LMFDB - Embedded newform 1110.2.l.b.697.8

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:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			697.8
Character	$\chi$	$=$	1110.697
Dual form			1110.2.l.b.43.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(-0.220830 + 2.22514i) q^{5} +(0.707107 - 0.707107i) q^{6} +(-1.18593 - 1.18593i) q^{7} -1.00000i q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(-0.220830 + 2.22514i) q^{5} +(0.707107 - 0.707107i) q^{6} +(-1.18593 - 1.18593i) q^{7} -1.00000i q^{8} +1.00000i q^{9} +(-2.22514 - 0.220830i) q^{10} +4.79879i q^{11} +(0.707107 + 0.707107i) q^{12} -4.44661i q^{13} +(1.18593 - 1.18593i) q^{14} +(1.72956 - 1.41726i) q^{15} +1.00000 q^{16} -1.30290 q^{17} -1.00000 q^{18} +(-4.46151 - 4.46151i) q^{19} +(0.220830 - 2.22514i) q^{20} +1.67716i q^{21} -4.79879 q^{22} +0.933219i 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} +1.00000i q^{32} +(3.39326 - 3.39326i) q^{33} -1.30290i q^{34} +(2.90075 - 2.37697i) q^{35} -1.00000i q^{36} +(3.31197 - 5.10204i) q^{37} +(4.46151 - 4.46151i) q^{38} +(-3.14423 + 3.14423i) q^{39} +(2.22514 + 0.220830i) q^{40} -7.79237i q^{41} -1.67716 q^{42} -2.02422i q^{43} -4.79879i q^{44} +(-2.22514 - 0.220830i) q^{45} -0.933219 q^{46} +(-6.81249 - 6.81249i) q^{47} +(-0.707107 - 0.707107i) q^{48} -4.18713i q^{49} +(0.982756 - 4.90247i) q^{50} +(0.921286 + 0.921286i) q^{51} +4.44661i q^{52} +(5.08803 - 5.08803i) q^{53} +(0.707107 + 0.707107i) q^{54} +(-10.6780 - 1.05972i) q^{55} +(-1.18593 + 1.18593i) q^{56} +6.30953i q^{57} +(-3.66959 - 3.66959i) q^{58} +(-3.87716 - 3.87716i) q^{59} +(-1.72956 + 1.41726i) 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} +1.30290 q^{68} +(0.659885 - 0.659885i) q^{69} +(2.37697 + 2.90075i) q^{70} -8.94910 q^{71} +1.00000 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} +(-0.220830 + 2.22514i) q^{80} -1.00000 q^{81} +7.79237 q^{82} +(-6.32708 + 6.32708i) q^{83} -1.67716i q^{84} +(0.287719 - 2.89912i) q^{85} +2.02422 q^{86} +5.18959 q^{87} +4.79879 q^{88} +(3.11309 - 3.11309i) q^{89} +(0.220830 - 2.22514i) q^{90} +(-5.27338 + 5.27338i) q^{91} -0.933219i q^{92} -6.42572i q^{93} +(6.81249 - 6.81249i) q^{94} +(10.9127 - 8.94223i) q^{95} +(0.707107 - 0.707107i) q^{96} +0.0235287 q^{97} +4.18713 q^{98} -4.79879 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 40 q^{4} - 4 q^{7}+O(q^{10}) $ 40 * q - 40 * q^4 - 4 * q^7	$ 40 q - 40 q^{4} - 4 q^{7} + 4 q^{14} + 40 q^{16} + 24 q^{17} - 40 q^{18} + 4 q^{19} + 8 q^{22} + 8 q^{25} + 8 q^{26} + 4 q^{28} + 28 q^{31} - 4 q^{33} + 20 q^{35} + 20 q^{37} - 4 q^{38} + 4 q^{39} + 16 q^{42} - 16 q^{47} + 16 q^{51} + 20 q^{53} + 16 q^{55} - 4 q^{56} - 4 q^{59} - 8 q^{61} - 28 q^{62} + 4 q^{63} - 40 q^{64} - 4 q^{65} - 4 q^{66} + 16 q^{67} - 24 q^{68} - 8 q^{69} + 12 q^{70} + 40 q^{71} + 40 q^{72} + 8 q^{73} - 8 q^{74} + 16 q^{75} - 4 q^{76} - 24 q^{77} + 4 q^{78} - 12 q^{79} - 40 q^{81} - 24 q^{82} - 8 q^{83} - 8 q^{85} + 8 q^{87} - 8 q^{88} + 12 q^{89} - 24 q^{91} + 16 q^{94} - 28 q^{95} + 40 q^{97} - 56 q^{98} + 8 q^{99}+O(q^{100}) $ 40 * q - 40 * q^4 - 4 * q^7 + 4 * q^14 + 40 * q^16 + 24 * q^17 - 40 * q^18 + 4 * q^19 + 8 * q^22 + 8 * q^25 + 8 * q^26 + 4 * q^28 + 28 * q^31 - 4 * q^33 + 20 * q^35 + 20 * q^37 - 4 * q^38 + 4 * q^39 + 16 * q^42 - 16 * q^47 + 16 * q^51 + 20 * q^53 + 16 * q^55 - 4 * q^56 - 4 * q^59 - 8 * q^61 - 28 * q^62 + 4 * q^63 - 40 * q^64 - 4 * q^65 - 4 * q^66 + 16 * q^67 - 24 * q^68 - 8 * q^69 + 12 * q^70 + 40 * q^71 + 40 * q^72 + 8 * q^73 - 8 * q^74 + 16 * q^75 - 4 * q^76 - 24 * q^77 + 4 * q^78 - 12 * q^79 - 40 * q^81 - 24 * q^82 - 8 * q^83 - 8 * q^85 + 8 * q^87 - 8 * q^88 + 12 * q^89 - 24 * q^91 + 16 * q^94 - 28 * q^95 + 40 * q^97 - 56 * 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
$5$	−0.220830	+	2.22514i	−0.0987584	+	0.995111i
$5$	−0.220830	+	2.22514i	−0.0987584	+	0.995111i
$6$	0.707107	−	0.707107i	0.288675	−	0.288675i
$7$	−1.18593	−	1.18593i	−0.448240	−	0.448240i	0.446529	−	0.894769i	$-0.352660\pi$
$7$	−1.18593	−	1.18593i	−0.448240	−	0.448240i	−0.894769	+	0.446529i	$0.852660\pi$
$8$		−	1.00000i		−	0.353553i
$9$			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
$13$		−	4.44661i		−	1.23327i	−0.787250	−	0.616634i	$-0.788496\pi$
$13$		−	4.44661i		−	1.23327i	0.787250	−	0.616634i	$-0.211504\pi$
$14$	1.18593	−	1.18593i	0.316954	−	0.316954i
$15$	1.72956	−	1.41726i	0.446570	−	0.365935i
$16$	1.00000			0.250000
$17$	−1.30290			−0.315999			−0.157999	−	0.987439i	$-0.550504\pi$
$17$	−1.30290			−0.315999			−0.157999	+	0.987439i	$0.550504\pi$
$18$	−1.00000			−0.235702
$19$	−4.46151	−	4.46151i	−1.02354	−	1.02354i	−0.999716	−	0.0238243i	$-0.992416\pi$
$19$	−4.46151	−	4.46151i	−1.02354	−	1.02354i	−0.0238243	−	0.999716i	$-0.507584\pi$
$20$	0.220830	−	2.22514i	0.0493792	−	0.497556i
$21$			1.67716i			0.365987i
$22$	−4.79879			−1.02311
$23$			0.933219i			0.194590i	0.995256	+	0.0972948i	$0.0310190\pi$
$23$			0.933219i			0.194590i	−0.995256	+	0.0972948i	$0.968981\pi$
$24$	−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	−0.960322	−	0.278895i	$-0.910032\pi$
$29$	−3.66959	+	3.66959i	−0.681426	+	0.681426i	0.278895	+	0.960322i	$0.410032\pi$
$30$	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	$0.554205\pi$
$32$			1.00000i			0.176777i
$33$	3.39326	−	3.39326i	0.590691	−	0.590691i
$34$		−	1.30290i		−	0.223445i
$35$	2.90075	−	2.37697i	0.490316	−	0.401781i
$36$		−	1.00000i		−	0.166667i
$37$	3.31197	−	5.10204i	0.544484	−	0.838771i
$37$	3.31197	−	5.10204i	0.544484	−	0.838771i
$38$	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	$-0.208221\pi$
$42$	−1.67716			−0.258792
$43$		−	2.02422i		−	0.308690i	−0.988017	−	0.154345i	$-0.950673\pi$
$43$		−	2.02422i		−	0.308690i	0.988017	−	0.154345i	$-0.0493268\pi$
$44$		−	4.79879i		−	0.723445i
$45$	−2.22514	−	0.220830i	−0.331704	−	0.0329195i
$46$	−0.933219			−0.137596
$47$	−6.81249	−	6.81249i	−0.993704	−	0.993704i	0.00627644	−	0.999980i	$-0.498002\pi$
