LMFDB - Embedded newform 1110.2.u.e.191.2

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			191.2
Character	$\chi$	$=$	1110.191
Dual form			1110.2.u.e.401.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(0.347239 + 1.69689i) q^{3} +1.00000i q^{4} +(-0.707107 + 0.707107i) q^{5} +(0.954345 - 1.44542i) q^{6} -3.94859 q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.75885 + 1.17845i) q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(0.347239 + 1.69689i) q^{3} +1.00000i q^{4} +(-0.707107 + 0.707107i) q^{5} +(0.954345 - 1.44542i) 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} +(-1.44542 - 0.954345i) q^{15} -1.00000 q^{16} +(1.47653 - 1.47653i) q^{17} +(2.78409 + 1.11751i) 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} +(1.44542 + 0.954345i) 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} +(0.394465 - 0.597441i) q^{39} +1.00000i q^{40} +0.304236 q^{41} +(-3.76832 + 5.70736i) q^{42} +(-1.47908 - 1.47908i) q^{43} -0.734688i q^{44} +(1.11751 - 2.78409i) 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} +(3.01820 + 1.99279i) q^{51} +(0.292272 - 0.292272i) q^{52} +1.95939i q^{53} +(-0.929548 + 5.11233i) q^{54} +(0.519503 - 0.519503i) q^{55} +(-2.79208 + 2.79208i) q^{56} +(2.78750 - 4.22185i) q^{57} -7.80876i q^{58} +(3.79975 - 3.79975i) q^{59} +(0.954345 - 1.44542i) 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} +(-0.701146 + 1.06193i) q^{66} +0.864992i q^{67} +(1.47653 + 1.47653i) q^{68} +(7.63527 + 5.04124i) q^{69} -3.94859 q^{70} -0.933886i q^{71} +(-1.11751 + 2.78409i) 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} +(-7.45225 + 11.2869i) 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} +(6.10623 + 4.03168i) q^{93} +(-3.70499 + 3.70499i) q^{94} +2.92086 q^{95} +(-0.954345 + 1.44542i) 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
$6$	0.954345	−	1.44542i	0.389610	−	0.590088i
$7$	−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	$-0.535328\pi$
$11$	−0.734688			−0.221517			−0.110758	+	0.993847i	$0.535328\pi$
$12$	−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
$15$	−1.44542	−	0.954345i	−0.373205	−	0.246411i
$16$	−1.00000			−0.250000
$17$	1.47653	−	1.47653i	0.358110	−	0.358110i	−0.505006	−	0.863116i	$-0.668510\pi$
$17$	1.47653	−	1.47653i	0.358110	−	0.358110i	0.863116	+	0.505006i	$0.168510\pi$
$18$	2.78409	+	1.11751i	0.656217	+	0.263400i
$19$	−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	−0.200787	−	0.979635i	$-0.564350\pi$
$23$	3.73522	−	3.73522i	0.778848	−	0.778848i	0.979635	+	0.200787i	$0.0643499\pi$
$24$	1.44542	+	0.954345i	0.295044	+	0.194805i
$25$		−	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	$0.00817180\pi$
$29$	5.52163	+	5.52163i	1.02534	+	1.02534i	0.0256696	+	0.999670i	$0.491828\pi$
$30$	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
$39$	0.394465	−	0.597441i	0.0631649	−	0.0956671i
$40$			1.00000i			0.158114i
$41$	0.304236			0.0475137			0.0237569	−	0.999718i	$-0.492437\pi$
$41$	0.304236			0.0475137			0.0237569	+	0.999718i	$0.492437\pi$
$42$	−3.76832	+	5.70736i	−0.581465	+	0.880664i
$43$	−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
$45$	1.11751	−	2.78409i	0.166589	−	0.415028i
$46$	−5.28241			−0.778848
$47$		−	5.23964i		−	0.764281i	−0.924104	−	0.382140i	$-0.875187\pi$
$47$		−	5.23964i		−	0.764281i	0.924104	−	0.382140i	$-0.124813\pi$
$48$	−0.347239	−	1.69689i	−0.0501196	−	0.244925i
$49$	8.59139			1.22734
$50$	−0.707107	+	0.707107i	−0.100000	+	0.100000i
$51$	3.01820	+	1.99279i	0.422633	+	0.279046i
$52$	0.292272	−	0.292272i	0.0405308	−	0.0405308i
$53$			1.95939i			0.269143i	0.990904	+	0.134571i	$0.0429658\pi$
$53$			1.95939i			0.269143i	−0.990904	+	0.134571i	$0.957034\pi$
$54$	−0.929548	+	5.11233i	−0.126495	+	0.695700i
$55$	0.519503	−	0.519503i	0.0700497	−	0.0700497i
$56$	−2.79208	+	2.79208i	−0.373107	+	0.373107i
$57$	2.78750	−	4.22185i	0.369214	−	0.559197i
$58$		−	7.80876i		−	1.02534i
$59$	3.79975	−	3.79975i	0.494686	−	0.494686i	−0.415093	−	0.909779i	$-0.636251\pi$
$59$	3.79975	−	3.79975i	0.494686	−	0.494686i	0.909779	+	0.415093i	$0.136251\pi$
$60$	0.954345	−	1.44542i	0.123205	−	0.186602i
$61$	−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
$66$	−0.701146	+	1.06193i	−0.0863051	+	0.130714i
$67$			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
$69$	7.63527	+	5.04124i	0.919178	+	0.606894i
$70$	−3.94859			−0.471947
$71$		−	0.933886i		−	0.110832i	−0.998463	−	0.0554159i	$-0.982352\pi$
