LMFDB - Embedded newform 768.2.s.a.719.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [768,2,Mod(47,768)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("768.47"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(768, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([8, 11, 8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 768 = 2^{8} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	768.s (of order $16$, degree $8$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$6.13251087523$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{16})$
Twist minimal:	no (minimal twist has level 192)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			719.12
Character	$\chi$	$=$	768.719
Dual form			768.2.s.a.47.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.585574 + 1.63006i) q^{3} +(-3.57797 + 2.39072i) q^{5} +(0.994439 - 2.40079i) q^{7} +(-2.31421 - 1.90904i) q^{9} +(0.714367 - 3.59136i) q^{11} +(-1.38986 + 2.08008i) q^{13} +(-1.80186 - 7.23226i) q^{15} +(-0.951204 - 0.951204i) q^{17} +(0.214739 - 0.321380i) q^{19} +(3.33112 + 3.02684i) q^{21} +(1.14288 + 2.75916i) q^{23} +(5.17290 - 12.4885i) q^{25} +(4.46700 - 2.65442i) q^{27} +(-2.53398 + 0.504039i) q^{29} -2.03735 q^{31} +(5.43583 + 3.26747i) q^{33} +(2.18155 + 10.9674i) q^{35} +(4.28668 - 2.86427i) q^{37} +(-2.57679 - 3.48361i) q^{39} +(4.29457 - 1.77887i) q^{41} +(1.88124 - 9.45763i) q^{43} +(12.8442 + 1.29787i) q^{45} +(5.57116 - 5.57116i) q^{47} +(0.174869 + 0.174869i) q^{49} +(2.10752 - 0.993522i) q^{51} +(1.47041 + 0.292483i) q^{53} +(6.02998 + 14.5576i) q^{55} +(0.398124 + 0.538230i) q^{57} +(-3.66506 - 5.48515i) q^{59} +(-4.09381 + 0.814309i) q^{61} +(-6.88455 + 3.65750i) q^{63} -10.7652i q^{65} +(-1.50936 - 7.58806i) q^{67} +(-5.16684 + 0.247277i) q^{69} +(-6.27514 - 2.59925i) q^{71} +(-15.4732 + 6.40920i) q^{73} +(17.3279 + 15.7451i) q^{75} +(-7.91171 - 5.28644i) q^{77} +(-2.31400 + 2.31400i) q^{79} +(1.71111 + 8.83584i) q^{81} +(1.62719 + 1.08726i) q^{83} +(5.67744 + 1.12931i) q^{85} +(0.662214 - 4.42569i) q^{87} +(4.04231 + 1.67438i) q^{89} +(3.61170 + 5.40528i) q^{91} +(1.19302 - 3.32101i) q^{93} +1.66327i q^{95} +1.86899i q^{97} +(-8.50926 + 6.94740i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 8 q^{3} + 16 q^{7} - 8 q^{9} - 16 q^{13} + 8 q^{15} + 16 q^{19} - 8 q^{21} - 16 q^{25} + 8 q^{27} + 32 q^{31} - 16 q^{37} + 8 q^{39} + 16 q^{43} - 8 q^{45} - 16 q^{49} + 8 q^{51} + 80 q^{55} - 8 q^{57}+ \cdots + 8 q^{99}+O(q^{100}) $ 240 * q + 8 * q^3 + 16 * q^7 - 8 * q^9 - 16 * q^13 + 8 * q^15 + 16 * q^19 - 8 * q^21 - 16 * q^25 + 8 * q^27 + 32 * q^31 - 16 * q^37 + 8 * q^39 + 16 * q^43 - 8 * q^45 - 16 * q^49 + 8 * q^51 + 80 * q^55 - 8 * q^57 - 16 * q^61 + 144 * q^67 - 8 * q^69 - 16 * q^73 + 8 * q^75 + 48 * q^79 - 8 * q^81 - 16 * q^85 + 8 * q^87 + 16 * q^91 - 32 * q^93 + 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/768\mathbb{Z}\right)^\times$.

$n$	$257$	$511$	$517$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{16}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.585574	+	1.63006i	−0.338081	+	0.941117i
$3$	−0.585574	+	1.63006i	−0.338081	+	0.941117i
$4$		0			0
$5$	−3.57797	+	2.39072i	−1.60012	+	1.06916i	−0.648796	+	0.760963i	$0.724727\pi$
$5$	−3.57797	+	2.39072i	−1.60012	+	1.06916i	−0.951321	+	0.308201i	$0.900273\pi$
$6$		0			0
$7$	0.994439	−	2.40079i	0.375863	−	0.907413i	−0.616869	−	0.787066i	$-0.711599\pi$
$7$	0.994439	−	2.40079i	0.375863	−	0.907413i	0.992732	−	0.120347i	$-0.0384008\pi$
$8$		0			0
$9$	−2.31421	−	1.90904i	−0.771402	−	0.636348i
$10$		0			0
$11$	0.714367	−	3.59136i	0.215390	−	1.08284i	−0.710111	−	0.704090i	$-0.751355\pi$
$11$	0.714367	−	3.59136i	0.215390	−	1.08284i	0.925500	−	0.378747i	$-0.123645\pi$
$12$		0			0
$13$	−1.38986	+	2.08008i	−0.385479	+	0.576910i	−0.972570	−	0.232611i	$-0.925273\pi$
$13$	−1.38986	+	2.08008i	−0.385479	+	0.576910i	0.587091	+	0.809521i	$0.300273\pi$
$14$		0			0
$15$	−1.80186	−	7.23226i	−0.465239	−	1.86736i
$16$		0			0
$17$	−0.951204	−	0.951204i	−0.230701	−	0.230701i	0.582284	−	0.812985i	$-0.302159\pi$
$17$	−0.951204	−	0.951204i	−0.230701	−	0.230701i	−0.812985	+	0.582284i	$0.802159\pi$
$18$		0			0
$19$	0.214739	−	0.321380i	0.0492646	−	0.0737297i	−0.806020	−	0.591889i	$-0.798382\pi$
$19$	0.214739	−	0.321380i	0.0492646	−	0.0737297i	0.855284	+	0.518159i	$0.173382\pi$
$20$		0			0
$21$	3.33112	+	3.02684i	0.726910	+	0.660510i
$22$		0			0
$23$	1.14288	+	2.75916i	0.238307	+	0.575324i	0.997108	−	0.0759988i	$-0.0242145\pi$
$23$	1.14288	+	2.75916i	0.238307	+	0.575324i	−0.758801	+	0.651322i	$0.774215\pi$
$24$		0			0
$25$	5.17290	−	12.4885i	1.03458	−	2.49769i
$26$		0			0
$27$	4.46700	−	2.65442i	0.859674	−	0.510843i
$28$		0			0
$29$	−2.53398	+	0.504039i	−0.470548	+	0.0935978i	−0.424668	−	0.905349i	$-0.639609\pi$
$29$	−2.53398	+	0.504039i	−0.470548	+	0.0935978i	−0.0458799	+	0.998947i	$0.514609\pi$
$30$		0			0
$31$	−2.03735			−0.365919			−0.182959	−	0.983120i	$-0.558568\pi$
$31$	−2.03735			−0.365919			−0.182959	+	0.983120i	$0.558568\pi$
$32$		0			0
$33$	5.43583	+	3.26747i	0.946257	+	0.568794i
$34$		0			0
$35$	2.18155	+	10.9674i	0.368749	+	1.85383i
$36$		0			0
$37$	4.28668	−	2.86427i	0.704726	−	0.470883i	−0.150852	−	0.988556i	$-0.548202\pi$
$37$	4.28668	−	2.86427i	0.704726	−	0.470883i	0.855578	+	0.517674i	$0.173202\pi$
$38$		0			0
$39$	−2.57679	−	3.48361i	−0.412617	−	0.557823i
$40$		0			0
$41$	4.29457	−	1.77887i	0.670699	−	0.277813i	−0.0212338	−	0.999775i	$-0.506759\pi$
$41$	4.29457	−	1.77887i	0.670699	−	0.277813i	0.691933	+	0.721962i	$0.256759\pi$
$42$		0			0
$43$	1.88124	−	9.45763i	0.286886	−	1.44228i	−0.521312	−	0.853366i	$-0.674557\pi$
$43$	1.88124	−	9.45763i	0.286886	−	1.44228i	0.808199	−	0.588910i	$-0.200443\pi$
$44$		0			0
$45$	12.8442	+	1.29787i	1.91469	+	0.193475i
$46$		0			0
$47$	5.57116	−	5.57116i	0.812637	−	0.812637i	−0.172392	−	0.985028i	$-0.555150\pi$
$47$	5.57116	−	5.57116i	0.812637	−	0.812637i	0.985028	+	0.172392i	$0.0551495\pi$
$48$		0			0
$49$	0.174869	+	0.174869i	0.0249813	+	0.0249813i
$50$		0			0
$51$	2.10752	−	0.993522i	0.295112	−	0.139121i
$52$		0			0
$53$	1.47041	+	0.292483i	0.201977	+	0.0401757i	0.295042	−	0.955484i	$-0.404666\pi$
$53$	1.47041	+	0.292483i	0.201977	+	0.0401757i	−0.0930650	+	0.995660i	$0.529666\pi$
$54$		0			0
$55$	6.02998	+	14.5576i	0.813082	+	1.96295i
$56$		0			0
$57$	0.398124	+	0.538230i	0.0527328	+	0.0712903i
$58$		0			0
$59$	−3.66506	−	5.48515i	−0.477150	−	0.714105i	0.512328	−	0.858790i	$-0.328783\pi$
$59$	−3.66506	−	5.48515i	−0.477150	−	0.714105i	−0.989478	+	0.144685i	$0.953783\pi$
$60$		0			0
$61$	−4.09381	+	0.814309i	−0.524158	+	0.104262i	−0.450075	−	0.892991i	$-0.648603\pi$
$61$	−4.09381	+	0.814309i	−0.524158	+	0.104262i	−0.0740827	+	0.997252i	$0.523603\pi$
$62$		0			0
$63$	−6.88455	+	3.65750i	−0.867372	+	0.460801i
$64$		0			0
$65$		−	10.7652i		−	1.33526i
$66$		0			0
$67$	−1.50936	−	7.58806i	−0.184398	−	0.927029i	−0.956545	−	0.291585i	$-0.905817\pi$
