LMFDB - Embedded newform 1110.2.o.b.253.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(253,1110)]

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, 1]))

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

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

chi := DirichletCharacter("1110.253");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.o (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			253.13
Character	$\chi$	$=$	1110.253
Dual form			1110.2.o.b.487.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(0.707107 - 0.707107i) q^{3} +1.00000 q^{4} +(-2.22514 + 0.220830i) q^{5} +(0.707107 - 0.707107i) q^{6} +(-1.18593 + 1.18593i) q^{7} +1.00000 q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(0.707107 - 0.707107i) q^{3} +1.00000 q^{4} +(-2.22514 + 0.220830i) q^{5} +(0.707107 - 0.707107i) q^{6} +(-1.18593 + 1.18593i) q^{7} +1.00000 q^{8} -1.00000i q^{9} +(-2.22514 + 0.220830i) q^{10} +4.79879i q^{11} +(0.707107 - 0.707107i) q^{12} +4.44661 q^{13} +(-1.18593 + 1.18593i) q^{14} +(-1.41726 + 1.72956i) q^{15} +1.00000 q^{16} +1.30290i q^{17} -1.00000i q^{18} +(4.46151 + 4.46151i) q^{19} +(-2.22514 + 0.220830i) q^{20} +1.67716i q^{21} +4.79879i q^{22} -0.933219 q^{23} +(0.707107 - 0.707107i) q^{24} +(4.90247 - 0.982756i) q^{25} +4.44661 q^{26} +(-0.707107 - 0.707107i) q^{27} +(-1.18593 + 1.18593i) q^{28} +(3.66959 - 3.66959i) q^{29} +(-1.41726 + 1.72956i) q^{30} +(4.54367 + 4.54367i) q^{31} +1.00000 q^{32} +(3.39326 + 3.39326i) q^{33} +1.30290i q^{34} +(2.37697 - 2.90075i) q^{35} -1.00000i q^{36} +(-5.10204 - 3.31197i) q^{37} +(4.46151 + 4.46151i) q^{38} +(3.14423 - 3.14423i) q^{39} +(-2.22514 + 0.220830i) q^{40} -7.79237i q^{41} +1.67716i q^{42} +2.02422 q^{43} +4.79879i q^{44} +(0.220830 + 2.22514i) q^{45} -0.933219 q^{46} +(-6.81249 + 6.81249i) q^{47} +(0.707107 - 0.707107i) q^{48} +4.18713i q^{49} +(4.90247 - 0.982756i) q^{50} +(0.921286 + 0.921286i) q^{51} +4.44661 q^{52} +(5.08803 + 5.08803i) q^{53} +(-0.707107 - 0.707107i) q^{54} +(-1.05972 - 10.6780i) q^{55} +(-1.18593 + 1.18593i) q^{56} +6.30953 q^{57} +(3.66959 - 3.66959i) q^{58} +(3.87716 + 3.87716i) q^{59} +(-1.41726 + 1.72956i) q^{60} +(-6.36168 - 6.36168i) q^{61} +(4.54367 + 4.54367i) q^{62} +(1.18593 + 1.18593i) q^{63} +1.00000 q^{64} +(-9.89431 + 0.981946i) q^{65} +(3.39326 + 3.39326i) q^{66} +(-0.639879 - 0.639879i) q^{67} +1.30290i q^{68} +(-0.659885 + 0.659885i) q^{69} +(2.37697 - 2.90075i) q^{70} -8.94910 q^{71} -1.00000i q^{72} +(1.06393 - 1.06393i) q^{73} +(-5.10204 - 3.31197i) q^{74} +(2.77166 - 4.16148i) q^{75} +(4.46151 + 4.46151i) q^{76} +(-5.69104 - 5.69104i) q^{77} +(3.14423 - 3.14423i) q^{78} +(2.21244 + 2.21244i) q^{79} +(-2.22514 + 0.220830i) q^{80} -1.00000 q^{81} -7.79237i q^{82} +(-6.32708 - 6.32708i) q^{83} +1.67716i q^{84} +(-0.287719 - 2.89912i) q^{85} +2.02422 q^{86} -5.18959i q^{87} +4.79879i q^{88} +(-3.11309 + 3.11309i) q^{89} +(0.220830 + 2.22514i) q^{90} +(-5.27338 + 5.27338i) q^{91} -0.933219 q^{92} +6.42572 q^{93} +(-6.81249 + 6.81249i) q^{94} +(-10.9127 - 8.94223i) q^{95} +(0.707107 - 0.707107i) q^{96} -0.0235287i q^{97} +4.18713i q^{98} +4.79879 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 40 q^{2} + 40 q^{4} - 4 q^{7} + 40 q^{8}+O(q^{10}) $ 40 * q + 40 * q^2 + 40 * q^4 - 4 * q^7 + 40 * q^8	$ 40 q + 40 q^{2} + 40 q^{4} - 4 q^{7} + 40 q^{8} + 8 q^{13} - 4 q^{14} + 40 q^{16} - 4 q^{19} - 8 q^{25} + 8 q^{26} - 4 q^{28} + 28 q^{31} + 40 q^{32} - 4 q^{33} + 12 q^{35} + 8 q^{37} - 4 q^{38} - 4 q^{39} - 16 q^{47} - 8 q^{50} + 16 q^{51} + 8 q^{52} + 20 q^{53} - 8 q^{55} - 4 q^{56} - 8 q^{57} + 4 q^{59} - 8 q^{61} + 28 q^{62} + 4 q^{63} + 40 q^{64} + 4 q^{65} - 4 q^{66} - 16 q^{67} + 8 q^{69} + 12 q^{70} + 40 q^{71} - 8 q^{73} + 8 q^{74} + 16 q^{75} - 4 q^{76} + 24 q^{77} - 4 q^{78} + 12 q^{79} - 40 q^{81} - 8 q^{83} + 8 q^{85} - 12 q^{89} - 24 q^{91} - 8 q^{93} - 16 q^{94} + 28 q^{95} - 8 q^{99}+O(q^{100}) $ 40 * q + 40 * q^2 + 40 * q^4 - 4 * q^7 + 40 * q^8 + 8 * q^13 - 4 * q^14 + 40 * q^16 - 4 * q^19 - 8 * q^25 + 8 * q^26 - 4 * q^28 + 28 * q^31 + 40 * q^32 - 4 * q^33 + 12 * q^35 + 8 * q^37 - 4 * q^38 - 4 * q^39 - 16 * q^47 - 8 * q^50 + 16 * q^51 + 8 * q^52 + 20 * q^53 - 8 * q^55 - 4 * q^56 - 8 * q^57 + 4 * q^59 - 8 * q^61 + 28 * q^62 + 4 * q^63 + 40 * q^64 + 4 * q^65 - 4 * q^66 - 16 * q^67 + 8 * q^69 + 12 * q^70 + 40 * q^71 - 8 * q^73 + 8 * q^74 + 16 * q^75 - 4 * q^76 + 24 * q^77 - 4 * q^78 + 12 * q^79 - 40 * q^81 - 8 * q^83 + 8 * q^85 - 12 * q^89 - 24 * q^91 - 8 * q^93 - 16 * q^94 + 28 * q^95 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$4$	1.00000			0.500000
$5$	−2.22514	+	0.220830i	−0.995111	+	0.0987584i
$5$	−2.22514	+	0.220830i	−0.995111	+	0.0987584i
$6$	0.707107	−	0.707107i	0.288675	−	0.288675i
$7$	−1.18593	+	1.18593i	−0.448240	+	0.448240i	−0.894769	−	0.446529i	$-0.852660\pi$
$7$	−1.18593	+	1.18593i	−0.448240	+	0.448240i	0.446529	+	0.894769i	$0.352660\pi$
$8$	1.00000			0.353553
$9$		−	1.00000i		−	0.333333i
$10$	−2.22514	+	0.220830i	−0.703650	+	0.0698327i
$11$			4.79879i			1.44689i	0.690382	+	0.723445i	$0.257443\pi$
$11$			4.79879i			1.44689i	−0.690382	+	0.723445i	$0.742557\pi$
$12$	0.707107	−	0.707107i	0.204124	−	0.204124i
$13$	4.44661			1.23327			0.616634	−	0.787250i	$-0.288496\pi$
$13$	4.44661			1.23327			0.616634	+	0.787250i	$0.288496\pi$
$14$	−1.18593	+	1.18593i	−0.316954	+	0.316954i
$15$	−1.41726	+	1.72956i	−0.365935	+	0.446570i
$16$	1.00000			0.250000
$17$			1.30290i			0.315999i	0.987439	+	0.157999i	$0.0505044\pi$
$17$			1.30290i			0.315999i	−0.987439	+	0.157999i	$0.949496\pi$
$18$		−	1.00000i		−	0.235702i
$19$	4.46151	+	4.46151i	1.02354	+	1.02354i	0.999716	+	0.0238243i	$0.00758424\pi$
$19$	4.46151	+	4.46151i	1.02354	+	1.02354i	0.0238243	+	0.999716i	$0.492416\pi$
$20$	−2.22514	+	0.220830i	−0.497556	+	0.0493792i
$21$			1.67716i			0.365987i
$22$			4.79879i			1.02311i
$23$	−0.933219			−0.194590			−0.0972948	−	0.995256i	$-0.531019\pi$
$23$	−0.933219			−0.194590			−0.0972948	+	0.995256i	$0.531019\pi$
$24$	0.707107	−	0.707107i	0.144338	−	0.144338i
$25$	4.90247	−	0.982756i	0.980494	−	0.196551i
$26$	4.44661			0.872052
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$	−1.18593	+	1.18593i	−0.224120	+	0.224120i
$29$	3.66959	−	3.66959i	0.681426	−	0.681426i	−0.278895	−	0.960322i	$-0.589968\pi$
$29$	3.66959	−	3.66959i	0.681426	−	0.681426i	0.960322	+	0.278895i	$0.0899682\pi$
$30$	−1.41726	+	1.72956i	−0.258755	+	0.315773i
$31$	4.54367	+	4.54367i	0.816067	+	0.816067i	0.985536	−	0.169468i	$-0.0542051\pi$
$31$	4.54367	+	4.54367i	0.816067	+	0.816067i	−0.169468	+	0.985536i	$0.554205\pi$
$32$	1.00000			0.176777
$33$	3.39326	+	3.39326i	0.590691	+	0.590691i
$34$			1.30290i			0.223445i
$35$	2.37697	−	2.90075i	0.401781	−	0.490316i
$36$		−	1.00000i		−	0.166667i
$37$	−5.10204	−	3.31197i	−0.838771	−	0.544484i
$37$	−5.10204	−	3.31197i	−0.838771	−	0.544484i
$38$	4.46151	+	4.46151i	0.723752	+	0.723752i
$39$	3.14423	−	3.14423i	0.503479	−	0.503479i
$40$	−2.22514	+	0.220830i	−0.351825	+	0.0349164i
$41$		−	7.79237i		−	1.21696i	−0.793568	−	0.608482i	$-0.791779\pi$
$41$		−	7.79237i		−	1.21696i	0.793568	−	0.608482i	$-0.208221\pi$
$42$			1.67716i			0.258792i
$43$	2.02422			0.308690			0.154345	−	0.988017i	$-0.450673\pi$
$43$	2.02422			0.308690			0.154345	+	0.988017i	$0.450673\pi$
$44$			4.79879i			0.723445i
$45$	0.220830	+	2.22514i	0.0329195	+	0.331704i
$46$	−0.933219			−0.137596
$47$	−6.81249	+	6.81249i	−0.993704	+	0.993704i	−0.999980	−	0.00627644i	$-0.998002\pi$
$47$	−6.81249	+	6.81249i	−0.993704	+	0.993704i	0.00627644	+	0.999980i	$0.498002\pi$
$48$	0.707107	−	0.707107i	0.102062	−	0.102062i
$49$			4.18713i			0.598162i
$50$	4.90247	−	0.982756i	0.693314	−	0.138983i
$51$	0.921286	+	0.921286i	0.129006	+	0.129006i
$52$	4.44661			0.616634
$53$	5.08803	+	5.08803i	0.698895	+	0.698895i	0.964172	−	0.265277i	$-0.0854634\pi$
$53$	5.08803	+	5.08803i	0.698895	+	0.698895i	−0.265277	+	0.964172i	$0.585463\pi$
$54$	−0.707107	−	0.707107i	−0.0962250	−	0.0962250i
$55$	−1.05972	−	10.6780i	−0.142893	−	1.43982i
$56$	−1.18593	+	1.18593i	−0.158477	+	0.158477i
$57$	6.30953			0.835717
$58$	3.66959	−	3.66959i	0.481841	−	0.481841i
$59$	3.87716	+	3.87716i	0.504763	+	0.504763i	0.912914	−	0.408151i	$-0.133826\pi$
$59$	3.87716	+	3.87716i	0.504763	+	0.504763i	−0.408151	+	0.912914i	$0.633826\pi$
$60$	−1.41726	+	1.72956i	−0.182967	+	0.223285i
$61$	−6.36168	−	6.36168i	−0.814529	−	0.814529i	0.170780	−	0.985309i	$-0.445371\pi$
