LMFDB - Embedded newform 640.2.bm.a.101.21

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [640,2,Mod(21,640)] 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("640.21"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(640, base_ring=CyclotomicField(32)) chi = DirichletCharacter(H, H._module([0, 13, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 640 = 2^{7} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	640.bm (of order $32$, degree $16$, 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:	$5.11042572936$
Analytic rank:	$0$
Dimension:	$1024$
Relative dimension:	$64$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			101.21
Character	$\chi$	$=$	640.101
Dual form			640.2.bm.a.621.21

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.576107 + 1.29155i) q^{2} +(-0.0615529 + 0.0329007i) q^{3} +(-1.33620 - 1.48814i) q^{4} +(-0.634393 - 0.773010i) q^{5} +(-0.00703187 - 0.0984530i) q^{6} +(-1.25743 + 0.840186i) q^{7} +(2.69180 - 0.868443i) q^{8} +(-1.66400 + 2.49036i) q^{9} +(1.36386 - 0.374014i) q^{10} +(5.08865 - 1.54363i) q^{11} +(0.131208 + 0.0476374i) q^{12} +(-0.464904 - 0.381537i) q^{13} +(-0.360730 - 2.10807i) q^{14} +(0.0644814 + 0.0267091i) q^{15} +(-0.429128 + 3.97691i) q^{16} +(4.92463 - 2.03985i) q^{17} +(-2.25778 - 3.58386i) q^{18} +(0.335472 + 3.40610i) q^{19} +(-0.302671 + 1.97696i) q^{20} +(0.0497556 - 0.0930862i) q^{21} +(-0.937937 + 7.46154i) q^{22} +(-6.71447 + 1.33559i) q^{23} +(-0.137116 + 0.142018i) q^{24} +(-0.195090 + 0.980785i) q^{25} +(0.760609 - 0.380641i) q^{26} +(0.0410128 - 0.416410i) q^{27} +(2.93049 + 0.748571i) q^{28} +(-2.79179 + 9.20331i) q^{29} +(-0.0716442 + 0.0678936i) q^{30} +(3.49578 + 3.49578i) q^{31} +(-4.88916 - 2.84537i) q^{32} +(-0.262435 + 0.262435i) q^{33} +(-0.202546 + 7.53557i) q^{34} +(1.44718 + 0.438996i) q^{35} +(5.92945 - 0.851349i) q^{36} +(4.78122 + 0.470909i) q^{37} +(-4.59242 - 1.52900i) q^{38} +(0.0411691 + 0.00818904i) q^{39} +(-2.37898 - 1.52986i) q^{40} +(1.69945 + 8.54373i) q^{41} +(0.0915609 + 0.117889i) q^{42} +(3.87874 + 2.07323i) q^{43} +(-9.09660 - 5.51004i) q^{44} +(2.98071 - 0.293574i) q^{45} +(2.14327 - 9.44151i) q^{46} +(0.799802 + 1.93089i) q^{47} +(-0.104429 - 0.258909i) q^{48} +(-1.80357 + 4.35421i) q^{49} +(-1.15434 - 0.817006i) q^{50} +(-0.236013 + 0.287582i) q^{51} +(0.0534250 + 1.20165i) q^{52} +(2.06626 + 6.81153i) q^{53} +(0.514186 + 0.292867i) q^{54} +(-4.42145 - 2.95432i) q^{55} +(-2.65509 + 3.35362i) q^{56} +(-0.132712 - 0.198618i) q^{57} +(-10.2782 - 8.90783i) q^{58} +(4.23437 - 3.47506i) q^{59} +(-0.0464133 - 0.131646i) q^{60} +(3.86411 + 7.22925i) q^{61} +(-6.52892 + 2.50103i) q^{62} -4.52952i q^{63} +(6.49161 - 4.67536i) q^{64} +0.601421i q^{65} +(-0.187757 - 0.490139i) q^{66} +(-5.62754 - 10.5284i) q^{67} +(-9.61588 - 4.60289i) q^{68} +(0.369353 - 0.303120i) q^{69} +(-1.40071 + 1.61619i) q^{70} +(-2.63291 - 3.94043i) q^{71} +(-2.31644 + 8.14865i) q^{72} +(-2.36854 - 1.58261i) q^{73} +(-3.36269 + 5.90389i) q^{74} +(-0.0202602 - 0.0667888i) q^{75} +(4.62050 - 5.05047i) q^{76} +(-5.10168 + 6.21641i) q^{77} +(-0.0342943 + 0.0484541i) q^{78} +(4.06361 - 9.81043i) q^{79} +(3.34643 - 2.19121i) q^{80} +(-3.42738 - 8.27443i) q^{81} +(-12.0137 - 2.72717i) q^{82} +(-2.19565 + 0.216253i) q^{83} +(-0.205009 + 0.0503386i) q^{84} +(-4.70097 - 2.51272i) q^{85} +(-4.91224 + 3.81518i) q^{86} +(-0.130953 - 0.658343i) q^{87} +(12.3571 - 8.57435i) q^{88} +(12.8784 + 2.56166i) q^{89} +(-1.33804 + 4.01886i) q^{90} +(0.905146 + 0.0891491i) q^{91} +(10.9594 + 8.20746i) q^{92} +(-0.330189 - 0.100162i) q^{93} +(-2.95462 - 0.0794162i) q^{94} +(2.42013 - 2.42013i) q^{95} +(0.394557 + 0.0142838i) q^{96} +(-2.94079 - 2.94079i) q^{97} +(-4.58463 - 4.83789i) q^{98} +(-4.62336 + 15.2412i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1024 q - 192 q^{52} - 128 q^{54} - 32 q^{56} - 288 q^{58} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 288 q^{72} - 32 q^{74} - 128 q^{76} - 192 q^{78}+O(q^{100}) $ 1024 * q - 192 * q^52 - 128 * q^54 - 32 * q^56 - 288 * q^58 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 288 * q^72 - 32 * q^74 - 128 * q^76 - 192 * q^78

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/640\mathbb{Z}\right)^\times$.

$n$	$257$	$261$	$511$
$\chi(n)$	$1$	$e\left(\frac{9}{32}\right)$	$1$

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 $

$2$	−0.576107	+	1.29155i	−0.407369	+	0.913264i
$2$	−0.576107	+	1.29155i	−0.407369	+	0.913264i
$3$	−0.0615529	+	0.0329007i	−0.0355376	+	0.0189952i	−0.489070	−	0.872245i	$-0.662664\pi$
$3$	−0.0615529	+	0.0329007i	−0.0355376	+	0.0189952i	0.453532	+	0.891240i	$0.350164\pi$
$4$	−1.33620	−	1.48814i	−0.668101	−	0.744071i
$5$	−0.634393	−	0.773010i	−0.283709	−	0.345701i
$5$	−0.634393	−	0.773010i	−0.283709	−	0.345701i
$6$	−0.00703187	−	0.0984530i	−0.00287075	−	0.0401933i
$7$	−1.25743	+	0.840186i	−0.475263	+	0.317561i	−0.770029	−	0.638009i	$-0.779758\pi$
$7$	−1.25743	+	0.840186i	−0.475263	+	0.317561i	0.294766	+	0.955569i	$0.404758\pi$
$8$	2.69180	−	0.868443i	0.951696	−	0.307041i
$9$	−1.66400	+	2.49036i	−0.554668	+	0.830120i
$10$	1.36386	−	0.374014i	0.431290	−	0.118274i
$11$	5.08865	−	1.54363i	1.53429	−	0.465421i	0.593618	−	0.804747i	$-0.297699\pi$
$11$	5.08865	−	1.54363i	1.53429	−	0.465421i	0.940669	+	0.339326i	$0.110199\pi$
$12$	0.131208	+	0.0476374i	0.0378765	+	0.0137517i
$13$	−0.464904	−	0.381537i	−0.128941	−	0.105819i	0.567712	−	0.823227i	$-0.307829\pi$
$13$	−0.464904	−	0.381537i	−0.128941	−	0.105819i	−0.696654	+	0.717408i	$0.745329\pi$
$14$	−0.360730	−	2.10807i	−0.0964091	−	0.563405i
$15$	0.0644814	+	0.0267091i	0.0166490	+	0.00689625i
$16$	−0.429128	+	3.97691i	−0.107282	+	0.994229i
$17$	4.92463	−	2.03985i	1.19440	−	0.494736i	0.305213	−	0.952284i	$-0.401272\pi$
$17$	4.92463	−	2.03985i	1.19440	−	0.494736i	0.889185	+	0.457549i	$0.151272\pi$
$18$	−2.25778	−	3.58386i	−0.532163	−	0.844723i
$19$	0.335472	+	3.40610i	0.0769625	+	0.781413i	0.953763	+	0.300559i	$0.0971733\pi$
$19$	0.335472	+	3.40610i	0.0769625	+	0.781413i	−0.876801	+	0.480854i	$0.840327\pi$
$20$	−0.302671	+	1.97696i	−0.0676793	+	0.442063i
$21$	0.0497556	−	0.0930862i	0.0108576	−	0.0203131i
$22$	−0.937937	+	7.46154i	−0.199969	+	1.59081i
$23$	−6.71447	+	1.33559i	−1.40006	+	0.278490i	−0.836674	−	0.547701i	$-0.815503\pi$
$23$	−6.71447	+	1.33559i	−1.40006	+	0.278490i	−0.563390	+	0.826191i	$0.690503\pi$
$24$	−0.137116	+	0.142018i	−0.0279887	+	0.0289892i
$25$	−0.195090	+	0.980785i	−0.0390181	+	0.196157i
$26$	0.760609	−	0.380641i	0.149168	−	0.0746498i
$27$	0.0410128	−	0.416410i	0.00789292	−	0.0801381i
$28$	2.93049	+	0.748571i	0.553811	+	0.141467i
$29$	−2.79179	+	9.20331i	−0.518423	+	1.70901i	0.171549	+	0.985176i	$0.445123\pi$
$29$	−2.79179	+	9.20331i	−0.518423	+	1.70901i	−0.689972	+	0.723836i	$0.742377\pi$
$30$	−0.0716442	+	0.0678936i	−0.0130804	+	0.0123956i
$31$	3.49578	+	3.49578i	0.627861	+	0.627861i	0.947529	−	0.319669i	$-0.103572\pi$
$31$	3.49578	+	3.49578i	0.627861	+	0.627861i	−0.319669	+	0.947529i	$0.603572\pi$
$32$	−4.88916	−	2.84537i	−0.864289	−	0.502995i
$33$	−0.262435	+	0.262435i	−0.0456841	+	0.0456841i
$34$	−0.202546	+	7.53557i	−0.0347364	+	1.29234i
$35$	1.44718	+	0.438996i	0.244617	+	0.0742039i
$36$	5.92945	−	0.851349i	0.988242	−	0.141891i
$37$	4.78122	+	0.470909i	0.786027	+	0.0774169i	0.483064	−	0.875585i	$-0.339524\pi$
$37$	4.78122	+	0.470909i	0.786027	+	0.0774169i	0.302963	+	0.953002i	$0.402024\pi$
$38$	−4.59242	−	1.52900i	−0.744988	−	0.248036i
$39$	0.0411691	+	0.00818904i	0.00659233	+	0.00131130i
$40$	−2.37898	−	1.52986i	−0.376149	−	0.241892i
$41$	1.69945	+	8.54373i	0.265410	+	1.33431i	0.851625	+	0.524151i	$0.175617\pi$
$41$	1.69945	+	8.54373i	0.265410	+	1.33431i	−0.586215	+	0.810155i	$0.699383\pi$
$42$	0.0915609	+	0.117889i	0.0141282	+	0.0181907i
$43$	3.87874	+	2.07323i	0.591502	+	0.316164i	0.739851	−	0.672771i	$-0.234896\pi$
$43$	3.87874	+	2.07323i	0.591502	+	0.316164i	−0.148349	+	0.988935i	$0.547396\pi$
$44$	−9.09660	−	5.51004i	−1.37136	−	0.830670i
$45$	2.98071	−	0.293574i	0.444337	−	0.0437634i
$46$	2.14327	−	9.44151i	0.316008	−	1.39208i
$47$	0.799802	+	1.93089i	0.116663	+	0.281650i	0.971415	−	0.237387i	$-0.0762909\pi$
$47$	0.799802	+	1.93089i	0.116663	+	0.281650i	−0.854752	+	0.519036i	$0.826291\pi$
$48$	−0.104429	−	0.258909i	−0.0150731	−	0.0373703i
$49$	−1.80357	+	4.35421i	−0.257653	+	0.622030i
$50$	−1.15434	−	0.817006i	−0.163248	−	0.115542i
$51$	−0.236013	+	0.287582i	−0.0330484	+	0.0402696i
$52$	0.0534250	+	1.20165i	0.00740872	+	0.166639i
$53$	2.06626	+	6.81153i	0.283822	+	0.935636i	0.976705	+	0.214586i	$0.0688403\pi$
$53$	2.06626	+	6.81153i	0.283822	+	0.935636i	−0.692883	+	0.721050i	$0.743660\pi$
$54$	0.514186	+	0.292867i	0.0699719	+	0.0398541i
$55$	−4.42145	−	2.95432i	−0.596188	−	0.398360i
$56$	−2.65509	+	3.35362i	−0.354802	+	0.448146i
$57$	−0.132712	−	0.198618i	−0.0175782	−	0.0263076i
$58$	−10.2782	−	8.90783i	−1.34959	−	1.16966i
$59$	4.23437	−	3.47506i	0.551268	−	0.452414i	−0.317059	−	0.948406i	$-0.602695\pi$
$59$	4.23437	−	3.47506i	0.551268	−	0.452414i	0.868327	+	0.495992i	$0.165195\pi$
$60$	−0.0464133	−	0.131646i	−0.00599193	−	0.0169954i
$61$	3.86411	+	7.22925i	0.494749	+	0.925610i	0.998105	+	0.0615313i	$0.0195984\pi$
$61$	3.86411	+	7.22925i	0.494749	+	0.925610i	−0.503356	+	0.864079i	$0.667902\pi$
$62$	−6.52892	+	2.50103i	−0.829174	+	0.317631i
$63$		−	4.52952i		−	0.570666i
$64$	6.49161	−	4.67536i	0.811452	−	0.584420i
$65$			0.601421i			0.0745970i
$66$	−0.187757	−	0.490139i	−0.0231113	−	0.0603319i
$67$	−5.62754	−	10.5284i	−0.687513	−	1.28625i	−0.947228	−	0.320562i	$-0.896128\pi$
