LMFDB - Embedded newform 260.2.j.a.31.17

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			31.17
Character	$\chi$	$=$	260.31
Dual form			260.2.j.a.151.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.384637 + 1.36090i) q^{2} +1.17966i q^{3} +(-1.70411 + 1.04691i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(-1.60540 + 0.453740i) q^{6} +(-0.171101 + 0.171101i) q^{7} +(-2.08020 - 1.91645i) q^{8} +1.60841 q^{9} +O(q^{10})$	\(q+(0.384637 + 1.36090i) q^{2} +1.17966i q^{3} +(-1.70411 + 1.04691i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(-1.60540 + 0.453740i) q^{6} +(-0.171101 + 0.171101i) q^{7} +(-2.08020 - 1.91645i) 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} +(0.618653 + 2.18888i) q^{18} +(0.875738 + 0.875738i) q^{19} +(0.464712 - 1.94526i) q^{20} +(-0.201841 - 0.201841i) q^{21} +(-6.67683 - 3.73429i) q^{22} -0.244297 q^{23} +(2.26075 - 2.45393i) q^{24} -1.00000i q^{25} +(-5.08380 + 0.393632i) q^{26} +5.43634i q^{27} +(0.112448 - 0.470702i) q^{28} +8.54595 q^{29} +(0.814346 - 1.45603i) q^{30} +(6.94531 + 6.94531i) q^{31} +(5.55123 + 1.08806i) q^{32} +(-4.51229 - 4.51229i) q^{33} +(9.67357 - 2.73408i) 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} +(2.51385 - 10.5229i) q^{44} +(-1.13732 + 1.13732i) q^{45} +(-0.0939657 - 0.332464i) q^{46} +(2.57972 - 2.57972i) q^{47} +(4.20912 + 2.13279i) q^{48} +6.94145i q^{49} +(1.36090 - 0.384637i) q^{50} +8.38526 q^{51} +(-2.49111 - 6.76715i) q^{52} -1.29703 q^{53} +(-7.39833 + 2.09102i) q^{54} -5.40948i q^{55} +(0.683831 - 0.0280186i) q^{56} +(-1.03307 + 1.03307i) q^{57} +(3.28709 + 11.6302i) q^{58} +(8.15392 - 8.15392i) q^{59} +(2.29474 + 0.548201i) 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} +(0.329302 - 0.0930720i) q^{70} +(2.44932 + 2.44932i) q^{71} +(-3.34581 - 3.08242i) q^{72} +(5.81613 + 5.81613i) q^{73} +(-2.89869 + 5.18279i) q^{74} +1.17966 q^{75} +(-2.40917 - 0.575537i) q^{76} -1.30895i q^{77} +(-0.464352 - 5.99715i) q^{78} -15.8091i q^{79} +(1.24459 + 3.80145i) q^{80} -1.58781 q^{81} +(-5.56464 - 3.11226i) q^{82} +(-5.92703 - 5.92703i) q^{83} +(0.555267 + 0.132650i) q^{84} +(5.02626 + 5.02626i) q^{85} +(-3.32099 - 11.7502i) 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} +(-1.28353 + 6.54855i) q^{96} +(2.93876 - 2.93876i) q^{97} +(-9.44663 + 2.66994i) 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 $

$2$	0.384637	+	1.36090i	0.271979	+	0.962303i
$2$	0.384637	+	1.36090i	0.271979	+	0.962303i
$3$			1.17966i			0.681076i	0.940231	+	0.340538i	$0.110609\pi$
$3$			1.17966i			0.681076i	−0.940231	+	0.340538i	$0.889391\pi$
$4$	−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
$6$	−1.60540	+	0.453740i	−0.655402	+	0.185239i
$7$	−0.171101	+	0.171101i	−0.0646702	+	0.0646702i	−0.738702	−	0.674032i	$-0.764561\pi$
$7$	−0.171101	+	0.171101i	−0.0646702	+	0.0646702i	0.674032	+	0.738702i	$0.264561\pi$
$8$	−2.08020	−	1.91645i	−0.735462	−	0.677566i
$9$	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	$0.553544\pi$
$11$	−3.82508	+	3.82508i	−1.15331	+	1.15331i	−0.985886	+	0.167420i	$0.946456\pi$
$12$	−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	$-0.330786\pi$
$18$	0.618653	+	2.18888i	0.145818	+	0.515925i
$19$	0.875738	+	0.875738i	0.200908	+	0.200908i	0.800389	−	0.599481i	$-0.204626\pi$
$19$	0.875738	+	0.875738i	0.200908	+	0.200908i	−0.599481	+	0.800389i	$0.704626\pi$
$20$	0.464712	−	1.94526i	0.103913	−	0.434974i
$21$	−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	$-0.508108\pi$
$23$	−0.244297			−0.0509394			−0.0254697	+	0.999676i	$0.508108\pi$
$24$	2.26075	−	2.45393i	0.461474	−	0.500906i
$25$		−	1.00000i		−	0.200000i
$26$	−5.08380	+	0.393632i	−0.997016	+	0.0771977i
$27$			5.43634i			1.04623i
$28$	0.112448	−	0.470702i	0.0212507	−	0.0889543i
$29$	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	$0.0938407\pi$
$31$	6.94531	+	6.94531i	1.24741	+	1.24741i	0.290557	+	0.956858i	$0.406159\pi$
$32$	5.55123	+	1.08806i	0.981328	+	0.192343i
$33$	−4.51229	−	4.51229i	−0.785489	−	0.785489i
$34$	9.67357	−	2.73408i	1.65900	−	0.468891i
$35$		−	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	$-0.728742\pi$
$43$	−8.63409			−1.31669			−0.658343	+	0.752718i	$0.728742\pi$
$44$	2.51385	−	10.5229i	0.378977	−	1.58638i
$45$	−1.13732	+	1.13732i	−0.169541	+	0.169541i
$46$	−0.0939657	−	0.332464i	−0.0138545	−	0.0490192i
$47$	2.57972	−	2.57972i	0.376290	−	0.376290i	−0.493472	−	0.869762i	$-0.664272\pi$
$47$	2.57972	−	2.57972i	0.376290	−	0.376290i	0.869762	+	0.493472i	$0.164272\pi$
$48$	4.20912	+	2.13279i	0.607534	+	0.307842i
$49$			6.94145i			0.991636i
$50$	1.36090	−	0.384637i	0.192461	−	0.0543959i
$51$	8.38526			1.17417
$52$	−2.49111	−	6.76715i	−0.345455	−	0.938435i
$53$	−1.29703			−0.178160			−0.0890802	−	0.996024i	$-0.528393\pi$
$53$	−1.29703			−0.178160			−0.0890802	+	0.996024i	$0.528393\pi$
$54$	−7.39833	+	2.09102i	−1.00679	+	0.284552i
$55$		−	5.40948i		−	0.729415i
$56$	0.683831	−	0.0280186i	0.0913808	−	0.00374415i
$57$	−1.03307	+	1.03307i	−0.136834	+	0.136834i
$58$	3.28709	+	11.6302i	0.431616	+	1.52712i
$59$	8.15392	−	8.15392i	1.06155	−	1.06155i	0.0635727	−	0.997977i	$-0.479751\pi$
$59$	8.15392	−	8.15392i	1.06155	−	1.06155i	0.997977	−	0.0635727i	$-0.0202495\pi$
$60$	2.29474	+	0.548201i	0.296250	+	0.0707725i
$61$	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	0.652037	−	0.758187i	$-0.273915\pi$
$67$	−0.868882	−	0.868882i	−0.106151	−	0.106151i	−0.758187	+	0.652037i	$0.773915\pi$
$68$	7.44163	+	12.1132i	0.902430	+	1.46894i
$69$		−	0.288187i		−	0.0346936i
$70$	0.329302	−	0.0930720i	0.0393592	−	0.0111242i
$71$	2.44932	+	2.44932i	0.290680	+	0.290680i	0.837349	−	0.546669i	$-0.184104\pi$
$71$	2.44932	+	2.44932i	0.290680	+	0.290680i	−0.546669	+	0.837349i	$0.684104\pi$
$72$	−3.34581	−	3.08242i	−0.394307	−	0.363267i
