LMFDB - Embedded newform 324.3.f.r.55.5

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			55.5
Root			$1.08837 + 0.903022i$ of defining polynomial
Character	$\chi$	$=$	324.55
Dual form			324.3.f.r.271.5

$q$-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 $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

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	0.757697	−	0.652607i	$-0.226325\pi$
$5$	−0.931627	−	1.61363i	−0.186325	−	0.322725i	−0.944022	+	0.329881i	$0.892991\pi$
$6$		0			0
$7$	−9.80189	−	5.65913i	−1.40027	−	0.808447i	−0.405851	−	0.913939i	$-0.633025\pi$
$7$	−9.80189	−	5.65913i	−1.40027	−	0.808447i	−0.994420	+	0.105493i	$0.966358\pi$
$8$	−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	$-0.419337\pi$
$11$	−5.08539	−	2.93605i	−0.462308	−	0.266914i	−0.713014	+	0.701150i	$0.752670\pi$
$12$		0			0
$13$	6.96926	+	12.0711i	0.536097	+	0.928547i	0.999109	+	0.0421954i	$0.0134352\pi$
$13$	6.96926	+	12.0711i	0.536097	+	0.928547i	−0.463012	+	0.886352i	$0.653231\pi$
$14$	−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	$-0.920913\pi$
$19$		−	9.34459i		−	0.491820i	0.969293	−	0.245910i	$-0.0790868\pi$
$20$	−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	−0.948340	−	0.317257i	$-0.897238\pi$
$23$	−26.3984	+	15.2411i	−1.14776	+	0.662658i	−0.199418	+	0.979915i	$0.563905\pi$
$24$		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	−0.143667	−	0.989626i	$-0.545889\pi$
$29$	22.7710	−	39.4406i	0.785208	−	1.36002i	0.928875	−	0.370394i	$-0.120777\pi$
$30$		0			0
$31$	42.9526	−	24.7987i	1.38557	−	0.799958i	0.392756	−	0.919643i	$-0.371522\pi$
$31$	42.9526	−	24.7987i	1.38557	−	0.799958i	0.992812	+	0.119685i	$0.0381885\pi$
$32$	−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	0.942444	−	0.334363i	$-0.108521\pi$
$41$	7.44787	+	12.9001i	0.181655	+	0.314636i	−0.760789	+	0.648999i	$0.775188\pi$
$42$		0			0
$43$	4.34763	+	2.51011i	0.101108	+	0.0583745i	0.549701	−	0.835361i	$-0.314742\pi$
$43$	4.34763	+	2.51011i	0.101108	+	0.0583745i	−0.448594	+	0.893736i	$0.648075\pi$
$44$	−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	−0.999284	−	0.0378317i	$-0.987955\pi$
$47$	−71.9894	−	41.5631i	−1.53169	−	0.884321i	−0.532405	−	0.846490i	$-0.678712\pi$
$48$		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	0.445434	−	0.895315i	$-0.353050\pi$
$59$	85.1674	−	49.1714i	1.44352	−	0.833414i	0.998082	+	0.0619007i	$0.0197162\pi$
$60$		0			0
$61$	−10.2103	+	17.6847i	−0.167381	+	0.289913i	−0.937498	−	0.347990i	$-0.886864\pi$
$61$	−10.2103	+	17.6847i	−0.167381	+	0.289913i	0.770117	+	0.637903i	$0.220198\pi$
$62$	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	$-0.707731\pi$
$67$	−14.9296	+	8.61963i	−0.222830	+	0.128651i	0.384430	+	0.923154i	$0.374398\pi$
$68$	−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	$0.120893\pi$
$71$			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	$0.265296\pi$
$74$	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	0.483208	−	0.875505i	$-0.339471\pi$
$79$	−2.63838	−	1.52327i	−0.0333973	−	0.0192819i	−0.516606	+	0.856223i	$0.672805\pi$
$80$	−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	$-0.122919\pi$
$83$	88.2594	+	50.9566i	1.06337	+	0.613935i	0.137005	+	0.990570i	$0.456252\pi$
$84$		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	−0.700275	−	0.713873i	$-0.746939\pi$
$97$	26.0051	−	45.0422i	0.268094	−	0.464353i	0.968370	+	0.249520i	$0.0802728\pi$
$98$	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	−0.985233	−	0.171220i	$-0.945229\pi$
