LMFDB - Embedded newform 62.6.d.a.33.1

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			33.1
Character	$\chi$	$=$	62.33
Dual form			62.6.d.a.47.1

$q$-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} +(-20.9547 + 15.2245i) q^{3} +(4.94427 + 15.2169i) q^{4} +78.8224 q^{5} +103.606 q^{6} +(-0.961853 - 2.96028i) q^{7} +(19.7771 - 60.8676i) q^{8} +(132.224 - 406.944i) q^{9} +(-255.075 - 185.323i) q^{10} +(178.470 + 549.273i) q^{11} +(-335.276 - 243.592i) q^{12} +(-373.521 + 271.379i) q^{13} +(-3.84741 + 11.8411i) q^{14} +(-1651.70 + 1200.03i) q^{15} +(-207.108 + 150.473i) q^{16} +(-62.9273 + 193.670i) q^{17} +(-1384.67 + 1006.02i) q^{18} +(-997.639 - 724.827i) q^{19} +(389.719 + 1199.43i) q^{20} +(65.2242 + 47.3881i) q^{21} +(713.878 - 2197.09i) q^{22} +(-782.479 + 2408.22i) q^{23} +(512.256 + 1576.56i) q^{24} +3087.97 q^{25} +1846.79 q^{26} +(1479.83 + 4554.45i) q^{27} +(40.2906 - 29.2729i) q^{28} +(-6588.92 - 4787.13i) q^{29} +8166.46 q^{30} +(-2053.74 + 4940.78i) q^{31} +1024.00 q^{32} +(-12102.2 - 8792.75i) q^{33} +(658.984 - 478.780i) q^{34} +(-75.8156 - 233.336i) q^{35} +6846.18 q^{36} -10431.0 q^{37} +(1524.26 + 4691.18i) q^{38} +(3695.43 - 11373.4i) q^{39} +(1558.88 - 4797.73i) q^{40} +(7273.66 + 5284.62i) q^{41} +(-99.6537 - 306.702i) q^{42} +(11000.6 + 7992.41i) q^{43} +(-7475.83 + 5431.51i) q^{44} +(10422.2 - 32076.3i) q^{45} +(8194.23 - 5953.46i) q^{46} +(-17659.5 + 12830.3i) q^{47} +(2049.02 - 6306.24i) q^{48} +(13589.3 - 9873.21i) q^{49} +(-9992.88 - 7260.25i) q^{50} +(-1629.91 - 5016.35i) q^{51} +(-5976.34 - 4342.07i) q^{52} +(-3553.52 + 10936.6i) q^{53} +(5919.32 - 18217.8i) q^{54} +(14067.4 + 43295.0i) q^{55} -199.208 q^{56} +31940.4 q^{57} +(10067.0 + 30983.0i) q^{58} +(23175.7 - 16838.2i) q^{59} +(-26427.2 - 19200.5i) q^{60} +12903.6 q^{61} +(18262.5 - 11160.0i) q^{62} -1331.85 q^{63} +(-3313.73 - 2407.57i) q^{64} +(-29441.8 + 21390.7i) q^{65} +(18490.5 + 56907.9i) q^{66} -57807.7 q^{67} -3258.19 q^{68} +(-20267.4 - 62376.5i) q^{69} +(-303.262 + 933.345i) q^{70} +(7686.88 - 23657.8i) q^{71} +(-22154.7 - 16096.3i) q^{72} +(13235.8 + 40735.5i) q^{73} +(33755.3 + 24524.7i) q^{74} +(-64707.6 + 47012.8i) q^{75} +(6097.03 - 18764.7i) q^{76} +(1454.34 - 1056.64i) q^{77} +(-38699.0 + 28116.5i) q^{78} +(-32185.5 + 99056.9i) q^{79} +(-16324.8 + 11860.6i) q^{80} +(-16230.0 - 11791.8i) q^{81} +(-11113.2 - 34202.8i) q^{82} +(-81219.5 - 59009.4i) q^{83} +(-398.615 + 1226.81i) q^{84} +(-4960.08 + 15265.6i) q^{85} +(-16807.4 - 51728.0i) q^{86} +210951. q^{87} +36962.5 q^{88} +(-13166.0 - 40520.8i) q^{89} +(-109143. + 79297.0i) q^{90} +(1162.63 + 844.701i) q^{91} -40514.5 q^{92} +(-32185.2 - 134800. i) q^{93} +87313.2 q^{94} +(-78636.3 - 57132.6i) q^{95} +(-21457.6 + 15589.9i) q^{96} +(31480.1 + 96885.8i) q^{97} -67189.2 q^{98} +247121. 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
$3$	−20.9547	+	15.2245i	−1.34425	+	0.976652i	−0.344971	+	0.938614i	$0.612111\pi$
$3$	−20.9547	+	15.2245i	−1.34425	+	0.976652i	−0.999276	+	0.0380390i	$0.987889\pi$
$4$	4.94427	+	15.2169i	0.154508	+	0.475528i
$5$	78.8224			1.41002			0.705009	−	0.709198i	$-0.250943\pi$
$5$	78.8224			1.41002			0.705009	+	0.709198i	$0.250943\pi$
$6$	103.606			1.17491
$7$	−0.961853	−	2.96028i	−0.00741931	−	0.0228343i	0.947278	−	0.320412i	$-0.103821\pi$
$7$	−0.961853	−	2.96028i	−0.00741931	−	0.0228343i	−0.954698	+	0.297578i	$0.903821\pi$
$8$	19.7771	−	60.8676i	0.109254	−	0.336249i
$9$	132.224	−	406.944i	0.544132	−	1.67467i
$10$	−255.075	−	185.323i	−0.806617	−	0.586041i
$11$	178.470	+	549.273i	0.444716	+	1.36869i	0.882795	+	0.469758i	$0.155659\pi$
$11$	178.470	+	549.273i	0.444716	+	1.36869i	−0.438080	+	0.898936i	$0.644341\pi$
$12$	−335.276	−	243.592i	−0.672123	−	0.488326i
$13$	−373.521	+	271.379i	−0.612995	+	0.445367i	−0.850468	−	0.526027i	$-0.823681\pi$
$13$	−373.521	+	271.379i	−0.612995	+	0.445367i	0.237473	+	0.971394i	$0.423681\pi$
$14$	−3.84741	+	11.8411i	−0.00524625	+	0.0161463i
$15$	−1651.70	+	1200.03i	−1.89541	+	1.37710i
$16$	−207.108	+	150.473i	−0.202254	+	0.146946i
$17$	−62.9273	+	193.670i	−0.0528101	+	0.162533i	−0.973983	−	0.226620i	$-0.927232\pi$
$17$	−62.9273	+	193.670i	−0.0528101	+	0.162533i	0.921173	+	0.389153i	$0.127232\pi$
$18$	−1384.67	+	1006.02i	−1.00731	+	0.731856i
$19$	−997.639	−	724.827i	−0.634000	−	0.460628i	0.223783	−	0.974639i	$-0.428159\pi$
$19$	−997.639	−	724.827i	−0.634000	−	0.460628i	−0.857784	+	0.514011i	$0.828159\pi$
$20$	389.719	+	1199.43i	0.217860	+	0.670503i
$21$	65.2242	+	47.3881i	0.0322746	+	0.0234488i
$22$	713.878	−	2197.09i	0.314461	−	0.967813i
$23$	−782.479	+	2408.22i	−0.308428	+	0.949242i	0.669948	+	0.742408i	$0.266316\pi$
$23$	−782.479	+	2408.22i	−0.308428	+	0.949242i	−0.978376	+	0.206835i	$0.933684\pi$
$24$	512.256	+	1576.56i	0.181534	+	0.558705i
$25$	3087.97			0.988150
$26$	1846.79			0.535777
$27$	1479.83	+	4554.45i	0.390663	+	1.20234i
$28$	40.2906	−	29.2729i	0.00971201	−	0.00705619i
$29$	−6588.92	−	4787.13i	−1.45485	−	1.05701i	−0.984667	−	0.174446i	$-0.944186\pi$
$29$	−6588.92	−	4787.13i	−1.45485	−	1.05701i	−0.470187	−	0.882567i	$-0.655814\pi$
$30$	8166.46			1.65665
$31$	−2053.74	+	4940.78i	−0.383833	+	0.923403i
$31$	−2053.74	+	4940.78i	−0.383833	+	0.923403i
$32$	1024.00			0.176777
$33$	−12102.2	−	8792.75i	−1.93455	−	1.40553i
$34$	658.984	−	478.780i	0.0977636	−	0.0710294i
$35$	−75.8156	−	233.336i	−0.0104614	−	0.0321968i
$36$	6846.18			0.880425
$37$	−10431.0			−1.25262			−0.626311	−	0.779573i	$-0.715436\pi$
$37$	−10431.0			−1.25262			−0.626311	+	0.779573i	$0.715436\pi$
$38$	1524.26	+	4691.18i	0.171238	+	0.527015i
$39$	3695.43	−	11373.4i	0.389048	−	1.19737i
$40$	1558.88	−	4797.73i	0.154050	−	0.474117i
$41$	7273.66	+	5284.62i	0.675761	+	0.490969i	0.871949	−	0.489597i	$-0.162856\pi$
$41$	7273.66	+	5284.62i	0.675761	+	0.490969i	−0.196187	+	0.980566i	$0.562856\pi$
$42$	−99.6537	−	306.702i	−0.00871706	−	0.0268284i
$43$	11000.6	+	7992.41i	0.907289	+	0.659184i	0.940328	−	0.340270i	$-0.110519\pi$
$43$	11000.6	+	7992.41i	0.907289	+	0.659184i	−0.0330389	+	0.999454i	$0.510519\pi$
$44$	−7475.83	+	5431.51i	−0.582140	+	0.422950i
$45$	10422.2	−	32076.3i	0.767236	−	2.36131i
$46$	8194.23	−	5953.46i	0.570970	−	0.414834i
$47$	−17659.5	+	12830.3i	−1.16609	+	0.847215i	−0.990536	−	0.137254i	$-0.956172\pi$
$47$	−17659.5	+	12830.3i	−1.16609	+	0.847215i	−0.175556	+	0.984469i	$0.556172\pi$
$48$	2049.02	−	6306.24i	0.128364	−	0.395064i
$49$	13589.3	−	9873.21i	0.808551	−	0.587446i
$50$	−9992.88	−	7260.25i	−0.565282	−	0.410702i
$51$	−1629.91	−	5016.35i	−0.0877482	−	0.270061i
$52$	−5976.34	−	4342.07i	−0.306498	−	0.222684i
$53$	−3553.52	+	10936.6i	−0.173768	+	0.534803i	−0.999575	−	0.0291500i	$-0.990720\pi$
$53$	−3553.52	+	10936.6i	−0.173768	+	0.534803i	0.825807	+	0.563953i	$0.190720\pi$
$54$	5919.32	−	18217.8i	0.276241	−	0.850181i
$55$	14067.4	+	43295.0i	0.627057	+	1.92988i
$56$	−199.208			−0.00848860
$57$	31940.4			1.30213
$58$	10067.0	+	30983.0i	0.392943	+	1.20935i
$59$	23175.7	−	16838.2i	0.866769	−	0.629745i	−0.0629490	−	0.998017i	$-0.520051\pi$
$59$	23175.7	−	16838.2i	0.866769	−	0.629745i	0.929718	+	0.368272i	$0.120051\pi$
$60$	−26427.2	−	19200.5i	−0.947706	−	0.688549i
$61$	12903.6			0.444003			0.222001	−	0.975046i	$-0.428741\pi$
$61$	12903.6			0.444003			0.222001	+	0.975046i	$0.428741\pi$
$62$	18262.5	−	11160.0i	0.603367	−	0.368712i
$63$	−1331.85			−0.0422769
$64$	−3313.73	−	2407.57i	−0.101127	−	0.0734732i
$65$	−29441.8	+	21390.7i	−0.864334	+	0.627975i
$66$	18490.5	+	56907.9i	0.522503	+	1.60810i
$67$	−57807.7			−1.57325			−0.786627	−	0.617428i	$-0.788175\pi$
$67$	−57807.7			−1.57325			−0.786627	+	0.617428i	$0.788175\pi$
$68$	−3258.19			−0.0854485
$69$	−20267.4	−	62376.5i	−0.512477	−	1.57724i
$70$	−303.262	+	933.345i	−0.00739730	+	0.0227665i
$71$	7686.88	−	23657.8i	0.180969	−	0.556966i	−0.818887	−	0.573955i	$-0.805408\pi$
$71$	7686.88	−	23657.8i	0.180969	−	0.556966i	0.999856	+	0.0169897i	$0.00540826\pi$
$72$	−22154.7	−	16096.3i	−0.503657	−	0.365928i
$73$	13235.8	+	40735.5i	0.290698	+	0.894677i	0.984633	+	0.174639i	$0.0558758\pi$
$73$	13235.8	+	40735.5i	0.290698	+	0.894677i	−0.693934	+	0.720038i	$0.744124\pi$
$74$	33755.3	+	24524.7i	0.716577	+	0.520624i
$75$	−64707.6	+	47012.8i	−1.32832	+	0.965079i
$76$	6097.03	−	18764.7i	0.121083	−	0.372656i
$77$	1454.34	−	1056.64i	0.0279537	−	0.0203095i
$78$	−38699.0	+	28116.5i	−0.720217	+	0.523268i
$79$	−32185.5	+	99056.9i	−0.580220	+	1.78573i	0.0374517	+	0.999298i	$0.488076\pi$
$79$	−32185.5	+	99056.9i	−0.580220	+	1.78573i	−0.617672	+	0.786436i	$0.711924\pi$
$80$	−16324.8	+	11860.6i	−0.285182	+	0.207197i
$81$	−16230.0	−	11791.8i	−0.274857	−	0.199695i
$82$	−11113.2	−	34202.8i	−0.182517	−	0.561729i
$83$	−81219.5	−	59009.4i	−1.29409	−	0.940213i	−0.294212	−	0.955740i	$-0.595057\pi$
$83$	−81219.5	−	59009.4i	−1.29409	−	0.940213i	−0.999879	+	0.0155273i	$0.995057\pi$