$73$	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
$76$	−2.40917	−	0.575537i	−0.276351	−	0.0660186i
$77$		−	1.30895i		−	0.149169i
$78$	−0.464352	−	5.99715i	−0.0525775	−	0.679044i
$79$		−	15.8091i		−	1.77866i	−0.457265	−	0.889330i	$-0.651171\pi$
$79$		−	15.8091i		−	1.77866i	0.457265	−	0.889330i	$-0.348829\pi$
$80$	1.24459	+	3.80145i	0.139149	+	0.425015i
$81$	−1.58781			−0.176423
$82$	−5.56464	−	3.11226i	−0.614512	−	0.343691i
$83$	−5.92703	−	5.92703i	−0.650576	−	0.650576i	0.302556	−	0.953132i	$-0.402160\pi$
$83$	−5.92703	−	5.92703i	−0.650576	−	0.650576i	−0.953132	+	0.302556i	$0.902160\pi$
$84$	0.555267	+	0.132650i	0.0605846	+	0.0144733i
$85$	5.02626	+	5.02626i	0.545175	+	0.545175i
$86$	−3.32099	−	11.7502i	−0.358112	−	1.26705i
$87$			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
$96$	−1.28353	+	6.54855i	−0.131000	+	0.668359i
$97$	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	$0.182331\pi$
$98$	−9.44663	+	2.66994i	−0.954254	+	0.269704i
$99$	−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	$-0.0876377\pi$
$102$	3.22528	+	11.4115i	0.319350	+	1.12991i
$103$	6.98313			0.688068			0.344034	−	0.938957i	$-0.388206\pi$
$103$	6.98313			0.688068			0.344034	+	0.938957i	$0.388206\pi$
$104$	8.25126	−	5.99306i	0.809102	−	0.587668i
$105$	0.285446			0.0278567
$106$	−0.498885	−	1.76513i	−0.0484560	−	0.171444i
$107$		−	15.9729i		−	1.54415i	−0.635529	−	0.772077i	$-0.719218\pi$
$107$		−	15.9729i		−	1.54415i	0.635529	−	0.772077i	$-0.280782\pi$
$108$	−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	$0.0973802\pi$
$110$	7.36178	−	2.08069i	0.701918	−	0.198386i
$111$	−3.50260	+	3.50260i	−0.332452	+	0.332452i
$112$	0.301157	+	0.919850i	0.0284567	+	0.0869177i
$113$	−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
$122$	1.25492	+	4.44008i	0.113615	+	0.401986i
$123$	−3.76066	−	3.76066i	−0.339087	−	0.339087i
$124$	−19.1067	−	4.56447i	−1.71583	−	0.409902i
$125$	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	$-0.387147\pi$
$127$	7.82453			0.694315			0.347157	+	0.937807i	$0.387147\pi$
$128$	−10.5990	+	3.95745i	−0.936827	+	0.349793i
$129$		−	10.1853i		−	0.896764i
$130$	3.31645	−	3.87313i	0.290872	−	0.339696i
$131$			0.310483i			0.0271271i	0.999908	+	0.0135635i	$0.00431754\pi$
$131$			0.310483i			0.0271271i	−0.999908	+	0.0135635i	$0.995682\pi$
$132$	12.4134	+	2.96549i	1.08045	+	0.258112i
$133$	−0.299680			−0.0259855
$134$	0.848259	−	1.51667i	0.0732784	−	0.131020i
$135$	−3.84408	−	3.84408i	−0.330845	−	0.330845i
$136$	−13.6225	+	14.7865i	−1.16812	+	1.26793i
$137$	−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	$0.774233\pi$
$138$	0.392194	−	0.110847i	0.0333858	−	0.00943596i
$139$			14.4289i			1.22385i	0.790917	+	0.611923i	$0.209604\pi$
$139$			14.4289i			1.22385i	−0.790917	+	0.611923i	$0.790396\pi$
$140$	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
$148$	−8.16822	−	1.95134i	−0.671423	−	0.160399i
$149$	−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	$0.991328\pi$
$150$	0.453740	+	1.60540i	0.0370477	+	0.131080i
$151$	0.535648	−	0.535648i	0.0435904	−	0.0435904i	−0.684976	−	0.728566i	$-0.740187\pi$
$151$	0.535648	−	0.535648i	0.0435904	−	0.0435904i	0.728566	+	0.684976i	$0.240187\pi$
$152$	−0.143406	−	3.50002i	−0.0116318	−	0.283889i
$153$		−	11.4329i		−	0.924294i
$154$	1.78136	−	0.503472i	0.143546	−	0.0405709i
$155$	−9.82215			−0.788934
$156$	7.98293	−	2.93866i	0.639146	−	0.235281i
$157$	−5.91108			−0.471755			−0.235878	−	0.971783i	$-0.575796\pi$
$157$	−5.91108			−0.471755			−0.235878	+	0.971783i	$0.575796\pi$
$158$	21.5146	−	6.08076i	1.71161	−	0.483759i
$159$		−	1.53005i		−	0.121341i
$160$	−4.69468	+	3.15594i	−0.371147	+	0.249499i
$161$	0.0417995	−	0.0417995i	0.00329426	−	0.00329426i
$162$	−0.610730	−	2.16085i	−0.0479835	−	0.169773i
$163$	4.54967	−	4.54967i	0.356358	−	0.356358i	−0.506111	−	0.862468i	$-0.668917\pi$
$163$	4.54967	−	4.54967i	0.356358	−	0.356358i	0.862468	+	0.506111i	$0.168917\pi$
$164$	2.09511	−	8.77002i	0.163600	−	0.684823i
$165$	6.38134			0.496787
$166$	5.78635	−	10.3459i	0.449108	−	0.802994i
$167$	−4.08388	+	4.08388i	−0.316020	+	0.316020i	−0.847236	−	0.531216i	$-0.821735\pi$
$167$	−4.08388	+	4.08388i	−0.316020	+	0.316020i	0.531216	+	0.847236i	$0.321735\pi$
$168$	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	$-0.00196067\pi$
$174$	−13.7197	+	3.87764i	−1.04008	+	0.293963i
$175$	0.171101	+	0.171101i	0.0129340	+	0.0129340i
$176$	6.73258	+	20.5639i	0.507487	+	1.55006i
$177$	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	$-0.417530\pi$
$179$	6.85543			0.512399			0.256199	+	0.966624i	$0.417530\pi$
$180$	0.747446	−	3.12877i	0.0557113	−	0.233205i
$181$			2.85303i			0.212064i	0.994363	+	0.106032i	$0.0338146\pi$
$181$			2.85303i			0.212064i	−0.994363	+	0.106032i	$0.966185\pi$
$182$	0.802494	−	0.937196i	0.0594848	−	0.0694696i
$183$			3.84875i			0.284508i
$184$	0.508187	+	0.468182i	0.0374640	+	0.0345148i
$185$	−4.19903			−0.308719
$186$	−14.3014	−	7.99863i	−1.04863	−	0.586488i
$187$	27.1895	+	27.1895i	1.98829	+	1.98829i
$188$	−1.69539	+	7.09684i	−0.123649	+	0.517590i
$189$	−0.930165	−	0.930165i	−0.0676596	−	0.0676596i
$190$	−0.476366	−	1.68545i	−0.0345592	−	0.122275i
$191$			11.3008i			0.817700i	0.912602	+	0.408850i	$0.134070\pi$
$191$			11.3008i			0.817700i	−0.912602	+	0.408850i	$0.865930\pi$
$192$	−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	$-0.473478\pi$
$199$	2.34803			0.166447			0.0832237	+	0.996531i	$0.473478\pi$
$200$	−1.91645	+	2.08020i	−0.135513	+	0.147092i
$201$	1.02498	−	1.02498i	0.0722967	−	0.0722967i
$202$	7.43632	−	2.10175i	0.523217	−	0.147879i
$203$	−1.46222	+	1.46222i	−0.102628	+	0.102628i
$204$	−14.2894	+	8.77858i	−1.00046	+	0.614623i
$205$		−	4.50840i		−	0.314880i
$206$	2.68597	+	9.50335i	0.187140	+	0.662130i
$207$	−0.392929			−0.0273104
