LMFDB - Embedded newform 260.2.j.a.31.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [260,2,Mod(31,260)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(260, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("260.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 260 = 2^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	260.j (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:	$2.07611045255$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			31.2
Character	$\chi$	$=$	260.31
Dual form			260.2.j.a.151.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36090 - 0.384637i) q^{2} -1.17966i q^{3} +(1.70411 + 1.04691i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(-0.453740 + 1.60540i) q^{6} +(0.171101 - 0.171101i) q^{7} +(-1.91645 - 2.08020i) q^{8} +1.60841 q^{9} +O(q^{10})$	\(q+(-1.36090 - 0.384637i) q^{2} -1.17966i q^{3} +(1.70411 + 1.04691i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(-0.453740 + 1.60540i) q^{6} +(0.171101 - 0.171101i) q^{7} +(-1.91645 - 2.08020i) q^{8} +1.60841 q^{9} +(1.23428 - 0.690324i) q^{10} +(3.82508 - 3.82508i) q^{11} +(1.23499 - 2.01027i) q^{12} +(-0.709862 + 3.53498i) q^{13} +(-0.298664 + 0.167040i) q^{14} +(0.834144 + 0.834144i) q^{15} +(1.80797 + 3.56809i) q^{16} -7.10821i q^{17} +(-2.18888 - 0.618653i) q^{18} +(-0.875738 - 0.875738i) q^{19} +(-1.94526 + 0.464712i) q^{20} +(-0.201841 - 0.201841i) q^{21} +(-6.67683 + 3.73429i) q^{22} +0.244297 q^{23} +(-2.45393 + 2.26075i) q^{24} -1.00000i q^{25} +(2.32574 - 4.53772i) q^{26} -5.43634i q^{27} +(0.470702 - 0.112448i) q^{28} +8.54595 q^{29} +(-0.814346 - 1.45603i) q^{30} +(-6.94531 - 6.94531i) q^{31} +(-1.08806 - 5.55123i) q^{32} +(-4.51229 - 4.51229i) q^{33} +(-2.73408 + 9.67357i) q^{34} +0.241974i q^{35} +(2.74090 + 1.68385i) q^{36} +(2.96916 + 2.96916i) q^{37} +(0.854953 + 1.52864i) q^{38} +(4.17007 + 0.837394i) q^{39} +(2.82606 + 0.115792i) q^{40} +(-3.18792 + 3.18792i) q^{41} +(0.197050 + 0.352321i) q^{42} +8.63409 q^{43} +(10.5229 - 2.51385i) q^{44} +(-1.13732 + 1.13732i) q^{45} +(-0.332464 - 0.0939657i) q^{46} +(-2.57972 + 2.57972i) q^{47} +(4.20912 - 2.13279i) q^{48} +6.94145i q^{49} +(-0.384637 + 1.36090i) q^{50} -8.38526 q^{51} +(-4.91048 + 5.28083i) q^{52} -1.29703 q^{53} +(-2.09102 + 7.39833i) q^{54} +5.40948i q^{55} +(-0.683831 - 0.0280186i) q^{56} +(-1.03307 + 1.03307i) q^{57} +(-11.6302 - 3.28709i) q^{58} +(-8.15392 + 8.15392i) q^{59} +(0.548201 + 2.29474i) q^{60} +3.26260 q^{61} +(6.78047 + 12.1233i) q^{62} +(0.275200 - 0.275200i) q^{63} +(-0.654470 + 7.97318i) q^{64} +(-1.99766 - 3.00156i) q^{65} +(4.40519 + 7.87638i) q^{66} +(0.868882 + 0.868882i) q^{67} +(7.44163 - 12.1132i) q^{68} -0.288187i q^{69} +(0.0930720 - 0.329302i) q^{70} +(-2.44932 - 2.44932i) q^{71} +(-3.08242 - 3.34581i) q^{72} +(5.81613 + 5.81613i) q^{73} +(-2.89869 - 5.18279i) q^{74} -1.17966 q^{75} +(-0.575537 - 2.40917i) q^{76} -1.30895i q^{77} +(-5.35296 - 2.74358i) q^{78} +15.8091i q^{79} +(-3.80145 - 1.24459i) q^{80} -1.58781 q^{81} +(5.56464 - 3.11226i) q^{82} +(5.92703 + 5.92703i) q^{83} +(-0.132650 - 0.555267i) q^{84} +(5.02626 + 5.02626i) q^{85} +(-11.7502 - 3.32099i) q^{86} -10.0813i q^{87} +(-15.2875 - 0.626375i) q^{88} +(-5.79703 - 5.79703i) q^{89} +(1.98523 - 1.11032i) q^{90} +(0.483381 + 0.726298i) q^{91} +(0.416309 + 0.255756i) q^{92} +(-8.19309 + 8.19309i) q^{93} +(4.50300 - 2.51849i) q^{94} +1.23848 q^{95} +(-6.54855 + 1.28353i) q^{96} +(2.93876 - 2.93876i) q^{97} +(2.66994 - 9.44663i) q^{98} +(6.15229 - 6.15229i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 12 q^{6} + 12 q^{8} - 56 q^{9}+O(q^{10}) $ 56 * q - 12 * q^6 + 12 * q^8 - 56 * q^9	$ 56 q - 12 q^{6} + 12 q^{8} - 56 q^{9} + 16 q^{14} - 12 q^{18} - 8 q^{20} - 16 q^{21} - 40 q^{24} - 16 q^{26} - 44 q^{28} + 40 q^{32} - 4 q^{34} + 16 q^{37} + 8 q^{41} + 8 q^{42} + 28 q^{44} - 12 q^{46} + 104 q^{48} + 56 q^{52} - 16 q^{53} + 20 q^{54} - 48 q^{57} - 4 q^{58} + 16 q^{61} - 8 q^{65} + 64 q^{66} + 24 q^{68} - 8 q^{70} - 32 q^{72} + 48 q^{73} - 136 q^{74} - 88 q^{76} + 52 q^{78} - 32 q^{80} + 56 q^{81} - 20 q^{84} - 64 q^{86} - 8 q^{89} - 88 q^{92} - 48 q^{93} - 16 q^{94} - 4 q^{96} - 32 q^{97} + 16 q^{98}+O(q^{100}) $ 56 * q - 12 * q^6 + 12 * q^8 - 56 * q^9 + 16 * q^14 - 12 * q^18 - 8 * q^20 - 16 * q^21 - 40 * q^24 - 16 * q^26 - 44 * q^28 + 40 * q^32 - 4 * q^34 + 16 * q^37 + 8 * q^41 + 8 * q^42 + 28 * q^44 - 12 * q^46 + 104 * q^48 + 56 * q^52 - 16 * q^53 + 20 * q^54 - 48 * q^57 - 4 * q^58 + 16 * q^61 - 8 * q^65 + 64 * q^66 + 24 * q^68 - 8 * q^70 - 32 * q^72 + 48 * q^73 - 136 * q^74 - 88 * q^76 + 52 * q^78 - 32 * q^80 + 56 * q^81 - 20 * q^84 - 64 * q^86 - 8 * q^89 - 88 * q^92 - 48 * q^93 - 16 * q^94 - 4 * q^96 - 32 * q^97 + 16 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/260\mathbb{Z}\right)^\times$.

$n$	$41$	$131$	$157$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.36090	−	0.384637i	−0.962303	−	0.271979i
$2$	−1.36090	−	0.384637i	−0.962303	−	0.271979i
$3$		−	1.17966i		−	0.681076i	−0.940231	−	0.340538i	$-0.889391\pi$
$3$		−	1.17966i		−	0.681076i	0.940231	−	0.340538i	$-0.110609\pi$
$4$	1.70411	+	1.04691i	0.852054	+	0.523453i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$6$	−0.453740	+	1.60540i	−0.185239	+	0.655402i
$7$	0.171101	−	0.171101i	0.0646702	−	0.0646702i	−0.674032	−	0.738702i	$-0.735439\pi$
$7$	0.171101	−	0.171101i	0.0646702	−	0.0646702i	0.738702	+	0.674032i	$0.235439\pi$
$8$	−1.91645	−	2.08020i	−0.677566	−	0.735462i
$9$	1.60841			0.536135
$10$	1.23428	−	0.690324i	0.390314	−	0.218299i
$11$	3.82508	−	3.82508i	1.15331	−	1.15331i	0.167420	−	0.985886i	$-0.446456\pi$
$11$	3.82508	−	3.82508i	1.15331	−	1.15331i	0.985886	−	0.167420i	$-0.0535437\pi$
$12$	1.23499	−	2.01027i	0.356511	−	0.580314i
$13$	−0.709862	+	3.53498i	−0.196880	+	0.980428i
$13$	−0.709862	+	3.53498i	−0.196880	+	0.980428i
$14$	−0.298664	+	0.167040i	−0.0798213	+	0.0446433i
$15$	0.834144	+	0.834144i	0.215375	+	0.215375i
$16$	1.80797	+	3.56809i	0.451993	+	0.892021i
$17$		−	7.10821i		−	1.72399i	−0.506914	−	0.861997i	$-0.669214\pi$
$17$		−	7.10821i		−	1.72399i	0.506914	−	0.861997i	$-0.330786\pi$
$18$	−2.18888	−	0.618653i	−0.515925	−	0.145818i
$19$	−0.875738	−	0.875738i	−0.200908	−	0.200908i	0.599481	−	0.800389i	$-0.295374\pi$
$19$	−0.875738	−	0.875738i	−0.200908	−	0.200908i	−0.800389	+	0.599481i	$0.795374\pi$
$20$	−1.94526	+	0.464712i	−0.434974	+	0.103913i
$21$	−0.201841	−	0.201841i	−0.0440453	−	0.0440453i
$22$	−6.67683	+	3.73429i	−1.42351	+	0.796154i
$23$	0.244297			0.0509394			0.0254697	−	0.999676i	$-0.491892\pi$
$23$	0.244297			0.0509394			0.0254697	+	0.999676i	$0.491892\pi$
$24$	−2.45393	+	2.26075i	−0.500906	+	0.461474i
$25$		−	1.00000i		−	0.200000i
$26$	2.32574	−	4.53772i	0.456115	−	0.889921i
$27$		−	5.43634i		−	1.04623i
$28$	0.470702	−	0.112448i	0.0889543	−	0.0212507i
$29$	8.54595			1.58694			0.793471	−	0.608608i	$-0.208272\pi$
$29$	8.54595			1.58694			0.793471	+	0.608608i	$0.208272\pi$
$30$	−0.814346	−	1.45603i	−0.148679	−	0.265834i
$31$	−6.94531	−	6.94531i	−1.24741	−	1.24741i	−0.956858	−	0.290557i	$-0.906159\pi$
$31$	−6.94531	−	6.94531i	−1.24741	−	1.24741i	−0.290557	−	0.956858i	$-0.593841\pi$
$32$	−1.08806	−	5.55123i	−0.192343	−	0.981328i
$33$	−4.51229	−	4.51229i	−0.785489	−	0.785489i
$34$	−2.73408	+	9.67357i	−0.468891	+	1.65900i
$35$			0.241974i			0.0409010i
$36$	2.74090	+	1.68385i	0.456817	+	0.280642i
$37$	2.96916	+	2.96916i	0.488128	+	0.488128i	0.907715	−	0.419587i	$-0.137825\pi$
$37$	2.96916	+	2.96916i	0.488128	+	0.488128i	−0.419587	+	0.907715i	$0.637825\pi$
$38$	0.854953	+	1.52864i	0.138692	+	0.247977i
$39$	4.17007	+	0.837394i	0.667746	+	0.134090i
$40$	2.82606	+	0.115792i	0.446839	+	0.0183083i
$41$	−3.18792	+	3.18792i	−0.497870	+	0.497870i	−0.910774	−	0.412905i	$-0.864514\pi$
$41$	−3.18792	+	3.18792i	−0.497870	+	0.497870i	0.412905	+	0.910774i	$0.364514\pi$
$42$	0.197050	+	0.352321i	0.0304055	+	0.0543643i
$43$	8.63409			1.31669			0.658343	−	0.752718i	$-0.271258\pi$
$43$	8.63409			1.31669			0.658343	+	0.752718i	$0.271258\pi$
$44$	10.5229	−	2.51385i	1.58638	−	0.378977i
$45$	−1.13732	+	1.13732i	−0.169541	+	0.169541i
$46$	−0.332464	−	0.0939657i	−0.0490192	−	0.0138545i
$47$	−2.57972	+	2.57972i	−0.376290	+	0.376290i	−0.869762	−	0.493472i	$-0.835728\pi$
$47$	−2.57972	+	2.57972i	−0.376290	+	0.376290i	0.493472	+	0.869762i	$0.335728\pi$
$48$	4.20912	−	2.13279i	0.607534	−	0.307842i
$49$			6.94145i			0.991636i
$50$	−0.384637	+	1.36090i	−0.0543959	+	0.192461i
$51$	−8.38526			−1.17417
$52$	−4.91048	+	5.28083i	−0.680961	+	0.732320i
$53$	−1.29703			−0.178160			−0.0890802	−	0.996024i	$-0.528393\pi$
$53$	−1.29703			−0.178160			−0.0890802	+	0.996024i	$0.528393\pi$
$54$	−2.09102	+	7.39833i	−0.284552	+	1.00679i
$55$			5.40948i			0.729415i
$56$	−0.683831	−	0.0280186i	−0.0913808	−	0.00374415i
$57$	−1.03307	+	1.03307i	−0.136834	+	0.136834i
$58$	−11.6302	−	3.28709i	−1.52712	−	0.431616i
$59$	−8.15392	+	8.15392i	−1.06155	+	1.06155i	−0.0635727	+	0.997977i	$0.520249\pi$
