LMFDB - Embedded newform 783.2.k.f.136.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [783,2,Mod(82,783)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(783, base_ring=CyclotomicField(14)) chi = DirichletCharacter(H, H._module([0, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("783.82"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 783 = 3^{3} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	783.k (of order $7$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [60,0,0,-10,0,0,4,0,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(10)] == traces)

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

Self dual:	no
Analytic conductor:	$6.25228647827$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$10$ over $\Q(\zeta_{7})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			136.9
Character	$\chi$	$=$	783.136
Dual form			783.2.k.f.190.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.07439 - 0.998975i) q^{2} +(2.05818 - 2.58087i) q^{4} +(3.28060 - 1.57985i) q^{5} +(-0.480272 - 0.602242i) q^{7} +(0.666575 - 2.92046i) q^{8} +(5.22702 - 6.55447i) q^{10} +(0.658197 + 2.88375i) q^{11} +(-0.244037 - 1.06920i) q^{13} +(-1.59790 - 0.769507i) q^{14} +(-0.0656152 - 0.287479i) q^{16} -7.04868 q^{17} +(-0.225442 + 0.282695i) q^{19} +(2.67465 - 11.7184i) q^{20} +(4.24615 + 5.32451i) q^{22} +(5.36389 + 2.58312i) q^{23} +(5.14895 - 6.45657i) q^{25} +(-1.57433 - 1.97415i) q^{26} -2.54279 q^{28} +(-5.11165 - 1.69441i) q^{29} +(-6.78416 + 3.26708i) q^{31} +(3.31211 + 4.15325i) q^{32} +(-14.6217 + 7.04146i) q^{34} +(-2.52703 - 1.21696i) q^{35} +(-1.06504 + 4.66624i) q^{37} +(-0.185250 + 0.811632i) q^{38} +(-2.42713 - 10.6339i) q^{40} -2.58105 q^{41} +(5.10751 + 2.45965i) q^{43} +(8.79728 + 4.23654i) q^{44} +13.7073 q^{46} +(-1.97831 - 8.66752i) q^{47} +(1.42561 - 6.24602i) q^{49} +(4.23098 - 18.5371i) q^{50} +(-3.26174 - 1.57077i) q^{52} +(4.77573 - 2.29987i) q^{53} +(6.71518 + 8.42057i) q^{55} +(-2.07896 + 1.00117i) q^{56} +(-12.2962 + 1.59154i) q^{58} -4.02730 q^{59} +(-1.78011 - 2.23219i) q^{61} +(-10.8093 + 13.5544i) q^{62} +(11.5510 + 5.56265i) q^{64} +(-2.48977 - 3.12207i) q^{65} +(-2.21401 + 9.70022i) q^{67} +(-14.5074 + 18.1917i) q^{68} -6.45777 q^{70} +(-1.50142 - 6.57817i) q^{71} +(6.54889 + 3.15378i) q^{73} +(2.45215 + 10.7436i) q^{74} +(0.265601 + 1.16367i) q^{76} +(1.42060 - 1.78138i) q^{77} +(1.05869 - 4.63843i) q^{79} +(-0.669432 - 0.839441i) q^{80} +(-5.35410 + 2.57840i) q^{82} +(10.4949 - 13.1602i) q^{83} +(-23.1239 + 11.1359i) q^{85} +13.0521 q^{86} +8.86061 q^{88} +(-6.34265 + 3.05446i) q^{89} +(-0.526712 + 0.660475i) q^{91} +(17.7065 - 8.52702i) q^{92} +(-12.7624 - 16.0036i) q^{94} +(-0.292967 + 1.28357i) q^{95} +(-9.61159 + 12.0525i) q^{97} +(-3.28233 - 14.3808i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 10 q^{4} + 4 q^{7} + 4 q^{10} - 24 q^{13} - 26 q^{16} + 4 q^{19} - 8 q^{22} - 16 q^{25} + 112 q^{28} - 4 q^{31} + 26 q^{34} - 18 q^{37} - 78 q^{40} - 8 q^{43} + 72 q^{46} + 14 q^{49} - 12 q^{52}+ \cdots + 8 q^{97}+O(q^{100}) $ 60 * q - 10 * q^4 + 4 * q^7 + 4 * q^10 - 24 * q^13 - 26 * q^16 + 4 * q^19 - 8 * q^22 - 16 * q^25 + 112 * q^28 - 4 * q^31 + 26 * q^34 - 18 * q^37 - 78 * q^40 - 8 * q^43 + 72 * q^46 + 14 * q^49 - 12 * q^52 + 24 * q^55 - 162 * q^58 - 10 * q^61 + 116 * q^64 + 60 * q^67 - 12 * q^70 + 66 * q^73 - 120 * q^76 + 46 * q^79 - 84 * q^82 - 122 * q^85 - 152 * q^88 - 30 * q^91 - 68 * q^94 + 8 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/783\mathbb{Z}\right)^\times$.

$n$	$379$	$407$
$\chi(n)$	$e\left(\frac{6}{7}\right)$	$1$

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 $

$2$	2.07439	−	0.998975i	1.46682	−	0.706382i	0.481395	−	0.876504i	$-0.340130\pi$
$2$	2.07439	−	0.998975i	1.46682	−	0.706382i	0.985423	+	0.170122i	$0.0544162\pi$
$3$		0			0
$3$		0			0
$4$	2.05818	−	2.58087i	1.02909	−	1.29044i
$5$	3.28060	−	1.57985i	1.46713	−	0.706532i	0.481655	−	0.876361i	$-0.340036\pi$
$5$	3.28060	−	1.57985i	1.46713	−	0.706532i	0.985474	+	0.169829i	$0.0543215\pi$
$6$		0			0
$7$	−0.480272	−	0.602242i	−0.181526	−	0.227626i	0.682740	−	0.730661i	$-0.260788\pi$
$7$	−0.480272	−	0.602242i	−0.181526	−	0.227626i	−0.864266	+	0.503035i	$0.832217\pi$
$8$	0.666575	−	2.92046i	0.235670	−	1.03254i
$9$		0			0
$10$	5.22702	−	6.55447i	1.65293	−	2.07271i
$11$	0.658197	+	2.88375i	0.198454	+	0.869483i	0.971858	+	0.235570i	$0.0756955\pi$
$11$	0.658197	+	2.88375i	0.198454	+	0.869483i	−0.773404	+	0.633914i	$0.781447\pi$
$12$		0			0
$13$	−0.244037	−	1.06920i	−0.0676838	−	0.296542i	0.929745	−	0.368204i	$-0.120027\pi$
$13$	−0.244037	−	1.06920i	−0.0676838	−	0.296542i	−0.997429	+	0.0716614i	$0.977170\pi$
$14$	−1.59790	−	0.769507i	−0.427056	−	0.205659i
$15$		0			0
$16$	−0.0656152	−	0.287479i	−0.0164038	−	0.0718697i
$17$	−7.04868			−1.70956			−0.854778	−	0.518993i	$-0.826307\pi$
$17$	−7.04868			−1.70956			−0.854778	+	0.518993i	$0.826307\pi$
$18$		0			0
$19$	−0.225442	+	0.282695i	−0.0517199	+	0.0648547i	−0.807019	−	0.590526i	$-0.798920\pi$
$19$	−0.225442	+	0.282695i	−0.0517199	+	0.0648547i	0.755299	+	0.655381i	$0.227492\pi$
$20$	2.67465	−	11.7184i	0.598071	−	2.62032i
$21$		0			0
$22$	4.24615	+	5.32451i	0.905283	+	1.13519i
$23$	5.36389	+	2.58312i	1.11845	+	0.538617i	0.899413	−	0.437100i	$-0.143994\pi$
$23$	5.36389	+	2.58312i	1.11845	+	0.538617i	0.219036	+	0.975717i	$0.429709\pi$
$24$		0			0
$25$	5.14895	−	6.45657i	1.02979	−	1.29131i
$26$	−1.57433	−	1.97415i	−0.308752	−	0.387163i
$27$		0			0
$28$	−2.54279			−0.480543
$29$	−5.11165	−	1.69441i	−0.949210	−	0.314644i
$29$	−5.11165	−	1.69441i	−0.949210	−	0.314644i
$30$		0			0
$31$	−6.78416	+	3.26708i	−1.21847	+	0.586785i	−0.928886	−	0.370367i	$-0.879232\pi$
$31$	−6.78416	+	3.26708i	−1.21847	+	0.586785i	−0.289586	+	0.957152i	$0.593518\pi$
$32$	3.31211	+	4.15325i	0.585504	+	0.734198i
$33$		0			0
$34$	−14.6217	+	7.04146i	−2.50761	+	1.20760i
$35$	−2.52703	−	1.21696i	−0.427147	−	0.205703i
$36$		0			0
$37$	−1.06504	+	4.66624i	−0.175091	+	0.767125i	0.808760	+	0.588138i	$0.200139\pi$
$37$	−1.06504	+	4.66624i	−0.175091	+	0.767125i	−0.983852	+	0.178986i	$0.942718\pi$
$38$	−0.185250	+	0.811632i	−0.0300515	+	0.131664i
$39$		0			0
$40$	−2.42713	−	10.6339i	−0.383763	−	1.68137i
$41$	−2.58105			−0.403092			−0.201546	−	0.979479i	$-0.564596\pi$
$41$	−2.58105			−0.403092			−0.201546	+	0.979479i	$0.564596\pi$
$42$		0			0
$43$	5.10751	+	2.45965i	0.778887	+	0.375092i	0.780700	−	0.624906i	$-0.214863\pi$
$43$	5.10751	+	2.45965i	0.778887	+	0.375092i	−0.00181264	+	0.999998i	$0.500577\pi$
$44$	8.79728	+	4.23654i	1.32624	+	0.638683i
$45$		0			0
$46$	13.7073			2.02103
$47$	−1.97831	−	8.66752i	−0.288565	−	1.26429i	−0.886495	−	0.462739i	$-0.846867\pi$
$47$	−1.97831	−	8.66752i	−0.288565	−	1.26429i	0.597929	−	0.801549i	$-0.295990\pi$
$48$		0			0
$49$	1.42561	−	6.24602i	0.203659	−	0.892288i
$50$	4.23098	−	18.5371i	0.598351	−	2.62155i
$51$		0			0
$52$	−3.26174	−	1.57077i	−0.452321	−	0.217826i
$53$	4.77573	−	2.29987i	0.655997	−	0.315911i	−0.0761119	−	0.997099i	$-0.524251\pi$
$53$	4.77573	−	2.29987i	0.655997	−	0.315911i	0.732109	+	0.681188i	$0.238536\pi$
$54$		0			0
$55$	6.71518	+	8.42057i	0.905475	+	1.13543i
$56$	−2.07896	+	1.00117i	−0.277813	+	0.133787i
$57$		0			0
$58$	−12.2962	+	1.59154i	−1.61458	+	0.208980i
$59$	−4.02730			−0.524310			−0.262155	−	0.965026i	$-0.584433\pi$
$59$	−4.02730			−0.524310			−0.262155	+	0.965026i	$0.584433\pi$
$60$		0			0
$61$	−1.78011	−	2.23219i	−0.227920	−	0.285803i	0.654701	−	0.755888i	$-0.272795\pi$
$61$	−1.78011	−	2.23219i	−0.227920	−	0.285803i	−0.882621	+	0.470085i	$0.844223\pi$
