LMFDB - Embedded newform 230.2.l.a.57.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [230,2,Mod(7,230)] 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("230.7"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(230, base_ring=CyclotomicField(44)) chi = DirichletCharacter(H, H._module([11, 38])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	230.l (of order $44$, degree $20$, 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:	$1.83655924649$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			57.9
Character	$\chi$	$=$	230.57
Dual form			230.2.l.a.113.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.977147 + 0.212565i) q^{2} +(-0.390684 - 0.521893i) q^{3} +(0.909632 + 0.415415i) q^{4} +(-1.06032 - 1.96869i) q^{5} +(-0.270819 - 0.593012i) q^{6} +(2.75328 + 0.196919i) q^{7} +(0.800541 + 0.599278i) q^{8} +(0.725460 - 2.47069i) q^{9} +(-0.617610 - 2.14908i) q^{10} +(-0.171272 + 0.266505i) q^{11} +(-0.138577 - 0.637026i) q^{12} +(0.0436911 + 0.610881i) q^{13} +(2.64850 + 0.777670i) q^{14} +(-0.613195 + 1.32251i) q^{15} +(0.654861 + 0.755750i) q^{16} +(2.49510 + 0.930625i) q^{17} +(1.23406 - 2.26002i) q^{18} +(-1.33902 + 2.93205i) q^{19} +(-0.146675 - 2.23125i) q^{20} +(-0.972892 - 1.51385i) q^{21} +(-0.224008 + 0.224008i) q^{22} +(-1.29062 - 4.61891i) q^{23} -0.651925i q^{24} +(-2.75146 + 4.17486i) q^{25} +(-0.0871595 + 0.606208i) q^{26} +(-3.40532 + 1.27012i) q^{27} +(2.42267 + 1.32288i) q^{28} +(-5.55597 + 2.53733i) q^{29} +(-0.880300 + 1.16194i) q^{30} +(1.29230 + 8.98814i) q^{31} +(0.479249 + 0.877679i) q^{32} +(0.206000 - 0.0147334i) q^{33} +(2.24026 + 1.43973i) q^{34} +(-2.53168 - 5.62915i) q^{35} +(1.68626 - 1.94605i) q^{36} +(-2.11882 + 1.15696i) q^{37} +(-1.93167 + 2.58041i) q^{38} +(0.301745 - 0.261463i) q^{39} +(0.330964 - 2.21144i) q^{40} +(-7.62326 + 2.23839i) q^{41} +(-0.628867 - 1.68606i) q^{42} +(8.36389 - 6.26113i) q^{43} +(-0.266505 + 0.171272i) q^{44} +(-5.63323 + 1.19151i) q^{45} +(-0.279308 - 4.78769i) q^{46} +(4.91328 + 4.91328i) q^{47} +(0.138577 - 0.637026i) q^{48} +(0.613031 + 0.0881405i) q^{49} +(-3.57601 + 3.49459i) q^{50} +(-0.489110 - 1.66576i) q^{51} +(-0.214026 + 0.573827i) q^{52} +(0.413325 - 5.77904i) q^{53} +(-3.59748 + 0.517240i) q^{54} +(0.706268 + 0.0546022i) q^{55} +(2.08611 + 1.80762i) q^{56} +(2.05335 - 0.446679i) q^{57} +(-5.96835 + 1.29834i) q^{58} +(3.03630 + 2.63097i) q^{59} +(-1.10717 + 0.948263i) q^{60} +(-10.7039 + 1.53899i) q^{61} +(-0.647801 + 9.05743i) q^{62} +(2.48392 - 6.65964i) q^{63} +(0.281733 + 0.959493i) q^{64} +(1.15631 - 0.733741i) q^{65} +(0.204424 + 0.0293918i) q^{66} +(-1.63335 + 7.50837i) q^{67} +(1.88303 + 1.88303i) q^{68} +(-1.90635 + 2.47810i) q^{69} +(-1.27726 - 6.03865i) q^{70} +(7.02619 - 4.51545i) q^{71} +(2.06139 - 1.54314i) q^{72} +(3.36562 + 9.02358i) q^{73} +(-2.31633 + 0.680136i) q^{74} +(3.25378 - 0.195085i) q^{75} +(-2.43603 + 2.11083i) q^{76} +(-0.524041 + 0.700037i) q^{77} +(0.350427 - 0.191348i) q^{78} +(4.91108 - 5.66768i) q^{79} +(0.793475 - 2.09055i) q^{80} +(-4.50540 - 2.89544i) q^{81} +(-7.92485 + 0.566796i) q^{82} +(-0.489934 - 0.897247i) q^{83} +(-0.256098 - 1.78120i) q^{84} +(-0.813487 - 5.89883i) q^{85} +(9.50365 - 4.34017i) q^{86} +(3.49484 + 1.90833i) q^{87} +(-0.296821 + 0.110709i) q^{88} +(0.532679 - 3.70486i) q^{89} +(-5.75777 - 0.0331510i) q^{90} +1.69053i q^{91} +(0.744772 - 4.73765i) q^{92} +(4.18596 - 4.18596i) q^{93} +(3.75660 + 5.84539i) q^{94} +(7.19207 - 0.472783i) q^{95} +(0.270819 - 0.593012i) q^{96} +(5.77381 - 10.5739i) q^{97} +(0.580286 + 0.216435i) q^{98} +(0.534200 + 0.616500i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 8 q^{3} - 8 q^{6} - 8 q^{12} + 16 q^{13} + 24 q^{16} - 72 q^{18} - 80 q^{23} - 8 q^{26} + 16 q^{27} - 44 q^{28} + 24 q^{31} - 44 q^{33} - 8 q^{35} - 32 q^{36} - 88 q^{37} - 24 q^{41} - 8 q^{46}+ \cdots + 24 q^{98}+O(q^{100}) $ 240 * q - 8 * q^3 - 8 * q^6 - 8 * q^12 + 16 * q^13 + 24 * q^16 - 72 * q^18 - 80 * q^23 - 8 * q^26 + 16 * q^27 - 44 * q^28 + 24 * q^31 - 44 * q^33 - 8 * q^35 - 32 * q^36 - 88 * q^37 - 24 * q^41 - 8 * q^46 - 80 * q^47 + 8 * q^48 + 8 * q^50 + 16 * q^52 - 44 * q^56 - 88 * q^57 - 176 * q^61 - 32 * q^62 - 176 * q^66 + 24 * q^70 - 336 * q^71 + 16 * q^72 - 88 * q^73 - 36 * q^75 - 24 * q^77 + 40 * q^78 - 136 * q^81 + 40 * q^82 - 100 * q^85 - 44 * q^86 + 40 * q^87 + 8 * q^92 + 56 * q^93 + 52 * q^95 + 8 * q^96 + 132 * q^97 + 24 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{9}{22}\right)$

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 $

$2$	0.977147	+	0.212565i	0.690947	+	0.150306i
$2$	0.977147	+	0.212565i	0.690947	+	0.150306i
$3$	−0.390684	−	0.521893i	−0.225561	−	0.301315i	0.673456	−	0.739227i	$-0.264809\pi$
$3$	−0.390684	−	0.521893i	−0.225561	−	0.301315i	−0.899018	+	0.437912i	$0.855718\pi$
$4$	0.909632	+	0.415415i	0.454816	+	0.207708i
$5$	−1.06032	−	1.96869i	−0.474188	−	0.880424i
$5$	−1.06032	−	1.96869i	−0.474188	−	0.880424i
$6$	−0.270819	−	0.593012i	−0.110562	−	0.242096i
$7$	2.75328	+	0.196919i	1.04064	+	0.0744282i	0.581185	−	0.813772i	$-0.302589\pi$
$7$	2.75328	+	0.196919i	1.04064	+	0.0744282i	0.459458	+	0.888200i	$0.348044\pi$
$8$	0.800541	+	0.599278i	0.283034	+	0.211877i
$9$	0.725460	−	2.47069i	0.241820	−	0.823563i
$10$	−0.617610	−	2.14908i	−0.195305	−	0.679600i
$11$	−0.171272	+	0.266505i	−0.0516406	+	0.0803543i	−0.866114	−	0.499847i	$-0.833390\pi$
$11$	−0.171272	+	0.266505i	−0.0516406	+	0.0803543i	0.814473	+	0.580201i	$0.197026\pi$
$12$	−0.138577	−	0.637026i	−0.0400036	−	0.183894i
$13$	0.0436911	+	0.610881i	0.0121177	+	0.169428i	0.999907	+	0.0136325i	$0.00433950\pi$
$13$	0.0436911	+	0.610881i	0.0121177	+	0.169428i	−0.987789	+	0.155795i	$0.950206\pi$
$14$	2.64850	+	0.777670i	0.707842	+	0.207841i
$15$	−0.613195	+	1.32251i	−0.158326	+	0.341469i
$16$	0.654861	+	0.755750i	0.163715	+	0.188937i
$17$	2.49510	+	0.930625i	0.605151	+	0.225710i	0.633316	−	0.773894i	$-0.281693\pi$
$17$	2.49510	+	0.930625i	0.605151	+	0.225710i	−0.0281645	+	0.999603i	$0.508966\pi$
$18$	1.23406	−	2.26002i	0.290872	−	0.532691i
$19$	−1.33902	+	2.93205i	−0.307193	+	0.672658i	−0.998767	−	0.0496475i	$-0.984190\pi$
$19$	−1.33902	+	2.93205i	−0.307193	+	0.672658i	0.691574	+	0.722305i	$0.256917\pi$
$20$	−0.146675	−	2.23125i	−0.0327976	−	0.498923i
$21$	−0.972892	−	1.51385i	−0.212303	−	0.330349i
$22$	−0.224008	+	0.224008i	−0.0477587	+	0.0477587i
$23$	−1.29062	−	4.61891i	−0.269113	−	0.963109i
$23$	−1.29062	−	4.61891i	−0.269113	−	0.963109i
$24$		−	0.651925i		−	0.133074i
$25$	−2.75146	+	4.17486i	−0.550292	+	0.834972i
$26$	−0.0871595	+	0.606208i	−0.0170934	+	0.118887i
$27$	−3.40532	+	1.27012i	−0.655354	+	0.244435i
$28$	2.42267	+	1.32288i	0.457842	+	0.250000i
$29$	−5.55597	+	2.53733i	−1.03172	+	0.471170i	−0.858013	−	0.513628i	$-0.828301\pi$
$29$	−5.55597	+	2.53733i	−1.03172	+	0.471170i	−0.173705	+	0.984798i	$0.555574\pi$
$30$	−0.880300	+	1.16194i	−0.160720	+	0.212140i
$31$	1.29230	+	8.98814i	0.232104	+	1.61432i	0.688975	+	0.724785i	$0.258061\pi$
$31$	1.29230	+	8.98814i	0.232104	+	1.61432i	−0.456871	+	0.889533i	$0.651030\pi$
$32$	0.479249	+	0.877679i	0.0847201	+	0.155153i
$33$	0.206000	−	0.0147334i	0.0358601	−	0.00256476i
$34$	2.24026	+	1.43973i	0.384202	+	0.246912i
$35$	−2.53168	−	5.62915i	−0.427932	−	0.951499i
$36$	1.68626	−	1.94605i	0.281044	−	0.324342i
$37$	−2.11882	+	1.15696i	−0.348332	+	0.190204i	−0.643884	−	0.765123i	$-0.722678\pi$
$37$	−2.11882	+	1.15696i	−0.348332	+	0.190204i	0.295552	+	0.955327i	$0.404496\pi$
$38$	−1.93167	+	2.58041i	−0.313359	+	0.418598i
$39$	0.301745	−	0.261463i	0.0483178	−	0.0418676i
$40$	0.330964	−	2.21144i	0.0523299	−	0.349659i
$41$	−7.62326	+	2.23839i	−1.19055	+	0.349578i	−0.816234	−	0.577722i	$-0.803942\pi$
$41$	−7.62326	+	2.23839i	−1.19055	+	0.349578i	−0.374320	+	0.927300i	$0.622124\pi$
$42$	−0.628867	−	1.68606i	−0.0970362	−	0.260164i
$43$	8.36389	−	6.26113i	1.27548	−	0.954814i	0.275503	−	0.961300i	$-0.411156\pi$
$43$	8.36389	−	6.26113i	1.27548	−	0.954814i	0.999979	+	0.00648654i	$0.00206474\pi$
$44$	−0.266505	+	0.171272i	−0.0401772	+	0.0258203i
$45$	−5.63323	+	1.19151i	−0.839752	+	0.177620i
$46$	−0.279308	−	4.78769i	−0.0411818	−	0.705907i
$47$	4.91328	+	4.91328i	0.716675	+	0.716675i	0.967923	−	0.251248i	$-0.0808409\pi$
$47$	4.91328	+	4.91328i	0.716675	+	0.716675i	−0.251248	+	0.967923i	$0.580841\pi$
$48$	0.138577	−	0.637026i	0.0200018	−	0.0919468i
$49$	0.613031	+	0.0881405i	0.0875758	+	0.0125915i
$50$	−3.57601	+	3.49459i	−0.505724	+	0.494209i
$51$	−0.489110	−	1.66576i	−0.0684891	−	0.233252i
$52$	−0.214026	+	0.573827i	−0.0296801	+	0.0795755i
$53$	0.413325	−	5.77904i	0.0567746	−	0.793812i	−0.886695	−	0.462354i	$-0.847005\pi$
$53$	0.413325	−	5.77904i	0.0567746	−	0.793812i	0.943470	−	0.331458i	$-0.107541\pi$
$54$	−3.59748	+	0.517240i	−0.489555	+	0.0703874i
$55$	0.706268	+	0.0546022i	0.0952332	+	0.00736256i
$56$	2.08611	+	1.80762i	0.278768	+	0.241554i
$57$	2.05335	−	0.446679i	0.271973	−	0.0591640i
$58$	−5.96835	+	1.29834i	−0.783683	+	0.170480i
$59$	3.03630	+	2.63097i	0.395292	+	0.342523i	0.829716	−	0.558186i	$-0.188502\pi$
$59$	3.03630	+	2.63097i	0.395292	+	0.342523i	−0.434424	+	0.900709i	$0.643048\pi$
$60$	−1.10717	+	0.948263i	−0.142935	+	0.122420i
$61$	−10.7039	+	1.53899i	−1.37050	+	0.197048i	−0.787945	−	0.615745i	$-0.788855\pi$
$61$	−10.7039	+	1.53899i	−1.37050	+	0.197048i	−0.582553	+	0.812793i	$0.697946\pi$
$62$	−0.647801	+	9.05743i	−0.0822707	+	1.15030i
$63$	2.48392	−	6.65964i	0.312944	−	0.839036i
$64$	0.281733	+	0.959493i	0.0352166	+	0.119937i
$65$	1.15631	−	0.733741i	0.143422	−	0.0910094i
$66$	0.204424	+	0.0293918i	0.0251629	+	0.00361788i
