LMFDB - Embedded newform 930.2.d.h.559.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [930,2,Mod(559,930)] 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("930.559"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(930, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.d (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [6,0,0,-6,-6,-6,0,0,-6,2,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.3534400.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 3x^{4} + 16x^{3} + x^{2} - 12x + 40 $ x^6 - 2x^5 - 3x^4 + 16x^3 + x^2 - 12x + 40
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			559.3
Root			$2.19082 - 1.44755i$ of defining polynomial
Character	$\chi$	$=$	930.559
Dual form			930.2.d.h.559.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +(0.447553 + 2.19082i) q^{5} -1.00000 q^{6} -3.38164i q^{7} +1.00000i q^{8} -1.00000 q^{9} +(2.19082 - 0.447553i) q^{10} -6.27675 q^{11} +1.00000i q^{12} +6.89511i q^{13} -3.38164 q^{14} +(2.19082 - 0.447553i) q^{15} +1.00000 q^{16} -1.40857i q^{17} +1.00000i q^{18} -1.97307 q^{19} +(-0.447553 - 2.19082i) q^{20} -3.38164 q^{21} +6.27675i q^{22} -2.40857i q^{23} +1.00000 q^{24} +(-4.59939 + 1.96102i) q^{25} +6.89511 q^{26} +1.00000i q^{27} +3.38164i q^{28} -7.79021 q^{29} +(-0.447553 - 2.19082i) q^{30} +1.00000 q^{31} -1.00000i q^{32} +6.27675i q^{33} -1.40857 q^{34} +(7.40857 - 1.51346i) q^{35} +1.00000 q^{36} +1.97307i q^{38} +6.89511 q^{39} +(-2.19082 + 0.447553i) q^{40} -9.58043 q^{41} +3.38164i q^{42} +3.38164i q^{43} +6.27675 q^{44} +(-0.447553 - 2.19082i) q^{45} -2.40857 q^{46} +2.59143i q^{47} -1.00000i q^{48} -4.43550 q^{49} +(1.96102 + 4.59939i) q^{50} -1.40857 q^{51} -6.89511i q^{52} +8.40857i q^{53} +1.00000 q^{54} +(-2.80918 - 13.7512i) q^{55} +3.38164 q^{56} +1.97307i q^{57} +7.79021i q^{58} +0.973070 q^{59} +(-2.19082 + 0.447553i) q^{60} +7.40857 q^{61} -1.00000i q^{62} +3.38164i q^{63} -1.00000 q^{64} +(-15.1059 + 3.08593i) q^{65} +6.27675 q^{66} +1.92204i q^{67} +1.40857i q^{68} -2.40857 q^{69} +(-1.51346 - 7.40857i) q^{70} +0.540394 q^{71} -1.00000i q^{72} -1.43550i q^{73} +(1.96102 + 4.59939i) q^{75} +1.97307 q^{76} +21.2257i q^{77} -6.89511i q^{78} -6.94614 q^{79} +(0.447553 + 2.19082i) q^{80} +1.00000 q^{81} +9.58043i q^{82} -9.19878i q^{83} +3.38164 q^{84} +(3.08593 - 0.630411i) q^{85} +3.38164 q^{86} +7.79021i q^{87} -6.27675i q^{88} -13.3816 q^{89} +(-2.19082 + 0.447553i) q^{90} +23.3168 q^{91} +2.40857i q^{92} -1.00000i q^{93} +2.59143 q^{94} +(-0.883054 - 4.32264i) q^{95} -1.00000 q^{96} -10.6853i q^{97} +4.43550i q^{98} +6.27675 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{4} - 6 q^{5} - 6 q^{6} - 6 q^{9} + 2 q^{10} + 2 q^{11} + 2 q^{14} + 2 q^{15} + 6 q^{16} - 2 q^{19} + 6 q^{20} + 2 q^{21} + 6 q^{24} - 4 q^{25} + 24 q^{26} - 12 q^{29} + 6 q^{30} + 6 q^{31} + 4 q^{34}+ \cdots - 2 q^{99}+O(q^{100}) $ 6 * q - 6 * q^4 - 6 * q^5 - 6 * q^6 - 6 * q^9 + 2 * q^10 + 2 * q^11 + 2 * q^14 + 2 * q^15 + 6 * q^16 - 2 * q^19 + 6 * q^20 + 2 * q^21 + 6 * q^24 - 4 * q^25 + 24 * q^26 - 12 * q^29 + 6 * q^30 + 6 * q^31 + 4 * q^34 + 32 * q^35 + 6 * q^36 + 24 * q^39 - 2 * q^40 + 12 * q^41 - 2 * q^44 + 6 * q^45 - 2 * q^46 - 24 * q^49 + 8 * q^50 + 4 * q^51 + 6 * q^54 - 28 * q^55 - 2 * q^56 - 4 * q^59 - 2 * q^60 + 32 * q^61 - 6 * q^64 - 20 * q^65 - 2 * q^66 - 2 * q^69 - 14 * q^70 + 18 * q^71 + 8 * q^75 + 2 * q^76 - 22 * q^79 - 6 * q^80 + 6 * q^81 - 2 * q^84 - 10 * q^85 - 2 * q^86 - 58 * q^89 - 2 * q^90 + 16 * q^91 + 28 * q^94 + 6 * q^95 - 6 * q^96 - 2 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$-1$	$1$	$1$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	−1.00000			−0.500000
$5$	0.447553	+	2.19082i	0.200152	+	0.979765i
$5$	0.447553	+	2.19082i	0.200152	+	0.979765i
$6$	−1.00000			−0.408248
$7$		−	3.38164i		−	1.27814i	−0.769148	−	0.639070i	$-0.779319\pi$
$7$		−	3.38164i		−	1.27814i	0.769148	−	0.639070i	$-0.220681\pi$
$8$			1.00000i			0.353553i
$9$	−1.00000			−0.333333
$10$	2.19082	−	0.447553i	0.692798	−	0.141529i
$11$	−6.27675			−1.89251			−0.946255	−	0.323420i	$-0.895167\pi$
$11$	−6.27675			−1.89251			−0.946255	+	0.323420i	$0.895167\pi$
$12$			1.00000i			0.288675i
$13$			6.89511i			1.91236i	0.292782	+	0.956179i	$0.405419\pi$
$13$			6.89511i			1.91236i	−0.292782	+	0.956179i	$0.594581\pi$
$14$	−3.38164			−0.903782
$15$	2.19082	−	0.447553i	0.565668	−	0.115558i
$16$	1.00000			0.250000
$17$		−	1.40857i		−	0.341629i	−0.985303	−	0.170814i	$-0.945360\pi$
$17$		−	1.40857i		−	0.341629i	0.985303	−	0.170814i	$-0.0546398\pi$
$18$			1.00000i			0.235702i
$19$	−1.97307			−0.452653			−0.226327	−	0.974051i	$-0.572672\pi$
$19$	−1.97307			−0.452653			−0.226327	+	0.974051i	$0.572672\pi$
$20$	−0.447553	−	2.19082i	−0.100076	−	0.489882i
$21$	−3.38164			−0.737935
$22$			6.27675i			1.33821i
$23$		−	2.40857i		−	0.502222i	−0.967958	−	0.251111i	$-0.919204\pi$
$23$		−	2.40857i		−	0.502222i	0.967958	−	0.251111i	$-0.0807959\pi$
$24$	1.00000			0.204124
$25$	−4.59939	+	1.96102i	−0.919878	+	0.392204i
$26$	6.89511			1.35224
$27$			1.00000i			0.192450i
$28$			3.38164i			0.639070i
$29$	−7.79021			−1.44661			−0.723303	−	0.690531i	$-0.757377\pi$
$29$	−7.79021			−1.44661			−0.723303	+	0.690531i	$0.757377\pi$
$30$	−0.447553	−	2.19082i	−0.0817117	−	0.399987i
$31$	1.00000			0.179605
$31$	1.00000			0.179605
$32$		−	1.00000i		−	0.176777i
$33$			6.27675i			1.09264i
$34$	−1.40857			−0.241568
$35$	7.40857	−	1.51346i	1.25228	−	0.255822i
$36$	1.00000			0.166667
$37$		0			0		1.00000			$0$
$37$		0			0		−1.00000			$\pi$
$38$			1.97307i			0.320074i
$39$	6.89511			1.10410
$40$	−2.19082	+	0.447553i	−0.346399	+	0.0707644i
$41$	−9.58043			−1.49621			−0.748106	−	0.663580i	$-0.769036\pi$
$41$	−9.58043			−1.49621			−0.748106	+	0.663580i	$0.769036\pi$
$42$			3.38164i			0.521799i
$43$			3.38164i			0.515696i	0.966186	+	0.257848i	$0.0830133\pi$
$43$			3.38164i			0.515696i	−0.966186	+	0.257848i	$0.916987\pi$
$44$	6.27675			0.946255
$45$	−0.447553	−	2.19082i	−0.0667173	−	0.326588i
$46$	−2.40857			−0.355124
$47$			2.59143i			0.377999i	0.981977	+	0.188999i	$0.0605244\pi$
$47$			2.59143i			0.377999i	−0.981977	+	0.188999i	$0.939476\pi$
$48$		−	1.00000i		−	0.144338i
$49$	−4.43550			−0.633643
$50$	1.96102	+	4.59939i	0.277330	+	0.650452i
$51$	−1.40857			−0.197239
$52$		−	6.89511i		−	0.956179i
$53$			8.40857i			1.15501i	0.816389	+	0.577503i	$0.195973\pi$
$53$			8.40857i			1.15501i	−0.816389	+	0.577503i	$0.804027\pi$
$54$	1.00000			0.136083
$55$	−2.80918	−	13.7512i	−0.378790	−	1.85422i
$56$	3.38164			0.451891
$57$			1.97307i			0.261340i
$58$			7.79021i			1.02291i
$59$	0.973070			0.126683			0.0633415	−	0.997992i	$-0.479824\pi$
$59$	0.973070			0.126683			0.0633415	+	0.997992i	$0.479824\pi$
$60$	−2.19082	+	0.447553i	−0.282834	+	0.0577789i
$61$	7.40857			0.948570			0.474285	−	0.880371i	$-0.342707\pi$
$61$	7.40857			0.948570			0.474285	+	0.880371i	$0.342707\pi$
$62$		−	1.00000i		−	0.127000i
$63$			3.38164i			0.426047i
