LMFDB - Embedded newform 1110.2.u.e.191.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(191,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("1110.191");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.u (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:	$8.86339462436$
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			191.12
Character	$\chi$	$=$	1110.191
Dual form			1110.2.u.e.401.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(-0.347239 + 1.69689i) q^{3} +1.00000i q^{4} +(0.707107 - 0.707107i) q^{5} +(-1.44542 + 0.954345i) q^{6} -3.94859 q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.75885 - 1.17845i) q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(-0.347239 + 1.69689i) q^{3} +1.00000i q^{4} +(0.707107 - 0.707107i) q^{5} +(-1.44542 + 0.954345i) q^{6} -3.94859 q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.75885 - 1.17845i) q^{9} +1.00000 q^{10} +0.734688 q^{11} +(-1.69689 - 0.347239i) q^{12} +(-0.292272 - 0.292272i) q^{13} +(-2.79208 - 2.79208i) q^{14} +(0.954345 + 1.44542i) q^{15} -1.00000 q^{16} +(-1.47653 + 1.47653i) q^{17} +(-1.11751 - 2.78409i) q^{18} +(-2.06536 - 2.06536i) q^{19} +(0.707107 + 0.707107i) q^{20} +(1.37110 - 6.70032i) q^{21} +(0.519503 + 0.519503i) q^{22} +(-3.73522 + 3.73522i) q^{23} +(-0.954345 - 1.44542i) q^{24} -1.00000i q^{25} -0.413335i q^{26} +(2.95767 - 4.27225i) q^{27} -3.94859i q^{28} +(-5.52163 - 5.52163i) q^{29} +(-0.347239 + 1.69689i) q^{30} +(2.98721 - 2.98721i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-0.255112 + 1.24668i) q^{33} -2.08812 q^{34} +(-2.79208 + 2.79208i) q^{35} +(1.17845 - 2.75885i) q^{36} +(-4.35299 - 4.24870i) q^{37} -2.92086i q^{38} +(0.597441 - 0.394465i) q^{39} +1.00000i q^{40} -0.304236 q^{41} +(5.70736 - 3.76832i) q^{42} +(-1.47908 - 1.47908i) q^{43} +0.734688i q^{44} +(-2.78409 + 1.11751i) q^{45} -5.28241 q^{46} +5.23964i q^{47} +(0.347239 - 1.69689i) q^{48} +8.59139 q^{49} +(0.707107 - 0.707107i) q^{50} +(-1.99279 - 3.01820i) q^{51} +(0.292272 - 0.292272i) q^{52} -1.95939i q^{53} +(5.11233 - 0.929548i) q^{54} +(0.519503 - 0.519503i) q^{55} +(2.79208 - 2.79208i) q^{56} +(4.22185 - 2.78750i) q^{57} -7.80876i q^{58} +(-3.79975 + 3.79975i) q^{59} +(-1.44542 + 0.954345i) q^{60} +(-2.94499 + 2.94499i) q^{61} +4.22455 q^{62} +(10.8936 + 4.65322i) q^{63} -1.00000i q^{64} -0.413335 q^{65} +(-1.06193 + 0.701146i) q^{66} +0.864992i q^{67} +(-1.47653 - 1.47653i) q^{68} +(-5.04124 - 7.63527i) q^{69} -3.94859 q^{70} +0.933886i q^{71} +(2.78409 - 1.11751i) q^{72} +2.91706i q^{73} +(-0.0737400 - 6.08232i) q^{74} +(1.69689 + 0.347239i) q^{75} +(2.06536 - 2.06536i) q^{76} -2.90098 q^{77} +(0.701383 + 0.143526i) q^{78} +(7.13662 + 7.13662i) q^{79} +(-0.707107 + 0.707107i) q^{80} +(6.22251 + 6.50233i) q^{81} +(-0.215128 - 0.215128i) q^{82} +17.0240i q^{83} +(6.70032 + 1.37110i) q^{84} +2.08812i q^{85} -2.09173i q^{86} +(11.2869 - 7.45225i) q^{87} +(-0.519503 + 0.519503i) q^{88} +(-2.74463 - 2.74463i) q^{89} +(-2.75885 - 1.17845i) q^{90} +(1.15406 + 1.15406i) q^{91} +(-3.73522 - 3.73522i) q^{92} +(4.03168 + 6.10623i) q^{93} +(-3.70499 + 3.70499i) q^{94} -2.92086 q^{95} +(1.44542 - 0.954345i) q^{96} +(-9.44894 - 9.44894i) q^{97} +(6.07503 + 6.07503i) q^{98} +(-2.02689 - 0.865792i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 24 q^{7} - 8 q^{9}+O(q^{10}) $ 40 * q - 24 * q^7 - 8 * q^9	$ 40 q - 24 q^{7} - 8 q^{9} + 40 q^{10} - 8 q^{12} - 16 q^{13} - 40 q^{16} + 8 q^{18} + 16 q^{19} - 24 q^{31} + 24 q^{33} - 8 q^{34} + 16 q^{39} - 20 q^{42} - 32 q^{43} - 8 q^{45} + 72 q^{46} + 96 q^{49} + 20 q^{51} + 16 q^{52} + 24 q^{54} - 16 q^{57} + 40 q^{61} - 24 q^{63} - 44 q^{66} - 24 q^{70} + 8 q^{72} + 8 q^{75} - 16 q^{76} + 48 q^{79} + 24 q^{81} - 56 q^{82} - 8 q^{84} + 12 q^{87} - 8 q^{90} - 64 q^{91} + 12 q^{93} + 24 q^{94} + 8 q^{97}+O(q^{100}) $ 40 * q - 24 * q^7 - 8 * q^9 + 40 * q^10 - 8 * q^12 - 16 * q^13 - 40 * q^16 + 8 * q^18 + 16 * q^19 - 24 * q^31 + 24 * q^33 - 8 * q^34 + 16 * q^39 - 20 * q^42 - 32 * q^43 - 8 * q^45 + 72 * q^46 + 96 * q^49 + 20 * q^51 + 16 * q^52 + 24 * q^54 - 16 * q^57 + 40 * q^61 - 24 * q^63 - 44 * q^66 - 24 * q^70 + 8 * q^72 + 8 * q^75 - 16 * q^76 + 48 * q^79 + 24 * q^81 - 56 * q^82 - 8 * q^84 + 12 * q^87 - 8 * q^90 - 64 * q^91 + 12 * q^93 + 24 * q^94 + 8 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$

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
$3$	−0.347239	+	1.69689i	−0.200478	+	0.979698i
$3$	−0.347239	+	1.69689i	−0.200478	+	0.979698i
$4$			1.00000i			0.500000i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$6$	−1.44542	+	0.954345i	−0.590088	+	0.389610i
$7$	−3.94859			−1.49243			−0.746214	−	0.665706i	$-0.768130\pi$
$7$	−3.94859			−1.49243			−0.746214	+	0.665706i	$0.768130\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	−2.75885	−	1.17845i	−0.919617	−	0.392816i
$10$	1.00000			0.316228
$11$	0.734688			0.221517			0.110758	−	0.993847i	$-0.464672\pi$
$11$	0.734688			0.221517			0.110758	+	0.993847i	$0.464672\pi$
$12$	−1.69689	−	0.347239i	−0.489849	−	0.100239i
$13$	−0.292272	−	0.292272i	−0.0810617	−	0.0810617i	0.665413	−	0.746475i	$-0.268255\pi$
$13$	−0.292272	−	0.292272i	−0.0810617	−	0.0810617i	−0.746475	+	0.665413i	$0.768255\pi$
$14$	−2.79208	−	2.79208i	−0.746214	−	0.746214i
$15$	0.954345	+	1.44542i	0.246411	+	0.373205i
$16$	−1.00000			−0.250000
$17$	−1.47653	+	1.47653i	−0.358110	+	0.358110i	−0.863116	−	0.505006i	$-0.831490\pi$
$17$	−1.47653	+	1.47653i	−0.358110	+	0.358110i	0.505006	+	0.863116i	$0.331490\pi$
$18$	−1.11751	−	2.78409i	−0.263400	−	0.656217i
$19$	−2.06536	−	2.06536i	−0.473825	−	0.473825i	0.429325	−	0.903150i	$-0.358752\pi$
$19$	−2.06536	−	2.06536i	−0.473825	−	0.473825i	−0.903150	+	0.429325i	$0.858752\pi$
$20$	0.707107	+	0.707107i	0.158114	+	0.158114i
$21$	1.37110	−	6.70032i	0.299199	−	1.46213i
$22$	0.519503	+	0.519503i	0.110758	+	0.110758i
$23$	−3.73522	+	3.73522i	−0.778848	+	0.778848i	−0.979635	−	0.200787i	$-0.935650\pi$
$23$	−3.73522	+	3.73522i	−0.778848	+	0.778848i	0.200787	+	0.979635i	$0.435650\pi$
$24$	−0.954345	−	1.44542i	−0.194805	−	0.295044i
$25$		−	1.00000i		−	0.200000i
$26$		−	0.413335i		−	0.0810617i
$27$	2.95767	−	4.27225i	0.569205	−	0.822196i
$28$		−	3.94859i		−	0.746214i
$29$	−5.52163	−	5.52163i	−1.02534	−	1.02534i	−0.999670	−	0.0256696i	$-0.991828\pi$
$29$	−5.52163	−	5.52163i	−1.02534	−	1.02534i	−0.0256696	−	0.999670i	$-0.508172\pi$
$30$	−0.347239	+	1.69689i	−0.0633968	+	0.309808i
$31$	2.98721	−	2.98721i	0.536519	−	0.536519i	−0.385986	−	0.922505i	$-0.626139\pi$
$31$	2.98721	−	2.98721i	0.536519	−	0.536519i	0.922505	+	0.385986i	$0.126139\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	−0.255112	+	1.24668i	−0.0444093	+	0.217020i
$34$	−2.08812			−0.358110
$35$	−2.79208	+	2.79208i	−0.471947	+	0.471947i
$36$	1.17845	−	2.75885i	0.196408	−	0.459808i
$37$	−4.35299	−	4.24870i	−0.715627	−	0.698483i
$37$	−4.35299	−	4.24870i	−0.715627	−	0.698483i
$38$		−	2.92086i		−	0.473825i
$39$	0.597441	−	0.394465i	0.0956671	−	0.0631649i
$40$			1.00000i			0.158114i
$41$	−0.304236			−0.0475137			−0.0237569	−	0.999718i	$-0.507563\pi$
$41$	−0.304236			−0.0475137			−0.0237569	+	0.999718i	$0.507563\pi$
$42$	5.70736	−	3.76832i	0.880664	−	0.581465i
$43$	−1.47908	−	1.47908i	−0.225557	−	0.225557i	0.585276	−	0.810834i	$-0.300986\pi$
$43$	−1.47908	−	1.47908i	−0.225557	−	0.225557i	−0.810834	+	0.585276i	$0.800986\pi$
$44$			0.734688i			0.110758i
$45$	−2.78409	+	1.11751i	−0.415028	+	0.166589i
$46$	−5.28241			−0.778848
$47$			5.23964i			0.764281i	0.924104	+	0.382140i	$0.124813\pi$
$47$			5.23964i			0.764281i	−0.924104	+	0.382140i	$0.875187\pi$
$48$	0.347239	−	1.69689i	0.0501196	−	0.244925i
$49$	8.59139			1.22734
$50$	0.707107	−	0.707107i	0.100000	−	0.100000i
$51$	−1.99279	−	3.01820i	−0.279046	−	0.422633i
$52$	0.292272	−	0.292272i	0.0405308	−	0.0405308i
$53$		−	1.95939i		−	0.269143i	−0.990904	−	0.134571i	$-0.957034\pi$
$53$		−	1.95939i		−	0.269143i	0.990904	−	0.134571i	$-0.0429658\pi$
$54$	5.11233	−	0.929548i	0.695700	−	0.126495i
$55$	0.519503	−	0.519503i	0.0700497	−	0.0700497i
$56$	2.79208	−	2.79208i	0.373107	−	0.373107i
$57$	4.22185	−	2.78750i	0.559197	−	0.369214i
$58$		−	7.80876i		−	1.02534i
$59$	−3.79975	+	3.79975i	−0.494686	+	0.494686i	−0.909779	−	0.415093i	$-0.863749\pi$
$59$	−3.79975	+	3.79975i	−0.494686	+	0.494686i	0.415093	+	0.909779i	$0.363749\pi$
$60$	−1.44542	+	0.954345i	−0.186602	+	0.123205i
$61$	−2.94499	+	2.94499i	−0.377067	+	0.377067i	−0.870043	−	0.492976i	$-0.835909\pi$
$61$	−2.94499	+	2.94499i	−0.377067	+	0.377067i	0.492976	+	0.870043i	$0.335909\pi$
$62$	4.22455			0.536519
$63$	10.8936	+	4.65322i	1.37246	+	0.586250i