$59$	−8.15392	+	8.15392i	−1.06155	+	1.06155i	−0.997977	+	0.0635727i	$0.979751\pi$
$60$	0.548201	+	2.29474i	0.0707725	+	0.296250i
$61$	3.26260			0.417733			0.208866	−	0.977944i	$-0.433023\pi$
$61$	3.26260			0.417733			0.208866	+	0.977944i	$0.433023\pi$
$62$	6.78047	+	12.1233i	0.861120	+	1.53966i
$63$	0.275200	−	0.275200i	0.0346720	−	0.0346720i
$64$	−0.654470	+	7.97318i	−0.0818087	+	0.996648i
$65$	−1.99766	−	3.00156i	−0.247779	−	0.372297i
$66$	4.40519	+	7.87638i	0.542242	+	0.969515i
$67$	0.868882	+	0.868882i	0.106151	+	0.106151i	0.758187	−	0.652037i	$-0.226085\pi$
$67$	0.868882	+	0.868882i	0.106151	+	0.106151i	−0.652037	+	0.758187i	$0.726085\pi$
$68$	7.44163	−	12.1132i	0.902430	−	1.46894i
$69$		−	0.288187i		−	0.0346936i
$70$	0.0930720	−	0.329302i	0.0111242	−	0.0393592i
$71$	−2.44932	−	2.44932i	−0.290680	−	0.290680i	0.546669	−	0.837349i	$-0.315896\pi$
$71$	−2.44932	−	2.44932i	−0.290680	−	0.290680i	−0.837349	+	0.546669i	$0.815896\pi$
$72$	−3.08242	−	3.34581i	−0.363267	−	0.394307i
$73$	5.81613	+	5.81613i	0.680726	+	0.680726i	0.960164	−	0.279438i	$-0.0901480\pi$
$73$	5.81613	+	5.81613i	0.680726	+	0.680726i	−0.279438	+	0.960164i	$0.590148\pi$
$74$	−2.89869	−	5.18279i	−0.336966	−	0.602487i
$75$	−1.17966			−0.136215
$76$	−0.575537	−	2.40917i	−0.0660186	−	0.276351i
$77$		−	1.30895i		−	0.149169i
$78$	−5.35296	−	2.74358i	−0.606104	−	0.310649i
$79$			15.8091i			1.77866i	0.457265	+	0.889330i	$0.348829\pi$
$79$			15.8091i			1.77866i	−0.457265	+	0.889330i	$0.651171\pi$
$80$	−3.80145	−	1.24459i	−0.425015	−	0.139149i
$81$	−1.58781			−0.176423
$82$	5.56464	−	3.11226i	0.614512	−	0.343691i
$83$	5.92703	+	5.92703i	0.650576	+	0.650576i	0.953132	−	0.302556i	$-0.0978399\pi$
$83$	5.92703	+	5.92703i	0.650576	+	0.650576i	−0.302556	+	0.953132i	$0.597840\pi$
$84$	−0.132650	−	0.555267i	−0.0144733	−	0.0605846i
$85$	5.02626	+	5.02626i	0.545175	+	0.545175i
$86$	−11.7502	−	3.32099i	−1.26705	−	0.358112i
$87$		−	10.0813i		−	1.08083i
$88$	−15.2875	−	0.626375i	−1.62965	−	0.0667718i
$89$	−5.79703	−	5.79703i	−0.614484	−	0.614484i	0.329627	−	0.944111i	$-0.393077\pi$
$89$	−5.79703	−	5.79703i	−0.614484	−	0.614484i	−0.944111	+	0.329627i	$0.893077\pi$
$90$	1.98523	−	1.11032i	0.209261	−	0.117038i
$91$	0.483381	+	0.726298i	0.0506721	+	0.0761367i
$92$	0.416309	+	0.255756i	0.0434032	+	0.0266644i
$93$	−8.19309	+	8.19309i	−0.849584	+	0.849584i
$94$	4.50300	−	2.51849i	0.464449	−	0.259762i
$95$	1.23848			0.127065
$96$	−6.54855	+	1.28353i	−0.668359	+	0.131000i
$97$	2.93876	−	2.93876i	0.298386	−	0.298386i	−0.541995	−	0.840381i	$-0.682331\pi$
$97$	2.93876	−	2.93876i	0.298386	−	0.298386i	0.840381	+	0.541995i	$0.182331\pi$
$98$	2.66994	−	9.44663i	0.269704	−	0.954254i
$99$	6.15229	−	6.15229i	0.618328	−	0.618328i
$100$	1.04691	−	1.70411i	0.104691	−	0.170411i
$101$		−	5.46425i		−	0.543714i	−0.962338	−	0.271857i	$-0.912362\pi$
$101$		−	5.46425i		−	0.543714i	0.962338	−	0.271857i	$-0.0876377\pi$
$102$	11.4115	+	3.22528i	1.12991	+	0.319350i
$103$	−6.98313			−0.688068			−0.344034	−	0.938957i	$-0.611794\pi$
$103$	−6.98313			−0.688068			−0.344034	+	0.938957i	$0.611794\pi$
$104$	8.71388	−	5.29795i	0.854467	−	0.519506i
$105$	0.285446			0.0278567
$106$	1.76513	+	0.498885i	0.171444	+	0.0484560i
$107$			15.9729i			1.54415i	0.635529	+	0.772077i	$0.280782\pi$
$107$			15.9729i			1.54415i	−0.635529	+	0.772077i	$0.719218\pi$
$108$	5.69135	−	9.26412i	0.547650	−	0.891441i
$109$	6.81114	−	6.81114i	0.652389	−	0.652389i	−0.301179	−	0.953568i	$-0.597380\pi$
$109$	6.81114	−	6.81114i	0.652389	−	0.652389i	0.953568	+	0.301179i	$0.0973802\pi$
$110$	2.08069	−	7.36178i	0.198386	−	0.701918i
$111$	3.50260	−	3.50260i	0.332452	−	0.332452i
$112$	0.919850	+	0.301157i	0.0869177	+	0.0284567i
$113$	−14.9889			−1.41004			−0.705018	−	0.709190i	$-0.749061\pi$
$113$	−14.9889			−1.41004			−0.705018	+	0.709190i	$0.749061\pi$
$114$	1.80327	−	1.00855i	0.168891	−	0.0944595i
$115$	−0.172744	+	0.172744i	−0.0161085	+	0.0161085i
$116$	14.5632	+	8.94681i	1.35216	+	0.830690i
$117$	−1.14175	+	5.68569i	−0.105554	+	0.525642i
$118$	14.2330	−	7.96039i	1.31025	−	0.732813i
$119$	−1.21622	−	1.21622i	−0.111491	−	0.111491i
$120$	0.136595	−	3.33378i	0.0124694	−	0.304331i
$121$		−	18.2625i		−	1.66023i
$122$	−4.44008	−	1.25492i	−0.401986	−	0.113615i
$123$	3.76066	+	3.76066i	0.339087	+	0.339087i
$124$	−4.56447	−	19.1067i	−0.409902	−	1.71583i
$125$	0.707107	+	0.707107i	0.0632456	+	0.0632456i
$126$	−0.480373	+	0.268668i	−0.0427950	+	0.0239349i
$127$	−7.82453			−0.694315			−0.347157	−	0.937807i	$-0.612853\pi$
$127$	−7.82453			−0.694315			−0.347157	+	0.937807i	$0.612853\pi$
$128$	3.95745	−	10.5990i	0.349793	−	0.936827i
$129$		−	10.1853i		−	0.896764i
$130$	1.56411	+	4.85320i	0.137182	+	0.425654i
$131$		−	0.310483i		−	0.0271271i	−0.999908	−	0.0135635i	$-0.995682\pi$
$131$		−	0.310483i		−	0.0271271i	0.999908	−	0.0135635i	$-0.00431754\pi$
$132$	−2.96549	−	12.4134i	−0.258112	−	1.08045i
$133$	−0.299680			−0.0259855
$134$	−0.848259	−	1.51667i	−0.0732784	−	0.131020i
$135$	3.84408	+	3.84408i	0.330845	+	0.330845i
$136$	−14.7865	+	13.6225i	−1.26793	+	1.16812i
$137$	−1.25894	−	1.25894i	−0.107558	−	0.107558i	0.651279	−	0.758838i	$-0.274233\pi$
$137$	−1.25894	−	1.25894i	−0.107558	−	0.107558i	−0.758838	+	0.651279i	$0.774233\pi$
$138$	−0.110847	+	0.392194i	−0.00943596	+	0.0333858i
$139$		−	14.4289i		−	1.22385i	−0.790917	−	0.611923i	$-0.790396\pi$
$139$		−	14.4289i		−	1.22385i	0.790917	−	0.611923i	$-0.209604\pi$
$140$	−0.253324	+	0.412349i	−0.0214098	+	0.0348499i
$141$	3.04318	+	3.04318i	0.256282	+	0.256282i
$142$	2.39118	+	4.27538i	0.200663	+	0.358782i
$143$	10.8063	+	16.2369i	0.903670	+	1.35780i
$144$	2.90796	+	5.73893i	0.242330	+	0.478244i
$145$	−6.04290	+	6.04290i	−0.501835	+	0.501835i
$146$	−5.67808	−	10.1523i	−0.469921	−	0.840208i
$147$	8.18854			0.675379
$148$	1.95134	+	8.16822i	0.160399	+	0.671423i
$149$	−12.5345	+	12.5345i	−1.02687	+	1.02687i	−0.0272396	+	0.999629i	$0.508672\pi$
$149$	−12.5345	+	12.5345i	−1.02687	+	1.02687i	−0.999629	+	0.0272396i	$0.991328\pi$
$150$	1.60540	+	0.453740i	0.131080	+	0.0370477i
$151$	−0.535648	+	0.535648i	−0.0435904	+	0.0435904i	−0.728566	−	0.684976i	$-0.759813\pi$
$151$	−0.535648	+	0.535648i	−0.0435904	+	0.0435904i	0.684976	+	0.728566i	$0.259813\pi$
$152$	−0.143406	+	3.50002i	−0.0116318	+	0.283889i
$153$		−	11.4329i		−	0.924294i
$154$	−0.503472	+	1.78136i	−0.0405709	+	0.143546i
$155$	9.82215			0.788934
$156$	6.22958	+	5.79269i	0.498766	+	0.463786i
$157$	−5.91108			−0.471755			−0.235878	−	0.971783i	$-0.575796\pi$
$157$	−5.91108			−0.471755			−0.235878	+	0.971783i	$0.575796\pi$
$158$	6.08076	−	21.5146i	0.483759	−	1.71161i
$159$			1.53005i			0.121341i
$160$	4.69468	+	3.15594i	0.371147	+	0.249499i
$161$	0.0417995	−	0.0417995i	0.00329426	−	0.00329426i
$162$	2.16085	+	0.610730i	0.169773	+	0.0479835i
$163$	−4.54967	+	4.54967i	−0.356358	+	0.356358i	−0.862468	−	0.506111i	$-0.831083\pi$
$163$	−4.54967	+	4.54967i	−0.356358	+	0.356358i	0.506111	+	0.862468i	$0.331083\pi$
$164$	−8.77002	+	2.09511i	−0.684823	+	0.163600i
$165$	6.38134			0.496787
$166$	−5.78635	−	10.3459i	−0.449108	−	0.802994i
$167$	4.08388	−	4.08388i	0.316020	−	0.316020i	−0.531216	−	0.847236i	$-0.678265\pi$
$167$	4.08388	−	4.08388i	0.316020	−	0.316020i	0.847236	+	0.531216i	$0.178265\pi$
$168$	−0.0330524	+	0.806687i	−0.00255005	+	0.0622372i
$169$	−11.9922	−	5.01870i	−0.922476	−	0.386054i
$170$	−4.90696	−	8.77354i	−0.376347	−	0.672900i
$171$	−1.40854	−	1.40854i	−0.107714	−	0.107714i
$172$	14.7134	+	9.03909i	1.12189	+	0.689224i
$173$		−	0.162034i		−	0.0123192i	−0.999981	−	0.00615959i	$-0.998039\pi$
$173$		−	0.162034i		−	0.0123192i	0.999981	−	0.00615959i	$-0.00196067\pi$
$174$	−3.87764	+	13.7197i	−0.293963	+	1.04008i
$175$	−0.171101	−	0.171101i	−0.0129340	−	0.0129340i
$176$	20.5639	+	6.73258i	1.55006	+	0.507487i
$177$	9.61884	+	9.61884i	0.722996	+	0.722996i
$178$	5.65944	+	10.1189i	0.424193	+	0.758446i
$179$	−6.85543			−0.512399			−0.256199	−	0.966624i	$-0.582470\pi$
$179$	−6.85543			−0.512399			−0.256199	+	0.966624i	$0.582470\pi$
$180$	−3.12877	+	0.747446i	−0.233205	+	0.0557113i
$181$			2.85303i			0.212064i	0.994363	+	0.106032i	$0.0338146\pi$
$181$			2.85303i			0.212064i	−0.994363	+	0.106032i	$0.966185\pi$
$182$	−0.378474	−	1.17435i	−0.0280543	−	0.0870484i
$183$		−	3.84875i		−	0.284508i
$184$	−0.468182	−	0.508187i	−0.0345148	−	0.0374640i
$185$	−4.19903			−0.308719
$186$	14.3014	−	7.99863i	1.04863	−	0.586488i
$187$	−27.1895	−	27.1895i	−1.98829	−	1.98829i
$188$	−7.09684	+	1.69539i	−0.517590	+	0.123649i
$189$	−0.930165	−	0.930165i	−0.0676596	−	0.0676596i
$190$	−1.68545	−	0.476366i	−0.122275	−	0.0345592i
$191$		−	11.3008i		−	0.817700i	−0.912602	−	0.408850i	$-0.865930\pi$
$191$		−	11.3008i		−	0.817700i	0.912602	−	0.408850i	$-0.134070\pi$
$192$	9.40563	+	0.772051i	0.678793	+	0.0557180i
$193$	5.66921	+	5.66921i	0.408079	+	0.408079i	0.881068	−	0.472989i	$-0.156825\pi$
$193$	5.66921	+	5.66921i	0.408079	+	0.408079i	−0.472989	+	0.881068i	$0.656825\pi$
