LMFDB - Embedded newform 63.6.i.a.5.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [63,6,Mod(5,63)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("63.5"); S:= CuspForms(chi, 6); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(63, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 5])) N = Newforms(chi, 6, names="a")

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	63.i (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$10.1041806482$
Analytic rank:	$0$
Dimension:	$76$
Relative dimension:	$38$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			5.12
Character	$\chi$	$=$	63.5
Dual form			63.6.i.a.38.27

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-5.28457i q^{2} +(0.760712 + 15.5699i) q^{3} +4.07335 q^{4} +(-18.3459 - 31.7760i) q^{5} +(82.2801 - 4.02003i) q^{6} +(43.8244 + 122.010i) q^{7} -190.632i q^{8} +(-241.843 + 23.6884i) q^{9} +(-167.922 + 96.9499i) q^{10} +(510.471 + 294.720i) q^{11} +(3.09865 + 63.4216i) q^{12} +(874.017 + 504.614i) q^{13} +(644.770 - 231.593i) q^{14} +(480.792 - 309.815i) q^{15} -877.061 q^{16} +(-6.40516 - 11.0941i) q^{17} +(125.183 + 1278.03i) q^{18} +(786.320 + 453.982i) q^{19} +(-74.7291 - 129.435i) q^{20} +(-1866.34 + 775.155i) q^{21} +(1557.47 - 2697.62i) q^{22} +(1421.86 - 820.910i) q^{23} +(2968.12 - 145.016i) q^{24} +(889.359 - 1540.42i) q^{25} +(2666.67 - 4618.80i) q^{26} +(-552.798 - 3747.44i) q^{27} +(178.512 + 496.989i) q^{28} +(-539.931 + 311.729i) q^{29} +(-1637.24 - 2540.78i) q^{30} +5087.59i q^{31} -1465.34i q^{32} +(-4200.44 + 8172.17i) q^{33} +(-58.6273 + 33.8485i) q^{34} +(3072.99 - 3630.94i) q^{35} +(-985.110 + 96.4911i) q^{36} +(-5612.52 + 9721.18i) q^{37} +(2399.10 - 4155.36i) q^{38} +(-7191.90 + 13992.2i) q^{39} +(-6057.52 + 3497.31i) q^{40} +(-259.774 + 449.942i) q^{41} +(4096.36 + 9862.81i) q^{42} +(-8746.21 - 15148.9i) q^{43} +(2079.33 + 1200.50i) q^{44} +(5189.53 + 7250.20i) q^{45} +(-4338.15 - 7513.90i) q^{46} +12022.3 q^{47} +(-667.190 - 13655.7i) q^{48} +(-12965.8 + 10694.0i) q^{49} +(-8140.43 - 4699.88i) q^{50} +(167.861 - 108.167i) q^{51} +(3560.18 + 2055.47i) q^{52} +(-29007.7 + 16747.6i) q^{53} +(-19803.6 + 2921.30i) q^{54} -21627.6i q^{55} +(23259.0 - 8354.33i) q^{56} +(-6470.29 + 12588.3i) q^{57} +(1647.35 + 2853.30i) q^{58} +9146.38 q^{59} +(1958.44 - 1261.99i) q^{60} -33783.8i q^{61} +26885.7 q^{62} +(-13488.8 - 28469.1i) q^{63} -35809.6 q^{64} -37030.3i q^{65} +(43186.4 + 22197.5i) q^{66} -46497.0 q^{67} +(-26.0905 - 45.1900i) q^{68} +(13863.1 + 21513.7i) q^{69} +(-19187.9 - 16239.4i) q^{70} -79736.3i q^{71} +(4515.77 + 46103.0i) q^{72} +(22128.7 - 12776.0i) q^{73} +(51372.2 + 29659.8i) q^{74} +(24660.6 + 12675.4i) q^{75} +(3202.96 + 1849.23i) q^{76} +(-13587.8 + 75198.4i) q^{77} +(73942.8 + 38006.1i) q^{78} +407.717 q^{79} +(16090.4 + 27869.4i) q^{80} +(57926.7 - 11457.7i) q^{81} +(2377.75 + 1372.79i) q^{82} +(9086.59 + 15738.4i) q^{83} +(-7602.27 + 3157.48i) q^{84} +(-235.016 + 407.060i) q^{85} +(-80055.2 + 46219.9i) q^{86} +(-5264.32 - 8169.53i) q^{87} +(56183.1 - 97312.1i) q^{88} +(-16627.6 + 28799.9i) q^{89} +(38314.2 - 27424.4i) q^{90} +(-23264.7 + 128753. i) q^{91} +(5791.72 - 3343.85i) q^{92} +(-79213.2 + 3870.19i) q^{93} -63532.5i q^{94} -33314.8i q^{95} +(22815.2 - 1114.70i) q^{96} +(30413.4 - 17559.2i) q^{97} +(56513.3 + 68518.9i) q^{98} +(-130435. - 59183.7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q - 3 q^{3} - 1154 q^{4} - 3 q^{5} + 96 q^{6} - 30 q^{7} + 489 q^{9} - 6 q^{10} + 567 q^{11} - 1542 q^{12} + 543 q^{13} - 1638 q^{14} + 234 q^{15} + 16446 q^{16} - 801 q^{17} - 2022 q^{18} - 6 q^{19}+ \cdots - 144540 q^{99}+O(q^{100}) $ 76 * q - 3 * q^3 - 1154 * q^4 - 3 * q^5 + 96 * q^6 - 30 * q^7 + 489 * q^9 - 6 * q^10 + 567 * q^11 - 1542 * q^12 + 543 * q^13 - 1638 * q^14 + 234 * q^15 + 16446 * q^16 - 801 * q^17 - 2022 * q^18 - 6 * q^19 + 96 * q^20 - 4119 * q^21 + 62 * q^22 + 7806 * q^23 - 2346 * q^24 - 18749 * q^25 + 10128 * q^26 - 1539 * q^27 + 860 * q^28 + 17904 * q^29 + 11457 * q^30 - 3 * q^33 + 96 * q^34 + 3960 * q^35 - 57846 * q^36 + 2577 * q^37 + 14967 * q^38 - 16269 * q^39 + 9564 * q^40 + 28230 * q^41 + 15606 * q^42 - 9246 * q^43 - 69885 * q^44 - 23649 * q^45 - 9418 * q^46 - 56562 * q^47 + 48615 * q^48 + 7948 * q^49 - 67509 * q^50 - 103722 * q^51 - 40899 * q^52 + 25296 * q^53 + 176211 * q^54 + 104754 * q^56 + 33399 * q^57 - 4951 * q^58 - 59076 * q^59 + 33729 * q^60 + 79536 * q^62 - 95871 * q^63 - 198600 * q^64 + 114900 * q^66 + 1244 * q^67 + 191496 * q^68 + 3702 * q^69 - 127197 * q^70 + 183582 * q^72 - 6 * q^73 - 45681 * q^74 - 240486 * q^75 - 2880 * q^76 + 13854 * q^77 + 184431 * q^78 + 59984 * q^79 + 243225 * q^80 + 177117 * q^81 + 90 * q^82 - 246930 * q^83 + 56085 * q^84 + 11973 * q^85 + 291801 * q^86 + 205125 * q^87 - 34751 * q^88 - 6345 * q^89 - 269187 * q^90 - 120111 * q^91 - 463488 * q^92 + 200946 * q^93 - 382521 * q^96 - 104037 * q^97 - 646797 * q^98 - 144540 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

$n$	$10$	$29$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$		−	5.28457i		−	0.934188i	−0.884208	−	0.467094i	$-0.845301\pi$
$2$		−	5.28457i		−	0.934188i	0.884208	−	0.467094i	$-0.154699\pi$
$3$	0.760712	+	15.5699i	0.0487997	+	0.998809i
$3$	0.760712	+	15.5699i	0.0487997	+	0.998809i
$4$	4.07335			0.127292
$5$	−18.3459	−	31.7760i	−0.328181	−	0.568426i	0.653970	−	0.756520i	$-0.273102\pi$
$5$	−18.3459	−	31.7760i	−0.328181	−	0.568426i	−0.982151	+	0.188095i	$0.939769\pi$
$6$	82.2801	−	4.02003i	0.933075	−	0.0455881i
$7$	43.8244	+	122.010i	0.338042	+	0.941131i
$7$	43.8244	+	122.010i	0.338042	+	0.941131i
$8$		−	190.632i		−	1.05310i
$9$	−241.843	+	23.6884i	−0.995237	+	0.0974831i
$10$	−167.922	+	96.9499i	−0.531016	+	0.306583i
$11$	510.471	+	294.720i	1.27201	+	0.734393i	0.975365	−	0.220596i	$-0.0708004\pi$
$11$	510.471	+	294.720i	1.27201	+	0.734393i	0.296640	+	0.954989i	$0.404134\pi$
$12$	3.09865	+	63.4216i	0.00621182	+	0.127141i
$13$	874.017	+	504.614i	1.43437	+	0.828134i	0.997450	−	0.0713658i	$-0.0227358\pi$
$13$	874.017	+	504.614i	1.43437	+	0.828134i	0.436920	+	0.899500i	$0.356069\pi$
$14$	644.770	−	231.593i	0.879194	−	0.315795i
$15$	480.792	−	309.815i	0.551733	−	0.355529i
$16$	−877.061			−0.856504
$17$	−6.40516	−	11.0941i	−0.00537536	−	0.00931039i	0.863325	−	0.504648i	$-0.168378\pi$
$17$	−6.40516	−	11.0941i	−0.00537536	−	0.00931039i	−0.868701	+	0.495338i	$0.835044\pi$
$18$	125.183	+	1278.03i	0.0910675	+	0.929739i
$19$	786.320	+	453.982i	0.499707	+	0.288506i	0.728593	−	0.684947i	$-0.240175\pi$
$19$	786.320	+	453.982i	0.499707	+	0.288506i	−0.228885	+	0.973453i	$0.573508\pi$
$20$	−74.7291	−	129.435i	−0.0417749	−	0.0723562i
$21$	−1866.34	+	775.155i	−0.923513	+	0.383566i
$22$	1557.47	−	2697.62i	0.686061	−	1.18829i
$23$	1421.86	−	820.910i	0.560449	−	0.323576i	−0.192877	−	0.981223i	$-0.561782\pi$
$23$	1421.86	−	820.910i	0.560449	−	0.323576i	0.753326	+	0.657647i	$0.228448\pi$
$24$	2968.12	−	145.016i	1.05185	−	0.0513911i
$25$	889.359	−	1540.42i	0.284595	−	0.492933i
$26$	2666.67	−	4618.80i	0.773633	−	1.33997i
$27$	−552.798	−	3747.44i	−0.145934	−	0.989294i
$28$	178.512	+	496.989i	0.0430301	+	0.119799i
$29$	−539.931	+	311.729i	−0.119218	+	0.0688308i	−0.558423	−	0.829556i	$-0.688594\pi$
$29$	−539.931	+	311.729i	−0.119218	+	0.0688308i	0.439205	+	0.898387i	$0.355260\pi$
$30$	−1637.24	−	2540.78i	−0.332131	−	0.515423i
$31$			5087.59i			0.950841i	0.879759	+	0.475420i	$0.157704\pi$
$31$			5087.59i			0.950841i	−0.879759	+	0.475420i	$0.842296\pi$
$32$		−	1465.34i		−	0.252967i
$33$	−4200.44	+	8172.17i	−0.671444	+	1.30633i
$34$	−58.6273	+	33.8485i	−0.00869766	+	0.00502160i
$35$	3072.99	−	3630.94i	0.424024	−	0.501013i
$36$	−985.110	+	96.4911i	−0.126686	+	0.0124088i
$37$	−5612.52	+	9721.18i	−0.673991	+	1.16739i	0.302772	+	0.953063i	$0.402088\pi$
$37$	−5612.52	+	9721.18i	−0.673991	+	1.16739i	−0.976763	+	0.214323i	$0.931245\pi$
$38$	2399.10	−	4155.36i	0.269519	−	0.466821i
$39$	−7191.90	+	13992.2i	−0.757151	+	1.47307i
$40$	−6057.52	+	3497.31i	−0.598611	+	0.345608i
$41$	−259.774	+	449.942i	−0.0241344	+	0.0418020i	−0.877840	−	0.478953i	$-0.841016\pi$
$41$	−259.774	+	449.942i	−0.0241344	+	0.0418020i	0.853706	+	0.520755i	$0.174350\pi$
$42$	4096.36	+	9862.81i	0.358323	+	0.862735i
$43$	−8746.21	−	15148.9i	−0.721354	−	1.24942i	−0.960457	−	0.278428i	$-0.910187\pi$
$43$	−8746.21	−	15148.9i	−0.721354	−	1.24942i	0.239103	−	0.970994i	$-0.423147\pi$
$44$	2079.33	+	1200.50i	0.161916	+	0.0934825i
$45$	5189.53	+	7250.20i	0.382029	+	0.533726i
$46$	−4338.15	−	7513.90i	−0.302280	−	0.523565i
$47$	12022.3			0.793856			0.396928	−	0.917850i	$-0.370076\pi$
$47$	12022.3			0.793856			0.396928	+	0.917850i	$0.370076\pi$
$48$	−667.190	−	13655.7i	−0.0417971	−	0.855484i
$49$	−12965.8	+	10694.0i	−0.771455	+	0.636284i
$50$	−8140.43	−	4699.88i	−0.460492	−	0.265865i
$51$	167.861	−	108.167i	0.00903698	−	0.00582330i
$52$	3560.18	+	2055.47i	0.182584	+	0.105415i
$53$	−29007.7	+	16747.6i	−1.41848	+	0.818960i	−0.996165	−	0.0874896i	$-0.972116\pi$
$53$	−29007.7	+	16747.6i	−1.41848	+	0.818960i	−0.422315	+	0.906449i	$0.638782\pi$
$54$	−19803.6	+	2921.30i	−0.924187	+	0.136330i
$55$		−	21627.6i		−	0.964054i
$56$	23259.0	−	8354.33i	0.991108	−	0.355993i
$57$	−6470.29	+	12588.3i	−0.263777	+	0.513191i
$58$	1647.35	+	2853.30i	0.0643009	+	0.111372i
$59$	9146.38			0.342073			0.171037	−	0.985265i	$-0.445288\pi$
$59$	9146.38			0.342073			0.171037	+	0.985265i	$0.445288\pi$
$60$	1958.44	−	1261.99i	0.0702314	−	0.0452560i
