LMFDB - Embedded newform 192.2.s.a.107.26

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [192,2,Mod(11,192)] 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("192.11"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(192, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([8, 5, 8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 192 = 2^{6} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	192.s (of order $16$, degree $8$, 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:	$1.53312771881$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			107.26
Character	$\chi$	$=$	192.107
Dual form			192.2.s.a.131.26

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.17382 - 0.788758i) q^{2} +(0.00323701 + 1.73205i) q^{3} +(0.755721 - 1.85172i) q^{4} +(0.951414 + 1.42389i) q^{5} +(1.36997 + 2.03056i) q^{6} +(-0.304742 + 0.735711i) q^{7} +(-0.573480 - 2.76968i) q^{8} +(-2.99998 + 0.0112133i) q^{9} +(2.23990 + 0.920961i) q^{10} +(5.27874 + 1.05001i) q^{11} +(3.20972 + 1.30295i) q^{12} +(-2.38495 - 1.59357i) q^{13} +(0.222585 + 1.10396i) q^{14} +(-2.46317 + 1.65250i) q^{15} +(-2.85777 - 2.79878i) q^{16} +(-3.60610 - 3.60610i) q^{17} +(-3.51260 + 2.37942i) q^{18} +(-2.23180 - 1.49124i) q^{19} +(3.35566 - 0.685692i) q^{20} +(-1.27527 - 0.525445i) q^{21} +(7.02451 - 2.93113i) q^{22} +(2.89265 + 6.98348i) q^{23} +(4.79536 - 1.00226i) q^{24} +(0.791139 - 1.90998i) q^{25} +(-4.05645 + 0.0105764i) q^{26} +(-0.0291330 - 5.19607i) q^{27} +(1.13203 + 1.12029i) q^{28} +(-0.806254 - 4.05331i) q^{29} +(-1.58790 + 3.88259i) q^{30} -6.95599 q^{31} +(-5.56207 - 1.03118i) q^{32} +(-1.80158 + 9.14643i) q^{33} +(-7.07727 - 1.38858i) q^{34} +(-1.33751 + 0.266047i) q^{35} +(-2.24638 + 5.56361i) q^{36} +(-2.51344 - 3.76162i) q^{37} +(-3.79597 + 0.00989724i) q^{38} +(2.75242 - 4.13600i) q^{39} +(3.39810 - 3.45168i) q^{40} +(-1.08807 + 0.450693i) q^{41} +(-1.91139 + 0.389102i) q^{42} +(1.84512 + 0.367016i) q^{43} +(5.93358 - 8.98127i) q^{44} +(-2.87019 - 4.26097i) q^{45} +(8.90374 + 5.91577i) q^{46} +(-4.93192 + 4.93192i) q^{47} +(4.83836 - 4.95886i) q^{48} +(4.50134 + 4.50134i) q^{49} +(-0.577854 - 2.86600i) q^{50} +(6.23427 - 6.25761i) q^{51} +(-4.75321 + 3.21197i) q^{52} +(-1.88555 + 9.47932i) q^{53} +(-4.13264 - 6.07629i) q^{54} +(3.52717 + 8.51534i) q^{55} +(2.21245 + 0.422120i) q^{56} +(2.57568 - 3.87042i) q^{57} +(-4.14348 - 4.12193i) q^{58} +(2.08460 - 1.39288i) q^{59} +(1.19851 + 5.80994i) q^{60} +(-0.211398 - 1.06277i) q^{61} +(-8.16510 + 5.48659i) q^{62} +(0.905968 - 2.21053i) q^{63} +(-7.34224 + 3.17671i) q^{64} -4.91205i q^{65} +(5.09959 + 12.1573i) q^{66} +(13.8689 - 2.75869i) q^{67} +(-9.40272 + 3.95230i) q^{68} +(-12.0864 + 5.03282i) q^{69} +(-1.36015 + 1.36726i) q^{70} +(4.58122 + 1.89760i) q^{71} +(1.75149 + 8.30255i) q^{72} +(0.638643 - 0.264535i) q^{73} +(-5.91734 - 2.43299i) q^{74} +(3.31074 + 1.36411i) q^{75} +(-4.44799 + 3.00572i) q^{76} +(-2.38115 + 3.56365i) q^{77} +(-0.0314495 - 7.02592i) q^{78} +(2.62297 - 2.62297i) q^{79} +(1.26623 - 6.73195i) q^{80} +(8.99975 - 0.0672794i) q^{81} +(-0.921714 + 1.38726i) q^{82} +(-1.68471 + 2.52135i) q^{83} +(-1.93673 + 1.96437i) q^{84} +(1.70380 - 8.56559i) q^{85} +(2.45533 - 1.02454i) q^{86} +(7.01792 - 1.40959i) q^{87} +(-0.119072 - 15.2226i) q^{88} +(14.6543 + 6.06999i) q^{89} +(-6.72997 - 2.73775i) q^{90} +(1.89920 - 1.26900i) q^{91} +(15.1175 - 0.0788324i) q^{92} +(-0.0225166 - 12.0481i) q^{93} +(-1.89911 + 9.67928i) q^{94} -4.59663i q^{95} +(1.76804 - 9.63712i) q^{96} -0.149313i q^{97} +(8.83425 + 1.73331i) q^{98} +(-15.8479 - 3.09081i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 8 q^{3} - 16 q^{4} - 8 q^{6} - 16 q^{7} - 8 q^{9} - 16 q^{10} - 8 q^{12} - 16 q^{13} - 8 q^{15} - 16 q^{16} - 8 q^{18} - 16 q^{19} - 8 q^{21} - 16 q^{22} - 48 q^{24} - 16 q^{25} - 8 q^{27} - 16 q^{28}+ \cdots - 8 q^{99}+O(q^{100}) $ 240 * q - 8 * q^3 - 16 * q^4 - 8 * q^6 - 16 * q^7 - 8 * q^9 - 16 * q^10 - 8 * q^12 - 16 * q^13 - 8 * q^15 - 16 * q^16 - 8 * q^18 - 16 * q^19 - 8 * q^21 - 16 * q^22 - 48 * q^24 - 16 * q^25 - 8 * q^27 - 16 * q^28 - 88 * q^30 - 32 * q^31 - 16 * q^34 - 88 * q^36 - 16 * q^37 - 8 * q^39 - 16 * q^40 - 48 * q^42 - 16 * q^43 - 8 * q^45 - 16 * q^46 - 8 * q^48 - 16 * q^49 - 8 * q^51 + 32 * q^52 - 8 * q^54 - 80 * q^55 - 8 * q^57 + 128 * q^58 - 8 * q^60 - 16 * q^61 + 80 * q^64 - 24 * q^66 - 144 * q^67 - 8 * q^69 + 80 * q^70 - 8 * q^72 - 16 * q^73 - 8 * q^75 + 96 * q^76 + 16 * q^78 - 48 * q^79 - 8 * q^81 + 64 * q^82 + 104 * q^84 - 16 * q^85 - 8 * q^87 + 64 * q^88 + 136 * q^90 - 16 * q^91 - 32 * q^93 + 80 * q^94 + 128 * q^96 - 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/192\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$133$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{13}{16}\right)$

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 $

$2$	1.17382	−	0.788758i	0.830018	−	0.557736i
$2$	1.17382	−	0.788758i	0.830018	−	0.557736i
$3$	0.00323701	+	1.73205i	0.00186889	+	0.999998i
$3$	0.00323701	+	1.73205i	0.00186889	+	0.999998i
$4$	0.755721	−	1.85172i	0.377861	−	0.925862i
$5$	0.951414	+	1.42389i	0.425485	+	0.636783i	0.980837	−	0.194832i	$-0.0624163\pi$
$5$	0.951414	+	1.42389i	0.425485	+	0.636783i	−0.555351	+	0.831616i	$0.687416\pi$
$6$	1.36997	+	2.03056i	0.559286	+	0.828974i
$7$	−0.304742	+	0.735711i	−0.115181	+	0.278073i	−0.970948	−	0.239289i	$-0.923086\pi$
$7$	−0.304742	+	0.735711i	−0.115181	+	0.278073i	0.855767	+	0.517361i	$0.173086\pi$
$8$	−0.573480	−	2.76968i	−0.202756	−	0.979229i
$9$	−2.99998	+	0.0112133i	−0.999993	+	0.00373777i
$10$	2.23990	+	0.920961i	0.708318	+	0.291233i
$11$	5.27874	+	1.05001i	1.59160	+	0.316589i	0.909831	−	0.414978i	$-0.136211\pi$
$11$	5.27874	+	1.05001i	1.59160	+	0.316589i	0.681769	+	0.731567i	$0.261211\pi$
$12$	3.20972	+	1.30295i	0.926567	+	0.376130i
$13$	−2.38495	−	1.59357i	−0.661465	−	0.441977i	0.178995	−	0.983850i	$-0.442715\pi$
$13$	−2.38495	−	1.59357i	−0.661465	−	0.441977i	−0.840460	+	0.541873i	$0.817715\pi$
$14$	0.222585	+	1.10396i	0.0594885	+	0.295046i
$15$	−2.46317	+	1.65250i	−0.635987	+	0.426674i
$16$	−2.85777	−	2.79878i	−0.714443	−	0.699694i
$17$	−3.60610	−	3.60610i	−0.874608	−	0.874608i	0.118362	−	0.992970i	$-0.462236\pi$
$17$	−3.60610	−	3.60610i	−0.874608	−	0.874608i	−0.992970	+	0.118362i	$0.962236\pi$
$18$	−3.51260	+	2.37942i	−0.827928	+	0.560835i
$19$	−2.23180	−	1.49124i	−0.512011	−	0.342115i	0.272575	−	0.962134i	$-0.412125\pi$
$19$	−2.23180	−	1.49124i	−0.512011	−	0.342115i	−0.784586	+	0.620020i	$0.787125\pi$
$20$	3.35566	−	0.685692i	0.750348	−	0.153325i
$21$	−1.27527	−	0.525445i	−0.278287	−	0.114662i
$22$	7.02451	−	2.93113i	1.49763	−	0.624919i
$23$	2.89265	+	6.98348i	0.603160	+	1.45616i	0.870311	+	0.492502i	$0.163918\pi$
$23$	2.89265	+	6.98348i	0.603160	+	1.45616i	−0.267151	+	0.963655i	$0.586082\pi$
$24$	4.79536	−	1.00226i	0.978849	−	0.204586i
$25$	0.791139	−	1.90998i	0.158228	−	0.381996i
$26$	−4.05645	+	0.0105764i	−0.795534	+	0.00207420i
$27$	−0.0291330	−	5.19607i	−0.00560664	−	0.999984i
$28$	1.13203	+	1.12029i	0.213934	+	0.211715i
$29$	−0.806254	−	4.05331i	−0.149718	−	0.752681i	−0.980567	−	0.196184i	$-0.937145\pi$
$29$	−0.806254	−	4.05331i	−0.149718	−	0.752681i	0.830850	−	0.556497i	$-0.187855\pi$
$30$	−1.58790	+	3.88259i	−0.289909	+	0.708861i
$31$	−6.95599			−1.24933			−0.624666	−	0.780892i	$-0.714765\pi$
$31$	−6.95599			−1.24933			−0.624666	+	0.780892i	$0.714765\pi$
$32$	−5.56207	−	1.03118i	−0.983245	−	0.182288i
$33$	−1.80158	+	9.14643i	−0.313614	+	1.59219i
$34$	−7.07727	−	1.38858i	−1.21374	−	0.238140i
$35$	−1.33751	+	0.266047i	−0.226080	+	0.0449701i
$36$	−2.24638	+	5.56361i	−0.374397	+	0.927268i
$37$	−2.51344	−	3.76162i	−0.413206	−	0.618407i	0.565235	−	0.824930i	$-0.308785\pi$
$37$	−2.51344	−	3.76162i	−0.413206	−	0.618407i	−0.978442	+	0.206523i	$0.933785\pi$
$38$	−3.79597	+	0.00989724i	−0.615788	+	0.00160554i
$39$	2.75242	−	4.13600i	0.440740	−	0.662290i
$40$	3.39810	−	3.45168i	0.537287	−	0.545759i
$41$	−1.08807	+	0.450693i	−0.169928	+	0.0703865i	−0.466026	−	0.884771i	$-0.654315\pi$
$41$	−1.08807	+	0.450693i	−0.169928	+	0.0703865i	0.296098	+	0.955158i	$0.404315\pi$
$42$	−1.91139	+	0.389102i	−0.294935	+	0.0600398i
$43$	1.84512	+	0.367016i	0.281377	+	0.0559695i	0.333761	−	0.942658i	$-0.391682\pi$
$43$	1.84512	+	0.367016i	0.281377	+	0.0559695i	−0.0523840	+	0.998627i	$0.516682\pi$
$44$	5.93358	−	8.98127i	0.894521	−	1.35398i
$45$	−2.87019	−	4.26097i	−0.427862	−	0.635189i
$46$	8.90374	+	5.91577i	1.31279	+	0.872233i
$47$	−4.93192	+	4.93192i	−0.719394	+	0.719394i	−0.968481	−	0.249087i	$-0.919869\pi$
$47$	−4.93192	+	4.93192i	−0.719394	+	0.719394i	0.249087	+	0.968481i	$0.419869\pi$
$48$	4.83836	−	4.95886i	0.698357	−	0.715749i
$49$	4.50134	+	4.50134i	0.643049	+	0.643049i
$50$	−0.577854	−	2.86600i	−0.0817209	−	0.405313i
$51$	6.23427	−	6.25761i	0.872972	−	0.876241i
$52$	−4.75321	+	3.21197i	−0.659151	+	0.445420i
$53$	−1.88555	+	9.47932i	−0.259001	+	1.30208i	0.604041	+	0.796953i	$0.293556\pi$
$53$	−1.88555	+	9.47932i	−0.259001	+	1.30208i	−0.863042	+	0.505132i	$0.831444\pi$
$54$	−4.13264	−	6.07629i	−0.562381	−	0.826878i
$55$	3.52717	+	8.51534i	0.475604	+	1.14821i
$56$	2.21245	+	0.422120i	0.295651	+	0.0564082i
$57$	2.57568	−	3.87042i	0.341157	−	0.512649i
$58$	−4.14348	−	4.12193i	−0.544066	−	0.541236i
$59$	2.08460	−	1.39288i	0.271392	−	0.181338i	−0.412426	−	0.910991i	$-0.635318\pi$
$59$	2.08460	−	1.39288i	0.271392	−	0.181338i	0.683817	+	0.729653i	$0.260318\pi$
$60$	1.19851	+	5.80994i	0.154727	+	0.750060i
