LMFDB - Embedded newform 84.6.e.a.71.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [84,6,Mod(71,84)] 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("84.71"); S:= CuspForms(chi, 6); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(84, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 0])) N = Newforms(chi, 6, names="a")

Level:	$ N $	$=$	$ 84 = 2^{2} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	84.e (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$13.4722408643$
Analytic rank:	$0$
Dimension:	$60$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			71.10
Character	$\chi$	$=$	84.71
Dual form			84.6.e.a.71.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-4.66315 + 3.20235i) q^{2} +(15.3769 - 2.55934i) q^{3} +(11.4900 - 29.8660i) q^{4} +8.37395i q^{5} +(-63.5091 + 61.1768i) q^{6} -49.0000i q^{7} +(42.0619 + 176.065i) q^{8} +(229.900 - 78.7095i) q^{9} +(-26.8163 - 39.0490i) q^{10} +453.236 q^{11} +(100.243 - 488.655i) q^{12} -689.106 q^{13} +(156.915 + 228.494i) q^{14} +(21.4318 + 128.766i) q^{15} +(-759.961 - 686.320i) q^{16} -2117.22i q^{17} +(-820.002 + 1103.25i) q^{18} -129.730i q^{19} +(250.097 + 96.2165i) q^{20} +(-125.408 - 753.469i) q^{21} +(-2113.51 + 1451.42i) q^{22} +4271.28 q^{23} +(1097.39 + 2599.68i) q^{24} +3054.88 q^{25} +(3213.41 - 2206.76i) q^{26} +(3333.70 - 1798.70i) q^{27} +(-1463.44 - 563.009i) q^{28} +4938.67i q^{29} +(-512.292 - 531.822i) q^{30} -1625.35i q^{31} +(5741.65 + 766.757i) q^{32} +(6969.38 - 1159.98i) q^{33} +(6780.08 + 9872.93i) q^{34} +410.324 q^{35} +(290.799 - 7770.56i) q^{36} +4599.74 q^{37} +(415.439 + 604.949i) q^{38} +(-10596.3 + 1763.65i) q^{39} +(-1474.36 + 352.224i) q^{40} -675.877i q^{41} +(2997.66 + 3111.94i) q^{42} -18309.1i q^{43} +(5207.67 - 13536.4i) q^{44} +(659.110 + 1925.17i) q^{45} +(-19917.6 + 13678.1i) q^{46} +10496.4 q^{47} +(-13442.4 - 8608.49i) q^{48} -2401.00 q^{49} +(-14245.4 + 9782.77i) q^{50} +(-5418.69 - 32556.4i) q^{51} +(-7917.81 + 20580.9i) q^{52} +23317.1i q^{53} +(-9785.51 + 19063.3i) q^{54} +3795.38i q^{55} +(8627.17 - 2061.03i) q^{56} +(-332.022 - 1994.84i) q^{57} +(-15815.3 - 23029.8i) q^{58} -23669.0 q^{59} +(4091.97 + 839.432i) q^{60} -26379.2 q^{61} +(5204.94 + 7579.27i) q^{62} +(-3856.76 - 11265.1i) q^{63} +(-29229.6 + 14811.2i) q^{64} -5770.54i q^{65} +(-28784.6 + 27727.5i) q^{66} +16473.0i q^{67} +(-63233.1 - 24326.8i) q^{68} +(65679.2 - 10931.6i) q^{69} +(-1913.40 + 1314.00i) q^{70} -11101.4 q^{71} +(23528.0 + 37166.5i) q^{72} +18356.9 q^{73} +(-21449.3 + 14730.0i) q^{74} +(46974.6 - 7818.46i) q^{75} +(-3874.51 - 1490.59i) q^{76} -22208.6i q^{77} +(43764.5 - 42157.3i) q^{78} -84662.8i q^{79} +(5747.21 - 6363.88i) q^{80} +(46658.6 - 36190.6i) q^{81} +(2164.39 + 3151.72i) q^{82} -44361.0 q^{83} +(-23944.1 - 4911.91i) q^{84} +17729.5 q^{85} +(58632.1 + 85378.2i) q^{86} +(12639.7 + 75941.6i) q^{87} +(19064.0 + 79798.9i) q^{88} +117136. i q^{89} +(-9238.58 - 6866.66i) q^{90} +33766.2i q^{91} +(49076.9 - 127566. i) q^{92} +(-4159.83 - 24992.9i) q^{93} +(-48946.1 + 33613.0i) q^{94} +1086.35 q^{95} +(90251.3 - 2904.45i) q^{96} -113037. q^{97} +(11196.2 - 7688.83i) q^{98} +(104199. - 35674.0i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 20 q^{4} - 114 q^{6} + 44 q^{9} + 668 q^{10} + 786 q^{12} - 3004 q^{16} - 3320 q^{18} + 7120 q^{22} + 16466 q^{24} - 37500 q^{25} - 7448 q^{28} - 35236 q^{30} - 9424 q^{33} + 43360 q^{34} + 50524 q^{36}+ \cdots + 232584 q^{97}+O(q^{100}) $ 60 * q - 20 * q^4 - 114 * q^6 + 44 * q^9 + 668 * q^10 + 786 * q^12 - 3004 * q^16 - 3320 * q^18 + 7120 * q^22 + 16466 * q^24 - 37500 * q^25 - 7448 * q^28 - 35236 * q^30 - 9424 * q^33 + 43360 * q^34 + 50524 * q^36 - 15056 * q^37 - 35468 * q^40 - 20090 * q^42 + 36024 * q^45 + 124416 * q^46 + 88654 * q^48 - 144060 * q^49 - 140108 * q^52 + 19486 * q^54 - 65072 * q^57 + 115616 * q^58 + 164908 * q^60 - 169424 * q^61 + 20116 * q^64 - 98484 * q^66 + 142536 * q^69 + 35868 * q^70 + 121312 * q^72 + 107256 * q^73 + 214836 * q^76 + 263708 * q^78 - 114932 * q^81 - 479624 * q^82 + 40474 * q^84 - 383992 * q^85 - 107320 * q^88 + 423760 * q^90 + 545208 * q^93 - 448512 * q^94 - 751618 * q^96 + 232584 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/84\mathbb{Z}\right)^\times$.

$n$	$29$	$43$	$73$
$\chi(n)$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−4.66315	+	3.20235i	−0.824337	+	0.566100i
$2$	−4.66315	+	3.20235i	−0.824337	+	0.566100i
$3$	15.3769	−	2.55934i	0.986430	−	0.164182i
$3$	15.3769	−	2.55934i	0.986430	−	0.164182i
$4$	11.4900	−	29.8660i	0.359062	−	0.933314i
$5$			8.37395i			0.149798i	0.997191	+	0.0748989i	$0.0238634\pi$
$5$			8.37395i			0.149798i	−0.997191	+	0.0748989i	$0.976137\pi$
$6$	−63.5091	+	61.1768i	−0.720207	+	0.693759i
$7$		−	49.0000i		−	0.377964i
$7$		−	49.0000i		−	0.377964i
$8$	42.0619	+	176.065i	0.232361	+	0.972630i
$9$	229.900	−	78.7095i	0.946089	−	0.323907i
$10$	−26.8163	−	39.0490i	−0.0848006	−	0.123484i
$11$	453.236			1.12939			0.564694	−	0.825301i	$-0.308994\pi$
$11$	453.236			1.12939			0.564694	+	0.825301i	$0.308994\pi$
$12$	100.243	−	488.655i	0.200956	−	0.979600i
$13$	−689.106			−1.13091			−0.565455	−	0.824779i	$-0.691299\pi$
$13$	−689.106			−1.13091			−0.565455	+	0.824779i	$0.691299\pi$
$14$	156.915	+	228.494i	0.213966	+	0.311570i
$15$	21.4318	+	128.766i	0.0245940	+	0.147765i
$16$	−759.961	−	686.320i	−0.742149	−	0.670234i
$17$		−	2117.22i		−	1.77682i	−0.459047	−	0.888412i	$-0.651809\pi$
$17$		−	2117.22i		−	1.77682i	0.459047	−	0.888412i	$-0.348191\pi$
$18$	−820.002	+	1103.25i	−0.596532	+	0.802590i
$19$		−	129.730i		−	0.0824433i	−0.999150	−	0.0412216i	$-0.986875\pi$
$19$		−	129.730i		−	0.0824433i	0.999150	−	0.0412216i	$-0.0131250\pi$
$20$	250.097	+	96.2165i	0.139808	+	0.0537867i
$21$	−125.408	−	753.469i	−0.0620548	−	0.372836i
$22$	−2113.51	+	1451.42i	−0.930995	+	0.639346i
$23$	4271.28			1.68360			0.841799	−	0.539791i	$-0.181497\pi$
$23$	4271.28			1.68360			0.841799	+	0.539791i	$0.181497\pi$
$24$	1097.39	+	2599.68i	0.388896	+	0.921282i
$25$	3054.88			0.977561
$26$	3213.41	−	2206.76i	0.932250	−	0.640208i
$27$	3333.70	−	1798.70i	0.880071	−	0.474842i
$28$	−1463.44	−	563.009i	−0.352759	−	0.135713i
$29$			4938.67i			1.09047i	0.838282	+	0.545237i	$0.183560\pi$
$29$			4938.67i			1.09047i	−0.838282	+	0.545237i	$0.816440\pi$
$30$	−512.292	−	531.822i	−0.103924	−	0.107885i
$31$		−	1625.35i		−	0.303769i	−0.988398	−	0.151884i	$-0.951466\pi$
$31$		−	1625.35i		−	0.303769i	0.988398	−	0.151884i	$-0.0485342\pi$
$32$	5741.65	+	766.757i	0.991201	+	0.132368i
$33$	6969.38	−	1159.98i	1.11406	−	0.185425i
$34$	6780.08	+	9872.93i	1.00586	+	1.46470i
$35$	410.324			0.0566183
$36$	290.799	−	7770.56i	0.0373970	−	0.999300i
$37$	4599.74			0.552369			0.276184	−	0.961105i	$-0.410930\pi$
$37$	4599.74			0.552369			0.276184	+	0.961105i	$0.410930\pi$
$38$	415.439	+	604.949i	0.0466711	+	0.0679610i
$39$	−10596.3	+	1763.65i	−1.11556	+	0.185674i
$40$	−1474.36	+	352.224i	−0.145698	+	0.0348072i
$41$		−	675.877i		−	0.0627925i	−0.999507	−	0.0313963i	$-0.990005\pi$
$41$		−	675.877i		−	0.0627925i	0.999507	−	0.0313963i	$-0.00999539\pi$
$42$	2997.66	+	3111.94i	0.262216	+	0.272213i
$43$		−	18309.1i		−	1.51007i	−0.655686	−	0.755033i	$-0.727621\pi$
$43$		−	18309.1i		−	1.51007i	0.655686	−	0.755033i	$-0.272379\pi$
$44$	5207.67	−	13536.4i	0.405520	−	1.05407i
$45$	659.110	+	1925.17i	0.0485206	+	0.141722i
$46$	−19917.6	+	13678.1i	−1.38785	+	0.953085i
$47$	10496.4			0.693097			0.346549	−	0.938032i	$-0.387354\pi$
$47$	10496.4			0.693097			0.346549	+	0.938032i	$0.387354\pi$
$48$	−13442.4	−	8608.49i	−0.842119	−	0.539292i
$49$	−2401.00			−0.142857
$50$	−14245.4	+	9782.77i	−0.805839	+	0.553397i
$51$	−5418.69	−	32556.4i	−0.291722	−	1.75271i
$52$	−7917.81	+	20580.9i	−0.406066	+	1.05549i
$53$			23317.1i			1.14021i	0.821572	+	0.570105i	$0.193097\pi$
$53$			23317.1i			1.14021i	−0.821572	+	0.570105i	$0.806903\pi$
$54$	−9785.51	+	19063.3i	−0.456666	+	0.889638i
$55$			3795.38i			0.169180i
$56$	8627.17	−	2061.03i	0.367619	−	0.0878243i
$57$	−332.022	−	1994.84i	−0.0135357	−	0.0813245i
$58$	−15815.3	−	23029.8i	−0.617317	−	0.898917i
$59$	−23669.0			−0.885217			−0.442609	−	0.896715i	$-0.645947\pi$
$59$	−23669.0			−0.885217			−0.442609	+	0.896715i	$0.645947\pi$
$60$	4091.97	+	839.432i	0.146742	+	0.0301028i
$61$	−26379.2			−0.907690			−0.453845	−	0.891081i	$-0.649948\pi$
$61$	−26379.2			−0.907690			−0.453845	+	0.891081i	$0.649948\pi$
$62$	5204.94	+	7579.27i	0.171964	+	0.250408i
$63$	−3856.76	−	11265.1i	−0.122425	−	0.357588i
$64$	−29229.6	+	14811.2i	−0.892016	+	0.452003i
$65$		−	5770.54i		−	0.169408i
