LMFDB - Embedded newform 770.2.l.c.573.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(573,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3, 2, 0]))

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

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

chi := DirichletCharacter("770.573");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.l (of order $4$, degree $2$, 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:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			573.17
Character	$\chi$	$=$	770.573
Dual form			770.2.l.c.727.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(0.949748 - 0.949748i) q^{3} -1.00000i q^{4} +(2.23301 - 0.116862i) q^{5} -1.34315i q^{6} +(0.924898 - 2.47882i) q^{7} +(-0.707107 - 0.707107i) q^{8} +1.19596i q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(0.949748 - 0.949748i) q^{3} -1.00000i q^{4} +(2.23301 - 0.116862i) q^{5} -1.34315i q^{6} +(0.924898 - 2.47882i) q^{7} +(-0.707107 - 0.707107i) q^{8} +1.19596i q^{9} +(1.49634 - 1.66161i) q^{10} -1.00000 q^{11} +(-0.949748 - 0.949748i) q^{12} +(1.43289 - 1.43289i) q^{13} +(-1.09879 - 2.40679i) q^{14} +(2.00981 - 2.23179i) q^{15} -1.00000 q^{16} +(-2.12548 - 2.12548i) q^{17} +(0.845671 + 0.845671i) q^{18} -4.78247 q^{19} +(-0.116862 - 2.23301i) q^{20} +(-1.47584 - 3.23268i) q^{21} +(-0.707107 + 0.707107i) q^{22} +(5.43865 + 5.43865i) q^{23} -1.34315 q^{24} +(4.97269 - 0.521906i) q^{25} -2.02641i q^{26} +(3.98510 + 3.98510i) q^{27} +(-2.47882 - 0.924898i) q^{28} +4.88338i q^{29} +(-0.156962 - 2.99926i) q^{30} -3.61773i q^{31} +(-0.707107 + 0.707107i) q^{32} +(-0.949748 + 0.949748i) q^{33} -3.00588 q^{34} +(1.77563 - 5.64333i) q^{35} +1.19596 q^{36} +(-3.64261 + 3.64261i) q^{37} +(-3.38172 + 3.38172i) q^{38} -2.72176i q^{39} +(-1.66161 - 1.49634i) q^{40} -1.73025i q^{41} +(-3.32942 - 1.24227i) q^{42} +(-2.53166 - 2.53166i) q^{43} +1.00000i q^{44} +(0.139762 + 2.67059i) q^{45} +7.69142 q^{46} +(-5.99420 - 5.99420i) q^{47} +(-0.949748 + 0.949748i) q^{48} +(-5.28913 - 4.58531i) q^{49} +(3.14718 - 3.88526i) q^{50} -4.03733 q^{51} +(-1.43289 - 1.43289i) q^{52} +(8.00171 + 8.00171i) q^{53} +5.63579 q^{54} +(-2.23301 + 0.116862i) q^{55} +(-2.40679 + 1.09879i) q^{56} +(-4.54214 + 4.54214i) q^{57} +(3.45307 + 3.45307i) q^{58} -2.83786 q^{59} +(-2.23179 - 2.00981i) q^{60} +9.06025i q^{61} +(-2.55812 - 2.55812i) q^{62} +(2.96457 + 1.10614i) q^{63} +1.00000i q^{64} +(3.03221 - 3.36710i) q^{65} +1.34315i q^{66} +(2.09522 - 2.09522i) q^{67} +(-2.12548 + 2.12548i) q^{68} +10.3307 q^{69} +(-2.73488 - 5.24599i) q^{70} -3.95706 q^{71} +(0.845671 - 0.845671i) q^{72} +(-2.03080 + 2.03080i) q^{73} +5.15143i q^{74} +(4.22712 - 5.21848i) q^{75} +4.78247i q^{76} +(-0.924898 + 2.47882i) q^{77} +(-1.92458 - 1.92458i) q^{78} -2.07142i q^{79} +(-2.23301 + 0.116862i) q^{80} +3.98180 q^{81} +(-1.22347 - 1.22347i) q^{82} +(10.0744 - 10.0744i) q^{83} +(-3.23268 + 1.47584i) q^{84} +(-4.99460 - 4.49783i) q^{85} -3.58031 q^{86} +(4.63798 + 4.63798i) q^{87} +(0.707107 + 0.707107i) q^{88} +2.88427 q^{89} +(1.98722 + 1.78957i) q^{90} +(-2.22660 - 4.87715i) q^{91} +(5.43865 - 5.43865i) q^{92} +(-3.43593 - 3.43593i) q^{93} -8.47708 q^{94} +(-10.6793 + 0.558887i) q^{95} +1.34315i q^{96} +(4.99905 + 4.99905i) q^{97} +(-6.98229 + 0.497672i) q^{98} -1.19596i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q+O(q^{10}) $ 40 * q	$ 40 q - 40 q^{11} + 56 q^{15} - 40 q^{16} - 8 q^{18} - 4 q^{21} - 32 q^{25} - 24 q^{30} + 48 q^{35} - 48 q^{36} - 8 q^{37} - 40 q^{42} - 8 q^{43} + 32 q^{46} + 16 q^{50} - 8 q^{51} + 56 q^{53} + 4 q^{56} + 32 q^{57} - 8 q^{58} + 8 q^{60} - 16 q^{63} + 8 q^{65} - 24 q^{67} - 4 q^{70} - 24 q^{71} - 8 q^{72} - 16 q^{78} - 24 q^{81} + 96 q^{85} - 96 q^{86} + 64 q^{91} + 24 q^{93} - 112 q^{95} + 16 q^{98}+O(q^{100}) $ 40 * q - 40 * q^11 + 56 * q^15 - 40 * q^16 - 8 * q^18 - 4 * q^21 - 32 * q^25 - 24 * q^30 + 48 * q^35 - 48 * q^36 - 8 * q^37 - 40 * q^42 - 8 * q^43 + 32 * q^46 + 16 * q^50 - 8 * q^51 + 56 * q^53 + 4 * q^56 + 32 * q^57 - 8 * q^58 + 8 * q^60 - 16 * q^63 + 8 * q^65 - 24 * q^67 - 4 * q^70 - 24 * q^71 - 8 * q^72 - 16 * q^78 - 24 * q^81 + 96 * q^85 - 96 * q^86 + 64 * q^91 + 24 * q^93 - 112 * q^95 + 16 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$	0.949748	−	0.949748i	0.548337	−	0.548337i	−0.377623	−	0.925960i	$-0.623258\pi$
$3$	0.949748	−	0.949748i	0.548337	−	0.548337i	0.925960	+	0.377623i	$0.123258\pi$
$4$		−	1.00000i		−	0.500000i
$5$	2.23301	−	0.116862i	0.998633	−	0.0522621i
$5$	2.23301	−	0.116862i	0.998633	−	0.0522621i
$6$		−	1.34315i		−	0.548337i
$7$	0.924898	−	2.47882i	0.349578	−	0.936907i
$7$	0.924898	−	2.47882i	0.349578	−	0.936907i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$			1.19596i			0.398653i
$10$	1.49634	−	1.66161i	0.473186	−	0.525448i
$11$	−1.00000			−0.301511
$11$	−1.00000			−0.301511
$12$	−0.949748	−	0.949748i	−0.274168	−	0.274168i
$13$	1.43289	−	1.43289i	0.397411	−	0.397411i	−0.479908	−	0.877319i	$-0.659330\pi$
$13$	1.43289	−	1.43289i	0.397411	−	0.397411i	0.877319	+	0.479908i	$0.159330\pi$
$14$	−1.09879	−	2.40679i	−0.293664	−	0.643243i
$15$	2.00981	−	2.23179i	0.518930	−	0.576245i
$16$	−1.00000			−0.250000
$17$	−2.12548	−	2.12548i	−0.515504	−	0.515504i	0.400704	−	0.916208i	$-0.368766\pi$
$17$	−2.12548	−	2.12548i	−0.515504	−	0.515504i	−0.916208	+	0.400704i	$0.868766\pi$
$18$	0.845671	+	0.845671i	0.199327	+	0.199327i
$19$	−4.78247			−1.09717			−0.548587	−	0.836093i	$-0.684834\pi$
$19$	−4.78247			−1.09717			−0.548587	+	0.836093i	$0.684834\pi$
$20$	−0.116862	−	2.23301i	−0.0261310	−	0.499317i
$21$	−1.47584	−	3.23268i	−0.322054	−	0.705428i
$22$	−0.707107	+	0.707107i	−0.150756	+	0.150756i
$23$	5.43865	+	5.43865i	1.13404	+	1.13404i	0.989499	+	0.144539i	$0.0461699\pi$
$23$	5.43865	+	5.43865i	1.13404	+	1.13404i	0.144539	+	0.989499i	$0.453830\pi$
$24$	−1.34315			−0.274168
$25$	4.97269	−	0.521906i	0.994537	−	0.104381i
$26$		−	2.02641i		−	0.397411i
$27$	3.98510	+	3.98510i	0.766933	+	0.766933i
$28$	−2.47882	−	0.924898i	−0.468454	−	0.174789i
$29$			4.88338i			0.906821i	0.891302	+	0.453410i	$0.149793\pi$
$29$			4.88338i			0.906821i	−0.891302	+	0.453410i	$0.850207\pi$
$30$	−0.156962	−	2.99926i	−0.0286572	−	0.547588i
$31$		−	3.61773i		−	0.649763i	−0.945755	−	0.324882i	$-0.894676\pi$
$31$		−	3.61773i		−	0.649763i	0.945755	−	0.324882i	$-0.105324\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	−0.949748	+	0.949748i	−0.165330	+	0.165330i
$34$	−3.00588			−0.515504
$35$	1.77563	−	5.64333i	0.300136	−	0.953896i
$36$	1.19596			0.199327
$37$	−3.64261	+	3.64261i	−0.598842	+	0.598842i	−0.940004	−	0.341162i	$-0.889179\pi$
$37$	−3.64261	+	3.64261i	−0.598842	+	0.598842i	0.341162	+	0.940004i	$0.389179\pi$
$38$	−3.38172	+	3.38172i	−0.548587	+	0.548587i
$39$		−	2.72176i		−	0.435831i
$40$	−1.66161	−	1.49634i	−0.262724	−	0.236593i
$41$		−	1.73025i		−	0.270219i	−0.990831	−	0.135110i	$-0.956861\pi$
$41$		−	1.73025i		−	0.270219i	0.990831	−	0.135110i	$-0.0431386\pi$
$42$	−3.32942	−	1.24227i	−0.513741	−	0.191687i
$43$	−2.53166	−	2.53166i	−0.386075	−	0.386075i	0.487210	−	0.873285i	$-0.338015\pi$
$43$	−2.53166	−	2.53166i	−0.386075	−	0.386075i	−0.873285	+	0.487210i	$0.838015\pi$
$44$			1.00000i			0.150756i
$45$	0.139762	+	2.67059i	0.0208344	+	0.398108i
$46$	7.69142			1.13404
$47$	−5.99420	−	5.99420i	−0.874344	−	0.874344i	0.118599	−	0.992942i	$-0.462160\pi$
$47$	−5.99420	−	5.99420i	−0.874344	−	0.874344i	−0.992942	+	0.118599i	$0.962160\pi$
$48$	−0.949748	+	0.949748i	−0.137084	+	0.137084i
$49$	−5.28913	−	4.58531i	−0.755590	−	0.655045i
$50$	3.14718	−	3.88526i	0.445078	−	0.549459i
$51$	−4.03733			−0.565339
$52$	−1.43289	−	1.43289i	−0.198706	−	0.198706i
$53$	8.00171	+	8.00171i	1.09912	+	1.09912i	0.994514	+	0.104606i	$0.0333580\pi$
$53$	8.00171	+	8.00171i	1.09912	+	1.09912i	0.104606	+	0.994514i	$0.466642\pi$
$54$	5.63579			0.766933
$55$	−2.23301	+	0.116862i	−0.301099	+	0.0157576i
$56$	−2.40679	+	1.09879i	−0.321621	+	0.146832i
$57$	−4.54214	+	4.54214i	−0.601621	+	0.601621i
$58$	3.45307	+	3.45307i	0.453410	+	0.453410i
$59$	−2.83786			−0.369458			−0.184729	−	0.982789i	$-0.559141\pi$
$59$	−2.83786			−0.369458			−0.184729	+	0.982789i	$0.559141\pi$
$60$	−2.23179	−	2.00981i	−0.288122	−	0.259465i
$61$			9.06025i			1.16005i	0.814600	+	0.580023i	$0.196956\pi$
$61$			9.06025i			1.16005i	−0.814600	+	0.580023i	$0.803044\pi$
$62$	−2.55812	−	2.55812i	−0.324882	−	0.324882i
$63$	2.96457	+	1.10614i	0.373501	+	0.139361i
$64$			1.00000i			0.125000i
$65$	3.03221	−	3.36710i	0.376099	−	0.417638i