$61$	−0.211398	−	1.06277i	−0.0270668	−	0.136074i	0.964889	−	0.262657i	$-0.0845988\pi$
$61$	−0.211398	−	1.06277i	−0.0270668	−	0.136074i	−0.991956	+	0.126583i	$0.959599\pi$
$62$	−8.16510	+	5.48659i	−1.03697	+	0.696798i
$63$	0.905968	−	2.21053i	0.114141	−	0.278501i
$64$	−7.34224	+	3.17671i	−0.917780	+	0.397089i
$65$		−	4.91205i		−	0.609264i
$66$	5.09959	+	12.1573i	0.627716	+	1.49646i
$67$	13.8689	−	2.75869i	1.69435	−	0.337027i	0.748873	−	0.662714i	$-0.230595\pi$
$67$	13.8689	−	2.75869i	1.69435	−	0.337027i	0.945478	+	0.325687i	$0.105595\pi$
$68$	−9.40272	+	3.95230i	−1.14025	+	0.479287i
$69$	−12.0864	+	5.03282i	−1.45503	+	0.605880i
$70$	−1.36015	+	1.36726i	−0.162569	+	0.163419i
$71$	4.58122	+	1.89760i	0.543691	+	0.225204i	0.637588	−	0.770378i	$-0.279932\pi$
$71$	4.58122	+	1.89760i	0.543691	+	0.225204i	−0.0938968	+	0.995582i	$0.529932\pi$
$72$	1.75149	+	8.30255i	0.206415	+	0.978465i
$73$	0.638643	−	0.264535i	0.0747476	−	0.0309615i	−0.344996	−	0.938604i	$-0.612120\pi$
$73$	0.638643	−	0.264535i	0.0747476	−	0.0309615i	0.419744	+	0.907643i	$0.362120\pi$
$74$	−5.91734	−	2.43299i	−0.687877	−	0.282829i
$75$	3.31074	+	1.36411i	0.382291	+	0.157514i
$76$	−4.44799	+	3.00572i	−0.510220	+	0.344780i
$77$	−2.38115	+	3.56365i	−0.271358	+	0.406115i
$78$	−0.0314495	−	7.02592i	−0.00356096	−	0.795529i
$79$	2.62297	−	2.62297i	0.295108	−	0.295108i	−0.543986	−	0.839094i	$-0.683086\pi$
$79$	2.62297	−	2.62297i	0.295108	−	0.295108i	0.839094	+	0.543986i	$0.183086\pi$
$80$	1.26623	−	6.73195i	0.141569	−	0.752655i
$81$	8.99975	−	0.0672794i	0.999972	−	0.00747549i
$82$	−0.921714	+	1.38726i	−0.101786	+	0.153197i
$83$	−1.68471	+	2.52135i	−0.184921	+	0.276754i	−0.912335	−	0.409445i	$-0.865722\pi$
$83$	−1.68471	+	2.52135i	−0.184921	+	0.276754i	0.727414	+	0.686199i	$0.240722\pi$
$84$	−1.93673	+	1.96437i	−0.211315	+	0.214330i
$85$	1.70380	−	8.56559i	0.184803	−	0.929069i
$86$	2.45533	−	1.02454i	0.264765	−	0.110479i
$87$	7.01792	−	1.40959i	0.752400	−	0.151124i
$88$	−0.119072	−	15.2226i	−0.0126931	−	1.62273i
$89$	14.6543	+	6.06999i	1.55335	+	0.643418i	0.983918	−	0.178622i	$-0.0571639\pi$
$89$	14.6543	+	6.06999i	1.55335	+	0.643418i	0.569430	+	0.822040i	$0.307164\pi$
$90$	−6.72997	−	2.73775i	−0.709401	−	0.288584i
$91$	1.89920	−	1.26900i	0.199090	−	0.133028i
$92$	15.1175	−	0.0788324i	1.57611	−	0.00821885i
$93$	−0.0225166	−	12.0481i	−0.00233486	−	1.24933i
$94$	−1.89911	+	9.67928i	−0.195878	+	0.998342i
$95$		−	4.59663i		−	0.471605i
$96$	1.76804	−	9.63712i	0.180450	−	0.983584i
$97$		−	0.149313i		−	0.0151604i	−0.999971	−	0.00758022i	$-0.997587\pi$
$97$		−	0.149313i		−	0.0151604i	0.999971	−	0.00758022i	$-0.00241288\pi$
$98$	8.83425	+	1.73331i	0.892394	+	0.175091i
$99$	−15.8479	−	3.09081i	−1.59277	−	0.310638i
$100$	−2.93888	−	2.90838i	−0.293888	−	0.290838i
$101$	1.92669	−	1.28738i	0.191713	−	0.128099i	−0.456009	−	0.889975i	$-0.650722\pi$
$101$	1.92669	−	1.28738i	0.191713	−	0.128099i	0.647723	+	0.761876i	$0.275722\pi$
$102$	2.38218	−	12.2627i	0.235871	−	1.21418i
$103$	−16.6745	−	6.90682i	−1.64299	−	0.680549i	−0.646397	−	0.763002i	$-0.723725\pi$
$103$	−16.6745	−	6.90682i	−1.64299	−	0.680549i	−0.996595	+	0.0824521i	$0.973725\pi$
$104$	−3.04596	+	7.51941i	−0.298681	+	0.737339i
$105$	−0.465135	−	2.31577i	−0.0453926	−	0.225996i
$106$	5.26358	+	12.6143i	0.511245	+	1.22521i
$107$	1.86716	−	9.38684i	0.180505	−	0.907460i	−0.779270	−	0.626689i	$-0.784410\pi$
$107$	1.86716	−	9.38684i	0.180505	−	0.907460i	0.959775	−	0.280772i	$-0.0905903\pi$
$108$	−9.64371	−	3.87283i	−0.927966	−	0.372664i
$109$	3.82994	−	5.73191i	0.366842	−	0.549017i	−0.601427	−	0.798927i	$-0.705401\pi$
$109$	3.82994	−	5.73191i	0.366842	−	0.549017i	0.968269	+	0.249910i	$0.0804011\pi$
$110$	10.8568	+	7.21342i	1.03516	+	0.687773i
$111$	6.50718	−	4.36557i	0.617634	−	0.414361i
$112$	2.92997	−	1.24959i	0.276856	−	0.118075i
$113$	−10.9819	+	10.9819i	−1.03309	+	1.03309i	−0.0336525	+	0.999434i	$0.510714\pi$
$113$	−10.9819	+	10.9819i	−1.03309	+	1.03309i	−0.999434	+	0.0336525i	$0.989286\pi$
$114$	−0.0294301	−	6.57477i	−0.00275638	−	0.615784i
$115$	−7.19161	+	10.7630i	−0.670621	+	1.00366i
$116$	−8.11492	−	1.57021i	−0.753451	−	0.145791i
$117$	7.17266	+	4.75393i	0.663112	+	0.439501i
$118$	1.34830	−	3.27924i	0.124121	−	0.301879i
$119$	3.75198	−	1.55412i	0.343943	−	0.142466i
$120$	5.98948	+	5.87451i	0.546762	+	0.536266i
$121$	16.5999	+	6.87591i	1.50908	+	0.625083i
$122$	−1.08641	−	1.08076i	−0.0983592	−	0.0978476i
$123$	−0.784144	−	1.88313i	−0.0707039	−	0.169796i
$124$	−5.25679	+	12.8806i	−0.472074	+	1.15671i
$125$	11.8703	−	2.36114i	1.06171	−	0.211187i
$126$	−0.680131	−	3.30937i	−0.0605909	−	0.294822i
$127$			20.2770i			1.79929i	0.436624	+	0.899644i	$0.356174\pi$
$127$			20.2770i			1.79929i	−0.436624	+	0.899644i	$0.643826\pi$
$128$	−6.11283	+	9.52015i	−0.540303	+	0.841470i
$129$	−0.629717	+	3.19702i	−0.0554435	+	0.281482i
$130$	−3.87442	−	5.76587i	−0.339809	−	0.505701i
$131$	0.249189	+	1.25276i	0.0217717	+	0.109454i	0.990143	−	0.140059i	$-0.0447294\pi$
$131$	0.249189	+	1.25276i	0.0217717	+	0.109454i	−0.968371	+	0.249513i	$0.919729\pi$
$132$	15.5752	+	10.2482i	1.35565	+	0.891989i
$133$	1.77725	−	1.18752i	0.154107	−	0.102971i
$134$	14.1036	−	14.1774i	1.21837	−	1.22474i
$135$	7.37092	−	4.98509i	0.634388	−	0.429049i
$136$	−7.91972	+	12.0558i	−0.679110	+	1.03377i
$137$	−3.45449	−	8.33988i	−0.295137	−	0.712524i	−0.999995	−	0.00317519i	$-0.998989\pi$
$137$	−3.45449	−	8.33988i	−0.295137	−	0.712524i	0.704858	−	0.709348i	$-0.251011\pi$
$138$	−10.2176	+	15.4409i	−0.869778	+	1.31441i
$139$	−1.01764	+	5.11603i	−0.0863153	+	0.433936i	0.913328	+	0.407225i	$0.133503\pi$
$139$	−1.01764	+	5.11603i	−0.0863153	+	0.433936i	−0.999643	+	0.0267113i	$0.991497\pi$
$140$	−0.518137	+	2.67775i	−0.0437906	+	0.226311i
$141$	−8.55828	−	8.52635i	−0.720737	−	0.718048i
$142$	6.87429	−	1.38602i	0.576878	−	0.116313i
$143$	−10.9163	−	10.9163i	−0.912863	−	0.912863i
$144$	8.60464	+	8.36422i	0.717053	+	0.697019i
$145$	5.00439	−	5.00439i	0.415592	−	0.415592i
$146$	0.541000	−	0.814252i	0.0447735	−	0.0673880i
$147$	−7.78197	+	7.81111i	−0.641846	+	0.644250i
$148$	−8.86495	+	1.81145i	−0.728694	+	0.148901i
$149$	16.6513	+	3.31215i	1.36413	+	0.271342i	0.822255	−	0.569119i	$-0.192716\pi$
$149$	16.6513	+	3.31215i	1.36413	+	0.271342i	0.541872	+	0.840461i	$0.317716\pi$
$150$	4.96217	−	1.01015i	0.405160	−	0.0824783i
$151$	−5.96083	+	2.46906i	−0.485086	+	0.200929i	−0.611804	−	0.791010i	$-0.709556\pi$
$151$	−5.96083	+	2.46906i	−0.485086	+	0.200929i	0.126718	+	0.991939i	$0.459556\pi$
$152$	−2.85037	+	7.03658i	−0.231196	+	0.570742i
$153$	10.8587	+	10.7778i	0.877871	+	0.871333i
$154$	0.0158035	+	6.06125i	0.00127348	+	0.488429i
$155$	−6.61802	−	9.90457i	−0.531572	−	0.795554i
$156$	−5.57867	−	8.22238i	−0.446651	−	0.658318i
$157$	−13.1331	+	2.61233i	−1.04813	+	0.208487i	−0.688972	−	0.724788i	$-0.741938\pi$
$157$	−13.1331	+	2.61233i	−1.04813	+	0.208487i	−0.359162	+	0.933275i	$0.616938\pi$
$158$	1.01002	−	5.14780i	0.0803525	−	0.409537i
$159$	−16.4247	−	3.23519i	−1.30257	−	0.256567i
$160$	−3.82355	−	8.90086i	−0.302278	−	0.703675i
$161$	−6.01934			−0.474390
$162$	10.5110	−	7.17760i	0.825826	−	0.563925i
$163$	4.06143	+	20.4182i	0.318116	+	1.59928i	0.726965	+	0.686675i	$0.240930\pi$
$163$	4.06143	+	20.4182i	0.318116	+	1.59928i	−0.408849	+	0.912602i	$0.634070\pi$
$164$	0.0122826	+	2.35540i	0.000959108	+	0.183926i
$165$	−14.7376	+	6.13679i	−1.14732	+	0.477749i
$166$	0.0111813	+	4.28844i	0.000867835	+	0.332848i
$167$	−4.47253	+	10.7976i	−0.346095	+	0.835546i	0.650979	+	0.759096i	$0.274359\pi$
$167$	−4.47253	+	10.7976i	−0.346095	+	0.835546i	−0.997073	+	0.0764504i	$0.975641\pi$
$168$	−0.723971	+	3.83343i	−0.0558556	+	0.295756i
$169$	−1.82638	−	4.40928i	−0.140491	−	0.339175i
$170$	−4.75622	−	11.3984i	−0.364785	−	0.874215i
$171$	6.71209	+	4.44867i	0.513286	+	0.340199i
$172$	2.07401	−	3.13928i	0.158141	−	0.239368i
$173$	−10.2207	−	6.82923i	−0.777062	−	0.519217i	0.102653	−	0.994717i	$-0.467267\pi$
$173$	−10.2207	−	6.82923i	−0.777062	−	0.519217i	−0.879715	+	0.475501i	$0.842267\pi$
$174$	7.12597	−	7.19005i	0.540218	−	0.545076i
$175$	1.16410	+	1.16410i	0.0879977	+	0.0879977i
$176$	−12.1467	−	17.7747i	−0.915592	−	1.33982i
$177$	2.41929	+	3.60611i	0.181845	+	0.271052i
$178$	21.9893	−	4.43357i	1.64816	−	0.332310i
$179$	−6.50009	−	4.34322i	−0.485839	−	0.324627i	0.288411	−	0.957507i	$-0.406873\pi$
$179$	−6.50009	−	4.34322i	−0.485839	−	0.324627i	−0.774251	+	0.632879i	$0.781873\pi$
$180$	−10.0592	+	2.09469i	−0.749770	+	0.156129i
$181$	12.7875	+	2.54359i	0.950487	+	0.189064i	0.645901	−	0.763421i	$-0.276482\pi$
$181$	12.7875	+	2.54359i	0.950487	+	0.189064i	0.304586	+	0.952485i	$0.401482\pi$
$182$	1.22839	−	2.98759i	0.0910540	−	0.221455i
$183$	1.84008	−	0.369592i	0.136023	−	0.0273210i
$184$	17.6831	−	12.0166i	1.30362	−	0.885876i
$185$	2.96482	−	7.15772i	0.217978	−	0.526246i
$186$	−9.52947	−	14.1246i	−0.698735	−	1.03566i
$187$	−15.2492	−	22.8221i	−1.11514	−	1.66892i
$188$	5.40540	+	12.8597i	0.394229	+	0.937890i
$189$	3.83168	+	1.56202i	0.278714	+	0.113621i
$190$	−3.62563	−	5.39564i	−0.263031	−	0.391441i
$191$	−11.6080			−0.839922			−0.419961	−	0.907542i	$-0.637956\pi$
$191$	−11.6080			−0.839922			−0.419961	+	0.907542i	$0.637956\pi$
$192$	−5.52598	−	12.7068i	−0.398804	−	0.917036i
$193$	−23.6837			−1.70479			−0.852396	−	0.522896i	$-0.824852\pi$
$193$	−23.6837			−1.70479			−0.852396	+	0.522896i	$0.824852\pi$
$194$	−0.117772	−	0.175267i	−0.00845553	−	0.0125834i
$195$	8.50790	−	0.0159003i	0.609263	−	0.00113865i
$196$	11.7370	−	4.93349i	0.838358	−	0.352392i