$101$	−34.7779	+	60.2371i	−0.344336	+	0.596407i	0.640897	+	0.767627i	$0.278563\pi$
$102$		0			0
$103$	12.4403	−	7.18240i	0.120779	−	0.0697320i	−0.438393	−	0.898783i	$-0.644452\pi$
$103$	12.4403	−	7.18240i	0.120779	−	0.0697320i	0.559173	+	0.829051i	$0.311119\pi$
$104$	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	$-0.853801\pi$
$107$		−	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	$0.481690\pi$
$110$	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	0.994794	+	0.101910i	$0.0324953\pi$
$113$	66.1788	+	114.625i	0.585653	+	1.01438i	−0.409140	+	0.912471i	$0.634171\pi$
$114$		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	$-0.928965\pi$
$127$		−	56.2142i		−	0.442632i	0.975202	−	0.221316i	$-0.0710352\pi$
$128$	−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	−0.319573	−	0.947562i	$-0.603539\pi$
$131$	44.7042	−	25.8100i	0.341253	−	0.197023i	0.660826	+	0.750539i	$0.270206\pi$
$132$		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	−0.848336	−	0.529459i	$-0.822395\pi$
$137$	4.70687	−	8.15253i	0.0343567	−	0.0595075i	0.882692	+	0.469951i	$0.155728\pi$
$138$		0			0
$139$	−48.2294	+	27.8452i	−0.346974	+	0.200325i	−0.663352	−	0.748308i	$-0.730867\pi$
$139$	−48.2294	+	27.8452i	−0.346974	+	0.200325i	0.316378	+	0.948633i	$0.397533\pi$
$140$	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	−0.923623	−	0.383302i	$-0.874787\pi$
$149$	−118.270	−	204.850i	−0.793761	−	1.37483i	0.129863	−	0.991532i	$-0.458546\pi$
$150$		0			0
$151$	−84.0469	−	48.5245i	−0.556602	−	0.321354i	0.195178	−	0.980768i	$-0.437471\pi$
$151$	−84.0469	−	48.5245i	−0.556602	−	0.321354i	−0.751781	+	0.659413i	$0.770805\pi$
$152$	−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	0.622801	−	0.782380i	$-0.285995\pi$
$157$	−57.4873	−	99.5708i	−0.366161	−	0.634209i	−0.988962	+	0.148171i	$0.952661\pi$
$158$	−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	$0.404945\pi$
$163$			311.572i			1.91149i	−0.294204	+	0.955743i	$0.595055\pi$
$164$	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	−0.226741	−	0.973955i	$-0.572807\pi$
$167$	84.0608	−	48.5325i	0.503358	−	0.290614i	0.730099	+	0.683341i	$0.239474\pi$
$168$		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	−0.978057	−	0.208338i	$-0.933194\pi$
$173$	−53.3881	+	92.4710i	−0.308602	+	0.534514i	0.669455	+	0.742853i	$0.266528\pi$
$174$		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	$0.164379\pi$
$179$			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	$0.649287\pi$
$182$	−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	0.142535	−	0.989790i	$-0.454475\pi$
$191$	−122.886	−	70.9480i	−0.643380	−	0.371456i	−0.785915	+	0.618334i	$0.787808\pi$
$192$		0			0
$193$	20.8743	+	36.1553i	0.108157	+	0.187333i	0.915024	−	0.403400i	$-0.132172\pi$
$193$	20.8743	+	36.1553i	0.108157	+	0.187333i	−0.806867	+	0.590733i	$0.798838\pi$
$194$	−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	$0.140148\pi$
$199$			169.627i			0.852397i	−0.904630	+	0.426199i	$0.859852\pi$
$200$	−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	0.220385	−	0.975413i	$-0.429269\pi$
$211$	247.990	−	143.177i	1.17531	−	0.678565i	0.954925	+	0.296848i	$0.0959354\pi$
$212$	−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	0.971603	−	0.236618i	$-0.0760389\pi$
$223$	279.305	+	161.257i	1.25249	+	0.723124i	0.280885	+	0.959742i	$0.409372\pi$
$224$	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	$-0.376386\pi$
$227$	−53.0167	−	30.6092i	−0.233554	−	0.134842i	−0.612210	+	0.790695i	$0.709719\pi$
$228$		0			0