$66$	−28784.6	+	27727.5i	−0.813393	+	0.783523i
$67$			16473.0i			0.448318i	0.974553	+	0.224159i	$0.0719635\pi$
$67$			16473.0i			0.448318i	−0.974553	+	0.224159i	$0.928036\pi$
$68$	−63233.1	−	24326.8i	−1.65833	−	0.637989i
$69$	65679.2	−	10931.6i	1.66075	−	0.276416i
$70$	−1913.40	+	1314.00i	−0.0466725	+	0.0320516i
$71$	−11101.4			−0.261356			−0.130678	−	0.991425i	$-0.541715\pi$
$71$	−11101.4			−0.261356			−0.130678	+	0.991425i	$0.541715\pi$
$72$	23528.0	+	37166.5i	0.534876	+	0.844930i
$73$	18356.9			0.403173			0.201587	−	0.979471i	$-0.435390\pi$
$73$	18356.9			0.403173			0.201587	+	0.979471i	$0.435390\pi$
$74$	−21449.3	+	14730.0i	−0.455338	+	0.312696i
$75$	46974.6	−	7818.46i	0.964295	−	0.160497i
$76$	−3874.51	−	1490.59i	−0.0769454	−	0.0296022i
$77$		−	22208.6i		−	0.426868i
$78$	43764.5	−	42157.3i	0.814489	−	0.784578i
$79$		−	84662.8i		−	1.52625i	−0.646252	−	0.763124i	$-0.723665\pi$
$79$		−	84662.8i		−	1.52625i	0.646252	−	0.763124i	$-0.276335\pi$
$80$	5747.21	−	6363.88i	0.100400	−	0.111172i
$81$	46658.6	−	36190.6i	0.790168	−	0.612890i
$82$	2164.39	+	3151.72i	0.0355469	+	0.0517622i
$83$	−44361.0			−0.706815			−0.353408	−	0.935469i	$-0.614977\pi$
$83$	−44361.0			−0.706815			−0.353408	+	0.935469i	$0.614977\pi$
$84$	−23944.1	−	4911.91i	−0.370254	−	0.0759543i
$85$	17729.5			0.266164
$86$	58632.1	+	85378.2i	0.854849	+	1.24480i
$87$	12639.7	+	75941.6i	0.179036	+	1.07568i
$88$	19064.0	+	79798.9i	0.262426	+	1.09848i
$89$			117136.i			1.56753i	0.621055	+	0.783767i	$0.286704\pi$
$89$			117136.i			1.56753i	−0.621055	+	0.783767i	$0.713296\pi$
$90$	−9238.58	−	6866.66i	−0.120226	−	0.0893592i
$91$			33766.2i			0.427443i
$92$	49076.9	−	127566.i	0.604516	−	1.57133i
$93$	−4159.83	−	24992.9i	−0.0498733	−	0.299647i
$94$	−48946.1	+	33613.0i	−0.571346	+	0.392362i
$95$	1086.35			0.0123498
$96$	90251.3	−	2904.45i	0.999483	−	0.0321652i
$97$	−113037.			−1.21980			−0.609902	−	0.792477i	$-0.708791\pi$
$97$	−113037.			−1.21980			−0.609902	+	0.792477i	$0.708791\pi$
$98$	11196.2	−	7688.83i	0.117762	−	0.0808714i
$99$	104199.	−	35674.0i	1.06850	−	0.365817i
$100$	35100.5	−	91237.1i	0.351005	−	0.912371i
$101$		−	59404.2i		−	0.579447i	−0.957110	−	0.289723i	$-0.906437\pi$
$101$		−	59404.2i		−	0.579447i	0.957110	−	0.289723i	$-0.0935633\pi$
$102$	129525.	+	134463.i	1.23269	+	1.27968i
$103$			142064.i			1.31944i	0.751511	+	0.659721i	$0.229326\pi$
$103$			142064.i			1.31944i	−0.751511	+	0.659721i	$0.770674\pi$
$104$	−28985.1	−	121327.i	−0.262779	−	1.09996i
$105$	6309.52	−	1050.16i	0.0558500	−	0.00929568i
$106$	−74669.4	−	108731.i	−0.645473	−	0.939917i
$107$	−63745.0			−0.538254			−0.269127	−	0.963105i	$-0.586735\pi$
$107$	−63745.0			−0.538254			−0.269127	+	0.963105i	$0.586735\pi$
$108$	−15415.9	−	120232.i	−0.127177	−	0.991880i
$109$	−166009.			−1.33834			−0.669169	−	0.743110i	$-0.733350\pi$
$109$	−166009.			−1.33834			−0.669169	+	0.743110i	$0.733350\pi$
$110$	−12154.1	−	17698.4i	−0.0957727	−	0.139461i
$111$	70729.9	−	11772.3i	0.544873	−	0.0906888i
$112$	−33629.7	+	37238.1i	−0.253325	+	0.280506i
$113$		−	27283.6i		−	0.201004i	−0.994937	−	0.100502i	$-0.967955\pi$
$113$		−	27283.6i		−	0.201004i	0.994937	−	0.100502i	$-0.0320449\pi$
$114$	7936.44	+	8239.01i	0.0571957	+	0.0593762i
$115$			35767.5i			0.252199i
$116$	147499.	+	56745.2i	1.01775	+	0.391547i
$117$	−158425.	+	54239.2i	−1.06994	+	0.366310i
$118$	110372.	−	75796.3i	0.729717	−	0.501122i
$119$	−103744.			−0.671576
$120$	−21769.6	+	9189.51i	−0.138006	+	0.0582558i
$121$	44372.1			0.275516
$122$	123010.	−	84475.4i	0.748242	−	0.513843i
$123$	−1729.80	−	10392.9i	−0.0103094	−	0.0619405i
$124$	−48542.8	−	18675.3i	−0.283512	−	0.109072i
$125$			51750.0i			0.296234i
$126$	54059.4	+	40180.1i	0.303350	+	0.225468i
$127$			334663.i			1.84119i	0.390521	+	0.920594i	$0.372295\pi$
$127$			334663.i			1.84119i	−0.390521	+	0.920594i	$0.627705\pi$
$128$	88871.4	−	162670.i	0.479443	−	0.877573i
$129$	−46859.2	−	281538.i	−0.247925	−	1.48958i
$130$	18479.3	+	26908.9i	0.0959017	+	0.139649i
$131$	225705.			1.14912			0.574558	−	0.818464i	$-0.305174\pi$
$131$	225705.			1.14912			0.574558	+	0.818464i	$0.305174\pi$
$132$	45433.8	−	221476.i	0.226957	−	1.10635i
$133$	−6356.75			−0.0311606
$134$	−52752.3	−	76816.2i	−0.253793	−	0.369565i
$135$	15062.2	+	27916.3i	0.0711304	+	0.131833i
$136$	372768.	−	89054.4i	1.72819	−	0.412865i
$137$			360881.i			1.64272i	0.570411	+	0.821359i	$0.306784\pi$
$137$			360881.i			1.64272i	−0.570411	+	0.821359i	$0.693216\pi$
$138$	−271265.	+	261303.i	−1.21254	+	1.16801i
$139$		−	234021.i		−	1.02735i	−0.857985	−	0.513675i	$-0.828284\pi$
$139$		−	234021.i		−	1.02735i	0.857985	−	0.513675i	$-0.171716\pi$
$140$	4714.61	−	12254.7i	0.0203294	−	0.0528426i
$141$	161402.	−	26863.7i	0.683692	−	0.113794i
$142$	51767.6	−	35550.6i	0.215445	−	0.147954i
$143$	−312328.			−1.27723
$144$	−228735.	−	97968.5i	−0.919233	−	0.393714i
$145$	−41356.2			−0.163351
$146$	−85601.0	+	58785.1i	−0.332351	+	0.228236i
$147$	−36920.0	+	6144.97i	−0.140919	+	0.0234545i
$148$	52850.9	−	137376.i	0.198334	−	0.515533i
$149$			116592.i			0.430231i	0.976589	+	0.215116i	$0.0690128\pi$
$149$			116592.i			0.430231i	−0.976589	+	0.215116i	$0.930987\pi$
$150$	−194012.	+	186888.i	−0.704046	+	0.678191i
$151$			102126.i			0.364498i	0.983252	+	0.182249i	$0.0583378\pi$
$151$			102126.i			0.364498i	−0.983252	+	0.182249i	$0.941662\pi$
$152$	22840.8	−	5456.67i	0.0801867	−	0.0191566i
$153$	−166646.	−	486749.i	−0.575526	−	1.68103i
$154$	71119.5	+	103562.i	0.241650	+	0.351883i
$155$	13610.6			0.0455039
$156$	−69078.2	+	336735.i	−0.227263	+	1.10784i
$157$	231699.			0.750197			0.375098	−	0.926985i	$-0.377609\pi$
$157$	231699.			0.750197			0.375098	+	0.926985i	$0.377609\pi$
$158$	271120.	+	394796.i	0.864009	+	1.25814i
$159$	59676.3	+	358545.i	0.187201	+	1.12474i
$160$	−6420.79	+	48080.3i	−0.0198284	+	0.148480i
$161$		−	209293.i		−	0.636340i
$162$	−101682.	+	318179.i	−0.304407	+	0.952542i
$163$			180183.i			0.531184i	0.964086	+	0.265592i	$0.0855673\pi$
$163$			180183.i			0.531184i	−0.964086	+	0.265592i	$0.914433\pi$
$164$	−20185.8	−	7765.81i	−0.0586052	−	0.0225464i
$165$	9713.66	+	58361.3i	0.0277762	+	0.166884i
$166$	206862.	−	142059.i	0.582654	−	0.400128i
$167$	11036.8			0.0306233			0.0153116	−	0.999883i	$-0.495126\pi$
$167$	11036.8			0.0306233			0.0153116	+	0.999883i	$0.495126\pi$
$168$	127385.	−	53772.2i	0.348212	−	0.146989i
$169$	103574.			0.278955
$170$	−82675.5	+	56776.1i	−0.219409	+	0.150676i
$171$	−10211.0	−	29824.8i	−0.0267040	−	0.0779986i
$172$	−546821.	−	210371.i	−1.40937	−	0.542207i
$173$			437674.i			1.11182i	0.831241	+	0.555912i	$0.187631\pi$
$173$			437674.i			1.11182i	−0.831241	+	0.555912i	$0.812369\pi$
$174$	−302132.	−	313650.i	−0.756526	−	0.785367i
$175$		−	149689.i		−	0.369483i
$176$	−344442.	−	311065.i	−0.838174	−	0.756954i
$177$	−363956.	+	60577.0i	−0.873205	+	0.145336i
$178$	−375111.	−	546225.i	−0.887381	−	1.29218i
$179$	−328285.			−0.765806			−0.382903	−	0.923789i	$-0.625076\pi$
$179$	−328285.			−0.765806			−0.382903	+	0.923789i	$0.625076\pi$
$180$	65070.3	+	2435.14i	0.149693	+	0.00560199i
$181$	−6048.00			−0.0137219			−0.00686096	−	0.999976i	$-0.502184\pi$
$181$	−6048.00			−0.0137219			−0.00686096	+	0.999976i	$0.502184\pi$
$182$	−108131.	−	157457.i	−0.241976	−	0.352357i
$183$	−405631.	+	67513.4i	−0.895373	+	0.149026i
$184$	179658.	+	752022.i	0.391203	+	1.63752i
$185$			38518.0i			0.0827436i
$186$	99433.9	+	103225.i	0.210742	+	0.218777i
$187$		−	959602.i		−	2.00672i
$188$	120603.	−	313485.i	0.248865	−	0.646877i
$189$	−88136.3	−	163352.i	−0.179474	−	0.332636i
$190$	−5065.81	+	3478.87i	−0.0101804	+	0.00699123i
$191$	−259647.			−0.514991			−0.257495	−	0.966280i	$-0.582897\pi$
$191$	−259647.			−0.514991			−0.257495	+	0.966280i	$0.582897\pi$
$192$	−411554.	+	302560.i	−0.805701	+	0.592322i
$193$	672466.			1.29950			0.649751	−	0.760147i	$-0.274873\pi$
$193$	672466.			1.29950			0.649751	+	0.760147i	$0.274873\pi$
$194$	527107.	−	361982.i	1.00553	−	0.690530i
$195$	−14768.8	−	88733.2i	−0.0278136	−	0.167109i
$196$	−27587.4	+	71708.4i	−0.0512945	+	0.133331i
$197$			76641.6i			0.140702i	0.997522	+	0.0703508i	$0.0224119\pi$
$197$			76641.6i			0.140702i	−0.997522	+	0.0703508i	$0.977588\pi$
$198$	−371655.	+	500034.i	−0.673715	+	0.906435i
$199$		−	485442.i		−	0.868970i	−0.900679	−	0.434485i	$-0.856930\pi$
$199$		−	485442.i		−	0.868970i	0.900679	−	0.434485i	$-0.143070\pi$
$200$	128494.	+	537856.i	0.227147	+	0.950804i
$201$	42160.0	+	253305.i	0.0736056	+	0.442235i
$202$	190233.	+	277011.i	0.328025	+	0.477659i
$203$	241995.			0.412160
$204$	−1.03459e6	−	212237.i	−1.74058	−	0.357064i
$205$	5659.76			0.00940619
