LMFDB - Embedded newform 43.6.c.a.36.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,6,Mod(6,43)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(43, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4]))

N = Newforms(chi, 6, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("43.6");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	43.c (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$6.89650425196$
Analytic rank:	$0$
Dimension:	$34$
Relative dimension:	$17$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			36.14
Character	$\chi$	$=$	43.36
Dual form			43.6.c.a.6.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+6.70145 q^{2} +(-7.23861 - 12.5376i) q^{3} +12.9095 q^{4} +(-40.0400 - 69.3513i) q^{5} +(-48.5092 - 84.0205i) q^{6} +(-74.8208 + 129.593i) q^{7} -127.934 q^{8} +(16.7049 - 28.9338i) q^{9} +O(q^{10})$	\(q+6.70145 q^{2} +(-7.23861 - 12.5376i) q^{3} +12.9095 q^{4} +(-40.0400 - 69.3513i) q^{5} +(-48.5092 - 84.0205i) q^{6} +(-74.8208 + 129.593i) q^{7} -127.934 q^{8} +(16.7049 - 28.9338i) q^{9} +(-268.326 - 464.754i) q^{10} +126.467 q^{11} +(-93.4468 - 161.855i) q^{12} +(420.937 - 729.085i) q^{13} +(-501.408 + 868.464i) q^{14} +(-579.668 + 1004.01i) q^{15} -1270.45 q^{16} +(1123.97 - 1946.77i) q^{17} +(111.947 - 193.898i) q^{18} +(1462.95 + 2533.91i) q^{19} +(-516.896 - 895.290i) q^{20} +2166.40 q^{21} +847.515 q^{22} +(-1996.77 - 3458.50i) q^{23} +(926.066 + 1603.99i) q^{24} +(-1643.90 + 2847.32i) q^{25} +(2820.89 - 4885.93i) q^{26} -4001.65 q^{27} +(-965.898 + 1672.99i) q^{28} +(-1138.80 + 1972.46i) q^{29} +(-3884.62 + 6728.36i) q^{30} +(1142.42 + 1978.74i) q^{31} -4419.96 q^{32} +(-915.448 - 1585.60i) q^{33} +(7532.23 - 13046.2i) q^{34} +11983.3 q^{35} +(215.652 - 373.520i) q^{36} +(1256.01 + 2175.48i) q^{37} +(9803.91 + 16980.9i) q^{38} -12188.0 q^{39} +(5122.48 + 8872.40i) q^{40} +192.193 q^{41} +14518.0 q^{42} +(12115.9 - 462.816i) q^{43} +1632.63 q^{44} -2675.46 q^{45} +(-13381.2 - 23177.0i) q^{46} -6423.78 q^{47} +(9196.29 + 15928.4i) q^{48} +(-2792.80 - 4837.28i) q^{49} +(-11016.5 + 19081.2i) q^{50} -32543.9 q^{51} +(5434.09 - 9412.12i) q^{52} +(-11360.2 - 19676.4i) q^{53} -26816.9 q^{54} +(-5063.75 - 8770.67i) q^{55} +(9572.14 - 16579.4i) q^{56} +(21179.5 - 36684.0i) q^{57} +(-7631.60 + 13218.3i) q^{58} -17318.6 q^{59} +(-7483.22 + 12961.3i) q^{60} +(15021.4 - 26017.8i) q^{61} +(7655.91 + 13260.4i) q^{62} +(2499.75 + 4329.70i) q^{63} +11034.2 q^{64} -67417.3 q^{65} +(-6134.83 - 10625.8i) q^{66} +(726.753 + 1258.77i) q^{67} +(14509.9 - 25131.8i) q^{68} +(-28907.7 + 50069.5i) q^{69} +80305.5 q^{70} +(34539.7 - 59824.5i) q^{71} +(-2137.13 + 3701.62i) q^{72} +(-6368.40 + 11030.4i) q^{73} +(8417.12 + 14578.9i) q^{74} +47598.2 q^{75} +(18886.0 + 32711.5i) q^{76} +(-9462.38 + 16389.3i) q^{77} -81677.4 q^{78} +(13220.7 - 22898.9i) q^{79} +(50868.7 + 88107.2i) q^{80} +(24907.1 + 43140.4i) q^{81} +1287.98 q^{82} +(14962.4 + 25915.6i) q^{83} +27967.1 q^{84} -180015. q^{85} +(81193.9 - 3101.54i) q^{86} +32973.3 q^{87} -16179.5 q^{88} +(31589.4 + 54714.4i) q^{89} -17929.5 q^{90} +(62989.7 + 109101. i) q^{91} +(-25777.2 - 44647.5i) q^{92} +(16539.1 - 28646.6i) q^{93} -43048.7 q^{94} +(117153. - 202915. i) q^{95} +(31994.4 + 55415.9i) q^{96} +131247. q^{97} +(-18715.9 - 32416.8i) q^{98} +(2112.63 - 3659.17i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 14 q^{2} - 14 q^{3} + 454 q^{4} + 71 q^{5} + 15 q^{6} + 225 q^{7} - 936 q^{8} - 1011 q^{9}+O(q^{10}) $ 34 * q - 14 * q^2 - 14 * q^3 + 454 * q^4 + 71 * q^5 + 15 * q^6 + 225 * q^7 - 936 * q^8 - 1011 * q^9	\( 34 q - 14 q^{2} - 14 q^{3} + 454 q^{4} + 71 q^{5} + 15 q^{6} + 225 q^{7} - 936 q^{8} - 1011 q^{9} - 317 q^{10} + 1326 q^{11} - 648 q^{12} + 1006 q^{13} - 1272 q^{14} + 683 q^{15} + 3574 q^{16} + 200 q^{17} + 1861 q^{18} + 3361 q^{19} + 3825 q^{20} - 1320 q^{21} - 8768 q^{22} + 560 q^{23} - 7382 q^{24} - 3232 q^{25} - 3201 q^{26} - 122 q^{27} + 13934 q^{28} + 8887 q^{29} - 19449 q^{30} - 6749 q^{31} - 19086 q^{32} + 7106 q^{33} + 8423 q^{34} + 31118 q^{35} - 14112 q^{36} - 4514 q^{37} + 7072 q^{38} - 5404 q^{39} - 18519 q^{40} - 28996 q^{41} + 58118 q^{42} - 14998 q^{43} + 71050 q^{44} - 92096 q^{45} + 20052 q^{46} - 10742 q^{47} + 32927 q^{48} + 7472 q^{49} + 20362 q^{50} + 20250 q^{51} + 59532 q^{52} - 50572 q^{53} - 230084 q^{54} + 38544 q^{55} - 40355 q^{56} - 18087 q^{57} - 33436 q^{58} + 112654 q^{59} + 134093 q^{60} - 20120 q^{61} - 31491 q^{62} + 188227 q^{63} + 125164 q^{64} - 36578 q^{65} + 8803 q^{66} - 73824 q^{67} - 128456 q^{68} + 8005 q^{69} - 141610 q^{70} + 142842 q^{71} + 98466 q^{72} - 91624 q^{73} - 99720 q^{74} + 298358 q^{75} + 258288 q^{76} + 68051 q^{77} - 201116 q^{78} + 99734 q^{79} - 31261 q^{80} - 28441 q^{81} - 147772 q^{82} - 47340 q^{83} - 624232 q^{84} - 71734 q^{85} - 115526 q^{86} - 215924 q^{87} - 720684 q^{88} + 60402 q^{89} + 676108 q^{90} + 164172 q^{91} + 78997 q^{92} - 40793 q^{93} - 341874 q^{94} + 123541 q^{95} - 442140 q^{96} + 318476 q^{97} + 217473 q^{98} - 134770 q^{99}+O(q^{100}) \) 34 * q - 14 * q^2 - 14 * q^3 + 454 * q^4 + 71 * q^5 + 15 * q^6 + 225 * q^7 - 936 * q^8 - 1011 * q^9 - 317 * q^10 + 1326 * q^11 - 648 * q^12 + 1006 * q^13 - 1272 * q^14 + 683 * q^15 + 3574 * q^16 + 200 * q^17 + 1861 * q^18 + 3361 * q^19 + 3825 * q^20 - 1320 * q^21 - 8768 * q^22 + 560 * q^23 - 7382 * q^24 - 3232 * q^25 - 3201 * q^26 - 122 * q^27 + 13934 * q^28 + 8887 * q^29 - 19449 * q^30 - 6749 * q^31 - 19086 * q^32 + 7106 * q^33 + 8423 * q^34 + 31118 * q^35 - 14112 * q^36 - 4514 * q^37 + 7072 * q^38 - 5404 * q^39 - 18519 * q^40 - 28996 * q^41 + 58118 * q^42 - 14998 * q^43 + 71050 * q^44 - 92096 * q^45 + 20052 * q^46 - 10742 * q^47 + 32927 * q^48 + 7472 * q^49 + 20362 * q^50 + 20250 * q^51 + 59532 * q^52 - 50572 * q^53 - 230084 * q^54 + 38544 * q^55 - 40355 * q^56 - 18087 * q^57 - 33436 * q^58 + 112654 * q^59 + 134093 * q^60 - 20120 * q^61 - 31491 * q^62 + 188227 * q^63 + 125164 * q^64 - 36578 * q^65 + 8803 * q^66 - 73824 * q^67 - 128456 * q^68 + 8005 * q^69 - 141610 * q^70 + 142842 * q^71 + 98466 * q^72 - 91624 * q^73 - 99720 * q^74 + 298358 * q^75 + 258288 * q^76 + 68051 * q^77 - 201116 * q^78 + 99734 * q^79 - 31261 * q^80 - 28441 * q^81 - 147772 * q^82 - 47340 * q^83 - 624232 * q^84 - 71734 * q^85 - 115526 * q^86 - 215924 * q^87 - 720684 * q^88 + 60402 * q^89 + 676108 * q^90 + 164172 * q^91 + 78997 * q^92 - 40793 * q^93 - 341874 * q^94 + 123541 * q^95 - 442140 * q^96 + 318476 * q^97 + 217473 * q^98 - 134770 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/43\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	6.70145			1.18466			0.592330	−	0.805695i	$-0.298208\pi$
$2$	6.70145			1.18466			0.592330	+	0.805695i	$0.298208\pi$
$3$	−7.23861	−	12.5376i	−0.464357	−	0.804291i	0.534815	−	0.844969i	$-0.320381\pi$
$3$	−7.23861	−	12.5376i	−0.464357	−	0.804291i	−0.999172	+	0.0406787i	$0.987048\pi$
$4$	12.9095			0.403422
$5$	−40.0400	−	69.3513i	−0.716257	−	1.24059i	−0.962473	−	0.271378i	$-0.912521\pi$
$5$	−40.0400	−	69.3513i	−0.716257	−	1.24059i	0.246216	−	0.969215i	$-0.420813\pi$
$6$	−48.5092	−	84.0205i	−0.550106	−	0.952812i
$7$	−74.8208	+	129.593i	−0.577135	+	0.999627i	0.418671	+	0.908138i	$0.362496\pi$
$7$	−74.8208	+	129.593i	−0.577135	+	0.999627i	−0.995806	+	0.0914889i	$0.970837\pi$
$8$	−127.934			−0.706743
$9$	16.7049	−	28.9338i	0.0687445	−	0.119069i
$10$	−268.326	−	464.754i	−0.848522	−	1.46968i
$11$	126.467			0.315135			0.157567	−	0.987508i	$-0.449635\pi$
$11$	126.467			0.315135			0.157567	+	0.987508i	$0.449635\pi$
$12$	−93.4468	−	161.855i	−0.187332	−	0.324468i
$13$	420.937	−	729.085i	0.690811	−	1.19652i	−0.280762	−	0.959777i	$-0.590587\pi$
$13$	420.937	−	729.085i	0.690811	−	1.19652i	0.971573	−	0.236742i	$-0.0760796\pi$
$14$	−501.408	+	868.464i	−0.683709	+	1.18422i
$15$	−579.668	+	1004.01i	−0.665198	+	1.15216i
$16$	−1270.45			−1.24067
$17$	1123.97	−	1946.77i	0.943261	−	1.63378i	0.184066	−	0.982914i	$-0.441074\pi$
$17$	1123.97	−	1946.77i	0.943261	−	1.63378i	0.759195	−	0.650863i	$-0.225593\pi$
$18$	111.947	−	193.898i	0.0814389	−	0.141056i
$19$	1462.95	+	2533.91i	0.929707	+	1.61030i	0.783810	+	0.621000i	$0.213273\pi$
$19$	1462.95	+	2533.91i	0.929707	+	1.61030i	0.145897	+	0.989300i	$0.453393\pi$
$20$	−516.896	−	895.290i	−0.288953	−	0.500482i
$21$	2166.40			1.07199
$22$	847.515			0.373328
$23$	−1996.77	−	3458.50i	−0.787060	−	1.36323i	−0.927761	−	0.373176i	$-0.878269\pi$
$23$	−1996.77	−	3458.50i	−0.787060	−	1.36323i	0.140701	−	0.990052i	$-0.455064\pi$
$24$	926.066	+	1603.99i	0.328181	+	0.568427i
$25$	−1643.90	+	2847.32i	−0.526048	+	0.911142i
$26$	2820.89	−	4885.93i	0.818377	−	1.41747i
$27$	−4001.65			−1.05640
$28$	−965.898	+	1672.99i	−0.232829	+	0.403271i
$29$	−1138.80	+	1972.46i	−0.251450	+	0.435524i	−0.963925	−	0.266173i	$-0.914241\pi$
$29$	−1138.80	+	1972.46i	−0.251450	+	0.435524i	0.712475	+	0.701697i	$0.247574\pi$
$30$	−3884.62	+	6728.36i	−0.788034	+	1.36492i
$31$	1142.42	+	1978.74i	0.213513	+	0.369815i	0.952811	−	0.303563i	$-0.0981763\pi$
$31$	1142.42	+	1978.74i	0.213513	+	0.369815i	−0.739299	+	0.673377i	$0.764843\pi$
$32$	−4419.96			−0.763033
$33$	−915.448	−	1585.60i	−0.146335	−	0.253460i
$34$	7532.23	−	13046.2i	1.11745	−	1.93547i
$35$	11983.3			1.65351
$36$	215.652	−	373.520i	0.0277330	−	0.0480350i
$37$	1256.01	+	2175.48i	0.150831	+	0.261247i	0.931533	−	0.363656i	$-0.118472\pi$