$194$	−5.12972	+	2.86901i	−0.368292	+	0.205983i
$195$	−3.54081	+	2.35656i	−0.253563	+	0.168757i
$196$	−7.26705	+	11.8290i	−0.519075	+	0.844927i
$197$	−3.16165	+	3.16165i	−0.225258	+	0.225258i	−0.810708	−	0.585450i	$-0.800918\pi$
$197$	−3.16165	+	3.16165i	−0.225258	+	0.225258i	0.585450	+	0.810708i	$0.300918\pi$
$198$	−10.7391	+	6.00626i	−0.763192	+	0.426847i
$199$	−2.34803			−0.166447			−0.0832237	−	0.996531i	$-0.526522\pi$
$199$	−2.34803			−0.166447			−0.0832237	+	0.996531i	$0.526522\pi$
$200$	−2.08020	+	1.91645i	−0.147092	+	0.135513i
$201$	1.02498	−	1.02498i	0.0722967	−	0.0722967i
$202$	−2.10175	+	7.43632i	−0.147879	+	0.523217i
$203$	1.46222	−	1.46222i	0.102628	−	0.102628i
$204$	−14.2894	−	8.77858i	−1.00046	−	0.614623i
$205$		−	4.50840i		−	0.314880i
$206$	9.50335	+	2.68597i	0.662130	+	0.187140i
$207$	0.392929			0.0273104
$208$	−13.8965	+	3.85830i	−0.963551	+	0.267525i
$209$	−6.69954			−0.463417
$210$	−0.388464	−	0.109793i	−0.0268066	−	0.00757645i
$211$			16.4039i			1.12929i	0.825333	+	0.564646i	$0.190987\pi$
$211$			16.4039i			1.12929i	−0.825333	+	0.564646i	$0.809013\pi$
$212$	−2.21028	−	1.35787i	−0.151802	−	0.0932587i
$213$	−2.88936	+	2.88936i	−0.197975	+	0.197975i
$214$	6.14375	−	21.7375i	0.419978	−	1.48594i
$215$	−6.10522	+	6.10522i	−0.416373	+	0.416373i
$216$	−11.3087	+	10.4185i	−0.769459	+	0.708886i
$217$	−2.37670			−0.161341
$218$	−11.8891	+	6.64948i	−0.805232	+	0.450359i
$219$	6.86104	−	6.86104i	0.463626	−	0.463626i
$220$	−5.66322	+	9.21835i	−0.381815	+	0.621501i
$221$	25.1274	+	5.04585i	1.69025	+	0.339420i
$222$	−6.11392	+	3.41947i	−0.410340	+	0.229499i
$223$	14.1421	+	14.1421i	0.947027	+	0.947027i	0.998666	−	0.0516385i	$-0.0164444\pi$
$223$	14.1421	+	14.1421i	0.947027	+	0.947027i	−0.0516385	+	0.998666i	$0.516444\pi$
$224$	−1.13599	−	0.763654i	−0.0759015	−	0.0510238i
$225$		−	1.60841i		−	0.107227i
$226$	20.3984	+	5.76528i	1.35688	+	0.383501i
$227$	11.0746	+	11.0746i	0.735046	+	0.735046i	0.971615	−	0.236569i	$-0.0760228\pi$
$227$	11.0746	+	11.0746i	0.735046	+	0.735046i	−0.236569	+	0.971615i	$0.576023\pi$
$228$	−2.84200	+	0.678937i	−0.188216	+	0.0449637i
$229$	14.3900	+	14.3900i	0.950916	+	0.950916i	0.998851	−	0.0479341i	$-0.0152637\pi$
$229$	14.3900	+	14.3900i	0.950916	+	0.950916i	−0.0479341	+	0.998851i	$0.515264\pi$
$230$	0.301532	−	0.168644i	0.0198824	−	0.0111201i
$231$	−1.54412			−0.101595
$232$	−16.3778	−	17.7773i	−1.07526	−	1.16714i
$233$			0.905587i			0.0593270i	0.999560	+	0.0296635i	$0.00944357\pi$
$233$			0.905587i			0.0593270i	−0.999560	+	0.0296635i	$0.990556\pi$
$234$	3.74073	−	7.29851i	0.244539	−	0.477118i
$235$		−	3.64827i		−	0.237987i
$236$	−22.4316	+	5.35877i	−1.46017	+	0.348826i
$237$	18.6493			1.21140
$238$	1.18736	+	2.12296i	0.0769648	+	0.137611i
$239$	−10.2112	−	10.2112i	−0.660511	−	0.660511i	0.294990	−	0.955500i	$-0.404684\pi$
$239$	−10.2112	−	10.2112i	−0.660511	−	0.660511i	−0.955500	+	0.294990i	$0.904684\pi$
$240$	−1.46819	+	4.48441i	−0.0947711	+	0.289467i
$241$	6.31339	+	6.31339i	0.406681	+	0.406681i	0.880580	−	0.473898i	$-0.157154\pi$
$241$	6.31339	+	6.31339i	0.406681	+	0.406681i	−0.473898	+	0.880580i	$0.657154\pi$
$242$	−7.02444	+	24.8535i	−0.451548	+	1.59764i
$243$		−	14.4360i		−	0.926067i
$244$	5.55982	+	3.41564i	0.355931	+	0.218664i
$245$	−4.90835	−	4.90835i	−0.313583	−	0.313583i
$246$	−3.67140	−	6.56437i	−0.234080	−	0.418529i
$247$	3.71737	−	2.47407i	0.236531	−	0.157421i
$248$	−1.13733	+	27.7580i	−0.0722204	+	1.76263i
$249$	6.99187	−	6.99187i	0.443092	−	0.443092i
$250$	−0.690324	−	1.23428i	−0.0436599	−	0.0780629i
$251$	−3.59463			−0.226891			−0.113446	−	0.993544i	$-0.536189\pi$
$251$	−3.59463			−0.226891			−0.113446	+	0.993544i	$0.536189\pi$
$252$	0.757080	−	0.180862i	0.0476916	−	0.0113932i
$253$	0.934456	−	0.934456i	0.0587488	−	0.0587488i
$254$	10.6484	+	3.00960i	0.668141	+	0.188839i
$255$	5.92927	−	5.92927i	0.371305	−	0.371305i
$256$	−9.46247	+	12.9020i	−0.591404	+	0.806375i
$257$			12.2301i			0.762891i	0.924391	+	0.381445i	$0.124574\pi$
$257$			12.2301i			0.762891i	−0.924391	+	0.381445i	$0.875426\pi$
$258$	−3.91763	+	13.8612i	−0.243901	+	0.862958i
$259$	1.01606			0.0631346
$260$	−0.261882	−	7.20635i	−0.0162412	−	0.446919i
$261$	13.7454			0.850816
$262$	−0.119423	+	0.422538i	−0.00737800	+	0.0261045i
$263$			15.9843i			0.985636i	0.870132	+	0.492818i	$0.164033\pi$
$263$			15.9843i			0.985636i	−0.870132	+	0.492818i	$0.835967\pi$
$264$	−0.738909	+	18.0340i	−0.0454767	+	1.10992i
$265$	0.917137	−	0.917137i	0.0563393	−	0.0563393i
$266$	0.407835	+	0.115268i	0.0250060	+	0.00706753i
$267$	−6.83851	+	6.83851i	−0.418510	+	0.418510i
$268$	0.571031	+	2.39031i	0.0348813	+	0.146011i
$269$	21.7917			1.32866			0.664332	−	0.747438i	$-0.268716\pi$
$269$	21.7917			1.32866			0.664332	+	0.747438i	$0.268716\pi$
$270$	−3.75284	−	6.70999i	−0.228390	−	0.408357i
$271$	5.64353	−	5.64353i	0.342820	−	0.342820i	−0.514606	−	0.857427i	$-0.672062\pi$
$271$	5.64353	−	5.64353i	0.342820	−	0.342820i	0.857427	+	0.514606i	$0.172062\pi$
$272$	25.3627	−	12.8514i	1.53784	−	0.779233i
$273$	0.856783	−	0.570225i	0.0518549	−	0.0345116i
$274$	1.22906	+	2.19753i	0.0742502	+	0.132758i
$275$	−3.82508	−	3.82508i	−0.230661	−	0.230661i
$276$	0.301705	−	0.491102i	0.0181605	−	0.0295609i
$277$		−	3.86006i		−	0.231929i	−0.993253	−	0.115964i	$-0.963004\pi$
$277$		−	3.86006i		−	0.231929i	0.993253	−	0.115964i	$-0.0369958\pi$
$278$	−5.54990	+	19.6364i	−0.332861	+	1.17771i
$279$	−11.1709	−	11.1709i	−0.668783	−	0.668783i
$280$	0.503354	−	0.463729i	0.0300811	−	0.0277131i
$281$	−6.00896	−	6.00896i	−0.358465	−	0.358465i	0.504782	−	0.863247i	$-0.331573\pi$
$281$	−6.00896	−	6.00896i	−0.358465	−	0.358465i	−0.863247	+	0.504782i	$0.831573\pi$
$282$	−2.97095	−	5.31200i	−0.176918	−	0.316325i
$283$	−10.7185			−0.637147			−0.318573	−	0.947898i	$-0.603204\pi$
$283$	−10.7185			−0.637147			−0.318573	+	0.947898i	$0.603204\pi$
$284$	−1.60970	−	6.73810i	−0.0955178	−	0.399833i
$285$		−	1.46098i		−	0.0865412i
$286$	−8.46104	−	26.2533i	−0.500311	−	1.55239i
$287$			1.09091i			0.0643946i
$288$	−1.75004	−	8.92863i	−0.103122	−	0.526125i
$289$	−33.5266			−1.97215
$290$	10.5481	−	5.89947i	0.619406	−	0.346429i
$291$	−3.46673	−	3.46673i	−0.203223	−	0.203223i
$292$	3.82237	+	16.0003i	0.223687	+	0.936344i
$293$	5.97855	+	5.97855i	0.349270	+	0.349270i	0.859838	−	0.510567i	$-0.170565\pi$
$293$	5.97855	+	5.97855i	0.349270	+	0.349270i	−0.510567	+	0.859838i	$0.670565\pi$
$294$	−11.1438	−	3.14961i	−0.649919	−	0.183689i
$295$		−	11.5314i		−	0.671383i
$296$	0.486215	−	11.8667i	0.0282607	−	0.689738i
$297$	−20.7945	−	20.7945i	−1.20662	−	1.20662i
$298$	21.8795	−	12.2370i	1.26745	−	0.708872i
$299$	−0.173417	+	0.863585i	−0.0100290	+	0.0499424i
$300$	−2.01027	−	1.23499i	−0.116063	−	0.0713023i
$301$	1.47730	−	1.47730i	0.0851504	−	0.0851504i
$302$	0.934994	−	0.522934i	0.0538028	−	0.0300915i
$303$	−6.44595			−0.370310
$304$	1.54140	−	4.70802i	0.0884052	−	0.270024i
$305$	−2.30701	+	2.30701i	−0.132099	+	0.132099i
$306$	−4.39751	+	15.5590i	−0.251389	+	0.889451i
$307$	9.41527	−	9.41527i	0.537358	−	0.537358i	−0.385394	−	0.922752i	$-0.625935\pi$
$307$	9.41527	−	9.41527i	0.537358	−	0.537358i	0.922752	+	0.385394i	$0.125935\pi$
$308$	1.37035	−	2.23060i	0.0780830	−	0.127100i
$309$			8.23770i			0.468626i
$310$	−13.3670	−	3.77796i	−0.759194	−	0.214574i
$311$	−18.1931			−1.03163			−0.515817	−	0.856699i	$-0.672512\pi$
$311$	−18.1931			−1.03163			−0.515817	+	0.856699i	$0.672512\pi$
$312$	−6.24977	−	10.2794i	−0.353823	−	0.581957i
$313$	30.5156			1.72484			0.862422	−	0.506190i	$-0.168946\pi$
$313$	30.5156			1.72484			0.862422	+	0.506190i	$0.168946\pi$
$314$	8.04440	+	2.27362i	0.453972	+	0.128308i
$315$			0.389192i			0.0219285i
$316$	−16.5506	+	26.9404i	−0.931046	+	1.51552i
$317$	7.27121	−	7.27121i	0.408392	−	0.408392i	−0.472786	−	0.881178i	$-0.656751\pi$
$317$	7.27121	−	7.27121i	0.408392	−	0.408392i	0.881178	+	0.472786i	$0.156751\pi$
$318$	0.588514	−	2.08225i	0.0330022	−	0.116767i
$319$	32.6890	−	32.6890i	1.83023	−	1.83023i
$320$	−5.17511	−	6.10067i	−0.289298	−	0.341038i
$321$	18.8425			1.05169
$322$	−0.0729627	+	0.0408074i	−0.00406605	+	0.00227411i
$323$	−6.22493	+	6.22493i	−0.346364	+	0.346364i
$324$	−2.70580	−	1.66229i	−0.150322	−	0.0923493i
$325$	3.53498	+	0.709862i	0.196086	+	0.0393760i
$326$	7.94162	−	4.44168i	0.439846	−	0.246002i
$327$	−8.03481	−	8.03481i	−0.444326	−	0.444326i
$328$	12.7410	+	0.522037i	0.703504	+	0.0288247i
$329$			0.882785i			0.0486695i
$330$	−8.68438	−	2.45450i	−0.478059	−	0.135116i
$331$	2.07275	+	2.07275i	0.113928	+	0.113928i	0.761773	−	0.647844i	$-0.224329\pi$
$331$	2.07275	+	2.07275i	0.113928	+	0.113928i	−0.647844	+	0.761773i	$0.724329\pi$
$332$	3.89526	+	16.3053i	0.213780	+	0.894872i
$333$	4.77562	+	4.77562i	0.261703	+	0.261703i
$334$	−7.12858	+	3.98695i	−0.390058	+	0.218156i
$335$	−1.22878			−0.0671356
$336$	0.355263	−	1.08511i	0.0193812	−	0.0591975i
$337$		−	21.2847i		−	1.15945i	−0.814811	−	0.579726i	$-0.803160\pi$
$337$		−	21.2847i		−	1.15945i	0.814811	−	0.579726i	$-0.196840\pi$