$61$		−	33783.8i		−	1.16248i	−0.813734	−	0.581238i	$-0.802569\pi$
$61$		−	33783.8i		−	1.16248i	0.813734	−	0.581238i	$-0.197431\pi$
$62$	26885.7			0.888264
$63$	−13488.8	−	28469.1i	−0.428176	−	0.903695i
$64$	−35809.6			−1.09282
$65$		−	37030.3i		−	1.08711i
$66$	43186.4	+	22197.5i	1.22036	+	0.627255i
$67$	−46497.0			−1.26543			−0.632715	−	0.774385i	$-0.718059\pi$
$67$	−46497.0			−1.26543			−0.632715	+	0.774385i	$0.718059\pi$
$68$	−26.0905	−	45.1900i	−0.000684241	−	0.00118514i
$69$	13863.1	+	21513.7i	0.350540	+	0.543991i
$70$	−19187.9	−	16239.4i	−0.468040	−	0.396118i
$71$		−	79736.3i		−	1.87720i	−0.345011	−	0.938599i	$-0.612125\pi$
$71$		−	79736.3i		−	1.87720i	0.345011	−	0.938599i	$-0.387875\pi$
$72$	4515.77	+	46103.0i	0.102660	+	1.04809i
$73$	22128.7	−	12776.0i	0.486014	−	0.280601i	−0.236905	−	0.971533i	$-0.576133\pi$
$73$	22128.7	−	12776.0i	0.486014	−	0.280601i	0.722920	+	0.690932i	$0.242800\pi$
$74$	51372.2	+	29659.8i	1.09056	+	0.629634i
$75$	24660.6	+	12675.4i	0.506234	+	0.260201i
$76$	3202.96	+	1849.23i	0.0636088	+	0.0367246i
$77$	−13587.8	+	75198.4i	−0.261169	+	1.44538i
$78$	73942.8	+	38006.1i	1.37613	+	0.707321i
$79$	407.717			0.00735007			0.00367504	−	0.999993i	$-0.498830\pi$
$79$	407.717			0.00735007			0.00367504	+	0.999993i	$0.498830\pi$
$80$	16090.4	+	27869.4i	0.281088	+	0.486859i
$81$	57926.7	−	11457.7i	0.980994	−	0.194038i
$82$	2377.75	+	1372.79i	0.0390509	+	0.0225461i
$83$	9086.59	+	15738.4i	0.144779	+	0.250765i	0.929290	−	0.369350i	$-0.120420\pi$
$83$	9086.59	+	15738.4i	0.144779	+	0.250765i	−0.784511	+	0.620114i	$0.787086\pi$
$84$	−7602.27	+	3157.48i	−0.117556	+	0.0488250i
$85$	−235.016	+	407.060i	−0.00352818	+	0.00611098i
$86$	−80055.2	+	46219.9i	−1.16720	+	0.673881i
$87$	−5264.32	−	8169.53i	−0.0745666	−	0.115717i
$88$	56183.1	−	97312.1i	0.773391	−	1.33955i
$89$	−16627.6	+	28799.9i	−0.222513	+	0.385403i	−0.955570	−	0.294763i	$-0.904759\pi$
$89$	−16627.6	+	28799.9i	−0.222513	+	0.385403i	0.733058	+	0.680167i	$0.238093\pi$
$90$	38314.2	−	27424.4i	0.498601	−	0.356887i
$91$	−23264.7	+	128753.i	−0.294505	+	1.62987i
$92$	5791.72	−	3343.85i	0.0713408	−	0.0411887i
$93$	−79213.2	+	3870.19i	−0.949708	+	0.0464007i
$94$		−	63532.5i		−	0.741611i
$95$		−	33314.8i		−	0.378728i
$96$	22815.2	−	1114.70i	0.252665	−	0.0123447i
$97$	30413.4	−	17559.2i	0.328198	−	0.189485i	−0.326843	−	0.945079i	$-0.605985\pi$
$97$	30413.4	−	17559.2i	0.328198	−	0.189485i	0.655041	+	0.755593i	$0.272651\pi$
$98$	56513.3	+	68518.9i	0.594409	+	0.720684i
$99$	−130435.	−	59183.7i	−1.33754	−	0.606896i
$100$	3622.67	−	6274.65i	0.0362267	−	0.0627465i
$101$	62318.8	−	107939.i	0.607877	−	1.05287i	−0.383712	−	0.923453i	$-0.625355\pi$
$101$	62318.8	−	107939.i	0.607877	−	1.05287i	0.991590	−	0.129422i	$-0.0413121\pi$
$102$	−571.615	−	887.071i	−0.00544006	−	0.00844224i
$103$	−55729.5	+	32175.4i	−0.517597	+	0.298835i	−0.735951	−	0.677035i	$-0.763265\pi$
$103$	−55729.5	+	32175.4i	−0.517597	+	0.298835i	0.218354	+	0.975870i	$0.429931\pi$
$104$	96195.6	−	166616.i	0.872111	−	1.51054i
$105$	58870.9	+	45083.9i	0.521108	+	0.399070i
$106$	88503.7	+	153293.i	0.765063	+	1.32513i
$107$	9802.86	+	5659.68i	0.0827738	+	0.0477895i	0.540816	−	0.841141i	$-0.318116\pi$
$107$	9802.86	+	5659.68i	0.0827738	+	0.0477895i	−0.458042	+	0.888931i	$0.651449\pi$
$108$	−2251.74	−	15264.6i	−0.0185763	−	0.125929i
$109$	46154.7	+	79942.4i	0.372092	+	0.644482i	0.989887	−	0.141857i	$-0.0453073\pi$
$109$	46154.7	+	79942.4i	0.372092	+	0.644482i	−0.617795	+	0.786339i	$0.711974\pi$
$110$	−114292.			−0.900608
$111$	−155627.	−	79991.3i	−1.19889	−	0.616220i
$112$	−38436.6	−	107010.i	−0.289534	−	0.806083i
$113$	43926.9	+	25361.2i	0.323619	+	0.186842i	0.653005	−	0.757354i	$-0.273508\pi$
$113$	43926.9	+	25361.2i	0.323619	+	0.186842i	−0.329385	+	0.944196i	$0.606842\pi$
$114$	66523.5	+	34192.7i	0.479417	+	0.246417i
$115$	−52170.4	−	30120.6i	−0.367857	−	0.212382i
$116$	−2199.33	+	1269.78i	−0.0151756	+	0.00876162i
$117$	−223328.	−	101333.i	−1.50827	−	0.684363i
$118$		−	48334.6i		−	0.319561i
$119$	1072.88	−	1267.68i	0.00694520	−	0.00820622i
$120$	−59060.7	−	91654.4i	−0.374408	−	0.581032i
$121$	93194.7	+	161418.i	0.578666	+	1.00228i
$122$	−178533.			−1.08597
$123$	−7203.16	−	3702.38i	−0.0429299	−	0.0220657i
$124$			20723.5i			0.121035i
$125$	−179926.			−1.02996
$126$	−150447.	+	71282.6i	−0.844222	+	0.399997i
$127$	296331.			1.63030			0.815149	−	0.579251i	$-0.196655\pi$
$127$	296331.			1.63030			0.815149	+	0.579251i	$0.196655\pi$
$128$			142347.i			0.767936i
$129$	229213.	−	147701.i	1.21273	−	0.781466i
$130$	−195689.			−1.01557
$131$	−169953.	−	294368.i	−0.865270	−	1.49869i	−0.866779	−	0.498693i	$-0.833814\pi$
$131$	−169953.	−	294368.i	−0.865270	−	1.49869i	0.00150870	−	0.999999i	$-0.499520\pi$
$132$	−17109.9	+	33288.1i	−0.0854697	+	0.166285i
$133$	−20930.4	+	115834.i	−0.102600	+	0.567817i
$134$			245716.i			1.18215i
$135$	−108937.	+	86315.7i	−0.514447	+	0.407620i
$136$	−2114.88	+	1221.03i	−0.00980480	+	0.00566081i
$137$	−292099.	−	168644.i	−1.32962	−	0.767659i	−0.344383	−	0.938829i	$-0.611912\pi$
$137$	−292099.	−	168644.i	−1.32962	−	0.767659i	−0.985241	+	0.171170i	$0.945245\pi$
$138$	113690.	−	73260.4i	0.508190	−	0.327470i
$139$	320227.	+	184883.i	1.40579	+	0.811634i	0.994979	−	0.100085i	$-0.0319116\pi$
$139$	320227.	+	184883.i	1.40579	+	0.811634i	0.410813	+	0.911720i	$0.365245\pi$
$140$	12517.4	−	14790.1i	0.0539750	−	0.0637750i
$141$	9145.48	+	187185.i	0.0387399	+	0.792911i
$142$	−421372.			−1.75366
$143$	297440.	+	515181.i	1.21635	+	2.10678i
$144$	212111.	−	20776.1i	0.852425	−	0.0834947i
$145$	19811.0	+	11437.9i	0.0782503	+	0.0451778i
$146$	−67515.7	−	116941.i	−0.262134	−	0.454029i
$147$	−176368.	−	193742.i	−0.673172	−	0.739486i
$148$	−22861.8	+	39597.8i	−0.0857938	+	0.148599i
$149$	−135845.	+	78430.2i	−0.501277	+	0.289413i	−0.729241	−	0.684257i	$-0.760127\pi$
$149$	−135845.	+	78430.2i	−0.501277	+	0.289413i	0.227963	+	0.973670i	$0.426793\pi$
$150$	66984.0	−	130321.i	0.243077	−	0.472918i
$151$	151483.	−	262376.i	0.540655	−	0.936442i	−0.458211	−	0.888843i	$-0.651510\pi$
$151$	151483.	−	262376.i	0.540655	−	0.936442i	0.998867	−	0.0475990i	$-0.0151570\pi$
$152$	86543.6	−	149898.i	0.303827	−	0.526243i
$153$	1811.84	+	2531.29i	0.00625736	+	0.00874204i
$154$	397391.	+	71805.4i	1.35026	+	0.243981i
$155$	161663.	−	93336.2i	0.540482	−	0.312047i
$156$	−29295.2	+	56995.2i	−0.0963794	+	0.187511i
$157$		−	201640.i		−	0.652872i	−0.945219	−	0.326436i	$-0.894152\pi$
$157$		−	201640.i		−	0.652872i	0.945219	−	0.326436i	$-0.105848\pi$
$158$		−	2154.61i		−	0.00686635i
$159$	−282824.	−	438906.i	−0.887205	−	1.37682i
$160$	−46562.6	+	26882.9i	−0.143793	+	0.0830188i
$161$	162471.	+	137505.i	0.493982	+	0.418074i
$162$	−60549.1	−	306118.i	−0.181268	−	0.916433i
$163$	5251.78	−	9096.35i	0.0154824	−	0.0268163i	−0.858180	−	0.513348i	$-0.828405\pi$
$163$	5251.78	−	9096.35i	0.0154824	−	0.0268163i	0.873663	+	0.486532i	$0.161738\pi$
$164$	−1058.15	+	1832.77i	−0.00307212	+	0.00532107i
$165$	336739.	−	16452.4i	0.962905	−	0.0470455i
$166$	83170.8	−	48018.7i	0.234261	−	0.135251i
$167$	−347843.	+	602482.i	−0.965144	+	1.67168i	−0.255915	+	0.966699i	$0.582377\pi$
$167$	−347843.	+	602482.i	−0.965144	+	1.67168i	−0.709228	+	0.704979i	$0.750957\pi$
$168$	147769.	+	355785.i	0.403935	+	0.972555i
$169$	323624.	+	560533.i	0.871613	+	1.50968i
$170$	2151.13	+	1241.96i	0.00570881	+	0.00329598i
$171$	−200920.	−	91165.6i	−0.525452	−	0.238419i
$172$	−35626.4	−	61706.7i	−0.0918228	−	0.159042i
$173$	212731.			0.540400			0.270200	−	0.962804i	$-0.412910\pi$
$173$	212731.			0.540400			0.270200	+	0.962804i	$0.412910\pi$
$174$	−43172.4	+	27819.7i	−0.108102	+	0.0696592i
$175$	226922.	+	41002.9i	0.560119	+	0.101209i
$176$	−447714.	−	258488.i	−1.08948	−	0.629011i
$177$	6957.76	+	142408.i	0.0166931	+	0.341666i
$178$	152195.	+	87869.8i	0.360039	+	0.207869i
$179$	−498070.	+	287561.i	−1.16187	+	0.670807i	−0.951752	−	0.306869i	$-0.900719\pi$
$179$	−498070.	+	287561.i	−1.16187	+	0.670807i	−0.210120	+	0.977676i	$0.567385\pi$
$180$	21138.8	+	29532.6i	0.0486294	+	0.0679392i
$181$		−	486203.i		−	1.10312i	−0.834136	−	0.551558i	$-0.814033\pi$
$181$		−	486203.i		−	1.10312i	0.834136	−	0.551558i	$-0.185967\pi$
$182$	680404.	+	122944.i	1.52261	+	0.275124i
$183$	526010.	−	25699.7i	1.16109	−	0.0567284i
$184$	−156492.	−	271052.i	−0.340758	−	0.590211i
$185$	411866.			0.884763
$186$	20452.3	+	418607.i	0.0433470	+	0.887206i
$187$		−	7550.92i		−	0.0157905i
$188$	48971.0			0.101052
$189$	432999.	−	231676.i	0.881724	−	0.471766i
$190$	−176054.			−0.353804
$191$		−	518523.i		−	1.02845i	−0.857654	−	0.514227i	$-0.828079\pi$
$191$		−	518523.i		−	1.02845i	0.857654	−	0.514227i	$-0.171921\pi$
$192$	−27240.8	−	557552.i	−0.0533294	−	1.09152i
$193$	326832.			0.631585			0.315792	−	0.948828i	$-0.397730\pi$
$193$	326832.			0.631585			0.315792	+	0.948828i	$0.397730\pi$
$194$	−92792.8	−	160722.i	−0.177015	−	0.306599i
$195$	576557.	−	28169.4i	1.08582	−	0.0530506i
$196$	−52814.5	+	43560.5i	−0.0982003	+	0.0809940i
$197$		−	314024.i		−	0.576497i	−0.957556	−	0.288249i	$-0.906927\pi$
$197$		−	314024.i		−	0.576497i	0.957556	−	0.288249i	$-0.0930730\pi$
$198$	−312760.	+	689293.i	−0.566955	+	1.24951i
$199$	−547781.	+	316261.i	−0.980560	+	0.566127i	−0.902439	−	0.430817i	$-0.858225\pi$
$199$	−547781.	+	316261.i	−0.980560	+	0.566127i	−0.0781209	+	0.996944i	$0.524892\pi$
$200$	−293653.	−	169540.i	−0.519109	−	0.299708i
$201$	−35370.8	−	723953.i	−0.0617525	−	1.26392i