$66$			1.34315i			0.165330i
$67$	2.09522	−	2.09522i	0.255972	−	0.255972i	−0.567442	−	0.823414i	$-0.692067\pi$
$67$	2.09522	−	2.09522i	0.255972	−	0.255972i	0.823414	+	0.567442i	$0.192067\pi$
$68$	−2.12548	+	2.12548i	−0.257752	+	0.257752i
$69$	10.3307			1.24367
$70$	−2.73488	−	5.24599i	−0.326880	−	0.627016i
$71$	−3.95706			−0.469616			−0.234808	−	0.972042i	$-0.575446\pi$
$71$	−3.95706			−0.469616			−0.234808	+	0.972042i	$0.575446\pi$
$72$	0.845671	−	0.845671i	0.0996633	−	0.0996633i
$73$	−2.03080	+	2.03080i	−0.237687	+	0.237687i	−0.815892	−	0.578205i	$-0.803754\pi$
$73$	−2.03080	+	2.03080i	−0.237687	+	0.237687i	0.578205	+	0.815892i	$0.303754\pi$
$74$			5.15143i			0.598842i
$75$	4.22712	−	5.21848i	0.488106	−	0.602578i
$76$			4.78247i			0.548587i
$77$	−0.924898	+	2.47882i	−0.105402	+	0.282488i
$78$	−1.92458	−	1.92458i	−0.217915	−	0.217915i
$79$		−	2.07142i		−	0.233053i	−0.993188	−	0.116527i	$-0.962824\pi$
$79$		−	2.07142i		−	0.233053i	0.993188	−	0.116527i	$-0.0371761\pi$
$80$	−2.23301	+	0.116862i	−0.249658	+	0.0130655i
$81$	3.98180			0.442423
$82$	−1.22347	−	1.22347i	−0.135110	−	0.135110i
$83$	10.0744	−	10.0744i	1.10581	−	1.10581i	0.112114	−	0.993695i	$-0.464238\pi$
$83$	10.0744	−	10.0744i	1.10581	−	1.10581i	0.993695	−	0.112114i	$-0.0357623\pi$
$84$	−3.23268	+	1.47584i	−0.352714	+	0.161027i
$85$	−4.99460	−	4.49783i	−0.541740	−	0.487858i
$86$	−3.58031			−0.386075
$87$	4.63798	+	4.63798i	0.497243	+	0.497243i
$88$	0.707107	+	0.707107i	0.0753778	+	0.0753778i
$89$	2.88427			0.305732			0.152866	−	0.988247i	$-0.451150\pi$
$89$	2.88427			0.305732			0.152866	+	0.988247i	$0.451150\pi$
$90$	1.98722	+	1.78957i	0.209471	+	0.188637i
$91$	−2.22660	−	4.87715i	−0.233411	−	0.511264i
$92$	5.43865	−	5.43865i	0.567019	−	0.567019i
$93$	−3.43593	−	3.43593i	−0.356289	−	0.356289i
$94$	−8.47708			−0.874344
$95$	−10.6793	+	0.558887i	−1.09568	+	0.0573406i
$96$			1.34315i			0.137084i
$97$	4.99905	+	4.99905i	0.507577	+	0.507577i	0.913782	−	0.406205i	$-0.133148\pi$
$97$	4.99905	+	4.99905i	0.507577	+	0.507577i	−0.406205	+	0.913782i	$0.633148\pi$
$98$	−6.98229	+	0.497672i	−0.705317	+	0.0502725i
$99$		−	1.19596i		−	0.120198i
$100$	−0.521906	−	4.97269i	−0.0521906	−	0.497269i
$101$			16.4098i			1.63284i	0.577461	+	0.816418i	$0.304044\pi$
$101$			16.4098i			1.63284i	−0.577461	+	0.816418i	$0.695956\pi$
$102$	−2.85482	+	2.85482i	−0.282670	+	0.282670i
$103$	−2.19851	+	2.19851i	−0.216626	+	0.216626i	−0.807075	−	0.590449i	$-0.798951\pi$
$103$	−2.19851	+	2.19851i	−0.216626	+	0.216626i	0.590449	+	0.807075i	$0.298951\pi$
$104$	−2.02641			−0.198706
$105$	−3.67334	−	7.04613i	−0.358481	−	0.687632i
$106$	11.3161			1.09912
$107$	−7.11035	+	7.11035i	−0.687384	+	0.687384i	−0.961653	−	0.274269i	$-0.911564\pi$
$107$	−7.11035	+	7.11035i	−0.687384	+	0.687384i	0.274269	+	0.961653i	$0.411564\pi$
$108$	3.98510	−	3.98510i	0.383467	−	0.383467i
$109$		−	9.12988i		−	0.874484i	−0.899344	−	0.437242i	$-0.855955\pi$
$109$		−	9.12988i		−	0.874484i	0.899344	−	0.437242i	$-0.144045\pi$
$110$	−1.49634	+	1.66161i	−0.142671	+	0.158428i
$111$			6.91913i			0.656734i
$112$	−0.924898	+	2.47882i	−0.0873946	+	0.234227i
$113$	−0.954364	−	0.954364i	−0.0897790	−	0.0897790i	0.660791	−	0.750570i	$-0.270221\pi$
$113$	−0.954364	−	0.954364i	−0.0897790	−	0.0897790i	−0.750570	+	0.660791i	$0.770221\pi$
$114$			6.42356i			0.601621i
$115$	12.7802	+	11.5090i	1.19176	+	1.07322i
$116$	4.88338			0.453410
$117$	1.71368	+	1.71368i	0.158429	+	0.158429i
$118$	−2.00667	+	2.00667i	−0.184729	+	0.184729i
$119$	−7.23453	+	3.30283i	−0.663188	+	0.302770i
$120$	−2.99926	+	0.156962i	−0.273794	+	0.0143286i
$121$	1.00000			0.0909091
$122$	6.40656	+	6.40656i	0.580023	+	0.580023i
$123$	−1.64330	−	1.64330i	−0.148171	−	0.148171i
$124$	−3.61773			−0.324882
$125$	11.0431	−	1.74654i	0.987723	−	0.156215i
$126$	2.87843	−	1.31411i	0.256431	−	0.117070i
$127$	−2.02297	+	2.02297i	−0.179510	+	0.179510i	−0.791142	−	0.611632i	$-0.790513\pi$
$127$	−2.02297	+	2.02297i	−0.179510	+	0.179510i	0.611632	+	0.791142i	$0.290513\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	−4.80888			−0.423398
$130$	−0.236809	−	4.52500i	−0.0207695	−	0.396868i
$131$		−	2.61550i		−	0.228517i	−0.993451	−	0.114259i	$-0.963551\pi$
$131$		−	2.61550i		−	0.228517i	0.993451	−	0.114259i	$-0.0364493\pi$
$132$	0.949748	+	0.949748i	0.0826649	+	0.0826649i
$133$	−4.42330	+	11.8549i	−0.383549	+	1.02795i
$134$		−	2.96309i		−	0.255972i
$135$	9.36449	+	8.43308i	0.805967	+	0.725804i
$136$			3.00588i			0.257752i
$137$	−12.3068	+	12.3068i	−1.05144	+	1.05144i	−0.0528400	+	0.998603i	$0.516827\pi$
$137$	−12.3068	+	12.3068i	−1.05144	+	1.05144i	−0.998603	+	0.0528400i	$0.983173\pi$
$138$	7.30491	−	7.30491i	0.621835	−	0.621835i
$139$	13.5756			1.15146			0.575732	−	0.817638i	$-0.304717\pi$
$139$	13.5756			1.15146			0.575732	+	0.817638i	$0.304717\pi$
$140$	−5.64333	−	1.77563i	−0.476948	−	0.150068i
$141$	−11.3859			−0.958870
$142$	−2.79806	+	2.79806i	−0.234808	+	0.234808i
$143$	−1.43289	+	1.43289i	−0.119824	+	0.119824i
$144$		−	1.19596i		−	0.0996633i
$145$	0.570679	+	10.9046i	0.0473923	+	0.905581i
$146$			2.87198i			0.237687i
$147$	−9.37823	+	0.668446i	−0.773503	+	0.0551325i
$148$	3.64261	+	3.64261i	0.299421	+	0.299421i
$149$		−	17.5669i		−	1.43914i	−0.694422	−	0.719568i	$-0.744340\pi$
$149$		−	17.5669i		−	1.43914i	0.694422	−	0.719568i	$-0.255660\pi$
$150$	−0.700996	−	6.67904i	−0.0572361	−	0.545342i
$151$	5.18511			0.421958			0.210979	−	0.977491i	$-0.432335\pi$
$151$	5.18511			0.421958			0.210979	+	0.977491i	$0.432335\pi$
$152$	3.38172	+	3.38172i	0.274294	+	0.274294i
$153$	2.54198	−	2.54198i	0.205507	−	0.205507i
$154$	1.09879	+	2.40679i	0.0885431	+	0.193945i
$155$	−0.422773	−	8.07843i	−0.0339580	−	0.648875i
$156$	−2.72176			−0.217915
$157$	−10.8879	−	10.8879i	−0.868949	−	0.868949i	0.123407	−	0.992356i	$-0.460618\pi$
$157$	−10.8879	−	10.8879i	−0.868949	−	0.868949i	−0.992356	+	0.123407i	$0.960618\pi$
$158$	−1.46472	−	1.46472i	−0.116527	−	0.116527i
$159$	15.1992			1.20538
$160$	−1.49634	+	1.66161i	−0.118296	+	0.131362i
$161$	18.5117	−	8.45127i	1.45892	−	0.666053i
$162$	2.81556	−	2.81556i	0.221211	−	0.221211i
$163$	16.0344	+	16.0344i	1.25591	+	1.25591i	0.953029	+	0.302879i	$0.0979480\pi$
$163$	16.0344	+	16.0344i	1.25591	+	1.25591i	0.302879	+	0.953029i	$0.402052\pi$
$164$	−1.73025			−0.135110
$165$	−2.00981	+	2.23179i	−0.156463	+	0.173744i
$166$		−	14.2474i		−	1.10581i
$167$	12.4146	+	12.4146i	0.960668	+	0.960668i	0.999255	−	0.0385876i	$-0.0122859\pi$
$167$	12.4146	+	12.4146i	0.960668	+	0.960668i	−0.0385876	+	0.999255i	$0.512286\pi$
$168$	−1.24227	+	3.32942i	−0.0958434	+	0.256870i
$169$			8.89367i			0.684128i
$170$	−6.71216	+	0.351271i	−0.514799	+	0.0269413i
$171$		−	5.71964i		−	0.437392i
$172$	−2.53166	+	2.53166i	−0.193037	+	0.193037i
$173$	−5.53909	+	5.53909i	−0.421129	+	0.421129i	−0.885592	−	0.464463i	$-0.846247\pi$
$173$	−5.53909	+	5.53909i	−0.421129	+	0.421129i	0.464463	+	0.885592i	$0.346247\pi$
$174$	6.55909			0.497243
$175$	3.30551	−	12.8091i	0.249873	−	0.968279i
$176$	1.00000			0.0753778
$177$	−2.69525	+	2.69525i	−0.202588	+	0.202588i
$178$	2.03948	−	2.03948i	0.152866	−	0.152866i
$179$		−	3.83429i		−	0.286588i	−0.989680	−	0.143294i	$-0.954230\pi$
$179$		−	3.83429i		−	0.286588i	0.989680	−	0.143294i	$-0.0457695\pi$
$180$	2.67059	−	0.139762i	0.199054	−	0.0104172i
$181$			25.6033i			1.90308i	0.307529	+	0.951539i	$0.400498\pi$
$181$			25.6033i			1.90308i	−0.307529	+	0.951539i	$0.599502\pi$
$182$	−5.02311	−	1.87422i	−0.372338	−	0.138926i
$183$	8.60495	+	8.60495i	0.636096	+	0.636096i
$184$		−	7.69142i		−	0.567019i
$185$	−7.70832	+	8.55968i	−0.566727	+	0.629320i
$186$	−4.85914			−0.356289
$187$	2.12548	+	2.12548i	0.155430	+	0.155430i
$188$	−5.99420	+	5.99420i	−0.437172	+	0.437172i
$189$	13.5642	−	6.19255i	0.986648	−	0.450442i
$190$	−7.15623	+	7.94661i	−0.519167	+	0.576508i
$191$	9.24632			0.669040			0.334520	−	0.942389i	$-0.391426\pi$
$191$	9.24632			0.669040			0.334520	+	0.942389i	$0.391426\pi$
$192$	0.949748	+	0.949748i	0.0685421	+	0.0685421i
$193$	−7.47212	−	7.47212i	−0.537855	−	0.537855i	0.385043	−	0.922898i	$-0.374186\pi$
$193$	−7.47212	−	7.47212i	−0.537855	−	0.537855i	−0.922898	+	0.385043i	$0.874186\pi$
$194$	7.06973			0.507577
$195$	−0.318069	−	6.07773i	−0.0227774	−	0.435235i
$196$	−4.58531	+	5.28913i	−0.327522	+	0.377795i
$197$	7.14410	−	7.14410i	0.508996	−	0.508996i	−0.405222	−	0.914218i	$-0.632806\pi$
$197$	7.14410	−	7.14410i	0.508996	−	0.508996i	0.914218	+	0.405222i	$0.132806\pi$
