LMFDB - Embedded newform 324.3.f.r.271.5

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			271.5
Root			$1.08837 - 0.903022i$ of defining polynomial
Character	$\chi$	$=$	324.271
Dual form			324.3.f.r.55.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.70333 + 1.04817i) q^{2} +(1.80268 + 3.57076i) q^{4} +(-0.931627 + 1.61363i) q^{5} +(-9.80189 + 5.65913i) q^{7} +(-0.672219 + 7.97171i) q^{8} +O(q^{10})$	\(q+(1.70333 + 1.04817i) q^{2} +(1.80268 + 3.57076i) q^{4} +(-0.931627 + 1.61363i) q^{5} +(-9.80189 + 5.65913i) q^{7} +(-0.672219 + 7.97171i) q^{8} +(-3.27823 + 1.77203i) q^{10} +(-5.08539 + 2.93605i) q^{11} +(6.96926 - 12.0711i) q^{13} +(-22.6276 - 0.634694i) q^{14} +(-9.50072 + 12.8739i) q^{16} -11.0753 q^{17} +9.34459i q^{19} +(-7.44130 - 0.417779i) q^{20} +(-11.7396 - 0.329290i) q^{22} +(-26.3984 - 15.2411i) q^{23} +(10.7641 + 18.6440i) q^{25} +(24.5236 - 13.2561i) q^{26} +(-37.8770 - 24.7987i) q^{28} +(22.7710 + 39.4406i) q^{29} +(42.9526 + 24.7987i) q^{31} +(-29.6769 + 11.9701i) q^{32} +(-18.8648 - 11.6088i) q^{34} -21.0888i q^{35} +48.9848 q^{37} +(-9.79472 + 15.9169i) q^{38} +(-12.2371 - 8.51137i) q^{40} +(7.44787 - 12.9001i) q^{41} +(4.34763 - 2.51011i) q^{43} +(-19.6512 - 12.8660i) q^{44} +(-28.9899 - 53.6308i) q^{46} +(-71.9894 + 41.5631i) q^{47} +(39.5514 - 68.5051i) q^{49} +(-1.20724 + 43.0396i) q^{50} +(55.6664 + 3.12529i) q^{52} -53.6036 q^{53} -10.9412i q^{55} +(-38.5239 - 81.9420i) q^{56} +(-2.55386 + 91.0483i) q^{58} +(85.1674 + 49.1714i) q^{59} +(-10.2103 - 17.6847i) q^{61} +(47.1692 + 87.2621i) q^{62} +(-63.0962 - 10.7175i) q^{64} +(12.9855 + 22.4916i) q^{65} +(-14.9296 - 8.61963i) q^{67} +(-19.9651 - 39.5472i) q^{68} +(22.1046 - 35.9212i) q^{70} -52.6439i q^{71} +98.1594 q^{73} +(83.4373 + 51.3444i) q^{74} +(-33.3673 + 16.8453i) q^{76} +(33.2309 - 57.5577i) q^{77} +(-2.63838 + 1.52327i) q^{79} +(-11.9225 - 27.3242i) q^{80} +(26.2077 - 14.1665i) q^{82} +(88.2594 - 50.9566i) q^{83} +(10.3180 - 17.8713i) q^{85} +(10.0365 + 0.281518i) q^{86} +(-19.9868 - 42.5129i) q^{88} +17.0580 q^{89} +157.760i q^{91} +(6.83473 - 121.737i) q^{92} +(-166.187 - 4.66147i) q^{94} +(-15.0787 - 8.70567i) q^{95} +(26.0051 + 45.0422i) q^{97} +(139.174 - 75.2302i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.70333	+	1.04817i	0.851666	+	0.524085i
$2$	1.70333	+	1.04817i	0.851666	+	0.524085i
$3$		0			0
$3$		0			0
$4$	1.80268	+	3.57076i	0.450669	+	0.892691i
$5$	−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	−0.994420	−	0.105493i	$-0.966358\pi$
$7$	−9.80189	+	5.65913i	−1.40027	+	0.808447i	−0.405851	+	0.913939i	$0.633025\pi$
$8$	−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	−0.713014	−	0.701150i	$-0.752670\pi$
$11$	−5.08539	+	2.93605i	−0.462308	+	0.266914i	0.250706	+	0.968063i	$0.419337\pi$
$12$		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	$-0.0134352\pi$
$14$	−22.6276	−	0.634694i	−1.61626	−	0.0453353i
$15$		0			0
$16$	−9.50072	+	12.8739i	−0.593795	+	0.804616i
$17$	−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	$0.0790868\pi$
$19$			9.34459i			0.491820i	−0.969293	+	0.245910i	$0.920913\pi$
$20$	−7.44130	−	0.417779i	−0.372065	−	0.0208889i
$21$		0			0
$22$	−11.7396	−	0.329290i	−0.533617	−	0.0149677i
$23$	−26.3984	−	15.2411i	−1.14776	−	0.662658i	−0.199418	−	0.979915i	$-0.563905\pi$
$23$	−26.3984	−	15.2411i	−1.14776	−	0.662658i	−0.948340	+	0.317257i	$0.897238\pi$
$24$		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	0.992812	−	0.119685i	$-0.0381885\pi$
$31$	42.9526	+	24.7987i	1.38557	+	0.799958i	0.392756	+	0.919643i	$0.371522\pi$
$32$	−29.6769	+	11.9701i	−0.927403	+	0.374065i
$33$		0			0
$34$	−18.8648	−	11.6088i	−0.554848	−	0.341435i
$35$		−	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	$0.269726\pi$
$38$	−9.79472	+	15.9169i	−0.257756	+	0.418866i
$39$		0			0
$40$	−12.2371	−	8.51137i	−0.305927	−	0.212784i
$41$	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	−0.448594	−	0.893736i	$-0.648075\pi$
$43$	4.34763	−	2.51011i	0.101108	−	0.0583745i	0.549701	+	0.835361i	$0.314742\pi$
$44$	−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	$0.678712\pi$
$47$	−71.9894	+	41.5631i	−1.53169	+	0.884321i	−0.999284	+	0.0378317i	$0.987955\pi$
$48$		0			0
$49$	39.5514	−	68.5051i	0.807172	−	1.39806i
$50$	−1.20724	+	43.0396i	−0.0241448	+	0.860793i
$51$		0			0
$52$	55.6664	+	3.12529i	1.07051	+	0.0601018i
$53$	−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
$56$	−38.5239	−	81.9420i	−0.687926	−	1.46325i
$57$		0			0
$58$	−2.55386	+	91.0483i	−0.0440321	+	1.56980i
$59$	85.1674	+	49.1714i	1.44352	+	0.833414i	0.998082	−	0.0619007i	$-0.0197162\pi$
$59$	85.1674	+	49.1714i	1.44352	+	0.833414i	0.445434	+	0.895315i	$0.353050\pi$