$47$	−6.81249	−	6.81249i	−0.993704	−	0.993704i	−0.999980	+	0.00627644i	$0.998002\pi$
$48$	−0.707107	−	0.707107i	−0.102062	−	0.102062i
$49$		−	4.18713i		−	0.598162i
$50$	0.982756	−	4.90247i	0.138983	−	0.693314i
$51$	0.921286	+	0.921286i	0.129006	+	0.129006i
$52$			4.44661i			0.616634i
$53$	5.08803	−	5.08803i	0.698895	−	0.698895i	−0.265277	−	0.964172i	$-0.585463\pi$
$53$	5.08803	−	5.08803i	0.698895	−	0.698895i	0.964172	+	0.265277i	$0.0854634\pi$
$54$	0.707107	+	0.707107i	0.0962250	+	0.0962250i
$55$	−10.6780	−	1.05972i	−1.43982	−	0.142893i
$56$	−1.18593	+	1.18593i	−0.158477	+	0.158477i
$57$			6.30953i			0.835717i
$58$	−3.66959	−	3.66959i	−0.481841	−	0.481841i
$59$	−3.87716	−	3.87716i	−0.504763	−	0.504763i	0.408151	−	0.912914i	$-0.366174\pi$
$59$	−3.87716	−	3.87716i	−0.504763	−	0.504763i	−0.912914	+	0.408151i	$0.866174\pi$
$60$	−1.72956	+	1.41726i	−0.223285	+	0.182967i
$61$	−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	$-0.732396\pi$
$67$	0.639879	−	0.639879i	0.0781737	−	0.0781737i	0.745112	+	0.666939i	$0.232396\pi$
$68$	1.30290			0.157999
$69$	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	$0.678195\pi$
$72$	1.00000			0.117851
$73$	−1.06393	−	1.06393i	−0.124524	−	0.124524i	0.642098	−	0.766622i	$-0.278064\pi$
$73$	−1.06393	−	1.06393i	−0.124524	−	0.124524i	−0.766622	+	0.642098i	$0.778064\pi$
$74$	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	0.571608	−	0.820527i	$-0.306320\pi$
$79$	−2.21244	−	2.21244i	−0.248919	−	0.248919i	−0.820527	+	0.571608i	$0.806320\pi$
$80$	−0.220830	+	2.22514i	−0.0246896	+	0.248778i
$81$	−1.00000			−0.111111
$82$	7.79237			0.860524
$83$	−6.32708	+	6.32708i	−0.694488	+	0.694488i	−0.963216	−	0.268728i	$-0.913397\pi$
$83$	−6.32708	+	6.32708i	−0.694488	+	0.694488i	0.268728	+	0.963216i	$0.413397\pi$
$84$		−	1.67716i		−	0.182993i
$85$	0.287719	−	2.89912i	0.0312075	−	0.314454i
$86$	2.02422			0.218277
$87$	5.18959			0.556382
$88$	4.79879			0.511553
$89$	3.11309	−	3.11309i	0.329987	−	0.329987i	−0.522594	−	0.852582i	$-0.675036\pi$
$89$	3.11309	−	3.11309i	0.329987	−	0.329987i	0.852582	+	0.522594i	$0.175036\pi$
$90$	0.220830	−	2.22514i	0.0232776	−	0.234550i
$91$	−5.27338	+	5.27338i	−0.552800	+	0.552800i
$92$		−	0.933219i		−	0.0972948i
$93$		−	6.42572i		−	0.666316i
$94$	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
$97$	0.0235287			0.00238898			0.00119449	−	0.999999i	$-0.499620\pi$
$97$	0.0235287			0.00238898			0.00119449	+	0.999999i	$0.499620\pi$
$98$	4.18713			0.422964
$99$	−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
$103$	−10.4171			−1.02642			−0.513212	−	0.858262i	$-0.671545\pi$
$103$	−10.4171			−1.02642			−0.513212	+	0.858262i	$0.671545\pi$
$104$	−4.44661			−0.436026
$105$	−3.73191	−	0.370368i	−0.364197	−	0.0361442i
$106$	5.08803	+	5.08803i	0.494194	+	0.494194i
$107$	−3.87605	−	3.87605i	−0.374712	−	0.374712i	0.494478	−	0.869190i	$-0.335359\pi$
$107$	−3.87605	−	3.87605i	−0.374712	−	0.374712i	−0.869190	+	0.494478i	$0.835359\pi$
$108$	−0.707107	+	0.707107i	−0.0680414	+	0.0680414i
$109$	−0.670005	−	0.670005i	−0.0641748	−	0.0641748i	0.674291	−	0.738466i	$-0.264449\pi$
$109$	−0.670005	−	0.670005i	−0.0641748	−	0.0641748i	−0.738466	+	0.674291i	$0.764449\pi$
$110$	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
$113$	10.2693			0.966056			0.483028	−	0.875605i	$-0.339537\pi$
$113$	10.2693			0.966056			0.483028	+	0.875605i	$0.339537\pi$
$114$	−6.30953			−0.590941
$115$	−2.07654	−	0.206083i	−0.193638	−	0.0192173i
$116$	3.66959	−	3.66959i	0.340713	−	0.340713i
$117$	4.44661			0.411089
$118$	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
$125$	3.26938	−	10.6916i	0.292422	−	0.956289i
$126$	1.18593	+	1.18593i	0.105651	+	0.105651i
$127$	13.8004	+	13.8004i	1.22459	+	1.22459i	0.965983	+	0.258607i	$0.0832636\pi$
$127$	13.8004	+	13.8004i	1.22459	+	1.22459i	0.258607	+	0.965983i	$0.416736\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−1.43134	+	1.43134i	−0.126022	+	0.126022i
$130$	−0.981946	+	9.89431i	−0.0861224	+	0.867789i
$131$	−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
$133$			10.5821i			0.917584i
$134$	0.639879	+	0.639879i	0.0552771	+	0.0552771i
$135$	1.41726	+	1.72956i	0.121978	+	0.148857i
$136$			1.30290i			0.111722i
$137$	6.54303	+	6.54303i	0.559008	+	0.559008i	0.929025	−	0.370017i	$-0.120648\pi$
$137$	6.54303	+	6.54303i	0.559008	+	0.559008i	−0.370017	+	0.929025i	$0.620648\pi$
$138$	0.659885	+	0.659885i	0.0561732	+	0.0561732i
$139$	−13.1631			−1.11648			−0.558241	−	0.829679i	$-0.688524\pi$
$139$	−13.1631			−1.11648			−0.558241	+	0.829679i	$0.688524\pi$
$140$	−2.90075	+	2.37697i	−0.245158	+	0.200891i
$141$			9.63432i			0.811356i
$142$		−	8.94910i		−	0.750992i
$143$	21.3384			1.78440
$144$			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
$148$	−3.31197	+	5.10204i	−0.272242	+	0.419385i
$149$			5.19216i			0.425359i	0.977122	+	0.212679i	$0.0682189\pi$
$149$			5.19216i			0.425359i	−0.977122	+	0.212679i	$0.931781\pi$
$150$	−4.16148	+	2.77166i	−0.339784	+	0.226305i
$151$			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
$153$		−	1.30290i		−	0.105333i
$154$	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	0.608298	−	0.793709i	$-0.291853\pi$
$157$	−2.32320	−	2.32320i	−0.185411	−	0.185411i	−0.793709	+	0.608298i	$0.791853\pi$
$158$	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
$162$		−	1.00000i		−	0.0785674i
$163$	0.310642			0.0243314			0.0121657	−	0.999926i	$-0.496127\pi$
$163$	0.310642			0.0243314			0.0121657	+	0.999926i	$0.496127\pi$
$164$			7.79237i			0.608482i
$165$	6.80113	+	8.29980i	0.529467	+	0.646139i
$166$	−6.32708	−	6.32708i	−0.491077	−	0.491077i
$167$	21.2856			1.64713			0.823563	−	0.567225i	$-0.191983\pi$
$167$	21.2856			1.64713			0.823563	+	0.567225i	$0.191983\pi$
$168$	1.67716			0.129396
$169$	−6.77233			−0.520948
$170$	2.89912	+	0.287719i	0.222352	+	0.0220670i
$171$	4.46151	−	4.46151i	0.341180	−	0.341180i
$172$			2.02422i			0.154345i
$173$	−13.5623	−	13.5623i	−1.03112	−	1.03112i	−0.999500	−	0.0316231i	$-0.989932\pi$
