LMFDB - Embedded newform 26.5.f.a.19.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [26,5,Mod(7,26)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(26, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([11]))

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

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

chi := DirichletCharacter("26.7");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 26 = 2 \cdot 13 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	26.f (of order $12$, degree $4$, 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:	$2.68761904018$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	8.0.120336834816.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 2x^{6} + 46x^{5} + 445x^{4} + 68x^{3} + 32x^{2} + 1136x + 20164 $ x^8 - 2x^7 + 2x^6 + 46x^5 + 445x^4 + 68x^3 + 32x^2 + 1136*x + 20164
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			19.1
Root			$1.80078 - 1.80078i$ of defining polynomial
Character	$\chi$	$=$	26.19
Dual form			26.5.f.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)

$f(q)$	$=$	$q+(0.732051 + 2.73205i) q^{2} +(-3.39466 + 5.87972i) q^{3} +(-6.92820 + 4.00000i) q^{4} +(-10.7932 + 10.7932i) q^{5} +(-18.5487 - 4.97012i) q^{6} +(-4.14281 + 15.4612i) q^{7} +(-16.0000 - 16.0000i) q^{8} +(17.4526 + 30.2288i) q^{9} +O(q^{10})$	\(q+(0.732051 + 2.73205i) q^{2} +(-3.39466 + 5.87972i) q^{3} +(-6.92820 + 4.00000i) q^{4} +(-10.7932 + 10.7932i) q^{5} +(-18.5487 - 4.97012i) q^{6} +(-4.14281 + 15.4612i) q^{7} +(-16.0000 - 16.0000i) q^{8} +(17.4526 + 30.2288i) q^{9} +(-37.3887 - 21.5864i) q^{10} +(63.4031 - 16.9888i) q^{11} -54.3145i q^{12} +(147.515 + 82.4644i) q^{13} -45.2735 q^{14} +(-26.8217 - 100.100i) q^{15} +(32.0000 - 55.4256i) q^{16} +(260.411 - 150.348i) q^{17} +(-69.8105 + 69.8105i) q^{18} +(-6.07879 - 1.62881i) q^{19} +(31.6047 - 117.950i) q^{20} +(-76.8439 - 76.8439i) q^{21} +(92.8286 + 160.784i) q^{22} +(-336.766 - 194.432i) q^{23} +(148.390 - 39.7610i) q^{24} +392.014i q^{25} +(-117.309 + 463.386i) q^{26} -786.917 q^{27} +(-33.1425 - 123.689i) q^{28} +(-72.9490 + 126.351i) q^{29} +(253.844 - 146.557i) q^{30} +(-627.618 + 627.618i) q^{31} +(174.851 + 46.8513i) q^{32} +(-115.342 + 430.464i) q^{33} +(601.394 + 601.394i) q^{34} +(-122.161 - 211.590i) q^{35} +(-241.831 - 139.621i) q^{36} +(1947.04 - 521.708i) q^{37} -17.7999i q^{38} +(-985.629 + 587.407i) q^{39} +345.382 q^{40} +(-767.255 - 2863.43i) q^{41} +(153.688 - 266.195i) q^{42} +(2068.72 - 1194.37i) q^{43} +(-371.315 + 371.315i) q^{44} +(-514.635 - 137.896i) q^{45} +(284.668 - 1062.40i) q^{46} +(-951.593 - 951.593i) q^{47} +(217.258 + 376.302i) q^{48} +(1857.44 + 1072.39i) q^{49} +(-1071.00 + 286.974i) q^{50} +2041.53i q^{51} +(-1351.87 + 18.7293i) q^{52} +2641.26 q^{53} +(-576.063 - 2149.90i) q^{54} +(-500.959 + 867.686i) q^{55} +(313.664 - 181.094i) q^{56} +(30.2123 - 30.2123i) q^{57} +(-398.601 - 106.805i) q^{58} +(-1137.91 + 4246.75i) q^{59} +(586.227 + 586.227i) q^{60} +(2539.11 + 4397.86i) q^{61} +(-2174.13 - 1255.24i) q^{62} +(-539.676 + 144.606i) q^{63} +512.000i q^{64} +(-2482.21 + 702.102i) q^{65} -1260.49 q^{66} +(-1485.73 - 5544.82i) q^{67} +(-1202.79 + 2083.29i) q^{68} +(2286.41 - 1320.06i) q^{69} +(488.645 - 488.645i) q^{70} +(-7435.49 - 1992.33i) q^{71} +(204.419 - 762.903i) q^{72} +(-23.0864 - 23.0864i) q^{73} +(2850.66 + 4937.50i) q^{74} +(-2304.93 - 1330.75i) q^{75} +(48.6303 - 13.0304i) q^{76} +1050.67i q^{77} +(-2326.36 - 2262.78i) q^{78} +7919.96 q^{79} +(252.837 + 943.602i) q^{80} +(1257.65 - 2178.31i) q^{81} +(7261.38 - 4192.36i) q^{82} +(4637.16 - 4637.16i) q^{83} +(839.766 + 225.015i) q^{84} +(-1187.93 + 4433.41i) q^{85} +(4777.50 + 4777.50i) q^{86} +(-495.273 - 857.839i) q^{87} +(-1286.27 - 742.629i) q^{88} +(2696.21 - 722.446i) q^{89} -1506.96i q^{90} +(-1886.12 + 1939.12i) q^{91} +3110.91 q^{92} +(-1559.67 - 5820.76i) q^{93} +(1903.19 - 3296.41i) q^{94} +(83.1895 - 48.0295i) q^{95} +(-869.032 + 869.032i) q^{96} +(-13054.8 - 3498.02i) q^{97} +(-1570.09 + 5859.67i) q^{98} +(1620.10 + 1620.10i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} + 30 q^{5} + 36 q^{6} - 92 q^{7} - 128 q^{8} + 90 q^{9}+O(q^{10}) $ 8 * q - 8 * q^2 + 30 * q^5 + 36 * q^6 - 92 * q^7 - 128 * q^8 + 90 * q^9	\( 8 q - 8 q^{2} + 30 q^{5} + 36 q^{6} - 92 q^{7} - 128 q^{8} + 90 q^{9} + 132 q^{10} + 192 q^{11} - 78 q^{13} - 344 q^{14} + 132 q^{15} + 256 q^{16} - 870 q^{17} - 360 q^{18} - 218 q^{19} - 144 q^{20} + 1914 q^{21} + 948 q^{22} + 264 q^{23} - 288 q^{24} - 520 q^{26} - 2268 q^{27} - 736 q^{28} - 252 