LMFDB - Embedded newform 216.3.p.b.91.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,3,Mod(19,216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(216, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 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("216.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	216.p (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:	$5.88557371018$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 72)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			91.5
Character	$\chi$	$=$	216.91
Dual form			216.3.p.b.19.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.67744 - 1.08913i) q^{2} +(1.62758 + 3.65390i) q^{4} +(-5.42020 - 3.12935i) q^{5} +(5.96345 - 3.44300i) q^{7} +(1.24943 - 7.90183i) q^{8} +O(q^{10})$	\(q+(-1.67744 - 1.08913i) q^{2} +(1.62758 + 3.65390i) q^{4} +(-5.42020 - 3.12935i) q^{5} +(5.96345 - 3.44300i) q^{7} +(1.24943 - 7.90183i) q^{8} +(5.68375 + 11.1526i) q^{10} +(5.38524 + 9.32751i) q^{11} +(-15.3923 - 8.88677i) q^{13} +(-13.7532 - 0.719584i) q^{14} +(-10.7020 + 11.8940i) q^{16} +0.681004 q^{17} -26.6092 q^{19} +(2.61256 - 24.8981i) q^{20} +(1.12551 - 21.5115i) q^{22} +(-22.8204 - 13.1754i) q^{23} +(7.08571 + 12.2728i) q^{25} +(16.1408 + 31.6713i) q^{26} +(22.2863 + 16.1861i) q^{28} +(-26.8884 + 15.5240i) q^{29} +(-19.9096 - 11.4948i) q^{31} +(30.9061 - 8.29554i) q^{32} +(-1.14234 - 0.741704i) q^{34} -43.0974 q^{35} +33.4119i q^{37} +(44.6352 + 28.9810i) q^{38} +(-31.4998 + 38.9196i) q^{40} +(-13.4634 + 23.3192i) q^{41} +(-16.5202 - 28.6138i) q^{43} +(-25.3169 + 34.8584i) q^{44} +(23.9300 + 46.9553i) q^{46} +(10.6191 - 6.13093i) q^{47} +(-0.791537 + 1.37098i) q^{49} +(1.48091 - 28.3041i) q^{50} +(7.41917 - 70.7060i) q^{52} -49.2792i q^{53} -67.4093i q^{55} +(-19.7551 - 51.4239i) q^{56} +(62.0114 + 3.24451i) q^{58} +(19.0327 - 32.9656i) q^{59} +(65.7927 - 37.9854i) q^{61} +(20.8777 + 40.9660i) q^{62} +(-60.8778 - 19.7456i) q^{64} +(55.6197 + 96.3362i) q^{65} +(-27.4324 + 47.5143i) q^{67} +(1.10839 + 2.48832i) q^{68} +(72.2931 + 46.9389i) q^{70} -35.6080i q^{71} +113.344 q^{73} +(36.3900 - 56.0463i) q^{74} +(-43.3085 - 97.2274i) q^{76} +(64.2292 + 37.0827i) q^{77} +(30.8141 - 17.7905i) q^{79} +(95.2275 - 30.9776i) q^{80} +(47.9817 - 24.4531i) q^{82} +(-58.7309 - 101.725i) q^{83} +(-3.69118 - 2.13110i) q^{85} +(-3.45271 + 65.9905i) q^{86} +(80.4329 - 30.8992i) q^{88} +58.3120 q^{89} -122.389 q^{91} +(10.9995 - 104.827i) q^{92} +(-24.4902 - 1.28136i) q^{94} +(144.227 + 83.2696i) q^{95} +(-63.7809 - 110.472i) q^{97} +(2.82093 - 1.43764i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 5 q^{2} + 7 q^{4} - 46 q^{8}+O(q^{10}) $ 40 * q + 5 * q^2 + 7 * q^4 - 46 * q^8	$ 40 q + 5 q^{2} + 7 q^{4} - 46 q^{8} - 12 q^{10} + 16 q^{11} - 6 q^{14} + 31 q^{16} + 4 q^{17} - 76 q^{19} + 12 q^{20} + 35 q^{22} + 118 q^{25} + 72 q^{26} - 36 q^{28} + 5 q^{32} + 5 q^{34} + 108 q^{35} + 169 q^{38} - 6 q^{40} - 20 q^{41} - 16 q^{43} - 362 q^{44} - 96 q^{46} + 166 q^{49} - 73 q^{50} - 24 q^{52} - 186 q^{56} + 36 q^{58} + 64 q^{59} - 384 q^{62} - 518 q^{64} + 102 q^{65} - 64 q^{67} + 295 q^{68} - 6 q^{70} - 292 q^{73} - 318 q^{74} + 197 q^{76} + 720 q^{80} + 386 q^{82} - 554 q^{83} + 295 q^{86} + 59 q^{88} + 688 q^{89} - 204 q^{91} + 378 q^{92} - 66 q^{94} + 92 q^{97} + 614 q^{98}+O(q^{100}) $ 40 * q + 5 * q^2 + 7 * q^4 - 46 * q^8 - 12 * q^10 + 16 * q^11 - 6 * q^14 + 31 * q^16 + 4 * q^17 - 76 * q^19 + 12 * q^20 + 35 * q^22 + 118 * q^25 + 72 * q^26 - 36 * q^28 + 5 * q^32 + 5 * q^34 + 108 * q^35 + 169 * q^38 - 6 * q^40 - 20 * q^41 - 16 * q^43 - 362 * q^44 - 96 * q^46 + 166 * q^49 - 73 * q^50 - 24 * q^52 - 186 * q^56 + 36 * q^58 + 64 * q^59 - 384 * q^62 - 518 * q^64 + 102 * q^65 - 64 * q^67 + 295 * q^68 - 6 * q^70 - 292 * q^73 - 318 * q^74 + 197 * q^76 + 720 * q^80 + 386 * q^82 - 554 * q^83 + 295 * q^86 + 59 * q^88 + 688 * q^89 - 204 * q^91 + 378 * q^92 - 66 * q^94 + 92 * q^97 + 614 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.67744	−	1.08913i	−0.838718	−	0.544567i
$2$	−1.67744	−	1.08913i	−0.838718	−	0.544567i
$3$		0			0
$3$		0			0
$4$	1.62758	+	3.65390i	0.406894	+	0.913475i
$5$	−5.42020	−	3.12935i	−1.08404	−	0.625871i	−0.152057	−	0.988372i	$-0.548590\pi$
$5$	−5.42020	−	3.12935i	−1.08404	−	0.625871i	−0.931983	+	0.362501i	$0.881923\pi$
$6$		0			0
$7$	5.96345	−	3.44300i	0.851921	−	0.491857i	−0.00937760	−	0.999956i	$-0.502985\pi$
$7$	5.96345	−	3.44300i	0.851921	−	0.491857i	0.861299	+	0.508099i	$0.169652\pi$
$8$	1.24943	−	7.90183i	0.156179	−	0.987729i
$9$		0			0
$10$	5.68375	+	11.1526i	0.568375	+	1.11526i
$11$	5.38524	+	9.32751i	0.489567	+	0.847955i	0.999928	−	0.0120051i	$-0.00382145\pi$
$11$	5.38524	+	9.32751i	0.489567	+	0.847955i	−0.510361	+	0.859960i	$0.670488\pi$
$12$		0			0
$13$	−15.3923	−	8.88677i	−1.18403	−	0.683598i	−0.227084	−	0.973875i	$-0.572919\pi$
$13$	−15.3923	−	8.88677i	−1.18403	−	0.683598i	−0.956943	+	0.290277i	$0.906252\pi$
$14$	−13.7532	−	0.719584i	−0.982370	−	0.0513989i
$15$		0			0
$16$	−10.7020	+	11.8940i	−0.668874	+	0.743376i
$17$	0.681004			0.0400590			0.0200295	−	0.999799i	$-0.493624\pi$
$17$	0.681004			0.0400590			0.0200295	+	0.999799i	$0.493624\pi$
$18$		0			0
$19$	−26.6092			−1.40048			−0.700242	−	0.713905i	$-0.746925\pi$
$19$	−26.6092			−1.40048			−0.700242	+	0.713905i	$0.746925\pi$
$20$	2.61256	−	24.8981i	0.130628	−	1.24491i
$21$		0			0
$22$	1.12551	−	21.5115i	0.0511596	−	0.977797i
$23$	−22.8204	−	13.1754i	−0.992191	−	0.572842i	−0.0862626	−	0.996272i	$-0.527492\pi$
$23$	−22.8204	−	13.1754i	−0.992191	−	0.572842i	−0.905929	+	0.423431i	$0.860826\pi$
$24$		0			0
$25$	7.08571	+	12.2728i	0.283428	+	0.490913i
$26$	16.1408	+	31.6713i	0.620799	+	1.21813i
$27$		0			0
$28$	22.2863	+	16.1861i	0.795941	+	0.578075i
$29$	−26.8884	+	15.5240i	−0.927187	+	0.535312i	−0.885921	−	0.463836i	$-0.846473\pi$
$29$	−26.8884	+	15.5240i	−0.927187	+	0.535312i	−0.0412664	+	0.999148i	$0.513139\pi$
$30$		0			0
$31$	−19.9096	−	11.4948i	−0.642245	−	0.370800i	0.143234	−	0.989689i	$-0.454250\pi$
$31$	−19.9096	−	11.4948i	−0.642245	−	0.370800i	−0.785479	+	0.618889i	$0.787583\pi$
$32$	30.9061	−	8.29554i	0.965814	−	0.259236i
$33$		0			0
$34$	−1.14234	−	0.741704i	−0.0335982	−	0.0218148i
$35$	−43.0974			−1.23136
$36$		0			0
$37$			33.4119i			0.903025i	0.892265	+	0.451512i	$0.149115\pi$
$37$			33.4119i			0.903025i	−0.892265	+	0.451512i	$0.850885\pi$
$38$	44.6352	+	28.9810i	1.17461	+	0.762657i
$39$		0			0
$40$	−31.4998	+	38.9196i	−0.787495	+	0.972990i
$41$	−13.4634	+	23.3192i	−0.328375	+	0.568762i	−0.982190	−	0.187893i	$-0.939834\pi$
$41$	−13.4634	+	23.3192i	−0.328375	+	0.568762i	0.653815	+	0.756655i	$0.273168\pi$
$42$		0			0
$43$	−16.5202	−	28.6138i	−0.384190	−	0.665437i	0.607466	−	0.794346i	$-0.292186\pi$
$43$	−16.5202	−	28.6138i	−0.384190	−	0.665437i	−0.991657	+	0.128908i	$0.958853\pi$
$44$	−25.3169	+	34.8584i	−0.575384	+	0.792236i
$45$		0			0
$46$	23.9300	+	46.9553i	0.520218	+	1.02077i
$47$	10.6191	−	6.13093i	0.225938	−	0.130445i	−0.382759	−	0.923848i	$-0.625026\pi$
$47$	10.6191	−	6.13093i	0.225938	−	0.130445i	0.608697	+	0.793403i	$0.291693\pi$
$48$		0			0
$49$	−0.791537	+	1.37098i	−0.0161538	+	0.0279792i
$50$	1.48091	−	28.3041i	0.0296182	−	0.566083i
$51$		0			0
$52$	7.41917	−	70.7060i	0.142676	−	1.35973i
$53$		−	49.2792i		−	0.929797i	−0.885364	−	0.464898i	$-0.846091\pi$
$53$		−	49.2792i		−	0.929797i	0.885364	−	0.464898i	$-0.153909\pi$
$54$		0			0
$55$		−	67.4093i		−	1.22562i
$56$	−19.7551	−	51.4239i	−0.352769	−	0.918284i
$57$		0			0
$58$	62.0114	+	3.24451i	1.06916	+	0.0559399i
$59$	19.0327	−	32.9656i	0.322588	−	0.558739i	−0.658433	−	0.752639i	$-0.728780\pi$
$59$	19.0327	−	32.9656i	0.322588	−	0.558739i	0.981021	+	0.193900i	$0.0621137\pi$
$60$		0			0
$61$	65.7927	−	37.9854i	1.07857	−	0.622712i	0.148059	−	0.988979i	$-0.452698\pi$
