LMFDB - Embedded newform 18.5.d.a.5.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [18,5,Mod(5,18)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(18, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("18.5");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 18 = 2 \cdot 3^{2} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	18.d (of order $6$, 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:	$1.86065933551$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.221456830464.4
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 38x^{6} - 100x^{5} + 449x^{4} - 736x^{3} + 1900x^{2} - 1548x + 2307 $ x^8 - 4x^7 + 38x^6 - 100x^5 + 449x^4 - 736x^3 + 1900x^2 - 1548*x + 2307
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			5.1
Root			$0.500000 - 1.74753i$ of defining polynomial
Character	$\chi$	$=$	18.5
Dual form			18.5.d.a.11.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.44949 + 1.41421i) q^{2} +(-7.80760 - 4.47676i) q^{3} +(4.00000 - 6.92820i) q^{4} +(-32.5033 - 18.7658i) q^{5} +(25.4557 - 0.0758456i) q^{6} +(-1.35458 - 2.34620i) q^{7} +22.6274i q^{8} +(40.9173 + 69.9055i) q^{9} +O(q^{10})$	\(q+(-2.44949 + 1.41421i) q^{2} +(-7.80760 - 4.47676i) q^{3} +(4.00000 - 6.92820i) q^{4} +(-32.5033 - 18.7658i) q^{5} +(25.4557 - 0.0758456i) q^{6} +(-1.35458 - 2.34620i) q^{7} +22.6274i q^{8} +(40.9173 + 69.9055i) q^{9} +106.155 q^{10} +(-91.4988 + 52.8268i) q^{11} +(-62.2463 + 36.1856i) q^{12} +(97.9281 - 169.616i) q^{13} +(6.63606 + 3.83133i) q^{14} +(169.763 + 292.025i) q^{15} +(-32.0000 - 55.4256i) q^{16} -448.150i q^{17} +(-199.088 - 113.367i) q^{18} -501.845 q^{19} +(-260.026 + 150.126i) q^{20} +(0.0726474 + 24.3823i) q^{21} +(149.417 - 258.798i) q^{22} +(343.254 + 198.178i) q^{23} +(101.297 - 176.666i) q^{24} +(391.808 + 678.631i) q^{25} +553.965i q^{26} +(-6.51608 - 728.971i) q^{27} -21.6733 q^{28} +(466.948 - 269.593i) q^{29} +(-828.817 - 475.231i) q^{30} +(-297.859 + 515.907i) q^{31} +(156.767 + 90.5097i) q^{32} +(950.879 - 2.83315i) q^{33} +(633.780 + 1097.74i) q^{34} +101.679i q^{35} +(647.988 - 3.86141i) q^{36} -1844.02 q^{37} +(1229.26 - 709.716i) q^{38} +(-1523.91 + 885.897i) q^{39} +(424.621 - 735.465i) q^{40} +(-145.474 - 83.9896i) q^{41} +(-34.6598 - 59.6215i) q^{42} +(-310.535 - 537.862i) q^{43} +845.229i q^{44} +(-18.1156 - 3040.00i) q^{45} -1121.06 q^{46} +(-651.961 + 376.410i) q^{47} +(1.71619 + 575.997i) q^{48} +(1196.83 - 2072.97i) q^{49} +(-1919.46 - 1108.20i) q^{50} +(-2006.26 + 3498.98i) q^{51} +(-783.425 - 1356.93i) q^{52} -913.826i q^{53} +(1046.88 + 1776.39i) q^{54} +3965.34 q^{55} +(53.0885 - 30.6506i) q^{56} +(3918.21 + 2246.64i) q^{57} +(-762.523 + 1320.73i) q^{58} +(1142.44 + 659.590i) q^{59} +(2702.26 - 8.05141i) q^{60} +(2064.42 + 3575.68i) q^{61} -1684.94i q^{62} +(108.587 - 190.693i) q^{63} -512.000 q^{64} +(-6365.96 + 3675.39i) q^{65} +(-2325.16 + 1351.69i) q^{66} +(3341.65 - 5787.91i) q^{67} +(-3104.88 - 1792.60i) q^{68} +(-1792.80 - 3083.96i) q^{69} +(-143.796 - 249.061i) q^{70} +2887.29i q^{71} +(-1581.78 + 925.853i) q^{72} +118.825 q^{73} +(4516.92 - 2607.84i) q^{74} +(-21.0130 - 7052.51i) q^{75} +(-2007.38 + 3476.88i) q^{76} +(247.885 + 143.116i) q^{77} +(2479.97 - 4325.14i) q^{78} +(-3918.75 - 6787.48i) q^{79} +2402.02i q^{80} +(-3212.55 + 5720.69i) q^{81} +475.117 q^{82} +(4404.19 - 2542.76i) q^{83} +(169.216 + 97.0260i) q^{84} +(-8409.88 + 14566.3i) q^{85} +(1521.30 + 878.325i) q^{86} +(-4852.65 + 14.4585i) q^{87} +(-1195.33 - 2070.38i) q^{88} -10285.1i q^{89} +(4343.58 + 7420.83i) q^{90} -530.605 q^{91} +(2746.03 - 1585.42i) q^{92} +(4635.15 - 2694.55i) q^{93} +(1064.65 - 1844.02i) q^{94} +(16311.6 + 9417.50i) q^{95} +(-818.787 - 1408.47i) q^{96} +(440.403 + 762.801i) q^{97} +6770.29i q^{98} +(-7436.77 - 4234.73i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 6 q^{3} + 32 q^{4} + 18 q^{5} + 48 q^{6} - 26 q^{7} - 78 q^{9}+O(q^{10}) $ 8 * q + 6 * q^3 + 32 * q^4 + 18 * q^5 + 48 * q^6 - 26 * q^7 - 78 * q^9	\( 8 q + 6 q^{3} + 32 q^{4} + 18 q^{5} + 48 q^{6} - 26 q^{7} - 78 q^{9} - 720 q^{11} - 144 q^{12} + 10 q^{13} + 288 q^{14} + 1134 q^{15} - 256 q^{16} - 384 q^{18} + 100 q^{19} + 144 q^{20} + 438 q^{21} + 336 q^{22} + 1278 q^{23} + 384 q^{24} + 794 q^{25} - 1296 q^{27} - 416 q^{28} - 1854 q^{29} - 3456 q^{30} - 1478 q^{31} - 3384 q^{33} - 96 q^{34} + 1056 q^{36} - 32 q^{37} + 6768 q^{38} + 5274 q^{39} - 36 q^{41} + 2592 q^{42} - 68 q^{43} + 3402 q^{45} + 2112 q^{46} + 2214 q^{47} - 1536 q^{48} + 2442 q^{49} - 15552 q^{50} - 12006 q^{51} - 80 q^{52} + 7056 q^{54} - 3996 q^{55} + 2304 q^{56} + 10902 q^{57} - 2400 q^{58} + 9108 q^{59} + 6480 q^{60} - 4478 q^{61} - 6654 q^{63} - 4096 q^{64} - 22554 q^{65} - 19872 q^{66} + 7504 q^{67} - 11088 q^{68} - 5994 q^{69} + 6048 q^{70} + 5376 q^{72} + 20716 q^{73} + 15264 q^{74} + 16590 q^{75} + 400 q^{76} + 34434 q^{77} + 24096 q^{78} - 6050 q^{79} - 21150 q^{81} + 1152 q^{82} - 3834 q^{83} - 9600 q^{84} - 16092 q^{85} - 12528 q^{86} + 10170 q^{87} - 2688 q^{88} + 2592 q^{90} - 45868 q^{91} + 10224 q^{92} - 10926 q^{93} + 672 q^{94} + 20880 q^{95} + 31336 q^{97} - 22338 q^{99}+O(q^{100}) \) 8 * q + 6 * q^3 + 32 * q^4 + 18 * q^5 + 48 * q^6 - 26 * q^7 - 78 * q^9 - 720 * q^11 - 144 * q^12 + 10 * q^13 + 288 * q^14 + 1134 * q^15 - 256 * q^16 - 384 * q^18 + 100 * q^19 + 144 * q^20 + 438 * q^21 + 336 * q^22 + 1278 * q^23 + 384 * q^24 + 794 * q^25 - 1296 * q^27 - 416 * q^28 - 1854 * q^29 - 3456 * q^30 - 1478 * q^31 - 3384 * q^33 - 96 * q^34 + 1056 * q^36 - 32 * q^37 + 6768 * q^38 + 5274 * q^39 - 36 * q^41 + 2592 * q^42 - 68 * q^43 + 3402 * q^45 + 2112 * q^46 + 2214 * q^47 - 1536 * q^48 + 2442 * q^49 - 15552 * q^50 - 12006 * q^51 - 80 * q^52 + 7056 * q^54 - 3996 * q^55 + 2304 * q^56 + 10902 * q^57 - 2400 * q^58 + 9108 * q^59 + 6480 * q^60 - 4478 * q^61 - 6654 * q^63 - 4096 * q^64 - 22554 * q^65 - 19872 * q^66 + 7504 * q^67 - 11088 * q^68 - 5994 * q^69 + 6048 * q^70 + 5376 * q^72 + 20716 * q^73 + 15264 * q^74 + 16590 * q^75 + 400 * q^76 + 34434 * q^77 + 24096 * q^78 - 6050 * q^79 - 21150 * q^81 + 1152 * q^82 - 3834 * q^83 - 9600 * q^84 - 16092 * q^85 - 12528 * q^86 + 10170 * q^87 - 2688 * q^88 + 2592 * q^90 - 45868 * q^91 + 10224 * q^92 - 10926 * q^93 + 672 * q^94 + 20880 * q^95 + 31336 * q^97 - 22338 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/18\mathbb{Z}\right)^\times$.

$n$	$11$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−2.44949	+	1.41421i	−0.612372	+	0.353553i
$2$	−2.44949	+	1.41421i	−0.612372	+	0.353553i
$3$	−7.80760	−	4.47676i	−0.867511	−	0.497417i
$3$	−7.80760	−	4.47676i	−0.867511	−	0.497417i
$4$	4.00000	−	6.92820i	0.250000	−	0.433013i
$5$	−32.5033	−	18.7658i	−1.30013	−	0.750630i	−0.319704	−	0.947518i	$-0.603583\pi$
$5$	−32.5033	−	18.7658i	−1.30013	−	0.750630i	−0.980426	+	0.196887i	$0.936917\pi$
$6$	25.4557	−	0.0758456i	0.707104	−	0.00210682i
$7$	−1.35458	−	2.34620i	−0.0276445	−	0.0478816i	0.851872	−	0.523750i	$-0.175467\pi$
$7$	−1.35458	−	2.34620i	−0.0276445	−	0.0478816i	−0.879517	+	0.475868i	$0.842134\pi$
$8$			22.6274i			0.353553i
$9$	40.9173	+	69.9055i	0.505152	+	0.863031i
$10$	106.155			1.06155
$11$	−91.4988	+	52.8268i	−0.756188	+	0.436585i	−0.827925	−	0.560838i	$-0.810479\pi$
$11$	−91.4988	+	52.8268i	−0.756188	+	0.436585i	0.0717373	+	0.997424i	$0.477146\pi$
$12$	−62.2463	+	36.1856i	−0.432266	+	0.251289i
$13$	97.9281	−	169.616i	0.579456	−	1.00365i	−0.416086	−	0.909325i	$-0.636598\pi$
$13$	97.9281	−	169.616i	0.579456	−	1.00365i	0.995542	−	0.0943219i	$-0.0300683\pi$
$14$	6.63606	+	3.83133i	0.0338574	+	0.0195476i
$15$	169.763	+	292.025i	0.754501	+	1.29789i
$16$	−32.0000	−	55.4256i	−0.125000	−	0.216506i
$17$		−	448.150i		−	1.55069i	−0.631536	−	0.775347i	$-0.717575\pi$
$17$		−	448.150i		−	1.55069i	0.631536	−	0.775347i	$-0.282425\pi$
$18$	−199.088	−	113.367i	−0.614468	−	0.349898i
$19$	−501.845			−1.39015			−0.695076	−	0.718936i	$-0.744629\pi$
$19$	−501.845			−1.39015			−0.695076	+	0.718936i	$0.744629\pi$
$20$	−260.026	+	150.126i	−0.650065	+	0.375315i
$21$	0.0726474	+	24.3823i	0.000164733	+	0.0552887i
$22$	149.417	−	258.798i	0.308713	−	0.534706i
$23$	343.254	+	198.178i	0.648874	+	0.374628i	0.788025	−	0.615644i	$-0.211104\pi$
$23$	343.254	+	198.178i	0.648874	+	0.374628i	−0.139151	+	0.990271i	$0.544437\pi$
$24$	101.297	−	176.666i	0.175864	−	0.306712i
$25$	391.808	+	678.631i	0.626892	+	1.08581i
$26$			553.965i			0.819475i
$27$	−6.51608	−	728.971i	−0.00893839	−	0.999960i
$28$	−21.6733			−0.0276445
$29$	466.948	−	269.593i	0.555230	−	0.320562i	−0.195999	−	0.980604i	$-0.562795\pi$
$29$	466.948	−	269.593i	0.555230	−	0.320562i	0.751229	+	0.660042i	$0.229462\pi$
$30$	−828.817	−	475.231i	−0.920908	−	0.528034i
$31$	−297.859	+	515.907i	−0.309947	+	0.536844i	−0.978350	−	0.206955i	$-0.933645\pi$
$31$	−297.859	+	515.907i	−0.309947	+	0.536844i	0.668404	+	0.743799i	$0.266978\pi$
$32$	156.767	+	90.5097i	0.153093	+	0.0883883i
$33$	950.879	−	2.83315i	0.873167	−	0.00260161i
$34$	633.780	+	1097.74i	0.548253	+	0.949602i
$35$			101.679i			0.0830032i
$36$	647.988	−	3.86141i	0.499991	−	0.00297948i
$37$	−1844.02			−1.34699			−0.673493	−	0.739194i	$-0.735207\pi$
$37$	−1844.02			−1.34699			−0.673493	+	0.739194i	$0.735207\pi$
$38$	1229.26	−	709.716i	0.851291	−	0.491493i
$39$	−1523.91	+	885.897i	−1.00192	+	0.582444i
$40$	424.621	−	735.465i	0.265388	−	0.459665i
$41$	−145.474	−	83.9896i	−0.0865403	−	0.0499641i	0.456105	−	0.889926i	$-0.349244\pi$