q^{29} + 1728 q^{30} - 3376 q^{31} + 512 q^{32} + 1698 q^{33} + 1080 q^{34} + 6474 q^{35} + 2016 q^{36} + 2552 q^{37} - 5928 q^{39} - 960 q^{40} - 8472 q^{41} - 3828 q^{42} + 7290 q^{43} - 3792 q^{44} - 6282 q^{45} - 540 q^{46} + 4848 q^{47} + 9678 q^{49} + 2524 q^{50} - 832 q^{52} - 6840 q^{53} + 2268 q^{54} + 294 q^{55} + 4320 q^{56} - 4434 q^{57} - 7008 q^{58} - 4632 q^{59} + 9024 q^{60} + 8670 q^{61} + 3936 q^{62} + 8100 q^{63} - 2808 q^{65} - 984 q^{66} - 12446 q^{67} - 2160 q^{68} + 19206 q^{69} - 25896 q^{70} - 4554 q^{71} - 5472 q^{72} + 19294 q^{73} + 10112 q^{74} - 25992 q^{75} + 1744 q^{76} - 8580 q^{78} - 11328 q^{79} - 1152 q^{80} + 6048 q^{81} + 42672 q^{82} + 10344 q^{83} - 8592 q^{84} - 23178 q^{85} + 13536 q^{86} + 18372 q^{87} + 1440 q^{88} - 2538 q^{89} + 1456 q^{91} + 96 q^{92} - 162 q^{93} - 9696 q^{94} + 26568 q^{95} - 64282 q^{97} - 31676 q^{98} + 9504 q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 + 30 * q^5 + 36 * q^6 - 92 * q^7 - 128 * q^8 + 90 * q^9 + 132 * q^10 + 192 * q^11 - 78 * q^13 - 344 * q^14 + 132 * q^15 + 256 * q^16 - 870 * q^17 - 360 * q^18 - 218 * q^19 - 144 * q^20 + 1914 * q^21 + 948 * q^22 + 264 * q^23 - 288 * q^24 - 520 * q^26 - 2268 * q^27 - 736 * q^28 - 252 * q^29 + 1728 * q^30 - 3376 * q^31 + 512 * q^32 + 1698 * q^33 + 1080 * q^34 + 6474 * q^35 + 2016 * q^36 + 2552 * q^37 - 5928 * q^39 - 960 * q^40 - 8472 * q^41 - 3828 * q^42 + 7290 * q^43 - 3792 * q^44 - 6282 * q^45 - 540 * q^46 + 4848 * q^47 + 9678 * q^49 + 2524 * q^50 - 832 * q^52 - 6840 * q^53 + 2268 * q^54 + 294 * q^55 + 4320 * q^56 - 4434 * q^57 - 7008 * q^58 - 4632 * q^59 + 9024 * q^60 + 8670 * q^61 + 3936 * q^62 + 8100 * q^63 - 2808 * q^65 - 984 * q^66 - 12446 * q^67 - 2160 * q^68 + 19206 * q^69 - 25896 * q^70 - 4554 * q^71 - 5472 * q^72 + 19294 * q^73 + 10112 * q^74 - 25992 * q^75 + 1744 * q^76 - 8580 * q^78 - 11328 * q^79 - 1152 * q^80 + 6048 * q^81 + 42672 * q^82 + 10344 * q^83 - 8592 * q^84 - 23178 * q^85 + 13536 * q^86 + 18372 * q^87 + 1440 * q^88 - 2538 * q^89 + 1456 * q^91 + 96 * q^92 - 162 * q^93 - 9696 * q^94 + 26568 * q^95 - 64282 * q^97 - 31676 * q^98 + 9504 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/26\mathbb{Z}\right)^\times$.

$n$	$15$
$\chi(n)$	$e\left(\frac{5}{12}\right)$

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 $

$2$	0.732051	+	2.73205i	0.183013	+	0.683013i
$2$	0.732051	+	2.73205i	0.183013	+	0.683013i
$3$	−3.39466	+	5.87972i	−0.377184	+	0.653302i	−0.990651	−	0.136418i	$-0.956441\pi$
$3$	−3.39466	+	5.87972i	−0.377184	+	0.653302i	0.613467	+	0.789720i	$0.289774\pi$
$4$	−6.92820	+	4.00000i	−0.433013	+	0.250000i
$5$	−10.7932	+	10.7932i	−0.431728	+	0.431728i	−0.889216	−	0.457488i	$-0.848749\pi$
$5$	−10.7932	+	10.7932i	−0.431728	+	0.431728i	0.457488	+	0.889216i	$0.348749\pi$
$6$	−18.5487	−	4.97012i	−0.515243	−	0.138059i
$7$	−4.14281	+	15.4612i	−0.0845471	+	0.315534i	−0.995228	−	0.0975763i	$-0.968891\pi$
$7$	−4.14281	+	15.4612i	−0.0845471	+	0.315534i	0.910681	+	0.413110i	$0.135558\pi$
$8$	−16.0000	−	16.0000i	−0.250000	−	0.250000i
$9$	17.4526	+	30.2288i	0.215464	+	0.373195i
$10$	−37.3887	−	21.5864i	−0.373887	−	0.215864i
$11$	63.4031	−	16.9888i	0.523993	−	0.140403i	0.0128800	−	0.999917i	$-0.495900\pi$
$11$	63.4031	−	16.9888i	0.523993	−	0.140403i	0.511113	+	0.859514i	$0.329233\pi$
$12$		−	54.3145i		−	0.377184i
$13$	147.515	+	82.4644i	0.872869	+	0.487955i
$13$	147.515	+	82.4644i	0.872869	+	0.487955i
$14$	−45.2735			−0.230987
$15$	−26.8217	−	100.100i	−0.119208	−	0.444889i
$16$	32.0000	−	55.4256i	0.125000	−	0.216506i
$17$	260.411	−	150.348i	0.901077	−	0.520237i	0.0235275	−	0.999723i	$-0.492510\pi$
$17$	260.411	−	150.348i	0.901077	−	0.520237i	0.877549	+	0.479486i	$0.159177\pi$
$18$	−69.8105	+	69.8105i	−0.215464	+	0.215464i
$19$	−6.07879	−	1.62881i	−0.0168387	−	0.00451193i	0.250390	−	0.968145i	$-0.419441\pi$
$19$	−6.07879	−	1.62881i	−0.0168387	−	0.00451193i	−0.267229	+	0.963633i	$0.586108\pi$
$20$	31.6047	−	117.950i	0.0790117	−	0.294875i
$21$	−76.8439	−	76.8439i	−0.174249	−	0.174249i
$22$	92.8286	+	160.784i	0.191795	+	0.332198i
$23$	−336.766	−	194.432i	−0.636609	−	0.367546i	0.146698	−	0.989181i	$-0.453135\pi$
$23$	−336.766	−	194.432i	−0.636609	−	0.367546i	−0.783307	+	0.621635i	$0.786469\pi$
$24$	148.390	−	39.7610i	0.257621	−	0.0690295i
$25$			392.014i			0.627222i
$26$	−117.309	+	463.386i	−0.173533	+	0.685482i
$27$	−786.917			−1.07945
$28$	−33.1425	−	123.689i	−0.0422736	−	0.157767i
$29$	−72.9490	+	126.351i	−0.0867408	+	0.150239i	−0.906132	−	0.422996i	$-0.860979\pi$
