LMFDB - Embedded newform 768.2.s.a.431.14

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			431.14
Character	$\chi$	$=$	768.431
Dual form			768.2.s.a.335.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.00323701 + 1.73205i) q^{3} +(0.951414 - 1.42389i) q^{5} +(0.304742 + 0.735711i) q^{7} +(-2.99998 - 0.0112133i) q^{9} +(-5.27874 + 1.05001i) q^{11} +(-2.38495 + 1.59357i) q^{13} +(2.46317 + 1.65250i) q^{15} +(-3.60610 + 3.60610i) q^{17} +(2.23180 - 1.49124i) q^{19} +(-1.27527 + 0.525445i) q^{21} +(-2.89265 + 6.98348i) q^{23} +(0.791139 + 1.90998i) q^{25} +(0.0291330 - 5.19607i) q^{27} +(-0.806254 + 4.05331i) q^{29} +6.95599 q^{31} +(-1.80158 - 9.14643i) q^{33} +(1.33751 + 0.266047i) q^{35} +(-2.51344 + 3.76162i) q^{37} +(-2.75242 - 4.13600i) q^{39} +(-1.08807 - 0.450693i) q^{41} +(-1.84512 + 0.367016i) q^{43} +(-2.87019 + 4.26097i) q^{45} +(4.93192 + 4.93192i) q^{47} +(4.50134 - 4.50134i) q^{49} +(-6.23427 - 6.25761i) q^{51} +(-1.88555 - 9.47932i) q^{53} +(-3.52717 + 8.51534i) q^{55} +(2.57568 + 3.87042i) q^{57} +(-2.08460 - 1.39288i) q^{59} +(-0.211398 + 1.06277i) q^{61} +(-0.905968 - 2.21053i) q^{63} +4.91205i q^{65} +(-13.8689 - 2.75869i) q^{67} +(-12.0864 - 5.03282i) q^{69} +(-4.58122 + 1.89760i) q^{71} +(0.638643 + 0.264535i) q^{73} +(-3.31074 + 1.36411i) q^{75} +(-2.38115 - 3.56365i) q^{77} +(-2.62297 - 2.62297i) q^{79} +(8.99975 + 0.0672794i) q^{81} +(1.68471 + 2.52135i) q^{83} +(1.70380 + 8.56559i) q^{85} +(-7.01792 - 1.40959i) q^{87} +(14.6543 - 6.06999i) q^{89} +(-1.89920 - 1.26900i) q^{91} +(-0.0225166 + 12.0481i) q^{93} -4.59663i q^{95} +0.149313i q^{97} +(15.8479 - 3.09081i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/768\mathbb{Z}\right)^\times$.

$n$	$257$	$511$	$517$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{3}{16}\right)$

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
$3$	−0.00323701	+	1.73205i	−0.00186889	+	0.999998i
$3$	−0.00323701	+	1.73205i	−0.00186889	+	0.999998i
$4$		0			0
$5$	0.951414	−	1.42389i	0.425485	−	0.636783i	−0.555351	−	0.831616i	$-0.687416\pi$
$5$	0.951414	−	1.42389i	0.425485	−	0.636783i	0.980837	+	0.194832i	$0.0624163\pi$
$6$		0			0
$7$	0.304742	+	0.735711i	0.115181	+	0.278073i	0.970948	−	0.239289i	$-0.0769143\pi$
$7$	0.304742	+	0.735711i	0.115181	+	0.278073i	−0.855767	+	0.517361i	$0.826914\pi$
$8$		0			0
$9$	−2.99998	−	0.0112133i	−0.999993	−	0.00373777i
$10$		0			0
$11$	−5.27874	+	1.05001i	−1.59160	+	0.316589i	−0.909831	−	0.414978i	$-0.863789\pi$
$11$	−5.27874	+	1.05001i	−1.59160	+	0.316589i	−0.681769	+	0.731567i	$0.738789\pi$
$12$		0			0
$13$	−2.38495	+	1.59357i	−0.661465	+	0.441977i	−0.840460	−	0.541873i	$-0.817715\pi$
$13$	−2.38495	+	1.59357i	−0.661465	+	0.441977i	0.178995	+	0.983850i	$0.442715\pi$
$14$		0			0
$15$	2.46317	+	1.65250i	0.635987	+	0.426674i
$16$		0			0
$17$	−3.60610	+	3.60610i	−0.874608	+	0.874608i	−0.992970	−	0.118362i	$-0.962236\pi$
$17$	−3.60610	+	3.60610i	−0.874608	+	0.874608i	0.118362	+	0.992970i	$0.462236\pi$
$18$		0			0
$19$	2.23180	−	1.49124i	0.512011	−	0.342115i	−0.272575	−	0.962134i	$-0.587875\pi$
$19$	2.23180	−	1.49124i	0.512011	−	0.342115i	0.784586	+	0.620020i	$0.212875\pi$
$20$		0			0
$21$	−1.27527	+	0.525445i	−0.278287	+	0.114662i
$22$		0			0
$23$	−2.89265	+	6.98348i	−0.603160	+	1.45616i	0.267151	+	0.963655i	$0.413918\pi$
$23$	−2.89265	+	6.98348i	−0.603160	+	1.45616i	−0.870311	+	0.492502i	$0.836082\pi$
$24$		0			0
$25$	0.791139	+	1.90998i	0.158228	+	0.381996i
$26$		0			0
$27$	0.0291330	−	5.19607i	0.00560664	−	0.999984i
$28$		0			0
$29$	−0.806254	+	4.05331i	−0.149718	+	0.752681i	0.830850	+	0.556497i	$0.187855\pi$
$29$	−0.806254	+	4.05331i	−0.149718	+	0.752681i	−0.980567	+	0.196184i	$0.937145\pi$
$30$		0			0
$31$	6.95599			1.24933			0.624666	−	0.780892i	$-0.285235\pi$
$31$	6.95599			1.24933			0.624666	+	0.780892i	$0.285235\pi$
$32$		0			0
$33$	−1.80158	−	9.14643i	−0.313614	−	1.59219i
$34$		0			0
$35$	1.33751	+	0.266047i	0.226080	+	0.0449701i
$36$		0			0
$37$	−2.51344	+	3.76162i	−0.413206	+	0.618407i	−0.978442	−	0.206523i	$-0.933785\pi$
$37$	−2.51344	+	3.76162i	−0.413206	+	0.618407i	0.565235	+	0.824930i	$0.308785\pi$
$38$		0			0
$39$	−2.75242	−	4.13600i	−0.440740	−	0.662290i
$40$		0			0
$41$	−1.08807	−	0.450693i	−0.169928	−	0.0703865i	0.296098	−	0.955158i	$-0.404315\pi$
$41$	−1.08807	−	0.450693i	−0.169928	−	0.0703865i	−0.466026	+	0.884771i	$0.654315\pi$
$42$		0			0
$43$	−1.84512	+	0.367016i	−0.281377	+	0.0559695i	−0.333761	−	0.942658i	$-0.608318\pi$
$43$	−1.84512	+	0.367016i	−0.281377	+	0.0559695i	0.0523840	+	0.998627i	$0.483318\pi$
$44$		0			0
$45$	−2.87019	+	4.26097i	−0.427862	+	0.635189i
$46$		0			0
$47$	4.93192	+	4.93192i	0.719394	+	0.719394i	0.968481	−	0.249087i	$-0.0801306\pi$
$47$	4.93192	+	4.93192i	0.719394	+	0.719394i	−0.249087	+	0.968481i	$0.580131\pi$
$48$		0			0
$49$	4.50134	−	4.50134i	0.643049	−	0.643049i
$50$		0			0
$51$	−6.23427	−	6.25761i	−0.872972	−	0.876241i
$52$		0			0
$53$	−1.88555	−	9.47932i	−0.259001	−	1.30208i	−0.863042	−	0.505132i	$-0.831444\pi$
$53$	−1.88555	−	9.47932i	−0.259001	−	1.30208i	0.604041	−	0.796953i	$-0.293556\pi$
$54$		0			0
$55$	−3.52717	+	8.51534i	−0.475604	+	1.14821i
$56$		0			0
$57$	2.57568	+	3.87042i	0.341157	+	0.512649i
$58$		0			0
$59$	−2.08460	−	1.39288i	−0.271392	−	0.181338i	0.412426	−	0.910991i	$-0.364682\pi$
$59$	−2.08460	−	1.39288i	−0.271392	−	0.181338i	−0.683817	+	0.729653i	$0.739682\pi$
$60$		0			0
$61$	−0.211398	+	1.06277i	−0.0270668	+	0.136074i	−0.991956	−	0.126583i	$-0.959599\pi$
$61$	−0.211398	+	1.06277i	−0.0270668	+	0.136074i	0.964889	+	0.262657i	$0.0845988\pi$
$62$		0			0
$63$	−0.905968	−	2.21053i	−0.114141	−	0.278501i
$64$		0			0
$65$			4.91205i			0.609264i
$66$		0			0
$67$	−13.8689	−	2.75869i	−1.69435	−	0.337027i	−0.748873	−	0.662714i	$-0.769405\pi$
$67$	−13.8689	−	2.75869i	−1.69435	−	0.337027i	−0.945478	+	0.325687i	$0.894405\pi$
$68$		0			0
$69$	−12.0864	−	5.03282i	−1.45503	−	0.605880i
$70$		0			0
$71$	−4.58122	+	1.89760i	−0.543691	+	0.225204i	−0.637588	−	0.770378i	$-0.720068\pi$
$71$	−4.58122	+	1.89760i	−0.543691	+	0.225204i	0.0938968	+	0.995582i	$0.470068\pi$
$72$		0			0
$73$	0.638643	+	0.264535i	0.0747476	+	0.0309615i	0.419744	−	0.907643i	$-0.362120\pi$
$73$	0.638643	+	0.264535i	0.0747476	+	0.0309615i	−0.344996	+	0.938604i	$0.612120\pi$
$74$		0			0
$75$	−3.31074	+	1.36411i	−0.382291	+	0.157514i
$76$		0			0
$77$	−2.38115	−	3.56365i	−0.271358	−	0.406115i
$78$		0			0
$79$	−2.62297	−	2.62297i	−0.295108	−	0.295108i	0.543986	−	0.839094i	$-0.316914\pi$
$79$	−2.62297	−	2.62297i	−0.295108	−	0.295108i	−0.839094	+	0.543986i	$0.816914\pi$
$80$		0			0
$81$	8.99975	+	0.0672794i	0.999972	+	0.00747549i
$82$		0			0
$83$	1.68471	+	2.52135i	0.184921	+	0.276754i	0.912335	−	0.409445i	$-0.134278\pi$
