LMFDB - Embedded newform 216.3.b.b.163.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,3,Mod(163,216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(216, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

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

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

chi := DirichletCharacter("216.163");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	216.b (of order $2$, degree $1$, 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:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2x^{14} - 2x^{12} - 56x^{10} + 400x^{8} - 896x^{6} - 512x^{4} - 8192x^{2} + 65536 $ x^16 - 2x^14 - 2x^12 - 56x^10 + 400x^8 - 896x^6 - 512x^4 - 8192*x^2 + 65536
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			163.12
Root			$0.862987 + 1.80423i$ of defining polynomial
Character	$\chi$	$=$	216.163
Dual form			216.3.b.b.163.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.862987 + 1.80423i) q^{2} +(-2.51051 + 3.11406i) q^{4} +1.42436i q^{5} +4.94379i q^{7} +(-7.78502 - 1.84214i) q^{8} +O(q^{10})$	\(q+(0.862987 + 1.80423i) q^{2} +(-2.51051 + 3.11406i) q^{4} +1.42436i q^{5} +4.94379i q^{7} +(-7.78502 - 1.84214i) q^{8} +(-2.56987 + 1.22920i) q^{10} -2.70955 q^{11} +15.5806i q^{13} +(-8.91974 + 4.26643i) q^{14} +(-3.39473 - 15.6357i) q^{16} -28.9740 q^{17} +7.08332 q^{19} +(-4.43553 - 3.57585i) q^{20} +(-2.33831 - 4.88866i) q^{22} -10.1847i q^{23} +22.9712 q^{25} +(-28.1110 + 13.4459i) q^{26} +(-15.3953 - 12.4114i) q^{28} +34.4999i q^{29} +26.2444i q^{31} +(25.2809 - 19.6183i) q^{32} +(-25.0042 - 52.2758i) q^{34} -7.04172 q^{35} -4.36110i q^{37} +(6.11282 + 12.7800i) q^{38} +(2.62386 - 11.0886i) q^{40} +23.5591 q^{41} +46.0553 q^{43} +(6.80235 - 8.43771i) q^{44} +(18.3755 - 8.78923i) q^{46} -76.4010i q^{47} +24.5589 q^{49} +(19.8239 + 41.4454i) q^{50} +(-48.5189 - 39.1152i) q^{52} +69.6716i q^{53} -3.85937i q^{55} +(9.10715 - 38.4875i) q^{56} +(-62.2458 + 29.7730i) q^{58} +80.1517 q^{59} +85.1807i q^{61} +(-47.3510 + 22.6486i) q^{62} +(57.2130 + 28.6822i) q^{64} -22.1923 q^{65} +2.80385 q^{67} +(72.7394 - 90.2267i) q^{68} +(-6.07691 - 12.7049i) q^{70} -80.3947i q^{71} -59.9527 q^{73} +(7.86844 - 3.76358i) q^{74} +(-17.7827 + 22.0579i) q^{76} -13.3955i q^{77} +111.063i q^{79} +(22.2708 - 4.83530i) q^{80} +(20.3312 + 42.5060i) q^{82} +133.760 q^{83} -41.2693i q^{85} +(39.7451 + 83.0944i) q^{86} +(21.0939 + 4.99138i) q^{88} -65.2456 q^{89} -77.0272 q^{91} +(31.7156 + 25.5686i) q^{92} +(137.845 - 65.9331i) q^{94} +10.0892i q^{95} +74.3752 q^{97} +(21.1941 + 44.3100i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{4}+O(q^{10}) $ 16 * q + 4 * q^4	$ 16 q + 4 q^{4} + 24 q^{10} + 16 q^{16} - 64 q^{19} + 80 q^{22} - 80 q^{25} - 12 q^{28} + 8 q^{34} - 72 q^{40} - 64 q^{43} - 192 q^{46} - 128 q^{49} + 84 q^{52} - 96 q^{58} + 376 q^{64} + 128 q^{67} + 192 q^{70} + 80 q^{73} + 308 q^{76} + 272 q^{82} - 136 q^{88} + 192 q^{91} + 336 q^{94} + 80 q^{97}+O(q^{100}) $ 16 * q + 4 * q^4 + 24 * q^10 + 16 * q^16 - 64 * q^19 + 80 * q^22 - 80 * q^25 - 12 * q^28 + 8 * q^34 - 72 * q^40 - 64 * q^43 - 192 * q^46 - 128 * q^49 + 84 * q^52 - 96 * q^58 + 376 * q^64 + 128 * q^67 + 192 * q^70 + 80 * q^73 + 308 * q^76 + 272 * q^82 - 136 * q^88 + 192 * q^91 + 336 * q^94 + 80 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$55$	$109$	$137$
$\chi(n)$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	0.862987	+	1.80423i	0.431494	+	0.902116i
$2$	0.862987	+	1.80423i	0.431494	+	0.902116i
$3$		0			0
$3$		0			0
$4$	−2.51051	+	3.11406i	−0.627626	+	0.778515i
$5$			1.42436i			0.284871i	0.989804	+	0.142436i	$0.0454934\pi$
$5$			1.42436i			0.284871i	−0.989804	+	0.142436i	$0.954507\pi$
$6$		0			0
$7$			4.94379i			0.706256i	0.935575	+	0.353128i	$0.114882\pi$
$7$			4.94379i			0.706256i	−0.935575	+	0.353128i	$0.885118\pi$
$8$	−7.78502	−	1.84214i	−0.973127	−	0.230267i
$9$		0			0
$10$	−2.56987	+	1.22920i	−0.256987	+	0.122920i
$11$	−2.70955			−0.246323			−0.123162	−	0.992387i	$-0.539303\pi$
$11$	−2.70955			−0.246323			−0.123162	+	0.992387i	$0.539303\pi$
$12$		0			0
$13$			15.5806i			1.19851i	0.800559	+	0.599254i	$0.204536\pi$
$13$			15.5806i			1.19851i	−0.800559	+	0.599254i	$0.795464\pi$
$14$	−8.91974	+	4.26643i	−0.637124	+	0.304745i
$15$		0			0
$16$	−3.39473	−	15.6357i	−0.212170	−	0.977233i
$17$	−28.9740			−1.70435			−0.852176	−	0.523255i	$-0.824718\pi$
$17$	−28.9740			−1.70435			−0.852176	+	0.523255i	$0.824718\pi$
$18$		0			0
$19$	7.08332			0.372806			0.186403	−	0.982473i	$-0.440317\pi$
$19$	7.08332			0.372806			0.186403	+	0.982473i	$0.440317\pi$
$20$	−4.43553	−	3.57585i	−0.221776	−	0.178793i
$21$		0			0
$22$	−2.33831	−	4.88866i	−0.106287	−	0.222212i
$23$		−	10.1847i		−	0.442811i	−0.975182	−	0.221406i	$-0.928936\pi$
$23$		−	10.1847i		−	0.442811i	0.975182	−	0.221406i	$-0.0710645\pi$
$24$		0			0
$25$	22.9712			0.918848
$26$	−28.1110	+	13.4459i	−1.08119	+	0.517148i
$27$		0			0
$28$	−15.3953	−	12.4114i	−0.549830	−	0.443265i
$29$			34.4999i			1.18965i	0.803854	+	0.594826i	$0.202779\pi$
$29$			34.4999i			1.18965i	−0.803854	+	0.594826i	$0.797221\pi$
$30$		0			0
$31$			26.2444i			0.846593i	0.905991	+	0.423297i	$0.139127\pi$
$31$			26.2444i			0.846593i	−0.905991	+	0.423297i	$0.860873\pi$
$32$	25.2809	−	19.6183i	0.790027	−	0.613072i
$33$		0			0
$34$	−25.0042	−	52.2758i	−0.735417	−	1.53752i
$35$	−7.04172			−0.201192
$36$		0			0
$37$		−	4.36110i		−	0.117868i	−0.998262	−	0.0589338i	$-0.981230\pi$
$37$		−	4.36110i		−	0.117868i	0.998262	−	0.0589338i	$-0.0187701\pi$
$38$	6.11282	+	12.7800i	0.160864	+	0.336315i
$39$		0			0
$40$	2.62386	−	11.0886i	0.0655966	−	0.277216i
$41$	23.5591			0.574611			0.287306	−	0.957839i	$-0.407240\pi$
$41$	23.5591			0.574611			0.287306	+	0.957839i	$0.407240\pi$
$42$		0			0
$43$	46.0553			1.07105			0.535526	−	0.844519i	$-0.320113\pi$
$43$	46.0553			1.07105			0.535526	+	0.844519i	$0.320113\pi$
$44$	6.80235	−	8.43771i	0.154599	−	0.191766i
$45$		0			0
$46$	18.3755	−	8.78923i	0.399467	−	0.191070i
$47$		−	76.4010i		−	1.62555i	−0.582576	−	0.812777i	$-0.697955\pi$
$47$		−	76.4010i		−	1.62555i	0.582576	−	0.812777i	$-0.302045\pi$
$48$		0			0
$49$	24.5589			0.501203
$50$	19.8239	+	41.4454i	0.396477	+	0.828908i
$51$		0			0
$52$	−48.5189	−	39.1152i	−0.933056	−	0.752215i
$53$			69.6716i			1.31456i	0.753647	+	0.657279i	$0.228293\pi$
$53$			69.6716i			1.31456i	−0.753647	+	0.657279i	$0.771707\pi$
$54$		0			0
$55$		−	3.85937i		−	0.0701703i
$56$	9.10715	−	38.4875i	0.162628	−	0.687277i
$57$		0			0
$58$	−62.2458	+	29.7730i	−1.07320	+	0.513327i
$59$	80.1517			1.35850			0.679252	−	0.733905i	$-0.262304\pi$
$59$	80.1517			1.35850			0.679252	+	0.733905i	$0.262304\pi$
