LMFDB - Embedded newform 156.3.l.c.47.43

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [156,3,Mod(47,156)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("156.47"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(156, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 2, 1])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 156 = 2^{2} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	156.l (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [96,0,0,0,0,-36,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.25069212402$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$48$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			47.43
Character	$\chi$	$=$	156.47
Dual form			156.3.l.c.83.43

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.87876 - 0.685761i) q^{2} +(-2.74902 + 1.20121i) q^{3} +(3.05946 - 2.57676i) q^{4} +(2.23749 - 2.23749i) q^{5} +(-4.34099 + 4.14196i) q^{6} +(1.91723 + 1.91723i) q^{7} +(3.98095 - 6.93916i) q^{8} +(6.11417 - 6.60431i) q^{9} +(2.66932 - 5.73809i) q^{10} +(6.43837 - 6.43837i) q^{11} +(-5.31528 + 10.7586i) q^{12} +(12.9887 - 0.543102i) q^{13} +(4.91678 + 2.28725i) q^{14} +(-3.46320 + 8.83861i) q^{15} +(2.72064 - 15.7670i) q^{16} -7.93049 q^{17} +(6.95808 - 16.6008i) q^{18} +(-13.1475 + 13.1475i) q^{19} +(1.08005 - 12.6110i) q^{20} +(-7.57350 - 2.96749i) q^{21} +(7.68096 - 16.5113i) q^{22} -13.4703i q^{23} +(-2.60829 + 23.8578i) q^{24} +14.9872i q^{25} +(24.0301 - 9.92747i) q^{26} +(-8.87477 + 25.4998i) q^{27} +(10.8059 + 0.925460i) q^{28} +10.9793i q^{29} +(-0.445336 + 18.9805i) q^{30} +(-4.01999 + 4.01999i) q^{31} +(-5.70096 - 31.4881i) q^{32} +(-9.96532 + 25.4330i) q^{33} +(-14.8995 + 5.43842i) q^{34} +8.57958 q^{35} +(1.68839 - 35.9604i) q^{36} +(1.70839 - 1.70839i) q^{37} +(-15.6849 + 33.7170i) q^{38} +(-35.0536 + 17.0951i) q^{39} +(-6.61898 - 24.4337i) q^{40} +(-35.1614 + 35.1614i) q^{41} +(-16.2638 - 0.381593i) q^{42} -46.1935 q^{43} +(3.10784 - 36.2881i) q^{44} +(-1.09668 - 28.4575i) q^{45} +(-9.23738 - 25.3074i) q^{46} +(-45.9388 + 45.9388i) q^{47} +(11.4604 + 46.6118i) q^{48} -41.6485i q^{49} +(10.2777 + 28.1574i) q^{50} +(21.8010 - 9.52621i) q^{51} +(38.3389 - 35.1302i) q^{52} +96.7348i q^{53} +(0.813197 + 53.9939i) q^{54} -28.8116i q^{55} +(20.9364 - 5.67157i) q^{56} +(20.3497 - 51.9357i) q^{57} +(7.52915 + 20.6274i) q^{58} +(19.8925 - 19.8925i) q^{59} +(12.1794 + 35.9652i) q^{60} +107.892 q^{61} +(-4.79584 + 10.3094i) q^{62} +(24.3843 - 0.939704i) q^{63} +(-32.3040 - 55.2490i) q^{64} +(27.8468 - 30.2772i) q^{65} +(-1.28145 + 54.6163i) q^{66} +(57.5421 - 57.5421i) q^{67} +(-24.2631 + 20.4350i) q^{68} +(16.1807 + 37.0300i) q^{69} +(16.1190 - 5.88354i) q^{70} +(-15.3918 - 15.3918i) q^{71} +(-21.4881 - 68.7187i) q^{72} +(-52.5418 + 52.5418i) q^{73} +(2.03811 - 4.38120i) q^{74} +(-18.0029 - 41.2002i) q^{75} +(-6.34639 + 74.1023i) q^{76} +24.6877 q^{77} +(-54.1341 + 56.1560i) q^{78} -46.1756i q^{79} +(-29.1911 - 41.3660i) q^{80} +(-6.23379 - 80.7598i) q^{81} +(-41.9475 + 90.1721i) q^{82} +(88.7459 + 88.7459i) q^{83} +(-30.8174 + 10.4361i) q^{84} +(-17.7444 + 17.7444i) q^{85} +(-86.7865 + 31.6777i) q^{86} +(-13.1884 - 30.1822i) q^{87} +(-19.0461 - 70.3077i) q^{88} +(-96.2535 - 96.2535i) q^{89} +(-21.5754 - 52.7127i) q^{90} +(25.9435 + 23.8610i) q^{91} +(-34.7096 - 41.2118i) q^{92} +(6.22216 - 15.8799i) q^{93} +(-54.8049 + 117.811i) q^{94} +58.8349i q^{95} +(53.4959 + 79.7131i) q^{96} +(-42.4947 - 42.4947i) q^{97} +(-28.5609 - 78.2474i) q^{98} +(-3.15568 - 81.8863i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 36 q^{6} - 64 q^{9} - 8 q^{13} + 80 q^{16} + 48 q^{18} + 8 q^{21} + 124 q^{24} - 8 q^{28} + 24 q^{33} + 64 q^{34} - 128 q^{37} - 136 q^{40} - 140 q^{42} - 160 q^{45} + 88 q^{46} - 108 q^{48} - 320 q^{52}+ \cdots + 336 q^{97}+O(q^{100}) $ 96 * q - 36 * q^6 - 64 * q^9 - 8 * q^13 + 80 * q^16 + 48 * q^18 + 8 * q^21 + 124 * q^24 - 8 * q^28 + 24 * q^33 + 64 * q^34 - 128 * q^37 - 136 * q^40 - 140 * q^42 - 160 * q^45 + 88 * q^46 - 108 * q^48 - 320 * q^52 - 216 * q^54 + 136 * q^57 + 280 * q^58 + 80 * q^60 - 464 * q^61 - 240 * q^66 - 120 * q^70 - 32 * q^72 + 288 * q^73 + 88 * q^76 - 296 * q^78 - 144 * q^81 + 204 * q^84 + 848 * q^85 - 392 * q^93 + 1384 * q^94 - 204 * q^96 + 336 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/156\mathbb{Z}\right)^\times$.

$n$	$53$	$79$	$145$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	1.87876	−	0.685761i	0.939379	−	0.342880i
$2$	1.87876	−	0.685761i	0.939379	−	0.342880i
$3$	−2.74902	+	1.20121i	−0.916339	+	0.400404i
$3$	−2.74902	+	1.20121i	−0.916339	+	0.400404i
$4$	3.05946	−	2.57676i	0.764866	−	0.644189i
$5$	2.23749	−	2.23749i	0.447499	−	0.447499i	−0.447024	−	0.894522i	$-0.647516\pi$
$5$	2.23749	−	2.23749i	0.447499	−	0.447499i	0.894522	+	0.447024i	$0.147516\pi$
$6$	−4.34099	+	4.14196i	−0.723498	+	0.690326i
$7$	1.91723	+	1.91723i	0.273890	+	0.273890i	0.830664	−	0.556774i	$-0.187961\pi$
$7$	1.91723	+	1.91723i	0.273890	+	0.273890i	−0.556774	+	0.830664i	$0.687961\pi$
$8$	3.98095	−	6.93916i	0.497619	−	0.867396i
$9$	6.11417	−	6.60431i	0.679353	−	0.733812i
$10$	2.66932	−	5.73809i	0.266932	−	0.573809i
$11$	6.43837	−	6.43837i	0.585306	−	0.585306i	−0.351050	−	0.936357i	$-0.614175\pi$
$11$	6.43837	−	6.43837i	0.585306	−	0.585306i	0.936357	+	0.351050i	$0.114175\pi$
$12$	−5.31528	+	10.7586i	−0.442940	+	0.896551i
$13$	12.9887	−	0.543102i	0.999127	−	0.0417771i
$13$	12.9887	−	0.543102i	0.999127	−	0.0417771i
$14$	4.91678	+	2.28725i	0.351198	+	0.163375i
$15$	−3.46320	+	8.83861i	−0.230880	+	0.589241i
$16$	2.72064	−	15.7670i	0.170040	−	0.985437i
$17$	−7.93049			−0.466499			−0.233250	−	0.972417i	$-0.574936\pi$
$17$	−7.93049			−0.466499			−0.233250	+	0.972417i	$0.574936\pi$
$18$	6.95808	−	16.6008i	0.386560	−	0.922264i
$19$	−13.1475	+	13.1475i	−0.691974	+	0.691974i	−0.962666	−	0.270692i	$-0.912748\pi$
$19$	−13.1475	+	13.1475i	−0.691974	+	0.691974i	0.270692	+	0.962666i	$0.412748\pi$
$20$	1.08005	−	12.6110i	0.0540026	−	0.630550i
$21$	−7.57350	−	2.96749i	−0.360643	−	0.141309i
$22$	7.68096	−	16.5113i	0.349134	−	0.750514i
$23$		−	13.4703i		−	0.585664i	−0.956164	−	0.292832i	$-0.905402\pi$
$23$		−	13.4703i		−	0.585664i	0.956164	−	0.292832i	$-0.0945977\pi$
$24$	−2.60829	+	23.8578i	−0.108679	+	0.994077i
$25$			14.9872i			0.599490i
$26$	24.0301	−	9.92747i	0.924234	−	0.381826i
$27$	−8.87477	+	25.4998i	−0.328695	+	0.944436i
$28$	10.8059	+	0.925460i	0.385926	+	0.0330521i
$29$			10.9793i			0.378595i	0.981920	+	0.189298i	$0.0606211\pi$
$29$			10.9793i			0.378595i	−0.981920	+	0.189298i	$0.939379\pi$
$30$	−0.445336	+	18.9805i	−0.0148445	+	0.632685i
$31$	−4.01999	+	4.01999i	−0.129677	+	0.129677i	−0.768966	−	0.639289i	$-0.779229\pi$
$31$	−4.01999	+	4.01999i	−0.129677	+	0.129677i	0.639289	+	0.768966i	$0.279229\pi$
$32$	−5.70096	−	31.4881i	−0.178155	−	0.984002i
$33$	−9.96532	+	25.4330i	−0.301979	+	0.770698i
$34$	−14.8995	+	5.43842i	−0.438220	+	0.159954i
$35$	8.57958			0.245131
$36$	1.68839	−	35.9604i	0.0468997	−	0.998900i
$37$	1.70839	−	1.70839i	0.0461727	−	0.0461727i	−0.683643	−	0.729816i	$-0.739606\pi$
$37$	1.70839	−	1.70839i	0.0461727	−	0.0461727i	0.729816	+	0.683643i	$0.239606\pi$
$38$	−15.6849	+	33.7170i	−0.412762	+	0.887290i
$39$	−35.0536	+	17.0951i	−0.898811	+	0.438337i
$40$	−6.61898	−	24.4337i	−0.165474	−	0.610842i
$41$	−35.1614	+	35.1614i	−0.857595	+	0.857595i	−0.991054	−	0.133459i	$-0.957392\pi$
$41$	−35.1614	+	35.1614i	−0.857595	+	0.857595i	0.133459	+	0.991054i	$0.457392\pi$
$42$	−16.2638	−	0.381593i	−0.387233	−	0.00908555i
$43$	−46.1935			−1.07427			−0.537134	−	0.843497i	$-0.680493\pi$
$43$	−46.1935			−1.07427			−0.537134	+	0.843497i	$0.680493\pi$
$44$	3.10784	−	36.2881i	0.0706328	−	0.824729i
$45$	−1.09668	−	28.4575i	−0.0243706	−	0.632389i
$46$	−9.23738	−	25.3074i	−0.200813	−	0.550160i
$47$	−45.9388	+	45.9388i	−0.977422	+	0.977422i	−0.999751	−	0.0223285i	$-0.992892\pi$
$47$	−45.9388	+	45.9388i	−0.977422	+	0.977422i	0.0223285	+	0.999751i	$0.492892\pi$
$48$	11.4604	+	46.6118i	0.238759	+	0.971079i
$49$		−	41.6485i		−	0.849968i
$50$	10.2777	+	28.1574i	0.205553	+	0.563148i
$51$	21.8010	−	9.52621i	0.427471	−	0.186788i
$52$	38.3389	−	35.1302i	0.737286	−	0.675581i
$53$			96.7348i			1.82518i	0.408870	+	0.912592i	$0.365923\pi$
$53$			96.7348i			1.82518i	−0.408870	+	0.912592i	$0.634077\pi$
$54$	0.813197	+	53.9939i	0.0150592	+	0.999887i
$55$		−	28.8116i		−	0.523847i
$56$	20.9364	−	5.67157i	0.373864	−	0.101278i
$57$	20.3497	−	51.9357i	0.357013	−	0.911152i
$58$	7.52915	+	20.6274i	0.129813	+	0.355645i
$59$	19.8925	−	19.8925i	0.337162	−	0.337162i	−0.518136	−	0.855298i	$-0.673374\pi$
$59$	19.8925	−	19.8925i	0.337162	−	0.337162i	0.855298	+	0.518136i	$0.173374\pi$
$60$	12.1794	+	35.9652i	0.202990	+	0.599420i
$61$	107.892			1.76872			0.884360	−	0.466805i	$-0.154595\pi$
$61$	107.892			1.76872			0.884360	+	0.466805i	$0.154595\pi$
$62$	−4.79584	+	10.3094i	−0.0773523	+	0.166280i
$63$	24.3843	−	0.939704i	0.387052	−	0.0149159i
$64$	−32.3040	−	55.2490i	−0.504750	−	0.863265i