$173$	−13.5623	−	13.5623i	−1.03112	−	1.03112i	−0.0316231	−	0.999500i	$-0.510068\pi$
$174$			5.18959i			0.393422i
$175$	4.64851	+	6.97947i	0.351394	+	0.527599i
$176$			4.79879i			0.361723i
$177$			5.48313i			0.412137i
$178$	3.11309	+	3.11309i	0.233336	+	0.233336i
$179$	−9.91196	+	9.91196i	−0.740854	+	0.740854i	−0.972742	−	0.231888i	$-0.925510\pi$
$179$	−9.91196	+	9.91196i	−0.740854	+	0.740854i	0.231888	+	0.972742i	$0.425510\pi$
$180$	2.22514	+	0.220830i	0.165852	+	0.0164597i
$181$	−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
$183$			8.99677i			0.665060i
$184$	0.933219			0.0687978
$185$	10.6214	+	8.49627i	0.780898	+	0.624658i
$186$	6.42572			0.471157
$187$		−	6.25232i		−	0.457215i
$188$	6.81249	+	6.81249i	0.496852	+	0.496852i
$189$	−1.67716			−0.121996
$190$	8.94223	+	10.9127i	0.648738	+	0.791691i
$191$	−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
$193$			16.8985i			1.21638i	0.793790	+	0.608192i	$0.208105\pi$
$193$			16.8985i			1.21638i	−0.793790	+	0.608192i	$0.791895\pi$
$194$			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	0.485151	−	0.874430i	$-0.338764\pi$
$197$	−5.46379	−	5.46379i	−0.389279	−	0.389279i	−0.874430	+	0.485151i	$0.838764\pi$
$198$		−	4.79879i		−	0.341035i
$199$	−11.6938	+	11.6938i	−0.828949	+	0.828949i	−0.987371	−	0.158423i	$-0.949359\pi$
$199$	−11.6938	+	11.6938i	−0.828949	+	0.828949i	0.158423	+	0.987371i	$0.449359\pi$
$200$	−0.982756	+	4.90247i	−0.0694913	+	0.346657i
$201$	−0.904926			−0.0638285
$202$	−3.95084			−0.277980
$203$	8.70377			0.610885
$204$	−0.921286	−	0.921286i	−0.0645029	−	0.0645029i
$205$	17.3391	+	1.72079i	1.21101	+	0.120185i
$206$		−	10.4171i		−	0.725792i
$207$	−0.933219			−0.0648632
$208$		−	4.44661i		−	0.308317i
$209$	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
$217$		−	10.7770i		−	0.731588i
$218$	0.670005	−	0.670005i	0.0453784	−	0.0453784i
$219$			1.50463i			0.101673i
$220$	10.6780	+	1.05972i	0.719909	+	0.0714463i
$221$			5.79347i			0.389711i
$222$	−1.26577	−	5.94961i	−0.0849532	−	0.399311i
$223$	−10.7674	+	10.7674i	−0.721039	+	0.721039i	−0.968817	−	0.247778i	$-0.920300\pi$
$223$	−10.7674	+	10.7674i	−0.721039	+	0.721039i	0.247778	+	0.968817i	$0.420300\pi$
$224$	1.18593	−	1.18593i	0.0792384	−	0.0792384i
$225$	0.982756	−	4.90247i	0.0655170	−	0.326831i
$226$			10.2693i			0.683105i
$227$	−9.50039			−0.630563			−0.315282	−	0.948998i	$-0.602099\pi$
$227$	−9.50039			−0.630563			−0.315282	+	0.948998i	$0.602099\pi$
$228$		−	6.30953i		−	0.417859i
$229$		−	4.84055i		−	0.319873i	−0.987127	−	0.159936i	$-0.948871\pi$
$229$		−	4.84055i		−	0.319873i	0.987127	−	0.159936i	$-0.0511289\pi$
$230$	0.206083	−	2.07654i	0.0135887	−	0.136923i
$231$	−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	$-0.312310\pi$
$233$	−4.19880	−	4.19880i	−0.275072	−	0.275072i	−0.831138	+	0.556066i	$0.812310\pi$
$234$			4.44661i			0.290684i
$235$	16.6631	−	13.6543i	1.08698	−	0.890710i
$236$	3.87716	+	3.87716i	0.252382	+	0.252382i
$237$			3.12886i			0.203241i
$238$	−1.54515	+	1.54515i	−0.100157	+	0.100157i
$239$	5.62269	+	5.62269i	0.363701	+	0.363701i	0.865174	−	0.501472i	$-0.167208\pi$
$239$	5.62269	+	5.62269i	0.363701	+	0.363701i	−0.501472	+	0.865174i	$0.667208\pi$
$240$	1.72956	−	1.41726i	0.111643	−	0.0914837i
$241$	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	$0.0857510\pi$
$242$		−	12.0284i		−	0.773216i
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$	6.36168	+	6.36168i	0.407265	+	0.407265i
$245$	9.31694	+	0.924646i	0.595237	+	0.0590734i
$246$	−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
$253$	−4.47832			−0.281550
$254$	−13.8004	+	13.8004i	−0.865916	+	0.865916i
$255$	−2.25344	+	1.84654i	−0.141116	+	0.115635i
$256$	1.00000			0.0625000
$257$	11.2517			0.701861			0.350931	−	0.936401i	$-0.385865\pi$
$257$	11.2517			0.701861			0.350931	+	0.936401i	$0.385865\pi$
$258$	−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	$-0.396196\pi$
$263$	−10.1672	−	10.1672i	−0.626937	−	0.626937i	−0.947296	+	0.320359i	$0.896196\pi$
$264$	−3.39326	−	3.39326i	−0.208841	−	0.208841i
$265$	10.1980	+	12.4452i	0.626457	+	0.764500i
$266$	−10.5821			−0.648830
$267$	−4.40258			−0.269434
$268$	−0.639879	+	0.639879i	−0.0390868	+	0.0390868i
$269$			24.8306i			1.51395i	0.653445	+	0.756974i	$0.273323\pi$
$269$			24.8306i			1.51395i	−0.653445	+	0.756974i	$0.726677\pi$
$270$	−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	$0.461687\pi$
$272$	−1.30290			−0.0789996
$273$	7.45768			0.451359
$274$	−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
$277$		−	2.77329i		−	0.166631i	−0.996523	−	0.0833154i	$-0.973449\pi$
$277$		−	2.77329i		−	0.166631i	0.996523	−	0.0833154i	$-0.0265509\pi$
$278$		−	13.1631i		−	0.789472i
$279$	−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	$0.434470\pi$
$282$	−9.63432			−0.573715
$283$	−26.5212			−1.57652			−0.788261	−	0.615341i	$-0.789018\pi$
$283$	−26.5212			−1.57652			−0.788261	+	0.615341i	$0.789018\pi$
$284$	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
$288$	−1.00000			−0.0589256
$289$	−15.3025			−0.900145
$290$	8.97570	−	7.35499i	0.527071	−	0.431900i
$291$	−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	−0.0618185	+	0.998087i	$0.519690\pi$
$293$	−18.1427	+	18.1427i	−1.05991	+	1.05991i	−0.998087	+	0.0618185i	$0.980310\pi$
$294$	−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
$298$	−5.19216			−0.300774
$299$	4.14966			0.239981
$300$	−2.77166	−	4.16148i	−0.160022	−	0.240263i
$301$	−2.40058	+	2.40058i	−0.138367	+	0.138367i
$302$	−11.5161			−0.662679
$303$	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	$-0.781480\pi$
$307$	−2.44662	+	2.44662i	−0.139636	+	0.139636i	0.633833	+	0.773470i	$0.281480\pi$
$308$	−5.69104	+	5.69104i	−0.324277	+	0.324277i
$309$	7.36598	+	7.36598i	0.419036	+	0.419036i
$310$	−9.10691	−	11.1137i	−0.517238	−	0.631214i
$311$	−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
$313$			1.26968i			0.0717668i	0.999356	+	0.0358834i	$0.0114245\pi$
$313$			1.26968i			0.0717668i	−0.999356	+	0.0358834i	$0.988576\pi$
