LMFDB - Embedded newform 280.2.bj.e.171.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [280,2,Mod(131,280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(280, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 0, 5]))

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

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

chi := DirichletCharacter("280.131");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 280 = 2^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	280.bj (of order $6$, 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:	$2.23581125660$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			171.8
Character	$\chi$	$=$	280.171
Dual form			280.2.bj.e.131.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.617571 - 1.27224i) q^{2} +(0.725648 + 0.418953i) q^{3} +(-1.23721 - 1.57140i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.981150 - 0.664468i) q^{6} +(2.36913 + 1.17781i) q^{7} +(-2.76328 + 0.603581i) q^{8} +(-1.14896 - 1.99005i) q^{9} +O(q^{10})$	\(q+(0.617571 - 1.27224i) q^{2} +(0.725648 + 0.418953i) q^{3} +(-1.23721 - 1.57140i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.981150 - 0.664468i) q^{6} +(2.36913 + 1.17781i) q^{7} +(-2.76328 + 0.603581i) q^{8} +(-1.14896 - 1.99005i) q^{9} +(1.41058 - 0.101290i) q^{10} +(2.98938 - 5.17776i) q^{11} +(-0.239435 - 1.65862i) q^{12} +2.87544 q^{13} +(2.96157 - 2.28672i) q^{14} +0.837906i q^{15} +(-0.938618 + 3.88832i) q^{16} +(2.07668 + 1.19897i) q^{17} +(-3.24139 + 0.232755i) q^{18} +(-4.05564 + 2.34152i) q^{19} +(0.742270 - 1.85716i) q^{20} +(1.22570 + 1.84723i) q^{21} +(-4.74122 - 7.00086i) q^{22} +(-5.81623 + 3.35800i) q^{23} +(-2.25804 - 0.719696i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(1.77579 - 3.65827i) q^{26} -4.43915i q^{27} +(-1.08029 - 5.18006i) q^{28} +1.31035i q^{29} +(1.06602 + 0.517467i) q^{30} +(-4.34775 + 7.53053i) q^{31} +(4.36722 + 3.59546i) q^{32} +(4.33848 - 2.50482i) q^{33} +(2.80789 - 1.90160i) q^{34} +(0.164546 + 2.64063i) q^{35} +(-1.70567 + 4.26759i) q^{36} +(3.26889 - 1.88729i) q^{37} +(0.474344 + 6.60582i) q^{38} +(2.08656 + 1.20468i) q^{39} +(-1.90435 - 2.09128i) q^{40} +1.79404i q^{41} +(3.10709 - 0.418596i) q^{42} -6.73760 q^{43} +(-11.8348 + 1.70846i) q^{44} +(1.14896 - 1.99005i) q^{45} +(0.680261 + 9.47346i) q^{46} +(-0.874599 - 1.51485i) q^{47} +(-2.31013 + 2.42831i) q^{48} +(4.22551 + 5.58078i) q^{49} +(0.793010 + 1.17095i) q^{50} +(1.00463 + 1.74007i) q^{51} +(-3.55753 - 4.51848i) q^{52} +(0.0994447 + 0.0574144i) q^{53} +(-5.64769 - 2.74150i) q^{54} +5.97876 q^{55} +(-7.25745 - 1.82467i) q^{56} -3.92395 q^{57} +(1.66708 + 0.809232i) q^{58} +(2.61363 + 1.50898i) q^{59} +(1.31669 - 1.03667i) q^{60} +(-4.40120 - 7.62310i) q^{61} +(6.89562 + 10.1820i) q^{62} +(-0.378112 - 6.06794i) q^{63} +(7.27138 - 3.33572i) q^{64} +(1.43772 + 2.49021i) q^{65} +(-0.507425 - 7.06651i) q^{66} +(-2.83761 + 4.91489i) q^{67} +(-0.685224 - 4.74669i) q^{68} -5.62738 q^{69} +(3.46114 + 1.42144i) q^{70} +3.06734i q^{71} +(4.37604 + 4.80557i) q^{72} +(8.69332 + 5.01909i) q^{73} +(-0.382326 - 5.32436i) q^{74} +(-0.725648 + 0.418953i) q^{75} +(8.69716 + 3.47608i) q^{76} +(13.1807 - 8.74583i) q^{77} +(2.82124 - 1.91064i) q^{78} +(-11.9852 + 6.91965i) q^{79} +(-3.83669 + 1.13129i) q^{80} +(-1.58707 + 2.74889i) q^{81} +(2.28245 + 1.10795i) q^{82} -17.4215i q^{83} +(1.38629 - 4.21149i) q^{84} +2.39795i q^{85} +(-4.16095 + 8.57187i) q^{86} +(-0.548973 + 0.950850i) q^{87} +(-5.13529 + 16.1119i) q^{88} +(-11.0658 + 6.38886i) q^{89} +(-1.82227 - 2.69075i) q^{90} +(6.81228 + 3.38674i) q^{91} +(12.4727 + 4.98508i) q^{92} +(-6.30988 + 3.64301i) q^{93} +(-2.46739 + 0.177175i) q^{94} +(-4.05564 - 2.34152i) q^{95} +(1.66274 + 4.43870i) q^{96} +3.76431i q^{97} +(9.70967 - 1.92935i) q^{98} -13.7387 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 3 q^{2} + 12 q^{3} + q^{4} + 12 q^{5} + 2 q^{6} - 10 q^{7} - 6 q^{8} + 12 q^{9}+O(q^{10}) $ 24 * q - 3 * q^2 + 12 * q^3 + q^4 + 12 * q^5 + 2 * q^6 - 10 * q^7 - 6 * q^8 + 12 * q^9	\( 24 q - 3 q^{2} + 12 q^{3} + q^{4} + 12 q^{5} + 2 q^{6} - 10 q^{7} - 6 q^{8} + 12 q^{9} - 3 q^{10} + 8 q^{11} + 8 q^{12} - 20 q^{13} - 15 q^{14} - 3 q^{16} + 6 q^{17} - 27 q^{18} + 18 q^{19} + 2 q^{20} + 26 q^{21} - 16 q^{22} - 18 q^{23} + 6 q^{24} - 12 q^{25} - 29 q^{26} + 3 q^{28} + 10 q^{30} + 6 q^{31} - 33 q^{32} + 12 q^{33} + 20 q^{34} - 8 q^{35} - 22 q^{36} + 9 q^{38} + 18 q^{39} - 3 q^{40} - 12 q^{42} + 32 q^{43} - 25 q^{44} - 12 q^{45} + 53 q^{46} + 14 q^{48} + 8 q^{49} - 22 q^{51} - 31 q^{52} - 30 q^{53} + 10 q^{54} + 16 q^{55} + 16 q^{56} - 44 q^{57} + 30 q^{58} - 18 q^{59} + 10 q^{60} - 22 q^{61} - 8 q^{62} + 12 q^{63} + 58 q^{64} - 10 q^{65} - 8 q^{66} - 8 q^{67} - 6 q^{68} + 12 q^{69} + 3 q^{70} - 23 q^{72} + 30 q^{73} - 43 q^{74} - 12 q^{75} - 8 q^{76} + 32 q^{77} - 8 q^{78} - 6 q^{79} + 3 q^{80} - 4 q^{81} - 27 q^{82} - 16 q^{84} - 36 q^{86} - 14 q^{87} + 49 q^{88} - 60 q^{89} - 24 q^{90} + 18 q^{91} - 38 q^{92} + 18 q^{93} + 11 q^{94} + 18 q^{95} + 2 q^{96} - 19 q^{98} - 56 q^{99}+O(q^{100}) \) 24 * q - 3 * q^2 + 12 * q^3 + q^4 + 12 * q^5 + 2 * q^6 - 10 * q^7 - 6 * q^8 + 12 * q^9 - 3 * q^10 + 8 * q^11 + 8 * q^12 - 20 * q^13 - 15 * q^14 - 3 * q^16 + 6 * q^17 - 27 * q^18 + 18 * q^19 + 2 * q^20 + 26 * q^21 - 16 * q^22 - 18 * q^23 + 6 * q^24 - 12 * q^25 - 29 * q^26 + 3 * q^28 + 10 * q^30 + 6 * q^31 - 33 * q^32 + 12 * q^33 + 20 * q^34 - 8 * q^35 - 22 * q^36 + 9 * q^38 + 18 * q^39 - 3 * q^40 - 12 * q^42 + 32 * q^43 - 25 * q^44 - 12 * q^45 + 53 * q^46 + 14 * q^48 + 8 * q^49 - 22 * q^51 - 31 * q^52 - 30 * q^53 + 10 * q^54 + 16 * q^55 + 16 * q^56 - 44 * q^57 + 30 * q^58 - 18 * q^59 + 10 * q^60 - 22 * q^61 - 8 * q^62 + 12 * q^63 + 58 * q^64 - 10 * q^65 - 8 * q^66 - 8 * q^67 - 6 * q^68 + 12 * q^69 + 3 * q^70 - 23 * q^72 + 30 * q^73 - 43 * q^74 - 12 * q^75 - 8 * q^76 + 32 * q^77 - 8 * q^78 - 6 * q^79 + 3 * q^80 - 4 * q^81 - 27 * q^82 - 16 * q^84 - 36 * q^86 - 14 * q^87 + 49 * q^88 - 60 * q^89 - 24 * q^90 + 18 * q^91 - 38 * q^92 + 18 * q^93 + 11 * q^94 + 18 * q^95 + 2 * q^96 - 19 * q^98 - 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/280\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$141$	$241$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	0.617571	−	1.27224i	0.436689	−	0.899613i
$2$	0.617571	−	1.27224i	0.436689	−	0.899613i
$3$	0.725648	+	0.418953i	0.418953	+	0.241883i	0.694629	−	0.719368i	$-0.255568\pi$
$3$	0.725648	+	0.418953i	0.418953	+	0.241883i	−0.275676	+	0.961251i	$0.588902\pi$
$4$	−1.23721	−	1.57140i	−0.618606	−	0.785702i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	0.981150	−	0.664468i	0.400553	−	0.271268i
$7$	2.36913	+	1.17781i	0.895445	+	0.445172i
$7$	2.36913	+	1.17781i	0.895445	+	0.445172i
$8$	−2.76328	+	0.603581i	−0.976965	+	0.213398i
$9$	−1.14896	−	1.99005i	−0.382985	−	0.663350i
$10$	1.41058	−	0.101290i	0.446065	−	0.0320306i
$11$	2.98938	−	5.17776i	0.901332	−	1.56115i	0.0755665	−	0.997141i	$-0.475923\pi$
$11$	2.98938	−	5.17776i	0.901332	−	1.56115i	0.825766	−	0.564013i	$-0.190743\pi$
$12$	−0.239435	−	1.65862i	−0.0691191	−	0.478802i
$13$	2.87544			0.797504			0.398752	−	0.917059i	$-0.369443\pi$
$13$	2.87544			0.797504			0.398752	+	0.917059i	$0.369443\pi$
$14$	2.96157	−	2.28672i	0.791513	−	0.611152i
$15$			0.837906i			0.216346i
$16$	−0.938618	+	3.88832i	−0.234654	+	0.972079i
$17$	2.07668	+	1.19897i	0.503670	+	0.290794i	0.730228	−	0.683204i	$-0.239414\pi$
$17$	2.07668	+	1.19897i	0.503670	+	0.290794i	−0.226558	+	0.973998i	$0.572747\pi$
$18$	−3.24139	+	0.232755i	−0.764004	+	0.0548608i
$19$	−4.05564	+	2.34152i	−0.930427	+	0.537182i	−0.886947	−	0.461872i	$-0.847178\pi$
$19$	−4.05564	+	2.34152i	−0.930427	+	0.537182i	−0.0434803	+	0.999054i	$0.513845\pi$
$20$	0.742270	−	1.85716i	0.165977	−	0.415273i
$21$	1.22570	+	1.84723i	0.267470	+	0.403099i
$22$	−4.74122	−	7.00086i	−1.01083	−	1.49259i
$23$	−5.81623	+	3.35800i	−1.21277	+	0.700191i	−0.963361	−	0.268208i	$-0.913569\pi$
$23$	−5.81623	+	3.35800i	−1.21277	+	0.700191i	−0.249406	+	0.968399i	$0.580235\pi$
$24$	−2.25804	−	0.719696i	−0.460920	−	0.146907i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	1.77579	−	3.65827i	0.348261	−	0.717445i
$27$		−	4.43915i		−	0.854316i
$28$	−1.08029	−	5.18006i	−0.204155	−	0.978939i
$29$			1.31035i			0.243325i	0.992572	+	0.121663i	$0.0388226\pi$
$29$			1.31035i			0.243325i	−0.992572	+	0.121663i	$0.961177\pi$
$30$	1.06602	+	0.517467i	0.194628	+	0.0944761i
$31$	−4.34775	+	7.53053i	−0.780879	+	1.35252i	0.150551	+	0.988602i	$0.451895\pi$
$31$	−4.34775	+	7.53053i	−0.780879	+	1.35252i	−0.931430	+	0.363920i	$0.881438\pi$
$32$	4.36722	+	3.59546i	0.772023	+	0.635594i
$33$	4.33848	−	2.50482i	0.755232	−	0.436034i
$34$	2.80789	−	1.90160i	0.481549	−	0.326121i
$35$	0.164546	+	2.64063i	0.0278133	+	0.446348i
$36$	−1.70567	+	4.26759i	−0.284279	+	0.711265i
$37$	3.26889	−	1.88729i	0.537402	−	0.310269i	−0.206624	−	0.978421i	$-0.566248\pi$
$37$	3.26889	−	1.88729i	0.537402	−	0.310269i	0.744025	+	0.668151i	$0.232914\pi$
$38$	0.474344	+	6.60582i	0.0769487	+	1.07161i
$39$	2.08656	+	1.20468i	0.334117	+	0.192903i
$40$	−1.90435	−	2.09128i	−0.301105	−	0.330660i
$41$			1.79404i			0.280181i	0.990139	+	0.140091i	$0.0447394\pi$
$41$			1.79404i			0.280181i	−0.990139	+	0.140091i	$0.955261\pi$
$42$	3.10709	−	0.418596i	0.479434	−	0.0645907i
$43$	−6.73760			−1.02747			−0.513737	−	0.857948i	$-0.671739\pi$
$43$	−6.73760			−1.02747			−0.513737	+	0.857948i	$0.671739\pi$
$44$	−11.8348	+	1.70846i	−1.78417	+	0.257560i
$45$	1.14896	−	1.99005i	0.171276	−	0.296659i