$29$	−72.9490	+	126.351i	−0.0867408	+	0.150239i	0.819391	+	0.573235i	$0.194312\pi$
$30$	253.844	−	146.557i	0.282049	−	0.162841i
$31$	−627.618	+	627.618i	−0.653088	+	0.653088i	−0.953735	−	0.300647i	$-0.902797\pi$
$31$	−627.618	+	627.618i	−0.653088	+	0.653088i	0.300647	+	0.953735i	$0.402797\pi$
$32$	174.851	+	46.8513i	0.170753	+	0.0457532i
$33$	−115.342	+	430.464i	−0.105916	+	0.395283i
$34$	601.394	+	601.394i	0.520237	+	0.520237i
$35$	−122.161	−	211.590i	−0.0997235	−	0.172726i
$36$	−241.831	−	139.621i	−0.186598	−	0.107732i
$37$	1947.04	−	521.708i	1.42224	−	0.381087i	0.535959	−	0.844244i	$-0.319950\pi$
$37$	1947.04	−	521.708i	1.42224	−	0.381087i	0.886276	+	0.463157i	$0.153283\pi$
$38$		−	17.7999i		−	0.0123268i
$39$	−985.629	+	587.407i	−0.648014	+	0.386198i
$40$	345.382			0.215864
$41$	−767.255	−	2863.43i	−0.456428	−	1.70341i	−0.683857	−	0.729616i	$-0.739699\pi$
$41$	−767.255	−	2863.43i	−0.456428	−	1.70341i	0.227429	−	0.973795i	$-0.426968\pi$
$42$	153.688	−	266.195i	0.0871246	−	0.150904i
$43$	2068.72	−	1194.37i	1.11883	−	0.645957i	0.177728	−	0.984080i	$-0.443125\pi$
$43$	2068.72	−	1194.37i	1.11883	−	0.645957i	0.941102	+	0.338123i	$0.109792\pi$
$44$	−371.315	+	371.315i	−0.191795	+	0.191795i
$45$	−514.635	−	137.896i	−0.254141	−	0.0680968i
$46$	284.668	−	1062.40i	0.134531	−	0.502078i
$47$	−951.593	−	951.593i	−0.430780	−	0.430780i	0.458114	−	0.888894i	$-0.348525\pi$
$47$	−951.593	−	951.593i	−0.430780	−	0.430780i	−0.888894	+	0.458114i	$0.848525\pi$
$48$	217.258	+	376.302i	0.0942960	+	0.163325i
$49$	1857.44	+	1072.39i	0.773612	+	0.446645i
$50$	−1071.00	+	286.974i	−0.428401	+	0.114790i
$51$			2041.53i			0.784900i
$52$	−1351.87	+	18.7293i	−0.499952	+	0.00692650i
$53$	2641.26			0.940285			0.470142	−	0.882591i	$-0.344203\pi$
$53$	2641.26			0.940285			0.470142	+	0.882591i	$0.344203\pi$
$54$	−576.063	−	2149.90i	−0.197553	−	0.737276i
$55$	−500.959	+	867.686i	−0.165606	+	0.286838i
$56$	313.664	−	181.094i	0.100020	−	0.0577468i
$57$	30.2123	−	30.2123i	0.00929896	−	0.00929896i
$58$	−398.601	−	106.805i	−0.118490	−	0.0317493i
$59$	−1137.91	+	4246.75i	−0.326893	+	1.21998i	0.585502	+	0.810671i	$0.300897\pi$
$59$	−1137.91	+	4246.75i	−0.326893	+	1.21998i	−0.912395	+	0.409310i	$0.865769\pi$
$60$	586.227	+	586.227i	0.162841	+	0.162841i
$61$	2539.11	+	4397.86i	0.682372	+	1.18190i	0.974255	+	0.225449i	$0.0723848\pi$
$61$	2539.11	+	4397.86i	0.682372	+	1.18190i	−0.291883	+	0.956454i	$0.594282\pi$
$62$	−2174.13	−	1255.24i	−0.565591	−	0.326544i
$63$	−539.676	+	144.606i	−0.135973	+	0.0364338i
$64$			512.000i			0.125000i
$65$	−2482.21	+	702.102i	−0.587505	+	0.166178i
$66$	−1260.49			−0.289368
$67$	−1485.73	−	5544.82i	−0.330971	−	1.23520i	−0.908171	−	0.418599i	$-0.862521\pi$
$67$	−1485.73	−	5544.82i	−0.330971	−	1.23520i	0.577200	−	0.816603i	$-0.304145\pi$
$68$	−1202.79	+	2083.29i	−0.260118	+	0.450538i
$69$	2286.41	−	1320.06i	0.480237	−	0.277265i
$70$	488.645	−	488.645i	0.0997235	−	0.0997235i
$71$	−7435.49	−	1992.33i	−1.47500	−	0.395226i	−0.570359	−	0.821395i	$-0.693196\pi$
$71$	−7435.49	−	1992.33i	−1.47500	−	0.395226i	−0.904643	+	0.426170i	$0.859863\pi$
$72$	204.419	−	762.903i	0.0394327	−	0.147165i
$73$	−23.0864	−	23.0864i	−0.00433221	−	0.00433221i	0.704937	−	0.709270i	$-0.250975\pi$
$73$	−23.0864	−	23.0864i	−0.00433221	−	0.00433221i	−0.709270	+	0.704937i	$0.750975\pi$
$74$	2850.66	+	4937.50i	0.520574	+	0.901661i
$75$	−2304.93	−	1330.75i	−0.409766	−	0.236578i
$76$	48.6303	−	13.0304i	0.00841937	−	0.00225596i
$77$			1050.67i			0.177208i
$78$	−2326.36	−	2262.78i	−0.382373	−	0.371923i
$79$	7919.96			1.26902			0.634511	−	0.772914i	$-0.281202\pi$
$79$	7919.96			1.26902			0.634511	+	0.772914i	$0.281202\pi$
$80$	252.837	+	943.602i	0.0395058	+	0.147438i
$81$	1257.65	−	2178.31i	0.191686	−	0.332009i
$82$	7261.38	−	4192.36i	1.07992	−	0.623492i
$83$	4637.16	−	4637.16i	0.673125	−	0.673125i	−0.285310	−	0.958435i	$-0.592097\pi$
$83$	4637.16	−	4637.16i	0.673125	−	0.673125i	0.958435	+	0.285310i	$0.0920966\pi$
$84$	839.766	+	225.015i	0.119014	+	0.0318898i
$85$	−1187.93	+	4433.41i	−0.164419	+	0.613621i
$86$	4777.50	+	4777.50i	0.645957	+	0.645957i
$87$	−495.273	−	857.839i	−0.0654345	−	0.113336i
$88$	−1286.27	−	742.629i	−0.166099	−	0.0958974i
$89$	2696.21	−	722.446i	0.340387	−	0.0912064i	−0.0845763	−	0.996417i	$-0.526954\pi$
$89$	2696.21	−	722.446i	0.340387	−	0.0912064i	0.424963	+	0.905211i	$0.360287\pi$
$90$		−	1506.96i		−	0.186044i
$91$	−1886.12	+	1939.12i	−0.227765	+	0.234165i
$92$	3110.91			0.367546
$93$	−1559.67	−	5820.76i	−0.180329	−	0.672998i
$94$	1903.19	−	3296.41i	0.215390	−	0.373066i
$95$	83.1895	−	48.0295i	0.00921768	−	0.00532183i
