LMFDB - Embedded newform 82.6.d.a.57.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [82,6,Mod(37,82)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(82, 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("82.37"); S:= CuspForms(chi, 6); N := Newforms(S);

Level:	$ N $	$=$	$ 82 = 2 \cdot 41 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	82.d (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [36,-36] 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:	$13.1514732247$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$9$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			57.8
Character	$\chi$	$=$	82.57
Dual form			82.6.d.a.59.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.23607 - 3.80423i) q^{2} +19.9677 q^{3} +(-12.9443 - 9.40456i) q^{4} +(-63.9053 - 46.4299i) q^{5} +(24.6815 - 75.9618i) q^{6} +(-26.6561 - 82.0390i) q^{7} +(-51.7771 + 37.6183i) q^{8} +155.710 q^{9} +(-255.621 + 185.720i) q^{10} +(-606.379 + 440.560i) q^{11} +(-258.468 - 187.788i) q^{12} +(108.100 - 332.699i) q^{13} -345.044 q^{14} +(-1276.04 - 927.100i) q^{15} +(79.1084 + 243.470i) q^{16} +(954.652 - 693.595i) q^{17} +(192.469 - 592.358i) q^{18} +(-35.3093 - 108.671i) q^{19} +(390.554 + 1202.00i) q^{20} +(-532.262 - 1638.13i) q^{21} +(926.464 + 2851.36i) q^{22} +(709.648 - 2184.07i) q^{23} +(-1033.87 + 751.151i) q^{24} +(962.472 + 2962.18i) q^{25} +(-1132.04 - 822.477i) q^{26} -1742.98 q^{27} +(-426.498 + 1312.62i) q^{28} +(-4112.14 - 2987.64i) q^{29} +(-5104.18 + 3708.40i) q^{30} +(5652.28 - 4106.62i) q^{31} +1024.00 q^{32} +(-12108.0 + 8796.98i) q^{33} +(-1458.58 - 4489.04i) q^{34} +(-2105.60 + 6480.37i) q^{35} +(-2015.56 - 1464.39i) q^{36} +(-2090.57 - 1518.89i) q^{37} -457.054 q^{38} +(2158.52 - 6643.24i) q^{39} +5055.44 q^{40} +(-1630.95 + 10639.4i) q^{41} -6889.74 q^{42} +(1432.43 - 4408.56i) q^{43} +11992.4 q^{44} +(-9950.72 - 7229.62i) q^{45} +(-7431.53 - 5399.33i) q^{46} +(1277.86 - 3932.84i) q^{47} +(1579.61 + 4861.55i) q^{48} +(7577.29 - 5505.23i) q^{49} +12458.5 q^{50} +(19062.2 - 13849.5i) q^{51} +(-4528.17 + 3289.91i) q^{52} +(21689.5 + 15758.3i) q^{53} +(-2154.44 + 6630.67i) q^{54} +59206.0 q^{55} +(4466.34 + 3244.99i) q^{56} +(-705.047 - 2169.91i) q^{57} +(-16448.5 + 11950.6i) q^{58} +(9536.50 - 29350.3i) q^{59} +(7798.49 + 24001.3i) q^{60} +(-5600.21 - 17235.7i) q^{61} +(-8635.91 - 26578.6i) q^{62} +(-4150.63 - 12774.3i) q^{63} +(1265.73 - 3895.53i) q^{64} +(-22355.4 + 16242.1i) q^{65} +(18499.4 + 56935.3i) q^{66} +(-55072.9 - 40012.8i) q^{67} -18880.2 q^{68} +(14170.1 - 43611.0i) q^{69} +(22050.1 + 16020.4i) q^{70} +(-18644.1 + 13545.8i) q^{71} +(-8062.23 + 5857.55i) q^{72} +62099.9 q^{73} +(-8362.28 + 6075.55i) q^{74} +(19218.4 + 59148.1i) q^{75} +(-564.949 + 1738.74i) q^{76} +(52306.8 + 38003.1i) q^{77} +(-22604.3 - 16423.0i) q^{78} +69089.2 q^{79} +(6248.87 - 19232.0i) q^{80} -72640.9 q^{81} +(38458.6 + 19355.5i) q^{82} +14033.5 q^{83} +(-8516.19 + 26210.1i) q^{84} -93210.9 q^{85} +(-15000.6 - 10898.6i) q^{86} +(-82110.1 - 59656.5i) q^{87} +(14823.4 - 45621.8i) q^{88} +(28203.2 + 86800.6i) q^{89} +(-39802.9 + 28918.5i) q^{90} -30175.8 q^{91} +(-29726.1 + 21597.3i) q^{92} +(112863. - 81999.9i) q^{93} +(-13381.9 - 9722.50i) q^{94} +(-2789.13 + 8584.06i) q^{95} +20447.0 q^{96} +(10196.9 + 7408.48i) q^{97} +(-11577.1 - 35630.6i) q^{98} +(-94419.5 + 68599.8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 36 q^{2} + 20 q^{3} - 144 q^{4} - 98 q^{5} - 20 q^{6} + 120 q^{7} - 576 q^{8} + 2876 q^{9} - 392 q^{10} - 436 q^{11} - 80 q^{12} - 617 q^{13} + 280 q^{14} + 789 q^{15} - 2304 q^{16} + 1359 q^{17}+ \cdots + 261106 q^{99}+O(q^{100}) $ 36 * q - 36 * q^2 + 20 * q^3 - 144 * q^4 - 98 * q^5 - 20 * q^6 + 120 * q^7 - 576 * q^8 + 2876 * q^9 - 392 * q^10 - 436 * q^11 - 80 * q^12 - 617 * q^13 + 280 * q^14 + 789 * q^15 - 2304 * q^16 + 1359 * q^17 - 4976 * q^18 + 4876 * q^19 + 352 * q^20 - 13529 * q^21 + 2476 * q^22 + 819 * q^23 - 320 * q^24 - 10487 * q^25 - 2088 * q^26 + 1592 * q^27 + 1920 * q^28 + 5249 * q^29 + 3156 * q^30 - 2992 * q^31 + 36864 * q^32 - 5676 * q^33 + 4136 * q^34 + 21607 * q^35 - 3104 * q^36 - 11508 * q^37 + 10664 * q^38 + 8144 * q^39 + 9728 * q^40 - 44187 * q^41 + 97464 * q^42 - 88677 * q^43 - 5856 * q^44 - 45045 * q^45 - 6864 * q^46 - 56670 * q^47 - 1280 * q^48 - 59417 * q^49 + 88352 * q^50 - 26259 * q^51 - 8352 * q^52 + 21963 * q^53 + 29968 * q^54 + 128202 * q^55 - 9920 * q^56 + 16428 * q^57 + 20996 * q^58 - 77668 * q^59 - 7856 * q^60 - 168787 * q^61 - 34428 * q^62 + 247961 * q^63 - 36864 * q^64 - 74533 * q^65 + 48036 * q^66 - 40269 * q^67 - 76576 * q^68 + 242095 * q^69 - 20492 * q^70 - 44665 * q^71 - 12416 * q^72 - 76360 * q^73 - 46032 * q^74 - 154234 * q^75 + 78016 * q^76 - 8441 * q^77 - 71044 * q^78 + 230228 * q^79 + 5632 * q^80 + 184156 * q^81 + 36752 * q^82 + 673200 * q^83 - 216464 * q^84 - 130180 * q^85 + 194192 * q^86 - 398341 * q^87 + 39616 * q^88 - 409131 * q^89 - 180180 * q^90 + 355046 * q^91 - 27456 * q^92 - 51949 * q^93 + 234960 * q^94 - 588753 * q^95 + 20480 * q^96 + 138500 * q^97 - 43248 * q^98 + 261106 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/82\mathbb{Z}\right)^\times$.

$n$	$47$
$\chi(n)$	$e\left(\frac{3}{5}\right)$

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 $

$2$	1.23607	−	3.80423i	0.218508	−	0.672499i
$2$	1.23607	−	3.80423i	0.218508	−	0.672499i
$3$	19.9677			1.28093			0.640465	−	0.767987i	$-0.278741\pi$
$3$	19.9677			1.28093			0.640465	+	0.767987i	$0.278741\pi$
$4$	−12.9443	−	9.40456i	−0.404508	−	0.293893i
$5$	−63.9053	−	46.4299i	−1.14317	−	0.830564i	−0.155615	−	0.987818i	$-0.549736\pi$
$5$	−63.9053	−	46.4299i	−1.14317	−	0.830564i	−0.987558	+	0.157254i	$0.949736\pi$
$6$	24.6815	−	75.9618i	0.279894	−	0.861424i
$7$	−26.6561	−	82.0390i	−0.205613	−	0.632813i	−0.999688	−	0.0249923i	$-0.992044\pi$
$7$	−26.6561	−	82.0390i	−0.205613	−	0.632813i	0.794074	−	0.607821i	$-0.207956\pi$
$8$	−51.7771	+	37.6183i	−0.286031	+	0.207813i
$9$	155.710			0.640784
$10$	−255.621	+	185.720i	−0.808345	+	0.587297i
$11$	−606.379	+	440.560i	−1.51099	+	1.09780i	−0.545257	+	0.838269i	$0.683568\pi$
$11$	−606.379	+	440.560i	−1.51099	+	1.09780i	−0.965735	+	0.259531i	$0.916432\pi$
$12$	−258.468	−	187.788i	−0.518147	−	0.376456i
$13$	108.100	−	332.699i	0.177406	−	0.546001i	−0.822329	−	0.569013i	$-0.807326\pi$
$13$	108.100	−	332.699i	0.177406	−	0.546001i	0.999735	+	0.0230120i	$0.00732559\pi$
$14$	−345.044			−0.470494
$15$	−1276.04	−	927.100i	−1.46433	−	1.06389i
$16$	79.1084	+	243.470i	0.0772542	+	0.237764i
$17$	954.652	−	693.595i	0.801166	−	0.582081i	−0.110090	−	0.993922i	$-0.535114\pi$
$17$	954.652	−	693.595i	0.801166	−	0.582081i	0.911256	+	0.411840i	$0.135114\pi$
$18$	192.469	−	592.358i	0.140016	−	0.430926i
$19$	−35.3093	−	108.671i	−0.0224391	−	0.0690605i	0.939210	−	0.343343i	$-0.111559\pi$
$19$	−35.3093	−	108.671i	−0.0224391	−	0.0690605i	−0.961649	+	0.274283i	$0.911559\pi$
$20$	390.554	+	1202.00i	0.218327	+	0.671940i
$21$	−532.262	−	1638.13i	−0.263377	−	0.810590i
$22$	926.464	+	2851.36i	0.408105	+	1.25602i
$23$	709.648	−	2184.07i	0.279720	−	0.860890i	−0.708212	−	0.706000i	$-0.750498\pi$
$23$	709.648	−	2184.07i	0.279720	−	0.860890i	0.987932	−	0.154890i	$-0.0495022\pi$
$24$	−1033.87	+	751.151i	−0.366386	+	0.266195i
$25$	962.472	+	2962.18i	0.307991	+	0.947899i
$26$	−1132.04	−	822.477i	−0.328420	−	0.238611i
$27$	−1742.98			−0.460131
$28$	−426.498	+	1312.62i	−0.102807	+	0.316407i
$29$	−4112.14	−	2987.64i	−0.907972	−	0.659681i	0.0325289	−	0.999471i	$-0.489644\pi$
$29$	−4112.14	−	2987.64i	−0.907972	−	0.659681i	−0.940501	+	0.339790i	$0.889644\pi$
$30$	−5104.18	+	3708.40i	−1.03543	+	0.752287i
$31$	5652.28	−	4106.62i	1.05638	−	0.767503i	0.0829629	−	0.996553i	$-0.473562\pi$
$31$	5652.28	−	4106.62i	1.05638	−	0.767503i	0.973415	+	0.229049i	$0.0735617\pi$
$32$	1024.00			0.176777
$33$	−12108.0	+	8796.98i	−1.93548	+	1.40621i
$34$	−1458.58	−	4489.04i	−0.216388	−	0.665973i
$35$	−2105.60	+	6480.37i	−0.290540	+	0.894190i
$36$	−2015.56	−	1464.39i	−0.259202	−	0.188322i
$37$	−2090.57	−	1518.89i	−0.251050	−	0.182399i	0.455142	−	0.890419i	$-0.349589\pi$
$37$	−2090.57	−	1518.89i	−0.251050	−	0.182399i	−0.706192	+	0.708020i	$0.749589\pi$
$38$	−457.054			−0.0513462
$39$	2158.52	−	6643.24i	0.227245	−	0.699389i
$40$	5055.44			0.499585
$41$	−1630.95	+	10639.4i	−0.151524	+	0.988454i
$41$	−1630.95	+	10639.4i	−0.151524	+	0.988454i
$42$	−6889.74			−0.602670
$43$	1432.43	−	4408.56i	0.118141	−	0.363602i	−0.874448	−	0.485119i	$-0.838776\pi$
$43$	1432.43	−	4408.56i	0.118141	−	0.363602i	0.992589	+	0.121518i	$0.0387762\pi$
$44$	11992.4			0.933845
$45$	−9950.72	−	7229.62i	−0.732526	−	0.532212i
$46$	−7431.53	−	5399.33i	−0.517826	−	0.376223i
$47$	1277.86	−	3932.84i	0.0843795	−	0.259694i	−0.899961	−	0.435970i	$-0.856405\pi$
$47$	1277.86	−	3932.84i	0.0843795	−	0.259694i	0.984341	+	0.176277i	$0.0564053\pi$
$48$	1579.61	+	4861.55i	0.0989573	+	0.304559i
$49$	7577.29	−	5505.23i	0.450841	−	0.327555i
$50$	12458.5			0.704759
$51$	19062.2	−	13849.5i	1.02624	−	0.745606i
$52$	−4528.17	+	3289.91i	−0.232228	+	0.168723i
$53$	21689.5	+	15758.3i	1.06062	+	0.770586i	0.974203	−	0.225674i	$-0.0724583\pi$
$53$	21689.5	+	15758.3i	1.06062	+	0.770586i	0.0864170	+	0.996259i	$0.472458\pi$
$54$	−2154.44	+	6630.67i	−0.100542	+	0.309438i
$55$	59206.0			2.63912
$56$	4466.34	+	3244.99i	0.190319	+	0.138275i
$57$	−705.047	−	2169.91i	−0.0287429	−	0.0884617i