$197$	5.94160	+	8.89224i	0.423322	+	0.633546i	0.980424	−	0.196898i	$-0.0630869\pi$
$197$	5.94160	+	8.89224i	0.423322	+	0.633546i	−0.557102	+	0.830444i	$0.688087\pi$
$198$	−21.0405	+	8.87209i	−1.49528	+	0.630512i
$199$	−0.0481228	+	0.116179i	−0.00341134	+	0.00823569i	−0.925576	−	0.378562i	$-0.876419\pi$
$199$	−0.0481228	+	0.116179i	−0.00341134	+	0.00823569i	0.922165	+	0.386797i	$0.126419\pi$
$200$	−5.74373	−	1.09587i	−0.406143	−	0.0774895i
$201$	4.82307	+	24.0126i	0.340193	+	1.69372i
$202$	1.24617	−	3.03085i	0.0876802	−	0.213250i
$203$	3.22776	+	0.642042i	0.226545	+	0.0450625i
$204$	−6.87601	−	16.2732i	−0.481417	−	1.13935i
$205$	−1.67694	−	1.12050i	−0.117123	−	0.0782589i
$206$	−25.0208	+	5.04480i	−1.74328	+	0.351488i
$207$	−8.75621	−	20.9179i	−0.608598	−	1.45389i
$208$	2.35558	+	11.2290i	0.163330	+	0.778590i
$209$	−10.2153	−	10.2153i	−0.706607	−	0.706607i
$210$	−2.37257	−	2.35142i	−0.163723	−	0.162263i
$211$	−11.9918	−	8.01268i	−0.825551	−	0.551615i	0.0694988	−	0.997582i	$-0.477860\pi$
$211$	−11.9918	−	8.01268i	−0.825551	−	0.551615i	−0.895050	+	0.445967i	$0.852860\pi$
$212$	16.1281	+	10.6553i	1.10769	+	0.731806i
$213$	−3.27191	+	7.94104i	−0.224188	+	0.544111i
$214$	−5.21223	−	12.4912i	−0.356301	−	0.853883i
$215$	1.23288	+	2.97643i	0.0840815	+	0.202991i
$216$	−14.3747	+	3.06053i	−0.978077	+	0.208243i
$217$	2.11978	−	5.11760i	0.143900	−	0.347405i
$218$	−0.0254189	−	9.74914i	−0.00172159	−	0.660295i
$219$	0.460254	+	1.10530i	0.0311011	+	0.0746896i
$220$	18.4336	−	0.0961247i	1.24280	−	0.00648073i
$221$	2.85378	+	14.3469i	0.191966	+	0.965079i
$222$	4.19490	−	10.2570i	0.281543	−	0.688404i
$223$	15.4594			1.03524			0.517618	−	0.855612i	$-0.326819\pi$
$223$	15.4594			1.03524			0.517618	+	0.855612i	$0.326819\pi$
$224$	2.45364	−	3.77784i	0.163941	−	0.252417i
$225$	−2.35198	+	5.73877i	−0.156799	+	0.382585i
$226$	−4.22873	+	21.5528i	−0.281291	+	1.43367i
$227$	8.37592	−	1.66607i	0.555929	−	0.110581i	0.0908733	−	0.995862i	$-0.471034\pi$
$227$	8.37592	−	1.66607i	0.555929	−	0.110581i	0.465056	+	0.885281i	$0.346034\pi$
$228$	−5.22045	−	7.69441i	−0.345733	−	0.509575i
$229$	1.16297	+	1.74050i	0.0768510	+	0.115016i	0.867904	−	0.496732i	$-0.165467\pi$
$229$	1.16297	+	1.74050i	0.0768510	+	0.115016i	−0.791053	+	0.611748i	$0.790467\pi$
$230$	0.0477300	+	18.3063i	0.00314723	+	1.20708i
$231$	−6.18012	−	4.11274i	−0.406622	−	0.270598i
$232$	−10.7640	+	4.55756i	−0.706691	+	0.299218i
$233$	9.34754	−	3.87188i	0.612378	−	0.253655i	−0.0548670	−	0.998494i	$-0.517473\pi$
$233$	9.34754	−	3.87188i	0.612378	−	0.253655i	0.667245	+	0.744839i	$0.267473\pi$
$234$	12.1691	−	0.0772151i	0.795521	−	0.00504771i
$235$	−11.7148	−	2.33022i	−0.764189	−	0.152007i
$236$	−1.00386	−	4.91273i	−0.0653459	−	0.319792i
$237$	4.55161	+	4.53463i	0.295659	+	0.294556i
$238$	3.17833	−	4.78367i	0.206021	−	0.310079i
$239$	−8.11977	+	8.11977i	−0.525224	+	0.525224i	−0.919145	−	0.393920i	$-0.871119\pi$
$239$	−8.11977	+	8.11977i	−0.525224	+	0.525224i	0.393920	+	0.919145i	$0.371119\pi$
$240$	11.6642	+	2.17138i	0.752918	+	0.140162i
$241$	−20.6545	−	20.6545i	−1.33047	−	1.33047i	−0.904948	−	0.425523i	$-0.860090\pi$
$241$	−20.6545	−	20.6545i	−1.33047	−	1.33047i	−0.425523	−	0.904948i	$-0.639910\pi$
$242$	24.9088	−	5.02222i	1.60120	−	0.322840i
$243$	0.145663	+	15.5878i	0.00934431	+	0.999956i
$244$	−2.12772	−	0.411707i	−0.136213	−	0.0263568i
$245$	−2.12678	+	10.6921i	−0.135875	+	0.683091i
$246$	−2.40578	−	1.59196i	−0.153387	−	0.101500i
$247$	2.94633	+	7.11307i	0.187470	+	0.452594i
$248$	3.98912	+	19.2659i	0.253310	+	1.22338i
$249$	−4.37255	−	2.90984i	−0.277099	−	0.184403i
$250$	12.0712	−	12.1343i	0.763452	−	0.767443i
$251$	6.36129	−	4.25048i	0.401521	−	0.268288i	−0.338372	−	0.941013i	$-0.609876\pi$
$251$	6.36129	−	4.25048i	0.401521	−	0.268288i	0.739893	+	0.672725i	$0.234876\pi$
$252$	−3.40864	−	3.34815i	−0.214724	−	0.210914i
$253$	7.93686	+	39.9013i	0.498986	+	2.50857i
$254$	15.9936	+	23.8016i	1.00353	+	1.49344i
$255$	14.8415	+	2.92334i	0.929412	+	0.183067i
$256$	0.333710	+	15.9965i	0.0208568	+	0.999782i
$257$			2.41242i			0.150483i	0.997165	+	0.0752414i	$0.0239727\pi$
$257$			2.41242i			0.150483i	−0.997165	+	0.0752414i	$0.976027\pi$
$258$	1.78250	+	4.24943i	0.110973	+	0.264558i
$259$	3.53342	−	0.702840i	0.219556	−	0.0436724i
$260$	−9.09576	−	3.71214i	−0.564095	−	0.230217i
$261$	2.46420	+	12.1508i	0.152530	+	0.752116i
$262$	1.28063	+	1.27397i	0.0791173	+	0.0787058i
$263$	−15.6931	−	6.50028i	−0.967676	−	0.400825i	−0.157830	−	0.987466i	$-0.550450\pi$
$263$	−15.6931	−	6.50028i	−0.967676	−	0.400825i	−0.809847	+	0.586642i	$0.800450\pi$
$264$	26.3658	−	0.255513i	1.62271	−	0.0157258i
$265$	−15.2915	+	6.33393i	−0.939347	+	0.389090i
$266$	1.14951	−	2.79576i	0.0704809	−	0.171419i
$267$	−10.4661	+	25.4015i	−0.640514	+	1.55455i
$268$	5.37266	−	27.7661i	0.328187	−	1.69608i
$269$	9.94484	−	14.8835i	0.606348	−	0.907464i	−0.393582	−	0.919289i	$-0.628764\pi$
$269$	9.94484	−	14.8835i	0.606348	−	0.907464i	0.999930	+	0.0118258i	$0.00376437\pi$
$270$	4.72012	−	11.6655i	0.287258	−	0.709939i
$271$	20.7141	−	20.7141i	1.25829	−	1.25829i	0.306382	−	0.951909i	$-0.400882\pi$
$271$	20.7141	−	20.7141i	1.25829	−	1.25829i	0.951909	−	0.306382i	$-0.0991183\pi$
$272$	0.212743	+	20.3981i	0.0128994	+	1.23682i
$273$	2.20412	+	3.28540i	0.133400	+	0.198841i
$274$	−10.6331	−	7.06478i	−0.642369	−	0.426799i
$275$	6.18171	−	9.25159i	0.372771	−	0.557892i
$276$	0.185477	+	26.1840i	0.0111644	+	1.57609i
$277$	4.98281	−	25.0503i	0.299388	−	1.50513i	−0.479264	−	0.877671i	$-0.659096\pi$
$277$	4.98281	−	25.0503i	0.299388	−	1.50513i	0.778652	−	0.627456i	$-0.215904\pi$
$278$	2.84078	+	6.80799i	0.170379	+	0.408316i
$279$	20.8678	−	0.0779997i	1.24932	−	0.00466972i
$280$	1.50390	+	3.55189i	0.0898751	+	0.212266i
$281$	−28.1242	−	11.6494i	−1.67775	−	0.694947i	−0.678535	−	0.734568i	$-0.737385\pi$
$281$	−28.1242	−	11.6494i	−1.67775	−	0.694947i	−0.999215	+	0.0396211i	$0.987385\pi$
$282$	−16.7711	−	3.25801i	−0.998706	−	0.194012i
$283$	9.93766	−	6.64013i	0.590732	−	0.394715i	−0.223968	−	0.974596i	$-0.571901\pi$
$283$	9.93766	−	6.64013i	0.590732	−	0.394715i	0.814701	+	0.579882i	$0.196901\pi$
$284$	6.97597	−	7.04910i	0.413947	−	0.418287i
$285$	7.96159	−	0.0148793i	0.471604	−	0.000881377i
$286$	−21.4240	−	4.20347i	−1.26683	−	0.248556i
$287$		−	0.937850i		−	0.0553595i
$288$	16.6977	+	3.03114i	0.983920	+	0.178612i
$289$			9.00794i			0.529879i
$290$	1.92702	−	9.82153i	0.113158	−	0.576740i
$291$	0.258617		0.000483328i	0.0151604		2.83332e-5i
$292$	−0.00720927	−	1.38251i	−0.000421891	−	0.0809051i
$293$	7.07296	−	4.72600i	0.413207	−	0.276096i	−0.331542	−	0.943440i	$-0.607569\pi$
$293$	7.07296	−	4.72600i	0.413207	−	0.276096i	0.744749	+	0.667344i	$0.232569\pi$
$294$	−2.97358	+	15.3070i	−0.173423	+	0.892720i
$295$	3.96663	+	1.64303i	0.230946	+	0.0956610i
$296$	−8.97708	+	9.11863i	−0.521782	+	0.530010i
$297$	5.30213	−	27.4593i	0.307661	−	1.59335i
$298$	22.1582	−	9.24597i	1.28359	−	0.535604i
$299$	4.22985	−	21.2649i	0.244618	−	1.22978i
$300$	5.02795	−	5.09969i	0.290289	−	0.294431i
$301$	−0.832301	+	1.24563i	−0.0479730	+	0.0717967i
$302$	−5.04947	+	7.59989i	−0.290564	+	0.437325i
$303$	2.23603	+	3.33296i	0.128457	+	0.191474i
$304$	2.20433	+	10.5079i	0.126427	+	0.602672i
$305$	1.31214	−	1.31214i	0.0751330	−	0.0751330i
$306$	21.2472	+	4.08636i	1.21462	+	0.233602i
$307$	−6.07810	+	9.09652i	−0.346895	+	0.519166i	−0.963358	−	0.268218i	$-0.913565\pi$
$307$	−6.07810	+	9.09652i	−0.346895	+	0.519166i	0.616463	+	0.787384i	$0.288565\pi$
$308$	4.79941	+	7.10237i	0.273472	+	0.404695i
$309$	11.9090	−	28.9035i	0.677478	−	1.64426i
$310$	−15.5807	−	6.40619i	−0.884924	−	0.363847i
$311$	11.0707	−	4.58563i	0.627761	−	0.260027i	−0.0460403	−	0.998940i	$-0.514660\pi$
$311$	11.0707	−	4.58563i	0.627761	−	0.260027i	0.673802	+	0.738912i	$0.264660\pi$
$312$	−13.0338	−	5.25140i	−0.737896	−	0.297302i
$313$	20.1965	+	8.36565i	1.14157	+	0.472855i	0.871699	−	0.490041i	$-0.163018\pi$
$313$	20.1965	+	8.36565i	1.14157	+	0.472855i	0.269873	+	0.962896i	$0.413018\pi$
$314$	−13.3554	+	13.4252i	−0.753690	+	0.757630i
$315$	4.00951	−	0.813133i	0.225910	−	0.0458148i
$316$	−2.87479	−	6.83926i	−0.161720	−	0.384739i
$317$	0.376393	−	0.0748693i	0.0211404	−	0.00420508i	−0.184509	−	0.982831i	$-0.559069\pi$
$317$	0.376393	−	0.0748693i	0.0211404	−	0.00420508i	0.205649	+	0.978626i	$0.434069\pi$
$318$	−21.8315	+	9.15761i	−1.22425	+	0.513533i
$319$		−	22.2430i		−	1.24537i
$320$	−11.5088	−	7.43218i	−0.643361	−	0.415472i
$321$	16.2645	+	3.20362i	0.907796	+	0.178809i
$322$	−7.06564	+	4.74780i	−0.393753	+	0.264585i
$323$	2.67053	+	13.4257i	0.148593	+	0.747025i
$324$	6.67672	−	16.7159i	0.370929	−	0.928661i
$325$	−4.93051	+	3.29446i	−0.273495	+	0.182744i
$326$	20.8724	+	20.7639i	1.15602	+	1.15000i
$327$	9.94034	+	6.61508i	0.549702	+	0.365815i
$328$	1.87226	+	2.75514i	0.103378	+	0.152127i
$329$	−2.12551	−	5.13142i	−0.117183	−	0.282905i
$330$	−12.4588	+	18.8279i	−0.685837	+	1.03644i
$331$	1.37154	−	6.89518i	0.0753865	−	0.378994i	−0.924612	−	0.380911i	$-0.875610\pi$
$331$	1.37154	−	6.89518i	0.0753865	−	0.378994i	0.999998	+	0.00191754i	$0.000610372\pi$
$332$	3.39567	+	5.02506i	0.186362	+	0.275786i
$333$	7.58244	+	11.2566i	0.415515	+	0.616858i
$334$	3.26677	+	16.2023i	0.178750	+	0.886548i
$335$	17.1231	+	17.1231i	0.935534	+	0.935534i
$336$	2.17384	+	5.07081i	0.118592	+	0.276635i
$337$	17.3354	−	17.3354i	0.944318	−	0.944318i	−0.0542113	−	0.998529i	$-0.517264\pi$
$337$	17.3354	−	17.3354i	0.944318	−	0.944318i	0.998529	+	0.0542113i	$0.0172645\pi$
$338$	−5.62171	−	3.73514i	−0.305780	−	0.203165i