$60$		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	0.384430	−	0.923154i	$-0.374398\pi$
$67$	−14.9296	−	8.61963i	−0.222830	−	0.128651i	−0.607260	+	0.794503i	$0.707731\pi$
$68$	−19.9651	−	39.5472i	−0.293605	−	0.581576i
$69$		0			0
$70$	22.1046	−	35.9212i	0.315781	−	0.513160i
$71$		−	52.6439i		−	0.741464i	−0.928740	−	0.370732i	$-0.879107\pi$
$71$		−	52.6439i		−	0.741464i	0.928740	−	0.370732i	$-0.120893\pi$
$72$		0			0
$73$	98.1594			1.34465			0.672325	−	0.740256i	$-0.265296\pi$
$73$	98.1594			1.34465			0.672325	+	0.740256i	$0.265296\pi$
$74$	83.4373	+	51.3444i	1.12753	+	0.693844i
$75$		0			0
$76$	−33.3673	+	16.8453i	−0.439044	+	0.221648i
$77$	33.2309	−	57.5577i	0.431571	−	0.747502i
$78$		0			0
$79$	−2.63838	+	1.52327i	−0.0333973	+	0.0192819i	−0.516606	−	0.856223i	$-0.672805\pi$
$79$	−2.63838	+	1.52327i	−0.0333973	+	0.0192819i	0.483208	+	0.875505i	$0.339471\pi$
$80$	−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	0.137005	−	0.990570i	$-0.456252\pi$
$83$	88.2594	−	50.9566i	1.06337	−	0.613935i	0.926362	+	0.376636i	$0.122919\pi$
$84$		0			0
$85$	10.3180	−	17.8713i	0.121388	−	0.210251i
$86$	10.0365	+	0.281518i	0.116703	+	0.00327347i
$87$		0			0
$88$	−19.9868	−	42.5129i	−0.227123	−	0.483101i
$89$	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
$92$	6.83473	−	121.737i	0.0742905	−	1.32323i
$93$		0			0
$94$	−166.187	−	4.66147i	−1.76795	−	0.0495901i
$95$	−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	0.559173	−	0.829051i	$-0.311119\pi$
$103$	12.4403	+	7.18240i	0.120779	+	0.0697320i	−0.438393	+	0.898783i	$0.644452\pi$
$104$	91.5425	+	63.6713i	0.880217	+	0.612224i
$105$		0			0
$106$	−91.3046	−	56.1857i	−0.861364	−	0.530054i
$107$			94.8704i			0.886639i	0.896364	+	0.443320i	$0.146199\pi$
$107$			94.8704i			0.886639i	−0.896364	+	0.443320i	$0.853801\pi$
$108$		0			0
$109$	12.5332			0.114983			0.0574917	−	0.998346i	$-0.481690\pi$
$109$	12.5332			0.114983			0.0574917	+	0.998346i	$0.481690\pi$
$110$	11.4683	−	18.6365i	0.104257	−	0.169423i
$111$		0			0
$112$	20.2703	−	179.954i	0.180985	−	1.60673i
$113$	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
$122$	1.14512	−	40.8250i	0.00938625	−	0.334631i
$123$		0			0
$124$	−11.1207	+	198.078i	−0.0896832	+	1.59740i
$125$	−86.6940			−0.693552
$126$		0			0
$127$			56.2142i			0.442632i	0.975202	+	0.221316i	$0.0710352\pi$
$127$			56.2142i			0.442632i	−0.975202	+	0.221316i	$0.928965\pi$
$128$	−96.2401	−	84.3910i	−0.751876	−	0.659305i
$129$		0			0
$130$	−1.45638	+	51.9216i	−0.0112029	+	0.399397i
$131$	44.7042	+	25.8100i	0.341253	+	0.197023i	0.660826	−	0.750539i	$-0.270206\pi$
$131$	44.7042	+	25.8100i	0.341253	+	0.197023i	−0.319573	+	0.947562i	$0.603539\pi$
$132$		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	0.316378	−	0.948633i	$-0.397533\pi$
$139$	−48.2294	−	27.8452i	−0.346974	−	0.200325i	−0.663352	+	0.748308i	$0.730867\pi$
$140$	75.3031	−	38.0162i	0.537879	−	0.271544i
$141$		0			0
$142$	55.1798	−	89.6701i	0.388590	−	0.631479i
$143$			81.8484i			0.572366i
$144$		0			0
$145$	−84.8565			−0.585217
$146$	167.198	+	102.888i	1.14519	+	0.704711i
$147$		0			0
$148$	88.3037	+	174.913i	0.596646	+	1.18185i
$149$	−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	−0.751781	−	0.659413i	$-0.770805\pi$
$151$	−84.0469	+	48.5245i	−0.556602	+	0.321354i	0.195178	+	0.980768i	$0.437471\pi$
$152$	−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	$0.285995\pi$
$158$	−6.09069	−	0.170841i	−0.0385487	−	0.00108127i
$159$		0			0
$160$	8.33259	−	59.0390i	0.0520787	−	0.368994i
$161$	345.006			2.14289
$162$		0			0
$163$		−	311.572i		−	1.91149i	−0.294204	−	0.955743i	$-0.595055\pi$
$163$		−	311.572i		−	1.91149i	0.294204	−	0.955743i	$-0.404945\pi$
$164$	59.4893	+	3.33992i	0.362740	+	0.0203654i
$165$		0			0
$166$	203.746	+	5.71499i	1.22739	+	0.0344276i
$167$	84.0608	+	48.5325i	0.503358	+	0.290614i	0.730099	−	0.683341i	$-0.239474\pi$
$167$	84.0608	+	48.5325i	0.503358	+	0.290614i	−0.226741	+	0.973955i	$0.572807\pi$
$168$		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
$176$	10.5166	−	93.3631i	0.0597532	−	0.530472i
$177$		0			0
$178$	29.0554	+	17.8797i	0.163233	+	0.100448i
$179$		−	176.768i		−	0.987529i	−0.869596	−	0.493764i	$-0.835621\pi$
$179$		−	176.768i		−	0.987529i	0.869596	−	0.493764i	$-0.164379\pi$
$180$		0			0
$181$	−163.621			−0.903985			−0.451993	−	0.892022i	$-0.649287\pi$
$181$	−163.621			−0.903985			−0.451993	+	0.892022i	$0.649287\pi$
$182$	−165.359	+	268.717i	−0.908567	+	1.47647i
$183$		0			0
$184$	139.243	−	200.195i	0.756758	−	1.08802i
$185$	−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	−0.785915	−	0.618334i	$-0.787808\pi$