$67$	−5.62754	−	10.5284i	−0.687513	−	1.28625i	0.259714	−	0.965686i	$-0.416372\pi$
$68$	−9.61588	−	4.60289i	−1.16610	−	0.558183i
$69$	0.369353	−	0.303120i	0.0444649	−	0.0364914i
$70$	−1.40071	+	1.61619i	−0.167417	+	0.193172i
$71$	−2.63291	−	3.94043i	−0.312469	−	0.467643i	0.641681	−	0.766972i	$-0.278237\pi$
$71$	−2.63291	−	3.94043i	−0.312469	−	0.467643i	−0.954150	+	0.299329i	$0.903237\pi$
$72$	−2.31644	+	8.14865i	−0.272995	+	0.960328i
$73$	−2.36854	−	1.58261i	−0.277217	−	0.185230i	0.409188	−	0.912450i	$-0.365812\pi$
$73$	−2.36854	−	1.58261i	−0.277217	−	0.185230i	−0.686405	+	0.727220i	$0.740812\pi$
$74$	−3.36269	+	5.90389i	−0.390905	+	0.686313i
$75$	−0.0202602	−	0.0667888i	−0.00233944	−	0.00771211i
$76$	4.62050	−	5.05047i	0.530008	−	0.579328i
$77$	−5.10168	+	6.21641i	−0.581390	+	0.708426i
$78$	−0.0342943	+	0.0484541i	−0.00388307	+	0.00548635i
$79$	4.06361	−	9.81043i	0.457192	−	1.10376i	−0.512337	−	0.858784i	$-0.671220\pi$
$79$	4.06361	−	9.81043i	0.457192	−	1.10376i	0.969529	−	0.244975i	$-0.0787798\pi$
$80$	3.34643	−	2.19121i	0.374143	−	0.244984i
$81$	−3.42738	−	8.27443i	−0.380820	−	0.919382i
$82$	−12.0137	−	2.72717i	−1.32669	−	0.301166i
$83$	−2.19565	+	0.216253i	−0.241004	+	0.0237368i	−0.217798	−	0.975994i	$-0.569887\pi$
$83$	−2.19565	+	0.216253i	−0.241004	+	0.0237368i	−0.0232062	+	0.999731i	$0.507387\pi$
$84$	−0.205009	+	0.0503386i	−0.0223683	+	0.00549239i
$85$	−4.70097	−	2.51272i	−0.509892	−	0.272543i
$86$	−4.91224	+	3.81518i	−0.529701	+	0.411402i
$87$	−0.130953	−	0.658343i	−0.0140396	−	0.0705817i
$88$	12.3571	−	8.57435i	1.31727	−	0.914028i
$89$	12.8784	+	2.56166i	1.36510	+	0.271536i	0.822649	−	0.568550i	$-0.192495\pi$
$89$	12.8784	+	2.56166i	1.36510	+	0.271536i	0.542454	+	0.840086i	$0.317495\pi$
$90$	−1.33804	+	4.01886i	−0.141042	+	0.423625i
$91$	0.905146	+	0.0891491i	0.0948851	+	0.00934536i
$92$	10.9594	+	8.20746i	1.14260	+	0.855687i
$93$	−0.330189	−	0.100162i	−0.0342390	−	0.0103863i
$94$	−2.95462	−	0.0794162i	−0.304745	−	0.00819116i
$95$	2.42013	−	2.42013i	0.248300	−	0.248300i
$96$	0.394557	+	0.0142838i	0.0402693	+	0.00145784i
$97$	−2.94079	−	2.94079i	−0.298592	−	0.298592i	0.541870	−	0.840462i	$-0.317717\pi$
$97$	−2.94079	−	2.94079i	−0.298592	−	0.298592i	−0.840462	+	0.541870i	$0.817717\pi$
$98$	−4.58463	−	4.83789i	−0.463118	−	0.488701i
$99$	−4.62336	+	15.2412i	−0.464665	+	1.53180i
$100$	1.72023	−	1.02021i	0.172023	−	0.102021i
$101$	−0.818425	+	8.30960i	−0.0814363	+	0.826836i	0.864532	+	0.502578i	$0.167615\pi$
$101$	−0.818425	+	8.30960i	−0.0814363	+	0.826836i	−0.945968	+	0.324259i	$0.894885\pi$
$102$	−0.235458	−	0.470500i	−0.0233139	−	0.0465865i
$103$	2.87637	−	14.4605i	0.283417	−	1.42484i	−0.532384	−	0.846503i	$-0.678704\pi$
$103$	2.87637	−	14.4605i	0.283417	−	1.42484i	0.815801	−	0.578332i	$-0.196296\pi$
$104$	−1.58277	−	0.623280i	−0.155204	−	0.0611176i
$105$	−0.103521	+	0.0205917i	−0.0101026	+	0.00200954i
$106$	−9.98782	−	1.25550i	−0.970103	−	0.121945i
$107$	−3.95350	+	7.39648i	−0.382199	+	0.715045i	−0.997302	−	0.0734021i	$-0.976614\pi$
$107$	−3.95350	+	7.39648i	−0.382199	+	0.715045i	0.615103	+	0.788447i	$0.289114\pi$
$108$	−0.674478	+	0.495375i	−0.0649017	+	0.0476675i
$109$	−0.910185	−	9.24127i	−0.0871799	−	0.885153i	−0.934948	−	0.354785i	$-0.884554\pi$
$109$	−0.910185	−	9.24127i	−0.0871799	−	0.885153i	0.847768	−	0.530367i	$-0.177946\pi$
$110$	6.36287	−	4.00852i	0.606676	−	0.382197i
$111$	−0.309791	+	0.128320i	−0.0294041	+	0.0121796i
$112$	−2.80175	−	5.36123i	−0.264741	−	0.506589i
$113$	8.46167	+	3.50494i	0.796007	+	0.329717i	0.743356	−	0.668896i	$-0.233233\pi$
$113$	8.46167	+	3.50494i	0.796007	+	0.329717i	0.0526511	+	0.998613i	$0.483233\pi$
$114$	0.332982	−	0.0569794i	0.0311866	−	0.00533661i
$115$	5.29204	+	4.34306i	0.493485	+	0.404993i
$116$	17.4262	−	8.14290i	1.61798	−	0.756049i
$117$	1.72377	−	0.522899i	0.159362	−	0.0483420i
$118$	2.04876	+	7.47091i	0.188604	+	0.687753i
$119$	−4.47851	+	6.70256i	−0.410544	+	0.614423i
$120$	0.196766	+	0.0158971i	0.0179622	+	0.00145120i
$121$	14.3654	−	9.59868i	1.30595	−	0.872608i
$122$	−11.5631	+	0.825877i	−1.04687	+	0.0747714i
$123$	−0.385701	−	0.469978i	−0.0347775	−	0.0423765i
$124$	0.531146	−	9.87329i	0.0476983	−	0.886647i
$125$	0.881921	−	0.471397i	0.0788814	−	0.0421630i
$126$	5.85010	+	2.60949i	0.521168	+	0.232472i
$127$	−8.70583			−0.772518			−0.386259	−	0.922390i	$-0.626233\pi$
$127$	−8.70583			−0.772518			−0.386259	+	0.922390i	$0.626233\pi$
$128$	2.29860	+	11.0777i	0.203169	+	0.979144i
$129$	−0.306958			−0.0270262
$130$	−0.776765	−	0.346482i	−0.0681268	−	0.0303885i
$131$	1.74300	−	0.931652i	0.152286	−	0.0813988i	−0.393493	−	0.919327i	$-0.628734\pi$
$131$	1.74300	−	0.931652i	0.152286	−	0.0813988i	0.545780	+	0.837929i	$0.316234\pi$
$132$	0.741207	+	0.0398742i	0.0645138	+	0.00347060i
$133$	−3.28359	−	4.00107i	−0.284723	−	0.346936i
$134$	16.8400	−	1.20277i	1.45475	−	0.103904i
$135$	−0.347907	+	0.232464i	−0.0299431	+	0.0200073i
$136$	11.4846	−	9.76763i	0.984799	−	0.837567i
$137$	7.95161	−	11.9004i	0.679352	−	1.01672i	−0.318284	−	0.947996i	$-0.603106\pi$
$137$	7.95161	−	11.9004i	0.679352	−	1.01672i	0.997636	−	0.0687264i	$-0.0218935\pi$
$138$	0.178708	+	0.651668i	0.0152127	+	0.0554737i
$139$	−5.76854	+	1.74987i	−0.489282	+	0.148422i	−0.525279	−	0.850930i	$-0.676039\pi$
$139$	−5.76854	+	1.74987i	−0.489282	+	0.148422i	0.0359976	+	0.999352i	$0.488539\pi$
$140$	−1.28043	−	2.74019i	−0.108216	−	0.231588i
$141$	−0.112758	−	0.0925380i	−0.00949593	−	0.00779311i
$142$	6.60610	−	1.13043i	0.554372	−	0.0948634i
$143$	−2.95469	−	1.22387i	−0.247083	−	0.102345i
$144$	−9.18987	−	7.68629i	−0.765823	−	0.640524i
$145$	8.88535	−	3.68043i	0.737888	−	0.305643i
$146$	3.40855	−	2.14734i	0.282094	−	0.177715i
$147$	−0.0322415	−	0.327353i	−0.00265923	−	0.0269996i
$148$	−5.68789	−	7.74435i	−0.467542	−	0.636582i
$149$	−0.871020	+	1.62956i	−0.0713567	+	0.133499i	−0.915070	−	0.403295i	$-0.867865\pi$
$149$	−0.871020	+	1.62956i	−0.0713567	+	0.133499i	0.843713	+	0.536794i	$0.180365\pi$
$150$	0.0979331	+	0.0123105i	0.00799620	+	0.00100515i
$151$	19.9211	−	3.96256i	1.62116	−	0.322468i	0.700743	−	0.713414i	$-0.252852\pi$
$151$	19.9211	−	3.96256i	1.62116	−	0.322468i	0.920414	+	0.390945i	$0.127852\pi$
$152$	3.86103	+	8.87722i	0.313171	+	0.720037i
$153$	−3.11465	+	15.6584i	−0.251804	+	1.26591i
$154$	−5.08970	−	10.1704i	−0.410139	−	0.819553i
$155$	0.484575	−	4.91998i	0.0389220	−	0.395182i
$156$	−0.0428238	−	0.0722076i	−0.00342864	−	0.00578123i
$157$	−5.51430	+	18.1782i	−0.440089	+	1.45078i	0.404091	+	0.914719i	$0.367588\pi$
$157$	−5.51430	+	18.1782i	−0.440089	+	1.45078i	−0.844180	+	0.536060i	$0.819912\pi$
$158$	10.3296	+	10.9002i	0.821777	+	0.867174i
$159$	−0.351289	−	0.351289i	−0.0278590	−	0.0278590i
$160$	0.902151	+	5.58445i	0.0713213	+	0.441490i
$161$	7.32081	−	7.32081i	0.576961	−	0.576961i
$162$	12.6614	+	0.340321i	0.994772	+	0.0267382i
$163$	9.06062	+	2.74851i	0.709683	+	0.215280i	0.624431	−	0.781080i	$-0.285331\pi$
$163$	9.06062	+	2.74851i	0.709683	+	0.215280i	0.0852512	+	0.996359i	$0.472831\pi$
$164$	10.4435	−	13.9452i	0.815497	−	1.08894i
$165$	0.369352	+	0.0363780i	0.0287540	+	0.00283202i
$166$	0.985629	−	2.96038i	0.0764996	−	0.229770i
$167$	−20.8640	−	4.15010i	−1.61450	−	0.321145i	−0.696451	−	0.717604i	$-0.745239\pi$
$167$	−20.8640	−	4.15010i	−1.61450	−	0.321145i	−0.918052	+	0.396459i	$0.870239\pi$
$168$	0.0530922	−	0.293780i	0.00409615	−	0.0226656i
$169$	−2.46561	−	12.3955i	−0.189662	−	0.953496i
$170$	5.95357	−	4.62394i	0.456618	−	0.354640i
$171$	−9.04064	−	4.83232i	−0.691355	−	0.369537i
$172$	−2.09752	−	8.54236i	−0.159934	−	0.651349i
$173$	−7.47336	+	0.736062i	−0.568189	+	0.0559618i	−0.378033	−	0.925792i	$-0.623399\pi$
$173$	−7.47336	+	0.736062i	−0.568189	+	0.0559618i	−0.190156	+	0.981754i	$0.560899\pi$
$174$	0.925725	+	0.210144i	0.0701790	+	0.0159310i
$175$	−0.578730	−	1.39718i	−0.0437479	−	0.105617i
$176$	3.95518	+	20.8996i	0.298133	+	1.57536i
$177$	−0.146306	+	0.353214i	−0.0109970	+	0.0265492i
$178$	−10.7278	+	15.1572i	−0.804084	+	1.13608i
$179$	−9.37782	+	11.4269i	−0.700931	+	0.854087i	−0.994809	−	0.101756i	$-0.967554\pi$
$179$	−9.37782	+	11.4269i	−0.700931	+	0.854087i	0.293879	+	0.955843i	$0.405054\pi$
$180$	−4.41971	−	4.04344i	−0.329425	−	0.301380i
$181$	6.30559	+	20.7868i	0.468691	+	1.54507i	0.799081	+	0.601223i	$0.205320\pi$
$181$	6.30559	+	20.7868i	0.468691	+	1.54507i	−0.330390	+	0.943844i	$0.607180\pi$
$182$	−0.636601	+	1.11768i	−0.0471880	+	0.0828481i
$183$	−0.475695	−	0.317849i	−0.0351644	−	0.0234961i
$184$	−16.9141	+	9.42628i	−1.24693	+	0.694915i
$185$	−2.66915	−	3.99467i	−0.196240	−	0.293694i
$186$	0.319588	−	0.368752i	0.0234334	−	0.0270382i
$187$	21.9110	−	17.9819i	1.60229	−	1.31496i
$188$	1.80474	−	3.77028i	0.131624	−	0.274976i
$189$	0.298291	+	0.558064i	0.0216975	+	0.0405932i
$190$	1.73147	+	4.51997i	0.125614	+	0.327913i
$191$		−	2.87989i		−	0.208381i	−0.994557	−	0.104191i	$-0.966775\pi$
$191$		−	2.87989i		−	0.208381i	0.994557	−	0.104191i	$-0.0332252\pi$
$192$	−0.245755	+	0.501361i	−0.0177358	+	0.0361826i
$193$			11.0175i			0.793056i	0.918023	+	0.396528i	$0.129785\pi$
$193$			11.0175i			0.793056i	−0.918023	+	0.396528i	$0.870215\pi$
$194$	5.49239	−	2.10397i	0.394331	−	0.151056i
$195$	−0.0197872	−	0.0370192i	−0.00141699	−	0.00265100i
$196$	8.88962	−	3.13413i	0.634973	−	0.223867i
$197$	−4.16005	+	3.41406i	−0.296391	+	0.243242i	−0.770822	−	0.637051i	$-0.780154\pi$
$197$	−4.16005	+	3.41406i	−0.296391	+	0.243242i	0.474431	+	0.880293i	$0.342654\pi$
$198$	−17.0212	−	14.7518i	−1.20964	−	1.04837i
