.328903	+	0.420469i
$353$	284.054	+	491.996i	0.804685	+	1.39375i	0.916504	+	0.400026i	$0.130999\pi$
$353$	284.054	+	491.996i	0.804685	+	1.39375i	−0.111819	+	0.993729i	$0.535668\pi$
$354$		0			0
$355$	−84.9476	−	49.0445i	−0.239289	−	0.138154i
$356$	−68.1247	+	3.82474i	−0.191361	+	0.0107436i
$357$		0			0
$358$	−353.396	+	9.91260i	−0.987141	+	0.0276888i
$359$			414.158i			1.15364i	0.816871	+	0.576821i	$0.195707\pi$
$359$			414.158i			1.15364i	−0.816871	+	0.576821i	$0.804293\pi$
$360$		0			0
$361$	273.679			0.758113
$362$	−9.17539	−	327.114i	−0.0253464	−	0.903630i
$363$		0			0
$364$	35.3729	+	630.047i	0.0971782	+	1.73090i
$365$	−91.4480	+	158.393i	−0.250542	+	0.433952i
$366$		0			0
$367$	−275.106	+	158.833i	−0.749608	+	0.432786i	−0.825552	−	0.564326i	$-0.809136\pi$
$367$	−275.106	+	158.833i	−0.749608	+	0.432786i	0.0759443	+	0.997112i	$0.475803\pi$
$368$	447.016	+	195.048i	1.21472	+	0.530021i
$369$		0			0
$370$	−160.583	−	86.8027i	−0.434009	−	0.234602i
$371$	−525.416	+	303.349i	−1.41622	+	0.817653i
$372$		0			0
$373$	−53.3693	+	92.4384i	−0.143081	+	0.247824i	−0.928655	−	0.370943i	$-0.879034\pi$
$373$	−53.3693	+	92.4384i	−0.143081	+	0.247824i	0.785574	+	0.618768i	$0.212368\pi$
$374$	−68.1679	−	110.776i	−0.182267	−	0.296193i
$375$		0			0
$376$	−379.722	−	545.939i	−1.00990	−	1.45197i
$377$	634.789			1.68379
$378$		0			0
$379$		−	33.8080i		−	0.0892033i	−0.999005	−	0.0446016i	$-0.985798\pi$
$379$		−	33.8080i		−	0.0892033i	0.999005	−	0.0446016i	$-0.0142019\pi$
$380$	−62.1718	−	31.3870i	−0.163610	−	0.0825973i
$381$		0			0
$382$	148.731	+	241.696i	0.389349	+	0.632712i
$383$	−159.158	−	91.8901i	−0.415557	−	0.239922i	0.277618	−	0.960692i	$-0.410455\pi$
$383$	−159.158	−	91.8901i	−0.415557	−	0.239922i	−0.693175	+	0.720770i	$0.743789\pi$
$384$		0			0
$385$	61.9177	+	107.245i	0.160825	+	0.278557i
$386$	73.4527	+	39.7046i	0.190292	+	0.102862i
$387$		0			0
$388$	−113.956	−	174.055i	−0.293702	−	0.448595i
$389$	−26.0192	−	45.0665i	−0.0668873	−	0.115852i	0.830642	−	0.556806i	$-0.187973\pi$
$389$	−26.0192	−	45.0665i	−0.0668873	−	0.115852i	−0.897530	+	0.440954i	$0.854640\pi$
$390$		0			0
$391$	−292.370	−	168.800i	−0.747748	−	0.431713i
$392$	−572.690	−	269.242i	−1.46094	−	0.686842i
$393$		0			0
$394$	−9.56032	−	340.837i	−0.0242648	−	0.865068i
$395$			5.67648i			0.0143708i
$396$		0			0
$397$	585.222			1.47411			0.737055	−	0.675833i	$-0.236216\pi$
$397$	585.222			1.47411			0.737055	+	0.675833i	$0.236216\pi$
$398$	−339.121	+	9.51218i	−0.852062	+	0.0238999i
$399$		0			0
$400$	204.534	+	277.152i	0.511336	+	0.692880i
$401$	267.477	−	463.284i	0.667025	−	1.15532i	−0.311708	−	0.950178i	$-0.600901\pi$
$401$	267.477	−	463.284i	0.667025	−	1.15532i	0.978732	−	0.205142i	$-0.0657657\pi$
$402$		0			0
$403$	−598.696	+	345.657i	−1.48560	+	0.857710i
$404$	152.399	+	232.772i	0.377226	+	0.576168i
$405$		0			0
$406$	−490.221	+	906.899i	−1.20744	+	2.23374i
$407$	249.107	−	143.822i	0.612056	−	0.353370i
$408$		0			0
$409$	165.972	−	287.473i	0.405800	−	0.702867i	−0.588614	−	0.808414i	$-0.700326\pi$
$409$	165.972	−	287.473i	0.405800	−	0.702867i	0.994414	+	0.105547i	$0.0336595\pi$
$410$	−47.2752	+	29.0915i	−0.115305	+	0.0709549i
$411$		0			0
$412$	51.2933	+	25.8951i	0.124498	+	0.0628521i
$413$	−1113.07			−2.69508
$414$		0			0
$415$		−	189.890i		−	0.457567i
$416$	413.652	+	166.845i	0.994356	+	0.401070i
$417$		0			0
$418$	93.4657	−	57.5156i	0.223602	−	0.137597i
$419$	−606.327	−	350.063i	−1.44708	−	0.835472i	−0.448774	−	0.893645i	$-0.648139\pi$
$419$	−606.327	−	350.063i	−1.44708	−	0.835472i	−0.998307	+	0.0581732i	$0.981472\pi$
$420$		0			0
$421$	221.791	+	384.153i	0.526820	+	0.912479i	0.999512	+	0.0312507i	$0.00994904\pi$
$421$	221.791	+	384.153i	0.526820	+	0.912479i	−0.472692	+	0.881228i	$0.656718\pi$
$422$	272.335	−	503.815i	0.645345	−	1.19387i
$423$		0			0
$424$	36.0333	+	427.312i	0.0849842	+	1.00781i
$425$	−119.216	−	206.488i	−0.280508	−	0.485853i
$426$		0			0
$427$	−200.160	−	115.562i	−0.468758	−	0.270638i
$428$	21.2718	+	378.885i	0.0497005	+	0.885245i
$429$		0			0
$430$	18.7005	−	0.524540i	0.0434895	−	0.00121986i
$431$		−	535.531i		−	1.24253i	−0.783600	−	0.621265i	$-0.786619\pi$
$431$		−	535.531i		−	1.24253i	0.783600	−	0.621265i	$-0.213381\pi$
$432$		0			0
$433$	151.504			0.349895			0.174947	−	0.984578i	$-0.444024\pi$
$433$	151.504			0.349895			0.174947	+	0.984578i	$0.444024\pi$
$434$	−31.4792	−	1122.27i	−0.0725326	−	2.58588i
$435$		0			0
$436$	−50.0540	+	2.81019i	−0.114803	+	0.00644539i
$437$	142.422	−	246.682i	0.325909	−	0.564490i
$438$		0			0
$439$	76.5284	−	44.1837i	0.174324	−	0.100646i	−0.410299	−	0.911951i	$-0.634576\pi$
$439$	76.5284	−	44.1837i	0.174324	−	0.100646i	0.584623	+	0.811305i	$0.301242\pi$
