LMFDB - Embedded newform 198.3.k.a.53.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [198,3,Mod(53,198)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(198, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 6])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("198.53"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 198 = 2 \cdot 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	198.k (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,8,0,0,-24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.39510923433$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
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} + 14 x^{14} + 255 x^{12} + 3946 x^{10} + 33929 x^{8} + 477466 x^{6} + 3733455 x^{4} + \cdots + 214358881 $ x^16 + 14x^14 + 255x^12 + 3946x^10 + 33929x^8 + 477466x^6 + 3733455x^4 + 24801854*x^2 + 214358881
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			53.4
Root			$2.40294 + 2.28602i$ of defining polynomial
Character	$\chi$	$=$	198.53
Dual form			198.3.k.a.71.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.34500 + 0.437016i) q^{2} +(1.61803 + 1.17557i) q^{4} +(2.68314 - 0.871805i) q^{5} +(1.80392 + 1.31063i) q^{7} +(1.66251 + 2.28825i) q^{8} +3.98981 q^{10} +(10.9772 - 0.707957i) q^{11} +(-1.39798 + 4.30255i) q^{13} +(1.85351 + 2.55113i) q^{14} +(1.23607 + 3.80423i) q^{16} +(14.0058 - 4.55076i) q^{17} +(-8.97019 + 6.51722i) q^{19} +(5.36628 + 1.74361i) q^{20} +(15.0737 + 3.84501i) q^{22} -11.0813i q^{23} +(-13.7862 + 10.0163i) q^{25} +(-3.76057 + 5.17598i) q^{26} +(1.37807 + 4.24128i) q^{28} +(13.3045 - 18.3121i) q^{29} +(-7.11534 + 21.8988i) q^{31} +5.65685i q^{32} +20.8265 q^{34} +(5.98279 + 1.94393i) q^{35} +(-16.2058 - 11.7742i) q^{37} +(-14.9130 + 4.84553i) q^{38} +(6.45565 + 4.69030i) q^{40} +(-23.8256 - 32.7931i) q^{41} -45.6612 q^{43} +(18.5937 + 11.7590i) q^{44} +(4.84271 - 14.9043i) q^{46} +(-6.81426 - 9.37903i) q^{47} +(-13.6054 - 41.8732i) q^{49} +(-22.9197 + 7.44706i) q^{50} +(-7.31994 + 5.31825i) q^{52} +(-37.2253 - 12.0952i) q^{53} +(28.8362 - 11.4695i) q^{55} +6.30674i q^{56} +(25.8972 - 18.8154i) q^{58} +(-54.7514 + 75.3588i) q^{59} +(-22.9159 - 70.5280i) q^{61} +(-19.1402 + 26.3443i) q^{62} +(-2.47214 + 7.60845i) q^{64} +12.7631i q^{65} +87.7093 q^{67} +(28.0116 + 9.10152i) q^{68} +(7.19731 + 5.22915i) q^{70} +(-63.8893 + 20.7589i) q^{71} +(-28.8781 - 20.9811i) q^{73} +(-16.6512 - 22.9184i) q^{74} -22.1755 q^{76} +(20.7299 + 13.1099i) q^{77} +(7.84946 - 24.1582i) q^{79} +(6.63309 + 9.12967i) q^{80} +(-17.7142 - 54.5188i) q^{82} +(20.8375 - 6.77051i) q^{83} +(33.6122 - 24.4207i) q^{85} +(-61.4141 - 19.9547i) q^{86} +(19.8697 + 23.9415i) q^{88} -34.9908i q^{89} +(-8.16089 + 5.92924i) q^{91} +(13.0269 - 17.9299i) q^{92} +(-5.06638 - 15.5927i) q^{94} +(-18.3865 + 25.3069i) q^{95} +(-33.7192 + 103.777i) q^{97} -62.2652i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} - 24 q^{7} - 24 q^{10} + 48 q^{13} - 16 q^{16} - 36 q^{19} + 48 q^{22} + 192 q^{25} - 32 q^{28} + 4 q^{31} - 112 q^{34} + 76 q^{37} - 72 q^{40} - 440 q^{43} - 36 q^{46} - 168 q^{49} + 24 q^{52}+ \cdots + 156 q^{97}+O(q^{100}) $ 16 * q + 8 * q^4 - 24 * q^7 - 24 * q^10 + 48 * q^13 - 16 * q^16 - 36 * q^19 + 48 * q^22 + 192 * q^25 - 32 * q^28 + 4 * q^31 - 112 * q^34 + 76 * q^37 - 72 * q^40 - 440 * q^43 - 36 * q^46 - 168 * q^49 + 24 * q^52 + 836 * q^55 - 96 * q^58 + 40 * q^61 + 32 * q^64 - 552 * q^67 + 516 * q^70 - 316 * q^73 - 288 * q^76 + 604 * q^79 - 36 * q^82 + 36 * q^85 - 16 * q^88 - 352 * q^91 - 220 * q^94 + 156 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/198\mathbb{Z}\right)^\times$.

$n$	$145$	$155$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$-1$

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 $

$2$	1.34500	+	0.437016i	0.672499	+	0.218508i
$2$	1.34500	+	0.437016i	0.672499	+	0.218508i
$3$		0			0
$3$		0			0
$4$	1.61803	+	1.17557i	0.404508	+	0.293893i
$5$	2.68314	−	0.871805i	0.536628	−	0.174361i	−0.0281501	−	0.999604i	$-0.508962\pi$
$5$	2.68314	−	0.871805i	0.536628	−	0.174361i	0.564778	+	0.825243i	$0.308962\pi$
$6$		0			0
$7$	1.80392	+	1.31063i	0.257703	+	0.187232i	0.709134	−	0.705074i	$-0.249086\pi$
$7$	1.80392	+	1.31063i	0.257703	+	0.187232i	−0.451431	+	0.892306i	$0.649086\pi$
$8$	1.66251	+	2.28825i	0.207813	+	0.286031i
$9$		0			0
$10$	3.98981			0.398981
$11$	10.9772	−	0.707957i	0.997927	−	0.0643598i
$11$	10.9772	−	0.707957i	0.997927	−	0.0643598i
$12$		0			0
$13$	−1.39798	+	4.30255i	−0.107537	+	0.330966i	−0.990318	−	0.138820i	$-0.955669\pi$
$13$	−1.39798	+	4.30255i	−0.107537	+	0.330966i	0.882780	+	0.469786i	$0.155669\pi$
$14$	1.85351	+	2.55113i	0.132393	+	0.182224i
$15$		0			0
$16$	1.23607	+	3.80423i	0.0772542	+	0.237764i
$17$	14.0058	−	4.55076i	0.823871	−	0.267692i	0.133409	−	0.991061i	$-0.457408\pi$
$17$	14.0058	−	4.55076i	0.823871	−	0.267692i	0.690461	+	0.723369i	$0.257408\pi$
$18$		0			0
$19$	−8.97019	+	6.51722i	−0.472115	+	0.343012i	−0.798265	−	0.602306i	$-0.794249\pi$
$19$	−8.97019	+	6.51722i	−0.472115	+	0.343012i	0.326150	+	0.945318i	$0.394249\pi$
$20$	5.36628	+	1.74361i	0.268314	+	0.0871805i
$21$		0			0
$22$	15.0737	+	3.84501i	0.685167	+	0.174773i
$23$		−	11.0813i		−	0.481796i	−0.970550	−	0.240898i	$-0.922558\pi$
$23$		−	11.0813i		−	0.481796i	0.970550	−	0.240898i	$-0.0774419\pi$
$24$		0			0
$25$	−13.7862	+	10.0163i	−0.551449	+	0.400651i
$26$	−3.76057	+	5.17598i	−0.144637	+	0.199076i
$27$		0			0
$28$	1.37807	+	4.24128i	0.0492169	+	0.151474i
$29$	13.3045	−	18.3121i	0.458776	−	0.631452i	−0.515478	−	0.856903i	$-0.672386\pi$
$29$	13.3045	−	18.3121i	0.458776	−	0.631452i	0.974254	+	0.225451i	$0.0723856\pi$
$30$		0			0
$31$	−7.11534	+	21.8988i	−0.229527	+	0.706412i	0.768273	+	0.640122i	$0.221116\pi$
$31$	−7.11534	+	21.8988i	−0.229527	+	0.706412i	−0.997800	+	0.0662901i	$0.978884\pi$
$32$			5.65685i			0.176777i
$33$		0			0
$34$	20.8265			0.612545
$35$	5.98279	+	1.94393i	0.170937	+	0.0555407i
$36$		0			0
$37$	−16.2058	−	11.7742i	−0.437994	−	0.318221i	0.346843	−	0.937923i	$-0.387254\pi$
$37$	−16.2058	−	11.7742i	−0.437994	−	0.318221i	−0.784837	+	0.619702i	$0.787254\pi$
$38$	−14.9130	+	4.84553i	−0.392448	+	0.127514i
$39$		0			0
$40$	6.45565	+	4.69030i	0.161391	+	0.117258i
$41$	−23.8256	−	32.7931i	−0.581111	−	0.799831i	0.412705	−	0.910865i	$-0.364584\pi$
$41$	−23.8256	−	32.7931i	−0.581111	−	0.799831i	−0.993817	+	0.111033i	$0.964584\pi$
$42$		0			0
$43$	−45.6612			−1.06189			−0.530944	−	0.847407i	$-0.678163\pi$
$43$	−45.6612			−1.06189			−0.530944	+	0.847407i	$0.678163\pi$
$44$	18.5937	+	11.7590i	0.422585	+	0.267249i
$45$		0			0
$46$	4.84271	−	14.9043i	0.105276	−	0.324007i
$47$	−6.81426	−	9.37903i	−0.144984	−	0.199554i	0.730348	−	0.683075i	$-0.239358\pi$
$47$	−6.81426	−	9.37903i	−0.144984	−	0.199554i	−0.875333	+	0.483521i	$0.839358\pi$
$48$		0			0
$49$	−13.6054	−	41.8732i	−0.277662	−	0.854556i
$50$	−22.9197	+	7.44706i	−0.458394	+	0.148941i
$51$		0			0
$52$	−7.31994	+	5.31825i	−0.140768	+	0.102274i
$53$	−37.2253	−	12.0952i	−0.702365	−	0.228212i	−0.0640042	−	0.997950i	$-0.520387\pi$
$53$	−37.2253	−	12.0952i	−0.702365	−	0.228212i	−0.638361	+	0.769737i	$0.720387\pi$
$54$		0			0
$55$	28.8362	−	11.4695i	0.524294	−	0.208537i
$56$			6.30674i			0.112620i
$57$		0			0
$58$	25.8972	−	18.8154i	0.446504	−	0.324404i
$59$	−54.7514	+	75.3588i	−0.927990	+	1.27727i	0.0326490	+	0.999467i	$0.489606\pi$
$59$	−54.7514	+	75.3588i	−0.927990	+	1.27727i	−0.960639	+	0.277801i	$0.910394\pi$
$60$		0			0
$61$	−22.9159	−	70.5280i	−0.375671	−	1.15620i	−0.943025	−	0.332723i	$-0.892033\pi$