$198$	−0.845671	−	0.845671i	−0.0600992	−	0.0600992i
$199$	−6.17800			−0.437946			−0.218973	−	0.975731i	$-0.570271\pi$
$199$	−6.17800			−0.437946			−0.218973	+	0.975731i	$0.570271\pi$
$200$	−3.88526	−	3.14718i	−0.274730	−	0.222539i
$201$		−	3.97986i		−	0.280718i
$202$	11.6035	+	11.6035i	0.816418	+	0.816418i
$203$	12.1050	+	4.51662i	0.849607	+	0.317005i
$204$			4.03733i			0.282670i
$205$	−0.202199	−	3.86366i	−0.0141222	−	0.269850i
$206$			3.10916i			0.216626i
$207$	−6.50441	+	6.50441i	−0.452088	+	0.452088i
$208$	−1.43289	+	1.43289i	−0.0993529	+	0.0993529i
$209$	4.78247			0.330811
$210$	−7.57981	−	2.38493i	−0.523057	−	0.164576i
$211$	−13.2613			−0.912944			−0.456472	−	0.889738i	$-0.650887\pi$
$211$	−13.2613			−0.912944			−0.456472	+	0.889738i	$0.650887\pi$
$212$	8.00171	−	8.00171i	0.549560	−	0.549560i
$213$	−3.75821	+	3.75821i	−0.257508	+	0.257508i
$214$			10.0556i			0.687384i
$215$	−5.94908	−	5.35737i	−0.405724	−	0.365370i
$216$		−	5.63579i		−	0.383467i
$217$	−8.96771	−	3.34603i	−0.608768	−	0.227143i
$218$	−6.45580	−	6.45580i	−0.437242	−	0.437242i
$219$			3.85749i			0.260665i
$220$	0.116862	+	2.23301i	0.00787880	+	0.150550i
$221$	−6.09114			−0.409734
$222$	4.89256	+	4.89256i	0.328367	+	0.328367i
$223$	2.44171	−	2.44171i	0.163509	−	0.163509i	−0.620610	−	0.784119i	$-0.713115\pi$
$223$	2.44171	−	2.44171i	0.163509	−	0.163509i	0.784119	+	0.620610i	$0.213115\pi$
$224$	1.09879	+	2.40679i	0.0734161	+	0.160811i
$225$	0.624179	+	5.94713i	0.0416119	+	0.396475i
$226$	−1.34967			−0.0897790
$227$	−19.8638	−	19.8638i	−1.31840	−	1.31840i	−0.915039	−	0.403364i	$-0.867841\pi$
$227$	−19.8638	−	19.8638i	−1.31840	−	1.31840i	−0.403364	−	0.915039i	$-0.632159\pi$
$228$	4.54214	+	4.54214i	0.300811	+	0.300811i
$229$	−5.89330			−0.389440			−0.194720	−	0.980859i	$-0.562380\pi$
$229$	−5.89330			−0.389440			−0.194720	+	0.980859i	$0.562380\pi$
$230$	17.1750	−	0.898831i	1.13249	−	0.0592672i
$231$	1.47584	+	3.23268i	0.0971030	+	0.212694i
$232$	3.45307	−	3.45307i	0.226705	−	0.226705i
$233$	5.79724	+	5.79724i	0.379790	+	0.379790i	0.871026	−	0.491236i	$-0.163455\pi$
$233$	5.79724	+	5.79724i	0.379790	+	0.379790i	−0.491236	+	0.871026i	$0.663455\pi$
$234$	2.42350			0.158429
$235$	−14.0856	−	12.6846i	−0.918844	−	0.827454i
$236$			2.83786i			0.184729i
$237$	−1.96733	−	1.96733i	−0.127792	−	0.127792i
$238$	−2.78013	+	7.45104i	−0.180209	+	0.482979i
$239$		−	17.2126i		−	1.11339i	−0.830717	−	0.556695i	$-0.812069\pi$
$239$		−	17.2126i		−	1.11339i	0.830717	−	0.556695i	$-0.187931\pi$
$240$	−2.00981	+	2.23179i	−0.129733	+	0.144061i
$241$			10.1701i			0.655116i	0.944831	+	0.327558i	$0.106226\pi$
$241$			10.1701i			0.655116i	−0.944831	+	0.327558i	$0.893774\pi$
$242$	0.707107	−	0.707107i	0.0454545	−	0.0454545i
$243$	−8.17360	+	8.17360i	−0.524337	+	0.524337i
$244$	9.06025			0.580023
$245$	−12.3465	−	9.62097i	−0.788791	−	0.614661i
$246$	−2.32397			−0.148171
$247$	−6.85275	+	6.85275i	−0.436030	+	0.436030i
$248$	−2.55812	+	2.55812i	−0.162441	+	0.162441i
$249$		−	19.1363i		−	1.21271i
$250$	6.57365	−	9.04363i	0.415754	−	0.571969i
$251$		−	15.2433i		−	0.962150i	−0.876679	−	0.481075i	$-0.840246\pi$
$251$		−	15.2433i		−	0.962150i	0.876679	−	0.481075i	$-0.159754\pi$
$252$	1.10614	−	2.96457i	0.0696803	−	0.186750i
$253$	−5.43865	−	5.43865i	−0.341925	−	0.341925i
$254$			2.86091i			0.179510i
$255$	−9.01541	+	0.471809i	−0.564567	+	0.0295458i
$256$	1.00000			0.0625000
$257$	−5.04404	−	5.04404i	−0.314639	−	0.314639i	0.532065	−	0.846704i	$-0.321416\pi$
$257$	−5.04404	−	5.04404i	−0.314639	−	0.314639i	−0.846704	+	0.532065i	$0.821416\pi$
$258$	−3.40039	+	3.40039i	−0.211699	+	0.211699i
$259$	5.66035	+	12.3984i	0.351717	+	0.770402i
$260$	−3.36710	−	3.03221i	−0.208819	−	0.188049i
$261$	−5.84032			−0.361507
$262$	−1.84944	−	1.84944i	−0.114259	−	0.114259i
$263$	10.6291	+	10.6291i	0.655421	+	0.655421i	0.954293	−	0.298872i	$-0.0966103\pi$
$263$	10.6291	+	10.6291i	0.655421	+	0.655421i	−0.298872	+	0.954293i	$0.596610\pi$
$264$	1.34315			0.0826649
$265$	18.8030	+	16.9328i	1.15506	+	1.04018i
$266$	5.25494	+	11.5104i	0.322201	+	0.705750i
$267$	2.73932	−	2.73932i	0.167644	−	0.167644i
$268$	−2.09522	−	2.09522i	−0.127986	−	0.127986i
$269$	6.12973			0.373736			0.186868	−	0.982385i	$-0.440166\pi$
$269$	6.12973			0.373736			0.186868	+	0.982385i	$0.440166\pi$
$270$	12.5848	−	0.658606i	0.765885	−	0.0400815i
$271$		−	30.3091i		−	1.84115i	−0.390567	−	0.920574i	$-0.627721\pi$
$271$		−	30.3091i		−	1.84115i	0.390567	−	0.920574i	$-0.372279\pi$
$272$	2.12548	+	2.12548i	0.128876	+	0.128876i
$273$	−6.74677	−	2.51735i	−0.408333	−	0.152357i
$274$			17.4045i			1.05144i
$275$	−4.97269	+	0.521906i	−0.299864	+	0.0314721i
$276$		−	10.3307i		−	0.621835i
$277$	−17.7616	+	17.7616i	−1.06719	+	1.06719i	−0.0696171	+	0.997574i	$0.522178\pi$
$277$	−17.7616	+	17.7616i	−1.06719	+	1.06719i	−0.997574	+	0.0696171i	$0.977822\pi$
$278$	9.59937	−	9.59937i	0.575732	−	0.575732i
$279$	4.32666			0.259030
$280$	−5.24599	+	2.73488i	−0.313508	+	0.163440i
$281$	18.8423			1.12404			0.562019	−	0.827125i	$-0.310025\pi$
$281$	18.8423			1.12404			0.562019	+	0.827125i	$0.310025\pi$
$282$	−8.05108	+	8.05108i	−0.479435	+	0.479435i
$283$	−10.9430	+	10.9430i	−0.650495	+	0.650495i	−0.953112	−	0.302617i	$-0.902140\pi$
$283$	−10.9430	+	10.9430i	−0.650495	+	0.650495i	0.302617	+	0.953112i	$0.402140\pi$
$284$			3.95706i			0.234808i
$285$	−9.61186	+	10.6735i	−0.569357	+	0.632241i
$286$			2.02641i			0.119824i
$287$	−4.28897	−	1.60030i	−0.253170	−	0.0944627i
$288$	−0.845671	−	0.845671i	−0.0498316	−	0.0498316i
$289$		−	7.96471i		−	0.468512i
$290$	8.11428	+	7.30722i	0.476487	+	0.429095i
$291$	9.49568			0.556647
$292$	2.03080	+	2.03080i	0.118844	+	0.118844i
$293$	8.93858	−	8.93858i	0.522198	−	0.522198i	−0.396037	−	0.918235i	$-0.629615\pi$
$293$	8.93858	−	8.93858i	0.522198	−	0.522198i	0.918235	+	0.396037i	$0.129615\pi$
$294$	−6.15875	+	7.10407i	−0.359185	+	0.414318i
$295$	−6.33698	+	0.331637i	−0.368953	+	0.0193086i
$296$	5.15143			0.299421
$297$	−3.98510	−	3.98510i	−0.231239	−	0.231239i
$298$	−12.4217	−	12.4217i	−0.719568	−	0.719568i
$299$	15.5860			0.901359
$300$	−5.21848	−	4.22712i	−0.301289	−	0.244053i
$301$	−8.61706	+	3.93401i	−0.496679	+	0.226753i
$302$	3.66642	−	3.66642i	0.210979	−	0.210979i
$303$	15.5852	+	15.5852i	0.895345	+	0.895345i
$304$	4.78247			0.274294
$305$	1.05879	+	20.2316i	0.0606264	+	1.15846i
$306$		−	3.59491i		−	0.205507i
$307$	−9.83891	−	9.83891i	−0.561536	−	0.561536i	0.368208	−	0.929744i	$-0.379972\pi$
$307$	−9.83891	−	9.83891i	−0.561536	−	0.561536i	−0.929744	+	0.368208i	$0.879972\pi$
$308$	2.47882	+	0.924898i	0.141244	+	0.0527009i
$309$			4.17606i			0.237568i
$310$	−6.01126	−	5.41337i	−0.341417	−	0.307459i
$311$		−	12.4820i		−	0.707788i	−0.935286	−	0.353894i	$-0.884857\pi$
$311$		−	12.4820i		−	0.707788i	0.935286	−	0.353894i	$-0.115143\pi$
$312$	−1.92458	+	1.92458i	−0.108958	+	0.108958i
$313$	−13.6375	+	13.6375i	−0.770835	+	0.770835i	−0.978253	−	0.207417i	$-0.933494\pi$
$313$	−13.6375	+	13.6375i	−0.770835	+	0.770835i	0.207417	+	0.978253i	$0.433494\pi$
$314$	−15.3978			−0.868949
$315$	6.74919	+	2.12358i	0.380274	+	0.119650i
$316$	−2.07142			−0.116527
$317$	17.9297	−	17.9297i	1.00703	−	1.00703i	0.00705463	−	0.999975i	$-0.497754\pi$
$317$	17.9297	−	17.9297i	1.00703	−	1.00703i	0.999975	−	0.00705463i	$-0.00224558\pi$
$318$	10.7475	−	10.7475i	0.602688	−	0.602688i
$319$		−	4.88338i		−	0.273417i
$320$	0.116862	+	2.23301i	0.00653276	+	0.124829i
$321$			13.5061i			0.753836i
$322$	7.11377	−	19.0657i	0.396435	−	1.06249i
$323$	10.1650	+	10.1650i	0.565597	+	0.565597i
$324$		−	3.98180i		−	0.221211i
$325$	6.37747	−	7.87313i	0.353758	−	0.436723i
$326$	22.6760			1.25591
$327$	−8.67108	−	8.67108i	−0.479512	−	0.479512i
$328$	−1.22347	+	1.22347i	−0.0675548	+	0.0675548i
$329$	−20.4026	+	9.31454i	−1.12483	+	0.513527i
$330$	0.156962	+	2.99926i	0.00864048	+	0.165104i
$331$	−9.63958			−0.529839			−0.264920	−	0.964271i	$-0.585345\pi$
$331$	−9.63958			−0.529839			−0.264920	+	0.964271i	$0.585345\pi$
$332$	−10.0744	−	10.0744i	−0.552905	−	0.552905i
$333$	−4.35642	−	4.35642i	−0.238730	−	0.238730i
$334$	17.5568			0.960668
$335$	4.43380	−	4.92350i	0.242244	−	0.269000i
$336$	1.47584	+	3.23268i	0.0805135	+	0.176357i
$337$	4.80672	−	4.80672i	0.261838	−	0.261838i	−0.563962	−	0.825801i	$-0.690724\pi$
$337$	4.80672	−	4.80672i	0.261838	−	0.261838i	0.825801	+	0.563962i	$0.190724\pi$
$338$	6.28877	+	6.28877i	0.342064	+	0.342064i
$339$	−1.81281			−0.0984583
$340$	−4.49783	+	4.99460i	−0.243929	+	0.270870i
$341$			3.61773i			0.195911i
