LMFDB - Embedded newform 43.6.c.a.36.8

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			36.8
Character	$\chi$	$=$	43.36
Dual form			43.6.c.a.6.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.35784 q^{2} +(-4.70904 - 8.15629i) q^{3} -26.4406 q^{4} +(15.5528 + 26.9382i) q^{5} +(11.1032 + 19.2313i) q^{6} +(-36.1175 + 62.5573i) q^{7} +137.794 q^{8} +(77.1499 - 133.628i) q^{9} +O(q^{10})$	\(q-2.35784 q^{2} +(-4.70904 - 8.15629i) q^{3} -26.4406 q^{4} +(15.5528 + 26.9382i) q^{5} +(11.1032 + 19.2313i) q^{6} +(-36.1175 + 62.5573i) q^{7} +137.794 q^{8} +(77.1499 - 133.628i) q^{9} +(-36.6710 - 63.5160i) q^{10} +785.739 q^{11} +(124.510 + 215.657i) q^{12} +(-374.054 + 647.881i) q^{13} +(85.1594 - 147.500i) q^{14} +(146.477 - 253.706i) q^{15} +521.202 q^{16} +(198.545 - 343.889i) q^{17} +(-181.907 + 315.073i) q^{18} +(1247.23 + 2160.26i) q^{19} +(-411.224 - 712.261i) q^{20} +680.315 q^{21} -1852.65 q^{22} +(628.566 + 1088.71i) q^{23} +(-648.876 - 1123.89i) q^{24} +(1078.72 - 1868.40i) q^{25} +(881.961 - 1527.60i) q^{26} -3741.80 q^{27} +(954.967 - 1654.05i) q^{28} +(-2011.40 + 3483.85i) q^{29} +(-345.370 + 598.199i) q^{30} +(-3397.41 - 5884.48i) q^{31} -5638.31 q^{32} +(-3700.07 - 6408.72i) q^{33} +(-468.137 + 810.838i) q^{34} -2246.91 q^{35} +(-2039.89 + 3533.19i) q^{36} +(5808.25 + 10060.2i) q^{37} +(-2940.77 - 5093.56i) q^{38} +7045.74 q^{39} +(2143.07 + 3711.91i) q^{40} +18171.5 q^{41} -1604.08 q^{42} +(-11480.7 - 3898.98i) q^{43} -20775.4 q^{44} +4799.58 q^{45} +(-1482.06 - 2567.01i) q^{46} +17311.6 q^{47} +(-2454.36 - 4251.08i) q^{48} +(5794.55 + 10036.5i) q^{49} +(-2543.46 + 4405.40i) q^{50} -3739.82 q^{51} +(9890.21 - 17130.3i) q^{52} +(10053.7 + 17413.5i) q^{53} +8822.58 q^{54} +(12220.4 + 21166.4i) q^{55} +(-4976.76 + 8620.01i) q^{56} +(11746.5 - 20345.5i) q^{57} +(4742.57 - 8214.37i) q^{58} -27080.7 q^{59} +(-3872.94 + 6708.13i) q^{60} +(23684.1 - 41022.1i) q^{61} +(8010.56 + 13874.7i) q^{62} +(5572.92 + 9652.58i) q^{63} -3384.21 q^{64} -23270.3 q^{65} +(8724.20 + 15110.8i) q^{66} +(18579.1 + 32179.9i) q^{67} +(-5249.64 + 9092.63i) q^{68} +(5919.89 - 10253.5i) q^{69} +5297.85 q^{70} +(-25191.9 + 43633.6i) q^{71} +(10630.8 - 18413.0i) q^{72} +(17654.3 - 30578.2i) q^{73} +(-13695.0 - 23720.4i) q^{74} -20319.0 q^{75} +(-32977.4 - 57118.6i) q^{76} +(-28378.9 + 49153.7i) q^{77} -16612.8 q^{78} +(4905.21 - 8496.08i) q^{79} +(8106.13 + 14040.2i) q^{80} +(-1127.14 - 1952.26i) q^{81} -42845.5 q^{82} +(-24391.4 - 42247.2i) q^{83} -17987.9 q^{84} +12351.7 q^{85} +(27069.7 + 9193.18i) q^{86} +37887.0 q^{87} +108270. q^{88} +(-36792.6 - 63726.6i) q^{89} -11316.7 q^{90} +(-27019.8 - 46799.6i) q^{91} +(-16619.7 - 28786.1i) q^{92} +(-31997.1 + 55420.5i) q^{93} -40818.0 q^{94} +(-38795.7 + 67196.1i) q^{95} +(26551.0 + 45987.7i) q^{96} -14665.7 q^{97} +(-13662.7 - 23664.4i) q^{98} +(60619.7 - 104996. i) 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 $

$2$	−2.35784			−0.416812			−0.208406	−	0.978042i	$-0.566828\pi$
$2$	−2.35784			−0.416812			−0.208406	+	0.978042i	$0.566828\pi$
$3$	−4.70904	−	8.15629i	−0.302085	−	0.523227i	0.674523	−	0.738254i	$-0.264349\pi$
$3$	−4.70904	−	8.15629i	−0.302085	−	0.523227i	−0.976608	+	0.215027i	$0.931016\pi$
$4$	−26.4406			−0.826268
$5$	15.5528	+	26.9382i	0.278216	+	0.481885i	0.970942	−	0.239317i	$-0.0769235\pi$
$5$	15.5528	+	26.9382i	0.278216	+	0.481885i	−0.692725	+	0.721202i	$0.743590\pi$
$6$	11.1032	+	19.2313i	0.125913	+	0.218087i
$7$	−36.1175	+	62.5573i	−0.278594	+	0.482540i	−0.971036	−	0.238935i	$-0.923202\pi$
$7$	−36.1175	+	62.5573i	−0.278594	+	0.482540i	0.692441	+	0.721474i	$0.256535\pi$
$8$	137.794			0.761210
$9$	77.1499	−	133.628i	0.317489	−	0.549908i
$10$	−36.6710	−	63.5160i	−0.115964	−	0.200855i
$11$	785.739			1.95793			0.978963	−	0.204037i	$-0.0654063\pi$
$11$	785.739			1.95793			0.978963	+	0.204037i	$0.0654063\pi$
$12$	124.510	+	215.657i	0.249603	+	0.432325i
$13$	−374.054	+	647.881i	−0.613870	+	1.06325i	0.376712	+	0.926330i	$0.377055\pi$
$13$	−374.054	+	647.881i	−0.613870	+	1.06325i	−0.990582	+	0.136923i	$0.956279\pi$
$14$	85.1594	−	147.500i	0.116121	−	0.201128i
$15$	146.477	−	253.706i	0.168090	−	0.291140i
$16$	521.202			0.508986
$17$	198.545	−	343.889i	0.166623	−	0.288600i	−0.770607	−	0.637310i	$-0.780047\pi$
$17$	198.545	−	343.889i	0.166623	−	0.288600i	0.937231	+	0.348710i	$0.113380\pi$
$18$	−181.907	+	315.073i	−0.132333	+	0.229208i
$19$	1247.23	+	2160.26i	0.792614	+	1.37285i	0.924343	+	0.381562i	$0.124614\pi$
$19$	1247.23	+	2160.26i	0.792614	+	1.37285i	−0.131729	+	0.991286i	$0.542053\pi$
$20$	−411.224	−	712.261i	−0.229881	−	0.398166i
$21$	680.315			0.336637
$22$	−1852.65			−0.816087
$23$	628.566	+	1088.71i	0.247760	+	0.429133i	0.962904	−	0.269844i	$-0.0869722\pi$
$23$	628.566	+	1088.71i	0.247760	+	0.429133i	−0.715144	+	0.698977i	$0.753639\pi$
$24$	−648.876	−	1123.89i	−0.229950	−	0.398285i
$25$	1078.72	−	1868.40i	0.345191	−	0.597889i
$26$	881.961	−	1527.60i	0.255868	−	0.443177i
$27$	−3741.80			−0.987805
$28$	954.967	−	1654.05i	0.230194	−	0.398707i
$29$	−2011.40	+	3483.85i	−0.444123	+	0.769244i	−0.997991	−	0.0633608i	$-0.979818\pi$
$29$	−2011.40	+	3483.85i	−0.444123	+	0.769244i	0.553867	+	0.832605i	$0.313151\pi$
$30$	−345.370	+	598.199i	−0.0700619	+	0.121351i
$31$	−3397.41	−	5884.48i	−0.634956	−	1.09978i	−0.986525	−	0.163614i	$-0.947685\pi$
$31$	−3397.41	−	5884.48i	−0.634956	−	1.09978i	0.351569	−	0.936162i	$-0.385648\pi$
$32$	−5638.31			−0.973362
$33$	−3700.07	−	6408.72i	−0.591460	−	1.02444i
$34$	−468.137	+	810.838i	−0.0694506	+	0.120292i
$35$	−2246.91			−0.310038
$36$	−2039.89	+	3533.19i	−0.262331	+	0.454371i
$37$	5808.25	+	10060.2i	0.697495	+	1.20810i	0.969332	+	0.245754i	$0.0790356\pi$
$37$	5808.25	+	10060.2i	0.697495	+	1.20810i	−0.271837	+	0.962343i	$0.587631\pi$
$38$	−2940.77	−	5093.56i	−0.330371	−	0.572219i
$39$	7045.74			0.741763
$40$	2143.07	+	3711.91i	0.211781	+	0.366815i
$41$	18171.5			1.68823			0.844113	−	0.536166i	$-0.180128\pi$
$41$	18171.5			1.68823			0.844113	+	0.536166i	$0.180128\pi$
$42$	−1604.08			−0.140314
$43$	−11480.7	−	3898.98i	−0.946885	−	0.321573i
$43$	−11480.7	−	3898.98i	−0.946885	−	0.321573i
$44$	−20775.4			−1.61777
$45$	4799.58			0.353323
$46$	−1482.06	−	2567.01i	−0.103269	−	0.178868i
$47$	17311.6			1.14312			0.571560	−	0.820560i	$-0.306338\pi$
$47$	17311.6			1.14312			0.571560	+	0.820560i	$0.306338\pi$
$48$	−2454.36	−	4251.08i	−0.153757	−	0.266315i
$49$	5794.55	+	10036.5i	0.344770	+	0.597160i
$50$	−2543.46	+	4405.40i	−0.143880	+	0.249207i
$51$	−3739.82			−0.201338
$52$	9890.21	−	17130.3i	0.507221	−	0.878532i
$53$	10053.7	+	17413.5i	0.491626	+	0.851521i	0.999954	−	0.00964287i	$-0.00306947\pi$
$53$	10053.7	+	17413.5i	0.491626	+	0.851521i	−0.508328	+	0.861164i	$0.669736\pi$
$54$	8822.58			0.411729
$55$	12220.4	+	21166.4i	0.544727	+	0.943495i
$56$	−4976.76	+	8620.01i	−0.212069	+	0.367314i
$57$	11746.5	−	20345.5i	0.478874	−	0.829433i
$58$	4742.57	−	8214.37i	0.185116	−	0.320630i
$59$	−27080.7			−1.01281			−0.506407	−	0.862294i	$-0.669027\pi$
$59$	−27080.7			−1.01281			−0.506407	+	0.862294i	$0.669027\pi$
$60$	−3872.94	+	6708.13i	−0.138887	+	0.240560i
$61$	23684.1	−	41022.1i	0.814953	−	1.41154i	−0.0944089	−	0.995534i	$-0.530096\pi$
$61$	23684.1	−	41022.1i	0.814953	−	1.41154i	0.909362	−	0.416006i	$-0.136571\pi$
$62$	8010.56	+	13874.7i	0.264657	+	0.458400i
$63$	5572.92	+	9652.58i	0.176901	+	0.306402i
$64$	−3384.21			−0.103278
$65$	−23270.3			−0.683154
$66$	8724.20	+	15110.8i	0.246528	+	0.426998i
$67$	18579.1	+	32179.9i	0.505635	+	0.875785i	0.999979	+	0.00651894i	$0.00207506\pi$
$67$	18579.1	+	32179.9i	0.505635	+	0.875785i	−0.494344	+	0.869266i	$0.664592\pi$
$68$	−5249.64	+	9092.63i	−0.137676	+	0.238461i
$69$	5919.89	−	10253.5i	0.149689	−	0.259269i
$70$	5297.85			0.129227
$71$	−25191.9	+	43633.6i	−0.593082	+	1.02725i	0.400732	+	0.916195i	$0.368756\pi$
$71$	−25191.9	+	43633.6i	−0.593082	+	1.02725i	−0.993814	+	0.111053i	$0.964578\pi$
$72$	10630.8	−	18413.0i	0.241676	−	0.418595i
$73$	17654.3	−	30578.2i	0.387743	−	0.671590i	−0.604403	−	0.796679i	$-0.706588\pi$
$73$	17654.3	−	30578.2i	0.387743	−	0.671590i	0.992146	+	0.125089i	$0.0399216\pi$
$74$	−13695.0	−	23720.4i	−0.290724	−	0.503549i
$75$	−20319.0			−0.417109
$76$	−32977.4	−	57118.6i	−0.654911	−	1.13434i
$77$	−28378.9	+	49153.7i	−0.545467	+	0.944777i
$78$	−16612.8			−0.309176
$79$	4905.21	−	8496.08i	0.0884281	−	0.153162i	−0.818419	−	0.574622i	$-0.805149\pi$
$79$	4905.21	−	8496.08i	0.0884281	−	0.153162i	0.906847	+	0.421460i	$0.138482\pi$