$37$	1256.01	+	2175.48i	0.150831	+	0.261247i	−0.780702	+	0.624903i	$0.785138\pi$
$38$	9803.91	+	16980.9i	1.10139	+	1.90766i
$39$	−12188.0			−1.28313
$40$	5122.48	+	8872.40i	0.506210	+	0.876781i
$41$	192.193			0.0178558			0.00892789	−	0.999960i	$-0.497158\pi$
$41$	192.193			0.0178558			0.00892789	+	0.999960i	$0.497158\pi$
$42$	14518.0			1.26994
$43$	12115.9	−	462.816i	0.999271	−	0.0381713i
$43$	12115.9	−	462.816i	0.999271	−	0.0381713i
$44$	1632.63			0.127132
$45$	−2675.46			−0.196955
$46$	−13381.2	−	23177.0i	−0.932399	−	1.61496i
$47$	−6423.78			−0.424176			−0.212088	−	0.977251i	$-0.568026\pi$
$47$	−6423.78			−0.424176			−0.212088	+	0.977251i	$0.568026\pi$
$48$	9196.29	+	15928.4i	0.576115	+	0.997861i
$49$	−2792.80	−	4837.28i	−0.166169	−	0.287813i
$50$	−11016.5	+	19081.2i	−0.623188	+	1.07939i
$51$	−32543.9			−1.75204
$52$	5434.09	−	9412.12i	0.278688	−	0.482702i
$53$	−11360.2	−	19676.4i	−0.555515	−	0.962180i	−0.997863	−	0.0653366i	$-0.979188\pi$
$53$	−11360.2	−	19676.4i	−0.555515	−	0.962180i	0.442348	−	0.896843i	$-0.354145\pi$
$54$	−26816.9			−1.25148
$55$	−5063.75	−	8770.67i	−0.225718	−	0.390954i
$56$	9572.14	−	16579.4i	0.407886	−	0.706479i
$57$	21179.5	−	36684.0i	0.863433	−	1.49551i
$58$	−7631.60	+	13218.3i	−0.297883	+	0.515948i
$59$	−17318.6			−0.647714			−0.323857	−	0.946106i	$-0.604980\pi$
$59$	−17318.6			−0.647714			−0.323857	+	0.946106i	$0.604980\pi$
$60$	−7483.22	+	12961.3i	−0.268355	+	0.464805i
$61$	15021.4	−	26017.8i	0.516875	−	0.895253i	−0.482933	−	0.875657i	$-0.660429\pi$
$61$	15021.4	−	26017.8i	0.516875	−	0.895253i	0.999808	−	0.0195959i	$-0.00623798\pi$
$62$	7655.91	+	13260.4i	0.252940	+	0.438105i
$63$	2499.75	+	4329.70i	0.0793497	+	0.137438i
$64$	11034.2			0.336737
$65$	−67417.3			−1.97919
$66$	−6134.83	−	10625.8i	−0.173358	−	0.300264i
$67$	726.753	+	1258.77i	0.0197788	+	0.0342579i	0.875745	−	0.482773i	$-0.160370\pi$
$67$	726.753	+	1258.77i	0.0197788	+	0.0342579i	−0.855967	+	0.517031i	$0.827037\pi$
$68$	14509.9	−	25131.8i	0.380532	−	0.659101i
$69$	−28907.7	+	50069.5i	−0.730954	+	1.26605i
$70$	80305.5			1.95885
$71$	34539.7	−	59824.5i	0.813154	−	1.40842i	−0.0974922	−	0.995236i	$-0.531082\pi$
$71$	34539.7	−	59824.5i	0.813154	−	1.40842i	0.910646	−	0.413187i	$-0.135585\pi$
$72$	−2137.13	+	3701.62i	−0.0485847	+	0.0841512i
$73$	−6368.40	+	11030.4i	−0.139870	+	0.242261i	−0.927447	−	0.373954i	$-0.878002\pi$
$73$	−6368.40	+	11030.4i	−0.139870	+	0.242261i	0.787578	+	0.616216i	$0.211335\pi$
$74$	8417.12	+	14578.9i	0.178683	+	0.309489i
$75$	47598.2			0.977097
$76$	18886.0	+	32711.5i	0.375064	+	0.649630i
$77$	−9462.38	+	16389.3i	−0.181875	+	0.315017i
$78$	−81677.4			−1.52008
$79$	13220.7	−	22898.9i	0.238334	−	0.412807i	−0.721902	−	0.691995i	$-0.756732\pi$
$79$	13220.7	−	22898.9i	0.238334	−	0.412807i	0.960236	+	0.279188i	$0.0900653\pi$
$80$	50868.7	+	88107.2i	0.888640	+	1.53917i
$81$	24907.1	+	43140.4i	0.421804	+	0.730586i
$82$	1287.98			0.0211530
$83$	14962.4	+	25915.6i	0.238399	+	0.412920i	0.960255	−	0.279124i	$-0.0900439\pi$
$83$	14962.4	+	25915.6i	0.238399	+	0.412920i	−0.721856	+	0.692044i	$0.756711\pi$
$84$	27967.1			0.432463
$85$	−180015.			−2.70247
$86$	81193.9	−	3101.54i	1.18380	−	0.0452201i
$87$	32973.3			0.467051
$88$	−16179.5			−0.222719
$89$	31589.4	+	54714.4i	0.422733	+	0.732195i	0.996206	−	0.0870298i	$-0.0277375\pi$
$89$	31589.4	+	54714.4i	0.422733	+	0.732195i	−0.573473	+	0.819225i	$0.694404\pi$
$90$	−17929.5			−0.233325
$91$	62989.7	+	109101.i	0.797382	+	1.38111i
$92$	−25777.2	−	44647.5i	−0.317517	−	0.549955i
$93$	16539.1	−	28646.6i	0.198292	−	0.343452i
$94$	−43048.7			−0.502505
$95$	117153.	−	202915.i	1.33182	−	2.30678i
$96$	31994.4	+	55415.9i	0.354320	+	0.613700i
$97$	131247.			1.41632			0.708159	−	0.706053i	$-0.249526\pi$
$97$	131247.			1.41632			0.708159	+	0.706053i	$0.249526\pi$
$98$	−18715.9	−	32416.8i	−0.196854	−	0.340961i
$99$	2112.63	−	3659.17i	0.0216638	−	0.0375228i
$100$	−21221.9	+	36757.4i	−0.212219	+	0.367574i
$101$	−2685.19	+	4650.88i	−0.0261921	+	0.0453661i	−0.878824	−	0.477145i	$-0.841672\pi$
$101$	−2685.19	+	4650.88i	−0.0261921	+	0.0453661i	0.852632	+	0.522512i	$0.175005\pi$
$102$	−218092.			−2.07558
$103$	−19680.1	+	34086.9i	−0.182782	+	0.316588i	−0.942827	−	0.333282i	$-0.891844\pi$
$103$	−19680.1	+	34086.9i	−0.182782	+	0.316588i	0.760045	+	0.649871i	$0.225177\pi$
$104$	−53852.3	+	93274.9i	−0.488226	+	0.845632i
$105$	−86742.4	−	150242.i	−0.767818	−	1.32990i
$106$	−76129.7	−	131861.i	−0.658097	−	1.13986i
$107$	−28671.5			−0.242098			−0.121049	−	0.992647i	$-0.538626\pi$
$107$	−28671.5			−0.242098			−0.121049	+	0.992647i	$0.538626\pi$
$108$	−51659.2			−0.426176
$109$	64211.8	+	111218.i	0.517665	+	0.896621i	0.999789	+	0.0205189i	$0.00653183\pi$
$109$	64211.8	+	111218.i	0.517665	+	0.896621i	−0.482125	+	0.876103i	$0.660135\pi$
$110$	−33934.5	−	58776.2i	−0.267399	−	0.463148i
$111$	18183.6	−	31494.9i	0.140079	−	0.242624i
$112$	95056.0	−	164642.i	0.716035	−	1.24021i
$113$	−20570.7			−0.151549			−0.0757744	−	0.997125i	$-0.524143\pi$
$113$	−20570.7			−0.151549			−0.0757744	+	0.997125i	$0.524143\pi$
$114$	141933.	−	245836.i	1.02288	−	1.77167i
$115$	−159901.	+	276957.i	−1.12747	+	1.95284i
$116$	−14701.3	+	25463.4i	−0.101440	+	0.175700i
$117$	−14063.4	−	24358.6i	−0.0949789	−	0.164508i
$118$	−116060.			−0.767321
$119$	168193.	+	291318.i	1.08878	+	1.88582i
$120$	74159.3	−	128448.i	0.470124	−	0.814279i
$121$	−145057.			−0.900690
$122$	100665.	−	174357.i	0.612321	−	1.06057i
$123$	−1391.21	−	2409.65i	−0.00829146	−	0.0143612i
$124$	14748.1	+	25544.5i	0.0861356	+	0.149191i
$125$	13037.0			0.0746282
$126$	16752.0	+	29015.3i	0.0940025	+	0.162817i
$127$	98267.2			0.540629			0.270314	−	0.962772i	$-0.412872\pi$
$127$	98267.2			0.540629			0.270314	+	0.962772i	$0.412872\pi$
$128$	215384.			1.16195
$129$	−93504.7	−	148554.i	−0.494720	−	0.785979i
$130$	−451794.			−2.34467
$131$	94616.1			0.481711			0.240856	−	0.970561i	$-0.422572\pi$
$131$	94616.1			0.481711			0.240856	+	0.970561i	$0.422572\pi$
$132$	−11818.0	−	20469.3i	−0.0590348	−	0.102251i
$133$	−437837.			−2.14627
$134$	4870.30	+	8435.62i	0.0234312	+	0.0405840i
$135$	160226.	+	277519.i	0.756656	+	1.31057i
$136$	−143794.	+	249059.i	−0.666644	+	1.15466i
$137$	435056.			1.98036			0.990180	−	0.139800i	$-0.0446459\pi$
$137$	435056.			1.98036			0.990180	+	0.139800i	$0.0446459\pi$
$138$	−193723.	+	335539.i	−0.865933	+	1.49984i
$139$	−105765.	−	183191.i	−0.464309	−	0.804206i	0.534861	−	0.844940i	$-0.320364\pi$
$139$	−105765.	−	183191.i	−0.464309	−	0.804206i	−0.999170	+	0.0407336i	$0.987031\pi$
$140$	154698.			0.667060
$141$	46499.3	+	80539.1i	0.196969	+	0.341161i
$142$	231466.	−	400911.i	0.963312	−	1.66850i
$143$	53234.8	−	92205.4i	0.217699	−	0.377065i
$144$	−21222.7	+	36758.9i	−0.0852894	+	0.147726i
$145$	182390.			0.720411
$146$	−42677.6	+	73919.7i	−0.165698	+	0.286997i
$147$	−40432.1	+	70030.4i	−0.154324	+	0.267296i
$148$	16214.5	+	28084.3i	0.0608484	+	0.105393i
$149$	−141616.	−	245287.i	−0.522574	−	0.905125i	−0.999655	−	0.0262655i	$-0.991638\pi$
$149$	−141616.	−	245287.i	−0.522574	−	0.905125i	0.477081	−	0.878859i	$-0.341695\pi$
$150$	318977.			1.15753
$151$	17751.1			0.0633555			0.0316777	−	0.999498i	$-0.489915\pi$
$151$	17751.1			0.0633555			0.0316777	+	0.999498i	$0.489915\pi$
$152$	−187162.	−	324173.i	−0.657064	−	1.13807i
$153$	−37551.6	−	65041.3i	−0.129688	−	0.224626i
$154$	−63411.7	+	109832.i	−0.215461	+	0.373189i
$155$	91485.3	−	158457.i	0.305860	−	0.529764i
$156$	−157341.			−0.517643
$157$	79369.5	−	137472.i	0.256983	−	0.445107i	−0.708449	−	0.705762i	$-0.750605\pi$
$157$	79369.5	−	137472.i	0.256983	−	0.445107i	0.965432	+	0.260654i	$0.0839383\pi$
$158$	88597.8	−	153456.i	0.282345	−	0.489036i
$159$	−164464.	+	284860.i	−0.515915	+	0.893591i
$160$	176975.	+	306530.i	0.546528	+	0.946614i
$161$	597599.			1.81696
$162$	166914.	+	289103.i	0.499695	+	0.865496i
$163$	−104878.	+	181653.i	−0.309182	+	0.535518i	−0.978184	−	0.207742i	$-0.933388\pi$
$163$	−104878.	+	181653.i	−0.309182	+	0.535518i	0.669002	+	0.743261i	$0.266722\pi$
$164$	2481.12			0.00720341
$165$	−73309.0	+	126975.i	−0.209627	+	0.363085i
$166$	100270.	+	173672.i	0.282422	+	0.489170i
$167$	102954.	+	178321.i	0.285661	+	0.494779i	0.972769	−	0.231776i	$-0.0744537\pi$
$167$	102954.	+	178321.i	0.285661	+	0.494779i	−0.687109	+	0.726555i	$0.741120\pi$
$168$	−277156.			−0.757620
$169$	−168730.	−	292249.i	−0.454439	−	0.787112i
$170$	−1.20636e6			−3.20151
$171$	97754.0			0.255649
$172$	156410.	−	5974.72i	0.403128	−	0.0153991i
$173$	192007.			0.487755			0.243877	−	0.969806i	$-0.421581\pi$
$173$	192007.			0.487755			0.243877	+	0.969806i	$0.421581\pi$
$174$	220969.			0.553296
$175$	−245996.	−	426077.i	−0.607201	−	1.05170i
$176$	−160670.			−0.390979
$177$	125363.	+	217135.i	0.300771	+	0.520950i
$178$	211695.	+	366666.i	0.500795	+	0.867402i
$179$	−159511.	+	276280.i	−0.372098	+	0.644492i	−0.989888	−	0.141851i	$-0.954695\pi$
$179$	−159511.	+	276280.i	−0.372098	+	0.644492i	0.617790	+	0.786343i	$0.288028\pi$
$180$	−34538.8			−0.0794559
$181$	42272.5	−	73218.1i	0.0959094	−	0.166120i	−0.814078	−	0.580755i	$-0.802757\pi$
$181$	42272.5	−	73218.1i	0.0959094	−	0.166120i	0.909988	+	0.414635i	$0.136091\pi$
$182$	422123.	+	731138.i	0.944627	+	1.63614i
$183$	−434936.			−0.960058
$184$	255455.	+	442461.i	0.556249	+	0.963452i