$314$	2.32320	−	2.32320i	0.131106	−	0.131106i
$315$	2.37697	+	2.90075i	0.133927	+	0.163439i
$316$	2.21244	+	2.21244i	0.124459	+	0.124459i
$317$	11.5508	−	11.5508i	0.648757	−	0.648757i	−0.303936	−	0.952693i	$-0.598301\pi$
$317$	11.5508	−	11.5508i	0.648757	−	0.648757i	0.952693	+	0.303936i	$0.0983008\pi$
$318$		−	7.19557i		−	0.403507i
$319$	−17.6096	−	17.6096i	−0.985949	−	0.985949i
$320$	0.220830	−	2.22514i	0.0123448	−	0.124389i
$321$			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
$325$	−4.36993	+	21.7994i	−0.242400	+	1.20921i
$326$			0.310642i			0.0172049i
$327$			0.947530i			0.0523985i
$328$	−7.79237			−0.430262
$329$			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
$333$	5.10204	+	3.31197i	0.279590	+	0.181495i
$334$			21.2856i			1.16469i
$335$	1.28251	+	1.56512i	0.0700712	+	0.0855118i
$336$			1.67716i			0.0914966i
$337$	3.80408	−	3.80408i	0.207222	−	0.207222i	−0.595864	−	0.803085i	$-0.703190\pi$
$337$	3.80408	−	3.80408i	0.207222	−	0.207222i	0.803085	+	0.595864i	$0.203190\pi$
$338$		−	6.77233i		−	0.368366i
$339$	−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
$347$		−	32.1513i		−	1.72597i	−0.505226	−	0.862987i	$-0.668591\pi$
$347$		−	32.1513i		−	1.72597i	0.505226	−	0.862987i	$-0.331409\pi$
$348$	−5.18959			−0.278191
$349$			4.32501i			0.231512i	0.993278	+	0.115756i	$0.0369291\pi$
$349$			4.32501i			0.231512i	−0.993278	+	0.115756i	$0.963071\pi$
$350$	−6.97947	+	4.64851i	−0.373069	+	0.248473i
$351$	−3.14423	−	3.14423i	−0.167826	−	0.167826i
$352$	−4.79879			−0.255777
$353$	−16.0457			−0.854028			−0.427014	−	0.904245i	$-0.640434\pi$
$353$	−16.0457			−0.854028			−0.427014	+	0.904245i	$0.640434\pi$
$354$	−5.48313			−0.291425
$355$	1.97623	−	19.9130i	0.104888	−	1.05687i
$356$	−3.11309	+	3.11309i	−0.164994	+	0.164994i
$357$		−	2.18517i		−	0.115651i
$358$	−9.91196	−	9.91196i	−0.523863	−	0.523863i
$359$		−	15.7185i		−	0.829591i	−0.909915	−	0.414795i	$-0.863853\pi$
$359$		−	15.7185i		−	0.829591i	0.909915	−	0.414795i	$-0.136147\pi$
$360$	−0.220830	+	2.22514i	−0.0116388	+	0.117275i
$361$			20.8101i			1.09527i
$362$		−	1.52458i		−	0.0801302i
$363$	8.50537	+	8.50537i	0.446416	+	0.446416i
$364$	5.27338	−	5.27338i	0.276400	−	0.276400i
$365$	2.60234	−	2.13245i	0.136213	−	0.111617i
$366$	−8.99677			−0.470269
$367$	17.3935	+	17.3935i	0.907935	+	0.907935i	0.996105	−	0.0881705i	$-0.0281020\pi$
$367$	17.3935	+	17.3935i	0.907935	+	0.907935i	−0.0881705	+	0.996105i	$0.528102\pi$
$368$			0.933219i			0.0486474i
$369$	7.79237			0.405655
$370$	−8.49627	+	10.6214i	−0.441700	+	0.552178i
$371$	−12.0681			−0.626546
$372$			6.42572i			0.333158i
$373$	−24.4469	−	24.4469i	−1.26581	−	1.26581i	−0.948231	−	0.317582i	$-0.897129\pi$
$373$	−24.4469	−	24.4469i	−1.26581	−	1.26581i	−0.317582	−	0.948231i	$-0.602871\pi$
$374$	6.25232			0.323300
$375$	−9.87193	+	5.24833i	−0.509784	+	0.271023i
$376$	−6.81249	+	6.81249i	−0.351327	+	0.351327i
$377$	16.3172	+	16.3172i	0.840381	+	0.840381i
$378$		−	1.67716i		−	0.0862639i
$379$		−	28.8766i		−	1.48329i	−0.670793	−	0.741645i	$-0.734046\pi$
$379$		−	28.8766i		−	1.48329i	0.670793	−	0.741645i	$-0.265954\pi$
$380$	−10.9127	+	8.94223i	−0.559810	+	0.458727i
$381$		−	19.5168i		−	0.999873i
$382$	−15.7574	−	15.7574i	−0.806218	−	0.806218i
$383$		−	36.9567i		−	1.88840i	−0.329374	−	0.944200i	$-0.606838\pi$
$383$		−	36.9567i		−	1.88840i	0.329374	−	0.944200i	$-0.393162\pi$
$384$	−0.707107	+	0.707107i	−0.0360844	+	0.0360844i
$385$	11.4066	+	13.9201i	0.581334	+	0.709434i
$386$	−16.8985			−0.860113
$387$	2.02422			0.102897
$388$	−0.0235287			−0.00119449
$389$	21.5492	+	21.5492i	1.09259	+	1.09259i	0.995252	+	0.0973355i	$0.0310320\pi$
$389$	21.5492	+	21.5492i	1.09259	+	1.09259i	0.0973355	+	0.995252i	$0.468968\pi$
$390$	7.69068	−	6.30199i	0.389433	−	0.319114i
$391$		−	1.21589i		−	0.0614900i
$392$	−4.18713			−0.211482
$393$			10.1035i			0.509652i
$394$	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	0.461894	−	0.886935i	$-0.347170\pi$
$397$	26.8752	−	26.8752i	1.34883	−	1.34883i	0.886935	−	0.461894i	$-0.152830\pi$
$398$	−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	$0.553935\pi$
$402$		−	0.904926i		−	0.0451336i
$403$	20.2039	−	20.2039i	1.00643	−	1.00643i
$404$		−	3.95084i		−	0.196562i
$405$	0.220830	−	2.22514i	0.0109732	−	0.110568i
$406$			8.70377i			0.431961i
$407$	24.4837	+	15.8935i	1.21361	+	0.787809i
$408$	0.921286	−	0.921286i	0.0456105	−	0.0456105i
$409$	−1.75957	+	1.75957i	−0.0870050	+	0.0870050i	−0.749270	−	0.662265i	$-0.769595\pi$
$409$	−1.75957	+	1.75957i	−0.0870050	+	0.0870050i	0.662265	+	0.749270i	$0.269595\pi$
$410$	−1.72079	+	17.3391i	−0.0849839	+	0.856317i
$411$		−	9.25324i		−	0.456429i
$412$	10.4171			0.513212
$413$			9.19609i			0.452510i
$414$		−	0.933219i		−	0.0458652i
$415$	−12.6814	−	15.4758i	−0.622506	−	0.759679i
$416$	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	$0.0788601\pi$
$419$			10.0390i			0.490439i	−0.969468	+	0.245220i	$0.921140\pi$
$420$	3.73191	+	0.370368i	0.182099	+	0.0180721i
$421$	−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	$0.826189\pi$
$422$			25.9385i			1.26267i
$423$	6.81249	−	6.81249i	0.331235	−	0.331235i
$424$	−5.08803	−	5.08803i	−0.247097	−	0.247097i
$425$	6.38740	+	1.28043i	0.309835	+	0.0621099i
$426$	−6.32797	+	6.32797i	−0.306591	+	0.306591i
$427$			15.0890i			0.730209i
$428$	3.87605	+	3.87605i	0.187356	+	0.187356i
$429$	−15.0885	−	15.0885i	−0.728479	−	0.728479i
$430$	−0.447009	+	4.50416i	−0.0215567	+	0.217210i
$431$	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	−0.373616	−	0.927584i	$-0.621882\pi$
$433$	11.5273	−	11.5273i	0.553968	−	0.553968i	0.927584	+	0.373616i	$0.121882\pi$
$434$	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
$438$	−1.50463			−0.0718939
$439$	25.1084	−	25.1084i	1.19836	−	1.19836i	0.223702	−	0.974658i	$-0.428186\pi$
$439$	25.1084	−	25.1084i	1.19836	−	1.19836i	0.974658	−	0.223702i	$-0.0718144\pi$
$440$	−1.05972	+	10.6780i	−0.0505201	+	0.509052i
$441$	4.18713			0.199387
$442$	−5.79347			−0.275567