$67$	−1.50936	−	7.58806i	−0.184398	−	0.927029i	0.772147	−	0.635444i	$-0.219183\pi$
$68$		0			0
$69$	−5.16684	+	0.247277i	−0.622014	+	0.0297686i
$70$		0			0
$71$	−6.27514	−	2.59925i	−0.744722	−	0.308474i	−0.0221361	−	0.999755i	$-0.507047\pi$
$71$	−6.27514	−	2.59925i	−0.744722	−	0.308474i	−0.722586	+	0.691281i	$0.757047\pi$
$72$		0			0
$73$	−15.4732	+	6.40920i	−1.81100	+	0.750140i	−0.829543	+	0.558443i	$0.811399\pi$
$73$	−15.4732	+	6.40920i	−1.81100	+	0.750140i	−0.981454	+	0.191697i	$0.938601\pi$
$74$		0			0
$75$	17.3279	+	15.7451i	2.00085	+	1.81808i
$76$		0			0
$77$	−7.91171	−	5.28644i	−0.901623	−	0.602446i
$78$		0			0
$79$	−2.31400	+	2.31400i	−0.260345	+	0.260345i	−0.825194	−	0.564849i	$-0.808934\pi$
$79$	−2.31400	+	2.31400i	−0.260345	+	0.260345i	0.564849	+	0.825194i	$0.308934\pi$
$80$		0			0
$81$	1.71111	+	8.83584i	0.190123	+	0.981760i
$82$		0			0
$83$	1.62719	+	1.08726i	0.178608	+	0.119342i	0.641660	−	0.766989i	$-0.278246\pi$
$83$	1.62719	+	1.08726i	0.178608	+	0.119342i	−0.463053	+	0.886331i	$0.653246\pi$
$84$		0			0
$85$	5.67744	+	1.12931i	0.615805	+	0.122491i
$86$		0			0
$87$	0.662214	−	4.42569i	0.0709968	−	0.474484i
$88$		0			0
$89$	4.04231	+	1.67438i	0.428484	+	0.177484i	0.586494	−	0.809954i	$-0.300508\pi$
$89$	4.04231	+	1.67438i	0.428484	+	0.177484i	−0.158010	+	0.987438i	$0.550508\pi$
$90$		0			0
$91$	3.61170	+	5.40528i	0.378609	+	0.566628i
$92$		0			0
$93$	1.19302	−	3.32101i	0.123710	−	0.344372i
$94$		0			0
$95$			1.66327i			0.170648i
$96$		0			0
$97$			1.86899i			0.189767i	0.995488	+	0.0948834i	$0.0302478\pi$
$97$			1.86899i			0.189767i	−0.995488	+	0.0948834i	$0.969752\pi$
$98$		0			0
$99$	−8.50926	+	6.94740i	−0.855213	+	0.698240i
$100$		0			0
$101$	−7.63182	−	11.4218i	−0.759395	−	1.13651i	−0.986678	−	0.162686i	$-0.947984\pi$
$101$	−7.63182	−	11.4218i	−0.759395	−	1.13651i	0.227283	−	0.973829i	$-0.427016\pi$
$102$		0			0
$103$	−13.4251	−	5.56087i	−1.32282	−	0.547929i	−0.394220	−	0.919016i	$-0.628985\pi$
$103$	−13.4251	−	5.56087i	−1.32282	−	0.547929i	−0.928598	+	0.371087i	$0.878985\pi$
$104$		0			0
$105$	−19.1550	−	2.86615i	−1.86933	−	0.279708i
$106$		0			0
$107$	−2.15026	−	0.427713i	−0.207874	−	0.0413486i	0.0900550	−	0.995937i	$-0.471296\pi$
$107$	−2.15026	−	0.427713i	−0.207874	−	0.0413486i	−0.297929	+	0.954588i	$0.596296\pi$
$108$		0			0
$109$	−14.2766	−	9.53929i	−1.36745	−	0.913698i	−0.367579	−	0.929992i	$-0.619813\pi$
$109$	−14.2766	−	9.53929i	−1.36745	−	0.913698i	−0.999867	+	0.0162943i	$0.994813\pi$
$110$		0			0
$111$	2.15877	+	8.66479i	0.204901	+	0.822426i
$112$		0			0
$113$	8.95069	−	8.95069i	0.842010	−	0.842010i	−0.147110	−	0.989120i	$-0.546997\pi$
$113$	8.95069	−	8.95069i	0.842010	−	0.842010i	0.989120	+	0.147110i	$0.0469971\pi$
$114$		0			0
$115$	−10.6856	−	7.13987i	−0.996434	−	0.665796i
$116$		0			0
$117$	7.18740	−	2.16042i	0.664475	−	0.199731i
$118$		0			0
$119$	−3.22955	+	1.33773i	−0.296053	+	0.122629i
$120$		0			0
$121$	−2.22490	−	0.921585i	−0.202264	−	0.0837805i
$122$		0			0
$123$	0.384881	+	8.04207i	0.0347036	+	0.725129i
$124$		0			0
$125$	7.15047	+	35.9478i	0.639557	+	3.21527i
$126$		0			0
$127$		−	17.0863i		−	1.51617i	−0.652158	−	0.758083i	$-0.726136\pi$
$127$		−	17.0863i		−	1.51617i	0.652158	−	0.758083i	$-0.273864\pi$
$128$		0			0
$129$	14.3149	+	8.60468i	1.26036	+	0.757600i
$130$		0			0
$131$	1.56358	−	0.311016i	0.136611	−	0.0271736i	−0.126311	−	0.991991i	$-0.540314\pi$
$131$	1.56358	−	0.311016i	0.136611	−	0.0271736i	0.262922	+	0.964817i	$0.415314\pi$
$132$		0			0
$133$	−0.558021	−	0.835137i	−0.0483865	−	0.0724155i
$134$		0			0
$135$	−9.63681	+	20.1768i	−0.829404	+	1.73654i
$136$		0			0
$137$	−5.56434	−	13.4335i	−0.475393	−	1.14770i	−0.961747	−	0.273939i	$-0.911673\pi$
$137$	−5.56434	−	13.4335i	−0.475393	−	1.14770i	0.486354	−	0.873762i	$-0.338327\pi$
$138$		0			0
$139$	4.94256	+	0.983137i	0.419223	+	0.0833886i	0.400194	−	0.916430i	$-0.368943\pi$
$139$	4.94256	+	0.983137i	0.419223	+	0.0833886i	0.0190285	+	0.999819i	$0.493943\pi$
$140$		0			0
$141$	5.81901	+	12.3437i	0.490049	+	1.03952i
$142$		0			0
$143$	6.47745	+	6.47745i	0.541672	+	0.541672i
$144$		0			0
$145$	7.86148	−	7.86148i	0.652860	−	0.652860i
$146$		0			0
$147$	−0.387446	+	0.182649i	−0.0319560	+	0.0150646i
$148$		0			0
$149$	−0.473681	+	2.38135i	−0.0388054	+	0.195088i	−0.995325	−	0.0965790i	$-0.969210\pi$
$149$	−0.473681	+	2.38135i	−0.0388054	+	0.195088i	0.956520	+	0.291667i	$0.0942100\pi$
$150$		0			0
$151$	1.17767	−	0.487807i	0.0958374	−	0.0396972i	−0.334250	−	0.942485i	$-0.608483\pi$
$151$	1.17767	−	0.487807i	0.0958374	−	0.0396972i	0.430087	+	0.902787i	$0.358483\pi$
$152$		0			0
$153$	0.385394	+	4.01717i	0.0311572	+	0.324769i
$154$		0			0
$155$	7.28958	−	4.87074i	0.585513	−	0.391227i
$156$		0			0
$157$	2.08481	+	10.4811i	0.166386	+	0.836479i	0.970332	+	0.241777i	$0.0777302\pi$
$157$	2.08481	+	10.4811i	0.166386	+	0.836479i	−0.803946	+	0.594703i	$0.797270\pi$
$158$		0			0
$159$	−1.33780	+	2.22559i	−0.106094	+	0.176501i
$160$		0			0
$161$	7.76067			0.611627
$162$		0			0
$163$	7.80064	−	1.55164i	0.610993	−	0.121534i	0.120112	−	0.992760i	$-0.461675\pi$
$163$	7.80064	−	1.55164i	0.610993	−	0.121534i	0.490882	+	0.871226i	$0.336675\pi$
$164$		0			0
$165$	−27.2609	+	1.30466i	−2.12226	+	0.101568i
$166$		0			0
$167$	6.86336	−	16.5696i	0.531103	−	1.28220i	−0.399691	−	0.916650i	$-0.630882\pi$
$167$	6.86336	−	16.5696i	0.531103	−	1.28220i	0.930793	−	0.365545i	$-0.119118\pi$
$168$		0			0
$169$	2.57988	+	6.22838i	0.198452	+	0.479106i
$170$		0			0
$171$	−1.11048	+	0.333794i	−0.0849205	+	0.0255258i
$172$		0			0
$173$	−7.24199	+	10.8384i	−0.550598	+	0.824029i	−0.997508	−	0.0705503i	$-0.977524\pi$
$173$	−7.24199	+	10.8384i	−0.550598	+	0.824029i	0.446910	+	0.894579i	$0.352524\pi$
$174$		0			0
$175$	−24.8381	−	24.8381i	−1.87758	−	1.87758i
$176$		0			0
$177$	11.0873	−	2.76232i	0.833372	−	0.207628i
$178$		0			0
$179$	−3.45085	+	5.16456i	−0.257929	+	0.386018i	−0.937722	−	0.347386i	$-0.887069\pi$
$179$	−3.45085	+	5.16456i	−0.257929	+	0.386018i	0.679794	+	0.733404i	$0.262069\pi$
$180$		0			0
$181$	2.65101	−	13.3275i	0.197048	−	0.990627i	−0.748001	−	0.663698i	$-0.768986\pi$
$181$	2.65101	−	13.3275i	0.197048	−	0.990627i	0.945049	−	0.326929i	$-0.106014\pi$
$182$		0			0
$183$	1.06985	−	7.15000i	0.0790856	−	0.528543i
$184$		0			0
$185$	−8.48994	+	20.4965i	−0.624193	+	1.50693i
$186$		0			0
$187$	−4.09563	+	2.73661i	−0.299502	+	0.200121i
$188$		0			0
$189$	−1.93054	−	13.3640i	−0.140426	−	0.972086i
$190$		0			0
$191$	−13.5497			−0.980420			−0.490210	−	0.871604i	$-0.663080\pi$
$191$	−13.5497			−0.980420			−0.490210	+	0.871604i	$0.663080\pi$
$192$		0			0
$193$	−20.6394			−1.48566			−0.742830	−	0.669480i	$-0.766517\pi$
$193$	−20.6394			−1.48566			−0.742830	+	0.669480i	$0.766517\pi$
$194$		0			0
$195$	17.5480	+	6.30384i	1.25664	+	0.451427i
$196$		0			0
$197$	2.97611	−	1.98857i	0.212039	−	0.141680i	−0.445016	−	0.895523i	$-0.646802\pi$