$65$	27.8468	−	30.2772i	0.428413	−	0.465803i
$66$	−1.28145	+	54.6163i	−0.0194159	+	0.827520i
$67$	57.5421	−	57.5421i	0.858838	−	0.858838i	−0.132364	−	0.991201i	$-0.542257\pi$
$67$	57.5421	−	57.5421i	0.858838	−	0.858838i	0.991201	+	0.132364i	$0.0422567\pi$
$68$	−24.2631	+	20.4350i	−0.356810	+	0.300514i
$69$	16.1807	+	37.0300i	0.234502	+	0.536666i
$70$	16.1190	−	5.88354i	0.230271	−	0.0840506i
$71$	−15.3918	−	15.3918i	−0.216785	−	0.216785i	0.590357	−	0.807142i	$-0.298987\pi$
$71$	−15.3918	−	15.3918i	−0.216785	−	0.216785i	−0.807142	+	0.590357i	$0.798987\pi$
$72$	−21.4881	−	68.7187i	−0.298446	−	0.954426i
$73$	−52.5418	+	52.5418i	−0.719751	+	0.719751i	−0.968554	−	0.248803i	$-0.919963\pi$
$73$	−52.5418	+	52.5418i	−0.719751	+	0.719751i	0.248803	+	0.968554i	$0.419963\pi$
$74$	2.03811	−	4.38120i	0.0275420	−	0.0592054i
$75$	−18.0029	−	41.2002i	−0.240038	−	0.549336i
$76$	−6.34639	+	74.1023i	−0.0835051	+	0.975030i
$77$	24.6877			0.320619
$78$	−54.1341	+	56.1560i	−0.694027	+	0.719949i
$79$		−	46.1756i		−	0.584501i	−0.956342	−	0.292251i	$-0.905596\pi$
$79$		−	46.1756i		−	0.584501i	0.956342	−	0.292251i	$-0.0944042\pi$
$80$	−29.1911	−	41.3660i	−0.364889	−	0.517074i
$81$	−6.23379	−	80.7598i	−0.0769603	−	0.997034i
$82$	−41.9475	+	90.1721i	−0.511555	+	1.09966i
$83$	88.7459	+	88.7459i	1.06923	+	1.06923i	0.997418	+	0.0718100i	$0.0228775\pi$
$83$	88.7459	+	88.7459i	1.06923	+	1.06923i	0.0718100	+	0.997418i	$0.477122\pi$
$84$	−30.8174	+	10.4361i	−0.366873	+	0.124240i
$85$	−17.7444	+	17.7444i	−0.208758	+	0.208758i
$86$	−86.7865	+	31.6777i	−1.00915	+	0.368346i
$87$	−13.1884	−	30.1822i	−0.151591	−	0.346922i
$88$	−19.0461	−	70.3077i	−0.216432	−	0.798952i
$89$	−96.2535	−	96.2535i	−1.08150	−	1.08150i	−0.996370	−	0.0851298i	$-0.972869\pi$
$89$	−96.2535	−	96.2535i	−1.08150	−	1.08150i	−0.0851298	−	0.996370i	$-0.527131\pi$
$90$	−21.5754	−	52.7127i	−0.239727	−	0.585697i
$91$	25.9435	+	23.8610i	0.285093	+	0.262209i
$92$	−34.7096	−	41.2118i	−0.377279	−	0.447954i
$93$	6.22216	−	15.8799i	0.0669049	−	0.170752i
$94$	−54.8049	+	117.811i	−0.583031	+	1.25331i
$95$			58.8349i			0.619315i
$96$	53.4959	+	79.7131i	0.557249	+	0.830345i
$97$	−42.4947	−	42.4947i	−0.438090	−	0.438090i	0.453279	−	0.891369i	$-0.350254\pi$
$97$	−42.4947	−	42.4947i	−0.438090	−	0.438090i	−0.891369	+	0.453279i	$0.850254\pi$
$98$	−28.5609	−	78.2474i	−0.291438	−	0.798442i
$99$	−3.15568	−	81.8863i	−0.0318755	−	0.827134i
$100$	38.6185	+	45.8529i	0.386185	+	0.458529i
$101$	−82.7044			−0.818855			−0.409428	−	0.912343i	$-0.634272\pi$
$101$	−82.7044			−0.818855			−0.409428	+	0.912343i	$0.634272\pi$
$102$	34.4262	−	32.8477i	0.337512	−	0.322037i
$103$	136.814			1.32829			0.664144	−	0.747605i	$-0.268796\pi$
$103$	136.814			1.32829			0.664144	+	0.747605i	$0.268796\pi$
$104$	47.9385	−	92.2924i	0.460948	−	0.887427i
$105$	−23.5854	+	10.3059i	−0.224623	+	0.0981515i
$106$	66.3369	+	181.741i	0.625820	+	1.71454i
$107$	93.4017			0.872913			0.436457	−	0.899725i	$-0.356233\pi$
$107$	93.4017			0.872913			0.436457	+	0.899725i	$0.356233\pi$
$108$	38.5547	+	100.884i	0.356988	+	0.934109i
$109$	−98.4697	−	98.4697i	−0.903392	−	0.903392i	0.0923359	−	0.995728i	$-0.470567\pi$
$109$	−98.4697	−	98.4697i	−0.903392	−	0.903392i	−0.995728	+	0.0923359i	$0.970567\pi$
$110$	−19.7579	−	54.1300i	−0.179617	−	0.492091i
$111$	−2.64425	+	6.74854i	−0.0238221	+	0.0607976i
$112$	35.4451	−	25.0129i	0.316474	−	0.223329i
$113$			85.7284i			0.758658i	0.925262	+	0.379329i	$0.123845\pi$
$113$			85.7284i			0.758658i	−0.925262	+	0.379329i	$0.876155\pi$
$114$	2.61679	−	111.530i	0.0229543	−	0.978330i
$115$	−30.1396	−	30.1396i	−0.262084	−	0.262084i
$116$	28.2909	+	33.5907i	0.243887	+	0.289575i
$117$	75.8280	−	89.1017i	0.648103	−	0.761553i
$118$	23.7317	−	51.0148i	0.201116	−	0.432329i
$119$	−15.2046	−	15.2046i	−0.127770	−	0.127770i
$120$	47.5457	+	59.2178i	0.396215	+	0.493482i
$121$			38.0948i			0.314833i
$122$	202.703	−	73.9881i	1.66150	−	0.606460i
$123$	54.4229	−	138.896i	0.442463	−	1.12923i
$124$	−1.94048	+	22.6576i	−0.0156490	+	0.182722i
$125$	89.4712	+	89.4712i	0.715770	+	0.715770i
$126$	45.1677	−	18.4873i	0.358474	−	0.146724i
$127$	−93.7596			−0.738265			−0.369132	−	0.929377i	$-0.620345\pi$
$127$	−93.7596			−0.738265			−0.369132	+	0.929377i	$0.620345\pi$
$128$	−98.5790	−	81.6467i	−0.770149	−	0.637864i
$129$	126.987	−	55.4883i	0.984394	−	0.430142i
$130$	31.5545	−	75.9798i	0.242727	−	0.584460i
$131$	56.4833			0.431170			0.215585	−	0.976485i	$-0.430834\pi$
$131$	56.4833			0.431170			0.215585	+	0.976485i	$0.430834\pi$
$132$	35.0462	+	103.490i	0.265502	+	0.784013i
$133$	−50.4136			−0.379050
$134$	68.6476	−	147.568i	0.512295	−	1.10125i
$135$	37.1983	+	76.9128i	0.275543	+	0.569725i
$136$	−31.5709	+	55.0310i	−0.232139	+	0.404640i
$137$	−9.93664	−	9.93664i	−0.0725302	−	0.0725302i	0.669911	−	0.742441i	$-0.266332\pi$
$137$	−9.93664	−	9.93664i	−0.0725302	−	0.0725302i	−0.742441	+	0.669911i	$0.766332\pi$
$138$	55.7933	+	58.4743i	0.404299	+	0.423727i
$139$			157.438i			1.13265i	0.824183	+	0.566324i	$0.191635\pi$
$139$			157.438i			1.13265i	−0.824183	+	0.566324i	$0.808365\pi$
$140$	26.2489	−	22.1075i	0.187492	−	0.157911i
$141$	71.1042	−	181.469i	0.504285	−	1.28701i
$142$	−39.4725	−	18.3623i	−0.277975	−	0.129312i
$143$	80.1290	−	87.1224i	0.560343	−	0.609248i
$144$	−87.4956	−	114.370i	−0.607609	−	0.794237i
$145$	24.5660	+	24.5660i	0.169421	+	0.169421i
$146$	−62.6823	+	134.745i	−0.429331	+	0.922908i
$147$	50.0287	+	114.492i	0.340331	+	0.778859i
$148$	0.824652	−	9.62887i	0.00557197	−	0.0650599i
$149$	−73.2706	+	73.2706i	−0.491749	+	0.491749i	−0.908857	−	0.417108i	$-0.863044\pi$
$149$	−73.2706	+	73.2706i	−0.491749	+	0.491749i	0.417108	+	0.908857i	$0.363044\pi$
$150$	−62.0765	−	65.0595i	−0.413844	−	0.433730i
$151$	−95.2616	−	95.2616i	−0.630871	−	0.630871i	0.317415	−	0.948287i	$-0.397185\pi$
$151$	−95.2616	−	95.2616i	−0.630871	−	0.630871i	−0.948287	+	0.317415i	$0.897185\pi$
$152$	38.8931	+	143.572i	0.255876	+	0.944555i
$153$	−48.4884	+	52.3754i	−0.316918	+	0.342323i
$154$	46.3822	−	16.9298i	0.301183	−	0.109934i
$155$			17.9894i			0.116061i
$156$	−63.1953	+	142.627i	−0.405098	+	0.914273i
$157$	−174.497			−1.11145			−0.555724	−	0.831367i	$-0.687559\pi$
$157$	−174.497			−1.11145			−0.555724	+	0.831367i	$0.687559\pi$
$158$	−31.6654	−	86.7528i	−0.200414	−	0.549068i
$159$	−116.199	−	265.925i	−0.730812	−	1.67249i
$160$	−83.2102	−	57.6985i	−0.520064	−	0.360616i
$161$	25.8256	−	25.8256i	0.160408	−	0.160408i
$162$	−67.0937	−	147.453i	−0.414158	−	0.910205i
$163$	204.207	+	204.207i	1.25280	+	1.25280i	0.954459	+	0.298343i	$0.0964340\pi$
$163$	204.207	+	204.207i	1.25280	+	1.25280i	0.298343	+	0.954459i	$0.403566\pi$
$164$	−16.9726	+	198.178i	−0.103492	+	1.20840i
$165$	34.6089	+	79.2036i	0.209751	+	0.480022i
$166$	227.591	+	105.874i	1.37103	+	0.637793i
$167$	−73.3239	+	73.3239i	−0.439066	+	0.439066i	−0.891697	−	0.452632i	$-0.850485\pi$
$167$	−73.3239	+	73.3239i	−0.439066	+	0.439066i	0.452632	+	0.891697i	$0.350485\pi$
$168$	−50.7417	+	40.7403i	−0.302034	+	0.242502i
$169$	168.410	−	14.1083i	0.996509	−	0.0834812i
$170$	−21.1690	+	45.5059i	−0.124524	+	0.267682i
$171$	6.44407	+	167.216i	0.0376846	+	0.977873i
$172$	−141.328	+	119.030i	−0.821672	+	0.692032i
$173$	47.5804			0.275031			0.137516	−	0.990500i	$-0.456088\pi$
$173$	47.5804			0.275031			0.137516	+	0.990500i	$0.456088\pi$
$174$	−45.4756	−	47.6609i	−0.261354	−	0.273913i
$175$	−28.7340	+	28.7340i	−0.164194	+	0.164194i
$176$	−83.9972	−	119.030i	−0.477257	−	0.676308i
$177$	−30.7897	+	78.5801i	−0.173953	+	0.443955i
$178$	−246.844	−	114.830i	−1.38676	−	0.645113i
$179$		−	348.521i		−	1.94704i	−0.228591	−	0.973522i	$-0.573412\pi$
$179$		−	348.521i		−	1.94704i	0.228591	−	0.973522i	$-0.426588\pi$
$180$	−76.6834	−	84.2389i	−0.426019	−	0.467994i
$181$			170.140i			0.940001i	0.882666	+	0.470000i	$0.155746\pi$
$181$			170.140i			0.940001i	−0.882666	+	0.470000i	$0.844254\pi$
$182$	65.1045	+	27.0380i	0.357717	+	0.148560i
$183$	−296.597	+	129.601i	−1.62075	+	0.708204i
$184$	−93.4724	−	53.6245i	−0.508002	−	0.291438i
$185$		−	7.64503i		−	0.0413245i
$186$	0.800113	−	34.1014i	0.00430168	−	0.183341i
$187$	−51.0594	+	51.0594i	−0.273045	+	0.273045i
$188$	−22.1750	+	258.921i	−0.117952	+	1.37724i
$189$	−65.9039	+	31.8740i	−0.348698	+	0.168645i
$190$	40.3467	+	110.537i	0.212351	+	0.581771i
$191$	−364.231			−1.90697			−0.953483	−	0.301445i	$-0.902531\pi$
$191$	−364.231			−1.90697			−0.953483	+	0.301445i	$0.902531\pi$
$192$	155.170	+	113.076i	0.808177	+	0.588939i
$193$	27.5701	−	27.5701i	0.142850	−	0.142850i	−0.632065	−	0.774915i	$-0.717792\pi$
$193$	27.5701	−	27.5701i	0.142850	−	0.142850i	0.774915	+	0.632065i	$0.217792\pi$
$194$	−108.978	−	50.6961i	−0.561745	−	0.261320i
$195$	−40.1820	+	116.682i	−0.206061	+	0.598372i
$196$	−107.318	−	127.422i	−0.547541	−	0.650112i
$197$	174.867	−	174.867i	0.887650	−	0.887650i	−0.106647	−	0.994297i	$-0.534011\pi$
$197$	174.867	−	174.867i	0.887650	−	0.887650i	0.994297	+	0.106647i	$0.0340114\pi$
$198$	−62.0832	−	151.680i	−0.313551	−	0.766063i