$191$	−122.886	+	70.9480i	−0.643380	+	0.371456i	0.142535	+	0.989790i	$0.454475\pi$
$192$		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	$0.132172\pi$
$194$	−2.91658	+	103.980i	−0.0150339	+	0.535978i
$195$		0			0
$196$	315.914	+	17.7364i	1.61181	+	0.0904920i
$197$	−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	$-0.859852\pi$
$199$		−	169.627i		−	0.852397i	0.904630	−	0.426199i	$-0.140148\pi$
$200$	−155.861	+	73.2757i	−0.779303	+	0.366379i
$201$		0			0
$202$	3.90048	−	139.057i	0.0193093	−	0.688401i
$203$	−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	0.954925	−	0.296848i	$-0.0959354\pi$
$211$	247.990	+	143.177i	1.17531	+	0.678565i	0.220385	+	0.975413i	$0.429269\pi$
$212$	−96.6298	−	191.406i	−0.455801	−	0.902857i
$213$		0			0
$214$	−99.4404	+	161.596i	−0.464675	+	0.755120i
$215$			9.35393i			0.0435066i
$216$		0			0
$217$	−561.356			−2.58689
$218$	21.3482	+	13.1369i	0.0979275	+	0.0602612i
$219$		0			0
$220$	39.0685	−	19.7235i	0.177584	−	0.0896521i
$221$	−77.1864	+	133.691i	−0.349260	+	0.604936i
$222$		0			0
$223$	279.305	−	161.257i	1.25249	−	0.723124i	0.280885	−	0.959742i	$-0.409372\pi$
$223$	279.305	−	161.257i	1.25249	−	0.723124i	0.971603	+	0.236618i	$0.0760389\pi$
$224$	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	−0.612210	−	0.790695i	$-0.709719\pi$
$227$	−53.0167	+	30.6092i	−0.233554	+	0.134842i	0.378657	+	0.925537i	$0.376386\pi$
$228$		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	$0.878501\pi$
$230$	113.548	+	3.18496i	0.493686	+	0.0138477i
$231$		0			0
$232$	−329.716	+	155.011i	−1.42119	+	0.668152i
$233$	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
$236$	−22.0504	+	392.753i	−0.0934340	+	1.66421i
$237$		0			0
$238$	250.607	+	7.02940i	1.05297	+	0.0295353i
$239$	−15.3913	−	8.88617i	−0.0643988	−	0.0371806i	0.467455	−	0.884017i	$-0.345171\pi$
$239$	−15.3913	−	8.88617i	−0.0643988	−	0.0371806i	−0.531854	+	0.846836i	$0.678504\pi$
$240$		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
$248$	−226.561	+	325.735i	−0.913554	+	1.31345i
$249$		0			0
$250$	−147.669	−	90.8702i	−0.590675	−	0.363481i
$251$			221.345i			0.881852i	0.897543	+	0.440926i	$0.145350\pi$
$251$			221.345i			0.881852i	−0.897543	+	0.440926i	$0.854650\pi$
$252$		0			0
$253$	178.995			0.707490
$254$	−58.9221	+	95.7514i	−0.231977	+	0.376974i
$255$		0			0
$256$	−75.4725	−	244.622i	−0.294814	−	0.955555i
$257$	−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	0.491747	−	0.870738i	$-0.336358\pi$
$263$	392.318	−	226.505i	1.49170	−	0.861234i	0.999955	+	0.00950362i	$0.00302514\pi$
$264$		0			0
$265$	49.9385	−	86.4961i	0.188447	−	0.326400i
$266$	5.93095	−	211.446i	0.0222968	−	0.794908i
$267$		0			0
$268$	3.86538	−	68.8486i	0.0144231	−	0.256898i
$269$	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	$0.0148480\pi$
$271$			25.2731i			0.0932588i	−0.998912	+	0.0466294i	$0.985152\pi$
$272$	105.223	−	142.581i	0.386849	−	0.524196i
$273$		0			0
$274$	−0.527894	+	18.8201i	−0.00192662	+	0.0686864i
$275$	−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	−0.0891949	−	0.996014i	$-0.528429\pi$
$283$	−281.972	−	162.796i	−0.996366	−	0.575252i	−0.907171	+	0.420762i	$0.861763\pi$
$284$	187.979	−	94.8999i	0.661898	−	0.334155i
$285$		0			0
$286$	−85.7911	+	139.415i	−0.299969	+	0.487465i
$287$			168.594i			0.587435i
$288$		0			0
$289$	−166.338			−0.575566
$290$	−144.539	−	88.9441i	−0.498409	−	0.306704i
$291$		0			0
$292$	176.950	+	350.504i	0.605992	+	1.20036i
$293$	−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
$302$	−194.022	−	5.44222i	−0.642456	−	0.0180206i
$303$		0			0
$304$	−120.301	−	88.7803i	−0.395727	−	0.292041i
$305$	38.0486			0.124750
$306$		0			0
$307$			193.311i			0.629678i	0.949145	+	0.314839i	$0.101950\pi$
$307$			193.311i			0.629678i	−0.949145	+	0.314839i	$0.898050\pi$
$308$	265.430	+	14.9021i	0.861784	+	0.0483834i
$309$		0			0
$310$	−184.752	−	5.18222i	−0.595976	−	0.0167168i
$311$	132.119	+	76.2790i	0.424820	+	0.245270i	0.697138	−	0.716937i	$-0.254457\pi$
$311$	132.119	+	76.2790i	0.424820	+	0.245270i	−0.272317	+	0.962208i	$0.587790\pi$
$312$		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
$320$	76.0761	−	91.8290i	0.237738	−	0.286966i
$321$		0			0
$322$	587.660	+	361.625i	1.82503	+	1.12306i
$323$		−	103.494i		−	0.320414i
$324$		0			0
$325$	300.072			0.923300
$326$	326.581	−	530.710i	1.00178	−	1.62795i
$327$		0			0
$328$	97.8292	+	68.0439i	0.298260	+	0.207451i
$329$	470.422	−	814.794i	1.42985	−	2.47658i
$330$		0			0
$331$	135.318	−	78.1258i	0.408815	−	0.236030i	−0.281465	−	0.959571i	$-0.590820\pi$
$331$	135.318	−	78.1258i	0.408815	−	0.236030i	0.690281	+	0.723542i	$0.257487\pi$
$332$	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	$0.0348043\pi$
