LMFDB - Embedded newform 1110.2.l.a.697.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(43,1110)]

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([0, 3, 3]))

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

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

chi := DirichletCharacter("1110.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.l (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			697.4
Character	$\chi$	$=$	1110.697
Dual form			1110.2.l.a.43.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(1.11117 - 1.94044i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(0.636201 + 0.636201i) q^{7} +1.00000i q^{8} +1.00000i q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(1.11117 - 1.94044i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(0.636201 + 0.636201i) q^{7} +1.00000i q^{8} +1.00000i q^{9} +(-1.94044 - 1.11117i) q^{10} +2.26858i q^{11} +(0.707107 + 0.707107i) q^{12} -1.29147i q^{13} +(0.636201 - 0.636201i) q^{14} +(-2.15781 + 0.586380i) q^{15} +1.00000 q^{16} -5.74699 q^{17} +1.00000 q^{18} +(-4.10165 - 4.10165i) q^{19} +(-1.11117 + 1.94044i) q^{20} -0.899724i q^{21} +2.26858 q^{22} -8.53431i q^{23} +(0.707107 - 0.707107i) q^{24} +(-2.53060 - 4.31232i) q^{25} -1.29147 q^{26} +(0.707107 - 0.707107i) q^{27} +(-0.636201 - 0.636201i) q^{28} +(-1.70155 + 1.70155i) q^{29} +(0.586380 + 2.15781i) q^{30} +(-5.81155 - 5.81155i) q^{31} -1.00000i q^{32} +(1.60413 - 1.60413i) q^{33} +5.74699i q^{34} +(1.94144 - 0.527580i) q^{35} -1.00000i q^{36} +(5.19618 + 3.16223i) q^{37} +(-4.10165 + 4.10165i) q^{38} +(-0.913209 + 0.913209i) q^{39} +(1.94044 + 1.11117i) q^{40} +9.02011i q^{41} -0.899724 q^{42} -0.853087i q^{43} -2.26858i q^{44} +(1.94044 + 1.11117i) q^{45} -8.53431 q^{46} +(-0.326713 - 0.326713i) q^{47} +(-0.707107 - 0.707107i) q^{48} -6.19050i q^{49} +(-4.31232 + 2.53060i) q^{50} +(4.06374 + 4.06374i) q^{51} +1.29147i q^{52} +(-6.79864 + 6.79864i) q^{53} +(-0.707107 - 0.707107i) q^{54} +(4.40204 + 2.52078i) q^{55} +(-0.636201 + 0.636201i) q^{56} +5.80061i q^{57} +(1.70155 + 1.70155i) q^{58} +(3.51171 + 3.51171i) q^{59} +(2.15781 - 0.586380i) q^{60} +(-2.06460 - 2.06460i) q^{61} +(-5.81155 + 5.81155i) q^{62} +(-0.636201 + 0.636201i) q^{63} -1.00000 q^{64} +(-2.50602 - 1.43505i) q^{65} +(-1.60413 - 1.60413i) q^{66} +(3.98347 - 3.98347i) q^{67} +5.74699 q^{68} +(-6.03467 + 6.03467i) q^{69} +(-0.527580 - 1.94144i) q^{70} -15.2892 q^{71} -1.00000 q^{72} +(-11.8322 - 11.8322i) q^{73} +(3.16223 - 5.19618i) q^{74} +(-1.25987 + 4.83867i) q^{75} +(4.10165 + 4.10165i) q^{76} +(-1.44327 + 1.44327i) q^{77} +(0.913209 + 0.913209i) q^{78} +(9.04382 + 9.04382i) q^{79} +(1.11117 - 1.94044i) q^{80} -1.00000 q^{81} +9.02011 q^{82} +(9.12362 - 9.12362i) q^{83} +0.899724i q^{84} +(-6.38589 + 11.1517i) q^{85} -0.853087 q^{86} +2.40635 q^{87} -2.26858 q^{88} +(-6.32382 + 6.32382i) q^{89} +(1.11117 - 1.94044i) q^{90} +(0.821636 - 0.821636i) q^{91} +8.53431i q^{92} +8.21877i q^{93} +(-0.326713 + 0.326713i) q^{94} +(-12.5166 + 3.40136i) q^{95} +(-0.707107 + 0.707107i) q^{96} +9.28197 q^{97} -6.19050 q^{98} -2.26858 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 36 q^{4} + 4 q^{7}+O(q^{10}) $ 36 * q - 36 * q^4 + 4 * q^7	$ 36 q - 36 q^{4} + 4 q^{7} - 4 q^{10} + 4 q^{14} + 36 q^{16} - 32 q^{17} + 36 q^{18} + 4 q^{19} + 8 q^{22} - 4 q^{25} + 8 q^{26} - 4 q^{28} + 36 q^{29} - 4 q^{31} + 4 q^{33} - 12 q^{35} - 4 q^{37} + 4 q^{38} + 4 q^{39} + 4 q^{40} - 16 q^{42} + 4 q^{45} + 16 q^{47} - 16 q^{50} - 8 q^{53} + 16 q^{55} - 4 q^{56} - 36 q^{58} - 4 q^{59} - 4 q^{61} - 4 q^{62} - 4 q^{63} - 36 q^{64} + 52 q^{65} - 4 q^{66} + 16 q^{67} + 32 q^{68} - 8 q^{69} - 28 q^{70} - 8 q^{71} - 36 q^{72} - 4 q^{73} + 28 q^{74} + 16 q^{75} - 4 q^{76} + 8 q^{77} - 4 q^{78} - 12 q^{79} - 36 q^{81} - 8 q^{82} + 8 q^{83} + 8 q^{85} + 32 q^{86} - 8 q^{87} - 8 q^{88} - 24 q^{89} + 56 q^{91} + 16 q^{94} - 20 q^{95} + 40 q^{97} - 12 q^{98} - 8 q^{99}+O(q^{100}) $ 36 * q - 36 * q^4 + 4 * q^7 - 4 * q^10 + 4 * q^14 + 36 * q^16 - 32 * q^17 + 36 * q^18 + 4 * q^19 + 8 * q^22 - 4 * q^25 + 8 * q^26 - 4 * q^28 + 36 * q^29 - 4 * q^31 + 4 * q^33 - 12 * q^35 - 4 * q^37 + 4 * q^38 + 4 * q^39 + 4 * q^40 - 16 * q^42 + 4 * q^45 + 16 * q^47 - 16 * q^50 - 8 * q^53 + 16 * q^55 - 4 * q^56 - 36 * q^58 - 4 * q^59 - 4 * q^61 - 4 * q^62 - 4 * q^63 - 36 * q^64 + 52 * q^65 - 4 * q^66 + 16 * q^67 + 32 * q^68 - 8 * q^69 - 28 * q^70 - 8 * q^71 - 36 * q^72 - 4 * q^73 + 28 * q^74 + 16 * q^75 - 4 * q^76 + 8 * q^77 - 4 * q^78 - 12 * q^79 - 36 * q^81 - 8 * q^82 + 8 * q^83 + 8 * q^85 + 32 * q^86 - 8 * q^87 - 8 * q^88 - 24 * q^89 + 56 * q^91 + 16 * q^94 - 20 * q^95 + 40 * q^97 - 12 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$4$	−1.00000			−0.500000
$5$	1.11117	−	1.94044i	0.496931	−	0.867790i
$5$	1.11117	−	1.94044i	0.496931	−	0.867790i
$6$	−0.707107	+	0.707107i	−0.288675	+	0.288675i
$7$	0.636201	+	0.636201i	0.240461	+	0.240461i	0.817041	−	0.576580i	$-0.195613\pi$
$7$	0.636201	+	0.636201i	0.240461	+	0.240461i	−0.576580	+	0.817041i	$0.695613\pi$
$8$			1.00000i			0.353553i
$9$			1.00000i			0.333333i
$10$	−1.94044	−	1.11117i	−0.613620	−	0.351383i
$11$			2.26858i			0.684003i	0.939699	+	0.342002i	$0.111105\pi$
$11$			2.26858i			0.684003i	−0.939699	+	0.342002i	$0.888895\pi$
$12$	0.707107	+	0.707107i	0.204124	+	0.204124i
$13$		−	1.29147i		−	0.358190i	−0.983832	−	0.179095i	$-0.942683\pi$
$13$		−	1.29147i		−	0.358190i	0.983832	−	0.179095i	$-0.0573169\pi$
$14$	0.636201	−	0.636201i	0.170032	−	0.170032i
$15$	−2.15781	+	0.586380i	−0.557145	+	0.151403i
$16$	1.00000			0.250000
$17$	−5.74699			−1.39385			−0.696925	−	0.717144i	$-0.745449\pi$
$17$	−5.74699			−1.39385			−0.696925	+	0.717144i	$0.745449\pi$
$18$	1.00000			0.235702
$19$	−4.10165	−	4.10165i	−0.940982	−	0.940982i	0.0573705	−	0.998353i	$-0.481728\pi$
$19$	−4.10165	−	4.10165i	−0.940982	−	0.940982i	−0.998353	+	0.0573705i	$0.981728\pi$
$20$	−1.11117	+	1.94044i	−0.248465	+	0.433895i
$21$		−	0.899724i		−	0.196336i
$22$	2.26858			0.483663
$23$		−	8.53431i		−	1.77953i	−0.456423	−	0.889763i	$-0.650869\pi$
$23$		−	8.53431i		−	1.77953i	0.456423	−	0.889763i	$-0.349131\pi$
$24$	0.707107	−	0.707107i	0.144338	−	0.144338i
$25$	−2.53060	−	4.31232i	−0.506119	−	0.862464i
$26$	−1.29147			−0.253278
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	−0.636201	−	0.636201i	−0.120231	−	0.120231i
$29$	−1.70155	+	1.70155i	−0.315969	+	0.315969i	−0.847217	−	0.531247i	$-0.821723\pi$
$29$	−1.70155	+	1.70155i	−0.315969	+	0.315969i	0.531247	+	0.847217i	$0.321723\pi$
$30$	0.586380	+	2.15781i	0.107058	+	0.393961i
$31$	−5.81155	−	5.81155i	−1.04379	−	1.04379i	−0.998996	−	0.0447888i	$-0.985739\pi$
$31$	−5.81155	−	5.81155i	−1.04379	−	1.04379i	−0.0447888	−	0.998996i	$-0.514261\pi$
$32$		−	1.00000i		−	0.176777i
$33$	1.60413	−	1.60413i	0.279243	−	0.279243i
$34$			5.74699i			0.985601i
$35$	1.94144	−	0.527580i	0.328163	−	0.0891773i
$36$		−	1.00000i		−	0.166667i
$37$	5.19618	+	3.16223i	0.854247	+	0.519868i
$37$	5.19618	+	3.16223i	0.854247	+	0.519868i
$38$	−4.10165	+	4.10165i	−0.665375	+	0.665375i
$39$	−0.913209	+	0.913209i	−0.146230	+	0.146230i
$40$	1.94044	+	1.11117i	0.306810	+	0.175692i
$41$			9.02011i			1.40870i	0.709851	+	0.704352i	$0.248762\pi$
$41$			9.02011i			1.40870i	−0.709851	+	0.704352i	$0.751238\pi$
$42$	−0.899724			−0.138830
$43$		−	0.853087i		−	0.130094i	−0.997882	−	0.0650472i	$-0.979280\pi$
$43$		−	0.853087i		−	0.130094i	0.997882	−	0.0650472i	$-0.0207198\pi$
$44$		−	2.26858i		−	0.342002i
$45$	1.94044	+	1.11117i	0.289263	+	0.165644i
$46$	−8.53431			−1.25832
$47$	−0.326713	−	0.326713i	−0.0476560	−	0.0476560i	0.682877	−	0.730533i	$-0.260728\pi$
$47$	−0.326713	−	0.326713i	−0.0476560	−	0.0476560i	−0.730533	+	0.682877i	$0.760728\pi$
$48$	−0.707107	−	0.707107i	−0.102062	−	0.102062i
$49$		−	6.19050i		−	0.884357i
$50$	−4.31232	+	2.53060i	−0.609854	+	0.357880i
$51$	4.06374	+	4.06374i	0.569037	+	0.569037i
$52$			1.29147i			0.179095i
$53$	−6.79864	+	6.79864i	−0.933866	+	0.933866i	−0.997945	−	0.0640792i	$-0.979589\pi$
$53$	−6.79864	+	6.79864i	−0.933866	+	0.933866i	0.0640792	+	0.997945i	$0.479589\pi$
$54$	−0.707107	−	0.707107i	−0.0962250	−	0.0962250i
$55$	4.40204	+	2.52078i	0.593571	+	0.339902i
$56$	−0.636201	+	0.636201i	−0.0850159	+	0.0850159i
$57$			5.80061i			0.768309i
$58$	1.70155	+	1.70155i	0.223424	+	0.223424i
$59$	3.51171	+	3.51171i	0.457186	+	0.457186i	0.897731	−	0.440545i	$-0.145215\pi$
$59$	3.51171	+	3.51171i	0.457186	+	0.457186i	−0.440545	+	0.897731i	$0.645215\pi$