$41$	−145.474	−	83.9896i	−0.0865403	−	0.0499641i	−0.542646	+	0.839962i	$0.682577\pi$
$42$	−34.6598	−	59.6215i	−0.0196484	−	0.0337990i
$43$	−310.535	−	537.862i	−0.167947	−	0.290893i	0.769751	−	0.638345i	$-0.220381\pi$
$43$	−310.535	−	537.862i	−0.167947	−	0.290893i	−0.937698	+	0.347451i	$0.887047\pi$
$44$			845.229i			0.436585i
$45$	−18.1156	−	3040.00i	−0.00894597	−	1.50123i
$46$	−1121.06			−0.529803
$47$	−651.961	+	376.410i	−0.295138	+	0.170398i	−0.640257	−	0.768161i	$-0.721172\pi$
$47$	−651.961	+	376.410i	−0.295138	+	0.170398i	0.345118	+	0.938559i	$0.387839\pi$
$48$	1.71619	+	575.997i	0.000744874	+	0.249999i
$49$	1196.83	−	2072.97i	0.498472	−	0.863378i
$50$	−1919.46	−	1108.20i	−0.767783	−	0.443280i
$51$	−2006.26	+	3498.98i	−0.771342	+	1.34524i
$52$	−783.425	−	1356.93i	−0.289728	−	0.501824i
$53$		−	913.826i		−	0.325321i	−0.986682	−	0.162660i	$-0.947993\pi$
$53$		−	913.826i		−	0.325321i	0.986682	−	0.162660i	$-0.0520075\pi$
$54$	1046.88	+	1776.39i	0.359013	+	0.609188i
$55$	3965.34			1.31086
$56$	53.0885	−	30.6506i	0.0169287	−	0.00977380i
$57$	3918.21	+	2246.64i	1.20597	+	0.691486i
$58$	−762.523	+	1320.73i	−0.226672	+	0.392607i
$59$	1142.44	+	659.590i	0.328194	+	0.189483i	0.655039	−	0.755595i	$-0.272652\pi$
$59$	1142.44	+	659.590i	0.328194	+	0.189483i	−0.326845	+	0.945078i	$0.605986\pi$
$60$	2702.26	−	8.05141i	0.750627	−	0.00223650i
$61$	2064.42	+	3575.68i	0.554802	+	0.960946i	0.997919	+	0.0644817i	$0.0205394\pi$
$61$	2064.42	+	3575.68i	0.554802	+	0.960946i	−0.443117	+	0.896464i	$0.646127\pi$
$62$		−	1684.94i		−	0.438331i
$63$	108.587	−	190.693i	0.0273587	−	0.0480455i
$64$	−512.000			−0.125000
$65$	−6365.96	+	3675.39i	−1.50674	+	0.869915i
$66$	−2325.16	+	1351.69i	−0.533784	+	0.310304i
$67$	3341.65	−	5787.91i	0.744408	−	1.28935i	−0.206062	−	0.978539i	$-0.566065\pi$
$67$	3341.65	−	5787.91i	0.744408	−	1.28935i	0.950471	−	0.310814i	$-0.100602\pi$
$68$	−3104.88	−	1792.60i	−0.671470	−	0.387673i
$69$	−1792.80	−	3083.96i	−0.376559	−	0.647755i
$70$	−143.796	−	249.061i	−0.0293460	−	0.0508288i
$71$			2887.29i			0.572761i	0.958116	+	0.286380i	$0.0924521\pi$
$71$			2887.29i			0.572761i	−0.958116	+	0.286380i	$0.907548\pi$
$72$	−1581.78	+	925.853i	−0.305127	+	0.178598i
$73$	118.825			0.0222979			0.0111489	−	0.999938i	$-0.496451\pi$
$73$	118.825			0.0222979			0.0111489	+	0.999938i	$0.496451\pi$
$74$	4516.92	−	2607.84i	0.824857	−	0.476231i
$75$	−21.0130	−	7052.51i	−0.00373565	−	1.25378i
$76$	−2007.38	+	3476.88i	−0.347538	+	0.601954i
$77$	247.885	+	143.116i	0.0418089	+	0.0241384i
$78$	2479.97	−	4325.14i	0.407621	−	0.710903i
$79$	−3918.75	−	6787.48i	−0.627905	−	1.08756i	−0.987971	−	0.154636i	$-0.950579\pi$
$79$	−3918.75	−	6787.48i	−0.627905	−	1.08756i	0.360067	−	0.932927i	$-0.382754\pi$
$80$			2402.02i			0.375315i
$81$	−3212.55	+	5720.69i	−0.489643	+	0.871923i
$82$	475.117			0.0706599
$83$	4404.19	−	2542.76i	0.639308	−	0.369105i	−0.145040	−	0.989426i	$-0.546331\pi$
$83$	4404.19	−	2542.76i	0.639308	−	0.369105i	0.784348	+	0.620321i	$0.212998\pi$
$84$	169.216	+	97.0260i	0.0239819	+	0.0137508i
$85$	−8409.88	+	14566.3i	−1.16400	+	2.01610i
$86$	1521.30	+	878.325i	0.205693	+	0.118757i
$87$	−4852.65	+	14.4585i	−0.641121	+	0.00191023i
$88$	−1195.33	−	2070.38i	−0.154356	−	0.267353i
$89$		−	10285.1i		−	1.29846i	−0.760594	−	0.649228i	$-0.775092\pi$
$89$		−	10285.1i		−	1.29846i	0.760594	−	0.649228i	$-0.224908\pi$
$90$	4343.58	+	7420.83i	0.536245	+	0.916152i
$91$	−530.605			−0.0640750
$92$	2746.03	−	1585.42i	0.324437	−	0.187314i
$93$	4635.15	−	2694.55i	0.535918	−	0.311545i
$94$	1064.65	−	1844.02i	0.120490	−	0.208694i
$95$	16311.6	+	9417.50i	1.80738	+	1.04349i
$96$	−818.787	−	1408.47i	−0.0888441	−	0.152829i
$97$	440.403	+	762.801i	0.0468066	+	0.0810714i	0.888480	−	0.458916i	$-0.151762\pi$
$97$	440.403	+	762.801i	0.0468066	+	0.0810714i	−0.841673	+	0.539988i	$0.818429\pi$
$98$			6770.29i			0.704945i
$99$	−7436.77	−	4234.73i	−0.758776	−	0.432072i
$100$	6268.92			0.626892
$101$	−3574.35	+	2063.65i	−0.350393	+	0.202299i	−0.664858	−	0.746970i	$-0.731508\pi$
$101$	−3574.35	+	2063.65i	−0.350393	+	0.202299i	0.314466	+	0.949269i	$0.398175\pi$
$102$	−33.9902	−	11408.0i	−0.00326704	−	1.09650i
$103$	−3638.92	+	6302.79i	−0.343003	+	0.594098i	−0.984989	−	0.172618i	$-0.944777\pi$
$103$	−3638.92	+	6302.79i	−0.343003	+	0.594098i	0.641986	+	0.766716i	$0.278111\pi$
$104$	3837.98	+	2215.86i	0.354843	+	0.204869i
$105$	455.192	−	793.868i	0.0412872	−	0.0720062i
$106$	1292.34	+	2238.41i	0.115018	+	0.199217i
$107$		−	2345.46i		−	0.204861i	−0.994740	−	0.102431i	$-0.967338\pi$
$107$		−	2345.46i		−	0.204861i	0.994740	−	0.102431i	$-0.0326620\pi$
$108$	−5076.52	−	2870.74i	−0.435230	−	0.246120i
$109$	5878.01			0.494740			0.247370	−	0.968921i	$-0.420434\pi$
$109$	5878.01			0.494740			0.247370	+	0.968921i	$0.420434\pi$
$110$	−9713.07	+	5607.84i	−0.802733	+	0.463458i
$111$	14397.4	+	8255.24i	1.16853	+	0.670014i
$112$	−86.6931	+	150.157i	−0.00691112	+	0.0119704i
$113$	−12321.8	−	7113.99i	−0.964977	−	0.557130i	−0.0672755	−	0.997734i	$-0.521431\pi$
$113$	−12321.8	−	7113.99i	−0.964977	−	0.557130i	−0.897701	+	0.440605i	$0.854764\pi$
$114$	−12774.8	+	38.0627i	−0.982982	+	0.00292880i
$115$	−7437.92	−	12882.9i	−0.562414	−	0.974129i
$116$		−	4313.48i		−	0.320562i
$117$	15864.1	−	94.5351i	1.15889	−	0.00690592i
$118$	−3731.20			−0.267969
$119$	−1051.45	+	607.055i	−0.0742497	+	0.0428681i
$120$	−6607.77	+	3841.29i	−0.458873	+	0.266756i
$121$	−1739.15	+	3012.30i	−0.118786	+	0.205744i
$122$	−10113.5	−	5839.06i	−0.679491	−	0.392304i
$123$	759.804	+	1307.01i	0.0502217	+	0.0863911i
$124$	2382.87	+	4127.25i	0.154973	+	0.268422i
$125$		−	5953.07i		−	0.380996i
$126$	3.69858	+	620.664i	0.000232967	+	0.0390945i
$127$	10022.6			0.621402			0.310701	−	0.950508i	$-0.399436\pi$
$127$	10022.6			0.621402			0.310701	+	0.950508i	$0.399436\pi$
$128$	1254.14	−	724.077i	0.0765466	−	0.0441942i
$129$	16.6543	+	5589.60i	0.00100080	+	0.335893i
$130$	10395.6	−	18005.7i	0.615123	−	1.06542i
$131$	−19690.8	−	11368.5i	−1.14742	−	0.662461i	−0.199160	−	0.979967i	$-0.563821\pi$
$131$	−19690.8	−	11368.5i	−1.14742	−	0.662461i	−0.948256	+	0.317506i	$0.897155\pi$
$132$	3783.89	−	6599.21i	0.217165	−	0.378743i
$133$	679.789	+	1177.43i	0.0384300	+	0.0665628i
$134$			18903.2i			1.05275i
$135$	−13467.9	+	23816.2i	−0.738979	+	1.30679i
$136$	10140.5			0.548253
$137$	9464.53	−	5464.35i	0.504264	−	0.291137i	−0.226209	−	0.974079i	$-0.572633\pi$
$137$	9464.53	−	5464.35i	0.504264	−	0.291137i	0.730473	+	0.682942i	$0.239300\pi$
$138$	8752.82	+	5018.73i	0.459610	+	0.263533i
$139$	11963.9	−	20722.1i	0.619217	−	1.07251i	−0.370412	−	0.928868i	$-0.620784\pi$
$139$	11963.9	−	20722.1i	0.619217	−	1.07251i	0.989629	−	0.143647i	$-0.0458831\pi$
$140$	704.452	+	406.715i	0.0359414	+	0.0207508i
$141$	6775.35	−	20.1872i	0.340795	−	0.00101540i
$142$	−4083.24	−	7072.38i	−0.202502	−	0.350743i
$143$			20692.9i			1.01193i
$144$	2565.20	−	4504.84i	0.123708	−	0.217247i
$145$	−20236.4			−0.962495
$146$	−291.061	+	168.044i	−0.0136546	+	0.00788348i
$147$	−18624.6	+	10827.0i	−0.861889	+	0.501042i
$148$	−7376.09	+	12775.8i	−0.336746	+	0.583262i
$149$	5527.74	+	3191.44i	0.248986	+	0.143752i	0.619300	−	0.785155i	$-0.287417\pi$
$149$	5527.74	+	3191.44i	0.248986	+	0.143752i	−0.370314	+	0.928907i	$0.620750\pi$
$150$	10025.2	+	17245.3i	0.445565	+	0.766459i
$151$	15708.6	+	27208.2i	0.688945	+	1.19329i	0.972180	+	0.234237i	$0.0752592\pi$
$151$	15708.6	+	27208.2i	0.688945	+	1.19329i	−0.283235	+	0.959051i	$0.591408\pi$
$152$		−	11355.5i		−	0.491493i
$153$	31328.2	−	18337.1i	1.33830	−	0.783335i
$154$	−809.588			−0.0341368
$155$	19362.8	−	11179.1i	0.805942	−	0.465311i
$156$	42.0158	+	14101.6i	0.00172649	+	0.579453i
$157$	5772.07	−	9997.52i	0.234171	−	0.405595i	−0.724861	−	0.688896i	$-0.758096\pi$
$157$	5772.07	−	9997.52i	0.234171	−	0.405595i	0.959031	+	0.283300i	$0.0914292\pi$
$158$	19197.9	+	11083.9i	0.769023	+	0.443996i
$159$	−4090.98	+	7134.79i	−0.161820	+	0.282219i
$160$	−3396.97	−	5883.72i	−0.132694	−	0.229833i
$161$		−	1073.79i		−	0.0414255i
$162$	−221.161	−	18556.0i	−0.00842710	−	0.707057i
$163$	−42242.8			−1.58993			−0.794964	−	0.606657i	$-0.792510\pi$
$163$	−42242.8			−1.58993			−0.794964	+	0.606657i	$0.792510\pi$
$164$	−1163.79	+	671.917i	−0.0432702	+	0.0249820i
$165$	−30959.8	−	17751.9i	−1.13718	−	0.652043i
$166$	−7192.02	+	12456.9i	−0.260996	+	0.452059i
$167$	−17363.1	−	10024.6i	−0.622577	−	0.359445i	0.155294	−	0.987868i	$-0.450367\pi$
$167$	−17363.1	−	10024.6i	−0.622577	−	0.359445i	−0.777872	+	0.628423i	$0.783701\pi$
$168$	−551.709	+	1.64382i	−0.0195475	+	5.82420e-5i
$169$	−4899.32	−	8485.86i	−0.171539	−	0.297114i
$170$		−	47573.5i		−	1.64614i
$171$	−20534.1	−	35081.7i	−0.702238	−	1.19974i
$172$	−4968.55			−0.167947
$173$	−32954.3	+	19026.1i	−1.10108	+	0.635709i	−0.936505	−	0.350655i	$-0.885959\pi$
$173$	−32954.3	+	19026.1i	−1.10108	+	0.635709i	−0.164576	+	0.986364i	$0.552626\pi$
$174$	11866.1	−	6898.10i	0.391930	−	0.227840i
$175$	1061.47	−	1838.52i	0.0346602	−	0.0600333i
$176$	5855.92	+	3380.92i	0.189047	+	0.109146i
$177$	−5966.92	−	10264.3i	−0.190460	−	0.327628i
$178$	14545.3	+	25193.2i	0.459073	+	0.795138i
$179$			33794.9i			1.05474i	0.849636	+	0.527370i	$0.176822\pi$
$179$			33794.9i			1.05474i	−0.849636	+	0.527370i	$0.823178\pi$
$180$	−21134.2	−	12034.5i	−0.652290	−	0.371435i
$181$	44812.8			1.36787			0.683935	−	0.729543i	$-0.260267\pi$
$181$	44812.8			1.36787			0.683935	+	0.729543i	$0.260267\pi$
$182$	1299.71	−	750.389i	0.0392378	−	0.0226540i