$61$	−22.9159	−	70.5280i	−0.375671	−	1.15620i	0.567354	−	0.823474i	$-0.307967\pi$
$62$	−19.1402	+	26.3443i	−0.308713	+	0.424908i
$63$		0			0
$64$	−2.47214	+	7.60845i	−0.0386271	+	0.118882i
$65$			12.7631i			0.196356i
$66$		0			0
$67$	87.7093			1.30909			0.654547	−	0.756021i	$-0.272859\pi$
$67$	87.7093			1.30909			0.654547	+	0.756021i	$0.272859\pi$
$68$	28.0116	+	9.10152i	0.411935	+	0.133846i
$69$		0			0
$70$	7.19731	+	5.22915i	0.102819	+	0.0747021i
$71$	−63.8893	+	20.7589i	−0.899850	+	0.292379i	−0.722175	−	0.691710i	$-0.756857\pi$
$71$	−63.8893	+	20.7589i	−0.899850	+	0.292379i	−0.177675	+	0.984089i	$0.556857\pi$
$72$		0			0
$73$	−28.8781	−	20.9811i	−0.395590	−	0.287413i	0.372152	−	0.928172i	$-0.378620\pi$
$73$	−28.8781	−	20.9811i	−0.395590	−	0.287413i	−0.767742	+	0.640759i	$0.778620\pi$
$74$	−16.6512	−	22.9184i	−0.225017	−	0.309709i
$75$		0			0
$76$	−22.1755			−0.291783
$77$	20.7299	+	13.1099i	0.269219	+	0.170258i
$78$		0			0
$79$	7.84946	−	24.1582i	0.0993603	−	0.305800i	−0.889005	−	0.457897i	$-0.848603\pi$
$79$	7.84946	−	24.1582i	0.0993603	−	0.305800i	0.988365	+	0.152098i	$0.0486028\pi$
$80$	6.63309	+	9.12967i	0.0829136	+	0.114121i
$81$		0			0
$82$	−17.7142	−	54.5188i	−0.216027	−	0.664863i
$83$	20.8375	−	6.77051i	0.251054	−	0.0815724i	−0.180786	−	0.983522i	$-0.557864\pi$
$83$	20.8375	−	6.77051i	0.251054	−	0.0815724i	0.431841	+	0.901950i	$0.357864\pi$
$84$		0			0
$85$	33.6122	−	24.4207i	0.395437	−	0.287302i
$86$	−61.4141	−	19.9547i	−0.714118	−	0.232031i
$87$		0			0
$88$	19.8697	+	23.9415i	0.225791	+	0.272063i
$89$		−	34.9908i		−	0.393155i	−0.980488	−	0.196577i	$-0.937017\pi$
$89$		−	34.9908i		−	0.393155i	0.980488	−	0.196577i	$-0.0629827\pi$
$90$		0			0
$91$	−8.16089	+	5.92924i	−0.0896801	+	0.0651564i
$92$	13.0269	−	17.9299i	0.141596	−	0.194891i
$93$		0			0
$94$	−5.06638	−	15.5927i	−0.0538976	−	0.165880i
$95$	−18.3865	+	25.3069i	−0.193542	+	0.266388i
$96$		0			0
$97$	−33.7192	+	103.777i	−0.347621	+	1.06987i	0.612545	+	0.790436i	$0.290146\pi$
$97$	−33.7192	+	103.777i	−0.347621	+	1.06987i	−0.960166	+	0.279432i	$0.909854\pi$
$98$		−	62.2652i		−	0.635359i
$99$		0			0
$100$	−34.0814			−0.340814
$101$	171.987	+	55.8819i	1.70284	+	0.553286i	0.989116	−	0.147140i	$-0.0470067\pi$
$101$	171.987	+	55.8819i	1.70284	+	0.553286i	0.713725	+	0.700426i	$0.247007\pi$
$102$		0			0
$103$	163.062	+	118.472i	1.58313	+	1.15021i	0.912997	+	0.407967i	$0.133762\pi$
$103$	163.062	+	118.472i	1.58313	+	1.15021i	0.670131	+	0.742243i	$0.266238\pi$
$104$	−12.1695	+	3.95410i	−0.117014	+	0.0380202i
$105$		0			0
$106$	−44.7822	−	32.5361i	−0.422473	−	0.306945i
$107$	−53.7458	−	73.9747i	−0.502297	−	0.691353i	0.480300	−	0.877104i	$-0.340528\pi$
$107$	−53.7458	−	73.9747i	−0.502297	−	0.691353i	−0.982597	+	0.185752i	$0.940528\pi$
$108$		0			0
$109$	−207.818			−1.90659			−0.953295	−	0.302040i	$-0.902332\pi$
$109$	−207.818			−1.90659			−0.953295	+	0.302040i	$0.902332\pi$
$110$	43.7969	−	2.82462i	0.398154	−	0.0256783i
$111$		0			0
$112$	−2.75615	+	8.48255i	−0.0246085	+	0.0757371i
$113$	−37.3186	−	51.3646i	−0.330253	−	0.454554i	0.611310	−	0.791391i	$-0.290643\pi$
$113$	−37.3186	−	51.3646i	−0.330253	−	0.454554i	−0.941563	+	0.336837i	$0.890643\pi$
$114$		0			0
$115$	−9.66075	−	29.7327i	−0.0840065	−	0.258545i
$116$	43.0543	−	13.9892i	0.371158	−	0.120597i
$117$		0			0
$118$	−106.573	+	77.4302i	−0.903165	+	0.656188i
$119$	31.2297	+	10.1472i	0.262435	+	0.0852702i
$120$		0			0
$121$	119.998	−	15.5428i	0.991716	−	0.128453i
$122$		−	104.875i		−	0.859628i
$123$		0			0
$124$	−37.2564	+	27.0684i	−0.300455	+	0.218293i
$125$	−69.7150	+	95.9544i	−0.557720	+	0.767635i
$126$		0			0
$127$	20.3921	+	62.7604i	0.160568	+	0.494176i	0.998682	−	0.0513177i	$-0.0163421\pi$
$127$	20.3921	+	62.7604i	0.160568	+	0.494176i	−0.838115	+	0.545494i	$0.816342\pi$
$128$	−6.65003	+	9.15298i	−0.0519534	+	0.0715077i
$129$		0			0
$130$	−5.57769	+	17.1664i	−0.0429053	+	0.132049i
$131$			59.5648i			0.454693i	0.973814	+	0.227347i	$0.0730050\pi$
$131$			59.5648i			0.454693i	−0.973814	+	0.227347i	$0.926995\pi$
$132$		0			0
$133$	−24.7232			−0.185888
$134$	117.969	+	38.3304i	0.880364	+	0.286048i
$135$		0			0
$136$	33.6980	+	24.4830i	0.247780	+	0.180022i
$137$	180.893	−	58.7758i	1.32039	−	0.429020i	0.437761	−	0.899092i	$-0.355772\pi$
$137$	180.893	−	58.7758i	1.32039	−	0.429020i	0.882629	+	0.470071i	$0.155772\pi$
$138$		0			0
$139$	189.818	+	137.911i	1.36560	+	0.992165i	0.998067	+	0.0621540i	$0.0197970\pi$
$139$	189.818	+	137.911i	1.36560	+	0.992165i	0.367531	+	0.930011i	$0.380203\pi$
$140$	7.39513	+	10.1785i	0.0528224	+	0.0727038i
$141$		0			0
$142$	−95.0029			−0.669035
$143$	−12.2999	+	48.2197i	−0.0860134	+	0.337201i
$144$		0			0
$145$	19.7333	−	60.7329i	0.136092	−	0.418848i
$146$	−29.6718	−	40.8397i	−0.203232	−	0.279724i
$147$		0			0
$148$	−12.3801	−	38.1021i	−0.0836495	−	0.257447i
$149$	143.042	−	46.4770i	0.960011	−	0.311926i	0.213234	−	0.977001i	$-0.431600\pi$
$149$	143.042	−	46.4770i	0.960011	−	0.311926i	0.746777	+	0.665075i	$0.231600\pi$
$150$		0			0
$151$	41.1188	−	29.8745i	0.272310	−	0.197845i	−0.443246	−	0.896400i	$-0.646173\pi$
$151$	41.1188	−	29.8745i	0.272310	−	0.197845i	0.715556	+	0.698555i	$0.246173\pi$
$152$	−29.8260	−	9.69106i	−0.196224	−	0.0637570i
$153$		0			0
$154$	22.1524	+	26.6921i	0.143847	+	0.173325i
$155$			64.9607i			0.419101i
$156$		0			0
$157$	83.4844	−	60.6550i	0.531748	−	0.386338i	−0.289263	−	0.957250i	$-0.593410\pi$
$157$	83.4844	−	60.6550i	0.531748	−	0.386338i	0.821011	+	0.570912i	$0.193410\pi$
$158$	21.1150	−	29.0623i	0.133639	−	0.183939i
$159$		0			0
$160$	4.93168	+	15.1781i	0.0308230	+	0.0948634i
$161$	14.5235	−	19.9898i	0.0902078	−	0.124160i
$162$		0			0
$163$	−83.2710	+	256.282i	−0.510865	+	1.57228i	0.279817	+	0.960053i	$0.409726\pi$
$163$	−83.2710	+	256.282i	−0.510865	+	1.57228i	−0.790682	+	0.612227i	$0.790274\pi$
$164$		−	81.0690i		−	0.494323i
$165$		0			0
$166$	30.9852			0.186658
$167$	201.473	+	65.4625i	1.20642	+	0.391991i	0.842121	−	0.539289i	$-0.181307\pi$
$167$	201.473	+	65.4625i	1.20642	+	0.391991i	0.364304	+	0.931280i	$0.381307\pi$
$168$		0			0
$169$	120.166	+	87.3059i	0.711043	+	0.516603i
$170$	55.8805	−	18.1567i	0.328709	−	0.106804i
$171$		0			0
$172$	−73.8813	−	53.6779i	−0.429543	−	0.312081i
$173$	−71.0891	−	97.8458i	−0.410920	−	0.565583i	0.552523	−	0.833498i	$-0.313665\pi$
$173$	−71.0891	−	97.8458i	−0.410920	−	0.565583i	−0.963442	+	0.267915i	$0.913665\pi$
$174$		0			0
$175$	−37.9969			−0.217125
$176$	16.2618	+	40.8846i	0.0923965	+	0.232299i
$177$		0			0
$178$	15.2915	−	47.0625i	0.0859074	−	0.264396i
$179$	−27.4907	−	37.8377i	−0.153579	−	0.211384i	0.725294	−	0.688440i	$-0.241704\pi$
$179$	−27.4907	−	37.8377i	−0.153579	−	0.211384i	−0.878873	+	0.477056i	$0.841704\pi$
$180$		0			0
$181$	−87.2836	−	268.631i	−0.482230	−	1.48415i	−0.835953	−	0.548801i	$-0.815084\pi$
$181$	−87.2836	−	268.631i	−0.482230	−	1.48415i	0.353723	−	0.935350i	$-0.384916\pi$
$182$	−13.5675	+	4.40836i	−0.0745470	+	0.0242218i
$183$		0			0
$184$	25.3568	−	18.4228i	0.137808	−	0.100124i
$185$	−53.7472	−	17.4635i	−0.290526	−	0.0943975i
$186$		0			0
$187$	150.523	−	59.8701i	0.804934	−	0.320161i
$188$		−	23.1862i		−	0.123331i
$189$		0			0
$190$	−35.7894	+	26.0025i	−0.188365	+	0.136855i
$191$	−210.191	+	289.303i	−1.10048	+	1.51468i	−0.265727	+	0.964048i	$0.585612\pi$
$191$	−210.191	+	289.303i	−1.10048	+	1.51468i	−0.834750	+	0.550628i	$0.814388\pi$
$192$		0			0
$193$	−11.4931	−	35.3722i	−0.0595499	−	0.183276i	0.916856	−	0.399217i	$-0.130718\pi$
$193$	−11.4931	−	35.3722i	−0.0595499	−	0.183276i	−0.976406	+	0.215941i	$0.930718\pi$