$62$	−10.8093	+	13.5544i	−1.37278	+	1.72141i
$63$		0			0
$64$	11.5510	+	5.56265i	1.44387	+	0.695331i
$65$	−2.48977	−	3.12207i	−0.308817	−	0.387245i
$66$		0			0
$67$	−2.21401	+	9.70022i	−0.270485	+	1.18507i	0.638958	+	0.769241i	$0.279366\pi$
$67$	−2.21401	+	9.70022i	−0.270485	+	1.18507i	−0.909443	+	0.415829i	$0.863491\pi$
$68$	−14.5074	+	18.1917i	−1.75928	+	2.20607i
$69$		0			0
$70$	−6.45777			−0.771851
$71$	−1.50142	−	6.57817i	−0.178186	−	0.780685i	−0.982467	−	0.186436i	$-0.940306\pi$
$71$	−1.50142	−	6.57817i	−0.178186	−	0.780685i	0.804281	−	0.594249i	$-0.202551\pi$
$72$		0			0
$73$	6.54889	+	3.15378i	0.766489	+	0.369122i	0.775918	−	0.630834i	$-0.217287\pi$
$73$	6.54889	+	3.15378i	0.766489	+	0.369122i	−0.00942870	+	0.999956i	$0.503001\pi$
$74$	2.45215	+	10.7436i	0.285056	+	1.24891i
$75$		0			0
$76$	0.265601	+	1.16367i	0.0304665	+	0.133482i
$77$	1.42060	−	1.78138i	0.161893	−	0.203007i
$78$		0			0
$79$	1.05869	−	4.63843i	0.119112	−	0.521864i	−0.879805	−	0.475335i	$-0.842327\pi$
$79$	1.05869	−	4.63843i	0.119112	−	0.521864i	0.998917	−	0.0465288i	$-0.0148159\pi$
$80$	−0.669432	−	0.839441i	−0.0748447	−	0.0938523i
$81$		0			0
$82$	−5.35410	+	2.57840i	−0.591262	+	0.284737i
$83$	10.4949	−	13.1602i	1.15197	−	1.44452i	0.276648	−	0.960971i	$-0.410776\pi$
$83$	10.4949	−	13.1602i	1.15197	−	1.44452i	0.875318	−	0.483548i	$-0.160652\pi$
$84$		0			0
$85$	−23.1239	+	11.1359i	−2.50814	+	1.20786i
$86$	13.0521			1.40744
$87$		0			0
$88$	8.86061			0.944544
$89$	−6.34265	+	3.05446i	−0.672319	+	0.323772i	−0.738711	−	0.674022i	$-0.764565\pi$
$89$	−6.34265	+	3.05446i	−0.672319	+	0.323772i	0.0663924	+	0.997794i	$0.478851\pi$
$90$		0			0
$91$	−0.526712	+	0.660475i	−0.0552144	+	0.0692366i
$92$	17.7065	−	8.52702i	1.84603	−	0.889003i
$93$		0			0
$94$	−12.7624	−	16.0036i	−1.31634	−	1.65064i
$95$	−0.292967	+	1.28357i	−0.0300578	+	0.131692i
$96$		0			0
$97$	−9.61159	+	12.0525i	−0.975909	+	1.22375i	−0.00126249	+	0.999999i	$0.500402\pi$
$97$	−9.61159	+	12.0525i	−0.975909	+	1.22375i	−0.974646	+	0.223752i	$0.928170\pi$
$98$	−3.28233	−	14.3808i	−0.331566	−	1.45268i
$99$		0			0
$100$	−6.06615	−	26.5775i	−0.606615	−	2.65775i
$101$	11.4471	+	5.51263i	1.13903	+	0.548527i	0.905720	−	0.423876i	$-0.139331\pi$
$101$	11.4471	+	5.51263i	1.13903	+	0.548527i	0.233308	+	0.972403i	$0.425045\pi$
$102$		0			0
$103$	4.19106	+	18.3622i	0.412958	+	1.80929i	0.569942	+	0.821685i	$0.306966\pi$
$103$	4.19106	+	18.3622i	0.412958	+	1.80929i	−0.156984	+	0.987601i	$0.550177\pi$
$104$	−3.28522			−0.322142
$105$		0			0
$106$	7.60923	−	9.54167i	0.739073	−	0.926769i
$107$	−0.727600	+	3.18782i	−0.0703398	+	0.308179i	−0.997844	−	0.0656347i	$-0.979093\pi$
$107$	−0.727600	+	3.18782i	−0.0703398	+	0.308179i	0.927504	+	0.373813i	$0.121950\pi$
$108$		0			0
$109$	−0.756564	−	0.948701i	−0.0724657	−	0.0908691i	0.744277	−	0.667871i	$-0.232794\pi$
$109$	−0.756564	−	0.948701i	−0.0724657	−	0.0908691i	−0.816743	+	0.577002i	$0.804223\pi$
$110$	22.3419	+	10.7593i	2.13021	+	1.02586i
$111$		0			0
$112$	−0.141619	+	0.177584i	−0.0133817	+	0.0167801i
$113$	−8.88360	−	11.1397i	−0.835699	−	1.04793i	−0.998125	−	0.0612123i	$-0.980503\pi$
$113$	−8.88360	−	11.1397i	−0.835699	−	1.04793i	0.162426	−	0.986721i	$-0.448068\pi$
$114$		0			0
$115$	21.6777			2.02146
$116$	−14.8937	+	9.70512i	−1.38285	+	0.901098i
$117$		0			0
$118$	−8.35421	+	4.02318i	−0.769068	+	0.370363i
$119$	3.38528	+	4.24501i	0.310328	+	0.389140i
$120$		0			0
$121$	2.02786	−	0.976568i	0.184351	−	0.0887789i
$122$	−5.92256	−	2.85216i	−0.536204	−	0.258222i
$123$		0			0
$124$	−5.53109	+	24.2333i	−0.496706	+	2.17621i
$125$	2.63998	−	11.5665i	0.236127	−	1.03454i
$126$		0			0
$127$	−1.17190	−	5.13441i	−0.103989	−	0.455605i	−0.999935	−	0.0114416i	$-0.996358\pi$
$127$	−1.17190	−	5.13441i	−0.103989	−	0.455605i	0.895946	−	0.444164i	$-0.146499\pi$
$128$	18.8937			1.66999
$129$		0			0
$130$	−8.28362	−	3.98918i	−0.726522	−	0.349874i
$131$	−6.71389	−	3.23324i	−0.586596	−	0.282490i	0.116952	−	0.993138i	$-0.462688\pi$
$131$	−6.71389	−	3.23324i	−0.586596	−	0.282490i	−0.703548	+	0.710648i	$0.748402\pi$
$132$		0			0
$133$	0.278524			0.0241511
$134$	5.09755	+	22.3338i	0.440361	+	1.92935i
$135$		0			0
$136$	−4.69848	+	20.5854i	−0.402891	+	1.76518i
$137$	−1.29117	+	5.65699i	−0.110312	+	0.483309i	0.889348	+	0.457232i	$0.151159\pi$
$137$	−1.29117	+	5.65699i	−0.110312	+	0.483309i	−0.999660	+	0.0260779i	$0.991698\pi$
$138$		0			0
$139$	20.1544	+	9.70583i	1.70947	+	0.823238i	0.991940	+	0.126712i	$0.0404425\pi$
$139$	20.1544	+	9.70583i	1.70947	+	0.823238i	0.717532	+	0.696526i	$0.245272\pi$
$140$	−8.34189	+	4.01724i	−0.705018	+	0.339519i
$141$		0			0
$142$	−9.68597	−	12.1458i	−0.812828	−	1.01925i
$143$	2.92268	−	1.40749i	0.244406	−	0.117700i
$144$		0			0
$145$	−19.4462	+	2.51698i	−1.61492	+	0.209024i
$146$	16.7355			1.38504
$147$		0			0
$148$	9.85093	+	12.3527i	0.809741	+	1.01538i
$149$	−11.9400	+	14.9722i	−0.978159	+	1.22657i	−0.00416692	+	0.999991i	$0.501326\pi$
$149$	−11.9400	+	14.9722i	−0.978159	+	1.22657i	−0.973992	+	0.226581i	$0.927245\pi$
$150$		0			0
$151$	6.51747	+	3.13865i	0.530384	+	0.255420i	0.679855	−	0.733347i	$-0.262043\pi$
$151$	6.51747	+	3.13865i	0.530384	+	0.255420i	−0.149471	+	0.988766i	$0.547757\pi$
$152$	0.675325	+	0.846831i	0.0547761	+	0.0686870i
$153$		0			0
$154$	1.16733	−	5.11443i	0.0940665	−	0.412132i
$155$	−17.0946	+	21.4360i	−1.37307	+	1.72178i
$156$		0			0
$157$	−16.7517			−1.33693			−0.668465	−	0.743743i	$-0.733048\pi$
$157$	−16.7517			−1.33693			−0.668465	+	0.743743i	$0.733048\pi$
$158$	−2.43753	−	10.6795i	−0.193920	−	0.849617i
$159$		0			0
$160$	17.4272	+	8.39251i	1.37774	+	0.663486i
$161$	−1.02047	−	4.47096i	−0.0804241	−	0.352361i
$162$		0			0
$163$	0.284638	+	1.24708i	0.0222946	+	0.0976788i	0.984851	−	0.173402i	$-0.0554760\pi$
$163$	0.284638	+	1.24708i	0.0222946	+	0.0976788i	−0.962557	+	0.271081i	$0.912619\pi$
$164$	−5.31225	+	6.66135i	−0.414817	+	0.520164i
$165$		0			0
$166$	8.62386	−	37.7836i	0.669341	−	2.93257i
$167$	−8.84199	−	11.0875i	−0.684214	−	0.857977i	0.311521	−	0.950239i	$-0.399162\pi$
$167$	−8.84199	−	11.0875i	−0.684214	−	0.857977i	−0.995735	+	0.0922621i	$0.970590\pi$
$168$		0			0
$169$	10.6290	−	5.11864i	0.817613	−	0.393742i
$170$	−36.8436	+	46.2004i	−2.82577	+	3.54341i
$171$		0			0
$172$	16.8602	−	8.11943i	1.28558	−	0.619101i
$173$	−23.7612			−1.80653			−0.903265	−	0.429083i	$-0.858837\pi$
$173$	−23.7612			−1.80653			−0.903265	+	0.429083i	$0.858837\pi$
$174$		0			0
$175$	−6.36131			−0.480870
$176$	0.785830	−	0.378436i	0.0592341	−	0.0285257i
$177$		0			0
$178$	−10.1058	+	12.6723i	−0.757463	+	0.949828i
$179$	13.6153	−	6.55679i	1.01766	−	0.490078i	0.150763	−	0.988570i	$-0.451827\pi$
$179$	13.6153	−	6.55679i	1.01766	−	0.490078i	0.866894	+	0.498492i	$0.166113\pi$
$180$		0			0
$181$	0.0635702	+	0.0797146i	0.00472514	+	0.00592514i	0.784188	−	0.620523i	$-0.213080\pi$
$181$	0.0635702	+	0.0797146i	0.00472514	+	0.00592514i	−0.779463	+	0.626448i	$0.784508\pi$
$182$	−0.432808	+	1.89626i	−0.0320819	+	0.140560i
$183$		0			0
$184$	11.1193	−	13.9432i	0.819727	−	1.02790i
$185$	3.87801	+	16.9907i	0.285117	+	1.24918i
$186$		0			0
$187$	−4.63942	−	20.3266i	−0.339268	−	1.48643i
$188$	−26.4415	−	12.7335i	−1.92844	−	0.928689i
$189$		0			0
$190$	0.674529	+	2.95531i	0.0489355	+	0.214400i
$191$	7.85966			0.568705			0.284353	−	0.958720i	$-0.408221\pi$
$191$	7.85966			0.568705			0.284353	+	0.958720i	$0.408221\pi$
$192$		0			0
$193$	9.69997	−	12.1634i	0.698219	−	0.875539i	−0.298670	−	0.954356i	$-0.596543\pi$
$193$	9.69997	−	12.1634i	0.698219	−	0.875539i	0.996889	+	0.0788173i	$0.0251144\pi$