$202$	−570413.	−	329328.i	−0.983583	−	0.567872i
$203$	−61696.2	−	52215.6i	−0.105080	−	0.0889324i
$204$	683.756	−	440.602i	0.00115034	−	0.000741261i
$205$	19063.1			0.0316818
$206$	170033.	+	294506.i	0.279168	+	0.483533i
$207$	−324420.	+	232212.i	−0.526237	+	0.376669i
$208$	−766566.	−	442577.i	−1.22854	−	0.709301i
$209$	267596.	+	463489.i	0.423754	+	0.733963i
$210$	238249.	−	311107.i	0.372806	−	0.486813i
$211$	1890.07	−	3273.70i	0.00292262	−	0.00506212i	−0.864560	−	0.502529i	$-0.832403\pi$
$211$	1890.07	−	3273.70i	0.00292262	−	0.00506212i	0.867483	+	0.497467i	$0.165736\pi$
$212$	−118158.	+	68218.8i	−0.180561	+	0.104247i
$213$	1.24148e6	−	60656.3i	1.87496	−	0.0916066i
$214$	29909.0	−	51803.8i	0.0446444	−	0.0773264i
$215$	−320913.	+	555838.i	−0.473469	+	0.820072i
$216$	−714383.	+	105381.i	−1.04183	+	0.153684i
$217$	−620736.	+	222960.i	−0.894866	+	0.321424i
$218$	422461.	−	243908.i	0.602067	−	0.347604i
$219$	215755.	+	334823.i	0.303984	+	0.471742i
$220$		−	88096.8i		−	0.122717i
$221$		−	12928.5i		−	0.0178061i
$222$	−422720.	+	822422.i	−0.575665	+	1.11999i
$223$	290744.	−	167861.i	0.391516	−	0.226042i	−0.291301	−	0.956631i	$-0.594088\pi$
$223$	290744.	−	167861.i	0.391516	−	0.226042i	0.682817	+	0.730590i	$0.260755\pi$
$224$	178786.	−	64217.6i	0.238075	−	0.0855134i
$225$	−178595.	+	393606.i	−0.235187	+	0.518328i
$226$	134023.	−	232134.i	0.174545	−	0.302321i
$227$	−22883.9	+	39636.1i	−0.0294758	+	0.0510536i	−0.880387	−	0.474256i	$-0.842717\pi$
$227$	−22883.9	+	39636.1i	−0.0294758	+	0.0510536i	0.850911	+	0.525310i	$0.176050\pi$
$228$	−26355.8	+	51276.4i	−0.0335767	+	0.0653252i
$229$	291890.	−	168523.i	0.367816	−	0.212359i	−0.304688	−	0.952452i	$-0.598552\pi$
$229$	291890.	−	168523.i	0.367816	−	0.212359i	0.672504	+	0.740094i	$0.265219\pi$
$230$	−159174.	+	275698.i	−0.198405	+	0.343648i
$231$	−1.18117e6	−	154355.i	−1.45640	−	0.190323i
$232$	59425.6	+	102928.i	0.0724859	+	0.125549i
$233$	−355275.	−	205118.i	−0.428721	−	0.247522i	0.270081	−	0.962838i	$-0.412950\pi$
$233$	−355275.	−	205118.i	−0.428721	−	0.247522i	−0.698802	+	0.715315i	$0.746283\pi$
$234$	−535502.	+	1.18019e6i	−0.639324	+	1.40901i
$235$	−220559.	−	382019.i	−0.260528	−	0.451248i
$236$	37256.4			0.0435433
$237$	310.155	+	6348.11i	0.000358681	+	0.00734131i
$238$	−6699.15	−	5669.72i	−0.00766615	−	0.00648813i
$239$	−1.09671e6	−	633183.i	−1.24192	−	0.717026i	−0.272439	−	0.962173i	$-0.587830\pi$
$239$	−1.09671e6	−	633183.i	−1.24192	−	0.717026i	−0.969486	+	0.245148i	$0.921164\pi$
$240$	−421684.	+	271727.i	−0.472562	+	0.304512i
$241$	−962034.	−	555431.i	−1.06696	−	0.616009i	−0.139610	−	0.990207i	$-0.544585\pi$
$241$	−962034.	−	555431.i	−1.06696	−	0.616009i	−0.927349	+	0.374197i	$0.877918\pi$
$242$	853024.	−	492493.i	0.936316	−	0.540583i
$243$	222461.	+	893196.i	0.241679	+	0.970356i
$244$		−	137613.i		−	0.147974i
$245$	577682.	+	215811.i	0.614857	+	0.229699i
$246$	−19565.5	+	38065.6i	−0.0206135	+	0.0401047i
$247$	458171.	+	793576.i	0.477843	+	0.827649i
$248$	969857.			1.00133
$249$	−238133.	+	153449.i	−0.243401	+	0.156844i
$250$			950830.i			0.962172i
$251$	241428.			0.241882			0.120941	−	0.992660i	$-0.461409\pi$
$251$	241428.			0.241882			0.120941	+	0.992660i	$0.461409\pi$
$252$	−54944.7	−	115965.i	−0.0545035	−	0.115033i
$253$	967755.			0.950526
$254$		−	1.56598e6i		−	1.52301i
$255$	−6516.65	−	3349.52i	−0.00627587	−	0.00322576i
$256$	−393663.			−0.375427
$257$	3016.79	+	5225.23i	0.00284913	+	0.00493484i	0.867446	−	0.497531i	$-0.165760\pi$
$257$	3016.79	+	5225.23i	0.00284913	+	0.00493484i	−0.864597	+	0.502465i	$0.832426\pi$
$258$	−780538.	−	1.21129e6i	−0.730037	−	1.13292i
$259$	−1.43205e6	−	258759.i	−1.32650	−	0.239688i
$260$		−	150837.i		−	0.138381i
$261$	123194.	−	88179.5i	0.111941	−	0.0801247i
$262$	−1.55561e6	+	898130.i	−1.40006	+	0.808325i
$263$	−279458.	−	161345.i	−0.249130	−	0.143835i	0.370236	−	0.928938i	$-0.379277\pi$
$263$	−279458.	−	161345.i	−0.249130	−	0.143835i	−0.619366	+	0.785102i	$0.712610\pi$
$264$	1.55788e6	+	800739.i	1.37570	+	0.707100i
$265$	1.06434e6	+	614498.i	0.931035	+	0.537533i
$266$	612135.	+	110608.i	0.530448	+	0.0958477i
$267$	−461060.	−	236982.i	−0.395803	−	0.203440i
$268$	−189399.			−0.161079
$269$	−177714.	−	307809.i	−0.149741	−	0.259359i	0.781391	−	0.624042i	$-0.214511\pi$
$269$	−177714.	−	307809.i	−0.149741	−	0.259359i	−0.931132	+	0.364683i	$0.881177\pi$
$270$	456141.	+	575685.i	0.380794	+	0.480591i
$271$	−24063.0	−	13892.8i	−0.0199033	−	0.0114912i	0.490015	−	0.871714i	$-0.336991\pi$
$271$	−24063.0	−	13892.8i	−0.0199033	−	0.0114912i	−0.509919	+	0.860223i	$0.670325\pi$
$272$	5617.71	+	9730.16i	0.00460402	+	0.00797439i
$273$	−2.02237e6	−	264284.i	−1.64230	−	0.214617i
$274$	−891208.	+	1.54362e6i	−0.717138	+	1.24212i
$275$	907983.	−	524224.i	0.724013	−	0.418009i
$276$	56469.2	+	87632.8i	0.0446210	+	0.0692459i
$277$	93533.3	−	162004.i	0.0732431	−	0.126861i	−0.827078	−	0.562087i	$-0.809998\pi$
$277$	93533.3	−	162004.i	0.0732431	−	0.126861i	0.900321	+	0.435227i	$0.143332\pi$
$278$	977027.	−	1.69226e6i	0.758219	−	1.31327i
$279$	−120517.	−	1.23040e6i	−0.0926909	−	0.946312i
$280$	−692173.	−	585810.i	−0.527618	−	0.446541i
$281$	404858.	−	233745.i	0.305870	−	0.176594i	−0.339207	−	0.940712i	$-0.610159\pi$
$281$	404858.	−	233745.i	0.305870	−	0.176594i	0.645077	+	0.764118i	$0.276825\pi$
$282$	989194.	−	48329.9i	0.740728	−	0.0361904i
$283$		−	593731.i		−	0.440680i	−0.975423	−	0.220340i	$-0.929283\pi$
$283$		−	593731.i		−	0.440680i	0.975423	−	0.220340i	$-0.0707167\pi$
$284$		−	324794.i		−	0.238953i
$285$	518707.	−	25342.9i	0.378277	−	0.0184818i
$286$	2.72251e6	−	1.57184e6i	1.96813	−	1.13630i
$287$	−66281.9	−	11976.6i	−0.0474996	−	0.00858280i
$288$	34711.5	+	354382.i	0.0246600	+	0.251762i
$289$	709846.	−	1.22949e6i	0.499942	−	0.865925i
$290$	60444.2	−	104693.i	0.0422046	−	0.0731005i
$291$	296531.	+	460176.i	0.205276	+	0.318560i
$292$	90138.1	−	52041.2i	0.0618659	−	0.0357183i
$293$	−526576.	+	912056.i	−0.358337	+	0.620658i	−0.987683	−	0.156467i	$-0.949990\pi$
$293$	−526576.	+	912056.i	−0.358337	+	0.620658i	0.629346	+	0.777125i	$0.283323\pi$
$294$	−1.02384e6	+	932028.i	−0.690819	+	0.628870i
$295$	−167798.	−	290635.i	−0.112262	−	0.194443i
$296$	1.85317e6	+	1.06993e6i	1.22938	+	0.709782i
$297$	822260.	−	2.07588e6i	0.540902	−	1.36556i
$298$	414470.	+	717882.i	0.270366	+	0.468288i
$299$	1.65697e6			1.07186
$300$	100451.	+	51631.4i	0.0644396	+	0.0331216i
$301$	1.46502e6	−	1.73101e6i	0.932022	−	1.10125i
$302$	−1.38654e6	−	800520.i	−0.874813	−	0.505074i
$303$	1.72801e6	+	888187.i	1.08128	+	0.555773i
$304$	−689651.	−	398170.i	−0.428001	−	0.247107i
$305$	−1.07351e6	+	619792.i	−0.660781	+	0.381502i
$306$	13376.8	−	9574.79i	0.00816671	−	0.00584555i
$307$			2.67357e6i			1.61900i	0.587122	+	0.809499i	$0.300261\pi$
$307$			2.67357e6i			1.61900i	−0.587122	+	0.809499i	$0.699739\pi$
$308$	−55347.7	+	306310.i	−0.0332447	+	0.183986i
$309$	−543362.	−	843225.i	−0.323737	−	0.502397i
$310$	−493241.	−	854319.i	−0.291511	−	0.504912i
$311$	−1.93431e6			−1.13403			−0.567016	−	0.823707i	$-0.691902\pi$
$311$	−1.93431e6			−1.13403			−0.567016	+	0.823707i	$0.691902\pi$
$312$	2.66736e6	+	1.37101e6i	1.55130	+	0.797358i
$313$			2.27296e6i			1.31139i	0.755026	+	0.655695i	$0.227624\pi$
$313$			2.27296e6i			1.31139i	−0.755026	+	0.655695i	$0.772376\pi$
$314$	−1.06558e6			−0.609905
$315$	−657168.	+	950910.i	−0.373164	+	0.539962i
$316$	1660.78			0.000935607
$317$			343306.i			0.191882i	0.995387	+	0.0959408i	$0.0305860\pi$
$317$			343306.i			0.191882i	−0.995387	+	0.0959408i	$0.969414\pi$
$318$	−2.31943e6	+	1.49460e6i	−1.28621	+	0.828817i
$319$	−367492.			−0.202195
$320$	656958.	+	1.13789e6i	0.358643	+	0.621189i
$321$	−80663.4	+	156935.i	−0.0436932	+	0.0850073i
$322$	726654.	−	858589.i	0.390560	−	0.461473i
$323$		−	11631.3i		−	0.00620329i
$324$	235956.	−	46671.3i	0.124873	−	0.0246995i
$325$	1.55463e6	−	897566.i	0.816429	−	0.471366i
$326$	−48070.3	−	27753.4i	−0.0250514	−	0.0144635i
$327$	−1.20958e6	+	779437.i	−0.625556	+	0.403099i
$328$	85773.4	+	49521.3i	0.0440218	+	0.0254160i
$329$	526869.	+	1.46684e6i	0.268357	+	0.747123i
$330$	−86943.6	−	1.77952e6i	−0.0439494	−	0.899535i
$331$	−2.95768e6			−1.48382			−0.741910	−	0.670499i	$-0.766080\pi$
$331$	−2.95768e6			−1.48382			−0.741910	+	0.670499i	$0.766080\pi$
$332$	37012.9	+	64108.2i	0.0184292	+	0.0319204i
$333$	1.12707e6	−	2.48395e6i	0.556980	−	1.22753i
$334$	3.18385e6	+	1.83820e6i	1.56166	+	0.901626i
$335$	853027.	+	1.47749e6i	0.415289	+	0.719302i
$336$	1.63690e6	−	679858.i	0.790993	−	0.328526i
$337$	−763183.	+	1.32187e6i	−0.366061	+	0.634037i	−0.988946	−	0.148277i	$-0.952627\pi$
$337$	−763183.	+	1.32187e6i	−0.366061	+	0.634037i	0.622885	+	0.782314i	$0.285961\pi$
$338$	2.96217e6	−	1.71021e6i	1.41032	−	0.814251i
$339$	−361455.	+	703229.i	−0.170826	+	0.332351i
$340$	−957.303	+	1658.10i	−0.000449110	+	0.000777881i
$341$	−1.49942e6	+	2.59706e6i	−0.698290	+	1.20947i
$342$	−481771.	+	1.06177e6i	−0.222728	+	0.490871i
$343$	−1.87300e6	−	1.11330e6i	−0.859610	−	0.510950i
$344$	−2.88786e6	+	1.66731e6i	−1.31577	+	0.759661i
$345$	429287.	−	835200.i	0.194178	−	0.377783i
$346$		−	1.12419e6i		−	0.504835i
$347$			1.05767e6i			0.471549i	0.971808	+	0.235774i	$0.0757626\pi$
$347$			1.05767e6i			0.471549i	−0.971808	+	0.235774i	$0.924237\pi$
$348$	−21443.4	−	33277.4i	−0.00949175	−	0.0147299i
$349$	2.17863e6	−	1.25783e6i	0.957460	−	0.552790i	0.0620696	−	0.998072i	$-0.480230\pi$
$349$	2.17863e6	−	1.25783e6i	0.957460	−	0.552790i	0.895390	+	0.445282i	$0.146897\pi$