$206$	−454937.	−	662465.i	−0.746936	−	1.08766i
$207$	981966.	−	336190.i	1.59283	−	0.545330i
$208$	523694.	+	472947.i	0.839304	+	0.757974i
$209$		−	58798.2i		−	0.0931104i
$210$	−26059.3	+	25102.3i	−0.0407769	+	0.0392794i
$211$		−	9472.20i		−	0.0146469i	−0.999973	−	0.00732343i	$-0.997669\pi$
$211$		−	9472.20i		−	0.0146469i	0.999973	−	0.00732343i	$-0.00233114\pi$
$212$	696389.	+	267913.i	1.06417	+	0.409406i
$213$	−170706.	+	28412.3i	−0.257810	+	0.0429099i
$214$	297253.	−	204134.i	0.443702	−	0.304705i
$215$	153320.			0.226205
$216$	456910.	+	511291.i	0.666340	+	0.745648i
$217$	−79642.3			−0.114814
$218$	774126.	−	531619.i	1.10324	−	0.757633i
$219$	282272.	−	46981.5i	0.397702	−	0.0661936i
$220$	113353.	+	43608.8i	0.157898	+	0.0607460i
$221$			1.45899e6i			2.00943i
$222$	−292125.	+	281397.i	−0.397820	+	0.383211i
$223$			277755.i			0.374024i	0.982358	+	0.187012i	$0.0598804\pi$
$223$			277755.i			0.374024i	−0.982358	+	0.187012i	$0.940120\pi$
$224$	37571.1	−	281341.i	0.0500304	−	0.374639i
$225$	702315.	−	240448.i	0.924859	−	0.316639i
$226$	87371.5	+	127228.i	0.113789	+	0.165695i
$227$	97472.2			0.125550			0.0627749	−	0.998028i	$-0.480005\pi$
$227$	97472.2			0.125550			0.0627749	+	0.998028i	$0.480005\pi$
$228$	−63393.0	−	13004.5i	−0.0807614	−	0.0165675i
$229$	−752884.			−0.948723			−0.474362	−	0.880330i	$-0.657321\pi$
$229$	−752884.			−0.948723			−0.474362	+	0.880330i	$0.657321\pi$
$230$	−114540.	−	166789.i	−0.142770	−	0.207897i
$231$	−56839.2	−	341500.i	−0.0700839	−	0.421076i
$232$	−869526.	+	207730.i	−1.06063	+	0.253384i
$233$		−	586354.i		−	0.707571i	−0.935327	−	0.353786i	$-0.884894\pi$
$233$		−	586354.i		−	0.707571i	0.935327	−	0.353786i	$-0.115106\pi$
$234$	565068.	−	760258.i	0.674623	−	0.907656i
$235$			87896.1i			0.103824i
$236$	−271956.	+	706899.i	−0.317848	+	0.826186i
$237$	−216681.	−	1.30185e6i	−0.250582	−	1.50554i
$238$	483774.	−	332224.i	0.553605	−	0.380179i
$239$	−336122.			−0.380629			−0.190314	−	0.981723i	$-0.560951\pi$
$239$	−336122.			−0.380629			−0.190314	+	0.981723i	$0.560951\pi$
$240$	72087.1	−	112566.i	0.0807848	−	0.126148i
$241$	1.59393e6			1.76778			0.883888	−	0.467698i	$-0.154916\pi$
$241$	1.59393e6			1.76778			0.883888	+	0.467698i	$0.154916\pi$
$242$	−206914.	+	142095.i	−0.227118	+	0.155970i
$243$	624842.	−	675915.i	0.678820	−	0.734304i
$244$	−303097.	+	787843.i	−0.325917	+	0.847160i
$245$		−	20105.9i		−	0.0213997i
$246$	41348.0	+	42924.3i	0.0435629	+	0.0452237i
$247$			89397.5i			0.0932358i
$248$	286167.	−	68365.4i	0.295455	−	0.0705841i
$249$	−682135.	+	113535.i	−0.697224	+	0.116046i
$250$	−165721.	−	241318.i	−0.167698	−	0.244197i
$251$	−829684.			−0.831244			−0.415622	−	0.909537i	$-0.636436\pi$
$251$	−829684.			−0.831244			−0.415622	+	0.909537i	$0.636436\pi$
$252$	−380757.	−	14249.2i	−0.377700	−	0.0141347i
$253$	1.93590e6			1.90144
$254$	−1.07171e6	−	1.56058e6i	−1.04230	−	1.51776i
$255$	272626.	−	45375.9i	0.262553	−	0.0436993i
$256$	106506.	+	1.04315e6i	0.101572	+	0.994828i
$257$		−	1.46452e6i		−	1.38313i	−0.722315	−	0.691564i	$-0.756922\pi$
$257$		−	1.46452e6i		−	1.38313i	0.722315	−	0.691564i	$-0.243078\pi$
$258$	1.12009e6	+	1.16279e6i	1.04762	+	1.08756i
$259$		−	225387.i		−	0.208776i
$260$	−172343.	−	66303.4i	−0.158111	−	0.0608278i
$261$	388720.	+	1.13540e6i	0.353212	+	1.03168i
$262$	−1.05250e6	+	722786.i	−0.947258	+	0.650514i
$263$	1.39999e6			1.24806			0.624031	−	0.781399i	$-0.285494\pi$
$263$	1.39999e6			1.24806			0.624031	+	0.781399i	$0.285494\pi$
$264$	497378.	+	1.17827e6i	0.439214	+	1.04048i
$265$	−195256.			−0.170801
$266$	29642.5	−	20356.5i	0.0256868	−	0.0176400i
$267$	299792.	+	1.80120e6i	0.257360	+	1.54626i
$268$	491984.	+	189275.i	0.418422	+	0.160974i
$269$		−	140203.i		−	0.118134i	−0.998254	−	0.0590671i	$-0.981187\pi$
$269$		−	140203.i		−	0.118134i	0.998254	−	0.0590671i	$-0.0188126\pi$
$270$	−159635.	−	81943.4i	−0.133266	−	0.0684076i
$271$		−	1.60866e6i		−	1.33058i	−0.746585	−	0.665290i	$-0.768308\pi$
$271$		−	1.60866e6i		−	1.33058i	0.746585	−	0.665290i	$-0.231692\pi$
$272$	−1.45309e6	+	1.60901e6i	−1.19089	+	1.31867i
$273$	86419.1	+	519220.i	0.0701783	+	0.421643i
$274$	−1.15567e6	−	1.68285e6i	−0.929943	−	1.35415i
$275$	1.38458e6			1.10404
$276$	428167.	−	2.08718e6i	0.338330	−	1.64925i
$277$	−244076.			−0.191128			−0.0955641	−	0.995423i	$-0.530465\pi$
$277$	−244076.			−0.191128			−0.0955641	+	0.995423i	$0.530465\pi$
$278$	749417.	+	1.09128e6i	0.581583	+	0.846883i
$279$	−127931.	−	373668.i	−0.0983930	−	0.287392i
$280$	17259.0	+	72243.6i	0.0131559	+	0.0550686i
$281$		−	1.54687e6i		−	1.16866i	−0.811517	−	0.584329i	$-0.801358\pi$
$281$		−	1.54687e6i		−	1.16866i	0.811517	−	0.584329i	$-0.198642\pi$
$282$	−666614.	+	642134.i	−0.499174	+	0.480843i
$283$			1.93564e6i			1.43668i	0.695694	+	0.718338i	$0.255097\pi$
$283$			1.93564e6i			1.43668i	−0.695694	+	0.718338i	$0.744903\pi$
$284$	−127555.	+	331556.i	−0.0938430	+	0.243927i
$285$	16704.7	−	2780.34i	0.0121822	−	0.00202761i
$286$	1.45643e6	−	1.00018e6i	1.05287	−	0.723042i
$287$	−33118.0			−0.0237334
$288$	1.38035e6	−	275645.i	0.980639	−	0.195825i
$289$	−3.06278e6			−2.15710
$290$	192850.	−	132437.i	0.134656	−	0.0924727i
$291$	−1.73816e6	+	289299.i	−1.20325	+	0.200269i
$292$	210920.	−	548248.i	0.144764	−	0.376287i
$293$			1.98036e6i			1.34765i	0.738893	+	0.673823i	$0.235349\pi$
$293$			1.98036e6i			1.34765i	−0.738893	+	0.673823i	$0.764651\pi$
$294$	152485.	−	146885.i	0.102887	−	0.0991084i
$295$		−	198203.i		−	0.132604i
$296$	193474.	+	809852.i	0.128349	+	0.537250i
$297$	1.51096e6	−	815236.i	0.993941	−	0.536281i
$298$	−373367.	−	543685.i	−0.243554	−	0.354655i
$299$	−2.94337e6			−1.90400
$300$	306230.	−	1.49278e6i	0.196447	−	0.957619i
$301$	−897147.			−0.570752
$302$	−327044.	−	476231.i	−0.206343	−	0.300469i
$303$	−152035.	−	913453.i	−0.0951345	−	0.571584i
$304$	−89036.0	+	98589.5i	−0.0552563	+	0.0611852i
$305$		−	220898.i		−	0.135970i
$306$	2.33583e6	+	1.73613e6i	1.42606	+	1.05993i
$307$			131599.i			0.0796907i	0.999206	+	0.0398453i	$0.0126865\pi$
$307$			131599.i			0.0796907i	−0.999206	+	0.0398453i	$0.987313\pi$
$308$	−663282.	−	255176.i	−0.398402	−	0.153272i
$309$	363589.	+	2.18450e6i	0.216628	+	1.30154i
$310$	−63468.4	+	43585.9i	−0.0375106	+	0.0257598i
$311$	7906.18			0.00463517			0.00231758	−	0.999997i	$-0.499262\pi$
$311$	7906.18			0.00463517			0.00231758	+	0.999997i	$0.499262\pi$
$312$	−756219.	−	1.79146e6i	−0.439806	−	1.04189i
$313$	−2.39105e6			−1.37952			−0.689760	−	0.724038i	$-0.742284\pi$
$313$	−2.39105e6			−1.37952			−0.689760	+	0.724038i	$0.742284\pi$
$314$	−1.08045e6	+	741981.i	−0.618415	+	0.424686i
$315$	94333.3	−	32296.4i	0.0535659	−	0.0183391i
$316$	−2.52854e6	−	972774.i	−1.42447	−	0.548017i
$317$			194399.i			0.108654i	0.998523	+	0.0543270i	$0.0173014\pi$
$317$			194399.i			0.108654i	−0.998523	+	0.0543270i	$0.982699\pi$
$318$	−1.42647e6	−	1.48085e6i	−0.791031	−	0.821187i
$319$			2.23838e6i			1.23157i
$320$	−124029.	−	244767.i	−0.0677091	−	0.133622i
$321$	−980203.	+	163145.i	−0.530950	+	0.0883713i
$322$	670228.	+	975964.i	0.360232	+	0.524559i
$323$	−274667.			−0.146487
$324$	−544762.	−	1.80934e6i	−0.288300	−	0.957540i
$325$	−2.10513e6			−1.10553
$326$	−577008.	−	840220.i	−0.300703	−	0.437874i
$327$	−2.55271e6	+	424874.i	−1.32018	+	0.219731i
$328$	118998.	−	28428.7i	0.0610739	−	0.0145906i
$329$		−	514322.i		−	0.261966i
$330$	−232189.	−	241041.i	−0.117370	−	0.121845i
$331$			656002.i			0.329106i	0.986368	+	0.164553i	$0.0526181\pi$
$331$			656002.i			0.329106i	−0.986368	+	0.164553i	$0.947382\pi$
$332$	−509706.	+	1.32489e6i	−0.253790	+	0.659680i
$333$	1.05748e6	−	362043.i	0.522590	−	0.178916i
$334$	−51466.3	+	35343.6i	−0.0252439	+	0.0173358i
$335$	−137944.			−0.0671571
$336$	−421816.	+	658677.i	−0.203833	+	0.318291i
$337$	1.84657e6			0.885708			0.442854	−	0.896594i	$-0.353966\pi$
$337$	1.84657e6			0.885708			0.442854	+	0.896594i	$0.353966\pi$
$338$	−482982.	+	331680.i	−0.229953	+	0.157917i
$339$	−69827.9	−	419538.i	−0.0330012	−	0.198277i
$340$	203712.	−	529511.i	0.0955694	−	0.248415i
$341$		−	736669.i		−	0.343073i
$342$	143124.	+	106379.i	0.0661681	+	0.0491800i
$343$			117649.i			0.0539949i
$344$	3.22359e6	−	770116.i	1.46874	−	0.350881i
$345$	91541.1	+	549994.i	0.0414065	+	0.248777i
$346$	−1.40158e6	−	2.04094e6i	−0.629403	−	0.916517i
$347$	881271.			0.392903			0.196452	−	0.980514i	$-0.437058\pi$
$347$	881271.			0.392903			0.196452	+	0.980514i	$0.437058\pi$
$348$	2.41330e6	+	495068.i	1.06823	+	0.219137i
$349$	−3.19533e6			−1.40427			−0.702137	−	0.712042i	$-0.747771\pi$
$349$	−3.19533e6			−1.40427			−0.702137	+	0.712042i	$0.747771\pi$