$183$	−110.717	−	37159.4i	−0.00330606	−	1.10960i
$184$	−4484.26	+	7766.96i	−0.132451	+	0.229412i
$185$	59936.7	+	34604.5i	1.75126	+	1.01109i
$186$	−7543.09	+	13155.4i	−0.218034	+	0.380257i
$187$	23674.4	+	41005.2i	0.677010	+	1.17262i
$188$			6022.56i			0.170398i
$189$	−1701.49	+	1002.74i	−0.0476326	+	0.0280714i
$190$	−53273.4			−1.47572
$191$	11359.5	−	6558.40i	0.311381	−	0.179776i	−0.336163	−	0.941804i	$-0.609129\pi$
$191$	11359.5	−	6558.40i	0.311381	−	0.179776i	0.647544	+	0.762028i	$0.275796\pi$
$192$	3997.49	+	2292.10i	0.108439	+	0.0621772i
$193$	−1155.92	+	2002.11i	−0.0310322	+	0.0537493i	−0.881124	−	0.472885i	$-0.843213\pi$
$193$	−1155.92	+	2002.11i	−0.0310322	+	0.0537493i	0.850092	+	0.526634i	$0.176546\pi$
$194$	−2157.53	−	1245.65i	−0.0573262	−	0.0330973i
$195$	66156.7	−	197.115i	1.73982	−	0.00518382i
$196$	−9574.64	−	16583.8i	−0.249236	−	0.431689i
$197$		−	13110.0i		−	0.337808i	−0.985632	−	0.168904i	$-0.945977\pi$
$197$		−	13110.0i		−	0.337808i	0.985632	−	0.168904i	$-0.0540228\pi$
$198$	24205.1	−	144.240i	0.617414	−	0.00367922i
$199$	−10592.0			−0.267467			−0.133733	−	0.991017i	$-0.542697\pi$
$199$	−10592.0			−0.267467			−0.133733	+	0.991017i	$0.542697\pi$
$200$	−15355.7	+	8865.59i	−0.383891	+	0.221640i
$201$	−52001.3	+	30229.9i	−1.28713	+	0.748247i
$202$	5836.90	−	10109.8i	0.143047	−	0.247765i
$203$	−1265.04	−	730.370i	−0.0306981	−	0.0177235i
$204$	16216.6	+	27895.7i	0.389672	+	0.670312i
$205$	3152.26	+	5459.87i	0.0750091	+	0.129920i
$206$		−	20584.8i		−	0.485079i
$207$	191.312	+	32104.3i	0.00446479	+	0.749242i
$208$	−12534.8			−0.289728
$209$	45918.2	−	26510.9i	1.05122	−	0.606920i
$210$	7.71190	+	2588.31i	0.000174873	+	0.0586918i
$211$	6692.11	−	11591.1i	0.150314	−	0.260351i	−0.781029	−	0.624495i	$-0.785305\pi$
$211$	6692.11	−	11591.1i	0.150314	−	0.260351i	0.931343	+	0.364144i	$0.118638\pi$
$212$	−6331.17	−	3655.30i	−0.140868	−	0.0813302i
$213$	12925.7	−	22542.8i	0.284901	−	0.496876i
$214$	3316.98	+	5745.18i	0.0724295	+	0.125451i
$215$			23309.7i			0.504266i
$216$	16494.7	−	147.442i	0.353539	−	0.00316020i
$217$	1613.89			0.0342733
$218$	−14398.1	+	8312.75i	−0.302965	+	0.174917i
$219$	−927.741	−	531.952i	−0.0193436	−	0.0110913i
$220$	15861.4	−	27472.7i	0.327714	−	0.567618i
$221$	−76013.6	−	43886.5i	−1.55635	−	0.898558i
$222$	−46941.0	+	139.861i	−0.952458	+	0.00283786i
$223$	−28939.5	−	50124.7i	−0.581944	−	1.00796i	−0.995249	−	0.0973637i	$-0.968959\pi$
$223$	−28939.5	−	50124.7i	−0.581944	−	1.00796i	0.413305	−	0.910593i	$-0.364374\pi$
$224$		−	490.410i		−	0.00977380i
$225$	−31408.3	+	55157.2i	−0.620411	+	1.08953i
$226$	40242.8			0.787900
$227$	−24205.4	+	13975.0i	−0.469742	+	0.271206i	−0.716132	−	0.697965i	$-0.754089\pi$
$227$	−24205.4	+	13975.0i	−0.469742	+	0.271206i	0.246389	+	0.969171i	$0.420756\pi$
$228$	31238.0	−	18159.6i	0.600916	−	0.349330i
$229$	29733.6	−	51500.1i	0.566991	−	0.982058i	−0.429870	−	0.902891i	$-0.641441\pi$
$229$	29733.6	−	51500.1i	0.566991	−	0.982058i	0.996861	−	0.0791669i	$-0.0252260\pi$
$230$	36438.2	+	21037.6i	0.688813	+	0.397687i
$231$	−1294.69	−	2227.11i	−0.0242628	−	0.0417368i
$232$	6100.19	+	10565.8i	0.113336	+	0.196303i
$233$			17091.6i			0.314826i	0.987533	+	0.157413i	$0.0503154\pi$
$233$			17091.6i			0.314826i	−0.987533	+	0.157413i	$0.949685\pi$
$234$	−38725.2	+	22666.7i	−0.707232	+	0.413959i
$235$	28254.5			0.511624
$236$	9139.55	−	5276.72i	0.164097	−	0.0947415i
$237$	210.166	+	70537.2i	0.00374168	+	1.25580i
$238$	1717.01	−	2973.95i	0.0303123	−	0.0525025i
$239$	−76828.5	−	44356.9i	−1.34501	−	0.776543i	−0.357474	−	0.933923i	$-0.616362\pi$
$239$	−76828.5	−	44356.9i	−1.34501	−	0.776543i	−0.987538	+	0.157380i	$0.949695\pi$
$240$	10753.2	−	18754.0i	0.186688	−	0.325590i
$241$	−27553.4	−	47723.9i	−0.474396	−	0.821678i	0.525174	−	0.850995i	$-0.324000\pi$
$241$	−27553.4	−	47723.9i	−0.474396	−	0.821678i	−0.999570	+	0.0293170i	$0.990667\pi$
$242$		−	9838.12i		−	0.167989i
$243$	50692.4	−	30283.0i	0.858481	−	0.512846i
$244$	33030.7			0.554802
$245$	−77801.7	+	44918.9i	−1.29616	+	0.748336i
$246$	−3709.53	−	2126.98i	−0.0612983	−	0.0351475i
$247$	−49144.7	+	85121.1i	−0.805532	+	1.39522i
$248$	−11673.6	−	6739.78i	−0.189803	−	0.109583i
$249$	−45769.5	+	136.371i	−0.738206	+	0.00219949i
$250$	8418.91	+	14582.0i	0.134703	+	0.233312i
$251$		−	99498.8i		−	1.57932i	−0.613544	−	0.789661i	$-0.710257\pi$
$251$		−	99498.8i		−	1.57932i	0.613544	−	0.789661i	$-0.289743\pi$
$252$	−886.812	−	1515.08i	−0.0139647	−	0.0238580i
$253$	−41876.5			−0.654228
$254$	−24550.2	+	14174.1i	−0.380529	+	0.219699i
$255$	130871.	−	76079.2i	2.01263	−	1.17000i
$256$	−2048.00	+	3547.24i	−0.0312500	+	0.0541266i
$257$	105289.	+	60788.7i	1.59411	+	0.920357i	0.992592	+	0.121495i	$0.0387689\pi$
$257$	105289.	+	60788.7i	1.59411	+	0.920357i	0.601514	+	0.798862i	$0.294564\pi$
$258$	−7945.68	−	13668.1i	−0.119369	−	0.205338i
$259$	2497.88	+	4326.45i	0.0372367	+	0.0644959i
$260$			58806.2i			0.869915i
$261$	37952.3	+	21611.2i	0.557130	+	0.317248i
$262$	64309.9			0.936862
$263$	104388.	−	60268.5i	1.50917	−	0.871322i	0.509231	−	0.860630i	$-0.329930\pi$
$263$	104388.	−	60268.5i	1.50917	−	0.871322i	0.999943	−	0.0106920i	$-0.00340345\pi$
$264$	64.1069	+	21515.9i	0.000919808	+	0.308711i
$265$	−17148.6	+	29702.3i	−0.244196	+	0.422959i
$266$	−3330.27	−	1922.73i	−0.0470670	−	0.0271741i
$267$	−46043.7	+	80301.7i	−0.645874	+	1.12642i
$268$	−26733.2	−	46303.2i	−0.372204	−	0.644677i
$269$			66714.5i			0.921968i	0.887408	+	0.460984i	$0.152504\pi$
$269$			66714.5i			0.921968i	−0.887408	+	0.460984i	$0.847496\pi$
$270$	−691.716	−	77384.0i	−0.00948856	−	1.06151i
$271$	110531.			1.50503			0.752517	−	0.658573i	$-0.228839\pi$
$271$	110531.			1.50503			0.752517	+	0.658573i	$0.228839\pi$
$272$	−24839.0	+	14340.8i	−0.335735	+	0.193837i
$273$	4142.76	+	2375.39i	0.0555858	+	0.0318720i
$274$	−15455.5	+	26769.7i	−0.205865	+	0.356568i
$275$	−71699.8	−	41395.9i	−0.948097	−	0.547384i
$276$	−28537.5	+	85.0278i	−0.374626	+	0.00111620i
$277$	38191.1	+	66148.9i	0.497740	+	0.862110i	0.999997	−	0.00260812i	$-0.000830190\pi$
$277$	38191.1	+	66148.9i	0.497740	+	0.862110i	−0.502257	+	0.864718i	$0.667497\pi$
$278$			67678.0i			0.875705i
$279$	−48252.3	+	287.539i	−0.619883	+	0.00369393i
$280$	−2300.73			−0.0293460
$281$	28868.9	−	16667.5i	0.365610	−	0.211085i	−0.305929	−	0.952054i	$-0.598967\pi$
$281$	28868.9	−	16667.5i	0.365610	−	0.211085i	0.671539	+	0.740970i	$0.265634\pi$
$282$	−16567.6	+	9631.23i	−0.208334	+	0.121111i
$283$	−43833.2	+	75921.3i	−0.547306	+	0.947962i	0.451152	+	0.892447i	$0.351013\pi$
$283$	−43833.2	+	75921.3i	−0.547306	+	0.947962i	−0.998458	+	0.0555146i	$0.982320\pi$
$284$	20003.7	+	11549.1i	0.248013	+	0.143190i
$285$	−85194.6	−	146551.i	−1.04887	−	1.80426i
$286$	−29264.2	−	50687.1i	−0.357771	−	0.619677i
$287$			455.083i			0.00552493i
$288$	87.3738	+	14662.3i	0.00105341	+	0.176774i
$289$	−117318.			−1.40465
$290$	49569.0	−	28618.7i	0.589405	−	0.340293i
$291$	−23.6193	−	7927.23i	−0.000278920	−	0.0936128i
$292$	475.301	−	823.246i	0.00557447	−	0.00965526i
$293$	141866.	+	81906.4i	1.65251	+	0.954076i	0.976037	+	0.217606i	$0.0698249\pi$
$293$	141866.	+	81906.4i	1.65251	+	0.954076i	0.676471	+	0.736469i	$0.263508\pi$
$294$	30309.0	−	52859.8i	0.350652	−	0.611548i
$295$	−24755.4	−	42877.6i	−0.284463	−	0.492705i
$296$		−	41725.5i		−	0.476231i
$297$	39105.4	+	66355.7i	0.443327	+	0.752256i
$298$	−18053.5			−0.203296
$299$	67228.5	−	38814.4i	0.751988	−	0.434160i
$300$	−48945.2	−	28064.4i	−0.543836	−	0.311827i
$301$	−841.288	+	1457.15i	−0.00928564	+	0.0160832i
$302$	−76956.3	−	44430.7i	−0.843782	−	0.487158i
$303$	37145.6	−	110.676i	0.404597	−	0.00120550i
$304$	16059.0	+	27815.1i	0.173769	+	0.300977i
$305$		−	154962.i		−	1.66581i
$306$	−50805.4	+	89221.2i	−0.542584	+	0.952852i
$307$	−50704.2			−0.537981			−0.268991	−	0.963143i	$-0.586690\pi$
$307$	−50704.2			−0.537981			−0.268991	+	0.963143i	$0.586690\pi$
$308$	1983.08	−	1144.93i	0.0209044	−	0.0120692i
$309$	56627.3	−	32919.1i	0.593074	−	0.344771i
$310$	−31619.3	+	54766.2i	−0.329025	+	0.569887i
$311$	−32107.8	−	18537.4i	−0.331963	−	0.191659i	0.324749	−	0.945800i	$-0.394720\pi$
$311$	−32107.8	−	18537.4i	−0.331963	−	0.191659i	−0.656712	+	0.754141i	$0.728053\pi$
$312$	−20045.6	−	34482.3i	−0.205925	−	0.354231i
$313$	−88549.2	−	153372.i	−0.903849	−	1.56551i	−0.822454	−	0.568831i	$-0.807396\pi$
$313$	−88549.2	−	153372.i	−0.903849	−	1.56551i	−0.0813950	−	0.996682i	$-0.525938\pi$
$314$			32651.8i			0.331167i
$315$	−7107.91	+	4160.42i	−0.0716343	+	0.0419292i
$316$	−62700.1			−0.627905
$317$	−24457.9	+	14120.8i	−0.243389	+	0.140521i	−0.616733	−	0.787172i	$-0.711544\pi$
$317$	−24457.9	+	14120.8i	−0.243389	+	0.140521i	0.373344	+	0.927693i	$0.378211\pi$
$318$	−69.3097	−	23262.1i	−0.000685393	−	0.230035i
$319$	−28483.5	+	49334.8i	−0.279905	+	0.484810i
$320$	16641.7	+	9608.07i	0.162516	+	0.0938288i
$321$	−10500.0	+	18312.4i	−0.101902	+	0.177720i
$322$	1518.57	+	2630.24i	0.0146461	+	0.0253679i
$323$			224902.i			2.15570i
$324$	26783.9	+	45139.9i	0.255143	+	0.430003i
$325$	153476.			1.45303
$326$	103473.	−	59740.3i	0.973628	−	0.562124i
$327$	−45893.1	−	26314.4i	−0.429192	−	0.246092i
$328$	1900.47	−	3291.71i	0.0176650	−	0.0305966i
$329$	1766.27	+	1019.75i	0.0163179	+	0.00942114i
$330$	100941.	−	300.754i	0.926912	−	0.00276174i
$331$	81696.9	+	141503.i	0.745675	+	1.29155i	0.949879	+	0.312618i	$0.101206\pi$
$331$	81696.9	+	141503.i	0.745675	+	1.29155i	−0.204204	+	0.978928i	$0.565461\pi$
$332$		−	40684.2i		−	0.369105i