$199$	−217.321			−1.09207			−0.546033	−	0.837764i	$-0.683863\pi$
$199$	−217.321			−1.09207			−0.546033	+	0.837764i	$0.683863\pi$
$200$	103.999	+	59.6635i	0.519995	+	0.298318i
$201$	−89.0638	+	227.305i	−0.443103	+	1.13087i
$202$	−155.382	+	56.7154i	−0.769216	+	0.280769i
$203$	−21.0498	+	21.0498i	−0.103694	+	0.103694i
$204$	42.1528	−	85.3211i	0.206631	−	0.418241i
$205$			157.347i			0.767546i
$206$	257.040	−	93.8215i	1.24777	−	0.455444i
$207$	−88.9618	−	82.3596i	−0.429767	−	0.397872i
$208$	26.7744	−	206.270i	0.128723	−	0.991681i
$209$			169.297i			0.810034i
$210$	−37.2439	+	35.5363i	−0.177352	+	0.169220i
$211$		−	16.1284i		−	0.0764381i	−0.999269	−	0.0382191i	$-0.987832\pi$
$211$		−	16.1284i		−	0.0764381i	0.999269	−	0.0382191i	$-0.0121685\pi$
$212$	249.262	+	295.957i	1.17576	+	1.39602i
$213$	60.8010	+	23.8234i	0.285451	+	0.111847i
$214$	175.479	−	64.0512i	0.819996	−	0.299305i
$215$	−103.358	+	103.358i	−0.480734	+	0.480734i
$216$	141.617	+	163.097i	0.655635	+	0.755078i
$217$	−15.4145			−0.0710346
$218$	−252.527	−	117.474i	−1.15838	−	0.538872i
$219$	81.3244	−	207.552i	0.371344	−	0.947727i
$220$	−74.2405	−	88.1481i	−0.337457	−	0.400673i
$221$	−103.006	+	4.30707i	−0.466092	+	0.0194890i
$222$	−0.340027	+	14.4922i	−0.00153165	+	0.0652801i
$223$	216.887	−	216.887i	0.972590	−	0.972590i	−0.0270445	−	0.999634i	$-0.508610\pi$
$223$	216.887	−	216.887i	0.972590	−	0.972590i	0.999634	+	0.0270445i	$0.00860960\pi$
$224$	49.4399	−	71.3000i	0.220714	−	0.318303i
$225$	98.9804	+	91.6346i	0.439913	+	0.407265i
$226$	58.7891	+	161.063i	0.260129	+	0.712667i
$227$	170.053	+	170.053i	0.749133	+	0.749133i	0.974316	−	0.225184i	$-0.0722982\pi$
$227$	170.053	+	170.053i	0.749133	+	0.749133i	−0.225184	+	0.974316i	$0.572298\pi$
$228$	−71.5663	−	211.332i	−0.313887	−	0.926893i
$229$	−28.7277	+	28.7277i	−0.125448	+	0.125448i	−0.767044	−	0.641595i	$-0.778273\pi$
$229$	−28.7277	+	28.7277i	−0.125448	+	0.125448i	0.641595	+	0.767044i	$0.278273\pi$
$230$	−77.2937	−	35.9565i	−0.336059	−	0.156333i
$231$	−67.8668	+	29.6552i	−0.293796	+	0.128377i
$232$	76.1869	+	43.7079i	0.328392	+	0.188396i
$233$	127.409			0.546818			0.273409	−	0.961898i	$-0.411849\pi$
$233$	127.409			0.546818			0.273409	+	0.961898i	$0.411849\pi$
$234$	81.3601	−	219.400i	0.347693	−	0.937609i
$235$			205.576i			0.874790i
$236$	9.60226	−	112.119i	0.0406875	−	0.475080i
$237$	55.4668	+	126.937i	0.234037	+	0.535601i
$238$	−38.9924	−	18.1390i	−0.163834	−	0.0762144i
$239$	9.41795	+	9.41795i	0.0394057	+	0.0394057i	0.726535	−	0.687129i	$-0.241129\pi$
$239$	9.41795	+	9.41795i	0.0394057	+	0.0394057i	−0.687129	+	0.726535i	$0.741129\pi$
$240$	129.936	+	78.6509i	0.541401	+	0.327712i
$241$	330.162	−	330.162i	1.36997	−	1.36997i	0.509492	−	0.860475i	$-0.329833\pi$
$241$	330.162	−	330.162i	1.36997	−	1.36997i	0.860475	−	0.509492i	$-0.170167\pi$
$242$	26.1239	+	71.5709i	0.107950	+	0.295748i
$243$	114.146	+	214.522i	0.469739	+	0.882806i
$244$	330.092	−	278.011i	1.35283	−	1.13939i
$245$	−93.1881	−	93.1881i	−0.380360	−	0.380360i
$246$	6.99830	−	298.272i	0.0284484	−	1.21249i
$247$	−163.628	+	177.909i	−0.662461	+	0.720279i
$248$	11.8920	+	43.8988i	0.0479516	+	0.177011i
$249$	−350.567	−	137.361i	−1.40790	−	0.551651i
$250$	229.451	+	106.739i	0.917802	+	0.426956i
$251$		−	131.726i		−	0.524804i	−0.964959	−	0.262402i	$-0.915485\pi$
$251$		−	131.726i		−	0.524804i	0.964959	−	0.262402i	$-0.0845147\pi$
$252$	72.1814	−	65.7073i	0.286434	−	0.260743i
$253$	−86.7266	−	86.7266i	−0.342793	−	0.342793i
$254$	−176.152	+	64.2967i	−0.693510	+	0.253137i
$255$	27.4648	−	70.0945i	0.107705	−	0.274880i
$256$	−241.196	−	85.7927i	−0.942173	−	0.335128i
$257$	−145.078			−0.564505			−0.282252	−	0.959340i	$-0.591082\pi$
$257$	−145.078			−0.564505			−0.282252	+	0.959340i	$0.591082\pi$
$258$	200.526	−	191.332i	0.777232	−	0.741596i
$259$	6.55076			0.0252925
$260$	7.17936	−	164.387i	0.0276129	−	0.632256i
$261$	72.5105	+	67.1291i	0.277818	+	0.257200i
$262$	106.118	−	38.7340i	0.405032	−	0.147840i
$263$	−73.5496			−0.279656			−0.139828	−	0.990176i	$-0.544655\pi$
$263$	−73.5496			−0.279656			−0.139828	+	0.990176i	$0.544655\pi$
$264$	136.813	+	170.399i	0.518229	+	0.645450i
$265$	216.443	+	216.443i	0.816768	+	0.816768i
$266$	−94.7150	+	34.5717i	−0.356071	+	0.129969i
$267$	380.223	+	148.981i	1.42406	+	0.557982i
$268$	27.7760	−	324.320i	0.103642	−	1.21015i
$269$		−	329.441i		−	1.22469i	−0.790591	−	0.612345i	$-0.790226\pi$
$269$		−	329.441i		−	1.22469i	0.790591	−	0.612345i	$-0.209774\pi$
$270$	122.630	+	118.991i	0.454187	+	0.440709i
$271$	163.971	+	163.971i	0.605061	+	0.605061i	0.941651	−	0.336590i	$-0.109274\pi$
$271$	163.971	+	163.971i	0.605061	+	0.605061i	−0.336590	+	0.941651i	$0.609274\pi$
$272$	−21.5760	+	125.040i	−0.0793236	+	0.459706i
$273$	−99.9812	−	34.4306i	−0.366232	−	0.126119i
$274$	−25.4827	−	11.8544i	−0.0930026	−	0.0432642i
$275$	96.4934	+	96.4934i	0.350885	+	0.350885i
$276$	144.921	+	71.5982i	0.525078	+	0.259414i
$277$		−	165.945i		−	0.599078i	−0.954084	−	0.299539i	$-0.903167\pi$
$277$		−	165.945i		−	0.599078i	0.954084	−	0.299539i	$-0.0968329\pi$
$278$	107.965	+	295.788i	0.388363	+	1.06399i
$279$	1.97034	+	51.1282i	0.00706217	+	0.183255i
$280$	34.1549	−	59.5351i	0.121982	−	0.212625i
$281$	−13.7443	−	13.7443i	−0.0489121	−	0.0489121i	0.682228	−	0.731140i	$-0.261011\pi$
$281$	−13.7443	−	13.7443i	−0.0489121	−	0.0489121i	−0.731140	+	0.682228i	$0.761011\pi$
$282$	9.14337	−	389.697i	0.0324233	−	1.38190i
$283$	−330.563			−1.16807			−0.584033	−	0.811730i	$-0.698526\pi$
$283$	−330.563			−1.16807			−0.584033	+	0.811730i	$0.698526\pi$
$284$	−86.7514	−	7.42971i	−0.305463	−	0.0261609i
$285$	−70.6733	−	161.738i	−0.247976	−	0.567502i
$286$	90.7979	−	218.631i	0.317475	−	0.764445i
$287$	−134.825			−0.469774
$288$	−242.814	−	154.873i	−0.843103	−	0.537752i
$289$	−226.107			−0.782378
$290$	63.0001	+	29.3072i	0.217242	+	0.101059i
$291$	167.864	+	65.7734i	0.576851	+	0.226025i
$292$	−25.3623	+	296.137i	−0.0868572	+	1.01417i
$293$	−20.8531	−	20.8531i	−0.0711711	−	0.0711711i	0.670625	−	0.741796i	$-0.266026\pi$
$293$	−20.8531	−	20.8531i	−0.0711711	−	0.0711711i	−0.741796	+	0.670625i	$0.766026\pi$
$294$	172.506	+	180.796i	0.586755	+	0.614951i
$295$		−	89.0188i		−	0.301759i
$296$	−5.05378	−	18.6558i	−0.0170736	−	0.0630265i
$297$	107.038	+	221.316i	0.360397	+	0.745172i
$298$	−87.4117	+	187.904i	−0.293328	+	0.630550i
$299$	−7.31573	−	174.961i	−0.0244673	−	0.585153i
$300$	−161.242	−	79.6614i	−0.537473	−	0.265538i
$301$	−88.5637	−	88.5637i	−0.294232	−	0.294232i
$302$	−244.300	−	113.647i	−0.808941	−	0.376314i
$303$	227.356	−	99.3456i	0.750349	−	0.327873i
$304$	171.527	+	243.066i	0.564234	+	0.799560i
$305$	241.408	−	241.408i	0.791500	−	0.791500i
$306$	−55.1809	+	131.652i	−0.180330	+	0.430236i
$307$	−330.034	−	330.034i	−1.07503	−	1.07503i	−0.996947	−	0.0780834i	$-0.975120\pi$
$307$	−330.034	−	330.034i	−1.07503	−	1.07503i	−0.0780834	−	0.996947i	$-0.524880\pi$
$308$	75.5311	−	63.6142i	0.245231	−	0.206539i
$309$	−376.103	+	164.342i	−1.21716	+	0.531853i
$310$	12.3364	+	33.7978i	0.0397950	+	0.109025i
$311$			291.242i			0.936470i	0.883604	+	0.468235i	$0.155110\pi$
$311$			291.242i			0.936470i	−0.883604	+	0.468235i	$0.844890\pi$
$312$	−20.9209	+	311.298i	−0.0670541	+	0.997749i
$313$	342.505			1.09427			0.547133	−	0.837046i	$-0.315719\pi$
$313$	342.505			1.09427			0.547133	+	0.837046i	$0.315719\pi$
$314$	−327.838	+	119.663i	−1.04407	+	0.381094i
$315$	52.4570	−	56.6622i	0.166530	−	0.179880i
$316$	−118.983	−	141.273i	−0.376530	−	0.447065i
$317$	399.011	−	399.011i	1.25871	−	1.25871i	0.306999	−	0.951710i	$-0.400675\pi$
$317$	399.011	−	399.011i	1.25871	−	1.25871i	0.951710	−	0.306999i	$-0.0993249\pi$
$318$	−400.671	−	419.925i	−1.25997	−	1.32052i
$319$	70.6886	+	70.6886i	0.221594	+	0.221594i
$320$	−195.899	−	51.3392i	−0.612185	−	0.160435i
$321$	−256.763	+	112.195i	−0.799884	+	0.349518i
$322$	30.8099	−	66.2303i	0.0956829	−	0.205684i
$323$	104.266	−	104.266i	0.322806	−	0.322806i
$324$	−227.170	−	231.019i	−0.701143	−	0.713021i
$325$	8.13961	+	194.664i	0.0250449	+	0.598967i
$326$	523.692	+	243.618i	1.60642	+	0.747295i
$327$	388.978	+	152.412i	1.18954	+	0.466091i
$328$	104.015	+	383.967i	0.317119	+	1.17063i
$329$	−176.151			−0.535413
$330$	119.336	+	125.071i	0.361626	+	0.379003i
$331$	386.713	−	386.713i	1.16832	−	1.16832i	0.185715	−	0.982604i	$-0.440540\pi$
$331$	386.713	−	386.713i	1.16832	−	1.16832i	0.982604	−	0.185715i	$-0.0594601\pi$
$332$	500.192	+	42.8383i	1.50660	+	0.129031i
$333$	−0.837344	−	21.7281i	−0.00251455	−	0.0652497i
$334$	−87.4753	+	188.041i	−0.261902	+	0.562996i
$335$		−	257.500i		−	0.768657i
$336$	−67.3932	+	111.338i	−0.200575	+	0.331363i
$337$		−	61.3087i		−	0.181925i	−0.995854	−	0.0909625i	$-0.971006\pi$
$337$		−	61.3087i		−	0.181925i	0.995854	−	0.0909625i	$-0.0289944\pi$
$338$	306.727	−	141.995i	0.907476	−	0.420104i
$339$	−102.978	−	235.669i	−0.303770	−	0.695188i
$340$	−8.56535	+	100.011i	−0.0251922	+	0.294151i
$341$			51.7644i			0.151802i
$342$	126.777	+	309.740i	0.370694	+	0.905672i
$343$	173.794	−	173.794i	0.506688	−	0.506688i