$185$	100582.	−	174212.i	0.216067	−	0.374239i
$186$	110836.	−	191974.i	0.234909	−	0.406874i
$187$	142145.	−	246203.i	0.297255	−	0.514860i
$188$	−82927.7			−0.171122
$189$	299407.	−	518587.i	0.609687	−	1.05601i
$190$	785097.	−	1.35983e6i	1.57775	−	2.73275i
$191$	−103436.	−	179157.i	−0.205158	−	0.355344i	0.745025	−	0.667037i	$-0.232438\pi$
$191$	−103436.	−	179157.i	−0.205158	−	0.355344i	−0.950183	+	0.311692i	$0.899104\pi$
$192$	−79872.3	−	138343.i	−0.156366	−	0.270834i
$193$	−860957.			−1.66375			−0.831876	−	0.554962i	$-0.812733\pi$
$193$	−860957.			−1.66375			−0.831876	+	0.554962i	$0.812733\pi$
$194$	879548.			1.67786
$195$	488008.	+	845254.i	0.919052	+	1.59185i
$196$	−36053.7	−	62446.8i	−0.0670362	−	0.116110i
$197$	−155564.	+	269445.i	−0.285591	+	0.494657i	−0.972752	−	0.231847i	$-0.925523\pi$
$197$	−155564.	+	269445.i	−0.285591	+	0.494657i	0.687162	+	0.726505i	$0.258856\pi$
$198$	14157.7	−	24521.8i	0.0256643	−	0.0444518i
$199$	−109969.			−0.196851			−0.0984254	−	0.995144i	$-0.531381\pi$
$199$	−109969.			−0.196851			−0.0984254	+	0.995144i	$0.531381\pi$
$200$	210311.	−	364269.i	0.371781	−	0.643943i
$201$	10521.4	−	18223.6i	0.0183689	−	0.0318158i
$202$	−17994.6	+	31167.6i	−0.0310288	+	0.0537434i
$203$	−170411.	−	295161.i	−0.290241	−	0.502712i
$204$	−420125.			−0.706811
$205$	−7695.42	−	13328.9i	−0.0127893	−	0.0221518i
$206$	−131885.	+	228432.i	−0.216535	+	0.375050i
$207$	−133423.			−0.216424
$208$	−534779.	+	926265.i	−0.857070	+	1.48449i
$209$	185016.	+	320456.i	0.292983	+	0.507462i
$210$	−581301.	−	1.00684e6i	−0.909604	−	1.57548i
$211$	−922584.			−1.42659			−0.713296	−	0.700863i	$-0.752798\pi$
$211$	−922584.			−1.42659			−0.713296	+	0.700863i	$0.752798\pi$
$212$	−146654.	−	254012.i	−0.224107	−	0.388164i
$213$	−1.00008e6			−1.51038
$214$	−192141.			−0.286804
$215$	−517216.	−	821720.i	−0.763090	−	1.21235i
$216$	511948.			0.746605
$217$	−341909.			−0.492902
$218$	430312.	+	745323.i	0.613257	+	1.06219i
$219$	184394.			0.259798
$220$	−65370.4	−	113225.i	−0.0910593	−	0.157719i
$221$	−946241.	−	1.63894e6i	−1.30323	−	2.25726i
$222$	121857.	−	211062.i	0.165946	−	0.287427i
$223$	1.06974e6			1.44051			0.720254	−	0.693711i	$-0.244025\pi$
$223$	1.06974e6			1.44051			0.720254	+	0.693711i	$0.244025\pi$
$224$	330705.	−	572798.i	0.440373	−	0.762748i
$225$	54922.4	+	95128.4i	0.0723258	+	0.125272i
$226$	−137853.			−0.179534
$227$	22321.9	+	38662.7i	0.0287520	+	0.0497999i	0.880043	−	0.474893i	$-0.157513\pi$
$227$	22321.9	+	38662.7i	0.0287520	+	0.0497999i	−0.851291	+	0.524693i	$0.824180\pi$
$228$	273417.	−	473571.i	0.348327	−	0.603321i
$229$	−45194.2	+	78278.6i	−0.0569500	+	0.0986403i	−0.893095	−	0.449868i	$-0.851471\pi$
$229$	−45194.2	+	78278.6i	−0.0569500	+	0.0986403i	0.836145	+	0.548509i	$0.184804\pi$
$230$	−1.07157e6	+	1.85601e6i	−1.33567	+	2.31346i
$231$	273978.			0.337820
$232$	145691.	−	252344.i	0.177711	−	0.307804i
$233$	357205.	−	618696.i	0.431050	−	0.746600i	−0.565914	−	0.824464i	$-0.691477\pi$
$233$	357205.	−	618696.i	0.431050	−	0.746600i	0.996964	+	0.0778643i	$0.0248101\pi$
$234$	−94245.6	−	163238.i	−0.112518	−	0.194887i
$235$	257208.	+	445497.i	0.303819	+	0.526230i
$236$	−223574.			−0.261302
$237$	−382798.			−0.442689
$238$	1.12713e6	+	1.95225e6i	1.28983	+	2.23406i
$239$	429861.	+	744541.i	0.486781	+	0.843129i	0.999885	−	0.0151974i	$-0.00483768\pi$
$239$	429861.	+	744541.i	0.486781	+	0.843129i	−0.513104	+	0.858327i	$0.671504\pi$
$240$	736438.	−	1.27555e6i	0.825293	−	1.42945i
$241$	−160818.	+	278546.i	−0.178358	+	0.308926i	−0.941318	−	0.337520i	$-0.890412\pi$
$241$	−160818.	+	278546.i	−0.178358	+	0.308926i	0.762960	+	0.646446i	$0.223745\pi$
$242$	−972093.			−1.06701
$243$	−125615.	+	217571.i	−0.136466	+	0.236366i
$244$	193918.	−	335876.i	0.208518	−	0.361164i
$245$	−223648.	+	387369.i	−0.238040	+	0.412297i
$246$	−9323.16	−	16148.2i	−0.00982257	−	0.0170132i
$247$	2.46325e6			2.56901
$248$	−146155.	−	253148.i	−0.150899	−	0.261364i
$249$	216614.	−	375186.i	0.221405	−	0.383485i
$250$	87366.9			0.0884091
$251$	−710851.	+	1.23123e6i	−0.712187	+	1.23354i	0.251848	+	0.967767i	$0.418962\pi$
$251$	−710851.	+	1.23123e6i	−0.712187	+	1.23354i	−0.964035	+	0.265777i	$0.914372\pi$
$252$	32270.5	+	55894.2i	0.0320114	+	0.0554453i
$253$	−252526.	−	437387.i	−0.248030	−	0.429601i
$254$	658533.			0.640462
$255$	1.30306e6	+	2.25696e6i	1.25491	+	2.17357i
$256$	1.09029e6			1.03978
$257$	1.11378e6			1.05188			0.525942	−	0.850520i	$-0.323713\pi$
$257$	1.11378e6			1.05188			0.525942	+	0.850520i	$0.323713\pi$
$258$	−626618.	−	995530.i	−0.586075	−	0.931119i
$259$	−375904.			−0.348199
$260$	−870323.			−0.798449
$261$	38047.0	+	65899.4i	0.0345716	+	0.0598798i
$262$	634066.			0.570665
$263$	−137625.	−	238373.i	−0.122689	−	0.212504i	0.798138	−	0.602475i	$-0.205819\pi$
$263$	−137625.	−	238373.i	−0.122689	−	0.212504i	−0.920827	+	0.389971i	$0.872485\pi$
$264$	117117.	+	202853.i	0.103421	+	0.179131i
$265$	−909723.	+	1.57569e6i	−0.795783	+	1.37834i
$266$	−2.93415e6			−2.54260
$267$	457327.	−	792113.i	0.392598	−	0.680000i
$268$	9382.02	+	16250.1i	0.00797920	+	0.0138204i
$269$	1.40639e6			1.18502			0.592509	−	0.805564i	$-0.298137\pi$
$269$	1.40639e6			1.18502			0.592509	+	0.805564i	$0.298137\pi$
$270$	1.07375e6	+	1.85978e6i	0.896381	+	1.55258i
$271$	970874.	−	1.68160e6i	0.803044	−	1.39091i	−0.114559	−	0.993416i	$-0.536545\pi$
$271$	970874.	−	1.68160e6i	0.803044	−	1.39091i	0.917603	−	0.397497i	$-0.130121\pi$
$272$	−1.42795e6	+	2.47327e6i	−1.17028	+	2.02698i
$273$	911917.	−	1.57949e6i	0.740540	−	1.28265i
$274$	2.91551e6			2.34605
$275$	−207900.	+	360093.i	−0.165776	+	0.287133i
$276$	−373183.	+	646372.i	−0.294883	+	0.510752i
$277$	31373.2	+	54340.0i	0.0245674	+	0.0425521i	0.878048	−	0.478573i	$-0.158846\pi$
$277$	31373.2	+	54340.0i	0.0245674	+	0.0425521i	−0.853480	+	0.521125i	$0.825512\pi$
$278$	−708782.	−	1.22765e6i	−0.550048	−	0.952712i
$279$	76336.4			0.0587113
$280$	−1.53307e6			−1.16860
$281$	713099.	+	1.23512e6i	0.538746	+	0.933136i	0.998972	+	0.0453337i	$0.0144351\pi$
$281$	713099.	+	1.23512e6i	0.538746	+	0.933136i	−0.460226	+	0.887802i	$0.652232\pi$
$282$	311613.	+	539729.i	0.233342	+	0.404160i
$283$	653541.	−	1.13197e6i	0.485073	−	0.840170i	−0.514780	−	0.857322i	$-0.672127\pi$
$283$	653541.	−	1.13197e6i	0.485073	−	0.840170i	0.999853	+	0.0171517i	$0.00545984\pi$
$284$	445890.	−	772304.i	0.328044	−	0.568188i
$285$	−3.39211e6			−2.47376
$286$	356751.	−	617910.i	0.257899	−	0.446694i
$287$	−14380.1	+	24907.0i	−0.0103052	+	0.0178491i
$288$	−73835.1	+	127886.i	−0.0524544	+	0.0908536i
$289$	−1.81668e6	−	3.14659e6i	−1.27948	−	2.21613i
$290$	1.22228e6			0.853443
$291$	−950049.	−	1.64553e6i	−0.657678	−	1.13913i
$292$	−82212.8	+	142397.i	−0.0564264	+	0.0977334i
$293$	154259.			0.104974			0.0524870	−	0.998622i	$-0.483285\pi$
$293$	154259.			0.104974			0.0524870	+	0.998622i	$0.483285\pi$
$294$	−270954.	+	469306.i	−0.182821	+	0.316656i
$295$	693437.	+	1.20107e6i	0.463929	+	0.803549i
$296$	−160687.	−	278318.i	−0.106599	−	0.184634i
$297$	−506078.			−0.332909
$298$	−949036.	−	1.64378e6i	−0.619073	−	1.07227i
$299$	−3.36206e6			−2.17484
$300$	614469.			0.394182
$301$	−846541.	+	1.60477e6i	−0.538557	+	1.02093i
$302$	118959.			0.0750548
$303$	77748.1			0.0486500
$304$	−1.85861e6	−	3.21920e6i	−1.15346	−	1.99786i
$305$	−2.40582e6			−1.48086
$306$	−251651.	−	435871.i	−0.153636	−	0.266106i
$307$	914488.	+	1.58394e6i	0.553773	+	0.959163i	0.997998	+	0.0632479i	$0.0201459\pi$
$307$	914488.	+	1.58394e6i	0.553773	+	0.959163i	−0.444225	+	0.895915i	$0.646521\pi$
$308$	−122155.	+	211578.i	−0.0733724	+	0.127085i
$309$	569827.			0.339505
$310$	613085.	−	1.06189e6i	0.362340	−	0.627591i
$311$	515362.	+	892633.i	0.302142	+	0.523326i	0.976621	−	0.214969i	$-0.0689649\pi$
$311$	515362.	+	892633.i	0.302142	+	0.523326i	−0.674479	+	0.738294i	$0.735632\pi$
$312$	1.55926e6			0.906845
$313$	−906617.	−	1.57031e6i	−0.523074	−	0.905990i	−0.999639	−	0.0268513i	$-0.991452\pi$
$313$	−906617.	−	1.57031e6i	−0.523074	−	0.905990i	0.476566	−	0.879139i	$-0.341881\pi$
$314$	531891.	−	921262.i	0.304438	−	0.527301i
$315$	200180.	−	346722.i	0.113670	−	0.196881i
$316$	170672.	−	295613.i	0.0961491	−	0.166535i
$317$	−3.17573e6			−1.77499			−0.887495	−	0.460818i	$-0.847556\pi$
$317$	−3.17573e6			−1.77499			−0.887495	+	0.460818i	$0.847556\pi$
$318$	−1.10215e6	+	1.90898e6i	−0.611184	+	1.05860i
$319$	−144021.	+	249451.i	−0.0792406	+	0.137249i
$320$	−441809.	−	765236.i	−0.241190	−	0.417754i
$321$	207542.	+	359474.i	0.112420	+	0.194717i
$322$	4.00478e6			2.15248
$323$	6.57725e6			3.50783
$324$	321538.	+	556920.i	0.170165	+	0.294734i
$325$	1.38396e6	+	2.39709e6i	0.726799	+	1.25885i
$326$	−702832.	+	1.21734e6i	−0.366275	+	0.634407i
$327$	929609.	−	1.61013e6i	0.480763	−	0.832706i
$328$	−24588.1			−0.0126194
$329$	480632.	−	832480.i	0.244807	−	0.424018i
$330$	−491277.	+	850917.i	−0.248337	+	0.430133i
$331$	231514.	−	400994.i	0.116147	−	0.201172i	−0.802091	−	0.597202i	$-0.796279\pi$
$331$	231514.	−	400994.i	0.116147	−	0.201172i	0.918238	+	0.396030i	$0.129612\pi$
$332$	193157.	+	334557.i	0.0961755	+	0.166581i
$333$	83926.4			0.0414752
$334$	689939.	+	1.19501e6i	0.338411	+	0.586145i
$335$	58198.4	−	100803.i	0.0283334	−	0.0490749i
$336$	−2.75229e6			−1.32999
$337$	510042.	−	883419.i	0.244642	−	0.423733i	−0.717389	−	0.696673i	$-0.754663\pi$
$337$	510042.	−	883419.i	0.244642	−	0.423733i	0.962031	+	0.272940i	$0.0879962\pi$