$208$	11.3297	+	8.92400i	0.785574	+	0.618768i
$209$	−6.69954			−0.463417
$210$	0.109793	+	0.388464i	0.00757645	+	0.0268066i
$211$		−	16.4039i		−	1.12929i	−0.825333	−	0.564646i	$-0.809013\pi$
$211$		−	16.4039i		−	1.12929i	0.825333	−	0.564646i	$-0.190987\pi$
$212$	2.21028	−	1.35787i	0.151802	−	0.0932587i
$213$	−2.88936	+	2.88936i	−0.197975	+	0.197975i
$214$	21.7375	−	6.14375i	1.48594	−	0.419978i
$215$	6.10522	−	6.10522i	0.416373	−	0.416373i
$216$	10.4185	−	11.3087i	0.708886	−	0.769459i
$217$	−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	0.0516385	−	0.998666i	$-0.483556\pi$
$223$	−14.1421	−	14.1421i	−0.947027	−	0.947027i	−0.998666	+	0.0516385i	$0.983556\pi$
$224$	−1.13599	+	0.763654i	−0.0759015	+	0.0510238i
$225$		−	1.60841i		−	0.107227i
$226$	−5.76528	−	20.3984i	−0.383501	−	1.35688i
$227$	−11.0746	−	11.0746i	−0.735046	−	0.735046i	0.236569	−	0.971615i	$-0.423977\pi$
$227$	−11.0746	−	11.0746i	−0.735046	−	0.735046i	−0.971615	+	0.236569i	$0.923977\pi$
$228$	0.678937	−	2.84200i	0.0449637	−	0.188216i
$229$	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
$232$	−17.7773	−	16.3778i	−1.16714	−	1.07526i
$233$			0.905587i			0.0593270i	0.999560	+	0.0296635i	$0.00944357\pi$
$233$			0.905587i			0.0593270i	−0.999560	+	0.0296635i	$0.990556\pi$
$234$	−8.17682	+	0.633121i	−0.534536	+	0.0413884i
$235$			3.64827i			0.237987i
$236$	−5.35877	+	22.4316i	−0.348826	+	1.46017i
$237$	18.6493			1.21140
$238$	−1.18736	+	2.12296i	−0.0769648	+	0.137611i
$239$	10.2112	+	10.2112i	0.660511	+	0.660511i	0.955500	−	0.294990i	$-0.0953162\pi$
$239$	10.2112	+	10.2112i	0.660511	+	0.660511i	−0.294990	+	0.955500i	$0.595316\pi$
$240$	−4.48441	+	1.46819i	−0.289467	+	0.0947711i
$241$	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	$0.657154\pi$
$242$	24.8535	−	7.02444i	1.59764	−	0.451548i
$243$			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	$-0.463811\pi$
$251$	3.59463			0.226891			0.113446	+	0.993544i	$0.463811\pi$
$252$	0.180862	−	0.757080i	0.0113932	−	0.0476916i
$253$	0.934456	−	0.934456i	0.0587488	−	0.0587488i
$254$	3.00960	+	10.6484i	0.188839	+	0.668141i
$255$	−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	$0.875426\pi$
$258$	13.8612	−	3.91763i	0.862958	−	0.243901i
$259$	−1.01606			−0.0631346
$260$	6.54658	+	3.02362i	0.406002	+	0.187517i
$261$	13.7454			0.850816
$262$	−0.422538	+	0.119423i	−0.0261045	+	0.00737800i
$263$		−	15.9843i		−	0.985636i	−0.870132	−	0.492818i	$-0.835967\pi$
$263$		−	15.9843i		−	0.985636i	0.870132	−	0.492818i	$-0.164033\pi$
$264$	0.738909	+	18.0340i	0.0454767	+	1.10992i
$265$	0.917137	−	0.917137i	0.0563393	−	0.0563393i
$266$	−0.115268	−	0.407835i	−0.00706753	−	0.0250060i
$267$	6.83851	−	6.83851i	0.418510	−	0.418510i
$268$	2.39031	+	0.571031i	0.146011	+	0.0348813i
$269$	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	−0.857427	−	0.514606i	$-0.827938\pi$
$271$	−5.64353	+	5.64353i	−0.342820	+	0.342820i	0.514606	+	0.857427i	$0.327938\pi$
$272$	−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	$-0.0369958\pi$
$278$	−19.6364	+	5.54990i	−1.17771	+	0.332861i
$279$	11.1709	+	11.1709i	0.668783	+	0.668783i
$280$	−0.463729	+	0.503354i	−0.0277131	+	0.0300811i
$281$	−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	$-0.396796\pi$
$283$	10.7185			0.637147			0.318573	+	0.947898i	$0.396796\pi$
$284$	−6.73810	−	1.60970i	−0.399833	−	0.0955178i
$285$		−	1.46098i		−	0.0865412i
$286$	17.9403	−	20.9516i	1.06083	−	1.23890i
$287$		−	1.09091i		−	0.0643946i
$288$	8.92863	+	1.75004i	0.526125	+	0.103122i
$289$	−33.5266			−1.97215
$290$	−10.5481	−	5.89947i	−0.619406	−	0.346429i
$291$	3.46673	+	3.46673i	0.203223	+	0.203223i
$292$	−16.0003	−	3.82237i	−0.936344	−	0.223687i
$293$	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	$0.670565\pi$
$294$	−3.14961	−	11.1438i	−0.183689	−	0.649919i
$295$			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
$304$	4.70802	−	1.54140i	0.270024	−	0.0884052i
$305$	−2.30701	+	2.30701i	−0.132099	+	0.132099i
$306$	15.5590	−	4.39751i	0.889451	−	0.251389i
$307$	−9.41527	+	9.41527i	−0.537358	+	0.537358i	−0.922752	−	0.385394i	$-0.874065\pi$
$307$	−9.41527	+	9.41527i	−0.537358	+	0.537358i	0.385394	+	0.922752i	$0.374065\pi$
$308$	1.37035	+	2.23060i	0.0780830	+	0.127100i
$309$			8.23770i			0.468626i
$310$	−3.77796	−	13.3670i	−0.214574	−	0.759194i
$311$	18.1931			1.03163			0.515817	−	0.856699i	$-0.327488\pi$
$311$	18.1931			1.03163			0.515817	+	0.856699i	$0.327488\pi$
$312$	7.06976	+	9.73366i	0.400246	+	0.551060i
$313$	30.5156			1.72484			0.862422	−	0.506190i	$-0.168946\pi$
$313$	30.5156			1.72484			0.862422	+	0.506190i	$0.168946\pi$
$314$	−2.27362	−	8.04440i	−0.128308	−	0.453972i
$315$		−	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	$0.156751\pi$
$318$	2.08225	−	0.588514i	0.116767	−	0.0330022i
$319$	−32.6890	+	32.6890i	−1.83023	+	1.83023i
$320$	−6.10067	−	5.17511i	−0.341038	−	0.289298i
$321$	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
$330$	2.45450	+	8.68438i	0.135116	+	0.478059i
$331$	−2.07275	−	2.07275i	−0.113928	−	0.113928i	0.647844	−	0.761773i	$-0.275671\pi$
$331$	−2.07275	−	2.07275i	−0.113928	−	0.113928i	−0.761773	+	0.647844i	$0.775671\pi$
$332$	16.3053	+	3.89526i	0.894872	+	0.213780i
$333$	4.77562	+	4.77562i	0.261703	+	0.261703i
$334$	−7.12858	−	3.98695i	−0.390058	−	0.218156i
$335$	1.22878			0.0671356
$336$	−1.08511	+	0.355263i	−0.0591975	+	0.0193812i
$337$		−	21.2847i		−	1.15945i	−0.814811	−	0.579726i	$-0.803160\pi$
$337$		−	21.2847i		−	1.15945i	0.814811	−	0.579726i	$-0.196840\pi$
$338$	2.21731	−	18.2506i	0.120606	−	0.992700i
$339$		−	17.6818i		−	0.960341i
$340$	−13.8273	−	3.30327i	−0.749892	−	0.179145i
$341$	−53.1328			−2.87730
$342$	−1.37511	+	2.45867i	−0.0743575	+	0.132950i
$343$	−2.38540	−	2.38540i	−0.128799	−	0.128799i
$344$	17.9606	+	16.5468i	0.968373	+	0.892142i