$60$		0			0
$61$			85.1807i			1.39640i	0.715900	+	0.698202i	$0.246016\pi$
$61$			85.1807i			1.39640i	−0.715900	+	0.698202i	$0.753984\pi$
$62$	−47.3510	+	22.6486i	−0.763725	+	0.365300i
$63$		0			0
$64$	57.2130	+	28.6822i	0.893954	+	0.448159i
$65$	−22.1923			−0.341420
$66$		0			0
$67$	2.80385			0.0418485			0.0209242	−	0.999781i	$-0.493339\pi$
$67$	2.80385			0.0418485			0.0209242	+	0.999781i	$0.493339\pi$
$68$	72.7394	−	90.2267i	1.06970	−	1.32686i
$69$		0			0
$70$	−6.07691	−	12.7049i	−0.0868130	−	0.181498i
$71$		−	80.3947i		−	1.13232i	−0.824296	−	0.566160i	$-0.808429\pi$
$71$		−	80.3947i		−	1.13232i	0.824296	−	0.566160i	$-0.191571\pi$
$72$		0			0
$73$	−59.9527			−0.821270			−0.410635	−	0.911800i	$-0.634693\pi$
$73$	−59.9527			−0.821270			−0.410635	+	0.911800i	$0.634693\pi$
$74$	7.86844	−	3.76358i	0.106330	−	0.0508591i
$75$		0			0
$76$	−17.7827	+	22.0579i	−0.233983	+	0.290235i
$77$		−	13.3955i		−	0.173967i
$78$		0			0
$79$			111.063i			1.40586i	0.711259	+	0.702930i	$0.248125\pi$
$79$			111.063i			1.40586i	−0.711259	+	0.702930i	$0.751875\pi$
$80$	22.2708	−	4.83530i	0.278385	−	0.0604412i
$81$		0			0
$82$	20.3312	+	42.5060i	0.247941	+	0.518366i
$83$	133.760			1.61157			0.805785	−	0.592208i	$-0.201744\pi$
$83$	133.760			1.61157			0.805785	+	0.592208i	$0.201744\pi$
$84$		0			0
$85$		−	41.2693i		−	0.485521i
$86$	39.7451	+	83.0944i	0.462152	+	0.966213i
$87$		0			0
$88$	21.0939	+	4.99138i	0.239704	+	0.0567202i
$89$	−65.2456			−0.733096			−0.366548	−	0.930399i	$-0.619460\pi$
$89$	−65.2456			−0.733096			−0.366548	+	0.930399i	$0.619460\pi$
$90$		0			0
$91$	−77.0272			−0.846453
$92$	31.7156	+	25.5686i	0.344735	+	0.277920i
$93$		0			0
$94$	137.845	−	65.9331i	1.46644	−	0.701416i
$95$			10.0892i			0.106202i
$96$		0			0
$97$	74.3752			0.766755			0.383377	−	0.923592i	$-0.374761\pi$
$97$	74.3752			0.766755			0.383377	+	0.923592i	$0.374761\pi$
$98$	21.1941	+	44.3100i	0.216266	+	0.452143i
$99$		0			0
$100$	−57.6693	+	71.5337i	−0.576693	+	0.715337i
$101$			159.189i			1.57613i	0.615595	+	0.788063i	$0.288916\pi$
$101$			159.189i			1.57613i	−0.615595	+	0.788063i	$0.711084\pi$
$102$		0			0
$103$		−	149.805i		−	1.45441i	−0.686418	−	0.727207i	$-0.740818\pi$
$103$		−	149.805i		−	1.45441i	0.686418	−	0.727207i	$-0.259182\pi$
$104$	28.7016	−	121.295i	0.275977	−	1.16630i
$105$		0			0
$106$	−125.704	+	60.1257i	−1.18588	+	0.567224i
$107$	−17.8799			−0.167102			−0.0835511	−	0.996503i	$-0.526626\pi$
$107$	−17.8799			−0.167102			−0.0835511	+	0.996503i	$0.526626\pi$
$108$		0			0
$109$		−	150.420i		−	1.38000i	−0.723811	−	0.689999i	$-0.757611\pi$
$109$		−	150.420i		−	1.38000i	0.723811	−	0.689999i	$-0.242389\pi$
$110$	6.96319	−	3.33059i	0.0633018	−	0.0302781i
$111$		0			0
$112$	77.2997	−	16.7828i	0.690176	−	0.149847i
$113$	49.8163			0.440852			0.220426	−	0.975404i	$-0.429255\pi$
$113$	49.8163			0.440852			0.220426	+	0.975404i	$0.429255\pi$
$114$		0			0
$115$	14.5066			0.126144
$116$	−107.435	−	86.6122i	−0.926162	−	0.746657i
$117$		0			0
$118$	69.1699	+	144.612i	0.586186	+	1.22553i
$119$		−	143.241i		−	1.20371i
$120$		0			0
$121$	−113.658			−0.939325
$122$	−153.686	+	73.5099i	−1.25972	+	0.602540i
$123$		0			0
$124$	−81.7266	−	65.8867i	−0.659085	−	0.531344i
$125$			68.3281i			0.546625i
$126$		0			0
$127$		−	213.966i		−	1.68477i	−0.538875	−	0.842386i	$-0.681150\pi$
$127$		−	213.966i		−	1.68477i	0.538875	−	0.842386i	$-0.318850\pi$
$128$	−2.37518	+	127.978i	−0.0185561	+	0.999828i
$129$		0			0
$130$	−19.1517	−	40.0401i	−0.147321	−	0.308001i
$131$	−213.913			−1.63292			−0.816462	−	0.577399i	$-0.804068\pi$
$131$	−213.913			−1.63292			−0.816462	+	0.577399i	$0.804068\pi$
$132$		0			0
$133$			35.0184i			0.263297i
$134$	2.41969	+	5.05879i	0.0180574	+	0.0377522i
$135$		0			0
$136$	225.563	+	53.3741i	1.65855	+	0.392457i
$137$	−178.724			−1.30456			−0.652279	−	0.757979i	$-0.726187\pi$
$137$	−178.724			−1.30456			−0.652279	+	0.757979i	$0.726187\pi$
$138$		0			0
$139$	−83.2514			−0.598931			−0.299465	−	0.954107i	$-0.596808\pi$
$139$	−83.2514			−0.598931			−0.299465	+	0.954107i	$0.596808\pi$
$140$	17.6783	−	21.9283i	0.126273	−	0.156631i
$141$		0			0
$142$	145.051	−	69.3796i	1.02148	−	0.488589i
$143$		−	42.2165i		−	0.295220i
$144$		0			0
$145$	−49.1402			−0.338898
$146$	−51.7384	−	108.169i	−0.354373	−	0.740881i
$147$		0			0
$148$	13.5807	+	10.9486i	0.0917617	+	0.0739768i
$149$		−	137.904i		−	0.925531i	−0.886481	−	0.462766i	$-0.846857\pi$
$149$		−	137.904i		−	0.925531i	0.886481	−	0.462766i	$-0.153143\pi$
$150$		0			0
$151$			15.9729i			0.105781i	0.998600	+	0.0528905i	$0.0168434\pi$
$151$			15.9729i			0.105781i	−0.998600	+	0.0528905i	$0.983157\pi$
$152$	−55.1438	−	13.0485i	−0.362788	−	0.0858452i
$153$		0			0
$154$	24.1685	−	11.5601i	0.156938	−	0.0750657i
$155$	−37.3813			−0.241170
$156$		0			0
$157$		−	152.976i		−	0.974367i	−0.873300	−	0.487183i	$-0.838024\pi$
$157$		−	152.976i		−	0.974367i	0.873300	−	0.487183i	$-0.161976\pi$
$158$	−200.383	+	95.8459i	−1.26825	+	0.606620i
$159$		0			0
$160$	27.9434	+	36.0089i	0.174647	+	0.225056i
$161$	50.3508			0.312738
$162$		0			0
$163$	−144.537			−0.886732			−0.443366	−	0.896341i	$-0.646216\pi$
$163$	−144.537			−0.886732			−0.443366	+	0.896341i	$0.646216\pi$
$164$	−59.1452	+	73.3643i	−0.360641	+	0.447343i
$165$		0			0
$166$	115.433	+	241.335i	0.695382	+	1.45382i
$167$			290.113i			1.73720i	0.495510	+	0.868602i	$0.334981\pi$
$167$			290.113i			1.73720i	−0.495510	+	0.868602i	$0.665019\pi$
$168$		0			0
$169$	−73.7550			−0.436420
$170$	74.4593	−	35.6149i	0.437996	−	0.209499i
$171$		0			0
$172$	−115.622	+	143.419i	−0.672221	+	0.833830i
$173$			106.253i			0.614179i	0.951681	+	0.307089i	$0.0993551\pi$
$173$			106.253i			0.614179i	−0.951681	+	0.307089i	$0.900645\pi$
$174$		0			0
$175$			113.565i			0.648942i
$176$	9.19819	+	42.3658i	0.0522625	+	0.240715i
$177$		0			0
$178$	−56.3061	−	117.718i	−0.316326	−	0.661338i
$179$	160.840			0.898549			0.449274	−	0.893394i	$-0.351683\pi$
$179$	160.840			0.898549			0.449274	+	0.893394i	$0.351683\pi$
$180$		0			0
$181$			0.648697i			0.00358396i	0.999998	+	0.00179198i	$0.000570405\pi$
$181$			0.648697i			0.00358396i	−0.999998	+	0.00179198i	$0.999430\pi$
$182$	−66.4735	−	138.975i	−0.365239	−	0.763598i
$183$		0			0
$184$	−18.7616	+	79.2878i	−0.101965	+	0.430912i
$185$	6.21176			0.0335771
$186$		0			0
$187$	78.5066			0.419821
$188$	237.917	+	191.805i	1.26552	+	1.02024i
$189$		0			0
$190$	−18.2032	+	8.70683i	−0.0958063	+	0.0458254i
$191$		−	76.5664i		−	0.400871i	−0.979707	−	0.200436i	$-0.935764\pi$
$191$		−	76.5664i		−	0.400871i	0.979707	−	0.200436i	$-0.0642357\pi$
$192$		0			0
$193$	57.7940			0.299451			0.149725	−	0.988728i	$-0.452161\pi$
$193$	57.7940			0.299451			0.149725	+	0.988728i	$0.452161\pi$
