LMFDB - Embedded newform 62.6.d.a.33.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [62,6,Mod(33,62)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(62, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([8])) N = Newforms(chi, 6, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("62.33"); S:= CuspForms(chi, 6); N := Newforms(S);

Level:	$ N $	$=$	$ 62 = 2 \cdot 31 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	62.d (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [24,-24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$9.94379682840$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			33.5
Character	$\chi$	$=$	62.33
Dual form			62.6.d.a.47.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.23607 - 2.35114i) q^{2} +(10.2581 - 7.45295i) q^{3} +(4.94427 + 15.2169i) q^{4} +64.6757 q^{5} -50.7189 q^{6} +(40.4673 + 124.545i) q^{7} +(19.7771 - 60.8676i) q^{8} +(-25.4089 + 78.2004i) q^{9} +(-209.295 - 152.062i) q^{10} +(128.485 + 395.436i) q^{11} +(164.130 + 119.247i) q^{12} +(-93.6147 + 68.0150i) q^{13} +(161.869 - 498.182i) q^{14} +(663.450 - 482.025i) q^{15} +(-207.108 + 150.473i) q^{16} +(252.067 - 775.783i) q^{17} +(266.085 - 193.322i) q^{18} +(1492.16 + 1084.12i) q^{19} +(319.774 + 984.164i) q^{20} +(1343.35 + 976.000i) q^{21} +(513.940 - 1581.74i) q^{22} +(1550.89 - 4773.16i) q^{23} +(-250.768 - 771.784i) q^{24} +1057.95 q^{25} +462.856 q^{26} +(1274.31 + 3921.93i) q^{27} +(-1695.11 + 1231.57i) q^{28} +(2929.66 + 2128.52i) q^{29} -3280.28 q^{30} +(-1175.67 - 5219.86i) q^{31} +1024.00 q^{32} +(4265.18 + 3098.83i) q^{33} +(-2639.68 + 1917.84i) q^{34} +(2617.25 + 8055.06i) q^{35} -1315.60 q^{36} -7696.43 q^{37} +(-2279.82 - 7016.57i) q^{38} +(-453.396 + 1395.41i) q^{39} +(1279.10 - 3936.66i) q^{40} +(-2393.56 - 1739.02i) q^{41} +(-2052.45 - 6316.80i) q^{42} +(-13966.0 - 10146.9i) q^{43} +(-5382.05 + 3910.29i) q^{44} +(-1643.34 + 5057.67i) q^{45} +(-16241.2 + 11799.9i) q^{46} +(-12492.6 + 9076.40i) q^{47} +(-1003.07 + 3087.14i) q^{48} +(-276.812 + 201.116i) q^{49} +(-3423.59 - 2487.38i) q^{50} +(-3196.14 - 9836.70i) q^{51} +(-1497.83 - 1088.24i) q^{52} +(-2815.04 + 8663.79i) q^{53} +(5097.25 - 15687.7i) q^{54} +(8309.85 + 25575.1i) q^{55} +8381.11 q^{56} +23386.6 q^{57} +(-4476.12 - 13776.1i) q^{58} +(11150.6 - 8101.41i) q^{59} +(10615.2 + 7712.40i) q^{60} +42101.4 q^{61} +(-8468.07 + 19656.0i) q^{62} -10767.7 q^{63} +(-3313.73 - 2407.57i) q^{64} +(-6054.59 + 4398.92i) q^{65} +(-6516.61 - 20056.1i) q^{66} +4168.09 q^{67} +13051.3 q^{68} +(-19664.9 - 60522.3i) q^{69} +(10469.0 - 32220.3i) q^{70} +(-7371.89 + 22688.4i) q^{71} +(4257.36 + 3093.15i) q^{72} +(97.2229 + 299.221i) q^{73} +(24906.2 + 18095.4i) q^{74} +(10852.5 - 7884.83i) q^{75} +(-9119.28 + 28066.3i) q^{76} +(-44050.3 + 32004.4i) q^{77} +(4748.03 - 3449.65i) q^{78} +(15579.2 - 47947.7i) q^{79} +(-13394.9 + 9731.95i) q^{80} +(26137.3 + 18989.9i) q^{81} +(3657.03 + 11255.2i) q^{82} +(-36323.0 - 26390.2i) q^{83} +(-8209.81 + 25267.2i) q^{84} +(16302.6 - 50174.3i) q^{85} +(21338.1 + 65671.8i) q^{86} +45916.5 q^{87} +26610.3 q^{88} +(11707.0 + 36030.4i) q^{89} +(17209.2 - 12503.2i) q^{90} +(-12259.3 - 8906.89i) q^{91} +80300.7 q^{92} +(-50963.5 - 44783.7i) q^{93} +61766.8 q^{94} +(96506.6 + 70116.2i) q^{95} +(10504.3 - 7631.82i) q^{96} +(-28661.9 - 88212.1i) q^{97} +1368.64 q^{98} -34187.9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{2} - 20 q^{3} - 96 q^{4} + 120 q^{5} + 280 q^{6} - 180 q^{7} - 384 q^{8} - 200 q^{9} - 100 q^{10} + 354 q^{11} - 320 q^{12} + 39 q^{13} - 720 q^{14} + 535 q^{15} - 1536 q^{16} - 1027 q^{17}+ \cdots + 339042 q^{99}+O(q^{100}) $ 24 * q - 24 * q^2 - 20 * q^3 - 96 * q^4 + 120 * q^5 + 280 * q^6 - 180 * q^7 - 384 * q^8 - 200 * q^9 - 100 * q^10 + 354 * q^11 - 320 * q^12 + 39 * q^13 - 720 * q^14 + 535 * q^15 - 1536 * q^16 - 1027 * q^17 - 1420 * q^18 + 334 * q^19 - 560 * q^20 - 1867 * q^21 + 1416 * q^22 - 1051 * q^23 - 960 * q^24 + 4812 * q^25 + 12536 * q^26 - 5135 * q^27 + 4000 * q^28 - 1143 * q^29 + 9080 * q^30 - 8583 * q^31 + 24576 * q^32 - 24628 * q^33 - 8108 * q^34 - 7496 * q^35 + 17760 * q^36 - 25204 * q^37 - 2844 * q^38 - 20114 * q^39 - 2240 * q^40 + 19615 * q^41 + 3212 * q^42 + 22358 * q^43 - 20496 * q^44 + 6725 * q^45 - 5264 * q^46 + 4766 * q^47 - 3840 * q^48 - 12058 * q^49 + 4628 * q^50 + 6844 * q^51 + 624 * q^52 - 7393 * q^53 - 20540 * q^54 + 11861 * q^55 - 8960 * q^56 + 176704 * q^57 + 4268 * q^58 - 21070 * q^59 + 8560 * q^60 + 76556 * q^61 - 49652 * q^62 + 105854 * q^63 - 24576 * q^64 - 107146 * q^65 + 57968 * q^66 - 150906 * q^67 + 97728 * q^68 - 212560 * q^69 - 29984 * q^70 + 27475 * q^71 - 22720 * q^72 + 49671 * q^73 + 90124 * q^74 - 156002 * q^75 - 11376 * q^76 + 253908 * q^77 - 9036 * q^78 - 7162 * q^79 - 6400 * q^80 + 38329 * q^81 - 92940 * q^82 - 246088 * q^83 + 12848 * q^84 - 104879 * q^85 - 149088 * q^86 - 247668 * q^87 + 118656 * q^88 + 159253 * q^89 - 167880 * q^90 - 68566 * q^91 + 75744 * q^92 + 260391 * q^93 + 18784 * q^94 + 222814 * q^95 - 20480 * q^96 + 190 * q^97 - 144032 * q^98 + 339042 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/62\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−3.23607	−	2.35114i	−0.572061	−	0.415627i
$2$	−3.23607	−	2.35114i	−0.572061	−	0.415627i
$3$	10.2581	−	7.45295i	0.658058	−	0.478107i	−0.207949	−	0.978140i	$-0.566679\pi$
$3$	10.2581	−	7.45295i	0.658058	−	0.478107i	0.866007	+	0.500033i	$0.166679\pi$
$4$	4.94427	+	15.2169i	0.154508	+	0.475528i
$5$	64.6757			1.15695			0.578477	−	0.815699i	$-0.303647\pi$
$5$	64.6757			1.15695			0.578477	+	0.815699i	$0.303647\pi$
$6$	−50.7189			−0.575164
$7$	40.4673	+	124.545i	0.312147	+	0.960689i	0.976913	+	0.213637i	$0.0685311\pi$
$7$	40.4673	+	124.545i	0.312147	+	0.960689i	−0.664766	+	0.747051i	$0.731469\pi$
$8$	19.7771	−	60.8676i	0.109254	−	0.336249i
$9$	−25.4089	+	78.2004i	−0.104563	+	0.321812i
$10$	−209.295	−	152.062i	−0.661849	−	0.480861i
$11$	128.485	+	395.436i	0.320163	+	0.985359i	0.973577	+	0.228359i	$0.0733359\pi$
$11$	128.485	+	395.436i	0.320163	+	0.985359i	−0.653415	+	0.757000i	$0.726664\pi$
$12$	164.130	+	119.247i	0.329029	+	0.239054i
$13$	−93.6147	+	68.0150i	−0.153633	+	0.111621i	−0.661946	−	0.749551i	$-0.730269\pi$
$13$	−93.6147	+	68.0150i	−0.153633	+	0.111621i	0.508313	+	0.861172i	$0.330269\pi$
$14$	161.869	−	498.182i	0.220721	−	0.679309i
$15$	663.450	−	482.025i	0.761343	−	0.553148i
$16$	−207.108	+	150.473i	−0.202254	+	0.146946i
$17$	252.067	−	775.783i	0.211541	−	0.651055i	−0.787841	−	0.615879i	$-0.788801\pi$
$17$	252.067	−	775.783i	0.211541	−	0.651055i	0.999381	−	0.0351757i	$-0.0111991\pi$
$18$	266.085	−	193.322i	0.193570	−	0.140637i
$19$	1492.16	+	1084.12i	0.948270	+	0.688958i	0.950397	−	0.311039i	$-0.100677\pi$
$19$	1492.16	+	1084.12i	0.948270	+	0.688958i	−0.00212709	+	0.999998i	$0.500677\pi$
$20$	319.774	+	984.164i	0.178759	+	0.550164i
$21$	1343.35	+	976.000i	0.664723	+	0.482949i
$22$	513.940	−	1581.74i	0.226389	−	0.696754i
$23$	1550.89	−	4773.16i	0.611311	−	1.88142i	0.165757	−	0.986167i	$-0.446993\pi$
$23$	1550.89	−	4773.16i	0.611311	−	1.88142i	0.445554	−	0.895255i	$-0.353007\pi$
$24$	−250.768	−	771.784i	−0.0888677	−	0.273507i
$25$	1057.95			0.338543
$26$	462.856			0.134280
$27$	1274.31	+	3921.93i	0.336408	+	1.03536i
$28$	−1695.11	+	1231.57i	−0.408605	+	0.296869i
$29$	2929.66	+	2128.52i	0.646877	+	0.469983i	0.862206	−	0.506558i	$-0.169082\pi$
$29$	2929.66	+	2128.52i	0.646877	+	0.469983i	−0.215329	+	0.976542i	$0.569082\pi$
$30$	−3280.28			−0.665438
$31$	−1175.67	−	5219.86i	−0.219726	−	0.975562i
$31$	−1175.67	−	5219.86i	−0.219726	−	0.975562i
$32$	1024.00			0.176777
$33$	4265.18	+	3098.83i	0.681792	+	0.495351i
$34$	−2639.68	+	1917.84i	−0.391610	+	0.284521i
$35$	2617.25	+	8055.06i	0.361139	+	1.11147i
$36$	−1315.60			−0.169187
$37$	−7696.43			−0.924240			−0.462120	−	0.886817i	$-0.652911\pi$
$37$	−7696.43			−0.924240			−0.462120	+	0.886817i	$0.652911\pi$
$38$	−2279.82	−	7016.57i	−0.256119	−	0.788253i
$39$	−453.396	+	1395.41i	−0.0477328	+	0.146906i
$40$	1279.10	−	3936.66i	0.126402	−	0.389025i
$41$	−2393.56	−	1739.02i	−0.222374	−	0.161564i	0.471021	−	0.882122i	$-0.343886\pi$
$41$	−2393.56	−	1739.02i	−0.222374	−	0.161564i	−0.693395	+	0.720558i	$0.743886\pi$
$42$	−2052.45	−	6316.80i	−0.179535	−	0.552553i
$43$	−13966.0	−	10146.9i	−1.15186	−	0.836875i	−0.163132	−	0.986604i	$-0.552160\pi$
$43$	−13966.0	−	10146.9i	−1.15186	−	0.836875i	−0.988727	+	0.149730i	$0.952160\pi$
$44$	−5382.05	+	3910.29i	−0.419098	+	0.304493i
$45$	−1643.34	+	5057.67i	−0.120975	+	0.372322i
$46$	−16241.2	+	11799.9i	−1.13168	+	0.822211i
$47$	−12492.6	+	9076.40i	−0.824912	+	0.599334i	−0.918115	−	0.396313i	$-0.870289\pi$
$47$	−12492.6	+	9076.40i	−0.824912	+	0.599334i	0.0932029	+	0.995647i	$0.470289\pi$
$48$	−1003.07	+	3087.14i	−0.0628389	+	0.193398i
$49$	−276.812	+	201.116i	−0.0164701	+	0.0119662i
$50$	−3423.59	−	2487.38i	−0.193668	−	0.140708i
$51$	−3196.14	−	9836.70i	−0.172068	−	0.529571i
$52$	−1497.83	−	1088.24i	−0.0768167	−	0.0558106i
$53$	−2815.04	+	8663.79i	−0.137656	+	0.423661i	−0.995994	−	0.0894239i	$-0.971497\pi$
$53$	−2815.04	+	8663.79i	−0.137656	+	0.423661i	0.858338	+	0.513085i	$0.171497\pi$
$54$	5097.25	−	15687.7i	0.237876	−	0.732108i
$55$	8309.85	+	25575.1i	0.370413	+	1.14002i
$56$	8381.11			0.357134
$57$	23386.6			0.953412
$58$	−4476.12	−	13776.1i	−0.174715	−	0.537719i
$59$	11150.6	−	8101.41i	0.417032	−	0.302992i	−0.359410	−	0.933180i	$-0.617022\pi$