$194$	−90.7046	+	124.844i	−0.467549	+	0.643526i
$195$		0			0
$196$	27.2109	−	83.7465i	0.138831	−	0.427278i
$197$		−	129.220i		−	0.655937i	−0.944689	−	0.327969i	$-0.893636\pi$
$197$		−	129.220i		−	0.655937i	0.944689	−	0.327969i	$-0.106364\pi$
$198$		0			0
$199$	−93.6837			−0.470772			−0.235386	−	0.971902i	$-0.575635\pi$
$199$	−93.6837			−0.470772			−0.235386	+	0.971902i	$0.575635\pi$
$200$	−45.8394	−	14.8941i	−0.229197	−	0.0744706i
$201$		0			0
$202$	206.901	+	150.322i	1.02426	+	0.744169i
$203$	48.0006	−	15.5963i	0.236456	−	0.0768293i
$204$		0			0
$205$	−92.5166	−	67.2172i	−0.451300	−	0.327889i
$206$	167.544	+	230.605i	0.813321	+	1.11944i
$207$		0			0
$208$	−18.0959			−0.0869995
$209$	−93.8536	+	77.8914i	−0.449060	+	0.372686i
$210$		0			0
$211$	89.4980	−	275.447i	0.424161	−	1.30543i	−0.479634	−	0.877469i	$-0.659231\pi$
$211$	89.4980	−	275.447i	0.424161	−	1.30543i	0.903795	−	0.427965i	$-0.140769\pi$
$212$	−46.0130	−	63.3315i	−0.217043	−	0.298734i
$213$		0			0
$214$	−39.9598	−	122.984i	−0.186728	−	0.574689i
$215$	−122.515	+	39.8077i	−0.569839	+	0.185152i
$216$		0			0
$217$	−41.5366	+	30.1781i	−0.191413	+	0.139070i
$218$	−279.515	−	90.8199i	−1.28218	−	0.416605i
$219$		0			0
$220$	60.1411	+	15.3409i	0.273369	+	0.0697312i
$221$			66.6226i			0.301460i
$222$		0			0
$223$	−116.475	+	84.6244i	−0.522311	+	0.379481i	−0.817474	−	0.575966i	$-0.804626\pi$
$223$	−116.475	+	84.6244i	−0.522311	+	0.379481i	0.295163	+	0.955447i	$0.404626\pi$
$224$	−7.41402	+	10.2045i	−0.0330983	+	0.0455559i
$225$		0			0
$226$	−27.7462	−	85.3941i	−0.122771	−	0.377850i
$227$	24.4076	−	33.5941i	0.107522	−	0.147992i	−0.751865	−	0.659317i	$-0.770845\pi$
$227$	24.4076	−	33.5941i	0.107522	−	0.147992i	0.859387	+	0.511326i	$0.170845\pi$
$228$		0			0
$229$	−39.1019	+	120.343i	−0.170751	+	0.525516i	−0.999414	−	0.0342310i	$-0.989102\pi$
$229$	−39.1019	+	120.343i	−0.170751	+	0.525516i	0.828663	+	0.559747i	$0.189102\pi$
$230$		−	44.2123i		−	0.192227i
$231$		0			0
$232$	64.0214			0.275954
$233$	−189.364	−	61.5282i	−0.812723	−	0.264070i	−0.126972	−	0.991906i	$-0.540526\pi$
$233$	−189.364	−	61.5282i	−0.812723	−	0.264070i	−0.685751	+	0.727837i	$0.740526\pi$
$234$		0			0
$235$	−26.4603	−	19.2245i	−0.112597	−	0.0818066i
$236$	−177.179	+	57.5690i	−0.750759	+	0.243937i
$237$		0			0
$238$	37.5694	+	27.2958i	0.157855	+	0.114688i
$239$	−144.854	−	199.374i	−0.606084	−	0.834203i	0.390164	−	0.920745i	$-0.372418\pi$
$239$	−144.854	−	199.374i	−0.606084	−	0.834203i	−0.996248	+	0.0865424i	$0.972418\pi$
$240$		0			0
$241$	−439.621			−1.82415			−0.912076	−	0.410021i	$-0.865521\pi$
$241$	−439.621			−1.82415			−0.912076	+	0.410021i	$0.865521\pi$
$242$	168.189	+	31.5359i	0.694995	+	0.130314i
$243$		0			0
$244$	45.8319	−	141.056i	0.187836	−	0.578098i
$245$	−73.0106	−	100.491i	−0.298003	−	0.410165i
$246$		0			0
$247$	−15.5005	−	47.7057i	−0.0627551	−	0.193140i
$248$	−61.9391	+	20.1252i	−0.249754	+	0.0811501i
$249$		0			0
$250$	−135.700	+	98.5918i	−0.542800	+	0.394367i
$251$	−153.228	−	49.7869i	−0.610471	−	0.198354i	−0.0125660	−	0.999921i	$-0.504000\pi$
$251$	−153.228	−	49.7869i	−0.610471	−	0.198354i	−0.597905	+	0.801567i	$0.704000\pi$
$252$		0			0
$253$	−7.84509	−	121.642i	−0.0310083	−	0.480797i
$254$			93.3242i			0.367418i
$255$		0			0
$256$	−12.9443	+	9.40456i	−0.0505636	+	0.0367366i
$257$	−63.6815	+	87.6500i	−0.247788	+	0.341051i	−0.914735	−	0.404054i	$-0.867601\pi$
$257$	−63.6815	+	87.6500i	−0.247788	+	0.341051i	0.666947	+	0.745105i	$0.267601\pi$
$258$		0			0
$259$	−13.8024	−	42.4795i	−0.0532912	−	0.164013i
$260$	−15.0040	+	20.6512i	−0.0577075	+	0.0794276i
$261$		0			0
$262$	−26.0308	+	80.1145i	−0.0993541	+	0.305780i
$263$		−	263.126i		−	1.00048i	−0.865887	−	0.500240i	$-0.833245\pi$
$263$		−	263.126i		−	1.00048i	0.865887	−	0.500240i	$-0.166755\pi$
$264$		0			0
$265$	−110.426			−0.416700
$266$	−33.2526	−	10.8044i	−0.125010	−	0.0406181i
$267$		0			0
$268$	141.917	+	103.108i	0.529540	+	0.384733i
$269$	302.144	−	98.1724i	1.12321	−	0.364953i	0.312218	−	0.950010i	$-0.398928\pi$
$269$	302.144	−	98.1724i	1.12321	−	0.364953i	0.810992	+	0.585057i	$0.198928\pi$
$270$		0			0
$271$	−35.1264	−	25.5208i	−0.129618	−	0.0941729i	0.521087	−	0.853503i	$-0.325527\pi$
$271$	−35.1264	−	25.5208i	−0.129618	−	0.0941729i	−0.650705	+	0.759331i	$0.725527\pi$
$272$	34.6242	+	47.6562i	0.127295	+	0.175207i
$273$		0			0
$274$	268.987			0.981704
$275$	−144.243	+	119.711i	−0.524520	+	0.435312i
$276$		0			0
$277$	109.009	−	335.496i	0.393535	−	1.21118i	−0.536561	−	0.843862i	$-0.680277\pi$
$277$	109.009	−	335.496i	0.393535	−	1.21118i	0.930096	−	0.367316i	$-0.119723\pi$
$278$	195.036	+	268.443i	0.701567	+	0.965624i
$279$		0			0
$280$	5.49825	+	16.9219i	0.0196366	+	0.0604353i
$281$	−170.582	+	55.4255i	−0.607054	+	0.197244i	−0.596384	−	0.802699i	$-0.703396\pi$
$281$	−170.582	+	55.4255i	−0.607054	+	0.197244i	−0.0106699	+	0.999943i	$0.503396\pi$
$282$		0			0
$283$	−167.826	+	121.933i	−0.593026	+	0.430859i	−0.843397	−	0.537291i	$-0.819448\pi$
$283$	−167.826	+	121.933i	−0.593026	+	0.430859i	0.250370	+	0.968150i	$0.419448\pi$
$284$	−127.779	−	41.5178i	−0.449925	−	0.146189i
$285$		0			0
$286$	−37.6161	+	59.4801i	−0.131525	+	0.207972i
$287$		−	90.3826i		−	0.314922i
$288$		0			0
$289$	−58.3528	+	42.3958i	−0.201913	+	0.146698i
$290$	53.0825	−	73.0618i	0.183043	−	0.251937i
$291$		0			0
$292$	−22.0609	−	67.8964i	−0.0755509	−	0.232522i
$293$	230.223	−	316.875i	0.785745	−	1.08149i	−0.208880	−	0.977941i	$-0.566982\pi$
$293$	230.223	−	316.875i	0.785745	−	1.08149i	0.994625	−	0.103544i	$-0.0330183\pi$
$294$		0			0
$295$	−81.2075	+	249.931i	−0.275280	+	0.847223i
$296$		−	56.6575i		−	0.191411i
$297$		0			0
$298$	212.702			0.713764
$299$	47.6779	+	15.4915i	0.159458	+	0.0518110i
$300$		0			0
$301$	−82.3692	−	59.8447i	−0.273652	−	0.198820i
$302$	68.3603	−	22.2116i	0.226358	−	0.0735483i
$303$		0			0
$304$	−35.8808	−	26.0689i	−0.118029	−	0.0857530i
$305$	−122.973	−	169.258i	−0.403191	−	0.554945i
$306$		0			0
$307$	82.4090			0.268433			0.134217	−	0.990952i	$-0.457148\pi$
$307$	82.4090			0.268433			0.134217	+	0.990952i	$0.457148\pi$
$308$	18.1300	+	45.5817i	0.0588637	+	0.147992i
$309$		0			0
$310$	−28.3889	+	87.3720i	−0.0915770	+	0.281845i
$311$	210.988	+	290.400i	0.678418	+	0.933762i	0.999914	−	0.0131491i	$-0.00418561\pi$
$311$	210.988	+	290.400i	0.678418	+	0.933762i	−0.321496	+	0.946911i	$0.604186\pi$
$312$		0			0
$313$	130.603	+	401.956i	0.417264	+	1.28421i	0.910211	+	0.414146i	$0.135920\pi$
$313$	130.603	+	401.956i	0.417264	+	1.28421i	−0.492947	+	0.870059i	$0.664080\pi$
$314$	138.794	−	45.0968i	0.442018	−	0.143620i
$315$		0			0
$316$	41.1003	−	29.8611i	0.130064	−	0.0944973i
$317$	356.602	+	115.867i	1.12493	+	0.365511i	0.811646	−	0.584150i	$-0.198572\pi$
$317$	356.602	+	115.867i	1.12493	+	0.365511i	0.313281	+	0.949661i	$0.398572\pi$
$318$		0			0
$319$	133.082	−	210.434i	0.417185	−	0.659669i
$320$			22.5698i			0.0705305i
$321$		0			0
$322$	28.2699	−	20.5393i	0.0877946	−	0.0637865i
$323$	−95.9764	+	132.100i	−0.297140	+	0.408979i
$324$		0			0
$325$	−23.8226	−	73.3185i	−0.0733004	−	0.225596i
$326$	−223.999	+	308.307i	−0.687112	+	0.945729i
$327$		0			0
$328$	35.4284	−	109.038i	0.108014	−	0.332431i
$329$		−	25.8500i		−	0.0785714i
$330$		0			0
$331$	−166.263			−0.502305			−0.251152	−	0.967948i	$-0.580810\pi$
$331$	−166.263			−0.502305			−0.251152	+	0.967948i	$0.580810\pi$
$332$	41.6750	+	13.5410i	0.125527	+	0.0407862i
$333$		0			0
$334$	242.372	+	176.094i	0.725666	+	0.527227i
$335$	235.336	−	76.4655i	0.702497	−	0.228255i
$336$		0			0