$197$	2.97611	−	1.98857i	0.212039	−	0.141680i	0.657055	+	0.753843i	$0.271802\pi$
$198$		0			0
$199$	−5.60732	+	13.5373i	−0.397492	+	0.959631i	0.590767	+	0.806842i	$0.298825\pi$
$199$	−5.60732	+	13.5373i	−0.397492	+	0.959631i	−0.988259	+	0.152788i	$0.951175\pi$
$200$		0			0
$201$	13.2529	+	1.98302i	0.934784	+	0.139871i
$202$		0			0
$203$	−1.30979	+	6.58478i	−0.0919295	+	0.462161i
$204$		0			0
$205$	−11.1131	+	16.6319i	−0.776169	+	1.16162i
$206$		0			0
$207$	2.62249	−	8.56706i	0.182275	−	0.595452i
$208$		0			0
$209$	−1.00079	−	1.00079i	−0.0692261	−	0.0692261i
$210$		0			0
$211$	−10.2740	+	15.3761i	−0.707289	+	1.05853i	0.287619	+	0.957745i	$0.407136\pi$
$211$	−10.2740	+	15.3761i	−0.707289	+	1.05853i	−0.994908	+	0.100788i	$0.967864\pi$
$212$		0			0
$213$	7.91149	−	8.70682i	0.542087	−	0.596581i
$214$		0			0
$215$	15.8796	+	38.3367i	1.08298	+	2.61454i
$216$		0			0
$217$	−2.02602	+	4.89125i	−0.137535	+	0.332040i
$218$		0			0
$219$	−1.38671	−	28.9753i	−0.0937053	−	1.95797i
$220$		0			0
$221$	3.30062	−	0.656535i	0.222024	−	0.0441633i
$222$		0			0
$223$	19.2274			1.28756			0.643782	−	0.765209i	$-0.277364\pi$
$223$	19.2274			1.28756			0.643782	+	0.765209i	$0.277364\pi$
$224$		0			0
$225$	−35.8122	+	19.0256i	−2.38748	+	1.26838i
$226$		0			0
$227$	−1.97234	−	9.91561i	−0.130909	−	0.658122i	−0.989391	−	0.145279i	$-0.953592\pi$
$227$	−1.97234	−	9.91561i	−0.130909	−	0.658122i	0.858482	−	0.512844i	$-0.171408\pi$
$228$		0			0
$229$	14.4937	−	9.68436i	0.957768	−	0.639960i	0.0247136	−	0.999695i	$-0.492133\pi$
$229$	14.4937	−	9.68436i	0.957768	−	0.639960i	0.933055	+	0.359734i	$0.117133\pi$
$230$		0			0
$231$	13.2501	−	9.80099i	0.871794	−	0.644858i
$232$		0			0
$233$	7.39105	−	3.06147i	0.484203	−	0.200564i	−0.127209	−	0.991876i	$-0.540602\pi$
$233$	7.39105	−	3.06147i	0.484203	−	0.200564i	0.611412	+	0.791312i	$0.290602\pi$
$234$		0			0
$235$	−6.61434	+	33.2525i	−0.431472	+	2.16916i
$236$		0			0
$237$	−2.41694	−	5.12698i	−0.156997	−	0.333033i
$238$		0			0
$239$	−8.30613	+	8.30613i	−0.537279	+	0.537279i	−0.922729	−	0.385450i	$-0.874046\pi$
$239$	−8.30613	+	8.30613i	−0.537279	+	0.537279i	0.385450	+	0.922729i	$0.374046\pi$
$240$		0			0
$241$	3.01268	+	3.01268i	0.194063	+	0.194063i	0.797449	−	0.603386i	$-0.206182\pi$
$241$	3.01268	+	3.01268i	0.194063	+	0.194063i	−0.603386	+	0.797449i	$0.706182\pi$
$242$		0			0
$243$	−15.4050	−	2.38482i	−0.988228	−	0.152986i
$244$		0			0
$245$	−1.04374	−	0.207613i	−0.0666821	−	0.0132639i
$246$		0			0
$247$	0.370038	+	0.893350i	0.0235449	+	0.0568425i
$248$		0			0
$249$	−2.72514	+	2.01576i	−0.172698	+	0.127743i
$250$		0			0
$251$	−7.23109	−	10.8221i	−0.456422	−	0.683085i	0.529872	−	0.848077i	$-0.322240\pi$
$251$	−7.23109	−	10.8221i	−0.456422	−	0.683085i	−0.986295	+	0.164993i	$0.947240\pi$
$252$		0			0
$253$	10.7256	−	2.13345i	0.674311	−	0.134129i
$254$		0			0
$255$	−5.16541	+	8.59329i	−0.323471	+	0.538133i
$256$		0			0
$257$			27.8550i			1.73755i	0.495210	+	0.868773i	$0.335091\pi$
$257$			27.8550i			1.73755i	−0.495210	+	0.868773i	$0.664909\pi$
$258$		0			0
$259$	−2.61366	−	13.1398i	−0.162405	−	0.816464i
$260$		0			0
$261$	6.82638	+	3.67102i	0.422542	+	0.227230i
$262$		0			0
$263$	10.8728	+	4.50368i	0.670448	+	0.277709i	0.691828	−	0.722063i	$-0.256806\pi$
$263$	10.8728	+	4.50368i	0.670448	+	0.277709i	−0.0213794	+	0.999771i	$0.506806\pi$
$264$		0			0
$265$	−5.96034	+	2.46885i	−0.366141	+	0.151660i
$266$		0			0
$267$	−5.09641	+	5.60874i	−0.311895	+	0.343249i
$268$		0			0
$269$	3.40585	+	2.27572i	0.207658	+	0.138753i	0.655051	−	0.755585i	$-0.272647\pi$
$269$	3.40585	+	2.27572i	0.207658	+	0.138753i	−0.447392	+	0.894338i	$0.647647\pi$
$270$		0			0
$271$	1.68641	−	1.68641i	0.102442	−	0.102442i	−0.654028	−	0.756470i	$-0.726922\pi$
$271$	1.68641	−	1.68641i	0.102442	−	0.102442i	0.756470	+	0.654028i	$0.226922\pi$
$272$		0			0
$273$	−10.9259	+	2.72210i	−0.661263	+	0.164749i
$274$		0			0
$275$	−41.1553	−	27.4991i	−2.48176	−	1.65826i
$276$		0			0
$277$	3.18127	+	0.632795i	0.191144	+	0.0380210i	0.289734	−	0.957107i	$-0.406433\pi$
$277$	3.18127	+	0.632795i	0.191144	+	0.0380210i	−0.0985898	+	0.995128i	$0.531433\pi$
$278$		0			0
$279$	4.71485	+	3.88939i	0.282271	+	0.232852i
$280$		0			0
$281$	22.6232	+	9.37084i	1.34959	+	0.559018i	0.936178	−	0.351527i	$-0.114338\pi$
$281$	22.6232	+	9.37084i	1.34959	+	0.559018i	0.413410	+	0.910545i	$0.364338\pi$
$282$		0			0
$283$	−1.43456	−	2.14698i	−0.0852760	−	0.127625i	0.786379	−	0.617744i	$-0.211953\pi$
$283$	−1.43456	−	2.14698i	−0.0852760	−	0.127625i	−0.871655	+	0.490119i	$0.836953\pi$
$284$		0			0
$285$	−2.71123	−	0.973967i	−0.160600	−	0.0576928i
$286$		0			0
$287$		−	12.0793i		−	0.713020i
$288$		0			0
$289$		−	15.1904i		−	0.893554i
$290$		0			0
$291$	−3.04656	−	1.09443i	−0.178593	−	0.0641565i
$292$		0			0
$293$	9.50218	+	14.2210i	0.555123	+	0.830800i	0.997828	−	0.0658668i	$-0.0209812\pi$
$293$	9.50218	+	14.2210i	0.555123	+	0.830800i	−0.442705	+	0.896667i	$0.645981\pi$
$294$		0			0
$295$	26.2269	+	10.8636i	1.52699	+	0.632500i
$296$		0			0
$297$	−6.34190	−	17.9388i	−0.367995	−	1.04092i
$298$		0			0
$299$	−7.32771	−	1.45757i	−0.423772	−	0.0842936i
$300$		0			0
$301$	−20.8350	−	13.9215i	−1.20091	−	0.802422i
$302$		0			0
$303$	23.0873	−	5.75203i	1.32633	−	0.330445i
$304$		0			0
$305$	12.7007	−	12.7007i	0.727242	−	0.727242i
$306$		0			0
$307$	6.85681	+	4.58157i	0.391339	+	0.261484i	0.735637	−	0.677376i	$-0.236883\pi$
$307$	6.85681	+	4.58157i	0.391339	+	0.261484i	−0.344298	+	0.938860i	$0.611883\pi$
$308$		0			0
$309$	16.9260	−	18.6275i	0.962885	−	1.05968i
$310$		0			0
$311$	30.1840	−	12.5026i	1.71157	−	0.708958i	0.711595	−	0.702590i	$-0.247973\pi$
$311$	30.1840	−	12.5026i	1.71157	−	0.708958i	0.999980	−	0.00636791i	$-0.00202698\pi$
$312$		0			0
$313$	−6.61643	−	2.74061i	−0.373982	−	0.154909i	0.187772	−	0.982213i	$-0.439873\pi$
$313$	−6.61643	−	2.74061i	−0.373982	−	0.154909i	−0.561754	+	0.827304i	$0.689873\pi$
$314$		0			0
$315$	15.8886	−	29.5455i	0.895224	−	1.66470i
$316$		0			0
$317$	−3.68607	−	18.5311i	−0.207031	−	1.04081i	−0.934850	−	0.355044i	$-0.884466\pi$
$317$	−3.68607	−	18.5311i	−0.207031	−	1.04081i	0.727819	−	0.685769i	$-0.240534\pi$
$318$		0			0
$319$			9.46050i			0.529687i
$320$		0			0
$321$	1.95634	−	3.25460i	0.109192	−	0.181654i
$322$		0			0
$323$	−0.509959	+	0.101437i	−0.0283749	+	0.00564411i
$324$		0			0
$325$	18.7874	+	28.1173i	1.04214	+	1.55967i
$326$		0			0
$327$	23.9096	−	17.6857i	1.32220	−	0.978023i
$328$		0			0
$329$	−7.83499	−	18.9153i	−0.431957	−	1.04284i
$330$		0			0
$331$	−19.6169	−	3.90204i	−1.07824	−	0.214476i	−0.376147	−	0.926560i	$-0.622751\pi$
$331$	−19.6169	−	3.90204i	−1.07824	−	0.214476i	−0.702094	+	0.712084i	$0.747751\pi$
$332$		0			0
$333$	−15.3883	−	1.55495i	−0.843272	−	0.0852105i
$334$		0			0
$335$	23.5414	+	23.5414i	1.28620	+	1.28620i
$336$		0			0
$337$	3.84192	−	3.84192i	0.209283	−	0.209283i	−0.594680	−	0.803963i	$-0.702721\pi$
$337$	3.84192	−	3.84192i	0.209283	−	0.209283i	0.803963	+	0.594680i	$0.202721\pi$