$440$	87.2201	−	7.35489i	0.198228	−	0.0167157i
$441$		0			0
$442$	−271.605	−	146.815i	−0.614491	−	0.332161i
$443$	5.13583	−	2.96517i	0.0115933	−	0.00669339i	−0.494192	−	0.869353i	$-0.664536\pi$
$443$	5.13583	−	2.96517i	0.0115933	−	0.00669339i	0.505785	+	0.862659i	$0.331203\pi$
$444$		0			0
$445$	−15.8917	+	27.5252i	−0.0357116	+	0.0618544i
$446$	−338.049	−	549.347i	−0.757958	−	1.23172i
$447$		0			0
$448$	−557.811	+	462.121i	−1.24511	+	1.03152i
$449$	−218.344			−0.486290			−0.243145	−	0.969990i	$-0.578179\pi$
$449$	−218.344			−0.486290			−0.243145	+	0.969990i	$0.578179\pi$
$450$		0			0
$451$		−	87.4693i		−	0.193945i
$452$	−238.598	+	472.618i	−0.527871	+	1.04562i
$453$		0			0
$454$	64.1674	+	104.275i	0.141338	+	0.229681i
$455$	254.565	+	146.973i	0.559484	+	0.323018i
$456$		0			0
$457$	−53.0234	−	91.8392i	−0.116025	−	0.200961i	0.802164	−	0.597104i	$-0.203682\pi$
$457$	−53.0234	−	91.8392i	−0.116025	−	0.200961i	−0.918189	+	0.396143i	$0.870349\pi$
$458$	−633.858	−	342.630i	−1.38397	−	0.748100i
$459$		0			0
$460$	190.071	−	124.443i	0.413198	−	0.270527i
$461$	101.367	+	175.572i	0.219884	+	0.380850i	0.954772	−	0.297338i	$-0.0960988\pi$
$461$	101.367	+	175.572i	0.219884	+	0.380850i	−0.734888	+	0.678188i	$0.762765\pi$
$462$		0			0
$463$	−333.562	−	192.582i	−0.720437	−	0.415945i	0.0944763	−	0.995527i	$-0.469882\pi$
$463$	−333.562	−	192.582i	−0.720437	−	0.415945i	−0.814914	+	0.579582i	$0.803216\pi$
$464$	432.683	+	586.302i	0.932506	+	1.26358i
$465$		0			0
$466$	6.55734	+	233.777i	0.0140715	+	0.501668i
$467$			563.818i			1.20732i	0.797243	+	0.603659i	$0.206291\pi$
$467$			563.818i			1.20732i	−0.797243	+	0.603659i	$0.793709\pi$
$468$		0			0
$469$	195.118			0.416030
$470$	−309.649	+	8.68550i	−0.658827	+	0.0184798i
$471$		0			0
$472$	−334.729	+	711.984i	−0.709172	+	1.50844i
$473$	−14.7396	+	25.5297i	−0.0311619	+	0.0539740i
$474$		0			0
$475$	174.221	−	100.586i	0.366781	−	0.211761i
$476$	419.498	−	274.652i	0.881299	−	0.577000i
$477$		0			0
$478$	−16.9023	+	31.2688i	−0.0353604	+	0.0654159i
$479$	413.226	−	238.576i	0.862685	−	0.498071i	−0.00222581	−	0.999998i	$-0.500708\pi$
$479$	413.226	−	238.576i	0.862685	−	0.498071i	0.864910	+	0.501926i	$0.167375\pi$
$480$		0			0
$481$	341.388	−	591.301i	0.709746	−	1.22932i
$482$	−386.622	+	237.914i	−0.802120	+	0.493597i
$483$		0			0
$484$	155.965	−	308.937i	0.322241	−	0.638300i
$485$	−96.9084			−0.199811
$486$		0			0
$487$			432.682i			0.888464i	0.895912	+	0.444232i	$0.146523\pi$
$487$			432.682i			0.888464i	−0.895912	+	0.444232i	$0.853477\pi$
$488$	−134.114	+	93.2812i	−0.274823	+	0.191150i
$489$		0			0
$490$	−251.052	+	154.489i	−0.512351	+	0.315283i
$491$	−331.698	−	191.506i	−0.675557	−	0.390033i	0.122622	−	0.992453i	$-0.460870\pi$
$491$	−331.698	−	191.506i	−0.675557	−	0.390033i	−0.798179	+	0.602421i	$0.794203\pi$
$492$		0			0
$493$	−252.195	−	436.815i	−0.511552	−	0.886035i
$494$	123.873	−	229.162i	0.250755	−	0.463892i
$495$		0			0
$496$	−727.336	−	317.360i	−1.46640	−	0.639839i
$497$	297.919	+	516.010i	0.599434	+	1.03825i
$498$		0			0
$499$	386.720	+	223.273i	0.774990	+	0.447441i	0.834652	−	0.550778i	$-0.185669\pi$
$499$	386.720	+	223.273i	0.774990	+	0.447441i	−0.0596617	+	0.998219i	$0.519002\pi$
$500$	346.231	−	19.4385i	0.692462	−	0.0388770i
$501$		0			0
$502$	442.516	−	12.4124i	0.881505	−	0.0247258i
$503$			488.145i			0.970467i	0.874385	+	0.485234i	$0.161265\pi$
$503$			488.145i			0.970467i	−0.874385	+	0.485234i	$0.838735\pi$
$504$		0			0
$505$	129.600			0.256634
$506$	10.0375	+	357.849i	0.0198370	+	0.707212i
$507$		0			0
$508$	12.6043	+	224.503i	0.0248117	+	0.441936i
$509$	−40.2548	+	69.7233i	−0.0790860	+	0.136981i	−0.902856	−	0.429943i	$-0.858534\pi$
$509$	−40.2548	+	69.7233i	−0.0790860	+	0.136981i	0.823770	+	0.566924i	$0.191867\pi$
$510$		0			0
$511$	962.148	−	555.496i	1.88287	−	1.08708i
$512$	127.851	+	495.780i	0.249709	+	0.968321i
$513$		0			0
$514$	−127.386	−	68.8579i	−0.247832	−	0.133965i
$515$	23.1794	−	13.3826i	0.0450085	−	0.0259857i
$516$		0			0
$517$	244.063	−	422.729i	0.472075	−	0.817657i
$518$	581.129	+	944.365i	1.12187	+	1.82310i
$519$		0			0
$520$	170.567	−	118.636i	0.328013	−	0.228146i
$521$	841.106			1.61441			0.807204	−	0.590273i	$-0.200980\pi$
$521$	841.106			1.61441			0.807204	+	0.590273i	$0.200980\pi$
$522$		0			0
$523$		−	935.263i		−	1.78827i	−0.447802	−	0.894133i	$-0.647793\pi$
$523$		−	935.263i		−	1.78827i	0.447802	−	0.894133i	$-0.352207\pi$
$524$	184.323	+	93.0540i	0.351761	+	0.177584i
$525$		0			0
$526$	−474.831	−	771.625i	−0.902721	−	1.46697i
$527$	475.711	+	274.652i	0.902678	+	0.521162i
$528$		0			0
$529$	200.084	+	346.556i	0.378231	+	0.655116i
$530$	175.725	+	94.9873i	0.331556	+	0.179221i
$531$		0			0
