LMFDB - Embedded newform 930.2.be.a.37.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(37,930)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 10]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("930.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.be (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			37.3
Character	$\chi$	$=$	930.37
Dual form			930.2.be.a.553.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(-0.258819 + 0.965926i) q^{3} +1.00000i q^{4} +(-1.08971 - 1.95257i) q^{5} +(0.866025 - 0.500000i) q^{6} +(0.294543 - 1.09925i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.258819 + 0.965926i) q^{3} +1.00000i q^{4} +(-1.08971 - 1.95257i) q^{5} +(0.866025 - 0.500000i) q^{6} +(0.294543 - 1.09925i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(-0.610134 + 2.15122i) q^{10} +(-0.779058 - 0.449790i) q^{11} +(-0.965926 - 0.258819i) q^{12} +(-4.95292 + 1.32713i) q^{13} +(-0.985560 + 0.569014i) q^{14} +(2.16808 - 0.547217i) q^{15} -1.00000 q^{16} +(3.02565 + 0.810719i) q^{17} +(0.258819 + 0.965926i) q^{18} +(-2.07233 + 1.19646i) q^{19} +(1.95257 - 1.08971i) q^{20} +(0.985560 + 0.569014i) q^{21} +(0.232828 + 0.868927i) q^{22} +(5.46345 + 5.46345i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-2.62506 + 4.25547i) q^{25} +(4.44067 + 2.56382i) q^{26} +(0.707107 - 0.707107i) q^{27} +(1.09925 + 0.294543i) q^{28} -0.504809 q^{29} +(-1.92000 - 1.14612i) q^{30} +(-4.84599 - 2.74160i) q^{31} +(0.707107 + 0.707107i) q^{32} +(0.636098 - 0.636098i) q^{33} +(-1.56619 - 2.71272i) q^{34} +(-2.46733 + 0.622748i) q^{35} +(0.500000 - 0.866025i) q^{36} +(-3.75540 - 1.00626i) q^{37} +(2.31138 + 0.619332i) q^{38} -5.12764i q^{39} +(-2.15122 - 0.610134i) q^{40} +(3.00995 - 5.21339i) q^{41} +(-0.294543 - 1.09925i) q^{42} +(-2.90441 + 10.8394i) q^{43} +(0.449790 - 0.779058i) q^{44} +(-0.0325682 + 2.23583i) q^{45} -7.72648i q^{46} +(7.21364 + 7.21364i) q^{47} +(0.258819 - 0.965926i) q^{48} +(4.94058 + 2.85245i) q^{49} +(4.86527 - 1.15287i) q^{50} +(-1.56619 + 2.71272i) q^{51} +(-1.32713 - 4.95292i) q^{52} +(-13.0247 + 3.48994i) q^{53} -1.00000 q^{54} +(-0.0292977 + 2.01131i) q^{55} +(-0.569014 - 0.985560i) q^{56} +(-0.619332 - 2.31138i) q^{57} +(0.356954 + 0.356954i) q^{58} +(-9.82144 + 5.67041i) q^{59} +(0.547217 + 2.16808i) q^{60} +13.7802i q^{61} +(1.48803 + 5.36524i) q^{62} +(-0.804707 + 0.804707i) q^{63} -1.00000i q^{64} +(7.98856 + 8.22474i) q^{65} -0.899579 q^{66} +(0.879554 - 0.235676i) q^{67} +(-0.810719 + 3.02565i) q^{68} +(-6.69133 + 3.86324i) q^{69} +(2.18501 + 1.30432i) q^{70} +(4.82448 - 8.35624i) q^{71} +(-0.965926 + 0.258819i) q^{72} +(-13.5981 + 3.64360i) q^{73} +(1.94394 + 3.36700i) q^{74} +(-3.43106 - 3.63701i) q^{75} +(-1.19646 - 2.07233i) q^{76} +(-0.723897 + 0.723897i) q^{77} +(-3.62579 + 3.62579i) q^{78} +(-5.90133 - 10.2214i) q^{79} +(1.08971 + 1.95257i) q^{80} +(0.500000 + 0.866025i) q^{81} +(-5.81478 + 1.55806i) q^{82} +(2.04678 - 0.548433i) q^{83} +(-0.569014 + 0.985560i) q^{84} +(-1.71409 - 6.79124i) q^{85} +(9.71835 - 5.61089i) q^{86} +(0.130654 - 0.487608i) q^{87} +(-0.868927 + 0.232828i) q^{88} -15.1587 q^{89} +(1.60400 - 1.55794i) q^{90} +5.83539i q^{91} +(-5.46345 + 5.46345i) q^{92} +(3.90241 - 3.97129i) q^{93} -10.2016i q^{94} +(4.59440 + 2.74257i) q^{95} +(-0.866025 + 0.500000i) q^{96} +(10.5084 + 10.5084i) q^{97} +(-1.47654 - 5.51050i) q^{98} +(0.449790 + 0.779058i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 8 q^{7}+O(q^{10}) $ 64 * q - 8 * q^7	$ 64 q - 8 q^{7} - 4 q^{10} + 24 q^{14} + 8 q^{15} - 64 q^{16} + 4 q^{17} - 12 q^{20} - 24 q^{21} - 8 q^{22} + 32 q^{24} - 20 q^{25} - 4 q^{28} + 16 q^{29} + 8 q^{31} + 4 q^{33} + 24 q^{35} + 32 q^{36} + 56 q^{37} - 4 q^{38} - 8 q^{41} + 8 q^{42} - 56 q^{43} - 4 q^{44} + 12 q^{45} + 8 q^{47} - 60 q^{49} - 8 q^{50} + 24 q^{53} - 64 q^{54} + 16 q^{55} - 28 q^{57} + 52 q^{58} + 24 q^{59} - 4 q^{62} - 4 q^{63} + 100 q^{65} + 8 q^{66} + 76 q^{67} + 4 q^{68} - 12 q^{69} - 44 q^{70} + 8 q^{71} - 52 q^{73} + 12 q^{74} - 8 q^{75} - 8 q^{76} - 104 q^{77} + 56 q^{79} + 32 q^{81} + 32 q^{82} + 24 q^{83} + 32 q^{85} - 24 q^{86} - 20 q^{87} + 4 q^{88} - 176 q^{89} + 8 q^{93} + 64 q^{95} - 68 q^{97} - 64 q^{98} - 4 q^{99}+O(q^{100}) $ 64 * q - 8 * q^7 - 4 * q^10 + 24 * q^14 + 8 * q^15 - 64 * q^16 + 4 * q^17 - 12 * q^20 - 24 * q^21 - 8 * q^22 + 32 * q^24 - 20 * q^25 - 4 * q^28 + 16 * q^29 + 8 * q^31 + 4 * q^33 + 24 * q^35 + 32 * q^36 + 56 * q^37 - 4 * q^38 - 8 * q^41 + 8 * q^42 - 56 * q^43 - 4 * q^44 + 12 * q^45 + 8 * q^47 - 60 * q^49 - 8 * q^50 + 24 * q^53 - 64 * q^54 + 16 * q^55 - 28 * q^57 + 52 * q^58 + 24 * q^59 - 4 * q^62 - 4 * q^63 + 100 * q^65 + 8 * q^66 + 76 * q^67 + 4 * q^68 - 12 * q^69 - 44 * q^70 + 8 * q^71 - 52 * q^73 + 12 * q^74 - 8 * q^75 - 8 * q^76 - 104 * q^77 + 56 * q^79 + 32 * q^81 + 32 * q^82 + 24 * q^83 + 32 * q^85 - 24 * q^86 - 20 * q^87 + 4 * q^88 - 176 * q^89 + 8 * q^93 + 64 * q^95 - 68 * q^97 - 64 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$187$	$311$	$871$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$	−0.258819	+	0.965926i	−0.149429	+	0.557678i
$3$	−0.258819	+	0.965926i	−0.149429	+	0.557678i
$4$			1.00000i			0.500000i
$5$	−1.08971	−	1.95257i	−0.487333	−	0.873216i
$5$	−1.08971	−	1.95257i	−0.487333	−	0.873216i
$6$	0.866025	−	0.500000i	0.353553	−	0.204124i
$7$	0.294543	−	1.09925i	0.111327	−	0.415477i	−0.887659	−	0.460501i	$-0.847670\pi$
$7$	0.294543	−	1.09925i	0.111327	−	0.415477i	0.998986	+	0.0450238i	$0.0143364\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	−0.866025	−	0.500000i	−0.288675	−	0.166667i
$10$	−0.610134	+	2.15122i	−0.192941	+	0.680275i
$11$	−0.779058	−	0.449790i	−0.234895	−	0.135617i	0.377933	−	0.925833i	$-0.376635\pi$
$11$	−0.779058	−	0.449790i	−0.234895	−	0.135617i	−0.612828	+	0.790216i	$0.709968\pi$
$12$	−0.965926	−	0.258819i	−0.278839	−	0.0747146i
$13$	−4.95292	+	1.32713i	−1.37369	+	0.368080i	−0.868826	−	0.495117i	$-0.835125\pi$
$13$	−4.95292	+	1.32713i	−1.37369	+	0.368080i	−0.504867	+	0.863197i	$0.668458\pi$
$14$	−0.985560	+	0.569014i	−0.263402	+	0.152075i
$15$	2.16808	−	0.547217i	0.559795	−	0.141291i
$16$	−1.00000			−0.250000
$17$	3.02565	+	0.810719i	0.733827	+	0.196628i	0.606333	−	0.795211i	$-0.292640\pi$
$17$	3.02565	+	0.810719i	0.733827	+	0.196628i	0.127494	+	0.991839i	$0.459307\pi$
$18$	0.258819	+	0.965926i	0.0610042	+	0.227671i
$19$	−2.07233	+	1.19646i	−0.475424	+	0.274486i	−0.718508	−	0.695519i	$-0.755174\pi$
$19$	−2.07233	+	1.19646i	−0.475424	+	0.274486i	0.243084	+	0.970005i	$0.421841\pi$
$20$	1.95257	−	1.08971i	0.436608	−	0.243667i
$21$	0.985560	+	0.569014i	0.215067	+	0.124169i
$22$	0.232828	+	0.868927i	0.0496391	+	0.185256i
$23$	5.46345	+	5.46345i	1.13921	+	1.13921i	0.988592	+	0.150615i	$0.0481254\pi$
$23$	5.46345	+	5.46345i	1.13921	+	1.13921i	0.150615	+	0.988592i	$0.451875\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	−2.62506	+	4.25547i	−0.525012	+	0.851095i
$26$	4.44067	+	2.56382i	0.870886	+	0.502806i
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	1.09925	+	0.294543i	0.207739	+	0.0556634i
$29$	−0.504809			−0.0937406			−0.0468703	−	0.998901i	$-0.514925\pi$
$29$	−0.504809			−0.0937406			−0.0468703	+	0.998901i	$0.514925\pi$
$30$	−1.92000	−	1.14612i	−0.350543	−	0.209252i
$31$	−4.84599	−	2.74160i	−0.870366	−	0.492405i
$31$	−4.84599	−	2.74160i	−0.870366	−	0.492405i
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	0.636098	−	0.636098i	0.110731	−	0.110731i
$34$	−1.56619	−	2.71272i	−0.268599	−	0.465228i
$35$	−2.46733	+	0.622748i	−0.417055	+	0.105264i
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$	−3.75540	−	1.00626i	−0.617384	−	0.165427i	−0.0634455	−	0.997985i	$-0.520209\pi$
$37$	−3.75540	−	1.00626i	−0.617384	−	0.165427i	−0.553938	+	0.832558i	$0.686876\pi$
$38$	2.31138	+	0.619332i	0.374955	+	0.100469i
$39$		−	5.12764i		−	0.821079i
$40$	−2.15122	−	0.610134i	−0.340137	−	0.0964707i
$41$	3.00995	−	5.21339i	0.470075	−	0.814194i	−0.529339	−	0.848410i	$-0.677560\pi$
$41$	3.00995	−	5.21339i	0.470075	−	0.814194i	0.999414	+	0.0342161i	$0.0108935\pi$
$42$	−0.294543	−	1.09925i	−0.0454490	−	0.169618i
$43$	−2.90441	+	10.8394i	−0.442919	+	1.65299i	0.278455	+	0.960449i	$0.410178\pi$
$43$	−2.90441	+	10.8394i	−0.442919	+	1.65299i	−0.721374	+	0.692546i	$0.756489\pi$
$44$	0.449790	−	0.779058i	0.0678083	−	0.117447i
$45$	−0.0325682	+	2.23583i	−0.00485498	+	0.333298i
$46$		−	7.72648i		−	1.13921i
$47$	7.21364	+	7.21364i	1.05222	+	1.05222i	0.998559	+	0.0536583i	$0.0170882\pi$
$47$	7.21364	+	7.21364i	1.05222	+	1.05222i	0.0536583	+	0.998559i	$0.482912\pi$
$48$	0.258819	−	0.965926i	0.0373573	−	0.139419i
$49$	4.94058	+	2.85245i	0.705798	+	0.407492i
$50$	4.86527	−	1.15287i	0.688053	−	0.163041i
$51$	−1.56619	+	2.71272i	−0.219310	+	0.379857i
$52$	−1.32713	−	4.95292i	−0.184040	−	0.686846i
$53$	−13.0247	+	3.48994i	−1.78907	+	0.479381i	−0.992188	−	0.124750i	$-0.960187\pi$
$53$	−13.0247	+	3.48994i	−1.78907	+	0.479381i	−0.796885	+	0.604131i	$0.793520\pi$
$54$	−1.00000			−0.136083
$55$	−0.0292977	+	2.01131i	−0.00395050	+	0.271205i
$56$	−0.569014	−	0.985560i	−0.0760376	−	0.131701i
$57$	−0.619332	−	2.31138i	−0.0820325	−	0.306150i
$58$	0.356954	+	0.356954i	0.0468703	+	0.0468703i
$59$	−9.82144	+	5.67041i	−1.27864	+	0.738225i	−0.976599	−	0.215069i	$-0.931002\pi$
$59$	−9.82144	+	5.67041i	−1.27864	+	0.738225i	−0.302044	+	0.953294i	$0.597669\pi$
$60$	0.547217	+	2.16808i	0.0706454	+	0.279897i