$337$	508.288	+	369.293i	1.50827	+	1.09583i	0.966936	+	0.255021i	$0.0820823\pi$
$337$	508.288	+	369.293i	1.50827	+	1.09583i	0.541339	+	0.840805i	$0.317918\pi$
$338$	123.469	+	169.941i	0.365293	+	0.502783i
$339$		0			0
$340$	83.0939			0.244394
$341$	−62.6031	+	245.425i	−0.183587	+	0.719720i
$342$		0			0
$343$	64.0998	−	197.279i	0.186880	−	0.575157i
$344$	−75.9121	−	104.484i	−0.220675	−	0.303733i
$345$		0			0
$346$	−52.8545	−	162.669i	−0.152759	−	0.470143i
$347$	541.504	−	175.945i	1.56053	−	0.507047i	0.603580	−	0.797302i	$-0.293740\pi$
$347$	541.504	−	175.945i	1.56053	−	0.507047i	0.956949	+	0.290256i	$0.0937403\pi$
$348$		0			0
$349$	72.1627	−	52.4293i	0.206770	−	0.150227i	−0.479581	−	0.877498i	$-0.659211\pi$
$349$	72.1627	−	52.4293i	0.206770	−	0.150227i	0.686351	+	0.727270i	$0.259211\pi$
$350$	−51.1057	−	16.6052i	−0.146016	−	0.0474435i
$351$		0			0
$352$	4.00481	+	62.0964i	0.0113773	+	0.176410i
$353$			490.203i			1.38868i	0.719649	+	0.694338i	$0.244303\pi$
$353$			490.203i			1.38868i	−0.719649	+	0.694338i	$0.755697\pi$
$354$		0			0
$355$	−153.326	+	111.398i	−0.431905	+	0.313798i
$356$	41.1341	−	56.6162i	0.115545	−	0.159034i
$357$		0			0
$358$	−20.4392	−	62.9055i	−0.0570928	−	0.175714i
$359$	281.600	−	387.589i	0.784401	−	1.07964i	−0.210382	−	0.977619i	$-0.567471\pi$
$359$	281.600	−	387.589i	0.784401	−	1.07964i	0.994783	−	0.102016i	$-0.0325292\pi$
$360$		0			0
$361$	−73.5650	+	226.410i	−0.203781	+	0.627174i
$362$		−	399.453i		−	1.10346i
$363$		0			0
$364$	−20.1748			−0.0554254
$365$	−95.7754	−	31.1193i	−0.262398	−	0.0852584i
$366$		0			0
$367$	−3.71416	−	2.69850i	−0.0101203	−	0.00735285i	0.582714	−	0.812678i	$-0.301991\pi$
$367$	−3.71416	−	2.69850i	−0.0101203	−	0.00735285i	−0.592834	+	0.805325i	$0.701991\pi$
$368$	42.1558	−	13.6973i	0.114554	−	0.0372208i
$369$		0			0
$370$	−64.6580	−	46.9768i	−0.174751	−	0.126964i
$371$	−51.2993	−	70.6074i	−0.138273	−	0.190316i
$372$		0			0
$373$	−127.560			−0.341984			−0.170992	−	0.985272i	$-0.554697\pi$
$373$	−127.560			−0.341984			−0.170992	+	0.985272i	$0.554697\pi$
$374$	228.617	−	14.7443i	0.611275	−	0.0394232i
$375$		0			0
$376$	10.1328	−	31.1854i	0.0269488	−	0.0829399i
$377$	60.1893	+	82.8434i	0.159653	+	0.219744i
$378$		0			0
$379$	97.6391	+	300.502i	0.257623	+	0.792882i	0.993302	+	0.115551i	$0.0368635\pi$
$379$	97.6391	+	300.502i	0.257623	+	0.792882i	−0.735678	+	0.677331i	$0.763137\pi$
$380$	−59.5001	+	19.3327i	−0.156579	+	0.0508757i
$381$		0			0
$382$	−409.137	+	297.255i	−1.07104	+	0.778155i
$383$	269.358	+	87.5199i	0.703286	+	0.228511i	0.638762	−	0.769405i	$-0.279447\pi$
$383$	269.358	+	87.5199i	0.703286	+	0.228511i	0.0645242	+	0.997916i	$0.479447\pi$
$384$		0			0
$385$	67.0505	+	17.1033i	0.174157	+	0.0444241i
$386$		−	52.5982i		−	0.136265i
$387$		0			0
$388$	−176.556	+	128.276i	−0.455042	+	0.330607i
$389$	173.179	−	238.360i	0.445189	−	0.612750i	−0.526166	−	0.850382i	$-0.676371\pi$
$389$	173.179	−	238.360i	0.445189	−	0.612750i	0.971355	+	0.237632i	$0.0763711\pi$
$390$		0			0
$391$	−50.4284	−	155.203i	−0.128973	−	0.396938i
$392$	73.1971	−	100.747i	0.186727	−	0.257008i
$393$		0			0
$394$	56.4711	−	173.800i	0.143328	−	0.441117i
$395$		−	71.6630i		−	0.181425i
$396$		0			0
$397$	354.576			0.893138			0.446569	−	0.894749i	$-0.352646\pi$
$397$	354.576			0.893138			0.446569	+	0.894749i	$0.352646\pi$
$398$	−126.004	−	40.9413i	−0.316594	−	0.102867i
$399$		0			0
$400$	−55.1449	−	40.0651i	−0.137862	−	0.100163i
$401$	38.8054	−	12.6086i	0.0967715	−	0.0314430i	−0.260231	−	0.965546i	$-0.583799\pi$
$401$	38.8054	−	12.6086i	0.0967715	−	0.0314430i	0.357003	+	0.934103i	$0.383799\pi$
$402$		0			0
$403$	−84.2735	−	61.2283i	−0.209115	−	0.151931i
$404$	212.588	+	292.602i	0.526207	+	0.724261i
$405$		0			0
$406$	71.3765			0.175804
$407$	−186.230	−	117.775i	−0.457567	−	0.289373i
$408$		0			0
$409$	−147.530	+	454.050i	−0.360708	+	1.11015i	0.591917	+	0.805999i	$0.298371\pi$
$409$	−147.530	+	454.050i	−0.360708	+	1.11015i	−0.952625	+	0.304147i	$0.901629\pi$
$410$	−95.0595	−	130.838i	−0.231852	−	0.319118i
$411$		0			0
$412$	124.568	+	383.382i	0.302350	+	0.930539i
$413$	−197.534	+	64.1828i	−0.478292	+	0.155406i
$414$		0			0
$415$	50.0074	−	36.3325i	0.120500	−	0.0875482i
$416$	−24.3389	−	7.90819i	−0.0585070	−	0.0190101i
$417$		0			0
$418$	−160.273	+	63.7481i	−0.383427	+	0.152507i
$419$			75.9631i			0.181296i	0.995883	+	0.0906481i	$0.0288938\pi$
$419$			75.9631i			0.181296i	−0.995883	+	0.0906481i	$0.971106\pi$
$420$		0			0
$421$	225.960	−	164.170i	0.536722	−	0.389951i	−0.286144	−	0.958187i	$-0.592374\pi$
$421$	225.960	−	164.170i	0.536722	−	0.389951i	0.822866	+	0.568235i	$0.192374\pi$
$422$	240.749	−	331.363i	0.570496	−	0.785220i
$423$		0			0
$424$	−34.2105	−	105.289i	−0.0806852	−	0.248323i
$425$	−147.505	+	203.024i	−0.347072	+	0.477703i
$426$		0			0
$427$	51.0973	−	157.261i	0.119666	−	0.368293i
$428$		−	182.876i		−	0.427279i
$429$		0			0
$430$	−182.179			−0.423673
$431$	−565.456	−	183.728i	−1.31196	−	0.426282i	−0.432235	−	0.901761i	$-0.642275\pi$
$431$	−565.456	−	183.728i	−1.31196	−	0.426282i	−0.879727	+	0.475479i	$0.842275\pi$
$432$		0			0
$433$	127.561	+	92.6786i	0.294598	+	0.214038i	0.725260	−	0.688475i	$-0.241720\pi$
$433$	127.561	+	92.6786i	0.294598	+	0.214038i	−0.430661	+	0.902514i	$0.641720\pi$
$434$	−69.0550	+	22.4373i	−0.159113	+	0.0516989i
$435$		0			0
$436$	−336.257	−	244.305i	−0.771232	−	0.560333i
$437$	72.2194	+	99.4014i	0.165262	+	0.227463i
$438$		0			0
$439$	265.463			0.604699			0.302349	−	0.953197i	$-0.402229\pi$
$439$	265.463			0.604699			0.302349	+	0.953197i	$0.402229\pi$
$440$	74.1854	+	46.9160i	0.168603	+	0.106627i
$441$		0			0
$442$	−29.1151	+	89.6072i	−0.0658714	+	0.202731i
$443$	−35.1370	−	48.3619i	−0.0793160	−	0.109169i	0.767515	−	0.641030i	$-0.221493\pi$
$443$	−35.1370	−	48.3619i	−0.0793160	−	0.109169i	−0.846831	+	0.531861i	$0.821493\pi$
$444$		0			0
$445$	−30.5051	−	93.8852i	−0.0685509	−	0.210978i
$446$	−193.641	+	62.9179i	−0.434173	+	0.141071i
$447$		0			0
$448$	−14.4314	+	10.4850i	−0.0322129	+	0.0234040i
$449$	−264.409	−	85.9116i	−0.588884	−	0.191340i	−0.000607294	−	1.00000i	$-0.500193\pi$
$449$	−264.409	−	85.9116i	−0.588884	−	0.191340i	−0.588276	+	0.808660i	$0.700193\pi$
$450$		0			0
$451$	−284.754	−	343.109i	−0.631384	−	0.760773i
$452$		−	126.980i		−	0.280930i
$453$		0			0
$454$	47.5093	−	34.5175i	0.104646	−	0.0760297i
$455$	−16.7277	+	23.0237i	−0.0367642	+	0.0506015i
$456$		0			0
$457$	101.783	+	313.255i	0.222720	+	0.685460i	0.998515	+	0.0544760i	$0.0173488\pi$
$457$	101.783	+	313.255i	0.222720	+	0.685460i	−0.775795	+	0.630984i	$0.782651\pi$
$458$	−105.184	+	144.773i	−0.229659	+	0.316099i
$459$		0			0
$460$	19.3215	−	59.4654i	0.0420032	−	0.129273i
$461$			628.919i			1.36425i	0.731236	+	0.682124i	$0.238944\pi$
$461$			628.919i			1.36425i	−0.731236	+	0.682124i	$0.761056\pi$
$462$		0			0
$463$	−509.930			−1.10136			−0.550680	−	0.834716i	$-0.685632\pi$
$463$	−509.930			−1.10136			−0.550680	+	0.834716i	$0.685632\pi$
$464$	86.1086	+	27.9784i	0.185579	+	0.0602983i
$465$		0			0
$466$	−227.806	−	165.511i	−0.488854	−	0.355173i
$467$	−210.460	+	68.3826i	−0.450664	+	0.146430i	−0.525550	−	0.850762i	$-0.676141\pi$
$467$	−210.460	+	68.3826i	−0.450664	+	0.146430i	0.0748865	+	0.997192i	$0.476141\pi$
$468$		0			0
$469$	158.221	+	114.954i	0.337358	+	0.245105i
$470$	−27.1876	−	37.4205i	−0.0578460	−	0.0796182i
$471$		0			0
$472$	−263.464			−0.558187
$473$	−501.232	+	32.3262i	−1.05969	+	0.0683428i
$474$		0			0
$475$	58.3867	−	179.696i	0.122919	−	0.378307i
$476$	38.6021	+	53.1312i	0.0810968	+	0.111620i