$338$	1.41776	−	50.5449i	0.00419456	−	0.149541i
$339$		0			0
$340$	82.4144	+	4.62701i	0.242395	+	0.0136089i
$341$	−291.241			−0.854078
$342$		0			0
$343$			340.712i			0.993328i
$344$	17.0873	+	36.3454i	0.0496723	+	0.105655i
$345$		0			0
$346$	5.98769	−	213.469i	0.0173055	−	0.616961i
$347$	300.561	+	173.529i	0.866171	+	0.500084i	0.866074	−	0.499916i	$-0.166636\pi$
$347$	300.561	+	173.529i	0.866171	+	0.500084i	9.73706e−5		1.00000i	$0.499969\pi$
$348$		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
$356$	30.7500	+	60.9100i	0.0863764	+	0.171096i
$357$		0			0
$358$	185.283	−	301.094i	0.517550	−	0.841044i
$359$		−	414.158i		−	1.15364i	−0.816871	−	0.576821i	$-0.804293\pi$
$359$		−	414.158i		−	1.15364i	0.816871	−	0.576821i	$-0.195707\pi$
$360$		0			0
$361$	273.679			0.758113
$362$	−278.701	−	171.503i	−0.769893	−	0.473765i
$363$		0			0
$364$	−563.323	+	284.390i	−1.54759	+	0.781290i
$365$	−91.4480	+	158.393i	−0.250542	+	0.433952i
$366$		0			0
$367$	275.106	−	158.833i	0.749608	−	0.432786i	−0.0759443	−	0.997112i	$-0.524197\pi$
$367$	275.106	−	158.833i	0.749608	−	0.432786i	0.825552	+	0.564326i	$0.190864\pi$
$368$	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	$0.212368\pi$
$374$	130.019	+	3.64697i	0.347644	+	0.00975126i
$375$		0			0
$376$	−282.936	−	601.818i	−0.752490	−	1.60058i
$377$	634.789			1.68379
$378$		0			0
$379$			33.8080i			0.0892033i	0.999005	+	0.0446016i	$0.0142019\pi$
$379$			33.8080i			0.0892033i	−0.999005	+	0.0446016i	$0.985798\pi$
$380$	3.90397	−	69.5358i	0.0102736	−	0.182989i
$381$		0			0
$382$	−283.681	−	7.95711i	−0.742619	−	0.0208301i
$383$	159.158	+	91.8901i	0.415557	+	0.239922i	0.693175	−	0.720770i	$-0.256211\pi$
$383$	159.158	+	91.8901i	0.415557	+	0.239922i	−0.277618	+	0.960692i	$0.589545\pi$
$384$		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
$392$	519.515	+	361.343i	1.32529	+	0.921793i
$393$		0			0
$394$	−290.393	−	178.698i	−0.737039	−	0.453548i
$395$		−	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	$0.236216\pi$
$398$	177.798	−	288.931i	0.446729	−	0.725958i
$399$		0			0
$400$	−342.288	−	38.5558i	−0.855720	−	0.0963896i
$401$	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	$0.0336595\pi$
$410$	−1.55639	+	55.4873i	−0.00379608	+	0.135335i
$411$		0			0
$412$	−3.22087	+	57.3688i	−0.00781765	+	0.139245i
$413$	−1113.07			−2.69508
$414$		0			0
$415$			189.890i			0.457567i
$416$	−62.3339	+	441.656i	−0.149841	+	1.06167i
$417$		0			0
$418$	3.07708	−	109.702i	0.00736143	−	0.262444i
$419$	606.327	+	350.063i	1.44708	+	0.835472i	0.998307	−	0.0581732i	$-0.0185276\pi$
$419$	606.327	+	350.063i	1.44708	+	0.835472i	0.448774	+	0.893645i	$0.351861\pi$
$420$		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
$428$	−338.760	+	171.021i	−0.791495	+	0.399581i
$429$		0			0
$430$	−9.80452	+	15.9328i	−0.0228012	+	0.0370531i
$431$			535.531i			1.24253i	0.783600	+	0.621265i	$0.213381\pi$
$431$			535.531i			1.24253i	−0.783600	+	0.621265i	$0.786619\pi$
$432$		0			0
$433$	151.504			0.349895			0.174947	−	0.984578i	$-0.444024\pi$
$433$	151.504			0.349895			0.174947	+	0.984578i	$0.444024\pi$
$434$	−956.175	−	588.397i	−2.20317	−	1.35575i
$435$		0			0
$436$	22.5933	+	44.7531i	0.0518195	+	0.102645i
$437$	142.422	−	246.682i	0.325909	−	0.564490i
$438$		0			0
$439$	−76.5284	+	44.1837i	−0.174324	+	0.100646i	−0.584623	−	0.811305i	$-0.698758\pi$
$439$	−76.5284	+	44.1837i	−0.174324	+	0.100646i	0.410299	+	0.911951i	$0.365424\pi$
$440$	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	−0.505785	−	0.862659i	$-0.668797\pi$
$443$	−5.13583	+	2.96517i	−0.0115933	+	0.00669339i	0.494192	+	0.869353i	$0.335464\pi$
$444$		0			0
$445$	−15.8917	+	27.5252i	−0.0357116	+	0.0618544i
$446$	644.773	+	18.0856i	1.44568	+	0.0405506i
$447$		0			0
$448$	679.114	−	252.018i	1.51588	−	0.562541i
$449$	−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
$452$	528.598	+	29.6772i	1.16946	+	0.0656575i
$453$		0			0
$454$	−122.389	−	3.43295i	−0.269579	−	0.00756155i
$455$	−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	0.814914	−	0.579582i	$-0.196784\pi$
$463$	333.562	+	192.582i	0.720437	+	0.415945i	−0.0944763	+	0.995527i	$0.530118\pi$
$464$	−724.094	−	81.5630i	−1.56055	−	0.175782i
$465$		0			0
$466$	199.178	+	122.567i	0.427421	+	0.263020i
$467$		−	563.818i		−	1.20732i	−0.797243	−	0.603659i	$-0.793709\pi$
$467$		−	563.818i		−	1.20732i	0.797243	−	0.603659i	$-0.206291\pi$
$468$		0			0
$469$	195.118			0.416030
$470$	162.346	−	263.821i	0.345417	−	0.561321i
$471$		0			0
$472$	−449.232	+	645.876i	−0.951762	+	1.36838i
$473$	−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	−0.864910	−	0.501926i	$-0.832625\pi$