$350$	479356.	+	698022.i	0.209164	+	0.304579i
$351$	−2.29728e6	+	1.23950e6i	−0.995280	+	0.537003i
$352$	2.60232e6	+	347522.i	1.11945	+	0.149495i
$353$			817755.i			0.349290i	0.984631	+	0.174645i	$0.0558778\pi$
$353$			817755.i			0.349290i	−0.984631	+	0.174645i	$0.944122\pi$
$354$	1.50320e6	−	1.44799e6i	0.637540	−	0.614127i
$355$		−	92962.8i		−	0.0391506i
$356$	3.49840e6	+	1.34589e6i	1.46300	+	0.562841i
$357$	−1.59526e6	+	265516.i	−0.662463	+	0.110260i
$358$	1.53084e6	−	1.05128e6i	0.631282	−	0.433523i
$359$	920973.			0.377147			0.188573	−	0.982059i	$-0.439614\pi$
$359$	920973.			0.377147			0.188573	+	0.982059i	$0.439614\pi$
$360$	−311231.	+	197022.i	−0.126569	+	0.0801233i
$361$	2.45927e6			0.993203
$362$	28202.7	−	19367.8i	0.0113115	−	0.00776798i
$363$	682307.	−	113563.i	0.271777	−	0.0452347i
$364$	1.00846e6	+	387973.i	0.398939	+	0.153479i
$365$			153720.i			0.0603945i
$366$	1.67532e6	−	1.61380e6i	0.653725	−	0.629718i
$367$			4.45609e6i			1.72699i	0.504360	+	0.863493i	$0.331728\pi$
$367$			4.45609e6i			1.72699i	−0.504360	+	0.863493i	$0.668272\pi$
$368$	−3.24601e6	−	2.93147e6i	−1.24948	−	1.12841i
$369$	−53197.9	−	155384.i	−0.0203390	−	0.0594073i
$370$	−123348.	−	179615.i	−0.0468412	−	0.0682086i
$371$	1.14254e6			0.430959
$372$	−794236.	−	162930.i	−0.297572	−	0.0610443i
$373$	1.50232e6			0.559102			0.279551	−	0.960131i	$-0.409814\pi$
$373$	1.50232e6			0.559102			0.279551	+	0.960131i	$0.409814\pi$
$374$	3.07298e6	+	4.47477e6i	1.13601	+	1.65421i
$375$	132446.	+	795756.i	0.0486362	+	0.292214i
$376$	441497.	+	1.84804e6i	0.161049	+	0.674127i
$377$		−	3.40327e6i		−	1.23323i
$378$	934101.	+	479490.i	0.336252	+	0.172604i
$379$			4.56843e6i			1.63369i	0.576858	+	0.816844i	$0.304278\pi$
$379$			4.56843e6i			1.63369i	−0.576858	+	0.816844i	$0.695722\pi$
$380$	12482.1	−	32445.0i	0.00443435	−	0.0115263i
$381$	856515.	+	5.14608e6i	0.302289	+	1.81620i
$382$	1.21077e6	−	831478.i	0.424526	−	0.291536i
$383$	4.97312e6			1.73234			0.866168	−	0.499753i	$-0.166576\pi$
$383$	4.97312e6			1.73234			0.866168	+	0.499753i	$0.166576\pi$
$384$	950240.	−	2.72882e6i	0.328856	−	0.944380i
$385$	185974.			0.0639440
$386$	−3.13581e6	+	2.15347e6i	−1.07123	+	0.735648i
$387$	−1.44110e6	−	4.20926e6i	−0.489122	−	1.42866i
$388$	−1.29879e6	+	3.37596e6i	−0.437984	+	1.13846i
$389$		−	1.01635e6i		−	0.340540i	−0.985397	−	0.170270i	$-0.945536\pi$
$389$		−	1.01635e6i		−	0.340540i	0.985397	−	0.170270i	$-0.0544639\pi$
$390$	353023.	+	366482.i	0.117528	+	0.122009i
$391$		−	9.04326e6i		−	2.99146i
$392$	−100991.	−	422731.i	−0.0331945	−	0.138947i
$393$	3.47065e6	−	577656.i	1.13352	−	0.188664i
$394$	−245433.	−	357391.i	−0.0796512	−	0.115985i
$395$	708963.			0.228629
$396$	131801.	−	3.52190e6i	0.0422357	−	1.12860i
$397$	−2.37477e6			−0.756215			−0.378107	−	0.925762i	$-0.623425\pi$
$397$	−2.37477e6			−0.756215			−0.378107	+	0.925762i	$0.623425\pi$
$398$	1.55455e6	+	2.26369e6i	0.491924	+	0.716324i
$399$	−97747.3	+	16269.1i	−0.0307378	+	0.00511600i
$400$	−2.32159e6	−	2.09662e6i	−0.725496	−	0.655195i
$401$		−	4.84343e6i		−	1.50415i	−0.659076	−	0.752076i	$-0.729053\pi$
$401$		−	4.84343e6i		−	1.50415i	0.659076	−	0.752076i	$-0.270947\pi$
$402$	−1.00777e6	−	1.04619e6i	−0.311025	−	0.322882i
$403$			1.12004e6i			0.343535i
$404$	−1.77417e6	−	682552.i	−0.540806	−	0.208057i
$405$	303058.	+	390717.i	0.0918096	+	0.118365i
$406$	−1.12846e6	+	774951.i	−0.339759	+	0.233324i
$407$	2.08477e6			0.623838
$408$	5.50411e6	−	2.32342e6i	1.63696	−	0.691000i
$409$	1.05664e6			0.312335			0.156167	−	0.987731i	$-0.450086\pi$
$409$	1.05664e6			0.312335			0.156167	+	0.987731i	$0.450086\pi$
$410$	−26392.3	+	18124.5i	−0.00775387	+	0.00532484i
$411$	923618.	+	5.54925e6i	0.269704	+	1.62043i
$412$	4.24288e6	+	1.63231e6i	1.23145	+	0.473761i
$413$			1.15978e6i			0.334581i
$414$	−3.50246e6	+	4.71230e6i	−1.00432	+	1.35124i
$415$		−	371477.i		−	0.105879i
$416$	−3.95660e6	−	528377.i	−1.12096	−	0.149696i
$417$	−598940.	−	3.59853e6i	−0.168672	−	1.01341i
$418$	188292.	+	274185.i	0.0527098	+	0.0767543i
$419$	6.00014e6			1.66965			0.834827	−	0.550512i	$-0.185568\pi$
$419$	6.00014e6			1.66965			0.834827	+	0.550512i	$0.185568\pi$
$420$	41132.1	−	200507.i	0.0113778	−	0.0554633i
$421$	4.85605e6			1.33530			0.667648	−	0.744477i	$-0.267301\pi$
$421$	4.85605e6			1.33530			0.667648	+	0.744477i	$0.267301\pi$
$422$	30333.2	+	44170.3i	0.00829159	+	0.0120739i
$423$	2.41311e6	−	826163.i	0.655732	−	0.224499i
$424$	−4.10532e6	+	980761.i	−1.10900	+	0.264941i
$425$		−	6.46786e6i		−	1.73695i
$426$	705041.	−	679149.i	0.188231	−	0.181318i
$427$			1.29258e6i			0.343075i
$428$	−732429.	+	1.90381e6i	−0.193266	+	0.502360i
$429$	−4.80264e6	+	799352.i	−1.25990	+	0.209698i
$430$	−714953.	+	490983.i	−0.186469	+	0.128055i
$431$	−3.37703e6			−0.875672			−0.437836	−	0.899055i	$-0.644255\pi$
$431$	−3.37703e6			−0.875672			−0.437836	+	0.899055i	$0.644255\pi$
$432$	−3.76797e6	−	921046.i	−0.971400	−	0.237450i
$433$	−4.51092e6			−1.15623			−0.578116	−	0.815954i	$-0.696212\pi$
$433$	−4.51092e6			−1.15623			−0.578116	+	0.815954i	$0.696212\pi$
$434$	371384.	−	255042.i	0.0946453	−	0.0649961i
$435$	−635931.	+	105844.i	−0.161134	+	0.0268192i
$436$	−1.90744e6	+	4.95804e6i	−0.480546	+	1.24909i
$437$		−	554112.i		−	0.138801i
$438$	−1.16583e6	+	1.12302e6i	−0.290368	+	0.279705i
$439$		−	7.79066e6i		−	1.92936i	−0.263429	−	0.964679i	$-0.584854\pi$
$439$		−	7.79066e6i		−	1.92936i	0.263429	−	0.964679i	$-0.415146\pi$
$440$	−668233.	+	159641.i	−0.164549	+	0.0393108i
$441$	−551989.	+	188981.i	−0.135156	+	0.0462725i
$442$	−4.67219e6	−	6.80350e6i	−1.13754	−	1.65644i
$443$	−3.28241e6			−0.794663			−0.397331	−	0.917675i	$-0.630064\pi$
$443$	−3.28241e6			−0.794663			−0.397331	+	0.917675i	$0.630064\pi$
$444$	461093.	−	2.24768e6i	0.111002	−	0.541101i
$445$	−980895.			−0.234813
$446$	−889468.	−	1.29521e6i	−0.211735	−	0.308322i
$447$	298397.	+	1.79282e6i	0.0706360	+	0.424393i
$448$	725750.	+	1.43225e6i	0.170841	+	0.337151i
$449$			6.95316e6i			1.62767i	0.581095	+	0.813836i	$0.302624\pi$
$449$			6.95316e6i			1.62767i	−0.581095	+	0.813836i	$0.697376\pi$
$450$	−2.50500e6	+	3.37030e6i	−0.583146	+	0.784580i
$451$		−	306332.i		−	0.0709171i
$452$	−814853.	−	313488.i	−0.187600	−	0.0721729i
$453$	261376.	+	1.57039e6i	0.0598439	+	0.359552i
$454$	−454528.	+	312140.i	−0.103495	+	0.0710737i
$455$	−282757.			−0.0640301
$456$	337256.	−	142364.i	0.0759535	−	0.0320619i
$457$	6.52994e6			1.46258			0.731288	−	0.682068i	$-0.238919\pi$
$457$	6.52994e6			1.46258			0.731288	+	0.682068i	$0.238919\pi$
$458$	3.51081e6	−	2.41100e6i	0.782067	−	0.537072i
$459$	−3.80825e6	−	7.05820e6i	−0.843711	−	1.56373i
$460$	1.06823e6	+	410968.i	0.235381	+	0.0905551i
$461$			8.99176e6i			1.97057i	0.170915	+	0.985286i	$0.445328\pi$
$461$			8.99176e6i			1.97057i	−0.170915	+	0.985286i	$0.554672\pi$
$462$	1.35865e6	+	1.41045e6i	0.296144	+	0.307434i
$463$		−	851678.i		−	0.184639i	−0.995729	−	0.0923194i	$-0.970572\pi$
$463$		−	851678.i		−	0.184639i	0.995729	−	0.0923194i	$-0.0294281\pi$
$464$	3.38951e6	−	3.75320e6i	0.730873	−	0.809294i
$465$	209290.	−	34834.2i	0.0448864	−	0.00747091i
$466$	1.87771e6	+	2.73426e6i	0.400556	+	0.583277i
$467$	−954227.			−0.202469			−0.101235	−	0.994863i	$-0.532279\pi$
$467$	−954227.			−0.202469			−0.101235	+	0.994863i	$0.532279\pi$
$468$	−200391.	+	5.35474e6i	−0.0422926	+	1.13012i
$469$	807178.			0.169448
$470$	−281474.	−	409873.i	−0.0587750	−	0.0855863i
$471$	3.56282e6	−	592996.i	0.740017	−	0.123169i
$472$	−995563.	−	4.16728e6i	−0.205690	−	0.860989i
$473$		−	8.29835e6i		−	1.70545i
$474$	5.17940e6	+	5.37686e6i	1.05885	+	1.09921i
$475$		−	396308.i		−	0.0805933i
$476$	−1.19202e6	+	3.09842e6i	−0.241137	+	0.626791i
$477$	1.83528e6	+	5.36059e6i	0.369322	+	1.07874i
$478$	1.56739e6	−	1.07638e6i	0.313766	−	0.215474i
$479$	−8.23679e6			−1.64028			−0.820142	−	0.572160i	$-0.806106\pi$
$479$	−8.23679e6			−1.64028			−0.820142	+	0.572160i	$0.806106\pi$
$480$	24321.7	+	755760.i	0.00481827	+	0.149720i
$481$	−3.16971e6			−0.624679
$482$	−7.43275e6	+	5.10432e6i	−1.45724	+	1.00074i
$483$	−535651.	−	3.21828e6i	−0.104475	−	0.627705i
$484$	509835.	−	1.32522e6i	0.0989272	−	0.257143i
$485$		−	946563.i		−	0.182724i
$486$	−749224.	+	5.15285e6i	−0.143887	+	0.989594i
$487$			524200.i			0.100155i	0.998745	+	0.0500777i	$0.0159469\pi$
$487$			524200.i			0.100155i	−0.998745	+	0.0500777i	$0.984053\pi$
$488$	−1.10956e6	−	4.64445e6i	−0.210912	−	0.882846i
$489$	461149.	+	2.77066e6i	0.0872106	+	0.523976i
$490$	64385.9	+	93756.7i	0.0121144	+	0.0176405i
$491$	898039.			0.168109			0.0840546	−	0.996461i	$-0.473213\pi$
$491$	898039.			0.168109			0.0840546	+	0.996461i	$0.473213\pi$
