LMFDB - Embedded newform 43.6.c.a.6.17

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			6.17
Character	$\chi$	$=$	43.6
Dual form			43.6.c.a.36.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+9.96731 q^{2} +(-9.83333 + 17.0318i) q^{3} +67.3472 q^{4} +(6.65929 - 11.5342i) q^{5} +(-98.0118 + 169.761i) q^{6} +(61.0081 + 105.669i) q^{7} +352.316 q^{8} +(-71.8888 - 124.515i) q^{9} +O(q^{10})$	\(q+9.96731 q^{2} +(-9.83333 + 17.0318i) q^{3} +67.3472 q^{4} +(6.65929 - 11.5342i) q^{5} +(-98.0118 + 169.761i) q^{6} +(61.0081 + 105.669i) q^{7} +352.316 q^{8} +(-71.8888 - 124.515i) q^{9} +(66.3751 - 114.965i) q^{10} -64.2046 q^{11} +(-662.247 + 1147.05i) q^{12} +(38.2202 + 66.1993i) q^{13} +(608.087 + 1053.24i) q^{14} +(130.966 + 226.840i) q^{15} +1356.53 q^{16} +(-984.059 - 1704.44i) q^{17} +(-716.538 - 1241.08i) q^{18} +(1244.22 - 2155.06i) q^{19} +(448.484 - 776.797i) q^{20} -2399.65 q^{21} -639.947 q^{22} +(2292.28 - 3970.35i) q^{23} +(-3464.44 + 6000.59i) q^{24} +(1473.81 + 2552.71i) q^{25} +(380.952 + 659.828i) q^{26} -1951.37 q^{27} +(4108.72 + 7116.52i) q^{28} +(887.712 + 1537.56i) q^{29} +(1305.38 + 2260.98i) q^{30} +(-721.458 + 1249.60i) q^{31} +2246.86 q^{32} +(631.345 - 1093.52i) q^{33} +(-9808.42 - 16988.7i) q^{34} +1625.08 q^{35} +(-4841.51 - 8385.74i) q^{36} +(-4283.83 + 7419.81i) q^{37} +(12401.6 - 21480.1i) q^{38} -1503.33 q^{39} +(2346.17 - 4063.69i) q^{40} -4836.07 q^{41} -23918.1 q^{42} +(2285.74 + 11907.3i) q^{43} -4324.00 q^{44} -1914.91 q^{45} +(22847.9 - 39573.7i) q^{46} -9504.55 q^{47} +(-13339.2 + 23104.2i) q^{48} +(959.520 - 1661.94i) q^{49} +(14689.9 + 25443.6i) q^{50} +38706.3 q^{51} +(2574.02 + 4458.33i) q^{52} +(-10269.9 + 17787.9i) q^{53} -19449.9 q^{54} +(-427.557 + 740.550i) q^{55} +(21494.1 + 37228.9i) q^{56} +(24469.7 + 42382.8i) q^{57} +(8848.10 + 15325.4i) q^{58} -12309.9 q^{59} +(8820.19 + 15277.0i) q^{60} +(-9716.67 - 16829.8i) q^{61} +(-7190.99 + 12455.2i) q^{62} +(8771.60 - 15192.9i) q^{63} -21013.9 q^{64} +1018.08 q^{65} +(6292.81 - 10899.5i) q^{66} +(34280.7 - 59375.9i) q^{67} +(-66273.6 - 114789. i) q^{68} +(45081.6 + 78083.6i) q^{69} +16197.7 q^{70} +(21742.0 + 37658.3i) q^{71} +(-25327.6 - 43868.7i) q^{72} +(27405.2 + 47467.3i) q^{73} +(-42698.2 + 73955.5i) q^{74} -57969.8 q^{75} +(83795.0 - 145137. i) q^{76} +(-3917.00 - 6784.45i) q^{77} -14984.1 q^{78} +(-14291.6 - 24753.9i) q^{79} +(9033.54 - 15646.5i) q^{80} +(36657.5 - 63492.6i) q^{81} -48202.6 q^{82} +(-3057.73 + 5296.14i) q^{83} -161610. q^{84} -26212.5 q^{85} +(22782.7 + 118684. i) q^{86} -34916.7 q^{87} -22620.3 q^{88} +(-37106.7 + 64270.7i) q^{89} -19086.5 q^{90} +(-4663.48 + 8077.38i) q^{91} +(154379. - 267392. i) q^{92} +(-14188.7 - 24575.5i) q^{93} -94734.7 q^{94} +(-16571.3 - 28702.3i) q^{95} +(-22094.1 + 38268.1i) q^{96} +65857.2 q^{97} +(9563.82 - 16565.0i) q^{98} +(4615.60 + 7994.45i) 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 $\left(\mathbb{Z}/43\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	9.96731			1.76199			0.880994	−	0.473128i	$-0.156875\pi$
$2$	9.96731			1.76199			0.880994	+	0.473128i	$0.156875\pi$
$3$	−9.83333	+	17.0318i	−0.630809	+	1.09259i	0.356578	+	0.934265i	$0.383943\pi$
$3$	−9.83333	+	17.0318i	−0.630809	+	1.09259i	−0.987387	+	0.158327i	$0.949390\pi$
$4$	67.3472			2.10460
$5$	6.65929	−	11.5342i	0.119125	−	0.206330i	−0.800296	−	0.599605i	$-0.795324\pi$
$5$	6.65929	−	11.5342i	0.119125	−	0.206330i	0.919421	+	0.393274i	$0.128658\pi$
$6$	−98.0118	+	169.761i	−1.11148	+	1.92513i
$7$	61.0081	+	105.669i	0.470590	+	0.815085i	0.999434	−	0.0336333i	$-0.0107078\pi$
$7$	61.0081	+	105.669i	0.470590	+	0.815085i	−0.528844	+	0.848719i	$0.677375\pi$
$8$	352.316			1.94629
$9$	−71.8888	−	124.515i	−0.295839	−	0.512408i
$10$	66.3751	−	114.965i	0.209897	−	0.363552i
$11$	−64.2046			−0.159987			−0.0799935	−	0.996795i	$-0.525490\pi$
$11$	−64.2046			−0.159987			−0.0799935	+	0.996795i	$0.525490\pi$
$12$	−662.247	+	1147.05i	−1.32760	+	2.29947i
$13$	38.2202	+	66.1993i	0.0627241	+	0.108641i	0.895682	−	0.444695i	$-0.146688\pi$
$13$	38.2202	+	66.1993i	0.0627241	+	0.108641i	−0.832958	+	0.553336i	$0.813355\pi$
$14$	608.087	+	1053.24i	0.829173	+	1.43617i
$15$	130.966	+	226.840i	0.150290	+	0.260310i
$16$	1356.53			1.32474
$17$	−984.059	−	1704.44i	−0.825846	−	1.43041i	−0.901271	−	0.433255i	$-0.857365\pi$
$17$	−984.059	−	1704.44i	−0.825846	−	1.43041i	0.0754258	−	0.997151i	$-0.475968\pi$
$18$	−716.538	−	1241.08i	−0.521264	−	0.902856i
$19$	1244.22	−	2155.06i	0.790705	−	1.36954i	−0.134826	−	0.990869i	$-0.543048\pi$
$19$	1244.22	−	2155.06i	0.790705	−	1.36954i	0.925531	−	0.378672i	$-0.123619\pi$
$20$	448.484	−	776.797i	0.250710	−	0.434243i
$21$	−2399.65			−1.18741
$22$	−639.947			−0.281895
$23$	2292.28	−	3970.35i	0.903543	−	1.56498i	0.0806819	−	0.996740i	$-0.474290\pi$
$23$	2292.28	−	3970.35i	0.903543	−	1.56498i	0.822861	−	0.568243i	$-0.192376\pi$
$24$	−3464.44	+	6000.59i	−1.22774	+	2.12650i
$25$	1473.81	+	2552.71i	0.471619	+	0.816867i
$26$	380.952	+	659.828i	0.110519	+	0.191425i
$27$	−1951.37			−0.515146
$28$	4108.72	+	7116.52i	0.990403	+	1.71543i
$29$	887.712	+	1537.56i	0.196010	+	0.339499i	0.947231	−	0.320552i	$-0.103868\pi$
$29$	887.712	+	1537.56i	0.196010	+	0.339499i	−0.751221	+	0.660050i	$0.770535\pi$
$30$	1305.38	+	2260.98i	0.264809	+	0.458663i
$31$	−721.458	+	1249.60i	−0.134836	+	0.233543i	−0.925535	−	0.378662i	$-0.876384\pi$
$31$	−721.458	+	1249.60i	−0.134836	+	0.233543i	0.790699	+	0.612206i	$0.209718\pi$
$32$	2246.86			0.387883
$33$	631.345	−	1093.52i	0.100921	−	0.174801i
$34$	−9808.42	−	16988.7i	−1.45513	−	2.52036i
$35$	1625.08			0.224236
$36$	−4841.51	−	8385.74i	−0.622622	−	1.07841i
$37$	−4283.83	+	7419.81i	−0.514432	+	0.891022i	0.485428	+	0.874277i	$0.338664\pi$
$37$	−4283.83	+	7419.81i	−0.514432	+	0.891022i	−0.999860	+	0.0167456i	$0.994669\pi$
$38$	12401.6	−	21480.1i	1.39321	−	2.41311i
$39$	−1503.33			−0.158267
$40$	2346.17	−	4063.69i	0.231852	−	0.401579i
$41$	−4836.07			−0.449296			−0.224648	−	0.974440i	$-0.572123\pi$
$41$	−4836.07			−0.449296			−0.224648	+	0.974440i	$0.572123\pi$
$42$	−23918.1			−2.09220
$43$	2285.74	+	11907.3i	0.188519	+	0.982070i
$43$	2285.74	+	11907.3i	0.188519	+	0.982070i
$44$	−4324.00			−0.336708
$45$	−1914.91			−0.140967
$46$	22847.9	−	39573.7i	1.59203	−	2.75748i
$47$	−9504.55			−0.627606			−0.313803	−	0.949488i	$-0.601603\pi$
$47$	−9504.55			−0.627606			−0.313803	+	0.949488i	$0.601603\pi$
$48$	−13339.2	+	23104.2i	−0.835656	+	1.44740i
$49$	959.520	−	1661.94i	0.0570905	−	0.0988836i
$50$	14689.9	+	25443.6i	0.830986	+	1.43931i
$51$	38706.3			2.08380
$52$	2574.02	+	4458.33i	0.132009	+	0.228646i
$53$	−10269.9	+	17787.9i	−0.502198	+	0.869832i	0.497799	+	0.867292i	$0.334142\pi$
$53$	−10269.9	+	17787.9i	−0.502198	+	0.869832i	−0.999997	+	0.00253957i	$0.999192\pi$
$54$	−19449.9			−0.907681
$55$	−427.557	+	740.550i	−0.0190584	+	0.0330102i
$56$	21494.1	+	37228.9i	0.915904	+	1.58639i
$57$	24469.7	+	42382.8i	0.997567	+	1.72784i
$58$	8848.10	+	15325.4i	0.345366	+	0.598192i
$59$	−12309.9			−0.460388			−0.230194	−	0.973145i	$-0.573936\pi$
$59$	−12309.9			−0.460388			−0.230194	+	0.973145i	$0.573936\pi$
$60$	8820.19	+	15277.0i	0.316300	+	0.547848i
$61$	−9716.67	−	16829.8i	−0.334343	−	0.579100i	0.649015	−	0.760776i	$-0.275181\pi$
$61$	−9716.67	−	16829.8i	−0.334343	−	0.579100i	−0.983358	+	0.181676i	$0.941848\pi$
$62$	−7190.99	+	12455.2i	−0.237580	+	0.411500i
$63$	8771.60	−	15192.9i	0.278437	−	0.482268i
$64$	−21013.9			−0.641294
$65$	1018.08			0.0298880
$66$	6292.81	−	10899.5i	0.177822	−	0.307996i
$67$	34280.7	−	59375.9i	0.932959	−	1.61593i	0.154725	−	0.987958i	$-0.450551\pi$
$67$	34280.7	−	59375.9i	0.932959	−	1.61593i	0.778234	−	0.627974i	$-0.216116\pi$
$68$	−66273.6	−	114789.i	−1.73807	−	3.01043i
$69$	45081.6	+	78083.6i	1.13993	+	1.97441i
$70$	16197.7			0.395101
$71$	21742.0	+	37658.3i	0.511864	+	0.886574i	0.999905	+	0.0137540i	$0.00437817\pi$
$71$	21742.0	+	37658.3i	0.511864	+	0.886574i	−0.488041	+	0.872820i	$0.662289\pi$
$72$	−25327.6	−	43868.7i	−0.575788	−	0.997294i
$73$	27405.2	+	47467.3i	0.601903	+	1.04253i	0.992533	+	0.121978i	$0.0389238\pi$
$73$	27405.2	+	47467.3i	0.601903	+	1.04253i	−0.390630	+	0.920548i	$0.627743\pi$
$74$	−42698.2	+	73955.5i	−0.906423	+	1.56997i
$75$	−57969.8			−1.19000
$76$	83795.0	−	145137.i	1.66412	−	2.88234i
$77$	−3917.00	−	6784.45i	−0.0752882	−	0.130403i
$78$	−14984.1			−0.278865
$79$	−14291.6	−	24753.9i	−0.257641	−	0.446247i	0.707969	−	0.706244i	$-0.249612\pi$