$83$	1.68471	+	2.52135i	0.184921	+	0.276754i	−0.727414	+	0.686199i	$0.759278\pi$
$84$		0			0
$85$	1.70380	+	8.56559i	0.184803	+	0.929069i
$86$		0			0
$87$	−7.01792	−	1.40959i	−0.752400	−	0.151124i
$88$		0			0
$89$	14.6543	−	6.06999i	1.55335	−	0.643418i	0.569430	−	0.822040i	$-0.307164\pi$
$89$	14.6543	−	6.06999i	1.55335	−	0.643418i	0.983918	+	0.178622i	$0.0571639\pi$
$90$		0			0
$91$	−1.89920	−	1.26900i	−0.199090	−	0.133028i
$92$		0			0
$93$	−0.0225166	+	12.0481i	−0.00233486	+	1.24933i
$94$		0			0
$95$		−	4.59663i		−	0.471605i
$96$		0			0
$97$			0.149313i			0.0151604i	0.999971	+	0.00758022i	$0.00241288\pi$
$97$			0.149313i			0.0151604i	−0.999971	+	0.00758022i	$0.997587\pi$
$98$		0			0
$99$	15.8479	−	3.09081i	1.59277	−	0.310638i
$100$		0			0
$101$	1.92669	+	1.28738i	0.191713	+	0.128099i	0.647723	−	0.761876i	$-0.275722\pi$
$101$	1.92669	+	1.28738i	0.191713	+	0.128099i	−0.456009	+	0.889975i	$0.650722\pi$
$102$		0			0
$103$	16.6745	−	6.90682i	1.64299	−	0.680549i	0.646397	−	0.763002i	$-0.276275\pi$
$103$	16.6745	−	6.90682i	1.64299	−	0.680549i	0.996595	+	0.0824521i	$0.0262751\pi$
$104$		0			0
$105$	−0.465135	+	2.31577i	−0.0453926	+	0.225996i
$106$		0			0
$107$	−1.86716	−	9.38684i	−0.180505	−	0.907460i	−0.959775	−	0.280772i	$-0.909410\pi$
$107$	−1.86716	−	9.38684i	−0.180505	−	0.907460i	0.779270	−	0.626689i	$-0.215590\pi$
$108$		0			0
$109$	3.82994	+	5.73191i	0.366842	+	0.549017i	0.968269	−	0.249910i	$-0.0804011\pi$
$109$	3.82994	+	5.73191i	0.366842	+	0.549017i	−0.601427	+	0.798927i	$0.705401\pi$
$110$		0			0
$111$	−6.50718	−	4.36557i	−0.617634	−	0.414361i
$112$		0			0
$113$	−10.9819	−	10.9819i	−1.03309	−	1.03309i	−0.999434	−	0.0336525i	$-0.989286\pi$
$113$	−10.9819	−	10.9819i	−1.03309	−	1.03309i	−0.0336525	−	0.999434i	$-0.510714\pi$
$114$		0			0
$115$	7.19161	+	10.7630i	0.670621	+	1.00366i
$116$		0			0
$117$	7.17266	−	4.75393i	0.663112	−	0.439501i
$118$		0			0
$119$	−3.75198	−	1.55412i	−0.343943	−	0.142466i
$120$		0			0
$121$	16.5999	−	6.87591i	1.50908	−	0.625083i
$122$		0			0
$123$	0.784144	−	1.88313i	0.0707039	−	0.169796i
$124$		0			0
$125$	11.8703	+	2.36114i	1.06171	+	0.211187i
$126$		0			0
$127$			20.2770i			1.79929i	0.436624	+	0.899644i	$0.356174\pi$
$127$			20.2770i			1.79929i	−0.436624	+	0.899644i	$0.643826\pi$
$128$		0			0
$129$	−0.629717	−	3.19702i	−0.0554435	−	0.281482i
$130$		0			0
$131$	−0.249189	+	1.25276i	−0.0217717	+	0.109454i	−0.990143	−	0.140059i	$-0.955271\pi$
$131$	−0.249189	+	1.25276i	−0.0217717	+	0.109454i	0.968371	+	0.249513i	$0.0802706\pi$
$132$		0			0
$133$	1.77725	+	1.18752i	0.154107	+	0.102971i
$134$		0			0
$135$	−7.37092	−	4.98509i	−0.634388	−	0.429049i
$136$		0			0
$137$	−3.45449	+	8.33988i	−0.295137	+	0.712524i	0.704858	+	0.709348i	$0.251011\pi$
$137$	−3.45449	+	8.33988i	−0.295137	+	0.712524i	−0.999995	+	0.00317519i	$0.998989\pi$
$138$		0			0
$139$	1.01764	+	5.11603i	0.0863153	+	0.433936i	0.999643	+	0.0267113i	$0.00850349\pi$
$139$	1.01764	+	5.11603i	0.0863153	+	0.433936i	−0.913328	+	0.407225i	$0.866497\pi$
$140$		0			0
$141$	−8.55828	+	8.52635i	−0.720737	+	0.718048i
$142$		0			0
$143$	10.9163	−	10.9163i	0.912863	−	0.912863i
$144$		0			0
$145$	5.00439	+	5.00439i	0.415592	+	0.415592i
$146$		0			0
$147$	7.78197	+	7.81111i	0.641846	+	0.644250i
$148$		0			0
$149$	16.6513	−	3.31215i	1.36413	−	0.271342i	0.541872	−	0.840461i	$-0.317716\pi$
$149$	16.6513	−	3.31215i	1.36413	−	0.271342i	0.822255	+	0.569119i	$0.192716\pi$
$150$		0			0
$151$	5.96083	+	2.46906i	0.485086	+	0.200929i	0.611804	−	0.791010i	$-0.290444\pi$
$151$	5.96083	+	2.46906i	0.485086	+	0.200929i	−0.126718	+	0.991939i	$0.540444\pi$
$152$		0			0
$153$	10.8587	−	10.7778i	0.877871	−	0.871333i
$154$		0			0
$155$	6.61802	−	9.90457i	0.531572	−	0.795554i
$156$		0			0
$157$	−13.1331	−	2.61233i	−1.04813	−	0.208487i	−0.359162	−	0.933275i	$-0.616938\pi$
$157$	−13.1331	−	2.61233i	−1.04813	−	0.208487i	−0.688972	+	0.724788i	$0.741938\pi$
$158$		0			0
$159$	16.4247	−	3.23519i	1.30257	−	0.256567i
$160$		0			0
$161$	−6.01934			−0.474390
$162$		0			0
$163$	−4.06143	+	20.4182i	−0.318116	+	1.59928i	0.408849	+	0.912602i	$0.365930\pi$
$163$	−4.06143	+	20.4182i	−0.318116	+	1.59928i	−0.726965	+	0.686675i	$0.759070\pi$
$164$		0			0
$165$	−14.7376	−	6.13679i	−1.14732	−	0.477749i
$166$		0			0
$167$	4.47253	+	10.7976i	0.346095	+	0.835546i	0.997073	+	0.0764504i	$0.0243587\pi$
$167$	4.47253	+	10.7976i	0.346095	+	0.835546i	−0.650979	+	0.759096i	$0.725641\pi$
$168$		0			0
$169$	−1.82638	+	4.40928i	−0.140491	+	0.339175i
$170$		0			0
$171$	−6.71209	+	4.44867i	−0.513286	+	0.340199i
$172$		0			0
$173$	−10.2207	+	6.82923i	−0.777062	+	0.519217i	−0.879715	−	0.475501i	$-0.842267\pi$
$173$	−10.2207	+	6.82923i	−0.777062	+	0.519217i	0.102653	+	0.994717i	$0.467267\pi$
$174$		0			0
$175$	−1.16410	+	1.16410i	−0.0879977	+	0.0879977i
$176$		0			0
$177$	2.41929	−	3.60611i	0.181845	−	0.271052i
$178$		0			0
$179$	6.50009	−	4.34322i	0.485839	−	0.324627i	−0.288411	−	0.957507i	$-0.593127\pi$
$179$	6.50009	−	4.34322i	0.485839	−	0.324627i	0.774251	+	0.632879i	$0.218127\pi$
$180$		0			0
$181$	12.7875	−	2.54359i	0.950487	−	0.189064i	0.304586	−	0.952485i	$-0.401482\pi$
$181$	12.7875	−	2.54359i	0.950487	−	0.189064i	0.645901	+	0.763421i	$0.276482\pi$
$182$		0			0
$183$	−1.84008	−	0.369592i	−0.136023	−	0.0273210i
$184$		0			0
$185$	2.96482	+	7.15772i	0.217978	+	0.526246i
$186$		0			0
$187$	15.2492	−	22.8221i	1.11514	−	1.66892i
$188$		0			0
$189$	3.83168	−	1.56202i	0.278714	−	0.113621i
$190$		0			0
$191$	11.6080			0.839922			0.419961	−	0.907542i	$-0.362044\pi$
$191$	11.6080			0.839922			0.419961	+	0.907542i	$0.362044\pi$
$192$		0			0
$193$	−23.6837			−1.70479			−0.852396	−	0.522896i	$-0.824852\pi$
$193$	−23.6837			−1.70479			−0.852396	+	0.522896i	$0.824852\pi$
$194$		0			0
$195$	−8.50790	−	0.0159003i	−0.609263	−	0.00113865i
$196$		0			0
$197$	5.94160	−	8.89224i	0.423322	−	0.633546i	−0.557102	−	0.830444i	$-0.688087\pi$
$197$	5.94160	−	8.89224i	0.423322	−	0.633546i	0.980424	+	0.196898i	$0.0630869\pi$
$198$		0			0
$199$	0.0481228	+	0.116179i	0.00341134	+	0.00823569i	0.925576	−	0.378562i	$-0.123581\pi$
$199$	0.0481228	+	0.116179i	0.00341134	+	0.00823569i	−0.922165	+	0.386797i	$0.873581\pi$
$200$		0			0
$201$	4.82307	−	24.0126i	0.340193	−	1.69372i
$202$		0			0
$203$	−3.22776	+	0.642042i	−0.226545	+	0.0450625i
$204$		0			0
$205$	−1.67694	+	1.12050i	−0.117123	+	0.0782589i
$206$		0			0
$207$	8.75621	−	20.9179i	0.608598	−	1.45389i
$208$		0			0
$209$	−10.2153	+	10.2153i	−0.706607	+	0.706607i
$210$		0			0
$211$	11.9918	−	8.01268i	0.825551	−	0.551615i	−0.0694988	−	0.997582i	$-0.522140\pi$
$211$	11.9918	−	8.01268i	0.825551	−	0.551615i	0.895050	+	0.445967i	$0.147140\pi$
$212$		0			0
$213$	−3.27191	−	7.94104i	−0.224188	−	0.544111i