$338$	−1.13074e6	−	1.95849e6i	−0.538356	−	0.932461i
$339$	148903.	+	257908.i	0.0703728	+	0.121889i
$340$	−2.32390e6			−1.09023
$341$	144479.	+	250246.i	0.0672852	+	0.116541i
$342$	655094.			0.302858
$343$	−1.67919e6			−0.770662
$344$	−1.55003e6	+	59210.0i	−0.706228	+	0.0269773i
$345$	4.62985e6			2.09420
$346$	1.28673e6			0.577824
$347$	−879171.	−	1.52277e6i	−0.391967	−	0.678907i	0.600742	−	0.799443i	$-0.294872\pi$
$347$	−879171.	−	1.52277e6i	−0.391967	−	0.678907i	−0.992709	+	0.120536i	$0.961539\pi$
$348$	425668.			0.188418
$349$	1.53484e6	+	2.65843e6i	0.674529	+	1.16832i	0.976606	+	0.215036i	$0.0689868\pi$
$349$	1.53484e6	+	2.65843e6i	0.674529	+	1.16832i	−0.302077	+	0.953284i	$0.597680\pi$
$350$	−1.64853e6	−	2.85534e6i	−0.719328	−	1.24591i
$351$	−1.68444e6	+	2.91754e6i	−0.729774	+	1.26401i
$352$	−558980.			−0.240458
$353$	−999829.	+	1.73175e6i	−0.427060	+	0.739689i	−0.996610	−	0.0822669i	$-0.973784\pi$
$353$	−999829.	+	1.73175e6i	−0.427060	+	0.739689i	0.569550	+	0.821956i	$0.307117\pi$
$354$	840113.	+	1.45512e6i	0.356311	+	0.617149i
$355$	−5.53188e6			−2.32971
$356$	407803.	+	706335.i	0.170540	+	0.295383i
$357$	2.43496e6	−	4.21748e6i	1.01116	−	1.75139i
$358$	−1.06895e6	+	1.85148e6i	−0.440809	+	0.763504i
$359$	451611.	−	782214.i	0.184939	−	0.320324i	−0.758617	−	0.651537i	$-0.774125\pi$
$359$	451611.	−	782214.i	0.184939	−	0.320324i	0.943556	+	0.331213i	$0.107458\pi$
$360$	342283.			0.139197
$361$	−3.04241e6	+	5.26961e6i	−1.22871	+	2.12819i
$362$	283287.	−	490668.i	0.113620	−	0.196796i
$363$	1.05001e6	+	1.81867e6i	0.418242	+	0.724416i
$364$	813166.	+	1.40844e6i	0.321681	+	0.557168i
$365$	1.01996e6			0.400730
$366$	−2.91470e6			−1.13734
$367$	−841055.	−	1.45675e6i	−0.325956	−	0.564573i	0.655749	−	0.754979i	$-0.272353\pi$
$367$	−841055.	−	1.45675e6i	−0.325956	−	0.564573i	−0.981705	+	0.190406i	$0.939020\pi$
$368$	2.53679e6	+	4.39385e6i	0.976484	+	1.69132i
$369$	3210.57	−	5560.88i	0.00122749	−	0.00212607i
$370$	674043.	−	1.16748e6i	0.255966	−	0.443347i
$371$	3.39991e6			1.28243
$372$	213512.	−	369813.i	0.0799954	−	0.138556i
$373$	1.39183e6	−	2.41071e6i	0.517980	−	0.897167i	−0.481802	−	0.876280i	$-0.660018\pi$
$373$	1.39183e6	−	2.41071e6i	0.517980	−	0.897167i	0.999782	−	0.0208873i	$-0.00664912\pi$
$374$	952580.	−	1.64992e6i	0.352146	−	0.609935i
$375$	−94369.9	−	163453.i	−0.0346541	−	0.0600227i
$376$	821821.			0.299783
$377$	958725.	+	1.66056e6i	0.347409	+	0.601729i
$378$	2.00646e6	−	3.47529e6i	0.722272	−	1.25101i
$379$	1.42785e6			0.510603			0.255302	−	0.966861i	$-0.417825\pi$
$379$	1.42785e6			0.510603			0.255302	+	0.966861i	$0.417825\pi$
$380$	1.51239e6	−	2.61953e6i	0.537284	−	0.930604i
$381$	−711318.	−	1.23204e6i	−0.251045	−	0.434823i
$382$	−693172.	−	1.20061e6i	−0.243043	−	0.420962i
$383$	1.85487e6			0.646124			0.323062	−	0.946378i	$-0.395288\pi$
$383$	1.85487e6			0.646124			0.323062	+	0.946378i	$0.395288\pi$
$384$	−1.55908e6	−	2.70041e6i	−0.539561	−	0.934547i
$385$	1.51549e6			0.521078
$386$	−5.76967e6			−1.97098
$387$	189004.	−	358289.i	0.0641494	−	0.121606i
$388$	1.69434e6			0.571374
$389$	2.61813e6			0.877238			0.438619	−	0.898673i	$-0.355468\pi$
$389$	2.61813e6			0.877238			0.438619	+	0.898673i	$0.355468\pi$
$390$	3.27036e6	+	5.66443e6i	1.08877	+	1.88580i
$391$	−8.97722e6			−2.96961
$392$	357295.	+	618853.i	0.117439	+	0.203410i
$393$	−684890.	−	1.18626e6i	−0.223686	−	0.387436i
$394$	−1.04251e6	+	1.80567e6i	−0.338328	+	0.586001i
$395$	−2.11742e6			−0.682834
$396$	27272.9	−	47238.1i	0.00873964	−	0.0151375i
$397$	2.05810e6	+	3.56473e6i	0.655374	+	1.13514i	0.981800	+	0.189919i	$0.0608225\pi$
$397$	2.05810e6	+	3.56473e6i	0.655374	+	1.13514i	−0.326425	+	0.945223i	$0.605844\pi$
$398$	−736952.			−0.233201
$399$	3.16933e6	+	5.48945e6i	0.996634	+	1.72622i
$400$	2.08849e6	−	3.61737e6i	0.652653	−	1.13043i
$401$	267212.	−	462825.i	0.0829842	−	0.143733i	−0.821546	−	0.570142i	$-0.806888\pi$
$401$	267212.	−	462825.i	0.0829842	−	0.143733i	0.904530	+	0.426409i	$0.140222\pi$
$402$	70508.5	−	122124.i	0.0217609	−	0.0376909i
$403$	1.92356e6			0.589987
$404$	−34664.4	+	60040.5i	−0.0105665	+	0.0183017i
$405$	1.99456e6	−	3.45468e6i	0.604240	−	1.04657i
$406$	−1.14200e6	−	1.97801e6i	−0.343837	−	0.595543i
$407$	158845.	+	275127.i	0.0475321	+	0.0823279i
$408$	4.16348e6			1.23824
$409$	−2.78895e6			−0.824389			−0.412195	−	0.911096i	$-0.635238\pi$
$409$	−2.78895e6			−0.824389			−0.412195	+	0.911096i	$0.635238\pi$
$410$	−51570.5	−	89322.7i	−0.0151510	−	0.0262423i
$411$	−3.14920e6	−	5.45458e6i	−0.919595	−	1.59278i
$412$	−254060.	+	440045.i	−0.0737384	+	0.127719i
$413$	1.29579e6	−	2.24438e6i	0.373818	−	0.647472i
$414$	−894130.			−0.256389
$415$	1.19819e6	−	2.07532e6i	0.341510	−	0.591513i
$416$	−1.86053e6	+	3.22253e6i	−0.527112	+	0.912984i
$417$	−1.53119e6	+	2.65210e6i	−0.431210	+	0.746878i
$418$	1.23987e6	+	2.14752e6i	0.347086	+	0.601170i
$419$	−4.86995e6			−1.35516			−0.677578	−	0.735451i	$-0.736970\pi$
$419$	−4.86995e6			−1.35516			−0.677578	+	0.735451i	$0.736970\pi$
$420$	−1.11980e6	−	1.93955e6i	−0.309754	−	0.536510i
$421$	−2.26694e6	+	3.92645e6i	−0.623354	+	1.07968i	0.365503	+	0.930810i	$0.380897\pi$
$421$	−2.26694e6	+	3.92645e6i	−0.623354	+	1.07968i	−0.988857	+	0.148870i	$0.952436\pi$
$422$	−6.18265e6			−1.69003
$423$	−107309.	+	185864.i	−0.0291598	+	0.0505062i
$424$	1.45336e6	+	2.51729e6i	0.392606	+	0.680014i
$425$	3.69539e6	+	6.40060e6i	0.992402	+	1.71889i
$426$	−6.70198e6			−1.78928
$427$	2.24782e6	+	3.89334e6i	0.596613	+	1.03336i
$428$	−370135.			−0.0976676
$429$	−1.54138e6			−0.404360
$430$	−3.46610e6	−	5.50672e6i	−0.904003	−	1.43622i
$431$	1.87803e6			0.486977			0.243489	−	0.969904i	$-0.421708\pi$
$431$	1.87803e6			0.486977			0.243489	+	0.969904i	$0.421708\pi$
$432$	5.08389e6			1.31065
$433$	2.05652e6	+	3.56199e6i	0.527124	+	0.913006i	0.999500	+	0.0316087i	$0.0100630\pi$
$433$	2.05652e6	+	3.56199e6i	0.527124	+	0.913006i	−0.472376	+	0.881397i	$0.656604\pi$
$434$	−2.29128e6			−0.583922
$435$	−1.32025e6	−	2.28674e6i	−0.334528	−	0.579420i
$436$	828941.	+	1.43577e6i	0.208837	+	0.361716i
$437$	5.84235e6	−	1.01192e7i	1.46347	−	2.53481i
$438$	1.23571e6			0.307772
$439$	579055.	−	1.00295e6i	0.143403	−	0.248382i	−0.785373	−	0.619023i	$-0.787529\pi$
$439$	579055.	−	1.00295e6i	0.143403	−	0.248382i	0.928776	+	0.370641i	$0.120862\pi$
$440$	647826.	+	1.12207e6i	0.159524	+	0.276304i
$441$	−186614.			−0.0456929
$442$	−6.34119e6	−	1.09833e7i	−1.54389	−	2.67409i
$443$	−33352.8	+	57768.7i	−0.00807463	+	0.0139857i	−0.870034	−	0.492991i	$-0.835904\pi$
$443$	−33352.8	+	57768.7i	−0.00807463	+	0.0139857i	0.861960	+	0.506977i	$0.169237\pi$
$444$	234741.	−	406583.i	0.0565108	−	0.0978796i
$445$	2.52968e6	−	4.38153e6i	0.605571	−	1.04888i
$446$	7.16881e6			1.70651
$447$	−2.05021e6	+	3.55107e6i	−0.485322	+	0.840603i
$448$	−825587.	+	1.42996e6i	−0.194343	+	0.336611i
$449$	988357.	+	1.71188e6i	0.231365	+	0.400736i	0.958210	−	0.286065i	$-0.0923475\pi$
$449$	988357.	+	1.71188e6i	0.231365	+	0.400736i	−0.726845	+	0.686802i	$0.759014\pi$
$450$	368060.	+	637499.i	0.0856816	+	0.148405i
$451$	24306.2			0.00562698
$452$	−265557.			−0.0611381
$453$	−128494.	−	222558.i	−0.0294196	−	0.0509562i
$454$	149590.	+	259097.i	0.0340613	+	0.0589959i
$455$	5.04422e6	−	8.73684e6i	1.14226	−	1.97845i
$456$	−2.70958e6	+	4.69313e6i	−0.610225	+	1.05694i
$457$	−5.08786e6			−1.13958			−0.569790	−	0.821790i	$-0.692976\pi$
$457$	−5.08786e6			−1.13958			−0.569790	+	0.821790i	$0.692976\pi$
$458$	−302867.	+	524581.i	−0.0674665	+	0.116855i
$459$	−4.49773e6	+	7.79030e6i	−0.996464	+	1.72593i
$460$	−2.06424e6	+	3.57537e6i	−0.454847	+	0.787819i
$461$	−881697.	−	1.52714e6i	−0.193227	−	0.334678i	0.753091	−	0.657916i	$-0.228562\pi$
$461$	−881697.	−	1.52714e6i	−0.193227	−	0.334678i	−0.946318	+	0.323238i	$0.895229\pi$
$462$	1.83605e6			0.400203
$463$	−1.07000e6	−	1.85330e6i	−0.231970	−	0.401784i	0.726418	−	0.687254i	$-0.241184\pi$
$463$	−1.07000e6	−	1.85330e6i	−0.231970	−	0.401784i	−0.958388	+	0.285469i	$0.907851\pi$
$464$	1.44678e6	−	2.50590e6i	0.311967	−	0.540343i
$465$	−2.64891e6			−0.568113
$466$	2.39379e6	−	4.14617e6i	0.510648	−	0.884467i
$467$	1.55319e6	+	2.69020e6i	0.329558	+	0.570811i	0.982424	−	0.186662i	$-0.0597671\pi$
$467$	1.55319e6	+	2.69020e6i	0.329558	+	0.570811i	−0.652866	+	0.757473i	$0.726434\pi$
$468$	−181552.	−	314457.i	−0.0383165	−	0.0663662i
$469$	−217505.			−0.0456601
$470$	1.72367e6	+	2.98548e6i	0.359922	+	0.623404i
$471$	−2.29810e6			−0.477328
$472$	2.21564e6			0.457767
$473$	1.53226e6	−	58531.1i	0.314905	−	0.0120291i
$474$	−2.56530e6			−0.524436
$475$	−9.61979e6			−1.95628
$476$	2.17128e6	+	3.76077e6i	0.439237	+	0.760780i
$477$	−759084.			−0.152754
$478$	2.88070e6	+	4.98951e6i	0.576670	+	0.998822i
$479$	−4.43049e6	−	7.67384e6i	−0.882294	−	1.52818i	−0.848784	−	0.528739i	$-0.822665\pi$
$479$	−4.43049e6	−	7.67384e6i	−0.882294	−	1.52818i	−0.0335093	−	0.999438i	$-0.510668\pi$
$480$	2.56211e6	−	4.43770e6i	0.507568	−	0.879134i
$481$	2.11481e6			0.416782
$482$	−1.07772e6	+	1.86666e6i	−0.211294	+	0.365972i
$483$	−4.32579e6	−	7.49248e6i	−0.843718	−	1.46136i
$484$	−1.87261e6			−0.363358
$485$	−5.25514e6	−	9.10217e6i	−1.01445	−	1.75708i
$486$	−841800.	+	1.45804e6i	−0.161666	+	0.280014i
$487$	4.51371e6	−	7.81797e6i	0.862405	−	1.49373i	−0.00719675	−	0.999974i	$-0.502291\pi$