$71$		−	0.933886i		−	0.110832i	0.998463	−	0.0554159i	$-0.0176485\pi$
$72$	−1.11751	+	2.78409i	−0.131700	+	0.328108i
$73$			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	$-0.616015\pi$
$83$		−	17.0240i		−	1.86862i	0.356457	−	0.934312i	$-0.383985\pi$
$84$	6.70032	−	1.37110i	0.731065	−	0.149600i
$85$			2.08812i			0.226489i
$86$			2.09173i			0.225557i
$87$	−7.45225	+	11.2869i	−0.798965	+	1.21008i
$88$	−0.519503	+	0.519503i	−0.0553792	+	0.0553792i
$89$	2.74463	+	2.74463i	0.290931	+	0.290931i	0.837448	−	0.546517i	$-0.184047\pi$
$89$	2.74463	+	2.74463i	0.290931	+	0.290931i	−0.546517	+	0.837448i	$0.684047\pi$
$90$	−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
$93$	6.10623	+	4.03168i	0.633187	+	0.418066i
$94$	−3.70499	+	3.70499i	−0.382140	+	0.382140i
$95$	2.92086			0.299673
$96$	−0.954345	+	1.44542i	−0.0974025	+	0.147522i
$97$	−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	$-0.507282\pi$
$101$	−0.459789			−0.0457507			−0.0228753	+	0.999738i	$0.507282\pi$
$102$	−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
$105$	5.70736	+	3.76832i	0.556981	+	0.367751i
$106$	1.38550	−	1.38550i	0.134571	−	0.134571i
$107$		−	15.3582i		−	1.48473i	−0.669996	−	0.742365i	$-0.733704\pi$
$107$		−	15.3582i		−	1.48473i	0.669996	−	0.742365i	$-0.266296\pi$
$108$	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
$111$	5.69805	−	8.86184i	0.540835	−	0.841129i
$112$	3.94859			0.373107
$113$	−7.13192	−	7.13192i	−0.670914	−	0.670914i	0.287012	−	0.957927i	$-0.407338\pi$
$113$	−7.13192	−	7.13192i	−0.670914	−	0.670914i	−0.957927	+	0.287012i	$0.907338\pi$
$114$	−4.95636	+	1.01423i	−0.464206	+	0.0949917i
$115$			5.28241i			0.492587i
$116$	−5.52163	+	5.52163i	−0.512670	+	0.512670i
$117$	1.15076	+	0.461907i	0.106388	+	0.0427033i
$118$	−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
$126$	−10.9932	−	4.41260i	−0.979356	−	0.393106i
$127$	−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
$129$	1.99624	−	3.02342i	0.175759	−	0.266197i
$130$	−0.292272	−	0.292272i	−0.0256340	−	0.0256340i
$131$	−3.51428	−	3.51428i	−0.307044	−	0.307044i	0.536718	−	0.843762i	$-0.319664\pi$
$131$	−3.51428	−	3.51428i	−0.307044	−	0.307044i	−0.843762	+	0.536718i	$0.819664\pi$
$132$	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
$135$	5.11233	+	0.929548i	0.439999	+	0.0800028i
$136$		−	2.08812i		−	0.179055i
$137$			13.1680i			1.12502i	0.826790	+	0.562510i	$0.190164\pi$
$137$			13.1680i			1.12502i	−0.826790	+	0.562510i	$0.809836\pi$
$138$	−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	$-0.940766\pi$
$149$		−	4.51686i		−	0.370036i	0.982735	−	0.185018i	$-0.0592343\pi$
$150$	−1.44542	−	0.954345i	−0.118018	−	0.0779220i
$151$		−	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
$153$	−2.33350	+	5.81352i	−0.188653	+	0.469996i
$154$	−2.05131	−	2.05131i	−0.165299	−	0.165299i
$155$			4.22455i			0.339324i
$156$	0.597441	+	0.394465i	0.0478335	+	0.0315824i
$157$	−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
$162$	−8.99782	+	0.197861i	−0.706936	+	0.0155454i
$163$	−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
$165$	1.06193	+	0.701146i	0.0826710	+	0.0545841i
$166$	−12.0378	+	12.0378i	−0.934312	+	0.934312i
$167$	7.06001	−	7.06001i	0.546320	−	0.546320i	−0.379054	−	0.925374i	$-0.623751\pi$
$167$	7.06001	−	7.06001i	0.546320	−	0.546320i	0.925374	+	0.379054i	$0.123751\pi$
$168$	−5.70736	−	3.76832i	−0.440332	−	0.290732i
$169$		−	12.8292i		−	0.986858i
$170$	1.47653	−	1.47653i	0.113244	−	0.113244i
$171$	8.13193	+	3.26409i	0.621864	+	0.249611i
$172$	1.47908	−	1.47908i	0.112779	−	0.112779i
$173$	−8.24761			−0.627054			−0.313527	−	0.949579i	$-0.601511\pi$
$173$	−8.24761			−0.627054			−0.313527	+	0.949579i	$0.601511\pi$
$174$	13.2506	−	2.71150i	1.00452	−	0.205558i
$175$			3.94859i			0.298486i
$176$	0.734688			0.0553792
$177$	7.76717	+	5.12833i	0.583816	+	0.385469i
$178$		−	3.88150i		−	0.290931i
$179$	−0.908928	−	0.908928i	−0.0679365	−	0.0679365i	0.672322	−	0.740259i	$-0.265297\pi$
$179$	−0.908928	−	0.908928i	−0.0679365	−	0.0679365i	−0.740259	+	0.672322i	$0.765297\pi$
$180$	2.78409	+	1.11751i	0.207514	+	0.0832945i
$181$	−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
$183$	−6.01992	−	3.97470i	−0.445006	−	0.293818i
$184$		−	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	−0.819351	−	0.573292i	$-0.805666\pi$
$191$	−3.40059	+	3.40059i	−0.246058	+	0.246058i	0.573292	+	0.819351i	$0.305666\pi$