$79$	−14291.6	−	24753.9i	−0.257641	−	0.446247i	−0.965609	+	0.259997i	$0.916278\pi$
$80$	9033.54	−	15646.5i	0.157809	−	0.273334i
$81$	36657.5	−	63492.6i	0.620798	−	1.07525i
$82$	−48202.6			−0.791655
$83$	−3057.73	+	5296.14i	−0.0487196	+	0.0843848i	−0.889357	−	0.457214i	$-0.848847\pi$
$83$	−3057.73	+	5296.14i	−0.0487196	+	0.0843848i	0.840637	+	0.541599i	$0.182181\pi$
$84$	−161610.			−2.49902
$85$	−26212.5			−0.393515
$86$	22782.7	+	118684.i	0.332168	+	1.73039i
$87$	−34916.7			−0.494578
$88$	−22620.3			−0.311381
$89$	−37106.7	+	64270.7i	−0.496567	+	0.860078i	−0.999992	−	0.00396011i	$-0.998739\pi$
$89$	−37106.7	+	64270.7i	−0.496567	+	0.860078i	0.503426	+	0.864039i	$0.332073\pi$
$90$	−19086.5			−0.248382
$91$	−4663.48	+	8077.38i	−0.0590346	+	0.102251i
$92$	154379.	−	267392.i	1.90160	−	3.29366i
$93$	−14188.7	−	24575.5i	−0.170112	−	0.294642i
$94$	−94734.7			−1.10583
$95$	−16571.3	−	28702.3i	−0.188385	−	0.326293i
$96$	−22094.1	+	38268.1i	−0.244680	+	0.423798i
$97$	65857.2			0.710680			0.355340	−	0.934737i	$-0.384365\pi$
$97$	65857.2			0.710680			0.355340	+	0.934737i	$0.384365\pi$
$98$	9563.82	−	16565.0i	0.100593	−	0.174232i
$99$	4615.60	+	7994.45i	0.0473304	+	0.0819786i
$100$	99256.8	+	171918.i	0.992568	+	1.71918i
$101$	−99361.1	−	172098.i	−0.969199	−	1.67870i	−0.697885	−	0.716210i	$-0.745875\pi$
$101$	−99361.1	−	172098.i	−0.969199	−	1.67870i	−0.271314	−	0.962491i	$-0.587458\pi$
$102$	385798.			3.67163
$103$	−12190.9	−	21115.3i	−0.113225	−	0.196112i	0.803844	−	0.594841i	$-0.202785\pi$
$103$	−12190.9	−	21115.3i	−0.113225	−	0.196112i	−0.917069	+	0.398729i	$0.869451\pi$
$104$	13465.6	+	23323.1i	0.122079	+	0.211447i
$105$	−15980.0	+	27678.1i	−0.141450	+	0.244998i
$106$	−102363.	+	177298.i	−0.884866	+	1.53263i
$107$	184018.			1.55382			0.776912	−	0.629609i	$-0.216785\pi$
$107$	184018.			1.55382			0.776912	+	0.629609i	$0.216785\pi$
$108$	−131419.			−1.08418
$109$	−104049.	+	180219.i	−0.838828	+	1.45289i	0.0520468	+	0.998645i	$0.483425\pi$
$109$	−104049.	+	180219.i	−0.838828	+	1.45289i	−0.890875	+	0.454248i	$0.849908\pi$
$110$	−4261.59	+	7381.29i	−0.0335807	+	0.0581635i
$111$	−84248.7	−	145923.i	−0.649016	−	1.12413i
$112$	82759.5	+	143344.i	0.623409	+	1.07978i
$113$	40753.9			0.300243			0.150122	−	0.988668i	$-0.452033\pi$
$113$	40753.9			0.300243			0.150122	+	0.988668i	$0.452033\pi$
$114$	243897.	+	422442.i	1.75770	+	3.04443i
$115$	−30529.9	−	52879.4i	−0.215269	−	0.372857i
$116$	59784.9	+	103551.i	0.412522	+	0.714508i
$117$	5495.21	−	9517.98i	0.0371124	−	0.0642806i
$118$	−122696.			−0.811198
$119$	120071.	−	207969.i	0.777269	−	1.34627i
$120$	46141.4	+	79919.3i	0.292508	+	0.506639i
$121$	−156929.			−0.974404
$122$	−96849.0	−	167747.i	−0.589109	−	1.02037i
$123$	47554.7	−	82367.1i	0.283420	−	0.490898i
$124$	−48588.2	+	84157.2i	−0.283776	+	0.491515i
$125$	80878.6			0.462976
$126$	87429.3	−	151432.i	0.490603	−	0.849750i
$127$	−248512.			−1.36722			−0.683608	−	0.729849i	$-0.739590\pi$
$127$	−248512.			−1.36722			−0.683608	+	0.729849i	$0.739590\pi$
$128$	−281352.			−1.51783
$129$	−225280.	−	78158.1i	−1.19192	−	0.413523i
$130$	10147.5			0.0526623
$131$	−254368.			−1.29504			−0.647522	−	0.762047i	$-0.724195\pi$
$131$	−254368.			−1.29504			−0.647522	+	0.762047i	$0.724195\pi$
$132$	42519.3	−	73645.6i	0.212399	−	0.367885i
$133$	303631.			1.48839
$134$	341686.	−	591818.i	1.64386	−	2.84725i
$135$	−12994.7	+	22507.6i	−0.0613668	+	0.106290i
$136$	−346700.	−	600502.i	−1.60733	−	2.78399i
$137$	−89866.3			−0.409068			−0.204534	−	0.978859i	$-0.565568\pi$
$137$	−89866.3			−0.409068			−0.204534	+	0.978859i	$0.565568\pi$
$138$	449342.	+	778283.i	2.00853	+	3.47888i
$139$	−155524.	+	269376.i	−0.682748	+	1.18255i	0.291390	+	0.956604i	$0.405882\pi$
$139$	−155524.	+	269376.i	−0.682748	+	1.18255i	−0.974139	+	0.225951i	$0.927451\pi$
$140$	109445.			0.471927
$141$	93461.4	−	161880.i	0.395899	−	0.685717i
$142$	216710.	+	375352.i	0.901898	+	1.56213i
$143$	−2453.91	−	4250.30i	−0.0100350	−	0.0173812i
$144$	−97519.5	−	168909.i	−0.391909	−	0.678807i
$145$	23646.1			0.0933985
$146$	273156.	+	473121.i	1.06054	+	1.83692i
$147$	18870.5	+	32684.7i	0.0720263	+	0.124753i
$148$	−288504.	+	499703.i	−1.08267	+	1.87525i
$149$	67505.9	−	116924.i	0.249101	−	0.431456i	−0.714175	−	0.699967i	$-0.753198\pi$
$149$	67505.9	−	116924.i	0.249101	−	0.431456i	0.963277	+	0.268511i	$0.0865314\pi$
$150$	−577802.			−2.09677
$151$	233223.			0.832393			0.416197	−	0.909275i	$-0.363363\pi$
$151$	233223.			0.832393			0.416197	+	0.909275i	$0.363363\pi$
$152$	438360.	−	759262.i	1.53894	−	2.66552i
$153$	−141486.	+	245060.i	−0.488634	+	0.846340i
$154$	−39042.0	−	67622.7i	−0.132657	−	0.229769i
$155$	9608.79	+	16642.9i	0.0321247	+	0.0556417i
$156$	−101245.			−0.333090
$157$	171445.	+	296952.i	0.555107	+	0.961473i	0.997895	+	0.0648469i	$0.0206559\pi$
$157$	171445.	+	296952.i	0.555107	+	0.961473i	−0.442789	+	0.896626i	$0.646011\pi$
$158$	−142449.	−	246729.i	−0.453960	−	0.786281i
$159$	−201974.	−	349829.i	−0.633581	−	1.09739i
$160$	14962.5	−	25915.8i	0.0462065	−	0.0800321i
$161$	559392.			1.70079
$162$	365376.	−	632850.i	1.09384	−	1.89458i
$163$	28679.6	+	49674.5i	0.0845481	+	0.146442i	0.905199	−	0.424989i	$-0.139722\pi$
$163$	28679.6	+	49674.5i	0.0845481	+	0.146442i	−0.820650	+	0.571431i	$0.806389\pi$
$164$	−325696.			−0.945589
$165$	−8408.62	−	14564.2i	−0.0240444	−	0.0416462i
$166$	−30477.3	+	52788.2i	−0.0858432	+	0.148685i
$167$	66256.0	−	114759.i	0.183838	−	0.318416i	−0.759347	−	0.650686i	$-0.774481\pi$
$167$	66256.0	−	114759.i	0.183838	−	0.318416i	0.943184	+	0.332270i	$0.107815\pi$
$168$	−845436.			−2.31104
$169$	182725.	−	316489.i	0.492131	−	0.852397i
$170$	−261268.			−0.693369
$171$	−357783.			−0.935685
$172$	153938.	+	801923.i	0.396757	+	2.06686i
$173$	159660.			0.405585			0.202792	−	0.979222i	$-0.434998\pi$
$173$	159660.			0.405585			0.202792	+	0.979222i	$0.434998\pi$
$174$	−348025.			−0.871440
$175$	−179828.	+	311472.i	−0.443878	+	0.768819i
$176$	−87095.7			−0.211941
$177$	121047.	−	209660.i	0.290417	−	0.503016i
$178$	−369854.	+	640606.i	−0.874944	+	1.51545i
$179$	−41797.1	−	72394.7i	−0.0975020	−	0.168878i	0.813148	−	0.582057i	$-0.197752\pi$
$179$	−41797.1	−	72394.7i	−0.0975020	−	0.168878i	−0.910650	+	0.413178i	$0.864419\pi$
$180$	−128964.			−0.296679
$181$	155097.	+	268635.i	0.351889	+	0.609490i	0.986580	−	0.163276i	$-0.0522060\pi$
$181$	155097.	+	268635.i	0.351889	+	0.609490i	−0.634691	+	0.772766i	$0.718873\pi$
$182$	−46482.3	+	80509.8i	−0.104018	+	0.180165i
$183$	382189.			0.843627
$184$	807609.	−	1.39882e6i	1.75856	−	3.04591i
$185$	57054.5	+	98821.3i	0.122563	+	0.212286i
$186$	−141423.	−	244952.i	−0.299735	−	0.519156i
$187$	63181.1	+	109433.i	0.132125	+	0.228846i
$188$	−640104.			−1.32086
$189$	−119050.	−	206200.i	−0.242423	−	0.419888i
$190$	−165171.	−	286085.i	−0.331933	−	0.574924i
$191$	116587.	−	201934.i	0.231241	−	0.400521i	−0.726932	−	0.686709i	$-0.759055\pi$
$191$	116587.	−	201934.i	0.231241	−	0.400521i	0.958174	+	0.286187i	$0.0923880\pi$
$192$	206637.	−	357905.i	0.404534	−	0.700673i
$193$	−304008.			−0.587478			−0.293739	−	0.955886i	$-0.594900\pi$
$193$	−304008.			−0.587478			−0.293739	+	0.955886i	$0.594900\pi$
$194$	656419.			1.25221
$195$	−10011.1	+	17339.7i	−0.0188536	+	0.0326554i
$196$	64620.9	−	111927.i	0.120153	−	0.208110i
$197$	378642.	+	655827.i	0.695126	+	1.20399i	0.970138	+	0.242552i	$0.0779846\pi$
$197$	378642.	+	655827.i	0.695126	+	1.20399i	−0.275013	+	0.961441i	$0.588682\pi$
$198$	46005.1	+	79683.1i	0.0833955	+	0.144445i
$199$	−615727.			−1.10219			−0.551094	−	0.834443i	$-0.685789\pi$
$199$	−615727.			−1.10219			−0.551094	+	0.834443i	$0.685789\pi$
$200$	519246.	+	899361.i	0.917906	+	1.58986i
$201$	674187.	+	1.16773e6i	1.17704	+	2.03869i
$202$	−990362.	−	1.71536e6i	−1.70772	−	2.95785i
$203$	−108315.	+	187608.i	−0.184480	+	0.319529i
$204$	2.60676e6			4.38557
$205$	−32204.8	+	55780.3i	−0.0535224	+	0.0927035i
$206$	−121511.	−	210462.i	−0.199501	−	0.345547i
$207$	−659159.			−1.06921
$208$	51846.9	+	89801.4i	0.0830930	+	0.143921i
$209$	−79884.9	+	138365.i	−0.126502	+	0.219109i
$210$	−159277.	+	275876.i	−0.249233	+	0.431684i
$211$	511196.			0.790463			0.395232	−	0.918581i	$-0.370664\pi$
$211$	511196.			0.790463			0.395232	+	0.918581i	$0.370664\pi$
$212$	−691646.	+	1.19797e6i	−1.05692	+	1.83065i
$213$	−855187.			−1.29155
$214$	1.83417e6			2.73782
$215$	152563.	+	52929.9i	0.225088	+	0.0780917i
$216$	−687500.			−1.00262
$217$	−176059.			−0.253810
$218$	−1.03709e6	+	1.79630e6i	−1.47800	+	2.55998i
$219$	−1.07794e6			−1.51874