$80$	8106.13	+	14040.2i	0.141608	+	0.245273i
$81$	−1127.14	−	1952.26i	−0.0190882	−	0.0330618i
$82$	−42845.5			−0.703672
$83$	−24391.4	−	42247.2i	−0.388635	−	0.673136i	0.603631	−	0.797264i	$-0.293720\pi$
$83$	−24391.4	−	42247.2i	−0.388635	−	0.673136i	−0.992266	+	0.124128i	$0.960387\pi$
$84$	−17987.9			−0.278152
$85$	12351.7			0.185429
$86$	27069.7	+	9193.18i	0.394673	+	0.134035i
$87$	37887.0			0.536652
$88$	108270.			1.49039
$89$	−36792.6	−	63726.6i	−0.492363	−	0.852797i	0.507599	−	0.861594i	$-0.330533\pi$
$89$	−36792.6	−	63726.6i	−0.492363	−	0.852797i	−0.999961	+	0.00879659i	$0.997200\pi$
$90$	−11316.7			−0.147269
$91$	−27019.8	−	46799.6i	−0.342041	−	0.592433i
$92$	−16619.7	−	28786.1i	−0.204716	−	0.354579i
$93$	−31997.1	+	55420.5i	−0.383621	+	0.664451i
$94$	−40818.0			−0.476466
$95$	−38795.7	+	67196.1i	−0.441036	+	0.763897i
$96$	26551.0	+	45987.7i	0.294038	+	0.509289i
$97$	−14665.7			−0.158261			−0.0791305	−	0.996864i	$-0.525214\pi$
$97$	−14665.7			−0.158261			−0.0791305	+	0.996864i	$0.525214\pi$
$98$	−13662.7	−	23664.4i	−0.143704	−	0.248903i
$99$	60619.7	−	104996.i	0.621621	−	1.07668i
$100$	−28522.1	+	49401.7i	−0.285221	+	0.494017i
$101$	−24764.9	+	42894.1i	−0.241565	+	0.418402i	−0.961160	−	0.275991i	$-0.910994\pi$
$101$	−24764.9	+	42894.1i	−0.241565	+	0.418402i	0.719596	+	0.694393i	$0.244327\pi$
$102$	8817.91			0.0839199
$103$	19879.4	−	34432.1i	0.184633	−	0.319794i	−0.758820	−	0.651301i	$-0.774224\pi$
$103$	19879.4	−	34432.1i	0.184633	−	0.319794i	0.943453	+	0.331507i	$0.107557\pi$
$104$	−51542.3	+	89273.9i	−0.467284	+	0.809359i
$105$	10580.8	+	18326.4i	0.0936578	+	0.162220i
$106$	−23705.0	−	41058.2i	−0.204915	−	0.354924i
$107$	−118895.			−1.00394			−0.501968	−	0.864886i	$-0.667390\pi$
$107$	−118895.			−1.00394			−0.501968	+	0.864886i	$0.667390\pi$
$108$	98935.3			0.816192
$109$	26664.4	+	46184.1i	0.214964	+	0.372328i	0.953261	−	0.302147i	$-0.0977033\pi$
$109$	26664.4	+	46184.1i	0.214964	+	0.372328i	−0.738298	+	0.674475i	$0.764370\pi$
$110$	−28813.8	−	49907.0i	−0.227049	−	0.393260i
$111$	54702.6	−	94747.7i	0.421406	−	0.729896i
$112$	−18824.5	+	32605.0i	−0.141801	+	0.245606i
$113$	−15529.6			−0.114410			−0.0572052	−	0.998362i	$-0.518219\pi$
$113$	−15529.6			−0.114410			−0.0572052	+	0.998362i	$0.518219\pi$
$114$	−27696.4	+	47971.5i	−0.199600	+	0.345718i
$115$	−19551.9	+	33864.9i	−0.137862	+	0.238784i
$116$	53182.6	−	92114.9i	0.366965	−	0.635602i
$117$	57716.5	+	99967.9i	0.389794	+	0.675143i
$118$	63852.1			0.422153
$119$	14341.9	+	24840.8i	0.0928407	+	0.160805i
$120$	20183.6	−	34959.1i	0.127952	−	0.221619i
$121$	456334.			2.83348
$122$	−55843.4	+	96723.7i	−0.339682	+	0.588347i
$123$	−85570.2	−	148212.i	−0.509987	−	0.883324i
$124$	89829.4	+	155589.i	0.524644	+	0.908709i
$125$	164313.			0.940584
$126$	−13140.1	−	22759.3i	−0.0737346	−	0.127712i
$127$	−155519.			−0.855604			−0.427802	−	0.903872i	$-0.640712\pi$
$127$	−155519.			−0.855604			−0.427802	+	0.903872i	$0.640712\pi$
$128$	188405.			1.01641
$129$	22261.9	+	112000.i	0.117784	+	0.592578i
$130$	54867.7			0.284747
$131$	87048.1			0.443181			0.221591	−	0.975140i	$-0.428875\pi$
$131$	87048.1			0.443181			0.221591	+	0.975140i	$0.428875\pi$
$132$	97832.1	+	169450.i	0.488705	+	0.846461i
$133$	−180187.			−0.883271
$134$	−43806.6	−	75875.2i	−0.210755	−	0.365038i
$135$	−58195.3	−	100797.i	−0.274823	−	0.476008i
$136$	27358.2	−	47385.8i	0.126835	−	0.219685i
$137$	−157426.			−0.716596			−0.358298	−	0.933607i	$-0.616643\pi$
$137$	−157426.			−0.716596			−0.358298	+	0.933607i	$0.616643\pi$
$138$	−13958.2	+	24176.3i	−0.0623923	+	0.108067i
$139$	−59373.3	−	102838.i	−0.260648	−	0.451455i	0.705766	−	0.708445i	$-0.250603\pi$
$139$	−59373.3	−	102838.i	−0.260648	−	0.451455i	−0.966414	+	0.256989i	$0.917269\pi$
$140$	59409.5			0.256174
$141$	−81520.9	−	141198.i	−0.345320	−	0.598111i
$142$	59398.5	−	102881.i	0.247204	−	0.428169i
$143$	−293909.	+	509065.i	−1.20191	+	2.08177i
$144$	40210.7	−	69647.0i	0.161598	−	0.279896i
$145$	−125131.			−0.494249
$146$	−41626.1	+	72098.5i	−0.161616	+	0.279927i
$147$	54573.6	−	94524.2i	0.208300	−	0.360786i
$148$	−153574.	−	265997.i	−0.576318	−	0.998212i
$149$	−50677.4	−	87775.9i	−0.187003	−	0.323899i	0.757247	−	0.653129i	$-0.226544\pi$
$149$	−50677.4	−	87775.9i	−0.187003	−	0.323899i	−0.944250	+	0.329230i	$0.893211\pi$
$150$	47909.0			0.173856
$151$	−273662.			−0.976724			−0.488362	−	0.872641i	$-0.662405\pi$
$151$	−273662.			−0.976724			−0.488362	+	0.872641i	$0.662405\pi$
$152$	171860.	+	297671.i	0.603346	+	1.04503i
$153$	−30635.4	−	53062.1i	−0.105802	−	0.183255i
$154$	66913.0	−	115897.i	0.227357	−	0.393794i
$155$	105678.	−	183040.i	0.353310	−	0.611951i
$156$	−186293.			−0.612895
$157$	−85576.5	+	148223.i	−0.277080	+	0.479917i	−0.970658	−	0.240465i	$-0.922700\pi$
$157$	−85576.5	+	148223.i	−0.277080	+	0.479917i	0.693578	+	0.720382i	$0.256033\pi$
$158$	−11565.7	+	20032.4i	−0.0368579	+	0.0638397i
$159$	94686.2	−	164001.i	0.297026	−	0.514463i
$160$	−87691.3	−	151886.i	−0.270805	−	0.469048i
$161$	−90808.9			−0.276098
$162$	2657.62	+	4603.14i	0.00795620	+	0.0137805i
$163$	−195306.	+	338280.i	−0.575767	+	0.997258i	0.420191	+	0.907436i	$0.361963\pi$
$163$	−195306.	+	338280.i	−0.575767	+	0.997258i	−0.995958	+	0.0898219i	$0.971370\pi$
$164$	−480464.			−1.39493
$165$	115093.	−	199346.i	0.329108	−	0.570031i
$166$	57511.2	+	99612.3i	0.161988	+	0.280571i
$167$	−324947.	−	562825.i	−0.901616	−	1.56164i	−0.825397	−	0.564553i	$-0.809049\pi$
$167$	−324947.	−	562825.i	−0.901616	−	1.56164i	−0.0762185	−	0.997091i	$-0.524285\pi$
$168$	93743.1			0.256251
$169$	−94186.5	−	163136.i	−0.253672	−	0.439372i
$170$	−29123.3			−0.0772891
$171$	384894.			1.00659
$172$	303556.	+	103091.i	0.782381	+	0.265705i
$173$	113478.			0.288269			0.144135	−	0.989558i	$-0.453960\pi$
$173$	113478.			0.288269			0.144135	+	0.989558i	$0.453960\pi$
$174$	−89331.7			−0.223683
$175$	77921.5	+	134964.i	0.192337	+	0.333137i
$176$	409529.			0.996558
$177$	127524.	+	220878.i	0.305956	+	0.529931i
$178$	86751.1	+	150257.i	0.205223	+	0.355456i
$179$	−55577.1	+	96262.3i	−0.129647	+	0.224556i	−0.923540	−	0.383502i	$-0.874718\pi$
$179$	−55577.1	+	96262.3i	−0.129647	+	0.224556i	0.793893	+	0.608058i	$0.208051\pi$
$180$	−126904.			−0.291939
$181$	31209.6	−	54056.6i	0.0708095	−	0.122646i	−0.828447	−	0.560068i	$-0.810775\pi$
$181$	31209.6	−	54056.6i	0.0708095	−	0.122646i	0.899256	+	0.437422i	$0.144108\pi$
$182$	63708.4	+	110346.i	0.142567	+	0.246933i
$183$	−446118.			−0.984740
$184$	86612.5	+	150017.i	0.188598	+	0.326661i
$185$	−180669.	+	312928.i	−0.388109	+	0.672225i
$186$	75444.1	−	130673.i	0.159898	−	0.276951i
$187$	156004.	−	270207.i	0.326236	−	0.565058i
$188$	−457728.			−0.944524
$189$	135144.	−	234077.i	0.275197	−	0.476655i
$190$	91474.1	−	158438.i	0.183829	−	0.318401i
$191$	80509.0	+	139446.i	0.159684	+	0.276581i	0.934755	−	0.355294i	$-0.115619\pi$
$191$	80509.0	+	139446.i	0.159684	+	0.276581i	−0.775071	+	0.631874i	$0.782286\pi$
$192$	15936.4	+	27602.6i	0.0311987	+	0.0540377i
$193$	386516.			0.746919			0.373460	−	0.927646i	$-0.378171\pi$
$193$	386516.			0.746919			0.373460	+	0.927646i	$0.378171\pi$
$194$	34579.5			0.0659651
$195$	109581.	+	189799.i	0.206371	+	0.357444i
$196$	−153211.	−	265370.i	−0.284873	−	0.493414i
$197$	−164469.	+	284868.i	−0.301938	+	0.522972i	−0.976575	−	0.215178i	$-0.930967\pi$
$197$	−164469.	+	284868.i	−0.301938	+	0.522972i	0.674637	+	0.738150i	$0.264300\pi$
$198$	−142932.	+	247565.i	−0.259099	+	0.448772i
$199$	309184.			0.553457			0.276729	−	0.960948i	$-0.410750\pi$
$199$	309184.			0.553457			0.276729	+	0.960948i	$0.410750\pi$
$200$	148641.	−	257454.i	0.262763	−	0.455119i
$201$	174979.	−	303073.i	0.305489	−	0.529123i
$202$	58391.8	−	101138.i	0.100687	−	0.174395i
$203$	−145293.	−	251656.i	−0.247460	−	0.428614i
$204$	98882.9			0.166359
$205$	282616.	+	489506.i	0.469692	+	0.813530i
$206$	−46872.5	+	81185.6i	−0.0769573	+	0.133294i
$207$	193975.			0.314645
$208$	−194958.	+	337677.i	−0.312451	+	0.541182i
$209$	979995.	+	1.69740e6i	1.55188	+	2.68793i
$210$	−24947.8	−	43210.9i	−0.0390377	−	0.0676153i
$211$	146655.			0.226772			0.113386	−	0.993551i	$-0.463830\pi$
$211$	146655.			0.226772			0.113386	+	0.993551i	$0.463830\pi$
$212$	−265825.	−	460422.i	−0.406215	−	0.703584i
$213$	474518.			0.716645
$214$	280337.			0.418452
$215$	−73525.3	−	369909.i	−0.108478	−	0.545756i
$216$	−515597.			−0.751927
$217$	490823.			0.707580
$218$	−62870.4	−	108895.i	−0.0895994	−	0.155191i
$219$	−332539.			−0.468525