$479$	−413.226	+	238.576i	−0.862685	+	0.498071i	0.00222581	+	0.999998i	$0.499292\pi$
$480$		0			0
$481$	341.388	−	591.301i	0.709746	−	1.22932i
$482$	−12.7284	+	453.781i	−0.0264074	+	0.941455i
$483$		0			0
$484$	−345.530	−	19.3992i	−0.713904	−	0.0400809i
$485$	−96.9084			−0.199811
$486$		0			0
$487$		−	432.682i		−	0.888464i	−0.895912	−	0.444232i	$-0.853477\pi$
$487$		−	432.682i		−	0.888464i	0.895912	−	0.444232i	$-0.146523\pi$
$488$	147.841	−	69.5053i	0.302952	−	0.142429i
$489$		0			0
$490$	−8.26512	+	294.662i	−0.0168676	+	0.601350i
$491$	331.698	+	191.506i	0.675557	+	0.390033i	0.798179	−	0.602421i	$-0.205797\pi$
$491$	331.698	+	191.506i	0.675557	+	0.390033i	−0.122622	+	0.992453i	$0.539130\pi$
$492$		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	0.0596617	−	0.998219i	$-0.480998\pi$
$499$	−386.720	−	223.273i	−0.774990	−	0.447441i	−0.834652	+	0.550778i	$0.814331\pi$
$500$	−156.281	−	309.564i	−0.312562	−	0.619128i
$501$		0			0
$502$	−232.007	+	377.024i	−0.462166	+	0.751043i
$503$		−	488.145i		−	0.970467i	−0.874385	−	0.485234i	$-0.838735\pi$
$503$		−	488.145i		−	0.970467i	0.874385	−	0.485234i	$-0.161265\pi$
$504$		0			0
$505$	129.600			0.256634
$506$	304.888	+	187.617i	0.602545	+	0.370785i
$507$		0			0
$508$	−200.728	+	101.336i	−0.395133	+	0.199480i
$509$	−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
$518$	−1108.41	−	31.0903i	−2.13979	−	0.0600200i
$519$		0			0
$520$	−188.025	+	88.3974i	−0.361587	+	0.169995i
$521$	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	$0.352207\pi$
$523$			935.263i			1.78827i	−0.447802	+	0.894133i	$0.647793\pi$
$524$	−11.5742	+	206.155i	−0.0220882	+	0.393426i
$525$		0			0
$526$	905.662	+	25.4034i	1.72179	+	0.0482955i
$527$	−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
$536$	78.7491	−	113.220i	0.146920	−	0.211232i
$537$		0			0
$538$	150.746	+	92.7636i	0.280196	+	0.172423i
$539$			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	$0.278674\pi$
$542$	−26.4906	+	43.0485i	−0.0488756	+	0.0794253i
$543$		0			0
$544$	328.679	−	132.572i	0.604190	−	0.243698i
$545$	−11.6763	+	20.2239i	−0.0214243	+	0.0371080i
$546$		0			0
$547$	−332.640	+	192.050i	−0.608117	+	0.351096i	−0.772228	−	0.635345i	$-0.780858\pi$
$547$	−332.640	+	192.050i	−0.608117	+	0.351096i	0.164111	+	0.986442i	$0.447524\pi$
$548$	−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
$554$	14.5967	−	520.392i	0.0263479	−	0.939335i
$555$		0			0
$556$	12.4869	−	222.412i	0.0224585	−	0.400021i
$557$	−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
$560$	271.494	+	200.359i	0.484811	+	0.357783i
$561$		0			0
$562$	9.32616	−	332.489i	0.0165946	−	0.591618i
$563$	−882.086	−	509.273i	−1.56676	−	0.904570i	−0.996543	−	0.0830764i	$-0.973525\pi$
$563$	−882.086	−	509.273i	−1.56676	−	0.904570i	−0.570218	−	0.821493i	$-0.693141\pi$
$564$		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	0.627369	−	0.778722i	$-0.284132\pi$
$571$	152.264	+	87.9094i	0.266661	+	0.153957i	−0.360708	+	0.932679i	$0.617465\pi$
$572$	−292.261	+	147.546i	−0.510946	+	0.257948i
$573$		0			0
$574$	−176.715	+	287.171i	−0.307866	+	0.500298i
$575$		−	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	$0.733983\pi$
$578$	−283.330	−	174.351i	−0.490189	−	0.301646i
$579$		0			0
$580$	−152.969	−	303.002i	−0.263739	−	0.522418i
$581$	−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	−0.157104	−	0.987582i	$-0.550216\pi$
$587$	363.714	−	209.990i	0.619615	−	0.357735i	0.776719	+	0.629847i	$0.216882\pi$
$588$		0			0
$589$	−231.733	+	401.374i	−0.393435	+	0.681450i
$590$	−366.332	−	10.2754i	−0.620901	−	0.0174160i
$591$		0			0
$592$	−465.391	+	630.623i	−0.786133	+	1.06524i
$593$	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
$596$	−944.675	−	53.0371i	−1.58503	−	0.0889884i
$597$		0			0
$598$	−849.421	−	23.8259i	−1.42044	−	0.0398426i
$599$	−289.090	−	166.906i	−0.482622	−	0.278642i	0.238887	−	0.971047i	$-0.423218\pi$
$599$	−289.090	−	166.906i	−0.482622	−	0.278642i	−0.721508	+	0.692406i	$0.756551\pi$
$600$		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	0.932793	−	0.360412i	$-0.117364\pi$
$607$	659.847	+	380.963i	1.08706	+	0.627616i	0.154270	+	0.988029i	$0.450697\pi$
$608$	−111.855	−	277.318i	−0.183973	−	0.456115i
$609$		0			0
$610$	64.8094	+	39.8815i	0.106245	+	0.0653795i
$611$			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	$0.645145\pi$
$614$	−202.623	+	329.273i	−0.330005	+	0.536275i
$615$		0			0
$616$	436.495	+	303.599i	0.708595	+	0.492855i
$617$	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	−0.111170	−	0.993801i	$-0.535460\pi$
$619$	429.526	−	247.987i	0.693903	−	0.400625i	0.805073	+	0.593176i	$0.202126\pi$
$620$	−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