$61$	−6.36168	−	6.36168i	−0.814529	−	0.814529i	−0.985309	+	0.170780i	$0.945371\pi$
$62$	4.54367	+	4.54367i	0.577047	+	0.577047i
$63$	1.18593	+	1.18593i	0.149413	+	0.149413i
$64$	1.00000			0.125000
$65$	−9.89431	+	0.981946i	−1.22724	+	0.121795i
$66$	3.39326	+	3.39326i	0.417681	+	0.417681i
$67$	−0.639879	−	0.639879i	−0.0781737	−	0.0781737i	0.666939	−	0.745112i	$-0.267604\pi$
$67$	−0.639879	−	0.639879i	−0.0781737	−	0.0781737i	−0.745112	+	0.666939i	$0.767604\pi$
$68$			1.30290i			0.157999i
$69$	−0.659885	+	0.659885i	−0.0794409	+	0.0794409i
$70$	2.37697	−	2.90075i	0.284102	−	0.346706i
$71$	−8.94910			−1.06206			−0.531031	−	0.847352i	$-0.678195\pi$
$71$	−8.94910			−1.06206			−0.531031	+	0.847352i	$0.678195\pi$
$72$		−	1.00000i		−	0.117851i
$73$	1.06393	−	1.06393i	0.124524	−	0.124524i	−0.642098	−	0.766622i	$-0.721936\pi$
$73$	1.06393	−	1.06393i	0.124524	−	0.124524i	0.766622	+	0.642098i	$0.221936\pi$
$74$	−5.10204	−	3.31197i	−0.593101	−	0.385009i
$75$	2.77166	−	4.16148i	0.320043	−	0.480526i
$76$	4.46151	+	4.46151i	0.511770	+	0.511770i
$77$	−5.69104	−	5.69104i	−0.648554	−	0.648554i
$78$	3.14423	−	3.14423i	0.356014	−	0.356014i
$79$	2.21244	+	2.21244i	0.248919	+	0.248919i	0.820527	−	0.571608i	$-0.193680\pi$
$79$	2.21244	+	2.21244i	0.248919	+	0.248919i	−0.571608	+	0.820527i	$0.693680\pi$
$80$	−2.22514	+	0.220830i	−0.248778	+	0.0246896i
$81$	−1.00000			−0.111111
$82$		−	7.79237i		−	0.860524i
$83$	−6.32708	−	6.32708i	−0.694488	−	0.694488i	0.268728	−	0.963216i	$-0.413397\pi$
$83$	−6.32708	−	6.32708i	−0.694488	−	0.694488i	−0.963216	+	0.268728i	$0.913397\pi$
$84$			1.67716i			0.182993i
$85$	−0.287719	−	2.89912i	−0.0312075	−	0.314454i
$86$	2.02422			0.218277
$87$		−	5.18959i		−	0.556382i
$88$			4.79879i			0.511553i
$89$	−3.11309	+	3.11309i	−0.329987	+	0.329987i	−0.852582	−	0.522594i	$-0.824964\pi$
$89$	−3.11309	+	3.11309i	−0.329987	+	0.329987i	0.522594	+	0.852582i	$0.324964\pi$
$90$	0.220830	+	2.22514i	0.0232776	+	0.234550i
$91$	−5.27338	+	5.27338i	−0.552800	+	0.552800i
$92$	−0.933219			−0.0972948
$93$	6.42572			0.666316
$94$	−6.81249	+	6.81249i	−0.702655	+	0.702655i
$95$	−10.9127	−	8.94223i	−1.11962	−	0.917454i
$96$	0.707107	−	0.707107i	0.0721688	−	0.0721688i
$97$		−	0.0235287i		−	0.00238898i	−0.999999	−	0.00119449i	$-0.999620\pi$
$97$		−	0.0235287i		−	0.00238898i	0.999999	−	0.00119449i	$-0.000380218\pi$
$98$			4.18713i			0.422964i
$99$	4.79879			0.482297
$100$	4.90247	−	0.982756i	0.490247	−	0.0982756i
$101$			3.95084i			0.393124i	0.980491	+	0.196562i	$0.0629776\pi$
$101$			3.95084i			0.393124i	−0.980491	+	0.196562i	$0.937022\pi$
$102$	0.921286	+	0.921286i	0.0912209	+	0.0912209i
$103$		−	10.4171i		−	1.02642i	−0.858262	−	0.513212i	$-0.828455\pi$
$103$		−	10.4171i		−	1.02642i	0.858262	−	0.513212i	$-0.171545\pi$
$104$	4.44661			0.436026
$105$	−0.370368	−	3.73191i	−0.0361442	−	0.364197i
$106$	5.08803	+	5.08803i	0.494194	+	0.494194i
$107$	−3.87605	+	3.87605i	−0.374712	+	0.374712i	−0.869190	−	0.494478i	$-0.835359\pi$
$107$	−3.87605	+	3.87605i	−0.374712	+	0.374712i	0.494478	+	0.869190i	$0.335359\pi$
$108$	−0.707107	−	0.707107i	−0.0680414	−	0.0680414i
$109$	0.670005	+	0.670005i	0.0641748	+	0.0641748i	0.738466	−	0.674291i	$-0.235551\pi$
$109$	0.670005	+	0.670005i	0.0641748	+	0.0641748i	−0.674291	+	0.738466i	$0.735551\pi$
$110$	−1.05972	−	10.6780i	−0.101040	−	1.01810i
$111$	−5.94961	+	1.26577i	−0.564712	+	0.120142i
$112$	−1.18593	+	1.18593i	−0.112060	+	0.112060i
$113$			10.2693i			0.966056i	0.875605	+	0.483028i	$0.160463\pi$
$113$			10.2693i			0.966056i	−0.875605	+	0.483028i	$0.839537\pi$
$114$	6.30953			0.590941
$115$	2.07654	−	0.206083i	0.193638	−	0.0192173i
$116$	3.66959	−	3.66959i	0.340713	−	0.340713i
$117$		−	4.44661i		−	0.411089i
$118$	3.87716	+	3.87716i	0.356921	+	0.356921i
$119$	−1.54515	−	1.54515i	−0.141643	−	0.141643i
$120$	−1.41726	+	1.72956i	−0.129377	+	0.157887i
$121$	−12.0284			−1.09349
$122$	−6.36168	−	6.36168i	−0.575959	−	0.575959i
$123$	−5.51004	−	5.51004i	−0.496824	−	0.496824i
$124$	4.54367	+	4.54367i	0.408034	+	0.408034i
$125$	−10.6916	+	3.26938i	−0.956289	+	0.292422i
$126$	1.18593	+	1.18593i	0.105651	+	0.105651i
$127$	13.8004	−	13.8004i	1.22459	−	1.22459i	0.258607	−	0.965983i	$-0.416736\pi$
$127$	13.8004	−	13.8004i	1.22459	−	1.22459i	0.965983	−	0.258607i	$-0.0832636\pi$
$128$	1.00000			0.0883883
$129$	1.43134	−	1.43134i	0.126022	−	0.126022i
$130$	−9.89431	+	0.981946i	−0.867789	+	0.0861224i
$131$	−7.14423	−	7.14423i	−0.624194	−	0.624194i	0.322407	−	0.946601i	$-0.395508\pi$
$131$	−7.14423	−	7.14423i	−0.624194	−	0.624194i	−0.946601	+	0.322407i	$0.895508\pi$
$132$	3.39326	+	3.39326i	0.295345	+	0.295345i
$133$	−10.5821			−0.917584
$134$	−0.639879	−	0.639879i	−0.0552771	−	0.0552771i
$135$	1.72956	+	1.41726i	0.148857	+	0.121978i
$136$			1.30290i			0.111722i
$137$	6.54303	−	6.54303i	0.559008	−	0.559008i	−0.370017	−	0.929025i	$-0.620648\pi$
$137$	6.54303	−	6.54303i	0.559008	−	0.559008i	0.929025	+	0.370017i	$0.120648\pi$
$138$	−0.659885	+	0.659885i	−0.0561732	+	0.0561732i
$139$	13.1631			1.11648			0.558241	−	0.829679i	$-0.311476\pi$
$139$	13.1631			1.11648			0.558241	+	0.829679i	$0.311476\pi$
$140$	2.37697	−	2.90075i	0.200891	−	0.245158i
$141$			9.63432i			0.811356i
$142$	−8.94910			−0.750992
$143$			21.3384i			1.78440i
$144$		−	1.00000i		−	0.0833333i
$145$	−7.35499	+	8.97570i	−0.610798	+	0.745392i
$146$	1.06393	−	1.06393i	0.0880517	−	0.0880517i
$147$	2.96075	+	2.96075i	0.244198	+	0.244198i
$148$	−5.10204	−	3.31197i	−0.419385	−	0.272242i
$149$		−	5.19216i		−	0.425359i	−0.977122	−	0.212679i	$-0.931781\pi$
$149$		−	5.19216i		−	0.425359i	0.977122	−	0.212679i	$-0.0682189\pi$
$150$	2.77166	−	4.16148i	0.226305	−	0.339784i
$151$			11.5161i			0.937170i	0.883419	+	0.468585i	$0.155236\pi$
$151$			11.5161i			0.937170i	−0.883419	+	0.468585i	$0.844764\pi$
$152$	4.46151	+	4.46151i	0.361876	+	0.361876i
$153$	1.30290			0.105333
$154$	−5.69104	−	5.69104i	−0.458597	−	0.458597i
$155$	−11.1137	−	9.10691i	−0.892671	−	0.731484i
$156$	3.14423	−	3.14423i	0.251740	−	0.251740i
$157$	−2.32320	+	2.32320i	−0.185411	+	0.185411i	−0.793709	−	0.608298i	$-0.791853\pi$
$157$	−2.32320	+	2.32320i	−0.185411	+	0.185411i	0.608298	+	0.793709i	$0.291853\pi$
$158$	2.21244	+	2.21244i	0.176012	+	0.176012i
$159$	7.19557			0.570646
$160$	−2.22514	+	0.220830i	−0.175913	+	0.0174582i
$161$	1.10673	−	1.10673i	0.0872229	−	0.0872229i
$162$	−1.00000			−0.0785674
$163$			0.310642i			0.0243314i	0.999926	+	0.0121657i	$0.00387255\pi$
$163$			0.310642i			0.0243314i	−0.999926	+	0.0121657i	$0.996127\pi$
$164$		−	7.79237i		−	0.608482i
$165$	−8.29980	−	6.80113i	−0.646139	−	0.529467i
$166$	−6.32708	−	6.32708i	−0.491077	−	0.491077i
$167$		−	21.2856i		−	1.64713i	−0.567225	−	0.823563i	$-0.691983\pi$
$167$		−	21.2856i		−	1.64713i	0.567225	−	0.823563i	$-0.308017\pi$
$168$			1.67716i			0.129396i
$169$	6.77233			0.520948
$170$	−0.287719	−	2.89912i	−0.0220670	−	0.222352i
$171$	4.46151	−	4.46151i	0.341180	−	0.341180i
$172$	2.02422			0.154345
$173$	13.5623	−	13.5623i	1.03112	−	1.03112i	0.0316231	−	0.999500i	$-0.489932\pi$
$173$	13.5623	−	13.5623i	1.03112	−	1.03112i	0.999500	−	0.0316231i	$-0.0100676\pi$
$174$		−	5.18959i		−	0.393422i
$175$	−4.64851	+	6.97947i	−0.351394	+	0.527599i
$176$			4.79879i			0.361723i
$177$	5.48313			0.412137
$178$	−3.11309	+	3.11309i	−0.233336	+	0.233336i
$179$	9.91196	−	9.91196i	0.740854	−	0.740854i	−0.231888	−	0.972742i	$-0.574490\pi$
$179$	9.91196	−	9.91196i	0.740854	−	0.740854i	0.972742	+	0.231888i	$0.0744903\pi$
$180$	0.220830	+	2.22514i	0.0164597	+	0.165852i
$181$	−1.52458			−0.113321			−0.0566606	−	0.998393i	$-0.518045\pi$
$181$	−1.52458			−0.113321			−0.0566606	+	0.998393i	$0.518045\pi$
$182$	−5.27338	+	5.27338i	−0.390889	+	0.390889i
$183$	−8.99677			−0.665060
$184$	−0.933219			−0.0687978
$185$	12.0841	+	6.24290i	0.888443	+	0.458987i
$186$	6.42572			0.471157
$187$	−6.25232			−0.457215
$188$	−6.81249	+	6.81249i	−0.496852	+	0.496852i
$189$	1.67716			0.121996
$190$	−10.9127	−	8.94223i	−0.791691	−	0.648738i
$191$	−15.7574	+	15.7574i	−1.14016	+	1.14016i	−0.151745	+	0.988420i	$0.548489\pi$
$191$	−15.7574	+	15.7574i	−1.14016	+	1.14016i	−0.988420	+	0.151745i	$0.951511\pi$
$192$	0.707107	−	0.707107i	0.0510310	−	0.0510310i
$193$	−16.8985			−1.21638			−0.608192	−	0.793790i	$-0.708105\pi$
$193$	−16.8985			−1.21638			−0.608192	+	0.793790i	$0.708105\pi$
$194$		−	0.0235287i		−	0.00168926i
$195$	−6.30199	+	7.69068i	−0.451295	+	0.550741i
$196$			4.18713i			0.299081i