$199$	−7.87278	−	11.7824i	−0.558086	−	0.835235i	0.439940	−	0.898027i	$-0.355000\pi$
$199$	−7.87278	−	11.7824i	−0.558086	−	0.835235i	−0.998027	+	0.0627918i	$0.980000\pi$
$200$	0.326612	+	2.80951i	0.0230949	+	0.198662i
$201$	0.692783	+	0.462903i	0.0488652	+	0.0326507i
$202$	−10.2608	−	5.84425i	−0.721945	−	0.411200i
$203$	−4.22202	−	13.9181i	−0.296327	−	0.976861i
$204$	0.743324	−	0.0330479i	0.0520431	−	0.00231381i
$205$	5.52627	−	6.73378i	0.385971	−	0.470307i
$206$	17.0194	+	12.0458i	1.18579	+	0.839269i
$207$	7.84681	−	18.9439i	0.545391	−	1.31669i
$208$	1.71684	−	1.68516i	0.119042	−	0.116845i
$209$	6.96484	+	16.8146i	0.481768	+	1.16309i
$210$	0.0330441	−	0.145566i	0.00228026	−	0.0100450i
$211$	19.1608	−	1.88718i	1.31909	−	0.129919i	0.586143	−	0.810208i	$-0.300646\pi$
$211$	19.1608	−	1.88718i	1.31909	−	0.129919i	0.732944	+	0.680289i	$0.238146\pi$
$212$	7.37559	−	12.1765i	0.506558	−	0.836283i
$213$	0.291706	+	0.155920i	0.0199874	+	0.0106835i
$214$	−7.27528	−	9.36730i	−0.497328	−	0.640336i
$215$	−0.858018	−	4.31355i	−0.0585163	−	0.294181i
$216$	−0.251230	−	1.15651i	−0.0170940	−	0.0786906i
$217$	−7.33280	−	1.45858i	−0.497783	−	0.0990152i
$218$	12.4599	+	4.14841i	0.843892	+	0.280965i
$219$	0.197860	+	0.0194875i	0.0133701	+	0.00131684i
$220$	1.51151	+	10.5273i	0.101906	+	0.709750i
$221$	−3.06776	−	0.930594i	−0.206360	−	0.0625985i
$222$	0.0127415	−	0.474036i	0.000855152	−	0.0318152i
$223$	9.95548	−	9.95548i	0.666668	−	0.666668i	−0.290275	−	0.956943i	$-0.593747\pi$
$223$	9.95548	−	9.95548i	0.666668	−	0.666668i	0.956943	+	0.290275i	$0.0937468\pi$
$224$	8.53840	−	0.529961i	0.570496	−	0.0354095i
$225$	−2.11788	−	2.11788i	−0.141192	−	0.141192i
$226$	−9.40163	+	8.90945i	−0.625387	+	0.592648i
$227$	−2.67051	+	8.80351i	−0.177248	+	0.584309i	0.822628	+	0.568580i	$0.192507\pi$
$227$	−2.67051	+	8.80351i	−0.177248	+	0.584309i	−0.999876	+	0.0157293i	$0.994993\pi$
$228$	−0.118241	+	0.462889i	−0.00783072	+	0.0306556i
$229$	1.53368	−	15.5717i	0.101348	−	1.02901i	−0.801194	−	0.598404i	$-0.795802\pi$
$229$	1.53368	−	15.5717i	0.101348	−	1.02901i	0.902542	−	0.430601i	$-0.141698\pi$
$230$	−8.65806	+	4.33286i	−0.570896	+	0.285701i
$231$	0.109499	−	0.550487i	0.00720449	−	0.0362194i
$232$	0.477594	+	27.1980i	0.0313556	+	1.78564i
$233$	16.1993	−	3.22224i	1.06125	−	0.211096i	0.366552	−	0.930398i	$-0.380538\pi$
$233$	16.1993	−	3.22224i	1.06125	−	0.211096i	0.694698	+	0.719302i	$0.255538\pi$
$234$	−0.317724	+	2.52758i	−0.0207702	+	0.165233i
$235$	0.985211	−	1.84320i	0.0642681	−	0.120237i
$236$	−10.8294	−	1.65796i	−0.704931	−	0.107924i
$237$	0.0726430	+	0.737556i	0.00471867	+	0.0479094i
$238$	−6.07659	−	9.64561i	−0.393887	−	0.625232i
$239$	−11.5212	+	4.77225i	−0.745246	+	0.308691i	−0.722800	−	0.691057i	$-0.757145\pi$
$239$	−11.5212	+	4.77225i	−0.745246	+	0.308691i	−0.0224459	+	0.999748i	$0.507145\pi$
$240$	−0.133890	+	0.244975i	−0.00864259	+	0.0158131i
$241$	−19.5160	−	8.08378i	−1.25713	−	0.520722i	−0.348106	−	0.937455i	$-0.613175\pi$
$241$	−19.5160	−	8.08378i	−1.25713	−	0.520722i	−0.909029	+	0.416733i	$0.863175\pi$
$242$	4.12115	+	24.0836i	0.264917	+	1.54815i
$243$	1.45354	+	1.19289i	0.0932447	+	0.0765239i
$244$	5.59490	−	15.4101i	0.358177	−	0.986529i
$245$	4.51002	−	1.36810i	0.288135	−	0.0874048i
$246$	0.829205	−	0.227395i	0.0528682	−	0.0144982i
$247$	1.14359	−	1.71151i	0.0727650	−	0.108901i
$248$	12.4458	+	6.37407i	0.790312	+	0.404754i
$249$	0.128034	−	0.0855496i	0.00811382	−	0.00542148i
$250$	0.100752	+	1.41062i	0.00637209	+	0.0892154i
$251$	−14.5033	−	17.6723i	−0.915438	−	1.11546i	−0.992957	−	0.118473i	$-0.962200\pi$
$251$	−14.5033	−	17.6723i	−0.915438	−	1.11546i	0.0775196	−	0.996991i	$-0.475300\pi$
$252$	−6.74056	+	6.05235i	−0.424616	+	0.381262i
$253$	−32.1060	+	17.1610i	−2.01848	+	1.07890i
$254$	5.01549	−	11.2440i	0.314700	−	0.705512i
$255$	0.372029			0.0232974
$256$	−15.6317	−	3.41321i	−0.976981	−	0.213326i
$257$	−26.4992			−1.65298			−0.826489	−	0.562953i	$-0.809665\pi$
$257$	−26.4992			−1.65298			−0.826489	+	0.562953i	$0.809665\pi$
$258$	0.176841	−	0.396452i	0.0110096	−	0.0246820i
$259$	−6.40768	+	3.42498i	−0.398154	+	0.212818i
$260$	0.894999	−	0.803619i	0.0555055	−	0.0498384i
$261$	−18.2740	−	22.2669i	−1.13113	−	1.37829i
$262$	0.199122	+	2.78790i	0.0123018	+	0.172237i
$263$	−7.10484	+	4.74730i	−0.438103	+	0.292731i	−0.754995	−	0.655730i	$-0.772361\pi$
$263$	−7.10484	+	4.74730i	−0.438103	+	0.292731i	0.316892	+	0.948462i	$0.397361\pi$
$264$	−0.478514	+	0.934334i	−0.0294505	+	0.0575043i
$265$	3.95457	−	5.91843i	0.242927	−	0.363566i
$266$	7.05927	−	1.93588i	0.432832	−	0.118696i
$267$	−0.876981	+	0.266029i	−0.0536704	+	0.0162807i
$268$	−8.14820	+	22.4426i	−0.497730	+	1.37090i
$269$	5.71569	+	4.69075i	0.348492	+	0.286000i	0.792312	−	0.610116i	$-0.208877\pi$
$269$	5.71569	+	4.69075i	0.348492	+	0.286000i	−0.443820	+	0.896116i	$0.646377\pi$
$270$	−0.0998075	−	0.583264i	−0.00607409	−	0.0354963i
$271$	−4.46307	−	1.84866i	−0.271112	−	0.112298i	0.242986	−	0.970030i	$-0.421873\pi$
$271$	−4.46307	−	1.84866i	−0.271112	−	0.112298i	−0.514098	+	0.857732i	$0.671873\pi$
$272$	5.99900	+	20.4602i	0.363743	+	1.24058i
$273$	−0.0586474	+	0.0242926i	−0.00354950	+	0.00147025i
$274$	10.7890	+	17.1258i	0.651788	+	1.03461i
$275$	0.521219	+	5.29202i	0.0314307	+	0.319121i
$276$	−0.944617	−	0.144620i	−0.0568592	−	0.00870508i
$277$	11.5505	−	21.6094i	0.693999	−	1.29838i	−0.249939	−	0.968261i	$-0.580411\pi$
$277$	11.5505	−	21.6094i	0.693999	−	1.29838i	0.943939	−	0.330120i	$-0.107089\pi$
$278$	1.06325	−	8.45847i	0.0637698	−	0.507306i
$279$	−14.5227	+	2.88875i	−0.869454	+	0.172945i
$280$	4.27676	−	0.0750994i	0.255585	−	0.00448805i
$281$	−5.77725	+	29.0442i	−0.344642	+	1.73263i	0.287503	+	0.957780i	$0.407175\pi$
$281$	−5.77725	+	29.0442i	−0.344642	+	1.73263i	−0.632145	+	0.774850i	$0.717825\pi$
$282$	0.184478	−	0.0923207i	0.0109855	−	0.00549762i
$283$	−2.63202	+	26.7234i	−0.156458	+	1.58854i	0.521378	+	0.853326i	$0.325418\pi$
$283$	−2.63202	+	26.7234i	−0.156458	+	1.58854i	−0.677835	+	0.735214i	$0.737082\pi$
$284$	−2.34581	+	9.18335i	−0.139198	+	0.544932i
$285$	−0.0693421	+	0.228590i	−0.00410747	+	0.0135405i
$286$	3.28291	−	3.11105i	0.194122	−	0.183960i
$287$	−9.31526	−	9.31526i	−0.549862	−	0.549862i
$288$	15.2216	−	7.44106i	0.896940	−	0.438468i
$289$	8.07016	−	8.07016i	0.474715	−	0.474715i
$290$	−0.365448	+	13.5962i	−0.0214598	+	0.798396i
$291$	0.277769	+	0.0842602i	0.0162831	+	0.00493942i
$292$	0.809705	+	5.63941i	0.0473844	+	0.330022i
$293$	−6.87220	−	0.676853i	−0.401478	−	0.0395422i	−0.104737	−	0.994500i	$-0.533400\pi$
$293$	−6.87220	−	0.676853i	−0.401478	−	0.0395422i	−0.296742	+	0.954958i	$0.595900\pi$
$294$	0.441368	+	0.146949i	0.0257411	+	0.00857024i
$295$	−5.37251	−	1.06866i	−0.312800	−	0.0622198i
$296$	13.2791	−	2.88462i	0.771829	−	0.167665i
$297$	−0.434081	−	2.18227i	−0.0251880	−	0.126628i
$298$	−1.60286	−	2.06377i	−0.0928513	−	0.119551i
$299$	3.63116	+	1.94090i	0.209996	+	0.112245i
$300$	−0.0723195	+	0.119393i	−0.00417537	+	0.00689318i
$301$	−6.61913	+	0.651927i	−0.381520	+	0.0375765i
$302$	−6.35885	+	28.0120i	−0.365911	+	1.61191i
$303$	−0.223016	−	0.538407i	−0.0128119	−	0.0309307i
$304$	−13.6897	−	0.127512i	−0.785160	−	0.00731330i
$305$	3.13692	−	7.57319i	0.179619	−	0.433639i
$306$	−18.4292	−	13.0436i	−1.05353	−	0.745655i
$307$	16.0949	−	19.6117i	0.918585	−	1.11930i	−0.0739406	−	0.997263i	$-0.523558\pi$
$307$	16.0949	−	19.6117i	0.918585	−	1.11930i	0.992526	−	0.122036i	$-0.0389425\pi$
$308$	16.0678	−	0.714366i	0.915546	−	0.0407048i
$309$	0.298712	+	0.984721i	0.0169931	+	0.0560188i
$310$	6.07523	+	3.46028i	0.345050	+	0.196531i
$311$	−3.74728	−	2.50385i	−0.212489	−	0.141980i	0.444772	−	0.895644i	$-0.353285\pi$
$311$	−3.74728	−	2.50385i	−0.212489	−	0.141980i	−0.657260	+	0.753664i	$0.728285\pi$
$312$	0.117931	−	0.0137097i	0.00667651	−	0.000776161i
$313$	10.2130	+	15.2849i	0.577275	+	0.863953i	0.999087	−	0.0427304i	$-0.0136057\pi$
$313$	10.2130	+	15.2849i	0.577275	+	0.863953i	−0.421812	+	0.906683i	$0.638606\pi$
$314$	−20.3012	−	17.5946i	−1.14566	−	0.992919i
$315$	−3.50137	+	2.87350i	−0.197280	+	0.161903i
$316$	−20.0291	+	7.06149i	−1.12673	+	0.397240i
$317$	−5.88266	−	11.0057i	−0.330403	−	0.618141i	0.660789	−	0.750572i	$-0.270222\pi$
$317$	−5.88266	−	11.0057i	−0.330403	−	0.618141i	−0.991192	+	0.132431i	$0.957722\pi$
$318$	0.656086	−	0.251327i	0.0367915	−	0.0140937i
$319$			51.1419i			2.86340i
$320$	−7.73234	−	2.05207i	−0.432251	−	0.114714i
$321$		−	0.585348i		−	0.0326709i
$322$	5.23762	+	13.6728i	0.291881	+	0.761953i
$323$	8.60000	+	16.0895i	0.478517	+	0.895242i
$324$	−7.73385	+	16.1567i	−0.429658	+	0.897597i
$325$	0.464904	−	0.381537i	0.0257883	−	0.0211639i
$326$	−8.76972	+	10.1188i	−0.485710	+	0.560429i
$327$	0.360069	+	0.538881i	0.0199119	+	0.0298002i
$328$	11.9943	+	21.5222i	0.662276	+	1.18836i
$329$	−2.62800	−	1.75597i	−0.144886	−	0.0968100i
$330$	−0.259770	+	0.456079i	−0.0142999	+	0.0251063i
$331$	−3.00150	−	9.89462i	−0.164977	−	0.543857i	0.835002	−	0.550247i	$-0.185466\pi$
$331$	−3.00150	−	9.89462i	−0.164977	−	0.543857i	−0.999980	+	0.00638908i	$0.997966\pi$
$332$	3.25565	+	2.97848i	0.178677	+	0.163466i
$333$	−9.12870	+	11.1233i	−0.500249	+	0.609556i
$334$	17.3799	−	24.5560i	0.950988	−	1.34364i
$335$	−4.56848	+	11.0293i	−0.249603	+	0.602594i
$336$	0.348844	+	0.237820i	0.0190310	+	0.0129741i
$337$	−7.22377	−	17.4397i	−0.393504	−	0.950002i	−0.989171	−	0.146771i	$-0.953112\pi$
$337$	−7.22377	−	17.4397i	−0.393504	−	0.950002i	0.595667	−	0.803232i	$-0.296888\pi$
$338$	17.4298	+	3.95665i	0.948056	+	0.215213i
$339$	−0.636156	+	0.0626559i	−0.0345512	+	0.00340300i