$61$	65.7927	−	37.9854i	1.07857	−	0.622712i	0.930510	+	0.366267i	$0.119364\pi$
$62$	20.8777	+	40.9660i	0.336737	+	0.660742i
$63$		0			0
$64$	−60.8778	−	19.7456i	−0.951216	−	0.308525i
$65$	55.6197	+	96.3362i	0.855688	+	1.48210i
$66$		0			0
$67$	−27.4324	+	47.5143i	−0.409438	+	0.709168i	−0.994827	−	0.101585i	$-0.967609\pi$
$67$	−27.4324	+	47.5143i	−0.409438	+	0.709168i	0.585388	+	0.810753i	$0.300942\pi$
$68$	1.10839	+	2.48832i	0.0162998	+	0.0365929i
$69$		0			0
$70$	72.2931	+	46.9389i	1.03276	+	0.670555i
$71$		−	35.6080i		−	0.501521i	−0.968049	−	0.250760i	$-0.919319\pi$
$71$		−	35.6080i		−	0.501521i	0.968049	−	0.250760i	$-0.0806806\pi$
$72$		0			0
$73$	113.344			1.55265			0.776327	−	0.630330i	$-0.217080\pi$
$73$	113.344			1.55265			0.776327	+	0.630330i	$0.217080\pi$
$74$	36.3900	−	56.0463i	0.491757	−	0.757383i
$75$		0			0
$76$	−43.3085	−	97.2274i	−0.569849	−	1.27931i
$77$	64.2292	+	37.0827i	0.834145	+	0.481594i
$78$		0			0
$79$	30.8141	−	17.7905i	0.390052	−	0.225196i	−0.292131	−	0.956378i	$-0.594364\pi$
$79$	30.8141	−	17.7905i	0.390052	−	0.225196i	0.682182	+	0.731182i	$0.261031\pi$
$80$	95.2275	−	30.9776i	1.19034	−	0.387220i
$81$		0			0
$82$	47.9817	−	24.4531i	0.585143	−	0.298209i
$83$	−58.7309	−	101.725i	−0.707601	−	1.22560i	−0.965745	−	0.259494i	$-0.916444\pi$
$83$	−58.7309	−	101.725i	−0.707601	−	1.22560i	0.258144	−	0.966107i	$-0.416889\pi$
$84$		0			0
$85$	−3.69118	−	2.13110i	−0.0434256	−	0.0250718i
$86$	−3.45271	+	65.9905i	−0.0401478	+	0.767331i
$87$		0			0
$88$	80.4329	−	30.8992i	0.914010	−	0.351127i
$89$	58.3120			0.655191			0.327595	−	0.944818i	$-0.393762\pi$
$89$	58.3120			0.655191			0.327595	+	0.944818i	$0.393762\pi$
$90$		0			0
$91$	−122.389			−1.34493
$92$	10.9995	−	104.827i	0.119560	−	1.13943i
$93$		0			0
$94$	−24.4902	−	1.28136i	−0.260534	−	0.0136315i
$95$	144.227	+	83.2696i	1.51818	+	0.876522i
$96$		0			0
$97$	−63.7809	−	110.472i	−0.657535	−	1.13888i	−0.981252	−	0.192730i	$-0.938266\pi$
$97$	−63.7809	−	110.472i	−0.657535	−	1.13888i	0.323717	−	0.946154i	$-0.395068\pi$
$98$	2.82093	−	1.43764i	0.0287850	−	0.0146698i
$99$		0			0
$100$	−33.3111	+	45.8654i	−0.333111	+	0.458654i
$101$	−152.120	+	87.8265i	−1.50614	+	0.869570i	−0.506164	+	0.862437i	$0.668937\pi$
$101$	−152.120	+	87.8265i	−1.50614	+	0.869570i	−0.999975	+	0.00713253i	$0.997730\pi$
$102$		0			0
$103$	0.597041	+	0.344702i	0.00579652	+	0.00334662i	0.502895	−	0.864347i	$-0.332268\pi$
$103$	0.597041	+	0.344702i	0.00579652	+	0.00334662i	−0.497099	+	0.867694i	$0.665601\pi$
$104$	−89.4535	+	110.524i	−0.860129	+	1.06273i
$105$		0			0
$106$	−53.6717	+	82.6627i	−0.506336	+	0.779837i
$107$	−63.0505			−0.589257			−0.294629	−	0.955612i	$-0.595196\pi$
$107$	−63.0505			−0.589257			−0.294629	+	0.955612i	$0.595196\pi$
$108$		0			0
$109$			61.3097i			0.562474i	0.959638	+	0.281237i	$0.0907447\pi$
$109$			61.3097i			0.562474i	−0.959638	+	0.281237i	$0.909255\pi$
$110$	−73.4177	+	113.075i	−0.667434	+	1.02795i
$111$		0			0
$112$	−22.8697	+	107.776i	−0.204194	+	0.962288i
$113$	20.7387	−	35.9206i	0.183529	−	0.317881i	−0.759551	−	0.650448i	$-0.774581\pi$
$113$	20.7387	−	35.9206i	0.183529	−	0.317881i	0.943080	+	0.332567i	$0.107915\pi$
$114$		0			0
$115$	82.4607	+	142.826i	0.717050	+	1.24197i
$116$	−100.486	−	72.9811i	−0.866261	−	0.629147i
$117$		0			0
$118$	−67.8301	+	34.5685i	−0.574831	+	0.292954i
$119$	4.06113	−	2.34469i	0.0341271	−	0.0197033i
$120$		0			0
$121$	2.49839	−	4.32735i	0.0206479	−	0.0357632i
$122$	−151.734	−	7.93893i	−1.24372	−	0.0650732i
$123$		0			0
$124$	9.59650	−	91.4563i	0.0773911	−	0.737551i
$125$			67.7729i			0.542183i
$126$		0			0
$127$			139.360i			1.09732i	0.836044	+	0.548662i	$0.184863\pi$
$127$			139.360i			1.09732i	−0.836044	+	0.548662i	$0.815137\pi$
$128$	80.6130	+	99.4260i	0.629789	+	0.776766i
$129$		0			0
$130$	11.6245	−	222.175i	0.0894191	−	1.70904i
$131$	74.3430	−	128.766i	0.567504	−	0.982945i	−0.429308	−	0.903158i	$-0.641243\pi$
$131$	74.3430	−	128.766i	0.567504	−	0.982945i	0.996812	−	0.0797872i	$-0.0254241\pi$
$132$		0			0
$133$	−158.683	+	91.6154i	−1.19310	+	0.688838i
$134$	97.7654	−	49.8246i	0.729593	−	0.371825i
$135$		0			0
$136$	0.850867	−	5.38118i	0.00625638	−	0.0395675i
$137$	30.9902	+	53.6766i	0.226206	+	0.391800i	0.956681	−	0.291140i	$-0.0940344\pi$
$137$	30.9902	+	53.6766i	0.226206	+	0.391800i	−0.730475	+	0.682940i	$0.760701\pi$
$138$		0			0
$139$	93.2316	−	161.482i	0.670731	−	1.16174i	−0.306966	−	0.951720i	$-0.599314\pi$
$139$	93.2316	−	161.482i	0.670731	−	1.16174i	0.977697	−	0.210020i	$-0.0673529\pi$
$140$	−70.1444	−	157.474i	−0.501031	−	1.12481i
$141$		0			0
$142$	−38.7818	+	59.7301i	−0.273112	+	0.420634i
$143$		−	191.430i		−	1.33867i
$144$		0			0
$145$	194.321			1.34014
$146$	−190.127	−	123.446i	−1.30224	−	0.845524i
$147$		0			0
$148$	−122.084	+	54.3805i	−0.824891	+	0.367436i
$149$	−6.86711	−	3.96473i	−0.0460880	−	0.0266089i	0.476779	−	0.879023i	$-0.341804\pi$
$149$	−6.86711	−	3.96473i	−0.0460880	−	0.0266089i	−0.522867	+	0.852414i	$0.675138\pi$
$150$		0			0
$151$	−131.798	+	76.0936i	−0.872834	+	0.503931i	−0.868289	−	0.496059i	$-0.834780\pi$
$151$	−131.798	+	76.0936i	−0.872834	+	0.503931i	−0.00454500	+	0.999990i	$0.501447\pi$
$152$	−33.2464	+	210.261i	−0.218726	+	1.38330i
$153$		0			0
$154$	−67.3522	−	132.158i	−0.437352	−	0.858169i
$155$	71.9426	+	124.608i	0.464146	+	0.803924i
$156$		0			0
$157$	90.0406	+	51.9850i	0.573507	+	0.331114i	0.758549	−	0.651616i	$-0.225909\pi$
$157$	90.0406	+	51.9850i	0.573507	+	0.331114i	−0.185042	+	0.982731i	$0.559242\pi$
$158$	−71.0648	−	3.71820i	−0.449777	−	0.0235329i
$159$		0			0
$160$	−193.477	−	51.7525i	−1.20923	−	0.323453i
$161$	−181.451			−1.12702
$162$		0			0
$163$	−14.8285			−0.0909726			−0.0454863	−	0.998965i	$-0.514484\pi$
$163$	−14.8285			−0.0909726			−0.0454863	+	0.998965i	$0.514484\pi$
$164$	−107.119	−	11.2400i	−0.653164	−	0.0685364i
$165$		0			0
$166$	−12.2747	+	234.603i	−0.0739441	+	1.41327i
$167$	46.8185	+	27.0307i	0.280350	+	0.161860i	0.633582	−	0.773676i	$-0.281584\pi$
$167$	46.8185	+	27.0307i	0.280350	+	0.161860i	−0.353232	+	0.935536i	$0.614917\pi$
$168$		0			0
$169$	73.4495	+	127.218i	0.434612	+	0.752771i
$170$	3.87065	+	7.59497i	0.0227686	+	0.0446763i
$171$		0			0
$172$	77.6641	−	106.934i	0.451536	−	0.621711i
$173$	281.500	−	162.524i	1.62717	−	0.939446i	0.642236	−	0.766507i	$-0.278007\pi$
$173$	281.500	−	162.524i	1.62717	−	0.939446i	0.984933	−	0.172939i	$-0.0553263\pi$
$174$		0			0
$175$	84.5105	+	48.7922i	0.482917	+	0.278812i
$176$	−168.574	−	35.7708i	−0.957808	−	0.203243i
$177$		0			0
$178$	−97.8146	−	63.5095i	−0.549520	−	0.356795i
$179$	40.8446			0.228182			0.114091	−	0.993470i	$-0.463604\pi$
$179$	40.8446			0.228182			0.114091	+	0.993470i	$0.463604\pi$
$180$		0			0
$181$			116.258i			0.642310i	0.947027	+	0.321155i	$0.104071\pi$
$181$			116.258i			0.642310i	−0.947027	+	0.321155i	$0.895929\pi$
$182$	205.299	+	133.297i	1.12802	+	0.732404i
$183$		0			0
$184$	−132.622	+	163.861i	−0.720772	+	0.890550i
$185$	104.558	−	181.099i	0.565177	−	0.978915i
$186$		0			0
$187$	3.66737	+	6.35207i	0.0196116	+	0.0339683i
$188$	39.6852	+	28.8225i	0.211091	+	0.153311i
$189$		0			0
$190$	−151.240	−	296.762i	−0.796000	−	1.56191i
$191$	−255.240	+	147.363i	−1.33633	+	0.771533i	−0.986262	−	0.165189i	$-0.947177\pi$
$191$	−255.240	+	147.363i	−1.33633	+	0.771533i	−0.350073	+	0.936722i	$0.613843\pi$
$192$		0			0
$193$	−107.903	+	186.893i	−0.559080	+	0.968356i	0.438493	+	0.898735i	$0.355512\pi$
$193$	−107.903	+	186.893i	−0.559080	+	0.968356i	−0.997574	+	0.0696211i	$0.977821\pi$
$194$	−13.3302	+	254.775i	−0.0687122	+	1.31327i
$195$		0			0
$196$	−6.29772	−	0.660819i	−0.0321312	−	0.00337153i
$197$		−	114.028i		−	0.578820i	−0.957205	−	0.289410i	$-0.906541\pi$
$197$		−	114.028i		−	0.578820i	0.957205	−	0.289410i	$-0.0934591\pi$