$197$	−5.46379	+	5.46379i	−0.389279	+	0.389279i	−0.874430	−	0.485151i	$-0.838764\pi$
$197$	−5.46379	+	5.46379i	−0.389279	+	0.389279i	0.485151	+	0.874430i	$0.338764\pi$
$198$	4.79879			0.341035
$199$	11.6938	−	11.6938i	0.828949	−	0.828949i	−0.158423	−	0.987371i	$-0.550641\pi$
$199$	11.6938	−	11.6938i	0.828949	−	0.828949i	0.987371	+	0.158423i	$0.0506408\pi$
$200$	4.90247	−	0.982756i	0.346657	−	0.0694913i
$201$	−0.904926			−0.0638285
$202$			3.95084i			0.277980i
$203$			8.70377i			0.610885i
$204$	0.921286	+	0.921286i	0.0645029	+	0.0645029i
$205$	1.72079	+	17.3391i	0.120185	+	1.21101i
$206$		−	10.4171i		−	0.725792i
$207$			0.933219i			0.0648632i
$208$	4.44661			0.308317
$209$	−21.4099	+	21.4099i	−1.48095	+	1.48095i
$210$	−0.370368	−	3.73191i	−0.0255578	−	0.257526i
$211$	25.9385			1.78568			0.892841	−	0.450371i	$-0.148708\pi$
$211$	25.9385			1.78568			0.892841	+	0.450371i	$0.148708\pi$
$212$	5.08803	+	5.08803i	0.349448	+	0.349448i
$213$	−6.32797	+	6.32797i	−0.433585	+	0.433585i
$214$	−3.87605	+	3.87605i	−0.264962	+	0.264962i
$215$	−4.50416	+	0.447009i	−0.307181	+	0.0304857i
$216$	−0.707107	−	0.707107i	−0.0481125	−	0.0481125i
$217$	−10.7770			−0.731588
$218$	0.670005	+	0.670005i	0.0453784	+	0.0453784i
$219$		−	1.50463i		−	0.101673i
$220$	−1.05972	−	10.6780i	−0.0714463	−	0.719909i
$221$			5.79347i			0.389711i
$222$	−5.94961	+	1.26577i	−0.399311	+	0.0849532i
$223$	−10.7674	−	10.7674i	−0.721039	−	0.721039i	0.247778	−	0.968817i	$-0.420300\pi$
$223$	−10.7674	−	10.7674i	−0.721039	−	0.721039i	−0.968817	+	0.247778i	$0.920300\pi$
$224$	−1.18593	+	1.18593i	−0.0792384	+	0.0792384i
$225$	−0.982756	−	4.90247i	−0.0655170	−	0.326831i
$226$			10.2693i			0.683105i
$227$			9.50039i			0.630563i	0.948998	+	0.315282i	$0.102099\pi$
$227$			9.50039i			0.630563i	−0.948998	+	0.315282i	$0.897901\pi$
$228$	6.30953			0.417859
$229$			4.84055i			0.319873i	0.987127	+	0.159936i	$0.0511289\pi$
$229$			4.84055i			0.319873i	−0.987127	+	0.159936i	$0.948871\pi$
$230$	2.07654	−	0.206083i	0.136923	−	0.0135887i
$231$	−8.04835			−0.529542
$232$	3.66959	−	3.66959i	0.240921	−	0.240921i
$233$	4.19880	−	4.19880i	0.275072	−	0.275072i	−0.556066	−	0.831138i	$-0.687690\pi$
$233$	4.19880	−	4.19880i	0.275072	−	0.275072i	0.831138	+	0.556066i	$0.187690\pi$
$234$		−	4.44661i		−	0.290684i
$235$	13.6543	−	16.6631i	0.890710	−	1.08698i
$236$	3.87716	+	3.87716i	0.252382	+	0.252382i
$237$	3.12886			0.203241
$238$	−1.54515	−	1.54515i	−0.100157	−	0.100157i
$239$	−5.62269	−	5.62269i	−0.363701	−	0.363701i	0.501472	−	0.865174i	$-0.332792\pi$
$239$	−5.62269	−	5.62269i	−0.363701	−	0.363701i	−0.865174	+	0.501472i	$0.832792\pi$
$240$	−1.41726	+	1.72956i	−0.0914837	+	0.111643i
$241$	10.8325	−	10.8325i	0.697784	−	0.697784i	−0.266148	−	0.963932i	$-0.585751\pi$
$241$	10.8325	−	10.8325i	0.697784	−	0.697784i	0.963932	+	0.266148i	$0.0857510\pi$
$242$	−12.0284			−0.773216
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$	−6.36168	−	6.36168i	−0.407265	−	0.407265i
$245$	−0.924646	−	9.31694i	−0.0590734	−	0.595237i
$246$	−5.51004	−	5.51004i	−0.351307	−	0.351307i
$247$	19.8386	+	19.8386i	1.26230	+	1.26230i
$248$	4.54367	+	4.54367i	0.288523	+	0.288523i
$249$	−8.94785			−0.567047
$250$	−10.6916	+	3.26938i	−0.676199	+	0.206774i
$251$	14.8022	+	14.8022i	0.934305	+	0.934305i	0.997971	−	0.0636664i	$-0.0202794\pi$
$251$	14.8022	+	14.8022i	0.934305	+	0.934305i	−0.0636664	+	0.997971i	$0.520279\pi$
$252$	1.18593	+	1.18593i	0.0747067	+	0.0747067i
$253$		−	4.47832i		−	0.281550i
$254$	13.8004	−	13.8004i	0.865916	−	0.865916i
$255$	−2.25344	−	1.84654i	−0.141116	−	0.115635i
$256$	1.00000			0.0625000
$257$		−	11.2517i		−	0.701861i	−0.936401	−	0.350931i	$-0.885865\pi$
$257$		−	11.2517i		−	0.701861i	0.936401	−	0.350931i	$-0.114135\pi$
$258$	1.43134	−	1.43134i	0.0891112	−	0.0891112i
$259$	9.97845	−	2.12291i	0.620031	−	0.131911i
$260$	−9.89431	+	0.981946i	−0.613619	+	0.0608977i
$261$	−3.66959	−	3.66959i	−0.227142	−	0.227142i
$262$	−7.14423	−	7.14423i	−0.441372	−	0.441372i
$263$	10.1672	−	10.1672i	0.626937	−	0.626937i	−0.320359	−	0.947296i	$-0.603804\pi$
$263$	10.1672	−	10.1672i	0.626937	−	0.626937i	0.947296	+	0.320359i	$0.103804\pi$
$264$	3.39326	+	3.39326i	0.208841	+	0.208841i
$265$	−12.4452	−	10.1980i	−0.764500	−	0.626457i
$266$	−10.5821			−0.648830
$267$			4.40258i			0.269434i
$268$	−0.639879	−	0.639879i	−0.0390868	−	0.0390868i
$269$		−	24.8306i		−	1.51395i	−0.653445	−	0.756974i	$-0.726677\pi$
$269$		−	24.8306i		−	1.51395i	0.653445	−	0.756974i	$-0.273323\pi$
$270$	1.72956	+	1.41726i	0.105258	+	0.0862516i
$271$	3.95334			0.240148			0.120074	−	0.992765i	$-0.461687\pi$
$271$	3.95334			0.240148			0.120074	+	0.992765i	$0.461687\pi$
$272$			1.30290i			0.0789996i
$273$			7.45768i			0.451359i
$274$	6.54303	−	6.54303i	0.395279	−	0.395279i
$275$	4.71604	+	23.5259i	0.284388	+	1.41867i
$276$	−0.659885	+	0.659885i	−0.0397204	+	0.0397204i
$277$	−2.77329			−0.166631			−0.0833154	−	0.996523i	$-0.526551\pi$
$277$	−2.77329			−0.166631			−0.0833154	+	0.996523i	$0.526551\pi$
$278$	13.1631			0.789472
$279$	4.54367	−	4.54367i	0.272022	−	0.272022i
$280$	2.37697	−	2.90075i	0.142051	−	0.173353i
$281$	−12.9824	+	12.9824i	−0.774467	+	0.774467i	−0.978884	−	0.204417i	$-0.934470\pi$
$281$	−12.9824	+	12.9824i	−0.774467	+	0.774467i	0.204417	+	0.978884i	$0.434470\pi$
$282$			9.63432i			0.573715i
$283$		−	26.5212i		−	1.57652i	−0.615341	−	0.788261i	$-0.710982\pi$
$283$		−	26.5212i		−	1.57652i	0.615341	−	0.788261i	$-0.289018\pi$
$284$	−8.94910			−0.531031
$285$	−14.0396	+	1.39334i	−0.831632	+	0.0825341i
$286$			21.3384i			1.26176i
$287$	9.24122	+	9.24122i	0.545492	+	0.545492i
$288$		−	1.00000i		−	0.0589256i
$289$	15.3025			0.900145
$290$	−7.35499	+	8.97570i	−0.431900	+	0.527071i
$291$	−0.0166373	−	0.0166373i	−0.000975297	−	0.000975297i
$292$	1.06393	−	1.06393i	0.0622619	−	0.0622619i
$293$	−18.1427	−	18.1427i	−1.05991	−	1.05991i	−0.998087	−	0.0618185i	$-0.980310\pi$
$293$	−18.1427	−	18.1427i	−1.05991	−	1.05991i	−0.0618185	−	0.998087i	$-0.519690\pi$
$294$	2.96075	+	2.96075i	0.172674	+	0.172674i
$295$	−9.48340	−	7.77102i	−0.552145	−	0.452446i
$296$	−5.10204	−	3.31197i	−0.296550	−	0.192504i
$297$	3.39326	−	3.39326i	0.196897	−	0.196897i
$298$		−	5.19216i		−	0.300774i
$299$	−4.14966			−0.239981
$300$	2.77166	−	4.16148i	0.160022	−	0.240263i
$301$	−2.40058	+	2.40058i	−0.138367	+	0.138367i
$302$			11.5161i			0.662679i
$303$	2.79367	+	2.79367i	0.160492	+	0.160492i
$304$	4.46151	+	4.46151i	0.255885	+	0.255885i
$305$	15.5605	+	12.7507i	0.890989	+	0.730106i
$306$	1.30290			0.0744816
$307$	2.44662	+	2.44662i	0.139636	+	0.139636i	0.773470	−	0.633833i	$-0.218520\pi$
$307$	2.44662	+	2.44662i	0.139636	+	0.139636i	−0.633833	+	0.773470i	$0.718520\pi$
$308$	−5.69104	−	5.69104i	−0.324277	−	0.324277i
$309$	−7.36598	−	7.36598i	−0.419036	−	0.419036i
$310$	−11.1137	−	9.10691i	−0.631214	−	0.517238i
$311$	−22.4050	−	22.4050i	−1.27047	−	1.27047i	−0.945841	−	0.324631i	$-0.894760\pi$
$311$	−22.4050	−	22.4050i	−1.27047	−	1.27047i	−0.324631	−	0.945841i	$-0.605240\pi$
$312$	3.14423	−	3.14423i	0.178007	−	0.178007i
$313$	−1.26968			−0.0717668			−0.0358834	−	0.999356i	$-0.511424\pi$
$313$	−1.26968			−0.0717668			−0.0358834	+	0.999356i	$0.511424\pi$
$314$	−2.32320	+	2.32320i	−0.131106	+	0.131106i
$315$	−2.90075	−	2.37697i	−0.163439	−	0.133927i
$316$	2.21244	+	2.21244i	0.124459	+	0.124459i
$317$	−11.5508	−	11.5508i	−0.648757	−	0.648757i	0.303936	−	0.952693i	$-0.401699\pi$
$317$	−11.5508	−	11.5508i	−0.648757	−	0.648757i	−0.952693	+	0.303936i	$0.901699\pi$
$318$	7.19557			0.403507
$319$	17.6096	+	17.6096i	0.985949	+	0.985949i
$320$	−2.22514	+	0.220830i	−0.124389	+	0.0123448i
$321$			5.48157i			0.305951i
$322$	1.10673	−	1.10673i	0.0616759	−	0.0616759i
$323$	−5.81288	+	5.81288i	−0.323437	+	0.323437i
$324$	−1.00000			−0.0555556
$325$	21.7994	−	4.36993i	1.20921	−	0.242400i
$326$			0.310642i			0.0172049i
$327$	0.947530			0.0523985
$328$		−	7.79237i		−	0.430262i
$329$		−	16.1583i		−	0.890836i
$330$	−8.29980	−	6.80113i	−0.456889	−	0.374390i
$331$	−14.6794	+	14.6794i	−0.806851	+	0.806851i	−0.984156	−	0.177305i	$-0.943262\pi$
$331$	−14.6794	+	14.6794i	−0.806851	+	0.806851i	0.177305	+	0.984156i	$0.443262\pi$
$332$	−6.32708	−	6.32708i	−0.347244	−	0.347244i
$333$	−3.31197	+	5.10204i	−0.181495	+	0.279590i
$334$		−	21.2856i		−	1.16469i
$335$	1.56512	+	1.28251i	0.0855118	+	0.0700712i
$336$			1.67716i			0.0914966i
$337$	−3.80408	−	3.80408i	−0.207222	−	0.207222i	0.595864	−	0.803085i	$-0.296810\pi$
$337$	−3.80408	−	3.80408i	−0.207222	−	0.207222i	−0.803085	+	0.595864i	$0.796810\pi$