$220$	−323114.	−	559651.i	−0.450090	−	0.779579i
$221$	148533.	+	257267.i	0.204570	+	0.354326i
$222$	−128980.	+	223400.i	−0.175647	+	0.304229i
$223$	−794062.			−1.06928			−0.534641	−	0.845079i	$-0.679553\pi$
$223$	−794062.			−1.06928			−0.534641	+	0.845079i	$0.679553\pi$
$224$	203642.	−	352718.i	0.271173	−	0.469686i
$225$	−166447.	−	288294.i	−0.219189	−	0.379647i
$226$	36616.5			0.0476876
$227$	−18433.1	−	31927.0i	−0.0237429	−	0.0411239i	0.853910	−	0.520421i	$-0.174225\pi$
$227$	−18433.1	−	31927.0i	−0.0237429	−	0.0411239i	−0.877653	+	0.479297i	$0.840892\pi$
$228$	−310584.	+	537947.i	−0.395678	+	0.685334i
$229$	217075.	−	375985.i	0.273540	−	0.473786i	−0.696226	−	0.717823i	$-0.745139\pi$
$229$	217075.	−	375985.i	0.273540	−	0.473786i	0.969766	+	0.244037i	$0.0784720\pi$
$230$	46100.3	−	79848.0i	0.0574624	−	0.0995279i
$231$	534549.			0.659110
$232$	−277158.	+	480052.i	−0.338071	+	0.585556i
$233$	677907.	−	1.17417e6i	0.818051	−	1.41691i	−0.0890646	−	0.996026i	$-0.528388\pi$
$233$	677907.	−	1.17417e6i	0.818051	−	1.41691i	0.907116	−	0.420881i	$-0.138279\pi$
$234$	−136086.	−	235709.i	−0.162471	−	0.281408i
$235$	269243.	+	466342.i	0.318035	+	0.550852i
$236$	716029.			0.836856
$237$	−92395.4			−0.106851
$238$	−33815.9	−	58570.8i	−0.0386971	−	0.0670253i
$239$	−460249.	−	797175.i	−0.521193	−	0.902733i	−0.999696	−	0.0246469i	$-0.992154\pi$
$239$	−460249.	−	797175.i	−0.521193	−	0.902733i	0.478503	−	0.878086i	$-0.341179\pi$
$240$	76344.2	−	132232.i	0.0855555	−	0.148186i
$241$	524551.	−	908549.i	0.581761	−	1.00764i	−0.413509	−	0.910500i	$-0.635697\pi$
$241$	524551.	−	908549.i	0.581761	−	1.00764i	0.995271	−	0.0971404i	$-0.0309696\pi$
$242$	−1.07596e6			−1.18103
$243$	−465244.	+	805827.i	−0.505435	+	0.875439i
$244$	−626221.	+	1.08465e6i	−0.673369	+	1.16631i
$245$	−180243.	+	312189.i	−0.191841	+	0.332279i
$246$	201761.	+	349460.i	0.212569	+	0.368180i
$247$	−1.86612e6			−1.94625
$248$	−468142.	−	810845.i	−0.483335	−	0.837160i
$249$	−229720.	+	397888.i	−0.234802	+	0.406689i
$250$	−387425.			−0.392047
$251$	583378.	−	1.01044e6i	0.584475	−	1.01234i	−0.410466	−	0.911876i	$-0.634634\pi$
$251$	583378.	−	1.01044e6i	0.584475	−	1.01234i	0.994941	−	0.100464i	$-0.0320328\pi$
$252$	−147351.	−	255220.i	−0.146168	−	0.253170i
$253$	493889.	+	855440.i	0.485096	+	0.840211i
$254$	366689.			0.356626
$255$	−58164.5	−	100744.i	−0.0560154	−	0.0970216i
$256$	−335936.			−0.320374
$257$	−234774.			−0.221726			−0.110863	−	0.993836i	$-0.535361\pi$
$257$	−234774.			−0.221726			−0.110863	+	0.993836i	$0.535361\pi$
$258$	−52490.0	−	264079.i	−0.0490939	−	0.246993i
$259$	−839118.			−0.777273
$260$	615280.			0.564468
$261$	310359.	+	537557.i	0.282009	+	0.488454i
$262$	−205246.			−0.184723
$263$	1.07763e6	+	1.86652e6i	0.960686	+	1.66396i	0.720783	+	0.693160i	$0.243782\pi$
$263$	1.07763e6	+	1.86652e6i	0.960686	+	1.66396i	0.239903	+	0.970797i	$0.422884\pi$
$264$	−509847.	−	883081.i	−0.450225	−	0.779813i
$265$	−312724.	+	541655.i	−0.273557	+	0.473814i
$266$	424853.			0.368158
$267$	−346515.	+	600182.i	−0.297471	+	0.515234i
$268$	−491241.	−	850855.i	−0.417790	−	0.723633i
$269$	−374180.			−0.315282			−0.157641	−	0.987496i	$-0.550389\pi$
$269$	−374180.			−0.315282			−0.157641	+	0.987496i	$0.550389\pi$
$270$	137216.	+	237664.i	0.114550	+	0.198406i
$271$	1.00118e6	−	1.73410e6i	0.828112	−	1.43433i	−0.0714049	−	0.997447i	$-0.522748\pi$
$271$	1.00118e6	−	1.73410e6i	0.828112	−	1.43433i	0.899517	−	0.436885i	$-0.143918\pi$
$272$	103482.	−	179236.i	0.0848091	−	0.146894i
$273$	−254474.	+	440763.i	−0.206651	+	0.357930i
$274$	371185.			0.298686
$275$	847594.	−	1.46808e6i	0.675859	−	1.17062i
$276$	−156525.	+	271110.i	−0.123683	+	0.214226i
$277$	66019.1	+	114348.i	0.0516976	+	0.0895428i	0.890716	−	0.454560i	$-0.150203\pi$
$277$	66019.1	+	114348.i	0.0516976	+	0.0895428i	−0.839019	+	0.544103i	$0.816870\pi$
$278$	139993.	+	242475.i	0.108641	+	0.188172i
$279$	−1.04844e6			−0.806367
$280$	−309610.			−0.236004
$281$	−700236.	−	1.21285e6i	−0.529028	−	0.916304i	−0.999427	−	0.0338498i	$-0.989223\pi$
$281$	−700236.	−	1.21285e6i	−0.529028	−	0.916304i	0.470399	−	0.882454i	$-0.344110\pi$
$282$	192214.	+	332924.i	0.143933	+	0.249300i
$283$	289462.	−	501362.i	0.214845	−	0.372122i	−0.738380	−	0.674385i	$-0.764409\pi$
$283$	289462.	−	501362.i	0.214845	−	0.372122i	0.953225	+	0.302263i	$0.0977421\pi$
$284$	666088.	−	1.15370e6i	0.490045	−	0.848782i
$285$	730761.			0.532922
$286$	692991.	−	1.20030e6i	0.500971	−	0.867707i
$287$	−656308.	+	1.13676e6i	−0.470330	+	0.814636i
$288$	−434995.	+	753434.i	−0.309032	+	0.535259i
$289$	631089.	+	1.09308e6i	0.444473	+	0.769850i
$290$	295040.			0.206009
$291$	69061.4	+	119618.i	0.0478083	+	0.0828064i
$292$	−466790.	+	808504.i	−0.320379	+	0.554913i
$293$	357984.			0.243610			0.121805	−	0.992554i	$-0.461132\pi$
$293$	357984.			0.243610			0.121805	+	0.992554i	$0.461132\pi$
$294$	−128676.	+	222873.i	−0.0868219	+	0.150380i
$295$	−421180.	−	729505.i	−0.281781	−	0.488060i
$296$	800341.	+	1.38623e6i	0.530941	+	0.919616i
$297$	−2.94008e6			−1.93405
$298$	119489.	+	206962.i	0.0779451	+	0.135005i
$299$	−940471.			−0.608370
$300$	537246.			0.344643
$301$	658563.	−	577380.i	0.418968	−	0.367321i
$302$	645252.			0.407110
$303$	466476.			0.291892
$304$	650058.	+	1.12593e6i	0.403430	+	0.698761i
$305$	1.47341e6			0.906932
$306$	72233.5	+	125112.i	0.0440996	+	0.0763828i
$307$	27911.1	+	48343.5i	0.0169017	+	0.0292747i	0.874353	−	0.485291i	$-0.161286\pi$
$307$	27911.1	+	48343.5i	0.0169017	+	0.0292747i	−0.857451	+	0.514566i	$0.827953\pi$
$308$	750354.	−	1.29965e6i	0.450702	−	0.780639i
$309$	−374451.			−0.223100
$310$	−249173.	+	431580.i	−0.147264	+	0.255068i
$311$	245116.	+	424553.i	0.143704	+	0.248903i	0.928889	−	0.370359i	$-0.120765\pi$
$311$	245116.	+	424553.i	0.143704	+	0.248903i	−0.785184	+	0.619262i	$0.787432\pi$
$312$	970859.			0.564638
$313$	−1.08613e6	−	1.88123e6i	−0.626644	−	1.08538i	−0.988221	−	0.153036i	$-0.951095\pi$
$313$	−1.08613e6	−	1.88123e6i	−0.626644	−	1.08538i	0.361577	−	0.932342i	$-0.382239\pi$
$314$	201776.	−	349486.i	0.115490	−	0.200035i
$315$	−173349.	+	300249.i	−0.0984337	+	0.170492i
$316$	−129697.	+	224641.i	−0.0730653	+	0.126553i
$317$	853939.			0.477286			0.238643	−	0.971107i	$-0.423297\pi$
$317$	853939.			0.477286			0.238643	+	0.971107i	$0.423297\pi$
$318$	−223255.	+	386689.i	−0.123804	+	0.214434i
$319$	−1.58043e6	+	2.73739e6i	−0.869561	+	1.50612i
$320$	−52633.7	−	91164.3i	−0.0287336	−	0.0497680i
$321$	559883.	+	969746.i	0.303274	+	0.525286i
$322$	214113.			0.115081
$323$	990522.			0.528272
$324$	29802.2	+	51619.0i	0.0157720	+	0.0273179i
$325$	807002.	+	1.39777e6i	0.423805	+	0.734052i
$326$	460501.	−	797612.i	0.239987	−	0.415669i
$327$	251127.	−	434965.i	0.129875	−	0.224950i
$328$	2.50391e6			1.28509
$329$	−625251.	+	1.08297e6i	−0.318467	+	0.551601i
$330$	−271371.	+	470028.i	−0.137176	+	0.237596i
$331$	896639.	−	1.55303e6i	0.449829	−	0.779127i	−0.548545	−	0.836121i	$-0.684818\pi$
$331$	896639.	−	1.55303e6i	0.449829	−	0.779127i	0.998375	+	0.0569935i	$0.0181514\pi$
$332$	644924.	+	1.11704e6i	0.321117	+	0.556191i
$333$	1.79243e6			0.885789
$334$	766174.	+	1.32705e6i	0.375804	+	0.650912i
$335$	−577912.	+	1.00097e6i	−0.281352	+	0.487315i
$336$	354581.			0.171344
$337$	1.47938e6	−	2.56236e6i	0.709584	−	1.22904i	−0.255427	−	0.966828i	$-0.582216\pi$
$337$	1.47938e6	−	2.56236e6i	0.709584	−	1.22904i	0.965011	−	0.262208i	$-0.0844506\pi$
$338$	222077.	+	384649.i	0.105733	+	0.183136i
$339$	73129.7	+	126664.i	0.0345617	+	0.0598626i
$340$	−326585.			−0.153214
$341$	−2.66947e6	−	4.62367e6i	−1.24320	−	2.15328i
$342$	−907520.			−0.419557
$343$	−2.05119e6			−0.941393
$344$	−1.58197e6	−	537255.i	−0.720778	−	0.244785i
$345$	368282.			0.166584
$346$	−267564.			−0.120154
$347$	340583.	+	589907.i	0.151845	+	0.263002i	0.931906	−	0.362701i	$-0.118145\pi$
$347$	340583.	+	589907.i	0.151845	+	0.263002i	−0.780061	+	0.625703i	$0.784812\pi$
$348$	−1.00176e6			−0.443418
$349$	898075.	+	1.55551e6i	0.394683	+	0.683612i	0.993061	−	0.117603i	$-0.0375209\pi$
$349$	898075.	+	1.55551e6i	0.394683	+	0.683612i	−0.598377	+	0.801214i	$0.704188\pi$
$350$	−183727.	−	318224.i	−0.0801683	−	0.138855i
$351$	1.39964e6	−	2.42424e6i	0.606383	−	1.05029i
$352$	−4.43024e6			−1.90577
$353$	445.726	−	772.021i	0.000190384	−	0.000329756i	−0.865930	−	0.500165i	$-0.833273\pi$
$353$	445.726	−	772.021i	0.000190384	−	0.000329756i	0.866121	+	0.499835i	$0.166606\pi$
$354$	−300682.	−	520796.i	−0.127526	−	0.220882i
$355$	−1.56721e6			−0.660020
$356$	972816.	+	1.68497e6i	0.406823	+	0.704639i