$198$		0			0
$199$		−	218.723i		−	1.09911i	−0.835457	−	0.549556i	$-0.814797\pi$
$199$		−	218.723i		−	1.09911i	0.835457	−	0.549556i	$-0.185203\pi$
$200$	105.831	−	40.6561i	0.529154	−	0.203280i
$201$		0			0
$202$	350.826	+	18.3557i	1.73676	+	0.0908697i
$203$	−106.898	+	185.154i	−0.526594	+	0.912087i
$204$		0			0
$205$	145.948	−	84.2633i	0.711943	−	0.411040i
$206$	−0.626071	−	1.22847i	−0.00303918	−	0.00596346i
$207$		0			0
$208$	270.428	−	87.9705i	1.30013	−	0.422935i
$209$	−143.297	−	248.198i	−0.685631	−	1.18755i
$210$		0			0
$211$	120.870	−	209.353i	0.572844	−	0.992195i	−0.423428	−	0.905930i	$-0.639173\pi$
$211$	120.870	−	209.353i	0.572844	−	0.992195i	0.996272	−	0.0862651i	$-0.0274932\pi$
$212$	180.061	−	80.2057i	0.849346	−	0.378329i
$213$		0			0
$214$	105.763	+	68.6705i	0.494221	+	0.320890i
$215$			206.790i			0.961814i
$216$		0			0
$217$	−158.306			−0.729522
$218$	66.7744	−	102.843i	0.306305	−	0.471757i
$219$		0			0
$220$	246.307	−	109.714i	1.11958	−	0.498699i
$221$	−10.4822	−	6.05193i	−0.0474310	−	0.0273843i
$222$		0			0
$223$	−81.2853	+	46.9301i	−0.364508	+	0.210449i	−0.671056	−	0.741406i	$-0.734159\pi$
$223$	−81.2853	+	46.9301i	−0.364508	+	0.210449i	0.306548	+	0.951855i	$0.400826\pi$
$224$	155.745	−	155.879i	0.695291	−	0.695890i
$225$		0			0
$226$	−73.9102	+	37.6672i	−0.327036	+	0.166669i
$227$	11.9115	+	20.6313i	0.0524735	+	0.0908867i	0.891069	−	0.453868i	$-0.149956\pi$
$227$	11.9115	+	20.6313i	0.0524735	+	0.0908867i	−0.838596	+	0.544755i	$0.816623\pi$
$228$		0			0
$229$	−230.137	−	132.870i	−1.00497	−	0.580218i	−0.0952527	−	0.995453i	$-0.530366\pi$
$229$	−230.137	−	132.870i	−1.00497	−	0.580218i	−0.909714	+	0.415235i	$0.863699\pi$
$230$	17.2342	−	329.392i	0.0749315	−	1.43214i
$231$		0			0
$232$	89.0731	+	231.864i	0.383936	+	0.999414i
$233$	107.407			0.460974			0.230487	−	0.973075i	$-0.425968\pi$
$233$	107.407			0.460974			0.230487	+	0.973075i	$0.425968\pi$
$234$		0			0
$235$	−76.7434			−0.326568
$236$	151.430	+	15.8896i	0.641654	+	0.0673286i
$237$		0			0
$238$	−9.36597	−	0.490039i	−0.0393528	−	0.00205899i
$239$	−85.3033	−	49.2499i	−0.356918	−	0.206066i	0.310810	−	0.950472i	$-0.399400\pi$
$239$	−85.3033	−	49.2499i	−0.356918	−	0.206066i	−0.667728	+	0.744406i	$0.732733\pi$
$240$		0			0
$241$	−203.132	−	351.835i	−0.842872	−	1.45990i	−0.887456	−	0.460892i	$-0.847530\pi$
$241$	−203.132	−	351.835i	−0.842872	−	1.45990i	0.0445841	−	0.999006i	$-0.485804\pi$
$242$	−8.90395	+	4.53776i	−0.0367932	+	0.0187511i
$243$		0			0
$244$	245.878	+	178.576i	1.00770	+	0.731868i
$245$	8.58058	−	4.95400i	0.0350228	−	0.0202204i
$246$		0			0
$247$	409.578	+	236.470i	1.65821	+	0.957368i
$248$	−115.706	+	142.960i	−0.466555	+	0.576452i
$249$		0			0
$250$	73.8137	−	113.685i	0.295255	−	0.454738i
$251$	227.911			0.908012			0.454006	−	0.890999i	$-0.349995\pi$
$251$	227.911			0.908012			0.454006	+	0.890999i	$0.349995\pi$
$252$		0			0
$253$		−	283.810i		−	1.12178i
$254$	151.782	−	233.768i	0.597566	−	0.920345i
$255$		0			0
$256$	−26.9349	−	254.579i	−0.105215	−	0.994450i
$257$	−84.8354	+	146.939i	−0.330099	+	0.571748i	−0.982531	−	0.186099i	$-0.940415\pi$
$257$	−84.8354	+	146.939i	−0.330099	+	0.571748i	0.652432	+	0.757847i	$0.273749\pi$
$258$		0			0
$259$	115.037	+	199.250i	0.444159	+	0.769306i
$260$	−261.478	+	360.023i	−1.00568	+	1.38471i
$261$		0			0
$262$	−264.949	+	135.027i	−1.01125	+	0.515370i
$263$	111.758	−	64.5235i	0.424936	−	0.245337i	−0.272251	−	0.962226i	$-0.587768\pi$
$263$	111.758	−	64.5235i	0.424936	−	0.245337i	0.697187	+	0.716890i	$0.254435\pi$
$264$		0			0
$265$	−154.212	+	267.103i	−0.581933	+	1.00794i
$266$	365.961	+	19.1476i	1.37579	+	0.0719833i
$267$		0			0
$268$	−218.261	−	22.9021i	−0.814406	−	0.0854555i
$269$			145.712i			0.541679i	0.962624	+	0.270840i	$0.0873013\pi$
$269$			145.712i			0.541679i	−0.962624	+	0.270840i	$0.912699\pi$
$270$		0			0
$271$		−	382.507i		−	1.41147i	−0.708478	−	0.705733i	$-0.750618\pi$
$271$		−	382.507i		−	1.41147i	0.708478	−	0.705733i	$-0.249382\pi$
$272$	−7.28809	+	8.09987i	−0.0267945	+	0.0297789i
$273$		0			0
$274$	6.47694	−	123.792i	0.0236384	−	0.451794i
$275$	−76.3165	+	132.184i	−0.277515	+	0.480669i
$276$		0			0
$277$	353.918	−	204.335i	1.27768	−	0.737671i	0.301261	−	0.953542i	$-0.402592\pi$
$277$	353.918	−	204.335i	1.27768	−	0.737671i	0.976422	+	0.215871i	$0.0692590\pi$
$278$	−332.265	+	169.334i	−1.19520	+	0.609114i
$279$		0			0
$280$	−53.8473	+	340.549i	−0.192312	+	1.21624i
$281$	44.3064	+	76.7410i	0.157674	+	0.273100i	0.934030	−	0.357196i	$-0.116267\pi$
$281$	44.3064	+	76.7410i	0.157674	+	0.273100i	−0.776355	+	0.630295i	$0.782934\pi$
$282$		0			0
$283$	43.1941	−	74.8143i	0.152629	−	0.264362i	−0.779564	−	0.626323i	$-0.784559\pi$
$283$	43.1941	−	74.8143i	0.152629	−	0.264362i	0.932193	+	0.361961i	$0.117893\pi$
$284$	130.108	−	57.9547i	0.458127	−	0.204066i
$285$		0			0
$286$	−208.492	+	321.111i	−0.728994	+	1.12276i
$287$			185.417i			0.646054i
$288$		0			0
$289$	−288.536			−0.998395
$290$	−325.961	−	211.641i	−1.12400	−	0.729798i
$291$		0			0
$292$	184.476	+	414.147i	0.631766	+	1.41831i
$293$	112.358	+	64.8698i	0.383474	+	0.221399i	0.679329	−	0.733834i	$-0.262271\pi$
$293$	112.358	+	64.8698i	0.383474	+	0.221399i	−0.295855	+	0.955233i	$0.595604\pi$
$294$		0			0
$295$	−206.322	+	119.120i	−0.699397	+	0.403797i
$296$	264.015	+	41.7459i	0.891944	+	0.141033i
$297$		0			0
$298$	7.20101	+	14.1298i	0.0241645	+	0.0474153i
$299$	234.173	+	405.599i	0.783187	+	1.35652i
$300$		0			0
$301$	−197.034	−	113.758i	−0.654600	−	0.377933i
$302$	303.959	+	15.9035i	1.00649	+	0.0526606i
$303$		0			0
$304$	284.771	−	316.490i	0.936748	−	1.04109i
$305$	−475.479			−1.55895
$306$		0			0
$307$	116.566			0.379693			0.189847	−	0.981814i	$-0.439201\pi$
$307$	116.566			0.379693			0.189847	+	0.981814i	$0.439201\pi$
$308$	−30.9587	+	295.042i	−0.100515	+	0.957929i
$309$		0			0
$310$	15.0360	−	287.377i	0.0485031	−	0.927024i
$311$	−279.543	−	161.394i	−0.898851	−	0.518952i	−0.0220238	−	0.999757i	$-0.507011\pi$
$311$	−279.543	−	161.394i	−0.898851	−	0.518952i	−0.876827	+	0.480806i	$0.840344\pi$
$312$		0			0
$313$	−91.5107	−	158.501i	−0.292366	−	0.506393i	0.682002	−	0.731350i	$-0.261109\pi$
$313$	−91.5107	−	158.501i	−0.292366	−	0.506393i	−0.974369	+	0.224956i	$0.927776\pi$
$314$	−94.4187	−	185.268i	−0.300697	−	0.590024i
$315$		0			0
$316$	115.157	+	83.6361i	0.364421	+	0.264671i
$317$	−247.800	+	143.067i	−0.781704	+	0.451317i	−0.837034	−	0.547151i	$-0.815712\pi$
$317$	−247.800	+	143.067i	−0.781704	+	0.451317i	0.0553300	+	0.998468i	$0.482379\pi$
$318$		0			0
$319$	−289.601	−	167.201i	−0.907841	−	0.524142i
$320$	268.179	+	297.533i	0.838060	+	0.929792i
$321$		0			0
$322$	304.372	+	197.624i	0.945255	+	0.613740i
$323$	−18.1210			−0.0561021
$324$		0			0
$325$		−	251.876i		−	0.775005i
$326$	24.8739	+	16.1503i	0.0763003	+	0.0495407i
$327$		0			0
$328$	167.443	+	135.521i	0.510497	+	0.413174i
$329$	42.2176	−	73.1230i	0.128321	−	0.222258i
$330$		0			0
$331$	50.8782	+	88.1236i	0.153710	+	0.266234i	0.932589	−	0.360941i	$-0.117544\pi$
$331$	50.8782	+	88.1236i	0.153710	+	0.266234i	−0.778878	+	0.627175i	$0.784211\pi$
$332$	276.104	−	380.162i	0.831637	−	1.14507i
$333$		0			0
$334$	−49.0950	−	96.3338i	−0.146991	−	0.288425i
$335$	297.378	−	171.691i	0.887695	−	0.512511i
$336$		0			0
$337$	17.5224	−	30.3498i	0.0519954	−	0.0900587i	−0.838856	−	0.544353i	$-0.816775\pi$
$337$	17.5224	−	30.3498i	0.0519954	−	0.0900587i	0.890852	+	0.454294i	$0.150109\pi$
$338$	15.3509	−	293.397i	0.0454168	−	0.868037i
$339$		0			0
$340$	1.77916	−	16.9557i	0.00523283	−	0.0498698i
$341$		−	247.609i		−	0.726126i
$342$		0			0
$343$			348.315i			1.01550i
$344$	−246.742	+	94.7887i	−0.717274	+	0.275549i
$345$		0			0
$346$	−649.209	−	33.9674i	−1.87633	−	0.0981718i