$443$	10.8396	+	10.8396i	0.515004	+	0.515004i	0.916056	−	0.401051i	$-0.131355\pi$
$443$	10.8396	+	10.8396i	0.515004	+	0.515004i	−0.401051	+	0.916056i	$0.631355\pi$
$444$	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	0.184433	−	0.982845i	$-0.440955\pi$
$449$	−16.9181	−	16.9181i	−0.798413	−	0.798413i	−0.982845	+	0.184433i	$0.940955\pi$
$450$	4.90247	+	0.982756i	0.231105	+	0.0463275i
$451$	37.3940			1.76081
$452$	−10.2693			−0.483028
$453$	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
$457$	17.9114			0.837860			0.418930	−	0.908018i	$-0.362405\pi$
$457$	17.9114			0.837860			0.418930	+	0.908018i	$0.362405\pi$
$458$	4.84055			0.226184
$459$	−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	$0.224270\pi$
$462$		−	8.04835i		−	0.374443i
$463$		−	36.5028i		−	1.69643i	−0.529654	−	0.848214i	$-0.677678\pi$
$463$		−	36.5028i		−	1.69643i	0.529654	−	0.848214i	$-0.322322\pi$
$464$	−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
$467$	−20.8160			−0.963252			−0.481626	−	0.876377i	$-0.659954\pi$
$467$	−20.8160			−0.963252			−0.481626	+	0.876377i	$0.659954\pi$
$468$	−4.44661			−0.205545
$469$	−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
$473$	9.71380			0.446641
$474$	−3.12886			−0.143713
$475$	17.4878	+	26.2570i	0.802397	+	1.20475i
$476$	−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	0.0259899	−	0.999662i	$-0.491726\pi$
$479$	−21.3099	−	21.3099i	−0.973672	−	0.973672i	−0.999662	+	0.0259899i	$0.991726\pi$
$480$	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
$483$	−1.56516			−0.0712172
$484$	12.0284			0.546746
$485$	−0.00519586	+	0.0523546i	−0.000235932	+	0.00237730i
$486$	−0.707107	+	0.707107i	−0.0320750	+	0.0320750i
$487$	−31.2190			−1.41467			−0.707334	−	0.706880i	$-0.750102\pi$
$487$	−31.2190			−1.41467			−0.707334	+	0.706880i	$0.750102\pi$
$488$	−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
$495$	1.05972	−	10.6780i	0.0476308	−	0.479939i
$496$	4.54367	+	4.54367i	0.204017	+	0.204017i
$497$	10.6130	+	10.6130i	0.476059	+	0.476059i
$498$			8.94785i			0.400963i
$499$	1.77906	−	1.77906i	0.0796419	−	0.0796419i	−0.666164	−	0.745806i	$-0.732065\pi$
$499$	1.77906	−	1.77906i	0.0796419	−	0.0796419i	0.745806	+	0.666164i	$0.232065\pi$
$500$	−3.26938	+	10.6916i	−0.146211	+	0.478145i
$501$	−15.0512	−	15.0512i	−0.672436	−	0.672436i
$502$	−14.8022	+	14.8022i	−0.660653	+	0.660653i
$503$		−	10.5966i		−	0.472478i	−0.971695	−	0.236239i	$-0.924085\pi$
$503$		−	10.5966i		−	0.472478i	0.971695	−	0.236239i	$-0.0759148\pi$
$504$	−1.18593	−	1.18593i	−0.0528256	−	0.0528256i
$505$	−8.79117	−	0.872466i	−0.391202	−	0.0388242i
$506$		−	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	$-0.552410\pi$
$509$	−7.39583			−0.327814			−0.163907	+	0.986476i	$0.552410\pi$
$510$	−1.84654	−	2.25344i	−0.0817661	−	0.0997838i
$511$			2.52350i			0.111633i
$512$			1.00000i			0.0441942i
$513$	−6.30953			−0.278572
$514$			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
$518$	−2.12291	−	9.97845i	−0.0932752	−	0.438428i
$519$			19.1800i			0.841908i
$520$	0.981946	−	9.89431i	0.0430612	−	0.433894i
$521$			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
$523$			28.4562i			1.24430i	0.782897	+	0.622151i	$0.213741\pi$
$523$			28.4562i			1.24430i	−0.782897	+	0.622151i	$0.786259\pi$
$524$	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
$532$		−	10.5821i		−	0.458792i
$533$	−34.6496			−1.50084
$534$		−	4.40258i		−	0.190518i
$535$	9.48070	−	7.76880i	0.409887	−	0.335875i
$536$	−0.639879	−	0.639879i	−0.0276386	−	0.0276386i
$537$	14.0176			0.604905
$538$	−24.8306			−1.07052
$539$	20.0932			0.865474
$540$	−1.41726	−	1.72956i	−0.0609891	−	0.0744284i
$541$	−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	$0.441910\pi$
$542$			3.95334i			0.169810i
$543$	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
$547$		−	4.88671i		−	0.208941i	−0.994528	−	0.104470i	$-0.966685\pi$
$547$		−	4.88671i		−	0.208941i	0.994528	−	0.104470i	$-0.0333147\pi$
$548$	−6.54303	−	6.54303i	−0.279504	−	0.279504i
$549$	6.36168	−	6.36168i	0.271510	−	0.271510i
$550$	23.5259	+	4.71604i	1.00315	+	0.201093i
$551$	32.7438			1.39493
$552$	−0.659885	−	0.659885i	−0.0280866	−	0.0280866i
$553$			5.24761i			0.223151i
$554$	2.77329			0.117826
$555$	−1.50267	−	13.5182i	−0.0637847	−	0.573816i
$556$	13.1631			0.558241
$557$		−	41.5104i		−	1.75885i	−0.476037	−	0.879425i	$-0.657927\pi$
$557$		−	41.5104i		−	1.75885i	0.476037	−	0.879425i	$-0.342073\pi$
$558$	−4.54367	−	4.54367i	−0.192349	−	0.192349i
$559$	−9.00090			−0.380698
$560$	2.90075	−	2.37697i	0.122579	−	0.100445i
$561$	−4.42106	+	4.42106i	−0.186657	+	0.186657i
$562$	−12.9824	−	12.9824i	−0.547631	−	0.547631i
$563$		−	34.6086i		−	1.45858i	−0.684206	−	0.729288i	$-0.739851\pi$
$563$		−	34.6086i		−	1.45858i	0.684206	−	0.729288i	$-0.260149\pi$
$564$		−	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
$568$			8.94910i			0.375496i
$569$	−4.46452	+	4.46452i	−0.187162	+	0.187162i	−0.794468	−	0.607306i	$-0.792250\pi$
$569$	−4.46452	+	4.46452i	−0.187162	+	0.187162i	0.607306	+	0.794468i	$0.292250\pi$
$570$	1.39334	−	14.0396i	0.0583604	−	0.588053i
$571$	−16.6857			−0.698274			−0.349137	−	0.937072i	$-0.613525\pi$
$571$	−16.6857			−0.698274			−0.349137	+	0.937072i	$0.613525\pi$
$572$	−21.3384			−0.892201
$573$	22.2843			0.930940
$574$	−9.24122	−	9.24122i	−0.385721	−	0.385721i
$575$	0.917126	−	4.57508i	0.0382468	−	0.190794i
$576$		−	1.00000i		−	0.0416667i
$577$	17.2889			0.719745			0.359872	−	0.933002i	$-0.382820\pi$
$577$	17.2889			0.719745			0.359872	+	0.933002i	$0.382820\pi$
$578$		−	15.3025i		−	0.636499i
$579$	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
$587$			28.9501i			1.19490i	0.801907	+	0.597449i	$0.203819\pi$
$587$			28.9501i			1.19490i	−0.801907	+	0.597449i	$0.796181\pi$
$588$	2.96075	−	2.96075i	0.122099	−	0.122099i
$589$		−	40.5433i		−	1.67056i
$590$	7.77102	+	9.48340i	0.319928	+	0.390426i
$591$			7.72696i			0.317845i
$592$	3.31197	−	5.10204i	0.136121	−	0.209693i
$593$	33.1096	−	33.1096i	1.35965	−	1.35965i	0.485300	−	0.874347i	$-0.338710\pi$