$58$	−16448.5	+	11950.6i	−0.642033	+	0.466465i
$59$	9536.50	−	29350.3i	0.356664	−	1.09770i	−0.598375	−	0.801216i	$-0.704187\pi$
$59$	9536.50	−	29350.3i	0.356664	−	1.09770i	0.955039	−	0.296482i	$-0.0958134\pi$
$60$	7798.49	+	24001.3i	0.279661	+	0.860709i
$61$	−5600.21	−	17235.7i	−0.192699	−	0.593067i	−0.999996	−	0.00292106i	$-0.999070\pi$
$61$	−5600.21	−	17235.7i	−0.192699	−	0.593067i	0.807297	−	0.590146i	$-0.200930\pi$
$62$	−8635.91	−	26578.6i	−0.285318	−	0.878118i
$63$	−4150.63	−	12774.3i	−0.131754	−	0.405496i
$64$	1265.73	−	3895.53i	0.0386271	−	0.118882i
$65$	−22355.4	+	16242.1i	−0.656294	+	0.476826i
$66$	18499.4	+	56935.3i	0.522754	+	1.60887i
$67$	−55072.9	−	40012.8i	−1.49883	−	1.08896i	−0.970846	−	0.239703i	$-0.922950\pi$
$67$	−55072.9	−	40012.8i	−1.49883	−	1.08896i	−0.527979	−	0.849257i	$-0.677050\pi$
$68$	−18880.2			−0.495148
$69$	14170.1	−	43611.0i	0.358302	−	1.10274i
$70$	22050.1	+	16020.4i	0.537856	+	0.390775i
$71$	−18644.1	+	13545.8i	−0.438931	+	0.318902i	−0.785210	−	0.619229i	$-0.787445\pi$
$71$	−18644.1	+	13545.8i	−0.438931	+	0.318902i	0.346279	+	0.938132i	$0.387445\pi$
$72$	−8062.23	+	5857.55i	−0.183284	+	0.133163i
$73$	62099.9			1.36390			0.681952	−	0.731397i	$-0.261131\pi$
$73$	62099.9			1.36390			0.681952	+	0.731397i	$0.261131\pi$
$74$	−8362.28	+	6075.55i	−0.177519	+	0.128975i
$75$	19218.4	+	59148.1i	0.394515	+	1.21419i
$76$	−564.949	+	1738.74i	−0.0112196	+	0.0345302i
$77$	52306.8	+	38003.1i	1.00538	+	0.730453i
$78$	−22604.3	−	16423.0i	−0.420683	−	0.305644i
$79$	69089.2			1.24550			0.622748	−	0.782422i	$-0.286016\pi$
$79$	69089.2			1.24550			0.622748	+	0.782422i	$0.286016\pi$
$80$	6248.87	−	19232.0i	0.109163	−	0.335970i
$81$	−72640.9			−1.23018
$82$	38458.6	+	19355.5i	0.631624	+	0.317885i
$83$	14033.5			0.223599			0.111800	−	0.993731i	$-0.464339\pi$
$83$	14033.5			0.223599			0.111800	+	0.993731i	$0.464339\pi$
$84$	−8516.19	+	26210.1i	−0.131688	+	0.405295i
$85$	−93210.9			−1.39933
$86$	−15000.6	−	10898.6i	−0.218707	−	0.158900i
$87$	−82110.1	−	59656.5i	−1.16305	−	0.845005i
$88$	14823.4	−	45621.8i	0.204053	−	0.628009i
$89$	28203.2	+	86800.6i	0.377419	+	1.16158i	0.941832	+	0.336083i	$0.109102\pi$
$89$	28203.2	+	86800.6i	0.377419	+	1.16158i	−0.564413	+	0.825492i	$0.690898\pi$
$90$	−39802.9	+	28918.5i	−0.517974	+	0.376330i
$91$	−30175.8			−0.381993
$92$	−29726.1	+	21597.3i	−0.366158	+	0.266030i
$93$	112863.	−	81999.9i	1.35315	−	0.983119i
$94$	−13381.9	−	9722.50i	−0.156206	−	0.113490i
$95$	−2789.13	+	8584.06i	−0.0317073	+	0.0975851i
$96$	20447.0			0.226439
$97$	10196.9	+	7408.48i	0.110037	+	0.0799466i	0.641443	−	0.767171i	$-0.278336\pi$
$97$	10196.9	+	7408.48i	0.110037	+	0.0799466i	−0.531406	+	0.847117i	$0.678336\pi$
$98$	−11577.1	−	35630.6i	−0.121768	−	0.374764i
$99$	−94419.5	+	68599.8i	−0.968219	+	0.703452i
$100$	15399.5	−	47394.9i	0.153995	−	0.473949i
$101$	−24172.7	−	74395.9i	−0.235788	−	0.725681i	−0.997016	−	0.0771964i	$-0.975403\pi$
$101$	−24172.7	−	74395.9i	−0.235788	−	0.725681i	0.761228	−	0.648484i	$-0.224597\pi$
$102$	−29124.5	−	89636.0i	−0.277178	−	0.853065i
$103$	45812.8	+	140997.i	0.425494	+	1.30954i	0.902520	+	0.430647i	$0.141715\pi$
$103$	45812.8	+	140997.i	0.425494	+	1.30954i	−0.477026	+	0.878889i	$0.658285\pi$
$104$	6918.43	+	21292.7i	0.0627226	+	0.193040i
$105$	−42044.1	+	129398.i	−0.372161	+	1.14540i
$106$	86758.0	−	63033.4i	0.749972	−	0.544886i
$107$	28784.3	+	88588.8i	0.243050	+	0.748031i	0.995951	+	0.0898973i	$0.0286539\pi$
$107$	28784.3	+	88588.8i	0.243050	+	0.748031i	−0.752901	+	0.658134i	$0.771346\pi$
$108$	22561.5	+	16391.9i	0.186127	+	0.135229i
$109$	−212133.			−1.71018			−0.855089	−	0.518481i	$-0.826498\pi$
$109$	−212133.			−1.71018			−0.855089	+	0.518481i	$0.826498\pi$
$110$	73182.6	−	225233.i	0.576668	−	1.77480i
$111$	−41744.0	−	30328.8i	−0.321578	−	0.233640i
$112$	17865.4	−	12979.9i	0.134576	−	0.0977750i
$113$	56990.4	−	41406.0i	0.419861	−	0.305047i	−0.357721	−	0.933829i	$-0.616446\pi$
$113$	56990.4	−	41406.0i	0.419861	−	0.305047i	0.777582	+	0.628782i	$0.216446\pi$
$114$	−9126.33			−0.0657709
$115$	−146757.	+	106625.i	−1.03479	+	0.751820i
$116$	25131.1	+	77345.7i	0.173407	+	0.533693i
$117$	16832.4	−	51804.7i	0.113679	−	0.349868i
$118$	−99867.5	−	72558.0i	−0.660266	−	0.479712i
$119$	−82349.2	−	59830.2i	−0.533079	−	0.387305i
$120$	100946.			0.639934
$121$	123835.	−	381124.i	0.768915	−	2.36648i
$122$	−72490.7			−0.440943
$123$	−32566.4	+	212444.i	−0.194092	+	1.26614i
$124$	−111786.			−0.652877
$125$	−253.281	+	779.519i	−0.00144987	+	0.00446223i
$126$	−53726.9			−0.301485
$127$	−81761.3	−	59403.1i	−0.449820	−	0.326813i	0.339705	−	0.940532i	$-0.389673\pi$
$127$	−81761.3	−	59403.1i	−0.449820	−	0.326813i	−0.789525	+	0.613719i	$0.789673\pi$
$128$	−13254.9	−	9630.27i	−0.0715077	−	0.0519534i
$129$	28602.3	−	88029.0i	0.151331	−	0.465748i
$130$	34156.0	+	105121.i	0.177259	+	0.545547i
$131$	−219436.	+	159430.i	−1.11720	+	0.811692i	−0.983782	−	0.179368i	$-0.942595\pi$
$131$	−219436.	+	159430.i	−1.11720	+	0.811692i	−0.133416	+	0.991060i	$0.542595\pi$
$132$	239461.			1.19619
$133$	−7974.05	+	5793.49i	−0.0390886	+	0.0283995i
$134$	−220292.	+	160051.i	−1.05983	+	0.770011i
$135$	111385.	+	80926.2i	0.526010	+	0.382168i
$136$	−23337.3	+	71824.7i	−0.108194	+	0.332986i
$137$	−262320.			−1.19407			−0.597036	−	0.802214i	$-0.703655\pi$
$137$	−262320.			−1.19407			−0.597036	+	0.802214i	$0.703655\pi$
$138$	−148391.	−	107812.i	−0.663299	−	0.481915i
$139$	−48224.5	−	148420.i	−0.211705	−	0.651561i	−0.999371	−	0.0354586i	$-0.988711\pi$
$139$	−48224.5	−	148420.i	−0.211705	−	0.651561i	0.787666	−	0.616102i	$-0.211289\pi$
$140$	88200.5	−	64081.4i	0.380322	−	0.276320i
$141$	25515.9	−	78529.8i	0.108084	−	0.332649i
$142$	28485.7	+	87670.0i	0.118551	+	0.364863i
$143$	81024.0	+	249366.i	0.331340	+	1.01976i
$144$	12318.0	+	37910.9i	0.0495033	+	0.152355i
$145$	124071.	+	381852.i	0.490063	+	1.50826i
$146$	76759.7	−	236242.i	0.298024	−	0.917223i
$147$	151301.	−	109927.i	0.577497	−	0.419576i
$148$	12776.4	+	39321.8i	0.0479463	+	0.147564i
$149$	336829.	+	244720.i	1.24292	+	0.903035i	0.997789	−	0.0664550i	$-0.0211689\pi$
$149$	336829.	+	244720.i	1.24292	+	0.903035i	0.245131	+	0.969490i	$0.421169\pi$
$150$	248768.			0.902747
$151$	113348.	−	348848.i	0.404548	−	1.24507i	−0.516724	−	0.856152i	$-0.672849\pi$
$151$	113348.	−	348848.i	0.404548	−	1.24507i	0.921272	−	0.388919i	$-0.127151\pi$
$152$	5916.23	+	4298.39i	0.0207700	+	0.0150903i
$153$	148649.	−	108000.i	0.513374	−	0.372988i
$154$	209227.	−	152012.i	0.710913	−	0.516508i
$155$	−551880.			−1.84508
$156$	−90417.3	+	65692.0i	−0.297468	+	0.216123i
$157$	86586.5	+	266486.i	0.280350	+	0.862830i	0.987754	+	0.156020i	$0.0498664\pi$
$157$	86586.5	+	266486.i	0.280350	+	0.862830i	−0.707403	+	0.706810i	$0.750134\pi$
$158$	85398.9	−	262831.i	0.272151	−	0.837594i
$159$	433090.	+	314658.i	1.35858	+	0.987067i
$160$	−65439.0	−	47544.2i	−0.202086	−	0.146824i
$161$	−198096.			−0.602297
$162$	−89789.1	+	276342.i	−0.268804	+	0.827294i
$163$	146632.			0.432276			0.216138	−	0.976363i	$-0.430654\pi$
$163$	146632.			0.432276			0.216138	+	0.976363i	$0.430654\pi$
$164$	121170.	−	122381.i	0.351792	−	0.355306i
$165$	1.18221e6			3.38053
$166$	17346.3	−	53386.5i	0.0488582	−	0.150370i
$167$	−49986.1			−0.138694			−0.0693471	−	0.997593i	$-0.522092\pi$
$167$	−49986.1			−0.138694			−0.0693471	+	0.997593i	$0.522092\pi$
$168$	89182.7	+	64795.0i	0.243785	+	0.177120i
$169$	201379.	+	146311.i	0.542373	+	0.394057i
$170$	−115215.	+	354595.i	−0.305764	+	0.941045i
$171$	−5498.03	−	16921.2i	−0.0143786	−	0.0442528i
$172$	−60002.3	+	43594.2i	−0.154649	+	0.112359i
$173$	140924.			0.357988			0.178994	−	0.983850i	$-0.442716\pi$
$173$	140924.			0.357988			0.178994	+	0.983850i	$0.442716\pi$
$174$	−328440.	+	238626.i	−0.822400	+	0.597509i
$175$	217359.	−	157920.i	0.536516	−	0.389801i
$176$	−155233.	−	112783.i	−0.377748	−	0.274450i
$177$	190422.	−	586059.i	0.456861	−	1.40607i
$178$	365070.			0.863627
$179$	−654552.	−	475560.i	−1.52690	−	1.10936i	−0.957929	−	0.287005i	$-0.907340\pi$
$179$	−654552.	−	475560.i	−1.52690	−	1.10936i	−0.568974	−	0.822355i	$-0.692660\pi$
$180$	60813.4	+	187164.i	0.139900	+	0.430568i
$181$	498308.	−	362042.i	1.13058	−	0.821415i	0.144802	−	0.989461i	$-0.453745\pi$
$181$	498308.	−	362042.i	1.13058	−	0.821415i	0.985779	+	0.168045i	$0.0537455\pi$
$182$	−37299.4	+	114796.i	−0.0834686	+	0.256890i
$183$	−111824.	−	344157.i	−0.246834	−	0.759678i
$184$	45417.5	+	139781.i	0.0988960	+	0.304370i
$185$	63076.7	+	194130.i	0.135500	+	0.417026i
$186$	−172440.	−	530714.i	−0.365472	−	1.12481i
$187$	−273310.	+	841163.i	−0.571547	+	1.75904i
$188$	−53527.5	+	38890.0i	−0.110454	+	0.0802497i
$189$	46460.9	+	142992.i	0.0946092	+	0.291177i
$190$	29208.2	+	21221.0i	0.0586976	+	0.0426463i
$191$	−993660.			−1.97085			−0.985427	−	0.170101i	$-0.945591\pi$
$191$	−993660.			−1.97085			−0.985427	+	0.170101i	$0.945591\pi$
$192$	25273.8	−	77784.9i	0.0494787	−	0.152280i
$193$	−358207.	−	260253.i	−0.692215	−	0.502924i	0.185173	−	0.982706i	$-0.440716\pi$
$193$	−358207.	−	260253.i	−0.692215	−	0.502924i	−0.877387	+	0.479782i	$0.840716\pi$
$194$	40787.6	−	29633.9i	0.0778079	−	0.0565308i
$195$	−446386.	+	324319.i	−0.840667	+	0.610781i
$196$	−149857.			−0.278635
$197$	−161927.	+	117647.i	−0.297272	+	0.215980i	−0.726416	−	0.687256i	$-0.758815\pi$
$197$	−161927.	+	117647.i	−0.297272	+	0.215980i	0.429144	+	0.903236i	$0.358815\pi$
$198$	144260.	+	443987.i	0.261507	+	0.804836i