$84$	−398.615	+	1226.81i	−0.00616389	+	0.0189705i
$85$	−4960.08	+	15265.6i	−0.0744632	+	0.229174i
$86$	−16807.4	−	51728.0i	−0.245050	−	0.754187i
$87$	210951.			2.98802
$88$	36962.5			0.508809
$89$	−13166.0	−	40520.8i	−0.176189	−	0.542254i	0.823497	−	0.567321i	$-0.192020\pi$
$89$	−13166.0	−	40520.8i	−0.176189	−	0.542254i	−0.999686	+	0.0250671i	$0.992020\pi$
$90$	−109143.	+	79297.0i	−1.42033	+	1.03193i
$91$	1162.63	+	844.701i	0.0147176	+	0.0106930i
$92$	−40514.5			−0.499046
$93$	−32185.2	−	134800.i	−0.385877	−	1.61615i
$94$	87313.2			1.01920
$95$	−78636.3	−	57132.6i	−0.893952	−	0.649494i
$96$	−21457.6	+	15589.9i	−0.237632	+	0.172649i
$97$	31480.1	+	96885.8i	0.339709	+	1.04552i	0.964356	+	0.264609i	$0.0852429\pi$
$97$	31480.1	+	96885.8i	0.339709	+	1.04552i	−0.624647	+	0.780907i	$0.714757\pi$
$98$	−67189.2			−0.706699
$99$	247121.			2.53409
$100$	15267.8	+	46989.3i	0.152678	+	0.469893i
$101$	−22237.2	+	68439.2i	−0.216909	+	0.667577i	0.782104	+	0.623148i	$0.214147\pi$
$101$	−22237.2	+	68439.2i	−0.216909	+	0.667577i	−0.999013	+	0.0444285i	$0.985853\pi$
$102$	−6519.64	+	20065.4i	−0.0620474	+	0.190962i
$103$	13184.5	+	9579.10i	0.122453	+	0.0889675i	0.647326	−	0.762213i	$-0.275887\pi$
$103$	13184.5	+	9579.10i	0.122453	+	0.0889675i	−0.524873	+	0.851181i	$0.675887\pi$
$104$	9131.04	+	28102.4i	0.0827822	+	0.254777i
$105$	5141.12	+	3735.25i	0.0455077	+	0.0330633i
$106$	37213.0	−	27036.8i	0.321684	−	0.233717i
$107$	−18557.7	+	57114.6i	−0.156698	+	0.482267i	−0.998329	−	0.0577860i	$-0.981596\pi$
$107$	−18557.7	+	57114.6i	−0.156698	+	0.482267i	0.841631	+	0.540053i	$0.181596\pi$
$108$	−61987.9	+	45036.9i	−0.511385	+	0.371543i
$109$	106164.	−	77133.0i	0.855880	−	0.621833i	−0.0708808	−	0.997485i	$-0.522581\pi$
$109$	106164.	−	77133.0i	0.855880	−	0.621833i	0.926761	+	0.375651i	$0.122581\pi$
$110$	56269.6	−	173180.i	0.443396	−	1.36463i
$111$	218578.	−	158806.i	1.68383	−	1.22338i
$112$	644.650	+	468.366i	0.00485600	+	0.00352809i
$113$	−12291.0	−	37827.7i	−0.0905503	−	0.278685i	0.895518	−	0.445025i	$-0.146805\pi$
$113$	−12291.0	−	37827.7i	−0.0905503	−	0.278685i	−0.986068	+	0.166340i	$0.946805\pi$
$114$	−103361.	−	75096.4i	−0.744896	−	0.541199i
$115$	−61676.9	+	189822.i	−0.434888	+	1.33845i
$116$	40267.9	−	123932.i	0.277852	−	0.855142i
$117$	61047.6	+	187885.i	0.412291	+	1.26890i
$118$	−114587.			−0.757584
$119$	633.845			0.00410314
$120$	40377.2	+	124268.i	0.255967	+	0.787784i
$121$	−139556.	+	101393.i	−0.866533	+	0.629573i
$122$	−41756.9	−	30338.1i	−0.253997	−	0.184539i
$123$	−232873.			−1.38790
$124$	−85337.6	−	6823.09i	−0.498409	−	0.0398499i
$125$	−2918.90			−0.0167088
$126$	4309.95	+	3131.36i	0.0241850	+	0.0175714i
$127$	280362.	−	203695.i	1.54244	−	1.12065i	0.593662	−	0.804714i	$-0.297681\pi$
$127$	280362.	−	203695.i	1.54244	−	1.12065i	0.948780	−	0.315936i	$-0.102319\pi$
$128$	5062.93	+	15582.1i	0.0273135	+	0.0840623i
$129$	−352195.			−1.86341
$130$	145568.			0.755456
$131$	−53250.5	−	163888.i	−0.271110	−	0.834390i	−0.990223	−	0.139497i	$-0.955452\pi$
$131$	−53250.5	−	163888.i	−0.271110	−	0.834390i	0.719113	−	0.694893i	$-0.244548\pi$
$132$	73962.0	−	227632.i	0.369465	−	1.13710i
$133$	−1186.11	+	3650.47i	−0.00581427	+	0.0178945i
$134$	187070.	+	135914.i	0.899998	+	0.653887i
$135$	116644.	+	358993.i	0.550842	+	1.69532i
$136$	10543.7	+	7660.47i	0.0488818	+	0.0355147i
$137$	194966.	−	141651.i	0.887478	−	0.644790i	−0.0477415	−	0.998860i	$-0.515202\pi$
$137$	194966.	−	141651.i	0.887478	−	0.644790i	0.935219	+	0.354070i	$0.115202\pi$
$138$	−81069.5	+	249506.i	−0.362376	+	1.11528i
$139$	282755.	−	205434.i	1.24129	−	0.901850i	0.243606	−	0.969874i	$-0.421670\pi$
$139$	282755.	−	205434.i	1.24129	−	0.901850i	0.997684	+	0.0680243i	$0.0216695\pi$
$140$	3175.80	−	2307.36i	0.0136941	−	0.00994935i
$141$	174714.	−	537713.i	0.740080	−	2.27773i
$142$	−80498.1	+	58485.3i	−0.335015	+	0.243403i
$143$	−215723.	−	156732.i	−0.882179	−	0.640941i
$144$	33849.4	+	104178.i	0.136033	+	0.418667i
$145$	−519355.	−	377333.i	−2.05137	−	1.49041i
$146$	52943.1	−	162942.i	0.205555	−	0.632632i
$147$	−134446.	+	413781.i	−0.513161	+	1.57935i
$148$	−51573.5	−	158727.i	−0.193541	−	0.595657i
$149$	466831.			1.72264			0.861319	−	0.508065i	$-0.169639\pi$
$149$	466831.			1.72264			0.861319	+	0.508065i	$0.169639\pi$
$150$	319932.			1.16099
$151$	89407.2	+	275167.i	0.319103	+	0.982097i	0.974033	+	0.226407i	$0.0726980\pi$
$151$	89407.2	+	275167.i	0.319103	+	0.982097i	−0.654930	+	0.755689i	$0.727302\pi$
$152$	−63848.9	+	46388.9i	−0.224153	+	0.162857i
$153$	70492.5	+	51215.8i	0.243453	+	0.176879i
$154$	−7190.65			−0.0244324
$155$	−161881.	+	389444.i	−0.541211	+	1.30201i
$156$	191338.			0.629493
$157$	240547.	+	174768.i	0.778845	+	0.565864i	0.904632	−	0.426193i	$-0.140146\pi$
$157$	240547.	+	174768.i	0.778845	+	0.565864i	−0.125787	+	0.992057i	$0.540146\pi$
$158$	337051.	−	244882.i	1.07412	−	0.780394i
$159$	−92041.5	−	283275.i	−0.288729	−	0.888618i
$160$	80714.1			0.249258
$161$	7881.64			0.0239636
$162$	24797.2	+	76318.1i	0.0742362	+	0.228476i
$163$	−60571.0	+	186418.i	−0.178565	+	0.549566i	−0.999778	−	0.0210550i	$-0.993297\pi$
$163$	−60571.0	+	186418.i	−0.178565	+	0.549566i	0.821213	+	0.570621i	$0.193297\pi$
$164$	−44452.7	+	136811.i	−0.129059	+	0.397203i
$165$	−953923.	−	693066.i	−2.72774	−	1.98182i
$166$	124092.	+	381917.i	0.349522	+	1.07572i
$167$	−30430.0	−	22108.7i	−0.0844326	−	0.0613439i	0.544768	−	0.838587i	$-0.316618\pi$
$167$	−30430.0	−	22108.7i	−0.0844326	−	0.0613439i	−0.629201	+	0.777243i	$0.716618\pi$
$168$	4174.35	−	3032.84i	0.0114108	−	0.00829042i
$169$	−48864.3	+	150389.i	−0.131606	+	0.405041i
$170$	51942.7	−	37738.5i	0.137848	−	0.100153i
$171$	−426876.	+	310144.i	−1.11638	+	0.811097i
$172$	−67229.7	+	206912.i	−0.173277	+	0.533291i
$173$	−497280.	+	361295.i	−1.26324	+	0.917797i	−0.998912	−	0.0466360i	$-0.985150\pi$
$173$	−497280.	+	361295.i	−1.26324	+	0.917797i	−0.264327	+	0.964433i	$0.585150\pi$
$174$	−682651.	−	495975.i	−1.70933	−	1.24190i
$175$	−2970.17	−	9141.25i	−0.00733139	−	0.0225637i
$176$	−119613.	−	86904.1i	−0.291070	−	0.211475i
$177$	−229289.	+	705678.i	−0.550110	+	1.69306i
$178$	−52664.0	+	162083.i	−0.124584	+	0.383431i
$179$	61198.9	+	188351.i	0.142761	+	0.439375i	0.996716	−	0.0809725i	$-0.0258026\pi$
$179$	61198.9	+	188351.i	0.142761	+	0.439375i	−0.853955	+	0.520347i	$0.825803\pi$
$180$	539632.			1.24141
$181$	244199.			0.554048			0.277024	−	0.960863i	$-0.410652\pi$
$181$	244199.			0.554048			0.277024	+	0.960863i	$0.410652\pi$
$182$	−1776.34	−	5467.02i	−0.00397510	−	0.0122341i
$183$	−270391.	+	196451.i	−0.596849	+	0.433636i
$184$	131108.	+	95255.3i	0.285485	+	0.207417i
$185$	−822194.			−1.76622
$186$	−212780.	+	511894.i	−0.450971	+	1.08492i
$187$	−117608.			−0.245943
$188$	−282551.	−	205286.i	−0.583046	−	0.423608i
$189$	12059.1	−	8761.42i	0.0245561	−	0.0178410i
$190$	120146.	+	369770.i	0.241448	+	0.743101i
$191$	296839.			0.588759			0.294380	−	0.955689i	$-0.404887\pi$
$191$	296839.			0.588759			0.294380	+	0.955689i	$0.404887\pi$
$192$	106092.			0.207698
$193$	−93690.9	−	288351.i	−0.181052	−	0.557222i	0.818806	−	0.574071i	$-0.194637\pi$
$193$	−93690.9	−	288351.i	−0.181052	−	0.557222i	−0.999858	+	0.0168489i	$0.994637\pi$
$194$	125920.	−	387543.i	0.240210	−	0.739292i
$195$	291282.	−	896475.i	0.548564	−	1.68831i
$196$	217429.	+	157971.i	0.404275	+	0.293723i
$197$	170294.	+	524110.i	0.312632	+	0.962181i	0.976718	+	0.214526i	$0.0688206\pi$
$197$	170294.	+	524110.i	0.312632	+	0.962181i	−0.664087	+	0.747656i	$0.731179\pi$
$198$	−799701.	−	581017.i	−1.44966	−	1.05324i
$199$	−402695.	+	292575.i	−0.720848	+	0.523727i	−0.886655	−	0.462431i	$-0.846977\pi$
$199$	−402695.	+	292575.i	−0.720848	+	0.523727i	0.165807	+	0.986158i	$0.446977\pi$
$200$	61071.0	−	187957.i	0.107959	−	0.332265i
$201$	1.21135e6	−	880094.i	2.11484	−	1.53652i
$202$	232871.	−	169191.i	0.401548	−	0.291742i
$203$	−7833.67	+	24109.6i	−0.0133421	+	0.0410629i
$204$	68274.6	−	49604.4i	0.114864	−	0.0834535i
$205$	573327.	+	416547.i	0.952836	+	0.692276i
$206$	−20144.1	−	61997.2i	−0.0330735	−	0.101790i
$207$	876550.	+	636851.i	1.42184	+	1.03303i
$208$	36524.1	−	112410.i	0.0585358	−	0.180155i
$209$	220080.	−	677335.i	0.348509	−	1.07260i
$210$	−7854.94	−	24175.0i	−0.0122912	−	0.0378285i
$211$	658638.			1.01845			0.509226	−	0.860633i	$-0.329932\pi$
$211$	658638.			1.01845			0.509226	+	0.860633i	$0.329932\pi$
$212$	−183991.			−0.281162
$213$	199102.	+	612772.i	0.300695	+	0.925443i
$214$	194338.	−	141195.i	0.290084	−	0.210759i
$215$	867094.	+	629981.i	1.27929	+	0.929461i
$216$	306485.			0.446967
$217$	16601.5	+	1327.36i	0.0239330	+	0.00191354i
$218$	−524906.			−0.748067
$219$	−897531.	−	652094.i	−1.26456	−	0.918756i
$220$	−589263.	+	428124.i	−0.820828	+	0.596366i
$221$	−29053.4	−	89417.2i	−0.0400144	−	0.123152i
$222$	−1.08071e6			−1.47172
$223$	1.25641e6			1.69188			0.845942	−	0.533276i	$-0.179039\pi$