$338$	6.77233			0.368366
$339$	7.26150	+	7.26150i	0.394391	+	0.394391i
$340$	−0.287719	−	2.89912i	−0.0156037	−	0.157227i
$341$	−21.8041	+	21.8041i	−1.18076	+	1.18076i
$342$	4.46151	−	4.46151i	0.241251	−	0.241251i
$343$	−13.2672	−	13.2672i	−0.716360	−	0.716360i
$344$	2.02422			0.109138
$345$	1.32261	−	1.61406i	0.0712071	−	0.0868980i
$346$	13.5623	−	13.5623i	0.729114	−	0.729114i
$347$	−32.1513			−1.72597			−0.862987	−	0.505226i	$-0.831409\pi$
$347$	−32.1513			−1.72597			−0.862987	+	0.505226i	$0.831409\pi$
$348$		−	5.18959i		−	0.278191i
$349$		−	4.32501i		−	0.231512i	−0.993278	−	0.115756i	$-0.963071\pi$
$349$		−	4.32501i		−	0.231512i	0.993278	−	0.115756i	$-0.0369291\pi$
$350$	−4.64851	+	6.97947i	−0.248473	+	0.373069i
$351$	−3.14423	−	3.14423i	−0.167826	−	0.167826i
$352$			4.79879i			0.255777i
$353$		−	16.0457i		−	0.854028i	−0.904245	−	0.427014i	$-0.859566\pi$
$353$		−	16.0457i		−	0.854028i	0.904245	−	0.427014i	$-0.140434\pi$
$354$	5.48313			0.291425
$355$	19.9130	−	1.97623i	1.05687	−	0.104888i
$356$	−3.11309	+	3.11309i	−0.164994	+	0.164994i
$357$	−2.18517			−0.115651
$358$	9.91196	−	9.91196i	0.523863	−	0.523863i
$359$			15.7185i			0.829591i	0.909915	+	0.414795i	$0.136147\pi$
$359$			15.7185i			0.829591i	−0.909915	+	0.414795i	$0.863853\pi$
$360$	0.220830	+	2.22514i	0.0116388	+	0.117275i
$361$			20.8101i			1.09527i
$362$	−1.52458			−0.0801302
$363$	−8.50537	+	8.50537i	−0.446416	+	0.446416i
$364$	−5.27338	+	5.27338i	−0.276400	+	0.276400i
$365$	−2.13245	+	2.60234i	−0.111617	+	0.136213i
$366$	−8.99677			−0.470269
$367$	17.3935	−	17.3935i	0.907935	−	0.907935i	−0.0881705	−	0.996105i	$-0.528102\pi$
$367$	17.3935	−	17.3935i	0.907935	−	0.907935i	0.996105	+	0.0881705i	$0.0281020\pi$
$368$	−0.933219			−0.0486474
$369$	−7.79237			−0.405655
$370$	12.0841	+	6.24290i	0.628224	+	0.324553i
$371$	−12.0681			−0.626546
$372$	6.42572			0.333158
$373$	24.4469	−	24.4469i	1.26581	−	1.26581i	0.317582	−	0.948231i	$-0.397129\pi$
$373$	24.4469	−	24.4469i	1.26581	−	1.26581i	0.948231	−	0.317582i	$-0.102871\pi$
$374$	−6.25232			−0.323300
$375$	−5.24833	+	9.87193i	−0.271023	+	0.509784i
$376$	−6.81249	+	6.81249i	−0.351327	+	0.351327i
$377$	16.3172	−	16.3172i	0.840381	−	0.840381i
$378$	1.67716			0.0862639
$379$			28.8766i			1.48329i	0.670793	+	0.741645i	$0.265954\pi$
$379$			28.8766i			1.48329i	−0.670793	+	0.741645i	$0.734046\pi$
$380$	−10.9127	−	8.94223i	−0.559810	−	0.458727i
$381$		−	19.5168i		−	0.999873i
$382$	−15.7574	+	15.7574i	−0.806218	+	0.806218i
$383$	36.9567			1.88840			0.944200	−	0.329374i	$-0.106838\pi$
$383$	36.9567			1.88840			0.944200	+	0.329374i	$0.106838\pi$
$384$	0.707107	−	0.707107i	0.0360844	−	0.0360844i
$385$	13.9201	+	11.4066i	0.709434	+	0.581334i
$386$	−16.8985			−0.860113
$387$		−	2.02422i		−	0.102897i
$388$		−	0.0235287i		−	0.00119449i
$389$	−21.5492	−	21.5492i	−1.09259	−	1.09259i	−0.995252	−	0.0973355i	$-0.968968\pi$
$389$	−21.5492	−	21.5492i	−1.09259	−	1.09259i	−0.0973355	−	0.995252i	$-0.531032\pi$
$390$	−6.30199	+	7.69068i	−0.319114	+	0.389433i
$391$		−	1.21589i		−	0.0614900i
$392$			4.18713i			0.211482i
$393$	−10.1035			−0.509652
$394$	−5.46379	+	5.46379i	−0.275262	+	0.275262i
$395$	−5.41155	−	4.43441i	−0.272285	−	0.223119i
$396$	4.79879			0.241148
$397$	−26.8752	−	26.8752i	−1.34883	−	1.34883i	−0.886935	−	0.461894i	$-0.847170\pi$
$397$	−26.8752	−	26.8752i	−1.34883	−	1.34883i	−0.461894	−	0.886935i	$-0.652830\pi$
$398$	11.6938	−	11.6938i	0.586155	−	0.586155i
$399$	−7.48267	+	7.48267i	−0.374602	+	0.374602i
$400$	4.90247	−	0.982756i	0.245123	−	0.0491378i
$401$	16.3614	+	16.3614i	0.817048	+	0.817048i	0.985679	−	0.168631i	$-0.0539346\pi$
$401$	16.3614	+	16.3614i	0.817048	+	0.817048i	−0.168631	+	0.985679i	$0.553935\pi$
$402$	−0.904926			−0.0451336
$403$	20.2039	+	20.2039i	1.00643	+	1.00643i
$404$			3.95084i			0.196562i
$405$	2.22514	−	0.220830i	0.110568	−	0.0109732i
$406$			8.70377i			0.431961i
$407$	15.8935	−	24.4837i	0.787809	−	1.21361i
$408$	0.921286	+	0.921286i	0.0456105	+	0.0456105i
$409$	1.75957	−	1.75957i	0.0870050	−	0.0870050i	−0.662265	−	0.749270i	$-0.730405\pi$
$409$	1.75957	−	1.75957i	0.0870050	−	0.0870050i	0.749270	+	0.662265i	$0.230405\pi$
$410$	1.72079	+	17.3391i	0.0849839	+	0.856317i
$411$		−	9.25324i		−	0.456429i
$412$		−	10.4171i		−	0.513212i
$413$	−9.19609			−0.452510
$414$			0.933219i			0.0458652i
$415$	15.4758	+	12.6814i	0.759679	+	0.622506i
$416$	4.44661			0.218013
$417$	9.30774	−	9.30774i	0.455802	−	0.455802i
$418$	−21.4099	+	21.4099i	−1.04719	+	1.04719i
$419$		−	10.0390i		−	0.490439i	−0.969468	−	0.245220i	$-0.921140\pi$
$419$		−	10.0390i		−	0.490439i	0.969468	−	0.245220i	$-0.0788601\pi$
$420$	−0.370368	−	3.73191i	−0.0180721	−	0.182099i
$421$	−6.87930	−	6.87930i	−0.335277	−	0.335277i	0.519310	−	0.854586i	$-0.326189\pi$
$421$	−6.87930	−	6.87930i	−0.335277	−	0.335277i	−0.854586	+	0.519310i	$0.826189\pi$
$422$	25.9385			1.26267
$423$	6.81249	+	6.81249i	0.331235	+	0.331235i
$424$	5.08803	+	5.08803i	0.247097	+	0.247097i
$425$	1.28043	+	6.38740i	0.0621099	+	0.309835i
$426$	−6.32797	+	6.32797i	−0.306591	+	0.306591i
$427$	15.0890			0.730209
$428$	−3.87605	+	3.87605i	−0.187356	+	0.187356i
$429$	15.0885	+	15.0885i	0.728479	+	0.728479i
$430$	−4.50416	+	0.447009i	−0.217210	+	0.0215567i
$431$	6.62805	+	6.62805i	0.319262	+	0.319262i	0.848484	−	0.529222i	$-0.177516\pi$
$431$	6.62805	+	6.62805i	0.319262	+	0.319262i	−0.529222	+	0.848484i	$0.677516\pi$
$432$	−0.707107	−	0.707107i	−0.0340207	−	0.0340207i
$433$	11.5273	+	11.5273i	0.553968	+	0.553968i	0.927584	−	0.373616i	$-0.121882\pi$
$433$	11.5273	+	11.5273i	0.553968	+	0.553968i	−0.373616	+	0.927584i	$0.621882\pi$
$434$	−10.7770			−0.517311
$435$	1.14602	+	11.5475i	0.0549474	+	0.553662i
$436$	0.670005	+	0.670005i	0.0320874	+	0.0320874i
$437$	−4.16356	−	4.16356i	−0.199170	−	0.199170i
$438$		−	1.50463i		−	0.0718939i
$439$	−25.1084	+	25.1084i	−1.19836	+	1.19836i	−0.223702	+	0.974658i	$0.571814\pi$
$439$	−25.1084	+	25.1084i	−1.19836	+	1.19836i	−0.974658	+	0.223702i	$0.928186\pi$
$440$	−1.05972	−	10.6780i	−0.0505201	−	0.509052i
$441$	4.18713			0.199387
$442$			5.79347i			0.275567i
$443$	−10.8396	+	10.8396i	−0.515004	+	0.515004i	−0.916056	−	0.401051i	$-0.868645\pi$
$443$	−10.8396	+	10.8396i	−0.515004	+	0.515004i	0.401051	+	0.916056i	$0.368645\pi$
$444$	−5.94961	+	1.26577i	−0.282356	+	0.0600710i
$445$	6.23959	−	7.61453i	0.295785	−	0.360963i
$446$	−10.7674	−	10.7674i	−0.509852	−	0.509852i
$447$	−3.67141	−	3.67141i	−0.173652	−	0.173652i
$448$	−1.18593	+	1.18593i	−0.0560300	+	0.0560300i
$449$	16.9181	+	16.9181i	0.798413	+	0.798413i	0.982845	−	0.184433i	$-0.0590447\pi$
$449$	16.9181	+	16.9181i	0.798413	+	0.798413i	−0.184433	+	0.982845i	$0.559045\pi$
$450$	−0.982756	−	4.90247i	−0.0463275	−	0.231105i
$451$	37.3940			1.76081
$452$			10.2693i			0.483028i
$453$	8.14314	+	8.14314i	0.382598	+	0.382598i
$454$			9.50039i			0.445876i
$455$	10.5695	−	12.8985i	0.495504	−	0.604691i
$456$	6.30953			0.295471
$457$		−	17.9114i		−	0.837860i	−0.908018	−	0.418930i	$-0.862405\pi$
$457$		−	17.9114i		−	0.837860i	0.908018	−	0.418930i	$-0.137595\pi$
$458$			4.84055i			0.226184i
$459$	0.921286	−	0.921286i	0.0430020	−	0.0430020i
$460$	2.07654	−	0.206083i	0.0968192	−	0.00960867i
$461$	2.45180	−	2.45180i	0.114192	−	0.114192i	−0.647702	−	0.761894i	$-0.724270\pi$
$461$	2.45180	−	2.45180i	0.114192	−	0.114192i	0.761894	+	0.647702i	$0.224270\pi$
$462$	−8.04835			−0.374443
$463$	36.5028			1.69643			0.848214	−	0.529654i	$-0.177678\pi$
$463$	36.5028			1.69643			0.848214	+	0.529654i	$0.177678\pi$
$464$	3.66959	−	3.66959i	0.170357	−	0.170357i
$465$	−14.2981	+	1.41899i	−0.663059	+	0.0658043i
$466$	4.19880	−	4.19880i	0.194505	−	0.194505i
$467$			20.8160i			0.963252i	0.876377	+	0.481626i	$0.159954\pi$
$467$			20.8160i			0.963252i	−0.876377	+	0.481626i	$0.840046\pi$
$468$		−	4.44661i		−	0.205545i
$469$	1.51771			0.0700812
$470$	13.6543	−	16.6631i	0.629827	−	0.768613i
$471$			3.28550i			0.151388i
$472$	3.87716	+	3.87716i	0.178461	+	0.178461i
$473$			9.71380i			0.446641i
$474$	3.12886			0.143713
$475$	26.2570	+	17.4878i	1.20475	+	0.802397i
$476$	−1.54515	−	1.54515i	−0.0708216	−	0.0708216i
$477$	5.08803	−	5.08803i	0.232965	−	0.232965i
$478$	−5.62269	−	5.62269i	−0.257176	−	0.257176i
$479$	21.3099	+	21.3099i	0.973672	+	0.973672i	0.999662	−	0.0259899i	$-0.00827378\pi$
$479$	21.3099	+	21.3099i	0.973672	+	0.973672i	−0.0259899	+	0.999662i	$0.508274\pi$
$480$	−1.41726	+	1.72956i	−0.0646887	+	0.0789433i