$61$			13.7802i			1.76437i	0.470899	+	0.882187i	$0.343930\pi$
$61$			13.7802i			1.76437i	−0.470899	+	0.882187i	$0.656070\pi$
$62$	1.48803	+	5.36524i	0.188980	+	0.681386i
$63$	−0.804707	+	0.804707i	−0.101384	+	0.101384i
$64$		−	1.00000i		−	0.125000i
$65$	7.98856	+	8.22474i	0.990860	+	1.02015i
$66$	−0.899579			−0.110731
$67$	0.879554	−	0.235676i	0.107455	−	0.0287924i	−0.204691	−	0.978827i	$-0.565619\pi$
$67$	0.879554	−	0.235676i	0.107455	−	0.0287924i	0.312146	+	0.950034i	$0.398952\pi$
$68$	−0.810719	+	3.02565i	−0.0983142	+	0.366913i
$69$	−6.69133	+	3.86324i	−0.805541	+	0.465080i
$70$	2.18501	+	1.30432i	0.261159	+	0.155896i
$71$	4.82448	−	8.35624i	0.572560	−	0.991703i	−0.423742	−	0.905783i	$-0.639284\pi$
$71$	4.82448	−	8.35624i	0.572560	−	0.991703i	0.996302	−	0.0859203i	$-0.0273830\pi$
$72$	−0.965926	+	0.258819i	−0.113835	+	0.0305021i
$73$	−13.5981	+	3.64360i	−1.59154	+	0.426451i	−0.942473	−	0.334281i	$-0.891506\pi$
$73$	−13.5981	+	3.64360i	−1.59154	+	0.426451i	−0.649065	+	0.760733i	$0.724840\pi$
$74$	1.94394	+	3.36700i	0.225978	+	0.391406i
$75$	−3.43106	−	3.63701i	−0.396184	−	0.419966i
$76$	−1.19646	−	2.07233i	−0.137243	−	0.237712i
$77$	−0.723897	+	0.723897i	−0.0824958	+	0.0824958i
$78$	−3.62579	+	3.62579i	−0.410540	+	0.410540i
$79$	−5.90133	−	10.2214i	−0.663951	−	1.15000i	−0.979569	−	0.201111i	$-0.935545\pi$
$79$	−5.90133	−	10.2214i	−0.663951	−	1.15000i	0.315617	−	0.948887i	$-0.397788\pi$
$80$	1.08971	+	1.95257i	0.121833	+	0.218304i
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$	−5.81478	+	1.55806i	−0.642135	+	0.172059i
$83$	2.04678	−	0.548433i	0.224663	−	0.0601984i	−0.144731	−	0.989471i	$-0.546232\pi$
$83$	2.04678	−	0.548433i	0.224663	−	0.0601984i	0.369395	+	0.929273i	$0.379565\pi$
$84$	−0.569014	+	0.985560i	−0.0620845	+	0.107533i
$85$	−1.71409	−	6.79124i	−0.185919	−	0.736613i
$86$	9.71835	−	5.61089i	1.04796	−	0.605038i
$87$	0.130654	−	0.487608i	0.0140076	−	0.0522770i
$88$	−0.868927	+	0.232828i	−0.0926279	+	0.0248196i
$89$	−15.1587			−1.60682			−0.803410	−	0.595426i	$-0.796983\pi$
$89$	−15.1587			−1.60682			−0.803410	+	0.595426i	$0.796983\pi$
$90$	1.60400	−	1.55794i	0.169076	−	0.164221i
$91$			5.83539i			0.611715i
$92$	−5.46345	+	5.46345i	−0.569604	+	0.569604i
$93$	3.90241	−	3.97129i	0.404662	−	0.411804i
$94$		−	10.2016i		−	1.05222i
$95$	4.59440	+	2.74257i	0.471376	+	0.281382i
$96$	−0.866025	+	0.500000i	−0.0883883	+	0.0510310i
$97$	10.5084	+	10.5084i	1.06696	+	1.06696i	0.997591	+	0.0693738i	$0.0221001\pi$
$97$	10.5084	+	10.5084i	1.06696	+	1.06696i	0.0693738	+	0.997591i	$0.477900\pi$
$98$	−1.47654	−	5.51050i	−0.149153	−	0.556645i
$99$	0.449790	+	0.779058i	0.0452055	+	0.0782983i
$100$	−4.25547	−	2.62506i	−0.425547	−	0.262506i
$101$	1.78541			0.177655			0.0888276	−	0.996047i	$-0.471688\pi$
$101$	1.78541			0.177655			0.0888276	+	0.996047i	$0.471688\pi$
$102$	3.02565	−	0.810719i	0.299584	−	0.0802732i
$103$	0.806193	+	3.00875i	0.0794366	+	0.296461i	0.994203	−	0.107523i	$-0.0342918\pi$
$103$	0.806193	+	3.00875i	0.0794366	+	0.296461i	−0.914766	+	0.403984i	$0.867625\pi$
$104$	−2.56382	+	4.44067i	−0.251403	+	0.435443i
$105$	0.0370635	−	2.54444i	0.00361703	−	0.248312i
$106$	11.6776	+	6.74206i	1.13423	+	0.654846i
$107$	2.42906	−	9.06539i	0.234826	−	0.876384i	−0.743401	−	0.668847i	$-0.766788\pi$
$107$	2.42906	−	9.06539i	0.234826	−	0.876384i	0.978227	−	0.207538i	$-0.0665450\pi$
$108$	0.707107	+	0.707107i	0.0680414	+	0.0680414i
$109$			11.3741i			1.08944i	0.838617	+	0.544721i	$0.183365\pi$
$109$			11.3741i			1.08944i	−0.838617	+	0.544721i	$0.816635\pi$
$110$	1.44293	−	1.40149i	0.137578	−	0.133627i
$111$	1.94394	−	3.36700i	0.184510	−	0.319581i
$112$	−0.294543	+	1.09925i	−0.0278317	+	0.103869i
$113$	3.55591	+	13.2708i	0.334512	+	1.24841i	0.904398	+	0.426690i	$0.140321\pi$
$113$	3.55591	+	13.2708i	0.334512	+	1.24841i	−0.569886	+	0.821724i	$0.693013\pi$
$114$	−1.19646	+	2.07233i	−0.112059	+	0.194091i
$115$	4.71419	−	16.6213i	0.439600	−	1.54995i
$116$		−	0.504809i		−	0.0468703i
$117$	4.95292	+	1.32713i	0.457898	+	0.122693i
$118$	10.9544	+	2.93522i	1.00843	+	0.270209i
$119$	1.78237	−	3.08715i	0.163389	−	0.282998i
$120$	1.14612	−	1.92000i	0.104626	−	0.175271i
$121$	−5.09538	−	8.82545i	−0.463216	−	0.802314i
$122$	9.74407	−	9.74407i	0.882187	−	0.882187i
$123$	4.25671	+	4.25671i	0.383815	+	0.383815i
$124$	2.74160	−	4.84599i	0.246203	−	0.435183i
$125$	11.1697	+	0.488385i	0.999045	+	0.0436825i
$126$	1.13803			0.101384
$127$	−14.3284	−	3.83928i	−1.27144	−	0.340681i	−0.440856	−	0.897578i	$-0.645325\pi$
$127$	−14.3284	−	3.83928i	−1.27144	−	0.340681i	−0.830582	+	0.556897i	$0.811992\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	−9.71835	−	5.61089i	−0.855653	−	0.494012i
$130$	0.166998	−	11.4645i	0.0146467	−	1.00551i
$131$	−1.46077	−	2.53013i	−0.127628	−	0.221059i	0.795129	−	0.606440i	$-0.207403\pi$
$131$	−1.46077	−	2.53013i	−0.127628	−	0.221059i	−0.922757	+	0.385382i	$0.874070\pi$
$132$	0.636098	+	0.636098i	0.0553653	+	0.0553653i
$133$	0.704817	+	2.63041i	0.0611153	+	0.228086i
$134$	−0.788587	−	0.455291i	−0.0681235	−	0.0393311i
$135$	−2.15122	−	0.610134i	−0.185147	−	0.0525120i
$136$	2.71272	−	1.56619i	0.232614	−	0.134300i
$137$	1.69173	+	6.31364i	0.144535	+	0.539410i	0.999776	+	0.0211801i	$0.00674233\pi$
$137$	1.69173	+	6.31364i	0.144535	+	0.539410i	−0.855241	+	0.518230i	$0.826591\pi$
$138$	7.46321	+	1.99976i	0.635310	+	0.170231i
$139$	9.49389			0.805261			0.402631	−	0.915363i	$-0.368096\pi$
$139$	9.49389			0.805261			0.402631	+	0.915363i	$0.368096\pi$
$140$	−0.622748	−	2.46733i	−0.0526318	−	0.208527i
$141$	−8.83487	+	5.10081i	−0.744030	+	0.429566i
$142$	−9.32018	+	2.49733i	−0.782132	+	0.209572i
$143$	4.45554	+	1.19386i	0.372591	+	0.0998355i
$144$	0.866025	+	0.500000i	0.0721688	+	0.0416667i
$145$	0.550095	+	0.985675i	0.0456829	+	0.0818558i
$146$	12.1917	+	7.03890i	1.00899	+	0.582544i
$147$	−4.03397	+	4.03397i	−0.332716	+	0.332716i
$148$	1.00626	−	3.75540i	0.0827137	−	0.308692i
$149$	12.0296	−	6.94529i	0.985503	−	0.568980i	0.0815758	−	0.996667i	$-0.474005\pi$
$149$	12.0296	−	6.94529i	0.985503	−	0.568980i	0.903927	+	0.427687i	$0.140671\pi$
$150$	−0.145634	+	4.99788i	−0.0118910	+	0.408075i
$151$		−	9.57147i		−	0.778915i	−0.921044	−	0.389458i	$-0.872662\pi$
$151$		−	9.57147i		−	0.778915i	0.921044	−	0.389458i	$-0.127338\pi$
$152$	−0.619332	+	2.31138i	−0.0502345	+	0.187478i
$153$	−2.21493	−	2.21493i	−0.179066	−	0.179066i
$154$	1.02375			0.0824958
$155$	−0.0724325	+	12.4497i	−0.00581791	+	0.999983i
$156$	5.12764			0.410540
$157$	−0.376021	−	0.376021i	−0.0300097	−	0.0300097i	0.691943	−	0.721952i	$-0.256755\pi$
$157$	−0.376021	−	0.376021i	−0.0300097	−	0.0300097i	−0.721952	+	0.691943i	$0.756755\pi$
$158$	−3.05475	+	11.4005i	−0.243023	+	0.906974i
$159$		−	13.4841i		−	1.06936i
$160$	0.610134	−	2.15122i	0.0482353	−	0.170069i
$161$	7.61491	−	4.39647i	0.600139	−	0.346491i
$162$	0.258819	−	0.965926i	0.0203347	−	0.0758903i
$163$	1.36461	−	1.36461i	0.106885	−	0.106885i	−0.651642	−	0.758527i	$-0.725919\pi$
$163$	1.36461	−	1.36461i	0.106885	−	0.106885i	0.758527	+	0.651642i	$0.225919\pi$
$164$	5.21339	+	3.00995i	0.407097	+	0.235038i
$165$	−1.93519	−	0.548864i	−0.150654	−	0.0427290i
$166$	−1.83509	−	1.05949i	−0.142431	−	0.0822325i
$167$	−14.5814	−	3.90707i	−1.12834	−	0.302338i	−0.354087	−	0.935213i	$-0.615208\pi$
$167$	−14.5814	−	3.90707i	−1.12834	−	0.302338i	−0.774254	+	0.632874i	$0.781875\pi$
$168$	1.09925	−	0.294543i	0.0848090	−	0.0227245i
$169$	11.5118	−	6.64634i	0.885524	−	0.511257i
$170$	−3.59008	+	6.01417i	−0.275347	+	0.461266i
$171$	2.39292			0.182991
$172$	−10.8394	−	2.90441i	−0.826497	−	0.221459i
$173$	−1.97827	−	7.38299i	−0.150405	−	0.561318i	−0.999455	−	0.0330063i	$-0.989492\pi$
$173$	−1.97827	−	7.38299i	−0.150405	−	0.561318i	0.849050	−	0.528312i	$-0.177175\pi$
$174$	−0.437177	+	0.252404i	−0.0331423	+	0.0191347i
$175$	3.90463	+	4.13902i	0.295163	+	0.312880i
$176$	0.779058	+	0.449790i	0.0587237	+	0.0339042i
$177$	−2.93522	−	10.9544i	−0.220625	−	0.823383i
$178$	10.7188	+	10.7188i	0.803410	+	0.803410i
$179$	−4.82033	−	8.34906i	−0.360288	−	0.624038i	0.627720	−	0.778439i	$-0.283988\pi$
$179$	−4.82033	−	8.34906i	−0.360288	−	0.624038i	−0.988008	+	0.154402i	$0.950655\pi$
$180$	−2.23583	−	0.0325682i	−0.166649	−	0.00242749i
$181$	4.04899	+	2.33769i	0.300959	+	0.173759i	0.642874	−	0.765972i	$-0.277742\pi$
$181$	4.04899	+	2.33769i	0.300959	+	0.173759i	−0.341915	+	0.939731i	$0.611075\pi$
$182$	4.12625	−	4.12625i	0.305858	−	0.305858i
$183$	−13.3107	−	3.56658i	−0.983952	−	0.263649i
$184$	7.72648			0.569604
$185$	2.12751	+	8.42921i	0.156418	+	0.619728i
$186$	−5.56755	+	0.0487035i	−0.408233	+	0.00357111i
$187$	−1.99250	−	1.99250i	−0.145706	−	0.145706i
$188$	−7.21364	+	7.21364i	−0.526109	+	0.526109i
$189$	−0.569014	−	0.985560i	−0.0413896	−	0.0716890i
$190$	−1.30944	−	5.18802i	−0.0949971	−	0.376379i
$191$	6.35934	−	11.0147i	0.460146	−	0.796996i	−0.538822	−	0.842420i	$-0.681130\pi$
$191$	6.35934	−	11.0147i	0.460146	−	0.796996i	0.998968	+	0.0454238i	$0.0144638\pi$
$192$	0.965926	+	0.258819i	0.0697097	+	0.0186787i
$193$	17.7980	+	4.76895i	1.28113	+	0.343277i	0.834283	−	0.551336i	$-0.185882\pi$
$193$	17.7980	+	4.76895i	1.28113	+	0.343277i	0.446842	+	0.894613i	$0.352548\pi$
$194$		−	14.8611i		−	1.06696i
$195$	−10.0121	+	5.58764i	−0.716980	+	0.400139i
$196$	−2.85245	+	4.94058i	−0.203746	+	0.352899i
$197$	2.68882	+	10.0348i	0.191571	+	0.714952i	0.993128	+	0.117034i	$0.0373386\pi$