$333$	−75452.4	−	128907.i	−0.680432	−	1.16249i
$334$	56707.5			0.508332
$335$	−217229.	+	125417.i	−1.93566	+	1.11755i
$336$	1349.08	−	784.261i	0.0119498	−	0.00694676i
$337$	99115.2	−	171673.i	0.872731	−	1.51161i	0.0135713	−	0.999908i	$-0.495680\pi$
$337$	99115.2	−	171673.i	0.872731	−	1.51161i	0.859160	−	0.511707i	$-0.170987\pi$
$338$	24001.6	+	13857.4i	0.210091	+	0.121296i
$339$	64356.0	+	110705.i	0.560002	+	0.963312i
$340$	67279.1	+	116531.i	0.581999	+	1.00805i
$341$		−	62939.8i		−	0.541273i
$342$	99911.2	+	56892.6i	0.854205	+	0.486412i
$343$	−12989.5			−0.110409
$344$	12170.4	−	7026.60i	0.102846	−	0.0593784i
$345$	398.903	+	133882.i	0.00335142	+	1.12482i
$346$	53814.1	−	93208.7i	0.449514	−	0.778582i
$347$	28124.2	+	16237.5i	0.233572	+	0.134853i	0.612219	−	0.790688i	$-0.290277\pi$
$347$	28124.2	+	16237.5i	0.233572	+	0.134853i	−0.378647	+	0.925541i	$0.623610\pi$
$348$	−19310.4	+	33678.0i	−0.159453	+	0.278091i
$349$	73033.8	+	126498.i	0.599616	+	1.03856i	0.992878	+	0.119138i	$0.0380132\pi$
$349$	73033.8	+	126498.i	0.599616	+	1.03856i	−0.393262	+	0.919426i	$0.628653\pi$
$350$			6004.58i			0.0490169i
$351$	−124284.	−	70281.5i	−1.00879	−	0.570462i
$352$	−19125.4			−0.154356
$353$	−151652.	+	87556.5i	−1.21703	+	0.702650i	−0.964280	−	0.264883i	$-0.914667\pi$
$353$	−151652.	+	87556.5i	−1.21703	+	0.702650i	−0.252745	+	0.967533i	$0.581333\pi$
$354$	29131.8	+	16703.7i	0.232466	+	0.133293i
$355$	54182.1	−	93846.2i	0.429932	−	0.744663i
$356$	−71257.0	−	41140.3i	−0.562248	−	0.324614i
$357$	10926.9	−	32.5569i	0.0857358	−	0.000255451i
$358$	−47793.3	−	82780.4i	−0.372907	−	0.645894i
$359$		−	217198.i		−	1.68526i	−0.538492	−	0.842631i	$-0.681006\pi$
$359$		−	217198.i		−	1.68526i	0.538492	−	0.842631i	$-0.318994\pi$
$360$	68787.3	−	409.909i	0.530766	−	0.00316288i
$361$	121527.			0.932524
$362$	−109768.	+	63374.9i	−0.837646	+	0.483615i
$363$	27063.9	−	15733.1i	0.205389	−	0.119399i
$364$	−2122.42	+	3676.14i	−0.0160188	+	0.0277453i
$365$	−3862.21	−	2229.85i	−0.0289901	−	0.0167375i
$366$	52822.5	+	90864.9i	0.394327	+	0.678319i
$367$	−92816.7	−	160763.i	−0.689119	−	1.19359i	−0.972123	−	0.234470i	$-0.924664\pi$
$367$	−92816.7	−	160763.i	−0.689119	−	1.19359i	0.283004	−	0.959119i	$-0.408669\pi$
$368$		−	25366.8i		−	0.187314i
$369$	−81.0796	−	13606.1i	−0.000595469	−	0.0999264i
$370$	−195753.			−1.42989
$371$	−2144.02	+	1237.85i	−0.0155769	+	0.00899332i
$372$	−127.796	−	42891.5i	−0.000923486	−	0.309945i
$373$	−39939.9	+	69178.0i	−0.287071	+	0.497222i	−0.973109	−	0.230344i	$-0.926015\pi$
$373$	−39939.9	+	69178.0i	−0.287071	+	0.497222i	0.686038	+	0.727565i	$0.259348\pi$
$374$	−115980.	−	66961.2i	−0.829165	−	0.478718i
$375$	−26650.4	+	46479.2i	−0.189514	+	0.330519i
$376$	−8517.18	−	14752.2i	−0.0602449	−	0.104347i
$377$		−	105603.i		−	0.743007i
$378$	2749.69	−	4862.46i	0.0192442	−	0.0340308i
$379$	−56872.1			−0.395932			−0.197966	−	0.980209i	$-0.563434\pi$
$379$	−56872.1			−0.395932			−0.197966	+	0.980209i	$0.563434\pi$
$380$	130493.	−	75340.0i	0.903690	−	0.521745i
$381$	−78252.4	−	44868.7i	−0.539073	−	0.309096i
$382$	−18550.0	+	32129.5i	−0.127121	+	0.220180i
$383$	84583.3	+	48834.2i	0.576617	+	0.332910i	0.759788	−	0.650171i	$-0.225303\pi$
$383$	84583.3	+	48834.2i	0.576617	+	0.332910i	−0.183171	+	0.983081i	$0.558636\pi$
$384$	−13033.3	+	38.8330i	−0.0883880	+	0.000263353i
$385$	−5371.37	−	9303.49i	−0.0362380	−	0.0627660i
$386$		−	6538.86i		−	0.0438862i
$387$	24893.2	−	43715.9i	0.166211	−	0.291889i
$388$	7046.45			0.0468066
$389$	−74946.6	+	43270.4i	−0.495282	+	0.285951i	−0.726763	−	0.686888i	$-0.758976\pi$
$389$	−74946.6	+	43270.4i	−0.495282	+	0.285951i	0.231481	+	0.972839i	$0.425643\pi$
$390$	−161771.	+	94042.6i	−1.06359	+	0.618294i
$391$	88813.5	−	153830.i	0.580932	−	1.00620i
$392$	46906.0	+	27081.2i	0.305250	+	0.176236i
$393$	102844.	+	176912.i	0.665877	+	1.14544i
$394$	18540.3	+	32112.8i	0.119433	+	0.206864i
$395$			294154.i			1.88530i
$396$	−59086.2	+	34584.5i	−0.376787	+	0.220542i
$397$	−13531.3			−0.0858537			−0.0429268	−	0.999078i	$-0.513668\pi$
$397$	−13531.3			−0.0858537			−0.0429268	+	0.999078i	$0.513668\pi$
$398$	25944.9	−	14979.3i	0.163789	−	0.0945638i
$399$	−36.4577	−	12236.1i	−0.000229004	−	0.0768597i
$400$	25075.7	−	43432.4i	0.156723	−	0.271452i
$401$	22448.2	+	12960.5i	0.139603	+	0.0805996i	0.568175	−	0.822908i	$-0.307650\pi$
$401$	22448.2	+	12960.5i	0.139603	+	0.0805996i	−0.428572	+	0.903508i	$0.640983\pi$
$402$	84625.1	−	147589.i	0.523657	−	0.913275i
$403$	58337.5	+	101044.i	0.359201	+	0.622155i
$404$			33018.5i			0.202299i
$405$	211771.	−	125655.i	1.29109	−	0.766072i
$406$	4131.59			0.0250649
$407$	168726.	−	97413.9i	1.01857	−	0.588074i
$408$	−79172.9	−	45396.5i	−0.475616	−	0.272711i
$409$	20360.8	−	35266.0i	0.121716	−	0.210819i	−0.798728	−	0.601692i	$-0.794493\pi$
$409$	20360.8	−	35266.0i	0.121716	−	0.210819i	0.920445	+	0.390873i	$0.127827\pi$
$410$	−15442.9	−	8915.94i	−0.0918671	−	0.0530395i
$411$	−98357.8	+	293.058i	−0.582271	+	0.00173488i
$412$	29111.3	+	50422.3i	0.171501	+	0.297049i
$413$		−	3573.87i		−	0.0209526i
$414$	−45870.9	−	78368.5i	−0.267631	−	0.457237i
$415$	−190867.			−1.10824
$416$	30703.8	−	17726.9i	0.177421	−	0.102434i
$417$	−186177.	+	108230.i	−1.07067	+	0.622410i
$418$	−74984.1	+	129876.i	−0.429157	+	0.743323i
$419$	44556.0	+	25724.4i	0.253792	+	0.146527i	0.621499	−	0.783415i	$-0.286524\pi$
$419$	44556.0	+	25724.4i	0.253792	+	0.146527i	−0.367707	+	0.929942i	$0.619857\pi$
$420$	−3679.31	−	6329.13i	−0.0208578	−	0.0358794i
$421$	91333.7	+	158195.i	0.515308	+	0.892540i	0.999842	+	0.0177674i	$0.00565585\pi$
$421$	91333.7	+	158195.i	0.515308	+	0.892540i	−0.484534	+	0.874772i	$0.661011\pi$
$422$			37856.3i			0.212576i
$423$	−52989.6	−	30174.0i	−0.296149	−	0.168637i
$424$	20677.5			0.115018
$425$	304129.	−	175589.i	1.68376	−	0.972117i
$426$	218.988	+	73498.0i	0.00120671	+	0.405001i
$427$	5592.84	−	9687.08i	0.0306744	−	0.0531297i
$428$	−16249.8	−	9381.83i	−0.0887076	−	0.0512154i
$429$	92637.2	−	161562.i	0.503351	−	0.877859i
$430$	−32964.9	−	57096.8i	−0.178285	−	0.308798i
$431$			78404.3i			0.422071i	0.977478	+	0.211035i	$0.0676835\pi$
$431$			78404.3i			0.422071i	−0.977478	+	0.211035i	$0.932316\pi$
$432$	−40195.2	+	23688.2i	−0.215380	+	0.126930i
$433$	−330583.			−1.76321			−0.881606	−	0.471986i	$-0.843537\pi$
$433$	−330583.			−1.76321			−0.881606	+	0.471986i	$0.843537\pi$
$434$	−3953.22	+	2282.39i	−0.0209880	+	0.0121174i
$435$	157998.	+	90593.7i	0.834975	+	0.478762i
$436$	23512.0	−	40724.0i	0.123685	−	0.214229i
$437$	−172260.	−	99454.6i	−0.902034	−	0.520789i
$438$	3024.78	−	9.01238i	0.0157669	−	4.69776e-5i
$439$	123906.	+	214611.i	0.642927	+	1.11358i	0.984776	+	0.173828i	$0.0556136\pi$
$439$	123906.	+	214611.i	0.642927	+	1.11358i	−0.341849	+	0.939755i	$0.611053\pi$
$440$			89725.5i			0.463458i
$441$	193883.	−	1155.36i	0.996925	−	0.00594075i
$442$	248260.			1.27075
$443$	136274.	−	78678.0i	0.694395	−	0.400909i	−0.110862	−	0.993836i	$-0.535361\pi$
$443$	136274.	−	78678.0i	0.694395	−	0.400909i	0.805256	+	0.592927i	$0.202028\pi$
$444$	114784.	−	66727.1i	0.582256	−	0.338483i
$445$	−193007.	+	334298.i	−0.974660	+	1.68816i
$446$	141774.	+	81853.2i	0.712733	+	0.411496i
$447$	−28871.1	−	49663.8i	−0.144493	−	0.248557i
$448$	693.545	+	1201.25i	0.00345556	+	0.00598521i
$449$		−	27735.6i		−	0.137577i	−0.997631	−	0.0687883i	$-0.978087\pi$
$449$		−	27735.6i		−	0.137577i	0.997631	−	0.0687883i	$-0.0219133\pi$
$450$	−1069.80	−	179525.i	−0.00528298	−	0.886544i
$451$	17747.6			0.0872544
$452$	−98574.3	+	56911.9i	−0.482488	+	0.278565i
$453$	−842.469	−	282754.i	−0.00410542	−	1.37788i
$454$	39527.2	−	68463.1i	0.191772	−	0.332158i
$455$	17246.4	+	9957.22i	0.0833059	+	0.0480967i
$456$	−50835.6	+	88658.9i	−0.244477	+	0.426376i
$457$	−6958.48	−	12052.4i	−0.0333182	−	0.0577089i	0.848885	−	0.528577i	$-0.177274\pi$
$457$	−6958.48	−	12052.4i	−0.0333182	−	0.0577089i	−0.882204	+	0.470868i	$0.843941\pi$
$458$			168199.i			0.801847i
$459$	−326689.	+	2920.18i	−1.55063	+	0.0138607i
$460$	−119007.			−0.562414
$461$	−351627.	+	203012.i	−1.65455	+	0.955256i	−0.679386	+	0.733781i	$0.737754\pi$
$461$	−351627.	+	203012.i	−1.65455	+	0.955256i	−0.975166	+	0.221475i	$0.928913\pi$
$462$	6320.94	+	3624.33i	0.0296141	+	0.0169802i
$463$	137743.	−	238578.i	0.642550	−	1.11293i	−0.342311	−	0.939587i	$-0.611210\pi$
$463$	137743.	−	238578.i	0.642550	−	1.11293i	0.984862	−	0.173343i	$-0.0554569\pi$
$464$	−29884.7	−	17253.9i	−0.138807	−	0.0801405i
$465$	−201223.	+	599.546i	−0.930618	+	0.00277279i
$466$	−24171.2	−	41865.7i	−0.111308	−	0.192791i
$467$		−	327264.i		−	1.50060i	−0.661098	−	0.750300i	$-0.729909\pi$
$467$		−	327264.i		−	1.50060i	0.661098	−	0.750300i	$-0.270091\pi$
$468$	62801.3	−	110288.i	0.286733	−	0.503541i
$469$	−18106.1			−0.0823151
$470$	−69209.0	+	39957.8i	−0.313305	+	0.180887i
$471$	−89822.5	+	52216.5i	−0.404896	+	0.235378i
$472$	−14924.8	+	25850.5i	−0.0669923	+	0.116034i
$473$	56827.1	+	32809.1i	0.254000	+	0.146647i
$474$	−100270.	−	172483.i	−0.446285	−	0.767697i
$475$	−196627.	−	340567.i	−0.871476	−	1.50944i
$476$			9712.88i			0.0428681i
$477$	63881.4	−	37391.3i	0.280762	−	0.164336i
$478$	250921.			1.09820
$479$	5079.20	−	2932.48i	0.0221373	−	0.0127810i	−0.488891	−	0.872345i	$-0.662598\pi$
$479$	5079.20	−	2932.48i	0.0221373	−	0.0127810i	0.511028	+	0.859564i	$0.329265\pi$
$480$	182.182	+	61145.1i	0.000790723	+	0.265387i
$481$	−180582.	+	312777.i	−0.780519	+	1.35190i
$482$	134983.	+	77932.7i	0.581014	+	0.335449i
