LMFDB - Embedded newform 768.2.s.a.47.23

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			47.23
Character	$\chi$	$=$	768.47
Dual form			768.2.s.a.719.23

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.16480 - 1.28189i) q^{3} +(3.57797 + 2.39072i) q^{5} +(0.994439 + 2.40079i) q^{7} +(-0.286494 - 2.98629i) q^{9} +(-0.714367 - 3.59136i) q^{11} +(-1.38986 - 2.08008i) q^{13} +(7.23226 - 1.80186i) q^{15} +(0.951204 - 0.951204i) q^{17} +(0.214739 + 0.321380i) q^{19} +(4.23587 + 1.52167i) q^{21} +(-1.14288 + 2.75916i) q^{23} +(5.17290 + 12.4885i) q^{25} +(-4.16181 - 3.11117i) q^{27} +(2.53398 + 0.504039i) q^{29} -2.03735 q^{31} +(-5.43583 - 3.26747i) q^{33} +(-2.18155 + 10.9674i) q^{35} +(4.28668 + 2.86427i) q^{37} +(-4.28535 - 0.641215i) q^{39} +(-4.29457 - 1.77887i) q^{41} +(1.88124 + 9.45763i) q^{43} +(6.11432 - 11.3698i) q^{45} +(-5.57116 - 5.57116i) q^{47} +(0.174869 - 0.174869i) q^{49} +(-0.111381 - 2.32730i) q^{51} +(-1.47041 + 0.292483i) q^{53} +(6.02998 - 14.5576i) q^{55} +(0.662102 + 0.0990701i) q^{57} +(3.66506 - 5.48515i) q^{59} +(-4.09381 - 0.814309i) q^{61} +(6.88455 - 3.65750i) q^{63} -10.7652i q^{65} +(-1.50936 + 7.58806i) q^{67} +(2.20572 + 4.67890i) q^{69} +(6.27514 - 2.59925i) q^{71} +(-15.4732 - 6.40920i) q^{73} +(22.0342 + 7.91545i) q^{75} +(7.91171 - 5.28644i) q^{77} +(-2.31400 - 2.31400i) q^{79} +(-8.83584 + 1.71111i) q^{81} +(-1.62719 + 1.08726i) q^{83} +(5.67744 - 1.12931i) q^{85} +(3.59769 - 2.66118i) q^{87} +(-4.04231 + 1.67438i) q^{89} +(3.61170 - 5.40528i) q^{91} +(-2.37310 + 2.61166i) q^{93} +1.66327i q^{95} -1.86899i q^{97} +(-10.5202 + 3.16221i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/768\mathbb{Z}\right)^\times$.

$n$	$257$	$511$	$517$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{11}{16}\right)$

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
$3$	1.16480	−	1.28189i	0.672496	−	0.740101i
$3$	1.16480	−	1.28189i	0.672496	−	0.740101i
$4$		0			0
$5$	3.57797	+	2.39072i	1.60012	+	1.06916i	0.951321	+	0.308201i	$0.0997270\pi$
$5$	3.57797	+	2.39072i	1.60012	+	1.06916i	0.648796	+	0.760963i	$0.275273\pi$
$6$		0			0
$7$	0.994439	+	2.40079i	0.375863	+	0.907413i	0.992732	+	0.120347i	$0.0384008\pi$
$7$	0.994439	+	2.40079i	0.375863	+	0.907413i	−0.616869	+	0.787066i	$0.711599\pi$
$8$		0			0
$9$	−0.286494	−	2.98629i	−0.0954981	−	0.995430i
$10$		0			0
$11$	−0.714367	−	3.59136i	−0.215390	−	1.08284i	−0.925500	−	0.378747i	$-0.876355\pi$
$11$	−0.714367	−	3.59136i	−0.215390	−	1.08284i	0.710111	−	0.704090i	$-0.248645\pi$
$12$		0			0
$13$	−1.38986	−	2.08008i	−0.385479	−	0.576910i	0.587091	−	0.809521i	$-0.300273\pi$
$13$	−1.38986	−	2.08008i	−0.385479	−	0.576910i	−0.972570	+	0.232611i	$0.925273\pi$
$14$		0			0
$15$	7.23226	−	1.80186i	1.86736	−	0.465239i
$16$		0			0
$17$	0.951204	−	0.951204i	0.230701	−	0.230701i	−0.582284	−	0.812985i	$-0.697841\pi$
$17$	0.951204	−	0.951204i	0.230701	−	0.230701i	0.812985	+	0.582284i	$0.197841\pi$
$18$		0			0
$19$	0.214739	+	0.321380i	0.0492646	+	0.0737297i	0.855284	−	0.518159i	$-0.173382\pi$
$19$	0.214739	+	0.321380i	0.0492646	+	0.0737297i	−0.806020	+	0.591889i	$0.798382\pi$
$20$		0			0
$21$	4.23587	+	1.52167i	0.924343	+	0.332055i
$22$		0			0
$23$	−1.14288	+	2.75916i	−0.238307	+	0.575324i	−0.997108	−	0.0759988i	$-0.975785\pi$
$23$	−1.14288	+	2.75916i	−0.238307	+	0.575324i	0.758801	+	0.651322i	$0.225785\pi$
$24$		0			0
$25$	5.17290	+	12.4885i	1.03458	+	2.49769i
$26$		0			0
$27$	−4.16181	−	3.11117i	−0.800940	−	0.598744i
$28$		0			0
$29$	2.53398	+	0.504039i	0.470548	+	0.0935978i	0.424668	−	0.905349i	$-0.360391\pi$
$29$	2.53398	+	0.504039i	0.470548	+	0.0935978i	0.0458799	+	0.998947i	$0.485391\pi$
$30$		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	0.855578	−	0.517674i	$-0.173202\pi$
$37$	4.28668	+	2.86427i	0.704726	+	0.470883i	−0.150852	+	0.988556i	$0.548202\pi$
$38$		0			0
$39$	−4.28535	−	0.641215i	−0.686205	−	0.102676i
$40$		0			0
$41$	−4.29457	−	1.77887i	−0.670699	−	0.277813i	0.0212338	−	0.999775i	$-0.493241\pi$
$41$	−4.29457	−	1.77887i	−0.670699	−	0.277813i	−0.691933	+	0.721962i	$0.743241\pi$
$42$		0			0
$43$	1.88124	+	9.45763i	0.286886	+	1.44228i	0.808199	+	0.588910i	$0.200443\pi$
$43$	1.88124	+	9.45763i	0.286886	+	1.44228i	−0.521312	+	0.853366i	$0.674557\pi$
$44$		0			0
$45$	6.11432	−	11.3698i	0.911469	−	1.69491i
$46$		0			0
$47$	−5.57116	−	5.57116i	−0.812637	−	0.812637i	0.172392	−	0.985028i	$-0.444850\pi$
$47$	−5.57116	−	5.57116i	−0.812637	−	0.812637i	−0.985028	+	0.172392i	$0.944850\pi$
$48$		0			0
$49$	0.174869	−	0.174869i	0.0249813	−	0.0249813i
$50$		0			0
$51$	−0.111381	−	2.32730i	−0.0155965	−	0.325887i
$52$		0			0
$53$	−1.47041	+	0.292483i	−0.201977	+	0.0401757i	−0.295042	−	0.955484i	$-0.595334\pi$
$53$	−1.47041	+	0.292483i	−0.201977	+	0.0401757i	0.0930650	+	0.995660i	$0.470334\pi$
$54$		0			0
$55$	6.02998	−	14.5576i	0.813082	−	1.96295i
$56$		0			0
$57$	0.662102	+	0.0990701i	0.0876976	+	0.0131222i
$58$		0			0
$59$	3.66506	−	5.48515i	0.477150	−	0.714105i	−0.512328	−	0.858790i	$-0.671217\pi$
$59$	3.66506	−	5.48515i	0.477150	−	0.714105i	0.989478	+	0.144685i	$0.0462167\pi$
$60$		0			0
$61$	−4.09381	−	0.814309i	−0.524158	−	0.104262i	−0.0740827	−	0.997252i	$-0.523603\pi$
$61$	−4.09381	−	0.814309i	−0.524158	−	0.104262i	−0.450075	+	0.892991i	$0.648603\pi$
$62$		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	0.772147	+	0.635444i	$0.219183\pi$
$67$	−1.50936	+	7.58806i	−0.184398	+	0.927029i	−0.956545	+	0.291585i	$0.905817\pi$
$68$		0			0
$69$	2.20572	+	4.67890i	0.265537	+	0.563274i
$70$		0			0
$71$	6.27514	−	2.59925i	0.744722	−	0.308474i	0.0221361	−	0.999755i	$-0.492953\pi$
$71$	6.27514	−	2.59925i	0.744722	−	0.308474i	0.722586	+	0.691281i	$0.242953\pi$
$72$		0			0
$73$	−15.4732	−	6.40920i	−1.81100	−	0.750140i	−0.981454	−	0.191697i	$-0.938601\pi$
$73$	−15.4732	−	6.40920i	−1.81100	−	0.750140i	−0.829543	−	0.558443i	$-0.811399\pi$