$492$	−330270.	−	67752.1i	−0.0615116	−	0.0126186i
$493$	1.04563e7			1.93758
$494$	−286282.	−	416874.i	−0.0527808	−	0.0768577i
$495$	298732.	+	872556.i	0.0547986	+	0.160059i
$496$	−1.11551e6	+	1.23520e6i	−0.203596	+	0.225442i
$497$			543970.i			0.0987833i
$498$	2.81732e6	−	2.71386e6i	0.509053	−	0.490359i
$499$		−	5.14482e6i		−	0.924951i	−0.886632	−	0.462475i	$-0.846961\pi$
$499$		−	5.14482e6i		−	0.924951i	0.886632	−	0.462475i	$-0.153039\pi$
$500$	1.54557e6	+	594606.i	0.276480	+	0.106366i
$501$	169712.	−	28246.9i	0.0302077	−	0.00502778i
$502$	3.86894e6	−	2.65693e6i	0.685225	−	0.470567i
$503$	−2.21559e6			−0.390453			−0.195227	−	0.980758i	$-0.562544\pi$
$503$	−2.21559e6			−0.390453			−0.195227	+	0.980758i	$0.562544\pi$
$504$	1.82116e6	−	1.15287e6i	0.319354	−	0.202164i
$505$	497448.			0.0867999
$506$	−9.02739e6	+	6.19942e6i	−1.56742	+	1.07640i
$507$	1.59265e6	−	265081.i	0.275170	−	0.0457993i
$508$	9.99505e6	+	3.84527e6i	1.71841	+	0.661100i
$509$			7.25379e6i			1.24100i	0.784208	+	0.620498i	$0.213070\pi$
$509$			7.25379e6i			1.24100i	−0.784208	+	0.620498i	$0.786930\pi$
$510$	−1.12599e6	+	1.08464e6i	−0.191694	+	0.184654i
$511$		−	899487.i		−	0.152385i
$512$	−3.83719e6	−	4.52331e6i	−0.646901	−	0.762574i
$513$	−233345.	−	432480.i	−0.0391475	−	0.0725559i
$514$	4.68990e6	+	6.82928e6i	0.782989	+	1.14016i
$515$	−1.18964e6			−0.197650
$516$	−8.94683e6	−	1.83536e6i	−1.47926	−	0.303457i
$517$	4.75733e6			0.782776
$518$	721768.	+	1.05102e6i	0.118188	+	0.172101i
$519$	1.12016e6	+	6.73008e6i	0.182541	+	1.09674i
$520$	1.01599e6	−	242720.i	0.164771	−	0.0393638i
$521$		−	380392.i		−	0.0613956i	−0.999529	−	0.0306978i	$-0.990227\pi$
$521$		−	380392.i		−	0.0613956i	0.999529	−	0.0306978i	$-0.00977295\pi$
$522$	−5.44860e6	−	4.04972e6i	−0.875202	−	0.650502i
$523$		−	7.06775e6i		−	1.12987i	−0.825137	−	0.564933i	$-0.808902\pi$
$523$		−	7.06775e6i		−	1.12987i	0.825137	−	0.564933i	$-0.191098\pi$
$524$	2.59335e6	−	6.74093e6i	0.412603	−	1.07249i
$525$	−383105.	−	2.30176e6i	−0.0606623	−	0.364469i
$526$	−6.52838e6	+	4.48326e6i	−1.02882	+	0.706528i
$527$	−3.44123e6			−0.539744
$528$	−6.09258e6	−	3.90168e6i	−0.951078	−	0.609070i
$529$	1.18075e7			1.83450
$530$	910510.	−	625278.i	0.140797	−	0.0966904i
$531$	−5.44149e6	+	1.86297e6i	−0.837494	+	0.286728i
$532$	−73038.9	+	189851.i	−0.0111886	+	0.0290826i
$533$			465751.i			0.0710127i
$534$	−7.16603e6	−	7.43922e6i	−1.08749	−	1.12895i
$535$		−	533798.i		−	0.0806292i
$536$	−2.90032e6	+	692887.i	−0.436048	+	0.104172i
$537$	−5.04802e6	+	840193.i	−0.755414	+	0.125731i
$538$	448978.	+	653787.i	0.0668758	+	0.0973824i
$539$	−1.08822e6			−0.161341
$540$	1.00681e6	−	129092.i	0.148581	−	0.0190509i
$541$	−1.16918e7			−1.71746			−0.858730	−	0.512429i	$-0.828746\pi$
$541$	−1.16918e7			−1.71746			−0.858730	+	0.512429i	$0.828746\pi$
$542$	5.15148e6	+	7.50143e6i	0.753241	+	1.09685i
$543$	−92999.6	+	15478.9i	−0.0135357	+	0.00225289i
$544$	1.62340e6	−	1.21563e7i	0.235195	−	1.76119i
$545$		−	1.39015e6i		−	0.200480i
$546$	−2.06571e6	−	2.14446e6i	−0.296543	−	0.307848i
$547$		−	3.16762e6i		−	0.452653i	−0.974051	−	0.226327i	$-0.927328\pi$
$547$		−	3.16762e6i		−	0.452653i	0.974051	−	0.226327i	$-0.0726716\pi$
$548$	1.07781e7	+	4.14652e6i	1.53317	+	0.589837i
$549$	−6.06457e6	+	2.07630e6i	−0.858755	+	0.294007i
$550$	−6.45651e6	+	4.43391e6i	−0.910104	+	0.625000i
$551$	640692.			0.0899022
$552$	4.68727e6	+	1.11040e7i	0.654745	+	1.55107i
$553$	−4.14848e6			−0.576867
$554$	1.13816e6	−	781614.i	0.157554	−	0.108198i
$555$	98580.6	+	592289.i	0.0135850	+	0.0816208i
$556$	−6.98930e6	−	2.68890e6i	−0.958841	−	0.368882i
$557$		−	5.07202e6i		−	0.692696i	−0.938106	−	0.346348i	$-0.887422\pi$
$557$		−	5.07202e6i		−	0.692696i	0.938106	−	0.346348i	$-0.112578\pi$
$558$	1.79317e6	+	1.33279e6i	0.243802	+	0.181208i
$559$			1.26169e7i			1.70775i
$560$	−311830.	−	281613.i	−0.0420192	−	0.0379475i
$561$	−2.45595e6	−	1.47557e7i	−0.329467	−	1.97949i
$562$	4.95360e6	+	7.21328e6i	0.661577	+	0.963367i
$563$	3.64457e6			0.484591			0.242295	−	0.970203i	$-0.422100\pi$
$563$	3.64457e6			0.484591			0.242295	+	0.970203i	$0.422100\pi$
$564$	1.05219e6	−	5.12910e6i	0.139282	−	0.678958i
$565$	228472.			0.0301100
$566$	−6.19859e6	−	9.02619e6i	−0.813303	−	1.18431i
$567$	−1.77334e6	−	2.28627e6i	−0.231651	−	0.298655i
$568$	−466947.	−	1.95457e6i	−0.0607291	−	0.254203i
$569$			1.10699e6i			0.143339i	0.997428	+	0.0716693i	$0.0228326\pi$
$569$			1.10699e6i			0.143339i	−0.997428	+	0.0716693i	$0.977167\pi$
$570$	−68993.1	+	66459.4i	−0.00889443	+	0.00856780i
$571$			6.48281e6i			0.832095i	0.909343	+	0.416048i	$0.136585\pi$
$571$			6.48281e6i			0.832095i	−0.909343	+	0.416048i	$0.863415\pi$
$572$	−3.58864e6	+	9.32800e6i	−0.458606	+	1.19206i
$573$	−3.99257e6	+	664523.i	−0.508002	+	0.0845520i
$574$	154434.	−	106055.i	0.0195643	−	0.0134355i
$575$	1.30482e7			1.64582
$576$	−5.55409e6	+	5.70574e6i	−0.697520	+	0.716566i
$577$	−2.43686e6			−0.304713			−0.152357	−	0.988326i	$-0.548686\pi$
$577$	−2.43686e6			−0.304713			−0.152357	+	0.988326i	$0.548686\pi$
$578$	1.42822e7	−	9.80807e6i	1.77818	−	1.22114i
$579$	1.03405e7	−	1.72107e6i	1.28187	−	0.213354i
$580$	−475182.	+	1.23515e6i	−0.0586529	+	0.152457i
$581$			2.17369e6i			0.267151i
$582$	7.17885e6	−	6.91522e6i	0.878511	−	0.846249i
$583$			1.05682e7i			1.28774i
$584$	772125.	+	3.23200e6i	0.0936819	+	0.392138i
$585$	−454196.	−	1.32665e6i	−0.0548724	−	0.160275i
$586$	−6.34180e6	−	9.23473e6i	−0.762902	−	1.11091i
$587$	8.97828e6			1.07547			0.537735	−	0.843114i	$-0.319280\pi$
$587$	8.97828e6			1.07547			0.537735	+	0.843114i	$0.319280\pi$
$588$	−240684.	+	1.17326e6i	−0.0287080	+	0.139943i
$589$	−210856.			−0.0250437
$590$	634715.	+	924251.i	0.0750669	+	0.109310i
$591$	196152.	+	1.17851e6i	0.0231006	+	0.138792i
$592$	−3.49562e6	−	3.15689e6i	−0.409940	−	0.370217i
$593$		−	164480.i		−	0.0192078i	−0.999954	−	0.00960388i	$-0.996943\pi$
$593$		−	164480.i		−	0.0192078i	0.999954	−	0.00960388i	$-0.00305706\pi$
$594$	−4.43515e6	+	8.64017e6i	−0.515753	+	1.00475i
$595$		−	868747.i		−	0.100601i
$596$	3.48213e6	+	1.33964e6i	0.401541	+	0.154480i
$597$	−1.24241e6	−	7.46461e6i	−0.142669	−	0.857178i
$598$	1.37254e7	−	9.42567e6i	1.56953	−	1.07785i
$599$	−4.67805e6			−0.532718			−0.266359	−	0.963874i	$-0.585821\pi$
$599$	−4.67805e6			−0.532718			−0.266359	+	0.963874i	$0.585821\pi$
$600$	3.35240e6	+	7.94171e6i	0.380169	+	0.900609i
$601$	−4.85047e6			−0.547769			−0.273885	−	0.961763i	$-0.588309\pi$
$601$	−4.85047e6			−0.547769			−0.273885	+	0.961763i	$0.588309\pi$
$602$	4.18353e6	−	2.87297e6i	0.470491	−	0.323102i
$603$	1.29658e6	+	3.78714e6i	0.145214	+	0.424149i
$604$	3.05011e6	+	1.17343e6i	0.340191	+	0.130877i
$605$			371570.i			0.0412717i
$606$	3.63416e6	+	3.77270e6i	0.401996	+	0.417322i
$607$			2.82378e6i			0.311071i	0.987830	+	0.155536i	$0.0497103\pi$
$607$			2.82378e6i			0.311071i	−0.987830	+	0.155536i	$0.950290\pi$
$608$	99471.1	−	744862.i	0.0109128	−	0.0817178i
$609$	3.72114e6	−	619346.i	0.406567	−	0.0676691i
$610$	707393.	+	1.03008e6i	0.0769726	+	0.112085i
$611$	−7.23311e6			−0.783830
$612$	−1.64520e7	−	615687.i	−1.77558	−	0.0664479i
$613$	−1.10547e7			−1.18822			−0.594111	−	0.804383i	$-0.702496\pi$
$613$	−1.10547e7			−1.18822			−0.594111	+	0.804383i	$0.702496\pi$
$614$	−421426.	−	613667.i	−0.0451129	−	0.0656919i
$615$	87029.8	−	14485.2i	0.00927855	−	0.00154432i
$616$	3.91015e6	−	934135.i	0.415185	−	0.0991877i
$617$			5.50481e6i			0.582143i	0.956701	+	0.291072i	$0.0940118\pi$
$617$			5.50481e6i			0.582143i	−0.956701	+	0.291072i	$0.905988\pi$
$618$	−8.69101e6	−	9.02234e6i	−0.915375	−	0.950272i
$619$		−	3.99239e6i		−	0.418799i	−0.977830	−	0.209400i	$-0.932849\pi$
$619$		−	3.99239e6i		−	0.418799i	0.977830	−	0.209400i	$-0.0671510\pi$
$620$	156386.	−	406496.i	0.0163387	−	0.0424694i
$621$	1.42392e7	−	7.68275e6i	1.48169	−	0.799444i
$622$	−36867.7	+	25318.3i	−0.00382094	+	0.00262397i
$623$	5.73968e6			0.592472
$624$	9.26323e6	+	5.93217e6i	0.952360	+	0.609890i
$625$	9.11314e6			0.933185
$626$	1.11498e7	−	7.65697e6i	1.13719	−	0.780946i
$627$	−150484.	−	904135.i	−0.0152870	−	0.0918469i
$628$	2.66222e6	−	6.91994e6i	0.269367	−	0.700169i
$629$		−	9.73868e6i		−	0.981462i
$630$	−336466.	+	452691.i	−0.0337746	+	0.0454412i
$631$		−	2.67616e6i		−	0.267571i	−0.991010	−	0.133785i	$-0.957287\pi$
$631$		−	2.67616e6i		−	0.267571i	0.991010	−	0.133785i	$-0.0427133\pi$
$632$	1.49061e7	−	3.56108e6i	1.48447	−	0.354641i
$633$	−24242.5	−	145653.i	−0.00240474	−	0.0144481i
$634$	−622533.	−	906513.i	−0.0615091	−	0.0895675i
$635$	−2.80245e6			−0.275806
$636$	1.13940e7	+	2.33738e6i	1.11695	+	0.229132i
$637$	1.65454e6			0.161558