$487$	4.51371e6	−	7.81797e6i	0.862405	−	1.49373i	0.869601	−	0.493754i	$-0.164376\pi$
$488$	−1.92175e6	+	3.32856e6i	−0.365298	+	0.632714i
$489$	3.03667e6			0.574283
$490$	−1.49876e6	+	2.59594e6i	−0.281996	+	0.488432i
$491$	−1.09845e6	+	1.90256e6i	−0.205625	+	0.356152i	−0.950332	−	0.311239i	$-0.899256\pi$
$491$	−1.09845e6	+	1.90256e6i	−0.205625	+	0.356152i	0.744707	+	0.667392i	$0.232589\pi$
$492$	−17959.9	−	31107.4i	−0.00334495	−	0.00579363i
$493$	2.55995e6	+	4.43396e6i	0.474366	+	0.821626i
$494$	1.65073e7			3.04340
$495$	−338358.			−0.0620674
$496$	−1.45139e6	−	2.51388e6i	−0.264899	−	0.458819i
$497$	5.16858e6	+	8.95224e6i	0.938599	+	1.62570i
$498$	1.45163e6	−	2.51429e6i	0.262290	−	0.454299i
$499$	3.02136e6	−	5.23315e6i	0.543189	−	0.940832i	−0.455529	−	0.890221i	$-0.650550\pi$
$499$	3.02136e6	−	5.23315e6i	0.543189	−	0.940832i	0.998718	−	0.0506108i	$-0.0161168\pi$
$500$	168301.			0.0301066
$501$	1.49048e6	−	2.58159e6i	0.265297	−	0.459508i
$502$	−4.76373e6	+	8.25103e6i	−0.843700	+	1.46133i
$503$	−5.26666e6	+	9.12213e6i	−0.928145	+	1.60759i	−0.141720	+	0.989907i	$0.545263\pi$
$503$	−5.26666e6	+	9.12213e6i	−0.928145	+	1.60759i	−0.786424	+	0.617687i	$0.788070\pi$
$504$	−319804.	−	553916.i	−0.0560799	−	0.0971332i
$505$	430059.			0.0750412
$506$	−1.69229e6	−	2.93113e6i	−0.293831	−	0.508931i
$507$	−2.44274e6	+	4.23096e6i	−0.422044	+	0.731002i
$508$	1.26858e6			0.218101
$509$	−3.64087e6	+	6.30617e6i	−0.622889	+	1.07887i	0.366056	+	0.930593i	$0.380708\pi$
$509$	−3.64087e6	+	6.30617e6i	−0.622889	+	1.07887i	−0.988945	+	0.148282i	$0.952626\pi$
$510$	8.73238e6	+	1.51249e7i	1.48665	+	2.57494i
$511$	−952978.	−	1.65061e6i	−0.161447	−	0.279635i
$512$	414251.			0.0698375
$513$	−5.85422e6	−	1.01398e7i	−0.982145	−	1.70113i
$514$	7.46397e6			1.24613
$515$	3.15196e6			0.523677
$516$	−1.20710e6	−	1.91776e6i	−0.199581	−	0.317081i
$517$	−812398.			−0.133673
$518$	−2.51910e6			−0.412498
$519$	−1.38986e6	−	2.40731e6i	−0.226492	−	0.392296i
$520$	8.62498e6			1.39878
$521$	4.07788e6	+	7.06309e6i	0.658172	+	1.13999i	0.981088	+	0.193560i	$0.0620036\pi$
$521$	4.07788e6	+	7.06309e6i	0.658172	+	1.13999i	−0.322916	+	0.946428i	$0.604663\pi$
$522$	254971.	+	441622.i	0.0409556	+	0.0709372i
$523$	1.09579e6	−	1.89797e6i	0.175176	−	0.303414i	−0.765046	−	0.643975i	$-0.777284\pi$
$523$	1.09579e6	−	1.89797e6i	0.175176	−	0.303414i	0.940222	+	0.340562i	$0.110617\pi$
$524$	1.22145e6			0.194333
$525$	−3.56134e6	+	6.16842e6i	−0.563917	+	0.976732i
$526$	−922285.	−	1.59744e6i	−0.145345	−	0.251745i
$527$	5.13620e6			0.805593
$528$	1.16303e6	+	2.01443e6i	0.181554	+	0.314461i
$529$	−4.75598e6	+	8.23761e6i	−0.738926	+	1.27986i
$530$	−6.09647e6	+	1.05594e7i	−0.942733	+	1.63286i
$531$	−289306.	+	501093.i	−0.0445268	+	0.0771226i
$532$	−5.65225e6			−0.865850
$533$	80901.4	−	140125.i	0.0123350	−	0.0213648i
$534$	3.06475e6	−	5.30831e6i	0.465096	−	0.805569i
$535$	1.14801e6	+	1.98841e6i	0.173405	+	0.300345i
$536$	−92976.6	−	161040.i	−0.0139785	−	0.0242115i
$537$	4.61854e6			0.691145
$538$	9.42486e6			1.40384
$539$	−353198.	−	611757.i	−0.0523657	−	0.0907000i
$540$	2.06844e6	+	3.58263e6i	0.305251	+	0.528711i
$541$	326611.	−	565707.i	0.0479776	−	0.0830996i	−0.841039	−	0.540974i	$-0.818056\pi$
$541$	326611.	−	565707.i	0.0479776	−	0.0830996i	0.889017	+	0.457874i	$0.151389\pi$
$542$	6.50627e6	−	1.12692e7i	0.951335	−	1.64776i
$543$	−1.22398e6			−0.178145
$544$	−4.96790e6	+	8.60465e6i	−0.719740	+	1.24663i
$545$	5.14208e6	−	8.90634e6i	0.741562	−	1.28442i
$546$	6.11117e6	−	1.05849e7i	0.877289	−	1.51951i
$547$	−345049.	−	597643.i	−0.0493075	−	0.0854031i	0.840318	−	0.542093i	$-0.182368\pi$
$547$	−345049.	−	597643.i	−0.0493075	−	0.0854031i	−0.889626	+	0.456690i	$0.849035\pi$
$548$	5.61636e6			0.798920
$549$	−501862.	−	869250.i	−0.0710646	−	0.123087i
$550$	−1.39323e6	+	2.41314e6i	−0.196388	+	0.340155i
$551$	−6.66403e6			−0.935099
$552$	3.69828e6	−	6.40560e6i	0.516597	−	0.894772i
$553$	1.97836e6	+	3.42663e6i	0.275102	+	0.476490i
$554$	210246.	+	364157.i	0.0291041	+	0.0504098i
$555$	−2.91228e6			−0.401330
$556$	−1.36538e6	−	2.36490e6i	−0.187312	−	0.324434i
$557$	−8.71526e6			−1.19026			−0.595131	−	0.803629i	$-0.702900\pi$
$557$	−8.71526e6			−1.19026			−0.595131	+	0.803629i	$0.702900\pi$
$558$	511565.			0.0695529
$559$	4.76259e6	−	9.02831e6i	0.644635	−	1.22202i
$560$	−1.52242e7			−2.05146
$561$	−4.11574e6			−0.552129
$562$	4.77880e6	+	8.27713e6i	0.638231	+	1.10545i
$563$	3.56075e6			0.473447			0.236723	−	0.971577i	$-0.423927\pi$
$563$	3.56075e6			0.473447			0.236723	+	0.971577i	$0.423927\pi$
$564$	600282.	+	1.03972e6i	0.0794616	+	0.137632i
$565$	823650.	+	1.42660e6i	0.108548	+	0.188010i
$566$	4.37968e6	−	7.58582e6i	0.574647	−	0.995317i
$567$	−7.45428e6			−0.973751
$568$	−4.41881e6	+	7.65360e6i	−0.574691	+	0.995394i
$569$	−2.72714e6	−	4.72354e6i	−0.353123	−	0.611628i	0.633672	−	0.773602i	$-0.281547\pi$
$569$	−2.72714e6	−	4.72354e6i	−0.353123	−	0.611628i	−0.986795	+	0.161975i	$0.948214\pi$
$570$	−2.27320e7			−2.93057
$571$	2.43360e6	+	4.21512e6i	0.312362	+	0.541027i	0.978873	−	0.204468i	$-0.0655464\pi$
$571$	2.43360e6	+	4.21512e6i	0.312362	+	0.541027i	−0.666511	+	0.745495i	$0.732213\pi$
$572$	687234.	−	1.19032e6i	0.0878243	−	0.152116i
$573$	−1.49747e6	+	2.59369e6i	−0.190533	+	0.330013i
$574$	−96367.3	+	166913.i	−0.0122082	+	0.0211451i
$575$	1.31299e7			1.65612
$576$	184325.	−	319261.i	0.0231488	−	0.0400949i
$577$	5.49945e6	−	9.52532e6i	0.687669	−	1.19108i	−0.284921	−	0.958551i	$-0.591967\pi$
$577$	5.49945e6	−	9.52532e6i	0.687669	−	1.19108i	0.972590	−	0.232527i	$-0.0746993\pi$
$578$	−1.21744e7	−	2.10867e7i	−1.51576	−	2.62537i
$579$	6.23214e6	+	1.07944e7i	0.772575	+	1.33814i
$580$	2.35456e6			0.290629
$581$	−4.47799e6			−0.550354
$582$	−6.36671e6	−	1.10275e7i	−0.779125	−	1.34948i
$583$	−1.43669e6	−	2.48842e6i	−0.175062	−	0.303216i
$584$	814736.	−	1.41116e6i	0.0988519	−	0.171216i
$585$	−1.12620e6	+	1.95064e6i	−0.136059	+	0.235660i
$586$	1.03376e6			0.124358
$587$	−5.21729e6	+	9.03661e6i	−0.624956	+	1.08246i	0.363593	+	0.931558i	$0.381550\pi$
$587$	−5.21729e6	+	9.03661e6i	−0.624956	+	1.08246i	−0.988549	+	0.150898i	$0.951783\pi$
$588$	−521957.	+	904057.i	−0.0622575	+	0.107833i
$589$	−3.34263e6	+	5.78960e6i	−0.397008	+	0.687638i
$590$	4.64704e6	+	8.04890e6i	0.549599	+	0.951933i
$591$	4.50428e6			0.530464
$592$	−1.59570e6	−	2.76384e6i	−0.187132	−	0.324122i
$593$	3.21382e6	−	5.56651e6i	0.375306	−	0.650049i	−0.615067	−	0.788475i	$-0.710871\pi$
$593$	3.21382e6	−	5.56651e6i	0.375306	−	0.650049i	0.990373	+	0.138426i	$0.0442044\pi$
$594$	−3.39146e6			−0.394385
$595$	1.34689e7	−	2.33287e7i	1.55969	−	2.70146i
$596$	−1.82820e6	−	3.16653e6i	−0.210818	−	0.365147i
$597$	796022.	+	1.37875e6i	0.0914091	+	0.158325i
$598$	−2.25307e7			−2.57645
$599$	−6.80546e6	−	1.17874e7i	−0.774980	−	1.34231i	−0.934806	−	0.355160i	$-0.884426\pi$
$599$	−6.80546e6	−	1.17874e7i	−0.774980	−	1.34231i	0.159825	−	0.987145i	$-0.448907\pi$
$600$	−6.08944e6			−0.690557
$601$	7.75878e6			0.876209			0.438104	−	0.898924i	$-0.355650\pi$
$601$	7.75878e6			0.876209			0.438104	+	0.898924i	$0.355650\pi$
$602$	−5.67306e6	+	1.07543e7i	−0.638008	+	1.20945i
$603$	48561.4			0.00543874
$604$	229158.			0.0255590
$605$	5.80808e6	+	1.00599e7i	0.645125	+	1.11739i
$606$	521025.			0.0576338
$607$	−2.10666e6	−	3.64884e6i	−0.232072	−	0.401961i	0.726346	−	0.687330i	$-0.241217\pi$
$607$	−2.10666e6	−	3.64884e6i	−0.232072	−	0.401961i	−0.958418	+	0.285369i	$0.907884\pi$
$608$	−6.46619e6	−	1.11998e7i	−0.709397	−	1.22871i
$609$	−2.46709e6	+	4.27312e6i	−0.269551	+	0.466876i
$610$	−1.61225e7			−1.75432
$611$	−2.70401e6	+	4.68348e6i	−0.293025	+	0.507535i
$612$	−484772.	−	839650.i	−0.0523190	−	0.0906191i
$613$	5.01051e6			0.538556			0.269278	−	0.963062i	$-0.413215\pi$
$613$	5.01051e6			0.538556			0.269278	+	0.963062i	$0.413215\pi$
$614$	6.12840e6	+	1.06147e7i	0.656033	+	1.13628i
$615$	−111408.	+	192965.i	−0.0118776	+	0.0205727i
$616$	1.21056e6	−	2.09676e6i	0.128539	−	0.222636i
$617$	4.47750e6	−	7.75526e6i	0.473503	−	0.820131i	−0.526037	−	0.850462i	$-0.676323\pi$
$617$	4.47750e6	−	7.75526e6i	0.473503	−	0.820131i	0.999540	+	0.0303305i	$0.00965597\pi$
$618$	3.81867e6			0.402199
$619$	1.73192e6	−	2.99977e6i	0.181677	−	0.314674i	−0.760775	−	0.649016i	$-0.775181\pi$
$619$	1.73192e6	−	2.99977e6i	0.181677	−	0.314674i	0.942452	+	0.334342i	$0.108514\pi$
$620$	1.18103e6	−	2.04560e6i	0.123390	−	0.213718i
$621$	7.99036e6	+	1.38397e7i	0.831452	+	1.44012i
$622$	3.45367e6	+	5.98194e6i	0.357936	+	0.619963i
$623$	−9.45417e6			−0.975895
$624$	1.54842e7			1.59195
$625$	4.61519e6	+	7.99374e6i	0.472595	+	0.818559i
$626$	−6.07565e6	−	1.05233e7i	−0.619665	−	1.07329i
$627$	2.67851e6	−	4.63932e6i	0.272098	−	0.471287i
$628$	1.02462e6	−	1.77469e6i	0.103672	−	0.179566i
$629$	5.64688e6			0.569092
$630$	1.34150e6	−	2.32354e6i	0.134660	−	0.233238i
$631$	−9.19741e6	+	1.59304e7i	−0.919586	+	1.59277i	−0.119540	+	0.992829i	$0.538142\pi$
$631$	−9.19741e6	+	1.59304e7i	−0.919586	+	1.59277i	−0.800045	+	0.599940i	$0.795191\pi$
$632$	−1.69138e6	+	2.92955e6i	−0.168441	+	0.291748i
$633$	6.67823e6	+	1.15670e7i	0.662448	+	1.14739i
$634$	−2.12820e7			−2.10276
$635$	−3.93462e6	−	6.81495e6i	−0.387229	−	0.670701i
$636$	−2.12315e6	+	3.67740e6i	−0.208131	+	0.360494i
$637$	−4.70238e6			−0.459166
$638$	−965148.	+	1.67168e6i	−0.0938733	+	0.162593i
$639$	−1.15397e6	−	1.99873e6i	−0.111800	−	0.193643i