$338$	14.3898	+	11.4426i	0.782703	+	0.622395i
$339$			17.6818i			0.960341i
$340$	3.30327	+	13.8273i	0.179145	+	0.749892i
$341$	−53.1328			−2.87730
$342$	1.37511	+	2.45867i	0.0743575	+	0.132950i
$343$	2.38540	+	2.38540i	0.128799	+	0.128799i
$344$	−16.5468	−	17.9606i	−0.892142	−	0.968373i
$345$	0.203779	+	0.203779i	0.0109711	+	0.0109711i
$346$	−0.0623241	+	0.220512i	−0.00335056	+	0.0118548i
$347$			25.2092i			1.35330i	0.736303	+	0.676652i	$0.236570\pi$
$347$			25.2092i			1.35330i	−0.736303	+	0.676652i	$0.763430\pi$
$348$	10.5542	−	17.1796i	0.565763	−	0.920924i
$349$	4.23932	+	4.23932i	0.226926	+	0.226926i	0.811407	−	0.584481i	$-0.198702\pi$
$349$	4.23932	+	4.23932i	0.226926	+	0.226926i	−0.584481	+	0.811407i	$0.698702\pi$
$350$	0.167040	+	0.298664i	0.00892867	+	0.0159643i
$351$	19.2174	+	3.85905i	1.02575	+	0.205981i
$352$	−25.3958	−	17.0720i	−1.35360	−	0.909941i
$353$	10.0763	−	10.0763i	0.536309	−	0.536309i	−0.386134	−	0.922443i	$-0.626190\pi$
$353$	10.0763	−	10.0763i	0.536309	−	0.536309i	0.922443	+	0.386134i	$0.126190\pi$
$354$	−9.39054	−	16.7901i	−0.499101	−	0.892382i
$355$	3.46386			0.183842
$356$	−3.80982	−	15.9477i	−0.201920	−	0.845227i
$357$	−1.43473	+	1.43473i	−0.0759338	+	0.0759338i
$358$	9.32956	+	2.63685i	0.493083	+	0.139362i
$359$	17.9020	−	17.9020i	0.944832	−	0.944832i	−0.0537235	−	0.998556i	$-0.517109\pi$
$359$	17.9020	−	17.9020i	0.944832	−	0.944832i	0.998556	+	0.0537235i	$0.0171090\pi$
$360$	4.54545	+	0.186241i	0.239566	+	0.00981575i
$361$		−	17.4662i		−	0.919272i
$362$	1.09738	−	3.88270i	0.0576771	−	0.204070i
$363$	−21.5435			−1.13074
$364$	0.0633684	+	1.74375i	0.00332141	+	0.0913971i
$365$	−8.22524			−0.430529
$366$	−1.48037	+	5.23777i	−0.0773803	+	0.273783i
$367$		−	5.24363i		−	0.273715i	−0.990591	−	0.136858i	$-0.956300\pi$
$367$		−	5.24363i		−	0.273715i	0.990591	−	0.136858i	$-0.0437003\pi$
$368$	0.441682	+	0.871673i	0.0230243	+	0.0454391i
$369$	−5.12747	+	5.12747i	−0.266926	+	0.266926i
$370$	5.71447	+	1.61510i	0.297081	+	0.0839652i
$371$	−0.221923	+	0.221923i	−0.0115217	+	0.0115217i
$372$	−22.5393	+	5.38452i	−1.16861	+	0.279174i
$373$	−18.0407			−0.934112			−0.467056	−	0.884228i	$-0.654685\pi$
$373$	−18.0407			−0.934112			−0.467056	+	0.884228i	$0.654685\pi$
$374$	26.5441	+	47.4603i	1.37256	+	2.45411i
$375$	0.834144	−	0.834144i	0.0430750	−	0.0430750i
$376$	10.3102	+	0.422441i	0.531709	+	0.0217857i
$377$	−6.06644	+	30.2098i	−0.312438	+	1.55588i
$378$	0.908088	+	1.62364i	0.0467070	+	0.0835110i
$379$	11.7658	+	11.7658i	0.604368	+	0.604368i	0.941469	−	0.337101i	$-0.109446\pi$
$379$	11.7658	+	11.7658i	0.604368	+	0.604368i	−0.337101	+	0.941469i	$0.609446\pi$
$380$	2.11051	+	1.29657i	0.108267	+	0.0665128i
$381$			9.23027i			0.472881i
$382$	−4.34672	+	15.3793i	−0.222397	+	0.786875i
$383$	−13.6517	−	13.6517i	−0.697569	−	0.697569i	0.266316	−	0.963886i	$-0.414193\pi$
$383$	−13.6517	−	13.6517i	−0.697569	−	0.697569i	−0.963886	+	0.266316i	$0.914193\pi$
$384$	−12.5032	−	4.66844i	−0.638050	−	0.238235i
$385$	0.925569	+	0.925569i	0.0471714	+	0.0471714i
$386$	−5.53465	−	9.89583i	−0.281706	−	0.503685i
$387$	13.8871			0.705922
$388$	8.08457	−	1.93136i	0.410432	−	0.0980499i
$389$			8.98539i			0.455577i	0.973711	+	0.227789i	$0.0731495\pi$
$389$			8.98539i			0.455577i	−0.973711	+	0.227789i	$0.926850\pi$
$390$	5.72512	−	1.84512i	0.289903	−	0.0934311i
$391$		−	1.73651i		−	0.0878193i
$392$	14.4396	−	13.3029i	0.729310	−	0.671898i
$393$	−0.366264			−0.0184756
$394$	5.51878	−	3.08661i	0.278032	−	0.155501i
$395$	−11.1787	−	11.1787i	−0.562462	−	0.562462i
$396$	16.9250	−	4.04330i	0.850515	−	0.203183i
$397$	−13.0460	−	13.0460i	−0.654760	−	0.654760i	0.299375	−	0.954135i	$-0.403222\pi$
$397$	−13.0460	−	13.0460i	−0.654760	−	0.654760i	−0.954135	+	0.299375i	$0.903222\pi$
$398$	3.19544	+	0.903139i	0.160173	+	0.0452703i
$399$			0.353520i			0.0176981i
$400$	3.56809	−	1.80797i	0.178404	−	0.0903986i
$401$	−0.574761	−	0.574761i	−0.0287022	−	0.0287022i	0.692610	−	0.721312i	$-0.256461\pi$
$401$	−0.574761	−	0.574761i	−0.0287022	−	0.0287022i	−0.721312	+	0.692610i	$0.756461\pi$
$402$	−1.78915	+	1.00066i	−0.0892346	+	0.0499081i
$403$	29.4818	−	19.6213i	1.46859	−	0.977409i
$404$	5.72056	−	9.31168i	0.284609	−	0.463274i
$405$	1.12275	−	1.12275i	0.0557899	−	0.0557899i
$406$	−2.55236	+	1.42752i	−0.126672	+	0.0708464i
$407$	22.7146			1.12592
$408$	16.0699	+	17.4430i	0.795578	+	0.863558i
$409$	2.42715	−	2.42715i	0.120015	−	0.120015i	−0.644548	−	0.764564i	$-0.722955\pi$
$409$	2.42715	−	2.42715i	0.120015	−	0.120015i	0.764564	+	0.644548i	$0.222955\pi$
$410$	−1.73410	+	6.13549i	−0.0856410	+	0.303010i
$411$	−1.48512	+	1.48512i	−0.0732555	+	0.0732555i
$412$	−11.9000	−	7.31068i	−0.586271	−	0.360171i
$413$			2.79029i			0.137301i
$414$	−0.534738	−	0.151135i	−0.0262809	−	0.00742788i
$415$	−8.38208			−0.411460
$416$	20.3959	+	0.0943456i	0.999989	+	0.00462567i
$417$	−17.0212			−0.833533
$418$	9.11742	+	2.57689i	0.445948	+	0.126040i
$419$			7.49789i			0.366296i	0.983085	+	0.183148i	$0.0586287\pi$
$419$			7.49789i			0.366296i	−0.983085	+	0.183148i	$0.941371\pi$
$420$	0.486431	+	0.298835i	0.0237354	+	0.0145817i
$421$	−15.0259	+	15.0259i	−0.732319	+	0.732319i	−0.971079	−	0.238759i	$-0.923259\pi$
$421$	−15.0259	+	15.0259i	−0.732319	+	0.732319i	0.238759	+	0.971079i	$0.423259\pi$
$422$	6.30956	−	22.3241i	0.307144	−	1.08672i
$423$	−4.14923	+	4.14923i	−0.201743	+	0.201743i
$424$	2.48568	+	2.69808i	0.120715	+	0.131030i
$425$	−7.10821			−0.344799
$426$	5.04348	−	2.82078i	0.244358	−	0.136667i
$427$	0.558234	−	0.558234i	0.0270149	−	0.0270149i
$428$	−16.7221	+	27.2195i	−0.808292	+	1.31570i
$429$	19.1540	−	12.7478i	0.924762	−	0.615468i
$430$	10.6569	−	5.96032i	0.513922	−	0.287432i
$431$	24.2947	+	24.2947i	1.17024	+	1.17024i	0.982153	+	0.188083i	$0.0602275\pi$
$431$	24.2947	+	24.2947i	1.17024	+	1.17024i	0.188083	+	0.982153i	$0.439772\pi$
$432$	19.3973	−	9.82876i	0.933255	−	0.472887i
$433$			39.8407i			1.91462i	0.289062	+	0.957310i	$0.406657\pi$
$433$			39.8407i			1.91462i	−0.289062	+	0.957310i	$0.593343\pi$
$434$	3.23446	+	0.914168i	0.155259	+	0.0438815i
$435$	7.12855	+	7.12855i	0.341788	+	0.341788i
$436$	18.7375	−	4.47629i	0.897366	−	0.214376i
$437$	−0.213940	−	0.213940i	−0.0102342	−	0.0102342i
$438$	−11.9762	+	6.69819i	−0.572246	+	0.320052i
$439$	−29.3812			−1.40229			−0.701144	−	0.713019i	$-0.747327\pi$
$439$	−29.3812			−1.40229			−0.701144	+	0.713019i	$0.747327\pi$
$440$	11.2528	−	10.3670i	0.536457	−	0.494227i
$441$			11.1647i			0.531651i
$442$	−32.2551	−	16.5318i	−1.53422	−	0.786339i
$443$		−	33.9623i		−	1.61360i	−0.590828	−	0.806798i	$-0.701199\pi$
$443$		−	33.9623i		−	1.61360i	0.590828	−	0.806798i	$-0.298801\pi$
$444$	9.63571	−	2.30192i	0.457290	−	0.109244i
$445$	8.19823			0.388634
$446$	−13.8065	−	24.6856i	−0.653755	−	1.16890i
$447$	14.7865	+	14.7865i	0.699375	+	0.699375i
$448$	1.25224	+	1.47620i	0.0591628	+	0.0697440i
$449$	−19.3104	−	19.3104i	−0.911316	−	0.911316i	0.0850598	−	0.996376i	$-0.472892\pi$
$449$	−19.3104	−	19.3104i	−0.911316	−	0.911316i	−0.996376	+	0.0850598i	$0.972892\pi$
$450$	−0.618653	+	2.18888i	−0.0291636	+	0.103185i
$451$			24.3881i			1.14839i
$452$	−25.5427	−	15.6920i	−1.20143	−	0.738088i
$453$	0.631881	+	0.631881i	0.0296884	+	0.0296884i
$454$	−10.8117	−	19.3311i	−0.507420	−	0.907255i
$455$	−0.855372	−	0.171768i	−0.0401005	−	0.00805260i
$456$	4.12882	+	0.169170i	0.193350	+	0.00792213i
$457$	25.1832	−	25.1832i	1.17802	−	1.17802i	0.197774	−	0.980248i	$-0.436629\pi$
$457$	25.1832	−	25.1832i	1.17802	−	1.17802i	0.980248	−	0.197774i	$-0.0633711\pi$
$458$	−14.0484	−	25.1183i	−0.656440	−	1.17370i
$459$	−38.6427			−1.80369
$460$	−0.475222	+	0.113528i	−0.0221573	+	0.00529326i
$461$	−19.2035	+	19.2035i	−0.894396	+	0.894396i	−0.994933	−	0.100537i	$-0.967944\pi$
$461$	−19.2035	+	19.2035i	−0.894396	+	0.894396i	0.100537	+	0.994933i	$0.467944\pi$
$462$	2.10139	+	0.593924i	0.0977656	+	0.0276319i
$463$	−5.45056	+	5.45056i	−0.253309	+	0.253309i	−0.822326	−	0.569017i	$-0.807324\pi$
$463$	−5.45056	+	5.45056i	−0.253309	+	0.253309i	0.569017	+	0.822326i	$0.307324\pi$
$464$	15.4508	+	30.4927i	0.717287	+	1.41559i
$465$		−	11.5868i		−	0.537324i
$466$	0.348322	−	1.23242i	0.0161357	−	0.0570906i
$467$	−13.8452			−0.640678			−0.320339	−	0.947303i	$-0.603797\pi$
$467$	−13.8452			−0.640678			−0.320339	+	0.947303i	$0.603797\pi$
$468$	−7.89804	+	8.49373i	−0.365087	+	0.392623i
$469$	0.297333			0.0137296
$470$	−1.40326	+	4.96494i	−0.0647275	+	0.229016i
$471$			6.97305i			0.321301i
$472$	32.5883	+	1.33524i	1.50000	+	0.0614595i
$473$	33.0261	−	33.0261i	1.51854	−	1.51854i
$474$	−25.3799	−	7.17322i	−1.16574	−	0.329477i
$475$	−0.875738	+	0.875738i	−0.0401816	+	0.0401816i
$476$	−0.799304	−	3.34585i	−0.0366360	−	0.153357i
$477$	−2.08615			−0.0955182
$478$	9.96888	+	17.8241i	0.455966	+	0.815257i
$479$	−13.5767	+	13.5767i	−0.620333	+	0.620333i	−0.945617	−	0.325283i	$-0.894540\pi$
$479$	−13.5767	+	13.5767i	−0.620333	+	0.620333i	0.325283	+	0.945617i	$0.394540\pi$