$593$	33.1096	−	33.1096i	1.35965	−	1.35965i	0.874347	−	0.485300i	$-0.161290\pi$
$594$	−3.39326	+	3.39326i	−0.139227	+	0.139227i
$595$	−3.77937	+	3.09694i	−0.154939	+	0.126962i
$596$		−	5.19216i		−	0.212679i
$597$	16.5375			0.676834
$598$			4.14966i			0.169692i
$599$			19.5074i			0.797053i	0.917157	+	0.398526i	$0.130478\pi$
$599$			19.5074i			0.797053i	−0.917157	+	0.398526i	$0.869522\pi$
$600$	4.16148	−	2.77166i	0.169892	−	0.113152i
$601$	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
$605$	2.65624	−	26.7649i	0.107992	−	1.08815i
$606$	2.79367	+	2.79367i	0.113485	+	0.113485i
$607$		−	28.0484i		−	1.13845i	−0.822182	−	0.569225i	$-0.807243\pi$
$607$		−	28.0484i		−	1.13845i	0.822182	−	0.569225i	$-0.192757\pi$
$608$	4.46151	−	4.46151i	0.180938	−	0.180938i
$609$	−6.15450	−	6.15450i	−0.249393	−	0.249393i
$610$	12.7507	+	15.5605i	0.516263	+	0.630024i
$611$	−30.2925	+	30.2925i	−1.22550	+	1.22550i
$612$			1.30290i			0.0526664i
$613$	23.0006	+	23.0006i	0.928986	+	0.928986i	0.997640	−	0.0686549i	$-0.0218707\pi$
$613$	23.0006	+	23.0006i	0.928986	+	0.928986i	−0.0686549	+	0.997640i	$0.521871\pi$
$614$	−2.44662	−	2.44662i	−0.0987377	−	0.0987377i
$615$	−11.0438	−	13.4774i	−0.445329	−	0.543460i
$616$	−5.69104	−	5.69104i	−0.229299	−	0.229299i
$617$	−14.0932	+	14.0932i	−0.567369	+	0.567369i	−0.931391	−	0.364022i	$-0.881403\pi$
$617$	−14.0932	+	14.0932i	−0.567369	+	0.567369i	0.364022	+	0.931391i	$0.381403\pi$
$618$	−7.36598	+	7.36598i	−0.296303	+	0.296303i
$619$	22.6414			0.910037			0.455018	−	0.890482i	$-0.349633\pi$
$619$	22.6414			0.910037			0.455018	+	0.890482i	$0.349633\pi$
$620$	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
$623$	−7.38384			−0.295827
$624$	−3.14423	+	3.14423i	−0.125870	+	0.125870i
$625$	23.0684	+	9.63586i	0.922735	+	0.385434i
$626$	−1.26968			−0.0507468
$627$	−30.2781			−1.20919
$628$	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
$635$	−33.7554	+	27.6603i	−1.33954	+	1.09766i
$636$	7.19557			0.285323
$637$	−18.6185			−0.737693
$638$	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	$0.350911\pi$
$642$	−5.48157			−0.216340
$643$	−4.05269			−0.159822			−0.0799112	−	0.996802i	$-0.525464\pi$
$643$	−4.05269			−0.159822			−0.0799112	+	0.996802i	$0.525464\pi$
$644$	−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
$647$			40.5162i			1.59285i	0.604734	+	0.796427i	$0.293279\pi$
$647$			40.5162i			1.59285i	−0.604734	+	0.796427i	$0.706721\pi$
$648$			1.00000i			0.0392837i
$649$	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
$652$	−0.310642			−0.0121657
$653$	−3.85391			−0.150815			−0.0754076	−	0.997153i	$-0.524026\pi$
$653$	−3.85391			−0.150815			−0.0754076	+	0.997153i	$0.524026\pi$
$654$	−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
$658$	−16.1583			−0.629916
$659$	−38.4968			−1.49962			−0.749812	−	0.661651i	$-0.769856\pi$
$659$	−38.4968			−1.49962			−0.749812	+	0.661651i	$0.769856\pi$
$660$	−6.80113	−	8.29980i	−0.264734	−	0.323069i
$661$	−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
$668$	−21.2856			−0.823563
$669$	15.2274			0.588726
$670$	−1.56512	+	1.28251i	−0.0604660	+	0.0495478i
$671$	30.5284	−	30.5284i	1.17853	−	1.17853i
$672$	−1.67716			−0.0646979
$673$	0.532326	−	0.532326i	0.0205197	−	0.0205197i	−0.696773	−	0.717292i	$-0.745381\pi$
$673$	0.532326	−	0.532326i	0.0205197	−	0.0205197i	0.717292	+	0.696773i	$0.245381\pi$
$674$	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	$-0.799974\pi$
$677$	−5.75332	+	5.75332i	−0.221118	+	0.221118i	0.587851	+	0.808969i	$0.299974\pi$
$678$	7.26150	−	7.26150i	0.278876	−	0.278876i
$679$	−0.0279035	−	0.0279035i	−0.00107084	−	0.00107084i
$680$	−2.89912	−	0.287719i	−0.111176	−	0.0110335i
$681$	6.71779	+	6.71779i	0.257426	+	0.257426i
$682$	−21.8041	−	21.8041i	−0.834923	−	0.834923i
$683$			39.9256i			1.52771i	0.645388	+	0.763855i	$0.276696\pi$
$683$			39.9256i			1.52771i	−0.645388	+	0.763855i	$0.723304\pi$
$684$	−4.46151	+	4.46151i	−0.170590	+	0.170590i
$685$	−16.0040	+	13.1142i	−0.611482	+	0.501069i
$686$	−13.2672	−	13.2672i	−0.506543	−	0.506543i
$687$	−3.42279	+	3.42279i	−0.130587	+	0.130587i
$688$		−	2.02422i		−	0.0771726i
$689$	−22.6245	−	22.6245i	−0.861925	−	0.861925i
$690$	−1.61406	+	1.32261i	−0.0614461	+	0.0503510i
$691$			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
$695$	2.90682	−	29.2898i	0.110262	−	1.11102i
$696$		−	5.18959i		−	0.196711i
$697$			10.1526i			0.384559i
$698$	−4.32501			−0.163704
$699$			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
$703$	−37.5392	+	7.98644i	−1.41582	+	0.301214i
$704$		−	4.79879i		−	0.180861i
$705$	−21.4377	−	2.12755i	−0.807389	−	0.0801282i
$706$		−	16.0457i		−	0.603889i
$707$	4.68543	−	4.68543i	0.176214	−	0.176214i
$708$		−	5.48313i		−	0.206069i
$709$	−28.0496	−	28.0496i	−1.05342	−	1.05342i	−0.998490	−	0.0549332i	$-0.982505\pi$
$709$	−28.0496	−	28.0496i	−1.05342	−	1.05342i	−0.0549332	−	0.998490i	$-0.517495\pi$
$710$	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
$717$		−	7.95168i		−	0.296961i
$718$	15.7185			0.586609
$719$			22.1676i			0.826713i	0.910569	+	0.413357i	$0.135644\pi$
$719$			22.1676i			0.826713i	−0.910569	+	0.413357i	$0.864356\pi$
$720$	−2.22514	−	0.220830i	−0.0829260	−	0.00822986i
$721$	12.3539	+	12.3539i	0.460085	+	0.460085i
$722$	−20.8101			−0.774473
$723$	−15.3195			−0.569738
$724$	1.52458			0.0566606
$725$	21.5964	−	14.3837i	0.802069	−	0.534199i
$726$	−8.50537	+	8.50537i	−0.315664	+	0.315664i
$727$			29.7685i			1.10405i	0.833827	+	0.552026i	$0.186145\pi$
$727$			29.7685i			1.10405i	−0.833827	+	0.552026i	$0.813855\pi$
$728$	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
$732$		−	8.99677i		−	0.332530i
$733$	−27.3738	−	27.3738i	−1.01108	−	1.01108i	−0.999938	−	0.0111379i	$-0.996455\pi$
$733$	−27.3738	−	27.3738i	−1.01108	−	1.01108i	−0.0111379	−	0.999938i	$-0.503545\pi$
$734$	−17.3935	+	17.3935i	−0.642007	+	0.642007i
$735$	−5.93425	−	7.24189i	−0.218888	−	0.267121i
$736$	−0.933219			−0.0343989