$640$	−8.62397e6	−	1.49371e7i	−0.832256	−	1.44151i
$641$	1.82412e7			1.75351			0.876756	−	0.480936i	$-0.159703\pi$
$641$	1.82412e7			1.75351			0.876756	+	0.480936i	$0.159703\pi$
$642$	1.39083e6	+	2.40900e6i	0.133180	+	0.230674i
$643$	7.75417e6			0.739619			0.369809	−	0.929108i	$-0.379423\pi$
$643$	7.75417e6			0.739619			0.369809	+	0.929108i	$0.379423\pi$
$644$	7.71470e6			0.733000
$645$	−6.55851e6	+	1.24328e7i	−0.620734	+	1.17671i
$646$	4.40772e7			4.15559
$647$	1.50603e7			1.41440			0.707199	−	0.707014i	$-0.249958\pi$
$647$	1.50603e7			1.41440			0.707199	+	0.707014i	$0.249958\pi$
$648$	−3.18647e6	−	5.51913e6i	−0.298107	−	0.516336i
$649$	−2.19024e6			−0.204117
$650$	9.27453e6	+	1.60640e7i	0.861011	+	1.49131i
$651$	2.47494e6	+	4.28673e6i	0.228883	+	0.396436i
$652$	−1.35392e6	+	2.34505e6i	−0.124730	+	0.216040i
$653$	−1.72831e7			−1.58613			−0.793064	−	0.609138i	$-0.791515\pi$
$653$	−1.72831e7			−1.58613			−0.793064	+	0.609138i	$0.791515\pi$
$654$	6.22973e6	−	1.07902e7i	0.569541	−	0.986474i
$655$	−3.78843e6	−	6.56175e6i	−0.345029	−	0.597608i
$656$	−244172.			−0.0221532
$657$	212767.	+	368524.i	0.0192305	+	0.0333083i
$658$	3.22094e6	−	5.57882e6i	0.290013	−	0.502317i
$659$	−122541.	+	212248.i	−0.0109918	+	0.0190384i	−0.871469	−	0.490451i	$-0.836832\pi$
$659$	−122541.	+	212248.i	−0.0109918	+	0.0190384i	0.860477	+	0.509489i	$0.170166\pi$
$660$	−946382.	+	1.63918e6i	−0.0845681	+	0.146476i
$661$	1.24794e7			1.11093			0.555467	−	0.831538i	$-0.312539\pi$
$661$	1.24794e7			1.11093			0.555467	+	0.831538i	$0.312539\pi$
$662$	1.55148e6	−	2.68724e6i	0.137594	−	0.238321i
$663$	−1.36990e7	+	2.37273e7i	−1.21033	+	2.09635i
$664$	−1.91420e6	−	3.31549e6i	−0.168487	−	0.291828i
$665$	1.75310e7	+	3.03646e7i	1.53728	+	2.66264i
$666$	562429.			0.0491340
$667$	9.09565e6			0.791625
$668$	1.32908e6	+	2.30203e6i	0.115242	+	0.199604i
$669$	−7.74343e6	−	1.34120e7i	−0.668910	−	1.15859i
$670$	390014.	−	675524.i	0.0335655	−	0.0581371i
$671$	1.89971e6	−	3.29040e6i	0.162885	−	0.282125i
$672$	−9.57538e6			−0.817962
$673$	1.52145e6	−	2.63523e6i	0.129485	−	0.224275i	−0.793992	−	0.607928i	$-0.792001\pi$
$673$	1.52145e6	−	2.63523e6i	0.129485	−	0.224275i	0.923477	+	0.383653i	$0.125334\pi$
$674$	3.41802e6	−	5.92019e6i	0.289818	−	0.501979i
$675$	6.57831e6	−	1.13940e7i	0.555719	−	0.962533i
$676$	−2.17822e6	−	3.77279e6i	−0.183331	−	0.317538i
$677$	−9.51921e6			−0.798233			−0.399116	−	0.916900i	$-0.630683\pi$
$677$	−9.51921e6			−0.798233			−0.399116	+	0.916900i	$0.630683\pi$
$678$	997868.	+	1.72836e6i	0.0833679	+	0.144397i
$679$	−9.82003e6	+	1.70088e7i	−0.817407	+	1.41579i
$680$	2.30300e7			1.90995
$681$	323160.	−	559729.i	0.0267024	−	0.0462499i
$682$	968222.	+	1.67701e6i	0.0797102	+	0.138062i
$683$	1.94066e6	+	3.36132e6i	0.159183	+	0.275714i	0.934574	−	0.355768i	$-0.115781\pi$
$683$	1.94066e6	+	3.36132e6i	0.159183	+	0.275714i	−0.775391	+	0.631481i	$0.782447\pi$
$684$	1.26195e6			0.103134
$685$	−1.74196e7	−	3.01717e7i	−1.41845	−	2.45682i
$686$	−1.12530e7			−0.912973
$687$	1.30857e6			0.105781
$688$	−1.53926e7	+	587984.i	−1.23977	+	0.0473581i
$689$	−1.91277e7			−1.53502
$690$	3.10267e7			2.48092
$691$	6.28227e6	+	1.08812e7i	0.500520	+	0.866926i	1.00000		0.000600381i	$0.000191107\pi$
$691$	6.28227e6	+	1.08812e7i	0.500520	+	0.866926i	−0.499480	+	0.866325i	$0.666476\pi$
$692$	2.47871e6			0.196771
$693$	316137.	+	547565.i	0.0250059	+	0.0433114i
$694$	−5.89173e6	−	1.02048e7i	−0.464348	−	0.804275i
$695$	−8.46969e6	+	1.46699e7i	−0.665129	+	1.15204i
$696$	−4.21841e6			−0.330085
$697$	216019.	−	374157.i	0.0168427	−	0.0291724i
$698$	1.02857e7	+	1.78153e7i	0.799089	+	1.38406i
$699$	−1.03427e7			−0.800644
$700$	−3.17568e6	−	5.50044e6i	−0.244958	−	0.424280i
$701$	5.57285e6	−	9.65246e6i	0.428334	−	0.741896i	−0.568392	−	0.822758i	$-0.692434\pi$
$701$	5.57285e6	−	9.65246e6i	0.428334	−	0.741896i	0.996725	+	0.0808625i	$0.0257675\pi$
$702$	−1.12882e7	+	1.95518e7i	−0.864535	+	1.49742i
$703$	−3.67498e6	+	6.36525e6i	−0.280457	+	0.485766i
$704$	1.39546e6			0.106118
$705$	3.72366e6	−	6.44957e6i	0.282161	−	0.488717i
$706$	−6.70031e6	+	1.16053e7i	−0.505921	+	0.876281i
$707$	−401815.	−	695965.i	−0.0302328	−	0.0523647i
$708$	1.61837e6	+	2.80310e6i	0.121337	+	0.210162i
$709$	−1.12600e7			−0.841243			−0.420622	−	0.907236i	$-0.638188\pi$
$709$	−1.12600e7			−0.841243			−0.420622	+	0.907236i	$0.638188\pi$
$710$	−3.70716e7			−2.75991
$711$	−441701.	−	765049.i	−0.0327683	−	0.0567564i
$712$	−4.04136e6	−	6.99984e6i	−0.298764	−	0.517474i
$713$	4.56231e6	−	7.90215e6i	0.336094	−	0.582132i
$714$	1.63178e7	−	2.82632e7i	1.19789	−	2.07480i
$715$	−8.52608e6			−0.623712
$716$	−2.05920e6	+	3.56664e6i	−0.150112	+	0.260002i
$717$	6.22320e6	−	1.07789e7i	0.452081	−	0.783027i
$718$	3.02645e6	−	5.24197e6i	0.219090	−	0.379475i
$719$	−6.24554e6	−	1.08176e7i	−0.450555	−	0.780384i	0.547866	−	0.836566i	$-0.315441\pi$
$719$	−6.24554e6	−	1.08176e7i	−0.450555	−	0.780384i	−0.998421	+	0.0561824i	$0.982107\pi$
$720$	3.39903e6			0.244357
$721$	−2.94496e6	−	5.10082e6i	−0.210980	−	0.365428i
$722$	−2.03886e7	+	3.53140e7i	−1.45561	+	2.52118i
$723$	4.65641e6			0.331288
$724$	545716.	−	945208.i	0.0386919	−	0.0670164i
$725$	−3.74414e6	−	6.48504e6i	−0.264549	−	0.458213i
$726$	7.03661e6	+	1.21878e7i	0.495475	+	0.858188i
$727$	1.74704e7			1.22594			0.612968	−	0.790108i	$-0.289975\pi$
$727$	1.74704e7			1.22594			0.612968	+	0.790108i	$0.289975\pi$
$728$	−8.05854e6	−	1.39578e7i	−0.563544	−	0.976087i
$729$	1.57420e7			1.09708
$730$	6.83523e6			0.474729
$731$	1.27169e7	−	2.41070e7i	0.880211	−	1.66859i
$732$	−5.61480e6			−0.387308
$733$	2.31567e6			0.159190			0.0795952	−	0.996827i	$-0.474637\pi$
$733$	2.31567e6			0.159190			0.0795952	+	0.996827i	$0.474637\pi$
$734$	−5.63629e6	−	9.76234e6i	−0.386148	−	0.668827i
$735$	6.47560e6			0.442142
$736$	8.82563e6	+	1.52864e7i	0.600553	+	1.04019i
$737$	91910.5	+	159194.i	0.00623299	+	0.0107959i
$738$	21515.5	−	37266.0i	0.00145416	−	0.00251867i
$739$	3.84040e6			0.258682			0.129341	−	0.991600i	$-0.458714\pi$
$739$	3.84040e6			0.258682			0.129341	+	0.991600i	$0.458714\pi$
$740$	1.29846e6	−	2.24899e6i	0.0871662	−	0.150976i
$741$	−1.78305e7	−	3.08833e7i	−1.19294	−	2.06623i
$742$	2.27844e7			1.51924
$743$	6.41374e6	+	1.11089e7i	0.426225	+	0.738244i	0.996534	−	0.0831865i	$-0.0265097\pi$
$743$	6.41374e6	+	1.11089e7i	0.426225	+	0.738244i	−0.570309	+	0.821431i	$0.693176\pi$
$744$	−2.11592e6	+	3.66488e6i	−0.140142	+	0.242732i
$745$	−1.13406e7	+	1.96426e7i	−0.748595	+	1.29660i
$746$	9.32726e6	−	1.61553e7i	0.613631	−	1.06284i
$747$	999781.			0.0655546
$748$	1.83502e6	−	3.17835e6i	0.119919	−	0.207706i
$749$	2.14523e6	−	3.71564e6i	0.139723	−	0.242008i
$750$	−632415.	−	1.09538e6i	−0.0410534	−	0.0711066i
$751$	−4.50277e6	−	7.79902e6i	−0.291326	−	0.504592i	0.682797	−	0.730608i	$-0.260763\pi$
$751$	−4.50277e6	−	7.79902e6i	−0.291326	−	0.504592i	−0.974124	+	0.226016i	$0.927430\pi$
$752$	8.16108e6			0.526263
$753$	2.05823e7			1.32284
$754$	6.42485e6	+	1.11282e7i	0.411562	+	0.712845i
$755$	−710756.	−	1.23106e6i	−0.0453788	−	0.0785984i
$756$	3.86519e6	−	6.69470e6i	0.245961	−	0.426017i
$757$	−7.22813e6	+	1.25195e7i	−0.458444	+	0.794049i	−0.998879	−	0.0473372i	$-0.984926\pi$
$757$	−7.22813e6	+	1.25195e7i	−0.458444	+	0.794049i	0.540435	+	0.841386i	$0.318260\pi$
$758$	9.56865e6			0.604892
$759$	−3.65587e6	+	6.33216e6i	−0.230349	+	0.398976i
$760$	−1.49879e7	+	2.59598e7i	−0.941254	+	1.63030i
$761$	6.95980e6	−	1.20547e7i	0.435647	−	0.754563i	−0.561701	−	0.827340i	$-0.689853\pi$
$761$	6.95980e6	−	1.20547e7i	0.435647	−	0.754563i	0.997348	+	0.0727771i	$0.0231862\pi$
$762$	−4.76687e6	−	8.25646e6i	−0.297403	−	0.515117i
$763$	−1.92175e7			−1.19505
$764$	−1.33531e6	−	2.31282e6i	−0.0827652	−	0.143354i
$765$	−3.00713e6	+	5.20851e6i	−0.185780	+	0.321780i
$766$	1.24303e7			0.765438
$767$	−7.29005e6	+	1.26267e7i	−0.447448	+	0.775002i
$768$	−7.89220e6	−	1.36697e7i	−0.482831	−	0.836287i
$769$	1.31773e7	+	2.28237e7i	0.803545	+	1.39178i	0.917269	+	0.398268i	$0.130389\pi$
$769$	1.31773e7	+	2.28237e7i	0.803545	+	1.39178i	−0.113724	+	0.993512i	$0.536278\pi$
$770$	1.01560e7			0.617300
$771$	−8.06225e6	−	1.39642e7i	−0.488450	−	0.846020i
$772$	−1.11145e7			−0.671193
$773$	−2.13712e7			−1.28641			−0.643205	−	0.765694i	$-0.722396\pi$
$773$	−2.13712e7			−1.28641			−0.643205	+	0.765694i	$0.722396\pi$
$774$	1.26660e6	−	2.40106e6i	0.0759953	−	0.144062i
$775$	−7.51213e6			−0.449271
$776$	−1.67910e7			−1.00097
$777$	2.72102e6	+	4.71295e6i	0.161689	+	0.280053i
$778$	1.75453e7			1.03923
$779$	281170.	+	487000.i	0.0166006	+	0.0287532i
$780$	6.29993e6	+	1.09118e7i	0.370766	+	0.642185i
$781$	4.36814e6	−	7.56584e6i	0.256253	−	0.443843i
$782$	−6.01604e7			−3.51798
$783$	4.55707e6	−	7.89307e6i	0.265632	−	0.460089i
$784$	3.54811e6	+	6.14552e6i	0.206161	+	0.357082i
$785$	−1.27118e7			−0.736263
$786$	−4.58976e6	−	7.94969e6i	−0.264992	−	0.458980i
$787$	2.45063e6	−	4.24461e6i	0.141039	−	0.244287i	−0.786849	−	0.617146i	$-0.788289\pi$
$787$	2.45063e6	−	4.24461e6i	0.141039	−	0.244287i	0.927888	+	0.372858i	$0.121622\pi$
$788$	−2.00825e6	+	3.47840e6i	−0.115213	+	0.199555i
$789$	−1.99242e6	+	3.45098e6i	−0.113943	+	0.197356i
$790$	−1.41898e7			−0.808927
$791$	1.53911e6	−	2.66582e6i	0.0874641	−	0.151492i
$792$	−270277.	+	468133.i	−0.0153107	+	0.0265190i
$793$	−1.26461e7	−	2.19037e7i	−0.714125	−	1.23690i
$794$	1.37922e7	+	2.38889e7i	0.776396	+	1.34476i