$220$	−28794.8	+	49874.0i	−0.0401104	+	0.0694732i
$221$	75221.8	−	130288.i	0.103601	−	0.179442i
$222$	−839732.	−	1.45446e6i	−1.14356	−	1.98070i
$223$	256944.			0.346000			0.173000	−	0.984922i	$-0.444654\pi$
$223$	256944.			0.346000			0.173000	+	0.984922i	$0.444654\pi$
$224$	137077.	+	237424.i	0.182534	+	0.316158i
$225$	211901.	−	367023.i	0.279046	−	0.483322i
$226$	406207.			0.529025
$227$	220739.	−	382330.i	0.284324	−	0.492464i	−0.688121	−	0.725596i	$-0.741564\pi$
$227$	220739.	−	382330.i	0.284324	−	0.492464i	0.972445	+	0.233132i	$0.0748975\pi$
$228$	1.64797e6	+	2.85436e6i	2.09948	+	3.63640i
$229$	238261.	+	412680.i	0.300237	+	0.520025i	0.976189	−	0.216920i	$-0.0696010\pi$
$229$	238261.	+	412680.i	0.300237	+	0.520025i	−0.675953	+	0.736945i	$0.736268\pi$
$230$	−304301.	−	527065.i	−0.379301	−	0.656969i
$231$	154069.			0.189970
$232$	312755.	+	541708.i	0.381491	+	0.660762i
$233$	18109.0	+	31365.7i	0.0218527	+	0.0378500i	0.876745	−	0.480956i	$-0.159710\pi$
$233$	18109.0	+	31365.7i	0.0218527	+	0.0378500i	−0.854892	+	0.518806i	$0.826377\pi$
$234$	54772.4	−	94868.6i	0.0653916	−	0.113262i
$235$	−63293.5	+	109628.i	−0.0747635	+	0.129494i
$236$	−829036.			−0.968932
$237$	562138.			0.650088
$238$	1.19679e6	−	2.07289e6i	1.36954	−	2.37211i
$239$	333746.	−	578066.i	0.377939	−	0.654610i	−0.612823	−	0.790220i	$-0.709966\pi$
$239$	333746.	−	578066.i	0.377939	−	0.654610i	0.990762	+	0.135611i	$0.0432996\pi$
$240$	177660.	+	307715.i	0.199095	+	0.344843i
$241$	−109771.	−	190128.i	−0.121743	−	0.210865i	0.798712	−	0.601713i	$-0.205515\pi$
$241$	−109771.	−	190128.i	−0.121743	−	0.210865i	−0.920455	+	0.390848i	$0.872182\pi$
$242$	−1.56416e6			−1.71689
$243$	483839.	+	838033.i	0.525636	+	0.910428i
$244$	−654390.	−	1.13344e6i	−0.703659	−	1.21877i
$245$	−12779.4	−	22134.6i	−0.0136018	−	0.0235590i
$246$	473992.	−	820978.i	0.499382	−	0.864956i
$247$	190218.			0.198385
$248$	−254181.	+	440255.i	−0.262430	+	0.454543i
$249$	−60135.3	−	104157.i	−0.0614654	−	0.106461i
$250$	806141.			0.815758
$251$	−685995.	−	1.18818e6i	−0.687285	−	1.19041i	−0.972713	−	0.232012i	$-0.925469\pi$
$251$	−685995.	−	1.18818e6i	−0.687285	−	1.19041i	0.285428	−	0.958400i	$-0.407864\pi$
$252$	590743.	−	1.02320e6i	0.585999	−	1.01498i
$253$	−147175.	+	254915.i	−0.144555	+	0.250377i
$254$	−2.47699e6			−2.40902
$255$	257756.	−	446447.i	0.248233	−	0.429952i
$256$	−2.13187e6			−2.03311
$257$	794811.			0.750639			0.375320	−	0.926895i	$-0.377533\pi$
$257$	794811.			0.750639			0.375320	+	0.926895i	$0.377533\pi$
$258$	−2.24543e6	−	779026.i	−2.10015	−	0.728623i
$259$	−1.04539e6			−0.968346
$260$	68564.5			0.0629022
$261$	127633.	−	221067.i	0.115974	−	0.200874i
$262$	−2.53537e6			−2.28185
$263$	731593.	−	1.26716e6i	0.652199	−	1.12964i	−0.330389	−	0.943845i	$-0.607180\pi$
$263$	731593.	−	1.26716e6i	0.652199	−	1.12964i	0.982588	−	0.185797i	$-0.0594868\pi$
$264$	222433.	−	385265.i	0.196422	−	0.340213i
$265$	136780.	+	236910.i	0.119649	+	0.207237i
$266$	3.02638e6			2.62253
$267$	−729765.	−	1.26399e6i	−0.626477	−	1.08509i
$268$	2.30871e6	−	3.99880e6i	1.96350	−	3.40089i
$269$	107923.			0.0909357			0.0454679	−	0.998966i	$-0.485522\pi$
$269$	107923.			0.0909357			0.0454679	+	0.998966i	$0.485522\pi$
$270$	−129523.	+	224340.i	−0.108127	+	0.187282i
$271$	−730659.	−	1.26554e6i	−0.604354	−	1.04677i	−0.992153	−	0.125028i	$-0.960098\pi$
$271$	−730659.	−	1.26554e6i	−0.604354	−	1.04677i	0.387799	−	0.921744i	$-0.373235\pi$
$272$	−1.33491e6	−	2.31213e6i	−1.09403	−	1.89491i
$273$	−91715.1	−	158855.i	−0.0744791	−	0.129002i
$274$	−895725.			−0.720772
$275$	−94625.3	−	163896.i	−0.0754528	−	0.130688i
$276$	3.03612e6	+	5.25871e6i	2.39909	+	4.15534i
$277$	−363438.	+	629492.i	−0.284597	+	0.492937i	−0.972511	−	0.232855i	$-0.925193\pi$
$277$	−363438.	+	629492.i	−0.284597	+	0.492937i	0.687914	+	0.725792i	$0.258526\pi$
$278$	−1.55016e6	+	2.68495e6i	−1.20299	+	2.08365i
$279$	207459.			0.159559
$280$	572543.			0.436428
$281$	−395912.	+	685739.i	−0.299111	+	0.518076i	−0.975933	−	0.218071i	$-0.930023\pi$
$281$	−395912.	+	685739.i	−0.299111	+	0.518076i	0.676822	+	0.736147i	$0.263357\pi$
$282$	931558.	−	1.61351e6i	0.697569	−	1.20822i
$283$	1.28066e6	+	2.21818e6i	0.950538	+	1.64638i	0.744265	+	0.667885i	$0.232800\pi$
$283$	1.28066e6	+	2.21818e6i	0.950538	+	1.64638i	0.206273	+	0.978494i	$0.433866\pi$
$284$	1.46427e6	+	2.53618e6i	1.07727	+	1.86588i
$285$	651804.			0.475340
$286$	−24458.9	−	42364.0i	−0.0176816	−	0.0306254i
$287$	−295040.	−	511023.i	−0.211434	−	0.366215i
$288$	−161524.	−	279768.i	−0.114751	−	0.198754i
$289$	−1.22682e6	+	2.12491e6i	−0.864042	+	1.49656i
$290$	235688.			0.164567
$291$	−647596.	+	1.12167e6i	−0.448303	+	0.776484i
$292$	1.84566e6	+	3.19679e6i	1.26676	+	2.19410i
$293$	−42451.1			−0.0288881			−0.0144441	−	0.999896i	$-0.504598\pi$
$293$	−42451.1			−0.0288881			−0.0144441	+	0.999896i	$0.504598\pi$
$294$	188089.	+	325779.i	0.126909	+	0.219814i
$295$	−81975.1	+	141985.i	−0.0548437	+	0.0949921i
$296$	−1.50926e6	+	2.61412e6i	−1.00123	+	1.73419i
$297$	125287.			0.0824167
$298$	672852.	−	1.16541e6i	0.438914	−	0.760221i
$299$	350446.			0.226696
$300$	−3.90410e6			−2.50448
$301$	−1.11879e6	+	967974.i	−0.711755	+	0.615811i
$302$	2.32460e6			1.46667
$303$	3.90820e6			2.44551
$304$	1.68783e6	−	2.92341e6i	1.04748	−	1.81428i
$305$	−258824.			−0.159315
$306$	−1.41023e6	+	2.44259e6i	−0.860968	+	1.49124i
$307$	−82279.4	+	142512.i	−0.0498248	+	0.0862990i	−0.889862	−	0.456229i	$-0.849200\pi$
$307$	−82279.4	+	142512.i	−0.0498248	+	0.0862990i	0.840037	+	0.542529i	$0.182533\pi$
$308$	−263799.	−	456913.i	−0.158452	−	0.274446i
$309$	479509.			0.285694
$310$	95773.7	+	165885.i	0.0566034	+	0.0980399i
$311$	1.49086e6	−	2.58225e6i	0.874049	−	1.51390i	0.0162774	−	0.999868i	$-0.494819\pi$
$311$	1.49086e6	−	2.58225e6i	0.874049	−	1.51390i	0.857772	−	0.514030i	$-0.171848\pi$
$312$	−529646.			−0.308034
$313$	498808.	−	863960.i	0.287788	−	0.498463i	−0.685494	−	0.728079i	$-0.740414\pi$
$313$	498808.	−	863960.i	0.287788	−	0.498463i	0.973281	+	0.229616i	$0.0737469\pi$
$314$	1.70885e6	+	2.95981e6i	0.978091	+	1.69410i
$315$	−116825.	−	202347.i	−0.0663377	−	0.114900i
$316$	−962502.	−	1.66710e6i	−0.542231	−	0.939171i
$317$	2.04824e6			1.14481			0.572403	−	0.819972i	$-0.306011\pi$
$317$	2.04824e6			1.14481			0.572403	+	0.819972i	$0.306011\pi$
$318$	−2.01313e6	−	3.48685e6i	−1.11636	−	1.93360i
$319$	−56995.2	−	98718.6i	−0.0313590	−	0.0543153i
$320$	−139938.	+	242379.i	−0.0763941	+	0.132318i
$321$	−1.80951e6	+	3.13417e6i	−0.980165	+	1.69770i
$322$	5.57563e6			2.99677
$323$	−4.89756e6			−2.61200
$324$	2.46878e6	−	4.27605e6i	1.30653	−	2.26298i
$325$	−112658.	+	195130.i	−0.0591637	+	0.102474i
$326$	285858.	+	495121.i	0.148973	+	0.258028i
$327$	−2.04630e6	−	3.54430e6i	−1.05828	−	1.83299i
$328$	−1.70383e6			−0.874461
$329$	−579855.	−	1.00434e6i	−0.295345	−	0.511552i
$330$	−83811.3	−	145165.i	−0.0423660	−	0.0733801i
$331$	1.76103e6	+	3.05019e6i	0.883480	+	1.53023i	0.847446	+	0.530882i	$0.178139\pi$
$331$	1.76103e6	+	3.05019e6i	0.883480	+	1.53023i	0.0360345	+	0.999351i	$0.488527\pi$
$332$	−205929.	+	356680.i	−0.102535	+	0.177596i
$333$	1.23184e6			0.608756
$334$	660394.	−	1.14384e6i	0.323919	−	0.561045i
$335$	−456570.	−	790802.i	−0.222277	−	0.384996i
$336$	−3.25521e6			−1.57301
$337$	−1.59018e6	−	2.75427e6i	−0.762729	−	1.32109i	−0.941439	−	0.337184i	$-0.890526\pi$
$337$	−1.59018e6	−	2.75427e6i	−0.762729	−	1.32109i	0.178710	−	0.983902i	$-0.442808\pi$
$338$	1.82128e6	−	3.15454e6i	0.867129	−	1.50191i
$339$	−400747.	+	694114.i	−0.189396	+	0.328044i
$340$	−1.76534e6			−0.828192
$341$	46320.9	−	80230.2i	0.0215720	−	0.0373639i
$342$	−3.56613e6			−1.64867
$343$	2.28488e6			1.04864
$344$	805303.	+	4.19513e6i	0.366913	+	1.91139i
$345$	1.20084e6			0.543174
$346$	1.59138e6			0.714635
$347$	−806594.	+	1.39706e6i	−0.359609	+	0.622862i	−0.987896	−	0.155121i	$-0.950423\pi$
$347$	−806594.	+	1.39706e6i	−0.359609	+	0.622862i	0.628286	+	0.777982i	$0.283757\pi$
$348$	−2.35154e6			−1.04089
$349$	−1.30042e6	+	2.25239e6i	−0.571504	+	0.989874i	0.424908	+	0.905237i	$0.360307\pi$
$349$	−1.30042e6	+	2.25239e6i	−0.571504	+	0.989874i	−0.996412	+	0.0846375i	$0.973027\pi$
$350$	−1.79241e6	+	3.10454e6i	−0.782107	+	1.35465i
$351$	−74581.8	−	129179.i	−0.0323121	−	0.0559662i
$352$	−144259.			−0.0620562
$353$	−557211.	−	965117.i	−0.238003	−	0.412234i	0.722138	−	0.691749i	$-0.243160\pi$
$353$	−557211.	−	965117.i	−0.238003	−	0.412234i	−0.960141	+	0.279515i	$0.909826\pi$
$354$	1.20651e6	−	2.08974e6i	0.511711	−	0.886309i