$59$	11150.6	−	8101.41i	0.417032	−	0.302992i	0.776443	+	0.630188i	$0.217022\pi$
$60$	10615.2	+	7712.40i	0.380671	+	0.276574i
$61$	42101.4			1.44868			0.724340	−	0.689443i	$-0.242145\pi$
$61$	42101.4			1.44868			0.724340	+	0.689443i	$0.242145\pi$
$62$	−8468.07	+	19656.0i	−0.279773	+	0.649405i
$63$	−10767.7			−0.341801
$64$	−3313.73	−	2407.57i	−0.101127	−	0.0734732i
$65$	−6054.59	+	4398.92i	−0.177747	+	0.129141i
$66$	−6516.61	−	20056.1i	−0.184146	−	0.566743i
$67$	4168.09			0.113436			0.0567179	−	0.998390i	$-0.481936\pi$
$67$	4168.09			0.113436			0.0567179	+	0.998390i	$0.481936\pi$
$68$	13051.3			0.342280
$69$	−19664.9	−	60522.3i	−0.497243	−	1.53036i
$70$	10469.0	−	32220.3i	0.255364	−	0.785930i
$71$	−7371.89	+	22688.4i	−0.173553	+	0.534142i	−0.999564	−	0.0295115i	$-0.990605\pi$
$71$	−7371.89	+	22688.4i	−0.173553	+	0.534142i	0.826011	+	0.563654i	$0.190605\pi$
$72$	4257.36	+	3093.15i	0.0967852	+	0.0703186i
$73$	97.2229	+	299.221i	0.00213531	+	0.00657181i	0.952118	−	0.305729i	$-0.0989002\pi$
$73$	97.2229	+	299.221i	0.00213531	+	0.00657181i	−0.949983	+	0.312301i	$0.898900\pi$
$74$	24906.2	+	18095.4i	0.528722	+	0.384139i
$75$	10852.5	−	7884.83i	0.222781	−	0.161860i
$76$	−9119.28	+	28066.3i	−0.181103	+	0.557379i
$77$	−44050.3	+	32004.4i	−0.846685	+	0.615153i
$78$	4748.03	−	3449.65i	0.0883643	−	0.0642004i
$79$	15579.2	−	47947.7i	0.280851	−	0.864371i	−0.706761	−	0.707453i	$-0.749844\pi$
$79$	15579.2	−	47947.7i	0.280851	−	0.864371i	0.987612	−	0.156918i	$-0.0501558\pi$
$80$	−13394.9	+	9731.95i	−0.233999	+	0.170010i
$81$	26137.3	+	18989.9i	0.442637	+	0.321595i
$82$	3657.03	+	11255.2i	0.0600612	+	0.184849i
$83$	−36323.0	−	26390.2i	−0.578744	−	0.420482i	0.259527	−	0.965736i	$-0.416433\pi$
$83$	−36323.0	−	26390.2i	−0.578744	−	0.420482i	−0.838271	+	0.545253i	$0.816433\pi$
$84$	−8209.81	+	25267.2i	−0.126951	+	0.390714i
$85$	16302.6	−	50174.3i	0.244743	−	0.753241i
$86$	21338.1	+	65671.8i	0.311107	+	0.957487i
$87$	45916.5			0.650385
$88$	26610.3			0.366305
$89$	11707.0	+	36030.4i	0.156664	+	0.482163i	0.998326	−	0.0578426i	$-0.0184222\pi$
$89$	11707.0	+	36030.4i	0.156664	+	0.482163i	−0.841662	+	0.540005i	$0.818422\pi$
$90$	17209.2	−	12503.2i	0.223952	−	0.162711i
$91$	−12259.3	−	8906.89i	−0.155189	−	0.112752i
$92$	80300.7			0.989122
$93$	−50963.5	−	44783.7i	−0.611015	−	0.536923i
$94$	61766.8			0.721000
$95$	96506.6	+	70116.2i	1.09711	+	0.797093i
$96$	10504.3	−	7631.82i	0.116329	−	0.0845182i
$97$	−28661.9	−	88212.1i	−0.309296	−	0.951917i	−0.978039	−	0.208423i	$-0.933167\pi$
$97$	−28661.9	−	88212.1i	−0.309296	−	0.951917i	0.668742	−	0.743494i	$-0.266833\pi$
$98$	1368.64			0.0143954
$99$	−34187.9			−0.350578
$100$	5230.78	+	16098.7i	0.0523078	+	0.160987i
$101$	−43316.6	+	133315.i	−0.422523	+	1.30039i	0.482823	+	0.875718i	$0.339611\pi$
$101$	−43316.6	+	133315.i	−0.422523	+	1.30039i	−0.905346	+	0.424675i	$0.860389\pi$
$102$	−12784.6	+	39346.8i	−0.121670	+	0.374463i
$103$	−156847.	−	113956.i	−1.45675	−	1.05839i	−0.984196	−	0.177085i	$-0.943333\pi$
$103$	−156847.	−	113956.i	−1.45675	−	1.05839i	−0.472551	−	0.881303i	$-0.656667\pi$
$104$	2288.49	+	7043.24i	0.0207475	+	0.0638542i
$105$	86882.0	+	63123.5i	0.769054	+	0.558750i
$106$	29479.5	−	21418.1i	0.254832	−	0.185147i
$107$	17970.2	−	55306.7i	0.151738	−	0.467001i	−0.846078	−	0.533059i	$-0.821042\pi$
$107$	17970.2	−	55306.7i	0.151738	−	0.467001i	0.997816	+	0.0660580i	$0.0210422\pi$
$108$	−53379.0	+	38782.1i	−0.440364	+	0.319943i
$109$	−158664.	+	115276.i	−1.27912	+	0.929335i	−0.999526	−	0.0307835i	$-0.990200\pi$
$109$	−158664.	+	115276.i	−1.27912	+	0.929335i	−0.279594	+	0.960118i	$0.590200\pi$
$110$	33239.4	−	102300.i	0.261922	−	0.806113i
$111$	−78950.8	+	57361.1i	−0.608204	+	0.441886i
$112$	−27121.8	−	19705.2i	−0.204303	−	0.148435i
$113$	39835.2	+	122600.i	0.293475	+	0.903223i	0.983729	+	0.179657i	$0.0574986\pi$
$113$	39835.2	+	122600.i	0.293475	+	0.903223i	−0.690254	+	0.723567i	$0.742501\pi$
$114$	−75680.8	−	54985.3i	−0.545410	−	0.396264i
$115$	100305.	−	308707.i	0.707259	−	2.17672i
$116$	−17904.5	+	55104.3i	−0.123542	+	0.380225i
$117$	−2940.16	−	9048.89i	−0.0198567	−	0.0611126i
$118$	−55131.8			−0.364499
$119$	106821.			0.691493
$120$	−16218.6	−	49915.7i	−0.102816	−	0.316435i
$121$	−9568.24	+	6951.73i	−0.0594112	+	0.0431648i
$122$	−136243.	−	98986.4i	−0.828734	−	0.602110i
$123$	−37514.2			−0.223580
$124$	73617.3	−	43698.5i	0.429957	−	0.255219i
$125$	−133688.			−0.765275
$126$	34845.1	+	25316.4i	0.195531	+	0.142062i
$127$	235571.	−	171152.i	1.29602	−	0.941616i	0.296115	−	0.955152i	$-0.404309\pi$
$127$	235571.	−	171152.i	1.29602	−	0.941616i	0.999908	+	0.0135361i	$0.00430880\pi$
$128$	5062.93	+	15582.1i	0.0273135	+	0.0840623i
$129$	−218888.			−1.15811
$130$	29935.6			0.155356
$131$	−53313.0	−	164081.i	−0.271428	−	0.835371i	−0.990142	−	0.140065i	$-0.955269\pi$
$131$	−53313.0	−	164081.i	−0.271428	−	0.835371i	0.718714	−	0.695306i	$-0.244731\pi$
$132$	−26066.4	+	80224.3i	−0.130211	+	0.400748i
$133$	−74638.4	+	229713.i	−0.365875	+	1.12605i
$134$	−13488.2	−	9799.78i	−0.0648923	−	0.0471470i
$135$	82417.0	+	253653.i	0.389209	+	1.19786i
$136$	−42234.9	−	30685.4i	−0.195805	−	0.142261i
$137$	−121224.	+	88074.4i	−0.551807	+	0.400911i	−0.828451	−	0.560061i	$-0.810778\pi$
$137$	−121224.	+	88074.4i	−0.551807	+	0.400911i	0.276644	+	0.960972i	$0.410778\pi$
$138$	−78659.5	+	242089.i	−0.351604	+	1.08213i
$139$	−60590.0	+	44021.2i	−0.265989	+	0.193253i	−0.712783	−	0.701384i	$-0.752566\pi$
$139$	−60590.0	+	44021.2i	−0.265989	+	0.193253i	0.446794	+	0.894637i	$0.352566\pi$
$140$	−109633.	+	79652.8i	−0.472738	+	0.343464i
$141$	−60504.4	+	186213.i	−0.256294	+	0.788793i
$142$	77199.5	−	56088.7i	0.321287	−	0.233429i
$143$	−38923.7	−	28279.7i	−0.159175	−	0.115647i
$144$	−6504.67	−	20019.3i	−0.0261408	−	0.0804531i
$145$	189478.	+	137663.i	0.748407	+	0.543749i
$146$	388.892	−	1196.89i	0.00150989	−	0.00464697i
$147$	−1340.66	+	4126.14i	−0.00511713	+	0.0157489i
$148$	−38053.2	−	117116.i	−0.142803	−	0.439502i
$149$	−99133.0			−0.365807			−0.182904	−	0.983131i	$-0.558550\pi$
$149$	−99133.0			−0.365807			−0.182904	+	0.983131i	$0.558550\pi$
$150$	−53657.9			−0.194718
$151$	−147404.	−	453662.i	−0.526097	−	1.61916i	−0.762136	−	0.647417i	$-0.775849\pi$
$151$	−147404.	−	453662.i	−0.526097	−	1.61916i	0.236038	−	0.971744i	$-0.424151\pi$
$152$	95498.4	−	69383.6i	0.335264	−	0.243584i
$153$	54261.8	+	39423.5i	0.187398	+	0.136153i
$154$	217797.			0.740030
$155$	−76037.5	−	337598.i	−0.254213	−	1.12868i
$156$	−23475.5			−0.0772332
$157$	210218.	+	152733.i	0.680647	+	0.494519i	0.873572	−	0.486695i	$-0.161798\pi$
$157$	210218.	+	152733.i	0.680647	+	0.494519i	−0.192925	+	0.981213i	$0.561798\pi$
$158$	−163147.	+	118533.i	−0.519920	+	0.377744i
$159$	35693.9	+	109854.i	0.111970	+	0.344608i
$160$	66227.9			0.204523
$161$	657235.			1.99828
$162$	−39934.2	−	122905.i	−0.119552	−	0.367944i
$163$	80035.4	−	246324.i	0.235946	−	0.726168i	−0.761048	−	0.648695i	$-0.775315\pi$
$163$	80035.4	−	246324.i	0.235946	−	0.726168i	0.996994	−	0.0774727i	$-0.0246851\pi$
$164$	14628.1	−	45020.8i	0.0424697	−	0.130708i
$165$	275853.	+	200419.i	0.788803	+	0.573099i
$166$	55496.6	+	170801.i	0.156314	+	0.481084i
$167$	149063.	+	108300.i	0.413597	+	0.300496i	0.775057	−	0.631892i	$-0.217721\pi$
$167$	149063.	+	108300.i	0.413597	+	0.300496i	−0.361459	+	0.932388i	$0.617721\pi$
$168$	85974.3	−	62464.0i	0.235015	−	0.170748i
$169$	−110598.	+	340386.i	−0.297873	+	0.916759i
$170$	−170723.	+	124038.i	−0.453075	+	0.329178i
$171$	−122693.	+	89141.5i	−0.320869	+	0.233125i
$172$	85352.3	−	262687.i	0.219986	−	0.677046i
$173$	441604.	−	320844.i	1.12181	−	0.815039i	0.137323	−	0.990526i	$-0.456150\pi$
$173$	441604.	−	320844.i	1.12181	−	0.815039i	0.984482	+	0.175487i	$0.0561500\pi$
$174$	−148589.	−	107956.i	−0.372060	−	0.270317i
$175$	42812.2	+	131763.i	0.105675	+	0.325235i
$176$	−86112.8	−	62564.6i	−0.209549	−	0.152246i
$177$	54005.0	−	166210.i	0.129569	−	0.398772i
$178$	46827.9	−	144121.i	0.110778	−	0.340941i
$179$	84624.2	+	260447.i	0.197407	+	0.607556i	0.999940	+	0.0109483i	$0.00348504\pi$
$179$	84624.2	+	260447.i	0.197407	+	0.607556i	−0.802533	+	0.596607i	$0.796515\pi$
$180$	−85087.1			−0.195741
$181$	226426.			0.513723			0.256862	−	0.966448i	$-0.417312\pi$
$181$	226426.			0.513723			0.256862	+	0.966448i	$0.417312\pi$
$182$	18730.5	+	57646.6i	0.0419152	+	0.129002i
$183$	431881.	−	313780.i	0.953315	−	0.692624i
$184$	−259859.	−	188798.i	−0.565838	−	0.411106i
$185$	−497772.			−1.06930
$186$	59628.8	+	264745.i	0.126379	+	0.561108i
$187$	339159.			0.709250
$188$	−199881.	−	145222.i	−0.412456	−	0.299667i
$189$	−436890.	+	317419.i	−0.889647	+	0.646366i
$190$	−147449.	−	453801.i	−0.296318	−	0.911973i
$191$	937936.			1.86033			0.930165	−	0.367142i	$-0.119664\pi$
$191$	937936.			1.86033			0.930165	+	0.367142i	$0.119664\pi$
$192$	−51936.1			−0.101676
$193$	−227390.	−	699834.i	−0.439418	−	1.35239i	−0.888491	−	0.458894i	$-0.848246\pi$
$193$	−227390.	−	699834.i	−0.439418	−	1.35239i	0.449074	−	0.893495i	$-0.351754\pi$
$194$	−114647.	+	352848.i	−0.218706	+	0.673107i
$195$	−29323.7	+	90249.2i	−0.0552246	+	0.169964i
$196$	−4429.00	−	3217.85i	−0.00823503	−	0.00598310i
$197$	−99826.8	−	307235.i	−0.183266	−	0.564035i	0.816648	−	0.577136i	$-0.195830\pi$
$197$	−99826.8	−	307235.i	−0.183266	−	0.564035i	−0.999914	+	0.0131012i	$0.995830\pi$
$198$	110634.	+	80380.6i	0.200552	+	0.145710i