$67$	−1.63335	+	7.50837i	−0.199545	+	0.917294i	0.763048	+	0.646342i	$0.223702\pi$
$67$	−1.63335	+	7.50837i	−0.199545	+	0.917294i	−0.962593	+	0.270952i	$0.912662\pi$
$68$	1.88303	+	1.88303i	0.228351	+	0.228351i
$69$	−1.90635	+	2.47810i	−0.229497	+	0.298328i
$70$	−1.27726	−	6.03865i	−0.152662	−	0.721757i
$71$	7.02619	−	4.51545i	0.833855	−	0.535886i	−0.0526459	−	0.998613i	$-0.516765\pi$
$71$	7.02619	−	4.51545i	0.833855	−	0.535886i	0.886501	+	0.462727i	$0.153129\pi$
$72$	2.06139	−	1.54314i	0.242937	−	0.181860i
$73$	3.36562	+	9.02358i	0.393916	+	1.05613i	0.970923	+	0.239391i	$0.0769477\pi$
$73$	3.36562	+	9.02358i	0.393916	+	1.05613i	−0.577007	+	0.816739i	$0.695780\pi$
$74$	−2.31633	+	0.680136i	−0.269268	+	0.0790642i
$75$	3.25378	−	0.195085i	0.375714	−	0.0225265i
$76$	−2.43603	+	2.11083i	−0.279432	+	0.242129i
$77$	−0.524041	+	0.700037i	−0.0597200	+	0.0797766i
$78$	0.350427	−	0.191348i	0.0396781	−	0.0216659i
$79$	4.91108	−	5.66768i	0.552539	−	0.637664i	−0.408934	−	0.912564i	$-0.634099\pi$
$79$	4.91108	−	5.66768i	0.552539	−	0.637664i	0.961473	+	0.274900i	$0.0886447\pi$
$80$	0.793475	−	2.09055i	0.0887132	−	0.233731i
$81$	−4.50540	−	2.89544i	−0.500600	−	0.321716i
$82$	−7.92485	+	0.566796i	−0.875153	+	0.0625922i
$83$	−0.489934	−	0.897247i	−0.0537772	−	0.0984857i	0.849408	−	0.527737i	$-0.176959\pi$
$83$	−0.489934	−	0.897247i	−0.0537772	−	0.0984857i	−0.903185	+	0.429251i	$0.858777\pi$
$84$	−0.256098	−	1.78120i	−0.0279426	−	0.194345i
$85$	−0.813487	−	5.89883i	−0.0882351	−	0.639818i
$86$	9.50365	−	4.34017i	1.02481	−	0.468013i
$87$	3.49484	+	1.90833i	0.374686	+	0.204594i
$88$	−0.296821	+	0.110709i	−0.0316412	+	0.0118016i
$89$	0.532679	−	3.70486i	0.0564638	−	0.392715i	−0.941918	−	0.335844i	$-0.890979\pi$
$89$	0.532679	−	3.70486i	0.0564638	−	0.392715i	0.998382	−	0.0568709i	$-0.0181123\pi$
$90$	−5.75777	−	0.0331510i	−0.606922	−	0.00349442i
$91$			1.69053i			0.177216i
$92$	0.744772	−	4.73765i	0.0776478	−	0.493934i
$93$	4.18596	−	4.18596i	0.434064	−	0.434064i
$94$	3.75660	+	5.84539i	0.387464	+	0.602905i
$95$	7.19207	−	0.472783i	0.737891	−	0.0485065i
$96$	0.270819	−	0.593012i	0.0276404	−	0.0605240i
$97$	5.77381	−	10.5739i	0.586241	−	1.07362i	−0.401253	−	0.915967i	$-0.631425\pi$
$97$	5.77381	−	10.5739i	0.586241	−	1.07362i	0.987494	−	0.157654i	$-0.0503929\pi$
$98$	0.580286	+	0.216435i	0.0586177	+	0.0218633i
$99$	0.534200	+	0.616500i	0.0536891	+	0.0619605i
$100$	−4.23712	+	2.65459i	−0.423712	+	0.265459i
$101$	−8.74877	−	2.56887i	−0.870535	−	0.255612i	−0.184192	−	0.982890i	$-0.558967\pi$
$101$	−8.74877	−	2.56887i	−0.870535	−	0.255612i	−0.686343	+	0.727278i	$0.740785\pi$
$102$	−0.123850	−	1.73166i	−0.0122630	−	0.171459i
$103$	−0.981625	−	4.51246i	−0.0967224	−	0.444626i	−0.999883	−	0.0153220i	$-0.995123\pi$
$103$	−0.981625	−	4.51246i	−0.0967224	−	0.444626i	0.903160	−	0.429304i	$-0.141241\pi$
$104$	−0.331111	+	0.515218i	−0.0324681	+	0.0505213i
$105$	−1.94872	+	3.52048i	−0.190176	+	0.343564i
$106$	1.63230	−	5.55911i	0.158543	−	0.539949i
$107$	3.96069	+	2.96493i	0.382894	+	0.286631i	0.773336	−	0.633997i	$-0.218587\pi$
$107$	3.96069	+	2.96493i	0.382894	+	0.286631i	−0.390442	+	0.920628i	$0.627678\pi$
$108$	−3.62522	−	0.259281i	−0.348837	−	0.0249493i
$109$	3.31324	+	7.25499i	0.317351	+	0.694902i	0.999335	−	0.0364655i	$-0.0116099\pi$
$109$	3.31324	+	7.25499i	0.317351	+	0.694902i	−0.681984	+	0.731367i	$0.738883\pi$
$110$	0.678521	+	0.203482i	0.0646944	+	0.0194013i
$111$	1.43160	+	0.653790i	0.135882	+	0.0620550i
$112$	1.65419	+	2.20975i	0.156307	+	0.208801i
$113$	5.99568	+	1.30428i	0.564026	+	0.122696i	0.485533	−	0.874218i	$-0.338626\pi$
$113$	5.99568	+	1.30428i	0.564026	+	0.122696i	0.0784929	+	0.996915i	$0.474989\pi$
$114$	2.10137			0.196811
$115$	−7.72471	+	7.43833i	−0.720333	+	0.693628i
$116$	−6.10794			−0.567108
$117$	1.54099	+	0.335222i	0.142465	+	0.0309913i
$118$	2.40766	+	3.21625i	0.221643	+	0.296080i
$119$	6.68646	+	3.05360i	0.612947	+	0.279923i
$120$	−1.28344	+	0.691246i	−0.117161	+	0.0631019i
$121$	4.52787	+	9.91466i	0.411625	+	0.901333i
$122$	−10.7865	−	0.771462i	−0.976559	−	0.0698449i
$123$	4.14648	+	3.10402i	0.373876	+	0.279880i
$124$	−2.55829	+	8.71274i	−0.229741	+	0.782428i
$125$	11.1364	+	0.990090i	0.996071	+	0.0885563i
$126$	3.84276	−	5.97946i	0.342341	−	0.532692i
$127$	−2.85969	−	13.1458i	−0.253757	−	1.16650i	−0.910865	−	0.412704i	$-0.864584\pi$
$127$	−2.85969	−	13.1458i	−0.253757	−	1.16650i	0.657109	−	0.753796i	$-0.271779\pi$
$128$	0.0713392	+	0.997452i	0.00630555	+	0.0881631i
$129$	−6.53528	−	1.91893i	−0.575399	−	0.168952i
$130$	1.28585	−	0.471182i	0.112776	−	0.0413254i
$131$	−7.65537	−	8.83477i	−0.668853	−	0.771897i	0.315344	−	0.948978i	$-0.397880\pi$
$131$	−7.65537	−	8.83477i	−0.668853	−	0.771897i	−0.984196	+	0.177080i	$0.943335\pi$
$132$	0.193505	+	0.0721737i	0.0168425	+	0.00628191i
$133$	−4.26408	+	7.80907i	−0.369742	+	0.677133i
$134$	−3.19204	+	6.98959i	−0.275750	+	0.603809i
$135$	6.11119	+	5.35729i	0.525967	+	0.461082i
$136$	1.43973	+	2.24026i	0.123456	+	0.192101i
$137$	12.9973	−	12.9973i	1.11044	−	1.11044i	0.117346	−	0.993091i	$-0.462561\pi$
$137$	12.9973	−	12.9973i	1.11044	−	1.11044i	0.993091	−	0.117346i	$-0.0374386\pi$
$138$	−2.38954	+	2.01624i	−0.203411	+	0.171634i
$139$			6.25498i			0.530540i	0.964174	+	0.265270i	$0.0854612\pi$
$139$			6.25498i			0.530540i	−0.964174	+	0.265270i	$0.914539\pi$
$140$	0.0355368	−	6.17215i	0.00300341	−	0.521642i
$141$	0.644665	−	4.48374i	0.0542906	−	0.377599i
$142$	7.82544	−	2.91874i	0.656697	−	0.244935i
$143$	−0.170286	−	0.0929832i	−0.0142400	−	0.00777564i
$144$	2.34230	−	1.06969i	0.195191	−	0.0891409i
$145$	10.8863	+	8.24761i	0.904058	+	0.684926i
$146$	1.37061	+	9.53277i	0.113432	+	0.788938i
$147$	−0.193501	−	0.354371i	−0.0159597	−	0.0292281i
$148$	−2.40797	+	0.172221i	−0.197934	+	0.0141565i
$149$	−16.6602	−	10.7069i	−1.36486	−	0.877141i	−0.366283	−	0.930504i	$-0.619370\pi$
$149$	−16.6602	−	10.7069i	−1.36486	−	0.877141i	−0.998575	+	0.0533626i	$0.983006\pi$
$150$	3.22089	+	0.501014i	0.262985	+	0.0409076i
$151$	−3.91387	+	4.51685i	−0.318506	+	0.367576i	−0.892315	−	0.451413i	$-0.850920\pi$
$151$	−3.91387	+	4.51685i	−0.318506	+	0.367576i	0.573808	+	0.818990i	$0.305465\pi$
$152$	−2.82905	+	1.54478i	−0.229466	+	0.125298i
$153$	4.10938	−	5.48949i	0.332224	−	0.443799i
$154$	−0.660868	+	0.572646i	−0.0532543	+	0.0461451i
$155$	16.3246	−	12.0744i	1.31122	−	0.969840i
$156$	0.383093	−	0.112486i	0.0306720	−	0.00900610i
$157$	−4.98794	−	13.3732i	−0.398081	−	1.06730i	−0.969167	−	0.246406i	$-0.920750\pi$
$157$	−4.98794	−	13.3732i	−0.398081	−	1.06730i	0.571085	−	0.820891i	$-0.306522\pi$
$158$	6.00359	−	4.49423i	0.477620	−	0.357542i
$159$	−3.17752	+	2.04207i	−0.251994	+	0.161946i
$160$	1.21972	−	1.87411i	0.0964273	−	0.148161i
$161$	−2.64390	−	12.9713i	−0.208368	−	1.02228i
$162$	−3.78697	−	3.78697i	−0.297532	−	0.297532i
$163$	2.52181	−	11.5926i	0.197524	−	0.908002i	−0.766512	−	0.642230i	$-0.778010\pi$
$163$	2.52181	−	11.5926i	0.197524	−	0.908002i	0.964036	−	0.265772i	$-0.0856268\pi$
$164$	−7.86422	−	1.13070i	−0.614093	−	0.0882932i
$165$	−0.247431	−	0.389928i	−0.0192625	−	0.0303559i
$166$	−0.288014	−	0.980885i	−0.0223542	−	0.0761314i
$167$	−4.67014	+	12.5211i	−0.361386	+	0.968914i	0.621290	+	0.783581i	$0.286609\pi$
$167$	−4.67014	+	12.5211i	−0.361386	+	0.968914i	−0.982676	+	0.185333i	$0.940664\pi$
$168$	0.128376	−	1.79493i	0.00990443	−	0.138482i
$169$	12.4964	−	1.79671i	0.961262	−	0.138209i
$170$	0.458990	−	5.93694i	0.0352029	−	0.455343i
$171$	6.27277	+	5.43539i	0.479691	+	0.415654i
$172$	10.2090	−	2.22084i	0.778432	−	0.169337i
$173$	−11.3976	+	2.47939i	−0.866541	+	0.188504i	−0.623797	−	0.781586i	$-0.714411\pi$
$173$	−11.3976	+	2.47939i	−0.866541	+	0.188504i	−0.242743	+	0.970091i	$0.578047\pi$
$174$	3.00933	+	2.60760i	0.228137	+	0.197682i
$175$	−8.39765	+	10.9528i	−0.634803	+	0.827951i
$176$	−0.313571	+	0.0450847i	−0.0236363	+	0.00339838i
$177$	0.186849	−	2.61250i	0.0140445	−	0.196367i
$178$	1.30803	−	3.50697i	0.0980410	−	0.262858i
$179$	−2.86500	−	9.75728i	−0.214140	−	0.729293i	−0.994572	−	0.104053i	$-0.966819\pi$
$179$	−2.86500	−	9.75728i	−0.214140	−	0.729293i	0.780432	−	0.625241i	$-0.214999\pi$
$180$	−5.61914	−	1.25629i	−0.418826	−	0.0936387i
$181$	17.5918	+	2.52932i	1.30759	+	0.188003i	0.760646	−	0.649167i	$-0.224883\pi$
$181$	17.5918	+	2.52932i	1.30759	+	0.188003i	0.546942	+	0.837170i	$0.315792\pi$
$182$	−0.359348	+	1.65190i	−0.0266367	+	0.122447i
$183$	4.98504	+	4.98504i	0.368505	+	0.368505i
$184$	1.73481	−	4.47107i	0.127892	−	0.329611i
$185$	4.52432	+	2.94455i	0.332635	+	0.216488i
$186$	4.98009	−	3.20051i	0.365158	−	0.234673i
$187$	−0.675358	+	0.505567i	−0.0493871	+	0.0369707i
$188$	2.42822	+	6.51032i	0.177097	+	0.474814i
$189$	−9.62592	+	2.82642i	−0.700183	+	0.205592i
$190$	7.12821	+	1.06681i	0.517134	+	0.0773942i
$191$	−10.0659	+	8.72213i	−0.728341	+	0.631111i	−0.937989	−	0.346666i	$-0.887314\pi$
$191$	−10.0659	+	8.72213i	−0.728341	+	0.631111i	0.209648	+	0.977777i	$0.432768\pi$
$192$	0.390684	−	0.521893i	0.0281952	−	0.0376644i
$193$	−20.4619	+	11.1731i	−1.47288	+	0.804255i	−0.997158	−	0.0753387i	$-0.975996\pi$
$193$	−20.4619	+	11.1731i	−1.47288	+	0.804255i	−0.475725	+	0.879594i	$0.657814\pi$
$194$	7.88951	−	9.10498i	0.566434	−	0.653699i
$195$	−0.834685	−	0.316807i	−0.0597730	−	0.0226870i
$196$	0.521018	+	0.334838i	0.0372155	+	0.0239170i
$197$	−16.2218	+	1.16021i	−1.15576	+	0.0826614i	−0.636025	−	0.771668i	$-0.719423\pi$
$197$	−16.2218	+	1.16021i	−1.15576	+	0.0826614i	−0.519732	+	0.854330i	$0.673968\pi$
$198$	0.390945	+	0.715963i	0.0277833	+	0.0508813i