$342$	−4.04440	−	4.04440i	−0.218696	−	0.218696i
$343$	−16.2581	+	8.86987i	−0.877854	+	0.478928i
$344$			3.58031i			0.193037i
$345$	23.0686	−	1.20726i	1.24197	−	0.0649968i
$346$			7.83346i			0.421129i
$347$	−12.4252	+	12.4252i	−0.667021	+	0.667021i	−0.957025	−	0.290005i	$-0.906343\pi$
$347$	−12.4252	+	12.4252i	−0.667021	+	0.667021i	0.290005	+	0.957025i	$0.406343\pi$
$348$	4.63798	−	4.63798i	0.248622	−	0.248622i
$349$	−22.6716			−1.21358			−0.606791	−	0.794861i	$-0.707544\pi$
$349$	−22.6716			−1.21358			−0.606791	+	0.794861i	$0.707544\pi$
$350$	−6.72007	−	11.3948i	−0.359203	−	0.609076i
$351$	11.4204			0.609576
$352$	0.707107	−	0.707107i	0.0376889	−	0.0376889i
$353$	7.85732	−	7.85732i	0.418203	−	0.418203i	−0.466381	−	0.884584i	$-0.654442\pi$
$353$	7.85732	−	7.85732i	0.418203	−	0.418203i	0.884584	+	0.466381i	$0.154442\pi$
$354$			3.81166i			0.202588i
$355$	−8.83616	+	0.462428i	−0.468975	+	0.0245431i
$356$		−	2.88427i		−	0.152866i
$357$	−3.73412	+	10.0078i	−0.197630	+	0.529670i
$358$	−2.71125	−	2.71125i	−0.143294	−	0.143294i
$359$		−	28.2697i		−	1.49202i	−0.665936	−	0.746009i	$-0.731968\pi$
$359$		−	28.2697i		−	1.49202i	0.665936	−	0.746009i	$-0.268032\pi$
$360$	1.78957	−	1.98722i	0.0943185	−	0.104736i
$361$	3.87205			0.203792
$362$	18.1043	+	18.1043i	0.951539	+	0.951539i
$363$	0.949748	−	0.949748i	0.0498488	−	0.0498488i
$364$	−4.87715	+	2.22660i	−0.255632	+	0.116706i
$365$	−4.29748	+	4.77212i	−0.224940	+	0.249784i
$366$	12.1692			0.636096
$367$	−10.3543	−	10.3543i	−0.540490	−	0.540490i	0.383182	−	0.923673i	$-0.374828\pi$
$367$	−10.3543	−	10.3543i	−0.540490	−	0.540490i	−0.923673	+	0.383182i	$0.874828\pi$
$368$	−5.43865	−	5.43865i	−0.283509	−	0.283509i
$369$	2.06930			0.107724
$370$	0.602004	+	11.5032i	0.0312967	+	0.598024i
$371$	27.2356	−	12.4341i	1.41400	−	0.645544i
$372$	−3.43593	+	3.43593i	−0.178145	+	0.178145i
$373$	−23.8137	−	23.8137i	−1.23303	−	1.23303i	−0.962795	−	0.270233i	$-0.912899\pi$
$373$	−23.8137	−	23.8137i	−1.23303	−	1.23303i	−0.270233	−	0.962795i	$-0.587101\pi$
$374$	3.00588			0.155430
$375$	8.82937	−	12.1469i	0.455947	−	0.627264i
$376$			8.47708i			0.437172i
$377$	6.99733	+	6.99733i	0.360381	+	0.360381i
$378$	5.21252	−	13.9701i	0.268103	−	0.718545i
$379$		−	5.13552i		−	0.263794i	−0.991263	−	0.131897i	$-0.957893\pi$
$379$		−	5.13552i		−	0.263794i	0.991263	−	0.131897i	$-0.0421068\pi$
$380$	0.558887	+	10.6793i	0.0286703	+	0.547838i
$381$			3.84262i			0.196864i
$382$	6.53813	−	6.53813i	0.334520	−	0.334520i
$383$	−17.6671	+	17.6671i	−0.902749	+	0.902749i	−0.995673	−	0.0929243i	$-0.970379\pi$
$383$	−17.6671	+	17.6671i	−0.902749	+	0.902749i	0.0929243	+	0.995673i	$0.470379\pi$
$384$	1.34315			0.0685421
$385$	−1.77563	+	5.64333i	−0.0904944	+	0.287611i
$386$	−10.5672			−0.537855
$387$	3.02776	−	3.02776i	0.153910	−	0.153910i
$388$	4.99905	−	4.99905i	0.253789	−	0.253789i
$389$		−	38.4284i		−	1.94840i	−0.225693	−	0.974199i	$-0.572465\pi$
$389$		−	38.4284i		−	1.94840i	0.225693	−	0.974199i	$-0.427535\pi$
$390$	−4.52251	−	4.07269i	−0.229006	−	0.206229i
$391$		−	23.1195i		−	1.16920i
$392$	0.497672	+	6.98229i	0.0251362	+	0.352659i
$393$	−2.48407	−	2.48407i	−0.125305	−	0.125305i
$394$		−	10.1033i		−	0.508996i
$395$	−0.242070	−	4.62552i	−0.0121799	−	0.232735i
$396$	−1.19596			−0.0600992
$397$	−21.9507	−	21.9507i	−1.10167	−	1.10167i	−0.994209	−	0.107466i	$-0.965726\pi$
$397$	−21.9507	−	21.9507i	−1.10167	−	1.10167i	−0.107466	−	0.994209i	$-0.534274\pi$
$398$	−4.36850	+	4.36850i	−0.218973	+	0.218973i
$399$	7.05815	+	15.4602i	0.353350	+	0.773977i
$400$	−4.97269	+	0.521906i	−0.248634	+	0.0260953i
$401$	−36.6621			−1.83082			−0.915408	−	0.402526i	$-0.868132\pi$
$401$	−36.6621			−1.83082			−0.915408	+	0.402526i	$0.868132\pi$
$402$	−2.81418	−	2.81418i	−0.140359	−	0.140359i
$403$	−5.18380	−	5.18380i	−0.258223	−	0.258223i
$404$	16.4098			0.816418
$405$	8.89142	−	0.465320i	0.441818	−	0.0231219i
$406$	11.7533	−	5.36581i	0.583306	−	0.266301i
$407$	3.64261	−	3.64261i	0.180558	−	0.180558i
$408$	2.85482	+	2.85482i	0.141335	+	0.141335i
$409$	−18.1244			−0.896193			−0.448096	−	0.893985i	$-0.647898\pi$
$409$	−18.1244			−0.896193			−0.448096	+	0.893985i	$0.647898\pi$
$410$	−2.87500	−	2.58904i	−0.141986	−	0.127864i
$411$			23.3768i			1.15309i
$412$	2.19851	+	2.19851i	0.108313	+	0.108313i
$413$	−2.62473	+	7.03456i	−0.129155	+	0.346148i
$414$			9.19862i			0.452088i
$415$	21.3190	−	23.6736i	1.04651	−	1.16209i
$416$			2.02641i			0.0993529i
$417$	12.8934	−	12.8934i	0.631391	−	0.631391i
$418$	3.38172	−	3.38172i	0.165405	−	0.165405i
$419$	38.4130			1.87660			0.938299	−	0.345825i	$-0.112401\pi$
$419$	38.4130			1.87660			0.938299	+	0.345825i	$0.112401\pi$
$420$	−7.04613	+	3.67334i	−0.343816	+	0.179241i
$421$	14.0893			0.686672			0.343336	−	0.939213i	$-0.388443\pi$
$421$	14.0893			0.686672			0.343336	+	0.939213i	$0.388443\pi$
$422$	−9.37714	+	9.37714i	−0.456472	+	0.456472i
$423$	7.16882	−	7.16882i	0.348560	−	0.348560i
$424$		−	11.3161i		−	0.549560i
$425$	−11.6786	−	9.46003i	−0.566497	−	0.458879i
$426$			5.31491i			0.257508i
$427$	22.4588	+	8.37980i	1.08686	+	0.405527i
$428$	7.11035	+	7.11035i	0.343692	+	0.343692i
$429$			2.72176i			0.131408i
$430$	−7.99487	+	0.418400i	−0.385547	+	0.0201771i
$431$	−1.93248			−0.0930842			−0.0465421	−	0.998916i	$-0.514820\pi$
$431$	−1.93248			−0.0930842			−0.0465421	+	0.998916i	$0.514820\pi$
$432$	−3.98510	−	3.98510i	−0.191733	−	0.191733i
$433$	−6.22466	+	6.22466i	−0.299138	+	0.299138i	−0.840676	−	0.541538i	$-0.817842\pi$
$433$	−6.22466	+	6.22466i	−0.299138	+	0.299138i	0.541538	+	0.840676i	$0.317842\pi$
$434$	−8.70713	+	3.97513i	−0.417956	+	0.190812i
$435$	10.8987	+	9.81466i	0.522551	+	0.470577i
$436$	−9.12988			−0.437242
$437$	−26.0102	−	26.0102i	−1.24424	−	1.24424i
$438$	2.72766	+	2.72766i	0.130333	+	0.130333i
$439$	−30.6132			−1.46109			−0.730545	−	0.682864i	$-0.760734\pi$
$439$	−30.6132			−1.46109			−0.730545	+	0.682864i	$0.760734\pi$
$440$	1.66161	+	1.49634i	0.0792142	+	0.0713354i
$441$	5.48385	−	6.32558i	0.261136	−	0.301218i
$442$	−4.30708	+	4.30708i	−0.204867	+	0.204867i
$443$	−15.1351	−	15.1351i	−0.719088	−	0.719088i	0.249330	−	0.968418i	$-0.419789\pi$
$443$	−15.1351	−	15.1351i	−0.719088	−	0.719088i	−0.968418	+	0.249330i	$0.919789\pi$
$444$	6.91913			0.328367
$445$	6.44060	−	0.337060i	0.305314	−	0.0159782i
$446$		−	3.45310i		−	0.163509i
$447$	−16.6841	−	16.6841i	−0.789132	−	0.789132i
$448$	2.47882	+	0.924898i	0.117113	+	0.0436973i
$449$			7.77206i			0.366786i	0.983040	+	0.183393i	$0.0587081\pi$
$449$			7.77206i			0.366786i	−0.983040	+	0.183393i	$0.941292\pi$
$450$	4.64662	+	3.76390i	0.219044	+	0.177432i
$451$			1.73025i			0.0814741i
$452$	−0.954364	+	0.954364i	−0.0448895	+	0.0448895i
$453$	4.92454	−	4.92454i	0.231375	−	0.231375i
$454$	−28.0916			−1.31840
$455$	−5.54198	−	10.6305i	−0.259812	−	0.498367i
$456$	6.42356			0.300811
$457$	−15.3410	+	15.3410i	−0.717622	+	0.717622i	−0.968118	−	0.250496i	$-0.919406\pi$
$457$	−15.3410	+	15.3410i	−0.717622	+	0.717622i	0.250496	+	0.968118i	$0.419406\pi$
$458$	−4.16719	+	4.16719i	−0.194720	+	0.194720i
$459$		−	16.9405i		−	0.790714i
$460$	11.5090	−	12.7802i	0.536611	−	0.595878i
$461$			0.181199i			0.00843929i	0.999991	+	0.00421964i	$0.00134316\pi$
$461$			0.181199i			0.00843929i	−0.999991	+	0.00421964i	$0.998657\pi$
$462$	3.32942	+	1.24227i	0.154899	+	0.0577957i
$463$	−26.9113	−	26.9113i	−1.25067	−	1.25067i	−0.955418	−	0.295256i	$-0.904595\pi$
$463$	−26.9113	−	26.9113i	−1.25067	−	1.25067i	−0.295256	−	0.955418i	$-0.595405\pi$
$464$		−	4.88338i		−	0.226705i
$465$	−8.07400	−	7.27094i	−0.374423	−	0.337182i
$466$	8.19854			0.379790
$467$	26.1838	+	26.1838i	1.21164	+	1.21164i	0.970486	+	0.241157i	$0.0775269\pi$
$467$	26.1838	+	26.1838i	1.21164	+	1.21164i	0.241157	+	0.970486i	$0.422473\pi$
$468$	1.71368	−	1.71368i	0.0792147	−	0.0792147i
$469$	−3.25581	−	7.13154i	−0.150340	−	0.329304i
$470$	−18.9294	+	0.990644i	−0.873149	+	0.0456950i
$471$	−20.6815			−0.952954
$472$	2.00667	+	2.00667i	0.0923646	+	0.0923646i
$473$	2.53166	+	2.53166i	0.116406	+	0.116406i
$474$	−2.78222			−0.127792
$475$	−23.7817	+	2.49600i	−1.09118	+	0.114524i
$476$	3.30283	+	7.23453i	0.151385	+	0.331594i
$477$	−9.56972	+	9.56972i	−0.438167	+	0.438167i
$478$	−12.1711	−	12.1711i	−0.556695	−	0.556695i
$479$	−38.1124			−1.74140			−0.870701	−	0.491813i	$-0.836334\pi$
$479$	−38.1124			−1.74140			−0.870701	+	0.491813i	$0.836334\pi$
$480$	0.156962	+	2.99926i	0.00716431	+	0.136897i
$481$			10.4389i			0.475973i
$482$	7.19137	+	7.19137i	0.327558	+	0.327558i