$532$	231.733	+	353.945i	0.435589	+	0.665311i
$533$	−103.812	−	179.808i	−0.194770	−	0.337351i
$534$		0			0
$535$	153.085	+	88.3838i	0.286141	+	0.165203i
$536$	58.6772	−	124.809i	0.109472	−	0.232853i
$537$		0			0
$538$	4.96284	+	176.931i	0.00922461	+	0.328869i
$539$		−	464.500i		−	0.861780i
$540$		0			0
$541$	693.160			1.28126			0.640629	−	0.767851i	$-0.278674\pi$
$541$	693.160			1.28126			0.640629	+	0.767851i	$0.278674\pi$
$542$	50.5264	−	1.41724i	0.0932221	−	0.00261484i
$543$		0			0
$544$	−49.5293	−	350.931i	−0.0910465	−	0.645093i
$545$	−11.6763	+	20.2239i	−0.0214243	+	0.0371080i
$546$		0			0
$547$	332.640	−	192.050i	0.608117	−	0.351096i	−0.164111	−	0.986442i	$-0.552476\pi$
$547$	332.640	−	192.050i	0.608117	−	0.351096i	0.772228	+	0.635345i	$0.219142\pi$
$548$	−20.6258	−	31.5035i	−0.0376384	−	0.0574881i
$549$		0			0
$550$	−120.227	+	222.418i	−0.218595	+	0.404396i
$551$	368.556	−	212.786i	0.668886	−	0.386181i
$552$		0			0
$553$	17.2408	−	29.8619i	0.0311768	−	0.0539998i
$554$	443.374	−	272.837i	0.800314	−	0.492486i
$555$		0			0
$556$	−198.858	−	100.392i	−0.357658	−	0.180561i
$557$	−684.610			−1.22910			−0.614551	−	0.788877i	$-0.710663\pi$
$557$	−684.610			−1.22910			−0.614551	+	0.788877i	$0.710663\pi$
$558$		0			0
$559$			69.9743i			0.125178i
$560$	37.7687	+	335.300i	0.0674441	+	0.598750i
$561$		0			0
$562$	283.281	−	174.321i	0.504059	−	0.310180i
$563$	882.086	+	509.273i	1.56676	+	0.904570i	0.996543	+	0.0830764i	$0.0264746\pi$
$563$	882.086	+	509.273i	1.56676	+	0.904570i	0.570218	+	0.821493i	$0.306859\pi$
$564$		0			0
$565$	123.308	+	213.576i	0.218244	+	0.378010i
$566$	−309.653	+	572.851i	−0.547089	+	1.01210i
$567$		0			0
$568$	419.662	−	35.3882i	0.738842	−	0.0623032i
$569$	353.027	+	611.460i	0.620433	+	1.07462i	0.989405	+	0.145181i	$0.0463766\pi$
$569$	353.027	+	611.460i	0.620433	+	1.07462i	−0.368972	+	0.929441i	$0.620290\pi$
$570$		0			0
$571$	−152.264	−	87.9094i	−0.266661	−	0.153957i	0.360708	−	0.932679i	$-0.382535\pi$
$571$	−152.264	−	87.9094i	−0.266661	−	0.153957i	−0.627369	+	0.778722i	$0.715868\pi$
$572$	18.3520	+	326.879i	0.0320840	+	0.571466i
$573$		0			0
$574$	337.055	−	9.45423i	0.587204	−	0.0164708i
$575$			656.231i			1.14127i
$576$		0			0
$577$	−773.925			−1.34129			−0.670645	−	0.741778i	$-0.733983\pi$
$577$	−773.925			−1.34129			−0.670645	+	0.741778i	$0.733983\pi$
$578$	−9.32776	−	332.546i	−0.0161380	−	0.575339i
$579$		0			0
$580$	338.892	−	19.0265i	0.584297	−	0.0328043i
$581$	−576.740	+	998.942i	−0.992667	+	1.71935i
$582$		0			0
$583$	−272.595	+	157.383i	−0.467572	+	0.269953i
$584$	−65.9846	−	782.498i	−0.112987	−	1.33989i
$585$		0			0
$586$	−804.974	−	435.126i	−1.37368	−	0.742536i
$587$	−363.714	+	209.990i	−0.619615	+	0.357735i	−0.776719	−	0.629847i	$-0.783118\pi$
$587$	−363.714	+	209.990i	−0.619615	+	0.357735i	0.157104	+	0.987582i	$0.449784\pi$
$588$		0			0
$589$	−231.733	+	401.374i	−0.393435	+	0.681450i
$590$	192.065	+	312.115i	0.325533	+	0.529008i
$591$		0			0
$592$	778.831	−	87.7288i	1.31559	−	0.148190i
$593$	393.181			0.663038			0.331519	−	0.943449i	$-0.392439\pi$
$593$	393.181			0.663038			0.331519	+	0.943449i	$0.392439\pi$
$594$		0			0
$595$		−	233.564i		−	0.392544i
$596$	426.406	−	844.631i	0.715446	−	1.41717i
$597$		0			0
$598$	445.345	+	723.708i	0.744723	+	1.21021i
$599$	289.090	+	166.906i	0.482622	+	0.278642i	0.721508	−	0.692406i	$-0.243449\pi$
$599$	289.090	+	166.906i	0.482622	+	0.278642i	−0.238887	+	0.971047i	$0.576782\pi$
$600$		0			0
$601$	426.635	+	738.954i	0.709875	+	1.22954i	0.964903	+	0.262606i	$0.0845821\pi$
$601$	426.635	+	738.954i	0.709875	+	1.22954i	−0.255028	+	0.966934i	$0.582085\pi$
$602$	−99.9696	−	54.0383i	−0.166062	−	0.0897645i
$603$		0			0
$604$	−324.779	+	212.638i	−0.537713	+	0.352049i
$605$	−80.6029	−	139.608i	−0.133228	−	0.230758i
$606$		0			0
$607$	−659.847	−	380.963i	−1.08706	−	0.627616i	−0.154270	−	0.988029i	$-0.549303\pi$
$607$	−659.847	−	380.963i	−1.08706	−	0.627616i	−0.932793	+	0.360412i	$0.882636\pi$
$608$	296.092	−	41.7896i	0.486994	−	0.0687328i
$609$		0			0
$610$	2.13365	+	76.0674i	0.00349779	+	0.124701i
$611$		−	1158.66i		−	1.89633i
$612$		0			0
$613$	−539.868			−0.880698			−0.440349	−	0.897827i	$-0.645145\pi$
$613$	−539.868			−0.880698			−0.440349	+	0.897827i	$0.645145\pi$
$614$	386.470	−	10.8403i	0.629430	−	0.0176552i
$615$		0			0
$616$	−481.172	−	226.216i	−0.781123	−	0.367234i
$617$	363.389	−	629.409i	0.588961	−	1.02011i	−0.405407	−	0.914136i	$-0.632870\pi$
$617$	363.389	−	629.409i	0.588961	−	1.02011i	0.994369	−	0.105975i	$-0.0337963\pi$
$618$		0			0
$619$	−429.526	+	247.987i	−0.693903	+	0.400625i	−0.805073	−	0.593176i	$-0.797874\pi$
$619$	−429.526	+	247.987i	−0.693903	+	0.400625i	0.111170	+	0.993801i	$0.464540\pi$