$481$	−22.6868	−	14.7270i	−1.03443	−	0.671495i
$482$	10.8325	−	10.8325i	0.493408	−	0.493408i
$483$		−	1.56516i		−	0.0712172i
$484$	−12.0284			−0.546746
$485$	0.00519586	+	0.0523546i	0.000235932	+	0.00237730i
$486$	−0.707107	+	0.707107i	−0.0320750	+	0.0320750i
$487$			31.2190i			1.41467i	0.706880	+	0.707334i	$0.250102\pi$
$487$			31.2190i			1.41467i	−0.706880	+	0.707334i	$0.749898\pi$
$488$	−6.36168	−	6.36168i	−0.287980	−	0.287980i
$489$	0.219657	+	0.219657i	0.00993323	+	0.00993323i
$490$	−0.924646	−	9.31694i	−0.0417712	−	0.420896i
$491$	1.46818			0.0662579			0.0331289	−	0.999451i	$-0.489453\pi$
$491$	1.46818			0.0662579			0.0331289	+	0.999451i	$0.489453\pi$
$492$	−5.51004	−	5.51004i	−0.248412	−	0.248412i
$493$	4.78109	+	4.78109i	0.215330	+	0.215330i
$494$	19.8386	+	19.8386i	0.892580	+	0.892580i
$495$	−10.6780	+	1.05972i	−0.479939	+	0.0476308i
$496$	4.54367	+	4.54367i	0.204017	+	0.204017i
$497$	10.6130	−	10.6130i	0.476059	−	0.476059i
$498$	−8.94785			−0.400963
$499$	−1.77906	+	1.77906i	−0.0796419	+	0.0796419i	−0.745806	−	0.666164i	$-0.767935\pi$
$499$	−1.77906	+	1.77906i	−0.0796419	+	0.0796419i	0.666164	+	0.745806i	$0.267935\pi$
$500$	−10.6916	+	3.26938i	−0.478145	+	0.146211i
$501$	−15.0512	−	15.0512i	−0.672436	−	0.672436i
$502$	14.8022	+	14.8022i	0.660653	+	0.660653i
$503$	10.5966			0.472478			0.236239	−	0.971695i	$-0.424085\pi$
$503$	10.5966			0.472478			0.236239	+	0.971695i	$0.424085\pi$
$504$	1.18593	+	1.18593i	0.0528256	+	0.0528256i
$505$	−0.872466	−	8.79117i	−0.0388242	−	0.391202i
$506$		−	4.47832i		−	0.199086i
$507$	4.78876	−	4.78876i	0.212676	−	0.212676i
$508$	13.8004	−	13.8004i	0.612295	−	0.612295i
$509$	7.39583			0.327814			0.163907	−	0.986476i	$-0.447590\pi$
$509$	7.39583			0.327814			0.163907	+	0.986476i	$0.447590\pi$
$510$	−2.25344	−	1.84654i	−0.0997838	−	0.0817661i
$511$			2.52350i			0.111633i
$512$	1.00000			0.0441942
$513$		−	6.30953i		−	0.278572i
$514$		−	11.2517i		−	0.496291i
$515$	2.30041	+	23.1794i	0.101368	+	1.02141i
$516$	1.43134	−	1.43134i	0.0630111	−	0.0630111i
$517$	−32.6917	−	32.6917i	−1.43778	−	1.43778i
$518$	9.97845	−	2.12291i	0.438428	−	0.0932752i
$519$		−	19.1800i		−	0.841908i
$520$	−9.89431	+	0.981946i	−0.433894	+	0.0430612i
$521$			42.7186i			1.87154i	0.352614	+	0.935769i	$0.385293\pi$
$521$			42.7186i			1.87154i	−0.352614	+	0.935769i	$0.614707\pi$
$522$	−3.66959	−	3.66959i	−0.160614	−	0.160614i
$523$	−28.4562			−1.24430			−0.622151	−	0.782897i	$-0.713741\pi$
$523$	−28.4562			−1.24430			−0.622151	+	0.782897i	$0.713741\pi$
$524$	−7.14423	−	7.14423i	−0.312097	−	0.312097i
$525$	1.64824	+	8.22223i	0.0719351	+	0.358847i
$526$	10.1672	−	10.1672i	0.443311	−	0.443311i
$527$	−5.91993	+	5.91993i	−0.257876	+	0.257876i
$528$	3.39326	+	3.39326i	0.147673	+	0.147673i
$529$	−22.1291			−0.962135
$530$	−12.4452	−	10.1980i	−0.540583	−	0.442972i
$531$	3.87716	−	3.87716i	0.168254	−	0.168254i
$532$	−10.5821			−0.458792
$533$		−	34.6496i		−	1.50084i
$534$			4.40258i			0.190518i
$535$	7.76880	−	9.48070i	0.335875	−	0.409887i
$536$	−0.639879	−	0.639879i	−0.0276386	−	0.0276386i
$537$		−	14.0176i		−	0.604905i
$538$		−	24.8306i		−	1.07052i
$539$	−20.0932			−0.865474
$540$	1.72956	+	1.41726i	0.0744284	+	0.0609891i
$541$	−18.6520	+	18.6520i	−0.801912	+	0.801912i	−0.983394	−	0.181482i	$-0.941910\pi$
$541$	−18.6520	+	18.6520i	−0.801912	+	0.801912i	0.181482	+	0.983394i	$0.441910\pi$
$542$	3.95334			0.169810
$543$	−1.07804	+	1.07804i	−0.0462632	+	0.0462632i
$544$			1.30290i			0.0558612i
$545$	−1.63881	−	1.34289i	−0.0701989	−	0.0575233i
$546$			7.45768i			0.319159i
$547$	−4.88671			−0.208941			−0.104470	−	0.994528i	$-0.533315\pi$
$547$	−4.88671			−0.208941			−0.104470	+	0.994528i	$0.533315\pi$
$548$	6.54303	−	6.54303i	0.279504	−	0.279504i
$549$	−6.36168	+	6.36168i	−0.271510	+	0.271510i
$550$	4.71604	+	23.5259i	0.201093	+	1.00315i
$551$	32.7438			1.39493
$552$	−0.659885	+	0.659885i	−0.0280866	+	0.0280866i
$553$	−5.24761			−0.223151
$554$	−2.77329			−0.117826
$555$	12.9592	−	4.13038i	0.550086	−	0.175325i
$556$	13.1631			0.558241
$557$	−41.5104			−1.75885			−0.879425	−	0.476037i	$-0.842073\pi$
$557$	−41.5104			−1.75885			−0.879425	+	0.476037i	$0.842073\pi$
$558$	4.54367	−	4.54367i	0.192349	−	0.192349i
$559$	9.00090			0.380698
$560$	2.37697	−	2.90075i	0.100445	−	0.122579i
$561$	−4.42106	+	4.42106i	−0.186657	+	0.186657i
$562$	−12.9824	+	12.9824i	−0.547631	+	0.547631i
$563$	34.6086			1.45858			0.729288	−	0.684206i	$-0.239851\pi$
$563$	34.6086			1.45858			0.729288	+	0.684206i	$0.239851\pi$
$564$			9.63432i			0.405678i
$565$	−2.26778	−	22.8506i	−0.0954061	−	0.961333i
$566$		−	26.5212i		−	1.11477i
$567$	1.18593	−	1.18593i	0.0498045	−	0.0498045i
$568$	−8.94910			−0.375496
$569$	4.46452	−	4.46452i	0.187162	−	0.187162i	−0.607306	−	0.794468i	$-0.707750\pi$
$569$	4.46452	−	4.46452i	0.187162	−	0.187162i	0.794468	+	0.607306i	$0.207750\pi$
$570$	−14.0396	+	1.39334i	−0.588053	+	0.0583604i
$571$	−16.6857			−0.698274			−0.349137	−	0.937072i	$-0.613525\pi$
$571$	−16.6857			−0.698274			−0.349137	+	0.937072i	$0.613525\pi$
$572$			21.3384i			0.892201i
$573$			22.2843i			0.930940i
$574$	9.24122	+	9.24122i	0.385721	+	0.385721i
$575$	−4.57508	+	0.917126i	−0.190794	+	0.0382468i
$576$		−	1.00000i		−	0.0416667i
$577$		−	17.2889i		−	0.719745i	−0.933002	−	0.359872i	$-0.882820\pi$
$577$		−	17.2889i		−	0.719745i	0.933002	−	0.359872i	$-0.117180\pi$
$578$	15.3025			0.636499
$579$	−11.9491	+	11.9491i	−0.496587	+	0.496587i
$580$	−7.35499	+	8.97570i	−0.305399	+	0.372696i
$581$	15.0070			0.622595
$582$	−0.0166373	−	0.0166373i	−0.000689639	−	0.000689639i
$583$	−24.4164	+	24.4164i	−1.01122	+	1.01122i
$584$	1.06393	−	1.06393i	0.0440258	−	0.0440258i
$585$	0.981946	+	9.89431i	0.0405985	+	0.409079i
$586$	−18.1427	−	18.1427i	−0.749467	−	0.749467i
$587$	28.9501			1.19490			0.597449	−	0.801907i	$-0.296181\pi$
$587$	28.9501			1.19490			0.597449	+	0.801907i	$0.296181\pi$
$588$	2.96075	+	2.96075i	0.122099	+	0.122099i
$589$			40.5433i			1.67056i
$590$	−9.48340	−	7.77102i	−0.390426	−	0.319928i
$591$			7.72696i			0.317845i
$592$	−5.10204	−	3.31197i	−0.209693	−	0.136121i
$593$	33.1096	+	33.1096i	1.35965	+	1.35965i	0.874347	+	0.485300i	$0.161290\pi$
$593$	33.1096	+	33.1096i	1.35965	+	1.35965i	0.485300	+	0.874347i	$0.338710\pi$
$594$	3.39326	−	3.39326i	0.139227	−	0.139227i
$595$	3.77937	+	3.09694i	0.154939	+	0.126962i
$596$		−	5.19216i		−	0.212679i
$597$		−	16.5375i		−	0.676834i
$598$	−4.14966			−0.169692
$599$		−	19.5074i		−	0.797053i	−0.917157	−	0.398526i	$-0.869522\pi$
$599$		−	19.5074i		−	0.797053i	0.917157	−	0.398526i	$-0.130478\pi$
$600$	2.77166	−	4.16148i	0.113152	−	0.169892i
$601$	41.8679			1.70783			0.853913	−	0.520415i	$-0.174223\pi$
$601$	41.8679			1.70783			0.853913	+	0.520415i	$0.174223\pi$
$602$	−2.40058	+	2.40058i	−0.0978405	+	0.0978405i
$603$	−0.639879	+	0.639879i	−0.0260579	+	0.0260579i
$604$			11.5161i			0.468585i
$605$	26.7649	−	2.65624i	1.08815	−	0.107992i
$606$	2.79367	+	2.79367i	0.113485	+	0.113485i
$607$	−28.0484			−1.13845			−0.569225	−	0.822182i	$-0.692757\pi$
$607$	−28.0484			−1.13845			−0.569225	+	0.822182i	$0.692757\pi$
$608$	4.46151	+	4.46151i	0.180938	+	0.180938i
$609$	6.15450	+	6.15450i	0.249393	+	0.249393i
$610$	15.5605	+	12.7507i	0.630024	+	0.516263i
$611$	−30.2925	+	30.2925i	−1.22550	+	1.22550i
$612$	1.30290			0.0526664
$613$	−23.0006	+	23.0006i	−0.928986	+	0.928986i	−0.997640	−	0.0686549i	$-0.978129\pi$
$613$	−23.0006	+	23.0006i	−0.928986	+	0.928986i	0.0686549	+	0.997640i	$0.478129\pi$
$614$	2.44662	+	2.44662i	0.0987377	+	0.0987377i
$615$	13.4774	+	11.0438i	0.543460	+	0.445329i
$616$	−5.69104	−	5.69104i	−0.229299	−	0.229299i
$617$	14.0932	+	14.0932i	0.567369	+	0.567369i	0.931391	−	0.364022i	$-0.118597\pi$
$617$	14.0932	+	14.0932i	0.567369	+	0.567369i	−0.364022	+	0.931391i	$0.618597\pi$
$618$	−7.36598	−	7.36598i	−0.296303	−	0.296303i
$619$	−22.6414			−0.910037			−0.455018	−	0.890482i	$-0.650367\pi$
$619$	−22.6414			−0.910037			−0.455018	+	0.890482i	$0.650367\pi$
$620$	−11.1137	−	9.10691i	−0.446336	−	0.365742i
$621$	0.659885	+	0.659885i	0.0264803	+	0.0264803i
$622$	−22.4050	−	22.4050i	−0.898359	−	0.898359i
$623$		−	7.38384i		−	0.295827i
$624$	3.14423	−	3.14423i	0.125870	−	0.125870i
$625$	23.0684	−	9.63586i	0.922735	−	0.385434i
$626$	−1.26968			−0.0507468
$627$			30.2781i			1.20919i
$628$	−2.32320	+	2.32320i	−0.0927057	+	0.0927057i
$629$	4.31515	−	6.64743i	0.172056	−	0.265050i
$630$	−2.90075	−	2.37697i	−0.115569	−	0.0947008i