$345$	0.203779	+	0.203779i	0.0109711	+	0.0109711i
$346$	0.220512	−	0.0623241i	0.0118548	−	0.00335056i
$347$		−	25.2092i		−	1.35330i	−0.736303	−	0.676652i	$-0.763430\pi$
$347$		−	25.2092i		−	1.35330i	0.736303	−	0.676652i	$-0.236570\pi$
$348$	−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
$356$	15.9477	+	3.80982i	0.845227	+	0.201920i
$357$	−1.43473	+	1.43473i	−0.0759338	+	0.0759338i
$358$	2.63685	+	9.32956i	0.139362	+	0.493083i
$359$	−17.9020	+	17.9020i	−0.944832	+	0.944832i	−0.998556	−	0.0537235i	$-0.982891\pi$
$359$	−17.9020	+	17.9020i	−0.944832	+	0.944832i	0.0537235	+	0.998556i	$0.482891\pi$
$360$	4.54545	−	0.186241i	0.239566	−	0.00981575i
$361$		−	17.4662i		−	0.919272i
$362$	−3.88270	+	1.09738i	−0.204070	+	0.0576771i
$363$	21.5435			1.13074
$364$	1.58410	+	0.731635i	0.0830294	+	0.0383481i
$365$	−8.22524			−0.430529
$366$	−5.23777	+	1.48037i	−0.273783	+	0.0773803i
$367$			5.24363i			0.273715i	0.990591	+	0.136858i	$0.0437003\pi$
$367$			5.24363i			0.273715i	−0.990591	+	0.136858i	$0.956300\pi$
$368$	−0.441682	+	0.871673i	−0.0230243	+	0.0454391i
$369$	−5.12747	+	5.12747i	−0.266926	+	0.266926i
$370$	−1.61510	−	5.71447i	−0.0839652	−	0.297081i
$371$	0.221923	−	0.221923i	0.0115217	−	0.0115217i
$372$	5.38452	−	22.5393i	0.279174	−	1.16861i
$373$	−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	0.337101	−	0.941469i	$-0.390554\pi$
$379$	−11.7658	−	11.7658i	−0.604368	−	0.604368i	−0.941469	+	0.337101i	$0.890554\pi$
$380$	2.11051	−	1.29657i	0.108267	−	0.0665128i
$381$			9.23027i			0.472881i
$382$	−15.3793	+	4.34672i	−0.786875	+	0.222397i
$383$	13.6517	+	13.6517i	0.697569	+	0.697569i	0.963886	−	0.266316i	$-0.0858066\pi$
$383$	13.6517	+	13.6517i	0.697569	+	0.697569i	−0.266316	+	0.963886i	$0.585807\pi$
$384$	−4.66844	−	12.5032i	−0.238235	−	0.638050i
$385$	0.925569	+	0.925569i	0.0471714	+	0.0471714i
$386$	−5.53465	+	9.89583i	−0.281706	+	0.503685i
$387$	−13.8871			−0.705922
$388$	−1.93136	+	8.08457i	−0.0980499	+	0.410432i
$389$			8.98539i			0.455577i	0.973711	+	0.227789i	$0.0731495\pi$
$389$			8.98539i			0.455577i	−0.973711	+	0.227789i	$0.926850\pi$
$390$	4.56897	+	3.91228i	0.231359	+	0.198106i
$391$			1.73651i			0.0878193i
$392$	13.3029	−	14.4396i	0.671898	−	0.729310i
$393$	−0.366264			−0.0184756
$394$	−5.51878	−	3.08661i	−0.278032	−	0.155501i
$395$	11.1787	+	11.1787i	0.562462	+	0.562462i
$396$	4.04330	−	16.9250i	0.203183	−	0.850515i
$397$	−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	$0.903222\pi$
$398$	0.903139	+	3.19544i	0.0452703	+	0.160173i
$399$		−	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
$408$	−17.4430	−	16.0699i	−0.863558	−	0.795578i
$409$	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	$0.222955\pi$
$410$	6.13549	−	1.73410i	0.303010	−	0.0856410i
$411$	1.48512	−	1.48512i	0.0732555	−	0.0732555i
$412$	−11.9000	+	7.31068i	−0.586271	+	0.360171i
$413$			2.79029i			0.137301i
$414$	−0.151135	−	0.534738i	−0.00742788	−	0.0262809i
$415$	8.38208			0.411460
$416$	−7.78686	+	18.8511i	−0.381782	+	0.924252i
$417$	−17.0212			−0.833533
$418$	−2.57689	−	9.11742i	−0.126040	−	0.445948i
$419$		−	7.49789i		−	0.366296i	−0.983085	−	0.183148i	$-0.941371\pi$
$419$		−	7.49789i		−	0.366296i	0.983085	−	0.183148i	$-0.0586287\pi$
$420$	−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	$0.423259\pi$
$422$	22.3241	−	6.30956i	1.08672	−	0.307144i
$423$	4.14923	−	4.14923i	0.201743	−	0.201743i
$424$	2.69808	+	2.48568i	0.131030	+	0.120715i
$425$	−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	$-0.939772\pi$
$431$	−24.2947	−	24.2947i	−1.17024	−	1.17024i	−0.188083	−	0.982153i	$-0.560228\pi$
$432$	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	$0.593343\pi$
$434$	−0.914168	−	3.23446i	−0.0438815	−	0.155259i
$435$	−7.12855	−	7.12855i	−0.341788	−	0.341788i
$436$	−4.47629	+	18.7375i	−0.214376	+	0.897366i
$437$	−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	$-0.252673\pi$
$439$	29.3812			1.40229			0.701144	+	0.713019i	$0.252673\pi$
$440$	−10.3670	+	11.2528i	−0.494227	+	0.536457i
$441$			11.1647i			0.531651i
$442$	2.79802	+	36.1367i	0.133088	+	1.71885i
$443$			33.9623i			1.61360i	0.590828	+	0.806798i	$0.298801\pi$
$443$			33.9623i			1.61360i	−0.590828	+	0.806798i	$0.701199\pi$
$444$	2.30192	−	9.63571i	0.109244	−	0.457290i
$445$	8.19823			0.388634
$446$	13.8065	−	24.6856i	0.653755	−	1.16890i
$447$	−14.7865	−	14.7865i	−0.699375	−	0.699375i
$448$	−1.47620	−	1.25224i	−0.0697440	−	0.0591628i
$449$	−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	$0.972892\pi$
$450$	2.18888	−	0.618653i	0.103185	−	0.0291636i
$451$		−	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
$460$	−0.113528	+	0.475222i	−0.00529326	+	0.0221573i
$461$	−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	$0.467944\pi$
$462$	0.593924	+	2.10139i	0.0276319	+	0.0977656i
$463$	5.45056	−	5.45056i	0.253309	−	0.253309i	−0.569017	−	0.822326i	$-0.692676\pi$
$463$	5.45056	−	5.45056i	0.253309	−	0.253309i	0.822326	+	0.569017i	$0.192676\pi$
$464$	15.4508	−	30.4927i	0.717287	−	1.41559i
$465$		−	11.5868i		−	0.537324i
$466$	−1.23242	+	0.348322i	−0.0570906	+	0.0161357i
$467$	13.8452			0.640678			0.320339	−	0.947303i	$-0.396203\pi$
$467$	13.8452			0.640678			0.320339	+	0.947303i	$0.396203\pi$
$468$	−4.00672	−	10.8843i	−0.185211	−	0.503128i
$469$	0.297333			0.0137296
$470$	−4.96494	+	1.40326i	−0.229016	+	0.0647275i
$471$		−	6.97305i		−	0.321301i
$472$	−32.5883	+	1.33524i	−1.50000	+	0.0614595i
$473$	33.0261	−	33.0261i	1.51854	−	1.51854i
$474$	7.17322	+	25.3799i	0.329477	+	1.16574i
$475$	0.875738	−	0.875738i	0.0401816	−	0.0401816i
$476$	−3.34585	−	0.799304i	−0.153357	−	0.0366360i
$477$	−2.08615			−0.0955182
$478$	−9.96888	+	17.8241i	−0.455966	+	0.815257i
$479$	13.5767	−	13.5767i	0.620333	−	0.620333i	−0.325283	−	0.945617i	$-0.605460\pi$