$64$		−	1.00000i		−	0.125000i
$65$	−0.413335			−0.0512679
$66$	−1.06193	+	0.701146i	−0.130714	+	0.0863051i
$67$			0.864992i			0.105676i	0.998603	+	0.0528378i	$0.0168266\pi$
$67$			0.864992i			0.105676i	−0.998603	+	0.0528378i	$0.983173\pi$
$68$	−1.47653	−	1.47653i	−0.179055	−	0.179055i
$69$	−5.04124	−	7.63527i	−0.606894	−	0.919178i
$70$	−3.94859			−0.471947
$71$			0.933886i			0.110832i	0.998463	+	0.0554159i	$0.0176485\pi$
$71$			0.933886i			0.110832i	−0.998463	+	0.0554159i	$0.982352\pi$
$72$	2.78409	−	1.11751i	0.328108	−	0.131700i
$73$			2.91706i			0.341416i	0.985322	+	0.170708i	$0.0546056\pi$
$73$			2.91706i			0.341416i	−0.985322	+	0.170708i	$0.945394\pi$
$74$	−0.0737400	−	6.08232i	−0.00857210	−	0.707055i
$75$	1.69689	+	0.347239i	0.195940	+	0.0400957i
$76$	2.06536	−	2.06536i	0.236913	−	0.236913i
$77$	−2.90098			−0.330598
$78$	0.701383	+	0.143526i	0.0794160	+	0.0162511i
$79$	7.13662	+	7.13662i	0.802932	+	0.802932i	0.983553	−	0.180621i	$-0.0578107\pi$
$79$	7.13662	+	7.13662i	0.802932	+	0.802932i	−0.180621	+	0.983553i	$0.557811\pi$
$80$	−0.707107	+	0.707107i	−0.0790569	+	0.0790569i
$81$	6.22251	+	6.50233i	0.691390	+	0.722481i
$82$	−0.215128	−	0.215128i	−0.0237569	−	0.0237569i
$83$			17.0240i			1.86862i	0.356457	+	0.934312i	$0.383985\pi$
$83$			17.0240i			1.86862i	−0.356457	+	0.934312i	$0.616015\pi$
$84$	6.70032	+	1.37110i	0.731065	+	0.149600i
$85$			2.08812i			0.226489i
$86$		−	2.09173i		−	0.225557i
$87$	11.2869	−	7.45225i	1.21008	−	0.798965i
$88$	−0.519503	+	0.519503i	−0.0553792	+	0.0553792i
$89$	−2.74463	−	2.74463i	−0.290931	−	0.290931i	0.546517	−	0.837448i	$-0.315953\pi$
$89$	−2.74463	−	2.74463i	−0.290931	−	0.290931i	−0.837448	+	0.546517i	$0.815953\pi$
$90$	−2.75885	−	1.17845i	−0.290808	−	0.124219i
$91$	1.15406	+	1.15406i	0.120979	+	0.120979i
$92$	−3.73522	−	3.73522i	−0.389424	−	0.389424i
$93$	4.03168	+	6.10623i	0.418066	+	0.633187i
$94$	−3.70499	+	3.70499i	−0.382140	+	0.382140i
$95$	−2.92086			−0.299673
$96$	1.44542	−	0.954345i	0.147522	−	0.0974025i
$97$	−9.44894	−	9.44894i	−0.959395	−	0.959395i	0.0398122	−	0.999207i	$-0.487324\pi$
$97$	−9.44894	−	9.44894i	−0.959395	−	0.959395i	−0.999207	+	0.0398122i	$0.987324\pi$
$98$	6.07503	+	6.07503i	0.613671	+	0.613671i
$99$	−2.02689	−	0.865792i	−0.203711	−	0.0870154i
$100$	1.00000			0.100000
$101$	0.459789			0.0457507			0.0228753	−	0.999738i	$-0.492718\pi$
$101$	0.459789			0.0457507			0.0228753	+	0.999738i	$0.492718\pi$
$102$	0.725077	−	3.54331i	0.0717933	−	0.350840i
$103$	1.84691	−	1.84691i	0.181982	−	0.181982i	−0.610237	−	0.792219i	$-0.708926\pi$
$103$	1.84691	−	1.84691i	0.181982	−	0.181982i	0.792219	+	0.610237i	$0.208926\pi$
$104$	0.413335			0.0405308
$105$	−3.76832	−	5.70736i	−0.367751	−	0.556981i
$106$	1.38550	−	1.38550i	0.134571	−	0.134571i
$107$			15.3582i			1.48473i	0.669996	+	0.742365i	$0.266296\pi$
$107$			15.3582i			1.48473i	−0.669996	+	0.742365i	$0.733704\pi$
$108$	4.27225	+	2.95767i	0.411098	+	0.284602i
$109$	−6.88464	−	6.88464i	−0.659429	−	0.659429i	0.295816	−	0.955245i	$-0.404409\pi$
$109$	−6.88464	−	6.88464i	−0.659429	−	0.659429i	−0.955245	+	0.295816i	$0.904409\pi$
$110$	0.734688			0.0700497
$111$	8.72110	−	5.91122i	0.827770	−	0.561068i
$112$	3.94859			0.373107
$113$	7.13192	+	7.13192i	0.670914	+	0.670914i	0.957927	−	0.287012i	$-0.0926621\pi$
$113$	7.13192	+	7.13192i	0.670914	+	0.670914i	−0.287012	+	0.957927i	$0.592662\pi$
$114$	4.95636	+	1.01423i	0.464206	+	0.0949917i
$115$			5.28241i			0.492587i
$116$	5.52163	−	5.52163i	0.512670	−	0.512670i
$117$	0.461907	+	1.15076i	0.0427033	+	0.106388i
$118$	−5.37366			−0.494686
$119$	5.83020	−	5.83020i	0.534454	−	0.534454i
$120$	−1.69689	−	0.347239i	−0.154904	−	0.0316984i
$121$	−10.4602			−0.950930
$122$	−4.16484			−0.377067
$123$	0.105643	−	0.516255i	0.00952547	−	0.0465491i
$124$	2.98721	+	2.98721i	0.268259	+	0.268259i
$125$	−0.707107	−	0.707107i	−0.0632456	−	0.0632456i
$126$	4.41260	+	10.9932i	0.393106	+	0.979356i
$127$	−19.9698			−1.77204			−0.886018	−	0.463650i	$-0.846539\pi$
$127$	−19.9698			−1.77204			−0.886018	+	0.463650i	$0.846539\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	3.02342	−	1.99624i	0.266197	−	0.175759i
$130$	−0.292272	−	0.292272i	−0.0256340	−	0.0256340i
$131$	3.51428	+	3.51428i	0.307044	+	0.307044i	0.843762	−	0.536718i	$-0.180336\pi$
$131$	3.51428	+	3.51428i	0.307044	+	0.307044i	−0.536718	+	0.843762i	$0.680336\pi$
$132$	−1.24668	−	0.255112i	−0.108510	−	0.0222046i
$133$	8.15525	+	8.15525i	0.707150	+	0.707150i
$134$	−0.611642	+	0.611642i	−0.0528378	+	0.0528378i
$135$	−0.929548	−	5.11233i	−0.0800028	−	0.439999i
$136$		−	2.08812i		−	0.179055i
$137$		−	13.1680i		−	1.12502i	−0.826790	−	0.562510i	$-0.809836\pi$
$137$		−	13.1680i		−	1.12502i	0.826790	−	0.562510i	$-0.190164\pi$
$138$	1.83426	−	8.96364i	0.156142	−	0.763036i
$139$		−	16.3562i		−	1.38731i	−0.720306	−	0.693657i	$-0.755999\pi$
$139$		−	16.3562i		−	1.38731i	0.720306	−	0.693657i	$-0.244001\pi$
$140$	−2.79208	−	2.79208i	−0.235974	−	0.235974i
$141$	−8.89108	−	1.81941i	−0.748764	−	0.153222i
$142$	−0.660357	+	0.660357i	−0.0554159	+	0.0554159i
$143$	−0.214729	−	0.214729i	−0.0179565	−	0.0179565i
$144$	2.75885	+	1.17845i	0.229904	+	0.0982041i
$145$	−7.80876			−0.648482
$146$	−2.06268	+	2.06268i	−0.170708	+	0.170708i
$147$	−2.98326	+	14.5786i	−0.246055	+	1.20242i
$148$	4.24870	−	4.35299i	0.349241	−	0.357813i
$149$			4.51686i			0.370036i	0.982735	+	0.185018i	$0.0592343\pi$
$149$			4.51686i			0.370036i	−0.982735	+	0.185018i	$0.940766\pi$
$150$	0.954345	+	1.44542i	0.0779220	+	0.118018i
$151$		−	0.666704i		−	0.0542556i	−0.999632	−	0.0271278i	$-0.991364\pi$
$151$		−	0.666704i		−	0.0542556i	0.999632	−	0.0271278i	$-0.00863611\pi$
$152$	2.92086			0.236913
$153$	5.81352	−	2.33350i	0.469996	−	0.188653i
$154$	−2.05131	−	2.05131i	−0.165299	−	0.165299i
$155$		−	4.22455i		−	0.339324i
$156$	0.394465	+	0.597441i	0.0315824	+	0.0478335i
$157$	−4.51846			−0.360613			−0.180306	−	0.983611i	$-0.557709\pi$
$157$	−4.51846			−0.360613			−0.180306	+	0.983611i	$0.557709\pi$
$158$			10.0927i			0.802932i
$159$	3.32486	+	0.680376i	0.263679	+	0.0539573i
$160$	−1.00000			−0.0790569
$161$	14.7489	−	14.7489i	1.16237	−	1.16237i
$162$	−0.197861	+	8.99782i	−0.0155454	+	0.706936i
$163$	−7.73462	+	7.73462i	−0.605822	+	0.605822i	−0.941851	−	0.336029i	$-0.890916\pi$
$163$	−7.73462	+	7.73462i	−0.605822	+	0.605822i	0.336029	+	0.941851i	$0.390916\pi$
$164$		−	0.304236i		−	0.0237569i
$165$	0.701146	+	1.06193i	0.0545841	+	0.0826710i
$166$	−12.0378	+	12.0378i	−0.934312	+	0.934312i
$167$	−7.06001	+	7.06001i	−0.546320	+	0.546320i	−0.925374	−	0.379054i	$-0.876249\pi$
$167$	−7.06001	+	7.06001i	−0.546320	+	0.546320i	0.379054	+	0.925374i	$0.376249\pi$
$168$	3.76832	+	5.70736i	0.290732	+	0.440332i
$169$		−	12.8292i		−	0.986858i
$170$	−1.47653	+	1.47653i	−0.113244	+	0.113244i
$171$	3.26409	+	8.13193i	0.249611	+	0.621864i
$172$	1.47908	−	1.47908i	0.112779	−	0.112779i
$173$	8.24761			0.627054			0.313527	−	0.949579i	$-0.398489\pi$
$173$	8.24761			0.627054			0.313527	+	0.949579i	$0.398489\pi$
$174$	13.2506	+	2.71150i	1.00452	+	0.205558i
$175$			3.94859i			0.298486i
$176$	−0.734688			−0.0553792
$177$	−5.12833	−	7.76717i	−0.385469	−	0.583816i
$178$		−	3.88150i		−	0.290931i
$179$	0.908928	+	0.908928i	0.0679365	+	0.0679365i	0.740259	−	0.672322i	$-0.234703\pi$
$179$	0.908928	+	0.908928i	0.0679365	+	0.0679365i	−0.672322	+	0.740259i	$0.734703\pi$
$180$	−1.11751	−	2.78409i	−0.0832945	−	0.207514i
$181$	−18.8543			−1.40143			−0.700714	−	0.713443i	$-0.747135\pi$
$181$	−18.8543			−1.40143			−0.700714	+	0.713443i	$0.747135\pi$
$182$			1.63209i			0.120979i
$183$	−3.97470	−	6.01992i	−0.293818	−	0.445006i
$184$		−	5.28241i		−	0.389424i
$185$	−6.08232	+	0.0737400i	−0.447181	+	0.00542147i
$186$	−1.46693	+	7.16859i	−0.107560	+	0.525626i
$187$	−1.08479	+	1.08479i	−0.0793274	+	0.0793274i
$188$	−5.23964			−0.382140
$189$	−11.6787	+	16.8694i	−0.849497	+	1.22707i
$190$	−2.06536	−	2.06536i	−0.149837	−	0.149837i
$191$	3.40059	−	3.40059i	0.246058	−	0.246058i	−0.573292	−	0.819351i	$-0.694334\pi$
$191$	3.40059	−	3.40059i	0.246058	−	0.246058i	0.819351	+	0.573292i	$0.194334\pi$
$192$	1.69689	+	0.347239i	0.122462	+	0.0250598i
$193$	12.1531	+	12.1531i	0.874802	+	0.874802i	0.992991	−	0.118189i	$-0.0377090\pi$
$193$	12.1531	+	12.1531i	0.874802	+	0.874802i	−0.118189	+	0.992991i	$0.537709\pi$
$194$		−	13.3628i		−	0.959395i
$195$	0.143526	−	0.701383i	0.0102781	−	0.0502271i
$196$			8.59139i			0.613671i
$197$			10.0263i			0.714343i	0.934039	+	0.357172i	$0.116259\pi$
$197$			10.0263i			0.714343i	−0.934039	+	0.357172i	$0.883741\pi$
$198$	−0.821023	−	2.04544i	−0.0583475	−	0.145363i
$199$	−17.8385	+	17.8385i	−1.26454	+	1.26454i	−0.315673	+	0.948868i	$0.602230\pi$