$60$	2.15781	−	0.586380i	0.278573	−	0.0757013i
$61$	−2.06460	−	2.06460i	−0.264345	−	0.264345i	0.562472	−	0.826817i	$-0.309851\pi$
$61$	−2.06460	−	2.06460i	−0.264345	−	0.264345i	−0.826817	+	0.562472i	$0.809851\pi$
$62$	−5.81155	+	5.81155i	−0.738068	+	0.738068i
$63$	−0.636201	+	0.636201i	−0.0801538	+	0.0801538i
$64$	−1.00000			−0.125000
$65$	−2.50602	−	1.43505i	−0.310834	−	0.177996i
$66$	−1.60413	−	1.60413i	−0.197455	−	0.197455i
$67$	3.98347	−	3.98347i	0.486659	−	0.486659i	−0.420591	−	0.907250i	$-0.638177\pi$
$67$	3.98347	−	3.98347i	0.486659	−	0.486659i	0.907250	+	0.420591i	$0.138177\pi$
$68$	5.74699			0.696925
$69$	−6.03467	+	6.03467i	−0.726489	+	0.726489i
$70$	−0.527580	−	1.94144i	−0.0630579	−	0.232046i
$71$	−15.2892			−1.81450			−0.907248	−	0.420596i	$-0.861821\pi$
$71$	−15.2892			−1.81450			−0.907248	+	0.420596i	$0.861821\pi$
$72$	−1.00000			−0.117851
$73$	−11.8322	−	11.8322i	−1.38486	−	1.38486i	−0.835751	−	0.549108i	$-0.814968\pi$
$73$	−11.8322	−	11.8322i	−1.38486	−	1.38486i	−0.549108	−	0.835751i	$-0.685032\pi$
$74$	3.16223	−	5.19618i	0.367602	−	0.604044i
$75$	−1.25987	+	4.83867i	−0.145477	+	0.558722i
$76$	4.10165	+	4.10165i	0.470491	+	0.470491i
$77$	−1.44327	+	1.44327i	−0.164476	+	0.164476i
$78$	0.913209	+	0.913209i	0.103401	+	0.103401i
$79$	9.04382	+	9.04382i	1.01751	+	1.01751i	0.999844	+	0.0176652i	$0.00562329\pi$
$79$	9.04382	+	9.04382i	1.01751	+	1.01751i	0.0176652	+	0.999844i	$0.494377\pi$
$80$	1.11117	−	1.94044i	0.124233	−	0.216948i
$81$	−1.00000			−0.111111
$82$	9.02011			0.996104
$83$	9.12362	−	9.12362i	1.00145	−	1.00145i	0.00144791	−	0.999999i	$-0.499539\pi$
$83$	9.12362	−	9.12362i	1.00145	−	1.00145i	0.999999	−	0.00144791i	$-0.000460883\pi$
$84$			0.899724i			0.0981680i
$85$	−6.38589	+	11.1517i	−0.692647	+	1.20957i
$86$	−0.853087			−0.0919907
$87$	2.40635			0.257988
$88$	−2.26858			−0.241832
$89$	−6.32382	+	6.32382i	−0.670323	+	0.670323i	−0.957791	−	0.287467i	$-0.907187\pi$
$89$	−6.32382	+	6.32382i	−0.670323	+	0.670323i	0.287467	+	0.957791i	$0.407187\pi$
$90$	1.11117	−	1.94044i	0.117128	−	0.204540i
$91$	0.821636	−	0.821636i	0.0861308	−	0.0861308i
$92$			8.53431i			0.889763i
$93$			8.21877i			0.852247i
$94$	−0.326713	+	0.326713i	−0.0336979	+	0.0336979i
$95$	−12.5166	+	3.40136i	−1.28418	+	0.348972i
$96$	−0.707107	+	0.707107i	−0.0721688	+	0.0721688i
$97$	9.28197			0.942441			0.471220	−	0.882015i	$-0.343814\pi$
$97$	9.28197			0.942441			0.471220	+	0.882015i	$0.343814\pi$
$98$	−6.19050			−0.625335
$99$	−2.26858			−0.228001
$100$	2.53060	+	4.31232i	0.253060	+	0.431232i
$101$			1.47408i			0.146677i	0.997307	+	0.0733383i	$0.0233653\pi$
$101$			1.47408i			0.146677i	−0.997307	+	0.0733383i	$0.976635\pi$
$102$	4.06374	−	4.06374i	0.402370	−	0.402370i
$103$	1.02968			0.101458			0.0507289	−	0.998712i	$-0.483846\pi$
$103$	1.02968			0.101458			0.0507289	+	0.998712i	$0.483846\pi$
$104$	1.29147			0.126639
$105$	−1.74586	−	0.999748i	−0.170378	−	0.0975654i
$106$	6.79864	+	6.79864i	0.660343	+	0.660343i
$107$	−13.8598	−	13.8598i	−1.33988	−	1.33988i	−0.896171	−	0.443708i	$-0.853663\pi$
$107$	−13.8598	−	13.8598i	−1.33988	−	1.33988i	−0.443708	−	0.896171i	$-0.646337\pi$
$108$	−0.707107	+	0.707107i	−0.0680414	+	0.0680414i
$109$	5.32683	+	5.32683i	0.510218	+	0.510218i	0.914593	−	0.404375i	$-0.132511\pi$
$109$	5.32683	+	5.32683i	0.510218	+	0.510218i	−0.404375	+	0.914593i	$0.632511\pi$
$110$	2.52078	−	4.40204i	0.240347	−	0.419718i
$111$	−1.43822	−	5.91029i	−0.136510	−	0.560980i
$112$	0.636201	+	0.636201i	0.0601153	+	0.0601153i
$113$	17.2755			1.62515			0.812573	−	0.582859i	$-0.198066\pi$
$113$	17.2755			1.62515			0.812573	+	0.582859i	$0.198066\pi$
$114$	5.80061			0.543276
$115$	−16.5603	−	9.48308i	−1.54426	−	0.884302i
$116$	1.70155	−	1.70155i	0.157985	−	0.157985i
$117$	1.29147			0.119397
$118$	3.51171	−	3.51171i	0.323279	−	0.323279i
$119$	−3.65624	−	3.65624i	−0.335167	−	0.335167i
$120$	−0.586380	−	2.15781i	−0.0535289	−	0.196981i
$121$	5.85354			0.532140
$122$	−2.06460	+	2.06460i	−0.186920	+	0.186920i
$123$	6.37818	−	6.37818i	0.575101	−	0.575101i
$124$	5.81155	+	5.81155i	0.521893	+	0.521893i
$125$	−11.1797	+	0.118740i	−0.999944	+	0.0106204i
$126$	0.636201	+	0.636201i	0.0566773	+	0.0566773i
$127$	0.916380	+	0.916380i	0.0813156	+	0.0813156i	0.746595	−	0.665279i	$-0.231687\pi$
$127$	0.916380	+	0.916380i	0.0813156	+	0.0813156i	−0.665279	+	0.746595i	$0.731687\pi$
$128$			1.00000i			0.0883883i
$129$	−0.603223	+	0.603223i	−0.0531109	+	0.0531109i
$130$	−1.43505	+	2.50602i	−0.125862	+	0.219793i
$131$	−6.28943	−	6.28943i	−0.549510	−	0.549510i	0.376789	−	0.926299i	$-0.377028\pi$
$131$	−6.28943	−	6.28943i	−0.549510	−	0.549510i	−0.926299	+	0.376789i	$0.877028\pi$
$132$	−1.60413	+	1.60413i	−0.139622	+	0.139622i
$133$		−	5.21895i		−	0.452540i
$134$	−3.98347	−	3.98347i	−0.344120	−	0.344120i
$135$	−0.586380	−	2.15781i	−0.0504675	−	0.185715i
$136$		−	5.74699i		−	0.492800i
$137$	10.4523	+	10.4523i	0.893004	+	0.893004i	0.994805	−	0.101801i	$-0.0324605\pi$
$137$	10.4523	+	10.4523i	0.893004	+	0.893004i	−0.101801	+	0.994805i	$0.532461\pi$
$138$	6.03467	+	6.03467i	0.513705	+	0.513705i
$139$	−14.4443			−1.22515			−0.612574	−	0.790414i	$-0.709866\pi$
$139$	−14.4443			−1.22515			−0.612574	+	0.790414i	$0.709866\pi$
$140$	−1.94144	+	0.527580i	−0.164081	+	0.0445887i
$141$			0.462042i			0.0389110i
$142$			15.2892i			1.28304i
$143$	2.92981			0.245003
$144$			1.00000i			0.0833333i
$145$	1.41104	+	5.19246i	0.117180	+	0.431210i
$146$	−11.8322	+	11.8322i	−0.979243	+	0.979243i
$147$	−4.37734	+	4.37734i	−0.361037	+	0.361037i
$148$	−5.19618	−	3.16223i	−0.427123	−	0.259934i
$149$		−	19.0997i		−	1.56471i	−0.622831	−	0.782356i	$-0.714018\pi$
$149$		−	19.0997i		−	1.56471i	0.622831	−	0.782356i	$-0.285982\pi$
$150$	4.83867	+	1.25987i	0.395076	+	0.102868i
$151$		−	3.42513i		−	0.278733i	−0.990241	−	0.139367i	$-0.955493\pi$
$151$		−	3.42513i		−	0.278733i	0.990241	−	0.139367i	$-0.0445067\pi$
$152$	4.10165	−	4.10165i	0.332688	−	0.332688i
$153$		−	5.74699i		−	0.464617i
$154$	1.44327	+	1.44327i	0.116302	+	0.116302i
$155$	−17.7346	+	4.81932i	−1.42448	+	0.387097i
$156$	0.913209	−	0.913209i	0.0731152	−	0.0731152i
$157$	12.1068	+	12.1068i	0.966232	+	0.966232i	0.999448	−	0.0332164i	$-0.0105751\pi$
$157$	12.1068	+	12.1068i	0.966232	+	0.966232i	−0.0332164	+	0.999448i	$0.510575\pi$
$158$	9.04382	−	9.04382i	0.719488	−	0.719488i
$159$	9.61473			0.762498
$160$	−1.94044	−	1.11117i	−0.153405	−	0.0878458i
$161$	5.42954	−	5.42954i	0.427907	−	0.427907i
$162$			1.00000i			0.0785674i
$163$	24.2268			1.89759			0.948795	−	0.315894i	$-0.102304\pi$
$163$	24.2268			1.89759			0.948795	+	0.315894i	$0.102304\pi$
$164$		−	9.02011i		−	0.704352i
$165$	−1.33025	−	4.89518i	−0.103560	−	0.381089i
$166$	−9.12362	−	9.12362i	−0.708130	−	0.708130i
$167$	9.66372			0.747801			0.373900	−	0.927469i	$-0.378020\pi$
$167$	9.66372			0.747801			0.373900	+	0.927469i	$0.378020\pi$
$168$	0.899724			0.0694152
$169$	11.3321			0.871700
$170$	11.1517	+	6.38589i	0.855295	+	0.489776i
$171$	4.10165	−	4.10165i	0.313661	−	0.313661i
$172$			0.853087i			0.0650472i
$173$	−6.77556	−	6.77556i	−0.515136	−	0.515136i	0.400959	−	0.916096i	$-0.368677\pi$
$173$	−6.77556	−	6.77556i	−0.515136	−	0.515136i	−0.916096	+	0.400959i	$0.868677\pi$
$174$		−	2.40635i		−	0.182425i
$175$	1.13353	−	4.35347i	0.0856870	−	0.329091i
$176$			2.26858i			0.171001i
$177$		−	4.96631i		−	0.373290i
$178$	6.32382	+	6.32382i	0.473990	+	0.473990i
$179$	7.36463	−	7.36463i	0.550458	−	0.550458i	−0.376115	−	0.926573i	$-0.622740\pi$
$179$	7.36463	−	7.36463i	0.550458	−	0.550458i	0.926573	+	0.376115i	$0.122740\pi$
$180$	−1.94044	−	1.11117i	−0.144632	−	0.0828218i
$181$	−13.9651			−1.03802			−0.519008	−	0.854769i	$-0.673699\pi$
$181$	−13.9651			−1.03802			−0.519008	+	0.854769i	$0.673699\pi$
$182$	−0.821636	−	0.821636i	−0.0609037	−	0.0609037i
$183$			2.91979i			0.215837i
$184$	8.53431			0.629158
$185$	11.9100	−	6.56908i	0.875638	−	0.482969i
$186$	8.21877			0.602630
$187$		−	13.0375i		−	0.953398i
$188$	0.326713	+	0.326713i	0.0238280	+	0.0238280i
$189$	0.899724			0.0654453
$190$	3.40136	+	12.5166i	0.246760	+	0.908051i
$191$	−11.6459	+	11.6459i	−0.842665	+	0.842665i	−0.989205	−	0.146540i	$-0.953186\pi$
$191$	−11.6459	+	11.6459i	−0.842665	+	0.842665i	0.146540	+	0.989205i	$0.453186\pi$
$192$	0.707107	+	0.707107i	0.0510310	+	0.0510310i
$193$			2.80664i			0.202026i	0.994885	+	0.101013i	$0.0322084\pi$
$193$			2.80664i			0.202026i	−0.994885	+	0.101013i	$0.967792\pi$
$194$		−	9.28197i		−	0.666406i
$195$	0.757293	+	2.78676i	0.0542309	+	0.199564i