$355$	579146.			0.243903
$356$	−2.49903e6	+	4.32845e6i	−1.04507	+	1.81012i
$357$	2.36140e6	+	4.09006e6i	0.980616	+	1.69848i
$358$	−416604.	−	721580.i	−0.171797	−	0.297561i
$359$	661665.	+	1.14604e6i	0.270958	+	0.469313i	0.969107	−	0.246639i	$-0.0793262\pi$
$359$	661665.	+	1.14604e6i	0.270958	+	0.469313i	−0.698149	+	0.715952i	$0.745993\pi$
$360$	−674655.			−0.274363
$361$	−1.85814e6	−	3.21839e6i	−0.750429	−	1.29978i
$362$	1.54590e6	+	2.67757e6i	0.620025	+	1.07391i
$363$	1.54313e6	−	2.67278e6i	0.614662	−	1.06463i
$364$	−314072.	+	543989.i	−0.124244	+	0.215197i
$365$	729997.			0.286806
$366$	3.80939e6			1.48646
$367$	811350.	−	1.40530e6i	0.314444	−	0.544633i	−0.664875	−	0.746954i	$-0.731515\pi$
$367$	811350.	−	1.40530e6i	0.314444	−	0.544633i	0.979319	+	0.202322i	$0.0648487\pi$
$368$	3.10956e6	−	5.38591e6i	1.19696	−	2.07319i
$369$	347659.	+	602164.i	0.132919	+	0.230223i
$370$	568680.	+	984982.i	0.215955	+	0.374045i
$371$	−2.50618e6			−0.945316
$372$	−955567.	−	1.65509e6i	−0.358017	−	0.620104i
$373$	−543097.	−	940671.i	−0.202118	−	0.350079i	0.747093	−	0.664720i	$-0.231449\pi$
$373$	−543097.	−	940671.i	−0.202118	−	0.350079i	−0.949211	+	0.314641i	$0.898116\pi$
$374$	629746.	+	1.09075e6i	0.232802	+	0.403224i
$375$	−795306.	+	1.37751e6i	−0.292049	+	0.505844i
$376$	−3.34860e6			−1.22150
$377$	−67857.0	+	117532.i	−0.0245890	+	0.0425894i
$378$	−1.18660e6	−	2.05526e6i	−0.427146	−	0.739838i
$379$	−3.16873e6			−1.13315			−0.566575	−	0.824010i	$-0.691732\pi$
$379$	−3.16873e6			−1.13315			−0.566575	+	0.824010i	$0.691732\pi$
$380$	−1.11603e6	−	1.93302e6i	−0.396476	−	0.686716i
$381$	2.44370e6	−	4.23261e6i	0.862452	−	1.49381i
$382$	1.16205e6	−	2.01274e6i	0.407444	−	0.705714i
$383$	5.07150e6			1.76661			0.883303	−	0.468802i	$-0.155314\pi$
$383$	5.07150e6			1.76661			0.883303	+	0.468802i	$0.155314\pi$
$384$	2.76662e6	−	4.79193e6i	0.957463	−	1.65837i
$385$	−104338.			−0.0358748
$386$	−3.03014e6			−1.03513
$387$	1.31832e6	−	1.14061e6i	0.447449	−	0.387133i
$388$	4.43530e6			1.49570
$389$	−4.34521e6			−1.45592			−0.727959	−	0.685621i	$-0.759531\pi$
$389$	−4.34521e6			−1.45592			−0.727959	+	0.685621i	$0.759531\pi$
$390$	−99783.5	+	172830.i	−0.0332198	+	0.0575384i
$391$	−9.02297e6			−2.98475
$392$	338054.	−	585527.i	0.111115	−	0.192456i
$393$	2.50129e6	−	4.33236e6i	0.816925	−	1.41496i
$394$	3.77404e6	+	6.53683e6i	1.22480	+	2.12142i
$395$	−380689.			−0.122766
$396$	310847.	+	538403.i	0.0996114	+	0.172532i
$397$	−2.37845e6	+	4.11960e6i	−0.757387	+	1.31183i	0.186792	+	0.982400i	$0.440191\pi$
$397$	−2.37845e6	+	4.11960e6i	−0.757387	+	1.31183i	−0.944179	+	0.329433i	$0.893142\pi$
$398$	−6.13714e6			−1.94204
$399$	−2.98570e6	+	5.17139e6i	−0.938890	+	1.62620i
$400$	1.99927e6	+	3.46283e6i	0.624771	+	1.08214i
$401$	1.74745e6	+	3.02667e6i	0.542680	+	0.939949i	0.998749	+	0.0500049i	$0.0159237\pi$
$401$	1.74745e6	+	3.02667e6i	0.542680	+	0.939949i	−0.456069	+	0.889944i	$0.650743\pi$
$402$	6.71982e6	+	1.16391e7i	2.07392	+	3.59214i
$403$	−110297.			−0.0338299
$404$	−6.69169e6	−	1.15903e7i	−2.03977	−	3.53299i
$405$	−488225.	−	845631.i	−0.147905	−	0.256179i
$406$	−1.07961e6	+	1.86994e6i	−0.325052	+	0.563006i
$407$	275042.	−	476386.i	0.0823024	−	0.142552i
$408$	1.36369e7			4.05568
$409$	2.15155e6			0.635981			0.317990	−	0.948094i	$-0.396992\pi$
$409$	2.15155e6			0.635981			0.317990	+	0.948094i	$0.396992\pi$
$410$	−320995.	+	555979.i	−0.0943058	+	0.163342i
$411$	883685.	−	1.53059e6i	0.258043	−	0.446944i
$412$	−821024.	−	1.42205e6i	−0.238294	−	0.412737i
$413$	−751003.	−	1.30078e6i	−0.216654	−	0.375256i
$414$	−6.57003e6			−1.88394
$415$	40724.5	+	70537.0i	0.0116074	+	0.0201047i
$416$	85875.3	+	148740.i	0.0243296	+	0.0421401i
$417$	−3.05864e6	−	5.29772e6i	−0.861367	−	1.49193i
$418$	−796237.	+	1.37912e6i	−0.222896	+	0.386067i
$419$	5.86423e6			1.63183			0.815917	−	0.578168i	$-0.196232\pi$
$419$	5.86423e6			1.63183			0.815917	+	0.578168i	$0.196232\pi$
$420$	−1.07621e6	+	1.86404e6i	−0.297695	+	0.515624i
$421$	−381550.	−	660864.i	−0.104917	−	0.181722i	0.808787	−	0.588101i	$-0.200124\pi$
$421$	−381550.	−	660864.i	−0.104917	−	0.181722i	−0.913704	+	0.406380i	$0.866791\pi$
$422$	5.09525e6			1.39279
$423$	683271.	+	1.18346e6i	0.185670	+	0.321590i
$424$	−3.61824e6	+	6.26697e6i	−0.977422	+	1.69295i
$425$	2.90063e6	−	5.02403e6i	0.778968	−	1.34921i
$426$	−8.52391e6			−2.27570
$427$	1.18559e6	−	2.05350e6i	0.314677	−	0.545037i
$428$	1.23931e7			3.27018
$429$	96520.5			0.0253207
$430$	1.52064e6	+	527569.i	0.396602	+	0.137597i
$431$	4.90960e6			1.27307			0.636536	−	0.771247i	$-0.280367\pi$
$431$	4.90960e6			1.27307			0.636536	+	0.771247i	$0.280367\pi$
$432$	−2.64710e6			−0.682434
$433$	−757783.	+	1.31252e6i	−0.194234	+	0.336423i	−0.946649	−	0.322266i	$-0.895555\pi$
$433$	−757783.	+	1.31252e6i	−0.194234	+	0.336423i	0.752415	+	0.658689i	$0.228889\pi$
$434$	−1.75484e6			−0.447211
$435$	−232520.	+	402737.i	−0.0589166	+	0.102046i
$436$	−7.00743e6	+	1.21372e7i	−1.76540	+	3.05776i
$437$	−5.70423e6	−	9.88001e6i	−1.42887	−	2.47488i
$438$	−1.07441e7			−2.67600
$439$	1.13980e6	+	1.97420e6i	0.282273	+	0.488911i	0.971944	−	0.235212i	$-0.0755784\pi$
$439$	1.13980e6	+	1.97420e6i	0.282273	+	0.488911i	−0.689671	+	0.724122i	$0.742245\pi$
$440$	−150635.	+	260908.i	−0.0370932	+	0.0642474i
$441$	−275915.			−0.0675583
$442$	749759.	−	1.29862e6i	0.182543	−	0.316174i
$443$	−1.45095e6	−	2.51312e6i	−0.351271	−	0.608420i	0.635201	−	0.772347i	$-0.280917\pi$
$443$	−1.45095e6	−	2.51312e6i	−0.351271	−	0.608420i	−0.986472	+	0.163927i	$0.947584\pi$
$444$	−5.67391e6	−	9.82750e6i	−1.36592	−	2.36584i
$445$	494208.	+	855994.i	0.118307	+	0.204914i
$446$	2.56104e6			0.609648
$447$	1.32762e6	+	2.29950e6i	0.314271	+	0.544333i
$448$	−1.28202e6	−	2.22052e6i	−0.301786	−	0.522709i
$449$	186135.	−	322396.i	0.0435726	−	0.0754699i	−0.843417	−	0.537260i	$-0.819459\pi$
$449$	186135.	−	322396.i	0.0435726	−	0.0754699i	0.886989	+	0.461790i	$0.152793\pi$
$450$	2.11208e6	−	3.65823e6i	0.491676	−	0.851607i
$451$	310498.			0.0718816
$452$	2.74466e6			0.631892
$453$	−2.29336e6	+	3.97221e6i	−0.525081	+	0.909466i
$454$	2.20017e6	−	3.81080e6i	0.500975	−	0.867715i
$455$	62110.9	+	107579.i	0.0140650	+	0.0243613i
$456$	8.62108e6	+	1.49321e7i	1.94155	+	3.36287i
$457$	3.73465e6			0.836487			0.418244	−	0.908335i	$-0.362646\pi$
$457$	3.73465e6			0.836487			0.418244	+	0.908335i	$0.362646\pi$
$458$	2.37482e6	+	4.11330e6i	0.529013	+	0.916278i
$459$	1.92027e6	+	3.32600e6i	0.425431	+	0.736869i
$460$	−2.05611e6	−	3.56128e6i	−0.453055	−	0.784714i
$461$	−2.49556e6	+	4.32244e6i	−0.546910	+	0.947276i	0.451574	+	0.892234i	$0.350863\pi$
$461$	−2.49556e6	+	4.32244e6i	−0.546910	+	0.947276i	−0.998484	+	0.0550424i	$0.982471\pi$
$462$	1.53565e6			0.334724
$463$	−165773.	+	287127.i	−0.0359385	+	0.0622474i	−0.883435	−	0.468553i	$-0.844775\pi$
$463$	−165773.	+	287127.i	−0.0359385	+	0.0622474i	0.847497	+	0.530801i	$0.178109\pi$
$464$	1.20421e6	+	2.08575e6i	0.259661	+	0.449747i
$465$	−377946.			−0.0810582
$466$	180498.	+	312632.i	0.0385042	+	0.0666912i
$467$	−2.18649e6	+	3.78710e6i	−0.463932	+	0.803554i	−0.999153	−	0.0411584i	$-0.986895\pi$
$467$	−2.18649e6	+	3.78710e6i	−0.463932	+	0.803554i	0.535221	+	0.844712i	$0.320228\pi$
$468$	370087.	−	641009.i	0.0781068	−	0.135285i
$469$	8.36560e6			1.75616
$470$	−630866.	+	1.09269e6i	−0.131732	+	0.228167i
$471$	−6.74351e6			−1.40066
$472$	−4.33697e6			−0.896049
$473$	−146755.	−	764504.i	−0.0301606	−	0.157118i
$474$	5.60300e6			1.14545
$475$	7.33499e6			1.49164
$476$	8.08645e6	−	1.40061e7i	1.63584	−	2.83336i
$477$	2.95315e6			0.594278
$478$	3.32655e6	−	5.76176e6i	0.665924	−	1.15341i
$479$	−1.21317e6	+	2.10127e6i	−0.241592	+	0.418449i	−0.961168	−	0.275965i	$-0.911003\pi$
$479$	−1.21317e6	+	2.10127e6i	−0.241592	+	0.418449i	0.719576	+	0.694413i	$0.244336\pi$
$480$	294262.	+	509676.i	0.0582949	+	0.100970i
$481$	−654915.			−0.129069
$482$	−1.09412e6	−	1.89507e6i	−0.214509	−	0.371541i
$483$	−5.50068e6	+	9.52746e6i	−1.07287	+	1.85827i
$484$	−1.05687e7			−2.05073
$485$	438562.	−	759612.i	0.0846597	−	0.146635i
$486$	4.82257e6	+	8.35293e6i	0.926163	+	1.60416i
$487$	−78130.6	−	135326.i	−0.0149279	−	0.0258559i	0.858465	−	0.512872i	$-0.171419\pi$
$487$	−78130.6	−	135326.i	−0.0149279	−	0.0258559i	−0.873393	+	0.487016i	$0.838085\pi$
$488$	−3.42334e6	−	5.92940e6i	−0.650729	−	1.12710i
$489$	−1.12806e6			−0.213335
$490$	−127376.	−	220623.i	−0.0239662	−	0.0415107i
$491$	2.49338e6	+	4.31866e6i	0.466750	+	0.808435i	0.999279	−	0.0379773i	$-0.0120915\pi$