$340$	2.54216	+	10.3532i	0.137868	+	0.561482i
$341$	23.1850	+	12.3926i	1.25554	+	0.671099i
$342$	11.4496	−	8.89250i	0.619121	−	0.480851i
$343$	−3.45572	−	17.3731i	−0.186592	−	0.938059i
$344$	12.2413	+	2.21226i	0.660006	+	0.119277i
$345$	−0.468631	−	0.0932164i	−0.0252302	−	0.00501860i
$346$	3.35479	−	10.0763i	0.180355	−	0.541704i
$347$	14.0563	+	1.38443i	0.754582	+	0.0743199i	0.467991	−	0.883733i	$-0.344978\pi$
$347$	14.0563	+	1.38443i	0.754582	+	0.0743199i	0.286591	+	0.958053i	$0.407478\pi$
$348$	−0.804728	+	1.07455i	−0.0431379	+	0.0576022i
$349$	−1.75408	−	0.532093i	−0.0938935	−	0.0284823i	0.242988	−	0.970029i	$-0.421872\pi$
$349$	−1.75408	−	0.532093i	−0.0938935	−	0.0284823i	−0.336882	+	0.941547i	$0.609372\pi$
$350$	2.13794	+	0.0574649i	0.114277	+	0.00307163i
$351$	−0.177943	+	0.177943i	−0.00949789	+	0.00949789i
$352$	−29.2714	−	6.93206i	−1.56017	−	0.369480i
$353$	−10.9345	−	10.9345i	−0.581984	−	0.581984i	0.353464	−	0.935448i	$-0.385004\pi$
$353$	−10.9345	−	10.9345i	−0.581984	−	0.581984i	−0.935448	+	0.353464i	$0.885004\pi$
$354$	−0.371906	−	0.392451i	−0.0197666	−	0.0208585i
$355$	−1.37569	+	4.53505i	−0.0730142	+	0.240695i
$356$	−13.3960	−	22.5877i	−0.709985	−	1.19715i
$357$	0.0551462	−	0.559909i	0.00291865	−	0.0296335i
$358$	−9.35579	−	18.6950i	−0.494469	−	0.988063i
$359$	−6.71311	+	33.7491i	−0.354304	+	1.78121i	0.233657	+	0.972319i	$0.424931\pi$
$359$	−6.71311	+	33.7491i	−0.354304	+	1.78121i	−0.587962	+	0.808889i	$0.700069\pi$
$360$	7.76852	−	3.37882i	0.409437	−	0.178079i
$361$	7.14594	−	1.42142i	0.376102	−	0.0748114i
$362$	−30.4798	−	3.83140i	−1.60198	−	0.201374i
$363$	−0.568432	+	1.06346i	−0.0298349	+	0.0558172i
$364$	−1.07679	−	1.46611i	−0.0564392	−	0.0768448i
$365$	0.279214	+	2.83490i	0.0146147	+	0.148386i
$366$	0.684569	−	0.431269i	0.0357830	−	0.0225428i
$367$	2.49696	−	1.03428i	0.130340	−	0.0539888i	−0.316560	−	0.948573i	$-0.602528\pi$
$367$	2.49696	−	1.03428i	0.130340	−	0.0539888i	0.446900	+	0.894584i	$0.352528\pi$
$368$	−2.43016	−	27.2760i	−0.126681	−	1.42186i
$369$	−24.1048	−	9.98455i	−1.25485	−	0.519775i
$370$	6.69703	−	1.14599i	0.348162	−	0.0595771i
$371$	−8.32112	−	6.82897i	−0.432011	−	0.354542i
$372$	0.292145	+	0.625205i	0.0151470	+	0.0324154i
$373$	−11.0105	+	3.34001i	−0.570104	+	0.172939i	−0.562159	−	0.827029i	$-0.690029\pi$
$373$	−11.0105	+	3.34001i	−0.570104	+	0.172939i	−0.00794533	+	0.999968i	$0.502529\pi$
$374$	10.6014	+	38.6586i	0.548186	+	1.99899i
$375$	−0.0387755	+	0.0580317i	−0.00200236	+	0.00299674i
$376$	3.82978	+	4.50300i	0.197506	+	0.232225i
$377$	4.80932	−	3.21349i	0.247693	−	0.165503i
$378$	−0.892615	+	0.0637538i	−0.0459111	+	0.00327914i
$379$	17.5539	+	21.3895i	0.901685	+	1.09871i	0.994677	+	0.103039i	$0.0328568\pi$
$379$	17.5539	+	21.3895i	0.901685	+	1.09871i	−0.0929924	+	0.995667i	$0.529643\pi$
$380$	−6.83528	−	0.367712i	−0.350642	−	0.0188633i
$381$	0.535869	−	0.286428i	0.0274534	−	0.0146742i
$382$	3.71952	+	1.65912i	0.190307	+	0.0848881i
$383$	25.3480			1.29522			0.647612	−	0.761971i	$-0.275768\pi$
$383$	25.3480			1.29522			0.647612	+	0.761971i	$0.275768\pi$
$384$	−0.505951	−	0.606242i	−0.0258192	−	0.0309372i
$385$	8.04182			0.409849
$386$	−14.2296	−	6.34725i	−0.724270	−	0.323067i
$387$	−11.6173	+	6.20959i	−0.590542	+	0.315651i
$388$	−0.446821	+	8.30581i	−0.0226839	+	0.421664i
$389$	4.64900	+	5.66482i	0.235714	+	0.287218i	0.877410	−	0.479741i	$-0.159269\pi$
$389$	4.64900	+	5.66482i	0.235714	+	0.287218i	−0.641697	+	0.766958i	$0.721769\pi$
$390$	0.0592117	−	0.00422911i	0.00299830	−	0.000214149i
$391$	−30.3419	+	20.2738i	−1.53445	+	1.02529i
$392$	−1.07348	+	13.2870i	−0.0542189	+	0.671094i
$393$	−0.0766346	+	0.114692i	−0.00386570	+	0.00578543i
$394$	−2.01280	−	7.33977i	−0.101403	−	0.369772i
$395$	−10.1615	+	3.08245i	−0.511280	+	0.155095i
$396$	28.8588	−	13.4851i	1.45021	−	0.677650i
$397$	−10.9830	−	9.01355i	−0.551223	−	0.452377i	0.317089	−	0.948396i	$-0.397295\pi$
$397$	−10.9830	−	9.01355i	−0.551223	−	0.452377i	−0.868312	+	0.496019i	$0.834795\pi$
$398$	19.7532	−	3.38014i	0.990137	−	0.169431i
$399$	0.333753	+	0.138245i	0.0167085	+	0.00692090i
$400$	−3.81678	−	1.19674i	−0.190839	−	0.0598370i
$401$	−0.262544	+	0.108749i	−0.0131108	+	0.00543069i	−0.389229	−	0.921141i	$-0.627259\pi$
$401$	−0.262544	+	0.108749i	−0.0131108	+	0.00543069i	0.376118	+	0.926572i	$0.377259\pi$
$402$	−0.996979	+	0.628082i	−0.0497248	+	0.0313259i
$403$	−0.291434	−	2.95897i	−0.0145173	−	0.147397i
$404$	13.4594	−	9.88538i	0.669632	−	0.491816i
$405$	−4.22192	+	7.89865i	−0.209789	+	0.392487i
$406$	20.4083	+	2.56538i	1.01285	+	0.127318i
$407$	25.0569	−	4.98412i	1.24202	−	0.247054i
$408$	−0.385551	+	0.979079i	−0.0190876	+	0.0484716i
$409$	−0.783182	+	3.93732i	−0.0387259	+	0.194688i	−0.995306	−	0.0967830i	$-0.969145\pi$
$409$	−0.783182	+	3.93732i	−0.0387259	+	0.194688i	0.956580	+	0.291471i	$0.0941447\pi$
$410$	5.51329	+	11.0168i	0.272282	+	0.544082i
$411$	−0.0979122	+	0.994120i	−0.00482965	+	0.0490363i
$412$	−25.3627	+	15.0417i	−1.24953	+	0.741051i
$413$	−2.40472	+	7.92730i	−0.118328	+	0.390077i
$414$	19.9463	+	21.0482i	0.980310	+	1.03446i
$415$	1.56007	+	1.56007i	0.0765810	+	0.0765810i
$416$	1.18738	+	3.18822i	0.0582160	+	0.156315i
$417$	0.297499	−	0.297499i	0.0145686	−	0.0145686i
$418$	−25.7294	−	0.691573i	−1.25847	−	0.0338260i
$419$	21.0036	+	6.37137i	1.02609	+	0.311262i	0.758086	−	0.652155i	$-0.226135\pi$
$419$	21.0036	+	6.37137i	1.02609	+	0.311262i	0.268007	+	0.963417i	$0.413635\pi$
$420$	0.168969	+	0.126540i	0.00824482	+	0.00617450i
$421$	−2.55512	−	0.251658i	−0.124529	−	0.0122651i	0.0355605	−	0.999368i	$-0.488678\pi$
$421$	−2.55512	−	0.251658i	−0.124529	−	0.0122651i	−0.160090	+	0.987102i	$0.551178\pi$
$422$	−8.60130	+	25.8344i	−0.418705	+	1.25760i
$423$	−6.13949	−	1.22122i	−0.298512	−	0.0593778i
$424$	11.4774	+	16.5409i	0.557391	+	0.803296i
$425$	1.03991	+	5.22796i	0.0504428	+	0.253593i
$426$	−0.369433	+	0.286927i	−0.0178991	+	0.0139016i
$427$	−10.9328	−	5.84368i	−0.529073	−	0.282795i
$428$	16.2897	−	3.99982i	0.787391	−	0.193339i
$429$	0.222136	−	0.0218785i	0.0107248	−	0.00105630i
$430$	6.06547	+	1.37689i	0.292503	+	0.0663996i
$431$	−4.01510	−	9.69330i	−0.193400	−	0.466910i	0.797197	−	0.603719i	$-0.206315\pi$
$431$	−4.01510	−	9.69330i	−0.193400	−	0.466910i	−0.990597	+	0.136809i	$0.956315\pi$
$432$	1.63843	+	0.341798i	0.0788289	+	0.0164447i
$433$	13.2939	−	32.0943i	0.638864	−	1.54235i	−0.189330	−	0.981914i	$-0.560632\pi$
$433$	13.2939	−	32.0943i	0.638864	−	1.54235i	0.828194	−	0.560441i	$-0.189368\pi$
$434$	6.10831	−	8.63037i	0.293208	−	0.414271i
$435$	−0.425830	+	0.518876i	−0.0204170	+	0.0248782i
$436$	−12.5361	+	13.7027i	−0.600371	+	0.656239i
$437$	−6.80167	−	22.4221i	−0.325368	−	1.07259i
$438$	−0.139157	+	0.244319i	−0.00664919	+	0.0116740i
$439$	−21.5272	−	14.3840i	−1.02744	−	0.686511i	−0.0768728	−	0.997041i	$-0.524494\pi$
$439$	−21.5272	−	14.3840i	−1.02744	−	0.686511i	−0.950564	+	0.310530i	$0.899494\pi$
$440$	−14.4673	−	4.11266i	−0.689703	−	0.196063i
$441$	−7.84239	−	11.7370i	−0.373447	−	0.558903i
$442$	2.96926	−	3.42604i	0.141234	−	0.162960i
$443$	−8.53637	+	7.00562i	−0.405575	+	0.332847i	−0.814962	−	0.579514i	$-0.803242\pi$
$443$	−8.53637	+	7.00562i	−0.405575	+	0.332847i	0.409387	+	0.912361i	$0.365742\pi$
$444$	0.604901	+	0.289552i	0.0287073	+	0.0137415i
$445$	−6.18975	−	11.5802i	−0.293422	−	0.548954i
$446$	7.12258	+	18.5934i	0.337264	+	0.880424i
$447$		−	0.128962i		−	0.00609967i
$448$	−4.23456	+	11.3331i	−0.200064	+	0.535438i
$449$		−	36.1790i		−	1.70739i	−0.520770	−	0.853697i	$-0.674355\pi$
$449$		−	36.1790i		−	1.70739i	0.520770	−	0.853697i	$-0.325645\pi$
$450$	3.95546	−	1.51522i	0.186462	−	0.0714281i
$451$	21.8362	+	40.8527i	1.02823	+	1.92368i
$452$	−6.09066	−	17.2755i	−0.286480	−	0.812570i
$453$	−1.09583	+	0.899326i	−0.0514867	+	0.0422540i
$454$	−9.83167	−	8.52086i	−0.461423	−	0.399904i
$455$	−0.505305	−	0.756243i	−0.0236891	−	0.0354532i
$456$	−0.529724	−	0.419388i	−0.0248066	−	0.0196396i
$457$	17.2908	+	11.5534i	0.808831	+	0.540444i	0.889842	−	0.456270i	$-0.150815\pi$
$457$	17.2908	+	11.5534i	0.808831	+	0.540444i	−0.0810104	+	0.996713i	$0.525815\pi$
$458$	19.2280	+	10.9518i	0.898467	+	0.511742i
$459$	−0.647440	−	2.13432i	−0.0302199	−	0.0996217i
$460$	−0.608141	−	13.6785i	−0.0283547	−	0.637764i
$461$	18.3651	−	22.3779i	0.855348	−	1.04224i	−0.143270	−	0.989684i	$-0.545762\pi$
$461$	18.3651	−	22.3779i	0.855348	−	1.04224i	0.998618	−	0.0525607i	$-0.0167383\pi$
$462$	0.647899	+	0.458563i	0.0301430	+	0.0213343i
$463$	10.3204	−	24.9157i	0.479631	−	1.15793i	−0.480152	−	0.877186i	$-0.659418\pi$
$463$	10.3204	−	24.9157i	0.479631	−	1.15793i	0.959782	−	0.280745i	$-0.0905817\pi$
$464$	−35.4027	−	15.0521i	−1.64353	−	0.698777i
$465$	0.132044	+	0.318782i	0.00612338	+	0.0147832i
$466$	−5.17083	+	22.7785i	−0.239534	+	1.05519i
$467$	−32.5010	+	3.20107i	−1.50397	+	0.148128i	−0.816185	−	0.577790i	$-0.803915\pi$
$467$	−32.5010	+	3.20107i	−1.50397	+	0.148128i	−0.687781	+	0.725918i	$0.741415\pi$
$468$	−3.08145	−	1.86651i	−0.142440	−	0.0862795i
$469$	15.9220	+	8.51050i	0.735211	+	0.392978i
$470$	1.81300	+	2.33433i	0.0836274	+	0.107675i
$471$	−0.258655	−	1.30035i	−0.0119182	−	0.0599168i
$472$	8.38021	−	13.0315i	0.385730	−	0.599823i
$473$	22.9378	+	4.56262i	1.05468	+	0.209790i
$474$	−0.994441	−	0.331089i	−0.0456762	−	0.0152074i
$475$	−3.40610	−	0.335472i	−0.156283	−	0.0153925i
$476$	15.9586	−	2.29132i	0.731459	−	0.105023i
$477$	−20.4014	−	6.18870i	−0.934117	−	0.283361i
$478$	0.473860	−	17.6296i	0.0216738	−	0.806357i
$479$	15.9619	−	15.9619i	0.729316	−	0.729316i	−0.241167	−	0.970484i	$-0.577530\pi$