$338$		0			0
$339$	9.34890	+	19.8315i	0.507762	+	1.07710i
$340$		0			0
$341$	−1.45542	+	7.31687i	−0.0788152	+	0.396231i
$342$		0			0
$343$	17.3992	−	7.20700i	0.939471	−	0.389142i
$344$		0			0
$345$	17.8956	−	13.2372i	0.963467	−	0.712668i
$346$		0			0
$347$	−14.6437	+	9.78460i	−0.786114	+	0.525265i	−0.882631	−	0.470067i	$-0.844230\pi$
$347$	−14.6437	+	9.78460i	−0.786114	+	0.525265i	0.0965168	+	0.995331i	$0.469230\pi$
$348$		0			0
$349$	−0.173660	−	0.873047i	−0.00929580	−	0.0467332i	0.975859	−	0.218402i	$-0.0700842\pi$
$349$	−0.173660	−	0.873047i	−0.00929580	−	0.0467332i	−0.985155	+	0.171668i	$0.945084\pi$
$350$		0			0
$351$	−0.687124	+	12.9810i	−0.0366760	+	0.692874i
$352$		0			0
$353$	−33.0774			−1.76053			−0.880266	−	0.474481i	$-0.842636\pi$
$353$	−33.0774			−1.76053			−0.880266	+	0.474481i	$0.842636\pi$
$354$		0			0
$355$	28.6663	−	5.70209i	1.52145	−	0.302636i
$356$		0			0
$357$	−0.289434	−	6.04771i	−0.0153185	−	0.320079i
$358$		0			0
$359$	−4.91221	+	11.8591i	−0.259257	+	0.625901i	−0.998890	−	0.0471093i	$-0.984999\pi$
$359$	−4.91221	+	11.8591i	−0.259257	+	0.625901i	0.739633	+	0.673010i	$0.234999\pi$
$360$		0			0
$361$	7.21381	+	17.4157i	0.379674	+	0.916615i
$362$		0			0
$363$	2.80509	−	3.08708i	0.147229	−	0.162030i
$364$		0			0
$365$	40.0399	−	59.9240i	2.09579	−	3.13656i
$366$		0			0
$367$	−0.647822	−	0.647822i	−0.0338161	−	0.0338161i	0.689997	−	0.723813i	$-0.257612\pi$
$367$	−0.647822	−	0.647822i	−0.0338161	−	0.0338161i	−0.723813	+	0.689997i	$0.757612\pi$
$368$		0			0
$369$	−13.3345	−	4.08185i	−0.694164	−	0.212492i
$370$		0			0
$371$	2.16443	−	3.23929i	0.112371	−	0.168176i
$372$		0			0
$373$	3.01645	−	15.1647i	0.156186	−	0.785200i	−0.820687	−	0.571378i	$-0.806409\pi$
$373$	3.01645	−	15.1647i	0.156186	−	0.785200i	0.976873	−	0.213821i	$-0.0685911\pi$
$374$		0			0
$375$	−62.7843	−	9.39439i	−3.24217	−	0.485124i
$376$		0			0
$377$	2.47344	−	5.97142i	0.127389	−	0.307544i
$378$		0			0
$379$	2.79369	−	1.86669i	0.143502	−	0.0958852i	−0.481747	−	0.876311i	$-0.659997\pi$
$379$	2.79369	−	1.86669i	0.143502	−	0.0958852i	0.625249	+	0.780425i	$0.284997\pi$
$380$		0			0
$381$	27.8518	+	10.0053i	1.42689	+	0.512587i
$382$		0			0
$383$	−23.3643			−1.19386			−0.596931	−	0.802293i	$-0.703613\pi$
$383$	−23.3643			−1.19386			−0.596931	+	0.802293i	$0.703613\pi$
$384$		0			0
$385$	40.9463			2.08682
$386$		0			0
$387$	−22.4086	+	18.2956i	−1.13909	+	0.930015i
$388$		0			0
$389$	−10.1512	+	6.78284i	−0.514688	+	0.343904i	−0.785635	−	0.618691i	$-0.787663\pi$
$389$	−10.1512	+	6.78284i	−0.514688	+	0.343904i	0.270946	+	0.962594i	$0.412663\pi$
$390$		0			0
$391$	1.53741	−	3.71163i	0.0777501	−	0.187705i
$392$		0			0
$393$	−0.408617	+	2.73086i	−0.0206120	+	0.137754i
$394$		0			0
$395$	2.74729	−	13.8115i	0.138231	−	0.694934i
$396$		0			0
$397$	15.0250	−	22.4865i	0.754083	−	1.12856i	−0.233636	−	0.972324i	$-0.575062\pi$
$397$	15.0250	−	22.4865i	0.754083	−	1.12856i	0.987719	−	0.156241i	$-0.0499376\pi$
$398$		0			0
$399$	1.68809	−	0.420574i	0.0845101	−	0.0210551i
$400$		0			0
$401$	−1.77953	−	1.77953i	−0.0888656	−	0.0888656i	0.661277	−	0.750142i	$-0.270015\pi$
$401$	−1.77953	−	1.77953i	−0.0888656	−	0.0888656i	−0.750142	+	0.661277i	$0.770015\pi$
$402$		0			0
$403$	2.83164	−	4.23785i	0.141054	−	0.211102i
$404$		0			0
$405$	−27.2464	−	27.5236i	−1.35388	−	1.36766i
$406$		0			0
$407$	−7.22437	−	17.4412i	−0.358099	−	0.864526i
$408$		0			0
$409$	−7.30266	+	17.6302i	−0.361093	+	0.871756i	0.634048	+	0.773294i	$0.281392\pi$
$409$	−7.30266	+	17.6302i	−0.361093	+	0.871756i	−0.995141	+	0.0984620i	$0.968608\pi$
$410$		0			0
$411$	25.1558	−	1.20392i	1.24084	−	0.0593848i
$412$		0			0
$413$	−16.8134	+	3.34439i	−0.827331	+	0.164566i
$414$		0			0
$415$	−8.42137			−0.413389
$416$		0			0
$417$	−4.49681	+	7.48099i	−0.220210	+	0.366345i
$418$		0			0
$419$	2.89265	+	14.5424i	0.141315	+	0.710440i	0.984856	+	0.173375i	$0.0554672\pi$
$419$	2.89265	+	14.5424i	0.141315	+	0.710440i	−0.843541	+	0.537066i	$0.819533\pi$
$420$		0			0
$421$	−9.40305	+	6.28291i	−0.458276	+	0.306211i	−0.763195	−	0.646168i	$-0.776371\pi$
$421$	−9.40305	+	6.28291i	−0.458276	+	0.306211i	0.304919	+	0.952378i	$0.401371\pi$
$422$		0			0
$423$	−23.5284	+	2.25723i	−1.14399	+	0.109750i
$424$		0			0
$425$	−16.7996	+	6.95861i	−0.814898	+	0.337542i
$426$		0			0
$427$	−2.11606	+	10.6381i	−0.102403	+	0.514816i
$428$		0			0
$429$	−14.3517	+	6.76562i	−0.692905	+	0.326647i
$430$		0			0
$431$	0.840930	−	0.840930i	0.0405062	−	0.0405062i	−0.686564	−	0.727070i	$-0.740882\pi$
$431$	0.840930	−	0.840930i	0.0405062	−	0.0405062i	0.727070	+	0.686564i	$0.240882\pi$
$432$		0			0
$433$	0.498959	+	0.498959i	0.0239785	+	0.0239785i	0.718994	−	0.695016i	$-0.244603\pi$
$433$	0.498959	+	0.498959i	0.0239785	+	0.0239785i	−0.695016	+	0.718994i	$0.744603\pi$
$434$		0			0
$435$	8.21122	+	17.4182i	0.393698	+	0.835137i
$436$		0			0
$437$	1.13216	+	0.225200i	0.0541585	+	0.0107728i
$438$		0			0
$439$	5.55530	+	13.4117i	0.265140	+	0.640105i	0.999242	−	0.0389347i	$-0.0123964\pi$
$439$	5.55530	+	13.4117i	0.265140	+	0.640105i	−0.734102	+	0.679040i	$0.762396\pi$
$440$		0			0
$441$	−0.0708507	−	0.738516i	−0.00337384	−	0.0351674i
$442$		0			0
$443$	−1.97447	−	2.95500i	−0.0938100	−	0.140397i	0.781596	−	0.623785i	$-0.214406\pi$
$443$	−1.97447	−	2.95500i	−0.0938100	−	0.140397i	−0.875406	+	0.483388i	$0.839406\pi$
$444$		0			0
$445$	−18.4662	+	3.67316i	−0.875383	+	0.174125i
$446$		0			0
$447$	−3.60438	−	2.16659i	−0.170481	−	0.102476i
$448$		0			0
$449$		−	5.09669i		−	0.240527i	−0.992742	−	0.120264i	$-0.961626\pi$
$449$		−	5.09669i		−	0.240527i	0.992742	−	0.120264i	$-0.0383740\pi$
$450$		0			0
$451$	−3.32067	−	16.6941i	−0.156364	−	0.786096i
$452$		0			0
$453$	0.105543	+	2.20532i	0.00495885	+	0.103615i
$454$		0			0
$455$	−25.8451	−	10.7054i	−1.21164	−	0.501876i
$456$		0			0
$457$	32.8641	−	13.6128i	1.53732	−	0.636779i	0.556351	−	0.830947i	$-0.312201\pi$
$457$	32.8641	−	13.6128i	1.53732	−	0.636779i	0.980968	+	0.194169i	$0.0622009\pi$
$458$		0			0
$459$	−6.77392	−	1.72413i	−0.316179	−	0.0804757i
$460$		0			0
$461$	−8.02408	−	5.36152i	−0.373719	−	0.249711i	0.354500	−	0.935056i	$-0.384651\pi$
$461$	−8.02408	−	5.36152i	−0.373719	−	0.249711i	−0.728218	+	0.685345i	$0.759651\pi$
$462$		0			0
$463$	13.9676	−	13.9676i	0.649129	−	0.649129i	−0.303654	−	0.952782i	$-0.598207\pi$
$463$	13.9676	−	13.9676i	0.649129	−	0.649129i	0.952782	+	0.303654i	$0.0982066\pi$
$464$		0			0
$465$	3.67103	+	14.7346i	0.170240	+	0.683303i
$466$		0			0
$467$	−26.7190	−	17.8531i	−1.23641	−	0.826141i	−0.246678	−	0.969097i	$-0.579339\pi$
$467$	−26.7190	−	17.8531i	−1.23641	−	0.826141i	−0.989729	+	0.142957i	$0.954339\pi$
$468$		0			0
$469$	−19.7183	−	3.92221i	−0.910506	−	0.181111i
$470$		0			0
$471$	−18.3056	−	2.73906i	−0.843477	−	0.126209i
$472$		0			0
$473$	−32.6219	−	13.5124i	−1.49996	−	0.621303i
$474$		0			0
$475$	−2.90272	−	4.34423i	−0.133186	−	0.199327i
$476$		0			0