$74$		0			0
$75$	22.0342	+	7.91545i	2.54430	+	0.913997i
$76$		0			0
$77$	7.91171	−	5.28644i	0.901623	−	0.602446i
$78$		0			0
$79$	−2.31400	−	2.31400i	−0.260345	−	0.260345i	0.564849	−	0.825194i	$-0.308934\pi$
$79$	−2.31400	−	2.31400i	−0.260345	−	0.260345i	−0.825194	+	0.564849i	$0.808934\pi$
$80$		0			0
$81$	−8.83584	+	1.71111i	−0.981760	+	0.190123i
$82$		0			0
$83$	−1.62719	+	1.08726i	−0.178608	+	0.119342i	−0.641660	−	0.766989i	$-0.721754\pi$
$83$	−1.62719	+	1.08726i	−0.178608	+	0.119342i	0.463053	+	0.886331i	$0.346754\pi$
$84$		0			0
$85$	5.67744	−	1.12931i	0.615805	−	0.122491i
$86$		0			0
$87$	3.59769	−	2.66118i	0.385713	−	0.285309i
$88$		0			0
$89$	−4.04231	+	1.67438i	−0.428484	+	0.177484i	−0.586494	−	0.809954i	$-0.699492\pi$
$89$	−4.04231	+	1.67438i	−0.428484	+	0.177484i	0.158010	+	0.987438i	$0.449492\pi$
$90$		0			0
$91$	3.61170	−	5.40528i	0.378609	−	0.566628i
$92$		0			0
$93$	−2.37310	+	2.61166i	−0.246079	+	0.270817i
$94$		0			0
$95$			1.66327i			0.170648i
$96$		0			0
$97$		−	1.86899i		−	0.189767i	−0.995488	−	0.0948834i	$-0.969752\pi$
$97$		−	1.86899i		−	0.189767i	0.995488	−	0.0948834i	$-0.0302478\pi$
$98$		0			0
$99$	−10.5202	+	3.16221i	−1.05732	+	0.317814i
$100$		0			0
$101$	7.63182	−	11.4218i	0.759395	−	1.13651i	−0.227283	−	0.973829i	$-0.572984\pi$
$101$	7.63182	−	11.4218i	0.759395	−	1.13651i	0.986678	−	0.162686i	$-0.0520157\pi$
$102$		0			0
$103$	−13.4251	+	5.56087i	−1.32282	+	0.547929i	−0.928598	−	0.371087i	$-0.878985\pi$
$103$	−13.4251	+	5.56087i	−1.32282	+	0.547929i	−0.394220	+	0.919016i	$0.628985\pi$
$104$		0			0
$105$	11.5179	+	15.5713i	1.12404	+	1.51960i
$106$		0			0
$107$	2.15026	−	0.427713i	0.207874	−	0.0413486i	−0.0900550	−	0.995937i	$-0.528704\pi$
$107$	2.15026	−	0.427713i	0.207874	−	0.0413486i	0.297929	+	0.954588i	$0.403704\pi$
$108$		0			0
$109$	−14.2766	+	9.53929i	−1.36745	+	0.913698i	−0.999867	−	0.0162943i	$-0.994813\pi$
$109$	−14.2766	+	9.53929i	−1.36745	+	0.913698i	−0.367579	+	0.929992i	$0.619813\pi$
$110$		0			0
$111$	8.66479	−	2.15877i	0.822426	−	0.204901i
$112$		0			0
$113$	−8.95069	−	8.95069i	−0.842010	−	0.842010i	0.147110	−	0.989120i	$-0.453003\pi$
$113$	−8.95069	−	8.95069i	−0.842010	−	0.842010i	−0.989120	+	0.147110i	$0.953003\pi$
$114$		0			0
$115$	−10.6856	+	7.13987i	−0.996434	+	0.665796i
$116$		0			0
$117$	−5.81353	+	4.74647i	−0.537461	+	0.438811i
$118$		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
$123$	−7.28262	+	3.43315i	−0.656652	+	0.309557i
$124$		0			0
$125$	−7.15047	+	35.9478i	−0.639557	+	3.21527i
$126$		0			0
$127$			17.0863i			1.51617i	0.652158	+	0.758083i	$0.273864\pi$
$127$			17.0863i			1.51617i	−0.652158	+	0.758083i	$0.726136\pi$
$128$		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	$-0.459686\pi$
$131$	−1.56358	−	0.311016i	−0.136611	−	0.0271736i	−0.262922	+	0.964817i	$0.584686\pi$
$132$		0			0
$133$	−0.558021	+	0.835137i	−0.0483865	+	0.0724155i
$134$		0			0
$135$	−7.45289	−	21.0814i	−0.641442	−	1.81440i
$136$		0			0
$137$	5.56434	−	13.4335i	0.475393	−	1.14770i	−0.486354	−	0.873762i	$-0.661673\pi$
$137$	5.56434	−	13.4335i	0.475393	−	1.14770i	0.961747	−	0.273939i	$-0.0883267\pi$
$138$		0			0
$139$	4.94256	−	0.983137i	0.419223	−	0.0833886i	0.0190285	−	0.999819i	$-0.493943\pi$
$139$	4.94256	−	0.983137i	0.419223	−	0.0833886i	0.400194	+	0.916430i	$0.368943\pi$
$140$		0			0
$141$	−13.6309	+	0.652353i	−1.14793	+	0.0549380i
$142$		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
$147$	−0.0204763	−	0.427850i	−0.00168885	−	0.0352885i
$148$		0			0
$149$	0.473681	+	2.38135i	0.0388054	+	0.195088i	0.995325	−	0.0965790i	$-0.0307900\pi$
$149$	0.473681	+	2.38135i	0.0388054	+	0.195088i	−0.956520	+	0.291667i	$0.905790\pi$
$150$		0			0
$151$	1.17767	+	0.487807i	0.0958374	+	0.0396972i	0.430087	−	0.902787i	$-0.358483\pi$
$151$	1.17767	+	0.487807i	0.0958374	+	0.0396972i	−0.334250	+	0.942485i	$0.608483\pi$
$152$		0			0
$153$	−3.11308	−	2.56806i	−0.251678	−	0.207615i
$154$		0			0
$155$	−7.28958	−	4.87074i	−0.585513	−	0.391227i
$156$		0			0
$157$	2.08481	−	10.4811i	0.166386	−	0.836479i	−0.803946	−	0.594703i	$-0.797270\pi$
$157$	2.08481	−	10.4811i	0.166386	−	0.836479i	0.970332	−	0.241777i	$-0.0777302\pi$
$158$		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	0.490882	−	0.871226i	$-0.336675\pi$
$163$	7.80064	+	1.55164i	0.610993	+	0.121534i	0.120112	+	0.992760i	$0.461675\pi$
$164$		0			0
$165$	−11.6376	−	24.6865i	−0.905989	−	1.92184i
$166$		0			0
$167$	−6.86336	−	16.5696i	−0.531103	−	1.28220i	−0.930793	−	0.365545i	$-0.880882\pi$
$167$	−6.86336	−	16.5696i	−0.531103	−	1.28220i	0.399691	−	0.916650i	$-0.369118\pi$
$168$		0			0
$169$	2.57988	−	6.22838i	0.198452	−	0.479106i
$170$		0			0
$171$	0.898212	−	0.733347i	0.0686880	−	0.0560805i
$172$		0			0
$173$	7.24199	+	10.8384i	0.550598	+	0.824029i	0.997508	−	0.0705503i	$-0.0224755\pi$
$173$	7.24199	+	10.8384i	0.550598	+	0.824029i	−0.446910	+	0.894579i	$0.647476\pi$
$174$		0			0
$175$	−24.8381	+	24.8381i	−1.87758	+	1.87758i
$176$		0			0
$177$	−2.76232	−	11.0873i	−0.207628	−	0.833372i
$178$		0			0
$179$	3.45085	+	5.16456i	0.257929	+	0.386018i	0.937722	−	0.347386i	$-0.112931\pi$
$179$	3.45085	+	5.16456i	0.257929	+	0.386018i	−0.679794	+	0.733404i	$0.737931\pi$
$180$		0			0
$181$	2.65101	+	13.3275i	0.197048	+	0.990627i	0.945049	+	0.326929i	$0.106014\pi$
$181$	2.65101	+	13.3275i	0.197048	+	0.990627i	−0.748001	+	0.663698i	$0.768986\pi$
$182$		0			0
$183$	−5.81231	+	4.29931i	−0.429658	+	0.317814i
$184$		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
$189$	3.33059	−	13.0855i	0.242265	−	0.951829i
$190$		0			0
$191$	13.5497			0.980420			0.490210	−	0.871604i	$-0.336920\pi$
$191$	13.5497			0.980420			0.490210	+	0.871604i	$0.336920\pi$
$192$		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
$195$	−13.7999	−	12.5393i	−0.988230	−	0.897960i
$196$		0			0
$197$	−2.97611	−	1.98857i	−0.212039	−	0.141680i	0.445016	−	0.895523i	$-0.353198\pi$