$199$	−412760.	+	299888.i	−0.738864	+	0.536816i	−0.892355	−	0.451334i	$-0.850948\pi$
$199$	−412760.	+	299888.i	−0.738864	+	0.536816i	0.153491	+	0.988150i	$0.450948\pi$
$200$	20923.1	−	64394.7i	0.0369872	−	0.113835i
$201$	42756.7	−	31064.6i	0.0746474	−	0.0542345i
$202$	453617.	−	329572.i	0.782187	−	0.568292i
$203$	−146542.	+	451010.i	−0.249587	+	0.768151i
$204$	133882.	−	97270.7i	0.225240	−	0.163646i
$205$	−154805.	−	112472.i	−0.257277	−	0.186923i
$206$	239641.	+	737540.i	0.393454	+	1.21093i
$207$	333856.	+	242561.i	0.541544	+	0.393455i
$208$	9153.95	−	28173.0i	0.0146707	−	0.0451517i
$209$	−236979.	+	729348.i	−0.375271	+	1.15496i
$210$	−132744.	−	408544.i	−0.207714	−	0.639279i
$211$	−195332.			−0.302042			−0.151021	−	0.988531i	$-0.548256\pi$
$211$	−195332.			−0.302042			−0.151021	+	0.988531i	$0.548256\pi$
$212$	−145754.			−0.222732
$213$	93473.5	+	287682.i	0.141169	+	0.434474i
$214$	−188187.	+	136726.i	−0.280902	+	0.204087i
$215$	−903258.	−	656255.i	−1.33265	−	0.968226i
$216$	263921.			0.384892
$217$	602533.	−	357658.i	0.868624	−	0.515607i
$218$	784476.			1.11799
$219$	3227.40	+	2344.85i	0.00454719	+	0.00330373i
$220$	−348088.	+	252901.i	−0.484877	+	0.352284i
$221$	29167.7	+	89769.0i	0.0401718	+	0.123636i
$222$	390354.			0.531589
$223$	−744357.			−1.00235			−0.501175	−	0.865346i	$-0.667099\pi$
$223$	−744357.			−1.00235			−0.501175	+	0.865346i	$0.667099\pi$
$224$	41438.5	+	127535.i	0.0551803	+	0.169827i
$225$	−26881.2	+	82731.9i	−0.0353992	+	0.108947i
$226$	159341.	−	490401.i	0.207518	−	0.638675i
$227$	−430618.	−	312862.i	−0.554661	−	0.402985i	0.274840	−	0.961490i	$-0.411375\pi$
$227$	−430618.	−	312862.i	−0.554661	−	0.402985i	−0.829501	+	0.558505i	$0.811375\pi$
$228$	115630.	+	355872.i	0.147310	+	0.453375i
$229$	−587026.	−	426499.i	−0.739722	−	0.537440i	0.152902	−	0.988241i	$-0.451138\pi$
$229$	−587026.	−	426499.i	−0.739722	−	0.537440i	−0.892624	+	0.450802i	$0.851138\pi$
$230$	−1.05041e6	+	763167.i	−1.30930	+	0.951261i
$231$	−213345.	+	656609.i	−0.263059	+	0.809613i
$232$	187498.	−	136225.i	0.228705	−	0.166164i
$233$	−1.17344e6	+	852552.i	−1.41602	+	1.02880i	−0.423610	+	0.905845i	$0.639237\pi$
$233$	−1.17344e6	+	852552.i	−1.41602	+	1.02880i	−0.992412	+	0.122955i	$0.960763\pi$
$234$	−11760.6	+	36195.6i	−0.0140408	+	0.0432131i
$235$	−807967.	+	587023.i	−0.954386	+	0.693402i
$236$	178410.	+	129623.i	0.208516	+	0.151496i
$237$	−197539.	−	607963.i	−0.228445	−	0.703083i
$238$	−345679.	−	251150.i	−0.395576	−	0.287403i
$239$	369956.	−	1.13861e6i	0.418943	−	1.28937i	−0.489733	−	0.871872i	$-0.662906\pi$
$239$	369956.	−	1.13861e6i	0.418943	−	1.28937i	0.908676	−	0.417502i	$-0.137094\pi$
$240$	−64874.4	+	199663.i	−0.0727018	+	0.223753i
$241$	−226934.	−	698432.i	−0.251685	−	0.774607i	−0.994465	−	0.105071i	$-0.966493\pi$
$241$	−226934.	−	698432.i	−0.251685	−	0.774607i	0.742780	−	0.669536i	$-0.233507\pi$
$242$	47308.0			0.0519273
$243$	−592424.			−0.643601
$244$	208161.	+	640654.i	0.223833	+	0.688888i
$245$	−17903.0	+	13007.3i	−0.0190551	+	0.0138443i
$246$	121399.	+	88201.2i	0.127902	+	0.0929259i
$247$	−213425.			−0.222588
$248$	−340972.	−	31673.3i	−0.352038	−	0.0327012i
$249$	−569291.			−0.581883
$250$	432624.	+	314320.i	0.437784	+	0.318069i
$251$	−458289.	+	332967.i	−0.459151	+	0.333593i	−0.793198	−	0.608964i	$-0.791586\pi$
$251$	−458289.	+	332967.i	−0.459151	+	0.333593i	0.334047	+	0.942556i	$0.391586\pi$
$252$	−53238.6	−	163851.i	−0.0528111	−	0.162536i
$253$	2.08674e6			2.04959
$254$	−1.16473e6			−1.13277
$255$	−206713.	−	636196.i	−0.199075	−	0.612689i
$256$	20251.7	−	62328.4i	0.0193136	−	0.0594410i
$257$	90901.2	−	279765.i	0.0858493	−	0.264217i	−0.898912	−	0.438130i	$-0.855641\pi$
$257$	90901.2	−	279765.i	0.0858493	−	0.264217i	0.984761	+	0.173913i	$0.0556411\pi$
$258$	708337.	+	514637.i	0.662508	+	0.481340i
$259$	−311453.	−	958555.i	−0.288499	−	0.887907i
$260$	−96873.5	−	70382.7i	−0.0888734	−	0.0645703i
$261$	−240890.	+	175017.i	−0.218886	+	0.159030i
$262$	−213252.	+	656323.i	−0.191929	+	0.590696i
$263$	1.51442e6	−	1.10029e6i	1.35007	−	0.980884i	0.351063	−	0.936352i	$-0.385820\pi$
$263$	1.51442e6	−	1.10029e6i	1.35007	−	0.980884i	0.999008	−	0.0445321i	$-0.0141797\pi$
$264$	272971.	−	198325.i	0.241050	−	0.175133i
$265$	−182065.	+	560337.i	−0.159261	+	0.490156i
$266$	781623.	−	567882.i	0.677319	−	0.492101i
$267$	388624.	+	282352.i	0.333620	+	0.242389i
$268$	20608.2	+	63425.5i	0.0175268	+	0.0539420i
$269$	−189413.	−	137617.i	−0.159599	−	0.115955i	0.505119	−	0.863049i	$-0.331448\pi$
$269$	−189413.	−	137617.i	−0.159599	−	0.115955i	−0.664718	+	0.747094i	$0.731448\pi$
$270$	329668.	−	1.01461e6i	0.275212	−	0.847015i
$271$	−266578.	+	820442.i	−0.220496	+	0.678617i	0.778222	+	0.627990i	$0.216122\pi$
$271$	−266578.	+	820442.i	−0.220496	+	0.678617i	−0.998718	+	0.0506271i	$0.983878\pi$
$272$	64529.2	+	198600.i	0.0528852	+	0.162764i
$273$	−192140.			−0.156031
$274$	599364.			0.482297
$275$	135930.	+	418351.i	0.108389	+	0.333587i
$276$	823733.	−	598477.i	0.650899	−	0.472906i
$277$	1.68890e6	+	1.22706e6i	1.32253	+	0.960874i	0.999897	+	0.0143503i	$0.00456799\pi$
$277$	1.68890e6	+	1.22706e6i	1.32253	+	0.960874i	0.322633	+	0.946524i	$0.395432\pi$
$278$	299574.			0.232483
$279$	438068.	+	40692.6i	0.336923	+	0.0312972i
$280$	542054.			0.413188
$281$	−590545.	−	429056.i	−0.446156	−	0.324151i	0.341920	−	0.939729i	$-0.388923\pi$
$281$	−590545.	−	429056.i	−0.446156	−	0.324151i	−0.788076	+	0.615578i	$0.788923\pi$
$282$	633610.	−	460345.i	0.474460	−	0.344715i
$283$	−140971.	−	433865.i	−0.104632	−	0.322024i	0.885012	−	0.465568i	$-0.154150\pi$
$283$	−140971.	−	433865.i	−0.104632	−	0.322024i	−0.989644	+	0.143544i	$0.954150\pi$
$284$	−381695.			−0.280815
$285$	1.51255e6			1.10305
$286$	59470.1	+	183030.i	0.0429916	+	0.132314i
$287$	119726.	−	368480.i	0.0857996	−	0.264064i
$288$	−26018.7	+	80077.2i	−0.0184843	+	0.0568889i
$289$	610388.	+	443473.i	0.429894	+	0.312336i
$290$	−289496.	−	890977.i	−0.202138	−	0.622116i
$291$	−951457.	−	691274.i	−0.658653	−	0.478539i
$292$	−4072.52	+	2958.86i	−0.00279516	+	0.00203080i
$293$	173537.	−	534092.i	0.118093	−	0.363452i	−0.874487	−	0.485049i	$-0.838802\pi$
$293$	173537.	−	534092.i	0.118093	−	0.363452i	0.992580	+	0.121597i	$0.0388016\pi$
$294$	14039.6	−	10200.4i	0.00947298	−	0.00688252i
$295$	721175.	−	523964.i	0.482487	−	0.350547i
$296$	−152213.	+	468463.i	−0.100977	+	0.310775i
$297$	−1.38714e6	+	1.00782e6i	−0.912493	+	0.662965i
$298$	320801.	+	233076.i	0.209264	+	0.152039i
$299$	179460.	+	552321.i	0.116089	+	0.357284i
$300$	173641.	+	126157.i	0.111391	+	0.0809299i
$301$	698581.	−	2.15001e6i	0.444427	−	1.36781i
$302$	−589615.	+	1.81465e6i	−0.372007	+	1.14492i
$303$	549242.	+	1.69039e6i	0.343682	+	1.05774i
$304$	−472170.			−0.293032
$305$	2.72294e6			1.67606
$306$	−82904.6	−	255154.i	−0.0506145	−	0.155775i
$307$	740526.	−	538024.i	0.448430	−	0.325803i	−0.340546	−	0.940228i	$-0.610612\pi$
$307$	740526.	−	538024.i	0.448430	−	0.325803i	0.788976	+	0.614425i	$0.210612\pi$
$308$	−704805.	−	512071.i	−0.423343	−	0.307576i
$309$	−2.45827e6			−1.46465
$310$	−547679.	+	1.27127e6i	−0.323684	+	0.751332i
$311$	2.27657e6			1.33469			0.667344	−	0.744749i	$-0.267431\pi$
$311$	2.27657e6			1.33469			0.667344	+	0.744749i	$0.267431\pi$
$312$	75968.5	+	55194.3i	0.0441822	+	0.0321002i
$313$	−2.35113e6	+	1.70819e6i	−1.35649	+	0.985545i	−0.357826	+	0.933788i	$0.616482\pi$
$313$	−2.35113e6	+	1.70819e6i	−1.35649	+	0.985545i	−0.998660	+	0.0517565i	$0.983518\pi$
$314$	−321185.	−	988507.i	−0.183836	−	0.565790i
$315$	−696411.			−0.395448
$316$	806643.			0.454427
$317$	560987.	+	1.72654e6i	0.313548	+	0.965003i	0.976348	+	0.216206i	$0.0693682\pi$
$317$	560987.	+	1.72654e6i	0.313548	+	0.965003i	−0.662799	+	0.748797i	$0.730632\pi$
$318$	142776.	−	439418.i	0.0791746	−	0.243674i
$319$	−465276.	+	1.43197e6i	−0.255997	+	0.787877i
$320$	−214318.	−	155711.i	−0.116999	−	0.0850051i
$321$	−227857.	−	701273.i	−0.123424	−	0.379861i
$322$	−2.12686e6	−	1.54525e6i	−1.14314	−	0.830539i
$323$	1.21717e6	−	884323.i	0.649147	−	0.471633i
$324$	−159737.	+	491620.i	−0.0845362	+	0.260176i
$325$	−99039.4	+	71956.3i	−0.0520115	+	0.0377886i
$326$	−838142.	+	608946.i	−0.436791	+	0.317347i
$327$	−768443.	+	2.36502e6i	−0.397413	+	1.22311i
$328$	−153188.	+	111297.i	−0.0786212	+	0.0571216i
$329$	−1.63596e6	−	1.18860e6i	−0.833267	−	0.605404i
$330$	−421466.	−	1.29714e6i	−0.213048	−	0.655695i
$331$	−243021.	−	176565.i	−0.121920	−	0.0885798i	0.525154	−	0.851007i	$-0.324008\pi$
$331$	−243021.	−	176565.i	−0.121920	−	0.0885798i	−0.647074	+	0.762427i	$0.724008\pi$
$332$	221987.	−	683204.i	0.110530	−	0.340177i
$333$	195557.	−	601864.i	0.0966415	−	0.297432i
$334$	−227748.	−	700935.i	−0.111709	−	0.343804i
$335$	269574.			0.131240
$336$	−425080.			−0.205411
$337$	−166226.	−	511591.i	−0.0797305	−	0.245385i	0.903244	−	0.429127i	$-0.141179\pi$
$337$	−166226.	−	511591.i	−0.0797305	−	0.245385i	−0.982974	+	0.183742i	$0.941179\pi$
$338$	1.15820e6	−	841481.i	0.551431	−	0.400638i
$339$	1.32237e6	+	960756.i	0.624961	+	0.454061i
$340$	844102.			0.396002
$341$	1.91306e6	−	1.13558e6i	0.890930	−	0.528848i
$342$	606626.			0.280450
$343$	1.74436e6	+	1.26735e6i	0.800574	+	0.581651i
$344$	−893821.	+	649399.i	−0.407244	+	0.295880i
$345$	−1.27184e6	−	3.91432e6i	−0.575287	−	1.77055i
$346$	−2.18341e6			−0.980494
$347$	2.88511e6			1.28629			0.643144	−	0.765745i	$-0.277630\pi$
$347$	2.88511e6			1.28629			0.643144	+	0.765745i	$0.277630\pi$