$626$	−4.90400	+	174.833i	−0.00783386	+	0.279287i
$627$		0			0
$628$	−459.175	−	25.7796i	−0.731170	−	0.0410503i
$629$	−542.520			−0.862511
$630$		0			0
$631$		−	895.486i		−	1.41915i	−0.704628	−	0.709576i	$-0.748886\pi$
$631$		−	895.486i		−	1.41915i	0.704628	−	0.709576i	$-0.251114\pi$
$632$	−10.3695	−	22.0564i	−0.0164074	−	0.0348994i
$633$		0			0
$634$	16.3864	−	584.195i	0.0258461	−	0.921444i
$635$	−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	0.726628	−	0.687032i	$-0.241087\pi$
$643$	318.256	+	183.745i	0.494955	+	0.285762i	−0.231673	+	0.972794i	$0.574420\pi$
$644$	621.934	+	1231.94i	0.965736	+	1.91294i
$645$		0			0
$646$	108.479	−	176.284i	0.167924	−	0.272886i
$647$			762.797i			1.17897i	0.807778	+	0.589487i	$0.200670\pi$
$647$			762.797i			1.17897i	−0.807778	+	0.589487i	$0.799330\pi$
$648$		0			0
$649$	−577.479			−0.889798
$650$	511.123	+	314.527i	0.786343	+	0.483888i
$651$		0			0
$652$	1112.55	−	561.663i	1.70637	−	0.861447i
$653$	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	−0.624890	−	0.780713i	$-0.714856\pi$
$659$	−172.143	+	99.3866i	−0.261218	+	0.150814i	0.363672	+	0.931527i	$0.381523\pi$
$660$		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	$0.218849\pi$
$662$	312.380	+	8.76212i	0.471873	+	0.0132358i
$663$		0			0
$664$	346.881	+	737.832i	0.522412	+	1.11119i
$665$	197.066			0.296340
$666$		0			0
$667$		−	1388.23i		−	2.08130i
$668$	−21.7639	+	387.650i	−0.0325807	+	0.580314i
$669$		0			0
$670$	64.2170	+	1.80126i	0.0958462	+	0.00268844i
$671$	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
$680$	135.529	+	94.2657i	0.199307	+	0.138626i
$681$		0			0
$682$	−496.079	−	305.270i	−0.727389	−	0.447610i
$683$		−	1186.83i		−	1.73767i	−0.495103	−	0.868834i	$-0.664870\pi$
$683$		−	1186.83i		−	1.73767i	0.495103	−	0.868834i	$-0.335130\pi$
$684$		0			0
$685$	−17.5402			−0.0256061
$686$	−357.124	+	580.345i	−0.520589	+	0.845984i
$687$		0			0
$688$	−8.99089	+	79.8186i	−0.0130682	+	0.116015i
$689$	−373.577	+	647.055i	−0.542202	+	0.939121i
$690$		0			0
$691$	3.26716	−	1.88630i	0.00472817	−	0.00272981i	−0.497634	−	0.867387i	$-0.665798\pi$
$691$	3.26716	−	1.88630i	0.00472817	−	0.00272981i	0.502362	+	0.864657i	$0.332464\pi$
$692$	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
$698$	16.7409	−	596.833i	0.0239841	−	0.855062i
$699$		0			0
$700$	54.6340	−	973.118i	0.0780485	−	1.39017i
$701$	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
$704$	352.336	−	130.751i	0.500477	−	0.185726i
$705$		0			0
$706$	−31.8578	+	1135.77i	−0.0451243	+	1.60874i
$707$	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
$716$	631.196	−	318.655i	0.881558	−	0.445048i
$717$		0			0
$718$	434.108	−	705.448i	0.604607	−	0.982517i
$719$		−	500.230i		−	0.695730i	−0.937545	−	0.347865i	$-0.886907\pi$
$719$		−	500.230i		−	0.695730i	0.937545	−	0.347865i	$-0.113093\pi$
$720$		0			0
$721$	−162.584			−0.225498
$722$	466.166	+	286.862i	0.645659	+	0.397316i
$723$		0			0
$724$	−294.956	−	584.253i	−0.407398	−	0.806980i
$725$	−490.221	+	849.088i	−0.676167	+	1.17116i
$726$		0			0
$727$	541.817	−	312.818i	0.745278	−	0.430287i	−0.0787070	−	0.996898i	$-0.525079\pi$
$727$	541.817	−	312.818i	0.745278	−	0.430287i	0.823985	+	0.566611i	$0.191746\pi$
$728$	−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	$0.864050\pi$
$734$	635.081	+	17.8137i	0.865232	+	0.0242694i
$735$		0			0
$736$	965.860	+	136.319i	1.31231	+	0.185216i
$737$	101.231			0.137355
$738$		0			0
$739$		−	850.984i		−	1.15154i	−0.817613	−	0.575768i	$-0.804703\pi$
$739$		−	850.984i		−	1.15154i	0.817613	−	0.575768i	$-0.195297\pi$
$740$	−364.510	−	20.4648i	−0.492582	−	0.0276551i
$741$		0			0
$742$	1212.92	+	34.0218i	1.63466	+	0.0458515i
$743$	209.853	+	121.159i	0.282440	+	0.163067i	0.634527	−	0.772900i	$-0.281195\pi$
$743$	209.853	+	121.159i	0.282440	+	0.163067i	−0.352088	+	0.935967i	$0.614528\pi$
$744$		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	−0.462007	−	0.886876i	$-0.652871\pi$
$751$	−1097.26	−	633.505i	−1.46107	−	0.843548i	−0.999061	+	0.0433279i	$0.986204\pi$
$752$	148.874	−	1321.66i	0.197971	−	1.75753i
$753$		0			0
$754$	1081.26	+	665.368i	1.43403	+	0.882450i
$755$		−	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	$0.740059\pi$
$758$	−35.4366	+	57.5863i	−0.0467501	+	0.0759714i
$759$		0			0
$760$	79.5352	−	114.351i	0.104652	−	0.150461i
$761$	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	$-0.0411155\pi$
$770$	−6.94432	+	247.573i	−0.00901860	+	0.321524i
$771$		0			0
$772$	166.731	+	9.36084i	0.215973	+	0.0121254i
$773$	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
$776$	−376.545	+	177.027i	−0.485238	+	0.228128i
$777$		0			0
$778$	2.91815	−	104.036i	0.00375084	−	0.133722i