$196$			6.19050i			0.442178i
$197$	11.5183	+	11.5183i	0.820643	+	0.820643i	0.986200	−	0.165557i	$-0.0529422\pi$
$197$	11.5183	+	11.5183i	0.820643	+	0.820643i	−0.165557	+	0.986200i	$0.552942\pi$
$198$			2.26858i			0.161221i
$199$	10.3470	−	10.3470i	0.733481	−	0.733481i	−0.237827	−	0.971308i	$-0.576435\pi$
$199$	10.3470	−	10.3470i	0.733481	−	0.733481i	0.971308	+	0.237827i	$0.0764350\pi$
$200$	4.31232	−	2.53060i	0.304927	−	0.178940i
$201$	−5.63348			−0.397355
$202$	1.47408			0.103716
$203$	−2.16505			−0.151957
$204$	−4.06374	−	4.06374i	−0.284518	−	0.284518i
$205$	17.5030	+	10.0229i	1.22246	+	0.700029i
$206$		−	1.02968i		−	0.0717414i
$207$	8.53431			0.593175
$208$		−	1.29147i		−	0.0895475i
$209$	9.30492	−	9.30492i	0.643635	−	0.643635i
$210$	−0.999748	+	1.74586i	−0.0689892	+	0.120476i
$211$	−3.80993			−0.262286			−0.131143	−	0.991363i	$-0.541865\pi$
$211$	−3.80993			−0.262286			−0.131143	+	0.991363i	$0.541865\pi$
$212$	6.79864	−	6.79864i	0.466933	−	0.466933i
$213$	10.8111	+	10.8111i	0.740765	+	0.740765i
$214$	−13.8598	+	13.8598i	−0.947438	+	0.947438i
$215$	−1.65536	−	0.947925i	−0.112895	−	0.0646480i
$216$	0.707107	+	0.707107i	0.0481125	+	0.0481125i
$217$		−	7.39463i		−	0.501980i
$218$	5.32683	−	5.32683i	0.360779	−	0.360779i
$219$			16.7333i			1.13073i
$220$	−4.40204	−	2.52078i	−0.296786	−	0.169951i
$221$			7.42208i			0.499263i
$222$	−5.91029	+	1.43822i	−0.396673	+	0.0965269i
$223$	16.8923	−	16.8923i	1.13119	−	1.13119i	0.141210	−	0.989980i	$-0.454901\pi$
$223$	16.8923	−	16.8923i	1.13119	−	1.13119i	0.989980	−	0.141210i	$-0.0450992\pi$
$224$	0.636201	−	0.636201i	0.0425080	−	0.0425080i
$225$	4.31232	−	2.53060i	0.287488	−	0.168706i
$226$		−	17.2755i		−	1.14915i
$227$	−25.0030			−1.65950			−0.829752	−	0.558132i	$-0.811518\pi$
$227$	−25.0030			−1.65950			−0.829752	+	0.558132i	$0.811518\pi$
$228$		−	5.80061i		−	0.384154i
$229$		−	11.3572i		−	0.750503i	−0.926923	−	0.375252i	$-0.877556\pi$
$229$		−	11.3572i		−	0.750503i	0.926923	−	0.375252i	$-0.122444\pi$
$230$	−9.48308	+	16.5603i	−0.625296	+	1.09195i
$231$	2.04110			0.134294
$232$	−1.70155	−	1.70155i	−0.111712	−	0.111712i
$233$	4.77274	+	4.77274i	0.312673	+	0.312673i	0.845944	−	0.533271i	$-0.179038\pi$
$233$	4.77274	+	4.77274i	0.312673	+	0.312673i	−0.533271	+	0.845944i	$0.679038\pi$
$234$		−	1.29147i		−	0.0844262i
$235$	−0.997001	+	0.270932i	−0.0650371	+	0.0176737i
$236$	−3.51171	−	3.51171i	−0.228593	−	0.228593i
$237$		−	12.7899i		−	0.830793i
$238$	−3.65624	+	3.65624i	−0.236999	+	0.236999i
$239$	−2.96858	−	2.96858i	−0.192022	−	0.192022i	0.604547	−	0.796569i	$-0.293354\pi$
$239$	−2.96858	−	2.96858i	−0.192022	−	0.192022i	−0.796569	+	0.604547i	$0.793354\pi$
$240$	−2.15781	+	0.586380i	−0.139286	+	0.0378507i
$241$	−5.75647	+	5.75647i	−0.370807	+	0.370807i	−0.867771	−	0.496964i	$-0.834448\pi$
$241$	−5.75647	+	5.75647i	−0.370807	+	0.370807i	0.496964	+	0.867771i	$0.334448\pi$
$242$		−	5.85354i		−	0.376279i
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$	2.06460	+	2.06460i	0.132172	+	0.132172i
$245$	−12.0123	−	6.87870i	−0.767436	−	0.439464i
$246$	−6.37818	−	6.37818i	−0.406658	−	0.406658i
$247$	−5.29716	+	5.29716i	−0.337050	+	0.337050i
$248$	5.81155	−	5.81155i	0.369034	−	0.369034i
$249$	−12.9027			−0.817678
$250$	0.118740	+	11.1797i	0.00750979	+	0.707067i
$251$	−14.7749	−	14.7749i	−0.932584	−	0.932584i	0.0652824	−	0.997867i	$-0.479205\pi$
$251$	−14.7749	−	14.7749i	−0.932584	−	0.932584i	−0.997867	+	0.0652824i	$0.979205\pi$
$252$	0.636201	−	0.636201i	0.0400769	−	0.0400769i
$253$	19.3608			1.21720
$254$	0.916380	−	0.916380i	0.0574988	−	0.0574988i
$255$	12.4009	−	3.36992i	0.776577	−	0.211033i
$256$	1.00000			0.0625000
$257$	1.80027			0.112298			0.0561488	−	0.998422i	$-0.482118\pi$
$257$	1.80027			0.112298			0.0561488	+	0.998422i	$0.482118\pi$
$258$	0.603223	+	0.603223i	0.0375550	+	0.0375550i
$259$	1.29400	+	5.31763i	0.0804053	+	0.330421i
$260$	2.50602	+	1.43505i	0.155417	+	0.0889978i
$261$	−1.70155	−	1.70155i	−0.105323	−	0.105323i
$262$	−6.28943	+	6.28943i	−0.388563	+	0.388563i
$263$	−9.25899	−	9.25899i	−0.570934	−	0.570934i	0.361456	−	0.932389i	$-0.382280\pi$
$263$	−9.25899	−	9.25899i	−0.570934	−	0.570934i	−0.932389	+	0.361456i	$0.882280\pi$
$264$	1.60413	+	1.60413i	0.0987274	+	0.0987274i
$265$	5.63789	+	20.7468i	0.346333	+	1.27447i
$266$	−5.21895			−0.319994
$267$	8.94323			0.547317
$268$	−3.98347	+	3.98347i	−0.243329	+	0.243329i
$269$			0.689017i			0.0420101i	0.999779	+	0.0210051i	$0.00668661\pi$
$269$			0.689017i			0.0420101i	−0.999779	+	0.0210051i	$0.993313\pi$
$270$	−2.15781	+	0.586380i	−0.131320	+	0.0356859i
$271$	−14.7629			−0.896783			−0.448392	−	0.893837i	$-0.648003\pi$
$271$	−14.7629			−0.896783			−0.448392	+	0.893837i	$0.648003\pi$
$272$	−5.74699			−0.348462
$273$	−1.16197			−0.0703255
$274$	10.4523	−	10.4523i	0.631449	−	0.631449i
$275$	9.78285	−	5.74087i	0.589928	−	0.346187i
$276$	6.03467	−	6.03467i	0.363244	−	0.363244i
$277$		−	32.3771i		−	1.94535i	−0.232172	−	0.972675i	$-0.574583\pi$
$277$		−	32.3771i		−	1.94535i	0.232172	−	0.972675i	$-0.425417\pi$
$278$			14.4443i			0.866310i
$279$	5.81155	−	5.81155i	0.347928	−	0.347928i
$280$	0.527580	+	1.94144i	0.0315289	+	0.116023i
$281$	5.74725	−	5.74725i	0.342852	−	0.342852i	−0.514586	−	0.857439i	$-0.672054\pi$
$281$	5.74725	−	5.74725i	0.342852	−	0.342852i	0.857439	+	0.514586i	$0.172054\pi$
$282$	0.462042			0.0275142
$283$	6.56809			0.390433			0.195216	−	0.980760i	$-0.437459\pi$
$283$	6.56809			0.390433			0.195216	+	0.980760i	$0.437459\pi$
$284$	15.2892			0.907248
$285$	11.2557	+	6.44547i	0.666731	+	0.381797i
$286$		−	2.92981i		−	0.173243i
$287$	−5.73860	+	5.73860i	−0.338739	+	0.338739i
$288$	1.00000			0.0589256
$289$	16.0279			0.942818
$290$	5.19246	−	1.41104i	0.304912	−	0.0828589i
$291$	−6.56334	−	6.56334i	−0.384750	−	0.384750i
$292$	11.8322	+	11.8322i	0.692430	+	0.692430i
$293$	−22.0187	+	22.0187i	−1.28634	+	1.28634i	−0.349353	+	0.936991i	$0.613599\pi$
$293$	−22.0187	+	22.0187i	−1.28634	+	1.28634i	−0.936991	+	0.349353i	$0.886401\pi$
$294$	4.37734	+	4.37734i	0.255292	+	0.255292i
$295$	10.7164	−	2.91214i	0.623931	−	0.169551i
$296$	−3.16223	+	5.19618i	−0.183801	+	0.302022i
$297$	1.60413	+	1.60413i	0.0930811	+	0.0930811i
$298$	−19.0997			−1.10642
$299$	−11.0218			−0.637408
$300$	1.25987	−	4.83867i	0.0727385	−	0.279361i
$301$	0.542735	−	0.542735i	0.0312827	−	0.0312827i
$302$	−3.42513			−0.197094
$303$	1.04233	−	1.04233i	0.0598805	−	0.0598805i
$304$	−4.10165	−	4.10165i	−0.235246	−	0.235246i
$305$	−6.30035	+	1.71210i	−0.360757	+	0.0980347i
$306$	−5.74699			−0.328534
$307$	5.03677	−	5.03677i	0.287464	−	0.287464i	−0.548613	−	0.836077i	$-0.684844\pi$
$307$	5.03677	−	5.03677i	0.287464	−	0.287464i	0.836077	+	0.548613i	$0.184844\pi$
$308$	1.44327	−	1.44327i	0.0822382	−	0.0822382i
$309$	−0.728096	−	0.728096i	−0.0414199	−	0.0414199i
$310$	4.81932	+	17.7346i	0.273719	+	1.00726i
$311$	3.85553	+	3.85553i	0.218627	+	0.218627i	0.807920	−	0.589293i	$-0.200594\pi$
$311$	3.85553	+	3.85553i	0.218627	+	0.218627i	−0.589293	+	0.807920i	$0.700594\pi$
$312$	−0.913209	−	0.913209i	−0.0517003	−	0.0517003i
$313$		−	19.5460i		−	1.10481i	−0.833577	−	0.552404i	$-0.813711\pi$
$313$		−	19.5460i		−	1.10481i	0.833577	−	0.552404i	$-0.186289\pi$
$314$	12.1068	−	12.1068i	0.683229	−	0.683229i
$315$	0.527580	+	1.94144i	0.0297258	+	0.109388i
$316$	−9.04382	−	9.04382i	−0.508755	−	0.508755i
$317$	5.03252	−	5.03252i	0.282655	−	0.282655i	−0.551512	−	0.834167i	$-0.685949\pi$
$317$	5.03252	−	5.03252i	0.282655	−	0.282655i	0.834167	+	0.551512i	$0.185949\pi$
$318$		−	9.61473i		−	0.539168i
$319$	−3.86010	−	3.86010i	−0.216124	−	0.216124i
$320$	−1.11117	+	1.94044i	−0.0621164	+	0.108474i
$321$			19.6007i			1.09401i
$322$	−5.42954	−	5.42954i	−0.302576	−	0.302576i
$323$	23.5721	+	23.5721i	1.31159	+	1.31159i
$324$	1.00000			0.0555556
$325$	−5.56924	+	3.26819i	−0.308926	+	0.181287i
$326$		−	24.2268i		−	1.34180i
$327$		−	7.53328i		−	0.416591i
$328$	−9.02011			−0.498052
$329$		−	0.415710i		−	0.0229189i
$330$	−4.89518	+	1.33025i	−0.269471	+	0.0732279i
$331$	−3.25748	+	3.25748i	−0.179048	+	0.179048i	−0.790941	−	0.611893i	$-0.790408\pi$
$331$	−3.25748	+	3.25748i	−0.179048	+	0.179048i	0.611893	+	0.790941i	$0.290408\pi$
$332$	−9.12362	+	9.12362i	−0.500723	+	0.500723i
$333$	−3.16223	+	5.19618i	−0.173289	+	0.284749i
$334$		−	9.66372i		−	0.528775i
$335$	−3.30336	−	12.1560i	−0.180482	−	0.664154i
$336$		−	0.899724i		−	0.0490840i
$337$	15.5648	−	15.5648i	0.847866	−	0.847866i	−0.142000	−	0.989867i	$-0.545353\pi$