$199$	−17.8385	+	17.8385i	−1.26454	+	1.26454i	−0.948868	+	0.315673i	$0.897770\pi$
$200$	0.707107	+	0.707107i	0.0500000	+	0.0500000i
$201$	−1.46779	−	0.300359i	−0.103530	−	0.0211857i
$202$	0.325120	+	0.325120i	0.0228753	+	0.0228753i
$203$	21.8027	+	21.8027i	1.53025	+	1.53025i
$204$	3.01820	−	1.99279i	0.211317	−	0.139523i
$205$	−0.215128	+	0.215128i	−0.0150252	+	0.0150252i
$206$	2.61193			0.181982
$207$	14.7067	−	5.90315i	1.02219	−	0.410298i
$208$	0.292272	+	0.292272i	0.0202654	+	0.0202654i
$209$	−1.51739	−	1.51739i	−0.104960	−	0.104960i
$210$	1.37110	−	6.70032i	0.0946152	−	0.462366i
$211$	23.4805			1.61646			0.808231	−	0.588865i	$-0.200425\pi$
$211$	23.4805			1.61646			0.808231	+	0.588865i	$0.200425\pi$
$212$	1.95939			0.134571
$213$	−1.58470	−	0.324281i	−0.108582	−	0.0222194i
$214$	−10.8599	+	10.8599i	−0.742365	+	0.742365i
$215$	−2.09173			−0.142655
$216$	0.929548	+	5.11233i	0.0632477	+	0.347850i
$217$	−11.7953	+	11.7953i	−0.800715	+	0.800715i
$218$		−	9.73635i		−	0.659429i
$219$	−4.94993	−	1.01292i	−0.334485	−	0.0684466i
$220$	0.519503	+	0.519503i	0.0350249	+	0.0350249i
$221$	0.863094			0.0580580
$222$	10.3466	+	1.98689i	0.694419	+	0.133351i
$223$	−10.3252			−0.691426			−0.345713	−	0.938340i	$-0.612363\pi$
$223$	−10.3252			−0.691426			−0.345713	+	0.938340i	$0.612363\pi$
$224$	2.79208	+	2.79208i	0.186554	+	0.186554i
$225$	−1.17845	+	2.75885i	−0.0785633	+	0.183923i
$226$			10.0861i			0.670914i
$227$	−19.2638	+	19.2638i	−1.27859	+	1.27859i	−0.337125	+	0.941460i	$0.609455\pi$
$227$	−19.2638	+	19.2638i	−1.27859	+	1.27859i	−0.941460	+	0.337125i	$0.890545\pi$
$228$	2.78750	+	4.22185i	0.184607	+	0.279599i
$229$	5.12830			0.338888			0.169444	−	0.985540i	$-0.445803\pi$
$229$	5.12830			0.338888			0.169444	+	0.985540i	$0.445803\pi$
$230$	−3.73522	+	3.73522i	−0.246293	+	0.246293i
$231$	1.00733	−	4.92264i	0.0662777	−	0.323886i
$232$	7.80876			0.512670
$233$	3.70833			0.242941			0.121471	−	0.992595i	$-0.461239\pi$
$233$	3.70833			0.242941			0.121471	+	0.992595i	$0.461239\pi$
$234$	−0.487095	+	1.14033i	−0.0318424	+	0.0745457i
$235$	3.70499	+	3.70499i	0.241687	+	0.241687i
$236$	−3.79975	−	3.79975i	−0.247343	−	0.247343i
$237$	−14.5881	+	9.63192i	−0.947601	+	0.625661i
$238$	8.24515			0.534454
$239$	−18.5198	+	18.5198i	−1.19795	+	1.19795i	−0.223165	+	0.974781i	$0.571639\pi$
$239$	−18.5198	+	18.5198i	−1.19795	+	1.19795i	−0.974781	+	0.223165i	$0.928361\pi$
$240$	−0.954345	−	1.44542i	−0.0616027	−	0.0933011i
$241$	8.62974	+	8.62974i	0.555890	+	0.555890i	0.928135	−	0.372245i	$-0.121412\pi$
$241$	8.62974	+	8.62974i	0.555890	+	0.555890i	−0.372245	+	0.928135i	$0.621412\pi$
$242$	−7.39650	−	7.39650i	−0.475465	−	0.475465i
$243$	−13.1944	+	8.30104i	−0.846422	+	0.532512i
$244$	−2.94499	−	2.94499i	−0.188533	−	0.188533i
$245$	6.07503	−	6.07503i	0.388120	−	0.388120i
$246$	0.439748	−	0.290347i	0.0280373	−	0.0185118i
$247$			1.20729i			0.0768182i
$248$			4.22455i			0.268259i
$249$	−28.8878	−	5.91138i	−1.83069	−	0.374618i
$250$		−	1.00000i		−	0.0632456i
$251$	4.62056	+	4.62056i	0.291647	+	0.291647i	0.837731	−	0.546084i	$-0.183882\pi$
$251$	4.62056	+	4.62056i	0.291647	+	0.291647i	−0.546084	+	0.837731i	$0.683882\pi$
$252$	−4.65322	+	10.8936i	−0.293125	+	0.686231i
$253$	−2.74422	+	2.74422i	−0.172528	+	0.172528i
$254$	−14.1208	−	14.1208i	−0.886018	−	0.886018i
$255$	−3.54331	−	0.725077i	−0.221891	−	0.0454061i
$256$	1.00000			0.0625000
$257$	−2.19029	+	2.19029i	−0.136627	+	0.136627i	−0.772112	−	0.635486i	$-0.780800\pi$
$257$	−2.19029	+	2.19029i	−0.136627	+	0.136627i	0.635486	+	0.772112i	$0.280800\pi$
$258$	3.54943	+	0.726330i	0.220978	+	0.0452194i
$259$	17.1882	+	16.7764i	1.06802	+	1.04244i
$260$		−	0.413335i		−	0.0256340i
$261$	8.72638	+	21.7403i	0.540150	+	1.34569i
$262$			4.96994i			0.307044i
$263$	21.1251			1.30263			0.651313	−	0.758809i	$-0.274218\pi$
$263$	21.1251			1.30263			0.651313	+	0.758809i	$0.274218\pi$
$264$	−0.701146	−	1.06193i	−0.0431526	−	0.0653572i
$265$	−1.38550	−	1.38550i	−0.0851105	−	0.0851105i
$266$			11.5333i			0.707150i
$267$	5.61038	−	3.70429i	0.343350	−	0.226699i
$268$	−0.864992			−0.0528378
$269$		−	29.9724i		−	1.82745i	−0.406337	−	0.913723i	$-0.633194\pi$
$269$		−	29.9724i		−	1.82745i	0.406337	−	0.913723i	$-0.366806\pi$
$270$	2.95767	−	4.27225i	0.179998	−	0.260001i
$271$	27.2422			1.65485			0.827424	−	0.561577i	$-0.189805\pi$
$271$	27.2422			1.65485			0.827424	+	0.561577i	$0.189805\pi$
$272$	1.47653	−	1.47653i	0.0895275	−	0.0895275i
$273$	−2.35905	+	1.55758i	−0.142776	+	0.0942690i
$274$	9.31120	−	9.31120i	0.562510	−	0.562510i
$275$		−	0.734688i		−	0.0443033i
$276$	7.63527	−	5.04124i	0.459589	−	0.303447i
$277$	7.66046	−	7.66046i	0.460272	−	0.460272i	−0.438472	−	0.898745i	$-0.644480\pi$
$277$	7.66046	−	7.66046i	0.460272	−	0.460272i	0.898745	+	0.438472i	$0.144480\pi$
$278$	11.5656	−	11.5656i	0.693657	−	0.693657i
$279$	−11.7615	+	4.72099i	−0.704145	+	0.282638i
$280$		−	3.94859i		−	0.235974i
$281$	−1.71864	+	1.71864i	−0.102525	+	0.102525i	−0.756509	−	0.653984i	$-0.773097\pi$
$281$	−1.71864	+	1.71864i	−0.102525	+	0.102525i	0.653984	+	0.756509i	$0.273097\pi$
$282$	−5.00043	−	7.57346i	−0.297771	−	0.450993i
$283$	−1.71910	+	1.71910i	−0.102190	+	0.102190i	−0.756353	−	0.654163i	$-0.773021\pi$
$283$	−1.71910	+	1.71910i	−0.102190	+	0.102190i	0.654163	+	0.756353i	$0.273021\pi$
$284$	−0.933886			−0.0554159
$285$	1.01423	−	4.95636i	0.0600780	−	0.293589i
$286$		−	0.303672i		−	0.0179565i
$287$	1.20131			0.0709108
$288$	1.11751	+	2.78409i	0.0658501	+	0.164054i
$289$			12.6397i			0.743514i
$290$	−5.52163	−	5.52163i	−0.324241	−	0.324241i
$291$	19.3148	−	12.7528i	1.13226	−	0.747580i
$292$	−2.91706			−0.170708
$293$		−	17.1591i		−	1.00245i	−0.865318	−	0.501223i	$-0.832884\pi$
$293$		−	17.1591i		−	1.00245i	0.865318	−	0.501223i	$-0.167116\pi$
$294$	−12.4181	+	8.19916i	−0.724240	+	0.478185i
$295$			5.37366i			0.312867i
$296$	6.08232	−	0.0737400i	0.353527	−	0.00428605i
$297$	2.17297	−	3.13877i	0.126088	−	0.182130i
$298$	−3.19390	+	3.19390i	−0.185018	+	0.185018i
$299$	2.18340			0.126269
$300$	−0.347239	+	1.69689i	−0.0200478	+	0.0979698i
$301$	5.84028	+	5.84028i	0.336628	+	0.336628i
$302$	0.471431	−	0.471431i	0.0271278	−	0.0271278i
$303$	−0.159656	+	0.780209i	−0.00917202	+	0.0448219i
$304$	2.06536	+	2.06536i	0.118456	+	0.118456i
$305$			4.16484i			0.238478i
$306$	5.76082	+	2.46075i	0.329324	+	0.140672i
$307$		−	19.7974i		−	1.12990i	−0.825127	−	0.564948i	$-0.808896\pi$
$307$		−	19.7974i		−	1.12990i	0.825127	−	0.564948i	$-0.191104\pi$
$308$		−	2.90098i		−	0.165299i
$309$	2.49268	+	3.77532i	0.141804	+	0.214770i
$310$	2.98721	−	2.98721i	0.169662	−	0.169662i
$311$	−13.6776	−	13.6776i	−0.775586	−	0.775586i	0.203491	−	0.979077i	$-0.434771\pi$
$311$	−13.6776	−	13.6776i	−0.775586	−	0.775586i	−0.979077	+	0.203491i	$0.934771\pi$
$312$	−0.143526	+	0.701383i	−0.00812556	+	0.0397080i
$313$	−5.76423	−	5.76423i	−0.325814	−	0.325814i	0.525178	−	0.850992i	$-0.323999\pi$
$313$	−5.76423	−	5.76423i	−0.325814	−	0.325814i	−0.850992	+	0.525178i	$0.823999\pi$
$314$	−3.19504	−	3.19504i	−0.180306	−	0.180306i
$315$	10.9932	−	4.41260i	0.619399	−	0.248622i
$316$	−7.13662	+	7.13662i	−0.401466	+	0.401466i
$317$	6.61486			0.371527			0.185764	−	0.982594i	$-0.440524\pi$
$317$	6.61486			0.371527			0.185764	+	0.982594i	$0.440524\pi$
$318$	1.86994	+	2.83213i	0.104861	+	0.158818i
$319$	−4.05667	−	4.05667i	−0.227130	−	0.227130i
$320$	−0.707107	−	0.707107i	−0.0395285	−	0.0395285i
$321$	−26.0611	−	5.33295i	−1.45459	−	0.297656i
$322$	20.8581			1.16237
$323$	6.09910			0.339363
$324$	−6.50233	+	6.22251i	−0.361241	+	0.345695i
$325$	−0.292272	+	0.292272i	−0.0162123	+	0.0162123i
$326$	−10.9384			−0.605822
$327$	14.0731	−	9.29185i	0.778243	−	0.513840i
$328$	0.215128	−	0.215128i	0.0118784	−	0.0118784i
$329$		−	20.6892i		−	1.14063i
$330$	−0.255112	+	1.24668i	−0.0140435	+	0.0686276i
$331$	−24.1839	−	24.1839i	−1.32927	−	1.32927i	−0.906008	−	0.423260i	$-0.860886\pi$
$331$	−24.1839	−	24.1839i	−1.32927	−	1.32927i	−0.423260	−	0.906008i	$-0.639114\pi$
$332$	−17.0240			−0.934312
$333$	7.00236	+	16.8513i	0.383727	+	0.923447i
$334$	−9.98436			−0.546320
$335$	0.611642	+	0.611642i	0.0334176	+	0.0334176i
$336$	−1.37110	+	6.70032i	−0.0747999	+	0.365532i
$337$			21.1146i			1.15019i	0.818088	+	0.575093i	$0.195034\pi$
$337$			21.1146i			1.15019i	−0.818088	+	0.575093i	$0.804966\pi$
$338$	9.07158	−	9.07158i	0.493429	−	0.493429i
$339$	−14.5785	+	9.62558i	−0.791797	+	0.522790i
$340$	−2.08812			−0.113244
$341$	2.19467	−	2.19467i	0.118848	−	0.118848i
$342$	−3.44208	+	8.05820i	−0.186126	+	0.435738i
$343$	−6.28377			−0.339292
$344$	2.09173			0.112779