$483$	9.55484	−	25.6080i	0.434760	−	1.16520i
$484$		−	1.00000i		−	0.0454545i
$485$	11.7471	+	10.5788i	0.533410	+	0.480356i
$486$			11.5592i			0.524337i
$487$	17.9528	−	17.9528i	0.813519	−	0.813519i	−0.171641	−	0.985160i	$-0.554907\pi$
$487$	17.9528	−	17.9528i	0.813519	−	0.813519i	0.985160	+	0.171641i	$0.0549069\pi$
$488$	6.40656	−	6.40656i	0.290011	−	0.290011i
$489$	30.4572			1.37732
$490$	−15.5334	+	1.92727i	−0.701726	+	0.0870651i
$491$	28.6533			1.29310			0.646552	−	0.762870i	$-0.276210\pi$
$491$	28.6533			1.29310			0.646552	+	0.762870i	$0.276210\pi$
$492$	−1.64330	+	1.64330i	−0.0740856	+	0.0740856i
$493$	10.3795	−	10.3795i	0.467469	−	0.467469i
$494$			9.69125i			0.436030i
$495$	−0.139762	−	2.67059i	−0.00628182	−	0.120034i
$496$			3.61773i			0.162441i
$497$	−3.65987	+	9.80885i	−0.164168	+	0.439987i
$498$	−13.5314	−	13.5314i	−0.606356	−	0.606356i
$499$			22.4528i			1.00512i	0.864541	+	0.502562i	$0.167609\pi$
$499$			22.4528i			1.00512i	−0.864541	+	0.502562i	$0.832391\pi$
$500$	−1.74654	−	11.0431i	−0.0781076	−	0.493862i
$501$	23.5814			1.05354
$502$	−10.7787	−	10.7787i	−0.481075	−	0.481075i
$503$	16.6561	−	16.6561i	0.742657	−	0.742657i	−0.230431	−	0.973089i	$-0.574014\pi$
$503$	16.6561	−	16.6561i	0.742657	−	0.742657i	0.973089	+	0.230431i	$0.0740137\pi$
$504$	−1.31411	−	2.87843i	−0.0585351	−	0.128215i
$505$	1.91767	+	36.6433i	0.0853354	+	1.63061i
$506$	−7.69142			−0.341925
$507$	8.44674	+	8.44674i	0.375133	+	0.375133i
$508$	2.02297	+	2.02297i	0.0897549	+	0.0897549i
$509$	35.1644			1.55864			0.779318	−	0.626629i	$-0.215566\pi$
$509$	35.1644			1.55864			0.779318	+	0.626629i	$0.215566\pi$
$510$	−6.04124	+	6.70848i	−0.267510	+	0.297056i
$511$	3.15571	+	6.91228i	0.139600	+	0.305781i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−19.0586	−	19.0586i	−0.841460	−	0.841460i
$514$	−7.13335			−0.314639
$515$	−4.65238	+	5.16622i	−0.205008	+	0.227651i
$516$			4.80888i			0.211699i
$517$	5.99420	+	5.99420i	0.263625	+	0.263625i
$518$	12.7695	+	4.76455i	0.561059	+	0.209342i
$519$			10.5215i			0.461842i
$520$	−4.52500	+	0.236809i	−0.198434	+	0.0103848i
$521$		−	19.3553i		−	0.847971i	−0.905669	−	0.423985i	$-0.860631\pi$
$521$		−	19.3553i		−	0.847971i	0.905669	−	0.423985i	$-0.139369\pi$
$522$	−4.12973	+	4.12973i	−0.180753	+	0.180753i
$523$	21.9672	−	21.9672i	0.960560	−	0.960560i	−0.0386909	−	0.999251i	$-0.512319\pi$
$523$	21.9672	−	21.9672i	0.960560	−	0.960560i	0.999251	+	0.0386909i	$0.0123188\pi$
$524$	−2.61550			−0.114259
$525$	−9.02603	−	15.3048i	−0.393928	−	0.667958i
$526$	15.0319			0.655421
$527$	−7.68940	+	7.68940i	−0.334955	+	0.334955i
$528$	0.949748	−	0.949748i	0.0413325	−	0.0413325i
$529$			36.1579i			1.57208i
$530$	25.2691	−	1.32242i	1.09762	−	0.0574422i
$531$		−	3.39397i		−	0.147286i
$532$	11.8549	+	4.42330i	0.513975	+	0.191774i
$533$	−2.47925	−	2.47925i	−0.107388	−	0.107388i
$534$		−	3.87399i		−	0.167644i
$535$	−15.0466	+	16.7084i	−0.650520	+	0.722369i
$536$	−2.96309			−0.127986
$537$	−3.64161	−	3.64161i	−0.157147	−	0.157147i
$538$	4.33438	−	4.33438i	0.186868	−	0.186868i
$539$	5.28913	+	4.58531i	0.227819	+	0.197503i
$540$	8.43308	−	9.36449i	0.362902	−	0.402983i
$541$	27.7429			1.19276			0.596381	−	0.802702i	$-0.296605\pi$
$541$	27.7429			1.19276			0.596381	+	0.802702i	$0.296605\pi$
$542$	−21.4318	−	21.4318i	−0.920574	−	0.920574i
$543$	24.3167	+	24.3167i	1.04353	+	1.04353i
$544$	3.00588			0.128876
$545$	−1.06693	−	20.3871i	−0.0457024	−	0.873289i
$546$	−6.55072	+	2.99065i	−0.280345	+	0.127988i
$547$	26.7013	−	26.7013i	1.14166	−	1.14166i	0.153517	−	0.988146i	$-0.450940\pi$
$547$	26.7013	−	26.7013i	1.14166	−	1.14166i	0.988146	−	0.153517i	$-0.0490600\pi$
$548$	12.3068	+	12.3068i	0.525721	+	0.525721i
$549$	−10.8357			−0.462456
$550$	−3.14718	+	3.88526i	−0.134196	+	0.165668i
$551$		−	23.3546i		−	0.994941i
$552$	−7.30491	−	7.30491i	−0.310917	−	0.310917i
$553$	−5.13469	−	1.91586i	−0.218349	−	0.0814704i
$554$			25.1187i			1.06719i
$555$	0.808580	+	15.4505i	0.0343223	+	0.655837i
$556$		−	13.5756i		−	0.575732i
$557$	−17.0454	+	17.0454i	−0.722237	+	0.722237i	−0.969060	−	0.246824i	$-0.920613\pi$
$557$	−17.0454	+	17.0454i	−0.722237	+	0.722237i	0.246824	+	0.969060i	$0.420613\pi$
$558$	3.05941	−	3.05941i	0.129515	−	0.129515i
$559$	−7.25517			−0.306861
$560$	−1.77563	+	5.64333i	−0.0750340	+	0.238474i
$561$	4.03733			0.170456
$562$	13.3235	−	13.3235i	0.562019	−	0.562019i
$563$	1.20575	−	1.20575i	0.0508161	−	0.0508161i	−0.681242	−	0.732058i	$-0.738560\pi$
$563$	1.20575	−	1.20575i	0.0508161	−	0.0508161i	0.732058	+	0.681242i	$0.238560\pi$
$564$			11.3859i			0.479435i
$565$	−2.24263	−	2.01958i	−0.0943483	−	0.0849643i
$566$			15.4758i			0.650495i
$567$	3.68276	−	9.87019i	0.154661	−	0.414509i
$568$	2.79806	+	2.79806i	0.117404	+	0.117404i
$569$		−	24.5821i		−	1.03054i	−0.857029	−	0.515268i	$-0.827692\pi$
$569$		−	24.5821i		−	1.03054i	0.857029	−	0.515268i	$-0.172308\pi$
$570$	0.750667	+	14.3439i	0.0314420	+	0.600799i
$571$	−26.6697			−1.11609			−0.558047	−	0.829809i	$-0.688449\pi$
$571$	−26.6697			−1.11609			−0.558047	+	0.829809i	$0.688449\pi$
$572$	1.43289	+	1.43289i	0.0599120	+	0.0599120i
$573$	8.78167	−	8.78167i	0.366859	−	0.366859i
$574$	−4.16435	+	1.90118i	−0.173816	+	0.0793537i
$575$	29.8832	+	24.2063i	1.24622	+	1.00947i
$576$	−1.19596			−0.0498316
$577$	21.1375	+	21.1375i	0.879967	+	0.879967i	0.993531	−	0.113564i	$-0.0362267\pi$
$577$	21.1375	+	21.1375i	0.879967	+	0.879967i	−0.113564	+	0.993531i	$0.536227\pi$
$578$	−5.63190	−	5.63190i	−0.234256	−	0.234256i
$579$	−14.1933			−0.589852
$580$	10.9046	−	0.570679i	0.452791	−	0.0236962i
$581$	−15.6549	−	34.2905i	−0.649474	−	1.42261i
$582$	6.71446	−	6.71446i	0.278323	−	0.278323i
$583$	−8.00171	−	8.00171i	−0.331397	−	0.331397i
$584$	2.87198			0.118844
$585$	4.02692	+	3.62639i	0.166493	+	0.149933i
$586$		−	12.6411i		−	0.522198i
$587$	−9.22072	−	9.22072i	−0.380580	−	0.380580i	0.490731	−	0.871311i	$-0.336730\pi$
$587$	−9.22072	−	9.22072i	−0.380580	−	0.380580i	−0.871311	+	0.490731i	$0.836730\pi$
$588$	0.668446	+	9.37823i	0.0275662	+	0.386752i
$589$			17.3017i			0.712904i
$590$	−4.24642	+	4.71543i	−0.174822	+	0.194131i
$591$		−	13.5702i		−	0.558203i
$592$	3.64261	−	3.64261i	0.149710	−	0.149710i
$593$	−23.5647	+	23.5647i	−0.967687	+	0.967687i	−0.999494	−	0.0318066i	$-0.989874\pi$
$593$	−23.5647	+	23.5647i	−0.967687	+	0.967687i	0.0318066	+	0.999494i	$0.489874\pi$
$594$	−5.63579			−0.231239
$595$	−15.7688	+	8.22070i	−0.646458	+	0.337016i
$596$	−17.5669			−0.719568
$597$	−5.86754	+	5.86754i	−0.240142	+	0.240142i
$598$	11.0209	−	11.0209i	0.450680	−	0.450680i
$599$		−	16.9455i		−	0.692373i	−0.938166	−	0.346187i	$-0.887476\pi$
$599$		−	16.9455i		−	0.692373i	0.938166	−	0.346187i	$-0.112524\pi$
$600$	−6.67904	+	0.700996i	−0.272671	+	0.0286181i
$601$			32.2702i			1.31633i	0.752875	+	0.658164i	$0.228667\pi$
$601$			32.2702i			1.31633i	−0.752875	+	0.658164i	$0.771333\pi$
$602$	−3.31142	+	8.87495i	−0.134963	+	0.361716i
$603$	2.50580	+	2.50580i	0.102044	+	0.102044i
$604$		−	5.18511i		−	0.210979i
$605$	2.23301	−	0.116862i	0.0907849	−	0.00475110i
$606$	22.0408			0.895345
$607$	27.2362	+	27.2362i	1.10548	+	1.10548i	0.993737	+	0.111748i	$0.0356450\pi$
$607$	27.2362	+	27.2362i	1.10548	+	1.10548i	0.111748	+	0.993737i	$0.464355\pi$
$608$	3.38172	−	3.38172i	0.137147	−	0.137147i
$609$	15.7864	−	7.20707i	0.639696	−	0.292045i
$610$	15.0546	+	13.5573i	0.609543	+	0.548917i
$611$	−17.1780			−0.694948
$612$	−2.54198	−	2.54198i	−0.102754	−	0.102754i
$613$	27.5022	+	27.5022i	1.11080	+	1.11080i	0.993042	+	0.117761i	$0.0375717\pi$
$613$	27.5022	+	27.5022i	1.11080	+	1.11080i	0.117761	+	0.993042i	$0.462428\pi$
$614$	−13.9143			−0.561536
$615$	−3.86154	−	3.47746i	−0.155712	−	0.140225i
$616$	2.40679	−	1.09879i	0.0969725	−	0.0442716i
$617$	−0.627978	+	0.627978i	−0.0252815	+	0.0252815i	−0.719635	−	0.694353i	$-0.755691\pi$
$617$	−0.627978	+	0.627978i	−0.0252815	+	0.0252815i	0.694353	+	0.719635i	$0.255691\pi$
$618$	2.95292	+	2.95292i	0.118784	+	0.118784i
$619$	−9.55756			−0.384151			−0.192075	−	0.981380i	$-0.561522\pi$
$619$	−9.55756			−0.384151			−0.192075	+	0.981380i	$0.561522\pi$
$620$	−8.07843	+	0.422773i	−0.324438	+	0.0169790i
$621$			43.3472i			1.73946i
$622$	−8.82608	−	8.82608i	−0.353894	−	0.353894i
$623$	2.66765	−	7.14959i	0.106877	−	0.286442i
$624$			2.72176i			0.108958i
$625$	24.4552	−	5.19055i	0.978209	−	0.207622i
$626$			19.2863i			0.770835i
$627$	4.54214	−	4.54214i	0.181396	−	0.181396i
$628$	−10.8879	+	10.8879i	−0.434475	+	0.434475i
$629$	15.4846			0.617410