$192$	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	$-0.883741\pi$
$197$		−	10.0263i		−	0.714343i	0.934039	−	0.357172i	$-0.116259\pi$
$198$	−2.04544	−	0.821023i	−0.145363	−	0.0583475i
$199$	−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
$204$	−1.99279	+	3.01820i	−0.139523	+	0.211317i
$205$	−0.215128	+	0.215128i	−0.0150252	+	0.0150252i
$206$	−2.61193			−0.181982
$207$	−5.90315	+	14.7067i	−0.410298	+	1.02219i
$208$	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
$216$	−5.11233	−	0.929548i	−0.347850	−	0.0632477i
$217$	−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
$222$	−10.2954	+	2.23714i	−0.690982	+	0.150147i
$223$	−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	$-0.390545\pi$
$227$	19.2638	−	19.2638i	1.27859	−	1.27859i	0.941460	−	0.337125i	$-0.109455\pi$
$228$	4.22185	+	2.78750i	0.279599	+	0.184607i
$229$	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	$-0.538761\pi$
$233$	−3.70833			−0.242941			−0.121471	+	0.992595i	$0.538761\pi$
$234$	−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
$237$	−9.63192	+	14.5881i	−0.625661	+	0.947601i
$238$	8.24515			0.534454
$239$	18.5198	−	18.5198i	1.19795	−	1.19795i	0.223165	−	0.974781i	$-0.428361\pi$
$239$	18.5198	−	18.5198i	1.19795	−	1.19795i	0.974781	−	0.223165i	$-0.0716388\pi$
$240$	1.44542	+	0.954345i	0.0933011	+	0.0616027i
$241$	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
$246$	0.290347	−	0.439748i	0.0185118	−	0.0280373i
$247$			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	0.546084	−	0.837731i	$-0.316118\pi$
$251$	−4.62056	−	4.62056i	−0.291647	−	0.291647i	−0.837731	+	0.546084i	$0.816118\pi$
$252$	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	−0.635486	−	0.772112i	$-0.719200\pi$
$257$	2.19029	−	2.19029i	0.136627	−	0.136627i	0.772112	+	0.635486i	$0.219200\pi$
$258$	−3.54943	+	0.726330i	−0.220978	+	0.0452194i
$259$	17.1882	+	16.7764i	1.06802	+	1.04244i
$260$			0.413335i			0.0256340i
$261$	−21.7403	−	8.72638i	−1.34569	−	0.540150i
$262$			4.96994i			0.307044i
$263$	−21.1251			−1.30263			−0.651313	−	0.758809i	$-0.725782\pi$
$263$	−21.1251			−1.30263			−0.651313	+	0.758809i	$0.725782\pi$
$264$	−1.06193	−	0.701146i	−0.0653572	−	0.0431526i
$265$	−1.38550	−	1.38550i	−0.0851105	−	0.0851105i
$266$		−	11.5333i		−	0.707150i
$267$	−3.70429	+	5.61038i	−0.226699	+	0.343350i
$268$	−0.864992			−0.0528378
$269$			29.9724i			1.82745i	0.406337	+	0.913723i	$0.366806\pi$
$269$			29.9724i			1.82745i	−0.406337	+	0.913723i	$0.633194\pi$
$270$	−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
$273$	−1.55758	+	2.35905i	−0.0942690	+	0.142776i
$274$	9.31120	−	9.31120i	0.562510	−	0.562510i
$275$			0.734688i			0.0443033i
$276$	−5.04124	+	7.63527i	−0.303447	+	0.459589i
$277$	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
$279$	−4.72099	+	11.7615i	−0.282638	+	0.704145i
$280$		−	3.94859i		−	0.235974i
$281$	1.71864	−	1.71864i	0.102525	−	0.102525i	−0.653984	−	0.756509i	$-0.726903\pi$
$281$	1.71864	−	1.71864i	0.102525	−	0.102525i	0.756509	+	0.653984i	$0.226903\pi$
$282$	−7.57346	−	5.00043i	−0.450993	−	0.297771i
$283$	−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
$288$	−2.78409	−	1.11751i	−0.164054	−	0.0658501i
$289$			12.6397i			0.743514i
$290$	5.52163	+	5.52163i	0.324241	+	0.324241i
$291$	12.7528	−	19.3148i	0.747580	−	1.13226i
$292$	−2.91706			−0.170708
$293$			17.1591i			1.00245i	0.865318	+	0.501223i	$0.167116\pi$
$293$			17.1591i			1.00245i	−0.865318	+	0.501223i	$0.832884\pi$
$294$	8.19916	−	12.4181i	0.478185	−	0.724240i
$295$			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
$309$	3.77532	+	2.49268i	0.214770	+	0.141804i
$310$	2.98721	−	2.98721i	0.169662	−	0.169662i
$311$	13.6776	+	13.6776i	0.775586	+	0.775586i	0.979077	−	0.203491i	$-0.0652288\pi$
$311$	13.6776	+	13.6776i	0.775586	+	0.775586i	−0.203491	+	0.979077i	$0.565229\pi$
$312$	−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
$315$	−4.41260	+	10.9932i	−0.248622	+	0.619399i
$316$	−7.13662	+	7.13662i	−0.401466	+	0.401466i
$317$	−6.61486			−0.371527			−0.185764	−	0.982594i	$-0.559476\pi$
$317$	−6.61486			−0.371527			−0.185764	+	0.982594i	$0.559476\pi$
$318$	2.83213	+	1.86994i	0.158818	+	0.104861i
$319$	−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
$327$	9.29185	−	14.0731i	0.513840	−	0.778243i
$328$	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
$333$	17.0161	+	6.59176i	0.932478	+	0.361226i
$334$	−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