$477$		0			0
$478$	−107.698	−	331.462i	−0.225310	−	0.693434i
$479$	245.892	−	79.8953i	0.513345	−	0.166796i	−0.0408778	−	0.999164i	$-0.513015\pi$
$479$	245.892	−	79.8953i	0.513345	−	0.166796i	0.554223	+	0.832368i	$0.313015\pi$
$480$		0			0
$481$	73.3145	−	53.2661i	0.152421	−	0.110740i
$482$	−591.288	−	192.121i	−1.22674	−	0.398592i
$483$		0			0
$484$	212.432	+	115.917i	0.438909	+	0.239498i
$485$			307.845i			0.634733i
$486$		0			0
$487$	361.333	−	262.523i	0.741956	−	0.539063i	−0.151367	−	0.988478i	$-0.548368\pi$
$487$	361.333	−	262.523i	0.741956	−	0.539063i	0.893323	+	0.449415i	$0.148368\pi$
$488$	123.287	−	169.691i	0.252638	−	0.347727i
$489$		0			0
$490$	−54.2831	−	167.066i	−0.110782	−	0.340952i
$491$	−261.208	+	359.522i	−0.531992	+	0.732224i	−0.987432	−	0.158042i	$-0.949482\pi$
$491$	−261.208	+	359.522i	−0.531992	+	0.732224i	0.455441	+	0.890266i	$0.349482\pi$
$492$		0			0
$493$	103.006	−	317.021i	0.208938	−	0.643045i
$494$		−	70.9380i		−	0.143599i
$495$		0			0
$496$	−92.1030			−0.185691
$497$	−142.459	−	46.2876i	−0.286637	−	0.0931340i
$498$		0			0
$499$	−608.499	−	442.100i	−1.21944	−	0.885973i	−0.223384	−	0.974731i	$-0.571710\pi$
$499$	−608.499	−	442.100i	−1.21944	−	0.885973i	−0.996053	+	0.0887576i	$0.971710\pi$
$500$	−225.602	+	73.3026i	−0.451205	+	0.146605i
$501$		0			0
$502$	−184.334	−	133.926i	−0.367199	−	0.266786i
$503$	−196.115	−	269.929i	−0.389890	−	0.536638i	0.568280	−	0.822835i	$-0.307609\pi$
$503$	−196.115	−	269.929i	−0.389890	−	0.536638i	−0.958171	+	0.286197i	$0.907609\pi$
$504$		0			0
$505$	510.183			1.01026
$506$	42.6077	−	167.036i	0.0842050	−	0.330111i
$507$		0			0
$508$	−40.7842	+	125.521i	−0.0802838	+	0.247088i
$509$	−208.025	−	286.322i	−0.408693	−	0.562518i	0.554206	−	0.832380i	$-0.313022\pi$
$509$	−208.025	−	286.322i	−0.408693	−	0.562518i	−0.962899	+	0.269862i	$0.913022\pi$
$510$		0			0
$511$	−24.5953	−	75.6967i	−0.0481318	−	0.148134i
$512$	−21.5200	+	6.99226i	−0.0420312	+	0.0136568i
$513$		0			0
$514$	−123.956	+	90.0592i	−0.241159	+	0.175212i
$515$	540.803	+	175.718i	1.05010	+	0.341199i
$516$		0			0
$517$	−81.4414	−	98.1312i	−0.157527	−	0.189809i
$518$		−	63.1666i		−	0.121943i
$519$		0			0
$520$	−29.2052	+	21.2188i	−0.0561638	+	0.0408054i
$521$	−460.803	+	634.240i	−0.884458	+	1.21735i	0.0907083	+	0.995878i	$0.471087\pi$
$521$	−460.803	+	634.240i	−0.884458	+	1.21735i	−0.975166	+	0.221474i	$0.928913\pi$
$522$		0			0
$523$	129.129	+	397.420i	0.246902	+	0.759885i	0.995318	+	0.0966555i	$0.0308145\pi$
$523$	129.129	+	397.420i	0.246902	+	0.759885i	−0.748416	+	0.663229i	$0.769185\pi$
$524$	−70.0226	+	96.3779i	−0.133631	+	0.183927i
$525$		0			0
$526$	114.990	−	353.904i	0.218613	−	0.672821i
$527$			339.090i			0.643435i
$528$		0			0
$529$	406.205			0.767873
$530$	−148.522	−	48.2577i	−0.280230	−	0.0910523i
$531$		0			0
$532$	−40.0029	−	29.0638i	−0.0751935	−	0.0546313i
$533$	174.402	−	56.6666i	0.327208	−	0.106316i
$534$		0			0
$535$	−208.699	−	151.629i	−0.390092	−	0.283418i
$536$	145.817	+	200.700i	0.272047	+	0.374441i
$537$		0			0
$538$	449.285			0.835103
$539$	−178.994	−	450.019i	−0.332085	−	0.834914i
$540$		0			0
$541$	−11.8020	+	36.3229i	−0.0218152	+	0.0671404i	−0.961371	−	0.275254i	$-0.911238\pi$
$541$	−11.8020	+	36.3229i	−0.0218152	+	0.0671404i	0.939556	+	0.342395i	$0.111238\pi$
$542$	−36.0919	−	49.6763i	−0.0665903	−	0.0916536i
$543$		0			0
$544$	25.7430	+	79.2288i	0.0473217	+	0.145641i
$545$	−557.606	+	181.177i	−1.02313	+	0.332435i
$546$		0			0
$547$	741.060	−	538.411i	1.35477	−	0.984299i	0.356013	−	0.934481i	$-0.384136\pi$
$547$	741.060	−	538.411i	1.35477	−	0.984299i	0.998758	−	0.0498175i	$-0.0158640\pi$
$548$	361.787	+	117.552i	0.660195	+	0.214510i
$549$		0			0
$550$	−246.322	+	97.9740i	−0.447858	+	0.178135i
$551$			250.972i			0.455484i
$552$		0			0
$553$	45.8221	−	33.2917i	0.0828610	−	0.0602021i
$554$	293.234	−	403.603i	0.529304	−	0.728524i
$555$		0			0
$556$	145.008	+	446.289i	0.260806	+	0.802678i
$557$	456.163	−	627.854i	0.818964	−	1.12721i	−0.170914	−	0.985286i	$-0.554672\pi$
$557$	456.163	−	627.854i	0.818964	−	1.12721i	0.989878	−	0.141921i	$-0.0453280\pi$
$558$		0			0
$559$	63.8336	−	196.460i	0.114192	−	0.351448i
$560$			25.1627i			0.0449334i
$561$		0			0
$562$	−253.654			−0.451342
$563$	371.042	+	120.559i	0.659045	+	0.214137i	0.619398	−	0.785077i	$-0.287377\pi$
$563$	371.042	+	120.559i	0.659045	+	0.214137i	0.0396470	+	0.999214i	$0.487377\pi$
$564$		0			0
$565$	−144.911	−	105.284i	−0.256480	−	0.186343i
$566$	−279.013	+	90.6567i	−0.492955	+	0.160171i
$567$		0			0
$568$	−153.718	−	111.683i	−0.270630	−	0.196624i
$569$	61.3644	+	84.4609i	0.107846	+	0.148437i	0.859528	−	0.511088i	$-0.170757\pi$
$569$	61.3644	+	84.4609i	0.107846	+	0.148437i	−0.751682	+	0.659525i	$0.770757\pi$
$570$		0			0
$571$	−66.1095			−0.115778			−0.0578892	−	0.998323i	$-0.518437\pi$
$571$	−66.1095			−0.115778			−0.0578892	+	0.998323i	$0.518437\pi$
$572$	−76.5873	+	63.5616i	−0.133894	+	0.111122i
$573$		0			0
$574$	39.4986	−	121.564i	0.0688130	−	0.211785i
$575$	110.993	+	152.769i	0.193032	+	0.265686i
$576$		0			0
$577$	297.125	+	914.456i	0.514948	+	1.58485i	0.783377	+	0.621547i	$0.213495\pi$
$577$	297.125	+	914.456i	0.514948	+	1.58485i	−0.268429	+	0.963299i	$0.586505\pi$
$578$	−97.0120	+	31.5211i	−0.167841	+	0.0545348i
$579$		0			0
$580$	103.325	−	75.0700i	0.178147	−	0.129431i
$581$	46.4628	+	15.0967i	0.0799704	+	0.0259840i
$582$		0			0
$583$	−417.193	−	106.418i	−0.715596	−	0.182535i
$584$		−	100.961i		−	0.172879i
$585$		0			0
$586$	448.129	−	325.585i	0.764726	−	0.555606i
$587$	387.993	−	534.026i	0.660976	−	0.909755i	−0.338537	−	0.940953i	$-0.609932\pi$
$587$	387.993	−	534.026i	0.660976	−	0.909755i	0.999513	+	0.0311975i	$0.00993209\pi$
$588$		0			0
$589$	−78.8933	−	242.809i	−0.133944	−	0.412239i
$590$	−218.448	+	300.667i	−0.370250	+	0.509606i
$591$		0			0
$592$	24.7602	−	76.2042i	0.0418247	−	0.128723i
$593$			883.670i			1.49017i	0.666970	+	0.745084i	$0.267591\pi$
$593$			883.670i			1.49017i	−0.666970	+	0.745084i	$0.732409\pi$
$594$		0			0
$595$	92.6401			0.155698
$596$	286.083	+	92.9541i	0.480005	+	0.155963i
$597$		0			0
$598$	57.3566	+	41.6720i	0.0959141	+	0.0696857i
$599$	−223.184	+	72.5169i	−0.372595	+	0.121063i	−0.489328	−	0.872100i	$-0.662758\pi$
$599$	−223.184	+	72.5169i	−0.372595	+	0.121063i	0.116733	+	0.993163i	$0.462758\pi$
$600$		0			0
$601$	126.159	+	91.6602i	0.209916	+	0.152513i	0.687776	−	0.725923i	$-0.258587\pi$
$601$	126.159	+	91.6602i	0.209916	+	0.152513i	−0.477860	+	0.878436i	$0.658587\pi$
$602$	−84.6332	−	116.488i	−0.140587	−	0.193501i
$603$		0			0
$604$	101.651			0.168297
$605$	308.420	−	146.318i	0.509786	−	0.241848i
$606$		0			0
$607$	−322.483	+	992.500i	−0.531273	+	1.63509i	0.220293	+	0.975434i	$0.429298\pi$
$607$	−322.483	+	992.500i	−0.531273	+	1.63509i	−0.751567	+	0.659657i	$0.770702\pi$
$608$	−36.8670	−	50.7431i	−0.0606365	−	0.0834590i
$609$		0			0
$610$	−91.4302	−	281.393i	−0.149886	−	0.461301i
$611$	49.8800	−	16.2070i	0.0816367	−	0.0265254i
$612$		0			0
$613$	667.207	−	484.754i	1.08843	−	0.790790i	0.109296	−	0.994009i	$-0.465140\pi$
$613$	667.207	−	484.754i	1.08843	−	0.790790i	0.979133	+	0.203219i	$0.0651403\pi$
$614$	110.840	+	36.0141i	0.180521	+	0.0586548i
$615$		0			0
$616$	4.46490	+	69.2303i	0.00724822	+	0.112387i
$617$		−	513.392i		−	0.832078i	−0.909347	−	0.416039i	$-0.863418\pi$
$617$		−	513.392i		−	0.832078i	0.909347	−	0.416039i	$-0.136582\pi$
$618$		0			0
$619$	−657.376	+	477.612i	−1.06200	+	0.771586i	−0.974457	−	0.224575i	$-0.927901\pi$
$619$	−657.376	+	477.612i	−1.06200	+	0.771586i	−0.0875403	+	0.996161i	$0.527901\pi$