$350$	216683.	−	1.19918e6i	0.0945484	−	0.523257i
$351$	1.40786e6	−	3.55428e6i	0.609945	−	1.53987i
$352$	431866.	−	748013.i	0.185777	−	0.321775i
$353$	−1.21656e6	+	2.10715e6i	−0.519634	+	0.900032i	0.480106	+	0.877211i	$0.340598\pi$
$353$	−1.21656e6	+	2.10715e6i	−0.519634	+	0.900032i	−0.999740	+	0.0228217i	$0.992735\pi$
$354$	752565.	−	36768.7i	0.319180	−	0.0155945i
$355$	−2.53370e6	+	1.46283e6i	−1.06705	+	0.616060i
$356$	−67730.1	+	117312.i	−0.0283242	+	0.0490589i
$357$	20553.8	+	15740.3i	0.00853537	+	0.00653647i
$358$	1.51964e6	+	2.63209e6i	0.626660	+	1.08541i
$359$	−2.01017e6	−	1.16057e6i	−0.823183	−	0.475265i	0.0283298	−	0.999599i	$-0.490981\pi$
$359$	−2.01017e6	−	1.16057e6i	−0.823183	−	0.475265i	−0.851513	+	0.524334i	$0.824314\pi$
$360$	1.38212e6	−	989291.i	0.562069	−	0.402316i
$361$	−825850.	−	1.43041e6i	−0.333529	−	0.577688i
$362$	−2.56937e6			−1.03052
$363$	−2.44236e6	+	1.57382e6i	−0.972845	+	0.626887i
$364$	−94765.2	+	524457.i	−0.0374883	+	0.207470i
$365$	−811941.	−	468774.i	−0.319001	−	0.184175i
$366$	−135812.	−	2.77973e6i	−0.0529950	−	1.08468i
$367$	−299741.	−	173055.i	−0.116166	−	0.0670687i	0.440791	−	0.897610i	$-0.354698\pi$
$367$	−299741.	−	173055.i	−0.116166	−	0.0670687i	−0.556957	+	0.830541i	$0.688031\pi$
$368$	−1.24705e6	+	719987.i	−0.480027	+	0.277144i
$369$	52166.1	−	114969.i	0.0199445	−	0.0439556i
$370$		−	2.17653e6i		−	0.826535i
$371$	−3.31462e6	−	2.80527e6i	−1.25025	−	1.05813i
$372$	−322663.	+	15764.6i	−0.120890	+	0.00590645i
$373$	−863044.	−	1.49484e6i	−0.321189	−	0.556316i	0.659545	−	0.751665i	$-0.270749\pi$
$373$	−863044.	−	1.49484e6i	−0.321189	−	0.556316i	−0.980734	+	0.195350i	$0.937416\pi$
$374$	−39903.3			−0.0147513
$375$	−136872.	−	2.80142e6i	−0.0502615	−	1.02873i
$376$		−	2.29183e6i		−	0.836013i
$377$	−629212.			−0.228004
$378$	−1.22431e6	−	2.28821e6i	−0.440718	−	0.823696i
$379$	1.34667e6			0.481573			0.240787	−	0.970578i	$-0.422595\pi$
$379$	1.34667e6			0.481573			0.240787	+	0.970578i	$0.422595\pi$
$380$		−	135703.i		−	0.0482092i
$381$	225422.	+	4.61383e6i	0.0795580	+	1.62836i
$382$	−2.74017e6			−0.960770
$383$	47554.1	+	82366.0i	0.0165650	+	0.0286914i	0.874189	−	0.485586i	$-0.161394\pi$
$383$	47554.1	+	82366.0i	0.0165650	+	0.0286914i	−0.857624	+	0.514277i	$0.828060\pi$
$384$	−2.21633e6	+	108285.i	−0.767021	+	0.0374750i
$385$	2.63878e6	−	947815.i	0.907301	−	0.325891i
$386$		−	1.72717e6i		−	0.590019i
$387$	2.47406e6	+	3.45646e6i	0.839716	+	1.17315i
$388$	123885.	−	71524.8i	0.0417771	−	0.0241200i
$389$	−1.53608e6	−	886854.i	−0.514682	−	0.297152i	0.220074	−	0.975483i	$-0.429370\pi$
$389$	−1.53608e6	−	886854.i	−0.514682	−	0.297152i	−0.734756	+	0.678331i	$0.762703\pi$
$390$	−148863.	−	3.04686e6i	−0.0495593	−	1.01436i
$391$	−18214.4	−	10516.1i	−0.00602523	−	0.00347867i
$392$	2.03862e6	+	2.47171e6i	0.670072	+	0.812422i
$393$	4.45399e6	−	2.87008e6i	1.45468	−	0.937375i
$394$	−1.65948e6			−0.538557
$395$	−7479.92	−	12955.6i	−0.00241215	−	0.00417797i
$396$	−531308.	−	241076.i	−0.170258	−	0.0772532i
$397$	3.85284e6	+	2.22444e6i	1.22689	+	0.708344i	0.966378	−	0.257127i	$-0.0827758\pi$
$397$	3.85284e6	+	2.22444e6i	1.22689	+	0.708344i	0.260511	+	0.965471i	$0.416109\pi$
$398$	1.67130e6	+	2.89479e6i	0.528869	+	0.916028i
$399$	−1.81945e6	−	237767.i	−0.572147	−	0.0747685i
$400$	−780022.	+	1.35104e6i	−0.243757	+	0.422199i
$401$	4.10880e6	−	2.37222e6i	1.27601	−	0.736705i	0.299899	−	0.953971i	$-0.403047\pi$
$401$	4.10880e6	−	2.37222e6i	1.27601	−	0.736705i	0.976112	+	0.217266i	$0.0697138\pi$
$402$	−3.82578e6	+	186919.i	−1.18074	+	0.0576885i
$403$	−2.56727e6	+	4.44664e6i	−0.787424	+	1.36386i
$404$	253847.	−	439675.i	0.0773781	−	0.134023i
$405$	−1.42680e6	−	1.63048e6i	−0.432239	−	0.493943i
$406$	−275937.	+	326038.i	−0.0830796	+	0.0981641i
$407$	−5.73006e6	+	3.30825e6i	−1.71464	+	0.989948i
$408$	−20620.1	−	31999.6i	−0.00613253	−	0.00951688i
$409$			1.88826e6i			0.558154i	0.960269	+	0.279077i	$0.0900285\pi$
$409$			1.88826e6i			0.558154i	−0.960269	+	0.279077i	$0.909971\pi$
$410$		−	100740.i		−	0.0295967i
$411$	2.40356e6	−	4.67624e6i	0.701859	−	1.36550i
$412$	−227006.	+	131062.i	−0.0658861	+	0.0380393i
$413$	400834.	+	1.11595e6i	0.115635	+	0.321936i
$414$	1.22714e6	+	1.71442e6i	0.351880	+	0.491604i
$415$	333402.	−	577470.i	0.0950273	−	0.164592i
$416$	739431.	−	1.28073e6i	0.209490	−	0.362848i
$417$	−2.63501e6	+	5.12654e6i	−0.742065	+	1.44372i
$418$	2.44934e6	−	1.41413e6i	0.685659	−	0.395866i
$419$	−1.17116e6	+	2.02851e6i	−0.325898	+	0.564472i	−0.981694	−	0.190466i	$-0.939000\pi$
$419$	−1.17116e6	+	2.02851e6i	−0.325898	+	0.564472i	0.655795	+	0.754939i	$0.272333\pi$
$420$	239802.	+	183643.i	0.0663330	+	0.0507985i
$421$	1.71886e6	+	2.97716e6i	0.472646	+	0.818646i	0.999510	−	0.0313032i	$-0.00996573\pi$
$421$	1.71886e6	+	2.97716e6i	0.472646	+	0.818646i	−0.526864	+	0.849949i	$0.676632\pi$
$422$	−17300.1	−	9988.20i	−0.00472897	−	0.00273027i
$423$	−2.90750e6	+	284788.i	−0.790075	+	0.0773876i
$424$	3.19263e6	+	5.52979e6i	0.862449	+	1.49381i
$425$	−22785.9			−0.00611920
$426$	−320542.	−	6.56071e6i	−0.0855778	−	1.75157i
$427$	4.12196e6	−	1.48055e6i	1.09404	−	0.392965i
$428$	39930.5	+	23053.9i	0.0105365	+	0.00608323i
$429$	−7.79504e6	+	5.02301e6i	−2.04492	+	1.31771i
$430$	2.93736e6	+	1.69589e6i	0.766102	+	0.442309i
$431$	5.10986e6	−	2.95018e6i	1.32500	−	0.764988i	0.340477	−	0.940253i	$-0.389411\pi$
$431$	5.10986e6	−	2.95018e6i	1.32500	−	0.764988i	0.984521	+	0.175264i	$0.0560780\pi$
$432$	484837.	+	3.28673e6i	0.124993	+	0.847335i
$433$			5.26100e6i			1.34849i	0.738507	+	0.674246i	$0.235531\pi$
$433$			5.26100e6i			1.34849i	−0.738507	+	0.674246i	$0.764469\pi$
$434$	1.17825e6	+	3.28032e6i	0.300271	+	0.835973i
$435$	−163016.	+	317156.i	−0.0413054	+	0.0803618i
$436$	188005.	+	325633.i	0.0473644	+	0.0820375i
$437$	1.49071e6			0.373414
$438$	1.76939e6	−	1.14017e6i	0.440696	−	0.283978i
$439$		−	7.52561e6i		−	1.86372i	−0.362821	−	0.931859i	$-0.618186\pi$
$439$		−	7.52561e6i		−	1.86372i	0.362821	−	0.931859i	$-0.381814\pi$
$440$	−4.12291e6			−1.01525
$441$	2.88237e6	−	2.89341e6i	0.705754	−	0.708457i
$442$	−68321.6			−0.0166342
$443$			842692.i			0.204014i	0.994784	+	0.102007i	$0.0325264\pi$
$443$			842692.i			0.204014i	−0.994784	+	0.102007i	$0.967474\pi$
$444$	−633924.	−	325833.i	−0.152609	−	0.0784400i
$445$	1.22019e6			0.292098
$446$	−887075.	−	1.53646e6i	−0.211166	−	0.365749i
$447$	−1.32449e6	−	2.05543e6i	−0.313530	−	0.486557i
$448$	−1.56933e6	−	4.36913e6i	−0.369420	−	1.02849i
$449$		−	2.79946e6i		−	0.655328i	−0.944794	−	0.327664i	$-0.893739\pi$
$449$		−	2.79946e6i		−	0.655328i	0.944794	−	0.327664i	$-0.106261\pi$
$450$	2.08003e6	+	943797.i	0.484216	+	0.219709i
$451$	−265214.	+	153122.i	−0.0613982	+	0.0354483i
$452$	178930.	+	103305.i	0.0411942	+	0.0237835i
$453$	4.20039e6	+	2.15897e6i	0.961710	+	0.494313i
$454$	209460.	+	120932.i	0.0476936	+	0.0275359i
$455$	4.51806e6	−	1.62283e6i	1.02311	−	0.367489i
$456$	2.39973e6	+	1.23344e6i	0.540443	+	0.277784i
$457$	−804025.			−0.180086			−0.0900428	−	0.995938i	$-0.528700\pi$
$457$	−804025.			−0.180086			−0.0900428	+	0.995938i	$0.528700\pi$
$458$	−890570.	−	1.54251e6i	−0.198383	−	0.343609i
$459$	−38033.6	+	30135.7i	−0.00842627	+	0.00667652i
$460$	−212508.	−	122692.i	−0.0468254	−	0.0270346i
$461$	3.20919e6	+	5.55848e6i	0.703305	+	1.21816i	0.967300	+	0.253635i	$0.0816263\pi$
$461$	3.20919e6	+	5.55848e6i	0.703305	+	1.21816i	−0.263995	+	0.964524i	$0.585040\pi$
$462$	−815702.	+	6.24196e6i	−0.177798	+	1.36055i
$463$	2.79796e6	−	4.84621e6i	0.606582	−	1.05063i	−0.385217	−	0.922826i	$-0.625874\pi$
$463$	2.79796e6	−	4.84621e6i	0.606582	−	1.05063i	0.991799	−	0.127805i	$-0.0407931\pi$
$464$	473552.	−	273405.i	0.102111	−	0.0589539i
$465$	1.57621e6	+	2.44607e6i	0.338051	+	0.524610i
$466$	−1.08396e6	+	1.87747e6i	−0.231232	+	0.400506i
$467$	1.42965e6	−	2.47622e6i	0.303345	−	0.525408i	−0.673547	−	0.739145i	$-0.735230\pi$
$467$	1.42965e6	−	2.47622e6i	0.303345	−	0.525408i	0.976891	+	0.213736i	$0.0685633\pi$
$468$	−909694.	−	412765.i	−0.191991	−	0.0871141i
$469$	−2.03770e6	−	5.67309e6i	−0.427768	−	1.19093i
$470$	−2.01881e6	+	1.16556e6i	−0.421551	+	0.243383i
$471$	3.13951e6	−	153390.i	0.652094	−	0.0318599i
$472$		−	1.74359e6i		−	0.360238i
$473$		−	1.03107e7i		−	2.11903i
$474$	33547.0	−	1639.04i	0.00685817	−	0.000335076i
$475$	1.39864e6	−	807507.i	0.284428	−	0.164215i
$476$	4370.23	−	5163.72i	0.000884070	−	0.00104459i
$477$	6.61857e6	−	4.73743e6i	1.33189	−	0.953337i
$478$	−3.34610e6	+	5.79561e6i	−0.669837	+	1.16019i
$479$	4.82841e6	−	8.36305e6i	0.961536	−	1.66543i	0.242888	−	0.970054i	$-0.421905\pi$
$479$	4.82841e6	−	8.36305e6i	0.961536	−	1.66543i	0.718648	−	0.695374i	$-0.244761\pi$
$480$	−453985.	−	704524.i	−0.0899369	−	0.139570i
$481$	−9.81088e6	+	5.66432e6i	−1.93351	+	1.11631i
$482$	−2.93521e6	+	5.08393e6i	−0.575469	+	0.996741i
$483$	−2.01734e6	+	2.63426e6i	−0.393470	+	0.513796i
$484$	379615.	+	657512.i	0.0736596	+	0.127582i
$485$	−1.11592e6	−	644277.i	−0.215417	−	0.124371i
$486$	4.72016e6	−	1.17561e6i	0.906496	−	0.225773i
$487$	−300650.	−	520740.i	−0.0574432	−	0.0994945i	0.835874	−	0.548922i	$-0.184961\pi$
$487$	−300650.	−	520740.i	−0.0574432	−	0.0994945i	−0.893317	+	0.449427i	$0.851628\pi$
$488$	−6.44027e6			−1.22421
$489$	145624.	+	74849.9i	0.0275399	+	0.0141553i
$490$	1.14047e6	−	3.05280e6i	0.214582	−	0.574392i
$491$	2.74551e6	+	1.58512e6i	0.513948	+	0.296728i	0.734455	−	0.678657i	$-0.237438\pi$