$194$	−7.89801	+	34.6035i	−0.567044	+	2.48438i
$195$		0			0
$196$	−13.1860	−	16.5347i	−0.941857	−	1.18105i
$197$	−11.1235	−	5.35678i	−0.792515	−	0.381655i	−0.00659102	−	0.999978i	$-0.502098\pi$
$197$	−11.1235	−	5.35678i	−0.792515	−	0.381655i	−0.785924	+	0.618323i	$0.787812\pi$
$198$		0			0
$199$	5.44085	−	6.82261i	0.385692	−	0.483642i	−0.550648	−	0.834737i	$-0.685619\pi$
$199$	5.44085	−	6.82261i	0.385692	−	0.483642i	0.936340	+	0.351096i	$0.114191\pi$
$200$	−15.4240	−	19.3411i	−1.09064	−	1.36762i
$201$		0			0
$202$	29.2527			2.05822
$203$	1.43454	+	3.89223i	0.100685	+	0.273181i
$204$		0			0
$205$	−8.46738	+	4.07767i	−0.591387	+	0.284797i
$206$	27.0373	+	33.9038i	1.88378	+	2.36219i
$207$		0			0
$208$	−0.291359	+	0.140311i	−0.0202021	+	0.00972883i
$209$	−0.963607	−	0.464049i	−0.0666541	−	0.0320989i
$210$		0			0
$211$	−2.17454	+	9.52727i	−0.149701	+	0.655884i	0.843266	+	0.537496i	$0.180630\pi$
$211$	−2.17454	+	9.52727i	−0.149701	+	0.655884i	−0.992967	+	0.118388i	$0.962227\pi$
$212$	3.89362	−	17.0591i	0.267415	−	1.17162i
$213$		0			0
$214$	1.67523	+	7.33966i	0.114516	+	0.501728i
$215$	20.6416			1.40774
$216$		0			0
$217$	5.22582	+	2.51662i	0.354752	+	0.170839i
$218$	−2.51714	−	1.21219i	−0.170482	−	0.0820999i
$219$		0			0
$220$	35.5535			2.39701
$221$	1.72014	+	7.53644i	0.115709	+	0.506956i
$222$		0			0
$223$	2.40309	−	10.5286i	0.160923	−	0.705050i	−0.828500	−	0.559989i	$-0.810805\pi$
$223$	2.40309	−	10.5286i	0.160923	−	0.705050i	0.989423	−	0.145061i	$-0.0463377\pi$
$224$	0.910550	−	3.98938i	0.0608387	−	0.266552i
$225$		0			0
$226$	−29.5563	−	14.2336i	−1.96606	−	0.946804i
$227$	4.42073	−	2.12891i	0.293414	−	0.141301i	−0.281386	−	0.959595i	$-0.590794\pi$
$227$	4.42073	−	2.12891i	0.293414	−	0.141301i	0.574800	+	0.818294i	$0.305080\pi$
$228$		0			0
$229$	2.02914	+	2.54446i	0.134089	+	0.168143i	0.844343	−	0.535803i	$-0.179991\pi$
$229$	2.02914	+	2.54446i	0.134089	+	0.168143i	−0.710253	+	0.703946i	$0.751420\pi$
$230$	44.9681	−	21.6555i	2.96511	−	1.42792i
$231$		0			0
$232$	−8.35575	+	13.7989i	−0.548582	+	0.905942i
$233$	−5.32357			−0.348759			−0.174379	−	0.984679i	$-0.555792\pi$
$233$	−5.32357			−0.348759			−0.174379	+	0.984679i	$0.555792\pi$
$234$		0			0
$235$	−20.1834	−	25.3092i	−1.31662	−	1.65099i
$236$	−8.28890	+	10.3940i	−0.539562	+	0.676589i
$237$		0			0
$238$	11.2631	+	5.42401i	0.730077	+	0.351586i
$239$	−6.37356	−	7.99220i	−0.412272	−	0.516972i	0.531730	−	0.846914i	$-0.321542\pi$
$239$	−6.37356	−	7.99220i	−0.412272	−	0.516972i	−0.944001	+	0.329942i	$0.892971\pi$
$240$		0			0
$241$	6.69956	−	29.3527i	0.431556	−	1.89077i	−0.0224023	−	0.999749i	$-0.507131\pi$
$241$	6.69956	−	29.3527i	0.431556	−	1.89077i	0.453959	−	0.891023i	$-0.350011\pi$
$242$	3.23102	−	4.05157i	0.207698	−	0.260445i
$243$		0			0
$244$	−9.42479			−0.603361
$245$	−5.19093	−	22.7429i	−0.331636	−	1.45299i
$246$		0			0
$247$	0.357273	+	0.172054i	0.0227328	+	0.0109475i
$248$	5.01921	+	21.9906i	0.318720	+	1.39641i
$249$		0			0
$250$	−6.07831	−	26.6308i	−0.384426	−	1.68428i
$251$	9.94334	−	12.4686i	0.627618	−	0.787008i	−0.361776	−	0.932265i	$-0.617829\pi$
$251$	9.94334	−	12.4686i	0.627618	−	0.787008i	0.989394	+	0.145257i	$0.0464009\pi$
$252$		0			0
$253$	−3.91856	+	17.1683i	−0.246358	+	1.07936i
$254$	−7.56012	−	9.48010i	−0.474364	−	0.594834i
$255$		0			0
$256$	16.0912	−	7.74909i	1.00570	−	0.484318i
$257$	−12.7006	+	15.9260i	−0.792239	+	0.993436i	0.207645	+	0.978204i	$0.433420\pi$
$257$	−12.7006	+	15.9260i	−0.792239	+	0.993436i	−0.999884	+	0.0152317i	$0.995151\pi$
$258$		0			0
$259$	3.32171	−	1.59965i	0.206401	−	0.0993976i
$260$	−13.1820			−0.817515
$261$		0			0
$262$	−17.1572			−1.05997
$263$	3.51526	−	1.69286i	0.216760	−	0.104386i	−0.322353	−	0.946620i	$-0.604474\pi$
$263$	3.51526	−	1.69286i	0.216760	−	0.104386i	0.539113	+	0.842233i	$0.318760\pi$
$264$		0			0
$265$	12.0338	−	15.0899i	0.739230	−	0.926965i
$266$	0.577769	−	0.278239i	0.0354253	−	0.0170599i
$267$		0			0
$268$	20.4782	+	25.6788i	1.25090	+	1.56859i
$269$	3.98885	−	17.4763i	0.243204	−	1.06555i	−0.694876	−	0.719130i	$-0.744541\pi$
$269$	3.98885	−	17.4763i	0.243204	−	1.06555i	0.938080	−	0.346418i	$-0.112602\pi$
$270$		0			0
$271$	13.0639	−	16.3816i	0.793576	−	0.995113i	−0.206286	−	0.978492i	$-0.566138\pi$
$271$	13.0639	−	16.3816i	0.793576	−	0.995113i	0.999862	−	0.0166210i	$-0.00529089\pi$
$272$	0.462501	+	2.02635i	0.0280432	+	0.122865i
$273$		0			0
$274$	2.97280	+	13.0247i	0.179593	+	0.786849i
$275$	22.0082	+	10.5986i	1.32714	+	0.639118i
$276$		0			0
$277$	−0.629159	−	2.75653i	−0.0378025	−	0.165624i	0.952503	−	0.304529i	$-0.0984989\pi$
$277$	−0.629159	−	2.75653i	−0.0378025	−	0.165624i	−0.990306	+	0.138905i	$0.955642\pi$
$278$	51.5040			3.08900
$279$		0			0
$280$	−5.23852	+	6.56890i	−0.313062	+	0.392567i
$281$	4.71792	−	20.6706i	0.281448	−	1.23310i	−0.614491	−	0.788924i	$-0.710639\pi$
$281$	4.71792	−	20.6706i	0.281448	−	1.23310i	0.895938	−	0.444178i	$-0.146504\pi$
$282$		0			0
$283$	18.2892	+	22.9339i	1.08718	+	1.36328i	0.926509	+	0.376273i	$0.122795\pi$
$283$	18.2892	+	22.9339i	1.08718	+	1.36328i	0.160672	+	0.987008i	$0.448634\pi$
$284$	−20.0676	−	9.66405i	−1.19079	−	0.573456i
$285$		0			0
$286$	4.65673	−	5.83936i	0.275358	−	0.345289i
$287$	1.23960	+	1.55441i	0.0731715	+	0.0917541i
$288$		0			0
$289$	32.6839			1.92258
$290$	−37.8247	+	24.6475i	−2.22114	+	1.44735i
$291$		0			0
$292$	21.6183	−	10.4108i	1.26511	−	0.609246i
$293$	−10.4426	−	13.0947i	−0.610066	−	0.764998i	0.376843	−	0.926277i	$-0.377010\pi$
$293$	−10.4426	−	13.0947i	−0.610066	−	0.764998i	−0.986909	+	0.161279i	$0.948438\pi$
$294$		0			0
$295$	−13.2120	+	6.36255i	−0.769231	+	0.370442i
$296$	12.9176	+	6.22080i	0.750821	+	0.361576i
$297$		0			0
$298$	−9.81128	+	42.9860i	−0.568352	+	2.49011i
$299$	1.45287	−	6.36544i	0.0840217	−	0.368123i
$300$		0			0
$301$	−0.971690	−	4.25725i	−0.0560073	−	0.245384i
$302$	16.6552			0.958401
$303$		0			0
$304$	0.0960613	+	0.0462607i	0.00550949	+	0.00265323i
$305$	−9.36638	−	4.51061i	−0.536317	−	0.258277i
$306$		0			0
$307$	−27.4865			−1.56874			−0.784368	−	0.620295i	$-0.787013\pi$
$307$	−27.4865			−1.56874			−0.784368	+	0.620295i	$0.787013\pi$
$308$	−1.67366	−	7.33278i	−0.0953656	−	0.417824i
$309$		0			0
$310$	−14.0470	+	61.5437i	−0.797813	+	3.49545i
$311$	−0.262236	+	1.14893i	−0.0148701	+	0.0651500i	−0.981819	−	0.189822i	$-0.939209\pi$
$311$	−0.262236	+	1.14893i	−0.0148701	+	0.0651500i	0.966949	+	0.254972i	$0.0820662\pi$
$312$		0			0
$313$	5.18769	+	2.49826i	0.293226	+	0.141210i	0.574713	−	0.818355i	$-0.305114\pi$
$313$	5.18769	+	2.49826i	0.293226	+	0.141210i	−0.281488	+	0.959565i	$0.590828\pi$
$314$	−34.7496	+	16.7345i	−1.96103	+	0.944384i
$315$		0			0
$316$	−9.79221	−	12.2790i	−0.550855	−	0.690750i
$317$	−4.08783	+	1.96860i	−0.229596	+	0.110567i	−0.545145	−	0.838342i	$-0.683525\pi$
$317$	−4.08783	+	1.96860i	−0.229596	+	0.110567i	0.315549	+	0.948909i	$0.397811\pi$
$318$		0			0
$319$	1.52178	−	15.8560i	0.0852033	−	0.887765i
$320$	46.6822			2.60961
$321$		0			0
$322$	−6.58323	−	8.25511i	−0.366869	−	0.460039i
$323$	1.58907	−	1.99263i	0.0884181	−	0.110873i
$324$		0			0
$325$	−8.15989	−	3.92960i	−0.452629	−	0.217975i
$326$	1.83625	+	2.30259i	0.101701	+	0.127529i
$327$		0			0
$328$	−1.72046	+	7.53783i	−0.0949966	+	0.416207i
$329$	−4.26982	+	5.35418i	−0.235403	+	0.295186i
$330$		0			0
$331$	−9.69839			−0.533072			−0.266536	−	0.963825i	$-0.585879\pi$
$331$	−9.69839			−0.533072			−0.266536	+	0.963825i	$0.585879\pi$
$332$	−12.3644	−	54.1720i	−0.678585	−	2.97308i
$333$		0			0
$334$	−29.4179	−	14.1669i	−1.60968	−	0.775180i