$197$	2.68882	+	10.0348i	0.191571	+	0.714952i	−0.801557	+	0.597918i	$0.795995\pi$
$198$	0.232828	−	0.868927i	0.0165464	−	0.0617519i
$199$	0.0232391	−	0.0402513i	0.00164738	−	0.00285334i	−0.865201	−	0.501426i	$-0.832809\pi$
$199$	0.0232391	−	0.0402513i	0.00164738	−	0.00285334i	0.866848	+	0.498573i	$0.166142\pi$
$200$	1.15287	+	4.86527i	0.0815205	+	0.344027i
$201$			0.910582i			0.0642275i
$202$	−1.26248	−	1.26248i	−0.0888276	−	0.0888276i
$203$	−0.148688	+	0.554911i	−0.0104358	+	0.0389471i
$204$	−2.71272	−	1.56619i	−0.189928	−	0.109655i
$205$	−13.4595	−	0.196057i	−0.940051	−	0.0136932i
$206$	1.55745	−	2.69757i	0.108512	−	0.187949i
$207$	−1.99976	−	7.46321i	−0.138993	−	0.518729i
$208$	4.95292	−	1.32713i	0.343423	−	0.0920200i
$209$	2.15262			0.148900
$210$	−1.82540	+	1.77298i	−0.125964	+	0.122347i
$211$	−1.14080	−	1.97592i	−0.0785359	−	0.136028i	0.824083	−	0.566470i	$-0.191691\pi$
$211$	−1.14080	−	1.97592i	−0.0785359	−	0.136028i	−0.902618	+	0.430442i	$0.858358\pi$
$212$	−3.48994	−	13.0247i	−0.239690	−	0.894537i
$213$	6.82284	+	6.82284i	0.467493	+	0.467493i
$214$	−8.12781	+	4.69259i	−0.555605	+	0.320779i
$215$	24.3297	−	6.14075i	1.65927	−	0.418796i
$216$		−	1.00000i		−	0.0680414i
$217$	−4.44105	+	4.51944i	−0.301478	+	0.306799i
$218$	8.04271	−	8.04271i	0.544721	−	0.544721i
$219$		−	14.0778i		−	0.951290i
$220$	−2.01131	−	0.0292977i	−0.135602	−	0.00197525i
$221$	−16.0617			−1.08043
$222$	−3.75540	+	1.00626i	−0.252046	+	0.0675355i
$223$	4.57313	−	17.0672i	0.306240	−	1.14290i	−0.625634	−	0.780117i	$-0.715159\pi$
$223$	4.57313	−	17.0672i	0.306240	−	1.14290i	0.931873	−	0.362784i	$-0.118174\pi$
$224$	0.985560	−	0.569014i	0.0658505	−	0.0380188i
$225$	4.40111	−	2.37282i	0.293407	−	0.158188i
$226$	6.86948	−	11.8983i	0.456951	−	0.791463i
$227$	−12.6504	+	3.38965i	−0.839634	+	0.224979i	−0.652912	−	0.757434i	$-0.726453\pi$
$227$	−12.6504	+	3.38965i	−0.839634	+	0.224979i	−0.186722	+	0.982413i	$0.559786\pi$
$228$	2.31138	−	0.619332i	0.153075	−	0.0410163i
$229$	−14.5052	−	25.1238i	−0.958532	−	1.66023i	−0.726070	−	0.687621i	$-0.758655\pi$
$229$	−14.5052	−	25.1238i	−0.958532	−	1.66023i	−0.232462	−	0.972605i	$-0.574678\pi$
$230$	−15.0865	+	8.41963i	−0.994774	+	0.555174i
$231$	−0.511873	−	0.886589i	−0.0336787	−	0.0583333i
$232$	−0.356954	+	0.356954i	−0.0234352	+	0.0234352i
$233$	8.69103	−	8.69103i	0.569369	−	0.569369i	−0.362583	−	0.931952i	$-0.618105\pi$
$233$	8.69103	−	8.69103i	0.569369	−	0.569369i	0.931952	+	0.362583i	$0.118105\pi$
$234$	−2.56382	−	4.44067i	−0.167602	−	0.290295i
$235$	6.22436	−	21.9459i	0.406033	−	1.43159i
$236$	−5.67041	−	9.82144i	−0.369112	−	0.639321i
$237$	11.4005	−	3.05475i	0.740541	−	0.198427i
$238$	−3.44327	+	0.922621i	−0.223194	+	0.0598046i
$239$	2.08869	−	3.61771i	0.135106	−	0.234010i	−0.790532	−	0.612421i	$-0.790196\pi$
$239$	2.08869	−	3.61771i	0.135106	−	0.234010i	0.925638	+	0.378410i	$0.123529\pi$
$240$	−2.16808	+	0.547217i	−0.139949	+	0.0353227i
$241$	−20.5745	+	11.8787i	−1.32532	+	0.765175i	−0.984572	−	0.174979i	$-0.944014\pi$
$241$	−20.5745	+	11.8787i	−1.32532	+	0.765175i	−0.340749	+	0.940154i	$0.610681\pi$
$242$	−2.63756	+	9.84352i	−0.169549	+	0.632765i
$243$	−0.965926	+	0.258819i	−0.0619642	+	0.0166032i
$244$	−13.7802			−0.882187
$245$	0.185798	−	12.7552i	0.0118702	−	0.814898i
$246$		−	6.01990i		−	0.383815i
$247$	8.67620	−	8.67620i	0.552054	−	0.552054i
$248$	−5.36524	+	1.48803i	−0.340693	+	0.0944901i
$249$			2.11898i			0.134285i
$250$	−7.55281	−	8.24349i	−0.477681	−	0.521364i
$251$	−8.63232	+	4.98387i	−0.544867	+	0.314579i	−0.747049	−	0.664769i	$-0.768530\pi$
$251$	−8.63232	+	4.98387i	−0.544867	+	0.314579i	0.202182	+	0.979348i	$0.435197\pi$
$252$	−0.804707	−	0.804707i	−0.0506918	−	0.0506918i
$253$	−1.79894	−	6.71375i	−0.113099	−	0.422090i
$254$	7.41691	+	12.8465i	0.465379	+	0.806059i
$255$	7.00347	+	0.102016i	0.438574	+	0.00638849i
$256$	1.00000			0.0625000
$257$	−17.2675	+	4.62682i	−1.07712	+	0.288613i	−0.753414	−	0.657546i	$-0.771595\pi$
$257$	−17.2675	+	4.62682i	−1.07712	+	0.288613i	−0.323703	+	0.946159i	$0.604928\pi$
$258$	2.90441	+	10.8394i	0.180821	+	0.674832i
$259$	−2.21225	+	3.83173i	−0.137463	+	0.238092i
$260$	−8.22474	+	7.98856i	−0.510076	+	0.495430i
$261$	0.437177	+	0.252404i	0.0270606	+	0.0156234i
$262$	−0.756152	+	2.82200i	−0.0467152	+	0.174344i
$263$	5.75402	+	5.75402i	0.354808	+	0.354808i	0.861895	−	0.507087i	$-0.169278\pi$
$263$	5.75402	+	5.75402i	0.354808	+	0.354808i	−0.507087	+	0.861895i	$0.669278\pi$
$264$		−	0.899579i		−	0.0553653i
$265$	21.0075	+	21.6285i	1.29048	+	1.32863i
$266$	1.36160	−	2.35836i	0.0834851	−	0.144600i
$267$	3.92336	−	14.6422i	0.240106	−	0.896087i
$268$	0.235676	+	0.879554i	0.0143962	+	0.0537273i
$269$	−0.228430	+	0.395653i	−0.0139276	+	0.0241234i	−0.872905	−	0.487890i	$-0.837767\pi$
$269$	−0.228430	+	0.395653i	−0.0139276	+	0.0241234i	0.858978	+	0.512013i	$0.171100\pi$
$270$	1.08971	+	1.95257i	0.0663177	+	0.118830i
$271$		−	9.09703i		−	0.552605i	−0.961071	−	0.276303i	$-0.910891\pi$
$271$		−	9.09703i		−	0.552605i	0.961071	−	0.276303i	$-0.0891092\pi$
$272$	−3.02565	−	0.810719i	−0.183457	−	0.0491571i
$273$	−5.63656	−	1.51031i	−0.341140	−	0.0914082i
$274$	3.26818	−	5.66065i	0.197438	−	0.341972i
$275$	3.95914	−	2.13454i	0.238745	−	0.128717i
$276$	−3.86324	−	6.69133i	−0.232540	−	0.402771i
$277$	2.84308	−	2.84308i	0.170824	−	0.170824i	−0.616517	−	0.787341i	$-0.711457\pi$
$277$	2.84308	−	2.84308i	0.170824	−	0.170824i	0.787341	+	0.616517i	$0.211457\pi$
$278$	−6.71319	−	6.71319i	−0.402631	−	0.402631i
$279$	2.82595	+	4.79729i	0.169185	+	0.287206i
$280$	−1.30432	+	2.18501i	−0.0779478	+	0.130580i
$281$	30.8049			1.83766			0.918832	−	0.394649i	$-0.129134\pi$
$281$	30.8049			1.83766			0.918832	+	0.394649i	$0.129134\pi$
$282$	9.85402	+	2.64038i	0.586798	+	0.157232i
$283$	−13.1611	+	13.1611i	−0.782349	+	0.782349i	−0.980227	−	0.197878i	$-0.936595\pi$
$283$	−13.1611	+	13.1611i	−0.782349	+	0.782349i	0.197878	+	0.980227i	$0.436595\pi$
$284$	8.35624	+	4.82448i	0.495852	+	0.286280i
$285$	−3.83824	+	3.72802i	−0.227358	+	0.220829i
$286$	−2.30636	−	3.99473i	−0.136378	−	0.236213i
$287$	−4.84425	−	4.84425i	−0.285947	−	0.285947i
$288$	−0.258819	−	0.965926i	−0.0152511	−	0.0569177i
$289$	−6.22517	−	3.59410i	−0.366186	−	0.211418i
$290$	0.308001	−	1.08595i	0.0180864	−	0.0637694i
$291$	−12.8701	+	7.43055i	−0.754458	+	0.435586i
$292$	−3.64360	−	13.5981i	−0.213226	−	0.795769i
$293$	0.606551	+	0.162525i	0.0354351	+	0.00949481i	0.276493	−	0.961016i	$-0.410828\pi$
$293$	0.606551	+	0.162525i	0.0354351	+	0.00949481i	−0.241058	+	0.970511i	$0.577494\pi$
$294$	5.70489			0.332716
$295$	21.7744	+	12.9979i	1.26776	+	0.756770i
$296$	−3.36700	+	1.94394i	−0.195703	+	0.112989i
$297$	−0.868927	+	0.232828i	−0.0504202	+	0.0135101i
$298$	−13.4173	−	3.59515i	−0.777241	−	0.208261i
$299$	−34.3107	−	19.8093i	−1.98424	−	1.14560i
$300$	3.63701	−	3.43106i	0.209983	−	0.198092i
$301$	11.0597	+	6.38535i	0.637473	+	0.368045i
$302$	−6.76805	+	6.76805i	−0.389458	+	0.389458i
$303$	−0.462099	+	1.72458i	−0.0265469	+	0.0990743i
$304$	2.07233	−	1.19646i	0.118856	−	0.0686215i
$305$	26.9068	−	15.0164i	1.54068	−	0.859838i
$306$			3.13238i			0.179066i
$307$	−2.89153	+	10.7913i	−0.165028	+	0.615893i	0.833008	+	0.553260i	$0.186616\pi$
$307$	−2.89153	+	10.7913i	−0.165028	+	0.615893i	−0.998037	+	0.0626332i	$0.980050\pi$
$308$	−0.723897	−	0.723897i	−0.0412479	−	0.0412479i
$309$	−3.11489			−0.177200
$310$	8.85448	−	8.75204i	0.502900	−	0.497083i
$311$	−20.3998			−1.15677			−0.578384	−	0.815765i	$-0.696316\pi$
$311$	−20.3998			−1.15677			−0.578384	+	0.815765i	$0.696316\pi$
$312$	−3.62579	−	3.62579i	−0.205270	−	0.205270i
$313$	−6.76552	+	25.2493i	−0.382410	+	1.42717i	0.459800	+	0.888022i	$0.347921\pi$
$313$	−6.76552	+	25.2493i	−0.382410	+	1.42717i	−0.842210	+	0.539150i	$0.818746\pi$
$314$			0.531773i			0.0300097i
$315$	2.44814	+	0.694349i	0.137937	+	0.0391221i
$316$	10.2214	−	5.90133i	0.574999	−	0.331976i
$317$	3.67196	−	13.7039i	0.206238	−	0.769690i	−0.782831	−	0.622235i	$-0.786225\pi$
$317$	3.67196	−	13.7039i	0.206238	−	0.769690i	0.989069	−	0.147456i	$-0.0471084\pi$
$318$	−9.53471	+	9.53471i	−0.534680	+	0.534680i
$319$	0.393275	+	0.227058i	0.0220192	+	0.0127128i
$320$	−1.95257	+	1.08971i	−0.109152	+	0.0609167i
$321$	8.12781	+	4.69259i	0.453650	+	0.261915i
$322$	−8.49333	−	2.27578i	−0.473315	−	0.126824i
$323$	−7.24011	+	1.93998i	−0.402851	+	0.107944i
$324$	−0.866025	+	0.500000i	−0.0481125	+	0.0277778i
$325$	7.35415	−	24.5608i	0.407935	−	1.36239i
$326$	−1.92986			−0.106885
$327$	−10.9866	−	2.94384i	−0.607558	−	0.162795i
$328$	−1.55806	−	5.81478i	−0.0860297	−	0.321067i
$329$	10.0543	−	5.80486i	0.554313	−	0.320033i
$330$	0.980281	+	1.75649i	0.0539627	+	0.0966917i
$331$	1.94556	+	1.12327i	0.106938	+	0.0617406i	0.552515	−	0.833503i	$-0.313668\pi$
$331$	1.94556	+	1.12327i	0.106938	+	0.0617406i	−0.445577	+	0.895244i	$0.647002\pi$
$332$	0.548433	+	2.04678i	0.0300992	+	0.112332i
$333$	2.74914	+	2.74914i	0.150652	+	0.150652i
$334$	7.54788	+	13.0733i	0.413002	+	0.715340i
$335$	−1.41863	−	1.46057i	−0.0775082	−	0.0797996i
$336$	−0.985560	−	0.569014i	−0.0537667	−	0.0310422i
$337$	−10.9628	+	10.9628i	−0.597181	+	0.597181i	−0.939561	−	0.342380i	$-0.888767\pi$
$337$	−10.9628	+	10.9628i	−0.597181	+	0.597181i	0.342380	+	0.939561i	$0.388767\pi$
$338$	−12.8398	−	3.44040i	−0.698390	−	0.187133i
$339$	−13.7390			−0.746198
$340$	6.79124	−	1.71409i	0.368306	−	0.0929597i
$341$	2.54217	+	4.31554i	0.137666	+	0.233700i