$477$	−2.84448	−	3.48395i	−0.130240	−	0.159519i
$478$		0			0
$479$		−	6.21762i		−	0.284090i	−0.989860	−	0.142045i	$-0.954632\pi$
$479$		−	6.21762i		−	0.284090i	0.989860	−	0.142045i	$-0.0453678\pi$
$480$		0			0
$481$			12.8976i			0.588079i
$482$		0			0
$483$	−4.54445	+	12.6504i	−0.206779	+	0.575612i
$484$		0			0
$485$	−4.46823	−	6.68717i	−0.202892	−	0.303649i
$486$		0			0
$487$	−1.30351	−	0.539930i	−0.0590676	−	0.0244666i	0.352954	−	0.935641i	$-0.385177\pi$
$487$	−1.30351	−	0.539930i	−0.0590676	−	0.0244666i	−0.412022	+	0.911174i	$0.635177\pi$
$488$		0			0
$489$	−2.03857	+	13.6241i	−0.0921874	+	0.616105i
$490$		0			0
$491$	10.3424	+	2.05722i	0.466744	+	0.0928411i	0.422859	−	0.906195i	$-0.361027\pi$
$491$	10.3424	+	2.05722i	0.466744	+	0.0928411i	0.0438848	+	0.999037i	$0.486027\pi$
$492$		0			0
$493$	2.88977	+	1.93088i	0.130149	+	0.0869627i
$494$		0			0
$495$	13.8366	−	45.2009i	0.621907	−	2.03163i
$496$		0			0
$497$	−12.4805	+	12.4805i	−0.559827	+	0.559827i
$498$		0			0
$499$	10.5229	+	7.03120i	0.471071	+	0.314760i	0.768349	−	0.640031i	$-0.221079\pi$
$499$	10.5229	+	7.03120i	0.471071	+	0.314760i	−0.297277	+	0.954791i	$0.596079\pi$
$500$		0			0
$501$	22.9905	+	20.8904i	1.02714	+	0.933316i
$502$		0			0
$503$	6.66908	−	2.76242i	0.297360	−	0.123170i	−0.229016	−	0.973423i	$-0.573551\pi$
$503$	6.66908	−	2.76242i	0.297360	−	0.123170i	0.526375	+	0.850252i	$0.323551\pi$
$504$		0			0
$505$	54.6129	+	22.6214i	2.43024	+	1.00664i
$506$		0			0
$507$	−11.6634	+	0.558190i	−0.517988	+	0.0247901i
$508$		0			0
$509$	1.85153	+	9.30829i	0.0820678	+	0.412583i	0.999879	+	0.0155653i	$0.00495480\pi$
$509$	1.85153	+	9.30829i	0.0820678	+	0.412583i	−0.917811	+	0.397018i	$0.870045\pi$
$510$		0			0
$511$			43.5214i			1.92527i
$512$		0			0
$513$	0.106163	−	2.00561i	0.00468722	−	0.0885499i
$514$		0			0
$515$	61.3293	−	12.1991i	2.70249	−	0.537559i
$516$		0			0
$517$	−16.0282	−	23.9879i	−0.704920	−	1.05499i
$518$		0			0
$519$	−13.4266	−	18.1516i	−0.589361	−	0.796766i
$520$		0			0
$521$	−6.13573	−	14.8130i	−0.268811	−	0.648968i	0.730617	−	0.682788i	$-0.239233\pi$
$521$	−6.13573	−	14.8130i	−0.268811	−	0.648968i	−0.999428	+	0.0338199i	$0.989233\pi$
$522$		0			0
$523$	31.6109	+	6.28780i	1.38225	+	0.274946i	0.829548	−	0.558435i	$-0.188598\pi$
$523$	31.6109	+	6.28780i	1.38225	+	0.274946i	0.552699	+	0.833381i	$0.313598\pi$
$524$		0			0
$525$	55.0321	−	25.9431i	2.40180	−	1.13225i
$526$		0			0
$527$	1.93794	+	1.93794i	0.0844178	+	0.0844178i
$528$		0			0
$529$	9.95669	−	9.95669i	0.432900	−	0.432900i
$530$		0			0
$531$	−1.98968	+	19.6905i	−0.0863447	+	0.854496i
$532$		0			0
$533$	−2.26868	+	11.4054i	−0.0982675	+	0.494024i
$534$		0			0
$535$	8.71611	−	3.61033i	0.376830	−	0.156088i
$536$		0			0
$537$	−6.39783	−	8.64933i	−0.276087	−	0.373246i
$538$		0			0
$539$	0.752940	−	0.503098i	0.0324314	−	0.0216700i
$540$		0			0
$541$	5.30294	+	26.6597i	0.227991	+	1.14619i	0.909924	+	0.414774i	$0.136139\pi$
$541$	5.30294	+	26.6597i	0.227991	+	1.14619i	−0.681933	+	0.731414i	$0.738861\pi$
$542$		0			0
$543$	20.1723	+	12.1256i	0.865678	+	0.520357i
$544$		0			0
$545$	73.8869			3.16497
$546$		0			0
$547$	−2.89843	+	0.576533i	−0.123928	+	0.0246508i	−0.256664	−	0.966501i	$-0.582624\pi$
$547$	−2.89843	+	0.576533i	−0.123928	+	0.0246508i	0.132737	+	0.991151i	$0.457624\pi$
$548$		0			0
$549$	11.0285	+	5.93077i	0.470683	+	0.253119i
$550$		0			0
$551$	−0.382156	+	0.922607i	−0.0162804	+	0.0393044i
$552$		0			0
$553$	3.25429	+	7.85655i	0.138386	+	0.334095i
$554$		0			0
$555$	−28.4391	−	25.8414i	−1.20717	−	1.09690i
$556$		0			0
$557$	−9.09602	+	13.6132i	−0.385411	+	0.576808i	−0.972555	−	0.232675i	$-0.925252\pi$
$557$	−9.09602	+	13.6132i	−0.385411	+	0.576808i	0.587144	+	0.809483i	$0.300252\pi$
$558$		0			0
$559$	17.0580	+	17.0580i	0.721475	+	0.721475i
$560$		0			0
$561$	−2.06256	−	8.27862i	−0.0870812	−	0.349524i
$562$		0			0
$563$	19.5452	−	29.2515i	0.823732	−	1.23280i	−0.146159	−	0.989261i	$-0.546691\pi$
$563$	19.5452	−	29.2515i	0.823732	−	1.23280i	0.969891	−	0.243541i	$-0.0783089\pi$
$564$		0			0
$565$	−10.6267	+	53.4239i	−0.447068	+	2.24756i
$566$		0			0
$567$	22.9146	+	4.67870i	0.962322	+	0.196487i
$568$		0			0
$569$	−7.42318	+	17.9211i	−0.311196	+	0.751293i	0.688465	+	0.725269i	$0.258285\pi$
$569$	−7.42318	+	17.9211i	−0.311196	+	0.751293i	−0.999661	+	0.0260241i	$0.991715\pi$
$570$		0			0
$571$	−25.4369	+	16.9964i	−1.06450	+	0.711277i	−0.959076	−	0.283150i	$-0.908621\pi$
$571$	−25.4369	+	16.9964i	−1.06450	+	0.711277i	−0.105426	+	0.994427i	$0.533621\pi$
$572$		0			0
$573$	7.93433	−	22.0868i	0.331462	−	0.922690i
$574$		0			0
$575$	40.3696			1.68353
$576$		0			0
$577$	−13.6429			−0.567963			−0.283982	−	0.958830i	$-0.591655\pi$
$577$	−13.6429			−0.567963			−0.283982	+	0.958830i	$0.591655\pi$
$578$		0			0
$579$	12.0859	−	33.6436i	0.502273	−	1.39818i
$580$		0			0
$581$	4.22842	−	2.82534i	0.175424	−	0.117215i
$582$		0			0
$583$	2.10083	−	5.07185i	0.0870074	−	0.210054i
$584$		0			0
$585$	−20.5513	+	24.9130i	−0.849692	+	1.03003i
$586$		0			0
$587$	−4.83875	+	24.3260i	−0.199717	+	1.00404i	0.742706	+	0.669618i	$0.233542\pi$
$587$	−4.83875	+	24.3260i	−0.199717	+	1.00404i	−0.942422	+	0.334425i	$0.891458\pi$
$588$		0			0
$589$	−0.437499	+	0.654764i	−0.0180268	+	0.0269791i
$590$		0			0
$591$	1.49877	+	6.01569i	0.0616510	+	0.247453i
$592$		0			0
$593$	−9.31734	−	9.31734i	−0.382617	−	0.382617i	0.489427	−	0.872044i	$-0.337206\pi$
$593$	−9.31734	−	9.31734i	−0.382617	−	0.382617i	−0.872044	+	0.489427i	$0.837206\pi$
$594$		0			0
$595$	8.35712	−	12.5073i	0.342608	−	0.512750i
$596$		0			0
$597$	−18.7831	−	17.0673i	−0.768740	−	0.698520i
$598$		0			0
$599$	0.450558	+	1.08774i	0.0184093	+	0.0444440i	0.932817	−	0.360351i	$-0.117343\pi$
$599$	0.450558	+	1.08774i	0.0184093	+	0.0444440i	−0.914408	+	0.404795i	$0.867343\pi$
$600$		0			0
$601$	−9.25984	+	22.3552i	−0.377717	+	0.911889i	0.614676	+	0.788780i	$0.289287\pi$
$601$	−9.25984	+	22.3552i	−0.377717	+	0.911889i	−0.992393	+	0.123110i	$0.960713\pi$
$602$		0			0
$603$	−10.9930	+	20.4418i	−0.447668	+	0.832453i
$604$		0			0
$605$	10.1639	−	2.02172i	0.413221	−	0.0821948i
$606$		0			0
$607$	−47.3452			−1.92168			−0.960840	−	0.277103i	$-0.910626\pi$
$607$	−47.3452			−1.92168			−0.960840	+	0.277103i	$0.910626\pi$
$608$		0			0
$609$	−9.96662	−	5.99092i	−0.403868	−	0.242764i
$610$		0			0
$611$	3.84529	+	19.3316i	0.155564	+	0.782073i
$612$		0			0
$613$	0.532520	−	0.355818i	0.0215083	−	0.0143714i	−0.544770	−	0.838586i	$-0.683383\pi$
$613$	0.532520	−	0.355818i	0.0215083	−	0.0143714i	0.566278	+	0.824214i	$0.308383\pi$
$614$		0			0
$615$	−20.6035	−	27.8542i	−0.830812	−	1.12319i
$616$		0			0
$617$	15.4604	−	6.40389i	0.622411	−	0.257811i	−0.0491140	−	0.998793i	$-0.515640\pi$
$617$	15.4604	−	6.40389i	0.622411	−	0.257811i	0.671525	+	0.740982i	$0.265640\pi$
$618$		0			0
$619$	8.36961	−	42.0769i	0.336403	−	1.69121i	−0.328678	−	0.944442i	$-0.606603\pi$
$619$	8.36961	−	42.0769i	0.336403	−	1.69121i	0.665081	−	0.746771i	$-0.268397\pi$