$214$		0			0
$215$	−1.23288	+	2.97643i	−0.0840815	+	0.202991i
$216$		0			0
$217$	2.11978	+	5.11760i	0.143900	+	0.347405i
$218$		0			0
$219$	−0.460254	+	1.10530i	−0.0311011	+	0.0746896i
$220$		0			0
$221$	2.85378	−	14.3469i	0.191966	−	0.965079i
$222$		0			0
$223$	−15.4594			−1.03524			−0.517618	−	0.855612i	$-0.673181\pi$
$223$	−15.4594			−1.03524			−0.517618	+	0.855612i	$0.673181\pi$
$224$		0			0
$225$	−2.35198	−	5.73877i	−0.156799	−	0.382585i
$226$		0			0
$227$	−8.37592	−	1.66607i	−0.555929	−	0.110581i	−0.0908733	−	0.995862i	$-0.528966\pi$
$227$	−8.37592	−	1.66607i	−0.555929	−	0.110581i	−0.465056	+	0.885281i	$0.653966\pi$
$228$		0			0
$229$	1.16297	−	1.74050i	0.0768510	−	0.115016i	−0.791053	−	0.611748i	$-0.790467\pi$
$229$	1.16297	−	1.74050i	0.0768510	−	0.115016i	0.867904	+	0.496732i	$0.165467\pi$
$230$		0			0
$231$	6.18012	−	4.11274i	0.406622	−	0.270598i
$232$		0			0
$233$	9.34754	+	3.87188i	0.612378	+	0.253655i	0.667245	−	0.744839i	$-0.267473\pi$
$233$	9.34754	+	3.87188i	0.612378	+	0.253655i	−0.0548670	+	0.998494i	$0.517473\pi$
$234$		0			0
$235$	11.7148	−	2.33022i	0.764189	−	0.152007i
$236$		0			0
$237$	4.55161	−	4.53463i	0.295659	−	0.294556i
$238$		0			0
$239$	8.11977	+	8.11977i	0.525224	+	0.525224i	0.919145	−	0.393920i	$-0.128881\pi$
$239$	8.11977	+	8.11977i	0.525224	+	0.525224i	−0.393920	+	0.919145i	$0.628881\pi$
$240$		0			0
$241$	−20.6545	+	20.6545i	−1.33047	+	1.33047i	−0.425523	+	0.904948i	$0.639910\pi$
$241$	−20.6545	+	20.6545i	−1.33047	+	1.33047i	−0.904948	+	0.425523i	$0.860090\pi$
$242$		0			0
$243$	−0.145663	+	15.5878i	−0.00934431	+	0.999956i
$244$		0			0
$245$	−2.12678	−	10.6921i	−0.135875	−	0.683091i
$246$		0			0
$247$	−2.94633	+	7.11307i	−0.187470	+	0.452594i
$248$		0			0
$249$	−4.37255	+	2.90984i	−0.277099	+	0.184403i
$250$		0			0
$251$	−6.36129	−	4.25048i	−0.401521	−	0.268288i	0.338372	−	0.941013i	$-0.390124\pi$
$251$	−6.36129	−	4.25048i	−0.401521	−	0.268288i	−0.739893	+	0.672725i	$0.765124\pi$
$252$		0			0
$253$	7.93686	−	39.9013i	0.498986	−	2.50857i
$254$		0			0
$255$	−14.8415	+	2.92334i	−0.929412	+	0.183067i
$256$		0			0
$257$		−	2.41242i		−	0.150483i	−0.997165	−	0.0752414i	$-0.976027\pi$
$257$		−	2.41242i		−	0.150483i	0.997165	−	0.0752414i	$-0.0239727\pi$
$258$		0			0
$259$	−3.53342	−	0.702840i	−0.219556	−	0.0436724i
$260$		0			0
$261$	2.46420	−	12.1508i	0.152530	−	0.752116i
$262$		0			0
$263$	15.6931	−	6.50028i	0.967676	−	0.400825i	0.157830	−	0.987466i	$-0.449550\pi$
$263$	15.6931	−	6.50028i	0.967676	−	0.400825i	0.809847	+	0.586642i	$0.199550\pi$
$264$		0			0
$265$	−15.2915	−	6.33393i	−0.939347	−	0.389090i
$266$		0			0
$267$	10.4661	+	25.4015i	0.640514	+	1.55455i
$268$		0			0
$269$	9.94484	+	14.8835i	0.606348	+	0.907464i	0.999930	−	0.0118258i	$-0.00376437\pi$
$269$	9.94484	+	14.8835i	0.606348	+	0.907464i	−0.393582	+	0.919289i	$0.628764\pi$
$270$		0			0
$271$	−20.7141	−	20.7141i	−1.25829	−	1.25829i	−0.951909	−	0.306382i	$-0.900882\pi$
$271$	−20.7141	−	20.7141i	−1.25829	−	1.25829i	−0.306382	−	0.951909i	$-0.599118\pi$
$272$		0			0
$273$	2.20412	−	3.28540i	0.133400	−	0.198841i
$274$		0			0
$275$	−6.18171	−	9.25159i	−0.372771	−	0.557892i
$276$		0			0
$277$	4.98281	+	25.0503i	0.299388	+	1.50513i	0.778652	+	0.627456i	$0.215904\pi$
$277$	4.98281	+	25.0503i	0.299388	+	1.50513i	−0.479264	+	0.877671i	$0.659096\pi$
$278$		0			0
$279$	−20.8678	−	0.0779997i	−1.24932	−	0.00466972i
$280$		0			0
$281$	−28.1242	+	11.6494i	−1.67775	+	0.694947i	−0.999215	−	0.0396211i	$-0.987385\pi$
$281$	−28.1242	+	11.6494i	−1.67775	+	0.694947i	−0.678535	+	0.734568i	$0.737385\pi$
$282$		0			0
$283$	−9.93766	−	6.64013i	−0.590732	−	0.394715i	0.223968	−	0.974596i	$-0.428099\pi$
$283$	−9.93766	−	6.64013i	−0.590732	−	0.394715i	−0.814701	+	0.579882i	$0.803099\pi$
$284$		0			0
$285$	7.96159	+	0.0148793i	0.471604	+	0.000881377i
$286$		0			0
$287$		−	0.937850i		−	0.0553595i
$288$		0			0
$289$		−	9.00794i		−	0.529879i
$290$		0			0
$291$	−0.258617		0.000483328i	−0.0151604		2.83332e-5i
$292$		0			0
$293$	7.07296	+	4.72600i	0.413207	+	0.276096i	0.744749	−	0.667344i	$-0.232569\pi$
$293$	7.07296	+	4.72600i	0.413207	+	0.276096i	−0.331542	+	0.943440i	$0.607569\pi$
$294$		0			0
$295$	−3.96663	+	1.64303i	−0.230946	+	0.0956610i
$296$		0			0
$297$	5.30213	+	27.4593i	0.307661	+	1.59335i
$298$		0			0
$299$	−4.22985	−	21.2649i	−0.244618	−	1.22978i
$300$		0			0
$301$	−0.832301	−	1.24563i	−0.0479730	−	0.0717967i
$302$		0			0
$303$	−2.23603	+	3.33296i	−0.128457	+	0.191474i
$304$		0			0
$305$	1.31214	+	1.31214i	0.0751330	+	0.0751330i
$306$		0			0
$307$	6.07810	+	9.09652i	0.346895	+	0.519166i	0.963358	−	0.268218i	$-0.0864349\pi$
$307$	6.07810	+	9.09652i	0.346895	+	0.519166i	−0.616463	+	0.787384i	$0.711435\pi$
$308$		0			0
$309$	11.9090	+	28.9035i	0.677478	+	1.64426i
$310$		0			0
$311$	−11.0707	−	4.58563i	−0.627761	−	0.260027i	0.0460403	−	0.998940i	$-0.485340\pi$
$311$	−11.0707	−	4.58563i	−0.627761	−	0.260027i	−0.673802	+	0.738912i	$0.735340\pi$
$312$		0			0
$313$	20.1965	−	8.36565i	1.14157	−	0.472855i	0.269873	−	0.962896i	$-0.413018\pi$
$313$	20.1965	−	8.36565i	1.14157	−	0.472855i	0.871699	+	0.490041i	$0.163018\pi$
$314$		0			0
$315$	−4.00951	−	0.813133i	−0.225910	−	0.0458148i
$316$		0			0
$317$	0.376393	+	0.0748693i	0.0211404	+	0.00420508i	0.205649	−	0.978626i	$-0.434069\pi$
$317$	0.376393	+	0.0748693i	0.0211404	+	0.00420508i	−0.184509	+	0.982831i	$0.559069\pi$
$318$		0			0
$319$		−	22.2430i		−	1.24537i
$320$		0			0
$321$	16.2645	−	3.20362i	0.907796	−	0.178809i
$322$		0			0
$323$	−2.67053	+	13.4257i	−0.148593	+	0.747025i
$324$		0			0
$325$	−4.93051	−	3.29446i	−0.273495	−	0.182744i
$326$		0			0
$327$	−9.94034	+	6.61508i	−0.549702	+	0.365815i
$328$		0			0
$329$	−2.12551	+	5.13142i	−0.117183	+	0.282905i
$330$		0			0
$331$	−1.37154	−	6.89518i	−0.0753865	−	0.378994i	0.924612	−	0.380911i	$-0.124390\pi$
$331$	−1.37154	−	6.89518i	−0.0753865	−	0.378994i	−0.999998	+	0.00191754i	$0.999390\pi$
$332$		0			0
$333$	7.58244	−	11.2566i	0.415515	−	0.616858i
$334$		0			0
$335$	−17.1231	+	17.1231i	−0.935534	+	0.935534i
$336$		0			0
$337$	17.3354	+	17.3354i	0.944318	+	0.944318i	0.998529	−	0.0542113i	$-0.0172645\pi$
$337$	17.3354	+	17.3354i	0.944318	+	0.944318i	−0.0542113	+	0.998529i	$0.517264\pi$
$338$		0			0
$339$	19.0566	−	18.9856i	1.03502	−	1.03115i
$340$		0			0
$341$	−36.7189	+	7.30384i	−1.98844	+	0.395525i
$342$		0			0
$343$	9.83341	+	4.07313i	0.530954	+	0.219929i
$344$		0			0
$345$	−18.6653	+	12.4214i	−1.00491	+	0.668744i
$346$		0			0
$347$	−10.1675	+	15.2167i	−0.545819	+	0.816875i	−0.997147	−	0.0754825i	$-0.975950\pi$
$347$	−10.1675	+	15.2167i	−0.545819	+	0.816875i	0.451328	+	0.892358i	$0.350950\pi$
$348$		0			0
$349$	13.3260	+	2.65070i	0.713322	+	0.141889i	0.538395	−	0.842693i	$-0.319031\pi$