$197$	−2.97611	−	1.98857i	−0.212039	−	0.141680i	−0.657055	+	0.753843i	$0.728198\pi$
$198$		0			0
$199$	−5.60732	−	13.5373i	−0.397492	−	0.959631i	−0.988259	−	0.152788i	$-0.951175\pi$
$199$	−5.60732	−	13.5373i	−0.397492	−	0.959631i	0.590767	−	0.806842i	$-0.298825\pi$
$200$		0			0
$201$	7.96898	+	10.7734i	0.562088	+	0.759896i
$202$		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
$207$	8.56706	+	2.62249i	0.595452	+	0.182275i
$208$		0			0
$209$	1.00079	−	1.00079i	0.0692261	−	0.0692261i
$210$		0			0
$211$	−10.2740	−	15.3761i	−0.707289	−	1.05853i	−0.994908	−	0.100788i	$-0.967864\pi$
$211$	−10.2740	−	15.3761i	−0.707289	−	1.05853i	0.287619	−	0.957745i	$-0.407136\pi$
$212$		0			0
$213$	3.97731	−	11.0717i	0.272521	−	0.758617i
$214$		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
$219$	−26.2390	+	12.3695i	−1.77307	+	0.835854i
$220$		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	−0.858482	−	0.512844i	$-0.828592\pi$
$227$	1.97234	−	9.91561i	0.130909	−	0.658122i	0.989391	−	0.145279i	$-0.0464079\pi$
$228$		0			0
$229$	14.4937	+	9.68436i	0.957768	+	0.639960i	0.933055	−	0.359734i	$-0.117133\pi$
$229$	14.4937	+	9.68436i	0.957768	+	0.639960i	0.0247136	+	0.999695i	$0.492133\pi$
$230$		0			0
$231$	2.43890	−	16.2996i	0.160468	−	1.07243i
$232$		0			0
$233$	−7.39105	−	3.06147i	−0.484203	−	0.200564i	0.127209	−	0.991876i	$-0.459398\pi$
$233$	−7.39105	−	3.06147i	−0.484203	−	0.200564i	−0.611412	+	0.791312i	$0.709398\pi$
$234$		0			0
$235$	−6.61434	−	33.2525i	−0.431472	−	2.16916i
$236$		0			0
$237$	−5.66163	+	0.270957i	−0.367763	+	0.0176005i
$238$		0			0
$239$	8.30613	+	8.30613i	0.537279	+	0.537279i	0.922729	−	0.385450i	$-0.125954\pi$
$239$	8.30613	+	8.30613i	0.537279	+	0.537279i	−0.385450	+	0.922729i	$0.625954\pi$
$240$		0			0
$241$	3.01268	−	3.01268i	0.194063	−	0.194063i	−0.603386	−	0.797449i	$-0.706182\pi$
$241$	3.01268	−	3.01268i	0.194063	−	0.194063i	0.797449	+	0.603386i	$0.206182\pi$
$242$		0			0
$243$	−8.09851	+	13.3197i	−0.519519	+	0.854459i
$244$		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
$249$	−0.501606	+	3.35232i	−0.0317880	+	0.212445i
$250$		0			0
$251$	7.23109	−	10.8221i	0.456422	−	0.683085i	−0.529872	−	0.848077i	$-0.677760\pi$
$251$	7.23109	−	10.8221i	0.456422	−	0.683085i	0.986295	+	0.164993i	$0.0527601\pi$
$252$		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
$261$	0.779237	−	7.71159i	0.0482336	−	0.477336i
$262$		0			0
$263$	−10.8728	+	4.50368i	−0.670448	+	0.277709i	−0.691828	−	0.722063i	$-0.743194\pi$
$263$	−10.8728	+	4.50368i	−0.670448	+	0.277709i	0.0213794	+	0.999771i	$0.493194\pi$
$264$		0			0
$265$	−5.96034	−	2.46885i	−0.366141	−	0.151660i
$266$		0			0
$267$	−2.56210	+	7.13211i	−0.156798	+	0.436478i
$268$		0			0
$269$	−3.40585	+	2.27572i	−0.207658	+	0.138753i	−0.655051	−	0.755585i	$-0.727353\pi$
$269$	−3.40585	+	2.27572i	−0.207658	+	0.138753i	0.447392	+	0.894338i	$0.352353\pi$
$270$		0			0
$271$	1.68641	+	1.68641i	0.102442	+	0.102442i	0.756470	−	0.654028i	$-0.226922\pi$
$271$	1.68641	+	1.68641i	0.102442	+	0.102442i	−0.654028	+	0.756470i	$0.726922\pi$
$272$		0			0
$273$	−2.72210	−	10.9259i	−0.164749	−	0.661263i
$274$		0			0
$275$	41.1553	−	27.4991i	2.48176	−	1.65826i
$276$		0			0
$277$	3.18127	−	0.632795i	0.191144	−	0.0380210i	−0.0985898	−	0.995128i	$-0.531433\pi$
$277$	3.18127	−	0.632795i	0.191144	−	0.0380210i	0.289734	+	0.957107i	$0.406433\pi$
$278$		0			0
$279$	0.583689	+	6.08412i	0.0349446	+	0.364246i
$280$		0			0
$281$	−22.6232	+	9.37084i	−1.34959	+	0.559018i	−0.936178	−	0.351527i	$-0.885662\pi$
$281$	−22.6232	+	9.37084i	−1.34959	+	0.559018i	−0.413410	+	0.910545i	$0.635662\pi$
$282$		0			0
$283$	−1.43456	+	2.14698i	−0.0852760	+	0.127625i	−0.871655	−	0.490119i	$-0.836953\pi$
$283$	−1.43456	+	2.14698i	−0.0852760	+	0.127625i	0.786379	+	0.617744i	$0.211953\pi$
$284$		0			0
$285$	2.13213	+	1.93737i	0.126297	+	0.114760i
$286$		0			0
$287$		−	12.0793i		−	0.713020i
$288$		0			0
$289$			15.1904i			0.893554i
$290$		0			0
$291$	−2.39584	−	2.17699i	−0.140447	−	0.127617i
$292$		0			0
$293$	−9.50218	+	14.2210i	−0.555123	+	0.830800i	−0.997828	−	0.0658668i	$-0.979019\pi$
$293$	−9.50218	+	14.2210i	−0.555123	+	0.830800i	0.442705	+	0.896667i	$0.354019\pi$
$294$		0			0
$295$	26.2269	−	10.8636i	1.52699	−	0.632500i
$296$		0			0
$297$	−8.20028	+	17.1691i	−0.475828	+	0.996251i
$298$		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
$303$	−5.75203	−	23.0873i	−0.330445	−	1.32633i
$304$		0			0
$305$	−12.7007	−	12.7007i	−0.727242	−	0.727242i
$306$		0			0
$307$	6.85681	−	4.58157i	0.391339	−	0.261484i	−0.344298	−	0.938860i	$-0.611883\pi$
$307$	6.85681	−	4.58157i	0.391339	−	0.261484i	0.735637	+	0.677376i	$0.236883\pi$
$308$		0			0
$309$	−8.50912	+	23.6869i	−0.484067	+	1.34750i
$310$		0			0
$311$	−30.1840	−	12.5026i	−1.71157	−	0.708958i	−0.999980	−	0.00636791i	$-0.997973\pi$
$311$	−30.1840	−	12.5026i	−1.71157	−	0.708958i	−0.711595	−	0.702590i	$-0.752027\pi$
$312$		0			0
$313$	−6.61643	+	2.74061i	−0.373982	+	0.154909i	−0.561754	−	0.827304i	$-0.689873\pi$
$313$	−6.61643	+	2.74061i	−0.373982	+	0.154909i	0.187772	+	0.982213i	$0.439873\pi$
$314$		0			0
$315$	33.3768	+	3.37264i	1.88057	+	0.190027i
$316$		0			0
$317$	3.68607	−	18.5311i	0.207031	−	1.04081i	−0.727819	−	0.685769i	$-0.759466\pi$
$317$	3.68607	−	18.5311i	0.207031	−	1.04081i	0.934850	−	0.355044i	$-0.115534\pi$
$318$		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
$327$	−4.40095	+	29.4123i	−0.243373	+	1.62651i
$328$		0			0
$329$	7.83499	−	18.9153i	0.431957	−	1.04284i
$330$		0			0
$331$	−19.6169	+	3.90204i	−1.07824	+	0.214476i	−0.702094	−	0.712084i	$-0.747751\pi$
$331$	−19.6169	+	3.90204i	−1.07824	+	0.214476i	−0.376147	+	0.926560i	$0.622751\pi$
$332$		0			0
$333$	7.32542	−	13.6219i	0.401431	−	0.746473i
$334$		0			0
$335$	−23.5414	+	23.5414i	−1.28620	+	1.28620i
$336$		0			0
$337$	3.84192	+	3.84192i	0.209283	+	0.209283i	0.803963	−	0.594680i	$-0.202721\pi$