$737$	3.07065	+	3.07065i	0.113109	+	0.113109i
$738$			7.79237i			0.286841i
$739$	3.45235			0.126997			0.0634984	−	0.997982i	$-0.479774\pi$
$739$	3.45235			0.126997			0.0634984	+	0.997982i	$0.479774\pi$
$740$	−10.6214	−	8.49627i	−0.390449	−	0.312329i
$741$	28.0560			1.03066
$742$		−	12.0681i		−	0.443035i
$743$	6.95019	+	6.95019i	0.254978	+	0.254978i	0.823008	−	0.568030i	$-0.192294\pi$
$743$	6.95019	+	6.95019i	0.254978	+	0.254978i	−0.568030	+	0.823008i	$0.692294\pi$
$744$	−6.42572			−0.235578
$745$	−11.5533	−	1.14659i	−0.423279	−	0.0420077i
$746$	24.4469	−	24.4469i	0.895065	−	0.895065i
$747$	−6.32708	−	6.32708i	−0.231496	−	0.231496i
$748$			6.25232i			0.228608i
$749$			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
$753$		−	20.9334i		−	0.762857i
$754$	−16.3172	+	16.3172i	−0.594239	+	0.594239i
$755$	−25.6250	−	2.54311i	−0.932588	−	0.0925533i
$756$	1.67716			0.0609978
$757$	−24.9414			−0.906511			−0.453256	−	0.891381i	$-0.649737\pi$
$757$	−24.9414			−0.906511			−0.453256	+	0.891381i	$0.649737\pi$
$758$	28.8766			1.04884
$759$	3.16665	+	3.16665i	0.114942	+	0.114942i
$760$	−8.94223	−	10.9127i	−0.324369	−	0.395845i
$761$			38.6923i			1.40260i	0.712868	+	0.701298i	$0.247396\pi$
$761$			38.6923i			1.40260i	−0.712868	+	0.701298i	$0.752604\pi$
$762$	19.5168			0.707017
$763$			1.58916i			0.0575315i
$764$	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	−0.373055	−	0.927809i	$-0.621690\pi$
$769$	15.3838	−	15.3838i	0.554755	−	0.554755i	0.927809	+	0.373055i	$0.121690\pi$
$770$	−13.9201	+	11.4066i	−0.501646	+	0.411065i
$771$	−7.95615	−	7.95615i	−0.286534	−	0.286534i
$772$		−	16.8985i		−	0.608192i
$773$	−19.3766	+	19.3766i	−0.696929	+	0.696929i	−0.963747	−	0.266818i	$-0.914028\pi$
$773$	−19.3766	+	19.3766i	−0.696929	+	0.696929i	0.266818	+	0.963747i	$0.414028\pi$
$774$			2.02422i			0.0727590i
$775$	−17.8099	−	26.7405i	−0.639750	−	0.960548i
$776$		−	0.0235287i		−	0.000844632i
$777$	8.55695	+	5.55471i	0.306979	+	0.199274i
$778$	−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
$782$	1.21589			0.0434800
$783$			5.18959i			0.185461i
$784$		−	4.18713i		−	0.149540i
$785$	5.68247	−	4.65640i	0.202816	−	0.166194i
$786$	−10.1035			−0.360379
$787$	−9.19564	−	9.19564i	−0.327789	−	0.327789i	0.523956	−	0.851745i	$-0.324456\pi$
$787$	−9.19564	−	9.19564i	−0.327789	−	0.327789i	−0.851745	+	0.523956i	$0.824456\pi$
$788$	5.46379	+	5.46379i	0.194639	+	0.194639i
$789$			14.3786i			0.511892i
$790$	4.43441	+	5.41155i	0.157769	+	0.192534i
$791$	−12.1787	−	12.1787i	−0.433025	−	0.433025i
$792$			4.79879i			0.170518i
$793$	−28.2879	+	28.2879i	−1.00453	+	1.00453i
$794$	26.8752	+	26.8752i	0.953766	+	0.953766i
$795$	1.58900	−	16.0111i	0.0563560	−	0.567856i
$796$	11.6938	−	11.6938i	0.414474	−	0.414474i
$797$			15.2753i			0.541079i	0.962709	+	0.270539i	$0.0872020\pi$
$797$			15.2753i			0.541079i	−0.962709	+	0.270539i	$0.912798\pi$
$798$	7.48267	+	7.48267i	0.264884	+	0.264884i
$799$	8.87596	+	8.87596i	0.314009	+	0.314009i
$800$	0.982756	−	4.90247i	0.0347457	−	0.173328i
$801$	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
$808$	3.95084			0.138990
$809$	9.44473	−	9.44473i	0.332059	−	0.332059i	−0.521309	−	0.853368i	$-0.674556\pi$
$809$	9.44473	−	9.44473i	0.332059	−	0.332059i	0.853368	+	0.521309i	$0.174556\pi$
$810$	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	$0.140524\pi$
$812$	−8.70377			−0.305443
$813$	−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
$820$	−17.3391	−	1.72079i	−0.605507	−	0.0600927i
$821$	30.7870			1.07447			0.537237	−	0.843431i	$-0.319468\pi$
$821$	30.7870			1.07447			0.537237	+	0.843431i	$0.319468\pi$
$822$	9.25324			0.322744
$823$	−14.1184	+	14.1184i	−0.492135	+	0.492135i	−0.908978	−	0.416843i	$-0.863136\pi$
$823$	−14.1184	+	14.1184i	−0.492135	+	0.492135i	0.416843	+	0.908978i	$0.363136\pi$
$824$			10.4171i			0.362896i
$825$	−19.9701	+	13.3006i	−0.695269	+	0.463067i
$826$	−9.19609			−0.319973
$827$	−7.05530			−0.245337			−0.122668	−	0.992448i	$-0.539145\pi$
$827$	−7.05530			−0.245337			−0.122668	+	0.992448i	$0.539145\pi$
$828$	0.933219			0.0324316
$829$	32.0957	−	32.0957i	1.11473	−	1.11473i	0.122227	−	0.992502i	$-0.460996\pi$
$829$	32.0957	−	32.0957i	1.11473	−	1.11473i	0.992502	−	0.122227i	$-0.0390036\pi$
$830$	15.4758	−	12.6814i	0.537174	−	0.440178i
$831$	−1.96101	+	1.96101i	−0.0680268	+	0.0680268i
$832$			4.44661i			0.154158i
$833$			5.45539i			0.189018i
$834$	−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
$837$	6.42572			0.222105
$838$	−10.0390			−0.346793
$839$	−9.87040			−0.340764			−0.170382	−	0.985378i	$-0.554500\pi$
$839$	−9.87040			−0.340764			−0.170382	+	0.985378i	$0.554500\pi$
$840$	−0.370368	+	3.73191i	−0.0127789	+	0.128763i
$841$			2.06818i			0.0713166i
$842$	6.87930	−	6.87930i	0.237076	−	0.237076i
$843$	18.3599			0.632350
$844$	−25.9385			−0.892841
$845$	1.49554	−	15.0694i	0.0514480	−	0.518402i
$846$	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
$853$	−47.6548			−1.63167			−0.815834	−	0.578286i	$-0.803722\pi$
$853$	−47.6548			−1.63167			−0.815834	+	0.578286i	$0.803722\pi$
$854$	−15.0890			−0.516336
$855$	8.94223	+	10.9127i	0.305818	+	0.373207i
$856$	−3.87605	+	3.87605i	−0.132481	+	0.132481i
$857$	26.8502			0.917185			0.458593	−	0.888647i	$-0.348354\pi$
$857$	26.8502			0.917185			0.458593	+	0.888647i	$0.348354\pi$
$858$	15.0885	−	15.0885i	0.515113	−	0.515113i
$859$	20.2206	+	20.2206i	0.689918	+	0.689918i	0.962214	−	0.272295i	$-0.0877828\pi$
$859$	20.2206	+	20.2206i	0.689918	+	0.689918i	−0.272295	+	0.962214i	$0.587783\pi$
$860$	−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	−0.437850	−	0.899048i	$-0.644260\pi$
$863$	13.5486	−	13.5486i	0.461198	−	0.461198i	0.899048	+	0.437850i	$0.144260\pi$
$864$	0.707107	+	0.707107i	0.0240563	+	0.0240563i
$865$	33.1730	−	27.1830i	1.12791	−	0.924250i
$866$	11.5273	+	11.5273i	0.391715	+	0.391715i
$867$	10.8205	+	10.8205i	0.367483	+	0.367483i
$868$			10.7770i			0.365794i
$869$	10.6170	−	10.6170i	0.360158	−	0.360158i
$870$	−11.5475	−	1.14602i	−0.391498	−	0.0388537i