$223$	1.25641e6			1.69188			0.845942	+	0.533276i	$0.179039\pi$
$224$	−984.938	−	3031.33i	−0.00131156	−	0.00403657i
$225$	408304.	−	1.25663e6i	0.537684	−	1.65482i
$226$	−49163.8	+	151311.i	−0.0640287	+	0.197060i
$227$	−648520.	−	471177.i	−0.835331	−	0.606904i	0.0857312	−	0.996318i	$-0.472677\pi$
$227$	−648520.	−	471177.i	−0.835331	−	0.606904i	−0.921063	+	0.389415i	$0.872677\pi$
$228$	157922.	+	486034.i	0.201190	+	0.619198i
$229$	128063.	+	93043.4i	0.161375	+	0.117246i	0.665542	−	0.746360i	$-0.268200\pi$
$229$	128063.	+	93043.4i	0.161375	+	0.117246i	−0.504167	+	0.863606i	$0.668200\pi$
$230$	645889.	−	469266.i	0.805078	−	0.584924i
$231$	−14388.5	+	44283.2i	−0.0177413	+	0.0546020i
$232$	−421691.	+	306376.i	−0.514369	+	0.373711i
$233$	25069.2	−	18213.8i	0.0302518	−	0.0219792i	−0.572557	−	0.819865i	$-0.694048\pi$
$233$	25069.2	−	18213.8i	0.0302518	−	0.0219792i	0.602808	+	0.797886i	$0.294048\pi$
$234$	244190.	−	751541.i	0.291534	−	0.897249i
$235$	−1.39196e6	+	1.01132e6i	−1.64421	+	1.19459i
$236$	370812.	+	269410.i	0.433385	+	0.314872i
$237$	−833653.	−	2.56572e6i	−0.964083	−	2.96714i
$238$	−2051.17	−	1490.26i	−0.00234725	−	0.00170537i
$239$	−43056.2	+	132513.i	−0.0487575	+	0.150060i	−0.972471	−	0.233024i	$-0.925138\pi$
$239$	−43056.2	+	132513.i	−0.0487575	+	0.150060i	0.923714	+	0.383084i	$0.125138\pi$
$240$	161509.	−	497073.i	0.180996	−	0.557048i
$241$	−127613.	−	392752.i	−0.141531	−	0.435587i	0.855018	−	0.518599i	$-0.173546\pi$
$241$	−127613.	−	392752.i	−0.141531	−	0.435587i	−0.996549	+	0.0830115i	$0.973546\pi$
$242$	690003.			0.757378
$243$	−644066.			−0.699705
$244$	63798.8	+	196353.i	0.0686022	+	0.211136i
$245$	1.07114e6	−	778230.i	1.14007	−	0.828310i
$246$	753594.	+	547518.i	0.793962	+	0.576847i
$247$	569342.			0.593788
$248$	260116.	+	222721.i	0.268558	+	0.229949i
$249$	2.60032e6			2.65784
$250$	9445.77	+	6862.75i	0.00955845	+	0.00694462i
$251$	−660880.	+	480157.i	−0.662122	+	0.481060i	−0.867379	−	0.497648i	$-0.834197\pi$
$251$	−660880.	+	480157.i	−0.662122	+	0.481060i	0.205257	+	0.978708i	$0.434197\pi$
$252$	−6585.02	−	20266.6i	−0.00653215	−	0.0201039i
$253$	−1.46242e6			−1.43638
$254$	−1.38618e6			−1.34814
$255$	−128473.	−	395401.i	−0.123727	−	0.380791i
$256$	20251.7	−	62328.4i	0.0193136	−	0.0594410i
$257$	133054.	−	409499.i	0.125660	−	0.386741i	−0.868361	−	0.495933i	$-0.834826\pi$
$257$	133054.	−	409499.i	0.125660	−	0.386741i	0.994021	+	0.109192i	$0.0348262\pi$
$258$	1.13973e6	+	828061.i	1.06599	+	0.774485i
$259$	10033.1	+	30878.6i	0.00929360	+	0.0286028i
$260$	−471069.	−	342252.i	−0.432167	−	0.313988i
$261$	−2.81931e6	+	2.04835e6i	−2.56178	+	1.86124i
$262$	−213002.	+	655552.i	−0.191704	+	0.590003i
$263$	678721.	−	493119.i	0.605065	−	0.439605i	−0.242608	−	0.970124i	$-0.578003\pi$
$263$	678721.	−	493119.i	0.605065	−	0.439605i	0.847673	+	0.530519i	$0.178003\pi$
$264$	−774540.	+	562736.i	−0.683965	+	0.496930i
$265$	−280097.	+	862051.i	−0.245016	+	0.754081i
$266$	12421.1	−	9024.45i	0.0107636	−	0.00782018i
$267$	892798.	+	648656.i	0.766435	+	0.556847i
$268$	−285817.	−	879655.i	−0.243081	−	0.748127i
$269$	−449561.	−	326625.i	−0.378799	−	0.275213i	0.382051	−	0.924141i	$-0.375218\pi$
$269$	−449561.	−	326625.i	−0.378799	−	0.275213i	−0.760850	+	0.648928i	$0.775218\pi$
$270$	466575.	−	1.43597e6i	0.389504	−	1.19877i
$271$	−23121.1	+	71159.4i	−0.0191243	+	0.0588585i	−0.960163	−	0.279440i	$-0.909851\pi$
$271$	−23121.1	+	71159.4i	−0.0191243	+	0.0588585i	0.941039	+	0.338298i	$0.109851\pi$
$272$	−16109.4	−	49579.6i	−0.0132025	−	0.0406332i
$273$	−37222.8			−0.0302275
$274$	−963965.			−0.775684
$275$	551108.	+	1.69614e6i	0.439446	+	1.35247i
$276$	848970.	−	616813.i	0.670841	−	0.487395i
$277$	−908157.	−	659815.i	−0.711150	−	0.516681i	0.172394	−	0.985028i	$-0.444850\pi$
$277$	−908157.	−	659815.i	−0.711150	−	0.516681i	−0.883545	+	0.468347i	$0.844850\pi$
$278$	−1.39802e6			−1.08493
$279$	1.73907e6	+	1.48905e6i	1.33754	+	1.14525i
$280$	−15702.0			−0.0119691
$281$	1.00611e6	+	730984.i	0.760118	+	0.552258i	0.898947	−	0.438058i	$-0.144334\pi$
$281$	1.00611e6	+	730984.i	0.760118	+	0.552258i	−0.138828	+	0.990316i	$0.544334\pi$
$282$	−1.82962e6	+	1.32930e6i	−1.37006	+	0.995406i
$283$	68366.6	+	210411.i	0.0507432	+	0.156171i	0.973217	−	0.229888i	$-0.0738360\pi$
$283$	68366.6	+	210411.i	0.0507432	+	0.156171i	−0.922474	+	0.386059i	$0.873836\pi$
$284$	398004.			0.292814
$285$	2.51762e6			1.83602
$286$	329596.	+	1.01439e6i	0.238269	+	0.733315i
$287$	8647.77	−	26615.1i	0.00619726	−	0.0190732i
$288$	135398.	−	416711.i	0.0961899	−	0.296042i
$289$	1.11514e6	+	810197.i	0.785389	+	0.570619i
$290$	793503.	+	2.44215e6i	0.554056	+	1.70521i
$291$	−2.13470e6	−	1.55095e6i	−1.47776	−	1.07365i
$292$	−554427.	+	402815.i	−0.380529	+	0.276470i
$293$	−569670.	+	1.75326e6i	−0.387663	+	1.19310i	0.546867	+	0.837220i	$0.315820\pi$
$293$	−569670.	+	1.75326e6i	−0.387663	+	1.19310i	−0.934530	+	0.355885i	$0.884180\pi$
$294$	1.40793e6	−	1.02292e6i	0.949978	−	0.690199i
$295$	1.82677e6	−	1.32722e6i	1.22216	−	0.887951i
$296$	−206294.	+	634908.i	−0.136854	+	0.421193i
$297$	−2.23753e6	+	1.62566e6i	−1.47190	+	1.06940i
$298$	−1.51070e6	−	1.09759e6i	−0.985454	−	0.715974i
$299$	−361269.	−	1.11187e6i	−0.233697	−	0.719244i
$300$	−1.03532e6	−	752205.i	−0.664159	−	0.482540i
$301$	13078.8	−	40252.4i	0.00832054	−	0.0256080i
$302$	357629.	−	1.10067e6i	0.225640	−	0.694447i
$303$	−575977.	−	1.77268e6i	−0.360411	−	1.10923i
$304$	315686.			0.195917
$305$	1.01709e6			0.626052
$306$	−107703.	−	331476.i	−0.0657543	−	0.202371i
$307$	131188.	−	95314.0i	0.0794419	−	0.0577179i	−0.547355	−	0.836900i	$-0.684365\pi$
$307$	131188.	−	95314.0i	0.0794419	−	0.0577179i	0.626797	+	0.779182i	$0.284365\pi$
$308$	23269.4	+	16906.2i	0.0139768	+	0.0101548i
$309$	−422115.			−0.251498
$310$	1.43950e6	−	879662.i	0.850758	−	0.519890i
$311$	−2.33452e6			−1.36866			−0.684331	−	0.729171i	$-0.739906\pi$
$311$	−2.33452e6			−1.36866			−0.684331	+	0.729171i	$0.739906\pi$
$312$	−619184.	−	449864.i	−0.360108	−	0.261634i
$313$	235893.	−	171386.i	0.136099	−	0.0988814i	−0.517653	−	0.855591i	$-0.673194\pi$
$313$	235893.	−	171386.i	0.136099	−	0.0988814i	0.653752	+	0.756709i	$0.273194\pi$
$314$	−367523.	−	1.13112e6i	−0.210359	−	0.647418i
$315$	−104979.			−0.0596112
$316$	−1.66647e6			−0.938816
$317$	623501.	+	1.91894e6i	0.348489	+	1.07254i	0.959689	+	0.281063i	$0.0906871\pi$
$317$	623501.	+	1.91894e6i	0.348489	+	1.07254i	−0.611200	+	0.791476i	$0.709313\pi$
$318$	−368166.	+	1.13310e6i	−0.204163	+	0.628348i
$319$	1.45352e6	−	4.47347e6i	0.799731	−	2.46132i
$320$	−261196.	−	189770.i	−0.142591	−	0.103598i
$321$	−480671.	−	1.47935e6i	−0.260367	−	0.801326i
$322$	−25505.5	−	18530.9i	−0.0137087	−	0.00995992i
$323$	203156.	−	147602.i	0.108349	−	0.0787200i
$324$	99189.0	−	305272.i	0.0524929	−	0.161557i
$325$	−1.15342e6	+	838010.i	−0.605731	+	0.440089i
$326$	634308.	−	460852.i	0.330565	−	0.240169i
$327$	−1.05034e6	+	3.23260e6i	−0.543199	+	1.67180i
$328$	465514.	−	338216.i	0.238918	−	0.173584i
$329$	54967.2	+	39936.0i	0.0279972	+	0.0203411i
$330$	1.45746e6	+	4.48562e6i	0.736738	+	2.26745i
$331$	−1.71194e6	−	1.24380e6i	−0.858853	−	0.623993i	0.0687199	−	0.997636i	$-0.478109\pi$
$331$	−1.71194e6	−	1.24380e6i	−0.858853	−	0.623993i	−0.927573	+	0.373643i	$0.878109\pi$
$332$	496369.	−	1.52767e6i	0.247150	−	0.760648i
$333$	−1.37923e6	+	4.24482e6i	−0.681592	+	2.09773i
$334$	46492.8	+	143090.i	0.0228045	+	0.0701849i
$335$	−4.55654e6			−2.21832
$336$	−20639.1			−0.00997339
$337$	965169.	+	2.97048e6i	0.462944	+	1.42479i	0.861550	+	0.507673i	$0.169494\pi$
$337$	965169.	+	2.97048e6i	0.462944	+	1.42479i	−0.398606	+	0.917122i	$0.630506\pi$
$338$	511714.	−	371782.i	0.243633	−	0.177009i
$339$	833462.	+	605545.i	0.393900	+	0.286185i
$340$	−256819.			−0.120484
$341$	−3.08036e6	−	246288.i	−1.43455	−	0.114698i
$342$	2.11059e6			0.975751
$343$	−84621.2	−	61480.9i	−0.0388368	−	0.0282166i
$344$	704039.	−	511514.i	0.320775	−	0.233057i
$345$	−1.59752e6	−	4.91667e6i	−0.722602	−	2.22394i
$346$	2.45869e6			1.10411
$347$	2.51067e6			1.11935			0.559675	−	0.828712i	$-0.310926\pi$
$347$	2.51067e6			1.11935			0.559675	+	0.828712i	$0.310926\pi$
$348$	1.04300e6	+	3.21002e6i	0.461674	+	1.42089i
$349$	59747.7	−	183884.i	0.0262577	−	0.0808130i	−0.937069	−	0.349144i	$-0.886472\pi$
$349$	59747.7	−	183884.i	0.0262577	−	0.0808130i	0.963327	+	0.268331i	$0.0864722\pi$
$350$	−11880.7	+	36565.0i	−0.00518408	+	0.0159550i
$351$	−1.78873e6	−	1.29959e6i	−0.774956	−	0.563039i
$352$	182753.	+	562455.i	0.0786153	+	0.241953i
$353$	2.51560e6	+	1.82769e6i	1.07449	+	0.780666i	0.976715	−	0.214542i	$-0.0688260\pi$
$353$	2.51560e6	+	1.82769e6i	1.07449	+	0.780666i	0.0977794	+	0.995208i	$0.468826\pi$
$354$	2.40114e6	−	1.74453e6i	1.01838	−	0.739896i
$355$	605899.	−	1.86476e6i	0.255170	−	0.785331i
$356$	551504.	−	400691.i	0.230634	−	0.167566i
$357$	−13282.1	+	9649.98i	−0.00551563	+	0.00400734i
$358$	244796.	−	753403.i	0.100948	−	0.310685i