$479$	13.5767	−	13.5767i	0.620333	−	0.620333i	0.945617	+	0.325283i	$0.105460\pi$
$480$	−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
$486$	−19.6459	+	5.55261i	−0.891157	+	0.251871i
$487$	−10.4019	−	10.4019i	−0.471356	−	0.471356i	0.430997	−	0.902353i	$-0.358162\pi$
$487$	−10.4019	−	10.4019i	−0.471356	−	0.471356i	−0.902353	+	0.430997i	$0.858162\pi$
$488$	−6.78686	−	6.25259i	−0.307227	−	0.283042i
$489$	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	$-0.612508\pi$
$491$	−15.3399			−0.692281			−0.346140	+	0.938183i	$0.612508\pi$
$492$	10.3456	+	2.47151i	0.466417	+	0.111424i
$493$		−	60.7464i		−	2.73588i
$494$	−4.79680	−	4.10736i	−0.215818	−	0.184799i
$495$		−	8.70065i		−	0.391065i
$496$	37.3384	−	12.2245i	1.67654	−	0.548898i
$497$	−0.838162			−0.0375967
$498$	12.2046	+	6.82592i	0.546900	+	0.305877i
$499$	−16.6603	−	16.6603i	−0.745816	−	0.745816i	0.227875	−	0.973690i	$-0.426822\pi$
$499$	−16.6603	−	16.6603i	−0.745816	−	0.745816i	−0.973690	+	0.227875i	$0.926822\pi$
$500$	−1.94526	−	0.464712i	−0.0869947	−	0.0207826i
$501$	−4.81759	−	4.81759i	−0.215234	−	0.215234i
$502$	1.38263	+	4.89194i	0.0617098	+	0.218338i
$503$			2.89555i			0.129106i	0.997914	+	0.0645530i	$0.0205622\pi$
$503$			2.89555i			0.129106i	−0.997914	+	0.0645530i	$0.979438\pi$
$504$	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
$512$	13.9187	−	17.8401i	0.615128	−	0.788428i
$513$	−4.76082	+	4.76082i	−0.210195	+	0.210195i
$514$	−16.6439	+	4.70414i	−0.734132	+	0.207491i
$515$	−4.93782	+	4.93782i	−0.217586	+	0.217586i
$516$	10.6630	+	17.3568i	0.469414	+	0.764091i
$517$			19.7353i			0.867956i
$518$	−0.390812	−	1.38275i	−0.0171713	−	0.0607546i
$519$	0.191144			0.00839030
$520$	−1.59679	+	10.0723i	−0.0700237	+	0.441697i
$521$	21.0246			0.921105			0.460552	−	0.887633i	$-0.347651\pi$
$521$	21.0246			0.921105			0.460552	+	0.887633i	$0.347651\pi$
$522$	5.28697	+	18.7061i	0.231405	+	0.818743i
$523$			4.25536i			0.186074i	0.995663	+	0.0930370i	$0.0296575\pi$
$523$			4.25536i			0.186074i	−0.995663	+	0.0930370i	$0.970343\pi$
$524$	−0.325047	−	0.529098i	−0.0141998	−	0.0231137i
$525$	−0.201841	+	0.201841i	−0.00880906	+	0.00880906i
$526$	21.7531	−	6.14816i	0.948480	−	0.268073i
$527$	49.3687	−	49.3687i	2.15054	−	2.15054i
$528$	−24.2583	+	7.94214i	−1.05571	+	0.345637i
$529$	−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
$538$	8.38190	+	29.6564i	0.361369	+	1.27858i
$539$	−26.5516	−	26.5516i	−1.14366	−	1.14366i
$540$	10.5751	+	2.52633i	0.455080	+	0.108716i
$541$	−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
$544$	7.73413	−	39.4593i	0.331598	−	1.69180i
$545$			9.63240i			0.412607i
$546$	1.10557	+	0.946668i	0.0473141	+	0.0405137i
$547$			27.5083i			1.17617i	0.808799	+	0.588085i	$0.200118\pi$
$547$			27.5083i			1.17617i	−0.808799	+	0.588085i	$0.799882\pi$
$548$	3.46336	+	0.827378i	0.147948	+	0.0353438i
$549$	5.24758			0.223961
$550$	−3.73429	+	6.67683i	−0.159231	+	0.284701i
$551$	7.48401	+	7.48401i	0.318830	+	0.318830i
$552$	−0.552295	+	0.599487i	−0.0235072	+	0.0255159i
$553$	2.70495	+	2.70495i	0.115026	+	0.115026i
$554$	5.25317	−	1.48472i	0.223186	−	0.0630799i
$555$		−	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	$-0.0923032\pi$
$563$	45.4740			1.91650			0.958250	+	0.285932i	$0.0923032\pi$
$564$	−8.37184	−	1.99999i	−0.352518	−	0.0842146i
$565$	10.5987	−	10.5987i	0.445892	−	0.445892i
$566$	4.12272	+	14.5868i	0.173291	+	0.613128i
$567$	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	$-0.0227634\pi$
$570$	1.98826	−	0.561949i	0.0832789	−	0.0235374i
$571$	−11.8904			−0.497596			−0.248798	−	0.968555i	$-0.580036\pi$
$571$	−11.8904			−0.497596			−0.248798	+	0.968555i	$0.580036\pi$
$572$	35.4136	+	16.3562i	1.48072	+	0.683887i
$573$	−13.3311			−0.556916
$574$	1.48463	−	0.419606i	0.0619671	−	0.0175140i
$575$			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	$0.303241\pi$
$578$	−12.8956	−	45.6264i	−0.536385	−	1.89781i
$579$	−6.68773	+	6.68773i	−0.277933	+	0.277933i
$580$	3.97140	−	16.6241i	0.164904	−	0.690278i
$581$	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	0.506796	−	0.862066i	$-0.330830\pi$
$587$	−8.60753	−	8.60753i	−0.355271	−	0.355271i	−0.862066	+	0.506796i	$0.830830\pi$
$588$	13.9542	−	8.57263i	0.575460	−	0.353529i
$589$			12.1646i			0.501232i
$590$	−15.6931	+	4.43540i	−0.646074	+	0.182602i
$591$	−3.72966	−	3.72966i	−0.153418	−	0.153418i
$592$	15.9624	−	5.22606i	0.656051	−	0.214790i
$593$	−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
$596$	8.23772	−	34.4827i	0.337430	−	1.41247i
$597$			2.76987i			0.113363i
$598$	1.24196	−	0.0961632i	0.0507874	−	0.00393241i
$599$		−	36.6483i		−	1.49741i	−0.662905	−	0.748704i	$-0.730677\pi$
$599$		−	36.6483i		−	1.49741i	0.662905	−	0.748704i	$-0.269323\pi$
$600$	−2.45393	−	2.26075i	−0.100181	−	0.0922948i
$601$	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
$604$	−0.352029	+	1.47357i	−0.0143238	+	0.0599589i
$605$	12.9135	+	12.9135i	0.525010	+	0.525010i
$606$	2.47935	+	8.77231i	0.100717	+	0.356351i
$607$			30.1452i			1.22356i	0.791029	+	0.611778i	$0.209545\pi$
$607$			30.1452i			1.22356i	−0.791029	+	0.611778i	$0.790455\pi$
$608$	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
$616$	−2.50854	+	2.72288i	−0.101072	+	0.109708i
$617$	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	$0.131428\pi$
$618$	−11.2107	+	3.16852i	−0.450961	+	0.127457i
$619$	−20.3294	+	20.3294i	−0.817106	+	0.817106i	−0.985688	−	0.168581i	$-0.946081\pi$
$619$	−20.3294	+	20.3294i	−0.817106	+	0.817106i	0.168581	+	0.985688i	$0.446081\pi$
$620$	16.7380	−	10.2829i	0.672215	−	0.412970i
$621$		−	1.32808i		−	0.0532941i
$622$	6.99773	+	24.7590i	0.280583	+	0.992745i
$623$	1.98376			0.0794775
$624$	−10.5273	+	13.3652i	−0.421428	+	0.535035i
$625$	−1.00000			−0.0400000