$348$	227023.	+	698706.i	0.100490	+	0.309276i
$349$	−414208.	+	1.27480e6i	−0.182035	+	0.560246i	−0.999885	−	0.0151861i	$-0.995166\pi$
$349$	−414208.	+	1.27480e6i	−0.182035	+	0.560246i	0.817850	+	0.575432i	$0.195166\pi$
$350$	171249.	−	527050.i	0.0747236	−	0.229976i
$351$	−386044.	−	280478.i	−0.167251	−	0.121515i
$352$	131569.	+	404926.i	0.0565973	+	0.174189i
$353$	−1.33359e6	−	968913.i	−0.569622	−	0.413855i	0.265346	−	0.964153i	$-0.414514\pi$
$353$	−1.33359e6	−	968913.i	−0.569622	−	0.413855i	−0.834968	+	0.550299i	$0.814514\pi$
$354$	−565548.	+	410894.i	−0.239862	+	0.174270i
$355$	−476782.	+	1.46739e6i	−0.200793	+	0.617978i
$356$	−490388.	+	356288.i	−0.205076	+	0.148997i
$357$	1.09578e6	−	796129.i	0.455042	−	0.330608i
$358$	338497.	−	1.04179e6i	0.139588	−	0.429607i
$359$	−3.03090e6	+	2.20208e6i	−1.24118	+	0.901771i	−0.997677	−	0.0681290i	$-0.978297\pi$
$359$	−3.03090e6	+	2.20208e6i	−1.24118	+	0.901771i	−0.243504	+	0.969900i	$0.578297\pi$
$360$	275348.	+	200052.i	0.111976	+	0.0813554i
$361$	286077.	+	880453.i	0.115535	+	0.355581i
$362$	−732729.	−	532359.i	−0.293881	−	0.213517i
$363$	−46341.1	+	142623.i	−0.0184586	+	0.0568099i
$364$	74922.1	−	230587.i	0.0296385	−	0.0912180i
$365$	6287.96	+	19352.3i	0.00247046	+	0.00760329i
$366$	−2.13534e6			−0.833228
$367$	−3.60554e6			−1.39735			−0.698675	−	0.715439i	$-0.746227\pi$
$367$	−3.60554e6			−1.39735			−0.698675	+	0.715439i	$0.746227\pi$
$368$	397029.	+	1.22193e6i	0.152828	+	0.470355i
$369$	196810.	−	142991.i	0.0752456	−	0.0546691i
$370$	1.61082e6	+	1.17033e6i	0.611707	+	0.444431i
$371$	−1.19295e6			−0.449975
$372$	429491.	−	996930.i	0.160915	−	0.373514i
$373$	3.47080e6			1.29169			0.645845	−	0.763469i	$-0.276505\pi$
$373$	3.47080e6			1.29169			0.645845	+	0.763469i	$0.276505\pi$
$374$	−1.09754e6	−	797411.i	−0.405735	−	0.294784i
$375$	−1.37139e6	+	996371.i	−0.503595	+	0.365883i
$376$	305392.	+	939899.i	0.111401	+	0.342856i
$377$	−419030.			−0.151842
$378$	2.16010e6			0.777580
$379$	−151015.	−	464777.i	−0.0540036	−	0.166206i	0.920417	−	0.390938i	$-0.127849\pi$
$379$	−151015.	−	464777.i	−0.0540036	−	0.166206i	−0.974421	+	0.224732i	$0.927849\pi$
$380$	−589796.	+	1.81521e6i	−0.209528	+	0.644862i
$381$	1.14092e6	−	3.51140e6i	0.402665	−	1.23928i
$382$	−3.03523e6	−	2.20522e6i	−1.06422	−	0.773203i
$383$	1.62734e6	+	5.00845e6i	0.566869	+	1.74464i	0.662333	+	0.749210i	$0.269567\pi$
$383$	1.62734e6	+	5.00845e6i	0.566869	+	1.74464i	−0.0954637	+	0.995433i	$0.530433\pi$
$384$	168069.	+	122109.i	0.0581646	+	0.0422591i
$385$	−2.84898e6	+	2.06991e6i	−0.979576	+	0.711704i
$386$	−909559.	+	2.79933e6i	−0.310715	+	0.956283i
$387$	1.14835e6	−	834323.i	0.389759	−	0.283176i
$388$	1.20060e6	−	872289.i	0.404874	−	0.294158i
$389$	1.24079e6	−	3.81876e6i	0.415743	−	1.27953i	−0.495842	−	0.868413i	$-0.665140\pi$
$389$	1.24079e6	−	3.81876e6i	0.415743	−	1.27953i	0.911585	−	0.411112i	$-0.134860\pi$
$390$	307082.	−	223108.i	0.102233	−	0.0742770i
$391$	−3.31200e6	−	2.40631e6i	−1.09559	−	0.795994i
$392$	6766.90	+	20826.4i	0.00222421	+	0.00684540i
$393$	−1.76978e6	−	1.28582e6i	−0.578012	−	0.419950i
$394$	−399307.	+	1.22894e6i	−0.129589	+	0.398833i
$395$	1.00759e6	−	3.10105e6i	0.324932	−	1.00004i
$396$	−169034.	−	520234.i	−0.0541673	−	0.166710i
$397$	−189818.			−0.0604451			−0.0302225	−	0.999543i	$-0.509622\pi$
$397$	−189818.			−0.0604451			−0.0302225	+	0.999543i	$0.509622\pi$
$398$	2.04080e6			0.645791
$399$	946393.	+	2.91270e6i	0.297604	+	0.915932i
$400$	−219110.	+	159193.i	−0.0684718	+	0.0497477i
$401$	999529.	+	726200.i	0.310409	+	0.225525i	0.732072	−	0.681227i	$-0.238553\pi$
$401$	999529.	+	726200.i	0.310409	+	0.225525i	−0.421663	+	0.906753i	$0.638553\pi$
$402$	−211401.			−0.0652442
$403$	465089.	+	408692.i	0.142651	+	0.125353i
$404$	−2.24281e6			−0.683657
$405$	1.69045e6	+	1.22818e6i	0.512111	+	0.372070i
$406$	1.53461e6	−	1.11496e6i	0.462043	−	0.335694i
$407$	−988875.	−	3.04344e6i	−0.295907	−	0.910708i
$408$	−661947.			−0.196867
$409$	−1.55556e6			−0.459811			−0.229905	−	0.973213i	$-0.573842\pi$
$409$	−1.55556e6			−0.459811			−0.229905	+	0.973213i	$0.573842\pi$
$410$	236521.	+	727937.i	0.0694881	+	0.213862i
$411$	−587115.	+	1.80695e6i	−0.171442	+	0.527646i
$412$	958566.	−	2.95016e6i	0.278214	−	0.856254i
$413$	1.46023e6	+	1.06092e6i	0.421256	+	0.306060i
$414$	−510087.	−	1.56989e6i	−0.146266	−	0.450161i
$415$	−2.34922e6	−	1.70681e6i	−0.669581	−	0.486479i
$416$	−95861.4	+	69647.4i	−0.0271588	+	0.0197320i
$417$	−293451.	+	903149.i	−0.0826410	+	0.254343i
$418$	2.48168e6	−	1.80305e6i	0.694713	−	0.504738i
$419$	−3.78463e6	+	2.74970e6i	−1.05315	+	0.765155i	−0.972808	−	0.231612i	$-0.925600\pi$
$419$	−3.78463e6	+	2.74970e6i	−1.05315	+	0.765155i	−0.0803378	+	0.996768i	$0.525600\pi$
$420$	−530976.	+	1.63417e6i	−0.146876	+	0.452038i
$421$	−3.36610e6	+	2.44562e6i	−0.925597	+	0.672486i	−0.944911	−	0.327328i	$-0.893852\pi$
$421$	−3.36610e6	+	2.44562e6i	−0.925597	+	0.672486i	0.0193136	+	0.999813i	$0.493852\pi$
$422$	632108.	+	459253.i	0.172787	+	0.125537i
$423$	−392356.	−	1.20755e6i	−0.106618	−	0.328135i
$424$	471671.	+	342689.i	0.127416	+	0.0925733i
$425$	266674.	−	820737.i	0.0716156	−	0.220410i
$426$	373894.	−	1.15073e6i	0.0998216	−	0.307219i
$427$	1.70373e6	+	5.24354e6i	0.452200	+	1.39173i
$428$	930446.			0.245517
$429$	−610050.			−0.160038
$430$	1.38006e6	+	4.24737e6i	0.359936	+	1.10777i
$431$	3.98626e6	−	2.89619e6i	1.03365	−	0.750989i	0.0646123	−	0.997910i	$-0.479419\pi$
$431$	3.98626e6	−	2.89619e6i	1.03365	−	0.750989i	0.969036	+	0.246921i	$0.0794189\pi$
$432$	−854065.	−	620514.i	−0.220182	−	0.159971i
$433$	4.08445e6			1.04692			0.523460	−	0.852050i	$-0.324641\pi$
$433$	4.08445e6			1.04692			0.523460	+	0.852050i	$0.324641\pi$
$434$	−2.79074e6	−	259235.i	−0.711206	−	0.0660648i
$435$	2.96968e6			0.752465
$436$	−2.53862e6	−	1.84441e6i	−0.639560	−	0.464667i
$437$	7.48885e6	−	5.44097e6i	1.87591	−	1.36293i
$438$	−4931.03	−	15176.2i	−0.00122815	−	0.00377987i
$439$	−5.28725e6			−1.30939			−0.654694	−	0.755894i	$-0.727202\pi$
$439$	−5.28725e6			−1.30939			−0.654694	+	0.755894i	$0.727202\pi$
$440$	1.72104e6			0.423798
$441$	−8693.86	−	26757.0i	−0.00212871	−	0.00655149i
$442$	116671.	−	359076.i	0.0284058	−	0.0874240i
$443$	−1.21566e6	+	3.74142e6i	−0.294309	+	0.905789i	0.689144	+	0.724624i	$0.257987\pi$
$443$	−1.21566e6	+	3.74142e6i	−0.294309	+	0.905789i	−0.983453	+	0.181165i	$0.942013\pi$
$444$	−1.26321e6	−	917778.i	−0.304102	−	0.220943i
$445$	757157.	+	2.33029e6i	0.181253	+	0.557840i
$446$	2.40879e6	+	1.75009e6i	0.573405	+	0.416603i
$447$	−1.01692e6	+	738833.i	−0.240722	+	0.174895i
$448$	165754.	−	510138.i	0.0390183	−	0.120086i
$449$	2.74955e6	−	1.99767e6i	0.643645	−	0.467636i	−0.217455	−	0.976070i	$-0.569776\pi$
$449$	2.74955e6	−	1.99767e6i	0.643645	−	0.467636i	0.861101	+	0.508435i	$0.169776\pi$
$450$	281504.	−	204525.i	0.0655320	−	0.0476118i
$451$	380136.	−	1.16994e6i	0.0880030	−	0.270845i
$452$	−1.66864e6	+	1.21234e6i	−0.384164	+	0.279111i
$453$	−4.89320e6	−	3.55512e6i	−1.12033	−	0.813971i
$454$	657926.	+	2.02489e6i	0.149809	+	0.461064i
$455$	−792878.	−	576060.i	−0.179547	−	0.130448i
$456$	462520.	−	1.42349e6i	0.104164	−	0.320584i
$457$	−645060.	+	1.98529e6i	−0.144481	+	0.444666i	−0.996944	−	0.0781215i	$-0.975108\pi$
$457$	−645060.	+	1.98529e6i	−0.144481	+	0.444666i	0.852463	+	0.522787i	$0.175108\pi$
$458$	896896.	+	2.76036e6i	0.199792	+	0.614897i
$459$	3.36377e6			0.745238
$460$	5.19351e6			1.14437
$461$	2.18108e6	+	6.71268e6i	0.477991	+	1.47111i	0.841881	+	0.539663i	$0.181448\pi$
$461$	2.18108e6	+	6.71268e6i	0.477991	+	1.47111i	−0.363890	+	0.931442i	$0.618552\pi$
$462$	2.23418e6	−	1.62323e6i	0.486983	−	0.353814i
$463$	4.97470e6	+	3.61433e6i	1.07849	+	0.783566i	0.977418	−	0.211313i	$-0.0677740\pi$
$463$	4.97470e6	+	3.61433e6i	1.07849	+	0.783566i	0.101068	+	0.994880i	$0.467774\pi$
$464$	−927041.			−0.199896
$465$	−3.29610e6	−	2.89641e6i	−0.706917	−	0.621196i
$466$	5.80179e6			1.23765
$467$	−6.71859e6	−	4.88134e6i	−1.42556	−	1.03573i	−0.990822	−	0.135176i	$-0.956840\pi$
$467$	−6.71859e6	−	4.88134e6i	−1.42556	−	1.03573i	−0.434741	−	0.900556i	$-0.643160\pi$
$468$	123159.	−	89480.3i	0.0259927	−	0.0188848i
$469$	168671.	+	519117.i	0.0354086	+	0.108977i
$470$	3.99481e6			0.834164
$471$	3.29475e6			0.684338
$472$	−272586.	−	838935.i	−0.0563183	−	0.173330i
$473$	2.21802e6	−	6.82636e6i	0.455840	−	1.40293i
$474$	−790157.	+	2.43185e6i	−0.161535	+	0.497155i
$475$	1.57863e6	+	1.14694e6i	0.321030	+	0.233242i
$476$	528150.	+	1.62548e6i	0.106842	+	0.328824i
$477$	−605985.	−	440274.i	−0.121946	−	0.0885987i
$478$	−3.87423e6	+	2.81479e6i	−0.775560	+	0.563477i
$479$	−806863.	+	2.48327e6i	−0.160680	+	0.494521i	−0.998692	−	0.0511300i	$-0.983718\pi$
$479$	−806863.	+	2.48327e6i	−0.160680	+	0.494521i	0.838012	+	0.545651i	$0.183718\pi$
$480$	679373.	−	493593.i	0.134588	−	0.0977837i
$481$	720498.	−	523473.i	0.141994	−	0.103165i
$482$	−907737.	+	2.79373e6i	−0.177968	+	0.547730i
$483$	6.74199e6	−	4.89834e6i	1.31498	−	0.955391i
$484$	−153092.	−	111228.i	−0.0297056	−	0.0215824i
$485$	−1.85373e6	−	5.70518e6i	−0.357842	−	1.10132i
$486$	1.91712e6	+	1.39287e6i	0.368179	+	0.267498i
$487$	720938.	−	2.21882e6i	0.137745	−	0.423935i	−0.858262	−	0.513212i	$-0.828456\pi$
$487$	720938.	−	2.21882e6i	0.137745	−	0.423935i	0.996007	+	0.0892767i	$0.0284555\pi$
$488$	832644.	−	2.56261e6i	0.158274	−	0.487117i
$489$	−1.01483e6	−	3.12331e6i	−0.191920	−	0.590668i