$359$	1.62552e6	−	1.18101e6i	0.665664	−	0.483633i	−0.202907	−	0.979198i	$-0.565039\pi$
$359$	1.62552e6	−	1.18101e6i	0.665664	−	0.483633i	0.868571	+	0.495565i	$0.165039\pi$
$360$	−1.74629e6	−	1.26875e6i	−0.710165	−	0.515965i
$361$	−295247.	−	908678.i	−0.119239	−	0.366980i
$362$	−790245.	−	574146.i	−0.316950	−	0.230277i
$363$	1.38070e6	−	4.24934e6i	0.549960	−	1.69260i
$364$	−7105.37	+	21868.1i	−0.00281082	+	0.00865081i
$365$	1.04328e6	+	3.21087e6i	0.409890	+	1.26151i
$366$	1.33689e6			0.521665
$367$	−252681.			−0.0979283			−0.0489641	−	0.998801i	$-0.515592\pi$
$367$	−252681.			−0.0979283			−0.0489641	+	0.998801i	$0.515592\pi$
$368$	−200315.	−	616505.i	−0.0771069	−	0.237311i
$369$	3.11230e6	−	2.26122e6i	1.18991	−	0.864523i
$370$	2.66067e6	+	1.93309e6i	1.01039	+	0.734089i
$371$	35793.4			0.0135011
$372$	1.89211e6	−	1.15625e6i	0.708905	−	0.433205i
$373$	1.41235e6			0.525619			0.262809	−	0.964848i	$-0.415351\pi$
$373$	1.41235e6			0.525619			0.262809	+	0.964848i	$0.415351\pi$
$374$	380589.	+	276514.i	0.140695	+	0.102221i
$375$	61164.8	−	44438.9i	0.0224607	−	0.0163187i
$376$	431700.	+	1.32864e6i	0.157475	+	0.484659i
$377$	3.76023e6			1.36258
$378$	−59623.3			−0.0214628
$379$	−1.20304e6	−	3.70259e6i	−0.430213	−	1.32406i	−0.897913	−	0.440172i	$-0.854917\pi$
$379$	−1.20304e6	−	3.70259e6i	−0.430213	−	1.32406i	0.467700	−	0.883887i	$-0.345083\pi$
$380$	480582.	−	1.47908e6i	0.170730	−	0.525452i
$381$	−2.77375e6	+	8.53673e6i	−0.978938	+	3.01286i
$382$	−960592.	−	697911.i	−0.336807	−	0.244704i
$383$	−801620.	−	2.46713e6i	−0.279236	−	0.859401i	−0.988067	−	0.154022i	$-0.950777\pi$
$383$	−801620.	−	2.46713e6i	−0.279236	−	0.859401i	0.708831	−	0.705378i	$-0.249223\pi$
$384$	−343322.	−	249438.i	−0.118816	−	0.0863247i
$385$	114634.	−	83286.8i	0.0394152	−	0.0286368i
$386$	−374764.	+	1.15340e6i	−0.128023	+	0.394015i
$387$	4.70701e6	−	3.41984e6i	1.59760	−	1.16072i
$388$	−1.31866e6	+	958059.i	−0.444685	+	0.323082i
$389$	701517.	−	2.15905e6i	0.235052	−	0.723416i	−0.762062	−	0.647504i	$-0.775813\pi$
$389$	701517.	−	2.15905e6i	0.235052	−	0.723416i	0.997114	−	0.0759124i	$-0.0241870\pi$
$390$	−3.05035e6	+	2.21621e6i	−1.01552	+	0.737818i
$391$	−417162.	−	303086.i	−0.137995	−	0.100259i
$392$	−332202.	−	1.02241e6i	−0.109191	−	0.336055i
$393$	3.61096e6	+	2.62352e6i	1.17935	+	0.856846i
$394$	681175.	−	2.09644e6i	0.221064	−	0.680365i
$395$	−2.53694e6	+	7.80790e6i	−0.818121	+	2.51792i
$396$	1.22183e6	+	3.76042e6i	0.391539	+	1.20503i
$397$	−3.63960e6			−1.15898			−0.579492	−	0.814978i	$-0.696749\pi$
$397$	−3.63960e6			−1.15898			−0.579492	+	0.814978i	$0.696749\pi$
$398$	1.99104e6			0.630045
$399$	−30722.0	−	94552.5i	−0.00966088	−	0.0297331i
$400$	−639544.	+	464656.i	−0.199858	+	0.145205i
$401$	−4.02721e6	−	2.92594e6i	−1.25067	−	0.908665i	−0.252410	−	0.967620i	$-0.581223\pi$
$401$	−4.02721e6	−	2.92594e6i	−1.25067	−	0.908665i	−0.998261	+	0.0589550i	$0.981223\pi$
$402$	−5.98922e6			−1.84844
$403$	−573706.	−	2.40283e6i	−0.175965	−	0.736988i
$404$	−1.15138e6			−0.350966
$405$	−1.27929e6	−	929457.i	−0.387553	−	0.281573i
$406$	82035.3	−	59602.1i	0.0246994	−	0.0179451i
$407$	−1.86161e6	−	5.72944e6i	−0.557061	−	1.71446i
$408$	−337568.			−0.100395
$409$	2.21386e6			0.654397			0.327199	−	0.944956i	$-0.393895\pi$
$409$	2.21386e6			0.654397			0.327199	+	0.944956i	$0.393895\pi$
$410$	−875966.	−	2.69595e6i	−0.257352	−	0.792048i
$411$	−1.92889e6	+	5.93652e6i	−0.563253	+	1.73351i
$412$	−80576.5	+	247989.i	−0.0233865	+	0.0719763i
$413$	−72137.3	−	52410.8i	−0.0208106	−	0.0151198i
$414$	−1.33925e6	−	4.12178e6i	−0.384026	−	1.18191i
$415$	−6.40192e6	−	4.65126e6i	−1.82469	−	1.32572i
$416$	−382486.	+	277892.i	−0.108363	+	0.0787305i
$417$	−2.79743e6	+	8.60961e6i	−0.787806	+	2.42462i
$418$	−2.30470e6	+	1.67447e6i	−0.645170	+	0.468744i
$419$	−1.93273e6	+	1.40421e6i	−0.537819	+	0.390748i	−0.823274	−	0.567644i	$-0.807855\pi$
$419$	−1.93273e6	+	1.40421e6i	−0.537819	+	0.390748i	0.285455	+	0.958392i	$0.407855\pi$
$420$	−31419.8	+	96700.1i	−0.00869120	+	0.0267488i
$421$	5.29131e6	−	3.84436e6i	1.45498	−	1.05711i	0.470350	−	0.882480i	$-0.344128\pi$
$421$	5.29131e6	−	3.84436e6i	1.45498	−	1.05711i	0.984635	−	0.174628i	$-0.0558722\pi$
$422$	−2.13140e6	−	1.54855e6i	−0.582617	−	0.423296i
$423$	2.88623e6	+	8.88290e6i	0.784296	+	2.41381i
$424$	595408.	+	432589.i	0.160842	+	0.116859i
$425$	−194318.	+	598048.i	−0.0521843	+	0.160607i
$426$	796407.	−	2.45109e6i	0.212623	−	0.654387i
$427$	−12411.3	−	38198.2i	−0.00329419	−	0.0101385i
$428$	−960862.			−0.253543
$429$	6.90659e6			1.81184
$430$	−1.32480e6	−	4.07732e6i	−0.345525	−	1.06342i
$431$	−1.91420e6	+	1.39075e6i	−0.496356	+	0.360624i	−0.807623	−	0.589699i	$-0.799247\pi$
$431$	−1.91420e6	+	1.39075e6i	−0.496356	+	0.360624i	0.311267	+	0.950322i	$0.399247\pi$
$432$	−991807.	−	720590.i	−0.255692	−	0.185771i
$433$	1.55854e6			0.399484			0.199742	−	0.979849i	$-0.435990\pi$
$433$	1.55854e6			0.399484			0.199742	+	0.979849i	$0.435990\pi$
$434$	−50602.7	−	43327.8i	−0.0128958	−	0.0110419i
$435$	1.66276e7			4.21316
$436$	1.69863e6	+	1.23413e6i	0.427940	+	0.310917i
$437$	2.52618e6	−	1.83538e6i	0.632791	−	0.459750i
$438$	1.37130e6	+	4.22044e6i	0.341546	+	1.05117i
$439$	931984.			0.230806			0.115403	−	0.993319i	$-0.463184\pi$
$439$	931984.			0.230806			0.115403	+	0.993319i	$0.463184\pi$
$440$	2.91347e6			0.717430
$441$	−2.22101e6	−	6.83557e6i	−0.543819	−	1.67370i
$442$	−116214.	+	357669.i	−0.0282945	+	0.0870814i
$443$	1.19701e6	−	3.68400e6i	0.289792	−	0.891889i	−0.695129	−	0.718885i	$-0.744653\pi$
$443$	1.19701e6	−	3.68400e6i	0.289792	−	0.891889i	0.984921	−	0.173004i	$-0.0553473\pi$
$444$	3.49725e6	+	2.54090e6i	0.841917	+	0.611688i
$445$	−1.03777e6	−	3.19394e6i	−0.248429	−	0.764587i
$446$	−4.06584e6	−	2.95400e6i	−0.967861	−	0.703192i
$447$	−9.78232e6	+	7.10727e6i	−2.31565	+	1.68242i
$448$	−3939.75	+	12125.3i	−0.000927414	+	0.00285429i
$449$	−1.76198e6	+	1.28016e6i	−0.412464	+	0.299673i	−0.774599	−	0.632453i	$-0.782048\pi$
$449$	−1.76198e6	+	1.28016e6i	−0.412464	+	0.299673i	0.362134	+	0.932126i	$0.382048\pi$
$450$	−4.27582e6	+	3.10656e6i	−0.995377	+	0.723184i
$451$	−1.60457e6	+	4.93837e6i	−0.371465	+	1.14325i
$452$	514850.	−	374061.i	0.118532	−	0.0861184i
$453$	−6.06279e6	−	4.40487e6i	−1.38812	−	1.00853i
$454$	990851.	+	3.04952e6i	0.225615	+	0.694372i
$455$	91641.3	+	66581.3i	0.0207521	+	0.0150773i
$456$	631688.	−	1.94414e6i	0.142263	−	0.437839i
$457$	1.29718e6	−	3.99232e6i	0.290543	−	0.894200i	−0.694139	−	0.719841i	$-0.744215\pi$
$457$	1.29718e6	−	3.99232e6i	0.290543	−	0.894200i	0.984682	−	0.174359i	$-0.0557853\pi$
$458$	−195663.	−	602189.i	−0.0435858	−	0.134143i
$459$	−975184.			−0.216050
$460$	−3.19345e6			−0.703664
$461$	1.43123e6	+	4.40488e6i	0.313659	+	0.965343i	0.976303	+	0.216409i	$0.0694343\pi$
$461$	1.43123e6	+	4.40488e6i	0.313659	+	0.965343i	−0.662644	+	0.748935i	$0.730566\pi$
$462$	150678.	−	109474.i	0.0328432	−	0.0238620i
$463$	5.21304e6	+	3.78750e6i	1.13016	+	0.821107i	0.985718	−	0.168407i	$-0.0538622\pi$
$463$	5.21304e6	+	3.78750e6i	1.13016	+	0.821107i	0.144439	+	0.989514i	$0.453862\pi$
$464$	2.08495e6			0.449575
$465$	−2.53692e6	−	1.06253e7i	−0.544094	−	2.27880i
$466$	−123949.			−0.0264410
$467$	2.64357e6	+	1.92067e6i	0.560917	+	0.407530i	0.831795	−	0.555084i	$-0.187314\pi$
$467$	2.64357e6	+	1.92067e6i	0.560917	+	0.407530i	−0.270877	+	0.962614i	$0.587314\pi$
$468$	−2.55720e6	+	1.85791e6i	−0.539696	+	0.392112i
$469$	55602.6	+	171127.i	0.0116725	+	0.0359242i
$470$	6.88223e6			1.43709
$471$	−7.70135e6			−1.59961
$472$	−566550.	−	1.74366e6i	−0.117053	−	0.360253i
$473$	−2.42674e6	+	7.46874e6i	−0.498735	+	1.53495i
$474$	−3.33461e6	+	1.02629e7i	−0.681709	+	2.09809i
$475$	−3.08068e6	−	2.23824e6i	−0.626487	−	0.455170i
$476$	3133.90	+	9645.16i	0.000633969	+	0.00195116i
$477$	3.98073e6	+	2.89217e6i	0.801064	+	0.582007i
$478$	450891.	−	327591.i	0.0902613	−	0.0655786i
$479$	−1.02055e6	+	3.14093e6i	−0.203234	+	0.625489i	0.796547	+	0.604576i	$0.206657\pi$
$479$	−1.02055e6	+	3.14093e6i	−0.203234	+	0.625489i	−0.999781	+	0.0209134i	$0.993343\pi$
$480$	−1.69134e6	+	1.22883e6i	−0.335065	+	0.243439i
$481$	3.89619e6	−	2.83075e6i	0.767851	−	0.557877i
$482$	−510451.	+	1.57101e6i	−0.100077	+	0.308007i
$483$	−165158.	+	119994.i	−0.0322130	+	0.0234041i
$484$	−2.23290e6	−	1.62229e6i	−0.433267	−	0.314787i
$485$	2.48134e6	+	7.63677e6i	0.478995	+	1.47420i
$486$	2.08424e6	+	1.51429e6i	0.400274	+	0.290816i
$487$	88524.2	−	272449.i	0.0169137	−	0.0520551i	−0.942243	−	0.334929i	$-0.891288\pi$
$487$	88524.2	−	272449.i	0.0169137	−	0.0520551i	0.959157	+	0.282874i	$0.0912877\pi$
$488$	255195.	−	785410.i	0.0485091	−	0.149296i
$489$	−1.56888e6	−	4.82851e6i	−0.296700	−	0.913148i
$490$	−5.29602e6			−0.996458
$491$	−3.29135e6			−0.616126			−0.308063	−	0.951366i	$-0.599681\pi$
$491$	−3.29135e6			−0.616126			−0.308063	+	0.951366i	$0.599681\pi$
$492$	−1.15139e6	−	3.54361e6i	−0.214442	−	0.659984i