$479$	15.9619	−	15.9619i	0.729316	−	0.729316i	0.970484	+	0.241167i	$0.0775302\pi$
$480$	−0.239263	−	0.314058i	−0.0109208	−	0.0143347i
$481$	−2.04314	−	2.04314i	−0.0931591	−	0.0931591i
$482$	21.6839	−	20.5487i	0.987674	−	0.935969i
$483$	−0.209757	+	0.691477i	−0.00954429	+	0.0314633i
$484$	−33.4793	−	8.55203i	−1.52179	−	0.388729i
$485$	−0.407644	+	4.13888i	−0.0185102	+	0.187937i
$486$	−2.37807	+	1.19009i	−0.107871	+	0.0539835i
$487$	2.06077	−	10.3602i	0.0933822	−	0.469464i	−0.905591	−	0.424153i	$-0.860572\pi$
$487$	2.06077	−	10.3602i	0.0933822	−	0.469464i	0.998973	−	0.0453114i	$-0.0144280\pi$
$488$	16.6796	+	16.1040i	0.755051	+	0.728992i
$489$	−0.648136	+	0.128922i	−0.0293097	+	0.00583006i
$490$	−0.831285	+	6.61309i	−0.0375536	+	0.298749i
$491$	13.0276	−	24.3729i	0.587927	−	1.09993i	−0.395472	−	0.918478i	$-0.629419\pi$
$491$	13.0276	−	24.3729i	0.587927	−	1.09993i	0.983399	−	0.181457i	$-0.0580812\pi$
$492$	−0.184019	+	1.20196i	−0.00829623	+	0.0541887i
$493$	5.02480	+	51.0177i	0.226306	+	2.29772i
$494$	1.55166	+	2.46302i	0.0698127	+	0.110816i
$495$	14.7146	−	6.09499i	0.661373	−	0.273950i
$496$	−15.4026	+	12.4023i	−0.691595	+	0.556879i
$497$	6.62139	+	2.74267i	0.297010	+	0.123026i
$498$	0.0367303	+	0.214648i	0.00164592	+	0.00961860i
$499$	−12.7374	−	10.4533i	−0.570203	−	0.467953i	0.304568	−	0.952491i	$-0.401488\pi$
$499$	−12.7374	−	10.4533i	−0.570203	−	0.467953i	−0.874771	+	0.484537i	$0.838988\pi$
$500$	−1.87993	−	0.682542i	−0.0840730	−	0.0305242i
$501$	1.42078	−	0.430989i	0.0634758	−	0.0192552i
$502$	31.1800	−	8.55057i	1.39163	−	0.381630i
$503$	13.8500	−	20.7281i	0.617543	−	0.924218i	−0.382457	−	0.923973i	$-0.624922\pi$
$503$	13.8500	−	20.7281i	0.617543	−	0.924218i	1.00000		0.000244985i	$-7.79810e-5\pi$
$504$	−3.93363	−	12.1926i	−0.175218	−	0.543100i
$505$	6.94261	−	4.63891i	0.308942	−	0.206429i
$506$	−3.66782	−	51.3530i	−0.163054	−	2.28292i
$507$	0.559585	+	0.681856i	0.0248520	+	0.0302823i
$508$	11.6328	+	12.9555i	0.516120	+	0.574808i
$509$	8.21507	−	4.39105i	0.364126	−	0.194630i	−0.279179	−	0.960239i	$-0.590062\pi$
$509$	8.21507	−	4.39105i	0.364126	−	0.194630i	0.643306	+	0.765609i	$0.277562\pi$
$510$	−0.214328	+	0.480494i	−0.00949062	+	0.0212766i
$511$	4.30796			0.190573
$512$	13.4139	−	18.2227i	0.592814	−	0.805339i
$513$	1.43209			0.0632284
$514$	15.2664	−	34.2251i	0.673372	−	1.50960i
$515$	−13.0029	+	6.95018i	−0.572975	+	0.306261i
$516$	0.410158	+	0.456797i	0.0180562	+	0.0201094i
$517$	7.05049	+	8.59105i	0.310080	+	0.377834i
$518$	−0.732020	−	10.2490i	−0.0321631	−	0.450315i
$519$	0.435790	−	0.291186i	0.0191291	−	0.0127816i
$520$	0.522300	+	1.61891i	0.0229044	+	0.0709937i
$521$	−10.1252	+	15.1534i	−0.443593	+	0.663884i	−0.984133	−	0.177435i	$-0.943220\pi$
$521$	−10.1252	+	15.1534i	−0.443593	+	0.663884i	0.540539	+	0.841319i	$0.318220\pi$
$522$	39.2866	−	10.7736i	1.71953	−	0.471550i
$523$	−2.18976	+	0.664257i	−0.0957517	+	0.0290459i	−0.337797	−	0.941219i	$-0.609682\pi$
$523$	−2.18976	+	0.664257i	−0.0957517	+	0.0290459i	0.242045	+	0.970265i	$0.422182\pi$
$524$	−3.71543	−	1.34895i	−0.162309	−	0.0589292i
$525$	0.0815907	+	0.0669598i	0.00356091	+	0.00292236i
$526$	−2.03823	−	11.9112i	−0.0888712	−	0.519354i
$527$	24.3463	+	10.0846i	1.06054	+	0.439290i
$528$	−0.931064	−	1.15630i	−0.0405193	−	0.0503215i
$529$	22.0511	−	9.13385i	0.958742	−	0.397124i
$530$	5.36569	+	8.51717i	0.233071	+	0.369962i
$531$	1.60813	+	16.3276i	0.0697869	+	0.708558i
$532$	−1.56661	+	10.2327i	−0.0679212	+	0.443643i
$533$	2.46967	−	4.62042i	0.106973	−	0.200133i
$534$	0.161645	−	1.28593i	0.00699505	−	0.0556475i
$535$	8.22563	−	1.63618i	0.355625	−	0.0707382i
$536$	−24.2915	−	23.4531i	−1.04923	−	1.01302i
$537$	0.201279	−	1.01190i	0.00868581	−	0.0436665i
$538$	−9.35119	+	4.67973i	−0.403158	+	0.201758i
$539$	−2.45649	+	24.9411i	−0.105808	+	1.07429i
$540$	0.810814	+	0.207116i	0.0348919	+	0.00891286i
$541$	−2.79323	+	9.20805i	−0.120090	+	0.395885i	−0.996290	−	0.0860641i	$-0.972571\pi$
$541$	−2.79323	+	9.20805i	−0.120090	+	0.395885i	0.876199	+	0.481949i	$0.160071\pi$
$542$	4.95884	−	4.69924i	0.213000	−	0.201850i
$543$	−1.07203	−	1.07203i	−0.0460051	−	0.0460051i
$544$	−29.8814	−	4.03924i	−1.28115	−	0.173181i
$545$	−6.56618	+	6.56618i	−0.281264	+	0.281264i
$546$	0.00241213	−	0.0897412i	0.000103229	−	0.00384057i
$547$	33.9721	+	10.3053i	1.45254	+	0.440624i	0.915289	−	0.402798i	$-0.131962\pi$
$547$	33.9721	+	10.3053i	1.45254	+	0.440624i	0.537252	+	0.843422i	$0.319462\pi$
$548$	−28.3345	+	4.06825i	−1.21039	+	0.173787i
$549$	−24.4333	−	2.40647i	−1.04279	−	0.102706i
$550$	−7.13519	−	2.37559i	−0.304245	−	0.101295i
$551$	−32.2840	−	6.42168i	−1.37534	−	0.273573i
$552$	0.730984	−	1.13670i	0.0311127	−	0.0483813i
$553$	3.13289	+	15.7501i	0.133224	+	0.669762i
$554$	21.2553	+	27.3673i	0.903051	+	1.16272i
$555$	0.295722	+	0.158067i	0.0125527	+	0.00670955i
$556$	10.3120	+	6.24623i	0.437326	+	0.264899i
$557$	39.8164	−	3.92157i	1.68708	−	0.166162i	0.791529	−	0.611131i	$-0.209285\pi$
$557$	39.8164	−	3.92157i	1.68708	−	0.166162i	0.895546	+	0.444969i	$0.146785\pi$
$558$	4.63568	−	20.4211i	0.196244	−	0.864493i
$559$	−1.01223	−	2.44374i	−0.0428127	−	0.103359i
$560$	−2.36687	+	5.56691i	−0.100019	+	0.235245i
$561$	−0.757067	+	1.82772i	−0.0319634	+	0.0771665i
$562$	−34.1837	−	24.1941i	−1.44195	−	1.02057i
$563$	16.4100	−	19.9957i	0.691600	−	0.842717i	−0.302276	−	0.953221i	$-0.597746\pi$
$563$	16.4100	−	19.9957i	0.691600	−	0.842717i	0.993876	+	0.110503i	$0.0352463\pi$
$564$	0.0129577	+	0.291449i	0.000545618	+	0.0122722i
$565$	−2.65867	−	8.76447i	−0.111851	−	0.368724i
$566$	−32.9982	−	18.7949i	−1.38702	−	0.790009i
$567$	11.2617	+	7.52486i	0.472949	+	0.316014i
$568$	−10.5093	−	8.32033i	−0.440961	−	0.349113i
$569$	−1.92474	−	2.88057i	−0.0806891	−	0.120760i	0.788930	−	0.614483i	$-0.210635\pi$
$569$	−1.92474	−	2.88057i	−0.0806891	−	0.120760i	−0.869619	+	0.493724i	$0.835635\pi$
$570$	−0.255287	−	0.221251i	−0.0106928	−	0.00926719i
$571$	12.6816	−	10.4075i	0.530709	−	0.435542i	−0.330490	−	0.943810i	$-0.607214\pi$
$571$	12.6816	−	10.4075i	0.530709	−	0.435542i	0.861199	+	0.508268i	$0.169714\pi$
$572$	2.12677	+	6.03233i	0.0889246	+	0.252224i
$573$	0.0947504	+	0.177265i	0.00395825	+	0.00740537i
$574$	17.3977	−	6.66454i	0.726166	−	0.278172i
$575$		−	6.84601i		−	0.285498i
$576$	0.841247	+	23.9463i	0.0350519	+	0.997761i
$577$			8.95023i			0.372603i	0.982493	+	0.186302i	$0.0596501\pi$
$577$			8.95023i			0.372603i	−0.982493	+	0.186302i	$0.940350\pi$
$578$	5.77374	+	15.0723i	0.240156	+	0.626924i
$579$	−0.362483	−	0.678159i	−0.0150643	−	0.0281833i
$580$	−17.3496	−	8.30485i	−0.720404	−	0.344840i
$581$	2.57918	−	2.11668i	0.107002	−	0.0878147i
$582$	−0.268851	+	0.310209i	−0.0111442	+	0.0128586i
$583$	21.0289	+	31.4720i	0.870929	+	1.30344i
$584$	−7.75006	−	2.20313i	−0.320700	−	0.0911661i
$585$	−1.49775	−	1.00077i	−0.0619245	−	0.0413766i
$586$	4.83331	−	8.48585i	0.199662	−	0.350547i
$587$	10.4209	+	34.3530i	0.430115	+	1.41790i	0.857805	+	0.513975i	$0.171827\pi$
$587$	10.4209	+	34.3530i	0.430115	+	1.41790i	−0.427690	+	0.903925i	$0.640673\pi$
$588$	−0.444067	+	0.485390i	−0.0183130	+	0.0200171i
$589$	−10.7342	+	13.0797i	−0.442297	+	0.538940i
$590$	4.47537	−	6.32321i	0.184248	−	0.260322i
$591$	0.143738	−	0.347014i	0.00591259	−	0.0142742i
$592$	−3.92452	+	18.8124i	−0.161297	+	0.773185i
$593$	2.77785	+	6.70633i	0.114073	+	0.275396i	0.970597	−	0.240711i	$-0.0773806\pi$
$593$	2.77785	+	6.70633i	0.114073	+	0.275396i	−0.856524	+	0.516107i	$0.827381\pi$
$594$	3.06859	+	0.696585i	0.125906	+	0.0285812i
$595$	8.02229	−	0.790126i	0.328882	−	0.0323920i
$596$	3.58888	−	0.881226i	0.147006	−	0.0360964i
$597$	0.872243	+	0.466224i	0.0356985	+	0.0190813i
$598$	−4.59870	+	3.57166i	−0.188055	+	0.146056i
$599$	1.90124	+	9.55817i	0.0776825	+	0.390536i	0.999992	+	0.00408342i	$0.00129980\pi$
$599$	1.90124	+	9.55817i	0.0776825	+	0.390536i	−0.922309	+	0.386453i	$0.873700\pi$
$600$	−0.112539	−	0.162188i	−0.00459437	−	0.00662128i
$601$	−44.9654	−	8.94418i	−1.83418	−	0.364841i	−0.847930	−	0.530109i	$-0.822151\pi$
$601$	−44.9654	−	8.94418i	−1.83418	−	0.364841i	−0.986249	+	0.165268i	$0.947151\pi$
$602$	2.97133	−	8.92451i	0.121102	−	0.363736i
$603$	35.5837	+	3.50469i	1.44908	+	0.142722i
$604$	−32.5155	−	24.3507i	−1.32304	−	0.990814i
$605$	−16.5332	−	5.01530i	−0.672171	−	0.203901i
$606$	0.823860	+	0.0221443i	0.0334670	+	0.000899551i
$607$	−14.6715	+	14.6715i	−0.595496	+	0.595496i	−0.939111	−	0.343615i	$-0.888349\pi$
$607$	−14.6715	+	14.6715i	−0.595496	+	0.595496i	0.343615	+	0.939111i	$0.388349\pi$
$608$	8.05143	−	17.6075i	0.326529	−	0.714079i
$609$	0.717794	+	0.717794i	0.0290865	+	0.0290865i
$610$	7.97395	+	8.41445i	0.322856	+	0.340691i
$611$	0.364876	−	1.20283i	0.0147613	−	0.0486615i
$612$	27.4637	−	16.2877i	1.11015	−	0.658393i
$613$	2.19463	−	22.2824i	0.0886402	−	0.899979i	−0.843319	−	0.537414i	$-0.819401\pi$
$613$	2.19463	−	22.2824i	0.0886402	−	0.899979i	0.931959	−	0.362565i	$-0.118099\pi$
$614$	16.0571	+	32.0858i	0.648012	+	1.29488i
$615$	−0.118612	+	0.596302i	−0.00478289	+	0.0240452i
$616$	−8.33411	+	21.1639i	−0.335791	+	0.852717i
$617$	2.75169	−	0.547346i	0.110779	−	0.0220353i	−0.139389	−	0.990238i	$-0.544514\pi$
$617$	2.75169	−	0.547346i	0.110779	−	0.0220353i	0.250168	+	0.968202i	$0.419514\pi$
$618$	−1.44391	−	0.181503i	−0.0580824	−	0.00730113i
$619$	11.8682	−	22.2039i	0.477024	−	0.892449i	−0.522191	−	0.852829i	$-0.674885\pi$
$619$	11.8682	−	22.2039i	0.477024	−	0.892449i	0.999215	−	0.0396201i	$-0.0126148\pi$
$620$	−7.96911	+	5.85297i	−0.320047	+	0.235061i
$621$	0.280774	+	2.85075i	0.0112671	+	0.114397i