$339$	9.62558	−	14.5785i	0.522790	−	0.791797i
$340$	−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	0.464135	−	0.885765i	$-0.346365\pi$
$347$	−7.85410	−	7.85410i	−0.421630	−	0.421630i	−0.885765	+	0.464135i	$0.846365\pi$
$348$	−11.2869	−	7.45225i	−0.605041	−	0.399483i
$349$	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
$351$	−0.384215	+	2.11311i	−0.0205079	+	0.112789i
$352$	−0.519503	−	0.519503i	−0.0276896	−	0.0276896i
$353$	−7.22156	−	7.22156i	−0.384365	−	0.384365i	0.488307	−	0.872672i	$-0.337615\pi$
$353$	−7.22156	−	7.22156i	−0.384365	−	0.384365i	−0.872672	+	0.488307i	$0.837615\pi$
$354$	−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
$357$	−11.9177	−	7.86872i	−0.630750	−	0.416457i
$358$			1.28542i			0.0679365i
$359$			34.9275i			1.84340i	0.387902	+	0.921701i	$0.373200\pi$
$359$			34.9275i			1.84340i	−0.387902	+	0.921701i	$0.626800\pi$
$360$	−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
$372$	−4.03168	+	6.10623i	−0.209033	+	0.316593i
$373$			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
$375$	−0.954345	+	1.44542i	−0.0492822	+	0.0746409i
$376$	−3.70499	−	3.70499i	−0.191070	−	0.191070i
$377$		−	3.22763i		−	0.166232i
$378$	3.67041	−	20.1865i	0.188785	−	1.03828i
$379$	−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	−0.993850	−	0.110737i	$-0.964679\pi$
$383$	−17.2829	+	17.2829i	−0.883112	+	0.883112i	0.110737	+	0.993850i	$0.464679\pi$
$384$	−1.44542	−	0.954345i	−0.0737610	−	0.0487012i
$385$	−2.05131	+	2.05131i	−0.104544	+	0.104544i
$386$		−	17.1871i		−	0.874802i
$387$	5.82358	+	2.33754i	0.296029	+	0.118824i
$388$	9.44894	−	9.44894i	0.479697	−	0.479697i
$389$	−13.9985	+	13.9985i	−0.709755	+	0.709755i	−0.966483	−	0.256729i	$-0.917355\pi$
$389$	−13.9985	+	13.9985i	−0.709755	+	0.709755i	0.256729	+	0.966483i	$0.417355\pi$
$390$	0.394465	−	0.597441i	0.0199745	−	0.0302526i
$391$		−	11.0303i		−	0.557827i
$392$	6.07503	−	6.07503i	0.306835	−	0.306835i
$393$	4.74304	−	7.18363i	0.239255	−	0.362366i
$394$	−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
$399$	−11.0067	+	16.6704i	−0.551025	+	0.834562i
$400$			1.00000i			0.0500000i
$401$	−18.5427	−	18.5427i	−0.925979	−	0.925979i	0.0714644	−	0.997443i	$-0.477233\pi$
$401$	−18.5427	−	18.5427i	−0.925979	−	0.925979i	−0.997443	+	0.0714644i	$0.977233\pi$
$402$	1.25027	+	0.825502i	0.0623580	+	0.0411723i
$403$	−1.74616			−0.0869822
$404$		−	0.459789i		−	0.0228753i
$405$	0.197861	+	8.99782i	0.00983179	+	0.447106i
$406$			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	$0.119905\pi$
$419$			15.0592i			0.735692i	−0.929887	+	0.367846i	$0.880095\pi$
$420$	−3.76832	+	5.70736i	−0.183875	+	0.278491i
$421$	−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
$426$	−1.34985	−	0.891250i	−0.0654006	−	0.0431812i
$427$	11.6286	−	11.6286i	0.562745	−	0.562745i
$428$	15.3582			0.742365
$429$	−0.289808	+	0.438932i	−0.0139921	+	0.0211919i
$430$	−1.47908	−	1.47908i	−0.0713275	−	0.0713275i
$431$	−6.81039	−	6.81039i	−0.328045	−	0.328045i	0.523798	−	0.851843i	$-0.324515\pi$
$431$	−6.81039	−	6.81039i	−0.328045	−	0.328045i	−0.851843	+	0.523798i	$0.824515\pi$
$432$	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
$438$	4.21637	+	2.78389i	0.201466	+	0.133019i
$439$	−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	$-0.451106\pi$
$443$	6.44067			0.306006			0.153003	+	0.988226i	$0.451106\pi$
$444$	8.86184	+	5.69805i	0.420565	+	0.270417i
$445$	−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	$-0.493365\pi$
$449$	21.6267	−	21.6267i	1.02063	−	1.02063i	0.999783	−	0.0208427i	$-0.00663492\pi$
$450$	1.11751	−	2.78409i	0.0526800	−	0.131243i
$451$	−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
$459$	−10.6752	−	1.94101i	−0.498275	−	0.0905986i
$460$	−5.28241			−0.246293
$461$	15.6337	−	15.6337i	0.728136	−	0.728136i	−0.242112	−	0.970248i	$-0.577840\pi$
$461$	15.6337	−	15.6337i	0.728136	−	0.728136i	0.970248	+	0.242112i	$0.0778403\pi$
$462$	2.76854	−	4.19313i	0.128804	−	0.195082i
$463$	−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	−0.918688	−	0.394984i	$-0.870750\pi$
$467$	−11.3173	+	11.3173i	−0.523704	+	0.523704i	0.394984	+	0.918688i	$0.370750\pi$
$468$	−0.461907	+	1.15076i	−0.0213517	+	0.0531940i
$469$		−	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	$0.578123\pi$
$479$	−26.5480	+	26.5480i	−1.21301	+	1.21301i	−0.970033	+	0.242974i	$0.921877\pi$
$480$	−0.347239	−	1.69689i	−0.0158492	−	0.0774519i
$481$	0.0304793	+	2.51403i	0.00138974	+	0.114630i