$64$	−1.00000			−0.125000
$65$	−15.1059	+	3.08593i	−1.87366	+	0.382762i
$66$	6.27675			0.772614
$67$			1.92204i			0.234814i	0.993084	+	0.117407i	$0.0374582\pi$
$67$			1.92204i			0.234814i	−0.993084	+	0.117407i	$0.962542\pi$
$68$			1.40857i			0.170814i
$69$	−2.40857			−0.289958
$70$	−1.51346	−	7.40857i	−0.180894	−	0.885494i
$71$	0.540394			0.0641330			0.0320665	−	0.999486i	$-0.489791\pi$
$71$	0.540394			0.0641330			0.0320665	+	0.999486i	$0.489791\pi$
$72$		−	1.00000i		−	0.117851i
$73$		−	1.43550i		−	0.168013i	−0.996465	−	0.0840063i	$-0.973228\pi$
$73$		−	1.43550i		−	0.168013i	0.996465	−	0.0840063i	$-0.0267716\pi$
$74$		0			0
$75$	1.96102	+	4.59939i	0.226439	+	0.531092i
$76$	1.97307			0.226327
$77$			21.2257i			2.41889i
$78$		−	6.89511i		−	0.780717i
$79$	−6.94614			−0.781502			−0.390751	−	0.920496i	$-0.627785\pi$
$79$	−6.94614			−0.781502			−0.390751	+	0.920496i	$0.627785\pi$
$80$	0.447553	+	2.19082i	0.0500380	+	0.244941i
$81$	1.00000			0.111111
$82$			9.58043i			1.05798i
$83$		−	9.19878i		−	1.00970i	−0.863208	−	0.504849i	$-0.831548\pi$
$83$		−	9.19878i		−	1.00970i	0.863208	−	0.504849i	$-0.168452\pi$
$84$	3.38164			0.368967
$85$	3.08593	−	0.630411i	0.334716	−	0.0683776i
$86$	3.38164			0.364652
$87$			7.79021i			0.835199i
$88$		−	6.27675i		−	0.669104i
$89$	−13.3816			−1.41845			−0.709226	−	0.704982i	$-0.750955\pi$
$89$	−13.3816			−1.41845			−0.709226	+	0.704982i	$0.750955\pi$
$90$	−2.19082	+	0.447553i	−0.230933	+	0.0471763i
$91$	23.3168			2.44426
$92$			2.40857i			0.251111i
$93$		−	1.00000i		−	0.103695i
$94$	2.59143			0.267285
$95$	−0.883054	−	4.32264i	−0.0905994	−	0.443494i
$96$	−1.00000			−0.102062
$97$		−	10.6853i		−	1.08493i	−0.840078	−	0.542465i	$-0.817491\pi$
$97$		−	10.6853i		−	1.08493i	0.840078	−	0.542465i	$-0.182509\pi$
$98$			4.43550i			0.448053i
$99$	6.27675			0.630837
$100$	4.59939	−	1.96102i	0.459939	−	0.196102i
$101$	18.1988			1.81085			0.905423	−	0.424510i	$-0.139554\pi$
$101$	18.1988			1.81085			0.905423	+	0.424510i	$0.139554\pi$
$102$			1.40857i			0.139469i
$103$		−	0.763283i		−	0.0752086i	−0.999293	−	0.0376043i	$-0.988027\pi$
$103$		−	0.763283i		−	0.0752086i	0.999293	−	0.0376043i	$-0.0119726\pi$
$104$	−6.89511			−0.676121
$105$	−1.51346	−	7.40857i	−0.147699	−	0.723003i
$106$	8.40857			0.816713
$107$			12.3547i			1.19438i	0.802102	+	0.597188i	$0.203715\pi$
$107$			12.3547i			1.19438i	−0.802102	+	0.597188i	$0.796285\pi$
$108$		−	1.00000i		−	0.0962250i
$109$	18.6074			1.78226			0.891131	−	0.453747i	$-0.149913\pi$
$109$	18.6074			1.78226			0.891131	+	0.453747i	$0.149913\pi$
$110$	−13.7512	+	2.80918i	−1.31113	+	0.267845i
$111$		0			0
$112$		−	3.38164i		−	0.319535i
$113$		−	3.38164i		−	0.318118i	−0.987269	−	0.159059i	$-0.949154\pi$
$113$		−	3.38164i		−	0.318118i	0.987269	−	0.159059i	$-0.0508460\pi$
$114$	1.97307			0.184795
$115$	5.27675	−	1.07796i	0.492059	−	0.100521i
$116$	7.79021			0.723303
$117$		−	6.89511i		−	0.637453i
$118$		−	0.973070i		−	0.0895784i
$119$	−4.76328			−0.436649
$120$	0.447553	+	2.19082i	0.0408558	+	0.199994i
$121$	28.3976			2.58160
$122$		−	7.40857i		−	0.670741i
$123$			9.58043i			0.863838i
$124$	−1.00000			−0.0898027
$125$	−6.35471	−	9.19878i	−0.568383	−	0.822764i
$126$	3.38164			0.301261
$127$		−	17.7902i		−	1.57863i	−0.613991	−	0.789313i	$-0.710437\pi$
$127$		−	17.7902i		−	1.57863i	0.613991	−	0.789313i	$-0.289563\pi$
$128$			1.00000i			0.0883883i
$129$	3.38164			0.297737
$130$	3.08593	+	15.1059i	0.270654	+	1.32488i
$131$	−20.1339			−1.75911			−0.879554	−	0.475798i	$-0.842159\pi$
$131$	−20.1339			−1.75911			−0.879554	+	0.475798i	$0.842159\pi$
$132$		−	6.27675i		−	0.546321i
$133$			6.67222i			0.578555i
$134$	1.92204			0.166039
$135$	−2.19082	+	0.447553i	−0.188556	+	0.0385193i
$136$	1.40857			0.120784
$137$			7.94614i			0.678885i	0.940627	+	0.339442i	$0.110238\pi$
$137$			7.94614i			0.678885i	−0.940627	+	0.339442i	$0.889762\pi$
$138$			2.40857i			0.205031i
$139$	−10.9731			−0.930724			−0.465362	−	0.885121i	$-0.654076\pi$
$139$	−10.9731			−0.930724			−0.465362	+	0.885121i	$0.654076\pi$
$140$	−7.40857	+	1.51346i	−0.626139	+	0.127911i
$141$	2.59143			0.218238
$142$		−	0.540394i		−	0.0453489i
$143$		−	43.2788i		−	3.61916i
$144$	−1.00000			−0.0833333
$145$	−3.48654	−	17.0670i	−0.289541	−	1.41733i
$146$	−1.43550			−0.118803
$147$			4.43550i			0.365834i
$148$		0			0
$149$	−15.5135			−1.27091			−0.635456	−	0.772137i	$-0.719188\pi$
$149$	−15.5135			−1.27091			−0.635456	+	0.772137i	$0.719188\pi$
$150$	4.59939	−	1.96102i	0.375539	−	0.160116i
$151$	−10.4355			−0.849229			−0.424615	−	0.905374i	$-0.639590\pi$
$151$	−10.4355			−0.849229			−0.424615	+	0.905374i	$0.639590\pi$
$152$		−	1.97307i		−	0.160037i
$153$			1.40857i			0.113876i
$154$	21.2257			1.71042
$155$	0.447553	+	2.19082i	0.0359483	+	0.175971i
$156$	−6.89511			−0.552050
$157$			0.354712i			0.0283091i	0.999900	+	0.0141546i	$0.00450569\pi$
$157$			0.354712i			0.0283091i	−0.999900	+	0.0141546i	$0.995494\pi$
$158$			6.94614i			0.552605i
$159$	8.40857			0.666843
$160$	2.19082	−	0.447553i	0.173200	−	0.0353822i
$161$	−8.14493			−0.641910
$162$		−	1.00000i		−	0.0785674i
$163$		−	7.05103i		−	0.552280i	−0.961117	−	0.276140i	$-0.910945\pi$
$163$		−	7.05103i		−	0.552280i	0.961117	−	0.276140i	$-0.0890553\pi$
$164$	9.58043			0.748106
$165$	−13.7512	+	2.80918i	−1.07053	+	0.218694i
$166$	−9.19878			−0.713964
$167$			8.19878i			0.634441i	0.948352	+	0.317220i	$0.102750\pi$
$167$			8.19878i			0.634441i	−0.948352	+	0.317220i	$0.897250\pi$
$168$		−	3.38164i		−	0.260899i
$169$	−34.5425			−2.65711
$170$	−0.630411	−	3.08593i	−0.0483503	−	0.236680i
$171$	1.97307			0.150884
$172$		−	3.38164i		−	0.257848i
$173$		−	5.19878i		−	0.395256i	−0.980277	−	0.197628i	$-0.936676\pi$
$173$		−	5.19878i		−	0.395256i	0.980277	−	0.197628i	$-0.0633238\pi$
$174$	7.79021			0.590575
$175$	6.63146	+	15.5535i	0.501291	+	1.17573i
$176$	−6.27675			−0.473128
$177$		−	0.973070i		−	0.0731405i
$178$			13.3816i			1.00300i
$179$	−19.9220			−1.48904			−0.744521	−	0.667599i	$-0.767322\pi$
$179$	−19.9220			−1.48904			−0.744521	+	0.667599i	$0.767322\pi$
$180$	0.447553	+	2.19082i	0.0333587	+	0.163294i
$181$	−22.5425			−1.67557			−0.837785	−	0.546000i	$-0.816150\pi$
$181$	−22.5425			−1.67557			−0.837785	+	0.546000i	$0.816150\pi$
$182$		−	23.3168i		−	1.72835i
$183$		−	7.40857i		−	0.547657i
$184$	2.40857			0.177562
$185$		0			0
$186$	−1.00000			−0.0733236
$187$			8.84125i			0.646536i
$188$		−	2.59143i		−	0.188999i
$189$	3.38164			0.245978
$190$	−4.32264	+	0.883054i	−0.313598	+	0.0640635i
$191$	25.3706			1.83576			0.917878	−	0.396864i	$-0.129901\pi$
$191$	25.3706			1.83576			0.917878	+	0.396864i	$0.129901\pi$
$192$			1.00000i			0.0721688i
$193$			10.8412i			0.780370i	0.920736	+	0.390185i	$0.127589\pi$
$193$			10.8412i			0.780370i	−0.920736	+	0.390185i	$0.872411\pi$
$194$	−10.6853			−0.767161
$195$	3.08593	+	15.1059i	0.220988	+	1.08176i
$196$	4.43550			0.316821
$197$		−	19.1070i		−	1.36132i	−0.732601	−	0.680658i	$-0.761694\pi$