$344$	−183.894	+	320.545i	−0.534577	+	0.931816i
$345$	119.058	+	46.6502i	0.345097	+	0.135218i
$346$	89.3921	−	32.6288i	0.258359	−	0.0943028i
$347$	27.4780			0.0791872			0.0395936	−	0.999216i	$-0.487394\pi$
$347$	27.4780			0.0791872			0.0395936	+	0.999216i	$0.487394\pi$
$348$	−118.122	−	58.3579i	−0.339430	−	0.167695i
$349$	−241.315	+	241.315i	−0.691447	+	0.691447i	−0.962550	−	0.271103i	$-0.912612\pi$
$349$	−241.315	+	241.315i	−0.691447	+	0.691447i	0.271103	+	0.962550i	$0.412612\pi$
$350$	−34.2796	+	73.6889i	−0.0979417	+	0.210540i
$351$	−101.422	+	336.028i	−0.288952	+	0.957343i
$352$	−239.437	−	166.027i	−0.680218	−	0.471668i
$353$	268.532	−	268.532i	0.760715	−	0.760715i	−0.215737	−	0.976452i	$-0.569215\pi$
$353$	268.532	−	268.532i	0.760715	−	0.760715i	0.976452	+	0.215737i	$0.0692153\pi$
$354$	−3.95928	+	168.747i	−0.0111844	+	0.476687i
$355$	−68.8779			−0.194022
$356$	−542.506	−	46.4622i	−1.52389	−	0.130512i
$357$	60.0616	+	23.5337i	0.168240	+	0.0659207i
$358$	−239.002	−	654.787i	−0.667604	−	1.82901i
$359$	−43.0730	+	43.0730i	−0.119981	+	0.119981i	−0.764548	−	0.644567i	$-0.777038\pi$
$359$	−43.0730	+	43.0730i	−0.119981	+	0.119981i	0.644567	+	0.764548i	$0.277038\pi$
$360$	−201.837	−	105.678i	−0.560659	−	0.293550i
$361$			15.2861i			0.0423437i
$362$	116.675	+	319.652i	0.322308	+	0.883017i
$363$	−45.7600	−	104.723i	−0.126061	−	0.288494i
$364$	140.857	+	6.15175i	0.386970	+	0.0169004i
$365$			235.124i			0.644175i
$366$	−468.358	+	446.884i	−1.27967	+	1.22099i
$367$		−	499.591i		−	1.36128i	−0.732616	−	0.680642i	$-0.761701\pi$
$367$		−	499.591i		−	1.36128i	0.732616	−	0.680642i	$-0.238299\pi$
$368$	−212.386	−	36.6478i	−0.577135	−	0.0995864i
$369$	17.2339	+	447.200i	0.0467043	+	1.21192i
$370$	−5.24266	−	14.3632i	−0.0141694	−	0.0388193i
$371$	−185.463	+	185.463i	−0.499900	+	0.499900i
$372$	−21.8822	−	64.6170i	−0.0588231	−	0.173702i
$373$	−332.025			−0.890147			−0.445073	−	0.895494i	$-0.646822\pi$
$373$	−332.025			−0.890147			−0.445073	+	0.895494i	$0.646822\pi$
$374$	−60.9138	+	130.943i	−0.162871	+	0.350115i
$375$	−353.432	−	138.484i	−0.942485	−	0.369290i
$376$	135.897	+	501.658i	0.361428	+	1.33420i
$377$	5.96286	+	142.606i	0.0158166	+	0.378265i
$378$	−101.960	+	105.078i	−0.269735	+	0.277984i
$379$	468.317	−	468.317i	1.23567	−	1.23567i	0.273911	−	0.961755i	$-0.411683\pi$
$379$	468.317	−	468.317i	1.23567	−	1.23567i	0.961755	−	0.273911i	$-0.0883173\pi$
$380$	151.603	+	180.003i	0.398956	+	0.473693i
$381$	257.747	−	112.625i	0.676500	−	0.295605i
$382$	−684.301	+	249.775i	−1.79136	+	0.653862i
$383$	−101.144	−	101.144i	−0.264083	−	0.264083i	0.562627	−	0.826711i	$-0.309791\pi$
$383$	−101.144	−	101.144i	−0.264083	−	0.264083i	−0.826711	+	0.562627i	$0.809791\pi$
$384$	369.070	+	106.033i	0.961121	+	0.276129i
$385$	55.2385	−	55.2385i	0.143477	−	0.143477i
$386$	32.8911	−	70.7041i	0.0852100	−	0.183171i
$387$	−282.435	+	305.076i	−0.729807	+	0.788311i
$388$	−239.509	−	20.5125i	−0.617293	−	0.0528672i
$389$	−456.268			−1.17293			−0.586463	−	0.809976i	$-0.699480\pi$
$389$	−456.268			−1.17293			−0.586463	+	0.809976i	$0.699480\pi$
$390$	4.52405	+	246.773i	0.0116001	+	0.632752i
$391$			106.826i			0.273212i
$392$	−289.005	−	165.801i	−0.737259	−	0.422961i
$393$	−155.273	+	67.8485i	−0.395098	+	0.172642i
$394$	208.616	−	448.450i	0.529482	−	1.13820i
$395$	−103.318	−	103.318i	−0.261564	−	0.261564i
$396$	−220.656	−	242.397i	−0.557211	−	0.612113i
$397$	300.957	−	300.957i	0.758078	−	0.758078i	−0.217895	−	0.975972i	$-0.569919\pi$
$397$	300.957	−	300.957i	0.758078	−	0.758078i	0.975972	+	0.217895i	$0.0699189\pi$
$398$	−408.294	+	149.030i	−1.02586	+	0.374448i
$399$	138.588	−	60.5575i	0.347338	−	0.151773i
$400$	236.304	+	40.7749i	0.590760	+	0.101937i
$401$	252.305	+	252.305i	0.629190	+	0.629190i	0.947864	−	0.318674i	$-0.103238\pi$
$401$	252.305	+	252.305i	0.629190	+	0.629190i	−0.318674	+	0.947864i	$0.603238\pi$
$402$	−11.4528	+	488.127i	−0.0284896	+	1.21425i
$403$	−50.0310	+	54.3976i	−0.124146	+	0.134982i
$404$	−253.031	+	213.109i	−0.626315	+	0.527498i
$405$	−194.647	−	166.751i	−0.480611	−	0.411732i
$406$	−25.1123	+	53.9826i	−0.0618531	+	0.132962i
$407$		−	21.9985i		−	0.0540504i
$408$	20.6850	−	189.204i	0.0506985	−	0.463736i
$409$	−75.5531	−	75.5531i	−0.184726	−	0.184726i	0.608685	−	0.793412i	$-0.291697\pi$
$409$	−75.5531	−	75.5531i	−0.184726	−	0.184726i	−0.793412	+	0.608685i	$0.791697\pi$
$410$	107.902	+	295.617i	0.263176	+	0.721016i
$411$	39.2520	+	15.3800i	0.0955036	+	0.0374208i
$412$	418.577	−	352.536i	1.01596	−	0.855669i
$413$	76.2772			0.184691
$414$	−223.617	−	93.7272i	−0.540137	−	0.226394i
$415$	397.137			0.956956
$416$	−91.1490	−	405.891i	−0.219108	−	0.975701i
$417$	−189.117	−	432.799i	−0.453517	−	1.03789i
$418$	116.097	+	318.068i	0.277745	+	0.760929i
$419$	354.855			0.846909			0.423454	−	0.905917i	$-0.360817\pi$
$419$	354.855			0.846909			0.423454	+	0.905917i	$0.360817\pi$
$420$	−45.6029	+	92.3044i	−0.108578	+	0.219772i
$421$	−148.325	−	148.325i	−0.352315	−	0.352315i	0.508655	−	0.860970i	$-0.330143\pi$
$421$	−148.325	−	148.325i	−0.352315	−	0.352315i	−0.860970	+	0.508655i	$0.830143\pi$
$422$	−11.0603	−	30.3014i	−0.0262091	−	0.0718044i
$423$	22.5163	+	584.272i	0.0532300	+	1.38126i
$424$	671.259	+	385.097i	1.58316	+	0.908247i
$425$		−	118.856i		−	0.279662i
$426$	130.568	+	3.06348i	0.306496	+	0.00719126i
$427$	206.854	+	206.854i	0.484435	+	0.484435i
$428$	285.759	−	240.674i	0.667662	−	0.562321i
$429$	−115.623	+	335.753i	−0.269518	+	0.782641i
$430$	−123.306	+	265.063i	−0.286757	+	0.616425i
$431$	−129.751	−	129.751i	−0.301047	−	0.301047i	0.540376	−	0.841424i	$-0.318282\pi$
$431$	−129.751	−	129.751i	−0.301047	−	0.301047i	−0.841424	+	0.540376i	$0.818282\pi$
$432$	377.910	+	209.304i	0.874791	+	0.484500i
$433$		−	277.129i		−	0.640020i	−0.947414	−	0.320010i	$-0.896314\pi$
$433$		−	277.129i		−	0.640020i	0.947414	−	0.320010i	$-0.103686\pi$
$434$	−28.9601	+	10.5707i	−0.0667285	+	0.0243564i
$435$	−97.0414	−	38.0234i	−0.223084	−	0.0874100i
$436$	−554.997	−	47.5320i	−1.27293	−	0.109018i
$437$	177.101	+	177.101i	0.405264	+	0.405264i
$438$	10.4576	−	445.710i	0.0238758	−	1.01760i
$439$	−824.382			−1.87786			−0.938932	−	0.344104i	$-0.888183\pi$
$439$	−824.382			−1.87786			−0.938932	+	0.344104i	$0.888183\pi$
$440$	−199.929	−	114.698i	−0.454383	−	0.260677i
$441$	−275.059	−	254.646i	−0.623717	−	0.577428i
$442$	−190.570	+	78.7297i	−0.431155	+	0.178121i
$443$	296.524			0.669354			0.334677	−	0.942333i	$-0.391373\pi$
$443$	296.524			0.669354			0.334677	+	0.942333i	$0.391373\pi$
$444$	9.29935	+	27.4605i	0.0209445	+	0.0618480i
$445$	−430.733			−0.967939
$446$	258.746	−	556.212i	0.580148	−	1.24711i
$447$	113.408	−	289.436i	0.253710	−	0.647507i
$448$	43.9908	−	167.859i	0.0981938	−	0.374686i
$449$	102.052	+	102.052i	0.227288	+	0.227288i	0.811559	−	0.584271i	$-0.198619\pi$
$449$	102.052	+	102.052i	0.227288	+	0.227288i	−0.584271	+	0.811559i	$0.698619\pi$
$450$	248.800	+	104.282i	0.552888	+	0.231739i
$451$			452.764i			1.00391i
$452$	220.901	+	262.283i	0.488719	+	0.580272i
$453$	376.305	+	147.446i	0.830695	+	0.325488i
$454$	436.104	+	202.873i	0.960583	+	0.446857i
$455$	111.437	−	4.65959i	0.244917	−	0.0102409i
$456$	−279.379	−	347.964i	−0.612673	−	0.763078i
$457$	297.399	+	297.399i	0.650763	+	0.650763i	0.953177	−	0.302414i	$-0.0977925\pi$
$457$	297.399	+	297.399i	0.650763	+	0.650763i	−0.302414	+	0.953177i	$0.597792\pi$
$458$	−34.2721	+	73.6727i	−0.0748298	+	0.160857i
$459$	70.3813	−	202.226i	0.153336	−	0.440579i
$460$	−169.874	−	14.5486i	−0.369291	−	0.0316274i
$461$	304.031	−	304.031i	0.659503	−	0.659503i	−0.295759	−	0.955262i	$-0.595573\pi$
$461$	304.031	−	304.031i	0.659503	−	0.659503i	0.955262	+	0.295759i	$0.0955727\pi$
$462$	−107.169	+	102.255i	−0.231967	+	0.221332i
$463$	141.035	+	141.035i	0.304612	+	0.304612i	0.842815	−	0.538203i	$-0.180897\pi$
$463$	141.035	+	141.035i	0.304612	+	0.304612i	−0.538203	+	0.842815i	$0.680897\pi$
$464$	173.110	+	29.8706i	0.373082	+	0.0643764i
$465$	−21.6091	−	49.4532i	−0.0464713	−	0.106351i
$466$	239.370	−	87.3718i	0.513669	−	0.187493i
$467$			546.532i			1.17030i	0.810923	+	0.585152i	$0.198965\pi$
$467$			546.532i			1.17030i	−0.810923	+	0.585152i	$0.801035\pi$
$468$	2.39975	−	467.994i	0.00512767	−	0.999987i
$469$	220.643			0.470454
$470$	140.976	+	386.227i	0.299948	+	0.821760i
$471$	479.696	−	209.609i	1.01846	−	0.445029i
$472$	−58.8463	−	217.229i	−0.124674	−	0.460231i
$473$	−297.411	+	297.411i	−0.628776	+	0.628776i
$474$	191.257	+	200.448i	0.403497	+	0.422886i
$475$	−197.045	−	197.045i	−0.414832	−	0.414832i
$476$	−85.6964	−	7.33935i	−0.180034	−	0.0154188i
$477$	638.866	+	591.453i	1.33934	+	1.23994i
$478$	24.1525	+	11.2356i	0.0505283	+	0.0235054i
$479$	−111.887	+	111.887i	−0.233585	+	0.233585i	−0.814187	−	0.580602i	$-0.802817\pi$
$479$	−111.887	+	111.887i	−0.233585	+	0.233585i	0.580602	+	0.814187i	$0.302817\pi$
$480$	298.054	+	58.6608i	0.620947	+	0.122210i
$481$	21.2619	−	23.1175i	0.0442035	−	0.0480614i
$482$	393.883	−	846.707i	0.817184	−	1.75665i
$483$	−39.9730	+	102.017i	−0.0827597	+	0.211216i