$46$	0.680261	+	9.47346i	0.100299	+	1.39679i
$47$	−0.874599	−	1.51485i	−0.127573	−	0.220963i	0.795163	−	0.606396i	$-0.207385\pi$
$47$	−0.874599	−	1.51485i	−0.127573	−	0.220963i	−0.922736	+	0.385433i	$0.874052\pi$
$48$	−2.31013	+	2.42831i	−0.333438	+	0.350497i
$49$	4.22551	+	5.58078i	0.603644	+	0.797254i
$50$	0.793010	+	1.17095i	0.112149	+	0.165598i
$51$	1.00463	+	1.74007i	0.140676	+	0.243658i
$52$	−3.55753	−	4.51848i	−0.493341	−	0.626601i
$53$	0.0994447	+	0.0574144i	0.0136598	+	0.00788648i	0.506814	−	0.862055i	$-0.330823\pi$
$53$	0.0994447	+	0.0574144i	0.0136598	+	0.00788648i	−0.493155	+	0.869942i	$0.664156\pi$
$54$	−5.64769	−	2.74150i	−0.768553	−	0.373070i
$55$	5.97876			0.806176
$56$	−7.25745	−	1.82467i	−0.969818	−	0.243831i
$57$	−3.92395			−0.519740
$58$	1.66708	+	0.809232i	0.218898	+	0.106257i
$59$	2.61363	+	1.50898i	0.340266	+	0.196453i	0.660390	−	0.750923i	$-0.270391\pi$
$59$	2.61363	+	1.50898i	0.340266	+	0.196453i	−0.320124	+	0.947376i	$0.603724\pi$
$60$	1.31669	−	1.03667i	0.169984	−	0.133833i
$61$	−4.40120	−	7.62310i	−0.563516	−	0.976038i	−0.997186	−	0.0749664i	$-0.976115\pi$
$61$	−4.40120	−	7.62310i	−0.563516	−	0.976038i	0.433670	−	0.901072i	$-0.357218\pi$
$62$	6.89562	+	10.1820i	0.875745	+	1.29312i
$63$	−0.378112	−	6.06794i	−0.0476376	−	0.764488i
$64$	7.27138	−	3.33572i	0.908923	−	0.416965i
$65$	1.43772	+	2.49021i	0.178327	+	0.308872i
$66$	−0.507425	−	7.06651i	−0.0624597	−	0.869827i
$67$	−2.83761	+	4.91489i	−0.346670	+	0.600449i	−0.985656	−	0.168769i	$-0.946021\pi$
$67$	−2.83761	+	4.91489i	−0.346670	+	0.600449i	0.638986	+	0.769218i	$0.279354\pi$
$68$	−0.685224	−	4.74669i	−0.0830956	−	0.575621i
$69$	−5.62738			−0.677457
$70$	3.46114	+	1.42144i	0.413686	+	0.169894i
$71$			3.06734i			0.364026i	0.983296	+	0.182013i	$0.0582613\pi$
$71$			3.06734i			0.364026i	−0.983296	+	0.182013i	$0.941739\pi$
$72$	4.37604	+	4.80557i	0.515721	+	0.566342i
$73$	8.69332	+	5.01909i	1.01748	+	0.587440i	0.913372	−	0.407126i	$-0.133469\pi$
$73$	8.69332	+	5.01909i	1.01748	+	0.587440i	0.104104	+	0.994566i	$0.466802\pi$
$74$	−0.382326	−	5.32436i	−0.0444445	−	0.618944i
$75$	−0.725648	+	0.418953i	−0.0837906	+	0.0483765i
$76$	8.69716	+	3.47608i	0.997632	+	0.398734i
$77$	13.1807	−	8.74583i	1.50208	−	0.996680i
$78$	2.82124	−	1.91064i	0.319443	−	0.216337i
$79$	−11.9852	+	6.91965i	−1.34844	+	0.778522i	−0.988028	−	0.154272i	$-0.950697\pi$
$79$	−11.9852	+	6.91965i	−1.34844	+	0.778522i	−0.360411	+	0.932794i	$0.617364\pi$
$80$	−3.83669	+	1.13129i	−0.428955	+	0.126482i
$81$	−1.58707	+	2.74889i	−0.176341	+	0.305432i
$82$	2.28245	+	1.10795i	0.252055	+	0.122352i
$83$		−	17.4215i		−	1.91226i	−0.292940	−	0.956131i	$-0.594634\pi$
$83$		−	17.4215i		−	1.91226i	0.292940	−	0.956131i	$-0.405366\pi$
$84$	1.38629	−	4.21149i	0.151257	−	0.459511i
$85$			2.39795i			0.260094i
$86$	−4.16095	+	8.57187i	−0.448687	+	0.924329i
$87$	−0.548973	+	0.950850i	−0.0588561	+	0.101942i
$88$	−5.13529	+	16.1119i	−0.547423	+	1.71754i
$89$	−11.0658	+	6.38886i	−1.17297	+	0.677217i	−0.954379	−	0.298598i	$-0.903481\pi$
$89$	−11.0658	+	6.38886i	−1.17297	+	0.677217i	−0.218596	+	0.975815i	$0.570148\pi$
$90$	−1.82227	−	2.69075i	−0.192084	−	0.283630i
$91$	6.81228	+	3.38674i	0.714121	+	0.355026i
$92$	12.4727	+	4.98508i	1.30037	+	0.519731i
$93$	−6.30988	+	3.64301i	−0.654304	+	0.377762i
$94$	−2.46739	+	0.177175i	−0.254491	+	0.0182743i
$95$	−4.05564	−	2.34152i	−0.416100	−	0.240235i
$96$	1.66274	+	4.43870i	0.169702	+	0.453023i
$97$			3.76431i			0.382208i	0.981570	+	0.191104i	$0.0612067\pi$
$97$			3.76431i			0.382208i	−0.981570	+	0.191104i	$0.938793\pi$
$98$	9.70967	−	1.92935i	0.980824	−	0.194894i
$99$	−13.7387			−1.38079
$100$	1.97948	−	0.285754i	0.197948	−	0.0285754i
$101$	8.14097	−	14.1006i	0.810057	−	1.40306i	−0.102767	−	0.994705i	$-0.532770\pi$
$101$	8.14097	−	14.1006i	0.810057	−	1.40306i	0.912824	−	0.408354i	$-0.133897\pi$
$102$	2.83422	−	0.203517i	0.280629	−	0.0201511i
$103$	−1.13180	−	1.96034i	−0.111520	−	0.193158i	0.804864	−	0.593460i	$-0.202238\pi$
$103$	−1.13180	−	1.96034i	−0.111520	−	0.193158i	−0.916383	+	0.400302i	$0.868905\pi$
$104$	−7.94564	+	1.73556i	−0.779134	+	0.170186i
$105$	−0.986898	+	1.98511i	−0.0963114	+	0.193726i
$106$	0.134459	−	0.0910605i	0.0130599	−	0.00884458i
$107$	1.21095	+	2.09743i	0.117067	+	0.202766i	0.918604	−	0.395179i	$-0.129317\pi$
$107$	1.21095	+	2.09743i	0.117067	+	0.202766i	−0.801537	+	0.597945i	$0.795984\pi$
$108$	−6.97570	+	5.49217i	−0.671237	+	0.528484i
$109$	6.35090	+	3.66669i	0.608306	+	0.351206i	0.772302	−	0.635255i	$-0.219105\pi$
$109$	6.35090	+	3.66669i	0.608306	+	0.351206i	−0.163996	+	0.986461i	$0.552439\pi$
$110$	3.69231	−	7.60645i	0.352048	−	0.725246i
$111$	3.16275			0.300195
$112$	−6.80342	+	8.10639i	−0.642862	+	0.765982i
$113$	15.0661			1.41730			0.708651	−	0.705559i	$-0.249304\pi$
$113$	15.0661			1.41730			0.708651	+	0.705559i	$0.249304\pi$
$114$	−2.42332	+	4.99223i	−0.226965	+	0.467565i
$115$	−5.81623	−	3.35800i	−0.542366	−	0.313135i
$116$	2.05908	−	1.62117i	0.191181	−	0.150522i
$117$	−3.30376	−	5.72228i	−0.305433	−	0.529025i
$118$	3.53390	−	2.39328i	0.325322	−	0.220319i
$119$	3.50775	+	5.28646i	0.321555	+	0.484609i
$120$	−0.505744	−	2.31537i	−0.0461679	−	0.211363i
$121$	−12.3728	−	21.4303i	−1.12480	−	1.94821i
$122$	−12.4165	+	0.891591i	−1.12414	+	0.0807209i
$123$	−0.751617	+	1.30184i	−0.0677710	+	0.117383i
$124$	17.2126	−	2.48478i	1.54574	−	0.223140i
$125$	−1.00000			−0.0894427
$126$	−7.95341	−	3.26633i	−0.708546	−	0.290988i
$127$		−	5.22434i		−	0.463585i	−0.972765	−	0.231793i	$-0.925541\pi$
$127$		−	5.22434i		−	0.463585i	0.972765	−	0.231793i	$-0.0744591\pi$
$128$	0.246747	−	11.3110i	0.0218095	−	0.999762i
$129$	−4.88913	−	2.82274i	−0.430464	−	0.248528i
$130$	4.05605	−	0.291252i	0.355739	−	0.0255445i
$131$	7.76094	−	4.48078i	0.678076	−	0.391487i	−0.121054	−	0.992646i	$-0.538627\pi$
$131$	7.76094	−	4.48078i	0.678076	−	0.391487i	0.799130	+	0.601159i	$0.205294\pi$
$132$	−9.30370	−	3.71851i	−0.809783	−	0.323655i
$133$	−12.3662	+	0.770575i	−1.07228	+	0.0668173i
$134$	4.50051	+	6.64543i	0.388785	+	0.574078i
$135$	3.84442	−	2.21958i	0.330875	−	0.191031i
$136$	−6.46212	−	2.05965i	−0.554123	−	0.176613i
$137$	10.4348	−	18.0735i	0.891502	−	1.54413i	0.0534263	−	0.998572i	$-0.482986\pi$
$137$	10.4348	−	18.0735i	0.891502	−	1.54413i	0.838075	−	0.545554i	$-0.183681\pi$
$138$	−3.47531	+	7.15940i	−0.295838	+	0.609449i
$139$			12.8189i			1.08728i	0.839318	+	0.543641i	$0.182955\pi$
$139$			12.8189i			1.08728i	−0.839318	+	0.543641i	$0.817045\pi$
$140$	3.94592	−	3.52558i	0.333491	−	0.297966i
$141$		−	1.46566i		−	0.123431i
$142$	3.90240	+	1.89430i	0.327482	+	0.158966i
$143$	8.59580	−	14.8884i	0.718817	−	1.24503i
$144$	8.81638	−	2.59961i	0.734698	−	0.216634i
$145$	−1.13479	+	0.655173i	−0.0942394	+	0.0544091i
$146$	11.7543	−	7.96038i	0.972789	−	0.658806i
$147$	0.728148	+	5.81997i	0.0600566	+	0.480023i
$148$	−7.01000	−	2.80176i	−0.576219	−	0.230303i
$149$	0.696284	−	0.402000i	0.0570418	−	0.0329331i	−0.471208	−	0.882022i	$-0.656182\pi$
$149$	0.696284	−	0.402000i	0.0570418	−	0.0329331i	0.528250	+	0.849089i	$0.322849\pi$
$150$	0.0848712	+	1.18194i	0.00692970	+	0.0965046i
$151$	−11.3405	−	6.54743i	−0.922875	−	0.532822i	−0.0383242	−	0.999265i	$-0.512202\pi$
$151$	−11.3405	−	6.54743i	−0.922875	−	0.532822i	−0.884551	+	0.466443i	$0.845535\pi$
$152$	9.79354	−	8.91818i	0.794361	−	0.723360i
$153$		−	5.51027i		−	0.445479i
$154$	−2.98683	−	22.1702i	−0.240686	−	1.78652i
$155$	−8.69550			−0.698440
$156$	−0.688483	−	4.76927i	−0.0551228	−	0.381847i
$157$	−8.58489	+	14.8695i	−0.685149	+	1.18671i	0.288241	+	0.957558i	$0.406930\pi$
$157$	−8.58489	+	14.8695i	−0.685149	+	1.18671i	−0.973390	+	0.229155i	$0.926404\pi$
$158$	1.40178	+	19.5215i	0.111519	+	1.55305i
$159$	0.0481079	+	0.0833254i	0.00381521	+	0.00660813i
$160$	−0.930151	+	5.57986i	−0.0735349	+	0.441127i
$161$	−17.7345	+	1.10509i	−1.39767	+	0.0870932i
$162$	2.51713	+	3.71678i	0.197764	+	0.292018i
$163$	−2.93458	−	5.08284i	−0.229854	−	0.398119i	0.727911	−	0.685672i	$-0.240492\pi$
$163$	−2.93458	−	5.08284i	−0.229854	−	0.398119i	−0.957765	+	0.287553i	$0.907158\pi$
$164$	2.81915	−	2.21960i	0.220139	−	0.173322i
$165$	4.33848	+	2.50482i	0.337750	+	0.195000i
$166$	−22.1644	−	10.7590i	−1.72029	−	0.835063i
$167$	−6.02260			−0.466043			−0.233022	−	0.972472i	$-0.574861\pi$
$167$	−6.02260			−0.466043			−0.233022	+	0.972472i	$0.574861\pi$
$168$	−4.50191	−	4.36460i	−0.347330	−	0.336736i
$169$	−4.73183			−0.363987
$170$	3.05077	+	1.48090i	0.233984	+	0.113580i
$171$	9.31950	+	5.38062i	0.712680	+	0.411466i
$172$	8.33583	+	10.5875i	0.635601	+	0.807288i
$173$	−1.08168	−	1.87352i	−0.0822385	−	0.142441i	0.821973	−	0.569527i	$-0.192874\pi$
$173$	−1.08168	−	1.87352i	−0.0822385	−	0.142441i	−0.904211	+	0.427086i	$0.859540\pi$
$174$	0.870683	+	1.28565i	0.0660063	+	0.0974646i
$175$	−2.20458	+	1.46282i	−0.166651	+	0.110578i
$176$	17.3269	+	16.4836i	1.30606	+	1.24250i
$177$	1.26439	+	2.18998i	0.0950371	+	0.164609i
$178$	1.29425	+	18.0240i	0.0970081	+	1.35096i
$179$	5.63498	−	9.76008i	0.421178	−	0.729502i	−0.574877	−	0.818240i	$-0.694950\pi$
$179$	5.63498	−	9.76008i	0.421178	−	0.729502i	0.996055	+	0.0887377i	$0.0282833\pi$
$180$	−4.54867	+	0.656639i	−0.339038	+	0.0489430i
$181$	−15.2369			−1.13255			−0.566274	−	0.824217i	$-0.691616\pi$
$181$	−15.2369			−1.13255			−0.566274	+	0.824217i	$0.691616\pi$
$182$	8.51583	−	6.57534i	0.631235	−	0.487396i
$183$		−	7.37559i		−	0.545219i
$184$	14.0450	−	12.7896i	1.03541	−	0.942865i
$185$	3.26889	+	1.88729i	0.240333	+	0.138757i
$186$	0.737998	+	10.2775i	0.0541126	+	0.753585i
$187$	12.4160	−	7.16838i	0.907948	−	0.524204i