$622$	5.39268	−	3.39731i	0.216227	−	0.136220i
$623$	−18.3459	+	7.59911i	−0.735012	+	0.304452i
$624$	−0.0502339	+	0.160212i	−0.00201097	+	0.00641360i
$625$	−0.923880	−	0.382683i	−0.0369552	−	0.0153073i
$626$	−25.6250	+	4.38492i	−1.02418	+	0.175257i
$627$	−0.981920	−	0.805841i	−0.0392141	−	0.0321822i
$628$	34.4199	−	16.0837i	1.37351	−	0.641809i
$629$	24.5063	−	7.43390i	0.977130	−	0.296409i
$630$	−1.69410	−	6.17763i	−0.0674947	−	0.246123i
$631$	−19.9559	+	29.8660i	−0.794430	+	1.18895i	0.184113	+	0.982905i	$0.441059\pi$
$631$	−19.9559	+	29.8660i	−0.794430	+	1.18895i	−0.978543	+	0.206043i	$0.933941\pi$
$632$	2.41864	−	29.9368i	0.0962085	−	1.19082i
$633$	−1.11732	+	0.746567i	−0.0444093	+	0.0296734i
$634$	17.6034	−	1.25730i	0.699121	−	0.0499338i
$635$	5.52292	+	6.72970i	0.219170	+	0.267060i
$636$	−0.0533745	+	0.992159i	−0.00211644	+	0.0393417i
$637$	2.49978	−	1.33616i	0.0990450	−	0.0529406i
$638$	−66.0524	−	29.4632i	−2.61504	−	1.16646i
$639$	14.1943			0.561516
$640$	7.10500	−	8.80449i	0.280850	−	0.348028i
$641$	−22.6830			−0.895926			−0.447963	−	0.894052i	$-0.647850\pi$
$641$	−22.6830			−0.895926			−0.447963	+	0.894052i	$0.647850\pi$
$642$	0.756006	+	0.337223i	0.0298372	+	0.0133091i
$643$	−39.5887	+	21.1606i	−1.56122	+	0.834492i	−0.561248	+	0.827647i	$0.689679\pi$
$643$	−39.5887	+	21.1606i	−1.56122	+	0.834492i	−0.999977	+	0.00684468i	$0.997821\pi$
$644$	−20.6765	−	1.11232i	−0.814768	−	0.0438315i
$645$	0.194732	+	0.237282i	0.00766758	+	0.00934297i
$646$	−25.7349	+	1.83808i	−1.01252	+	0.0723182i
$647$	−8.93406	+	5.96955i	−0.351234	+	0.234687i	−0.718654	−	0.695368i	$-0.755241\pi$
$647$	−8.93406	+	5.96955i	−0.351234	+	0.234687i	0.367419	+	0.930055i	$0.380241\pi$
$648$	−16.4117	−	19.2967i	−0.644713	−	0.758044i
$649$	16.1831	−	24.2197i	0.635241	−	0.950705i
$650$	0.224940	+	0.820253i	0.00882286	+	0.0321730i
$651$	0.499344	−	0.151474i	0.0195708	−	0.00593674i
$652$	−8.01665	−	17.1560i	−0.313956	−	0.671883i
$653$	−33.3297	−	27.3530i	−1.30429	−	1.07040i	−0.992753	−	0.120171i	$-0.961656\pi$
$653$	−33.3297	−	27.3530i	−1.30429	−	1.07040i	−0.311538	−	0.950234i	$-0.600844\pi$
$654$	−0.903430	+	0.154594i	−0.0353269	+	0.00604510i
$655$	−1.82592	−	0.756322i	−0.0713447	−	0.0295519i
$656$	−34.7070	+	3.09223i	−1.35508	+	0.120731i
$657$	7.88253	−	3.26505i	0.307527	−	0.127382i
$658$	3.78194	−	2.38257i	0.147435	−	0.0928821i
$659$	0.932517	+	9.46801i	0.0363257	+	0.368821i	0.996112	+	0.0880910i	$0.0280766\pi$
$659$	0.932517	+	9.46801i	0.0363257	+	0.368821i	−0.959787	+	0.280730i	$0.909423\pi$
$660$	−0.439393	−	0.598256i	−0.0171034	−	0.0232871i
$661$	4.88721	−	9.14333i	0.190090	−	0.355634i	−0.768764	−	0.639533i	$-0.779128\pi$
$661$	4.88721	−	9.14333i	0.190090	−	0.355634i	0.958854	+	0.283899i	$0.0916279\pi$
$662$	14.5086	+	1.82377i	0.563892	+	0.0708828i
$663$	0.219447	−	0.0436507i	0.00852260	−	0.00169525i
$664$	−5.72246	+	2.48891i	−0.222075	+	0.0965885i
$665$	−1.00978	+	5.07650i	−0.0391575	+	0.196858i
$666$	−9.10726	−	18.1984i	−0.352899	−	0.705174i
$667$	6.45355	−	65.5240i	0.249883	−	2.53710i
$668$	21.7026	+	36.5939i	0.839697	+	1.41586i
$669$	−0.285246	+	0.940332i	−0.0110283	+	0.0363553i
$670$	−11.6129	−	12.2545i	−0.448647	−	0.473431i
$671$	30.8224	+	30.8224i	1.18989	+	1.18989i
$672$	−0.508128	+	0.313540i	−0.0196014	+	0.0120951i
$673$	7.04545	−	7.04545i	0.271582	−	0.271582i	−0.558155	−	0.829737i	$-0.688490\pi$
$673$	7.04545	−	7.04545i	0.271582	−	0.271582i	0.829737	+	0.558155i	$0.188490\pi$
$674$	26.6859	+	0.717283i	1.02790	+	0.0276287i
$675$	0.400408	+	0.121462i	0.0154117	+	0.00467509i
$676$	−15.1516	+	20.2320i	−0.582755	+	0.778154i
$677$	18.1967	+	1.79222i	0.699358	+	0.0688807i	0.441446	−	0.897288i	$-0.354466\pi$
$677$	18.1967	+	1.79222i	0.699358	+	0.0688807i	0.257912	+	0.966169i	$0.416966\pi$
$678$	0.285570	−	0.857723i	0.0109673	−	0.0329407i
$679$	6.16865	+	1.22702i	0.236731	+	0.0470887i
$680$	−14.8363	−	2.68123i	−0.568944	−	0.102820i
$681$	−0.125264	−	0.629743i	−0.00480012	−	0.0241318i
$682$	−29.3627	+	22.8051i	−1.12436	+	0.873252i
$683$	−19.6473	−	10.5017i	−0.751783	−	0.401836i	0.0505435	−	0.998722i	$-0.483905\pi$
$683$	−19.6473	−	10.5017i	−0.751783	−	0.401836i	−0.802326	+	0.596886i	$0.796405\pi$
$684$	4.88894	+	19.9107i	0.186933	+	0.761305i
$685$	−14.2436	+	1.40287i	−0.544220	+	0.0536010i
$686$	24.4291	+	5.54552i	0.932707	+	0.211729i
$687$	0.417917	+	1.00894i	0.0159445	+	0.0384935i
$688$	−9.90953	+	14.5357i	−0.377797	+	0.554169i
$689$	1.63824	−	3.95507i	0.0624120	−	0.150676i
$690$	0.390375	−	0.551557i	0.0148613	−	0.0209974i
$691$	8.73084	−	10.6386i	0.332137	−	0.404710i	−0.579986	−	0.814626i	$-0.696942\pi$
$691$	8.73084	−	10.6386i	0.332137	−	0.404710i	0.912123	+	0.409916i	$0.134442\pi$
$692$	11.0813	+	10.1379i	0.421247	+	0.385385i
$693$	−6.99188	−	23.0491i	−0.265600	−	0.875565i
$694$	−9.88599	+	17.3568i	−0.375267	+	0.658857i
$695$	5.01219	+	3.34904i	0.190123	+	0.127036i
$696$	−0.924232	−	1.65840i	−0.0350329	−	0.0628617i
$697$	25.7971	+	38.6080i	0.977134	+	1.46238i
$698$	1.69776	−	1.95893i	0.0642612	−	0.0741468i
$699$	−0.891099	+	0.731306i	−0.0337045	+	0.0276605i
$700$	−1.30590	+	2.72815i	−0.0493583	+	0.103114i
$701$	−4.47674	−	8.37539i	−0.169084	−	0.316334i	0.783080	−	0.621921i	$-0.213647\pi$
$701$	−4.47674	−	8.37539i	−0.169084	−	0.316334i	−0.952164	+	0.305587i	$0.901147\pi$
$702$	−0.127308	−	0.332336i	−0.00480493	−	0.0125432i
$703$			16.4433i			0.620170i
$704$	25.8166	−	33.8119i	0.972998	−	1.27433i
$705$			0.145869i			0.00549373i
$706$	20.4219	−	7.82300i	0.768586	−	0.294422i
$707$	−5.95250	−	11.1364i	−0.223867	−	0.418826i
$708$	0.721127	−	0.254241i	0.0271016	−	0.00955497i
$709$	25.8953	−	21.2518i	0.972520	−	0.798126i	−0.00689665	−	0.999976i	$-0.502195\pi$
$709$	25.8953	−	21.2518i	0.972520	−	0.798126i	0.979416	+	0.201850i	$0.0646953\pi$
$710$	−5.06470	−	4.38945i	−0.190075	−	0.164733i
$711$	17.6696	+	26.4444i	0.662662	+	0.991744i
$712$	36.8907	−	4.28863i	1.38254	−	0.160723i
$713$	−28.1413	−	18.8034i	−1.05390	−	0.704192i
$714$	0.691380	+	0.393791i	0.0258742	+	0.0147373i
$715$	0.928368	+	3.06042i	0.0347190	+	0.114453i
$716$	29.5355	−	1.31314i	1.10379	−	0.0490742i
$717$	0.552155	−	0.672803i	0.0206206	−	0.0251263i
$718$	−39.7211	−	28.1134i	−1.48238	−	1.04918i
$719$	−9.60658	+	23.1923i	−0.358265	+	0.864928i	0.637279	+	0.770633i	$0.280060\pi$
$719$	−9.60658	+	23.1923i	−0.358265	+	0.864928i	−0.995544	+	0.0942952i	$0.969940\pi$
$720$	−0.111587	+	11.9800i	−0.00415859	+	0.446468i
$721$	8.53268	+	20.5997i	0.317774	+	0.767174i
$722$	−2.28099	+	10.0482i	−0.0848898	+	0.373956i
$723$	1.46723	−	0.144509i	0.0545668	−	0.00537436i
$724$	22.5081	−	37.1589i	0.836506	−	1.38100i
$725$	−8.48182	−	4.53363i	−0.315007	−	0.168375i
$726$	−1.04604	−	1.34682i	−0.0388220	−	0.0499853i
$727$	0.926691	+	4.65879i	0.0343691	+	0.172785i	0.994157	−	0.107940i	$-0.0344253\pi$
$727$	0.926691	+	4.65879i	0.0343691	+	0.172785i	−0.959788	+	0.280724i	$0.909425\pi$
$728$	2.51390	−	0.546096i	0.0931712	−	0.0202397i
$729$	26.2236	+	5.21619i	0.971243	+	0.193192i
$730$	−3.82228	−	1.27259i	−0.141469	−	0.0471006i
$731$	23.3304	+	2.29784i	0.862906	+	0.0849888i
$732$	0.162620	+	1.13261i	0.00601061	+	0.0418625i
$733$	11.0080	+	3.33923i	0.406588	+	0.123337i	0.486953	−	0.873428i	$-0.338108\pi$
$733$	11.0080	+	3.33923i	0.406588	+	0.123337i	−0.0803644	+	0.996766i	$0.525608\pi$
$734$	−0.102698	+	3.82081i	−0.00379066	+	0.141029i
$735$	−0.232594	+	0.232594i	−0.00857935	+	0.00857935i
$736$	36.6284	+	12.5752i	1.35014	+	0.463529i
$737$	−44.8885	−	44.8885i	−1.65349	−	1.65349i
$738$	26.7825	−	25.3804i	0.985878	−	0.934267i
$739$	−0.686975	+	2.26465i	−0.0252708	+	0.0833066i	−0.968669	−	0.248356i	$-0.920110\pi$
$739$	−0.686975	+	2.26465i	−0.0252708	+	0.0833066i	0.943398	+	0.331663i	$0.107610\pi$
$740$	−2.37811	+	9.30977i	−0.0874209	+	0.342234i
$741$	−0.0140816	+	0.142973i	−0.000517302	+	0.00525225i
$742$	13.6138	−	6.81293i	0.499779	−	0.250111i
$743$	7.31324	−	36.7661i	0.268297	−	1.34882i	−0.577969	−	0.816059i	$-0.696155\pi$
$743$	7.31324	−	36.7661i	0.268297	−	1.34882i	0.846266	−	0.532761i	$-0.178845\pi$
$744$	−0.975790	+	0.0171348i	−0.0357742	+	0.000628191i
$745$	1.81224	−	0.360477i	0.0663953	−	0.0132068i
$746$	2.02946	−	16.1449i	0.0743037	−	0.591106i
$747$	3.11503	−	5.82781i	0.113973	−	0.213228i
$748$	−56.0370	−	8.57920i	−2.04892	−	0.313687i
$749$	−1.24318	−	12.6222i	−0.0454248	−	0.461206i
$750$	−0.0526120	−	0.0835130i	−0.00192112	−	0.00304946i
$751$	14.4048	−	5.96664i	0.525637	−	0.217726i	−0.104054	−	0.994572i	$-0.533182\pi$
$751$	14.4048	−	5.96664i	0.525637	−	0.217726i	0.629691	+	0.776846i	$0.283182\pi$
$752$	−8.02221	+	2.35214i	−0.292540	+	0.0857738i
$753$	1.47415	+	0.610612i	0.0537210	+	0.0222520i
$754$	1.37969	+	8.06279i	0.0502455	+	0.293629i
$755$	−15.7009	−	12.8854i	−0.571415	−	0.468948i
$756$	0.431900	−	1.18959i	0.0157081	−	0.0432648i
$757$	22.7267	−	6.89406i	0.826015	−	0.250569i	0.151151	−	0.988511i	$-0.451702\pi$
$757$	22.7267	−	6.89406i	0.826015	−	0.250569i	0.674864	+	0.737942i	$0.264202\pi$
$758$	−37.7386	+	10.3491i	−1.37073	+	0.375897i
$759$	1.41161	−	2.11262i	0.0512381	−	0.0766832i
$760$	4.41277	−	8.61626i	0.160068	−	0.312545i
$761$	−27.2748	+	18.2244i	−0.988711	+	0.660636i	−0.941064	−	0.338229i	$-0.890172\pi$
$761$	−27.2748	+	18.2244i	−0.988711	+	0.660636i	−0.0476472	+	0.998864i	$0.515172\pi$
$762$	0.0612183	+	0.857115i	0.00221770	+	0.0310500i
$763$	8.90887	+	10.8555i	0.322523	+	0.392995i
$764$	−4.28568	+	3.84811i	−0.155050	+	0.139220i
$765$	14.0800	−	7.52593i	0.509064	−	0.272100i
$766$	−14.6032	+	32.7382i	−0.527634	+	1.18288i
$767$	−3.29444			−0.118955