$96$	−869.032	+	869.032i	−0.0942960	+	0.0942960i
$97$	−13054.8	−	3498.02i	−1.38748	−	0.371774i	−0.513647	−	0.858002i	$-0.671706\pi$
$97$	−13054.8	−	3498.02i	−1.38748	−	0.371774i	−0.873832	+	0.486228i	$0.838372\pi$
$98$	−1570.09	+	5859.67i	−0.163483	+	0.610128i
$99$	1620.10	+	1620.10i	0.165300	+	0.165300i
$100$	−1568.06	−	2715.95i	−0.156806	−	0.271595i
$101$	−7726.44	−	4460.86i	−0.757420	−	0.437296i	0.0709488	−	0.997480i	$-0.477397\pi$
$101$	−7726.44	−	4460.86i	−0.757420	−	0.437296i	−0.828369	+	0.560183i	$0.810731\pi$
$102$	−5577.55	+	1494.50i	−0.536097	+	0.143647i
$103$			13007.9i			1.22612i	0.790038	+	0.613058i	$0.210061\pi$
$103$			13007.9i			1.22612i	−0.790038	+	0.613058i	$0.789939\pi$
$104$	−1040.81	−	3679.67i	−0.0962285	−	0.340206i
$105$	1658.78			0.150456
$106$	1933.54	+	7216.06i	0.172084	+	0.642226i
$107$	7278.58	−	12606.9i	0.635739	−	1.10113i	−0.350618	−	0.936518i	$-0.614029\pi$
$107$	7278.58	−	12606.9i	0.635739	−	1.10113i	0.986358	−	0.164615i	$-0.0526381\pi$
$108$	5451.92	−	3147.67i	0.467414	−	0.269862i
$109$	−2562.24	+	2562.24i	−0.215659	+	0.215659i	−0.806666	−	0.591007i	$-0.798730\pi$
$109$	−2562.24	+	2562.24i	−0.215659	+	0.215659i	0.591007	+	0.806666i	$0.298730\pi$
$110$	−2737.29	−	733.454i	−0.226222	−	0.0606161i
$111$	−3542.04	+	13219.1i	−0.287480	+	1.07289i
$112$	724.375	+	724.375i	0.0577468	+	0.0577468i
$113$	1346.21	+	2331.70i	0.105428	+	0.182606i	0.913913	−	0.405910i	$-0.133045\pi$
$113$	1346.21	+	2331.70i	0.105428	+	0.182606i	−0.808485	+	0.588517i	$0.799712\pi$
$114$	104.659	+	60.4246i	0.00805313	+	0.00464948i
$115$	5733.32	−	1536.24i	0.433522	−	0.116162i
$116$		−	1167.18i		−	0.0867408i
$117$	81.7186	+	5898.42i	0.00596966	+	0.430887i
$118$	−12435.4			−0.893088
$119$	1245.73	+	4649.13i	0.0879691	+	0.328305i
$120$	−1172.45	+	2030.75i	−0.0814204	+	0.141024i
$121$	−8948.14	+	5166.21i	−0.611170	+	0.352859i
$122$	−10156.4	+	10156.4i	−0.682372	+	0.682372i
$123$	19440.7	+	5209.13i	1.28500	+	0.344314i
$124$	1837.79	−	6858.74i	0.119523	−	0.446068i
$125$	−10976.8	−	10976.8i	−0.702517	−	0.702517i
$126$	−790.140	−	1368.56i	−0.0497695	−	0.0862033i
$127$	−10627.1	−	6135.57i	−0.658883	−	0.380406i	0.132968	−	0.991120i	$-0.457549\pi$
$127$	−10627.1	−	6135.57i	−0.658883	−	0.380406i	−0.791851	+	0.610714i	$0.790882\pi$
$128$	−1398.81	+	374.810i	−0.0853766	+	0.0228766i
$129$			16218.0i			0.974578i
$130$	−3735.28	−	6267.55i	−0.221023	−	0.370861i
$131$	29295.2			1.70708			0.853539	−	0.521029i	$-0.174452\pi$
$131$	29295.2			1.70708			0.853539	+	0.521029i	$0.174452\pi$
$132$	−922.739	−	3443.71i	−0.0529579	−	0.197642i
$133$	50.3665	−	87.2373i	0.00284733	−	0.00493173i
$134$	14061.1	−	8118.18i	0.783087	−	0.452115i
$135$	8493.35	−	8493.35i	0.466027	−	0.466027i
$136$	−6572.16	−	1761.00i	−0.355328	−	0.0952100i
$137$	4462.91	−	16655.8i	0.237781	−	0.887411i	−0.739094	−	0.673602i	$-0.764746\pi$
$137$	4462.91	−	16655.8i	0.237781	−	0.887411i	0.976875	−	0.213809i	$-0.0685870\pi$
$138$	5280.24	+	5280.24i	0.277265	+	0.277265i
$139$	−4160.34	−	7205.92i	−0.215327	−	0.372958i	0.738046	−	0.674750i	$-0.235748\pi$
$139$	−4160.34	−	7205.92i	−0.215327	−	0.372958i	−0.953374	+	0.301792i	$0.902415\pi$
$140$	1692.72	+	977.290i	0.0863631	+	0.0498617i
$141$	8825.43	−	2364.77i	0.443913	−	0.118946i
$142$		−	21772.6i		−	1.07978i
$143$	10753.9	+	2722.40i	0.525888	+	0.133131i
$144$	2233.94			0.107732
$145$	−576.382	−	2151.09i	−0.0274141	−	0.102311i
$146$	46.1727	−	79.9735i	0.00216611	−	0.00375181i
$147$	−12610.8	+	7280.82i	−0.583588	+	0.336935i
$148$	−11402.7	+	11402.7i	−0.520574	+	0.520574i
$149$	9908.00	+	2654.84i	0.446286	+	0.119582i	0.474961	−	0.880007i	$-0.342462\pi$
$149$	9908.00	+	2654.84i	0.446286	+	0.119582i	−0.0286750	+	0.999589i	$0.509129\pi$
$150$	1948.36	−	7271.37i	0.0865937	−	0.323172i
$151$	−9659.87	−	9659.87i	−0.423660	−	0.423660i	0.462802	−	0.886462i	$-0.346844\pi$
$151$	−9659.87	−	9659.87i	−0.423660	−	0.423660i	−0.886462	+	0.462802i	$0.846844\pi$
$152$	71.1997	+	123.321i	0.00308170	+	0.00533767i
$153$	9089.72	+	5247.95i	0.388300	+	0.224185i
$154$	−2870.48	+	769.143i	−0.121036	+	0.0324314i
$155$		−	13548.0i		−	0.563913i
$156$	4479.01	−	8012.19i	0.184049	−	0.329232i
$157$	−31367.6			−1.27257			−0.636285	−	0.771454i	$-0.719530\pi$
$157$	−31367.6			−1.27257			−0.636285	+	0.771454i	$0.719530\pi$
$158$	5797.82	+	21637.7i	0.232247	+	0.866758i
$159$	−8966.17	+	15529.9i	−0.354660	+	0.614290i
$160$	−2392.88	+	1381.53i	−0.0934718	+	0.0539660i
$161$	4401.31	−	4401.31i	0.169797	−	0.169797i
$162$	6871.93	+	1841.33i	0.261848	+	0.0701619i