$337$	3.84192	+	3.84192i	0.209283	+	0.209283i	−0.594680	+	0.803963i	$0.702721\pi$
$338$		0			0
$339$	−21.8996	+	1.04808i	−1.18942	+	0.0569238i
$340$		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
$345$	−3.29398	+	22.0142i	−0.177342	+	1.18521i
$346$		0			0
$347$	14.6437	+	9.78460i	0.786114	+	0.525265i	0.882631	−	0.470067i	$-0.155770\pi$
$347$	14.6437	+	9.78460i	0.786114	+	0.525265i	−0.0965168	+	0.995331i	$0.530770\pi$
$348$		0			0
$349$	−0.173660	+	0.873047i	−0.00929580	+	0.0467332i	−0.985155	−	0.171668i	$-0.945084\pi$
$349$	−0.173660	+	0.873047i	−0.00929580	+	0.0467332i	0.975859	+	0.218402i	$0.0700842\pi$
$350$		0			0
$351$	−0.687124	+	12.9810i	−0.0366760	+	0.692874i
$352$		0			0
$353$	33.0774			1.76053			0.880266	−	0.474481i	$-0.157364\pi$
$353$	33.0774			1.76053			0.880266	+	0.474481i	$0.157364\pi$
$354$		0			0
$355$	28.6663	+	5.70209i	1.52145	+	0.302636i
$356$		0			0
$357$	5.47660	−	2.58176i	0.289852	−	0.136641i
$358$		0			0
$359$	4.91221	+	11.8591i	0.259257	+	0.625901i	0.998890	−	0.0471093i	$-0.0150009\pi$
$359$	4.91221	+	11.8591i	0.259257	+	0.625901i	−0.739633	+	0.673010i	$0.765001\pi$
$360$		0			0
$361$	7.21381	−	17.4157i	0.379674	−	0.916615i
$362$		0			0
$363$	−1.41019	+	3.92555i	−0.0740157	+	0.206038i
$364$		0			0
$365$	−40.0399	−	59.9240i	−2.09579	−	3.13656i
$366$		0			0
$367$	−0.647822	+	0.647822i	−0.0338161	+	0.0338161i	−0.723813	−	0.689997i	$-0.757612\pi$
$367$	−0.647822	+	0.647822i	−0.0338161	+	0.0338161i	0.689997	+	0.723813i	$0.257612\pi$
$368$		0			0
$369$	−4.08185	+	13.3345i	−0.212492	+	0.694164i
$370$		0			0
$371$	−2.16443	−	3.23929i	−0.112371	−	0.168176i
$372$		0			0
$373$	3.01645	+	15.1647i	0.156186	+	0.785200i	0.976873	+	0.213821i	$0.0685911\pi$
$373$	3.01645	+	15.1647i	0.156186	+	0.785200i	−0.820687	+	0.571378i	$0.806409\pi$
$374$		0			0
$375$	37.7524	+	51.0381i	1.94952	+	2.63559i
$376$		0			0
$377$	−2.47344	−	5.97142i	−0.127389	−	0.307544i
$378$		0			0
$379$	2.79369	+	1.86669i	0.143502	+	0.0958852i	0.625249	−	0.780425i	$-0.284997\pi$
$379$	2.79369	+	1.86669i	0.143502	+	0.0958852i	−0.481747	+	0.876311i	$0.659997\pi$
$380$		0			0
$381$	21.9028	+	19.9021i	1.12212	+	1.01962i
$382$		0			0
$383$	23.3643			1.19386			0.596931	−	0.802293i	$-0.296387\pi$
$383$	23.3643			1.19386			0.596931	+	0.802293i	$0.296387\pi$
$384$		0			0
$385$	40.9463			2.08682
$386$		0			0
$387$	27.7043	−	8.32749i	1.40829	−	0.423310i
$388$		0			0
$389$	10.1512	+	6.78284i	0.514688	+	0.343904i	0.785635	−	0.618691i	$-0.212337\pi$
$389$	10.1512	+	6.78284i	0.514688	+	0.343904i	−0.270946	+	0.962594i	$0.587337\pi$
$390$		0			0
$391$	1.53741	+	3.71163i	0.0777501	+	0.187705i
$392$		0			0
$393$	−2.21995	+	1.64207i	−0.111981	+	0.0828316i
$394$		0			0
$395$	−2.74729	−	13.8115i	−0.138231	−	0.694934i
$396$		0			0
$397$	15.0250	+	22.4865i	0.754083	+	1.12856i	0.987719	+	0.156241i	$0.0499376\pi$
$397$	15.0250	+	22.4865i	0.754083	+	1.12856i	−0.233636	+	0.972324i	$0.575062\pi$
$398$		0			0
$399$	0.420574	+	1.68809i	0.0210551	+	0.0845101i
$400$		0			0
$401$	1.77953	−	1.77953i	0.0888656	−	0.0888656i	−0.661277	−	0.750142i	$-0.729985\pi$
$401$	1.77953	−	1.77953i	0.0888656	−	0.0888656i	0.750142	+	0.661277i	$0.229985\pi$
$402$		0			0
$403$	2.83164	+	4.23785i	0.141054	+	0.211102i
$404$		0			0
$405$	−35.7052	−	15.0018i	−1.77420	−	0.745443i
$406$		0			0
$407$	7.22437	−	17.4412i	0.358099	−	0.864526i
$408$		0			0
$409$	−7.30266	−	17.6302i	−0.361093	−	0.871756i	−0.995141	−	0.0984620i	$-0.968608\pi$
$409$	−7.30266	−	17.6302i	−0.361093	−	0.871756i	0.634048	−	0.773294i	$-0.281392\pi$
$410$		0			0
$411$	−10.7390	−	22.7802i	−0.529714	−	1.12366i
$412$		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	0.843541	+	0.537066i	$0.180467\pi$
$419$	−2.89265	+	14.5424i	−0.141315	+	0.710440i	−0.984856	+	0.173375i	$0.944533\pi$
$420$		0			0
$421$	−9.40305	−	6.28291i	−0.458276	−	0.306211i	0.304919	−	0.952378i	$-0.401371\pi$
$421$	−9.40305	−	6.28291i	−0.458276	−	0.306211i	−0.763195	+	0.646168i	$0.776371\pi$
$422$		0			0
$423$	−15.0410	+	18.2332i	−0.731317	+	0.886528i
$424$		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
$429$	0.758475	+	15.8483i	0.0366195	+	0.765164i
$430$		0			0
$431$	−0.840930	−	0.840930i	−0.0405062	−	0.0405062i	0.686564	−	0.727070i	$-0.259118\pi$
$431$	−0.840930	−	0.840930i	−0.0405062	−	0.0405062i	−0.727070	+	0.686564i	$0.759118\pi$
$432$		0			0
$433$	0.498959	−	0.498959i	0.0239785	−	0.0239785i	−0.695016	−	0.718994i	$-0.744603\pi$
$433$	0.498959	−	0.498959i	0.0239785	−	0.0239785i	0.718994	+	0.695016i	$0.244603\pi$
$434$		0			0
$435$	19.2346	−	0.920537i	0.922228	−	0.0441364i
$436$		0			0
$437$	−1.13216	+	0.225200i	−0.0541585	+	0.0107728i
$438$		0			0
$439$	5.55530	−	13.4117i	0.265140	−	0.640105i	−0.734102	−	0.679040i	$-0.762396\pi$
$439$	5.55530	−	13.4117i	0.265140	−	0.640105i	0.999242	+	0.0389347i	$0.0123964\pi$
$440$		0			0
$441$	−0.572309	−	0.472111i	−0.0272528	−	0.0224815i
$442$		0			0
$443$	1.97447	−	2.95500i	0.0938100	−	0.140397i	−0.781596	−	0.623785i	$-0.785594\pi$
$443$	1.97447	−	2.95500i	0.0938100	−	0.140397i	0.875406	+	0.483388i	$0.160594\pi$
$444$		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
$453$	1.99706	−	0.941450i	0.0938302	−	0.0442332i
$454$		0			0
$455$	25.8451	−	10.7054i	1.21164	−	0.501876i
$456$		0			0
$457$	32.8641	+	13.6128i	1.53732	+	0.636779i	0.980968	−	0.194169i	$-0.0622009\pi$
$457$	32.8641	+	13.6128i	1.53732	+	0.636779i	0.556351	+	0.830947i	$0.312201\pi$
$458$		0			0
$459$	−6.91808	+	0.999374i	−0.322908	+	0.0466468i
$460$		0			0
$461$	8.02408	−	5.36152i	0.373719	−	0.249711i	−0.354500	−	0.935056i	$-0.615349\pi$
$461$	8.02408	−	5.36152i	0.373719	−	0.249711i	0.728218	+	0.685345i	$0.240349\pi$
$462$		0			0
$463$	13.9676	+	13.9676i	0.649129	+	0.649129i	0.952782	−	0.303654i	$-0.0982066\pi$
$463$	13.9676	+	13.9676i	0.649129	+	0.649129i	−0.303654	+	0.952782i	$0.598207\pi$
$464$		0			0