$188$	−1.29838	+	3.24854i	−0.0946938	+	0.236924i
$189$	5.22850	−	10.5169i	0.380317	−	0.764993i
$190$	−5.48363	+	3.71370i	−0.397825	+	0.269420i
$191$	5.33642	−	3.08099i	0.386130	−	0.222932i	−0.294352	−	0.955697i	$-0.595104\pi$
$191$	5.33642	−	3.08099i	0.386130	−	0.222932i	0.680482	+	0.732765i	$0.261770\pi$
$192$	6.67397	+	0.625809i	0.481653	+	0.0451639i
$193$	5.79750	−	10.0416i	0.417313	−	0.722808i	−0.578355	−	0.815785i	$-0.696305\pi$
$193$	5.79750	−	10.0416i	0.417313	−	0.722808i	0.995668	+	0.0929776i	$0.0296385\pi$
$194$	4.78912	+	2.32473i	0.343839	+	0.166906i
$195$			2.40935i			0.172537i
$196$	3.54181	−	13.5446i	0.252986	−	0.967470i
$197$			13.1499i			0.936892i	0.883492	+	0.468446i	$0.155186\pi$
$197$			13.1499i			0.936892i	−0.883492	+	0.468446i	$0.844814\pi$
$198$	−8.48461	+	17.4790i	−0.602975	+	1.24218i
$199$	10.0683	−	17.4388i	0.713724	−	1.23621i	−0.249726	−	0.968317i	$-0.580341\pi$
$199$	10.0683	−	17.4388i	0.713724	−	1.23621i	0.963450	−	0.267889i	$-0.0863261\pi$
$200$	0.858921	−	2.69486i	0.0607349	−	0.190555i
$201$	−4.11822	+	2.37765i	−0.290477	+	0.167707i
$202$	−12.9117	−	19.0654i	−0.908467	−	1.34144i
$203$	−1.54334	+	3.10437i	−0.108321	+	0.217884i
$204$	1.49141	−	3.73150i	0.104420	−	0.261258i
$205$	−1.55368	+	0.897018i	−0.108514	+	0.0626504i
$206$	−3.19299	+	0.229279i	−0.222466	+	0.0159746i
$207$	13.3652	+	7.71639i	0.928944	+	0.536326i
$208$	−2.69894	+	11.1806i	−0.187138	+	0.775237i
$209$			27.9988i			1.93672i
$210$	1.91606	+	2.48152i	0.132221	+	0.171241i
$211$	4.31289			0.296912			0.148456	−	0.988919i	$-0.452570\pi$
$211$	4.31289			0.296912			0.148456	+	0.988919i	$0.452570\pi$
$212$	−0.0328129	−	0.227302i	−0.00225360	−	0.0156111i
$213$	−1.28507	+	2.22581i	−0.0880516	+	0.152510i
$214$	3.41629	−	0.245314i	0.233533	−	0.0167693i
$215$	−3.36880	−	5.83493i	−0.229750	−	0.397939i
$216$	2.67939	+	12.2666i	0.182309	+	0.834637i
$217$	−19.1699	+	12.7199i	−1.30134	+	0.863484i
$218$	8.58706	−	5.81545i	0.581589	−	0.393872i
$219$	4.20553	+	7.28419i	0.284183	+	0.492220i
$220$	−7.39699	−	9.39505i	−0.498705	−	0.633414i
$221$	5.97138	+	3.44758i	0.401679	+	0.231909i
$222$	1.95322	−	4.02379i	0.131092	−	0.270059i
$223$	11.5948			0.776447			0.388224	−	0.921565i	$-0.373089\pi$
$223$	11.5948			0.776447			0.388224	+	0.921565i	$0.373089\pi$
$224$	6.11171	+	13.6619i	0.408356	+	0.912823i
$225$	2.29791			0.153194
$226$	9.30441	−	19.1678i	0.618920	−	1.27502i
$227$	16.7181	+	9.65222i	1.10962	+	0.640640i	0.938731	−	0.344650i	$-0.112002\pi$
$227$	16.7181	+	9.65222i	1.10962	+	0.640640i	0.170890	+	0.985290i	$0.445336\pi$
$228$	4.85476	+	6.16611i	0.321514	+	0.408361i
$229$	8.54131	+	14.7940i	0.564425	+	0.977613i	0.997103	+	0.0760647i	$0.0242355\pi$
$229$	8.54131	+	14.7940i	0.564425	+	0.977613i	−0.432678	+	0.901549i	$0.642431\pi$
$230$	−7.86413	+	5.32585i	−0.518545	+	0.351176i
$231$	13.2286	−	0.824315i	0.870379	−	0.0542360i
$232$	−0.790899	−	3.62085i	−0.0519251	−	0.237720i
$233$	−6.11671	−	10.5945i	−0.400719	−	0.694066i	0.593094	−	0.805133i	$-0.297906\pi$
$233$	−6.11671	−	10.5945i	−0.400719	−	0.694066i	−0.993813	+	0.111068i	$0.964573\pi$
$234$	−9.32044	+	0.669273i	−0.609296	+	0.0437517i
$235$	0.874599	−	1.51485i	0.0570525	−	0.0988179i
$236$	−0.862397	−	5.97400i	−0.0561373	−	0.388875i
$237$	−11.5960			−0.753244
$238$	8.89196	−	1.19795i	0.576380	−	0.0776516i
$239$			1.56688i			0.101353i	0.998715	+	0.0506767i	$0.0161378\pi$
$239$			1.56688i			0.101353i	−0.998715	+	0.0506767i	$0.983862\pi$
$240$	−3.25804	−	0.786474i	−0.210306	−	0.0507667i
$241$	19.0828	+	11.0174i	1.22923	+	0.709695i	0.966869	−	0.255275i	$-0.0821659\pi$
$241$	19.0828	+	11.0174i	1.22923	+	0.709695i	0.262360	+	0.964970i	$0.415499\pi$
$242$	−34.9057	+	2.50647i	−2.24382	+	0.161122i
$243$	−13.8366	+	7.98855i	−0.887617	+	0.512466i
$244$	−6.53376	+	16.3474i	−0.418281	+	1.04654i
$245$	−2.72034	+	6.44979i	−0.173796	+	0.412062i
$246$	1.19208	+	1.76022i	0.0760042	+	0.112227i
$247$	−11.6618	+	6.73291i	−0.742019	+	0.428405i
$248$	7.46875	−	23.4331i	0.474266	−	1.48801i
$249$	7.29881	−	12.6419i	0.462543	−	0.801148i
$250$	−0.617571	+	1.27224i	−0.0390586	+	0.0804638i
$251$		−	7.68553i		−	0.485106i	−0.970138	−	0.242553i	$-0.922015\pi$
$251$		−	7.68553i		−	0.485106i	0.970138	−	0.242553i	$-0.0779849\pi$
$252$	−9.06737	+	8.10148i	−0.571191	+	0.510346i
$253$			40.1534i			2.52442i
$254$	−6.64664	−	3.22640i	−0.417047	−	0.202443i
$255$	−1.00463	+	1.74007i	−0.0629122	+	0.108967i
$256$	−14.2380	−	7.29928i	−0.889875	−	0.456205i
$257$	1.93788	−	1.11883i	0.120881	−	0.0697909i	−0.438340	−	0.898809i	$-0.644433\pi$
$257$	1.93788	−	1.11883i	0.120881	−	0.0697909i	0.559221	+	0.829018i	$0.311100\pi$
$258$	−6.61060	+	4.47692i	−0.411558	+	0.278721i
$259$	9.96728	−	0.621092i	0.619337	−	0.0385928i
$260$	2.13435	−	5.34015i	0.132367	−	0.331182i
$261$	2.60765	−	1.50553i	0.161410	−	0.0931900i
$262$	−0.907712	−	12.6410i	−0.0560787	−	0.780964i
$263$	−15.0365	−	8.68130i	−0.927188	−	0.535312i	−0.0412668	−	0.999148i	$-0.513139\pi$
$263$	−15.0365	−	8.68130i	−0.927188	−	0.535312i	−0.885921	+	0.463836i	$0.846473\pi$
$264$	−10.4765	+	9.54013i	−0.644787	+	0.587155i
$265$			0.114829i			0.00705388i
$266$	−6.65665	+	16.2087i	−0.408145	+	0.993819i
$267$	−10.7065			−0.655229
$268$	11.2340	−	1.62172i	0.686226	−	0.0990624i
$269$	0.374476	−	0.648612i	0.0228322	−	0.0395466i	−0.854384	−	0.519643i	$-0.826065\pi$
$269$	0.374476	−	0.648612i	0.0228322	−	0.0395466i	0.877216	+	0.480096i	$0.159398\pi$
$270$	−0.449640	−	6.26179i	−0.0273642	−	0.381080i
$271$	10.8572	+	18.8052i	0.659527	+	1.14233i	0.980738	+	0.195327i	$0.0625767\pi$
$271$	10.8572	+	18.8052i	0.659527	+	1.14233i	−0.321211	+	0.947008i	$0.604090\pi$
$272$	−6.61120	+	6.94942i	−0.400863	+	0.421370i
$273$	3.52444	+	5.31161i	0.213309	+	0.321473i
$274$	−16.5497	−	24.4373i	−0.999806	−	1.47631i
$275$	2.98938	+	5.17776i	0.180266	+	0.312231i
$276$	6.96225	+	8.84288i	0.419078	+	0.532279i
$277$	−20.4537	−	11.8089i	−1.22894	−	0.709531i	−0.262135	−	0.965031i	$-0.584426\pi$
$277$	−20.4537	−	11.8089i	−1.22894	−	0.709531i	−0.966809	+	0.255500i	$0.917760\pi$
$278$	16.3087	+	7.91657i	0.978133	+	0.474804i
$279$	19.9815			1.19626
$280$	−2.04852	−	7.19747i	−0.122422	−	0.430131i
$281$	−14.4129			−0.859803			−0.429901	−	0.902876i	$-0.641452\pi$
$281$	−14.4129			−0.859803			−0.429901	+	0.902876i	$0.641452\pi$
$282$	−1.86468	−	0.905152i	−0.111040	−	0.0539010i
$283$	10.7892	+	6.22915i	0.641351	+	0.370284i	0.785135	−	0.619325i	$-0.212594\pi$
$283$	10.7892	+	6.22915i	0.641351	+	0.370284i	−0.143784	+	0.989609i	$0.545927\pi$
$284$	4.82002	−	3.79494i	0.286016	−	0.225188i
$285$	−1.96198	−	3.39824i	−0.116217	−	0.201295i
$286$	−13.6331	−	20.1306i	−0.806143	−	1.19035i
$287$	−2.11304	+	4.25030i	−0.124729	+	0.250887i
$288$	2.13741	−	12.8220i	0.125948	−	0.755545i
$289$	−5.62493	−	9.74266i	−0.330878	−	0.573097i
$290$	0.132724	+	1.84835i	0.00779384	+	0.108539i
$291$	−1.57707	+	2.73157i	−0.0924495	+	0.160127i
$292$	−2.86846	−	19.8704i	−0.167864	−	1.16283i
$293$	8.47355			0.495030			0.247515	−	0.968884i	$-0.420386\pi$
$293$	8.47355			0.495030			0.247515	+	0.968884i	$0.420386\pi$
$294$	7.85411	+	2.66787i	0.458061	+	0.155593i
$295$			3.01797i			0.175713i
$296$	−7.89370	+	7.18815i	−0.458812	+	0.417803i
$297$	−22.9849	−	13.2703i	−1.33372	−	0.770023i
$298$	−0.0814368	−	1.13411i	−0.00471751	−	0.0656971i
$299$	−16.7242	+	9.65573i	−0.967187	+	0.558406i
$300$	1.55612	+	0.621953i	0.0898429	+	0.0359084i
$301$	−15.9622	−	7.93564i	−0.920047	−	0.457403i
$302$	−15.3335	+	10.3844i	−0.882343	+	0.597553i
$303$	11.8150	−	6.82137i	0.678752	−	0.391877i
$304$	−5.29789	−	17.9674i	−0.303855	−	1.03050i
$305$	4.40120	−	7.62310i	0.252012	−	0.436498i
$306$	−7.01041	−	3.40299i	−0.400759	−	0.194536i
$307$		−	11.9420i		−	0.681565i	−0.940142	−	0.340783i	$-0.889308\pi$
$307$		−	11.9420i		−	0.681565i	0.940142	−	0.340783i	$-0.110692\pi$
$308$	−30.0505	−	9.89170i	−1.71229	−	0.563632i
$309$		−	1.89668i		−	0.107899i
$310$	−5.37009	+	11.0628i	−0.305001	+	0.628325i
$311$	−7.74793	+	13.4198i	−0.439345	+	0.760967i	−0.997639	−	0.0686757i	$-0.978123\pi$
$311$	−7.74793	+	13.4198i	−0.439345	+	0.760967i	0.558294	+	0.829643i	$0.311456\pi$
$312$	−6.49286	−	2.06944i	−0.367586	−	0.117159i
$313$	14.9712	−	8.64360i	0.846220	−	0.488565i	−0.0131537	−	0.999913i	$-0.504187\pi$
$313$	14.9712	−	8.64360i	0.846220	−	0.488565i	0.859374	+	0.511348i	$0.170854\pi$
$314$	13.6158	+	20.1050i	0.768385	+	1.13459i
$315$	5.06593	−	3.36142i	0.285433	−	0.189395i
$316$	25.7018	+	10.2725i	1.44584	+	0.577873i
$317$	7.20732	−	4.16115i	0.404803	−	0.233713i	−0.283751	−	0.958898i	$-0.591579\pi$
$317$	7.20732	−	4.16115i	0.404803	−	0.233713i	0.688554	+	0.725185i	$0.258246\pi$
$318$	0.135720	−	0.00974566i	0.00761082	−	0.000546510i
$319$	6.78466	+	3.91712i	0.379868	+	0.219317i
$320$	6.52451	+	4.62934i	0.364731	+	0.258788i
$321$			2.02933i			0.113266i
$322$	−9.54636	+	23.2450i	−0.531998	+	1.29540i
$323$	−11.2297			−0.624837
$324$	6.28315	−	0.907025i	0.349064	−	0.0503903i
$325$	−1.43772	+	2.49021i	−0.0797504	+	0.138132i
$326$	−8.27893	+	0.594485i	−0.458527	+	0.0329255i
$327$	3.07235	+	5.32146i	0.169901	+	0.294277i
$328$	−1.08285	−	4.95741i	−0.0597901	−	0.273727i
$329$	−0.287823	−	4.61898i	−0.0158682	−	0.254653i
$330$	5.86607	−	3.97270i	0.322916	−	0.218690i
$331$	12.6436	+	21.8993i	0.694953	+	1.20369i	0.970197	+	0.242319i	$0.0779082\pi$
$331$	12.6436	+	21.8993i	0.694953	+	1.20369i	−0.275244	+	0.961375i	$0.588759\pi$
$332$	−27.3763	+	21.5541i	−1.50247	+	1.18294i
$333$	−7.51162	−	4.33683i	−0.411634	−	0.237657i
$334$	−3.71939	+	7.66222i	−0.203516	+	0.419258i
$335$	−5.67523			−0.310071