$620$	−309.263	+	202.479i	−0.498811	+	0.326579i
$621$		0			0
$622$	145.089	−	268.412i	0.233262	−	0.431530i
$623$	167.201	−	96.5333i	0.268380	−	0.154949i
$624$		0			0
$625$	−188.337	+	326.209i	−0.301339	+	0.521935i
$626$	−148.958	+	91.6637i	−0.237952	+	0.146428i
$627$		0			0
$628$	207.262	−	410.547i	0.330035	−	0.653737i
$629$	−542.520			−0.862511
$630$		0			0
$631$			895.486i			1.41915i	0.704628	+	0.709576i	$0.251114\pi$
$631$			895.486i			1.41915i	−0.704628	+	0.709576i	$0.748886\pi$
$632$	−13.9166	−	20.0084i	−0.0220200	−	0.0316589i
$633$		0			0
$634$	497.735	−	306.289i	0.785070	−	0.483105i
$635$	90.7087	+	52.3707i	0.142848	+	0.0824735i
$636$		0			0
$637$	−551.288	−	954.859i	−0.865445	−	1.49899i
$638$	−254.335	+	470.514i	−0.398644	+	0.737483i
$639$		0			0
$640$	225.835	+	76.6745i	0.352868	+	0.119804i
$641$	−311.644	−	539.783i	−0.486184	−	0.842095i	0.513690	−	0.857976i	$-0.328278\pi$
$641$	−311.644	−	539.783i	−0.486184	−	0.842095i	−0.999874	+	0.0158810i	$0.994945\pi$
$642$		0			0
$643$	−318.256	−	183.745i	−0.494955	−	0.285762i	0.231673	−	0.972794i	$-0.425580\pi$
$643$	−318.256	−	183.745i	−0.494955	−	0.285762i	−0.726628	+	0.687032i	$0.758913\pi$
$644$	−1377.85	+	77.3572i	−2.13953	+	0.120120i
$645$		0			0
$646$	−206.906	+	5.80362i	−0.320288	+	0.00898393i
$647$		−	762.797i		−	1.17897i	−0.807778	−	0.589487i	$-0.799330\pi$
$647$		−	762.797i		−	1.17897i	0.807778	−	0.589487i	$-0.200670\pi$
$648$		0			0
$649$	−577.479			−0.889798
$650$	16.8272	+	599.909i	0.0258879	+	0.922937i
$651$		0			0
$652$	−69.8606	−	1244.33i	−0.107148	−	1.90848i
$653$	0.668056	−	1.15711i	0.00102306	−	0.00177199i	−0.865513	−	0.500886i	$-0.833008\pi$
$653$	0.668056	−	1.15711i	0.00102306	−	0.00177199i	0.866536	+	0.499114i	$0.166341\pi$
$654$		0			0
$655$	83.2953	−	48.0906i	0.127168	−	0.0734207i
$656$	95.3138	−	218.443i	0.145295	−	0.332992i
$657$		0			0
$658$	1655.33	+	894.782i	2.51570	+	1.35985i
$659$	172.143	−	99.3866i	0.261218	−	0.150814i	−0.363672	−	0.931527i	$-0.618477\pi$
$659$	172.143	−	99.3866i	0.261218	−	0.150814i	0.624890	+	0.780713i	$0.285144\pi$
$660$		0			0
$661$	−107.877	+	186.849i	−0.163203	+	0.282676i	−0.936016	−	0.351958i	$-0.885516\pi$
$661$	−107.877	+	186.849i	−0.163203	+	0.282676i	0.772813	+	0.634634i	$0.218849\pi$
$662$	−163.778	−	266.148i	−0.247399	−	0.402036i
$663$		0			0
$664$	465.541	+	669.324i	0.701115	+	1.00802i
$665$	197.066			0.296340
$666$		0			0
$667$			1388.23i			2.08130i
$668$	346.596	+	174.977i	0.518857	+	0.261941i
$669$		0			0
$670$	−33.6684	−	54.7129i	−0.0502514	−	0.0816610i
$671$	−103.846	−	59.9557i	−0.154763	−	0.0893527i
$672$		0			0
$673$	101.787	+	176.301i	0.151244	+	0.261962i	0.931685	−	0.363267i	$-0.118339\pi$
$673$	101.787	+	176.301i	0.151244	+	0.261962i	−0.780441	+	0.625229i	$0.785005\pi$
$674$	477.314	+	258.010i	0.708181	+	0.382805i
$675$		0			0
$676$	55.3946	+	84.6086i	0.0819446	+	0.125161i
$677$	505.490	+	875.534i	0.746662	+	1.29326i	0.949414	+	0.314026i	$0.101678\pi$
$677$	505.490	+	875.534i	0.746662	+	1.29326i	−0.202753	+	0.979230i	$0.564989\pi$
$678$		0			0
$679$	509.799	+	294.333i	0.750809	+	0.433480i
$680$	−149.401	−	70.2388i	−0.219707	−	0.103292i
$681$		0			0
$682$	−16.3319	−	582.252i	−0.0239471	−	0.853743i
$683$			1186.83i			1.73767i	0.495103	+	0.868834i	$0.335130\pi$
$683$			1186.83i			1.73767i	−0.495103	+	0.868834i	$0.664870\pi$
$684$		0			0
$685$	−17.5402			−0.0256061
$686$	681.155	−	19.1061i	0.992938	−	0.0278514i
$687$		0			0
$688$	−64.6295	+	47.6956i	−0.0939382	+	0.0693250i
$689$	−373.577	+	647.055i	−0.542202	+	0.939121i
$690$		0			0
$691$	−3.26716	+	1.88630i	−0.00472817	+	0.00272981i	−0.502362	−	0.864657i	$-0.667536\pi$
$691$	−3.26716	+	1.88630i	−0.00472817	+	0.00272981i	0.497634	+	0.867387i	$0.334202\pi$
$692$	233.951	+	357.332i	0.338079	+	0.516375i
$693$		0			0
$694$	330.067	−	610.618i	0.475602	−	0.879853i
$695$	−89.8636	+	51.8828i	−0.129300	+	0.0746514i
$696$		0			0
$697$	−82.4872	+	142.872i	−0.118346	+	0.204981i
$698$	508.502	−	312.915i	0.728513	−	0.448302i
$699$		0			0
$700$	−870.062	−	439.244i	−1.24295	−	0.627492i
$701$	970.063			1.38383			0.691913	−	0.721980i	$-0.256768\pi$
$701$	970.063			1.38383			0.691913	+	0.721980i	$0.256768\pi$
$702$		0			0
$703$		−	457.743i		−	0.651127i
$704$	−289.402	+	239.756i	−0.411082	+	0.340563i
$705$		0			0
$706$	−967.675	+	595.474i	−1.37064	+	0.843447i
$707$	−681.779	−	393.625i	−0.964327	−	0.556754i
$708$		0			0
$709$	−122.626	−	212.395i	−0.172956	−	0.299569i	0.766496	−	0.642249i	$-0.221999\pi$
$709$	−122.626	−	212.395i	−0.172956	−	0.299569i	−0.939452	+	0.342680i	$0.888665\pi$
$710$	93.2869	−	172.579i	0.131390	−	0.243069i
$711$		0			0
$712$	−11.4667	−	135.981i	−0.0161049	−	0.190985i
$713$	−755.920	−	1309.29i	−1.06020	−	1.83632i