$779$	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	−0.440846	−	0.897583i	$-0.645321\pi$
$787$	−1132.18	−	653.663i	−1.43860	−	0.830575i	−0.997752	+	0.0670077i	$0.978655\pi$
$788$	−307.330	−	608.764i	−0.390013	−	0.772543i
$789$		0			0
$790$	5.94993	−	9.66893i	0.00753155	−	0.0122392i
$791$			1498.06i			1.89388i
$792$		0			0
$793$	−284.632			−0.358931
$794$	996.827	+	613.413i	1.25545	+	0.772560i
$795$		0			0
$796$	605.698	−	305.783i	0.760928	−	0.384149i
$797$	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
$806$	1382.08	+	38.7668i	1.71475	+	0.0480978i
$807$		0			0
$808$	503.571	−	236.747i	0.623232	−	0.293004i
$809$	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	$0.0230291\pi$
$811$			117.246i			0.144570i	−0.997384	+	0.0722851i	$0.976971\pi$
$812$	115.576	−	2058.58i	0.142335	−	2.53520i
$813$		0			0
$814$	−575.061	−	16.1302i	−0.706463	−	0.0198160i
$815$	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	0.439160	−	0.898409i	$-0.355276\pi$
$823$	−98.1876	−	56.6887i	−0.119305	−	0.0688805i	−0.558465	+	0.829528i	$0.688609\pi$
$824$	−65.6186	+	94.3421i	−0.0796342	+	0.114493i
$825$		0			0
$826$	−1895.93	−	1166.69i	−2.29531	−	1.41245i
$827$		−	467.270i		−	0.565018i	−0.959265	−	0.282509i	$-0.908833\pi$
$827$		−	467.270i		−	0.565018i	0.959265	−	0.282509i	$-0.0911667\pi$
$828$		0			0
$829$	−359.806			−0.434025			−0.217012	−	0.976169i	$-0.569631\pi$
$829$	−359.806			−0.434025			−0.217012	+	0.976169i	$0.569631\pi$
$830$	−199.037	+	323.446i	−0.239804	+	0.389694i
$831$		0			0
$832$	−569.106	+	686.949i	−0.684021	+	0.825660i
$833$	−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	−0.0677709	−	0.997701i	$-0.521589\pi$
$839$	639.635	−	369.294i	0.762378	−	0.440159i	0.830149	+	0.557542i	$0.188255\pi$
$840$		0			0
$841$	−616.540	+	1067.88i	−0.733104	+	1.26977i
$842$	−24.8748	+	886.816i	−0.0295425	+	1.05323i
$843$		0			0
$844$	−64.2064	+	1143.62i	−0.0760739	+	1.35500i
$845$	47.1075			0.0557485
$846$		0			0
$847$		−	979.238i		−	1.15612i
$848$	509.273	−	690.085i	0.600557	−	0.813779i
$849$		0			0
$850$	13.3705	−	476.675i	0.0157300	−	0.560795i
$851$	−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	0.869132	−	0.494581i	$-0.164678\pi$
$859$	751.950	+	434.138i	0.875378	+	0.505400i	0.00624629	+	0.999980i	$0.498012\pi$
$860$	−33.4007	+	16.8621i	−0.0388380	+	0.0196071i
$861$		0			0
$862$	−561.328	+	912.186i	−0.651192	+	1.05822i
$863$		−	136.786i		−	0.158500i	−0.996855	−	0.0792500i	$-0.974747\pi$
$863$		−	136.786i		−	0.158500i	0.996855	−	0.0792500i	$-0.0252526\pi$
$864$		0			0
$865$	198.951			0.230002
$866$	258.062	+	158.803i	0.297993	+	0.183375i
$867$		0			0
$868$	−1011.94	−	2004.47i	−1.16583	−	2.30930i
$869$	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	$0.308422\pi$
$878$	−176.665	−	4.95538i	−0.201213	−	0.00564394i
$879$		0			0
$880$	140.856	+	103.949i	0.160063	+	0.118124i
$881$	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	$0.161993\pi$
$883$			860.448i			0.974460i	−0.873274	+	0.487230i	$0.838007\pi$
$884$	−616.520	−	34.6135i	−0.697421	−	0.0391555i
$885$		0			0
$886$	−11.8560	−	0.332556i	−0.0133815	−	0.000375345i
$887$	1048.85	+	605.552i	1.18247	+	0.682697i	0.956584	−	0.291458i	$-0.0941402\pi$
$887$	1048.85	+	605.552i	1.18247	+	0.682697i	0.225882	+	0.974155i	$0.427474\pi$
$888$		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
$896$	1420.91	+	282.557i	1.58584	+	0.315354i
$897$		0			0
$898$	−371.912	−	228.862i	−0.414156	−	0.254857i
$899$			2258.77i			2.51253i
$900$		0			0
$901$	593.674			0.658905
$902$	−91.6827	+	148.989i	−0.101644	+	0.165176i
$903$		0			0
$904$	869.271	+	604.611i	0.961583	+	0.668818i
$905$	152.434	−	264.024i	0.168435	−	0.291739i
$906$		0			0
$907$	−278.678	+	160.895i	−0.307252	+	0.177392i	−0.645696	−	0.763594i	$-0.723433\pi$
$907$	−278.678	+	160.895i	−0.307252	+	0.177392i	0.338444	+	0.940987i	$0.390099\pi$
$908$	−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	0.481610	−	0.876386i	$-0.340052\pi$
$911$	1349.54	−	779.160i	1.48139	−	0.855279i	0.999777	+	0.0211061i	$0.00671877\pi$
$912$		0			0
$913$	−299.222	+	518.268i	−0.327735	+	0.567654i
$914$	5.94678	−	212.010i	0.00650633	−	0.231959i
$915$		0			0
$916$	−1438.80	−	80.7792i	−1.57075	−	0.0881869i
$917$	−584.248			−0.637129
$918$		0			0
$919$			1338.32i			1.45628i	0.685428	+	0.728140i	$0.259615\pi$
$919$			1338.32i			1.45628i	−0.685428	+	0.728140i	$0.740385\pi$
$920$	193.317	+	411.194i	0.210127	+	0.446950i
$921$		0			0
$922$	−11.3687	+	405.307i	−0.0123304	+	0.439595i
$923$	−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
$932$	210.795	+	417.546i	0.226175	+	0.448011i
$933$		0			0
$934$	590.977	−	960.368i	0.632738	−	1.02823i