$336$	−8.33308	+	3.03207i	−0.454607	+	0.165413i
$337$	−0.379048			−0.0206481			−0.0103240	−	0.999947i	$-0.503286\pi$
$337$	−0.379048			−0.0206481			−0.0103240	+	0.999947i	$0.503286\pi$
$338$	−2.92224	+	6.02004i	−0.158949	+	0.327447i
$339$	10.9327	+	6.31200i	0.593783	+	0.342821i
$340$	3.76814	−	2.96677i	0.204356	−	0.160895i
$341$	25.9942	+	45.0232i	1.40766	+	2.43815i
$342$	12.6009	−	8.53377i	0.681379	−	0.461453i
$343$	3.43764	+	18.1984i	0.185615	+	0.982623i
$344$	18.6178	−	4.06668i	1.00381	−	0.219261i
$345$	−2.81369	−	4.87345i	−0.151484	−	0.262378i
$346$	−3.05159	+	0.219125i	−0.164055	+	0.0117803i
$347$	4.89803	−	8.48364i	0.262940	−	0.455426i	−0.704082	−	0.710119i	$-0.748641\pi$
$347$	4.89803	−	8.48364i	0.262940	−	0.455426i	0.967022	+	0.254693i	$0.0819745\pi$
$348$	2.17336	−	0.313743i	0.116505	−	0.0168184i
$349$	−6.73905			−0.360733			−0.180366	−	0.983599i	$-0.557728\pi$
$349$	−6.73905			−0.360733			−0.180366	+	0.983599i	$0.557728\pi$
$350$	0.499573	+	3.70816i	0.0267033	+	0.198209i
$351$		−	12.7645i		−	0.681321i
$352$	31.6717	−	11.8642i	1.68811	−	0.632365i
$353$	18.5926	+	10.7345i	0.989587	+	0.571338i	0.905151	−	0.425091i	$-0.139758\pi$
$353$	18.5926	+	10.7345i	0.989587	+	0.571338i	0.0844361	+	0.996429i	$0.473091\pi$
$354$	3.56704	−	0.256138i	0.189586	−	0.0136136i
$355$	−2.65639	+	1.53367i	−0.140987	+	0.0813986i
$356$	23.7302	+	9.48451i	1.25770	+	0.502678i
$357$	0.330614	+	5.30570i	0.0174980	+	0.280807i
$358$	−8.93720	−	13.1966i	−0.472346	−	0.697463i
$359$	−4.15852	+	2.40092i	−0.219478	+	0.126716i	−0.605709	−	0.795687i	$-0.707110\pi$
$359$	−4.15852	+	2.40092i	−0.219478	+	0.126716i	0.386231	+	0.922402i	$0.373777\pi$
$360$	−1.97373	+	6.19255i	−0.104025	+	0.326376i
$361$	1.46546	−	2.53825i	0.0771294	−	0.133592i
$362$	−9.40986	+	19.3850i	−0.494571	+	1.01885i
$363$		−	20.7345i		−	1.08828i
$364$	−3.10630	−	14.8950i	−0.162815	−	0.780708i
$365$			10.0382i			0.525423i
$366$	−9.38355	−	4.55495i	−0.490486	−	0.238091i
$367$	−5.81465	+	10.0713i	−0.303522	+	0.525716i	−0.976931	−	0.213554i	$-0.931496\pi$
$367$	−5.81465	+	10.0713i	−0.303522	+	0.525716i	0.673409	+	0.739270i	$0.264829\pi$
$368$	−7.59775	−	25.7672i	−0.396060	−	1.34321i
$369$	3.57022	−	2.06127i	0.185858	−	0.107305i
$370$	4.41987	−	2.99328i	0.229778	−	0.155613i
$371$	0.167973	+	0.253149i	0.00872075	+	0.0131429i
$372$	13.5313	+	5.40819i	0.701564	+	0.280402i
$373$	25.2282	−	14.5655i	1.30627	−	0.754174i	0.324797	−	0.945784i	$-0.394704\pi$
$373$	25.2282	−	14.5655i	1.30627	−	0.754174i	0.981471	+	0.191610i	$0.0613707\pi$
$374$	−1.45216	−	20.2232i	−0.0750896	−	1.04571i
$375$	−0.725648	−	0.418953i	−0.0374723	−	0.0216346i
$376$	3.33109	+	3.65805i	0.171788	+	0.188650i
$377$			3.76782i			0.194053i
$378$	−10.1511	−	13.1469i	−0.522117	−	0.676202i
$379$	2.52399			0.129649			0.0648243	−	0.997897i	$-0.479351\pi$
$379$	2.52399			0.129649			0.0648243	+	0.997897i	$0.479351\pi$
$380$	1.33820	+	9.27000i	0.0686483	+	0.475541i
$381$	2.18875	−	3.79103i	0.112133	−	0.194221i
$382$	−0.624144	−	8.69197i	−0.0319340	−	0.444720i
$383$	−11.6539	−	20.1851i	−0.595485	−	1.03141i	−0.993478	−	0.114022i	$-0.963627\pi$
$383$	−11.6539	−	20.1851i	−0.595485	−	1.03141i	0.397993	−	0.917388i	$-0.369707\pi$
$384$	4.91784	−	8.10444i	0.250962	−	0.413578i
$385$	14.1644	+	7.04187i	0.721887	+	0.358887i
$386$	−9.19495	−	13.5772i	−0.468011	−	0.691062i
$387$	7.74121	+	13.4082i	0.393508	+	0.681575i
$388$	5.91525	−	4.65725i	0.300301	−	0.236436i
$389$	−0.383453	−	0.221387i	−0.0194418	−	0.0112248i	0.490248	−	0.871583i	$-0.336906\pi$
$389$	−0.383453	−	0.221387i	−0.0194418	−	0.0112248i	−0.509689	+	0.860358i	$0.670240\pi$
$390$	3.06528	+	1.48795i	0.155217	+	0.0753451i
$391$	−16.1046			−0.814445
$392$	−15.0447	−	12.8708i	−0.759872	−	0.650073i
$393$	7.50895			0.378776
$394$	16.7299	+	8.12101i	0.842840	+	0.409130i
$395$	−11.9852	−	6.91965i	−0.603041	−	0.348166i
$396$	16.9976	+	21.5890i	0.854164	+	1.08489i
$397$	−4.05153	−	7.01745i	−0.203340	−	0.352196i	0.746262	−	0.665652i	$-0.231846\pi$
$397$	−4.05153	−	7.01745i	−0.203340	−	0.352196i	−0.949603	+	0.313456i	$0.898513\pi$
$398$	−15.9685	−	23.5791i	−0.800431	−	1.18191i
$399$	−9.29634	−	4.62169i	−0.465399	−	0.231374i
$400$	−2.89807	−	2.75702i	−0.144904	−	0.137851i
$401$	−1.01905	−	1.76504i	−0.0508889	−	0.0881421i	0.839459	−	0.543423i	$-0.182872\pi$
$401$	−1.01905	−	1.76504i	−0.0508889	−	0.0881421i	−0.890348	+	0.455281i	$0.849539\pi$
$402$	0.481663	+	6.70775i	0.0240232	+	0.334552i
$403$	−12.5017	+	21.6536i	−0.622755	+	1.07864i
$404$	−32.2298	+	4.65264i	−1.60349	+	0.231477i
$405$	−3.17414			−0.157724
$406$	2.99640	+	3.88068i	0.148709	+	0.192595i
$407$		−	22.5674i		−	1.11862i
$408$	−3.82633	−	4.20191i	−0.189432	−	0.208025i
$409$	−27.1993	−	15.7035i	−1.34492	−	0.776490i	−0.357395	−	0.933953i	$-0.616335\pi$
$409$	−27.1993	−	15.7035i	−1.34492	−	0.776490i	−0.987525	+	0.157463i	$0.949668\pi$
$410$	0.181717	+	2.53063i	0.00897437	+	0.124979i
$411$	15.1439	−	8.74335i	0.746995	−	0.431278i
$412$	−1.68020	+	4.20386i	−0.0827776	+	0.207109i
$413$	4.41473	+	6.65334i	0.217235	+	0.327390i
$414$	18.0711	−	12.2384i	0.888145	−	0.601482i
$415$	15.0875	−	8.71077i	0.740616	−	0.427595i
$416$	12.5577	+	10.3386i	0.615692	+	0.506889i
$417$	−5.37051	+	9.30199i	−0.262995	+	0.455521i
$418$	35.6213	+	17.2913i	1.74230	+	0.845744i
$419$		−	18.1384i		−	0.886117i	−0.896493	−	0.443059i	$-0.853893\pi$
$419$		−	18.1384i		−	0.886117i	0.896493	−	0.443059i	$-0.146107\pi$
$420$	4.34040	−	0.905179i	0.211790	−	0.0441682i
$421$		−	38.6453i		−	1.88345i	−0.336377	−	0.941727i	$-0.609202\pi$
$421$		−	38.6453i		−	1.88345i	0.336377	−	0.941727i	$-0.390798\pi$
$422$	2.66352	−	5.48705i	0.129658	−	0.267105i
$423$	−2.00975	+	3.48099i	−0.0977175	+	0.169252i
$424$	−0.309447	−	0.0986290i	−0.0150281	−	0.00478985i
$425$	−2.07668	+	1.19897i	−0.100734	+	0.0581588i
$426$	2.03815	+	3.00952i	0.0987486	+	0.145812i
$427$	−1.44840	−	23.2439i	−0.0700928	−	1.12485i
$428$	1.79771	−	4.49786i	0.0868954	−	0.217412i
$429$	12.4750	−	7.20247i	0.602301	−	0.347739i
$430$	−9.50393	+	0.682449i	−0.458320	+	0.0329106i
$431$	−3.59352	−	2.07472i	−0.173094	−	0.0999358i	0.410950	−	0.911658i	$-0.365197\pi$
$431$	−3.59352	−	2.07472i	−0.173094	−	0.0999358i	−0.584044	+	0.811722i	$0.698530\pi$
$432$	17.2608	+	4.16667i	0.830462	+	0.200469i
$433$			21.7089i			1.04326i	0.853170	+	0.521632i	$0.174677\pi$
$433$			21.7089i			1.04326i	−0.853170	+	0.521632i	$0.825323\pi$
$434$	4.34404	+	32.2443i	0.208521	+	1.54778i
$435$	−1.09795			−0.0526425
$436$	−2.09555	−	14.5163i	−0.100359	−	0.695205i
$437$	15.7257	−	27.2376i	0.752260	−	1.30295i
$438$	11.8645	−	0.851953i	0.566907	−	0.0407079i
$439$	3.86516	+	6.69465i	0.184474	+	0.319518i	0.943399	−	0.331660i	$-0.107609\pi$
$439$	3.86516	+	6.69465i	0.184474	+	0.319518i	−0.758925	+	0.651178i	$0.774275\pi$
$440$	−16.5210	+	3.60867i	−0.787606	+	0.172036i
$441$	6.25111	−	14.8210i	0.297672	−	0.705764i
$442$	8.07392	−	5.46793i	0.384037	−	0.260083i
$443$	−8.93181	−	15.4704i	−0.424363	−	0.735019i	0.571998	−	0.820255i	$-0.306169\pi$
$443$	−8.93181	−	15.4704i	−0.424363	−	0.735019i	−0.996361	+	0.0852368i	$0.972835\pi$
$444$	−3.91299	−	4.96996i	−0.185702	−	0.235864i
$445$	−11.0658	−	6.38886i	−0.524570	−	0.302861i
$446$	7.16064	−	14.7515i	0.339066	−	0.698502i
$447$	0.673676			0.0318638
$448$	21.1557	+	0.661597i	0.999511	+	0.0312575i
$449$	29.3236			1.38387			0.691933	−	0.721961i	$-0.256759\pi$
$449$	29.3236			1.38387			0.691933	+	0.721961i	$0.256759\pi$
$450$	1.41913	−	2.92351i	0.0668982	−	0.137815i
$451$	9.28909	+	5.36306i	0.437406	+	0.252537i
$452$	−18.6400	−	23.6750i	−0.876751	−	1.11358i
$453$	−5.48613	−	9.50226i	−0.257761	−	0.446455i
$454$	22.6046	−	15.3086i	1.06089	−	0.718469i
$455$	0.473142	+	7.59298i	0.0221812	+	0.355964i
$456$	10.8430	−	2.36842i	0.507768	−	0.110912i
$457$	−4.64207	−	8.04029i	−0.217147	−	0.376109i	0.736788	−	0.676124i	$-0.236342\pi$
$457$	−4.64207	−	8.04029i	−0.217147	−	0.376109i	−0.953935	+	0.300015i	$0.903008\pi$
$458$	24.0964	−	1.73029i	1.12595	−	0.0808512i
$459$	5.32243	−	9.21872i	0.248430	−	0.430293i
$460$	1.91913	+	13.2942i	0.0894797	+	0.619845i
$461$	−0.401756			−0.0187116			−0.00935582	−	0.999956i	$-0.502978\pi$
$461$	−0.401756			−0.0187116			−0.00935582	+	0.999956i	$0.502978\pi$
$462$	7.12088	−	17.3391i	0.331293	−	0.806688i
$463$			9.04694i			0.420447i	0.977653	+	0.210223i	$0.0674191\pi$
$463$			9.04694i			0.420447i	−0.977653	+	0.210223i	$0.932581\pi$
$464$	−5.09504	−	1.22991i	−0.236531	−	0.0570973i
$465$	−6.30988	−	3.64301i	−0.292614	−	0.168940i
$466$	−17.2562	+	1.23912i	−0.799380	+	0.0574011i
$467$	−10.4257	+	6.01931i	−0.482446	+	0.278540i	−0.721435	−	0.692482i	$-0.756517\pi$
$467$	−10.4257	+	6.01931i	−0.482446	+	0.278540i	0.238989	+	0.971022i	$0.423184\pi$
$468$	−4.90456	+	12.2712i	−0.226713	+	0.567237i
$469$	−12.5115	+	8.30181i	−0.577727	+	0.383342i
$470$	−1.38713	−	2.04823i	−0.0639836	−	0.0944778i
$471$	−12.4592	+	7.19333i	−0.574091	+	0.331451i
$472$	−8.13299	−	2.59220i	−0.374351	−	0.119315i
$473$	−20.1413	+	34.8857i	−0.926096	+	1.60405i
$474$	−7.16139	+	14.7530i	−0.328933	+	0.677628i
$475$		−	4.68305i		−	0.214873i
$476$	3.96734	−	12.0526i	0.181843	−	0.552429i
$477$		−	0.263867i		−	0.0120816i
$478$	1.99346	+	0.967663i	0.0911788	+	0.0442599i
$479$	1.59624	−	2.76477i	0.0729340	−	0.126325i	−0.827252	−	0.561831i	$-0.810097\pi$
$479$	1.59624	−	2.76477i	0.0729340	−	0.126325i	0.900186	+	0.435506i	$0.143430\pi$
$480$	−3.01266	+	3.65932i	−0.137509	+	0.167025i
$481$	9.39950	−	5.42680i	0.428580	−	0.247441i
$482$	25.8018	−	17.4739i	1.17524	−	0.795913i
$483$	−13.3320	−	6.62800i	−0.606625	−	0.301585i