$465$	−14.7346	+	3.67103i	−0.683303	+	0.170240i
$466$		0			0
$467$	26.7190	−	17.8531i	1.23641	−	0.826141i	0.246678	−	0.969097i	$-0.420661\pi$
$467$	26.7190	−	17.8531i	1.23641	−	0.826141i	0.989729	+	0.142957i	$0.0456610\pi$
$468$		0			0
$469$	−19.7183	+	3.92221i	−0.910506	+	0.181111i
$470$		0			0
$471$	−11.0072	−	14.8808i	−0.507185	−	0.685672i
$472$		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
$477$	1.29470	+	4.30728i	0.0592804	+	0.197217i
$478$		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
$483$	−9.03961	+	9.94835i	−0.411317	+	0.452665i
$484$		0			0
$485$	4.46823	−	6.68717i	0.202892	−	0.303649i
$486$		0			0
$487$	−1.30351	+	0.539930i	−0.0590676	+	0.0244666i	−0.412022	−	0.911174i	$-0.635177\pi$
$487$	−1.30351	+	0.539930i	−0.0590676	+	0.0244666i	0.352954	+	0.935641i	$0.385177\pi$
$488$		0			0
$489$	11.0752	−	8.19223i	0.500838	−	0.370465i
$490$		0			0
$491$	−10.3424	+	2.05722i	−0.466744	+	0.0928411i	−0.422859	−	0.906195i	$-0.638973\pi$
$491$	−10.3424	+	2.05722i	−0.466744	+	0.0928411i	−0.0438848	+	0.999037i	$0.513973\pi$
$492$		0			0
$493$	2.88977	−	1.93088i	0.130149	−	0.0869627i
$494$		0			0
$495$	−45.2009	−	13.8366i	−2.03163	−	0.621907i
$496$		0			0
$497$	12.4805	+	12.4805i	0.559827	+	0.559827i
$498$		0			0
$499$	10.5229	−	7.03120i	0.471071	−	0.314760i	−0.297277	−	0.954791i	$-0.596079\pi$
$499$	10.5229	−	7.03120i	0.471071	−	0.314760i	0.768349	+	0.640031i	$0.221079\pi$
$500$		0			0
$501$	−29.2349	−	10.5022i	−1.30612	−	0.469202i
$502$		0			0
$503$	−6.66908	−	2.76242i	−0.297360	−	0.123170i	0.229016	−	0.973423i	$-0.426449\pi$
$503$	−6.66908	−	2.76242i	−0.297360	−	0.123170i	−0.526375	+	0.850252i	$0.676449\pi$
$504$		0			0
$505$	54.6129	−	22.6214i	2.43024	−	1.00664i
$506$		0			0
$507$	−4.97907	−	10.5619i	−0.221128	−	0.469071i
$508$		0			0
$509$	−1.85153	+	9.30829i	−0.0820678	+	0.412583i	0.917811	+	0.397018i	$0.129955\pi$
$509$	−1.85153	+	9.30829i	−0.0820678	+	0.412583i	−0.999879	+	0.0155653i	$0.995045\pi$
$510$		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
$519$	22.3291	+	3.34110i	0.980140	+	0.146658i
$520$		0			0
$521$	6.13573	−	14.8130i	0.268811	−	0.648968i	−0.730617	−	0.682788i	$-0.760767\pi$
$521$	6.13573	−	14.8130i	0.268811	−	0.648968i	0.999428	+	0.0338199i	$0.0107673\pi$
$522$		0			0
$523$	31.6109	−	6.28780i	1.38225	−	0.274946i	0.552699	−	0.833381i	$-0.313598\pi$
$523$	31.6109	−	6.28780i	1.38225	−	0.274946i	0.829548	+	0.558435i	$0.188598\pi$
$524$		0			0
$525$	2.90841	+	60.7710i	0.126933	+	2.65226i
$526$		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
$531$	−17.4303	−	9.37346i	−0.756409	−	0.406773i
$532$		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
$537$	10.6400	+	1.59205i	0.459148	+	0.0687021i
$538$		0			0
$539$	−0.752940	−	0.503098i	−0.0324314	−	0.0216700i
$540$		0			0
$541$	5.30294	−	26.6597i	0.227991	−	1.14619i	−0.681933	−	0.731414i	$-0.738861\pi$
$541$	5.30294	−	26.6597i	0.227991	−	1.14619i	0.909924	−	0.414774i	$-0.136139\pi$
$542$		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	0.132737	−	0.991151i	$-0.457624\pi$
$547$	−2.89843	−	0.576533i	−0.123928	−	0.0246508i	−0.256664	+	0.966501i	$0.582624\pi$
$548$		0			0
$549$	−1.25891	+	12.4586i	−0.0537289	+	0.531719i
$550$		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
$555$	36.1634	+	12.9911i	1.53505	+	0.551442i
$556$		0			0
$557$	9.09602	+	13.6132i	0.385411	+	0.576808i	0.972555	−	0.232675i	$-0.0747477\pi$
$557$	9.09602	+	13.6132i	0.385411	+	0.576808i	−0.587144	+	0.809483i	$0.699748\pi$
$558$		0			0
$559$	17.0580	−	17.0580i	0.721475	−	0.721475i
$560$		0			0
$561$	−8.27862	+	2.06256i	−0.349524	+	0.0870812i
$562$		0			0
$563$	−19.5452	−	29.2515i	−0.823732	−	1.23280i	−0.969891	−	0.243541i	$-0.921691\pi$
$563$	−19.5452	−	29.2515i	−0.823732	−	1.23280i	0.146159	−	0.989261i	$-0.453309\pi$
$564$		0			0
$565$	−10.6267	−	53.4239i	−0.447068	−	2.24756i
$566$		0			0
$567$	−12.8947	−	19.5114i	−0.541527	−	0.819402i
$568$		0			0
$569$	7.42318	+	17.9211i	0.311196	+	0.751293i	0.999661	+	0.0260241i	$0.00828468\pi$
$569$	7.42318	+	17.9211i	0.311196	+	0.751293i	−0.688465	+	0.725269i	$0.741715\pi$
$570$		0			0
$571$	−25.4369	−	16.9964i	−1.06450	−	0.711277i	−0.105426	−	0.994427i	$-0.533621\pi$
$571$	−25.4369	−	16.9964i	−1.06450	−	0.711277i	−0.959076	+	0.283150i	$0.908621\pi$
$572$		0			0
$573$	15.7826	−	17.3692i	0.659329	−	0.725610i
$574$		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
$579$	−24.0408	+	26.4575i	−0.999100	+	1.09954i
$580$		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
$585$	−32.1481	+	3.08418i	−1.32916	+	0.127515i
$586$		0			0
$587$	4.83875	+	24.3260i	0.199717	+	1.00404i	0.942422	+	0.334425i	$0.108542\pi$
$587$	4.83875	+	24.3260i	0.199717	+	1.00404i	−0.742706	+	0.669618i	$0.766458\pi$
$588$		0			0
$589$	−0.437499	−	0.654764i	−0.0180268	−	0.0269791i
$590$		0			0
$591$	−6.01569	+	1.49877i	−0.247453	+	0.0616510i
$592$		0			0
$593$	9.31734	−	9.31734i	0.382617	−	0.382617i	−0.489427	−	0.872044i	$-0.662794\pi$
$593$	9.31734	−	9.31734i	0.382617	−	0.382617i	0.872044	+	0.489427i	$0.162794\pi$
$594$		0			0
$595$	8.35712	+	12.5073i	0.342608	+	0.512750i
$596$		0			0
$597$	−23.8847	−	8.58019i	−0.977535	−	0.351164i
$598$		0			0
$599$	−0.450558	+	1.08774i	−0.0184093	+	0.0444440i	−0.932817	−	0.360351i	$-0.882657\pi$
$599$	−0.450558	+	1.08774i	−0.0184093	+	0.0444440i	0.914408	+	0.404795i	$0.132657\pi$
$600$		0			0
$601$	−9.25984	−	22.3552i	−0.377717	−	0.911889i	−0.992393	−	0.123110i	$-0.960713\pi$
$601$	−9.25984	−	22.3552i	−0.377717	−	0.911889i	0.614676	−	0.788780i	$-0.289287\pi$
$602$		0			0
$603$	23.0926	+	2.33345i	0.940402	+	0.0950252i
$604$		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	0.566278	−	0.824214i	$-0.308383\pi$
$613$	0.532520	+	0.355818i	0.0215083	+	0.0143714i	−0.544770	+	0.838586i	$0.683383\pi$
$614$		0			0
$615$	−34.2647	−	5.12701i	−1.38169	−	0.206741i
$616$		0			0