$631$	5.51471	+	5.51471i	0.219537	+	0.219537i	0.808303	−	0.588766i	$-0.200386\pi$
$631$	5.51471	+	5.51471i	0.219537	+	0.219537i	−0.588766	+	0.808303i	$0.700386\pi$
$632$	2.21244	+	2.21244i	0.0880061	+	0.0880061i
$633$	18.3413	−	18.3413i	0.729002	−	0.729002i
$634$	−11.5508	−	11.5508i	−0.458740	−	0.458740i
$635$	−27.6603	+	33.7554i	−1.09766	+	1.33954i
$636$	7.19557			0.285323
$637$			18.6185i			0.737693i
$638$	17.6096	+	17.6096i	0.697171	+	0.697171i
$639$			8.94910i			0.354021i
$640$	−2.22514	+	0.220830i	−0.0879563	+	0.00872909i
$641$	22.8591			0.902878			0.451439	−	0.892302i	$-0.350911\pi$
$641$	22.8591			0.902878			0.451439	+	0.892302i	$0.350911\pi$
$642$			5.48157i			0.216340i
$643$		−	4.05269i		−	0.159822i	−0.996802	−	0.0799112i	$-0.974536\pi$
$643$		−	4.05269i		−	0.159822i	0.996802	−	0.0799112i	$-0.0254637\pi$
$644$	1.10673	−	1.10673i	0.0436114	−	0.0436114i
$645$	−2.86884	+	3.50101i	−0.112960	+	0.137852i
$646$	−5.81288	+	5.81288i	−0.228705	+	0.228705i
$647$	40.5162			1.59285			0.796427	−	0.604734i	$-0.206721\pi$
$647$	40.5162			1.59285			0.796427	+	0.604734i	$0.206721\pi$
$648$	−1.00000			−0.0392837
$649$	−18.6057	+	18.6057i	−0.730337	+	0.730337i
$650$	21.7994	−	4.36993i	0.855041	−	0.171403i
$651$	−7.62047	+	7.62047i	−0.298670	+	0.298670i
$652$			0.310642i			0.0121657i
$653$		−	3.85391i		−	0.150815i	−0.997153	−	0.0754076i	$-0.975974\pi$
$653$		−	3.85391i		−	0.150815i	0.997153	−	0.0754076i	$-0.0240258\pi$
$654$	0.947530			0.0370513
$655$	17.4745	+	14.3192i	0.682787	+	0.559498i
$656$		−	7.79237i		−	0.304241i
$657$	−1.06393	−	1.06393i	−0.0415079	−	0.0415079i
$658$		−	16.1583i		−	0.629916i
$659$	38.4968			1.49962			0.749812	−	0.661651i	$-0.230144\pi$
$659$	38.4968			1.49962			0.749812	+	0.661651i	$0.230144\pi$
$660$	−8.29980	−	6.80113i	−0.323069	−	0.264734i
$661$	−34.7273	−	34.7273i	−1.35073	−	1.35073i	−0.884841	−	0.465894i	$-0.845733\pi$
$661$	−34.7273	−	34.7273i	−1.35073	−	1.35073i	−0.465894	−	0.884841i	$-0.654267\pi$
$662$	−14.6794	+	14.6794i	−0.570530	+	0.570530i
$663$	4.09660	+	4.09660i	0.159099	+	0.159099i
$664$	−6.32708	−	6.32708i	−0.245539	−	0.245539i
$665$	23.5466	−	2.33685i	0.913098	−	0.0906191i
$666$	−3.31197	+	5.10204i	−0.128336	+	0.197700i
$667$	−3.42453	+	3.42453i	−0.132598	+	0.132598i
$668$		−	21.2856i		−	0.823563i
$669$	−15.2274			−0.588726
$670$	1.56512	+	1.28251i	0.0604660	+	0.0495478i
$671$	30.5284	−	30.5284i	1.17853	−	1.17853i
$672$			1.67716i			0.0646979i
$673$	0.532326	+	0.532326i	0.0205197	+	0.0205197i	0.717292	−	0.696773i	$-0.245381\pi$
$673$	0.532326	+	0.532326i	0.0205197	+	0.0205197i	−0.696773	+	0.717292i	$0.745381\pi$
$674$	−3.80408	−	3.80408i	−0.146528	−	0.146528i
$675$	−4.16148	−	2.77166i	−0.160175	−	0.106681i
$676$	6.77233			0.260474
$677$	5.75332	+	5.75332i	0.221118	+	0.221118i	0.808969	−	0.587851i	$-0.200026\pi$
$677$	5.75332	+	5.75332i	0.221118	+	0.221118i	−0.587851	+	0.808969i	$0.700026\pi$
$678$	7.26150	+	7.26150i	0.278876	+	0.278876i
$679$	0.0279035	+	0.0279035i	0.00107084	+	0.00107084i
$680$	−0.287719	−	2.89912i	−0.0110335	−	0.111176i
$681$	6.71779	+	6.71779i	0.257426	+	0.257426i
$682$	−21.8041	+	21.8041i	−0.834923	+	0.834923i
$683$	−39.9256			−1.52771			−0.763855	−	0.645388i	$-0.776696\pi$
$683$	−39.9256			−1.52771			−0.763855	+	0.645388i	$0.776696\pi$
$684$	4.46151	−	4.46151i	0.170590	−	0.170590i
$685$	−13.1142	+	16.0040i	−0.501069	+	0.611482i
$686$	−13.2672	−	13.2672i	−0.506543	−	0.506543i
$687$	3.42279	+	3.42279i	0.130587	+	0.130587i
$688$	2.02422			0.0771726
$689$	22.6245	+	22.6245i	0.861925	+	0.861925i
$690$	1.32261	−	1.61406i	0.0503510	−	0.0614461i
$691$			17.1171i			0.651166i	0.945513	+	0.325583i	$0.105561\pi$
$691$			17.1171i			0.651166i	−0.945513	+	0.325583i	$0.894439\pi$
$692$	13.5623	−	13.5623i	0.515562	−	0.515562i
$693$	−5.69104	+	5.69104i	−0.216185	+	0.216185i
$694$	−32.1513			−1.22045
$695$	−29.2898	+	2.90682i	−1.11102	+	0.110262i
$696$		−	5.18959i		−	0.196711i
$697$	10.1526			0.384559
$698$		−	4.32501i		−	0.163704i
$699$		−	5.93799i		−	0.224596i
$700$	−4.64851	+	6.97947i	−0.175697	+	0.263799i
$701$	−22.1259	+	22.1259i	−0.835684	+	0.835684i	−0.988288	−	0.152603i	$-0.951234\pi$
$701$	−22.1259	+	22.1259i	−0.835684	+	0.835684i	0.152603	+	0.988288i	$0.451234\pi$
$702$	−3.14423	−	3.14423i	−0.118671	−	0.118671i
$703$	−7.98644	−	37.5392i	−0.301214	−	1.41582i
$704$			4.79879i			0.180861i
$705$	−2.12755	−	21.4377i	−0.0801282	−	0.807389i
$706$		−	16.0457i		−	0.603889i
$707$	−4.68543	−	4.68543i	−0.176214	−	0.176214i
$708$	5.48313			0.206069
$709$	28.0496	+	28.0496i	1.05342	+	1.05342i	0.998490	+	0.0549332i	$0.0174946\pi$
$709$	28.0496	+	28.0496i	1.05342	+	1.05342i	0.0549332	+	0.998490i	$0.482505\pi$
$710$	19.9130	−	1.97623i	0.747321	−	0.0741667i
$711$	2.21244	−	2.21244i	0.0829730	−	0.0829730i
$712$	−3.11309	+	3.11309i	−0.116668	+	0.116668i
$713$	−4.24024	−	4.24024i	−0.158798	−	0.158798i
$714$	−2.18517			−0.0817778
$715$	−4.71216	−	47.4808i	−0.176225	−	1.77568i
$716$	9.91196	−	9.91196i	0.370427	−	0.370427i
$717$	−7.95168			−0.296961
$718$			15.7185i			0.586609i
$719$		−	22.1676i		−	0.826713i	−0.910569	−	0.413357i	$-0.864356\pi$
$719$		−	22.1676i		−	0.826713i	0.910569	−	0.413357i	$-0.135644\pi$
$720$	0.220830	+	2.22514i	0.00822986	+	0.0829260i
$721$	12.3539	+	12.3539i	0.460085	+	0.460085i
$722$			20.8101i			0.774473i
$723$		−	15.3195i		−	0.569738i
$724$	−1.52458			−0.0566606
$725$	14.3837	−	21.5964i	0.534199	−	0.802069i
$726$	−8.50537	+	8.50537i	−0.315664	+	0.315664i
$727$	29.7685			1.10405			0.552026	−	0.833827i	$-0.313855\pi$
$727$	29.7685			1.10405			0.552026	+	0.833827i	$0.313855\pi$
$728$	−5.27338	+	5.27338i	−0.195444	+	0.195444i
$729$			1.00000i			0.0370370i
$730$	−2.13245	+	2.60234i	−0.0789254	+	0.0963170i
$731$			2.63734i			0.0975457i
$732$	−8.99677			−0.332530
$733$	27.3738	−	27.3738i	1.01108	−	1.01108i	0.0111379	−	0.999938i	$-0.496455\pi$
$733$	27.3738	−	27.3738i	1.01108	−	1.01108i	0.999938	−	0.0111379i	$-0.00354539\pi$
$734$	17.3935	−	17.3935i	0.642007	−	0.642007i
$735$	−7.24189	−	5.93425i	−0.267121	−	0.218888i
$736$	−0.933219			−0.0343989
$737$	3.07065	−	3.07065i	0.113109	−	0.113109i
$738$	−7.79237			−0.286841
$739$	−3.45235			−0.126997			−0.0634984	−	0.997982i	$-0.520226\pi$
$739$	−3.45235			−0.126997			−0.0634984	+	0.997982i	$0.520226\pi$
$740$	12.0841	+	6.24290i	0.444221	+	0.229494i
$741$	28.0560			1.03066
$742$	−12.0681			−0.443035
$743$	−6.95019	+	6.95019i	−0.254978	+	0.254978i	−0.823008	−	0.568030i	$-0.807706\pi$
$743$	−6.95019	+	6.95019i	−0.254978	+	0.254978i	0.568030	+	0.823008i	$0.307706\pi$
$744$	6.42572			0.235578
$745$	1.14659	+	11.5533i	0.0420077	+	0.423279i
$746$	24.4469	−	24.4469i	0.895065	−	0.895065i
$747$	−6.32708	+	6.32708i	−0.231496	+	0.231496i
$748$	−6.25232			−0.228608
$749$		−	9.19347i		−	0.335922i
$750$	−5.24833	+	9.87193i	−0.191642	+	0.360472i
$751$		−	48.5947i		−	1.77325i	−0.462491	−	0.886624i	$-0.653044\pi$
$751$		−	48.5947i		−	1.77325i	0.462491	−	0.886624i	$-0.346956\pi$
$752$	−6.81249	+	6.81249i	−0.248426	+	0.248426i
$753$	20.9334			0.762857
$754$	16.3172	−	16.3172i	0.594239	−	0.594239i
$755$	−2.54311	−	25.6250i	−0.0925533	−	0.932588i
$756$	1.67716			0.0609978
$757$			24.9414i			0.906511i	0.891381	+	0.453256i	$0.149737\pi$
$757$			24.9414i			0.906511i	−0.891381	+	0.453256i	$0.850263\pi$
$758$			28.8766i			1.04884i
$759$	−3.16665	−	3.16665i	−0.114942	−	0.114942i
$760$	−10.9127	−	8.94223i	−0.395845	−	0.324369i
$761$			38.6923i			1.40260i	0.712868	+	0.701298i	$0.247396\pi$
$761$			38.6923i			1.40260i	−0.712868	+	0.701298i	$0.752604\pi$
$762$		−	19.5168i		−	0.707017i
$763$	−1.58916			−0.0575315
$764$	−15.7574	+	15.7574i	−0.570082	+	0.570082i
$765$	−2.89912	+	0.287719i	−0.104818	+	0.0104025i
$766$	36.9567			1.33530
$767$	17.2402	+	17.2402i	0.622508	+	0.622508i
$768$	0.707107	−	0.707107i	0.0255155	−	0.0255155i
$769$	−15.3838	+	15.3838i	−0.554755	+	0.554755i	−0.927809	−	0.373055i	$-0.878310\pi$
$769$	−15.3838	+	15.3838i	−0.554755	+	0.554755i	0.373055	+	0.927809i	$0.378310\pi$
$770$	13.9201	+	11.4066i	0.501646	+	0.411065i
$771$	−7.95615	−	7.95615i	−0.286534	−	0.286534i
$772$	−16.8985			−0.608192
$773$	−19.3766	−	19.3766i	−0.696929	−	0.696929i	0.266818	−	0.963747i	$-0.414028\pi$
$773$	−19.3766	−	19.3766i	−0.696929	−	0.696929i	−0.963747	+	0.266818i	$0.914028\pi$
$774$		−	2.02422i		−	0.0727590i
$775$	26.7405	+	17.8099i	0.960548	+	0.639750i
$776$		−	0.0235287i		−	0.000844632i
$777$	5.55471	−	8.55695i	0.199274	−	0.306979i
$778$	−21.5492	−	21.5492i	−0.772576	−	0.772576i