$620$	−76.3659	+	105.109i	−0.123171	+	0.169530i
$621$		0			0
$622$	156.869	+	482.792i	0.252200	+	0.776193i
$623$	45.8598	−	63.1206i	0.0736112	−	0.101317i
$624$		0			0
$625$	28.2452	−	86.9298i	0.0451923	−	0.139088i
$626$			597.706i			0.954802i
$627$		0			0
$628$	206.385			0.328638
$629$	−280.557	−	91.1584i	−0.446036	−	0.144926i
$630$		0			0
$631$	−483.503	−	351.286i	−0.766249	−	0.556713i	0.134572	−	0.990904i	$-0.457034\pi$
$631$	−483.503	−	351.286i	−0.766249	−	0.556713i	−0.900821	+	0.434191i	$0.857034\pi$
$632$	68.3296	−	22.2016i	0.108116	−	0.0351292i
$633$		0			0
$634$	428.992	+	311.681i	0.676644	+	0.491611i
$635$	109.430	+	150.617i	0.172330	+	0.237192i
$636$		0			0
$637$	199.182			0.312688
$638$	270.958	−	224.875i	0.424699	−	0.352468i
$639$		0			0
$640$	−9.86335	+	30.3563i	−0.0154115	+	0.0474317i
$641$	−479.564	−	660.063i	−0.748150	−	1.02974i	−0.998108	−	0.0614833i	$-0.980417\pi$
$641$	−479.564	−	660.063i	−0.748150	−	1.02974i	0.249958	−	0.968257i	$-0.419583\pi$
$642$		0			0
$643$	−143.098	−	440.409i	−0.222547	−	0.684928i	−0.998531	−	0.0541765i	$-0.982747\pi$
$643$	−143.098	−	440.409i	−0.222547	−	0.684928i	0.775985	−	0.630752i	$-0.217253\pi$
$644$	46.9989	−	15.2709i	0.0729796	−	0.0237125i
$645$		0			0
$646$	−186.818	+	135.731i	−0.289192	+	0.210110i
$647$	945.308	+	307.149i	1.46106	+	0.474728i	0.928395	−	0.371596i	$-0.121189\pi$
$647$	945.308	+	307.149i	1.46106	+	0.474728i	0.532668	+	0.846324i	$0.321189\pi$
$648$		0			0
$649$	−547.666	+	865.990i	−0.843861	+	1.33435i
$650$		−	109.024i		−	0.167729i
$651$		0			0
$652$	−436.013	+	316.782i	−0.668731	+	0.485862i
$653$	359.048	−	494.187i	0.549843	−	0.756794i	−0.440148	−	0.897925i	$-0.645074\pi$
$653$	359.048	−	494.187i	0.549843	−	0.756794i	0.989991	+	0.141131i	$0.0450739\pi$
$654$		0			0
$655$	51.9289	+	159.821i	0.0792808	+	0.244001i
$656$	95.3023	−	131.172i	0.145278	−	0.199958i
$657$		0			0
$658$	11.2969	−	34.7682i	0.0171685	−	0.0528391i
$659$		−	249.471i		−	0.378560i	−0.981923	−	0.189280i	$-0.939385\pi$
$659$		−	249.471i		−	0.378560i	0.981923	−	0.189280i	$-0.0606154\pi$
$660$		0			0
$661$	−1210.43			−1.83121			−0.915604	−	0.402081i	$-0.868287\pi$
$661$	−1210.43			−1.83121			−0.915604	+	0.402081i	$0.868287\pi$
$662$	−223.623	−	72.6595i	−0.337799	−	0.109758i
$663$		0			0
$664$	50.1351	+	36.4253i	0.0755047	+	0.0548573i
$665$	−66.3358	+	21.5538i	−0.0997530	+	0.0324117i
$666$		0			0
$667$	−202.922	−	147.431i	−0.304231	−	0.221037i
$668$	249.034	+	342.766i	0.372806	+	0.513123i
$669$		0			0
$670$	349.943			0.522304
$671$	−301.484	−	757.976i	−0.449305	−	1.12962i
$672$		0			0
$673$	−346.565	+	1066.62i	−0.514955	+	1.58487i	0.268409	+	0.963305i	$0.413502\pi$
$673$	−346.565	+	1066.62i	−0.514955	+	1.58487i	−0.783364	+	0.621563i	$0.786498\pi$
$674$	522.259	+	718.828i	0.774866	+	1.06651i
$675$		0			0
$676$	91.7989	+	282.528i	0.135797	+	0.417941i
$677$	227.144	−	73.8036i	0.335516	−	0.109016i	−0.136414	−	0.990652i	$-0.543558\pi$
$677$	227.144	−	73.8036i	0.335516	−	0.109016i	0.471930	+	0.881636i	$0.343558\pi$
$678$		0			0
$679$	−196.840	+	143.013i	−0.289897	+	0.210622i
$680$	111.761	+	36.3133i	0.164354	+	0.0534020i
$681$		0			0
$682$	−191.455	+	302.737i	−0.280726	+	0.443895i
$683$		−	1328.40i		−	1.94494i	−0.233023	−	0.972471i	$-0.574862\pi$
$683$		−	1328.40i		−	1.94494i	0.233023	−	0.972471i	$-0.425138\pi$
$684$		0			0
$685$	434.121	−	315.408i	0.633754	−	0.460449i
$686$	172.428	−	237.327i	0.251353	−	0.345958i
$687$		0			0
$688$	−56.4403	−	173.705i	−0.0820354	−	0.252479i
$689$	104.081	−	143.255i	0.151061	−	0.207917i
$690$		0			0
$691$	−12.6560	+	38.9513i	−0.0183155	+	0.0563694i	−0.959797	−	0.280697i	$-0.909435\pi$
$691$	−12.6560	+	38.9513i	−0.0183155	+	0.0563694i	0.941481	+	0.337066i	$0.109435\pi$
$692$		−	241.888i		−	0.349549i
$693$		0			0
$694$	805.212			1.16025
$695$	629.540	+	204.550i	0.905814	+	0.294317i
$696$		0			0
$697$	−482.930	−	350.869i	−0.692869	−	0.503399i
$698$	119.971	−	38.9810i	0.171878	−	0.0558466i
$699$		0			0
$700$	−61.4802	−	44.6680i	−0.0878289	−	0.0638114i
$701$	136.416	+	187.761i	0.194602	+	0.267847i	0.895156	−	0.445752i	$-0.147064\pi$
$701$	136.416	+	187.761i	0.194602	+	0.267847i	−0.700554	+	0.713599i	$0.747064\pi$
$702$		0			0
$703$	222.104			0.315938
$704$	−21.7507	+	85.2696i	−0.0308958	+	0.121122i
$705$		0			0
$706$	−214.226	+	659.321i	−0.303437	+	0.933883i
$707$	237.011	+	326.217i	0.335234	+	0.461410i
$708$		0			0
$709$	66.5049	+	204.681i	0.0938010	+	0.288690i	0.986939	−	0.161092i	$-0.0515017\pi$
$709$	66.5049	+	204.681i	0.0938010	+	0.288690i	−0.893138	+	0.449782i	$0.851502\pi$
$710$	−254.906	+	82.8241i	−0.359023	+	0.116654i
$711$		0			0
$712$	80.0675	−	58.1724i	0.112454	−	0.0817028i
$713$	242.667	+	78.8473i	0.340347	+	0.110585i
$714$		0			0
$715$	9.03575	+	140.103i	0.0126374	+	0.195949i
$716$		−	93.5399i		−	0.130642i
$717$		0			0
$718$	548.134	−	398.242i	0.763417	−	0.554655i
$719$	−89.7795	+	123.571i	−0.124867	+	0.171865i	−0.866874	−	0.498528i	$-0.833874\pi$
$719$	−89.7795	+	123.571i	−0.124867	+	0.171865i	0.742007	+	0.670393i	$0.233874\pi$
$720$		0			0
$721$	138.879	+	427.427i	0.192621	+	0.592825i
$722$	−197.890	+	272.372i	−0.274085	+	0.377246i
$723$		0			0
$724$	174.567	−	537.263i	0.241115	−	0.742076i
$725$			385.716i			0.532023i
$726$		0			0
$727$	610.733			0.840073			0.420037	−	0.907507i	$-0.362017\pi$
$727$	610.733			0.840073			0.420037	+	0.907507i	$0.362017\pi$
$728$	−27.1351	−	8.81673i	−0.0372735	−	0.0121109i
$729$		0			0
$730$	−115.218	−	83.7108i	−0.157833	−	0.114672i
$731$	−639.521	+	207.793i	−0.874858	+	0.284259i
$732$		0			0
$733$	180.227	+	130.943i	0.245876	+	0.178640i	0.703897	−	0.710302i	$-0.251442\pi$
$733$	180.227	+	130.943i	0.245876	+	0.178640i	−0.458021	+	0.888941i	$0.651442\pi$
$734$	−3.81625	−	5.25262i	−0.00519925	−	0.00715616i
$735$		0			0
$736$	62.6853			0.0851703
$737$	962.802	−	62.0944i	1.30638	−	0.0842530i
$738$		0			0
$739$	−99.1503	+	305.153i	−0.134168	+	0.412927i	−0.995460	−	0.0951838i	$-0.969656\pi$
$739$	−99.1503	+	305.153i	−0.134168	+	0.412927i	0.861291	+	0.508111i	$0.169656\pi$
$740$	−66.4352	−	91.4402i	−0.0897773	−	0.123568i
$741$		0			0
$742$	−38.1408	−	117.385i	−0.0514027	−	0.158201i
$743$	263.302	−	85.5519i	0.354377	−	0.115144i	−0.126418	−	0.991977i	$-0.540348\pi$
$743$	263.302	−	85.5519i	0.354377	−	0.115144i	0.480795	+	0.876833i	$0.340348\pi$
$744$		0			0
$745$	343.282	−	249.409i	0.460781	−	0.334777i
$746$	−171.568	−	55.7457i	−0.229983	−	0.0747262i
$747$		0			0
$748$	313.932	+	80.0782i	0.419696	+	0.107056i
$749$		−	203.885i		−	0.272210i
$750$		0			0
$751$	−433.264	+	314.785i	−0.576916	+	0.419154i	−0.837611	−	0.546267i	$-0.816048\pi$
$751$	−433.264	+	314.785i	−0.576916	+	0.419154i	0.260695	+	0.965421i	$0.416048\pi$
$752$	27.2570	−	37.5161i	0.0362461	−	0.0498884i
$753$		0			0
$754$	44.7505	+	137.728i	0.0593508	+	0.182663i
$755$	84.2827	−	116.005i	0.111633	−	0.153649i
$756$		0			0
$757$	209.813	−	645.737i	0.277163	−	0.853021i	−0.711476	−	0.702711i	$-0.751973\pi$
$757$	209.813	−	645.737i	0.277163	−	0.853021i	0.988639	−	0.150310i	$-0.0480272\pi$
$758$			446.845i			0.589505i
$759$		0			0
$760$	−88.4762			−0.116416
$761$	−534.529	−	173.679i	−0.702404	−	0.228225i	−0.0640263	−	0.997948i	$-0.520394\pi$
$761$	−534.529	−	173.679i	−0.702404	−	0.228225i	−0.638378	+	0.769723i	$0.720394\pi$
$762$		0			0
$763$	−374.888	−	272.372i	−0.491334	−	0.356975i
$764$	−680.193	+	221.008i	−0.890305	+	0.289278i
$765$		0			0
$766$	324.039	+	235.428i	0.423027	+	0.307347i
$767$	−247.694	−	340.921i	−0.322938	−	0.444487i
$768$		0			0