$357$	135073.	−	233953.i	0.0560916	−	0.0971534i
$358$	131042.	−	226972.i	0.0540385	−	0.0935974i
$359$	−7293.51	+	12632.7i	−0.00298676	+	0.00517322i	−0.867515	−	0.497411i	$-0.834284\pi$
$359$	−7293.51	+	12632.7i	−0.00298676	+	0.00517322i	0.864528	+	0.502584i	$0.167617\pi$
$360$	661352.			0.268953
$361$	−1.87310e6	+	3.24431e6i	−0.756474	+	1.31025i
$362$	−73587.3	+	127457.i	−0.0295142	+	0.0511201i
$363$	−2.14889e6	−	3.72200e6i	−0.855950	−	1.48255i
$364$	714419.	+	1.23741e6i	0.282618	+	0.489508i
$365$	1.09829e6			0.431505
$366$	1.05188e6			0.410451
$367$	219283.	+	379809.i	0.0849845	+	0.147197i	0.905385	−	0.424592i	$-0.139583\pi$
$367$	219283.	+	379809.i	0.0849845	+	0.147197i	−0.820400	+	0.571790i	$0.806249\pi$
$368$	327610.	+	567437.i	0.126107	+	0.218423i
$369$	1.40193e6	−	2.42821e6i	0.535993	−	0.928368i
$370$	425989.	−	737834.i	0.161768	−	0.280191i
$371$	−1.45245e6			−0.547857
$372$	846020.	−	1.46535e6i	0.316974	−	0.549015i
$373$	−1.84218e6	+	3.19074e6i	−0.685582	+	1.18746i	0.287672	+	0.957729i	$0.407119\pi$
$373$	−1.84218e6	+	3.19074e6i	−0.685582	+	1.18746i	−0.973254	+	0.229733i	$0.926215\pi$
$374$	−367834.	+	637106.i	−0.135979	+	0.235523i
$375$	−773758.	−	1.34019e6i	−0.284136	−	0.492139i
$376$	2.38543e6			0.870155
$377$	−1.50475e6	−	2.60630e6i	−0.545267	−	0.944431i
$378$	−318649.	+	551917.i	−0.114705	+	0.198675i
$379$	−4.33977e6			−1.55192			−0.775959	−	0.630784i	$-0.782734\pi$
$379$	−4.33977e6			−1.55192			−0.775959	+	0.630784i	$0.782734\pi$
$380$	1.02578e6	−	1.77670e6i	0.364414	−	0.631184i
$381$	732343.	+	1.26846e6i	0.258465	+	0.447675i
$382$	−189828.	−	328791.i	−0.0665581	−	0.115282i
$383$	826932.			0.288053			0.144027	−	0.989574i	$-0.453995\pi$
$383$	826932.			0.288053			0.144027	+	0.989574i	$0.453995\pi$
$384$	−887209.	−	1.53669e6i	−0.307042	−	0.531812i
$385$	−1.76548e6			−0.607031
$386$	−911343.			−0.311325
$387$	−1.40675e6	+	1.23333e6i	−0.477461	+	0.418603i
$388$	387770.			0.130766
$389$	−2.23266e6			−0.748080			−0.374040	−	0.927413i	$-0.622028\pi$
$389$	−2.23266e6			−0.748080			−0.374040	+	0.927413i	$0.622028\pi$
$390$	−258374.	−	447517.i	−0.0860177	−	0.148987i
$391$	499194.			0.165131
$392$	798453.	+	1.38296e6i	0.262443	+	0.454564i
$393$	−409913.	−	709990.i	−0.133878	−	0.231884i
$394$	387791.	−	671674.i	0.125851	−	0.217981i
$395$	305159.			0.0984085
$396$	−1.60282e6	+	2.77616e6i	−0.513625	+	0.889625i
$397$	−1.86790e6	−	3.23529e6i	−0.594808	−	1.03024i	−0.993574	−	0.113184i	$-0.963895\pi$
$397$	−1.86790e6	−	3.23529e6i	−0.594808	−	1.03024i	0.398766	−	0.917053i	$-0.369438\pi$
$398$	−729007.			−0.230687
$399$	848507.	+	1.46966e6i	0.266823	+	0.462151i
$400$	562233.	−	973816.i	0.175698	−	0.304317i
$401$	−894571.	+	1.54944e6i	−0.277814	+	0.481188i	−0.970841	−	0.239724i	$-0.922943\pi$
$401$	−894571.	+	1.54944e6i	−0.277814	+	0.481188i	0.693027	+	0.720911i	$0.256276\pi$
$402$	−412574.	+	714598.i	−0.127332	+	0.220545i
$403$	5.08326e6			1.55912
$404$	654798.	−	1.13414e6i	0.199597	−	0.345712i
$405$	35060.3	−	60726.2i	0.0106213	−	0.0183966i
$406$	342579.	+	593365.i	0.103144	+	0.178651i
$407$	4.56377e6	+	7.90468e6i	1.36564	+	2.36537i
$408$	−515324.			−0.153260
$409$	−531028.			−0.156967			−0.0784836	−	0.996915i	$-0.525008\pi$
$409$	−531028.			−0.156967			−0.0784836	+	0.996915i	$0.525008\pi$
$410$	−666366.	−	1.15418e6i	−0.195773	−	0.339089i
$411$	741324.	+	1.28401e6i	0.216473	+	0.374942i
$412$	−525622.	+	910405.i	−0.152557	+	0.264236i
$413$	978087.	−	1.69410e6i	0.282164	−	0.488723i
$414$	−457364.			−0.131148
$415$	758708.	−	1.31412e6i	0.216249	−	0.374555i
$416$	2.10903e6	−	3.65295e6i	0.597517	−	1.03493i
$417$	−559182.	+	968532.i	−0.157476	+	0.272756i
$418$	−2.31067e6	−	4.00221e6i	−0.646842	−	1.12036i
$419$	−4.56915e6			−1.27145			−0.635726	−	0.771915i	$-0.719299\pi$
$419$	−4.56915e6			−1.27145			−0.635726	+	0.771915i	$0.719299\pi$
$420$	−279762.	−	484561.i	−0.0773864	−	0.134037i
$421$	1.50987e6	−	2.61516e6i	0.415177	−	0.719107i	−0.580270	−	0.814424i	$-0.697053\pi$
$421$	1.50987e6	−	2.61516e6i	0.415177	−	0.719107i	0.995447	+	0.0953168i	$0.0303864\pi$
$422$	−345789.			−0.0945214
$423$	1.33559e6	−	2.31330e6i	0.362929	−	0.628611i
$424$	1.38533e6	+	2.39947e6i	0.374231	+	0.648186i
$425$	−428350.	−	741923.i	−0.115034	−	0.199245i
$426$	−1.11884e6			−0.298706
$427$	1.71082e6	+	2.96323e6i	0.454083	+	0.786494i
$428$	3.14366e6			0.829519
$429$	5.53611e6			1.45232
$430$	173361.	+	872187.i	0.0452148	+	0.227478i
$431$	−453602.			−0.117620			−0.0588101	−	0.998269i	$-0.518731\pi$
$431$	−453602.			−0.117620			−0.0588101	+	0.998269i	$0.518731\pi$
$432$	−1.95023e6			−0.502779
$433$	2.91468e6	+	5.04838e6i	0.747087	+	1.29399i	0.949213	+	0.314634i	$0.101882\pi$
$433$	2.91468e6	+	5.04838e6i	0.747087	+	1.29399i	−0.202126	+	0.979360i	$0.564785\pi$
$434$	−1.15728e6			−0.294928
$435$	589248.	+	1.02061e6i	0.149305	+	0.258604i
$436$	−705021.	−	1.22113e6i	−0.177618	−	0.307643i
$437$	−1.56793e6	+	2.71574e6i	−0.392756	+	0.680274i
$438$	784076.			0.195287
$439$	3.31046e6	−	5.73388e6i	0.819835	−	1.42000i	−0.0859683	−	0.996298i	$-0.527398\pi$
$439$	3.31046e6	−	5.73388e6i	0.819835	−	1.42000i	0.905803	−	0.423698i	$-0.139268\pi$
$440$	1.68390e6	+	2.91659e6i	0.414652	+	0.718198i
$441$	1.78820e6			0.437844
$442$	−350217.	−	606594.i	−0.0852672	−	0.147687i
$443$	−1.63844e6	+	2.83786e6i	−0.396662	+	0.687039i	−0.993312	−	0.115463i	$-0.963165\pi$
$443$	−1.63844e6	+	2.83786e6i	−0.396662	+	0.687039i	0.596650	+	0.802502i	$0.296498\pi$
$444$	−1.44637e6	+	2.50518e6i	−0.348194	+	0.603090i
$445$	1.14445e6	−	1.98225e6i	0.273967	−	0.474524i
$446$	1.87228e6			0.445690
$447$	−477284.	+	826680.i	−0.112982	+	0.195690i
$448$	122229.	−	211707.i	0.0287726	−	0.0498356i
$449$	1.03947e6	+	1.80042e6i	0.243331	+	0.421462i	0.961661	−	0.274241i	$-0.0884265\pi$
$449$	1.03947e6	+	1.80042e6i	0.243331	+	0.421462i	−0.718330	+	0.695703i	$0.755093\pi$
$450$	392456.	+	679753.i	0.0913607	+	0.158241i
$451$	1.42780e7			3.30542
$452$	410613.			0.0945336
$453$	1.28868e6	+	2.23207e6i	0.295054	+	0.511048i
$454$	43462.3	+	75278.9i	0.00989631	+	0.0171409i
$455$	840465.	−	1.45573e6i	0.190323	−	0.329649i
$456$	1.61859e6	−	2.80348e6i	0.364523	−	0.631373i
$457$	−7.10479e6			−1.59133			−0.795665	−	0.605736i	$-0.792879\pi$
$457$	−7.10479e6			−1.59133			−0.795665	+	0.605736i	$0.792879\pi$
$458$	−511829.	+	886514.i	−0.114015	+	0.197479i
$459$	−742915.	+	1.28677e6i	−0.164591	+	0.285081i
$460$	516963.	−	895406.i	0.113911	−	0.197299i
$461$	−386731.	−	669838.i	−0.0847534	−	0.146797i	0.820533	−	0.571600i	$-0.193677\pi$
$461$	−386731.	−	669838.i	−0.0847534	−	0.146797i	−0.905286	+	0.424802i	$0.860344\pi$
$462$	−1.26038e6			−0.274725
$463$	−1.35158e6	−	2.34100e6i	−0.293014	−	0.507516i	0.681507	−	0.731812i	$-0.261325\pi$
$463$	−1.35158e6	−	2.34100e6i	−0.293014	−	0.507516i	−0.974521	+	0.224296i	$0.927992\pi$
$464$	−1.04835e6	+	1.81579e6i	−0.226053	+	0.391535i
$465$	−1.99057e6			−0.426919
$466$	−1.59840e6	+	2.76851e6i	−0.340974	+	0.590583i
$467$	1.45585e6	+	2.52161e6i	0.308905	+	0.535039i	0.978123	−	0.208027i	$-0.0667043\pi$
$467$	1.45585e6	+	2.52161e6i	0.308905	+	0.535039i	−0.669218	+	0.743066i	$0.733371\pi$
$468$	−1.52606e6	−	2.64321e6i	−0.322074	−	0.557849i
$469$	−2.68412e6			−0.563468
$470$	−634833.	−	1.09956e6i	−0.132561	−	0.229602i
$471$	1.61193e6			0.334807
$472$	−3.73155e6			−0.770965
$473$	−9.02083e6	−	3.06358e6i	−1.85393	−	0.629616i
$474$	217854.			0.0445369
$475$	5.38165e6			1.09441
$476$	−379207.	−	656806.i	−0.0767113	−	0.132868i
$477$	3.10256e6			0.624344
$478$	1.08520e6	+	1.87962e6i	0.217239	+	0.376270i
$479$	−2.26063e6	−	3.91553e6i	−0.450185	−	0.779743i	0.548212	−	0.836339i	$-0.315309\pi$
$479$	−2.26063e6	−	3.91553e6i	−0.450185	−	0.779743i	−0.998397	+	0.0565964i	$0.981975\pi$
$480$	−825884.	+	1.43047e6i	−0.163612	+	0.283385i
$481$	−8.69041e6			−1.71268
$482$	−1.23681e6	+	2.14222e6i	−0.242485	+	0.419996i
$483$	427623.	+	740664.i	0.0834052	+	0.144462i
$484$	−1.20657e7			−2.34121
$485$	−228092.	−	395068.i	−0.0440308	−	0.0762636i
$486$	1.09697e6	−	1.90001e6i	0.210671	−	0.364893i
$487$	−2.41774e6	+	4.18764e6i	−0.461941	+	0.800105i	−0.999058	−	0.0434028i	$-0.986180\pi$
$487$	−2.41774e6	+	4.18764e6i	−0.461941	+	0.800105i	0.537117	+	0.843508i	$0.319513\pi$
$488$	3.26352e6	−	5.65259e6i	0.620350	−	1.07448i
$489$	3.67882e6			0.695722
$490$	424984.	−	736094.i	0.0799618	−	0.138498i
$491$	3.77568e6	−	6.53967e6i	0.706792	−	1.22420i	−0.259249	−	0.965810i	$-0.583475\pi$
$491$	3.77568e6	−	6.53967e6i	0.706792	−	1.22420i	0.966041	−	0.258389i	$-0.0831916\pi$