$490$	88517.4			0.0166548
$491$	−1.46079e6			−0.273453			−0.136727	−	0.990609i	$-0.543658\pi$
$491$	−1.46079e6			−0.273453			−0.136727	+	0.990609i	$0.543658\pi$
$492$	−185481.	−	570850.i	−0.0345450	−	0.106319i
$493$	2.38974e6	−	1.73625e6i	0.442826	−	0.321732i
$494$	690657.	+	501791.i	0.127334	+	0.0925137i
$495$	−2.21113e6			−0.405603
$496$	1.02894e6	+	904170.i	0.187796	+	0.165023i
$497$	−3.12405e6			−0.567319
$498$	1.84226e6	+	1.33848e6i	0.332873	+	0.241846i
$499$	−3.98439e6	+	2.89483e6i	−0.716326	+	0.520441i	−0.885208	−	0.465195i	$-0.845984\pi$
$499$	−3.98439e6	+	2.89483e6i	−0.716326	+	0.520441i	0.168882	+	0.985636i	$0.445984\pi$
$500$	−660990.	−	2.03432e6i	−0.118242	−	0.363910i
$501$	2.33626e6			0.415840
$502$	2.26591e6			0.401313
$503$	−2.60949e6	−	8.03118e6i	−0.459871	−	1.41534i	−0.865321	−	0.501219i	$-0.832885\pi$
$503$	−2.60949e6	−	8.03118e6i	−0.459871	−	1.41534i	0.405450	−	0.914117i	$-0.367115\pi$
$504$	−212954.	+	655406.i	−0.0373431	+	0.114930i
$505$	−2.80153e6	+	8.62222e6i	−0.488840	+	1.50449i
$506$	−6.75285e6	−	4.90623e6i	−1.17249	−	0.851867i
$507$	1.40235e6	+	4.31600e6i	0.242291	+	0.745696i
$508$	3.76914e6	+	2.73844e6i	0.648012	+	0.470808i
$509$	−4.66675e6	+	3.39059e6i	−0.798399	+	0.580071i	−0.910444	−	0.413632i	$-0.864260\pi$
$509$	−4.66675e6	+	3.39059e6i	−0.798399	+	0.580071i	0.112045	+	0.993703i	$0.464260\pi$
$510$	−826850.	+	2.54478e6i	−0.140767	+	0.433237i
$511$	−33332.3	+	24217.3i	−0.00564694	+	0.00410274i
$512$	−212079.	+	154084.i	−0.0357538	+	0.0259767i
$513$	−2.35036e6	+	7.23366e6i	−0.394312	+	1.21357i
$514$	−951930.	+	691617.i	−0.158927	+	0.115467i
$515$	−1.01442e7	−	7.37020e6i	−1.68539	−	1.22451i
$516$	−1.08224e6	−	3.33080e6i	−0.178937	−	0.550712i
$517$	−5.19424e6	−	3.77384e6i	−0.854665	−	0.620951i
$518$	−1.24581e6	+	3.83422e6i	−0.203999	+	0.627845i
$519$	2.13878e6	−	6.58250e6i	0.348537	−	1.07269i
$520$	148010.	+	455527.i	0.0240039	+	0.0738763i
$521$	7.41006e6			1.19599			0.597994	−	0.801500i	$-0.295964\pi$
$521$	7.41006e6			1.19599			0.597994	+	0.801500i	$0.295964\pi$
$522$	1.19103e6			0.191313
$523$	1.67810e6	+	5.16465e6i	0.268264	+	0.825633i	0.990923	+	0.134428i	$0.0429197\pi$
$523$	1.67810e6	+	5.16465e6i	0.268264	+	0.825633i	−0.722659	+	0.691205i	$0.757080\pi$
$524$	2.23321e6	−	1.62252e6i	0.355304	−	0.258144i
$525$	1.42119e6	+	1.03256e6i	0.225037	+	0.163499i
$526$	−7.48770e6			−1.18001
$527$	−4.34582e6	−	403689.i	−0.681625	−	0.0633169i
$528$	−1.34964e6			−0.210685
$529$	−1.51707e7	−	1.10221e7i	−2.35703	−	1.71248i
$530$	1.90660e6	−	1.38523e6i	0.294830	−	0.214206i
$531$	350209.	+	1.07783e6i	0.0539002	+	0.165888i
$532$	−3.86456e6			−0.591999
$533$	342352.			0.0521981
$534$	−593765.	−	1.82742e6i	−0.0901076	−	0.277323i
$535$	1.16224e6	−	3.57700e6i	0.175554	−	0.540299i
$536$	82432.7	−	253702.i	0.0123933	−	0.0381427i
$537$	2.80918e6	+	2.04099e6i	0.420382	+	0.305425i
$538$	289398.	+	890674.i	0.0431062	+	0.132667i
$539$	−115095.	−	83621.2i	−0.0170641	−	0.0123978i
$540$	−3.45233e6	+	2.50826e6i	−0.509481	+	0.370159i
$541$	−3.69572e6	+	1.13743e7i	−0.542883	+	1.67082i	0.183088	+	0.983096i	$0.441391\pi$
$541$	−3.69572e6	+	1.13743e7i	−0.542883	+	1.67082i	−0.725971	+	0.687725i	$0.758609\pi$
$542$	2.79164e6	−	2.02824e6i	0.408189	−	0.296566i
$543$	2.32270e6	−	1.68754e6i	0.338060	−	0.245615i
$544$	258117.	−	794401.i	0.0373954	−	0.115091i
$545$	−1.02617e7	+	7.45555e6i	−1.47988	+	1.07520i
$546$	621777.	+	451748.i	0.0892592	+	0.0648506i
$547$	3.44322e6	+	1.05971e7i	0.492035	+	1.51433i	0.821527	+	0.570170i	$0.193123\pi$
$547$	3.44322e6	+	1.05971e7i	0.492035	+	1.51433i	−0.329492	+	0.944158i	$0.606877\pi$
$548$	−1.93958e6	−	1.40919e6i	−0.275903	−	0.200456i
$549$	−1.06975e6	+	3.29235e6i	−0.151479	+	0.466203i
$550$	543721.	−	1.67340e6i	0.0766425	−	0.235881i
$551$	2.06395e6	+	6.35219e6i	0.289615	+	0.891342i
$552$	−4.07276e6			−0.568907
$553$	6.60211e6			0.918058
$554$	−2.58042e6	−	7.94170e6i	−0.357203	−	1.09936i
$555$	−5.10620e6	+	3.70987e6i	−0.703664	+	0.511242i
$556$	−969441.	−	704340.i	−0.132995	−	0.0966263i
$557$	9.44064e6			1.28933			0.644664	−	0.764466i	$-0.276997\pi$
$557$	9.44064e6			1.28933			0.644664	+	0.764466i	$0.276997\pi$
$558$	−1.32194e6	−	1.16164e6i	−0.179733	−	0.157938i
$559$	1.99756e6			0.270377
$560$	−1.75412e6	−	1.27445e6i	−0.236369	−	0.171732i
$561$	3.47913e6	−	2.52774e6i	0.466728	−	0.339098i
$562$	902272.	+	2.77691e6i	0.120503	+	0.370869i
$563$	9.96821e6			1.32540			0.662699	−	0.748886i	$-0.269411\pi$
$563$	9.96821e6			1.32540			0.662699	+	0.748886i	$0.269411\pi$
$564$	−3.13274e6			−0.414693
$565$	2.57637e6	+	7.92926e6i	0.339537	+	1.04499i
$566$	−563885.	+	1.73546e6i	−0.0739860	+	0.227706i
$567$	−1.30739e6	+	4.02375e6i	−0.170785	+	0.525621i
$568$	1.23519e6	+	897419.i	0.160644	+	0.116714i
$569$	3.74539e6	+	1.15271e7i	0.484972	+	1.49259i	0.832022	+	0.554743i	$0.187183\pi$
$569$	3.74539e6	+	1.15271e7i	0.484972	+	1.49259i	−0.347050	+	0.937846i	$0.612817\pi$
$570$	−4.89471e6	−	3.55621e6i	−0.631015	−	0.458459i
$571$	−2.68958e6	+	1.95409e6i	−0.345218	+	0.250816i	−0.746860	−	0.664981i	$-0.768440\pi$
$571$	−2.68958e6	+	1.95409e6i	−0.345218	+	0.250816i	0.401642	+	0.915797i	$0.368440\pi$
$572$	237880.	−	732120.i	0.0303996	−	0.0935604i
$573$	9.62145e6	−	6.99039e6i	1.22420	−	0.889437i
$574$	−1.25379e6	+	910933.i	−0.158835	+	0.115400i
$575$	1.64076e6	−	5.04975e6i	0.206955	−	0.636943i
$576$	272471.	−	197962.i	0.0342187	−	0.0248614i
$577$	−2.28945e6	−	1.66338e6i	−0.286280	−	0.207995i	0.435372	−	0.900251i	$-0.356617\pi$
$577$	−2.28945e6	−	1.66338e6i	−0.286280	−	0.207995i	−0.721652	+	0.692256i	$0.756617\pi$
$578$	−932589.	−	2.87022e6i	−0.116110	−	0.357351i
$579$	−7.54841e6	−	5.48424e6i	−0.935749	−	0.679861i
$580$	−1.15798e6	+	3.56391e6i	−0.142933	+	0.439902i
$581$	1.81689e6	−	5.59181e6i	0.223300	−	0.687245i
$582$	1.45370e6	+	4.47402e6i	0.177896	+	0.547508i
$583$	−3.78767e6			−0.461530
$584$	20135.7			0.00244306
$585$	−190157.	−	585243.i	−0.0229733	−	0.0707045i
$586$	−1.81730e6	+	1.32035e6i	−0.218617	+	0.158834i
$587$	4.38394e6	+	3.18512e6i	0.525133	+	0.381532i	0.818534	−	0.574458i	$-0.194787\pi$
$587$	4.38394e6	+	3.18512e6i	0.525133	+	0.381532i	−0.293401	+	0.955990i	$0.594787\pi$
$588$	−69415.6			−0.00827969
$589$	3.90466e6	−	9.06345e6i	0.463761	−	1.07648i
$590$	−3.56569e6			−0.421709
$591$	−3.31384e6	−	2.40765e6i	−0.390268	−	0.283547i
$592$	1.59399e6	−	1.15810e6i	0.186932	−	0.135814i
$593$	−2.88501e6	−	8.87916e6i	−0.336908	−	1.03690i	−0.965775	−	0.259382i	$-0.916481\pi$
$593$	−2.88501e6	−	8.87916e6i	−0.336908	−	1.03690i	0.628867	−	0.777513i	$-0.283519\pi$
$594$	6.85840e6			0.797548
$595$	6.90870e6			0.800026
$596$	−490140.	−	1.50850e6i	−0.0565204	−	0.173952i
$597$	−1.99909e6	+	6.15256e6i	−0.229560	+	0.706512i
$598$	717841.	−	2.20929e6i	0.0820871	−	0.252638i
$599$	−6.32269e6	−	4.59370e6i	−0.720004	−	0.523113i	0.166382	−	0.986061i	$-0.446792\pi$
$599$	−6.32269e6	−	4.59370e6i	−0.720004	−	0.523113i	−0.886385	+	0.462948i	$0.846792\pi$
$600$	−265299.	−	816507.i	−0.0300855	−	0.0925938i
$601$	311847.	+	226570.i	0.0352172	+	0.0255868i	0.605255	−	0.796032i	$-0.293071\pi$
$601$	311847.	+	226570.i	0.0352172	+	0.0255868i	−0.570037	+	0.821619i	$0.693071\pi$
$602$	−7.31563e6	+	5.31512e6i	−0.822736	+	0.597753i
$603$	−105906.	+	325947.i	−0.0118612	+	0.0365051i
$604$	6.17453e6	−	4.48606e6i	0.688670	−	0.500348i
$605$	−618833.	+	449608.i	−0.0687361	+	0.0499397i
$606$	2.19697e6	−	6.76157e6i	0.243020	−	0.747939i
$607$	1.37098e7	−	9.96075e6i	1.51029	−	1.09729i	0.544237	−	0.838931i	$-0.316819\pi$
$607$	1.37098e7	−	9.96075e6i	1.51029	−	1.09729i	0.966050	−	0.258356i	$-0.0831809\pi$
$608$	1.52797e6	+	1.11014e6i	0.167632	+	0.121792i
$609$	1.85811e6	+	5.71869e6i	0.203015	+	0.624817i
$610$	−8.81162e6	−	6.40202e6i	−0.958807	−	0.696614i
$611$	552158.	−	1.69937e6i	0.0598357	−	0.184155i
$612$	−331618.	+	1.02062e6i	−0.0357899	+	0.110150i
$613$	−2.21879e6	−	6.82875e6i	−0.238488	−	0.733990i	−0.996640	−	0.0819116i	$-0.973897\pi$
$613$	−2.21879e6	−	6.82875e6i	−0.238488	−	0.733990i	0.758152	−	0.652078i	$-0.226103\pi$
$614$	−3.66136e6			−0.391942
$615$	−2.42626e6			−0.258672
$616$	1.07685e6	+	3.31419e6i	0.114341	+	0.351905i
$617$	−1.33764e7	+	9.71849e6i	−1.41457	+	1.02775i	−0.421933	+	0.906627i	$0.638648\pi$
$617$	−1.33764e7	+	9.71849e6i	−1.41457	+	1.02775i	−0.992638	+	0.121119i	$0.961352\pi$
$618$	7.95512e6	+	5.77973e6i	0.837868	+	0.608747i
$619$	1.15192e7			1.20836			0.604182	−	0.796847i	$-0.293500\pi$
$619$	1.15192e7			1.20836			0.604182	+	0.796847i	$0.293500\pi$
$620$	4.76125e6	−	2.82623e6i	0.497441	−	0.295276i
$621$	2.06963e7			2.15359
$622$	−7.36713e6	−	5.35254e6i	−0.763524	−	0.554733i
$623$	−4.01367e6	+	2.91610e6i	−0.414306	+	0.301011i
$624$	−116069.	−	357225.i	−0.0119332	−	0.0367266i
$625$	−1.19525e7			−1.22393
$626$	1.16246e7			1.18561
$627$	3.00483e6	+	9.24792e6i	0.305247	+	0.939453i
$628$	−1.28474e6	+	3.95403e6i	−0.129992	+	0.400074i
$629$	−1.94002e6	+	5.97075e6i	−0.195514	+	0.601731i
$630$	2.25363e6	+	1.63736e6i	0.226220	+	0.164359i
$631$	−2.27687e6	−	7.00749e6i	−0.227649	−	0.700631i	−0.998012	−	0.0630255i	$-0.979925\pi$
$631$	−2.27687e6	−	7.00749e6i	−0.227649	−	0.700631i	0.770363	−	0.637605i	$-0.220075\pi$
$632$	−2.61035e6	−	1.89653e6i	−0.259960	−	0.188872i
$633$	−2.00374e6	+	1.45580e6i	−0.198761	+	0.144408i
$634$	2.24395e6	−	6.90616e6i	0.221712	−	0.682360i
$635$	1.52357e7	−	1.10694e7i	1.49944	−	1.08941i
$636$	−1.49516e6	+	1.08630e6i	−0.146570	+	0.106490i