$795$	2.63405e7			1.47811
$796$	−1.41964e6			−0.0794139
$797$	357156.	+	618612.i	0.0199164	+	0.0344963i	0.875812	−	0.482653i	$-0.160327\pi$
$797$	357156.	+	618612.i	0.0199164	+	0.0344963i	−0.855895	+	0.517149i	$0.826993\pi$
$798$	2.12391e7	+	3.67873e7i	1.18067	+	2.04499i
$799$	−7.22013e6	+	1.25056e7i	−0.400109	+	0.693009i
$800$	7.26597e6	−	1.25850e7i	0.401392	−	0.695231i
$801$	2.11079e6			0.116242
$802$	1.79071e6	−	3.10160e6i	0.0983081	−	0.170275i
$803$	−805394.	+	1.39498e6i	−0.0440778	+	0.0763450i
$804$	135826.	−	235257.i	0.00741040	−	0.0128352i
$805$	−2.39278e7	−	4.14442e7i	−1.30141	−	2.25411i
$806$	1.28906e7			0.698935
$807$	−1.01803e7	−	1.76328e7i	−0.550272	−	0.953099i
$808$	343527.	−	595006.i	0.0185111	−	0.0320622i
$809$	−1.35024e7			−0.725337			−0.362669	−	0.931918i	$-0.618134\pi$
$809$	−1.35024e7			−0.725337			−0.362669	+	0.931918i	$0.618134\pi$
$810$	1.33664e7	−	2.31514e7i	0.715819	−	1.23984i
$811$	1.65308e7	+	2.86322e7i	0.882556	+	1.52863i	0.848490	+	0.529212i	$0.177512\pi$
$811$	1.65308e7	+	2.86322e7i	0.882556	+	1.52863i	0.0340660	+	0.999420i	$0.489154\pi$
$812$	−2.19993e6	−	3.81038e6i	−0.117089	−	0.202805i
$813$	−2.81111e7			−1.49160
$814$	1.06449e6	+	1.84375e6i	0.0563094	+	0.0975307i
$815$	1.67972e7			0.885814
$816$	4.13454e7			2.17371
$817$	1.88977e7	+	3.00234e7i	0.990497	+	1.57364i
$818$	−1.86900e7			−0.976622
$819$	4.20895e6			0.219263
$820$	−99343.9	−	172069.i	−0.00515949	−	0.00893650i
$821$	2.51338e7			1.30137			0.650685	−	0.759348i	$-0.274482\pi$
$821$	2.51338e7			1.30137			0.650685	+	0.759348i	$0.274482\pi$
$822$	−2.11043e7	−	3.65536e7i	−1.08941	−	1.88691i
$823$	70044.8	+	121321.i	0.00360476	+	0.00624362i	0.867822	−	0.496875i	$-0.165519\pi$
$823$	70044.8	+	121321.i	0.00360476	+	0.00624362i	−0.864217	+	0.503119i	$0.832186\pi$
$824$	2.51776e6	−	4.36089e6i	0.129180	−	0.223747i
$825$	6.01962e6			0.307917
$826$	8.68369e6	−	1.50406e7i	0.442848	−	0.767035i
$827$	−3.93111e6	−	6.80889e6i	−0.199872	−	0.346188i	0.748615	−	0.663005i	$-0.230719\pi$
$827$	−3.93111e6	−	6.80889e6i	−0.199872	−	0.346188i	−0.948487	+	0.316817i	$0.897386\pi$
$828$	−1.72243e6			−0.0873102
$829$	−1.38930e6	−	2.40634e6i	−0.0702119	−	0.121610i	0.828782	−	0.559571i	$-0.189034\pi$
$829$	−1.38930e6	−	2.40634e6i	−0.0702119	−	0.121610i	−0.898994	+	0.437961i	$0.855701\pi$
$830$	8.02959e6	−	1.39077e7i	0.404574	−	0.700743i
$831$	454198.	−	786693.i	0.0228161	−	0.0395187i
$832$	4.64471e6	−	8.04487e6i	0.232622	−	0.402912i
$833$	−1.25561e7			−0.626964
$834$	−1.02612e7	+	1.77729e7i	−0.510838	+	0.884797i
$835$	8.24452e6	−	1.42799e7i	0.409213	−	0.708777i
$836$	2.38846e6	+	4.13693e6i	0.118196	+	0.204721i
$837$	−4.57158e6	−	7.91821e6i	−0.225555	−	0.390673i
$838$	−3.26357e7			−1.60540
$839$	−3.13532e7			−1.53772			−0.768860	−	0.639417i	$-0.779176\pi$
$839$	−3.13532e7			−1.53772			−0.768860	+	0.639417i	$0.779176\pi$
$840$	1.10973e7	+	1.92211e7i	0.542650	+	0.939898i
$841$	7.66185e6	+	1.32707e7i	0.373546	+	0.647000i
$842$	−1.51918e7	+	2.63130e7i	−0.738463	+	1.27906i
$843$	1.03237e7	−	1.78812e7i	0.500341	−	0.866617i
$844$	−1.19101e7			−0.575518
$845$	−1.35119e7	+	2.34033e7i	−0.650990	+	1.12755i
$846$	−719124.	+	1.24556e6i	−0.0345444	+	0.0598327i
$847$	1.08533e7	−	1.87984e7i	0.519820	−	0.900354i
$848$	1.44325e7	+	2.49979e7i	0.689212	+	1.19375i
$849$	−1.89229e7			−0.900988
$850$	2.47645e7	+	4.28933e7i	1.17566	+	2.03630i
$851$	5.01593e6	−	8.68785e6i	0.237426	−	0.411234i
$852$	−1.29105e7			−0.609318
$853$	1.14610e7	−	1.98511e7i	0.539326	−	0.934140i	−0.459614	−	0.888119i	$-0.652012\pi$
$853$	1.14610e7	−	1.98511e7i	0.539326	−	0.934140i	0.998940	−	0.0460215i	$-0.0146543\pi$
$854$	1.50637e7	+	2.60911e7i	0.706784	+	1.22419i
$855$	−3.91407e6	−	6.77936e6i	−0.183110	−	0.317157i
$856$	3.66807e6			0.171101
$857$	1.21459e7	+	2.10372e7i	0.564906	+	0.978445i	0.997058	+	0.0766449i	$0.0244208\pi$
$857$	1.21459e7	+	2.10372e7i	0.564906	+	0.978445i	−0.432153	+	0.901800i	$0.642246\pi$
$858$	−1.03295e7			−0.479029
$859$	6.79860e6			0.314367			0.157183	−	0.987569i	$-0.449759\pi$
$859$	6.79860e6			0.314367			0.157183	+	0.987569i	$0.449759\pi$
$860$	−6.67699e6	−	1.06080e7i	−0.307847	−	0.489088i
$861$	416367.			0.0191412
$862$	1.25855e7			0.576903
$863$	1.31013e7	+	2.26922e7i	0.598809	+	1.03717i	0.992997	+	0.118138i	$0.0376924\pi$
$863$	1.31013e7	+	2.26922e7i	0.598809	+	1.03717i	−0.394189	+	0.919030i	$0.628974\pi$
$864$	1.76871e7			0.806070
$865$	−7.68795e6	−	1.33159e7i	−0.349358	−	0.605105i
$866$	1.37817e7	+	2.38705e7i	0.624463	+	1.08160i
$867$	−2.63006e7	+	4.55539e7i	−1.18828	+	2.05815i
$868$	−4.41386e6			−0.198847
$869$	1.67198e6	−	2.89596e6i	0.0751074	−	0.130090i
$870$	−8.84759e6	−	1.53245e7i	−0.396302	−	0.686416i
$871$	1.22367e6			0.0546537
$872$	−8.21488e6	−	1.42286e7i	−0.365856	−	0.633681i
$873$	2.19248e6	−	3.79748e6i	0.0973642	−	0.168640i
$874$	3.91522e7	−	6.78137e7i	1.73372	−	3.00288i
$875$	−975439.	+	1.68951e6i	−0.0430705	+	0.0746003i
$876$	2.38043e6			0.104808
$877$	−668743.	+	1.15830e6i	−0.0293603	+	0.0508535i	−0.880332	−	0.474358i	$-0.842680\pi$
$877$	−668743.	+	1.15830e6i	−0.0293603	+	0.0508535i	0.850972	+	0.525211i	$0.176014\pi$
$878$	3.88051e6	−	6.72124e6i	0.169884	−	0.294248i
$879$	−1.11662e6	−	1.93404e6i	−0.0487454	−	0.0844295i
$880$	6.43323e6	+	1.11427e7i	0.280042	+	0.485046i
$881$	2.55902e7			1.11079			0.555397	−	0.831585i	$-0.312566\pi$
$881$	2.55902e7			1.11079			0.555397	+	0.831585i	$0.312566\pi$
$882$	−1.25059e6			−0.0541306
$883$	1.79489e7	+	3.10883e7i	0.774703	+	1.34182i	0.934961	+	0.354749i	$0.115434\pi$
$883$	1.79489e7	+	3.10883e7i	0.774703	+	1.34182i	−0.160259	+	0.987075i	$0.551233\pi$
$884$	−1.22155e7	−	2.11579e7i	−0.525751	−	0.910628i
$885$	1.00390e7	−	1.73881e7i	0.430858	−	0.746268i
$886$	−223512.	+	387134.i	−0.00956570	+	0.0165683i
$887$	1.39773e7			0.596505			0.298253	−	0.954487i	$-0.403596\pi$
$887$	1.39773e7			0.596505			0.298253	+	0.954487i	$0.403596\pi$
$888$	−2.32630e6	+	4.02928e6i	−0.0989997	+	0.171473i
$889$	−7.35243e6	+	1.27348e7i	−0.312016	+	0.540427i
$890$	1.69525e7	−	2.93626e7i	0.717396	−	1.24257i
$891$	3.14993e6	+	5.45584e6i	0.132925	+	0.230233i
$892$	1.38098e7			0.581132
$893$	−9.39768e6	−	1.62773e7i	−0.394359	−	0.683050i
$894$	−1.37394e7	+	2.37974e7i	−0.574942	+	0.995829i
$895$	2.55472e7			1.06607
$896$	−1.61152e7	+	2.79123e7i	−0.670603	+	1.16152i
$897$	2.43366e7	+	4.21523e7i	1.00990	+	1.74920i
$898$	6.62343e6	+	1.14721e7i	0.274089	+	0.474736i
$899$	−5.20396e6			−0.214751
$900$	709021.	+	1.22806e6i	0.0291778	+	0.0505374i
$901$	−5.10740e7			−2.09598
$902$	162887.			0.00666606
$903$	2.62478e7	−	1.00264e6i	1.07121	−	0.0409192i
$904$	2.63169e6			0.107106
$905$	−6.77036e6			−0.274783
$906$	−861095.	−	1.49146e6i	−0.0348522	−	0.0603658i
$907$	−3.51929e7			−1.42049			−0.710244	−	0.703956i	$-0.751415\pi$
$907$	−3.51929e7			−1.42049			−0.710244	+	0.703956i	$0.751415\pi$
$908$	288165.	+	499116.i	0.0115992	+	0.0200903i
$909$	89711.6	+	155385.i	0.00360113	+	0.00623734i
$910$	3.38036e7	−	5.85495e7i	1.35319	−	2.34380i
$911$	−9.27200e6			−0.370150			−0.185075	−	0.982724i	$-0.559253\pi$
$911$	−9.27200e6			−0.370150			−0.185075	+	0.982724i	$0.559253\pi$
$912$	−2.69075e7	+	4.66051e7i	−1.07124	+	1.85544i
$913$	1.89225e6	+	3.27747e6i	0.0751280	+	0.130125i
$914$	−3.40961e7			−1.35002
$915$	1.74148e7	+	3.01634e7i	0.687648	+	1.19104i
$916$	−583434.	+	1.01054e6i	−0.0229749	+	0.0397936i
$917$	−7.07925e6	+	1.22616e7i	−0.278012	+	0.481532i
$918$	−3.01413e7	+	5.22063e7i	−1.18047	+	2.04464i
$919$	482262.			0.0188362			0.00941811	−	0.999956i	$-0.497002\pi$
$919$	482262.			0.0188362			0.00941811	+	0.999956i	$0.497002\pi$
$920$	2.04568e7	−	3.54322e7i	0.796835	−	1.38016i
$921$	1.32392e7	−	2.29311e7i	0.514297	−	0.890789i
$922$	−5.90865e6	−	1.02341e7i	−0.228908	−	0.396481i
$923$	−2.90781e7	−	5.03648e7i	−1.12347	−	1.94591i
$924$	3.53692e6			0.136284
$925$	−8.25904e6			−0.317377
$926$	−7.17058e6	−	1.24198e7i	−0.274806	−	0.475978i
$927$	657509.	+	1.13884e6i	0.0251306	+	0.0435274i
$928$	5.03344e6	−	8.71817e6i	0.191865	−	0.332319i
$929$	5.37891e6	−	9.31654e6i	0.204482	−	0.354173i	−0.745486	−	0.666522i	$-0.767782\pi$
$929$	5.37891e6	−	9.31654e6i	0.204482	−	0.354173i	0.949968	+	0.312349i	$0.101116\pi$
$930$	−1.77515e7			−0.673021
$931$	8.17148e6	−	1.41534e7i	0.308977	−	0.535164i
$932$	4.61133e6	−	7.98706e6i	0.173895	−	0.301194i
$933$	7.46101e6	−	1.29229e7i	0.280604	−	0.486020i
$934$	1.04086e7	+	1.80282e7i	0.390414	+	0.676217i
$935$	−2.27660e7			−0.851643
$936$	1.79920e6	+	3.11630e6i	0.0671257	+	0.116265i
$937$	2.44181e7	−	4.22934e7i	0.908581	−	1.57371i	0.0925431	−	0.995709i	$-0.470500\pi$
$937$	2.44181e7	−	4.22934e7i	0.908581	−	1.57371i	0.816037	−	0.577999i	$-0.196166\pi$
$938$	−1.45760e6			−0.0540918
$939$	−1.31253e7	+	2.27337e7i	−0.485786	+	0.841406i
$940$	3.32042e6	+	5.75114e6i	0.122567	+	0.212292i
$941$	−6.15307e6	−	1.06574e7i	−0.226526	−	0.392354i	0.730250	−	0.683180i	$-0.239403\pi$
$941$	−6.15307e6	−	1.06574e7i	−0.226526	−	0.392354i	−0.956776	+	0.290825i	$0.906070\pi$
$942$	−1.54006e7			−0.565471
$943$	−383765.	−	664701.i	−0.0140536	−	0.0243415i
$944$	2.20024e7			0.803601
$945$	−4.79529e7			−1.74677
$946$	1.02684e7	−	392244.i	0.373056	−	0.0142504i
$947$	2.36458e7			0.856799			0.428400	−	0.903589i	$-0.359078\pi$
$947$	2.36458e7			0.856799			0.428400	+	0.903589i	$0.359078\pi$
$948$	−4.94172e6			−0.178590