$493$	1.34175e6	−	974838.i	0.248630	−	0.180640i
$494$	−1.84243e6	−	1.33860e6i	−0.339683	−	0.246794i
$495$	1.94787e7			3.57311
$496$	−318106.	−	1.33231e6i	−0.0580588	−	0.243165i
$497$	−77427.3			−0.0140606
$498$	−8.41482e6	−	6.11372e6i	−1.52045	−	1.10467i
$499$	−7.39881e6	+	5.37555e6i	−1.33018	+	0.966432i	−0.330436	+	0.943829i	$0.607196\pi$
$499$	−7.39881e6	+	5.37555e6i	−1.33018	+	0.966432i	−0.999744	+	0.0226039i	$0.992804\pi$
$500$	−14431.9	−	44416.7i	−0.00258165	−	0.00794550i
$501$	974245.			0.173410
$502$	3.26757e6			0.578716
$503$	608387.	+	1.87242e6i	0.107216	+	0.329977i	0.990244	−	0.139343i	$-0.0444990\pi$
$503$	608387.	+	1.87242e6i	0.107216	+	0.329977i	−0.883028	+	0.469320i	$0.844499\pi$
$504$	−26340.1	+	81066.5i	−0.00461892	+	0.0142156i
$505$	−1.75279e6	+	5.39454e6i	−0.305845	+	0.941295i
$506$	4.73249e6	+	3.43836e6i	0.821700	+	0.597000i
$507$	−1.26566e6	−	3.89529e6i	−0.218674	−	0.673008i
$508$	4.48578e6	+	3.25911e6i	0.771221	+	0.560325i
$509$	−5.88927e6	+	4.27881e6i	−1.00755	+	0.732029i	−0.963694	−	0.267009i	$-0.913965\pi$
$509$	−5.88927e6	+	4.27881e6i	−1.00755	+	0.732029i	−0.0438570	+	0.999038i	$0.513965\pi$
$510$	−513894.	+	1.58160e6i	−0.0874879	+	0.269260i
$511$	107858.	−	78363.2i	0.0182725	−	0.0132758i
$512$	−212079.	+	154084.i	−0.0357538	+	0.0259767i
$513$	1.82485e6	−	5.61632e6i	0.306150	−	0.942233i
$514$	−1.39336e6	+	1.01234e6i	−0.232625	+	0.169012i
$515$	1.03923e6	+	755047.i	0.172661	+	0.125446i
$516$	−1.74135e6	−	5.35932e6i	−0.287913	−	0.886106i
$517$	−1.01990e7	−	7.41003e6i	−1.67816	−	1.21925i
$518$	40132.2	−	123514.i	0.00657157	−	0.0202252i
$519$	4.91983e6	−	1.51417e7i	0.801737	−	2.46749i
$520$	719730.	+	2.21510e6i	0.116724	+	0.359240i
$521$	4.05288e6			0.654137			0.327069	−	0.945001i	$-0.393939\pi$
$521$	4.05288e6			0.654137			0.327069	+	0.945001i	$0.393939\pi$
$522$	1.39394e7			2.23908
$523$	−1.48458e6	−	4.56906e6i	−0.237328	−	0.730420i	−0.996804	−	0.0798849i	$-0.974545\pi$
$523$	−1.48458e6	−	4.56906e6i	−0.237328	−	0.730420i	0.759476	−	0.650535i	$-0.225455\pi$
$524$	2.23058e6	−	1.62061e6i	0.354887	−	0.257841i
$525$	201410.	+	146333.i	0.0318921	+	0.0231710i
$526$	−3.35578e6			−0.528846
$527$	−827646.	−	708659.i	−0.129813	−	0.111150i
$528$	3.82954e6			0.597807
$529$	19845.3	+	14418.4i	0.00308332	+	0.00224016i
$530$	2.93322e6	−	2.13111e6i	0.453581	−	0.329546i
$531$	−3.78780e6	−	1.16576e7i	−0.582976	−	1.79421i
$532$	−61413.3			−0.00940769
$533$	−4.15100e6			−0.632900
$534$	−1.36407e6	−	4.19819e6i	−0.207007	−	0.637102i
$535$	−1.46276e6	+	4.50191e6i	−0.220947	+	0.680005i
$536$	−1.14327e6	+	3.51862e6i	−0.171884	+	0.529006i
$537$	−4.14995e6	−	3.01512e6i	−0.621023	−	0.451199i
$538$	686869.	+	2.11396e6i	0.102310	+	0.314878i
$539$	7.84836e6	+	5.70217e6i	1.16361	+	0.845412i
$540$	−4.88604e6	+	3.54991e6i	−0.721062	+	0.523882i
$541$	−1.26382e6	+	3.88965e6i	−0.185649	+	0.571369i	−0.999959	−	0.00906114i	$-0.997116\pi$
$541$	−1.26382e6	+	3.88965e6i	−0.185649	+	0.571369i	0.814310	+	0.580431i	$0.197116\pi$
$542$	242127.	−	175916.i	0.0354034	−	0.0257221i
$543$	−5.11713e6	+	3.71781e6i	−0.744778	+	0.541113i
$544$	−64437.6	+	198318.i	−0.00933559	+	0.0287320i
$545$	8.36814e6	−	6.07981e6i	1.20681	−	0.876796i
$546$	120455.	+	87516.0i	0.0172920	+	0.0125634i
$547$	1.38800e6	+	4.27182e6i	0.198345	+	0.610442i	0.999921	+	0.0125500i	$0.00399491\pi$
$547$	1.38800e6	+	4.27182e6i	0.198345	+	0.610442i	−0.801577	+	0.597892i	$0.796005\pi$
$548$	3.11946e6	+	2.26642e6i	0.443739	+	0.322395i
$549$	1.70617e6	−	5.25104e6i	0.241596	−	0.743557i
$550$	2.20443e6	−	6.78455e6i	0.310735	−	0.956344i
$551$	3.10352e6	+	9.55166e6i	0.435488	+	1.34029i
$552$	−4.19754e6			−0.586337
$553$	324194.			0.0450808
$554$	1.38754e6	+	4.27041e6i	0.192075	+	0.591146i
$555$	1.72288e7	−	1.25175e7i	2.37424	−	1.72498i
$556$	4.52408e6	+	3.28694e6i	0.620645	+	0.450925i
$557$	8.42223e6			1.15024			0.575121	−	0.818069i	$-0.304955\pi$
$557$	8.42223e6			1.15024			0.575121	+	0.818069i	$0.304955\pi$
$558$	−2.12677e6	−	8.90746e6i	−0.289158	−	1.21107i
$559$	−6.27793e6			−0.849742
$560$	50812.9	+	36917.7i	0.00684705	+	0.00497467i
$561$	2.46445e6	−	1.79053e6i	0.330608	−	0.240201i
$562$	−1.53720e6	−	4.73103e6i	−0.205301	−	0.631851i
$563$	4.39288e6			0.584088			0.292044	−	0.956405i	$-0.405665\pi$
$563$	4.39288e6			0.584088			0.292044	+	0.956405i	$0.405665\pi$
$564$	9.04616e6			1.19748
$565$	−968803.	−	2.98167e6i	−0.127677	−	0.392951i
$566$	273466.	−	841643.i	0.0358809	−	0.110430i
$567$	−19296.1	+	59387.3i	−0.00252065	+	0.00775776i
$568$	−1.28797e6	−	935765.i	−0.167508	−	0.121701i
$569$	2.58740e6	+	7.96320e6i	0.335030	+	1.03112i	0.966707	+	0.255884i	$0.0823666\pi$
$569$	2.58740e6	+	7.96320e6i	0.335030	+	1.03112i	−0.631678	+	0.775231i	$0.717633\pi$
$570$	−8.14718e6	−	5.91928e6i	−1.05032	−	0.763100i
$571$	−539121.	+	391694.i	−0.0691984	+	0.0502756i	−0.621847	−	0.783139i	$-0.713617\pi$
$571$	−539121.	+	391694.i	−0.0691984	+	0.0502756i	0.552648	+	0.833415i	$0.313617\pi$
$572$	1.31838e6	−	4.05757e6i	0.168481	−	0.518532i
$573$	−6.22019e6	+	4.51923e6i	−0.791438	+	0.575013i
$574$	−90560.6	+	65796.1i	−0.0114725	+	0.00833529i
$575$	−2.41627e6	+	7.43652e6i	−0.304773	+	0.937994i
$576$	−1.41790e6	+	1.03017e6i	−0.178070	+	0.129375i
$577$	213402.	+	155046.i	0.0266845	+	0.0193874i	0.601048	−	0.799213i	$-0.294750\pi$
$577$	213402.	+	155046.i	0.0266845	+	0.0193874i	−0.574363	+	0.818601i	$0.694750\pi$
$578$	−1.70378e6	−	5.24370e6i	−0.212126	−	0.652858i
$579$	6.35327e6	+	4.61592e6i	0.787591	+	0.572218i
$580$	3.17401e6	−	9.76861e6i	0.391777	−	1.20576i
$581$	−96563.2	+	297191.i	−0.0118678	+	0.0365254i
$582$	3.26152e6	+	1.00379e7i	0.399129	+	1.22839i
$583$	−6.64138e6			−0.809258
$584$	2.74124e6			0.332594
$585$	4.81192e6	+	1.48096e7i	0.581338	+	1.78917i
$586$	5.96566e6	−	4.33431e6i	0.717653	−	0.521406i
$587$	−1.19456e7	−	8.67898e6i	−1.43091	−	1.03962i	−0.989846	−	0.142142i	$-0.954601\pi$
$587$	−1.19456e7	−	8.67898e6i	−1.43091	−	1.03962i	−0.441064	−	0.897476i	$-0.645399\pi$
$588$	−6.96120e6			−0.830311
$589$	5.63011e6	−	3.44050e6i	0.668695	−	0.408633i
$590$	−9.03203e6			−1.06821
$591$	−1.15478e7	−	8.38995e6i	−1.35997	−	0.988077i
$592$	2.16034e6	−	1.56958e6i	0.253348	−	0.184068i
$593$	−3.43333e6	−	1.05667e7i	−0.400939	−	1.23396i	−0.924239	−	0.381815i	$-0.875299\pi$
$593$	−3.43333e6	−	1.05667e7i	−0.400939	−	1.23396i	0.523300	−	0.852149i	$-0.324701\pi$
$594$	1.10630e7			1.28649
$595$	49961.2			0.00578549
$596$	2.30814e6	+	7.10372e6i	0.266162	+	0.819163i
$597$	3.98406e6	−	1.22617e7i	0.457499	−	1.40804i
$598$	−1.44508e6	+	4.44748e6i	−0.165249	+	0.508583i
$599$	836139.	+	607491.i	0.0952163	+	0.0691787i	0.634375	−	0.773026i	$-0.281258\pi$
$599$	836139.	+	607491.i	0.0952163	+	0.0691787i	−0.539158	+	0.842204i	$0.681258\pi$
$600$	1.58183e6	+	4.86837e6i	0.179383	+	0.552084i
$601$	7.69033e6	+	5.58735e6i	0.868478	+	0.630986i	0.930178	−	0.367109i	$-0.119652\pi$
$601$	7.69033e6	+	5.58735e6i	0.868478	+	0.630986i	−0.0617004	+	0.998095i	$0.519652\pi$
$602$	−136963.	+	99509.4i	−0.0154032	+	0.0111911i
$603$	−7.64358e6	+	2.35245e7i	−0.856059	+	2.63468i
$604$	−3.74514e6	+	2.72100e6i	−0.417711	+	0.303485i
$605$	−1.10001e7	+	7.99207e6i	−1.22183	+	0.887710i
$606$	−2.30391e6	+	7.09070e6i	−0.254849	+	0.784346i
$607$	535612.	−	389145.i	0.0590037	−	0.0428687i	−0.557892	−	0.829913i	$-0.688390\pi$
$607$	535612.	−	389145.i	0.0590037	−	0.0428687i	0.616896	+	0.787045i	$0.288390\pi$
$608$	−1.02158e6	−	742223.i	−0.112076	−	0.0814283i
$609$	−202904.	−	624473.i	−0.0221690	−	0.0682293i
$610$	−3.29138e6	−	2.39132e6i	−0.358140	−	0.260204i
$611$	3.11430e6	−	9.58482e6i	0.337487	−	1.03868i
$612$	−430812.	+	1.32590e6i	−0.0464953	+	0.143098i
$613$	2.64172e6	+	8.13037e6i	0.283946	+	0.873895i	0.986713	+	0.162475i	$0.0519476\pi$
$613$	2.64172e6	+	8.13037e6i	0.283946	+	0.873895i	−0.702767	+	0.711420i	$0.748052\pi$
$614$	−648631.			−0.0694348
$615$	−1.83556e7			−1.95696
$616$	−35552.5	−	109419.i	−0.00377501	−	0.0116183i
$617$	−3.48713e6	+	2.53355e6i	−0.368769	+	0.267927i	−0.756700	−	0.653762i	$-0.773190\pi$
$617$	−3.48713e6	+	2.53355e6i	−0.368769	+	0.267927i	0.387931	+	0.921688i	$0.373190\pi$
$618$	1.36599e6	+	992451.i	0.143872	+	0.104529i
$619$	1.42264e6			0.149234			0.0746170	−	0.997212i	$-0.476227\pi$
$619$	1.42264e6			0.149234			0.0746170	+	0.997212i	$0.476227\pi$
$620$	−6.72651e6	−	537812.i	−0.702766	−	0.0561890i
$621$	−1.21261e7			−1.26180
$622$	7.55466e6	+	5.48878e6i	0.782959	+	0.568853i
$623$	−107289.	+	77950.0i	−0.0110748	+	0.00804630i
$624$	946029.	+	2.91158e6i	0.0972620	+	0.299342i
$625$	−9.87998e6			−1.01171
$626$	−1.16632e6			−0.118954
$627$	5.70039e6	+	1.75440e7i	0.579076	+	1.78221i
$628$	−1.47009e6	+	4.52448e6i	−0.148746	+	0.457793i
$629$	656393.	−	2.02017e6i	0.0661511	−	0.203592i
$630$	339721.	+	246822.i	0.0341013	+	0.0247760i
$631$	497854.	+	1.53224e6i	0.0497770	+	0.153198i	0.972855	−	0.231414i	$-0.0743353\pi$