$229$	−180.134	−	312.001i	−0.786611	−	1.36245i	−0.928032	−	0.372500i	$-0.878501\pi$
$229$	−180.134	−	312.001i	−0.786611	−	1.36245i	0.141422	−	0.989949i	$-0.454833\pi$
$230$	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	−0.531854	−	0.846836i	$-0.678504\pi$
$239$	−15.3913	+	8.88617i	−0.0643988	+	0.0371806i	0.467455	+	0.884017i	$0.345171\pi$
$240$		0			0
$241$	113.490	−	196.570i	0.470913	−	0.815645i	−0.528534	−	0.848912i	$-0.677258\pi$
$241$	113.490	−	196.570i	0.470913	−	0.815645i	0.999446	+	0.0332676i	$0.0105914\pi$
$242$	−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	$-0.854650\pi$
$251$		−	221.345i		−	0.881852i	0.897543	−	0.440926i	$-0.145350\pi$
$252$		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	0.786960	−	0.617004i	$-0.211654\pi$
$257$	−36.2012	−	62.7024i	−0.140861	−	0.243978i	−0.927821	+	0.373026i	$0.878320\pi$
$258$		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	$-0.00302514\pi$
$263$	392.318	+	226.505i	1.49170	+	0.861234i	0.491747	+	0.870738i	$0.336358\pi$
$264$		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	$-0.985152\pi$
$271$		−	25.2731i		−	0.0932588i	0.998912	−	0.0466294i	$-0.0148480\pi$
$272$	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	−0.999406	−	0.0344684i	$-0.989026\pi$
$277$	−130.149	+	225.425i	−0.469852	+	0.813808i	0.529553	+	0.848277i	$0.322360\pi$
$278$	−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	−0.975200	−	0.221327i	$-0.928961\pi$
$281$	−83.1550	+	144.029i	−0.295925	+	0.512557i	0.679275	+	0.733884i	$0.262295\pi$
$282$		0			0
$283$	−281.972	+	162.796i	−0.996366	+	0.575252i	−0.907171	−	0.420762i	$-0.861763\pi$
$283$	−281.972	+	162.796i	−0.996366	+	0.575252i	−0.0891949	+	0.996014i	$0.528429\pi$
$284$	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	−0.931500	−	0.363742i	$-0.881499\pi$
$293$	−228.763	−	396.228i	−0.780760	−	1.35232i	0.150740	−	0.988573i	$-0.451834\pi$
$294$		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	$-0.898050\pi$
$307$		−	193.311i		−	0.629678i	0.949145	−	0.314839i	$-0.101950\pi$
$308$	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	−0.272317	−	0.962208i	$-0.587790\pi$
$311$	132.119	−	76.2790i	0.424820	−	0.245270i	0.697138	+	0.716937i	$0.254457\pi$
$312$		0			0
$313$	43.7256	−	75.7349i	0.139698	−	0.241965i	−0.787684	−	0.616079i	$-0.788720\pi$
$313$	43.7256	−	75.7349i	0.139698	−	0.241965i	0.927382	+	0.374115i	$0.122053\pi$
$314$	−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	−0.999006	−	0.0445716i	$-0.985808\pi$
$317$	−146.106	+	253.063i	−0.460903	+	0.798307i	0.538103	+	0.842879i	$0.319141\pi$
$318$		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	0.690281	−	0.723542i	$-0.257487\pi$
$331$	135.318	+	78.1258i	0.408815	+	0.236030i	−0.281465	+	0.959571i	$0.590820\pi$
$332$	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	0.994028	−	0.109123i	$-0.0348043\pi$
$337$	135.646	+	234.946i	0.402511	+	0.697169i	−0.591518	+	0.806292i	$0.701471\pi$
$338$	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	9.73706e−5	−	1.00000i	$-0.499969\pi$
$347$	300.561	−	173.529i	0.866171	−	0.500084i	0.866074	+	0.499916i	$0.166636\pi$
$348$		0			0
$349$	−149.267	+	258.538i	−0.427699	+	0.740796i	−0.996668	−	0.0815625i	$-0.974009\pi$
$349$	−149.267	+	258.538i	−0.427699	+	0.740796i	0.568969	+	0.822359i	$0.307342\pi$
$350$	−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	−0.111819	−	0.993729i	$-0.535668\pi$
$353$	284.054	−	491.996i	0.804685	−	1.39375i	0.916504	−	0.400026i	$-0.130999\pi$
$354$		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	$0.195707\pi$