$484$	98.1611	+	116.550i	0.202812	+	0.240805i
$485$	−190.163			−0.392089
$486$	361.564	+	324.757i	0.743959	+	0.668225i
$487$	−149.033	+	149.033i	−0.306022	+	0.306022i	−0.843364	−	0.537343i	$-0.819428\pi$
$487$	−149.033	+	149.033i	−0.306022	+	0.306022i	0.537343	+	0.843364i	$0.319428\pi$
$488$	429.513	−	748.680i	0.880149	−	1.53418i
$489$	−806.663	−	316.072i	−1.64962	−	0.646363i
$490$	−238.983	−	111.173i	−0.487720	−	0.226884i
$491$		−	431.862i		−	0.879555i	−0.898107	−	0.439778i	$-0.855057\pi$
$491$		−	431.862i		−	0.879555i	0.898107	−	0.439778i	$-0.144943\pi$
$492$	−191.395	−	565.181i	−0.389015	−	1.14874i
$493$		−	87.0710i		−	0.176615i
$494$	−185.414	+	446.457i	−0.375333	+	0.903760i
$495$	−190.281	−	176.159i	−0.384406	−	0.355877i
$496$	52.4463	+	74.3202i	0.105738	+	0.149839i
$497$		−	59.0191i		−	0.118751i
$498$	−752.827	−	17.6634i	−1.51170	−	0.0354687i
$499$	−249.737	+	249.737i	−0.500475	+	0.500475i	−0.911586	−	0.411111i	$-0.865141\pi$
$499$	−249.737	+	249.737i	−0.500475	+	0.500475i	0.411111	+	0.911586i	$0.365141\pi$
$500$	504.279	+	43.1883i	1.00856	+	0.0863767i
$501$	113.491	−	289.646i	0.226529	−	0.578136i
$502$	−90.3324	−	247.481i	−0.179945	−	0.492990i
$503$	19.5125			0.0387923			0.0193961	−	0.999812i	$-0.493826\pi$
$503$	19.5125			0.0387923			0.0193961	+	0.999812i	$0.493826\pi$
$504$	90.5519	−	172.947i	0.179666	−	0.343150i
$505$	−185.051	+	185.051i	−0.366437	+	0.366437i
$506$	−222.412	−	103.465i	−0.439549	−	0.204475i
$507$	−446.015	+	241.080i	−0.879714	+	0.475504i
$508$	−286.854	+	241.596i	−0.564674	+	0.475582i
$509$	−291.110	+	291.110i	−0.571926	+	0.571926i	−0.932666	−	0.360740i	$-0.882524\pi$
$509$	−291.110	+	291.110i	−0.571926	+	0.571926i	0.360740	+	0.932666i	$0.382524\pi$
$510$	3.53173	−	150.525i	0.00692497	−	0.295147i
$511$	−201.470			−0.394265
$512$	−511.983	+	4.21922i	−0.999966	+	0.00824067i
$513$	−218.577	−	451.940i	−0.426077	−	0.880974i
$514$	−272.566	+	99.4886i	−0.530284	+	0.193558i
$515$	306.120	−	306.120i	0.594407	−	0.594407i
$516$	245.532	−	496.979i	0.475836	−	0.963137i
$517$			591.542i			1.14418i
$518$	12.3073	−	4.49225i	0.0237593	−	0.00867231i
$519$	−130.799	+	57.1542i	−0.252022	+	0.110124i
$520$	−99.2416	−	313.766i	−0.190849	−	0.603396i
$521$		−	554.046i		−	1.06343i	−0.846924	−	0.531714i	$-0.821548\pi$
$521$		−	554.046i		−	1.06343i	0.846924	−	0.531714i	$-0.178452\pi$
$522$	182.264	+	76.3946i	0.349165	+	0.146350i
$523$			565.353i			1.08098i	0.841350	+	0.540491i	$0.181761\pi$
$523$			565.353i			1.08098i	−0.841350	+	0.540491i	$0.818239\pi$
$524$	172.809	−	145.544i	0.329787	−	0.277755i
$525$	44.4746	−	113.506i	0.0847135	−	0.216202i
$526$	−138.182	+	50.4374i	−0.262703	+	0.0958887i
$527$	31.8805	−	31.8805i	0.0604944	−	0.0604944i
$528$	373.890	+	226.317i	0.708126	+	0.428631i
$529$	347.552			0.656998
$530$	555.073	+	258.216i	1.04731	+	0.487201i
$531$	−9.75005	−	253.003i	−0.0183617	−	0.476465i
$532$	−154.239	+	129.904i	−0.289922	+	0.244180i
$533$	−437.603	+	475.796i	−0.821019	+	0.892675i
$534$	816.513	+	19.1577i	1.52905	+	0.0358758i
$535$	208.986	−	208.986i	0.390627	−	0.390627i
$536$	−170.222	−	628.367i	−0.317578	−	1.17233i
$537$	418.648	+	958.090i	0.779606	+	1.78415i
$538$	−225.918	−	618.941i	−0.419922	−	1.15045i
$539$	−268.148	−	268.148i	−0.497492	−	0.497492i
$540$	311.993	+	139.461i	0.577764	+	0.258261i
$541$	−173.050	+	173.050i	−0.319870	+	0.319870i	−0.848717	−	0.528847i	$-0.822624\pi$
$541$	−173.050	+	173.050i	−0.319870	+	0.319870i	0.528847	+	0.848717i	$0.322624\pi$
$542$	420.508	+	195.618i	0.775845	+	0.360918i
$543$	−204.375	−	467.718i	−0.376380	−	0.861359i
$544$	45.2114	+	249.716i	0.0831092	+	0.459037i
$545$	−440.651			−0.808533
$546$	−211.452	+	3.87651i	−0.387274	+	0.00709983i
$547$			745.007i			1.36199i	0.732289	+	0.680994i	$0.238452\pi$
$547$			745.007i			1.36199i	−0.732289	+	0.680994i	$0.761548\pi$
$548$	−56.0051	−	4.79648i	−0.102199	−	0.00875270i
$549$	659.670	−	712.552i	1.20158	−	1.29791i
$550$	247.459	+	115.116i	0.449926	+	0.209303i
$551$	−144.350	−	144.350i	−0.261978	−	0.261978i
$552$	321.372	+	35.1343i	0.582195	+	0.0636491i
$553$	88.5293	−	88.5293i	0.160089	−	0.160089i
$554$	−113.798	−	311.770i	−0.205412	−	0.562761i
$555$	9.18331	+	21.0163i	0.0165465	+	0.0378672i
$556$	405.679	+	481.676i	0.729639	+	0.866323i
$557$	−343.993	−	343.993i	−0.617582	−	0.617582i	0.327328	−	0.944911i	$-0.393852\pi$
$557$	−343.993	−	343.993i	−0.617582	−	0.617582i	−0.944911	+	0.327328i	$0.893852\pi$
$558$	38.7635	+	94.7064i	0.0694687	+	0.169725i
$559$	−599.992	+	25.0878i	−1.07333	+	0.0448798i
$560$	23.3420	−	135.274i	0.0416821	−	0.241561i
$561$	79.0299	−	201.696i	0.140873	−	0.359530i
$562$	−35.2475	−	16.3969i	−0.0627180	−	0.0291760i
$563$			904.253i			1.60613i	0.595890	+	0.803066i	$0.296800\pi$
$563$			904.253i			1.60613i	−0.595890	+	0.803066i	$0.703200\pi$
$564$	−250.061	−	738.416i	−0.443370	−	1.30925i
$565$	191.817	+	191.817i	0.339498	+	0.339498i
$566$	−621.047	+	226.687i	−1.09726	+	0.400507i
$567$	142.884	−	166.787i	0.251999	−	0.294157i
$568$	−168.080	+	45.5321i	−0.295915	+	0.0801621i
$569$	938.529			1.64944			0.824718	−	0.565545i	$-0.191334\pi$
$569$	938.529			1.64944			0.824718	+	0.565545i	$0.191334\pi$
$570$	−243.692	−	255.402i	−0.427529	−	0.448073i
$571$	472.192			0.826956			0.413478	−	0.910514i	$-0.364314\pi$
$571$	472.192			0.826956			0.413478	+	0.910514i	$0.364314\pi$
$572$	20.6586	−	473.021i	0.0361164	−	0.826960i
$573$	1001.28	−	437.519i	1.74743	−	0.763558i
$574$	−253.304	+	92.4578i	−0.441296	+	0.161076i
$575$	201.882			0.351100
$576$	−562.394	−	124.456i	−0.976378	−	0.216070i
$577$	27.8631	+	27.8631i	0.0482896	+	0.0482896i	0.730839	−	0.682550i	$-0.239129\pi$
$577$	27.8631	+	27.8631i	0.0482896	+	0.0482896i	−0.682550	+	0.730839i	$0.739129\pi$
$578$	−424.801	+	155.056i	−0.734950	+	0.268262i
$579$	−42.6731	+	108.908i	−0.0737013	+	0.188097i
$580$	138.460	+	11.8582i	0.238723	+	0.0204451i
$581$			340.293i			0.585702i
$582$	360.480	+	8.45786i	0.619382	+	0.0145324i
$583$	622.814	+	622.814i	1.06829	+	1.06829i
$584$	155.430	+	573.763i	0.266147	+	0.982471i
$585$	−29.6997	−	369.029i	−0.0507687	−	0.630819i
$586$	−53.4783	−	24.8777i	−0.0912598	−	0.0424535i
$587$	−478.108	−	478.108i	−0.814494	−	0.814494i	0.170810	−	0.985304i	$-0.445362\pi$
$587$	−478.108	−	478.108i	−0.814494	−	0.814494i	−0.985304	+	0.170810i	$0.945362\pi$
$588$	448.080	+	221.373i	0.762040	+	0.376485i
$589$		−	105.706i		−	0.179467i
$590$	−61.0456	−	167.245i	−0.103467	−	0.283466i
$591$	−270.660	+	690.765i	−0.457969	+	1.16881i
$592$	−22.2883	−	31.5841i	−0.0376491	−	0.0533515i
$593$	−80.9828	−	80.9828i	−0.136565	−	0.136565i	0.635520	−	0.772084i	$-0.280786\pi$
$593$	−80.9828	−	80.9828i	−0.136565	−	0.136565i	−0.772084	+	0.635520i	$0.780786\pi$
$594$	352.868	+	342.397i	0.594054	+	0.576426i
$595$	−68.0403			−0.114353
$596$	−35.3682	+	412.970i	−0.0593427	+	0.692902i
$597$	597.419	−	261.049i	1.00070	−	0.437268i
$598$	−133.726	−	323.692i	−0.223621	−	0.541291i
$599$	686.856			1.14667			0.573336	−	0.819321i	$-0.305649\pi$
$599$	686.856			1.14667			0.573336	+	0.819321i	$0.305649\pi$
$600$	−357.563	−	39.0910i	−0.595939	−	0.0651517i
$601$	−294.571			−0.490135			−0.245067	−	0.969506i	$-0.578810\pi$
$601$	−294.571			−0.490135			−0.245067	+	0.969506i	$0.578810\pi$
$602$	−227.123	−	105.656i	−0.377281	−	0.175509i
$603$	−28.2035	−	731.848i	−0.0467719	−	1.21368i
$604$	−536.915	−	45.9834i	−0.888933	−	0.0761314i
$605$	85.2369	+	85.2369i	0.140887	+	0.140887i
$606$	359.019	−	342.558i	0.592440	−	0.565277i
$607$			834.152i			1.37422i	0.726553	+	0.687110i	$0.241121\pi$
$607$			834.152i			1.37422i	−0.726553	+	0.687110i	$0.758879\pi$
$608$	488.943	+	339.036i	0.804183	+	0.557626i
$609$	32.5809	−	83.1515i	0.0534990	−	0.136538i
$610$	287.999	−	619.094i	0.472129	−	1.01491i
$611$	−571.734	+	621.633i	−0.935735	+	1.01740i
$612$	−13.3898	+	285.183i	−0.0218787	+	0.465986i
$613$	71.3441	+	71.3441i	0.116385	+	0.116385i	0.762901	−	0.646516i	$-0.223774\pi$
$613$	71.3441	+	71.3441i	0.116385	+	0.116385i	−0.646516	+	0.762901i	$0.723774\pi$
$614$	−846.379	−	393.730i	−1.37847	−	0.641254i
$615$	−189.007	−	432.549i	−0.307329	−	0.703332i
$616$	98.2805	−	171.312i	0.159546	−	0.278104i
$617$	−222.842	+	222.842i	−0.361169	+	0.361169i	−0.864243	−	0.503074i	$-0.832202\pi$
$617$	−222.842	+	222.842i	−0.361169	+	0.361169i	0.503074	+	0.864243i	$0.332202\pi$
$618$	−593.907	+	566.676i	−0.961014	+	0.916952i
$619$	−534.752	−	534.752i	−0.863896	−	0.863896i	0.127892	−	0.991788i	$-0.459179\pi$
$619$	−534.752	−	534.752i	−0.863896	−	0.863896i	−0.991788	+	0.127892i	$0.959179\pi$
$620$	46.3544	+	55.0380i	0.0747651	+	0.0887709i
$621$	343.489	+	119.546i	0.553122	+	0.192505i
$622$	199.722	+	547.173i	0.321097	+	0.879700i
$623$		−	369.080i		−	0.592424i
$624$	174.171	+	599.200i	0.279120	+	0.960256i
$625$	25.7012			0.0411219
$626$	643.484	−	234.877i	1.02793	−	0.375202i
$627$	−203.362	−	465.400i	−0.324341	−	0.742265i
$628$	−533.869	+	449.638i	−0.850109	+	0.715983i
$629$	−13.5484	+	13.5484i	−0.0215396	+	0.0215396i
$630$	59.6974	−	142.428i	0.0947577	−	0.226076i