$345$	−8.96364	−	1.83426i	−0.482586	−	0.0987530i
$346$	5.83194	+	5.83194i	0.313527	+	0.313527i
$347$	7.85410	+	7.85410i	0.421630	+	0.421630i	0.885765	−	0.464135i	$-0.153635\pi$
$347$	7.85410	+	7.85410i	0.421630	+	0.421630i	−0.464135	+	0.885765i	$0.653635\pi$
$348$	7.45225	+	11.2869i	0.399483	+	0.605041i
$349$	16.5499			0.885896			0.442948	−	0.896547i	$-0.353933\pi$
$349$	16.5499			0.885896			0.442948	+	0.896547i	$0.353933\pi$
$350$	−2.79208	+	2.79208i	−0.149243	+	0.149243i
$351$	−2.11311	+	0.384215i	−0.112789	+	0.0205079i
$352$	−0.519503	−	0.519503i	−0.0276896	−	0.0276896i
$353$	7.22156	+	7.22156i	0.384365	+	0.384365i	0.872672	−	0.488307i	$-0.162385\pi$
$353$	7.22156	+	7.22156i	0.384365	+	0.384365i	−0.488307	+	0.872672i	$0.662385\pi$
$354$	1.86594	−	9.11850i	0.0991738	−	0.484643i
$355$	0.660357	+	0.660357i	0.0350481	+	0.0350481i
$356$	2.74463	−	2.74463i	0.145465	−	0.145465i
$357$	7.86872	+	11.9177i	0.416457	+	0.630750i
$358$			1.28542i			0.0679365i
$359$		−	34.9275i		−	1.84340i	−0.387902	−	0.921701i	$-0.626800\pi$
$359$		−	34.9275i		−	1.84340i	0.387902	−	0.921701i	$-0.373200\pi$
$360$	1.17845	−	2.75885i	0.0621097	−	0.145404i
$361$		−	10.4686i		−	0.550979i
$362$	−13.3320	−	13.3320i	−0.700714	−	0.700714i
$363$	3.63220	−	17.7498i	0.190641	−	0.931625i
$364$	−1.15406	+	1.15406i	−0.0604894	+	0.0604894i
$365$	2.06268	+	2.06268i	0.107965	+	0.107965i
$366$	1.44619	−	7.06726i	0.0755938	−	0.369412i
$367$	1.37685			0.0718709			0.0359354	−	0.999354i	$-0.488559\pi$
$367$	1.37685			0.0718709			0.0359354	+	0.999354i	$0.488559\pi$
$368$	3.73522	−	3.73522i	0.194712	−	0.194712i
$369$	0.839343	+	0.358527i	0.0436944	+	0.0186642i
$370$	−4.35299	−	4.24870i	−0.226301	−	0.220880i
$371$			7.73684i			0.401677i
$372$	−6.10623	+	4.03168i	−0.316593	+	0.209033i
$373$			9.83627i			0.509303i	0.967033	+	0.254651i	$0.0819607\pi$
$373$			9.83627i			0.509303i	−0.967033	+	0.254651i	$0.918039\pi$
$374$	−1.53412			−0.0793274
$375$	1.44542	−	0.954345i	0.0746409	−	0.0492822i
$376$	−3.70499	−	3.70499i	−0.191070	−	0.191070i
$377$			3.22763i			0.166232i
$378$	−20.1865	+	3.67041i	−1.03828	+	0.188785i
$379$	−6.94587			−0.356785			−0.178393	−	0.983959i	$-0.557090\pi$
$379$	−6.94587			−0.356785			−0.178393	+	0.983959i	$0.557090\pi$
$380$		−	2.92086i		−	0.149837i
$381$	6.93430	−	33.8866i	0.355255	−	1.73606i
$382$	4.80917			0.246058
$383$	17.2829	−	17.2829i	0.883112	−	0.883112i	−0.110737	−	0.993850i	$-0.535321\pi$
$383$	17.2829	−	17.2829i	0.883112	−	0.883112i	0.993850	+	0.110737i	$0.0353212\pi$
$384$	0.954345	+	1.44542i	0.0487012	+	0.0737610i
$385$	−2.05131	+	2.05131i	−0.104544	+	0.104544i
$386$			17.1871i			0.874802i
$387$	2.33754	+	5.82358i	0.118824	+	0.296029i
$388$	9.44894	−	9.44894i	0.479697	−	0.479697i
$389$	13.9985	−	13.9985i	0.709755	−	0.709755i	−0.256729	−	0.966483i	$-0.582645\pi$
$389$	13.9985	−	13.9985i	0.709755	−	0.709755i	0.966483	+	0.256729i	$0.0826447\pi$
$390$	0.597441	−	0.394465i	0.0302526	−	0.0199745i
$391$		−	11.0303i		−	0.557827i
$392$	−6.07503	+	6.07503i	−0.306835	+	0.306835i
$393$	−7.18363	+	4.74304i	−0.362366	+	0.239255i
$394$	−7.08965	+	7.08965i	−0.357172	+	0.357172i
$395$	10.0927			0.507819
$396$	0.865792	−	2.02689i	0.0435077	−	0.101855i
$397$		−	26.4716i		−	1.32857i	−0.747479	−	0.664285i	$-0.768736\pi$
$397$		−	26.4716i		−	1.32857i	0.747479	−	0.664285i	$-0.231264\pi$
$398$	−25.2275			−1.26454
$399$	−16.6704	+	11.0067i	−0.834562	+	0.551025i
$400$			1.00000i			0.0500000i
$401$	18.5427	+	18.5427i	0.925979	+	0.925979i	0.997443	−	0.0714644i	$-0.0227672\pi$
$401$	18.5427	+	18.5427i	0.925979	+	0.925979i	−0.0714644	+	0.997443i	$0.522767\pi$
$402$	−0.825502	−	1.25027i	−0.0411723	−	0.0623580i
$403$	−1.74616			−0.0869822
$404$			0.459789i			0.0228753i
$405$	8.99782	+	0.197861i	0.447106	+	0.00983179i
$406$			30.8336i			1.53025i
$407$	−3.19809	−	3.12147i	−0.158523	−	0.154726i
$408$	3.54331	+	0.725077i	0.175420	+	0.0358967i
$409$	16.1415	−	16.1415i	0.798144	−	0.798144i	−0.184659	−	0.982803i	$-0.559118\pi$
$409$	16.1415	−	16.1415i	0.798144	−	0.798144i	0.982803	+	0.184659i	$0.0591179\pi$
$410$	−0.304236			−0.0150252
$411$	22.3446	+	4.57245i	1.10218	+	0.225542i
$412$	1.84691	+	1.84691i	0.0909908	+	0.0909908i
$413$	15.0037	−	15.0037i	0.738283	−	0.738283i
$414$	14.5734	+	6.22505i	0.716242	+	0.305944i
$415$	12.0378	+	12.0378i	0.590911	+	0.590911i
$416$			0.413335i			0.0202654i
$417$	27.7546	+	5.67950i	1.35915	+	0.278126i
$418$		−	2.14592i		−	0.104960i
$419$		−	15.0592i		−	0.735692i	−0.929887	−	0.367846i	$-0.880095\pi$
$419$		−	15.0592i		−	0.735692i	0.929887	−	0.367846i	$-0.119905\pi$
$420$	5.70736	−	3.76832i	0.278491	−	0.183875i
$421$	−18.3585	+	18.3585i	−0.894741	+	0.894741i	−0.994965	−	0.100224i	$-0.968044\pi$
$421$	−18.3585	+	18.3585i	−0.894741	+	0.894741i	0.100224	+	0.994965i	$0.468044\pi$
$422$	16.6032	+	16.6032i	0.808231	+	0.808231i
$423$	6.17465	−	14.4554i	0.300222	−	0.702845i
$424$	1.38550	+	1.38550i	0.0672857	+	0.0672857i
$425$	1.47653	+	1.47653i	0.0716220	+	0.0716220i
$426$	−0.891250	−	1.34985i	−0.0431812	−	0.0654006i
$427$	11.6286	−	11.6286i	0.562745	−	0.562745i
$428$	−15.3582			−0.742365
$429$	0.438932	−	0.289808i	0.0211919	−	0.0139921i
$430$	−1.47908	−	1.47908i	−0.0713275	−	0.0713275i
$431$	6.81039	+	6.81039i	0.328045	+	0.328045i	0.851843	−	0.523798i	$-0.175485\pi$
$431$	6.81039	+	6.81039i	0.328045	+	0.328045i	−0.523798	+	0.851843i	$0.675485\pi$
$432$	−2.95767	+	4.27225i	−0.142301	+	0.205549i
$433$	9.53056			0.458009			0.229005	−	0.973425i	$-0.426453\pi$
$433$	9.53056			0.458009			0.229005	+	0.973425i	$0.426453\pi$
$434$	−16.6810			−0.800715
$435$	2.71150	−	13.2506i	0.130007	−	0.635317i
$436$	6.88464	−	6.88464i	0.329715	−	0.329715i
$437$	15.4291			0.738076
$438$	−2.78389	−	4.21637i	−0.133019	−	0.201466i
$439$	−22.4216	+	22.4216i	−1.07012	+	1.07012i	−0.0727759	+	0.997348i	$0.523186\pi$
$439$	−22.4216	+	22.4216i	−1.07012	+	1.07012i	−0.997348	+	0.0727759i	$0.976814\pi$
$440$			0.734688i			0.0350249i
$441$	−23.7024	−	10.1245i	−1.12868	−	0.482120i
$442$	0.610300	+	0.610300i	0.0290290	+	0.0290290i
$443$	−6.44067			−0.306006			−0.153003	−	0.988226i	$-0.548894\pi$
$443$	−6.44067			−0.306006			−0.153003	+	0.988226i	$0.548894\pi$
$444$	5.91122	+	8.72110i	0.280534	+	0.413885i
$445$	−3.88150			−0.184001
$446$	−7.30102	−	7.30102i	−0.345713	−	0.345713i
$447$	−7.66460	−	1.56843i	−0.362523	−	0.0741841i
$448$			3.94859i			0.186554i
$449$	−21.6267	+	21.6267i	−1.02063	+	1.02063i	−0.0208427	+	0.999783i	$0.506635\pi$
$449$	−21.6267	+	21.6267i	−1.02063	+	1.02063i	−0.999783	+	0.0208427i	$0.993365\pi$
$450$	−2.78409	+	1.11751i	−0.131243	+	0.0526800i
$451$	−0.223519			−0.0105251
$452$	−7.13192	+	7.13192i	−0.335457	+	0.335457i
$453$	1.13132	+	0.231505i	0.0531541	+	0.0108771i
$454$	−27.2432			−1.27859
$455$	1.63209			0.0765137
$456$	−1.01423	+	4.95636i	−0.0474958	+	0.232103i
$457$	23.1144	+	23.1144i	1.08125	+	1.08125i	0.996393	+	0.0848531i	$0.0270421\pi$
$457$	23.1144	+	23.1144i	1.08125	+	1.08125i	0.0848531	+	0.996393i	$0.472958\pi$
$458$	3.62626	+	3.62626i	0.169444	+	0.169444i
$459$	1.94101	+	10.6752i	0.0905986	+	0.498275i
$460$	−5.28241			−0.246293
$461$	−15.6337	+	15.6337i	−0.728136	+	0.728136i	−0.970248	−	0.242112i	$-0.922160\pi$
$461$	−15.6337	+	15.6337i	−0.728136	+	0.728136i	0.242112	+	0.970248i	$0.422160\pi$
$462$	4.19313	−	2.76854i	0.195082	−	0.128804i
$463$	−17.1735	−	17.1735i	−0.798121	−	0.798121i	0.184678	−	0.982799i	$-0.440876\pi$
$463$	−17.1735	−	17.1735i	−0.798121	−	0.798121i	−0.982799	+	0.184678i	$0.940876\pi$
$464$	5.52163	+	5.52163i	0.256335	+	0.256335i
$465$	7.16859	+	1.46693i	0.332435	+	0.0680271i
$466$	2.62219	+	2.62219i	0.121471	+	0.121471i
$467$	11.3173	−	11.3173i	0.523704	−	0.523704i	−0.394984	−	0.918688i	$-0.629250\pi$
$467$	11.3173	−	11.3173i	0.523704	−	0.523704i	0.918688	+	0.394984i	$0.129250\pi$
$468$	−1.15076	+	0.461907i	−0.0531940	+	0.0213517i
$469$		−	3.41550i		−	0.157713i
$470$			5.23964i			0.241687i
$471$	1.56899	−	7.66732i	0.0722950	−	0.353292i
$472$		−	5.37366i		−	0.247343i
$473$	−1.08666	−	1.08666i	−0.0499647	−	0.0499647i
$474$	−17.1262	−	3.50458i	−0.786631	−	0.160970i
$475$	−2.06536	+	2.06536i	−0.0947651	+	0.0947651i
$476$	5.83020	+	5.83020i	0.267227	+	0.267227i
$477$	−2.30904	+	5.40566i	−0.105724	+	0.247508i
$478$	−26.1909			−1.19795
$479$	26.5480	−	26.5480i	1.21301	−	1.21301i	0.242974	−	0.970033i	$-0.421877\pi$
$479$	26.5480	−	26.5480i	1.21301	−	1.21301i	0.970033	−	0.242974i	$-0.0781231\pi$
$480$	0.347239	−	1.69689i	0.0158492	−	0.0774519i
$481$	0.0304793	+	2.51403i	0.00138974	+	0.114630i
$482$			12.2043i			0.555890i
$483$	19.9058	+	30.1486i	0.905746	+	1.37181i
$484$		−	10.4602i		−	0.475465i
$485$	−13.3628			−0.606775