$630$	6.27399	−	3.27080i	0.249962	−	0.130312i
$631$	−13.5254			−0.538440			−0.269220	−	0.963079i	$-0.586766\pi$
$631$	−13.5254			−0.538440			−0.269220	+	0.963079i	$0.586766\pi$
$632$	−1.46472	+	1.46472i	−0.0582634	+	0.0582634i
$633$	−12.5949	+	12.5949i	−0.500601	+	0.500601i
$634$		−	25.3564i		−	1.00703i
$635$	−4.28091	+	4.75373i	−0.169883	+	0.188646i
$636$		−	15.1992i		−	0.602688i
$637$	−14.1490	+	1.00849i	−0.560603	+	0.0399577i
$638$	−3.45307	−	3.45307i	−0.136708	−	0.136708i
$639$		−	4.73248i		−	0.187214i
$640$	1.66161	+	1.49634i	0.0656810	+	0.0591482i
$641$	−22.0487			−0.870873			−0.435436	−	0.900220i	$-0.643406\pi$
$641$	−22.0487			−0.870873			−0.435436	+	0.900220i	$0.643406\pi$
$642$	9.55024	+	9.55024i	0.376918	+	0.376918i
$643$	7.86017	−	7.86017i	0.309975	−	0.309975i	−0.534925	−	0.844900i	$-0.679660\pi$
$643$	7.86017	−	7.86017i	0.309975	−	0.309975i	0.844900	+	0.534925i	$0.179660\pi$
$644$	−8.45127	−	18.5117i	−0.333027	−	0.729462i
$645$	−10.7383	+	0.561973i	−0.422819	+	0.0221276i
$646$	14.3755			0.565597
$647$	32.2543	+	32.2543i	1.26805	+	1.26805i	0.947096	+	0.320950i	$0.104002\pi$
$647$	32.2543	+	32.2543i	1.26805	+	1.26805i	0.320950	+	0.947096i	$0.395998\pi$
$648$	−2.81556	−	2.81556i	−0.110606	−	0.110606i
$649$	2.83786			0.111396
$650$	−1.05760	−	10.0767i	−0.0414823	−	0.395241i
$651$	−11.6949	+	5.33918i	−0.458361	+	0.209259i
$652$	16.0344	−	16.0344i	0.627954	−	0.627954i
$653$	4.98787	+	4.98787i	0.195190	+	0.195190i	0.797935	−	0.602744i	$-0.205926\pi$
$653$	4.98787	+	4.98787i	0.195190	+	0.195190i	−0.602744	+	0.797935i	$0.705926\pi$
$654$	−12.2628			−0.479512
$655$	−0.305651	−	5.84044i	−0.0119428	−	0.228205i
$656$			1.73025i			0.0675548i
$657$	−2.42875	−	2.42875i	−0.0947547	−	0.0947547i
$658$	−7.84043	+	21.0132i	−0.305652	+	0.819179i
$659$		−	6.66323i		−	0.259563i	−0.991543	−	0.129781i	$-0.958572\pi$
$659$		−	6.66323i		−	0.259563i	0.991543	−	0.129781i	$-0.0414275\pi$
$660$	2.23179	+	2.00981i	0.0868722	+	0.0782317i
$661$		−	20.8957i		−	0.812747i	−0.913707	−	0.406373i	$-0.866793\pi$
$661$		−	20.8957i		−	0.812747i	0.913707	−	0.406373i	$-0.133207\pi$
$662$	−6.81621	+	6.81621i	−0.264920	+	0.264920i
$663$	−5.78504	+	5.78504i	−0.224672	+	0.224672i
$664$	−14.2474			−0.552905
$665$	−8.49190	+	26.9891i	−0.329302	+	1.04659i
$666$	−6.16090			−0.238730
$667$	−26.5590	+	26.5590i	−1.02837	+	1.02837i
$668$	12.4146	−	12.4146i	0.480334	−	0.480334i
$669$		−	4.63802i		−	0.179316i
$670$	−0.346271	−	6.61661i	−0.0133776	−	0.255622i
$671$		−	9.06025i		−	0.349767i
$672$	3.32942	+	1.24227i	0.128435	+	0.0479217i
$673$	−19.3410	−	19.3410i	−0.745542	−	0.745542i	0.228096	−	0.973639i	$-0.426750\pi$
$673$	−19.3410	−	19.3410i	−0.745542	−	0.745542i	−0.973639	+	0.228096i	$0.926750\pi$
$674$		−	6.79772i		−	0.261838i
$675$	21.8965	+	17.7368i	0.842797	+	0.682690i
$676$	8.89367			0.342064
$677$	31.2937	+	31.2937i	1.20271	+	1.20271i	0.973338	+	0.229375i	$0.0736681\pi$
$677$	31.2937	+	31.2937i	1.20271	+	1.20271i	0.229375	+	0.973338i	$0.426332\pi$
$678$	−1.28185	+	1.28185i	−0.0492291	+	0.0492291i
$679$	17.0154	−	7.76816i	0.652990	−	0.298115i
$680$	0.351271	+	6.71216i	0.0134706	+	0.257400i
$681$	−37.7311			−1.44586
$682$	2.55812	+	2.55812i	0.0979555	+	0.0979555i
$683$	22.6051	+	22.6051i	0.864960	+	0.864960i	0.991909	−	0.126949i	$-0.0405186\pi$
$683$	22.6051	+	22.6051i	0.864960	+	0.864960i	−0.126949	+	0.991909i	$0.540519\pi$
$684$	−5.71964			−0.218696
$685$	−26.0431	+	28.9195i	−0.995055	+	1.10496i
$686$	−5.22426	+	17.7681i	−0.199463	+	0.678391i
$687$	−5.59715	+	5.59715i	−0.213545	+	0.213545i
$688$	2.53166	+	2.53166i	0.0965186	+	0.0965186i
$689$	22.9311			0.873605
$690$	15.4583	−	17.1656i	0.588487	−	0.653484i
$691$			16.2122i			0.616741i	0.951266	+	0.308371i	$0.0997837\pi$
$691$			16.2122i			0.616741i	−0.951266	+	0.308371i	$0.900216\pi$
$692$	5.53909	+	5.53909i	0.210565	+	0.210565i
$693$	−2.96457	−	1.10614i	−0.112615	−	0.0420188i
$694$			17.5719i			0.667021i
$695$	30.3144	−	1.58646i	1.14989	−	0.0601779i
$696$		−	6.55909i		−	0.248622i
$697$	−3.67760	+	3.67760i	−0.139299	+	0.139299i
$698$	−16.0312	+	16.0312i	−0.606791	+	0.606791i
$699$	11.0118			0.416506
$700$	−12.8091	−	3.30551i	−0.484139	−	0.124937i
$701$	−23.7589			−0.897360			−0.448680	−	0.893692i	$-0.648106\pi$
$701$	−23.7589			−0.897360			−0.448680	+	0.893692i	$0.648106\pi$
$702$	8.07545	−	8.07545i	0.304788	−	0.304788i
$703$	17.4207	−	17.4207i	0.657034	−	0.657034i
$704$		−	1.00000i		−	0.0376889i
$705$	−25.4250	+	1.33058i	−0.957559	+	0.0501125i
$706$		−	11.1119i		−	0.418203i
$707$	40.6770	+	15.1774i	1.52982	+	0.570804i
$708$	2.69525	+	2.69525i	0.101294	+	0.101294i
$709$		−	30.8469i		−	1.15848i	−0.815158	−	0.579239i	$-0.803350\pi$
$709$		−	30.8469i		−	1.15848i	0.815158	−	0.579239i	$-0.196650\pi$
$710$	−5.92112	+	6.57509i	−0.222216	+	0.246759i
$711$	2.47734			0.0929075
$712$	−2.03948	−	2.03948i	−0.0764329	−	0.0764329i
$713$	19.6756	−	19.6756i	0.736856	−	0.736856i
$714$	4.43618	+	9.71702i	0.166020	+	0.363650i
$715$	−3.03221	+	3.36710i	−0.113398	+	0.125923i
$716$	−3.83429			−0.143294
$717$	−16.3476	−	16.3476i	−0.610513	−	0.610513i
$718$	−19.9897	−	19.9897i	−0.746009	−	0.746009i
$719$	−12.5887			−0.469481			−0.234740	−	0.972058i	$-0.575424\pi$
$719$	−12.5887			−0.469481			−0.234740	+	0.972058i	$0.575424\pi$
$720$	−0.139762	−	2.67059i	−0.00520861	−	0.0995271i
$721$	3.41632	+	7.48311i	0.127230	+	0.278686i
$722$	2.73795	−	2.73795i	0.101896	−	0.101896i
$723$	9.65906	+	9.65906i	0.359224	+	0.359224i
$724$	25.6033			0.951539
$725$	2.54867	+	24.2835i	0.0946551	+	0.901867i
$726$		−	1.34315i		−	0.0498488i
$727$	4.78343	+	4.78343i	0.177408	+	0.177408i	0.790225	−	0.612817i	$-0.209964\pi$
$727$	4.78343	+	4.78343i	0.177408	+	0.177408i	−0.612817	+	0.790225i	$0.709964\pi$
$728$	−1.87422	+	5.02311i	−0.0694632	+	0.186169i
$729$			27.4711i			1.01745i
$730$	0.335625	+	6.41318i	0.0124220	+	0.237362i
$731$			10.7620i			0.398046i
$732$	8.60495	−	8.60495i	0.318048	−	0.318048i
$733$	−20.4104	+	20.4104i	−0.753874	+	0.753874i	−0.975200	−	0.221326i	$-0.928961\pi$
$733$	−20.4104	+	20.4104i	−0.753874	+	0.753874i	0.221326	+	0.975200i	$0.428961\pi$
$734$	−14.6432			−0.540490
$735$	−20.8636	+	2.58860i	−0.769565	+	0.0954820i
$736$	−7.69142			−0.283509
$737$	−2.09522	+	2.09522i	−0.0771784	+	0.0771784i
$738$	1.46322	−	1.46322i	0.0538618	−	0.0538618i
$739$			25.4609i			0.936594i	0.883571	+	0.468297i	$0.155132\pi$
$739$			25.4609i			0.936594i	−0.883571	+	0.468297i	$0.844868\pi$
$740$	8.55968	+	7.70832i	0.314660	+	0.283363i
$741$			13.0168i			0.478183i
$742$	10.4663	−	28.0507i	0.384228	−	1.02977i
$743$	−15.3238	−	15.3238i	−0.562174	−	0.562174i	0.367750	−	0.929925i	$-0.380128\pi$
$743$	−15.3238	−	15.3238i	−0.562174	−	0.562174i	−0.929925	+	0.367750i	$0.880128\pi$
$744$			4.85914i			0.178145i
$745$	−2.05289	−	39.2271i	−0.0752122	−	1.43717i
$746$	−33.6777			−1.23303
$747$	12.0486	+	12.0486i	0.440834	+	0.440834i
$748$	2.12548	−	2.12548i	0.0777151	−	0.0777151i
$749$	11.0490	+	24.2017i	0.403720	+	0.884310i
$750$	−2.34586	−	14.8325i	−0.0856586	−	0.541605i
$751$	−47.9832			−1.75093			−0.875465	−	0.483281i	$-0.839445\pi$
$751$	−47.9832			−1.75093			−0.875465	+	0.483281i	$0.839445\pi$
$752$	5.99420	+	5.99420i	0.218586	+	0.218586i
$753$	−14.4773	−	14.4773i	−0.527582	−	0.527582i
$754$	9.89572			0.360381
$755$	11.5784	−	0.605939i	0.421381	−	0.0220524i
$756$	−6.19255	−	13.5642i	−0.225221	−	0.493324i
$757$	36.7680	−	36.7680i	1.33636	−	1.33636i	0.436794	−	0.899561i	$-0.356114\pi$
$757$	36.7680	−	36.7680i	1.33636	−	1.33636i	0.899561	−	0.436794i	$-0.143886\pi$
$758$	−3.63136	−	3.63136i	−0.131897	−	0.131897i
$759$	−10.3307			−0.374981
$760$	7.94661	+	7.15623i	0.288254	+	0.259584i
$761$		−	18.9721i		−	0.687738i	−0.939018	−	0.343869i	$-0.888262\pi$
$761$		−	18.9721i		−	0.687738i	0.939018	−	0.343869i	$-0.111738\pi$
$762$	2.71715	+	2.71715i	0.0984318	+	0.0984318i
$763$	−22.6314	−	8.44421i	−0.819311	−	0.305701i
$764$		−	9.24632i		−	0.334520i
$765$	5.37922	−	5.97334i	0.194486	−	0.215966i
$766$			24.9851i			0.902749i
$767$	−4.06634	+	4.06634i	−0.146827	+	0.146827i
$768$	0.949748	−	0.949748i	0.0342711	−	0.0342711i
$769$	−7.37227			−0.265851			−0.132925	−	0.991126i	$-0.542437\pi$
$769$	−7.37227			−0.265851			−0.132925	+	0.991126i	$0.542437\pi$
$770$	2.73488	+	5.24599i	0.0985581	+	0.189052i
$771$	−9.58113			−0.345056
$772$	−7.47212	+	7.47212i	−0.268927	+	0.268927i
$773$	−0.623999	+	0.623999i	−0.0224437	+	0.0224437i	−0.718240	−	0.695796i	$-0.755052\pi$
$773$	−0.623999	+	0.623999i	−0.0224437	+	0.0224437i	0.695796	+	0.718240i	$0.255052\pi$