$199$	72257.3	−	222385.i	0.129345	−	0.398083i	−0.865323	−	0.501215i	$-0.832887\pi$
$199$	72257.3	−	222385.i	0.129345	−	0.398083i	0.994668	+	0.103132i	$0.0328865\pi$
$200$	−161266.	−	117167.i	−0.285081	−	0.207123i
$201$	−1.09968e6	−	798965.i	−1.91989	−	1.39488i
$202$	−312898.			−0.539541
$203$	−135490.	+	416995.i	−0.230763	+	0.710216i
$204$	−376995.			−0.634250
$205$	598212.	−	604187.i	0.994192	−	1.00412i
$206$	593013.			0.973635
$207$	110500.	−	340083.i	0.179240	−	0.551644i
$208$	89554.0			0.143525
$209$	69286.9	+	50339.9i	0.109720	+	0.0797162i
$210$	440291.	+	319890.i	0.688956	+	0.500556i
$211$	164844.	−	507337.i	0.254898	−	0.784496i	−0.738952	−	0.673758i	$-0.764679\pi$
$211$	164844.	−	507337.i	0.254898	−	0.784496i	0.993850	−	0.110737i	$-0.0353212\pi$
$212$	−132554.	−	407961.i	−0.202560	−	0.623417i
$213$	−372281.	+	270478.i	−0.562240	+	0.408492i
$214$	372591.			0.556158
$215$	−296229.	+	215223.i	−0.437050	+	0.317535i
$216$	90246.2	−	65567.7i	0.131612	−	0.0956215i
$217$	−487571.	−	354241.i	−0.702892	−	0.510681i
$218$	−262210.	+	807001.i	−0.373688	+	1.15009i
$219$	1.23999e6			1.74707
$220$	−766378.	−	556806.i	−1.06755	−	0.775617i
$221$	−127560.	−	392590.i	−0.175685	−	0.540702i
$222$	−166976.	+	121315.i	−0.227390	+	0.165208i
$223$	−430223.	+	1.32409e6i	−0.579338	+	1.78302i	0.0415723	+	0.999135i	$0.486763\pi$
$223$	−430223.	+	1.32409e6i	−0.579338	+	1.78302i	−0.620910	+	0.783882i	$0.713237\pi$
$224$	−27295.8	−	84008.0i	−0.0363477	−	0.111867i
$225$	149867.	+	461243.i	0.197356	+	0.607398i
$226$	−87073.6	−	267985.i	−0.113401	−	0.349011i
$227$	−207798.	−	639535.i	−0.267655	−	0.823759i	−0.991070	−	0.133344i	$-0.957428\pi$
$227$	−207798.	−	639535.i	−0.267655	−	0.823759i	0.723414	−	0.690414i	$-0.242572\pi$
$228$	−11280.8	+	34718.6i	−0.0143715	+	0.0442308i
$229$	959797.	−	697334.i	1.20946	−	0.878723i	0.214277	−	0.976773i	$-0.431261\pi$
$229$	959797.	−	697334.i	1.20946	−	0.878723i	0.995181	+	0.0980503i	$0.0312606\pi$
$230$	224224.	+	690091.i	0.279488	+	0.860175i
$231$	1.04445e6	+	758836.i	1.28783	+	0.935660i
$232$	325304.			0.396798
$233$	−157958.	+	486146.i	−0.190613	+	0.586647i	−1.00000		0.000629013i	$-0.999800\pi$
$233$	−157958.	+	486146.i	−0.190613	+	0.586647i	0.809387	+	0.587276i	$0.199800\pi$
$234$	−176271.	−	128068.i	−0.210446	−	0.152898i
$235$	−264263.	+	191998.i	−0.312152	+	0.226792i
$236$	−399470.	+	290232.i	−0.466879	+	0.339207i
$237$	1.37955e6			1.59539
$238$	−329397.	+	239321.i	−0.376944	+	0.273866i
$239$	−274874.	−	845975.i	−0.311271	−	0.957994i	−0.977262	−	0.212035i	$-0.931991\pi$
$239$	−274874.	−	845975.i	−0.311271	−	0.957994i	0.665991	−	0.745960i	$-0.268009\pi$
$240$	124776.	−	384020.i	0.139831	−	0.430354i
$241$	−120826.	−	87785.2i	−0.134004	−	0.0973596i	0.518764	−	0.854917i	$-0.326392\pi$
$241$	−120826.	−	87785.2i	−0.134004	−	0.0973596i	−0.652768	+	0.757558i	$0.726392\pi$
$242$	−1.29681e6	−	942189.i	−1.42344	−	1.03419i
$243$	−1.02693e6			−1.11564
$244$	−89603.4	+	275771.i	−0.0963496	+	0.296533i
$245$	−739836.			−0.787445
$246$	767931.	+	386485.i	0.809067	+	0.407188i
$247$	−39971.7			−0.0416879
$248$	−138175.	+	425258.i	−0.142659	+	0.439059i
$249$	280217.			0.286415
$250$	2652.39	+	1927.08i	0.00268403	+	0.00195007i
$251$	−100660.	−	73133.7i	−0.100849	−	0.0732712i	0.536218	−	0.844080i	$-0.319853\pi$
$251$	−100660.	−	73133.7i	−0.100849	−	0.0732712i	−0.637067	+	0.770808i	$0.719853\pi$
$252$	−66410.1	+	204389.i	−0.0658769	+	0.202748i
$253$	531899.	+	1.63702e6i	0.522430	+	1.60787i
$254$	−327045.	+	237612.i	−0.318071	+	0.231092i
$255$	−1.86121e6			−1.79244
$256$	−53019.7	+	38521.1i	−0.0505636	+	0.0367366i
$257$	−39385.1	+	28615.0i	−0.0371963	+	0.0270247i	−0.606228	−	0.795291i	$-0.707318\pi$
$257$	−39385.1	+	28615.0i	−0.0371963	+	0.0270247i	0.569032	+	0.822316i	$0.307318\pi$
$258$	−299528.	−	217620.i	−0.280148	−	0.203540i
$259$	−68881.7	+	211996.i	−0.0638049	+	0.196371i
$260$	442124.			0.405612
$261$	−640303.	−	465207.i	−0.581814	−	0.422712i
$262$	335269.	+	1.03185e6i	0.301745	+	0.928676i
$263$	1.47771e6	−	1.07362e6i	1.31734	−	0.957105i	0.317380	−	0.948298i	$-0.397197\pi$
$263$	1.47771e6	−	1.07362e6i	1.31734	−	0.957105i	0.999961	−	0.00880642i	$-0.00280321\pi$
$264$	295990.	−	910964.i	0.261377	−	0.804436i
$265$	−654415.	−	2.01408e6i	−0.572452	−	1.76182i
$266$	12183.3	+	37496.2i	0.0105575	+	0.0324925i
$267$	563154.	+	1.73321e6i	0.483447	+	1.48790i
$268$	336576.	+	1.03587e6i	0.286250	+	0.880987i
$269$	185294.	−	570277.i	0.156128	−	0.480513i	−0.842145	−	0.539251i	$-0.818708\pi$
$269$	185294.	−	570277.i	0.156128	−	0.480513i	0.998273	+	0.0587375i	$0.0187075\pi$
$270$	445541.	−	323705.i	0.371945	−	0.270234i
$271$	283933.	+	873855.i	0.234851	+	0.722797i	0.997141	+	0.0755615i	$0.0240749\pi$
$271$	283933.	+	873855.i	0.234851	+	0.722797i	−0.762290	+	0.647235i	$0.775925\pi$
$272$	244391.	+	177560.i	0.200292	+	0.145520i
$273$	−602543.			−0.489307
$274$	−324246.	+	997926.i	−0.260914	+	0.803012i
$275$	−1.88864e6	−	1.37218e6i	−1.50598	−	1.09415i
$276$	−593564.	+	431249.i	−0.469023	+	0.340765i
$277$	420844.	−	305761.i	0.329550	−	0.239432i	−0.410690	−	0.911775i	$-0.634712\pi$
$277$	420844.	−	305761.i	0.329550	−	0.239432i	0.740240	+	0.672343i	$0.234712\pi$
$278$	−624231.			−0.484433
$279$	880118.	−	639443.i	0.676909	−	0.491804i
$280$	−134758.	−	414744.i	−0.102721	−	0.316144i
$281$	−33159.3	+	102054.i	−0.0250519	+	0.0771017i	−0.962801	−	0.270212i	$-0.912906\pi$
$281$	−33159.3	+	102054.i	−0.0250519	+	0.0771017i	0.937749	+	0.347314i	$0.112906\pi$
$282$	−267206.	−	194136.i	−0.200089	−	0.145373i
$283$	1.83314e6	+	1.33185e6i	1.36060	+	0.988531i	0.998407	+	0.0564265i	$0.0179707\pi$
$283$	1.83314e6	+	1.33185e6i	1.36060	+	0.988531i	0.362189	+	0.932104i	$0.382029\pi$
$284$	368727.			0.271274
$285$	−55692.6	+	171404.i	−0.0406149	+	0.125000i
$286$	1.04880e6			0.758187
$287$	916319.	−	149802.i	0.656662	−	0.107353i
$288$	159447.			0.113276
$289$	−8474.05	+	26080.4i	−0.00596824	+	0.0183684i
$290$	1.60601e6			1.12138
$291$	203609.	+	147931.i	0.140950	+	0.102406i
$292$	−803838.	−	584022.i	−0.551711	−	0.400841i
$293$	856848.	−	2.63711e6i	0.583089	−	1.79456i	−0.0237239	−	0.999719i	$-0.507552\pi$
$293$	856848.	−	2.63711e6i	0.583089	−	1.79456i	0.606813	−	0.794845i	$-0.292448\pi$
$294$	−231168.	−	711462.i	−0.155977	−	0.480046i
$295$	−1.97217e6	+	1.43286e6i	−1.31944	+	0.958626i
$296$	165382.			0.109713
$297$	1.05690e6	−	767885.i	0.695255	−	0.505132i
$298$	1.34731e6	−	978882.i	0.878878	−	0.638542i
$299$	−649926.	−	472199.i	−0.420422	−	0.305455i
$300$	307494.	−	946369.i	0.197258	−	0.607096i
$301$	−399857.			−0.254383
$302$	−1.18699e6	−	862400.i	−0.748911	−	0.544116i
$303$	−482674.	−	1.48552e6i	−0.302028	−	0.929547i
$304$	23664.9	−	17193.6i	0.0146866	−	0.0106704i
$305$	−442368.	+	1.36147e6i	−0.272291	+	0.838027i
$306$	−227116.	−	698991.i	−0.138658	−	0.426744i
$307$	−67639.6	−	208173.i	−0.0409595	−	0.126061i	0.928486	−	0.371368i	$-0.121111\pi$
$307$	−67639.6	−	208173.i	−0.0409595	−	0.126061i	−0.969445	+	0.245307i	$0.921111\pi$
$308$	−319671.	−	983845.i	−0.192011	−	0.590949i
$309$	914777.	+	2.81540e6i	0.545029	+	1.67743i
$310$	−682162.	+	2.09948e6i	−0.403165	+	1.24082i
$311$	1.80954e6	−	1.31471e6i	1.06088	−	0.770777i	0.0866319	−	0.996240i	$-0.472390\pi$
$311$	1.80954e6	−	1.31471e6i	1.06088	−	0.770777i	0.974252	+	0.225463i	$0.0723896\pi$
$312$	138145.	+	425168.i	0.0803433	+	0.247271i
$313$	786380.	+	571339.i	0.453703	+	0.329635i	0.791056	−	0.611744i	$-0.209532\pi$
$313$	786380.	+	571339.i	0.453703	+	0.329635i	−0.337353	+	0.941378i	$0.609532\pi$
$314$	1.12080e6			0.641511
$315$	−327864.	+	1.00906e6i	−0.186173	+	0.572982i
$316$	−894309.	−	649754.i	−0.503814	−	0.366042i
$317$	−998669.	+	725576.i	−0.558179	+	0.405541i	−0.830792	−	0.556583i	$-0.812112\pi$
$317$	−998669.	+	725576.i	−0.558179	+	0.405541i	0.272613	+	0.962124i	$0.412112\pi$
$318$	1.73236e6	−	1.25863e6i	0.960662	−	0.697962i
$319$	3.80975e6			2.09614
$320$	−261756.	+	190177.i	−0.142897	+	0.103820i
$321$	574756.	+	1.76892e6i	0.311330	+	0.958176i
$322$	−244860.	+	753601.i	−0.131607	+	0.405044i
$323$	−109082.	−	79252.6i	−0.0581763	−	0.0422675i
$324$	940284.	+	683156.i	0.497618	+	0.361541i
$325$	1.08956e6			0.572193
$326$	181248.	−	557822.i	0.0944557	−	0.290705i
$327$	−4.23581e6			−2.19062
$328$	−315789.	−	612229.i	−0.162073	−	0.314217i
$329$	−356709.			−0.181687
$330$	1.46129e6	−	4.49739e6i	0.738672	−	2.27340i
$331$	203340.			0.102012			0.0510061	−	0.998698i	$-0.483757\pi$
$331$	203340.			0.102012			0.0510061	+	0.998698i	$0.483757\pi$
$332$	−181653.	−	131979.i	−0.0904477	−	0.0657141i
$333$	−325524.	−	236507.i	−0.160869	−	0.116878i
$334$	−61786.2	+	190158.i	−0.0303058	+	0.0932716i
$335$	1.66166e6	+	5.11406e6i	0.808965	+	2.48974i
$336$	356731.	−	259180.i	0.172382	−	0.125243i
$337$	1.71052e6			0.820455			0.410227	−	0.911983i	$-0.365449\pi$
$337$	1.71052e6			0.820455			0.410227	+	0.911983i	$0.365449\pi$
$338$	805518.	−	585243.i	0.383516	−	0.278641i
$339$	1.13797e6	−	826783.i	0.537813	−	0.390744i
$340$	1.20655e6	+	876608.i	0.566040	+	0.411252i
$341$	−1.61821e6	+	4.98033e6i	−0.753613	+	2.31938i
$342$	−71168.0			−0.0329018
$343$	−1.82653e6	−	1.32705e6i	−0.838283	−	0.609049i
$344$	91675.4	+	282148.i	0.0417693	+	0.128553i
$345$	−2.93040e6	+	2.12906e6i	−1.32550	+	0.963030i
$346$	174191.	−	536106.i	0.0782233	−	0.240747i
$347$	1.16332e6	+	3.58032e6i	0.518650	+	1.59624i	0.776541	+	0.630067i	$0.216972\pi$