$492$	2.26252e6	+	3.91881e6i	0.421386	+	0.729862i
$493$	798706.	+	1.38340e6i	0.148003	+	0.256348i
$494$	4.40003e6			0.811219
$495$	3.77121e6			0.691780
$496$	−1.77074e6	−	3.06701e6i	−0.323184	−	0.559771i
$497$	−1.81974e6	−	3.15187e6i	−0.330459	−	0.572371i
$498$	541645.	−	938157.i	0.0978682	−	0.169513i
$499$	4.16824e6	−	7.21960e6i	0.749379	−	1.29796i	−0.198742	−	0.980052i	$-0.563686\pi$
$499$	4.16824e6	−	7.21960e6i	0.749379	−	1.29796i	0.948121	−	0.317910i	$-0.102981\pi$
$500$	−4.34454e6			−0.777174
$501$	−3.06038e6	+	5.30073e6i	−0.544729	+	0.943498i
$502$	−1.37551e6	+	2.38246e6i	−0.243616	+	0.421955i
$503$	−5.50014e6	+	9.52651e6i	−0.969289	+	1.67886i	−0.271669	+	0.962391i	$0.587576\pi$
$503$	−5.50014e6	+	9.52651e6i	−0.969289	+	1.67886i	−0.697620	+	0.716468i	$0.745758\pi$
$504$	767914.	+	1.33007e6i	0.134659	+	0.233237i
$505$	−1.54065e6			−0.268829
$506$	−1.16451e6	−	2.01699e6i	−0.202194	−	0.350210i
$507$	−887056.	+	1.53643e6i	−0.153261	+	0.265456i
$508$	4.11200e6			0.706958
$509$	−525773.	+	910665.i	−0.0899505	+	0.155799i	−0.907490	−	0.420074i	$-0.862004\pi$
$509$	−525773.	+	910665.i	−0.0899505	+	0.155799i	0.817540	+	0.575873i	$0.195338\pi$
$510$	137143.	+	237538.i	0.0233479	+	0.0404397i
$511$	1.27526e6	+	2.20881e6i	0.216046	+	0.374202i
$512$	−5.23689e6			−0.882874
$513$	−4.66688e6	−	8.08327e6i	−0.782948	−	1.35611i
$514$	553560.			0.0924180
$515$	1.23672e6			0.205472
$516$	−588616.	−	2.96135e6i	−0.0973213	−	0.489628i
$517$	1.36024e7			2.23815
$518$	1.97851e6			0.323977
$519$	−534374.	−	925563.i	−0.0870818	−	0.150830i
$520$	−3.20650e6			−0.520024
$521$	−286252.	−	495803.i	−0.0462013	−	0.0800230i	0.842000	−	0.539478i	$-0.181378\pi$
$521$	−286252.	−	495803.i	−0.0462013	−	0.0800230i	−0.888201	+	0.459455i	$0.848045\pi$
$522$	−731777.	−	1.26748e6i	−0.117545	−	0.203593i
$523$	2.93659e6	−	5.08632e6i	0.469450	−	0.813111i	−0.529940	−	0.848035i	$-0.677786\pi$
$523$	2.93659e6	−	5.08632e6i	0.469450	−	0.813111i	0.999390	+	0.0349242i	$0.0111190\pi$
$524$	−2.30160e6			−0.366186
$525$	733871.	−	1.27110e6i	0.116204	−	0.201271i
$526$	−2.54089e6	−	4.40095e6i	−0.400425	−	0.693557i
$527$	−2.69815e6			−0.423194
$528$	−1.92849e6	−	3.34024e6i	−0.301045	−	0.521426i
$529$	2.42798e6	−	4.20539e6i	0.377230	−	0.653381i
$530$	737355.	−	1.27714e6i	0.114022	−	0.197491i
$531$	−2.08927e6	+	3.61873e6i	−0.321558	+	0.556954i
$532$	4.76424e6			0.729819
$533$	−6.79711e6	+	1.17729e7i	−1.03635	+	1.79501i
$534$	817029.	−	1.41514e6i	0.123989	−	0.214756i
$535$	−1.84915e6	−	3.20283e6i	−0.279311	−	0.483781i
$536$	2.56008e6	+	4.43419e6i	0.384894	+	0.666657i
$537$	1.04686e6			0.156658
$538$	882258.			0.131413
$539$	4.55301e6	+	7.88604e6i	0.675035	+	1.16919i
$540$	1.53872e6	+	2.66514e6i	0.227078	+	0.393310i
$541$	163410.	−	283035.i	0.0240042	−	0.0415764i	−0.853774	−	0.520644i	$-0.825692\pi$
$541$	163410.	−	283035.i	0.0240042	−	0.0415764i	0.877778	+	0.479068i	$0.159025\pi$
$542$	−2.36063e6	+	4.08873e6i	−0.345167	+	0.597847i
$543$	−587868.			−0.0855619
$544$	−1.11946e6	+	1.93896e6i	−0.162185	+	0.280912i
$545$	−829409.	+	1.43658e6i	−0.119613	+	0.207175i
$546$	600011.	−	1.03925e6i	0.0861346	−	0.149190i
$547$	−691457.	−	1.19764e6i	−0.0988090	−	0.171142i	0.812383	−	0.583124i	$-0.198170\pi$
$547$	−691457.	−	1.19764e6i	−0.0988090	−	0.171142i	−0.911192	+	0.411982i	$0.864837\pi$
$548$	4.16243e6			0.592100
$549$	−3.65445e6	−	6.32970e6i	−0.517478	−	0.896298i
$550$	−1.99850e6	+	3.46150e6i	−0.281706	+	0.487929i
$551$	−1.00347e7			−1.40807
$552$	815723.	−	1.41287e6i	0.113945	−	0.197358i
$553$	354328.	+	613714.i	0.0492711	+	0.0853401i
$554$	−155663.	−	269616.i	−0.0215482	−	0.0373225i
$555$	3.40311e6			0.468968
$556$	1.56986e6	+	2.71908e6i	0.215365	+	0.373023i
$557$	−9.53674e6			−1.30245			−0.651226	−	0.758883i	$-0.725745\pi$
$557$	−9.53674e6			−1.30245			−0.651226	+	0.758883i	$0.725745\pi$
$558$	2.47205e6			0.336103
$559$	6.82047e6	−	5.97970e6i	0.923177	−	0.809375i
$560$	−1.17109e6			−0.157805
$561$	−2.93852e6			−0.394204
$562$	1.65105e6	+	2.85970e6i	0.220505	+	0.381926i
$563$	−5.53863e6			−0.736430			−0.368215	−	0.929741i	$-0.620031\pi$
$563$	−5.53863e6			−0.736430			−0.368215	+	0.929741i	$0.620031\pi$
$564$	2.15546e6	+	3.73337e6i	0.285327	+	0.494200i
$565$	−241529.	−	418340.i	−0.0318308	−	0.0551326i
$566$	−682506.	+	1.18213e6i	−0.0895499	+	0.155105i
$567$	162838.			0.0212715
$568$	−3.47128e6	+	6.01244e6i	−0.451460	+	0.781952i
$569$	4.21862e6	+	7.30687e6i	0.546248	+	0.946130i	0.998527	+	0.0542531i	$0.0172778\pi$
$569$	4.21862e6	+	7.30687e6i	0.546248	+	0.946130i	−0.452279	+	0.891876i	$0.649389\pi$
$570$	−1.72302e6			−0.222128
$571$	−1.00713e6	−	1.74439e6i	−0.129269	−	0.223900i	0.794125	−	0.607755i	$-0.207930\pi$
$571$	−1.00713e6	−	1.74439e6i	−0.129269	−	0.223900i	−0.923393	+	0.383855i	$0.874596\pi$
$572$	7.77112e6	−	1.34600e7i	0.993101	−	1.72010i
$573$	758240.	−	1.31331e6i	0.0964762	−	0.167102i
$574$	1.54747e6	−	2.68030e6i	0.196039	−	0.339550i
$575$	2.71220e6			0.342099
$576$	−261091.	+	452223.i	−0.0327896	+	0.0567932i
$577$	3.63995e6	−	6.30458e6i	0.455152	−	0.788346i	−0.543545	−	0.839380i	$-0.682918\pi$
$577$	3.63995e6	−	6.30458e6i	0.455152	−	0.788346i	0.998697	+	0.0510342i	$0.0162517\pi$
$578$	−1.48801e6	−	2.57731e6i	−0.185262	−	0.320883i
$579$	−1.82012e6	−	3.15254e6i	−0.225633	−	0.390808i
$580$	3.30854e6			0.408382
$581$	3.52383e6			0.433086
$582$	−162836.	−	282040.i	−0.0199271	−	0.0345147i
$583$	7.89955e6	+	1.36824e7i	0.962567	+	1.66722i
$584$	2.43265e6	−	4.21348e6i	0.295154	−	0.511221i
$585$	−1.79530e6	+	3.10955e6i	−0.216894	+	0.375672i
$586$	−844070.			−0.101539
$587$	−2.18347e6	+	3.78187e6i	−0.261548	+	0.453014i	−0.966653	−	0.256088i	$-0.917566\pi$
$587$	−2.18347e6	+	3.78187e6i	−0.261548	+	0.453014i	0.705106	+	0.709102i	$0.250900\pi$
$588$	−1.44296e6	+	2.49927e6i	−0.172112	+	0.298106i
$589$	8.47468e6	−	1.46786e7i	1.00655	−	1.74340i
$590$	993076.	+	1.72006e6i	0.117450	+	0.203429i
$591$	3.09796e6			0.364844
$592$	3.02727e6	+	5.24339e6i	0.355016	+	0.614905i
$593$	−2.44473e6	+	4.23439e6i	−0.285492	+	0.494486i	−0.972728	−	0.231947i	$-0.925490\pi$
$593$	−2.44473e6	+	4.23439e6i	−0.285492	+	0.494486i	0.687237	+	0.726434i	$0.258824\pi$
$594$	6.93224e6			0.806135
$595$	−446111.	+	772687.i	−0.0516596	+	0.0894770i
$596$	1.33994e6	+	2.32084e6i	0.154515	+	0.267627i
$597$	−1.45596e6	−	2.52179e6i	−0.167191	−	0.289583i
$598$	2.21748e6			0.253576
$599$	−100075.	−	173334.i	−0.0113961	−	0.0197387i	0.860271	−	0.509837i	$-0.170294\pi$
$599$	−100075.	−	173334.i	−0.0113961	−	0.0197387i	−0.871667	+	0.490098i	$0.836961\pi$
$600$	−2.79983e6			−0.317507
$601$	−3.52160e6			−0.397699			−0.198849	−	0.980030i	$-0.563720\pi$
$601$	−3.52160e6			−0.397699			−0.198849	+	0.980030i	$0.563720\pi$
$602$	−1.55279e6	+	1.36137e6i	−0.174631	+	0.153104i
$603$	5.73350e6			0.642135
$604$	7.23578e6			0.807036
$605$	7.09725e6	+	1.22928e7i	0.788319	+	1.36541i
$606$	−1.09988e6			−0.121664
$607$	−869571.	−	1.50614e6i	−0.0957929	−	0.165918i	0.814146	−	0.580660i	$-0.197205\pi$
$607$	−869571.	−	1.50614e6i	−0.0957929	−	0.165918i	−0.909939	+	0.414742i	$0.863872\pi$
$608$	−7.03226e6	−	1.21802e7i	−0.771500	−	1.33628i
$609$	−1.36838e6	+	2.37011e6i	−0.149508	+	0.258956i
$610$	−3.47408e6			−0.378020
$611$	−6.47547e6	+	1.12158e7i	−0.701727	+	1.21543i
$612$	810018.	+	1.40299e6i	0.0874210	+	0.151418i
$613$	3.79841e6			0.408273			0.204136	−	0.978942i	$-0.434561\pi$
$613$	3.79841e6			0.408273			0.204136	+	0.978942i	$0.434561\pi$
$614$	−65810.0	−	113986.i	−0.00704484	−	0.0122020i
$615$	2.66170e6	−	4.61021e6i	0.283774	−	0.491510i
$616$	−3.91043e6	+	6.77307e6i	−0.415215	+	0.719174i
$617$	8.10025e6	−	1.40300e7i	0.856615	−	1.48370i	−0.0185241	−	0.999828i	$-0.505897\pi$
$617$	8.10025e6	−	1.40300e7i	0.856615	−	1.48370i	0.875139	−	0.483872i	$-0.160770\pi$
$618$	882898.			0.0929906
$619$	−6.36414e6	+	1.10230e7i	−0.667595	+	1.15631i	0.310980	+	0.950417i	$0.399343\pi$
$619$	−6.36414e6	+	1.10230e7i	−0.667595	+	1.15631i	−0.978575	+	0.205892i	$0.933990\pi$
$620$	−2.79419e6	+	4.83968e6i	−0.291929	+	0.505635i
$621$	−2.35197e6	−	4.07373e6i	−0.244739	−	0.423900i
$622$	−577945.	−	1.00103e6i	−0.0598977	−	0.103746i
$623$	5.31542e6			0.548678
$624$	3.67226e6			0.377547
$625$	−815485.	−	1.41246e6i	−0.0835057	−	0.144636i
$626$	2.56092e6	+	4.43565e6i	0.261193	+	0.452399i
$627$	9.22967e6	−	1.59863e7i	0.937599	−	1.62397i
$628$	2.26269e6	−	3.91910e6i	0.228942	−	0.396540i
$629$	4.61279e6			0.464876
$630$	408729.	−	707939.i	0.0410283	−	0.0710632i