$194$	64.1849	+	134.190i	0.330850	+	0.691702i
$195$		0			0
$196$	−61.6554	+	76.4780i	−0.314568	+	0.390194i
$197$		−	82.2299i		−	0.417411i	−0.977979	−	0.208705i	$-0.933075\pi$
$197$		−	82.2299i		−	0.417411i	0.977979	−	0.208705i	$-0.0669249\pi$
$198$		0			0
$199$			40.2673i			0.202348i	0.994869	+	0.101174i	$0.0322599\pi$
$199$			40.2673i			0.202348i	−0.994869	+	0.101174i	$0.967740\pi$
$200$	−178.831	−	42.3162i	−0.894157	−	0.211581i
$201$		0			0
$202$	−287.213	+	137.378i	−1.42185	+	0.680088i
$203$	−170.560			−0.840199
$204$		0			0
$205$			33.5565i			0.163690i
$206$	270.282	−	129.280i	1.31205	−	0.627571i
$207$		0			0
$208$	243.614	−	52.8919i	1.17122	−	0.254288i
$209$	−19.1926			−0.0918308
$210$		0			0
$211$	76.4845			0.362486			0.181243	−	0.983438i	$-0.441988\pi$
$211$	76.4845			0.362486			0.181243	+	0.983438i	$0.441988\pi$
$212$	−216.961	−	174.911i	−1.02340	−	0.825051i
$213$		0			0
$214$	−15.4302	−	32.2595i	−0.0721035	−	0.150745i
$215$			65.5991i			0.305112i
$216$		0			0
$217$	−129.747			−0.597911
$218$	271.392	−	129.810i	1.24492	−	0.595460i
$219$		0			0
$220$	12.0183	+	9.68896i	0.0546286	+	0.0440407i
$221$		−	451.432i		−	2.04268i
$222$		0			0
$223$		−	86.3440i		−	0.387193i	−0.981081	−	0.193596i	$-0.937985\pi$
$223$		−	86.3440i		−	0.387193i	0.981081	−	0.193596i	$-0.0620152\pi$
$224$	96.9888	+	124.983i	0.432986	+	0.557961i
$225$		0			0
$226$	42.9908	+	89.8801i	0.190225	+	0.397700i
$227$	−4.88232			−0.0215080			−0.0107540	−	0.999942i	$-0.503423\pi$
$227$	−4.88232			−0.0215080			−0.0107540	+	0.999942i	$0.503423\pi$
$228$		0			0
$229$			257.116i			1.12278i	0.827552	+	0.561389i	$0.189733\pi$
$229$			257.116i			1.12278i	−0.827552	+	0.561389i	$0.810267\pi$
$230$	12.5190	+	26.1732i	0.0544304	+	0.113797i
$231$		0			0
$232$	63.5537	−	268.582i	0.273938	−	1.15768i
$233$	359.069			1.54107			0.770534	−	0.637398i	$-0.219989\pi$
$233$	359.069			1.54107			0.770534	+	0.637398i	$0.219989\pi$
$234$		0			0
$235$	108.822			0.463073
$236$	−201.221	+	249.597i	−0.852633	+	1.05762i
$237$		0			0
$238$	258.441	−	123.615i	1.08588	−	0.519393i
$239$			437.851i			1.83201i	0.401162	+	0.916007i	$0.368606\pi$
$239$			437.851i			1.83201i	−0.401162	+	0.916007i	$0.631394\pi$
$240$		0			0
$241$	246.366			1.02227			0.511133	−	0.859502i	$-0.329226\pi$
$241$	246.366			1.02227			0.511133	+	0.859502i	$0.329226\pi$
$242$	−98.0857	−	205.066i	−0.405313	−	0.847380i
$243$		0			0
$244$	−265.258	−	213.847i	−1.08712	−	0.876420i
$245$			34.9807i			0.142778i
$246$		0			0
$247$			110.362i			0.446811i
$248$	48.3458	−	204.313i	0.194943	−	0.823843i
$249$		0			0
$250$	−123.280	+	58.9663i	−0.493119	+	0.235865i
$251$	127.838			0.509314			0.254657	−	0.967031i	$-0.418037\pi$
$251$	127.838			0.509314			0.254657	+	0.967031i	$0.418037\pi$
$252$		0			0
$253$			27.5959i			0.109075i
$254$	386.044	−	184.650i	1.51986	−	0.726969i
$255$		0			0
$256$	−232.952	+	106.158i	−0.909967	+	0.414680i
$257$	76.0568			0.295941			0.147970	−	0.988992i	$-0.452726\pi$
$257$	76.0568			0.295941			0.147970	+	0.988992i	$0.452726\pi$
$258$		0			0
$259$	21.5604			0.0832447
$260$	55.7139	−	69.1082i	0.214284	−	0.265801i
$261$		0			0
$262$	−184.604	−	385.949i	−0.704597	−	1.47309i
$263$		−	87.8347i		−	0.333972i	−0.985959	−	0.166986i	$-0.946597\pi$
$263$		−	87.8347i		−	0.333972i	0.985959	−	0.166986i	$-0.0534035\pi$
$264$		0			0
$265$	−99.2371			−0.374480
$266$	−63.1814	+	30.2205i	−0.237524	+	0.113611i
$267$		0			0
$268$	−7.03907	+	8.73135i	−0.0262652	+	0.0325797i
$269$		−	251.470i		−	0.934832i	−0.884037	−	0.467416i	$-0.845185\pi$
$269$		−	251.470i		−	0.934832i	0.884037	−	0.467416i	$-0.154815\pi$
$270$		0			0
$271$			143.262i			0.528642i	0.964435	+	0.264321i	$0.0851478\pi$
$271$			143.262i			0.528642i	−0.964435	+	0.264321i	$0.914852\pi$
$272$	98.3588	+	453.029i	0.361613	+	1.66555i
$273$		0			0
$274$	−154.237	−	322.460i	−0.562908	−	1.17686i
$275$	−62.2417			−0.226334
$276$		0			0
$277$		−	264.625i		−	0.955325i	−0.878543	−	0.477662i	$-0.841484\pi$
$277$		−	264.625i		−	0.955325i	0.878543	−	0.477662i	$-0.158516\pi$
$278$	−71.8449	−	150.205i	−0.258435	−	0.540305i
$279$		0			0
$280$	54.8199	+	12.9718i	0.195785	+	0.0463279i
$281$	296.505			1.05518			0.527589	−	0.849500i	$-0.323096\pi$
$281$	296.505			1.05518			0.527589	+	0.849500i	$0.323096\pi$
$282$		0			0
$283$	55.5093			0.196146			0.0980730	−	0.995179i	$-0.468732\pi$
$283$	55.5093			0.196146			0.0980730	+	0.995179i	$0.468732\pi$
$284$	250.354	+	201.831i	0.881527	+	0.710673i
$285$		0			0
$286$	76.1683	−	36.4323i	0.266323	−	0.127386i
$287$			116.471i			0.405823i
$288$		0			0
$289$	550.492			1.90482
$290$	−42.4073	−	88.6602i	−0.146232	−	0.305725i
$291$		0			0
$292$	150.512	−	186.696i	0.515451	−	0.639371i
$293$		−	364.614i		−	1.24442i	−0.782852	−	0.622208i	$-0.786236\pi$
$293$		−	364.614i		−	1.24442i	0.782852	−	0.622208i	$-0.213764\pi$
$294$		0			0
$295$			114.165i			0.386999i
$296$	−8.03376	+	33.9513i	−0.0271411	+	0.114700i
$297$		0			0
$298$	248.811	−	119.010i	0.834936	−	0.399361i
$299$	158.683			0.530713
$300$		0			0
$301$			227.687i			0.756437i
$302$	−28.8189	+	13.7844i	−0.0954268	+	0.0456439i
$303$		0			0
$304$	−24.0459	−	110.753i	−0.0790985	−	0.364319i
$305$	−121.328			−0.397795
$306$		0			0
$307$	199.204			0.648872			0.324436	−	0.945908i	$-0.394825\pi$
$307$	199.204			0.648872			0.324436	+	0.945908i	$0.394825\pi$
$308$	41.7143	+	33.6294i	0.135436	+	0.109186i
$309$		0			0
$310$	−32.2596	−	67.4446i	−0.104063	−	0.217563i
$311$			391.789i			1.25977i	0.776688	+	0.629885i	$0.216898\pi$
$311$			391.789i			1.25977i	−0.776688	+	0.629885i	$0.783102\pi$
$312$		0			0
$313$	−315.898			−1.00926			−0.504630	−	0.863336i	$-0.668371\pi$
$313$	−315.898			−1.00926			−0.504630	+	0.863336i	$0.668371\pi$
$314$	276.003	−	132.016i	0.878992	−	0.420433i
$315$		0			0
$316$	−345.856	−	278.824i	−1.09448	−	0.882354i
$317$			119.157i			0.375889i	0.982180	+	0.187944i	$0.0601825\pi$
$317$			119.157i			0.375889i	−0.982180	+	0.187944i	$0.939818\pi$
$318$		0			0
$319$		−	93.4793i		−	0.293039i
$320$	−40.8536	+	81.4917i	−0.127668	+	0.254662i
$321$		0			0
$322$	43.4521	+	90.8445i	0.134944	+	0.282126i
$323$	−205.232			−0.635393
$324$		0			0
$325$			357.905i			1.10125i
$326$	−124.734	−	260.779i	−0.382619	−	0.799935i
$327$		0			0
$328$	−183.408	−	43.3991i	−0.559170	−	0.132314i
$329$	377.710			1.14806
$330$		0			0
$331$	−144.486			−0.436512			−0.218256	−	0.975892i	$-0.570037\pi$
$331$	−144.486			−0.436512			−0.218256	+	0.975892i	$0.570037\pi$
$332$	−335.806	+	416.537i	−1.01146	+	1.25463i
$333$		0			0
$334$	−523.432	+	250.364i	−1.56716	+	0.749593i
$335$			3.99368i			0.0119214i
$336$		0			0
$337$	500.012			1.48371			0.741857	−	0.670558i	$-0.233945\pi$