$197$		−	19.1070i		−	1.36132i	0.732601	−	0.680658i	$-0.238306\pi$
$198$		−	6.27675i		−	0.446069i
$199$	−5.87100			−0.416184			−0.208092	−	0.978109i	$-0.566725\pi$
$199$	−5.87100			−0.416184			−0.208092	+	0.978109i	$0.566725\pi$
$200$	−1.96102	−	4.59939i	−0.138665	−	0.325226i
$201$	1.92204			0.135570
$202$		−	18.1988i		−	1.28046i
$203$			26.3437i			1.84897i
$204$	1.40857			0.0986197
$205$	−4.28775	−	20.9890i	−0.299470	−	1.46594i
$206$	−0.763283			−0.0531805
$207$			2.40857i			0.167407i
$208$			6.89511i			0.478090i
$209$	12.3845			0.856651
$210$	−7.40857	+	1.51346i	−0.511240	+	0.104439i
$211$	0.144925			0.00997706			0.00498853	−	0.999988i	$-0.498412\pi$
$211$	0.144925			0.00997706			0.00498853	+	0.999988i	$0.498412\pi$
$212$		−	8.40857i		−	0.577503i
$213$		−	0.540394i		−	0.0370272i
$214$	12.3547			0.844551
$215$	−7.40857	+	1.51346i	−0.505260	+	0.103217i
$216$	−1.00000			−0.0680414
$217$		−	3.38164i		−	0.229561i
$218$		−	18.6074i		−	1.26025i
$219$	−1.43550			−0.0970022
$220$	2.80918	+	13.7512i	0.189395	+	0.927108i
$221$	9.71225			0.653317
$222$		0			0
$223$		−	15.2388i		−	1.02047i	−0.860036	−	0.510233i	$-0.829559\pi$
$223$		−	15.2388i		−	1.02047i	0.860036	−	0.510233i	$-0.170441\pi$
$224$	−3.38164			−0.225945
$225$	4.59939	−	1.96102i	0.306626	−	0.130735i
$226$	−3.38164			−0.224943
$227$		−	16.4086i		−	1.08908i	−0.838736	−	0.544538i	$-0.816705\pi$
$227$		−	16.4086i		−	1.08908i	0.838736	−	0.544538i	$-0.183295\pi$
$228$		−	1.97307i		−	0.130670i
$229$	6.73635			0.445151			0.222575	−	0.974915i	$-0.428554\pi$
$229$	6.73635			0.445151			0.222575	+	0.974915i	$0.428554\pi$
$230$	−1.07796	−	5.27675i	−0.0710788	−	0.347938i
$231$	21.2257			1.39655
$232$		−	7.79021i		−	0.511453i
$233$		−	7.32778i		−	0.480059i	−0.970766	−	0.240030i	$-0.922843\pi$
$233$		−	7.32778i		−	0.480059i	0.970766	−	0.240030i	$-0.0771571\pi$
$234$	−6.89511			−0.450747
$235$	−5.67736	+	1.15980i	−0.370350	+	0.0756572i
$236$	−0.973070			−0.0633415
$237$			6.94614i			0.451200i
$238$			4.76328i			0.308758i
$239$	−2.15593			−0.139455			−0.0697277	−	0.997566i	$-0.522213\pi$
$239$	−2.15593			−0.139455			−0.0697277	+	0.997566i	$0.522213\pi$
$240$	2.19082	−	0.447553i	0.141417	−	0.0288894i
$241$	−5.79021			−0.372980			−0.186490	−	0.982457i	$-0.559711\pi$
$241$	−5.79021			−0.372980			−0.186490	+	0.982457i	$0.559711\pi$
$242$		−	28.3976i		−	1.82546i
$243$		−	1.00000i		−	0.0641500i
$244$	−7.40857			−0.474285
$245$	−1.98512	−	9.71739i	−0.126825	−	0.620821i
$246$	9.58043			0.610826
$247$		−	13.6045i		−	0.865636i
$248$			1.00000i			0.0635001i
$249$	−9.19878			−0.582949
$250$	−9.19878	+	6.35471i	−0.581782	+	0.401907i
$251$	15.7364			0.993270			0.496635	−	0.867960i	$-0.334569\pi$
$251$	15.7364			0.993270			0.496635	+	0.867960i	$0.334569\pi$
$252$		−	3.38164i		−	0.213023i
$253$			15.1180i			0.950460i
$254$	−17.7902			−1.11626
$255$	−0.630411	−	3.08593i	−0.0394778	−	0.193248i
$256$	1.00000			0.0625000
$257$		−	9.38164i		−	0.585211i	−0.956233	−	0.292605i	$-0.905478\pi$
$257$		−	9.38164i		−	0.585211i	0.956233	−	0.292605i	$-0.0945222\pi$
$258$		−	3.38164i		−	0.210532i
$259$		0			0
$260$	15.1059	−	3.08593i	0.936831	−	0.191381i
$261$	7.79021			0.482202
$262$			20.1339i			1.24388i
$263$			25.2147i			1.55481i	0.629003	+	0.777403i	$0.283463\pi$
$263$			25.2147i			1.55481i	−0.629003	+	0.777403i	$0.716537\pi$
$264$	−6.27675			−0.386307
$265$	−18.4217	+	3.76328i	−1.13163	+	0.231177i
$266$	6.67222			0.409100
$267$			13.3816i			0.818943i
$268$		−	1.92204i		−	0.117407i
$269$	5.58043			0.340245			0.170122	−	0.985423i	$-0.445584\pi$
$269$	5.58043			0.340245			0.170122	+	0.985423i	$0.445584\pi$
$270$	0.447553	+	2.19082i	0.0272372	+	0.133329i
$271$	11.7633			0.714569			0.357284	−	0.933996i	$-0.383703\pi$
$271$	11.7633			0.714569			0.357284	+	0.933996i	$0.383703\pi$
$272$		−	1.40857i		−	0.0854072i
$273$		−	23.3168i		−	1.41120i
$274$	7.94614			0.480044
$275$	28.8692	−	12.3088i	1.74088	−	0.742250i
$276$	2.40857			0.144979
$277$			21.3465i			1.28259i	0.767295	+	0.641294i	$0.221602\pi$
$277$			21.3465i			1.28259i	−0.767295	+	0.641294i	$0.778398\pi$
$278$			10.9731i			0.658121i
$279$	−1.00000			−0.0598684
$280$	1.51346	+	7.40857i	0.0904468	+	0.442747i
$281$	−0.871002			−0.0519596			−0.0259798	−	0.999662i	$-0.508271\pi$
$281$	−0.871002			−0.0519596			−0.0259798	+	0.999662i	$0.508271\pi$
$282$		−	2.59143i		−	0.154317i
$283$			1.76611i			0.104984i	0.998621	+	0.0524921i	$0.0167164\pi$
$283$			1.76611i			0.104984i	−0.998621	+	0.0524921i	$0.983284\pi$
$284$	−0.540394			−0.0320665
$285$	−4.32264	+	0.883054i	−0.256051	+	0.0523076i
$286$	−43.2788			−2.55913
$287$			32.3976i			1.91237i
$288$			1.00000i			0.0589256i
$289$	15.0159			0.883290
$290$	−17.0670	+	3.48654i	−1.00221	+	0.204736i
$291$	−10.6853			−0.626385
$292$			1.43550i			0.0840063i
$293$		−	15.6343i		−	0.913365i	−0.889630	−	0.456682i	$-0.849038\pi$
$293$		−	15.6343i		−	0.913365i	0.889630	−	0.456682i	$-0.150962\pi$
$294$	4.43550			0.258684
$295$	0.435501	+	2.13182i	0.0253558	+	0.124120i
$296$		0			0
$297$		−	6.27675i		−	0.364214i
$298$			15.5135i			0.898671i
$299$	16.6074			0.960428
$300$	−1.96102	−	4.59939i	−0.113219	−	0.265546i
$301$	11.4355			0.659131
$302$			10.4355i			0.600496i
$303$		−	18.1988i		−	1.04549i
$304$	−1.97307			−0.113163
$305$	3.31573	+	16.2309i	0.189858	+	0.929376i
$306$	1.40857			0.0805227
$307$		−	0.155928i		−	0.00889927i	−0.999990	−	0.00444964i	$-0.998584\pi$
$307$		−	0.155928i		−	0.00889927i	0.999990	−	0.00444964i	$-0.00141637\pi$
$308$		−	21.2257i		−	1.20945i
$309$	−0.763283			−0.0434217
$310$	2.19082	−	0.447553i	0.124430	−	0.0254193i
$311$	−9.10489			−0.516291			−0.258146	−	0.966106i	$-0.583111\pi$
$311$	−9.10489			−0.516291			−0.258146	+	0.966106i	$0.583111\pi$
$312$			6.89511i			0.390359i
$313$		−	1.58043i		−	0.0893310i	−0.999002	−	0.0446655i	$-0.985778\pi$
$313$		−	1.58043i		−	0.0893310i	0.999002	−	0.0446655i	$-0.0142222\pi$
$314$	0.354712			0.0200176
$315$	−7.40857	+	1.51346i	−0.417426	+	0.0852741i
$316$	6.94614			0.390751
$317$			6.80122i			0.381994i	0.981591	+	0.190997i	$0.0611721\pi$
$317$			6.80122i			0.381994i	−0.981591	+	0.190997i	$0.938828\pi$
$318$		−	8.40857i		−	0.471529i
$319$	48.8972			2.73772
$320$	−0.447553	−	2.19082i	−0.0250190	−	0.122471i
$321$	12.3547			0.689573
$322$			8.14493i			0.453899i
$323$			2.77921i			0.154639i
$324$	−1.00000			−0.0555556
$325$	−13.5214	−	31.7133i	−0.750034	−	1.75914i
$326$	−7.05103			−0.390521
$327$		−	18.6074i		−	1.02899i
$328$		−	9.58043i		−	0.528991i
$329$	8.76328			0.483135
$330$	2.80918	+	13.7512i	0.154640	+	0.756980i
$331$	30.1339			1.65631			0.828155	−	0.560499i	$-0.189391\pi$
$331$	30.1339			1.65631			0.828155	+	0.560499i	$0.189391\pi$
$332$			9.19878i			0.504849i
$333$		0			0
$334$	8.19878			0.448618
$335$	−4.21084	+	0.860214i	−0.230063	+	0.0469985i
$336$	−3.38164			−0.184484
$337$		−	22.7633i		−	1.24000i	−0.784604	−	0.619998i	$-0.787134\pi$
$337$		−	22.7633i		−	1.24000i	0.784604	−	0.619998i	$-0.212866\pi$