$631$	−5.58801e6	+	9.67872e6i	−0.558707	+	0.967708i	0.438898	+	0.898537i	$0.355369\pi$
$631$	−5.58801e6	+	9.67872e6i	−0.558707	+	0.967708i	−0.997605	+	0.0691716i	$0.977964\pi$
$632$	675908.	−	1.17071e6i	0.0673124	−	0.116588i
$633$	−690603.	−	1.19616e6i	−0.0685045	−	0.118653i
$634$	−2.01346e6			−0.198938
$635$	−2.41874e6	−	4.18939e6i	−0.238043	−	0.412303i
$636$	−2.50356e6	+	4.33629e6i	−0.245423	+	0.425085i
$637$	−8.66991e6			−0.846576
$638$	3.72642e6	−	6.45435e6i	0.362443	−	0.627770i
$639$	3.88710e6	+	6.73266e6i	0.376594	+	0.652281i
$640$	2.93022e6	+	5.07530e6i	0.282782	+	0.489792i
$641$	−1.39604e7			−1.34200			−0.671002	−	0.741456i	$-0.734136\pi$
$641$	−1.39604e7			−1.34200			−0.671002	+	0.741456i	$0.734136\pi$
$642$	−1.32012e6	−	2.28651e6i	−0.126408	−	0.218945i
$643$	−1.15185e7			−1.09867			−0.549337	−	0.835601i	$-0.685120\pi$
$643$	−1.15185e7			−1.09867			−0.549337	+	0.835601i	$0.685120\pi$
$644$	2.40104e6			0.228131
$645$	−2.67085e6	+	2.34161e6i	−0.252785	+	0.221623i
$646$	−2.33550e6			−0.220190
$647$	7.86031e6			0.738209			0.369104	−	0.929388i	$-0.379665\pi$
$647$	7.86031e6			0.738209			0.369104	+	0.929388i	$0.379665\pi$
$648$	−155313.	−	269010.i	−0.0145302	−	0.0251670i
$649$	−2.12784e7			−1.98302
$650$	−1.90278e6	−	3.29572e6i	−0.176647	−	0.305962i
$651$	−2.31131e6	−	4.00330e6i	−0.213749	−	0.370225i
$652$	5.16400e6	−	8.94432e6i	0.475738	−	0.824002i
$653$	−1.39211e7			−1.27758			−0.638792	−	0.769379i	$-0.720566\pi$
$653$	−1.39211e7			−1.27758			−0.638792	+	0.769379i	$0.720566\pi$
$654$	−592119.	+	1.02558e6i	−0.0541333	+	0.0937616i
$655$	1.35384e6	+	2.34492e6i	0.123300	+	0.213562i
$656$	9.47101e6			0.859284
$657$	−2.72406e6	−	4.71820e6i	−0.246208	−	0.426445i
$658$	1.47424e6	−	2.55347e6i	0.132741	−	0.229914i
$659$	−6.30343e6	+	1.09179e7i	−0.565410	+	0.979319i	0.431601	+	0.902064i	$0.357949\pi$
$659$	−6.30343e6	+	1.09179e7i	−0.565410	+	0.979319i	−0.997011	+	0.0772545i	$0.975385\pi$
$660$	−3.04312e6	+	5.27083e6i	−0.271931	+	0.470998i
$661$	−111996.			−0.00997012			−0.00498506	−	0.999988i	$-0.501587\pi$
$661$	−111996.			−0.00997012			−0.00498506	+	0.999988i	$0.501587\pi$
$662$	−2.11414e6	+	3.66179e6i	−0.187494	+	0.324750i
$663$	1.39889e6	−	2.42296e6i	0.123595	−	0.214073i
$664$	−3.36099e6	−	5.82140e6i	−0.295833	−	0.512398i
$665$	−2.80240e6	−	4.85391e6i	−0.245740	−	0.425635i
$666$	−4.22626e6			−0.369207
$667$	−5.05719e6			−0.440144
$668$	8.59178e6	+	1.48814e7i	0.744976	+	1.29034i
$669$	3.73927e6	+	6.47661e6i	0.323014	+	0.559477i
$670$	1.36263e6	−	2.36014e6i	0.117271	−	0.203119i
$671$	1.86095e7	−	3.22326e7i	1.59562	−	2.76369i
$672$	−3.83583e6			−0.327669
$673$	6.26611e6	−	1.08532e7i	0.533286	−	0.923678i	−0.465958	−	0.884807i	$-0.654290\pi$
$673$	6.26611e6	−	1.08532e7i	0.533286	−	0.923678i	0.999244	−	0.0388717i	$-0.0123764\pi$
$674$	−3.48814e6	+	6.04163e6i	−0.295763	+	0.512277i
$675$	−4.03637e6	+	6.99119e6i	−0.340982	+	0.590598i
$676$	2.49035e6	+	4.31341e6i	0.209601	+	0.363039i
$677$	1.27948e7			1.07291			0.536455	−	0.843929i	$-0.319763\pi$
$677$	1.27948e7			1.07291			0.536455	+	0.843929i	$0.319763\pi$
$678$	−172428.	−	298655.i	−0.0144057	−	0.0249514i
$679$	529689.	−	917448.i	0.0440906	−	0.0763672i
$680$	1.70198e6			0.141151
$681$	−173604.	+	300691.i	−0.0143447	+	0.0248458i
$682$	6.29420e6	+	1.09019e7i	0.518179	+	0.897512i
$683$	−1.94779e6	−	3.37367e6i	−0.159768	−	0.276727i	0.775017	−	0.631941i	$-0.217741\pi$
$683$	−1.94779e6	−	3.37367e6i	−0.159768	−	0.276727i	−0.934785	+	0.355214i	$0.884408\pi$
$684$	−1.01768e7			−0.831710
$685$	−2.44841e6	−	4.24076e6i	−0.199369	−	0.345317i
$686$	4.83639e6			0.392384
$687$	−4.08886e6			−0.330530
$688$	−5.98376e6	−	2.03215e6i	−0.481952	−	0.163676i
$689$	−1.50425e7			−1.20718
$690$	−868352.			−0.0694342
$691$	284444.	+	492671.i	0.0226622	+	0.0392520i	0.877134	−	0.480246i	$-0.159452\pi$
$691$	284444.	+	492671.i	0.0226622	+	0.0392520i	−0.854472	+	0.519498i	$0.826119\pi$
$692$	−3.00043e6			−0.238187
$693$	4.37886e6	+	7.58441e6i	0.346360	+	0.599913i
$694$	−803041.	−	1.39091e6i	−0.0632906	−	0.109623i
$695$	1.84684e6	−	3.19882e6i	0.145033	−	0.251204i
$696$	5.22060e6			0.408505
$697$	3.60785e6	−	6.24898e6i	0.281298	−	0.487222i
$698$	−2.11752e6	−	3.66765e6i	−0.164509	−	0.284937i
$699$	−1.27692e7			−0.988484
$700$	−2.06029e6	−	3.56853e6i	−0.158922	−	0.275260i
$701$	6.57247e6	−	1.13839e7i	0.505166	−	0.874973i	−0.494816	−	0.868998i	$-0.664765\pi$
$701$	6.57247e6	−	1.13839e7i	0.505166	−	0.874973i	0.999982	−	0.00597517i	$-0.00190197\pi$
$702$	−3.30012e6	+	5.71598e6i	−0.252748	+	0.437772i
$703$	−1.44884e7	+	2.50947e7i	−1.10569	+	1.91511i
$704$	−2.65910e6			−0.202210
$705$	2.53575e6	−	4.39205e6i	0.192147	−	0.332808i
$706$	−1050.95	+	1820.30i	−7.93545e−5	+	0.000137446i
$707$	−1.78889e6	−	3.09845e6i	−0.134597	−	0.233129i
$708$	−3.37181e6	−	5.84015e6i	−0.252802	−	0.437865i
$709$	1.54954e7			1.15767			0.578836	−	0.815444i	$-0.303507\pi$
$709$	1.54954e7			1.15767			0.578836	+	0.815444i	$0.303507\pi$
$710$	3.69524e6			0.275104
$711$	−756874.	−	1.31094e6i	−0.0561500	−	0.0972546i
$712$	−5.06979e6	−	8.78113e6i	−0.374791	−	0.649158i
$713$	4.27099e6	−	7.39758e6i	0.314633	−	0.544961i
$714$	−318481.	+	551625.i	−0.0233796	+	0.0404947i
$715$	−1.82844e7			−1.33757
$716$	1.46949e6	−	2.54523e6i	0.107123	−	0.185543i
$717$	−4.33467e6	+	7.50786e6i	−0.314889	+	0.545404i
$718$	17197.0	−	29786.0i	0.00124492	−	0.00215626i
$719$	−6.63582e6	−	1.14936e7i	−0.478710	−	0.829150i	0.520992	−	0.853562i	$-0.325562\pi$
$719$	−6.63582e6	−	1.14936e7i	−0.478710	−	0.829150i	−0.999702	+	0.0244114i	$0.992229\pi$
$720$	2.50155e6			0.179836
$721$	1.43599e6	+	2.48720e6i	0.102876	+	0.178186i
$722$	4.41649e6	−	7.64958e6i	0.315307	−	0.546128i
$723$	−9.88052e6			−0.702966
$724$	−825199.	+	1.42929e6i	−0.0585076	+	0.101338i
$725$	4.33949e6	+	7.51621e6i	0.306615	+	0.531073i
$726$	5.06676e6	+	8.77588e6i	0.356770	+	0.617944i
$727$	7.27001e6			0.510151			0.255076	−	0.966921i	$-0.417900\pi$
$727$	7.27001e6			0.510151			0.255076	+	0.966921i	$0.417900\pi$
$728$	−3.72316e6	−	6.44870e6i	−0.260365	−	0.450966i
$729$	8.21562e6			0.572561
$730$	−2.58960e6			−0.179856
$731$	−3.62025e6	+	3.17397e6i	−0.250579	+	0.219690i
$732$	1.17956e7			0.813659
$733$	1.00580e7			0.691438			0.345719	−	0.938338i	$-0.387635\pi$
$733$	1.00580e7			0.691438			0.345719	+	0.938338i	$0.387635\pi$
$734$	−517035.	−	895531.i	−0.0354225	−	0.0613536i
$735$	3.39508e6			0.231810
$736$	−3.54405e6	−	6.13848e6i	−0.241160	−	0.417702i
$737$	1.45983e7	+	2.52850e7i	0.989996	+	1.71472i
$738$	−3.30552e6	+	5.72534e6i	−0.223408	+	0.386955i
$739$	7.58208e6			0.510713			0.255357	−	0.966847i	$-0.417807\pi$
$739$	7.58208e6			0.510713			0.255357	+	0.966847i	$0.417807\pi$
$740$	4.77699e6	−	8.27398e6i	0.320682	−	0.555438i
$741$	8.78765e6	+	1.52206e7i	0.587932	+	1.01833i
$742$	3.42466e6			0.228353
$743$	3.36685e6	+	5.83156e6i	0.223744	+	0.387536i	0.955942	−	0.293556i	$-0.0948386\pi$
$743$	3.36685e6	+	5.83156e6i	0.223744	+	0.387536i	−0.732198	+	0.681092i	$0.761505\pi$
$744$	−4.40899e6	+	7.63660e6i	−0.292016	+	0.505787i
$745$	1.57635e6	−	2.73031e6i	0.104055	−	0.180228i
$746$	4.34356e6	−	7.52327e6i	0.285759	−	0.494948i
$747$	−7.52719e6			−0.493550
$748$	−4.12484e6	+	7.14443e6i	−0.269559	+	0.466889i
$749$	4.29420e6	−	7.43778e6i	0.279691	−	0.484438i
$750$	1.82440e6	+	3.15995e6i	0.118431	+	0.205129i
$751$	6.84753e6	+	1.18603e7i	0.443031	+	0.767352i	0.997913	−	0.0645774i	$-0.0205699\pi$
$751$	6.84753e6	+	1.18603e7i	0.443031	+	0.767352i	−0.554882	+	0.831929i	$0.687237\pi$
$752$	9.02283e6			0.581833
$753$	−1.09886e7			−0.706244
$754$	3.54795e6	+	6.14524e6i	0.227274	+	0.393650i
$755$	−4.25620e6	−	7.37195e6i	−0.271741	−	0.470668i
$756$	−3.57330e6	+	6.18913e6i	−0.227386	+	0.393845i
$757$	−254645.	+	441058.i	−0.0161508	+	0.0279741i	−0.873988	−	0.485948i	$-0.838475\pi$
$757$	−254645.	+	441058.i	−0.0161508	+	0.0279741i	0.857837	+	0.513922i	$0.171808\pi$
$758$	1.02325e7			0.646858
$759$	4.65148e6	−	8.05660e6i	0.293081	−	0.507630i
$760$	−5.34580e6	+	9.25920e6i	−0.335721	+	0.581486i
$761$	−2.37927e6	+	4.12102e6i	−0.148930	+	0.257955i	−0.930832	−	0.365446i	$-0.880916\pi$
$761$	−2.37927e6	+	4.12102e6i	−0.148930	+	0.257955i	0.781902	+	0.623401i	$0.214250\pi$
$762$	−1.72675e6	−	2.99082e6i	−0.107731	−	0.186596i
$763$	−3.85220e6			−0.239551
$764$	−2.12870e6	−	3.68702e6i	−0.131942	−	0.228530i
$765$	952930.	−	1.65052e6i	0.0588718	−	0.101969i
$766$	−1.94978e6			−0.120064
$767$	1.01296e7	−	1.75451e7i	0.621736	−	1.07688i
$768$	1.58194e6	+	2.73999e6i	0.0967801	+	0.167628i