$337$	500.012			1.48371			0.741857	+	0.670558i	$0.233945\pi$
$338$	−63.6496	−	133.071i	−0.188312	−	0.393701i
$339$		0			0
$340$	128.515	+	103.607i	0.377985	+	0.304726i
$341$		−	71.1106i		−	0.208535i
$342$		0			0
$343$			363.660i			1.06023i
$344$	−358.541	−	84.8402i	−1.04227	−	0.246629i
$345$		0			0
$346$	−191.705	+	91.6950i	−0.554061	+	0.265014i
$347$	−603.316			−1.73866			−0.869331	−	0.494230i	$-0.835450\pi$
$347$	−603.316			−1.73866			−0.869331	+	0.494230i	$0.835450\pi$
$348$		0			0
$349$			418.624i			1.19950i	0.800189	+	0.599748i	$0.204732\pi$
$349$			418.624i			1.19950i	−0.800189	+	0.599748i	$0.795268\pi$
$350$	−204.897	+	98.0050i	−0.585421	+	0.280014i
$351$		0			0
$352$	−68.4998	+	53.1568i	−0.194602	+	0.151014i
$353$	−164.645			−0.466417			−0.233208	−	0.972427i	$-0.574922\pi$
$353$	−164.645			−0.466417			−0.233208	+	0.972427i	$0.574922\pi$
$354$		0			0
$355$	114.511			0.322565
$356$	163.799	−	203.179i	0.460110	−	0.570726i
$357$		0			0
$358$	138.803	+	290.193i	0.387718	+	0.810595i
$359$			65.5404i			0.182564i	0.995825	+	0.0912819i	$0.0290964\pi$
$359$			65.5404i			0.182564i	−0.995825	+	0.0912819i	$0.970904\pi$
$360$		0			0
$361$	−310.827			−0.861015
$362$	−1.17040	+	0.559817i	−0.00323315	+	0.00154646i
$363$		0			0
$364$	193.377	−	239.867i	0.531256	−	0.658976i
$365$		−	85.3940i		−	0.233956i
$366$		0			0
$367$		−	188.436i		−	0.513449i	−0.966485	−	0.256724i	$-0.917357\pi$
$367$		−	188.436i		−	0.513449i	0.966485	−	0.256724i	$-0.0826433\pi$
$368$	−159.245	+	34.5741i	−0.432730	+	0.0939515i
$369$		0			0
$370$	5.36067	+	11.2075i	0.0144883	+	0.0302904i
$371$	−344.442			−0.928414
$372$		0			0
$373$		−	399.943i		−	1.07223i	−0.844144	−	0.536116i	$-0.819891\pi$
$373$		−	399.943i		−	1.07223i	0.844144	−	0.536116i	$-0.180109\pi$
$374$	67.7502	+	141.644i	0.181150	+	0.378727i
$375$		0			0
$376$	−140.741	+	594.783i	−0.374312	+	1.58187i
$377$	−537.529			−1.42581
$378$		0			0
$379$	370.998			0.978886			0.489443	−	0.872035i	$-0.337200\pi$
$379$	370.998			0.978886			0.489443	+	0.872035i	$0.337200\pi$
$380$	−31.4183	−	25.3289i	−0.0826797	−	0.0666550i
$381$		0			0
$382$	138.144	−	66.0758i	0.361632	−	0.172973i
$383$		−	39.1265i		−	0.102158i	−0.998695	−	0.0510790i	$-0.983734\pi$
$383$		−	39.1265i		−	0.102158i	0.998695	−	0.0510790i	$-0.0162660\pi$
$384$		0			0
$385$	19.0799			0.0495582
$386$	49.8755	+	104.274i	0.129211	+	0.270139i
$387$		0			0
$388$	−186.719	+	231.609i	−0.481236	+	0.596930i
$389$		−	119.226i		−	0.306493i	−0.988188	−	0.153247i	$-0.951027\pi$
$389$		−	119.226i		−	0.306493i	0.988188	−	0.153247i	$-0.0489729\pi$
$390$		0			0
$391$			295.090i			0.754707i
$392$	−191.192	−	45.2410i	−0.487734	−	0.115411i
$393$		0			0
$394$	148.362	−	70.9634i	0.376553	−	0.180110i
$395$	−158.193			−0.400489
$396$		0			0
$397$			143.202i			0.360711i	0.983601	+	0.180356i	$0.0577248\pi$
$397$			143.202i			0.360711i	−0.983601	+	0.180356i	$0.942275\pi$
$398$	−72.6515	+	34.7501i	−0.182541	+	0.0873119i
$399$		0			0
$400$	−77.9810	−	359.171i	−0.194952	−	0.897929i
$401$	142.969			0.356530			0.178265	−	0.983982i	$-0.442952\pi$
$401$	142.969			0.356530			0.178265	+	0.983982i	$0.442952\pi$
$402$		0			0
$403$	−408.903			−1.01465
$404$	−495.723	−	399.644i	−1.22704	−	0.989218i
$405$		0			0
$406$	−147.191	−	307.730i	−0.362540	−	0.757956i
$407$			11.8166i			0.0290335i
$408$		0			0
$409$	−288.751			−0.705992			−0.352996	−	0.935625i	$-0.614837\pi$
$409$	−288.751			−0.705992			−0.352996	+	0.935625i	$0.614837\pi$
$410$	−60.5437	+	28.9588i	−0.147668	+	0.0706313i
$411$		0			0
$412$	466.501	+	376.086i	1.13228	+	0.912829i
$413$			396.253i			0.959451i
$414$		0			0
$415$			190.522i			0.459090i
$416$	305.665	+	393.891i	0.734771	+	0.946853i
$417$		0			0
$418$	−16.5630	−	34.6280i	−0.0396244	−	0.0828420i
$419$	668.281			1.59494			0.797472	−	0.603356i	$-0.206170\pi$
$419$	668.281			1.59494			0.797472	+	0.603356i	$0.206170\pi$
$420$		0			0
$421$		−	457.020i		−	1.08556i	−0.839876	−	0.542779i	$-0.817372\pi$
$421$		−	457.020i		−	1.08556i	0.839876	−	0.542779i	$-0.182628\pi$
$422$	66.0051	+	137.996i	0.156410	+	0.327004i
$423$		0			0
$424$	128.345	−	542.395i	0.302700	−	1.27923i
$425$	−665.568			−1.56604
$426$		0			0
$427$	−421.115			−0.986219
$428$	44.8877	−	55.6792i	0.104878	−	0.130091i
$429$		0			0
$430$	−118.356	+	56.6112i	−0.275246	+	0.131654i
$431$			291.189i			0.675613i	0.941216	+	0.337806i	$0.109685\pi$
$431$			291.189i			0.675613i	−0.941216	+	0.337806i	$0.890315\pi$
$432$		0			0
$433$	298.330			0.688984			0.344492	−	0.938789i	$-0.388051\pi$
$433$	298.330			0.688984			0.344492	+	0.938789i	$0.388051\pi$
$434$	−111.970	−	234.093i	−0.257995	−	0.539385i
$435$		0			0
$436$	468.416	+	377.629i	1.07435	+	0.866123i
$437$		−	72.1412i		−	0.165083i
$438$		0			0
$439$		−	411.905i		−	0.938281i	−0.883123	−	0.469141i	$-0.844564\pi$
$439$		−	411.905i		−	0.938281i	0.883123	−	0.469141i	$-0.155436\pi$
$440$	−7.10950	+	30.0453i	−0.0161579	+	0.0682847i
$441$		0			0
$442$	814.488	−	389.580i	1.84273	−	0.881403i
$443$	545.893			1.23226			0.616132	−	0.787643i	$-0.288699\pi$
$443$	545.893			1.23226			0.616132	+	0.787643i	$0.288699\pi$
$444$		0			0
$445$		−	92.9329i		−	0.208838i
$446$	155.785	−	74.5138i	0.349293	−	0.167071i
$447$		0			0
$448$	−141.799	+	282.849i	−0.316515	+	0.631360i
$449$	208.017			0.463289			0.231644	−	0.972801i	$-0.425589\pi$
$449$	208.017			0.463289			0.231644	+	0.972801i	$0.425589\pi$
$450$		0			0
$451$	−63.8345			−0.141540
$452$	−125.064	+	155.131i	−0.276690	+	0.343210i
$453$		0			0
$454$	−4.21338	−	8.80884i	−0.00928058	−	0.0194027i
$455$		−	109.714i		−	0.241130i
$456$		0			0
$457$	−739.827			−1.61888			−0.809439	−	0.587205i	$-0.800228\pi$
$457$	−739.827			−1.61888			−0.809439	+	0.587205i	$0.800228\pi$
$458$	−463.897	+	221.888i	−1.01288	+	0.484472i
$459$		0			0
$460$	−36.4188	+	45.1743i	−0.0791714	+	0.0982051i
$461$			61.7163i			0.133875i	0.997757	+	0.0669374i	$0.0213228\pi$
$461$			61.7163i			0.133875i	−0.997757	+	0.0669374i	$0.978677\pi$
$462$		0			0
$463$		−	675.030i		−	1.45795i	−0.684541	−	0.728974i	$-0.739997\pi$
$463$		−	675.030i		−	1.45795i	0.684541	−	0.728974i	$-0.260003\pi$
$464$	539.431	−	117.118i	1.16257	−	0.252409i
$465$		0			0
$466$	309.872	+	647.844i	0.664962	+	1.39022i
$467$	−559.474			−1.19802			−0.599009	−	0.800743i	$-0.704438\pi$
$467$	−559.474			−1.19802			−0.599009	+	0.800743i	$0.704438\pi$
$468$		0			0
$469$			13.8616i			0.0295557i
$470$	93.9122	+	196.340i	0.199813	+	0.417746i
$471$		0			0
$472$	−623.983	−	147.651i	−1.32200	−	0.312819i
$473$	−124.789			−0.263825
$474$		0			0
$475$	162.712			0.342553
$476$	446.062	+	359.608i	0.937105	+	0.755479i
$477$		0			0
$478$	−789.985	+	377.860i	−1.65269	+	0.790503i