$338$			34.5425i			1.87886i
$339$	−3.38164			−0.183666
$340$	−3.08593	+	0.630411i	−0.167358	+	0.0341888i
$341$	−6.27675			−0.339905
$342$		−	1.97307i		−	0.106691i
$343$		−	8.67222i		−	0.468256i
$344$	−3.38164			−0.182326
$345$	−1.07796	−	5.27675i	−0.0580356	−	0.284091i
$346$	−5.19878			−0.279488
$347$			19.9082i			1.06873i	0.845254	+	0.534364i	$0.179449\pi$
$347$			19.9082i			1.06873i	−0.845254	+	0.534364i	$0.820551\pi$
$348$		−	7.79021i		−	0.417599i
$349$	13.1070			0.701601			0.350801	−	0.936450i	$-0.385909\pi$
$349$	13.1070			0.701601			0.350801	+	0.936450i	$0.385909\pi$
$350$	15.5535	−	6.63146i	0.831369	−	0.354466i
$351$	−6.89511			−0.368034
$352$			6.27675i			0.334552i
$353$			26.0960i			1.38895i	0.719517	+	0.694475i	$0.244363\pi$
$353$			26.0960i			1.38895i	−0.719517	+	0.694475i	$0.755637\pi$
$354$	−0.973070			−0.0517181
$355$	0.241855	+	1.18391i	0.0128363	+	0.0628353i
$356$	13.3816			0.709226
$357$			4.76328i			0.252100i
$358$			19.9220i			1.05291i
$359$	−18.0670			−0.953538			−0.476769	−	0.879029i	$-0.658192\pi$
$359$	−18.0670			−0.953538			−0.476769	+	0.879029i	$0.658192\pi$
$360$	2.19082	−	0.447553i	0.115466	−	0.0235881i
$361$	−15.1070			−0.795105
$362$			22.5425i			1.18481i
$363$		−	28.3976i		−	1.49049i
$364$	−23.3168			−1.22213
$365$	3.14493	−	0.642463i	0.164613	−	0.0336281i
$366$	−7.40857			−0.387252
$367$			16.7874i			0.876295i	0.898903	+	0.438147i	$0.144365\pi$
$367$			16.7874i			0.876295i	−0.898903	+	0.438147i	$0.855635\pi$
$368$		−	2.40857i		−	0.125555i
$369$	9.58043			0.498737
$370$		0			0
$371$	28.4348			1.47626
$372$			1.00000i			0.0518476i
$373$			14.6184i			0.756910i	0.925620	+	0.378455i	$0.123545\pi$
$373$			14.6184i			0.756910i	−0.925620	+	0.378455i	$0.876455\pi$
$374$	8.84125			0.457170
$375$	−9.19878	+	6.35471i	−0.475023	+	0.328156i
$376$	−2.59143			−0.133643
$377$		−	53.7143i		−	2.76643i
$378$		−	3.38164i		−	0.173933i
$379$	7.15593			0.367575			0.183788	−	0.982966i	$-0.441164\pi$
$379$	7.15593			0.367575			0.183788	+	0.982966i	$0.441164\pi$
$380$	0.883054	+	4.32264i	0.0452997	+	0.221747i
$381$	−17.7902			−0.911420
$382$		−	25.3706i		−	1.29807i
$383$			13.6825i			0.699143i	0.936910	+	0.349571i	$0.113673\pi$
$383$			13.6825i			0.699143i	−0.936910	+	0.349571i	$0.886327\pi$
$384$	1.00000			0.0510310
$385$	−46.5017	+	9.49964i	−2.36995	+	0.484146i
$386$	10.8412			0.551805
$387$		−	3.38164i		−	0.171899i
$388$			10.6853i			0.542465i
$389$	−15.4245			−0.782053			−0.391027	−	0.920379i	$-0.627880\pi$
$389$	−15.4245			−0.782053			−0.391027	+	0.920379i	$0.627880\pi$
$390$	15.1059	−	3.08593i	0.764919	−	0.156262i
$391$	−3.39264			−0.171573
$392$		−	4.43550i		−	0.224027i
$393$			20.1339i			1.01562i
$394$	−19.1070			−0.962596
$395$	−3.10877	−	15.2178i	−0.156419	−	0.765688i
$396$	−6.27675			−0.315418
$397$			3.17185i			0.159191i	0.996827	+	0.0795954i	$0.0253628\pi$
$397$			3.17185i			0.159191i	−0.996827	+	0.0795954i	$0.974637\pi$
$398$			5.87100i			0.294287i
$399$	6.67222			0.334029
$400$	−4.59939	+	1.96102i	−0.229970	+	0.0980509i
$401$	31.5935			1.57771			0.788853	−	0.614582i	$-0.210675\pi$
$401$	31.5935			1.57771			0.788853	+	0.614582i	$0.210675\pi$
$402$		−	1.92204i		−	0.0958624i
$403$			6.89511i			0.343470i
$404$	−18.1988			−0.905423
$405$	0.447553	+	2.19082i	0.0222391	+	0.108863i
$406$	26.3437			1.30742
$407$		0			0
$408$		−	1.40857i		−	0.0697347i
$409$	15.8441			0.783439			0.391719	−	0.920085i	$-0.371880\pi$
$409$	15.8441			0.783439			0.391719	+	0.920085i	$0.371880\pi$
$410$	−20.9890	+	4.28775i	−1.03657	+	0.211757i
$411$	7.94614			0.391954
$412$			0.763283i			0.0376043i
$413$		−	3.29058i		−	0.161919i
$414$	2.40857			0.118375
$415$	20.1529	−	4.11695i	0.989266	−	0.202093i
$416$	6.89511			0.338060
$417$			10.9731i			0.537354i
$418$		−	12.3845i		−	0.605744i
$419$	−25.0049			−1.22157			−0.610785	−	0.791796i	$-0.709146\pi$
$419$	−25.0049			−1.22157			−0.610785	+	0.791796i	$0.709146\pi$
$420$	1.51346	+	7.40857i	0.0738495	+	0.361501i
$421$	−29.1609			−1.42121			−0.710606	−	0.703590i	$-0.751579\pi$
$421$	−29.1609			−1.42121			−0.710606	+	0.703590i	$0.751579\pi$
$422$		−	0.144925i		−	0.00705485i
$423$		−	2.59143i		−	0.126000i
$424$	−8.40857			−0.408356
$425$	2.76223	+	6.47857i	0.133988	+	0.314257i
$426$	−0.540394			−0.0261822
$427$		−	25.0531i		−	1.21241i
$428$		−	12.3547i		−	0.597188i
$429$	−43.2788			−2.08952
$430$	1.51346	+	7.40857i	0.0729858	+	0.357273i
$431$	−27.4245			−1.32099			−0.660496	−	0.750830i	$-0.729654\pi$
$431$	−27.4245			−1.32099			−0.660496	+	0.750830i	$0.729654\pi$
$432$			1.00000i			0.0481125i
$433$			20.1449i			0.968103i	0.875039	+	0.484052i	$0.160835\pi$
$433$			20.1449i			0.968103i	−0.875039	+	0.484052i	$0.839165\pi$
$434$	−3.38164			−0.162324
$435$	−17.0670	+	3.48654i	−0.818298	+	0.167167i
$436$	−18.6074			−0.891131
$437$			4.75228i			0.227332i
$438$			1.43550i			0.0685909i
$439$	−14.1339			−0.674575			−0.337288	−	0.941402i	$-0.609509\pi$
$439$	−14.1339			−0.674575			−0.337288	+	0.941402i	$0.609509\pi$
$440$	13.7512	−	2.80918i	0.655564	−	0.133922i
$441$	4.43550			0.211214
$442$		−	9.71225i		−	0.461965i
$443$		−	29.3278i		−	1.39341i	−0.717360	−	0.696703i	$-0.754650\pi$
$443$		−	29.3278i		−	1.39341i	0.717360	−	0.696703i	$-0.245350\pi$
$444$		0			0
$445$	−5.98900	−	29.3168i	−0.283906	−	1.38975i
$446$	−15.2388			−0.721579
$447$			15.5135i			0.733762i
$448$			3.38164i			0.159768i
$449$	5.50246			0.259677			0.129839	−	0.991535i	$-0.458554\pi$
$449$	5.50246			0.259677			0.129839	+	0.991535i	$0.458554\pi$
$450$	−1.96102	−	4.59939i	−0.0924433	−	0.216817i
$451$	60.1339			2.83160
$452$			3.38164i			0.159059i
$453$			10.4355i			0.490303i
$454$	−16.4086			−0.770092
$455$	10.4355	+	51.0829i	0.489224	+	2.39480i
$456$	−1.97307			−0.0923975
$457$			38.4996i			1.80094i	0.434921	+	0.900469i	$0.356776\pi$
$457$			38.4996i			1.80094i	−0.434921	+	0.900469i	$0.643224\pi$
$458$		−	6.73635i		−	0.314769i
$459$	1.40857			0.0657465
$460$	−5.27675	+	1.07796i	−0.246030	+	0.0502603i
$461$	−4.15593			−0.193561			−0.0967804	−	0.995306i	$-0.530854\pi$
$461$	−4.15593			−0.193561			−0.0967804	+	0.995306i	$0.530854\pi$
$462$		−	21.2257i		−	0.987510i
$463$			19.7923i			0.919827i	0.887964	+	0.459913i	$0.152120\pi$
$463$			19.7923i			0.919827i	−0.887964	+	0.459913i	$0.847880\pi$
$464$	−7.79021			−0.361652
$465$	2.19082	−	0.447553i	0.101597	−	0.0207548i
$466$	−7.32778			−0.339453
$467$			36.6874i			1.69769i	0.528641	+	0.848846i	$0.322702\pi$
$467$			36.6874i			1.69769i	−0.528641	+	0.848846i	$0.677298\pi$
$468$			6.89511i			0.318726i
$469$	6.49964			0.300125
$470$	1.15980	+	5.67736i	0.0534977	+	0.261877i
$471$	0.354712			0.0163443
$472$			0.973070i			0.0447892i
$473$		−	21.2257i		−	0.975959i
$474$	6.94614			0.319047
$475$	9.07492	−	3.86923i	0.416386	−	0.177532i
$476$	4.76328			0.218325
$477$		−	8.40857i		−	0.385002i
$478$			2.15593i			0.0986098i
$479$	17.9330			0.819381			0.409691	−	0.912224i	$-0.365637\pi$
$479$	17.9330			0.819381			0.409691	+	0.912224i	$0.365637\pi$