$342$	−1.69205	−	1.69205i	−0.0914954	−	0.0914954i
$343$	10.2237	−	10.2237i	0.552029	−	0.552029i
$344$	5.61089	+	9.71835i	0.302519	+	0.523978i
$345$	14.8349	+	8.85548i	0.798682	+	0.476763i
$346$	−3.82172	+	6.61941i	−0.205457	+	0.355862i
$347$	19.0652	+	5.10850i	1.02347	+	0.274238i	0.731248	−	0.682112i	$-0.238938\pi$
$347$	19.0652	+	5.10850i	1.02347	+	0.274238i	0.292224	+	0.956350i	$0.405605\pi$
$348$	0.487608	+	0.130654i	0.0261385	+	0.00700380i
$349$			16.9622i			0.907965i	0.891011	+	0.453982i	$0.149997\pi$
$349$			16.9622i			0.907965i	−0.891011	+	0.453982i	$0.850003\pi$
$350$	0.165735	−	5.68772i	0.00885893	−	0.304021i
$351$	−2.56382	+	4.44067i	−0.136847	+	0.237025i
$352$	−0.232828	−	0.868927i	−0.0124098	−	0.0463139i
$353$	8.70771	−	32.4976i	0.463465	−	1.72967i	−0.198465	−	0.980108i	$-0.563596\pi$
$353$	8.70771	−	32.4976i	0.463465	−	1.72967i	0.661930	−	0.749566i	$-0.269738\pi$
$354$	−5.67041	+	9.82144i	−0.301379	+	0.522004i
$355$	−21.5734	−	0.314249i	−1.14500	−	0.0166786i
$356$		−	15.1587i		−	0.803410i
$357$	2.52065	+	2.52065i	0.133407	+	0.133407i
$358$	−2.49519	+	9.31216i	−0.131875	+	0.492163i
$359$	−23.9036	−	13.8008i	−1.26159	−	0.728377i	−0.288204	−	0.957569i	$-0.593058\pi$
$359$	−23.9036	−	13.8008i	−1.26159	−	0.728377i	−0.973381	+	0.229192i	$0.926392\pi$
$360$	1.55794	+	1.60400i	0.0821107	+	0.0845382i
$361$	−6.63698	+	11.4956i	−0.349315	+	0.605031i
$362$	−1.21008	−	4.51606i	−0.0636002	−	0.237359i
$363$	9.84352	−	2.63756i	0.516651	−	0.138436i
$364$	−5.83539			−0.305858
$365$	21.9324	+	22.5808i	1.14799	+	1.18193i
$366$	6.89010	+	11.9340i	0.360151	+	0.623800i
$367$	3.43802	+	12.8309i	0.179463	+	0.669767i	0.995748	+	0.0921169i	$0.0293633\pi$
$367$	3.43802	+	12.8309i	0.179463	+	0.669767i	−0.816285	+	0.577650i	$0.803970\pi$
$368$	−5.46345	−	5.46345i	−0.284802	−	0.284802i
$369$	−5.21339	+	3.00995i	−0.271398	+	0.156692i
$370$	4.45597	−	7.46473i	0.231655	−	0.388073i
$371$			15.3453i			0.796687i
$372$	3.97129	+	3.90241i	0.205902	+	0.202331i
$373$	16.1688	−	16.1688i	0.837186	−	0.837186i	−0.151301	−	0.988488i	$-0.548346\pi$
$373$	16.1688	−	16.1688i	0.837186	−	0.837186i	0.988488	+	0.151301i	$0.0483464\pi$
$374$			2.81782i			0.145706i
$375$	−3.36267	+	10.6627i	−0.173647	+	0.550618i
$376$	10.2016			0.526109
$377$	2.50028	−	0.669947i	0.128771	−	0.0345040i
$378$	−0.294543	+	1.09925i	−0.0151497	+	0.0565393i
$379$	9.09160	−	5.24904i	0.467004	−	0.269625i	−0.247981	−	0.968765i	$-0.579767\pi$
$379$	9.09160	−	5.24904i	0.467004	−	0.269625i	0.714985	+	0.699140i	$0.246434\pi$
$380$	−2.74257	+	4.59440i	−0.140691	+	0.235688i
$381$	7.41691	−	12.8465i	0.379980	−	0.658145i
$382$	−12.2853	+	3.29184i	−0.628571	+	0.168425i
$383$	5.82728	−	1.56142i	0.297760	−	0.0797846i	−0.106846	−	0.994276i	$-0.534075\pi$
$383$	5.82728	−	1.56142i	0.297760	−	0.0797846i	0.404606	+	0.914491i	$0.367409\pi$
$384$	−0.500000	−	0.866025i	−0.0255155	−	0.0441942i
$385$	2.20230	+	0.624622i	0.112240	+	0.0318337i
$386$	−9.21290	−	15.9572i	−0.468924	−	0.812201i
$387$	7.93500	−	7.93500i	0.403359	−	0.403359i
$388$	−10.5084	+	10.5084i	−0.533482	+	0.533482i
$389$	0.468167	+	0.810889i	0.0237370	+	0.0411137i	0.877650	−	0.479302i	$-0.159110\pi$
$389$	0.468167	+	0.810889i	0.0237370	+	0.0411137i	−0.853913	+	0.520416i	$0.825777\pi$
$390$	11.0307	+	3.12855i	0.558560	+	0.158420i
$391$	12.1011	+	20.9598i	0.611981	+	1.05998i
$392$	5.51050	−	1.47654i	0.278323	−	0.0745763i
$393$	2.82200	−	0.756152i	0.142351	−	0.0381428i
$394$	5.19441	−	8.99698i	0.261691	−	0.453261i
$395$	−13.5273	+	22.6611i	−0.680630	+	1.14020i
$396$	−0.779058	+	0.449790i	−0.0391492	+	0.0226028i
$397$	−1.40801	+	5.25476i	−0.0706659	+	0.263729i	−0.992216	−	0.124532i	$-0.960257\pi$
$397$	−1.40801	+	5.25476i	−0.0706659	+	0.263729i	0.921550	+	0.388260i	$0.126924\pi$
$398$	−0.0448945	+	0.0120294i	−0.00225036	+	0.000602981i
$399$	−2.72320			−0.136331
$400$	2.62506	−	4.25547i	0.131253	−	0.212774i
$401$			24.4103i			1.21899i	0.792790	+	0.609495i	$0.208628\pi$
$401$			24.4103i			1.21899i	−0.792790	+	0.609495i	$0.791372\pi$
$402$	0.643878	−	0.643878i	0.0321137	−	0.0321137i
$403$	27.6403	+	7.14764i	1.37686	+	0.356050i
$404$			1.78541i			0.0888276i
$405$	1.14612	−	1.92000i	0.0569512	−	0.0954057i
$406$	0.497520	−	0.287243i	0.0246915	−	0.0142556i
$407$	2.47307	+	2.47307i	0.122586	+	0.122586i
$408$	0.810719	+	3.02565i	0.0401366	+	0.149792i
$409$	7.66702	+	13.2797i	0.379110	+	0.656637i	0.990933	−	0.134357i	$-0.0428970\pi$
$409$	7.66702	+	13.2797i	0.379110	+	0.656637i	−0.611823	+	0.790994i	$0.709564\pi$
$410$	9.37865	+	9.65592i	0.463179	+	0.476872i
$411$	−6.53636			−0.322415
$412$	−3.00875	+	0.806193i	−0.148231	+	0.0397183i
$413$	3.34036	+	12.4664i	0.164368	+	0.613431i
$414$	−3.86324	+	6.69133i	−0.189868	+	0.328861i
$415$	−3.30125	−	3.39885i	−0.162052	−	0.166843i
$416$	−4.44067	−	2.56382i	−0.217722	−	0.125702i
$417$	−2.45720	+	9.17039i	−0.120330	+	0.449076i
$418$	−1.52213	−	1.52213i	−0.0744498	−	0.0744498i
$419$			8.33493i			0.407188i	0.979055	+	0.203594i	$0.0652623\pi$
$419$			8.33493i			0.407188i	−0.979055	+	0.203594i	$0.934738\pi$
$420$	2.54444	+	0.0370635i	0.124156	+	0.00180851i
$421$	−10.6193	+	18.3931i	−0.517551	+	0.896425i	0.482241	+	0.876038i	$0.339823\pi$
$421$	−10.6193	+	18.3931i	−0.517551	+	0.896425i	−0.999792	+	0.0203861i	$0.993510\pi$
$422$	−0.590522	+	2.20386i	−0.0287462	+	0.107282i
$423$	−2.64038	−	9.85402i	−0.128379	−	0.479119i
$424$	−6.74206	+	11.6776i	−0.327423	+	0.567114i
$425$	−11.3925	+	10.7474i	−0.552617	+	0.521324i
$426$		−	9.64896i		−	0.467493i
$427$	15.1479	+	4.05886i	0.733058	+	0.196422i
$428$	9.06539	+	2.42906i	0.438192	+	0.117413i
$429$	−2.30636	+	3.99473i	−0.111352	+	0.192867i
$430$	−21.5459	−	12.8615i	−1.03903	−	0.620237i
$431$	−0.261276	−	0.452543i	−0.0125852	−	0.0217982i	0.859664	−	0.510860i	$-0.170673\pi$
$431$	−0.261276	−	0.452543i	−0.0125852	−	0.0217982i	−0.872249	+	0.489061i	$0.837339\pi$
$432$	−0.707107	+	0.707107i	−0.0340207	+	0.0340207i
$433$	2.80648	+	2.80648i	0.134871	+	0.134871i	0.771319	−	0.636449i	$-0.219597\pi$
$433$	2.80648	+	2.80648i	0.134871	+	0.134871i	−0.636449	+	0.771319i	$0.719597\pi$
$434$	6.33602	−	0.0554259i	0.304139	−	0.00266053i
$435$	−1.09446	+	0.276240i	−0.0524755	+	0.0132447i
$436$	−11.3741			−0.544721
$437$	−17.8588	−	4.78526i	−0.854303	−	0.228910i
$438$	−9.95451	+	9.95451i	−0.475645	+	0.475645i
$439$	25.1410	+	14.5152i	1.19992	+	0.692772i	0.960537	−	0.278154i	$-0.0897225\pi$
$439$	25.1410	+	14.5152i	1.19992	+	0.692772i	0.239380	+	0.970926i	$0.423056\pi$
$440$	1.40149	+	1.44293i	0.0668135	+	0.0687888i
$441$	−2.85245	−	4.94058i	−0.135831	−	0.235266i
$442$	11.3573	+	11.3573i	0.540214	+	0.540214i
$443$	3.90187	+	14.5620i	0.185384	+	0.691861i	0.994548	+	0.104279i	$0.0332534\pi$
$443$	3.90187	+	14.5620i	0.185384	+	0.691861i	−0.809165	+	0.587582i	$0.800080\pi$
$444$	3.36700	+	1.94394i	0.159791	+	0.0922552i
$445$	16.5186	+	29.5984i	0.783057	+	1.40310i
$446$	−15.3020	+	8.83461i	−0.724571	+	0.418331i
$447$	3.59515	+	13.4173i	0.170045	+	0.634615i
$448$	−1.09925	−	0.294543i	−0.0519347	−	0.0139159i
$449$	−0.00987934			−0.000466235			−0.000233117	−	1.00000i	$-0.500074\pi$
$449$	−0.00987934			−0.000466235			−0.000233117		1.00000i	$0.500074\pi$
$450$	−4.78989	−	1.43422i	−0.225797	−	0.0676097i
$451$	−4.68985	+	2.70769i	−0.220837	+	0.127500i
$452$	−13.2708	+	3.55591i	−0.624207	+	0.167256i
$453$	9.24533	+	2.47728i	0.434383	+	0.116393i
$454$	11.3420	+	6.54831i	0.532306	+	0.307327i
$455$	11.3940	−	6.35889i	0.534160	−	0.298109i
$456$	−2.07233	−	1.19646i	−0.0970455	−	0.0560293i
$457$	−4.09127	+	4.09127i	−0.191382	+	0.191382i	−0.796293	−	0.604911i	$-0.793209\pi$
$457$	−4.09127	+	4.09127i	−0.191382	+	0.191382i	0.604911	+	0.796293i	$0.293209\pi$
$458$	−7.50846	+	28.0219i	−0.350847	+	1.30938i
$459$	2.71272	−	1.56619i	0.126619	−	0.0731035i
$460$	16.6213	+	4.71419i	0.774974	+	0.219800i
$461$		−	31.4192i		−	1.46334i	−0.681661	−	0.731668i	$-0.738742\pi$
$461$		−	31.4192i		−	1.46334i	0.681661	−	0.731668i	$-0.261258\pi$
$462$	−0.264965	+	0.988862i	−0.0123273	+	0.0460060i
$463$	−24.5885	−	24.5885i	−1.14272	−	1.14272i	−0.987950	−	0.154773i	$-0.950536\pi$
$463$	−24.5885	−	24.5885i	−1.14272	−	1.14272i	−0.154773	−	0.987950i	$-0.549464\pi$
$464$	0.504809			0.0234352
$465$	−12.0067	−	3.29218i	−0.556799	−	0.152671i
$466$	−12.2910			−0.569369
$467$	5.70729	+	5.70729i	0.264102	+	0.264102i	0.826718	−	0.562616i	$-0.190205\pi$
$467$	5.70729	+	5.70729i	0.264102	+	0.264102i	−0.562616	+	0.826718i	$0.690205\pi$
$468$	−1.32713	+	4.95292i	−0.0613466	+	0.228949i
$469$		−	1.03627i		−	0.0478503i
$470$	−19.9194	+	11.1168i	−0.918813	+	0.512781i
$471$	0.460529	−	0.265887i	0.0212201	−	0.0122514i
$472$	−2.93522	+	10.9544i	−0.135105	+	0.504217i
$473$	7.13816	−	7.13816i	0.328213	−	0.328213i
$474$	−10.2214	−	5.90133i	−0.469484	−	0.271057i
$475$	0.348490	−	11.9595i	0.0159898	−	0.548739i
$476$	3.08715	+	1.78237i	0.141499	+	0.0816946i
$477$	13.0247	+	3.48994i	0.596358	+	0.159794i
$478$	−4.03503	+	1.08118i	−0.184558	+	0.0494522i
$479$	14.8751	−	8.58815i	0.679661	−	0.392403i	−0.120066	−	0.992766i	$-0.538311\pi$
$479$	14.8751	−	8.58815i	0.679661	−	0.392403i	0.799727	+	0.600363i	$0.204977\pi$
$480$	1.92000	+	1.14612i	0.0876357	+	0.0523130i
$481$	19.9356			0.908986
$482$	22.9479	+	6.14887i	1.04525	+	0.280073i
$483$	2.27578	+	8.49333i	0.103552	+	0.386460i
$484$	8.82545	−	5.09538i	0.401157	−	0.231608i
$485$	9.06726	−	31.9694i	0.411723	−	1.45166i
$486$	0.866025	+	0.500000i	0.0392837	+	0.0226805i