$479$		−	287.292i		−	0.599774i	−0.953975	−	0.299887i	$-0.903051\pi$
$479$		−	287.292i		−	0.599774i	0.953975	−	0.299887i	$-0.0969490\pi$
$480$		0			0
$481$	67.9486			0.141265
$482$	212.611	+	444.501i	0.441101	+	0.922202i
$483$		0			0
$484$	285.340	−	353.939i	0.589545	−	0.731278i
$485$			105.937i			0.218426i
$486$		0			0
$487$		−	489.110i		−	1.00433i	−0.864771	−	0.502166i	$-0.832537\pi$
$487$		−	489.110i		−	1.00433i	0.864771	−	0.502166i	$-0.167463\pi$
$488$	156.915	−	663.133i	0.321547	−	1.35888i
$489$		0			0
$490$	−63.1133	+	30.1879i	−0.128803	+	0.0616079i
$491$	525.888			1.07106			0.535528	−	0.844518i	$-0.320113\pi$
$491$	525.888			1.07106			0.535528	+	0.844518i	$0.320113\pi$
$492$		0			0
$493$		−	999.600i		−	2.02759i
$494$	−199.119	+	95.2413i	−0.403075	+	0.192796i
$495$		0			0
$496$	410.350	−	89.0925i	0.827318	−	0.179622i
$497$	397.454			0.799707
$498$		0			0
$499$	687.095			1.37694			0.688472	−	0.725263i	$-0.258282\pi$
$499$	687.095			1.37694			0.688472	+	0.725263i	$0.258282\pi$
$500$	−212.778	−	171.538i	−0.425555	−	0.343076i
$501$		0			0
$502$	110.322	+	230.649i	0.219766	+	0.459460i
$503$		−	872.525i		−	1.73464i	−0.497750	−	0.867321i	$-0.665840\pi$
$503$		−	872.525i		−	1.73464i	0.497750	−	0.867321i	$-0.334160\pi$
$504$		0			0
$505$	−226.741			−0.448993
$506$	−49.7894	+	23.8149i	−0.0983980	+	0.0470650i
$507$		0			0
$508$	666.303	+	537.163i	1.31162	+	1.05741i
$509$			402.266i			0.790307i	0.918615	+	0.395153i	$0.129309\pi$
$509$			402.266i			0.790307i	−0.918615	+	0.395153i	$0.870691\pi$
$510$		0			0
$511$		−	296.393i		−	0.580026i
$512$	−392.568	−	328.686i	−0.766734	−	0.641964i
$513$		0			0
$514$	65.6360	+	137.224i	0.127697	+	0.266973i
$515$	213.375			0.414321
$516$		0			0
$517$			207.013i			0.400411i
$518$	18.6063	+	38.8999i	0.0359196	+	0.0750963i
$519$		0			0
$520$	172.768	+	40.8813i	0.332245	+	0.0786180i
$521$	−28.9740			−0.0556123			−0.0278061	−	0.999613i	$-0.508852\pi$
$521$	−28.9740			−0.0556123			−0.0278061	+	0.999613i	$0.508852\pi$
$522$		0			0
$523$	−454.653			−0.869318			−0.434659	−	0.900595i	$-0.643131\pi$
$523$	−454.653			−0.869318			−0.434659	+	0.900595i	$0.643131\pi$
$524$	537.030	−	666.138i	1.02487	−	1.27126i
$525$		0			0
$526$	158.474	−	75.8002i	0.301282	−	0.144107i
$527$		−	760.405i		−	1.44289i
$528$		0			0
$529$	425.273			0.803918
$530$	−85.6404	−	179.047i	−0.161586	−	0.337824i
$531$		0			0
$532$	−109.050	−	87.9140i	−0.204980	−	0.165252i
$533$			367.064i			0.688676i
$534$		0			0
$535$		−	25.4674i		−	0.0476026i
$536$	−21.8280	−	5.16508i	−0.0407239	−	0.00963634i
$537$		0			0
$538$	453.710	−	217.015i	0.843327	−	0.403374i
$539$	−66.5438			−0.123458
$540$		0			0
$541$		−	215.095i		−	0.397587i	−0.980041	−	0.198793i	$-0.936298\pi$
$541$		−	215.095i		−	0.397587i	0.980041	−	0.198793i	$-0.0637023\pi$
$542$	−258.478	+	123.633i	−0.476896	+	0.228106i
$543$		0			0
$544$	−732.488	+	568.421i	−1.34648	+	1.04489i
$545$	214.251			0.393121
$546$		0			0
$547$	−1003.34			−1.83426			−0.917132	−	0.398583i	$-0.869502\pi$
$547$	−1003.34			−1.83426			−0.917132	+	0.398583i	$0.869502\pi$
$548$	448.688	−	556.558i	0.818775	−	1.01562i
$549$		0			0
$550$	−53.7138	−	112.298i	−0.0976615	−	0.204179i
$551$			244.374i			0.443510i
$552$		0			0
$553$	−549.072			−0.992896
$554$	477.445	−	228.368i	0.861814	−	0.412217i
$555$		0			0
$556$	209.003	−	259.250i	0.375905	−	0.466277i
$557$			367.873i			0.660455i	0.943901	+	0.330227i	$0.107125\pi$
$557$			367.873i			0.660455i	−0.943901	+	0.330227i	$0.892875\pi$
$558$		0			0
$559$			717.568i			1.28366i
$560$	23.9047	+	110.102i	0.0426870	+	0.196611i
$561$		0			0
$562$	255.880	+	534.964i	0.455303	+	0.951893i
$563$	146.204			0.259688			0.129844	−	0.991534i	$-0.458552\pi$
$563$	146.204			0.259688			0.129844	+	0.991534i	$0.458552\pi$
$564$		0			0
$565$			70.9561i			0.125586i
$566$	47.9038	+	100.152i	0.0846358	+	0.176946i
$567$		0			0
$568$	−148.098	+	625.874i	−0.260736	+	1.10189i
$569$	703.306			1.23604			0.618019	−	0.786163i	$-0.287935\pi$
$569$	703.306			1.23604			0.618019	+	0.786163i	$0.287935\pi$
$570$		0			0
$571$	−643.806			−1.12751			−0.563753	−	0.825943i	$-0.690643\pi$
$571$	−643.806			−1.12751			−0.563753	+	0.825943i	$0.690643\pi$
$572$	131.465	+	105.985i	0.229833	+	0.185288i
$573$		0			0
$574$	−210.141	+	100.513i	−0.366099	+	0.175110i
$575$		−	233.954i		−	0.406876i
$576$		0			0
$577$	350.872			0.608097			0.304049	−	0.952657i	$-0.401661\pi$
$577$	350.872			0.608097			0.304049	+	0.952657i	$0.401661\pi$
$578$	475.068	+	993.216i	0.821917	+	1.71837i
$579$		0			0
$580$	123.367	−	153.025i	0.212701	−	0.263837i
$581$			661.283i			1.13818i
$582$		0			0
$583$		−	188.779i		−	0.323806i
$584$	466.733	+	110.441i	0.799200	+	0.189112i
$585$		0			0
$586$	657.848	−	314.657i	1.12261	−	0.536958i
$587$	−120.781			−0.205759			−0.102879	−	0.994694i	$-0.532806\pi$
$587$	−120.781			−0.205759			−0.102879	+	0.994694i	$0.532806\pi$
$588$		0			0
$589$			185.897i			0.315615i
$590$	−205.979	+	98.5226i	−0.349118	+	0.166987i
$591$		0			0
$592$	−68.1890	+	14.8047i	−0.115184	+	0.0250080i
$593$	−350.072			−0.590340			−0.295170	−	0.955445i	$-0.595376\pi$
$593$	−350.072			−0.590340			−0.295170	+	0.955445i	$0.595376\pi$
$594$		0			0
$595$	204.027			0.342902
$596$	429.442	+	346.209i	0.720540	+	0.580888i
$597$		0			0
$598$	136.942	+	286.301i	0.228999	+	0.478764i
$599$		−	638.722i		−	1.06631i	−0.846016	−	0.533157i	$-0.821006\pi$
$599$		−	638.722i		−	1.06631i	0.846016	−	0.533157i	$-0.178994\pi$
$600$		0			0
$601$	−639.359			−1.06383			−0.531913	−	0.846799i	$-0.678527\pi$
$601$	−639.359			−1.06383			−0.531913	+	0.846799i	$0.678527\pi$
$602$	−410.801	+	196.491i	−0.682394	+	0.326398i
$603$		0			0
$604$	−49.7407	−	40.1001i	−0.0823521	−	0.0663910i
$605$		−	161.890i		−	0.267587i
$606$		0			0
$607$			872.976i			1.43818i	0.694916	+	0.719090i	$0.255441\pi$
$607$			872.976i			1.43818i	−0.694916	+	0.719090i	$0.744559\pi$
$608$	179.072	−	138.963i	0.294527	−	0.228557i
$609$		0			0
$610$	−104.704	−	218.903i	−0.171646	−	0.358858i
$611$	1190.37			1.94824
$612$		0			0
$613$			215.160i			0.350995i	0.984480	+	0.175497i	$0.0561534\pi$
$613$			215.160i			0.350995i	−0.984480	+	0.175497i	$0.943847\pi$
$614$	171.910	+	359.410i	0.279984	+	0.585358i
$615$		0			0
$616$	−24.6763	+	104.284i	−0.0400589	+	0.169292i
$617$	−657.172			−1.06511			−0.532554	−	0.846396i	$-0.678768\pi$
$617$	−657.172			−1.06511			−0.532554	+	0.846396i	$0.678768\pi$
$618$		0			0
$619$	823.016			1.32959			0.664795	−	0.747026i	$-0.268519\pi$
$619$	823.016			1.32959			0.664795	+	0.747026i	$0.268519\pi$
$620$	93.8461	−	116.408i	0.151365	−	0.187754i
$621$		0			0
$622$	−706.878	+	338.109i	−1.13646	+	0.543583i
$623$		−	322.560i		−	0.517753i