$199$	−1.06727	−	7.42305i	−0.0756570	−	0.526206i	−0.992042	−	0.125908i	$-0.959816\pi$
$199$	−1.06727	−	7.42305i	−0.0756570	−	0.526206i	0.916385	−	0.400298i	$-0.131093\pi$
$200$	−4.70456	+	1.69326i	−0.332662	+	0.119732i
$201$	4.55669	−	2.08097i	0.321404	−	0.146780i
$202$	−8.00278	−	4.36985i	−0.563073	−	0.307461i
$203$	−15.7968	+	5.89190i	−1.10872	+	0.413531i
$204$	0.247070	−	1.71841i	0.0172983	−	0.120313i
$205$	12.4898	+	12.6344i	0.872323	+	0.882426i
$206$		−	4.61799i		−	0.321751i
$207$	−12.3482	−	0.162104i	−0.858257	−	0.0112670i
$208$	−0.433061	+	0.433061i	−0.0300274	+	0.0300274i
$209$	−0.552068	−	0.859035i	−0.0381874	−	0.0594207i
$210$	−2.65252	+	3.02580i	−0.183041	+	0.208800i
$211$	−9.66421	+	21.1617i	−0.665312	+	1.45683i	0.212177	+	0.977231i	$0.431945\pi$
$211$	−9.66421	+	21.1617i	−0.665312	+	1.45683i	−0.877488	+	0.479598i	$0.840783\pi$
$212$	2.77667	−	5.08510i	0.190703	−	0.349246i
$213$	−5.10160	−	1.90280i	−0.349556	−	0.130378i
$214$	3.23993	+	3.73908i	0.221477	+	0.255598i
$215$	−21.1946	−	9.82711i	−1.44546	−	0.670203i
$216$	−3.48725	−	1.02395i	−0.237278	−	0.0696710i
$217$	1.78813	+	25.0014i	0.121386	+	1.69720i
$218$	1.69536	+	7.79347i	0.114825	+	0.527840i
$219$	3.39444	−	5.28186i	0.229375	−	0.356915i
$220$	0.619761	+	0.343062i	0.0417843	+	0.0231293i
$221$	−0.459487	+	1.56487i	−0.0309085	+	0.105265i
$222$	1.25991	+	0.943158i	0.0845597	+	0.0633006i
$223$	−6.59961	−	0.472013i	−0.441942	−	0.0316083i	−0.151405	−	0.988472i	$-0.548380\pi$
$223$	−6.59961	−	0.472013i	−0.441942	−	0.0316083i	−0.290538	+	0.956864i	$0.593834\pi$
$224$	1.14668	+	2.51087i	0.0766155	+	0.167765i
$225$	8.31871	+	9.82669i	0.554581	+	0.655113i
$226$	5.58141	+	2.54895i	0.371270	+	0.169553i
$227$	8.27641	+	11.0560i	0.549325	+	0.733812i	0.986172	−	0.165724i	$-0.0529960\pi$
$227$	8.27641	+	11.0560i	0.549325	+	0.733812i	−0.436847	+	0.899536i	$0.643905\pi$
$228$	2.05335	+	0.446679i	0.135986	+	0.0295820i
$229$	−22.9134			−1.51416			−0.757080	−	0.653322i	$-0.773375\pi$
$229$	−22.9134			−1.51416			−0.757080	+	0.653322i	$0.773375\pi$
$230$	−9.12931	+	5.62634i	−0.601969	+	0.370990i
$231$	0.570078			0.0375084
$232$	−5.96835	−	1.29834i	−0.391841	−	0.0852399i
$233$	−1.41794	−	1.89415i	−0.0928926	−	0.124090i	0.751687	−	0.659520i	$-0.229240\pi$
$233$	−1.41794	−	1.89415i	−0.0928926	−	0.124090i	−0.844580	+	0.535430i	$0.820150\pi$
$234$	1.43452	+	0.655123i	0.0937775	+	0.0428267i
$235$	4.46308	−	14.8823i	0.291139	−	0.970816i
$236$	1.66897	+	3.65453i	0.108641	+	0.237890i
$237$	−4.87660	−	0.348781i	−0.316769	−	0.0226558i
$238$	5.88456	+	4.40513i	0.381440	+	0.285542i
$239$	5.05977	−	17.2320i	0.327290	−	1.11465i	−0.617392	−	0.786656i	$-0.711811\pi$
$239$	5.05977	−	17.2320i	0.327290	−	1.11465i	0.944681	−	0.327990i	$-0.106371\pi$
$240$	−1.40104	+	0.402635i	−0.0904368	+	0.0259900i
$241$	−0.312423	+	0.486139i	−0.0201249	+	0.0313150i	−0.851170	−	0.524890i	$-0.824107\pi$
$241$	−0.312423	+	0.486139i	−0.0201249	+	0.0313150i	0.831045	+	0.556205i	$0.187743\pi$
$242$	2.31689	+	10.6505i	0.148935	+	0.684643i
$243$	1.02692	+	14.3582i	0.0658768	+	0.921078i
$244$	−10.3760	−	3.04666i	−0.664253	−	0.195042i
$245$	−0.476485	−	1.30032i	−0.0304415	−	0.0830746i
$246$	3.39192	+	3.91448i	0.216261	+	0.249578i
$247$	−1.84964	−	0.689878i	−0.117689	−	0.0438959i
$248$	−4.35185	+	7.96983i	−0.276343	+	0.506084i
$249$	−0.276857	+	0.606233i	−0.0175451	+	0.0384184i
$250$	10.6715	+	3.33468i	0.674922	+	0.210904i
$251$	3.97999	+	6.19299i	0.251215	+	0.390898i	0.943842	−	0.330398i	$-0.107183\pi$
$251$	3.97999	+	6.19299i	0.251215	+	0.390898i	−0.692627	+	0.721296i	$0.743547\pi$
$252$	5.02597	−	5.02597i	0.316606	−	0.316606i
$253$	1.45201	+	0.447134i	0.0912871	+	0.0281111i
$254$		−	13.4532i		−	0.844131i
$255$	−2.76074	+	2.72913i	−0.172884	+	0.170905i
$256$	−0.142315	+	0.989821i	−0.00889468	+	0.0618638i
$257$	−6.60411	+	2.46321i	−0.411953	+	0.153651i	−0.546892	−	0.837203i	$-0.684189\pi$
$257$	−6.60411	+	2.46321i	−0.411953	+	0.153651i	0.134938	+	0.990854i	$0.456916\pi$
$258$	−5.97803	−	3.26425i	−0.372176	−	0.203223i
$259$	−6.06154	+	2.76821i	−0.376646	+	0.172008i
$260$	1.35662	−	0.187087i	0.0841341	−	0.0116026i
$261$	2.23831	+	15.5678i	0.138548	+	0.963624i
$262$	−5.60246	−	10.2601i	−0.346121	−	0.633873i
$263$	−17.8175	+	1.27433i	−1.09867	+	0.0785787i	−0.608882	−	0.793261i	$-0.708382\pi$
$263$	−17.8175	+	1.27433i	−1.09867	+	0.0785787i	−0.489792	+	0.871839i	$0.662927\pi$
$264$	0.173741	+	0.111657i	0.0106930	+	0.00687200i
$265$	−11.8154	+	5.31390i	−0.725813	+	0.326430i
$266$	−5.82657	+	6.72422i	−0.357250	+	0.412288i
$267$	−2.14165	+	1.16943i	−0.131067	+	0.0715679i
$268$	−4.60484	+	6.15134i	−0.281285	+	0.375753i
$269$	13.3924	−	11.6046i	0.816550	−	0.707545i	−0.142803	−	0.989751i	$-0.545612\pi$
$269$	13.3924	−	11.6046i	0.816550	−	0.707545i	0.959354	+	0.282206i	$0.0910662\pi$
$270$	4.83275	+	6.53388i	0.294112	+	0.397639i
$271$	27.9409	−	8.20418i	1.69729	−	0.498368i	0.717188	−	0.696880i	$-0.245429\pi$
$271$	27.9409	−	8.20418i	1.69729	−	0.498368i	0.980098	+	0.198512i	$0.0636109\pi$
$272$	0.930625	+	2.49510i	0.0564274	+	0.151288i
$273$	0.882275	−	0.660463i	0.0533977	−	0.0399730i
$274$	15.4631	−	9.93752i	0.934159	−	0.600348i
$275$	−0.641373	−	1.44832i	−0.0386762	−	0.0873368i
$276$	−2.76351	+	1.46223i	−0.166344	+	0.0880160i
$277$	−16.6398	−	16.6398i	−0.999786	−	0.999786i	0.000213691	−	1.00000i	$-0.499932\pi$
$277$	−16.6398	−	16.6398i	−0.999786	−	0.999786i	−1.00000		0.000213691i	$0.999932\pi$
$278$	−1.32959	+	6.11203i	−0.0797436	+	0.366575i
$279$	23.1444	+	3.32766i	1.38562	+	0.199222i
$280$	1.34671	−	6.02354i	0.0804813	−	0.359975i
$281$	−6.85360	−	23.3412i	−0.408852	−	1.39242i	−0.864666	−	0.502346i	$-0.832470\pi$
$281$	−6.85360	−	23.3412i	−0.408852	−	1.39242i	0.455815	−	0.890075i	$-0.349348\pi$
$282$	1.58302	−	4.24424i	0.0942675	−	0.252741i
$283$	−0.159029	+	2.22352i	−0.00945332	+	0.132175i	−0.999987	−	0.00509507i	$-0.998378\pi$
$283$	−0.159029	+	2.22352i	−0.00945332	+	0.132175i	0.990534	+	0.137270i	$0.0438327\pi$
$284$	8.26703	−	1.18862i	0.490558	−	0.0705316i
$285$	−3.05657	−	3.56878i	−0.181055	−	0.211396i
$286$	−0.146629	−	0.127055i	−0.00867038	−	0.00751292i
$287$	−21.4298	+	4.66176i	−1.26496	+	0.275175i
$288$	2.51615	−	0.547354i	0.148265	−	0.0322532i
$289$	−7.48827	−	6.48862i	−0.440487	−	0.381684i
$290$	8.88436	+	10.3732i	0.521707	+	0.609134i
$291$	−7.77419	+	1.11776i	−0.455731	+	0.0655243i
$292$	−0.687054	+	9.60626i	−0.0402068	+	0.562164i
$293$	8.94896	−	23.9931i	0.522804	−	1.40169i	−0.360442	−	0.932782i	$-0.617374\pi$
$293$	8.94896	−	23.9931i	0.522804	−	1.40169i	0.883246	−	0.468910i	$-0.155353\pi$
$294$	−0.113752	−	0.387405i	−0.00663417	−	0.0225939i
$295$	1.96011	−	8.76717i	0.114122	−	0.510445i
$296$	−2.38955	−	0.343565i	−0.138890	−	0.0199693i
$297$	0.244744	−	1.12507i	0.0142015	−	0.0652833i
$298$	−14.0036	−	14.0036i	−0.811205	−	0.811205i
$299$	2.76521	−	0.990222i	0.159916	−	0.0572660i
$300$	3.04078	+	1.17421i	0.175560	+	0.0677933i
$301$	24.2611	−	15.5917i	1.39839	−	0.898688i
$302$	−4.78455	+	3.58167i	−0.275320	+	0.206102i
$303$	2.07733	+	5.56953i	0.119339	+	0.319961i
$304$	−3.09277	+	0.908118i	−0.177382	+	0.0520841i
$305$	14.3793	+	19.4409i	0.823359	+	1.11318i
$306$	5.18234	−	4.49053i	0.296255	−	0.256706i
$307$	7.20516	−	9.62496i	0.411220	−	0.549326i	−0.546339	−	0.837564i	$-0.683979\pi$
$307$	7.20516	−	9.62496i	0.411220	−	0.549326i	0.957559	+	0.288239i	$0.0930697\pi$
$308$	−0.767490	+	0.419081i	−0.0437318	+	0.0238794i
$309$	−1.97151	+	2.27525i	−0.112155	+	0.129434i
$310$	18.5181	−	8.32843i	1.05176	−	0.473023i
$311$	−14.2553	−	9.16132i	−0.808344	−	0.519491i	0.0699851	−	0.997548i	$-0.477705\pi$
$311$	−14.2553	−	9.16132i	−0.808344	−	0.519491i	−0.878329	+	0.478057i	$0.841341\pi$
$312$	0.398248	−	0.0284833i	0.0225464	−	0.00161255i
$313$	8.53594	+	15.6324i	0.482480	+	0.883596i	0.999616	+	0.0276933i	$0.00881619\pi$
$313$	8.53594	+	15.6324i	0.482480	+	0.883596i	−0.517136	+	0.855903i	$0.673002\pi$
$314$	−2.03128	−	14.1278i	−0.114632	−	0.797280i
$315$	−15.7445	+	2.17127i	−0.887102	+	0.122337i
$316$	6.82171	−	3.11537i	0.383751	−	0.175253i
$317$	17.3153	+	9.45486i	0.972523	+	0.531038i	0.885234	−	0.465145i	$-0.153998\pi$
$317$	17.3153	+	9.45486i	0.972523	+	0.531038i	0.0872888	+	0.996183i	$0.472180\pi$
$318$	−3.53897	+	1.31997i	−0.198456	+	0.0740202i
$319$	0.275374	−	1.91527i	0.0154180	−	0.107235i
$320$	1.59022	−	1.57201i	0.0888958	−	0.0878780i
$321$		−	3.22540i		−	0.180024i
$322$	0.173770	−	13.2369i	0.00968385	−	0.737661i
$323$	−6.06963	+	6.06963i	−0.337723	+	0.337723i
$324$	−2.89544	−	4.50540i	−0.160858	−	0.250300i
$325$	−2.67056	−	1.49841i	−0.148136	−	0.0831168i
$326$	4.92836	−	10.7916i	0.272957	−	0.597692i
$327$	2.49189	−	4.56356i	0.137802	−	0.252366i
$328$	−7.44415	−	2.77653i	−0.411035	−	0.153308i
$329$	12.5601	+	14.4951i	0.692462	+	0.799143i
$330$	−0.158891	−	0.433612i	−0.00874668	−	0.0238696i
$331$	17.2261	+	5.05804i	0.946831	+	0.278015i	0.718467	−	0.695561i	$-0.244844\pi$
$331$	17.2261	+	5.05804i	0.946831	+	0.278015i	0.228364	+	0.973576i	$0.426662\pi$
$332$	−0.0729297	−	1.01969i	−0.00400254	−	0.0559628i
$333$	1.32138	+	6.07428i	0.0724111	+	0.332869i
$334$	−7.22497	+	11.2423i	−0.395333	+	0.615150i
$335$	16.5135	−	4.74570i	0.902229	−	0.259285i
$336$	0.506983	−	1.72662i	0.0276582	−	0.0941951i
$337$	14.6813	+	10.9903i	0.799743	+	0.598680i	0.919034	−	0.394179i	$-0.128971\pi$
$337$	14.6813	+	10.9903i	0.799743	+	0.598680i	−0.119291	+	0.992859i	$0.538062\pi$
$338$	12.5927	+	0.900651i	0.684955	+	0.0489890i
$339$	−1.66172	−	3.63866i	−0.0902523	−	0.197625i
$340$	1.71049	−	5.70370i	0.0927643	−	0.309327i
$341$	−2.61672	−	1.19502i	−0.141703	−	0.0647138i