$714$		0			0
$715$	132.073	+	76.2522i	0.184717	+	0.106646i
$716$	−39.6348	−	705.959i	−0.0553559	−	0.985976i
$717$		0			0
$718$	−827.989	+	23.2247i	−1.15319	+	0.0323464i
$719$			500.230i			0.695730i	0.937545	+	0.347865i	$0.113093\pi$
$719$			500.230i			0.695730i	−0.937545	+	0.347865i	$0.886907\pi$
$720$		0			0
$721$	−162.584			−0.225498
$722$	15.3471	+	547.142i	0.0212564	+	0.757815i
$723$		0			0
$724$	653.456	−	36.6871i	0.902564	−	0.0506729i
$725$	−490.221	+	849.088i	−0.676167	+	1.17116i
$726$		0			0
$727$	−541.817	+	312.818i	−0.745278	+	0.430287i	−0.823985	−	0.566611i	$-0.808254\pi$
$727$	−541.817	+	312.818i	−0.745278	+	0.430287i	0.0787070	+	0.996898i	$0.474921\pi$
$728$	−1257.61	+	106.049i	−1.72749	+	0.145672i
$729$		0			0
$730$	−321.789	−	173.942i	−0.440806	−	0.238277i
$731$	48.1512	−	27.8001i	0.0658703	−	0.0380302i
$732$		0			0
$733$	−596.531	+	1033.22i	−0.813821	+	1.40958i	0.0963510	+	0.995347i	$0.469283\pi$
$733$	−596.531	+	1033.22i	−0.813821	+	1.40958i	−0.910172	+	0.414231i	$0.864050\pi$
$734$	−332.967	−	541.089i	−0.453634	−	0.737178i
$735$		0			0
$736$	−364.875	+	904.619i	−0.495754	+	1.22910i
$737$	101.231			0.137355
$738$		0			0
$739$			850.984i			1.15154i	0.817613	+	0.575768i	$0.195297\pi$
$739$			850.984i			1.15154i	−0.817613	+	0.575768i	$0.804703\pi$
$740$	164.532	−	325.908i	0.222341	−	0.440416i
$741$		0			0
$742$	−635.924	−	1033.41i	−0.857040	−	1.39273i
$743$	−209.853	−	121.159i	−0.282440	−	0.163067i	0.352088	−	0.935967i	$-0.385472\pi$
$743$	−209.853	−	121.159i	−0.282440	−	0.163067i	−0.634527	+	0.772900i	$0.718805\pi$
$744$		0			0
$745$	−220.368	−	381.688i	−0.295796	−	0.512333i
$746$	−187.797	−	101.513i	−0.251739	−	0.136076i
$747$		0			0
$748$	217.643	−	142.494i	0.290966	−	0.190500i
$749$	−536.884	−	929.910i	−0.716800	−	1.24153i
$750$		0			0
$751$	1097.26	+	633.505i	1.46107	+	0.843548i	0.999061	−	0.0433279i	$-0.0137960\pi$
$751$	1097.26	+	633.505i	1.46107	+	0.843548i	0.462007	+	0.886876i	$0.347129\pi$
$752$	1070.15	−	789.759i	1.42308	−	1.05021i
$753$		0			0
$754$	35.5971	+	1269.08i	0.0472110	+	1.68313i
$755$			180.827i			0.239506i
$756$		0			0
$757$	−1036.61			−1.36936			−0.684682	−	0.728842i	$-0.740059\pi$
$757$	−1036.61			−1.36936			−0.684682	+	0.728842i	$0.740059\pi$
$758$	67.5895	−	1.89585i	0.0891682	−	0.00250113i
$759$		0			0
$760$	59.2629	−	126.055i	0.0779775	−	0.165862i
$761$	484.626	−	839.396i	0.636827	−	1.10302i	−0.349298	−	0.937012i	$-0.613580\pi$
$761$	484.626	−	839.396i	0.636827	−	1.10302i	0.986125	−	0.166005i	$-0.0530869\pi$
$762$		0			0
$763$	122.849	−	70.9269i	0.161008	−	0.0929580i
$764$	−474.862	+	310.899i	−0.621547	+	0.406936i
$765$		0			0
$766$	174.783	−	323.344i	0.228176	−	0.422121i
$767$	−1187.11	+	685.377i	−1.54773	+	0.893582i
$768$		0			0
$769$	467.080	−	809.007i	0.607387	−	1.05202i	−0.384283	−	0.923215i	$-0.625551\pi$
$769$	467.080	−	809.007i	0.607387	−	1.05202i	0.991669	−	0.128809i	$-0.0411155\pi$
$770$	−210.933	+	129.801i	−0.273939	+	0.168572i
$771$		0			0
$772$	−75.2590	+	149.074i	−0.0974858	+	0.193101i
$773$	69.8230			0.0903273			0.0451637	−	0.998980i	$-0.485619\pi$
$773$	69.8230			0.0903273			0.0451637	+	0.998980i	$0.485619\pi$
$774$		0			0
$775$		−	1067.75i		−	1.37774i
$776$	341.582	−	237.584i	0.440183	−	0.306165i
$777$		0			0
$778$	88.6385	−	54.5451i	0.113931	−	0.0701093i
$779$	−120.546	−	69.5973i	−0.154745	−	0.0893418i
$780$		0			0
$781$	154.565	+	267.715i	0.197907	+	0.342785i
$782$	321.071	−	593.975i	0.410577	−	0.759559i
$783$		0			0
$784$	506.158	−	1160.03i	0.645609	−	1.47963i
$785$	−107.113	−	185.526i	−0.136450	−	0.236339i
$786$		0			0
$787$	1132.18	+	653.663i	1.43860	+	0.830575i	0.997752	−	0.0670077i	$-0.0213452\pi$
$787$	1132.18	+	653.663i	1.43860	+	0.830575i	0.440846	+	0.897583i	$0.354679\pi$
$788$	680.870	−	38.2262i	0.864048	−	0.0485105i
$789$		0			0
$790$	−11.3485	+	0.318320i	−0.0143652	+	0.000402937i
$791$		−	1498.06i		−	1.89388i
$792$		0			0
$793$	−284.632			−0.358931
$794$	32.8175	+	1169.98i	0.0413319	+	1.47353i
$795$		0			0
$796$	−38.0338	−	677.441i	−0.0477811	−	0.851057i
$797$	379.279	−	656.931i	0.475884	−	0.824255i	−0.523734	−	0.851882i	$-0.675462\pi$
$797$	379.279	−	656.931i	0.475884	−	0.824255i	0.999618	+	0.0276265i	$0.00879490\pi$
$798$		0			0
$799$	−797.302	+	460.322i	−0.997875	+	0.576123i
$800$	−542.617	+	424.450i	−0.678271	+	0.530562i
$801$		0			0
$802$	941.202	+	508.764i	1.17357	+	0.634369i
$803$	499.179	−	288.201i	0.621642	−	0.358905i
$804$		0			0
$805$	−321.417	+	556.711i	−0.399276	+	0.691566i
$806$	−724.615	−	1177.54i	−0.899027	−	1.46096i
$807$		0			0
$808$	−456.814	+	317.732i	−0.565364	+	0.393233i
$809$	574.403			0.710016			0.355008	−	0.934863i	$-0.384478\pi$