$631$	497854.	+	1.53224e6i	0.0497770	+	0.153198i	−0.923078	+	0.384612i	$0.874335\pi$
$632$	5.39282e6	+	3.91811e6i	0.537060	+	0.390197i
$633$	−1.38016e7	+	1.00274e7i	−1.36905	+	0.994673i
$634$	2.49401e6	−	7.67576e6i	0.246419	−	0.758400i
$635$	2.20988e7	−	1.60557e7i	2.17487	−	1.58014i
$636$	3.85549e6	−	2.80117e6i	0.377952	−	0.274598i
$637$	−2.39651e6	+	7.37571e6i	−0.234008	+	0.720204i
$638$	−1.52214e7	+	1.10590e7i	−1.48049	+	1.07564i
$639$	−8.61101e6	−	6.25627e6i	−0.834261	−	0.606126i
$640$	399073.	+	1.22822e6i	0.0385125	+	0.118529i
$641$	−1.42139e7	−	1.03270e7i	−1.36637	−	0.992723i	−0.998011	−	0.0630371i	$-0.979921\pi$
$641$	−1.42139e7	−	1.03270e7i	−1.36637	−	0.992723i	−0.368354	−	0.929686i	$-0.620079\pi$
$642$	−1.92268e6	+	5.91741e6i	−0.184107	+	0.566623i
$643$	−5.37629e6	+	1.65465e7i	−0.512808	+	1.57826i	0.274427	+	0.961608i	$0.411512\pi$
$643$	−5.37629e6	+	1.65465e7i	−0.512808	+	1.57826i	−0.787235	+	0.616653i	$0.788488\pi$
$644$	38969.0	+	119934.i	0.00370258	+	0.0113954i
$645$	−2.77609e7			−2.62745
$646$	−1.00446e6			−0.0947003
$647$	−4.41012e6	−	1.35730e7i	−0.414181	−	1.27472i	−0.912982	−	0.408000i	$-0.866226\pi$
$647$	−4.41012e6	−	1.35730e7i	−0.414181	−	1.27472i	0.498801	−	0.866716i	$-0.333774\pi$
$648$	−1.03872e6	+	754675.i	−0.0971765	+	0.0706028i
$649$	1.33849e7	+	9.72470e6i	1.24739	+	0.906284i
$650$	5.70283e6			0.529428
$651$	−368088.	+	224935.i	−0.0340408	+	0.0208020i
$652$	−3.13619e6			−0.288924
$653$	−5.08508e6	−	3.69452e6i	−0.466675	−	0.339059i	0.329469	−	0.944166i	$-0.393130\pi$
$653$	−5.08508e6	−	3.69452e6i	−0.466675	−	0.339059i	−0.796144	+	0.605107i	$0.793130\pi$
$654$	1.09993e7	−	7.99144e6i	1.00559	−	0.730601i
$655$	−4.19733e6	−	1.29181e7i	−0.382270	−	1.17651i
$656$	−2.30163e6			−0.208822
$657$	1.83272e7			1.65646
$658$	−83982.5	−	258471.i	−0.00756178	−	0.0232728i
$659$	5.46566e6	−	1.68216e7i	0.490263	−	1.50887i	−0.333949	−	0.942591i	$-0.608381\pi$
$659$	5.46566e6	−	1.68216e7i	0.490263	−	1.50887i	0.824212	−	0.566282i	$-0.191619\pi$
$660$	5.82986e6	−	1.79425e7i	0.520953	−	1.60333i
$661$	5.04515e6	+	3.66552e6i	0.449128	+	0.326311i	0.789252	−	0.614070i	$-0.210469\pi$
$661$	5.04515e6	+	3.66552e6i	0.449128	+	0.326311i	−0.340123	+	0.940381i	$0.610469\pi$
$662$	2.61561e6	+	8.05003e6i	0.231968	+	0.713925i
$663$	1.97014e6	+	1.43139e6i	0.174066	+	0.126466i
$664$	−5.19805e6	+	3.77660e6i	−0.457531	+	0.332415i
$665$	−93491.9	+	287739.i	−0.00819823	+	0.0252316i
$666$	1.44434e7	−	1.04938e7i	1.26178	−	0.916740i
$667$	1.66842e7	−	1.21218e7i	1.45208	−	1.05500i
$668$	185971.	−	572361.i	0.0161252	−	0.0496282i
$669$	−2.63278e7	+	1.91283e7i	−2.27431	+	1.65238i
$670$	1.47453e7	+	1.07131e7i	1.26901	+	0.921992i
$671$	2.30290e6	+	7.08758e6i	0.197455	+	0.607704i
$672$	66789.5	+	48525.4i	0.00570539	+	0.00414521i
$673$	1.46891e6	−	4.52084e6i	0.125014	−	0.384752i	−0.868890	−	0.495005i	$-0.835166\pi$
$673$	1.46891e6	−	4.52084e6i	0.125014	−	0.384752i	0.993904	+	0.110253i	$0.0351661\pi$
$674$	3.86067e6	−	1.18819e7i	0.327351	−	1.00748i
$675$	4.56967e6	+	1.40640e7i	0.386034	+	1.18809i
$676$	−2.53005e6			−0.212943
$677$	2.92780e6			0.245510			0.122755	−	0.992437i	$-0.460827\pi$
$677$	2.92780e6			0.245510			0.122755	+	0.992437i	$0.460827\pi$
$678$	−1.27342e6	−	3.91917e6i	−0.106389	−	0.327431i
$679$	256530.	−	186380.i	0.0213532	−	0.0155140i
$680$	831082.	+	603817.i	0.0689242	+	0.0500764i
$681$	2.07630e7			1.71563
$682$	9.38921e6	+	8.03938e6i	0.772980	+	0.661853i
$683$	−4.76347e6			−0.390725			−0.195363	−	0.980731i	$-0.562588\pi$
$683$	−4.76347e6			−0.390725			−0.195363	+	0.980731i	$0.562588\pi$
$684$	−6.83002e6	−	4.96230e6i	−0.558190	−	0.405548i
$685$	1.53677e7	−	1.11653e7i	1.25136	−	0.909166i
$686$	129290.	+	397913.i	0.0104895	+	0.0322833i
$687$	−4.10007e6			−0.331436
$688$	−3.48096e6			−0.280368
$689$	−1.64065e6	−	5.04941e6i	−0.131665	−	0.405222i
$690$	−6.39009e6	+	1.96667e7i	−0.510957	+	1.57256i
$691$	−6.82152e6	+	2.09945e7i	−0.543483	+	1.67267i	0.181085	+	0.983467i	$0.442039\pi$
$691$	−6.82152e6	+	2.09945e7i	−0.543483	+	1.67267i	−0.724569	+	0.689202i	$0.757961\pi$
$692$	−7.95648e6	−	5.78072e6i	−0.631620	−	0.458899i
$693$	−237694.	−	731548.i	−0.0188012	−	0.0578642i
$694$	−8.12470e6	−	5.90294e6i	−0.640337	−	0.465232i
$695$	2.22874e7	−	1.61928e7i	1.75024	−	1.27162i
$696$	4.17199e6	−	1.28401e7i	0.326453	−	1.00472i
$697$	−1.48119e6	+	1.07615e6i	−0.115486	+	0.0839052i
$698$	−625686.	+	454587.i	−0.0486091	+	0.0353166i
$699$	−248022.	+	763333.i	−0.0191998	+	0.0590909i
$700$	124416.	−	90393.7i	0.00959692	−	0.00697257i
$701$	−5.19540e6	−	3.77468e6i	−0.399323	−	0.290125i	0.369942	−	0.929055i	$-0.379377\pi$
$701$	−5.19540e6	−	3.77468e6i	−0.399323	−	0.290125i	−0.769265	+	0.638930i	$0.779377\pi$
$702$	2.73294e6	+	8.41112e6i	0.209308	+	0.644185i
$703$	1.04063e7	+	7.56065e6i	0.794163	+	0.576993i
$704$	731011.	−	2.24982e6i	0.0555894	−	0.171087i
$705$	1.37713e7	−	4.23838e7i	1.04353	−	3.21164i
$706$	−3.84349e6	−	1.18290e7i	−0.290211	−	0.893177i
$707$	223988.			0.0168530
$708$	−1.18719e7			−0.890097
$709$	2.94377e6	+	9.06000e6i	0.219932	+	0.676881i	0.998767	+	0.0496519i	$0.0158112\pi$
$709$	2.94377e6	+	9.06000e6i	0.219932	+	0.676881i	−0.778835	+	0.627229i	$0.784189\pi$
$710$	−6.34505e6	+	4.60995e6i	−0.472378	+	0.343202i
$711$	3.60549e7	+	2.61954e7i	2.67479	+	1.94335i
$712$	−2.72679e6			−0.201582
$713$	−1.02915e7	−	8.81193e6i	−0.758148	−	0.649153i
$714$	65670.1			0.00482084
$715$	−1.70038e7	−	1.23540e7i	−1.24389	−	0.903738i
$716$	−2.56353e6	+	1.86252e6i	−0.186877	+	0.135774i
$717$	−1.11522e6	−	3.43229e6i	−0.0810144	−	0.249337i
$718$	−8.03700e6			−0.581812
$719$	8.38441e6			0.604853			0.302427	−	0.953173i	$-0.402203\pi$
$719$	8.38441e6			0.604853			0.302427	+	0.953173i	$0.402203\pi$
$720$	2.66809e6	+	8.21154e6i	0.191809	+	0.590328i
$721$	15675.3	−	48243.5i	0.00112299	−	0.00345621i
$722$	−1.18099e6	+	3.63471e6i	−0.0843147	+	0.259494i
$723$	8.65354e6	+	6.28716e6i	0.615670	+	0.447310i
$724$	1.20739e6	+	3.71595e6i	0.0856052	+	0.263466i
$725$	−2.03464e7	−	1.47825e7i	−1.43761	−	1.04449i
$726$	−1.44588e7	+	1.05050e7i	−1.01810	+	0.739695i
$727$	809500.	−	2.49139e6i	0.0568043	−	0.174826i	−0.918629	−	0.395122i	$-0.870702\pi$
$727$	809500.	−	2.49139e6i	0.0568043	−	0.174826i	0.975433	+	0.220296i	$0.0707024\pi$
$728$	74408.4	−	54060.8i	0.00520347	−	0.00378054i
$729$	1.74401e7	−	1.26710e7i	1.21543	−	0.883064i
$730$	4.17310e6	−	1.28435e7i	0.289836	−	0.892023i
$731$	−2.24013e6	+	1.62755e6i	−0.155053	+	0.112653i
$732$	−4.32626e6	−	3.14321e6i	−0.298425	−	0.216818i
$733$	−310702.	−	956243.i	−0.0213592	−	0.0657367i	0.939809	−	0.341701i	$-0.111003\pi$
$733$	−310702.	−	956243.i	−0.0213592	−	0.0657367i	−0.961168	+	0.275964i	$0.911003\pi$
$734$	817694.	+	594090.i	0.0560210	+	0.0407016i
$735$	−1.05973e7	+	3.26152e7i	−0.723566	+	2.22691i
$736$	−801259.	+	2.46602e6i	−0.0545228	+	0.167804i
$737$	−1.03169e7	−	3.17522e7i	−0.699651	−	2.15330i
$738$	−1.53881e7			−1.04002
$739$	7.53967e6			0.507857			0.253929	−	0.967223i	$-0.418277\pi$
$739$	7.53967e6			0.507857			0.253929	+	0.967223i	$0.418277\pi$
$740$	−4.06515e6	−	1.25112e7i	−0.272896	−	0.839887i
$741$	−1.19304e7	+	8.66796e6i	−0.798197	+	0.579924i
$742$	−115830.	−	84155.4i	−0.00772345	−	0.00561141i
$743$	−3.65905e6			−0.243162			−0.121581	−	0.992581i	$-0.538796\pi$
$743$	−3.65905e6			−0.243162			−0.121581	+	0.992581i	$0.538796\pi$
$744$	−8.84148e6	−	706912.i	−0.585589	−	0.0468202i
$745$	3.67967e7			2.42895
$746$	−4.57047e6	−	3.32064e6i	−0.300686	−	0.218461i
$747$	−3.47527e7	+	2.52493e7i	−2.27870	+	1.65557i
$748$	−581488.	−	1.78964e6i	−0.0380003	−	0.116953i
$749$	186925.			0.0121748
$750$	−302416.			−0.0196314
$751$	6.51598e6	+	2.00541e7i	0.421580	+	1.29749i	0.906231	+	0.422782i	$0.138946\pi$
$751$	6.51598e6	+	2.00541e7i	0.421580	+	1.29749i	−0.484651	+	0.874707i	$0.661054\pi$
$752$	1.72680e6	−	5.31454e6i	0.111352	−	0.342706i
$753$	6.53841e6	−	2.01231e7i	0.420227	−	1.29333i
$754$	−1.21684e7	−	8.84083e6i	−0.779478	−	0.566324i
$755$	7.04729e6	+	2.16893e7i	0.449940	+	1.38477i
$756$	192945.	+	140183.i	0.0122780	+	0.00892052i
$757$	4.01984e6	−	2.92058e6i	0.254958	−	0.185238i	−0.452963	−	0.891529i	$-0.649633\pi$
$757$	4.01984e6	−	2.92058e6i	0.254958	−	0.185238i	0.707921	+	0.706291i	$0.249633\pi$
$758$	−4.81218e6	+	1.48104e7i	−0.304207	+	0.936252i
$759$	3.06446e7	−	2.22646e7i	1.93086	−	1.40285i
$760$	−5.03272e6	+	3.65649e6i	−0.316060	+	0.229631i
$761$	3.41895e6	−	1.05224e7i	0.214008	−	0.658650i	−0.785214	−	0.619224i	$-0.787447\pi$
$761$	3.41895e6	−	1.05224e7i	0.214008	−	0.658650i	0.999223	−	0.0394258i	$-0.0125529\pi$
$762$	2.90471e7	−	2.11040e7i	1.81224	−	1.31667i
$763$	−330450.	−	240086.i	−0.0205492	−	0.0149298i
$764$	1.46765e6	+	4.51697e6i	0.0909683	+	0.279972i
$765$	5.55639e6	+	4.03695e6i	0.343273	+	0.249402i
$766$	−3.20648e6	+	9.86853e6i	−0.197450	+	0.607688i
$767$	−4.08711e6	+	1.25788e7i	−0.250858	+	0.772061i