$359$			414.158i			1.15364i	−0.816871	+	0.576821i	$0.804293\pi$
$360$		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	0.825552	−	0.564326i	$-0.190864\pi$
$367$	275.106	+	158.833i	0.749608	+	0.432786i	−0.0759443	+	0.997112i	$0.524197\pi$
$368$	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	0.785574	−	0.618768i	$-0.212368\pi$
$373$	−53.3693	−	92.4384i	−0.143081	−	0.247824i	−0.928655	+	0.370943i	$0.879034\pi$
$374$	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	$-0.985798\pi$
$379$		−	33.8080i		−	0.0892033i	0.999005	−	0.0446016i	$-0.0142019\pi$
$380$	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	−0.277618	−	0.960692i	$-0.589545\pi$
$383$	159.158	−	91.8901i	0.415557	−	0.239922i	0.693175	+	0.720770i	$0.256211\pi$
$384$		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	−0.897530	−	0.440954i	$-0.854640\pi$
$389$	−26.0192	+	45.0665i	−0.0668873	+	0.115852i	0.830642	+	0.556806i	$0.187973\pi$
$390$		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	0.978732	+	0.205142i	$0.0657657\pi$
$401$	267.477	+	463.284i	0.667025	+	1.15532i	−0.311708	+	0.950178i	$0.600901\pi$
$402$		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	0.994414	−	0.105547i	$-0.0336595\pi$
$409$	165.972	+	287.473i	0.405800	+	0.702867i	−0.588614	+	0.808414i	$0.700326\pi$
$410$	−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	0.448774	−	0.893645i	$-0.351861\pi$
$419$	606.327	−	350.063i	1.44708	−	0.835472i	0.998307	+	0.0581732i	$0.0185276\pi$
$420$		0			0
$421$	221.791	−	384.153i	0.526820	−	0.912479i	−0.472692	−	0.881228i	$-0.656718\pi$
$421$	221.791	−	384.153i	0.526820	−	0.912479i	0.999512	−	0.0312507i	$-0.00994904\pi$
$422$	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	$-0.786619\pi$
$431$		−	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	$0.444024\pi$
$434$	−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	0.410299	−	0.911951i	$-0.365424\pi$
$439$	−76.5284	−	44.1837i	−0.174324	−	0.100646i	−0.584623	+	0.811305i	$0.698758\pi$
$440$	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	$-0.335464\pi$
$443$	−5.13583	−	2.96517i	−0.0115933	−	0.00669339i	−0.505785	+	0.862659i	$0.668797\pi$
$444$		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	−0.918189	−	0.396143i	$-0.870349\pi$
$457$	−53.0234	+	91.8392i	−0.116025	+	0.200961i	0.802164	+	0.597104i	$0.203682\pi$
$458$	−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	−0.734888	−	0.678188i	$-0.762765\pi$
$461$	101.367	−	175.572i	0.219884	−	0.380850i	0.954772	+	0.297338i	$0.0960988\pi$
$462$		0			0
$463$	333.562	−	192.582i	0.720437	−	0.415945i	−0.0944763	−	0.995527i	$-0.530118\pi$
$463$	333.562	−	192.582i	0.720437	−	0.415945i	0.814914	+	0.579582i	$0.196784\pi$
$464$	−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	$0.206291\pi$
$467$			563.818i			1.20732i	−0.797243	+	0.603659i	$0.793709\pi$
$468$		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	0.00222581	−	0.999998i	$-0.499292\pi$
$479$	−413.226	−	238.576i	−0.862685	−	0.498071i	−0.864910	+	0.501926i	$0.832625\pi$
$480$		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	$0.146523\pi$
$487$			432.682i			0.888464i	−0.895912	+	0.444232i	$0.853477\pi$
$488$	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	−0.122622	−	0.992453i	$-0.539130\pi$
$491$	331.698	−	191.506i	0.675557	−	0.390033i	0.798179	+	0.602421i	$0.205797\pi$
$492$		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	$-0.814331\pi$
$499$	−386.720	+	223.273i	−0.774990	+	0.447441i	0.0596617	+	0.998219i	$0.480998\pi$