$620$		0			0
$621$	12.4292	+	9.29146i	0.498766	+	0.372854i
$622$		0			0
$623$	8.03966	−	8.03966i	0.322102	−	0.322102i
$624$		0			0
$625$	−63.7341	−	63.7341i	−2.54937	−	2.54937i
$626$		0			0
$627$	2.21739	−	1.04531i	0.0885539	−	0.0417458i
$628$		0			0
$629$	−6.80201	−	1.35300i	−0.271214	−	0.0539478i
$630$		0			0
$631$	−8.07387	−	19.4920i	−0.321416	−	0.775966i	−0.999172	−	0.0406796i	$-0.987048\pi$
$631$	−8.07387	−	19.4920i	−0.321416	−	0.775966i	0.677757	−	0.735286i	$-0.262952\pi$
$632$		0			0
$633$	−19.0478	−	25.7510i	−0.757082	−	1.02351i
$634$		0			0
$635$	40.8487	+	61.1344i	1.62103	+	2.42604i
$636$		0			0
$637$	−0.606786	+	0.120697i	−0.0240417	+	0.00478220i
$638$		0			0
$639$	9.55990	+	17.9947i	0.378184	+	0.711860i
$640$		0			0
$641$			37.3054i			1.47347i	0.676180	+	0.736736i	$0.263634\pi$
$641$			37.3054i			1.47347i	−0.676180	+	0.736736i	$0.736366\pi$
$642$		0			0
$643$	0.437593	+	2.19993i	0.0172570	+	0.0867567i	0.988454	−	0.151521i	$-0.0484171\pi$
$643$	0.437593	+	2.19993i	0.0172570	+	0.0867567i	−0.971197	+	0.238278i	$0.923417\pi$
$644$		0			0
$645$	−71.7898	+	3.43575i	−2.82672	+	0.135282i
$646$		0			0
$647$	−13.8914	−	5.75400i	−0.546126	−	0.226213i	0.0925234	−	0.995711i	$-0.470507\pi$
$647$	−13.8914	−	5.75400i	−0.546126	−	0.226213i	−0.638650	+	0.769498i	$0.720507\pi$
$648$		0			0
$649$	−22.3174	+	9.24415i	−0.876033	+	0.362865i
$650$		0			0
$651$	−6.78665	−	6.16673i	−0.265990	−	0.241693i
$652$		0			0
$653$	−20.8375	−	13.9232i	−0.815433	−	0.544855i	0.0764751	−	0.997071i	$-0.475633\pi$
$653$	−20.8375	−	13.9232i	−0.815433	−	0.544855i	−0.891908	+	0.452216i	$0.850633\pi$
$654$		0			0
$655$	−4.85090	+	4.85090i	−0.189540	+	0.189540i
$656$		0			0
$657$	48.0435	+	14.7067i	1.87436	+	0.573764i
$658$		0			0
$659$	24.4240	+	16.3196i	0.951426	+	0.635722i	0.931369	−	0.364076i	$-0.118615\pi$
$659$	24.4240	+	16.3196i	0.951426	+	0.635722i	0.0200567	+	0.999799i	$0.493615\pi$
$660$		0			0
$661$	37.5355	+	7.46628i	1.45996	+	0.290405i	0.860275	−	0.509830i	$-0.170292\pi$
$661$	37.5355	+	7.46628i	1.45996	+	0.290405i	0.599687	+	0.800235i	$0.295292\pi$
$662$		0			0
$663$	−0.862565	+	5.76467i	−0.0334993	+	0.223881i
$664$		0			0
$665$	3.99316	+	1.65402i	0.154848	+	0.0641402i
$666$		0			0
$667$	−4.28675	−	6.41558i	−0.165984	−	0.248412i
$668$		0			0
$669$	−11.2591	+	31.3419i	−0.435301	+	1.21175i
$670$		0			0
$671$			15.2841i			0.590035i
$672$		0			0
$673$			17.2901i			0.666486i	0.942841	+	0.333243i	$0.108143\pi$
$673$			17.2901i			0.666486i	−0.942841	+	0.333243i	$0.891857\pi$
$674$		0			0
$675$	−10.0423	−	69.5170i	−0.386529	−	2.67571i
$676$		0			0
$677$	0.0350577	+	0.0524676i	0.00134738	+	0.00201649i	0.832143	−	0.554562i	$-0.187114\pi$
$677$	0.0350577	+	0.0524676i	0.00134738	+	0.00201649i	−0.830795	+	0.556578i	$0.812114\pi$
$678$		0			0
$679$	4.48704	+	1.85859i	0.172197	+	0.0713263i
$680$		0			0
$681$	17.3180	+	2.59129i	0.663628	+	0.0992983i
$682$		0			0
$683$	−25.4364	−	5.05961i	−0.973297	−	0.193601i	−0.317267	−	0.948336i	$-0.602765\pi$
$683$	−25.4364	−	5.05961i	−0.973297	−	0.193601i	−0.656029	+	0.754735i	$0.727765\pi$
$684$		0			0
$685$	52.0248	+	34.7619i	1.98777	+	1.32818i
$686$		0			0
$687$	7.29900	+	29.2965i	0.278474	+	1.11773i
$688$		0			0
$689$	−2.65206	+	2.65206i	−0.101036	+	0.101036i
$690$		0			0
$691$	31.0818	+	20.7682i	1.18241	+	0.790059i	0.981857	−	0.189624i	$-0.0607270\pi$
$691$	31.0818	+	20.7682i	1.18241	+	0.790059i	0.200550	+	0.979683i	$0.435727\pi$
$692$		0			0
$693$	8.21731	+	27.3377i	0.312150	+	1.03847i
$694$		0			0
$695$	−20.0347	+	8.29866i	−0.759961	+	0.314786i
$696$		0			0
$697$	−5.77708	−	2.39294i	−0.218822	−	0.0906392i
$698$		0			0
$699$	0.662388	+	13.8406i	0.0250538	+	0.523499i
$700$		0			0
$701$	6.43348	+	32.3433i	0.242989	+	1.22159i	0.888873	+	0.458154i	$0.151489\pi$
$701$	6.43348	+	32.3433i	0.242989	+	1.22159i	−0.645884	+	0.763436i	$0.723511\pi$
$702$		0			0
$703$		−	1.99272i		−	0.0751570i
$704$		0			0
$705$	−50.3305	−	30.2536i	−1.89556	−	1.13942i
$706$		0			0
$707$	−35.0108	+	6.96408i	−1.31672	+	0.261911i
$708$		0			0
$709$	13.2204	+	19.7857i	0.496502	+	0.743067i	0.992095	−	0.125487i	$-0.0400494\pi$
$709$	13.2204	+	19.7857i	0.496502	+	0.743067i	−0.495593	+	0.868555i	$0.665049\pi$
$710$		0			0
$711$	9.77259	−	0.937549i	0.366501	−	0.0351608i
$712$		0			0
$713$	−2.32845	−	5.62136i	−0.0872010	−	0.210522i
$714$		0			0
$715$	−38.6619	−	7.69033i	−1.44587	−	0.287602i
$716$		0			0
$717$	−8.67566	−	18.4034i	−0.323999	−	0.687286i
$718$		0			0
$719$	−17.8047	−	17.8047i	−0.664002	−	0.664002i	0.292319	−	0.956321i	$-0.405573\pi$
$719$	−17.8047	−	17.8047i	−0.664002	−	0.664002i	−0.956321	+	0.292319i	$0.905573\pi$
$720$		0			0
$721$	−26.7010	+	26.7010i	−0.994396	+	0.994396i
$722$		0			0
$723$	−6.67499	+	3.14671i	−0.248246	+	0.117027i
$724$		0			0
$725$	−6.81332	+	34.2529i	−0.253040	+	1.27212i
$726$		0			0
$727$	−22.6315	+	9.37426i	−0.839355	+	0.347672i	−0.760599	−	0.649222i	$-0.775095\pi$
$727$	−22.6315	+	9.37426i	−0.839355	+	0.347672i	−0.0787556	+	0.996894i	$0.525095\pi$
$728$		0			0
$729$	12.9081	−	23.7146i	0.478079	−	0.878317i
$730$		0			0
$731$	−10.7856	+	7.20670i	−0.398919	+	0.266549i
$732$		0			0
$733$	−9.77199	−	49.1271i	−0.360937	−	1.81455i	−0.553015	−	0.833171i	$-0.686523\pi$
$733$	−9.77199	−	49.1271i	−0.360937	−	1.81455i	0.192078	−	0.981380i	$-0.438477\pi$
$734$		0			0
$735$	0.949609	−	1.57979i	0.0350268	−	0.0582714i
$736$		0			0
$737$	−28.3297			−1.04354
$738$		0			0
$739$	−28.8194	+	5.73254i	−1.06014	+	0.210875i	−0.694214	−	0.719769i	$-0.744248\pi$
$739$	−28.8194	+	5.73254i	−1.06014	+	0.210875i	−0.365926	+	0.930644i	$0.619248\pi$
$740$		0			0
$741$	−1.67290	+	0.0800624i	−0.0614555	+	0.00294116i
$742$		0			0
$743$	−15.3189	+	36.9832i	−0.561997	+	1.35678i	0.346169	+	0.938172i	$0.387482\pi$
$743$	−15.3189	+	36.9832i	−0.561997	+	1.35678i	−0.908166	+	0.418609i	$0.862518\pi$
$744$		0			0
$745$	−3.99834	−	9.65285i	−0.146488	−	0.353653i
$746$		0			0
$747$	−1.69004	−	5.62252i	−0.0618355	−	0.205717i
$748$		0			0
$749$	−3.16515	+	4.73699i	−0.115652	+	0.173086i
$750$		0			0
$751$	0.644925	+	0.644925i	0.0235337	+	0.0235337i	0.718776	−	0.695242i	$-0.244703\pi$
$751$	0.644925	+	0.644925i	0.0235337	+	0.0235337i	−0.695242	+	0.718776i	$0.744703\pi$
$752$		0			0
$753$	21.8750	−	5.45000i	0.797170	−	0.198609i
$754$		0			0
$755$	−3.04746	+	4.56084i	−0.110908	+	0.165986i
$756$		0			0
$757$	2.74459	−	13.7980i	0.0997538	−	0.501496i	−0.898314	−	0.439355i	$-0.855207\pi$
$757$	2.74459	−	13.7980i	0.0997538	−	0.501496i	0.998067	−	0.0621412i	$-0.0197929\pi$
$758$		0			0
$759$	−2.80296	+	18.7326i	−0.101741	+	0.679952i
$760$		0			0
$761$	−0.456572	+	1.10226i	−0.0165507	+	0.0399570i	−0.931939	−	0.362615i	$-0.881884\pi$
$761$	−0.456572	+	1.10226i	−0.0165507	+	0.0399570i	0.915388	+	0.402572i	$0.131884\pi$
$762$		0			0
$763$	−37.0990	+	24.7888i	−1.34307	+	0.897413i
$764$		0			0
$765$	−10.9829	−	13.4520i	−0.397087	−	0.486356i
$766$		0			0