$487$	−1.22896	−	4.58653i	−0.0556893	−	0.207835i	0.932475	−	0.361235i	$-0.117645\pi$
$487$	−1.22896	−	4.58653i	−0.0556893	−	0.207835i	−0.988164	+	0.153399i	$0.950978\pi$
$488$	9.74407	+	9.74407i	0.441094	+	0.441094i
$489$	0.964928	+	1.67130i	0.0436356	+	0.0755790i
$490$	−9.15065	+	8.88789i	−0.413384	+	0.401514i
$491$	−17.5860	−	10.1533i	−0.793645	−	0.458211i	0.0475990	−	0.998867i	$-0.484843\pi$
$491$	−17.5860	−	10.1533i	−0.793645	−	0.458211i	−0.841244	+	0.540655i	$0.818176\pi$
$492$	−4.25671	+	4.25671i	−0.191907	+	0.191907i
$493$	−1.52737	−	0.409258i	−0.0687894	−	0.0184321i
$494$	−12.2700			−0.552054
$495$	1.03103	−	1.72719i	0.0463412	−	0.0776316i
$496$	4.84599	+	2.74160i	0.217591	+	0.123101i
$497$	−7.76458	−	7.76458i	−0.348289	−	0.348289i
$498$	1.49835	−	1.49835i	0.0671426	−	0.0671426i
$499$	19.0209	+	32.9451i	0.851491	+	1.47483i	0.879862	+	0.475229i	$0.157635\pi$
$499$	19.0209	+	32.9451i	0.851491	+	1.47483i	−0.0283712	+	0.999597i	$0.509032\pi$
$500$	−0.488385	+	11.1697i	−0.0218412	+	0.499523i
$501$	7.54788	−	13.0733i	0.337214	−	0.584072i
$502$	9.62810	+	2.57984i	0.429723	+	0.115144i
$503$	−31.6944	−	8.49249i	−1.41318	−	0.378661i	−0.530123	−	0.847921i	$-0.677854\pi$
$503$	−31.6944	−	8.49249i	−1.41318	−	0.378661i	−0.883060	+	0.469259i	$0.844521\pi$
$504$			1.13803i			0.0506918i
$505$	−1.94558	−	3.48614i	−0.0865773	−	0.155131i
$506$	−3.47529	+	6.01938i	−0.154496	+	0.267594i
$507$	3.44040	+	12.8398i	0.152794	+	0.570233i
$508$	3.83928	−	14.3284i	0.170340	−	0.635719i
$509$	−8.29571	+	14.3686i	−0.367701	+	0.636877i	−0.989206	−	0.146534i	$-0.953188\pi$
$509$	−8.29571	+	14.3686i	−0.367701	+	0.636877i	0.621505	+	0.783410i	$0.286522\pi$
$510$	−4.88006	−	5.02434i	−0.216093	−	0.222481i
$511$			16.0209i			0.708724i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−0.619332	+	2.31138i	−0.0273442	+	0.102050i
$514$	15.4816	+	8.93832i	0.682865	+	0.394252i
$515$	4.99629	−	4.85282i	0.220163	−	0.213841i
$516$	5.61089	−	9.71835i	0.247006	−	0.427827i
$517$	−2.37523	−	8.86447i	−0.104462	−	0.389859i
$518$	4.27374	−	1.14515i	0.187778	−	0.0503148i
$519$	7.64343			0.335509
$520$	11.4645	+	0.166998i	0.502753	+	0.00732335i
$521$	−2.65857	−	4.60478i	−0.116474	−	0.201739i	0.801894	−	0.597466i	$-0.203826\pi$
$521$	−2.65857	−	4.60478i	−0.116474	−	0.201739i	−0.918368	+	0.395727i	$0.870493\pi$
$522$	−0.130654	−	0.487608i	−0.00571858	−	0.0213420i
$523$	−26.9819	−	26.9819i	−1.17984	−	1.17984i	−0.979785	−	0.200051i	$-0.935889\pi$
$523$	−26.9819	−	26.9819i	−1.17984	−	1.17984i	−0.200051	−	0.979785i	$-0.564111\pi$
$524$	2.53013	−	1.46077i	0.110529	−	0.0638142i
$525$	−5.00858	+	2.70033i	−0.218592	+	0.117852i
$526$		−	8.13741i		−	0.354808i
$527$	−12.4396	−	12.2238i	−0.541877	−	0.532479i
$528$	−0.636098	+	0.636098i	−0.0276826	+	0.0276826i
$529$			36.6985i			1.59559i
$530$	0.439153	−	30.1482i	0.0190756	−	1.30955i
$531$	11.3408			0.492150
$532$	−2.63041	+	0.704817i	−0.114043	+	0.0305577i
$533$	−7.98919	+	29.8161i	−0.346050	+	1.29148i
$534$	−13.1278	+	7.57935i	−0.568097	+	0.327991i
$535$	−20.3478	+	5.13573i	−0.879712	+	0.222037i
$536$	0.455291	−	0.788587i	0.0196656	−	0.0340618i
$537$	9.31216	−	2.49519i	0.401850	−	0.107675i
$538$	0.441294	−	0.118244i	0.0190255	−	0.00509787i
$539$	−2.56600	−	4.44445i	−0.110526	−	0.191436i
$540$	0.610134	−	2.15122i	0.0262560	−	0.0925737i
$541$	−10.2049	−	17.6755i	−0.438744	−	0.759927i	0.558849	−	0.829270i	$-0.311243\pi$
$541$	−10.2049	−	17.6755i	−0.438744	−	0.759927i	−0.997593	+	0.0693423i	$0.977910\pi$
$542$	−6.43257	+	6.43257i	−0.276303	+	0.276303i
$543$	−3.30599	+	3.30599i	−0.141874	+	0.141874i
$544$	1.56619	+	2.71272i	0.0671498	+	0.116307i
$545$	22.2088	−	12.3945i	0.951319	−	0.530922i
$546$	2.91770	+	5.05360i	0.124866	+	0.216274i
$547$	16.8168	−	4.50604i	0.719033	−	0.192664i	0.119293	−	0.992859i	$-0.461937\pi$
$547$	16.8168	−	4.50604i	0.719033	−	0.192664i	0.599740	+	0.800195i	$0.295271\pi$
$548$	−6.31364	+	1.69173i	−0.269705	+	0.0722673i
$549$	6.89010	−	11.9340i	0.294062	−	0.509331i
$550$	−4.30888	−	1.29019i	−0.183731	−	0.0550140i
$551$	1.04613	−	0.603982i	0.0445665	−	0.0257305i
$552$	−1.99976	+	7.46321i	−0.0851155	+	0.317655i
$553$	−12.9741	+	3.47639i	−0.551713	+	0.147831i
$554$	−4.02073			−0.170824
$555$	−8.69263	−	0.126621i	−0.368982	−	0.00537477i
$556$			9.49389i			0.402631i
$557$	−22.0941	+	22.0941i	−0.936157	+	0.936157i	−0.998081	−	0.0619240i	$-0.980276\pi$
$557$	−22.0941	+	22.0941i	−0.936157	+	0.936157i	0.0619240	+	0.998081i	$0.480276\pi$
$558$	1.39394	−	5.39045i	0.0590104	−	0.228196i
$559$		−	57.5413i		−	2.43374i
$560$	2.46733	−	0.622748i	0.104264	−	0.0263159i
$561$	2.44031	−	1.40891i	0.103030	−	0.0594843i
$562$	−21.7823	−	21.7823i	−0.918832	−	0.918832i
$563$	−1.71353	−	6.39498i	−0.0722167	−	0.269516i	0.920371	−	0.391046i	$-0.127887\pi$
$563$	−1.71353	−	6.39498i	−0.0722167	−	0.269516i	−0.992588	+	0.121530i	$0.961220\pi$
$564$	−5.10081	−	8.83487i	−0.214783	−	0.372015i
$565$	22.0373	−	21.4045i	0.927117	−	0.900495i
$566$	18.6127			0.782349
$567$	1.09925	−	0.294543i	0.0461642	−	0.0123696i
$568$	−2.49733	−	9.32018i	−0.104786	−	0.391066i
$569$	−16.6293	+	28.8027i	−0.697135	+	1.20747i	0.272321	+	0.962206i	$0.412209\pi$
$569$	−16.6293	+	28.8027i	−0.697135	+	1.20747i	−0.969456	+	0.245266i	$0.921125\pi$
$570$	5.35015	+	0.0779329i	0.224093	+	0.00326425i
$571$	28.7699	+	16.6103i	1.20398	+	0.695120i	0.961439	−	0.275020i	$-0.0886844\pi$
$571$	28.7699	+	16.6103i	1.20398	+	0.695120i	0.242545	+	0.970140i	$0.422018\pi$
$572$	−1.19386	+	4.45554i	−0.0499178	+	0.186296i
$573$	8.99347	+	8.99347i	0.375707	+	0.375707i
$574$			6.85081i			0.285947i
$575$	−37.5914	+	8.90766i	−1.56767	+	0.371475i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−1.52703	+	5.69896i	−0.0635711	+	0.237251i	−0.990400	−	0.138234i	$-0.955857\pi$
$577$	−1.52703	+	5.69896i	−0.0635711	+	0.237251i	0.926828	+	0.375485i	$0.122524\pi$
$578$	1.86044	+	6.94327i	0.0773843	+	0.288802i
$579$	−9.21290	+	15.9572i	−0.382875	+	0.663159i
$580$	−0.985675	+	0.550095i	−0.0409279	+	0.0228415i
$581$		−	2.41146i		−	0.100044i
$582$	14.3547	+	3.84633i	0.595022	+	0.159436i
$583$	11.7167	+	3.13948i	0.485256	+	0.130024i
$584$	−7.03890	+	12.1917i	−0.291272	+	0.504497i
$585$	−2.80593	−	11.1171i	−0.116011	−	0.459636i
$586$	−0.313974	−	0.543819i	−0.0129702	−	0.0224650i
$587$	16.6410	−	16.6410i	0.686847	−	0.686847i	−0.274687	−	0.961534i	$-0.588574\pi$
$587$	16.6410	−	16.6410i	0.686847	−	0.686847i	0.961534	+	0.274687i	$0.0885741\pi$
$588$	−4.03397	−	4.03397i	−0.166358	−	0.166358i
$589$	13.3227	−	0.116543i	0.548951	−	0.00480208i
$590$	−6.20589	−	24.5878i	−0.255493	−	1.01226i
$591$	−10.3888			−0.427339
$592$	3.75540	+	1.00626i	0.154346	+	0.0413569i
$593$	−10.1086	+	10.1086i	−0.415111	+	0.415111i	−0.883515	−	0.468404i	$-0.844829\pi$
$593$	−10.1086	+	10.1086i	−0.415111	+	0.415111i	0.468404	+	0.883515i	$0.344829\pi$
$594$	0.779058	+	0.449790i	0.0319652	+	0.0184551i
$595$	−7.97014	−	0.116097i	−0.326744	−	0.00475951i
$596$	6.94529	+	12.0296i	0.284490	+	0.492751i
$597$	0.0328650	+	0.0328650i	0.00134508	+	0.00134508i
$598$	10.2541	+	38.2686i	0.419319	+	1.56492i
$599$	−36.9834	−	21.3524i	−1.51110	−	0.872435i	−0.999916	−	0.0129647i	$-0.995873\pi$
$599$	−36.9834	−	21.3524i	−1.51110	−	0.872435i	−0.511186	−	0.859470i	$-0.670794\pi$
$600$	−4.99788	−	0.145634i	−0.204038	−	0.00594548i
$601$	−25.1849	+	14.5405i	−1.02731	+	0.593119i	−0.916214	−	0.400690i	$-0.868770\pi$
$601$	−25.1849	+	14.5405i	−1.02731	+	0.593119i	−0.111099	+	0.993809i	$0.535437\pi$
$602$	−3.30530	−	12.3355i	−0.134714	−	0.502759i
$603$	−0.879554	−	0.235676i	−0.0358182	−	0.00959746i
$604$	9.57147			0.389458
$605$	−11.6798	+	19.5663i	−0.474853	+	0.795482i
$606$	1.54621	−	0.892706i	0.0628106	−	0.0362637i
$607$	34.7672	−	9.31584i	1.41116	−	0.378118i	0.528819	−	0.848734i	$-0.322635\pi$
$607$	34.7672	−	9.31584i	1.41116	−	0.378118i	0.882338	+	0.470616i	$0.155968\pi$
$608$	−2.31138	−	0.619332i	−0.0937388	−	0.0251172i
$609$	−0.497520	−	0.287243i	−0.0201605	−	0.0116397i
$610$	−29.6442	−	8.40777i	−1.20026	−	0.340421i
$611$	−45.3020	−	26.1551i	−1.83272	−	1.05812i
$612$	2.21493	−	2.21493i	0.0895331	−	0.0895331i
$613$	0.465982	−	1.73907i	0.0188208	−	0.0702403i	−0.955877	−	0.293768i	$-0.905091\pi$
$613$	0.465982	−	1.73907i	0.0188208	−	0.0702403i	0.974698	+	0.223528i	$0.0717573\pi$
$614$	9.67524	−	5.58600i	0.390461	−	0.225433i
$615$	3.67295	−	12.9501i	0.148107	−	0.522199i
$616$			1.02375i			0.0412479i
$617$	−7.33331	+	27.3683i	−0.295228	+	1.10181i	0.645809	+	0.763499i	$0.276520\pi$
$617$	−7.33331	+	27.3683i	−0.295228	+	1.10181i	−0.941036	+	0.338306i	$0.890146\pi$
$618$	2.20256	+	2.20256i	0.0886000	+	0.0886000i
$619$	26.6023			1.06924			0.534618	−	0.845094i	$-0.320456\pi$
$619$	26.6023			1.06924			0.534618	+	0.845094i	$0.320456\pi$
$620$	−12.4497	−	0.0724325i	−0.499992	−	0.00290896i
$621$	7.72648			0.310053
$622$	14.4248	+	14.4248i	0.578384	+	0.578384i
$623$	−4.46489	+	16.6632i	−0.178882	+	0.667597i
$624$			5.12764i			0.205270i
$625$	−11.2181	−	22.3418i	−0.448724	−	0.893670i
$626$	22.6379	−	13.0700i	0.904791	−	0.522381i
$627$	−0.557138	+	2.07927i	−0.0222500	+	0.0830380i
$628$	0.376021	−	0.376021i	0.0150049	−	0.0150049i
$629$	−10.5467	−	6.08915i	−0.420525	−	0.242790i
$630$	−1.24012	−	2.22208i	−0.0494076	−	0.0885297i
$631$	−6.82606	−	3.94103i	−0.271741	−	0.156890i	0.357938	−	0.933746i	$-0.383480\pi$
$631$	−6.82606	−	3.94103i	−0.271741	−	0.156890i	−0.629679	+	0.776856i	$0.716813\pi$