$484$	−18.3679	+	45.9565i	−0.834905	+	2.08893i
$485$	−3.25999	+	1.88216i	−0.148028	+	0.0854643i
$486$	1.61831	+	22.5370i	0.0734082	+	1.02230i
$487$	−3.30907	−	1.91049i	−0.149948	−	0.0865727i	0.423149	−	0.906060i	$-0.360925\pi$
$487$	−3.30907	−	1.91049i	−0.149948	−	0.0865727i	−0.573097	+	0.819488i	$0.694258\pi$
$488$	16.7629	+	18.4082i	0.758820	+	0.833302i
$489$		−	4.91781i		−	0.222391i
$490$	6.52570	+	7.44414i	0.294801	+	0.336292i
$491$	−42.7678			−1.93008			−0.965041	−	0.262097i	$-0.915586\pi$
$491$	−42.7678			−1.93008			−0.965041	+	0.262097i	$0.915586\pi$
$492$	2.97562	−	0.429556i	0.134151	−	0.0193659i
$493$	−1.57107	+	2.72117i	−0.0707574	+	0.122555i
$494$	1.36395	+	18.9947i	0.0613669	+	0.854610i
$495$	−6.86934	−	11.8980i	−0.308754	−	0.534777i
$496$	−25.2002	−	23.9737i	−1.13152	−	1.07645i
$497$	−3.61275	+	7.26690i	−0.162054	+	0.325965i
$498$	−11.5761	−	17.0931i	−0.518735	−	0.765962i
$499$	−3.71383	−	6.43253i	−0.166254	−	0.287960i	0.770846	−	0.637021i	$-0.219834\pi$
$499$	−3.71383	−	6.43253i	−0.166254	−	0.287960i	−0.937100	+	0.349062i	$0.886500\pi$
$500$	1.23721	+	1.57140i	0.0553298	+	0.0702753i
$501$	−4.37029	−	2.52319i	−0.195250	−	0.112728i
$502$	−9.77787	−	4.74636i	−0.436408	−	0.211840i
$503$	41.0916			1.83219			0.916093	−	0.400966i	$-0.131326\pi$
$503$	41.0916			1.83219			0.916093	+	0.400966i	$0.131326\pi$
$504$	4.70732	+	16.5392i	0.209681	+	0.736713i
$505$	16.2819			0.724537
$506$	51.0849	+	24.7976i	2.27100	+	1.10239i
$507$	−3.43364	−	1.98241i	−0.152493	−	0.0880421i
$508$	−8.20955	+	6.46361i	−0.364240	+	0.286776i
$509$	−17.7683	−	30.7755i	−0.787564	−	1.36410i	−0.927455	−	0.373934i	$-0.878009\pi$
$509$	−17.7683	−	30.7755i	−0.787564	−	1.36410i	0.139891	−	0.990167i	$-0.455325\pi$
$510$	1.59336	+	2.35275i	0.0705551	+	0.104181i
$511$	14.6840	+	22.1300i	0.649582	+	0.978972i
$512$	−18.0794	+	13.6064i	−0.799006	+	0.601323i
$513$	10.3944	+	18.0036i	0.458923	+	0.794878i
$514$	−0.226652	−	3.15641i	−0.00999720	−	0.139223i
$515$	1.13180	−	1.96034i	0.0498731	−	0.0863827i
$516$	1.61322	+	11.1751i	0.0710181	+	0.491957i
$517$	−10.4580			−0.459944
$518$	5.36533	−	13.0644i	0.235739	−	0.574016i
$519$		−	1.81269i		−	0.0795683i
$520$	−5.47586	−	6.01335i	−0.240132	−	0.263703i
$521$	−31.1264	−	17.9708i	−1.36367	−	0.787316i	−0.373561	−	0.927606i	$-0.621863\pi$
$521$	−31.1264	−	17.9708i	−1.36367	−	0.787316i	−0.990111	+	0.140289i	$0.955197\pi$
$522$	−0.304989	−	4.24735i	−0.0133490	−	0.185901i
$523$	−26.6453	+	15.3837i	−1.16512	+	0.672681i	−0.952525	−	0.304460i	$-0.901524\pi$
$523$	−26.6453	+	15.3837i	−1.16512	+	0.672681i	−0.212592	+	0.977141i	$0.568191\pi$
$524$	−16.6430	−	6.65189i	−0.727054	−	0.290589i
$525$	−2.21260	+	0.137874i	−0.0965658	+	0.00601731i
$526$	−20.3308	+	13.7687i	−0.886466	+	0.600345i
$527$	−18.0578	+	10.4257i	−0.786610	+	0.454150i
$528$	5.66736	+	19.2204i	0.246640	+	0.836462i
$529$	11.0523	−	19.1432i	0.480536	−	0.832312i
$530$	0.146090	+	0.0709150i	0.00634576	+	0.00308035i
$531$		−	6.93502i		−	0.300954i
$532$	16.5105	+	18.4789i	0.715820	+	0.801162i
$533$			5.15865i			0.223446i
$534$	−6.61204	+	13.6213i	−0.286131	+	0.589452i
$535$	−1.21095	+	2.09743i	−0.0523540	+	0.0906798i
$536$	4.87457	−	15.2939i	0.210550	−	0.660597i
$537$	8.17803	−	4.72159i	0.352908	−	0.203752i
$538$	−0.593927	−	0.876990i	−0.0256060	−	0.0378097i
$539$	41.5276	−	5.19560i	1.78872	−	0.223790i
$540$	−8.24421	−	3.29505i	−0.354774	−	0.141796i
$541$	−6.51224	+	3.75984i	−0.279983	+	0.161648i	−0.633416	−	0.773812i	$-0.718348\pi$
$541$	−6.51224	+	3.75984i	−0.279983	+	0.161648i	0.353433	+	0.935460i	$0.385014\pi$
$542$	30.6299	−	2.19944i	1.31567	−	0.0944740i
$543$	−11.0566	−	6.38354i	−0.474484	−	0.273944i
$544$	4.75847	+	12.7028i	0.204018	+	0.544629i
$545$			7.33339i			0.314128i
$546$	8.93425	−	1.20365i	0.382351	−	0.0515114i
$547$	10.8177			0.462531			0.231265	−	0.972891i	$-0.425713\pi$
$547$	10.8177			0.462531			0.231265	+	0.972891i	$0.425713\pi$
$548$	−41.3108	+	5.96356i	−1.76471	+	0.254751i
$549$	−10.1136	+	17.5172i	−0.431637	+	0.747617i
$550$	8.43353	−	0.605586i	0.359607	−	0.0258223i
$551$	−3.06820	−	5.31428i	−0.130710	−	0.226396i
$552$	15.5500	−	3.39658i	0.661852	−	0.144568i
$553$	−36.5445	+	2.27720i	−1.55403	+	0.0968364i
$554$	−27.6555	+	18.7292i	−1.17497	+	0.795729i
$555$	1.58137	+	2.73902i	0.0671256	+	0.116265i
$556$	20.1436	−	15.8597i	0.854280	−	0.672599i
$557$	20.6521	+	11.9235i	0.875057	+	0.505214i	0.869025	−	0.494767i	$-0.164747\pi$
$557$	20.6521	+	11.9235i	0.875057	+	0.505214i	0.00603158	+	0.999982i	$0.498080\pi$
$558$	12.3400	−	25.4214i	0.522394	−	1.07617i
$559$	−19.3736			−0.819415
$560$	−10.4220	−	1.83874i	−0.440412	−	0.0777008i
$561$	12.0129			0.507183
$562$	−8.90101	+	18.3368i	−0.375466	+	0.773489i
$563$	−1.24064	−	0.716284i	−0.0522868	−	0.0301878i	0.473629	−	0.880725i	$-0.342944\pi$
$563$	−1.24064	−	0.716284i	−0.0522868	−	0.0301878i	−0.525916	+	0.850537i	$0.676277\pi$
$564$	−2.30315	+	1.81334i	−0.0969801	+	0.0763552i
$565$	7.53306	+	13.0476i	0.316918	+	0.548919i
$566$	14.5881	−	9.87955i	0.613183	−	0.415269i
$567$	−6.99765	+	4.64319i	−0.293874	+	0.194995i
$568$	−1.85138	−	8.47589i	−0.0776824	−	0.355641i
$569$	13.6099	+	23.5731i	0.570558	+	0.988235i	0.996509	+	0.0834885i	$0.0266062\pi$
$569$	13.6099	+	23.5731i	0.570558	+	0.988235i	−0.425951	+	0.904746i	$0.640060\pi$
$570$	−5.53506	+	0.397456i	−0.231838	+	0.0166476i
$571$	−6.19271	+	10.7261i	−0.259157	+	0.448873i	−0.966016	−	0.258481i	$-0.916778\pi$
$571$	−6.19271	+	10.7261i	−0.259157	+	0.448873i	0.706859	+	0.707354i	$0.250111\pi$
$572$	−34.0304	+	4.91257i	−1.42288	+	0.205405i
$573$	5.16316			0.215694
$574$	4.10246	+	5.31316i	0.171233	+	0.221767i
$575$		−	6.71600i		−	0.280076i
$576$	−14.9928	−	10.6378i	−0.624698	−	0.443243i
$577$	20.3920	+	11.7733i	0.848929	+	0.490130i	0.860289	−	0.509806i	$-0.170283\pi$
$577$	20.3920	+	11.7733i	0.848929	+	0.490130i	−0.0113602	+	0.999935i	$0.503616\pi$
$578$	−15.8688	+	1.13949i	−0.660056	+	0.0473966i
$579$	8.41389	−	4.85776i	0.349669	−	0.201882i
$580$	2.43352	+	0.972630i	0.101046	+	0.0403863i
$581$	20.5193	−	41.2738i	0.851285	−	1.71233i
$582$	2.50126	+	3.69335i	0.103681	+	0.153094i
$583$	0.594557	−	0.343267i	0.0246240	−	0.0142167i
$584$	−27.0515	−	8.62201i	−1.11940	−	0.356781i
$585$	3.30376	−	5.72228i	0.136594	−	0.236587i
$586$	5.23302	−	10.7804i	0.216174	−	0.445335i
$587$			28.0077i			1.15600i	0.816036	+	0.578001i	$0.196167\pi$
$587$			28.0077i			1.15600i	−0.816036	+	0.578001i	$0.803833\pi$
$588$	8.24465	−	8.34475i	0.340004	−	0.344132i
$589$		−	40.7214i		−	1.67790i
$590$	3.83959	+	1.86381i	0.158073	+	0.0767318i
$591$	−5.50920	+	9.54221i	−0.226618	+	0.392514i
$592$	4.27015	+	14.4819i	0.175502	+	0.595203i
$593$	−28.9741	+	16.7282i	−1.18982	+	0.686945i	−0.958266	−	0.285877i	$-0.907715\pi$
$593$	−28.9741	+	16.7282i	−1.18982	+	0.686945i	−0.231557	+	0.972821i	$0.574382\pi$
$594$	−31.0779	+	21.0470i	−1.27514	+	0.863569i
$595$	−2.82434	+	5.68104i	−0.115786	+	0.232900i
$596$	−1.49315	−	0.596785i	−0.0611620	−	0.0244452i
$597$	14.6121	−	8.43630i	0.598034	−	0.345275i
$598$	1.95605	+	27.2404i	0.0799889	+	1.11394i
$599$	−37.2436	−	21.5026i	−1.52173	−	0.878571i	−0.999671	−	0.0256625i	$-0.991830\pi$
$599$	−37.2436	−	21.5026i	−1.52173	−	0.878571i	−0.522060	−	0.852909i	$-0.674836\pi$
$600$	1.75229	−	1.59567i	0.0715371	−	0.0651430i
$601$			32.3145i			1.31813i	0.752084	+	0.659067i	$0.229049\pi$
$601$			32.3145i			1.31813i	−0.752084	+	0.659067i	$0.770951\pi$
$602$	−19.9539	+	15.4070i	−0.813259	+	0.627943i
$603$	13.0412			0.531078
$604$	3.74192	+	25.9210i	0.152256	+	1.05471i
$605$	12.3728	−	21.4303i	0.503026	−	0.871267i
$606$	−1.38187	−	19.2442i	−0.0561345	−	0.781742i
$607$	6.75765	+	11.7046i	0.274285	+	0.475075i	0.969954	−	0.243287i	$-0.0782256\pi$
$607$	6.75765	+	11.7046i	0.274285	+	0.475075i	−0.695670	+	0.718362i	$0.744892\pi$
$608$	−26.1307	−	4.35594i	−1.05974	−	0.176657i
$609$	−2.42051	+	1.60609i	−0.0980841	+	0.0650822i
$610$	−6.98039	−	10.3072i	−0.282628	−	0.417327i
$611$	−2.51486	−	4.35586i	−0.101740	−	0.176219i
$612$	−8.65886	+	6.81737i	−0.350014	+	0.275576i
$613$	5.63444	+	3.25304i	0.227573	+	0.131389i	0.609452	−	0.792823i	$-0.291390\pi$
$613$	5.63444	+	3.25304i	0.227573	+	0.131389i	−0.381879	+	0.924212i	$0.624723\pi$
$614$	−15.1931	−	7.37503i	−0.613145	−	0.297632i
$615$	−1.50323			−0.0606162
$616$	−31.1430	+	32.1227i	−1.25479	+	1.29426i
$617$	−1.66184			−0.0669033			−0.0334516	−	0.999440i	$-0.510650\pi$
$617$	−1.66184			−0.0669033			−0.0334516	+	0.999440i	$0.510650\pi$
$618$	−2.41305	−	1.17134i	−0.0970670	−	0.0471181i
$619$	−24.5080	−	14.1497i	−0.985061	−	0.568725i	−0.0812670	−	0.996692i	$-0.525897\pi$
$619$	−24.5080	−	14.1497i	−0.985061	−	0.568725i	−0.903794	+	0.427967i	$0.859230\pi$
$620$	10.7582	+	13.6641i	0.432059	+	0.548765i
$621$	14.9067	+	25.8191i	0.598184	+	1.03609i
$622$	12.2884	+	18.1449i	0.492719	+	0.727546i
$623$	−33.7412	+	2.10252i	−1.35181	+	0.0842356i
$624$	−6.64264	+	6.98247i	−0.265919	+	0.279523i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−1.75101	−	24.3850i	−0.0699846	−	0.974621i
$627$	−11.7302	+	20.3173i	−0.468459	+	0.811395i
$628$	33.9873	−	4.90634i	1.35624	−	0.195784i
$629$	9.05126			0.360897
$630$	−1.14798	−	8.52102i	−0.0457365	−	0.339486i
$631$		−	48.7721i		−	1.94159i	−0.239918	−	0.970793i	$-0.577121\pi$
$631$		−	48.7721i		−	1.94159i	0.239918	−	0.970793i	$-0.422879\pi$
$632$	28.9418	−	26.3549i	1.15124	−	1.04834i
$633$	3.12964	+	1.80690i	0.124392	+	0.0718178i
$634$	−0.842961	−	11.7393i	−0.0334783	−	0.466226i
$635$	4.52441	−	2.61217i	0.179546	−	0.103661i
$636$	0.0714181	−	0.178688i	0.00283191	−	0.00708544i