$631$	−35.0852	−	35.0852i	−0.0556025	−	0.0556025i	0.678759	−	0.734361i	$-0.262518\pi$
$631$	−35.0852	−	35.0852i	−0.0556025	−	0.0556025i	−0.734361	+	0.678759i	$0.762518\pi$
$632$	−320.420	−	183.823i	−0.506994	−	0.290859i
$633$	19.3737	+	44.3373i	0.0306062	+	0.0700432i
$634$	476.019	−	1023.27i	0.750818	−	1.61399i
$635$	−209.787	+	209.787i	−0.330372	+	0.330372i
$636$	−1040.73	−	514.172i	−1.63637	−	0.808447i
$637$	−22.6194	−	540.957i	−0.0355092	−	0.849226i
$638$	181.282	+	84.3313i	0.284141	+	0.132181i
$639$	−195.760	+	7.54406i	−0.306353	+	0.0118060i
$640$	−403.254	+	37.8861i	−0.630084	+	0.0591970i
$641$	−918.436			−1.43282			−0.716409	−	0.697680i	$-0.754216\pi$
$641$	−918.436			−1.43282			−0.716409	+	0.697680i	$0.754216\pi$
$642$	−405.456	+	386.866i	−0.631551	+	0.602595i
$643$	174.939	−	174.939i	0.272066	−	0.272066i	−0.557865	−	0.829932i	$-0.688379\pi$
$643$	174.939	−	174.939i	0.272066	−	0.272066i	0.829932	+	0.557865i	$0.188379\pi$
$644$	12.4662	−	145.559i	0.0193575	−	0.226023i
$645$	159.977	−	408.287i	0.248027	−	0.633003i
$646$	124.389	−	267.393i	0.192553	−	0.413920i
$647$			1087.32i			1.68056i	0.542151	+	0.840281i	$0.317610\pi$
$647$			1087.32i			1.68056i	−0.542151	+	0.840281i	$0.682390\pi$
$648$	−585.222	−	278.244i	−0.903120	−	0.429388i
$649$		−	256.151i		−	0.394686i
$650$	148.785	+	360.145i	0.228901	+	0.554069i
$651$	42.3747	−	18.5161i	0.0650918	−	0.0284426i
$652$	1150.95	+	98.5719i	1.76527	+	0.151184i
$653$			915.597i			1.40214i	0.713093	+	0.701070i	$0.247294\pi$
$653$			915.597i			1.40214i	−0.713093	+	0.701070i	$0.752706\pi$
$654$	835.313	+	19.5988i	1.27724	+	0.0299675i
$655$	126.381	−	126.381i	0.192948	−	0.192948i
$656$	458.728	+	650.051i	0.699281	+	0.990932i
$657$	25.7526	+	668.252i	0.0391973	+	1.01713i
$658$	−330.945	+	120.797i	−0.502955	+	0.183582i
$659$	−330.590			−0.501653			−0.250827	−	0.968032i	$-0.580702\pi$
$659$	−330.590			−0.501653			−0.250827	+	0.968032i	$0.580702\pi$
$660$	309.973	+	153.142i	0.469656	+	0.232033i
$661$	−388.081	+	388.081i	−0.587112	+	0.587112i	−0.936848	−	0.349736i	$-0.886271\pi$
$661$	−388.081	+	388.081i	−0.587112	+	0.587112i	0.349736	+	0.936848i	$0.386271\pi$
$662$	461.348	−	991.734i	0.696900	−	1.49809i
$663$	277.992	−	135.573i	0.419295	−	0.204484i
$664$	969.116	−	262.529i	1.45951	−	0.395375i
$665$	−112.800	+	112.800i	−0.169624	+	0.169624i
$666$	−16.4735	−	40.2477i	−0.0247349	−	0.0604320i
$667$	147.894			0.221730
$668$	−35.3940	+	413.270i	−0.0529850	+	0.618668i
$669$	−335.699	+	856.755i	−0.501792	+	1.28065i
$670$	−176.584	−	483.781i	−0.263558	−	0.722061i
$671$	694.648	−	694.648i	1.03524	−	1.03524i
$672$	−50.2645	+	255.393i	−0.0747983	+	0.380048i
$673$		−	186.978i		−	0.277827i	−0.990304	−	0.138914i	$-0.955639\pi$
$673$		−	186.978i		−	0.277827i	0.990304	−	0.138914i	$-0.0443611\pi$
$674$	−42.0431	−	115.184i	−0.0623785	−	0.170897i
$675$	−382.171	−	133.008i	−0.566180	−	0.197049i
$676$	478.891	−	477.116i	0.708418	−	0.705793i
$677$			368.883i			0.544879i	0.962173	+	0.272440i	$0.0878305\pi$
$677$			368.883i			0.544879i	−0.962173	+	0.272440i	$0.912170\pi$
$678$	−355.083	−	372.146i	−0.523721	−	0.548888i
$679$		−	162.944i		−	0.239977i
$680$	52.4917	+	193.771i	0.0771937	+	0.284958i
$681$	−671.749	−	263.209i	−0.986415	−	0.386503i
$682$	35.4980	+	97.2528i	0.0520499	+	0.142599i
$683$	−455.745	+	455.745i	−0.667269	+	0.667269i	−0.957083	−	0.289814i	$-0.906407\pi$
$683$	−455.745	+	455.745i	−0.667269	+	0.667269i	0.289814	+	0.957083i	$0.406407\pi$
$684$	450.591	+	494.988i	0.658759	+	0.723666i
$685$	−44.4663			−0.0649143
$686$	207.336	−	445.698i	0.302239	−	0.649706i
$687$	44.4648	−	113.481i	0.0647231	−	0.165183i
$688$	−125.676	+	728.333i	−0.182669	+	1.05862i
$689$	52.5369	+	1256.45i	0.0762509	+	1.82359i
$690$	255.673	+	5.99880i	0.370541	+	0.00869391i
$691$	252.600	−	252.600i	0.365557	−	0.365557i	−0.500297	−	0.865854i	$-0.666776\pi$
$691$	252.600	−	252.600i	0.365557	−	0.365557i	0.865854	+	0.500297i	$0.166776\pi$
$692$	145.571	−	122.603i	0.210362	−	0.177172i
$693$	150.945	−	163.045i	0.217813	−	0.235274i
$694$	51.6244	−	18.8433i	0.0743868	−	0.0271517i
$695$	352.266	+	352.266i	0.506858	+	0.506858i
$696$	−261.942	−	28.6371i	−0.376353	−	0.0411452i
$697$	278.847	−	278.847i	0.400068	−	0.400068i
$698$	−287.888	+	618.857i	−0.412447	+	0.886615i
$699$	−350.248	+	153.045i	−0.501070	+	0.218948i
$700$	−13.8701	+	161.951i	−0.0198144	+	0.231359i
$701$	684.290			0.976162			0.488081	−	0.872798i	$-0.337697\pi$
$701$	684.290			0.976162			0.488081	+	0.872798i	$0.337697\pi$
$702$	39.8865	+	700.866i	0.0568184	+	0.998385i
$703$			44.9222i			0.0639007i
$704$	−563.699	−	147.728i	−0.800708	−	0.209841i
$705$	−246.940	−	565.131i	−0.350270	−	0.801604i
$706$	320.358	−	688.656i	0.453765	−	0.975434i
$707$	−158.563	−	158.563i	−0.224276	−	0.224276i
$708$	108.282	+	319.751i	0.152940	+	0.451625i
$709$	−801.423	+	801.423i	−1.13036	+	1.13036i	−0.140240	+	0.990118i	$0.544787\pi$
$709$	−801.423	+	801.423i	−1.13036	+	1.13036i	−0.990118	+	0.140240i	$0.955213\pi$
$710$	−129.405	+	47.2338i	−0.182261	+	0.0665265i
$711$	−304.958	−	282.326i	−0.428914	−	0.397083i
$712$	−1051.10	+	284.738i	−1.47626	+	0.399913i
$713$	54.1504	+	54.1504i	0.0759473	+	0.0759473i
$714$	128.980	+	3.02622i	0.180644	+	0.00423840i
$715$	−15.6476	−	374.224i	−0.0218848	−	0.523390i
$716$	−898.054	−	1066.29i	−1.25427	−	1.48923i
$717$	−37.2031	−	14.5771i	−0.0518871	−	0.0203307i
$718$	−51.3860	+	110.462i	−0.0715683	+	0.153846i
$719$		−	931.573i		−	1.29565i	−0.761789	−	0.647825i	$-0.775679\pi$
$719$		−	931.573i		−	1.29565i	0.761789	−	0.647825i	$-0.224321\pi$
$720$	−451.673	−	60.1314i	−0.627324	−	0.0835159i
$721$	262.303	+	262.303i	0.363805	+	0.363805i
$722$	10.4826	+	28.7188i	0.0145188	+	0.0397767i
$723$	−511.026	+	1304.22i	−0.706813	+	1.80390i
$724$	438.410	+	520.538i	0.605538	+	0.718975i
$725$	−164.549			−0.226964
$726$	−157.787	−	165.369i	−0.217338	−	0.227781i
$727$	−364.106			−0.500833			−0.250417	−	0.968138i	$-0.580568\pi$
$727$	−364.106			−0.500833			−0.250417	+	0.968138i	$0.580568\pi$
$728$	268.855	−	85.0367i	0.369307	−	0.116809i
$729$	−571.477	−	452.609i	−0.783919	−	0.620863i
$730$	161.239	+	441.741i	0.220875	+	0.605125i
$731$	366.337			0.501146
$732$	−573.476	+	1160.77i	−0.783437	+	1.58575i
$733$	−857.363	−	857.363i	−1.16966	−	1.16966i	−0.982288	−	0.187375i	$-0.940002\pi$
$733$	−857.363	−	857.363i	−1.16966	−	1.16966i	−0.187375	−	0.982288i	$-0.559998\pi$
$734$	−342.600	−	938.611i	−0.466758	−	1.27876i
$735$	368.114	+	144.237i	0.500836	+	0.196241i
$736$	−424.153	+	76.7935i	−0.576295	+	0.104339i
$737$		−	740.955i		−	1.00537i
$738$	339.050	+	828.362i	0.459418	+	1.12244i
$739$	−963.677	−	963.677i	−1.30403	−	1.30403i	−0.925651	−	0.378378i	$-0.876482\pi$
$739$	−963.677	−	963.677i	−1.30403	−	1.30403i	−0.378378	−	0.925651i	$-0.623518\pi$
$740$	−19.6994	−	23.3897i	−0.0266208	−	0.0316077i
$741$	236.109	−	685.626i	0.318636	−	0.925272i
$742$	−221.257	+	475.623i	−0.298190	+	0.641002i
$743$	935.304	+	935.304i	1.25882	+	1.25882i	0.951656	+	0.307165i	$0.0993803\pi$
$743$	935.304	+	935.304i	1.25882	+	1.25882i	0.307165	+	0.951656i	$0.400620\pi$
$744$	−85.4231	−	106.394i	−0.114816	−	0.143002i
$745$			327.885i			0.440114i
$746$	−623.794	+	227.690i	−0.836185	+	0.305214i
$747$	1128.71	−	43.4976i	1.51100	−	0.0582297i
$748$	−24.6467	+	287.782i	−0.0329502	+	0.384736i
$749$	179.073	+	179.073i	0.239082	+	0.239082i
$750$	−758.979	−	17.8078i	−1.01197	−	0.0237437i
$751$	1140.94			1.51923			0.759613	−	0.650376i	$-0.225389\pi$
$751$	1140.94			1.51923			0.759613	+	0.650376i	$0.225389\pi$
$752$	599.334	+	849.301i	0.796987	+	1.12939i
$753$	158.231	+	362.116i	0.210134	+	0.480898i
$754$	108.996	+	263.833i	0.144557	+	0.349911i
$755$	−426.294			−0.564628
$756$	−119.499	+	267.336i	−0.158068	+	0.353619i
$757$	−383.846			−0.507062			−0.253531	−	0.967327i	$-0.581592\pi$
$757$	−383.846			−0.507062			−0.253531	+	0.967327i	$0.581592\pi$
$758$	558.701	−	1201.01i	0.737073	−	1.58444i
$759$	342.590	+	134.236i	0.451370	+	0.176858i
$760$	408.265	+	234.219i	0.537191	+	0.308183i
$761$	4.79917	+	4.79917i	0.00630639	+	0.00630639i	0.710253	−	0.703947i	$-0.248581\pi$
$761$	4.79917	+	4.79917i	0.00630639	+	0.00630639i	−0.703947	+	0.710253i	$0.748581\pi$
$762$	407.010	−	388.348i	0.534133	−	0.509643i
$763$		−	377.578i		−	0.494860i
$764$	−1114.35	+	938.534i	−1.45857	+	1.22845i
$765$	8.69718	+	225.682i	0.0113689	+	0.295009i
$766$	−259.385	−	120.664i	−0.338623	−	0.157525i
$767$	247.574	−	269.181i	0.322782	−	0.350953i
$768$	766.107	−	53.8827i	0.997536	−	0.0701598i
$769$	7.46155	+	7.46155i	0.00970292	+	0.00970292i	0.711942	−	0.702239i	$-0.247816\pi$
$769$	7.46155	+	7.46155i	0.00970292	+	0.00970292i	−0.702239	+	0.711942i	$0.747816\pi$
$770$	65.8994	−	141.660i	0.0855836	−	0.183974i
$771$	398.821	−	174.269i	0.517277	−	0.226030i
$772$	13.3083	−	155.391i	0.0172387	−	0.201284i
$773$	566.815	−	566.815i	0.733267	−	0.733267i	−0.237999	−	0.971266i	$-0.576491\pi$
$773$	566.815	−	566.815i	0.733267	−	0.733267i	0.971266	+	0.237999i	$0.0764914\pi$
$774$	−321.418	+	766.848i	−0.415269	+	0.990760i