$335$	8.06164	+	35.3203i	0.440454	+	1.92976i
$336$		0			0
$337$	−6.87809	−	30.1349i	−0.374673	−	1.64155i	−0.713466	−	0.700690i	$-0.752876\pi$
$337$	−6.87809	−	30.1349i	−0.374673	−	1.64155i	0.338793	−	0.940861i	$-0.389981\pi$
$338$	16.9353	−	21.2361i	0.921157	−	1.15509i
$339$		0			0
$340$	−18.8528	+	82.5994i	−1.02244	+	4.47958i
$341$	−13.8868	−	17.4135i	−0.752010	−	0.942991i
$342$		0			0
$343$	−9.30439	+	4.48076i	−0.502390	+	0.241938i
$344$	10.5878	−	13.2767i	0.570857	−	0.715832i
$345$		0			0
$346$	−49.2901	+	23.7368i	−2.64985	+	1.27610i
$347$	30.0220			1.61167			0.805833	−	0.592142i	$-0.201718\pi$
$347$	30.0220			1.61167			0.805833	+	0.592142i	$0.201718\pi$
$348$		0			0
$349$	−26.0590			−1.39491			−0.697454	−	0.716630i	$-0.745684\pi$
$349$	−26.0590			−1.39491			−0.697454	+	0.716630i	$0.745684\pi$
$350$	−13.1959	+	6.35480i	−0.705349	+	0.339678i
$351$		0			0
$352$	−9.79692	+	12.2850i	−0.522178	+	0.654790i
$353$	13.6243	−	6.56112i	0.725149	−	0.349213i	−0.0346253	−	0.999400i	$-0.511024\pi$
$353$	13.6243	−	6.56112i	0.725149	−	0.349213i	0.759774	+	0.650187i	$0.225309\pi$
$354$		0			0
$355$	−15.3181	−	19.2083i	−0.813001	−	1.01947i
$356$	−5.17112	+	22.6562i	−0.274069	+	1.20077i
$357$		0			0
$358$	21.6935	−	27.2027i	1.14653	−	1.43771i
$359$	1.01482	+	4.44622i	0.0535602	+	0.234662i	0.994622	−	0.103572i	$-0.0330273\pi$
$359$	1.01482	+	4.44622i	0.0535602	+	0.234662i	−0.941062	+	0.338235i	$0.890170\pi$
$360$		0			0
$361$	4.19881	+	18.3962i	0.220990	+	0.968219i
$362$	0.211503	+	0.101854i	0.0111163	+	0.00535334i
$363$		0			0
$364$	0.620537	+	2.71875i	0.0325250	+	0.142501i
$365$	26.4668			1.38533
$366$		0			0
$367$	5.50227	−	6.89963i	0.287216	−	0.360158i	−0.617202	−	0.786805i	$-0.711734\pi$
$367$	5.50227	−	6.89963i	0.287216	−	0.360158i	0.904418	+	0.426647i	$0.140305\pi$
$368$	0.390638	−	1.71150i	0.0203634	−	0.0892180i
$369$		0			0
$370$	25.0178	+	31.3713i	1.30061	+	1.63092i
$371$	−3.67873	−	1.77158i	−0.190990	−	0.0919759i
$372$		0			0
$373$	−13.5551	+	16.9976i	−0.701857	+	0.880101i	−0.997161	−	0.0753021i	$-0.976008\pi$
$373$	−13.5551	+	16.9976i	−0.701857	+	0.880101i	0.295303	+	0.955404i	$0.404579\pi$
$374$	−29.9298	−	37.5308i	−1.54763	−	1.94067i
$375$		0			0
$376$	−26.6318			−1.37343
$377$	−0.564225	+	5.87887i	−0.0290591	+	0.302777i
$378$		0			0
$379$	−16.9047	+	8.14088i	−0.868337	+	0.418169i	−0.814351	−	0.580373i	$-0.802907\pi$
$379$	−16.9047	+	8.14088i	−0.868337	+	0.418169i	−0.0539861	+	0.998542i	$0.517193\pi$
$380$	2.70976	+	3.39793i	0.139008	+	0.174310i
$381$		0			0
$382$	16.3040	−	7.85161i	0.834187	−	0.401723i
$383$	−32.7559	−	15.7744i	−1.67375	−	0.806035i	−0.997598	−	0.0692728i	$-0.977932\pi$
$383$	−32.7559	−	15.7744i	−1.67375	−	0.806035i	−0.676152	−	0.736762i	$-0.736354\pi$
$384$		0			0
$385$	1.84611	−	8.08833i	0.0940864	−	0.412220i
$386$	7.97064	−	34.9217i	0.405695	−	1.77747i
$387$		0			0
$388$	11.3237	+	49.6125i	0.574876	+	2.51870i
$389$	7.01594			0.355722			0.177861	−	0.984056i	$-0.443082\pi$
$389$	7.01594			0.355722			0.177861	+	0.984056i	$0.443082\pi$
$390$		0			0
$391$	−37.8084	−	18.2076i	−1.91205	−	0.920796i
$392$	−17.2909	−	8.32688i	−0.873324	−	0.420571i
$393$		0			0
$394$	−28.4258			−1.43207
$395$	−3.85489	−	16.8894i	−0.193961	−	0.849798i
$396$		0			0
$397$	7.78785	−	34.1208i	0.390861	−	1.71247i	−0.270771	−	0.962644i	$-0.587279\pi$
$397$	7.78785	−	34.1208i	0.390861	−	1.71247i	0.661632	−	0.749829i	$-0.269864\pi$
$398$	4.47084	−	19.5880i	0.224103	−	0.981860i
$399$		0			0
$400$	−2.19398	−	1.05656i	−0.109699	−	0.0528282i
$401$	3.88389	−	1.87038i	0.193952	−	0.0934025i	−0.334387	−	0.942436i	$-0.608529\pi$
$401$	3.88389	−	1.87038i	0.193952	−	0.0934025i	0.528339	+	0.849033i	$0.322815\pi$
$402$		0			0
$403$	5.14875	+	6.45632i	0.256477	+	0.321612i
$404$	37.7875	−	18.1975i	1.88000	−	0.905360i
$405$		0			0
$406$	6.86404	+	6.64094i	0.340656	+	0.329584i
$407$	−14.1573			−0.701750
$408$		0			0
$409$	13.3553	+	16.7470i	0.660376	+	0.828085i	0.993384	−	0.114839i	$-0.0366352\pi$
$409$	13.3553	+	16.7470i	0.660376	+	0.828085i	−0.333008	+	0.942924i	$0.608064\pi$
$410$	−13.4912	+	16.9174i	−0.666282	+	0.835491i
$411$		0			0
$412$	56.0166	+	26.9761i	2.75974	+	1.32902i
$413$	1.93420	+	2.42541i	0.0951758	+	0.119347i
$414$		0			0
$415$	13.6384	−	59.7538i	0.669483	−	2.93320i
$416$	3.63237	−	4.55485i	0.178092	−	0.223320i
$417$		0			0
$418$	−2.46247			−0.120444
$419$	5.76940	+	25.2774i	0.281854	+	1.23488i	0.895414	+	0.445234i	$0.146879\pi$
$419$	5.76940	+	25.2774i	0.281854	+	1.23488i	−0.613561	+	0.789648i	$0.710263\pi$
$420$		0			0
$421$	24.0003	+	11.5579i	1.16970	+	0.563299i	0.914895	−	0.403692i	$-0.132273\pi$
$421$	24.0003	+	11.5579i	1.16970	+	0.563299i	0.254808	+	0.966992i	$0.417988\pi$
$422$	5.00666	+	21.9356i	0.243720	+	1.06781i
$423$		0			0
$424$	−3.53329	−	15.4803i	−0.171592	−	0.751792i
$425$	−36.2933	+	45.5103i	−1.76048	+	2.20758i
$426$		0			0
$427$	−0.489381	+	2.14412i	−0.0236828	+	0.103761i
$428$	6.72984	+	8.43895i	0.325299	+	0.407912i
$429$		0			0
$430$	42.8187	−	20.6204i	2.06490	−	0.994404i
$431$	−5.50492	+	6.90295i	−0.265163	+	0.332503i	−0.896532	−	0.442979i	$-0.853922\pi$
$431$	−5.50492	+	6.90295i	−0.265163	+	0.332503i	0.631370	+	0.775482i	$0.282493\pi$
$432$		0			0
$433$	−24.9676	+	12.0238i	−1.19987	+	0.577825i	−0.923637	−	0.383267i	$-0.874799\pi$
$433$	−24.9676	+	12.0238i	−1.19987	+	0.577825i	−0.276228	+	0.961092i	$0.589084\pi$
$434$	13.3544			0.641034
$435$		0			0
$436$	−4.00562			−0.191834
$437$	−1.93948	+	0.934004i	−0.0927779	+	0.0446795i
$438$		0			0
$439$	−18.7714	+	23.5386i	−0.895910	+	1.12344i	0.0958585	+	0.995395i	$0.469440\pi$
$439$	−18.7714	+	23.5386i	−0.895910	+	1.12344i	−0.991769	+	0.128041i	$0.959131\pi$
$440$	29.0681	−	13.9985i	1.38577	−	0.667350i
$441$		0			0
$442$	11.0970	+	13.9152i	0.527829	+	0.661876i
$443$	4.73026	−	20.7246i	0.224742	−	0.984658i	−0.729114	−	0.684392i	$-0.760068\pi$
$443$	4.73026	−	20.7246i	0.224742	−	0.984658i	0.953856	−	0.300265i	$-0.0970752\pi$
$444$		0			0
$445$	−15.9821	+	20.0409i	−0.757623	+	0.950030i
$446$	−5.53289	−	24.2412i	−0.261990	−	1.14785i
$447$		0			0
$448$	−2.19754	−	9.62805i	−0.103824	−	0.454883i
$449$	27.4918	+	13.2394i	1.29742	+	0.624805i	0.949808	−	0.312834i	$-0.101278\pi$
$449$	27.4918	+	13.2394i	1.29742	+	0.624805i	0.347612	+	0.937638i	$0.386993\pi$
$450$		0			0
$451$	−1.69884	−	7.44309i	−0.0799951	−	0.350481i
$452$	−47.0341			−2.21230
$453$		0			0
$454$	7.04361	−	8.83240i	0.330573	−	0.414525i
$455$	−0.684475	+	2.99888i	−0.0320887	+	0.140590i
$456$		0			0
$457$	−2.28489	−	2.86516i	−0.106882	−	0.134026i	0.725513	−	0.688208i	$-0.241603\pi$
$457$	−2.28489	−	2.86516i	−0.106882	−	0.134026i	−0.832395	+	0.554182i	$0.813031\pi$
$458$	6.75109	+	3.25116i	0.315458	+	0.151917i
$459$		0			0
$460$	44.6166	−	55.9474i	2.08026	−	2.60856i
$461$	−20.7699	−	26.0446i	−0.967348	−	1.21302i	−0.977038	−	0.213064i	$-0.931656\pi$
$461$	−20.7699	−	26.0446i	−0.967348	−	1.21302i	0.00968987	−	0.999953i	$-0.496916\pi$
$462$		0			0
$463$	−18.0503			−0.838868			−0.419434	−	0.907786i	$-0.637771\pi$
$463$	−18.0503			−0.838868			−0.419434	+	0.907786i	$0.637771\pi$
$464$	−0.151705	+	1.58067i	−0.00704273	+	0.0733808i
$465$		0			0
$466$	−11.0432	+	5.31812i	−0.511566	+	0.246357i
$467$	−13.1851	−	16.5336i	−0.610133	−	0.765083i	0.376786	−	0.926300i	$-0.377029\pi$
$467$	−13.1851	−	16.5336i	−0.610133	−	0.765083i	−0.986919	+	0.161218i	$0.948458\pi$
$468$		0			0
$469$	6.90521	−	3.32537i	0.318853	−	0.153551i
$470$	−67.1517	−	32.3385i	−3.09748	−	1.49167i
$471$		0			0
$472$	−2.68450	+	11.7616i	−0.123564	+	0.541370i
$473$	−3.73126	+	16.3477i	−0.171563	+	0.751668i