$491$	2.49338e6	+	4.31866e6i	0.466750	+	0.808435i	−0.532529	+	0.846412i	$0.678758\pi$
$492$	3.20267e6	−	5.54719e6i	0.596486	−	1.03314i
$493$	1.74712e6	−	3.02610e6i	0.323747	−	0.560747i
$494$	1.89596e6			0.349552
$495$	122946.			0.0225529
$496$	−978681.	+	1.69513e6i	−0.178623	+	0.309384i
$497$	−2.65288e6	+	4.59493e6i	−0.481756	+	0.834426i
$498$	−599387.	−	1.03817e6i	−0.108301	−	0.187583i
$499$	1.11429e6	+	1.93001e6i	0.200331	+	0.346983i	0.948635	−	0.316372i	$-0.102465\pi$
$499$	1.11429e6	+	1.93001e6i	0.200331	+	0.346983i	−0.748304	+	0.663356i	$0.769132\pi$
$500$	5.44694e6			0.974379
$501$	1.30303e6	+	2.25692e6i	0.231933	+	0.401719i
$502$	−6.83752e6	−	1.18429e7i	−1.21099	−	2.09749i
$503$	2.13628e6	+	3.70015e6i	0.376477	+	0.652078i	0.990547	−	0.137174i	$-0.0438020\pi$
$503$	2.13628e6	+	3.70015e6i	0.376477	+	0.652078i	−0.614070	+	0.789252i	$0.710469\pi$
$504$	3.09038e6	−	5.35269e6i	0.541920	−	0.938633i
$505$	−2.64669e6			−0.461823
$506$	−1.46694e6	+	2.54082e6i	−0.254704	+	0.441161i
$507$	3.59359e6	+	6.22428e6i	0.620881	+	1.07540i
$508$	−1.67366e7			−2.87744
$509$	1.97221e6	+	3.41596e6i	0.337410	+	0.584411i	0.983945	−	0.178473i	$-0.0571159\pi$
$509$	1.97221e6	+	3.41596e6i	0.337410	+	0.584411i	−0.646535	+	0.762884i	$0.723783\pi$
$510$	2.56914e6	−	4.44988e6i	0.437383	−	0.757569i
$511$	−3.34388e6	+	5.79178e6i	−0.566499	+	0.981204i
$512$	−1.22458e7			−2.06448
$513$	−2.42794e6	+	4.20532e6i	−0.407329	+	0.705514i
$514$	7.92213e6			1.32262
$515$	−324731.			−0.0539518
$516$	−1.51719e7	−	5.26373e6i	−2.50852	−	0.870301i
$517$	610236.			0.100409
$518$	−1.04198e7			−1.70621
$519$	−1.56999e6	+	2.71931e6i	−0.255846	+	0.443139i
$520$	358685.			0.0581707
$521$	4.25817e6	−	7.37536e6i	0.687271	−	1.19039i	−0.285446	−	0.958395i	$-0.592142\pi$
$521$	4.25817e6	−	7.37536e6i	0.687271	−	1.19039i	0.972717	−	0.231994i	$-0.0745250\pi$
$522$	1.27216e6	−	2.20344e6i	0.204346	−	0.353937i
$523$	1.33171e6	+	2.30660e6i	0.212891	+	0.368738i	0.952618	−	0.304169i	$-0.0983788\pi$
$523$	1.33171e6	+	2.30660e6i	0.212891	+	0.368738i	−0.739727	+	0.672907i	$0.765045\pi$
$524$	−1.71310e7			−2.72555
$525$	−3.53663e6	−	6.12562e6i	−0.560004	−	0.969955i
$526$	7.29201e6	−	1.26301e7i	1.14917	−	1.99042i
$527$	2.83983e6			0.445416
$528$	856440.	−	1.48340e6i	0.133694	−	0.231565i
$529$	−7.29096e6	−	1.26283e7i	−1.13278	−	1.96203i
$530$	1.36333e6	+	2.36135e6i	0.210819	+	0.365150i
$531$	884943.	+	1.53277e6i	0.136201	+	0.235906i
$532$	2.04487e7			3.13247
$533$	−184835.	−	320144.i	−0.0281817	−	0.0488121i
$534$	−7.27379e6	−	1.25986e7i	−1.10384	−	1.91191i
$535$	1.22543e6	−	2.12251e6i	0.185099	−	0.320601i
$536$	1.20776e7	−	2.09191e7i	1.81581	−	3.14507i
$537$	1.64402e6			0.246020
$538$	1.07570e6			0.160228
$539$	−61605.6	+	106704.i	−0.00913373	+	0.0158201i
$540$	−875159.	+	1.51582e6i	−0.129152	+	0.223699i
$541$	4.65356e6	+	8.06020e6i	0.683584	+	1.18400i	0.973880	+	0.227065i	$0.0729130\pi$
$541$	4.65356e6	+	8.06020e6i	0.683584	+	1.18400i	−0.290296	+	0.956937i	$0.593754\pi$
$542$	−7.28270e6	−	1.26140e7i	−1.06486	−	1.84440i
$543$	−6.10047e6			−0.887899
$544$	−2.21104e6	−	3.82963e6i	−0.320331	−	0.554830i
$545$	1.38579e6	+	2.40026e6i	0.199851	+	0.346152i
$546$	−914152.	−	1.58336e6i	−0.131231	−	0.227299i
$547$	3.05092e6	−	5.28435e6i	0.435976	−	0.755132i	−0.561399	−	0.827545i	$-0.689737\pi$
$547$	3.05092e6	−	5.28435e6i	0.435976	−	0.755132i	0.997375	+	0.0724130i	$0.0230700\pi$
$548$	−6.05224e6			−0.860924
$549$	−1.39704e6	+	2.41974e6i	−0.197824	+	0.342640i
$550$	−943159.	−	1.63360e6i	−0.132947	−	0.230271i
$551$	4.41805e6			0.619943
$552$	1.58830e7	+	2.75101e7i	2.21863	+	3.84277i
$553$	1.74381e6	−	3.02037e6i	0.242486	−	0.419998i
$554$	−3.62249e6	+	6.27434e6i	−0.501456	+	0.868548i
$555$	−2.24414e6			−0.309256
$556$	−1.04741e7	+	1.81417e7i	−1.43691	+	2.48880i
$557$	−5.98575e6			−0.817486			−0.408743	−	0.912650i	$-0.634033\pi$
$557$	−5.98575e6			−0.817486			−0.408743	+	0.912650i	$0.634033\pi$
$558$	2.06781e6			0.281141
$559$	−700893.	+	606413.i	−0.0948686	+	0.0820803i
$560$	2.20448e6			0.297054
$561$	−2.48512e6			−0.333381
$562$	−3.94617e6	+	6.83497e6i	−0.527030	+	0.912843i
$563$	3.57765e6			0.475694			0.237847	−	0.971303i	$-0.423558\pi$
$563$	3.57765e6			0.475694			0.237847	+	0.971303i	$0.423558\pi$
$564$	6.29436e6	−	1.09022e7i	0.833209	−	1.44316i
$565$	271392.	−	470065.i	0.0357665	−	0.0619494i
$566$	1.27648e7	+	2.21092e7i	1.67484	+	2.90090i
$567$	8.94561e6			1.16856
$568$	7.66007e6	+	1.32676e7i	0.996236	+	1.72553i
$569$	−555792.	+	962661.i	−0.0719668	+	0.124650i	−0.899763	−	0.436378i	$-0.856261\pi$
$569$	−555792.	+	962661.i	−0.0719668	+	0.124650i	0.827796	+	0.561029i	$0.189594\pi$
$570$	6.49673e6			0.837544
$571$	7.27086e6	−	1.25935e7i	0.933245	−	1.61643i	0.155511	−	0.987834i	$-0.450298\pi$
$571$	7.27086e6	−	1.25935e7i	0.933245	−	1.61643i	0.777734	−	0.628594i	$-0.216369\pi$
$572$	−165264.	−	286246.i	−0.0211197	−	0.0365804i
$573$	2.29287e6	+	3.97137e6i	0.291738	+	0.505305i
$574$	−2.94075e6	−	5.09353e6i	−0.372545	−	0.645266i
$575$	1.35135e7			1.70451
$576$	1.51067e6	+	2.61655e6i	0.189720	+	0.328604i
$577$	−3.12595e6	−	5.41430e6i	−0.390879	−	0.677022i	0.601687	−	0.798732i	$-0.294495\pi$
$577$	−3.12595e6	−	5.41430e6i	−0.390879	−	0.677022i	−0.992566	+	0.121710i	$0.961162\pi$
$578$	−1.22280e7	+	2.11796e7i	−1.52243	+	2.63693i
$579$	2.98941e6	−	5.17782e6i	0.370586	−	0.641875i
$580$	1.59250e6			0.196566
$581$	−746184.			−0.0917077
$582$	−6.45479e6	+	1.11800e7i	−0.789904	+	1.36815i
$583$	659372.	−	1.14207e6i	0.0803451	−	0.139162i
$584$	9.65530e6	+	1.67235e7i	1.17148	+	2.02906i
$585$	−73188.3	−	126766.i	−0.00884203	−	0.0153148i
$586$	−423123.			−0.0509005
$587$	−2.75602e6	−	4.77357e6i	−0.330132	−	0.571805i	0.652406	−	0.757870i	$-0.273760\pi$
$587$	−2.75602e6	−	4.77357e6i	−0.330132	−	0.571805i	−0.982537	+	0.186065i	$0.940426\pi$
$588$	1.27088e6	+	2.20123e6i	0.151587	+	0.262556i
$589$	1.79531e6	+	3.10957e6i	0.213231	+	0.369328i
$590$	−817070.	+	1.41521e6i	−0.0966339	+	0.167375i
$591$	−1.48933e7			−1.75396
$592$	−5.81116e6	+	1.00652e7i	−0.681488	+	1.18037i
$593$	−5.03378e6	−	8.71876e6i	−0.587837	−	1.01816i	−0.994515	−	0.104592i	$-0.966646\pi$
$593$	−5.03378e6	−	8.71876e6i	−0.587837	−	1.01816i	0.406678	−	0.913572i	$-0.366687\pi$
$594$	1.24877e6			0.145217
$595$	−1.59918e6	−	2.76985e6i	−0.185184	−	0.320748i
$596$	4.54633e6	−	7.87448e6i	0.524259	−	0.908043i
$597$	6.05465e6	−	1.04870e7i	0.695269	−	1.20424i
$598$	3.49300e6			0.399435
$599$	−4.08485e6	+	7.07516e6i	−0.465167	+	0.805692i	−0.999209	−	0.0397654i	$-0.987339\pi$
$599$	−4.08485e6	+	7.07516e6i	−0.465167	+	0.805692i	0.534042	+	0.845458i	$0.320672\pi$
$600$	−2.04237e7			−2.31609
$601$	−1.13683e7			−1.28383			−0.641916	−	0.766775i	$-0.721860\pi$
$601$	−1.13683e7			−1.28383			−0.641916	+	0.766775i	$0.721860\pi$
$602$	−1.11513e7	+	9.64809e6i	−1.25410	+	1.08505i
$603$	−9.85759e6			−1.10402
$604$	1.57069e7			1.75185
$605$	−1.04503e6	+	1.81005e6i	−0.116076	+	0.201049i
$606$	3.89542e7			4.30897
$607$	3.99736e6	−	6.92364e6i	0.440354	−	0.762716i	−0.557362	−	0.830270i	$-0.688186\pi$
$607$	3.99736e6	−	6.92364e6i	0.440354	−	0.762716i	0.997716	+	0.0675543i	$0.0215196\pi$
$608$	2.79559e6	−	4.84211e6i	0.306701	−	0.531222i
$609$	−2.13020e6	−	3.68962e6i	−0.232743	−	0.403123i
$610$	−2.57978e6			−0.280710
$611$	−363265.	−	629194.i	−0.0393660	−	0.0681839i
$612$	−9.52866e6	+	1.65041e7i	−1.02838	+	1.78121i
$613$	6.94295e6			0.746265			0.373132	−	0.927778i	$-0.378284\pi$
$613$	6.94295e6			0.746265			0.373132	+	0.927778i	$0.378284\pi$
$614$	−820104.	+	1.42046e6i	−0.0877906	+	0.152058i
$615$	−633360.	−	1.09701e6i	−0.0675248	−	0.116956i
$616$	−1.38002e6	−	2.39027e6i	−0.146533	−	0.253802i
$617$	−8.84860e6	−	1.53262e7i	−0.935754	−	1.62077i	−0.773283	−	0.634061i	$-0.781387\pi$
$617$	−8.84860e6	−	1.53262e7i	−0.935754	−	1.62077i	−0.162471	−	0.986713i	$-0.551946\pi$
$618$	4.77941e6			0.503389
$619$	3.44611e6	+	5.96884e6i	0.361496	+	0.626129i	0.988207	−	0.153123i	$-0.0489329\pi$
$619$	3.44611e6	+	5.96884e6i	0.361496	+	0.626129i	−0.626712	+	0.779251i	$0.715600\pi$
$620$	647125.	+	1.12085e6i	0.0676097	+	0.117103i
$621$	−4.47310e6	+	7.74764e6i	−0.465457	+	0.806195i
$622$	1.48599e7	−	2.57380e7i	1.54006	−	2.66747i
$623$	−9.05524e6			−0.934717
$624$	−2.03931e6			−0.209663
$625$	−4.06706e6	+	7.04435e6i	−0.416467	+	0.721341i
$626$	4.97177e6	−	8.61136e6i	0.507078	−	0.878285i
$627$	−1.57107e6	−	2.72117e6i	−0.159598	−	0.276431i
$628$	1.15464e7	+	1.99989e7i	1.16828	+	2.02352i
$629$	1.68622e7			1.69937