$768$	524550.	+	1.61440e6i	0.0320910	+	0.0987661i
$769$	8.91398e6			0.543570			0.271785	−	0.962358i	$-0.412386\pi$
$769$	8.91398e6			0.543570			0.271785	+	0.962358i	$0.412386\pi$
$770$	−566784.			−0.0344501
$771$	3.44630e6	+	1.06066e7i	0.208794	+	0.642601i
$772$	3.92458e6	−	2.85137e6i	0.237001	−	0.172191i
$773$	1.65426e7	+	1.20189e7i	0.995758	+	0.723461i	0.961175	−	0.275941i	$-0.0889895\pi$
$773$	1.65426e7	+	1.20189e7i	0.995758	+	0.723461i	0.0345837	+	0.999402i	$0.488989\pi$
$774$	−2.32727e7			−1.39635
$775$	−6.34190e6	+	1.52570e7i	−0.379284	+	0.912460i
$776$	6.51979e6			0.388669
$777$	−680351.	−	494304.i	−0.0404278	−	0.0293725i
$778$	−7.34638e6	+	5.33746e6i	−0.435135	+	0.316144i
$779$	−3.42605e6	−	1.05443e7i	−0.202279	−	0.622549i
$780$	1.50818e7			0.887596
$781$	1.43665e7			0.842795
$782$	637367.	+	1.96161e6i	0.0372712	+	0.114709i
$783$	1.20523e7	−	3.70931e7i	0.702529	−	2.16216i
$784$	−1.32881e6	+	4.08965e6i	−0.0772097	+	0.237627i
$785$	1.89605e7	+	1.37756e7i	1.09818	+	0.797878i
$786$	−5.51706e6	−	1.69798e7i	−0.318531	−	0.980337i
$787$	−2.42482e7	−	1.76174e7i	−1.39554	−	1.01392i	−0.995231	−	0.0975417i	$-0.968902\pi$
$787$	−2.42482e7	−	1.76174e7i	−1.39554	−	1.01392i	−0.400311	−	0.916379i	$-0.631098\pi$
$788$	−7.13335e6	+	5.18269e6i	−0.409240	+	0.297330i
$789$	−6.71491e6	+	2.06664e7i	−0.384015	+	1.18188i
$790$	2.65672e7	−	1.93022e7i	1.51453	−	1.10037i
$791$	−100158.	+	72769.4i	−0.00569176	+	0.00413530i
$792$	4.88734e6	−	1.50417e7i	0.276860	−	0.852086i
$793$	−4.81976e6	+	3.50176e6i	−0.272171	+	0.197744i
$794$	1.17780e7	+	8.55721e6i	0.663010	+	0.481705i
$795$	−7.25493e6	−	2.23284e7i	−0.407114	−	1.25297i
$796$	−6.44313e6	−	4.68120e6i	−0.360424	−	0.261863i
$797$	1.54737e6	−	4.76231e6i	0.0862875	−	0.265566i	−0.898598	−	0.438773i	$-0.855413\pi$
$797$	1.54737e6	−	4.76231e6i	0.0862875	−	0.265566i	0.984885	+	0.173208i	$0.0554131\pi$
$798$	−122888.	+	378210.i	−0.00683128	+	0.0210245i
$799$	−1.37360e6	−	4.22749e6i	−0.0761188	−	0.234270i
$800$	3.16208e6			0.174682
$801$	−1.82305e7			−1.00396
$802$	6.15302e6	+	1.89371e7i	0.337795	+	1.03962i
$803$	−2.00127e7	+	1.45401e7i	−1.09526	+	0.795754i
$804$	1.93815e7	+	1.40815e7i	1.05742	+	0.768261i
$805$	621250.			0.0337891
$806$	−3.79284e6	+	9.12458e6i	−0.205649	+	0.494738i
$807$	1.43932e7			0.777986
$808$	3.72594e6	+	2.70705e6i	0.200774	+	0.145871i
$809$	−7.72009e6	+	5.60898e6i	−0.414716	+	0.301309i	−0.775508	−	0.631337i	$-0.782506\pi$
$809$	−7.72009e6	+	5.60898e6i	−0.414716	+	0.301309i	0.360792	+	0.932646i	$0.382506\pi$
$810$	1.95458e6	+	6.01557e6i	0.104674	+	0.322155i
$811$	−1.89826e7			−1.01345			−0.506726	−	0.862107i	$-0.669144\pi$
$811$	−1.89826e7			−1.01345			−0.506726	+	0.862107i	$0.669144\pi$
$812$	−405605.			−0.0215880
$813$	−598870.	−	1.84313e6i	−0.0317765	−	0.0977981i
$814$	−7.44644e6	+	2.29178e7i	−0.393901	+	1.21230i
$815$	−4.77435e6	+	1.46940e7i	−0.251780	+	0.774898i
$816$	1.09239e6	+	793670.i	0.0574320	+	0.0417268i
$817$	−5.18152e6	−	1.59471e7i	−0.271583	−	0.835846i
$818$	−7.16419e6	−	5.20509e6i	−0.374355	−	0.271985i
$819$	497474.	−	361436.i	0.0259156	−	0.0188288i
$820$	−3.50386e6	+	1.07838e7i	−0.181975	+	0.560063i
$821$	2.67681e7	−	1.94482e7i	1.38599	−	1.00698i	0.389696	−	0.920943i	$-0.372580\pi$
$821$	2.67681e7	−	1.94482e7i	1.38599	−	1.00698i	0.996292	−	0.0860359i	$-0.0274200\pi$
$822$	2.01996e7	−	1.46759e7i	1.04271	−	0.757574i
$823$	752772.	−	2.31679e6i	0.0387404	−	0.119231i	−0.929816	−	0.368025i	$-0.880034\pi$
$823$	752772.	−	2.31679e6i	0.0387404	−	0.119231i	0.968556	+	0.248794i	$0.0800342\pi$
$824$	843808.	−	613062.i	0.0432938	−	0.0314548i
$825$	−3.73712e7	−	2.71517e7i	−1.91162	−	1.38887i
$826$	110216.	+	339210.i	0.00562075	+	0.0172989i
$827$	−1.54914e6	−	1.12552e6i	−0.0787640	−	0.0572254i	0.547706	−	0.836671i	$-0.315501\pi$
$827$	−1.54914e6	−	1.12552e6i	−0.0787640	−	0.0572254i	−0.626470	+	0.779445i	$0.715501\pi$
$828$	−5.35700e6	+	1.64871e7i	−0.271547	+	0.835737i
$829$	−5.56202e6	+	1.71181e7i	−0.281090	+	0.865107i	0.706453	+	0.707760i	$0.250294\pi$
$829$	−5.56202e6	+	1.71181e7i	−0.281090	+	0.865107i	−0.987543	+	0.157347i	$0.949706\pi$
$830$	9.78126e6	+	3.01036e7i	0.492833	+	1.51678i
$831$	2.90755e7			1.46058
$832$	1.89111e6			0.0947129
$833$	1.05701e6	+	3.25314e6i	0.0527797	+	0.162439i
$834$	2.92951e7	−	2.12841e7i	1.45841	−	1.05960i
$835$	−2.39856e6	−	1.74266e6i	−0.119051	−	0.0864960i
$836$	1.13951e7			0.563900
$837$	−2.55417e7	−	2.04216e6i	−1.26019	−	0.100757i
$838$	9.55594e6			0.470071
$839$	−1.98309e7	−	1.44080e7i	−0.972606	−	0.706640i	−0.0165620	−	0.999863i	$-0.505272\pi$
$839$	−1.98309e7	−	1.44080e7i	−0.972606	−	0.706640i	−0.956044	+	0.293223i	$0.905272\pi$
$840$	329032.	−	239056.i	0.0160894	−	0.0116896i
$841$	1.41590e7	+	4.35768e7i	0.690306	+	2.12454i
$842$	−2.61617e7			−1.27170
$843$	−3.22117e7			−1.56115
$844$	3.25648e6	+	1.00224e7i	0.157359	+	0.484302i
$845$	−3.85160e6	+	1.18540e7i	−0.185566	+	0.571115i
$846$	1.15449e7	−	3.55316e7i	0.554581	−	1.70682i
$847$	434385.	+	315599.i	0.0208049	+	0.0151157i
$848$	−909702.	−	2.79978e6i	−0.0434420	−	0.133701i
$849$	−4.63600e6	−	3.36825e6i	−0.220737	−	0.160375i
$850$	2.03492e6	−	1.47846e6i	0.0966051	−	0.0701877i
$851$	8.16201e6	−	2.51201e7i	0.386343	−	1.18904i
$852$	−8.34008e6	+	6.05942e6i	−0.393615	+	0.285978i
$853$	4.81586e6	−	3.49893e6i	0.226622	−	0.164650i	−0.468681	−	0.883368i	$-0.655271\pi$
$853$	4.81586e6	−	3.49893e6i	0.226622	−	0.164650i	0.695302	+	0.718717i	$0.255271\pi$
$854$	−49645.4	+	152793.i	−0.00232935	+	0.00716899i
$855$	−3.36474e7	+	2.44463e7i	−1.57411	+	1.14366i
$856$	3.10941e6	+	2.25912e6i	0.145042	+	0.105379i
$857$	−938017.	−	2.88692e6i	−0.0436273	−	0.134271i	0.926870	−	0.375382i	$-0.122488\pi$
$857$	−938017.	−	2.88692e6i	−0.0436273	−	0.134271i	−0.970498	+	0.241111i	$0.922488\pi$
$858$	−2.23502e7	−	1.62384e7i	−1.03649	−	0.753051i
$859$	−6.11749e6	+	1.88277e7i	−0.282872	+	0.870591i	0.704156	+	0.710045i	$0.251325\pi$
$859$	−6.11749e6	+	1.88277e7i	−0.282872	+	0.870591i	−0.987028	+	0.160546i	$0.948675\pi$
$860$	−5.29921e6	+	1.63093e7i	−0.244323	+	0.751950i
$861$	223990.	+	689370.i	0.0102972	+	0.0316916i
$862$	9.46431e6			0.433831
$863$	1.77965e7			0.813406			0.406703	−	0.913560i	$-0.366678\pi$
$863$	1.77965e7			0.813406			0.406703	+	0.913560i	$0.366678\pi$
$864$	1.51535e6	+	4.66376e6i	0.0690601	+	0.212545i
$865$	−3.91968e7	+	2.84781e7i	−1.78119	+	1.29411i
$866$	−5.04356e6	−	3.66436e6i	−0.228529	−	0.166036i
$867$	−3.57023e7			−1.61305
$868$	61884.0	+	259186.i	0.00278791	+	0.0116765i
$869$	−6.01534e7			−2.70216
$870$	−5.38082e7	−	3.90939e7i	−2.41018	−	1.75110i
$871$	2.15924e7	−	1.56878e7i	0.964397	−	0.700676i
$872$	−2.59528e6	−	7.98745e6i	−0.115583	−	0.355727i
$873$	4.35895e7			1.93574
$874$	−1.24901e7			−0.553080
$875$	2807.56	+	8640.77i	0.000123968	+	0.000381533i
$876$	5.48522e6	−	1.68818e7i	0.241509	−	0.743289i
$877$	−1.95495e6	+	6.01671e6i	−0.0858294	+	0.264156i	−0.984755	−	0.173945i	$-0.944349\pi$
$877$	−1.95495e6	+	6.01671e6i	−0.0858294	+	0.264156i	0.898926	+	0.438100i	$0.144349\pi$
$878$	−3.01596e6	−	2.19123e6i	−0.132035	−	0.0959292i
$879$	−1.47553e7	−	4.54121e7i	−0.644133	−	1.98244i
$880$	−9.42820e6	−	6.84999e6i	−0.410414	−	0.298183i
$881$	−1.66799e7	+	1.21186e7i	−0.724025	+	0.526035i	−0.887668	−	0.460485i	$-0.847676\pi$
$881$	−1.66799e7	+	1.21186e7i	−0.724025	+	0.526035i	0.163643	+	0.986520i	$0.447676\pi$
$882$	−8.88404e6	+	2.73423e7i	−0.384538	+	1.18349i
$883$	1.34612e7	−	9.78012e6i	0.581007	−	0.422126i	−0.258080	−	0.966124i	$-0.583090\pi$
$883$	1.34612e7	−	9.78012e6i	0.581007	−	0.422126i	0.839087	+	0.543997i	$0.183090\pi$
$884$	1.21700e6	−	884206.i	0.0523795	−	0.0380560i
$885$	−1.80731e7	+	5.56232e7i	−0.775665	+	2.38725i
$886$	−1.25352e7	+	9.10736e6i	−0.536472	+	0.389770i
$887$	5.80157e6	+	4.21509e6i	0.247592	+	0.179886i	0.704659	−	0.709546i	$-0.251100\pi$
$887$	5.80157e6	+	4.21509e6i	0.247592	+	0.179886i	−0.457067	+	0.889432i	$0.651100\pi$
$888$	−5.34332e6	−	1.64451e7i	−0.227394	−	0.699847i
$889$	−872659.	−	634024.i	−0.0370331	−	0.0269061i
$890$	−4.15110e6	+	1.27758e7i	−0.175666	+	0.540645i
$891$	3.58035e6	−	1.10192e7i	0.151088	−	0.465002i
$892$	6.21205e6	+	1.91187e7i	0.261410	+	0.804538i
$893$	2.69176e7			1.12955
$894$	4.83664e7			2.02395
$895$	4.82384e6	+	1.48463e7i	0.201296	+	0.619526i
$896$	41257.6	−	29975.4i	0.00171686	−	0.00124737i
$897$	2.44980e7	+	1.77988e7i	1.01660	+	0.738602i
$898$	8.71173e6			0.360507
$899$	3.71841e7	−	2.27229e7i	1.53447	−	0.937699i
$900$	2.11408e7			0.869992
$901$	−1.89449e6	−	1.37642e6i	−0.0777463	−	0.0564860i
$902$	1.68033e7	−	1.22083e7i	0.687667	−	0.499619i
$903$	338760.	+	1.04260e6i	0.0138252	+	0.0425497i
$904$	−2.54556e6			−0.103601
$905$	1.92484e7			0.781218
$906$	9.26312e6	+	2.85089e7i	0.374918	+	1.15388i
$907$	6.67898e6	−	2.05558e7i	0.269583	−	0.829690i	−0.721020	−	0.692915i	$-0.756326\pi$
$907$	6.67898e6	−	2.05558e7i	0.269583	−	0.829690i	0.990602	−	0.136775i	$-0.0436738\pi$