$163$	3325.57	−	12411.2i	0.125167	−	0.467131i	−0.874678	−	0.484704i	$-0.838927\pi$
$163$	3325.57	−	12411.2i	0.125167	−	0.467131i	0.999846	+	0.0175733i	$0.00559403\pi$
$164$	16769.4	+	16769.4i	0.623492	+	0.623492i
$165$	−3401.16	−	5890.99i	−0.124928	−	0.216382i
$166$	16063.6	+	9274.32i	0.582943	+	0.336563i
$167$	−29136.8	+	7807.19i	−1.04474	+	0.279938i	−0.740078	−	0.672521i	$-0.765211\pi$
$167$	−29136.8	+	7807.19i	−1.04474	+	0.279938i	−0.304665	+	0.952459i	$0.598545\pi$
$168$			2459.01i			0.0871246i
$169$	14960.2	+	24329.4i	0.523800	+	0.851841i
$170$	−12981.9			−0.449201
$171$	−56.8539	−	212.181i	−0.00194432	−	0.00725630i
$172$	−9554.99	+	16549.7i	−0.322978	+	0.559415i
$173$	−30572.2	+	17650.9i	−1.02149	+	0.589758i	−0.914535	−	0.404506i	$-0.867443\pi$
$173$	−30572.2	+	17650.9i	−1.02149	+	0.589758i	−0.106955	+	0.994264i	$0.534110\pi$
$174$	1981.09	−	1981.09i	0.0654345	−	0.0654345i
$175$	−6061.00	−	1624.04i	−0.197910	−	0.0530298i
$176$	1087.28	−	4057.80i	0.0351009	−	0.130998i
$177$	−21106.9	−	21106.9i	−0.673717	−	0.673717i
$178$	3947.52	+	6837.30i	0.124590	+	0.215797i
$179$	36685.2	+	21180.2i	1.14495	+	0.661035i	0.947651	−	0.319309i	$-0.103451\pi$
$179$	36685.2	+	21180.2i	1.14495	+	0.661035i	0.197296	+	0.980344i	$0.436784\pi$
$180$	4117.08	−	1103.17i	0.127070	−	0.0340484i
$181$		−	7769.43i		−	0.237155i	−0.992945	−	0.118577i	$-0.962167\pi$
$181$		−	7769.43i		−	0.237155i	0.992945	−	0.118577i	$-0.0378334\pi$
$182$	−6678.51	−	3733.45i	−0.201621	−	0.112711i
$183$	−34477.6			−1.02952
$184$	2277.35	+	8499.17i	0.0672657	+	0.251039i
$185$	−15383.9	+	26645.7i	−0.449493	+	0.778544i
$186$	14760.9	−	8522.19i	0.426664	−	0.246335i
$187$	13956.6	−	13956.6i	0.399115	−	0.399115i
$188$	10399.2	+	2786.46i	0.294228	+	0.0788382i
$189$	3260.05	−	12166.7i	0.0912641	−	0.340602i
$190$	192.118	+	192.118i	0.00532183	+	0.00532183i
$191$	−9039.17	−	15656.3i	−0.247778	−	0.429163i	0.715131	−	0.698990i	$-0.246367\pi$
$191$	−9039.17	−	15656.3i	−0.247778	−	0.429163i	−0.962909	+	0.269827i	$0.913034\pi$
$192$	−3010.42	−	1738.06i	−0.0816627	−	0.0471480i
$193$	47016.6	−	12598.1i	1.26222	−	0.338212i	0.435177	−	0.900345i	$-0.356686\pi$
$193$	47016.6	−	12598.1i	1.26222	−	0.338212i	0.827047	+	0.562133i	$0.190019\pi$
$194$		−	38227.1i		−	1.01570i
$195$	4298.09	−	16978.1i	0.113033	−	0.446498i
$196$	−17158.3			−0.446645
$197$	−3427.81	−	12792.7i	−0.0883251	−	0.329634i	0.907598	−	0.419840i	$-0.137914\pi$
$197$	−3427.81	−	12792.7i	−0.0883251	−	0.329634i	−0.995923	+	0.0902067i	$0.971247\pi$
$198$	−3240.21	+	5612.20i	−0.0826499	+	0.143154i
$199$	−53142.1	+	30681.6i	−1.34194	+	0.774768i	−0.987092	−	0.160156i	$-0.948800\pi$
$199$	−53142.1	+	30681.6i	−1.34194	+	0.774768i	−0.354847	+	0.934925i	$0.615467\pi$
$200$	6272.22	−	6272.22i	0.156806	−	0.156806i
$201$	37645.5	+	10087.1i	0.931797	+	0.249674i
$202$	6531.15	−	24374.6i	0.160062	−	0.597358i
$203$	−1651.33	−	1651.33i	−0.0400720	−	0.0400720i
$204$	−8166.10	−	14144.1i	−0.196225	−	0.339872i
$205$	39186.7	+	22624.5i	0.932462	+	0.538357i
$206$	−35538.2	+	9522.42i	−0.837453	+	0.224395i
$207$		−	13573.4i		−	0.316773i
$208$	9291.11	−	5537.24i	0.214754	−	0.127987i
$209$	−413.086			−0.00945687
$210$	1214.31	+	4531.88i	0.0275354	+	0.102764i
$211$	25628.4	−	44389.8i	0.575648	−	0.997052i	−0.420323	−	0.907375i	$-0.638083\pi$
$211$	25628.4	−	44389.8i	0.575648	−	0.997052i	0.995971	−	0.0896774i	$-0.0285836\pi$
$212$	−18299.2	+	10565.0i	−0.407155	+	0.235071i
$213$	36955.3	−	36955.3i	0.814549	−	0.814549i
$214$	39770.9	+	10656.6i	0.868436	+	0.232697i
$215$	−9436.95	+	35219.2i	−0.204152	+	0.761907i
$216$	12590.7	+	12590.7i	0.269862	+	0.269862i
$217$	−7103.61	−	12303.8i	−0.150855	−	0.261288i
$218$	−8875.87	−	5124.49i	−0.186766	−	0.107829i
$219$	214.111	−	57.3710i	0.00446428	−	0.00119620i
$220$		−	8015.34i		−	0.165606i
$221$	50812.9	−	703.979i	1.04037	−	0.0144137i
$222$	−38708.1			−0.785409
$223$	11567.5	+	43170.5i	0.232611	+	0.868115i	0.979211	+	0.202843i	$0.0650180\pi$
$223$	11567.5	+	43170.5i	0.232611	+	0.868115i	−0.746601	+	0.665272i	$0.768315\pi$
$224$	−1448.75	+	2509.31i	−0.0288734	+	0.0500102i
$225$	−11850.1	+	6841.67i	−0.234076	+	0.135144i
$226$	−5384.83	+	5384.83i	−0.105428	+	0.105428i
$227$	16176.6	+	4334.50i	0.313931	+	0.0841176i	0.412344	−	0.911028i	$-0.364710\pi$
$227$	16176.6	+	4334.50i	0.313931	+	0.0841176i	−0.0984133	+	0.995146i	$0.531377\pi$
$228$	−88.4678	+	330.166i	−0.00170183	+	0.00635131i
$229$	14835.3	+	14835.3i	0.282896	+	0.282896i	0.834263	−	0.551367i	$-0.185894\pi$
$229$	14835.3	+	14835.3i	0.282896	+	0.282896i	−0.551367	+	0.834263i	$0.685894\pi$