$637$	12.1502	+	16.0472i	0.481409	+	0.635814i
$638$	9.17355	−	6.21264i	0.363184	−	0.245961i
$639$	6.10415	−	3.52424i	0.241477	−	0.139417i
$640$	9.91900	−	5.44182i	0.392083	−	0.215107i
$641$	−10.8633	+	18.8158i	−0.429074	+	0.743178i	−0.996791	−	0.0800459i	$-0.974493\pi$
$641$	−10.8633	+	18.8158i	−0.429074	+	0.743178i	0.567717	+	0.823224i	$0.307827\pi$
$642$	2.58180	+	1.25326i	0.101896	+	0.0494620i
$643$			7.13929i			0.281546i	0.990042	+	0.140773i	$0.0449588\pi$
$643$			7.13929i			0.281546i	−0.990042	+	0.140773i	$0.955041\pi$
$644$	23.6778	+	26.5008i	0.933037	+	1.04428i
$645$		−	5.64548i		−	0.222290i
$646$	−6.93514	+	14.2869i	−0.272859	+	0.562111i
$647$	4.58700	−	7.94492i	0.180334	−	0.312347i	−0.761661	−	0.647976i	$-0.775616\pi$
$647$	4.58700	−	7.94492i	0.180334	−	0.312347i	0.941994	+	0.335629i	$0.108949\pi$
$648$	2.72634	−	8.55386i	0.107101	−	0.336027i
$649$	15.6263	−	9.02185i	0.613386	−	0.354139i
$650$	2.28026	+	3.36701i	0.0894390	+	0.132065i
$651$	−19.2397	+	1.19888i	−0.754062	+	0.0469879i
$652$	−4.35650	+	10.9000i	−0.170614	+	0.426875i
$653$	−0.710174	+	0.410019i	−0.0277913	+	0.0160453i	−0.513831	−	0.857891i	$-0.671774\pi$
$653$	−0.710174	+	0.410019i	−0.0277913	+	0.0160453i	0.486040	+	0.873937i	$0.338441\pi$
$654$	8.66759	−	0.622393i	0.338930	−	0.0243375i
$655$	7.76094	+	4.48078i	0.303245	+	0.175079i
$656$	−6.97578	−	1.68391i	−0.272358	−	0.0657458i
$657$		−	23.0669i		−	0.899924i
$658$	−6.05422	−	2.48637i	−0.236018	−	0.0969288i
$659$	−10.4133			−0.405645			−0.202823	−	0.979216i	$-0.565011\pi$
$659$	−10.4133			−0.405645			−0.202823	+	0.979216i	$0.565011\pi$
$660$	−1.43153	−	9.91649i	−0.0557222	−	0.385999i
$661$	−2.76908	+	4.79619i	−0.107705	+	0.186550i	−0.914840	−	0.403816i	$-0.867683\pi$
$661$	−2.76908	+	4.79619i	−0.107705	+	0.186550i	0.807135	+	0.590367i	$0.201017\pi$
$662$	35.6695	−	2.56132i	1.38634	−	0.0995486i
$663$	2.88875	+	5.00346i	0.112190	+	0.194318i
$664$	10.5153	+	48.1405i	0.408073	+	1.86821i
$665$	−6.85043	−	10.3241i	−0.265648	−	0.400353i
$666$	−10.1565	+	6.87831i	−0.393555	+	0.266529i
$667$	−4.40014	−	7.62126i	−0.170374	−	0.295097i
$668$	7.45123	+	9.46394i	0.288297	+	0.366171i
$669$	8.41377	+	4.85769i	0.325295	+	0.187809i
$670$	−3.50486	+	7.22027i	−0.135404	+	0.278944i
$671$	−52.6275			−2.03166
$672$	−1.28874	+	12.4742i	−0.0497141	+	0.481204i
$673$	28.9492			1.11591			0.557956	−	0.829871i	$-0.311586\pi$
$673$	28.9492			1.11591			0.557956	+	0.829871i	$0.311586\pi$
$674$	−0.234089	+	0.482242i	−0.00901679	+	0.0185753i
$675$	3.84442	+	2.21958i	0.147972	+	0.0854316i
$676$	5.85427	+	7.43561i	0.225164	+	0.285985i
$677$	−2.77831	−	4.81218i	−0.106779	−	0.184947i	0.807685	−	0.589615i	$-0.200720\pi$
$677$	−2.77831	−	4.81218i	−0.106779	−	0.184947i	−0.914464	+	0.404668i	$0.867387\pi$
$678$	14.7821	−	10.0110i	0.567705	−	0.384469i
$679$	−4.43366	+	8.91812i	−0.170148	+	0.342246i
$680$	−1.44735	−	6.62619i	−0.0555035	−	0.254103i
$681$	8.08766	+	14.0082i	0.309920	+	0.536797i
$682$	73.3338	−	5.26588i	2.80810	−	0.201641i
$683$	−17.5473	+	30.3928i	−0.671428	+	1.16295i	0.306071	+	0.952009i	$0.400986\pi$
$683$	−17.5473	+	30.3928i	−0.671428	+	1.16295i	−0.977499	+	0.210939i	$0.932348\pi$
$684$	−3.07507	−	21.3017i	−0.117578	−	0.814489i
$685$	20.8695			0.797383
$686$	25.2758	+	6.86531i	0.965036	+	0.262119i
$687$			14.3136i			0.546099i
$688$	6.32403	−	26.1979i	0.241101	−	0.998786i
$689$	0.285948	+	0.165092i	0.0108937	+	0.00628950i
$690$	−7.93788	+	0.569995i	−0.302190	+	0.0216993i
$691$	6.28794	−	3.63035i	0.239205	−	0.138105i	−0.375606	−	0.926779i	$-0.622566\pi$
$691$	6.28794	−	3.63035i	0.239205	−	0.138105i	0.614811	+	0.788674i	$0.289232\pi$
$692$	−1.60579	+	4.01769i	−0.0610431	+	0.152730i
$693$	−32.5486	−	16.1816i	−1.23642	−	0.614688i
$694$	−7.76838	−	11.4707i	−0.294884	−	0.435424i
$695$	−11.1015	+	6.40944i	−0.421103	+	0.243124i
$696$	0.943050	−	2.95881i	0.0357462	−	0.112153i
$697$	−2.15100	+	3.72564i	−0.0814750	+	0.141119i
$698$	−4.16184	+	8.57372i	−0.157528	+	0.324520i
$699$		−	10.2505i		−	0.387708i
$700$	5.02620	+	1.65447i	0.189973	+	0.0625332i
$701$		−	2.84288i		−	0.107374i	−0.998558	−	0.0536870i	$-0.982903\pi$
$701$		−	2.84288i		−	0.107374i	0.998558	−	0.0536870i	$-0.0170973\pi$
$702$	−16.2396	−	7.88301i	−0.612925	−	0.297525i
$703$	−8.83828	+	15.3083i	−0.333342	+	0.577365i
$704$	4.46537	−	47.6212i	0.168295	−	1.79479i
$705$	1.26930	−	0.732832i	0.0478047	−	0.0276000i
$706$	25.1392	−	17.0251i	0.946125	−	0.640748i
$707$	35.8948	−	23.8175i	1.34996	−	0.895748i
$708$	1.87703	−	4.69633i	0.0705432	−	0.176499i
$709$	−14.8464	+	8.57155i	−0.557567	+	0.321911i	−0.752168	−	0.658971i	$-0.770992\pi$
$709$	−14.8464	+	8.57155i	−0.557567	+	0.321911i	0.194601	+	0.980882i	$0.437659\pi$
$710$	0.310689	+	4.32673i	0.0116600	+	0.162379i
$711$	27.5409	+	15.9008i	1.03287	+	0.596325i
$712$	26.7217	−	24.3333i	1.00144	−	0.911928i
$713$		−	58.3990i		−	2.18706i
$714$	6.95432	+	2.85603i	0.260259	+	0.106884i
$715$	17.1916			0.642929
$716$	−22.3087	+	3.22044i	−0.833715	+	0.120354i
$717$	−0.656451	+	1.13701i	−0.0245156	+	0.0424623i
$718$	0.486376	+	6.77339i	0.0181514	+	0.252781i
$719$	11.0395	+	19.1210i	0.411705	+	0.713094i	0.995076	−	0.0991116i	$-0.0316001\pi$
$719$	11.0395	+	19.1210i	0.411705	+	0.713094i	−0.583371	+	0.812206i	$0.698267\pi$
$720$	6.65951	+	6.33540i	0.248185	+	0.236107i
$721$	−0.372466	−	5.97733i	−0.0138713	−	0.222607i
$722$	−2.32425	−	3.43197i	−0.0864995	−	0.127725i
$723$	9.23158	+	15.9896i	0.343326	+	0.594658i
$724$	18.8512	+	23.9433i	0.700600	+	0.889845i
$725$	−1.13479	−	0.655173i	−0.0421451	−	0.0243325i
$726$	−26.3794	−	12.8050i	−0.979030	−	0.475240i
$727$	52.6712			1.95347			0.976733	−	0.214459i	$-0.0687990\pi$
$727$	52.6712			1.95347			0.976733	+	0.214459i	$0.0687990\pi$
$728$	−20.8684	−	5.24672i	−0.773434	−	0.194456i
$729$	−3.86488			−0.143144
$730$	12.7710	+	6.19930i	0.472677	+	0.229446i
$731$	−13.9919	−	8.07820i	−0.517507	−	0.298783i
$732$	−11.5900	+	9.12516i	−0.428380	+	0.337275i
$733$	−0.876721	−	1.51853i	−0.0323824	−	0.0560880i	0.849380	−	0.527782i	$-0.176976\pi$
$733$	−0.876721	−	1.51853i	−0.0323824	−	0.0560880i	−0.881762	+	0.471694i	$0.843643\pi$
$734$	9.22215	+	13.6174i	0.340396	+	0.502627i
$735$	−4.67617	+	3.54058i	−0.172483	+	0.130596i
$736$	−37.4743	−	6.24689i	−1.38132	−	0.230264i
$737$	16.9654	+	29.3850i	0.624929	+	1.08241i
$738$	−0.417570	−	5.81518i	−0.0153710	−	0.214060i
$739$	9.69575	−	16.7935i	0.356664	−	0.617760i	−0.630737	−	0.775996i	$-0.717248\pi$
$739$	9.69575	−	16.7935i	0.356664	−	0.617760i	0.987401	+	0.158237i	$0.0505808\pi$
$740$	−1.07860	−	7.47172i	−0.0396503	−	0.274666i
$741$	−11.2831			−0.414495
$742$	0.425804	−	0.0573655i	0.0156317	−	0.00210595i
$743$			44.8603i			1.64576i	0.568213	+	0.822882i	$0.307635\pi$
$743$			44.8603i			1.64576i	−0.568213	+	0.822882i	$0.692365\pi$
$744$	15.2371	−	13.8752i	0.558618	−	0.508688i
$745$	0.696284	+	0.402000i	0.0255099	+	0.0147281i
$746$	−2.95067	−	41.0917i	−0.108032	−	1.50447i
$747$	−34.6697	+	20.0166i	−1.26850	+	0.732368i
$748$	−26.6256	−	10.6417i	−0.973529	−	0.389101i
$749$	0.398514	+	6.39535i	0.0145614	+	0.233681i
$750$	−0.981150	+	0.664468i	−0.0358265	+	0.0242629i
$751$	40.9012	−	23.6143i	1.49250	−	0.861698i	0.492542	−	0.870289i	$-0.336068\pi$
$751$	40.9012	−	23.6143i	1.49250	−	0.861698i	0.999963	+	0.00859066i	$0.00273453\pi$
$752$	6.71113	−	1.97885i	0.244730	−	0.0721613i
$753$	3.21988	−	5.57699i	0.117339	−	0.203237i
$754$	4.79359	+	2.32690i	0.174572	+	0.0847407i
$755$		−	13.0949i		−	0.476571i
$756$	−22.9951	+	4.79556i	−0.836323	+	0.174413i
$757$		−	1.52456i		−	0.0554110i	−0.999616	−	0.0277055i	$-0.991180\pi$
$757$		−	1.52456i		−	0.0554110i	0.999616	−	0.0277055i	$-0.00882007\pi$
$758$	1.55874	−	3.21113i	0.0566161	−	0.116634i
$759$	−16.8224	+	29.1372i	−0.610614	+	1.05761i
$760$	12.6201	+	4.02237i	0.457781	+	0.145907i
$761$	−28.6395	+	16.5350i	−1.03818	+	0.599394i	−0.919317	−	0.393517i	$-0.871258\pi$
$761$	−28.6395	+	16.5350i	−1.03818	+	0.599394i	−0.118863	+	0.992911i	$0.537925\pi$
$762$	−3.47141	−	5.12586i	−0.125756	−	0.185690i
$763$	10.7274	+	16.1670i	0.388358	+	0.585286i
$764$	−11.4438	−	4.57385i	−0.414021	−	0.165476i
$765$	4.77204	−	2.75514i	0.172533	−	0.0996122i
$766$	−32.8775	+	2.36083i	−1.18791	+	0.0853003i
$767$	7.51536	+	4.33899i	0.271364	+	0.156672i
$768$	−7.27372	−	11.2618i	−0.262468	−	0.406374i
$769$		−	1.31233i		−	0.0473238i	−0.999720	−	0.0236619i	$-0.992467\pi$
$769$		−	1.31233i		−	0.0473238i	0.999720	−	0.0236619i	$-0.00753252\pi$
$770$	17.7065	−	13.6718i	0.638099	−	0.492696i
$771$	1.87495			0.0675248
$772$	−22.9521	+	3.31332i	−0.826063	+	0.119249i
$773$	8.51479	−	14.7480i	0.306256	−	0.530450i	−0.671284	−	0.741200i	$-0.734257\pi$
$773$	8.51479	−	14.7480i	0.306256	−	0.530450i	0.977540	+	0.210749i	$0.0675904\pi$
$774$	21.8392	−	1.56821i	0.784994	−	0.0563681i
$775$	−4.34775	−	7.53053i	−0.156176	−	0.270505i
$776$	−2.27207	−	10.4018i	−0.0815624	−	0.373404i
$777$	7.49295	+	3.72513i	0.268808	+	0.133638i
$778$	−0.518468	+	0.351124i	−0.0185880	+	0.0125884i
$779$	−4.20078	−	7.27596i	−0.150508	−	0.260688i
$780$	3.78606	−	2.98088i	0.135563	−	0.106733i
$781$	15.8819	+	9.16944i	0.568300	+	0.328108i
$782$	−9.94575	+	20.4890i	−0.355659	+	0.732685i
$783$	5.81683			0.207876
$784$	−25.6660	+	11.1919i	−0.916641	+	0.399710i
$785$	−17.1698			−0.612816
$786$	4.63731	−	9.55321i	0.165407	−	0.340752i
$787$	−26.0083	−	15.0159i	−0.927097	−	0.535260i	−0.0412045	−	0.999151i	$-0.513120\pi$
$787$	−26.0083	−	15.0159i	−0.927097	−	0.535260i	−0.885892	+	0.463891i	$0.846453\pi$
$788$	20.6638	−	16.2692i	0.736118	−	0.579567i
$789$	−7.27412	−	12.5991i	−0.258966	−	0.448541i