$342$	4.97404	+	6.64455i	0.268966	+	0.359296i
$343$	−17.2101	−	3.74384i	−0.929260	−	0.202148i
$344$	10.4478			0.563308
$345$	6.89993	+	1.12543i	0.371480	+	0.0605913i
$346$	−11.6641			−0.627067
$347$	25.5769	+	5.56392i	1.37304	+	0.298687i	0.837784	−	0.546002i	$-0.183851\pi$
$347$	25.5769	+	5.56392i	1.37304	+	0.298687i	0.535258	+	0.844689i	$0.320214\pi$
$348$	2.38627	+	3.18769i	0.127918	+	0.170878i
$349$	−20.3982	−	9.31555i	−1.09189	−	0.498650i	−0.213671	−	0.976906i	$-0.568542\pi$
$349$	−20.3982	−	9.31555i	−1.09189	−	0.498650i	−0.878221	+	0.478256i	$0.841269\pi$
$350$	−10.5339	+	8.91740i	−0.563061	+	0.476655i
$351$	−0.924674	−	2.02475i	−0.0493554	−	0.108073i
$352$	−0.315988	−	0.0225999i	−0.0168422	−	0.00120458i
$353$	10.0726	+	7.54025i	0.536110	+	0.401327i	0.832739	−	0.553666i	$-0.186771\pi$
$353$	10.0726	+	7.54025i	0.536110	+	0.401327i	−0.296629	+	0.954993i	$0.595862\pi$
$354$	0.737905	−	2.51307i	0.0392192	−	0.133568i
$355$	−16.3395	−	9.04455i	−0.867210	−	0.480035i
$356$	2.02360	−	3.14878i	0.107250	−	0.166885i
$357$	−1.01864	−	4.68261i	−0.0539121	−	0.247830i
$358$	−0.725463	−	10.1433i	−0.0383419	−	0.536090i
$359$	20.2928	+	5.95851i	1.07101	+	0.314478i	0.769279	−	0.638914i	$-0.220616\pi$
$359$	20.2928	+	5.95851i	1.07101	+	0.314478i	0.301736	+	0.953392i	$0.402434\pi$
$360$	−5.22368	−	2.42202i	−0.275312	−	0.127652i
$361$	5.63843	+	6.50709i	0.296759	+	0.342479i
$362$	16.6521	+	6.21092i	0.875216	+	0.326439i
$363$	3.40542	−	6.23656i	0.178738	−	0.327335i
$364$	−0.702272	+	1.53776i	−0.0368090	+	0.0806006i
$365$	14.1960	−	16.1937i	0.743052	−	0.847617i
$366$	3.81147	+	5.93077i	0.199229	+	0.310006i
$367$	13.6323	−	13.6323i	0.711598	−	0.711598i	−0.255271	−	0.966869i	$-0.582165\pi$
$367$	13.6323	−	13.6323i	0.711598	−	0.711598i	0.966869	+	0.255271i	$0.0821648\pi$
$368$	2.64556	−	4.00013i	0.137909	−	0.208521i
$369$			20.4586i			1.06503i
$370$	3.79502	+	3.83897i	0.197294	+	0.199579i
$371$	2.27600	−	15.8299i	0.118164	−	0.821849i
$372$	5.54660	−	2.06877i	0.287578	−	0.107261i
$373$	−0.0427868	−	0.0233634i	−0.00221542	−	0.00120971i	0.478141	−	0.878283i	$-0.341311\pi$
$373$	−0.0427868	−	0.0233634i	−0.00221542	−	0.00120971i	−0.480356	+	0.877073i	$0.659493\pi$
$374$	−0.767390	+	0.350455i	−0.0396808	+	0.0181216i
$375$	−3.83410	−	6.19882i	−0.197992	−	0.320106i
$376$	0.988864	+	6.87770i	0.0509968	+	0.354690i
$377$	−1.79275	−	3.28318i	−0.0923314	−	0.169092i
$378$	−10.0067	+	0.715696i	−0.514691	+	0.0368114i
$379$	11.0138	+	7.07816i	0.565742	+	0.363580i	0.792032	−	0.610480i	$-0.209023\pi$
$379$	11.0138	+	7.07816i	0.565742	+	0.363580i	−0.226290	+	0.974060i	$0.572660\pi$
$380$	6.73854	+	2.55764i	0.345680	+	0.131204i
$381$	−5.74345	+	6.62830i	−0.294246	+	0.339578i
$382$	−11.6899	+	6.38315i	−0.598105	+	0.326590i
$383$	−16.1948	+	21.6338i	−0.827517	+	1.10543i	0.165353	+	0.986234i	$0.447124\pi$
$383$	−16.1948	+	21.6338i	−0.827517	+	1.10543i	−0.992870	+	0.119199i	$0.961967\pi$
$384$	0.492692	−	0.426920i	0.0251426	−	0.0217862i
$385$	1.93380	+	0.289412i	0.0985557	+	0.0147498i
$386$	−22.3693	+	6.56823i	−1.13857	+	0.334314i
$387$	−9.40164	−	25.2068i	−0.477912	−	1.28133i
$388$	9.64461	−	7.21987i	0.489631	−	0.366533i
$389$	10.3405	−	6.64544i	0.524285	−	0.336937i	−0.251580	−	0.967836i	$-0.580950\pi$
$389$	10.3405	−	6.64544i	0.524285	−	0.336937i	0.775865	+	0.630899i	$0.217314\pi$
$390$	−0.748267	−	0.486992i	−0.0378900	−	0.0246598i
$391$	1.07823	−	12.7257i	0.0545287	−	0.643568i
$392$	0.437936	+	0.437936i	0.0221191	+	0.0221191i
$393$	−1.61997	+	7.44688i	−0.0817167	+	0.375646i
$394$	−16.0977	−	2.31450i	−0.810991	−	0.116603i
$395$	−16.3652	−	3.65884i	−0.823422	−	0.184096i
$396$	0.229822	+	0.782702i	0.0115490	+	0.0393323i
$397$	2.76946	−	7.42520i	0.138995	−	0.372660i	−0.848738	−	0.528814i	$-0.822637\pi$
$397$	2.76946	−	7.42520i	0.138995	−	0.372660i	0.987733	+	0.156154i	$0.0499096\pi$
$398$	0.535000	−	7.48027i	0.0268171	−	0.374952i
$399$	5.74140	−	0.825489i	0.287430	−	0.0413262i
$400$	−4.95697	+	0.654539i	−0.247849	+	0.0327269i
$401$	10.5343	+	9.12804i	0.526059	+	0.455832i	0.876948	−	0.480584i	$-0.159575\pi$
$401$	10.5343	+	9.12804i	0.526059	+	0.455832i	−0.350890	+	0.936417i	$0.614121\pi$
$402$	4.89489	−	1.06482i	0.244135	−	0.0531083i
$403$	−5.43422	+	1.18214i	−0.270698	+	0.0588867i
$404$	−6.89101	−	5.97109i	−0.342841	−	0.297073i
$405$	−0.923077	+	11.9398i	−0.0458681	+	0.593294i
$406$	−16.6882	+	2.39940i	−0.828222	+	0.119080i
$407$	0.0545589	−	0.762833i	0.00270438	−	0.0378122i
$408$	0.606697	−	1.62662i	0.0300360	−	0.0805296i
$409$	−0.412691	−	1.40550i	−0.0204062	−	0.0694973i	0.948660	−	0.316296i	$-0.102439\pi$
$409$	−0.412691	−	1.40550i	−0.0204062	−	0.0694973i	−0.969067	+	0.246799i	$0.920621\pi$
$410$	9.51869	+	15.0006i	0.470095	+	0.740825i
$411$	−11.8611	−	1.70536i	−0.585063	−	0.0841193i
$412$	0.981625	−	4.51246i	0.0483612	−	0.222313i
$413$	7.84169	+	7.84169i	0.385864	+	0.385864i
$414$	−12.0315	−	2.78319i	−0.591317	−	0.136786i
$415$	−1.24691	+	1.91589i	−0.0612086	+	0.0940474i
$416$	−0.515218	+	0.331111i	−0.0252607	+	0.0162340i
$417$	3.26443	−	2.44372i	0.159860	−	0.119669i
$418$	−0.356851	−	0.956754i	−0.0174541	−	0.0467964i
$419$	0.132001	−	0.0387591i	0.00644868	−	0.00189350i	−0.278507	−	0.960434i	$-0.589839\pi$
$419$	0.132001	−	0.0387591i	0.00644868	−	0.00189350i	0.284955	+	0.958541i	$0.408021\pi$
$420$	−3.23508	+	2.39281i	−0.157856	+	0.116757i
$421$	25.0172	−	21.6775i	1.21926	−	1.05650i	0.222599	−	0.974910i	$-0.428546\pi$
$421$	25.0172	−	21.6775i	1.21926	−	1.05650i	0.996666	−	0.0815888i	$-0.0259994\pi$
$422$	−13.9416	+	18.6238i	−0.678666	+	0.906591i
$423$	15.7036	−	8.57479i	0.763533	−	0.416921i
$424$	3.79413	−	4.37866i	0.184259	−	0.212647i
$425$	−10.7504	+	7.85613i	−0.521471	+	0.381078i
$426$	−4.58054	−	2.94374i	−0.221928	−	0.142625i
$427$	−29.7740	+	2.12948i	−1.44086	+	0.103053i
$428$	2.37109	+	4.34232i	0.114611	+	0.209894i
$429$	0.0180008	+	0.125198i	0.000869085	+	0.00604462i
$430$	−18.6213	−	14.1078i	−0.898000	−	0.680337i
$431$	−28.8071	+	13.1558i	−1.38759	+	0.633691i	−0.962456	−	0.271439i	$-0.912501\pi$
$431$	−28.8071	+	13.1558i	−1.38759	+	0.633691i	−0.425135	+	0.905130i	$0.639773\pi$
$432$	−3.18990	−	1.74182i	−0.153474	−	0.0838033i
$433$	34.7592	−	12.9645i	1.67042	−	0.623034i	0.676836	−	0.736134i	$-0.263351\pi$
$433$	34.7592	−	12.9645i	1.67042	−	0.623034i	0.993584	+	0.113100i	$0.0360781\pi$
$434$	−3.56715	+	24.8101i	−0.171229	+	1.19092i
$435$	0.0512639	−	8.90368i	0.00245792	−	0.426899i
$436$			7.97574i			0.381969i
$437$	15.2710	+	2.40065i	0.730512	+	0.114839i
$438$	4.43961	−	4.43961i	0.212133	−	0.212133i
$439$	−5.37599	−	8.36521i	−0.256582	−	0.399250i	0.688934	−	0.724824i	$-0.258079\pi$
$439$	−5.37599	−	8.36521i	−0.256582	−	0.399250i	−0.945517	+	0.325574i	$0.894442\pi$
$440$	0.532675	+	0.466962i	0.0253943	+	0.0222615i
$441$	0.662497	−	1.45067i	0.0315475	−	0.0690793i
$442$	−0.781624	+	1.43144i	−0.0371781	+	0.0680865i
$443$	36.2330	+	13.5142i	1.72148	+	0.642079i	0.998794	−	0.0490953i	$-0.0156338\pi$
$443$	36.2330	+	13.5142i	1.72148	+	0.642079i	0.722688	+	0.691175i	$0.242907\pi$
$444$	1.03064	+	1.18942i	0.0489118	+	0.0564472i
$445$	−7.85852	+	2.87965i	−0.372530	+	0.136508i
$446$	−6.34845	−	1.86407i	−0.300608	−	0.0882664i
$447$	0.921042	+	12.8778i	0.0435638	+	0.609101i
$448$	0.586747	+	2.69723i	0.0277212	+	0.127432i
$449$	10.0638	−	15.6596i	0.474941	−	0.739022i	−0.518287	−	0.855207i	$-0.673430\pi$
$449$	10.0638	−	15.6596i	0.474941	−	0.739022i	0.993228	+	0.116185i	$0.0370665\pi$
$450$	6.03979	+	11.3704i	0.284718	+	0.536005i
$451$	0.709112	−	2.41501i	0.0333908	−	0.113718i
$452$	4.91204	+	3.67711i	0.231043	+	0.172957i
$453$	3.88640	+	0.277961i	0.182599	+	0.0130597i
$454$	5.73715	+	12.5626i	0.269258	+	0.589592i
$455$	3.32813	−	1.79250i	0.156025	−	0.0840336i
$456$	1.91147	+	0.872941i	0.0895130	+	0.0408792i
$457$	−2.96732	−	3.96387i	−0.138805	−	0.185422i	0.725752	−	0.687956i	$-0.241492\pi$
$457$	−2.96732	−	3.96387i	−0.138805	−	0.185422i	−0.864557	+	0.502534i	$0.832401\pi$
$458$	−22.3898	−	4.87059i	−1.04620	−	0.227588i
$459$	−9.67863			−0.451760
$460$	−10.1166	+	3.55718i	−0.471691	+	0.165855i
$461$	19.7385			0.919315			0.459658	−	0.888096i	$-0.347972\pi$
$461$	19.7385			0.919315			0.459658	+	0.888096i	$0.347972\pi$
$462$	0.557050	+	0.121179i	0.0259163	+	0.00563775i
$463$	−8.50050	−	11.3553i	−0.395052	−	0.527727i	0.558280	−	0.829653i	$-0.311462\pi$
$463$	−8.50050	−	11.3553i	−0.395052	−	0.527727i	−0.953332	+	0.301925i	$0.902371\pi$
$464$	−5.55597	−	2.53733i	−0.257930	−	0.117793i
$465$	−12.6793	−	3.80241i	−0.587989	−	0.176333i
$466$	−0.982909	−	2.15227i	−0.0455324	−	0.0997020i
$467$	−21.7205	−	1.55348i	−1.00510	−	0.0718864i	−0.440929	−	0.897542i	$-0.645351\pi$
$467$	−21.7205	−	1.55348i	−1.00510	−	0.0718864i	−0.564174	+	0.825656i	$0.690805\pi$
$468$	1.26248	+	0.945081i	0.0583582	+	0.0436864i
$469$	−5.97560	+	20.3510i	−0.275928	+	0.939723i
$470$	7.52455	−	13.5935i	0.347082	−	0.627023i
$471$	−5.03066	+	7.82786i	−0.231801	+	0.360689i
$472$	0.854001	+	3.92578i	0.0393086	+	0.180699i
$473$	0.236119	+	3.30138i	0.0108568	+	0.151798i
$474$	−4.69102	−	1.37741i	−0.215465	−	0.0632664i
$475$	−8.55663	−	13.6576i	−0.392605	−	0.626655i
$476$	4.81371	+	5.55531i	0.220636	+	0.254627i
$477$	−13.9784	−	5.21366i	−0.640025	−	0.238717i
$478$	8.60707	−	15.7627i	0.393678	−	0.720968i
$479$	−12.6195	+	27.6329i	−0.576600	+	1.26258i	0.366608	+	0.930376i	$0.380519\pi$
$479$	−12.6195	+	27.6329i	−0.576600	+	1.26258i	−0.943208	+	0.332203i	$0.892208\pi$
$480$	−1.45461	+	0.0956212i	−0.0663935	+	0.00436449i
$481$	−0.799341	−	1.24380i	−0.0364468	−	0.0567123i