$624$		0			0
$625$	476.957			0.763131
$626$	−272.616	−	569.954i	−0.435489	−	0.910469i
$627$		0			0
$628$	476.375	+	384.046i	0.758559	+	0.611538i
$629$			126.359i			0.200888i
$630$		0			0
$631$		−	870.590i		−	1.37970i	−0.723953	−	0.689849i	$-0.757677\pi$
$631$		−	870.590i		−	1.37970i	0.723953	−	0.689849i	$-0.242323\pi$
$632$	204.593	−	864.627i	0.323724	−	1.36808i
$633$		0			0
$634$	−214.986	+	102.831i	−0.339095	+	0.162194i
$635$	304.764			0.479943
$636$		0			0
$637$			382.643i			0.600695i
$638$	168.658	−	80.6715i	0.264355	−	0.126444i
$639$		0			0
$640$	−182.286	−	3.38310i	−0.284822	−	0.00528609i
$641$	−675.353			−1.05359			−0.526797	−	0.849991i	$-0.676607\pi$
$641$	−675.353			−1.05359			−0.526797	+	0.849991i	$0.676607\pi$
$642$		0			0
$643$	−94.7253			−0.147318			−0.0736589	−	0.997283i	$-0.523468\pi$
$643$	−94.7253			−0.147318			−0.0736589	+	0.997283i	$0.523468\pi$
$644$	−126.406	+	156.795i	−0.196283	+	0.243471i
$645$		0			0
$646$	−177.113	−	370.286i	−0.274168	−	0.573199i
$647$			477.571i			0.738131i	0.929403	+	0.369065i	$0.120322\pi$
$647$			477.571i			0.738131i	−0.929403	+	0.369065i	$0.879678\pi$
$648$		0			0
$649$	−217.175			−0.334631
$650$	−645.744	+	308.868i	−0.993452	+	0.475181i
$651$		0			0
$652$	362.862	−	450.098i	0.556537	−	0.690334i
$653$			840.259i			1.28677i	0.765544	+	0.643384i	$0.222470\pi$
$653$			840.259i			1.28677i	−0.765544	+	0.643384i	$0.777530\pi$
$654$		0			0
$655$		−	304.688i		−	0.465173i
$656$	−79.9766	−	368.363i	−0.121916	−	0.561529i
$657$		0			0
$658$	325.959	+	681.477i	0.495379	+	1.03568i
$659$	−167.854			−0.254710			−0.127355	−	0.991857i	$-0.540649\pi$
$659$	−167.854			−0.254710			−0.127355	+	0.991857i	$0.540649\pi$
$660$		0			0
$661$			257.248i			0.389179i	0.980885	+	0.194590i	$0.0623375\pi$
$661$			257.248i			0.389179i	−0.980885	+	0.194590i	$0.937662\pi$
$662$	−124.689	−	260.685i	−0.188352	−	0.393785i
$663$		0			0
$664$	−1041.33	−	246.405i	−1.56826	−	0.371092i
$665$	−49.8787			−0.0750056
$666$		0			0
$667$	351.370			0.526791
$668$	−903.430	−	728.331i	−1.35244	−	1.09032i
$669$		0			0
$670$	−7.20552	+	3.44649i	−0.0107545	+	0.00514402i
$671$		−	230.802i		−	0.343967i
$672$		0			0
$673$	829.748			1.23291			0.616455	−	0.787390i	$-0.288568\pi$
$673$	829.748			1.23291			0.616455	+	0.787390i	$0.288568\pi$
$674$	431.504	+	902.137i	0.640213	+	1.33848i
$675$		0			0
$676$	185.162	−	229.677i	0.273909	−	0.339759i
$677$		−	157.740i		−	0.232999i	−0.993191	−	0.116500i	$-0.962833\pi$
$677$		−	157.740i		−	0.232999i	0.993191	−	0.116500i	$-0.0371674\pi$
$678$		0			0
$679$			367.695i			0.541525i
$680$	−76.0238	+	321.282i	−0.111800	+	0.472474i
$681$		0			0
$682$	128.300	−	61.3675i	0.188123	−	0.0899817i
$683$	443.451			0.649269			0.324635	−	0.945839i	$-0.394759\pi$
$683$	443.451			0.649269			0.324635	+	0.945839i	$0.394759\pi$
$684$		0			0
$685$		−	254.567i		−	0.371631i
$686$	−656.127	+	313.834i	−0.956453	+	0.457484i
$687$		0			0
$688$	−156.345	−	720.107i	−0.227246	−	1.04667i
$689$	−1085.52			−1.57551
$690$		0			0
$691$	364.887			0.528056			0.264028	−	0.964515i	$-0.414949\pi$
$691$	364.887			0.528056			0.264028	+	0.964515i	$0.414949\pi$
$692$	−330.878	−	266.749i	−0.478147	−	0.385475i
$693$		0			0
$694$	−520.654	−	1088.52i	−0.750222	−	1.56847i
$695$		−	118.580i		−	0.170618i
$696$		0			0
$697$	−682.600			−0.979340
$698$	−755.295	+	361.267i	−1.08208	+	0.517575i
$699$		0			0
$700$	−353.648	−	285.105i	−0.505211	−	0.407293i
$701$		−	835.592i		−	1.19200i	−0.802984	−	0.596000i	$-0.796756\pi$
$701$		−	835.592i		−	1.19200i	0.802984	−	0.596000i	$-0.203244\pi$
$702$		0			0
$703$		−	30.8911i		−	0.0439418i
$704$	−155.022	−	77.7159i	−0.220201	−	0.110392i
$705$		0			0
$706$	−142.087	−	297.058i	−0.201256	−	0.420762i
$707$	−786.995			−1.11315
$708$		0			0
$709$			695.967i			0.981617i	0.871267	+	0.490809i	$0.163299\pi$
$709$			695.967i			0.981617i	−0.871267	+	0.490809i	$0.836701\pi$
$710$	98.8212	+	206.604i	0.139185	+	0.290991i
$711$		0			0
$712$	507.938	+	120.191i	0.713396	+	0.168808i
$713$	267.290			0.374881
$714$		0			0
$715$	60.1313			0.0840997
$716$	−403.790	+	500.866i	−0.563953	+	0.699533i
$717$		0			0
$718$	−118.250	+	56.5605i	−0.164694	+	0.0787751i
$719$		−	214.444i		−	0.298253i	−0.988818	−	0.149127i	$-0.952354\pi$
$719$		−	214.444i		−	0.298253i	0.988818	−	0.149127i	$-0.0476462\pi$
$720$		0			0
$721$	740.603			1.02719
$722$	−268.239	−	560.803i	−0.371523	−	0.776736i
$723$		0			0
$724$	−2.02008	−	1.62856i	−0.00279017	−	0.00224939i
$725$			792.505i			1.09311i
$726$		0			0
$727$			798.004i			1.09767i	0.835932	+	0.548834i	$0.184928\pi$
$727$			798.004i			1.09767i	−0.835932	+	0.548834i	$0.815072\pi$
$728$	599.658	+	141.895i	0.823706	+	0.194911i
$729$		0			0
$730$	154.071	−	73.6939i	0.211056	−	0.100951i
$731$	−1334.40			−1.82545
$732$		0			0
$733$		−	841.501i		−	1.14802i	−0.818847	−	0.574012i	$-0.805386\pi$
$733$		−	841.501i		−	1.14802i	0.818847	−	0.574012i	$-0.194614\pi$
$734$	339.982	−	162.618i	0.463190	−	0.221550i
$735$		0			0
$736$	−199.806	−	257.477i	−0.271475	−	0.349833i
$737$	−7.59717			−0.0103082
$738$		0			0
$739$	−607.559			−0.822136			−0.411068	−	0.911605i	$-0.634844\pi$
$739$	−607.559			−0.822136			−0.411068	+	0.911605i	$0.634844\pi$
$740$	−15.5947	+	19.3438i	−0.0210739	+	0.0261403i
$741$		0			0
$742$	−297.249	−	621.452i	−0.400605	−	0.837537i
$743$		−	933.780i		−	1.25677i	−0.777902	−	0.628385i	$-0.783716\pi$
$743$		−	933.780i		−	1.25677i	0.777902	−	0.628385i	$-0.216284\pi$
$744$		0			0
$745$	196.425			0.263657
$746$	721.589	−	345.145i	0.967278	−	0.462661i
$747$		0			0
$748$	−197.091	+	244.474i	−0.263491	+	0.326837i
$749$		−	88.3946i		−	0.118017i
$750$		0			0
$751$		−	588.542i		−	0.783678i	−0.920034	−	0.391839i	$-0.871839\pi$
$751$		−	588.542i		−	0.783678i	0.920034	−	0.391839i	$-0.128161\pi$
$752$	−1194.58	+	259.360i	−1.58854	+	0.344894i
$753$		0			0
$754$	−463.881	−	969.827i	−0.615227	−	1.28624i
$755$	−22.7511			−0.0301340
$756$		0			0
$757$		−	365.635i		−	0.483005i	−0.970400	−	0.241503i	$-0.922360\pi$
$757$		−	365.635i		−	0.483005i	0.970400	−	0.241503i	$-0.0776402\pi$
$758$	320.167	+	669.366i	0.422383	+	0.883069i
$759$		0			0
$760$	18.5857	−	78.5444i	0.0244548	−	0.103348i
$761$	−221.260			−0.290749			−0.145374	−	0.989377i	$-0.546439\pi$
$761$	−221.260			−0.290749			−0.145374	+	0.989377i	$0.546439\pi$
$762$		0			0
$763$	743.643			0.974631
$764$	238.432	+	192.220i	0.312084	+	0.251597i
$765$		0			0
$766$	70.5933	−	33.7657i	0.0921584	−	0.0440805i
$767$			1248.81i			1.62818i
$768$		0			0
$769$	1313.45			1.70800			0.854002	−	0.520270i	$-0.174169\pi$
$769$	1313.45			1.70800			0.854002	+	0.520270i	$0.174169\pi$
$770$	16.4657	+	34.4246i	0.0213840	+	0.0447072i
$771$		0			0