$347$	1.16332e6	+	3.58032e6i	0.518650	+	1.59624i	−0.257891	+	0.966174i	$0.583028\pi$
$348$	501812.	+	1.54442e6i	0.222123	+	0.683623i
$349$	−221799.	−	682627.i	−0.0974756	−	0.299999i	0.890415	−	0.455149i	$-0.150414\pi$
$349$	−221799.	−	682627.i	−0.0974756	−	0.299999i	−0.987891	+	0.155150i	$0.950414\pi$
$350$	−332095.	−	1.02208e6i	−0.144908	−	0.445981i
$351$	−188416.	+	579886.i	−0.0816302	+	0.251232i
$352$	−620932.	+	451133.i	−0.267108	+	0.194065i
$353$	155700.	+	479195.i	0.0665046	+	0.204680i	0.978787	−	0.204883i	$-0.0656813\pi$
$353$	155700.	+	479195.i	0.0665046	+	0.204680i	−0.912282	+	0.409563i	$0.865681\pi$
$354$	−1.99413e6	−	1.44882e6i	−0.845755	−	0.614477i
$355$	1.82039e6			0.766642
$356$	451251.	−	1.38881e6i	0.188709	−	0.580788i
$357$	−1.64433e6	−	1.19467e6i	−0.682838	−	0.496111i
$358$	−2.61821e6	+	1.90224e6i	−1.07968	+	0.784436i
$359$	−734256.	+	533468.i	−0.300685	+	0.218460i	−0.727889	−	0.685695i	$-0.759498\pi$
$359$	−734256.	+	533468.i	−0.300685	+	0.218460i	0.427204	+	0.904155i	$0.359498\pi$
$360$	787185.			0.320126
$361$	1.99264e6	−	1.44774e6i	0.804751	−	0.584686i
$362$	−761348.	−	2.34319e6i	−0.305360	−	0.939800i
$363$	2.47270e6	−	7.61018e6i	0.984927	−	3.03129i
$364$	390604.	+	283791.i	0.154520	+	0.112265i
$365$	−3.96851e6	−	2.88329e6i	−1.55918	−	1.13281i
$366$	−1.44747e6			−0.564817
$367$	175531.	−	540229.i	0.0680282	−	0.209369i	−0.911263	−	0.411824i	$-0.864892\pi$
$367$	175531.	−	540229.i	0.0680282	−	0.209369i	0.979292	+	0.202455i	$0.0648919\pi$
$368$	587896.			0.226298
$369$	−253956.	+	1.65666e6i	−0.0970942	+	0.633385i
$370$	816481.			0.310057
$371$	714642.	−	2.19944e6i	0.269559	−	0.829617i
$372$	−2.23210e6			−0.836291
$373$	585798.	+	425607.i	0.218010	+	0.158393i	0.691430	−	0.722443i	$-0.256981\pi$
$373$	585798.	+	425607.i	0.218010	+	0.158393i	−0.473421	+	0.880836i	$0.656981\pi$
$374$	2.86214e6	+	2.07947e6i	1.05806	+	0.768729i
$375$	−5057.45	+	15565.2i	−0.00185718	+	0.00571581i
$376$	81782.8	+	251701.i	0.0298327	+	0.0918155i
$377$	−1.43851e6	+	1.04514e6i	−0.521266	+	0.378722i
$378$	601403.			0.216489
$379$	−3.16770e6	+	2.30147e6i	−1.13278	+	0.823013i	−0.986097	−	0.166171i	$-0.946860\pi$
$379$	−3.16770e6	+	2.30147e6i	−1.13278	+	0.823013i	−0.146683	+	0.989184i	$0.546860\pi$
$380$	116833.	−	84883.9i	0.0415054	−	0.0301555i
$381$	−1.63259e6	−	1.18614e6i	−0.576188	−	0.418625i
$382$	−1.22823e6	+	3.78011e6i	−0.430647	+	1.32540i
$383$	−245578.			−0.0855447			−0.0427724	−	0.999085i	$-0.513619\pi$
$383$	−245578.			−0.0855447			−0.0427724	+	0.999085i	$0.513619\pi$
$384$	−264671.	−	192295.i	−0.0915964	−	0.0665487i
$385$	−1.57820e6	−	4.85720e6i	−0.542638	−	1.67007i
$386$	−1.43283e6	+	1.04101e6i	−0.489470	+	0.355621i
$387$	223044.	−	686459.i	0.0757030	−	0.232990i
$388$	−62317.9	−	191795.i	−0.0210152	−	0.0646781i
$389$	1.55709e6	+	4.79224e6i	0.521723	+	1.60570i	0.770706	+	0.637191i	$0.219904\pi$
$389$	1.55709e6	+	4.79224e6i	0.521723	+	1.60570i	−0.248983	+	0.968508i	$0.580096\pi$
$390$	682017.	+	2.09903e6i	0.227057	+	0.698808i
$391$	−837395.	−	2.57724e6i	−0.277006	−	0.852536i
$392$	−185233.	+	570089.i	−0.0608841	+	0.187382i
$393$	−4.38165e6	+	3.18345e6i	−1.43105	+	1.03972i
$394$	247402.	+	761426.i	0.0802903	+	0.247108i
$395$	−4.41517e6	−	3.20781e6i	−1.42382	−	1.03446i
$396$	1.86734e6			0.598392
$397$	761357.	−	2.34322e6i	0.242444	−	0.746167i	−0.753602	−	0.657331i	$-0.771685\pi$
$397$	761357.	−	2.34322e6i	0.242444	−	0.746167i	0.996046	−	0.0888360i	$-0.0283147\pi$
$398$	−756689.	−	549767.i	−0.239447	−	0.173969i
$399$	−159224.	+	115683.i	−0.0500698	+	0.0363778i
$400$	−645065.	+	468667.i	−0.201583	+	0.146458i
$401$	418551.			0.129983			0.0649916	−	0.997886i	$-0.479298\pi$
$401$	418551.			0.129983			0.0649916	+	0.997886i	$0.479298\pi$
$402$	−4.39872e6	+	3.19586e6i	−1.35757	+	0.986331i
$403$	−755254.	−	2.32443e6i	−0.231649	−	0.712943i
$404$	−386763.	+	1.19033e6i	−0.117894	+	0.362840i
$405$	4.64214e6	+	3.37271e6i	1.40631	+	1.02174i
$406$	1.41887e6	+	1.03087e6i	0.427196	+	0.310376i
$407$	1.93684e6			0.579572
$408$	−465992.	+	1.43418e6i	−0.138589	+	0.426532i
$409$	−1.26282e6			−0.373278			−0.186639	−	0.982429i	$-0.559760\pi$
$409$	−1.26282e6			−0.373278			−0.186639	+	0.982429i	$0.559760\pi$
$410$	−1.55903e6	−	3.02255e6i	−0.458032	−	0.888001i
$411$	−5.23794e6			−1.52952
$412$	733004.	−	2.25596e6i	0.212747	−	0.654768i
$413$	−2.66208e6			−0.767972
$414$	−1.15717e6	−	840731.i	−0.331814	−	0.241077i
$415$	−896813.	−	651573.i	−0.255612	−	0.185713i
$416$	110695.	−	340684.i	0.0313613	−	0.0965202i
$417$	−962934.	−	2.96361e6i	−0.271179	−	0.834604i
$418$	277148.	−	201360.i	0.0775837	−	0.0563678i
$419$	1.69399e6			0.471384			0.235692	−	0.971828i	$-0.424264\pi$
$419$	1.69399e6			0.471384			0.235692	+	0.971828i	$0.424264\pi$
$420$	1.76116e6	−	1.27956e6i	0.487166	−	0.353947i
$421$	4.47996e6	−	3.25488e6i	1.23188	−	0.895015i	0.234853	−	0.972031i	$-0.424539\pi$
$421$	4.47996e6	−	3.25488e6i	1.23188	−	0.895015i	0.997030	+	0.0770160i	$0.0245392\pi$
$422$	−1.72627e6	−	1.25421e6i	−0.471875	−	0.342837i
$423$	198975.	−	612383.i	0.0540690	−	0.166407i
$424$	−1.71582e6			−0.463508
$425$	2.97338e6	+	2.16029e6i	0.798506	+	0.580149i
$426$	568795.	+	1.75057e6i	0.151856	+	0.467364i
$427$	−1.26472e6	+	918872.i	−0.335679	+	0.243885i
$428$	460548.	−	1.41742e6i	0.121525	−	0.374016i
$429$	1.61787e6	+	4.97928e6i	0.424423	+	1.30624i
$430$	452597.	+	1.39295e6i	0.118043	+	0.363300i
$431$	277516.	+	854105.i	0.0719605	+	0.221472i	0.980568	−	0.196179i	$-0.0628535\pi$
$431$	277516.	+	854105.i	0.0719605	+	0.221472i	−0.908608	+	0.417651i	$0.862853\pi$
$432$	−137884.	−	424363.i	−0.0355471	−	0.109403i
$433$	2.11584e6	−	6.51188e6i	0.542329	−	1.66912i	−0.184930	−	0.982752i	$-0.559206\pi$
$433$	2.11584e6	−	6.51188e6i	0.542329	−	1.66912i	0.727258	−	0.686364i	$-0.240794\pi$
$434$	−1.95028e6	+	1.41696e6i	−0.497019	+	0.361106i
$435$	2.47742e6	+	7.62473e6i	0.627736	+	1.93197i
$436$	2.74590e6	+	1.99502e6i	0.691782	+	0.502609i
$437$	−262403.			−0.0657301
$438$	1.53272e6	−	4.71722e6i	0.381748	−	1.17490i
$439$	306290.	+	222533.i	0.0758528	+	0.0551103i	0.625065	−	0.780572i	$-0.285072\pi$
$439$	306290.	+	222533.i	0.0758528	+	0.0551103i	−0.549213	+	0.835683i	$0.685072\pi$
$440$	−3.06551e6	+	2.22723e6i	−0.754869	+	0.548444i
$441$	1.17986e6	−	857221.i	0.288892	−	0.209892i
$442$	−1.65117e6			−0.402010
$443$	5.40772e6	−	3.92894e6i	1.30920	−	0.951187i	0.309197	−	0.950998i	$-0.399940\pi$
$443$	5.40772e6	−	3.92894e6i	1.30920	−	0.951187i	1.00000		0.000189315i	$-6.02607e-5\pi$
$444$	255116.	+	785167.i	0.0614159	+	0.189019i
$445$	2.22781e6	−	6.85649e6i	0.533308	−	1.64135i
$446$	4.50536e6	+	3.27333e6i	1.07249	+	0.779207i
$447$	6.72571e6	+	4.88651e6i	1.59210	+	1.15673i
$448$	−353325.			−0.0831724
$449$	1.32823e6	−	4.08787e6i	0.310926	−	0.956932i	−0.666473	−	0.745529i	$-0.732197\pi$
$449$	1.32823e6	−	4.08787e6i	0.310926	−	0.956932i	0.977399	−	0.211403i	$-0.0678032\pi$
$450$	1.93992e6			0.451598
$451$	−3.69830e6	−	7.17002e6i	−0.856173	−	1.65989i
$452$	−1.12710e6			−0.259489
$453$	2.26330e6	−	6.96571e6i	0.518198	−	1.59485i
$454$	−2.68979e6			−0.612461
$455$	1.92840e6	+	1.40106e6i	0.436684	+	0.317270i
$456$	118134.	+	85829.1i	0.0266049	+	0.0193296i
$457$	−622476.	+	1.91578e6i	−0.139422	+	0.429098i	−0.996252	−	0.0865025i	$-0.972431\pi$
$457$	−622476.	+	1.91578e6i	−0.139422	+	0.429098i	0.856829	+	0.515600i	$0.172431\pi$
$458$	−1.46644e6	−	4.51324e6i	−0.326663	−	1.00537i
$459$	−1.66393e6	+	1.20892e6i	−0.368642	+	0.267834i
$460$	2.90242e6			0.639537
$461$	−276515.	+	200900.i	−0.0605990	+	0.0440278i	−0.617672	−	0.786436i	$-0.711924\pi$
$461$	−276515.	+	200900.i	−0.0605990	+	0.0440278i	0.557073	+	0.830463i	$0.311924\pi$
$462$	4.17779e6	−	3.03534e6i	0.910630	−	0.661611i
$463$	2.12140e6	+	1.54129e6i	0.459906	+	0.334142i	0.793495	−	0.608577i	$-0.208259\pi$
$463$	2.12140e6	+	1.54129e6i	0.459906	+	0.334142i	−0.333588	+	0.942719i	$0.608259\pi$
$464$	402098.	−	1.23753e6i	0.0867036	−	0.266846i
$465$	−1.10198e7			−2.36342
$466$	1.65416e6	+	1.20182e6i	0.352869	+	0.256374i
$467$	215355.	+	662795.i	0.0456944	+	0.140633i	0.971301	−	0.237855i	$-0.0764442\pi$
$467$	215355.	+	662795.i	0.0456944	+	0.140633i	−0.925606	+	0.378488i	$0.876444\pi$
$468$	−705083.	+	512273.i	−0.148808	+	0.108115i
$469$	−1.81458e6	+	5.58471e6i	−0.380930	+	1.17238i
$470$	403758.	+	1.24264e6i	0.0843095	+	0.259478i
$471$	1.72894e6	+	5.32112e6i	0.359109	+	1.10523i
$472$	610336.	+	1.87842e6i	0.126100	+	0.388095i
$473$	1.07364e6	+	3.30433e6i	0.220651	+	0.679095i
$474$	1.70522e6	−	5.24814e6i	0.348606	−	1.07290i
$475$	287919.	−	209185.i	0.0585513	−	0.0425400i
$476$	503273.	+	1.54892e6i	0.101809	+	0.313336i
$477$	3.37728e6	+	2.45374e6i	0.679628	+	0.493779i
$478$	−3.55804e6			−0.712265
$479$	−1.47132e6	+	4.52827e6i	−0.293001	+	0.901765i	0.690884	+	0.722965i	$0.257221\pi$
$479$	−1.47132e6	+	4.52827e6i	−0.293001	+	0.901765i	−0.983886	+	0.178800i	$0.942779\pi$
$480$	−1.30667e6	−	949351.i	−0.258859	−	0.188072i
$481$	−731324.	+	531338.i	−0.144128	+	0.104715i
$482$	−483304.	+	351141.i	−0.0947551	+	0.0688436i
$483$	−3.95552e6			−0.771500
$484$	−5.18725e6	+	3.76876e6i	−1.00652	+	0.731282i
$485$	−307661.	−	946882.i	−0.0593906	−	0.182785i
$486$	−1.26936e6	+	3.90668e6i	−0.243777	+	0.750269i
$487$	−4.80863e6	−	3.49367e6i	−0.918754	−	0.667514i	0.0244599	−	0.999701i	$-0.492213\pi$
$487$	−4.80863e6	−	3.49367e6i	−0.918754	−	0.667514i	−0.943213	+	0.332187i	$0.892213\pi$
$488$	938339.	+	681743.i	0.178365	+	0.129590i
$489$	2.92792e6			0.553715