$480$	3.72293	−	5.53812i	0.169928	−	0.252780i
$481$	−12.6036	+	8.38825i	−0.574677	+	0.382471i
$482$	−6.16354	−	11.0203i	−0.280742	−	0.501960i
$483$	−0.0493091	−	0.0493091i	−0.00224364	−	0.00224364i
$484$	19.1191	−	31.1213i	0.869052	−	1.41461i
$485$			4.15603i			0.188716i
$486$	−5.55261	+	19.6459i	−0.251871	+	0.891157i
$487$	10.4019	+	10.4019i	0.471356	+	0.471356i	0.902353	−	0.430997i	$-0.141838\pi$
$487$	10.4019	+	10.4019i	0.471356	+	0.471356i	−0.430997	+	0.902353i	$0.641838\pi$
$488$	−6.25259	−	6.78686i	−0.283042	−	0.307227i
$489$	5.36705	+	5.36705i	0.242707	+	0.242707i
$490$	4.79185	+	8.56771i	0.216474	+	0.387050i
$491$	15.3399			0.692281			0.346140	−	0.938183i	$-0.387492\pi$
$491$	15.3399			0.692281			0.346140	+	0.938183i	$0.387492\pi$
$492$	2.47151	+	10.3456i	0.111424	+	0.466417i
$493$		−	60.7464i		−	2.73588i
$494$	−6.01060	+	1.93712i	−0.270430	+	0.0871553i
$495$			8.70065i			0.391065i
$496$	12.2245	−	37.3384i	0.548898	−	1.67654i
$497$	−0.838162			−0.0375967
$498$	−12.2046	+	6.82592i	−0.546900	+	0.305877i
$499$	16.6603	+	16.6603i	0.745816	+	0.745816i	0.973690	−	0.227875i	$-0.0731777\pi$
$499$	16.6603	+	16.6603i	0.745816	+	0.745816i	−0.227875	+	0.973690i	$0.573178\pi$
$500$	0.464712	+	1.94526i	0.0207826	+	0.0869947i
$501$	−4.81759	−	4.81759i	−0.215234	−	0.215234i
$502$	4.89194	+	1.38263i	0.218338	+	0.0617098i
$503$		−	2.89555i		−	0.129106i	−0.997914	−	0.0645530i	$-0.979438\pi$
$503$		−	2.89555i		−	0.129106i	0.997914	−	0.0645530i	$-0.0205622\pi$
$504$	−1.09988	−	0.0450653i	−0.0489925	−	0.00200737i
$505$	3.86381	+	3.86381i	0.171937	+	0.171937i
$506$	−1.63113	+	0.912277i	−0.0725126	+	0.0405557i
$507$	−5.92035	+	14.1467i	−0.262932	+	0.628276i
$508$	−13.3339	−	8.19155i	−0.591594	−	0.363441i
$509$	9.00023	−	9.00023i	0.398928	−	0.398928i	−0.478927	−	0.877855i	$-0.658974\pi$
$509$	9.00023	−	9.00023i	0.398928	−	0.398928i	0.877855	+	0.478927i	$0.158974\pi$
$510$	−10.3498	+	5.78854i	−0.458296	+	0.256321i
$511$	1.99029			0.0880453
$512$	17.8401	−	13.9187i	0.788428	−	0.615128i
$513$	−4.76082	+	4.76082i	−0.210195	+	0.210195i
$514$	4.70414	−	16.6439i	0.207491	−	0.734132i
$515$	4.93782	−	4.93782i	0.217586	−	0.217586i
$516$	10.6630	−	17.3568i	0.469414	−	0.764091i
$517$			19.7353i			0.867956i
$518$	−1.38275	−	0.390812i	−0.0607546	−	0.0171713i
$519$	−0.191144			−0.00839030
$520$	−2.41543	+	9.90786i	−0.105924	+	0.434488i
$521$	21.0246			0.921105			0.460552	−	0.887633i	$-0.347651\pi$
$521$	21.0246			0.921105			0.460552	+	0.887633i	$0.347651\pi$
$522$	−18.7061	−	5.28697i	−0.818743	−	0.231405i
$523$		−	4.25536i		−	0.186074i	−0.995663	−	0.0930370i	$-0.970343\pi$
$523$		−	4.25536i		−	0.186074i	0.995663	−	0.0930370i	$-0.0296575\pi$
$524$	0.325047	−	0.529098i	0.0141998	−	0.0231137i
$525$	−0.201841	+	0.201841i	−0.00880906	+	0.00880906i
$526$	6.14816	−	21.7531i	0.268073	−	0.948480i
$527$	−49.3687	+	49.3687i	−2.15054	+	2.15054i
$528$	7.94214	−	24.2583i	0.345637	−	1.05571i
$529$	−22.9403			−0.997405
$530$	−1.60090	+	0.895369i	−0.0695386	+	0.0388923i
$531$	−13.1148	+	13.1148i	−0.569135	+	0.569135i
$532$	−0.510687	−	0.313737i	−0.0221411	−	0.0136022i
$533$	−9.00626	−	13.5322i	−0.390104	−	0.586146i
$534$	11.9369	−	6.67620i	0.516560	−	0.288907i
$535$	−11.2945	−	11.2945i	−0.488304	−	0.488304i
$536$	0.142283	−	3.47261i	0.00614571	−	0.149994i
$537$			8.08706i			0.348982i
$538$	−29.6564	−	8.38190i	−1.27858	−	0.361369i
$539$	26.5516	+	26.5516i	1.14366	+	1.14366i
$540$	2.52633	+	10.5751i	0.108716	+	0.455080i
$541$	−10.9455	−	10.9455i	−0.470583	−	0.470583i	0.431520	−	0.902103i	$-0.357977\pi$
$541$	−10.9455	−	10.9455i	−0.470583	−	0.470583i	−0.902103	+	0.431520i	$0.857977\pi$
$542$	−9.85101	+	5.50958i	−0.423137	+	0.236657i
$543$	3.36560			0.144432
$544$	−39.4593	+	7.73413i	−1.69180	+	0.331598i
$545$			9.63240i			0.412607i
$546$	−1.38533	+	0.446470i	−0.0592865	+	0.0191071i
$547$		−	27.5083i		−	1.17617i	−0.808799	−	0.588085i	$-0.799882\pi$
$547$		−	27.5083i		−	1.17617i	0.808799	−	0.588085i	$-0.200118\pi$
$548$	−0.827378	−	3.46336i	−0.0353438	−	0.147948i
$549$	5.24758			0.223961
$550$	3.73429	+	6.67683i	0.159231	+	0.284701i
$551$	−7.48401	−	7.48401i	−0.318830	−	0.318830i
$552$	−0.599487	+	0.552295i	−0.0255159	+	0.0235072i
$553$	2.70495	+	2.70495i	0.115026	+	0.115026i
$554$	−1.48472	+	5.25317i	−0.0630799	+	0.223186i
$555$			4.95342i			0.210261i
$556$	15.1058	−	24.5885i	0.640627	−	1.04278i
$557$	27.6855	+	27.6855i	1.17307	+	1.17307i	0.981474	+	0.191598i	$0.0613669\pi$
$557$	27.6855	+	27.6855i	1.17307	+	1.17307i	0.191598	+	0.981474i	$0.438633\pi$
$558$	10.9057	+	19.4992i	0.461677	+	0.825468i
$559$	−6.12901	+	30.5214i	−0.259230	+	1.29092i
$560$	−0.863383	+	0.437482i	−0.0364846	+	0.0184870i
$561$	−32.0743	+	32.0743i	−1.35418	+	1.35418i
$562$	5.86634	+	10.4889i	0.247457	+	0.442447i
$563$	−45.4740			−1.91650			−0.958250	−	0.285932i	$-0.907697\pi$
$563$	−45.4740			−1.91650			−0.958250	+	0.285932i	$0.907697\pi$
$564$	1.99999	+	8.37184i	0.0842146	+	0.352518i
$565$	10.5987	−	10.5987i	0.445892	−	0.445892i
$566$	14.5868	+	4.12272i	0.613128	+	0.173291i
$567$	−0.271676	+	0.271676i	−0.0114093	+	0.0114093i
$568$	−0.401087	+	9.78905i	−0.0168292	+	0.410739i
$569$		−	3.40881i		−	0.142905i	−0.997444	−	0.0714523i	$-0.977237\pi$
$569$		−	3.40881i		−	0.142905i	0.997444	−	0.0714523i	$-0.0227634\pi$
$570$	−0.561949	+	1.98826i	−0.0235374	+	0.0832789i
$571$	11.8904			0.497596			0.248798	−	0.968555i	$-0.419964\pi$
$571$	11.8904			0.497596			0.248798	+	0.968555i	$0.419964\pi$
$572$	1.41664	+	38.9826i	0.0592329	+	1.62994i
$573$	−13.3311			−0.556916
$574$	0.419606	−	1.48463i	0.0175140	−	0.0619671i
$575$		−	0.244297i		−	0.0101879i
$576$	−1.05265	+	12.8241i	−0.0438606	+	0.534338i
$577$	−5.65553	+	5.65553i	−0.235443	+	0.235443i	−0.814960	−	0.579517i	$-0.803241\pi$
$577$	−5.65553	+	5.65553i	−0.235443	+	0.235443i	0.579517	+	0.814960i	$0.303241\pi$
$578$	45.6264	+	12.8956i	1.89781	+	0.536385i
$579$	6.68773	−	6.68773i	0.277933	−	0.277933i
$580$	−16.6241	+	3.97140i	−0.690278	+	0.164904i
$581$	2.02824			0.0841457
$582$	3.38445	+	6.05132i	0.140290	+	0.250835i
$583$	−4.96124	+	4.96124i	−0.205474	+	0.205474i
$584$	0.952418	−	23.2450i	0.0394113	−	0.961885i
$585$	−3.21305	−	4.82772i	−0.132843	−	0.199602i
$586$	−5.83665	−	10.4358i	−0.241110	−	0.431098i
$587$	8.60753	+	8.60753i	0.355271	+	0.355271i	0.862066	−	0.506796i	$-0.169170\pi$
$587$	8.60753	+	8.60753i	0.355271	+	0.355271i	−0.506796	+	0.862066i	$0.669170\pi$
$588$	13.9542	+	8.57263i	0.575460	+	0.353529i
$589$			12.1646i			0.501232i
$590$	−4.43540	+	15.6931i	−0.182602	+	0.646074i
$591$	3.72966	+	3.72966i	0.153418	+	0.153418i
$592$	−5.22606	+	15.9624i	−0.214790	+	0.656051i
$593$	−11.6988	−	11.6988i	−0.480414	−	0.480414i	0.424850	−	0.905264i	$-0.360327\pi$
$593$	−11.6988	−	11.6988i	−0.480414	−	0.480414i	−0.905264	+	0.424850i	$0.860327\pi$
$594$	20.3009	+	36.2976i	0.832956	+	1.48931i
$595$	1.72000			0.0705131
$596$	−34.4827	+	8.23772i	−1.41247	+	0.337430i
$597$			2.76987i			0.113363i
$598$	0.568171	−	1.10855i	0.0232342	−	0.0453321i
$599$			36.6483i			1.49741i	0.662905	+	0.748704i	$0.269323\pi$
$599$			36.6483i			1.49741i	−0.662905	+	0.748704i	$0.730677\pi$
$600$	2.26075	+	2.45393i	0.0922948	+	0.100181i
$601$	26.7542			1.09133			0.545663	−	0.838004i	$-0.316278\pi$
$601$	26.7542			1.09133			0.545663	+	0.838004i	$0.316278\pi$
$602$	−2.57869	+	1.44224i	−0.105100	+	0.0587813i
$603$	1.39751	+	1.39751i	0.0569112	+	0.0569112i
$604$	−1.47357	+	0.352029i	−0.0599589	+	0.0143238i
$605$	12.9135	+	12.9135i	0.525010	+	0.525010i
$606$	8.77231	+	2.47935i	0.356351	+	0.100717i
$607$		−	30.1452i		−	1.22356i	−0.791029	−	0.611778i	$-0.790455\pi$
$607$		−	30.1452i		−	1.22356i	0.791029	−	0.611778i	$-0.209545\pi$
$608$	−3.90857	+	5.81428i	−0.158513	+	0.235800i
$609$	−1.72492	−	1.72492i	−0.0698974	−	0.0698974i
$610$	4.02697	−	2.25225i	0.163047	−	0.0911909i
$611$	−7.28801	−	10.9505i	−0.294841	−	0.443010i
$612$	11.9692	−	19.4829i	0.483825	−	0.787549i
$613$	−21.8672	+	21.8672i	−0.883208	+	0.883208i	−0.993859	−	0.110651i	$-0.964706\pi$
$613$	−21.8672	+	21.8672i	−0.883208	+	0.883208i	0.110651	+	0.993859i	$0.464706\pi$
$614$	−16.4347	+	9.19180i	−0.663251	+	0.370951i
$615$	−5.31837			−0.214457
$616$	−2.72288	+	2.50854i	−0.109708	+	0.101072i
$617$	12.7850	−	12.7850i	0.514703	−	0.514703i	−0.401261	−	0.915964i	$-0.631428\pi$
$617$	12.7850	−	12.7850i	0.514703	−	0.514703i	0.915964	+	0.401261i	$0.131428\pi$
$618$	3.16852	−	11.2107i	0.127457	−	0.450961i
$619$	20.3294	−	20.3294i	0.817106	−	0.817106i	−0.168581	−	0.985688i	$-0.553919\pi$
$619$	20.3294	−	20.3294i	0.817106	−	0.817106i	0.985688	+	0.168581i	$0.0539186\pi$
$620$	16.7380	+	10.2829i	0.672215	+	0.412970i
$621$		−	1.32808i		−	0.0532941i
$622$	24.7590	+	6.99773i	0.992745	+	0.280583i
$623$	−1.98376			−0.0794775
$624$	4.55148	+	16.3932i	0.182205	+	0.656251i
$625$	−1.00000			−0.0400000
$626$	−41.5288	−	11.7374i	−1.65982	−	0.469122i
$627$			7.90317i			0.315622i
$628$	−10.0731	−	6.18835i	−0.401961	−	0.246942i
$629$	21.1054	−	21.1054i	0.841529	−	0.841529i