$337$	15.5648	−	15.5648i	0.847866	−	0.847866i	0.989867	+	0.142000i	$0.0453534\pi$
$338$		−	11.3321i		−	0.616385i
$339$	−12.2157	−	12.2157i	−0.663463	−	0.663463i
$340$	6.38589	−	11.1517i	0.346324	−	0.604785i
$341$	13.1840	−	13.1840i	0.713953	−	0.713953i
$342$	−4.10165	−	4.10165i	−0.221792	−	0.221792i
$343$	8.39181	−	8.39181i	0.453115	−	0.453115i
$344$	0.853087			0.0459953
$345$	5.00435	+	18.4154i	0.269425	+	0.991454i
$346$	−6.77556	+	6.77556i	−0.364256	+	0.364256i
$347$		−	19.7799i		−	1.06184i	−0.847422	−	0.530920i	$-0.821846\pi$
$347$		−	19.7799i		−	1.06184i	0.847422	−	0.530920i	$-0.178154\pi$
$348$	−2.40635			−0.128994
$349$			5.47518i			0.293080i	0.989205	+	0.146540i	$0.0468137\pi$
$349$			5.47518i			0.293080i	−0.989205	+	0.146540i	$0.953186\pi$
$350$	−4.35347	−	1.13353i	−0.232703	−	0.0605899i
$351$	−0.913209	−	0.913209i	−0.0487435	−	0.0487435i
$352$	2.26858			0.120916
$353$	28.1816			1.49995			0.749976	−	0.661465i	$-0.230065\pi$
$353$	28.1816			1.49995			0.749976	+	0.661465i	$0.230065\pi$
$354$	−4.96631			−0.263956
$355$	−16.9889	+	29.6678i	−0.901679	+	1.57460i
$356$	6.32382	−	6.32382i	0.335162	−	0.335162i
$357$			5.17071i			0.273663i
$358$	−7.36463	−	7.36463i	−0.389233	−	0.389233i
$359$			2.05043i			0.108218i	0.998535	+	0.0541089i	$0.0172318\pi$
$359$			2.05043i			0.108218i	−0.998535	+	0.0541089i	$0.982768\pi$
$360$	−1.11117	+	1.94044i	−0.0585639	+	0.102270i
$361$			14.6470i			0.770896i
$362$			13.9651i			0.733988i
$363$	−4.13907	−	4.13907i	−0.217245	−	0.217245i
$364$	−0.821636	+	0.821636i	−0.0430654	+	0.0430654i
$365$	−36.1074	+	9.81208i	−1.88995	+	0.513588i
$366$	2.91979			0.152620
$367$	−8.13886	−	8.13886i	−0.424845	−	0.424845i	0.462023	−	0.886868i	$-0.347124\pi$
$367$	−8.13886	−	8.13886i	−0.424845	−	0.424845i	−0.886868	+	0.462023i	$0.847124\pi$
$368$		−	8.53431i		−	0.444882i
$369$	−9.02011			−0.469568
$370$	−6.56908	−	11.9100i	−0.341510	−	0.619169i
$371$	−8.65061			−0.449117
$372$		−	8.21877i		−	0.426124i
$373$	−9.78820	−	9.78820i	−0.506814	−	0.506814i	0.406733	−	0.913547i	$-0.366668\pi$
$373$	−9.78820	−	9.78820i	−0.506814	−	0.506814i	−0.913547	+	0.406733i	$0.866668\pi$
$374$	−13.0375			−0.674154
$375$	7.98921	+	7.82129i	0.412561	+	0.403889i
$376$	0.326713	−	0.326713i	0.0168489	−	0.0168489i
$377$	2.19750	+	2.19750i	0.113177	+	0.113177i
$378$		−	0.899724i		−	0.0462768i
$379$		−	22.6146i		−	1.16164i	−0.814034	−	0.580818i	$-0.802733\pi$
$379$		−	22.6146i		−	1.16164i	0.814034	−	0.580818i	$-0.197267\pi$
$380$	12.5166	−	3.40136i	0.642089	−	0.174486i
$381$		−	1.29596i		−	0.0663939i
$382$	11.6459	+	11.6459i	0.595854	+	0.595854i
$383$			9.52538i			0.486724i	0.969936	+	0.243362i	$0.0782503\pi$
$383$			9.52538i			0.486724i	−0.969936	+	0.243362i	$0.921750\pi$
$384$	0.707107	−	0.707107i	0.0360844	−	0.0360844i
$385$	1.19686	+	4.40431i	0.0609976	+	0.224464i
$386$	2.80664			0.142854
$387$	0.853087			0.0433648
$388$	−9.28197			−0.471220
$389$	7.75553	+	7.75553i	0.393221	+	0.393221i	0.875834	−	0.482613i	$-0.160312\pi$
$389$	7.75553	+	7.75553i	0.393221	+	0.393221i	−0.482613	+	0.875834i	$0.660312\pi$
$390$	2.78676	−	0.757293i	0.141113	−	0.0383470i
$391$			49.0466i			2.48039i
$392$	6.19050			0.312667
$393$			8.89460i			0.448673i
$394$	11.5183	−	11.5183i	0.580282	−	0.580282i
$395$	27.5982	−	7.49973i	1.38862	−	0.377353i
$396$	2.26858			0.114001
$397$	−18.6690	+	18.6690i	−0.936970	+	0.936970i	−0.998128	−	0.0611581i	$-0.980521\pi$
$397$	−18.6690	+	18.6690i	−0.936970	+	0.936970i	0.0611581	+	0.998128i	$0.480521\pi$
$398$	−10.3470	−	10.3470i	−0.518649	−	0.518649i
$399$	−3.69035	+	3.69035i	−0.184749	+	0.184749i
$400$	−2.53060	−	4.31232i	−0.126530	−	0.215616i
$401$	13.9114	+	13.9114i	0.694702	+	0.694702i	0.963263	−	0.268561i	$-0.0865481\pi$
$401$	13.9114	+	13.9114i	0.694702	+	0.694702i	−0.268561	+	0.963263i	$0.586548\pi$
$402$			5.63348i			0.280973i
$403$	−7.50545	+	7.50545i	−0.373873	+	0.373873i
$404$		−	1.47408i		−	0.0733383i
$405$	−1.11117	+	1.94044i	−0.0552146	+	0.0964211i
$406$			2.16505i			0.107450i
$407$	−7.17378	+	11.7880i	−0.355591	+	0.584308i
$408$	−4.06374	+	4.06374i	−0.201185	+	0.201185i
$409$	−7.16339	+	7.16339i	−0.354207	+	0.354207i	−0.861672	−	0.507465i	$-0.830582\pi$
$409$	−7.16339	+	7.16339i	−0.354207	+	0.354207i	0.507465	+	0.861672i	$0.330582\pi$
$410$	10.0229	−	17.5030i	0.494995	−	0.864409i
$411$		−	14.7818i		−	0.729134i
$412$	−1.02968			−0.0507289
$413$			4.46831i			0.219871i
$414$		−	8.53431i		−	0.419438i
$415$	−7.56591	−	27.8417i	−0.371396	−	1.36670i
$416$	−1.29147			−0.0633196
$417$	10.2136	+	10.2136i	0.500164	+	0.500164i
$418$	−9.30492	−	9.30492i	−0.455119	−	0.455119i
$419$			23.8546i			1.16537i	0.812698	+	0.582686i	$0.197998\pi$
$419$			23.8546i			1.16537i	−0.812698	+	0.582686i	$0.802002\pi$
$420$	1.74586	+	0.999748i	0.0851892	+	0.0487827i
$421$	−12.3787	−	12.3787i	−0.603301	−	0.603301i	0.337886	−	0.941187i	$-0.390288\pi$
$421$	−12.3787	−	12.3787i	−0.603301	−	0.603301i	−0.941187	+	0.337886i	$0.890288\pi$
$422$			3.80993i			0.185464i
$423$	0.326713	−	0.326713i	0.0158853	−	0.0158853i
$424$	−6.79864	−	6.79864i	−0.330171	−	0.330171i
$425$	14.5433	+	24.7828i	0.705454	+	1.20214i
$426$	10.8111	−	10.8111i	0.523800	−	0.523800i
$427$		−	2.62700i		−	0.127130i
$428$	13.8598	+	13.8598i	0.669940	+	0.669940i
$429$	−2.07169	−	2.07169i	−0.100022	−	0.100022i
$430$	−0.947925	+	1.65536i	−0.0457130	+	0.0798286i
$431$	5.50143	+	5.50143i	0.264995	+	0.264995i	0.827080	−	0.562085i	$-0.190001\pi$
$431$	5.50143	+	5.50143i	0.264995	+	0.264995i	−0.562085	+	0.827080i	$0.690001\pi$
$432$	0.707107	−	0.707107i	0.0340207	−	0.0340207i
$433$	4.53175	−	4.53175i	0.217782	−	0.217782i	−0.589781	−	0.807563i	$-0.700786\pi$
$433$	4.53175	−	4.53175i	0.217782	−	0.217782i	0.807563	+	0.589781i	$0.200786\pi$
$434$	−7.39463			−0.354954
$435$	2.67387	−	4.66938i	0.128202	−	0.223879i
$436$	−5.32683	−	5.32683i	−0.255109	−	0.255109i
$437$	−35.0047	+	35.0047i	−1.67450	+	1.67450i
$438$	16.7333			0.799549
$439$	22.7618	−	22.7618i	1.08636	−	1.08636i	0.0904591	−	0.995900i	$-0.471167\pi$
$439$	22.7618	−	22.7618i	1.08636	−	1.08636i	0.995900	−	0.0904591i	$-0.0288334\pi$
$440$	−2.52078	+	4.40204i	−0.120174	+	0.209859i
$441$	6.19050			0.294786
$442$	7.42208			0.353032
$443$	−18.5368	−	18.5368i	−0.880708	−	0.880708i	0.112899	−	0.993606i	$-0.463986\pi$
$443$	−18.5368	−	18.5368i	−0.880708	−	0.880708i	−0.993606	+	0.112899i	$0.963986\pi$
$444$	1.43822	+	5.91029i	0.0682549	+	0.280490i
$445$	5.24413	+	19.2978i	0.248596	+	0.914804i
$446$	−16.8923	−	16.8923i	−0.799872	−	0.799872i
$447$	−13.5056	+	13.5056i	−0.638791	+	0.638791i
$448$	−0.636201	−	0.636201i	−0.0300577	−	0.0300577i
$449$	9.96142	+	9.96142i	0.470109	+	0.470109i	0.901950	−	0.431841i	$-0.142136\pi$
$449$	9.96142	+	9.96142i	0.470109	+	0.470109i	−0.431841	+	0.901950i	$0.642136\pi$
$450$	−2.53060	−	4.31232i	−0.119293	−	0.203285i
$451$	−20.4629			−0.963558
$452$	−17.2755			−0.812573
$453$	−2.42193	+	2.42193i	−0.113792	+	0.113792i
$454$			25.0030i			1.17345i
$455$	−0.681355	−	2.50731i	−0.0319424	−	0.117545i
$456$	−5.80061			−0.271638
$457$	−6.81678			−0.318876			−0.159438	−	0.987208i	$-0.550968\pi$
$457$	−6.81678			−0.318876			−0.159438	+	0.987208i	$0.550968\pi$
$458$	−11.3572			−0.530686
$459$	−4.06374	+	4.06374i	−0.189679	+	0.189679i
$460$	16.5603	+	9.48308i	0.772128	+	0.442151i
$461$	24.7125	−	24.7125i	1.15097	−	1.15097i	0.164617	−	0.986358i	$-0.447361\pi$
$461$	24.7125	−	24.7125i	1.15097	−	1.15097i	0.986358	−	0.164617i	$-0.0526389\pi$
$462$		−	2.04110i		−	0.0949605i
$463$			32.0736i			1.49059i	0.666737	+	0.745293i	$0.267690\pi$
$463$			32.0736i			1.49059i	−0.666737	+	0.745293i	$0.732310\pi$
$464$	−1.70155	+	1.70155i	−0.0789924	+	0.0789924i
$465$	15.9480	+	9.13247i	0.739572	+	0.423508i
$466$	4.77274	−	4.77274i	0.221093	−	0.221093i
$467$	13.7531			0.636416			0.318208	−	0.948021i	$-0.396919\pi$
$467$	13.7531			0.636416			0.318208	+	0.948021i	$0.396919\pi$
$468$	−1.29147			−0.0596983
$469$	5.06858			0.234045
$470$	0.270932	+	0.997001i	0.0124972	+	0.0459882i
$471$		−	17.1217i		−	0.788925i
$472$	−3.51171	+	3.51171i	−0.161640	+	0.161640i
$473$	1.93530			0.0889851
$474$	−12.7899			−0.587459
$475$	−7.30799	+	28.0672i	−0.335314	+	1.28781i
$476$	3.65624	+	3.65624i	0.167584	+	0.167584i
$477$	−6.79864	−	6.79864i	−0.311289	−	0.311289i
$478$	−2.96858	+	2.96858i	−0.135780	+	0.135780i
$479$	15.9554	+	15.9554i	0.729021	+	0.729021i	0.970425	−	0.241404i	$-0.0776079\pi$
$479$	15.9554	+	15.9554i	0.729021	+	0.729021i	−0.241404	+	0.970425i	$0.577608\pi$
$480$	0.586380	+	2.15781i	0.0267645	+	0.0984903i