$790$	−16.2052	+	10.9747i	−0.576555	+	0.390463i
$791$	35.6935	+	17.7451i	1.26912	+	0.630943i
$792$	37.9637	−	8.29240i	1.34898	−	0.294658i
$793$	−12.6554	−	21.9198i	−0.449406	−	0.778395i
$794$	−11.4300	+	0.820755i	−0.405636	+	0.0291275i
$795$	−0.0481079	+	0.0833254i	−0.00170621	+	0.00295525i
$796$	−39.8601	+	5.75413i	−1.41280	+	0.203950i
$797$	−34.7798			−1.23196			−0.615981	−	0.787761i	$-0.711240\pi$
$797$	−34.7798			−1.23196			−0.615981	+	0.787761i	$0.711240\pi$
$798$	−11.6211	+	8.97299i	−0.411381	+	0.317640i
$799$		−	4.19448i		−	0.148390i
$800$	−5.29737	+	1.98439i	−0.187290	+	0.0701589i
$801$	25.4283	+	14.6810i	0.898465	+	0.518729i
$802$	−2.87490	+	0.206438i	−0.101516	+	0.00728958i
$803$	51.9753	−	30.0080i	1.83417	−	1.05896i
$804$	8.83136	+	3.52972i	0.311458	+	0.124484i
$805$	−9.82427	−	14.8060i	−0.346260	−	0.521841i
$806$	19.8280	+	29.2779i	0.698410	+	1.03127i
$807$	0.543476	−	0.313776i	0.0191313	−	0.0110454i
$808$	−13.9849	+	43.8775i	−0.491987	+	1.54360i
$809$	6.61556	−	11.4585i	0.232591	−	0.402859i	−0.725979	−	0.687717i	$-0.758613\pi$
$809$	6.61556	−	11.4585i	0.232591	−	0.402859i	0.958570	+	0.284858i	$0.0919464\pi$
$810$	−1.96026	+	4.03828i	−0.0688765	+	0.141891i
$811$		−	17.4547i		−	0.612917i	−0.951884	−	0.306459i	$-0.900856\pi$
$811$		−	17.4547i		−	0.612917i	0.951884	−	0.306459i	$-0.0991441\pi$
$812$	6.78766	−	1.41555i	0.238200	−	0.0496760i
$813$			18.1946i			0.638113i
$814$	−28.7112	−	13.9370i	−1.00633	−	0.488490i
$815$	2.93458	−	5.08284i	0.102794	−	0.178044i
$816$	−7.70889	+	2.27305i	−0.269865	+	0.0795727i
$817$	27.3253	−	15.7762i	0.955990	−	0.551941i
$818$	−36.7763	+	24.9061i	−1.28585	+	0.870823i
$819$	−1.08724	−	17.4480i	−0.0379912	−	0.609683i
$820$	3.33181	+	1.33166i	0.116352	+	0.0465035i
$821$	−40.5407	+	23.4062i	−1.41488	+	0.816882i	−0.995843	−	0.0910860i	$-0.970966\pi$
$821$	−40.5407	+	23.4062i	−1.41488	+	0.816882i	−0.419039	+	0.907968i	$0.637633\pi$
$822$	−1.77122	−	24.6664i	−0.0617784	−	0.860340i
$823$	13.7735	+	7.95213i	0.480114	+	0.277194i	0.720464	−	0.693492i	$-0.243929\pi$
$823$	13.7735	+	7.95213i	0.480114	+	0.277194i	−0.240350	+	0.970686i	$0.577262\pi$
$824$	4.31070	+	4.73381i	0.150170	+	0.164910i
$825$			5.00964i			0.174413i
$826$	11.1911	−	1.50770i	0.389388	−	0.0524594i
$827$	14.9258			0.519021			0.259511	−	0.965740i	$-0.416439\pi$
$827$	14.9258			0.519021			0.259511	+	0.965740i	$0.416439\pi$
$828$	−4.40999	−	30.5489i	−0.153258	−	1.06165i
$829$	9.10972	−	15.7785i	0.316394	−	0.548010i	−0.663339	−	0.748319i	$-0.730861\pi$
$829$	9.10972	−	15.7785i	0.316394	−	0.548010i	0.979733	+	0.200309i	$0.0641946\pi$
$830$	−1.76462	−	24.5745i	−0.0612508	−	0.852993i
$831$	−9.89479	−	17.1383i	−0.343247	−	0.594520i
$832$	20.9084	−	9.59167i	0.724870	−	0.332531i
$833$	2.08384	+	16.6558i	0.0722007	+	0.577088i
$834$	8.51773	+	12.5772i	0.294945	+	0.435514i
$835$	−3.01130	−	5.21573i	−0.104210	−	0.180498i
$836$	43.9974	−	34.6405i	1.52168	−	1.19807i
$837$	33.4292	+	19.3003i	1.15548	+	0.667117i
$838$	−23.0764	−	11.2017i	−0.797162	−	0.386958i
$839$	−28.2947			−0.976843			−0.488421	−	0.872608i	$-0.662427\pi$
$839$	−28.2947			−0.976843			−0.488421	+	0.872608i	$0.662427\pi$
$840$	1.52890	−	6.08106i	0.0527520	−	0.209817i
$841$	27.2830			0.940793
$842$	−49.1662	−	23.8662i	−1.69438	−	0.822484i
$843$	−10.4587	−	6.03834i	−0.360217	−	0.207971i
$844$	−5.33596	−	6.77729i	−0.183671	−	0.233284i
$845$	−2.36591	−	4.09788i	−0.0813899	−	0.140971i
$846$	3.18751	+	4.70666i	0.109589	+	0.161818i
$847$	−4.07178	−	65.3440i	−0.139908	−	2.24525i
$848$	−0.316586	+	0.332782i	−0.0108716	+	0.0114278i
$849$	5.21944	+	9.04034i	0.179131	+	0.310264i
$850$	0.242887	+	3.38250i	0.00833096	+	0.116019i
$851$	−12.6751	+	21.9538i	−0.434495	+	0.752568i
$852$	5.08754	−	0.734429i	0.174296	−	0.0251611i
$853$	39.5247			1.35330			0.676650	−	0.736305i	$-0.263431\pi$
$853$	39.5247			1.35330			0.676650	+	0.736305i	$0.263431\pi$
$854$	−30.4664	−	12.5120i	−1.04254	−	0.428153i
$855$			10.7612i			0.368026i
$856$	−4.61216	−	5.06487i	−0.157640	−	0.173114i
$857$	2.50342	+	1.44535i	0.0855151	+	0.0493722i	0.542148	−	0.840283i	$-0.317611\pi$
$857$	2.50342	+	1.44535i	0.0855151	+	0.0493722i	−0.456633	+	0.889655i	$0.650945\pi$
$858$	−1.45907	−	20.3193i	−0.0498119	−	0.693691i
$859$	12.6042	−	7.27704i	0.430050	−	0.248290i	−0.269318	−	0.963051i	$-0.586798\pi$
$859$	12.6042	−	7.27704i	0.430050	−	0.248290i	0.699368	+	0.714762i	$0.253465\pi$
$860$	−5.00112	+	12.5128i	−0.170537	+	0.426682i
$861$	−3.31400	+	2.19895i	−0.112941	+	0.0749402i
$862$	−4.85881	+	3.29055i	−0.165492	+	0.112077i
$863$	−12.0583	+	6.96188i	−0.410470	+	0.236985i	−0.690992	−	0.722863i	$-0.742826\pi$
$863$	−12.0583	+	6.96188i	−0.410470	+	0.236985i	0.280521	+	0.959848i	$0.409493\pi$
$864$	15.9608	−	19.3868i	0.542998	−	0.659552i
$865$	1.08168	−	1.87352i	0.0367782	−	0.0637016i
$866$	27.6191	+	13.4068i	0.938534	+	0.455582i
$867$		−	9.42632i		−	0.320135i
$868$	43.7054	+	14.3865i	1.48346	+	0.488309i
$869$			82.7420i			2.80683i
$870$	−0.678061	+	1.39686i	−0.0229884	+	0.0473579i
$871$	−8.15939	+	14.1325i	−0.276471	+	0.478861i
$872$	−19.7624	−	6.29880i	−0.669240	−	0.213304i
$873$	7.49117	−	4.32503i	0.253538	−	0.146380i
$874$	−24.9412	−	36.8281i	−0.843649	−	1.24573i
$875$	−2.36913	−	1.17781i	−0.0800910	−	0.0398174i
$876$	6.24327	−	15.6207i	0.210941	−	0.527773i
$877$	13.6311	−	7.86992i	0.460289	−	0.265748i	−0.251877	−	0.967759i	$-0.581048\pi$
$877$	13.6311	−	7.86992i	0.460289	−	0.265748i	0.712166	+	0.702011i	$0.247714\pi$
$878$	10.9042	−	0.783000i	0.368000	−	0.0264250i
$879$	6.14882	+	3.55002i	0.207394	+	0.119739i
$880$	−5.61177	+	23.2473i	−0.189173	+	0.783667i
$881$			4.77034i			0.160717i	0.996766	+	0.0803584i	$0.0256065\pi$
$881$			4.77034i			0.160717i	−0.996766	+	0.0803584i	$0.974394\pi$
$882$	−14.9955	−	17.1060i	−0.504924	−	0.575989i
$883$	31.2410			1.05134			0.525672	−	0.850688i	$-0.323814\pi$
$883$	31.2410			1.05134			0.525672	+	0.850688i	$0.323814\pi$
$884$	−1.97032	−	13.6488i	−0.0662691	−	0.459060i
$885$	−1.26439	+	2.18998i	−0.0425019	+	0.0736154i
$886$	−25.1981	+	1.80940i	−0.846547	+	0.0607879i
$887$	18.4386	+	31.9365i	0.619106	+	1.07232i	0.989649	+	0.143508i	$0.0458384\pi$
$887$	18.4386	+	31.9365i	0.619106	+	1.07232i	−0.370543	+	0.928815i	$0.620828\pi$
$888$	−8.73955	+	1.90897i	−0.293280	+	0.0640610i
$889$	6.15330	−	12.3771i	0.206375	−	0.415115i
$890$	−14.9621	+	10.1329i	−0.501531	+	0.339654i
$891$	9.48872	+	16.4350i	0.317884	+	0.550592i
$892$	−14.3453	−	18.2202i	−0.480315	−	0.610056i
$893$	7.09411	+	4.09579i	0.237395	+	0.137060i
$894$	0.416043	−	0.857081i	0.0139146	−	0.0286651i
$895$	11.2700			0.376713
$896$	13.9068	−	26.5066i	0.464595	−	0.885523i
$897$	−16.1812			−0.540275
$898$	18.1094	−	37.3068i	0.604319	−	1.24494i
$899$	−9.86759	−	5.69706i	−0.329103	−	0.190007i
$900$	−2.84300	−	3.61095i	−0.0947668	−	0.120365i
$901$	0.137677	+	0.238463i	0.00458668	+	0.00794436i
$902$	12.5598	−	8.50592i	0.418195	−	0.283216i
$903$	−8.25829	−	12.4459i	−0.274819	−	0.414174i
$904$	−41.6319	+	9.09362i	−1.38466	+	0.302449i
$905$	−7.61844	−	13.1955i	−0.253245	−	0.438634i
$906$	−15.4773	+	1.11138i	−0.514198	+	0.0369230i
$907$	−0.588928	+	1.02005i	−0.0195550	+	0.0338703i	−0.875637	−	0.482969i	$-0.839558\pi$
$907$	−0.588928	+	1.02005i	−0.0195550	+	0.0338703i	0.856082	+	0.516840i	$0.172892\pi$
$908$	−5.51633	−	38.2128i	−0.183066	−	1.26814i
$909$	−37.4145			−1.24096
$910$	9.95232	+	4.08726i	0.329916	+	0.135491i
$911$			37.7931i			1.25214i	0.779766	+	0.626071i	$0.215338\pi$
$911$			37.7931i			1.25214i	−0.779766	+	0.626071i	$0.784662\pi$
$912$	3.68309	−	15.2576i	0.121959	−	0.505229i
$913$	−90.2045	−	52.0796i	−2.98533	−	1.72358i
$914$	−13.0960	+	0.940386i	−0.433178	+	0.0311052i
$915$	6.38745	−	3.68779i	0.211162	−	0.121915i
$916$	12.6799	−	31.7251i	0.418956	−	1.04823i
$917$	23.6642	−	1.47459i	0.781459	−	0.0486951i
$918$	−8.44148	−	12.4646i	−0.278610	−	0.411395i
$919$	−37.4585	+	21.6267i	−1.23564	+	0.713398i	−0.968200	−	0.250177i	$-0.919511\pi$
$919$	−37.4585	+	21.6267i	−1.23564	+	0.713398i	−0.267441	+	0.963574i	$0.586178\pi$
$920$	18.0987	+	5.76851i	0.596695	+	0.190182i
$921$	5.00313	−	8.66568i	0.164859	−	0.285544i
$922$	−0.248113	+	0.511132i	−0.00817116	+	0.0168332i
$923$			8.81995i			0.290312i
$924$	−17.6619	−	19.7676i	−0.581034	−	0.650308i
$925$			3.77459i			0.124108i
$926$	11.5099	+	5.58713i	0.378239	+	0.183604i
$927$	−2.60078	+	4.50468i	−0.0854208	+	0.147953i
$928$	−4.71130	+	5.72257i	−0.154656	+	0.187853i
$929$	30.3878	−	17.5444i	0.996992	−	0.575614i	0.0896350	−	0.995975i	$-0.471430\pi$
$929$	30.3878	−	17.5444i	0.996992	−	0.575614i	0.907357	+	0.420361i	$0.138097\pi$
$930$	−8.53160	+	5.77789i	−0.279762	+	0.189464i
$931$	−30.2046	−	12.7395i	−0.989917	−	0.417520i
$932$	−9.08050	+	22.7194i	−0.297442	+	0.744199i
$933$	−11.2445	+	6.49204i	−0.368130	+	0.212540i
$934$	1.21939	+	16.9815i	0.0398996	+	0.555650i
$935$	12.4160	+	7.16838i	0.406046	+	0.234431i
$936$	12.5831	+	13.8181i	0.411290	+	0.451660i
$937$			44.8914i			1.46654i	0.679938	+	0.733270i	$0.262007\pi$
$937$			44.8914i			1.46654i	−0.679938	+	0.733270i	$0.737993\pi$
$938$	2.83519	+	21.0446i	0.0925723	+	0.687132i
$939$	14.4851			0.472702
$940$	−3.46250	+	0.499841i	−0.112934	+	0.0163030i
$941$	−28.7781	+	49.8451i	−0.938138	+	1.62490i	−0.169197	+	0.985582i	$0.554118\pi$
$941$	−28.7781	+	49.8451i	−0.938138	+	1.62490i	−0.768941	+	0.639320i	$0.779216\pi$
$942$	1.45722	+	20.2936i	0.0474788	+	0.661200i
$943$	−6.02437	−	10.4345i	−0.196180	−	0.339795i
$944$	−8.32060	+	8.74628i	−0.270813	+	0.284667i
$945$	11.7222	−	0.730444i	0.381322	−	0.0237613i