$768$	1.07447	−	0.304201i	0.0387717	−	0.0109769i
$769$	−17.1737			−0.619300			−0.309650	−	0.950851i	$-0.600212\pi$
$769$	−17.1737			−0.619300			−0.309650	+	0.950851i	$0.600212\pi$
$770$	−4.63295	+	10.3864i	−0.166960	+	0.374300i
$771$	1.63111	−	0.871844i	0.0587428	−	0.0313987i
$772$	16.3956	−	14.7216i	0.590090	−	0.529842i
$773$	6.35425	+	7.74268i	0.228547	+	0.278485i	0.874639	−	0.484774i	$-0.161098\pi$
$773$	6.35425	+	7.74268i	0.228547	+	0.278485i	−0.646093	+	0.763259i	$0.723598\pi$
$774$	−1.32717	−	18.5817i	−0.0477043	−	0.667907i
$775$	−4.11060	+	2.74662i	−0.147657	+	0.0986614i
$776$	−10.4699	−	5.36212i	−0.375849	−	0.192489i
$777$	0.281727	−	0.421635i	0.0101069	−	0.0151261i
$778$	−9.99472	+	2.74087i	−0.358328	+	0.0982650i
$779$	−28.5307	+	8.65469i	−1.02222	+	0.310086i
$780$	−0.0286501	+	0.0789112i	−0.00102584	+	0.00282548i
$781$	−19.4805	−	15.9873i	−0.697068	−	0.572069i
$782$	−8.70445	−	50.8679i	−0.311270	−	1.81903i
$783$	3.71785	+	1.53998i	0.132865	+	0.0550345i
$784$	−16.5424	−	9.04117i	−0.590799	−	0.322899i
$785$	17.5502	−	7.26952i	0.626392	−	0.259460i
$786$	−0.103980	−	0.165052i	−0.00370886	−	0.00588721i
$787$	1.95004	+	19.7990i	0.0695113	+	0.705760i	0.965276	+	0.261232i	$0.0841286\pi$
$787$	1.95004	+	19.7990i	0.0695113	+	0.705760i	−0.895765	+	0.444528i	$0.853371\pi$
$788$	10.6393	+	1.62886i	0.379008	+	0.0580257i
$789$	0.281134	−	0.525965i	0.0100086	−	0.0187248i
$790$	1.87296	−	14.8999i	0.0666369	−	0.530115i
$791$	−13.5847	+	2.70217i	−0.483018	+	0.0960782i
$792$	0.790922	+	45.0414i	0.0281042	+	1.60048i
$793$	0.961783	−	4.83521i	0.0341539	−	0.171703i
$794$	17.9689	−	8.99238i	0.637691	−	0.319128i
$795$	−0.0486946	+	0.494405i	−0.00172702	+	0.0175347i
$796$	−7.01432	+	27.4595i	−0.248616	+	0.973277i
$797$	−12.6144	+	41.5841i	−0.446825	+	1.47298i	0.387582	+	0.921835i	$0.373310\pi$
$797$	−12.6144	+	41.5841i	−0.446825	+	1.47298i	−0.834407	+	0.551149i	$0.814190\pi$
$798$	−0.370827	+	0.351414i	−0.0131271	+	0.0124399i
$799$	7.87745	+	7.87745i	0.278684	+	0.278684i
$800$	3.74452	−	4.24011i	0.132389	−	0.149911i
$801$	−27.8091	+	27.8091i	−0.982586	+	0.982586i
$802$	0.0107983	−	0.401741i	0.000381300	−	0.0141860i
$803$	−14.4956	−	4.39721i	−0.511540	−	0.155174i
$804$	−0.236833	−	1.64949i	−0.00835247	−	0.0581731i
$805$	−10.3033	−	1.01479i	−0.363145	−	0.0357667i
$806$	3.98956	+	1.32828i	0.140526	+	0.0467868i
$807$	−0.506147	−	0.100679i	−0.0178172	−	0.00354406i
$808$	5.01338	+	23.0786i	0.176370	+	0.811901i
$809$	3.46711	+	17.4303i	0.121897	+	0.612818i	0.992642	+	0.121083i	$0.0386369\pi$
$809$	3.46711	+	17.4303i	0.121897	+	0.612818i	−0.870745	+	0.491734i	$0.836363\pi$
$810$	−7.76922	−	10.0033i	−0.272983	−	0.351479i
$811$	7.40134	+	3.95610i	0.259896	+	0.138917i	0.596199	−	0.802836i	$-0.296677\pi$
$811$	7.40134	+	3.95610i	0.259896	+	0.138917i	−0.336303	+	0.941754i	$0.609177\pi$
$812$	−15.0707	+	24.8804i	−0.528877	+	0.873130i
$813$	0.335537	−	0.0330475i	0.0117678	−	0.00115903i
$814$	−7.99819	+	35.2336i	−0.280336	+	1.23494i
$815$	−3.62337	−	8.74759i	−0.126921	−	0.306415i
$816$	−1.04241	−	1.06201i	−0.0364917	−	0.0371779i
$817$	−5.76042	+	13.9069i	−0.201532	+	0.486540i
$818$	−4.63405	−	3.27984i	−0.162026	−	0.114677i
$819$	−1.72818	+	2.10579i	−0.0603875	+	0.0735824i
$820$	−17.4050	+	0.773820i	−0.607810	+	0.0270230i
$821$	12.3889	+	40.8409i	0.432377	+	1.42536i	0.854800	+	0.518958i	$0.173680\pi$
$821$	12.3889	+	40.8409i	0.432377	+	1.42536i	−0.422423	+	0.906399i	$0.638820\pi$
$822$	−1.22755	−	0.699178i	−0.0428156	−	0.0243866i
$823$	−7.58233	−	5.06635i	−0.264303	−	0.176602i	0.416356	−	0.909201i	$-0.363307\pi$
$823$	−7.58233	−	5.06635i	−0.264303	−	0.176602i	−0.680660	+	0.732600i	$0.738307\pi$
$824$	−4.81550	−	41.4228i	−0.167756	−	1.44303i
$825$	−0.206194	−	0.308591i	−0.00717875	−	0.0107438i
$826$	−8.85312	−	7.67278i	−0.308040	−	0.266970i
$827$	−6.76895	+	5.55513i	−0.235379	+	0.193171i	−0.744687	−	0.667413i	$-0.767401\pi$
$827$	−6.76895	+	5.55513i	−0.235379	+	0.193171i	0.509308	+	0.860584i	$0.329901\pi$
$828$	−38.6761	+	13.6357i	−1.34409	+	0.473873i
$829$	13.5868	+	25.4191i	0.471889	+	0.882843i	0.999445	+	0.0333223i	$0.0106088\pi$
$829$	13.5868	+	25.4191i	0.471889	+	0.882843i	−0.527555	+	0.849521i	$0.676891\pi$
$830$	−2.91368	+	1.11614i	−0.101135	+	0.0387419i
$831$			1.71014i			0.0593241i
$832$	−4.80180	−	0.303197i	−0.166473	−	0.0105115i
$833$			25.1219i			0.870421i
$834$	0.212844	+	0.555626i	0.00737017	+	0.0192397i
$835$	10.0279	+	18.7609i	0.347030	+	0.649247i
$836$	15.7161	−	32.8324i	0.543552	−	1.13553i
$837$	1.59905	−	1.31231i	0.0552713	−	0.0453599i
$838$	−20.3293	+	23.4566i	−0.702263	+	0.810295i
$839$	12.4346	+	18.6097i	0.429291	+	0.642479i	0.981553	−	0.191192i	$-0.0612352\pi$
$839$	12.4346	+	18.6097i	0.429291	+	0.642479i	−0.552262	+	0.833671i	$0.686235\pi$
$840$	−0.260776	+	0.145331i	−0.00899763	+	0.00501440i
$841$	−52.7942	−	35.2760i	−1.82049	−	1.21641i
$842$	1.79705	−	3.15509i	0.0619305	−	0.108732i
$843$	−0.599968	−	1.97783i	−0.0206640	−	0.0681201i
$844$	−28.4111	−	25.9924i	−0.977952	−	0.894695i
$845$	−8.01765	+	9.76953i	−0.275815	+	0.336082i
$846$	5.11427	−	7.22590i	0.175832	−	0.248432i
$847$	−9.99882	+	24.1393i	−0.343564	+	0.829436i
$848$	−27.9756	+	5.29430i	−0.960685	+	0.181807i
$849$	−0.717210	−	1.73150i	−0.0246146	−	0.0594248i
$850$	−7.35126	−	1.66877i	−0.252146	−	0.0572384i
$851$	−32.7323	+	3.22385i	−1.12205	+	0.110512i
$852$	−0.157747	−	0.642441i	−0.00540433	−	0.0220097i
$853$	15.6657	+	8.37348i	0.536383	+	0.286703i	0.717263	−	0.696803i	$-0.245395\pi$
$853$	15.6657	+	8.37348i	0.536383	+	0.286703i	−0.180880	+	0.983505i	$0.557895\pi$
$854$	13.8458	−	10.7536i	0.473795	−	0.367981i
$855$	1.99988	+	10.0541i	0.0683946	+	0.343843i
$856$	−4.21862	+	23.3433i	−0.144190	+	0.797856i
$857$	18.7517	+	3.72994i	0.640544	+	0.127412i	0.504668	−	0.863314i	$-0.331615\pi$
$857$	18.7517	+	3.72994i	0.640544	+	0.127412i	0.135876	+	0.990726i	$0.456615\pi$
$858$	−0.0997169	+	0.299504i	−0.00340428	+	0.0102249i
$859$	−23.6541	−	2.32972i	−0.807067	−	0.0794891i	−0.313936	−	0.949444i	$-0.601648\pi$
$859$	−23.6541	−	2.32972i	−0.807067	−	0.0794891i	−0.493131	+	0.869955i	$0.664148\pi$
$860$	−5.27268	+	7.04062i	−0.179797	+	0.240083i
$861$	0.879860	+	0.266903i	0.0299856	+	0.00909602i
$862$	14.8325	+	0.398678i	0.505197	+	0.0135790i
$863$	−4.50409	+	4.50409i	−0.153321	+	0.153321i	−0.779599	−	0.626278i	$-0.784577\pi$
$863$	−4.50409	+	4.50409i	−0.153321	+	0.153321i	0.626278	+	0.779599i	$0.284577\pi$
$864$	−1.38536	+	1.91920i	−0.0471308	+	0.0652925i
$865$	5.31003	+	5.31003i	0.180547	+	0.180547i
$866$	33.7927	+	35.6595i	1.14832	+	1.21176i
$867$	−0.231228	+	0.762256i	−0.00785291	+	0.0258876i
$868$	7.62752	+	12.8612i	0.258895	+	0.436538i
$869$	5.53468	−	56.1946i	0.187751	−	1.90627i
$870$	−0.424830	−	0.848909i	−0.0144031	−	0.0287807i
$871$	−1.40070	+	7.04181i	−0.0474610	+	0.238603i
$872$	−10.4756	−	24.0852i	−0.354747	−	0.815629i
$873$	12.2171	−	2.43014i	0.413487	−	0.0822477i
$874$	32.8778	+	4.13283i	1.11211	+	0.139795i
$875$	−0.712891	+	1.33373i	−0.0241001	+	0.0450881i
$876$	−0.235380	−	0.320482i	−0.00795277	−	0.0108281i
$877$	−0.956839	−	9.71495i	−0.0323101	−	0.328050i	−0.997730	−	0.0673486i	$-0.978546\pi$
$877$	−0.956839	−	9.71495i	−0.0323101	−	0.328050i	0.965419	−	0.260702i	$-0.0839540\pi$
$878$	30.9796	−	19.5167i	1.04551	−	0.658657i
$879$	0.445273	−	0.184438i	0.0150187	−	0.00622094i
$880$	13.6464	−	16.3159i	0.460021	−	0.550010i
$881$	48.0900	+	19.9195i	1.62019	+	0.671106i	0.994082	−	0.108629i	$-0.0346462\pi$
$881$	48.0900	+	19.9195i	1.62019	+	0.671106i	0.626110	+	0.779735i	$0.284646\pi$
$882$	19.6769	−	3.36709i	0.662557	−	0.113376i
$883$	41.8776	+	34.3680i	1.40929	+	1.15658i	0.965487	+	0.260453i	$0.0838718\pi$
$883$	41.8776	+	34.3680i	1.40929	+	1.15658i	0.443805	+	0.896123i	$0.353628\pi$
$884$	2.71429	+	5.80872i	0.0912914	+	0.195368i
$885$	0.365854	−	0.110981i	0.0122980	−	0.00373057i
$886$	−4.13024	−	15.0611i	−0.138758	−	0.505989i
$887$	14.3980	−	21.5481i	0.483437	−	0.723515i	−0.506929	−	0.861988i	$-0.669219\pi$
$887$	14.3980	−	21.5481i	0.483437	−	0.723515i	0.990366	+	0.138473i	$0.0442194\pi$
$888$	−0.722458	+	0.614447i	−0.0242441	+	0.0206195i
$889$	10.9470	−	7.31452i	0.367149	−	0.245321i
$890$	18.5224	−	1.32293i	0.620871	−	0.0443449i
$891$	−30.2134	−	36.8151i	−1.01219	−	1.23335i
$892$	−28.1177	−	1.51263i	−0.941450	−	0.0506465i
$893$	−6.30850	+	3.37197i	−0.211106	+	0.112839i
$894$	0.166560	+	0.0742956i	0.00557061	+	0.00248482i
$895$	14.7823			0.494119
$896$	−12.1977	−	11.9982i	−0.407496	−	0.400832i
$897$	−0.287366			−0.00959486
$898$	46.7270	+	20.8430i	1.55930	+	0.695539i
$899$	−41.9323	+	22.4133i	−1.39852	+	0.747524i
$900$	−0.321788	+	5.98161i	−0.0107263	+	0.199387i
$901$	24.0700	+	29.3294i	0.801889	+	0.977105i
$902$	−65.3434	+	4.66706i	−2.17570	+	0.155396i
$903$	0.385978	−	0.257902i	0.0128445	−	0.00858245i
$904$	25.8210	+	2.08612i	0.858794	+	0.0693835i
$905$	12.0682	−	18.0613i	0.401159	−	0.600377i
$906$	−0.530208	−	1.93343i	−0.0176150	−	0.0642339i
$907$	−22.5223	+	6.83206i	−0.747840	+	0.226855i	−0.641127	−	0.767435i	$-0.721533\pi$
$907$	−22.5223	+	6.83206i	−0.747840	+	0.226855i	−0.106713	+	0.994290i	$0.534033\pi$
$908$	16.6692	−	7.78916i	0.553187	−	0.258492i
$909$	−19.3320	−	15.8654i	−0.641203	−	0.526222i
$910$	1.26783	−	0.216950i	0.0420283	−	0.00719183i
$911$	33.2006	+	13.7521i	1.09999	+	0.455629i	0.857478	−	0.514521i	$-0.172030\pi$
$911$	33.2006	+	13.7521i	1.09999	+	0.455629i	0.242507	+	0.970150i	$0.422030\pi$
$912$	0.846838	−	0.442553i	0.0280416	−	0.0146544i
$913$	−10.8391	+	4.48970i	−0.358722	+	0.148587i