$638$	−7.16808e6	−	1.04379e7i	−0.697190	−	1.01523i
$639$	−2.55221e6	+	873787.i	−0.247266	+	0.0846552i
$640$	1.36219e6	+	744205.i	0.131459	+	0.0718195i
$641$			1.83364e7i			1.76266i	0.472503	+	0.881329i	$0.343351\pi$
$641$			1.83364e7i			1.76266i	−0.472503	+	0.881329i	$0.656649\pi$
$642$	4.04839e6	−	3.89972e6i	0.387654	−	0.373418i
$643$			1.35723e6i			0.129457i	0.997903	+	0.0647284i	$0.0206181\pi$
$643$			1.35723e6i			0.129457i	−0.997903	+	0.0647284i	$0.979382\pi$
$644$	−6.25075e6	−	2.40477e6i	−0.593905	−	0.228485i
$645$	2.35759e6	−	392397.i	0.223135	−	0.0371387i
$646$	1.28081e6	−	879577.i	0.120755	−	0.0829264i
$647$	−197730.			−0.0185700			−0.00928499	−	0.999957i	$-0.502956\pi$
$647$	−197730.			−0.0185700			−0.00928499	+	0.999957i	$0.502956\pi$
$648$	8.33443e6	+	6.69270e6i	0.779720	+	0.626129i
$649$	−1.07277e7			−0.999753
$650$	9.81656e6	−	6.74137e6i	0.911331	−	0.625842i
$651$	−1.22465e6	+	203831.i	−0.113256	+	0.0188503i
$652$	5.38135e6	+	2.07030e6i	0.495761	+	0.190728i
$653$			8.41551e6i			0.772320i	0.922432	+	0.386160i	$0.126199\pi$
$653$			8.41551e6i			0.772320i	−0.922432	+	0.386160i	$0.873801\pi$
$654$	1.05431e7	−	1.01559e7i	0.963881	−	0.928484i
$655$			1.89005e6i			0.172135i
$656$	−463868.	+	513640.i	−0.0420857	+	0.0466015i
$657$	4.22024e6	−	1.44486e6i	0.381438	−	0.130591i
$658$	1.64704e6	+	2.39836e6i	0.148299	+	0.215948i
$659$	−1.77751e7			−1.59440			−0.797202	−	0.603713i	$-0.793687\pi$
$659$	−1.77751e7			−1.59440			−0.797202	+	0.603713i	$0.793687\pi$
$660$	1.85463e6	+	380461.i	0.165729	+	0.0339977i
$661$	−2.43728e6			−0.216971			−0.108486	−	0.994098i	$-0.534600\pi$
$661$	−2.43728e6			−0.216971			−0.108486	+	0.994098i	$0.534600\pi$
$662$	−2.10075e6	−	3.05904e6i	−0.186307	−	0.271294i
$663$	3.73405e6	+	2.24348e7i	0.329911	+	1.98216i
$664$	−1.86591e6	−	7.81040e6i	−0.164236	−	0.687469i
$665$		−	53231.1i		−	0.00466779i
$666$	−3.77180e6	+	5.07467e6i	−0.329505	+	0.443325i
$667$			2.10944e7i			1.83592i
$668$	126812.	−	329625.i	0.0109956	−	0.0285811i
$669$	710869.	+	4.27102e6i	0.0614079	+	0.368949i
$670$	643256.	−	441746.i	0.0553601	−	0.0380176i
$671$	−1.19560e7			−1.02513
$672$	−142318.	−	4.42231e6i	−0.0121573	−	0.377769i
$673$	−1.90352e7			−1.62001			−0.810007	−	0.586420i	$-0.800537\pi$
$673$	−1.90352e7			−1.62001			−0.810007	+	0.586420i	$0.800537\pi$
$674$	−8.61082e6	+	5.91335e6i	−0.730121	+	0.501399i
$675$	1.01841e7	−	5.49481e6i	0.860323	−	0.464187i
$676$	1.19006e6	−	3.09335e6i	0.100162	−	0.260353i
$677$			1.52729e7i			1.28071i	0.768081	+	0.640353i	$0.221212\pi$
$677$			1.52729e7i			1.28071i	−0.768081	+	0.640353i	$0.778788\pi$
$678$	1.66912e6	+	1.73275e6i	0.139449	+	0.144765i
$679$			5.53879e6i			0.461042i
$680$	745738.	+	3.12155e6i	0.0618463	+	0.258879i
$681$	1.49882e6	−	249464.i	0.123846	−	0.0206130i
$682$	2.35907e6	+	3.43520e6i	0.194213	+	0.282807i
$683$	2.23444e7			1.83281			0.916405	−	0.400251i	$-0.131077\pi$
$683$	2.23444e7			1.83281			0.916405	+	0.400251i	$0.131077\pi$
$684$	−1.00807e6	−	37725.3i	−0.0823856	−	0.00308313i
$685$	−3.02201e6			−0.246076
$686$	−376753.	−	548615.i	−0.0305665	−	0.0445100i
$687$	−1.15770e7	+	1.92689e6i	−0.935849	+	0.155763i
$688$	−1.25659e7	+	1.39142e7i	−1.01210	+	1.12070i
$689$		−	1.60680e7i		−	1.28947i
$690$	−2.18814e6	−	2.27156e6i	−0.174966	−	0.181636i
$691$		−	1.29017e7i		−	1.02790i	−0.857820	−	0.513951i	$-0.828181\pi$
$691$		−	1.29017e7i		−	1.02790i	0.857820	−	0.513951i	$-0.171819\pi$
$692$	1.30716e7	+	5.02887e6i	1.03768	+	0.399213i
$693$	−1.74803e6	−	5.10574e6i	−0.138266	−	0.403855i
$694$	−4.10950e6	+	2.82213e6i	−0.323885	+	0.222423i
$695$	1.95968e6			0.153895
$696$	−1.28390e7	+	5.41966e6i	−1.00463	+	0.424081i
$697$	−1.43098e6			−0.111571
$698$	1.49003e7	−	1.02325e7i	1.15759	−	0.794960i
$699$	−1.50068e6	−	9.01632e6i	−0.116170	−	0.697970i
$700$	−4.47062e6	−	1.71992e6i	−0.344844	−	0.132667i
$701$			9.32173e6i			0.716475i	0.933630	+	0.358238i	$0.116622\pi$
$701$			9.32173e6i			0.716475i	−0.933630	+	0.358238i	$0.883378\pi$
$702$	6.74325e6	−	1.31366e7i	0.516448	−	1.00610i
$703$		−	596723.i		−	0.0455391i
$704$	−1.32479e7	+	6.71299e6i	−1.00743	+	0.510486i
$705$	224956.	+	1.35157e6i	0.0170461	+	0.102416i
$706$	−2.61873e6	−	3.81332e6i	−0.197733	−	0.287933i
$707$	−2.91080e6			−0.219010
$708$	−2.37266e6	+	1.15660e7i	−0.177890	+	0.867159i
$709$	−1.85586e6			−0.138653			−0.0693264	−	0.997594i	$-0.522085\pi$
$709$	−1.85586e6			−0.138653			−0.0693264	+	0.997594i	$0.522085\pi$
$710$	297699.	+	433500.i	0.0221631	+	0.0322733i
$711$	−6.66377e6	−	1.94639e7i	−0.494363	−	1.44397i
$712$	−2.06236e7	+	4.92698e6i	−1.52463	+	0.364234i
$713$		−	6.94234e6i		−	0.511425i
$714$	6.58868e6	−	6.34672e6i	0.483674	−	0.465912i
$715$		−	2.61542e6i		−	0.191327i
$716$	−3.77199e6	+	9.80458e6i	−0.274971	+	0.714737i
$717$	−5.16852e6	+	860248.i	−0.375464	+	0.0624922i
$718$	−4.29464e6	+	2.94927e6i	−0.310896	+	0.213503i
$719$	−1.95537e7			−1.41061			−0.705303	−	0.708906i	$-0.749189\pi$
$719$	−1.95537e7			−1.41061			−0.705303	+	0.708906i	$0.749189\pi$
$720$	820384.	−	1.91541e6i	0.0589775	−	0.137699i
$721$	6.96113e6			0.498702
$722$	−1.14679e7	+	7.87543e6i	−0.818734	+	0.562252i
$723$	2.45098e7	−	4.07941e6i	1.74379	−	0.290236i
$724$	−69491.3	+	180630.i	−0.00492702	+	0.0128069i
$725$			1.50870e7i			1.06600i
$726$	−2.81803e6	+	2.71454e6i	−0.198429	+	0.191142i
$727$		−	1.42834e7i		−	1.00229i	−0.865362	−	0.501147i	$-0.832912\pi$
$727$		−	1.42834e7i		−	1.00229i	0.865362	−	0.501147i	$-0.167088\pi$
$728$	−5.94504e6	+	1.42027e6i	−0.415744	+	0.0993213i
$729$	7.87826e6	−	1.19927e7i	0.549050	−	0.835790i
$730$	−492264.	−	716818.i	−0.0341893	−	0.0497854i
$731$	−3.87645e7			−2.68312
$732$	−2.64434e6	+	1.28903e7i	−0.182406	+	0.889173i
$733$	1.56773e7			1.07773			0.538865	−	0.842392i	$-0.318853\pi$
$733$	1.56773e7			1.07773			0.538865	+	0.842392i	$0.318853\pi$
$734$	−1.42699e7	−	2.07794e7i	−0.977647	−	1.42362i
$735$	−51457.7	−	309166.i	−0.00351344	−	0.0211093i
$736$	2.45242e7	+	3.27503e6i	1.66878	+	0.222854i
$737$			7.46617e6i			0.506325i
$738$	745663.	+	554220.i	0.0503966	+	0.0374577i
$739$			1.55444e7i			1.04704i	0.852013	+	0.523520i	$0.175381\pi$
$739$			1.55444e7i			1.04704i	−0.852013	+	0.523520i	$0.824619\pi$
$740$	1.15038e6	+	442571.i	0.0772258	+	0.0297101i
$741$	228798.	+	1.37466e6i	0.0153076	+	0.0919706i
$742$	−5.32783e6	+	3.65880e6i	−0.355255	+	0.243966i
$743$	−4.14309e6			−0.275329			−0.137664	−	0.990479i	$-0.543960\pi$
$743$	−4.14309e6			−0.275329			−0.137664	+	0.990479i	$0.543960\pi$
$744$	4.22540e6	−	1.78365e6i	0.279857	−	0.118135i
$745$	−976333.			−0.0644477
$746$	−7.00555e6	+	4.81095e6i	−0.460888	+	0.316507i
$747$	−1.01986e7	+	3.49163e6i	−0.668710	+	0.228943i
$748$	−2.86595e7	−	1.10258e7i	−1.87290	−	0.720537i
$749$			3.12351e6i			0.203441i
$750$	−3.16590e6	−	3.28659e6i	−0.205515	−	0.213350i
$751$		−	2.09047e7i		−	1.35252i	−0.736663	−	0.676260i	$-0.763599\pi$
$751$		−	2.09047e7i		−	1.35252i	0.736663	−	0.676260i	$-0.236401\pi$
$752$	−7.97683e6	−	7.20387e6i	−0.514382	−	0.464538i
$753$	−1.27580e7	+	2.12344e6i	−0.819964	+	0.136475i
$754$	1.08984e7	+	1.58700e7i	0.698129	+	1.01659i
$755$	−855202.			−0.0546011
$756$	−5.89135e6	+	755379.i	−0.374895	+	0.0480685i
$757$	−1.53911e7			−0.976181			−0.488090	−	0.872793i	$-0.662306\pi$
$757$	−1.53911e7			−0.976181			−0.488090	+	0.872793i	$0.662306\pi$
$758$	−1.46297e7	−	2.13033e7i	−0.924831	−	1.34671i
$759$	2.97682e7	−	4.95462e6i	1.87563	−	0.312181i
$760$	45693.9	+	191268.i	0.00286962	+	0.0120118i
$761$		−	1.39304e7i		−	0.871969i	−0.899954	−	0.435984i	$-0.856400\pi$
$761$		−	1.39304e7i		−	0.871969i	0.899954	−	0.435984i	$-0.143600\pi$
$762$	−2.04736e7	−	2.12541e7i	−1.27734	−	1.32604i
$763$			8.13445e6i			0.505844i
$764$	−2.98333e6	+	7.75462e6i	−0.184913	+	0.480648i
$765$	4.07601e6	−	1.39548e6i	0.251815	−	0.0862126i
$766$	−2.31904e7	+	1.59256e7i	−1.42803	+	0.980675i
$767$	1.63105e7			1.00110
$768$	4.30751e6	+	1.57679e7i	0.263526	+	0.964652i
$769$	2.33154e7			1.42176			0.710881	−	0.703312i	$-0.248296\pi$
$769$	2.33154e7			1.42176			0.710881	+	0.703312i	$0.248296\pi$
$770$	−867223.	+	595552.i	−0.0527113	+	0.0361987i
$771$	−3.74820e6	−	2.25198e7i	−0.227084	−	1.36436i
$772$	7.72661e6	−	2.00839e7i	0.466601	−	1.21284i
$773$		−	2.21698e7i		−	1.33448i	−0.744841	−	0.667242i	$-0.767475\pi$
$773$		−	2.21698e7i		−	1.33448i	0.744841	−	0.667242i	$-0.232525\pi$
$774$	2.01996e7	+	1.50135e7i	1.21196	+	0.900803i
$775$		−	4.96525e6i		−	0.296953i
$776$	−4.75453e6	−	1.99018e7i	−0.283435	−	1.18642i
$777$	−576842.	−	3.46576e6i	−0.0342771	−	0.205943i
$778$	3.25469e6	+	4.73938e6i	0.192779	+	0.280719i
$779$	−87681.3			−0.00517682