$347$	31.6703	−	54.8545i	0.0912687	−	0.158082i	−0.816777	−	0.576954i	$-0.804241\pi$
$347$	31.6703	−	54.8545i	0.0912687	−	0.158082i	0.908045	+	0.418872i	$0.137574\pi$
$348$		0			0
$349$	−397.904	+	229.730i	−1.14012	+	0.658251i	−0.946461	−	0.322817i	$-0.895370\pi$
$349$	−397.904	+	229.730i	−1.14012	+	0.658251i	−0.193663	+	0.981068i	$0.562037\pi$
$350$	−88.6197	−	173.889i	−0.253199	−	0.496826i
$351$		0			0
$352$	243.813	+	243.603i	0.692651	+	0.692054i
$353$	−186.318	−	322.713i	−0.527814	−	0.914201i	−0.999474	−	0.0324202i	$-0.989679\pi$
$353$	−186.318	−	322.713i	−0.527814	−	0.914201i	0.471660	−	0.881780i	$-0.343655\pi$
$354$		0			0
$355$	−111.430	+	193.002i	−0.313887	+	0.543669i
$356$	94.9072	+	213.066i	0.266593	+	0.598501i
$357$		0			0
$358$	−68.5141	−	44.4852i	−0.191380	−	0.124260i
$359$		−	208.385i		−	0.580458i	−0.956957	−	0.290229i	$-0.906268\pi$
$359$		−	208.385i		−	0.580458i	0.956957	−	0.290229i	$-0.0937315\pi$
$360$		0			0
$361$	347.050			0.961357
$362$	126.621	−	195.015i	0.349781	−	0.538716i
$363$		0			0
$364$	−199.197	−	447.196i	−0.547244	−	1.22856i
$365$	−614.346	−	354.693i	−1.68314	−	0.971761i
$366$		0			0
$367$	306.309	−	176.848i	0.834630	−	0.481874i	−0.0208051	−	0.999784i	$-0.506623\pi$
$367$	306.309	−	176.848i	0.834630	−	0.481874i	0.855435	+	0.517910i	$0.173290\pi$
$368$	400.931	−	130.423i	1.08949	−	0.354412i
$369$		0			0
$370$	−372.630	+	189.905i	−1.00711	+	0.513257i
$371$	−169.668	−	293.874i	−0.457327	−	0.792113i
$372$		0			0
$373$	242.982	+	140.286i	0.651426	+	0.376101i	0.789003	−	0.614390i	$-0.210598\pi$
$373$	242.982	+	140.286i	0.651426	+	0.376101i	−0.137576	+	0.990491i	$0.543931\pi$
$374$	0.766477	−	14.6494i	0.00204941	−	0.0391696i
$375$		0			0
$376$	−35.1778	−	91.5704i	−0.0935579	−	0.243538i
$377$	551.835			1.46375
$378$		0			0
$379$	91.6531			0.241829			0.120914	−	0.992663i	$-0.461417\pi$
$379$	91.6531			0.241829			0.120914	+	0.992663i	$0.461417\pi$
$380$	−69.5181	+	662.520i	−0.182942	+	1.74347i
$381$		0			0
$382$	588.646	+	30.7987i	1.54096	+	0.0806250i
$383$	−479.834	−	277.032i	−1.25283	−	0.723322i	−0.281159	−	0.959661i	$-0.590719\pi$
$383$	−479.834	−	277.032i	−1.25283	−	0.723322i	−0.971671	+	0.236339i	$0.924052\pi$
$384$		0			0
$385$	−232.090	−	401.992i	−0.602831	−	1.04413i
$386$	384.550	−	195.980i	0.996245	−	0.507720i
$387$		0			0
$388$	299.845	−	412.850i	0.772795	−	1.06405i
$389$	157.124	−	90.7158i	0.403919	−	0.233203i	−0.284255	−	0.958749i	$-0.591746\pi$
$389$	157.124	−	90.7158i	0.403919	−	0.233203i	0.688173	+	0.725546i	$0.258413\pi$
$390$		0			0
$391$	−15.5408	−	8.97247i	−0.0397462	−	0.0229475i
$392$	9.84430	+	7.96754i	0.0251130	+	0.0203254i
$393$		0			0
$394$	−124.191	+	191.274i	−0.315206	+	0.485466i
$395$	−222.691			−0.563775
$396$		0			0
$397$			418.944i			1.05527i	0.849470	+	0.527637i	$0.176922\pi$
$397$			418.944i			1.05527i	−0.849470	+	0.527637i	$0.823078\pi$
$398$	−238.219	+	366.894i	−0.598540	+	0.921844i
$399$		0			0
$400$	−221.804	−	47.0660i	−0.554510	−	0.117665i
$401$	−365.914	+	633.781i	−0.912503	+	1.58050i	−0.101987	+	0.994786i	$0.532520\pi$
$401$	−365.914	+	633.781i	−0.912503	+	1.58050i	−0.810516	+	0.585717i	$0.800813\pi$
$402$		0			0
$403$	204.303	+	353.864i	0.506957	+	0.878074i
$404$	−568.496	−	412.887i	−1.40717	−	1.02200i
$405$		0			0
$406$	380.972	−	194.156i	0.938355	−	0.478218i
$407$	−311.650	+	179.931i	−0.765725	+	0.442091i
$408$		0			0
$409$	−215.705	+	373.611i	−0.527395	+	0.913475i	0.472095	+	0.881548i	$0.343498\pi$
$409$	−215.705	+	373.611i	−0.527395	+	0.913475i	−0.999490	+	0.0319276i	$0.989835\pi$
$410$	−336.593	−	17.6110i	−0.820958	−	0.0429536i
$411$		0			0
$412$	−0.287776	+	2.74256i	−0.000698486	+	0.00665669i
$413$		−	262.118i		−	0.634669i
$414$		0			0
$415$			735.159i			1.77147i
$416$	−549.437	−	146.967i	−1.32076	−	0.353287i
$417$		0			0
$418$	−29.9490	+	572.405i	−0.0716482	+	1.36939i
$419$	−82.7933	+	143.402i	−0.197597	+	0.342249i	−0.947749	−	0.319017i	$-0.896647\pi$
$419$	−82.7933	+	143.402i	−0.197597	+	0.342249i	0.750151	+	0.661266i	$0.229981\pi$
$420$		0			0
$421$	356.679	−	205.929i	0.847219	−	0.489142i	−0.0124926	−	0.999922i	$-0.503977\pi$
$421$	356.679	−	205.929i	0.847219	−	0.489142i	0.859711	+	0.510780i	$0.170643\pi$
$422$	−430.765	+	219.533i	−1.02077	+	0.520219i
$423$		0			0
$424$	−389.396	−	61.5710i	−0.918387	−	0.145215i
$425$	4.82540	+	8.35783i	0.0113539	+	0.0196655i
$426$		0			0
$427$	261.567	−	453.048i	0.612570	−	1.06100i
$428$	−102.620	−	230.380i	−0.239765	−	0.538272i
$429$		0			0
$430$	225.222	−	346.877i	0.523772	−	0.806690i
$431$			469.824i			1.09008i	0.838411	+	0.545039i	$0.183485\pi$
$431$			469.824i			1.09008i	−0.838411	+	0.545039i	$0.816515\pi$
$432$		0			0
$433$	−243.729			−0.562884			−0.281442	−	0.959578i	$-0.590813\pi$
$433$	−243.729			−0.562884			−0.281442	+	0.959578i	$0.590813\pi$
$434$	265.549	+	172.417i	0.611863	+	0.397274i
$435$		0			0
$436$	−224.019	+	99.7862i	−0.513806	+	0.228867i
$437$	607.233	+	350.586i	1.38955	+	0.802256i
$438$		0			0
$439$	−330.243	+	190.666i	−0.752262	+	0.434318i	−0.826510	−	0.562921i	$-0.809677\pi$
$439$	−330.243	+	190.666i	−0.752262	+	0.434318i	0.0742490	+	0.997240i	$0.476344\pi$
$440$	−532.657	−	84.2233i	−1.21058	−	0.191417i
$441$		0			0
$442$	10.9919	+	21.5683i	0.0248686	+	0.0487970i
$443$	−174.881	−	302.903i	−0.394765	−	0.683753i	0.598306	−	0.801268i	$-0.295841\pi$
$443$	−174.881	−	302.903i	−0.394765	−	0.683753i	−0.993071	+	0.117515i	$0.962507\pi$
$444$		0			0
$445$	−316.063	−	182.479i	−0.710253	−	0.410065i
$446$	187.464	+	9.80835i	0.420323	+	0.0219918i
$447$		0			0
$448$	−431.026	+	91.8505i	−0.962111	+	0.205023i
$449$	473.179			1.05385			0.526926	−	0.849911i	$-0.323345\pi$
$449$	473.179			1.05385			0.526926	+	0.849911i	$0.323345\pi$
$450$		0			0
$451$	−290.014			−0.643046
$452$	165.004	+	17.3139i	0.365053	+	0.0383050i
$453$		0			0
$454$	2.48949	−	47.5808i	0.00548346	−	0.104804i
$455$	663.370	+	382.997i	1.45796	+	0.841752i
$456$		0			0
$457$	374.230	+	648.186i	0.818885	+	1.41835i	0.906505	+	0.422196i	$0.138740\pi$
$457$	374.230	+	648.186i	0.818885	+	1.41835i	−0.0876202	+	0.996154i	$0.527926\pi$
$458$	241.327	+	473.531i	0.526916	+	1.03391i
$459$		0			0
$460$	−387.662	+	533.764i	−0.842743	+	1.16036i
$461$	166.642	−	96.2107i	0.361479	−	0.208700i	−0.308250	−	0.951305i	$-0.599743\pi$
$461$	166.642	−	96.2107i	0.361479	−	0.208700i	0.669729	+	0.742605i	$0.266410\pi$
$462$		0			0
$463$	−474.121	−	273.734i	−1.02402	−	0.591218i	−0.108754	−	0.994069i	$-0.534686\pi$
$463$	−474.121	−	273.734i	−1.02402	−	0.591218i	−0.915266	+	0.402851i	$0.868019\pi$
$464$	103.117	−	485.949i	0.222234	−	1.04730i
$465$		0			0
$466$	−180.168	−	116.980i	−0.386627	−	0.251031i
$467$	510.071			1.09223			0.546115	−	0.837710i	$-0.316106\pi$
$467$	510.071			1.09223			0.546115	+	0.837710i	$0.316106\pi$
$468$		0			0
$469$			377.798i			0.805540i
$470$	128.732	+	83.5838i	0.273898	+	0.177838i
$471$		0			0
$472$	−236.709	−	191.582i	−0.501501	−	0.405893i
$473$	177.930	−	308.184i	0.376174	−	0.651552i
$474$		0			0
$475$	−188.545	−	326.570i	−0.396937	−	0.687516i
$476$	15.1771	+	11.0228i	0.0318846	+	0.0231571i
$477$		0			0
$478$	89.4510	+	175.520i	0.187136	+	0.367197i
$479$	218.351	−	126.065i	0.455849	−	0.263184i	−0.254449	−	0.967086i	$-0.581894\pi$
$479$	218.351	−	126.065i	0.455849	−	0.263184i	0.710297	+	0.703902i	$0.248561\pi$
$480$		0			0
$481$	296.924	−	514.288i	0.617306	−	1.06921i
$482$	−42.4545	+	811.419i	−0.0880799	+	1.68344i
$483$		0			0
$484$	19.8780	+	2.08580i	0.0410703	+	0.00430950i
$485$			798.372i			1.64613i
$486$		0			0
$487$		−	839.912i		−	1.72467i	−0.506342	−	0.862333i	$-0.669003\pi$
$487$		−	839.912i		−	1.72467i	0.506342	−	0.862333i	$-0.330997\pi$
$488$	−217.951	−	567.343i	−0.446621	−	1.16259i
$489$		0			0
$490$	−19.7889	−	1.03538i	−0.0403856	−	0.00211303i
$491$	133.450	−	231.142i	0.271792	−	0.470758i	−0.697529	−	0.716557i	$-0.745717\pi$