$490$	−914488.	+	2.81450e6i	−0.172063	+	0.529556i
$491$	−1.86425e6			−0.348979			−0.174490	−	0.984659i	$-0.555828\pi$
$491$	−1.86425e6			−0.348979			−0.174490	+	0.984659i	$0.555828\pi$
$492$	2.41949e6	−	2.44366e6i	0.450621	−	0.455122i
$493$	−5.99787e6			−1.11142
$494$	−49407.7	+	152061.i	−0.00910914	+	0.0280350i
$495$	9.21899e6			1.69110
$496$	1.44698e6	+	1.05129e6i	0.264094	+	0.191876i
$497$	1.60826e6	+	1.16847e6i	0.292056	+	0.212191i
$498$	346367.	−	1.06601e6i	0.0625839	−	0.192614i
$499$	2.45716e6	+	7.56237e6i	0.441756	+	1.35959i	0.886002	+	0.463681i	$0.153472\pi$
$499$	2.45716e6	+	7.56237e6i	0.441756	+	1.35959i	−0.444246	+	0.895905i	$0.646528\pi$
$500$	10609.6	−	7708.31i	0.00189790	−	0.00137890i
$501$	−998109.			−0.177658
$502$	−402640.	+	292535.i	−0.0713111	+	0.0518106i
$503$	−3.83793e6	+	2.78842e6i	−0.676358	+	0.491403i	−0.872147	−	0.489243i	$-0.837273\pi$
$503$	−3.83793e6	+	2.78842e6i	−0.676358	+	0.491403i	0.195789	+	0.980646i	$0.437273\pi$
$504$	695456.	+	505278.i	0.121953	+	0.0886042i
$505$	−1.90943e6	+	5.87663e6i	−0.333178	+	1.02542i
$506$	6.88505e6			1.19545
$507$	4.02109e6	+	2.92149e6i	0.694743	+	0.504760i
$508$	499681.	+	1.53786e6i	0.0859079	+	0.264397i
$509$	7.10435e6	−	5.16161e6i	1.21543	−	0.883061i	0.219717	−	0.975564i	$-0.429486\pi$
$509$	7.10435e6	−	5.16161e6i	1.21543	−	0.883061i	0.995712	+	0.0925021i	$0.0294865\pi$
$510$	−2.30058e6	+	7.08046e6i	−0.391663	+	1.20541i
$511$	−1.65534e6	−	5.09462e6i	−0.280437	−	0.863096i
$512$	81007.0	+	249314.i	0.0136568	+	0.0420312i
$513$	61543.3	+	189411.i	0.0103249	+	0.0317769i
$514$	60175.1	+	185200.i	0.0100464	+	0.0309195i
$515$	3.61881e6	−	1.11376e7i	0.601240	−	1.85043i
$516$	−1.19811e6	+	870478.i	−0.198095	+	0.143924i
$517$	957785.	+	2.94776e6i	0.157595	+	0.485027i
$518$	721338.	+	524083.i	0.118118	+	0.0858175i
$519$	2.81393e6			0.458558
$520$	546496.	−	1.68194e6i	0.0886295	−	0.272774i
$521$	−4.24051e6	−	3.08091e6i	−0.684422	−	0.497262i	0.190400	−	0.981707i	$-0.439022\pi$
$521$	−4.24051e6	−	3.08091e6i	−0.684422	−	0.497262i	−0.874822	+	0.484445i	$0.839022\pi$
$522$	−2.56121e6	+	1.86083e6i	−0.411404	+	0.298903i
$523$	4.40123e6	−	3.19768e6i	0.703590	−	0.511188i	−0.177509	−	0.984119i	$-0.556804\pi$
$523$	4.40123e6	−	3.19768e6i	0.703590	−	0.511188i	0.881099	+	0.472931i	$0.156804\pi$
$524$	4.33981e6			0.690467
$525$	4.34017e6	−	3.15331e6i	0.687239	−	0.499309i
$526$	−2.25773e6	−	6.94859e6i	−0.355802	−	1.09505i
$527$	2.54763e6	−	7.84078e6i	0.399585	−	1.22980i
$528$	−3.09965e6	−	2.25203e6i	−0.483869	−	0.351551i
$529$	940537.	+	683340.i	0.146129	+	0.106169i
$530$	−8.47093e6			−1.30991
$531$	1.48493e6	−	4.57015e6i	0.228544	−	0.703387i
$532$	157704.			0.0241581
$533$	3.36340e6	+	1.69274e6i	0.512815	+	0.258090i
$534$	7.28962e6			1.10625
$535$	2.27371e6	−	6.99775e6i	0.343439	−	1.05700i
$536$	4.35673e6			0.655011
$537$	−1.30699e7	−	9.49585e6i	−1.95586	−	1.42101i
$538$	−1.94043e6	−	1.40980e6i	−0.289029	−	0.209992i
$539$	−2.16933e6	+	6.67650e6i	−0.321627	+	0.989868i
$540$	−680727.	−	2.09506e6i	−0.100459	−	0.309181i
$541$	−6.17420e6	+	4.48582e6i	−0.906959	+	0.658944i	−0.940244	−	0.340502i	$-0.889403\pi$
$541$	−6.17420e6	+	4.48582e6i	−0.906959	+	0.658944i	0.0332850	+	0.999446i	$0.489403\pi$
$542$	3.67530e6			0.537397
$543$	9.95009e6	−	7.22916e6i	1.44820	−	1.05218i
$544$	977563.	−	710241.i	0.141628	−	0.102898i
$545$	1.35564e7	+	9.84930e6i	1.95503	+	1.42041i
$546$	−744784.	+	2.29221e6i	−0.106918	+	0.329058i
$547$	−5.60328e6			−0.800708			−0.400354	−	0.916361i	$-0.631113\pi$
$547$	−5.60328e6			−0.800708			−0.400354	+	0.916361i	$0.631113\pi$
$548$	3.39555e6	+	2.46701e6i	0.483012	+	0.350929i
$549$	−872011.	−	2.68377e6i	−0.123478	−	0.380028i
$550$	−7.55457e6	+	5.48871e6i	−1.06489	+	0.773684i
$551$	−179473.	+	552362.i	−0.0251838	+	0.0775076i
$552$	906884.	+	2.79110e6i	0.126679	+	0.389878i
$553$	−1.84165e6	−	5.66801e6i	−0.256091	−	0.788166i
$554$	−642992.	−	1.97893e6i	−0.0890085	−	0.273940i
$555$	1.25950e6	+	3.87634e6i	0.173566	+	0.534182i
$556$	−771592.	+	2.37472e6i	−0.105852	+	0.325780i
$557$	1.92189e6	−	1.39634e6i	0.262477	−	0.190701i	−0.448761	−	0.893652i	$-0.648135\pi$
$557$	1.92189e6	−	1.39634e6i	0.262477	−	0.190701i	0.711238	+	0.702951i	$0.248135\pi$
$558$	−1.34470e6	−	4.13857e6i	−0.182827	−	0.562684i
$559$	−1.31188e6	−	953135.i	−0.177568	−	0.129010i
$560$	−1.74435e6			−0.235052
$561$	−5.45739e6	+	1.67961e7i	−0.732112	+	2.25321i
$562$	347249.	+	252291.i	0.0463767	+	0.0336947i
$563$	3.97684e6	−	2.88934e6i	0.528770	−	0.384174i	−0.291127	−	0.956684i	$-0.594030\pi$
$563$	3.97684e6	−	2.88934e6i	0.528770	−	0.384174i	0.819898	+	0.572510i	$0.194030\pi$
$564$	−1.06882e6	+	776546.i	−0.141484	+	0.102794i
$565$	−5.56447e6			−0.733335
$566$	7.33256e6	−	5.32741e6i	0.962087	−	0.698997i
$567$	1.93632e6	+	5.95939e6i	0.252942	+	0.778474i
$568$	455771.	−	1.40272e6i	0.0592756	−	0.182432i
$569$	8.21365e6	+	5.96757e6i	1.06354	+	0.772710i	0.974741	−	0.223339i	$-0.0716957\pi$
$569$	8.21365e6	+	5.96757e6i	1.06354	+	0.772710i	0.0888035	+	0.996049i	$0.471696\pi$
$570$	583221.	+	423735.i	0.0751875	+	0.0546269i
$571$	3.84738e6			0.493827			0.246913	−	0.969038i	$-0.420584\pi$
$571$	3.84738e6			0.493827			0.246913	+	0.969038i	$0.420584\pi$
$572$	1.29638e6	−	3.98986e6i	0.165670	−	0.509880i
$573$	−1.98411e7			−2.52453
$574$	562750.	−	3.67105e6i	0.0712912	−	0.465062i
$575$	7.15264e6			0.902187
$576$	197088.	−	606574.i	0.0247516	−	0.0761777i
$577$	1.76816e6			0.221097			0.110548	−	0.993871i	$-0.464739\pi$
$577$	1.76816e6			0.221097			0.110548	+	0.993871i	$0.464739\pi$
$578$	88741.4	+	64474.4i	0.0110486	+	0.00802726i
$579$	−7.15258e6	−	5.19666e6i	−0.886679	−	0.644210i
$580$	1.98514e6	−	6.10964e6i	0.245031	−	0.754129i
$581$	−374078.	−	1.15129e6i	−0.0459750	−	0.141496i
$582$	814436.	−	591722.i	0.0996666	−	0.0724120i
$583$	−2.00945e7			−2.44854
$584$	−3.21535e6	+	2.33609e6i	−0.390118	+	0.283438i
$585$	−3.48096e6	+	2.52907e6i	−0.420543	+	0.305542i
$586$	−8.97303e6	−	6.51929e6i	−1.07943	−	0.784253i
$587$	−3.81905e6	+	1.17538e7i	−0.457467	+	1.40794i	0.410747	+	0.911750i	$0.365268\pi$
$587$	−3.81905e6	+	1.17538e7i	−0.457467	+	1.40794i	−0.868214	+	0.496190i	$0.834732\pi$
$588$	−2.99230e6			−0.356913
$589$	−645849.	−	469236.i	−0.0767083	−	0.0557319i
$590$	3.01320e6	+	9.27368e6i	0.356367	+	1.09679i
$591$	−3.23331e6	+	2.34914e6i	−0.380784	+	0.276656i
$592$	204423.	−	629149.i	0.0239732	−	0.0737818i
$593$	−3.19864e6	−	9.84439e6i	−0.373532	−	1.14961i	−0.944463	−	0.328616i	$-0.893418\pi$
$593$	−3.19864e6	−	9.84439e6i	−0.373532	−	1.14961i	0.570931	−	0.820998i	$-0.306582\pi$
$594$	−1.61480e6	−	4.96986e6i	−0.187782	−	0.577933i
$595$	2.48464e6	+	7.64693e6i	0.287720	+	0.885513i
$596$	−2.05851e6	−	6.33546e6i	−0.237377	−	0.730571i
$597$	1.44282e6	−	4.44053e6i	0.165682	−	0.509916i
$598$	−2.59970e6	+	1.88879e6i	−0.297283	+	0.215989i
$599$	−4.37865e6	−	1.34761e7i	−0.498624	−	1.53461i	−0.811232	−	0.584725i	$-0.801202\pi$
$599$	−4.37865e6	−	1.34761e7i	−0.498624	−	1.53461i	0.312607	−	0.949882i	$-0.398798\pi$
$600$	−3.22012e6	−	2.33955e6i	−0.365169	−	0.265311i
$601$	−1.42104e6			−0.160480			−0.0802400	−	0.996776i	$-0.525569\pi$
$601$	−1.42104e6			−0.160480			−0.0802400	+	0.996776i	$0.525569\pi$
$602$	−494250.	+	1.52115e6i	−0.0555848	+	0.171072i
$603$	−8.57543e6	−	6.23041e6i	−0.960423	−	0.697788i
$604$	−4.74797e6	+	3.44960e6i	−0.529560	+	0.384748i
$605$	−2.56092e7	+	1.86062e7i	−2.84451	+	2.06666i
$606$	−6.24786e6			−0.691114
$607$	2.19922e6	−	1.59782e6i	0.242268	−	0.176018i	−0.460025	−	0.887906i	$-0.652160\pi$
$607$	2.19922e6	−	1.59782e6i	0.242268	−	0.176018i	0.702293	+	0.711888i	$0.252160\pi$
$608$	−36156.8	−	111279.i	−0.00396671	−	0.0122083i
$609$	−2.70542e6	+	8.32644e6i	−0.295592	+	0.909737i
$610$	4.63254e6	+	3.36573e6i	0.504074	+	0.366231i
$611$	−1.17031e6	−	850283.i	−0.126823	−	0.0921426i
$612$	−2.93985e6			−0.317283
$613$	−45055.7	+	138667.i	−0.00484282	+	0.0149047i	−0.953449	−	0.301555i	$-0.902494\pi$
$613$	−45055.7	+	138667.i	−0.00484282	+	0.0149047i	0.948606	+	0.316460i	$0.102494\pi$
$614$	−875545.			−0.0937255
$615$	1.19449e7	−	1.20642e7i	1.27349	−	1.28621i
$616$	−4.13790e6			−0.439368
$617$	−1.97933e6	+	6.09175e6i	−0.209317	+	0.644212i	0.790191	+	0.612861i	$0.209981\pi$
$617$	−1.97933e6	+	6.09175e6i	−0.209317	+	0.644212i	−0.999508	+	0.0313519i	$0.990019\pi$
$618$	1.18411e7			1.24716
$619$	−5.03163e6	−	3.65569e6i	−0.527815	−	0.383480i	0.291725	−	0.956502i	$-0.405771\pi$
$619$	−5.03163e6	−	3.65569e6i	−0.527815	−	0.383480i	−0.819540	+	0.573022i	$0.805771\pi$
$620$	7.14369e6	+	5.19019e6i	0.746351	+	0.542256i
$621$	−1.23690e6	+	3.80678e6i	−0.128708	+	0.396122i
$622$	−2.76473e6	−	8.50898e6i	−0.286535	−	0.881864i
$623$	6.36925e6	−	4.62753e6i	0.657458	−	0.477671i
$624$	1.78819e6			0.183845
$625$	7.92670e6	−	5.75909e6i	0.811694	−	0.589730i
$626$	3.14552e6	−	2.28535e6i	0.320816	−	0.233087i
$627$	1.38350e6	+	1.00517e6i	0.140544	+	0.102111i
$628$	1.38538e6	−	4.26378e6i	0.140175	−	0.431415i
$629$	−3.04926e6			−0.307304
$630$	3.43343e6	+	2.49454e6i	0.344649	+	0.250402i
$631$	5.32981e6	+	1.64035e7i	0.532891	+	1.64007i	0.748163	+	0.663516i	$0.230936\pi$
$631$	5.32981e6	+	1.64035e7i	0.532891	+	1.64007i	−0.215272	+	0.976554i	$0.569064\pi$
$632$	−3.57724e6	+	2.59902e6i	−0.356250	+	0.258831i
$633$	3.29156e6	−	1.01304e7i	0.326507	−	1.00488i
$634$	1.52583e6	+	4.69602e6i	0.150759	+	0.463988i
$635$	2.46690e6	+	7.59234e6i	0.242783	+	0.747208i
$636$	−2.64681e6	−	8.14605e6i	−0.259466	−	0.798554i