$491$	2.74551e6	+	1.58512e6i	0.513948	+	0.296728i	−0.220507	+	0.975385i	$0.570771\pi$
$492$	−29341.0	−	15081.1i	−0.00546465	−	0.00280879i
$493$	6916.68	+	3993.35i	0.00128168	+	0.000739980i
$494$	4.19371e6	−	2.42124e6i	0.773180	−	0.446396i
$495$	512323.	+	5.23047e6i	0.0939789	+	0.959462i
$496$		−	4.46212e6i		−	0.814399i
$497$	9.72862e6	−	3.49439e6i	1.76669	−	0.634572i
$498$	810914.	+	1.25843e6i	0.146522	+	0.227382i
$499$	1.74702e6	+	3.02593e6i	0.314084	+	0.544010i	0.979242	−	0.202692i	$-0.0649691\pi$
$499$	1.74702e6	+	3.02593e6i	0.314084	+	0.544010i	−0.665158	+	0.746703i	$0.731636\pi$
$500$	−732901.			−0.131105
$501$	−9.64518e6	−	4.95756e6i	−1.71678	−	0.882416i
$502$		−	1.27584e6i		−	0.225963i
$503$	2.45238e6			0.432183			0.216092	−	0.976373i	$-0.430669\pi$
$503$	2.45238e6			0.432183			0.216092	+	0.976373i	$0.430669\pi$
$504$	−5.42712e6	+	2.57140e6i	−0.951684	+	0.450914i
$505$	−4.57317e6			−0.797974
$506$		−	5.11417e6i		−	0.887970i
$507$	−8.48125e6	+	5.46519e6i	−1.46534	+	0.944246i
$508$	1.20706e6			0.207524
$509$	336208.	+	582330.i	0.0575193	+	0.0996264i	0.893351	−	0.449359i	$-0.148348\pi$
$509$	336208.	+	582330.i	0.0575193	+	0.0996264i	−0.835832	+	0.548985i	$0.815014\pi$
$510$	−17700.8	+	34437.7i	−0.00301347	+	0.00586285i
$511$	2.52858e6	+	2.14002e6i	0.428375	+	0.362548i
$512$			6.63546e6i			1.11865i
$513$	1.26660e6	−	3.19765e6i	0.212493	−	0.536460i
$514$	27613.1	−	15942.4i	0.00461007	−	0.00266162i
$515$	2.04481e6	+	1.18057e6i	0.339731	+	0.196144i
$516$	933665.	−	601640.i	0.154371	−	0.0994746i
$517$	6.13702e6	+	3.54321e6i	1.00979	+	0.583002i
$518$	−1.36743e6	+	7.56774e6i	−0.223914	+	1.23920i
$519$	161827.	+	3.31220e6i	0.0263714	+	0.539756i
$520$	−7.05916e6			−1.14484
$521$	−1.98294e6	−	3.43456e6i	−0.320049	−	0.554341i	0.660449	−	0.750871i	$-0.270366\pi$
$521$	−1.98294e6	−	3.43456e6i	−0.320049	−	0.554341i	−0.980498	+	0.196530i	$0.937033\pi$
$522$	−465991.	−	651027.i	−0.0748516	−	0.104574i
$523$	−8.23532e6	−	4.75467e6i	−1.31652	−	0.760091i	−0.333350	−	0.942803i	$-0.608179\pi$
$523$	−8.23532e6	−	4.75467e6i	−1.31652	−	0.760091i	−0.983167	+	0.182712i	$0.941513\pi$
$524$	−692280.	−	1.19906e6i	−0.110142	−	0.190772i
$525$	−465789.	+	3.56433e6i	−0.0737549	+	0.564391i
$526$	−852638.	+	1.47681e6i	−0.134369	+	0.232735i
$527$	56442.0	−	32586.8i	0.00885270	−	0.00511111i
$528$	3.68404e6	−	7.16748e6i	0.575095	−	1.11888i
$529$	−1.87039e6	+	3.23960e6i	−0.290598	+	0.503330i
$530$	3.24735e6	−	5.62458e6i	0.502157	−	0.869762i
$531$	−2.21198e6	+	216663.i	−0.340444	+	0.0333463i
$532$	−85256.7	+	471834.i	−0.0130602	+	0.0722787i
$533$	−454094.	+	262171.i	−0.0692353	+	0.0399730i
$534$	−1.25235e6	+	2.43650e6i	−0.190051	+	0.369754i
$535$		−	415327.i		−	0.0627344i
$536$			8.86382e6i			1.33263i
$537$	−4.85618e6	−	7.53615e6i	−0.726706	−	1.12775i
$538$	−1.62664e6	+	939140.i	−0.242290	+	0.139886i
$539$	−9.77043e6	+	1.63768e6i	−1.44858	+	0.242805i
$540$	−443739.	+	351594.i	−0.0654852	+	0.0518869i
$541$	2.10781e6	−	3.65083e6i	0.309626	−	0.536289i	−0.668654	−	0.743573i	$-0.733129\pi$
$541$	2.10781e6	−	3.65083e6i	0.309626	−	0.536289i	0.978281	+	0.207285i	$0.0664627\pi$
$542$	−73417.2	+	127162.i	−0.0107349	+	0.0185935i
$543$	7.57013e6	−	369860.i	1.10180	−	0.0538317i
$544$	−16256.6	+	9385.73i	−0.00235522	+	0.00135979i
$545$	1.69350e6	−	2.93322e6i	0.244227	−	0.423013i
$546$	−1.39663e6	+	1.06873e7i	−0.200493	+	1.53422i
$547$	1.14882e6	+	1.98981e6i	0.164166	+	0.284344i	0.936359	−	0.351044i	$-0.114173\pi$
$547$	1.14882e6	+	1.98981e6i	0.164166	+	0.284344i	−0.772193	+	0.635388i	$0.780840\pi$
$548$	−1.18982e6	−	686944.i	−0.169251	−	0.0977170i
$549$	800283.	+	8.17036e6i	0.113322	+	1.15694i
$550$	−2.77030e6	−	4.79830e6i	−0.390499	−	0.676364i
$551$	−566078.			−0.0794324
$552$	4.10120e6	−	2.64275e6i	0.572879	−	0.369155i
$553$	17868.0	+	49745.6i	0.00248463	+	0.00691738i
$554$	−856123.	−	494283.i	−0.118512	−	0.0684228i
$555$	313311.	+	6.41271e6i	0.0431761	+	0.883709i
$556$	1.30440e6	+	753094.i	0.178946	+	0.103315i
$557$	6.67557e6	−	3.85414e6i	0.911696	−	0.526368i	0.0307199	−	0.999528i	$-0.490220\pi$
$557$	6.67557e6	−	3.85414e6i	0.911696	−	0.526368i	0.880977	+	0.473160i	$0.156887\pi$
$558$	−6.50211e6	+	636879.i	−0.884033	+	0.0865907i
$559$		−	1.76538e7i		−	2.38951i
$560$	−2.69520e6	+	3.18455e6i	−0.363179	+	0.429120i
$561$	117567.	−	5744.07i	0.0157717	−	0.000770571i
$562$	−1.23524e6	−	2.13950e6i	−0.164972	−	0.285740i
$563$	5.56745e6			0.740262			0.370131	−	0.928980i	$-0.379313\pi$
$563$	5.56745e6			0.740262			0.370131	+	0.928980i	$0.379313\pi$
$564$	37252.8	+	762472.i	0.00493129	+	0.100931i
$565$		−	1.86109e6i		−	0.245271i
$566$	−3.13761e6			−0.411678
$567$	3.93656e6	+	6.56551e6i	0.514232	+	0.857651i
$568$	−1.52003e7			−1.97688
$569$			1.10776e7i			1.43438i	0.696876	+	0.717192i	$0.254573\pi$
$569$			1.10776e7i			1.43438i	−0.696876	+	0.717192i	$0.745427\pi$
$570$	−133926.	−	2.74114e6i	−0.0172655	−	0.353382i
$571$	−5.72848e6			−0.735274			−0.367637	−	0.929969i	$-0.619833\pi$
$571$	−5.72848e6			−0.735274			−0.367637	+	0.929969i	$0.619833\pi$
$572$	1.21158e6	+	2.09851e6i	0.154832	+	0.268177i
$573$	8.07335e6	−	394447.i	1.02723	−	0.0501882i
$574$	−63291.2	+	350271.i	−0.00801795	+	0.0443736i
$575$		−	2.92033e6i		−	0.368352i
$576$	8.66029e6	−	848272.i	1.08762	−	0.106532i
$577$	−4.75244e6	+	2.74382e6i	−0.594261	+	0.343097i	−0.766780	−	0.641909i	$-0.778142\pi$
$577$	−4.75244e6	+	2.74382e6i	−0.594261	+	0.343097i	0.172520	+	0.985006i	$0.444809\pi$
$578$	−6.49732e6	−	3.75123e6i	−0.808937	−	0.467040i
$579$	248625.	+	5.08874e6i	0.0308211	+	0.630833i
$580$	80697.1	+	46590.5i	0.00996066	+	0.00575079i
$581$	−1.52203e6	+	1.79838e6i	−0.187061	+	0.221025i
$582$	2.43183e6	−	1.56704e6i	0.297595	−	0.191766i
$583$	−1.97434e7			−2.40575
$584$	−2.43552e6	−	4.21844e6i	−0.295501	−	0.511823i
$585$	877188.	+	8.95550e6i	0.105975	+	1.08193i
$586$	4.81982e6	+	2.78273e6i	0.579812	+	0.334754i
$587$	3.11452e6	+	5.39450e6i	0.373075	+	0.646184i	0.990037	−	0.140809i	$-0.0449702\pi$
$587$	3.11452e6	+	5.39450e6i	0.373075	+	0.646184i	−0.616962	+	0.786993i	$0.711637\pi$
$588$	−718409.	−	789178.i	−0.0856896	−	0.0941308i
$589$	−2.30967e6	+	4.00047e6i	−0.274323	+	0.475142i
$590$	−1.53588e6	+	886740.i	−0.181647	+	0.104874i
$591$	4.88932e6	−	238882.i	0.575811	−	0.0281329i
$592$	4.92252e6	−	8.52606e6i	0.577276	−	0.999872i
$593$	−6.47756e6	+	1.12195e7i	−0.756440	+	1.31019i	0.188215	+	0.982128i	$0.439730\pi$
$593$	−6.47756e6	+	1.12195e7i	−0.756440	+	1.31019i	−0.944655	+	0.328065i	$0.893603\pi$
$594$	−1.09701e7	−	4.34529e6i	−1.27569	−	0.505304i
$595$	−59964.8	−	10835.2i	−0.00694391	−	0.00125471i
$596$	−553345.	+	319474.i	−0.0638087	+	0.0368400i
$597$	−5.34086e6	−	8.28830e6i	−0.613303	−	0.951765i
$598$		−	8.75636e6i		−	1.00132i
$599$		−	2.19325e6i		−	0.249760i	−0.992172	−	0.124880i	$-0.960145\pi$
$599$		−	2.19325e6i		−	0.249760i	0.992172	−	0.124880i	$-0.0398545\pi$
$600$	2.41634e6	−	4.70111e6i	0.274018	−	0.533116i
$601$	1.39414e7	−	8.04904e6i	1.57441	−	0.908988i	0.578795	−	0.815473i	$-0.303523\pi$
$601$	1.39414e7	−	8.04904e6i	1.57441	−	0.908988i	0.995618	−	0.0935151i	$-0.0298103\pi$
$602$	−9.14766e6	−	7.74198e6i	−1.02877	−	0.870684i
$603$	1.12450e7	−	1.10144e6i	1.25940	−	0.123358i
$604$	617042.	−	1.06875e6i	0.0688212	−	0.119202i
$605$	3.41947e6	−	5.92270e6i	0.379814	−	0.657857i
$606$	4.69368e6	−	9.13179e6i	0.519197	−	1.01012i
$607$	−3.48748e6	+	2.01350e6i	−0.384184	+	0.221809i	−0.679637	−	0.733548i	$-0.737863\pi$
$607$	−3.48748e6	+	2.01350e6i	−0.384184	+	0.221809i	0.295453	+	0.955357i	$0.404529\pi$
$608$	665239.	−	1.15223e6i	0.0729824	−	0.126409i
$609$	766058.	−	1.00032e6i	0.0836986	−	0.109294i
$610$	3.27533e6	+	5.67305e6i	0.356395	+	0.617294i
$611$	1.05077e7	+	6.06661e6i	1.13868	+	0.657420i
$612$	7380.26	+	10310.8i	0.000796514	+	0.00111279i
$613$	4.47033e6	+	7.74283e6i	0.480494	+	0.832240i	0.999750	−	0.0223789i	$-0.00712401\pi$
$613$	4.47033e6	+	7.74283e6i	0.480494	+	0.832240i	−0.519255	+	0.854619i	$0.673791\pi$
$614$	1.41287e7			1.51245
$615$	14501.5	+	296811.i	0.00154606	+	0.0316440i
$616$	1.43352e7	+	2.59026e6i	1.52213	+	0.275037i
$617$	−1.27575e7	−	7.36557e6i	−1.34913	−	0.778921i	−0.361005	−	0.932564i	$-0.617566\pi$
$617$	−1.27575e7	−	7.36557e6i	−1.34913	−	0.778921i	−0.988126	+	0.153643i	$0.950900\pi$
$618$	−4.45608e6	+	2.87143e6i	−0.469334	+	0.302432i
$619$	1.23975e7	+	7.15771e6i	1.30049	+	0.750840i	0.980489	−	0.196576i	$-0.0629823\pi$
$619$	1.23975e7	+	7.15771e6i	1.30049	+	0.750840i	0.320004	+	0.947416i	$0.396316\pi$
$620$	658510.	−	380191.i	0.0687992	−	0.0397212i
$621$	−3.86231e6	−	4.87453e6i	−0.401900	−	0.507229i
$622$			1.02220e7i			1.05940i
$623$	−4.24257e6	−	766598.i	−0.437934	−	0.0791312i
$624$	6.30774e6	−	1.22720e7i	0.648503	−	1.26169i
$625$	521646.	+	903517.i	0.0534165	+	0.0925201i
$626$	1.20116e7			1.22509
$627$	−7.01291e6	+	4.51901e6i	−0.712409	+	0.459066i
$628$		−	821351.i		−	0.0831055i
$629$	143796.			0.0144918
$630$	5.02515e6	+	3.47285e6i	0.504426	+	0.348606i
$631$	1.20159e7			1.20138			0.600691	−	0.799481i	$-0.294892\pi$
$631$	1.20159e7			1.20138			0.600691	+	0.799481i	$0.294892\pi$
$632$		−	77724.0i		−	0.00774038i
$633$	52408.9	+	26937.8i	0.00519871	+	0.00267210i
$634$	1.81422e6			0.179254
$635$	−5.43644e6	−	9.41619e6i	−0.535032	−	0.926703i
$636$	−1.15204e6	−	1.78782e6i	−0.112934	−	0.175259i
$637$	−1.67287e7	+	2.80400e6i	−1.63348	+	0.273798i
$638$			1.94204e6i			0.188888i
$639$	1.88882e6	+	1.92836e7i	0.182995	+	1.86826i
$640$	4.52323e6	−	2.61149e6i	0.436514	−	0.252022i