$474$		0			0
$475$	0.664454	+	2.91116i	0.0304872	+	0.133573i
$476$	17.9233			0.821515
$477$		0			0
$478$	−21.2053	−	10.2119i	−0.969907	−	0.467083i
$479$	10.7410	+	5.17260i	0.490769	+	0.236342i	0.662866	−	0.748738i	$-0.269340\pi$
$479$	10.7410	+	5.17260i	0.490769	+	0.236342i	−0.172097	+	0.985080i	$0.555054\pi$
$480$		0			0
$481$	5.24904			0.239336
$482$	−15.4251	−	67.5817i	−0.702593	−	3.07826i
$483$		0			0
$484$	1.65331	−	7.24361i	0.0751503	−	0.329255i
$485$	−12.4905	+	54.7245i	−0.567165	+	2.48491i
$486$		0			0
$487$	2.18739	+	1.05339i	0.0991199	+	0.0477336i	0.482787	−	0.875738i	$-0.339625\pi$
$487$	2.18739	+	1.05339i	0.0991199	+	0.0477336i	−0.383667	+	0.923472i	$0.625339\pi$
$488$	−7.70560	+	3.71082i	−0.348816	+	0.167981i
$489$		0			0
$490$	−33.4876	−	41.9922i	−1.51282	−	1.89701i
$491$	−20.3987	+	9.82349i	−0.920580	+	0.443328i	−0.833278	−	0.552854i	$-0.813539\pi$
$491$	−20.3987	+	9.82349i	−0.920580	+	0.443328i	−0.0873016	+	0.996182i	$0.527824\pi$
$492$		0			0
$493$	36.0304	+	11.9434i	1.62273	+	0.537902i
$494$	0.913003			0.0410779
$495$		0			0
$496$	1.38436	+	1.73593i	0.0621596	+	0.0779457i
$497$	−3.24056	+	4.06353i	−0.145359	+	0.182274i
$498$		0			0
$499$	11.8896	+	5.72571i	0.532250	+	0.256318i	0.680649	−	0.732610i	$-0.261698\pi$
$499$	11.8896	+	5.72571i	0.532250	+	0.256318i	−0.148399	+	0.988928i	$0.547412\pi$
$500$	−24.4182	−	30.6194i	−1.09201	−	1.36934i
$501$		0			0
$502$	8.17062	−	35.7978i	0.364673	−	1.59774i
$503$	−3.59106	+	4.50305i	−0.160118	+	0.200781i	−0.855418	−	0.517938i	$-0.826700\pi$
$503$	−3.59106	+	4.50305i	−0.160118	+	0.200781i	0.695301	+	0.718719i	$0.255271\pi$
$504$		0			0
$505$	46.2625			2.05865
$506$	9.02210	+	39.5284i	0.401081	+	1.75725i
$507$		0			0
$508$	−15.6632	−	7.54301i	−0.694943	−	0.334667i
$509$	4.34035	+	19.0163i	0.192383	+	0.842884i	0.975322	+	0.220786i	$0.0708622\pi$
$509$	4.34035	+	19.0163i	0.192383	+	0.842884i	−0.782940	+	0.622098i	$0.786281\pi$
$510$		0			0
$511$	−1.24591	−	5.45869i	−0.0551158	−	0.241478i
$512$	2.07811	−	2.60587i	0.0918405	−	0.115164i
$513$		0			0
$514$	−10.4363	+	45.7243i	−0.460324	+	2.01681i
$515$	42.7589	+	53.6179i	1.88418	+	2.36269i
$516$		0			0
$517$	23.6929	−	11.4099i	1.04201	−	0.501806i
$518$	5.29253	−	6.63662i	0.232540	−	0.291596i
$519$		0			0
$520$	−10.7775	+	5.19016i	−0.472624	+	0.227604i
$521$	−12.8724			−0.563950			−0.281975	−	0.959422i	$-0.590989\pi$
$521$	−12.8724			−0.563950			−0.281975	+	0.959422i	$0.590989\pi$
$522$		0			0
$523$	37.1488			1.62440			0.812202	−	0.583377i	$-0.198269\pi$
$523$	37.1488			1.62440			0.812202	+	0.583377i	$0.198269\pi$
$524$	−22.1630	+	10.6731i	−0.968193	+	0.466257i
$525$		0			0
$526$	5.60090	−	7.02331i	0.244211	−	0.306231i
$527$	47.8194	−	23.0286i	2.08305	−	1.00314i
$528$		0			0
$529$	7.75861	+	9.72899i	0.337331	+	0.422999i
$530$	9.88839	−	43.3239i	0.429524	−	1.88187i
$531$		0			0
$532$	0.573252	−	0.718835i	0.0248536	−	0.0311655i
$533$	0.629872	+	2.75965i	0.0272828	+	0.119534i
$534$		0			0
$535$	2.64933	+	11.6075i	0.114541	+	0.501835i
$536$	26.8533	+	12.9319i	1.15988	+	0.558571i
$537$		0			0
$538$	−9.18394	−	40.2375i	−0.395948	−	1.73476i
$539$	18.9503			0.816247
$540$		0			0
$541$	−0.771832	+	0.967846i	−0.0331836	+	0.0416110i	−0.798146	−	0.602464i	$-0.794186\pi$
$541$	−0.771832	+	0.967846i	−0.0331836	+	0.0416110i	0.764963	+	0.644074i	$0.222757\pi$
$542$	10.7349	−	47.0325i	0.461101	−	2.02022i
$543$		0			0
$544$	−23.3460	−	29.2750i	−1.00095	−	1.25515i
$545$	−3.98079	−	1.91705i	−0.170518	−	0.0821173i
$546$		0			0
$547$	−15.2640	+	19.1405i	−0.652643	+	0.818388i	−0.992520	−	0.122082i	$-0.961043\pi$
$547$	−15.2640	+	19.1405i	−0.652643	+	0.818388i	0.339877	+	0.940470i	$0.389614\pi$
$548$	11.9425	+	14.9754i	0.510159	+	0.639719i
$549$		0			0
$550$	56.2413			2.39814
$551$	1.63138	−	1.06305i	0.0694992	−	0.0452874i
$552$		0			0
$553$	−3.30191	+	1.59012i	−0.140412	+	0.0676187i
$554$	−4.05882	−	5.08960i	−0.172443	−	0.216237i
$555$		0			0
$556$	66.5308	−	32.0395i	2.82153	−	1.35878i
$557$	−6.76892	−	3.25974i	−0.286808	−	0.138120i	0.284948	−	0.958543i	$-0.408024\pi$
$557$	−6.76892	−	3.25974i	−0.286808	−	0.138120i	−0.571757	+	0.820423i	$0.693738\pi$
$558$		0			0
$559$	1.38343	−	6.06118i	0.0585126	−	0.256361i
$560$	−0.184037	+	0.806320i	−0.00777699	+	0.0340732i
$561$		0			0
$562$	−10.8626	−	47.5920i	−0.458209	−	2.00755i
$563$	0.0530158			0.00223435			0.00111717	−	0.999999i	$-0.499644\pi$
$563$	0.0530158			0.00223435			0.00111717	+	0.999999i	$0.499644\pi$
$564$		0			0
$565$	−46.7426	−	22.5100i	−1.96648	−	0.947005i
$566$	60.8494	+	29.3035i	2.55769	+	1.23172i
$567$		0			0
$568$	−20.2121			−0.848079
$569$	−6.00338	−	26.3025i	−0.251675	−	1.10266i	−0.929902	−	0.367807i	$-0.880109\pi$
$569$	−6.00338	−	26.3025i	−0.251675	−	1.10266i	0.678227	−	0.734852i	$-0.262748\pi$
$570$		0			0
$571$	0.0985468	−	0.431762i	0.00412405	−	0.0180687i	−0.972824	−	0.231546i	$-0.925622\pi$
$571$	0.0985468	−	0.431762i	0.00412405	−	0.0180687i	0.976948	+	0.213477i	$0.0684789\pi$
$572$	2.38284	−	10.4399i	0.0996316	−	0.436514i
$573$		0			0
$574$	4.12425	+	1.98613i	0.172143	+	0.0828996i
$575$	44.2965	−	21.3321i	1.84729	−	0.889608i
$576$		0			0
$577$	15.8054	+	19.8194i	0.657989	+	0.825092i	0.993123	−	0.117078i	$-0.0373529\pi$
$577$	15.8054	+	19.8194i	0.657989	+	0.825092i	−0.335134	+	0.942171i	$0.608781\pi$
$578$	67.7993	−	32.6504i	2.82008	−	1.35808i
$579$		0			0
$580$	−33.5277	+	55.3685i	−1.39216	+	2.29905i
$581$	−12.9660			−0.537922
$582$		0			0
$583$	9.77562	+	12.2582i	0.404865	+	0.507685i
$584$	13.5758	−	17.0235i	0.561771	−	0.704438i
$585$		0			0
$586$	−34.7434	−	16.7315i	−1.43524	−	0.691173i
$587$	10.5083	+	13.1770i	0.433725	+	0.543874i	0.949877	−	0.312623i	$-0.101207\pi$
$587$	10.5083	+	13.1770i	0.433725	+	0.543874i	−0.516152	+	0.856497i	$0.672636\pi$
$588$		0			0
$589$	0.605846	−	2.65439i	0.0249635	−	0.109372i
$590$	−21.0508	+	26.3969i	−0.866647	+	1.08674i
$591$		0			0
$592$	1.41133			0.0580052
$593$	−9.11752	−	39.9464i	−0.374411	−	1.64040i	−0.714229	−	0.699912i	$-0.753222\pi$
$593$	−9.11752	−	39.9464i	−0.374411	−	1.64040i	0.339817	−	0.940491i	$-0.389635\pi$
$594$		0			0
$595$	17.8123	+	8.57793i	0.730231	+	0.351661i
$596$	14.0669	+	61.6310i	0.576201	+	2.52450i
$597$		0			0
$598$	−3.34509	−	14.6558i	−0.136791	−	0.599321i
$599$	−9.55967	+	11.9874i	−0.390597	+	0.489794i	−0.937785	−	0.347216i	$-0.887127\pi$
$599$	−9.55967	+	11.9874i	−0.390597	+	0.489794i	0.547188	+	0.837010i	$0.315698\pi$
$600$		0			0
$601$	5.21924	−	22.8670i	0.212897	−	0.932764i	−0.749689	−	0.661790i	$-0.769797\pi$
$601$	5.21924	−	22.8670i	0.212897	−	0.932764i	0.962587	−	0.270974i	$-0.0873458\pi$
$602$	−6.26856	−	7.86052i	−0.255487	−	0.320371i
$603$		0			0
$604$	21.5146	−	10.3609i	0.875415	−	0.421578i
$605$	5.10978	−	6.40746i	0.207742	−	0.260500i
$606$		0			0
$607$	−13.1732	+	6.34390i	−0.534685	+	0.257491i	−0.681685	−	0.731646i	$-0.738753\pi$
$607$	−13.1732	+	6.34390i	−0.534685	+	0.257491i	0.147000	+	0.989137i	$0.453038\pi$
$608$	−1.92079			−0.0778984
$609$		0			0
$610$	−23.9355			−0.969122
$611$	−8.78452	+	4.23040i	−0.355383	+	0.171144i
$612$		0			0
$613$	−20.5363	+	25.7517i	−0.829453	+	1.04010i	0.169061	+	0.985606i	$0.445926\pi$
$613$	−20.5363	+	25.7517i	−0.829453	+	1.04010i	−0.998514	+	0.0544951i	$0.982645\pi$
$614$	−57.0178	+	27.4583i	−2.30105	+	1.10813i
$615$		0			0
$616$	−4.25550	−	5.33623i	−0.171459	−	0.215003i
$617$	3.27811	−	14.3623i	0.131972	−	0.578206i	−0.865091	−	0.501615i	$-0.832739\pi$
$617$	3.27811	−	14.3623i	0.131972	−	0.578206i	0.997063	−	0.0765909i	$-0.0244036\pi$
$618$		0			0