$230$	8394.17	+	14539.1i	0.158680	+	0.274842i
$231$	−6177.63	−	3566.66i	−0.115771	−	0.0668402i
$232$	3188.80	−	854.438i	0.0592450	−	0.0158747i
$233$		−	46102.8i		−	0.849211i	−0.905378	−	0.424606i	$-0.860413\pi$
$233$		−	46102.8i		−	0.849211i	0.905378	−	0.424606i	$-0.139587\pi$
$234$	−16055.0	+	4541.20i	−0.293209	+	0.0829352i
$235$	20541.5			0.371959
$236$	−9103.31	−	33974.0i	−0.163446	−	0.609991i
$237$	−26885.6	+	46567.1i	−0.478655	+	0.829054i
$238$	−11789.7	+	6806.80i	−0.208137	+	0.120168i
$239$	−67703.2	+	67703.2i	−1.18526	+	1.18526i	−0.206897	+	0.978363i	$0.566337\pi$
$239$	−67703.2	+	67703.2i	−1.18526	+	1.18526i	−0.978363	+	0.206897i	$0.933663\pi$
$240$	−6406.41	−	1716.59i	−0.111222	−	0.0298019i
$241$	7692.12	−	28707.4i	0.132438	−	0.494265i	−0.867557	−	0.497337i	$-0.834311\pi$
$241$	7692.12	−	28707.4i	0.132438	−	0.494265i	0.999995	+	0.00307221i	$0.000977917\pi$
$242$	−20664.8	−	20664.8i	−0.352859	−	0.352859i
$243$	−23331.6	−	40411.4i	−0.395122	−	0.684371i
$244$	−35182.9	−	20312.8i	−0.590951	−	0.341186i
$245$	−31622.3	+	8473.17i	−0.526819	+	0.141161i
$246$			56926.5i			0.940684i
$247$	−762.393	−	741.556i	−0.0124964	−	0.0121549i
$248$	20083.8			0.326544
$249$	11523.6	+	43006.7i	0.185862	+	0.693646i
$250$	21953.7	−	38024.8i	0.351258	−	0.608398i
$251$	−48608.7	+	28064.2i	−0.771554	+	0.445457i	−0.833429	−	0.552627i	$-0.813625\pi$
$251$	−48608.7	+	28064.2i	−0.771554	+	0.445457i	0.0618749	+	0.998084i	$0.480292\pi$
$252$	3160.56	−	3160.56i	0.0497695	−	0.0497695i
$253$	−24655.2	−	6606.34i	−0.385183	−	0.103210i
$254$	8983.10	−	33525.4i	0.139238	−	0.519644i
$255$	−22034.6	−	22034.6i	−0.338863	−	0.338863i
$256$	−2048.00	−	3547.24i	−0.0312500	−	0.0541266i
$257$	21717.0	+	12538.3i	0.328802	+	0.189834i	0.655309	−	0.755361i	$-0.272538\pi$
$257$	21717.0	+	12538.3i	0.328802	+	0.189834i	−0.326507	+	0.945195i	$0.605872\pi$
$258$	−44308.3	+	11872.4i	−0.665649	+	0.178360i
$259$			32264.9i			0.480984i
$260$	14388.8	−	14793.1i	0.212853	−	0.218833i
$261$	−5092.60			−0.0747582
$262$	21445.5	+	80035.9i	0.312417	+	1.16596i
$263$	27492.0	−	47617.6i	0.397462	−	0.688424i	−0.595950	−	0.803021i	$-0.703224\pi$
$263$	27492.0	−	47617.6i	0.397462	−	0.688424i	0.993412	+	0.114597i	$0.0365577\pi$
$264$	8732.90	−	5041.94i	0.125300	−	0.0723419i
$265$	−28507.6	+	28507.6i	−0.405947	+	0.405947i
$266$	275.208	+	73.7417i	0.00388953	+	0.00104220i
$267$	−4904.91	+	18305.4i	−0.0688032	+	0.256777i
$268$	32472.7	+	32472.7i	0.452115	+	0.452115i
$269$	7262.85	+	12579.6i	0.100370	+	0.173845i	0.911837	−	0.410552i	$-0.134664\pi$
$269$	7262.85	+	12579.6i	0.100370	+	0.173845i	−0.811467	+	0.584398i	$0.801331\pi$
$270$	29421.8	+	16986.7i	0.403591	+	0.233014i
$271$	34964.2	−	9368.63i	0.476086	−	0.127567i	−0.0127937	−	0.999918i	$-0.504072\pi$
$271$	34964.2	−	9368.63i	0.476086	−	0.127567i	0.488879	+	0.872351i	$0.337406\pi$
$272$		−	19244.6i		−	0.260118i
$273$	−4998.73	−	17672.5i	−0.0670709	−	0.237123i
$274$	48771.6			0.649630
$275$	6659.86	+	24854.9i	0.0880642	+	0.328660i
$276$	−10560.5	+	18291.3i	−0.138633	+	0.240119i
$277$	130422.	−	75299.0i	1.69977	−	0.981363i	0.753805	−	0.657098i	$-0.228216\pi$
$277$	130422.	−	75299.0i	1.69977	−	0.981363i	0.945966	−	0.324265i	$-0.105117\pi$
$278$	16641.4	−	16641.4i	0.215327	−	0.215327i
$279$	−29925.7	−	8018.58i	−0.384447	−	0.103012i
$280$	−1430.85	+	5340.01i	−0.0182507	+	0.0681124i
$281$	−44923.7	−	44923.7i	−0.568935	−	0.568935i	0.362895	−	0.931830i	$-0.381788\pi$
$281$	−44923.7	−	44923.7i	−0.568935	−	0.568935i	−0.931830	+	0.362895i	$0.881788\pi$
$282$	12921.3	+	22380.4i	0.162483	+	0.281429i
$283$	−84222.0	−	48625.6i	−1.05160	−	0.607144i	−0.128506	−	0.991709i	$-0.541018\pi$
$283$	−84222.0	−	48625.6i	−1.05160	−	0.607144i	−0.923098	+	0.384564i	$0.874352\pi$
$284$	59483.9	−	15938.7i	0.737501	−	0.197613i
$285$			652.175i			0.00802923i
$286$	434.653	+	31373.1i	0.00531386	+	0.383553i
$287$	47450.6			0.576074
$288$	1635.35	+	6103.22i	0.0197164	+	0.0735825i
$289$	3448.84	−	5973.56i	0.0412930	−	0.0715217i
$290$	5454.94	−	3149.41i	0.0648625	−	0.0374484i
$291$	64883.9	−	64883.9i	0.766215	−	0.766215i
$292$	252.292	+	67.6015i	0.00295896	+	0.000792850i
$293$	−1029.00	+	3840.27i	−0.0119861	+	0.0447329i	−0.971660	−	0.236383i	$-0.924038\pi$
$293$	−1029.00	+	3840.27i	−0.0119861	+	0.0447329i	0.959674	+	0.281116i	$0.0907046\pi$
$294$	−29123.3	−	29123.3i	−0.336935	−	0.336935i
$295$	−33554.3	−	58117.8i	−0.385571	−	0.667828i
$296$	−39500.0	−	22805.3i	−0.450831	−	0.260287i
$297$	−49893.0	+	13368.8i	−0.565623	+	0.151558i
$298$			29012.6i			0.326704i
$299$	−33644.3	−	56452.8i	−0.376330	−	0.631456i