$774$		−	4.28190i		−	0.153910i
$775$	−1.88812	−	17.9898i	−0.0678231	−	0.646214i
$776$		−	7.06973i		−	0.253789i
$777$	17.1513	+	6.39948i	0.615299	+	0.229580i
$778$	−27.1730	−	27.1730i	−0.974199	−	0.974199i
$779$			8.27486i			0.296477i
$780$	−6.07773	+	0.318069i	−0.217618	+	0.0113887i
$781$	3.95706			0.141595
$782$	−16.3479	−	16.3479i	−0.584601	−	0.584601i
$783$	−19.4608	+	19.4608i	−0.695471	+	0.695471i
$784$	5.28913	+	4.58531i	0.188897	+	0.163761i
$785$	−25.5852	−	23.0404i	−0.913175	−	0.822349i
$786$	−3.51300			−0.125305
$787$	34.7755	+	34.7755i	1.23961	+	1.23961i	0.960159	+	0.279455i	$0.0901539\pi$
$787$	34.7755	+	34.7755i	1.23961	+	1.23961i	0.279455	+	0.960159i	$0.409846\pi$
$788$	−7.14410	−	7.14410i	−0.254498	−	0.254498i
$789$	20.1900			0.718784
$790$	−3.44190	−	3.09956i	−0.122457	−	0.110278i
$791$	−3.24839	+	1.48301i	−0.115499	+	0.0527298i
$792$	−0.845671	+	0.845671i	−0.0300496	+	0.0300496i
$793$	12.9823	+	12.9823i	0.461016	+	0.461016i
$794$	−31.0430			−1.10167
$795$	33.9400	−	1.77620i	1.20373	−	0.0629954i
$796$			6.17800i			0.218973i
$797$	14.0141	+	14.0141i	0.496404	+	0.496404i	0.910317	−	0.413913i	$-0.135838\pi$
$797$	14.0141	+	14.0141i	0.496404	+	0.496404i	−0.413913	+	0.910317i	$0.635838\pi$
$798$	15.9229	+	5.94113i	0.563663	+	0.210314i
$799$			25.4810i			0.901455i
$800$	−3.14718	+	3.88526i	−0.111270	+	0.137365i
$801$			3.44946i			0.121881i
$802$	−25.9240	+	25.9240i	−0.915408	+	0.915408i
$803$	2.03080	−	2.03080i	0.0716654	−	0.0716654i
$804$	−3.97986			−0.140359
$805$	40.3491	−	21.0351i	1.42212	−	0.741389i
$806$	−7.33100			−0.258223
$807$	5.82170	−	5.82170i	0.204934	−	0.204934i
$808$	11.6035	−	11.6035i	0.408209	−	0.408209i
$809$		−	18.0086i		−	0.633147i	−0.948568	−	0.316573i	$-0.897468\pi$
$809$		−	18.0086i		−	0.633147i	0.948568	−	0.316573i	$-0.102532\pi$
$810$	5.95815	−	6.61621i	0.209348	−	0.232470i
$811$		−	4.98746i		−	0.175133i	−0.996159	−	0.0875667i	$-0.972091\pi$
$811$		−	4.98746i		−	0.175133i	0.996159	−	0.0875667i	$-0.0279091\pi$
$812$	4.51662	−	12.1050i	0.158502	−	0.424803i
$813$	−28.7860	−	28.7860i	−1.00957	−	1.00957i
$814$		−	5.15143i		−	0.180558i
$815$	37.6787	+	33.9311i	1.31983	+	1.18856i
$816$	4.03733			0.141335
$817$	12.1076	+	12.1076i	0.423591	+	0.423591i
$818$	−12.8159	+	12.8159i	−0.448096	+	0.448096i
$819$	5.83287	−	2.66292i	0.203817	−	0.0930501i
$820$	−3.86366	+	0.202199i	−0.134925	+	0.00706110i
$821$	42.8555			1.49567			0.747833	−	0.663887i	$-0.231094\pi$
$821$	42.8555			1.49567			0.747833	+	0.663887i	$0.231094\pi$
$822$	16.5299	+	16.5299i	0.576545	+	0.576545i
$823$	−15.2626	−	15.2626i	−0.532022	−	0.532022i	0.389152	−	0.921174i	$-0.372768\pi$
$823$	−15.2626	−	15.2626i	−0.532022	−	0.532022i	−0.921174	+	0.389152i	$0.872768\pi$
$824$	3.10916			0.108313
$825$	−4.22712	+	5.21848i	−0.147169	+	0.181684i
$826$	3.11822	+	6.83015i	0.108497	+	0.237651i
$827$	20.9697	−	20.9697i	0.729187	−	0.729187i	−0.241271	−	0.970458i	$-0.577564\pi$
$827$	20.9697	−	20.9697i	0.729187	−	0.729187i	0.970458	+	0.241271i	$0.0775643\pi$
$828$	6.50441	+	6.50441i	0.226044	+	0.226044i
$829$	−40.2043			−1.39635			−0.698177	−	0.715925i	$-0.746005\pi$
$829$	−40.2043			−1.39635			−0.698177	+	0.715925i	$0.746005\pi$
$830$	−1.66497	−	31.8145i	−0.0577919	−	1.10430i
$831$			33.7381i			1.17036i
$832$	1.43289	+	1.43289i	0.0496764	+	0.0496764i
$833$	1.49594	+	20.9879i	0.0518313	+	0.727187i
$834$		−	18.2340i		−	0.631391i
$835$	29.1727	+	26.2711i	1.00956	+	0.909148i
$836$		−	4.78247i		−	0.165405i
$837$	14.4170	−	14.4170i	0.498325	−	0.498325i
$838$	27.1621	−	27.1621i	0.938299	−	0.938299i
$839$	−17.7994			−0.614503			−0.307252	−	0.951628i	$-0.599409\pi$
$839$	−17.7994			−0.614503			−0.307252	+	0.951628i	$0.599409\pi$
$840$	−2.38493	+	7.57981i	−0.0822878	+	0.261528i
$841$	5.15261			0.177676
$842$	9.96266	−	9.96266i	0.343336	−	0.343336i
$843$	17.8954	−	17.8954i	0.616351	−	0.616351i
$844$			13.2613i			0.456472i
$845$	1.03933	+	19.8597i	0.0357540	+	0.683193i
$846$		−	10.1382i		−	0.348560i
$847$	0.924898	−	2.47882i	0.0317799	−	0.0851734i
$848$	−8.00171	−	8.00171i	−0.274780	−	0.274780i
$849$			20.7862i			0.713381i
$850$	−14.9473	+	1.56879i	−0.512688	+	0.0538089i
$851$	−39.6218			−1.35822
$852$	3.75821	+	3.75821i	0.128754	+	0.128754i
$853$	3.32565	−	3.32565i	0.113868	−	0.113868i	−0.647877	−	0.761745i	$-0.724343\pi$
$853$	3.32565	−	3.32565i	0.113868	−	0.113868i	0.761745	+	0.647877i	$0.224343\pi$
$854$	21.8061	−	9.95532i	0.746191	−	0.340664i
$855$	−0.668406	−	12.7720i	−0.0228590	−	0.436794i
$856$	10.0556			0.343692
$857$	7.22713	+	7.22713i	0.246874	+	0.246874i	0.819686	−	0.572812i	$-0.194148\pi$
$857$	7.22713	+	7.22713i	0.246874	+	0.246874i	−0.572812	+	0.819686i	$0.694148\pi$
$858$	1.92458	+	1.92458i	0.0657040	+	0.0657040i
$859$	−32.5217			−1.10963			−0.554814	−	0.831975i	$-0.687211\pi$
$859$	−32.5217			−1.10963			−0.554814	+	0.831975i	$0.687211\pi$
$860$	−5.35737	+	5.94908i	−0.182685	+	0.202862i
$861$	−5.59332	+	2.55356i	−0.190620	+	0.0870251i
$862$	−1.36647	+	1.36647i	−0.0465421	+	0.0465421i
$863$	27.2040	+	27.2040i	0.926034	+	0.926034i	0.997447	−	0.0714131i	$-0.0227509\pi$
$863$	27.2040	+	27.2040i	0.926034	+	0.926034i	−0.0714131	+	0.997447i	$0.522751\pi$
$864$	−5.63579			−0.191733
$865$	−11.7216	+	13.0162i	−0.398545	+	0.442563i
$866$			8.80299i			0.299138i
$867$	−7.56446	−	7.56446i	−0.256903	−	0.256903i
$868$	−3.34603	+	8.96771i	−0.113572	+	0.304384i
$869$			2.07142i			0.0702683i
$870$	14.6465	−	0.766505i	0.496564	−	0.0259870i
$871$		−	6.00443i		−	0.203452i
$872$	−6.45580	+	6.45580i	−0.218621	+	0.218621i
$873$	−5.97866	+	5.97866i	−0.202347	+	0.202347i
$874$	−36.7840			−1.24424
$875$	5.88435	−	28.9892i	0.198927	−	0.980014i
$876$	3.85749			0.130333
$877$	−2.01885	+	2.01885i	−0.0681718	+	0.0681718i	−0.740371	−	0.672199i	$-0.765350\pi$
$877$	−2.01885	+	2.01885i	−0.0681718	+	0.0681718i	0.672199	+	0.740371i	$0.265350\pi$
$878$	−21.6468	+	21.6468i	−0.730545	+	0.730545i
$879$		−	16.9788i		−	0.572680i
$880$	2.23301	−	0.116862i	0.0752748	−	0.00393940i
$881$		−	11.6120i		−	0.391220i	−0.980682	−	0.195610i	$-0.937331\pi$
$881$		−	11.6120i		−	0.391220i	0.980682	−	0.195610i	$-0.0626686\pi$
$882$	−0.595195	−	8.35053i	−0.0200413	−	0.281177i
$883$	13.9206	+	13.9206i	0.468467	+	0.468467i	0.901418	−	0.432951i	$-0.142528\pi$
$883$	13.9206	+	13.9206i	0.468467	+	0.468467i	−0.432951	+	0.901418i	$0.642528\pi$
$884$			6.09114i			0.204867i
$885$	−5.70356	+	6.33350i	−0.191723	+	0.212898i
$886$	−21.4042			−0.719088
$887$	−26.4164	−	26.4164i	−0.886977	−	0.886977i	0.107255	−	0.994232i	$-0.465794\pi$
$887$	−26.4164	−	26.4164i	−0.886977	−	0.886977i	−0.994232	+	0.107255i	$0.965794\pi$
$888$	4.89256	−	4.89256i	0.164184	−	0.164184i
$889$	3.14355	+	6.88563i	0.105431	+	0.230937i
$890$	4.31586	−	4.79253i	0.144668	−	0.160646i
$891$	−3.98180			−0.133395
$892$	−2.44171	−	2.44171i	−0.0817546	−	0.0817546i
$893$	28.6671	+	28.6671i	0.959308	+	0.959308i
$894$	−23.5949			−0.789132
$895$	−0.448081	−	8.56202i	−0.0149777	−	0.286197i
$896$	2.40679	−	1.09879i	0.0804053	−	0.0367080i
$897$	14.8027	−	14.8027i	0.494249	−	0.494249i
$898$	5.49567	+	5.49567i	0.183393	+	0.183393i
$899$	17.6667			0.589219
$900$	5.94713	−	0.624179i	0.198238	−	0.0208060i
$901$		−	34.0149i		−	1.13320i
$902$	1.22347	+	1.22347i	0.0407371	+	0.0407371i
$903$	−4.44772	+	11.9204i	−0.148011	+	0.396685i
$904$			1.34967i			0.0448895i
$905$	2.99204	+	57.1725i	0.0994587	+	1.90048i
$906$		−	6.96435i		−	0.231375i
$907$	−16.9615	+	16.9615i	−0.563198	+	0.563198i	−0.930214	−	0.367016i	$-0.880379\pi$
$907$	−16.9615	+	16.9615i	−0.563198	+	0.563198i	0.367016	+	0.930214i	$0.380379\pi$
$908$	−19.8638	+	19.8638i	−0.659202	+	0.659202i
$909$	−19.6255			−0.650935
$910$	−11.4357	−	3.59815i	−0.379089	−	0.119277i
$911$	−58.3499			−1.93322			−0.966610	−	0.256252i	$-0.917512\pi$
$911$	−58.3499			−1.93322			−0.966610	+	0.256252i	$0.917512\pi$
$912$	4.54214	−	4.54214i	0.150405	−	0.150405i
$913$	−10.0744	+	10.0744i	−0.333414	+	0.333414i
$914$			21.6955i			0.717622i
$915$	20.2205	+	18.2094i	0.668470	+	0.601983i
$916$			5.89330i			0.194720i
$917$	−6.48336	−	2.41907i	−0.214100	−	0.0798847i
$918$	−11.9787	−	11.9787i	−0.395357	−	0.395357i
$919$			23.7933i			0.784870i	0.919780	+	0.392435i	$0.128367\pi$
$919$			23.7933i			0.784870i	−0.919780	+	0.392435i	$0.871633\pi$
$920$	−0.898831	−	17.1750i	−0.0296336	−	0.566244i
$921$	−18.6890			−0.615822
$922$	0.128127	+	0.128127i	0.00421964	+	0.00421964i
$923$	−5.67002	+	5.67002i	−0.186631	+	0.186631i
$924$	3.23268	−	1.47584i	0.106347	−	0.0485515i