$767$	16.5035			0.595906
$768$		0			0
$769$	17.8345			0.643128			0.321564	−	0.946888i	$-0.395792\pi$
$769$	17.8345			0.643128			0.321564	+	0.946888i	$0.395792\pi$
$770$		0			0
$771$	−45.4054	−	16.3111i	−1.63523	−	0.587431i
$772$		0			0
$773$	30.0410	−	20.0728i	1.08050	−	0.721968i	0.117937	−	0.993021i	$-0.462372\pi$
$773$	30.0410	−	20.0728i	1.08050	−	0.721968i	0.962564	+	0.271053i	$0.0873720\pi$
$774$		0			0
$775$	−10.5390	+	25.4434i	−0.378572	+	0.913954i
$776$		0			0
$777$	22.9491	+	3.43386i	0.823295	+	0.123189i
$778$		0			0
$779$	0.350520	−	1.76218i	0.0125587	−	0.0631367i
$780$		0			0
$781$	−13.8176	+	20.6795i	−0.494433	+	0.739971i
$782$		0			0
$783$	−9.98134	+	8.97778i	−0.356704	+	0.320840i
$784$		0			0
$785$	−32.5167	−	32.5167i	−1.16057	−	1.16057i
$786$		0			0
$787$	28.9404	−	43.3124i	1.03161	−	1.54392i	0.206906	−	0.978361i	$-0.433661\pi$
$787$	28.9404	−	43.3124i	1.03161	−	1.54392i	0.824708	−	0.565558i	$-0.191339\pi$
$788$		0			0
$789$	−13.7081	+	15.0862i	−0.488022	+	0.537082i
$790$		0			0
$791$	−12.5878	−	30.3896i	−0.447571	−	1.08053i
$792$		0			0
$793$	3.99601	−	9.64722i	0.141902	−	0.342583i
$794$		0			0
$795$	−0.534168	−	11.1614i	−0.0189450	−	0.395855i
$796$		0			0
$797$	−16.5418	+	3.29037i	−0.585942	+	0.116551i	−0.479154	−	0.877731i	$-0.659056\pi$
$797$	−16.5418	+	3.29037i	−0.585942	+	0.116551i	−0.106788	+	0.994282i	$0.534056\pi$
$798$		0			0
$799$	−10.5986			−0.374952
$800$		0			0
$801$	−6.15828	−	11.5918i	−0.217592	−	0.409576i
$802$		0			0
$803$	11.9642	+	60.1483i	0.422209	+	2.12259i
$804$		0			0
$805$	−27.7675	+	18.5536i	−0.978674	+	0.653929i
$806$		0			0
$807$	−5.70394	+	4.21915i	−0.200788	+	0.148521i
$808$		0			0
$809$	39.8340	−	16.4998i	1.40049	−	0.580102i	0.450611	−	0.892721i	$-0.351206\pi$
$809$	39.8340	−	16.4998i	1.40049	−	0.580102i	0.949879	+	0.312619i	$0.101206\pi$
$810$		0			0
$811$	−9.67058	+	48.6173i	−0.339580	+	1.70718i	0.313243	+	0.949673i	$0.398584\pi$
$811$	−9.67058	+	48.6173i	−0.339580	+	1.70718i	−0.652823	+	0.757510i	$0.726416\pi$
$812$		0			0
$813$	1.76144	+	3.73648i	0.0617765	+	0.131044i
$814$		0			0
$815$	−24.2009	+	24.2009i	−0.847721	+	0.847721i
$816$		0			0
$817$	−2.63552	−	2.63552i	−0.0922051	−	0.0922051i
$818$		0			0
$819$	1.96071	−	19.4038i	0.0685127	−	0.678025i
$820$		0			0
$821$	−17.9426	−	3.56901i	−0.626203	−	0.124559i	−0.128219	−	0.991746i	$-0.540926\pi$
$821$	−17.9426	−	3.56901i	−0.626203	−	0.124559i	−0.497984	+	0.867186i	$0.665926\pi$
$822$		0			0
$823$	−5.19727	−	12.5473i	−0.181165	−	0.437372i	0.807042	−	0.590494i	$-0.201067\pi$
$823$	−5.19727	−	12.5473i	−0.181165	−	0.437372i	−0.988207	+	0.153122i	$0.951067\pi$
$824$		0			0
$825$	68.9247	−	50.9830i	2.39965	−	1.77500i
$826$		0			0
$827$	−16.4642	−	24.6404i	−0.572516	−	0.856831i	0.426344	−	0.904561i	$-0.359801\pi$
$827$	−16.4642	−	24.6404i	−0.572516	−	0.856831i	−0.998860	+	0.0477298i	$0.984801\pi$
$828$		0			0
$829$	−16.2671	+	3.23572i	−0.564979	+	0.112381i	−0.469312	−	0.883032i	$-0.655498\pi$
$829$	−16.2671	+	3.23572i	−0.564979	+	0.112381i	−0.0956663	+	0.995413i	$0.530498\pi$
$830$		0			0
$831$	−2.89436	+	4.81513i	−0.100404	+	0.167035i
$832$		0			0
$833$		−	0.332672i		−	0.0115264i
$834$		0			0
$835$	15.0565	+	75.6940i	0.521051	+	2.61950i
$836$		0			0
$837$	−9.10084	+	5.40798i	−0.314571	+	0.186927i
$838$		0			0
$839$	−45.1745	−	18.7119i	−1.55960	−	0.646006i	−0.574578	−	0.818450i	$-0.694834\pi$
$839$	−45.1745	−	18.7119i	−1.55960	−	0.646006i	−0.985019	+	0.172444i	$0.944834\pi$
$840$		0			0
$841$	−20.6255	+	8.54337i	−0.711225	+	0.294599i
$842$		0			0
$843$	−28.5226	+	31.3899i	−0.982371	+	1.08113i
$844$		0			0
$845$	−24.1211	−	16.1172i	−0.829789	−	0.554448i
$846$		0			0
$847$	−4.42506	+	4.42506i	−0.152047	+	0.152047i
$848$		0			0
$849$	4.33975	−	1.08122i	0.148940	−	0.0371073i
$850$		0			0
$851$	12.8021	+	8.55410i	0.438851	+	0.293231i
$852$		0			0
$853$	25.6899	+	5.11004i	0.879606	+	0.174965i	0.614179	−	0.789166i	$-0.289487\pi$
$853$	25.6899	+	5.11004i	0.879606	+	0.174965i	0.265427	+	0.964131i	$0.414487\pi$
$854$		0			0
$855$	3.17526	−	3.84915i	0.108591	−	0.131638i
$856$		0			0
$857$	30.8971	+	12.7980i	1.05543	+	0.437172i	0.841826	−	0.539749i	$-0.181481\pi$
$857$	30.8971	+	12.7980i	1.05543	+	0.437172i	0.213600	+	0.976921i	$0.431481\pi$
$858$		0			0
$859$	−16.0686	−	24.0483i	−0.548252	−	0.820517i	0.449082	−	0.893491i	$-0.351751\pi$
$859$	−16.0686	−	24.0483i	−0.548252	−	0.820517i	−0.997334	+	0.0729736i	$0.976751\pi$
$860$		0			0
$861$	19.6901	+	7.07334i	0.671036	+	0.241059i
$862$		0			0
$863$		−	44.8567i		−	1.52694i	−0.645843	−	0.763470i	$-0.723494\pi$
$863$		−	44.8567i		−	1.52694i	0.645843	−	0.763470i	$-0.276506\pi$
$864$		0			0
$865$		−	56.0931i		−	1.90722i
$866$		0			0
$867$	24.7613	+	8.89511i	0.840939	+	0.302094i
$868$		0			0
$869$	6.65737	+	9.96345i	0.225836	+	0.337987i
$870$		0			0
$871$	17.8816	+	7.40679i	0.605894	+	0.250969i
$872$		0			0
$873$	3.56797	−	4.32522i	0.120758	−	0.146387i
$874$		0			0
$875$	93.4139	+	18.5812i	3.15796	+	0.628158i
$876$		0			0
$877$	−16.5425	−	11.0534i	−0.558602	−	0.373246i	0.243987	−	0.969779i	$-0.421545\pi$
$877$	−16.5425	−	11.0534i	−0.558602	−	0.373246i	−0.802589	+	0.596533i	$0.796545\pi$
$878$		0			0
$879$	−28.7454	+	7.16169i	−0.969557	+	0.241558i
$880$		0			0
$881$	−29.6126	+	29.6126i	−0.997673	+	0.997673i	−0.999997	−	0.00232406i	$-0.999260\pi$
$881$	−29.6126	+	29.6126i	−0.997673	+	0.997673i	0.00232406	+	0.999997i	$0.499260\pi$
$882$		0			0
$883$	34.3003	+	22.9187i	1.15430	+	0.771277i	0.977075	−	0.212894i	$-0.0682889\pi$
$883$	34.3003	+	22.9187i	1.15430	+	0.771277i	0.177222	+	0.984171i	$0.443289\pi$
$884$		0			0
$885$	−33.0661	+	36.3901i	−1.11150	+	1.22324i
$886$		0			0
$887$	17.2802	−	7.15771i	0.580214	−	0.240332i	−0.0732204	−	0.997316i	$-0.523328\pi$
$887$	17.2802	−	7.15771i	0.580214	−	0.240332i	0.653434	+	0.756983i	$0.273328\pi$
$888$		0			0
$889$	−41.0207	−	16.9913i	−1.37579	−	0.569871i
$890$		0			0
$891$	32.9551	+	0.166813i	1.10404	+	0.00558845i
$892$		0			0
$893$	−0.594112	−	2.98680i	−0.0198812	−	0.0999496i
$894$		0			0
$895$		−	26.7287i		−	0.893441i
$896$		0			0
$897$	6.66685	−	11.0911i	0.222600	−	0.370321i
$898$		0			0
$899$	5.16260	−	1.02690i	0.172182	−	0.0342492i
$900$		0			0
$901$	−1.12045	−	1.67687i	−0.0373276	−	0.0558648i
$902$		0			0
$903$	34.8934	−	25.8103i	1.16118	−	0.858913i
$904$		0			0
$905$	22.3772	+	54.0233i	0.743843	+	1.79580i
$906$		0			0
$907$	6.74321	+	1.34131i	0.223905	+	0.0445374i	0.305768	−	0.952106i	$-0.401087\pi$
$907$	6.74321	+	1.34131i	0.223905	+	0.0445374i	−0.0818628	+	0.996644i	$0.526087\pi$
$908$		0			0
$909$	−4.14315	+	41.0020i	−0.137419	+	1.35995i
$910$		0			0
$911$	−7.04481	−	7.04481i	−0.233405	−	0.233405i	0.580707	−	0.814112i	$-0.302776\pi$
$911$	−7.04481	−	7.04481i	−0.233405	−	0.233405i	−0.814112	+	0.580707i	$0.802776\pi$
$912$		0			0
$913$	5.06714	−	5.06714i	0.167698	−	0.167698i
$914$		0			0
$915$	13.2658	+	28.1402i	0.438553	+	0.930286i
$916$		0			0