$480$	−0.447553	−	2.19082i	−0.0204279	−	0.0999968i
$481$		0			0
$482$			5.79021i			0.263737i
$483$			8.14493i			0.370607i
$484$	−28.3976			−1.29080
$485$	23.4096	−	4.78225i	1.06298	−	0.217151i
$486$	−1.00000			−0.0453609
$487$		−	11.6102i		−	0.526107i	−0.964781	−	0.263054i	$-0.915270\pi$
$487$		−	11.6102i		−	0.526107i	0.964781	−	0.263054i	$-0.0847297\pi$
$488$			7.40857i			0.335370i
$489$	−7.05103			−0.318859
$490$	−9.71739	+	1.98512i	−0.438987	+	0.0896787i
$491$	−3.98900			−0.180021			−0.0900105	−	0.995941i	$-0.528690\pi$
$491$	−3.98900			−0.180021			−0.0900105	+	0.995941i	$0.528690\pi$
$492$		−	9.58043i		−	0.431919i
$493$			10.9731i			0.494202i
$494$	−13.6045			−0.612097
$495$	2.80918	+	13.7512i	0.126263	+	0.618072i
$496$	1.00000			0.0449013
$497$		−	1.82742i		−	0.0819710i
$498$			9.19878i			0.412207i
$499$	22.3437			1.00024			0.500121	−	0.865956i	$-0.333289\pi$
$499$	22.3437			1.00024			0.500121	+	0.865956i	$0.333289\pi$
$500$	6.35471	+	9.19878i	0.284191	+	0.411382i
$501$	8.19878			0.366295
$502$		−	15.7364i		−	0.702348i
$503$			21.6984i			0.967485i	0.875210	+	0.483742i	$0.160723\pi$
$503$			21.6984i			0.967485i	−0.875210	+	0.483742i	$0.839277\pi$
$504$	−3.38164			−0.150630
$505$	8.14493	+	39.8703i	0.362444	+	1.77420i
$506$	15.1180			0.672077
$507$			34.5425i			1.53409i
$508$			17.7902i			0.789313i
$509$	12.4196			0.550488			0.275244	−	0.961374i	$-0.411241\pi$
$509$	12.4196			0.550488			0.275244	+	0.961374i	$0.411241\pi$
$510$	−3.08593	+	0.630411i	−0.136647	+	0.0279151i
$511$	−4.85435			−0.214744
$512$		−	1.00000i		−	0.0441942i
$513$		−	1.97307i		−	0.0871132i
$514$	−9.38164			−0.413806
$515$	1.67222	−	0.341610i	0.0736867	−	0.0150531i
$516$	−3.38164			−0.148868
$517$		−	16.2657i		−	0.715367i
$518$		0			0
$519$	−5.19878			−0.228201
$520$	−3.08593	−	15.1059i	−0.135327	−	0.662439i
$521$	37.7143			1.65230			0.826148	−	0.563453i	$-0.190528\pi$
$521$	37.7143			1.65230			0.826148	+	0.563453i	$0.190528\pi$
$522$		−	7.79021i		−	0.340968i
$523$			26.5425i			1.16062i	0.814395	+	0.580311i	$0.197069\pi$
$523$			26.5425i			1.16062i	−0.814395	+	0.580311i	$0.802931\pi$
$524$	20.1339			0.879554
$525$	15.5535	−	6.63146i	0.678810	−	0.289421i
$526$	25.2147			1.09941
$527$		−	1.40857i		−	0.0613583i
$528$			6.27675i			0.273160i
$529$	17.1988			0.747773
$530$	3.76328	+	18.4217i	0.163467	+	0.800186i
$531$	−0.973070			−0.0422277
$532$		−	6.67222i		−	0.289277i
$533$		−	66.0581i		−	2.86129i
$534$	13.3816			0.579080
$535$	−27.0670	+	5.52939i	−1.17021	+	0.239056i
$536$	−1.92204			−0.0830193
$537$			19.9220i			0.859699i
$538$		−	5.58043i		−	0.240589i
$539$	27.8405			1.19918
$540$	2.19082	−	0.447553i	0.0942779	−	0.0192596i
$541$	−22.6612			−0.974282			−0.487141	−	0.873323i	$-0.661960\pi$
$541$	−22.6612			−0.974282			−0.487141	+	0.873323i	$0.661960\pi$
$542$		−	11.7633i		−	0.505276i
$543$			22.5425i			0.967391i
$544$	−1.40857			−0.0603920
$545$	8.32778	+	40.7654i	0.356723	+	1.74620i
$546$	−23.3168			−0.997866
$547$			27.4245i			1.17259i	0.810099	+	0.586293i	$0.199413\pi$
$547$			27.4245i			1.17259i	−0.810099	+	0.586293i	$0.800587\pi$
$548$		−	7.94614i		−	0.339442i
$549$	−7.40857			−0.316190
$550$	−12.3088	−	28.8692i	−0.524850	−	1.23099i
$551$	15.3706			0.654811
$552$		−	2.40857i		−	0.102516i
$553$			23.4894i			0.998869i
$554$	21.3465			0.906927
$555$		0			0
$556$	10.9731			0.465362
$557$			24.5425i			1.03990i	0.854197	+	0.519949i	$0.174049\pi$
$557$			24.5425i			1.03990i	−0.854197	+	0.519949i	$0.825951\pi$
$558$			1.00000i			0.0423334i
$559$	−23.3168			−0.986195
$560$	7.40857	−	1.51346i	0.313069	−	0.0639556i
$561$	8.84125			0.373278
$562$			0.871002i			0.0367410i
$563$		−	33.0269i		−	1.39192i	−0.718081	−	0.695960i	$-0.754979\pi$
$563$		−	33.0269i		−	1.39192i	0.718081	−	0.695960i	$-0.245021\pi$
$564$	−2.59143			−0.109119
$565$	7.40857	−	1.51346i	0.311681	−	0.0636719i
$566$	1.76611			0.0742351
$567$		−	3.38164i		−	0.142016i
$568$			0.540394i			0.0226744i
$569$	−14.9082			−0.624985			−0.312492	−	0.949920i	$-0.601164\pi$
$569$	−14.9082			−0.624985			−0.312492	+	0.949920i	$0.601164\pi$
$570$	0.883054	+	4.32264i	0.0369871	+	0.181056i
$571$	−14.3437			−0.600266			−0.300133	−	0.953897i	$-0.597031\pi$
$571$	−14.3437			−0.600266			−0.300133	+	0.953897i	$0.597031\pi$
$572$			43.2788i			1.80958i
$573$		−	25.3706i		−	1.05987i
$574$	32.3976			1.35225
$575$	4.72325	+	11.0780i	0.196973	+	0.461983i
$576$	1.00000			0.0416667
$577$			32.1637i			1.33899i	0.742816	+	0.669496i	$0.233490\pi$
$577$			32.1637i			1.33899i	−0.742816	+	0.669496i	$0.766510\pi$
$578$		−	15.0159i		−	0.624580i
$579$	10.8412			0.450547
$580$	3.48654	+	17.0670i	0.144770	+	0.708667i
$581$	−31.1070			−1.29054
$582$			10.6853i			0.442921i
$583$		−	52.7785i		−	2.18586i
$584$	1.43550			0.0594014
$585$	15.1059	−	3.08593i	0.624554	−	0.127587i
$586$	−15.6343			−0.645846
$587$			41.4348i			1.71020i	0.518466	+	0.855098i	$0.326503\pi$
$587$			41.4348i			1.71020i	−0.518466	+	0.855098i	$0.673497\pi$
$588$		−	4.43550i		−	0.182917i
$589$	−1.97307			−0.0812990
$590$	2.13182	−	0.435501i	0.0877658	−	0.0179293i
$591$	−19.1070			−0.785957
$592$		0			0
$593$		−	26.0801i		−	1.07098i	−0.844542	−	0.535490i	$-0.820127\pi$
$593$		−	26.0801i		−	1.07098i	0.844542	−	0.535490i	$-0.179873\pi$
$594$	−6.27675			−0.257538
$595$	−2.13182	−	10.4355i	−0.0873962	−	0.427814i
$596$	15.5135			0.635456
$597$			5.87100i			0.240284i
$598$		−	16.6074i		−	0.679125i
$599$	21.8033			0.890859			0.445430	−	0.895317i	$-0.353051\pi$
$599$	21.8033			0.890859			0.445430	+	0.895317i	$0.353051\pi$
$600$	−4.59939	+	1.96102i	−0.187769	+	0.0800582i
$601$	−3.92414			−0.160069			−0.0800344	−	0.996792i	$-0.525503\pi$
$601$	−3.92414			−0.160069			−0.0800344	+	0.996792i	$0.525503\pi$
$602$		−	11.4355i		−	0.466076i
$603$		−	1.92204i		−	0.0782714i
$604$	10.4355			0.424615
$605$	12.7094	+	62.2140i	0.516712	+	2.52936i
$606$	−18.1988			−0.739275
$607$		−	18.9621i		−	0.769647i	−0.922990	−	0.384823i	$-0.874262\pi$
$607$		−	18.9621i		−	0.769647i	0.922990	−	0.384823i	$-0.125738\pi$
$608$			1.97307i			0.0800186i
$609$	26.3437			1.06750
$610$	16.2309	−	3.31573i	0.657168	−	0.134250i
$611$	−17.8682			−0.722869
$612$		−	1.40857i		−	0.0569381i
$613$		−	18.0560i		−	0.729273i	−0.931150	−	0.364637i	$-0.881193\pi$
$613$		−	18.0560i		−	0.729273i	0.931150	−	0.364637i	$-0.118807\pi$
$614$	−0.155928			−0.00629274
$615$	−20.9890	+	4.28775i	−0.846358	+	0.172899i
$616$	−21.2257			−0.855208
$617$		−	15.7792i		−	0.635247i	−0.948217	−	0.317624i	$-0.897115\pi$
$617$		−	15.7792i		−	0.635247i	0.948217	−	0.317624i	$-0.102885\pi$
$618$			0.763283i			0.0307038i
$619$	−33.5266			−1.34755			−0.673773	−	0.738938i	$-0.735328\pi$
$619$	−33.5266			−1.34755			−0.673773	+	0.738938i	$0.735328\pi$
$620$	−0.447553	−	2.19082i	−0.0179742	−	0.0879855i
$621$	2.40857			0.0966526
$622$			9.10489i			0.365073i
$623$			45.2519i			1.81298i
$624$	6.89511			0.276025
$625$	17.3088	−	18.0390i	0.692353	−	0.721559i