$491$	133.450	−	231.142i	0.271792	−	0.470758i	0.969321	+	0.245799i	$0.0790504\pi$
$492$		0			0
$493$	−18.3111	+	10.5719i	−0.0371422	+	0.0214441i
$494$	−429.493	−	842.748i	−0.869420	−	1.70597i
$495$		0			0
$496$	349.791	−	113.788i	0.705225	−	0.229410i
$497$	−122.598	−	212.346i	−0.246676	−	0.427256i
$498$		0			0
$499$	58.1397	−	100.701i	0.116512	−	0.201805i	−0.801871	−	0.597497i	$-0.796162\pi$
$499$	58.1397	−	100.701i	0.116512	−	0.201805i	0.918383	+	0.395692i	$0.129495\pi$
$500$	−247.635	+	110.306i	−0.495271	+	0.220611i
$501$		0			0
$502$	−382.306	−	248.225i	−0.761565	−	0.494473i
$503$			304.204i			0.604780i	0.953184	+	0.302390i	$0.0977844\pi$
$503$			304.204i			0.604780i	−0.953184	+	0.302390i	$0.902216\pi$
$504$		0			0
$505$	1099.36			2.17695
$506$	−309.107	+	476.073i	−0.610883	+	0.940855i
$507$		0			0
$508$	−509.208	+	226.819i	−1.00238	+	0.446495i
$509$	145.986	+	84.2850i	0.286809	+	0.165589i	0.636502	−	0.771275i	$-0.280381\pi$
$509$	145.986	+	84.2850i	0.286809	+	0.165589i	−0.349693	+	0.936864i	$0.613714\pi$
$510$		0			0
$511$	675.919	−	390.242i	1.32274	−	0.763684i
$512$	−232.089	+	456.376i	−0.453299	+	0.891359i
$513$		0			0
$514$	302.342	−	154.084i	0.588215	−	0.299774i
$515$	−2.15739	−	3.73671i	−0.00418910	−	0.00725574i
$516$		0			0
$517$	114.373	+	66.0331i	0.221224	+	0.127724i
$518$	24.0427	−	459.520i	0.0464145	−	0.887104i
$519$		0			0
$520$	830.725	−	319.132i	1.59755	−	0.613716i
$521$	55.4427			0.106416			0.0532080	−	0.998583i	$-0.483055\pi$
$521$	55.4427			0.106416			0.0532080	+	0.998583i	$0.483055\pi$
$522$		0			0
$523$	−295.471			−0.564954			−0.282477	−	0.959274i	$-0.591156\pi$
$523$	−295.471			−0.564954			−0.282477	+	0.959274i	$0.591156\pi$
$524$	591.497	+	62.0656i	1.12881	+	0.118446i
$525$		0			0
$526$	−257.742	−	13.4854i	−0.490003	−	0.0256376i
$527$	−13.5585	−	7.82801i	−0.0257277	−	0.0148539i
$528$		0			0
$529$	82.6803	+	143.207i	0.156296	+	0.270712i
$530$	549.592	−	280.091i	1.03697	−	0.528473i
$531$		0			0
$532$	−593.022	−	430.699i	−1.11470	−	0.809585i
$533$	414.466	−	239.292i	0.777609	−	0.448953i
$534$		0			0
$535$	341.747	+	197.307i	0.638779	+	0.368799i
$536$	341.175	+	276.132i	0.636520	+	0.515171i
$537$		0			0
$538$	158.700	−	244.422i	0.294981	−	0.454316i
$539$	−17.0505			−0.0316335
$540$		0			0
$541$			579.072i			1.07037i	0.844734	+	0.535186i	$0.179759\pi$
$541$			579.072i			1.07037i	−0.844734	+	0.535186i	$0.820241\pi$
$542$	−416.602	+	641.631i	−0.768638	+	1.18382i
$543$		0			0
$544$	21.0471	−	5.64929i	0.0386896	−	0.0103847i
$545$	191.860	−	332.311i	0.352036	−	0.609744i
$546$		0			0
$547$	−448.149	−	776.217i	−0.819285	−	1.41904i	−0.906210	−	0.422828i	$-0.861037\pi$
$547$	−448.149	−	776.217i	−0.819285	−	1.41904i	0.0869249	−	0.996215i	$-0.472296\pi$
$548$	−145.690	+	200.598i	−0.265858	+	0.366055i
$549$		0			0
$550$	271.982	−	138.611i	0.494513	−	0.252021i
$551$	715.480	−	413.083i	1.29851	−	0.749696i
$552$		0			0
$553$	122.505	−	212.186i	0.221529	−	0.383699i
$554$	−816.223	−	42.7058i	−1.47333	−	0.0770864i
$555$		0			0
$556$	741.781	+	77.8349i	1.33414	+	0.139991i
$557$			736.451i			1.32217i	0.750309	+	0.661087i	$0.229905\pi$
$557$			736.451i			1.32217i	−0.750309	+	0.661087i	$0.770095\pi$
$558$		0			0
$559$			587.245i			1.05053i
$560$	461.228	−	512.601i	0.823622	−	0.915359i
$561$		0			0
$562$	9.26001	−	176.984i	0.0164769	−	0.314917i
$563$	−124.818	+	216.191i	−0.221701	+	0.383998i	−0.955325	−	0.295559i	$-0.904494\pi$
$563$	−124.818	+	216.191i	−0.221701	+	0.383998i	0.733624	+	0.679556i	$0.237828\pi$
$564$		0			0
$565$	−224.816	+	129.798i	−0.397905	+	0.229731i
$566$	−153.938	+	78.4521i	−0.271975	+	0.138608i
$567$		0			0
$568$	−281.368	−	44.4897i	−0.495367	−	0.0783270i
$569$	185.689	+	321.622i	0.326342	+	0.565241i	0.981783	−	0.190005i	$-0.0608506\pi$
$569$	185.689	+	321.622i	0.326342	+	0.565241i	−0.655441	+	0.755246i	$0.727517\pi$
$570$		0			0
$571$	−503.426	+	871.960i	−0.881658	+	1.52708i	−0.0321603	+	0.999483i	$0.510239\pi$
$571$	−503.426	+	871.960i	−0.881658	+	1.52708i	−0.849497	+	0.527593i	$0.823095\pi$
$572$	699.465	−	311.566i	1.22284	−	0.544697i
$573$		0			0
$574$	201.944	−	311.026i	0.351819	−	0.541857i
$575$		−	373.427i		−	0.649439i
$576$		0			0
$577$	−585.056			−1.01396			−0.506981	−	0.861957i	$-0.669238\pi$
$577$	−585.056			−1.01396			−0.506981	+	0.861957i	$0.669238\pi$
$578$	484.001	+	314.254i	0.837372	+	0.543693i
$579$		0			0
$580$	316.272	+	710.029i	0.545297	+	1.22419i
$581$	−700.477	−	404.420i	−1.20564	−	0.696077i
$582$		0			0
$583$	459.652	−	265.380i	0.788426	−	0.455198i
$584$	141.615	−	895.623i	0.242492	−	1.53360i
$585$		0			0
$586$	−117.821	−	231.188i	−0.201060	−	0.394518i
$587$	−174.768	−	302.707i	−0.297731	−	0.515685i	0.677886	−	0.735167i	$-0.262896\pi$
$587$	−174.768	−	302.707i	−0.297731	−	0.515685i	−0.975616	+	0.219483i	$0.929563\pi$
$588$		0			0
$589$	529.778	+	305.868i	0.899454	+	0.519300i
$590$	475.830	+	24.8960i	0.806491	+	0.0421967i
$591$		0			0
$592$	−397.402	−	357.574i	−0.671287	−	0.604010i
$593$	−983.452			−1.65844			−0.829218	−	0.558926i	$-0.811214\pi$
$593$	−983.452			−1.65844			−0.829218	+	0.558926i	$0.811214\pi$
$594$		0			0
$595$	−29.3495			−0.0493269
$596$	3.30997	−	31.5446i	0.00555365	−	0.0529272i
$597$		0			0
$598$	48.9420	−	935.412i	0.0818428	−	1.56423i
$599$	−72.7768	−	42.0177i	−0.121497	−	0.0701464i	0.438020	−	0.898965i	$-0.355680\pi$
$599$	−72.7768	−	42.0177i	−0.121497	−	0.0701464i	−0.559517	+	0.828819i	$0.689013\pi$
$600$		0			0
$601$	521.747	+	903.693i	0.868132	+	1.50365i	0.863903	+	0.503658i	$0.168013\pi$
$601$	521.747	+	903.693i	0.868132	+	1.50365i	0.00422856	+	0.999991i	$0.498654\pi$
$602$	206.615	+	405.418i	0.343214	+	0.673452i
$603$		0			0
$604$	−492.550	−	357.728i	−0.815480	−	0.592266i
$605$	−27.0836	+	15.6367i	−0.0447663	+	0.0258458i
$606$		0			0
$607$	462.637	+	267.103i	0.762169	+	0.440038i	0.830074	−	0.557653i	$-0.188298\pi$
$607$	462.637	+	267.103i	0.762169	+	0.440038i	−0.0679050	+	0.997692i	$0.521631\pi$
$608$	−822.386	+	220.738i	−1.35261	+	0.363055i
$609$		0			0
$610$	797.586	+	517.861i	1.30752	+	0.848952i
$611$	−217.937			−0.356689
$612$		0			0
$613$		−	516.828i		−	0.843113i	−0.906802	−	0.421556i	$-0.861484\pi$
$613$		−	516.828i		−	0.843113i	0.906802	−	0.421556i	$-0.138516\pi$
$614$	−195.532	−	126.956i	−0.318456	−	0.206768i
$615$		0			0
$616$	373.271	−	461.196i	0.605960	−	0.748694i
$617$	151.566	−	262.520i	0.245650	−	0.425477i	−0.716665	−	0.697418i	$-0.754332\pi$
$617$	151.566	−	262.520i	0.245650	−	0.425477i	0.962314	+	0.271941i	$0.0876654\pi$
$618$		0			0
$619$	288.511	+	499.715i	0.466092	+	0.807295i	0.999250	−	0.0387208i	$-0.0123283\pi$
$619$	288.511	+	499.715i	0.466092	+	0.807295i	−0.533158	+	0.846016i	$0.678995\pi$
$620$	−338.214	+	465.681i	−0.545507	+	0.751098i
$621$		0			0
$622$	293.135	+	575.187i	0.471278	+	0.924738i
$623$	347.740	−	200.768i	0.558171	−	0.322260i
$624$		0			0
$625$	389.228	−	674.163i	0.622765	−	1.07866i
$626$	−19.1257	+	365.543i	−0.0305522	+	0.583934i
$627$		0			0
$628$	−43.3999	+	413.609i	−0.0691082	+	0.658613i
$629$			22.7536i			0.0361743i
$630$		0			0
$631$		−	101.296i		−	0.160532i	−0.996773	−	0.0802661i	$-0.974423\pi$
$631$		−	101.296i		−	0.160532i	0.996773	−	0.0802661i	$-0.0255770\pi$
$632$	−102.078	−	265.716i	−0.161515	−	0.420436i
$633$		0			0
$634$	571.488	+	29.9010i	0.901401	+	0.0471625i
$635$	436.107	−	755.360i	0.686783	−	1.18954i
$636$		0			0
$637$	24.3672	−	14.0684i	0.0382531	−	0.0220854i
$638$	303.683	+	595.884i	0.475992	+	0.933987i
$639$		0			0
$640$	−125.800	−	791.176i	−0.196562	−	1.23621i
$641$	575.546	+	996.875i	0.897888	+	1.55519i	0.830190	+	0.557481i	$0.188232\pi$
$641$	575.546	+	996.875i	0.897888	+	1.55519i	0.0676980	+	0.997706i	$0.478435\pi$
$642$		0			0
$643$	−87.5932	+	151.716i	−0.136226	+	0.235950i	−0.926065	−	0.377364i	$-0.876831\pi$