$617$	−15.4604	−	6.40389i	−0.622411	−	0.257811i	0.0491140	−	0.998793i	$-0.484360\pi$
$617$	−15.4604	−	6.40389i	−0.622411	−	0.257811i	−0.671525	+	0.740982i	$0.734360\pi$
$618$		0			0
$619$	8.36961	+	42.0769i	0.336403	+	1.69121i	0.665081	+	0.746771i	$0.268397\pi$
$619$	8.36961	+	42.0769i	0.336403	+	1.69121i	−0.328678	+	0.944442i	$0.606603\pi$
$620$		0			0
$621$	13.3406	−	7.92739i	0.535341	−	0.318115i
$622$		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
$627$	−0.117187	−	2.44862i	−0.00468001	−	0.0977886i
$628$		0			0
$629$	6.80201	−	1.35300i	0.271214	−	0.0539478i
$630$		0			0
$631$	−8.07387	+	19.4920i	−0.321416	+	0.775966i	0.677757	+	0.735286i	$0.262952\pi$
$631$	−8.07387	+	19.4920i	−0.321416	+	0.775966i	−0.999172	+	0.0406796i	$0.987048\pi$
$632$		0			0
$633$	−31.6775	−	4.73990i	−1.25907	−	0.188394i
$634$		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	−0.971197	−	0.238278i	$-0.923417\pi$
$643$	0.437593	−	2.19993i	0.0172570	−	0.0867567i	0.988454	+	0.151521i	$0.0484171\pi$
$644$		0			0
$645$	30.6470	+	65.0103i	1.20672	+	2.55978i
$646$		0			0
$647$	13.8914	−	5.75400i	0.546126	−	0.226213i	−0.0925234	−	0.995711i	$-0.529493\pi$
$647$	13.8914	−	5.75400i	0.546126	−	0.226213i	0.638650	+	0.769498i	$0.279493\pi$
$648$		0			0
$649$	−22.3174	−	9.24415i	−0.876033	−	0.362865i
$650$		0			0
$651$	−8.62995	−	3.10017i	−0.338235	−	0.121505i
$652$		0			0
$653$	20.8375	−	13.9232i	0.815433	−	0.544855i	−0.0764751	−	0.997071i	$-0.524367\pi$
$653$	20.8375	−	13.9232i	0.815433	−	0.544855i	0.891908	+	0.452216i	$0.149367\pi$
$654$		0			0
$655$	−4.85090	−	4.85090i	−0.189540	−	0.189540i
$656$		0			0
$657$	−14.7067	+	48.0435i	−0.573764	+	1.87436i
$658$		0			0
$659$	−24.4240	+	16.3196i	−0.951426	+	0.635722i	−0.931369	−	0.364076i	$-0.881385\pi$
$659$	−24.4240	+	16.3196i	−0.951426	+	0.635722i	−0.0200567	+	0.999799i	$0.506385\pi$
$660$		0			0
$661$	37.5355	−	7.46628i	1.45996	−	0.290405i	0.599687	−	0.800235i	$-0.295292\pi$
$661$	37.5355	−	7.46628i	1.45996	−	0.290405i	0.860275	+	0.509830i	$0.170292\pi$
$662$		0			0
$663$	−4.68617	+	3.46631i	−0.181996	+	0.134620i
$664$		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
$669$	22.3961	−	24.6475i	0.865881	−	0.952927i
$670$		0			0
$671$			15.2841i			0.590035i
$672$		0			0
$673$		−	17.2901i		−	0.666486i	−0.942841	−	0.333243i	$-0.891857\pi$
$673$		−	17.2901i		−	0.666486i	0.942841	−	0.333243i	$-0.108143\pi$
$674$		0			0
$675$	17.3251	−	68.0684i	0.666844	−	2.61995i
$676$		0			0
$677$	−0.0350577	+	0.0524676i	−0.00134738	+	0.00201649i	−0.832143	−	0.554562i	$-0.812886\pi$
$677$	−0.0350577	+	0.0524676i	−0.00134738	+	0.00201649i	0.830795	+	0.556578i	$0.187886\pi$
$678$		0			0
$679$	4.48704	−	1.85859i	0.172197	−	0.0713263i
$680$		0			0
$681$	−10.4134	−	14.0780i	−0.399041	−	0.539470i
$682$		0			0
$683$	25.4364	−	5.05961i	0.973297	−	0.193601i	0.317267	−	0.948336i	$-0.397235\pi$
$683$	25.4364	−	5.05961i	0.973297	−	0.193601i	0.656029	+	0.754735i	$0.272235\pi$
$684$		0			0
$685$	52.0248	−	34.7619i	1.98777	−	1.32818i
$686$		0			0
$687$	29.2965	−	7.29900i	1.11773	−	0.278474i
$688$		0			0
$689$	2.65206	+	2.65206i	0.101036	+	0.101036i
$690$		0			0
$691$	31.0818	−	20.7682i	1.18241	−	0.790059i	0.200550	−	0.979683i	$-0.435727\pi$
$691$	31.0818	−	20.7682i	1.18241	−	0.790059i	0.981857	+	0.189624i	$0.0607270\pi$
$692$		0			0
$693$	−18.0535	−	22.1121i	−0.685795	−	0.839970i
$694$		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
$699$	−12.5335	+	5.90853i	−0.474062	+	0.223481i
$700$		0			0
$701$	−6.43348	+	32.3433i	−0.242989	+	1.22159i	0.645884	+	0.763436i	$0.276489\pi$
$701$	−6.43348	+	32.3433i	−0.242989	+	1.22159i	−0.888873	+	0.458154i	$0.848511\pi$
$702$		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	−0.495593	−	0.868555i	$-0.665049\pi$
$709$	13.2204	−	19.7857i	0.496502	−	0.743067i	0.992095	+	0.125487i	$0.0400494\pi$
$710$		0			0
$711$	−6.24732	+	7.57321i	−0.234293	+	0.284018i
$712$		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
$717$	20.3225	−	0.972604i	0.758958	−	0.0363226i
$718$		0			0
$719$	17.8047	−	17.8047i	0.664002	−	0.664002i	−0.292319	−	0.956321i	$-0.594427\pi$
$719$	17.8047	−	17.8047i	0.664002	−	0.664002i	0.956321	+	0.292319i	$0.0944270\pi$
$720$		0			0
$721$	−26.7010	−	26.7010i	−0.994396	−	0.994396i
$722$		0			0
$723$	−0.352768	−	7.37108i	−0.0131196	−	0.274133i
$724$		0			0
$725$	6.81332	+	34.2529i	0.253040	+	1.27212i
$726$		0			0
$727$	−22.6315	−	9.37426i	−0.839355	−	0.347672i	−0.0787556	−	0.996894i	$-0.525095\pi$
$727$	−22.6315	−	9.37426i	−0.839355	−	0.347672i	−0.760599	+	0.649222i	$0.775095\pi$
$728$		0			0
$729$	7.64129	+	25.8962i	0.283011	+	0.959117i
$730$		0			0
$731$	10.7856	+	7.20670i	0.398919	+	0.266549i
$732$		0			0
$733$	−9.77199	+	49.1271i	−0.360937	+	1.81455i	0.192078	+	0.981380i	$0.438477\pi$
$733$	−9.77199	+	49.1271i	−0.360937	+	1.81455i	−0.553015	+	0.833171i	$0.686523\pi$
$734$		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	−0.365926	−	0.930644i	$-0.619248\pi$
$739$	−28.8194	−	5.73254i	−1.06014	−	0.210875i	−0.694214	+	0.719769i	$0.744248\pi$
$740$		0			0
$741$	−0.714159	−	1.51492i	−0.0262353	−	0.0556520i
$742$		0			0
$743$	15.3189	+	36.9832i	0.561997	+	1.35678i	0.908166	+	0.418609i	$0.137482\pi$
$743$	15.3189	+	36.9832i	0.561997	+	1.35678i	−0.346169	+	0.938172i	$0.612518\pi$
$744$		0			0
$745$	−3.99834	+	9.65285i	−0.146488	+	0.353653i
$746$		0			0
$747$	3.71304	+	4.54778i	0.135853	+	0.166394i
$748$		0			0
$749$	3.16515	+	4.73699i	0.115652	+	0.173086i
$750$		0			0
$751$	0.644925	−	0.644925i	0.0235337	−	0.0235337i	−0.695242	−	0.718776i	$-0.744703\pi$
$751$	0.644925	−	0.644925i	0.0235337	−	0.0235337i	0.718776	+	0.695242i	$0.244703\pi$
$752$		0			0
$753$	−5.45000	−	21.8750i	−0.198609	−	0.797170i
$754$		0			0
$755$	3.04746	+	4.56084i	0.110908	+	0.165986i
$756$		0			0
$757$	2.74459	+	13.7980i	0.0997538	+	0.501496i	0.998067	+	0.0621412i	$0.0197929\pi$
$757$	2.74459	+	13.7980i	0.0997538	+	0.501496i	−0.898314	+	0.439355i	$0.855207\pi$