$483$	−4807.10	+	8383.74i	−0.0206058	+	0.0359371i
$484$	13913.2	+	24098.4i	0.0593932	+	0.102872i
$485$		−	33058.0i		−	0.140538i
$486$	−81343.9	+	145868.i	−0.344392	+	0.617571i
$487$	119183.			0.502524			0.251262	−	0.967919i	$-0.419154\pi$
$487$	119183.			0.502524			0.251262	+	0.967919i	$0.419154\pi$
$488$	−80908.4	+	46712.5i	−0.339746	+	0.196152i
$489$	329815.	+	189111.i	1.37928	+	0.790858i
$490$	127050.	−	220057.i	0.529153	−	0.916521i
$491$	−134236.	−	77501.3i	−0.556810	−	0.321474i	0.195054	−	0.980792i	$-0.437512\pi$
$491$	−134236.	−	77501.3i	−0.556810	−	0.321474i	−0.751864	+	0.659318i	$0.770845\pi$
$492$	12094.5	−	36.0356i	0.0499639	−	0.000148868i
$493$	−120818.	−	209263.i	−0.497093	−	0.860991i
$494$		−	278005.i		−	1.13919i
$495$	162251.	+	277199.i	0.662182	+	1.13131i
$496$	38125.9			0.154973
$497$	6774.15	−	3911.06i	0.0274247	−	0.0158337i
$498$	111919.	−	65061.9i	0.451279	−	0.262342i
$499$	51906.9	−	89905.4i	0.208461	−	0.361065i	−0.742769	−	0.669548i	$-0.766488\pi$
$499$	51906.9	−	89905.4i	0.208461	−	0.361065i	0.951230	+	0.308483i	$0.0998213\pi$
$500$	−41244.1	−	23812.3i	−0.164976	−	0.0952491i
$501$	90686.3	+	155998.i	0.361299	+	0.621504i
$502$	140713.	+	243721.i	0.558374	+	0.967133i
$503$			48040.5i			0.189876i	0.995483	+	0.0949382i	$0.0302654\pi$
$503$			48040.5i			0.189876i	−0.995483	+	0.0949382i	$0.969735\pi$
$504$	4314.88	+	2457.03i	0.0169867	+	0.00967275i
$505$	154904.			0.607408
$506$	102576.	−	59222.3i	0.400631	−	0.231304i
$507$	262.755	+	88187.3i	0.00102220	+	0.343076i
$508$	40090.4	−	69438.6i	0.155350	−	0.269075i
$509$	−245324.	−	141638.i	−0.946902	−	0.546694i	−0.0547847	−	0.998498i	$-0.517447\pi$
$509$	−245324.	−	141638.i	−0.946902	−	0.546694i	−0.892117	+	0.451804i	$0.850781\pi$
$510$	−212975.	+	371435.i	−0.818819	+	1.42805i
$511$	−160.958	−	278.788i	−0.000616413	−	0.00106766i
$512$		−	11585.2i		−	0.0441942i
$513$	3270.06	+	365830.i	0.0124257	+	1.39010i
$514$	−343873.			−1.30158
$515$	236553.	−	136574.i	0.891896	−	0.514937i
$516$	38792.5	+	22243.0i	0.145696	+	0.0835399i
$517$	39769.1	−	68882.1i	0.148787	−	0.257706i
$518$	−12237.0	−	7065.06i	−0.0456055	−	0.0263303i
$519$	342469.	−	1020.39i	1.27141	−	0.00378819i
$520$	−83164.6	−	144045.i	−0.307561	−	0.532712i
$521$			253304.i			0.933183i	0.884473	+	0.466591i	$0.154518\pi$
$521$			253304.i			0.933183i	−0.884473	+	0.466591i	$0.845482\pi$
$522$	−123527.	+	736.104i	−0.453335	+	0.00270146i
$523$	418405.			1.52966			0.764828	−	0.644234i	$-0.222824\pi$
$523$	418405.			1.52966			0.764828	+	0.644234i	$0.222824\pi$
$524$	−157527.	+	90948.0i	−0.573708	+	0.331231i
$525$	−16518.1	+	9602.48i	−0.0599297	+	0.0348389i
$526$	−170465.	+	295254.i	−0.616118	+	1.06715i
$527$	231204.	+	133486.i	0.832480	+	0.480632i
$528$	−30585.2	−	52612.4i	−0.109709	−	0.188721i
$529$	−61371.5	−	106299.i	−0.219308	−	0.379853i
$530$		−	97007.3i		−	0.345345i
$531$	636.737	+	106852.i	0.00225825	+	0.378959i
$532$	10876.6			0.0384300
$533$	−28492.0	+	16449.9i	−0.100293	+	0.0579040i
$534$	−780.077	−	261814.i	−0.00273561	−	0.918142i
$535$	−44014.3	+	76235.0i	−0.153775	+	0.266347i
$536$	130965.	+	75612.9i	0.455855	+	0.263188i
$537$	151292.	−	263857.i	0.524646	−	0.914999i
$538$	−94348.6	−	163417.i	−0.325965	−	0.564588i
$539$			252899.i			0.870502i
$540$	111132.	+	188573.i	0.381111	+	0.646684i
$541$	496984.			1.69804			0.849020	−	0.528360i	$-0.177193\pi$
$541$	496984.			1.69804			0.849020	+	0.528360i	$0.177193\pi$
$542$	−270745.	+	156315.i	−0.921642	+	0.532110i
$543$	−349880.	−	200616.i	−1.18664	−	0.680402i
$544$	40561.9	−	70255.3i	0.137063	−	0.237400i
$545$	−191054.	−	110305.i	−0.643226	−	0.371367i
$546$	−13507.0	+	40.2441i	−0.0453077	+	0.000134995i
$547$	−214561.	−	371631.i	−0.717094	−	1.24204i	−0.962146	−	0.272534i	$-0.912138\pi$
$547$	−214561.	−	371631.i	−0.717094	−	1.24204i	0.245052	−	0.969510i	$-0.421195\pi$
$548$		−	87429.6i		−	0.291137i
$549$	−165489.	+	290621.i	−0.549066	+	0.964235i
$550$	234171.			0.774118
$551$	−234336.	+	135294.i	−0.771854	+	0.445630i
$552$	69782.1	−	40566.4i	0.229016	−	0.133134i
$553$	−10616.5	+	18388.4i	−0.0347162	+	0.0601302i
$554$	−187097.	−	108021.i	−0.609604	−	0.351955i
$555$	−313046.	−	538500.i	−1.01630	−	1.74824i
$556$	−95711.1	−	165776.i	−0.309608	−	0.536257i
$557$		−	208947.i		−	0.673482i	−0.941597	−	0.336741i	$-0.890675\pi$
$557$		−	208947.i		−	0.673482i	0.941597	−	0.336741i	$-0.109325\pi$
$558$	117787.	−	68943.4i	0.378293	−	0.221424i
$559$	−121640.			−0.389272
$560$	5635.61	−	3253.72i	0.0179707	−	0.0103754i
$561$	−1269.68	−	426137.i	−0.00403430	−	1.35401i
$562$	−47142.7	+	81653.6i	−0.149259	+	0.258525i
$563$	−73412.4	−	42384.6i	−0.231607	−	0.133719i	0.379706	−	0.925107i	$-0.376025\pi$
$563$	−73412.4	−	42384.6i	−0.231607	−	0.133719i	−0.611313	+	0.791389i	$0.709358\pi$
$564$	26961.5	−	47021.7i	0.0847591	−	0.147822i
$565$	266999.	+	462455.i	0.836397	+	1.44868i
$566$		−	247958.i		−	0.774008i
$567$	17773.5	−	211.835i	0.0552850	−	0.000658919i
$568$	−65331.8			−0.202502
$569$	283998.	−	163966.i	0.877185	−	0.506443i	0.00745565	−	0.999972i	$-0.497627\pi$
$569$	283998.	−	163966.i	0.877185	−	0.506443i	0.869729	+	0.493529i	$0.164293\pi$
$570$	415938.	+	238492.i	1.28020	+	0.734048i
$571$	−196916.	+	341069.i	−0.603962	+	1.04609i	0.388252	+	0.921553i	$0.373079\pi$
$571$	−196916.	+	341069.i	−0.603962	+	1.04609i	−0.992215	+	0.124540i	$0.960254\pi$
$572$	143365.	+	82771.7i	0.438178	+	0.252982i
$573$	−118051.	+	351.733i	−0.359550	+	0.00107128i
$574$	−643.584	−	1114.72i	−0.00195336	−	0.00338331i
$575$			310591.i			0.939404i
$576$	−20949.7	−	35791.6i	−0.0631440	−	0.107879i
$577$	−405942.			−1.21931			−0.609653	−	0.792669i	$-0.708691\pi$
$577$	−405942.			−1.21931			−0.609653	+	0.792669i	$0.708691\pi$
$578$	287368.	−	165912.i	0.860168	−	0.496618i
$579$	17987.9	−	10456.9i	0.0536566	−	0.0311922i
$580$	−80945.8	+	140202.i	−0.240624	+	0.416772i
$581$	−11931.7	−	6888.75i	−0.0353467	−	0.0204074i
$582$	11268.6	+	19384.3i	0.0332679	+	0.0572273i
$583$	48274.5	+	83613.9i	0.142030	+	0.246004i
$584$			2688.71i			0.00788348i
$585$	−517408.	−	294629.i	−1.51189	−	0.860921i
$586$	−463333.			−1.34927
$587$	−251224.	+	145044.i	−0.729096	+	0.420944i	−0.818091	−	0.575088i	$-0.804968\pi$
$587$	−251224.	+	145044.i	−0.729096	+	0.420944i	0.0889955	+	0.996032i	$0.471634\pi$
$588$	513.497	+	172343.i	0.00148519	+	0.498469i
$589$	149479.	−	258905.i	0.430873	−	0.746295i
$590$	121276.	+	70018.9i	0.348395	+	0.201146i
$591$	−58690.3	+	102358.i	−0.168032	+	0.293052i
$592$	59008.7	+	102206.i	0.168373	+	0.291631i
$593$		−	217450.i		−	0.618372i	−0.951002	−	0.309186i	$-0.899943\pi$
$593$		−	217450.i		−	0.618372i	0.951002	−	0.309186i	$-0.100057\pi$
$594$	−189630.	−	107234.i	−0.537444	−	0.303921i
$595$	45567.4			0.128712
$596$	44221.9	−	25531.5i	0.124493	−	0.0718761i
$597$	82697.7	+	47417.6i	0.232030	+	0.133043i
$598$	−109784.	+	190151.i	−0.306998	+	0.531736i
$599$	414884.	+	239534.i	1.15631	+	0.667595i	0.950416	−	0.310980i	$-0.100657\pi$
$599$	414884.	+	239534.i	1.15631	+	0.667595i	0.205892	+	0.978575i	$0.433991\pi$
$600$	159580.	−	475.470i	0.443278	−	0.00132075i
$601$	93655.9	+	162217.i	0.259290	+	0.449104i	0.966052	−	0.258348i	$-0.0831780\pi$
$601$	93655.9	+	162217.i	0.259290	+	0.449104i	−0.706762	+	0.707452i	$0.749845\pi$
$602$		−	4759.04i		−	0.0131319i
$603$	541338.	−	3225.87i	1.48879	−	0.00887181i
$604$	251338.			0.688945
$605$	113056.	−	65273.0i	0.308875	−	0.178329i
$606$	−90831.3	+	52802.9i	−0.247338	+	0.143785i
$607$	−13139.1	+	22757.6i	−0.0356606	+	0.0617661i	−0.883305	−	0.468799i	$-0.844687\pi$
$607$	−13139.1	+	22757.6i	−0.0356606	+	0.0617661i	0.847644	+	0.530565i	$0.178020\pi$
$608$	−78672.9	−	45421.8i	−0.212823	−	0.122873i
$609$	6607.22	+	11365.7i	0.0178149	+	0.0306451i
$610$	219149.	+	379577.i	0.588951	+	1.02009i
$611$			147444.i			0.394953i
$612$	−1730.49	−	290396.i	−0.00462027	−	0.775333i
$613$	144548.			0.384672			0.192336	−	0.981329i	$-0.438394\pi$
$613$	144548.			0.384672			0.192336	+	0.981329i	$0.438394\pi$
$614$	124199.	−	71706.6i	0.329445	−	0.190205i
$615$	−169.059	−	56740.4i	−0.000446979	−	0.150018i
$616$	−3238.35	+	5608.99i	−0.00853420	+	0.0147817i
$617$	398472.	+	230058.i	1.04671	+	0.604319i	0.921727	−	0.387839i	$-0.126778\pi$
$617$	398472.	+	230058.i	1.04671	+	0.604319i	0.124985	+	0.992159i	$0.460112\pi$
$618$	−92153.2	+	160718.i	−0.241287	+	0.420812i
$619$	−53625.4	−	92881.9i	−0.139955	−	0.242410i	0.787524	−	0.616284i	$-0.211363\pi$
$619$	−53625.4	−	92881.9i	−0.139955	−	0.242410i	−0.927479	+	0.373874i	$0.878029\pi$
$620$		−	178866.i		−	0.465311i
$621$	142229.	−	251514.i	0.368813	−	0.652197i
$622$	104864.			0.271047
$623$	−24130.8	+	13931.9i	−0.0621722	+	0.0358951i
$624$	97866.7	+	56115.2i	0.251342	+	0.144116i
$625$	133166.	−	230650.i	0.340905	−	0.590464i
$626$	433801.	+	250455.i	1.10698	+	0.639118i
$627$	−477194.	+	1421.80i	−1.21384	+	0.00361663i
$628$	−46176.6	−	79980.2i	−0.117085	−	0.202798i
$629$			826399.i			2.08876i
$630$	11527.0	−	20243.0i	0.0290426	−	0.0510028i
$631$	−585714.			−1.47105			−0.735524	−	0.677498i	$-0.763064\pi$
$631$	−585714.			−1.47105			−0.735524	+	0.677498i	$0.763064\pi$
$632$	153583.	−	88671.3i	0.384512	−	0.221998i
$633$	−104140.	+	60539.6i	−0.259902	+	0.151089i
$634$	39939.7	−	69177.5i	0.0993632	−	0.172102i
$635$	−325767.	−	188082.i	−0.807903	−	0.466443i
$636$	33067.4	+	56882.3i	0.0817495	+	0.140625i
$637$	−234407.	−	406004.i	−0.577685	−	1.00058i
$638$		−	161127.i		−	0.395846i
$639$	−201837.	+	118140.i	−0.494310	+	0.289331i