$780$	−2.81980e6	−	578457.i	−0.165952	−	0.0340435i
$781$	−5.03157e6			−0.295172
$782$	2.89596e7	+	4.21701e7i	1.69346	+	2.46597i
$783$	8.88319e6	+	1.64641e7i	0.517803	+	0.959694i
$784$	1.82467e6	+	1.64785e6i	0.106021	+	0.0957478i
$785$			1.94024e6i			0.112378i
$786$	−1.43343e7	+	1.38079e7i	−0.827601	+	0.797209i
$787$			2.03874e7i			1.17335i	0.809824	+	0.586673i	$0.199563\pi$
$787$			2.03874e7i			1.17335i	−0.809824	+	0.586673i	$0.800437\pi$
$788$	2.28898e6	+	880610.i	0.131319	+	0.0505205i
$789$	2.15276e7	−	3.58305e6i	1.23113	−	0.204909i
$790$	−3.30600e6	+	2.27034e6i	−0.188467	+	0.129427i
$791$	−1.33690e6			−0.0759725
$792$	1.06637e7	+	1.68452e7i	0.604083	+	0.954254i
$793$	1.81781e7			1.02651
$794$	1.10739e7	−	7.60483e6i	0.623376	−	0.428093i
$795$	−3.00244e6	+	499727.i	−0.168483	+	0.0280424i
$796$	−1.44982e7	−	5.57772e6i	−0.811022	−	0.312014i
$797$		−	1.27632e7i		−	0.711727i	−0.934538	−	0.355864i	$-0.884187\pi$
$797$		−	1.27632e7i		−	0.711727i	0.934538	−	0.355864i	$-0.115813\pi$
$798$	403711.	−	388886.i	0.0224421	−	0.0216180i
$799$		−	2.22231e7i		−	1.23151i
$800$	1.75400e7	+	2.34235e6i	0.968959	+	0.129398i
$801$	9.21974e6	+	2.69296e7i	0.507736	+	1.48303i
$802$	1.55103e7	+	2.25856e7i	0.851501	+	1.23993i
$803$	8.32001e6			0.455339
$804$	8.04962e6	+	1.65131e6i	0.439173	+	0.0900924i
$805$	1.75261e6			0.0953224
$806$	−3.58676e6	−	5.22292e6i	−0.194475	−	0.283188i
$807$	−358826.	−	2.15589e6i	−0.0193955	−	0.116531i
$808$	1.04590e7	−	2.49865e6i	0.563587	−	0.134641i
$809$			2.60306e7i			1.39834i	0.714955	+	0.699171i	$0.246447\pi$
$809$			2.60306e7i			1.39834i	−0.714955	+	0.699171i	$0.753553\pi$
$810$	−2.66442e6	−	851478.i	−0.142689	−	0.0455996i
$811$		−	7.32451e6i		−	0.391045i	−0.980699	−	0.195522i	$-0.937360\pi$
$811$		−	7.32451e6i		−	0.391045i	0.980699	−	0.195522i	$-0.0626402\pi$
$812$	2.78051e6	−	7.22743e6i	0.147991	−	0.384675i
$813$	−4.11710e6	−	2.47362e7i	−0.218457	−	1.31252i
$814$	−9.72160e6	+	6.67615e6i	−0.514253	+	0.353155i
$815$	−1.50884e6			−0.0795702
$816$	−1.82261e7	+	2.84605e7i	−0.958227	+	1.49630i
$817$	−2.37523e6			−0.124495
$818$	−4.92729e6	+	3.38374e6i	−0.257469	+	0.176813i
$819$	2.65772e6	+	7.76283e6i	0.138452	+	0.404399i
$820$	65030.5	−	169035.i	0.00337740	−	0.00877893i
$821$			9.06360e6i			0.469292i	0.972081	+	0.234646i	$0.0753931\pi$
$821$			9.06360e6i			0.469292i	−0.972081	+	0.234646i	$0.924607\pi$
$822$	−2.20776e7	−	2.29192e7i	−1.13965	−	1.18310i
$823$		−	2.65152e7i		−	1.36457i	−0.731086	−	0.682285i	$-0.760986\pi$
$823$		−	2.65152e7i		−	1.36457i	0.731086	−	0.682285i	$-0.239014\pi$
$824$	−2.50124e7	+	5.97547e6i	−1.28333	+	0.306587i
$825$	2.12906e7	−	3.54361e6i	1.08906	−	0.181264i
$826$	−3.71402e6	−	5.40824e6i	−0.189406	−	0.275807i
$827$	2.68499e7			1.36515			0.682573	−	0.730818i	$-0.260861\pi$
$827$	2.68499e7			1.36515			0.682573	+	0.730818i	$0.260861\pi$
$828$	1.24209e6	−	3.31902e7i	0.0629616	−	1.68242i
$829$	−2.05212e7			−1.03709			−0.518546	−	0.855050i	$-0.673527\pi$
$829$	−2.05212e7			−1.03709			−0.518546	+	0.855050i	$0.673527\pi$
$830$	1.18960e6	+	1.73225e6i	0.0599383	+	0.0872803i
$831$	−3.75313e6	+	624672.i	−0.188535	+	0.0313797i
$832$	2.01423e7	−	1.02065e7i	1.00879	−	0.511174i
$833$			5.08345e6i			0.253832i
$834$	1.43167e7	+	1.48625e7i	0.712734	+	0.739905i
$835$			92421.6i			0.00458730i
$836$	−1.75607e6	−	675589.i	−0.0869012	−	0.0334324i
$837$	−2.92352e6	−	5.41844e6i	−0.144242	−	0.267338i
$838$	−2.79796e7	+	1.92145e7i	−1.37636	+	0.945191i
$839$	1.13348e7			0.555915			0.277958	−	0.960593i	$-0.410343\pi$
$839$	1.13348e7			0.555915			0.277958	+	0.960593i	$0.410343\pi$
$840$	450286.	+	1.06671e6i	0.0220186	+	0.0521614i
$841$	−3.87932e6			−0.189132
$842$	−2.26445e7	+	1.55507e7i	−1.10073	+	0.755911i
$843$	−3.95896e6	−	2.37861e7i	−0.191872	−	1.15280i
$844$	−282897.	−	108835.i	−0.0136701	−	0.00525913i
$845$			867325.i			0.0417869i
$846$	−8.60704e6	+	1.15801e7i	−0.413455	+	0.556273i
$847$		−	2.17423e6i		−	0.104135i
$848$	1.60030e7	−	1.77201e7i	0.764208	−	0.846206i
$849$	4.95396e6	+	2.97642e7i	0.235876	+	1.41718i
$850$	2.07123e7	+	3.01606e7i	0.983289	+	1.43183i
$851$	1.96468e7			0.929967
$852$	−1.11284e6	+	5.42476e6i	−0.0525212	+	0.256025i
$853$	3.21406e7			1.51245			0.756226	−	0.654310i	$-0.227041\pi$
$853$	3.21406e7			1.51245			0.756226	+	0.654310i	$0.227041\pi$
$854$	−4.13930e6	−	6.02751e6i	−0.194215	−	0.282809i
$855$	249751.	−	85506.0i	0.0116840	−	0.00400020i
$856$	−2.68124e6	−	1.12233e7i	−0.125069	−	0.523521i
$857$		−	2.75329e6i		−	0.128056i	−0.997948	−	0.0640281i	$-0.979605\pi$
$857$		−	2.75329e6i		−	0.128056i	0.997948	−	0.0640281i	$-0.0203947\pi$
$858$	1.98356e7	−	1.91072e7i	0.919874	−	0.886093i
$859$			3.39979e7i			1.57206i	0.618188	+	0.786031i	$0.287867\pi$
$859$			3.39979e7i			1.57206i	−0.618188	+	0.786031i	$0.712133\pi$
$860$	1.76164e6	−	4.57905e6i	0.0812215	−	0.211120i
$861$	−509253.	+	84760.1i	−0.0234113	+	0.00389658i
$862$	1.57476e7	−	1.08144e7i	0.721848	−	0.495718i
$863$	−416296.			−0.0190272			−0.00951360	−	0.999955i	$-0.503028\pi$
$863$	−416296.			−0.0190272			−0.00951360	+	0.999955i	$0.503028\pi$
$864$	2.05201e7	−	7.77136e6i	0.935181	−	0.354171i
$865$	−3.66506e6			−0.166549
$866$	2.10351e7	−	1.44455e7i	0.953125	−	0.654543i
$867$	−4.70961e7	+	7.83868e6i	−2.12783	+	0.354157i
$868$	−915087.	+	2.37860e6i	−0.0412252	+	0.107157i
$869$		−	3.83723e7i		−	1.72373i
$870$	2.62649e6	−	2.53004e6i	0.117646	−	0.113326i
$871$		−	1.13517e7i		−	0.507007i
$872$	−6.98266e6	−	2.92284e7i	−0.310978	−	1.30171i
$873$	−2.59871e7	+	8.89705e6i	−1.15404	+	0.395103i
$874$	1.77446e6	+	2.58391e6i	0.0785754	+	0.114419i
$875$	2.53575e6			0.111966
$876$	1.84015e6	−	8.97018e6i	0.0810202	−	0.394949i
$877$	−9.63202e6			−0.422881			−0.211441	−	0.977391i	$-0.567815\pi$
$877$	−9.63202e6			−0.422881			−0.211441	+	0.977391i	$0.567815\pi$
$878$	2.49484e7	+	3.63290e7i	1.09221	+	1.59044i
$879$	5.06842e6	+	3.04519e7i	0.221259	+	1.32936i
$880$	2.60485e6	−	2.88434e6i	0.113390	−	0.125557i
$881$			1.23236e7i			0.534931i	0.963567	+	0.267465i	$0.0861861\pi$
$881$			1.23236e7i			0.534931i	−0.963567	+	0.267465i	$0.913814\pi$
$882$	1.96882e6	−	2.64891e6i	0.0852188	−	0.114656i
$883$		−	3.02442e7i		−	1.30539i	−0.757621	−	0.652695i	$-0.773638\pi$
$883$		−	3.02442e7i		−	1.30539i	0.757621	−	0.652695i	$-0.226362\pi$
$884$	4.35743e7	+	1.67638e7i	1.87543	+	0.721508i
$885$	−507269.	−	3.04775e6i	−0.0217711	−	0.130804i
$886$	1.53064e7	−	1.05114e7i	0.655070	−	0.449859i
$887$	−1.71955e7			−0.733847			−0.366924	−	0.930251i	$-0.619589\pi$
$887$	−1.71955e7			−0.733847			−0.366924	+	0.930251i	$0.619589\pi$
$888$	5.04772e6	+	1.19579e7i	0.214814	+	0.508887i
$889$	1.63985e7			0.695904
$890$	4.57406e6	−	3.14116e6i	0.193565	−	0.132928i
$891$	2.11474e7	−	1.64029e7i	0.892406	−	0.692190i
$892$	8.29545e6	+	3.19140e6i	0.349082	+	0.134298i
$893$		−	1.36169e6i		−	0.0571412i
$894$	−7.13270e6	−	7.40463e6i	−0.298477	−	0.309856i
$895$		−	2.74904e6i		−	0.114716i
$896$	−7.97084e6	−	4.35470e6i	−0.331691	−	0.181212i
$897$	−4.52599e7	+	7.53307e6i	−1.87816	+	0.312601i
$898$	−2.22664e7	−	3.24237e7i	−0.921425	−	1.34175i
$899$	8.02708e6			0.331252
$900$	888356.	−	2.37381e7i	0.0365579	−	0.976877i
$901$	4.93675e7			2.02595
$902$	980981.	+	1.42847e6i	0.0401462	+	0.0584596i
$903$	−1.37954e7	+	2.29610e6i	−0.563007	+	0.0937069i
$904$	4.80368e6	−	1.14760e6i	0.195503	−	0.0467056i
$905$		−	50645.6i		−	0.00205551i
$906$	−6.24777e6	−	6.48595e6i	−0.252874	−	0.262514i
$907$			1.13488e7i			0.458069i	0.973418	+	0.229034i	$0.0735568\pi$
$907$			1.13488e7i			0.458069i	−0.973418	+	0.229034i	$0.926443\pi$
$908$	1.11995e6	−	2.91111e6i	0.0450801	−	0.117177i
$909$	−4.67567e6	−	1.36570e7i	−0.187687	−	0.548208i
$910$	1.31854e6	−	905484.i	0.0527824	−	0.0362474i
$911$	2.77713e7			1.10867			0.554333	−	0.832295i	$-0.312973\pi$
$911$	2.77713e7			1.10867			0.554333	+	0.832295i	$0.312973\pi$
$912$	−1.11678e6	+	1.74388e6i	−0.0444610	+	0.0694270i
$913$	−2.01060e7			−0.798268
$914$	−3.04501e7	+	2.09111e7i	−1.20566	+	0.827965i
$915$	−565354.	−	3.39674e6i	−0.0223238	−	0.134125i
$916$	−8.65062e6	+	2.24857e7i	−0.340650	+	0.885457i
$917$		−	1.10596e7i		−	0.434325i
$918$	4.03612e7	+	2.07181e7i	1.58073	+	0.811416i
$919$			1.38857e6i			0.0542351i	0.999632	+	0.0271175i	$0.00863284\pi$
$919$			1.38857e6i			0.0542351i	−0.999632	+	0.0271175i	$0.991367\pi$
$920$	−6.29740e6	+	1.50445e6i	−0.245297	+	0.0586014i
$921$	336807.	+	2.02359e6i	0.0130837	+	0.0786093i
$922$	−2.87947e7	−	4.19299e7i	−1.11554	−	1.62441i
$923$	7.65006e6			0.295570
$924$	−1.08523e7	−	2.22626e6i	−0.418160	−	0.0857819i
$925$	1.40516e7			0.539974
$926$	2.72737e6	+	3.97151e6i	0.104524	+	0.152205i