$339$	−19.0566	−	18.9856i	−1.03502	−	1.03115i
$340$	−14.5735	−	9.62817i	−0.790360	−	0.522161i
$341$	−36.7189	−	7.30384i	−1.98844	−	0.395525i
$342$	11.3877	−	0.0722569i	0.615778	−	0.00390721i
$343$	−9.83341	+	4.07313i	−0.530954	+	0.219929i
$344$	−0.0416200	−	5.32085i	−0.00224400	−	0.286881i
$345$	−18.6653	−	12.4214i	−1.00491	−	0.668744i
$346$	−17.3839	+	0.0453249i	−0.934562	+	0.00243668i
$347$	10.1675	+	15.2167i	0.545819	+	0.816875i	0.997147	−	0.0754825i	$-0.0240497\pi$
$347$	10.1675	+	15.2167i	0.545819	+	0.816875i	−0.451328	+	0.892358i	$0.649050\pi$
$348$	2.69342	−	14.0605i	0.144382	−	0.753723i
$349$	13.3260	−	2.65070i	0.713322	−	0.141889i	0.174927	−	0.984581i	$-0.444031\pi$
$349$	13.3260	−	2.65070i	0.713322	−	0.141889i	0.538395	+	0.842693i	$0.319031\pi$
$350$	2.28464	+	0.448254i	0.122119	+	0.0239602i
$351$	−8.21082	+	12.4388i	−0.438261	+	0.663933i
$352$	−28.2780	−	11.2835i	−1.50722	−	0.601415i
$353$	13.2033			0.702743			0.351372	−	0.936236i	$-0.385715\pi$
$353$	13.2033			0.702743			0.351372	+	0.936236i	$0.385715\pi$
$354$	5.68417	+	2.32471i	0.302110	+	0.123557i
$355$	1.65665	+	8.32857i	0.0879261	+	0.442034i
$356$	22.3145	−	22.5484i	1.18267	−	1.19506i
$357$	2.70396	+	6.49357i	0.143108	+	0.343676i
$358$	−11.0557	+	0.0288255i	−0.584312	+	0.00152348i
$359$	−9.51903	+	22.9810i	−0.502395	+	1.21289i	0.445780	+	0.895142i	$0.352926\pi$
$359$	−9.51903	+	22.9810i	−0.502395	+	1.21289i	−0.948176	+	0.317747i	$0.897074\pi$
$360$	−10.1555	+	10.3931i	−0.535244	+	0.547763i
$361$	−4.51385	−	10.8974i	−0.237571	−	0.573547i
$362$	17.0165	−	7.10051i	0.894369	−	0.373195i
$363$	−11.8557	+	28.7741i	−0.622262	+	1.51025i
$364$	−0.914582	−	4.47581i	−0.0479371	−	0.234596i
$365$	0.984283	+	0.657677i	0.0515197	+	0.0344244i
$366$	1.86842	−	1.88522i	0.0976636	−	0.0985419i
$367$	6.04728	+	6.04728i	0.315665	+	0.315665i	0.847100	−	0.531434i	$-0.178347\pi$
$367$	6.04728	+	6.04728i	0.315665	+	0.315665i	−0.531434	+	0.847100i	$0.678347\pi$
$368$	11.2787	−	28.0531i	0.587941	−	1.46237i
$369$	3.25913	−	1.36427i	0.169664	−	0.0710211i
$370$	−2.16553	−	10.7404i	−0.112581	−	0.558368i
$371$	−6.39943	−	4.27597i	−0.332242	−	0.221997i
$372$	−22.3268	−	9.06331i	−1.15759	−	0.469911i
$373$	26.8149	+	5.33382i	1.38842	+	0.276175i	0.832024	−	0.554739i	$-0.187182\pi$
$373$	26.8149	+	5.33382i	1.38842	+	0.276175i	0.556401	+	0.830914i	$0.312182\pi$
$374$	−35.9010	−	14.7612i	−1.85640	−	0.763281i
$375$	4.12804	+	20.5522i	0.213171	+	1.06131i
$376$	16.4882	+	10.8315i	0.850313	+	0.558590i
$377$	−4.53636	+	10.9517i	−0.233635	+	0.564044i
$378$	5.72978	−	1.18873i	0.294708	−	0.0611418i
$379$	5.46511	+	8.17912i	0.280724	+	0.420133i	0.944858	−	0.327481i	$-0.106200\pi$
$379$	5.46511	+	8.17912i	0.280724	+	0.420133i	−0.664134	+	0.747614i	$0.731200\pi$
$380$	−8.51170	−	3.47377i	−0.436641	−	0.178201i
$381$	−35.1207	+	0.0656367i	−1.79929	+	0.00336267i
$382$	−13.6257	+	9.15587i	−0.697150	+	0.468455i
$383$	−9.12965			−0.466503			−0.233252	−	0.972416i	$-0.574937\pi$
$383$	−9.12965			−0.466503			−0.233252	+	0.972416i	$0.574937\pi$
$384$	−16.5091	−	10.5569i	−0.842479	−	0.538730i
$385$	−7.33971			−0.374066
$386$	−27.8005	+	18.6807i	−1.41501	+	0.950825i
$387$	−5.53942	−	1.08035i	−0.281585	−	0.0549173i
$388$	−0.276487	−	0.112839i	−0.0140365	−	0.00572853i
$389$	−0.446040	−	0.667546i	−0.0226151	−	0.0338459i	0.819990	−	0.572378i	$-0.193979\pi$
$389$	−0.446040	−	0.667546i	−0.0226151	−	0.0338459i	−0.842605	+	0.538532i	$0.818979\pi$
$390$	9.97423	−	6.72934i	0.505065	−	0.340753i
$391$	14.7519	−	35.6143i	0.746038	−	1.80110i
$392$	9.88585	−	15.0487i	0.499311	−	0.760075i
$393$	−2.16903	+	0.435662i	−0.109413	+	0.0219763i
$394$	13.9882	+	5.75142i	0.704716	+	0.289753i
$395$	6.23036	+	1.23930i	0.313484	+	0.0623558i
$396$	−17.6999	+	27.0101i	−0.889454	+	1.35731i
$397$	−26.1544	−	17.4758i	−1.31265	−	0.877086i	−0.315242	−	0.949011i	$-0.602086\pi$
$397$	−26.1544	−	17.4758i	−1.31265	−	0.877086i	−0.997410	+	0.0719252i	$0.977086\pi$
$398$	0.0351493	+	0.174331i	0.00176187	+	0.00873840i
$399$	2.06259	+	3.07443i	0.103259	+	0.153914i
$400$	−7.60650	+	3.24406i	−0.380325	+	0.162203i
$401$	−12.4507	−	12.4507i	−0.621757	−	0.621757i	0.324223	−	0.945981i	$-0.394897\pi$
$401$	−12.4507	−	12.4507i	−0.621757	−	0.621757i	−0.945981	+	0.324223i	$0.894897\pi$
$402$	24.6016	+	24.3823i	1.22701	+	1.21608i
$403$	16.5897	+	11.0849i	0.826390	+	0.552176i
$404$	−0.927823	−	4.54061i	−0.0461609	−	0.225904i
$405$	8.65828	+	12.7507i	0.430233	+	0.633585i
$406$	4.29524	−	1.79228i	0.213169	−	0.0889494i
$407$	−9.31805	−	22.4958i	−0.461879	−	1.11507i
$408$	−20.9068	−	13.6783i	−1.03504	−	0.677177i
$409$	−6.02622	+	14.5486i	−0.297977	+	0.719381i	0.701997	+	0.712180i	$0.252292\pi$
$409$	−6.02622	+	14.5486i	−0.297977	+	0.719381i	−0.999974	+	0.00720056i	$0.997708\pi$
$410$	−2.85224	+	0.00743664i	−0.140862	+	0.000367269i
$411$	14.4339	−	6.01034i	0.711971	−	0.296468i
$412$	−25.3908	+	25.6570i	−1.25092	+	1.26403i
$413$	0.389497	+	1.95813i	0.0191659	+	0.0963534i
$414$	−26.7774	−	17.6473i	−1.31604	−	0.867320i
$415$	−5.19298			−0.254913
$416$	11.6220	+	11.3229i	0.569815	+	0.555149i
$417$	−8.86451	−	1.74604i	−0.434097	−	0.0855042i
$418$	−20.0484	−	3.93355i	−0.980597	−	0.192396i
$419$	20.4761	−	4.07294i	1.00032	−	0.198976i	0.332344	−	0.943158i	$-0.392160\pi$
$419$	20.4761	−	4.07294i	1.00032	−	0.198976i	0.667977	+	0.744182i	$0.267160\pi$
$420$	−4.63967	−	0.888771i	−0.226393	−	0.0433676i
$421$	4.56603	+	6.83355i	0.222535	+	0.333047i	0.925891	−	0.377791i	$-0.123316\pi$
$421$	4.56603	+	6.83355i	0.222535	+	0.333047i	−0.703356	+	0.710838i	$0.748316\pi$
$422$	−20.3963	+	0.0531794i	−0.992878	+	0.00258873i
$423$	14.7403	−	14.8509i	0.716700	−	0.722078i
$424$	27.3360	−	0.213823i	1.32755	−	0.0103842i
$425$	−9.74051	+	4.03465i	−0.472484	+	0.195709i
$426$	2.42291	+	11.9021i	0.117390	+	0.576660i
$427$	0.846314	+	0.168342i	0.0409560	+	0.00814665i
$428$	−15.9708	−	10.5513i	−0.771978	−	0.510016i
$429$	18.8721	−	18.9428i	0.911155	−	0.914567i
$430$	3.79486	+	2.52136i	0.183004	+	0.121591i
$431$	22.1459	−	22.1459i	1.06673	−	1.06673i	0.0691236	−	0.997608i	$-0.477980\pi$
$431$	22.1459	−	22.1459i	1.06673	−	1.06673i	0.997608	−	0.0691236i	$-0.0220203\pi$
$432$	−14.4594	+	14.9307i	−0.695677	+	0.718354i
$433$	−7.75001	−	7.75001i	−0.372442	−	0.372442i	0.495924	−	0.868366i	$-0.334829\pi$
$433$	−7.75001	−	7.75001i	−0.372442	−	0.372442i	−0.868366	+	0.495924i	$0.834829\pi$
$434$	−1.54830	−	7.67915i	−0.0743209	−	0.368611i
$435$	8.68405	+	8.65165i	0.416368	+	0.414815i
$436$	−7.71955	−	11.4237i	−0.369700	−	0.547097i
$437$	3.95824	−	19.8994i	0.189348	−	0.951918i
$438$	1.41207	+	0.934403i	0.0674715	+	0.0446475i
$439$	−1.60466	−	3.87398i	−0.0765861	−	0.184895i	0.880950	−	0.473210i	$-0.156905\pi$
$439$	−1.60466	−	3.87398i	−0.0765861	−	0.184895i	−0.957536	+	0.288315i	$0.906905\pi$
$440$	21.5620	−	14.6525i	1.02793	−	0.698531i
$441$	−13.5544	−	13.4535i	−0.645448	−	0.640641i
$442$	14.6661	+	14.5898i	0.697595	+	0.693967i
$443$	−13.5119	+	9.02838i	−0.641971	+	0.428951i	−0.833488	−	0.552538i	$-0.813659\pi$
$443$	−13.5119	+	9.02838i	−0.641971	+	0.428951i	0.191517	+	0.981489i	$0.438659\pi$
$444$	−3.16622	−	15.3487i	−0.150262	−	0.728415i
$445$	5.29925	+	26.6411i	0.251209	+	1.26291i
$446$	18.1466	−	12.1937i	0.859265	−	0.577388i
$447$	−5.68290	+	28.8516i	−0.268792	+	1.36463i
$448$	−0.0996565	−	6.36984i	−0.00470833	−	0.300947i
$449$		−	4.44342i		−	0.209698i	−0.994488	−	0.104849i	$-0.966564\pi$
$449$		−	4.44342i		−	0.209698i	0.994488	−	0.104849i	$-0.0334359\pi$
$450$	1.76569	+	8.59145i	0.0832353	+	0.405005i
$451$	−6.21687	+	1.23661i	−0.292741	+	0.0582298i
$452$	12.0362	+	28.6346i	0.566133	+	1.34686i
$453$	−4.29582	−	10.3165i	−0.201835	−	0.484709i
$454$	8.51772	−	8.56225i	0.399756	−	0.401846i
$455$	3.61385	+	1.49690i	0.169420	+	0.0701760i
$456$	−12.1969	−	4.91420i	−0.571173	−	0.230128i
$457$	3.26785	−	1.35359i	0.152864	−	0.0633182i	−0.304940	−	0.952372i	$-0.598636\pi$
$457$	3.26785	−	1.35359i	0.152864	−	0.0633182i	0.457803	+	0.889053i	$0.348636\pi$
$458$	2.73795	+	1.12574i	0.127936	+	0.0526025i
$459$	−18.6325	+	18.8426i	−0.869691	+	0.879498i
$460$	14.4953	+	21.4507i	0.675845	+	1.00014i
$461$	−0.445238	+	0.666345i	−0.0207368	+	0.0310348i	−0.841693	−	0.539956i	$-0.818441\pi$
$461$	−0.445238	+	0.666345i	−0.0207368	+	0.0310348i	0.820956	+	0.570991i	$0.193441\pi$
$462$	−10.4983	+	0.0469927i	−0.488426	+	0.00218630i
$463$	13.5750	−	13.5750i	0.630885	−	0.630885i	−0.317405	−	0.948290i	$-0.602811\pi$
$463$	13.5750	−	13.5750i	0.630885	−	0.630885i	0.948290	+	0.317405i	$0.102811\pi$
$464$	−9.04022	+	13.8400i	−0.419682	+	0.642504i
$465$	17.1338	−	11.4948i	0.794559	−	0.533058i
$466$	7.91838	−	11.9178i	0.366812	−	0.552084i
$467$	−22.5240	+	33.7096i	−1.04229	+	1.55989i	−0.233003	+	0.972476i	$0.574855\pi$
$467$	−22.5240	+	33.7096i	−1.04229	+	1.55989i	−0.809284	+	0.587417i	$0.800145\pi$
$468$	14.2235	−	9.68914i	0.657482	−	0.447881i
$469$	−2.19682	+	11.0442i	−0.101440	+	0.509972i
$470$	−15.5891	+	6.50488i	−0.719071	+	0.300048i
$471$	−4.56720	−	22.7387i	−0.210445	−	1.04774i
$472$	−5.05332	−	4.97488i	−0.232598	−	0.228987i
$473$	9.35452	+	3.87477i	0.430121	+	0.178162i
$474$	8.91951	+	1.73273i	0.409686	+	0.0795870i
$475$	−4.61391	+	3.08292i	−0.211701	+	0.141454i
$476$	−0.0423539	−	8.12211i	−0.00194129	−	0.372276i
$477$	5.55033	−	28.4589i	0.254132	−	1.30304i
$478$	−3.12664	+	15.9357i	−0.143009	+	0.728882i
$479$			0.596301i			0.0272457i	0.999907	+	0.0136228i	$0.00433642\pi$
$479$			0.596301i			0.0272457i	−0.999907	+	0.0136228i	$0.995664\pi$
$480$	15.4043	−	6.65138i	0.703109	−	0.303593i
$481$			12.9766i			0.591682i