$758$		0			0
$759$	15.2280	−	11.2640i	0.552740	−	0.408857i
$760$		0			0
$761$	0.456572	+	1.10226i	0.0165507	+	0.0399570i	0.931939	−	0.362615i	$-0.118116\pi$
$761$	0.456572	+	1.10226i	0.0165507	+	0.0399570i	−0.915388	+	0.402572i	$0.868116\pi$
$762$		0			0
$763$	−37.0990	−	24.7888i	−1.34307	−	0.897413i
$764$		0			0
$765$	−4.99901	−	16.6309i	−0.180740	−	0.601293i
$766$		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
$771$	35.7071	+	32.4454i	1.28596	+	1.16849i
$772$		0			0
$773$	−30.0410	−	20.0728i	−1.08050	−	0.721968i	−0.117937	−	0.993021i	$-0.537628\pi$
$773$	−30.0410	−	20.0728i	−1.08050	−	0.721968i	−0.962564	+	0.271053i	$0.912628\pi$
$774$		0			0
$775$	−10.5390	−	25.4434i	−0.378572	−	0.913954i
$776$		0			0
$777$	13.7994	+	18.6556i	0.495049	+	0.669265i
$778$		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
$783$	−8.97778	−	9.98134i	−0.320840	−	0.356704i
$784$		0			0
$785$	32.5167	−	32.5167i	1.16057	−	1.16057i
$786$		0			0
$787$	28.9404	+	43.3124i	1.03161	+	1.54392i	0.824708	+	0.565558i	$0.191339\pi$
$787$	28.9404	+	43.3124i	1.03161	+	1.54392i	0.206906	+	0.978361i	$0.433661\pi$
$788$		0			0
$789$	−6.89143	+	19.1837i	−0.245341	+	0.682957i
$790$		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
$795$	−10.1074	+	4.76480i	−0.358472	+	0.168990i
$796$		0			0
$797$	16.5418	+	3.29037i	0.585942	+	0.116551i	0.479154	−	0.877731i	$-0.340944\pi$
$797$	16.5418	+	3.29037i	0.585942	+	0.116551i	0.106788	+	0.994282i	$0.465944\pi$
$798$		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
$807$	−1.04990	+	7.01668i	−0.0369583	+	0.246999i
$808$		0			0
$809$	−39.8340	−	16.4998i	−1.40049	−	0.580102i	−0.450611	−	0.892721i	$-0.648794\pi$
$809$	−39.8340	−	16.4998i	−1.40049	−	0.580102i	−0.949879	+	0.312619i	$0.898794\pi$
$810$		0			0
$811$	−9.67058	−	48.6173i	−0.339580	−	1.70718i	−0.652823	−	0.757510i	$-0.726416\pi$
$811$	−9.67058	−	48.6173i	−0.339580	−	1.70718i	0.313243	−	0.949673i	$-0.398584\pi$
$812$		0			0
$813$	4.12613	−	0.197470i	0.144710	−	0.00692558i
$814$		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
$819$	−17.1765	−	9.23698i	−0.600194	−	0.322766i
$820$		0			0
$821$	17.9426	−	3.56901i	0.626203	−	0.124559i	0.128219	−	0.991746i	$-0.459074\pi$
$821$	17.9426	−	3.56901i	0.626203	−	0.124559i	0.497984	+	0.867186i	$0.334074\pi$
$822$		0			0
$823$	−5.19727	+	12.5473i	−0.181165	+	0.437372i	−0.988207	−	0.153122i	$-0.951067\pi$
$823$	−5.19727	+	12.5473i	−0.181165	+	0.437372i	0.807042	+	0.590494i	$0.201067\pi$
$824$		0			0
$825$	12.6867	−	84.7876i	0.441695	−	2.95192i
$826$		0			0
$827$	16.4642	−	24.6404i	0.572516	−	0.856831i	−0.426344	−	0.904561i	$-0.640199\pi$
$827$	16.4642	−	24.6404i	0.572516	−	0.856831i	0.998860	+	0.0477298i	$0.0151986\pi$
$828$		0			0
$829$	−16.2671	−	3.23572i	−0.564979	−	0.112381i	−0.0956663	−	0.995413i	$-0.530498\pi$
$829$	−16.2671	−	3.23572i	−0.564979	−	0.112381i	−0.469312	+	0.883032i	$0.655498\pi$
$830$		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
$837$	8.47906	+	6.33853i	0.293079	+	0.219092i
$838$		0			0
$839$	45.1745	−	18.7119i	1.55960	−	0.646006i	0.574578	−	0.818450i	$-0.305166\pi$
$839$	45.1745	−	18.7119i	1.55960	−	0.646006i	0.985019	+	0.172444i	$0.0551662\pi$
$840$		0			0
$841$	−20.6255	−	8.54337i	−0.711225	−	0.294599i
$842$		0			0
$843$	−14.3391	+	39.9157i	−0.493863	+	1.37477i
$844$		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
$849$	1.08122	+	4.33975i	0.0371073	+	0.148940i
$850$		0			0
$851$	−12.8021	+	8.55410i	−0.438851	+	0.293231i
$852$		0			0
$853$	25.6899	−	5.11004i	0.879606	−	0.174965i	0.265427	−	0.964131i	$-0.414487\pi$
$853$	25.6899	−	5.11004i	0.879606	−	0.174965i	0.614179	+	0.789166i	$0.289487\pi$
$854$		0			0
$855$	4.96701	−	0.476518i	0.169868	−	0.0162966i
$856$		0			0
$857$	−30.8971	+	12.7980i	−1.05543	+	0.437172i	−0.841826	−	0.539749i	$-0.818519\pi$
$857$	−30.8971	+	12.7980i	−1.05543	+	0.437172i	−0.213600	+	0.976921i	$0.568519\pi$
$858$		0			0
$859$	−16.0686	+	24.0483i	−0.548252	+	0.820517i	−0.997334	−	0.0729736i	$-0.976751\pi$
$859$	−16.0686	+	24.0483i	−0.548252	+	0.820517i	0.449082	+	0.893491i	$0.351751\pi$
$860$		0			0
$861$	−15.4844	−	14.0700i	−0.527707	−	0.479503i
$862$		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
$867$	19.4725	+	17.6938i	0.661320	+	0.600912i
$868$		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
$873$	−5.58133	+	0.535454i	−0.188899	+	0.0181224i
$874$		0			0
$875$	−93.4139	+	18.5812i	−3.15796	+	0.628158i
$876$		0			0
$877$	−16.5425	+	11.0534i	−0.558602	+	0.373246i	−0.802589	−	0.596533i	$-0.796545\pi$
$877$	−16.5425	+	11.0534i	−0.558602	+	0.373246i	0.243987	+	0.969779i	$0.421545\pi$
$878$		0			0
$879$	7.16169	+	28.7454i	0.241558	+	0.969557i
$880$		0			0
$881$	29.6126	+	29.6126i	0.997673	+	0.997673i	0.999997	−	0.00232406i	$-0.000739773\pi$
$881$	29.6126	+	29.6126i	0.997673	+	0.997673i	−0.00232406	+	0.999997i	$0.500740\pi$
$882$		0			0
$883$	34.3003	−	22.9187i	1.15430	−	0.771277i	0.177222	−	0.984171i	$-0.443289\pi$
$883$	34.3003	−	22.9187i	1.15430	−	0.771277i	0.977075	+	0.212894i	$0.0682889\pi$
$884$		0			0
$885$	16.6232	−	46.2739i	0.558782	−	1.55548i
$886$		0			0
$887$	−17.2802	−	7.15771i	−0.580214	−	0.240332i	0.0732204	−	0.997316i	$-0.476672\pi$
$887$	−17.2802	−	7.15771i	−0.580214	−	0.240332i	−0.653434	+	0.756983i	$0.726672\pi$
$888$		0			0
$889$	−41.0207	+	16.9913i	−1.37579	+	0.569871i
$890$		0			0
$891$	12.4573	+	30.5104i	0.417334	+	1.02214i
$892$		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
$903$	−6.42269	+	42.9240i	−0.213734	+	1.42842i
$904$		0			0
$905$	−22.3772	+	54.0233i	−0.743843	+	1.79580i
$906$		0			0
$907$	6.74321	−	1.34131i	0.223905	−	0.0445374i	−0.0818628	−	0.996644i	$-0.526087\pi$
$907$	6.74321	−	1.34131i	0.223905	−	0.0445374i	0.305768	+	0.952106i	$0.401087\pi$
$908$		0			0
$909$	−36.2954	−	19.5185i	−1.20384	−	0.647389i
$910$		0			0