$935$			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	$0.462917\pi$
$938$	332.351	+	204.517i	0.354319	+	0.218035i
$939$		0			0
$940$	553.059	−	279.208i	0.588360	−	0.297030i
$941$	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	−0.991370	−	0.131095i	$-0.958151\pi$
$947$	−1300.73	+	750.974i	−1.37352	+	0.793004i	−0.382153	+	0.924099i	$0.624817\pi$
$948$		0			0
$949$	684.098	−	1184.89i	0.720862	−	1.24857i
$950$	−402.188	−	11.2812i	−0.423355	−	0.0118749i
$951$		0			0
$952$	426.662	+	907.530i	0.448175	+	0.953287i
$953$	−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
$956$	3.98491	−	70.9776i	0.00416832	−	0.0742444i
$957$		0			0
$958$	−953.929	−	26.7573i	−0.995751	−	0.0279303i
$959$	−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	0.273167	−	0.961967i	$-0.411929\pi$
$967$	−409.368	−	236.349i	−0.423338	−	0.244414i	−0.696504	+	0.717553i	$0.745262\pi$
$968$	−568.218	−	395.217i	−0.587002	−	0.408282i
$969$		0			0
$970$	−165.067	−	101.577i	−0.170172	−	0.104718i
$971$		−	595.910i		−	0.613707i	−0.951757	−	0.306854i	$-0.900724\pi$
$971$		−	595.910i		−	0.613707i	0.951757	−	0.306854i	$-0.0992762\pi$
$972$		0			0
$973$	630.319			0.647810
$974$	453.525	−	737.001i	0.465631	−	0.756675i
$975$		0			0
$976$	324.675	+	36.5719i	0.332659	+	0.0374712i
$977$	−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	−0.977680	−	0.210100i	$-0.932621\pi$
$983$	−1262.73	+	729.038i	−1.28457	+	0.741645i	−0.306888	+	0.951746i	$0.599288\pi$
$984$		0			0
$985$	158.829	−	275.100i	0.161248	−	0.279289i
$986$	28.2847	−	1008.38i	0.0286863	−	1.02270i
$987$		0			0
$988$	−29.2046	+	520.180i	−0.0295593	+	0.526498i
$989$	−153.027			−0.154729
$990$		0			0
$991$		−	569.118i		−	0.574287i	−0.957888	−	0.287143i	$-0.907294\pi$
$991$		−	569.118i		−	0.574287i	0.957888	−	0.287143i	$-0.0927056\pi$
$992$	−1571.54	−	221.803i	−1.58421	−	0.223591i
$993$		0			0
$994$	−33.4128	+	1191.21i	−0.0336145	+	1.19840i
$995$	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.271.5		12
3.2	odd	2		324.3.f.q.271.2		12
4.3	odd	2	inner	324.3.f.r.271.3		12
9.2	odd	6		324.3.f.q.55.4		12
9.4	even	3		324.3.d.e.163.2	yes	6
9.5	odd	6		324.3.d.f.163.5	yes	6
9.7	even	3	inner	324.3.f.r.55.3		12
12.11	even	2		324.3.f.q.271.4		12
36.7	odd	6	inner	324.3.f.r.55.5		12
36.11	even	6		324.3.f.q.55.2		12
36.23	even	6		324.3.d.f.163.6	yes	6
36.31	odd	6		324.3.d.e.163.1	✓	6

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

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)

\(f(q)\)	\(=\)	\(q+(1.70333 + 1.04817i) q^{2} +(1.80268 + 3.57076i) q^{4} +(-0.931627 + 1.61363i) q^{5} +(-9.80189 + 5.65913i) q^{7} +(-0.672219 + 7.97171i) q^{8} +O(q^{10})\)	\(q+(1.70333 + 1.04817i) q^{2} +(1.80268 + 3.57076i) q^{4} +(-0.931627 + 1.61363i) q^{5} +(-9.80189 + 5.65913i) q^{7} +(-0.672219 + 7.97171i) q^{8} +(-3.27823 + 1.77203i) q^{10} +(-5.08539 + 2.93605i) q^{11} +(6.96926 - 12.0711i) q^{13} +(-22.6276 - 0.634694i) q^{14} +(-9.50072 + 12.8739i) q^{16} -11.0753 q^{17} +9.34459i q^{19} +(-7.44130 - 0.417779i) q^{20} +(-11.7396 - 0.329290i) q^{22} +(-26.3984 - 15.2411i) q^{23} +(10.7641 + 18.6440i) q^{25} +(24.5236 - 13.2561i) q^{26} +(-37.8770 - 24.7987i) q^{28} +(22.7710 + 39.4406i) q^{29} +(42.9526 + 24.7987i) q^{31} +(-29.6769 + 11.9701i) q^{32} +(-18.8648 - 11.6088i) q^{34} -21.0888i q^{35} +48.9848 q^{37} +(-9.79472 + 15.9169i) q^{38} +(-12.2371 - 8.51137i) q^{40} +(7.44787 - 12.9001i) q^{41} +(4.34763 - 2.51011i) q^{43} +(-19.6512 - 12.8660i) q^{44} +(-28.9899 - 53.6308i) q^{46} +(-71.9894 + 41.5631i) q^{47} +(39.5514 - 68.5051i) q^{49} +(-1.20724 + 43.0396i) q^{50} +(55.6664 + 3.12529i) q^{52} -53.6036 q^{53} -10.9412i q^{55} +(-38.5239 - 81.9420i) q^{56} +(-2.55386 + 91.0483i) q^{58} +(85.1674 + 49.1714i) q^{59} +(-10.2103 - 17.6847i) q^{61} +(47.1692 + 87.2621i) q^{62} +(-63.0962 - 10.7175i) q^{64} +(12.9855 + 22.4916i) q^{65} +(-14.9296 - 8.61963i) q^{67} +(-19.9651 - 39.5472i) q^{68} +(22.1046 - 35.9212i) q^{70} -52.6439i q^{71} +98.1594 q^{73} +(83.4373 + 51.3444i) q^{74} +(-33.3673 + 16.8453i) q^{76} +(33.2309 - 57.5577i) q^{77} +(-2.63838 + 1.52327i) q^{79} +(-11.9225 - 27.3242i) q^{80} +(26.2077 - 14.1665i) q^{82} +(88.2594 - 50.9566i) q^{83} +(10.3180 - 17.8713i) q^{85} +(10.0365 + 0.281518i) q^{86} +(-19.9868 - 42.5129i) q^{88} +17.0580 q^{89} +157.760i q^{91} +(6.83473 - 121.737i) q^{92} +(-166.187 - 4.66147i) q^{94} +(-15.0787 - 8.70567i) q^{95} +(26.0051 + 45.0422i) q^{97} +(139.174 - 75.2302i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + q^{2} + 3 q^{4} + 2 q^{5} - 14 q^{8}+O(q^{10}) \) 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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