$500$	−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	$0.161265\pi$
$503$			488.145i			0.970467i	−0.874385	+	0.485234i	$0.838735\pi$
$504$		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	0.823770	−	0.566924i	$-0.191867\pi$
$509$	−40.2548	−	69.7233i	−0.0790860	−	0.136981i	−0.902856	+	0.429943i	$0.858534\pi$
$510$		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	$-0.647793\pi$
$523$		−	935.263i		−	1.78827i	0.447802	−	0.894133i	$-0.352207\pi$
$524$	−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	0.164111	−	0.986442i	$-0.447524\pi$
$547$	−332.640	−	192.050i	−0.608117	−	0.351096i	−0.772228	+	0.635345i	$0.780858\pi$
$548$	−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	−0.570218	+	0.821493i	$0.693141\pi$
$563$	−882.086	+	509.273i	−1.56676	+	0.904570i	−0.996543	+	0.0830764i	$0.973525\pi$
$564$		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	−0.368972	−	0.929441i	$-0.620290\pi$
$569$	353.027	−	611.460i	0.620433	−	1.07462i	0.989405	−	0.145181i	$-0.0463766\pi$
$570$		0			0
$571$	152.264	−	87.9094i	0.266661	−	0.153957i	−0.360708	−	0.932679i	$-0.617465\pi$
$571$	152.264	−	87.9094i	0.266661	−	0.153957i	0.627369	+	0.778722i	$0.284132\pi$
$572$	−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	0.776719	−	0.629847i	$-0.216882\pi$
$587$	363.714	+	209.990i	0.619615	+	0.357735i	−0.157104	+	0.987582i	$0.550216\pi$
$588$		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	−0.721508	−	0.692406i	$-0.756551\pi$
$599$	−289.090	+	166.906i	−0.482622	+	0.278642i	0.238887	+	0.971047i	$0.423218\pi$
$600$		0			0
$601$	426.635	−	738.954i	0.709875	−	1.22954i	−0.255028	−	0.966934i	$-0.582085\pi$
$601$	426.635	−	738.954i	0.709875	−	1.22954i	0.964903	−	0.262606i	$-0.0845821\pi$
$602$	−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	$-0.450697\pi$
$607$	659.847	−	380.963i	1.08706	−	0.627616i	0.932793	+	0.360412i	$0.117364\pi$
$608$	−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	0.994369	+	0.105975i	$0.0337963\pi$
$617$	363.389	+	629.409i	0.588961	+	1.02011i	−0.405407	+	0.914136i	$0.632870\pi$
$618$		0			0
$619$	429.526	+	247.987i	0.693903	+	0.400625i	0.805073	−	0.593176i	$-0.202126\pi$
$619$	429.526	+	247.987i	0.693903	+	0.400625i	−0.111170	+	0.993801i	$0.535460\pi$
$620$	−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	$0.251114\pi$
$631$			895.486i			1.41915i	−0.704628	+	0.709576i	$0.748886\pi$
$632$	−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	−0.999874	−	0.0158810i	$-0.994945\pi$
$641$	−311.644	+	539.783i	−0.486184	+	0.842095i	0.513690	+	0.857976i	$0.328278\pi$
$642$		0			0
$643$	318.256	−	183.745i	0.494955	−	0.285762i	−0.231673	−	0.972794i	$-0.574420\pi$
$643$	318.256	−	183.745i	0.494955	−	0.285762i	0.726628	+	0.687032i	$0.241087\pi$
$644$	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	$-0.799330\pi$
$647$		−	762.797i		−	1.17897i	0.807778	−	0.589487i	$-0.200670\pi$
$648$		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	0.866536	−	0.499114i	$-0.166341\pi$
$653$	0.668056	+	1.15711i	0.00102306	+	0.00177199i	−0.865513	+	0.500886i	$0.833008\pi$
$654$		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	$-0.381523\pi$
$659$	−172.143	−	99.3866i	−0.261218	−	0.150814i	−0.624890	+	0.780713i	$0.714856\pi$
$660$		0			0
$661$	−107.877	−	186.849i	−0.163203	−	0.282676i	0.772813	−	0.634634i	$-0.218849\pi$
$661$	−107.877	−	186.849i	−0.163203	−	0.282676i	−0.936016	+	0.351958i	$0.885516\pi$
$662$	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	−0.780441	−	0.625229i	$-0.785005\pi$