$481$	4.08393	−	6.71072i	0.186211	−	0.305983i
$482$	5.75647	+	5.75647i	0.262200	+	0.262200i
$483$	−7.67852			−0.349385
$484$	−5.85354			−0.266070
$485$	10.3139	−	18.0111i	0.468328	−	0.817841i
$486$	0.707107	−	0.707107i	0.0320750	−	0.0320750i
$487$	22.5078			1.01992			0.509962	−	0.860197i	$-0.329659\pi$
$487$	22.5078			1.01992			0.509962	+	0.860197i	$0.329659\pi$
$488$	2.06460	−	2.06460i	0.0934600	−	0.0934600i
$489$	−17.1309	−	17.1309i	−0.774688	−	0.774688i
$490$	−6.87870	+	12.0123i	−0.310748	+	0.542659i
$491$	31.0223			1.40002			0.700008	−	0.714135i	$-0.253180\pi$
$491$	31.0223			1.40002			0.700008	+	0.714135i	$0.253180\pi$
$492$	−6.37818	+	6.37818i	−0.287550	+	0.287550i
$493$	9.77878	−	9.77878i	0.440414	−	0.440414i
$494$	5.29716	+	5.29716i	0.238331	+	0.238331i
$495$	−2.52078	+	4.40204i	−0.113301	+	0.197857i
$496$	−5.81155	−	5.81155i	−0.260946	−	0.260946i
$497$	−9.72702	−	9.72702i	−0.436316	−	0.436316i
$498$			12.9027i			0.578186i
$499$	5.68409	−	5.68409i	0.254455	−	0.254455i	−0.568339	−	0.822794i	$-0.692414\pi$
$499$	5.68409	−	5.68409i	0.254455	−	0.254455i	0.822794	+	0.568339i	$0.192414\pi$
$500$	11.1797	−	0.118740i	0.499972	−	0.00531022i
$501$	−6.83328	−	6.83328i	−0.305288	−	0.305288i
$502$	−14.7749	+	14.7749i	−0.659437	+	0.659437i
$503$		−	3.69027i		−	0.164541i	−0.996610	−	0.0822705i	$-0.973783\pi$
$503$		−	3.69027i		−	0.164541i	0.996610	−	0.0822705i	$-0.0262171\pi$
$504$	−0.636201	−	0.636201i	−0.0283386	−	0.0283386i
$505$	2.86036	+	1.63796i	0.127285	+	0.0728882i
$506$		−	19.3608i		−	0.860692i
$507$	−8.01300	−	8.01300i	−0.355870	−	0.355870i
$508$	−0.916380	−	0.916380i	−0.0406578	−	0.0406578i
$509$	5.91876			0.262345			0.131172	−	0.991360i	$-0.458126\pi$
$509$	5.91876			0.262345			0.131172	+	0.991360i	$0.458126\pi$
$510$	−3.36992	−	12.4009i	−0.149223	−	0.549123i
$511$		−	15.0554i		−	0.666010i
$512$		−	1.00000i		−	0.0441942i
$513$	−5.80061			−0.256103
$514$		−	1.80027i		−	0.0794064i
$515$	1.14415	−	1.99804i	0.0504175	−	0.0880440i
$516$	0.603223	−	0.603223i	0.0265554	−	0.0265554i
$517$	0.741175	−	0.741175i	0.0325969	−	0.0325969i
$518$	5.31763	−	1.29400i	0.233643	−	0.0568551i
$519$			9.58209i			0.420607i
$520$	1.43505	−	2.50602i	0.0629310	−	0.109896i
$521$			21.8007i			0.955107i	0.878603	+	0.477554i	$0.158476\pi$
$521$			21.8007i			0.955107i	−0.878603	+	0.477554i	$0.841524\pi$
$522$	−1.70155	+	1.70155i	−0.0744747	+	0.0744747i
$523$			17.1466i			0.749767i	0.927072	+	0.374883i	$0.122317\pi$
$523$			17.1466i			0.749767i	−0.927072	+	0.374883i	$0.877683\pi$
$524$	6.28943	+	6.28943i	0.274755	+	0.274755i
$525$	−3.87990	+	2.27684i	−0.169333	+	0.0993694i
$526$	−9.25899	+	9.25899i	−0.403711	+	0.403711i
$527$	33.3989	+	33.3989i	1.45488	+	1.45488i
$528$	1.60413	−	1.60413i	0.0698108	−	0.0698108i
$529$	−49.8344			−2.16671
$530$	20.7468	−	5.63789i	0.901184	−	0.244894i
$531$	−3.51171	+	3.51171i	−0.152395	+	0.152395i
$532$			5.21895i			0.226270i
$533$	11.6492			0.504583
$534$		−	8.94323i		−	0.387011i
$535$	−42.2948	+	11.4935i	−1.82856	+	0.496907i
$536$	3.98347	+	3.98347i	0.172060	+	0.172060i
$537$	−10.4152			−0.449447
$538$	0.689017			0.0297056
$539$	14.0436			0.604903
$540$	0.586380	+	2.15781i	0.0252338	+	0.0928575i
$541$	−11.6362	+	11.6362i	−0.500279	+	0.500279i	−0.911525	−	0.411245i	$-0.865094\pi$
$541$	−11.6362	+	11.6362i	−0.500279	+	0.500279i	0.411245	+	0.911525i	$0.365094\pi$
$542$			14.7629i			0.634122i
$543$	9.87480	+	9.87480i	0.423768	+	0.423768i
$544$			5.74699i			0.246400i
$545$	16.2554	−	4.41736i	0.696305	−	0.189219i
$546$			1.16197i			0.0497277i
$547$			37.0105i			1.58245i	0.611523	+	0.791226i	$0.290557\pi$
$547$			37.0105i			1.58245i	−0.611523	+	0.791226i	$0.709443\pi$
$548$	−10.4523	−	10.4523i	−0.446502	−	0.446502i
$549$	2.06460	−	2.06460i	0.0881150	−	0.0881150i
$550$	−5.74087	−	9.78285i	−0.244791	−	0.417142i
$551$	13.9583			0.594643
$552$	−6.03467	−	6.03467i	−0.256853	−	0.256853i
$553$			11.5074i			0.489343i
$554$	−32.3771			−1.37557
$555$	−13.0667	−	3.77657i	−0.554649	−	0.160307i
$556$	14.4443			0.612574
$557$		−	5.02764i		−	0.213028i	−0.994311	−	0.106514i	$-0.966031\pi$
$557$		−	5.02764i		−	0.213028i	0.994311	−	0.106514i	$-0.0339689\pi$
$558$	−5.81155	−	5.81155i	−0.246023	−	0.246023i
$559$	−1.10174			−0.0465985
$560$	1.94144	−	0.527580i	0.0820407	−	0.0222943i
$561$	−9.21892	+	9.21892i	−0.389223	+	0.389223i
$562$	−5.74725	−	5.74725i	−0.242433	−	0.242433i
$563$			14.7235i			0.620522i	0.950651	+	0.310261i	$0.100416\pi$
$563$			14.7235i			0.620522i	−0.950651	+	0.310261i	$0.899584\pi$
$564$		−	0.462042i		−	0.0194555i
$565$	19.1961	−	33.5221i	0.807586	−	1.41029i
$566$		−	6.56809i		−	0.276078i
$567$	−0.636201	−	0.636201i	−0.0267179	−	0.0267179i
$568$		−	15.2892i		−	0.641521i
$569$	−15.1302	+	15.1302i	−0.634291	+	0.634291i	−0.949141	−	0.314850i	$-0.898046\pi$
$569$	−15.1302	+	15.1302i	−0.634291	+	0.634291i	0.314850	+	0.949141i	$0.398046\pi$
$570$	6.44547	−	11.2557i	0.269971	−	0.471450i
$571$	−0.732604			−0.0306585			−0.0153293	−	0.999882i	$-0.504880\pi$
$571$	−0.732604			−0.0306585			−0.0153293	+	0.999882i	$0.504880\pi$
$572$	−2.92981			−0.122502
$573$	16.4697			0.688033
$574$	5.73860	+	5.73860i	0.239525	+	0.239525i
$575$	−36.8026	+	21.5969i	−1.53478	+	0.900653i
$576$		−	1.00000i		−	0.0416667i
$577$	13.0938			0.545102			0.272551	−	0.962141i	$-0.412133\pi$
$577$	13.0938			0.545102			0.272551	+	0.962141i	$0.412133\pi$
$578$		−	16.0279i		−	0.666673i
$579$	1.98459	−	1.98459i	0.0824768	−	0.0824768i
$580$	−1.41104	−	5.19246i	−0.0585901	−	0.215605i
$581$	11.6089			0.481619
$582$	−6.56334	+	6.56334i	−0.272059	+	0.272059i
$583$	−15.4233	−	15.4233i	−0.638767	−	0.638767i
$584$	11.8322	−	11.8322i	0.489622	−	0.489622i
$585$	1.43505	−	2.50602i	0.0593319	−	0.103611i
$586$	22.0187	+	22.0187i	0.909583	+	0.909583i
$587$		−	25.6946i		−	1.06053i	−0.847832	−	0.530265i	$-0.822092\pi$
$587$		−	25.6946i		−	1.06053i	0.847832	−	0.530265i	$-0.177908\pi$
$588$	4.37734	−	4.37734i	0.180519	−	0.180519i
$589$			47.6739i			1.96437i
$590$	−2.91214	−	10.7164i	−0.119891	−	0.441186i
$591$		−	16.2893i		−	0.670052i
$592$	5.19618	+	3.16223i	0.213562	+	0.129967i
$593$	−32.7884	+	32.7884i	−1.34646	+	1.34646i	−0.456986	+	0.889474i	$0.651071\pi$
$593$	−32.7884	+	32.7884i	−1.34646	+	1.34646i	−0.889474	+	0.456986i	$0.848929\pi$
$594$	1.60413	−	1.60413i	0.0658182	−	0.0658182i
$595$	−11.1574	+	3.03200i	−0.457410	+	0.124300i
$596$			19.0997i			0.782356i
$597$	−14.6329			−0.598885
$598$			11.0218i			0.450716i
$599$		−	32.7946i		−	1.33995i	−0.742383	−	0.669975i	$-0.766305\pi$
$599$		−	32.7946i		−	1.33995i	0.742383	−	0.669975i	$-0.233695\pi$
$600$	−4.83867	−	1.25987i	−0.197538	−	0.0514339i
$601$	27.3053			1.11381			0.556904	−	0.830577i	$-0.311989\pi$
$601$	27.3053			1.11381			0.556904	+	0.830577i	$0.311989\pi$
$602$	−0.542735	−	0.542735i	−0.0221202	−	0.0221202i
$603$	3.98347	+	3.98347i	0.162220	+	0.162220i
$604$			3.42513i			0.139367i
$605$	6.50428	−	11.3584i	0.264437	−	0.461785i
$606$	−1.04233	−	1.04233i	−0.0423419	−	0.0423419i
$607$		−	26.7432i		−	1.08547i	−0.839903	−	0.542737i	$-0.817388\pi$
$607$		−	26.7432i		−	1.08547i	0.839903	−	0.542737i	$-0.182612\pi$
$608$	−4.10165	+	4.10165i	−0.166344	+	0.166344i
$609$	1.53092	+	1.53092i	0.0620362	+	0.0620362i
$610$	1.71210	+	6.30035i	0.0693210	+	0.255094i
$611$	−0.421941	+	0.421941i	−0.0170699	+	0.0170699i
$612$			5.74699i			0.232308i
$613$	−23.6704	−	23.6704i	−0.956040	−	0.956040i	0.0430339	−	0.999074i	$-0.486298\pi$
$613$	−23.6704	−	23.6704i	−0.956040	−	0.956040i	−0.999074	+	0.0430339i	$0.986298\pi$
$614$	−5.03677	−	5.03677i	−0.203268	−	0.203268i
$615$	−5.28921	−	19.4637i	−0.213281	−	0.784852i
$616$	−1.44327	−	1.44327i	−0.0581512	−	0.0581512i
$617$	3.77510	−	3.77510i	0.151980	−	0.151980i	−0.627022	−	0.779002i	$-0.715726\pi$
$617$	3.77510	−	3.77510i	0.151980	−	0.151980i	0.779002	+	0.627022i	$0.215726\pi$
$618$	−0.728096	+	0.728096i	−0.0292883	+	0.0292883i
$619$	9.65130			0.387918			0.193959	−	0.981010i	$-0.437867\pi$
$619$	9.65130			0.387918			0.193959	+	0.981010i	$0.437867\pi$
$620$	17.7346	−	4.81932i	0.712238	−	0.193549i
$621$	−6.03467	−	6.03467i	−0.242163	−	0.242163i
$622$	3.85553	−	3.85553i	0.154593	−	0.154593i
$623$	−8.04644			−0.322374
$624$	−0.913209	+	0.913209i	−0.0365576	+	0.0365576i
$625$	−12.1922	+	21.8255i	−0.487687	+	0.873019i
$626$	−19.5460			−0.781217
$627$	−13.1592			−0.525526
$628$	−12.1068	−	12.1068i	−0.483116	−	0.483116i
$629$	−29.8624	−	18.1733i	−1.19069	−	0.724618i
$630$	1.94144	−	0.527580i	0.0773487	−	0.0210193i
$631$	9.32454	+	9.32454i	0.371204	+	0.371204i	0.867916	−	0.496712i	$-0.165459\pi$