$626$	−1.58043			−0.0631665
$627$		−	12.3845i		−	0.494588i
$628$		−	0.354712i		−	0.0141546i
$629$		0			0
$630$	1.51346	+	7.40857i	0.0602979	+	0.295165i
$631$	−33.2739			−1.32461			−0.662307	−	0.749233i	$-0.730423\pi$
$631$	−33.2739			−1.32461			−0.662307	+	0.749233i	$0.730423\pi$
$632$		−	6.94614i		−	0.276303i
$633$		−	0.144925i		−	0.00576026i
$634$	6.80122			0.270111
$635$	38.9752	−	7.96207i	1.54668	−	0.315965i
$636$	−8.40857			−0.333422
$637$		−	30.5833i		−	1.21175i
$638$		−	48.8972i		−	1.93586i
$639$	−0.540394			−0.0213777
$640$	−2.19082	+	0.447553i	−0.0865998	+	0.0176911i
$641$	−32.9270			−1.30054			−0.650268	−	0.759705i	$-0.725344\pi$
$641$	−32.9270			−1.30054			−0.650268	+	0.759705i	$0.725344\pi$
$642$		−	12.3547i		−	0.487602i
$643$		−	13.6991i		−	0.540242i	−0.962826	−	0.270121i	$-0.912936\pi$
$643$		−	13.6991i		−	0.540242i	0.962826	−	0.270121i	$-0.0870636\pi$
$644$	8.14493			0.320955
$645$	1.51346	+	7.40857i	0.0595926	+	0.291712i
$646$	2.77921			0.109347
$647$			5.32778i			0.209457i	0.994501	+	0.104728i	$0.0333973\pi$
$647$			5.32778i			0.209457i	−0.994501	+	0.104728i	$0.966603\pi$
$648$			1.00000i			0.0392837i
$649$	−6.10772			−0.239749
$650$	−31.7133	+	13.5214i	−1.24390	+	0.530354i
$651$	−3.38164			−0.132537
$652$			7.05103i			0.276140i
$653$			47.1768i			1.84617i	0.384596	+	0.923085i	$0.374341\pi$
$653$			47.1768i			1.84617i	−0.384596	+	0.923085i	$0.625659\pi$
$654$	−18.6074			−0.727605
$655$	−9.01100	−	44.1098i	−0.352089	−	1.72351i
$656$	−9.58043			−0.374053
$657$			1.43550i			0.0560042i
$658$		−	8.76328i		−	0.341628i
$659$	21.4727			0.836458			0.418229	−	0.908342i	$-0.362651\pi$
$659$	21.4727			0.836458			0.418229	+	0.908342i	$0.362651\pi$
$660$	13.7512	−	2.80918i	0.535266	−	0.109347i
$661$	−36.4996			−1.41967			−0.709836	−	0.704367i	$-0.751231\pi$
$661$	−36.4996			−1.41967			−0.709836	+	0.704367i	$0.751231\pi$
$662$		−	30.1339i		−	1.17119i
$663$		−	9.71225i		−	0.377192i
$664$	9.19878			0.356982
$665$	−14.6176	+	2.98617i	−0.566847	+	0.115799i
$666$		0			0
$667$			18.7633i			0.726517i
$668$		−	8.19878i		−	0.317220i
$669$	−15.2388			−0.589167
$670$	0.860214	+	4.21084i	0.0332329	+	0.162679i
$671$	−46.5017			−1.79518
$672$			3.38164i			0.130450i
$673$		−	13.3168i		−	0.513324i	−0.966501	−	0.256662i	$-0.917377\pi$
$673$		−	13.3168i		−	0.513324i	0.966501	−	0.256662i	$-0.0826227\pi$
$674$	−22.7633			−0.876809
$675$	−1.96102	−	4.59939i	−0.0754796	−	0.177031i
$676$	34.5425			1.32856
$677$			28.5425i			1.09698i	0.836158	+	0.548489i	$0.184797\pi$
$677$			28.5425i			1.09698i	−0.836158	+	0.548489i	$0.815203\pi$
$678$			3.38164i			0.129871i
$679$	−36.1339			−1.38669
$680$	0.630411	+	3.08593i	0.0241751	+	0.118340i
$681$	−16.4086			−0.628778
$682$			6.27675i			0.240349i
$683$		−	13.8012i		−	0.528089i	−0.964511	−	0.264044i	$-0.914943\pi$
$683$		−	13.8012i		−	0.528089i	0.964511	−	0.264044i	$-0.0850566\pi$
$684$	−1.97307			−0.0754422
$685$	−17.4086	+	3.55632i	−0.665147	+	0.135880i
$686$	−8.67222			−0.331107
$687$		−	6.73635i		−	0.257008i
$688$			3.38164i			0.128924i
$689$	−57.9780			−2.20879
$690$	−5.27675	+	1.07796i	−0.200882	+	0.0410374i
$691$	17.6612			0.671864			0.335932	−	0.941886i	$-0.390949\pi$
$691$	17.6612			0.671864			0.335932	+	0.941886i	$0.390949\pi$
$692$			5.19878i			0.197628i
$693$		−	21.2257i		−	0.806298i
$694$	19.9082			0.755705
$695$	−4.91103	−	24.0400i	−0.186286	−	0.911890i
$696$	−7.79021			−0.295287
$697$			13.4947i			0.511149i
$698$		−	13.1070i		−	0.496107i
$699$	−7.32778			−0.277162
$700$	−6.63146	−	15.5535i	−0.250646	−	0.587867i
$701$	−10.1428			−0.383089			−0.191545	−	0.981484i	$-0.561350\pi$
$701$	−10.1428			−0.383089			−0.191545	+	0.981484i	$0.561350\pi$
$702$			6.89511i			0.260239i
$703$		0			0
$704$	6.27675			0.236564
$705$	1.15980	+	5.67736i	0.0436807	+	0.213822i
$706$	26.0960			0.982136
$707$		−	61.5418i		−	2.31452i
$708$			0.973070i			0.0365702i
$709$	−9.97307			−0.374547			−0.187273	−	0.982308i	$-0.559965\pi$
$709$	−9.97307			−0.374547			−0.187273	+	0.982308i	$0.559965\pi$
$710$	1.18391	−	0.241855i	0.0444312	−	0.00907667i
$711$	6.94614			0.260501
$712$		−	13.3816i		−	0.501498i
$713$		−	2.40857i		−	0.0902017i
$714$	4.76328			0.178261
$715$	94.8162	−	19.3696i	3.54592	−	0.724382i
$716$	19.9220			0.744521
$717$			2.15593i			0.0805146i
$718$			18.0670i			0.674253i
$719$	−21.7364			−0.810629			−0.405315	−	0.914177i	$-0.632838\pi$
$719$	−21.7364			−0.810629			−0.405315	+	0.914177i	$0.632838\pi$
$720$	−0.447553	−	2.19082i	−0.0166793	−	0.0816471i
$721$	−2.58115			−0.0961271
$722$			15.1070i			0.562224i
$723$			5.79021i			0.215340i
$724$	22.5425			0.837785
$725$	35.8302	−	15.2767i	1.33070	−	0.567364i
$726$	−28.3976			−1.05393
$727$			35.0159i			1.29867i	0.760503	+	0.649334i	$0.224952\pi$
$727$			35.0159i			1.29867i	−0.760503	+	0.649334i	$0.775048\pi$
$728$			23.3168i			0.864177i
$729$	−1.00000			−0.0370370
$730$	−0.642463	−	3.14493i	−0.0237786	−	0.116399i
$731$	4.76328			0.176176
$732$			7.40857i			0.273829i
$733$			14.6074i			0.539535i	0.962925	+	0.269767i	$0.0869468\pi$
$733$			14.6074i			0.539535i	−0.962925	+	0.269767i	$0.913053\pi$
$734$	16.7874			0.619634
$735$	−9.71739	+	1.98512i	−0.358431	+	0.0732224i
$736$	−2.40857			−0.0887811
$737$		−	12.0641i		−	0.444388i
$738$		−	9.58043i		−	0.352660i
$739$	25.4245			0.935255			0.467628	−	0.883926i	$-0.345109\pi$
$739$	25.4245			0.935255			0.467628	+	0.883926i	$0.345109\pi$
$740$		0			0
$741$	−13.6045			−0.499775
$742$		−	28.4348i		−	1.04387i
$743$		−	20.0372i		−	0.735094i	−0.930005	−	0.367547i	$-0.880198\pi$
$743$		−	20.0372i		−	0.735094i	0.930005	−	0.367547i	$-0.119802\pi$
$744$	1.00000			0.0366618
$745$	−6.94310	−	33.9872i	−0.254376	−	1.24520i
$746$	14.6184			0.535216
$747$			9.19878i			0.336566i
$748$		−	8.84125i		−	0.323268i
$749$	41.7792			1.52658
$750$	6.35471	+	9.19878i	0.232041	+	0.335892i
$751$	−13.5804			−0.495557			−0.247778	−	0.968817i	$-0.579700\pi$
$751$	−13.5804			−0.495557			−0.247778	+	0.968817i	$0.579700\pi$
$752$			2.59143i			0.0944997i
$753$		−	15.7364i		−	0.573465i
$754$	−53.7143			−1.95616
$755$	−4.67044	−	22.8623i	−0.169975	−	0.832045i
$756$	−3.38164			−0.122989
$757$			43.4727i			1.58004i	0.613079	+	0.790021i	$0.289931\pi$
$757$			43.4727i			1.58004i	−0.613079	+	0.790021i	$0.710069\pi$
$758$		−	7.15593i		−	0.259915i
$759$	15.1180			0.548748
$760$	4.32264	−	0.883054i	0.156799	−	0.0320317i
$761$	27.5453			0.998517			0.499259	−	0.866453i	$-0.333606\pi$
$761$	27.5453			0.998517			0.499259	+	0.866453i	$0.333606\pi$
$762$			17.7902i			0.644471i
$763$		−	62.9234i		−	2.27798i
$764$	−25.3706			−0.917878
$765$	−3.08593	+	0.630411i	−0.111572	+	0.0227925i
$766$	13.6825			0.494369
$767$			6.70942i			0.242263i
$768$		−	1.00000i		−	0.0360844i
$769$	−12.6184			−0.455030			−0.227515	−	0.973775i	$-0.573060\pi$
$769$	−12.6184			−0.455030			−0.227515	+	0.973775i	$0.573060\pi$
$770$	9.49964	+	46.5017i	0.342343	+	1.67581i
$771$	−9.38164			−0.337872
$772$		−	10.8412i		−	0.390185i