$626$	11.7374	+	41.5288i	0.469122	+	1.65982i
$627$		−	7.90317i		−	0.315622i
$628$	10.0731	−	6.18835i	0.401961	−	0.246942i
$629$	21.1054	−	21.1054i	0.841529	−	0.841529i
$630$	0.529652	−	0.149698i	0.0211018	−	0.00596410i
$631$	−5.42446	+	5.42446i	−0.215944	+	0.215944i	−0.806787	−	0.590843i	$-0.798795\pi$
$631$	−5.42446	+	5.42446i	−0.215944	+	0.215944i	0.590843	+	0.806787i	$0.298795\pi$
$632$	−30.2973	+	32.8861i	−1.20516	+	1.30814i
$633$	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	$0.923113\pi$
$642$	7.24752	+	25.6428i	0.286037	+	1.01204i
$643$	28.4178	+	28.4178i	1.12069	+	1.12069i	0.991638	+	0.129050i	$0.0411929\pi$
$643$	28.4178	+	28.4178i	1.12069	+	1.12069i	0.129050	+	0.991638i	$0.458807\pi$
$644$	−0.0274707	+	0.114991i	−0.00108250	+	0.00453128i
$645$	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	$-0.736332\pi$
$647$	−34.3949			−1.35220			−0.676102	+	0.736808i	$0.736332\pi$
$648$	3.30296	+	3.04295i	0.129753	+	0.119538i
$649$			62.3788i			2.44858i
$650$	0.393632	+	5.08380i	0.0154395	+	0.199403i
$651$		−	2.80370i		−	0.109886i
$652$	−2.99005	+	12.5162i	−0.117099	+	0.490172i
$653$	−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
$656$	5.61110	+	17.1384i	0.219077	+	0.669144i
$657$	9.35470	+	9.35470i	0.364961	+	0.364961i
$658$	−1.20138	+	0.339552i	−0.0468348	+	0.0132371i
$659$			25.9578i			1.01117i	0.862776	+	0.505586i	$0.168724\pi$
$659$			25.9578i			1.01117i	−0.862776	+	0.505586i	$0.831276\pi$
$660$	−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
$668$	2.68394	−	11.2348i	0.103845	−	0.434688i
$669$	16.6829	−	16.6829i	0.644998	−	0.644998i
$670$	0.472636	+	1.67225i	0.0182595	+	0.0646048i
$671$	−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	$0.930210\pi$
$674$	28.9664	−	8.18689i	1.11574	−	0.315347i
$675$	5.43634			0.209245
$676$	25.6901	−	4.00230i	0.988081	−	0.153935i
$677$	−18.8203			−0.723323			−0.361661	−	0.932310i	$-0.617790\pi$
$677$	−18.8203			−0.723323			−0.361661	+	0.932310i	$0.617790\pi$
$678$	24.0631	−	6.80106i	0.924139	−	0.261193i
$679$			1.00565i			0.0385933i
$680$	−0.823074	−	20.0882i	−0.0315635	−	0.770347i
$681$	13.0642	−	13.0642i	0.500622	−	0.500622i
$682$	−20.4368	−	72.3085i	−0.782567	−	2.76884i
$683$	−8.57437	+	8.57437i	−0.328089	+	0.328089i	−0.851859	−	0.523770i	$-0.824525\pi$
$683$	−8.57437	+	8.57437i	−0.328089	+	0.328089i	0.523770	+	0.851859i	$0.324525\pi$
$684$	−3.87492	−	0.925698i	−0.148161	−	0.0353949i
$685$	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	0.308230	−	0.951312i	$-0.400263\pi$
$691$	−16.9046	−	16.9046i	−0.643082	−	0.643082i	−0.951312	+	0.308230i	$0.900263\pi$
$692$	0.169634	+	0.276123i	0.00644852	+	0.0104966i
$693$		−	2.10533i		−	0.0799748i
$694$	34.3073	−	9.69641i	1.30229	−	0.368071i
$695$	−10.2028	−	10.2028i	−0.387014	−	0.387014i
$696$	19.3203	−	20.9711i	0.732332	−	0.794908i
$697$	22.6604	+	22.6604i	0.858324	+	0.858324i
$698$	−4.13870	+	7.39991i	−0.156652	+	0.280091i
$699$	−1.06828			−0.0404062
$700$	−0.470702	−	0.112448i	−0.0177909	−	0.00425014i
$701$		−	37.2994i		−	1.40878i	−0.709814	−	0.704390i	$-0.751221\pi$
$701$		−	37.2994i		−	1.40878i	0.709814	−	0.704390i	$-0.248779\pi$
$702$	−2.13992	−	27.6373i	−0.0807661	−	1.04310i
$703$			5.20042i			0.196138i
$704$	−33.0015	−	27.9947i	−1.24379	−	1.05509i
$705$	−4.30371			−0.162087
$706$	17.5886	+	9.83718i	0.661957	+	0.370227i
$707$	0.934940	+	0.934940i	0.0351621	+	0.0351621i
$708$	−26.4616	−	6.32152i	−0.994487	−	0.237577i
$709$	−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	$-0.507757\pi$
$710$	−1.33233	−	4.71397i	−0.0500013	−	0.176912i
$711$		−	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	$-0.386362\pi$
$719$	18.7415			0.698939			0.349470	+	0.936948i	$0.386362\pi$
$720$	2.00180	+	6.11427i	0.0746028	+	0.227865i
$721$	−1.19482	+	1.19482i	−0.0444975	+	0.0444975i
$722$	23.7697	−	6.71813i	0.884618	−	0.250023i
$723$	−7.44765	+	7.44765i	−0.276981	+	0.276981i
$724$	−2.98686	−	4.86187i	−0.111006	−	0.180690i
$725$		−	8.54595i		−	0.317388i
$726$	8.28644	+	29.3186i	0.307539	+	1.08812i
$727$	3.35848			0.124559			0.0622796	−	0.998059i	$-0.480163\pi$
$727$	3.35848			0.124559			0.0622796	+	0.998059i	$0.480163\pi$
$728$	−0.386380	+	2.43722i	−0.0143202	+	0.0903294i
$729$	−21.7929			−0.807145
$730$	−3.16373	−	11.1938i	−0.117095	−	0.414299i
$731$			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	$0.224641\pi$
$734$	−7.13606	+	2.01689i	−0.263397	+	0.0744449i
$735$	5.79017	−	5.79017i	0.213574	−	0.213574i
$736$	−1.35615	−	0.265809i	−0.0499883	−	0.00979785i
$737$	6.64709			0.244849
$738$	−8.95020	−	5.00577i	−0.329462	−	0.184265i
$739$	10.6855	−	10.6855i	0.393072	−	0.393072i	−0.482709	−	0.875781i	$-0.660347\pi$
$739$	10.6855	−	10.6855i	0.393072	−	0.393072i	0.875781	+	0.482709i	$0.160347\pi$
$740$	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	0.859535	−	0.511076i	$-0.170753\pi$
$743$	9.49831	+	9.49831i	0.348459	+	0.348459i	−0.511076	+	0.859535i	$0.670753\pi$
$744$	32.7449	−	1.34166i	1.20049	−	0.0491876i
$745$		−	17.7265i		−	0.649449i
$746$	−6.93912	−	24.5516i	−0.254059	−	0.898899i
$747$	−9.53307	−	9.53307i	−0.348797	−	0.348797i
$748$	−74.7987	−	17.8690i	−2.73491	−	0.653355i
$749$	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	$-0.356291\pi$
$751$	23.9126			0.872585			0.436292	+	0.899805i	$0.356291\pi$
$752$	−4.54059	−	13.8687i	−0.165578	−	0.505740i
$753$			4.24044i			0.154530i
$754$	−43.4459	+	3.36396i	−1.58221	+	0.122508i
$755$			0.757520i			0.0275690i
$756$	2.55890	+	0.611306i	0.0930662	+	0.0222330i
$757$	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
$760$	2.57629	+	2.37348i	0.0934518	+	0.0860952i
$761$	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	$0.743100\pi$
$762$	−12.5615	+	3.55030i	−0.455055	+	0.128614i
$763$			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