$630$	−1.16443e6	−	2.01686e6i	−0.116886	−	0.202453i
$631$	−5.65192e6	−	9.78941e6i	−0.565096	−	0.978776i	−0.997041	−	0.0768754i	$-0.975506\pi$
$631$	−5.65192e6	−	9.78941e6i	−0.565096	−	0.978776i	0.431944	−	0.901900i	$-0.357828\pi$
$632$	−5.03518e6	−	8.72118e6i	−0.501444	−	0.868526i
$633$	−5.02676e6	+	8.70661e6i	−0.498631	+	0.863654i
$634$	2.04154e7			2.01713
$635$	−1.65491e6	+	2.86639e6i	−0.162870	+	0.282098i
$636$	−1.36024e7	−	2.35600e7i	−1.33343	−	2.30958i
$637$	146692.			0.0143238
$638$	−568089.	−	983959.i	−0.0552541	−	0.0957029i
$639$	3.12602e6	−	5.41443e6i	0.302858	−	0.524566i
$640$	−1.87360e6	+	3.24517e6i	−0.180812	+	0.313175i
$641$	−1.40110e7			−1.34687			−0.673433	−	0.739248i	$-0.735181\pi$
$641$	−1.40110e7			−1.34687			−0.673433	+	0.739248i	$0.735181\pi$
$642$	−1.80360e7	+	3.12392e7i	−1.72704	+	2.99132i
$643$	−4.27504e6			−0.407767			−0.203884	−	0.978995i	$-0.565356\pi$
$643$	−4.27504e6			−0.407767			−0.203884	+	0.978995i	$0.565356\pi$
$644$	3.76735e7			3.57949
$645$	−2.40169e6	+	2.07795e6i	−0.227310	+	0.196669i
$646$	−4.88155e7			−4.60231
$647$	−7.88684e6			−0.740700			−0.370350	−	0.928892i	$-0.620762\pi$
$647$	−7.88684e6			−0.740700			−0.370350	+	0.928892i	$0.620762\pi$
$648$	1.29150e7	−	2.23695e7i	1.20825	−	2.09275i
$649$	790352.			0.0736561
$650$	−1.12290e6	+	1.94492e6i	−0.104246	+	0.180559i
$651$	1.73125e6	−	2.99861e6i	0.160106	−	0.277311i
$652$	1.93149e6	+	3.34544e6i	0.177940	+	0.308201i
$653$	1.39028e7			1.27591			0.637954	−	0.770075i	$-0.279781\pi$
$653$	1.39028e7			1.27591			0.637954	+	0.770075i	$0.279781\pi$
$654$	−2.03961e7	−	3.53271e7i	−1.86468	−	3.22971i
$655$	−1.69391e6	+	2.93394e6i	−0.154272	+	0.267207i
$656$	−6.56029e6			−0.595200
$657$	3.94026e6	−	6.82473e6i	0.356132	−	0.616839i
$658$	−5.77959e6	−	1.00105e7i	−0.520394	−	0.901348i
$659$	−755746.	−	1.30899e6i	−0.0677895	−	0.117415i	0.830138	−	0.557557i	$-0.188261\pi$
$659$	−755746.	−	1.30899e6i	−0.0677895	−	0.117415i	−0.897928	+	0.440142i	$0.854928\pi$
$660$	−566297.	−	980855.i	−0.0506039	−	0.0876486i
$661$	670631.			0.0597008			0.0298504	−	0.999554i	$-0.490497\pi$
$661$	670631.			0.0597008			0.0298504	+	0.999554i	$0.490497\pi$
$662$	1.75527e7	+	3.04022e7i	1.55668	+	2.69625i
$663$	1.47936e6	+	2.56233e6i	0.130704	+	0.226387i
$664$	−1.07729e6	+	1.86591e6i	−0.0948224	+	0.164237i
$665$	2.02197e6	−	3.50215e6i	0.177304	−	0.307100i
$666$	1.22781e7			1.07262
$667$	8.13955e6			0.708412
$668$	4.46216e6	−	7.72868e6i	0.386904	−	0.670138i
$669$	−2.52662e6	+	4.37623e6i	−0.218260	+	0.378037i
$670$	−4.55077e6	−	7.88216e6i	−0.391650	−	0.678357i
$671$	623855.	+	1.08055e6i	0.0534906	+	0.0926484i
$672$	−5.39168e6			−0.460575
$673$	−5.24651e6	−	9.08723e6i	−0.446512	−	0.773381i	0.551644	−	0.834080i	$-0.314001\pi$
$673$	−5.24651e6	−	9.08723e6i	−0.446512	−	0.773381i	−0.998156	+	0.0606981i	$0.980667\pi$
$674$	−1.58498e7	−	2.74526e7i	−1.34392	−	2.32774i
$675$	−2.87595e6	−	4.98129e6i	−0.242953	−	0.420806i
$676$	1.23060e7	−	2.13146e7i	1.03574	−	1.79395i
$677$	−1.21425e7			−1.01821			−0.509103	−	0.860706i	$-0.670023\pi$
$677$	−1.21425e7			−1.01821			−0.509103	+	0.860706i	$0.670023\pi$
$678$	−3.99437e6	+	6.91845e6i	−0.333714	+	0.578009i
$679$	4.01783e6	+	6.95908e6i	0.334439	+	0.579265i
$680$	−9.23509e6			−0.765895
$681$	4.34119e6	+	7.51916e6i	0.358708	+	0.621301i
$682$	461695.	−	799679.i	0.0380097	−	0.0658347i
$683$	8.82663e6	−	1.52882e7i	0.724008	−	1.25402i	−0.235374	−	0.971905i	$-0.575631\pi$
$683$	8.82663e6	−	1.52882e7i	0.724008	−	1.25402i	0.959381	−	0.282113i	$-0.0910353\pi$
$684$	−2.40957e7			−1.96924
$685$	−598445.	+	1.03654e6i	−0.0487302	+	0.0844031i
$686$	2.27741e7			1.84770
$687$	−9.37159e6			−0.757567
$688$	3.10068e6	+	1.61526e7i	0.249739	+	1.30099i
$689$	−1.57006e6			−0.126000
$690$	1.19692e7			0.957066
$691$	5.81354e6	−	1.00693e7i	0.463175	−	0.802243i	−0.535942	−	0.844255i	$-0.680043\pi$
$691$	5.81354e6	−	1.00693e7i	0.463175	−	0.802243i	0.999117	+	0.0420116i	$0.0133766\pi$
$692$	1.07527e7			0.853593
$693$	−563178.	+	975452.i	−0.0445464	+	0.0771566i
$694$	−8.03957e6	+	1.39249e7i	−0.633627	+	1.09747i
$695$	2.07136e6	+	3.58770e6i	0.162665	+	0.281744i
$696$	−1.23017e7			−0.962592
$697$	4.75898e6	+	8.24279e6i	0.371049	+	0.642676i
$698$	−1.29617e7	+	2.24503e7i	−1.00698	+	1.74415i
$699$	−712288.			−0.0551395
$700$	−1.21109e7	+	2.09768e7i	−0.934185	+	1.61806i
$701$	2.87557e6	+	4.98064e6i	0.221019	+	0.382816i	0.955118	−	0.296227i	$-0.0957284\pi$
$701$	2.87557e6	+	4.98064e6i	0.221019	+	0.382816i	−0.734099	+	0.679043i	$0.762395\pi$
$702$	−743379.	−	1.28757e6i	−0.0569335	−	0.0986117i
$703$	1.06601e7	+	1.84638e7i	0.813528	+	1.40907i
$704$	1.34919e6			0.102599
$705$	−1.24477e6	−	2.15601e6i	−0.0943229	−	0.163372i
$706$	−5.55389e6	−	9.61962e6i	−0.419358	−	0.726350i
$707$	1.21237e7	−	2.09988e7i	0.912190	−	1.57996i
$708$	8.15219e6	−	1.41200e7i	0.611211	−	1.05865i
$709$	−2.30040e7			−1.71865			−0.859326	−	0.511428i	$-0.829117\pi$
$709$	−2.30040e7			−1.71865			−0.859326	+	0.511428i	$0.829117\pi$
$710$	5.77253e6			0.429754
$711$	−2.05482e6	+	3.55905e6i	−0.152440	+	0.264034i
$712$	−1.30733e7	+	2.26436e7i	−0.966462	+	1.67396i
$713$	3.30757e6	+	5.72888e6i	0.243661	+	0.422033i
$714$	2.35368e7	+	4.07669e7i	1.72783	+	2.99269i
$715$	−65365.2			−0.00478169
$716$	−2.81491e6	−	4.87558e6i	−0.205203	−	0.355421i
$717$	6.56368e6	+	1.13686e7i	0.476814	+	0.825867i
$718$	6.59502e6	+	1.14229e7i	0.477425	+	0.826924i
$719$	−1.26494e7	+	2.19095e7i	−0.912533	+	1.58055i	−0.102061	+	0.994778i	$0.532544\pi$
$719$	−1.26494e7	+	2.19095e7i	−0.912533	+	1.58055i	−0.810473	+	0.585776i	$0.800790\pi$
$720$	−2.59764e6			−0.186745
$721$	1.48749e6	−	2.57641e6i	0.106565	−	0.184576i
$722$	−1.85206e7	−	3.20786e7i	−1.32225	−	2.29020i
$723$	4.31764e6			0.307186
$724$	1.04453e7	+	1.80918e7i	0.740586	+	1.28273i
$725$	−2.61663e6	+	4.53214e6i	−0.184883	+	0.320228i
$726$	1.53809e7	−	2.66405e7i	1.08303	−	1.87586i
$727$	2.19269e7			1.53865			0.769326	−	0.638856i	$-0.220592\pi$
$727$	2.19269e7			1.53865			0.769326	+	0.638856i	$0.220592\pi$
$728$	−1.64302e6	+	2.84579e6i	−0.114898	+	0.199010i
$729$	−1.21545e6			−0.0847066
$730$	7.27610e6			0.505349
$731$	1.80460e7	−	1.56134e7i	1.24907	−	1.08070i
$732$	2.57393e7			1.77550
$733$	−1.44070e7			−0.990406			−0.495203	−	0.868777i	$-0.664906\pi$
$733$	−1.44070e7			−0.990406			−0.495203	+	0.868777i	$0.664906\pi$
$734$	8.08697e6	−	1.40070e7i	0.554046	−	0.959636i
$735$	502658.			0.0343205
$736$	5.15044e6	−	8.92082e6i	0.350469	−	0.607030i
$737$	−2.20098e6	+	3.81221e6i	−0.149261	+	0.258528i
$738$	3.46523e6	+	6.00195e6i	0.234202	+	0.405650i
$739$	−7.09096e6			−0.477633			−0.238816	−	0.971065i	$-0.576759\pi$
$739$	−7.09096e6			−0.477633			−0.238816	+	0.971065i	$0.576759\pi$
$740$	3.84246e6	+	6.65534e6i	0.257947	+	0.446777i
$741$	−1.87047e6	+	3.23976e6i	−0.125143	+	0.216754i
$742$	−2.49798e7			−1.66564
$743$	−7.74297e6	+	1.34112e7i	−0.514559	+	0.891243i	0.485298	+	0.874349i	$0.338711\pi$
$743$	−7.74297e6	+	1.34112e7i	−0.514559	+	0.891243i	−0.999857	+	0.0168942i	$0.994622\pi$
$744$	−4.99890e6	−	8.65834e6i	−0.331087	−	0.573459i
$745$	−899082.	−	1.55726e6i	−0.0593484	−	0.102794i
$746$	−5.41321e6	−	9.37596e6i	−0.356130	−	0.616834i
$747$	879265.			0.0576526
$748$	4.25507e6	+	7.37000e6i	0.278069	+	0.481630i
$749$	1.12266e7	+	1.94451e7i	0.731214	+	1.26650i
$750$	−7.92706e6	+	1.37301e7i	−0.514587	+	0.891291i
$751$	6.94541e6	−	1.20298e7i	0.449364	−	0.778321i	−0.548981	−	0.835835i	$-0.684984\pi$
$751$	6.94541e6	−	1.20298e7i	0.449364	−	0.778321i	0.998345	+	0.0575139i	$0.0183174\pi$
$752$	−1.28932e7			−0.831413
$753$	2.69825e7			1.73418
$754$	−676352.	+	1.17148e6i	−0.0433256	+	0.0750421i
$755$	1.55310e6	−	2.69004e6i	0.0991588	−	0.171748i
$756$	−8.01765e6	−	1.38870e7i	−0.510203	−	0.883697i
$757$	590046.	+	1.02199e6i	0.0374237	+	0.0648197i	0.884131	−	0.467240i	$-0.154752\pi$
$757$	590046.	+	1.02199e6i	0.0374237	+	0.0648197i	−0.846707	+	0.532060i	$0.821418\pi$
$758$	−3.15837e7			−1.99660
$759$	−2.89445e6	−	5.01333e6i	−0.182373	−	0.315880i
$760$	−5.83833e6	−	1.01123e7i	−0.366653	−	0.635061i
$761$	−1.39544e7	−	2.41698e7i	−0.873475	−	1.51290i	−0.858378	−	0.513018i	$-0.828528\pi$
$761$	−1.39544e7	−	2.41698e7i	−0.873475	−	1.51290i	−0.0150972	−	0.999886i	$-0.504806\pi$
$762$	2.43571e7	−	4.21877e7i	1.51963	−	2.63208i
$763$	−2.53914e7			−1.57898
$764$	7.85178e6	−	1.35997e7i	0.486670	−	0.842937i
$765$	1.88439e6	+	3.26386e6i	0.116417	+	0.201640i
$766$	5.05492e7			3.11274
$767$	−470486.	−	814905.i	−0.0288774	−	0.0500171i
$768$	2.09634e7	−	3.63097e7i	1.28250	−	2.22136i