$773$		−	35.6176i		−	1.28108i	−0.767926	−	0.640539i	$-0.778711\pi$
$773$		−	35.6176i		−	1.28108i	0.767926	−	0.640539i	$-0.221289\pi$
$774$	−3.38164			−0.121551
$775$	−4.59939	+	1.96102i	−0.165215	+	0.0704418i
$776$	10.6853			0.383581
$777$		0			0
$778$			15.4245i			0.552995i
$779$	18.9029			0.677265
$780$	−3.08593	−	15.1059i	−0.110494	−	0.540880i
$781$	−3.39192			−0.121372
$782$			3.39264i			0.121321i
$783$		−	7.79021i		−	0.278400i
$784$	−4.43550			−0.158411
$785$	−0.777111	+	0.158753i	−0.0277363	+	0.00566612i
$786$	20.1339			0.718153
$787$			21.9890i			0.783823i	0.920003	+	0.391912i	$0.128186\pi$
$787$			21.9890i			0.783823i	−0.920003	+	0.391912i	$0.871814\pi$
$788$			19.1070i			0.680658i
$789$	25.2147			0.897667
$790$	−15.2178	+	3.10877i	−0.541423	+	0.110605i
$791$	−11.4355			−0.406600
$792$			6.27675i			0.223035i
$793$			51.0829i			1.81401i
$794$	3.17185			0.112565
$795$	3.76328	+	18.4217i	0.133470	+	0.653349i
$796$	5.87100			0.208092
$797$		−	3.79021i		−	0.134256i	−0.997744	−	0.0671281i	$-0.978616\pi$
$797$		−	3.79021i		−	0.134256i	0.997744	−	0.0671281i	$-0.0213836\pi$
$798$		−	6.67222i		−	0.236194i
$799$	3.65021			0.129135
$800$	1.96102	+	4.59939i	0.0693325	+	0.162613i
$801$	13.3816			0.472817
$802$		−	31.5935i		−	1.11561i
$803$			9.01028i			0.317966i
$804$	−1.92204			−0.0677850
$805$	−3.64529	−	17.8441i	−0.128480	−	0.628921i
$806$	6.89511			0.242870
$807$		−	5.58043i		−	0.196440i
$808$			18.1988i			0.640231i
$809$	25.6694			0.902488			0.451244	−	0.892401i	$-0.350980\pi$
$809$	25.6694			0.902488			0.451244	+	0.892401i	$0.350980\pi$
$810$	2.19082	−	0.447553i	0.0769776	−	0.0157254i
$811$	−37.0698			−1.30170			−0.650848	−	0.759208i	$-0.725587\pi$
$811$	−37.0698			−1.30170			−0.650848	+	0.759208i	$0.725587\pi$
$812$		−	26.3437i		−	0.924483i
$813$		−	11.7633i		−	0.412556i
$814$		0			0
$815$	15.4476	−	3.15571i	0.541104	−	0.110540i
$816$	−1.40857			−0.0493099
$817$		−	6.67222i		−	0.233431i
$818$		−	15.8441i		−	0.553975i
$819$	−23.3168			−0.814754
$820$	4.28775	+	20.9890i	0.149735	+	0.732968i
$821$	−43.2147			−1.50820			−0.754102	−	0.656757i	$-0.771928\pi$
$821$	−43.2147			−1.50820			−0.754102	+	0.656757i	$0.771928\pi$
$822$		−	7.94614i		−	0.277153i
$823$			22.9972i			0.801631i	0.916159	+	0.400816i	$0.131273\pi$
$823$			22.9972i			0.801631i	−0.916159	+	0.400816i	$0.868727\pi$
$824$	0.763283			0.0265902
$825$	−12.3088	−	28.8692i	−0.428538	−	1.00510i
$826$	−3.29058			−0.114494
$827$			26.3816i			0.917380i	0.888596	+	0.458690i	$0.151681\pi$
$827$			26.3816i			0.917380i	−0.888596	+	0.458690i	$0.848319\pi$
$828$		−	2.40857i		−	0.0837036i
$829$	31.2739			1.08619			0.543094	−	0.839672i	$-0.317253\pi$
$829$	31.2739			1.08619			0.543094	+	0.839672i	$0.317253\pi$
$830$	−4.11695	−	20.1529i	−0.142901	−	0.699517i
$831$	21.3465			0.740503
$832$		−	6.89511i		−	0.239045i
$833$			6.24772i			0.216471i
$834$	10.9731			0.379966
$835$	−17.9621	+	3.66939i	−0.621603	+	0.126985i
$836$	−12.3845			−0.428326
$837$			1.00000i			0.0345651i
$838$			25.0049i			0.863781i
$839$	21.0960			0.728314			0.364157	−	0.931337i	$-0.381357\pi$
$839$	21.0960			0.728314			0.364157	+	0.931337i	$0.381357\pi$
$840$	7.40857	−	1.51346i	0.255620	−	0.0522195i
$841$	31.6874			1.09267
$842$			29.1609i			1.00495i
$843$			0.871002i			0.0299989i
$844$	−0.144925			−0.00498853
$845$	−15.4596	−	75.6764i	−0.531827	−	2.60335i
$846$	−2.59143			−0.0890952
$847$		−	96.0304i		−	3.29964i
$848$			8.40857i			0.288752i
$849$	1.76611			0.0606127
$850$	6.47857	−	2.76223i	0.222213	−	0.0947438i
$851$		0			0
$852$			0.540394i			0.0185136i
$853$		−	52.3866i		−	1.79368i	−0.442353	−	0.896841i	$-0.645856\pi$
$853$		−	52.3866i		−	1.79368i	0.442353	−	0.896841i	$-0.354144\pi$
$854$	−25.0531			−0.857301
$855$	0.883054	+	4.32264i	0.0301998	+	0.147831i
$856$	−12.3547			−0.422275
$857$		−	19.9780i		−	0.682435i	−0.939984	−	0.341218i	$-0.889161\pi$
$857$		−	19.9780i		−	0.682435i	0.939984	−	0.341218i	$-0.110839\pi$
$858$			43.2788i			1.47752i
$859$	−45.0311			−1.53644			−0.768221	−	0.640185i	$-0.778858\pi$
$859$	−45.0311			−1.53644			−0.768221	+	0.640185i	$0.778858\pi$
$860$	7.40857	−	1.51346i	0.252630	−	0.0516087i
$861$	32.3976			1.10411
$862$			27.4245i			0.934082i
$863$		−	29.2037i		−	0.994106i	−0.867720	−	0.497053i	$-0.834415\pi$
$863$		−	29.2037i		−	0.994106i	0.867720	−	0.497053i	$-0.165585\pi$
$864$	1.00000			0.0340207
$865$	11.3896	−	2.32673i	0.387258	−	0.0791113i
$866$	20.1449			0.684552
$867$		−	15.0159i		−	0.509968i
$868$			3.38164i			0.114780i
$869$	43.5992			1.47900
$870$	3.48654	+	17.0670i	0.118205	+	0.578624i
$871$	−13.2526			−0.449049
$872$			18.6074i			0.630125i
$873$			10.6853i			0.361643i
$874$	4.75228			0.160748
$875$	−31.1070	+	21.4894i	−1.05161	+	0.726473i
$876$	1.43550			0.0485011
$877$		−	38.1559i		−	1.28843i	−0.764843	−	0.644217i	$-0.777183\pi$
$877$		−	38.1559i		−	1.28843i	0.764843	−	0.644217i	$-0.222817\pi$
$878$			14.1339i			0.476997i
$879$	−15.6343			−0.527331
$880$	−2.80918	−	13.7512i	−0.0946974	−	0.463554i
$881$	32.9752			1.11096			0.555481	−	0.831529i	$-0.312534\pi$
$881$	32.9752			1.11096			0.555481	+	0.831529i	$0.312534\pi$
$882$		−	4.43550i		−	0.149351i
$883$		−	47.8813i		−	1.61133i	−0.592369	−	0.805667i	$-0.701807\pi$
$883$		−	47.8813i		−	1.61133i	0.592369	−	0.805667i	$-0.298193\pi$
$884$	−9.71225			−0.326658
$885$	2.13182	−	0.435501i	0.0716604	−	0.0146392i
$886$	−29.3278			−0.985286
$887$		−	12.1077i		−	0.406537i	−0.979123	−	0.203269i	$-0.934844\pi$
$887$		−	12.1077i		−	0.406537i	0.979123	−	0.203269i	$-0.0651565\pi$
$888$		0			0
$889$	−60.1601			−2.01771
$890$	−29.3168	+	5.98900i	−0.982701	+	0.200752i
$891$	−6.27675			−0.210279
$892$			15.2388i			0.510233i
$893$		−	5.11307i		−	0.171102i
$894$	15.5135			0.518848
$895$	−8.91617	−	43.6456i	−0.298035	−	1.45891i
$896$	3.38164			0.112973
$897$		−	16.6074i		−	0.554503i
$898$		−	5.50246i		−	0.183620i
$899$	−7.79021			−0.259818
$900$	−4.59939	+	1.96102i	−0.153313	+	0.0653673i
$901$	11.8441			0.394583
$902$		−	60.1339i		−	2.00224i
$903$		−	11.4355i		−	0.380550i
$904$	3.38164			0.112472
$905$	−10.0890	−	49.3866i	−0.335369	−	1.64167i
$906$	10.4355			0.346696
$907$			1.10489i			0.0366874i	0.999832	+	0.0183437i	$0.00583931\pi$
$907$			1.10489i			0.0366874i	−0.999832	+	0.0183437i	$0.994161\pi$
$908$			16.4086i			0.544538i
$909$	−18.1988			−0.603616
$910$	51.0829	−	10.4355i	1.69338	−	0.345933i
$911$	57.0850			1.89131			0.945655	−	0.325172i	$-0.105422\pi$
$911$	57.0850			1.89131			0.945655	+	0.325172i	$0.105422\pi$
$912$			1.97307i			0.0653349i
$913$			57.7385i			1.91086i
$914$	38.4996			1.27345
$915$	16.2309	−	3.31573i	0.536575	−	0.109615i
$916$	−6.73635			−0.222575
$917$			68.0857i			2.24839i
$918$		−	1.40857i		−	0.0464898i
$919$	40.4996			1.33596			0.667980	−	0.744179i	$-0.267159\pi$
$919$	40.4996			1.33596			0.667980	+	0.744179i	$0.267159\pi$
$920$	1.07796	+	5.27675i	0.0355394	+	0.173969i
$921$	−0.155928			−0.00513800
$922$			4.15593i			0.136868i