$482$	−40.5361	−	7.95331i	−1.84637	−	0.362263i
$483$	−0.0194847	−	10.4258i	−0.000886582	−	0.474389i
$484$	25.2772	−	25.5422i	1.14896	−	1.16101i
$485$	0.212605	−	0.142058i	0.00965392	−	0.00645054i
$486$	12.4660	+	18.1824i	0.565468	+	0.824770i
$487$	−14.1819	−	5.87434i	−0.642644	−	0.266192i	0.0374708	−	0.999298i	$-0.488070\pi$
$487$	−14.1819	−	5.87434i	−0.642644	−	0.266192i	−0.680114	+	0.733106i	$0.738070\pi$
$488$	−2.82230	+	1.19498i	−0.127760	+	0.0540943i
$489$	−35.3521	+	7.10069i	−1.59868	+	0.321104i
$490$	5.93698	+	14.2281i	0.268206	+	0.642760i
$491$	0.00640918	−	0.0322211i	0.000289242	−	0.00145412i	−0.980640	−	0.195817i	$-0.937264\pi$
$491$	0.00640918	−	0.0322211i	0.000289242	−	0.00145412i	0.980930	+	0.194363i	$0.0622640\pi$
$492$	−4.07963	+	0.0288985i	−0.183924	+	0.00130284i
$493$	−11.7092	+	17.5241i	−0.527357	+	0.789245i
$494$	9.06896	+	6.02554i	0.408032	+	0.271102i
$495$	−10.6769	−	25.5063i	−0.479892	−	1.14642i
$496$	19.8786	+	19.4683i	0.892577	+	0.874150i
$497$	−2.79218	+	2.79218i	−0.125246	+	0.125246i
$498$	−7.42776	+	0.0332482i	−0.332846	+	0.00148989i
$499$	5.40096	−	8.08311i	0.241780	−	0.361850i	−0.690656	−	0.723183i	$-0.742678\pi$
$499$	5.40096	−	8.08311i	0.241780	−	0.361850i	0.932437	+	0.361333i	$0.117678\pi$
$500$	4.59843	−	23.7648i	0.205648	−	1.06280i
$501$	−18.7165	−	7.71168i	−0.836192	−	0.344532i
$502$	4.11443	−	10.0068i	0.183636	−	0.446627i
$503$	8.11650	−	3.36197i	0.361897	−	0.149903i	−0.194323	−	0.980938i	$-0.562251\pi$
$503$	8.11650	−	3.36197i	0.361897	−	0.149903i	0.556220	+	0.831035i	$0.312251\pi$
$504$	−6.64203	−	1.24154i	−0.295859	−	0.0553027i
$505$	3.66617	+	1.51858i	0.163142	+	0.0675758i
$506$	40.7890	+	40.5768i	1.81329	+	1.80386i
$507$	7.63117	−	3.17766i	0.338912	−	0.141125i
$508$	37.5473	+	15.3237i	1.66589	+	0.679880i
$509$	26.0046	−	5.17263i	1.15263	−	0.229273i	0.418460	−	0.908235i	$-0.362570\pi$
$509$	26.0046	−	5.17263i	1.15263	−	0.229273i	0.734173	+	0.678962i	$0.237570\pi$
$510$	19.7271	−	8.27489i	0.873532	−	0.366418i
$511$			0.550472i			0.0243514i
$512$	13.0091	+	18.5139i	0.574926	+	0.818205i
$513$	−7.68359	+	11.6401i	−0.339239	+	0.513921i
$514$	1.90282	+	2.83176i	0.0839297	+	0.124903i
$515$	−6.02983	−	30.3140i	−0.265706	−	1.33579i
$516$	5.44410	+	3.58212i	0.239663	+	0.157694i
$517$	−31.2129	+	20.8558i	−1.37274	+	0.917235i
$518$	3.59323	−	3.61202i	0.157878	−	0.158703i
$519$	11.7955	−	17.7248i	0.517763	−	0.778031i
$520$	−13.6048	+	2.81696i	−0.596610	+	0.123532i
$521$	1.81662	+	4.38572i	0.0795877	+	0.192142i	0.958665	−	0.284538i	$-0.0918402\pi$
$521$	1.81662	+	4.38572i	0.0795877	+	0.192142i	−0.879077	+	0.476680i	$0.841840\pi$
$522$	12.4766	+	12.3192i	0.546085	+	0.539199i
$523$	−4.42990	+	22.2706i	−0.193706	+	0.973826i	0.754531	+	0.656264i	$0.227864\pi$
$523$	−4.42990	+	22.2706i	−0.193706	+	0.973826i	−0.948237	+	0.317562i	$0.897136\pi$
$524$	2.50808	+	0.485306i	0.109566	+	0.0212007i
$525$	−2.01251	+	2.02004i	−0.0878331	+	0.0881620i
$526$	−23.5480	+	4.74786i	−1.02674	+	0.207016i
$527$	25.0840	+	25.0840i	1.09268	+	1.09268i
$528$	30.7473	−	21.0962i	1.33810	−	0.918094i
$529$	−24.1381	+	24.1381i	−1.04948	+	1.04948i
$530$	−12.9535	+	19.4962i	−0.562665	+	0.846860i
$531$	−6.23813	+	4.20200i	−0.270712	+	0.182351i
$532$	−0.855855	−	4.18841i	−0.0371060	−	0.181590i
$533$	3.31320	+	0.659036i	0.143511	+	0.0285460i
$534$	7.75033	+	38.0721i	0.335390	+	1.64754i
$535$	15.1423	−	6.27214i	0.654658	−	0.271168i
$536$	−15.5942	−	36.8302i	−0.673567	−	1.59082i
$537$	7.50162	−	11.2725i	0.323719	−	0.486445i
$538$	−0.0660030	−	25.3147i	−0.00284559	−	1.09139i
$539$	19.0350	+	28.4879i	0.819895	+	1.22706i
$540$	−3.66066	−	17.4163i	−0.157530	−	0.749476i
$541$	−1.34295	+	0.267129i	−0.0577379	+	0.0114848i	−0.223875	−	0.974618i	$-0.571871\pi$
$541$	−1.34295	+	0.267129i	−0.0577379	+	0.0114848i	0.166137	+	0.986103i	$0.446871\pi$
$542$	7.97626	−	40.6531i	0.342610	−	1.74620i
$543$	−4.36423	+	22.1568i	−0.187287	+	0.950838i
$544$	16.3389	+	23.7759i	0.700524	+	1.01938i
$545$	11.8055			0.505691
$546$	5.17863	+	2.11795i	0.221625	+	0.0906400i
$547$	−5.22689	−	26.2774i	−0.223486	−	1.12354i	−0.915705	−	0.401851i	$-0.868367\pi$
$547$	−5.22689	−	26.2774i	−0.223486	−	1.12354i	0.692219	−	0.721687i	$-0.256633\pi$
$548$	−18.0538	+	0.0941439i	−0.771220	+	0.00402163i
$549$	0.646107	+	3.18592i	0.0275752	+	0.135972i
$550$	−0.0410274	−	15.7356i	−0.00174942	−	0.670968i
$551$	−4.24507	+	10.2485i	−0.180846	+	0.436601i
$552$	20.8706	+	30.5891i	0.888311	+	1.30196i
$553$	1.13042	+	2.72908i	0.0480704	+	0.116052i
$554$	−13.9097	−	33.3349i	−0.590966	−	1.41626i
$555$	12.4071	+	5.11205i	0.526652	+	0.216994i
$556$	8.70443	+	5.75069i	0.369150	+	0.243883i
$557$	−6.81107	−	4.55101i	−0.288594	−	0.192833i	0.402843	−	0.915269i	$-0.368022\pi$
$557$	−6.81107	−	4.55101i	−0.288594	−	0.192833i	−0.691437	+	0.722437i	$0.743022\pi$
$558$	24.4336	−	16.5512i	1.03436	−	0.700669i
$559$	−3.81563	−	3.81563i	−0.161384	−	0.161384i
$560$	4.56690	+	2.98308i	0.192987	+	0.126058i
$561$	39.4796	−	26.4863i	1.66683	−	1.11825i
$562$	−42.2014	+	8.50883i	−1.78016	+	0.358923i
$563$	−1.37594	−	0.919371i	−0.0579888	−	0.0387469i	0.526238	−	0.850337i	$-0.323602\pi$
$563$	−1.37594	−	0.919371i	−0.0579888	−	0.0387469i	−0.584227	+	0.811590i	$0.698602\pi$
$564$	−22.2561	+	9.40403i	−0.937152	+	0.395981i
$565$	−26.0853	−	5.18868i	−1.09741	−	0.218289i
$566$	6.42759	−	15.6327i	0.270172	−	0.657093i
$567$	−2.69310	+	6.64172i	−0.113100	+	0.278926i
$568$	2.62851	−	13.7767i	0.110290	−	0.578060i
$569$	−8.37450	+	20.2178i	−0.351077	+	0.847575i	0.645410	+	0.763836i	$0.276686\pi$
$569$	−8.37450	+	20.2178i	−0.351077	+	0.847575i	−0.996488	+	0.0837394i	$0.973314\pi$
$570$	9.33376	−	6.29723i	0.390948	−	0.263762i
$571$	−12.6472	−	18.9278i	−0.529267	−	0.792104i	0.466451	−	0.884547i	$-0.345532\pi$
$571$	−12.6472	−	18.9278i	−0.529267	−	0.792104i	−0.995718	+	0.0924431i	$0.970532\pi$
$572$	−28.4635	+	11.9643i	−1.19012	+	0.500251i
$573$	−0.0375751	−	20.1055i	−0.00156972	−	0.839920i
$574$	−0.739737	−	1.10087i	−0.0308760	−	0.0459494i
$575$	15.6268			0.651683
$576$	21.9909	−	9.61240i	0.916289	−	0.400517i
$577$	3.02364			0.125876			0.0629378	−	0.998017i	$-0.479953\pi$
$577$	3.02364			0.125876			0.0629378	+	0.998017i	$0.479953\pi$
$578$	7.10509	+	10.5737i	0.295533	+	0.439809i
$579$	−0.0766645	−	41.0214i	−0.00318607	−	1.70479i
$580$	−5.48483	−	13.0487i	−0.227745	−	0.541817i
$581$	−1.34158	−	2.00782i	−0.0556582	−	0.0832984i
$582$	0.303190	−	0.204554i	0.0125676	−	0.00847903i
$583$	−19.9067	+	48.0590i	−0.824452	+	1.99040i
$584$	−1.09893	−	1.61713i	−0.0454739	−	0.0669174i
$585$	0.0550803	+	14.7360i	0.00227729	+	0.609260i
$586$	4.57473	−	11.1263i	0.188981	−	0.459625i
$587$	−20.2802	−	4.03398i	−0.837054	−	0.166500i	−0.242091	−	0.970254i	$-0.577833\pi$
$587$	−20.2802	−	4.03398i	−0.837054	−	0.166500i	−0.594963	+	0.803753i	$0.702833\pi$
$588$	8.58303	+	20.3131i	0.353958	+	0.837698i
$589$	15.5244	+	10.3731i	0.639672	+	0.427415i
$590$	5.95208	−	1.20008i	0.245043	−	0.0494066i
$591$	−15.3825	+	10.3199i	−0.632753	+	0.424505i
$592$	−3.34511	+	17.7844i	−0.137483	+	0.730934i
$593$	25.5322	+	25.5322i	1.04848	+	1.04848i	0.998763	+	0.0497164i	$0.0158318\pi$
$593$	25.5322	+	25.5322i	1.04848	+	1.04848i	0.0497164	+	0.998763i	$0.484168\pi$
$594$	−15.4350	−	36.4145i	−0.633305	−	1.49410i
$595$	5.78258	+	3.86380i	0.237063	+	0.158400i
$596$	18.7169	−	28.3306i	0.766675	−	1.16046i
$597$	−0.201383	−	0.0829749i	−0.00824205	−	0.00339594i
$598$	−11.8077	−	28.2975i	−0.482855	−	1.15717i
$599$	−2.81924	−	6.80624i	−0.115191	−	0.278095i	0.855761	−	0.517372i	$-0.173090\pi$
$599$	−2.81924	−	6.80624i	−0.115191	−	0.278095i	−0.970951	+	0.239277i	$0.923090\pi$
$600$	1.87950	−	9.95197i	0.0767303	−	0.406287i
$601$	−2.76305	+	6.67058i	−0.112707	+	0.272099i	−0.970161	−	0.242462i	$-0.922045\pi$
$601$	−2.76305	+	6.67058i	−0.112707	+	0.272099i	0.857454	+	0.514561i	$0.172045\pi$
$602$	0.00552391	+	2.11863i	0.000225138	+	0.0863489i
$603$	−41.5753	+	8.43152i	−1.69308	+	0.343358i
$604$	0.0672883	+	12.9037i	0.00273792	+	0.525046i
$605$	6.00284	+	30.1783i	0.244050	+	1.22692i
$606$	5.25361	+	2.14862i	0.213413	+	0.0872815i
$607$	−12.5060			−0.507603			−0.253802	−	0.967256i	$-0.581681\pi$
$607$	−12.5060			−0.507603			−0.253802	+	0.967256i	$0.581681\pi$
$608$	10.8757	+	10.5958i	0.441069	+	0.429716i
$609$	−1.10160	+	5.59272i	−0.0446391	+	0.226628i
$610$	0.505260	−	2.57519i	0.0204574	−	0.104266i
$611$	19.6217	−	3.90300i	0.793809	−	0.157898i
$612$	28.1636	−	11.9623i	1.13845	−	0.483546i
$613$	−21.1070	−	31.5888i	−0.852503	−	1.27586i	−0.959530	−	0.281605i	$-0.909133\pi$
$613$	−21.1070	−	31.5888i	−0.852503	−	1.27586i	0.107027	−	0.994256i	$-0.465867\pi$
$614$	0.0403398	+	15.4719i	0.00162798	+	0.624393i
$615$	1.93533	−	2.90817i	0.0780399	−	0.117269i
$616$	11.2357	+	4.55135i	0.452699	+	0.183379i
$617$	−1.55951	+	0.645969i	−0.0627834	+	0.0260057i	−0.413854	−	0.910343i	$-0.635818\pi$
$617$	−1.55951	+	0.645969i	−0.0627834	+	0.0260057i	0.351071	+	0.936349i	$0.385818\pi$
$618$	−8.81882	−	43.3209i	−0.354745	−	1.74262i
$619$	−12.4267	−	2.47182i	−0.499469	−	0.0993507i	−0.0610747	−	0.998133i	$-0.519453\pi$
$619$	−12.4267	−	2.47182i	−0.499469	−	0.0993507i	−0.438395	+	0.898783i	$0.644453\pi$
$620$	−23.3419	+	4.76966i	−0.937434	+	0.191554i
$621$	36.2024	−	15.2339i	1.45275	−	0.611315i
$622$	9.37808	−	14.1148i	0.376027	−	0.565952i
$623$	−8.93152	+	8.93152i	−0.357834	+	0.357834i
$624$	−19.4415	+	4.11633i	−0.778283	+	0.164785i
$625$	7.34638	+	7.34638i	0.293855	+	0.293855i
$626$	30.3056	−	6.11034i	1.21125	−	0.244218i