$619$	−9.17298	+	11.5026i	−0.368693	+	0.462327i	−0.931223	−	0.364450i	$-0.881257\pi$
$619$	−9.17298	+	11.5026i	−0.368693	+	0.462327i	0.562529	+	0.826777i	$0.309828\pi$
$620$	20.1397	+	88.2380i	0.808832	+	3.54372i
$621$		0			0
$622$	0.603774	+	2.64531i	0.0242091	+	0.106067i
$623$	4.88572	+	2.35284i	0.195742	+	0.0942644i
$624$		0			0
$625$	−0.424495	−	1.85983i	−0.0169798	−	0.0743934i
$626$	13.2570			0.529857
$627$		0			0
$628$	−34.4779	+	43.2340i	−1.37582	+	1.72522i
$629$	7.50712	−	32.8908i	0.299328	−	1.31144i
$630$		0			0
$631$	23.0230	+	28.8699i	0.916532	+	1.14929i	0.988399	+	0.151880i	$0.0485328\pi$
$631$	23.0230	+	28.8699i	0.916532	+	1.14929i	−0.0718673	+	0.997414i	$0.522896\pi$
$632$	−12.8406	−	6.18372i	−0.510773	−	0.245975i
$633$		0			0
$634$	−6.51320	+	8.16729i	−0.258672	+	0.324365i
$635$	−11.9561	−	14.9925i	−0.474465	−	0.594960i
$636$		0			0
$637$	−7.02613			−0.278385
$638$	−12.6830	−	34.4118i	−0.502123	−	1.36237i
$639$		0			0
$640$	61.9828	−	29.8493i	2.45009	−	1.17990i
$641$	26.5895	+	33.3422i	1.05022	+	1.31694i	0.946632	+	0.322317i	$0.104462\pi$
$641$	26.5895	+	33.3422i	1.05022	+	1.31694i	0.103591	+	0.994620i	$0.466967\pi$
$642$		0			0
$643$	−3.14831	+	1.51615i	−0.124157	+	0.0597910i	−0.494931	−	0.868932i	$-0.664807\pi$
$643$	−3.14831	+	1.51615i	−0.124157	+	0.0597910i	0.370774	+	0.928723i	$0.379092\pi$
$644$	−13.6393	−	6.56833i	−0.537463	−	0.258828i
$645$		0			0
$646$	1.30577	−	5.72093i	0.0513747	−	0.225087i
$647$	−3.98049	+	17.4397i	−0.156489	+	0.685625i	0.834424	+	0.551123i	$0.185800\pi$
$647$	−3.98049	+	17.4397i	−0.156489	+	0.685625i	−0.990913	+	0.134502i	$0.957057\pi$
$648$		0			0
$649$	−2.65076	−	11.6137i	−0.104051	−	0.455879i
$650$	−20.8524			−0.817898
$651$		0			0
$652$	3.80439	+	1.83210i	0.148991	+	0.0717505i
$653$	21.9220	+	10.5571i	0.857873	+	0.413130i	0.810494	−	0.585747i	$-0.199199\pi$
$653$	21.9220	+	10.5571i	0.857873	+	0.413130i	0.0473790	+	0.998877i	$0.484913\pi$
$654$		0			0
$655$	−27.1336			−1.06020
$656$	0.169356	+	0.741996i	0.00661223	+	0.0289701i
$657$		0			0
$658$	−3.50859	+	15.3721i	−0.136779	+	0.599268i
$659$	4.48212	−	19.6374i	0.174598	−	0.764966i	−0.809468	−	0.587164i	$-0.800244\pi$
$659$	4.48212	−	19.6374i	0.174598	−	0.764966i	0.984066	−	0.177802i	$-0.0568985\pi$
$660$		0			0
$661$	20.2302	+	9.74233i	0.786862	+	0.378933i	0.783761	−	0.621063i	$-0.213299\pi$
$661$	20.2302	+	9.74233i	0.786862	+	0.378933i	0.00310069	+	0.999995i	$0.499013\pi$
$662$	−20.1183	+	9.68845i	−0.781919	+	0.376552i
$663$		0			0
$664$	−31.4381	−	39.4222i	−1.22004	−	1.52988i
$665$	0.913726	−	0.440027i	0.0354328	−	0.0170635i
$666$		0			0
$667$	−23.0415	−	22.2926i	−0.892170	−	0.863174i
$668$	−46.8138			−1.81128
$669$		0			0
$670$	52.0072	+	65.2149i	2.00921	+	2.51947i
$671$	5.26542	−	6.60263i	0.203269	−	0.254892i
$672$		0			0
$673$	0.866965	+	0.417509i	0.0334191	+	0.0160938i	0.450519	−	0.892767i	$-0.351239\pi$
$673$	0.866965	+	0.417509i	0.0334191	+	0.0160938i	−0.417100	+	0.908861i	$0.636953\pi$
$674$	−44.3718	−	55.6405i	−1.70914	−	2.14319i
$675$		0			0
$676$	8.66573	−	37.9671i	0.333297	−	1.46027i
$677$	7.63427	−	9.57307i	0.293409	−	0.367923i	−0.613176	−	0.789946i	$-0.710108\pi$
$677$	7.63427	−	9.57307i	0.293409	−	0.367923i	0.906585	+	0.422023i	$0.138680\pi$
$678$		0			0
$679$	11.8747			0.455710
$680$	17.1080	+	74.9553i	0.656064	+	2.87440i
$681$		0			0
$682$	−46.2022	−	22.2498i	−1.76917	−	0.851989i
$683$	10.5464	+	46.2069i	0.403548	+	1.76806i	0.612842	+	0.790206i	$0.290026\pi$
$683$	10.5464	+	46.2069i	0.403548	+	1.76806i	−0.209294	+	0.977853i	$0.567117\pi$
$684$		0			0
$685$	4.70140	+	20.5982i	0.179631	+	0.787016i
$686$	−14.8248	+	18.5897i	−0.566013	+	0.709758i
$687$		0			0
$688$	0.371966	−	1.62969i	0.0141811	−	0.0621314i
$689$	−3.62447	−	4.54495i	−0.138081	−	0.173149i
$690$		0			0
$691$	4.27851	−	2.06042i	0.162762	−	0.0783822i	−0.350729	−	0.936477i	$-0.614066\pi$
$691$	4.27851	−	2.06042i	0.162762	−	0.0783822i	0.513491	+	0.858095i	$0.328352\pi$
$692$	−48.9047	+	61.3246i	−1.85908	+	2.33121i
$693$		0			0
$694$	62.2775	−	29.9913i	2.36402	−	1.13845i
$695$	81.4522			3.08966
$696$		0			0
$697$	18.1930			0.689108
$698$	−54.0567	+	26.0323i	−2.04608	+	0.985338i
$699$		0			0
$700$	−13.0927	+	16.4177i	−0.494858	+	0.620532i
$701$	3.35536	−	1.61586i	0.126730	−	0.0610301i	−0.369444	−	0.929253i	$-0.620452\pi$
$701$	3.35536	−	1.61586i	0.126730	−	0.0610301i	0.496175	+	0.868223i	$0.334738\pi$
$702$		0			0
$703$	−1.07902	−	1.35305i	−0.0406960	−	0.0510311i
$704$	−8.43848	+	36.9714i	−0.318037	+	1.39341i
$705$		0			0
$706$	21.7078	−	27.2207i	0.816983	−	1.02446i
$707$	−2.17778	−	9.54148i	−0.0819039	−	0.358844i
$708$		0			0
$709$	−1.06035	−	4.64570i	−0.0398223	−	0.174473i	0.951106	−	0.308865i	$-0.0999491\pi$
$709$	−1.06035	−	4.64570i	−0.0398223	−	0.174473i	−0.990928	+	0.134392i	$0.957092\pi$
$710$	−50.9644	−	24.5432i	−1.91266	−	0.921088i
$711$		0			0
$712$	4.69256	+	20.5594i	0.175861	+	0.770498i
$713$	−44.8288			−1.67885
$714$		0			0
$715$	7.36451	−	9.23480i	0.275417	−	0.345362i
$716$	11.1005	−	48.6344i	0.414845	−	1.81755i
$717$		0			0
$718$	6.54680	+	8.20943i	0.244324	+	0.306373i
$719$	−10.1082	−	4.86785i	−0.376972	−	0.181540i	0.235797	−	0.971802i	$-0.424230\pi$
$719$	−10.1082	−	4.86785i	−0.376972	−	0.181540i	−0.612769	+	0.790262i	$0.709944\pi$
$720$		0			0
$721$	9.04566	−	11.3429i	0.336878	−	0.422432i
$722$	27.0873	+	33.9664i	1.00808	+	1.26410i
$723$		0			0
$724$	0.336572			0.0125086
$725$	−37.2597	+	24.2793i	−1.38379	+	0.901712i
$726$		0			0
$727$	38.2910	−	18.4400i	1.42013	−	0.683901i	0.443000	−	0.896522i	$-0.353914\pi$
$727$	38.2910	−	18.4400i	1.42013	−	0.683901i	0.977135	+	0.212621i	$0.0681999\pi$
$728$	1.57780	+	1.97849i	0.0584770	+	0.0733279i
$729$		0			0
$730$	54.9025	−	26.4397i	2.03203	−	0.978576i
$731$	−36.0012	−	17.3373i	−1.33155	−	0.641242i
$732$		0			0
$733$	1.89309	−	8.29416i	0.0699228	−	0.306352i	−0.927858	−	0.372933i	$-0.878352\pi$
$733$	1.89309	−	8.29416i	0.0699228	−	0.306352i	0.997781	+	0.0665813i	$0.0212092\pi$
$734$	4.52132	−	19.8092i	0.166885	−	0.731170i
$735$		0			0
$736$	7.03747	+	30.8332i	0.259405	+	1.13653i
$737$	−29.4303			−1.08408
$738$		0			0
$739$	−10.7096	−	5.15748i	−0.393960	−	0.189721i	0.226407	−	0.974033i	$-0.427302\pi$
$739$	−10.7096	−	5.15748i	−0.393960	−	0.189721i	−0.620367	+	0.784312i	$0.713016\pi$
$740$	51.8323	+	24.9611i	1.90540	+	0.917590i
$741$		0			0
$742$	−9.40089			−0.345118
$743$	5.36567	+	23.5086i	0.196848	+	0.862445i	0.972799	+	0.231652i	$0.0744132\pi$
$743$	5.36567	+	23.5086i	0.196848	+	0.862445i	−0.775951	+	0.630793i	$0.782730\pi$
$744$		0			0
$745$	−15.5163	+	67.9813i	−0.568472	+	2.49064i
$746$	−11.1385	+	48.8009i	−0.407809	+	1.78673i
$747$		0			0
$748$	−62.0092	−	29.8621i	−2.26728	−	1.09186i
$749$	2.26929	−	1.09283i	0.0829179	−	0.0399312i
$750$		0			0
$751$	−15.1433	−	18.9892i	−0.552589	−	0.692924i	0.424580	−	0.905391i	$-0.360422\pi$
$751$	−15.1433	−	18.9892i	−0.552589	−	0.692924i	−0.977168	+	0.212466i	$0.931850\pi$
$752$	−2.36192	+	1.13744i	−0.0861304	+	0.0414782i
$753$		0			0
$754$	4.70242	+	12.7587i	0.171252	+	0.464645i
$755$	26.3398			0.958604
$756$		0			0
$757$	7.41301	+	9.29563i	0.269431	+	0.337855i	0.898079	−	0.439834i	$-0.144963\pi$
$757$	7.41301	+	9.29563i	0.269431	+	0.337855i	−0.628648	+	0.777690i	$0.716391\pi$
$758$	−26.9345	+	33.7748i	−0.978305	+	1.22676i
$759$		0			0
$760$	3.55334	+	1.71120i	0.128893	+	0.0620717i
$761$	16.9478	+	21.2518i	0.614356	+	0.770378i	0.987538	−	0.157380i	$-0.0503049\pi$
$761$	16.9478	+	21.2518i	0.614356	+	0.770378i	−0.373182	+	0.927758i	$0.621733\pi$
$762$		0			0
$763$	−0.207991	+	0.911269i	−0.00752979	+	0.0329901i