$640$	−54351.4			−0.132694
$641$	269007.	−	155311.i	0.654707	−	0.377995i	−0.135550	−	0.990770i	$-0.543280\pi$
$641$	269007.	−	155311.i	0.654707	−	0.377995i	0.790257	+	0.612775i	$0.209947\pi$
$642$	−177.893	−	59705.4i	−0.000431607	−	0.144858i
$643$	−217352.	+	376464.i	−0.525704	+	0.910546i	0.473848	+	0.880607i	$0.342865\pi$
$643$	−217352.	+	376464.i	−0.525704	+	0.910546i	−0.999552	+	0.0299390i	$0.990469\pi$
$644$	−7439.45	−	4295.17i	−0.0179378	−	0.0103564i
$645$	104352.	−	181993.i	0.250831	−	0.437456i
$646$	−318059.	−	550895.i	−0.762155	−	1.32009i
$647$		−	491590.i		−	1.17434i	−0.809463	−	0.587171i	$-0.800242\pi$
$647$		−	491590.i		−	1.17434i	0.809463	−	0.587171i	$-0.199758\pi$
$648$	−129444.	−	72691.7i	−0.308271	−	0.173115i
$649$	−139376.			−0.330902
$650$	−375938.	+	217048.i	−0.889793	+	0.513722i
$651$	−12600.6	−	7225.01i	−0.0297325	−	0.0170481i
$652$	−168971.	+	292667.i	−0.397482	+	0.688459i
$653$	−394771.	−	227921.i	−0.925805	−	0.534514i	−0.0403223	−	0.999187i	$-0.512838\pi$
$653$	−394771.	−	227921.i	−0.925805	−	0.534514i	−0.885482	+	0.464673i	$0.846172\pi$
$654$	149629.	−	445.821i	0.349832	−	0.00104233i
$655$	426677.	+	739026.i	0.994527	+	1.72257i
$656$			10750.7i			0.0249820i
$657$	4862.01	+	8306.54i	0.0112638	+	0.0192437i
$658$	−5768.60			−0.0133235
$659$	241349.	−	139343.i	0.555744	−	0.320859i	−0.195692	−	0.980665i	$-0.562695\pi$
$659$	241349.	−	139343.i	0.555744	−	0.320859i	0.751435	+	0.659807i	$0.229362\pi$
$660$	−246828.	+	143488.i	−0.566639	+	0.329404i
$661$	422668.	−	732082.i	0.967378	−	1.67555i	0.264291	−	0.964443i	$-0.414862\pi$
$661$	422668.	−	732082.i	0.967378	−	1.67555i	0.703087	−	0.711104i	$-0.251805\pi$
$662$	−400231.	−	231074.i	−0.913261	−	0.527272i
$663$	397015.	+	682943.i	0.903192	+	1.55366i
$664$	57536.1	+	99655.5i	0.130498	+	0.226030i
$665$		−	51027.0i		−	0.115387i
$666$	367122.	+	209051.i	0.827680	+	0.471308i
$667$	213709.			0.480366
$668$	−138904.	+	80196.5i	−0.311289	+	0.179723i
$669$	1552.05	+	520908.i	0.00346780	+	1.16388i
$670$	354733.	−	614416.i	0.790228	−	1.36872i
$671$	−377784.	−	218113.i	−0.839070	−	0.484437i
$672$	−2195.45	+	3828.93i	−0.00486166	+	0.00847888i
$673$	−48001.2	−	83140.5i	−0.105980	−	0.183562i	0.808158	−	0.588965i	$-0.200464\pi$
$673$	−48001.2	−	83140.5i	−0.105980	−	0.183562i	−0.914138	+	0.405403i	$0.867131\pi$
$674$			560680.i			1.23423i
$675$	492149.	−	290038.i	1.08016	−	0.636572i
$676$	−78389.0			−0.171539
$677$	389771.	−	225034.i	0.850416	−	0.490988i	−0.0103749	−	0.999946i	$-0.503302\pi$
$677$	389771.	−	225034.i	0.850416	−	0.490988i	0.860791	+	0.508958i	$0.169969\pi$
$678$	−314200.	−	180157.i	−0.683512	−	0.391915i
$679$	1193.12	−	2066.55i	0.00258789	−	0.00448236i
$680$	−329599.	−	190294.i	−0.712800	−	0.411535i
$681$	251548.	−	749.491i	0.542409	−	0.00161611i
$682$	89010.3	+	154170.i	0.191369	+	0.331461i
$683$		−	429135.i		−	0.919926i	−0.887938	−	0.459963i	$-0.847863\pi$
$683$		−	429135.i		−	0.919926i	0.887938	−	0.459963i	$-0.152137\pi$
$684$	−325190.	+	1937.83i	−0.695064	+	0.00414194i
$685$	−410171.			−0.874145
$686$	31817.6	−	18369.9i	0.0676114	−	0.0390354i
$687$	−462701.	+	268982.i	−0.980364	+	0.569915i
$688$	−19874.2	+	34423.2i	−0.0419868	+	0.0727233i
$689$	−155000.	−	89489.2i	−0.326507	−	0.188509i
$690$	−190315.	−	327378.i	−0.399737	−	0.687625i
$691$	24875.5	+	43085.6i	0.0520973	+	0.0902352i	0.890898	−	0.454203i	$-0.150076\pi$
$691$	24875.5	+	43085.6i	0.0520973	+	0.0902352i	−0.838801	+	0.544439i	$0.816743\pi$
$692$			304418.i			0.635709i
$693$	138.158	+	23184.4i	0.000287679	+	0.0482759i
$694$	−91853.2			−0.190711
$695$	−777731.	+	449023.i	−1.61012	+	0.929606i
$696$	−327.159	−	109803.i	−0.000675367	−	0.226671i
$697$	−37640.0	+	65194.4i	−0.0774790	+	0.134198i
$698$	−357791.	−	206571.i	−0.734376	−	0.423992i
$699$	76514.9	−	133444.i	0.156600	−	0.273115i
$700$	−8491.75	−	14708.1i	−0.0173301	−	0.0300166i
$701$			291866.i			0.593946i	0.954886	+	0.296973i	$0.0959771\pi$
$701$			291866.i			0.593946i	−0.954886	+	0.296973i	$0.904023\pi$
$702$	403824.	−	3609.68i	0.819442	−	0.00732478i
$703$	925414.			1.87252
$704$	46847.4	−	27047.3i	0.0945235	−	0.0545732i
$705$	−220600.	−	126488.i	−0.443840	−	0.254491i
$706$	247647.	−	428937.i	0.496848	−	0.860567i
$707$	9683.50	+	5590.77i	0.0193728	+	0.0111849i
$708$	−94980.5	+	282.996i	−0.189482	+	0.000564564i
$709$	103058.	+	178501.i	0.205016	+	0.355099i	0.950138	−	0.311830i	$-0.100942\pi$
$709$	103058.	+	178501.i	0.205016	+	0.355099i	−0.745122	+	0.666929i	$0.767609\pi$
$710$			306500.i			0.608015i
$711$	314137.	−	551668.i	0.621413	−	1.09129i
$712$	232724.			0.459073
$713$	−204483.	+	118058.i	−0.402233	+	0.232229i
$714$	−26719.4	+	15532.8i	−0.0524119	+	0.0304686i
$715$	388318.	−	672587.i	0.759584	−	1.31564i
$716$	234138.	+	135180.i	0.456716	+	0.263685i
$717$	401271.	+	690264.i	0.780547	+	1.34269i
$718$	307165.	+	532025.i	0.595830	+	1.03201i
$719$		−	736226.i		−	1.42414i	−0.702108	−	0.712071i	$-0.747757\pi$
$719$		−	736226.i		−	1.42414i	0.702108	−	0.712071i	$-0.252243\pi$
$720$	−167914.	+	98284.0i	−0.323909	+	0.189591i
$721$	19716.8			0.0379285
$722$	−297680.	+	171866.i	−0.571052	+	0.329697i
$723$	1477.71	+	495959.i	0.00282692	+	0.948787i
$724$	179251.	−	310472.i	0.341967	−	0.592305i
$725$	365908.	+	211257.i	0.696138	+	0.401916i
$726$	−44042.9	+	76812.1i	−0.0835608	+	0.145733i
$727$	−68590.3	−	118802.i	−0.129776	−	0.224778i	0.793814	−	0.608161i	$-0.208092\pi$
$727$	−68590.3	−	118802.i	−0.129776	−	0.224778i	−0.923590	+	0.383382i	$0.874759\pi$
$728$		−	12006.2i		−	0.0226540i
$729$	−531356.	+	9500.07i	−0.999840	+	0.0178761i
$730$	12613.9			0.0236703
$731$	−241043.	+	139166.i	−0.451086	+	0.260435i
$732$	−257891.	−	147870.i	−0.481297	−	0.275968i
$733$	−419306.	+	726258.i	−0.780410	+	1.35171i	0.151294	+	0.988489i	$0.451656\pi$
$733$	−419306.	+	726258.i	−0.780410	+	1.35171i	−0.931703	+	0.363220i	$0.881677\pi$
$734$	454707.	+	262525.i	0.843995	+	0.487281i
$735$	808536.	−	2409.04i	1.49667	−	0.00445933i
$736$	35874.0	+	62135.7i	0.0662254	+	0.114706i
$737$			706115.i			1.29999i
$738$	19440.5	+	33213.3i	0.0356940	+	0.0609817i
$739$	−1.05122e6			−1.92488			−0.962442	−	0.271488i	$-0.912484\pi$
$739$	−1.05122e6			−1.92488			−0.962442	+	0.271488i	$0.912484\pi$
$740$	479494.	−	276836.i	0.875628	−	0.505544i
$741$	764769.	−	444583.i	1.39282	−	0.809686i
$742$	3501.17	−	6064.20i	0.00635924	−	0.0110145i
$743$	191179.	+	110377.i	0.346308	+	0.199941i	0.663058	−	0.748568i	$-0.269258\pi$
$743$	191179.	+	110377.i	0.346308	+	0.199941i	−0.316750	+	0.948509i	$0.602592\pi$
$744$	60970.8	+	104882.i	0.110148	+	0.189476i
$745$	−119780.	−	207464.i	−0.215809	−	0.373793i
$746$		−	225934.i		−	0.405980i
$747$	357961.	+	203834.i	0.641496	+	0.365289i
$748$	378790.			0.677010
$749$	−5502.92	+	3177.11i	−0.00980910	+	0.00566329i
$750$	−451.514	−	151540.i	−0.000802692	−	0.269404i
$751$	−218252.	+	378023.i	−0.386970	+	0.670252i	−0.992040	−	0.125920i	$-0.959812\pi$
$751$	−218252.	+	378023.i	−0.386970	+	0.670252i	0.605070	+	0.796172i	$0.293145\pi$
$752$	41725.5	+	24090.2i	0.0737846	+	0.0425996i
$753$	−445432.	+	776847.i	−0.785582	+	1.37008i
$754$	149345.	+	258673.i	0.262692	+	0.454997i
$755$		−	1.17914e6i		−	2.06857i
$756$	141.225	+	15799.2i	0.000247097	+	0.0276434i
$757$	−689032.			−1.20240			−0.601198	−	0.799100i	$-0.705310\pi$
$757$	−689032.			−1.20240			−0.601198	+	0.799100i	$0.705310\pi$
$758$	139308.	−	80429.3i	0.242458	−	0.139983i
$759$	326955.	+	187471.i	0.567550	+	0.325424i
$760$	−213094.	+	369089.i	−0.368930	+	0.639005i
$761$	367695.	+	212289.i	0.634920	+	0.366571i	0.782655	−	0.622456i	$-0.213865\pi$
$761$	367695.	+	212289.i	0.634920	+	0.366571i	−0.147735	+	0.989027i	$0.547198\pi$
$762$	255132.	−	760.170i	0.439396	−	0.00130918i
$763$	−7962.23	−	13791.0i	−0.0136768	−	0.0236890i
$764$		−	104934.i		−	0.179776i
$765$	−1.36238e6	+	8118.50i	−2.32795	+	0.0138724i
$766$	−276248.			−0.470806
$767$	223755.	−	129185.i	0.380348	−	0.219594i
$768$	31870.1	−	18527.0i	0.0540332	−	0.0314111i
$769$	372620.	−	645396.i	0.630105	−	1.09137i	−0.357425	−	0.933942i	$-0.616345\pi$
$769$	372620.	−	645396.i	0.630105	−	1.09137i	0.987530	−	0.157432i	$-0.0503215\pi$
$770$	26314.2	+	15192.5i	0.0443823	+	0.0256241i
$771$	−549919.	−	945968.i	−0.925103	−	1.59136i
$772$	9247.35	+	16016.9i	0.0155161	+	0.0268747i
$773$		−	757068.i		−	1.26700i	−0.773743	−	0.633499i	$-0.781618\pi$
$773$		−	757068.i		−	1.26700i	0.773743	−	0.633499i	$-0.218382\pi$
$774$	847.893	+	142286.i	0.00141533	+	0.237509i
$775$	−466814.			−0.777213
$776$	−17260.2	+	9965.19i	−0.0286631	+	0.0165486i
$777$	−133.963	−	44961.6i	−0.000221893	−	0.0744731i
$778$	122387.	−	211981.i	0.202198	−	0.350217i
$779$	73005.6	+	42149.8i	0.120304	+	0.0694577i
$780$	263261.	−	459136.i	0.432711	−	0.754661i
$781$	−152526.	−	264183.i	−0.250059	−	0.433115i
$782$			502405.i			0.821562i
$783$	−199568.	−	338635.i	−0.325512	−	0.552342i
$784$	−153194.			−0.249236
$785$	−375222.	+	216635.i	−0.608905	+	0.351551i
$786$	−502106.	−	287900.i	−0.812738	−	0.466011i
$787$	−387371.	+	670945.i	−0.625428	+	1.08327i	0.363030	+	0.931777i	$0.381742\pi$
$787$	−387371.	+	670945.i	−0.625428	+	1.08327i	−0.988458	+	0.151495i	$0.951591\pi$
$788$	−90828.7	−	52440.0i	−0.146275	−	0.0844520i
$789$	−1.08483e6	+	3232.26i	−1.74264	+	0.00519220i
$790$	−415996.	−	720526.i	−0.666553	−	1.15450i
$791$			38545.8i			0.0616062i
$792$	95821.1	−	168275.i	0.152760	−	0.268268i
$793$	808658.			1.28593
$794$	33144.8	−	19136.2i	0.0525744	−	0.0303539i