$809$	574.403			0.710016			0.355008	+	0.934863i	$0.384478\pi$
$810$		0			0
$811$		−	117.246i		−	0.144570i	−0.997384	−	0.0722851i	$-0.976971\pi$
$811$		−	117.246i		−	0.144570i	0.997384	−	0.0722851i	$-0.0230291\pi$
$812$	−1840.57	−	929.201i	−2.26672	−	1.14434i
$813$		0			0
$814$	301.500	+	489.952i	0.370393	+	0.601907i
$815$	−502.761	−	290.269i	−0.616884	−	0.356158i
$816$		0			0
$817$	23.4559	+	40.6268i	0.0287098	+	0.0497268i
$818$	584.026	+	315.694i	0.713969	+	0.385934i
$819$		0			0
$820$	−60.8112	−	92.8819i	−0.0741600	−	0.113271i
$821$	−25.7065	−	44.5249i	−0.0313112	−	0.0542326i	0.849945	−	0.526871i	$-0.176635\pi$
$821$	−25.7065	−	44.5249i	−0.0313112	−	0.0542326i	−0.881256	+	0.472639i	$0.843302\pi$
$822$		0			0
$823$	98.1876	+	56.6887i	0.119305	+	0.0688805i	0.558465	−	0.829528i	$-0.311391\pi$
$823$	98.1876	+	56.6887i	0.119305	+	0.0688805i	−0.439160	+	0.898409i	$0.644724\pi$
$824$	−48.8934	+	103.998i	−0.0593366	+	0.126212i
$825$		0			0
$826$	−62.4176	−	2225.26i	−0.0755661	−	2.69402i
$827$			467.270i			0.565018i	0.959265	+	0.282509i	$0.0911667\pi$
$827$			467.270i			0.565018i	−0.959265	+	0.282509i	$0.908833\pi$
$828$		0			0
$829$	−359.806			−0.434025			−0.217012	−	0.976169i	$-0.569631\pi$
$829$	−359.806			−0.434025			−0.217012	+	0.976169i	$0.569631\pi$
$830$	379.631	−	10.6485i	0.457387	−	0.0128295i
$831$		0			0
$832$	−310.362	+	836.335i	−0.373032	+	1.00521i
$833$	−438.043	+	758.712i	−0.525861	+	0.910819i
$834$		0			0
$835$	156.627	−	90.4284i	0.187577	−	0.108298i
$836$	120.227	+	183.633i	0.143812	+	0.219656i
$837$		0			0
$838$	665.849	−	1231.81i	0.794570	−	1.46994i
$839$	−639.635	+	369.294i	−0.762378	+	0.440159i	−0.830149	−	0.557542i	$-0.811745\pi$
$839$	−639.635	+	369.294i	−0.762378	+	0.440159i	0.0677709	+	0.997701i	$0.478411\pi$
$840$		0			0
$841$	−616.540	+	1067.88i	−0.733104	+	1.26977i
$842$	−755.567	+	464.950i	−0.897349	+	0.552197i
$843$		0			0
$844$	1022.50	+	516.204i	1.21150	+	0.611616i
$845$	47.1075			0.0557485
$846$		0			0
$847$			979.238i			1.15612i
$848$	−852.267	+	96.0007i	−1.00503	+	0.113208i
$849$		0			0
$850$	406.128	−	249.917i	0.477797	−	0.294020i
$851$	1293.12	+	746.584i	1.51953	+	0.877302i
$852$		0			0
$853$	−578.418	−	1001.85i	−0.678099	−	1.17450i	−0.975553	−	0.219766i	$-0.929471\pi$
$853$	−578.418	−	1001.85i	−0.678099	−	1.17450i	0.297454	−	0.954736i	$-0.403863\pi$
$854$	219.809	−	406.643i	0.257388	−	0.476162i
$855$		0			0
$856$	−756.279	+	63.7737i	−0.883504	+	0.0745019i
$857$	180.503	+	312.641i	0.210623	+	0.364809i	0.951910	−	0.306379i	$-0.0991176\pi$
$857$	180.503	+	312.641i	0.210623	+	0.364809i	−0.741287	+	0.671188i	$0.765784\pi$
$858$		0			0
$859$	−751.950	−	434.138i	−0.875378	−	0.505400i	−0.00624629	−	0.999980i	$-0.501988\pi$
$859$	−751.950	−	434.138i	−0.875378	−	0.505400i	−0.869132	+	0.494581i	$0.835322\pi$
$860$	2.09734	+	37.3569i	0.00243876	+	0.0434382i
$861$		0			0
$862$	1070.64	−	30.0310i	1.24204	−	0.0348387i
$863$			136.786i			0.158500i	0.996855	+	0.0792500i	$0.0252526\pi$
$863$			136.786i			0.158500i	−0.996855	+	0.0792500i	$0.974747\pi$
$864$		0			0
$865$	198.951			0.230002
$866$	8.49591	+	302.890i	0.00981052	+	0.349757i
$867$		0			0
$868$	2241.89	−	125.867i	2.58283	−	0.145008i
$869$	8.94480	−	15.4928i	0.0102932	−	0.0178284i
$870$		0			0
$871$	208.097	−	120.145i	0.238917	−	0.137939i
$872$	−8.42505	−	99.9110i	−0.00966175	−	0.114577i
$873$		0			0
$874$	501.157	+	270.899i	0.573406	+	0.309953i
$875$	−849.766	+	490.612i	−0.971161	+	0.560700i
$876$		0			0
$877$	−377.780	+	654.334i	−0.430764	+	0.746104i	−0.996939	−	0.0781802i	$-0.975089\pi$
$877$	−377.780	+	654.334i	−0.430764	+	0.746104i	0.566176	+	0.824285i	$0.308422\pi$
$878$	92.6241	+	150.519i	0.105494	+	0.171434i
$879$		0			0
$880$	19.5950	+	173.959i	0.0222671	+	0.197681i
$881$	845.499			0.959703			0.479852	−	0.877350i	$-0.340690\pi$
$881$	845.499			0.959703			0.479852	+	0.877350i	$0.340690\pi$
$882$		0			0
$883$		−	860.448i		−	0.974460i	−0.873274	−	0.487230i	$-0.838007\pi$
$883$		−	860.448i		−	0.974460i	0.873274	−	0.487230i	$-0.161993\pi$
$884$	278.284	−	551.229i	0.314801	−	0.623562i
$885$		0			0
$886$	6.21601	+	10.1013i	0.00701582	+	0.0114011i
$887$	−1048.85	−	605.552i	−1.18247	−	0.682697i	−0.225882	−	0.974155i	$-0.572526\pi$
$887$	−1048.85	−	605.552i	−1.18247	−	0.682697i	−0.956584	+	0.291458i	$0.905860\pi$
$888$		0			0
$889$	−318.123	−	551.006i	−0.357844	−	0.619804i
$890$	−55.9199	−	30.2273i	−0.0628314	−	0.0339633i
$891$		0			0
$892$	1079.31	−	706.638i	1.20998	−	0.792195i
$893$	−388.390	−	672.711i	−0.434927	−	0.753316i
$894$		0			0
$895$	−285.237	−	164.682i	−0.318700	−	0.184002i
$896$	−955.159	−	1089.27i	−1.06603	−	1.21570i
$897$		0			0
$898$	−12.2441	−	436.516i	−0.0136348	−	0.486098i
$899$		−	2258.77i		−	2.51253i