$349$	13.3260	+	2.65070i	0.713322	+	0.141889i	0.174927	+	0.984581i	$0.444031\pi$
$350$		0			0
$351$	8.21082	+	12.4388i	0.438261	+	0.663933i
$352$		0			0
$353$	13.2033			0.702743			0.351372	−	0.936236i	$-0.385715\pi$
$353$	13.2033			0.702743			0.351372	+	0.936236i	$0.385715\pi$
$354$		0			0
$355$	−1.65665	+	8.32857i	−0.0879261	+	0.442034i
$356$		0			0
$357$	2.70396	−	6.49357i	0.143108	−	0.343676i
$358$		0			0
$359$	9.51903	+	22.9810i	0.502395	+	1.21289i	0.948176	+	0.317747i	$0.102926\pi$
$359$	9.51903	+	22.9810i	0.502395	+	1.21289i	−0.445780	+	0.895142i	$0.647074\pi$
$360$		0			0
$361$	−4.51385	+	10.8974i	−0.237571	+	0.573547i
$362$		0			0
$363$	11.8557	+	28.7741i	0.622262	+	1.51025i
$364$		0			0
$365$	0.984283	−	0.657677i	0.0515197	−	0.0344244i
$366$		0			0
$367$	−6.04728	+	6.04728i	−0.315665	+	0.315665i	−0.847100	−	0.531434i	$-0.821653\pi$
$367$	−6.04728	+	6.04728i	−0.315665	+	0.315665i	0.531434	+	0.847100i	$0.321653\pi$
$368$		0			0
$369$	3.25913	+	1.36427i	0.169664	+	0.0710211i
$370$		0			0
$371$	6.39943	−	4.27597i	0.332242	−	0.221997i
$372$		0			0
$373$	26.8149	−	5.33382i	1.38842	−	0.276175i	0.556401	−	0.830914i	$-0.312182\pi$
$373$	26.8149	−	5.33382i	1.38842	−	0.276175i	0.832024	+	0.554739i	$0.187182\pi$
$374$		0			0
$375$	−4.12804	+	20.5522i	−0.213171	+	1.06131i
$376$		0			0
$377$	−4.53636	−	10.9517i	−0.233635	−	0.564044i
$378$		0			0
$379$	−5.46511	+	8.17912i	−0.280724	+	0.420133i	−0.944858	−	0.327481i	$-0.893800\pi$
$379$	−5.46511	+	8.17912i	−0.280724	+	0.420133i	0.664134	+	0.747614i	$0.268800\pi$
$380$		0			0
$381$	−35.1207	−	0.0656367i	−1.79929	−	0.00336267i
$382$		0			0
$383$	9.12965			0.466503			0.233252	−	0.972416i	$-0.425063\pi$
$383$	9.12965			0.466503			0.233252	+	0.972416i	$0.425063\pi$
$384$		0			0
$385$	−7.33971			−0.374066
$386$		0			0
$387$	5.53942	−	1.08035i	0.281585	−	0.0549173i
$388$		0			0
$389$	−0.446040	+	0.667546i	−0.0226151	+	0.0338459i	−0.842605	−	0.538532i	$-0.818979\pi$
$389$	−0.446040	+	0.667546i	−0.0226151	+	0.0338459i	0.819990	+	0.572378i	$0.193979\pi$
$390$		0			0
$391$	−14.7519	−	35.6143i	−0.746038	−	1.80110i
$392$		0			0
$393$	−2.16903	−	0.435662i	−0.109413	−	0.0219763i
$394$		0			0
$395$	−6.23036	+	1.23930i	−0.313484	+	0.0623558i
$396$		0			0
$397$	−26.1544	+	17.4758i	−1.31265	+	0.877086i	−0.997410	−	0.0719252i	$-0.977086\pi$
$397$	−26.1544	+	17.4758i	−1.31265	+	0.877086i	−0.315242	+	0.949011i	$0.602086\pi$
$398$		0			0
$399$	−2.06259	+	3.07443i	−0.103259	+	0.153914i
$400$		0			0
$401$	−12.4507	+	12.4507i	−0.621757	+	0.621757i	−0.945981	−	0.324223i	$-0.894897\pi$
$401$	−12.4507	+	12.4507i	−0.621757	+	0.621757i	0.324223	+	0.945981i	$0.394897\pi$
$402$		0			0
$403$	−16.5897	+	11.0849i	−0.826390	+	0.552176i
$404$		0			0
$405$	8.65828	−	12.7507i	0.430233	−	0.633585i
$406$		0			0
$407$	9.31805	−	22.4958i	0.461879	−	1.11507i
$408$		0			0
$409$	−6.02622	−	14.5486i	−0.297977	−	0.719381i	−0.999974	−	0.00720056i	$-0.997708\pi$
$409$	−6.02622	−	14.5486i	−0.297977	−	0.719381i	0.701997	−	0.712180i	$-0.252292\pi$
$410$		0			0
$411$	−14.4339	−	6.01034i	−0.711971	−	0.296468i
$412$		0			0
$413$	0.389497	−	1.95813i	0.0191659	−	0.0963534i
$414$		0			0
$415$	5.19298			0.254913
$416$		0			0
$417$	−8.86451	+	1.74604i	−0.434097	+	0.0855042i
$418$		0			0
$419$	−20.4761	−	4.07294i	−1.00032	−	0.198976i	−0.332344	−	0.943158i	$-0.607840\pi$
$419$	−20.4761	−	4.07294i	−1.00032	−	0.198976i	−0.667977	+	0.744182i	$0.732840\pi$
$420$		0			0
$421$	4.56603	−	6.83355i	0.222535	−	0.333047i	−0.703356	−	0.710838i	$-0.748316\pi$
$421$	4.56603	−	6.83355i	0.222535	−	0.333047i	0.925891	+	0.377791i	$0.123316\pi$
$422$		0			0
$423$	−14.7403	−	14.8509i	−0.716700	−	0.722078i
$424$		0			0
$425$	−9.74051	−	4.03465i	−0.472484	−	0.195709i
$426$		0			0
$427$	−0.846314	+	0.168342i	−0.0409560	+	0.00814665i
$428$		0			0
$429$	18.8721	+	18.9428i	0.911155	+	0.914567i
$430$		0			0
$431$	−22.1459	−	22.1459i	−1.06673	−	1.06673i	−0.997608	−	0.0691236i	$-0.977980\pi$
$431$	−22.1459	−	22.1459i	−1.06673	−	1.06673i	−0.0691236	−	0.997608i	$-0.522020\pi$
$432$		0			0
$433$	−7.75001	+	7.75001i	−0.372442	+	0.372442i	−0.868366	−	0.495924i	$-0.834829\pi$
$433$	−7.75001	+	7.75001i	−0.372442	+	0.372442i	0.495924	+	0.868366i	$0.334829\pi$
$434$		0			0
$435$	−8.68405	+	8.65165i	−0.416368	+	0.414815i
$436$		0			0
$437$	3.95824	+	19.8994i	0.189348	+	0.951918i
$438$		0			0
$439$	1.60466	−	3.87398i	0.0765861	−	0.184895i	−0.880950	−	0.473210i	$-0.843095\pi$
$439$	1.60466	−	3.87398i	0.0765861	−	0.184895i	0.957536	+	0.288315i	$0.0930951\pi$
$440$		0			0
$441$	−13.5544	+	13.4535i	−0.645448	+	0.640641i
$442$		0			0
$443$	13.5119	+	9.02838i	0.641971	+	0.428951i	0.833488	−	0.552538i	$-0.186341\pi$
$443$	13.5119	+	9.02838i	0.641971	+	0.428951i	−0.191517	+	0.981489i	$0.561341\pi$
$444$		0			0
$445$	5.29925	−	26.6411i	0.251209	−	1.26291i
$446$		0			0
$447$	5.68290	+	28.8516i	0.268792	+	1.36463i
$448$		0			0
$449$			4.44342i			0.209698i	0.994488	+	0.104849i	$0.0334359\pi$
$449$			4.44342i			0.209698i	−0.994488	+	0.104849i	$0.966564\pi$
$450$		0			0
$451$	6.21687	+	1.23661i	0.292741	+	0.0582298i
$452$		0			0
$453$	−4.29582	+	10.3165i	−0.201835	+	0.484709i
$454$		0			0
$455$	−3.61385	+	1.49690i	−0.169420	+	0.0701760i
$456$		0			0
$457$	3.26785	+	1.35359i	0.152864	+	0.0633182i	0.457803	−	0.889053i	$-0.348636\pi$
$457$	3.26785	+	1.35359i	0.152864	+	0.0633182i	−0.304940	+	0.952372i	$0.598636\pi$
$458$		0			0
$459$	18.6325	+	18.8426i	0.869691	+	0.879498i
$460$		0			0
$461$	−0.445238	−	0.666345i	−0.0207368	−	0.0310348i	0.820956	−	0.570991i	$-0.193441\pi$
$461$	−0.445238	−	0.666345i	−0.0207368	−	0.0310348i	−0.841693	+	0.539956i	$0.818441\pi$
$462$		0			0
$463$	−13.5750	−	13.5750i	−0.630885	−	0.630885i	0.317405	−	0.948290i	$-0.397189\pi$
$463$	−13.5750	−	13.5750i	−0.630885	−	0.630885i	−0.948290	+	0.317405i	$0.897189\pi$
$464$		0			0
$465$	17.1338	+	11.4948i	0.794559	+	0.533058i
$466$		0			0
$467$	22.5240	+	33.7096i	1.04229	+	1.55989i	0.809284	+	0.587417i	$0.199855\pi$
$467$	22.5240	+	33.7096i	1.04229	+	1.55989i	0.233003	+	0.972476i	$0.425145\pi$
$468$		0			0
$469$	−2.19682	−	11.0442i	−0.101440	−	0.509972i
$470$		0			0
$471$	4.56720	−	22.7387i	0.210445	−	1.04774i
$472$		0			0
$473$	9.35452	−	3.87477i	0.430121	−	0.178162i
$474$		0			0
$475$	4.61391	+	3.08292i	0.211701	+	0.141454i
$476$		0			0
$477$	5.55033	+	28.4589i	0.254132	+	1.30304i
$478$		0			0
$479$			0.596301i			0.0272457i	0.999907	+	0.0136228i	$0.00433642\pi$
$479$			0.596301i			0.0272457i	−0.999907	+	0.0136228i	$0.995664\pi$
$480$		0			0
$481$		−	12.9766i		−	0.591682i
$482$		0			0
$483$	0.0194847	−	10.4258i	0.000886582	−	0.474389i
$484$		0			0
$485$	0.212605	+	0.142058i	0.00965392	+	0.00645054i
$486$		0			0