$779$	34.7657	−	34.7657i	1.24561	−	1.24561i
$780$	−6.30199	+	7.69068i	−0.225648	+	0.275370i
$781$		−	42.9449i		−	1.53669i
$782$		−	1.21589i		−	0.0434800i
$783$	−5.18959			−0.185461
$784$			4.18713i			0.149540i
$785$	4.65640	−	5.68247i	0.166194	−	0.202816i
$786$	−10.1035			−0.360379
$787$	−9.19564	+	9.19564i	−0.327789	+	0.327789i	−0.851745	−	0.523956i	$-0.824456\pi$
$787$	−9.19564	+	9.19564i	−0.327789	+	0.327789i	0.523956	+	0.851745i	$0.324456\pi$
$788$	−5.46379	+	5.46379i	−0.194639	+	0.194639i
$789$		−	14.3786i		−	0.511892i
$790$	−5.41155	−	4.43441i	−0.192534	−	0.157769i
$791$	−12.1787	−	12.1787i	−0.433025	−	0.433025i
$792$	4.79879			0.170518
$793$	−28.2879	−	28.2879i	−1.00453	−	1.00453i
$794$	−26.8752	−	26.8752i	−0.953766	−	0.953766i
$795$	−16.0111	+	1.58900i	−0.567856	+	0.0563560i
$796$	11.6938	−	11.6938i	0.414474	−	0.414474i
$797$	15.2753			0.541079			0.270539	−	0.962709i	$-0.412798\pi$
$797$	15.2753			0.541079			0.270539	+	0.962709i	$0.412798\pi$
$798$	−7.48267	+	7.48267i	−0.264884	+	0.264884i
$799$	−8.87596	−	8.87596i	−0.314009	−	0.314009i
$800$	4.90247	−	0.982756i	0.173328	−	0.0347457i
$801$	3.11309	+	3.11309i	0.109996	+	0.109996i
$802$	16.3614	+	16.3614i	0.577740	+	0.577740i
$803$	5.10559	+	5.10559i	0.180172	+	0.180172i
$804$	−0.904926			−0.0319143
$805$	−2.21823	+	2.70704i	−0.0781825	+	0.0954105i
$806$	20.2039	+	20.2039i	0.711653	+	0.711653i
$807$	−17.5579	−	17.5579i	−0.618067	−	0.618067i
$808$			3.95084i			0.138990i
$809$	−9.44473	+	9.44473i	−0.332059	+	0.332059i	−0.853368	−	0.521309i	$-0.825444\pi$
$809$	−9.44473	+	9.44473i	−0.332059	+	0.332059i	0.521309	+	0.853368i	$0.325444\pi$
$810$	2.22514	−	0.220830i	0.0781833	−	0.00775919i
$811$	51.4955			1.80825			0.904125	−	0.427267i	$-0.140524\pi$
$811$	51.4955			1.80825			0.904125	+	0.427267i	$0.140524\pi$
$812$			8.70377i			0.305443i
$813$	2.79543	−	2.79543i	0.0980400	−	0.0980400i
$814$	15.8935	−	24.4837i	0.557065	−	0.858152i
$815$	−0.0685992	−	0.691221i	−0.00240292	−	0.0242124i
$816$	0.921286	+	0.921286i	0.0322515	+	0.0322515i
$817$	9.03106	+	9.03106i	0.315957	+	0.315957i
$818$	1.75957	−	1.75957i	0.0615218	−	0.0615218i
$819$	5.27338	+	5.27338i	0.184267	+	0.184267i
$820$	1.72079	+	17.3391i	0.0600927	+	0.605507i
$821$	30.7870			1.07447			0.537237	−	0.843431i	$-0.319468\pi$
$821$	30.7870			1.07447			0.537237	+	0.843431i	$0.319468\pi$
$822$		−	9.25324i		−	0.322744i
$823$	−14.1184	−	14.1184i	−0.492135	−	0.492135i	0.416843	−	0.908978i	$-0.363136\pi$
$823$	−14.1184	−	14.1184i	−0.492135	−	0.492135i	−0.908978	+	0.416843i	$0.863136\pi$
$824$		−	10.4171i		−	0.362896i
$825$	19.9701	+	13.3006i	0.695269	+	0.463067i
$826$	−9.19609			−0.319973
$827$			7.05530i			0.245337i	0.992448	+	0.122668i	$0.0391452\pi$
$827$			7.05530i			0.245337i	−0.992448	+	0.122668i	$0.960855\pi$
$828$			0.933219i			0.0324316i
$829$	−32.0957	+	32.0957i	−1.11473	+	1.11473i	−0.122227	+	0.992502i	$0.539004\pi$
$829$	−32.0957	+	32.0957i	−1.11473	+	1.11473i	−0.992502	+	0.122227i	$0.960996\pi$
$830$	15.4758	+	12.6814i	0.537174	+	0.440178i
$831$	−1.96101	+	1.96101i	−0.0680268	+	0.0680268i
$832$	4.44661			0.154158
$833$	−5.45539			−0.189018
$834$	9.30774	−	9.30774i	0.322301	−	0.322301i
$835$	4.70050	+	47.3633i	0.162667	+	1.63907i
$836$	−21.4099	+	21.4099i	−0.740476	+	0.740476i
$837$		−	6.42572i		−	0.222105i
$838$		−	10.0390i		−	0.346793i
$839$	9.87040			0.340764			0.170382	−	0.985378i	$-0.445500\pi$
$839$	9.87040			0.340764			0.170382	+	0.985378i	$0.445500\pi$
$840$	−0.370368	−	3.73191i	−0.0127789	−	0.128763i
$841$			2.06818i			0.0713166i
$842$	−6.87930	−	6.87930i	−0.237076	−	0.237076i
$843$			18.3599i			0.632350i
$844$	25.9385			0.892841
$845$	−15.0694	+	1.49554i	−0.518402	+	0.0514480i
$846$	6.81249	+	6.81249i	0.234218	+	0.234218i
$847$	14.2649	−	14.2649i	0.490147	−	0.490147i
$848$	5.08803	+	5.08803i	0.174724	+	0.174724i
$849$	−18.7533	−	18.7533i	−0.643612	−	0.643612i
$850$	1.28043	+	6.38740i	0.0439183	+	0.219086i
$851$	4.76132	+	3.09079i	0.163216	+	0.105951i
$852$	−6.32797	+	6.32797i	−0.216793	+	0.216793i
$853$		−	47.6548i		−	1.63167i	−0.578286	−	0.815834i	$-0.696278\pi$
$853$		−	47.6548i		−	1.63167i	0.578286	−	0.815834i	$-0.303722\pi$
$854$	15.0890			0.516336
$855$	−8.94223	+	10.9127i	−0.305818	+	0.373207i
$856$	−3.87605	+	3.87605i	−0.132481	+	0.132481i
$857$		−	26.8502i		−	0.917185i	−0.888647	−	0.458593i	$-0.848354\pi$
$857$		−	26.8502i		−	0.917185i	0.888647	−	0.458593i	$-0.151646\pi$
$858$	15.0885	+	15.0885i	0.515113	+	0.515113i
$859$	−20.2206	−	20.2206i	−0.689918	−	0.689918i	0.272295	−	0.962214i	$-0.412217\pi$
$859$	−20.2206	−	20.2206i	−0.689918	−	0.689918i	−0.962214	+	0.272295i	$0.912217\pi$
$860$	−4.50416	+	0.447009i	−0.153591	+	0.0152429i
$861$	13.0691			0.445393
$862$	6.62805	+	6.62805i	0.225752	+	0.225752i
$863$	13.5486	+	13.5486i	0.461198	+	0.461198i	0.899048	−	0.437850i	$-0.144260\pi$
$863$	13.5486	+	13.5486i	0.461198	+	0.461198i	−0.437850	+	0.899048i	$0.644260\pi$
$864$	−0.707107	−	0.707107i	−0.0240563	−	0.0240563i
$865$	−27.1830	+	33.1730i	−0.924250	+	1.12791i
$866$	11.5273	+	11.5273i	0.391715	+	0.391715i
$867$	10.8205	−	10.8205i	0.367483	−	0.367483i
$868$	−10.7770			−0.365794
$869$	−10.6170	+	10.6170i	−0.360158	+	0.360158i
$870$	1.14602	+	11.5475i	0.0388537	+	0.391498i
$871$	−2.84529	−	2.84529i	−0.0964090	−	0.0964090i
$872$	0.670005	+	0.670005i	0.0226892	+	0.0226892i
$873$	−0.0235287			−0.000796327
$874$	−4.16356	−	4.16356i	−0.140835	−	0.140835i
$875$	8.80230	−	16.5568i	0.297572	−	0.559723i
$876$		−	1.50463i		−	0.0508366i
$877$	−29.0568	+	29.0568i	−0.981180	+	0.981180i	−0.999826	−	0.0186460i	$-0.994064\pi$
$877$	−29.0568	+	29.0568i	−0.981180	+	0.981180i	0.0186460	+	0.999826i	$0.494064\pi$
$878$	−25.1084	+	25.1084i	−0.847368	+	0.847368i
$879$	−25.6576			−0.865410
$880$	−1.05972	−	10.6780i	−0.0357231	−	0.359954i
$881$		−	37.9507i		−	1.27859i	−0.768961	−	0.639296i	$-0.779226\pi$
$881$		−	37.9507i		−	1.27859i	0.768961	−	0.639296i	$-0.220774\pi$
$882$	4.18713			0.140988
$883$			35.9876i			1.21108i	0.795815	+	0.605540i	$0.207043\pi$
$883$			35.9876i			1.21108i	−0.795815	+	0.605540i	$0.792957\pi$
$884$			5.79347i			0.194855i
$885$	−12.2007	+	1.21084i	−0.410123	+	0.0407020i
$886$	−10.8396	+	10.8396i	−0.364163	+	0.364163i
$887$	4.20003	+	4.20003i	0.141023	+	0.141023i	0.774094	−	0.633071i	$-0.218206\pi$
$887$	4.20003	+	4.20003i	0.141023	+	0.141023i	−0.633071	+	0.774094i	$0.718206\pi$
$888$	−5.94961	+	1.26577i	−0.199656	+	0.0424766i
$889$			32.7327i			1.09782i
$890$	6.23959	−	7.61453i	0.209152	−	0.255239i
$891$		−	4.79879i		−	0.160766i
$892$	−10.7674	−	10.7674i	−0.360520	−	0.360520i
$893$	−60.7880			−2.03419
$894$	−3.67141	−	3.67141i	−0.122790	−	0.122790i
$895$	−19.8666	+	24.2443i	−0.664067	+	0.810398i
$896$	−1.18593	+	1.18593i	−0.0396192	+	0.0396192i
$897$	−2.93425	+	2.93425i	−0.0979718	+	0.0979718i
$898$	16.9181	+	16.9181i	0.564563	+	0.564563i
$899$	33.3468			1.11218
$900$	−0.982756	−	4.90247i	−0.0327585	−	0.163416i
$901$	−6.62918	+	6.62918i	−0.220850	+	0.220850i
$902$	37.3940			1.24508
$903$			3.39494i			0.112976i
$904$			10.2693i			0.341552i
$905$	3.39240	−	0.336674i	0.112767	−	0.0111914i
$906$	8.14314	+	8.14314i	0.270538	+	0.270538i
$907$			4.45102i			0.147794i	0.997266	+	0.0738969i	$0.0235436\pi$
$907$			4.45102i			0.147794i	−0.997266	+	0.0738969i	$0.976456\pi$
$908$			9.50039i			0.315282i
$909$	3.95084			0.131041
$910$	10.5695	−	12.8985i	0.350374	−	0.427581i
$911$	−7.73985	+	7.73985i	−0.256433	+	0.256433i	−0.823602	−	0.567169i	$-0.808039\pi$
$911$	−7.73985	+	7.73985i	−0.256433	+	0.256433i	0.567169	+	0.823602i	$0.308039\pi$
$912$	6.30953			0.208929
$913$	30.3624	−	30.3624i	1.00485	−	1.00485i
$914$		−	17.9114i		−	0.592457i
$915$	20.0190	−	1.98676i	0.661809	−	0.0656803i
$916$			4.84055i			0.159936i
$917$	16.9451			0.559578
$918$	0.921286	−	0.921286i	0.0304070	−	0.0304070i
$919$	−32.7456	+	32.7456i	−1.08018	+	1.08018i	−0.0836854	+	0.996492i	$0.526669\pi$
$919$	−32.7456	+	32.7456i	−1.08018	+	1.08018i	−0.996492	+	0.0836854i	$0.973331\pi$
$920$	2.07654	−	0.206083i	0.0684615	−	0.00679436i
$921$	3.46005			0.114012
$922$	2.45180	−	2.45180i	0.0807456	−	0.0807456i
$923$	−39.7932			−1.30981
$924$	−8.04835			−0.264771
$925$	−28.2675	−	11.2228i	−0.929429	−	0.369002i
$926$	36.5028			1.19956
$927$	−10.4171			−0.342142
$928$	3.66959	−	3.66959i	0.120460	−	0.120460i
$929$	−2.92392			−0.0959307			−0.0479653	−	0.998849i	$-0.515274\pi$
$929$	−2.92392			−0.0959307			−0.0479653	+	0.998849i	$0.515274\pi$
$930$	−14.2981	+	1.41899i	−0.468853	+	0.0465307i