$637$	−1.01247e6	−	3.11607e6i	−0.0988633	−	0.304270i
$638$	4.70911e6	−	1.44931e7i	0.458023	−	1.40965i
$639$	−2.90309e6	+	2.10922e6i	−0.281260	+	0.204347i
$640$	399928.	+	1.23085e6i	0.0385950	+	0.118783i
$641$	1.34203e7	+	9.75040e6i	1.29008	+	0.937297i	0.999807	−	0.0196473i	$-0.00625434\pi$
$641$	1.34203e7	+	9.75040e6i	1.29008	+	0.937297i	0.290272	+	0.956944i	$0.406254\pi$
$642$	7.43980e6			0.712400
$643$	−2.59848e6	+	7.99731e6i	−0.247852	+	0.762810i	0.747302	+	0.664484i	$0.231349\pi$
$643$	−2.59848e6	+	7.99731e6i	−0.247852	+	0.762810i	−0.995154	+	0.0983258i	$0.968651\pi$
$644$	2.56420e6	+	1.86300e6i	0.243634	+	0.177011i
$645$	−5.91502e6	+	4.29751e6i	−0.559831	+	0.406741i
$646$	−436327.	+	317010.i	−0.0411368	+	0.0298877i
$647$	1.52695e7			1.43405			0.717024	−	0.697048i	$-0.245504\pi$
$647$	1.52695e7			1.43405			0.717024	+	0.697048i	$0.245504\pi$
$648$	3.76113e6	−	2.73262e6i	0.351869	−	0.255648i
$649$	7.14785e6	+	2.19988e7i	0.666137	+	2.05016i
$650$	1.34677e6	−	4.14493e6i	0.125029	−	0.384799i
$651$	−9.73568e6	−	7.07339e6i	−0.900355	−	0.654147i
$652$	−1.89805e6	−	1.37901e6i	−0.174859	−	0.127043i
$653$	−2.06377e7			−1.89399			−0.946996	−	0.321246i	$-0.895899\pi$
$653$	−2.06377e7			−1.89399			−0.946996	+	0.321246i	$0.895899\pi$
$654$	−5.23575e6	+	1.61140e7i	−0.478668	+	1.47319i
$655$	2.14255e7			1.95131
$656$	−2.71939e6	+	444574.i	−0.246725	+	0.0403352i
$657$	9.66960e6			0.873967
$658$	−440916.	+	1.35700e6i	−0.0397001	+	0.122184i
$659$	3.81395e6			0.342107			0.171053	−	0.985262i	$-0.445283\pi$
$659$	3.81395e6			0.342107			0.171053	+	0.985262i	$0.445283\pi$
$660$	−1.53028e7	−	1.11182e7i	−1.36745	−	0.993512i
$661$	−9.29673e6	−	6.75447e6i	−0.827611	−	0.601295i	0.0912712	−	0.995826i	$-0.470907\pi$
$661$	−9.29673e6	−	6.75447e6i	−0.827611	−	0.601295i	−0.918883	+	0.394531i	$0.870907\pi$
$662$	251342.	−	773550.i	0.0222905	−	0.0686031i
$663$	−2.54709e6	−	7.83913e6i	−0.225040	−	0.692602i
$664$	−726612.	+	527915.i	−0.0639562	+	0.0464669i
$665$	778575.			0.0682726
$666$	−1.30209e6	+	946027.i	−0.113751	+	0.0826452i
$667$	−9.44340e6	+	6.86103e6i	−0.821890	+	0.597138i
$668$	647034.	+	470098.i	0.0561030	+	0.0407612i
$669$	−8.59058e6	+	2.64391e7i	−0.742091	+	2.28392i
$670$	2.15090e7			1.85111
$671$	1.09892e7	+	7.98412e6i	0.942236	+	0.684574i
$672$	−545036.	−	1.67745e6i	−0.0465588	−	0.143293i
$673$	1.12663e7	−	8.18546e6i	0.958836	−	0.696635i	0.00595554	−	0.999982i	$-0.498104\pi$
$673$	1.12663e7	−	8.18546e6i	0.958836	−	0.696635i	0.952880	+	0.303347i	$0.0981043\pi$
$674$	2.11432e6	−	6.50722e6i	0.179276	−	0.551754i
$675$	−1.67756e6	−	5.16301e6i	−0.141716	−	0.436158i
$676$	−1.23072e6	−	3.78777e6i	−0.103584	−	0.318799i
$677$	−3.43055e6	−	1.05581e7i	−0.287668	−	0.885352i	−0.985586	−	0.169174i	$-0.945890\pi$
$677$	−3.43055e6	−	1.05581e7i	−0.287668	−	0.885352i	0.697918	−	0.716178i	$-0.254110\pi$
$678$	−1.73866e6	−	5.35106e6i	−0.145258	−	0.447059i
$679$	335975.	−	1.03402e6i	0.0279661	−	0.0860710i
$680$	4.82619e6	−	3.50643e6i	0.400251	−	0.290799i
$681$	−4.14925e6	−	1.27701e7i	−0.342848	−	1.05518i
$682$	1.69461e7	+	1.23121e7i	1.39511	+	1.01361i
$683$	−2.13915e7			−1.75465			−0.877324	−	0.479899i	$-0.840673\pi$
$683$	−2.13915e7			−1.75465			−0.877324	+	0.479899i	$0.840673\pi$
$684$	−87968.5	+	270739.i	−0.00718931	+	0.0221264i
$685$	1.67637e7	+	1.21795e7i	1.36503	+	0.991753i
$686$	−7.30611e6	+	5.30820e6i	−0.592756	+	0.430662i
$687$	1.91650e7	−	1.39242e7i	1.54923	−	1.12558i
$688$	1.18667e6			0.0955783
$689$	7.58743e6	−	5.51259e6i	0.608901	−	0.442392i
$690$	4.47725e6	+	1.37796e7i	0.358004	+	1.10182i
$691$	5.49583e6	−	1.69144e7i	0.437863	−	1.34760i	−0.452262	−	0.891885i	$-0.649383\pi$
$691$	5.49583e6	−	1.69144e7i	0.437863	−	1.34760i	0.890125	−	0.455717i	$-0.150617\pi$
$692$	−1.82416e6	−	1.32533e6i	−0.144809	−	0.105210i
$693$	8.14471e6	+	5.91748e6i	0.644233	+	0.468062i
$694$	1.50583e7			1.18680
$695$	−3.80932e6	+	1.17239e7i	−0.299147	+	0.920681i
$696$	6.49559e6			0.508271
$697$	5.82242e6	+	1.12881e7i	0.453964	+	0.880115i
$698$	−2.87103e6			−0.223048
$699$	−3.15407e6	+	9.70724e6i	−0.244162	+	0.751454i
$700$	−4.29873e6			−0.331585
$701$	−1.02895e7	−	7.47575e6i	−0.790859	−	0.574592i	0.117359	−	0.993090i	$-0.462557\pi$
$701$	−1.02895e7	−	7.47575e6i	−0.790859	−	0.574592i	−0.908218	+	0.418497i	$0.862557\pi$
$702$	1.97312e6	+	1.43356e6i	0.151116	+	0.109792i
$703$	−91242.4	+	280815.i	−0.00696319	+	0.0214305i
$704$	948699.	+	2.91980e6i	0.0721435	+	0.222035i
$705$	−5.27673e6	+	3.83377e6i	−0.399846	+	0.290505i
$706$	2.01542e6			0.152179
$707$	−5.45902e6	+	3.96621e6i	−0.410739	+	0.298419i
$708$	−7.97651e6	+	5.79527e6i	−0.598039	+	0.434501i
$709$	6.06243e6	+	4.40461e6i	0.452930	+	0.329073i	0.790751	−	0.612137i	$-0.209690\pi$
$709$	6.06243e6	+	4.40461e6i	0.452930	+	0.329073i	−0.337822	+	0.941210i	$0.609690\pi$
$710$	2.25012e6	−	6.92516e6i	0.167518	−	0.515566i
$711$	1.07579e7			0.798094
$712$	−4.72557e6	−	3.43332e6i	−0.349344	−	0.253814i
$713$	−4.95803e6	−	1.52592e7i	−0.365246	−	1.12411i
$714$	−6.57731e6	+	4.77869e6i	−0.482839	+	0.350803i
$715$	6.40019e6	−	1.96978e7i	0.468196	−	1.44096i
$716$	4.00027e6	+	1.23116e7i	0.291613	+	0.897491i
$717$	−5.48861e6	−	1.68922e7i	−0.398717	−	1.22712i
$718$	1.12184e6	+	3.45268e6i	0.0812121	+	0.249945i
$719$	3.36440e6	+	1.03546e7i	0.242709	+	0.746981i	0.996005	+	0.0892994i	$0.0284628\pi$
$719$	3.36440e6	+	1.03546e7i	0.242709	+	0.746981i	−0.753296	+	0.657682i	$0.771537\pi$
$720$	973014.	−	2.99463e6i	0.0699500	−	0.215284i
$721$	1.03461e7	−	7.51687e6i	0.741204	−	0.538517i
$722$	−3.04449e6	−	9.36997e6i	−0.217356	−	0.668953i
$723$	−2.41262e6	−	1.75287e6i	−0.171650	−	0.124711i
$724$	−9.85509e6			−0.698738
$725$	4.89213e6	−	1.50564e7i	0.345663	−	1.06384i
$726$	−2.58944e7	−	1.88134e7i	−1.82333	−	1.32472i
$727$	3.54553e6	−	2.57598e6i	0.248797	−	0.180762i	−0.456397	−	0.889777i	$-0.650860\pi$
$727$	3.54553e6	−	2.57598e6i	0.248797	−	0.180762i	0.705193	+	0.709015i	$0.250860\pi$
$728$	1.56242e6	−	1.13516e6i	0.109262	−	0.0793834i
$729$	−2.85375e6			−0.198883
$730$	−1.58740e7	+	1.15332e7i	−1.10250	+	0.801017i
$731$	−1.69029e6	−	5.20217e6i	−0.116995	−	0.360073i
$732$	−1.78918e6	+	5.50652e6i	−0.123417	+	0.379839i
$733$	6.39950e6	+	4.64951e6i	0.439932	+	0.319630i	0.785608	−	0.618724i	$-0.212350\pi$
$733$	6.39950e6	+	4.64951e6i	0.439932	+	0.319630i	−0.345676	+	0.938354i	$0.612350\pi$
$734$	−1.83819e6	−	1.33552e6i	−0.125936	−	0.0914977i
$735$	−1.47729e7			−1.00866
$736$	726680.	−	2.23649e6i	0.0494480	−	0.152185i
$737$	5.10231e7			3.46017
$738$	5.98840e6	+	3.01385e6i	0.404735	+	0.203695i
$739$	−1.86625e7			−1.25707			−0.628535	−	0.777781i	$-0.716345\pi$
$739$	−1.86625e7			−1.25707			−0.628535	+	0.777781i	$0.716345\pi$
$740$	1.00923e6	−	3.10608e6i	0.0677500	−	0.208513i
$741$	−798144.			−0.0533993
$742$	−7.48383e6	−	5.43732e6i	−0.499015	−	0.362556i
$743$	8.97290e6	+	6.51919e6i	0.596295	+	0.433233i	0.844562	−	0.535458i	$-0.179861\pi$
$743$	8.97290e6	+	6.51919e6i	0.596295	+	0.433233i	−0.248267	+	0.968692i	$0.579861\pi$
$744$	−2.75903e6	+	8.49143e6i	−0.182736	+	0.562404i
$745$	−1.01628e7	−	3.12779e7i	−0.670845	−	2.06465i
$746$	2.34319e6	−	1.70243e6i	0.154156	−	0.112001i
$747$	2.18516e6			0.143279
$748$	1.14486e7	−	8.31787e6i	0.748165	−	0.543574i
$749$	6.50047e6	−	4.72287e6i	0.423389	−	0.307610i
$750$	52962.3	+	38479.4i	0.00343806	+	0.00249790i
$751$	2.81590e6	−	8.66644e6i	0.182187	−	0.560713i	−0.817702	−	0.575642i	$-0.804752\pi$
$751$	2.81590e6	−	8.66644e6i	0.182187	−	0.560713i	0.999889	+	0.0149287i	$0.00475214\pi$
$752$	1.05862e6			0.0682645
$753$	−2.00995e6	−	1.46031e6i	−0.129181	−	0.0938554i
$754$	2.19785e6	+	6.76428e6i	0.140789	+	0.433304i
$755$	−2.34405e7	+	1.70305e7i	−1.49658	+	1.08733i
$756$	743375.	−	2.28787e6i	0.0473046	−	0.145589i
$757$	−3.89205e6	−	1.19785e7i	−0.246853	−	0.759736i	−0.995326	−	0.0965708i	$-0.969213\pi$
$757$	−3.89205e6	−	1.19785e7i	−0.246853	−	0.759736i	0.748473	−	0.663165i	$-0.230787\pi$
$758$	4.83981e6	+	1.48954e7i	0.305953	+	0.941627i
$759$	1.06208e7	+	3.26875e7i	0.669197	+	2.05958i
$760$	−178504.	−	549380.i	−0.0112102	−	0.0345016i
$761$	−3.05562e6	+	9.40422e6i	−0.191266	+	0.588656i	0.808734	+	0.588174i	$0.200153\pi$
$761$	−3.05562e6	+	9.40422e6i	−0.191266	+	0.588656i	−1.00000		0.000481177i	$0.999847\pi$
$762$	−6.53035e6	+	4.74458e6i	−0.407426	+	0.296013i
$763$	5.65463e6	+	1.74032e7i	0.351636	+	1.08222i
$764$	1.28622e7	+	9.34494e6i	0.797227	+	0.579219i
$765$	−1.45139e7			−0.896666
$766$	−303552.	+	934236.i	−0.0186922	+	0.0575287i
$767$	−8.73392e6	−	6.34557e6i	−0.536069	−	0.389477i
$768$	−1.05868e6	+	769179.i	−0.0647684	+	0.0470570i
$769$	−1.06900e7	+	7.76674e6i	−0.651871	+	0.473612i	−0.863908	−	0.503650i	$-0.831990\pi$
$769$	−1.06900e7	+	7.76674e6i	−0.651871	+	0.473612i	0.212037	+	0.977262i	$0.431990\pi$
$770$	−2.04287e7			−1.24169
$771$	−786432.	+	571376.i	−0.0476458	+	0.0346167i
$772$	2.18917e6	+	6.73756e6i	0.132201	+	0.406874i
$773$	5.28842e6	−	1.62761e7i	0.318330	−	0.979718i	−0.656032	−	0.754733i	$-0.727767\pi$
$773$	5.28842e6	−	1.62761e7i	0.318330	−	0.979718i	0.974362	−	0.224985i	$-0.0722335\pi$
$774$	−2.33575e6	−	1.69702e6i	−0.140144	−	0.101820i
$775$	1.76047e7	+	1.27906e7i	1.05287	+	0.764955i
$776$	−806660.			−0.0480879
$777$	−1.37541e6	+	4.23308e6i	−0.0817297	+	0.251538i
$778$	2.01554e7			1.19383
$779$	1.21378e6	−	198432.i	0.0716631	−	0.0117157i
$780$	8.82822e6			0.519561
$781$	5.33769e6	−	1.64277e7i	0.313131	−	0.963717i