$637$	12234.8	−	37654.8i	0.00119467	−	0.00367681i
$638$	4.87244e6	−	3.54003e6i	0.473909	−	0.344315i
$639$	−1.58693e6	−	1.15297e6i	−0.153746	−	0.111703i
$640$	327449.	+	1.00778e6i	0.0316005	+	0.0972563i
$641$	1.02144e7	+	7.42117e6i	0.981898	+	0.713390i	0.958132	−	0.286327i	$-0.0924344\pi$
$641$	1.02144e7	+	7.42117e6i	0.981898	+	0.713390i	0.0237657	+	0.999718i	$0.492434\pi$
$642$	−911430.	+	2.80509e6i	−0.0872742	+	0.268602i
$643$	2.92551e6	−	9.00379e6i	0.279045	−	0.858811i	−0.709076	−	0.705132i	$-0.750888\pi$
$643$	2.92551e6	−	9.00379e6i	0.279045	−	0.858811i	0.988121	−	0.153679i	$-0.0491123\pi$
$644$	3.24955e6	+	1.00011e7i	0.308751	+	0.950238i
$645$	−1.41568e7			−1.33988
$646$	−6.01800e6			−0.567376
$647$	1.80887e6	+	5.56713e6i	0.169882	+	0.522842i	0.999363	−	0.0356925i	$-0.0113637\pi$
$647$	1.80887e6	+	5.56713e6i	0.169882	+	0.522842i	−0.829481	+	0.558535i	$0.811364\pi$
$648$	1.67279e6	−	1.21535e6i	0.156496	−	0.113701i
$649$	4.63628e6	+	3.36845e6i	0.432074	+	0.313920i
$650$	489678.			0.0454597
$651$	3.51524e6	−	8.15955e6i	0.325090	−	0.754594i
$652$	4.14400e6			0.381769
$653$	5.75340e6	+	4.18009e6i	0.528009	+	0.383621i	0.819613	−	0.572918i	$-0.194189\pi$
$653$	5.75340e6	+	4.18009e6i	0.528009	+	0.383621i	−0.291603	+	0.956539i	$0.594189\pi$
$654$	8.04724e6	−	5.84666e6i	0.735703	−	0.534520i
$655$	−3.44806e6	−	1.06120e7i	−0.314030	−	0.966485i
$656$	757402.			0.0687174
$657$	−25869.5			−0.00233817
$658$	2.49953e6	+	7.69277e6i	0.225058	+	0.692656i
$659$	3.06942e6	−	9.44671e6i	0.275323	−	0.847359i	−0.713810	−	0.700339i	$-0.753032\pi$
$659$	3.06942e6	−	9.44671e6i	0.275323	−	0.847359i	0.989134	−	0.147019i	$-0.0469679\pi$
$660$	−1.68587e6	+	5.18856e6i	−0.150648	+	0.463647i
$661$	1.29316e7	+	9.39536e6i	1.15119	+	0.836392i	0.988639	−	0.150308i	$-0.0480265\pi$
$661$	1.29316e7	+	9.39536e6i	1.15119	+	0.836392i	0.162555	+	0.986699i	$0.448027\pi$
$662$	371303.	+	1.14275e6i	0.0329294	+	0.101346i
$663$	968249.	+	703474.i	0.0855467	+	0.0621533i
$664$	−2.32467e6	+	1.68897e6i	−0.204617	+	0.148663i
$665$	−4.82729e6	+	1.48569e7i	−0.423301	+	1.30279i
$666$	−2.04790e6	+	1.48789e6i	−0.178906	+	0.129983i
$667$	1.47033e7	−	1.06826e7i	1.27968	−	0.929742i
$668$	−910990.	+	2.80374e6i	−0.0789901	+	0.243106i
$669$	−7.63569e6	+	5.54766e6i	−0.659604	+	0.479230i
$670$	−872361.	−	633807.i	−0.0750774	−	0.0545469i
$671$	5.40940e6	+	1.66484e7i	0.463813	+	1.42747i
$672$	1.37559e6	+	999424.i	0.117507	+	0.0853742i
$673$	4.34549e6	−	1.33740e7i	0.369829	−	1.13822i	−0.577073	−	0.816693i	$-0.695805\pi$
$673$	4.34549e6	−	1.33740e7i	0.369829	−	1.13822i	0.946902	−	0.321523i	$-0.104195\pi$
$674$	−664904.	+	2.04637e6i	−0.0563780	+	0.173514i
$675$	1.34815e6	+	4.14919e6i	0.113889	+	0.350513i
$676$	−5.72645e6			−0.481969
$677$	3.50518e6			0.293926			0.146963	−	0.989142i	$-0.453050\pi$
$677$	3.50518e6			0.293926			0.146963	+	0.989142i	$0.453050\pi$
$678$	−2.02040e6	−	6.21814e6i	−0.168796	−	0.519501i
$679$	9.82655e6	−	7.13941e6i	0.817950	−	0.594275i
$680$	−2.73157e6	−	1.98460e6i	−0.226538	−	0.164589i
$681$	−6.74907e6			−0.557669
$682$	−8.86071e6	−	823081.i	−0.729470	−	0.0677613i
$683$	−2.15686e7			−1.76917			−0.884586	−	0.466376i	$-0.845559\pi$
$683$	−2.15686e7			−1.76917			−0.884586	+	0.466376i	$0.845559\pi$
$684$	−1.96308e6	−	1.42626e6i	−0.160435	−	0.116563i
$685$	−7.84025e6	+	5.69627e6i	−0.638415	+	0.463836i
$686$	−2.66515e6	−	8.20248e6i	−0.216228	−	0.665480i
$687$	−9.20046e6			−0.743734
$688$	4.41929e6			0.355944
$689$	−325739.	−	1.00252e6i	−0.0261410	−	0.0804537i
$690$	−5.08736e6	+	1.56573e7i	−0.406790	+	1.25197i
$691$	4.54158e6	−	1.39775e7i	0.361836	−	1.11362i	−0.590103	−	0.807328i	$-0.700913\pi$
$691$	4.54158e6	−	1.39775e7i	0.361836	−	1.11362i	0.951939	−	0.306289i	$-0.0990873\pi$
$692$	7.06566e6	+	5.13350e6i	0.560903	+	0.407520i
$693$	−1.38349e6	−	4.25795e6i	−0.109432	−	0.336796i
$694$	−9.33640e6	−	6.78329e6i	−0.735836	−	0.534616i
$695$	−3.91870e6	+	2.84711e6i	−0.307738	+	0.223584i
$696$	908094.	−	2.79483e6i	0.0710571	−	0.218691i
$697$	−1.95244e6	+	1.41853e6i	−0.152228	+	0.110600i
$698$	4.33764e6	−	3.15148e6i	0.336988	−	0.244836i
$699$	−5.68321e6	+	1.74911e7i	−0.439948	+	1.35402i
$700$	−1.79334e6	+	1.30294e6i	−0.138331	+	0.100503i
$701$	7.72226e6	+	5.61055e6i	0.593539	+	0.431231i	0.843580	−	0.537004i	$-0.180444\pi$
$701$	7.72226e6	+	5.61055e6i	0.593539	+	0.431231i	−0.250041	+	0.968235i	$0.580444\pi$
$702$	589823.	+	1.81529e6i	0.0451730	+	0.139028i
$703$	−1.14843e7	−	8.34385e6i	−0.876429	−	0.636763i
$704$	526274.	−	1.61971e6i	0.0400203	−	0.123170i
$705$	−3.91316e6	+	1.20435e7i	−0.296521	+	0.912597i
$706$	2.03755e6	+	6.27093e6i	0.153850	+	0.473501i
$707$	−1.83566e7			−1.38116
$708$	2.79622e6			0.209647
$709$	1.65551e6	+	5.09514e6i	0.123685	+	0.380663i	0.993659	−	0.112434i	$-0.0358647\pi$
$709$	1.65551e6	+	5.09514e6i	0.123685	+	0.380663i	−0.869974	+	0.493097i	$0.835865\pi$
$710$	4.99293e6	−	3.62758e6i	0.371715	−	0.270066i
$711$	3.35368e6	+	2.43659e6i	0.248799	+	0.180763i
$712$	2.42461e6			0.179243
$713$	−2.67386e7	−	2.48377e6i	−1.96976	−	0.182974i
$714$	−5.41782e6			−0.397722
$715$	−2.51742e6	−	1.82901e6i	−0.184158	−	0.133798i
$716$	−3.54479e6	+	2.57544e6i	−0.258409	+	0.187745i
$717$	−4.69093e6	−	1.44372e7i	−0.340770	−	1.04878i
$718$	1.49856e7			1.08483
$719$	2.87893e6			0.207687			0.103843	−	0.994594i	$-0.466886\pi$
$719$	2.87893e6			0.207687			0.103843	+	0.994594i	$0.466886\pi$
$720$	−420694.	−	1.29476e6i	−0.0302437	−	0.0930806i
$721$	7.84555e6	−	2.41461e7i	0.562063	−	1.72985i
$722$	1.14431e6	−	3.52181e6i	0.0816957	−	0.251434i
$723$	−7.53329e6	−	5.47326e6i	−0.535968	−	0.389404i
$724$	1.11951e6	+	3.44550e6i	0.0793746	+	0.244290i
$725$	3.09942e6	+	2.25186e6i	0.218996	+	0.159110i
$726$	485290.	−	352584.i	0.0341712	−	0.0248268i
$727$	−2.92003e6	+	8.98692e6i	−0.204904	+	0.630630i	0.794813	+	0.606854i	$0.207569\pi$
$727$	−2.92003e6	+	8.98692e6i	−0.204904	+	0.630630i	−0.999717	+	0.0237760i	$0.992431\pi$
$728$	−784594.	+	570041.i	−0.0548677	+	0.0398637i
$729$	−1.24285e7	+	9.02984e6i	−0.866164	+	0.629305i
$730$	25151.8	−	77409.4i	0.00174688	−	0.00537634i
$731$	−1.13921e7	+	8.27685e6i	−0.788516	+	0.572891i
$732$	6.91010e6	+	5.02048e6i	0.476657	+	0.346312i
$733$	−1.29706e6	−	3.99195e6i	−0.0891663	−	0.274426i	0.896523	−	0.442997i	$-0.146085\pi$
$733$	−1.29706e6	−	3.99195e6i	−0.0891663	−	0.274426i	−0.985689	+	0.168571i	$0.946085\pi$
$734$	1.16678e7	+	8.47714e6i	0.799370	+	0.580777i
$735$	−86708.3	+	266861.i	−0.00592028	+	0.0182208i
$736$	1.58811e6	−	4.88771e6i	0.108066	−	0.332592i
$737$	535537.	+	1.64821e6i	0.0363179	+	0.111775i
$738$	−973081.			−0.0657670
$739$	−8.65631e6			−0.583072			−0.291536	−	0.956560i	$-0.594166\pi$
$739$	−8.65631e6			−0.583072			−0.291536	+	0.956560i	$0.594166\pi$
$740$	−2.46112e6	−	7.57455e6i	−0.165217	−	0.508484i
$741$	−2.18933e6	+	1.59064e6i	−0.146476	+	0.106421i
$742$	3.86048e6	+	2.80480e6i	0.257413	+	0.187022i
$743$	1.56966e7			1.04312			0.521560	−	0.853215i	$-0.325350\pi$
$743$	1.56966e7			1.04312			0.521560	+	0.853215i	$0.325350\pi$
$744$	−3.73378e6	+	2.21634e6i	−0.247296	+	0.146792i
$745$	−6.41150e6			−0.423223
$746$	−1.12318e7	−	8.16035e6i	−0.738926	−	0.536861i
$747$	2.98665e6	−	2.16993e6i	0.195832	−	0.142280i
$748$	1.67690e6	+	5.16095e6i	0.109585	+	0.337269i
$749$	7.61540e6			0.496007
$750$	6.78051e6			0.440159
$751$	3.77650e6	+	1.16229e7i	0.244337	+	0.751992i	0.995745	+	0.0921537i	$0.0293751\pi$
$751$	3.77650e6	+	1.16229e7i	0.244337	+	0.751992i	−0.751408	+	0.659838i	$0.770625\pi$
$752$	1.22157e6	−	3.75960e6i	0.0787721	−	0.242436i
$753$	−2.21960e6	+	6.83122e6i	−0.142655	+	0.439047i
$754$	1.35601e6	+	985199.i	0.0868629	+	0.0631096i
$755$	−9.53344e6	−	2.93409e7i	−0.608671	−	1.87330i
$756$	−6.99024e6	−	5.07871e6i	−0.444824	−	0.323183i
$757$	4.68546e6	−	3.40419e6i	0.297175	−	0.215910i	−0.429199	−	0.903210i	$-0.641204\pi$
$757$	4.68546e6	−	3.40419e6i	0.297175	−	0.215910i	0.726374	+	0.687300i	$0.241204\pi$
$758$	−604060.	+	1.85911e6i	−0.0381863	+	0.117525i
$759$	2.14060e7	−	1.55524e7i	1.34875	−	0.979926i
$760$	6.17643e6	−	4.48744e6i	0.387885	−	0.281815i
$761$	−2.19205e6	+	6.74645e6i	−0.137211	+	0.422293i	−0.995927	−	0.0901587i	$-0.971263\pi$
$761$	−2.19205e6	+	6.74645e6i	−0.137211	+	0.422293i	0.858716	+	0.512452i	$0.171263\pi$
$762$	−1.19479e7	+	8.68066e6i	−0.745426	+	0.541583i
$763$	−2.07778e7	−	1.50959e7i	−1.29207	−	0.938747i
$764$	4.63741e6	+	1.42725e7i	0.287437	+	0.884639i
$765$	3.50942e6	+	2.54974e6i	0.216811	+	0.157523i
$766$	6.50938e6	−	2.00338e7i	0.400837	−	1.23365i
$767$	−492845.	+	1.51682e6i	−0.0302498	+	0.0930992i
$768$	−256786.	−	790307.i	−0.0157097	−	0.0483496i
$769$	−3.26236e7			−1.98937			−0.994685	−	0.102962i	$-0.967168\pi$
$769$	−3.26236e7			−1.98937			−0.994685	+	0.102962i	$0.967168\pi$
$770$	1.40862e7			0.856181
$771$	−1.15260e6	−	3.54734e6i	−0.0698302	−	0.214915i
$772$	9.52502e6	−	6.92033e6i	0.575205	−	0.417911i
$773$	1.88364e7	+	1.36854e7i	1.13383	+	0.823778i	0.986248	−	0.165271i	$-0.0528499\pi$
$773$	1.88364e7	+	1.36854e7i	1.13383	+	0.823778i	0.147585	+	0.989049i	$0.452850\pi$
$774$	−5.67774e6			−0.340662
$775$	−1.24380e6	−	5.52234e6i	−0.0743869	−	0.330270i
$776$	−5.93611e6			−0.353873
$777$	−1.03390e7	−	7.51171e6i	−0.614363	−	0.446361i
$778$	−1.29937e7	+	9.44050e6i	−0.769636	+	0.559173i
$779$	−1.68627e6	−	5.18981e6i	−0.0995597	−	0.306413i
$780$	−1.51830e6			−0.0893553
$781$	−9.91897e6			−0.581887
$782$	5.06029e6	+	1.55740e7i	0.295909	+	0.910715i