$632$	−11.4005	−	3.05475i	−0.453487	−	0.121511i
$633$	2.20386	−	0.590522i	0.0875955	−	0.0234711i
$634$	−12.2866	+	7.09368i	−0.487964	+	0.281726i
$635$	8.11732	+	32.1609i	0.322126	+	1.27626i
$636$	13.4841			0.534680
$637$	−28.2559	−	7.57114i	−1.11954	−	0.299980i
$638$	−0.117534	−	0.438642i	−0.00465320	−	0.0173660i
$639$	−8.35624	+	4.82448i	−0.330568	+	0.190853i
$640$	2.15122	+	0.610134i	0.0850343	+	0.0241177i
$641$	−5.43744	−	3.13931i	−0.214766	−	0.123995i	0.388758	−	0.921340i	$-0.372904\pi$
$641$	−5.43744	−	3.13931i	−0.214766	−	0.123995i	−0.603524	+	0.797344i	$0.706237\pi$
$642$	−2.42906	−	9.06539i	−0.0958675	−	0.357782i
$643$	−34.4434	−	34.4434i	−1.35832	−	1.35832i	−0.875993	−	0.482323i	$-0.839793\pi$
$643$	−34.4434	−	34.4434i	−1.35832	−	1.35832i	−0.482323	−	0.875993i	$-0.660207\pi$
$644$	4.39647	+	7.61491i	0.173245	+	0.300070i
$645$	−0.365473	+	25.0900i	−0.0143905	+	0.987918i
$646$	6.49131	+	3.74776i	0.255397	+	0.147454i
$647$	−27.3248	+	27.3248i	−1.07425	+	1.07425i	−0.0772376	+	0.997013i	$0.524610\pi$
$647$	−27.3248	+	27.3248i	−1.07425	+	1.07425i	−0.997013	+	0.0772376i	$0.975390\pi$
$648$	0.965926	+	0.258819i	0.0379452	+	0.0101674i
$649$	10.2020			0.400462
$650$	−22.5673	+	12.1669i	−0.885162	+	0.477227i
$651$	−3.21601	−	5.45945i	−0.126045	−	0.213973i
$652$	1.36461	+	1.36461i	0.0534424	+	0.0534424i
$653$	11.4134	−	11.4134i	0.446640	−	0.446640i	−0.447596	−	0.894236i	$-0.647720\pi$
$653$	11.4134	−	11.4134i	0.446640	−	0.446640i	0.894236	+	0.447596i	$0.147720\pi$
$654$	5.68706	+	9.85027i	0.222382	+	0.385176i
$655$	−3.34845	+	5.60938i	−0.130835	+	0.219177i
$656$	−3.00995	+	5.21339i	−0.117519	+	0.203549i
$657$	13.5981	+	3.64360i	0.530513	+	0.142150i
$658$	−11.2141	−	3.00482i	−0.437173	−	0.117140i
$659$			0.526658i			0.0205157i	0.999947	+	0.0102578i	$0.00326523\pi$
$659$			0.526658i			0.0205157i	−0.999947	+	0.0102578i	$0.996735\pi$
$660$	0.548864	−	1.93519i	0.0213645	−	0.0753272i
$661$	−12.7603	+	22.1015i	−0.496318	+	0.859648i	−0.999991	−	0.00424614i	$-0.998648\pi$
$661$	−12.7603	+	22.1015i	−0.496318	+	0.859648i	0.503673	+	0.863895i	$0.331982\pi$
$662$	−0.581448	−	2.16999i	−0.0225986	−	0.0843392i
$663$	4.15708	−	15.5144i	0.161447	−	0.602530i
$664$	1.05949	−	1.83509i	0.0411163	−	0.0712154i
$665$	4.36802	−	4.24259i	0.169384	−	0.164521i
$666$		−	3.88787i		−	0.150652i
$667$	−2.75800	−	2.75800i	−0.106790	−	0.106790i
$668$	3.90707	−	14.5814i	0.151169	−	0.564171i
$669$	15.3020	+	8.83461i	0.591609	+	0.341566i
$670$	−0.0296560	+	2.03591i	−0.00114571	+	0.0786539i
$671$	6.19819	−	10.7356i	0.239279	−	0.414443i
$672$	0.294543	+	1.09925i	0.0113622	+	0.0424045i
$673$	−14.1208	+	3.78367i	−0.544318	+	0.145850i	−0.520492	−	0.853866i	$-0.674252\pi$
$673$	−14.1208	+	3.78367i	−0.544318	+	0.145850i	−0.0238262	+	0.999716i	$0.507585\pi$
$674$	15.5037			0.597181
$675$	1.15287	+	4.86527i	0.0443742	+	0.187264i
$676$	6.64634	+	11.5118i	0.255629	+	0.442762i
$677$	−12.2900	−	45.8668i	−0.472342	−	1.76280i	−0.631320	−	0.775523i	$-0.717486\pi$
$677$	−12.2900	−	45.8668i	−0.472342	−	1.76280i	0.158977	−	0.987282i	$-0.449180\pi$
$678$	9.71492	+	9.71492i	0.373099	+	0.373099i
$679$	14.6465	−	8.45616i	0.562081	−	0.324518i
$680$	−6.01417	−	3.59008i	−0.230633	−	0.137673i
$681$		−	13.0966i		−	0.501863i
$682$	1.25396	−	4.84913i	0.0480167	−	0.185683i
$683$	24.8879	−	24.8879i	0.952308	−	0.952308i	−0.0466053	−	0.998913i	$-0.514840\pi$
$683$	24.8879	−	24.8879i	0.952308	−	0.952308i	0.998913	+	0.0466053i	$0.0148403\pi$
$684$			2.39292i			0.0914954i
$685$	10.4843	−	10.1833i	0.400585	−	0.389083i
$686$	−14.4585			−0.552029
$687$	28.0219	−	7.50846i	1.06910	−	0.286465i
$688$	2.90441	−	10.8394i	0.110730	−	0.413249i
$689$	59.8784	−	34.5708i	2.28119	−	1.31704i
$690$	−4.22806	−	16.7516i	−0.160960	−	0.637723i
$691$	−3.52702	+	6.10898i	−0.134174	+	0.232396i	−0.925282	−	0.379281i	$-0.876171\pi$
$691$	−3.52702	+	6.10898i	−0.134174	+	0.232396i	0.791108	+	0.611677i	$0.209505\pi$
$692$	7.38299	−	1.97827i	0.280659	−	0.0752024i
$693$	0.988862	−	0.264965i	0.0375638	−	0.0100652i
$694$	−9.86886	−	17.0934i	−0.374617	−	0.648855i
$695$	−10.3456	−	18.5375i	−0.392431	−	0.703167i
$696$	−0.252404	−	0.437177i	−0.00956736	−	0.0165712i
$697$	13.3336	−	13.3336i	0.505047	−	0.505047i
$698$	11.9941	−	11.9941i	0.453982	−	0.453982i
$699$	6.14549	+	10.6443i	0.232444	+	0.402604i
$700$	−4.13902	+	3.90463i	−0.156440	+	0.147581i
$701$	18.8146	+	32.5879i	0.710618	+	1.23083i	0.964626	+	0.263624i	$0.0849178\pi$
$701$	18.8146	+	32.5879i	0.710618	+	1.23083i	−0.254008	+	0.967202i	$0.581749\pi$
$702$	4.95292	−	1.32713i	0.186936	−	0.0500893i
$703$	8.98635	−	2.40788i	0.338927	−	0.0908151i
$704$	−0.449790	+	0.779058i	−0.0169521	+	0.0293619i
$705$	19.5871	+	11.6923i	0.737695	+	0.440357i
$706$	−29.1366	+	16.8220i	−1.09657	+	0.633105i
$707$	0.525881	−	1.96261i	0.0197778	−	0.0738117i
$708$	10.9544	−	2.93522i	0.411691	−	0.110312i
$709$	7.10997			0.267021			0.133510	−	0.991047i	$-0.457375\pi$
$709$	7.10997			0.267021			0.133510	+	0.991047i	$0.457375\pi$
$710$	15.0325	+	15.4769i	0.564160	+	0.580839i
$711$			11.8027i			0.442634i
$712$	−10.7188	+	10.7188i	−0.401705	+	0.401705i
$713$	−11.4973	−	41.4544i	−0.430576	−	1.55248i
$714$		−	3.56473i		−	0.133407i
$715$	−2.52416	−	10.0007i	−0.0943982	−	0.374006i
$716$	8.34906	−	4.82033i	0.312019	−	0.180144i
$717$	2.95385	+	2.95385i	0.110313	+	0.110313i
$718$	7.14380	+	26.6610i	0.266604	+	0.994981i
$719$	1.62998	+	2.82322i	0.0607882	+	0.105288i	0.894818	−	0.446431i	$-0.147305\pi$
$719$	1.62998	+	2.82322i	0.0607882	+	0.105288i	−0.834030	+	0.551719i	$0.813972\pi$
$720$	0.0325682	−	2.23583i	0.00121375	−	0.0833245i
$721$	3.54483			0.132016
$722$	12.8217	−	3.43555i	0.477173	−	0.127858i
$723$	−6.14887	−	22.9479i	−0.228679	−	0.853442i
$724$	−2.33769	+	4.04899i	−0.0868794	+	0.150480i
$725$	1.32515	−	2.14820i	0.0492150	−	0.0797821i
$726$	−8.82545	−	5.09538i	−0.327543	−	0.189107i
$727$	−9.25077	+	34.5244i	−0.343092	+	1.28044i	0.551733	+	0.834021i	$0.313967\pi$
$727$	−9.25077	+	34.5244i	−0.343092	+	1.28044i	−0.894825	+	0.446417i	$0.852700\pi$
$728$	4.12625	+	4.12625i	0.152929	+	0.152929i
$729$		−	1.00000i		−	0.0370370i
$730$	0.458489	−	31.4756i	0.0169694	−	1.16496i
$731$	−17.5754	+	30.4416i	−0.650051	+	1.12592i
$732$	3.56658	−	13.3107i	0.131825	−	0.491976i
$733$	−2.65768	−	9.91858i	−0.0981635	−	0.366351i	0.899317	−	0.437298i	$-0.144065\pi$
$733$	−2.65768	−	9.91858i	−0.0981635	−	0.366351i	−0.997480	+	0.0709470i	$0.977398\pi$
$734$	6.64175	−	11.5039i	0.245152	−	0.424615i
$735$	12.2725	+	3.48075i	0.452677	+	0.128389i
$736$			7.72648i			0.284802i
$737$	−0.791229	−	0.212009i	−0.0291453	−	0.00780945i
$738$	5.81478	+	1.55806i	0.214045	+	0.0573532i
$739$	−22.4615	+	38.9044i	−0.826259	+	1.43112i	0.0746948	+	0.997206i	$0.476202\pi$
$739$	−22.4615	+	38.9044i	−0.826259	+	1.43112i	−0.900954	+	0.433916i	$0.857132\pi$
$740$	−8.42921	+	2.12751i	−0.309864	+	0.0782089i
$741$	6.13500	+	10.6261i	0.225375	+	0.390361i
$742$	10.8508	−	10.8508i	0.398344	−	0.398344i
$743$	9.32650	+	9.32650i	0.342156	+	0.342156i	0.857177	−	0.515021i	$-0.172216\pi$
$743$	9.32650	+	9.32650i	0.342156	+	0.342156i	−0.515021	+	0.857177i	$0.672216\pi$
$744$	−0.0487035	−	5.56755i	−0.00178556	−	0.204116i
$745$	−26.6699	−	15.9203i	−0.977111	−	0.583274i
$746$	−22.8661			−0.837186
$747$	−2.04678	−	0.548433i	−0.0748878	−	0.0200661i
$748$	1.99250	−	1.99250i	0.0728531	−	0.0728531i
$749$	−9.24966	−	5.34030i	−0.337975	−	0.195130i
$750$	9.91741	−	5.16188i	0.362133	−	0.188485i
$751$	19.6178	+	33.9790i	0.715863	+	1.23991i	0.962626	+	0.270835i	$0.0872997\pi$
$751$	19.6178	+	33.9790i	0.715863	+	1.23991i	−0.246763	+	0.969076i	$0.579367\pi$
$752$	−7.21364	−	7.21364i	−0.263054	−	0.263054i
$753$	−2.57984	−	9.62810i	−0.0940146	−	0.350867i
$754$	−2.24169	−	1.29424i	−0.0816374	−	0.0471334i
$755$	−18.6890	+	10.4301i	−0.680161	+	0.379591i
$756$	0.985560	−	0.569014i	0.0358445	−	0.0206948i
$757$	2.88002	+	10.7484i	0.104676	+	0.390657i	0.998308	−	0.0581434i	$-0.0185181\pi$
$757$	2.88002	+	10.7484i	0.104676	+	0.390657i	−0.893632	+	0.448800i	$0.851851\pi$
$758$	−10.1404	−	2.71710i	−0.368315	−	0.0986896i
$759$	6.95058			0.252290
$760$	5.18802	−	1.30944i	0.188189	−	0.0474985i
$761$	−15.9541	+	9.21111i	−0.578336	+	0.333903i	−0.760472	−	0.649371i	$-0.775032\pi$
$761$	−15.9541	+	9.21111i	−0.578336	+	0.333903i	0.182136	+	0.983273i	$0.441699\pi$
$762$	−14.3284	+	3.83928i	−0.519062	+	0.139082i
$763$	12.5030	+	3.35017i	0.452639	+	0.121284i
$764$	11.0147	+	6.35934i	0.398498	+	0.230073i
$765$	−1.91117	+	6.73843i	−0.0690985	+	0.243628i
$766$	−5.22460	−	3.01642i	−0.188772	−	0.108988i
$767$	41.1194	−	41.1194i	1.48474	−	1.48474i
$768$	−0.258819	+	0.965926i	−0.00933933	+	0.0348548i
$769$	4.04508	−	2.33543i	0.145869	−	0.0842176i	−0.425289	−	0.905058i	$-0.639828\pi$
$769$	4.04508	−	2.33543i	0.145869	−	0.0842176i	0.571158	+	0.820840i	$0.306494\pi$
$770$	−1.11559	−	1.99893i	−0.0402029	−	0.0720366i
$771$		−	17.8766i		−	0.643812i
$772$	−4.76895	+	17.7980i	−0.171638	+	0.640563i
$773$	−6.99782	−	6.99782i	−0.251694	−	0.251694i	0.569971	−	0.821665i	$-0.306954\pi$
$773$	−6.99782	−	6.99782i	−0.251694	−	0.251694i	−0.821665	+	0.569971i	$0.806954\pi$
$774$	−11.2218			−0.403359
$775$	24.3878	−	13.4251i	0.876036	−	0.482245i
$776$	14.8611			0.533482
$777$	−3.12860	−	3.12860i	−0.112238	−	0.112238i
$778$	0.242341	−	0.904429i	0.00868835	−	0.0324254i
$779$			14.4051i			0.516117i
$780$	−5.58764	−	10.0121i	−0.200070	−	0.358490i