$673$	101.787	−	176.301i	0.151244	−	0.261962i	0.931685	+	0.363267i	$0.118339\pi$
$674$	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	−0.202753	−	0.979230i	$-0.564989\pi$
$677$	505.490	−	875.534i	0.746662	−	1.29326i	0.949414	−	0.314026i	$-0.101678\pi$
$678$		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	$0.335130\pi$
$683$			1186.83i			1.73767i	−0.495103	+	0.868834i	$0.664870\pi$
$684$		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	0.502362	−	0.864657i	$-0.332464\pi$
$691$	3.26716	+	1.88630i	0.00472817	+	0.00272981i	−0.497634	+	0.867387i	$0.665798\pi$
$692$	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	−0.939452	−	0.342680i	$-0.888665\pi$
$709$	−122.626	+	212.395i	−0.172956	+	0.299569i	0.766496	+	0.642249i	$0.221999\pi$
$710$	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	$0.113093\pi$
$719$			500.230i			0.695730i	−0.937545	+	0.347865i	$0.886907\pi$
$720$		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	0.823985	−	0.566611i	$-0.191746\pi$
$727$	541.817	+	312.818i	0.745278	+	0.430287i	−0.0787070	+	0.996898i	$0.525079\pi$
$728$	−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	−0.910172	−	0.414231i	$-0.864050\pi$
$733$	−596.531	−	1033.22i	−0.813821	−	1.40958i	0.0963510	−	0.995347i	$-0.469283\pi$
$734$	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	$0.195297\pi$
$739$			850.984i			1.15154i	−0.817613	+	0.575768i	$0.804703\pi$
$740$	−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	−0.352088	−	0.935967i	$-0.614528\pi$
$743$	209.853	−	121.159i	0.282440	−	0.163067i	0.634527	+	0.772900i	$0.281195\pi$
$744$		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	$-0.986204\pi$
$751$	−1097.26	+	633.505i	−1.46107	+	0.843548i	−0.462007	+	0.886876i	$0.652871\pi$
$752$	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	0.986125	+	0.166005i	$0.0530869\pi$
$761$	484.626	+	839.396i	0.636827	+	1.10302i	−0.349298	+	0.937012i	$0.613580\pi$
$762$		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	0.991669	+	0.128809i	$0.0411155\pi$
$769$	467.080	+	809.007i	0.607387	+	1.05202i	−0.384283	+	0.923215i	$0.625551\pi$
$770$	−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	−0.997752	−	0.0670077i	$-0.978655\pi$
$787$	−1132.18	+	653.663i	−1.43860	+	0.830575i	−0.440846	+	0.897583i	$0.645321\pi$
$788$	−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	0.999618	−	0.0276265i	$-0.00879490\pi$
$797$	379.279	+	656.931i	0.475884	+	0.824255i	−0.523734	+	0.851882i	$0.675462\pi$
$798$		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	$-0.976971\pi$
$811$		−	117.246i		−	0.144570i	0.997384	−	0.0722851i	$-0.0230291\pi$
$812$	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	−0.881256	−	0.472639i	$-0.843302\pi$
$821$	−25.7065	+	44.5249i	−0.0313112	+	0.0542326i	0.849945	+	0.526871i	$0.176635\pi$
$822$		0			0
$823$	−98.1876	+	56.6887i	−0.119305	+	0.0688805i	−0.558465	−	0.829528i	$-0.688609\pi$
$823$	−98.1876	+	56.6887i	−0.119305	+	0.0688805i	0.439160	+	0.898409i	$0.355276\pi$
$824$	−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	$0.0911667\pi$
$827$			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	$0.569631\pi$
$830$	−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	0.830149	−	0.557542i	$-0.188255\pi$
$839$	639.635	+	369.294i	0.762378	+	0.440159i	−0.0677709	+	0.997701i	$0.521589\pi$
$840$		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	0.297454	+	0.954736i	$0.403863\pi$
$853$	−578.418	+	1001.85i	−0.678099	+	1.17450i	−0.975553	+	0.219766i	$0.929471\pi$