$900$		0			0
$901$	593.674			0.658905
$902$	174.870	−	4.90501i	0.193869	−	0.00543793i
$903$		0			0
$904$	−958.244	−	450.505i	−1.06000	−	0.498346i
$905$	152.434	−	264.024i	0.168435	−	0.291739i
$906$		0			0
$907$	278.678	−	160.895i	0.307252	−	0.177392i	−0.338444	−	0.940987i	$-0.609901\pi$
$907$	278.678	−	160.895i	0.307252	−	0.177392i	0.645696	+	0.763594i	$0.276567\pi$
$908$	−204.870	+	134.132i	−0.225628	+	0.147722i
$909$		0			0
$910$	−279.556	+	517.172i	−0.307204	+	0.568321i
$911$	−1349.54	+	779.160i	−1.48139	+	0.855279i	−0.999777	−	0.0211061i	$-0.993281\pi$
$911$	−1349.54	+	779.160i	−1.48139	+	0.855279i	−0.481610	+	0.876386i	$0.659948\pi$
$912$		0			0
$913$	−299.222	+	518.268i	−0.327735	+	0.567654i
$914$	180.633	−	111.155i	0.197629	−	0.121614i
$915$		0			0
$916$	649.446	−	1286.43i	0.709002	−	1.40440i
$917$	−584.248			−0.637129
$918$		0			0
$919$		−	1338.32i		−	1.45628i	−0.685428	−	0.728140i	$-0.740385\pi$
$919$		−	1338.32i		−	1.45628i	0.685428	−	0.728140i	$-0.259615\pi$
$920$	259.446	+	373.014i	0.282006	+	0.405450i
$921$		0			0
$922$	−345.322	+	212.499i	−0.374535	+	0.230476i
$923$	635.471	+	366.889i	0.688484	+	0.397496i
$924$		0			0
$925$	527.279	+	913.275i	0.570032	+	0.987324i
$926$	366.308	−	677.662i	0.395581	−	0.731817i
$927$		0			0
$928$	−1147.88	+	897.903i	−1.23694	+	0.967568i
$929$	549.200	+	951.243i	0.591174	+	1.02394i	0.994075	+	0.108699i	$0.0346686\pi$
$929$	549.200	+	951.243i	0.591174	+	1.02394i	−0.402901	+	0.915244i	$0.631998\pi$
$930$		0			0
$931$	−640.151	−	369.592i	−0.687596	−	0.396983i
$932$	−467.003	+	26.2190i	−0.501076	+	0.0281320i
$933$		0			0
$934$	−1127.19	+	31.6172i	−1.20684	+	0.0338514i
$935$		−	121.177i		−	0.129601i
$936$		0			0
$937$	217.829			0.232474			0.116237	−	0.993221i	$-0.462917\pi$
$937$	217.829			0.232474			0.116237	+	0.993221i	$0.462917\pi$
$938$	10.9416	+	390.083i	0.0116649	+	0.415867i
$939$		0			0
$940$	−34.7283	−	618.567i	−0.0369450	−	0.658050i
$941$	160.263	−	277.583i	0.170311	−	0.294987i	−0.768218	−	0.640189i	$-0.778856\pi$
$941$	160.263	−	277.583i	0.170311	−	0.294987i	0.938529	+	0.345202i	$0.112189\pi$
$942$		0			0
$943$	393.224	−	227.028i	0.416993	−	0.240751i
$944$	−1442.18	−	629.269i	−1.52773	−	0.666599i
$945$		0			0
$946$	−51.8659	−	28.0359i	−0.0548265	−	0.0296363i
$947$	1300.73	−	750.974i	1.37352	−	0.793004i	0.382153	−	0.924099i	$-0.375183\pi$
$947$	1300.73	−	750.974i	1.37352	−	0.793004i	0.991370	+	0.131095i	$0.0418495\pi$
$948$		0			0
$949$	684.098	−	1184.89i	0.720862	−	1.24857i
$950$	210.864	+	342.664i	0.221962	+	0.360699i
$951$		0			0
$952$	572.613	+	823.265i	0.601484	+	0.864774i
$953$	−1053.40			−1.10535			−0.552675	−	0.833397i	$-0.686393\pi$
$953$	−1053.40			−1.10535			−0.552675	+	0.833397i	$0.686393\pi$
$954$		0			0
$955$			264.388i			0.276847i
$956$	−63.4609	−	32.0378i	−0.0663817	−	0.0335123i
$957$		0			0
$958$	500.137	+	812.748i	0.522064	+	0.848380i
$959$	92.2724	+	53.2735i	0.0962173	+	0.0555511i
$960$		0			0
$961$	749.450	+	1298.09i	0.779865	+	1.35077i
$962$	1201.28	+	649.349i	1.24873	+	0.674999i
$963$		0			0
$964$	−497.321	−	759.598i	−0.515893	−	0.787965i
$965$	38.8940	+	67.3665i	0.0403047	+	0.0698098i
$966$		0			0
$967$	409.368	+	236.349i	0.423338	+	0.244414i	0.696504	−	0.717553i	$-0.254738\pi$
$967$	409.368	+	236.349i	0.423338	+	0.244414i	−0.273167	+	0.961967i	$0.588071\pi$
$968$	626.377	+	294.482i	0.647084	+	0.304217i
$969$		0			0
$970$	−5.43433	−	193.741i	−0.00560241	−	0.199733i
$971$			595.910i			0.613707i	0.951757	+	0.306854i	$0.0992762\pi$
$971$			595.910i			0.613707i	−0.951757	+	0.306854i	$0.900724\pi$
$972$		0			0
$973$	630.319			0.647810
$974$	−865.024	+	24.2635i	−0.888115	+	0.0249112i
$975$		0			0
$976$	−194.010	−	262.891i	−0.198781	−	0.269356i
$977$	−96.8999	+	167.836i	−0.0991811	+	0.171787i	−0.911346	−	0.411641i	$-0.864956\pi$
$977$	−96.8999	+	167.836i	−0.0991811	+	0.171787i	0.812165	+	0.583428i	$0.198289\pi$
$978$		0			0
$979$	86.7464	−	50.0831i	0.0886072	−	0.0511574i
$980$	−322.934	−	493.243i	−0.329524	−	0.503309i
$981$		0			0
$982$	364.261	−	673.875i	0.370938	−	0.686227i
$983$	1262.73	−	729.038i	1.28457	−	0.741645i	0.306888	−	0.951746i	$-0.400712\pi$
$983$	1262.73	−	729.038i	1.28457	−	0.741645i	0.977680	+	0.210100i	$0.0673790\pi$
$984$		0			0
$985$	158.829	−	275.100i	0.161248	−	0.279289i
$986$	859.144	−	528.688i	0.871343	−	0.536194i
$987$		0			0
$988$	465.091	+	234.798i	0.470740	+	0.237650i
$989$	−153.027			−0.154729
$990$		0			0
$991$			569.118i			0.574287i	0.957888	+	0.287143i	$0.0927056\pi$
$991$			569.118i			0.574287i	−0.957888	+	0.287143i	$0.907294\pi$
$992$	593.684	−	1471.90i	0.598472	−	1.48377i
$993$		0			0
$994$	−1014.91	+	624.539i	−1.02103	+	0.628309i