$482$		−	12.2043i		−	0.555890i
$483$	−30.1486	−	19.9058i	−1.37181	−	0.905746i
$484$		−	10.4602i		−	0.475465i
$485$	13.3628			0.606775
$486$	−3.46014	−	15.1996i	−0.156955	−	0.689467i
$487$	−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
$489$	−15.8105	−	10.4390i	−0.714977	−	0.472069i
$490$	8.59139			0.388120
$491$		−	34.3485i		−	1.55013i	−0.631884	−	0.775063i	$-0.717718\pi$
$491$		−	34.3485i		−	1.55013i	0.631884	−	0.775063i	$-0.282282\pi$
$492$	−0.516255	+	0.105643i	−0.0232746	+	0.00476274i
$493$	16.3056			0.734369
$494$	0.853684	−	0.853684i	0.0384091	−	0.0384091i
$495$	−0.821023	+	2.04544i	−0.0369022	+	0.0919356i
$496$	−2.98721	+	2.98721i	−0.134130	+	0.134130i
$497$			3.68754i			0.165409i
$498$	−24.6067	−	16.2467i	−1.10265	−	0.728034i
$499$	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
$501$	14.4315	+	9.52853i	0.644754	+	0.425703i
$502$			6.53446i			0.291647i
$503$	2.10055	−	2.10055i	0.0936591	−	0.0936591i	−0.658725	−	0.752384i	$-0.728904\pi$
$503$	2.10055	−	2.10055i	0.0936591	−	0.0936591i	0.752384	+	0.658725i	$0.228904\pi$
$504$	4.41260	−	10.9932i	0.196553	−	0.489678i
$505$	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	$-0.425449\pi$
$509$	10.4717			0.464149			0.232074	+	0.972698i	$0.425449\pi$
$510$	3.01820	+	1.99279i	0.133648	+	0.0882422i
$511$		−	11.5183i		−	0.509540i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−2.71508	+	14.9324i	−0.119874	+	0.659281i
$514$	−3.09754			−0.136627
$515$			2.61193i			0.115095i
$516$	3.02342	+	1.99624i	0.133099	+	0.0878794i
$517$			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	$-0.157572\pi$
$521$	40.1707			1.75991			0.879956	+	0.475056i	$0.157572\pi$
$522$	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
$531$	−6.00513	+	14.9608i	−0.260601	+	0.649242i
$532$	−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
$537$	1.22673	−	1.85796i	0.0529375	−	0.0801770i
$538$	21.1937	−	21.1937i	0.913723	−	0.913723i
$539$	−6.31199			−0.271877
$540$	−0.929548	+	5.11233i	−0.0400014	+	0.220000i
$541$	−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
$549$	4.65426	−	11.5953i	0.198639	−	0.494875i
$550$	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
$555$	2.23714	+	10.2954i	0.0949614	+	0.437015i
$556$	16.3562			0.693657
$557$	6.19261	+	6.19261i	0.262389	+	0.262389i	0.826024	−	0.563635i	$-0.190597\pi$
$557$	6.19261	+	6.19261i	0.262389	+	0.262389i	−0.563635	+	0.826024i	$0.690597\pi$
$558$	11.6549	−	4.97842i	0.493392	−	0.210753i
$559$			0.864587i			0.0365681i
$560$	−2.79208	+	2.79208i	−0.117987	+	0.117987i
$561$	−2.21744	−	1.46408i	−0.0936203	−	0.0618135i
$562$	−2.43052			−0.102525
$563$	−10.5672	+	10.5672i	−0.445356	+	0.445356i	−0.893807	−	0.448452i	$-0.851976\pi$
$563$	−10.5672	+	10.5672i	−0.445356	+	0.445356i	0.448452	+	0.893807i	$0.351976\pi$
$564$	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	0.243742	−	0.969840i	$-0.421625\pi$
$569$	−17.3202	−	17.3202i	−0.726098	−	0.726098i	−0.969840	+	0.243742i	$0.921625\pi$
$570$	2.78750	−	4.22185i	0.116756	−	0.176834i
$571$	−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
$573$	−6.95124	−	4.58961i	−0.290392	−	0.191734i
$574$	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
$579$	−16.4025	+	24.8425i	−0.681663	+	1.03242i
$580$		−	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	0.378726	−	0.925509i	$-0.376362\pi$
$587$	−13.2475	−	13.2475i	−0.546783	−	0.546783i	−0.925509	+	0.378726i	$0.876362\pi$
$588$	−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	$0.288746\pi$
$593$			38.3651i			1.57547i	−0.616016	+	0.787734i	$0.711254\pi$
$594$	0.682928	−	3.75597i	0.0280209	−	0.154109i
$595$		−	8.24515i		−	0.338018i
$596$	4.51686			0.185018
$597$	−36.4642	−	24.0758i	−1.49238	−	0.985356i
$598$	1.54390	+	1.54390i	0.0631347	+	0.0631347i
$599$		−	37.1450i		−	1.51770i	−0.651264	−	0.758851i	$-0.725761\pi$
$599$		−	37.1450i		−	1.51770i	0.651264	−	0.758851i	$-0.274239\pi$
$600$	0.954345	−	1.44542i	0.0389610	−	0.0590088i
$601$	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
$606$	−0.438797	+	0.664585i	−0.0178249	+	0.0269969i
$607$	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
$609$	29.4259	−	44.5674i	1.19240	−	1.80596i
$610$	−2.94499	+	2.94499i	−0.119239	+	0.119239i
$611$	−1.53140	+	1.53140i	−0.0619539	+	0.0619539i
$612$	−5.81352	−	2.33350i	−0.234998	−	0.0943263i
$613$		−	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
$615$	−0.439748	−	0.290347i	−0.0177323	−	0.0117079i