$631$	9.32454	+	9.32454i	0.371204	+	0.371204i	−0.496712	+	0.867916i	$0.665459\pi$
$632$	−9.04382	+	9.04382i	−0.359744	+	0.359744i
$633$	2.69402	+	2.69402i	0.107078	+	0.107078i
$634$	−5.03252	−	5.03252i	−0.199867	−	0.199867i
$635$	2.79643	−	0.759923i	0.110973	−	0.0301566i
$636$	−9.61473			−0.381249
$637$	−7.99485			−0.316768
$638$	−3.86010	+	3.86010i	−0.152823	+	0.152823i
$639$		−	15.2892i		−	0.604832i
$640$	1.94044	+	1.11117i	0.0767025	+	0.0439229i
$641$	−7.81012			−0.308481			−0.154241	−	0.988033i	$-0.549293\pi$
$641$	−7.81012			−0.308481			−0.154241	+	0.988033i	$0.549293\pi$
$642$	19.6007			0.773580
$643$	−39.3070			−1.55012			−0.775058	−	0.631890i	$-0.782279\pi$
$643$	−39.3070			−1.55012			−0.775058	+	0.631890i	$0.782279\pi$
$644$	−5.42954	+	5.42954i	−0.213954	+	0.213954i
$645$	0.500233	+	1.84080i	0.0196966	+	0.0724815i
$646$	23.5721	−	23.5721i	0.927433	−	0.927433i
$647$		−	31.8619i		−	1.25262i	−0.779573	−	0.626311i	$-0.784564\pi$
$647$		−	31.8619i		−	1.25262i	0.779573	−	0.626311i	$-0.215436\pi$
$648$		−	1.00000i		−	0.0392837i
$649$	−7.96660	+	7.96660i	−0.312716	+	0.312716i
$650$	3.26819	+	5.56924i	0.128189	+	0.218443i
$651$	−5.22879	+	5.22879i	−0.204933	+	0.204933i
$652$	−24.2268			−0.948795
$653$	40.2027			1.57325			0.786626	−	0.617430i	$-0.211826\pi$
$653$	40.2027			1.57325			0.786626	+	0.617430i	$0.211826\pi$
$654$	−7.53328			−0.294575
$655$	−19.1929	+	5.21562i	−0.749929	+	0.203791i
$656$			9.02011i			0.352176i
$657$	11.8322	−	11.8322i	0.461620	−	0.461620i
$658$	−0.415710			−0.0162061
$659$	−22.6033			−0.880499			−0.440250	−	0.897875i	$-0.645110\pi$
$659$	−22.6033			−0.880499			−0.440250	+	0.897875i	$0.645110\pi$
$660$	1.33025	+	4.89518i	0.0517799	+	0.190545i
$661$	20.1421	+	20.1421i	0.783436	+	0.783436i	0.980409	−	0.196973i	$-0.0631111\pi$
$661$	20.1421	+	20.1421i	0.783436	+	0.783436i	−0.196973	+	0.980409i	$0.563111\pi$
$662$	3.25748	+	3.25748i	0.126606	+	0.126606i
$663$	5.24820	−	5.24820i	0.203823	−	0.203823i
$664$	9.12362	+	9.12362i	0.354065	+	0.354065i
$665$	−10.1270	−	5.79914i	−0.392710	−	0.224881i
$666$	5.19618	+	3.16223i	0.201348	+	0.122534i
$667$	14.5215	+	14.5215i	0.562276	+	0.562276i
$668$	−9.66372			−0.373900
$669$	−23.8893			−0.923612
$670$	−12.1560	+	3.30336i	−0.469628	+	0.127620i
$671$	4.68371	−	4.68371i	0.180813	−	0.180813i
$672$	−0.899724			−0.0347076
$673$	23.9631	−	23.9631i	0.923709	−	0.923709i	−0.0735806	−	0.997289i	$-0.523443\pi$
$673$	23.9631	−	23.9631i	0.923709	−	0.923709i	0.997289	+	0.0735806i	$0.0234426\pi$
$674$	−15.5648	−	15.5648i	−0.599532	−	0.599532i
$675$	−4.83867	−	1.25987i	−0.186241	−	0.0484923i
$676$	−11.3321			−0.435850
$677$	−18.3439	+	18.3439i	−0.705012	+	0.705012i	−0.965482	−	0.260470i	$-0.916122\pi$
$677$	−18.3439	+	18.3439i	−0.705012	+	0.705012i	0.260470	+	0.965482i	$0.416122\pi$
$678$	−12.2157	+	12.2157i	−0.469139	+	0.469139i
$679$	5.90520	+	5.90520i	0.226621	+	0.226621i
$680$	−11.1517	−	6.38589i	−0.427647	−	0.244888i
$681$	17.6798	+	17.6798i	0.677490	+	0.677490i
$682$	−13.1840	−	13.1840i	−0.504841	−	0.504841i
$683$		−	2.79715i		−	0.107030i	−0.998567	−	0.0535149i	$-0.982958\pi$
$683$		−	2.79715i		−	0.107030i	0.998567	−	0.0535149i	$-0.0170425\pi$
$684$	−4.10165	+	4.10165i	−0.156830	+	0.156830i
$685$	31.8965	−	8.66777i	1.21870	−	0.331179i
$686$	−8.39181	−	8.39181i	−0.320401	−	0.320401i
$687$	−8.03073	+	8.03073i	−0.306392	+	0.306392i
$688$		−	0.853087i		−	0.0325236i
$689$	8.78026	+	8.78026i	0.334501	+	0.334501i
$690$	18.4154	−	5.00435i	0.701064	−	0.190512i
$691$			7.07761i			0.269245i	0.990897	+	0.134623i	$0.0429822\pi$
$691$			7.07761i			0.269245i	−0.990897	+	0.134623i	$0.957018\pi$
$692$	6.77556	+	6.77556i	0.257568	+	0.257568i
$693$	−1.44327	−	1.44327i	−0.0548255	−	0.0548255i
$694$	−19.7799			−0.750835
$695$	−16.0501	+	28.0282i	−0.608813	+	1.06317i
$696$			2.40635i			0.0912125i
$697$		−	51.8385i		−	1.96352i
$698$	5.47518			0.207239
$699$		−	6.74968i		−	0.255296i
$700$	−1.13353	+	4.35347i	−0.0428435	+	0.164546i
$701$	−25.0871	+	25.0871i	−0.947527	+	0.947527i	−0.998690	−	0.0511635i	$-0.983707\pi$
$701$	−25.0871	+	25.0871i	−0.947527	+	0.947527i	0.0511635	+	0.998690i	$0.483707\pi$
$702$	−0.913209	+	0.913209i	−0.0344668	+	0.0344668i
$703$	−8.34254	−	34.2833i	−0.314645	−	1.29302i
$704$		−	2.26858i		−	0.0855004i
$705$	0.896564	+	0.513408i	0.0337665	+	0.0193361i
$706$		−	28.1816i		−	1.06063i
$707$	−0.937812	+	0.937812i	−0.0352701	+	0.0352701i
$708$			4.96631i			0.186645i
$709$	−6.08101	−	6.08101i	−0.228377	−	0.228377i	0.583637	−	0.812014i	$-0.301629\pi$
$709$	−6.08101	−	6.08101i	−0.228377	−	0.228377i	−0.812014	+	0.583637i	$0.801629\pi$
$710$	29.6678	+	16.9889i	1.11341	+	0.637584i
$711$	−9.04382	+	9.04382i	−0.339170	+	0.339170i
$712$	−6.32382	−	6.32382i	−0.236995	−	0.236995i
$713$	−49.5976	+	49.5976i	−1.85744	+	1.85744i
$714$	5.17071			0.193509
$715$	3.25552	−	5.68511i	0.121750	−	0.212611i
$716$	−7.36463	+	7.36463i	−0.275229	+	0.275229i
$717$			4.19821i			0.156785i
$718$	2.05043			0.0765215
$719$			37.1763i			1.38644i	0.720724	+	0.693222i	$0.243809\pi$
$719$			37.1763i			1.38644i	−0.720724	+	0.693222i	$0.756191\pi$
$720$	1.94044	+	1.11117i	0.0723158	+	0.0414109i
$721$	0.655086	+	0.655086i	0.0243967	+	0.0243967i
$722$	14.6470			0.545106
$723$	8.14088			0.302762
$724$	13.9651			0.519008
$725$	11.6435	+	3.03168i	0.432430	+	0.112594i
$726$	−4.13907	+	4.13907i	−0.153615	+	0.153615i
$727$		−	10.8041i		−	0.400701i	−0.979724	−	0.200350i	$-0.935792\pi$
$727$		−	10.8041i		−	0.400701i	0.979724	−	0.200350i	$-0.0642081\pi$
$728$	0.821636	+	0.821636i	0.0304519	+	0.0304519i
$729$		−	1.00000i		−	0.0370370i
$730$	9.81208	+	36.1074i	0.363161	+	1.33639i
$731$			4.90268i			0.181332i
$732$		−	2.91979i		−	0.107918i
$733$	−2.31409	−	2.31409i	−0.0854728	−	0.0854728i	0.663078	−	0.748551i	$-0.269250\pi$
$733$	−2.31409	−	2.31409i	−0.0854728	−	0.0854728i	−0.748551	+	0.663078i	$0.769250\pi$
$734$	−8.13886	+	8.13886i	−0.300411	+	0.300411i
$735$	3.62998	+	13.3579i	0.133894	+	0.492715i
$736$	−8.53431			−0.314579
$737$	9.03684	+	9.03684i	0.332876	+	0.332876i
$738$			9.02011i			0.332035i
$739$	−3.59606			−0.132283			−0.0661416	−	0.997810i	$-0.521069\pi$
$739$	−3.59606			−0.132283			−0.0661416	+	0.997810i	$0.521069\pi$
$740$	−11.9100	+	6.56908i	−0.437819	+	0.241484i
$741$	7.49132			0.275201
$742$			8.65061i			0.317574i
$743$	7.78930	+	7.78930i	0.285762	+	0.285762i	0.835402	−	0.549640i	$-0.185235\pi$
$743$	7.78930	+	7.78930i	0.285762	+	0.285762i	−0.549640	+	0.835402i	$0.685235\pi$
$744$	−8.21877			−0.301315
$745$	−37.0619	−	21.2231i	−1.35784	−	0.777554i
$746$	−9.78820	+	9.78820i	−0.358371	+	0.358371i
$747$	9.12362	+	9.12362i	0.333816	+	0.333816i
$748$			13.0375i			0.476699i
$749$		−	17.6353i		−	0.644379i
$750$	7.82129	−	7.98921i	0.285593	−	0.291725i
$751$			31.8319i			1.16156i	0.814059	+	0.580782i	$0.197253\pi$
$751$			31.8319i			1.16156i	−0.814059	+	0.580782i	$0.802747\pi$
$752$	−0.326713	−	0.326713i	−0.0119140	−	0.0119140i
$753$			20.8949i			0.761452i
$754$	2.19750	−	2.19750i	0.0800283	−	0.0800283i
$755$	−6.64625	−	3.80591i	−0.241882	−	0.138511i
$756$	−0.899724			−0.0327227
$757$	2.85691			0.103836			0.0519182	−	0.998651i	$-0.483467\pi$
$757$	2.85691			0.103836			0.0519182	+	0.998651i	$0.483467\pi$
$758$	−22.6146			−0.821400
$759$	−13.6901	−	13.6901i	−0.496921	−	0.496921i
$760$	−3.40136	−	12.5166i	−0.123380	−	0.454026i
$761$		−	3.11943i		−	0.113079i	−0.998400	−	0.0565396i	$-0.981993\pi$
$761$		−	3.11943i		−	0.113079i	0.998400	−	0.0565396i	$-0.0180067\pi$
$762$	−1.29596			−0.0469476
$763$			6.77787i			0.245376i
$764$	11.6459	−	11.6459i	0.421332	−	0.421332i
$765$	−11.1517	−	6.38589i	−0.403190	−	0.230882i
$766$	9.52538			0.344166
$767$	4.53527	−	4.53527i	0.163759	−	0.163759i
$768$	−0.707107	−	0.707107i	−0.0255155	−	0.0255155i
$769$	22.4056	−	22.4056i	0.807966	−	0.807966i	−0.176360	−	0.984326i	$-0.556432\pi$
$769$	22.4056	−	22.4056i	0.807966	−	0.807966i	0.984326	+	0.176360i	$0.0564322\pi$
$770$	4.40431	−	1.19686i	0.158720	−	0.0431318i
$771$	−1.27298	−	1.27298i	−0.0458453	−	0.0458453i
$772$		−	2.80664i		−	0.101013i
$773$	−1.90608	+	1.90608i	−0.0685571	+	0.0685571i	−0.740554	−	0.671997i	$-0.765437\pi$
$773$	−1.90608	+	1.90608i	−0.0685571	+	0.0685571i	0.671997	+	0.740554i	$0.265437\pi$
$774$		−	0.853087i		−	0.0306636i
$775$	−10.3546	+	39.7679i	−0.371947	+	1.42851i
$776$			9.28197i			0.333203i
$777$	2.84514	−	4.67513i	0.102069	−	0.167719i
$778$	7.75553	−	7.75553i	0.278049	−	0.278049i
$779$	36.9973	−	36.9973i	1.32557	−	1.32557i