$995$	−273.715	−	158.029i	−0.275090	−	0.158823i
$996$		0			0
$997$	−5.23685	−	9.07049i	−0.00525261	−	0.00909779i	0.863387	−	0.504542i	$-0.168339\pi$
$997$	−5.23685	−	9.07049i	−0.00525261	−	0.00909779i	−0.868640	+	0.495444i	$0.835005\pi$
$998$	−424.684	+	785.657i	−0.425535	+	0.787231i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.3.f.r.271.3		12
3.2	odd	2		324.3.f.q.271.4		12
4.3	odd	2	inner	324.3.f.r.271.5		12
9.2	odd	6		324.3.f.q.55.2		12
9.4	even	3		324.3.d.e.163.1	✓	6
9.5	odd	6		324.3.d.f.163.6	yes	6
9.7	even	3	inner	324.3.f.r.55.5		12
12.11	even	2		324.3.f.q.271.2		12
36.7	odd	6	inner	324.3.f.r.55.3		12
36.11	even	6		324.3.f.q.55.4		12
36.23	even	6		324.3.d.f.163.5	yes	6
36.31	odd	6		324.3.d.e.163.2	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
324.3.d.e.163.1	✓	6	9.4	even	3
324.3.d.e.163.2	yes	6	36.31	odd	6
324.3.d.f.163.5	yes	6	36.23	even	6
324.3.d.f.163.6	yes	6	9.5	odd	6
324.3.f.q.55.2		12	9.2	odd	6
324.3.f.q.55.4		12	36.11	even	6
324.3.f.q.271.2		12	12.11	even	2
324.3.f.q.271.4		12	3.2	odd	2
324.3.f.r.55.3		12	36.7	odd	6	inner
324.3.f.r.55.5		12	9.7	even	3	inner
324.3.f.r.271.3		12	1.1	even	1	trivial
324.3.f.r.271.5		12	4.3	odd	2	inner

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:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	324.f (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.0560770 + 1.99921i) q^{2} +(-3.99371 + 0.224220i) q^{4} +(-0.931627 + 1.61363i) q^{5} +(9.80189 - 5.65913i) q^{7} +(-0.672219 - 7.97171i) q^{8} +O(q^{10})\)	\(q+(0.0560770 + 1.99921i) q^{2} +(-3.99371 + 0.224220i) q^{4} +(-0.931627 + 1.61363i) q^{5} +(9.80189 - 5.65913i) q^{7} +(-0.672219 - 7.97171i) q^{8} +(-3.27823 - 1.77203i) q^{10} +(5.08539 - 2.93605i) q^{11} +(6.96926 - 12.0711i) q^{13} +(11.8635 + 19.2787i) q^{14} +(15.8995 - 1.79094i) q^{16} -11.0753 q^{17} -9.34459i q^{19} +(3.35884 - 6.65324i) q^{20} +(6.15496 + 10.0021i) q^{22} +(26.3984 + 15.2411i) q^{23} +(10.7641 + 18.6440i) q^{25} +(24.5236 + 13.2561i) q^{26} +(-37.8770 + 24.7987i) q^{28} +(22.7710 + 39.4406i) q^{29} +(-42.9526 - 24.7987i) q^{31} +(4.47206 + 31.6860i) q^{32} +(-0.621068 - 22.1418i) q^{34} +21.0888i q^{35} +48.9848 q^{37} +(18.6818 - 0.524016i) q^{38} +(13.4896 + 6.34195i) q^{40} +(7.44787 - 12.9001i) q^{41} +(-4.34763 + 2.51011i) q^{43} +(-19.6512 + 12.8660i) q^{44} +(-28.9899 + 53.6308i) q^{46} +(71.9894 - 41.5631i) q^{47} +(39.5514 - 68.5051i) q^{49} +(-36.6698 + 22.5653i) q^{50} +(-25.1266 + 49.7712i) q^{52} -53.6036 q^{53} +10.9412i q^{55} +(-51.7019 - 74.3337i) q^{56} +(-77.5732 + 47.7359i) q^{58} +(-85.1674 - 49.1714i) q^{59} +(-10.2103 - 17.6847i) q^{61} +(47.1692 - 87.2621i) q^{62} +(-63.0962 + 10.7175i) q^{64} +(12.9855 + 22.4916i) q^{65} +(14.9296 + 8.61963i) q^{67} +(44.2314 - 2.48329i) q^{68} +(-42.1610 + 1.18260i) q^{70} +52.6439i q^{71} +98.1594 q^{73} +(2.74692 + 97.9311i) q^{74} +(2.09524 + 37.3196i) q^{76} +(33.2309 - 57.5577i) q^{77} +(2.63838 - 1.52327i) q^{79} +(-11.9225 + 27.3242i) q^{80} +(26.2077 + 14.1665i) q^{82} +(-88.2594 + 50.9566i) q^{83} +(10.3180 - 17.8713i) q^{85} +(-5.26204 - 8.55108i) q^{86} +(-26.8238 - 38.5655i) q^{88} +17.0580 q^{89} -157.760i q^{91} +(-108.845 - 54.9496i) q^{92} +(87.1305 + 141.591i) q^{94} +(15.0787 + 8.70567i) q^{95} +(26.0051 + 45.0422i) q^{97} +(139.174 + 75.2302i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + q^{2} + 3 q^{4} + 2 q^{5} - 14 q^{8}+O(q^{10}) \) 12 * q + q^2 + 3 * q^4 + 2 * q^5 - 14 * q^8	\( 12 q + q^{2} + 3 q^{4} + 2 q^{5} - 14 q^{8} + 18 q^{10} - 6 q^{13} + 15 q^{16} + 20 q^{17} - 67 q^{20} - 48 q^{22} + 146 q^{26} - 96 q^{28} - 22 q^{29} + 31 q^{32} - 81 q^{34} + 108 q^{37} + 168 q^{38} + 81 q^{40} + 92 q^{41} - 336 q^{44} + 240 q^{46} + 66 q^{49} - 48 q^{50} + 117 q^{52} - 232 q^{53} - 312 q^{56} - 201 q^{58} - 54 q^{61} + 624 q^{62} - 510 q^{64} + 82 q^{65} + 53 q^{68} - 264 q^{70} - 156 q^{73} + 383 q^{74} + 192 q^{76} - 168 q^{77} - 754 q^{80} + 300 q^{82} - 66 q^{85} - 144 q^{86} + 336 q^{88} + 500 q^{89} - 504 q^{92} - 216 q^{94} + 204 q^{97} + 814 q^{98}+O(q^{100}) \) 12 * q + q^2 + 3 * q^4 + 2 * q^5 - 14 * q^8 + 18 * q^10 - 6 * q^13 + 15 * q^16 + 20 * q^17 - 67 * q^20 - 48 * q^22 + 146 * q^26 - 96 * q^28 - 22 * q^29 + 31 * q^32 - 81 * q^34 + 108 * q^37 + 168 * q^38 + 81 * q^40 + 92 * q^41 - 336 * q^44 + 240 * q^46 + 66 * q^49 - 48 * q^50 + 117 * q^52 - 232 * q^53 - 312 * q^56 - 201 * q^58 - 54 * q^61 + 624 * q^62 - 510 * q^64 + 82 * q^65 + 53 * q^68 - 264 * q^70 - 156 * q^73 + 383 * q^74 + 192 * q^76 - 168 * q^77 - 754 * q^80 + 300 * q^82 - 66 * q^85 - 144 * q^86 + 336 * q^88 + 500 * q^89 - 504 * q^92 - 216 * q^94 + 204 * q^97 + 814 * q^98

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