$772$	−15.5961	−	3.72582i	−0.561316	−	0.134095i
$773$	−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	$0.315399\pi$
$774$	−5.34150	−	18.8990i	−0.191996	−	0.679311i
$775$	6.94531	−	6.94531i	0.249483	−	0.249483i
$776$	−11.7452	+	0.481236i	−0.421628	+	0.0172754i
$777$		−	1.19860i		−	0.0429995i
$778$	−12.2282	+	3.45611i	−0.438403	+	0.123908i
$779$	−5.58357			−0.200052
$780$	−3.56683	+	7.72273i	−0.127713	+	0.276518i
$781$	−18.7377			−0.670486
$782$	−2.36323	+	0.667928i	−0.0845088	+	0.0238850i
$783$			46.4587i			1.66030i
$784$	24.7677	+	12.5500i	0.884560	+	0.448213i
$785$	4.17976	−	4.17976i	0.149182	−	0.149182i
$786$	−0.140879	−	0.498450i	−0.00502498	−	0.0177791i
$787$	−19.0399	+	19.0399i	−0.678698	+	0.678698i	−0.959706	−	0.281008i	$-0.909331\pi$
$787$	−19.0399	+	19.0399i	−0.678698	+	0.678698i	0.281008	+	0.959706i	$0.409331\pi$
$788$	2.07784	−	8.69774i	0.0740200	−	0.309844i
$789$	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	$-0.279842\pi$
$798$	0.481106	−	0.135977i	0.0170310	−	0.00481353i
$799$	−18.3372	−	18.3372i	−0.648722	−	0.648722i
$800$	1.08806	−	5.55123i	0.0384686	−	0.196266i
$801$	−9.32398	−	9.32398i	−0.329447	−	0.329447i
$802$	0.561119	−	1.00327i	0.0198138	−	0.0354266i
$803$	−44.4943			−1.57017
$804$	−0.673621	+	2.81974i	−0.0237568	+	0.0994447i
$805$			0.0591134i			0.00208347i
$806$	−38.0425	−	32.5747i	−1.33999	−	1.14739i
$807$			25.7068i			0.904921i
$808$	−10.4719	+	11.3667i	−0.368402	+	0.399881i
$809$	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	$-0.946901\pi$
$811$	−32.8113	−	32.8113i	−1.15216	−	1.15216i	−0.166044	−	0.986118i	$-0.553099\pi$
$812$	0.960975	−	4.02259i	0.0337236	−	0.141165i
$813$	−6.65744	−	6.65744i	−0.233487	−	0.233487i
$814$	−8.73688	−	30.9123i	−0.306227	−	1.08348i
$815$			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	$-0.587933\pi$
$823$	−15.6493			−0.545500			−0.272750	+	0.962085i	$0.587933\pi$
$824$	−14.5263	−	13.3828i	−0.506048	−	0.466211i
$825$	−4.51229	+	4.51229i	−0.157098	+	0.157098i
$826$	−3.79731	+	1.07325i	−0.132125	+	0.0373431i
$827$	−20.4874	+	20.4874i	−0.712417	+	0.712417i	−0.967040	−	0.254623i	$-0.918049\pi$
$827$	−20.4874	+	20.4874i	−0.712417	+	0.712417i	0.254623	+	0.967040i	$0.418049\pi$
$828$	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	$-0.208437\pi$
$830$	3.22406	+	11.4072i	0.111909	+	0.395950i
$831$	4.55356			0.157961
$832$	−28.6496	−	3.34632i	−0.993248	−	0.116013i
$833$	49.3413			1.70957
$834$	−6.54699	−	23.1642i	−0.226704	−	0.802111i
$835$		−	5.77548i		−	0.199869i
$836$	11.4168	−	7.01380i	0.394857	−	0.242577i
$837$	−37.7571	+	37.7571i	−1.30508	+	1.30508i
$838$	10.2039	−	2.88397i	0.352488	−	0.0996250i
$839$	−25.2583	+	25.2583i	−0.872013	+	0.872013i	−0.992692	−	0.120679i	$-0.961493\pi$
$839$	−25.2583	+	25.2583i	−0.872013	+	0.872013i	0.120679	+	0.992692i	$0.461493\pi$
$840$	−0.593785	−	0.547042i	−0.0204875	−	0.0188747i
$841$	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
$850$	−2.73408	−	9.67357i	−0.0937782	−	0.331801i
$851$	−0.725358	−	0.725358i	−0.0248650	−	0.0248650i
$852$	1.89889	−	7.94866i	0.0650549	−	0.272317i
$853$	−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
$856$	−30.6111	+	33.2267i	−1.04627	+	1.13567i
$857$			17.1773i			0.586764i	0.955995	+	0.293382i	$0.0947808\pi$
$857$			17.1773i			0.586764i	−0.955995	+	0.293382i	$0.905219\pi$
$858$	24.7158	+	21.1634i	0.843783	+	0.722507i
$859$		−	43.8884i		−	1.49745i	−0.662879	−	0.748727i	$-0.730666\pi$
$859$		−	43.8884i		−	1.49745i	0.662879	−	0.748727i	$-0.269334\pi$
$860$	−4.01237	+	16.7956i	−0.136821	+	0.572724i
$861$	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	$0.0569908\pi$
$863$	34.1389	+	34.1389i	1.16210	+	1.16210i	0.178087	+	0.984015i	$0.443009\pi$
$864$	−5.91505	+	30.1784i	−0.201234	+	1.02669i
$865$	0.114575	+	0.114575i	0.00389567	+	0.00389567i
$866$	−54.2193	+	15.3242i	−1.84245	+	0.520737i
$867$		−	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
$876$	4.50909	−	18.8748i	0.152348	−	0.637721i
$877$	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	$0.0379730\pi$
$878$	11.3011	+	39.9850i	0.381394	+	1.34943i
$879$	−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	$0.858069\pi$
$882$	−15.1940	+	4.29435i	−0.511609	+	0.144598i
$883$	9.90603			0.333365			0.166682	−	0.986011i	$-0.446695\pi$
$883$	9.90603			0.333365			0.166682	+	0.986011i	$0.446695\pi$
$884$	−48.1023	+	17.7074i	−1.61786	+	0.595563i
$885$	−13.6031			−0.457263
$886$	−46.2193	+	13.0631i	−1.55277	+	0.438865i
$887$		−	57.1646i		−	1.91940i	−0.281027	−	0.959700i	$-0.590675\pi$
$887$		−	57.1646i		−	1.91940i	0.281027	−	0.959700i	$-0.409325\pi$
$888$	13.9987	−	0.573567i	0.469764	−	0.0192477i
$889$	−1.33879	+	1.33879i	−0.0449015	+	0.0449015i
$890$	3.15334	+	11.1570i	0.105700	+	0.373983i
$891$	6.07350	−	6.07350i	0.203470	−	0.203470i
$892$	38.9052	+	9.29424i	1.30264	+	0.311194i
$893$	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
$902$	33.1898	−	9.38057i	1.10510	−	0.312339i
$903$	1.74271	+	1.74271i	0.0579939	+	0.0579939i
$904$	31.1799	+	28.7254i	1.03703	+	0.955392i
$905$	−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	$-0.262899\pi$
$907$	40.8307			1.35576			0.677880	+	0.735172i	$0.262899\pi$
$908$	30.4664	+	7.27824i	1.01106	+	0.241537i
$909$		−	8.78874i		−	0.291504i
$910$	0.0952487	+	1.23015i	0.00315746	+	0.0407790i
$911$			35.1011i			1.16295i	0.813563	+	0.581476i	$0.197525\pi$
$911$			35.1011i			1.16295i	−0.813563	+	0.581476i	$0.802475\pi$
$912$	1.81832	+	5.55386i	0.0602107	+	0.183907i
$913$	45.3427			1.50063
$914$	43.9583	+	24.5855i	1.45401	+	0.813216i
$915$	−2.72148	−	2.72148i	−0.0899693	−	0.0899693i
$916$	−39.5870	−	9.45712i	−1.30799	−	0.312472i
$917$	−0.0531241	−	0.0531241i	−0.00175431	−	0.00175431i
$918$	14.8634	+	52.5889i	0.490565	+	1.73569i
$919$		−	30.3991i		−	1.00277i	−0.865223	−	0.501386i	$-0.832824\pi$