$486$	−15.1996	−	3.46014i	−0.689467	−	0.156955i
$487$	−30.6600	−	30.6600i	−1.38934	−	1.38934i	−0.826712	−	0.562625i	$-0.809792\pi$
$487$	−30.6600	−	30.6600i	−1.38934	−	1.38934i	−0.562625	−	0.826712i	$-0.690208\pi$
$488$		−	4.16484i		−	0.188533i
$489$	−10.4390	−	15.8105i	−0.472069	−	0.714977i
$490$	8.59139			0.388120
$491$			34.3485i			1.55013i	0.631884	+	0.775063i	$0.282282\pi$
$491$			34.3485i			1.55013i	−0.631884	+	0.775063i	$0.717718\pi$
$492$	0.516255	+	0.105643i	0.0232746	+	0.00476274i
$493$	16.3056			0.734369
$494$	−0.853684	+	0.853684i	−0.0384091	+	0.0384091i
$495$	−2.04544	+	0.821023i	−0.0919356	+	0.0369022i
$496$	−2.98721	+	2.98721i	−0.134130	+	0.134130i
$497$		−	3.68754i		−	0.165409i
$498$	−16.2467	−	24.6067i	−0.728034	−	1.10265i
$499$	2.34473	−	2.34473i	0.104965	−	0.104965i	−0.652674	−	0.757639i	$-0.726353\pi$
$499$	2.34473	−	2.34473i	0.104965	−	0.104965i	0.757639	+	0.652674i	$0.226353\pi$
$500$	0.707107	−	0.707107i	0.0316228	−	0.0316228i
$501$	−9.52853	−	14.4315i	−0.425703	−	0.644754i
$502$			6.53446i			0.291647i
$503$	−2.10055	+	2.10055i	−0.0936591	+	0.0936591i	−0.752384	−	0.658725i	$-0.771096\pi$
$503$	−2.10055	+	2.10055i	−0.0936591	+	0.0936591i	0.658725	+	0.752384i	$0.271096\pi$
$504$	−10.9932	+	4.41260i	−0.489678	+	0.196553i
$505$	0.325120	−	0.325120i	0.0144676	−	0.0144676i
$506$	−3.88092			−0.172528
$507$	21.7696	+	4.45478i	0.966823	+	0.197844i
$508$		−	19.9698i		−	0.886018i
$509$	−10.4717			−0.464149			−0.232074	−	0.972698i	$-0.574551\pi$
$509$	−10.4717			−0.464149			−0.232074	+	0.972698i	$0.574551\pi$
$510$	−1.99279	−	3.01820i	−0.0882422	−	0.133648i
$511$		−	11.5183i		−	0.509540i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−14.9324	+	2.71508i	−0.659281	+	0.119874i
$514$	−3.09754			−0.136627
$515$		−	2.61193i		−	0.115095i
$516$	1.99624	+	3.02342i	0.0878794	+	0.133099i
$517$			3.84950i			0.169301i
$518$	0.291169	+	24.0166i	0.0127932	+	1.05523i
$519$	−2.86389	+	13.9953i	−0.125711	+	0.614324i
$520$	0.292272	−	0.292272i	0.0128170	−	0.0128170i
$521$	−40.1707			−1.75991			−0.879956	−	0.475056i	$-0.842428\pi$
$521$	−40.1707			−1.75991			−0.879956	+	0.475056i	$0.842428\pi$
$522$	−9.20223	+	21.5432i	−0.402770	+	0.942920i
$523$	6.70260	+	6.70260i	0.293084	+	0.293084i	0.838297	−	0.545213i	$-0.183551\pi$
$523$	6.70260	+	6.70260i	0.293084	+	0.293084i	−0.545213	+	0.838297i	$0.683551\pi$
$524$	−3.51428	+	3.51428i	−0.153522	+	0.153522i
$525$	−6.70032	−	1.37110i	−0.292426	−	0.0598399i
$526$	14.9377	+	14.9377i	0.651313	+	0.651313i
$527$			8.82138i			0.384265i
$528$	0.255112	−	1.24668i	0.0111023	−	0.0542549i
$529$		−	4.90380i		−	0.213209i
$530$		−	1.95939i		−	0.0851105i
$531$	14.9608	−	6.00513i	0.649242	−	0.260601i
$532$	−8.15525	+	8.15525i	−0.353575	+	0.353575i
$533$	0.0889198	+	0.0889198i	0.00385154	+	0.00385154i
$534$	6.58647	+	1.34781i	0.285024	+	0.0583253i
$535$	10.8599	+	10.8599i	0.469513	+	0.469513i
$536$	−0.611642	−	0.611642i	−0.0264189	−	0.0264189i
$537$	−1.85796	+	1.22673i	−0.0801770	+	0.0529375i
$538$	21.1937	−	21.1937i	0.913723	−	0.913723i
$539$	6.31199			0.271877
$540$	5.11233	−	0.929548i	0.220000	−	0.0400014i
$541$	−15.4007	−	15.4007i	−0.662129	−	0.662129i	0.293752	−	0.955882i	$-0.405096\pi$
$541$	−15.4007	−	15.4007i	−0.662129	−	0.662129i	−0.955882	+	0.293752i	$0.905096\pi$
$542$	19.2632	+	19.2632i	0.827424	+	0.827424i
$543$	6.54693	−	31.9936i	0.280956	−	1.37298i
$544$	2.08812			0.0895275
$545$	−9.73635			−0.417060
$546$	−2.76948	−	0.566726i	−0.118523	−	0.0242536i
$547$	11.5338	−	11.5338i	0.493149	−	0.493149i	−0.416148	−	0.909297i	$-0.636620\pi$
$547$	11.5338	−	11.5338i	0.493149	−	0.493149i	0.909297	+	0.416148i	$0.136620\pi$
$548$	13.1680			0.562510
$549$	11.5953	−	4.65426i	0.494875	−	0.198639i
$550$	0.519503	−	0.519503i	0.0221517	−	0.0221517i
$551$			22.8082i			0.971664i
$552$	8.96364	+	1.83426i	0.381518	+	0.0780711i
$553$	−28.1796	−	28.1796i	−1.19832	−	1.19832i
$554$	10.8335			0.460272
$555$	1.98689	−	10.3466i	0.0843386	−	0.439189i
$556$	16.3562			0.693657
$557$	−6.19261	−	6.19261i	−0.262389	−	0.262389i	0.563635	−	0.826024i	$-0.309403\pi$
$557$	−6.19261	−	6.19261i	−0.262389	−	0.262389i	−0.826024	+	0.563635i	$0.809403\pi$
$558$	−11.6549	−	4.97842i	−0.493392	−	0.210753i
$559$			0.864587i			0.0365681i
$560$	2.79208	−	2.79208i	0.117987	−	0.117987i
$561$	−1.46408	−	2.21744i	−0.0618135	−	0.0936203i
$562$	−2.43052			−0.102525
$563$	10.5672	−	10.5672i	0.445356	−	0.445356i	−0.448452	−	0.893807i	$-0.648024\pi$
$563$	10.5672	−	10.5672i	0.445356	−	0.445356i	0.893807	+	0.448452i	$0.148024\pi$
$564$	1.81941	−	8.89108i	0.0766108	−	0.374382i
$565$	10.0861			0.424324
$566$	−2.43118			−0.102190
$567$	−24.5702	−	25.6751i	−1.03185	−	1.07825i
$568$	−0.660357	−	0.660357i	−0.0277080	−	0.0277080i
$569$	17.3202	+	17.3202i	0.726098	+	0.726098i	0.969840	−	0.243742i	$-0.0783749\pi$
$569$	17.3202	+	17.3202i	0.726098	+	0.726098i	−0.243742	+	0.969840i	$0.578375\pi$
$570$	4.22185	−	2.78750i	0.176834	−	0.116756i
$571$	−6.09808			−0.255196			−0.127598	−	0.991826i	$-0.540727\pi$
$571$	−6.09808			−0.255196			−0.127598	+	0.991826i	$0.540727\pi$
$572$	0.214729	−	0.214729i	0.00897826	−	0.00897826i
$573$	4.58961	+	6.95124i	0.191734	+	0.290392i
$574$	0.849451	+	0.849451i	0.0354554	+	0.0354554i
$575$	3.73522	+	3.73522i	0.155770	+	0.155770i
$576$	−1.17845	+	2.75885i	−0.0491021	+	0.114952i
$577$	−1.00454	−	1.00454i	−0.0418197	−	0.0418197i	0.685888	−	0.727707i	$-0.259414\pi$
$577$	−1.00454	−	1.00454i	−0.0418197	−	0.0418197i	−0.727707	+	0.685888i	$0.759414\pi$
$578$	−8.93765	+	8.93765i	−0.371757	+	0.371757i
$579$	−24.8425	+	16.4025i	−1.03242	+	0.681663i
$580$		−	7.80876i		−	0.324241i
$581$		−	67.2207i		−	2.78879i
$582$	22.6752	+	4.64009i	0.939917	+	0.192338i
$583$		−	1.43954i		−	0.0596197i
$584$	−2.06268	−	2.06268i	−0.0853541	−	0.0853541i
$585$	1.14033	+	0.487095i	0.0471468	+	0.0201389i
$586$	12.1333	−	12.1333i	0.501223	−	0.501223i
$587$	13.2475	+	13.2475i	0.546783	+	0.546783i	0.925509	−	0.378726i	$-0.123638\pi$
$587$	13.2475	+	13.2475i	0.546783	+	0.546783i	−0.378726	+	0.925509i	$0.623638\pi$
$588$	−14.5786	−	2.98326i	−0.601212	−	0.123028i
$589$	−12.3393			−0.508432
$590$	−3.79975	+	3.79975i	−0.156433	+	0.156433i
$591$	−17.0135	−	3.48151i	−0.699841	−	0.143210i
$592$	4.35299	+	4.24870i	0.178907	+	0.174621i
$593$		−	38.3651i		−	1.57547i	−0.616016	−	0.787734i	$-0.711254\pi$
$593$		−	38.3651i		−	1.57547i	0.616016	−	0.787734i	$-0.288746\pi$
$594$	3.75597	−	0.682928i	0.154109	−	0.0280209i
$595$		−	8.24515i		−	0.338018i
$596$	−4.51686			−0.185018
$597$	−24.0758	−	36.4642i	−0.985356	−	1.49238i
$598$	1.54390	+	1.54390i	0.0631347	+	0.0631347i
$599$			37.1450i			1.51770i	0.651264	+	0.758851i	$0.274239\pi$
$599$			37.1450i			1.51770i	−0.651264	+	0.758851i	$0.725761\pi$
$600$	−1.44542	+	0.954345i	−0.0590088	+	0.0389610i
$601$	44.0501			1.79684			0.898420	−	0.439137i	$-0.144716\pi$
$601$	44.0501			1.79684			0.898420	+	0.439137i	$0.144716\pi$
$602$			8.25940i			0.336628i
$603$	1.01935	−	2.38638i	0.0415111	−	0.0971811i
$604$	0.666704			0.0271278
$605$	−7.39650	+	7.39650i	−0.300711	+	0.300711i
$606$	−0.664585	+	0.438797i	−0.0269969	+	0.0178249i
$607$	23.7723	−	23.7723i	0.964888	−	0.964888i	−0.0345157	−	0.999404i	$-0.510989\pi$
$607$	23.7723	−	23.7723i	0.964888	−	0.964888i	0.999404	+	0.0345157i	$0.0109889\pi$
$608$			2.92086i			0.118456i
$609$	−44.5674	+	29.4259i	−1.80596	+	1.19240i
$610$	−2.94499	+	2.94499i	−0.119239	+	0.119239i
$611$	1.53140	−	1.53140i	0.0619539	−	0.0619539i
$612$	2.33350	+	5.81352i	0.0943263	+	0.234998i
$613$		−	20.1947i		−	0.815657i	−0.913059	−	0.407828i	$-0.866286\pi$
$613$		−	20.1947i		−	0.815657i	0.913059	−	0.407828i	$-0.133714\pi$
$614$	13.9989	−	13.9989i	0.564948	−	0.564948i
$615$	−0.290347	−	0.439748i	−0.0117079	−	0.0177323i
$616$	2.05131	−	2.05131i	0.0826494	−	0.0826494i
$617$	−1.38704			−0.0558402			−0.0279201	−	0.999610i	$-0.508888\pi$
$617$	−1.38704			−0.0558402			−0.0279201	+	0.999610i	$0.508888\pi$
$618$	−0.906962	+	4.43214i	−0.0364834	+	0.178287i
$619$		−	36.0337i		−	1.44831i	−0.689635	−	0.724157i	$-0.742229\pi$
$619$		−	36.0337i		−	1.44831i	0.689635	−	0.724157i	$-0.257771\pi$
$620$	4.22455			0.169662
$621$	4.91025	+	27.0054i	0.197042	+	1.08369i
$622$		−	19.3431i		−	0.775586i
$623$	10.8374	+	10.8374i	0.434193	+	0.434193i
$624$	−0.597441	+	0.394465i	−0.0239168	+	0.0157912i
$625$	−1.00000			−0.0400000
$626$		−	8.15186i		−	0.325814i
$627$	3.10174	−	2.04795i	0.123872	−	0.0817871i
$628$		−	4.51846i		−	0.180306i
$629$	12.7006	−	0.153978i	0.506407	−	0.00613951i
$630$	10.8936	+	4.65322i	0.434011	+	0.185389i
$631$	−3.67529	+	3.67529i	−0.146311	+	0.146311i	−0.776468	−	0.630157i	$-0.782991\pi$