$616$	2.05131	−	2.05131i	0.0826494	−	0.0826494i
$617$	1.38704			0.0558402			0.0279201	−	0.999610i	$-0.491112\pi$
$617$	1.38704			0.0558402			0.0279201	+	0.999610i	$0.491112\pi$
$618$	−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
$621$	−27.0054	−	4.91025i	−1.08369	−	0.197042i
$622$		−	19.3431i		−	0.775586i
$623$	−10.8374	−	10.8374i	−0.434193	−	0.434193i
$624$	−0.394465	+	0.597441i	−0.0157912	+	0.0239168i
$625$	−1.00000			−0.0400000
$626$			8.15186i			0.325814i
$627$	−2.04795	+	3.10174i	−0.0817871	+	0.123872i
$628$		−	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	$-0.799585\pi$
$641$		−	29.8165i		−	1.17768i	0.808249	−	0.588840i	$-0.200415\pi$
$642$	−22.1989	−	14.6570i	−0.876121	−	0.578465i
$643$	−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	0.845822	−	0.533465i	$-0.179110\pi$
$647$	7.94518	+	7.94518i	0.312357	+	0.312357i	−0.533465	+	0.845822i	$0.679110\pi$
$648$	−0.197861	−	8.99782i	−0.00777271	−	0.353468i
$649$	−2.79163	+	2.79163i	−0.109581	+	0.109581i
$650$	0.413335			0.0162123
$651$	−24.1110	−	15.9195i	−0.944986	−	0.623933i
$652$	−7.73462	−	7.73462i	−0.302911	−	0.302911i
$653$	1.70851	+	1.70851i	0.0668591	+	0.0668591i	0.739746	−	0.672887i	$-0.234946\pi$
$653$	1.70851	+	1.70851i	0.0668591	+	0.0668591i	−0.672887	+	0.739746i	$0.734946\pi$
$654$	−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	$-0.888431\pi$
$659$	−48.2204			−1.87840			−0.939199	+	0.343372i	$0.888431\pi$
$660$	−0.701146	+	1.06193i	−0.0272921	+	0.0413355i
$661$	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
$666$	−7.37114	−	16.6933i	−0.285626	−	0.646852i
$667$	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
$672$	3.76832	−	5.70736i	0.145366	−	0.220166i
$673$	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	$-0.321635\pi$
$677$	27.6576			1.06297			0.531484	+	0.847068i	$0.321635\pi$
$678$	−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
$681$	39.3777	+	25.9994i	1.50896	+	0.996299i
$682$	3.10373			0.118848
$683$	−8.19870	+	8.19870i	−0.313715	+	0.313715i	−0.846347	−	0.532632i	$-0.821203\pi$
$683$	−8.19870	+	8.19870i	−0.313715	+	0.313715i	0.532632	+	0.846347i	$0.321203\pi$
$684$	−3.26409	+	8.13193i	−0.124806	+	0.310932i
$685$	−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
$690$	7.63527	+	5.04124i	0.290670	+	0.191917i
$691$			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	−0.565311	−	0.824878i	$-0.691244\pi$
$701$	6.87240	−	6.87240i	0.259567	−	0.259567i	0.824878	+	0.565311i	$0.191244\pi$
$702$	1.76587	−	1.22251i	0.0666486	−	0.0461407i
$703$	0.215384	+	17.7656i	0.00812336	+	0.670041i
$704$			0.734688i			0.0276896i
$705$	−5.00043	+	7.57346i	−0.188327	+	0.285233i
$706$			10.2128i			0.384365i
$707$	1.81552			0.0682796
$708$	−5.12833	+	7.76717i	−0.192734	+	0.291908i
$709$	−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
$711$	−28.0990	−	11.2787i	−1.05379	−	0.422985i
$712$	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
$717$	37.8568	+	24.9952i	1.41379	+	0.933463i
$718$	24.6974	−	24.6974i	0.921701	−	0.921701i
$719$			0.0958633i			0.00357510i	0.999998	+	0.00178755i	$0.000568995\pi$
$719$			0.0958633i			0.00357510i	−0.999998	+	0.00178755i	$0.999431\pi$
$720$	−1.11751	+	2.78409i	−0.0416472	+	0.103757i
$721$	−7.29270	+	7.29270i	−0.271594	+	0.271594i
$722$	−7.40242	+	7.40242i	−0.275490	+	0.275490i
$723$	−11.6471	+	17.6403i	−0.433161	+	0.656048i
$724$		−	18.8543i		−	0.700714i
$725$	5.52163	−	5.52163i	0.205068	−	0.205068i
$726$	−9.98268	+	15.1194i	−0.370492	+	0.561133i
$727$	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
$732$	3.97470	−	6.01992i	0.146909	−	0.222503i
$733$			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
$735$	−12.4181	−	8.19916i	−0.458050	−	0.302431i
$736$	5.28241			0.194712
$737$		−	0.635499i		−	0.0234089i
$738$	0.847022	+	0.339988i	0.0311793	+	0.0125151i
$739$		−	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	$-0.170413\pi$
$743$	46.8882			1.72016			0.860081	+	0.510158i	$0.170413\pi$
$744$	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
$753$	6.23613	−	9.44500i	0.227257	−	0.344195i
$754$	−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
$759$	−5.60954	−	3.70374i	−0.203613	−	0.134437i
$760$	2.06536	−	2.06536i	0.0749184	−	0.0749184i
$761$	−7.45409			−0.270211			−0.135105	−	0.990831i	$-0.543137\pi$
$761$	−7.45409			−0.270211			−0.135105	+	0.990831i	$0.543137\pi$
$762$	−19.0581	+	28.8647i	−0.690403	+	1.04566i