$487$	14.1819	−	5.87434i	0.642644	−	0.266192i	−0.0374708	−	0.999298i	$-0.511930\pi$
$487$	14.1819	−	5.87434i	0.642644	−	0.266192i	0.680114	+	0.733106i	$0.261930\pi$
$488$		0			0
$489$	−35.3521	−	7.10069i	−1.59868	−	0.321104i
$490$		0			0
$491$	−0.00640918	−	0.0322211i	−0.000289242	−	0.00145412i	0.980640	−	0.195817i	$-0.0627360\pi$
$491$	−0.00640918	−	0.0322211i	−0.000289242	−	0.00145412i	−0.980930	+	0.194363i	$0.937736\pi$
$492$		0			0
$493$	−11.7092	−	17.5241i	−0.527357	−	0.789245i
$494$		0			0
$495$	10.6769	−	25.5063i	0.479892	−	1.14642i
$496$		0			0
$497$	−2.79218	−	2.79218i	−0.125246	−	0.125246i
$498$		0			0
$499$	−5.40096	−	8.08311i	−0.241780	−	0.361850i	0.690656	−	0.723183i	$-0.257322\pi$
$499$	−5.40096	−	8.08311i	−0.241780	−	0.361850i	−0.932437	+	0.361333i	$0.882322\pi$
$500$		0			0
$501$	−18.7165	+	7.71168i	−0.836192	+	0.344532i
$502$		0			0
$503$	−8.11650	−	3.36197i	−0.361897	−	0.149903i	0.194323	−	0.980938i	$-0.437749\pi$
$503$	−8.11650	−	3.36197i	−0.361897	−	0.149903i	−0.556220	+	0.831035i	$0.687749\pi$
$504$		0			0
$505$	3.66617	−	1.51858i	0.163142	−	0.0675758i
$506$		0			0
$507$	−7.63117	−	3.17766i	−0.338912	−	0.141125i
$508$		0			0
$509$	26.0046	+	5.17263i	1.15263	+	0.229273i	0.734173	−	0.678962i	$-0.237570\pi$
$509$	26.0046	+	5.17263i	1.15263	+	0.229273i	0.418460	+	0.908235i	$0.362570\pi$
$510$		0			0
$511$			0.550472i			0.0243514i
$512$		0			0
$513$	−7.68359	−	11.6401i	−0.339239	−	0.513921i
$514$		0			0
$515$	6.02983	−	30.3140i	0.265706	−	1.33579i
$516$		0			0
$517$	−31.2129	−	20.8558i	−1.37274	−	0.917235i
$518$		0			0
$519$	−11.7955	−	17.7248i	−0.517763	−	0.778031i
$520$		0			0
$521$	1.81662	−	4.38572i	0.0795877	−	0.192142i	−0.879077	−	0.476680i	$-0.841840\pi$
$521$	1.81662	−	4.38572i	0.0795877	−	0.192142i	0.958665	+	0.284538i	$0.0918402\pi$
$522$		0			0
$523$	4.42990	+	22.2706i	0.193706	+	0.973826i	0.948237	+	0.317562i	$0.102864\pi$
$523$	4.42990	+	22.2706i	0.193706	+	0.973826i	−0.754531	+	0.656264i	$0.772136\pi$
$524$		0			0
$525$	−2.01251	−	2.02004i	−0.0878331	−	0.0881620i
$526$		0			0
$527$	−25.0840	+	25.0840i	−1.09268	+	1.09268i
$528$		0			0
$529$	−24.1381	−	24.1381i	−1.04948	−	1.04948i
$530$		0			0
$531$	6.23813	+	4.20200i	0.270712	+	0.182351i
$532$		0			0
$533$	3.31320	−	0.659036i	0.143511	−	0.0285460i
$534$		0			0
$535$	−15.1423	−	6.27214i	−0.654658	−	0.271168i
$536$		0			0
$537$	7.50162	+	11.2725i	0.323719	+	0.486445i
$538$		0			0
$539$	−19.0350	+	28.4879i	−0.819895	+	1.22706i
$540$		0			0
$541$	−1.34295	−	0.267129i	−0.0577379	−	0.0114848i	0.166137	−	0.986103i	$-0.446871\pi$
$541$	−1.34295	−	0.267129i	−0.0577379	−	0.0114848i	−0.223875	+	0.974618i	$0.571871\pi$
$542$		0			0
$543$	4.36423	+	22.1568i	0.187287	+	0.950838i
$544$		0			0
$545$	11.8055			0.505691
$546$		0			0
$547$	5.22689	−	26.2774i	0.223486	−	1.12354i	−0.692219	−	0.721687i	$-0.743367\pi$
$547$	5.22689	−	26.2774i	0.223486	−	1.12354i	0.915705	−	0.401851i	$-0.131633\pi$
$548$		0			0
$549$	0.646107	−	3.18592i	0.0275752	−	0.135972i
$550$		0			0
$551$	4.24507	+	10.2485i	0.180846	+	0.436601i
$552$		0			0
$553$	1.13042	−	2.72908i	0.0480704	−	0.116052i
$554$		0			0
$555$	−12.4071	+	5.11205i	−0.526652	+	0.216994i
$556$		0			0
$557$	−6.81107	+	4.55101i	−0.288594	+	0.192833i	−0.691437	−	0.722437i	$-0.743022\pi$
$557$	−6.81107	+	4.55101i	−0.288594	+	0.192833i	0.402843	+	0.915269i	$0.368022\pi$
$558$		0			0
$559$	3.81563	−	3.81563i	0.161384	−	0.161384i
$560$		0			0
$561$	39.4796	+	26.4863i	1.66683	+	1.11825i
$562$		0			0
$563$	1.37594	−	0.919371i	0.0579888	−	0.0387469i	−0.526238	−	0.850337i	$-0.676398\pi$
$563$	1.37594	−	0.919371i	0.0579888	−	0.0387469i	0.584227	+	0.811590i	$0.301398\pi$
$564$		0			0
$565$	−26.0853	+	5.18868i	−1.09741	+	0.218289i
$566$		0			0
$567$	2.69310	+	6.64172i	0.113100	+	0.278926i
$568$		0			0
$569$	−8.37450	−	20.2178i	−0.351077	−	0.847575i	−0.996488	−	0.0837394i	$-0.973314\pi$
$569$	−8.37450	−	20.2178i	−0.351077	−	0.847575i	0.645410	−	0.763836i	$-0.276686\pi$
$570$		0			0
$571$	12.6472	−	18.9278i	0.529267	−	0.792104i	−0.466451	−	0.884547i	$-0.654468\pi$
$571$	12.6472	−	18.9278i	0.529267	−	0.792104i	0.995718	+	0.0924431i	$0.0294676\pi$
$572$		0			0
$573$	−0.0375751	+	20.1055i	−0.00156972	+	0.839920i
$574$		0			0
$575$	−15.6268			−0.651683
$576$		0			0
$577$	3.02364			0.125876			0.0629378	−	0.998017i	$-0.479953\pi$
$577$	3.02364			0.125876			0.0629378	+	0.998017i	$0.479953\pi$
$578$		0			0
$579$	0.0766645	−	41.0214i	0.00318607	−	1.70479i
$580$		0			0
$581$	−1.34158	+	2.00782i	−0.0556582	+	0.0832984i
$582$		0			0
$583$	19.9067	+	48.0590i	0.824452	+	1.99040i
$584$		0			0
$585$	0.0550803	−	14.7360i	0.00227729	−	0.609260i
$586$		0			0
$587$	20.2802	−	4.03398i	0.837054	−	0.166500i	0.242091	−	0.970254i	$-0.422167\pi$
$587$	20.2802	−	4.03398i	0.837054	−	0.166500i	0.594963	+	0.803753i	$0.297167\pi$
$588$		0			0
$589$	15.5244	−	10.3731i	0.639672	−	0.427415i
$590$		0			0
$591$	15.3825	+	10.3199i	0.632753	+	0.424505i
$592$		0			0
$593$	25.5322	−	25.5322i	1.04848	−	1.04848i	0.0497164	−	0.998763i	$-0.484168\pi$
$593$	25.5322	−	25.5322i	1.04848	−	1.04848i	0.998763	−	0.0497164i	$-0.0158318\pi$
$594$		0			0
$595$	−5.78258	+	3.86380i	−0.237063	+	0.158400i
$596$		0			0
$597$	−0.201383	+	0.0829749i	−0.00824205	+	0.00339594i
$598$		0			0
$599$	2.81924	−	6.80624i	0.115191	−	0.278095i	−0.855761	−	0.517372i	$-0.826910\pi$
$599$	2.81924	−	6.80624i	0.115191	−	0.278095i	0.970951	+	0.239277i	$0.0769103\pi$
$600$		0			0
$601$	−2.76305	−	6.67058i	−0.112707	−	0.272099i	0.857454	−	0.514561i	$-0.172045\pi$
$601$	−2.76305	−	6.67058i	−0.112707	−	0.272099i	−0.970161	+	0.242462i	$0.922045\pi$
$602$		0			0
$603$	41.5753	+	8.43152i	1.69308	+	0.343358i
$604$		0			0
$605$	6.00284	−	30.1783i	0.244050	−	1.22692i
$606$		0			0
$607$	12.5060			0.507603			0.253802	−	0.967256i	$-0.418319\pi$
$607$	12.5060			0.507603			0.253802	+	0.967256i	$0.418319\pi$
$608$		0			0
$609$	−1.10160	−	5.59272i	−0.0446391	−	0.226628i
$610$		0			0
$611$	−19.6217	−	3.90300i	−0.793809	−	0.157898i
$612$		0			0
$613$	−21.1070	+	31.5888i	−0.852503	+	1.27586i	0.107027	+	0.994256i	$0.465867\pi$
$613$	−21.1070	+	31.5888i	−0.852503	+	1.27586i	−0.959530	+	0.281605i	$0.909133\pi$
$614$		0			0
$615$	−1.93533	−	2.90817i	−0.0780399	−	0.117269i
$616$		0			0
$617$	−1.55951	−	0.645969i	−0.0627834	−	0.0260057i	0.351071	−	0.936349i	$-0.385818\pi$
$617$	−1.55951	−	0.645969i	−0.0627834	−	0.0260057i	−0.413854	+	0.910343i	$0.635818\pi$
$618$		0			0
$619$	12.4267	−	2.47182i	0.499469	−	0.0993507i	0.0610747	−	0.998133i	$-0.480547\pi$
$619$	12.4267	−	2.47182i	0.499469	−	0.0993507i	0.438395	+	0.898783i	$0.355547\pi$
$620$		0			0
$621$	36.2024	+	15.2339i	1.45275	+	0.611315i
$622$		0			0
$623$	8.93152	+	8.93152i	0.357834	+	0.357834i