$914$	−24.8831	+	15.6760i	−0.823060	+	0.518516i
$915$	0.0560769	+	0.569359i	0.00185385	+	0.0188224i
$916$	−25.2221	+	18.5246i	−0.833363	+	0.612069i
$917$	−1.40893	+	2.63593i	−0.0465270	+	0.0870460i
$918$	3.12958	+	0.393397i	0.103292	+	0.0129840i
$919$	45.7603	−	9.10229i	1.50949	−	0.300257i	0.630160	−	0.776465i	$-0.282989\pi$
$919$	45.7603	−	9.10229i	1.50949	−	0.300257i	0.879333	+	0.476208i	$0.157989\pi$
$920$	18.0168	+	7.09484i	0.593998	+	0.233910i
$921$	−0.345450	+	1.73669i	−0.0113829	+	0.0572259i
$922$	18.3220	+	36.6115i	0.603402	+	1.20574i
$923$	−0.279369	+	2.83648i	−0.00919553	+	0.0933637i
$924$	−0.965515	+	0.572613i	−0.0317631	+	0.0188376i
$925$	−1.39463	+	4.59748i	−0.0458551	+	0.151164i
$926$	26.2342	+	27.6834i	0.862110	+	0.909734i
$927$	31.2255	+	31.2255i	1.02558	+	1.02558i
$928$	39.8363	−	37.0528i	1.30769	−	1.21632i
$929$	−9.53719	+	9.53719i	−0.312905	+	0.312905i	−0.846034	−	0.533129i	$-0.821016\pi$
$929$	−9.53719	+	9.53719i	−0.312905	+	0.312905i	0.533129	+	0.846034i	$0.321016\pi$
$930$	−0.487794	−	0.0131113i	−0.0159954	−	0.000429935i
$931$	−15.4359	−	4.68244i	−0.505892	−	0.153461i
$932$	−26.4406	−	19.8012i	−0.866092	−	0.648612i
$933$	0.313035	+	0.0308312i	0.0102483	+	0.00100937i
$934$	14.5897	−	43.8208i	0.477389	−	1.43386i
$935$	−27.8003	−	5.52983i	−0.909168	−	0.180845i
$936$	4.18593	−	2.90454i	0.136822	−	0.0949377i
$937$	−1.91675	−	9.63616i	−0.0626175	−	0.314800i	0.936764	−	0.349961i	$-0.113805\pi$
$937$	−1.91675	−	9.63616i	−0.0626175	−	0.314800i	−0.999382	+	0.0351619i	$0.988805\pi$
$938$	−20.1645	+	15.6611i	−0.658395	+	0.511354i
$939$	−1.13153	−	0.604813i	−0.0369260	−	0.0197373i
$940$	−4.05938	+	0.996755i	−0.132402	+	0.0325106i
$941$	60.3325	−	5.94223i	1.96678	−	0.193711i	0.968346	−	0.249611i	$-0.0803028\pi$
$941$	60.3325	−	5.94223i	1.96678	−	0.193711i	0.998436	+	0.0559000i	$0.0178028\pi$
$942$	1.82847	+	0.415072i	0.0595749	+	0.0135238i
$943$	−22.8219	−	55.0968i	−0.743182	−	1.79420i
$944$	12.0029	+	18.3310i	0.390662	+	0.596623i
$945$	0.242155	−	0.584614i	0.00787731	−	0.0190175i
$946$	−19.1075	+	26.9968i	−0.621238	+	0.877742i
$947$	19.7530	−	24.0690i	0.641885	−	0.782139i	−0.345848	−	0.938290i	$-0.612409\pi$
$947$	19.7530	−	24.0690i	0.641885	−	0.782139i	0.987733	+	0.156152i	$0.0499089\pi$
$948$	1.00052	−	1.09363i	0.0324955	−	0.0355194i
$949$	0.497321	+	1.63945i	0.0161437	+	0.0532188i
$950$	2.39556	−	4.20588i	0.0777221	−	0.136457i
$951$	0.724190	+	0.483888i	0.0234835	+	0.0156912i
$952$	−6.23447	+	21.9313i	−0.202060	+	0.710798i
$953$	18.4876	+	27.6687i	0.598873	+	0.896276i	0.999803	−	0.0198322i	$-0.00631320\pi$
$953$	18.4876	+	27.6687i	0.598873	+	0.896276i	−0.400931	+	0.916108i	$0.631313\pi$
$954$	19.7464	−	22.7841i	0.639314	−	0.737663i
$955$	−2.22618	+	1.82698i	−0.0720376	+	0.0591197i
$956$	22.4965	+	10.7685i	0.727588	+	0.348279i
$957$	−1.68261	−	3.14794i	−0.0543910	−	0.101758i
$958$	11.4198	+	29.8113i	0.368957	+	0.963159i
$959$			21.6448i			0.698945i
$960$	0.543462	−	0.128089i	0.0175402	−	0.00413404i
$961$		−	6.55902i		−	0.211581i
$962$	3.81588	−	1.46175i	0.123029	−	0.0471287i
$963$	−11.8412	−	22.1534i	−0.381579	−	0.713884i
$964$	14.0475	+	39.8441i	0.452439	+	1.28329i
$965$	8.51664	−	6.98942i	0.274160	−	0.224998i
$966$	−0.772235	−	0.669277i	−0.0248463	−	0.0215336i
$967$	13.9991	+	20.9511i	0.450180	+	0.673742i	0.985261	−	0.171059i	$-0.0547188\pi$
$967$	13.9991	+	20.9511i	0.450180	+	0.673742i	−0.535081	+	0.844801i	$0.679719\pi$
$968$	30.3330	−	38.3133i	0.974941	−	1.23144i
$969$	−1.05871	−	0.707407i	−0.0340107	−	0.0227252i
$970$	−5.11073	−	2.91093i	−0.164096	−	0.0934644i
$971$	−10.6178	−	35.0020i	−0.340740	−	1.12327i	−0.945161	−	0.326604i	$-0.894096\pi$
$971$	−10.6178	−	35.0020i	−0.340740	−	1.12327i	0.604421	−	0.796665i	$-0.293404\pi$
$972$	−0.167035	−	3.75702i	−0.00535766	−	0.120506i
$973$	5.78331	−	7.04698i	0.185404	−	0.225916i
$974$	12.1935	+	8.63014i	0.390703	+	0.276528i
$975$	−0.0160634	+	0.0387804i	−0.000514440	+	0.00124197i
$976$	−30.4083	+	12.2650i	−0.973346	+	0.392592i
$977$	1.38008	+	3.33181i	0.0441527	+	0.106594i	0.944417	−	0.328749i	$-0.106627\pi$
$977$	1.38008	+	3.33181i	0.0441527	+	0.106594i	−0.900265	+	0.435343i	$0.856627\pi$
$978$	0.206886	−	0.911373i	0.00661548	−	0.0291425i
$979$	69.4877	−	6.84394i	2.22084	−	0.218733i
$980$	−8.06223	−	4.88349i	−0.257539	−	0.155998i
$981$	24.5286	+	13.1108i	0.783138	+	0.418596i
$982$	23.9736	+	30.8672i	0.765027	+	0.985012i
$983$	−6.51728	−	32.7646i	−0.207869	−	1.04503i	−0.933946	−	0.357414i	$-0.883659\pi$
$983$	−6.51728	−	32.7646i	−0.207869	−	1.04503i	0.726077	−	0.687613i	$-0.241341\pi$
$984$	−1.44638	−	0.930129i	−0.0461089	−	0.0296514i
$985$	5.27821	+	1.04990i	0.168178	+	0.0334526i
$986$	−68.7867	−	22.9019i	−2.19062	−	0.729344i
$987$	0.219534	+	0.0216222i	0.00698785	+	0.000688243i
$988$	−4.07503	+	0.585092i	−0.129644	+	0.0186143i
$989$	−28.8127	−	8.74022i	−0.916189	−	0.277923i
$990$	−0.605201	+	22.5160i	−0.0192346	+	0.715606i
$991$	26.3184	−	26.3184i	0.836032	−	0.836032i	−0.152302	−	0.988334i	$-0.548669\pi$
$991$	26.3184	−	26.3184i	0.836032	−	0.836032i	0.988334	+	0.152302i	$0.0486687\pi$
$992$	−7.14465	−	27.0382i	−0.226843	−	0.858464i
$993$	0.510291	+	0.510291i	0.0161936	+	0.0161936i
$994$	−7.35692	+	6.97178i	−0.233347	+	0.221132i
$995$	−4.11351	+	13.5604i	−0.130407	+	0.429895i
$996$	−0.298389	−	0.0762211i	−0.00945482	−	0.00241516i
$997$	3.39278	−	34.4474i	0.107450	−	1.09096i	−0.778647	−	0.627462i	$-0.784094\pi$
$997$	3.39278	−	34.4474i	0.107450	−	1.09096i	0.886097	−	0.463499i	$-0.153406\pi$
$998$	20.8390	−	10.4287i	0.659648	−	0.330116i
$999$	0.392182	−	1.97163i	0.0124081	−	0.0623797i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	640.2.bm.a.101.21	✓	1024
128.109	even	32	inner	640.2.bm.a.621.21	yes	1024

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
640.2.bm.a.101.21	✓	1024	1.1	even	1	trivial
640.2.bm.a.621.21	yes	1024	128.109	even	32	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:	\( N \)	\(=\)	\( 640 = 2^{7} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	640.bm (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.576107 + 1.29155i) q^{2} +(-0.0615529 + 0.0329007i) q^{3} +(-1.33620 - 1.48814i) q^{4} +(-0.634393 - 0.773010i) q^{5} +(-0.00703187 - 0.0984530i) q^{6} +(-1.25743 + 0.840186i) q^{7} +(2.69180 - 0.868443i) q^{8} +(-1.66400 + 2.49036i) q^{9} +(1.36386 - 0.374014i) q^{10} +(5.08865 - 1.54363i) q^{11} +(0.131208 + 0.0476374i) q^{12} +(-0.464904 - 0.381537i) q^{13} +(-0.360730 - 2.10807i) q^{14} +(0.0644814 + 0.0267091i) q^{15} +(-0.429128 + 3.97691i) q^{16} +(4.92463 - 2.03985i) q^{17} +(-2.25778 - 3.58386i) q^{18} +(0.335472 + 3.40610i) q^{19} +(-0.302671 + 1.97696i) q^{20} +(0.0497556 - 0.0930862i) q^{21} +(-0.937937 + 7.46154i) q^{22} +(-6.71447 + 1.33559i) q^{23} +(-0.137116 + 0.142018i) q^{24} +(-0.195090 + 0.980785i) q^{25} +(0.760609 - 0.380641i) q^{26} +(0.0410128 - 0.416410i) q^{27} +(2.93049 + 0.748571i) q^{28} +(-2.79179 + 9.20331i) q^{29} +(-0.0716442 + 0.0678936i) q^{30} +(3.49578 + 3.49578i) q^{31} +(-4.88916 - 2.84537i) q^{32} +(-0.262435 + 0.262435i) q^{33} +(-0.202546 + 7.53557i) q^{34} +(1.44718 + 0.438996i) q^{35} +(5.92945 - 0.851349i) q^{36} +(4.78122 + 0.470909i) q^{37} +(-4.59242 - 1.52900i) q^{38} +(0.0411691 + 0.00818904i) q^{39} +(-2.37898 - 1.52986i) q^{40} +(1.69945 + 8.54373i) q^{41} +(0.0915609 + 0.117889i) q^{42} +(3.87874 + 2.07323i) q^{43} +(-9.09660 - 5.51004i) q^{44} +(2.98071 - 0.293574i) q^{45} +(2.14327 - 9.44151i) q^{46} +(0.799802 + 1.93089i) q^{47} +(-0.104429 - 0.258909i) q^{48} +(-1.80357 + 4.35421i) q^{49} +(-1.15434 - 0.817006i) q^{50} +(-0.236013 + 0.287582i) q^{51} +(0.0534250 + 1.20165i) q^{52} +(2.06626 + 6.81153i) q^{53} +(0.514186 + 0.292867i) q^{54} +(-4.42145 - 2.95432i) q^{55} +(-2.65509 + 3.35362i) q^{56} +(-0.132712 - 0.198618i) q^{57} +(-10.2782 - 8.90783i) q^{58} +(4.23437 - 3.47506i) q^{59} +(-0.0464133 - 0.131646i) q^{60} +(3.86411 + 7.22925i) q^{61} +(-6.52892 + 2.50103i) q^{62} -4.52952i q^{63} +(6.49161 - 4.67536i) q^{64} +0.601421i q^{65} +(-0.187757 - 0.490139i) q^{66} +(-5.62754 - 10.5284i) q^{67} +(-9.61588 - 4.60289i) q^{68} +(0.369353 - 0.303120i) q^{69} +(-1.40071 + 1.61619i) q^{70} +(-2.63291 - 3.94043i) q^{71} +(-2.31644 + 8.14865i) q^{72} +(-2.36854 - 1.58261i) q^{73} +(-3.36269 + 5.90389i) q^{74} +(-0.0202602 - 0.0667888i) q^{75} +(4.62050 - 5.05047i) q^{76} +(-5.10168 + 6.21641i) q^{77} +(-0.0342943 + 0.0484541i) q^{78} +(4.06361 - 9.81043i) q^{79} +(3.34643 - 2.19121i) q^{80} +(-3.42738 - 8.27443i) q^{81} +(-12.0137 - 2.72717i) q^{82} +(-2.19565 + 0.216253i) q^{83} +(-0.205009 + 0.0503386i) q^{84} +(-4.70097 - 2.51272i) q^{85} +(-4.91224 + 3.81518i) q^{86} +(-0.130953 - 0.658343i) q^{87} +(12.3571 - 8.57435i) q^{88} +(12.8784 + 2.56166i) q^{89} +(-1.33804 + 4.01886i) q^{90} +(0.905146 + 0.0891491i) q^{91} +(10.9594 + 8.20746i) q^{92} +(-0.330189 - 0.100162i) q^{93} +(-2.95462 - 0.0794162i) q^{94} +(2.42013 - 2.42013i) q^{95} +(0.394557 + 0.0142838i) q^{96} +(-2.94079 - 2.94079i) q^{97} +(-4.58463 - 4.83789i) q^{98} +(-4.62336 + 15.2412i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1024 q - 192 q^{52} - 128 q^{54} - 32 q^{56} - 288 q^{58} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 288 q^{72} - 32 q^{74} - 128 q^{76} - 192 q^{78}+O(q^{100}) \) 1024 * q - 192 * q^52 - 128 * q^54 - 32 * q^56 - 288 * q^58 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 288 * q^72 - 32 * q^74 - 128 * q^76 - 192 * q^78

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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