$919$		−	30.3991i		−	1.00277i	0.865223	−	0.501386i	$-0.167176\pi$
$920$	−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
$928$	47.4405	+	9.29847i	1.55731	+	0.305237i
$929$	−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	$0.496076\pi$
$930$	15.7685	−	4.45671i	0.517069	−	0.146141i
$931$	−6.07889	+	6.07889i	−0.199228	+	0.199228i
$932$	−0.948066	−	1.54322i	−0.0310549	−	0.0505498i
$933$			21.4616i			0.702621i
$934$	5.32536	+	18.8419i	0.174251	+	0.616526i
$935$	−38.4517			−1.25751
$936$	13.2714	−	9.63928i	0.433788	−	0.315070i
$937$	13.6627			0.446341			0.223171	−	0.974779i	$-0.428359\pi$
$937$	13.6627			0.446341			0.223171	+	0.974779i	$0.428359\pi$
$938$	0.114365	+	0.404642i	0.00373416	+	0.0132120i
$939$			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	$0.451439\pi$
$942$	9.48964	−	2.68209i	0.309189	−	0.0873873i
$943$	0.778799	−	0.778799i	0.0253612	−	0.0253612i
$944$	−14.3518	−	43.8359i	−0.467112	−	1.42674i
$945$	1.31545			0.0427917
$946$	57.6484	+	32.2422i	1.87431	+	1.04829i
$947$	−3.90870	+	3.90870i	−0.127016	+	0.127016i	−0.767757	−	0.640741i	$-0.778627\pi$
$947$	−3.90870	+	3.90870i	−0.127016	+	0.127016i	0.640741	+	0.767757i	$0.278627\pi$
$948$	−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	$-0.0317300\pi$
$954$	−0.802410	−	2.83904i	−0.0259790	−	0.0919174i
$955$	−7.99090	−	7.99090i	−0.258579	−	0.258579i
$956$	−28.0913	−	6.71085i	−0.908538	−	0.217044i
$957$	−38.5618	−	38.5618i	−1.24653	−	1.24653i
$958$	23.6986	+	13.2544i	0.765667	+	0.428231i
$959$	0.430812			0.0139117
$960$	6.10486	−	7.19671i	0.197034	−	0.232273i
$961$			65.4747i			2.11209i
$962$	−16.2634	−	13.9259i	−0.524353	−	0.448989i
$963$		−	25.6908i		−	0.827876i
$964$	−17.3682	−	4.14917i	−0.559393	−	0.133636i
$965$	−8.01748			−0.258092
$966$	−0.0481388	+	0.0860710i	−0.00154884	+	0.00276929i
$967$	3.66529	+	3.66529i	0.117868	+	0.117868i	0.763581	−	0.645713i	$-0.223440\pi$
$967$	3.66529	+	3.66529i	0.117868	+	0.117868i	−0.645713	+	0.763581i	$0.723440\pi$
$968$	−34.9991	+	37.9897i	−1.12491	+	1.22104i
$969$	7.34329	+	7.34329i	0.235900	+	0.235900i
$970$	−5.65596	+	1.59856i	−0.181602	+	0.0513268i
$971$			5.51132i			0.176867i	0.996082	+	0.0884334i	$0.0281860\pi$
$971$			5.51132i			0.176867i	−0.996082	+	0.0884334i	$0.971814\pi$
$972$	−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
$980$	13.5029	+	3.22577i	0.431335	+	0.103044i
$981$	10.9551	−	10.9551i	0.349769	−	0.349769i
$982$	−5.90030	−	20.8761i	−0.188286	−	0.666184i
$983$	37.6373	−	37.6373i	1.20044	−	1.20044i	0.226413	−	0.974031i	$-0.427300\pi$
$983$	37.6373	−	37.6373i	1.20044	−	1.20044i	0.974031	−	0.226413i	$-0.0726999\pi$
$984$	0.615825	+	15.0300i	0.0196318	+	0.479139i
$985$		−	4.47124i		−	0.142466i
$986$	82.6698	−	23.3653i	2.63274	−	0.744103i
$987$	−1.04138			−0.0331476
$988$	3.74469	−	8.10782i	0.119134	−	0.257944i
$989$	2.10928			0.0670713
$990$	11.8407	−	3.34659i	0.376323	−	0.106362i
$991$		−	33.6708i		−	1.06959i	−0.844982	−	0.534794i	$-0.820389\pi$
$991$		−	33.6708i		−	1.06959i	0.844982	−	0.534794i	$-0.179611\pi$
$992$	30.9981	+	46.1119i	0.984191	+	1.46405i
$993$	2.44513	−	2.44513i	0.0775939	−	0.0775939i
$994$	−0.322388	−	1.14066i	−0.0102255	−	0.0361794i
$995$	−1.66031	+	1.66031i	−0.0526353	+	0.0526353i
$996$	−4.59507	+	19.2347i	−0.145600	+	0.609476i
$997$	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.31.17	yes	56
4.3	odd	2	inner	260.2.j.a.31.2	✓	56
13.8	odd	4	inner	260.2.j.a.151.2	yes	56
52.47	even	4	inner	260.2.j.a.151.17	yes	56

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.384637 + 1.36090i) q^{2} +1.17966i q^{3} +(-1.70411 + 1.04691i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(-1.60540 + 0.453740i) q^{6} +(-0.171101 + 0.171101i) q^{7} +(-2.08020 - 1.91645i) q^{8} +1.60841 q^{9} +O(q^{10})\)	\(q+(0.384637 + 1.36090i) q^{2} +1.17966i q^{3} +(-1.70411 + 1.04691i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(-1.60540 + 0.453740i) q^{6} +(-0.171101 + 0.171101i) q^{7} +(-2.08020 - 1.91645i) 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} +(0.618653 + 2.18888i) q^{18} +(0.875738 + 0.875738i) q^{19} +(0.464712 - 1.94526i) q^{20} +(-0.201841 - 0.201841i) q^{21} +(-6.67683 - 3.73429i) q^{22} -0.244297 q^{23} +(2.26075 - 2.45393i) q^{24} -1.00000i q^{25} +(-5.08380 + 0.393632i) q^{26} +5.43634i q^{27} +(0.112448 - 0.470702i) q^{28} +8.54595 q^{29} +(0.814346 - 1.45603i) q^{30} +(6.94531 + 6.94531i) q^{31} +(5.55123 + 1.08806i) q^{32} +(-4.51229 - 4.51229i) q^{33} +(9.67357 - 2.73408i) 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} +(2.51385 - 10.5229i) q^{44} +(-1.13732 + 1.13732i) q^{45} +(-0.0939657 - 0.332464i) q^{46} +(2.57972 - 2.57972i) q^{47} +(4.20912 + 2.13279i) q^{48} +6.94145i q^{49} +(1.36090 - 0.384637i) q^{50} +8.38526 q^{51} +(-2.49111 - 6.76715i) q^{52} -1.29703 q^{53} +(-7.39833 + 2.09102i) q^{54} -5.40948i q^{55} +(0.683831 - 0.0280186i) q^{56} +(-1.03307 + 1.03307i) q^{57} +(3.28709 + 11.6302i) q^{58} +(8.15392 - 8.15392i) q^{59} +(2.29474 + 0.548201i) 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} +(0.329302 - 0.0930720i) q^{70} +(2.44932 + 2.44932i) q^{71} +(-3.34581 - 3.08242i) q^{72} +(5.81613 + 5.81613i) q^{73} +(-2.89869 + 5.18279i) q^{74} +1.17966 q^{75} +(-2.40917 - 0.575537i) q^{76} -1.30895i q^{77} +(-0.464352 - 5.99715i) q^{78} -15.8091i q^{79} +(1.24459 + 3.80145i) q^{80} -1.58781 q^{81} +(-5.56464 - 3.11226i) q^{82} +(-5.92703 - 5.92703i) q^{83} +(0.555267 + 0.132650i) q^{84} +(5.02626 + 5.02626i) q^{85} +(-3.32099 - 11.7502i) 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} +(-1.28353 + 6.54855i) q^{96} +(2.93876 - 2.93876i) q^{97} +(-9.44663 + 2.66994i) 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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