$769$	−1.09877e7	+	1.90313e7i	−0.670027	+	1.16052i	0.307869	+	0.951429i	$0.400384\pi$
$769$	−1.09877e7	+	1.90313e7i	−0.670027	+	1.16052i	−0.977896	+	0.209092i	$0.932949\pi$
$770$	−1.03997e6			−0.0632110
$771$	−7.81565e6	+	1.35371e7i	−0.473510	+	0.820143i
$772$	−2.04741e7			−1.23641
$773$	3.40639e6			0.205043			0.102522	−	0.994731i	$-0.467309\pi$
$773$	3.40639e6			0.205043			0.102522	+	0.994731i	$0.467309\pi$
$774$	1.31401e7	−	1.13688e7i	0.788399	−	0.682123i
$775$	−4.25316e6			−0.254365
$776$	2.32026e7			1.38319
$777$	1.02797e7	−	1.78050e7i	0.610841	−	1.05801i
$778$	−4.33100e7			−2.56531
$779$	−6.01715e6	+	1.04220e7i	−0.355261	+	0.615330i
$780$	−674218.	+	1.16778e6i	−0.0396793	+	0.0687265i
$781$	−1.39594e6	−	2.41784e6i	−0.0818916	−	0.141840i
$782$	−8.99347e7			−5.25909
$783$	−1.73226e6	−	3.00036e6i	−0.100974	−	0.174891i
$784$	1.30162e6	−	2.25447e6i	0.0756300	−	0.130995i
$785$	4.56681e6			0.264508
$786$	2.49311e7	−	4.31819e7i	1.43941	−	2.49313i
$787$	8.48650e6	+	1.46990e7i	0.488418	+	0.845965i	0.999911	−	0.0133224i	$-0.00424077\pi$
$787$	8.48650e6	+	1.46990e7i	0.488418	+	0.845965i	−0.511493	+	0.859287i	$0.670907\pi$
$788$	2.55005e7	+	4.41681e7i	1.46296	+	2.53392i
$789$	1.43880e7	+	2.49207e7i	0.822826	+	1.42518i
$790$	−3.79444e6			−0.216312
$791$	2.48632e6	+	4.30643e6i	0.141291	+	0.244724i
$792$	1.62615e6	+	2.81657e6i	0.0921186	+	0.159554i
$793$	742745.	−	1.28647e6i	0.0419428	−	0.0726470i
$794$	−2.37067e7	+	4.10613e7i	−1.33451	+	2.31143i
$795$	−5.38001e6			−0.301901
$796$	−4.14675e7			−2.31966
$797$	1.28751e7	−	2.23003e7i	0.717967	−	1.24355i	−0.243837	−	0.969816i	$-0.578406\pi$
$797$	1.28751e7	−	2.23003e7i	0.717967	−	1.24355i	0.961804	−	0.273739i	$-0.0882603\pi$
$798$	−2.97594e7	+	5.15448e7i	−1.65431	+	2.86535i
$799$	9.35304e6	+	1.61999e7i	0.518305	+	0.897731i
$800$	3.31144e6	+	5.73558e6i	0.182933	+	0.316849i
$801$	1.06702e7			0.587615
$802$	1.74174e7	+	3.01678e7i	0.956195	+	1.65618i
$803$	−1.75954e6	−	3.04762e6i	−0.0962966	−	0.166791i
$804$	4.54046e7	+	7.86430e7i	2.47719	+	4.29062i
$805$	3.72515e6	−	6.45215e6i	0.202607	−	0.350925i
$806$	−1.09936e6			−0.0596079
$807$	−1.06125e6	+	1.83813e6i	−0.0573630	+	0.0993557i
$808$	−3.50065e7	−	6.06330e7i	−1.88634	−	3.26724i
$809$	−7.51409e6			−0.403650			−0.201825	−	0.979422i	$-0.564687\pi$
$809$	−7.51409e6			−0.403650			−0.201825	+	0.979422i	$0.564687\pi$
$810$	−4.86629e6	−	8.42866e6i	−0.260607	−	0.451384i
$811$	1.59404e6	−	2.76095e6i	0.0851032	−	0.147403i	−0.820332	−	0.571888i	$-0.806211\pi$
$811$	1.59404e6	−	2.76095e6i	0.0851032	−	0.147403i	0.905435	+	0.424484i	$0.139545\pi$
$812$	−7.29473e6	+	1.26348e7i	−0.388257	+	0.672481i
$813$	2.87392e7			1.52493
$814$	2.74143e6	−	4.74829e6i	0.145016	−	0.251175i
$815$	763942.			0.0402871
$816$	5.25064e7			2.76049
$817$	2.85049e7	+	9.88945e6i	1.49405	+	0.518343i
$818$	2.14452e7			1.12059
$819$	1.34101e6			0.0698589
$820$	−2.16890e6	+	3.75665e6i	−0.112643	+	0.195104i
$821$	1.23540e7			0.639662			0.319831	−	0.947475i	$-0.396374\pi$
$821$	1.23540e7			0.639662			0.319831	+	0.947475i	$0.396374\pi$
$822$	8.80796e6	−	1.52558e7i	0.454669	−	0.787510i
$823$	8.40509e6	−	1.45580e7i	0.432557	−	0.749210i	−0.564536	−	0.825408i	$-0.690945\pi$
$823$	8.40509e6	−	1.45580e7i	0.432557	−	0.749210i	0.997093	+	0.0761985i	$0.0242783\pi$
$824$	−4.29506e6	−	7.43925e6i	−0.220369	−	0.381690i
$825$	3.72193e6			0.190385
$826$	−7.48548e6	−	1.29652e7i	−0.381741	−	0.661196i
$827$	−1.26785e7	+	2.19598e7i	−0.644621	+	1.11652i	0.339768	+	0.940509i	$0.389652\pi$
$827$	−1.26785e7	+	2.19598e7i	−0.644621	+	1.11652i	−0.984389	+	0.176007i	$0.943682\pi$
$828$	−4.43925e7			−2.25026
$829$	−6.43498e6	+	1.11457e7i	−0.325207	+	0.563276i	−0.981554	−	0.191183i	$-0.938767\pi$
$829$	−6.43498e6	+	1.11457e7i	−0.325207	+	0.563276i	0.656347	+	0.754459i	$0.272101\pi$
$830$	405914.	+	703064.i	0.0204521	+	0.0354241i
$831$	−7.14760e6	−	1.23800e7i	−0.359052	−	0.621897i
$832$	−803155.	−	1.39111e6i	−0.0402246	−	0.0696710i
$833$	−3.77690e6			−0.188592
$834$	−3.04864e7	−	5.28040e7i	−1.51772	−	2.62876i
$835$	−882436.	−	1.52842e6i	−0.0437993	−	0.0758626i
$836$	−5.38002e6	+	9.31847e6i	−0.266237	+	0.461136i
$837$	1.40783e6	−	2.43844e6i	0.0694604	−	0.120309i
$838$	5.84506e7			2.87527
$839$	−2.64776e7			−1.29859			−0.649296	−	0.760536i	$-0.724937\pi$
$839$	−2.64776e7			−1.29859			−0.649296	+	0.760536i	$0.724937\pi$
$840$	−5.63000e6	+	9.75145e6i	−0.275303	+	0.476838i
$841$	8.67951e6	−	1.50333e7i	0.423161	−	0.732936i
$842$	−3.80303e6	−	6.58703e6i	−0.184863	−	0.320191i
$843$	−7.78626e6	−	1.34862e7i	−0.377364	−	0.653613i
$844$	3.44276e7			1.66361
$845$	−2.43364e6	−	4.21518e6i	−0.117250	−	0.203083i
$846$	6.81037e6	+	1.17959e7i	0.327148	+	0.566638i
$847$	−9.57393e6	−	1.65825e7i	−0.458545	−	0.794223i
$848$	−1.39314e7	+	2.41299e7i	−0.665281	+	1.15230i
$849$	−5.03728e7			−2.39843
$850$	2.89114e7	−	5.00761e7i	1.37253	−	2.37729i
$851$	1.96395e7	+	3.40166e7i	0.929623	+	1.61015i
$852$	−5.75944e7			−2.71820
$853$	1.38697e6	+	2.40229e6i	0.0652669	+	0.113046i	0.896812	−	0.442411i	$-0.145877\pi$
$853$	1.38697e6	+	2.40229e6i	0.0652669	+	0.113046i	−0.831545	+	0.555457i	$0.812543\pi$
$854$	1.18172e7	−	2.04679e7i	0.554457	−	0.960348i
$855$	−2.38258e6	+	4.12675e6i	−0.111463	+	0.193060i
$856$	6.48326e7			3.02419
$857$	−3.36540e6	+	5.82904e6i	−0.156525	+	0.271110i	−0.933613	−	0.358282i	$-0.883363\pi$
$857$	−3.36540e6	+	5.82904e6i	−0.156525	+	0.271110i	0.777088	+	0.629392i	$0.216696\pi$
$858$	962049.			0.0446148
$859$	−2.90254e7			−1.34213			−0.671066	−	0.741397i	$-0.734163\pi$
$859$	−2.90254e7			−1.34213			−0.671066	+	0.741397i	$0.734163\pi$
$860$	1.02747e7	+	3.56468e6i	0.473720	+	0.164352i
$861$	1.16049e7			0.533498
$862$	4.89355e7			2.24314
$863$	6.23289e6	−	1.07957e7i	0.284880	−	0.493427i	−0.687700	−	0.725995i	$-0.741379\pi$
$863$	6.23289e6	−	1.07957e7i	0.284880	−	0.493427i	0.972580	+	0.232568i	$0.0747128\pi$
$864$	−4.38446e6			−0.199817
$865$	1.06322e6	−	1.84156e6i	0.0483153	−	0.0836845i
$866$	−7.55306e6	+	1.30823e7i	−0.342238	+	0.592773i
$867$	−2.41274e7	−	4.17898e7i	−1.09009	−	1.88809i
$868$	−1.18571e7			−0.534169
$869$	917590.	+	1.58931e6i	0.0412192	+	0.0713937i
$870$	−2.31760e6	+	4.01420e6i	−0.103810	+	0.179805i
$871$	5.24085e6			0.234076
$872$	−3.66583e7	+	6.34940e7i	−1.63260	+	2.82775i
$873$	−4.73440e6	−	8.20022e6i	−0.210247	−	0.364158i
$874$	−5.68558e7	−	9.84771e7i	−2.51765	−	4.36071i
$875$	4.93425e6	+	8.54637e6i	0.217872	+	0.377365i
$876$	−7.25961e7			−3.19634
$877$	6.68062e6	+	1.15712e7i	0.293304	+	0.508017i	0.974589	−	0.224001i	$-0.0719119\pi$
$877$	6.68062e6	+	1.15712e7i	0.293304	+	0.508017i	−0.681285	+	0.732018i	$0.738579\pi$
$878$	1.13608e7	+	1.96774e7i	0.497361	+	0.861454i
$879$	417435.	−	723019.i	0.0182229	−	0.0315630i
$880$	−579995.	+	1.00458e6i	−0.0252474	+	0.0437299i
$881$	2.97673e7			1.29211			0.646056	−	0.763290i	$-0.276417\pi$
$881$	2.97673e7			1.29211			0.646056	+	0.763290i	$0.276417\pi$
$882$	−2.75013e6			−0.119037
$883$	1.06356e6	−	1.84215e6i	0.0459052	−	0.0795101i	−0.842160	−	0.539228i	$-0.818716\pi$
$883$	1.06356e6	−	1.84215e6i	0.0459052	−	0.0795101i	0.888065	+	0.459718i	$0.152049\pi$
$884$	5.06597e6	−	8.77453e6i	0.218038	−	0.377653i
$885$	−1.61218e6	−	2.79237e6i	−0.0691917	−	0.119844i
$886$	−1.44620e7	−	2.50490e7i	−0.618936	−	1.07203i
$887$	2.35571e7			1.00534			0.502670	−	0.864478i	$-0.332351\pi$
$887$	2.35571e7			1.00534			0.502670	+	0.864478i	$0.332351\pi$
$888$	−2.96822e7	−	5.14110e7i	−1.26317	−	2.18788i
$889$	−1.51612e7	−	2.62600e7i	−0.643398	−	1.11440i
$890$	4.92593e6	+	8.53195e6i	0.208455	+	0.361055i
$891$	−2.35358e6	+	4.07652e6i	−0.0993195	+	0.172026i
$892$	1.73045e7			0.728192
$893$	−1.18258e7	+	2.04829e7i	−0.496251	+	0.859532i
$894$	1.32328e7	+	2.29198e7i	0.553741	+	0.959107i
$895$	−1.11335e6			−0.0464597
$896$	−1.71647e7	−	2.97302e7i	−0.714277	−	1.23716i
$897$	−3.44605e6	+	5.96873e6i	−0.143001	+	0.247686i
$898$	1.85527e6	−	3.21342e6i	0.0767743	−	0.132977i
$899$	−2.56179e6			−0.105717
$900$	1.42709e7	−	2.47179e7i	0.587280	−	1.01720i
$901$	4.04246e7			1.65895
$902$	3.09483e6			0.126654
$903$	−5.48498e6	−	2.85734e7i	−0.223849	−	1.16612i
$904$	1.43583e7			0.584361
$905$	4.13133e6			0.167675
$906$	−2.28586e7	+	3.95922e7i	−0.925185	+	1.60247i
$907$	−1.56908e7			−0.633327			−0.316663	−	0.948538i	$-0.602563\pi$
$907$	−1.56908e7			−0.633327			−0.316663	+	0.948538i	$0.602563\pi$
$908$	1.48661e7	−	2.57489e7i	0.598388	−	1.03644i
$909$	−1.42859e7	+	2.47439e7i	−0.573453	+	0.993250i
$910$	619078.	+	1.07227e6i	0.0247823	+	0.0429242i