$627$	17.6603	−	17.7265i	0.705285	−	0.707926i
$628$	−5.08763	+	26.2930i	−0.203018	+	1.04921i
$629$	−4.50109	+	22.6285i	−0.179470	+	0.902258i
$630$	4.06509	−	4.11701i	0.161957	−	0.164026i
$631$	−0.496224	−	1.19799i	−0.0197544	−	0.0476912i	0.913695	−	0.406402i	$-0.133217\pi$
$631$	−0.496224	−	1.19799i	−0.0197544	−	0.0476912i	−0.933449	+	0.358710i	$0.883217\pi$
$632$	−8.76902	−	5.76057i	−0.348813	−	0.229143i
$633$	13.8395	−	20.7963i	0.550072	−	0.826580i
$634$	0.382765	−	0.384767i	0.0152016	−	0.0152810i
$635$	−28.8722	+	19.2918i	−1.14576	+	0.765570i
$636$	−18.4032	+	27.9692i	−0.729734	+	1.10905i
$637$	−3.56226	−	17.9087i	−0.141142	−	0.709567i
$638$	−17.5443	−	26.1093i	−0.694586	−	1.03368i
$639$	−13.7648	−	5.64140i	−0.544529	−	0.223170i
$640$	−19.3715	+	0.353590i	−0.765725	+	0.0139769i
$641$			36.7026i			1.44967i	0.688925	+	0.724833i	$0.258083\pi$
$641$			36.7026i			1.44967i	−0.688925	+	0.724833i	$0.741917\pi$
$642$	21.6185	−	9.06827i	0.853216	−	0.357896i
$643$	24.2814	−	4.82988i	0.957566	−	0.190472i	0.308518	−	0.951219i	$-0.400167\pi$
$643$	24.2814	−	4.82988i	0.957566	−	0.190472i	0.649049	+	0.760747i	$0.275167\pi$
$644$	−4.54894	+	11.1462i	−0.179253	+	0.439220i
$645$	−5.15132	+	2.14504i	−0.202833	+	0.0844607i
$646$	13.7244	+	13.6530i	0.539978	+	0.537169i
$647$	−30.2121	−	12.5143i	−1.18776	−	0.491987i	−0.300736	−	0.953707i	$-0.597232\pi$
$647$	−30.2121	−	12.5143i	−1.18776	−	0.491987i	−0.887026	+	0.461720i	$0.847232\pi$
$648$	−5.34752	−	24.8878i	−0.210070	−	0.977686i
$649$	12.4666	−	5.16383i	0.489357	−	0.202698i
$650$	−3.18901	+	7.75609i	−0.125083	+	0.304219i
$651$	8.87079	+	3.65499i	0.347674	+	0.143250i
$652$	40.8782	+	7.90981i	1.60091	+	0.309772i
$653$	−20.6065	+	30.8399i	−0.806396	+	1.20686i	0.168830	+	0.985645i	$0.446001\pi$
$653$	−20.6065	+	30.8399i	−0.806396	+	1.20686i	−0.975226	+	0.221212i	$0.928999\pi$
$654$	16.8859	−	0.0755849i	0.660291	−	0.00295560i
$655$	−1.54671	+	1.54671i	−0.0604349	+	0.0604349i
$656$	4.37084	+	1.75729i	0.170653	+	0.0686105i
$657$	−1.91295	+	0.800760i	−0.0746313	+	0.0312406i
$658$	−6.54242	−	4.34687i	−0.255050	−	0.169459i
$659$	9.69701	−	14.5126i	0.377742	−	0.565330i	−0.593077	−	0.805146i	$-0.702087\pi$
$659$	9.69701	−	14.5126i	0.377742	−	0.565330i	0.970818	+	0.239815i	$0.0770869\pi$
$660$	0.226162	+	31.9276i	0.00880336	+	1.24278i
$661$	−6.05894	+	30.4603i	−0.235665	+	1.18477i	0.663845	+	0.747870i	$0.268924\pi$
$661$	−6.05894	+	30.4603i	−0.235665	+	1.18477i	−0.899510	+	0.436900i	$0.856076\pi$
$662$	−3.82869	−	9.17554i	−0.148806	−	0.356617i
$663$	−24.8403	+	4.98933i	−0.964719	+	0.193769i
$664$	7.94947	+	3.22016i	0.308499	+	0.124967i
$665$	3.38179	+	1.40079i	0.131140	+	0.0543201i
$666$	17.7792	+	7.23256i	0.688929	+	0.280256i
$667$	25.9740	−	17.3553i	1.00572	−	0.671999i
$668$	16.6143	+	16.4419i	0.642826	+	0.636156i
$669$	0.0500421	+	26.7764i	0.00193474	+	1.03523i
$670$	33.6055	+	6.59350i	1.29829	+	0.254729i
$671$		−	5.83206i		−	0.225144i
$672$	6.55134	+	4.23760i	0.252723	+	0.163469i
$673$		−	1.42269i		−	0.0548405i	−0.999624	−	0.0274203i	$-0.991271\pi$
$673$		−	1.42269i		−	0.0548405i	0.999624	−	0.0274203i	$-0.00872923\pi$
$674$	6.67525	−	34.0221i	0.257121	−	1.31048i
$675$	−9.94744	−	4.05517i	−0.382877	−	0.156084i
$676$	−9.54501	+	0.0497738i	−0.367116	+	0.00191438i
$677$	30.5664	−	20.4238i	1.17476	−	0.784951i	0.194161	−	0.980970i	$-0.437801\pi$
$677$	30.5664	−	20.4238i	1.17476	−	0.784951i	0.980600	+	0.196019i	$0.0628014\pi$
$678$	−37.3441	−	7.25459i	−1.43419	−	0.278611i
$679$	0.109851	+	0.0455019i	0.00421570	+	0.00174620i
$680$	−24.7010	+	0.193213i	−0.947241	+	0.00740936i
$681$	2.91283	+	14.5021i	0.111620	+	0.555722i
$682$	−48.8624	+	20.3889i	−1.87104	+	0.780731i
$683$	0.0811176	−	0.407806i	0.00310388	−	0.0156043i	−0.979202	−	0.202886i	$-0.934968\pi$
$683$	0.0811176	−	0.407806i	0.00310388	−	0.0156043i	0.982306	+	0.187282i	$0.0599678\pi$
$684$	13.3102	−	9.06698i	0.508928	−	0.346685i
$685$	8.58843	−	12.8535i	0.328147	−	0.491106i
$686$	−8.32997	+	12.5373i	−0.318040	+	0.478677i
$687$	−3.01087	+	2.01995i	−0.114872	+	0.0770659i
$688$	−4.24572	−	6.21291i	−0.161867	−	0.236865i
$689$	19.6029	−	19.6029i	0.746811	−	0.746811i
$690$	−31.7072	+	0.141928i	−1.20707	+	0.00540312i
$691$	−6.46900	+	9.68155i	−0.246093	+	0.368303i	−0.933867	−	0.357621i	$-0.883588\pi$
$691$	−6.46900	+	9.68155i	−0.246093	+	0.368303i	0.687774	+	0.725925i	$0.258588\pi$
$692$	−20.3698	+	13.7649i	−0.774344	+	0.523262i
$693$	7.10345	−	10.7176i	0.269838	−	0.407127i
$694$	23.9371	+	9.84204i	0.908640	+	0.373599i
$695$	−8.25287	+	3.41845i	−0.313049	+	0.129669i
$696$	−7.92875	−	18.6290i	−0.300538	−	0.706131i
$697$	5.54894	+	2.29844i	0.210181	+	0.0870598i
$698$	13.5516	−	13.6224i	0.512934	−	0.515616i
$699$	6.73654	+	16.1779i	0.254799	+	0.611903i
$700$	3.03533	−	1.27586i	0.114725	−	0.0482229i
$701$	−37.1691	+	7.39339i	−1.40386	+	0.279244i	−0.838185	−	0.545386i	$-0.816383\pi$
$701$	−37.1691	+	7.39339i	−1.40386	+	0.279244i	−0.565672	+	0.824631i	$0.691383\pi$
$702$	0.173132	+	21.0773i	0.00653444	+	0.795510i
$703$			12.1434i			0.457995i
$704$	−42.0934	+	9.05964i	−1.58645	+	0.341448i
$705$	3.99813	−	20.2981i	0.150578	−	0.764472i
$706$	15.4984	−	10.4142i	0.583290	−	0.391945i
$707$	0.359993	+	1.80981i	0.0135389	+	0.0680648i
$708$	8.50584	−	1.75464i	0.319669	−	0.0659435i
$709$	38.1803	−	25.5113i	1.43389	−	0.958096i	0.435573	−	0.900154i	$-0.356546\pi$
$709$	38.1803	−	25.5113i	1.43389	−	0.958096i	0.998320	−	0.0579428i	$-0.0184541\pi$
$710$	8.51384	+	8.46956i	0.319519	+	0.317857i
$711$	−7.83946	+	7.89828i	−0.294003	+	0.296209i
$712$	8.40800	−	44.0686i	0.315103	−	1.65154i
$713$	−20.1213	−	48.5770i	−0.753547	−	1.81922i
$714$	8.29582	+	5.48954i	0.310463	+	0.205441i
$715$	5.15768	−	25.9294i	0.192886	−	0.969706i
$716$	−12.9547	+	8.75411i	−0.484140	+	0.327156i
$717$	−14.0901	−	14.0375i	−0.526205	−	0.524242i
$718$	6.95277	+	34.4838i	0.259475	+	1.28692i
$719$	15.3249	+	15.3249i	0.571523	+	0.571523i	0.932554	−	0.361031i	$-0.117575\pi$
$719$	15.3249	+	15.3249i	0.571523	+	0.571523i	−0.361031	+	0.932554i	$0.617575\pi$
$720$	−3.72317	+	20.2099i	−0.138755	+	0.753178i
$721$	10.1629	−	10.1629i	0.378484	−	0.378484i
$722$	−13.8939	−	9.23127i	−0.517076	−	0.343552i
$723$	35.7076	−	35.8414i	1.32798	−	1.33295i
$724$	14.3738	−	21.7567i	0.534198	−	0.808580i
$725$	−8.37960	−	1.66681i	−0.311210	−	0.0619036i
$726$	8.77935	+	43.1270i	0.325832	+	1.60059i
$727$	−5.58340	+	2.31272i	−0.207077	+	0.0857740i	−0.483811	−	0.875172i	$-0.660748\pi$
$727$	−5.58340	+	2.31272i	−0.207077	+	0.0857740i	0.276734	+	0.960946i	$0.410748\pi$
$728$	−4.60389	−	4.53242i	−0.170631	−	0.167983i
$729$	−26.9983	+	0.302754i	−0.999937	+	0.0112131i
$730$	1.67412	−	0.00436494i	0.0619620	−	0.000161554i
$731$	−5.33018	−	7.97717i	−0.197144	−	0.295046i
$732$	0.706208	−	3.68664i	0.0261022	−	0.136262i
$733$	−16.4103	+	3.26422i	−0.606130	+	0.120567i	−0.488608	−	0.872504i	$-0.662495\pi$
$733$	−16.4103	+	3.26422i	−0.606130	+	0.120567i	−0.117522	+	0.993070i	$0.537495\pi$
$734$	11.8683	+	2.32860i	0.438066	+	0.0859500i
$735$	−18.5260	−	3.64908i	−0.683344	−	0.134598i
$736$	−8.88794	−	41.8255i	−0.327614	−	1.54171i
$737$	76.1068			2.80343
$738$	2.74957	−	4.17208i	0.101213	−	0.153576i
$739$	4.06626	+	20.4425i	0.149580	+	0.751988i	0.980642	+	0.195809i	$0.0627332\pi$
$739$	4.06626	+	20.4425i	0.149580	+	0.751988i	−0.831062	+	0.556179i	$0.812267\pi$
$740$	−11.0135	−	10.8993i	−0.404866	−	0.400665i
$741$	−12.3106	+	5.12621i	−0.452243	+	0.188316i
$742$	−10.8845	+	0.0283792i	−0.399583	+	0.00104183i
$743$	11.3675	−	27.4437i	0.417035	−	1.00681i	−0.566167	−	0.824290i	$-0.691574\pi$
$743$	11.3675	−	27.4437i	0.417035	−	1.00681i	0.983202	−	0.182521i	$-0.0584257\pi$
$744$	−33.3565	+	6.97171i	−1.22291	+	0.255595i
$745$	11.1261	+	26.8608i	0.407630	+	0.984105i
$746$	35.6831	−	14.8895i	1.30645	−	0.545145i
$747$	5.02582	−	7.58288i	0.183885	−	0.277443i
$748$	−53.7845	+	10.9903i	−1.96655	+	0.401844i
$749$	6.33700	+	4.23425i	0.231549	+	0.154716i
$750$	21.0563	+	20.8687i	0.768868	+	0.762016i
$751$	9.88591	+	9.88591i	0.360742	+	0.360742i	0.864086	−	0.503344i	$-0.167897\pi$
$751$	9.88591	+	9.88591i	0.360742	+	0.360742i	−0.503344	+	0.864086i	$0.667897\pi$
$752$	27.8976	−	0.290960i	1.01732	−	0.0106102i
$753$	7.38262	+	11.0043i	0.269038	+	0.401019i
$754$	3.31339	+	16.4335i	0.120667	+	0.598473i
$755$	−9.18688	−	6.13848i	−0.334345	−	0.223402i
$756$	5.78813	−	5.91477i	0.210512	−	0.215118i
$757$	−2.43551	−	0.484453i	−0.0885202	−	0.0176078i	0.150631	−	0.988590i	$-0.451869\pi$
$757$	−2.43551	−	0.484453i	−0.0885202	−	0.0176078i	−0.239152	+	0.970982i	$0.576869\pi$
$758$	12.8664	+	5.29019i	0.467329	+	0.192148i
$759$	−69.0853	+	13.8762i	−2.50764	+	0.503674i
$760$	−12.7312	+	2.63608i	−0.461809	+	0.0956206i
$761$	−14.2896	+	34.4982i	−0.517999	+	1.25056i	0.421132	+	0.906999i	$0.361633\pi$
$761$	−14.2896	+	34.4982i	−0.517999	+	1.25056i	−0.939131	+	0.343560i	$0.888367\pi$
$762$	−41.1737	+	27.7787i	−1.49156	+	1.00632i
$763$	3.04989	+	4.56448i	0.110413	+	0.165245i
$764$	−8.77237	+	21.4947i	−0.317373	+	0.777652i
$765$	−5.01532	+	25.7157i	−0.181329	+	0.929753i
$766$	−10.7166	+	7.20108i	−0.387206	+	0.260186i
$767$	−7.19131			−0.259663
$768$	−27.7057	+	0.629782i	−0.999742	+	0.0227253i
$769$	8.19388			0.295479			0.147739	−	0.989026i	$-0.452800\pi$
$769$	8.19388			0.295479			0.147739	+	0.989026i	$0.452800\pi$
$770$	−8.61552	+	5.78925i	−0.310482	+	0.208630i
$771$	−4.17843	+	0.00780903i	−0.150482	+	0.000281235i
$772$	−17.8983	+	43.8558i	−0.644174	+	1.57840i
$773$	−11.9974	−	17.9553i	−0.431515	−	0.645808i	0.550451	−	0.834868i	$-0.314456\pi$