$946$	31.9444	+	47.1690i	1.03860	+	1.53360i
$947$	−8.60454	−	14.9035i	−0.279610	−	0.484299i	0.691678	−	0.722206i	$-0.256872\pi$
$947$	−8.60454	−	14.9035i	−0.279610	−	0.484299i	−0.971288	+	0.237908i	$0.923538\pi$
$948$	14.3468	+	18.2221i	0.465961	+	0.591825i
$949$	24.9972	+	14.4321i	0.811442	+	0.468486i
$950$	−5.95798	−	2.89212i	−0.193302	−	0.0938326i
$951$	6.97330			0.226125
$952$	−12.8837	−	12.4907i	−0.417563	−	0.404827i
$953$	11.6755			0.378207			0.189103	−	0.981957i	$-0.439442\pi$
$953$	11.6755			0.378207			0.189103	+	0.981957i	$0.439442\pi$
$954$	−0.335703	−	0.162957i	−0.0108688	−	0.00527591i
$955$	5.33642	+	3.08099i	0.172683	+	0.0996984i
$956$	2.46221	−	1.93857i	0.0796335	−	0.0626977i
$957$	3.28218	+	5.68491i	0.106098	+	0.183767i
$958$	−2.53167	−	3.73825i	−0.0817944	−	0.120777i
$959$	46.0085	−	30.5283i	1.48569	−	0.985809i
$960$	2.79502	+	6.09274i	0.0902089	+	0.196642i
$961$	−22.3059	−	38.6349i	−0.719545	−	1.24629i
$962$	−1.09936	−	15.3099i	−0.0354447	−	0.493611i
$963$	2.78266	−	4.81971i	0.0896700	−	0.155313i
$964$	−6.29656	−	43.6176i	−0.202799	−	1.40483i
$965$	11.5950			0.373256
$966$	−16.6659	+	12.8682i	−0.536216	+	0.414029i
$967$		−	52.1618i		−	1.67741i	−0.544586	−	0.838705i	$-0.683313\pi$
$967$		−	52.1618i		−	1.67741i	0.544586	−	0.838705i	$-0.316687\pi$
$968$	47.1244	+	51.7499i	1.51464	+	1.66331i
$969$	−8.14881	−	4.70472i	−0.261777	−	0.151137i
$970$	0.381285	+	5.30987i	0.0122423	+	0.170490i
$971$	14.6994	−	8.48673i	0.471728	−	0.272352i	−0.245235	−	0.969464i	$-0.578865\pi$
$971$	14.6994	−	8.48673i	0.471728	−	0.272352i	0.716963	+	0.697112i	$0.245532\pi$
$972$	29.6720	+	11.8593i	0.951730	+	0.380388i
$973$	−15.0982	+	30.3695i	−0.484028	+	0.973602i
$974$	−4.47420	+	3.03008i	−0.143363	+	0.0970901i
$975$	−2.08656	+	1.20468i	−0.0668234	+	0.0385805i
$976$	33.7721	−	9.95807i	1.08102	−	0.318750i
$977$	−11.5148	+	19.9442i	−0.368390	+	0.638071i	−0.989314	−	0.145800i	$-0.953424\pi$
$977$	−11.5148	+	19.9442i	−0.368390	+	0.638071i	0.620924	+	0.783871i	$0.286758\pi$
$978$	−6.25665	−	3.03710i	−0.200066	−	0.0971156i
$979$			76.3949i			2.44159i
$980$	13.5009	−	3.70499i	0.431269	−	0.118352i
$981$		−	16.8515i		−	0.538027i
$982$	−26.4122	+	54.4111i	−0.842846	+	1.73633i
$983$	19.4921	−	33.7613i	0.621701	−	1.07682i	−0.367468	−	0.930036i	$-0.619775\pi$
$983$	19.4921	−	33.7613i	0.621701	−	1.07682i	0.989169	−	0.146782i	$-0.0468915\pi$
$984$	1.29116	−	4.05100i	0.0411607	−	0.129141i
$985$	−11.3882	+	6.57495i	−0.362857	+	0.209495i
$986$	2.49175	+	3.67930i	0.0793534	+	0.117173i
$987$	1.72628	−	3.47234i	0.0549481	−	0.110526i
$988$	25.0082	+	9.99528i	0.795616	+	0.317992i
$989$	39.1874	−	22.6249i	1.24609	−	0.719428i
$990$	−19.3795	+	1.39158i	−0.615922	+	0.0442275i
$991$	13.9773	+	8.06982i	0.444005	+	0.256346i	0.705295	−	0.708914i	$-0.250815\pi$
$991$	13.9773	+	8.06982i	0.444005	+	0.256346i	−0.261290	+	0.965260i	$0.584148\pi$
$992$	−46.0633	+	17.2553i	−1.46251	+	0.547857i
$993$			21.1882i			0.672388i
$994$	7.01414	+	9.08413i	0.222475	+	0.288131i
$995$	20.1366			0.638374
$996$	−28.8957	+	4.17133i	−0.915595	+	0.132174i
$997$	−23.3556	+	40.4531i	−0.739679	+	1.28116i	0.212960	+	0.977061i	$0.431690\pi$
$997$	−23.3556	+	40.4531i	−0.739679	+	1.28116i	−0.952640	+	0.304102i	$0.901644\pi$
$998$	−10.4773	+	0.752344i	−0.331653	+	0.0238150i
$999$	−8.37799	−	14.5111i	−0.265068	−	0.459111i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.bj.e.171.8	yes	24
4.3	odd	2		1120.2.bz.f.591.7		24
7.5	odd	6		280.2.bj.f.131.1	yes	24
8.3	odd	2		280.2.bj.f.171.1	yes	24
8.5	even	2		1120.2.bz.e.591.7		24
28.19	even	6		1120.2.bz.e.271.7		24
56.5	odd	6		1120.2.bz.f.271.7		24
56.19	even	6	inner	280.2.bj.e.131.8	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.bj.e.131.8	✓	24	56.19	even	6	inner
280.2.bj.e.171.8	yes	24	1.1	even	1	trivial
280.2.bj.f.131.1	yes	24	7.5	odd	6
280.2.bj.f.171.1	yes	24	8.3	odd	2
1120.2.bz.e.271.7		24	28.19	even	6
1120.2.bz.e.591.7		24	8.5	even	2
1120.2.bz.f.271.7		24	56.5	odd	6
1120.2.bz.f.591.7		24	4.3	odd	2

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:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	280.bj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.617571 - 1.27224i) q^{2} +(0.725648 + 0.418953i) q^{3} +(-1.23721 - 1.57140i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.981150 - 0.664468i) q^{6} +(2.36913 + 1.17781i) q^{7} +(-2.76328 + 0.603581i) q^{8} +(-1.14896 - 1.99005i) q^{9} +O(q^{10})\)	\(q+(0.617571 - 1.27224i) q^{2} +(0.725648 + 0.418953i) q^{3} +(-1.23721 - 1.57140i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.981150 - 0.664468i) q^{6} +(2.36913 + 1.17781i) q^{7} +(-2.76328 + 0.603581i) q^{8} +(-1.14896 - 1.99005i) q^{9} +(1.41058 - 0.101290i) q^{10} +(2.98938 - 5.17776i) q^{11} +(-0.239435 - 1.65862i) q^{12} +2.87544 q^{13} +(2.96157 - 2.28672i) q^{14} +0.837906i q^{15} +(-0.938618 + 3.88832i) q^{16} +(2.07668 + 1.19897i) q^{17} +(-3.24139 + 0.232755i) q^{18} +(-4.05564 + 2.34152i) q^{19} +(0.742270 - 1.85716i) q^{20} +(1.22570 + 1.84723i) q^{21} +(-4.74122 - 7.00086i) q^{22} +(-5.81623 + 3.35800i) q^{23} +(-2.25804 - 0.719696i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(1.77579 - 3.65827i) q^{26} -4.43915i q^{27} +(-1.08029 - 5.18006i) q^{28} +1.31035i q^{29} +(1.06602 + 0.517467i) q^{30} +(-4.34775 + 7.53053i) q^{31} +(4.36722 + 3.59546i) q^{32} +(4.33848 - 2.50482i) q^{33} +(2.80789 - 1.90160i) q^{34} +(0.164546 + 2.64063i) q^{35} +(-1.70567 + 4.26759i) q^{36} +(3.26889 - 1.88729i) q^{37} +(0.474344 + 6.60582i) q^{38} +(2.08656 + 1.20468i) q^{39} +(-1.90435 - 2.09128i) q^{40} +1.79404i q^{41} +(3.10709 - 0.418596i) q^{42} -6.73760 q^{43} +(-11.8348 + 1.70846i) q^{44} +(1.14896 - 1.99005i) q^{45} +(0.680261 + 9.47346i) q^{46} +(-0.874599 - 1.51485i) q^{47} +(-2.31013 + 2.42831i) q^{48} +(4.22551 + 5.58078i) q^{49} +(0.793010 + 1.17095i) q^{50} +(1.00463 + 1.74007i) q^{51} +(-3.55753 - 4.51848i) q^{52} +(0.0994447 + 0.0574144i) q^{53} +(-5.64769 - 2.74150i) q^{54} +5.97876 q^{55} +(-7.25745 - 1.82467i) q^{56} -3.92395 q^{57} +(1.66708 + 0.809232i) q^{58} +(2.61363 + 1.50898i) q^{59} +(1.31669 - 1.03667i) q^{60} +(-4.40120 - 7.62310i) q^{61} +(6.89562 + 10.1820i) q^{62} +(-0.378112 - 6.06794i) q^{63} +(7.27138 - 3.33572i) q^{64} +(1.43772 + 2.49021i) q^{65} +(-0.507425 - 7.06651i) q^{66} +(-2.83761 + 4.91489i) q^{67} +(-0.685224 - 4.74669i) q^{68} -5.62738 q^{69} +(3.46114 + 1.42144i) q^{70} +3.06734i q^{71} +(4.37604 + 4.80557i) q^{72} +(8.69332 + 5.01909i) q^{73} +(-0.382326 - 5.32436i) q^{74} +(-0.725648 + 0.418953i) q^{75} +(8.69716 + 3.47608i) q^{76} +(13.1807 - 8.74583i) q^{77} +(2.82124 - 1.91064i) q^{78} +(-11.9852 + 6.91965i) q^{79} +(-3.83669 + 1.13129i) q^{80} +(-1.58707 + 2.74889i) q^{81} +(2.28245 + 1.10795i) q^{82} -17.4215i q^{83} +(1.38629 - 4.21149i) q^{84} +2.39795i q^{85} +(-4.16095 + 8.57187i) q^{86} +(-0.548973 + 0.950850i) q^{87} +(-5.13529 + 16.1119i) q^{88} +(-11.0658 + 6.38886i) q^{89} +(-1.82227 - 2.69075i) q^{90} +(6.81228 + 3.38674i) q^{91} +(12.4727 + 4.98508i) q^{92} +(-6.30988 + 3.64301i) q^{93} +(-2.46739 + 0.177175i) q^{94} +(-4.05564 - 2.34152i) q^{95} +(1.66274 + 4.43870i) q^{96} +3.76431i q^{97} +(9.70967 - 1.92935i) q^{98} -13.7387 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 3 q^{2} + 12 q^{3} + q^{4} + 12 q^{5} + 2 q^{6} - 10 q^{7} - 6 q^{8} + 12 q^{9}+O(q^{10}) \) 24 * q - 3 * q^2 + 12 * q^3 + q^4 + 12 * q^5 + 2 * q^6 - 10 * q^7 - 6 * q^8 + 12 * q^9	\( 24 q - 3 q^{2} + 12 q^{3} + q^{4} + 12 q^{5} + 2 q^{6} - 10 q^{7} - 6 q^{8} + 12 q^{9} - 3 q^{10} + 8 q^{11} + 8 q^{12} - 20 q^{13} - 15 q^{14} - 3 q^{16} + 6 q^{17} - 27 q^{18} + 18 q^{19} + 2 q^{20} + 26 q^{21} - 16 q^{22} - 18 q^{23} + 6 q^{24} - 12 q^{25} - 29 q^{26} + 3 q^{28} + 10 q^{30} + 6 q^{31} - 33 q^{32} + 12 q^{33} + 20 q^{34} - 8 q^{35} - 22 q^{36} + 9 q^{38} + 18 q^{39} - 3 q^{40} - 12 q^{42} + 32 q^{43} - 25 q^{44} - 12 q^{45} + 53 q^{46} + 14 q^{48} + 8 q^{49} - 22 q^{51} - 31 q^{52} - 30 q^{53} + 10 q^{54} + 16 q^{55} + 16 q^{56} - 44 q^{57} + 30 q^{58} - 18 q^{59} + 10 q^{60} - 22 q^{61} - 8 q^{62} + 12 q^{63} + 58 q^{64} - 10 q^{65} - 8 q^{66} - 8 q^{67} - 6 q^{68} + 12 q^{69} + 3 q^{70} - 23 q^{72} + 30 q^{73} - 43 q^{74} - 12 q^{75} - 8 q^{76} + 32 q^{77} - 8 q^{78} - 6 q^{79} + 3 q^{80} - 4 q^{81} - 27 q^{82} - 16 q^{84} - 36 q^{86} - 14 q^{87} + 49 q^{88} - 60 q^{89} - 24 q^{90} + 18 q^{91} - 38 q^{92} + 18 q^{93} + 11 q^{94} + 18 q^{95} + 2 q^{96} - 19 q^{98} - 56 q^{99}+O(q^{100}) \) 24 * q - 3 * q^2 + 12 * q^3 + q^4 + 12 * q^5 + 2 * q^6 - 10 * q^7 - 6 * q^8 + 12 * q^9 - 3 * q^10 + 8 * q^11 + 8 * q^12 - 20 * q^13 - 15 * q^14 - 3 * q^16 + 6 * q^17 - 27 * q^18 + 18 * q^19 + 2 * q^20 + 26 * q^21 - 16 * q^22 - 18 * q^23 + 6 * q^24 - 12 * q^25 - 29 * q^26 + 3 * q^28 + 10 * q^30 + 6 * q^31 - 33 * q^32 + 12 * q^33 + 20 * q^34 - 8 * q^35 - 22 * q^36 + 9 * q^38 + 18 * q^39 - 3 * q^40 - 12 * q^42 + 32 * q^43 - 25 * q^44 - 12 * q^45 + 53 * q^46 + 14 * q^48 + 8 * q^49 - 22 * q^51 - 31 * q^52 - 30 * q^53 + 10 * q^54 + 16 * q^55 + 16 * q^56 - 44 * q^57 + 30 * q^58 - 18 * q^59 + 10 * q^60 - 22 * q^61 - 8 * q^62 + 12 * q^63 + 58 * q^64 - 10 * q^65 - 8 * q^66 - 8 * q^67 - 6 * q^68 + 12 * q^69 + 3 * q^70 - 23 * q^72 + 30 * q^73 - 43 * q^74 - 12 * q^75 - 8 * q^76 + 32 * q^77 - 8 * q^78 - 6 * q^79 + 3 * q^80 - 4 * q^81 - 27 * q^82 - 16 * q^84 - 36 * q^86 - 14 * q^87 + 49 * q^88 - 60 * q^89 - 24 * q^90 + 18 * q^91 - 38 * q^92 + 18 * q^93 + 11 * q^94 + 18 * q^95 + 2 * q^96 - 19 * q^98 - 56 * q^99

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