$783$	−4.61460e6	+	1.42023e7i	−0.268986	+	0.827854i
$784$	27067.6	−	83305.6i	0.00157275	−	0.00484043i
$785$	1.35960e7	+	9.87809e6i	0.787477	+	0.572136i
$786$	2.70398e6	+	8.32199e6i	0.156116	+	0.480475i
$787$	1.04333e7	+	7.58022e6i	0.600460	+	0.436260i	0.846042	−	0.533116i	$-0.178979\pi$
$787$	1.04333e7	+	7.58022e6i	0.600460	+	0.436260i	−0.245582	+	0.969376i	$0.578979\pi$
$788$	4.18160e6	−	3.03811e6i	0.239898	−	0.174296i
$789$	7.33466e6	−	2.25738e7i	0.419457	−	1.29096i
$790$	−1.05516e7	+	7.66622e6i	−0.601523	+	0.437032i
$791$	−1.36573e7	+	9.92259e6i	−0.776109	+	0.563876i
$792$	−676137.	+	2.08094e6i	−0.0383020	+	0.117882i
$793$	−3.94131e6	+	2.86353e6i	−0.222565	+	0.161703i
$794$	614264.	+	446289.i	0.0345783	+	0.0251226i
$795$	2.30853e6	+	7.10492e6i	0.129544	+	0.398695i
$796$	−6.60416e6	−	4.79820e6i	−0.369432	−	0.268408i
$797$	−434600.	+	1.33756e6i	−0.0242350	+	0.0745878i	−0.962443	−	0.271485i	$-0.912485\pi$
$797$	−434600.	+	1.33756e6i	−0.0242350	+	0.0745878i	0.938208	+	0.346073i	$0.112485\pi$
$798$	3.78557e6	−	1.16508e7i	0.210438	−	0.647662i
$799$	3.89234e6	+	1.19794e7i	0.215697	+	0.663847i
$800$	1.08334e6			0.0598466
$801$	−3.11505e6			−0.171547
$802$	−1.52714e6	−	4.70007e6i	−0.0838386	−	0.258029i
$803$	−105831.	+	76890.9i	−0.00579195	+	0.00420810i
$804$	684108.	+	497034.i	0.0373237	+	0.0271172i
$805$	4.25072e7			2.31192
$806$	−544167.	−	2.41605e6i	−0.0295050	−	0.130999i
$807$	−2.96867e6			−0.160464
$808$	7.25787e6	+	5.27315e6i	0.391094	+	0.284146i
$809$	−1.16935e7	+	8.49586e6i	−0.628167	+	0.456390i	−0.855765	−	0.517365i	$-0.826913\pi$
$809$	−1.16935e7	+	8.49586e6i	−0.628167	+	0.456390i	0.227598	+	0.973755i	$0.426913\pi$
$810$	−2.58277e6	−	7.94896e6i	−0.138316	−	0.425694i
$811$	1.37941e7			0.736448			0.368224	−	0.929737i	$-0.379966\pi$
$811$	1.37941e7			0.736448			0.368224	+	0.929737i	$0.379966\pi$
$812$	−7.58753e6			−0.403841
$813$	3.38013e6	+	1.04030e7i	0.179352	+	0.551990i
$814$	−3.95550e6	+	1.21738e7i	−0.209238	+	0.643968i
$815$	5.17635e6	−	1.59312e7i	0.272979	−	0.840143i
$816$	2.14211e6	+	1.55633e6i	0.112620	+	0.0818232i
$817$	−9.83906e6	−	3.02815e7i	−0.515702	−	1.58717i
$818$	5.03391e6	+	3.65735e6i	0.263040	+	0.191110i
$819$	1.00802e6	−	732367.i	0.0525120	−	0.0381522i
$820$	946085.	−	2.91175e6i	0.0491355	−	0.151224i
$821$	2.12873e7	−	1.54661e7i	1.10220	−	0.800798i	0.120786	−	0.992679i	$-0.461458\pi$
$821$	2.12873e7	−	1.54661e7i	1.10220	−	0.800798i	0.981418	+	0.191880i	$0.0614585\pi$
$822$	6.14834e6	−	4.46703e6i	0.317379	−	0.230590i
$823$	−6.17810e6	+	1.90142e7i	−0.317947	+	0.978541i	0.656577	+	0.754259i	$0.272004\pi$
$823$	−6.17810e6	+	1.90142e7i	−0.317947	+	0.978541i	−0.974524	+	0.224282i	$0.927996\pi$
$824$	−1.00382e7	+	7.29320e6i	−0.515038	+	0.374197i
$825$	4.51233e6	+	3.27840e6i	0.230816	+	0.167698i
$826$	−2.23103e6	−	6.86641e6i	−0.113777	−	0.350171i
$827$	2.51659e6	+	1.82841e6i	0.127952	+	0.0929628i	0.649921	−	0.760002i	$-0.274802\pi$
$827$	2.51659e6	+	1.82841e6i	0.127952	+	0.0929628i	−0.521968	+	0.852965i	$0.674802\pi$
$828$	−2.04035e6	+	6.27955e6i	−0.103426	+	0.318312i
$829$	9.20203e6	−	2.83209e7i	0.465047	−	1.43127i	−0.393875	−	0.919164i	$-0.628866\pi$
$829$	9.20203e6	−	2.83209e7i	0.465047	−	1.43127i	0.858923	−	0.512105i	$-0.171134\pi$
$830$	3.58929e6	+	1.10467e7i	0.180848	+	0.556592i
$831$	2.64702e7			1.32970
$832$	473965.			0.0237377
$833$	86246.9	+	265441.i	0.00430657	+	0.0132543i
$834$	3.07306e6	−	2.23271e6i	0.152987	−	0.111152i
$835$	9.64074e6	+	7.00440e6i	0.478513	+	0.347660i
$836$	−1.22701e7			−0.607201
$837$	1.89737e7	−	1.12626e7i	0.936137	−	0.555682i
$838$	1.87122e7			0.920483
$839$	9.31625e6	+	6.76865e6i	0.456916	+	0.331969i	0.792320	−	0.610105i	$-0.208873\pi$
$839$	9.31625e6	+	6.76865e6i	0.456916	+	0.331969i	−0.335404	+	0.942074i	$0.608873\pi$
$840$	5.56045e6	−	4.03990e6i	0.271901	−	0.197548i
$841$	−2.28601e6	−	7.03561e6i	−0.111452	−	0.343014i
$842$	1.66429e7			0.809002
$843$	−9.25560e6			−0.448576
$844$	−965775.	−	2.97235e6i	−0.0466681	−	0.143630i
$845$	−7.15302e6	+	2.20147e7i	−0.344626	+	1.06065i
$846$	−1.56942e6	+	4.83019e6i	−0.0753900	+	0.232027i
$847$	−1.25301e6	−	910363.i	−0.0600129	−	0.0436020i
$848$	−720650.	−	2.21793e6i	−0.0344139	−	0.105915i
$849$	−4.67967e6	−	3.39998e6i	−0.222816	−	0.161885i
$850$	−2.79264e6	+	2.02897e6i	−0.132577	+	0.0963228i
$851$	−1.19363e7	+	3.67363e7i	−0.564998	+	1.73889i
$852$	−3.91547e6	+	2.84475e6i	−0.184793	+	0.134260i
$853$	−3.89921e6	+	2.83294e6i	−0.183487	+	0.133311i	−0.675737	−	0.737143i	$-0.736174\pi$
$853$	−3.89921e6	+	2.83294e6i	−0.183487	+	0.133311i	0.492250	+	0.870454i	$0.336174\pi$
$854$	6.81492e6	−	2.09742e7i	0.319754	−	0.984102i
$855$	−7.93524e6	+	5.76529e6i	−0.371231	+	0.269715i
$856$	−3.01099e6	−	2.18761e6i	−0.140451	−	0.102044i
$857$	−5.11878e6	−	1.57540e7i	−0.238075	−	0.732720i	−0.996699	−	0.0811908i	$-0.974128\pi$
$857$	−5.11878e6	−	1.57540e7i	−0.238075	−	0.732720i	0.758623	−	0.651529i	$-0.225872\pi$
$858$	1.97416e6	+	1.43431e6i	0.0915514	+	0.0665160i
$859$	−3.14428e6	+	9.67709e6i	−0.145391	+	0.447468i	−0.997061	−	0.0766105i	$-0.975590\pi$
$859$	−3.14428e6	+	9.67709e6i	−0.145391	+	0.447468i	0.851670	+	0.524079i	$0.175590\pi$
$860$	5.52022e6	−	1.69895e7i	0.254513	−	0.783311i
$861$	−1.51810e6	−	4.67222e6i	−0.0697898	−	0.214791i
$862$	−1.97092e7			−0.903441
$863$	−3.49591e7			−1.59784			−0.798921	−	0.601437i	$-0.794595\pi$
$863$	−3.49591e7			−1.59784			−0.798921	+	0.601437i	$0.794595\pi$
$864$	1.30489e6	+	4.01605e6i	0.0594691	+	0.183027i
$865$	2.85610e7	−	2.07508e7i	1.29788	−	0.942963i
$866$	−1.32175e7	−	9.60311e6i	−0.598903	−	0.435128i
$867$	9.56660e6			0.432225
$868$	8.42154e6	+	7.40034e6i	0.379395	+	0.333390i
$869$	2.09619e7			0.941633
$870$	−9.61009e6	−	6.98214e6i	−0.430456	−	0.312745i
$871$	−390195.	+	283493.i	−0.0174275	+	0.0126618i
$872$	3.87866e6	+	1.19373e7i	0.172739	+	0.531637i
$873$	7.62649e6			0.338680
$874$	−3.70269e7			−1.63960
$875$	−5.40999e6	−	1.66502e7i	−0.238878	−	0.735191i
$876$	−19724.1	+	60704.7i	−0.000868436	+	0.00267277i
$877$	−8.13968e6	+	2.50514e7i	−0.357362	+	1.09985i	0.597265	+	0.802044i	$0.296254\pi$
$877$	−8.13968e6	+	2.50514e7i	−0.357362	+	1.09985i	−0.954627	+	0.297803i	$0.903746\pi$
$878$	1.71099e7	+	1.24311e7i	0.749050	+	0.544217i
$879$	−2.20040e6	−	6.77214e6i	−0.0960572	−	0.295634i
$880$	−5.56940e6	−	4.04641e6i	−0.242439	−	0.176142i
$881$	−2.31435e7	+	1.68147e7i	−1.00459	+	0.729878i	−0.963068	−	0.269259i	$-0.913221\pi$
$881$	−2.31435e7	+	1.68147e7i	−1.00459	+	0.729878i	−0.0415237	+	0.999138i	$0.513221\pi$
$882$	−34775.4	+	107028.i	−0.00150522	+	0.00463260i
$883$	−1.82886e7	+	1.32874e7i	−0.789365	+	0.573507i	−0.907775	−	0.419458i	$-0.862220\pi$
$883$	−1.82886e7	+	1.32874e7i	−0.789365	+	0.573507i	0.118410	+	0.992965i	$0.462220\pi$
$884$	−1.22179e6	+	887684.i	−0.0525856	+	0.0382057i
$885$	3.49281e6	−	1.07498e7i	0.149905	−	0.461361i
$886$	1.27306e7	−	9.24930e6i	0.544833	−	0.395844i
$887$	2.05999e7	+	1.49667e7i	0.879137	+	0.638730i	0.933023	−	0.359817i	$-0.117161\pi$
$887$	2.05999e7	+	1.49667e7i	0.879137	+	0.638730i	−0.0538861	+	0.998547i	$0.517161\pi$
$888$	1.93002e6	+	5.93998e6i	0.0821351	+	0.252786i
$889$	3.08492e7	+	2.24132e7i	1.30915	+	0.951153i
$890$	3.02863e6	−	9.32116e6i	0.128165	−	0.394453i
$891$	−4.15102e6	+	1.27755e7i	−0.175170	+	0.539119i
$892$	−3.68030e6	−	1.13268e7i	−0.154871	−	0.476645i
$893$	−2.84809e7			−1.19516
$894$	5.02791e6			0.210399
$895$	5.47313e6	+	1.68446e7i	0.228391	+	0.702914i
$896$	−1.73580e6	+	1.26113e6i	−0.0722319	+	0.0524795i
$897$	5.95735e6	+	4.32827e6i	0.247213	+	0.179611i
$898$	−1.35945e7			−0.562567
$899$	7.66626e6	−	1.77948e7i	0.316362	−	0.734336i
$900$	−1.39183e6			−0.0572770
$901$	6.01164e6	+	4.36771e6i	0.246707	+	0.179243i
$902$	−3.98083e6	+	2.89224e6i	−0.162914	+	0.118364i
$903$	−8.85781e6	−	2.72615e7i	−0.361499	−	1.11258i
$904$	8.25021e6			0.335771
$905$	1.46442e7			0.594354
$906$	7.47615e6	+	2.30092e7i	0.302592	+	0.931283i
$907$	587374.	−	1.80775e6i	0.0237081	−	0.0729660i	−0.938502	−	0.345273i	$-0.887786\pi$
$907$	587374.	−	1.80775e6i	0.0237081	−	0.0729660i	0.962211	+	0.272307i	$0.0877865\pi$
$908$	2.63170e6	−	8.09955e6i	0.105931	−	0.326021i
$909$	−9.32464e6	−	6.77475e6i	−0.374302	−	0.271946i
$910$	1.21141e6	+	3.72834e6i	0.0484940	+	0.149249i
$911$	4.62329e6	+	3.35901e6i	0.184567	+	0.134096i	0.676232	−	0.736688i	$-0.263612\pi$
$911$	4.62329e6	+	3.35901e6i	0.184567	+	0.134096i	−0.491665	+	0.870784i	$0.663612\pi$
$912$	−4.84357e6	+	3.51906e6i	−0.192832	+	0.140100i
$913$	5.76868e6	−	1.77542e7i	0.229034	−	0.704894i
$914$	6.75516e6	−	4.90791e6i	0.267467	−	0.194326i
$915$	2.79322e7	−	2.02939e7i	1.10294	−	0.801334i
$916$	3.58758e6	−	1.10414e7i	0.141274	−	0.434798i
$917$	1.82781e7	−	1.32798e7i	0.717805	−	0.521516i
$918$	−1.08854e7	−	7.90871e6i	−0.426322	−	0.309741i
$919$	4.12271e6	+	1.26884e7i	0.161025	+	0.495584i	0.998721	−	0.0505520i	$-0.0160981\pi$
$919$	4.12271e6	+	1.26884e7i	0.161025	+	0.495584i	−0.837696	+	0.546136i	$0.816098\pi$
$920$	−1.68065e7	−	1.22107e7i	−0.654649	−	0.475631i
$921$	3.58653e6	−	1.10382e7i	0.139324	−	0.428795i
$922$	8.72433e6	−	2.68507e7i	0.337991	−	1.04023i
$923$	−853032.	−	2.62536e6i	−0.0329580	−	0.101434i
$924$	−1.10464e7			−0.425638
$925$	−8.14242e6			−0.312895
$926$	−7.60067e6	−	2.33925e7i	−0.291289	−	0.896496i
$927$	1.28967e7	−	9.37003e6i	0.492925	−	0.358131i
$928$	2.99997e6	+	2.17960e6i	0.114353	+	0.0830821i
$929$	9.16398e6			0.348373			0.174187	−	0.984713i	$-0.444270\pi$