$782$	−1.08395e7			−0.633857
$783$	7.16735e6	+	5.20739e6i	0.417787	+	0.303540i
$784$	1.93979e6	+	1.40934e6i	0.112710	+	0.0818889i
$785$	6.83958e6	−	2.10501e7i	0.396146	−	1.21921i
$786$	6.69456e6	+	2.06037e7i	0.386514	+	1.18957i
$787$	−2.04750e7	+	1.48759e7i	−1.17838	+	0.856145i	−0.991988	−	0.126330i	$-0.959680\pi$
$787$	−2.04750e7	+	1.48759e7i	−1.17838	+	0.856145i	−0.186394	+	0.982475i	$0.559680\pi$
$788$	3.20244e6			0.183724
$789$	2.95064e7	−	2.14377e7i	1.68742	−	1.22598i
$790$	−1.76607e7	+	1.28312e7i	−1.00679	+	0.731476i
$791$	−4.91605e6	−	3.57172e6i	−0.279367	−	0.202972i
$792$	2.30816e6	−	7.10379e6i	0.130754	−	0.402418i
$793$	−6.33968e6			−0.358001
$794$	−7.97304e6	−	5.79275e6i	−0.448820	−	0.326087i
$795$	−1.30672e7	−	4.02167e7i	−0.733271	−	2.25678i
$796$	−3.02676e6	+	2.19907e6i	−0.169315	+	0.123014i
$797$	1.71318e6	−	5.27263e6i	0.0955340	−	0.294023i	−0.891859	−	0.452314i	$-0.850598\pi$
$797$	1.71318e6	−	5.27263e6i	0.0955340	−	0.294023i	0.987392	+	0.158291i	$0.0505985\pi$
$798$	243272.	+	748715.i	0.0135234	+	0.0416207i
$799$	−1.50789e6	−	4.64080e6i	−0.0835607	−	0.257173i
$800$	985571.	+	3.03328e6i	0.0544456	+	0.167566i
$801$	4.39153e6	+	1.35158e7i	0.241844	+	0.744319i
$802$	517357.	−	1.59226e6i	0.0284024	−	0.0874135i
$803$	−3.76560e7	+	2.73587e7i	−2.06085	+	1.49729i
$804$	6.72065e6	+	2.06840e7i	0.366667	+	1.12848i
$805$	1.26594e7	+	9.19757e6i	0.688529	+	0.500246i
$806$	−9.77622e6			−0.530070
$807$	3.69991e6	−	1.13871e7i	0.199989	−	0.615504i
$808$	4.05024e6	+	2.94267e6i	0.218249	+	0.158567i
$809$	2.09014e7	−	1.51858e7i	1.12281	−	0.815767i	0.138175	−	0.990408i	$-0.455876\pi$
$809$	2.09014e7	−	1.51858e7i	1.12281	−	0.815767i	0.984632	+	0.174641i	$0.0558765\pi$
$810$	1.85686e7	−	1.34908e7i	0.994410	−	0.722481i
$811$	−2.96201e7			−1.58138			−0.790688	−	0.612220i	$-0.790277\pi$
$811$	−2.96201e7			−1.58138			−0.790688	+	0.612220i	$0.790277\pi$
$812$	5.67547e6	−	4.12347e6i	0.302073	−	0.219469i
$813$	5.66949e6	+	1.74489e7i	0.300828	+	0.925853i
$814$	2.39406e6	−	7.36817e6i	0.126641	−	0.389761i
$815$	−9.37058e6	−	6.80813e6i	−0.494166	−	0.359032i
$816$	4.87993e6	+	3.54548e6i	0.256560	+	0.186402i
$817$	−529661.			−0.0277615
$818$	−1.56093e6	+	4.80405e6i	−0.0815643	+	0.251029i
$819$	−4.69869e6			−0.244775
$820$	−1.34255e7	+	2.19484e6i	−0.697263	+	0.113991i
$821$	3.71873e7			1.92547			0.962736	−	0.270445i	$-0.0871707\pi$
$821$	3.71873e7			1.92547			0.962736	+	0.270445i	$0.0871707\pi$
$822$	−6.47445e6	+	1.99263e7i	−0.334213	+	1.02860i
$823$	−1.12316e7			−0.578020			−0.289010	−	0.957326i	$-0.593326\pi$
$823$	−1.12316e7			−0.578020			−0.289010	+	0.957326i	$0.593326\pi$
$824$	−7.67612e6	−	5.57703e6i	−0.393844	−	0.286144i
$825$	−3.77119e7	−	2.73993e7i	−1.92905	−	1.40154i
$826$	−3.29051e6	+	1.01271e7i	−0.167808	+	0.516460i
$827$	5.34404e6	+	1.64473e7i	0.271710	+	0.836238i	0.990071	+	0.140568i	$0.0448927\pi$
$827$	5.34404e6	+	1.64473e7i	0.271710	+	0.836238i	−0.718361	+	0.695671i	$0.755107\pi$
$828$	−4.62867e6	+	3.36292e6i	−0.234628	+	0.170467i
$829$	2.21660e7			1.12021			0.560106	−	0.828421i	$-0.310760\pi$
$829$	2.21660e7			1.12021			0.560106	+	0.828421i	$0.310760\pi$
$830$	−3.58725e6	+	2.60629e6i	−0.180745	+	0.131319i
$831$	8.40330e6	−	6.10535e6i	0.422131	−	0.306696i
$832$	−1.15921e6	−	842217.i	−0.0580570	−	0.0421809i
$833$	3.41528e6	−	1.05111e7i	0.170535	−	0.524853i
$834$	−1.24645e7			−0.620525
$835$	3.19438e6	+	2.32085e6i	0.158551	+	0.115194i
$836$	−423444.	−	1.30323e6i	−0.0209546	−	0.0644917i
$837$	−9.85178e6	+	7.15774e6i	−0.486072	+	0.353152i
$838$	2.09388e6	−	6.44431e6i	0.103001	−	0.317005i
$839$	447967.	+	1.37870e6i	0.0219705	+	0.0676184i	0.961441	−	0.275012i	$-0.0886820\pi$
$839$	447967.	+	1.37870e6i	0.0219705	+	0.0676184i	−0.939470	+	0.342631i	$0.888682\pi$
$840$	−2.69082e6	−	8.28149e6i	−0.131579	−	0.404958i
$841$	1.64537e6	+	5.06393e6i	0.0802184	+	0.246887i
$842$	−6.84478e6	−	2.10661e7i	−0.332720	−	1.02401i
$843$	−662117.	+	2.03779e6i	−0.0320897	+	0.0987619i
$844$	−6.90507e6	+	5.01683e6i	−0.333666	+	0.242422i
$845$	−6.07602e6	−	1.87001e7i	−0.292737	−	0.900951i
$846$	−2.08370e6	−	1.51390e6i	−0.100094	−	0.0727227i
$847$	−3.45680e7			−1.65564
$848$	−2.12087e6	+	6.52737e6i	−0.101280	+	0.311708i
$849$	3.66036e7	+	2.65941e7i	1.74283	+	1.26624i
$850$	1.18935e7	−	8.64115e6i	0.564629	−	0.410227i
$851$	−4.80093e6	+	3.48808e6i	−0.227249	+	0.165106i
$852$	7.36264e6			0.347484
$853$	−1.48837e7	+	1.08136e7i	−0.700385	+	0.508860i	−0.880058	−	0.474867i	$-0.842496\pi$
$853$	−1.48837e7	+	1.08136e7i	−0.700385	+	0.508860i	0.179672	+	0.983727i	$0.442496\pi$
$854$	1.93232e6	+	5.94706e6i	0.0906638	+	0.279034i
$855$	−434297.	+	1.33663e6i	−0.0203175	+	0.0625310i
$856$	−4.82292e6	−	3.50406e6i	−0.224971	−	0.163451i
$857$	2.24638e7	+	1.63209e7i	1.04480	+	0.759090i	0.971216	−	0.238200i	$-0.0765573\pi$
$857$	2.24638e7	+	1.63209e7i	1.04480	+	0.759090i	0.0735810	+	0.997289i	$0.476557\pi$
$858$	2.09421e7			0.971185
$859$	−8.03589e6	+	2.47319e7i	−0.371579	+	1.14360i	0.574179	+	0.818730i	$0.305321\pi$
$859$	−8.03589e6	+	2.47319e7i	−0.371579	+	1.14360i	−0.945758	+	0.324872i	$0.894679\pi$
$860$	5.85854e6			0.270112
$861$	1.82968e7	−	2.99121e6i	0.841138	−	0.137512i
$862$	3.59224e6			0.164663
$863$	−5.95022e6	+	1.83129e7i	−0.271961	+	0.837009i	0.718047	+	0.695995i	$0.245036\pi$
$863$	−5.95022e6	+	1.83129e7i	−0.271961	+	0.837009i	−0.990008	+	0.141014i	$0.954964\pi$
$864$	−1.78481e6			−0.0813405
$865$	−9.00578e6	−	6.54308e6i	−0.409243	−	0.297332i
$866$	−2.21573e7	−	1.60982e7i	−1.00397	−	0.729430i
$867$	−169208.	+	520767.i	−0.00764490	+	0.0235286i
$868$	2.97977e6	+	9.17078e6i	0.134240	+	0.413149i
$869$	−4.18942e7	+	3.04379e7i	−1.88194	+	1.36731i
$870$	3.20684e7			1.43641
$871$	−1.92656e7	+	1.39973e7i	−0.860474	+	0.625171i
$872$	1.09836e7	−	7.98006e6i	0.489163	−	0.355398i
$873$	1.58776e6	+	1.15358e6i	0.0705099	+	0.0512285i
$874$	−324347.	+	998239.i	−0.0143626	+	0.0442034i
$875$	70702.5			0.00312187
$876$	−1.60508e7	−	1.16616e7i	−0.706703	−	0.513450i
$877$	−2.47935e6	−	7.63065e6i	−0.108853	−	0.335014i	0.881763	−	0.471693i	$-0.156357\pi$
$877$	−2.47935e6	−	7.63065e6i	−0.108853	−	0.335014i	−0.990615	+	0.136679i	$0.956357\pi$
$878$	1.22516e6	−	890131.i	0.0536360	−	0.0389689i
$879$	1.71093e7	−	5.26571e7i	0.746897	−	2.29871i
$880$	4.68369e6	+	1.44149e7i	0.203883	+	0.627488i
$881$	−90679.8	−	279084.i	−0.00393614	−	0.0121142i	0.949069	−	0.315068i	$-0.102027\pi$
$881$	−90679.8	−	279084.i	−0.00393614	−	0.0121142i	−0.953005	+	0.302954i	$0.902027\pi$
$882$	−1.80267e6	−	5.54805e6i	−0.0780270	−	0.240142i
$883$	−1.28890e7	−	3.96682e7i	−0.556310	−	1.71214i	−0.692460	−	0.721457i	$-0.743473\pi$
$883$	−1.28890e7	−	3.96682e7i	−0.556310	−	1.71214i	0.136150	−	0.990688i	$-0.456527\pi$
$884$	−2.04096e6	+	6.28143e6i	−0.0878424	+	0.270351i
$885$	−3.93797e7	+	2.86110e7i	−1.69011	+	1.22793i
$886$	−8.26226e6	−	2.54286e7i	−0.353602	−	1.08828i
$887$	−2.94240e7	−	2.13778e7i	−1.25572	−	0.912333i	−0.257179	−	0.966364i	$-0.582793\pi$
$887$	−2.94240e7	−	2.13778e7i	−1.25572	−	0.912333i	−0.998539	+	0.0540309i	$0.982793\pi$
$888$	3.30230e6			0.140535
$889$	−2.69393e6	+	8.29107e6i	−0.114323	+	0.351849i
$890$	−2.33299e7	−	1.69502e7i	−0.987275	−	0.717297i
$891$	4.40479e7	−	3.20027e7i	1.85879	−	1.35049i
$892$	1.80214e7	−	1.30933e7i	0.758363	−	0.550983i
$893$	−472505.			−0.0198280
$894$	2.69028e7	−	1.95460e7i	1.12578	−	0.817928i
$895$	1.97491e7	+	6.07816e7i	0.824120	+	2.53638i
$896$	−436734.	+	1.34413e6i	−0.0181738	+	0.0559333i
$897$	−1.29775e7	−	9.42873e6i	−0.538532	−	0.391266i
$898$	−1.39094e7	−	1.01058e7i	−0.575596	−	0.418195i
$899$	−3.55121e7			−1.46547
$900$	2.39787e6	−	7.37988e6i	0.0986778	−	0.303699i
$901$	3.16358e7			1.29828
$902$	−3.18477e7	+	5.20656e6i	−1.30335	+	0.213076i
$903$	−7.98424e6			−0.325847
$904$	−1.39318e6	+	4.28776e6i	−0.0567003	+	0.174506i
$905$	−4.86541e7			−1.97469
$906$	−2.37015e7	−	1.72202e7i	−0.959304	−	0.696975i
$907$	1.18494e6	+	860907.i	0.0478274	+	0.0347486i	0.611442	−	0.791289i	$-0.290590\pi$
$907$	1.18494e6	+	860907.i	0.0478274	+	0.0347486i	−0.563615	+	0.826038i	$0.690590\pi$
$908$	−3.32476e6	+	1.02326e7i	−0.133828	+	0.411879i
$909$	−3.76394e6	−	1.15842e7i	−0.151089	−	0.465004i
$910$	7.71358e6	−	5.60425e6i	0.308783	−	0.224344i
$911$	5.18409e6			0.206955			0.103478	−	0.994632i	$-0.467003\pi$
$911$	5.18409e6			0.206955			0.103478	+	0.994632i	$0.467003\pi$
$912$	472535.	−	343316.i	0.0188125	−	0.0136681i
$913$	−8.50960e6	+	6.18258e6i	−0.337856	+	0.245467i
$914$	6.51865e6	+	4.73608e6i	0.258103	+	0.187523i
$915$	−8.83308e6	+	2.71854e7i	−0.348786	+	1.07345i
$916$	−1.89820e7			−0.747486
$917$	1.89288e7	+	1.37526e7i	0.743360	+	0.540083i
$918$	2.54227e6	+	7.82429e6i	0.0995667	+	0.306435i
$919$	−156051.	+	113377.i	−0.00609504	+	0.00442831i	−0.590829	−	0.806797i	$-0.701199\pi$
$919$	−156051.	+	113377.i	−0.00609504	+	0.00442831i	0.584734	+	0.811225i	$0.301199\pi$
$920$	3.58759e6	−	1.10415e7i	0.139744	−	0.430087i
$921$	−1.35061e6	−	4.15675e6i	−0.0524663	−	0.161475i
$922$	422477.	+	1.30025e6i	0.0163672	+	0.0503732i
$923$	2.49122e6	+	7.66719e6i	0.0962516	+	0.296232i
$924$	−6.38310e6	−	1.96452e7i	−0.245953	−	0.756965i
$925$	2.48711e6	−	7.65454e6i	0.0955742	−	0.294147i
$926$	8.48559e6	−	6.16514e6i	0.325203	−	0.236274i
$927$	7.13353e6	+	2.19547e7i	0.272650	+	0.839129i
$928$	−4.21083e6	−	3.05935e6i	−0.160508	−	0.116616i
$929$	−3.36701e7			−1.27999			−0.639993	−	0.768381i	$-0.721063\pi$