$482$	−0.408619	+	0.408619i	−0.0186121	+	0.0186121i
$483$	−5.73669	+	6.44751i	−0.261029	+	0.293372i
$484$			10.8996i			0.495438i
$485$	−26.9388	−	0.155103i	−1.22323	−	0.00704288i
$486$	−2.04860	+	14.2483i	−0.0929265	+	0.646318i
$487$	−18.6538	+	6.95752i	−0.845286	+	0.315275i	−0.734533	−	0.678573i	$-0.762599\pi$
$487$	−18.6538	+	6.95752i	−0.845286	+	0.315275i	−0.110753	+	0.993848i	$0.535326\pi$
$488$	−9.49122	−	5.18260i	−0.429648	−	0.234605i
$489$	−7.03532	+	3.21292i	−0.318148	+	0.145293i
$490$	−0.189193	−	1.37189i	−0.00854685	−	0.0619757i
$491$	4.55533	+	31.6830i	0.205579	+	1.42984i	0.787362	+	0.616491i	$0.211446\pi$
$491$	4.55533	+	31.6830i	0.205579	+	1.42984i	−0.581782	+	0.813344i	$0.697644\pi$
$492$	2.48232	+	4.54603i	0.111912	+	0.204951i
$493$	−16.2240	+	1.16037i	−0.730693	+	0.0522602i
$494$	−1.66072	−	1.06728i	−0.0747194	−	0.0480192i
$495$	0.647274	−	1.70536i	0.0290928	−	0.0766501i
$496$	−5.94651	+	6.86264i	−0.267006	+	0.308142i
$497$	20.2342	−	11.0487i	0.907630	−	0.495603i
$498$	−0.399394	+	0.533528i	−0.0178973	+	0.0239080i
$499$	25.6825	−	22.2540i	1.14971	−	0.996227i	0.149735	−	0.988726i	$-0.452158\pi$
$499$	25.6825	−	22.2540i	1.14971	−	0.996227i	0.999972	−	0.00750072i	$-0.00238758\pi$
$500$	9.71874	+	5.52685i	0.434635	+	0.247168i
$501$	8.35923	−	2.45449i	0.373463	−	0.109659i
$502$	2.57262	+	6.89747i	0.114822	+	0.307849i
$503$	−15.4671	+	11.5785i	−0.689645	+	0.516261i	−0.885657	−	0.464340i	$-0.846292\pi$
$503$	−15.4671	+	11.5785i	−0.689645	+	0.516261i	0.196012	+	0.980601i	$0.437201\pi$
$504$	5.97946	−	3.84276i	0.266346	−	0.171170i
$505$	4.21916	+	19.9474i	0.187750	+	0.887647i
$506$	1.32378	+	0.745562i	0.0588493	+	0.0331443i
$507$	−5.81984	−	5.81984i	−0.258468	−	0.258468i
$508$	2.85969	−	13.1458i	0.126878	−	0.583250i
$509$	−4.65529	−	0.669329i	−0.206342	−	0.0296675i	0.0383687	−	0.999264i	$-0.487784\pi$
$509$	−4.65529	−	0.669329i	−0.206342	−	0.0296675i	−0.244711	+	0.969596i	$0.578693\pi$
$510$	−3.27777	+	2.07993i	−0.145142	+	0.0921006i
$511$	7.48959	+	25.5072i	0.331320	+	1.12837i
$512$	−0.349464	+	0.936950i	−0.0154443	+	0.0414077i
$513$	0.835748	−	11.6853i	0.0368992	−	0.515918i
$514$	−6.97678	+	1.00311i	−0.307733	+	0.0442453i
$515$	−7.84278	+	6.71714i	−0.345594	+	0.295993i
$516$	−5.14754	−	4.46037i	−0.226608	−	0.196357i
$517$	−2.15092	+	0.467904i	−0.0945974	+	0.0205784i
$518$	−6.51144	+	1.41648i	−0.286096	+	0.0622364i
$519$	5.74682	+	4.97965i	0.252257	+	0.218582i
$520$	1.36539	+	0.105559i	0.0598761	+	0.00462908i
$521$	−18.1659	+	2.61186i	−0.795861	+	0.114428i	−0.528238	−	0.849096i	$-0.677147\pi$
$521$	−18.1659	+	2.61186i	−0.795861	+	0.114428i	−0.267623	+	0.963524i	$0.586238\pi$
$522$	−1.12202	+	15.6878i	−0.0491093	+	0.686638i
$523$	4.95911	−	13.2959i	0.216847	−	0.581389i	−0.782291	−	0.622914i	$-0.785949\pi$
$523$	4.95911	−	13.2959i	0.216847	−	0.581389i	0.999137	+	0.0415246i	$0.0132215\pi$
$524$	−3.29347	−	11.2165i	−0.143876	−	0.489997i
$525$	8.99699	+	0.103606i	0.392661	+	0.00452172i
$526$	−17.6812	−	2.54217i	−0.770937	−	0.110844i
$527$	−5.14017	+	23.6290i	−0.223909	+	1.02929i
$528$	0.146036	+	0.146036i	0.00635542	+	0.00635542i
$529$	−19.6686	+	11.9225i	−0.855156	+	0.518371i
$530$	−12.6749	+	2.68092i	−0.550563	+	0.116452i
$531$	8.70301	−	5.59308i	0.377678	−	0.242719i
$532$	−7.12275	+	5.33202i	−0.308810	+	0.231172i
$533$	−1.70046	−	4.55911i	−0.0736550	−	0.197477i
$534$	−2.34129	+	0.687464i	−0.101317	+	0.0297495i
$535$	1.63745	−	10.9411i	0.0707929	−	0.473026i
$536$	−5.80716	+	5.03193i	−0.250831	+	0.217346i
$537$	−3.97294	+	5.30723i	−0.171445	+	0.229024i
$538$	15.5531	−	8.49263i	0.670542	−	0.366143i
$539$	−0.128485	+	0.148280i	−0.00553425	+	0.00638686i
$540$	3.33343	+	7.41184i	0.143448	+	0.318955i
$541$	−21.1489	−	13.5916i	−0.909263	−	0.584348i	0.000260505	−	1.00000i	$-0.499917\pi$
$541$	−21.1489	−	13.5916i	−0.909263	−	0.584348i	−0.909524	+	0.415652i	$0.863553\pi$
$542$	29.0462	−	2.07743i	1.24764	−	0.0892332i
$543$	−5.55280	−	10.1692i	−0.238293	−	0.436402i
$544$	0.378985	+	2.63590i	0.0162489	+	0.113013i
$545$	10.7697	−	14.2153i	0.461324	−	0.608917i
$546$	1.00250	−	0.457828i	0.0429032	−	0.0195932i
$547$	2.60982	+	1.42507i	0.111588	+	0.0609315i	0.534074	−	0.845438i	$-0.320661\pi$
$547$	2.60982	+	1.42507i	0.111588	+	0.0609315i	−0.422486	+	0.906370i	$0.638842\pi$
$548$	17.2221	−	6.42350i	0.735691	−	0.274398i
$549$	−3.96290	+	27.5626i	−0.169132	+	1.17634i
$550$	−0.318854	−	1.55155i	−0.0135960	−	0.0661584i
$551$		−	19.6879i		−	0.838734i
$552$	−3.01118	+	0.841389i	−0.128164	+	0.0358119i
$553$	14.6376	−	14.6376i	0.622456	−	0.622456i
$554$	−12.7225	−	19.7965i	−0.540525	−	0.841074i
$555$	−0.230841	−	3.51160i	−0.00979865	−	0.149059i
$556$	−2.59841	+	5.68973i	−0.110197	+	0.241298i
$557$	3.81764	−	6.99149i	0.161759	−	0.296239i	−0.784211	−	0.620494i	$-0.786932\pi$
$557$	3.81764	−	6.99149i	0.161759	−	0.296239i	0.945970	+	0.324256i	$0.105114\pi$
$558$	21.9081	+	8.17132i	0.927446	+	0.345919i
$559$	4.19023	+	4.83579i	0.177228	+	0.204532i
$560$	2.59633	−	5.59962i	0.109715	−	0.236627i
$561$	0.527703	+	0.154948i	0.0222797	+	0.00654190i
$562$	−1.73544	−	24.2646i	−0.0732052	−	1.02354i
$563$	−3.22035	−	14.8037i	−0.135721	−	0.623901i	−0.993875	−	0.110509i	$-0.964752\pi$
$563$	−3.22035	−	14.8037i	−0.135721	−	0.623901i	0.858154	−	0.513393i	$-0.171612\pi$
$564$	2.44902	−	3.81075i	0.103122	−	0.160462i
$565$	−3.78959	−	13.1866i	−0.159429	−	0.554763i
$566$	−0.628039	+	2.13890i	−0.0263984	+	0.0899049i
$567$	−11.8345	−	8.85917i	−0.497001	−	0.372050i
$568$	8.33076	+	0.595828i	0.349551	+	0.0250004i
$569$	8.90868	+	19.5073i	0.373471	+	0.817788i	0.999285	+	0.0378154i	$0.0120399\pi$
$569$	8.90868	+	19.5073i	0.373471	+	0.817788i	−0.625813	+	0.779973i	$0.715233\pi$
$570$	−2.22812	−	4.13694i	−0.0933256	−	0.173277i
$571$	−13.1374	−	5.99965i	−0.549783	−	0.251077i	0.121101	−	0.992640i	$-0.461358\pi$
$571$	−13.1374	−	5.99965i	−0.549783	−	0.251077i	−0.670883	+	0.741563i	$0.734085\pi$
$572$	−0.116271	−	0.155320i	−0.00486153	−	0.00649425i
$573$	8.48459	+	1.84571i	0.354449	+	0.0771056i
$574$	−21.9310			−0.915380
$575$	22.8344	+	7.32056i	0.952260	+	0.305289i
$576$	2.57499			0.107291
$577$	38.9854	+	8.48076i	1.62298	+	0.353059i	0.929904	−	0.367802i	$-0.119889\pi$
$577$	38.9854	+	8.48076i	1.62298	+	0.353059i	0.693080	+	0.720860i	$0.256253\pi$
$578$	−5.93788	−	7.93208i	−0.246983	−	0.329931i
$579$	13.8253	+	6.31380i	0.574560	+	0.262393i
$580$	6.47634	+	12.0246i	0.268916	+	0.499295i
$581$	−1.17224	−	2.56685i	−0.0486328	−	0.106491i
$582$	−7.83413	−	0.560308i	−0.324735	−	0.0232255i
$583$	1.46935	+	1.09994i	0.0608543	+	0.0455550i
$584$	−2.71331	+	9.24069i	−0.112278	+	0.382382i
$585$	−0.973991	−	3.38917i	−0.0402696	−	0.140125i
$586$	13.8445	−	21.5425i	0.571913	−	0.889914i
$587$	4.40434	+	20.2464i	0.181786	+	0.835659i	0.974202	+	0.225677i	$0.0724595\pi$
$587$	4.40434	+	20.2464i	0.181786	+	0.835659i	−0.792416	+	0.609981i	$0.791177\pi$
$588$	−0.0288039	−	0.402731i	−0.00118785	−	0.0166083i
$589$	−28.0841	−	8.24623i	−1.15718	−	0.339780i
$590$	3.77892	−	8.15016i	0.155576	−	0.335537i
$591$	6.94311	+	8.01277i	0.285601	+	0.329601i
$592$	−2.26191	−	0.843648i	−0.0929639	−	0.0346737i
$593$	−17.2067	+	31.5118i	−0.706596	+	1.29403i	0.239737	+	0.970838i	$0.422939\pi$
$593$	−17.2067	+	31.5118i	−0.706596	+	1.29403i	−0.946332	+	0.323195i	$0.895243\pi$
$594$	0.478302	−	1.04734i	0.0196250	−	0.0429727i
$595$	−1.07817	−	16.4013i	−0.0442007	−	0.672389i
$596$	−10.7069	−	16.6602i	−0.438570	−	0.682429i
$597$	−3.45707	+	3.45707i	−0.141488	+	0.141488i
$598$	2.91251	−	0.379804i	0.119101	−	0.0155313i
$599$			45.2263i			1.84790i	0.382517	+	0.923948i	$0.375057\pi$
$599$			45.2263i			1.84790i	−0.382517	+	0.923948i	$0.624943\pi$
$600$	2.72170	+	1.79374i	0.111113	+	0.0732293i
$601$	5.82478	−	40.5122i	0.237598	−	1.65253i	−0.426209	−	0.904625i	$-0.640151\pi$
$601$	5.82478	−	40.5122i	0.237598	−	1.65253i	0.663807	−	0.747904i	$-0.268940\pi$
$602$	27.0209	−	10.0783i	1.10129	−	0.410760i
$603$	17.3659	+	9.48251i	0.707195	+	0.386158i
$604$	−5.43655	+	2.48279i	−0.221210	+	0.101023i
$605$	14.7179	−	19.4266i	0.598367	−	0.789805i
$606$	0.845965	+	5.88382i	0.0343650	+	0.239014i
$607$	0.212897	+	0.389892i	0.00864123	+	0.0158252i	0.881964	−	0.471317i	$-0.156221\pi$
$607$	0.212897	+	0.389892i	0.00864123	+	0.0158252i	−0.873323	+	0.487142i	$0.838039\pi$
$608$	−3.21512	+	0.229950i	−0.130390	+	0.00932570i
$609$	9.24650	+	5.94236i	0.374687	+	0.240797i
$610$	9.91828	+	22.0531i	0.401579	+	0.892906i
$611$	−2.78676	+	3.21609i	−0.112740	+	0.130109i
$612$	6.01844	−	3.28632i	0.243281	−	0.132842i
$613$	22.0177	−	29.4122i	0.889285	−	1.18795i	−0.0920719	−	0.995752i	$-0.529349\pi$
$613$	22.0177	−	29.4122i	0.889285	−	1.18795i	0.981357	−	0.192193i	$-0.0615601\pi$
$614$	9.08643	−	7.87344i	0.366698	−	0.317746i
$615$	1.71426	−	11.4544i	0.0691256	−	0.461885i
$616$	−0.839033	+	0.246362i	−0.0338056	+	0.00992622i
$617$	−3.59098	−	9.62779i	−0.144567	−	0.387600i	0.844404	−	0.535707i	$-0.179955\pi$
$617$	−3.59098	−	9.62779i	−0.144567	−	0.387600i	−0.988971	+	0.148107i	$0.952682\pi$
$618$	−2.41010	+	1.80418i	−0.0969483	+	0.0725746i
$619$	−15.7999	+	10.1540i	−0.635053	+	0.408124i	−0.818177	−	0.574966i	$-0.805015\pi$
$619$	−15.7999	+	10.1540i	−0.635053	+	0.408124i	0.183124	+	0.983090i	$0.441379\pi$
$620$	19.8653	−	4.20179i	0.797808	−	0.168748i
$621$	10.2615	+	14.0896i	0.411782	+	0.565397i
$622$	−11.9821	−	11.9821i	−0.480440	−	0.480440i
$623$	2.19617	−	10.0956i	0.0879877	−	0.404473i
$624$	0.395202	+	0.0568214i	0.0158207	+	0.00227468i
$625$	−9.85894	−	22.9739i	−0.394358	−	0.918957i
$626$	5.01796	+	17.0896i	0.200558	+	0.683038i