$631$	−3.67529	+	3.67529i	−0.146311	+	0.146311i	0.630157	+	0.776468i	$0.282991\pi$
$632$	−10.0927			−0.401466
$633$	−8.15333	+	39.8437i	−0.324066	+	1.58365i
$634$	4.67741	+	4.67741i	0.185764	+	0.185764i
$635$	−14.1208	+	14.1208i	−0.560367	+	0.560367i
$636$	−0.680376	+	3.32486i	−0.0269787	+	0.131839i
$637$	−2.51102	−	2.51102i	−0.0994904	−	0.0994904i
$638$		−	5.73700i		−	0.227130i
$639$	1.10054	−	2.57645i	0.0435366	−	0.101923i
$640$		−	1.00000i		−	0.0395285i
$641$			29.8165i			1.17768i	0.808249	+	0.588840i	$0.200415\pi$
$641$			29.8165i			1.17768i	−0.808249	+	0.588840i	$0.799585\pi$
$642$	−14.6570	−	22.1989i	−0.578465	−	0.876121i
$643$	−21.8005	+	21.8005i	−0.859729	+	0.859729i	−0.991306	−	0.131577i	$-0.957996\pi$
$643$	−21.8005	+	21.8005i	−0.859729	+	0.859729i	0.131577	+	0.991306i	$0.457996\pi$
$644$	14.7489	+	14.7489i	0.581187	+	0.581187i
$645$	0.726330	−	3.54943i	0.0285992	−	0.139759i
$646$	4.31272	+	4.31272i	0.169682	+	0.169682i
$647$	−7.94518	−	7.94518i	−0.312357	−	0.312357i	0.533465	−	0.845822i	$-0.320890\pi$
$647$	−7.94518	−	7.94518i	−0.312357	−	0.312357i	−0.845822	+	0.533465i	$0.820890\pi$
$648$	−8.99782	−	0.197861i	−0.353468	−	0.00777271i
$649$	−2.79163	+	2.79163i	−0.109581	+	0.109581i
$650$	−0.413335			−0.0162123
$651$	−15.9195	−	24.1110i	−0.623933	−	0.944986i
$652$	−7.73462	−	7.73462i	−0.302911	−	0.302911i
$653$	−1.70851	−	1.70851i	−0.0668591	−	0.0668591i	0.672887	−	0.739746i	$-0.265054\pi$
$653$	−1.70851	−	1.70851i	−0.0668591	−	0.0668591i	−0.739746	+	0.672887i	$0.765054\pi$
$654$	16.5215	+	3.38084i	0.646041	+	0.132201i
$655$	4.96994			0.194192
$656$	0.304236			0.0118784
$657$	3.43761	−	8.04774i	0.134114	−	0.313972i
$658$	14.6295	−	14.6295i	0.570317	−	0.570317i
$659$	48.2204			1.87840			0.939199	−	0.343372i	$-0.111569\pi$
$659$	48.2204			1.87840			0.939199	+	0.343372i	$0.111569\pi$
$660$	−1.06193	+	0.701146i	−0.0413355	+	0.0272921i
$661$	2.02628	−	2.02628i	0.0788133	−	0.0788133i	−0.666601	−	0.745415i	$-0.732252\pi$
$661$	2.02628	−	2.02628i	0.0788133	−	0.0788133i	0.745415	+	0.666601i	$0.232252\pi$
$662$		−	34.2012i		−	1.32927i
$663$	−0.299700	+	1.46457i	−0.0116394	+	0.0568793i
$664$	−12.0378	−	12.0378i	−0.467156	−	0.467156i
$665$	11.5333			0.447241
$666$	−6.96426	+	16.8671i	−0.269860	+	0.653587i
$667$	41.2490			1.59717
$668$	−7.06001	−	7.06001i	−0.273160	−	0.273160i
$669$	3.58531	−	17.5207i	0.138616	−	0.677389i
$670$			0.864992i			0.0334176i
$671$	−2.16365	+	2.16365i	−0.0835266	+	0.0835266i
$672$	−5.70736	+	3.76832i	−0.220166	+	0.145366i
$673$	11.4027			0.439542			0.219771	−	0.975552i	$-0.429469\pi$
$673$	11.4027			0.439542			0.219771	+	0.975552i	$0.429469\pi$
$674$	−14.9303	+	14.9303i	−0.575093	+	0.575093i
$675$	−4.27225	−	2.95767i	−0.164439	−	0.113841i
$676$	12.8292			0.493429
$677$	−27.6576			−1.06297			−0.531484	−	0.847068i	$-0.678365\pi$
$677$	−27.6576			−1.06297			−0.531484	+	0.847068i	$0.678365\pi$
$678$	−17.1149	−	3.50227i	−0.657294	−	0.134504i
$679$	37.3100	+	37.3100i	1.43183	+	1.43183i
$680$	−1.47653	−	1.47653i	−0.0566222	−	0.0566222i
$681$	−25.9994	−	39.3777i	−0.996299	−	1.50896i
$682$	3.10373			0.118848
$683$	8.19870	−	8.19870i	0.313715	−	0.313715i	−0.532632	−	0.846347i	$-0.678797\pi$
$683$	8.19870	−	8.19870i	0.313715	−	0.313715i	0.846347	+	0.532632i	$0.178797\pi$
$684$	−8.13193	+	3.26409i	−0.310932	+	0.124806i
$685$	−9.31120	−	9.31120i	−0.355763	−	0.355763i
$686$	−4.44330	−	4.44330i	−0.169646	−	0.169646i
$687$	−1.78074	+	8.70215i	−0.0679396	+	0.332008i
$688$	1.47908	+	1.47908i	0.0563893	+	0.0563893i
$689$	−0.572675	+	0.572675i	−0.0218172	+	0.0218172i
$690$	−5.04124	−	7.63527i	−0.191917	−	0.290670i
$691$			4.68841i			0.178356i	0.996016	+	0.0891778i	$0.0284239\pi$
$691$			4.68841i			0.178356i	−0.996016	+	0.0891778i	$0.971576\pi$
$692$			8.24761i			0.313527i
$693$	8.00338	+	3.41866i	0.304023	+	0.129864i
$694$			11.1074i			0.421630i
$695$	−11.5656	−	11.5656i	−0.438707	−	0.438707i
$696$	−2.71150	+	13.2506i	−0.102779	+	0.502262i
$697$	0.449213	−	0.449213i	0.0170151	−	0.0170151i
$698$	11.7026	+	11.7026i	0.442948	+	0.442948i
$699$	−1.28768	+	6.29262i	−0.0487044	+	0.238009i
$700$	−3.94859			−0.149243
$701$	−6.87240	+	6.87240i	−0.259567	+	0.259567i	−0.824878	−	0.565311i	$-0.808756\pi$
$701$	−6.87240	+	6.87240i	−0.259567	+	0.259567i	0.565311	+	0.824878i	$0.308756\pi$
$702$	−1.76587	−	1.22251i	−0.0666486	−	0.0461407i
$703$	0.215384	+	17.7656i	0.00812336	+	0.670041i
$704$		−	0.734688i		−	0.0276896i
$705$	−7.57346	+	5.00043i	−0.285233	+	0.188327i
$706$			10.2128i			0.384365i
$707$	−1.81552			−0.0682796
$708$	7.76717	−	5.12833i	0.291908	−	0.192734i
$709$	−14.7250	−	14.7250i	−0.553008	−	0.553008i	0.374300	−	0.927308i	$-0.377883\pi$
$709$	−14.7250	−	14.7250i	−0.553008	−	0.553008i	−0.927308	+	0.374300i	$0.877883\pi$
$710$			0.933886i			0.0350481i
$711$	−11.2787	−	28.0990i	−0.422985	−	1.05379i
$712$	3.88150			0.145465
$713$			22.3158i			0.835733i
$714$	−2.86303	+	13.9911i	−0.107146	+	0.523603i
$715$	−0.303672			−0.0113567
$716$	−0.908928	+	0.908928i	−0.0339682	+	0.0339682i
$717$	−24.9952	−	37.8568i	−0.933463	−	1.41379i
$718$	24.6974	−	24.6974i	0.921701	−	0.921701i
$719$		−	0.0958633i		−	0.00357510i	−0.999998	−	0.00178755i	$-0.999431\pi$
$719$		−	0.0958633i		−	0.00357510i	0.999998	−	0.00178755i	$-0.000568995\pi$
$720$	2.78409	−	1.11751i	0.103757	−	0.0416472i
$721$	−7.29270	+	7.29270i	−0.271594	+	0.271594i
$722$	7.40242	−	7.40242i	0.275490	−	0.275490i
$723$	−17.6403	+	11.6471i	−0.656048	+	0.433161i
$724$		−	18.8543i		−	0.700714i
$725$	−5.52163	+	5.52163i	−0.205068	+	0.205068i
$726$	15.1194	−	9.98268i	0.561133	−	0.370492i
$727$	23.2832	−	23.2832i	0.863524	−	0.863524i	−0.128221	−	0.991746i	$-0.540927\pi$
$727$	23.2832	−	23.2832i	0.863524	−	0.863524i	0.991746	+	0.128221i	$0.0409267\pi$
$728$	−1.63209			−0.0604894
$729$	−9.50432	−	25.2719i	−0.352012	−	0.935996i
$730$			2.91706i			0.107965i
$731$	4.36780			0.161549
$732$	6.01992	−	3.97470i	0.222503	−	0.146909i
$733$			26.4058i			0.975321i	0.873033	+	0.487660i	$0.162150\pi$
$733$			26.4058i			0.975321i	−0.873033	+	0.487660i	$0.837850\pi$
$734$	0.973579	+	0.973579i	0.0359354	+	0.0359354i
$735$	8.19916	+	12.4181i	0.302431	+	0.458050i
$736$	5.28241			0.194712
$737$			0.635499i			0.0234089i
$738$	0.339988	+	0.847022i	0.0125151	+	0.0311793i
$739$		−	29.6045i		−	1.08902i	−0.838755	−	0.544510i	$-0.816716\pi$
$739$		−	29.6045i		−	1.08902i	0.838755	−	0.544510i	$-0.183284\pi$
$740$	−0.0737400	−	6.08232i	−0.00271074	−	0.223590i
$741$	−2.04864	−	0.419218i	−0.0752586	−	0.0154004i
$742$	−5.47077	+	5.47077i	−0.200838	+	0.200838i
$743$	−46.8882			−1.72016			−0.860081	−	0.510158i	$-0.829587\pi$
$743$	−46.8882			−1.72016			−0.860081	+	0.510158i	$0.829587\pi$
$744$	−7.16859	−	1.46693i	−0.262813	−	0.0537802i
$745$	3.19390	+	3.19390i	0.117016	+	0.117016i
$746$	−6.95529	+	6.95529i	−0.254651	+	0.254651i
$747$	20.0619	−	46.9666i	0.734026	−	1.71842i
$748$	−1.08479	−	1.08479i	−0.0396637	−	0.0396637i
$749$		−	60.6431i		−	2.21585i
$750$	1.69689	+	0.347239i	0.0619616	+	0.0126794i
$751$			6.41589i			0.234119i	0.993125	+	0.117060i	$0.0373468\pi$
$751$			6.41589i			0.234119i	−0.993125	+	0.117060i	$0.962653\pi$
$752$		−	5.23964i		−	0.191070i
$753$	−9.44500	+	6.23613i	−0.344195	+	0.227257i
$754$	−2.28228	+	2.28228i	−0.0831158	+	0.0831158i
$755$	−0.471431	−	0.471431i	−0.0171571	−	0.0171571i
$756$	−16.8694	−	11.6787i	−0.613534	−	0.424749i
$757$	17.5804	+	17.5804i	0.638970	+	0.638970i	0.950301	−	0.311331i	$-0.100775\pi$
$757$	17.5804	+	17.5804i	0.638970	+	0.638970i	−0.311331	+	0.950301i	$0.600775\pi$
$758$	−4.91147	−	4.91147i	−0.178393	−	0.178393i
$759$	−3.70374	−	5.60954i	−0.134437	−	0.203613i
$760$	2.06536	−	2.06536i	0.0749184	−	0.0749184i
$761$	7.45409			0.270211			0.135105	−	0.990831i	$-0.456863\pi$
$761$	7.45409			0.270211			0.135105	+	0.990831i	$0.456863\pi$
$762$	28.8647	−	19.0581i	1.04566	−	0.690403i
$763$	27.1847	+	27.1847i	0.984151	+	0.984151i
$764$	3.40059	+	3.40059i	0.123029	+	0.123029i
$765$	2.46075	−	5.76082i	0.0889685	−	0.208283i
$766$	24.4416			0.883112
$767$	2.22112			0.0802001
$768$	−0.347239	+	1.69689i	−0.0125299	+	0.0612311i
$769$	13.6259	−	13.6259i	0.491364	−	0.491364i	−0.417372	−	0.908736i	$-0.637049\pi$
$769$	13.6259	−	13.6259i	0.491364	−	0.491364i	0.908736	+	0.417372i	$0.137049\pi$
$770$	−2.90098			−0.104544
$771$	−2.95612	−	4.47723i	−0.106462	−	0.161243i
$772$	−12.1531	+	12.1531i	−0.437401	+	0.437401i
$773$		−	16.5922i		−	0.596781i	−0.954444	−	0.298390i	$-0.903550\pi$
$773$		−	16.5922i		−	0.596781i	0.954444	−	0.298390i	$-0.0964497\pi$
$774$	−2.46500	+	5.77078i	−0.0886026	+	0.207426i
$775$	−2.98721	−	2.98721i	−0.107304	−	0.107304i
$776$	13.3628			0.479697