$764$	16.1766	−	20.2848i	0.585248	−	0.733878i
$765$		0			0
$766$	−83.7069			−3.02445
$767$	0.982813	+	4.30599i	0.0354873	+	0.155480i
$768$		0			0
$769$	−11.2515	−	5.41845i	−0.405740	−	0.195394i	0.219871	−	0.975529i	$-0.429436\pi$
$769$	−11.2515	−	5.41845i	−0.405740	−	0.195394i	−0.625612	+	0.780135i	$0.715151\pi$
$770$	−4.25049	−	18.6226i	−0.153177	−	0.671112i
$771$		0			0
$772$	−11.4279	−	50.0688i	−0.411298	−	1.80201i
$773$	20.5967	−	25.8274i	0.740811	−	0.928948i	−0.258502	−	0.966011i	$-0.583229\pi$
$773$	20.5967	−	25.8274i	0.740811	−	0.928948i	0.999313	+	0.0370632i	$0.0118003\pi$
$774$		0			0
$775$	−13.8371	+	60.6245i	−0.497045	+	2.17770i
$776$	28.7921	+	36.1041i	1.03358	+	1.29606i
$777$		0			0
$778$	14.5538	−	7.00875i	0.521780	−	0.251276i
$779$	0.581876	−	0.729649i	0.0208479	−	0.0261424i
$780$		0			0
$781$	17.9816	−	8.65946i	0.643431	−	0.309860i
$782$	−96.6184			−3.45507
$783$		0			0
$784$	−1.88914			−0.0674693
$785$	−54.9556	+	26.4652i	−1.96145	+	0.944584i
$786$		0			0
$787$	−6.39485	+	8.01888i	−0.227952	+	0.285842i	−0.882633	−	0.470063i	$-0.844231\pi$
$787$	−6.39485	+	8.01888i	−0.227952	+	0.285842i	0.654681	+	0.755905i	$0.272803\pi$
$788$	−36.7193	+	17.6831i	−1.30807	+	0.629933i
$789$		0			0
$790$	−24.8686	−	31.1843i	−0.884787	−	1.10949i
$791$	−2.44224	+	10.7002i	−0.0868361	+	0.380454i
$792$		0			0
$793$	−1.95224	+	2.44803i	−0.0693261	+	0.0869322i
$794$	−17.9308	−	78.5598i	−0.636339	−	2.78798i
$795$		0			0
$796$	−6.41005	−	28.0843i	−0.227198	−	0.995420i
$797$	18.0958	+	8.71448i	0.640986	+	0.308683i	0.725997	−	0.687697i	$-0.241378\pi$
$797$	18.0958	+	8.71448i	0.640986	+	0.308683i	−0.0850115	+	0.996380i	$0.527093\pi$
$798$		0			0
$799$	13.9444	+	61.0946i	0.493319	+	2.16137i
$800$	43.8697			1.55103
$801$		0			0
$802$	6.18825	−	7.75983i	0.218515	−	0.274009i
$803$	−4.78425	+	20.9612i	−0.168832	+	0.739703i
$804$		0			0
$805$	−10.4112	−	13.0552i	−0.366947	−	0.460137i
$806$	17.1302	+	8.24949i	0.603387	+	0.290576i
$807$		0			0
$808$	23.7297	−	29.7562i	0.834809	−	1.04682i
$809$	−2.35678	−	2.95530i	−0.0828598	−	0.103903i	0.738674	−	0.674063i	$-0.235453\pi$
$809$	−2.35678	−	2.95530i	−0.0828598	−	0.103903i	−0.821533	+	0.570160i	$0.806881\pi$
$810$		0			0
$811$	−23.1047			−0.811314			−0.405657	−	0.914025i	$-0.632957\pi$
$811$	−23.1047			−0.811314			−0.405657	+	0.914025i	$0.632957\pi$
$812$	12.9979	+	4.30853i	0.456136	+	0.151200i
$813$		0			0
$814$	−29.3678	+	14.1428i	−1.02934	+	0.495704i
$815$	2.90399	+	3.64148i	0.101722	+	0.127556i
$816$		0			0
$817$	−1.84678	+	0.889360i	−0.0646105	+	0.0311148i
$818$	44.4339	+	21.3982i	1.55359	+	0.748172i
$819$		0			0
$820$	−6.90340	+	30.2458i	−0.241077	+	1.05623i
$821$	−4.34274	+	19.0268i	−0.151563	+	0.664039i	0.840869	+	0.541239i	$0.182045\pi$
$821$	−4.34274	+	19.0268i	−0.151563	+	0.664039i	−0.992431	+	0.122800i	$0.960813\pi$
$822$		0			0
$823$	1.64107	+	7.18999i	0.0572040	+	0.250627i	0.995443	−	0.0953614i	$-0.0304007\pi$
$823$	1.64107	+	7.18999i	0.0572040	+	0.250627i	−0.938239	+	0.345989i	$0.887544\pi$
$824$	56.4198			1.96548
$825$		0			0
$826$	6.43522	+	3.09904i	0.223910	+	0.107829i
$827$	−0.392890	−	0.189206i	−0.0136621	−	0.00657934i	0.427040	−	0.904233i	$-0.359556\pi$
$827$	−0.392890	−	0.189206i	−0.0136621	−	0.00657934i	−0.440702	+	0.897653i	$0.645271\pi$
$828$		0			0
$829$	31.6819			1.10036			0.550180	−	0.835046i	$-0.314559\pi$
$829$	31.6819			1.10036			0.550180	+	0.835046i	$0.314559\pi$
$830$	−31.4011	−	137.577i	−1.08995	−	4.77538i
$831$		0			0
$832$	3.12870	−	13.7077i	0.108468	−	0.475231i
$833$	−10.0487	+	44.0262i	−0.348166	+	1.52542i
$834$		0			0
$835$	−46.5237	−	22.4046i	−1.61002	−	0.775344i
$836$	−3.18092	+	1.53185i	−0.110015	+	0.0529802i
$837$		0			0
$838$	37.2195	+	46.6718i	1.28573	+	1.61225i
$839$	−8.73420	+	4.20617i	−0.301538	+	0.145213i	−0.578535	−	0.815658i	$-0.696375\pi$
$839$	−8.73420	+	4.20617i	−0.301538	+	0.145213i	0.276997	+	0.960871i	$0.410661\pi$
$840$		0			0
$841$	23.2580	+	17.3225i	0.801998	+	0.597326i
$842$	61.3321			2.11365
$843$		0			0
$844$	20.1131	+	25.2210i	0.692321	+	0.868143i
$845$	26.7827	−	33.5844i	0.921352	−	1.15534i
$846$		0			0
$847$	−1.56206	−	0.752247i	−0.0536729	−	0.0258475i
$848$	−0.974524	−	1.22201i	−0.0334653	−	0.0419642i
$849$		0			0
$850$	−29.8228	+	130.662i	−1.02292	+	4.48168i
$851$	−17.7662	+	22.2781i	−0.609017	+	0.763683i
$852$		0			0
$853$	−17.1659			−0.587750			−0.293875	−	0.955844i	$-0.594945\pi$
$853$	−17.1659			−0.587750			−0.293875	+	0.955844i	$0.594945\pi$
$854$	1.12675	+	4.93663i	0.0385567	+	0.168928i
$855$		0			0
$856$	8.82490	+	4.24985i	0.301629	+	0.145257i
$857$	−5.63717	−	24.6981i	−0.192562	−	0.843670i	−0.975223	−	0.221222i	$-0.928995\pi$
$857$	−5.63717	−	24.6981i	−0.192562	−	0.843670i	0.782661	−	0.622448i	$-0.213862\pi$
$858$		0			0
$859$	3.25796	+	14.2740i	0.111160	+	0.487024i	0.999607	+	0.0280441i	$0.00892790\pi$
$859$	3.25796	+	14.2740i	0.111160	+	0.487024i	−0.888447	+	0.458980i	$0.848215\pi$
$860$	42.4840	−	53.2732i	1.44869	−	1.81660i
$861$		0			0
$862$	−4.52349	+	19.8187i	−0.154071	+	0.675028i
$863$	9.95290	+	12.4805i	0.338801	+	0.424843i	0.921822	−	0.387615i	$-0.126701\pi$
$863$	9.95290	+	12.4805i	0.338801	+	0.424843i	−0.583021	+	0.812457i	$0.698129\pi$
$864$		0			0
$865$	−77.9510	+	37.5392i	−2.65041	+	1.27637i
$866$	−39.7812	+	49.8840i	−1.35182	+	1.69513i
$867$		0			0
$868$	17.2507	−	8.30751i	0.585528	−	0.281975i
$869$	14.0729			0.477390
$870$		0			0
$871$	10.9118			0.369731
$872$	−3.27495	+	1.57713i	−0.110904	+	0.0534084i
$873$		0			0
$874$	−3.09020	+	3.87498i	−0.104527	+	0.131073i
$875$	−8.23376	+	3.96517i	−0.278352	+	0.134047i
$876$		0			0
$877$	−18.7255	−	23.4810i	−0.632314	−	0.792896i	0.357705	−	0.933835i	$-0.383559\pi$
$877$	−18.7255	−	23.4810i	−0.632314	−	0.792896i	−0.990018	+	0.140939i	$0.954988\pi$
$878$	−15.4248	+	67.5805i	−0.520562	+	2.28073i
$879$		0			0
$880$	1.98012	−	2.48299i	0.0667498	−	0.0837016i
$881$	6.62865	+	29.0420i	0.223325	+	0.978450i	0.954956	+	0.296749i	$0.0959023\pi$
$881$	6.62865	+	29.0420i	0.223325	+	0.978450i	−0.731631	+	0.681701i	$0.761241\pi$
$882$		0			0
$883$	4.82282	+	21.1302i	0.162301	+	0.711087i	0.988935	+	0.148347i	$0.0473954\pi$
$883$	4.82282	+	21.1302i	0.162301	+	0.711087i	−0.826634	+	0.562739i	$0.809747\pi$
$884$	22.9909	+	11.0719i	0.773269	+	0.372387i
$885$		0			0
$886$	−10.8910	−	47.7165i	−0.365889	−	1.60307i
$887$	24.4750			0.821791			0.410896	−	0.911682i	$-0.365216\pi$
$887$	24.4750			0.821791			0.410896	+	0.911682i	$0.365216\pi$
$888$		0			0
$889$	−2.52933	+	3.17168i	−0.0848310	+	0.106375i
$890$	−13.1328	+	57.5384i	−0.440211	+	1.92869i
$891$		0			0
$892$	−22.2271	−	27.8719i	−0.744218	−	0.933220i
$893$	2.89626	+	1.39476i	0.0969196	+	0.0466740i
$894$		0			0
$895$	34.3076	−	43.0204i	1.14678	−	1.43801i
$896$	−9.07413	−	11.3786i	−0.303146	−	0.380133i
$897$		0			0
$898$	70.2547			2.34443
$899$	40.2140	−	5.20503i	1.34121	−	0.173597i
$900$		0			0
$901$	−33.6626	+	16.2111i	−1.12146	+	0.540068i
$902$	−10.9595	−	13.7428i	−0.364912	−	0.457585i
$903$		0			0
$904$	−38.4545	+	18.5187i	−1.27898	+	0.615924i
$905$	0.334486	+	0.161080i	0.0111187	+	0.00535448i
$906$		0			0
$907$	−2.22712	+	9.75765i	−0.0739503	+	0.323998i	−0.998350	−	0.0574287i	$-0.981710\pi$
$907$	−2.22712	+	9.75765i	−0.0739503	+	0.323998i	0.924399	+	0.381426i	$0.124567\pi$
$908$	3.60420	−	15.7910i	0.119610	−	0.524044i
$909$		0			0
$910$	1.57594	+	6.90464i	0.0522418	+	0.228886i
$911$	11.6915			0.387357			0.193678	−	0.981065i	$-0.437958\pi$
$911$	11.6915			0.387357			0.193678	+	0.981065i	$0.437958\pi$
$912$		0			0