$769$	−6.90091e6	−	1.19527e7i	−0.420814	−	0.728871i	0.575205	−	0.818009i	$-0.304922\pi$
$769$	−6.90091e6	−	1.19527e7i	−0.420814	−	0.728871i	−0.996019	+	0.0891377i	$0.971589\pi$
$770$	4.16273e6			0.253018
$771$	1.10556e6	+	1.91488e6i	0.0669801	+	0.116013i
$772$	−1.02197e7			−0.617156
$773$	2.81246e7			1.69293			0.846463	−	0.532447i	$-0.178727\pi$
$773$	2.81246e7			1.69293			0.846463	+	0.532447i	$0.178727\pi$
$774$	3.31689e6	−	2.90800e6i	0.199011	−	0.174479i
$775$	−1.46595e7			−0.876725
$776$	−2.02084e6			−0.120470
$777$	3.95144e6	+	6.84410e6i	0.234803	+	0.406690i
$778$	5.26425e6			0.311808
$779$	2.26640e7	+	3.92551e7i	1.33811	+	2.31768i
$780$	−2.89738e6	−	5.01841e6i	−0.170517	−	0.295345i
$781$	−1.97942e7	+	3.42846e7i	−1.16121	+	2.01128i
$782$	−1.17702e6			−0.0688284
$783$	7.52626e6	−	1.30359e7i	0.438707	−	0.759863i
$784$	3.02013e6	+	5.23103e6i	0.175483	+	0.303946i
$785$	−5.32380e6			−0.308353
$786$	966511.	+	1.67405e6i	0.0558021	+	0.0966520i
$787$	1.36896e7	−	2.37111e7i	0.787871	−	1.36463i	−0.139398	−	0.990236i	$-0.544517\pi$
$787$	1.36896e7	−	2.37111e7i	0.787871	−	1.36463i	0.927269	−	0.374396i	$-0.122150\pi$
$788$	4.34865e6	−	7.53208e6i	0.249482	−	0.432115i
$789$	1.01492e7	−	1.75790e7i	0.580418	−	1.00531i
$790$	−719516.			−0.0410178
$791$	560892.	−	971493.i	0.0318741	−	0.0552076i
$792$	8.35301e6	−	1.44678e7i	0.473184	−	0.819579i
$793$	1.77183e7	+	3.06890e7i	1.00055	+	1.73300i
$794$	4.40421e6	+	7.62831e6i	0.247923	+	0.429415i
$795$	5.89053e6			0.330549
$796$	−8.17500e6			−0.457304
$797$	−1.29354e6	−	2.24048e6i	−0.0721333	−	0.124938i	0.827703	−	0.561167i	$-0.189647\pi$
$797$	−1.29354e6	−	2.24048e6i	−0.0721333	−	0.124938i	−0.899836	+	0.436228i	$0.856314\pi$
$798$	−2.00065e6	−	3.46522e6i	−0.111215	−	0.192630i
$799$	3.43712e6	−	5.95327e6i	0.190471	−	0.329905i
$800$	−6.08218e6	+	1.05346e7i	−0.335996	+	0.581962i
$801$	−1.13542e7			−0.625279
$802$	2.10926e6	−	3.65334e6i	0.115796	−	0.200565i
$803$	1.38717e7	−	2.40264e7i	0.759172	−	1.31492i
$804$	−4.62655e6	+	8.01342e6i	−0.252416	+	0.437198i
$805$	−1.41233e6	−	2.44623e6i	−0.0768151	−	0.133048i
$806$	−1.19855e7			−0.649860
$807$	1.76203e6	+	3.05192e6i	0.0952421	+	0.164964i
$808$	−3.41245e6	+	5.91054e6i	−0.183881	+	0.318492i
$809$	971190.			0.0521715			0.0260857	−	0.999660i	$-0.491696\pi$
$809$	971190.			0.0521715			0.0260857	+	0.999660i	$0.491696\pi$
$810$	−82666.7	+	143183.i	−0.00442709	+	0.00766794i
$811$	9.97266e6	+	1.72731e7i	0.532425	+	0.922188i	0.999283	+	0.0378554i	$0.0120526\pi$
$811$	9.97266e6	+	1.72731e7i	0.532425	+	0.922188i	−0.466858	+	0.884332i	$0.654614\pi$
$812$	3.84164e6	+	6.65392e6i	0.204469	+	0.354150i
$813$	−1.88584e7			−1.00064
$814$	−1.07607e7	−	1.86380e7i	−0.569217	−	0.985913i
$815$	−1.21502e7			−0.640751
$816$	−1.94920e6			−0.102478
$817$	−5.89624e6	−	2.96642e7i	−0.309044	−	1.55481i
$818$	1.25208e6			0.0654258
$819$	−8.33830e6			−0.434378
$820$	−7.47254e6	−	1.29428e7i	−0.388091	−	0.672194i
$821$	−2.34166e7			−1.21245			−0.606227	−	0.795292i	$-0.707318\pi$
$821$	−2.34166e7			−1.21245			−0.606227	+	0.795292i	$0.707318\pi$
$822$	−1.74793e6	−	3.02750e6i	−0.0902285	−	0.156280i
$823$	−1.06666e7	−	1.84751e7i	−0.548943	−	0.950796i	−0.998347	−	0.0574681i	$-0.981697\pi$
$823$	−1.06666e7	−	1.84751e7i	−0.548943	−	0.950796i	0.449405	−	0.893328i	$-0.351636\pi$
$824$	2.73926e6	−	4.74453e6i	0.140545	−	0.243431i
$825$	−1.59654e7			−0.816668
$826$	−2.30618e6	+	3.99441e6i	−0.117609	+	0.203706i
$827$	−6.22611e6	−	1.07839e7i	−0.316558	−	0.548294i	0.663210	−	0.748434i	$-0.269194\pi$
$827$	−6.22611e6	−	1.07839e7i	−0.316558	−	0.548294i	−0.979767	+	0.200139i	$0.935860\pi$
$828$	−5.12882e6			−0.259981
$829$	1.69617e7	+	2.93784e7i	0.857199	+	1.48471i	0.874590	+	0.484864i	$0.161131\pi$
$829$	1.69617e7	+	2.93784e7i	0.857199	+	1.48471i	−0.0173903	+	0.999849i	$0.505536\pi$
$830$	−1.78892e6	+	3.09849e6i	−0.0901353	+	0.156119i
$831$	621773.	−	1.07694e6i	0.0312341	−	0.0540991i
$832$	1.26588e6	−	2.19256e6i	0.0633991	−	0.109810i
$833$	4.60191e6			0.229787
$834$	1.31846e6	−	2.28365e6i	0.0656377	−	0.113688i
$835$	1.01076e7	−	1.75070e7i	0.501688	−	0.868949i
$836$	−2.59116e7	−	4.48803e7i	−1.28227	−	2.22095i
$837$	1.27124e7	+	2.20186e7i	0.627212	+	1.08636i
$838$	1.07733e7			0.529956
$839$	−381374.			−0.0187045			−0.00935226	−	0.999956i	$-0.502977\pi$
$839$	−381374.			−0.0187045			−0.00935226	+	0.999956i	$0.502977\pi$
$840$	1.45796e6	+	2.52527e6i	0.0712933	+	0.123484i
$841$	2.16411e6	+	3.74835e6i	0.105509	+	0.182747i
$842$	−3.56003e6	+	6.16615e6i	−0.173051	+	0.299732i
$843$	−6.59488e6	+	1.14227e7i	−0.319623	+	0.553603i
$844$	−3.87764e6			−0.187375
$845$	2.92972e6	−	5.07443e6i	0.141151	−	0.244481i
$846$	−3.14911e6	+	5.45441e6i	−0.151273	+	0.262012i
$847$	−1.64816e7	+	2.85470e7i	−0.789390	+	1.36726i
$848$	5.23999e6	+	9.07593e6i	0.250231	+	0.433413i
$849$	−5.45235e6			−0.259606
$850$	1.00998e6	+	1.74934e6i	0.0479475	+	0.0830475i
$851$	−7.30175e6	+	1.26470e7i	−0.345623	+	0.598637i
$852$	−1.25465e7			−0.592141
$853$	160333.	−	277704.i	0.00754482	−	0.0130680i	−0.862228	−	0.506520i	$-0.830932\pi$
$853$	160333.	−	277704.i	0.00754482	−	0.0130680i	0.869773	+	0.493452i	$0.164265\pi$
$854$	−4.03385e6	−	6.98683e6i	−0.189267	−	0.327820i
$855$	5.98616e6	+	1.03683e7i	0.280049	+	0.485058i
$856$	−1.63830e7			−0.764206
$857$	−6.03271e6	−	1.04490e7i	−0.280583	−	0.485983i	0.690946	−	0.722907i	$-0.257194\pi$
$857$	−6.03271e6	−	1.04490e7i	−0.280583	−	0.485983i	−0.971528	+	0.236923i	$0.923861\pi$
$858$	−1.30533e7			−0.605343
$859$	−759379.			−0.0351136			−0.0175568	−	0.999846i	$-0.505589\pi$
$859$	−759379.			−0.0351136			−0.0175568	+	0.999846i	$0.505589\pi$
$860$	1.94405e6	+	9.78060e6i	0.0896316	+	0.450941i
$861$	1.23623e7			0.568319
$862$	1.06952e6			0.0490255
$863$	−8.53763e6	−	1.47876e7i	−0.390221	−	0.675882i	0.602258	−	0.798302i	$-0.294268\pi$
$863$	−8.53763e6	−	1.47876e7i	−0.390221	−	0.675882i	−0.992478	+	0.122420i	$0.960935\pi$
$864$	2.10974e7			0.961492
$865$	1.76490e6	+	3.05690e6i	0.0802011	+	0.138912i
$866$	−6.87236e6	−	1.19033e7i	−0.311395	−	0.539352i
$867$	5.94364e6	−	1.02947e7i	0.268537	−	0.465120i
$868$	−1.29776e7			−0.584651
$869$	3.85422e6	−	6.67570e6i	0.173136	−	0.299880i
$870$	−1.38936e6	−	2.40643e6i	−0.0622322	−	0.107789i
$871$	−2.77983e7			−1.24158
$872$	3.67418e6	+	6.36387e6i	0.163633	+	0.283420i
$873$	−1.13146e6	+	1.95974e6i	−0.0502462	+	0.0870289i
$874$	3.69694e6	−	6.40328e6i	0.163706	−	0.283546i
$875$	−5.93458e6	+	1.02790e7i	−0.262041	+	0.453869i
$876$	8.79253e6			0.387127
$877$	2.23854e7	−	3.87727e7i	0.982804	−	1.70227i	0.331487	−	0.943460i	$-0.392450\pi$
$877$	2.23854e7	−	3.87727e7i	0.982804	−	1.70227i	0.651316	−	0.758806i	$-0.274217\pi$
$878$	−7.80554e6	+	1.35196e7i	−0.341717	+	0.591871i
$879$	−1.68576e6	−	2.91982e6i	−0.0735908	−	0.127463i
$880$	6.36930e6	+	1.10320e7i	0.277259	+	0.480226i
$881$	−1.72138e7			−0.747202			−0.373601	−	0.927590i	$-0.621877\pi$
$881$	−1.72138e7			−0.747202			−0.373601	+	0.927590i	$0.621877\pi$
$882$	−4.21629e6			−0.182498
$883$	3.32656e6	+	5.76177e6i	0.143580	+	0.248688i	0.928842	−	0.370476i	$-0.120805\pi$
$883$	3.32656e6	+	5.76177e6i	0.143580	+	0.248688i	−0.785262	+	0.619163i	$0.787472\pi$
$884$	−3.92730e6	−	6.80228e6i	−0.169030	−	0.292768i
$885$	−3.96670e6	+	6.87053e6i	−0.170244	+	0.294871i
$886$	3.86318e6	−	6.69123e6i	0.165334	−	0.286366i
$887$	7.44897e6			0.317897			0.158949	−	0.987287i	$-0.449190\pi$
$887$	7.44897e6			0.317897			0.158949	+	0.987287i	$0.449190\pi$
$888$	7.53768e6	−	1.30556e7i	0.320778	−	0.555604i
$889$	5.61694e6	−	9.72882e6i	0.238367	−	0.412863i
$890$	−2.69844e6	+	4.67383e6i	−0.114193	+	0.197787i
$891$	−885638.	−	1.53397e6i	−0.0373733	−	0.0647325i
$892$	2.09955e7			0.883514
$893$	2.15915e7	+	3.73975e7i	0.906054	+	1.56933i
$894$	1.12536e6	−	1.94918e6i	0.0470921	−	0.0815659i
$895$	−3.45751e6			−0.144280
$896$	−6.80473e6	+	1.17861e7i	−0.283166	+	0.490458i
$897$	4.42872e6	+	7.67076e6i	0.183779	+	0.318315i
$898$	−2.45092e6	−	4.24511e6i	−0.101423	−	0.175670i
$899$	2.73342e7			1.12799
$900$	4.40095e6	+	7.62267e6i	0.181109	+	0.313690i
$901$	7.98441e6			0.327665
$902$	−3.36653e7			−1.37774
$903$	−7.81049e6	−	2.65253e6i	−0.318756	−	0.108253i
$904$	−2.13989e6			−0.0870904
$905$	1.94158e6			0.0788014
$906$	−3.03852e6	−	5.26287e6i	−0.122982	−	0.213011i
$907$	2.91117e7			1.17503			0.587515	−	0.809213i	$-0.300106\pi$
$907$	2.91117e7			1.17503			0.587515	+	0.809213i	$0.300106\pi$
$908$	487381.	+	844169.i	0.0196180	+	0.0339793i
$909$	3.82122e6	+	6.61855e6i	0.153388	+	0.265676i
$910$	−1.98168e6	+	3.43238e6i	−0.0793288	+	0.137402i