$627$	−0.232640	+	0.623731i	−0.00929074	+	0.0249094i
$628$	1.01823	−	14.2367i	0.0406319	−	0.568108i
$629$	−6.36338	+	0.914915i	−0.253724	+	0.0364801i
$630$	−15.8462	−	1.22509i	−0.631329	−	0.0488086i
$631$	3.05021	+	2.64302i	0.121427	+	0.105217i	0.713458	−	0.700698i	$-0.247128\pi$
$631$	3.05021	+	2.64302i	0.121427	+	0.105217i	−0.592031	+	0.805915i	$0.701674\pi$
$632$	7.32803	−	1.59412i	0.291494	−	0.0634105i
$633$	14.8198	−	3.22384i	0.589033	−	0.128136i
$634$	14.9098	+	12.9194i	0.592144	+	0.513095i
$635$	−22.8478	+	19.5685i	−0.906686	+	0.776553i
$636$	−3.73868	+	0.537541i	−0.148248	+	0.0213149i
$637$	−0.0270594	+	0.378340i	−0.00107213	+	0.0149904i
$638$	0.676201	−	1.81296i	0.0267711	−	0.0717760i
$639$	−6.05907	−	20.6353i	−0.239693	−	0.816320i
$640$	1.88803	−	1.19806i	0.0746309	−	0.0473574i
$641$	−37.1849	−	5.34639i	−1.46872	−	0.211170i	−0.638936	−	0.769260i	$-0.720625\pi$
$641$	−37.1849	−	5.34639i	−1.46872	−	0.211170i	−0.829780	+	0.558090i	$0.811534\pi$
$642$	0.685609	−	3.15169i	0.0270588	−	0.124387i
$643$	−12.6523	−	12.6523i	−0.498957	−	0.498957i	0.412156	−	0.911113i	$-0.364776\pi$
$643$	−12.6523	−	12.6523i	−0.498957	−	0.498957i	−0.911113	+	0.412156i	$0.864776\pi$
$644$	2.98350	−	12.8974i	0.117566	−	0.508230i
$645$	3.15169	+	14.9006i	0.124098	+	0.586710i
$646$	−7.22111	+	4.64073i	−0.284111	+	0.182587i
$647$	2.42792	−	1.81752i	0.0954512	−	0.0714539i	−0.550486	−	0.834844i	$-0.685558\pi$
$647$	2.42792	−	1.81752i	0.0954512	−	0.0714539i	0.645937	+	0.763390i	$0.276467\pi$
$648$	−1.87158	−	5.01791i	−0.0735227	−	0.197122i
$649$	−1.22120	+	0.358576i	−0.0479363	+	0.0140754i
$650$	−2.29102	−	2.03183i	−0.0898611	−	0.0796951i
$651$	12.3494	−	10.7008i	0.484012	−	0.419399i
$652$	7.10966	−	9.49739i	0.278436	−	0.371947i
$653$	−13.5202	+	7.38259i	−0.529087	+	0.288903i	−0.721504	−	0.692410i	$-0.756549\pi$
$653$	−13.5202	+	7.38259i	−0.529087	+	0.288903i	0.192418	+	0.981313i	$0.438367\pi$
$654$	3.40500	−	3.92958i	0.133146	−	0.153659i
$655$	−9.27578	+	24.4387i	−0.362435	+	0.954898i
$656$	−6.68384	−	4.29544i	−0.260960	−	0.167709i
$657$	24.7361	−	1.76916i	0.965046	−	0.0690215i
$658$	9.19191	+	16.8337i	0.358338	+	0.656247i
$659$	4.87682	+	33.9190i	0.189974	+	1.32130i	0.832069	+	0.554673i	$0.187156\pi$
$659$	4.87682	+	33.9190i	0.189974	+	1.32130i	−0.642095	+	0.766625i	$0.721934\pi$
$660$	−0.0630892	−	0.457478i	−0.00245574	−	0.0178073i
$661$	−34.1974	+	15.6174i	−1.33012	+	0.607447i	−0.948473	−	0.316859i	$-0.897372\pi$
$661$	−34.1974	+	15.6174i	−1.33012	+	0.607447i	−0.381651	+	0.924306i	$0.624645\pi$
$662$	15.7573	+	8.60411i	0.612423	+	0.334408i
$663$	0.996209	−	0.371567i	0.0386895	−	0.0144304i
$664$	0.145488	−	1.01189i	0.00564602	−	0.0392689i
$665$	19.8949	+	0.114547i	0.771491	+	0.00444194i
$666$			6.21634i			0.240878i
$667$	18.8903	+	22.3878i	0.731437	+	0.866859i
$668$	−9.44957	+	9.44957i	−0.365615	+	0.365615i
$669$	2.33202	+	3.62869i	0.0901611	+	0.140293i
$670$	17.1449	−	1.12705i	0.662365	−	0.0435417i
$671$	1.42314	−	3.11624i	0.0549397	−	0.120301i
$672$	0.862417	−	1.57940i	0.0332684	−	0.0609266i
$673$	17.2579	+	6.43685i	0.665241	+	0.248122i	0.659322	−	0.751860i	$-0.270843\pi$
$673$	17.2579	+	6.43685i	0.665241	+	0.248122i	0.00591883	+	0.999982i	$0.498116\pi$
$674$	12.0097	+	13.8599i	0.462595	+	0.533863i
$675$	4.06703	−	17.7114i	0.156540	−	0.681713i
$676$	12.1135	+	3.55685i	0.465905	+	0.136802i
$677$	0.469401	+	6.56309i	0.0180406	+	0.252240i	0.998467	+	0.0553533i	$0.0176285\pi$
$677$	0.469401	+	6.56309i	0.0180406	+	0.252240i	−0.980426	+	0.196887i	$0.936917\pi$
$678$	−0.850292	−	3.90873i	−0.0326553	−	0.150114i
$679$	17.9791	−	27.9761i	0.689975	−	1.07362i
$680$	2.88381	−	5.20976i	0.110589	−	0.199785i
$681$	2.53658	−	8.63880i	0.0972019	−	0.331039i
$682$	−2.30290	−	1.72393i	−0.0881827	−	0.0660127i
$683$	−33.6263	−	2.40500i	−1.28667	−	0.0920248i	−0.588820	−	0.808264i	$-0.700407\pi$
$683$	−33.6263	−	2.40500i	−1.28667	−	0.0920248i	−0.697855	+	0.716239i	$0.745862\pi$
$684$	3.44797	+	7.55001i	0.131837	+	0.288682i
$685$	−39.3690	−	11.8064i	−1.50421	−	0.451099i
$686$	−16.0210	−	7.31656i	−0.611685	−	0.279347i
$687$	8.95189	+	11.9583i	0.341536	+	0.456239i
$688$	10.2090	+	2.22084i	0.389216	+	0.0846687i
$689$	3.54836			0.135182
$690$	6.50302	+	2.56640i	0.247566	+	0.0977012i
$691$	−11.7111			−0.445510			−0.222755	−	0.974874i	$-0.571505\pi$
$691$	−11.7111			−0.445510			−0.222755	+	0.974874i	$0.571505\pi$
$692$	−11.3976	−	2.47939i	−0.433270	−	0.0942522i
$693$	1.34940	+	1.80259i	0.0512596	+	0.0684748i
$694$	23.8097	+	10.8735i	0.903805	+	0.412754i
$695$	12.3141	−	6.63225i	0.467100	−	0.251576i
$696$	1.65415	+	3.62208i	0.0627003	+	0.137294i
$697$	−21.1039	−	1.50938i	−0.799368	−	0.0571719i
$698$	−17.9519	−	13.4386i	−0.679489	−	0.508659i
$699$	−0.434576	+	1.48003i	−0.0164372	+	0.0559799i
$700$	−12.1887	+	6.47447i	−0.460690	+	0.244712i
$701$	7.90767	−	12.3046i	0.298669	−	0.464737i	−0.659191	−	0.751976i	$-0.729101\pi$
$701$	7.90767	−	12.3046i	0.298669	−	0.464737i	0.957859	+	0.287239i	$0.0927373\pi$
$702$	−0.473150	−	2.17503i	−0.0178579	−	0.0820914i
$703$	−0.555127	−	7.76169i	−0.0209370	−	0.292738i
$704$	−0.303963	−	0.0892515i	−0.0114560	−	0.00336379i
$705$	−9.51063	+	3.48504i	−0.358191	+	0.131254i
$706$	8.23961	+	9.50902i	0.310102	+	0.357877i
$707$	−23.5820	−	8.79561i	−0.886891	−	0.330793i
$708$	1.25523	−	2.29879i	0.0471746	−	0.0863938i
$709$	0.106146	−	0.232428i	0.00398641	−	0.00872901i	−0.907628	−	0.419775i	$-0.862109\pi$
$709$	0.106146	−	0.232428i	0.00398641	−	0.00872901i	0.911615	+	0.411046i	$0.134836\pi$
$710$	−14.0435	−	12.3111i	−0.527044	−	0.462026i
$711$	−10.4403	−	16.2454i	−0.391542	−	0.609251i
$712$	2.64667	−	2.64667i	0.0991883	−	0.0991883i
$713$	39.8475	−	17.5693i	1.49230	−	0.657976i
$714$		−	4.79212i		−	0.179341i
$715$	−0.00249783	+	0.433831i	−9.34136e−5	+	0.0162244i
$716$	1.44723	−	10.0657i	0.0540855	−	0.376173i
$717$	−10.9700	+	4.09161i	−0.409683	+	0.152804i
$718$	18.5625	+	10.1359i	0.692746	+	0.378268i
$719$	−11.2789	+	5.15090i	−0.420632	+	0.192096i	−0.614475	−	0.788936i	$-0.710632\pi$
$719$	−11.2789	+	5.15090i	−0.420632	+	0.192096i	0.193843	+	0.981033i	$0.437905\pi$
$720$	−4.58946	−	3.47704i	−0.171039	−	0.129582i
$721$	−1.81410	−	12.6174i	−0.0675607	−	0.469895i
$722$	4.12639	+	7.55692i	0.153568	+	0.281239i
$723$	0.375771	−	0.0268757i	0.0139751	−	0.000999517i
$724$	14.9513	+	9.60865i	0.555662	+	0.357103i
$725$	4.69404	−	30.1768i	0.174332	−	1.12074i
$726$	4.65327	−	5.37016i	0.172699	−	0.199305i
$727$	27.0585	−	14.7751i	1.00355	−	0.547977i	0.108568	−	0.994089i	$-0.465373\pi$
$727$	27.0585	−	14.7751i	1.00355	−	0.547977i	0.894977	+	0.446112i	$0.147192\pi$
$728$	−1.01310	+	1.35334i	−0.0375479	+	0.0501581i
$729$	−5.05020	+	4.37602i	−0.187044	+	0.162075i
$730$	17.3138	−	12.8060i	0.640812	−	0.473973i
$731$	26.6955	−	7.83852i	0.987370	−	0.289918i
$732$	2.46369	+	6.60542i	0.0910607	+	0.244143i
$733$	−37.1002	+	27.7729i	−1.37033	+	1.02581i	−0.375228	+	0.926932i	$0.622436\pi$
$733$	−37.1002	+	27.7729i	−1.37033	+	1.02581i	−0.995099	+	0.0988817i	$0.968473\pi$
$734$	16.2185	−	10.4230i	0.598634	−	0.384719i
$735$	−0.492474	+	0.756689i	−0.0181652	+	0.0279109i
$736$	3.43539	−	3.34636i	0.126630	−	0.123348i
$737$	−1.72127	−	1.72127i	−0.0634039	−	0.0634039i
$738$	−4.34878	+	19.9910i	−0.160081	+	0.735880i
$739$	−11.5958	−	1.66723i	−0.426559	−	0.0613300i	−0.0743078	−	0.997235i	$-0.523675\pi$
$739$	−11.5958	−	1.66723i	−0.426559	−	0.0613300i	−0.352251	+	0.935905i	$0.614584\pi$
$740$	2.89226	+	4.55793i	0.106322	+	0.167553i
$741$	0.362580	+	1.23484i	0.0133197	+	0.0453628i
$742$	5.58888	−	14.9844i	0.205174	−	0.550093i
$743$	1.40207	−	19.6035i	0.0514369	−	0.719182i	−0.904660	−	0.426133i	$-0.859875\pi$
$743$	1.40207	−	19.6035i	0.0514369	−	0.719182i	0.956097	−	0.293049i	$-0.0946700\pi$
$744$	5.85959	−	0.842482i	0.214823	−	0.0308869i
$745$	−3.41338	+	44.1514i	−0.125057	+	1.61758i
$746$	−0.0368427	−	0.0319244i	−0.00134891	−	0.00116884i
$747$	−2.57225	+	0.559558i	−0.0941135	+	0.0204731i
$748$	−0.824348	+	0.179326i	−0.0301411	+	0.00655680i
$749$	10.3210	+	8.94322i	0.377122	+	0.326778i
$750$	−2.42882	−	6.87216i	−0.0886880	−	0.250936i
$751$	40.7610	−	5.86055i	1.48739	−	0.213855i	0.649780	−	0.760122i	$-0.274861\pi$
$751$	40.7610	−	5.86055i	1.48739	−	0.213855i	0.837611	+	0.546267i	$0.183952\pi$
$752$	−0.495695	+	6.93072i	−0.0180761	+	0.252737i
$753$	1.67716	−	4.49663i	0.0611190	−	0.163866i
$754$	−1.05389	−	3.58923i	−0.0383805	−	0.130712i
$755$	13.0422	+	2.91590i	0.474655	+	0.106121i
$756$	−9.93018	−	1.42774i	−0.361157	−	0.0519266i
$757$	−2.57161	+	11.8215i	−0.0934669	+	0.429660i	0.906505	+	0.422195i	$0.138740\pi$
$757$	−2.57161	+	11.8215i	−0.0934669	+	0.429660i	−0.999972	+	0.00746575i	$0.997624\pi$
$758$	9.25755	+	9.25755i	0.336250	+	0.336250i
$759$	−0.333921	−	0.932481i	−0.0121206	−	0.0338469i
$760$	6.04088	+	3.93156i	0.219126	+	0.142613i
$761$	−24.3584	+	15.6542i	−0.882991	+	0.567464i	−0.901701	−	0.432361i	$-0.857681\pi$
$761$	−24.3584	+	15.6542i	−0.882991	+	0.567464i	0.0187095	+	0.999825i	$0.494044\pi$
$762$	−7.02114	+	5.25596i	−0.254349	+	0.190403i
$763$	7.69364	+	20.6275i	0.278529	+	0.746764i
$764$	−12.7795	+	3.75241i	−0.462348	+	0.135758i
$765$	−15.1643	−	2.26949i	−0.548268	−	0.0820536i
$766$	−20.4233	+	17.6969i	−0.737924	+	0.639415i
$767$	−1.47455	+	1.96976i	−0.0532428	+	0.0711241i
$768$	0.572181	−	0.312434i	0.0206468	−	0.0112740i
$769$	24.3410	−	28.0910i	0.877757	−	1.01299i	−0.122033	−	0.992526i	$-0.538942\pi$
$769$	24.3410	−	28.0910i	0.877757	−	1.01299i	0.999791	−	0.0204598i	$-0.00651301\pi$
$770$	1.82809	+	0.693858i	0.0658798	+	0.0250049i
$771$	3.86565	+	2.48430i	0.139218	+	0.0894700i