$780$	−0.757293	−	2.78676i	−0.0271154	−	0.0997819i
$781$		−	34.6848i		−	1.24112i
$782$	49.0466			1.75390
$783$			2.40635i			0.0859960i
$784$		−	6.19050i		−	0.221089i
$785$	36.9454	−	10.0398i	1.31864	−	0.358336i
$786$	8.89460			0.317260
$787$	−24.9409	−	24.9409i	−0.889045	−	0.889045i	0.105386	−	0.994431i	$-0.466392\pi$
$787$	−24.9409	−	24.9409i	−0.889045	−	0.889045i	−0.994431	+	0.105386i	$0.966392\pi$
$788$	−11.5183	−	11.5183i	−0.410322	−	0.410322i
$789$			13.0942i			0.466165i
$790$	−7.49973	−	27.5982i	−0.266829	−	0.981900i
$791$	10.9907	+	10.9907i	0.390785	+	0.390785i
$792$		−	2.26858i		−	0.0806106i
$793$	−2.66637	+	2.66637i	−0.0946857	+	0.0946857i
$794$	18.6690	+	18.6690i	0.662538	+	0.662538i
$795$	10.6836	−	18.6568i	0.378909	−	0.661688i
$796$	−10.3470	+	10.3470i	−0.366740	+	0.366740i
$797$		−	33.5854i		−	1.18966i	−0.803853	−	0.594828i	$-0.797220\pi$
$797$		−	33.5854i		−	1.18966i	0.803853	−	0.594828i	$-0.202780\pi$
$798$	3.69035	+	3.69035i	0.130637	+	0.130637i
$799$	1.87762	+	1.87762i	0.0664253	+	0.0664253i
$800$	−4.31232	+	2.53060i	−0.152463	+	0.0894701i
$801$	−6.32382	−	6.32382i	−0.223441	−	0.223441i
$802$	13.9114	−	13.9114i	0.491228	−	0.491228i
$803$	26.8424	−	26.8424i	0.947248	−	0.947248i
$804$	5.63348			0.198678
$805$	−4.50253	−	16.5688i	−0.158693	−	0.583974i
$806$	7.50545	+	7.50545i	0.264368	+	0.264368i
$807$	0.487209	−	0.487209i	0.0171506	−	0.0171506i
$808$	−1.47408			−0.0518580
$809$	−4.59489	+	4.59489i	−0.161548	+	0.161548i	−0.783252	−	0.621704i	$-0.786441\pi$
$809$	−4.59489	+	4.59489i	−0.161548	+	0.161548i	0.621704	+	0.783252i	$0.286441\pi$
$810$	1.94044	+	1.11117i	0.0681800	+	0.0390426i
$811$	−26.4363			−0.928304			−0.464152	−	0.885756i	$-0.653641\pi$
$811$	−26.4363			−0.928304			−0.464152	+	0.885756i	$0.653641\pi$
$812$	2.16505			0.0759785
$813$	10.4390	+	10.4390i	0.366110	+	0.366110i
$814$	11.7880	+	7.17378i	0.413168	+	0.251441i
$815$	26.9201	−	47.0106i	0.942971	−	1.64671i
$816$	4.06374	+	4.06374i	0.142259	+	0.142259i
$817$	−3.49906	+	3.49906i	−0.122417	+	0.122417i
$818$	7.16339	+	7.16339i	0.250462	+	0.250462i
$819$	0.821636	+	0.821636i	0.0287103	+	0.0287103i
$820$	−17.5030	−	10.0229i	−0.611230	−	0.350014i
$821$	38.5813			1.34650			0.673248	−	0.739417i	$-0.264899\pi$
$821$	38.5813			1.34650			0.673248	+	0.739417i	$0.264899\pi$
$822$	−14.7818			−0.515576
$823$	9.95130	−	9.95130i	0.346881	−	0.346881i	−0.512066	−	0.858946i	$-0.671120\pi$
$823$	9.95130	−	9.95130i	0.346881	−	0.346881i	0.858946	+	0.512066i	$0.171120\pi$
$824$			1.02968i			0.0358707i
$825$	−10.9769	−	2.85811i	−0.382167	−	0.0995067i
$826$	4.46831			0.155472
$827$	3.10451			0.107954			0.0539772	−	0.998542i	$-0.482810\pi$
$827$	3.10451			0.107954			0.0539772	+	0.998542i	$0.482810\pi$
$828$	−8.53431			−0.296588
$829$	−8.47013	+	8.47013i	−0.294180	+	0.294180i	−0.838729	−	0.544549i	$-0.816701\pi$
$829$	−8.47013	+	8.47013i	−0.294180	+	0.294180i	0.544549	+	0.838729i	$0.316701\pi$
$830$	−27.8417	+	7.56591i	−0.966400	+	0.262616i
$831$	−22.8940	+	22.8940i	−0.794186	+	0.794186i
$832$			1.29147i			0.0447737i
$833$			35.5767i			1.23266i
$834$	10.2136	−	10.2136i	0.353669	−	0.353669i
$835$	10.7380	−	18.7518i	0.371605	−	0.648934i
$836$	−9.30492	+	9.30492i	−0.321818	+	0.321818i
$837$	−8.21877			−0.284082
$838$	23.8546			0.824042
$839$	6.41357			0.221421			0.110711	−	0.993853i	$-0.464687\pi$
$839$	6.41357			0.221421			0.110711	+	0.993853i	$0.464687\pi$
$840$	0.999748	−	1.74586i	0.0344946	−	0.0602378i
$841$			23.2095i			0.800327i
$842$	−12.3787	+	12.3787i	−0.426598	+	0.426598i
$843$	−8.12784			−0.279938
$844$	3.80993			0.131143
$845$	12.5919	−	21.9892i	0.433175	−	0.756453i
$846$	−0.326713	−	0.326713i	−0.0112326	−	0.0112326i
$847$	3.72403	+	3.72403i	0.127959	+	0.127959i
$848$	−6.79864	+	6.79864i	−0.233466	+	0.233466i
$849$	−4.64434	−	4.64434i	−0.159393	−	0.159393i
$850$	24.7828	−	14.5433i	0.850045	−	0.498832i
$851$	26.9875	−	44.3458i	0.925118	−	1.52015i
$852$	−10.8111	−	10.8111i	−0.370382	−	0.370382i
$853$	−46.7208			−1.59969			−0.799845	−	0.600207i	$-0.795085\pi$
$853$	−46.7208			−1.59969			−0.799845	+	0.600207i	$0.795085\pi$
$854$	−2.62700			−0.0898941
$855$	−3.40136	−	12.5166i	−0.116324	−	0.428060i
$856$	13.8598	−	13.8598i	0.473719	−	0.473719i
$857$	−36.8302			−1.25810			−0.629048	−	0.777367i	$-0.716555\pi$
$857$	−36.8302			−1.25810			−0.629048	+	0.777367i	$0.716555\pi$
$858$	−2.07169	+	2.07169i	−0.0707263	+	0.0707263i
$859$	33.3859	+	33.3859i	1.13911	+	1.13911i	0.988610	+	0.150502i	$0.0480891\pi$
$859$	33.3859	+	33.3859i	1.13911	+	1.13911i	0.150502	+	0.988610i	$0.451911\pi$
$860$	1.65536	+	0.947925i	0.0564474	+	0.0323240i
$861$	8.11561			0.276579
$862$	5.50143	−	5.50143i	0.187379	−	0.187379i
$863$	−1.49779	+	1.49779i	−0.0509855	+	0.0509855i	−0.732140	−	0.681154i	$-0.761478\pi$
$863$	−1.49779	+	1.49779i	−0.0509855	+	0.0509855i	0.681154	+	0.732140i	$0.261478\pi$
$864$	−0.707107	−	0.707107i	−0.0240563	−	0.0240563i
$865$	−20.6764	+	5.61875i	−0.703018	+	0.191043i
$866$	−4.53175	−	4.53175i	−0.153995	−	0.153995i
$867$	−11.3334	−	11.3334i	−0.384904	−	0.384904i
$868$			7.39463i			0.250990i
$869$	−20.5166	+	20.5166i	−0.695980	+	0.695980i
$870$	−4.66938	−	2.67387i	−0.158307	−	0.0906527i
$871$	−5.14455	−	5.14455i	−0.174316	−	0.174316i
$872$	−5.32683	+	5.32683i	−0.180389	+	0.180389i
$873$			9.28197i			0.314147i
$874$	35.0047	+	35.0047i	1.18405	+	1.18405i
$875$	−7.18809	−	7.03700i	−0.243002	−	0.237894i
$876$		−	16.7333i		−	0.565366i
$877$	8.78482	+	8.78482i	0.296642	+	0.296642i	0.839697	−	0.543055i	$-0.182732\pi$
$877$	8.78482	+	8.78482i	0.296642	+	0.296642i	−0.543055	+	0.839697i	$0.682732\pi$
$878$	−22.7618	−	22.7618i	−0.768172	−	0.768172i
$879$	31.1391			1.05030
$880$	4.40204	+	2.52078i	0.148393	+	0.0849756i
$881$		−	19.0001i		−	0.640128i	−0.947396	−	0.320064i	$-0.896296\pi$
$881$		−	19.0001i		−	0.640128i	0.947396	−	0.320064i	$-0.103704\pi$
$882$		−	6.19050i		−	0.208445i
$883$	−10.1981			−0.343193			−0.171596	−	0.985167i	$-0.554892\pi$
$883$	−10.1981			−0.343193			−0.171596	+	0.985167i	$0.554892\pi$
$884$		−	7.42208i		−	0.249631i
$885$	−9.63681	−	5.51842i	−0.323938	−	0.185500i
$886$	−18.5368	+	18.5368i	−0.622754	+	0.622754i
$887$	12.1095	−	12.1095i	0.406597	−	0.406597i	−0.473953	−	0.880550i	$-0.657173\pi$
$887$	12.1095	−	12.1095i	0.406597	−	0.406597i	0.880550	+	0.473953i	$0.157173\pi$
$888$	5.91029	−	1.43822i	0.198336	−	0.0482635i
$889$			1.16600i			0.0391065i
$890$	19.2978	−	5.24413i	0.646864	−	0.175784i
$891$		−	2.26858i		−	0.0760004i
$892$	−16.8923	+	16.8923i	−0.565595	+	0.565595i
$893$			2.68012i			0.0896869i
$894$	13.5056	+	13.5056i	0.451694	+	0.451694i
$895$	−6.10724	−	22.4740i	−0.204143	−	0.751222i
$896$	−0.636201	+	0.636201i	−0.0212540	+	0.0212540i
$897$	7.79360	+	7.79360i	0.260221	+	0.260221i
$898$	9.96142	−	9.96142i	0.332417	−	0.332417i
$899$	19.7773			0.659609
$900$	−4.31232	+	2.53060i	−0.143744	+	0.0843532i
$901$	39.0717	−	39.0717i	1.30167	−	1.30167i
$902$			20.4629i			0.681338i
$903$	−0.767543			−0.0255422
$904$			17.2755i			0.574576i
$905$	−15.5176	+	27.0984i	−0.515822	+	0.900780i
$906$	2.42193	+	2.42193i	0.0804634	+	0.0804634i
$907$	0.471868			0.0156681			0.00783407	−	0.999969i	$-0.497506\pi$
$907$	0.471868			0.0156681			0.00783407	+	0.999969i	$0.497506\pi$
$908$	25.0030			0.829752
$909$	−1.47408			−0.0488922
$910$	−2.50731	+	0.681355i	−0.0831166	+	0.0225867i
$911$	18.6659	−	18.6659i	0.618430	−	0.618430i	−0.326698	−	0.945129i	$-0.605936\pi$
$911$	18.6659	−	18.6659i	0.618430	−	0.618430i	0.945129	+	0.326698i	$0.105936\pi$
$912$			5.80061i			0.192077i
$913$	20.6977	+	20.6977i	0.684993	+	0.684993i
$914$			6.81678i			0.225479i
$915$	5.66566	+	3.24438i	0.187301	+	0.107256i
$916$			11.3572i			0.375252i
$917$		−	8.00269i		−	0.264272i
$918$	4.06374	+	4.06374i	0.134123	+	0.134123i
$919$	24.0718	−	24.0718i	0.794054	−	0.794054i	−0.188096	−	0.982151i	$-0.560232\pi$
$919$	24.0718	−	24.0718i	0.794054	−	0.794054i	0.982151	+	0.188096i	$0.0602317\pi$
$920$	9.48308	−	16.5603i	0.312648	−	0.545977i
$921$	−7.12307			−0.234713
$922$	−24.7125	−	24.7125i	−0.813862	−	0.813862i
$923$			19.7456i			0.649934i
$924$	−2.04110			−0.0671472
$925$	0.487112	−	30.4099i	0.0160161	−	0.999872i
$926$	32.0736			1.05400
$927$			1.02968i			0.0338192i
$928$	1.70155	+	1.70155i	0.0558560	+	0.0558560i
$929$	−8.12677			−0.266631			−0.133315	−	0.991074i	$-0.542562\pi$
$929$	−8.12677			−0.266631			−0.133315	+	0.991074i	$0.542562\pi$
$930$	9.13247	−	15.9480i	0.299465	−	0.522956i
$931$	−25.3912	+	25.3912i	−0.832164	+	0.832164i