$911$	7.04481	−	7.04481i	0.233405	−	0.233405i	−0.580707	−	0.814112i	$-0.697224\pi$
$911$	7.04481	−	7.04481i	0.233405	−	0.233405i	0.814112	+	0.580707i	$0.197224\pi$
$912$		0			0
$913$	5.06714	+	5.06714i	0.167698	+	0.167698i
$914$		0			0
$915$	−31.0747	+	1.48719i	−1.02730	+	0.0491649i
$916$		0			0
$917$	−0.808204	−	4.06312i	−0.0266893	−	0.134176i
$918$		0			0
$919$	47.5960	+	19.7149i	1.57005	+	0.650335i	0.986798	−	0.161959i	$-0.0517811\pi$
$919$	47.5960	+	19.7149i	1.57005	+	0.650335i	0.583249	+	0.812293i	$0.301781\pi$
$920$		0			0
$921$	2.11371	−	14.1263i	0.0696491	−	0.465477i
$922$		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	$-0.489418\pi$
$929$	2.02612			0.0664748			0.0332374	+	0.999447i	$0.489418\pi$
$930$		0			0
$931$	0.0937507	+	0.0186482i	0.00307256	+	0.000611169i
$932$		0			0
$933$	−51.1852	+	24.1296i	−1.67573	+	0.789967i
$934$		0			0
$935$	−8.11156	−	19.5830i	−0.265276	−	0.640433i
$936$		0			0
$937$	−0.987795	+	2.38475i	−0.0322699	+	0.0779063i	−0.939193	−	0.343390i	$-0.888425\pi$
$937$	−0.987795	+	2.38475i	−0.0322699	+	0.0779063i	0.906923	+	0.421296i	$0.138425\pi$
$938$		0			0
$939$	−4.19362	+	11.6738i	−0.136854	+	0.380960i
$940$		0			0
$941$	2.09080	+	3.12910i	0.0681580	+	0.102006i	0.863983	−	0.503521i	$-0.167962\pi$
$941$	2.09080	+	3.12910i	0.0681580	+	0.102006i	−0.795825	+	0.605527i	$0.792962\pi$
$942$		0			0
$943$	9.81635	−	9.81635i	0.319664	−	0.319664i
$944$		0			0
$945$	43.2005	−	38.8570i	1.40531	−	1.26402i
$946$		0			0
$947$	16.2924	+	24.3833i	0.529432	+	0.792352i	0.995734	−	0.0922743i	$-0.0294137\pi$
$947$	16.2924	+	24.3833i	0.529432	+	0.792352i	−0.466301	+	0.884626i	$0.654414\pi$
$948$		0			0
$949$	8.17397	+	41.0933i	0.265338	+	1.33395i
$950$		0			0
$951$	−19.4614	−	26.3102i	−0.631079	−	0.853166i
$952$		0			0
$953$	−12.0888	−	29.1848i	−0.391593	−	0.945389i	−0.989593	−	0.143893i	$-0.954038\pi$
$953$	−12.0888	−	29.1848i	−0.391593	−	0.945389i	0.598000	−	0.801496i	$-0.295962\pi$
$954$		0			0
$955$	48.4803	+	32.3935i	1.56879	+	1.04823i
$956$		0			0
$957$	−12.1273	−	11.0196i	−0.392021	−	0.356212i
$958$		0			0
$959$	37.7844			1.22012
$960$		0			0
$961$	−26.8492			−0.866103
$962$		0			0
$963$	−1.89331	−	6.29876i	−0.0610112	−	0.202975i
$964$		0			0
$965$	−73.8473	−	49.3432i	−2.37723	−	1.58841i
$966$		0			0
$967$	16.2050	+	39.1222i	0.521116	+	1.25809i	0.937210	+	0.348764i	$0.113399\pi$
$967$	16.2050	+	39.1222i	0.521116	+	1.25809i	−0.416094	+	0.909321i	$0.636601\pi$
$968$		0			0
$969$	0.724030	−	0.535559i	0.0232592	−	0.0172046i
$970$		0			0
$971$	−8.80545	−	44.2680i	−0.282580	−	1.42063i	−0.817600	−	0.575787i	$-0.804696\pi$
$971$	−8.80545	−	44.2680i	−0.282580	−	1.42063i	0.535019	−	0.844840i	$-0.320304\pi$
$972$		0			0
$973$	7.27538	+	10.8884i	0.233238	+	0.349065i
$974$		0			0
$975$	−14.1599	−	56.8344i	−0.453479	−	1.82016i
$976$		0			0
$977$	−8.81730	+	8.81730i	−0.282090	+	0.282090i	−0.833942	−	0.551852i	$-0.813921\pi$
$977$	−8.81730	+	8.81730i	−0.282090	+	0.282090i	0.551852	+	0.833942i	$0.313921\pi$
$978$		0			0
$979$	8.90099	+	13.3213i	0.284477	+	0.425750i
$980$		0			0
$981$	32.5772	+	39.9010i	1.04011	+	1.27394i
$982$		0			0
$983$	−16.0320	+	38.7047i	−0.511341	+	1.23449i	0.431762	+	0.901988i	$0.357892\pi$
$983$	−16.0320	+	38.7047i	−0.511341	+	1.23449i	−0.943103	+	0.332500i	$0.892108\pi$
$984$		0			0
$985$	−5.89430	−	14.2301i	−0.187808	−	0.453408i
$986$		0			0
$987$	−15.1213	−	32.0762i	−0.481315	−	1.02100i
$988$		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	0.512561	−	0.858651i	$-0.328697\pi$
$997$	−2.67064	−	1.78447i	−0.0845801	−	0.0565146i	−0.597141	+	0.802136i	$0.703697\pi$
$998$		0			0
$999$	−8.92912	−	25.2571i	−0.282505	−	0.799099i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
192.2.s.a.11.11	✓	240	64.53	even	16
192.2.s.a.11.20	yes	240	192.53	odd	16
192.2.s.a.35.11	yes	240	12.11	even	2
192.2.s.a.35.20	yes	240	4.3	odd	2
768.2.s.a.47.12		240	3.2	odd	2	inner
768.2.s.a.47.23		240	1.1	even	1	trivial
768.2.s.a.719.12		240	64.11	odd	16	inner
768.2.s.a.719.23		240	192.11	even	16	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)

\(f(q)\)	\(=\)	\(q+(1.16480 - 1.28189i) q^{3} +(3.57797 + 2.39072i) q^{5} +(0.994439 + 2.40079i) q^{7} +(-0.286494 - 2.98629i) q^{9} +(-0.714367 - 3.59136i) q^{11} +(-1.38986 - 2.08008i) q^{13} +(7.23226 - 1.80186i) q^{15} +(0.951204 - 0.951204i) q^{17} +(0.214739 + 0.321380i) q^{19} +(4.23587 + 1.52167i) q^{21} +(-1.14288 + 2.75916i) q^{23} +(5.17290 + 12.4885i) q^{25} +(-4.16181 - 3.11117i) q^{27} +(2.53398 + 0.504039i) q^{29} -2.03735 q^{31} +(-5.43583 - 3.26747i) q^{33} +(-2.18155 + 10.9674i) q^{35} +(4.28668 + 2.86427i) q^{37} +(-4.28535 - 0.641215i) q^{39} +(-4.29457 - 1.77887i) q^{41} +(1.88124 + 9.45763i) q^{43} +(6.11432 - 11.3698i) q^{45} +(-5.57116 - 5.57116i) q^{47} +(0.174869 - 0.174869i) q^{49} +(-0.111381 - 2.32730i) q^{51} +(-1.47041 + 0.292483i) q^{53} +(6.02998 - 14.5576i) q^{55} +(0.662102 + 0.0990701i) q^{57} +(3.66506 - 5.48515i) q^{59} +(-4.09381 - 0.814309i) q^{61} +(6.88455 - 3.65750i) q^{63} -10.7652i q^{65} +(-1.50936 + 7.58806i) q^{67} +(2.20572 + 4.67890i) q^{69} +(6.27514 - 2.59925i) q^{71} +(-15.4732 - 6.40920i) q^{73} +(22.0342 + 7.91545i) q^{75} +(7.91171 - 5.28644i) q^{77} +(-2.31400 - 2.31400i) q^{79} +(-8.83584 + 1.71111i) q^{81} +(-1.62719 + 1.08726i) q^{83} +(5.67744 - 1.12931i) q^{85} +(3.59769 - 2.66118i) q^{87} +(-4.04231 + 1.67438i) q^{89} +(3.61170 - 5.40528i) q^{91} +(-2.37310 + 2.61166i) q^{93} +1.66327i q^{95} -1.86899i q^{97} +(-10.5202 + 3.16221i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 8 q^{3} + 16 q^{7} - 8 q^{9} - 16 q^{13} + 8 q^{15} + 16 q^{19} - 8 q^{21} - 16 q^{25} + 8 q^{27} + 32 q^{31} - 16 q^{37} + 8 q^{39} + 16 q^{43} - 8 q^{45} - 16 q^{49} + 8 q^{51} + 80 q^{55} - 8 q^{57}+ \cdots + 8 q^{99}+O(q^{100}) \) 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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