$775$	−60.2487	−	60.2487i	−0.0777402	−	0.0777402i
$776$	−464.047	+	125.708i	−0.597999	+	0.161995i
$777$	−18.0081	+	7.86886i	−0.0231765	+	0.0101272i
$778$	−857.217	+	312.891i	−1.10182	+	0.402173i
$779$		−	924.570i		−	1.18687i
$780$	177.727	+	460.525i	0.227855	+	0.590417i
$781$	−198.196			−0.253772
$782$	73.2570	+	200.700i	0.0936790	+	0.256650i
$783$	−279.969	−	97.4385i	−0.357559	−	0.124442i
$784$	−656.671	−	113.311i	−0.837590	−	0.144529i
$785$	−390.437	+	390.437i	−0.497372	+	0.497372i
$786$	−245.193	+	233.951i	−0.311951	+	0.297648i
$787$	−322.116	−	322.116i	−0.409296	−	0.409296i	0.472197	−	0.881493i	$-0.343461\pi$
$787$	−322.116	−	322.116i	−0.409296	−	0.409296i	−0.881493	+	0.472197i	$0.843461\pi$
$788$	84.4095	−	985.590i	0.107119	−	1.25075i
$789$	202.189	−	88.3488i	0.256260	−	0.111976i
$790$	−264.960	−	123.258i	−0.335392	−	0.156022i
$791$	−164.361	+	164.361i	−0.207789	+	0.207789i
$792$	−580.785	−	304.088i	−0.733314	−	0.383949i
$793$	1401.37	−	58.5964i	1.76718	−	0.0738920i
$794$	359.041	−	771.810i	0.452192	−	0.972052i
$795$	−855.001	−	335.012i	−1.07547	−	0.421398i
$796$	−664.886	+	559.984i	−0.835284	+	0.703498i
$797$	−1338.55			−1.67949			−0.839746	−	0.542980i	$-0.817296\pi$
$797$	−1338.55			−1.67949			−0.839746	+	0.542980i	$0.817296\pi$
$798$	218.845	−	208.811i	0.274242	−	0.261668i
$799$	364.318	−	364.318i	0.455967	−	0.455967i
$800$	471.920	−	85.4417i	0.589900	−	0.106802i
$801$	−1224.20	+	47.1773i	−1.52834	+	0.0588980i
$802$	647.041	+	300.999i	0.806785	+	0.375311i
$803$			676.567i			0.842550i
$804$	313.221	+	924.926i	0.389578	+	1.15041i
$805$		−	115.569i		−	0.143564i
$806$	−56.6925	+	136.509i	−0.0703381	+	0.169366i
$807$	395.730	+	905.640i	0.490371	+	1.12223i
$808$	−329.242	+	573.899i	−0.407478	+	0.710271i
$809$		−	615.167i		−	0.760404i	−0.924903	−	0.380202i	$-0.875854\pi$
$809$		−	615.167i		−	0.760404i	0.924903	−	0.380202i	$-0.124146\pi$
$810$	−480.047	−	179.804i	−0.592651	−	0.221980i
$811$	322.284	−	322.284i	0.397391	−	0.397391i	−0.479921	−	0.877312i	$-0.659335\pi$
$811$	322.284	−	322.284i	0.397391	−	0.397391i	0.877312	+	0.479921i	$0.159335\pi$
$812$	−10.1609	+	118.641i	−0.0125134	+	0.146110i
$813$	−647.725	−	253.795i	−0.796710	−	0.312171i
$814$	−15.0857	−	41.3299i	−0.0185328	−	0.0507738i
$815$	913.822			1.12125
$816$	−90.8869	−	369.654i	−0.111381	−	0.453008i
$817$	607.330	−	607.330i	0.743366	−	0.743366i
$818$	−193.757	−	90.1346i	−0.236867	−	0.110189i
$819$	316.208	−	25.4486i	0.386091	−	0.0310728i
$820$	405.445	+	481.397i	0.494445	+	0.587070i
$821$	353.910	−	353.910i	0.431072	−	0.431072i	−0.457921	−	0.888993i	$-0.651406\pi$
$821$	353.910	−	353.910i	0.431072	−	0.431072i	0.888993	+	0.457921i	$0.151406\pi$
$822$	84.2920	+	1.97772i	0.102545	+	0.00240599i
$823$	−155.082			−0.188435			−0.0942176	−	0.995552i	$-0.530035\pi$
$823$	−155.082			−0.188435			−0.0942176	+	0.995552i	$0.530035\pi$
$824$	544.649	−	949.373i	0.660982	−	1.15215i
$825$	−381.171	−	149.353i	−0.462026	−	0.181034i
$826$	143.306	−	52.3079i	0.173494	−	0.0633268i
$827$	453.337	−	453.337i	0.548170	−	0.548170i	−0.377741	−	0.925911i	$-0.623299\pi$
$827$	453.337	−	453.337i	0.548170	−	0.548170i	0.925911	+	0.377741i	$0.123299\pi$
$828$	−484.396	−	22.7431i	−0.585020	−	0.0274675i
$829$			277.026i			0.334169i	0.985943	+	0.167084i	$0.0534352\pi$
$829$			277.026i			0.334169i	−0.985943	+	0.167084i	$0.946565\pi$
$830$	746.124	−	272.341i	0.898945	−	0.328122i
$831$	199.335	+	456.184i	0.239874	+	0.548958i
$832$	−449.591	−	700.065i	−0.540374	−	0.841425i
$833$			330.293i			0.396510i
$834$	−652.101	−	683.437i	−0.781896	−	0.819468i
$835$			328.124i			0.392962i
$836$	436.237	+	517.958i	0.521815	+	0.619567i
$837$	−66.8324	−	138.185i	−0.0798476	−	0.165096i
$838$	666.686	−	243.345i	0.795568	−	0.290388i
$839$	548.135	−	548.135i	0.653319	−	0.653319i	−0.300471	−	0.953791i	$-0.597144\pi$
$839$	548.135	−	548.135i	0.653319	−	0.653319i	0.953791	+	0.300471i	$0.0971440\pi$
$840$	−22.3780	+	204.690i	−0.0266405	+	0.243679i
$841$	720.456			0.856666
$842$	−380.382	−	176.951i	−0.451760	−	0.210156i
$843$	54.2932	+	21.2735i	0.0644047	+	0.0252354i
$844$	−41.5591	−	49.3444i	−0.0492406	−	0.0584649i
$845$	345.249	−	408.384i	0.408579	−	0.483294i
$846$	442.974	+	1082.27i	0.523610	+	1.27927i
$847$	−73.0366	+	73.0366i	−0.0862297	+	0.0862297i
$848$	1525.22	+	263.181i	1.79861	+	0.310355i
$849$	908.722	−	397.076i	1.07034	−	0.467699i
$850$	−81.5069	−	223.302i	−0.0958905	−	0.262708i
$851$	−23.0125	−	23.0125i	−0.0270417	−	0.0270417i
$852$	247.406	−	83.7825i	0.290382	−	0.0983363i
$853$	671.485	−	671.485i	0.787204	−	0.787204i	−0.193831	−	0.981035i	$-0.562091\pi$
$853$	671.485	−	671.485i	0.787204	−	0.787204i	0.981035	+	0.193831i	$0.0620913\pi$
$854$	530.481	+	246.776i	0.621172	+	0.288965i
$855$	388.564	+	359.727i	0.454461	+	0.420733i
$856$	371.828	−	648.130i	0.434378	−	0.757161i
$857$	465.906			0.543647			0.271824	−	0.962347i	$-0.412373\pi$
$857$	465.906			0.543647			0.271824	+	0.962347i	$0.412373\pi$
$858$	13.0179	+	710.088i	0.0151724	+	0.827609i
$859$		−	646.398i		−	0.752500i	−0.926518	−	0.376250i	$-0.877213\pi$
$859$		−	646.398i		−	0.752500i	0.926518	−	0.376250i	$-0.122787\pi$
$860$	−49.8915	+	582.547i	−0.0580133	+	0.677380i
$861$	370.636	−	161.954i	0.430472	−	0.188100i
$862$	−332.750	−	154.793i	−0.386021	−	0.179574i
$863$	−80.0865	−	80.0865i	−0.0928001	−	0.0928001i	0.659183	−	0.751983i	$-0.270902\pi$
$863$	−80.0865	−	80.0865i	−0.0928001	−	0.0928001i	−0.751983	+	0.659183i	$0.770902\pi$
$864$	853.534	+	134.076i	0.987886	+	0.155181i
$865$	106.461	−	106.461i	0.123076	−	0.123076i
$866$	−190.044	−	520.658i	−0.219450	−	0.601222i
$867$	621.573	−	271.603i	0.716923	−	0.313268i
$868$	−47.1602	+	39.7195i	−0.0543320	+	0.0457598i
$869$	−297.296	−	297.296i	−0.342112	−	0.342112i
$870$	−208.392	−	4.88946i	−0.239531	−	0.00562007i
$871$	716.143	−	778.646i	0.822208	−	0.893967i
$872$	−1075.30	+	291.294i	−1.23314	+	0.334053i
$873$	−540.468	+	20.8282i	−0.619093	+	0.0238582i
$874$	454.178	+	211.280i	0.519654	+	0.241740i
$875$			343.074i			0.392084i
$876$	−286.003	−	844.552i	−0.326487	−	0.964100i
$877$	492.434	+	492.434i	0.561498	+	0.561498i	0.929733	−	0.368235i	$-0.120038\pi$
$877$	492.434	+	492.434i	0.561498	+	0.561498i	−0.368235	+	0.929733i	$0.620038\pi$
$878$	−1548.81	+	565.329i	−1.76403	+	0.643883i
$879$	82.3747	+	32.2765i	0.0937141	+	0.0367196i
$880$	−454.273	−	78.3861i	−0.516219	−	0.0890751i
$881$	582.104			0.660730			0.330365	−	0.943853i	$-0.392828\pi$
$881$	582.104			0.660730			0.330365	+	0.943853i	$0.392828\pi$
$882$	−691.396	−	289.793i	−0.783896	−	0.328564i
$883$	751.578			0.851164			0.425582	−	0.904920i	$-0.360069\pi$
$883$	751.578			0.851164			0.425582	+	0.904920i	$0.360069\pi$
$884$	−304.046	+	278.600i	−0.343943	+	0.315158i
$885$	106.931	+	244.714i	0.120826	+	0.276513i
$886$	557.096	−	203.344i	0.628777	−	0.229508i
$887$	−227.550			−0.256539			−0.128270	−	0.991739i	$-0.540942\pi$
$887$	−227.550			−0.256539			−0.128270	+	0.991739i	$0.540942\pi$
$888$	36.3026	+	45.2145i	0.0408813	+	0.0509172i
$889$	−179.759	−	179.759i	−0.202203	−	0.202203i
$890$	−809.243	+	295.380i	−0.909262	+	0.331887i
$891$	−560.097	−	479.826i	−0.628616	−	0.538525i
$892$	104.693	−	1222.43i	0.117369	−	1.37043i
$893$		−	1207.96i		−	1.35270i
$894$	14.5833	−	621.551i	0.0163124	−	0.695247i
$895$	−779.813	−	779.813i	−0.871300	−	0.871300i
$896$	−32.4633	−	345.534i	−0.0362313	−	0.385641i
$897$	230.276	+	472.182i	0.256718	+	0.526401i
$898$	261.715	+	121.748i	0.291442	+	0.135577i
$899$	−44.1366	−	44.1366i	−0.0490952	−	0.0490952i
$900$	538.947	+	25.3043i	0.598830	+	0.0281159i
$901$		−	767.154i		−	0.851448i
$902$	310.488	+	850.635i	0.344222	+	0.943054i
$903$	349.847	+	137.079i	0.387427	+	0.151804i
$904$	594.883	+	341.281i	0.658057	+	0.377523i
$905$	380.687	+	380.687i	0.420649	+	0.420649i
$906$	808.099	+	18.9602i	0.891941	+	0.0209274i
$907$	−83.6189			−0.0921929			−0.0460964	−	0.998937i	$-0.514678\pi$
$907$	−83.6189			−0.0921929			−0.0460964	+	0.998937i	$0.514678\pi$
$908$	958.457	+	82.0858i	1.05557	+	0.0904028i
$909$	−505.669	+	546.205i	−0.556291	+	0.600886i
$910$	206.168	−	85.1735i	0.226558	−	0.0935973i
$911$	−141.993			−0.155865			−0.0779323	−	0.996959i	$-0.524832\pi$
$911$	−141.993			−0.155865			−0.0779323	+	0.996959i	$0.524832\pi$
$912$	−763.505	−	462.153i	−0.837177	−	0.506746i
$913$	1142.76			1.25165
$914$	762.684	+	354.796i	0.834447	+	0.388179i
$915$	−373.651	+	953.615i	−0.408362	+	1.04220i
$916$	−13.8670	+	161.916i	−0.0151387	+	0.176764i
$917$	108.292	+	108.292i	0.118093	+	0.118093i
$918$	−6.44905	−	428.198i	−0.00702511	−	0.466447i
$919$		−	31.4087i		−	0.0341771i	−0.999854	−	0.0170885i	$-0.994560\pi$
$919$		−	31.4087i		−	0.0341771i	0.999854	−	0.0170885i	$-0.00543972\pi$
$920$	−329.128	+	89.1594i	−0.357748	+	0.0969124i
$921$	1303.71	+	510.828i	1.41554	+	0.554645i
$922$	362.708	−	779.693i	0.393393	−	0.845654i
$923$	−208.278	−	191.559i	−0.225653	−	0.207539i
$924$	−131.222	+	265.605i	−0.142015	+	0.287452i
$925$	25.6041	+	25.6041i	0.0276801	+	0.0276801i
$926$	361.688	+	168.255i	0.390592	+	0.181701i