$624$		0			0
$625$	7.34638	−	7.34638i	0.293855	−	0.293855i
$626$		0			0
$627$	−17.6603	−	17.7265i	−0.705285	−	0.707926i
$628$		0			0
$629$	−4.50109	−	22.6285i	−0.179470	−	0.902258i
$630$		0			0
$631$	0.496224	−	1.19799i	0.0197544	−	0.0476912i	−0.913695	−	0.406402i	$-0.866783\pi$
$631$	0.496224	−	1.19799i	0.0197544	−	0.0476912i	0.933449	+	0.358710i	$0.116783\pi$
$632$		0			0
$633$	13.8395	+	20.7963i	0.550072	+	0.826580i
$634$		0			0
$635$	28.8722	+	19.2918i	1.14576	+	0.765570i
$636$		0			0
$637$	−3.56226	+	17.9087i	−0.141142	+	0.709567i
$638$		0			0
$639$	13.7648	−	5.64140i	0.544529	−	0.223170i
$640$		0			0
$641$		−	36.7026i		−	1.44967i	−0.688925	−	0.724833i	$-0.741917\pi$
$641$		−	36.7026i		−	1.44967i	0.688925	−	0.724833i	$-0.258083\pi$
$642$		0			0
$643$	−24.2814	−	4.82988i	−0.957566	−	0.190472i	−0.308518	−	0.951219i	$-0.599833\pi$
$643$	−24.2814	−	4.82988i	−0.957566	−	0.190472i	−0.649049	+	0.760747i	$0.724833\pi$
$644$		0			0
$645$	−5.15132	−	2.14504i	−0.202833	−	0.0844607i
$646$		0			0
$647$	30.2121	−	12.5143i	1.18776	−	0.491987i	0.300736	−	0.953707i	$-0.402768\pi$
$647$	30.2121	−	12.5143i	1.18776	−	0.491987i	0.887026	+	0.461720i	$0.152768\pi$
$648$		0			0
$649$	12.4666	+	5.16383i	0.489357	+	0.202698i
$650$		0			0
$651$	−8.87079	+	3.65499i	−0.347674	+	0.143250i
$652$		0			0
$653$	−20.6065	−	30.8399i	−0.806396	−	1.20686i	−0.975226	−	0.221212i	$-0.928999\pi$
$653$	−20.6065	−	30.8399i	−0.806396	−	1.20686i	0.168830	−	0.985645i	$-0.446001\pi$
$654$		0			0
$655$	1.54671	+	1.54671i	0.0604349	+	0.0604349i
$656$		0			0
$657$	−1.91295	−	0.800760i	−0.0746313	−	0.0312406i
$658$		0			0
$659$	−9.69701	−	14.5126i	−0.377742	−	0.565330i	0.593077	−	0.805146i	$-0.297913\pi$
$659$	−9.69701	−	14.5126i	−0.377742	−	0.565330i	−0.970818	+	0.239815i	$0.922913\pi$
$660$		0			0
$661$	−6.05894	−	30.4603i	−0.235665	−	1.18477i	−0.899510	−	0.436900i	$-0.856076\pi$
$661$	−6.05894	−	30.4603i	−0.235665	−	1.18477i	0.663845	−	0.747870i	$-0.268924\pi$
$662$		0			0
$663$	24.8403	+	4.98933i	0.964719	+	0.193769i
$664$		0			0
$665$	3.38179	−	1.40079i	0.131140	−	0.0543201i
$666$		0			0
$667$	−25.9740	−	17.3553i	−1.00572	−	0.671999i
$668$		0			0
$669$	0.0500421	−	26.7764i	0.00193474	−	1.03523i
$670$		0			0
$671$		−	5.83206i		−	0.225144i
$672$		0			0
$673$			1.42269i			0.0548405i	0.999624	+	0.0274203i	$0.00872923\pi$
$673$			1.42269i			0.0548405i	−0.999624	+	0.0274203i	$0.991271\pi$
$674$		0			0
$675$	9.94744	−	4.05517i	0.382877	−	0.156084i
$676$		0			0
$677$	30.5664	+	20.4238i	1.17476	+	0.784951i	0.980600	−	0.196019i	$-0.0628014\pi$
$677$	30.5664	+	20.4238i	1.17476	+	0.784951i	0.194161	+	0.980970i	$0.437801\pi$
$678$		0			0
$679$	−0.109851	+	0.0455019i	−0.00421570	+	0.00174620i
$680$		0			0
$681$	2.91283	−	14.5021i	0.111620	−	0.555722i
$682$		0			0
$683$	−0.0811176	−	0.407806i	−0.00310388	−	0.0156043i	0.979202	−	0.202886i	$-0.0650322\pi$
$683$	−0.0811176	−	0.407806i	−0.00310388	−	0.0156043i	−0.982306	+	0.187282i	$0.940032\pi$
$684$		0			0
$685$	8.58843	+	12.8535i	0.328147	+	0.491106i
$686$		0			0
$687$	3.01087	+	2.01995i	0.114872	+	0.0770659i
$688$		0			0
$689$	19.6029	+	19.6029i	0.746811	+	0.746811i
$690$		0			0
$691$	6.46900	+	9.68155i	0.246093	+	0.368303i	0.933867	−	0.357621i	$-0.116412\pi$
$691$	6.46900	+	9.68155i	0.246093	+	0.368303i	−0.687774	+	0.725925i	$0.741412\pi$
$692$		0			0
$693$	7.10345	+	10.7176i	0.269838	+	0.407127i
$694$		0			0
$695$	8.25287	+	3.41845i	0.313049	+	0.129669i
$696$		0			0
$697$	5.54894	−	2.29844i	0.210181	−	0.0870598i
$698$		0			0
$699$	−6.73654	+	16.1779i	−0.254799	+	0.611903i
$700$		0			0
$701$	−37.1691	−	7.39339i	−1.40386	−	0.279244i	−0.565672	−	0.824631i	$-0.691383\pi$
$701$	−37.1691	−	7.39339i	−1.40386	−	0.279244i	−0.838185	+	0.545386i	$0.816383\pi$
$702$		0			0
$703$			12.1434i			0.457995i
$704$		0			0
$705$	3.99813	+	20.2981i	0.150578	+	0.764472i
$706$		0			0
$707$	−0.359993	+	1.80981i	−0.0135389	+	0.0680648i
$708$		0			0
$709$	38.1803	+	25.5113i	1.43389	+	0.958096i	0.998320	+	0.0579428i	$0.0184541\pi$
$709$	38.1803	+	25.5113i	1.43389	+	0.958096i	0.435573	+	0.900154i	$0.356546\pi$
$710$		0			0
$711$	7.83946	+	7.89828i	0.294003	+	0.296209i
$712$		0			0
$713$	−20.1213	+	48.5770i	−0.753547	+	1.81922i
$714$		0			0
$715$	−5.15768	−	25.9294i	−0.192886	−	0.969706i
$716$		0			0
$717$	−14.0901	+	14.0375i	−0.526205	+	0.524242i
$718$		0			0
$719$	−15.3249	+	15.3249i	−0.571523	+	0.571523i	−0.932554	−	0.361031i	$-0.882425\pi$
$719$	−15.3249	+	15.3249i	−0.571523	+	0.571523i	0.361031	+	0.932554i	$0.382425\pi$
$720$		0			0
$721$	10.1629	+	10.1629i	0.378484	+	0.378484i
$722$		0			0
$723$	−35.7076	−	35.8414i	−1.32798	−	1.33295i
$724$		0			0
$725$	−8.37960	+	1.66681i	−0.311210	+	0.0619036i
$726$		0			0
$727$	5.58340	+	2.31272i	0.207077	+	0.0857740i	0.483811	−	0.875172i	$-0.339252\pi$
$727$	5.58340	+	2.31272i	0.207077	+	0.0857740i	−0.276734	+	0.960946i	$0.589252\pi$
$728$		0			0
$729$	−26.9983	−	0.302754i	−0.999937	−	0.0112131i
$730$		0			0
$731$	5.33018	−	7.97717i	0.197144	−	0.295046i
$732$		0			0
$733$	−16.4103	−	3.26422i	−0.606130	−	0.120567i	−0.117522	−	0.993070i	$-0.537495\pi$
$733$	−16.4103	−	3.26422i	−0.606130	−	0.120567i	−0.488608	+	0.872504i	$0.662495\pi$
$734$		0			0
$735$	18.5260	−	3.64908i	0.683344	−	0.134598i
$736$		0			0
$737$	76.1068			2.80343
$738$		0			0
$739$	−4.06626	+	20.4425i	−0.149580	+	0.751988i	0.831062	+	0.556179i	$0.187733\pi$
$739$	−4.06626	+	20.4425i	−0.149580	+	0.751988i	−0.980642	+	0.195809i	$0.937267\pi$
$740$		0			0
$741$	−12.3106	−	5.12621i	−0.452243	−	0.188316i
$742$		0			0
$743$	−11.3675	−	27.4437i	−0.417035	−	1.00681i	−0.983202	−	0.182521i	$-0.941574\pi$
$743$	−11.3675	−	27.4437i	−0.417035	−	1.00681i	0.566167	−	0.824290i	$-0.308426\pi$
$744$		0			0
$745$	11.1261	−	26.8608i	0.407630	−	0.984105i
$746$		0			0
$747$	−5.02582	−	7.58288i	−0.183885	−	0.277443i
$748$		0			0
$749$	6.33700	−	4.23425i	0.231549	−	0.154716i
$750$		0			0
$751$	−9.88591	+	9.88591i	−0.360742	+	0.360742i	−0.864086	−	0.503344i	$-0.832103\pi$
$751$	−9.88591	+	9.88591i	−0.360742	+	0.360742i	0.503344	+	0.864086i	$0.332103\pi$
$752$		0			0
$753$	7.38262	−	11.0043i	0.269038	−	0.401019i
$754$		0			0
$755$	9.18688	−	6.13848i	0.334345	−	0.223402i
$756$		0			0
$757$	−2.43551	+	0.484453i	−0.0885202	+	0.0176078i	−0.239152	−	0.970982i	$-0.576869\pi$
$757$	−2.43551	+	0.484453i	−0.0885202	+	0.0176078i	0.150631	+	0.988590i	$0.451869\pi$
$758$		0			0
$759$	69.0853	+	13.8762i	2.50764	+	0.503674i
$760$		0			0
$761$	−14.2896	−	34.4982i	−0.517999	−	1.25056i	−0.939131	−	0.343560i	$-0.888367\pi$
$761$	−14.2896	−	34.4982i	−0.517999	−	1.25056i	0.421132	−	0.906999i	$-0.361633\pi$
$762$		0			0
$763$	−3.04989	+	4.56448i	−0.110413	+	0.165245i
$764$		0			0