$949$	5.36140e6	+	9.28621e6i	0.193247	+	0.334713i
$950$	−6.44666e7			−2.31753
$951$	2.29879e7	+	3.98162e7i	0.824230	+	1.42761i
$952$	−2.15176e7	−	3.72695e7i	−0.769486	−	1.33279i
$953$	−1.58773e6	+	2.75002e6i	−0.0566296	+	0.0980854i	−0.892950	−	0.450155i	$-0.851369\pi$
$953$	−1.58773e6	+	2.75002e6i	−0.0566296	+	0.0980854i	0.836321	+	0.548240i	$0.184702\pi$
$954$	−5.08696e6			−0.180962
$955$	−8.28316e6	+	1.43469e7i	−0.293892	+	0.509036i
$956$	5.54929e6	+	9.61165e6i	0.196378	+	0.340137i
$957$	4.17004e6			0.147184
$958$	−2.96907e7	−	5.14259e7i	−1.04522	−	1.81037i
$959$	−3.25513e7	+	5.63804e7i	−1.14293	+	1.97962i
$960$	−6.39617e6	+	1.10785e7i	−0.223997	+	0.387974i
$961$	1.17043e7	−	2.02725e7i	0.408825	−	0.708105i
$962$	1.41723e7			0.493746
$963$	−478956.	+	829576.i	−0.0166429	+	0.0288264i
$964$	−2.07608e6	+	3.59588e6i	−0.0719536	+	0.124627i
$965$	3.44727e7	+	5.97085e7i	1.19167	+	2.06404i
$966$	−2.89891e7	−	5.02105e7i	−0.999520	−	1.73122i
$967$	−2.30138e7			−0.791447			−0.395724	−	0.918370i	$-0.629506\pi$
$967$	−2.30138e7			−0.791447			−0.395724	+	0.918370i	$0.629506\pi$
$968$	1.85578e7			0.636557
$969$	−4.76102e7	−	8.24633e7i	−1.62889	−	2.82131i
$970$	−3.52171e7	−	6.09978e7i	−1.20178	−	2.08154i
$971$	1.48150e7	−	2.56603e7i	0.504258	−	0.873401i	−0.495730	−	0.868477i	$-0.665099\pi$
$971$	1.48150e7	−	2.56603e7i	0.504258	−	0.873401i	0.999988	−	0.00492403i	$-0.00156737\pi$
$972$	−1.62162e6	+	2.80873e6i	−0.0550533	+	0.0953551i
$973$	3.16538e7			1.07187
$974$	3.02484e7	−	5.23918e7i	1.02166	−	1.76956i
$975$	2.00359e7	−	3.47032e7i	0.674989	−	1.16912i
$976$	−1.90839e7	+	3.30543e7i	−0.641272	+	1.11072i
$977$	1.57030e6	+	2.71983e6i	0.0526315	+	0.0911604i	0.891141	−	0.453727i	$-0.149906\pi$
$977$	1.57030e6	+	2.71983e6i	0.0526315	+	0.0911604i	−0.838509	+	0.544887i	$0.816572\pi$
$978$	2.03501e7			0.680330
$979$	3.99502e6	+	6.91958e6i	0.133218	+	0.230740i
$980$	−2.88718e6	+	5.00074e6i	−0.0960303	+	0.166329i
$981$	4.29061e6			0.142346
$982$	−7.36118e6	+	1.27499e7i	−0.243595	+	0.421919i
$983$	−959179.	−	1.66135e6i	−0.0316604	−	0.0548374i	0.849761	−	0.527168i	$-0.176746\pi$
$983$	−959179.	−	1.66135e6i	−0.0316604	−	0.0548374i	−0.881421	+	0.472331i	$0.843413\pi$
$984$	177984.	+	308277.i	0.00585993	+	0.0101497i
$985$	2.49151e7			0.818225
$986$	1.71554e7	+	2.97140e7i	0.561963	+	0.973348i
$987$	−1.39164e7			−0.454711
$988$	3.17992e7			1.03639
$989$	−2.57932e7	−	4.09786e7i	−0.838522	−	1.33219i
$990$	−2.26749e6			−0.0735288
$991$	3.01657e7			0.975728			0.487864	−	0.872920i	$-0.337776\pi$
$991$	3.01657e7			0.975728			0.487864	+	0.872920i	$0.337776\pi$
$992$	−5.04947e6	−	8.74594e6i	−0.162917	−	0.282181i
$993$	−6.70336e6			−0.215734
$994$	3.46370e7	+	5.99930e7i	1.11192	+	1.92590i
$995$	4.40315e6	+	7.62648e6i	0.140996	+	0.244212i
$996$	2.79637e6	−	4.84346e6i	0.0893196	−	0.154706i
$997$	3.82271e7			1.21796			0.608980	−	0.793185i	$-0.291579\pi$
$997$	3.82271e7			1.21796			0.608980	+	0.793185i	$0.291579\pi$
$998$	2.02475e7	−	3.50697e7i	0.643495	−	1.11457i
$999$	−5.02613e6	−	8.70551e6i	−0.159338	−	0.275982i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.6.c.a.36.14	yes	34
43.6	even	3	inner	43.6.c.a.6.14	✓	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.6.c.a.6.14	✓	34	43.6	even	3	inner
43.6.c.a.36.14	yes	34	1.1	even	1	trivial

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	43.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+6.70145 q^{2} +(-7.23861 - 12.5376i) q^{3} +12.9095 q^{4} +(-40.0400 - 69.3513i) q^{5} +(-48.5092 - 84.0205i) q^{6} +(-74.8208 + 129.593i) q^{7} -127.934 q^{8} +(16.7049 - 28.9338i) q^{9} +O(q^{10})\)	\(q+6.70145 q^{2} +(-7.23861 - 12.5376i) q^{3} +12.9095 q^{4} +(-40.0400 - 69.3513i) q^{5} +(-48.5092 - 84.0205i) q^{6} +(-74.8208 + 129.593i) q^{7} -127.934 q^{8} +(16.7049 - 28.9338i) q^{9} +(-268.326 - 464.754i) q^{10} +126.467 q^{11} +(-93.4468 - 161.855i) q^{12} +(420.937 - 729.085i) q^{13} +(-501.408 + 868.464i) q^{14} +(-579.668 + 1004.01i) q^{15} -1270.45 q^{16} +(1123.97 - 1946.77i) q^{17} +(111.947 - 193.898i) q^{18} +(1462.95 + 2533.91i) q^{19} +(-516.896 - 895.290i) q^{20} +2166.40 q^{21} +847.515 q^{22} +(-1996.77 - 3458.50i) q^{23} +(926.066 + 1603.99i) q^{24} +(-1643.90 + 2847.32i) q^{25} +(2820.89 - 4885.93i) q^{26} -4001.65 q^{27} +(-965.898 + 1672.99i) q^{28} +(-1138.80 + 1972.46i) q^{29} +(-3884.62 + 6728.36i) q^{30} +(1142.42 + 1978.74i) q^{31} -4419.96 q^{32} +(-915.448 - 1585.60i) q^{33} +(7532.23 - 13046.2i) q^{34} +11983.3 q^{35} +(215.652 - 373.520i) q^{36} +(1256.01 + 2175.48i) q^{37} +(9803.91 + 16980.9i) q^{38} -12188.0 q^{39} +(5122.48 + 8872.40i) q^{40} +192.193 q^{41} +14518.0 q^{42} +(12115.9 - 462.816i) q^{43} +1632.63 q^{44} -2675.46 q^{45} +(-13381.2 - 23177.0i) q^{46} -6423.78 q^{47} +(9196.29 + 15928.4i) q^{48} +(-2792.80 - 4837.28i) q^{49} +(-11016.5 + 19081.2i) q^{50} -32543.9 q^{51} +(5434.09 - 9412.12i) q^{52} +(-11360.2 - 19676.4i) q^{53} -26816.9 q^{54} +(-5063.75 - 8770.67i) q^{55} +(9572.14 - 16579.4i) q^{56} +(21179.5 - 36684.0i) q^{57} +(-7631.60 + 13218.3i) q^{58} -17318.6 q^{59} +(-7483.22 + 12961.3i) q^{60} +(15021.4 - 26017.8i) q^{61} +(7655.91 + 13260.4i) q^{62} +(2499.75 + 4329.70i) q^{63} +11034.2 q^{64} -67417.3 q^{65} +(-6134.83 - 10625.8i) q^{66} +(726.753 + 1258.77i) q^{67} +(14509.9 - 25131.8i) q^{68} +(-28907.7 + 50069.5i) q^{69} +80305.5 q^{70} +(34539.7 - 59824.5i) q^{71} +(-2137.13 + 3701.62i) q^{72} +(-6368.40 + 11030.4i) q^{73} +(8417.12 + 14578.9i) q^{74} +47598.2 q^{75} +(18886.0 + 32711.5i) q^{76} +(-9462.38 + 16389.3i) q^{77} -81677.4 q^{78} +(13220.7 - 22898.9i) q^{79} +(50868.7 + 88107.2i) q^{80} +(24907.1 + 43140.4i) q^{81} +1287.98 q^{82} +(14962.4 + 25915.6i) q^{83} +27967.1 q^{84} -180015. q^{85} +(81193.9 - 3101.54i) q^{86} +32973.3 q^{87} -16179.5 q^{88} +(31589.4 + 54714.4i) q^{89} -17929.5 q^{90} +(62989.7 + 109101. i) q^{91} +(-25777.2 - 44647.5i) q^{92} +(16539.1 - 28646.6i) q^{93} -43048.7 q^{94} +(117153. - 202915. i) q^{95} +(31994.4 + 55415.9i) q^{96} +131247. q^{97} +(-18715.9 - 32416.8i) q^{98} +(2112.63 - 3659.17i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 14 q^{2} - 14 q^{3} + 454 q^{4} + 71 q^{5} + 15 q^{6} + 225 q^{7} - 936 q^{8} - 1011 q^{9}+O(q^{10}) \) 34 * q - 14 * q^2 - 14 * q^3 + 454 * q^4 + 71 * q^5 + 15 * q^6 + 225 * q^7 - 936 * q^8 - 1011 * q^9	\( 34 q - 14 q^{2} - 14 q^{3} + 454 q^{4} + 71 q^{5} + 15 q^{6} + 225 q^{7} - 936 q^{8} - 1011 q^{9} - 317 q^{10} + 1326 q^{11} - 648 q^{12} + 1006 q^{13} - 1272 q^{14} + 683 q^{15} + 3574 q^{16} + 200 q^{17} + 1861 q^{18} + 3361 q^{19} + 3825 q^{20} - 1320 q^{21} - 8768 q^{22} + 560 q^{23} - 7382 q^{24} - 3232 q^{25} - 3201 q^{26} - 122 q^{27} + 13934 q^{28} + 8887 q^{29} - 19449 q^{30} - 6749 q^{31} - 19086 q^{32} + 7106 q^{33} + 8423 q^{34} + 31118 q^{35} - 14112 q^{36} - 4514 q^{37} + 7072 q^{38} - 5404 q^{39} - 18519 q^{40} - 28996 q^{41} + 58118 q^{42} - 14998 q^{43} + 71050 q^{44} - 92096 q^{45} + 20052 q^{46} - 10742 q^{47} + 32927 q^{48} + 7472 q^{49} + 20362 q^{50} + 20250 q^{51} + 59532 q^{52} - 50572 q^{53} - 230084 q^{54} + 38544 q^{55} - 40355 q^{56} - 18087 q^{57} - 33436 q^{58} + 112654 q^{59} + 134093 q^{60} - 20120 q^{61} - 31491 q^{62} + 188227 q^{63} + 125164 q^{64} - 36578 q^{65} + 8803 q^{66} - 73824 q^{67} - 128456 q^{68} + 8005 q^{69} - 141610 q^{70} + 142842 q^{71} + 98466 q^{72} - 91624 q^{73} - 99720 q^{74} + 298358 q^{75} + 258288 q^{76} + 68051 q^{77} - 201116 q^{78} + 99734 q^{79} - 31261 q^{80} - 28441 q^{81} - 147772 q^{82} - 47340 q^{83} - 624232 q^{84} - 71734 q^{85} - 115526 q^{86} - 215924 q^{87} - 720684 q^{88} + 60402 q^{89} + 676108 q^{90} + 164172 q^{91} + 78997 q^{92} - 40793 q^{93} - 341874 q^{94} + 123541 q^{95} - 442140 q^{96} + 318476 q^{97} + 217473 q^{98} - 134770 q^{99}+O(q^{100}) \) 34 * q - 14 * q^2 - 14 * q^3 + 454 * q^4 + 71 * q^5 + 15 * q^6 + 225 * q^7 - 936 * q^8 - 1011 * q^9 - 317 * q^10 + 1326 * q^11 - 648 * q^12 + 1006 * q^13 - 1272 * q^14 + 683 * q^15 + 3574 * q^16 + 200 * q^17 + 1861 * q^18 + 3361 * q^19 + 3825 * q^20 - 1320 * q^21 - 8768 * q^22 + 560 * q^23 - 7382 * q^24 - 3232 * q^25 - 3201 * q^26 - 122 * q^27 + 13934 * q^28 + 8887 * q^29 - 19449 * q^30 - 6749 * q^31 - 19086 * q^32 + 7106 * q^33 + 8423 * q^34 + 31118 * q^35 - 14112 * q^36 - 4514 * q^37 + 7072 * q^38 - 5404 * q^39 - 18519 * q^40 - 28996 * q^41 + 58118 * q^42 - 14998 * q^43 + 71050 * q^44 - 92096 * q^45 + 20052 * q^46 - 10742 * q^47 + 32927 * q^48 + 7472 * q^49 + 20362 * q^50 + 20250 * q^51 + 59532 * q^52 - 50572 * q^53 - 230084 * q^54 + 38544 * q^55 - 40355 * q^56 - 18087 * q^57 - 33436 * q^58 + 112654 * q^59 + 134093 * q^60 - 20120 * q^61 - 31491 * q^62 + 188227 * q^63 + 125164 * q^64 - 36578 * q^65 + 8803 * q^66 - 73824 * q^67 - 128456 * q^68 + 8005 * q^69 - 141610 * q^70 + 142842 * q^71 + 98466 * q^72 - 91624 * q^73 - 99720 * q^74 + 298358 * q^75 + 258288 * q^76 + 68051 * q^77 - 201116 * q^78 + 99734 * q^79 - 31261 * q^80 - 28441 * q^81 - 147772 * q^82 - 47340 * q^83 - 624232 * q^84 - 71734 * q^85 - 115526 * q^86 - 215924 * q^87 - 720684 * q^88 + 60402 * q^89 + 676108 * q^90 + 164172 * q^91 + 78997 * q^92 - 40793 * q^93 - 341874 * q^94 + 123541 * q^95 - 442140 * q^96 + 318476 * q^97 + 217473 * q^98 - 134770 * q^99

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