$772$	−145.092	+	179.974i	−0.187943	+	0.233127i
$773$			468.140i			0.605614i	0.953052	+	0.302807i	$0.0979238\pi$
$773$			468.140i			0.605614i	−0.953052	+	0.302807i	$0.902076\pi$
$774$		0			0
$775$			602.865i			0.777891i
$776$	−579.013	−	137.010i	−0.746150	−	0.176559i
$777$		0			0
$778$	215.111	−	102.890i	0.276492	−	0.132250i
$779$	166.876			0.214219
$780$		0			0
$781$			217.834i			0.278916i
$782$	−532.411	+	254.659i	−0.680833	+	0.325651i
$783$		0			0
$784$	−83.3709	−	383.997i	−0.106340	−	0.489792i
$785$	217.892			0.277569
$786$		0			0
$787$	1425.09			1.81078			0.905392	−	0.424577i	$-0.139577\pi$
$787$	1425.09			1.81078			0.905392	+	0.424577i	$0.139577\pi$
$788$	256.069	+	206.439i	0.324960	+	0.261978i
$789$		0			0
$790$	−136.519	−	285.417i	−0.172808	−	0.361287i
$791$			246.281i			0.311354i
$792$		0			0
$793$	−1327.17			−1.67360
$794$	−258.370	+	123.582i	−0.325403	+	0.155645i
$795$		0			0
$796$	−125.395	−	101.091i	−0.157531	−	0.126999i
$797$			895.977i			1.12419i	0.827074	+	0.562093i	$0.190004\pi$
$797$			895.977i			1.12419i	−0.827074	+	0.562093i	$0.809996\pi$
$798$		0			0
$799$			2213.64i			2.77052i
$800$	580.732	−	450.656i	0.725915	−	0.563320i
$801$		0			0
$802$	123.380	+	257.949i	0.153841	+	0.321632i
$803$	162.445			0.202298
$804$		0			0
$805$			71.7175i			0.0890900i
$806$	−352.878	−	737.756i	−0.437814	−	0.915330i
$807$		0			0
$808$	293.248	−	1239.29i	0.362930	−	1.53377i
$809$	1034.32			1.27852			0.639261	−	0.768990i	$-0.279240\pi$
$809$	1034.32			1.27852			0.639261	+	0.768990i	$0.279240\pi$
$810$		0			0
$811$	−197.171			−0.243121			−0.121561	−	0.992584i	$-0.538790\pi$
$811$	−197.171			−0.243121			−0.121561	+	0.992584i	$0.538790\pi$
$812$	428.193	−	531.135i	0.527331	−	0.654107i
$813$		0			0
$814$	−21.3200	+	10.1976i	−0.0261916	+	0.0125278i
$815$		−	205.873i		−	0.252604i
$816$		0			0
$817$	326.224			0.399295
$818$	−249.188	−	520.973i	−0.304631	−	0.636887i
$819$		0			0
$820$	−104.497	−	84.2438i	−0.127435	−	0.102736i
$821$		−	1568.65i		−	1.91065i	−0.295551	−	0.955327i	$-0.595503\pi$
$821$		−	1568.65i		−	1.91065i	0.295551	−	0.955327i	$-0.404497\pi$
$822$		0			0
$823$		−	965.377i		−	1.17300i	−0.809950	−	0.586499i	$-0.800506\pi$
$823$		−	965.377i		−	1.17300i	0.809950	−	0.586499i	$-0.199494\pi$
$824$	−275.961	+	1166.23i	−0.334904	+	1.41533i
$825$		0			0
$826$	−714.933	+	341.962i	−0.865536	+	0.413997i
$827$	2.79204			0.00337611			0.00168805	−	0.999999i	$-0.499463\pi$
$827$	2.79204			0.00337611			0.00168805	+	0.999999i	$0.499463\pi$
$828$		0			0
$829$			1463.39i			1.76524i	0.470084	+	0.882622i	$0.344224\pi$
$829$			1463.39i			1.76524i	−0.470084	+	0.882622i	$0.655776\pi$
$830$	−343.746	+	164.418i	−0.414152	+	0.198094i
$831$		0			0
$832$	−446.886	+	891.413i	−0.537122	+	1.07141i
$833$	−711.571			−0.854227
$834$		0			0
$835$	−413.224			−0.494880
$836$	48.1832	−	59.7670i	0.0576354	−	0.0714916i
$837$		0			0
$838$	576.719	+	1205.73i	0.688208	+	1.43882i
$839$			608.761i			0.725579i	0.931871	+	0.362790i	$0.118176\pi$
$839$			608.761i			0.725579i	−0.931871	+	0.362790i	$0.881824\pi$
$840$		0			0
$841$	−349.244			−0.415272
$842$	824.569	−	394.402i	0.979298	−	0.468411i
$843$		0			0
$844$	−192.015	+	238.177i	−0.227505	+	0.282200i
$845$		−	105.053i		−	0.124323i
$846$		0			0
$847$		−	561.903i		−	0.663404i
$848$	1089.37	−	236.516i	1.28463	−	0.278910i
$849$		0			0
$850$	−574.377	−	1200.84i	−0.675737	−	1.41275i
$851$	−44.4163			−0.0521931
$852$		0			0
$853$			1450.55i			1.70052i	0.526361	+	0.850261i	$0.323556\pi$
$853$			1450.55i			1.70052i	−0.526361	+	0.850261i	$0.676444\pi$
$854$	−363.417	−	759.790i	−0.425547	−	0.889684i
$855$		0			0
$856$	139.196	+	32.9373i	0.162612	+	0.0384782i
$857$	−17.9925			−0.0209948			−0.0104974	−	0.999945i	$-0.503341\pi$
$857$	−17.9925			−0.0209948			−0.0104974	+	0.999945i	$0.503341\pi$
$858$		0			0
$859$	−825.824			−0.961379			−0.480689	−	0.876891i	$-0.659614\pi$
$859$	−825.824			−0.961379			−0.480689	+	0.876891i	$0.659614\pi$
$860$	−204.279	−	164.687i	−0.237534	−	0.191496i
$861$		0			0
$862$	−525.373	+	251.293i	−0.609481	+	0.291523i
$863$			8.17746i			0.00947562i	0.999989	+	0.00473781i	$0.00150810\pi$
$863$			8.17746i			0.00947562i	−0.999989	+	0.00473781i	$0.998492\pi$
$864$		0			0
$865$	−151.342			−0.174962
$866$	257.455	+	538.257i	0.297292	+	0.621544i
$867$		0			0
$868$	325.730	−	404.039i	0.375265	−	0.465483i
$869$		−	300.931i		−	0.346296i
$870$		0			0
$871$			43.6856i			0.0501557i
$872$	−277.094	+	1171.02i	−0.317768	+	1.34291i
$873$		0			0
$874$	130.159	−	62.2570i	0.148924	−	0.0712322i
$875$	−337.800			−0.386057
$876$		0			0
$877$			1085.59i			1.23784i	0.785452	+	0.618922i	$0.212430\pi$
$877$			1085.59i			1.23784i	−0.785452	+	0.618922i	$0.787570\pi$
$878$	743.173	−	355.469i	0.846438	−	0.404862i
$879$		0			0
$880$	−60.3440	+	13.1015i	−0.0685727	+	0.0148881i
$881$	1072.61			1.21749			0.608746	−	0.793366i	$-0.291673\pi$
$881$	1072.61			1.21749			0.608746	+	0.793366i	$0.291673\pi$
$882$		0			0
$883$	279.338			0.316351			0.158175	−	0.987411i	$-0.449439\pi$
$883$	279.338			0.316351			0.158175	+	0.987411i	$0.449439\pi$
$884$	1405.79	+	1133.32i	1.59026	+	1.28204i
$885$		0			0
$886$	471.099	+	984.917i	0.531714	+	1.11164i
$887$			195.699i			0.220630i	0.993897	+	0.110315i	$0.0351860\pi$
$887$			195.699i			0.220630i	−0.993897	+	0.110315i	$0.964814\pi$
$888$		0			0
$889$	1057.80			1.18988
$890$	167.672	−	80.1999i	0.188396	−	0.0901123i
$891$		0			0
$892$	268.880	+	216.767i	0.301435	+	0.243012i
$893$		−	541.173i		−	0.606016i
$894$		0			0
$895$			229.094i			0.255971i
$896$	−632.696	−	11.7424i	−0.706134	−	0.0131053i
$897$		0			0
$898$	179.516	+	375.310i	0.199906	+	0.417940i
$899$	−905.429			−1.00715
$900$		0			0
$901$		−	2018.66i		−	2.24047i
$902$	−55.0884	−	115.172i	−0.0610736	−	0.127686i
$903$		0			0
$904$	−387.821	−	91.7685i	−0.429005	−	0.101514i
$905$	−0.923975			−0.00102097
$906$		0			0
$907$	420.896			0.464053			0.232027	−	0.972709i	$-0.425464\pi$
$907$	420.896			0.464053			0.232027	+	0.972709i	$0.425464\pi$
$908$	12.2571	−	15.2038i	0.0134990	−	0.0167443i
$909$		0			0
$910$	197.950	−	94.6819i	0.217527	−	0.104046i
$911$			1331.84i			1.46195i	0.682404	+	0.730975i	$0.260934\pi$
$911$			1331.84i			1.46195i	−0.682404	+	0.730975i	$0.739066\pi$
$912$		0			0
$913$	−362.431			−0.396967
$914$	−638.461	−	1334.82i	−0.698535	−	1.46041i
$915$		0			0
$916$	−800.675	−	645.492i	−0.874099	−	0.704685i
$917$		−	1057.54i		−	1.15326i
$918$		0			0
$919$			502.618i			0.546918i	0.961884	+	0.273459i	$0.0881679\pi$
$919$			502.618i			0.546918i	−0.961884	+	0.273459i	$0.911832\pi$
$920$	−112.934	−	26.7231i	−0.122754	−	0.0290469i
$921$		0			0
$922$	−111.351	+	53.2604i	−0.120771	+	0.0577662i
$923$	1252.60			1.35709