$772$	−23.2543	+	1.66318i	−0.836941	+	0.0598592i
$773$	−5.16562	−	9.46013i	−0.185794	−	0.340257i	0.768135	−	0.640288i	$-0.221185\pi$
$773$	−5.16562	−	9.46013i	−0.185794	−	0.340257i	−0.953930	+	0.300031i	$0.903003\pi$
$774$	−3.82870	−	26.6292i	−0.137620	−	0.957166i
$775$	−41.0800	−	19.3353i	−1.47564	−	0.694546i
$776$	10.9589	−	5.00476i	0.393401	−	0.179660i
$777$	3.81286	+	2.08198i	0.136785	+	0.0746905i
$778$	11.5168	−	4.29554i	0.412897	−	0.154003i
$779$	3.64464	−	25.3490i	0.130583	−	0.908223i
$780$	−0.627649	−	0.634919i	−0.0224734	−	0.0227337i
$781$			2.64589i			0.0946773i
$782$	3.75864	−	12.2057i	0.134409	−	0.436475i
$783$	15.6972	−	15.6972i	0.560971	−	0.560971i
$784$	0.334838	+	0.521018i	0.0119585	+	0.0186078i
$785$	−21.0388	+	23.9995i	−0.750908	+	0.856579i
$786$	−3.16590	+	6.93235i	−0.112924	+	0.247269i
$787$	12.0079	−	21.9909i	0.428036	−	0.783890i	−0.571284	−	0.820752i	$-0.693554\pi$
$787$	12.0079	−	21.9909i	0.428036	−	0.783890i	0.999320	+	0.0368623i	$0.0117363\pi$
$788$	−15.2379	−	5.68343i	−0.542826	−	0.202464i
$789$	7.62607	+	8.80096i	0.271495	+	0.313322i
$790$	−15.2135	−	7.05389i	−0.541270	−	0.250966i
$791$	16.2509	+	4.77171i	0.577817	+	0.169662i
$792$	0.0581946	+	0.813667i	0.00206786	+	0.0289124i
$793$	−1.40781	−	6.47159i	−0.0499927	−	0.229813i
$794$	4.28451	−	6.66682i	0.152052	−	0.236597i
$795$	7.38936	+	4.09030i	0.262074	+	0.145068i
$796$	2.11282	−	7.19560i	0.0748869	−	0.255041i
$797$	39.0653	+	29.2439i	1.38376	+	1.03587i	0.993338	+	0.115237i	$0.0367628\pi$
$797$	39.0653	+	29.2439i	1.38376	+	1.03587i	0.390425	+	0.920635i	$0.372328\pi$
$798$	5.78567	+	0.413799i	0.204810	+	0.0146483i
$799$	7.68671	+	16.8315i	0.271936	+	0.595457i
$800$	−4.98282	−	0.414100i	−0.176169	−	0.0146406i
$801$	−8.76713	−	4.00381i	−0.309771	−	0.141468i
$802$	8.35327	+	11.1587i	0.294964	+	0.394026i
$803$	−2.98127	−	0.648535i	−0.105207	−	0.0228863i
$804$	5.00937			0.176667
$805$	−22.7331	+	18.9587i	−0.801235	+	0.668206i
$806$	−5.56132			−0.195889
$807$	−11.2886	−	2.45568i	−0.397376	−	0.0864439i
$808$	−5.46428	−	7.29943i	−0.192233	−	0.256793i
$809$	−26.4368	−	12.0733i	−0.929468	−	0.424474i	−0.107627	−	0.994191i	$-0.534325\pi$
$809$	−26.4368	−	12.0733i	−0.929468	−	0.424474i	−0.821841	+	0.569718i	$0.807053\pi$
$810$	−3.43997	+	11.4707i	−0.120868	+	0.403040i
$811$	−6.40557	−	14.0262i	−0.224930	−	0.492528i	0.763197	−	0.646166i	$-0.223628\pi$
$811$	−6.40557	−	14.0262i	−0.224930	−	0.492528i	−0.988127	+	0.153637i	$0.950901\pi$
$812$	−16.8169	−	1.20277i	−0.590156	−	0.0422088i
$813$	−15.1977	−	11.3769i	−0.533008	−	0.399005i
$814$	0.215464	−	0.733802i	0.00755200	−	0.0257198i
$815$	−25.4961	+	7.32715i	−0.893090	+	0.256659i
$816$	0.938595	−	1.46048i	0.0328574	−	0.0511271i
$817$	7.15851	+	32.9071i	0.250444	+	1.15127i
$818$	−0.104500	−	1.46110i	−0.00365375	−	0.0510861i
$819$	4.17678	+	1.22641i	0.145948	+	0.0428543i
$820$	6.11256	+	16.6811i	0.213460	+	0.582529i
$821$	34.3007	+	39.5851i	1.19710	+	1.38153i	0.905147	+	0.425099i	$0.139761\pi$
$821$	34.3007	+	39.5851i	1.19710	+	1.38153i	0.291956	+	0.956432i	$0.405694\pi$
$822$	−11.2275	−	4.18764i	−0.391604	−	0.146061i
$823$	1.64702	−	3.01630i	0.0574116	−	0.105142i	−0.847397	−	0.530959i	$-0.821832\pi$
$823$	1.64702	−	3.01630i	0.0574116	−	0.105142i	0.904809	+	0.425818i	$0.140014\pi$
$824$	1.91838	−	4.20067i	0.0668301	−	0.146337i
$825$	−0.505292	+	0.900562i	−0.0175920	+	0.0313535i
$826$	5.99561	+	9.32935i	0.208614	+	0.324610i
$827$	−27.7239	+	27.7239i	−0.964054	+	0.964054i	−0.999376	−	0.0353224i	$-0.988754\pi$
$827$	−27.7239	+	27.7239i	−0.964054	+	0.964054i	0.0353224	+	0.999376i	$0.488754\pi$
$828$	−11.1650	−	5.27707i	−0.388009	−	0.183391i
$829$			5.54125i			0.192455i	0.995359	+	0.0962277i	$0.0306777\pi$
$829$			5.54125i			0.192455i	−0.995359	+	0.0962277i	$0.969322\pi$
$830$	−1.62567	+	1.60706i	−0.0564278	+	0.0557818i
$831$	−2.18328	+	15.1851i	−0.0757372	+	0.526764i
$832$	−0.573827	+	0.214026i	−0.0198939	+	0.00742003i
$833$	1.44755	+	0.790422i	0.0501546	+	0.0273865i
$834$	3.70927	−	1.69397i	0.128442	−	0.0586573i
$835$	29.6020	−	4.08231i	1.02442	−	0.141274i
$836$	−0.145323	−	1.01074i	−0.00502610	−	0.0349573i
$837$	−15.8167	−	28.9661i	−0.546706	−	1.00122i
$838$	0.137223	−	0.00981441i	0.00474030	−	0.000339033i
$839$	−17.9179	−	11.5151i	−0.618595	−	0.397547i	0.193477	−	0.981105i	$-0.438024\pi$
$839$	−17.9179	−	11.5151i	−0.618595	−	0.397547i	−0.812071	+	0.583558i	$0.801660\pi$
$840$	−3.66978	+	1.65046i	−0.126619	+	0.0569464i
$841$	5.43986	−	6.27793i	0.187581	−	0.216480i
$842$	29.0534	−	15.8644i	1.00125	−	0.546722i
$843$	−9.50402	+	12.6959i	−0.327336	+	0.437270i
$844$	−17.5817	+	15.2347i	−0.605189	+	0.524399i
$845$	−16.7873	−	22.6964i	−0.577501	−	0.780781i
$846$	17.1674	−	5.04080i	0.590227	−	0.173306i
$847$	10.5141	+	28.1895i	0.361270	+	0.968602i
$848$	4.63818	−	3.47210i	0.159276	−	0.119232i
$849$	1.22257	−	0.785698i	0.0419585	−	0.0269651i
$850$	−12.1747	+	5.39143i	−0.417587	+	0.184925i
$851$	8.07851	+	8.29344i	0.276928	+	0.284295i
$852$	−3.85013	−	3.85013i	−0.131903	−	0.131903i
$853$	−11.6244	+	53.4367i	−0.398013	+	1.82964i	0.144394	+	0.989520i	$0.453877\pi$
$853$	−11.6244	+	53.4367i	−0.398013	+	1.82964i	−0.542407	+	0.840116i	$0.682487\pi$
$854$	−29.5462	−	4.24811i	−1.01105	−	0.145367i
$855$	4.04946	−	18.1124i	0.138489	−	0.619429i
$856$	1.39387	+	4.74710i	0.0476416	+	0.162253i
$857$	8.04263	−	21.5631i	0.274731	−	0.736583i	−0.724166	−	0.689626i	$-0.757775\pi$
$857$	8.04263	−	21.5631i	0.274731	−	0.736583i	0.998897	−	0.0469568i	$-0.0149523\pi$
$858$	−0.00902337	+	0.126163i	−0.000308053	+	0.00430714i
$859$	54.0648	−	7.77335i	1.84467	−	0.265223i	0.870684	−	0.491842i	$-0.163676\pi$
$859$	54.0648	−	7.77335i	1.84467	−	0.265223i	0.973983	+	0.226619i	$0.0727673\pi$
$860$	−15.1969	−	17.7436i	−0.518211	−	0.605052i
$861$	10.8052	+	9.36276i	0.368240	+	0.319082i
$862$	−30.9453	+	6.73173i	−1.05400	+	0.229284i
$863$	45.7977	−	9.96267i	1.55897	−	0.339133i	0.651301	−	0.758819i	$-0.274223\pi$
$863$	45.7977	−	9.96267i	1.55897	−	0.339133i	0.907669	+	0.419686i	$0.137860\pi$
$864$	−2.74675	−	2.38008i	−0.0934465	−	0.0809718i
$865$	16.9662	+	19.8093i	0.576867	+	0.673537i
$866$	36.7206	−	5.27963i	1.24782	−	0.179409i
$867$	−0.460818	+	6.44307i	−0.0156502	+	0.218818i
$868$	−8.75940	+	23.4849i	−0.297313	+	0.797128i
$869$	0.669335	+	2.27954i	0.0227056	+	0.0773282i
$870$	1.94271	−	8.68931i	0.0658639	−	0.294595i
$871$	−4.65808	−	0.669731i	−0.157833	−	0.0226930i
$872$	−1.69536	+	7.79347i	−0.0574123	+	0.263920i
$873$	−21.9362	−	21.9362i	−0.742429	−	0.742429i
$874$	14.4117	+	5.59187i	0.487484	+	0.189148i
$875$	30.4667	+	4.91896i	1.02996	+	0.166291i
$876$	5.28186	−	3.39444i	0.178457	−	0.114688i
$877$	1.43747	−	1.07608i	0.0485399	−	0.0363365i	−0.574732	−	0.818342i	$-0.694894\pi$
$877$	1.43747	−	1.07608i	0.0485399	−	0.0363365i	0.623272	+	0.782005i	$0.285803\pi$
$878$	−3.47498	−	9.31678i	−0.117275	−	0.314426i
$879$	−16.0180	+	4.70332i	−0.540275	+	0.158639i
$880$	0.421242	+	0.569519i	0.0142001	+	0.0191985i
$881$	−36.2934	+	31.4484i	−1.22276	+	1.05952i	−0.226418	+	0.974030i	$0.572702\pi$
$881$	−36.2934	+	31.4484i	−1.22276	+	1.05952i	−0.996339	+	0.0854948i	$0.972753\pi$
$882$	0.955718	−	1.27669i	0.0321807	−	0.0429884i
$883$	−4.43813	+	2.42340i	−0.149355	+	0.0815540i	−0.552189	−	0.833719i	$-0.686207\pi$
$883$	−4.43813	+	2.42340i	−0.149355	+	0.0815540i	0.402834	+	0.915273i	$0.368025\pi$
$884$	−1.06804	+	1.23258i	−0.0359219	+	0.0414561i
$885$	−5.34131	+	2.40222i	−0.179546	+	0.0807499i
$886$	32.5323	+	20.9072i	1.09294	+	0.702393i
$887$	−21.2290	+	1.51833i	−0.712802	+	0.0509806i	−0.423031	−	0.906115i	$-0.639034\pi$
$887$	−21.2290	+	1.51833i	−0.712802	+	0.0509806i	−0.289771	+	0.957096i	$0.593579\pi$
$888$	0.754254	+	1.38131i	0.0253111	+	0.0463538i
$889$	−5.28488	−	36.7572i	−0.177249	−	1.23280i
$890$	−8.29105	+	1.14339i	−0.277916	+	0.0383265i
$891$	1.54330	−	0.704802i	0.0517025	−	0.0236118i
$892$	−5.80713	−	3.17093i	−0.194437	−	0.106171i
$893$	−20.9849	+	7.82698i	−0.702234	+	0.261920i
$894$	−1.83739	+	12.7793i	−0.0614515	+	0.427405i
$895$	−16.1712	+	15.9861i	−0.540545	+	0.534356i
$896$			2.76031i			0.0922156i
$897$	−1.59711	−	1.05628i	−0.0533261	−	0.0352682i
$898$	13.1625	−	13.1625i	0.439239	−	0.439239i
$899$	−29.9859	−	46.6589i	−1.00008	−	1.55616i
$900$	3.48481	+	12.3944i	0.116160	+	0.413146i
$901$	6.40941	−	14.0346i	0.213528	−	0.467562i
$902$	1.20625	−	2.20909i	0.0401639	−	0.0735546i
$903$	−17.6156	−	6.57027i	−0.586210	−	0.218645i
$904$	4.01816	+	4.63720i	0.133642	+	0.154231i
$905$	−13.6734	−	37.3146i	−0.454520	−	1.24038i
$906$	3.73850	+	1.09772i	0.124203	+	0.0364694i
$907$	2.00472	+	28.0297i	0.0665657	+	0.930710i	0.915527	+	0.402256i	$0.131774\pi$
$907$	2.00472	+	28.0297i	0.0665657	+	0.930710i	−0.848962	+	0.528454i	$0.822772\pi$
$908$	2.93566	+	13.4950i	0.0974234	+	0.447848i
$909$	−12.6938	+	19.7519i	−0.421025	+	0.655128i
$910$	3.63309	−	1.04409i	0.120436	−	0.0346112i
$911$	1.96962	−	6.70790i	0.0652563	−	0.222243i	−0.920408	−	0.390958i	$-0.872144\pi$
$911$	1.96962	−	6.70790i	0.0652563	−	0.222243i	0.985665	+	0.168715i	$0.0539619\pi$
$912$	1.68223	+	1.25930i	0.0557043	+	0.0416997i
$913$	0.323033	+	0.0231038i	0.0106908	+	0.000764624i
$914$	−2.05692	−	4.50403i	−0.0680370	−	0.148980i
$915$	4.52827	−	15.0997i	0.149700	−	0.499181i
$916$	−20.8428	−	9.51857i	−0.688664	−	0.314502i
$917$	−19.3377	−	25.8321i	−0.638586	−	0.853051i
$918$	−9.45744	−	2.05734i	−0.312142	−	0.0679024i
$919$	−7.24774			−0.239081			−0.119540	−	0.992829i	$-0.538142\pi$
$919$	−7.24774			−0.239081			−0.119540	+	0.992829i	$0.538142\pi$
$920$	−10.6416	+	1.32544i	−0.350842	+	0.0436986i