$927$	836.503	−	903.560i	0.902376	−	0.974714i
$928$	345.716	−	62.5923i	0.372539	−	0.0674487i
$929$	1062.36	−	1062.36i	1.14355	−	1.14355i	0.155755	−	0.987796i	$-0.450219\pi$
$929$	1062.36	−	1062.36i	1.14355	−	1.14355i	0.987796	−	0.155755i	$-0.0497811\pi$
$930$	−74.5114	−	78.0919i	−0.0801198	−	0.0839698i
$931$	547.573	+	547.573i	0.588156	+	0.588156i
$932$	389.802	−	328.301i	0.418243	−	0.352254i
$933$	−349.844	−	800.629i	−0.374967	−	0.858123i
$934$	374.791	+	1026.80i	0.401275	+	1.09936i
$935$			228.490i			0.244375i
$936$	−316.423	−	880.893i	−0.338059	−	0.941125i
$937$	−1441.85			−1.53879			−0.769395	−	0.638773i	$-0.779442\pi$
$937$	−1441.85			−1.53879			−0.769395	+	0.638773i	$0.779442\pi$
$938$	414.535	−	151.308i	0.441935	−	0.161310i
$939$	−941.552	+	411.422i	−1.00272	+	0.438149i
$940$	529.719	+	628.951i	0.563531	+	0.669097i
$941$	−203.881	+	203.881i	−0.216664	+	0.216664i	−0.807091	−	0.590427i	$-0.798959\pi$
$941$	−203.881	+	203.881i	−0.216664	+	0.216664i	0.590427	+	0.807091i	$0.298959\pi$
$942$	757.492	−	722.761i	0.804131	−	0.767262i
$943$	473.634	+	473.634i	0.502263	+	0.502263i
$944$	−259.525	−	367.766i	−0.274921	−	0.389583i
$945$	−76.1418	+	218.777i	−0.0805734	+	0.231510i
$946$	−354.811	+	762.716i	−0.375064	+	0.806254i
$947$	−280.005	+	280.005i	−0.295676	+	0.295676i	−0.839318	−	0.543641i	$-0.817045\pi$
$947$	−280.005	+	280.005i	−0.295676	+	0.295676i	0.543641	+	0.839318i	$0.317045\pi$
$948$	496.786	+	245.436i	0.524036	+	0.258899i
$949$	−653.912	+	710.983i	−0.689054	+	0.749192i
$950$	−505.326	−	235.074i	−0.531922	−	0.247446i
$951$	−617.590	+	1576.18i	−0.649411	+	1.65740i
$952$	−166.036	+	44.9784i	−0.174407	+	0.0472462i
$953$	−1500.26			−1.57425			−0.787123	−	0.616796i	$-0.788430\pi$
$953$	−1500.26			−1.57425			−0.787123	+	0.616796i	$0.788430\pi$
$954$	1605.87	+	673.088i	1.68330	+	0.705543i
$955$	−814.964	+	814.964i	−0.853365	+	0.853365i
$956$	53.0817	+	4.54611i	0.0555248	+	0.00475534i
$957$	−279.236	−	109.412i	−0.291783	−	0.114328i
$958$	−133.481	+	286.937i	−0.139333	+	0.299517i
$959$		−	38.1017i		−	0.0397306i
$960$	600.199	−	94.1845i	0.625208	−	0.0981088i
$961$			928.679i			0.966368i
$962$	24.0928	−	58.0128i	0.0250445	−	0.0603044i
$963$	571.074	−	616.854i	0.593016	−	0.640554i
$964$	159.371	−	1860.87i	0.165323	−	1.93036i
$965$		−	123.376i		−	0.127851i
$966$	−5.14016	+	219.077i	−0.00532108	+	0.226788i
$967$	−302.480	+	302.480i	−0.312803	+	0.312803i	−0.845994	−	0.533192i	$-0.820992\pi$
$967$	−302.480	+	302.480i	−0.312803	+	0.312803i	0.533192	+	0.845994i	$0.320992\pi$
$968$	264.346	+	151.654i	0.273085	+	0.156667i
$969$	−161.383	+	411.875i	−0.166546	+	0.425052i
$970$	−357.271	+	130.406i	−0.368320	+	0.134440i
$971$	−1484.57			−1.52891			−0.764453	−	0.644679i	$-0.776991\pi$
$971$	−1484.57			−1.52891			−0.764453	+	0.644679i	$0.776991\pi$
$972$	901.998	+	362.194i	0.927981	+	0.372627i
$973$	−301.845	+	301.845i	−0.310221	+	0.310221i
$974$	−177.795	+	382.197i	−0.182541	+	0.392399i
$975$	−256.209	−	525.357i	−0.262779	−	0.538828i
$976$	293.535	−	1701.13i	0.300753	−	1.74296i
$977$	−680.203	+	680.203i	−0.696216	+	0.696216i	−0.963592	−	0.267376i	$-0.913843\pi$
$977$	−680.203	+	680.203i	−0.696216	+	0.696216i	0.267376	+	0.963592i	$0.413843\pi$
$978$	−1732.27	−	40.6440i	−1.77124	−	0.0415582i
$979$	−1239.43			−1.26602
$980$	−525.229	−	44.9825i	−0.535948	−	0.0459005i
$981$	−1252.39	+	48.2636i	−1.27664	+	0.0491983i
$982$	−296.154	−	811.363i	−0.301582	−	0.826236i
$983$	178.438	−	178.438i	0.181524	−	0.181524i	−0.610496	−	0.792019i	$-0.709030\pi$
$983$	178.438	−	178.438i	0.181524	−	0.181524i	0.792019	+	0.610496i	$0.209030\pi$
$984$	−747.165	−	930.587i	−0.759314	−	0.945718i
$985$		−	782.528i		−	0.794444i
$986$	−59.7099	−	163.585i	−0.0605577	−	0.165908i
$987$	484.241	−	211.595i	0.490619	−	0.214382i
$988$	−42.1859	+	965.935i	−0.0426983	+	0.977667i
$989$			622.240i			0.629160i
$990$	−478.295	−	200.473i	−0.483126	−	0.202498i
$991$			1209.46i			1.22045i	0.792230	+	0.610223i	$0.208920\pi$
$991$			1209.46i			1.22045i	−0.792230	+	0.610223i	$0.791080\pi$
$992$	149.500	+	103.664i	0.150705	+	0.104500i
$993$	−598.556	+	1527.61i	−0.602775	+	1.53838i
$994$	−40.4730	−	110.883i	−0.0407173	−	0.111552i
$995$	−486.255	+	486.255i	−0.488698	+	0.488698i
$996$	−1426.49	+	483.074i	−1.43222	+	0.485014i
$997$	−901.595			−0.904308			−0.452154	−	0.891940i	$-0.649344\pi$
$997$	−901.595			−0.904308			−0.452154	+	0.891940i	$0.649344\pi$
$998$	−297.936	+	640.455i	−0.298533	+	0.641739i
$999$	28.4020	+	58.7252i	0.0284304	+	0.0587839i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	156.3.l.c.47.43	yes	96
3.2	odd	2	inner	156.3.l.c.47.6	✓	96
4.3	odd	2	inner	156.3.l.c.47.30	yes	96
12.11	even	2	inner	156.3.l.c.47.19	yes	96
13.5	odd	4	inner	156.3.l.c.83.19	yes	96
39.5	even	4	inner	156.3.l.c.83.30	yes	96
52.31	even	4	inner	156.3.l.c.83.6	yes	96
156.83	odd	4	inner	156.3.l.c.83.43	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
156.3.l.c.47.6	✓	96	3.2	odd	2	inner
156.3.l.c.47.19	yes	96	12.11	even	2	inner
156.3.l.c.47.30	yes	96	4.3	odd	2	inner
156.3.l.c.47.43	yes	96	1.1	even	1	trivial
156.3.l.c.83.6	yes	96	52.31	even	4	inner
156.3.l.c.83.19	yes	96	13.5	odd	4	inner
156.3.l.c.83.30	yes	96	39.5	even	4	inner
156.3.l.c.83.43	yes	96	156.83	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 156 = 2^{2} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	156.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.87876 - 0.685761i) q^{2} +(-2.74902 + 1.20121i) q^{3} +(3.05946 - 2.57676i) q^{4} +(2.23749 - 2.23749i) q^{5} +(-4.34099 + 4.14196i) q^{6} +(1.91723 + 1.91723i) q^{7} +(3.98095 - 6.93916i) q^{8} +(6.11417 - 6.60431i) q^{9} +(2.66932 - 5.73809i) q^{10} +(6.43837 - 6.43837i) q^{11} +(-5.31528 + 10.7586i) q^{12} +(12.9887 - 0.543102i) q^{13} +(4.91678 + 2.28725i) q^{14} +(-3.46320 + 8.83861i) q^{15} +(2.72064 - 15.7670i) q^{16} -7.93049 q^{17} +(6.95808 - 16.6008i) q^{18} +(-13.1475 + 13.1475i) q^{19} +(1.08005 - 12.6110i) q^{20} +(-7.57350 - 2.96749i) q^{21} +(7.68096 - 16.5113i) q^{22} -13.4703i q^{23} +(-2.60829 + 23.8578i) q^{24} +14.9872i q^{25} +(24.0301 - 9.92747i) q^{26} +(-8.87477 + 25.4998i) q^{27} +(10.8059 + 0.925460i) q^{28} +10.9793i q^{29} +(-0.445336 + 18.9805i) q^{30} +(-4.01999 + 4.01999i) q^{31} +(-5.70096 - 31.4881i) q^{32} +(-9.96532 + 25.4330i) q^{33} +(-14.8995 + 5.43842i) q^{34} +8.57958 q^{35} +(1.68839 - 35.9604i) q^{36} +(1.70839 - 1.70839i) q^{37} +(-15.6849 + 33.7170i) q^{38} +(-35.0536 + 17.0951i) q^{39} +(-6.61898 - 24.4337i) q^{40} +(-35.1614 + 35.1614i) q^{41} +(-16.2638 - 0.381593i) q^{42} -46.1935 q^{43} +(3.10784 - 36.2881i) q^{44} +(-1.09668 - 28.4575i) q^{45} +(-9.23738 - 25.3074i) q^{46} +(-45.9388 + 45.9388i) q^{47} +(11.4604 + 46.6118i) q^{48} -41.6485i q^{49} +(10.2777 + 28.1574i) q^{50} +(21.8010 - 9.52621i) q^{51} +(38.3389 - 35.1302i) q^{52} +96.7348i q^{53} +(0.813197 + 53.9939i) q^{54} -28.8116i q^{55} +(20.9364 - 5.67157i) q^{56} +(20.3497 - 51.9357i) q^{57} +(7.52915 + 20.6274i) q^{58} +(19.8925 - 19.8925i) q^{59} +(12.1794 + 35.9652i) q^{60} +107.892 q^{61} +(-4.79584 + 10.3094i) q^{62} +(24.3843 - 0.939704i) q^{63} +(-32.3040 - 55.2490i) q^{64} +(27.8468 - 30.2772i) q^{65} +(-1.28145 + 54.6163i) q^{66} +(57.5421 - 57.5421i) q^{67} +(-24.2631 + 20.4350i) q^{68} +(16.1807 + 37.0300i) q^{69} +(16.1190 - 5.88354i) q^{70} +(-15.3918 - 15.3918i) q^{71} +(-21.4881 - 68.7187i) q^{72} +(-52.5418 + 52.5418i) q^{73} +(2.03811 - 4.38120i) q^{74} +(-18.0029 - 41.2002i) q^{75} +(-6.34639 + 74.1023i) q^{76} +24.6877 q^{77} +(-54.1341 + 56.1560i) q^{78} -46.1756i q^{79} +(-29.1911 - 41.3660i) q^{80} +(-6.23379 - 80.7598i) q^{81} +(-41.9475 + 90.1721i) q^{82} +(88.7459 + 88.7459i) q^{83} +(-30.8174 + 10.4361i) q^{84} +(-17.7444 + 17.7444i) q^{85} +(-86.7865 + 31.6777i) q^{86} +(-13.1884 - 30.1822i) q^{87} +(-19.0461 - 70.3077i) q^{88} +(-96.2535 - 96.2535i) q^{89} +(-21.5754 - 52.7127i) q^{90} +(25.9435 + 23.8610i) q^{91} +(-34.7096 - 41.2118i) q^{92} +(6.22216 - 15.8799i) q^{93} +(-54.8049 + 117.811i) q^{94} +58.8349i q^{95} +(53.4959 + 79.7131i) q^{96} +(-42.4947 - 42.4947i) q^{97} +(-28.5609 - 78.2474i) q^{98} +(-3.15568 - 81.8863i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 36 q^{6} - 64 q^{9} - 8 q^{13} + 80 q^{16} + 48 q^{18} + 8 q^{21} + 124 q^{24} - 8 q^{28} + 24 q^{33} + 64 q^{34} - 128 q^{37} - 136 q^{40} - 140 q^{42} - 160 q^{45} + 88 q^{46} - 108 q^{48} - 320 q^{52}+ \cdots + 336 q^{97}+O(q^{100}) \) 96 * q - 36 * q^6 - 64 * q^9 - 8 * q^13 + 80 * q^16 + 48 * q^18 + 8 * q^21 + 124 * q^24 - 8 * q^28 + 24 * q^33 + 64 * q^34 - 128 * q^37 - 136 * q^40 - 140 * q^42 - 160 * q^45 + 88 * q^46 - 108 * q^48 - 320 * q^52 - 216 * q^54 + 136 * q^57 + 280 * q^58 + 80 * q^60 - 464 * q^61 - 240 * q^66 - 120 * q^70 - 32 * q^72 + 288 * q^73 + 88 * q^76 - 296 * q^78 - 144 * q^81 + 204 * q^84 + 848 * q^85 - 392 * q^93 + 1384 * q^94 - 204 * q^96 + 336 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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