$763$	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
$771$	4.47723	+	2.95612i	0.161243	+	0.106462i
$772$	−12.1531	+	12.1531i	−0.437401	+	0.437401i
$773$			16.5922i			0.596781i	0.954444	+	0.298390i	$0.0964497\pi$
$773$			16.5922i			0.596781i	−0.954444	+	0.298390i	$0.903550\pi$
$774$	−2.46500	−	5.77078i	−0.0886026	−	0.207426i
$775$	−2.98721	−	2.98721i	−0.107304	−	0.107304i
$776$	−13.3628			−0.479697
$777$	−22.4993	+	34.9918i	−0.807157	+	1.25532i
$778$	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
$783$	7.25862	−	39.9210i	0.259402	−	1.42666i
$784$	−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
$792$	0.821023	−	2.04544i	0.0291738	−	0.0726815i
$793$	1.72148			0.0611314
$794$	−18.7182	+	18.7182i	−0.664285	+	0.664285i
$795$	1.86994	−	2.83213i	0.0663198	−	0.100445i
$796$	−17.8385	−	17.8385i	−0.632271	−	0.632271i
$797$	22.9666	+	22.9666i	0.813518	+	0.813518i	0.985160	−	0.171641i	$-0.0549069\pi$
$797$	22.9666	+	22.9666i	0.813518	+	0.813518i	−0.171641	+	0.985160i	$0.554907\pi$
$798$	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
$801$	−10.8065	−	4.33762i	−0.381827	−	0.153262i
$802$			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	0.842575	−	0.538579i	$-0.181039\pi$
$809$	8.64653	+	8.64653i	0.303996	+	0.303996i	−0.538579	+	0.842575i	$0.681039\pi$
$810$	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
$816$	−3.01820	−	1.99279i	−0.105658	−	0.0697616i
$817$			6.10965i			0.213750i
$818$	−22.8275			−0.798144
$819$	−4.54390	−	1.82388i	−0.158777	−	0.0637317i
$820$	−0.215128	−	0.215128i	−0.00751258	−	0.00751258i
$821$		−	20.8710i		−	0.728402i	−0.931320	−	0.364201i	$-0.881342\pi$
$821$		−	20.8710i		−	0.728402i	0.931320	−	0.364201i	$-0.118658\pi$
$822$	19.0333	+	12.5668i	0.663861	+	0.438319i
$823$	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	−0.639430	−	0.768849i	$-0.720830\pi$
$827$	3.72180	−	3.72180i	0.129420	−	0.129420i	0.768849	+	0.639430i	$0.220830\pi$
$828$	−14.7067	−	5.90315i	−0.511093	−	0.205149i
$829$	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
$831$	15.6589	+	10.3389i	0.543203	+	0.358653i
$832$	−0.292272	+	0.292272i	−0.0101327	+	0.0101327i
$833$	12.6854	−	12.6854i	0.439524	−	0.439524i
$834$	−23.6415	−	15.6094i	−0.818637	−	0.540511i
$835$			9.98436i			0.345523i
$836$	−1.51739	+	1.51739i	−0.0524801	+	0.0524801i
$837$	−21.5973	−	3.92692i	−0.746512	−	0.135734i
$838$	10.6485	−	10.6485i	0.367846	−	0.367846i
$839$	−42.1619			−1.45559			−0.727796	−	0.685794i	$-0.759455\pi$
$839$	−42.1619			−1.45559			−0.727796	+	0.685794i	$0.759455\pi$
$840$	6.70032	−	1.37110i	0.231183	−	0.0473076i
$841$			31.9767i			1.10264i
$842$	25.9629			0.894741
$843$	3.51311	+	2.31955i	0.120998	+	0.0798897i
$844$			23.4805i			0.808231i
$845$	9.07158	+	9.07158i	0.312072	+	0.312072i
$846$	5.85537	−	14.5876i	0.201312	−	0.501534i
$847$	41.3032			1.41920
$848$		−	1.95939i		−	0.0672857i
$849$	−3.51406	−	2.32019i	−0.120602	−	0.0796286i
$850$			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	$-0.462097\pi$
$857$	32.5449	−	32.5449i	1.11171	−	1.11171i	0.992919	−	0.118795i	$-0.0379032\pi$
$858$	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	$-0.950457\pi$
$863$		−	9.10784i		−	0.310035i	0.987912	−	0.155017i	$-0.0495433\pi$
$864$	0.929548	−	5.11233i	0.0316239	−	0.173925i
$865$	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
$870$	−7.45225	+	11.2869i	−0.252655	+	0.382662i
$871$	0.252813	−	0.252813i	0.00856625	−	0.00856625i
$872$	−9.73635			−0.329715
$873$	37.2033	+	14.9331i	1.25914	+	0.505410i
$874$	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	$-0.587471\pi$
$881$	−16.1084			−0.542706			−0.271353	+	0.962480i	$0.587471\pi$
$882$	23.9192	+	9.60099i	0.805402	+	0.323282i
$883$	−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	$-0.0895019\pi$
$887$	57.2259			1.92146			0.960729	+	0.277488i	$0.0895019\pi$
$888$	−2.23714	−	10.2954i	−0.0750736	−	0.345491i
$889$	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
$894$	−6.52874	−	4.31065i	−0.218354	−	0.144170i
$895$	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
$903$	−7.88233	+	11.9383i	−0.262307	+	0.397281i
$904$	−10.0861			−0.335457
$905$	13.3320	−	13.3320i	0.443170	−	0.443170i
$906$	−0.963664	−	0.636266i	−0.0320156	−	0.0211385i
$907$	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	−0.981768	−	0.190083i	$-0.939124\pi$
$911$	−23.8953	+	23.8953i	−0.791685	+	0.791685i	0.190083	+	0.981768i	$0.439124\pi$