$913$	44.8584	+	21.6027i	1.48460	+	0.714945i
$914$	−7.60197	−	3.66092i	−0.251451	−	0.121092i
$915$		0			0
$916$	10.7433			0.354968
$917$	1.27730	+	5.59622i	0.0421802	+	0.184804i
$918$		0			0
$919$	1.87286	−	8.20555i	0.0617800	−	0.270676i	−0.934598	−	0.355704i	$-0.884241\pi$
$919$	1.87286	−	8.20555i	0.0617800	−	0.270676i	0.996379	+	0.0850284i	$0.0270981\pi$
$920$	14.4498	−	63.3089i	0.476397	−	2.08723i
$921$		0			0
$922$	−69.1027	−	33.2781i	−2.27578	−	1.09596i
$923$	−6.66696	+	3.21064i	−0.219446	+	0.105679i
$924$		0			0
$925$	24.6441	+	30.9027i	0.810293	+	1.01607i
$926$	−37.4434	+	18.0318i	−1.23047	+	0.592561i
$927$		0			0
$928$	−9.89303	−	26.8420i	−0.324755	−	0.881133i
$929$	−42.9195			−1.40814			−0.704072	−	0.710129i	$-0.748637\pi$
$929$	−42.9195			−1.40814			−0.704072	+	0.710129i	$0.748637\pi$
$930$		0			0
$931$	1.44433	+	1.81113i	0.0473359	+	0.0593573i
$932$	−10.9569	+	13.7395i	−0.358904	+	0.450051i
$933$		0			0
$934$	−43.8677	−	21.1256i	−1.43539	−	0.691250i
$935$	−47.3332	−	59.3540i	−1.54796	−	1.94108i
$936$		0			0
$937$	−0.00329238	+	0.0144249i	−0.000107557	+	0.000471240i	−0.974982	−	0.222285i	$-0.928648\pi$
$937$	−0.00329238	+	0.0144249i	−0.000107557	+	0.000471240i	0.974874	+	0.222757i	$0.0715055\pi$
$938$	11.0021	−	13.7963i	0.359233	−	0.450464i
$939$		0			0
$940$	−106.861			−3.48542
$941$	−2.85918	−	12.5269i	−0.0932065	−	0.408365i	0.906704	−	0.421768i	$-0.138590\pi$
$941$	−2.85918	−	12.5269i	−0.0932065	−	0.408365i	−0.999910	+	0.0134038i	$0.995733\pi$
$942$		0			0
$943$	−13.8445	−	6.66714i	−0.450837	−	0.217112i
$944$	0.264252	+	1.15776i	0.00860068	+	0.0376820i
$945$		0			0
$946$	8.59086	+	37.6390i	0.279313	+	1.22375i
$947$	−0.894121	+	1.12119i	−0.0290550	+	0.0364338i	−0.796147	−	0.605104i	$-0.793132\pi$
$947$	−0.894121	+	1.12119i	−0.0290550	+	0.0364338i	0.767092	+	0.641537i	$0.221703\pi$
$948$		0			0
$949$	1.77384	−	7.77170i	0.0575813	−	0.252280i
$950$	4.28652	+	5.37513i	0.139073	+	0.174392i
$951$		0			0
$952$	14.6539	−	7.05696i	0.474936	−	0.228717i
$953$	−20.7527	+	26.0231i	−0.672246	+	0.842970i	−0.994614	−	0.103644i	$-0.966950\pi$
$953$	−20.7527	+	26.0231i	−0.672246	+	0.842970i	0.322368	+	0.946614i	$0.395521\pi$
$954$		0			0
$955$	25.7844	−	12.4171i	0.834364	−	0.401808i
$956$	−33.7448			−1.09138
$957$		0			0
$958$	27.4484			0.886817
$959$	4.02699	−	1.93930i	0.130038	−	0.0626232i
$960$		0			0
$961$	16.0229	−	20.0920i	0.516867	−	0.648130i
$962$	10.8886	−	5.24366i	0.351062	−	0.169062i
$963$		0			0
$964$	−61.9666	−	77.7037i	−1.99581	−	2.50267i
$965$	12.6054	−	55.2277i	0.405781	−	1.77784i
$966$		0			0
$967$	−16.1134	+	20.2056i	−0.518172	+	0.649767i	−0.970220	−	0.242226i	$-0.922122\pi$
$967$	−16.1134	+	20.2056i	−0.518172	+	0.649767i	0.452048	+	0.891994i	$0.350694\pi$
$968$	−1.50030	−	6.57325i	−0.0482215	−	0.211272i
$969$		0			0
$970$	28.7582	+	125.998i	0.923369	+	4.04555i
$971$	45.9293	+	22.1184i	1.47394	+	0.709812i	0.986563	−	0.163380i	$-0.0522395\pi$
$971$	45.9293	+	22.1184i	1.47394	+	0.709812i	0.487377	+	0.873192i	$0.337954\pi$
$972$		0			0
$973$	−3.83432	−	16.7992i	−0.122923	−	0.538559i
$974$	5.58981			0.179109
$975$		0			0
$976$	−0.524906	+	0.658211i	−0.0168018	+	0.0210688i
$977$	−8.47901	+	37.1490i	−0.271268	+	1.18850i	0.637251	+	0.770656i	$0.280071\pi$
$977$	−8.47901	+	37.1490i	−0.271268	+	1.18850i	−0.908519	+	0.417844i	$0.862786\pi$
$978$		0			0
$979$	−12.9830	−	16.2802i	−0.414939	−	0.520317i
$980$	−69.3804	−	33.4119i	−2.21628	−	1.06730i
$981$		0			0
$982$	−32.5015	+	40.7556i	−1.03716	+	1.30056i
$983$	−18.4474	−	23.1323i	−0.588379	−	0.737804i	0.395137	−	0.918622i	$-0.370697\pi$
$983$	−18.4474	−	23.1323i	−0.588379	−	0.737804i	−0.983517	+	0.180818i	$0.942126\pi$
$984$		0			0
$985$	−44.9546			−1.43237
$986$	86.6723	−	11.2183i	2.76021	−	0.357262i
$987$		0			0
$988$	1.17938	−	0.567960i	0.0375211	−	0.0180692i
$989$	21.0426	+	26.3866i	0.669115	+	0.839044i
$990$		0			0
$991$	−12.4415	+	5.99153i	−0.395219	+	0.190327i	−0.620928	−	0.783867i	$-0.713244\pi$
$991$	−12.4415	+	5.99153i	−0.395219	+	0.190327i	0.225710	+	0.974195i	$0.427530\pi$
$992$	−36.0389	−	17.3554i	−1.14424	−	0.551035i
$993$		0			0
$994$	−2.66282	+	11.6666i	−0.0844596	+	0.370042i
$995$	7.07052	−	30.9780i	0.224151	−	0.982068i
$996$		0			0
$997$	−4.23365	−	18.5488i	−0.134081	−	0.587448i	−0.996670	−	0.0815420i	$-0.974016\pi$
$997$	−4.23365	−	18.5488i	−0.134081	−	0.587448i	0.862589	−	0.505906i	$-0.168842\pi$
$998$	30.3835			0.961772
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	783.2.k.f.136.9	yes	60
3.2	odd	2	inner	783.2.k.f.136.2	✓	60
29.16	even	7	inner	783.2.k.f.190.9	yes	60
87.74	odd	14	inner	783.2.k.f.190.2	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
783.2.k.f.136.2	✓	60	3.2	odd	2	inner
783.2.k.f.136.9	yes	60	1.1	even	1	trivial
783.2.k.f.190.2	yes	60	87.74	odd	14	inner
783.2.k.f.190.9	yes	60	29.16	even	7	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 783 = 3^{3} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	783.k (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(2.07439 - 0.998975i) q^{2} +(2.05818 - 2.58087i) q^{4} +(3.28060 - 1.57985i) q^{5} +(-0.480272 - 0.602242i) q^{7} +(0.666575 - 2.92046i) q^{8} +(5.22702 - 6.55447i) q^{10} +(0.658197 + 2.88375i) q^{11} +(-0.244037 - 1.06920i) q^{13} +(-1.59790 - 0.769507i) q^{14} +(-0.0656152 - 0.287479i) q^{16} -7.04868 q^{17} +(-0.225442 + 0.282695i) q^{19} +(2.67465 - 11.7184i) q^{20} +(4.24615 + 5.32451i) q^{22} +(5.36389 + 2.58312i) q^{23} +(5.14895 - 6.45657i) q^{25} +(-1.57433 - 1.97415i) q^{26} -2.54279 q^{28} +(-5.11165 - 1.69441i) q^{29} +(-6.78416 + 3.26708i) q^{31} +(3.31211 + 4.15325i) q^{32} +(-14.6217 + 7.04146i) q^{34} +(-2.52703 - 1.21696i) q^{35} +(-1.06504 + 4.66624i) q^{37} +(-0.185250 + 0.811632i) q^{38} +(-2.42713 - 10.6339i) q^{40} -2.58105 q^{41} +(5.10751 + 2.45965i) q^{43} +(8.79728 + 4.23654i) q^{44} +13.7073 q^{46} +(-1.97831 - 8.66752i) q^{47} +(1.42561 - 6.24602i) q^{49} +(4.23098 - 18.5371i) q^{50} +(-3.26174 - 1.57077i) q^{52} +(4.77573 - 2.29987i) q^{53} +(6.71518 + 8.42057i) q^{55} +(-2.07896 + 1.00117i) q^{56} +(-12.2962 + 1.59154i) q^{58} -4.02730 q^{59} +(-1.78011 - 2.23219i) q^{61} +(-10.8093 + 13.5544i) q^{62} +(11.5510 + 5.56265i) q^{64} +(-2.48977 - 3.12207i) q^{65} +(-2.21401 + 9.70022i) q^{67} +(-14.5074 + 18.1917i) q^{68} -6.45777 q^{70} +(-1.50142 - 6.57817i) q^{71} +(6.54889 + 3.15378i) q^{73} +(2.45215 + 10.7436i) q^{74} +(0.265601 + 1.16367i) q^{76} +(1.42060 - 1.78138i) q^{77} +(1.05869 - 4.63843i) q^{79} +(-0.669432 - 0.839441i) q^{80} +(-5.35410 + 2.57840i) q^{82} +(10.4949 - 13.1602i) q^{83} +(-23.1239 + 11.1359i) q^{85} +13.0521 q^{86} +8.86061 q^{88} +(-6.34265 + 3.05446i) q^{89} +(-0.526712 + 0.660475i) q^{91} +(17.7065 - 8.52702i) q^{92} +(-12.7624 - 16.0036i) q^{94} +(-0.292967 + 1.28357i) q^{95} +(-9.61159 + 12.0525i) q^{97} +(-3.28233 - 14.3808i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 10 q^{4} + 4 q^{7} + 4 q^{10} - 24 q^{13} - 26 q^{16} + 4 q^{19} - 8 q^{22} - 16 q^{25} + 112 q^{28} - 4 q^{31} + 26 q^{34} - 18 q^{37} - 78 q^{40} - 8 q^{43} + 72 q^{46} + 14 q^{49} - 12 q^{52}+ \cdots + 8 q^{97}+O(q^{100}) \) 60 * q - 10 * q^4 + 4 * q^7 + 4 * q^10 - 24 * q^13 - 26 * q^16 + 4 * q^19 - 8 * q^22 - 16 * q^25 + 112 * q^28 - 4 * q^31 + 26 * q^34 - 18 * q^37 - 78 * q^40 - 8 * q^43 + 72 * q^46 + 14 * q^49 - 12 * q^52 + 24 * q^55 - 162 * q^58 - 10 * q^61 + 116 * q^64 + 60 * q^67 - 12 * q^70 + 66 * q^73 - 120 * q^76 + 46 * q^79 - 84 * q^82 - 122 * q^85 - 152 * q^88 - 30 * q^91 - 68 * q^94 + 8 * q^97

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