$911$	2.00574e7			0.800715			0.400358	−	0.916359i	$-0.368886\pi$
$911$	2.00574e7			0.800715			0.400358	+	0.916359i	$0.368886\pi$
$912$	6.12229e6	−	1.06041e7i	0.243740	−	0.422170i
$913$	−1.91653e7	−	3.31953e7i	−0.760919	−	1.31795i
$914$	1.67520e7			0.663286
$915$	−6.93836e6	−	1.20176e7i	−0.273971	−	0.474531i
$916$	−5.73959e6	+	9.94126e6i	−0.226018	+	0.391474i
$917$	−3.14396e6	+	5.44550e6i	−0.123468	+	0.213852i
$918$	1.75168e6	−	3.03399e6i	0.0686037	−	0.118825i
$919$	6.60703e6			0.258058			0.129029	−	0.991641i	$-0.458814\pi$
$919$	6.60703e6			0.258058			0.129029	+	0.991641i	$0.458814\pi$
$920$	−2.69413e6	+	4.66637e6i	−0.104942	+	0.181765i
$921$	262869.	−	455302.i	0.0102115	−	0.0176869i
$922$	911852.	+	1.57937e6i	0.0353262	+	0.0611868i
$923$	−1.88463e7	−	3.26427e7i	−0.728150	−	1.26119i
$924$	−1.41338e7			−0.544601
$925$	2.50620e7			0.963078
$926$	3.18681e6	+	5.51972e6i	0.122132	+	0.211539i
$927$	−3.06739e6	−	5.31287e6i	−0.117238	−	0.203063i
$928$	1.13409e7	−	1.96430e7i	0.432293	−	0.748753i
$929$	7.58813e6	−	1.31430e7i	0.288467	−	0.499639i	−0.684977	−	0.728564i	$-0.740188\pi$
$929$	7.58813e6	−	1.31430e7i	0.288467	−	0.499639i	0.973444	+	0.228925i	$0.0735212\pi$
$930$	4.69345e6			0.177945
$931$	−1.44543e7	+	2.50355e7i	−0.546540	+	0.946634i
$932$	−1.79243e7	+	3.10457e7i	−0.675930	+	1.17074i
$933$	2.30852e6	−	3.99847e6i	0.0868219	−	0.150380i
$934$	−3.43267e6	−	5.94555e6i	−0.128755	−	0.223010i
$935$	9.70518e6			0.363057
$936$	7.95297e6	+	1.37749e7i	0.296715	+	0.513926i
$937$	2.73730e6	−	4.74114e6i	0.101853	−	0.176414i	−0.810595	−	0.585607i	$-0.800856\pi$
$937$	2.73730e6	−	4.74114e6i	0.101853	−	0.176414i	0.912448	+	0.409193i	$0.134190\pi$
$938$	6.32873e6			0.234860
$939$	−1.02293e7	+	1.77176e7i	−0.378599	+	0.655753i
$940$	−7.11894e6	−	1.23304e7i	−0.262782	−	0.455152i
$941$	−3.29319e6	−	5.70397e6i	−0.121239	−	0.209992i	0.799018	−	0.601308i	$-0.205353\pi$
$941$	−3.29319e6	−	5.70397e6i	−0.121239	−	0.209992i	−0.920257	+	0.391316i	$0.872020\pi$
$942$	−3.80068e6			−0.139552
$943$	1.14220e7	+	1.97834e7i	0.418275	+	0.724473i
$944$	−1.41145e7			−0.515509
$945$	8.40748e6			0.306257
$946$	2.12697e7	+	7.22343e6i	0.772740	+	0.262431i
$947$	1.91206e7			0.692831			0.346415	−	0.938081i	$-0.387399\pi$
$947$	1.91206e7			0.692831			0.346415	+	0.938081i	$0.387399\pi$
$948$	2.44299e6			0.0882877
$949$	1.32073e7	+	2.28758e7i	0.476047	+	0.824537i
$950$	−1.26891e7			−0.456165
$951$	−4.02123e6	−	6.96498e6i	−0.144181	−	0.249729i
$952$	1.97622e6	+	3.42291e6i	0.0706713	+	0.122406i
$953$	−6.72804e6	+	1.16533e7i	−0.239970	+	0.415640i	−0.960705	−	0.277570i	$-0.910471\pi$
$953$	−6.72804e6	+	1.16533e7i	−0.239970	+	0.415640i	0.720736	+	0.693210i	$0.243804\pi$
$954$	−7.31534e6			−0.260234
$955$	−2.50427e6	+	4.33753e6i	−0.0888533	+	0.153898i
$956$	1.21693e7	+	2.10778e7i	0.430645	+	0.745899i
$957$	2.97693e7			1.05072
$958$	5.33021e6	+	9.23220e6i	0.187642	+	0.325006i
$959$	5.68582e6	−	9.84814e6i	0.199640	−	0.345786i
$960$	−495709.	+	858593.i	−0.0173600	+	0.0300683i
$961$	−8.77018e6	+	1.51904e7i	−0.306338	+	0.530592i
$962$	2.04906e7			0.713867
$963$	−9.17277e6	+	1.58877e7i	−0.318739	+	0.552072i
$964$	−1.38694e7	+	2.40225e7i	−0.480691	+	0.832581i
$965$	6.01138e6	+	1.04120e7i	0.207805	+	0.359929i
$966$	−1.00827e6	−	1.74637e6i	−0.0347643	−	0.0602135i
$967$	−4.26507e7			−1.46676			−0.733382	−	0.679817i	$-0.762059\pi$
$967$	−4.26507e7			−1.46676			−0.733382	+	0.679817i	$0.762059\pi$
$968$	6.28800e7			2.15687
$969$	−4.66441e6	−	8.07899e6i	−0.159583	−	0.276406i
$970$	537806.	+	931508.i	0.0183526	+	0.0317876i
$971$	−2.01049e7	+	3.48227e7i	−0.684310	+	1.18526i	0.289343	+	0.957226i	$0.406563\pi$
$971$	−2.01049e7	+	3.48227e7i	−0.684310	+	1.18526i	−0.973653	+	0.228035i	$0.926770\pi$
$972$	1.23013e7	−	2.13065e7i	0.417625	−	0.723347i
$973$	8.57765e6			0.290460
$974$	5.70064e6	−	9.87380e6i	0.192542	−	0.333493i
$975$	7.60041e6	−	1.31643e7i	0.256050	−	0.443492i
$976$	1.23442e7	−	2.13808e7i	0.414800	−	0.718455i
$977$	2.08409e7	+	3.60974e7i	0.698521	+	1.20987i	0.968979	+	0.247142i	$0.0794913\pi$
$977$	2.08409e7	+	3.60974e7i	0.698521	+	1.20987i	−0.270459	+	0.962732i	$0.587175\pi$
$978$	−8.67407e6			−0.289985
$979$	−2.89093e7	−	5.00724e7i	−0.964010	−	1.66971i
$980$	4.76572e6	−	8.25447e6i	0.158512	−	0.274552i
$981$	8.22862e6			0.272995
$982$	−8.90246e6	+	1.54195e7i	−0.294599	+	0.510261i
$983$	−2.38251e7	−	4.12663e7i	−0.786414	−	1.36211i	−0.928151	−	0.372204i	$-0.878602\pi$
$983$	−2.38251e7	−	4.12663e7i	−0.786414	−	1.36211i	0.141737	−	0.989904i	$-0.454731\pi$
$984$	−1.17910e7	−	2.04227e7i	−0.388208	−	0.672395i
$985$	−1.02318e7			−0.336016
$986$	−1.88322e6	−	3.26184e6i	−0.0616893	−	0.106849i
$987$	1.17773e7			0.384816
$988$	4.93414e7			1.60812
$989$	−2.97153e6	−	1.49499e7i	−0.0966027	−	0.486013i
$990$	−8.89193e6			−0.288342
$991$	−3.40171e7			−1.10031			−0.550153	−	0.835064i	$-0.685431\pi$
$991$	−3.40171e7			−1.10031			−0.550153	+	0.835064i	$0.685431\pi$
$992$	1.91556e7	+	3.31786e7i	0.618042	+	1.07048i
$993$	−1.68892e7			−0.543547
$994$	4.29065e6	+	7.43163e6i	0.137739	+	0.238571i
$995$	4.80866e6	+	8.32884e6i	0.153981	+	0.266702i
$996$	6.07394e6	−	1.05204e7i	0.194009	−	0.336034i
$997$	−1.36706e7			−0.435560			−0.217780	−	0.975998i	$-0.569882\pi$
$997$	−1.36706e7			−0.435560			−0.217780	+	0.975998i	$0.569882\pi$
$998$	−9.82806e6	+	1.70227e7i	−0.312350	+	0.541006i
$999$	−2.17333e7	−	3.76432e7i	−0.688989	−	1.19336i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.6.c.a.36.8	yes	34
43.6	even	3	inner	43.6.c.a.6.8	✓	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.6.c.a.6.8	✓	34	43.6	even	3	inner
43.6.c.a.36.8	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)

\(f(q)\)	\(=\)	\(q-2.35784 q^{2} +(-4.70904 - 8.15629i) q^{3} -26.4406 q^{4} +(15.5528 + 26.9382i) q^{5} +(11.1032 + 19.2313i) q^{6} +(-36.1175 + 62.5573i) q^{7} +137.794 q^{8} +(77.1499 - 133.628i) q^{9} +O(q^{10})\)	\(q-2.35784 q^{2} +(-4.70904 - 8.15629i) q^{3} -26.4406 q^{4} +(15.5528 + 26.9382i) q^{5} +(11.1032 + 19.2313i) q^{6} +(-36.1175 + 62.5573i) q^{7} +137.794 q^{8} +(77.1499 - 133.628i) q^{9} +(-36.6710 - 63.5160i) q^{10} +785.739 q^{11} +(124.510 + 215.657i) q^{12} +(-374.054 + 647.881i) q^{13} +(85.1594 - 147.500i) q^{14} +(146.477 - 253.706i) q^{15} +521.202 q^{16} +(198.545 - 343.889i) q^{17} +(-181.907 + 315.073i) q^{18} +(1247.23 + 2160.26i) q^{19} +(-411.224 - 712.261i) q^{20} +680.315 q^{21} -1852.65 q^{22} +(628.566 + 1088.71i) q^{23} +(-648.876 - 1123.89i) q^{24} +(1078.72 - 1868.40i) q^{25} +(881.961 - 1527.60i) q^{26} -3741.80 q^{27} +(954.967 - 1654.05i) q^{28} +(-2011.40 + 3483.85i) q^{29} +(-345.370 + 598.199i) q^{30} +(-3397.41 - 5884.48i) q^{31} -5638.31 q^{32} +(-3700.07 - 6408.72i) q^{33} +(-468.137 + 810.838i) q^{34} -2246.91 q^{35} +(-2039.89 + 3533.19i) q^{36} +(5808.25 + 10060.2i) q^{37} +(-2940.77 - 5093.56i) q^{38} +7045.74 q^{39} +(2143.07 + 3711.91i) q^{40} +18171.5 q^{41} -1604.08 q^{42} +(-11480.7 - 3898.98i) q^{43} -20775.4 q^{44} +4799.58 q^{45} +(-1482.06 - 2567.01i) q^{46} +17311.6 q^{47} +(-2454.36 - 4251.08i) q^{48} +(5794.55 + 10036.5i) q^{49} +(-2543.46 + 4405.40i) q^{50} -3739.82 q^{51} +(9890.21 - 17130.3i) q^{52} +(10053.7 + 17413.5i) q^{53} +8822.58 q^{54} +(12220.4 + 21166.4i) q^{55} +(-4976.76 + 8620.01i) q^{56} +(11746.5 - 20345.5i) q^{57} +(4742.57 - 8214.37i) q^{58} -27080.7 q^{59} +(-3872.94 + 6708.13i) q^{60} +(23684.1 - 41022.1i) q^{61} +(8010.56 + 13874.7i) q^{62} +(5572.92 + 9652.58i) q^{63} -3384.21 q^{64} -23270.3 q^{65} +(8724.20 + 15110.8i) q^{66} +(18579.1 + 32179.9i) q^{67} +(-5249.64 + 9092.63i) q^{68} +(5919.89 - 10253.5i) q^{69} +5297.85 q^{70} +(-25191.9 + 43633.6i) q^{71} +(10630.8 - 18413.0i) q^{72} +(17654.3 - 30578.2i) q^{73} +(-13695.0 - 23720.4i) q^{74} -20319.0 q^{75} +(-32977.4 - 57118.6i) q^{76} +(-28378.9 + 49153.7i) q^{77} -16612.8 q^{78} +(4905.21 - 8496.08i) q^{79} +(8106.13 + 14040.2i) q^{80} +(-1127.14 - 1952.26i) q^{81} -42845.5 q^{82} +(-24391.4 - 42247.2i) q^{83} -17987.9 q^{84} +12351.7 q^{85} +(27069.7 + 9193.18i) q^{86} +37887.0 q^{87} +108270. q^{88} +(-36792.6 - 63726.6i) q^{89} -11316.7 q^{90} +(-27019.8 - 46799.6i) q^{91} +(-16619.7 - 28786.1i) q^{92} +(-31997.1 + 55420.5i) q^{93} -40818.0 q^{94} +(-38795.7 + 67196.1i) q^{95} +(26551.0 + 45987.7i) q^{96} -14665.7 q^{97} +(-13662.7 - 23664.4i) q^{98} +(60619.7 - 104996. i) 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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