$300$	21292.0			0.236578
$301$	9896.13	+	36932.9i	0.109228	+	0.407643i
$302$	19319.7	−	33462.8i	0.211830	−	0.366900i
$303$	52457.2	−	30286.2i	0.571373	−	0.329882i
$304$	−284.799	+	284.799i	−0.00308170	+	0.00308170i
$305$	−74872.0	−	20061.9i	−0.804859	−	0.215661i
$306$	−7683.53	+	28675.3i	−0.0820574	+	0.306243i
$307$	60578.8	+	60578.8i	0.642753	+	0.642753i	0.951231	−	0.308479i	$-0.0998198\pi$
$307$	60578.8	+	60578.8i	0.642753	+	0.642753i	−0.308479	+	0.951231i	$0.599820\pi$
$308$	−4202.67	−	7279.24i	−0.0443021	−	0.0767335i
$309$	−76482.6	−	44157.2i	−0.801024	−	0.462472i
$310$	37013.8	−	9917.83i	0.385160	−	0.103203i
$311$			79599.2i			0.822978i	0.911415	+	0.411489i	$0.134991\pi$
$311$			79599.2i			0.822978i	−0.911415	+	0.411489i	$0.865009\pi$
$312$	25168.6	+	6371.56i	0.258553	+	0.0654540i
$313$	27640.8			0.282139			0.141069	−	0.990000i	$-0.454946\pi$
$313$	27640.8			0.282139			0.141069	+	0.990000i	$0.454946\pi$
$314$	−22962.7	−	85697.9i	−0.232897	−	0.869182i
$315$	4264.07	−	7385.58i	0.0429737	−	0.0744327i
$316$	−54871.1	+	31679.9i	−0.549502	+	0.317255i
$317$	−14618.9	+	14618.9i	−0.145478	+	0.145478i	−0.776095	−	0.630617i	$-0.782802\pi$
$317$	−14618.9	+	14618.9i	−0.145478	+	0.145478i	0.630617	+	0.776095i	$0.282802\pi$
$318$	−48992.1	−	13127.4i	−0.484475	−	0.129815i
$319$	−2478.63	+	9250.39i	−0.0243574	+	0.0909031i
$320$	−5526.11	−	5526.11i	−0.0539660	−	0.0539660i
$321$	49416.6	+	85592.0i	0.479582	+	0.830660i
$322$	15246.6	+	8802.61i	0.147048	+	0.0848984i
$323$	−1827.87	+	489.777i	−0.0175203	+	0.00469454i
$324$			20122.4i			0.191686i
$325$	−32327.2	+	57827.9i	−0.306056	+	0.547483i
$326$	36342.5			0.341963
$327$	−6367.33	−	23763.2i	−0.0595473	−	0.222233i
$328$	−33538.9	+	58091.0i	−0.311746	+	0.539960i
$329$	18655.0	−	10770.5i	0.172347	−	0.0995046i
$330$	13604.7	−	13604.7i	0.124928	−	0.124928i
$331$	16296.9	+	4366.75i	0.148748	+	0.0398568i	0.332425	−	0.943130i	$-0.392133\pi$
$331$	16296.9	+	4366.75i	0.148748	+	0.0398568i	−0.183677	+	0.982987i	$0.558800\pi$
$332$	−13578.5	+	50675.8i	−0.123190	+	0.459753i
$333$	49751.6	+	49751.6i	0.448661	+	0.448661i
$334$	−42659.3	−	73888.1i	−0.382402	−	0.662340i
$335$	75882.1	+	43810.6i	0.676161	+	0.390382i
$336$	−6718.13	+	1800.12i	−0.0595072	+	0.0159449i
$337$			71134.1i			0.626352i	0.949695	+	0.313176i	$0.101393\pi$
$337$			71134.1i			0.626352i	−0.949695	+	0.313176i	$0.898607\pi$
$338$	−55517.6	+	58682.5i	−0.485956	+	0.513660i
$339$	−18279.6			−0.159063
$340$	−9503.43	−	35467.3i	−0.0822096	−	0.306810i
$341$	−29130.5	+	50455.4i	−0.250518	+	0.433910i
$342$	538.071	−	310.655i	0.00460031	−	0.00265599i
$343$	−51450.9	+	51450.9i	−0.437325	+	0.437325i
$344$	−52209.5	−	13989.5i	−0.441197	−	0.118218i
$345$	−10430.0	+	38925.3i	−0.0876287	+	0.327035i
$346$	−70603.5	−	70603.5i	−0.589758	−	0.589758i
$347$	114396.	+	198140.i	0.950061	+	1.64555i	0.745286	+	0.666745i	$0.232313\pi$
$347$	114396.	+	198140.i	0.950061	+	1.64555i	0.204776	+	0.978809i	$0.434354\pi$
$348$	6862.71	+	3962.19i	0.0566679	+	0.0327172i
$349$	−87268.2	+	23383.4i	−0.716482	+	0.191981i	−0.598601	−	0.801047i	$-0.704277\pi$
$349$	−87268.2	+	23383.4i	−0.716482	+	0.191981i	−0.117880	+	0.993028i	$0.537610\pi$
$350$		−	17747.8i		−	0.144880i
$351$	−116082.	−	64892.6i	−0.942216	−	0.526722i
$352$	11882.1			0.0958974
$353$	−53957.7	−	201373.i	−0.433016	−	1.61604i	−0.745770	−	0.666203i	$-0.767918\pi$
$353$	−53957.7	−	201373.i	−0.433016	−	1.61604i	0.312754	−	0.949834i	$-0.398748\pi$
$354$	42213.8	−	73116.4i	0.336859	−	0.583456i
$355$	101756.	−	58749.0i	0.807429	−	0.466170i
$356$	−15790.1	+	15790.1i	−0.124590	+	0.124590i
$357$	−31564.4	−	8457.65i	−0.247663	−	0.0663611i
$358$	−31010.0	+	115731.i	−0.241956	+	0.902991i
$359$	133777.	+	133777.i	1.03799	+	1.03799i	0.999249	+	0.0387427i	$0.0123353\pi$
$359$	133777.	+	133777.i	1.03799	+	1.03799i	0.0387427	+	0.999249i	$0.487665\pi$
$360$	6027.82	+	10440.5i	0.0465110	+	0.0805594i
$361$	−112827.	−	65140.7i	−0.865762	−	0.499848i
$362$	21226.5	−	5687.61i	0.161980	−	0.0434023i
$363$		−	70150.0i		−	0.532371i
$364$	5310.96	−	20979.1i	0.0400840	−	0.158338i
$365$	498.351			0.00374067
$366$	−25239.3	−	94194.5i	−0.188415	−	0.703175i
$367$	98167.2	−	170031.i	0.728844	−	1.26239i	−0.228528	−	0.973537i	$-0.573391\pi$
$367$	98167.2	−	170031.i	0.728844	−	1.26239i	0.957372	−	0.288857i	$-0.0932753\pi$
$368$	−21553.0	+	12443.6i	−0.159152	+	0.0918866i
$369$	73167.6	−	73167.6i	0.537361	−	0.537361i
$370$	−84059.1	−	22523.6i	−0.614018	−	0.164526i
$371$	−10942.2	+	40837.0i	−0.0794984	+	0.296692i
$372$	34088.8	+	34088.8i	0.246335	+	0.246335i