$643$	−87.5932	+	151.716i	−0.136226	+	0.235950i	0.789839	+	0.613314i	$0.210164\pi$
$644$	−295.325	−	663.004i	−0.458580	−	1.02951i
$645$		0			0
$646$	30.3968	+	19.7362i	0.0470538	+	0.0305513i
$647$		−	761.431i		−	1.17686i	−0.808547	−	0.588432i	$-0.799745\pi$
$647$		−	761.431i		−	1.17686i	0.808547	−	0.588432i	$-0.200255\pi$
$648$		0			0
$649$	409.983			0.631715
$650$	−274.327	+	422.506i	−0.422042	+	0.650010i
$651$		0			0
$652$	−24.1346	−	54.1820i	−0.0370162	−	0.0831013i
$653$	−229.877	−	132.720i	−0.352032	−	0.203246i	0.313548	−	0.949572i	$-0.398482\pi$
$653$	−229.877	−	132.720i	−0.352032	−	0.203246i	−0.665580	+	0.746327i	$0.731816\pi$
$654$		0			0
$655$	−805.908	+	465.291i	−1.23039	+	0.710368i
$656$	−133.274	−	409.696i	−0.203162	−	0.624536i
$657$		0			0
$658$	−150.458	+	76.6785i	−0.228659	+	0.116533i
$659$	−453.855	−	786.099i	−0.688702	−	1.19287i	−0.972258	−	0.233911i	$-0.924848\pi$
$659$	−453.855	−	786.099i	−0.688702	−	1.19287i	0.283556	−	0.958956i	$-0.408486\pi$
$660$		0			0
$661$	−123.063	−	71.0504i	−0.186177	−	0.107489i	0.404015	−	0.914753i	$-0.367614\pi$
$661$	−123.063	−	71.0504i	−0.186177	−	0.107489i	−0.590192	+	0.807263i	$0.700948\pi$
$662$	10.6335	−	203.235i	0.0160627	−	0.307001i
$663$		0			0
$664$	−877.193	+	336.983i	−1.32107	+	0.507505i
$665$	1146.79			1.72449
$666$		0			0
$667$	818.140			1.22660
$668$	−22.5667	+	215.065i	−0.0337825	+	0.321953i
$669$		0			0
$670$	−685.827	−	35.8834i	−1.02362	−	0.0535572i
$671$	708.619	+	409.121i	1.05606	+	0.609719i
$672$		0			0
$673$	−510.616	−	884.413i	−0.758717	−	1.31414i	−0.943505	−	0.331357i	$-0.892493\pi$
$673$	−510.616	−	884.413i	−0.758717	−	1.31414i	0.184789	−	0.982778i	$-0.440840\pi$
$674$	−62.4477	+	31.8255i	−0.0926524	+	0.0472188i
$675$		0			0
$676$	−345.298	+	475.435i	−0.510796	+	0.703306i
$677$	−441.094	+	254.666i	−0.651542	+	0.376168i	−0.789047	−	0.614333i	$-0.789425\pi$
$677$	−441.094	+	254.666i	−0.651542	+	0.376168i	0.137505	+	0.990501i	$0.456092\pi$
$678$		0			0
$679$	−760.708	−	439.195i	−1.12034	−	0.646826i
$680$	−21.4515	+	26.5044i	−0.0315463	+	0.0389770i
$681$		0			0
$682$	−269.679	+	415.348i	−0.395424	+	0.609015i
$683$	−956.848			−1.40095			−0.700475	−	0.713677i	$-0.747028\pi$
$683$	−956.848			−1.40095			−0.700475	+	0.713677i	$0.747028\pi$
$684$		0			0
$685$		−	387.917i		−	0.566303i
$686$	379.361	−	584.275i	0.553005	−	0.851713i
$687$		0			0
$688$	517.132	+	109.733i	0.751645	+	0.159496i
$689$	−437.933	+	758.523i	−0.635607	+	1.10090i
$690$		0			0
$691$	−567.491	−	982.924i	−0.821261	−	1.42247i	−0.904744	−	0.425956i	$-0.859938\pi$
$691$	−567.491	−	982.924i	−0.821261	−	1.42247i	0.0834830	−	0.996509i	$-0.473396\pi$
$692$	1052.01	+	764.053i	1.52025	+	1.10412i
$693$		0			0
$694$	−112.869	+	57.5217i	−0.162635	+	0.0828843i
$695$	−1010.67	+	583.509i	−1.45420	+	0.839582i
$696$		0			0
$697$	−9.16861	+	15.8805i	−0.0131544	+	0.0227841i
$698$	917.664	+	48.0134i	1.31470	+	0.0687870i
$699$		0			0
$700$	−40.7344	+	388.206i	−0.0581920	+	0.554580i
$701$		−	784.688i		−	1.11938i	−0.828701	−	0.559692i	$-0.810920\pi$
$701$		−	784.688i		−	1.11938i	0.828701	−	0.559692i	$-0.189080\pi$
$702$		0			0
$703$		−	889.065i		−	1.26467i
$704$	−143.665	−	674.173i	−0.204069	−	0.957633i
$705$		0			0
$706$	−38.9404	+	744.255i	−0.0551564	+	1.05419i
$707$	−604.773	+	1047.50i	−0.855407	+	1.48161i
$708$		0			0
$709$	−1126.52	+	650.396i	−1.58888	+	0.917343i	−0.595393	+	0.803435i	$0.703004\pi$
$709$	−1126.52	+	650.396i	−1.58888	+	0.917343i	−0.993491	+	0.113908i	$0.963663\pi$
$710$	397.122	−	202.387i	0.559327	−	0.285052i
$711$		0			0
$712$	72.8568	−	460.771i	0.102327	−	0.647151i
$713$	302.896	+	524.632i	0.424820	+	0.735809i
$714$		0			0
$715$	−599.051	+	1037.59i	−0.837834	+	1.45117i
$716$	66.4777	+	149.242i	0.0928460	+	0.208439i
$717$		0			0
$718$	−226.959	+	349.552i	−0.316098	+	0.486841i
$719$			178.101i			0.247706i	0.992301	+	0.123853i	$0.0395251\pi$
$719$			178.101i			0.247706i	−0.992301	+	0.123853i	$0.960475\pi$
$720$		0			0
$721$	4.74723			0.00658423
$722$	−582.154	−	377.984i	−0.806307	−	0.523523i
$723$		0			0
$724$	−424.795	+	189.219i	−0.586734	+	0.261352i
$725$	−381.047	−	219.998i	−0.525583	−	0.303445i
$726$		0			0
$727$	−443.988	+	256.337i	−0.610713	+	0.352595i	−0.773244	−	0.634108i	$-0.781367\pi$
$727$	−443.988	+	256.337i	−0.610713	+	0.352595i	0.162532	+	0.986703i	$0.448034\pi$
$728$	−152.916	+	967.094i	−0.210050	+	1.32843i
$729$		0			0
$730$	644.218	+	1264.08i	0.882490	+	1.73161i
$731$	−11.2503	−	19.4861i	−0.0153903	−	0.0266568i
$732$		0			0
$733$	143.091	+	82.6135i	0.195212	+	0.112706i	0.594420	−	0.804154i	$-0.297382\pi$
$733$	143.091	+	82.6135i	0.195212	+	0.112706i	−0.399208	+	0.916860i	$0.630715\pi$
$734$	−706.425	−	36.9611i	−0.962432	−	0.0503557i
$735$		0			0
$736$	−814.585	−	217.891i	−1.10677	−	0.296048i
$737$	−590.920			−0.801791
$738$		0			0
$739$	−287.818			−0.389469			−0.194735	−	0.980856i	$-0.562385\pi$
$739$	−287.818			−0.389469			−0.194735	+	0.980856i	$0.562385\pi$
$740$	831.895	+	87.2906i	1.12418	+	0.117960i
$741$		0			0
$742$	−35.4606	+	677.746i	−0.0477905	+	0.913404i
$743$	−852.872	−	492.406i	−1.14788	−	0.662726i	−0.199507	−	0.979896i	$-0.563934\pi$
$743$	−852.872	−	492.406i	−1.14788	−	0.662726i	−0.948369	+	0.317170i	$0.897267\pi$
$744$		0			0
$745$	24.8141	+	42.9792i	0.0333075	+	0.0576902i
$746$	−254.797	−	499.960i	−0.341551	−	0.670188i
$747$		0			0
$748$	−17.2409	+	23.7387i	−0.0230493	+	0.0317362i
$749$	−375.999	+	217.083i	−0.502001	+	0.289830i
$750$		0			0
$751$	−61.7319	−	35.6409i	−0.0821996	−	0.0474580i	0.458337	−	0.888779i	$-0.348445\pi$
$751$	−61.7319	−	35.6409i	−0.0821996	−	0.0474580i	−0.540536	+	0.841321i	$0.681779\pi$
$752$	−40.7240	+	191.917i	−0.0541542	+	0.255208i
$753$		0			0
$754$	−925.667	−	601.022i	−1.22767	−	0.797111i
$755$	952.495			1.26158
$756$		0			0
$757$		−	398.629i		−	0.526591i	−0.964715	−	0.263295i	$-0.915191\pi$
$757$		−	398.629i		−	0.526591i	0.964715	−	0.263295i	$-0.0848094\pi$
$758$	−153.742	−	99.8225i	−0.202826	−	0.131692i
$759$		0			0
$760$	838.185	−	1035.62i	1.10287	−	1.36266i
$761$	−260.245	+	450.758i	−0.341978	+	0.592323i	−0.984800	−	0.173692i	$-0.944430\pi$
$761$	−260.245	+	450.758i	−0.341978	+	0.592323i	0.642822	+	0.766016i	$0.277764\pi$
$762$		0			0
$763$	211.089	+	365.617i	0.276657	+	0.479183i
$764$	−953.872	−	692.777i	−1.24852	−	0.906777i
$765$		0			0
$766$	503.165	+	987.307i	0.656873	+	1.28891i
$767$	−585.916	+	338.279i	−0.763906	+	0.441041i
$768$		0			0
$769$	−28.9207	+	50.0921i	−0.0376082	+	0.0651393i	−0.884217	−	0.467077i	$-0.845307\pi$
$769$	−28.9207	+	50.0921i	−0.0376082	+	0.0651393i	0.846609	+	0.532216i	$0.178641\pi$
$770$	−48.5066	+	927.092i	−0.0629956	+	1.20402i
$771$		0			0
$772$	−858.507	−	90.0830i	−1.11206	−	0.116688i
$773$		−	42.8654i		−	0.0554532i	−0.999616	−	0.0277266i	$-0.991173\pi$
$773$		−	42.8654i		−	0.0554532i	0.999616	−	0.0277266i	$-0.00882679\pi$
$774$		0			0
$775$		−	325.796i		−	0.420381i
$776$	−952.619	+	365.959i	−1.22760	+	0.471597i
$777$		0			0
$778$	−362.368	−	18.9595i	−0.465768	−	0.0243696i
$779$	358.250	−	620.507i	0.459884	−	0.796542i
$780$		0			0
$781$	332.134	−	191.757i	0.425267	−	0.245528i
$782$	16.2964	+	31.9767i	0.0208394	+	0.0408909i
$783$		0			0
$784$	−7.83546	−	24.0868i	−0.00999421	−	0.0307229i
$785$	−325.359	−	563.538i	−0.414470	−	0.717883i
$786$		0			0
$787$	84.6130	−	146.554i	0.107513	−	0.186218i	−0.807249	−	0.590211i	$-0.799045\pi$
$787$	84.6130	−	146.554i	0.107513	−	0.186218i	0.914762	+	0.403993i	$0.132378\pi$
$788$	416.645	−	185.589i	0.528738	−	0.235518i
$789$		0			0
$790$	373.550	+	242.540i	0.472848	+	0.307013i
$791$		−	285.614i		−	0.361079i
$792$		0			0
$793$	−1350.27			−1.70274
$794$	456.286	−	702.751i	0.574667	−	0.885077i
$795$		0			0
$796$	799.193	−	355.989i	1.00401	−	0.447222i