$927$	1.11818e7	+	3.26604e7i	0.427377	+	1.24831i
$928$	−3.78676e6	+	2.83561e7i	−0.144344	+	1.08088i
$929$			2.72200e7i			1.03478i	0.855749	+	0.517391i	$0.173097\pi$
$929$			2.72200e7i			1.03478i	−0.855749	+	0.517391i	$0.826903\pi$
$930$	−864398.	+	832655.i	−0.0327723	+	0.0315688i
$931$			311481.i			0.0117776i
$932$	−1.75121e7	−	6.73719e6i	−0.660386	−	0.254062i
$933$	121573.	−	20234.6i	0.00457227	−	0.000761009i
$934$	4.44970e6	−	3.05576e6i	0.166903	−	0.114618i
$935$	8.03567e6			0.300603
$936$	−1.62133e7	−	2.56117e7i	−0.604896	−	0.955539i
$937$	−4.76984e7			−1.77482			−0.887411	−	0.460980i	$-0.847498\pi$
$937$	−4.76984e7			−1.77482			−0.887411	+	0.460980i	$0.847498\pi$
$938$	−3.76400e6	+	2.58486e6i	−0.139682	+	0.0959247i
$939$	−3.67670e7	+	6.11951e6i	−1.36080	+	0.226492i
$940$	2.62511e6	+	1.00992e6i	0.0969008	+	0.0372794i
$941$		−	2.43103e7i		−	0.894986i	−0.894287	−	0.447493i	$-0.852317\pi$
$941$		−	2.43103e7i		−	0.894986i	0.894287	−	0.447493i	$-0.147683\pi$
$942$	−1.47150e7	+	1.41746e7i	−0.540297	+	0.520456i
$943$		−	2.88686e6i		−	0.105717i
$944$	1.79875e7	+	1.62445e7i	0.656964	+	0.593303i
$945$	1.36790e6	−	738049.i	0.0498281	−	0.0268847i
$946$	2.65742e7	+	3.86965e7i	0.965456	+	1.40587i
$947$	−2.62596e7			−0.951510			−0.475755	−	0.879578i	$-0.657825\pi$
$947$	−2.62596e7			−0.951510			−0.475755	+	0.879578i	$0.657825\pi$
$948$	−4.13709e7	−	8.48687e6i	−1.49511	−	0.306709i
$949$	−1.26498e7			−0.455952
$950$	1.26912e6	+	1.84804e6i	0.0456239	+	0.0664360i
$951$	497533.	+	2.98926e6i	0.0178390	+	0.107180i
$952$	−4.36367e6	−	1.82657e7i	−0.156048	−	0.653195i
$953$			2.60528e6i			0.0929229i	0.998920	+	0.0464614i	$0.0147945\pi$
$953$			2.60528e6i			0.0929229i	−0.998920	+	0.0464614i	$0.985206\pi$
$954$	−2.57246e7	−	1.91201e7i	−0.915120	−	0.680171i
$955$		−	2.17427e6i		−	0.0771445i
$956$	−3.86203e6	+	1.00386e7i	−0.136669	+	0.355246i
$957$	5.72878e6	+	3.44195e7i	0.202201	+	1.21485i
$958$	3.84094e7	−	2.63770e7i	1.35215	−	0.928565i
$959$	1.76832e7			0.620889
$960$	−2.53362e6	−	3.44634e6i	−0.0887286	−	0.120692i
$961$	2.59874e7			0.907724
$962$	1.47808e7	−	1.01505e7i	0.514946	−	0.353631i
$963$	−1.46550e7	+	5.01734e6i	−0.509236	+	0.174344i
$964$	1.83142e7	−	4.76045e7i	0.634741	−	1.64989i
$965$			5.63120e6i			0.194663i
$966$	1.28039e7	+	1.32920e7i	0.441467	+	0.458297i
$967$		−	1.17060e7i		−	0.402571i	−0.979533	−	0.201286i	$-0.935488\pi$
$967$		−	1.17060e7i		−	0.402571i	0.979533	−	0.201286i	$-0.0645120\pi$
$968$	1.86638e6	+	7.81237e6i	0.0640193	+	0.267975i
$969$	−4.22353e6	+	702964.i	−0.144499	+	0.0240505i
$970$	3.03122e6	+	4.41397e6i	0.103440	+	0.150626i
$971$	1.13519e7			0.386385			0.193192	−	0.981161i	$-0.438116\pi$
$971$	1.13519e7			0.386385			0.193192	+	0.981161i	$0.438116\pi$
$972$	−1.30075e7	−	2.64278e7i	−0.441598	−	0.897213i
$973$	−1.14671e7			−0.388302
$974$	−1.67867e6	−	2.44442e6i	−0.0566979	−	0.0825617i
$975$	−3.23705e7	+	5.38775e6i	−1.09053	+	0.181508i
$976$	2.00472e7	+	1.81046e7i	0.673642	+	0.608365i
$977$		−	7.51760e6i		−	0.251966i	−0.992032	−	0.125983i	$-0.959791\pi$
$977$		−	7.51760e6i		−	0.251966i	0.992032	−	0.125983i	$-0.0402085\pi$
$978$	−1.10230e7	−	1.14432e7i	−0.368513	−	0.382562i
$979$			5.30905e7i			1.77035i
$980$	−600483.	−	231016.i	−0.0199726	−	0.00768381i
$981$	−3.81654e7	+	1.30665e7i	−1.26619	+	0.433498i
$982$	−4.18769e6	+	2.87583e6i	−0.138579	+	0.0951666i
$983$	−2.24767e7			−0.741906			−0.370953	−	0.928652i	$-0.620969\pi$
$983$	−2.24767e7			−0.741906			−0.370953	+	0.928652i	$0.620969\pi$
$984$	1.75707e6	−	741702.i	0.0578496	−	0.0244198i
$985$	−641793.			−0.0210768
$986$	−4.87592e7	+	3.34846e7i	−1.59722	+	1.09686i
$987$	−1.31632e6	−	7.90869e6i	−0.0430100	−	0.258411i
$988$	2.66995e6	+	1.02717e6i	0.0870183	+	0.0334774i
$989$		−	7.82034e7i		−	2.54235i
$990$	−4.18726e6	−	3.11222e6i	−0.135782	−	0.100921i
$991$		−	5.89464e6i		−	0.190666i	−0.995445	−	0.0953330i	$-0.969608\pi$
$991$		−	5.89464e6i		−	0.190666i	0.995445	−	0.0953330i	$-0.0303916\pi$
$992$	1.24625e6	−	9.33220e6i	0.0402093	−	0.301096i
$993$	1.67893e6	+	1.00873e7i	0.0540331	+	0.324640i
$994$	−1.74198e6	−	2.53661e6i	−0.0559212	−	0.0814307i
$995$	4.06507e6			0.130170
$996$	−4.44688e6	+	2.16772e7i	−0.142039	+	0.692396i
$997$	−1.77444e7			−0.565359			−0.282679	−	0.959214i	$-0.591223\pi$
$997$	−1.77444e7			−0.565359			−0.282679	+	0.959214i	$0.591223\pi$
$998$	1.64755e7	+	2.39911e7i	0.523615	+	0.762471i
$999$	1.53342e7	−	8.27356e6i	0.486124	−	0.262288i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	84.6.e.a.71.10	yes	60
3.2	odd	2	inner	84.6.e.a.71.51	yes	60
4.3	odd	2	inner	84.6.e.a.71.52	yes	60
12.11	even	2	inner	84.6.e.a.71.9	✓	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.6.e.a.71.9	✓	60	12.11	even	2	inner
84.6.e.a.71.10	yes	60	1.1	even	1	trivial
84.6.e.a.71.51	yes	60	3.2	odd	2	inner
84.6.e.a.71.52	yes	60	4.3	odd	2	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:	\( N \)	\(=\)	\( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	84.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.66315 + 3.20235i) q^{2} +(15.3769 - 2.55934i) q^{3} +(11.4900 - 29.8660i) q^{4} +8.37395i q^{5} +(-63.5091 + 61.1768i) q^{6} -49.0000i q^{7} +(42.0619 + 176.065i) q^{8} +(229.900 - 78.7095i) q^{9} +(-26.8163 - 39.0490i) q^{10} +453.236 q^{11} +(100.243 - 488.655i) q^{12} -689.106 q^{13} +(156.915 + 228.494i) q^{14} +(21.4318 + 128.766i) q^{15} +(-759.961 - 686.320i) q^{16} -2117.22i q^{17} +(-820.002 + 1103.25i) q^{18} -129.730i q^{19} +(250.097 + 96.2165i) q^{20} +(-125.408 - 753.469i) q^{21} +(-2113.51 + 1451.42i) q^{22} +4271.28 q^{23} +(1097.39 + 2599.68i) q^{24} +3054.88 q^{25} +(3213.41 - 2206.76i) q^{26} +(3333.70 - 1798.70i) q^{27} +(-1463.44 - 563.009i) q^{28} +4938.67i q^{29} +(-512.292 - 531.822i) q^{30} -1625.35i q^{31} +(5741.65 + 766.757i) q^{32} +(6969.38 - 1159.98i) q^{33} +(6780.08 + 9872.93i) q^{34} +410.324 q^{35} +(290.799 - 7770.56i) q^{36} +4599.74 q^{37} +(415.439 + 604.949i) q^{38} +(-10596.3 + 1763.65i) q^{39} +(-1474.36 + 352.224i) q^{40} -675.877i q^{41} +(2997.66 + 3111.94i) q^{42} -18309.1i q^{43} +(5207.67 - 13536.4i) q^{44} +(659.110 + 1925.17i) q^{45} +(-19917.6 + 13678.1i) q^{46} +10496.4 q^{47} +(-13442.4 - 8608.49i) q^{48} -2401.00 q^{49} +(-14245.4 + 9782.77i) q^{50} +(-5418.69 - 32556.4i) q^{51} +(-7917.81 + 20580.9i) q^{52} +23317.1i q^{53} +(-9785.51 + 19063.3i) q^{54} +3795.38i q^{55} +(8627.17 - 2061.03i) q^{56} +(-332.022 - 1994.84i) q^{57} +(-15815.3 - 23029.8i) q^{58} -23669.0 q^{59} +(4091.97 + 839.432i) q^{60} -26379.2 q^{61} +(5204.94 + 7579.27i) q^{62} +(-3856.76 - 11265.1i) q^{63} +(-29229.6 + 14811.2i) q^{64} -5770.54i q^{65} +(-28784.6 + 27727.5i) q^{66} +16473.0i q^{67} +(-63233.1 - 24326.8i) q^{68} +(65679.2 - 10931.6i) q^{69} +(-1913.40 + 1314.00i) q^{70} -11101.4 q^{71} +(23528.0 + 37166.5i) q^{72} +18356.9 q^{73} +(-21449.3 + 14730.0i) q^{74} +(46974.6 - 7818.46i) q^{75} +(-3874.51 - 1490.59i) q^{76} -22208.6i q^{77} +(43764.5 - 42157.3i) q^{78} -84662.8i q^{79} +(5747.21 - 6363.88i) q^{80} +(46658.6 - 36190.6i) q^{81} +(2164.39 + 3151.72i) q^{82} -44361.0 q^{83} +(-23944.1 - 4911.91i) q^{84} +17729.5 q^{85} +(58632.1 + 85378.2i) q^{86} +(12639.7 + 75941.6i) q^{87} +(19064.0 + 79798.9i) q^{88} +117136. i q^{89} +(-9238.58 - 6866.66i) q^{90} +33766.2i q^{91} +(49076.9 - 127566. i) q^{92} +(-4159.83 - 24992.9i) q^{93} +(-48946.1 + 33613.0i) q^{94} +1086.35 q^{95} +(90251.3 - 2904.45i) q^{96} -113037. q^{97} +(11196.2 - 7688.83i) q^{98} +(104199. - 35674.0i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 20 q^{4} - 114 q^{6} + 44 q^{9} + 668 q^{10} + 786 q^{12} - 3004 q^{16} - 3320 q^{18} + 7120 q^{22} + 16466 q^{24} - 37500 q^{25} - 7448 q^{28} - 35236 q^{30} - 9424 q^{33} + 43360 q^{34} + 50524 q^{36}+ \cdots + 232584 q^{97}+O(q^{100}) \) 60 * q - 20 * q^4 - 114 * q^6 + 44 * q^9 + 668 * q^10 + 786 * q^12 - 3004 * q^16 - 3320 * q^18 + 7120 * q^22 + 16466 * q^24 - 37500 * q^25 - 7448 * q^28 - 35236 * q^30 - 9424 * q^33 + 43360 * q^34 + 50524 * q^36 - 15056 * q^37 - 35468 * q^40 - 20090 * q^42 + 36024 * q^45 + 124416 * q^46 + 88654 * q^48 - 144060 * q^49 - 140108 * q^52 + 19486 * q^54 - 65072 * q^57 + 115616 * q^58 + 164908 * q^60 - 169424 * q^61 + 20116 * q^64 - 98484 * q^66 + 142536 * q^69 + 35868 * q^70 + 121312 * q^72 + 107256 * q^73 + 214836 * q^76 + 263708 * q^78 - 114932 * q^81 - 479624 * q^82 + 40474 * q^84 - 383992 * q^85 - 107320 * q^88 + 423760 * q^90 + 545208 * q^93 - 448512 * q^94 - 751618 * q^96 + 232584 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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