$931$	−18.6809	+	18.6809i	−0.612243	+	0.612243i
$932$	4.19880	−	4.19880i	0.137536	−	0.137536i
$933$	−31.6855			−1.03734
$934$			20.8160i			0.681122i
$935$	13.9123	−	1.38070i	0.454980	−	0.0451538i
$936$		−	4.44661i		−	0.145342i
$937$	−26.3926	+	26.3926i	−0.862209	+	0.862209i	−0.991594	−	0.129385i	$-0.958700\pi$
$937$	−26.3926	+	26.3926i	−0.862209	+	0.862209i	0.129385	+	0.991594i	$0.458700\pi$
$938$	1.51771			0.0495549
$939$	−0.897802	+	0.897802i	−0.0292987	+	0.0292987i
$940$	13.6543	−	16.6631i	0.445355	−	0.543491i
$941$	−14.1264			−0.460509			−0.230254	−	0.973130i	$-0.573956\pi$
$941$	−14.1264			−0.460509			−0.230254	+	0.973130i	$0.573956\pi$
$942$			3.28550i			0.107047i
$943$			7.27199i			0.236809i
$944$	3.87716	+	3.87716i	0.126191	+	0.126191i
$945$	−3.73191	+	0.370368i	−0.121399	+	0.0120481i
$946$			9.71380i			0.315823i
$947$		−	54.3478i		−	1.76607i	−0.469309	−	0.883034i	$-0.655497\pi$
$947$		−	54.3478i		−	1.76607i	0.469309	−	0.883034i	$-0.344503\pi$
$948$	3.12886			0.101621
$949$	4.73089	−	4.73089i	0.153571	−	0.153571i
$950$	26.2570	+	17.4878i	0.851889	+	0.567380i
$951$	−16.3353			−0.529708
$952$	−1.54515	−	1.54515i	−0.0500784	−	0.0500784i
$953$	16.0189	−	16.0189i	0.518904	−	0.518904i	−0.398336	−	0.917240i	$-0.630412\pi$
$953$	16.0189	−	16.0189i	0.518904	−	0.518904i	0.917240	+	0.398336i	$0.130412\pi$
$954$	5.08803	−	5.08803i	0.164731	−	0.164731i
$955$	31.5826	−	38.5420i	1.02199	−	1.24719i
$956$	−5.62269	−	5.62269i	−0.181851	−	0.181851i
$957$	24.9038			0.805024
$958$	21.3099	+	21.3099i	0.688490	+	0.688490i
$959$			15.5192i			0.501140i
$960$	−1.41726	+	1.72956i	−0.0457418	+	0.0558213i
$961$			10.2899i			0.331932i
$962$	−22.6868	−	14.7270i	−0.731452	−	0.474819i
$963$	3.87605	+	3.87605i	0.124904	+	0.124904i
$964$	10.8325	−	10.8325i	0.348892	−	0.348892i
$965$	37.6016	−	3.73171i	1.21044	−	0.120128i
$966$		−	1.56516i		−	0.0503581i
$967$		−	14.2557i		−	0.458432i	−0.973376	−	0.229216i	$-0.926384\pi$
$967$		−	14.2557i		−	0.458432i	0.973376	−	0.229216i	$-0.0736163\pi$
$968$	−12.0284			−0.386608
$969$			8.22065i			0.264085i
$970$	0.00519586	+	0.0523546i	0.000166829	+	0.00168101i
$971$	46.2814			1.48524			0.742621	−	0.669712i	$-0.233582\pi$
$971$	46.2814			1.48524			0.742621	+	0.669712i	$0.233582\pi$
$972$	−0.707107	+	0.707107i	−0.0226805	+	0.0226805i
$973$	−15.6106	+	15.6106i	−0.500452	+	0.500452i
$974$			31.2190i			1.00032i
$975$	12.3245	−	18.5045i	0.394699	−	0.592618i
$976$	−6.36168	−	6.36168i	−0.203632	−	0.203632i
$977$	−8.86551			−0.283633			−0.141816	−	0.989893i	$-0.545294\pi$
$977$	−8.86551			−0.283633			−0.141816	+	0.989893i	$0.545294\pi$
$978$	0.219657	+	0.219657i	0.00702386	+	0.00702386i
$979$	−14.9391	−	14.9391i	−0.477456	−	0.477456i
$980$	−0.924646	−	9.31694i	−0.0295367	−	0.297619i
$981$	0.670005	−	0.670005i	0.0213916	−	0.0213916i
$982$	1.46818			0.0468514
$983$	−14.4066	+	14.4066i	−0.459499	+	0.459499i	−0.898491	−	0.438992i	$-0.855336\pi$
$983$	−14.4066	+	14.4066i	−0.459499	+	0.459499i	0.438992	+	0.898491i	$0.355336\pi$
$984$	−5.51004	−	5.51004i	−0.175654	−	0.175654i
$985$	10.9511	−	13.3642i	0.348931	−	0.425820i
$986$	4.78109	+	4.78109i	0.152261	+	0.152261i
$987$	−11.4256	−	11.4256i	−0.363682	−	0.363682i
$988$	19.8386	+	19.8386i	0.631150	+	0.631150i
$989$	−1.88904			−0.0600679
$990$	−10.6780	+	1.05972i	−0.339368	+	0.0336801i
$991$	−22.6388	−	22.6388i	−0.719145	−	0.719145i	0.249285	−	0.968430i	$-0.419804\pi$
$991$	−22.6388	−	22.6388i	−0.719145	−	0.719145i	−0.968430	+	0.249285i	$0.919804\pi$
$992$	4.54367	+	4.54367i	0.144262	+	0.144262i
$993$			20.7598i			0.658791i
$994$	10.6130	−	10.6130i	0.336625	−	0.336625i
$995$	−23.4379	+	28.6026i	−0.743031	+	0.906762i
$996$	−8.94785			−0.283523
$997$			49.8348i			1.57828i	0.614210	+	0.789142i	$0.289475\pi$
$997$			49.8348i			1.57828i	−0.614210	+	0.789142i	$0.710525\pi$
$998$	−1.77906	+	1.77906i	−0.0563153	+	0.0563153i
$999$	1.26577	+	5.94961i	0.0400473	+	0.188237i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.o.b.253.13	yes	40
5.2	odd	4		1110.2.l.b.697.8	yes	40
37.6	odd	4		1110.2.l.b.43.8	✓	40
185.117	even	4	inner	1110.2.o.b.487.13	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.l.b.43.8	✓	40	37.6	odd	4
1110.2.l.b.697.8	yes	40	5.2	odd	4
1110.2.o.b.253.13	yes	40	1.1	even	1	trivial
1110.2.o.b.487.13	yes	40	185.117	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(0.707107 - 0.707107i) q^{3} +1.00000 q^{4} +(-2.22514 + 0.220830i) q^{5} +(0.707107 - 0.707107i) q^{6} +(-1.18593 + 1.18593i) q^{7} +1.00000 q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(0.707107 - 0.707107i) q^{3} +1.00000 q^{4} +(-2.22514 + 0.220830i) q^{5} +(0.707107 - 0.707107i) q^{6} +(-1.18593 + 1.18593i) q^{7} +1.00000 q^{8} -1.00000i q^{9} +(-2.22514 + 0.220830i) q^{10} +4.79879i q^{11} +(0.707107 - 0.707107i) q^{12} +4.44661 q^{13} +(-1.18593 + 1.18593i) q^{14} +(-1.41726 + 1.72956i) q^{15} +1.00000 q^{16} +1.30290i q^{17} -1.00000i q^{18} +(4.46151 + 4.46151i) q^{19} +(-2.22514 + 0.220830i) q^{20} +1.67716i q^{21} +4.79879i q^{22} -0.933219 q^{23} +(0.707107 - 0.707107i) q^{24} +(4.90247 - 0.982756i) q^{25} +4.44661 q^{26} +(-0.707107 - 0.707107i) q^{27} +(-1.18593 + 1.18593i) q^{28} +(3.66959 - 3.66959i) q^{29} +(-1.41726 + 1.72956i) q^{30} +(4.54367 + 4.54367i) q^{31} +1.00000 q^{32} +(3.39326 + 3.39326i) q^{33} +1.30290i q^{34} +(2.37697 - 2.90075i) q^{35} -1.00000i q^{36} +(-5.10204 - 3.31197i) q^{37} +(4.46151 + 4.46151i) q^{38} +(3.14423 - 3.14423i) q^{39} +(-2.22514 + 0.220830i) q^{40} -7.79237i q^{41} +1.67716i q^{42} +2.02422 q^{43} +4.79879i q^{44} +(0.220830 + 2.22514i) q^{45} -0.933219 q^{46} +(-6.81249 + 6.81249i) q^{47} +(0.707107 - 0.707107i) q^{48} +4.18713i q^{49} +(4.90247 - 0.982756i) q^{50} +(0.921286 + 0.921286i) q^{51} +4.44661 q^{52} +(5.08803 + 5.08803i) q^{53} +(-0.707107 - 0.707107i) q^{54} +(-1.05972 - 10.6780i) q^{55} +(-1.18593 + 1.18593i) q^{56} +6.30953 q^{57} +(3.66959 - 3.66959i) q^{58} +(3.87716 + 3.87716i) q^{59} +(-1.41726 + 1.72956i) q^{60} +(-6.36168 - 6.36168i) q^{61} +(4.54367 + 4.54367i) q^{62} +(1.18593 + 1.18593i) q^{63} +1.00000 q^{64} +(-9.89431 + 0.981946i) q^{65} +(3.39326 + 3.39326i) q^{66} +(-0.639879 - 0.639879i) q^{67} +1.30290i q^{68} +(-0.659885 + 0.659885i) q^{69} +(2.37697 - 2.90075i) q^{70} -8.94910 q^{71} -1.00000i q^{72} +(1.06393 - 1.06393i) q^{73} +(-5.10204 - 3.31197i) q^{74} +(2.77166 - 4.16148i) q^{75} +(4.46151 + 4.46151i) q^{76} +(-5.69104 - 5.69104i) q^{77} +(3.14423 - 3.14423i) q^{78} +(2.21244 + 2.21244i) q^{79} +(-2.22514 + 0.220830i) q^{80} -1.00000 q^{81} -7.79237i q^{82} +(-6.32708 - 6.32708i) q^{83} +1.67716i q^{84} +(-0.287719 - 2.89912i) q^{85} +2.02422 q^{86} -5.18959i q^{87} +4.79879i q^{88} +(-3.11309 + 3.11309i) q^{89} +(0.220830 + 2.22514i) q^{90} +(-5.27338 + 5.27338i) q^{91} -0.933219 q^{92} +6.42572 q^{93} +(-6.81249 + 6.81249i) q^{94} +(-10.9127 - 8.94223i) q^{95} +(0.707107 - 0.707107i) q^{96} -0.0235287i q^{97} +4.18713i q^{98} +4.79879 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 40 q^{2} + 40 q^{4} - 4 q^{7} + 40 q^{8}+O(q^{10}) \) 40 * q + 40 * q^2 + 40 * q^4 - 4 * q^7 + 40 * q^8	\( 40 q + 40 q^{2} + 40 q^{4} - 4 q^{7} + 40 q^{8} + 8 q^{13} - 4 q^{14} + 40 q^{16} - 4 q^{19} - 8 q^{25} + 8 q^{26} - 4 q^{28} + 28 q^{31} + 40 q^{32} - 4 q^{33} + 12 q^{35} + 8 q^{37} - 4 q^{38} - 4 q^{39} - 16 q^{47} - 8 q^{50} + 16 q^{51} + 8 q^{52} + 20 q^{53} - 8 q^{55} - 4 q^{56} - 8 q^{57} + 4 q^{59} - 8 q^{61} + 28 q^{62} + 4 q^{63} + 40 q^{64} + 4 q^{65} - 4 q^{66} - 16 q^{67} + 8 q^{69} + 12 q^{70} + 40 q^{71} - 8 q^{73} + 8 q^{74} + 16 q^{75} - 4 q^{76} + 24 q^{77} - 4 q^{78} + 12 q^{79} - 40 q^{81} - 8 q^{83} + 8 q^{85} - 12 q^{89} - 24 q^{91} - 8 q^{93} - 16 q^{94} + 28 q^{95} - 8 q^{99}+O(q^{100}) \) 40 * q + 40 * q^2 + 40 * q^4 - 4 * q^7 + 40 * q^8 + 8 * q^13 - 4 * q^14 + 40 * q^16 - 4 * q^19 - 8 * q^25 + 8 * q^26 - 4 * q^28 + 28 * q^31 + 40 * q^32 - 4 * q^33 + 12 * q^35 + 8 * q^37 - 4 * q^38 - 4 * q^39 - 16 * q^47 - 8 * q^50 + 16 * q^51 + 8 * q^52 + 20 * q^53 - 8 * q^55 - 4 * q^56 - 8 * q^57 + 4 * q^59 - 8 * q^61 + 28 * q^62 + 4 * q^63 + 40 * q^64 + 4 * q^65 - 4 * q^66 - 16 * q^67 + 8 * q^69 + 12 * q^70 + 40 * q^71 - 8 * q^73 + 8 * q^74 + 16 * q^75 - 4 * q^76 + 24 * q^77 - 4 * q^78 + 12 * q^79 - 40 * q^81 - 8 * q^83 + 8 * q^85 - 12 * q^89 - 24 * q^91 - 8 * q^93 - 16 * q^94 + 28 * q^95 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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