$921$	−7.83814			−0.258275
$922$	19.2875	+	4.19573i	0.635198	+	0.138179i
$923$	3.06539	+	4.09488i	0.100898	+	0.134785i
$924$	0.518561	+	0.236819i	0.0170594	+	0.00779078i
$925$	0.999686	−	12.0291i	0.0328695	−	0.395515i
$926$	−5.89248	−	12.9027i	−0.193639	−	0.424010i
$927$	−11.8610	−	0.848316i	−0.389567	−	0.0278624i
$928$	−4.88966	−	3.66035i	−0.160511	−	0.120157i
$929$	13.1265	−	44.7047i	0.430666	−	1.46671i	−0.403388	−	0.915029i	$-0.632167\pi$
$929$	13.1265	−	44.7047i	0.430666	−	1.46671i	0.834053	−	0.551684i	$-0.186014\pi$
$930$	−11.5813	−	6.41069i	−0.379765	−	0.210215i
$931$	−1.07929	+	1.67941i	−0.0353724	+	0.0550406i
$932$	−0.502948	−	2.31202i	−0.0164746	−	0.0757326i
$933$	0.788088	+	11.0189i	0.0258009	+	0.360743i
$934$	−20.8939	−	6.13499i	−0.683668	−	0.200743i
$935$	1.71140	+	0.793509i	0.0559687	+	0.0259505i
$936$	1.03274	+	1.19184i	0.0337561	+	0.0389566i
$937$	−42.8398	−	15.9784i	−1.39952	−	0.521992i	−0.467365	−	0.884064i	$-0.654797\pi$
$937$	−42.8398	−	15.9784i	−1.39952	−	0.521992i	−0.932150	+	0.362072i	$0.882069\pi$
$938$	−10.1650	+	18.6157i	−0.331898	+	0.607825i
$939$	4.82359	−	10.5622i	0.157412	−	0.344684i
$940$	10.2421	−	11.6834i	0.334061	−	0.381071i
$941$	5.27804	+	8.21278i	0.172059	+	0.267729i	0.916564	−	0.399888i	$-0.130951\pi$
$941$	5.27804	+	8.21278i	0.172059	+	0.267729i	−0.744505	+	0.667617i	$0.767315\pi$
$942$	−6.57963	+	6.57963i	−0.214376	+	0.214376i
$943$	20.1777	+	32.3222i	0.657075	+	1.05256i
$944$			4.01760i			0.130762i
$945$	15.7709	+	15.9535i	0.513026	+	0.518968i
$946$	−0.471035	+	3.27612i	−0.0153147	+	0.106516i
$947$	48.6375	−	18.1408i	1.58051	−	0.589498i	0.602508	−	0.798113i	$-0.294168\pi$
$947$	48.6375	−	18.1408i	1.58051	−	0.589498i	0.977998	+	0.208615i	$0.0668954\pi$
$948$	−4.29102	−	2.34308i	−0.139366	−	0.0760996i
$949$	−5.36528	+	2.45024i	−0.174164	+	0.0795383i
$950$	−5.45795	−	15.1644i	−0.177079	−	0.491997i
$951$	−1.83038	−	12.7306i	−0.0593542	−	0.412817i
$952$	3.52283	+	6.45158i	0.114176	+	0.209097i
$953$	−0.666798	+	0.0476903i	−0.0215997	+	0.00154484i	−0.0821349	−	0.996621i	$-0.526174\pi$
$953$	−0.666798	+	0.0476903i	−0.0215997	+	0.00154484i	0.0605352	+	0.998166i	$0.480719\pi$
$954$	−12.5507	−	8.06582i	−0.406343	−	0.261141i
$955$	27.8442	+	10.5683i	0.901016	+	0.341984i
$956$	11.7610	−	13.5729i	0.380377	−	0.438978i
$957$	−1.10715	+	0.604549i	−0.0357891	+	0.0195423i
$958$	−18.2049	+	24.3189i	−0.588174	+	0.785708i
$959$	38.3447	−	33.2259i	1.23822	−	1.07292i
$960$	−1.44169	−	0.215763i	−0.0465304	−	0.00696373i
$961$	−49.3724	+	14.4970i	−1.59266	+	0.467647i
$962$	−0.516685	−	1.38529i	−0.0166586	−	0.0446634i
$963$	10.1987	−	7.63468i	0.328650	−	0.246024i
$964$	−0.486139	+	0.312423i	−0.0156575	+	0.0100625i
$965$	43.6924	+	28.4362i	1.40651	+	0.915393i
$966$	−6.97611	+	5.08074i	−0.224453	+	0.163470i
$967$	−18.4956	−	18.4956i	−0.594777	−	0.594777i	0.344141	−	0.938918i	$-0.388170\pi$
$967$	−18.4956	−	18.4956i	−0.594777	−	0.594777i	−0.938918	+	0.344141i	$0.888170\pi$
$968$	−2.31689	+	10.6505i	−0.0744675	+	0.342322i
$969$	5.53900	+	0.796388i	0.177938	+	0.0255837i
$970$	−26.2902	−	5.87782i	−0.844128	−	0.188725i
$971$	7.37991	+	25.1337i	0.236833	+	0.806577i	0.989040	+	0.147651i	$0.0471711\pi$
$971$	7.37991	+	25.1337i	0.236833	+	0.806577i	−0.752207	+	0.658927i	$0.771011\pi$
$972$	−5.03049	+	13.4873i	−0.161353	+	0.432604i
$973$	−1.23172	+	17.2217i	−0.0394872	+	0.552103i
$974$	−19.7065	+	2.83336i	−0.631436	+	0.0907868i
$975$	0.261335	+	1.97915i	0.00836941	+	0.0633835i
$976$	−8.17268	−	7.08167i	−0.261601	−	0.226679i
$977$	−34.2489	+	7.45039i	−1.09572	+	0.238359i	−0.723872	−	0.689934i	$-0.757639\pi$
$977$	−34.2489	+	7.45039i	−1.09572	+	0.238359i	−0.371848	+	0.928294i	$0.621276\pi$
$978$	−7.55750	+	1.64403i	−0.241662	+	0.0525704i
$979$	0.896132	+	0.776502i	0.0286405	+	0.0248171i
$980$	0.106747	−	1.38075i	0.00340992	−	0.0441066i
$981$	20.3284	−	2.92279i	0.649037	−	0.0933174i
$982$	−2.28349	+	31.9273i	−0.0728689	+	1.01884i
$983$	−14.8605	+	39.8425i	−0.473975	+	1.27078i	0.451602	+	0.892219i	$0.350853\pi$
$983$	−14.8605	+	39.8425i	−0.473975	+	1.27078i	−0.925578	+	0.378558i	$0.876420\pi$
$984$	1.45926	+	4.96979i	0.0465196	+	0.158431i
$985$	19.4843	+	30.7055i	0.620823	+	0.978359i
$986$	−16.0999	−	2.31482i	−0.512726	−	0.0737188i
$987$	2.65787	−	12.2181i	0.0846011	−	0.388905i
$988$	−1.39590	−	1.39590i	−0.0444095	−	0.0444095i
$989$	−39.7142	−	30.5513i	−1.26284	−	0.971474i
$990$	0.994981	−	1.52880i	0.0316226	−	0.0485883i
$991$	−35.2269	+	22.6390i	−1.11902	+	0.719150i	−0.963240	−	0.268642i	$-0.913425\pi$
$991$	−35.2269	+	22.6390i	−1.11902	+	0.719150i	−0.155779	+	0.987792i	$0.549789\pi$
$992$	−7.26937	+	5.44178i	−0.230803	+	0.172777i
$993$	−4.09020	−	10.9663i	−0.129799	−	0.348004i
$994$	22.1204	−	6.49514i	0.701617	−	0.206013i
$995$	−13.4820	+	9.97190i	−0.427409	+	0.316131i
$996$	−0.503676	+	0.436438i	−0.0159596	+	0.0138291i
$997$	24.8726	−	33.2259i	0.787724	−	1.05228i	−0.209500	−	0.977809i	$-0.567184\pi$
$997$	24.8726	−	33.2259i	0.787724	−	1.05228i	0.997223	−	0.0744670i	$-0.0237255\pi$
$998$	29.8260	−	16.2862i	0.944126	−	0.515532i
$999$	5.74579	−	6.63099i	0.181789	−	0.209795i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.2.l.a.57.9	✓	240
5.3	odd	4	inner	230.2.l.a.103.10	yes	240
23.21	odd	22	inner	230.2.l.a.67.10	yes	240
115.113	even	44	inner	230.2.l.a.113.9	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.l.a.57.9	✓	240	1.1	even	1	trivial
230.2.l.a.67.10	yes	240	23.21	odd	22	inner
230.2.l.a.103.10	yes	240	5.3	odd	4	inner
230.2.l.a.113.9	yes	240	115.113	even	44	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:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	230.l (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.977147 + 0.212565i) q^{2} +(-0.390684 - 0.521893i) q^{3} +(0.909632 + 0.415415i) q^{4} +(-1.06032 - 1.96869i) q^{5} +(-0.270819 - 0.593012i) q^{6} +(2.75328 + 0.196919i) q^{7} +(0.800541 + 0.599278i) q^{8} +(0.725460 - 2.47069i) q^{9} +(-0.617610 - 2.14908i) q^{10} +(-0.171272 + 0.266505i) q^{11} +(-0.138577 - 0.637026i) q^{12} +(0.0436911 + 0.610881i) q^{13} +(2.64850 + 0.777670i) q^{14} +(-0.613195 + 1.32251i) q^{15} +(0.654861 + 0.755750i) q^{16} +(2.49510 + 0.930625i) q^{17} +(1.23406 - 2.26002i) q^{18} +(-1.33902 + 2.93205i) q^{19} +(-0.146675 - 2.23125i) q^{20} +(-0.972892 - 1.51385i) q^{21} +(-0.224008 + 0.224008i) q^{22} +(-1.29062 - 4.61891i) q^{23} -0.651925i q^{24} +(-2.75146 + 4.17486i) q^{25} +(-0.0871595 + 0.606208i) q^{26} +(-3.40532 + 1.27012i) q^{27} +(2.42267 + 1.32288i) q^{28} +(-5.55597 + 2.53733i) q^{29} +(-0.880300 + 1.16194i) q^{30} +(1.29230 + 8.98814i) q^{31} +(0.479249 + 0.877679i) q^{32} +(0.206000 - 0.0147334i) q^{33} +(2.24026 + 1.43973i) q^{34} +(-2.53168 - 5.62915i) q^{35} +(1.68626 - 1.94605i) q^{36} +(-2.11882 + 1.15696i) q^{37} +(-1.93167 + 2.58041i) q^{38} +(0.301745 - 0.261463i) q^{39} +(0.330964 - 2.21144i) q^{40} +(-7.62326 + 2.23839i) q^{41} +(-0.628867 - 1.68606i) q^{42} +(8.36389 - 6.26113i) q^{43} +(-0.266505 + 0.171272i) q^{44} +(-5.63323 + 1.19151i) q^{45} +(-0.279308 - 4.78769i) q^{46} +(4.91328 + 4.91328i) q^{47} +(0.138577 - 0.637026i) q^{48} +(0.613031 + 0.0881405i) q^{49} +(-3.57601 + 3.49459i) q^{50} +(-0.489110 - 1.66576i) q^{51} +(-0.214026 + 0.573827i) q^{52} +(0.413325 - 5.77904i) q^{53} +(-3.59748 + 0.517240i) q^{54} +(0.706268 + 0.0546022i) q^{55} +(2.08611 + 1.80762i) q^{56} +(2.05335 - 0.446679i) q^{57} +(-5.96835 + 1.29834i) q^{58} +(3.03630 + 2.63097i) q^{59} +(-1.10717 + 0.948263i) q^{60} +(-10.7039 + 1.53899i) q^{61} +(-0.647801 + 9.05743i) q^{62} +(2.48392 - 6.65964i) q^{63} +(0.281733 + 0.959493i) q^{64} +(1.15631 - 0.733741i) q^{65} +(0.204424 + 0.0293918i) q^{66} +(-1.63335 + 7.50837i) q^{67} +(1.88303 + 1.88303i) q^{68} +(-1.90635 + 2.47810i) q^{69} +(-1.27726 - 6.03865i) q^{70} +(7.02619 - 4.51545i) q^{71} +(2.06139 - 1.54314i) q^{72} +(3.36562 + 9.02358i) q^{73} +(-2.31633 + 0.680136i) q^{74} +(3.25378 - 0.195085i) q^{75} +(-2.43603 + 2.11083i) q^{76} +(-0.524041 + 0.700037i) q^{77} +(0.350427 - 0.191348i) q^{78} +(4.91108 - 5.66768i) q^{79} +(0.793475 - 2.09055i) q^{80} +(-4.50540 - 2.89544i) q^{81} +(-7.92485 + 0.566796i) q^{82} +(-0.489934 - 0.897247i) q^{83} +(-0.256098 - 1.78120i) q^{84} +(-0.813487 - 5.89883i) q^{85} +(9.50365 - 4.34017i) q^{86} +(3.49484 + 1.90833i) q^{87} +(-0.296821 + 0.110709i) q^{88} +(0.532679 - 3.70486i) q^{89} +(-5.75777 - 0.0331510i) q^{90} +1.69053i q^{91} +(0.744772 - 4.73765i) q^{92} +(4.18596 - 4.18596i) q^{93} +(3.75660 + 5.84539i) q^{94} +(7.19207 - 0.472783i) q^{95} +(0.270819 - 0.593012i) q^{96} +(5.77381 - 10.5739i) q^{97} +(0.580286 + 0.216435i) q^{98} +(0.534200 + 0.616500i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 8 q^{3} - 8 q^{6} - 8 q^{12} + 16 q^{13} + 24 q^{16} - 72 q^{18} - 80 q^{23} - 8 q^{26} + 16 q^{27} - 44 q^{28} + 24 q^{31} - 44 q^{33} - 8 q^{35} - 32 q^{36} - 88 q^{37} - 24 q^{41} - 8 q^{46}+ \cdots + 24 q^{98}+O(q^{100}) \) 240 * q - 8 * q^3 - 8 * q^6 - 8 * q^12 + 16 * q^13 + 24 * q^16 - 72 * q^18 - 80 * q^23 - 8 * q^26 + 16 * q^27 - 44 * q^28 + 24 * q^31 - 44 * q^33 - 8 * q^35 - 32 * q^36 - 88 * q^37 - 24 * q^41 - 8 * q^46 - 80 * q^47 + 8 * q^48 + 8 * q^50 + 16 * q^52 - 44 * q^56 - 88 * q^57 - 176 * q^61 - 32 * q^62 - 176 * q^66 + 24 * q^70 - 336 * q^71 + 16 * q^72 - 88 * q^73 - 36 * q^75 - 24 * q^77 + 40 * q^78 - 136 * q^81 + 40 * q^82 - 100 * q^85 - 44 * q^86 + 40 * q^87 + 8 * q^92 + 56 * q^93 + 52 * q^95 + 8 * q^96 + 132 * q^97 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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