$641$	734048.	+	423803.i	0.0705634	+	0.0407398i	0.534867	−	0.844937i	$-0.320362\pi$
$641$	734048.	+	423803.i	0.0705634	+	0.0407398i	−0.464303	+	0.885676i	$0.653695\pi$
$642$	829332.	+	426271.i	0.0794129	+	0.0408177i
$643$	−6.03301e6	−	3.48316e6i	−0.575449	−	0.332236i	0.183874	−	0.982950i	$-0.441136\pi$
$643$	−6.03301e6	−	3.48316e6i	−0.575449	−	0.332236i	−0.759323	+	0.650714i	$0.774470\pi$
$644$	661802.	+	560106.i	0.0628801	+	0.0532176i
$645$	−8.89846e6	−	4.57375e6i	−0.842201	−	0.432886i
$646$	−61466.4			−0.00579504
$647$	7.65112e6	+	1.32521e7i	0.718562	+	1.24459i	0.961570	+	0.274561i	$0.0885326\pi$
$647$	7.65112e6	+	1.32521e7i	0.718562	+	1.24459i	−0.243008	+	0.970024i	$0.578134\pi$
$648$	−2.18421e6	−	1.10427e7i	−0.204342	−	1.03309i
$649$	4.66896e6	+	2.69562e6i	0.435119	+	0.251216i
$650$	−4.74325e6	−	8.21554e6i	−0.440344	−	0.762699i
$651$	−3.94367e6	−	9.49518e6i	−0.364710	−	0.878114i
$652$	21392.4	−	37052.6i	0.00197079	−	0.00341350i
$653$	−6.31045e6	+	3.64334e6i	−0.579131	+	0.334362i	−0.760788	−	0.649000i	$-0.775187\pi$
$653$	−6.31045e6	+	3.64334e6i	−0.579131	+	0.334362i	0.181657	+	0.983362i	$0.441854\pi$
$654$	4.11899e6	+	6.39212e6i	0.376570	+	0.584387i
$655$	−6.23588e6	+	1.08009e7i	−0.567930	+	0.983683i
$656$	227838.	−	394627.i	0.0206712	−	0.0358036i
$657$	−5.04902e6	+	3.61398e6i	−0.456346	+	0.326642i
$658$	7.75160e6	−	2.78427e6i	0.697954	−	0.250696i
$659$	1.64378e7	−	9.49038e6i	1.47445	−	0.851275i	0.474866	−	0.880058i	$-0.342497\pi$
$659$	1.64378e7	−	9.49038e6i	1.47445	−	0.851275i	0.999586	+	0.0287830i	$0.00916317\pi$
$660$	1.37166e6	−	67016.2i	0.122570	−	0.00598853i
$661$		−	1.11614e7i		−	0.993611i	−0.867862	−	0.496806i	$-0.834506\pi$
$661$		−	1.11614e7i		−	0.993611i	0.867862	−	0.496806i	$-0.165494\pi$
$662$			1.56301e7i			1.38617i
$663$	201296.	−	9834.88i	0.0177849	−	0.000868931i
$664$	3.00025e6	−	1.73219e6i	0.264081	−	0.152467i
$665$	4.06473e6	−	1.46000e6i	0.356433	−	0.128026i
$666$	−1.31266e7	−	5.95607e6i	−1.14674	−	0.520324i
$667$	−511803.	+	886469.i	−0.0445439	+	0.0771523i
$668$	−1.41689e6	+	2.45412e6i	−0.122855	+	0.212792i
$669$	2.83475e6	+	4.39916e6i	0.244878	+	0.380019i
$670$	7.80787e6	−	4.50788e6i	0.671964	−	0.387958i
$671$	9.95677e6	−	1.72456e7i	0.853714	−	1.47868i
$672$	1.13587e6	+	2.73483e6i	0.0970295	+	0.233618i
$673$	−1.54841e6	−	2.68192e6i	−0.131780	−	0.228249i	0.792583	−	0.609764i	$-0.208736\pi$
$673$	−1.54841e6	−	2.68192e6i	−0.131780	−	0.228249i	−0.924363	+	0.381515i	$0.875402\pi$
$674$	6.98552e6	+	4.03309e6i	0.592310	+	0.341970i
$675$	−6.26425e6	−	2.48128e6i	−0.529188	−	0.209612i
$676$	1.31823e6	+	2.28325e6i	0.110950	+	0.192170i
$677$	−7.79557e6			−0.653697			−0.326848	−	0.945077i	$-0.605987\pi$
$677$	−7.79557e6			−0.653697			−0.326848	+	0.945077i	$0.605987\pi$
$678$	3.71626e6	+	1.91013e6i	0.310479	+	0.159584i
$679$	3.47525e6	+	2.94122e6i	0.289275	+	0.244824i
$680$	77598.6	+	44801.6i	0.00643549	+	0.00371553i
$681$	−634537.	−	326148.i	−0.0524312	−	0.0269493i
$682$	1.37244e7	+	7.92376e6i	1.12988	+	0.652335i
$683$	3.85289e6	−	2.22447e6i	0.316035	−	0.182463i	−0.333589	−	0.942719i	$-0.608260\pi$
$683$	3.85289e6	−	2.22447e6i	0.316035	−	0.182463i	0.649624	+	0.760256i	$0.274926\pi$
$684$	−818417.	−	371350.i	−0.0668859	−	0.0303489i
$685$			1.23756e7i			1.00772i
$686$	−5.88333e6	+	9.89798e6i	−0.477323	+	0.803038i
$687$	2.84592e6	+	4.41650e6i	0.230055	+	0.357015i
$688$	7.67095e6	+	1.32865e7i	0.617843	+	1.07014i
$689$	−3.38043e7			−2.71283
$690$	−4.41367e6	−	2.26860e6i	−0.352921	−	0.181399i
$691$		−	6.55423e6i		−	0.522188i	−0.965313	−	0.261094i	$-0.915917\pi$
$691$		−	6.55423e6i		−	0.522188i	0.965313	−	0.261094i	$-0.0840832\pi$
$692$	866528.			0.0687887
$693$	1.50477e6	−	1.85081e7i	0.119025	−	1.46395i
$694$	5.58933e6			0.440515
$695$		−	1.35674e7i		−	1.06545i
$696$	−1.55737e6	+	1.00355e6i	−0.121862	+	0.0785263i
$697$	6655.58			0.000518924
$698$	−6.64711e6	−	1.15131e7i	−0.516410	−	0.894448i
$699$	2.92340e6	−	5.68763e6i	0.226306	−	0.440289i
$700$	924331.	+	167019.i	0.0712989	+	0.0128831i
$701$			1.51493e7i			1.16439i	0.813051	+	0.582193i	$0.197805\pi$
$701$			1.51493e7i			1.16439i	−0.813051	+	0.582193i	$0.802195\pi$
$702$	−1.87828e7	−	7.43991e6i	−1.43853	−	0.569803i
$703$	−8.82649e6	+	5.09597e6i	−0.673596	+	0.388901i
$704$	−1.82798e7	−	1.05538e7i	−1.39008	−	0.802561i
$705$	5.78021e6	−	3.72468e6i	0.437997	−	0.282239i
$706$	1.11354e7	+	6.42900e6i	0.840800	+	0.485436i
$707$	1.59008e7	+	2.87314e6i	1.19638	+	0.216177i
$708$	28341.4	+	580078.i	0.00212490	+	0.0434914i
$709$	1.82749e7			1.36534			0.682669	−	0.730728i	$-0.260819\pi$
$709$	1.82749e7			1.36534			0.682669	+	0.730728i	$0.260819\pi$
$710$	7.73042e6	+	1.33895e7i	0.575516	+	0.996823i
$711$	−98603.4	+	9658.17i	−0.00731506	+	0.000716507i
$712$	5.49018e6	+	3.16976e6i	0.405870	+	0.234329i
$713$	4.17645e6	+	7.23382e6i	0.307669	+	0.532898i
$714$	83180.8	−	108618.i	0.00610629	−	0.00797364i
$715$	1.09136e7	−	1.89029e7i	0.798366	−	1.38281i
$716$	−2.02882e6	+	1.17134e6i	−0.147897	+	0.0853885i
$717$	9.02431e6	−	1.75572e7i	0.655566	−	1.27544i
$718$	−6.13312e6	+	1.06229e7i	−0.443987	+	0.769008i
$719$	−9.97884e6	+	1.72839e7i	−0.719876	+	1.24686i	0.241172	+	0.970482i	$0.422468\pi$
$719$	−9.97884e6	+	1.72839e7i	−0.719876	+	1.24686i	−0.961048	+	0.276380i	$0.910865\pi$
$720$	−4.55153e6	−	6.35886e6i	−0.327210	−	0.457139i
$721$	−6.36803e6	−	5.38948e6i	−0.456212	−	0.386108i
$722$	−7.55912e6	+	4.36426e6i	−0.539670	+	0.311578i
$723$	7.91616e6	−	1.54013e7i	0.563208	−	1.09575i
$724$		−	1.98048e6i		−	0.140418i
$725$			1.10896e6i			0.0783555i
$726$	8.31697e6	+	1.29068e7i	0.585630	+	0.908821i
$727$	−1.66750e7	+	9.62733e6i	−1.17012	+	0.675569i	−0.953708	−	0.300733i	$-0.902769\pi$
$727$	−1.66750e7	+	9.62733e6i	−1.17012	+	0.675569i	−0.216412	+	0.976302i	$0.569435\pi$
$728$	2.45445e7	+	4.43499e6i	1.71643	+	0.310145i
$729$	−1.37377e7	+	4.14316e6i	−0.957406	+	0.288744i
$730$	−2.47727e6	+	4.29075e6i	−0.172054	+	0.298007i
$731$	−112042.	+	194062.i	−0.00775507	+	0.0134322i
$732$	2.14262e6	−	104684.i	0.147798	−	0.00722109i
$733$	−1.54254e7	+	8.90587e6i	−1.06042	+	0.612232i	−0.925548	−	0.378631i	$-0.876395\pi$
$733$	−1.54254e7	+	8.90587e6i	−1.06042	+	0.612232i	−0.134870	+	0.990863i	$0.543062\pi$
$734$	−914523.	+	1.58400e6i	−0.0626548	+	0.108521i
$735$	−2.92071e6	+	9.15862e6i	−0.199420	+	0.625333i
$736$	−1.20291e6	−	2.08350e6i	−0.0818539	−	0.141775i
$737$	−2.37353e7	−	1.37036e7i	−1.60963	−	0.929322i
$738$	−607561.	−	275675.i	−0.0410628	−	0.0186319i
$739$	2.33023e6	+	4.03608e6i	0.156960	+	0.271862i	0.933771	−	0.357871i	$-0.116497\pi$
$739$	2.33023e6	+	4.03608e6i	0.156960	+	0.271862i	−0.776811	+	0.629734i	$0.783164\pi$
$740$	1.67768e6			0.112623
$741$	−1.20074e7	+	7.73736e6i	−0.803345	+	0.517663i
$742$	−1.48246e7	+	1.75163e7i	−0.988495	+	1.16797i
$743$	−8.87210e6	−	5.12231e6i	−0.589596	−	0.340403i	0.175342	−	0.984508i	$-0.443897\pi$
$743$	−8.87210e6	−	5.12231e6i	−0.589596	−	0.340403i	−0.764938	+	0.644104i	$0.777230\pi$
$744$	737782.	+	1.51006e7i	0.0488647	+	1.00014i
$745$	4.98439e6	+	2.87774e6i	0.329019	+	0.189959i
$746$	−7.89956e6	+	4.56081e6i	−0.519704	+	0.300051i
$747$	−2.57034e6	−	3.59098e6i	−0.168535	−	0.235457i
$748$		−	30757.5i		−	0.00201001i
$749$	−260933.	+	1.44408e6i	−0.0169952	+	0.0940559i
$750$	−1.48043e7	+	723307.i	−0.961026	+	0.0469537i
$751$	−1.24559e7	−	2.15742e7i	−0.805887	−	1.39584i	−0.915691	−	0.401883i	$-0.868356\pi$
$751$	−1.24559e7	−	2.15742e7i	−0.805887	−	1.39584i	0.109804	−	0.993953i	$-0.464978\pi$
$752$	−1.05443e7			−0.679942
$753$	183657.	+	3.75900e6i	0.0118038	+	0.241594i
$754$			3.32511e6i			0.212999i
$755$	−1.11163e7			−0.709730
$756$	1.76376e6	−	943698.i	0.112237	−	0.0600522i
$757$	1.13574e7			0.720342			0.360171	−	0.932886i	$-0.382718\pi$
$757$	1.13574e7			0.720342			0.360171	+	0.932886i	$0.382718\pi$
$758$		−	7.11655e6i		−	0.449880i
$759$	736182.	+	1.50678e7i	0.0463854	+	0.949394i
$760$	−6.35086e6			−0.398840
$761$	−6.57623e6	−	1.13904e7i	−0.411638	−	0.712978i	0.583431	−	0.812163i	$-0.301710\pi$
$761$	−6.57623e6	−	1.13904e7i	−0.411638	−	0.712978i	−0.995069	+	0.0991849i	$0.968376\pi$
$762$	2.43821e7	−	1.19126e6i	1.52119	−	0.0743222i
$763$	−7.73106e6	+	9.13476e6i	−0.480759	+	0.568049i
$764$		−	2.11213e6i		−	0.130914i
$765$	47194.3	−	104012.i	0.00291566	−	0.00642581i
$766$	435269.	−	251303.i	0.0268031	−	0.0154748i
$767$	7.99409e6	+	4.61539e6i	0.490660	+	0.283283i
$768$	−299464.	−	6.12929e6i	−0.0183207	−	0.374979i
$769$	−1.49490e7	−	8.63079e6i	−0.911582	−	0.526302i	−0.0306419	−	0.999530i	$-0.509755\pi$
$769$	−1.49490e7	−	8.63079e6i	−0.911582	−	0.526302i	−0.880940	+	0.473229i	$0.843088\pi$
$770$	−5.00879e6	−	1.39448e7i	−0.304443	−	0.847590i
$771$	−79061.3	+	50945.9i	−0.00478992	+	0.00308655i
$772$	1.33130e6			0.0803959
$773$	7.67220e6	+	1.32886e7i	0.461818	+	0.799893i	0.999052	−	0.0435409i	$-0.0138639\pi$
$773$	7.67220e6	+	1.32886e7i	0.461818	+	0.799893i	−0.537233	+	0.843434i	$0.680531\pi$
$774$	1.82659e7	−	1.30743e7i	1.09594	−	0.784453i
$775$	7.83700e6	+	4.52469e6i	0.468701	+	0.270604i
$776$	−3.34735e6	−	5.79778e6i	−0.199548	−	0.345627i
$777$	2.93948e6	−	2.24936e7i	0.174670	−	1.33662i
$778$	−4.68664e6	+	8.11750e6i	−0.277596	+	0.480810i
$779$	−408532.	+	235866.i	−0.0241203	+	0.0139258i
$780$	2.34852e6	−	114744.i	0.138216	−	0.00675294i
$781$	2.34999e7	−	4.07030e7i	1.37860	−	2.38781i
$782$	−55573.1	+	96255.4i	−0.00324973	+	0.00562870i
$783$	1.46666e6	+	1.85104e6i	0.0854919	+	0.107897i
$784$	1.13718e7	−	9.37930e6i	0.660755	−	0.544980i