$797$	685.260	+	395.635i	0.859799	+	0.496405i	0.863945	−	0.503586i	$-0.167986\pi$
$797$	685.260	+	395.635i	0.859799	+	0.496405i	−0.00414571	+	0.999991i	$0.501320\pi$
$798$		0			0
$799$	7.23164	−	4.17519i	0.00905086	−	0.00522552i
$800$	320.801	+	320.524i	0.401001	+	0.400656i
$801$		0			0
$802$	1304.07	−	664.598i	1.62602	−	0.828676i
$803$	610.383	+	1057.21i	0.760129	+	1.31658i
$804$		0			0
$805$	983.500	+	567.824i	1.22174	+	0.705372i
$806$	42.6993	−	816.098i	0.0529768	−	1.01253i
$807$		0			0
$808$	503.927	+	1311.76i	0.623672	+	1.62347i
$809$	875.148			1.08176			0.540882	−	0.841098i	$-0.318090\pi$
$809$	875.148			1.08176			0.540882	+	0.841098i	$0.318090\pi$
$810$		0			0
$811$	−768.727			−0.947875			−0.473938	−	0.880558i	$-0.657168\pi$
$811$	−768.727			−0.947875			−0.473938	+	0.880558i	$0.657168\pi$
$812$	−850.519	−	89.2448i	−1.04744	−	0.109907i
$813$		0			0
$814$	718.742	+	37.6055i	0.882975	+	0.0461984i
$815$	80.3737	+	46.4037i	0.0986180	+	0.0569371i
$816$		0			0
$817$	439.589	+	761.391i	0.538053	+	0.931935i
$818$	768.743	−	391.778i	0.939784	−	0.478946i
$819$		0			0
$820$	545.432	+	396.136i	0.665161	+	0.483092i
$821$	−925.893	+	534.565i	−1.12776	+	0.651114i	−0.943371	−	0.331739i	$-0.892365\pi$
$821$	−925.893	+	534.565i	−1.12776	+	0.651114i	−0.184392	+	0.982853i	$0.559031\pi$
$822$		0			0
$823$	−376.654	−	217.461i	−0.457659	−	0.264230i	0.253400	−	0.967362i	$-0.418451\pi$
$823$	−376.654	−	217.461i	−0.457659	−	0.264230i	−0.711060	+	0.703132i	$0.751784\pi$
$824$	3.46974	−	4.28704i	0.00421085	−	0.00520271i
$825$		0			0
$826$	−285.482	+	439.686i	−0.345620	+	0.532308i
$827$	−1476.00			−1.78476			−0.892381	−	0.451282i	$-0.850967\pi$
$827$	−1476.00			−1.78476			−0.892381	+	0.451282i	$0.850967\pi$
$828$		0			0
$829$		−	817.581i		−	0.986225i	−0.869965	−	0.493113i	$-0.835859\pi$
$829$		−	817.581i		−	0.986225i	0.869965	−	0.493113i	$-0.164141\pi$
$830$	800.686	−	1233.18i	0.964682	−	1.48576i
$831$		0			0
$832$	761.578	+	844.938i	0.915358	+	1.01555i
$833$	−0.539040	+	0.933644i	−0.000647107	+	0.00112082i
$834$		0			0
$835$	−169.177	−	293.023i	−0.202607	−	0.350926i
$836$	673.663	−	927.554i	0.805817	−	1.10951i
$837$		0			0
$838$	295.065	−	150.375i	0.352106	−	0.179445i
$839$	−573.525	+	331.125i	−0.683582	+	0.394666i	−0.801203	−	0.598392i	$-0.795806\pi$
$839$	−573.525	+	331.125i	−0.683582	+	0.394666i	0.117621	+	0.993059i	$0.462473\pi$
$840$		0			0
$841$	61.4919	−	106.507i	0.0731176	−	0.126643i
$842$	−822.590	−	43.0390i	−0.976948	−	0.0511152i
$843$		0			0
$844$	961.681	+	100.909i	1.13943	+	0.119560i
$845$		−	919.398i		−	1.08804i
$846$		0			0
$847$		−	34.4079i		−	0.0406232i
$848$	586.128	+	527.386i	0.691188	+	0.621917i
$849$		0			0
$850$	1.00850	−	19.2752i	0.00118648	−	0.0226767i
$851$	440.214	−	762.473i	0.517290	−	0.895973i
$852$		0			0
$853$	855.899	−	494.154i	1.00340	−	0.579313i	0.0941469	−	0.995558i	$-0.469988\pi$
$853$	855.899	−	494.154i	1.00340	−	0.579313i	0.909252	+	0.416246i	$0.136654\pi$
$854$	−932.192	+	475.077i	−1.09156	+	0.556296i
$855$		0			0
$856$	−78.7773	+	498.215i	−0.0920296	+	0.582026i
$857$	−19.4901	−	33.7578i	−0.0227422	−	0.0393906i	0.854430	−	0.519566i	$-0.173906\pi$
$857$	−19.4901	−	33.7578i	−0.0227422	−	0.0393906i	−0.877173	+	0.480175i	$0.840573\pi$
$858$		0			0
$859$	210.715	−	364.969i	0.245302	−	0.424876i	−0.716914	−	0.697161i	$-0.754446\pi$
$859$	210.715	−	364.969i	0.245302	−	0.424876i	0.962217	+	0.272285i	$0.0877794\pi$
$860$	−755.590	+	336.567i	−0.878593	+	0.391357i
$861$		0			0
$862$	511.701	−	788.099i	0.593620	−	0.914268i
$863$		−	646.843i		−	0.749528i	−0.927120	−	0.374764i	$-0.877724\pi$
$863$		−	646.843i		−	0.749528i	0.927120	−	0.374764i	$-0.122276\pi$
$864$		0			0
$865$	−2034.38			−2.35189
$866$	408.839	+	265.453i	0.472101	+	0.306528i
$867$		0			0
$868$	−257.656	−	578.436i	−0.296838	−	0.666401i
$869$	331.882	+	191.612i	0.381913	+	0.220497i
$870$		0			0
$871$	844.497	−	487.571i	0.969572	−	0.559783i
$872$	484.459	+	76.6022i	0.555572	+	0.0878466i
$873$		0			0
$874$	−636.759	−	1249.44i	−0.728557	−	1.42957i
$875$	233.342	+	404.160i	0.266676	+	0.461897i
$876$		0			0
$877$	−223.150	−	128.836i	−0.254447	−	0.146905i	0.367352	−	0.930082i	$-0.380264\pi$
$877$	−223.150	−	128.836i	−0.254447	−	0.146905i	−0.621799	+	0.783177i	$0.713598\pi$
$878$	761.621	+	39.8490i	0.867450	+	0.0453861i
$879$		0			0
$880$	801.767	+	721.413i	0.911098	+	0.819788i
$881$	−1633.28			−1.85389			−0.926947	−	0.375193i	$-0.877576\pi$
$881$	−1633.28			−1.85389			−0.926947	+	0.375193i	$0.877576\pi$
$882$		0			0
$883$	1353.38			1.53271			0.766355	−	0.642417i	$-0.222068\pi$
$883$	1353.38			1.53271			0.766355	+	0.642417i	$0.222068\pi$
$884$	5.05248	−	48.1511i	0.00571548	−	0.0544695i
$885$		0			0
$886$	−36.5500	+	698.568i	−0.0412528	+	0.788451i
$887$	282.071	+	162.854i	0.318006	+	0.183601i	0.650503	−	0.759503i	$-0.274558\pi$
$887$	282.071	+	162.854i	0.318006	+	0.183601i	−0.332498	+	0.943104i	$0.607891\pi$
$888$		0			0
$889$	479.817	+	831.067i	0.539726	+	0.934833i
$890$	331.431	+	650.331i	0.372394	+	0.730709i
$891$		0			0
$892$	−303.776	−	220.626i	−0.340556	−	0.247339i
$893$	−282.565	+	163.139i	−0.316423	+	0.182687i
$894$		0			0
$895$	−221.386	−	127.817i	−0.247358	−	0.142812i
$896$	823.055	+	315.371i	0.918588	+	0.351977i
$897$		0			0
$898$	−793.728	−	515.355i	−0.883884	−	0.573892i
$899$	713.783			0.793975
$900$		0			0
$901$		−	33.5593i		−	0.0372468i
$902$	486.479	+	315.864i	0.539334	+	0.350182i
$903$		0			0
$904$	−257.927	−	208.754i	−0.285317	−	0.230923i
$905$	363.813	−	630.142i	0.402003	−	0.696289i
$906$		0			0
$907$	−199.536	−	345.607i	−0.219996	−	0.381044i	0.734811	−	0.678272i	$-0.237271\pi$
$907$	−199.536	−	345.607i	−0.219996	−	0.381044i	−0.954806	+	0.297229i	$0.903938\pi$
$908$	−55.9978	+	77.1024i	−0.0616716	+	0.0849145i
$909$		0			0
$910$	−695.626	−	1364.95i	−0.764424	−	1.49995i
$911$	315.232	−	181.999i	0.346028	−	0.199779i	−0.316906	−	0.948457i	$-0.602644\pi$
$911$	315.232	−	181.999i	0.346028	−	0.199779i	0.662935	+	0.748677i	$0.269311\pi$
$912$		0			0
$913$	632.560	−	1095.63i	0.692836	−	1.20003i
$914$	78.2139	−	1494.88i	0.0855732	−	1.63553i
$915$		0			0
$916$	110.927	−	1057.16i	0.121099	−	1.15410i
$917$		−	1023.85i		−	1.11652i
$918$		0			0
$919$			1451.55i			1.57949i	0.613434	+	0.789746i	$0.289788\pi$
$919$			1451.55i			1.57949i	−0.613434	+	0.789746i	$0.710212\pi$
$920$	1231.62	−	473.139i	1.33871	−	0.514282i
$921$		0			0
$922$	−384.317	−	20.1080i	−0.416830	−	0.0218091i
$923$	−316.440	+	548.090i	−0.342839	+	0.593814i
$924$		0			0
$925$	−410.058	+	236.747i	−0.443306	+	0.255943i
$926$	497.174	+	975.552i	0.536905	+	1.05351i
$927$		0			0
$928$	−702.235	+	702.841i	−0.756719	+	0.757372i
$929$	−346.569	−	600.274i	−0.373055	−	0.646151i	0.616978	−	0.786980i	$-0.288357\pi$
$929$	−346.569	−	600.274i	−0.373055	−	0.646151i	−0.990034	+	0.140829i	$0.955023\pi$
$930$		0			0
$931$	21.0622	−	36.4808i	0.0226232	−	0.0391845i
$932$	174.813	+	392.454i	0.187568	+	0.421088i
$933$		0			0
$934$	−855.611	−	555.536i	−0.916072	−	0.594792i
$935$		−	45.9060i		−	0.0490973i
$936$		0			0
$937$	74.3295			0.0793272			0.0396636	−	0.999213i	$-0.487371\pi$
$937$	74.3295			0.0793272			0.0396636	+	0.999213i	$0.487371\pi$
$938$	411.473	−	633.732i	0.438670	−	0.675621i
$939$		0			0
$940$	−124.906	−	280.413i	−0.132879	−	0.298312i
$941$	1375.98	+	794.423i	1.46225	+	0.844233i	0.999115	−	0.0420533i	$-0.0133899\pi$
$941$	1375.98	+	794.423i	1.46225	+	0.844233i	0.463138	+	0.886286i	$0.346723\pi$
$942$		0			0
$943$	614.479	−	354.770i	0.651621	−	0.376214i
$944$	188.406	+	579.173i	0.199582	+	0.613531i
$945$		0			0
$946$	−634.120	+	323.169i	−0.670318	+	0.341617i
$947$	653.900	+	1132.59i	0.690497	+	1.19598i	0.971675	+	0.236320i	$0.0759414\pi$
$947$	653.900	+	1132.59i	0.690497	+	1.19598i	−0.281179	+	0.959655i	$0.590725\pi$
$948$		0			0