$781$	−7.51710	+	4.34000i	−0.268983	+	0.155297i
$782$	6.26401	−	23.3776i	0.224000	−	0.835981i
$783$	−0.356954	+	0.356954i	−0.0127565	+	0.0127565i
$784$	−4.94058	−	2.85245i	−0.176449	−	0.101873i
$785$	−0.324453	+	1.14396i	−0.0115802	+	0.0408297i
$786$	−2.53013	−	1.46077i	−0.0902469	−	0.0521041i
$787$	−44.9190	−	12.0360i	−1.60119	−	0.429038i	−0.655788	−	0.754945i	$-0.727664\pi$
$787$	−44.9190	−	12.0360i	−1.60119	−	0.429038i	−0.945402	+	0.325907i	$0.894330\pi$
$788$	−10.0348	+	2.68882i	−0.357476	+	0.0957854i
$789$	−7.04721	+	4.06871i	−0.250887	+	0.144850i
$790$	25.5890	−	6.45861i	0.910417	−	0.229787i
$791$	15.6353			0.555928
$792$	0.868927	+	0.232828i	0.0308760	+	0.00827319i
$793$	−18.2881	−	68.2522i	−0.649431	−	2.42371i
$794$	4.71129	−	2.72006i	0.167197	−	0.0965315i
$795$	−26.3287	+	14.6938i	−0.933782	+	0.521135i
$796$	0.0402513	+	0.0232391i	0.00142667	+	0.000823688i
$797$	8.21469	+	30.6576i	0.290979	+	1.08595i	0.944358	+	0.328918i	$0.106684\pi$
$797$	8.21469	+	30.6576i	0.290979	+	1.08595i	−0.653379	+	0.757031i	$0.726649\pi$
$798$	1.92559	+	1.92559i	0.0681653	+	0.0681653i
$799$	15.9777	+	27.6742i	0.565250	+	0.979041i
$800$	−4.86527	+	1.15287i	−0.172013	+	0.0407603i
$801$	13.1278	+	7.57935i	0.463849	+	0.267803i
$802$	17.2607	−	17.2607i	0.609495	−	0.609495i
$803$	12.2326	+	3.27771i	0.431678	+	0.115668i
$804$	−0.910582			−0.0321137
$805$	−16.8825	−	10.0778i	−0.595029	−	0.355195i
$806$	−14.4905	−	24.5988i	−0.510405	−	0.866455i
$807$	−0.323049	−	0.323049i	−0.0113719	−	0.0113719i
$808$	1.26248	−	1.26248i	0.0444138	−	0.0444138i
$809$	−2.38795	−	4.13604i	−0.0839557	−	0.145415i	0.820990	−	0.570942i	$-0.193422\pi$
$809$	−2.38795	−	4.13604i	−0.0839557	−	0.145415i	−0.904946	+	0.425527i	$0.860089\pi$
$810$	−2.16808	+	0.547217i	−0.0761784	+	0.0192272i
$811$	4.16634	−	7.21631i	0.146300	−	0.253399i	−0.783557	−	0.621320i	$-0.786597\pi$
$811$	4.16634	−	7.21631i	0.146300	−	0.253399i	0.929857	+	0.367921i	$0.119930\pi$
$812$	−0.554911	−	0.148688i	−0.0194736	−	0.00521792i
$813$	8.78705	+	2.35448i	0.308175	+	0.0825754i
$814$		−	3.49745i		−	0.122586i
$815$	−4.15154	−	1.17747i	−0.145422	−	0.0412450i
$816$	1.56619	−	2.71272i	0.0548276	−	0.0949642i
$817$	−6.95001	−	25.9378i	−0.243150	−	0.907448i
$818$	3.96874	−	14.8115i	0.138764	−	0.517873i
$819$	2.91770	−	5.05360i	0.101953	−	0.176587i
$820$	0.196057	−	13.4595i	0.00684662	−	0.470025i
$821$			3.55052i			0.123914i	0.998079	+	0.0619571i	$0.0197342\pi$
$821$			3.55052i			0.123914i	−0.998079	+	0.0619571i	$0.980266\pi$
$822$	4.62190	+	4.62190i	0.161207	+	0.161207i
$823$	4.06069	−	15.1547i	0.141547	−	0.528260i	−0.858338	−	0.513085i	$-0.828503\pi$
$823$	4.06069	−	15.1547i	0.141547	−	0.528260i	0.999885	−	0.0151755i	$-0.00483069\pi$
$824$	2.69757	+	1.55745i	0.0939745	+	0.0542562i
$825$	1.03710	+	4.37670i	0.0361073	+	0.152377i
$826$	6.45308	−	11.1771i	0.224531	−	0.388900i
$827$	−9.36179	−	34.9387i	−0.325541	−	1.21494i	−0.913767	−	0.406239i	$-0.866840\pi$
$827$	−9.36179	−	34.9387i	−0.325541	−	1.21494i	0.588225	−	0.808697i	$-0.299827\pi$
$828$	7.46321	−	1.99976i	0.259364	−	0.0694965i
$829$	−7.01201			−0.243537			−0.121769	−	0.992559i	$-0.538857\pi$
$829$	−7.01201			−0.243537			−0.121769	+	0.992559i	$0.538857\pi$
$830$	−0.0690115	+	4.73769i	−0.00239542	+	0.164448i
$831$	2.01036	+	3.48205i	0.0697387	+	0.120791i
$832$	1.32713	+	4.95292i	0.0460100	+	0.171712i
$833$	12.6359	+	12.6359i	0.437809	+	0.437809i
$834$	8.22195	−	4.74695i	0.284703	−	0.164373i
$835$	8.26066	+	32.7288i	0.285872	+	1.13263i
$836$			2.15262i			0.0744498i
$837$	−5.36524	+	1.48803i	−0.185450	+	0.0514339i
$838$	5.89369	−	5.89369i	0.203594	−	0.203594i
$839$		−	5.71857i		−	0.197427i	−0.995116	−	0.0987134i	$-0.968527\pi$
$839$		−	5.71857i		−	0.197427i	0.995116	−	0.0987134i	$-0.0314727\pi$
$840$	−1.77298	−	1.82540i	−0.0611736	−	0.0629821i
$841$	−28.7452			−0.991213
$842$	20.5148	−	5.49693i	0.706988	−	0.189437i
$843$	−7.97289	+	29.7552i	−0.274601	+	1.02482i
$844$	1.97592	−	1.14080i	0.0680141	−	0.0392680i
$845$	−25.5220	−	15.2350i	−0.877983	−	0.524101i
$846$	−5.10081	+	8.83487i	−0.175370	+	0.303749i
$847$	−11.2022	+	3.00162i	−0.384912	+	0.103137i
$848$	13.0247	−	3.48994i	0.447268	−	0.119845i
$849$	−9.30634	−	16.1190i	−0.319393	−	0.553204i
$850$	15.6552	+	0.456181i	0.536971	+	0.0156469i
$851$	−15.0198	−	26.0150i	−0.514872	−	0.891784i
$852$	−6.82284	+	6.82284i	−0.233747	+	0.233747i
$853$	−15.5594	+	15.5594i	−0.532742	+	0.532742i	−0.921387	−	0.388645i	$-0.872943\pi$
$853$	−15.5594	+	15.5594i	−0.532742	+	0.532742i	0.388645	+	0.921387i	$0.372943\pi$
$854$	−7.84112	−	13.5812i	−0.268318	−	0.464740i
$855$	−2.60758	−	4.67233i	−0.0891775	−	0.159790i
$856$	−4.69259	−	8.12781i	−0.160389	−	0.277803i
$857$	−25.0470	+	6.71134i	−0.855591	+	0.229255i	−0.659847	−	0.751400i	$-0.729379\pi$
$857$	−25.0470	+	6.71134i	−0.855591	+	0.229255i	−0.195744	+	0.980655i	$0.562712\pi$
$858$	4.45554	−	1.19386i	0.152110	−	0.0407577i
$859$	−6.82238	+	11.8167i	−0.232777	+	0.403181i	−0.958624	−	0.284675i	$-0.908114\pi$
$859$	−6.82238	+	11.8167i	−0.232777	+	0.403181i	0.725847	+	0.687856i	$0.241448\pi$
$860$	6.14075	+	24.3297i	0.209398	+	0.829635i
$861$	5.93297	−	3.42540i	0.202195	−	0.116737i
$862$	−0.135246	+	0.504746i	−0.00460651	+	0.0171917i
$863$	34.3085	−	9.19294i	1.16788	−	0.312931i	0.377769	−	0.925900i	$-0.376692\pi$
$863$	34.3085	−	9.19294i	1.16788	−	0.312931i	0.790107	+	0.612969i	$0.210025\pi$
$864$	1.00000			0.0340207
$865$	−12.2601	+	11.9080i	−0.416855	+	0.404885i
$866$		−	3.96896i		−	0.134871i
$867$	5.08283	−	5.08283i	0.172622	−	0.172622i
$868$	−4.51944	−	4.44105i	−0.153400	−	0.150739i
$869$			10.6174i			0.360171i
$870$	0.969234	+	0.578572i	0.0328601	+	0.0196154i
$871$	−4.04359	+	2.33457i	−0.137012	+	0.0791038i
$872$	8.04271	+	8.04271i	0.272361	+	0.272361i
$873$	−3.84633	−	14.3547i	−0.130179	−	0.485834i
$874$	9.24441	+	16.0118i	0.312697	+	0.541607i
$875$	3.82681	−	12.1344i	0.129370	−	0.410218i
$876$	14.0778			0.475645
$877$	−5.66197	+	1.51712i	−0.191191	+	0.0512295i	−0.353144	−	0.935569i	$-0.614887\pi$
$877$	−5.66197	+	1.51712i	−0.191191	+	0.0512295i	0.161953	+	0.986798i	$0.448221\pi$
$878$	−7.51362	−	28.0412i	−0.253572	−	0.946344i
$879$	−0.313974	+	0.543819i	−0.0105901	+	0.0183426i
$880$	0.0292977	−	2.01131i	0.000987624	−	0.0678011i
$881$	26.6182	+	15.3680i	0.896791	+	0.517763i	0.876158	−	0.482025i	$-0.160098\pi$
$881$	26.6182	+	15.3680i	0.896791	+	0.517763i	0.0206334	+	0.999787i	$0.493432\pi$
$882$	−1.47654	+	5.51050i	−0.0497175	+	0.185548i
$883$	16.1483	+	16.1483i	0.543434	+	0.543434i	0.924534	−	0.381100i	$-0.124455\pi$
$883$	16.1483	+	16.1483i	0.543434	+	0.543434i	−0.381100	+	0.924534i	$0.624455\pi$
$884$		−	16.0617i		−	0.540214i
$885$	−18.1907	+	17.6683i	−0.611473	+	0.593915i
$886$	7.53784	−	13.0559i	0.253239	−	0.438622i
$887$	0.716033	−	2.67227i	0.0240420	−	0.0897261i	−0.952862	−	0.303403i	$-0.901877\pi$
$887$	0.716033	−	2.67227i	0.0240420	−	0.0897261i	0.976904	+	0.213677i	$0.0685439\pi$
$888$	−1.00626	−	3.75540i	−0.0337677	−	0.126023i
$889$	−8.44065	+	14.6196i	−0.283090	+	0.490327i
$890$	9.24884	−	32.6097i	0.310022	−	1.09308i
$891$		−	0.899579i		−	0.0301370i
$892$	17.0672	+	4.57313i	0.571451	+	0.153120i
$893$	−23.5798	−	6.31819i	−0.789069	−	0.211430i
$894$	6.94529	−	12.0296i	0.232285	−	0.402330i
$895$	−11.0494	+	18.5101i	−0.369339	+	0.618724i
$896$	0.569014	+	0.985560i	0.0190094	+	0.0329253i
$897$	28.0146	−	28.0146i	0.935380	−	0.935380i
$898$	0.00698575	+	0.00698575i	0.000233117	+	0.000233117i
$899$	2.44630	+	1.38398i	0.0815887	+	0.0461584i
$900$	2.37282	+	4.40111i	0.0790939	+	0.146704i
$901$	−42.2373			−1.40713
$902$	5.23085	+	1.40160i	0.174168	+	0.0466683i
$903$	−9.03025	+	9.03025i	−0.300508	+	0.300508i
$904$	11.8983	+	6.86948i	0.395731	+	0.228476i
$905$	0.152269	−	10.4533i	0.00506158	−	0.347481i
$906$	−4.78573	−	8.28914i	−0.158995	−	0.275388i
$907$	−15.5834	−	15.5834i	−0.517439	−	0.517439i	0.399357	−	0.916796i	$-0.369233\pi$
$907$	−15.5834	−	15.5834i	−0.517439	−	0.517439i	−0.916796	+	0.399357i	$0.869233\pi$
$908$	−3.38965	−	12.6504i	−0.112490	−	0.419817i
$909$	−1.54621	−	0.892706i	−0.0512846	−	0.0296092i
$910$	−12.5532	−	3.56037i	−0.416135	−	0.118025i
$911$	25.0105	−	14.4398i	0.828634	−	0.478412i	−0.0247510	−	0.999694i	$-0.507879\pi$
$911$	25.0105	−	14.4398i	0.828634	−	0.478412i	0.853385	+	0.521282i	$0.174546\pi$
$912$	0.619332	+	2.31138i	0.0205081	+	0.0765374i
$913$	−1.84124	−	0.493359i	−0.0609362	−	0.0163278i
$914$	5.78593			0.191382
$915$	7.54076	+	29.8765i	0.249290	+	0.987687i
$916$	25.1238	−	14.5052i	0.830113	−	0.479266i
$917$	−3.21151	+	0.860522i	−0.106053	+	0.0284169i
$918$	−3.02565	−	0.810719i	−0.0998612	−	0.0267577i
$919$	−17.4110	−	10.0523i	−0.574337	−	0.331593i	0.184543	−	0.982824i	$-0.440920\pi$
$919$	−17.4110	−	10.0523i	−0.574337	−	0.331593i	−0.758880	+	0.651231i	$0.774253\pi$
$920$	−8.41963	−	15.0865i	−0.277587	−	0.497387i
$921$	−9.67524	−	5.58600i	−0.318810	−	0.184065i
$922$	−22.2167	+	22.2167i	−0.731668	+	0.731668i
$923$	−12.8054	+	47.7905i	−0.421496	+	1.57304i
$924$	0.886589	−	0.511873i	0.0291667	−	0.0168394i
$925$	14.1402	−	13.3395i	0.464928	−	0.438600i
$926$			34.7733i			1.14272i
$927$	0.806193	−	3.00875i	0.0264789	−	0.0988204i
$928$	−0.356954	−	0.356954i	−0.0117176	−	0.0117176i
$929$	−18.8245			−0.617612			−0.308806	−	0.951125i	$-0.599929\pi$
$929$	−18.8245			−0.617612			−0.308806	+	0.951125i	$0.599929\pi$
$930$	6.16212	+	10.8180i	0.202064	+	0.354735i
$931$	−13.6513			−0.447404