$911$	−2.53728e7			−1.01291			−0.506457	−	0.862265i	$-0.669045\pi$
$911$	−2.53728e7			−1.01291			−0.506457	+	0.862265i	$0.669045\pi$
$912$	3.31940e7	+	5.74937e7i	1.32152	+	2.28893i
$913$	196320.	−	340036.i	0.00779449	−	0.0135005i
$914$	3.72244e7			1.47388
$915$	2.54511e6	−	4.40825e6i	0.100497	−	0.174066i
$916$	1.60462e7	+	2.77928e7i	0.631878	+	1.09444i
$917$	−1.55185e7	−	2.68789e7i	−0.609435	−	1.05557i
$918$	1.91399e7	+	3.31512e7i	0.749605	+	1.29835i
$919$	8.85863e6			0.346002			0.173001	−	0.984922i	$-0.444654\pi$
$919$	8.85863e6			0.346002			0.173001	+	0.984922i	$0.444654\pi$
$920$	−1.07562e7	−	1.86303e7i	−0.418976	−	0.725687i
$921$	−1.61816e6	−	2.80274e6i	−0.0628598	−	0.108876i
$922$	−2.48740e7	+	4.30831e7i	−0.963649	+	1.66909i
$923$	−1.66197e6	+	2.87862e6i	−0.0642124	+	0.111219i
$924$	1.03761e7			0.399810
$925$	−2.52542e7			−0.970463
$926$	−1.65231e6	+	2.86188e6i	−0.0633232	+	0.109679i
$927$	−1.75278e6	+	3.03591e6i	−0.0669928	+	0.116035i
$928$	1.99456e6	+	3.45469e6i	0.0760288	+	0.131686i
$929$	−8.50638e6	−	1.47335e7i	−0.323374	−	0.560101i	0.657808	−	0.753186i	$-0.271484\pi$
$929$	−8.50638e6	−	1.47335e7i	−0.323374	−	0.560101i	−0.981182	+	0.193085i	$0.938151\pi$
$930$	−3.76710e6			−0.142824
$931$	−2.38771e6	−	4.13564e6i	−0.0902834	−	0.156376i
$932$	1.21959e6	+	2.11239e6i	0.0459912	+	0.0796591i
$933$	2.93202e7	+	5.07842e7i	1.10272	+	1.90996i
$934$	−2.17934e7	+	3.77472e7i	−0.817442	+	1.41585i
$935$	1.68297e6			0.0629573
$936$	1.93605e6	−	3.35334e6i	0.0722315	−	0.125109i
$937$	8.52950e6	+	1.47735e7i	0.317376	+	0.549712i	0.979940	−	0.199294i	$-0.0638649\pi$
$937$	8.52950e6	+	1.47735e7i	0.317376	+	0.549712i	−0.662564	+	0.749006i	$0.730532\pi$
$938$	8.33825e7			3.09434
$939$	9.80988e6	+	1.69912e7i	0.363078	+	0.628869i
$940$	−4.26264e6	+	7.38311e6i	−0.157347	+	0.272533i
$941$	−1.27842e7	+	2.21429e7i	−0.470652	+	0.815193i	−0.999437	−	0.0335630i	$-0.989315\pi$
$941$	−1.27842e7	+	2.21429e7i	−0.470652	+	0.815193i	0.528785	+	0.848756i	$0.322648\pi$
$942$	−6.72147e7			−2.46795
$943$	−1.10856e7	+	1.92009e7i	−0.405959	+	0.703141i
$944$	−1.66988e7			−0.609894
$945$	−3.17114e6			−0.115514
$946$	−1.46275e6	−	7.62004e6i	−0.0531426	−	0.276840i
$947$	−7.75549e6			−0.281018			−0.140509	−	0.990079i	$-0.544874\pi$
$947$	−7.75549e6			−0.281018			−0.140509	+	0.990079i	$0.544874\pi$
$948$	3.78584e7			1.36817
$949$	−2.09486e6	+	3.62841e6i	−0.0755076	+	0.130783i
$950$	7.31101e7			2.62826
$951$	−2.01410e7	+	3.48852e7i	−0.722154	+	1.25081i
$952$	4.23030e7	−	7.32710e7i	1.51279	−	2.62023i
$953$	−5.60800e6	−	9.71334e6i	−0.200021	−	0.346447i	0.748514	−	0.663119i	$-0.230768\pi$
$953$	−5.60800e6	−	9.71334e6i	−0.200021	−	0.346447i	−0.948535	+	0.316672i	$0.897434\pi$
$954$	2.94350e7			1.04711
$955$	−1.55277e6	−	2.68947e6i	−0.0550932	−	0.0954242i
$956$	2.24769e7	−	3.89311e7i	0.795410	−	1.37769i
$957$	2.24181e6			0.0791260
$958$	−1.20920e7	+	2.09440e7i	−0.425681	+	0.737302i
$959$	−5.48257e6	−	9.49609e6i	−0.192503	−	0.333425i
$960$	−2.75211e6	−	4.76679e6i	−0.0963801	−	0.166935i
$961$	1.32736e7	+	2.29905e7i	0.463638	+	0.803045i
$962$	−6.52774e6			−0.227418
$963$	−1.32289e7	−	2.29131e7i	−0.459681	−	0.796191i
$964$	−7.39274e6	−	1.28046e7i	−0.256220	−	0.443786i
$965$	−2.02448e6	+	3.50650e6i	−0.0699833	+	0.121215i
$966$	−5.48270e7	+	9.49632e7i	−1.89039	+	3.27425i
$967$	1.79514e7			0.617352			0.308676	−	0.951167i	$-0.400114\pi$
$967$	1.79514e7			0.617352			0.308676	+	0.951167i	$0.400114\pi$
$968$	−5.52885e7			−1.89647
$969$	4.81593e7	−	8.34144e7i	1.64767	−	2.85385i
$970$	4.37128e6	−	7.57128e6i	0.149169	−	0.258369i
$971$	−1.86247e7	−	3.22589e7i	−0.633930	−	1.09800i	−0.986741	−	0.162304i	$-0.948108\pi$
$971$	−1.86247e7	−	3.22589e7i	−0.633930	−	1.09800i	0.352811	−	0.935694i	$-0.385226\pi$
$972$	3.25852e7	+	5.64392e7i	1.10625	+	1.91609i
$973$	−3.79529e7			−1.28518
$974$	−778751.	−	1.34884e6i	−0.0263028	−	0.0455577i
$975$	−2.21561e6	−	3.83756e6i	−0.0746419	−	0.129284i
$976$	−1.31810e7	−	2.28301e7i	−0.442918	−	0.767156i
$977$	−1.56405e7	+	2.70902e7i	−0.524221	+	0.907978i	0.475381	+	0.879780i	$0.342310\pi$
$977$	−1.56405e7	+	2.70902e7i	−0.524221	+	0.907978i	−0.999602	+	0.0281977i	$0.991023\pi$
$978$	−1.12438e7			−0.375893
$979$	2.38242e6	−	4.12648e6i	0.0794442	−	0.137601i
$980$	−860659.	−	1.49070e6i	−0.0286263	−	0.0495823i
$981$	2.99199e7			0.992632
$982$	2.48523e7	+	4.30454e7i	0.822408	+	1.42445i
$983$	2.80313e7	−	4.85516e7i	0.925249	−	1.60258i	0.134089	−	0.990969i	$-0.457189\pi$
$983$	2.80313e7	−	4.85516e7i	0.925249	−	1.60258i	0.791160	−	0.611609i	$-0.209478\pi$
$984$	1.67543e7	−	2.90193e7i	0.551617	−	0.955429i
$985$	1.00859e7			0.331227
$986$	1.74141e7	−	3.01621e7i	0.570439	−	0.988028i
$987$	2.28076e7			0.745224
$988$	1.28106e7			0.417521
$989$	5.25157e7	+	1.82197e7i	1.70726	+	0.592313i
$990$	1.22544e6			0.0397379
$991$	−3.57931e7			−1.15775			−0.578875	−	0.815416i	$-0.696508\pi$
$991$	−3.57931e7			−1.15775			−0.578875	+	0.815416i	$0.696508\pi$
$992$	−1.62101e6	+	2.80768e6i	−0.0523007	+	0.0905875i
$993$	−6.92672e7			−2.22923
$994$	−2.64421e7	+	4.57990e7i	−0.848848	+	1.47025i
$995$	−4.10030e6	+	7.10193e6i	−0.131298	+	0.227415i
$996$	−4.04994e6	−	7.01470e6i	−0.129360	−	0.224058i
$997$	4.54026e7			1.44658			0.723291	−	0.690543i	$-0.242629\pi$
$997$	4.54026e7			1.44658			0.723291	+	0.690543i	$0.242629\pi$
$998$	1.11065e7	+	1.92370e7i	0.352981	+	0.611380i
$999$	8.35935e6	−	1.44788e7i	0.265008	−	0.459007i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.6.c.a.6.17	✓	34
43.36	even	3	inner	43.6.c.a.36.17	yes	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.6.c.a.6.17	✓	34	1.1	even	1	trivial
43.6.c.a.36.17	yes	34	43.36	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+9.96731 q^{2} +(-9.83333 + 17.0318i) q^{3} +67.3472 q^{4} +(6.65929 - 11.5342i) q^{5} +(-98.0118 + 169.761i) q^{6} +(61.0081 + 105.669i) q^{7} +352.316 q^{8} +(-71.8888 - 124.515i) q^{9} +O(q^{10})\)	\(q+9.96731 q^{2} +(-9.83333 + 17.0318i) q^{3} +67.3472 q^{4} +(6.65929 - 11.5342i) q^{5} +(-98.0118 + 169.761i) q^{6} +(61.0081 + 105.669i) q^{7} +352.316 q^{8} +(-71.8888 - 124.515i) q^{9} +(66.3751 - 114.965i) q^{10} -64.2046 q^{11} +(-662.247 + 1147.05i) q^{12} +(38.2202 + 66.1993i) q^{13} +(608.087 + 1053.24i) q^{14} +(130.966 + 226.840i) q^{15} +1356.53 q^{16} +(-984.059 - 1704.44i) q^{17} +(-716.538 - 1241.08i) q^{18} +(1244.22 - 2155.06i) q^{19} +(448.484 - 776.797i) q^{20} -2399.65 q^{21} -639.947 q^{22} +(2292.28 - 3970.35i) q^{23} +(-3464.44 + 6000.59i) q^{24} +(1473.81 + 2552.71i) q^{25} +(380.952 + 659.828i) q^{26} -1951.37 q^{27} +(4108.72 + 7116.52i) q^{28} +(887.712 + 1537.56i) q^{29} +(1305.38 + 2260.98i) q^{30} +(-721.458 + 1249.60i) q^{31} +2246.86 q^{32} +(631.345 - 1093.52i) q^{33} +(-9808.42 - 16988.7i) q^{34} +1625.08 q^{35} +(-4841.51 - 8385.74i) q^{36} +(-4283.83 + 7419.81i) q^{37} +(12401.6 - 21480.1i) q^{38} -1503.33 q^{39} +(2346.17 - 4063.69i) q^{40} -4836.07 q^{41} -23918.1 q^{42} +(2285.74 + 11907.3i) q^{43} -4324.00 q^{44} -1914.91 q^{45} +(22847.9 - 39573.7i) q^{46} -9504.55 q^{47} +(-13339.2 + 23104.2i) q^{48} +(959.520 - 1661.94i) q^{49} +(14689.9 + 25443.6i) q^{50} +38706.3 q^{51} +(2574.02 + 4458.33i) q^{52} +(-10269.9 + 17787.9i) q^{53} -19449.9 q^{54} +(-427.557 + 740.550i) q^{55} +(21494.1 + 37228.9i) q^{56} +(24469.7 + 42382.8i) q^{57} +(8848.10 + 15325.4i) q^{58} -12309.9 q^{59} +(8820.19 + 15277.0i) q^{60} +(-9716.67 - 16829.8i) q^{61} +(-7190.99 + 12455.2i) q^{62} +(8771.60 - 15192.9i) q^{63} -21013.9 q^{64} +1018.08 q^{65} +(6292.81 - 10899.5i) q^{66} +(34280.7 - 59375.9i) q^{67} +(-66273.6 - 114789. i) q^{68} +(45081.6 + 78083.6i) q^{69} +16197.7 q^{70} +(21742.0 + 37658.3i) q^{71} +(-25327.6 - 43868.7i) q^{72} +(27405.2 + 47467.3i) q^{73} +(-42698.2 + 73955.5i) q^{74} -57969.8 q^{75} +(83795.0 - 145137. i) q^{76} +(-3917.00 - 6784.45i) q^{77} -14984.1 q^{78} +(-14291.6 - 24753.9i) q^{79} +(9033.54 - 15646.5i) q^{80} +(36657.5 - 63492.6i) q^{81} -48202.6 q^{82} +(-3057.73 + 5296.14i) q^{83} -161610. q^{84} -26212.5 q^{85} +(22782.7 + 118684. i) q^{86} -34916.7 q^{87} -22620.3 q^{88} +(-37106.7 + 64270.7i) q^{89} -19086.5 q^{90} +(-4663.48 + 8077.38i) q^{91} +(154379. - 267392. i) q^{92} +(-14188.7 - 24575.5i) q^{93} -94734.7 q^{94} +(-16571.3 - 28702.3i) q^{95} +(-22094.1 + 38268.1i) q^{96} +65857.2 q^{97} +(9563.82 - 16565.0i) q^{98} +(4615.60 + 7994.45i) 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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