$630$	0.149698	−	0.529652i	0.00596410	−	0.0211018i
$631$	5.42446	−	5.42446i	0.215944	−	0.215944i	−0.590843	−	0.806787i	$-0.701205\pi$
$631$	5.42446	−	5.42446i	0.215944	−	0.215944i	0.806787	+	0.590843i	$0.201205\pi$
$632$	32.8861	−	30.2973i	1.30814	−	1.20516i
$633$	19.3510			0.769134
$634$	−12.6922	+	7.09863i	−0.504071	+	0.281923i
$635$	5.53278	−	5.53278i	0.219562	−	0.219562i
$636$	−1.60182	+	2.60737i	−0.0635163	+	0.103389i
$637$	−24.5379	−	4.92747i	−0.972227	−	0.195233i
$638$	−57.0598	+	31.9131i	−2.25902	+	1.26345i
$639$	−3.93949	−	3.93949i	−0.155844	−	0.155844i
$640$	4.69628	+	10.2930i	0.185637	+	0.406865i
$641$			12.1124i			0.478413i	0.970969	+	0.239206i	$0.0768873\pi$
$641$			12.1124i			0.478413i	−0.970969	+	0.239206i	$0.923113\pi$
$642$	−25.6428	−	7.24752i	−1.01204	−	0.286037i
$643$	−28.4178	−	28.4178i	−1.12069	−	1.12069i	−0.991638	−	0.129050i	$-0.958807\pi$
$643$	−28.4178	−	28.4178i	−1.12069	−	1.12069i	−0.129050	−	0.991638i	$-0.541193\pi$
$644$	0.114991	−	0.0274707i	0.00453128	−	0.00108250i
$645$	7.20208	+	7.20208i	0.283582	+	0.283582i
$646$	10.8659	−	6.07718i	0.427511	−	0.239104i
$647$	34.3949			1.35220			0.676102	−	0.736808i	$-0.263668\pi$
$647$	34.3949			1.35220			0.676102	+	0.736808i	$0.263668\pi$
$648$	3.04295	+	3.30296i	0.119538	+	0.129753i
$649$			62.3788i			2.44858i
$650$	−4.53772	−	2.32574i	−0.177984	−	0.0912229i
$651$			2.80370i			0.109886i
$652$	−12.5162	+	2.99005i	−0.490172	+	0.117099i
$653$	−10.9924			−0.430167			−0.215084	−	0.976596i	$-0.569002\pi$
$653$	−10.9924			−0.430167			−0.215084	+	0.976596i	$0.569002\pi$
$654$	7.84411	+	14.0251i	0.306729	+	0.548424i
$655$	0.219545	+	0.219545i	0.00857833	+	0.00857833i
$656$	−17.1384	−	5.61110i	−0.669144	−	0.219077i
$657$	9.35470	+	9.35470i	0.364961	+	0.364961i
$658$	0.339552	−	1.20138i	0.0132371	−	0.0468348i
$659$		−	25.9578i		−	1.01117i	−0.862776	−	0.505586i	$-0.831276\pi$
$659$		−	25.9578i		−	1.01117i	0.862776	−	0.505586i	$-0.168724\pi$
$660$	10.8745	+	6.68067i	0.423289	+	0.260045i
$661$	−7.62930	−	7.62930i	−0.296746	−	0.296746i	0.542992	−	0.839738i	$-0.317291\pi$
$661$	−7.62930	−	7.62930i	−0.296746	−	0.296746i	−0.839738	+	0.542992i	$0.817291\pi$
$662$	−2.02355	−	3.61806i	−0.0786475	−	0.140620i
$663$	5.95237	−	29.6417i	0.231171	−	1.15119i
$664$	0.970579	−	23.6882i	0.0376658	−	0.919282i
$665$	0.211906	−	0.211906i	0.00821735	−	0.00821735i
$666$	−4.66227	−	8.33604i	−0.180659	−	0.323015i
$667$	2.08775			0.0808380
$668$	11.2348	−	2.68394i	0.434688	−	0.103845i
$669$	16.6829	−	16.6829i	0.644998	−	0.644998i
$670$	1.67225	+	0.472636i	0.0646048	+	0.0182595i
$671$	12.4797	−	12.4797i	0.481774	−	0.481774i
$672$	−0.900851	+	1.34008i	−0.0347511	+	0.0516947i
$673$			11.2848i			0.434997i	0.976061	+	0.217499i	$0.0697898\pi$
$673$			11.2848i			0.434997i	−0.976061	+	0.217499i	$0.930210\pi$
$674$	−8.18689	+	28.9664i	−0.315347	+	1.11574i
$675$	−5.43634			−0.209245
$676$	−15.1819	−	21.1071i	−0.583919	−	0.811812i
$677$	−18.8203			−0.723323			−0.361661	−	0.932310i	$-0.617790\pi$
$677$	−18.8203			−0.723323			−0.361661	+	0.932310i	$0.617790\pi$
$678$	6.80106	−	24.0631i	0.261193	−	0.924139i
$679$		−	1.00565i		−	0.0385933i
$680$	0.823074	−	20.0882i	0.0315635	−	0.770347i
$681$	13.0642	−	13.0642i	0.500622	−	0.500622i
$682$	72.3085	+	20.4368i	2.76884	+	0.782567i
$683$	8.57437	−	8.57437i	0.328089	−	0.328089i	−0.523770	−	0.851859i	$-0.675475\pi$
$683$	8.57437	−	8.57437i	0.328089	−	0.328089i	0.851859	+	0.523770i	$0.175475\pi$
$684$	−0.925698	−	3.87492i	−0.0353949	−	0.148161i
$685$	1.78041			0.0680260
$686$	−2.32878	−	4.16381i	−0.0889133	−	0.158975i
$687$	16.9753	−	16.9753i	0.647646	−	0.647646i
$688$	15.6102	+	30.8072i	0.595133	+	1.17451i
$689$	0.920711	−	4.58497i	0.0350763	−	0.174673i
$690$	−0.198942	−	0.355704i	−0.00757360	−	0.0135414i
$691$	16.9046	+	16.9046i	0.643082	+	0.643082i	0.951312	−	0.308230i	$-0.0997366\pi$
$691$	16.9046	+	16.9046i	0.643082	+	0.643082i	−0.308230	+	0.951312i	$0.599737\pi$
$692$	0.169634	−	0.276123i	0.00644852	−	0.0104966i
$693$		−	2.10533i		−	0.0799748i
$694$	9.69641	−	34.3073i	0.368071	−	1.30229i
$695$	10.2028	+	10.2028i	0.387014	+	0.387014i
$696$	−20.9711	+	19.3203i	−0.794908	+	0.732332i
$697$	22.6604	+	22.6604i	0.858324	+	0.858324i
$698$	−4.13870	−	7.39991i	−0.156652	−	0.280091i
$699$	1.06828			0.0404062
$700$	−0.112448	−	0.470702i	−0.00425014	−	0.0177909i
$701$		−	37.2994i		−	1.40878i	−0.709814	−	0.704390i	$-0.751221\pi$
$701$		−	37.2994i		−	1.40878i	0.709814	−	0.704390i	$-0.248779\pi$
$702$	−24.6686	−	12.6435i	−0.931058	−	0.477199i
$703$		−	5.20042i		−	0.196138i
$704$	27.9947	+	33.0015i	1.05509	+	1.24379i
$705$	−4.30371			−0.162087
$706$	−17.5886	+	9.83718i	−0.661957	+	0.370227i
$707$	−0.934940	−	0.934940i	−0.0351621	−	0.0351621i
$708$	6.32152	+	26.4616i	0.237577	+	0.994487i
$709$	−27.2679	−	27.2679i	−1.02407	−	1.02407i	−0.999703	−	0.0243660i	$-0.992243\pi$
$709$	−27.2679	−	27.2679i	−1.02407	−	1.02407i	−0.0243660	−	0.999703i	$-0.507757\pi$
$710$	−4.71397	−	1.33233i	−0.176912	−	0.0500013i
$711$			25.4274i			0.953603i
$712$	−0.949291	+	23.1687i	−0.0355762	+	0.868283i
$713$	−1.69672	−	1.69672i	−0.0635426	−	0.0635426i
$714$	2.50437	−	1.40067i	0.0937238	−	0.0524189i
$715$	−19.1224	−	3.83999i	−0.715138	−	0.143607i
$716$	−11.6824	−	7.17699i	−0.436591	−	0.268217i
$717$	−12.0458	+	12.0458i	−0.449858	+	0.449858i
$718$	−31.2487	+	17.4771i	−1.16619	+	0.652240i
$719$	−18.7415			−0.698939			−0.349470	−	0.936948i	$-0.613638\pi$
$719$	−18.7415			−0.698939			−0.349470	+	0.936948i	$0.613638\pi$
$720$	−6.11427	−	2.00180i	−0.227865	−	0.0746028i
$721$	−1.19482	+	1.19482i	−0.0444975	+	0.0444975i
$722$	−6.71813	+	23.7697i	−0.250023	+	0.884618i
$723$	7.44765	−	7.44765i	0.276981	−	0.276981i
$724$	−2.98686	+	4.86187i	−0.111006	+	0.180690i
$725$		−	8.54595i		−	0.317388i
$726$	29.3186	+	8.28644i	1.08812	+	0.307539i
$727$	−3.35848			−0.124559			−0.0622796	−	0.998059i	$-0.519837\pi$
$727$	−3.35848			−0.124559			−0.0622796	+	0.998059i	$0.519837\pi$
$728$	0.584471	−	2.39744i	0.0216619	−	0.0888551i
$729$	−21.7929			−0.807145
$730$	11.1938	+	3.16373i	0.414299	+	0.117095i
$731$		−	61.3729i		−	2.26996i
$732$	4.02928	−	6.55869i	0.148927	−	0.242416i
$733$	3.04717	−	3.04717i	0.112550	−	0.112550i	−0.648589	−	0.761139i	$-0.724641\pi$
$733$	3.04717	−	3.04717i	0.112550	−	0.112550i	0.761139	+	0.648589i	$0.224641\pi$
$734$	−2.01689	+	7.13606i	−0.0744449	+	0.263397i
$735$	−5.79017	+	5.79017i	−0.213574	+	0.213574i
$736$	−0.265809	−	1.35615i	−0.00979785	−	0.0499883i
$737$	6.64709			0.244849
$738$	8.95020	−	5.00577i	0.329462	−	0.184265i
$739$	−10.6855	+	10.6855i	−0.393072	+	0.393072i	−0.875781	−	0.482709i	$-0.839653\pi$
$739$	−10.6855	+	10.6855i	−0.393072	+	0.393072i	0.482709	+	0.875781i	$0.339653\pi$
$740$	−7.15561	−	4.39600i	−0.263045	−	0.161600i
$741$	−2.91855	−	4.38523i	−0.107216	−	0.161095i
$742$	0.387375	−	0.216656i	0.0142210	−	0.00795368i
$743$	−9.49831	−	9.49831i	−0.348459	−	0.348459i	0.511076	−	0.859535i	$-0.329247\pi$
$743$	−9.49831	−	9.49831i	−0.348459	−	0.348459i	−0.859535	+	0.511076i	$0.829247\pi$
$744$	32.7449	+	1.34166i	1.20049	+	0.0491876i
$745$		−	17.7265i		−	0.649449i
$746$	24.5516	+	6.93912i	0.898899	+	0.254059i
$747$	9.53307	+	9.53307i	0.348797	+	0.348797i
$748$	−17.8690	−	74.7987i	−0.653355	−	2.73491i
$749$	2.73297	+	2.73297i	0.0998607	+	0.0998607i
$750$	−1.45603	+	0.814346i	−0.0531668	+	0.0297357i
$751$	−23.9126			−0.872585			−0.436292	−	0.899805i	$-0.643709\pi$
$751$	−23.9126			−0.872585			−0.436292	+	0.899805i	$0.643709\pi$
$752$	−13.8687	−	4.54059i	−0.505740	−	0.165578i
$753$			4.24044i			0.154530i
$754$	19.8756	−	38.7792i	0.723828	−	1.41225i
$755$		−	0.757520i		−	0.0275690i
$756$	−0.611306	−	2.55890i	−0.0222330	−	0.0930662i
$757$	2.13171			0.0774783			0.0387392	−	0.999249i	$-0.487666\pi$
$757$	2.13171			0.0774783			0.0387392	+	0.999249i	$0.487666\pi$
$758$	−11.4865	−	20.5376i	−0.417209	−	0.745960i
$759$	−1.10234	−	1.10234i	−0.0400124	−	0.0400124i
$760$	−2.37348	−	2.57629i	−0.0860952	−	0.0934518i
$761$	0.845594	+	0.845594i	0.0306527	+	0.0306527i	0.722267	−	0.691614i	$-0.243100\pi$
$761$	0.845594	+	0.845594i	0.0306527	+	0.0306527i	−0.691614	+	0.722267i	$0.743100\pi$
$762$	3.55030	−	12.5615i	0.128614	−	0.455055i
$763$		−	2.33079i		−	0.0843802i
$764$	11.8309	−	19.2578i	0.428028	−	0.696725i
$765$	8.08427	+	8.08427i	0.292287	+	0.292287i
$766$	13.3277	+	23.8296i	0.481549	+	0.860998i
$767$	−23.0358	−	34.6121i	−0.831775	−	1.24977i
$768$	15.2200	+	11.1625i	0.549203	+	0.402791i
$769$	15.1402	−	15.1402i	0.545971	−	0.545971i	−0.379302	−	0.925273i	$-0.623836\pi$
$769$	15.1402	−	15.1402i	0.545971	−	0.545971i	0.925273	+	0.379302i	$0.123836\pi$
$770$	−0.903601	−	1.61562i	−0.0325635	−	0.0582228i
$771$	14.4273			0.519587
$772$	3.72582	+	15.5961i	0.134095	+	0.561316i
$773$	−8.02171	+	8.02171i	−0.288521	+	0.288521i	−0.836495	−	0.547974i	$-0.815399\pi$
$773$	−8.02171	+	8.02171i	−0.288521	+	0.288521i	0.547974	+	0.836495i	$0.315399\pi$
$774$	−18.8990	−	5.34150i	−0.679311	−	0.191996i