$917$	0.808204	−	4.06312i	0.0266893	−	0.134176i
$918$		0			0
$919$	47.5960	−	19.7149i	1.57005	−	0.650335i	0.583249	−	0.812293i	$-0.301781\pi$
$919$	47.5960	−	19.7149i	1.57005	−	0.650335i	0.986798	+	0.161959i	$0.0517811\pi$
$920$		0			0
$921$	−11.4834	+	8.49418i	−0.378392	+	0.279893i
$922$		0			0
$923$	14.1282	−	9.44019i	0.465037	−	0.310728i
$924$		0			0
$925$	−13.5958	−	68.3506i	−0.447027	−	2.24735i
$926$		0			0
$927$	20.4526	+	38.4982i	0.671752	+	1.26445i
$928$		0			0
$929$	−2.02612			−0.0664748			−0.0332374	−	0.999447i	$-0.510582\pi$
$929$	−2.02612			−0.0664748			−0.0332374	+	0.999447i	$0.510582\pi$
$930$		0			0
$931$	0.0937507	−	0.0186482i	0.00307256	−	0.000611169i
$932$		0			0
$933$	2.70510	+	56.5229i	0.0885609	+	1.85048i
$934$		0			0
$935$	8.11156	−	19.5830i	0.265276	−	0.640433i
$936$		0			0
$937$	−0.987795	−	2.38475i	−0.0322699	−	0.0779063i	0.906923	−	0.421296i	$-0.138425\pi$
$937$	−0.987795	−	2.38475i	−0.0322699	−	0.0779063i	−0.939193	+	0.343390i	$0.888425\pi$
$938$		0			0
$939$	8.34177	−	9.18036i	0.272224	−	0.299590i
$940$		0			0
$941$	−2.09080	+	3.12910i	−0.0681580	+	0.102006i	−0.863983	−	0.503521i	$-0.832038\pi$
$941$	−2.09080	+	3.12910i	−0.0681580	+	0.102006i	0.795825	+	0.605527i	$0.207038\pi$
$942$		0			0
$943$	9.81635	+	9.81635i	0.319664	+	0.319664i
$944$		0			0
$945$	38.8570	+	43.2005i	1.26402	+	1.40531i
$946$		0			0
$947$	−16.2924	+	24.3833i	−0.529432	+	0.792352i	−0.995734	−	0.0922743i	$-0.970586\pi$
$947$	−16.2924	+	24.3833i	−0.529432	+	0.792352i	0.466301	+	0.884626i	$0.345586\pi$
$948$		0			0
$949$	8.17397	−	41.0933i	0.265338	−	1.33395i
$950$		0			0
$951$	32.3654	+	4.84282i	1.04952	+	0.157039i
$952$		0			0
$953$	12.0888	−	29.1848i	0.391593	−	0.945389i	−0.598000	−	0.801496i	$-0.704038\pi$
$953$	12.0888	−	29.1848i	0.391593	−	0.945389i	0.989593	−	0.143893i	$-0.0459622\pi$
$954$		0			0
$955$	48.4803	−	32.3935i	1.56879	−	1.04823i
$956$		0			0
$957$	−15.4212	−	5.53982i	−0.498497	−	0.179077i
$958$		0			0
$959$	−37.7844			−1.22012
$960$		0			0
$961$	−26.8492			−0.866103
$962$		0			0
$963$	4.15963	+	5.09476i	0.134042	+	0.164176i
$964$		0			0
$965$	73.8473	−	49.3432i	2.37723	−	1.58841i
$966$		0			0
$967$	16.2050	−	39.1222i	0.521116	−	1.25809i	−0.416094	−	0.909321i	$-0.636601\pi$
$967$	16.2050	−	39.1222i	0.521116	−	1.25809i	0.937210	−	0.348764i	$-0.113399\pi$
$968$		0			0
$969$	0.133270	−	0.890664i	0.00428124	−	0.0286122i
$970$		0			0
$971$	8.80545	−	44.2680i	0.282580	−	1.42063i	−0.535019	−	0.844840i	$-0.679696\pi$
$971$	8.80545	−	44.2680i	0.282580	−	1.42063i	0.817600	−	0.575787i	$-0.195304\pi$
$972$		0			0
$973$	7.27538	−	10.8884i	0.233238	−	0.349065i
$974$		0			0
$975$	−56.8344	+	14.1599i	−1.82016	+	0.453479i
$976$		0			0
$977$	8.81730	+	8.81730i	0.282090	+	0.282090i	0.833942	−	0.551852i	$-0.186079\pi$
$977$	8.81730	+	8.81730i	0.282090	+	0.282090i	−0.551852	+	0.833942i	$0.686079\pi$
$978$		0			0
$979$	8.90099	−	13.3213i	0.284477	−	0.425750i
$980$		0			0
$981$	14.8280	+	49.3304i	0.473421	+	1.57500i
$982$		0			0
$983$	16.0320	+	38.7047i	0.511341	+	1.23449i	0.943103	+	0.332500i	$0.107892\pi$
$983$	16.0320	+	38.7047i	0.511341	+	1.23449i	−0.431762	+	0.901988i	$0.642108\pi$
$984$		0			0
$985$	−5.89430	+	14.2301i	−0.187808	+	0.453408i
$986$		0			0
$987$	35.4212	−	1.69520i	1.12747	−	0.0539588i
$988$		0			0
$989$	28.2451	−	5.61830i	0.898142	−	0.178652i
$990$		0			0
$991$	−30.3970			−0.965592			−0.482796	−	0.875733i	$-0.660379\pi$
$991$	−30.3970			−0.965592			−0.482796	+	0.875733i	$0.660379\pi$
$992$		0			0
$993$	17.8477	−	29.6918i	0.566380	−	0.942241i
$994$		0			0
$995$	−12.3010	−	61.8414i	−0.389969	−	1.96051i
$996$		0			0
$997$	−2.67064	+	1.78447i	−0.0845801	+	0.0565146i	−0.597141	−	0.802136i	$-0.703697\pi$
$997$	−2.67064	+	1.78447i	−0.0845801	+	0.0565146i	0.512561	+	0.858651i	$0.328697\pi$
$998$		0			0
$999$	11.5456	−	24.1733i	0.365287	−	0.764810i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	768.2.s.a.719.12		240
3.2	odd	2	inner	768.2.s.a.719.23		240
4.3	odd	2		192.2.s.a.11.11	✓	240
12.11	even	2		192.2.s.a.11.20	yes	240
64.29	even	16		192.2.s.a.35.20	yes	240
64.35	odd	16	inner	768.2.s.a.47.23		240
192.29	odd	16		192.2.s.a.35.11	yes	240
192.35	even	16	inner	768.2.s.a.47.12		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
192.2.s.a.11.11	✓	240	4.3	odd	2
192.2.s.a.11.20	yes	240	12.11	even	2
192.2.s.a.35.11	yes	240	192.29	odd	16
192.2.s.a.35.20	yes	240	64.29	even	16
768.2.s.a.47.12		240	192.35	even	16	inner
768.2.s.a.47.23		240	64.35	odd	16	inner
768.2.s.a.719.12		240	1.1	even	1	trivial
768.2.s.a.719.23		240	3.2	odd	2	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:	\( N \)	\(=\)	\( 768 = 2^{8} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	768.s (of order \(16\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.585574 + 1.63006i) q^{3} +(-3.57797 + 2.39072i) q^{5} +(0.994439 - 2.40079i) q^{7} +(-2.31421 - 1.90904i) q^{9} +(0.714367 - 3.59136i) q^{11} +(-1.38986 + 2.08008i) q^{13} +(-1.80186 - 7.23226i) q^{15} +(-0.951204 - 0.951204i) q^{17} +(0.214739 - 0.321380i) q^{19} +(3.33112 + 3.02684i) q^{21} +(1.14288 + 2.75916i) q^{23} +(5.17290 - 12.4885i) q^{25} +(4.46700 - 2.65442i) q^{27} +(-2.53398 + 0.504039i) q^{29} -2.03735 q^{31} +(5.43583 + 3.26747i) q^{33} +(2.18155 + 10.9674i) q^{35} +(4.28668 - 2.86427i) q^{37} +(-2.57679 - 3.48361i) q^{39} +(4.29457 - 1.77887i) q^{41} +(1.88124 - 9.45763i) q^{43} +(12.8442 + 1.29787i) q^{45} +(5.57116 - 5.57116i) q^{47} +(0.174869 + 0.174869i) q^{49} +(2.10752 - 0.993522i) q^{51} +(1.47041 + 0.292483i) q^{53} +(6.02998 + 14.5576i) q^{55} +(0.398124 + 0.538230i) q^{57} +(-3.66506 - 5.48515i) q^{59} +(-4.09381 + 0.814309i) q^{61} +(-6.88455 + 3.65750i) q^{63} -10.7652i q^{65} +(-1.50936 - 7.58806i) q^{67} +(-5.16684 + 0.247277i) q^{69} +(-6.27514 - 2.59925i) q^{71} +(-15.4732 + 6.40920i) q^{73} +(17.3279 + 15.7451i) q^{75} +(-7.91171 - 5.28644i) q^{77} +(-2.31400 + 2.31400i) q^{79} +(1.71111 + 8.83584i) q^{81} +(1.62719 + 1.08726i) q^{83} +(5.67744 + 1.12931i) q^{85} +(0.662214 - 4.42569i) q^{87} +(4.04231 + 1.67438i) q^{89} +(3.61170 + 5.40528i) q^{91} +(1.19302 - 3.32101i) q^{93} +1.66327i q^{95} +1.86899i q^{97} +(-8.50926 + 6.94740i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 8 q^{3} + 16 q^{7} - 8 q^{9} - 16 q^{13} + 8 q^{15} + 16 q^{19} - 8 q^{21} - 16 q^{25} + 8 q^{27} + 32 q^{31} - 16 q^{37} + 8 q^{39} + 16 q^{43} - 8 q^{45} - 16 q^{49} + 8 q^{51} + 80 q^{55} - 8 q^{57}+ \cdots + 8 q^{99}+O(q^{100}) \) 240 * q + 8 * q^3 + 16 * q^7 - 8 * q^9 - 16 * q^13 + 8 * q^15 + 16 * q^19 - 8 * q^21 - 16 * q^25 + 8 * q^27 + 32 * q^31 - 16 * q^37 + 8 * q^39 + 16 * q^43 - 8 * q^45 - 16 * q^49 + 8 * q^51 + 80 * q^55 - 8 * q^57 - 16 * q^61 + 144 * q^67 - 8 * q^69 - 16 * q^73 + 8 * q^75 + 48 * q^79 - 8 * q^81 - 16 * q^85 + 8 * q^87 + 16 * q^91 - 32 * q^93 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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