$924$		0			0
$925$		−	100.180i		−	0.108302i
$926$	1217.91	−	582.542i	1.31524	−	0.629096i
$927$		0			0
$928$	676.830	+	872.188i	0.729342	+	0.939857i
$929$	954.669			1.02763			0.513816	−	0.857901i	$-0.328232\pi$
$929$	954.669			1.02763			0.513816	+	0.857901i	$0.328232\pi$
$930$		0			0
$931$	173.959			0.186852
$932$	−901.445	+	1118.16i	−0.967215	+	1.19974i
$933$		0			0
$934$	−482.819	−	1009.42i	−0.516937	−	1.08075i
$935$			111.821i			0.119595i
$936$		0			0
$937$	−71.0308			−0.0758067			−0.0379033	−	0.999281i	$-0.512068\pi$
$937$	−71.0308			−0.0758067			−0.0379033	+	0.999281i	$0.512068\pi$
$938$	−25.0096	+	11.9624i	−0.0266627	+	0.0127531i
$939$		0			0
$940$	−273.199	+	338.879i	−0.290637	+	0.360509i
$941$		−	1218.28i		−	1.29467i	−0.762207	−	0.647333i	$-0.775884\pi$
$941$		−	1218.28i		−	1.29467i	0.762207	−	0.647333i	$-0.224116\pi$
$942$		0			0
$943$		−	239.941i		−	0.254444i
$944$	−272.093	−	1253.23i	−0.288234	−	1.32757i
$945$		0			0
$946$	−107.691	−	225.149i	−0.113839	−	0.238001i
$947$	1102.20			1.16389			0.581944	−	0.813229i	$-0.302292\pi$
$947$	1102.20			1.16389			0.581944	+	0.813229i	$0.302292\pi$
$948$		0			0
$949$		−	934.099i		−	0.984298i
$950$	140.419	+	293.571i	0.147809	+	0.309022i
$951$		0			0
$952$	−263.871	+	1115.14i	−0.277175	+	1.17136i
$953$	−13.7111			−0.0143873			−0.00719365	−	0.999974i	$-0.502290\pi$
$953$	−13.7111			−0.0143873			−0.00719365	+	0.999974i	$0.502290\pi$
$954$		0			0
$955$	109.058			0.114197
$956$	−1363.50	−	1099.23i	−1.42625	−	1.14982i
$957$		0			0
$958$	518.341	−	247.929i	0.541066	−	0.258799i
$959$		−	883.576i		−	0.921351i
$960$		0			0
$961$	272.232			0.283280
$962$	58.6388	+	122.595i	0.0609551	+	0.127438i
$963$		0			0
$964$	−618.503	+	767.198i	−0.641601	+	0.795849i
$965$			82.3193i			0.0853049i
$966$		0			0
$967$			73.1595i			0.0756561i	0.999284	+	0.0378281i	$0.0120439\pi$
$967$			73.1595i			0.0756561i	−0.999284	+	0.0378281i	$0.987956\pi$
$968$	884.832	+	209.375i	0.914083	+	0.216296i
$969$		0			0
$970$	−191.135	+	91.4221i	−0.197046	+	0.0942496i
$971$	−924.445			−0.952055			−0.476027	−	0.879431i	$-0.657924\pi$
$971$	−924.445			−0.952055			−0.476027	+	0.879431i	$0.657924\pi$
$972$		0			0
$973$		−	411.577i		−	0.422998i
$974$	882.467	−	422.096i	0.906024	−	0.433363i
$975$		0			0
$976$	1331.86	−	289.165i	1.36461	−	0.296276i
$977$	1101.28			1.12720			0.563602	−	0.826047i	$-0.309415\pi$
$977$	1101.28			1.12720			0.563602	+	0.826047i	$0.309415\pi$
$978$		0			0
$979$	176.786			0.180578
$980$	−108.932	−	87.8192i	−0.111155	−	0.0896114i
$981$		0			0
$982$	453.835	+	948.824i	0.462154	+	0.966216i
$983$			919.615i			0.935519i	0.883856	+	0.467760i	$0.154939\pi$
$983$			919.615i			0.935519i	−0.883856	+	0.467760i	$0.845061\pi$
$984$		0			0
$985$	117.125			0.118908
$986$	1803.51	−	862.642i	1.82912	−	0.874891i
$987$		0			0
$988$	−343.675	−	277.065i	−0.347849	−	0.280430i
$989$		−	469.057i		−	0.474274i
$990$		0			0
$991$		−	1633.57i		−	1.64841i	−0.566292	−	0.824204i	$-0.691623\pi$
$991$		−	1633.57i		−	1.64841i	0.566292	−	0.824204i	$-0.308377\pi$
$992$	514.870	+	663.481i	0.519023	+	0.668831i
$993$		0			0
$994$	342.998	+	717.100i	0.345069	+	0.721428i
$995$	−57.3549			−0.0576431
$996$		0			0
$997$		−	320.009i		−	0.320972i	−0.987038	−	0.160486i	$-0.948694\pi$
$997$		−	320.009i		−	0.320972i	0.987038	−	0.160486i	$-0.0513061\pi$
$998$	592.954	+	1239.68i	0.594143	+	1.24216i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.3.b.b.163.12	yes	16
3.2	odd	2	inner	216.3.b.b.163.5	✓	16
4.3	odd	2		864.3.b.b.271.9		16
8.3	odd	2	inner	216.3.b.b.163.11	yes	16
8.5	even	2		864.3.b.b.271.8		16
12.11	even	2		864.3.b.b.271.7		16
24.5	odd	2		864.3.b.b.271.10		16
24.11	even	2	inner	216.3.b.b.163.6	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.3.b.b.163.5	✓	16	3.2	odd	2	inner
216.3.b.b.163.6	yes	16	24.11	even	2	inner
216.3.b.b.163.11	yes	16	8.3	odd	2	inner
216.3.b.b.163.12	yes	16	1.1	even	1	trivial
864.3.b.b.271.7		16	12.11	even	2
864.3.b.b.271.8		16	8.5	even	2
864.3.b.b.271.9		16	4.3	odd	2
864.3.b.b.271.10		16	24.5	odd	2

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.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.862987 + 1.80423i) q^{2} +(-2.51051 + 3.11406i) q^{4} +1.42436i q^{5} +4.94379i q^{7} +(-7.78502 - 1.84214i) q^{8} +O(q^{10})\)	\(q+(0.862987 + 1.80423i) q^{2} +(-2.51051 + 3.11406i) q^{4} +1.42436i q^{5} +4.94379i q^{7} +(-7.78502 - 1.84214i) q^{8} +(-2.56987 + 1.22920i) q^{10} -2.70955 q^{11} +15.5806i q^{13} +(-8.91974 + 4.26643i) q^{14} +(-3.39473 - 15.6357i) q^{16} -28.9740 q^{17} +7.08332 q^{19} +(-4.43553 - 3.57585i) q^{20} +(-2.33831 - 4.88866i) q^{22} -10.1847i q^{23} +22.9712 q^{25} +(-28.1110 + 13.4459i) q^{26} +(-15.3953 - 12.4114i) q^{28} +34.4999i q^{29} +26.2444i q^{31} +(25.2809 - 19.6183i) q^{32} +(-25.0042 - 52.2758i) q^{34} -7.04172 q^{35} -4.36110i q^{37} +(6.11282 + 12.7800i) q^{38} +(2.62386 - 11.0886i) q^{40} +23.5591 q^{41} +46.0553 q^{43} +(6.80235 - 8.43771i) q^{44} +(18.3755 - 8.78923i) q^{46} -76.4010i q^{47} +24.5589 q^{49} +(19.8239 + 41.4454i) q^{50} +(-48.5189 - 39.1152i) q^{52} +69.6716i q^{53} -3.85937i q^{55} +(9.10715 - 38.4875i) q^{56} +(-62.2458 + 29.7730i) q^{58} +80.1517 q^{59} +85.1807i q^{61} +(-47.3510 + 22.6486i) q^{62} +(57.2130 + 28.6822i) q^{64} -22.1923 q^{65} +2.80385 q^{67} +(72.7394 - 90.2267i) q^{68} +(-6.07691 - 12.7049i) q^{70} -80.3947i q^{71} -59.9527 q^{73} +(7.86844 - 3.76358i) q^{74} +(-17.7827 + 22.0579i) q^{76} -13.3955i q^{77} +111.063i q^{79} +(22.2708 - 4.83530i) q^{80} +(20.3312 + 42.5060i) q^{82} +133.760 q^{83} -41.2693i q^{85} +(39.7451 + 83.0944i) q^{86} +(21.0939 + 4.99138i) q^{88} -65.2456 q^{89} -77.0272 q^{91} +(31.7156 + 25.5686i) q^{92} +(137.845 - 65.9331i) q^{94} +10.0892i q^{95} +74.3752 q^{97} +(21.1941 + 44.3100i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{4}+O(q^{10}) \) 16 * q + 4 * q^4	\( 16 q + 4 q^{4} + 24 q^{10} + 16 q^{16} - 64 q^{19} + 80 q^{22} - 80 q^{25} - 12 q^{28} + 8 q^{34} - 72 q^{40} - 64 q^{43} - 192 q^{46} - 128 q^{49} + 84 q^{52} - 96 q^{58} + 376 q^{64} + 128 q^{67} + 192 q^{70} + 80 q^{73} + 308 q^{76} + 272 q^{82} - 136 q^{88} + 192 q^{91} + 336 q^{94} + 80 q^{97}+O(q^{100}) \) 16 * q + 4 * q^4 + 24 * q^10 + 16 * q^16 - 64 * q^19 + 80 * q^22 - 80 * q^25 - 12 * q^28 + 8 * q^34 - 72 * q^40 - 64 * q^43 - 192 * q^46 - 128 * q^49 + 84 * q^52 - 96 * q^58 + 376 * q^64 + 128 * q^67 + 192 * q^70 + 80 * q^73 + 308 * q^76 + 272 * q^82 - 136 * q^88 + 192 * q^91 + 336 * q^94 + 80 * q^97

Introduction

L-functions

Modular forms

Varieties

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Database

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