$929$	9.16398e6			0.348373			0.174187	+	0.984713i	$0.444270\pi$
$930$	3.85653e6	+	1.71226e7i	0.146214	+	0.649176i
$931$	−631082.			−0.0238623
$932$	−1.87750e7	−	1.36408e7i	−0.708011	−	0.514400i
$933$	2.33533e7	−	1.69672e7i	0.878302	−	0.638124i
$934$	1.02651e7	+	3.15927e7i	0.385031	+	1.18500i
$935$	2.19354e7			0.820570
$936$	−608932.			−0.0227185
$937$	−9.73014e6	−	2.99463e7i	−0.362051	−	1.11428i	−0.951807	−	0.306697i	$-0.900776\pi$
$937$	−9.73014e6	−	2.99463e7i	−0.362051	−	1.11428i	0.589756	−	0.807582i	$-0.299224\pi$
$938$	674685.	−	2.07647e6i	0.0250377	−	0.0770581i
$939$	−1.13870e7	+	3.50457e7i	−0.421450	+	1.29709i
$940$	−1.29275e7	−	9.39236e6i	−0.477193	−	0.346701i
$941$	9.37057e6	+	2.88397e7i	0.344979	+	1.06174i	0.961595	+	0.274471i	$0.0885029\pi$
$941$	9.37057e6	+	2.88397e7i	0.344979	+	1.06174i	−0.616617	+	0.787264i	$0.711497\pi$
$942$	−1.06620e7	−	7.74643e6i	−0.391483	−	0.284429i
$943$	−1.20128e7	+	8.72780e6i	−0.439910	+	0.319614i
$944$	−1.09035e6	+	3.35574e6i	−0.0398230	+	0.122563i
$945$	−2.82562e7	+	2.05293e7i	−1.02928	+	0.747816i
$946$	−2.32274e7	+	1.68757e7i	−0.843864	+	0.613103i
$947$	−8.53552e6	+	2.62696e7i	−0.309282	+	0.951873i	0.668762	+	0.743476i	$0.266824\pi$
$947$	−8.53552e6	+	2.62696e7i	−0.309282	+	0.951873i	−0.978044	+	0.208397i	$0.933176\pi$
$948$	8.27463e6	−	6.01187e6i	0.299039	−	0.217265i
$949$	−29453.0	−	21398.9i	−0.00106161	−	0.000771304i
$950$	−2.41193e6	−	7.42316e6i	−0.0867073	−	0.266858i
$951$	1.86225e7	+	1.35300e7i	0.667707	+	0.485118i
$952$	2.11260e6	−	6.50192e6i	0.0755484	−	0.232514i
$953$	−7.68092e6	+	2.36395e7i	−0.273956	+	0.843151i	0.715537	+	0.698574i	$0.246182\pi$
$953$	−7.68092e6	+	2.36395e7i	−0.273956	+	0.843151i	−0.989494	+	0.144576i	$0.953818\pi$
$954$	925863.	+	2.84951e6i	0.0329364	+	0.101368i
$955$	6.06617e7			2.15232
$956$	1.91552e7			0.677864
$957$	5.89957e6	+	1.81570e7i	0.208229	+	0.640862i
$958$	8.44958e6	−	6.13898e6i	0.297455	−	0.216114i
$959$	−1.58749e7	−	1.15338e7i	−0.557396	−	0.404972i
$960$	−3.35901e6			−0.117634
$961$	−2.58647e7	+	1.22737e7i	−0.903441	+	0.428713i
$962$	−3.56234e6			−0.124107
$963$	3.86840e6	+	2.81056e6i	0.134421	+	0.0976623i
$964$	9.50595e6	−	6.90647e6i	0.329460	−	0.239367i
$965$	−1.47066e7	−	4.52622e7i	−0.508386	−	1.56465i
$966$	−3.33342e7			−1.14934
$967$	−1.32290e6			−0.0454946			−0.0227473	−	0.999741i	$-0.507241\pi$
$967$	−1.32290e6			−0.0454946			−0.0227473	+	0.999741i	$0.507241\pi$
$968$	233904.	+	719881.i	0.00802321	+	0.0246929i
$969$	5.89500e6	−	1.81430e7i	0.201685	−	0.620724i
$970$	−7.41490e6	+	2.28207e7i	−0.253032	+	0.778754i
$971$	−1.38883e7	−	1.00904e7i	−0.472716	−	0.343448i	0.325783	−	0.945445i	$-0.394372\pi$
$971$	−1.38883e7	−	1.00904e7i	−0.472716	−	0.343448i	−0.798499	+	0.601996i	$0.794372\pi$
$972$	−2.92910e6	−	9.01485e6i	−0.0994418	−	0.306050i
$973$	−7.93456e6	−	5.76479e6i	−0.268683	−	0.195210i
$974$	−7.54976e6	+	5.48522e6i	−0.254997	+	0.185266i
$975$	−479670.	+	1.47627e6i	−0.0161596	+	0.0497341i
$976$	−8.71956e6	+	6.33513e6i	−0.293002	+	0.212878i
$977$	2.11842e6	−	1.53912e6i	0.0710029	−	0.0515866i	−0.551718	−	0.834031i	$-0.686027\pi$
$977$	2.11842e6	−	1.53912e6i	0.0710029	−	0.0515866i	0.622720	+	0.782444i	$0.286027\pi$
$978$	−4.05931e6	+	1.24933e7i	−0.135708	+	0.417666i
$979$	−1.27435e7	+	9.25872e6i	−0.424945	+	0.308741i
$980$	−286448.	−	208117.i	−0.00952755	−	0.00692217i
$981$	−4.98316e6	−	1.53366e7i	−0.165323	−	0.508811i
$982$	4.72721e6	+	3.43452e6i	0.156432	+	0.113655i
$983$	−6.95934e6	+	2.14186e7i	−0.229712	+	0.706981i	0.768067	+	0.640370i	$0.221219\pi$
$983$	−6.95934e6	+	2.14186e7i	−0.229712	+	0.706981i	−0.997779	+	0.0666117i	$0.978781\pi$
$984$	−741922.	+	2.28340e6i	−0.0244270	+	0.0751787i
$985$	−6.45637e6	−	1.98707e7i	−0.212030	−	0.652562i
$986$	−1.18155e7			−0.387044
$987$	−2.56405e7			−0.837786
$988$	−1.05523e6	−	3.24766e6i	−0.0343918	−	0.105847i
$989$	−7.00922e7	+	5.09250e7i	−2.27866	+	1.65554i
$990$	7.15536e6	+	5.19867e6i	0.232030	+	0.168579i
$991$	−5.10914e6			−0.165258			−0.0826292	−	0.996580i	$-0.526332\pi$
$991$	−5.10914e6			−0.165258			−0.0826292	+	0.996580i	$0.526332\pi$
$992$	−1.20389e6	−	5.34514e6i	−0.0388425	−	0.172457i
$993$	−3.80886e6			−0.122581
$994$	1.01096e7	+	7.34508e6i	0.324541	+	0.235793i
$995$	−2.66955e7	+	1.93954e7i	−0.854832	+	0.621072i
$996$	−2.81473e6	−	8.66284e6i	−0.0899059	−	0.276702i
$997$	−4.79343e7			−1.52724			−0.763622	−	0.645664i	$-0.776581\pi$
$997$	−4.79343e7			−1.52724			−0.763622	+	0.645664i	$0.776581\pi$
$998$	1.96999e7			0.626092
$999$	−9.80765e6	−	3.01848e7i	−0.310922	−	0.956919i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	62.6.d.a.33.5	✓	24
31.16	even	5	inner	62.6.d.a.47.5	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
62.6.d.a.33.5	✓	24	1.1	even	1	trivial
62.6.d.a.47.5	yes	24	31.16	even	5	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:	\( N \)	\(=\)	\( 62 = 2 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	62.d (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.23607 - 2.35114i) q^{2} +(10.2581 - 7.45295i) q^{3} +(4.94427 + 15.2169i) q^{4} +64.6757 q^{5} -50.7189 q^{6} +(40.4673 + 124.545i) q^{7} +(19.7771 - 60.8676i) q^{8} +(-25.4089 + 78.2004i) q^{9} +(-209.295 - 152.062i) q^{10} +(128.485 + 395.436i) q^{11} +(164.130 + 119.247i) q^{12} +(-93.6147 + 68.0150i) q^{13} +(161.869 - 498.182i) q^{14} +(663.450 - 482.025i) q^{15} +(-207.108 + 150.473i) q^{16} +(252.067 - 775.783i) q^{17} +(266.085 - 193.322i) q^{18} +(1492.16 + 1084.12i) q^{19} +(319.774 + 984.164i) q^{20} +(1343.35 + 976.000i) q^{21} +(513.940 - 1581.74i) q^{22} +(1550.89 - 4773.16i) q^{23} +(-250.768 - 771.784i) q^{24} +1057.95 q^{25} +462.856 q^{26} +(1274.31 + 3921.93i) q^{27} +(-1695.11 + 1231.57i) q^{28} +(2929.66 + 2128.52i) q^{29} -3280.28 q^{30} +(-1175.67 - 5219.86i) q^{31} +1024.00 q^{32} +(4265.18 + 3098.83i) q^{33} +(-2639.68 + 1917.84i) q^{34} +(2617.25 + 8055.06i) q^{35} -1315.60 q^{36} -7696.43 q^{37} +(-2279.82 - 7016.57i) q^{38} +(-453.396 + 1395.41i) q^{39} +(1279.10 - 3936.66i) q^{40} +(-2393.56 - 1739.02i) q^{41} +(-2052.45 - 6316.80i) q^{42} +(-13966.0 - 10146.9i) q^{43} +(-5382.05 + 3910.29i) q^{44} +(-1643.34 + 5057.67i) q^{45} +(-16241.2 + 11799.9i) q^{46} +(-12492.6 + 9076.40i) q^{47} +(-1003.07 + 3087.14i) q^{48} +(-276.812 + 201.116i) q^{49} +(-3423.59 - 2487.38i) q^{50} +(-3196.14 - 9836.70i) q^{51} +(-1497.83 - 1088.24i) q^{52} +(-2815.04 + 8663.79i) q^{53} +(5097.25 - 15687.7i) q^{54} +(8309.85 + 25575.1i) q^{55} +8381.11 q^{56} +23386.6 q^{57} +(-4476.12 - 13776.1i) q^{58} +(11150.6 - 8101.41i) q^{59} +(10615.2 + 7712.40i) q^{60} +42101.4 q^{61} +(-8468.07 + 19656.0i) q^{62} -10767.7 q^{63} +(-3313.73 - 2407.57i) q^{64} +(-6054.59 + 4398.92i) q^{65} +(-6516.61 - 20056.1i) q^{66} +4168.09 q^{67} +13051.3 q^{68} +(-19664.9 - 60522.3i) q^{69} +(10469.0 - 32220.3i) q^{70} +(-7371.89 + 22688.4i) q^{71} +(4257.36 + 3093.15i) q^{72} +(97.2229 + 299.221i) q^{73} +(24906.2 + 18095.4i) q^{74} +(10852.5 - 7884.83i) q^{75} +(-9119.28 + 28066.3i) q^{76} +(-44050.3 + 32004.4i) q^{77} +(4748.03 - 3449.65i) q^{78} +(15579.2 - 47947.7i) q^{79} +(-13394.9 + 9731.95i) q^{80} +(26137.3 + 18989.9i) q^{81} +(3657.03 + 11255.2i) q^{82} +(-36323.0 - 26390.2i) q^{83} +(-8209.81 + 25267.2i) q^{84} +(16302.6 - 50174.3i) q^{85} +(21338.1 + 65671.8i) q^{86} +45916.5 q^{87} +26610.3 q^{88} +(11707.0 + 36030.4i) q^{89} +(17209.2 - 12503.2i) q^{90} +(-12259.3 - 8906.89i) q^{91} +80300.7 q^{92} +(-50963.5 - 44783.7i) q^{93} +61766.8 q^{94} +(96506.6 + 70116.2i) q^{95} +(10504.3 - 7631.82i) q^{96} +(-28661.9 - 88212.1i) q^{97} +1368.64 q^{98} -34187.9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{2} - 20 q^{3} - 96 q^{4} + 120 q^{5} + 280 q^{6} - 180 q^{7} - 384 q^{8} - 200 q^{9} - 100 q^{10} + 354 q^{11} - 320 q^{12} + 39 q^{13} - 720 q^{14} + 535 q^{15} - 1536 q^{16} - 1027 q^{17}+ \cdots + 339042 q^{99}+O(q^{100}) \) 24 * q - 24 * q^2 - 20 * q^3 - 96 * q^4 + 120 * q^5 + 280 * q^6 - 180 * q^7 - 384 * q^8 - 200 * q^9 - 100 * q^10 + 354 * q^11 - 320 * q^12 + 39 * q^13 - 720 * q^14 + 535 * q^15 - 1536 * q^16 - 1027 * q^17 - 1420 * q^18 + 334 * q^19 - 560 * q^20 - 1867 * q^21 + 1416 * q^22 - 1051 * q^23 - 960 * q^24 + 4812 * q^25 + 12536 * q^26 - 5135 * q^27 + 4000 * q^28 - 1143 * q^29 + 9080 * q^30 - 8583 * q^31 + 24576 * q^32 - 24628 * q^33 - 8108 * q^34 - 7496 * q^35 + 17760 * q^36 - 25204 * q^37 - 2844 * q^38 - 20114 * q^39 - 2240 * q^40 + 19615 * q^41 + 3212 * q^42 + 22358 * q^43 - 20496 * q^44 + 6725 * q^45 - 5264 * q^46 + 4766 * q^47 - 3840 * q^48 - 12058 * q^49 + 4628 * q^50 + 6844 * q^51 + 624 * q^52 - 7393 * q^53 - 20540 * q^54 + 11861 * q^55 - 8960 * q^56 + 176704 * q^57 + 4268 * q^58 - 21070 * q^59 + 8560 * q^60 + 76556 * q^61 - 49652 * q^62 + 105854 * q^63 - 24576 * q^64 - 107146 * q^65 + 57968 * q^66 - 150906 * q^67 + 97728 * q^68 - 212560 * q^69 - 29984 * q^70 + 27475 * q^71 - 22720 * q^72 + 49671 * q^73 + 90124 * q^74 - 156002 * q^75 - 11376 * q^76 + 253908 * q^77 - 9036 * q^78 - 7162 * q^79 - 6400 * q^80 + 38329 * q^81 - 92940 * q^82 - 246088 * q^83 + 12848 * q^84 - 104879 * q^85 - 149088 * q^86 - 247668 * q^87 + 118656 * q^88 + 159253 * q^89 - 167880 * q^90 - 68566 * q^91 + 75744 * q^92 + 260391 * q^93 + 18784 * q^94 + 222814 * q^95 - 20480 * q^96 + 190 * q^97 - 144032 * q^98 + 339042 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more