$777$	−34.4361	+	23.3410i	−1.23539	+	0.837353i
$778$	19.7969			0.709755
$779$	0.628356	+	0.628356i	0.0225132	+	0.0225132i
$780$	0.701383	+	0.143526i	0.0251135	+	0.00513905i
$781$			0.686115i			0.0245511i
$782$	7.79961	−	7.79961i	0.278913	−	0.278913i
$783$	−39.9210	+	7.25862i	−1.42666	+	0.259402i
$784$	−8.59139			−0.306835
$785$	−3.19504	+	3.19504i	−0.114036	+	0.114036i
$786$	−8.43343	−	1.72576i	−0.300810	−	0.0615557i
$787$	5.11626			0.182375			0.0911876	−	0.995834i	$-0.470934\pi$
$787$	5.11626			0.182375			0.0911876	+	0.995834i	$0.470934\pi$
$788$	−10.0263			−0.357172
$789$	−7.33543	+	35.8468i	−0.261148	+	1.27618i
$790$	7.13662	+	7.13662i	0.253909	+	0.253909i
$791$	−28.1610	−	28.1610i	−1.00129	−	1.00129i
$792$	2.04544	−	0.821023i	0.0726815	−	0.0291738i
$793$	1.72148			0.0611314
$794$	18.7182	−	18.7182i	0.664285	−	0.664285i
$795$	2.83213	−	1.86994i	0.100445	−	0.0663198i
$796$	−17.8385	−	17.8385i	−0.632271	−	0.632271i
$797$	−22.9666	−	22.9666i	−0.813518	−	0.813518i	0.171641	−	0.985160i	$-0.445093\pi$
$797$	−22.9666	−	22.9666i	−0.813518	−	0.813518i	−0.985160	+	0.171641i	$0.945093\pi$
$798$	−19.5707	−	4.00480i	−0.692794	−	0.141768i
$799$	−7.73647	−	7.73647i	−0.273697	−	0.273697i
$800$	−0.707107	+	0.707107i	−0.0250000	+	0.0250000i
$801$	4.33762	+	10.8065i	0.153262	+	0.381827i
$802$			26.2234i			0.925979i
$803$			2.14313i			0.0756294i
$804$	0.300359	−	1.46779i	0.0105928	−	0.0517651i
$805$		−	20.8581i		−	0.735150i
$806$	−1.23472	−	1.23472i	−0.0434911	−	0.0434911i
$807$	50.8597	+	10.4076i	1.79035	+	0.366363i
$808$	−0.325120	+	0.325120i	−0.0114377	+	0.0114377i
$809$	−8.64653	−	8.64653i	−0.303996	−	0.303996i	0.538579	−	0.842575i	$-0.318961\pi$
$809$	−8.64653	−	8.64653i	−0.303996	−	0.303996i	−0.842575	+	0.538579i	$0.818961\pi$
$810$	6.22251	+	6.50233i	0.218637	+	0.228469i
$811$	−51.5148			−1.80893			−0.904464	−	0.426549i	$-0.859729\pi$
$811$	−51.5148			−1.80893			−0.904464	+	0.426549i	$0.859729\pi$
$812$	−21.8027	+	21.8027i	−0.765123	+	0.765123i
$813$	−9.45956	+	46.2270i	−0.331761	+	1.62125i
$814$	−0.0541759	−	4.46860i	−0.00189886	−	0.156624i
$815$			10.9384i			0.383156i
$816$	1.99279	+	3.01820i	0.0697616	+	0.105658i
$817$			6.10965i			0.213750i
$818$	22.8275			0.798144
$819$	−1.82388	−	4.54390i	−0.0637317	−	0.158777i
$820$	−0.215128	−	0.215128i	−0.00751258	−	0.00751258i
$821$			20.8710i			0.728402i	0.931320	+	0.364201i	$0.118658\pi$
$821$			20.8710i			0.728402i	−0.931320	+	0.364201i	$0.881342\pi$
$822$	12.5668	+	19.0333i	0.438319	+	0.663861i
$823$	19.9395			0.695046			0.347523	−	0.937671i	$-0.387023\pi$
$823$	19.9395			0.695046			0.347523	+	0.937671i	$0.387023\pi$
$824$			2.61193i			0.0909908i
$825$	1.24668	+	0.255112i	0.0434039	+	0.00888186i
$826$	21.2184			0.738283
$827$	−3.72180	+	3.72180i	−0.129420	+	0.129420i	−0.768849	−	0.639430i	$-0.779170\pi$
$827$	−3.72180	+	3.72180i	−0.129420	+	0.129420i	0.639430	+	0.768849i	$0.279170\pi$
$828$	5.90315	+	14.7067i	0.205149	+	0.511093i
$829$	4.55761	−	4.55761i	0.158292	−	0.158292i	−0.623517	−	0.781810i	$-0.714297\pi$
$829$	4.55761	−	4.55761i	0.158292	−	0.158292i	0.781810	+	0.623517i	$0.214297\pi$
$830$			17.0240i			0.590911i
$831$	10.3389	+	15.6589i	0.358653	+	0.543203i
$832$	−0.292272	+	0.292272i	−0.0101327	+	0.0101327i
$833$	−12.6854	+	12.6854i	−0.439524	+	0.439524i
$834$	15.6094	+	23.6415i	0.540511	+	0.818637i
$835$			9.98436i			0.345523i
$836$	1.51739	−	1.51739i	0.0524801	−	0.0524801i
$837$	−3.92692	−	21.5973i	−0.135734	−	0.746512i
$838$	10.6485	−	10.6485i	0.367846	−	0.367846i
$839$	42.1619			1.45559			0.727796	−	0.685794i	$-0.240545\pi$
$839$	42.1619			1.45559			0.727796	+	0.685794i	$0.240545\pi$
$840$	6.70032	+	1.37110i	0.231183	+	0.0473076i
$841$			31.9767i			1.10264i
$842$	−25.9629			−0.894741
$843$	−2.31955	−	3.51311i	−0.0798897	−	0.120998i
$844$			23.4805i			0.808231i
$845$	−9.07158	−	9.07158i	−0.312072	−	0.312072i
$846$	14.5876	−	5.85537i	0.501534	−	0.201312i
$847$	41.3032			1.41920
$848$			1.95939i			0.0672857i
$849$	−2.32019	−	3.51406i	−0.0796286	−	0.120602i
$850$			2.08812i			0.0716220i
$851$	32.1293	−	0.389525i	1.10138	−	0.0133527i
$852$	0.324281	−	1.58470i	0.0111097	−	0.0542909i
$853$	8.85424	−	8.85424i	0.303163	−	0.303163i	−0.539087	−	0.842250i	$-0.681231\pi$
$853$	8.85424	−	8.85424i	0.303163	−	0.303163i	0.842250	+	0.539087i	$0.181231\pi$
$854$	16.4453			0.562745
$855$	8.05820	+	3.44208i	0.275585	+	0.117717i
$856$	−10.8599	−	10.8599i	−0.371182	−	0.371182i
$857$	−32.5449	+	32.5449i	−1.11171	+	1.11171i	−0.118795	+	0.992919i	$0.537903\pi$
$857$	−32.5449	+	32.5449i	−1.11171	+	1.11171i	−0.992919	+	0.118795i	$0.962097\pi$
$858$	0.515298	+	0.105447i	0.0175920	+	0.00359989i
$859$	−23.2767	−	23.2767i	−0.794190	−	0.794190i	0.187982	−	0.982172i	$-0.439805\pi$
$859$	−23.2767	−	23.2767i	−0.794190	−	0.794190i	−0.982172	+	0.187982i	$0.939805\pi$
$860$		−	2.09173i		−	0.0713275i
$861$	−0.417140	+	2.03848i	−0.0142161	+	0.0694712i
$862$			9.63135i			0.328045i
$863$			9.10784i			0.310035i	0.987912	+	0.155017i	$0.0495433\pi$
$863$			9.10784i			0.310035i	−0.987912	+	0.155017i	$0.950457\pi$
$864$	−5.11233	+	0.929548i	−0.173925	+	0.0316239i
$865$	5.83194	−	5.83194i	0.198292	−	0.198292i
$866$	6.73912	+	6.73912i	0.229005	+	0.229005i
$867$	−21.4482	−	4.38901i	−0.728420	−	0.149058i
$868$	−11.7953	−	11.7953i	−0.400358	−	0.400358i
$869$	5.24318	+	5.24318i	0.177863	+	0.177863i
$870$	11.2869	−	7.45225i	0.382662	−	0.252655i
$871$	0.252813	−	0.252813i	0.00856625	−	0.00856625i
$872$	9.73635			0.329715
$873$	14.9331	+	37.2033i	0.505410	+	1.25914i
$874$	10.9100	+	10.9100i	0.369038	+	0.369038i
$875$	2.79208	+	2.79208i	0.0943894	+	0.0943894i
$876$	1.01292	−	4.94993i	0.0342233	−	0.167243i
$877$	−4.47215			−0.151014			−0.0755069	−	0.997145i	$-0.524057\pi$
$877$	−4.47215			−0.151014			−0.0755069	+	0.997145i	$0.524057\pi$
$878$	−31.7089			−1.07012
$879$	29.1171	+	5.95830i	0.982094	+	0.200969i
$880$	−0.519503	+	0.519503i	−0.0175124	+	0.0175124i
$881$	16.1084			0.542706			0.271353	−	0.962480i	$-0.412529\pi$
$881$	16.1084			0.542706			0.271353	+	0.962480i	$0.412529\pi$
$882$	−9.60099	−	23.9192i	−0.323282	−	0.805402i
$883$	−17.4874	+	17.4874i	−0.588498	+	0.588498i	−0.937224	−	0.348727i	$-0.886614\pi$
$883$	−17.4874	+	17.4874i	−0.588498	+	0.588498i	0.348727	+	0.937224i	$0.386614\pi$
$884$			0.863094i			0.0290290i
$885$	−9.11850	−	1.86594i	−0.306515	−	0.0627230i
$886$	−4.55424	−	4.55424i	−0.153003	−	0.153003i
$887$	−57.2259			−1.92146			−0.960729	−	0.277488i	$-0.910498\pi$
$887$	−57.2259			−1.92146			−0.960729	+	0.277488i	$0.910498\pi$
$888$	−1.98689	+	10.3466i	−0.0666755	+	0.347209i
$889$	78.8528			2.64464
$890$	−2.74463	−	2.74463i	−0.0920004	−	0.0920004i
$891$	4.57161	+	4.77718i	0.153155	+	0.160042i
$892$		−	10.3252i		−	0.345713i
$893$	10.8217	−	10.8217i	0.362135	−	0.362135i
$894$	−4.31065	−	6.52874i	−0.144170	−	0.218354i
$895$	1.28542			0.0429668
$896$	−2.79208	+	2.79208i	−0.0932768	+	0.0932768i
$897$	−0.758162	+	3.70499i	−0.0253143	+	0.123706i
$898$	−30.5847			−1.02063
$899$	−32.9885			−1.10023
$900$	−2.75885	−	1.17845i	−0.0919617	−	0.0392816i
$901$	2.89309	+	2.89309i	0.0963828	+	0.0963828i
$902$	−0.158052	−	0.158052i	−0.00526254	−	0.00526254i
$903$	−11.9383	+	7.88233i	−0.397281	+	0.262307i
$904$	−10.0861			−0.335457
$905$	−13.3320	+	13.3320i	−0.443170	+	0.443170i
$906$	0.636266	+	0.963664i	0.0211385	+	0.0320156i
$907$	22.8941	+	22.8941i	0.760187	+	0.760187i	0.976356	−	0.216169i	$-0.0693562\pi$
$907$	22.8941	+	22.8941i	0.760187	+	0.760187i	−0.216169	+	0.976356i	$0.569356\pi$
$908$	−19.2638	−	19.2638i	−0.639293	−	0.639293i
$909$	−1.26849	−	0.541838i	−0.0420731	−	0.0179716i
$910$	1.15406	+	1.15406i	0.0382568	+	0.0382568i
$911$	23.8953	−	23.8953i	0.791685	−	0.791685i	−0.190083	−	0.981768i	$-0.560876\pi$
$911$	23.8953	−	23.8953i	0.791685	−	0.791685i	0.981768	+	0.190083i	$0.0608756\pi$
$912$	−4.22185	+	2.78750i	−0.139799	+	0.0923035i
$913$			12.5073i			0.413931i
$914$			32.6887i			1.08125i
$915$	−7.06726	−	1.44619i	−0.233637	−	0.0478097i
$916$			5.12830i			0.169444i
$917$	−13.8765	−	13.8765i	−0.458241	−	0.458241i
$918$	−6.17599	+	8.92099i	−0.203838	+	0.294437i
$919$	−7.98360	+	7.98360i	−0.263355	+	0.263355i	−0.826416	−	0.563061i	$-0.809624\pi$
$919$	−7.98360	+	7.98360i	−0.263355	+	0.263355i	0.563061	+	0.826416i	$0.309624\pi$
$920$	−3.73522	−	3.73522i	−0.123147	−	0.123147i
$921$	33.5939	+	6.87441i	1.10696	+	0.226520i
$922$	−22.1094			−0.728136
$923$	0.272949	−	0.272949i	0.00898422	−	0.00898422i
$924$	4.92264	+	1.00733i	0.161943	+	0.0331388i
$925$	−4.24870	+	4.35299i	−0.139697	+	0.143125i
$926$		−	24.2870i		−	0.798121i
$927$	−7.27184	+	2.91886i	−0.238839	+	0.0958680i
$928$			7.80876i			0.256335i