$775$	−6.94531	+	6.94531i	−0.249483	+	0.249483i
$776$	−11.7452	−	0.481236i	−0.421628	−	0.0172754i
$777$		−	1.19860i		−	0.0429995i
$778$	3.45611	−	12.2282i	0.123908	−	0.438403i
$779$	5.58357			0.200052
$780$	−8.50102	+	0.308931i	−0.304386	+	0.0110615i
$781$	−18.7377			−0.670486
$782$	−0.667928	+	2.36323i	−0.0238850	+	0.0845088i
$783$		−	46.4587i		−	1.66030i
$784$	−24.7677	+	12.5500i	−0.884560	+	0.448213i
$785$	4.17976	−	4.17976i	0.149182	−	0.149182i
$786$	0.498450	+	0.140879i	0.0177791	+	0.00502498i
$787$	19.0399	−	19.0399i	0.678698	−	0.678698i	−0.281008	−	0.959706i	$-0.590669\pi$
$787$	19.0399	−	19.0399i	0.678698	−	0.678698i	0.959706	+	0.281008i	$0.0906687\pi$
$788$	−8.69774	+	2.07784i	−0.309844	+	0.0740200i
$789$	18.8560			0.671293
$790$	10.9134	+	19.5129i	0.388281	+	0.694237i
$791$	−2.56462	+	2.56462i	−0.0911872	+	0.0911872i
$792$	−24.5885	−	1.00747i	−0.873715	−	0.0357988i
$793$	−2.31599	+	11.5332i	−0.0822433	+	0.409557i
$794$	12.7364	+	22.7723i	0.451997	+	0.808159i
$795$	−1.08191	−	1.08191i	−0.0383713	−	0.0383713i
$796$	−4.00130	−	2.45817i	−0.141822	−	0.0871275i
$797$		−	43.4872i		−	1.54040i	−0.637805	−	0.770198i	$-0.720158\pi$
$797$		−	43.4872i		−	1.54040i	0.637805	−	0.770198i	$-0.279842\pi$
$798$	0.135977	−	0.481106i	0.00481353	−	0.0170310i
$799$	18.3372	+	18.3372i	0.648722	+	0.648722i
$800$	−5.55123	+	1.08806i	−0.196266	+	0.0384686i
$801$	−9.32398	−	9.32398i	−0.329447	−	0.329447i
$802$	0.561119	+	1.00327i	0.0198138	+	0.0354266i
$803$	44.4943			1.57017
$804$	2.81974	−	0.673621i	0.0994447	−	0.0237568i
$805$			0.0591134i			0.00208347i
$806$	−47.6689	+	15.3629i	−1.67906	+	0.541137i
$807$		−	25.7068i		−	0.904921i
$808$	−11.3667	+	10.4719i	−0.399881	+	0.368402i
$809$	2.11109			0.0742219			0.0371110	−	0.999311i	$-0.488185\pi$
$809$	2.11109			0.0742219			0.0371110	+	0.999311i	$0.488185\pi$
$810$	−1.95980	+	1.09610i	−0.0688605	+	0.0385131i
$811$	32.8113	+	32.8113i	1.15216	+	1.15216i	0.986118	+	0.166044i	$0.0530993\pi$
$811$	32.8113	+	32.8113i	1.15216	+	1.15216i	0.166044	+	0.986118i	$0.446901\pi$
$812$	4.02259	−	0.960975i	0.141165	−	0.0337236i
$813$	−6.65744	−	6.65744i	−0.233487	−	0.233487i
$814$	−30.9123	−	8.73688i	−1.08348	−	0.306227i
$815$		−	6.43420i		−	0.225380i
$816$	−15.1603	−	29.9193i	−0.530717	−	1.04739i
$817$	−7.56121	−	7.56121i	−0.264533	−	0.264533i
$818$	−4.23669	+	2.36955i	−0.148133	+	0.0828492i
$819$	0.777474	+	1.16818i	0.0271671	+	0.0408196i
$820$	4.71987	−	7.68280i	0.164825	−	0.268295i
$821$	28.7972	−	28.7972i	1.00503	−	1.00503i	0.00504177	−	0.999987i	$-0.498395\pi$
$821$	28.7972	−	28.7972i	1.00503	−	1.00503i	0.999987	−	0.00504177i	$-0.00160485\pi$
$822$	2.59233	−	1.44987i	0.0904180	−	0.0505700i
$823$	15.6493			0.545500			0.272750	−	0.962085i	$-0.412067\pi$
$823$	15.6493			0.545500			0.272750	+	0.962085i	$0.412067\pi$
$824$	13.3828	+	14.5263i	0.466211	+	0.506048i
$825$	−4.51229	+	4.51229i	−0.157098	+	0.157098i
$826$	1.07325	−	3.79731i	0.0373431	−	0.132125i
$827$	20.4874	−	20.4874i	0.712417	−	0.712417i	−0.254623	−	0.967040i	$-0.581951\pi$
$827$	20.4874	−	20.4874i	0.712417	−	0.712417i	0.967040	+	0.254623i	$0.0819515\pi$
$828$	0.669594	+	0.411360i	0.0232700	+	0.0142957i
$829$		−	35.0702i		−	1.21804i	−0.793155	−	0.609020i	$-0.791563\pi$
$829$		−	35.0702i		−	1.21804i	0.793155	−	0.609020i	$-0.208437\pi$
$830$	11.4072	+	3.22406i	0.395950	+	0.111909i
$831$	−4.55356			−0.157961
$832$	−27.7205	−	7.97340i	−0.961035	−	0.276428i
$833$	49.3413			1.70957
$834$	23.1642	+	6.54699i	0.802111	+	0.226704i
$835$			5.77548i			0.199869i
$836$	−11.4168	−	7.01380i	−0.394857	−	0.242577i
$837$	−37.7571	+	37.7571i	−1.30508	+	1.30508i
$838$	2.88397	−	10.2039i	0.0996250	−	0.352488i
$839$	25.2583	−	25.2583i	0.872013	−	0.872013i	−0.120679	−	0.992692i	$-0.538507\pi$
$839$	25.2583	−	25.2583i	0.872013	−	0.872013i	0.992692	+	0.120679i	$0.0385071\pi$
$840$	−0.547042	−	0.593785i	−0.0188747	−	0.0204875i
$841$	44.0332			1.51839
$842$	26.2284	−	14.6693i	0.903889	−	0.505537i
$843$	−7.08852	+	7.08852i	−0.244142	+	0.244142i
$844$	−17.1734	+	27.9541i	−0.591132	+	0.962219i
$845$	12.0285	−	4.93101i	0.413794	−	0.169632i
$846$	7.24265	−	4.05075i	0.249007	−	0.139268i
$847$	−3.12474	−	3.12474i	−0.107367	−	0.107367i
$848$	−2.34499	−	4.62791i	−0.0805273	−	0.158923i
$849$			12.6441i			0.433945i
$850$	9.67357	+	2.73408i	0.331801	+	0.0937782i
$851$	0.725358	+	0.725358i	0.0248650	+	0.0248650i
$852$	−7.94866	+	1.89889i	−0.272317	+	0.0650549i
$853$	−35.4861	−	35.4861i	−1.21502	−	1.21502i	−0.969354	−	0.245666i	$-0.920993\pi$
$853$	−35.4861	−	35.4861i	−1.21502	−	1.21502i	−0.245666	−	0.969354i	$-0.579007\pi$
$854$	−0.974420	+	0.544985i	−0.0333440	+	0.0186490i
$855$	1.99198			0.0681243
$856$	33.2267	−	30.6111i	1.13567	−	1.04627i
$857$			17.1773i			0.586764i	0.955995	+	0.293382i	$0.0947808\pi$
$857$			17.1773i			0.586764i	−0.955995	+	0.293382i	$0.905219\pi$
$858$	−30.9699	+	9.98113i	−1.05730	+	0.340750i
$859$			43.8884i			1.49745i	0.662879	+	0.748727i	$0.269334\pi$
$859$			43.8884i			1.49745i	−0.662879	+	0.748727i	$0.730666\pi$
$860$	−16.7956	+	4.01237i	−0.572724	+	0.136821i
$861$	1.28691			0.0438576
$862$	−23.7181	−	42.4074i	−0.807842	−	1.44440i
$863$	−34.1389	−	34.1389i	−1.16210	−	1.16210i	−0.984015	−	0.178087i	$-0.943009\pi$
$863$	−34.1389	−	34.1389i	−1.16210	−	1.16210i	−0.178087	−	0.984015i	$-0.556991\pi$
$864$	−30.1784	+	5.91505i	−1.02669	+	0.201234i
$865$	0.114575	+	0.114575i	0.00389567	+	0.00389567i
$866$	15.3242	−	54.2193i	0.520737	−	1.84245i
$867$			39.5499i			1.34319i
$868$	−4.05016	−	2.48819i	−0.137471	−	0.0844545i
$869$	60.4710	+	60.4710i	2.05134	+	2.05134i
$870$	−6.95936	−	12.4432i	−0.235944	−	0.421863i
$871$	−3.68827	+	2.45469i	−0.124972	+	0.0831741i
$872$	−27.2217	−	1.11536i	−0.921843	−	0.0377707i
$873$	4.72672	−	4.72672i	0.159975	−	0.159975i
$874$	0.208862	+	0.373441i	0.00706488	+	0.0126318i
$875$	0.241974			0.00818020
$876$	18.8748	−	4.50909i	0.637721	−	0.152348i
$877$	25.8792	−	25.8792i	0.873880	−	0.873880i	−0.119013	−	0.992893i	$-0.537973\pi$
$877$	25.8792	−	25.8792i	0.873880	−	0.873880i	0.992893	+	0.119013i	$0.0379730\pi$
$878$	39.9850	+	11.3011i	1.34943	+	0.381394i
$879$	7.05264	−	7.05264i	0.237880	−	0.237880i
$880$	−19.3015	+	9.78020i	−0.650653	+	0.329691i
$881$			25.6010i			0.862519i	0.902228	+	0.431260i	$0.141931\pi$
$881$			25.6010i			0.862519i	−0.902228	+	0.431260i	$0.858069\pi$
$882$	4.29435	−	15.1940i	0.144598	−	0.511609i
$883$	−9.90603			−0.333365			−0.166682	−	0.986011i	$-0.553305\pi$
$883$	−9.90603			−0.333365			−0.166682	+	0.986011i	$0.553305\pi$
$884$	37.5373	+	34.9047i	1.26251	+	1.17397i
$885$	−13.6031			−0.457263
$886$	−13.0631	+	46.2193i	−0.438865	+	1.55277i
$887$			57.1646i			1.91940i	0.281027	+	0.959700i	$0.409325\pi$
$887$			57.1646i			1.91940i	−0.281027	+	0.959700i	$0.590675\pi$
$888$	−13.9987	−	0.573567i	−0.469764	−	0.0192477i
$889$	−1.33879	+	1.33879i	−0.0449015	+	0.0449015i
$890$	−11.1570	−	3.15334i	−0.373983	−	0.105700i
$891$	−6.07350	+	6.07350i	−0.203470	+	0.203470i
$892$	9.29424	+	38.9052i	0.311194	+	1.30264i
$893$	4.51831			0.151200
$894$	−14.4355	−	25.8103i	−0.482795	−	0.863227i
$895$	4.84752	−	4.84752i	0.162035	−	0.162035i
$896$	−1.13638	−	2.49062i	−0.0379636	−	0.0832059i
$897$	1.01874	+	0.204573i	0.0340146	+	0.00683049i
$898$	18.8521	+	33.7071i	0.629103	+	1.12482i
$899$	−59.3543	−	59.3543i	−1.97958	−	1.97958i
$900$	1.68385	−	2.74090i	0.0561284	−	0.0913633i
$901$			9.21954i			0.307148i
$902$	9.38057	−	33.1898i	0.312339	−	1.10510i
$903$	−1.74271	−	1.74271i	−0.0579939	−	0.0579939i
$904$	28.7254	+	31.1799i	0.955392	+	1.03703i
$905$	−2.01740	−	2.01740i	−0.0670606	−	0.0670606i
$906$	−0.616883	−	1.10297i	−0.0204946	−	0.0366438i
$907$	−40.8307			−1.35576			−0.677880	−	0.735172i	$-0.737101\pi$
$907$	−40.8307			−1.35576			−0.677880	+	0.735172i	$0.737101\pi$
$908$	7.27824	+	30.4664i	0.241537	+	1.01106i
$909$		−	8.78874i		−	0.291504i
$910$	1.09801	+	0.562767i	0.0363987	+	0.0186555i
$911$		−	35.1011i		−	1.16295i	−0.813563	−	0.581476i	$-0.802475\pi$
$911$		−	35.1011i		−	1.16295i	0.813563	−	0.581476i	$-0.197525\pi$
$912$	−5.55386	−	1.81832i	−0.183907	−	0.0602107i
$913$	45.3427			1.50063
$914$	−43.9583	+	24.5855i	−1.45401	+	0.813216i
$915$	2.72148	+	2.72148i	0.0899693	+	0.0899693i
$916$	9.45712	+	39.5870i	0.312472	+	1.30799i
$917$	−0.0531241	−	0.0531241i	−0.00175431	−	0.00175431i
$918$	52.5889	+	14.8634i	1.73569	+	0.490565i
$919$			30.3991i			1.00277i	0.865223	+	0.501386i	$0.167176\pi$
$919$			30.3991i			1.00277i	−0.865223	+	0.501386i	$0.832824\pi$
$920$	0.690397	+	0.0282877i	0.0227617	+	0.000932616i
$921$	−11.1068	−	11.1068i	−0.365981	−	0.365981i
$922$	33.5204	−	18.7477i	1.10394	−	0.617423i
$923$	10.3970	−	6.91961i	0.342220	−	0.227762i
$924$	−2.63134	−	1.61655i	−0.0865648	−	0.0531805i
$925$	2.96916	−	2.96916i	0.0976255	−	0.0976255i
$926$	9.51417	−	5.32119i	0.312655	−	0.174865i
$927$	−11.2317			−0.368898
$928$	−9.29847	−	47.4405i	−0.305237	−	1.55731i
$929$	−30.1014	+	30.1014i	−0.987595	+	0.987595i	−0.999924	−	0.0123289i	$-0.996076\pi$