$773$	−11.9974	−	17.9553i	−0.431515	−	0.645808i	−0.981966	+	0.189060i	$0.939456\pi$
$774$	−7.35444	+	3.10112i	−0.264350	+	0.111468i
$775$	−5.50316	+	13.2858i	−0.197679	+	0.477240i
$776$	−0.413549	+	0.0856281i	−0.0148455	+	0.00307387i
$777$	1.22879	+	6.11777i	0.0440826	+	0.219474i
$778$	−1.05010	−	0.431763i	−0.0376481	−	0.0154795i
$779$	3.10045	+	0.616718i	0.111085	+	0.0220962i
$780$	6.40016	−	15.7663i	0.229162	−	0.564524i
$781$	22.1906	+	14.8273i	0.794042	+	0.530562i
$782$	−10.7749	−	53.4407i	−0.385311	−	1.91103i
$783$	−21.0378	+	4.30744i	−0.751830	+	0.153935i
$784$	−0.265558	−	25.4621i	−0.00948422	−	0.909359i
$785$	−16.2147	−	16.2147i	−0.578726	−	0.578726i
$786$	−2.20242	+	2.22223i	−0.0785579	+	0.0792643i
$787$	−35.1663	−	23.4974i	−1.25354	−	0.837591i	−0.261712	−	0.965146i	$-0.584287\pi$
$787$	−35.1663	−	23.4974i	−1.25354	−	0.837591i	−0.991832	+	0.127555i	$0.959287\pi$
$788$	20.9562	−	4.28216i	0.746533	−	0.152546i
$789$	11.2080	−	27.2022i	0.399016	−	0.968424i
$790$	8.29085	−	3.45953i	0.294975	−	0.123085i
$791$	−4.73285	−	11.4261i	−0.168281	−	0.406265i
$792$	0.527908	+	45.6661i	0.0187584	+	1.62267i
$793$	−1.18943	+	2.87153i	−0.0422377	+	0.101971i
$794$	−44.4848	+	0.115985i	−1.57871	+	0.00411617i
$795$	−11.0202	−	26.4650i	−0.390845	−	0.938618i
$796$	0.178764	+	0.176909i	0.00633611	+	0.00627037i
$797$	1.56119	+	7.84862i	0.0553001	+	0.278012i	0.998535	−	0.0541148i	$-0.0172337\pi$
$797$	1.56119	+	7.84862i	0.0553001	+	0.278012i	−0.943235	+	0.332127i	$0.892234\pi$
$798$	4.84610	+	1.98195i	0.171550	+	0.0701604i
$799$	35.5700			1.25838
$800$	−6.36990	+	9.80764i	−0.225210	+	0.346753i
$801$	−44.0305	−	18.0455i	−1.55574	−	0.637607i
$802$	−24.4355	−	4.79432i	−0.862846	−	0.169293i
$803$	3.64900	−	0.725831i	0.128770	−	0.0256140i
$804$	48.1096	+	9.21582i	1.69670	+	0.325017i
$805$	−5.72688	−	8.57088i	−0.201846	−	0.302084i
$806$	28.2166	−	0.0735692i	0.993887	−	0.00259136i
$807$	25.8111	+	17.1768i	0.908595	+	0.604651i
$808$	−4.67054	−	4.59804i	−0.164309	−	0.161759i
$809$	1.59008	−	0.658632i	0.0559042	−	0.0231563i	−0.354556	−	0.935035i	$-0.615368\pi$
$809$	1.59008	−	0.658632i	0.0559042	−	0.0231563i	0.410460	+	0.911878i	$0.365368\pi$
$810$	20.2205	+	8.13772i	0.710475	+	0.285930i
$811$	44.0264	+	8.75739i	1.54598	+	0.307514i	0.893067	−	0.449923i	$-0.148549\pi$
$811$	44.0264	+	8.75739i	1.54598	+	0.307514i	0.652908	+	0.757437i	$0.273549\pi$
$812$	3.62818	−	5.49173i	0.127324	−	0.192722i
$813$	35.9448	+	35.8107i	1.26064	+	1.25594i
$814$	−28.6815	−	19.0564i	−1.00528	−	0.667925i
$815$	−25.2092	+	25.2092i	−0.883039	+	0.883039i
$816$	−35.3298	+	0.434510i	−1.23679	+	0.0152109i
$817$	−3.57062	−	3.57062i	−0.124920	−	0.124920i
$818$	4.40159	+	21.8307i	0.153898	+	0.763292i
$819$	−5.68333	+	3.82828i	−0.198592	+	0.133771i
$820$	−3.34215	+	2.25845i	−0.116713	+	0.0788686i
$821$	5.35307	−	26.9117i	0.186824	−	0.939225i	−0.767636	−	0.640886i	$-0.778567\pi$
$821$	5.35307	−	26.9117i	0.186824	−	0.939225i	0.954460	−	0.298340i	$-0.0964328\pi$
$822$	12.2021	−	18.4399i	0.425598	−	0.643166i
$823$	−0.538169	−	1.29925i	−0.0187594	−	0.0452891i	0.914222	−	0.405213i	$-0.132803\pi$
$823$	−0.538169	−	1.29925i	−0.0187594	−	0.0452891i	−0.932982	+	0.359924i	$0.882803\pi$
$824$	−9.56716	+	50.1441i	−0.333288	+	1.74685i
$825$	16.0442	+	10.6771i	0.558587	+	0.371728i
$826$	2.00169	+	1.99128i	0.0696478	+	0.0692855i
$827$	−42.6108	+	28.4716i	−1.48172	+	0.990056i	−0.488660	+	0.872474i	$0.662514\pi$
$827$	−42.6108	+	28.4716i	−1.48172	+	0.990056i	−0.993063	+	0.117582i	$0.962486\pi$
$828$	−45.3514	+	0.406013i	−1.57607	+	0.0141099i
$829$	−10.7528	−	54.0581i	−0.373461	−	1.87752i	−0.470760	−	0.882262i	$-0.656020\pi$
$829$	−10.7528	−	54.0581i	−0.373461	−	1.87752i	0.0972982	−	0.995255i	$-0.468980\pi$
$830$	−6.09564	+	4.09601i	−0.211583	+	0.142174i
$831$	43.4044	+	8.54938i	1.50568	+	0.296575i
$832$	22.5732	+	4.12409i	0.782583	+	0.142977i
$833$		−	32.4646i		−	1.12483i
$834$	−11.7826	+	4.94241i	−0.407997	+	0.171141i
$835$	−19.6299	+	3.90463i	−0.679320	+	0.135125i
$836$	−26.6358	+	11.1960i	−0.921220	+	0.387222i
$837$	0.202649	+	36.1438i	0.00700456	+	1.24931i
$838$	20.8227	−	20.9316i	0.719309	−	0.723070i
$839$	−11.4210	−	4.73072i	−0.394296	−	0.163323i	0.176721	−	0.984261i	$-0.443451\pi$
$839$	−11.4210	−	4.73072i	−0.394296	−	0.163323i	−0.571017	+	0.820938i	$0.693451\pi$
$840$	−6.14718	+	2.61632i	−0.212098	+	0.0902717i
$841$	11.0132	−	4.56183i	0.379766	−	0.157304i
$842$	10.7497	+	4.41989i	0.370460	+	0.152319i
$843$	20.0863	−	48.7502i	0.691810	−	1.67905i
$844$	−23.8997	+	16.1502i	−0.822663	+	0.555913i
$845$	4.54069	−	6.79562i	0.156204	−	0.233776i
$846$	5.58875	−	29.0589i	0.192145	−	0.999067i
$847$	−10.1174	+	10.1174i	−0.347637	+	0.347637i
$848$	31.9190	−	21.8125i	1.09610	−	0.749044i
$849$	11.5332	+	17.1910i	0.395818	+	0.589994i
$850$	−8.25127	+	12.4189i	−0.283016	+	0.425964i
$851$	18.9987	−	28.4336i	0.651268	−	0.974692i
$852$	12.2320	+	12.0599i	0.419060	+	0.413165i
$853$	8.07843	−	40.6130i	0.276600	−	1.39056i	−0.553454	−	0.832880i	$-0.686691\pi$
$853$	8.07843	−	40.6130i	0.276600	−	1.39056i	0.830054	−	0.557683i	$-0.188309\pi$
$854$	1.12620	−	0.469933i	0.0385379	−	0.0160808i
$855$	0.0515435	+	13.7898i	0.00176275	+	0.471601i
$856$	−27.0693	+	0.211737i	−0.925210	+	0.00723704i
$857$	11.4578	+	4.74597i	0.391390	+	0.162119i	0.569695	−	0.821856i	$-0.307061\pi$
$857$	11.4578	+	4.74597i	0.391390	+	0.162119i	−0.178305	+	0.983975i	$0.557061\pi$
$858$	7.21125	−	37.1211i	0.246188	−	1.26729i
$859$	13.4982	−	9.01922i	0.460553	−	0.307732i	−0.303562	−	0.952812i	$-0.598176\pi$
$859$	13.4982	−	9.01922i	0.460553	−	0.307732i	0.764115	+	0.645080i	$0.223176\pi$
$860$	6.44324	−	0.0335991i	0.219713	−	0.00114572i
$861$	1.62440	−	0.00303583i	0.0553594	−	0.000103461i
$862$	8.52762	−	43.4632i	0.290452	−	1.48036i
$863$		−	25.3881i		−	0.864222i	−0.901820	−	0.432111i	$-0.857769\pi$
$863$		−	25.3881i		−	0.864222i	0.901820	−	0.432111i	$-0.142231\pi$
$864$	−5.19603	+	28.9310i	−0.176773	+	0.984252i
$865$		−	21.0505i		−	0.715739i
$866$	−15.2100	−	2.98426i	−0.516858	−	0.101409i
$867$	−15.6022	+	0.0291588i	−0.529878	+	0.000990284i
$868$	−7.87442	−	7.79273i	−0.267275	−	0.264502i
$869$	16.6001	−	11.0919i	0.563121	−	0.376266i
$870$	17.0176	+	3.30589i	0.576950	+	0.112080i
$871$	−37.4726	−	15.5217i	−1.26971	−	0.525932i
$872$	−18.0719	−	7.32056i	−0.611993	−	0.247906i
$873$	0.00167429	+	0.447936i	5.66663e−5	+	0.0151603i
$874$	−11.0496	−	26.4805i	−0.373757	−	0.895716i
$875$	−1.88024	+	9.45263i	−0.0635639	+	0.319557i
$876$	2.39454	−	0.0169620i	0.0809041	−	0.000573092i
$877$	−14.4959	+	21.6947i	−0.489492	+	0.732577i	−0.991187	−	0.132468i	$-0.957710\pi$
$877$	−14.4959	+	21.6947i	−0.489492	+	0.732577i	0.501695	+	0.865044i	$0.332710\pi$
$878$	−4.93922	−	3.28168i	−0.166691	−	0.110751i
$879$	8.20856	+	12.2354i	0.276868	+	0.412690i
$880$	13.7527	−	34.2067i	0.463603	−	1.15311i
$881$	−20.3613	+	20.3613i	−0.685990	+	0.685990i	−0.961343	−	0.275353i	$-0.911205\pi$
$881$	−20.3613	+	20.3613i	−0.685990	+	0.685990i	0.275353	+	0.961343i	$0.411205\pi$
$882$	−26.5220	−	5.10083i	−0.893043	−	0.171754i
$883$	16.0071	−	23.9562i	0.538680	−	0.806192i	−0.457884	−	0.889012i	$-0.651393\pi$
$883$	16.0071	−	23.9562i	0.538680	−	0.806192i	0.996565	+	0.0828199i	$0.0263926\pi$
$884$	28.7232	+	5.55786i	0.966067	+	0.186931i
$885$	−2.83297	+	6.87571i	−0.0952292	+	0.231124i
$886$	−8.73940	+	21.2554i	−0.293606	+	0.714088i
$887$	39.4628	−	16.3460i	1.32503	−	0.548845i	0.395796	−	0.918338i	$-0.370469\pi$
$887$	39.4628	−	16.3460i	1.32503	−	0.548845i	0.929234	+	0.369493i	$0.120469\pi$
$888$	−15.8230	−	15.5192i	−0.530984	−	0.520791i
$889$	−14.9180	−	6.17923i	−0.500333	−	0.207245i
$890$	27.2338	+	27.0922i	0.912879	+	0.908131i
$891$	47.5780	+	9.09465i	1.59392	+	0.304682i
$892$	11.6830	−	28.6265i	0.391175	−	0.958486i
$893$	18.3618	−	3.65238i	0.614453	−	0.122222i
$894$	16.0862	+	38.3491i	0.538002	+	1.28258i
$895$		−	13.3876i		−	0.447499i
$896$	−5.14125	−	7.39846i	−0.171757	−	0.247165i
$897$	36.8455	+	7.25746i	1.23023	+	0.242320i
$898$	−3.50479	−	5.21579i	−0.116956	−	0.174053i
$899$	5.60829	+	28.1948i	0.187047	+	0.940349i
$900$	8.84918	+	8.69214i	0.294973	+	0.289738i
$901$	40.9829	−	27.3839i	1.36534	−	0.912290i
$902$	−6.32212	+	6.35517i	−0.210504	+	0.211604i
$903$	−2.16018	−	1.43755i	−0.0718863	−	0.0478388i
$904$	36.7141	+	24.1183i	1.22109	+	0.802164i
$905$	8.54440	+	20.6280i	0.284025	+	0.685698i
$906$	−13.1797	−	8.72133i	−0.437867	−	0.289747i
$907$	3.37324	−	16.9584i	0.112007	−	0.563096i	−0.883502	−	0.468427i	$-0.844821\pi$
$907$	3.37324	−	16.9584i	0.112007	−	0.563096i	0.995509	−	0.0946685i	$-0.0301791\pi$
$908$	3.24475	−	16.7690i	0.107681	−	0.556498i
$909$	−5.76561	+	3.88371i	−0.191233	+	0.128814i
$910$	5.42271	−	1.09335i	0.179761	−	0.0362442i
$911$	2.54657	+	2.54657i	0.0843717	+	0.0843717i	0.748033	−	0.663661i	$-0.230998\pi$
$911$	2.54657	+	2.54657i	0.0843717	+	0.0843717i	−0.663661	+	0.748033i	$0.730998\pi$
$912$	−18.1931	+	3.85201i	−0.602435	+	0.127553i
$913$	−11.5406	+	11.5406i	−0.381938	+	0.381938i
$914$	2.76823	−	4.16642i	0.0915648	−	0.137813i
$915$	2.27694	+	2.26845i	0.0752733	+	0.0749925i
$916$	4.10181	−	0.838160i	0.135528	−	0.0276936i
$917$	−0.997605	−	0.198436i	−0.0329438	−	0.00655294i
$918$	−7.00900	+	36.8144i	−0.231331	+	1.21506i
$919$	−30.5861	+	12.6692i	−1.00894	+	0.417918i	−0.825069	−	0.565032i	$-0.808864\pi$
$919$	−30.5861	+	12.6692i	−1.00894	+	0.417918i	−0.183874	+	0.982950i	$0.558864\pi$
$920$	33.9343	+	13.7461i	1.11878	+	0.453195i
$921$	−15.7753	−	10.4981i	−0.519813	−	0.345925i
$922$	0.00295500	+	1.13336i	9.73178e−5	+	0.0373251i