$932$	−4.77274	−	4.77274i	−0.156336	−	0.156336i
$933$		−	5.45254i		−	0.178508i
$934$		−	13.7531i		−	0.450014i
$935$	−25.2985	−	14.4869i	−0.827349	−	0.473773i
$936$			1.29147i			0.0422131i
$937$	−21.4124	−	21.4124i	−0.699513	−	0.699513i	0.264793	−	0.964305i	$-0.414696\pi$
$937$	−21.4124	−	21.4124i	−0.699513	−	0.699513i	−0.964305	+	0.264793i	$0.914696\pi$
$938$		−	5.06858i		−	0.165495i
$939$	−13.8211	+	13.8211i	−0.451036	+	0.451036i
$940$	0.997001	−	0.270932i	0.0325186	−	0.00883683i
$941$	−6.32110			−0.206062			−0.103031	−	0.994678i	$-0.532854\pi$
$941$	−6.32110			−0.206062			−0.103031	+	0.994678i	$0.532854\pi$
$942$	−17.1217			−0.557854
$943$	76.9804			2.50683
$944$	3.51171	+	3.51171i	0.114296	+	0.114296i
$945$	0.999748	−	1.74586i	0.0325218	−	0.0567928i
$946$		−	1.93530i		−	0.0629219i
$947$	29.6137			0.962316			0.481158	−	0.876634i	$-0.340216\pi$
$947$	29.6137			0.962316			0.481158	+	0.876634i	$0.340216\pi$
$948$			12.7899i			0.415396i
$949$	−15.2810	+	15.2810i	−0.496043	+	0.496043i
$950$	28.0672	+	7.30799i	0.910621	+	0.237103i
$951$	−7.11706			−0.230787
$952$	3.65624	−	3.65624i	0.118499	−	0.118499i
$953$	25.1832	+	25.1832i	0.815765	+	0.815765i	0.985491	−	0.169727i	$-0.0542884\pi$
$953$	25.1832	+	25.1832i	0.815765	+	0.815765i	−0.169727	+	0.985491i	$0.554288\pi$
$954$	−6.79864	+	6.79864i	−0.220114	+	0.220114i
$955$	9.65751	+	35.5386i	0.312510	+	1.15000i
$956$	2.96858	+	2.96858i	0.0960109	+	0.0960109i
$957$			5.45901i			0.176465i
$958$	15.9554	−	15.9554i	0.515496	−	0.515496i
$959$			13.2996i			0.429466i
$960$	2.15781	−	0.586380i	0.0696431	−	0.0189253i
$961$			36.5482i			1.17898i
$962$	−6.71072	−	4.08393i	−0.216362	−	0.131671i
$963$	13.8598	−	13.8598i	0.446627	−	0.446627i
$964$	5.75647	−	5.75647i	0.185403	−	0.185403i
$965$	5.44611	+	3.11866i	0.175316	+	0.100393i
$966$			7.67852i			0.247052i
$967$	12.3262			0.396385			0.198192	−	0.980163i	$-0.436493\pi$
$967$	12.3262			0.396385			0.198192	+	0.980163i	$0.436493\pi$
$968$			5.85354i			0.188140i
$969$		−	33.3360i		−	1.07091i
$970$	−18.0111	−	10.3139i	−0.578301	−	0.331158i
$971$	4.53299			0.145471			0.0727353	−	0.997351i	$-0.476827\pi$
$971$	4.53299			0.145471			0.0727353	+	0.997351i	$0.476827\pi$
$972$	−0.707107	−	0.707107i	−0.0226805	−	0.0226805i
$973$	−9.18946	−	9.18946i	−0.294601	−	0.294601i
$974$		−	22.5078i		−	0.721195i
$975$	6.24901	+	1.62708i	0.200128	+	0.0521084i
$976$	−2.06460	−	2.06460i	−0.0660862	−	0.0660862i
$977$			42.8715i			1.37158i	0.727799	+	0.685790i	$0.240543\pi$
$977$			42.8715i			1.37158i	−0.727799	+	0.685790i	$0.759457\pi$
$978$	−17.1309	+	17.1309i	−0.547787	+	0.547787i
$979$	−14.3461	−	14.3461i	−0.458503	−	0.458503i
$980$	12.0123	+	6.87870i	0.383718	+	0.219732i
$981$	−5.32683	+	5.32683i	−0.170073	+	0.170073i
$982$		−	31.0223i		−	0.989961i
$983$	23.7970	+	23.7970i	0.759006	+	0.759006i	0.976141	−	0.217136i	$-0.0696714\pi$
$983$	23.7970	+	23.7970i	0.759006	+	0.759006i	−0.217136	+	0.976141i	$0.569671\pi$
$984$	6.37818	+	6.37818i	0.203329	+	0.203329i
$985$	35.1493	−	9.55172i	1.11995	−	0.304343i
$986$	−9.77878	−	9.77878i	−0.311420	−	0.311420i
$987$	−0.293952	+	0.293952i	−0.00935658	+	0.00935658i
$988$	5.29716	−	5.29716i	0.168525	−	0.168525i
$989$	−7.28050			−0.231507
$990$	4.40204	+	2.52078i	0.139906	+	0.0801158i
$991$	−3.21857	−	3.21857i	−0.102241	−	0.102241i	0.654136	−	0.756377i	$-0.273032\pi$
$991$	−3.21857	−	3.21857i	−0.102241	−	0.102241i	−0.756377	+	0.654136i	$0.773032\pi$
$992$	−5.81155	+	5.81155i	−0.184517	+	0.184517i
$993$	4.60678			0.146192
$994$	−9.72702	+	9.72702i	−0.308522	+	0.308522i
$995$	−8.58044	−	31.5751i	−0.272018	−	1.00100i
$996$	12.9027			0.408839
$997$	27.5415			0.872248			0.436124	−	0.899887i	$-0.356351\pi$
$997$	27.5415			0.872248			0.436124	+	0.899887i	$0.356351\pi$
$998$	−5.68409	−	5.68409i	−0.179927	−	0.179927i
$999$	5.91029	−	1.43822i	0.186993	−	0.0455032i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.l.a.697.4	yes	36
5.3	odd	4		1110.2.o.a.253.15	yes	36
37.6	odd	4		1110.2.o.a.487.15	yes	36
185.43	even	4	inner	1110.2.l.a.43.4	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.l.a.43.4	✓	36	185.43	even	4	inner
1110.2.l.a.697.4	yes	36	1.1	even	1	trivial
1110.2.o.a.253.15	yes	36	5.3	odd	4
1110.2.o.a.487.15	yes	36	37.6	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(1.11117 - 1.94044i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(0.636201 + 0.636201i) q^{7} +1.00000i q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(1.11117 - 1.94044i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(0.636201 + 0.636201i) q^{7} +1.00000i q^{8} +1.00000i q^{9} +(-1.94044 - 1.11117i) q^{10} +2.26858i q^{11} +(0.707107 + 0.707107i) q^{12} -1.29147i q^{13} +(0.636201 - 0.636201i) q^{14} +(-2.15781 + 0.586380i) q^{15} +1.00000 q^{16} -5.74699 q^{17} +1.00000 q^{18} +(-4.10165 - 4.10165i) q^{19} +(-1.11117 + 1.94044i) q^{20} -0.899724i q^{21} +2.26858 q^{22} -8.53431i q^{23} +(0.707107 - 0.707107i) q^{24} +(-2.53060 - 4.31232i) q^{25} -1.29147 q^{26} +(0.707107 - 0.707107i) q^{27} +(-0.636201 - 0.636201i) q^{28} +(-1.70155 + 1.70155i) q^{29} +(0.586380 + 2.15781i) q^{30} +(-5.81155 - 5.81155i) q^{31} -1.00000i q^{32} +(1.60413 - 1.60413i) q^{33} +5.74699i q^{34} +(1.94144 - 0.527580i) q^{35} -1.00000i q^{36} +(5.19618 + 3.16223i) q^{37} +(-4.10165 + 4.10165i) q^{38} +(-0.913209 + 0.913209i) q^{39} +(1.94044 + 1.11117i) q^{40} +9.02011i q^{41} -0.899724 q^{42} -0.853087i q^{43} -2.26858i q^{44} +(1.94044 + 1.11117i) q^{45} -8.53431 q^{46} +(-0.326713 - 0.326713i) q^{47} +(-0.707107 - 0.707107i) q^{48} -6.19050i q^{49} +(-4.31232 + 2.53060i) q^{50} +(4.06374 + 4.06374i) q^{51} +1.29147i q^{52} +(-6.79864 + 6.79864i) q^{53} +(-0.707107 - 0.707107i) q^{54} +(4.40204 + 2.52078i) q^{55} +(-0.636201 + 0.636201i) q^{56} +5.80061i q^{57} +(1.70155 + 1.70155i) q^{58} +(3.51171 + 3.51171i) q^{59} +(2.15781 - 0.586380i) q^{60} +(-2.06460 - 2.06460i) q^{61} +(-5.81155 + 5.81155i) q^{62} +(-0.636201 + 0.636201i) q^{63} -1.00000 q^{64} +(-2.50602 - 1.43505i) q^{65} +(-1.60413 - 1.60413i) q^{66} +(3.98347 - 3.98347i) q^{67} +5.74699 q^{68} +(-6.03467 + 6.03467i) q^{69} +(-0.527580 - 1.94144i) q^{70} -15.2892 q^{71} -1.00000 q^{72} +(-11.8322 - 11.8322i) q^{73} +(3.16223 - 5.19618i) q^{74} +(-1.25987 + 4.83867i) q^{75} +(4.10165 + 4.10165i) q^{76} +(-1.44327 + 1.44327i) q^{77} +(0.913209 + 0.913209i) q^{78} +(9.04382 + 9.04382i) q^{79} +(1.11117 - 1.94044i) q^{80} -1.00000 q^{81} +9.02011 q^{82} +(9.12362 - 9.12362i) q^{83} +0.899724i q^{84} +(-6.38589 + 11.1517i) q^{85} -0.853087 q^{86} +2.40635 q^{87} -2.26858 q^{88} +(-6.32382 + 6.32382i) q^{89} +(1.11117 - 1.94044i) q^{90} +(0.821636 - 0.821636i) q^{91} +8.53431i q^{92} +8.21877i q^{93} +(-0.326713 + 0.326713i) q^{94} +(-12.5166 + 3.40136i) q^{95} +(-0.707107 + 0.707107i) q^{96} +9.28197 q^{97} -6.19050 q^{98} -2.26858 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 36 q^{4} + 4 q^{7}+O(q^{10}) \) 36 * q - 36 * q^4 + 4 * q^7	\( 36 q - 36 q^{4} + 4 q^{7} - 4 q^{10} + 4 q^{14} + 36 q^{16} - 32 q^{17} + 36 q^{18} + 4 q^{19} + 8 q^{22} - 4 q^{25} + 8 q^{26} - 4 q^{28} + 36 q^{29} - 4 q^{31} + 4 q^{33} - 12 q^{35} - 4 q^{37} + 4 q^{38} + 4 q^{39} + 4 q^{40} - 16 q^{42} + 4 q^{45} + 16 q^{47} - 16 q^{50} - 8 q^{53} + 16 q^{55} - 4 q^{56} - 36 q^{58} - 4 q^{59} - 4 q^{61} - 4 q^{62} - 4 q^{63} - 36 q^{64} + 52 q^{65} - 4 q^{66} + 16 q^{67} + 32 q^{68} - 8 q^{69} - 28 q^{70} - 8 q^{71} - 36 q^{72} - 4 q^{73} + 28 q^{74} + 16 q^{75} - 4 q^{76} + 8 q^{77} - 4 q^{78} - 12 q^{79} - 36 q^{81} - 8 q^{82} + 8 q^{83} + 8 q^{85} + 32 q^{86} - 8 q^{87} - 8 q^{88} - 24 q^{89} + 56 q^{91} + 16 q^{94} - 20 q^{95} + 40 q^{97} - 12 q^{98} - 8 q^{99}+O(q^{100}) \) 36 * q - 36 * q^4 + 4 * q^7 - 4 * q^10 + 4 * q^14 + 36 * q^16 - 32 * q^17 + 36 * q^18 + 4 * q^19 + 8 * q^22 - 4 * q^25 + 8 * q^26 - 4 * q^28 + 36 * q^29 - 4 * q^31 + 4 * q^33 - 12 * q^35 - 4 * q^37 + 4 * q^38 + 4 * q^39 + 4 * q^40 - 16 * q^42 + 4 * q^45 + 16 * q^47 - 16 * q^50 - 8 * q^53 + 16 * q^55 - 4 * q^56 - 36 * q^58 - 4 * q^59 - 4 * q^61 - 4 * q^62 - 4 * q^63 - 36 * q^64 + 52 * q^65 - 4 * q^66 + 16 * q^67 + 32 * q^68 - 8 * q^69 - 28 * q^70 - 8 * q^71 - 36 * q^72 - 4 * q^73 + 28 * q^74 + 16 * q^75 - 4 * q^76 + 8 * q^77 - 4 * q^78 - 12 * q^79 - 36 * q^81 - 8 * q^82 + 8 * q^83 + 8 * q^85 + 32 * q^86 - 8 * q^87 - 8 * q^88 - 24 * q^89 + 56 * q^91 + 16 * q^94 - 20 * q^95 + 40 * q^97 - 12 * q^98 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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