$765$	−5.01532	−	25.7157i	−0.181329	−	0.929753i
$766$		0			0
$767$	7.19131			0.259663
$768$		0			0
$769$	8.19388			0.295479			0.147739	−	0.989026i	$-0.452800\pi$
$769$	8.19388			0.295479			0.147739	+	0.989026i	$0.452800\pi$
$770$		0			0
$771$	4.17843	+	0.00780903i	0.150482	+	0.000281235i
$772$		0			0
$773$	−11.9974	+	17.9553i	−0.431515	+	0.645808i	−0.981966	−	0.189060i	$-0.939456\pi$
$773$	−11.9974	+	17.9553i	−0.431515	+	0.645808i	0.550451	+	0.834868i	$0.314456\pi$
$774$		0			0
$775$	5.50316	+	13.2858i	0.197679	+	0.477240i
$776$		0			0
$777$	1.22879	−	6.11777i	0.0440826	−	0.219474i
$778$		0			0
$779$	−3.10045	+	0.616718i	−0.111085	+	0.0220962i
$780$		0			0
$781$	22.1906	−	14.8273i	0.794042	−	0.530562i
$782$		0			0
$783$	21.0378	+	4.30744i	0.751830	+	0.153935i
$784$		0			0
$785$	−16.2147	+	16.2147i	−0.578726	+	0.578726i
$786$		0			0
$787$	35.1663	−	23.4974i	1.25354	−	0.837591i	0.261712	−	0.965146i	$-0.415713\pi$
$787$	35.1663	−	23.4974i	1.25354	−	0.837591i	0.991832	+	0.127555i	$0.0407128\pi$
$788$		0			0
$789$	11.2080	+	27.2022i	0.399016	+	0.968424i
$790$		0			0
$791$	4.73285	−	11.4261i	0.168281	−	0.406265i
$792$		0			0
$793$	−1.18943	−	2.87153i	−0.0422377	−	0.101971i
$794$		0			0
$795$	11.0202	−	26.4650i	0.390845	−	0.938618i
$796$		0			0
$797$	1.56119	−	7.84862i	0.0553001	−	0.278012i	−0.943235	−	0.332127i	$-0.892234\pi$
$797$	1.56119	−	7.84862i	0.0553001	−	0.278012i	0.998535	+	0.0541148i	$0.0172337\pi$
$798$		0			0
$799$	−35.5700			−1.25838
$800$		0			0
$801$	−44.0305	+	18.0455i	−1.55574	+	0.637607i
$802$		0			0
$803$	−3.64900	−	0.725831i	−0.128770	−	0.0256140i
$804$		0			0
$805$	−5.72688	+	8.57088i	−0.201846	+	0.302084i
$806$		0			0
$807$	−25.8111	+	17.1768i	−0.908595	+	0.604651i
$808$		0			0
$809$	1.59008	+	0.658632i	0.0559042	+	0.0231563i	0.410460	−	0.911878i	$-0.365368\pi$
$809$	1.59008	+	0.658632i	0.0559042	+	0.0231563i	−0.354556	+	0.935035i	$0.615368\pi$
$810$		0			0
$811$	−44.0264	+	8.75739i	−1.54598	+	0.307514i	−0.893067	−	0.449923i	$-0.851451\pi$
$811$	−44.0264	+	8.75739i	−1.54598	+	0.307514i	−0.652908	+	0.757437i	$0.726451\pi$
$812$		0			0
$813$	35.9448	−	35.8107i	1.26064	−	1.25594i
$814$		0			0
$815$	25.2092	+	25.2092i	0.883039	+	0.883039i
$816$		0			0
$817$	−3.57062	+	3.57062i	−0.124920	+	0.124920i
$818$		0			0
$819$	5.68333	+	3.82828i	0.198592	+	0.133771i
$820$		0			0
$821$	5.35307	+	26.9117i	0.186824	+	0.939225i	0.954460	+	0.298340i	$0.0964328\pi$
$821$	5.35307	+	26.9117i	0.186824	+	0.939225i	−0.767636	+	0.640886i	$0.778567\pi$
$822$		0			0
$823$	0.538169	−	1.29925i	0.0187594	−	0.0452891i	−0.914222	−	0.405213i	$-0.867197\pi$
$823$	0.538169	−	1.29925i	0.0187594	−	0.0452891i	0.932982	+	0.359924i	$0.117197\pi$
$824$		0			0
$825$	16.0442	−	10.6771i	0.558587	−	0.371728i
$826$		0			0
$827$	42.6108	+	28.4716i	1.48172	+	0.990056i	0.993063	+	0.117582i	$0.0375142\pi$
$827$	42.6108	+	28.4716i	1.48172	+	0.990056i	0.488660	+	0.872474i	$0.337486\pi$
$828$		0			0
$829$	−10.7528	+	54.0581i	−0.373461	+	1.87752i	0.0972982	+	0.995255i	$0.468980\pi$
$829$	−10.7528	+	54.0581i	−0.373461	+	1.87752i	−0.470760	+	0.882262i	$0.656020\pi$
$830$		0			0
$831$	−43.4044	+	8.54938i	−1.50568	+	0.296575i
$832$		0			0
$833$			32.4646i			1.12483i
$834$		0			0
$835$	19.6299	+	3.90463i	0.679320	+	0.135125i
$836$		0			0
$837$	0.202649	−	36.1438i	0.00700456	−	1.24931i
$838$		0			0
$839$	11.4210	−	4.73072i	0.394296	−	0.163323i	−0.176721	−	0.984261i	$-0.556549\pi$
$839$	11.4210	−	4.73072i	0.394296	−	0.163323i	0.571017	+	0.820938i	$0.306549\pi$
$840$		0			0
$841$	11.0132	+	4.56183i	0.379766	+	0.157304i
$842$		0			0
$843$	−20.0863	−	48.7502i	−0.691810	−	1.67905i
$844$		0			0
$845$	4.54069	+	6.79562i	0.156204	+	0.233776i
$846$		0			0
$847$	10.1174	+	10.1174i	0.347637	+	0.347637i
$848$		0			0
$849$	11.5332	−	17.1910i	0.395818	−	0.589994i
$850$		0			0
$851$	−18.9987	−	28.4336i	−0.651268	−	0.974692i
$852$		0			0
$853$	8.07843	+	40.6130i	0.276600	+	1.39056i	0.830054	+	0.557683i	$0.188309\pi$
$853$	8.07843	+	40.6130i	0.276600	+	1.39056i	−0.553454	+	0.832880i	$0.686691\pi$
$854$		0			0
$855$	−0.0515435	+	13.7898i	−0.00176275	+	0.471601i
$856$		0			0
$857$	11.4578	−	4.74597i	0.391390	−	0.162119i	−0.178305	−	0.983975i	$-0.557061\pi$
$857$	11.4578	−	4.74597i	0.391390	−	0.162119i	0.569695	+	0.821856i	$0.307061\pi$
$858$		0			0
$859$	−13.4982	−	9.01922i	−0.460553	−	0.307732i	0.303562	−	0.952812i	$-0.401824\pi$
$859$	−13.4982	−	9.01922i	−0.460553	−	0.307732i	−0.764115	+	0.645080i	$0.776824\pi$
$860$		0			0
$861$	1.62440	+	0.00303583i	0.0553594	+	0.000103461i
$862$		0			0
$863$		−	25.3881i		−	0.864222i	−0.901820	−	0.432111i	$-0.857769\pi$
$863$		−	25.3881i		−	0.864222i	0.901820	−	0.432111i	$-0.142231\pi$
$864$		0			0
$865$			21.0505i			0.715739i
$866$		0			0
$867$	15.6022	+	0.0291588i	0.529878	+	0.000990284i
$868$		0			0
$869$	16.6001	+	11.0919i	0.563121	+	0.376266i
$870$		0			0
$871$	37.4726	−	15.5217i	1.26971	−	0.525932i
$872$		0			0
$873$	0.00167429	−	0.447936i	5.66663e−5	−	0.0151603i
$874$		0			0
$875$	1.88024	+	9.45263i	0.0635639	+	0.319557i
$876$		0			0
$877$	−14.4959	−	21.6947i	−0.489492	−	0.732577i	0.501695	−	0.865044i	$-0.332710\pi$
$877$	−14.4959	−	21.6947i	−0.489492	−	0.732577i	−0.991187	+	0.132468i	$0.957710\pi$
$878$		0			0
$879$	−8.20856	+	12.2354i	−0.276868	+	0.412690i
$880$		0			0
$881$	−20.3613	−	20.3613i	−0.685990	−	0.685990i	0.275353	−	0.961343i	$-0.411205\pi$
$881$	−20.3613	−	20.3613i	−0.685990	−	0.685990i	−0.961343	+	0.275353i	$0.911205\pi$
$882$		0			0
$883$	−16.0071	−	23.9562i	−0.538680	−	0.806192i	0.457884	−	0.889012i	$-0.348607\pi$
$883$	−16.0071	−	23.9562i	−0.538680	−	0.806192i	−0.996565	+	0.0828199i	$0.973607\pi$
$884$		0			0
$885$	−2.83297	−	6.87571i	−0.0952292	−	0.231124i
$886$		0			0
$887$	−39.4628	−	16.3460i	−1.32503	−	0.548845i	−0.395796	−	0.918338i	$-0.629531\pi$
$887$	−39.4628	−	16.3460i	−1.32503	−	0.548845i	−0.929234	+	0.369493i	$0.879531\pi$
$888$		0			0
$889$	−14.9180	+	6.17923i	−0.500333	+	0.207245i
$890$		0			0
$891$	−47.5780	+	9.09465i	−1.59392	+	0.304682i
$892$		0			0
$893$	18.3618	+	3.65238i	0.614453	+	0.122222i
$894$		0			0
$895$		−	13.3876i		−	0.447499i
$896$		0			0
$897$	36.8455	−	7.25746i	1.23023	−	0.242320i
$898$		0			0
$899$	−5.60829	+	28.1948i	−0.187047	+	0.940349i
$900$		0			0
$901$	40.9829	+	27.3839i	1.36534	+	0.912290i
$902$		0			0
$903$	2.16018	−	1.43755i	0.0718863	−	0.0478388i
$904$		0			0
$905$	8.54440	−	20.6280i	0.284025	−	0.685698i
$906$		0			0
$907$	−3.37324	−	16.9584i	−0.112007	−	0.563096i	−0.995509	−	0.0946685i	$-0.969821\pi$
$907$	−3.37324	−	16.9584i	−0.112007	−	0.563096i	0.883502	−	0.468427i	$-0.155179\pi$
$908$		0			0
$909$	−5.76561	−	3.88371i	−0.191233	−	0.128814i
$910$		0			0
$911$	−2.54657	+	2.54657i	−0.0843717	+	0.0843717i	−0.748033	−	0.663661i	$-0.769002\pi$