$769$	−113.242			−0.147258			−0.0736291	−	0.997286i	$-0.523458\pi$
$769$	−113.242			−0.147258			−0.0736291	+	0.997286i	$0.523458\pi$
$770$	82.7082	+	52.3060i	0.107413	+	0.0679299i
$771$		0			0
$772$	22.9863	−	70.7444i	0.0297749	−	0.0916378i
$773$	629.282	+	866.132i	0.814077	+	1.12048i	0.990681	+	0.136199i	$0.0434887\pi$
$773$	629.282	+	866.132i	0.814077	+	1.12048i	−0.176604	+	0.984282i	$0.556511\pi$
$774$		0			0
$775$	−121.251	−	373.171i	−0.156452	−	0.481511i
$776$	−293.526	+	95.3724i	−0.378255	+	0.122903i
$777$		0			0
$778$	337.092	−	244.911i	0.433280	−	0.314796i
$779$	427.440	+	138.884i	0.548703	+	0.178284i
$780$		0			0
$781$	−686.629	+	273.105i	−0.879167	+	0.349687i
$782$		−	230.785i		−	0.295122i
$783$		0			0
$784$	142.478	−	103.516i	0.181732	−	0.132036i
$785$	171.121	−	235.528i	0.217989	−	0.300036i
$786$		0			0
$787$	64.3376	+	198.011i	0.0817505	+	0.251602i	0.983575	−	0.180501i	$-0.0577718\pi$
$787$	64.3376	+	198.011i	0.0817505	+	0.251602i	−0.901824	+	0.432103i	$0.857772\pi$
$788$	151.907	−	209.082i	0.192775	−	0.265332i
$789$		0			0
$790$	31.3179	−	96.3865i	0.0396429	−	0.122008i
$791$		−	141.569i		−	0.178974i
$792$		0			0
$793$	335.487			0.423060
$794$	476.903	+	154.955i	0.600634	+	0.195158i
$795$		0			0
$796$	−151.583	−	110.132i	−0.190431	−	0.138356i
$797$	−250.710	+	81.4605i	−0.314567	+	0.102209i	−0.462045	−	0.886856i	$-0.652884\pi$
$797$	−250.710	+	81.4605i	−0.314567	+	0.102209i	0.147479	+	0.989065i	$0.452884\pi$
$798$		0			0
$799$	−138.121	−	100.351i	−0.172867	−	0.125595i
$800$	−56.6606	−	77.9866i	−0.0708258	−	0.0974833i
$801$		0			0
$802$	57.7033			0.0719492
$803$	−331.854	−	209.870i	−0.413267	−	0.261357i
$804$		0			0
$805$	21.5412	−	66.2971i	0.0267593	−	0.0823567i
$806$	−86.5899	−	119.181i	−0.107432	−	0.147867i
$807$		0			0
$808$	158.058	+	486.452i	0.195616	+	0.602045i
$809$	−920.341	+	299.037i	−1.13763	+	0.369638i	−0.816470	−	0.577388i	$-0.804072\pi$
$809$	−920.341	+	299.037i	−1.13763	+	0.369638i	−0.321158	+	0.947026i	$0.604072\pi$
$810$		0			0
$811$	354.977	−	257.906i	0.437703	−	0.318010i	−0.347019	−	0.937858i	$-0.612806\pi$
$811$	354.977	−	257.906i	0.437703	−	0.318010i	0.784721	+	0.619849i	$0.212806\pi$
$812$	96.0012	+	31.1927i	0.118228	+	0.0384146i
$813$		0			0
$814$	−199.009	−	239.792i	−0.244483	−	0.294585i
$815$			760.236i			0.932805i
$816$		0			0
$817$	409.589	−	297.584i	0.501333	−	0.364240i
$818$	−396.854	+	546.223i	−0.485152	+	0.667754i
$819$		0			0
$820$	−70.6764	−	217.519i	−0.0861907	−	0.265268i
$821$	−162.007	+	222.984i	−0.197329	+	0.271600i	−0.896202	−	0.443645i	$-0.853685\pi$
$821$	−162.007	+	222.984i	−0.197329	+	0.271600i	0.698874	+	0.715245i	$0.253685\pi$
$822$		0			0
$823$	374.035	−	1151.16i	0.454477	−	1.39874i	−0.417271	−	0.908782i	$-0.637013\pi$
$823$	374.035	−	1151.16i	0.454477	−	1.39874i	0.871748	−	0.489955i	$-0.162987\pi$
$824$			570.086i			0.691852i
$825$		0			0
$826$	−293.732			−0.355608
$827$	−1037.13	−	336.983i	−1.25408	−	0.407476i	−0.394701	−	0.918810i	$-0.629152\pi$
$827$	−1037.13	−	336.983i	−1.25408	−	0.407476i	−0.859382	+	0.511333i	$0.829152\pi$
$828$		0			0
$829$	−1038.92	−	754.823i	−1.25323	−	0.910522i	−0.254821	−	0.966988i	$-0.582017\pi$
$829$	−1038.92	−	754.823i	−1.25323	−	0.910522i	−0.998404	+	0.0564665i	$0.982017\pi$
$830$	83.1377	−	27.0131i	0.100166	−	0.0325459i
$831$		0			0
$832$	−29.2798	−	21.2730i	−0.0351920	−	0.0255685i
$833$	−381.110	−	524.553i	−0.457515	−	0.629716i
$834$		0			0
$835$	597.651			0.715750
$836$	−243.425	+	15.6993i	−0.291178	+	0.0187791i
$837$		0			0
$838$	−33.1971	+	102.170i	−0.0396147	+	0.121921i
$839$	−311.504	−	428.748i	−0.371280	−	0.511023i	0.581968	−	0.813211i	$-0.302283\pi$
$839$	−311.504	−	428.748i	−0.371280	−	0.511023i	−0.953248	+	0.302189i	$0.902283\pi$
$840$		0			0
$841$	101.561	+	312.571i	0.120762	+	0.371666i
$842$	375.660	−	122.059i	0.446152	−	0.144964i
$843$		0			0
$844$	468.618	−	340.471i	0.555234	−	0.403401i
$845$	398.537	+	129.492i	0.471641	+	0.153246i
$846$		0			0
$847$	236.837	+	129.234i	0.279619	+	0.152579i
$848$		−	156.564i		−	0.184628i
$849$		0			0
$850$	−287.119	+	208.604i	−0.337787	+	0.245417i
$851$	−130.473	+	179.581i	−0.153318	+	0.211024i
$852$		0			0
$853$	−377.749	−	1162.59i	−0.442847	−	1.36294i	−0.884828	−	0.465919i	$-0.845724\pi$
$853$	−377.749	−	1162.59i	−0.442847	−	1.36294i	0.441980	−	0.897025i	$-0.354276\pi$
$854$	137.451	−	189.186i	0.160950	−	0.221529i
$855$		0			0
$856$	79.9196	−	245.967i	0.0933640	−	0.287345i
$857$			1479.73i			1.72664i	0.504653	+	0.863322i	$0.331620\pi$
$857$			1479.73i			1.72664i	−0.504653	+	0.863322i	$0.668380\pi$
$858$		0			0
$859$	95.9499			0.111700			0.0558498	−	0.998439i	$-0.482213\pi$
$859$	95.9499			0.111700			0.0558498	+	0.998439i	$0.482213\pi$
$860$	−245.031	−	79.6153i	−0.284920	−	0.0925760i
$861$		0			0
$862$	−680.244	−	494.226i	−0.789147	−	0.573349i
$863$	−1214.69	+	394.678i	−1.40752	+	0.457332i	−0.911616	−	0.411043i	$-0.865165\pi$
$863$	−1214.69	+	394.678i	−1.40752	+	0.457332i	−0.495908	+	0.868375i	$0.665165\pi$
$864$		0			0
$865$	−276.045	−	200.558i	−0.319127	−	0.231859i
$866$	131.067	+	180.399i	0.151348	+	0.208313i
$867$		0			0
$868$	−102.684			−0.118300
$869$	69.0621	−	270.746i	0.0794731	−	0.311560i
$870$		0			0
$871$	−122.616	+	377.374i	−0.140776	+	0.433265i
$872$	−345.500	−	475.539i	−0.396215	−	0.545343i
$873$		0			0
$874$	53.6948	+	165.256i	0.0614357	+	0.189080i
$875$	−251.521	+	81.7240i	−0.287452	+	0.0933989i
$876$		0			0
$877$	−265.285	+	192.741i	−0.302491	+	0.219773i	−0.728668	−	0.684867i	$-0.759860\pi$
$877$	−265.285	+	192.741i	−0.302491	+	0.219773i	0.426177	+	0.904640i	$0.359860\pi$
$878$	357.047	+	116.011i	0.406659	+	0.132131i
$879$		0			0
$880$	79.2761	+	95.5222i	0.0900865	+	0.108548i
$881$		−	768.903i		−	0.872761i	−0.899762	−	0.436381i	$-0.856260\pi$
$881$		−	768.903i		−	0.872761i	0.899762	−	0.436381i	$-0.143740\pi$
$882$		0			0
$883$	564.755	−	410.318i	0.639586	−	0.464687i	−0.220122	−	0.975472i	$-0.570645\pi$
$883$	564.755	−	410.318i	0.639586	−	0.464687i	0.859708	+	0.510786i	$0.170645\pi$
$884$	−78.3196	+	107.798i	−0.0885968	+	0.121943i
$885$		0			0
$886$	−26.1242	−	80.4021i	−0.0294856	−	0.0907472i
$887$	−491.752	+	676.839i	−0.554399	+	0.763065i	−0.990601	−	0.136784i	$-0.956323\pi$
$887$	−491.752	+	676.839i	−0.554399	+	0.763065i	0.436202	+	0.899849i	$0.356323\pi$
$888$		0			0
$889$	−45.4697	+	139.941i	−0.0511470	+	0.157414i
$890$		−	139.607i		−	0.156861i
$891$		0			0
$892$	−287.943			−0.322806
$893$	122.250	+	39.7216i	0.136899	+	0.0444811i
$894$		0			0
$895$	−106.749	−	77.5573i	−0.119272	−	0.0866563i
$896$	−23.9923	+	7.79556i	−0.0267771	+	0.00870040i
$897$		0			0
$898$	−318.084	−	231.102i	−0.354214	−	0.257352i
$899$	306.346	+	421.650i	0.340763	+	0.469021i
$900$		0			0
$901$	−576.413			−0.639748
$902$	−233.049	−	585.922i	−0.258370	−	0.649581i
$903$		0			0
$904$	55.4925	−	170.788i	0.0613855	−	0.188925i
$905$	−468.389	−	644.682i	−0.517556	−	0.712355i
$906$		0			0
$907$	−33.9257	−	104.413i	−0.0374043	−	0.115119i	0.930611	−	0.366010i	$-0.119276\pi$
$907$	−33.9257	−	104.413i	−0.0374043	−	0.115119i	−0.968015	+	0.250891i	$0.919276\pi$
$908$	78.9845	−	25.6636i	0.0869874	−	0.0282639i
$909$		0			0
$910$	−32.5604	+	23.6565i	−0.0357807	+	0.0259962i
$911$	−961.698	−	312.475i	−1.05565	−	0.343002i	−0.270767	−	0.962645i	$-0.587277\pi$
$911$	−961.698	−	312.475i	−1.05565	−	0.343002i	−0.784884	+	0.619643i	$0.787277\pi$
$912$		0			0
$913$	223.944	−	89.0733i	0.245284	−	0.0975611i
$914$			465.808i			0.509637i
$915$		0			0
$916$	−204.740	+	148.752i	−0.223515	+	0.162393i
$917$	−78.0672	+	107.450i	−0.0851332	+	0.117176i