$795$	266860.	−	155134.i	0.422230	−	0.245455i
$796$	−42367.8	+	73383.2i	−0.0668667	+	0.115817i
$797$	380905.	+	219916.i	0.599653	+	0.346210i	0.768905	−	0.639363i	$-0.220802\pi$
$797$	380905.	+	219916.i	0.599653	+	0.346210i	−0.169252	+	0.985573i	$0.554135\pi$
$798$	17393.8	+	29920.8i	0.0273143	+	0.0469858i
$799$	168688.	+	292176.i	0.264235	+	0.457669i
$800$			141849.i			0.221640i
$801$	718982.	−	420837.i	1.12061	−	0.655917i
$802$	−73315.7			−0.113985
$803$	−10872.4	+	6277.16i	−0.0168614	+	0.00973492i
$804$	1433.73	+	481195.i	0.00221796	+	0.744405i
$805$	−20150.5	+	34901.7i	−0.0310953	+	0.0538586i
$806$	−285794.	−	165003.i	−0.439930	−	0.253994i
$807$	298665.	−	520881.i	0.458603	−	0.799818i
$808$	−46695.2	−	80878.4i	−0.0715236	−	0.123882i
$809$			45564.3i			0.0696189i	0.999394	+	0.0348095i	$0.0110824\pi$
$809$			45564.3i			0.0696189i	−0.999394	+	0.0348095i	$0.988918\pi$
$810$	−341029.	+	607280.i	−0.519782	+	0.925591i
$811$	262824.			0.399598			0.199799	−	0.979837i	$-0.435971\pi$
$811$	262824.			0.399598			0.199799	+	0.979837i	$0.435971\pi$
$812$	−10120.3	+	5842.96i	−0.0153490	+	0.00886177i
$813$	−862984.	−	494821.i	−1.30563	−	0.748630i
$814$	−275528.	+	477229.i	−0.415831	+	0.720241i
$815$	1.37303e6	+	792718.i	2.06711	+	1.19345i
$816$	258133.	−	769.111i	0.387672	−	0.00115507i
$817$	155840.	+	269923.i	0.233472	+	0.404386i
$818$			115178.i			0.172133i
$819$	−21710.9	−	37092.2i	−0.0323676	−	0.0552987i
$820$	50436.1			0.0750091
$821$	860622.	−	496881.i	1.27681	−	0.737167i	0.300550	−	0.953766i	$-0.402830\pi$
$821$	860622.	−	496881.i	1.27681	−	0.737167i	0.976261	+	0.216600i	$0.0694966\pi$
$822$	240512.	−	139817.i	0.355953	−	0.206926i
$823$	−148709.	+	257571.i	−0.219552	+	0.380275i	−0.954671	−	0.297663i	$-0.903793\pi$
$823$	−148709.	+	257571.i	−0.219552	+	0.380275i	0.735119	+	0.677938i	$0.237126\pi$
$824$	−142616.	−	82339.3i	−0.210045	−	0.121270i
$825$	374484.	+	644185.i	0.550206	+	0.946462i
$826$	5054.21	+	8754.15i	0.00740787	+	0.0128308i
$827$			1.33030e6i			1.94508i	0.232734	+	0.972540i	$0.425233\pi$
$827$			1.33030e6i			1.94508i	−0.232734	+	0.972540i	$0.574767\pi$
$828$	223190.	+	127092.i	0.325547	+	0.185377i
$829$	180009.			0.261931			0.130965	−	0.991387i	$-0.458192\pi$
$829$	180009.			0.261931			0.130965	+	0.991387i	$0.458192\pi$
$830$	467528.	−	269927.i	0.678659	−	0.391824i
$831$	−2048.22	−	687436.i	−0.00296603	−	0.995475i
$832$	−50139.2	+	86843.6i	−0.0724320	+	0.125456i
$833$	−929002.	−	536360.i	−1.33883	−	0.772976i
$834$	302978.	−	528403.i	0.435591	−	0.759684i
$835$	376237.	+	651662.i	0.539621	+	0.934651i
$836$		−	424174.i		−	0.606920i
$837$	378022.	+	213769.i	0.539593	+	0.305136i
$838$	−145519.			−0.207220
$839$	−434857.	+	251065.i	−0.617763	+	0.356666i	−0.775998	−	0.630736i	$-0.782753\pi$
$839$	−434857.	+	251065.i	−0.617763	+	0.356666i	0.158234	+	0.987402i	$0.449420\pi$
$840$	17963.2	+	10299.8i	0.0254580	+	0.0145972i
$841$	−208280.	+	360752.i	−0.294480	+	0.510054i
$842$	−447442.	−	258331.i	−0.631121	−	0.364378i
$843$	−300013.	+	893.892i	−0.422168	+	0.00125785i
$844$	−53536.9	−	92728.7i	−0.0751568	−	0.130175i
$845$			367758.i			0.515049i
$846$	172470.	−	1027.76i	0.240975	−	0.00143599i
$847$	9423.27			0.0131351
$848$	−50649.4	+	29242.4i	−0.0704340	+	0.0406651i
$849$	682113.	−	396533.i	0.946327	−	0.550128i
$850$	−496640.	+	860205.i	−0.687391	+	1.19060i
$851$	−632969.	−	365445.i	−0.874024	−	0.504618i
$852$	−104478.	−	179723.i	−0.143929	−	0.247585i
$853$	−198999.	−	344677.i	−0.273498	−	0.473712i	0.696257	−	0.717792i	$-0.254847\pi$
$853$	−198999.	−	344677.i	−0.273498	−	0.473712i	−0.969755	+	0.244080i	$0.921514\pi$
$854$			31637.9i			0.0433802i
$855$	9091.21	+	1.52561e6i	0.0124363	+	2.08694i
$856$	53071.7			0.0724295
$857$	−790484.	+	456386.i	−1.07630	+	0.621400i	−0.929895	−	0.367826i	$-0.880102\pi$
$857$	−790484.	+	456386.i	−1.07630	+	0.621400i	−0.146401	+	0.989225i	$0.546769\pi$
$858$	1569.47	+	526753.i	0.00213195	+	0.715538i
$859$	429824.	−	744477.i	0.582511	−	1.00894i	−0.412669	−	0.910881i	$-0.635403\pi$
$859$	429824.	−	744477.i	0.582511	−	1.00894i	0.995181	−	0.0980584i	$-0.0312632\pi$
$860$	161494.	+	93238.7i	0.218353	+	0.126066i
$861$	2037.29	−	3553.10i	0.00274819	−	0.00479294i
$862$	−110880.	−	192050.i	−0.149225	−	0.258464i
$863$		−	627697.i		−	0.842808i	−0.906873	−	0.421404i	$-0.861538\pi$
$863$		−	627697.i		−	0.842808i	0.906873	−	0.421404i	$-0.138462\pi$
$864$	64957.4	−	114869.i	0.0870164	−	0.153877i
$865$	1.42816e6			1.90873
$866$	809759.	−	467515.i	1.07974	−	0.623390i
$867$	915970.	+	525203.i	1.21855	+	0.698697i
$868$	6455.58	−	11181.4i	0.00856832	−	0.0148408i
$869$	717122.	+	414031.i	0.949628	+	0.548268i
$870$	−515134.	+	1534.85i	−0.680583	+	0.00202781i
$871$	−654483.	−	1.13360e6i	−0.862704	−	1.49425i
$872$			133004.i			0.174917i
$873$	−35303.9	+	61998.4i	−0.0463227	+	0.0813489i
$874$	562600.			0.736508
$875$	−13967.1	+	8063.91i	−0.0182427	+	0.0105324i
$876$	−7396.43	+	4299.77i	−0.00963860	+	0.00560321i
$877$	22590.9	−	39128.6i	0.0293720	−	0.0508739i	−0.850966	−	0.525221i	$-0.823983\pi$
$877$	22590.9	−	39128.6i	0.0293720	−	0.0508739i	0.880338	+	0.474347i	$0.157316\pi$
$878$	−607011.	−	350458.i	−0.787422	−	0.454618i
$879$	−740959.	−	1.27459e6i	−0.958995	−	1.64966i
$880$	−126891.	−	219782.i	−0.163857	−	0.283809i
$881$			694637.i			0.894966i	0.894293	+	0.447483i	$0.147679\pi$
$881$			694637.i			0.894966i	−0.894293	+	0.447483i	$0.852321\pi$
$882$	−473281.	+	277022.i	−0.608389	+	0.356104i
$883$	1.39415e6			1.78809			0.894044	−	0.447979i	$-0.147856\pi$
$883$	1.39415e6			1.78809			0.894044	+	0.447979i	$0.147856\pi$
$884$	−608109.	+	351092.i	−0.778174	+	0.449279i
$885$	1327.66	+	445596.i	0.00169512	+	0.568924i
$886$	−222535.	+	385442.i	−0.283485	+	0.491011i
$887$	−491320.	−	283664.i	−0.624478	−	0.360542i	0.154133	−	0.988050i	$-0.450742\pi$
$887$	−491320.	−	283664.i	−0.624478	−	0.360542i	−0.778610	+	0.627508i	$0.784075\pi$
$888$	−186795.	+	325776.i	−0.236886	+	0.413136i
$889$	−13576.4	−	23515.0i	−0.0171783	−	0.0297537i
$890$		−	1.09181e6i		−	1.37838i
$891$	−8261.29	−	693145.i	−0.0104062	−	0.873109i
$892$	−463032.			−0.581944
$893$	327183.	−	188899.i	0.410287	−	0.236880i
$894$	140955.	+	80821.2i	0.176362	+	0.101123i
$895$	634188.	−	1.09845e6i	0.791720	−	1.37130i
$896$	−3397.66	−	1961.64i	−0.00423218	−	0.00244345i
$897$	−698656.	+	2081.65i	−0.868317	+	0.00258716i
$898$	39224.0	+	67938.0i	0.0486407	+	0.0842481i
$899$			321202.i			0.397429i
$900$	256507.	+	438232.i	0.316676	+	0.541027i
$901$	−409531.			−0.504473
$902$	−43472.6	+	25098.9i	−0.0534322	+	0.0308491i
$903$	13091.8	−	7610.63i	0.0160555	−	0.00933351i
$904$	160971.	−	278810.i	0.196975	−	0.341171i
$905$	−1.45656e6	−	840946.i	−1.77841	−	1.02676i
$906$	401938.	+	691412.i	0.489669	+	0.842327i
$907$	−50704.7	−	87823.1i	−0.0616359	−	0.106756i	0.833561	−	0.552428i	$-0.186298\pi$
$907$	−50704.7	−	87823.1i	−0.0616359	−	0.106756i	−0.895197	+	0.445671i	$0.852965\pi$
$908$			223600.i			0.271206i
$909$	−290514.	−	165428.i	−0.351592	−	0.200208i
$910$	−56326.5			−0.0680190
$911$	−1.22389e6	+	706615.i	−1.47471	+	0.851424i	−0.999594	−	0.0284993i	$-0.990927\pi$
$911$	−1.22389e6	+	706615.i	−1.47471	+	0.851424i	−0.475116	+	0.879923i	$0.657594\pi$
$912$	−861.262	−	289061.i	−0.00103549	−	0.347537i
$913$	−268652.	+	465319.i	−0.322291	+	0.558225i
$914$	34089.5	+	19681.6i	0.0408063	+	0.0235596i
$915$	−693725.	+	1.20988e6i	−0.828601	+	1.44511i
$916$	−237869.	−	412001.i	−0.283496	−	0.491029i
$917$			61598.1i			0.0732536i
$918$	796090.	−	469160.i	0.944663	−	0.556719i
$919$	−870421.			−1.03062			−0.515310	−	0.857004i	$-0.672323\pi$
$919$	−870421.			−1.03062			−0.515310	+	0.857004i	$0.672323\pi$
$920$	291506.	−	168301.i	0.344407	−	0.198843i
$921$	395878.	+	226990.i	0.466705	+	0.267601i
$922$	574205.	−	994551.i	0.675468	−	1.16994i
$923$	489731.	+	282746.i	0.574850	+	0.331890i
$924$	−20608.7	+	61.4037i	−0.0241382	+	7.19202e-5i
$925$	−722502.	−	1.25141e6i	−0.844415	−	1.46257i
$926$			779191.i			0.908703i
$927$	−589494.	+	3512.84i	−0.685993	+	0.00408789i
$928$	97603.0			0.113336
$929$	496469.	−	286636.i	0.575255	−	0.332124i	−0.183990	−	0.982928i	$-0.558902\pi$
$929$	496469.	−	286636.i	0.575255	−	0.332124i	0.759245	+	0.650804i	$0.225568\pi$
$930$	492045.	−	286041.i	0.568904	−	0.330721i
$931$	−600623.	+	1.04031e6i	−0.692951	+	1.20023i
$932$	118414.	+	68366.4i	0.136324	+	0.0787065i
$933$	167697.	+	288472.i	0.192647	+	0.331390i
$934$	462821.	+	801630.i	0.530542	+	0.918926i
$935$		−	1.77707e6i		−	2.03274i
$936$	2139.09	+	358963.i	0.00244161	+	0.409730i
$937$	538264.			0.613079			0.306539	−	0.951858i	$-0.400829\pi$
$937$	538264.			0.613079			0.306539	+	0.951858i	$0.400829\pi$
$938$	44350.7	−	25605.9i	0.0504075	−	0.0291028i
$939$	4748.98	+	1.59388e6i	0.00538603	+	1.80769i
$940$	113018.	−	195753.i	0.127906	−	0.221540i
$941$	262454.	+	151528.i	0.296397	+	0.171125i	0.640823	−	0.767688i	$-0.278593\pi$
$941$	262454.	+	151528.i	0.296397	+	0.171125i	−0.344426	+	0.938813i	$0.611926\pi$
$942$	146174.	−	254932.i	0.164728	−	0.287291i
$943$	−33289.8	−	57659.6i	−0.0374359	−	0.0648408i
$944$		−	84427.5i		−	0.0947415i
$945$	74120.9	−	662.548i	0.0829998	−	0.000741914i
$946$	−185596.			−0.207390
$947$	661805.	−	382093.i	0.737955	−	0.426059i	−0.0833701	−	0.996519i	$-0.526568\pi$
$947$	661805.	−	382093.i	0.737955	−	0.426059i	0.821325	+	0.570460i	$0.193235\pi$
$948$	489537.	+	280693.i	0.544714	+	0.312331i
$949$	11636.3	−	20154.7i	0.0129206	−	0.0223792i
$950$	963270.	+	556144.i	1.06734	+	0.616226i