$911$	−2.54657	+	2.54657i	−0.0843717	+	0.0843717i	0.663661	+	0.748033i	$0.269002\pi$
$912$		0			0
$913$	−11.5406	−	11.5406i	−0.381938	−	0.381938i
$914$		0			0
$915$	−2.27694	+	2.26845i	−0.0752733	+	0.0749925i
$916$		0			0
$917$	−0.997605	+	0.198436i	−0.0329438	+	0.00655294i
$918$		0			0
$919$	30.5861	+	12.6692i	1.00894	+	0.417918i	0.825069	−	0.565032i	$-0.191136\pi$
$919$	30.5861	+	12.6692i	1.00894	+	0.417918i	0.183874	+	0.982950i	$0.441136\pi$
$920$		0			0
$921$	−15.7753	+	10.4981i	−0.519813	+	0.345925i
$922$		0			0
$923$	7.90200	−	11.8262i	0.260097	−	0.389263i
$924$		0			0
$925$	−9.17310	−	1.82464i	−0.301610	−	0.0599939i
$926$		0			0
$927$	−50.1007	+	20.5333i	−1.64552	+	0.674404i
$928$		0			0
$929$	−15.5822			−0.511236			−0.255618	−	0.966778i	$-0.582279\pi$
$929$	−15.5822			−0.511236			−0.255618	+	0.966778i	$0.582279\pi$
$930$		0			0
$931$	3.33352	−	16.7587i	0.109252	−	0.549245i
$932$		0			0
$933$	7.97837	−	19.1601i	0.261200	−	0.627274i
$934$		0			0
$935$	−17.9879	−	43.4265i	−0.588266	−	1.42020i
$936$		0			0
$937$	13.5497	−	32.7119i	0.442650	−	1.06865i	−0.532366	−	0.846514i	$-0.678697\pi$
$937$	13.5497	−	32.7119i	0.442650	−	1.06865i	0.975016	−	0.222136i	$-0.0713030\pi$
$938$		0			0
$939$	14.4243	+	35.0083i	0.470720	+	1.14245i
$940$		0			0
$941$	−15.8636	+	10.5997i	−0.517139	+	0.345541i	−0.786593	−	0.617472i	$-0.788157\pi$
$941$	−15.8636	+	10.5997i	−0.517139	+	0.345541i	0.269454	+	0.963013i	$0.413157\pi$
$942$		0			0
$943$	6.29482	−	6.29482i	0.204987	−	0.204987i
$944$		0			0
$945$	1.42136	−	6.94203i	0.0462370	−	0.225824i
$946$		0			0
$947$	3.79100	−	2.53307i	0.123191	−	0.0823136i	−0.492448	−	0.870342i	$-0.663898\pi$
$947$	3.79100	−	2.53307i	0.123191	−	0.0823136i	0.615639	+	0.788028i	$0.288898\pi$
$948$		0			0
$949$	−1.94468	+	0.386822i	−0.0631271	+	0.0125568i
$950$		0			0
$951$	−0.130896	+	0.651689i	−0.00424458	+	0.0211325i
$952$		0			0
$953$	2.16803	+	5.23408i	0.0702292	+	0.169548i	0.955097	−	0.296295i	$-0.0957511\pi$
$953$	2.16803	+	5.23408i	0.0702292	+	0.169548i	−0.884867	+	0.465843i	$0.845751\pi$
$954$		0			0
$955$	11.0440	−	16.5285i	0.357374	−	0.534848i
$956$		0			0
$957$	38.5259	+	0.0720007i	1.24536	+	0.00232745i
$958$		0			0
$959$	−7.18846			−0.232128
$960$		0			0
$961$	17.3858			0.560832
$962$		0			0
$963$	5.49618	+	28.1813i	0.177112	+	0.908129i
$964$		0			0
$965$	−22.5330	+	33.7231i	−0.725364	+	1.08558i
$966$		0			0
$967$	4.84384	+	11.6941i	0.155767	+	0.376056i	0.982427	−	0.186646i	$-0.0597618\pi$
$967$	4.84384	+	11.6941i	0.155767	+	0.376056i	−0.826660	+	0.562702i	$0.809762\pi$
$968$		0			0
$969$	−23.2453	−	4.66895i	−0.746746	−	0.149988i
$970$		0			0
$971$	14.2757	−	2.83961i	0.458129	−	0.0911275i	0.0393696	−	0.999225i	$-0.487465\pi$
$971$	14.2757	−	2.83961i	0.458129	−	0.0911275i	0.418760	+	0.908097i	$0.362465\pi$
$972$		0			0
$973$	−3.45380	+	2.30776i	−0.110724	+	0.0739833i
$974$		0			0
$975$	5.72212	−	8.52921i	0.183255	−	0.273153i
$976$		0			0
$977$	16.4215	−	16.4215i	0.525370	−	0.525370i	−0.393818	−	0.919188i	$-0.628846\pi$
$977$	16.4215	−	16.4215i	0.525370	−	0.525370i	0.919188	+	0.393818i	$0.128846\pi$
$978$		0			0
$979$	−70.9825	+	47.4290i	−2.26861	+	1.51584i
$980$		0			0
$981$	−11.4255	−	17.2386i	−0.364787	−	0.550385i
$982$		0			0
$983$	−16.4499	+	39.7135i	−0.524669	+	1.26666i	0.410306	+	0.911948i	$0.365422\pi$
$983$	−16.4499	+	39.7135i	−0.524669	+	1.26666i	−0.934975	+	0.354715i	$0.884578\pi$
$984$		0			0
$985$	−7.00865	−	16.9204i	−0.223314	−	0.539128i
$986$		0			0
$987$	−8.88099	−	3.69809i	−0.282685	−	0.117711i
$988$		0			0
$989$	2.77423	−	13.9470i	0.0882153	−	0.443488i
$990$		0			0
$991$	24.5959			0.781314			0.390657	−	0.920536i	$-0.372248\pi$
$991$	24.5959			0.781314			0.390657	+	0.920536i	$0.372248\pi$
$992$		0			0
$993$	11.9472	−	2.35325i	0.379134	−	0.0746781i
$994$		0			0
$995$	0.211211	+	0.0420124i	0.00669583	+	0.00133188i
$996$		0			0
$997$	10.5381	−	15.7713i	0.333744	−	0.499483i	−0.626205	−	0.779658i	$-0.715393\pi$
$997$	10.5381	−	15.7713i	0.333744	−	0.499483i	0.959949	+	0.280176i	$0.0903927\pi$
$998$		0			0
$999$	19.4724	+	13.1696i	0.616081	+	0.416667i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	768.2.s.a.431.14		240
3.2	odd	2	inner	768.2.s.a.431.18		240
4.3	odd	2		192.2.s.a.131.26	yes	240
12.11	even	2		192.2.s.a.131.5	yes	240
64.21	even	16		192.2.s.a.107.5	✓	240
64.43	odd	16	inner	768.2.s.a.335.18		240
192.107	even	16	inner	768.2.s.a.335.14		240
192.149	odd	16		192.2.s.a.107.26	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
192.2.s.a.107.5	✓	240	64.21	even	16
192.2.s.a.107.26	yes	240	192.149	odd	16
192.2.s.a.131.5	yes	240	12.11	even	2
192.2.s.a.131.26	yes	240	4.3	odd	2
768.2.s.a.335.14		240	192.107	even	16	inner
768.2.s.a.335.18		240	64.43	odd	16	inner
768.2.s.a.431.14		240	1.1	even	1	trivial
768.2.s.a.431.18		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)

\(f(q)\)	\(=\)	\(q+(-0.00323701 + 1.73205i) q^{3} +(0.951414 - 1.42389i) q^{5} +(0.304742 + 0.735711i) q^{7} +(-2.99998 - 0.0112133i) q^{9} +(-5.27874 + 1.05001i) q^{11} +(-2.38495 + 1.59357i) q^{13} +(2.46317 + 1.65250i) q^{15} +(-3.60610 + 3.60610i) q^{17} +(2.23180 - 1.49124i) q^{19} +(-1.27527 + 0.525445i) q^{21} +(-2.89265 + 6.98348i) q^{23} +(0.791139 + 1.90998i) q^{25} +(0.0291330 - 5.19607i) q^{27} +(-0.806254 + 4.05331i) q^{29} +6.95599 q^{31} +(-1.80158 - 9.14643i) q^{33} +(1.33751 + 0.266047i) q^{35} +(-2.51344 + 3.76162i) q^{37} +(-2.75242 - 4.13600i) q^{39} +(-1.08807 - 0.450693i) q^{41} +(-1.84512 + 0.367016i) q^{43} +(-2.87019 + 4.26097i) q^{45} +(4.93192 + 4.93192i) q^{47} +(4.50134 - 4.50134i) q^{49} +(-6.23427 - 6.25761i) q^{51} +(-1.88555 - 9.47932i) q^{53} +(-3.52717 + 8.51534i) q^{55} +(2.57568 + 3.87042i) q^{57} +(-2.08460 - 1.39288i) q^{59} +(-0.211398 + 1.06277i) q^{61} +(-0.905968 - 2.21053i) q^{63} +4.91205i q^{65} +(-13.8689 - 2.75869i) q^{67} +(-12.0864 - 5.03282i) q^{69} +(-4.58122 + 1.89760i) q^{71} +(0.638643 + 0.264535i) q^{73} +(-3.31074 + 1.36411i) q^{75} +(-2.38115 - 3.56365i) q^{77} +(-2.62297 - 2.62297i) q^{79} +(8.99975 + 0.0672794i) q^{81} +(1.68471 + 2.52135i) q^{83} +(1.70380 + 8.56559i) q^{85} +(-7.01792 - 1.40959i) q^{87} +(14.6543 - 6.06999i) q^{89} +(-1.89920 - 1.26900i) q^{91} +(-0.0225166 + 12.0481i) q^{93} -4.59663i q^{95} +0.149313i q^{97} +(15.8479 - 3.09081i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 8 q^{3} + 16 q^{7} - 8 q^{9} - 16 q^{13} + 8 q^{15} + 16 q^{19} - 8 q^{21} - 16 q^{25} + 8 q^{27} + 32 q^{31} - 16 q^{37} + 8 q^{39} + 16 q^{43} - 8 q^{45} - 16 q^{49} + 8 q^{51} + 80 q^{55} - 8 q^{57}+ \cdots + 8 q^{99}+O(q^{100}) \) 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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