$929$	−30.1014	+	30.1014i	−0.987595	+	0.987595i	0.0123289	+	0.999924i	$0.496076\pi$
$930$	−4.45671	+	15.7685i	−0.146141	+	0.517069i
$931$	6.07889	−	6.07889i	0.199228	−	0.199228i
$932$	−0.948066	+	1.54322i	−0.0310549	+	0.0505498i
$933$			21.4616i			0.702621i
$934$	18.8419	+	5.32536i	0.616526	+	0.174251i
$935$	38.4517			1.25751
$936$	14.0155	−	8.52125i	0.458110	−	0.278526i
$937$	13.6627			0.446341			0.223171	−	0.974779i	$-0.428359\pi$
$937$	13.6627			0.446341			0.223171	+	0.974779i	$0.428359\pi$
$938$	−0.404642	−	0.114365i	−0.0132120	−	0.00373416i
$939$		−	35.9980i		−	1.17475i
$940$	3.81940	−	6.21705i	0.124575	−	0.202778i
$941$	−25.6578	+	25.6578i	−0.836419	+	0.836419i	−0.988386	−	0.151967i	$-0.951439\pi$
$941$	−25.6578	+	25.6578i	−0.836419	+	0.836419i	0.151967	+	0.988386i	$0.451439\pi$
$942$	2.68209	−	9.48964i	0.0873873	−	0.309189i
$943$	−0.778799	+	0.778799i	−0.0253612	+	0.0253612i
$944$	−43.8359	−	14.3518i	−1.42674	−	0.467112i
$945$	1.31545			0.0427917
$946$	−57.6484	+	32.2422i	−1.87431	+	1.04829i
$947$	3.90870	−	3.90870i	0.127016	−	0.127016i	−0.640741	−	0.767757i	$-0.721373\pi$
$947$	3.90870	−	3.90870i	0.127016	−	0.127016i	0.767757	+	0.640741i	$0.221373\pi$
$948$	31.7805	+	19.5241i	1.03218	+	0.634113i
$949$	−24.6885	+	16.4313i	−0.801424	+	0.533381i
$950$	1.52864	−	0.854953i	0.0495955	−	0.0277383i
$951$	−8.57754	−	8.57754i	−0.278146	−	0.278146i
$952$	−0.199162	+	4.86081i	−0.00645489	+	0.157540i
$953$		−	6.14436i		−	0.199035i	−0.995036	−	0.0995177i	$-0.968270\pi$
$953$		−	6.14436i		−	0.199035i	0.995036	−	0.0995177i	$-0.0317300\pi$
$954$	2.83904	+	0.802410i	0.0919174	+	0.0259790i
$955$	7.99090	+	7.99090i	0.258579	+	0.258579i
$956$	−6.71085	−	28.0913i	−0.217044	−	0.908538i
$957$	−38.5618	−	38.5618i	−1.24653	−	1.24653i
$958$	23.6986	−	13.2544i	0.765667	−	0.428231i
$959$	−0.430812			−0.0139117
$960$	−7.19671	+	6.10486i	−0.232273	+	0.197034i
$961$			65.4747i			2.11209i
$962$	20.3787	−	6.56776i	0.657037	−	0.211753i
$963$			25.6908i			0.827876i
$964$	4.14917	+	17.3682i	0.133636	+	0.559393i
$965$	−8.01748			−0.258092
$966$	0.0481388	+	0.0860710i	0.00154884	+	0.00276929i
$967$	−3.66529	−	3.66529i	−0.117868	−	0.117868i	0.645713	−	0.763581i	$-0.276560\pi$
$967$	−3.66529	−	3.66529i	−0.117868	−	0.117868i	−0.763581	+	0.645713i	$0.776560\pi$
$968$	−37.9897	+	34.9991i	−1.22104	+	1.12491i
$969$	7.34329	+	7.34329i	0.235900	+	0.235900i
$970$	1.59856	−	5.65596i	0.0513268	−	0.181602i
$971$		−	5.51132i		−	0.176867i	−0.996082	−	0.0884334i	$-0.971814\pi$
$971$		−	5.51132i		−	0.176867i	0.996082	−	0.0884334i	$-0.0281860\pi$
$972$	15.1131	−	24.6004i	0.484753	−	0.789060i
$973$	−2.46881	−	2.46881i	−0.0791464	−	0.0791464i
$974$	−10.1550	−	18.1570i	−0.325388	−	0.581786i
$975$	0.837394	−	4.17007i	0.0268181	−	0.133549i
$976$	5.89869	+	11.6412i	0.188812	+	0.372627i
$977$	−33.2448	+	33.2448i	−1.06359	+	1.06359i	−0.0657587	+	0.997836i	$0.520947\pi$
$977$	−33.2448	+	33.2448i	−1.06359	+	1.06359i	−0.997836	+	0.0657587i	$0.979053\pi$
$978$	−5.23967	−	9.36840i	−0.167546	−	0.299568i
$979$	−44.3482			−1.41738
$980$	−3.22577	−	13.5029i	−0.103044	−	0.431335i
$981$	10.9551	−	10.9551i	0.349769	−	0.349769i
$982$	−20.8761	−	5.90030i	−0.666184	−	0.188286i
$983$	−37.6373	+	37.6373i	−1.20044	+	1.20044i	−0.226413	+	0.974031i	$0.572700\pi$
$983$	−37.6373	+	37.6373i	−1.20044	+	1.20044i	−0.974031	+	0.226413i	$0.927300\pi$
$984$	0.615825	−	15.0300i	0.0196318	−	0.479139i
$985$		−	4.47124i		−	0.142466i
$986$	−23.3653	+	82.6698i	−0.744103	+	2.63274i
$987$	1.04138			0.0331476
$988$	8.92492	−	0.324335i	0.283940	−	0.0103185i
$989$	2.10928			0.0670713
$990$	3.34659	−	11.8407i	0.106362	−	0.376323i
$991$			33.6708i			1.06959i	0.844982	+	0.534794i	$0.179611\pi$
$991$			33.6708i			1.06959i	−0.844982	+	0.534794i	$0.820389\pi$
$992$	−30.9981	+	46.1119i	−0.984191	+	1.46405i
$993$	2.44513	−	2.44513i	0.0775939	−	0.0775939i
$994$	1.14066	+	0.322388i	0.0361794	+	0.0102255i
$995$	1.66031	−	1.66031i	0.0526353	−	0.0526353i
$996$	19.2347	−	4.59507i	0.609476	−	0.145600i
$997$	11.7916			0.373442			0.186721	−	0.982413i	$-0.440214\pi$
$997$	11.7916			0.373442			0.186721	+	0.982413i	$0.440214\pi$
$998$	−16.2648	−	29.0811i	−0.514854	−	0.920547i
$999$	16.1414	−	16.1414i	0.510691	−	0.510691i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	260.2.j.a.31.2	✓	56
4.3	odd	2	inner	260.2.j.a.31.17	yes	56
13.8	odd	4	inner	260.2.j.a.151.17	yes	56
52.47	even	4	inner	260.2.j.a.151.2	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.j.a.31.2	✓	56	1.1	even	1	trivial
260.2.j.a.31.17	yes	56	4.3	odd	2	inner
260.2.j.a.151.2	yes	56	52.47	even	4	inner
260.2.j.a.151.17	yes	56	13.8	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	260.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36090 - 0.384637i) q^{2} -1.17966i q^{3} +(1.70411 + 1.04691i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(-0.453740 + 1.60540i) q^{6} +(0.171101 - 0.171101i) q^{7} +(-1.91645 - 2.08020i) q^{8} +1.60841 q^{9} +O(q^{10})\)	\(q+(-1.36090 - 0.384637i) q^{2} -1.17966i q^{3} +(1.70411 + 1.04691i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(-0.453740 + 1.60540i) q^{6} +(0.171101 - 0.171101i) q^{7} +(-1.91645 - 2.08020i) q^{8} +1.60841 q^{9} +(1.23428 - 0.690324i) q^{10} +(3.82508 - 3.82508i) q^{11} +(1.23499 - 2.01027i) q^{12} +(-0.709862 + 3.53498i) q^{13} +(-0.298664 + 0.167040i) q^{14} +(0.834144 + 0.834144i) q^{15} +(1.80797 + 3.56809i) q^{16} -7.10821i q^{17} +(-2.18888 - 0.618653i) q^{18} +(-0.875738 - 0.875738i) q^{19} +(-1.94526 + 0.464712i) q^{20} +(-0.201841 - 0.201841i) q^{21} +(-6.67683 + 3.73429i) q^{22} +0.244297 q^{23} +(-2.45393 + 2.26075i) q^{24} -1.00000i q^{25} +(2.32574 - 4.53772i) q^{26} -5.43634i q^{27} +(0.470702 - 0.112448i) q^{28} +8.54595 q^{29} +(-0.814346 - 1.45603i) q^{30} +(-6.94531 - 6.94531i) q^{31} +(-1.08806 - 5.55123i) q^{32} +(-4.51229 - 4.51229i) q^{33} +(-2.73408 + 9.67357i) q^{34} +0.241974i q^{35} +(2.74090 + 1.68385i) q^{36} +(2.96916 + 2.96916i) q^{37} +(0.854953 + 1.52864i) q^{38} +(4.17007 + 0.837394i) q^{39} +(2.82606 + 0.115792i) q^{40} +(-3.18792 + 3.18792i) q^{41} +(0.197050 + 0.352321i) q^{42} +8.63409 q^{43} +(10.5229 - 2.51385i) q^{44} +(-1.13732 + 1.13732i) q^{45} +(-0.332464 - 0.0939657i) q^{46} +(-2.57972 + 2.57972i) q^{47} +(4.20912 - 2.13279i) q^{48} +6.94145i q^{49} +(-0.384637 + 1.36090i) q^{50} -8.38526 q^{51} +(-4.91048 + 5.28083i) q^{52} -1.29703 q^{53} +(-2.09102 + 7.39833i) q^{54} +5.40948i q^{55} +(-0.683831 - 0.0280186i) q^{56} +(-1.03307 + 1.03307i) q^{57} +(-11.6302 - 3.28709i) q^{58} +(-8.15392 + 8.15392i) q^{59} +(0.548201 + 2.29474i) q^{60} +3.26260 q^{61} +(6.78047 + 12.1233i) q^{62} +(0.275200 - 0.275200i) q^{63} +(-0.654470 + 7.97318i) q^{64} +(-1.99766 - 3.00156i) q^{65} +(4.40519 + 7.87638i) q^{66} +(0.868882 + 0.868882i) q^{67} +(7.44163 - 12.1132i) q^{68} -0.288187i q^{69} +(0.0930720 - 0.329302i) q^{70} +(-2.44932 - 2.44932i) q^{71} +(-3.08242 - 3.34581i) q^{72} +(5.81613 + 5.81613i) q^{73} +(-2.89869 - 5.18279i) q^{74} -1.17966 q^{75} +(-0.575537 - 2.40917i) q^{76} -1.30895i q^{77} +(-5.35296 - 2.74358i) q^{78} +15.8091i q^{79} +(-3.80145 - 1.24459i) q^{80} -1.58781 q^{81} +(5.56464 - 3.11226i) q^{82} +(5.92703 + 5.92703i) q^{83} +(-0.132650 - 0.555267i) q^{84} +(5.02626 + 5.02626i) q^{85} +(-11.7502 - 3.32099i) q^{86} -10.0813i q^{87} +(-15.2875 - 0.626375i) q^{88} +(-5.79703 - 5.79703i) q^{89} +(1.98523 - 1.11032i) q^{90} +(0.483381 + 0.726298i) q^{91} +(0.416309 + 0.255756i) q^{92} +(-8.19309 + 8.19309i) q^{93} +(4.50300 - 2.51849i) q^{94} +1.23848 q^{95} +(-6.54855 + 1.28353i) q^{96} +(2.93876 - 2.93876i) q^{97} +(2.66994 - 9.44663i) q^{98} +(6.15229 - 6.15229i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 12 q^{6} + 12 q^{8} - 56 q^{9}+O(q^{10}) \) 56 * q - 12 * q^6 + 12 * q^8 - 56 * q^9	\( 56 q - 12 q^{6} + 12 q^{8} - 56 q^{9} + 16 q^{14} - 12 q^{18} - 8 q^{20} - 16 q^{21} - 40 q^{24} - 16 q^{26} - 44 q^{28} + 40 q^{32} - 4 q^{34} + 16 q^{37} + 8 q^{41} + 8 q^{42} + 28 q^{44} - 12 q^{46} + 104 q^{48} + 56 q^{52} - 16 q^{53} + 20 q^{54} - 48 q^{57} - 4 q^{58} + 16 q^{61} - 8 q^{65} + 64 q^{66} + 24 q^{68} - 8 q^{70} - 32 q^{72} + 48 q^{73} - 136 q^{74} - 88 q^{76} + 52 q^{78} - 32 q^{80} + 56 q^{81} - 20 q^{84} - 64 q^{86} - 8 q^{89} - 88 q^{92} - 48 q^{93} - 16 q^{94} - 4 q^{96} - 32 q^{97} + 16 q^{98}+O(q^{100}) \) 56 * q - 12 * q^6 + 12 * q^8 - 56 * q^9 + 16 * q^14 - 12 * q^18 - 8 * q^20 - 16 * q^21 - 40 * q^24 - 16 * q^26 - 44 * q^28 + 40 * q^32 - 4 * q^34 + 16 * q^37 + 8 * q^41 + 8 * q^42 + 28 * q^44 - 12 * q^46 + 104 * q^48 + 56 * q^52 - 16 * q^53 + 20 * q^54 - 48 * q^57 - 4 * q^58 + 16 * q^61 - 8 * q^65 + 64 * q^66 + 24 * q^68 - 8 * q^70 - 32 * q^72 + 48 * q^73 - 136 * q^74 - 88 * q^76 + 52 * q^78 - 32 * q^80 + 56 * q^81 - 20 * q^84 - 64 * q^86 - 8 * q^89 - 88 * q^92 - 48 * q^93 - 16 * q^94 - 4 * q^96 - 32 * q^97 + 16 * q^98

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