$785$	−6.40731e6	+	3.69926e6i	−0.371109	+	0.214260i
$786$	−1.51672e7	−	2.35374e7i	−0.875685	−	1.35895i
$787$		−	950927.i		−	0.0547281i	−0.999626	−	0.0273641i	$-0.991289\pi$
$787$		−	950927.i		−	0.0547281i	0.999626	−	0.0273641i	$-0.00871134\pi$
$788$		−	1.27913e6i		−	0.0733837i
$789$	2.29954e6	−	4.47386e6i	0.131507	−	0.255853i
$790$	−68464.8	+	39528.2i	−0.00390301	+	0.00225340i
$791$	−1.16925e6	+	6.47095e6i	−0.0664456	+	0.367728i
$792$	−1.12823e7	+	2.48651e7i	−0.639124	+	1.40857i
$793$	1.70478e7	−	2.95276e7i	0.962686	−	1.66742i
$794$	1.17552e7	−	2.03606e7i	0.661727	−	1.14614i
$795$	−8.75800e6	+	1.70391e7i	−0.491459	+	0.956158i
$796$	−2.23130e6	+	1.28824e6i	−0.124818	+	0.0720635i
$797$	−1.17846e7	+	2.04116e7i	−0.657159	+	1.13823i	0.324189	+	0.945992i	$0.394909\pi$
$797$	−1.17846e7	+	2.04116e7i	−0.657159	+	1.13823i	−0.981348	+	0.192240i	$0.938425\pi$
$798$	−1.25649e6	+	9.61501e6i	−0.0698478	+	0.534493i
$799$	−77004.5	−	133376.i	−0.00426726	−	0.00739112i
$800$	−2.25723e6	−	1.30321e6i	−0.124696	−	0.0719931i
$801$	3.33904e6	−	7.35892e6i	0.183883	−	0.405259i
$802$	−1.25361e7	−	2.17132e7i	−0.688222	−	1.19203i
$803$	1.50614e7			0.824284
$804$	−144078.	−	2.94891e6i	−0.00786062	−	0.160887i
$805$	1.38868e6	−	7.68532e6i	0.0755286	−	0.417996i
$806$	2.34986e7	+	1.35669e7i	1.27410	+	0.735602i
$807$	4.65737e6	−	3.00114e6i	0.251742	−	0.162219i
$808$	−2.05767e7	−	1.18800e7i	−1.10879	−	0.640158i
$809$	−2.03260e7	+	1.17352e7i	−1.09190	+	0.630406i	−0.934080	−	0.357063i	$-0.883778\pi$
$809$	−2.03260e7	+	1.17352e7i	−1.09190	+	0.630406i	−0.157815	+	0.987469i	$0.550445\pi$
$810$	−8.61635e6	+	7.54000e6i	−0.461436	+	0.403793i
$811$			2.48215e7i			1.32519i	0.748980	+	0.662593i	$0.230544\pi$
$811$			2.48215e7i			1.32519i	−0.748980	+	0.662593i	$0.769456\pi$
$812$	−251310.	−	212693.i	−0.0133758	−	0.0113204i
$813$	198004.	−	385226.i	0.0105062	−	0.0204404i
$814$	1.74827e7	+	3.02809e7i	0.924798	+	1.60180i
$815$	−385394.			−0.0203241
$816$	−147224.	+	94868.9i	−0.00774022	+	0.00498768i
$817$		−	1.58825e7i		−	0.832460i
$818$	9.97865e6			0.521421
$819$	2.57643e6	−	3.16891e7i	0.134218	−	1.65082i
$820$	77650.8			0.00403284
$821$			2.48695e7i			1.28768i	0.765159	+	0.643842i	$0.222660\pi$
$821$			2.48695e7i			1.28768i	−0.765159	+	0.643842i	$0.777340\pi$
$822$	−2.47119e7	−	1.27018e7i	−1.27564	−	0.655668i
$823$	4.47940e6			0.230526			0.115263	−	0.993335i	$-0.463229\pi$
$823$	4.47940e6			0.230526			0.115263	+	0.993335i	$0.463229\pi$
$824$	6.13367e6	+	1.06238e7i	0.314704	+	0.545083i
$825$	8.85283e6	+	1.37384e7i	0.452842	+	0.702751i
$826$	5.89731e6	−	2.11824e6i	0.300749	−	0.108025i
$827$		−	8.78880e6i		−	0.446854i	−0.974721	−	0.223427i	$-0.928276\pi$
$827$		−	8.78880e6i		−	0.446854i	0.974721	−	0.223427i	$-0.0717245\pi$
$828$	−1.32148e6	+	945883.i	−0.0669859	+	0.0479470i
$829$	−2.43422e7	+	1.40540e7i	−1.23019	+	0.710253i	−0.967070	−	0.254509i	$-0.918086\pi$
$829$	−2.43422e7	+	1.40540e7i	−1.23019	+	0.710253i	−0.263124	+	0.964762i	$0.584753\pi$
$830$	−3.05168e6	−	1.76189e6i	−0.153760	−	0.0887734i
$831$	2.59354e6	+	1.33306e6i	0.130284	+	0.0669651i
$832$	−3.12982e7	−	1.80700e7i	−1.56751	−	0.905004i
$833$	201688.	+	75347.0i	0.0100709	+	0.00376230i
$834$	2.70915e7	+	1.39249e7i	1.34871	+	0.693228i
$835$	2.55259e7			1.26697
$836$	1.09001e6	+	1.88795e6i	0.0539405	+	0.0934277i
$837$	1.90654e7	−	2.81241e6i	0.940661	−	0.138760i
$838$	1.07198e7	+	6.18909e6i	0.527323	+	0.304450i
$839$	191045.	+	330899.i	0.00936979	+	0.0162290i	0.870672	−	0.491864i	$-0.163684\pi$
$839$	191045.	+	330899.i	0.00936979	+	0.0162290i	−0.861302	+	0.508093i	$0.830351\pi$
$840$	8.59445e6	−	1.12227e7i	0.420262	−	0.548781i
$841$	−1.00612e7	+	1.74266e7i	−0.490525	+	0.849614i
$842$	1.57330e7	−	9.08344e6i	0.764770	−	0.441540i
$843$	3.94736e6	+	6.12578e6i	0.191310	+	0.296888i
$844$	7698.92	−	13334.9i	0.000372026	−	0.000644369i
$845$	1.18743e7	−	2.05669e7i	0.572093	−	0.990894i
$846$	1.50498e6	+	1.53649e7i	0.0722946	+	0.738079i
$847$	−1.56104e7	+	1.84447e7i	−0.747662	+	0.883412i
$848$	2.54415e7	−	1.46886e7i	1.21493	−	0.701443i
$849$	9.24432e6	−	451658.i	0.440155	−	0.0215050i
$850$			120414.i			0.00571648i
$851$			1.84295e7i			0.872348i
$852$	5.05700e6	−	247074.i	0.238668	−	0.0116608i
$853$	−7.52482e6	+	4.34446e6i	−0.354098	+	0.204439i	−0.666489	−	0.745515i	$-0.732204\pi$
$853$	−7.52482e6	+	4.34446e6i	−0.354098	+	0.204439i	0.312391	+	0.949954i	$0.398870\pi$
$854$	−7.82408e6	−	2.17828e7i	−0.367104	−	1.02204i
$855$	789173.	+	8.05693e6i	0.0369196	+	0.376925i
$856$	1.07892e6	−	1.86874e6i	0.0503273	−	0.0871694i
$857$	−5.18178e6	+	8.97510e6i	−0.241005	+	0.417434i	−0.961001	−	0.276545i	$-0.910810\pi$
$857$	−5.18178e6	+	8.97510e6i	−0.241005	+	0.417434i	0.719996	+	0.693979i	$0.244144\pi$
$858$	2.65444e7	+	4.11934e7i	1.23099	+	1.91034i
$859$	−650888.	+	375790.i	−0.0300970	+	0.0173765i	−0.514973	−	0.857206i	$-0.672198\pi$
$859$	−650888.	+	375790.i	−0.0300970	+	0.0173765i	0.484876	+	0.874583i	$0.338865\pi$
$860$	−1.30719e6	+	2.26412e6i	−0.0602689	+	0.104389i
$861$	136053.	−	1.04111e6i	0.00625461	−	0.0478618i
$862$	−1.55904e7	−	2.70034e7i	−0.714643	−	1.23780i
$863$	1.93528e7	+	1.11734e7i	0.884539	+	0.510689i	0.872152	−	0.489234i	$-0.162724\pi$
$863$	1.93528e7	+	1.11734e7i	0.884539	+	0.510689i	0.0123868	+	0.999923i	$0.496057\pi$
$864$	−5.49128e6	+	810037.i	−0.250259	+	0.0369165i
$865$	−3.90273e6	−	6.75973e6i	−0.177349	−	0.307177i
$866$	2.78021e7			1.25975
$867$	1.96830e7	+	1.01169e7i	0.889291	+	0.457090i
$868$	−2.52848e6	+	908196.i	−0.113909	+	0.0409148i
$869$	208128.	+	120163.i	0.00934933	+	0.00539784i
$870$	1.67603e6	+	861469.i	0.0750730	+	0.0385871i
$871$	−4.06391e7	−	2.34630e7i	−1.81509	−	1.04795i
$872$	1.52396e7	−	8.79857e6i	0.678706	−	0.391851i
$873$	−6.93932e6	+	4.96701e6i	−0.308163	+	0.220577i
$874$		−	7.87778e6i		−	0.348839i
$875$	−7.88514e6	−	2.19527e7i	−0.348168	−	0.969323i
$876$	878845.	+	1.36385e6i	0.0386948	+	0.0600491i
$877$	8.76130e6	+	1.51750e7i	0.384653	+	0.666239i	0.991721	−	0.128411i	$-0.0409877\pi$
$877$	8.76130e6	+	1.51750e7i	0.384653	+	0.666239i	−0.607068	+	0.794650i	$0.707654\pi$
$878$	−3.97696e7			−1.74106
$879$	−1.46012e7	−	7.50491e6i	−0.637406	−	0.327622i
$880$			1.89687e7i			0.825717i
$881$	−4.70284e6			−0.204136			−0.102068	−	0.994777i	$-0.532546\pi$
$881$	−4.70284e6			−0.204136			−0.102068	+	0.994777i	$0.532546\pi$
$882$	−1.52904e7	−	1.52321e7i	−0.661832	−	0.659307i
$883$	6.86685e6			0.296385			0.148192	−	0.988959i	$-0.452655\pi$
$883$	6.86685e6			0.296385			0.148192	+	0.988959i	$0.452655\pi$
$884$		−	52662.4i		−	0.00226657i
$885$	4.39751e6	−	2.83369e6i	0.188733	−	0.121617i
$886$	4.45326e6			0.190587
$887$	1.58052e7	+	2.73755e7i	0.674515	+	1.16829i	0.976610	+	0.215017i	$0.0689805\pi$
$887$	1.58052e7	+	2.73755e7i	0.674515	+	1.16829i	−0.302095	+	0.953278i	$0.597686\pi$
$888$	−1.52489e7	+	2.96675e7i	−0.648943	+	1.26255i
$889$	1.29865e7	+	3.61553e7i	0.551109	+	1.53432i
$890$		−	6.44818e6i		−	0.272874i
$891$	3.29467e7	+	1.12234e7i	1.39033	+	0.473618i
$892$	1.18430e6	−	683758.i	0.0498369	−	0.0287734i
$893$	9.45336e6	+	5.45790e6i	0.396696	+	0.229032i
$894$	−1.08621e7	+	6.99934e6i	−0.454536	+	0.292896i
$895$	1.82750e7	+	1.05511e7i	0.762607	+	0.440292i
$896$	−1.73678e7	+	6.23829e6i	−0.722728	+	0.259594i
$897$	1.26048e6	+	2.57988e7i	0.0523062	+	1.07058i
$898$	−1.47939e7			−0.612200
$899$	−1.58595e6	−	2.74695e6i	−0.0654471	−	0.113358i
$900$	−727480.	+	1.60329e6i	−0.0299375	+	0.0659792i
$901$	371597.	+	214542.i	0.0152497	+	0.00880440i
$902$	809181.	+	1.40154e6i	0.0331153	+	0.0573575i
$903$	2.80661e7	+	2.14933e7i	1.14542	+	0.877171i
$904$	4.83466e6	−	8.37387e6i	0.196763	−	0.340804i
$905$	−1.54496e7	+	8.91981e6i	−0.627039	+	0.362021i
$906$	1.14092e7	−	2.21973e7i	0.461781	−	0.898419i
$907$	2.10805e7	−	3.65125e7i	0.850870	−	1.47375i	−0.0295547	−	0.999563i	$-0.509409\pi$
$907$	2.10805e7	−	3.65125e7i	0.850870	−	1.47375i	0.880424	−	0.474186i	$-0.157258\pi$
$908$	−93214.2	+	161452.i	−0.00375204	+	0.00649872i
$909$	−1.25144e7	+	2.75806e7i	−0.502345	+	1.10712i
$910$	−8.57595e6	−	2.38760e7i	−0.343304	−	0.955781i
$911$	4.02102e7	−	2.32153e7i	1.60524	−	0.926785i	0.614824	−	0.788664i	$-0.289227\pi$
$911$	4.02102e7	−	2.32153e7i	1.60524	−	0.926785i	0.990415	−	0.138121i	$-0.0441063\pi$
$912$	5.67484e6	−	1.10407e7i	0.225926	−	0.439550i
$913$			1.07120e7i			0.425299i
$914$			4.24892e6i			0.168234i
$915$	−1.04667e7	−	1.62430e7i	−0.413293	−	0.641376i
$916$	1.18897e6	−	686452.i	0.0468201	−	0.0270316i
$917$	2.84677e7	−	3.36365e7i	1.11797	−	1.32095i
$918$	159254.	+	200991.i	0.00623712	+	0.00787172i
$919$	5.23367e6	−	9.06498e6i	0.204417	−	0.354061i	−0.745530	−	0.666472i	$-0.767803\pi$
$919$	5.23367e6	−	9.06498e6i	0.204417	−	0.354061i	0.949947	+	0.312411i	$0.101137\pi$
$920$	−5.74195e6	+	9.94534e6i	−0.223661	+	0.387392i
$921$	−4.16272e7	+	2.03382e6i	−1.61707	+	0.0790065i
$922$	2.93742e7	−	1.69592e7i	1.13799	−	0.657019i
$923$	4.02360e7	−	6.96908e7i	1.55457	−	2.69260i
$924$	−4.81131e6	−	628744.i	−0.185389	−	0.0242267i
$925$	9.98310e6	+	1.72912e7i	0.383629	+	0.664464i
$926$	−2.56101e7	−	1.47860e7i	−0.981487	−	0.566662i
$927$	1.27156e7	−	9.10153e6i	0.486000	−	0.347868i
$928$	456789.	+	791183.i	0.0174119	+	0.0301583i
$929$	8.24331e6			0.313374			0.156687	−	0.987648i	$-0.449919\pi$
$929$	8.24331e6			0.313374			0.156687	+	0.987648i	$0.449919\pi$
$930$	1.29264e7	−	8.32960e6i	0.490085	−	0.315803i
$931$	−1.50502e7	+	2.52266e6i	−0.569073	+	0.0953859i
$932$	−1.44716e6	−	835518.i	−0.0545729	−	0.0315077i