$925$	−16.2125	+	20.0147i	−0.533063	+	0.658079i
$926$	−38.0583			−1.25067
$927$	−2.62933	−	2.62933i	−0.0863584	−	0.0863584i
$928$	−3.45307	−	3.45307i	−0.113353	−	0.113353i
$929$	−14.0486			−0.460919			−0.230459	−	0.973082i	$-0.574023\pi$
$929$	−14.0486			−0.460919			−0.230459	+	0.973082i	$0.574023\pi$
$930$	−10.8505	+	0.567846i	−0.355802	+	0.0186204i
$931$	25.2951	+	21.9291i	0.829014	+	0.718699i
$932$	5.79724	−	5.79724i	0.189895	−	0.189895i
$933$	−11.8547	−	11.8547i	−0.388106	−	0.388106i
$934$	37.0295			1.21164
$935$	4.99460	+	4.49783i	0.163341	+	0.147095i
$936$		−	2.42350i		−	0.0792147i
$937$	−6.13818	−	6.13818i	−0.200526	−	0.200526i	0.599700	−	0.800225i	$-0.295287\pi$
$937$	−6.13818	−	6.13818i	−0.200526	−	0.200526i	−0.800225	+	0.599700i	$0.795287\pi$
$938$	−7.34497	−	2.74055i	−0.239822	−	0.0894822i
$939$			25.9043i			0.845355i
$940$	−12.6846	+	14.0856i	−0.413727	+	0.459422i
$941$			34.1336i			1.11273i	0.830940	+	0.556363i	$0.187803\pi$
$941$			34.1336i			1.11273i	−0.830940	+	0.556363i	$0.812197\pi$
$942$	−14.6240	+	14.6240i	−0.476477	+	0.476477i
$943$	9.41021	−	9.41021i	0.306439	−	0.306439i
$944$	2.83786			0.0923646
$945$	29.5653	−	15.4132i	0.961759	−	0.501391i
$946$	3.58031			0.116406
$947$	−6.40501	+	6.40501i	−0.208135	+	0.208135i	−0.803474	−	0.595339i	$-0.797018\pi$
$947$	−6.40501	+	6.40501i	−0.208135	+	0.208135i	0.595339	+	0.803474i	$0.297018\pi$
$948$	−1.96733	+	1.96733i	−0.0638959	+	0.0638959i
$949$			5.81982i			0.188919i
$950$	−15.0513	+	18.5812i	−0.488328	+	0.602853i
$951$		−	34.0573i		−	1.10438i
$952$	7.45104	+	2.78013i	0.241489	+	0.0901045i
$953$	24.9448	+	24.9448i	0.808042	+	0.808042i	0.984337	−	0.176296i	$-0.0564115\pi$
$953$	24.9448	+	24.9448i	0.808042	+	0.808042i	−0.176296	+	0.984337i	$0.556411\pi$
$954$			13.5336i			0.438167i
$955$	20.6471	−	1.08054i	0.668126	−	0.0349654i
$956$	−17.2126			−0.556695
$957$	−4.63798	−	4.63798i	−0.149924	−	0.149924i
$958$	−26.9496	+	26.9496i	−0.870701	+	0.870701i
$959$	19.1239	+	41.8890i	0.617543	+	1.35267i
$960$	2.23179	+	2.00981i	0.0720306	+	0.0648663i
$961$	17.9120			0.577808
$962$	7.38142	+	7.38142i	0.237987	+	0.237987i
$963$	−8.50369	−	8.50369i	−0.274028	−	0.274028i
$964$	10.1701			0.327558
$965$	−17.5585	−	15.8121i	−0.565229	−	0.509011i
$966$	−11.3513	−	24.8639i	−0.365222	−	0.799982i
$967$	33.5389	−	33.5389i	1.07854	−	1.07854i	0.0818990	−	0.996641i	$-0.473902\pi$
$967$	33.5389	−	33.5389i	1.07854	−	1.07854i	0.996641	−	0.0818990i	$-0.0260985\pi$
$968$	−0.707107	−	0.707107i	−0.0227273	−	0.0227273i
$969$	19.3084			0.620276
$970$	15.7868	−	0.826179i	0.506883	−	0.0265270i
$971$			0.808991i			0.0259618i	0.999916	+	0.0129809i	$0.00413206\pi$
$971$			0.808991i			0.0259618i	−0.999916	+	0.0129809i	$0.995868\pi$
$972$	8.17360	+	8.17360i	0.262168	+	0.262168i
$973$	12.5560	−	33.6514i	0.402527	−	1.07882i
$974$		−	25.3891i		−	0.813519i
$975$	−1.42051	−	13.5345i	−0.0454926	−	0.433450i
$976$		−	9.06025i		−	0.290011i
$977$	34.8911	−	34.8911i	1.11627	−	1.11627i	0.123982	−	0.992284i	$-0.460434\pi$
$977$	34.8911	−	34.8911i	1.11627	−	1.11627i	0.992284	−	0.123982i	$-0.0395665\pi$
$978$	21.5365	−	21.5365i	0.688661	−	0.688661i
$979$	−2.88427			−0.0921815
$980$	−9.62097	+	12.3465i	−0.307331	+	0.394396i
$981$	10.9190			0.348616
$982$	20.2609	−	20.2609i	0.646552	−	0.646552i
$983$	−44.2094	+	44.2094i	−1.41006	+	1.41006i	−0.650878	+	0.759183i	$0.725599\pi$
$983$	−44.2094	+	44.2094i	−1.41006	+	1.41006i	−0.759183	+	0.650878i	$0.774401\pi$
$984$			2.32397i			0.0740856i
$985$	15.1180	−	16.7877i	0.481699	−	0.534902i
$986$		−	14.6788i		−	0.467469i
$987$	−10.5308	+	28.2238i	−0.335200	+	0.898372i
$988$	6.85275	+	6.85275i	0.218015	+	0.218015i
$989$		−	27.5377i		−	0.875646i
$990$	−1.98722	−	1.78957i	−0.0631580	−	0.0568762i
$991$	10.9894			0.349089			0.174544	−	0.984649i	$-0.444155\pi$
$991$	10.9894			0.349089			0.174544	+	0.984649i	$0.444155\pi$
$992$	2.55812	+	2.55812i	0.0812204	+	0.0812204i
$993$	−9.15517	+	9.15517i	−0.290530	+	0.290530i
$994$	4.34798	+	9.52382i	0.137910	+	0.302077i
$995$	−13.7955	+	0.721970i	−0.437348	+	0.0228880i
$996$	−19.1363			−0.606356
$997$	6.69587	+	6.69587i	0.212060	+	0.212060i	0.805142	−	0.593082i	$-0.202089\pi$
$997$	6.69587	+	6.69587i	0.212060	+	0.212060i	−0.593082	+	0.805142i	$0.702089\pi$
$998$	15.8765	+	15.8765i	0.502562	+	0.502562i
$999$	−29.0324			−0.918544

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.l.c.573.17	yes	40
5.2	odd	4	inner	770.2.l.c.727.14	yes	40
7.6	odd	2	inner	770.2.l.c.573.14	✓	40
35.27	even	4	inner	770.2.l.c.727.17	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.l.c.573.14	✓	40	7.6	odd	2	inner
770.2.l.c.573.17	yes	40	1.1	even	1	trivial
770.2.l.c.727.14	yes	40	5.2	odd	4	inner
770.2.l.c.727.17	yes	40	35.27	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(0.949748 - 0.949748i) q^{3} -1.00000i q^{4} +(2.23301 - 0.116862i) q^{5} -1.34315i q^{6} +(0.924898 - 2.47882i) q^{7} +(-0.707107 - 0.707107i) q^{8} +1.19596i q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(0.949748 - 0.949748i) q^{3} -1.00000i q^{4} +(2.23301 - 0.116862i) q^{5} -1.34315i q^{6} +(0.924898 - 2.47882i) q^{7} +(-0.707107 - 0.707107i) q^{8} +1.19596i q^{9} +(1.49634 - 1.66161i) q^{10} -1.00000 q^{11} +(-0.949748 - 0.949748i) q^{12} +(1.43289 - 1.43289i) q^{13} +(-1.09879 - 2.40679i) q^{14} +(2.00981 - 2.23179i) q^{15} -1.00000 q^{16} +(-2.12548 - 2.12548i) q^{17} +(0.845671 + 0.845671i) q^{18} -4.78247 q^{19} +(-0.116862 - 2.23301i) q^{20} +(-1.47584 - 3.23268i) q^{21} +(-0.707107 + 0.707107i) q^{22} +(5.43865 + 5.43865i) q^{23} -1.34315 q^{24} +(4.97269 - 0.521906i) q^{25} -2.02641i q^{26} +(3.98510 + 3.98510i) q^{27} +(-2.47882 - 0.924898i) q^{28} +4.88338i q^{29} +(-0.156962 - 2.99926i) q^{30} -3.61773i q^{31} +(-0.707107 + 0.707107i) q^{32} +(-0.949748 + 0.949748i) q^{33} -3.00588 q^{34} +(1.77563 - 5.64333i) q^{35} +1.19596 q^{36} +(-3.64261 + 3.64261i) q^{37} +(-3.38172 + 3.38172i) q^{38} -2.72176i q^{39} +(-1.66161 - 1.49634i) q^{40} -1.73025i q^{41} +(-3.32942 - 1.24227i) q^{42} +(-2.53166 - 2.53166i) q^{43} +1.00000i q^{44} +(0.139762 + 2.67059i) q^{45} +7.69142 q^{46} +(-5.99420 - 5.99420i) q^{47} +(-0.949748 + 0.949748i) q^{48} +(-5.28913 - 4.58531i) q^{49} +(3.14718 - 3.88526i) q^{50} -4.03733 q^{51} +(-1.43289 - 1.43289i) q^{52} +(8.00171 + 8.00171i) q^{53} +5.63579 q^{54} +(-2.23301 + 0.116862i) q^{55} +(-2.40679 + 1.09879i) q^{56} +(-4.54214 + 4.54214i) q^{57} +(3.45307 + 3.45307i) q^{58} -2.83786 q^{59} +(-2.23179 - 2.00981i) q^{60} +9.06025i q^{61} +(-2.55812 - 2.55812i) q^{62} +(2.96457 + 1.10614i) q^{63} +1.00000i q^{64} +(3.03221 - 3.36710i) q^{65} +1.34315i q^{66} +(2.09522 - 2.09522i) q^{67} +(-2.12548 + 2.12548i) q^{68} +10.3307 q^{69} +(-2.73488 - 5.24599i) q^{70} -3.95706 q^{71} +(0.845671 - 0.845671i) q^{72} +(-2.03080 + 2.03080i) q^{73} +5.15143i q^{74} +(4.22712 - 5.21848i) q^{75} +4.78247i q^{76} +(-0.924898 + 2.47882i) q^{77} +(-1.92458 - 1.92458i) q^{78} -2.07142i q^{79} +(-2.23301 + 0.116862i) q^{80} +3.98180 q^{81} +(-1.22347 - 1.22347i) q^{82} +(10.0744 - 10.0744i) q^{83} +(-3.23268 + 1.47584i) q^{84} +(-4.99460 - 4.49783i) q^{85} -3.58031 q^{86} +(4.63798 + 4.63798i) q^{87} +(0.707107 + 0.707107i) q^{88} +2.88427 q^{89} +(1.98722 + 1.78957i) q^{90} +(-2.22660 - 4.87715i) q^{91} +(5.43865 - 5.43865i) q^{92} +(-3.43593 - 3.43593i) q^{93} -8.47708 q^{94} +(-10.6793 + 0.558887i) q^{95} +1.34315i q^{96} +(4.99905 + 4.99905i) q^{97} +(-6.98229 + 0.497672i) q^{98} -1.19596i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q+O(q^{10}) \) 40 * q	\( 40 q - 40 q^{11} + 56 q^{15} - 40 q^{16} - 8 q^{18} - 4 q^{21} - 32 q^{25} - 24 q^{30} + 48 q^{35} - 48 q^{36} - 8 q^{37} - 40 q^{42} - 8 q^{43} + 32 q^{46} + 16 q^{50} - 8 q^{51} + 56 q^{53} + 4 q^{56} + 32 q^{57} - 8 q^{58} + 8 q^{60} - 16 q^{63} + 8 q^{65} - 24 q^{67} - 4 q^{70} - 24 q^{71} - 8 q^{72} - 16 q^{78} - 24 q^{81} + 96 q^{85} - 96 q^{86} + 64 q^{91} + 24 q^{93} - 112 q^{95} + 16 q^{98}+O(q^{100}) \) 40 * q - 40 * q^11 + 56 * q^15 - 40 * q^16 - 8 * q^18 - 4 * q^21 - 32 * q^25 - 24 * q^30 + 48 * q^35 - 48 * q^36 - 8 * q^37 - 40 * q^42 - 8 * q^43 + 32 * q^46 + 16 * q^50 - 8 * q^51 + 56 * q^53 + 4 * q^56 + 32 * q^57 - 8 * q^58 + 8 * q^60 - 16 * q^63 + 8 * q^65 - 24 * q^67 - 4 * q^70 - 24 * q^71 - 8 * q^72 - 16 * q^78 - 24 * q^81 + 96 * q^85 - 96 * q^86 + 64 * q^91 + 24 * q^93 - 112 * q^95 + 16 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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