$929$	−33.0085			−1.08297			−0.541486	−	0.840709i	$-0.682138\pi$
$929$	−33.0085			−1.08297			−0.541486	+	0.840709i	$0.682138\pi$
$930$	4.03168	+	6.10623i	0.132204	+	0.200231i
$931$	−17.7443	−	17.7443i	−0.581546	−	0.581546i
$932$			3.70833i			0.121471i
$933$	27.9587	−	18.4600i	0.915328	−	0.604352i
$934$	16.0051			0.523704
$935$			1.53412i			0.0501710i
$936$	−1.14033	−	0.487095i	−0.0372728	−	0.0159212i
$937$	−37.3085			−1.21881			−0.609407	−	0.792858i	$-0.708592\pi$
$937$	−37.3085			−1.21881			−0.609407	+	0.792858i	$0.708592\pi$
$938$	2.41513	−	2.41513i	0.0788567	−	0.0788567i
$939$	11.7828	−	7.77969i	0.384518	−	0.253880i
$940$	−3.70499	+	3.70499i	−0.120843	+	0.120843i
$941$		−	6.85240i		−	0.223382i	−0.993743	−	0.111691i	$-0.964373\pi$
$941$		−	6.85240i		−	0.223382i	0.993743	−	0.111691i	$-0.0356267\pi$
$942$	6.53106	−	4.31218i	0.212793	−	0.140498i
$943$	1.13639	−	1.13639i	0.0370060	−	0.0370060i
$944$	3.79975	−	3.79975i	0.123671	−	0.123671i
$945$	3.67041	+	20.1865i	0.119398	+	0.656668i
$946$		−	1.53677i		−	0.0499647i
$947$	26.5403	−	26.5403i	0.862444	−	0.862444i	−0.129178	−	0.991621i	$-0.541234\pi$
$947$	26.5403	−	26.5403i	0.862444	−	0.862444i	0.991621	+	0.129178i	$0.0412338\pi$
$948$	−9.63192	−	14.5881i	−0.312830	−	0.473801i
$949$	0.852576	−	0.852576i	0.0276758	−	0.0276758i
$950$	−2.92086			−0.0947651
$951$	−2.29693	+	11.2247i	−0.0744832	+	0.363985i
$952$			8.24515i			0.267227i
$953$	−37.1910			−1.20474			−0.602368	−	0.798219i	$-0.705776\pi$
$953$	−37.1910			−1.20474			−0.602368	+	0.798219i	$0.705776\pi$
$954$	−5.45512	+	2.18964i	−0.176616	+	0.0708923i
$955$		−	4.80917i		−	0.155621i
$956$	−18.5198	−	18.5198i	−0.598973	−	0.598973i
$957$	8.29234	−	5.47508i	0.268053	−	0.176984i
$958$	37.5445			1.21301
$959$			51.9952i			1.67901i
$960$	1.44542	−	0.954345i	0.0466506	−	0.0308014i
$961$			13.1532i			0.424296i
$962$	−1.75614	+	1.79924i	−0.0566202	+	0.0580099i
$963$	18.0988	−	42.3709i	0.583226	−	1.36538i
$964$	−8.62974	+	8.62974i	−0.277945	+	0.277945i
$965$	17.1871			0.553273
$966$	−7.24273	+	35.3938i	−0.233031	+	1.13878i
$967$	12.6256	+	12.6256i	0.406010	+	0.406010i	0.880345	−	0.474334i	$-0.157311\pi$
$967$	12.6256	+	12.6256i	0.406010	+	0.406010i	−0.474334	+	0.880345i	$0.657311\pi$
$968$	7.39650	−	7.39650i	0.237733	−	0.237733i
$969$	−2.11784	+	10.3495i	−0.0680350	+	0.332474i
$970$	−9.44894	−	9.44894i	−0.303387	−	0.303387i
$971$			35.9561i			1.15389i	0.816785	+	0.576943i	$0.195754\pi$
$971$			35.9561i			1.15389i	−0.816785	+	0.576943i	$0.804246\pi$
$972$	−8.30104	−	13.1944i	−0.266256	−	0.423211i
$973$			64.5839i			2.07047i
$974$		−	43.3598i		−	1.38934i
$975$	−0.394465	−	0.597441i	−0.0126330	−	0.0191334i
$976$	2.94499	−	2.94499i	0.0942667	−	0.0942667i
$977$	19.0698	+	19.0698i	0.610098	+	0.610098i	0.942972	−	0.332873i	$-0.108018\pi$
$977$	19.0698	+	19.0698i	0.610098	+	0.610098i	−0.332873	+	0.942972i	$0.608018\pi$
$978$	3.79824	−	18.5612i	0.121454	−	0.593523i
$979$	−2.01645	−	2.01645i	−0.0644460	−	0.0644460i
$980$	6.07503	+	6.07503i	0.194060	+	0.194060i
$981$	10.8805	+	27.1069i	0.347388	+	0.865457i
$982$	−24.2881	+	24.2881i	−0.775063	+	0.775063i
$983$	−47.3904			−1.51152			−0.755759	−	0.654850i	$-0.772732\pi$
$983$	−47.3904			−1.51152			−0.755759	+	0.654850i	$0.772732\pi$
$984$	0.290347	+	0.439748i	0.00925591	+	0.0140186i
$985$	7.08965	+	7.08965i	0.225895	+	0.225895i
$986$	11.5298	+	11.5298i	0.367185	+	0.367185i
$987$	35.1073	+	7.18410i	1.11748	+	0.228672i
$988$	−1.20729			−0.0384091
$989$	11.0494			0.351350
$990$	−2.02689	−	0.865792i	−0.0644189	−	0.0275167i
$991$	3.91509	−	3.91509i	0.124367	−	0.124367i	−0.642184	−	0.766551i	$-0.721971\pi$
$991$	3.91509	−	3.91509i	0.124367	−	0.124367i	0.766551	+	0.642184i	$0.221971\pi$
$992$	−4.22455			−0.134130
$993$	49.4350	−	32.6398i	1.56877	−	1.03579i
$994$	2.60748	−	2.60748i	0.0827043	−	0.0827043i
$995$			25.2275i			0.799766i
$996$	5.91138	−	28.8878i	0.187309	−	0.915343i
$997$	−16.0959	−	16.0959i	−0.509764	−	0.509764i	0.404690	−	0.914454i	$-0.367379\pi$
$997$	−16.0959	−	16.0959i	−0.509764	−	0.509764i	−0.914454	+	0.404690i	$0.867379\pi$
$998$	3.31595			0.104965
$999$	−31.0263	+	6.03079i	−0.981628	+	0.190806i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.u.e.191.12	yes	40
3.2	odd	2	inner	1110.2.u.e.191.2	✓	40
37.31	odd	4	inner	1110.2.u.e.401.2	yes	40
111.68	even	4	inner	1110.2.u.e.401.12	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.u.e.191.2	✓	40	3.2	odd	2	inner
1110.2.u.e.191.12	yes	40	1.1	even	1	trivial
1110.2.u.e.401.2	yes	40	37.31	odd	4	inner
1110.2.u.e.401.12	yes	40	111.68	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:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.u (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(-0.347239 + 1.69689i) q^{3} +1.00000i q^{4} +(0.707107 - 0.707107i) q^{5} +(-1.44542 + 0.954345i) q^{6} -3.94859 q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.75885 - 1.17845i) q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(-0.347239 + 1.69689i) q^{3} +1.00000i q^{4} +(0.707107 - 0.707107i) q^{5} +(-1.44542 + 0.954345i) q^{6} -3.94859 q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.75885 - 1.17845i) q^{9} +1.00000 q^{10} +0.734688 q^{11} +(-1.69689 - 0.347239i) q^{12} +(-0.292272 - 0.292272i) q^{13} +(-2.79208 - 2.79208i) q^{14} +(0.954345 + 1.44542i) q^{15} -1.00000 q^{16} +(-1.47653 + 1.47653i) q^{17} +(-1.11751 - 2.78409i) q^{18} +(-2.06536 - 2.06536i) q^{19} +(0.707107 + 0.707107i) q^{20} +(1.37110 - 6.70032i) q^{21} +(0.519503 + 0.519503i) q^{22} +(-3.73522 + 3.73522i) q^{23} +(-0.954345 - 1.44542i) q^{24} -1.00000i q^{25} -0.413335i q^{26} +(2.95767 - 4.27225i) q^{27} -3.94859i q^{28} +(-5.52163 - 5.52163i) q^{29} +(-0.347239 + 1.69689i) q^{30} +(2.98721 - 2.98721i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-0.255112 + 1.24668i) q^{33} -2.08812 q^{34} +(-2.79208 + 2.79208i) q^{35} +(1.17845 - 2.75885i) q^{36} +(-4.35299 - 4.24870i) q^{37} -2.92086i q^{38} +(0.597441 - 0.394465i) q^{39} +1.00000i q^{40} -0.304236 q^{41} +(5.70736 - 3.76832i) q^{42} +(-1.47908 - 1.47908i) q^{43} +0.734688i q^{44} +(-2.78409 + 1.11751i) q^{45} -5.28241 q^{46} +5.23964i q^{47} +(0.347239 - 1.69689i) q^{48} +8.59139 q^{49} +(0.707107 - 0.707107i) q^{50} +(-1.99279 - 3.01820i) q^{51} +(0.292272 - 0.292272i) q^{52} -1.95939i q^{53} +(5.11233 - 0.929548i) q^{54} +(0.519503 - 0.519503i) q^{55} +(2.79208 - 2.79208i) q^{56} +(4.22185 - 2.78750i) q^{57} -7.80876i q^{58} +(-3.79975 + 3.79975i) q^{59} +(-1.44542 + 0.954345i) q^{60} +(-2.94499 + 2.94499i) q^{61} +4.22455 q^{62} +(10.8936 + 4.65322i) q^{63} -1.00000i q^{64} -0.413335 q^{65} +(-1.06193 + 0.701146i) q^{66} +0.864992i q^{67} +(-1.47653 - 1.47653i) q^{68} +(-5.04124 - 7.63527i) q^{69} -3.94859 q^{70} +0.933886i q^{71} +(2.78409 - 1.11751i) q^{72} +2.91706i q^{73} +(-0.0737400 - 6.08232i) q^{74} +(1.69689 + 0.347239i) q^{75} +(2.06536 - 2.06536i) q^{76} -2.90098 q^{77} +(0.701383 + 0.143526i) q^{78} +(7.13662 + 7.13662i) q^{79} +(-0.707107 + 0.707107i) q^{80} +(6.22251 + 6.50233i) q^{81} +(-0.215128 - 0.215128i) q^{82} +17.0240i q^{83} +(6.70032 + 1.37110i) q^{84} +2.08812i q^{85} -2.09173i q^{86} +(11.2869 - 7.45225i) q^{87} +(-0.519503 + 0.519503i) q^{88} +(-2.74463 - 2.74463i) q^{89} +(-2.75885 - 1.17845i) q^{90} +(1.15406 + 1.15406i) q^{91} +(-3.73522 - 3.73522i) q^{92} +(4.03168 + 6.10623i) q^{93} +(-3.70499 + 3.70499i) q^{94} -2.92086 q^{95} +(1.44542 - 0.954345i) q^{96} +(-9.44894 - 9.44894i) q^{97} +(6.07503 + 6.07503i) q^{98} +(-2.02689 - 0.865792i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 24 q^{7} - 8 q^{9}+O(q^{10}) \) 40 * q - 24 * q^7 - 8 * q^9	\( 40 q - 24 q^{7} - 8 q^{9} + 40 q^{10} - 8 q^{12} - 16 q^{13} - 40 q^{16} + 8 q^{18} + 16 q^{19} - 24 q^{31} + 24 q^{33} - 8 q^{34} + 16 q^{39} - 20 q^{42} - 32 q^{43} - 8 q^{45} + 72 q^{46} + 96 q^{49} + 20 q^{51} + 16 q^{52} + 24 q^{54} - 16 q^{57} + 40 q^{61} - 24 q^{63} - 44 q^{66} - 24 q^{70} + 8 q^{72} + 8 q^{75} - 16 q^{76} + 48 q^{79} + 24 q^{81} - 56 q^{82} - 8 q^{84} + 12 q^{87} - 8 q^{90} - 64 q^{91} + 12 q^{93} + 24 q^{94} + 8 q^{97}+O(q^{100}) \) 40 * q - 24 * q^7 - 8 * q^9 + 40 * q^10 - 8 * q^12 - 16 * q^13 - 40 * q^16 + 8 * q^18 + 16 * q^19 - 24 * q^31 + 24 * q^33 - 8 * q^34 + 16 * q^39 - 20 * q^42 - 32 * q^43 - 8 * q^45 + 72 * q^46 + 96 * q^49 + 20 * q^51 + 16 * q^52 + 24 * q^54 - 16 * q^57 + 40 * q^61 - 24 * q^63 - 44 * q^66 - 24 * q^70 + 8 * q^72 + 8 * q^75 - 16 * q^76 + 48 * q^79 + 24 * q^81 - 56 * q^82 - 8 * q^84 + 12 * q^87 - 8 * q^90 - 64 * q^91 + 12 * q^93 + 24 * q^94 + 8 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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