$923$			3.72608i			0.122645i
$924$	−21.2257			−0.698275
$925$		0			0
$926$	19.7923			0.650416
$927$			0.763283i			0.0250695i
$928$			7.79021i			0.255726i
$929$	−7.41350			−0.243229			−0.121614	−	0.992577i	$-0.538807\pi$
$929$	−7.41350			−0.243229			−0.121614	+	0.992577i	$0.538807\pi$
$930$	−0.447553	−	2.19082i	−0.0146758	−	0.0718398i
$931$	8.75156			0.286821
$932$			7.32778i			0.240030i
$933$			9.10489i			0.298081i
$934$	36.6874			1.20045
$935$	−19.3696	+	3.95693i	−0.633453	+	0.129405i
$936$	6.89511			0.225374
$937$			41.5343i			1.35687i	0.734662	+	0.678433i	$0.237341\pi$
$937$			41.5343i			1.35687i	−0.734662	+	0.678433i	$0.762659\pi$
$938$		−	6.49964i		−	0.212221i
$939$	−1.58043			−0.0515753
$940$	5.67736	−	1.15980i	0.185175	−	0.0378286i
$941$	−54.4458			−1.77488			−0.887441	−	0.460922i	$-0.847519\pi$
$941$	−54.4458			−1.77488			−0.887441	+	0.460922i	$0.847519\pi$
$942$		−	0.354712i		−	0.0115571i
$943$			23.0751i			0.751430i
$944$	0.973070			0.0316707
$945$	1.51346	+	7.40857i	0.0492330	+	0.241001i
$946$	−21.2257			−0.690107
$947$			3.59635i			0.116866i	0.998291	+	0.0584329i	$0.0186104\pi$
$947$			3.59635i			0.116866i	−0.998291	+	0.0584329i	$0.981390\pi$
$948$		−	6.94614i		−	0.225600i
$949$	9.89793			0.321300
$950$	−3.86923	−	9.07492i	−0.125534	−	0.294429i
$951$	6.80122			0.220545
$952$		−	4.76328i		−	0.154379i
$953$			51.1711i			1.65760i	0.559548	+	0.828798i	$0.310975\pi$
$953$			51.1711i			1.65760i	−0.559548	+	0.828798i	$0.689025\pi$
$954$	−8.40857			−0.272238
$955$	11.3547	+	55.5825i	0.367430	+	1.79861i
$956$	2.15593			0.0697277
$957$		−	48.8972i		−	1.58062i
$958$		−	17.9330i		−	0.579390i
$959$	26.8710			0.867710
$960$	−2.19082	+	0.447553i	−0.0707084	+	0.0144447i
$961$	1.00000			0.0322581
$962$		0			0
$963$		−	12.3547i		−	0.398125i
$964$	5.79021			0.186490
$965$	−23.7512	+	4.85204i	−0.764579	+	0.156193i
$966$	8.14493			0.262059
$967$			6.13182i			0.197186i	0.995128	+	0.0985931i	$0.0314342\pi$
$967$			6.13182i			0.197186i	−0.995128	+	0.0985931i	$0.968566\pi$
$968$			28.3976i			0.912732i
$969$	2.77921			0.0892811
$970$	−4.78225	−	23.4096i	−0.153549	−	0.751638i
$971$	31.8221			1.02122			0.510609	−	0.859813i	$-0.329420\pi$
$971$	31.8221			1.02122			0.510609	+	0.859813i	$0.329420\pi$
$972$			1.00000i			0.0320750i
$973$			37.1070i			1.18960i
$974$	−11.6102			−0.372014
$975$	−31.7133	+	13.5214i	−1.01564	+	0.433032i
$976$	7.40857			0.237143
$977$			15.1070i			0.483316i	0.970362	+	0.241658i	$0.0776911\pi$
$977$			15.1070i			0.483316i	−0.970362	+	0.241658i	$0.922309\pi$
$978$			7.05103i			0.225467i
$979$	83.9932			2.68443
$980$	1.98512	+	9.71739i	0.0634124	+	0.310411i
$981$	−18.6074			−0.594087
$982$			3.98900i			0.127294i
$983$		−	6.44578i		−	0.205588i	−0.994703	−	0.102794i	$-0.967222\pi$
$983$		−	6.44578i		−	0.205588i	0.994703	−	0.102794i	$-0.0327783\pi$
$984$	−9.58043			−0.305413
$985$	41.8600	−	8.55140i	1.33377	−	0.272470i
$986$	10.9731			0.349454
$987$		−	8.76328i		−	0.278938i
$988$			13.6045i			0.432818i
$989$	8.14493			0.258994
$990$	13.7512	−	2.80918i	0.437043	−	0.0892816i
$991$	−32.6722			−1.03787			−0.518934	−	0.854815i	$-0.673671\pi$
$991$	−32.6722			−1.03787			−0.518934	+	0.854815i	$0.673671\pi$
$992$		−	1.00000i		−	0.0317500i
$993$		−	30.1339i		−	0.956271i
$994$	−1.82742			−0.0579622
$995$	−2.62759	−	12.8623i	−0.0833001	−	0.407763i
$996$	9.19878			0.291475
$997$			30.0801i			0.952645i	0.879271	+	0.476323i	$0.158031\pi$
$997$			30.0801i			0.952645i	−0.879271	+	0.476323i	$0.841969\pi$
$998$		−	22.3437i		−	0.707278i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.d.h.559.3	✓	6
3.2	odd	2		2790.2.d.k.559.4		6
5.2	odd	4		4650.2.a.cn.1.3		3
5.3	odd	4		4650.2.a.ck.1.1		3
5.4	even	2	inner	930.2.d.h.559.6	yes	6
15.14	odd	2		2790.2.d.k.559.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.d.h.559.3	✓	6	1.1	even	1	trivial
930.2.d.h.559.6	yes	6	5.4	even	2	inner
2790.2.d.k.559.1		6	15.14	odd	2
2790.2.d.k.559.4		6	3.2	odd	2
4650.2.a.ck.1.1		3	5.3	odd	4
4650.2.a.cn.1.3		3	5.2	odd	4

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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +(0.447553 + 2.19082i) q^{5} -1.00000 q^{6} -3.38164i q^{7} +1.00000i q^{8} -1.00000 q^{9} +(2.19082 - 0.447553i) q^{10} -6.27675 q^{11} +1.00000i q^{12} +6.89511i q^{13} -3.38164 q^{14} +(2.19082 - 0.447553i) q^{15} +1.00000 q^{16} -1.40857i q^{17} +1.00000i q^{18} -1.97307 q^{19} +(-0.447553 - 2.19082i) q^{20} -3.38164 q^{21} +6.27675i q^{22} -2.40857i q^{23} +1.00000 q^{24} +(-4.59939 + 1.96102i) q^{25} +6.89511 q^{26} +1.00000i q^{27} +3.38164i q^{28} -7.79021 q^{29} +(-0.447553 - 2.19082i) q^{30} +1.00000 q^{31} -1.00000i q^{32} +6.27675i q^{33} -1.40857 q^{34} +(7.40857 - 1.51346i) q^{35} +1.00000 q^{36} +1.97307i q^{38} +6.89511 q^{39} +(-2.19082 + 0.447553i) q^{40} -9.58043 q^{41} +3.38164i q^{42} +3.38164i q^{43} +6.27675 q^{44} +(-0.447553 - 2.19082i) q^{45} -2.40857 q^{46} +2.59143i q^{47} -1.00000i q^{48} -4.43550 q^{49} +(1.96102 + 4.59939i) q^{50} -1.40857 q^{51} -6.89511i q^{52} +8.40857i q^{53} +1.00000 q^{54} +(-2.80918 - 13.7512i) q^{55} +3.38164 q^{56} +1.97307i q^{57} +7.79021i q^{58} +0.973070 q^{59} +(-2.19082 + 0.447553i) q^{60} +7.40857 q^{61} -1.00000i q^{62} +3.38164i q^{63} -1.00000 q^{64} +(-15.1059 + 3.08593i) q^{65} +6.27675 q^{66} +1.92204i q^{67} +1.40857i q^{68} -2.40857 q^{69} +(-1.51346 - 7.40857i) q^{70} +0.540394 q^{71} -1.00000i q^{72} -1.43550i q^{73} +(1.96102 + 4.59939i) q^{75} +1.97307 q^{76} +21.2257i q^{77} -6.89511i q^{78} -6.94614 q^{79} +(0.447553 + 2.19082i) q^{80} +1.00000 q^{81} +9.58043i q^{82} -9.19878i q^{83} +3.38164 q^{84} +(3.08593 - 0.630411i) q^{85} +3.38164 q^{86} +7.79021i q^{87} -6.27675i q^{88} -13.3816 q^{89} +(-2.19082 + 0.447553i) q^{90} +23.3168 q^{91} +2.40857i q^{92} -1.00000i q^{93} +2.59143 q^{94} +(-0.883054 - 4.32264i) q^{95} -1.00000 q^{96} -10.6853i q^{97} +4.43550i q^{98} +6.27675 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{4} - 6 q^{5} - 6 q^{6} - 6 q^{9} + 2 q^{10} + 2 q^{11} + 2 q^{14} + 2 q^{15} + 6 q^{16} - 2 q^{19} + 6 q^{20} + 2 q^{21} + 6 q^{24} - 4 q^{25} + 24 q^{26} - 12 q^{29} + 6 q^{30} + 6 q^{31} + 4 q^{34}+ \cdots - 2 q^{99}+O(q^{100}) \) 6 * q - 6 * q^4 - 6 * q^5 - 6 * q^6 - 6 * q^9 + 2 * q^10 + 2 * q^11 + 2 * q^14 + 2 * q^15 + 6 * q^16 - 2 * q^19 + 6 * q^20 + 2 * q^21 + 6 * q^24 - 4 * q^25 + 24 * q^26 - 12 * q^29 + 6 * q^30 + 6 * q^31 + 4 * q^34 + 32 * q^35 + 6 * q^36 + 24 * q^39 - 2 * q^40 + 12 * q^41 - 2 * q^44 + 6 * q^45 - 2 * q^46 - 24 * q^49 + 8 * q^50 + 4 * q^51 + 6 * q^54 - 28 * q^55 - 2 * q^56 - 4 * q^59 - 2 * q^60 + 32 * q^61 - 6 * q^64 - 20 * q^65 - 2 * q^66 - 2 * q^69 - 14 * q^70 + 18 * q^71 + 8 * q^75 + 2 * q^76 - 22 * q^79 - 6 * q^80 + 6 * q^81 - 2 * q^84 - 10 * q^85 - 2 * q^86 - 58 * q^89 - 2 * q^90 + 16 * q^91 + 28 * q^94 + 6 * q^95 - 6 * q^96 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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