$929$	−3.36701e7			−1.27999			−0.639993	+	0.768381i	$0.721063\pi$
$930$	−1.36212e7	+	4.19218e7i	−0.516427	+	1.58940i
$931$	−865807.	−	629046.i	−0.0327376	−	0.0237853i
$932$	6.61665e6	−	4.80728e6i	0.249516	−	0.181284i
$933$	3.61325e7	−	2.62518e7i	1.35892	−	0.987312i
$934$	2.78761e6			0.104560
$935$	5.65211e7	−	4.10650e7i	2.11437	−	1.53618i
$936$	1.07727e6	+	3.31550e6i	0.0401916	+	0.123697i
$937$	808613.	−	2.48866e6i	0.0300879	−	0.0926011i	−0.934885	−	0.354951i	$-0.884498\pi$
$937$	808613.	−	2.48866e6i	0.0300879	−	0.0926011i	0.964973	+	0.262350i	$0.0844975\pi$
$938$	1.90026e7	+	1.38062e7i	0.705188	+	0.512349i
$939$	1.57022e7	+	1.14083e7i	0.581162	+	0.422239i
$940$	5.22635e6			0.192921
$941$	7.35957e6	−	2.26504e7i	0.270943	−	0.833878i	−0.719321	−	0.694678i	$-0.755547\pi$
$941$	7.35957e6	−	2.26504e7i	0.270943	−	0.833878i	0.990264	−	0.139200i	$-0.0444531\pi$
$942$	2.23798e7			0.821731
$943$	2.20798e7	+	1.11123e7i	0.808565	+	0.406936i
$944$	7.90035e6			0.288547
$945$	3.67001e6	−	1.12951e7i	0.133686	−	0.411445i
$946$	1.38975e7			0.504904
$947$	−2.62709e7	−	1.90869e7i	−0.951919	−	0.691609i	−0.000658865	−	1.00000i	$-0.500210\pi$
$947$	−2.62709e7	−	1.90869e7i	−0.951919	−	0.691609i	−0.951260	+	0.308390i	$0.900210\pi$
$948$	−1.78573e7	−	1.29741e7i	−0.645351	−	0.468875i
$949$	6.71303e6	−	2.06606e7i	0.241965	−	0.744692i
$950$	−439901.	−	1.35388e6i	−0.0158142	−	0.0486710i
$951$	−1.99412e7	+	1.44881e7i	−0.714989	+	0.519470i
$952$	6.51451e6			0.232964
$953$	−1.77160e7	+	1.28715e7i	−0.631880	+	0.459087i	−0.857051	−	0.515232i	$-0.827706\pi$
$953$	−1.77160e7	+	1.28715e7i	−0.631880	+	0.459087i	0.225171	+	0.974319i	$0.427706\pi$
$954$	1.35091e7	−	9.81495e6i	0.480569	−	0.349154i
$955$	6.35001e7	+	4.61355e7i	2.25303	+	1.63692i
$956$	−4.39799e6	+	1.35356e7i	−0.155636	+	0.478997i
$957$	7.60720e7			2.68501
$958$	1.54079e7	+	1.11945e7i	0.542413	+	0.394086i
$959$	6.99244e6	+	2.15205e7i	0.245517	+	0.755625i
$960$	−5.22668e6	+	3.79740e6i	−0.183041	+	0.132987i
$961$	6.23702e6	−	1.91956e7i	0.217855	−	0.670490i
$962$	1.11736e6	+	3.43889e6i	0.0389275	+	0.119807i
$963$	4.48201e6	+	1.37942e7i	0.155742	+	0.479326i
$964$	738423.	+	2.27263e6i	0.0255925	+	0.0787655i
$965$	1.08078e7	+	3.32631e7i	0.373611	+	1.14986i
$966$	−4.88929e6	+	1.50477e7i	−0.168579	+	0.518833i
$967$	2.90323e7	−	2.10932e7i	0.998425	−	0.725399i	0.0366755	−	0.999327i	$-0.488323\pi$
$967$	2.90323e7	−	2.10932e7i	0.998425	−	0.725399i	0.961750	+	0.273929i	$0.0883232\pi$
$968$	7.92541e6	+	2.43919e7i	0.271853	+	0.836676i
$969$	−2.17812e6	−	1.58249e6i	−0.0745198	−	0.0541418i
$970$	−3.98244e6			−0.135900
$971$	9.32800e6	−	2.87086e7i	0.317498	−	0.977157i	−0.657217	−	0.753702i	$-0.728266\pi$
$971$	9.32800e6	−	2.87086e7i	0.317498	−	0.977157i	0.974714	−	0.223455i	$-0.0717337\pi$
$972$	1.32929e7	+	9.65784e6i	0.451287	+	0.327880i
$973$	−1.08907e7	+	7.91259e6i	−0.368787	+	0.267939i
$974$	−1.92345e7	+	1.39747e7i	−0.649657	+	0.472003i
$975$	2.17560e7			0.732939
$976$	3.75335e6	−	2.72697e6i	0.126123	−	0.0916339i
$977$	−9.16942e6	−	2.82206e7i	−0.307330	−	0.945866i	−0.978797	−	0.204831i	$-0.934335\pi$
$977$	−9.16942e6	−	2.82206e7i	−0.307330	−	0.945866i	0.671467	−	0.741035i	$-0.265665\pi$
$978$	3.61910e6	−	1.11385e7i	0.120991	−	0.372373i
$979$	−5.53427e7	−	4.02088e7i	−1.84545	−	1.34080i
$980$	9.57664e6	+	6.95784e6i	0.318528	+	0.231424i
$981$	−3.30313e7			−1.09585
$982$	−2.30434e6	+	7.09202e6i	−0.0762548	+	0.234688i
$983$	1.24769e7			0.411835			0.205917	−	0.978569i	$-0.433982\pi$
$983$	1.24769e7			0.411835			0.205917	+	0.978569i	$0.433982\pi$
$984$	−6.30558e6	−	1.22248e7i	−0.207605	−	0.402490i
$985$	1.58103e7			0.519218
$986$	−7.41378e6	+	2.28173e7i	−0.242855	+	0.747431i
$987$	−7.12266e6			−0.232729
$988$	517404.	+	375916.i	0.0168631	+	0.0122518i
$989$	−8.61210e6	−	6.25706e6i	−0.279974	−	0.203413i
$990$	1.13953e7	−	3.50711e7i	0.369520	−	1.13726i
$991$	−410364.	−	1.26297e6i	−0.0132735	−	0.0408516i	0.944200	−	0.329372i	$-0.106837\pi$
$991$	−410364.	−	1.26297e6i	−0.0132735	−	0.0408516i	−0.957474	+	0.288520i	$0.906837\pi$
$992$	5.78793e6	−	4.20518e6i	0.186743	−	0.135677i
$993$	4.06023e6			0.130671
$994$	6.43304e6	−	4.67388e6i	0.206514	−	0.150042i
$995$	−1.49430e7	+	1.08567e7i	−0.478497	+	0.347648i
$996$	−3.62720e6	−	2.63532e6i	−0.115857	−	0.0841752i
$997$	−3.18333e6	+	9.79729e6i	−0.101425	+	0.312153i	−0.988875	−	0.148751i	$-0.952475\pi$
$997$	−3.18333e6	+	9.79729e6i	−0.101425	+	0.312153i	0.887450	+	0.460904i	$0.152475\pi$
$998$	3.18062e7			1.01085
$999$	3.64381e6	+	2.64738e6i	0.115516	+	0.0839273i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	82.6.d.a.57.8	✓	36
41.18	even	5	inner	82.6.d.a.59.8	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
82.6.d.a.57.8	✓	36	1.1	even	1	trivial
82.6.d.a.59.8	yes	36	41.18	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:	\( N \)	\(=\)	\( 82 = 2 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	82.d (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.23607 - 3.80423i) q^{2} +19.9677 q^{3} +(-12.9443 - 9.40456i) q^{4} +(-63.9053 - 46.4299i) q^{5} +(24.6815 - 75.9618i) q^{6} +(-26.6561 - 82.0390i) q^{7} +(-51.7771 + 37.6183i) q^{8} +155.710 q^{9} +(-255.621 + 185.720i) q^{10} +(-606.379 + 440.560i) q^{11} +(-258.468 - 187.788i) q^{12} +(108.100 - 332.699i) q^{13} -345.044 q^{14} +(-1276.04 - 927.100i) q^{15} +(79.1084 + 243.470i) q^{16} +(954.652 - 693.595i) q^{17} +(192.469 - 592.358i) q^{18} +(-35.3093 - 108.671i) q^{19} +(390.554 + 1202.00i) q^{20} +(-532.262 - 1638.13i) q^{21} +(926.464 + 2851.36i) q^{22} +(709.648 - 2184.07i) q^{23} +(-1033.87 + 751.151i) q^{24} +(962.472 + 2962.18i) q^{25} +(-1132.04 - 822.477i) q^{26} -1742.98 q^{27} +(-426.498 + 1312.62i) q^{28} +(-4112.14 - 2987.64i) q^{29} +(-5104.18 + 3708.40i) q^{30} +(5652.28 - 4106.62i) q^{31} +1024.00 q^{32} +(-12108.0 + 8796.98i) q^{33} +(-1458.58 - 4489.04i) q^{34} +(-2105.60 + 6480.37i) q^{35} +(-2015.56 - 1464.39i) q^{36} +(-2090.57 - 1518.89i) q^{37} -457.054 q^{38} +(2158.52 - 6643.24i) q^{39} +5055.44 q^{40} +(-1630.95 + 10639.4i) q^{41} -6889.74 q^{42} +(1432.43 - 4408.56i) q^{43} +11992.4 q^{44} +(-9950.72 - 7229.62i) q^{45} +(-7431.53 - 5399.33i) q^{46} +(1277.86 - 3932.84i) q^{47} +(1579.61 + 4861.55i) q^{48} +(7577.29 - 5505.23i) q^{49} +12458.5 q^{50} +(19062.2 - 13849.5i) q^{51} +(-4528.17 + 3289.91i) q^{52} +(21689.5 + 15758.3i) q^{53} +(-2154.44 + 6630.67i) q^{54} +59206.0 q^{55} +(4466.34 + 3244.99i) q^{56} +(-705.047 - 2169.91i) q^{57} +(-16448.5 + 11950.6i) q^{58} +(9536.50 - 29350.3i) q^{59} +(7798.49 + 24001.3i) q^{60} +(-5600.21 - 17235.7i) q^{61} +(-8635.91 - 26578.6i) q^{62} +(-4150.63 - 12774.3i) q^{63} +(1265.73 - 3895.53i) q^{64} +(-22355.4 + 16242.1i) q^{65} +(18499.4 + 56935.3i) q^{66} +(-55072.9 - 40012.8i) q^{67} -18880.2 q^{68} +(14170.1 - 43611.0i) q^{69} +(22050.1 + 16020.4i) q^{70} +(-18644.1 + 13545.8i) q^{71} +(-8062.23 + 5857.55i) q^{72} +62099.9 q^{73} +(-8362.28 + 6075.55i) q^{74} +(19218.4 + 59148.1i) q^{75} +(-564.949 + 1738.74i) q^{76} +(52306.8 + 38003.1i) q^{77} +(-22604.3 - 16423.0i) q^{78} +69089.2 q^{79} +(6248.87 - 19232.0i) q^{80} -72640.9 q^{81} +(38458.6 + 19355.5i) q^{82} +14033.5 q^{83} +(-8516.19 + 26210.1i) q^{84} -93210.9 q^{85} +(-15000.6 - 10898.6i) q^{86} +(-82110.1 - 59656.5i) q^{87} +(14823.4 - 45621.8i) q^{88} +(28203.2 + 86800.6i) q^{89} +(-39802.9 + 28918.5i) q^{90} -30175.8 q^{91} +(-29726.1 + 21597.3i) q^{92} +(112863. - 81999.9i) q^{93} +(-13381.9 - 9722.50i) q^{94} +(-2789.13 + 8584.06i) q^{95} +20447.0 q^{96} +(10196.9 + 7408.48i) q^{97} +(-11577.1 - 35630.6i) q^{98} +(-94419.5 + 68599.8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 36 q^{2} + 20 q^{3} - 144 q^{4} - 98 q^{5} - 20 q^{6} + 120 q^{7} - 576 q^{8} + 2876 q^{9} - 392 q^{10} - 436 q^{11} - 80 q^{12} - 617 q^{13} + 280 q^{14} + 789 q^{15} - 2304 q^{16} + 1359 q^{17}+ \cdots + 261106 q^{99}+O(q^{100}) \) 36 * q - 36 * q^2 + 20 * q^3 - 144 * q^4 - 98 * q^5 - 20 * q^6 + 120 * q^7 - 576 * q^8 + 2876 * q^9 - 392 * q^10 - 436 * q^11 - 80 * q^12 - 617 * q^13 + 280 * q^14 + 789 * q^15 - 2304 * q^16 + 1359 * q^17 - 4976 * q^18 + 4876 * q^19 + 352 * q^20 - 13529 * q^21 + 2476 * q^22 + 819 * q^23 - 320 * q^24 - 10487 * q^25 - 2088 * q^26 + 1592 * q^27 + 1920 * q^28 + 5249 * q^29 + 3156 * q^30 - 2992 * q^31 + 36864 * q^32 - 5676 * q^33 + 4136 * q^34 + 21607 * q^35 - 3104 * q^36 - 11508 * q^37 + 10664 * q^38 + 8144 * q^39 + 9728 * q^40 - 44187 * q^41 + 97464 * q^42 - 88677 * q^43 - 5856 * q^44 - 45045 * q^45 - 6864 * q^46 - 56670 * q^47 - 1280 * q^48 - 59417 * q^49 + 88352 * q^50 - 26259 * q^51 - 8352 * q^52 + 21963 * q^53 + 29968 * q^54 + 128202 * q^55 - 9920 * q^56 + 16428 * q^57 + 20996 * q^58 - 77668 * q^59 - 7856 * q^60 - 168787 * q^61 - 34428 * q^62 + 247961 * q^63 - 36864 * q^64 - 74533 * q^65 + 48036 * q^66 - 40269 * q^67 - 76576 * q^68 + 242095 * q^69 - 20492 * q^70 - 44665 * q^71 - 12416 * q^72 - 76360 * q^73 - 46032 * q^74 - 154234 * q^75 + 78016 * q^76 - 8441 * q^77 - 71044 * q^78 + 230228 * q^79 + 5632 * q^80 + 184156 * q^81 + 36752 * q^82 + 673200 * q^83 - 216464 * q^84 - 130180 * q^85 + 194192 * q^86 - 398341 * q^87 + 39616 * q^88 - 409131 * q^89 - 180180 * q^90 + 355046 * q^91 - 27456 * q^92 - 51949 * q^93 + 234960 * q^94 - 588753 * q^95 + 20480 * q^96 + 138500 * q^97 - 43248 * q^98 + 261106 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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