$949$	−1744.63	−	1007.26i	−1.83838	−	1.06139i
$950$	−39.4058	+	753.151i	−0.0414798	+	0.792790i
$951$		0			0
$952$	−13.4533	−	35.0199i	−0.0141316	−	0.0367856i
$953$	−114.519			−0.120167			−0.0600837	−	0.998193i	$-0.519137\pi$
$953$	−114.519			−0.120167			−0.0600837	+	0.998193i	$0.519137\pi$
$954$		0			0
$955$	1844.60			1.93152
$956$	41.1165	−	391.848i	0.0430089	−	0.409883i
$957$		0			0
$958$	−503.572	−	26.3476i	−0.525650	−	0.0275027i
$959$	369.617	+	213.398i	0.385419	+	0.222522i
$960$		0			0
$961$	−216.239	−	374.537i	−0.225014	−	0.389736i
$962$	−1058.20	+	539.294i	−1.10000	+	0.560597i
$963$		0			0
$964$	954.958	−	1314.86i	0.990620	−	1.36397i
$965$	1169.71	−	675.330i	1.21213	−	0.699824i
$966$		0			0
$967$	1282.94	+	740.704i	1.32672	+	0.765981i	0.984791	−	0.173745i	$-0.0555867\pi$
$967$	1282.94	+	740.704i	1.32672	+	0.765981i	0.341928	+	0.939726i	$0.388920\pi$
$968$	−31.0724	−	25.1486i	−0.0320996	−	0.0259800i
$969$		0			0
$970$	869.534	−	1339.22i	0.896426	−	1.38064i
$971$	581.038			0.598392			0.299196	−	0.954192i	$-0.403282\pi$
$971$	581.038			0.598392			0.299196	+	0.954192i	$0.403282\pi$
$972$		0			0
$973$		−	1283.98i		−	1.31961i
$974$	−914.776	+	1408.90i	−0.939195	+	1.44651i
$975$		0			0
$976$	−252.314	+	1189.06i	−0.258518	+	1.21830i
$977$	728.468	−	1261.74i	0.745617	−	1.29145i	−0.204289	−	0.978911i	$-0.565488\pi$
$977$	728.468	−	1261.74i	0.745617	−	1.29145i	0.949906	−	0.312536i	$-0.101178\pi$
$978$		0			0
$979$	314.024	+	543.905i	0.320760	+	0.555572i
$980$	32.0670	+	23.2896i	0.0327214	+	0.0237649i
$981$		0			0
$982$	−475.598	+	242.381i	−0.484316	+	0.246824i
$983$	1331.25	−	768.600i	1.35428	−	0.781892i	0.365431	−	0.930838i	$-0.380922\pi$
$983$	1331.25	−	768.600i	1.35428	−	0.781892i	0.988845	+	0.148947i	$0.0475882\pi$
$984$		0			0
$985$	−356.832	+	618.052i	−0.362266	+	0.627464i
$986$	42.2300	+	2.20953i	0.0428296	+	0.00224090i
$987$		0			0
$988$	−197.418	+	1881.43i	−0.199816	+	1.90428i
$989$			870.638i			0.880321i
$990$		0			0
$991$			757.758i			0.764640i	0.924030	+	0.382320i	$0.124875\pi$
$991$			757.758i			0.764640i	−0.924030	+	0.382320i	$0.875125\pi$
$992$	−710.682	−	190.098i	−0.716414	−	0.191631i
$993$		0			0
$994$	−25.6229	+	489.723i	−0.0257776	+	0.492679i
$995$	−684.462	+	1185.52i	−0.687902	+	1.19148i
$996$		0			0
$997$	−1069.50	+	617.475i	−1.07272	+	0.619333i	−0.928922	−	0.370275i	$-0.879263\pi$
$997$	−1069.50	+	617.475i	−1.07272	+	0.619333i	−0.143794	+	0.989608i	$0.545930\pi$
$998$	−207.202	+	105.597i	−0.207618	+	0.105809i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.3.p.b.91.5		40
3.2	odd	2		72.3.p.b.67.16	yes	40
4.3	odd	2		864.3.t.b.847.4		40
8.3	odd	2	inner	216.3.p.b.91.8		40
8.5	even	2		864.3.t.b.847.17		40
9.2	odd	6		72.3.p.b.43.13	✓	40
9.4	even	3		648.3.b.e.163.19		20
9.5	odd	6		648.3.b.f.163.2		20
9.7	even	3	inner	216.3.p.b.19.8		40
12.11	even	2		288.3.t.b.175.16		40
24.5	odd	2		288.3.t.b.175.15		40
24.11	even	2		72.3.p.b.67.13	yes	40
36.7	odd	6		864.3.t.b.559.17		40
36.11	even	6		288.3.t.b.79.15		40
36.23	even	6		2592.3.b.e.1135.4		20
36.31	odd	6		2592.3.b.f.1135.17		20
72.5	odd	6		2592.3.b.e.1135.17		20
72.11	even	6		72.3.p.b.43.16	yes	40
72.13	even	6		2592.3.b.f.1135.4		20
72.29	odd	6		288.3.t.b.79.16		40
72.43	odd	6	inner	216.3.p.b.19.5		40
72.59	even	6		648.3.b.f.163.1		20
72.61	even	6		864.3.t.b.559.4		40
72.67	odd	6		648.3.b.e.163.20		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.3.p.b.43.13	✓	40	9.2	odd	6
72.3.p.b.43.16	yes	40	72.11	even	6
72.3.p.b.67.13	yes	40	24.11	even	2
72.3.p.b.67.16	yes	40	3.2	odd	2
216.3.p.b.19.5		40	72.43	odd	6	inner
216.3.p.b.19.8		40	9.7	even	3	inner
216.3.p.b.91.5		40	1.1	even	1	trivial
216.3.p.b.91.8		40	8.3	odd	2	inner
288.3.t.b.79.15		40	36.11	even	6
288.3.t.b.79.16		40	72.29	odd	6
288.3.t.b.175.15		40	24.5	odd	2
288.3.t.b.175.16		40	12.11	even	2
648.3.b.e.163.19		20	9.4	even	3
648.3.b.e.163.20		20	72.67	odd	6
648.3.b.f.163.1		20	72.59	even	6
648.3.b.f.163.2		20	9.5	odd	6
864.3.t.b.559.4		40	72.61	even	6
864.3.t.b.559.17		40	36.7	odd	6
864.3.t.b.847.4		40	4.3	odd	2
864.3.t.b.847.17		40	8.5	even	2
2592.3.b.e.1135.4		20	36.23	even	6
2592.3.b.e.1135.17		20	72.5	odd	6
2592.3.b.f.1135.4		20	72.13	even	6
2592.3.b.f.1135.17		20	36.31	odd	6

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:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	216.p (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.67744 - 1.08913i) q^{2} +(1.62758 + 3.65390i) q^{4} +(-5.42020 - 3.12935i) q^{5} +(5.96345 - 3.44300i) q^{7} +(1.24943 - 7.90183i) q^{8} +O(q^{10})\)	\(q+(-1.67744 - 1.08913i) q^{2} +(1.62758 + 3.65390i) q^{4} +(-5.42020 - 3.12935i) q^{5} +(5.96345 - 3.44300i) q^{7} +(1.24943 - 7.90183i) q^{8} +(5.68375 + 11.1526i) q^{10} +(5.38524 + 9.32751i) q^{11} +(-15.3923 - 8.88677i) q^{13} +(-13.7532 - 0.719584i) q^{14} +(-10.7020 + 11.8940i) q^{16} +0.681004 q^{17} -26.6092 q^{19} +(2.61256 - 24.8981i) q^{20} +(1.12551 - 21.5115i) q^{22} +(-22.8204 - 13.1754i) q^{23} +(7.08571 + 12.2728i) q^{25} +(16.1408 + 31.6713i) q^{26} +(22.2863 + 16.1861i) q^{28} +(-26.8884 + 15.5240i) q^{29} +(-19.9096 - 11.4948i) q^{31} +(30.9061 - 8.29554i) q^{32} +(-1.14234 - 0.741704i) q^{34} -43.0974 q^{35} +33.4119i q^{37} +(44.6352 + 28.9810i) q^{38} +(-31.4998 + 38.9196i) q^{40} +(-13.4634 + 23.3192i) q^{41} +(-16.5202 - 28.6138i) q^{43} +(-25.3169 + 34.8584i) q^{44} +(23.9300 + 46.9553i) q^{46} +(10.6191 - 6.13093i) q^{47} +(-0.791537 + 1.37098i) q^{49} +(1.48091 - 28.3041i) q^{50} +(7.41917 - 70.7060i) q^{52} -49.2792i q^{53} -67.4093i q^{55} +(-19.7551 - 51.4239i) q^{56} +(62.0114 + 3.24451i) q^{58} +(19.0327 - 32.9656i) q^{59} +(65.7927 - 37.9854i) q^{61} +(20.8777 + 40.9660i) q^{62} +(-60.8778 - 19.7456i) q^{64} +(55.6197 + 96.3362i) q^{65} +(-27.4324 + 47.5143i) q^{67} +(1.10839 + 2.48832i) q^{68} +(72.2931 + 46.9389i) q^{70} -35.6080i q^{71} +113.344 q^{73} +(36.3900 - 56.0463i) q^{74} +(-43.3085 - 97.2274i) q^{76} +(64.2292 + 37.0827i) q^{77} +(30.8141 - 17.7905i) q^{79} +(95.2275 - 30.9776i) q^{80} +(47.9817 - 24.4531i) q^{82} +(-58.7309 - 101.725i) q^{83} +(-3.69118 - 2.13110i) q^{85} +(-3.45271 + 65.9905i) q^{86} +(80.4329 - 30.8992i) q^{88} +58.3120 q^{89} -122.389 q^{91} +(10.9995 - 104.827i) q^{92} +(-24.4902 - 1.28136i) q^{94} +(144.227 + 83.2696i) q^{95} +(-63.7809 - 110.472i) q^{97} +(2.82093 - 1.43764i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 5 q^{2} + 7 q^{4} - 46 q^{8}+O(q^{10}) \) 40 * q + 5 * q^2 + 7 * q^4 - 46 * q^8	\( 40 q + 5 q^{2} + 7 q^{4} - 46 q^{8} - 12 q^{10} + 16 q^{11} - 6 q^{14} + 31 q^{16} + 4 q^{17} - 76 q^{19} + 12 q^{20} + 35 q^{22} + 118 q^{25} + 72 q^{26} - 36 q^{28} + 5 q^{32} + 5 q^{34} + 108 q^{35} + 169 q^{38} - 6 q^{40} - 20 q^{41} - 16 q^{43} - 362 q^{44} - 96 q^{46} + 166 q^{49} - 73 q^{50} - 24 q^{52} - 186 q^{56} + 36 q^{58} + 64 q^{59} - 384 q^{62} - 518 q^{64} + 102 q^{65} - 64 q^{67} + 295 q^{68} - 6 q^{70} - 292 q^{73} - 318 q^{74} + 197 q^{76} + 720 q^{80} + 386 q^{82} - 554 q^{83} + 295 q^{86} + 59 q^{88} + 688 q^{89} - 204 q^{91} + 378 q^{92} - 66 q^{94} + 92 q^{97} + 614 q^{98}+O(q^{100}) \) 40 * q + 5 * q^2 + 7 * q^4 - 46 * q^8 - 12 * q^10 + 16 * q^11 - 6 * q^14 + 31 * q^16 + 4 * q^17 - 76 * q^19 + 12 * q^20 + 35 * q^22 + 118 * q^25 + 72 * q^26 - 36 * q^28 + 5 * q^32 + 5 * q^34 + 108 * q^35 + 169 * q^38 - 6 * q^40 - 20 * q^41 - 16 * q^43 - 362 * q^44 - 96 * q^46 + 166 * q^49 - 73 * q^50 - 24 * q^52 - 186 * q^56 + 36 * q^58 + 64 * q^59 - 384 * q^62 - 518 * q^64 + 102 * q^65 - 64 * q^67 + 295 * q^68 - 6 * q^70 - 292 * q^73 - 318 * q^74 + 197 * q^76 + 720 * q^80 + 386 * q^82 - 554 * q^83 + 295 * q^86 + 59 * q^88 + 688 * q^89 - 204 * q^91 + 378 * q^92 - 66 * q^94 + 92 * q^97 + 614 * q^98

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