$923$	−7.90200	−	11.8262i	−0.260097	−	0.389263i
$924$	−12.2861	+	8.33579i	−0.404183	+	0.274228i
$925$	−9.17310	+	1.82464i	−0.301610	+	0.0599939i
$926$	5.22727	−	26.6421i	0.171779	−	0.875513i
$927$	50.1007	+	20.5333i	1.64552	+	0.674404i
$928$	0.304761	+	23.3762i	0.0100043	+	0.767362i
$929$	−15.5822			−0.511236			−0.255618	−	0.966778i	$-0.582279\pi$
$929$	−15.5822			−0.511236			−0.255618	+	0.966778i	$0.582279\pi$
$930$	11.0454	−	27.0073i	0.362193	−	0.885603i
$931$	−3.33352	−	16.7587i	−0.109252	−	0.549245i
$932$	−0.105519	−	20.2351i	−0.00345639	−	0.662824i
$933$	7.97837	+	19.1601i	0.261200	+	0.627274i
$934$	0.149490	+	57.3351i	0.00489146	+	1.87606i
$935$	17.9879	−	43.4265i	0.588266	−	1.42020i
$936$	9.05349	−	22.5922i	0.295923	−	0.738450i
$937$	13.5497	+	32.7119i	0.442650	+	1.06865i	0.975016	+	0.222136i	$0.0713030\pi$
$937$	13.5497	+	32.7119i	0.442650	+	1.06865i	−0.532366	+	0.846514i	$0.678697\pi$
$938$	6.13249	+	14.6966i	0.200233	+	0.479863i
$939$	−14.4243	+	35.0083i	−0.470720	+	1.14245i
$940$	−13.1680	+	19.9316i	−0.429494	+	0.650097i
$941$	−15.8636	−	10.5997i	−0.517139	−	0.345541i	0.269454	−	0.963013i	$-0.413157\pi$
$941$	−15.8636	−	10.5997i	−0.517139	−	0.345541i	−0.786593	+	0.617472i	$0.788157\pi$
$942$	−23.2964	−	23.0888i	−0.759037	−	0.752272i
$943$	−6.29482	−	6.29482i	−0.204987	−	0.204987i
$944$	−9.85567	−	1.85378i	−0.320775	−	0.0603354i
$945$	1.42136	+	6.94203i	0.0462370	+	0.225824i
$946$	14.0368	−	2.83016i	0.456376	−	0.0920164i
$947$	−3.79100	−	2.53307i	−0.123191	−	0.0823136i	0.492448	−	0.870342i	$-0.336102\pi$
$947$	−3.79100	−	2.53307i	−0.123191	−	0.0823136i	−0.615639	+	0.788028i	$0.711102\pi$
$948$	11.8366	−	5.00141i	0.384436	−	0.162438i
$949$	−1.94468	−	0.386822i	−0.0631271	−	0.0125568i
$950$	−2.98424	+	7.25806i	−0.0968215	+	0.235483i
$951$	0.130896	+	0.651689i	0.00424458	+	0.0211325i
$952$	−6.45610	−	9.50052i	−0.209243	−	0.307913i
$953$	2.16803	−	5.23408i	0.0702292	−	0.169548i	−0.884867	−	0.465843i	$-0.845751\pi$
$953$	2.16803	−	5.23408i	0.0702292	−	0.169548i	0.955097	+	0.296295i	$0.0957511\pi$
$954$	−15.9321	−	37.7836i	−0.515821	−	1.22329i
$955$	−11.0440	−	16.5285i	−0.357374	−	0.534848i
$956$	8.89930	+	21.1719i	0.287824	+	0.684747i
$957$	38.5259	−	0.0720007i	1.24536	−	0.00232745i
$958$	0.470337	+	0.699952i	0.0151959	+	0.0226144i
$959$	7.18846			0.232128
$960$	12.8356	−	19.9578i	0.414269	−	0.644137i
$961$	17.3858			0.560832
$962$	10.2354	+	15.2322i	0.330003	+	0.491107i
$963$	−5.49618	+	28.1813i	−0.177112	+	0.908129i
$964$	−53.8554	+	22.6374i	−1.73457	+	0.729100i
$965$	−22.5330	−	33.7231i	−0.725364	−	1.08558i
$966$	−8.24629	−	12.2227i	−0.265320	−	0.393257i
$967$	−4.84384	+	11.6941i	−0.155767	+	0.376056i	−0.982427	−	0.186646i	$-0.940238\pi$
$967$	−4.84384	+	11.6941i	−0.155767	+	0.376056i	0.826660	+	0.562702i	$0.190238\pi$
$968$	9.52435	−	49.9197i	0.306124	−	1.60448i
$969$	−23.2453	+	4.66895i	−0.746746	+	0.149988i
$970$	0.137511	−	0.334446i	0.00441523	−	0.0107384i
$971$	−14.2757	−	2.83961i	−0.458129	−	0.0911275i	−0.0393696	−	0.999225i	$-0.512535\pi$
$971$	−14.2757	−	2.83961i	−0.458129	−	0.0911275i	−0.418760	+	0.908097i	$0.637535\pi$
$972$	28.9744	+	11.5103i	0.929353	+	0.369193i
$973$	−3.45380	−	2.30776i	−0.110724	−	0.0739833i
$974$	−21.2805	+	4.29066i	−0.681871	+	0.137482i
$975$	−5.72212	−	8.52921i	−0.183255	−	0.273153i
$976$	−2.37033	+	3.62881i	−0.0758724	+	0.116155i
$977$	16.4215	+	16.4215i	0.525370	+	0.525370i	0.919188	−	0.393818i	$-0.128846\pi$
$977$	16.4215	+	16.4215i	0.525370	+	0.525370i	−0.393818	+	0.919188i	$0.628846\pi$
$978$	−35.8964	+	36.2192i	−1.14784	+	1.15816i
$979$	70.9825	+	47.4290i	2.26861	+	1.51584i
$980$	18.1915	+	12.0184i	0.581106	+	0.383915i
$981$	−11.4255	+	17.2386i	−0.364787	+	0.550385i
$982$	−0.0178914	−	0.0428772i	−0.000570939	−	0.00136827i
$983$	16.4499	+	39.7135i	0.524669	+	1.26666i	0.934975	+	0.354715i	$0.115422\pi$
$983$	16.4499	+	39.7135i	0.524669	+	1.26666i	−0.410306	+	0.911948i	$0.634578\pi$
$984$	−4.76597	+	3.25177i	−0.151934	+	0.103663i
$985$	−7.00865	+	16.9204i	−0.223314	+	0.539128i
$986$	0.0777130	+	29.8059i	0.00247489	+	0.949214i
$987$	8.88099	−	3.69809i	0.282685	−	0.117711i
$988$	15.3981	−	0.0802953i	0.489877	−	0.00255453i
$989$	2.77423	+	13.9470i	0.0882153	+	0.443488i
$990$	−32.6511	−	21.5184i	−1.03772	−	0.683899i
$991$	−24.5959			−0.781314			−0.390657	−	0.920536i	$-0.627752\pi$
$991$	−24.5959			−0.781314			−0.390657	+	0.920536i	$0.627752\pi$
$992$	38.6897	+	7.17286i	1.22840	+	0.227739i
$993$	11.9472	+	2.35325i	0.379134	+	0.0746781i
$994$	−1.07517	+	5.47987i	−0.0341023	+	0.173811i
$995$	−0.211211	+	0.0420124i	−0.00669583	+	0.00133188i
$996$	−8.69265	+	5.89773i	−0.275437	+	0.186877i
$997$	10.5381	+	15.7713i	0.333744	+	0.499483i	0.959949	−	0.280176i	$-0.0903927\pi$
$997$	10.5381	+	15.7713i	0.333744	+	0.499483i	−0.626205	+	0.779658i	$0.715393\pi$
$998$	−0.0358457	−	13.7482i	−0.00113468	−	0.435192i
$999$	−19.4724	+	13.1696i	−0.616081	+	0.416667i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
192.2.s.a.107.5	✓	240	3.2	odd	2	inner
192.2.s.a.107.26	yes	240	1.1	even	1	trivial
192.2.s.a.131.5	yes	240	64.3	odd	16	inner
192.2.s.a.131.26	yes	240	192.131	even	16	inner
768.2.s.a.335.14		240	4.3	odd	2
768.2.s.a.335.18		240	12.11	even	2
768.2.s.a.431.14		240	192.125	odd	16
768.2.s.a.431.18		240	64.61	even	16

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:	\( N \)	\(=\)	\( 192 = 2^{6} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	192.s (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.17382 - 0.788758i) q^{2} +(0.00323701 + 1.73205i) q^{3} +(0.755721 - 1.85172i) q^{4} +(0.951414 + 1.42389i) q^{5} +(1.36997 + 2.03056i) q^{6} +(-0.304742 + 0.735711i) q^{7} +(-0.573480 - 2.76968i) q^{8} +(-2.99998 + 0.0112133i) q^{9} +(2.23990 + 0.920961i) q^{10} +(5.27874 + 1.05001i) q^{11} +(3.20972 + 1.30295i) q^{12} +(-2.38495 - 1.59357i) q^{13} +(0.222585 + 1.10396i) q^{14} +(-2.46317 + 1.65250i) q^{15} +(-2.85777 - 2.79878i) q^{16} +(-3.60610 - 3.60610i) q^{17} +(-3.51260 + 2.37942i) q^{18} +(-2.23180 - 1.49124i) q^{19} +(3.35566 - 0.685692i) q^{20} +(-1.27527 - 0.525445i) q^{21} +(7.02451 - 2.93113i) q^{22} +(2.89265 + 6.98348i) q^{23} +(4.79536 - 1.00226i) q^{24} +(0.791139 - 1.90998i) q^{25} +(-4.05645 + 0.0105764i) q^{26} +(-0.0291330 - 5.19607i) q^{27} +(1.13203 + 1.12029i) q^{28} +(-0.806254 - 4.05331i) q^{29} +(-1.58790 + 3.88259i) q^{30} -6.95599 q^{31} +(-5.56207 - 1.03118i) q^{32} +(-1.80158 + 9.14643i) q^{33} +(-7.07727 - 1.38858i) q^{34} +(-1.33751 + 0.266047i) q^{35} +(-2.24638 + 5.56361i) q^{36} +(-2.51344 - 3.76162i) q^{37} +(-3.79597 + 0.00989724i) q^{38} +(2.75242 - 4.13600i) q^{39} +(3.39810 - 3.45168i) q^{40} +(-1.08807 + 0.450693i) q^{41} +(-1.91139 + 0.389102i) q^{42} +(1.84512 + 0.367016i) q^{43} +(5.93358 - 8.98127i) q^{44} +(-2.87019 - 4.26097i) q^{45} +(8.90374 + 5.91577i) q^{46} +(-4.93192 + 4.93192i) q^{47} +(4.83836 - 4.95886i) q^{48} +(4.50134 + 4.50134i) q^{49} +(-0.577854 - 2.86600i) q^{50} +(6.23427 - 6.25761i) q^{51} +(-4.75321 + 3.21197i) q^{52} +(-1.88555 + 9.47932i) q^{53} +(-4.13264 - 6.07629i) q^{54} +(3.52717 + 8.51534i) q^{55} +(2.21245 + 0.422120i) q^{56} +(2.57568 - 3.87042i) q^{57} +(-4.14348 - 4.12193i) q^{58} +(2.08460 - 1.39288i) q^{59} +(1.19851 + 5.80994i) q^{60} +(-0.211398 - 1.06277i) q^{61} +(-8.16510 + 5.48659i) q^{62} +(0.905968 - 2.21053i) q^{63} +(-7.34224 + 3.17671i) q^{64} -4.91205i q^{65} +(5.09959 + 12.1573i) q^{66} +(13.8689 - 2.75869i) q^{67} +(-9.40272 + 3.95230i) q^{68} +(-12.0864 + 5.03282i) q^{69} +(-1.36015 + 1.36726i) q^{70} +(4.58122 + 1.89760i) q^{71} +(1.75149 + 8.30255i) q^{72} +(0.638643 - 0.264535i) q^{73} +(-5.91734 - 2.43299i) q^{74} +(3.31074 + 1.36411i) q^{75} +(-4.44799 + 3.00572i) q^{76} +(-2.38115 + 3.56365i) q^{77} +(-0.0314495 - 7.02592i) q^{78} +(2.62297 - 2.62297i) q^{79} +(1.26623 - 6.73195i) q^{80} +(8.99975 - 0.0672794i) q^{81} +(-0.921714 + 1.38726i) q^{82} +(-1.68471 + 2.52135i) q^{83} +(-1.93673 + 1.96437i) q^{84} +(1.70380 - 8.56559i) q^{85} +(2.45533 - 1.02454i) q^{86} +(7.01792 - 1.40959i) q^{87} +(-0.119072 - 15.2226i) q^{88} +(14.6543 + 6.06999i) q^{89} +(-6.72997 - 2.73775i) q^{90} +(1.89920 - 1.26900i) q^{91} +(15.1175 - 0.0788324i) q^{92} +(-0.0225166 - 12.0481i) q^{93} +(-1.89911 + 9.67928i) q^{94} -4.59663i q^{95} +(1.76804 - 9.63712i) q^{96} -0.149313i q^{97} +(8.83425 + 1.73331i) q^{98} +(-15.8479 - 3.09081i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 8 q^{3} - 16 q^{4} - 8 q^{6} - 16 q^{7} - 8 q^{9} - 16 q^{10} - 8 q^{12} - 16 q^{13} - 8 q^{15} - 16 q^{16} - 8 q^{18} - 16 q^{19} - 8 q^{21} - 16 q^{22} - 48 q^{24} - 16 q^{25} - 8 q^{27} - 16 q^{28}+ \cdots - 8 q^{99}+O(q^{100}) \) 240 * q - 8 * q^3 - 16 * q^4 - 8 * q^6 - 16 * q^7 - 8 * q^9 - 16 * q^10 - 8 * q^12 - 16 * q^13 - 8 * q^15 - 16 * q^16 - 8 * q^18 - 16 * q^19 - 8 * q^21 - 16 * q^22 - 48 * q^24 - 16 * q^25 - 8 * q^27 - 16 * q^28 - 88 * q^30 - 32 * q^31 - 16 * q^34 - 88 * q^36 - 16 * q^37 - 8 * q^39 - 16 * q^40 - 48 * q^42 - 16 * q^43 - 8 * q^45 - 16 * q^46 - 8 * q^48 - 16 * q^49 - 8 * q^51 + 32 * q^52 - 8 * q^54 - 80 * q^55 - 8 * q^57 + 128 * q^58 - 8 * q^60 - 16 * q^61 + 80 * q^64 - 24 * q^66 - 144 * q^67 - 8 * q^69 + 80 * q^70 - 8 * q^72 - 16 * q^73 - 8 * q^75 + 96 * q^76 + 16 * q^78 - 48 * q^79 - 8 * q^81 + 64 * q^82 + 104 * q^84 - 16 * q^85 - 8 * q^87 + 64 * q^88 + 136 * q^90 - 16 * q^91 - 32 * q^93 + 80 * q^94 + 128 * q^96 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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