$871$	−2.84529	−	2.84529i	−0.0964090	−	0.0964090i
$872$	−0.670005	+	0.670005i	−0.0226892	+	0.0226892i
$873$			0.0235287i			0.000796327i
$874$	4.16356	+	4.16356i	0.140835	+	0.140835i
$875$	−16.5568	+	8.80230i	−0.559723	+	0.297572i
$876$		−	1.50463i		−	0.0508366i
$877$	−29.0568	−	29.0568i	−0.981180	−	0.981180i	0.0186460	−	0.999826i	$-0.494064\pi$
$877$	−29.0568	−	29.0568i	−0.981180	−	0.981180i	−0.999826	+	0.0186460i	$0.994064\pi$
$878$	25.1084	+	25.1084i	0.847368	+	0.847368i
$879$	25.6576			0.865410
$880$	−10.6780	−	1.05972i	−0.359954	−	0.0357231i
$881$		−	37.9507i		−	1.27859i	−0.768961	−	0.639296i	$-0.779226\pi$
$881$		−	37.9507i		−	1.27859i	0.768961	−	0.639296i	$-0.220774\pi$
$882$			4.18713i			0.140988i
$883$	35.9876			1.21108			0.605540	−	0.795815i	$-0.292957\pi$
$883$	35.9876			1.21108			0.605540	+	0.795815i	$0.292957\pi$
$884$		−	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	$-0.781794\pi$
$887$	−4.20003	+	4.20003i	−0.141023	+	0.141023i	0.633071	+	0.774094i	$0.281794\pi$
$888$	1.26577	+	5.94961i	0.0424766	+	0.199656i
$889$		−	32.7327i		−	1.09782i
$890$	−7.61453	+	6.23959i	−0.255239	+	0.209152i
$891$		−	4.79879i		−	0.160766i
$892$	10.7674	−	10.7674i	0.360520	−	0.360520i
$893$			60.7880i			2.03419i
$894$	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
$902$			37.3940i			1.24508i
$903$	3.39494			0.112976
$904$		−	10.2693i		−	0.341552i
$905$	0.336674	−	3.39240i	0.0111914	−	0.112767i
$906$	8.14314	+	8.14314i	0.270538	+	0.270538i
$907$	−4.45102			−0.147794			−0.0738969	−	0.997266i	$-0.523544\pi$
$907$	−4.45102			−0.147794			−0.0738969	+	0.997266i	$0.523544\pi$
$908$	9.50039			0.315282
$909$	−3.95084			−0.131041
$910$	12.8985	−	10.5695i	0.427581	−	0.350374i
$911$	−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	$0.308039\pi$
$912$			6.30953i			0.208929i
$913$	−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
$917$			16.9451i			0.559578i
$918$	−0.921286	−	0.921286i	−0.0304070	−	0.0304070i
$919$	32.7456	−	32.7456i	1.08018	−	1.08018i	0.0836854	−	0.996492i	$-0.473331\pi$
$919$	32.7456	−	32.7456i	1.08018	−	1.08018i	0.996492	−	0.0836854i	$-0.0266691\pi$
$920$	−0.206083	+	2.07654i	−0.00679436	+	0.0684615i
$921$	3.46005			0.114012
$922$	2.45180	+	2.45180i	0.0807456	+	0.0807456i
$923$			39.7932i			1.30981i
$924$	8.04835			0.264771
$925$	−21.2509	+	21.7578i	−0.698725	+	0.715391i
$926$	36.5028			1.19956
$927$		−	10.4171i		−	0.342142i
$928$	−3.66959	−	3.66959i	−0.120460	−	0.120460i
$929$	2.92392			0.0959307			0.0479653	−	0.998849i	$-0.484726\pi$
$929$	2.92392			0.0959307			0.0479653	+	0.998849i	$0.484726\pi$
$930$	−1.41899	+	14.2981i	−0.0465307	+	0.468853i
$931$	−18.6809	+	18.6809i	−0.612243	+	0.612243i
$932$	4.19880	+	4.19880i	0.137536	+	0.137536i
$933$			31.6855i			1.03734i
$934$		−	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	0.129385	−	0.991594i	$-0.458700\pi$
$937$	−26.3926	−	26.3926i	−0.862209	−	0.862209i	−0.991594	+	0.129385i	$0.958700\pi$
$938$		−	1.51771i		−	0.0495549i
$939$	0.897802	−	0.897802i	0.0292987	−	0.0292987i
$940$	−16.6631	+	13.6543i	−0.543491	+	0.445355i
$941$	−14.1264			−0.460509			−0.230254	−	0.973130i	$-0.573956\pi$
$941$	−14.1264			−0.460509			−0.230254	+	0.973130i	$0.573956\pi$
$942$	−3.28550			−0.107047
$943$	7.27199			0.236809
$944$	−3.87716	−	3.87716i	−0.126191	−	0.126191i
$945$	0.370368	−	3.73191i	0.0120481	−	0.121399i
$946$			9.71380i			0.315823i
$947$	54.3478			1.76607			0.883034	−	0.469309i	$-0.155497\pi$
$947$	54.3478			1.76607			0.883034	+	0.469309i	$0.155497\pi$
$948$		−	3.12886i		−	0.101621i
$949$	−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	$-0.369588\pi$
$953$	−16.0189	−	16.0189i	−0.518904	−	0.518904i	−0.917240	+	0.398336i	$0.869588\pi$
$954$	−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
$957$			24.9038i			0.805024i
$958$	21.3099	−	21.3099i	0.688490	−	0.688490i
$959$		−	15.5192i		−	0.501140i
$960$	−1.72956	+	1.41726i	−0.0558213	+	0.0457418i
$961$			10.2899i			0.331932i
$962$	14.7270	−	22.6868i	0.474819	−	0.731452i
$963$	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
$967$	14.2557			0.458432			0.229216	−	0.973376i	$-0.426384\pi$
$967$	14.2557			0.458432			0.229216	+	0.973376i	$0.426384\pi$
$968$			12.0284i			0.386608i
$969$		−	8.22065i		−	0.264085i
$970$	−0.0523546	−	0.00519586i	−0.00168101	−	0.000166829i
$971$	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
$975$	18.5045	−	12.3245i	0.592618	−	0.394699i
$976$	−6.36168	−	6.36168i	−0.203632	−	0.203632i
$977$		−	8.86551i		−	0.283633i	−0.989893	−	0.141816i	$-0.954706\pi$
$977$		−	8.86551i		−	0.283633i	0.989893	−	0.141816i	$-0.0452942\pi$
$978$	0.219657	−	0.219657i	0.00702386	−	0.00702386i
$979$	14.9391	+	14.9391i	0.477456	+	0.477456i
$980$	−9.31694	−	0.924646i	−0.297619	−	0.0295367i
$981$	0.670005	−	0.670005i	0.0213916	−	0.0213916i
$982$			1.46818i			0.0468514i
$983$	14.4066	+	14.4066i	0.459499	+	0.459499i	0.898491	−	0.438992i	$-0.144664\pi$
$983$	14.4066	+	14.4066i	0.459499	+	0.459499i	−0.438992	+	0.898491i	$0.644664\pi$
$984$	5.51004	+	5.51004i	0.175654	+	0.175654i
$985$	13.3642	−	10.9511i	0.425820	−	0.348931i
$986$	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
$993$	20.7598			0.658791
$994$	−10.6130	+	10.6130i	−0.336625	+	0.336625i
$995$	−23.4379	−	28.6026i	−0.743031	−	0.906762i
$996$	−8.94785			−0.283523
$997$	−49.8348			−1.57828			−0.789142	−	0.614210i	$-0.789475\pi$
$997$	−49.8348			−1.57828			−0.789142	+	0.614210i	$0.789475\pi$
$998$	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.l.b.697.8	yes	40
5.3	odd	4		1110.2.o.b.253.13	yes	40
37.6	odd	4		1110.2.o.b.487.13	yes	40
185.43	even	4	inner	1110.2.l.b.43.8	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.l.b.43.8	✓	40	185.43	even	4	inner
1110.2.l.b.697.8	yes	40	1.1	even	1	trivial
1110.2.o.b.253.13	yes	40	5.3	odd	4
1110.2.o.b.487.13	yes	40	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)

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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