$932$	8.69103	+	8.69103i	0.284684	+	0.284684i
$933$	5.27986	−	19.7047i	0.172855	−	0.645103i
$934$		−	8.07133i		−	0.264102i
$935$	−1.71925	+	6.06175i	−0.0562255	+	0.198240i
$936$	4.44067	−	2.56382i	0.145148	−	0.0838011i
$937$	5.28370	−	19.7190i	0.172611	−	0.644193i	−0.824335	−	0.566102i	$-0.808451\pi$
$937$	5.28370	−	19.7190i	0.172611	−	0.644193i	0.996946	−	0.0780912i	$-0.0248825\pi$
$938$	−0.732751	+	0.732751i	−0.0239252	+	0.0239252i
$939$	−22.6379	−	13.0700i	−0.738759	−	0.426523i
$940$	21.9459	+	6.22436i	0.715797	+	0.203016i
$941$	5.87445	+	3.39161i	0.191501	+	0.110563i	0.592685	−	0.805434i	$-0.298068\pi$
$941$	5.87445	+	3.39161i	0.191501	+	0.110563i	−0.401184	+	0.915998i	$0.631401\pi$
$942$	−0.513654	−	0.137633i	−0.0167357	−	0.00448433i
$943$	44.9278	−	12.0384i	1.46305	−	0.392023i
$944$	9.82144	−	5.67041i	0.319661	−	0.184556i
$945$	−1.30432	+	2.18501i	−0.0424294	+	0.0710785i
$946$	−10.0949			−0.328213
$947$	36.7980	+	9.85999i	1.19577	+	0.320407i	0.801166	−	0.598443i	$-0.204214\pi$
$947$	36.7980	+	9.85999i	1.19577	+	0.320407i	0.394608	+	0.918849i	$0.370880\pi$
$948$	3.05475	+	11.4005i	0.0992137	+	0.370271i
$949$	62.5148	−	36.0929i	2.02932	−	1.17163i
$950$	−8.70306	+	8.21022i	−0.282365	+	0.266375i
$951$	12.2866	+	7.09368i	0.398421	+	0.230028i
$952$	−0.922621	−	3.44327i	−0.0299023	−	0.111597i
$953$	25.7218	+	25.7218i	0.833212	+	0.833212i	0.987955	−	0.154742i	$-0.0494548\pi$
$953$	25.7218	+	25.7218i	0.833212	+	0.833212i	−0.154742	+	0.987955i	$0.549455\pi$
$954$	−6.74206	−	11.6776i	−0.218282	−	0.378076i
$955$	−28.4368	−	0.414225i	−0.920194	−	0.0134040i
$956$	3.61771	+	2.08869i	0.117005	+	0.0675529i
$957$	−0.321108	+	0.321108i	−0.0103800	+	0.0103800i
$958$	−16.5910	−	4.44555i	−0.536032	−	0.143629i
$959$	7.43855			0.240203
$960$	−0.547217	−	2.16808i	−0.0176614	−	0.0699744i
$961$	15.9673	+	26.5715i	0.515074	+	0.857146i
$962$	−14.0966	−	14.0966i	−0.454493	−	0.454493i
$963$	−6.63633	+	6.63633i	−0.213853	+	0.213853i
$964$	−11.8787	−	20.5745i	−0.382587	−	0.662661i
$965$	−10.0829	−	39.9486i	−0.324581	−	1.28599i
$966$	4.39647	−	7.61491i	0.141454	−	0.245006i
$967$	4.63362	+	1.24158i	0.149007	+	0.0399264i	0.332552	−	0.943085i	$-0.392090\pi$
$967$	4.63362	+	1.24158i	0.149007	+	0.0399264i	−0.183544	+	0.983011i	$0.558757\pi$
$968$	−9.84352	−	2.63756i	−0.316383	−	0.0847745i
$969$		−	7.49552i		−	0.240791i
$970$	−29.0173	+	16.1943i	−0.931690	+	0.519967i
$971$	16.7546	−	29.0199i	0.537682	−	0.931293i	−0.461346	−	0.887220i	$-0.652633\pi$
$971$	16.7546	−	29.0199i	0.537682	−	0.931293i	0.999028	−	0.0440725i	$-0.0140333\pi$
$972$	−0.258819	−	0.965926i	−0.00830162	−	0.0309821i
$973$	2.79636	−	10.4362i	0.0896472	−	0.334568i
$974$	−2.37416	+	4.11217i	−0.0760730	+	0.131762i
$975$	21.8205	+	13.4604i	0.698816	+	0.431077i
$976$		−	13.7802i		−	0.441094i
$977$	2.00961	+	2.00961i	0.0642932	+	0.0642932i	0.738522	−	0.674229i	$-0.235524\pi$
$977$	2.00961	+	2.00961i	0.0642932	+	0.0642932i	−0.674229	+	0.738522i	$0.735524\pi$
$978$	0.499483	−	1.86410i	0.0159717	−	0.0596073i
$979$	11.8095	+	6.81823i	0.377434	+	0.217912i
$980$	12.7552	+	0.185798i	0.407449	+	0.00593510i
$981$	5.68706	−	9.85027i	0.181574	−	0.314495i
$982$	5.25573	+	19.6146i	0.167717	+	0.625928i
$983$	58.4203	−	15.6537i	1.86332	−	0.499275i	0.863333	−	0.504635i	$-0.168373\pi$
$983$	58.4203	−	15.6537i	1.86332	−	0.499275i	0.999986	+	0.00536062i	$0.00170635\pi$
$984$	6.01990			0.191907
$985$	16.6637	−	16.1852i	0.530949	−	0.515703i
$986$	0.790626	+	1.36940i	0.0251787	+	0.0436107i
$987$	3.00482	+	11.2141i	0.0956444	+	0.356950i
$988$	8.67620	+	8.67620i	0.276027	+	0.276027i
$989$	−75.0887	+	43.3525i	−2.38768	+	1.37853i
$990$	−1.95036	+	0.492265i	−0.0619864	+	0.0156452i
$991$		−	10.3522i		−	0.328847i	−0.986390	−	0.164424i	$-0.947424\pi$
$991$		−	10.3522i		−	0.328847i	0.986390	−	0.164424i	$-0.0525764\pi$
$992$	−1.48803	−	5.36524i	−0.0472451	−	0.170346i
$993$	−1.58854	+	1.58854i	−0.0504109	+	0.0504109i
$994$			10.9808i			0.348289i
$995$	−0.103917	−	0.00151371i	−0.00329440	−	4.79879e-5i
$996$	−2.11898			−0.0671426
$997$	−4.33958	+	1.16279i	−0.137436	+	0.0368258i	−0.326881	−	0.945065i	$-0.605998\pi$
$997$	−4.33958	+	1.16279i	−0.137436	+	0.0368258i	0.189445	+	0.981891i	$0.439331\pi$
$998$	9.84593	−	36.7455i	0.311667	−	1.16316i
$999$	−3.36700	+	1.94394i	−0.106527	+	0.0615034i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.be.a.37.3	✓	64
5.3	odd	4		930.2.be.b.223.8	yes	64
31.26	odd	6		930.2.be.b.367.8	yes	64
155.88	even	12	inner	930.2.be.a.553.3	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.be.a.37.3	✓	64	1.1	even	1	trivial
930.2.be.a.553.3	yes	64	155.88	even	12	inner
930.2.be.b.223.8	yes	64	5.3	odd	4
930.2.be.b.367.8	yes	64	31.26	odd	6

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.be (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.258819 + 0.965926i) q^{3} +1.00000i q^{4} +(-1.08971 - 1.95257i) q^{5} +(0.866025 - 0.500000i) q^{6} +(0.294543 - 1.09925i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.258819 + 0.965926i) q^{3} +1.00000i q^{4} +(-1.08971 - 1.95257i) q^{5} +(0.866025 - 0.500000i) q^{6} +(0.294543 - 1.09925i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(-0.610134 + 2.15122i) q^{10} +(-0.779058 - 0.449790i) q^{11} +(-0.965926 - 0.258819i) q^{12} +(-4.95292 + 1.32713i) q^{13} +(-0.985560 + 0.569014i) q^{14} +(2.16808 - 0.547217i) q^{15} -1.00000 q^{16} +(3.02565 + 0.810719i) q^{17} +(0.258819 + 0.965926i) q^{18} +(-2.07233 + 1.19646i) q^{19} +(1.95257 - 1.08971i) q^{20} +(0.985560 + 0.569014i) q^{21} +(0.232828 + 0.868927i) q^{22} +(5.46345 + 5.46345i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-2.62506 + 4.25547i) q^{25} +(4.44067 + 2.56382i) q^{26} +(0.707107 - 0.707107i) q^{27} +(1.09925 + 0.294543i) q^{28} -0.504809 q^{29} +(-1.92000 - 1.14612i) q^{30} +(-4.84599 - 2.74160i) q^{31} +(0.707107 + 0.707107i) q^{32} +(0.636098 - 0.636098i) q^{33} +(-1.56619 - 2.71272i) q^{34} +(-2.46733 + 0.622748i) q^{35} +(0.500000 - 0.866025i) q^{36} +(-3.75540 - 1.00626i) q^{37} +(2.31138 + 0.619332i) q^{38} -5.12764i q^{39} +(-2.15122 - 0.610134i) q^{40} +(3.00995 - 5.21339i) q^{41} +(-0.294543 - 1.09925i) q^{42} +(-2.90441 + 10.8394i) q^{43} +(0.449790 - 0.779058i) q^{44} +(-0.0325682 + 2.23583i) q^{45} -7.72648i q^{46} +(7.21364 + 7.21364i) q^{47} +(0.258819 - 0.965926i) q^{48} +(4.94058 + 2.85245i) q^{49} +(4.86527 - 1.15287i) q^{50} +(-1.56619 + 2.71272i) q^{51} +(-1.32713 - 4.95292i) q^{52} +(-13.0247 + 3.48994i) q^{53} -1.00000 q^{54} +(-0.0292977 + 2.01131i) q^{55} +(-0.569014 - 0.985560i) q^{56} +(-0.619332 - 2.31138i) q^{57} +(0.356954 + 0.356954i) q^{58} +(-9.82144 + 5.67041i) q^{59} +(0.547217 + 2.16808i) q^{60} +13.7802i q^{61} +(1.48803 + 5.36524i) q^{62} +(-0.804707 + 0.804707i) q^{63} -1.00000i q^{64} +(7.98856 + 8.22474i) q^{65} -0.899579 q^{66} +(0.879554 - 0.235676i) q^{67} +(-0.810719 + 3.02565i) q^{68} +(-6.69133 + 3.86324i) q^{69} +(2.18501 + 1.30432i) q^{70} +(4.82448 - 8.35624i) q^{71} +(-0.965926 + 0.258819i) q^{72} +(-13.5981 + 3.64360i) q^{73} +(1.94394 + 3.36700i) q^{74} +(-3.43106 - 3.63701i) q^{75} +(-1.19646 - 2.07233i) q^{76} +(-0.723897 + 0.723897i) q^{77} +(-3.62579 + 3.62579i) q^{78} +(-5.90133 - 10.2214i) q^{79} +(1.08971 + 1.95257i) q^{80} +(0.500000 + 0.866025i) q^{81} +(-5.81478 + 1.55806i) q^{82} +(2.04678 - 0.548433i) q^{83} +(-0.569014 + 0.985560i) q^{84} +(-1.71409 - 6.79124i) q^{85} +(9.71835 - 5.61089i) q^{86} +(0.130654 - 0.487608i) q^{87} +(-0.868927 + 0.232828i) q^{88} -15.1587 q^{89} +(1.60400 - 1.55794i) q^{90} +5.83539i q^{91} +(-5.46345 + 5.46345i) q^{92} +(3.90241 - 3.97129i) q^{93} -10.2016i q^{94} +(4.59440 + 2.74257i) q^{95} +(-0.866025 + 0.500000i) q^{96} +(10.5084 + 10.5084i) q^{97} +(-1.47654 - 5.51050i) q^{98} +(0.449790 + 0.779058i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 8 q^{7}+O(q^{10}) \) 64 * q - 8 * q^7	\( 64 q - 8 q^{7} - 4 q^{10} + 24 q^{14} + 8 q^{15} - 64 q^{16} + 4 q^{17} - 12 q^{20} - 24 q^{21} - 8 q^{22} + 32 q^{24} - 20 q^{25} - 4 q^{28} + 16 q^{29} + 8 q^{31} + 4 q^{33} + 24 q^{35} + 32 q^{36} + 56 q^{37} - 4 q^{38} - 8 q^{41} + 8 q^{42} - 56 q^{43} - 4 q^{44} + 12 q^{45} + 8 q^{47} - 60 q^{49} - 8 q^{50} + 24 q^{53} - 64 q^{54} + 16 q^{55} - 28 q^{57} + 52 q^{58} + 24 q^{59} - 4 q^{62} - 4 q^{63} + 100 q^{65} + 8 q^{66} + 76 q^{67} + 4 q^{68} - 12 q^{69} - 44 q^{70} + 8 q^{71} - 52 q^{73} + 12 q^{74} - 8 q^{75} - 8 q^{76} - 104 q^{77} + 56 q^{79} + 32 q^{81} + 32 q^{82} + 24 q^{83} + 32 q^{85} - 24 q^{86} - 20 q^{87} + 4 q^{88} - 176 q^{89} + 8 q^{93} + 64 q^{95} - 68 q^{97} - 64 q^{98} - 4 q^{99}+O(q^{100}) \) 64 * q - 8 * q^7 - 4 * q^10 + 24 * q^14 + 8 * q^15 - 64 * q^16 + 4 * q^17 - 12 * q^20 - 24 * q^21 - 8 * q^22 + 32 * q^24 - 20 * q^25 - 4 * q^28 + 16 * q^29 + 8 * q^31 + 4 * q^33 + 24 * q^35 + 32 * q^36 + 56 * q^37 - 4 * q^38 - 8 * q^41 + 8 * q^42 - 56 * q^43 - 4 * q^44 + 12 * q^45 + 8 * q^47 - 60 * q^49 - 8 * q^50 + 24 * q^53 - 64 * q^54 + 16 * q^55 - 28 * q^57 + 52 * q^58 + 24 * q^59 - 4 * q^62 - 4 * q^63 + 100 * q^65 + 8 * q^66 + 76 * q^67 + 4 * q^68 - 12 * q^69 - 44 * q^70 + 8 * q^71 - 52 * q^73 + 12 * q^74 - 8 * q^75 - 8 * q^76 - 104 * q^77 + 56 * q^79 + 32 * q^81 + 32 * q^82 + 24 * q^83 + 32 * q^85 - 24 * q^86 - 20 * q^87 + 4 * q^88 - 176 * q^89 + 8 * q^93 + 64 * q^95 - 68 * q^97 - 64 * q^98 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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