$912$	−2.78750	+	4.22185i	−0.0923035	+	0.139799i
$913$			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
$927$	−2.91886	+	7.27184i	−0.0958680	+	0.238839i
$928$			7.80876i			0.256335i
$929$	33.0085			1.08297			0.541486	−	0.840709i	$-0.317862\pi$
$929$	33.0085			1.08297			0.541486	+	0.840709i	$0.317862\pi$
$930$	6.10623	+	4.03168i	0.200231	+	0.132204i
$931$	−17.7443	−	17.7443i	−0.581546	−	0.581546i
$932$		−	3.70833i		−	0.121471i
$933$	−18.4600	+	27.9587i	−0.604352	+	0.915328i
$934$	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
$939$	7.77969	−	11.7828i	0.253880	−	0.384518i
$940$	−3.70499	+	3.70499i	−0.120843	+	0.120843i
$941$			6.85240i			0.223382i	0.993743	+	0.111691i	$0.0356267\pi$
$941$			6.85240i			0.223382i	−0.993743	+	0.111691i	$0.964373\pi$
$942$	−4.31218	+	6.53106i	−0.140498	+	0.212793i
$943$	1.13639	−	1.13639i	0.0370060	−	0.0370060i
$944$	−3.79975	+	3.79975i	−0.123671	+	0.123671i
$945$	−20.1865	−	3.67041i	−0.656668	−	0.119398i
$946$		−	1.53677i		−	0.0499647i
$947$	−26.5403	+	26.5403i	−0.862444	+	0.862444i	−0.991621	−	0.129178i	$-0.958766\pi$
$947$	−26.5403	+	26.5403i	−0.862444	+	0.862444i	0.129178	+	0.991621i	$0.458766\pi$
$948$	−14.5881	−	9.63192i	−0.473801	−	0.312830i
$949$	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	$-0.294224\pi$
$953$	37.1910			1.20474			0.602368	+	0.798219i	$0.294224\pi$
$954$	−2.18964	+	5.45512i	−0.0708923	+	0.176616i
$955$		−	4.80917i		−	0.155621i
$956$	18.5198	+	18.5198i	0.598973	+	0.598973i
$957$	5.47508	−	8.29234i	0.176984	−	0.268053i
$958$	37.5445			1.21301
$959$		−	51.9952i		−	1.67901i
$960$	−0.954345	+	1.44542i	−0.0308014	+	0.0466506i
$961$			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	$-0.804246\pi$
$971$		−	35.9561i		−	1.15389i	0.816785	−	0.576943i	$-0.195754\pi$
$972$	−8.30104	+	13.1944i	−0.266256	+	0.423211i
$973$			64.5839i			2.07047i
$974$			43.3598i			1.38934i
$975$	−0.597441	−	0.394465i	−0.0191334	−	0.0126330i
$976$	2.94499	−	2.94499i	0.0942667	−	0.0942667i
$977$	−19.0698	−	19.0698i	−0.610098	−	0.610098i	0.332873	−	0.942972i	$-0.391982\pi$
$977$	−19.0698	−	19.0698i	−0.610098	−	0.610098i	−0.942972	+	0.332873i	$0.891982\pi$
$978$	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
$981$	27.1069	+	10.8805i	0.865457	+	0.347388i
$982$	−24.2881	+	24.2881i	−0.775063	+	0.775063i
$983$	47.3904			1.51152			0.755759	−	0.654850i	$-0.227268\pi$
$983$	47.3904			1.51152			0.755759	+	0.654850i	$0.227268\pi$
$984$	0.439748	+	0.290347i	0.0140186	+	0.00925591i
$985$	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
$993$	32.6398	−	49.4350i	1.03579	−	1.56877i
$994$	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
$999$	−5.27682	+	31.1634i	−0.166951	+	0.985965i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(0.347239 + 1.69689i) q^{3} +1.00000i q^{4} +(-0.707107 + 0.707107i) q^{5} +(0.954345 - 1.44542i) q^{6} -3.94859 q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.75885 + 1.17845i) q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(0.347239 + 1.69689i) q^{3} +1.00000i q^{4} +(-0.707107 + 0.707107i) q^{5} +(0.954345 - 1.44542i) 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} +(-1.44542 - 0.954345i) q^{15} -1.00000 q^{16} +(1.47653 - 1.47653i) q^{17} +(2.78409 + 1.11751i) 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} +(1.44542 + 0.954345i) 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} +(0.394465 - 0.597441i) q^{39} +1.00000i q^{40} +0.304236 q^{41} +(-3.76832 + 5.70736i) q^{42} +(-1.47908 - 1.47908i) q^{43} -0.734688i q^{44} +(1.11751 - 2.78409i) 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} +(3.01820 + 1.99279i) q^{51} +(0.292272 - 0.292272i) q^{52} +1.95939i q^{53} +(-0.929548 + 5.11233i) q^{54} +(0.519503 - 0.519503i) q^{55} +(-2.79208 + 2.79208i) q^{56} +(2.78750 - 4.22185i) q^{57} -7.80876i q^{58} +(3.79975 - 3.79975i) q^{59} +(0.954345 - 1.44542i) 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} +(-0.701146 + 1.06193i) q^{66} +0.864992i q^{67} +(1.47653 + 1.47653i) q^{68} +(7.63527 + 5.04124i) q^{69} -3.94859 q^{70} -0.933886i q^{71} +(-1.11751 + 2.78409i) 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} +(-7.45225 + 11.2869i) 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} +(6.10623 + 4.03168i) q^{93} +(-3.70499 + 3.70499i) q^{94} +2.92086 q^{95} +(-0.954345 + 1.44542i) 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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