$951$	254173.	−	757.312i	0.281040	−	0.000837363i
$952$	−13736.1	−	23791.6i	−0.0151562	−	0.0262512i
$953$		−	314531.i		−	0.346320i	−0.984894	−	0.173160i	$-0.944602\pi$
$953$		−	314531.i		−	0.346320i	0.984894	−	0.173160i	$-0.0553977\pi$
$954$	−103598.	+	181932.i	−0.113829	+	0.199899i
$955$	−492294.			−0.539781
$956$	−614628.	+	354855.i	−0.672506	+	0.388272i
$957$	443247.	−	257673.i	0.483974	−	0.281349i
$958$	−8294.30	+	14366.2i	−0.00903751	+	0.0156534i
$959$	−25640.9	−	14803.8i	−0.0278802	−	0.0160967i
$960$	−86918.5	−	149517.i	−0.0943126	−	0.162236i
$961$	284321.	+	492458.i	0.307866	+	0.533239i
$962$		−	1.02152e6i		−	1.10382i
$963$	163960.	−	95969.8i	0.176802	−	0.103486i
$964$	−440854.			−0.474396
$965$	75142.2	−	43383.4i	0.0806918	−	0.0465874i
$966$	−81.4424	−	27334.1i	−8.72763e−5	−	0.0292922i
$967$	−99369.6	+	172113.i	−0.106268	+	0.184061i	−0.914255	−	0.405138i	$-0.867223\pi$
$967$	−99369.6	+	172113.i	−0.106268	+	0.184061i	0.807988	+	0.589199i	$0.200557\pi$
$968$	−68160.5	−	39352.5i	−0.0727415	−	0.0419973i
$969$	1.00683e6	−	1.75595e6i	1.07228	−	1.87009i
$970$	46751.1	+	80975.3i	0.0496876	+	0.0860615i
$971$			1.81483e6i			1.92485i	0.271544	+	0.962426i	$0.412466\pi$
$971$			1.81483e6i			1.92485i	−0.271544	+	0.962426i	$0.587534\pi$
$972$	−7037.20	−	472340.i	−0.00744848	−	0.499945i
$973$	−64824.2			−0.0684717
$974$	−291938.	+	168550.i	−0.307732	+	0.177669i
$975$	−1.19828e6	−	687074.i	−1.26052	−	0.722760i
$976$	132123.	−	228843.i	0.138701	−	0.240236i
$977$	181807.	+	104967.i	0.190468	+	0.109967i	0.592202	−	0.805790i	$-0.298259\pi$
$977$	181807.	+	104967.i	0.190468	+	0.109967i	−0.401734	+	0.915757i	$0.631592\pi$
$978$	−1.07532e6	+	3203.93i	−1.12424	+	0.00334970i
$979$	543327.	+	941071.i	0.566887	+	0.981876i
$980$			718702.i			0.748336i
$981$	240512.	+	410905.i	0.249919	+	0.426976i
$982$	438414.			0.454633
$983$	247315.	−	142787.i	0.255943	−	0.147769i	−0.366540	−	0.930402i	$-0.619458\pi$
$983$	247315.	−	142787.i	0.255943	−	0.147769i	0.622482	+	0.782634i	$0.286124\pi$
$984$	−29574.3	+	17192.4i	−0.0305439	+	0.0177561i
$985$	−246019.	+	426118.i	−0.253569	+	0.439195i
$986$	591885.	+	341725.i	0.608813	+	0.351498i
$987$	−9225.11	−	15869.0i	−0.00946972	−	0.0162898i
$988$	393158.	+	680969.i	0.402766	+	0.697611i
$989$		−	246165.i		−	0.251671i
$990$	−789451.	−	449539.i	−0.805480	−	0.458666i
$991$	865158.			0.880944			0.440472	−	0.897766i	$-0.354811\pi$
$991$	865158.			0.880944			0.440472	+	0.897766i	$0.354811\pi$
$992$	−93389.1	+	53918.2i	−0.0949015	+	0.0547914i
$993$	−4381.48	−	1.47054e6i	−0.00444347	−	1.49134i
$994$	−11062.1	+	19160.2i	−0.0111961	+	0.0193922i
$995$	344273.	+	198766.i	0.347742	+	0.200769i
$996$	−182133.	+	317646.i	−0.183599	+	0.320202i
$997$	234861.	+	406791.i	0.236276	+	0.409243i	0.959643	−	0.281222i	$-0.0907396\pi$
$997$	234861.	+	406791.i	0.236276	+	0.409243i	−0.723366	+	0.690464i	$0.757406\pi$
$998$			293630.i			0.294808i
$999$	12015.8	+	1.34424e6i	0.0120399	+	1.34693i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	18.5.d.a.5.1	✓	8
3.2	odd	2		54.5.d.a.17.4		8
4.3	odd	2		144.5.q.b.113.4		8
9.2	odd	6	inner	18.5.d.a.11.1	yes	8
9.4	even	3		162.5.b.c.161.4		8
9.5	odd	6		162.5.b.c.161.5		8
9.7	even	3		54.5.d.a.35.4		8
12.11	even	2		432.5.q.b.17.4		8
36.7	odd	6		432.5.q.b.305.4		8
36.11	even	6		144.5.q.b.65.4		8
36.23	even	6		1296.5.e.e.161.2		8
36.31	odd	6		1296.5.e.e.161.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.5.d.a.5.1	✓	8	1.1	even	1	trivial
18.5.d.a.11.1	yes	8	9.2	odd	6	inner
54.5.d.a.17.4		8	3.2	odd	2
54.5.d.a.35.4		8	9.7	even	3
144.5.q.b.65.4		8	36.11	even	6
144.5.q.b.113.4		8	4.3	odd	2
162.5.b.c.161.4		8	9.4	even	3
162.5.b.c.161.5		8	9.5	odd	6
432.5.q.b.17.4		8	12.11	even	2
432.5.q.b.305.4		8	36.7	odd	6
1296.5.e.e.161.2		8	36.23	even	6
1296.5.e.e.161.7		8	36.31	odd	6

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:	\( N \)	\(=\)	\( 18 = 2 \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	18.d (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.44949 + 1.41421i) q^{2} +(-7.80760 - 4.47676i) q^{3} +(4.00000 - 6.92820i) q^{4} +(-32.5033 - 18.7658i) q^{5} +(25.4557 - 0.0758456i) q^{6} +(-1.35458 - 2.34620i) q^{7} +22.6274i q^{8} +(40.9173 + 69.9055i) q^{9} +O(q^{10})\)	\(q+(-2.44949 + 1.41421i) q^{2} +(-7.80760 - 4.47676i) q^{3} +(4.00000 - 6.92820i) q^{4} +(-32.5033 - 18.7658i) q^{5} +(25.4557 - 0.0758456i) q^{6} +(-1.35458 - 2.34620i) q^{7} +22.6274i q^{8} +(40.9173 + 69.9055i) q^{9} +106.155 q^{10} +(-91.4988 + 52.8268i) q^{11} +(-62.2463 + 36.1856i) q^{12} +(97.9281 - 169.616i) q^{13} +(6.63606 + 3.83133i) q^{14} +(169.763 + 292.025i) q^{15} +(-32.0000 - 55.4256i) q^{16} -448.150i q^{17} +(-199.088 - 113.367i) q^{18} -501.845 q^{19} +(-260.026 + 150.126i) q^{20} +(0.0726474 + 24.3823i) q^{21} +(149.417 - 258.798i) q^{22} +(343.254 + 198.178i) q^{23} +(101.297 - 176.666i) q^{24} +(391.808 + 678.631i) q^{25} +553.965i q^{26} +(-6.51608 - 728.971i) q^{27} -21.6733 q^{28} +(466.948 - 269.593i) q^{29} +(-828.817 - 475.231i) q^{30} +(-297.859 + 515.907i) q^{31} +(156.767 + 90.5097i) q^{32} +(950.879 - 2.83315i) q^{33} +(633.780 + 1097.74i) q^{34} +101.679i q^{35} +(647.988 - 3.86141i) q^{36} -1844.02 q^{37} +(1229.26 - 709.716i) q^{38} +(-1523.91 + 885.897i) q^{39} +(424.621 - 735.465i) q^{40} +(-145.474 - 83.9896i) q^{41} +(-34.6598 - 59.6215i) q^{42} +(-310.535 - 537.862i) q^{43} +845.229i q^{44} +(-18.1156 - 3040.00i) q^{45} -1121.06 q^{46} +(-651.961 + 376.410i) q^{47} +(1.71619 + 575.997i) q^{48} +(1196.83 - 2072.97i) q^{49} +(-1919.46 - 1108.20i) q^{50} +(-2006.26 + 3498.98i) q^{51} +(-783.425 - 1356.93i) q^{52} -913.826i q^{53} +(1046.88 + 1776.39i) q^{54} +3965.34 q^{55} +(53.0885 - 30.6506i) q^{56} +(3918.21 + 2246.64i) q^{57} +(-762.523 + 1320.73i) q^{58} +(1142.44 + 659.590i) q^{59} +(2702.26 - 8.05141i) q^{60} +(2064.42 + 3575.68i) q^{61} -1684.94i q^{62} +(108.587 - 190.693i) q^{63} -512.000 q^{64} +(-6365.96 + 3675.39i) q^{65} +(-2325.16 + 1351.69i) q^{66} +(3341.65 - 5787.91i) q^{67} +(-3104.88 - 1792.60i) q^{68} +(-1792.80 - 3083.96i) q^{69} +(-143.796 - 249.061i) q^{70} +2887.29i q^{71} +(-1581.78 + 925.853i) q^{72} +118.825 q^{73} +(4516.92 - 2607.84i) q^{74} +(-21.0130 - 7052.51i) q^{75} +(-2007.38 + 3476.88i) q^{76} +(247.885 + 143.116i) q^{77} +(2479.97 - 4325.14i) q^{78} +(-3918.75 - 6787.48i) q^{79} +2402.02i q^{80} +(-3212.55 + 5720.69i) q^{81} +475.117 q^{82} +(4404.19 - 2542.76i) q^{83} +(169.216 + 97.0260i) q^{84} +(-8409.88 + 14566.3i) q^{85} +(1521.30 + 878.325i) q^{86} +(-4852.65 + 14.4585i) q^{87} +(-1195.33 - 2070.38i) q^{88} -10285.1i q^{89} +(4343.58 + 7420.83i) q^{90} -530.605 q^{91} +(2746.03 - 1585.42i) q^{92} +(4635.15 - 2694.55i) q^{93} +(1064.65 - 1844.02i) q^{94} +(16311.6 + 9417.50i) q^{95} +(-818.787 - 1408.47i) q^{96} +(440.403 + 762.801i) q^{97} +6770.29i q^{98} +(-7436.77 - 4234.73i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 6 q^{3} + 32 q^{4} + 18 q^{5} + 48 q^{6} - 26 q^{7} - 78 q^{9}+O(q^{10}) \) 8 * q + 6 * q^3 + 32 * q^4 + 18 * q^5 + 48 * q^6 - 26 * q^7 - 78 * q^9	\( 8 q + 6 q^{3} + 32 q^{4} + 18 q^{5} + 48 q^{6} - 26 q^{7} - 78 q^{9} - 720 q^{11} - 144 q^{12} + 10 q^{13} + 288 q^{14} + 1134 q^{15} - 256 q^{16} - 384 q^{18} + 100 q^{19} + 144 q^{20} + 438 q^{21} + 336 q^{22} + 1278 q^{23} + 384 q^{24} + 794 q^{25} - 1296 q^{27} - 416 q^{28} - 1854 q^{29} - 3456 q^{30} - 1478 q^{31} - 3384 q^{33} - 96 q^{34} + 1056 q^{36} - 32 q^{37} + 6768 q^{38} + 5274 q^{39} - 36 q^{41} + 2592 q^{42} - 68 q^{43} + 3402 q^{45} + 2112 q^{46} + 2214 q^{47} - 1536 q^{48} + 2442 q^{49} - 15552 q^{50} - 12006 q^{51} - 80 q^{52} + 7056 q^{54} - 3996 q^{55} + 2304 q^{56} + 10902 q^{57} - 2400 q^{58} + 9108 q^{59} + 6480 q^{60} - 4478 q^{61} - 6654 q^{63} - 4096 q^{64} - 22554 q^{65} - 19872 q^{66} + 7504 q^{67} - 11088 q^{68} - 5994 q^{69} + 6048 q^{70} + 5376 q^{72} + 20716 q^{73} + 15264 q^{74} + 16590 q^{75} + 400 q^{76} + 34434 q^{77} + 24096 q^{78} - 6050 q^{79} - 21150 q^{81} + 1152 q^{82} - 3834 q^{83} - 9600 q^{84} - 16092 q^{85} - 12528 q^{86} + 10170 q^{87} - 2688 q^{88} + 2592 q^{90} - 45868 q^{91} + 10224 q^{92} - 10926 q^{93} + 672 q^{94} + 20880 q^{95} + 31336 q^{97} - 22338 q^{99}+O(q^{100}) \) 8 * q + 6 * q^3 + 32 * q^4 + 18 * q^5 + 48 * q^6 - 26 * q^7 - 78 * q^9 - 720 * q^11 - 144 * q^12 + 10 * q^13 + 288 * q^14 + 1134 * q^15 - 256 * q^16 - 384 * q^18 + 100 * q^19 + 144 * q^20 + 438 * q^21 + 336 * q^22 + 1278 * q^23 + 384 * q^24 + 794 * q^25 - 1296 * q^27 - 416 * q^28 - 1854 * q^29 - 3456 * q^30 - 1478 * q^31 - 3384 * q^33 - 96 * q^34 + 1056 * q^36 - 32 * q^37 + 6768 * q^38 + 5274 * q^39 - 36 * q^41 + 2592 * q^42 - 68 * q^43 + 3402 * q^45 + 2112 * q^46 + 2214 * q^47 - 1536 * q^48 + 2442 * q^49 - 15552 * q^50 - 12006 * q^51 - 80 * q^52 + 7056 * q^54 - 3996 * q^55 + 2304 * q^56 + 10902 * q^57 - 2400 * q^58 + 9108 * q^59 + 6480 * q^60 - 4478 * q^61 - 6654 * q^63 - 4096 * q^64 - 22554 * q^65 - 19872 * q^66 + 7504 * q^67 - 11088 * q^68 - 5994 * q^69 + 6048 * q^70 + 5376 * q^72 + 20716 * q^73 + 15264 * q^74 + 16590 * q^75 + 400 * q^76 + 34434 * q^77 + 24096 * q^78 - 6050 * q^79 - 21150 * q^81 + 1152 * q^82 - 3834 * q^83 - 9600 * q^84 - 16092 * q^85 - 12528 * q^86 + 10170 * q^87 - 2688 * q^88 + 2592 * q^90 - 45868 * q^91 + 10224 * q^92 - 10926 * q^93 + 672 * q^94 + 20880 * q^95 + 31336 * q^97 - 22338 * q^99

Introduction

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