$908$	3.96340e6	−	1.21981e7i	0.159534	−	0.490995i
$909$	2.49106e7	+	1.80986e7i	0.999942	+	0.726500i
$910$	−140015.	−	430923.i	−0.00560496	−	0.0172503i
$911$	2.10202e7	+	1.52720e7i	0.839151	+	0.609679i	0.922133	−	0.386872i	$-0.126445\pi$
$911$	2.10202e7	+	1.52720e7i	0.839151	+	0.609679i	−0.0829826	+	0.996551i	$0.526445\pi$
$912$	−6.61512e6	+	4.80617e6i	−0.263361	+	0.191343i
$913$	1.79171e7	−	5.51430e7i	0.711361	−	2.18934i
$914$	−1.35843e7	+	9.86955e6i	−0.537862	+	0.390780i
$915$	−2.13129e7	+	1.54847e7i	−0.841568	+	0.611435i
$916$	−782653.	+	2.40876e6i	−0.0308198	+	0.0948537i
$917$	−433935.	+	315273.i	−0.0170413	+	0.0123812i
$918$	3.15576e6	+	2.29279e6i	0.123594	+	0.0897963i
$919$	5.79232e6	+	1.78269e7i	0.226237	+	0.696286i	0.998164	+	0.0605743i	$0.0192932\pi$
$919$	5.79232e6	+	1.78269e7i	0.226237	+	0.696286i	−0.771927	+	0.635712i	$0.780707\pi$
$920$	1.03342e7	+	7.50825e6i	0.402539	+	0.292462i
$921$	−1.29791e6	+	3.99456e6i	−0.0504192	+	0.155174i
$922$	5.72493e6	−	1.76195e7i	0.221790	−	0.682601i
$923$	3.54902e6	+	1.09228e7i	0.137121	+	0.422015i
$924$	−744994.			−0.0287060
$925$	−3.22105e7			−1.23778
$926$	−7.96482e6	−	2.45132e7i	−0.305245	−	0.939447i
$927$	5.64147e6	−	4.09877e6i	0.215622	−	0.156658i
$928$	−6.74706e6	−	4.90202e6i	−0.257184	−	0.186855i
$929$	−2.86433e7			−1.08889			−0.544445	−	0.838797i	$-0.683260\pi$
$929$	−2.86433e7			−1.08889			−0.544445	+	0.838797i	$0.683260\pi$
$930$	−1.67718e7	+	4.03487e7i	−0.635877	+	1.52976i
$931$	−2.07136e7			−0.783216
$932$	401107.	+	291422.i	0.0151259	+	0.0109896i
$933$	4.89192e7	−	3.55419e7i	1.83982	−	1.33671i
$934$	−4.03902e6	−	1.24308e7i	−0.151499	−	0.466265i
$935$	−9.27018e6			−0.346784
$936$	1.26435e7			0.471712
$937$	4.74871e6	+	1.46150e7i	0.176696	+	0.543815i	0.999707	−	0.0242110i	$-0.00770735\pi$
$937$	4.74871e6	+	1.46150e7i	0.176696	+	0.543815i	−0.823011	+	0.568026i	$0.807707\pi$
$938$	222410.	−	684508.i	0.00825368	−	0.0254022i
$939$	−2.33380e6	+	7.18270e6i	−0.0863773	+	0.265842i
$940$	−2.22714e7	−	1.61811e7i	−0.822105	−	0.597294i
$941$	1.61663e7	+	4.97548e7i	0.595164	+	1.83173i	0.553907	+	0.832578i	$0.313136\pi$
$941$	1.61663e7	+	4.97548e7i	0.595164	+	1.83173i	0.0412568	+	0.999149i	$0.486864\pi$
$942$	2.49221e7	+	1.81070e7i	0.915076	+	0.664842i
$943$	−1.84180e7	+	1.33815e7i	−0.674472	+	0.490033i
$944$	−2.26620e6	+	6.97464e6i	−0.0827691	+	0.254737i
$945$	950524.	−	690596.i	0.0346245	−	0.0251562i
$946$	2.54131e7	−	1.84637e7i	0.923274	−	0.670798i
$947$	1.32475e7	−	4.07716e7i	0.480019	−	1.47735i	−0.359048	−	0.933319i	$-0.616899\pi$
$947$	1.32475e7	−	4.07716e7i	0.480019	−	1.47735i	0.839067	−	0.544027i	$-0.183101\pi$
$948$	3.49205e7	−	2.53712e7i	1.26200	−	0.916897i
$949$	−1.59986e7	−	1.16237e7i	−0.576656	−	0.418965i
$950$	4.70686e6	+	1.44862e7i	0.169208	+	0.520770i
$951$	−4.22802e7	−	3.07184e7i	−1.51595	−	1.10140i
$952$	12535.6	−	38580.7i	0.000448284	−	0.00137968i
$953$	1.46390e7	−	4.50542e7i	0.522131	−	1.60695i	−0.247789	−	0.968814i	$-0.579704\pi$
$953$	1.46390e7	−	4.50542e7i	0.522131	−	1.60695i	0.769920	−	0.638140i	$-0.220296\pi$
$954$	−6.08202e6	−	1.87185e7i	−0.216360	−	0.665887i
$955$	2.33976e7			0.830161
$956$	−2.22933e6			−0.0788912
$957$	3.76483e7	+	1.15870e8i	1.32882	+	4.08968i
$958$	1.06874e7	−	7.76481e6i	0.376232	−	0.273349i
$959$	−606855.	−	440906.i	−0.0213078	−	0.0154810i
$960$	8.36246e6			0.292857
$961$	−2.01934e7	−	2.02942e7i	−0.705345	−	0.708865i
$962$	−1.92638e7			−0.671127
$963$	2.07887e7	+	1.51039e7i	0.722373	+	0.524835i
$964$	5.34551e6	−	3.88374e6i	0.185266	−	0.134604i
$965$	−7.38494e6	−	2.27285e7i	−0.255287	−	0.785693i
$966$	816585.			0.0281552
$967$	−228470.			−0.00785711			−0.00392855	−	0.999992i	$-0.501251\pi$
$967$	−228470.			−0.00785711			−0.00392855	+	0.999992i	$0.501251\pi$
$968$	3.41156e6	+	1.04997e7i	0.117021	+	0.360155i
$969$	−2.00992e6	+	6.18591e6i	−0.0687654	+	0.211638i
$970$	9.92535e6	−	3.05471e7i	0.338701	−	1.04241i
$971$	−1.65967e7	−	1.20582e7i	−0.564903	−	0.410426i	0.268347	−	0.963322i	$-0.413523\pi$
$971$	−1.65967e7	−	1.20582e7i	−0.564903	−	0.410426i	−0.833250	+	0.552896i	$0.813523\pi$
$972$	−3.18444e6	−	9.80070e6i	−0.108110	−	0.332729i
$973$	−880109.	−	639437.i	−0.0298026	−	0.0216529i
$974$	−927037.	+	673532.i	−0.0313112	+	0.0227489i
$975$	1.14114e7	−	3.51206e7i	0.384438	−	1.18318i
$976$	−2.67244e6	+	1.94164e6i	−0.0898014	+	0.0652446i
$977$	−2.81183e7	+	2.04292e7i	−0.942439	+	0.684722i	−0.949007	−	0.315256i	$-0.897909\pi$
$977$	−2.81183e7	+	2.04292e7i	−0.942439	+	0.684722i	0.00656749	+	0.999978i	$0.497909\pi$
$978$	−6.27552e6	+	1.93141e7i	−0.209798	+	0.645693i
$979$	1.99072e7	−	1.44634e7i	0.663825	−	0.482297i
$980$	1.71383e7	+	1.24517e7i	0.570035	+	0.414155i
$981$	−1.73513e7	−	5.34019e7i	−0.575652	−	1.77167i
$982$	1.06510e7	+	7.73842e6i	0.352462	+	0.256079i
$983$	5.78845e6	−	1.78150e7i	0.191064	−	0.588034i	−0.808936	−	0.587897i	$-0.799956\pi$
$983$	5.78845e6	−	1.78150e7i	0.191064	−	0.588034i	1.00000		0.000137652i	$-4.38160e-5\pi$
$984$	−4.60556e6	+	1.41744e7i	−0.151633	+	0.466679i
$985$	1.34230e7	+	4.13116e7i	0.440816	+	1.35669i
$986$	−6.63397e6			−0.217311
$987$	−1.75983e6			−0.0575013
$988$	2.81498e6	+	8.66363e6i	0.0917452	+	0.282363i
$989$	−2.78553e7	+	2.02380e7i	−0.905558	+	0.657927i
$990$	−6.30344e7	−	4.57971e7i	−2.04404	−	1.48508i
$991$	−2.10259e7			−0.680096			−0.340048	−	0.940408i	$-0.610443\pi$
$991$	−2.10259e7			−0.680096			−0.340048	+	0.940408i	$0.610443\pi$
$992$	−2.10303e6	+	5.05936e6i	−0.0678527	+	0.163236i
$993$	5.48095e7			1.76393
$994$	250560.	+	182043.i	0.00804352	+	0.00584396i
$995$	−3.17414e7	+	2.30615e7i	−1.01641	+	0.738464i
$996$	1.28567e7	+	3.95689e7i	0.410659	+	1.26388i
$997$	−1.06523e7			−0.339395			−0.169698	−	0.985496i	$-0.554279\pi$
$997$	−1.06523e7			−0.339395			−0.169698	+	0.985496i	$0.554279\pi$
$998$	3.65817e7			1.16262
$999$	−1.54361e7	−	4.75073e7i	−0.489353	−	1.50608i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	62.6.d.a.33.1	✓	24
31.16	even	5	inner	62.6.d.a.47.1	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
62.6.d.a.33.1	✓	24	1.1	even	1	trivial
62.6.d.a.47.1	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} +(-20.9547 + 15.2245i) q^{3} +(4.94427 + 15.2169i) q^{4} +78.8224 q^{5} +103.606 q^{6} +(-0.961853 - 2.96028i) q^{7} +(19.7771 - 60.8676i) q^{8} +(132.224 - 406.944i) q^{9} +(-255.075 - 185.323i) q^{10} +(178.470 + 549.273i) q^{11} +(-335.276 - 243.592i) q^{12} +(-373.521 + 271.379i) q^{13} +(-3.84741 + 11.8411i) q^{14} +(-1651.70 + 1200.03i) q^{15} +(-207.108 + 150.473i) q^{16} +(-62.9273 + 193.670i) q^{17} +(-1384.67 + 1006.02i) q^{18} +(-997.639 - 724.827i) q^{19} +(389.719 + 1199.43i) q^{20} +(65.2242 + 47.3881i) q^{21} +(713.878 - 2197.09i) q^{22} +(-782.479 + 2408.22i) q^{23} +(512.256 + 1576.56i) q^{24} +3087.97 q^{25} +1846.79 q^{26} +(1479.83 + 4554.45i) q^{27} +(40.2906 - 29.2729i) q^{28} +(-6588.92 - 4787.13i) q^{29} +8166.46 q^{30} +(-2053.74 + 4940.78i) q^{31} +1024.00 q^{32} +(-12102.2 - 8792.75i) q^{33} +(658.984 - 478.780i) q^{34} +(-75.8156 - 233.336i) q^{35} +6846.18 q^{36} -10431.0 q^{37} +(1524.26 + 4691.18i) q^{38} +(3695.43 - 11373.4i) q^{39} +(1558.88 - 4797.73i) q^{40} +(7273.66 + 5284.62i) q^{41} +(-99.6537 - 306.702i) q^{42} +(11000.6 + 7992.41i) q^{43} +(-7475.83 + 5431.51i) q^{44} +(10422.2 - 32076.3i) q^{45} +(8194.23 - 5953.46i) q^{46} +(-17659.5 + 12830.3i) q^{47} +(2049.02 - 6306.24i) q^{48} +(13589.3 - 9873.21i) q^{49} +(-9992.88 - 7260.25i) q^{50} +(-1629.91 - 5016.35i) q^{51} +(-5976.34 - 4342.07i) q^{52} +(-3553.52 + 10936.6i) q^{53} +(5919.32 - 18217.8i) q^{54} +(14067.4 + 43295.0i) q^{55} -199.208 q^{56} +31940.4 q^{57} +(10067.0 + 30983.0i) q^{58} +(23175.7 - 16838.2i) q^{59} +(-26427.2 - 19200.5i) q^{60} +12903.6 q^{61} +(18262.5 - 11160.0i) q^{62} -1331.85 q^{63} +(-3313.73 - 2407.57i) q^{64} +(-29441.8 + 21390.7i) q^{65} +(18490.5 + 56907.9i) q^{66} -57807.7 q^{67} -3258.19 q^{68} +(-20267.4 - 62376.5i) q^{69} +(-303.262 + 933.345i) q^{70} +(7686.88 - 23657.8i) q^{71} +(-22154.7 - 16096.3i) q^{72} +(13235.8 + 40735.5i) q^{73} +(33755.3 + 24524.7i) q^{74} +(-64707.6 + 47012.8i) q^{75} +(6097.03 - 18764.7i) q^{76} +(1454.34 - 1056.64i) q^{77} +(-38699.0 + 28116.5i) q^{78} +(-32185.5 + 99056.9i) q^{79} +(-16324.8 + 11860.6i) q^{80} +(-16230.0 - 11791.8i) q^{81} +(-11113.2 - 34202.8i) q^{82} +(-81219.5 - 59009.4i) q^{83} +(-398.615 + 1226.81i) q^{84} +(-4960.08 + 15265.6i) q^{85} +(-16807.4 - 51728.0i) q^{86} +210951. q^{87} +36962.5 q^{88} +(-13166.0 - 40520.8i) q^{89} +(-109143. + 79297.0i) q^{90} +(1162.63 + 844.701i) q^{91} -40514.5 q^{92} +(-32185.2 - 134800. i) q^{93} +87313.2 q^{94} +(-78636.3 - 57132.6i) q^{95} +(-21457.6 + 15589.9i) q^{96} +(31480.1 + 96885.8i) q^{97} -67189.2 q^{98} +247121. 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

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