$854$	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	−0.741287	−	0.671188i	$-0.765784\pi$
$857$	180.503	−	312.641i	0.210623	−	0.364809i	0.951910	+	0.306379i	$0.0991176\pi$
$858$		0			0
$859$	751.950	−	434.138i	0.875378	−	0.505400i	0.00624629	−	0.999980i	$-0.498012\pi$
$859$	751.950	−	434.138i	0.875378	−	0.505400i	0.869132	+	0.494581i	$0.164678\pi$
$860$	−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	$0.0252526\pi$
$863$			136.786i			0.158500i	−0.996855	+	0.0792500i	$0.974747\pi$
$864$		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	0.566176	−	0.824285i	$-0.308422\pi$
$877$	−377.780	−	654.334i	−0.430764	−	0.746104i	−0.996939	+	0.0781802i	$0.975089\pi$
$878$	−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	$-0.838007\pi$
$883$		−	860.448i		−	0.974460i	0.873274	−	0.487230i	$-0.161993\pi$
$884$	−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	0.225882	−	0.974155i	$-0.427474\pi$
$887$	1048.85	−	605.552i	1.18247	−	0.682697i	0.956584	+	0.291458i	$0.0941402\pi$
$888$		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	0.338444	−	0.940987i	$-0.390099\pi$
$907$	−278.678	−	160.895i	−0.307252	−	0.177392i	−0.645696	+	0.763594i	$0.723433\pi$
$908$	−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	$-0.00671877\pi$
$911$	1349.54	+	779.160i	1.48139	+	0.855279i	0.481610	+	0.876386i	$0.340052\pi$
$912$		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	$-0.740385\pi$
$919$		−	1338.32i		−	1.45628i	0.685428	−	0.728140i	$-0.259615\pi$
$920$	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	−0.402901	−	0.915244i	$-0.631998\pi$
$929$	549.200	−	951.243i	0.591174	−	1.02394i	0.994075	−	0.108699i	$-0.0346686\pi$
$930$		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	0.938529	−	0.345202i	$-0.112189\pi$
$941$	160.263	+	277.583i	0.170311	+	0.294987i	−0.768218	+	0.640189i	$0.778856\pi$
$942$		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	$-0.624817\pi$
$947$	−1300.73	−	750.974i	−1.37352	−	0.793004i	−0.991370	+	0.131095i	$0.958151\pi$
$948$		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	−0.696504	−	0.717553i	$-0.745262\pi$
$967$	−409.368	+	236.349i	−0.423338	+	0.244414i	0.273167	+	0.961967i	$0.411929\pi$
$968$	−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	$0.0992762\pi$
$971$			595.910i			0.613707i	−0.951757	+	0.306854i	$0.900724\pi$
$972$		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	0.812165	−	0.583428i	$-0.198289\pi$
$977$	−96.8999	−	167.836i	−0.0991811	−	0.171787i	−0.911346	+	0.411641i	$0.864956\pi$
$978$		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	$-0.599288\pi$
$983$	−1262.73	−	729.038i	−1.28457	−	0.741645i	−0.977680	+	0.210100i	$0.932621\pi$
$984$		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	$0.0927056\pi$
$991$			569.118i			0.574287i	−0.957888	+	0.287143i	$0.907294\pi$
$992$	−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	−0.868640	−	0.495444i	$-0.835005\pi$
$997$	−5.23685	+	9.07049i	−0.00525261	+	0.00909779i	0.863387	+	0.504542i	$0.168339\pi$
$998$	−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.55.5		12
3.2	odd	2		324.3.f.q.55.2		12
4.3	odd	2	inner	324.3.f.r.55.3		12
9.2	odd	6		324.3.d.f.163.6	yes	6
9.4	even	3	inner	324.3.f.r.271.3		12
9.5	odd	6		324.3.f.q.271.4		12
9.7	even	3		324.3.d.e.163.1	✓	6
12.11	even	2		324.3.f.q.55.4		12
36.7	odd	6		324.3.d.e.163.2	yes	6
36.11	even	6		324.3.d.f.163.5	yes	6
36.23	even	6		324.3.f.q.271.2		12
36.31	odd	6	inner	324.3.f.r.271.5		12

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

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