$933$	−1.47145e6	−	3.01170e7i	−0.0553404	−	1.13268i
$934$	−1.30857e7	−	7.55506e6i	−0.490830	−	0.283381i
$935$	−239938.	+	138528.i	−0.00897572	+	0.00518213i
$936$	−1.93173e7	+	4.25735e7i	−0.720705	+	1.58836i
$937$		−	1.57581e7i		−	0.586348i	−0.956059	−	0.293174i	$-0.905288\pi$
$937$		−	1.57581e7i		−	0.586348i	0.956059	−	0.293174i	$-0.0947116\pi$
$938$	−2.99798e7	+	1.07684e7i	−1.11256	+	0.399616i
$939$	−3.53898e7	+	1.72907e6i	−1.30983	+	0.0639954i
$940$	−898414.	−	1.55610e6i	−0.0331632	−	0.0574404i
$941$	−1.30362e7			−0.479928			−0.239964	−	0.970782i	$-0.577136\pi$
$941$	−1.30362e7			−0.479928			−0.239964	+	0.970782i	$0.577136\pi$
$942$	−810600.	−	1.65910e7i	−0.0297632	−	0.609179i
$943$			853005.i			0.0312372i
$944$	−8.02193e6			−0.292987
$945$	−1.53055e7	−	9.50866e6i	−0.557529	−	0.346370i
$946$	−5.44878e7			−1.97957
$947$		−	3.58251e6i		−	0.129811i	−0.997891	−	0.0649056i	$-0.979325\pi$
$947$		−	3.58251e6i		−	0.129811i	0.997891	−	0.0649056i	$-0.0206746\pi$
$948$	1263.37	+	25858.1i	4.56573e−5	+	0.000934492i
$949$	2.57878e7			0.929500
$950$	−4.26732e6	−	7.39122e6i	−0.153407	−	0.265710i
$951$	−5.34524e6	+	261157.i	−0.191653	+	0.00936376i
$952$	−241661.	−	204526.i	−0.00864200	−	0.00731402i
$953$			2.00093e7i			0.713674i	0.934167	+	0.356837i	$0.116145\pi$
$953$			2.00093e7i			0.713674i	−0.934167	+	0.356837i	$0.883855\pi$
$954$	−2.50352e7	−	3.49763e7i	−0.890596	−	1.24424i
$955$	−1.64766e7	+	9.51276e6i	−0.584600	+	0.337519i
$956$	−4.46727e6	−	2.57918e6i	−0.158087	−	0.0912718i
$957$	−279555.	−	5.72181e6i	−0.00986706	−	0.201954i
$958$	−4.41951e7	−	2.55161e7i	−1.55582	−	0.898255i
$959$	7.77512e6	−	4.30297e7i	0.272999	−	1.51085i
$960$	−1.72170e7	+	1.10944e7i	−0.602947	+	0.388530i
$961$	2.74560e6			0.0959023
$962$	2.99335e7	+	5.18463e7i	1.04284	+	1.80626i
$963$	−2.50482e6	−	1.13654e6i	−0.0870383	−	0.0394928i
$964$	−3.91870e6	−	2.26246e6i	−0.135816	−	0.0784132i
$965$	−5.99602e6	−	1.03854e7i	−0.207274	−	0.359009i
$966$	1.39209e7	+	1.06608e7i	0.479982	+	0.367575i
$967$	1.27825e7	−	2.21400e7i	0.439593	−	0.761397i	−0.558065	−	0.829797i	$-0.688456\pi$
$967$	1.27825e7	−	2.21400e7i	0.439593	−	0.761397i	0.997658	+	0.0684003i	$0.0217895\pi$
$968$	3.07714e7	−	1.77659e7i	1.05550	−	0.609395i
$969$	181098.	−	8848.07i	0.00619590	−	0.000302719i
$970$	−3.40473e6	+	5.89716e6i	−0.116186	+	0.201240i
$971$	−1.59696e7	+	2.76602e7i	−0.543559	+	0.941471i	0.455138	+	0.890421i	$0.349590\pi$
$971$	−1.59696e7	+	2.76602e7i	−0.543559	+	0.941471i	−0.998696	+	0.0510499i	$0.983743\pi$
$972$	906162.	+	3.63830e6i	0.0307638	+	0.123519i
$973$	−8.52383e6	+	4.71733e7i	−0.288638	+	1.59740i
$974$	−2.75189e6	+	1.58880e6i	−0.0929466	+	0.0536627i
$975$	1.51576e7	+	2.35226e7i	0.510646	+	0.792454i
$976$			2.96304e7i			0.995665i
$977$			1.67121e7i			0.560138i	0.959980	+	0.280069i	$0.0903573\pi$
$977$			1.67121e7i			0.560138i	−0.959980	+	0.280069i	$0.909643\pi$
$978$	395549.	−	769561.i	0.0132237	−	0.0257274i
$979$	−1.69758e7	+	9.80099e6i	−0.566075	+	0.326824i
$980$	2.35310e6	+	879075.i	0.0782665	+	0.0292389i
$981$	−1.30559e7	−	1.82401e7i	−0.433146	−	0.605140i
$982$	8.37668e6	−	1.45088e7i	0.277200	−	0.480124i
$983$	2.21862e7	−	3.84277e7i	0.732318	−	1.26841i	−0.223572	−	0.974687i	$-0.571772\pi$
$983$	2.21862e7	−	3.84277e7i	0.732318	−	1.26841i	0.955890	−	0.293724i	$-0.0948947\pi$
$984$	−705792.	+	1.37315e6i	−0.0232375	+	0.0452097i
$985$	−9.97841e6	+	5.76104e6i	−0.327696	+	0.189195i
$986$	21103.1	−	36551.7i	0.000691281	−	0.00119733i
$987$	−2.24377e7	+	9.31912e6i	−0.733137	+	0.304496i
$988$	1.86629e6	+	3.23252e6i	0.0608258	+	0.105353i
$989$	−2.48717e7	−	1.43597e7i	−0.808565	−	0.466825i
$990$	2.76408e7	−	2.70740e6i	0.896319	−	0.0877940i
$991$	6.23182e6	+	1.07938e7i	0.201572	+	0.349134i	0.949035	−	0.315170i	$-0.102062\pi$
$991$	6.23182e6	+	1.07938e7i	0.201572	+	0.349134i	−0.747463	+	0.664304i	$0.768728\pi$
$992$	7.45505e6			0.240531
$993$	−2.24994e6	−	4.60507e7i	−0.0724099	−	1.48205i
$994$	−1.84663e7	−	5.14115e7i	−0.592809	−	1.65042i
$995$	2.00990e7	+	1.16042e7i	0.643602	+	0.371584i
$996$	−970000.	+	625054.i	−0.0309830	+	0.0199650i
$997$	5.22263e7	+	3.01529e7i	1.66399	+	0.960706i	0.970780	+	0.239973i	$0.0771387\pi$
$997$	5.22263e7	+	3.01529e7i	1.66399	+	0.960706i	0.693213	+	0.720733i	$0.256195\pi$
$998$	1.59907e7	−	9.23224e6i	0.508208	−	0.293414i
$999$	3.95321e7	+	1.56588e7i	1.25325	+	0.496414i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.6.i.a.5.12	✓	76
3.2	odd	2		189.6.i.a.152.27		76
7.3	odd	6		63.6.s.a.59.27	yes	76
9.2	odd	6		63.6.s.a.47.27	yes	76
9.7	even	3		189.6.s.a.89.12		76
21.17	even	6		189.6.s.a.17.12		76
63.38	even	6	inner	63.6.i.a.38.27	yes	76
63.52	odd	6		189.6.i.a.143.12		76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.6.i.a.5.12	✓	76	1.1	even	1	trivial
63.6.i.a.38.27	yes	76	63.38	even	6	inner
63.6.s.a.47.27	yes	76	9.2	odd	6
63.6.s.a.59.27	yes	76	7.3	odd	6
189.6.i.a.143.12		76	63.52	odd	6
189.6.i.a.152.27		76	3.2	odd	2
189.6.s.a.17.12		76	21.17	even	6
189.6.s.a.89.12		76	9.7	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	63.i (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-5.28457i q^{2} +(0.760712 + 15.5699i) q^{3} +4.07335 q^{4} +(-18.3459 - 31.7760i) q^{5} +(82.2801 - 4.02003i) q^{6} +(43.8244 + 122.010i) q^{7} -190.632i q^{8} +(-241.843 + 23.6884i) q^{9} +(-167.922 + 96.9499i) q^{10} +(510.471 + 294.720i) q^{11} +(3.09865 + 63.4216i) q^{12} +(874.017 + 504.614i) q^{13} +(644.770 - 231.593i) q^{14} +(480.792 - 309.815i) q^{15} -877.061 q^{16} +(-6.40516 - 11.0941i) q^{17} +(125.183 + 1278.03i) q^{18} +(786.320 + 453.982i) q^{19} +(-74.7291 - 129.435i) q^{20} +(-1866.34 + 775.155i) q^{21} +(1557.47 - 2697.62i) q^{22} +(1421.86 - 820.910i) q^{23} +(2968.12 - 145.016i) q^{24} +(889.359 - 1540.42i) q^{25} +(2666.67 - 4618.80i) q^{26} +(-552.798 - 3747.44i) q^{27} +(178.512 + 496.989i) q^{28} +(-539.931 + 311.729i) q^{29} +(-1637.24 - 2540.78i) q^{30} +5087.59i q^{31} -1465.34i q^{32} +(-4200.44 + 8172.17i) q^{33} +(-58.6273 + 33.8485i) q^{34} +(3072.99 - 3630.94i) q^{35} +(-985.110 + 96.4911i) q^{36} +(-5612.52 + 9721.18i) q^{37} +(2399.10 - 4155.36i) q^{38} +(-7191.90 + 13992.2i) q^{39} +(-6057.52 + 3497.31i) q^{40} +(-259.774 + 449.942i) q^{41} +(4096.36 + 9862.81i) q^{42} +(-8746.21 - 15148.9i) q^{43} +(2079.33 + 1200.50i) q^{44} +(5189.53 + 7250.20i) q^{45} +(-4338.15 - 7513.90i) q^{46} +12022.3 q^{47} +(-667.190 - 13655.7i) q^{48} +(-12965.8 + 10694.0i) q^{49} +(-8140.43 - 4699.88i) q^{50} +(167.861 - 108.167i) q^{51} +(3560.18 + 2055.47i) q^{52} +(-29007.7 + 16747.6i) q^{53} +(-19803.6 + 2921.30i) q^{54} -21627.6i q^{55} +(23259.0 - 8354.33i) q^{56} +(-6470.29 + 12588.3i) q^{57} +(1647.35 + 2853.30i) q^{58} +9146.38 q^{59} +(1958.44 - 1261.99i) q^{60} -33783.8i q^{61} +26885.7 q^{62} +(-13488.8 - 28469.1i) q^{63} -35809.6 q^{64} -37030.3i q^{65} +(43186.4 + 22197.5i) q^{66} -46497.0 q^{67} +(-26.0905 - 45.1900i) q^{68} +(13863.1 + 21513.7i) q^{69} +(-19187.9 - 16239.4i) q^{70} -79736.3i q^{71} +(4515.77 + 46103.0i) q^{72} +(22128.7 - 12776.0i) q^{73} +(51372.2 + 29659.8i) q^{74} +(24660.6 + 12675.4i) q^{75} +(3202.96 + 1849.23i) q^{76} +(-13587.8 + 75198.4i) q^{77} +(73942.8 + 38006.1i) q^{78} +407.717 q^{79} +(16090.4 + 27869.4i) q^{80} +(57926.7 - 11457.7i) q^{81} +(2377.75 + 1372.79i) q^{82} +(9086.59 + 15738.4i) q^{83} +(-7602.27 + 3157.48i) q^{84} +(-235.016 + 407.060i) q^{85} +(-80055.2 + 46219.9i) q^{86} +(-5264.32 - 8169.53i) q^{87} +(56183.1 - 97312.1i) q^{88} +(-16627.6 + 28799.9i) q^{89} +(38314.2 - 27424.4i) q^{90} +(-23264.7 + 128753. i) q^{91} +(5791.72 - 3343.85i) q^{92} +(-79213.2 + 3870.19i) q^{93} -63532.5i q^{94} -33314.8i q^{95} +(22815.2 - 1114.70i) q^{96} +(30413.4 - 17559.2i) q^{97} +(56513.3 + 68518.9i) q^{98} +(-130435. - 59183.7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q - 3 q^{3} - 1154 q^{4} - 3 q^{5} + 96 q^{6} - 30 q^{7} + 489 q^{9} - 6 q^{10} + 567 q^{11} - 1542 q^{12} + 543 q^{13} - 1638 q^{14} + 234 q^{15} + 16446 q^{16} - 801 q^{17} - 2022 q^{18} - 6 q^{19}+ \cdots - 144540 q^{99}+O(q^{100}) \) 76 * q - 3 * q^3 - 1154 * q^4 - 3 * q^5 + 96 * q^6 - 30 * q^7 + 489 * q^9 - 6 * q^10 + 567 * q^11 - 1542 * q^12 + 543 * q^13 - 1638 * q^14 + 234 * q^15 + 16446 * q^16 - 801 * q^17 - 2022 * q^18 - 6 * q^19 + 96 * q^20 - 4119 * q^21 + 62 * q^22 + 7806 * q^23 - 2346 * q^24 - 18749 * q^25 + 10128 * q^26 - 1539 * q^27 + 860 * q^28 + 17904 * q^29 + 11457 * q^30 - 3 * q^33 + 96 * q^34 + 3960 * q^35 - 57846 * q^36 + 2577 * q^37 + 14967 * q^38 - 16269 * q^39 + 9564 * q^40 + 28230 * q^41 + 15606 * q^42 - 9246 * q^43 - 69885 * q^44 - 23649 * q^45 - 9418 * q^46 - 56562 * q^47 + 48615 * q^48 + 7948 * q^49 - 67509 * q^50 - 103722 * q^51 - 40899 * q^52 + 25296 * q^53 + 176211 * q^54 + 104754 * q^56 + 33399 * q^57 - 4951 * q^58 - 59076 * q^59 + 33729 * q^60 + 79536 * q^62 - 95871 * q^63 - 198600 * q^64 + 114900 * q^66 + 1244 * q^67 + 191496 * q^68 + 3702 * q^69 - 127197 * q^70 + 183582 * q^72 - 6 * q^73 - 45681 * q^74 - 240486 * q^75 - 2880 * q^76 + 13854 * q^77 + 184431 * q^78 + 59984 * q^79 + 243225 * q^80 + 177117 * q^81 + 90 * q^82 - 246930 * q^83 + 56085 * q^84 + 11973 * q^85 + 291801 * q^86 + 205125 * q^87 - 34751 * q^88 - 6345 * q^89 - 269187 * q^90 - 120111 * q^91 - 463488 * q^92 + 200946 * q^93 - 382521 * q^96 - 104037 * q^97 - 646797 * q^98 - 144540 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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