$918$		0			0
$919$	229.979	+	707.803i	0.250249	+	0.770188i	0.994729	+	0.102542i	$0.0326977\pi$
$919$	229.979	+	707.803i	0.250249	+	0.770188i	−0.744479	+	0.667645i	$0.767302\pi$
$920$	51.9747	−	71.5370i	0.0564942	−	0.0777576i
$921$		0			0
$922$	−274.848	+	845.894i	−0.298099	+	0.917455i
$923$		−	303.908i		−	0.329261i
$924$		0			0
$925$	341.350			0.369027
$926$	−685.854	−	222.847i	−0.740663	−	0.240656i
$927$		0			0
$928$	103.589	+	75.2617i	0.111626	+	0.0811010i
$929$	−172.202	+	55.9519i	−0.185363	+	0.0602281i	−0.400228	−	0.916416i	$-0.631069\pi$
$929$	−172.202	+	55.9519i	−0.185363	+	0.0602281i	0.214865	+	0.976644i	$0.431069\pi$
$930$		0			0
$931$	394.941	+	286.941i	0.424211	+	0.308207i
$932$	−234.067	−	322.166i	−0.251145	−	0.345672i
$933$		0			0
$934$	−312.952			−0.335067
$935$	351.679	−	291.866i	0.376127	−	0.312157i
$936$		0			0
$937$	249.812	−	768.843i	0.266609	−	0.820537i	−0.724710	−	0.689054i	$-0.758026\pi$
$937$	249.812	−	768.843i	0.266609	−	0.820537i	0.991318	−	0.131483i	$-0.0419738\pi$
$938$	162.570	+	223.758i	0.173315	+	0.238548i
$939$		0			0
$940$	−20.2139	−	62.2119i	−0.0215041	−	0.0661829i
$941$	124.609	−	40.4881i	0.132422	−	0.0430266i	−0.242056	−	0.970262i	$-0.577822\pi$
$941$	124.609	−	40.4881i	0.132422	−	0.0430266i	0.374478	+	0.927236i	$0.377822\pi$
$942$		0			0
$943$	−363.390	+	264.018i	−0.385356	+	0.279977i
$944$	−354.358	−	115.138i	−0.375380	−	0.121968i
$945$		0			0
$946$	−688.282	−	175.568i	−0.727571	−	0.185589i
$947$			816.092i			0.861765i	0.902408	+	0.430883i	$0.141798\pi$
$947$			816.092i			0.861765i	−0.902408	+	0.430883i	$0.858202\pi$
$948$		0			0
$949$	130.644	−	94.9181i	0.137664	−	0.100019i
$950$	157.060	−	216.174i	0.165326	−	0.227552i
$951$		0			0
$952$	28.7005	+	88.3310i	0.0301476	+	0.0927847i
$953$	588.175	−	809.554i	0.617183	−	0.849480i	−0.379961	−	0.925003i	$-0.624063\pi$
$953$	588.175	−	809.554i	0.617183	−	0.849480i	0.997144	+	0.0755229i	$0.0240626\pi$
$954$		0			0
$955$	−311.756	+	959.487i	−0.326446	+	1.00470i
$956$		−	492.881i		−	0.515566i
$957$		0			0
$958$	365.640			0.381670
$959$	403.351	+	131.057i	0.420595	+	0.136660i
$960$		0			0
$961$	348.537	+	253.227i	0.362682	+	0.263504i
$962$	121.886	−	39.6032i	0.126701	−	0.0411675i
$963$		0			0
$964$	−711.321	−	516.805i	−0.737885	−	0.536105i
$965$	−61.6754	−	84.8889i	−0.0639123	−	0.0879677i
$966$		0			0
$967$	1675.29			1.73247			0.866233	−	0.499640i	$-0.166534\pi$
$967$	1675.29			1.73247			0.866233	+	0.499640i	$0.166534\pi$
$968$	235.063	+	248.744i	0.242833	+	0.256967i
$969$		0			0
$970$	−134.533	+	414.051i	−0.138694	+	0.426857i
$971$	828.699	+	1140.61i	0.853449	+	1.17467i	0.983092	+	0.183111i	$0.0586166\pi$
$971$	828.699	+	1140.61i	0.853449	+	1.17467i	−0.129644	+	0.991561i	$0.541383\pi$
$972$		0			0
$973$	161.667	+	497.561i	0.166154	+	0.511368i
$974$	600.718	−	195.185i	0.616754	−	0.200395i
$975$		0			0
$976$	239.979	−	174.355i	0.245880	−	0.178642i
$977$	−621.149	−	201.824i	−0.635772	−	0.206575i	−0.0266416	−	0.999645i	$-0.508481\pi$
$977$	−621.149	−	201.824i	−0.635772	−	0.206575i	−0.609130	+	0.793070i	$0.708481\pi$
$978$		0			0
$979$	−24.7720	−	384.100i	−0.0253033	−	0.392340i
$980$		−	248.426i		−	0.253496i
$981$		0			0
$982$	−508.441	+	369.404i	−0.517760	+	0.376175i
$983$	376.857	−	518.699i	0.383374	−	0.527669i	−0.573100	−	0.819485i	$-0.694259\pi$
$983$	376.857	−	518.699i	0.383374	−	0.527669i	0.956475	+	0.291816i	$0.0942595\pi$
$984$		0			0
$985$	−112.654	−	346.715i	−0.114370	−	0.351995i
$986$	277.087	−	381.377i	0.281021	−	0.386792i
$987$		0			0
$988$	31.0010	−	95.4114i	0.0313776	−	0.0965702i
$989$			505.986i			0.511613i
$990$		0			0
$991$	435.813			0.439771			0.219886	−	0.975526i	$-0.429432\pi$
$991$	435.813			0.439771			0.219886	+	0.975526i	$0.429432\pi$
$992$	−123.878	−	40.2505i	−0.124877	−	0.0405751i
$993$		0			0
$994$	−171.378	−	124.513i	−0.172412	−	0.125265i
$995$	−251.367	+	81.6739i	−0.252630	+	0.0820843i
$996$		0			0
$997$	−341.582	−	248.174i	−0.342610	−	0.248921i	0.403152	−	0.915133i	$-0.367915\pi$
$997$	−341.582	−	248.174i	−0.342610	−	0.248921i	−0.745762	+	0.666212i	$0.767915\pi$
$998$	−625.225	−	860.548i	−0.626477	−	0.862272i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	198.3.k.a.53.4	yes	16
3.2	odd	2	inner	198.3.k.a.53.1	✓	16
11.4	even	5		2178.3.c.p.485.6		8
11.5	even	5	inner	198.3.k.a.71.1	yes	16
11.7	odd	10		2178.3.c.m.485.2		8
33.5	odd	10	inner	198.3.k.a.71.4	yes	16
33.26	odd	10		2178.3.c.p.485.3		8
33.29	even	10		2178.3.c.m.485.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
198.3.k.a.53.1	✓	16	3.2	odd	2	inner
198.3.k.a.53.4	yes	16	1.1	even	1	trivial
198.3.k.a.71.1	yes	16	11.5	even	5	inner
198.3.k.a.71.4	yes	16	33.5	odd	10	inner
2178.3.c.m.485.2		8	11.7	odd	10
2178.3.c.m.485.7		8	33.29	even	10
2178.3.c.p.485.3		8	33.26	odd	10
2178.3.c.p.485.6		8	11.4	even	5

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 198 = 2 \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	198.k (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.34500 + 0.437016i) q^{2} +(1.61803 + 1.17557i) q^{4} +(2.68314 - 0.871805i) q^{5} +(1.80392 + 1.31063i) q^{7} +(1.66251 + 2.28825i) q^{8} +3.98981 q^{10} +(10.9772 - 0.707957i) q^{11} +(-1.39798 + 4.30255i) q^{13} +(1.85351 + 2.55113i) q^{14} +(1.23607 + 3.80423i) q^{16} +(14.0058 - 4.55076i) q^{17} +(-8.97019 + 6.51722i) q^{19} +(5.36628 + 1.74361i) q^{20} +(15.0737 + 3.84501i) q^{22} -11.0813i q^{23} +(-13.7862 + 10.0163i) q^{25} +(-3.76057 + 5.17598i) q^{26} +(1.37807 + 4.24128i) q^{28} +(13.3045 - 18.3121i) q^{29} +(-7.11534 + 21.8988i) q^{31} +5.65685i q^{32} +20.8265 q^{34} +(5.98279 + 1.94393i) q^{35} +(-16.2058 - 11.7742i) q^{37} +(-14.9130 + 4.84553i) q^{38} +(6.45565 + 4.69030i) q^{40} +(-23.8256 - 32.7931i) q^{41} -45.6612 q^{43} +(18.5937 + 11.7590i) q^{44} +(4.84271 - 14.9043i) q^{46} +(-6.81426 - 9.37903i) q^{47} +(-13.6054 - 41.8732i) q^{49} +(-22.9197 + 7.44706i) q^{50} +(-7.31994 + 5.31825i) q^{52} +(-37.2253 - 12.0952i) q^{53} +(28.8362 - 11.4695i) q^{55} +6.30674i q^{56} +(25.8972 - 18.8154i) q^{58} +(-54.7514 + 75.3588i) q^{59} +(-22.9159 - 70.5280i) q^{61} +(-19.1402 + 26.3443i) q^{62} +(-2.47214 + 7.60845i) q^{64} +12.7631i q^{65} +87.7093 q^{67} +(28.0116 + 9.10152i) q^{68} +(7.19731 + 5.22915i) q^{70} +(-63.8893 + 20.7589i) q^{71} +(-28.8781 - 20.9811i) q^{73} +(-16.6512 - 22.9184i) q^{74} -22.1755 q^{76} +(20.7299 + 13.1099i) q^{77} +(7.84946 - 24.1582i) q^{79} +(6.63309 + 9.12967i) q^{80} +(-17.7142 - 54.5188i) q^{82} +(20.8375 - 6.77051i) q^{83} +(33.6122 - 24.4207i) q^{85} +(-61.4141 - 19.9547i) q^{86} +(19.8697 + 23.9415i) q^{88} -34.9908i q^{89} +(-8.16089 + 5.92924i) q^{91} +(13.0269 - 17.9299i) q^{92} +(-5.06638 - 15.5927i) q^{94} +(-18.3865 + 25.3069i) q^{95} +(-33.7192 + 103.777i) q^{97} -62.2652i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} - 24 q^{7} - 24 q^{10} + 48 q^{13} - 16 q^{16} - 36 q^{19} + 48 q^{22} + 192 q^{25} - 32 q^{28} + 4 q^{31} - 112 q^{34} + 76 q^{37} - 72 q^{40} - 440 q^{43} - 36 q^{46} - 168 q^{49} + 24 q^{52}+ \cdots + 156 q^{97}+O(q^{100}) \) 16 * q + 8 * q^4 - 24 * q^7 - 24 * q^10 + 48 * q^13 - 16 * q^16 - 36 * q^19 + 48 * q^22 + 192 * q^25 - 32 * q^28 + 4 * q^31 - 112 * q^34 + 76 * q^37 - 72 * q^40 - 440 * q^43 - 36 * q^46 - 168 * q^49 + 24 * q^52 + 836 * q^55 - 96 * q^58 + 40 * q^61 + 32 * q^64 - 552 * q^67 + 516 * q^70 - 316 * q^73 - 288 * q^76 + 604 * q^79 - 36 * q^82 + 36 * q^85 - 16 * q^88 - 352 * q^91 - 220 * q^94 + 156 * q^97

Introduction

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