$373$	22973.3	+	39790.9i	0.165122	+	0.286000i	0.936699	−	0.350137i	$-0.113865\pi$
$373$	22973.3	+	39790.9i	0.165122	+	0.286000i	−0.771577	+	0.636137i	$0.780532\pi$
$374$	48347.2	+	27913.3i	0.345644	+	0.199557i
$375$	101803.	−	27278.1i	0.723934	−	0.193977i
$376$			30451.0i			0.215390i
$377$	−21180.5	+	12623.0i	−0.149023	+	0.0888137i
$378$	35626.4			0.249338
$379$	−46949.5	−	175218.i	−0.326853	−	1.21983i	−0.912436	−	0.409219i	$-0.865801\pi$
$379$	−46949.5	−	175218.i	−0.326853	−	1.21983i	0.585583	−	0.810612i	$-0.300866\pi$
$380$	−384.236	+	665.516i	−0.00266091	+	0.00460884i
$381$	72150.8	−	41656.3i	0.497040	−	0.286966i
$382$	36156.7	−	36156.7i	0.247778	−	0.247778i
$383$	188412.	+	50484.9i	1.28443	+	0.344163i	0.835544	−	0.549424i	$-0.185153\pi$
$383$	188412.	+	50484.9i	1.28443	+	0.344163i	0.448890	+	0.893587i	$0.351819\pi$
$384$	2544.70	−	9496.96i	0.0172574	−	0.0644054i
$385$	−11340.1	−	11340.1i	−0.0765058	−	0.0765058i
$386$	68837.1	+	119229.i	0.462006	+	0.800218i
$387$	72209.0	+	41689.9i	0.482136	+	0.278361i
$388$	104438.	−	27984.2i	0.693739	−	0.185887i
$389$		−	227700.i		−	1.50475i	−0.658734	−	0.752376i	$-0.728908\pi$
$389$		−	227700.i		−	1.50475i	0.658734	−	0.752376i	$-0.271092\pi$
$390$	49531.4	−	686.224i	0.325650	−	0.00451167i
$391$	−116930.			−0.764845
$392$	−12560.8	−	46877.4i	−0.0817417	−	0.305064i
$393$	−99447.0	+	172247.i	−0.643883	+	1.11524i
$394$	32441.1	−	18729.9i	0.208979	−	0.120654i
$395$	−85481.7	+	85481.7i	−0.547872	+	0.547872i
$396$	−17704.8	−	4743.99i	−0.112902	−	0.0302520i
$397$	17027.4	−	63547.2i	0.108036	−	0.403195i	−0.890636	−	0.454717i	$-0.849740\pi$
$397$	17027.4	−	63547.2i	0.108036	−	0.403195i	0.998672	+	0.0515218i	$0.0164072\pi$
$398$	−122726.	−	122726.i	−0.774768	−	0.774768i
$399$	341.954	+	592.282i	0.00214794	+	0.00372034i
$400$	21727.6	+	12544.4i	0.135798	+	0.0784028i
$401$	−40758.2	+	10921.1i	−0.253470	+	0.0679171i	−0.383317	−	0.923617i	$-0.625218\pi$
$401$	−40758.2	+	10921.1i	−0.253470	+	0.0679171i	0.129847	+	0.991534i	$0.458552\pi$
$402$			110234.i			0.682123i
$403$	−144339.	+	40826.8i	−0.888738	+	0.251383i
$404$	71373.8			0.437296
$405$	9936.90	+	37085.0i	0.0605816	+	0.226094i
$406$	3302.65	−	5720.36i	0.0200360	−	0.0347033i
$407$	114585.	−	66155.8i	0.691735	−	0.399374i
$408$	32664.4	−	32664.4i	0.196225	−	0.196225i
$409$	−201825.	−	54078.8i	−1.20650	−	0.323281i	−0.401114	−	0.916028i	$-0.631377\pi$
$409$	−201825.	−	54078.8i	−1.20650	−	0.323281i	−0.805389	+	0.592747i	$0.798043\pi$
$410$	−33124.5	+	123622.i	−0.197052	+	0.735410i
$411$	82781.4	+	82781.4i	0.490060	+	0.490060i
$412$	−52031.5	−	90121.2i	−0.306529	−	0.530924i
$413$	−60945.6	−	35187.0i	−0.357308	−	0.206292i
$414$	37083.2	−	9936.41i	0.216360	−	0.0579734i
$415$			100099.i			0.581214i
$416$	21929.6	+	21330.3i	0.126720	+	0.123256i
$417$	56491.7			0.324872
$418$	−302.400	−	1128.57i	−0.00173073	−	0.00645916i
$419$	−87267.3	+	151151.i	−0.497077	+	0.860962i	−0.999994	−	0.00337202i	$-0.998927\pi$
$419$	−87267.3	+	151151.i	−0.497077	+	0.860962i	0.502917	+	0.864334i	$0.332260\pi$
$420$	−11492.4	+	6635.13i	−0.0651496	+	0.0376141i
$421$	−105896.	+	105896.i	−0.597472	+	0.597472i	−0.939639	−	0.342167i	$-0.888839\pi$
$421$	−105896.	+	105896.i	−0.597472	+	0.597472i	0.342167	+	0.939639i	$0.388839\pi$
$422$	140036.	+	37522.6i	0.786350	+	0.210702i
$423$	12157.7	−	45373.3i	0.0679473	−	0.253583i
$424$	−42260.2	−	42260.2i	−0.235071	−	0.235071i
$425$	58938.7	+	102085.i	0.326304	+	0.565176i
$426$	128017.	+	73910.6i	0.705420	+	0.407275i
$427$	−78515.1	+	21038.1i	−0.430623	+	0.115385i
$428$			116457.i			0.635739i
$429$	−52512.6	+	53988.1i	−0.285331	+	0.293348i
$430$	−103129.			−0.557755
$431$	−59613.0	−	222479.i	−0.320912	−	1.19766i	−0.918358	−	0.395752i	$-0.870484\pi$
$431$	−59613.0	−	222479.i	−0.320912	−	1.19766i	0.597445	−	0.801910i	$-0.296183\pi$
$432$	−25181.3	+	43615.4i	−0.134931	+	0.233707i
$433$	181350.	−	104703.i	0.967258	−	0.558447i	0.0688587	−	0.997626i	$-0.478064\pi$
$433$	181350.	−	104703.i	0.967258	−	0.558447i	0.898399	+	0.439180i	$0.144731\pi$
$434$	28414.4	−	28414.4i	0.150855	−	0.150855i
$435$	14604.4	+	3913.24i	0.0771801	+	0.0206803i
$436$	7502.77	−	28000.7i	0.0394683	−	0.147298i
$437$	1730.44	+	1730.44i	0.00906135	+	0.00906135i
$438$	313.481	+	542.965i	0.00163404	+	0.00283024i
$439$	−155413.	−	89727.5i	−0.806412	−	0.465582i	0.0392962	−	0.999228i	$-0.487488\pi$
$439$	−155413.	−	89727.5i	−0.806412	−	0.465582i	−0.845708	+	0.533645i	$0.820822\pi$
$440$	21898.3	−	5867.64i	0.113111	−	0.0303080i
$441$			74864.4i			0.384944i
$442$	39120.9	+	138308.i	0.200246	+	0.707951i
$443$	−114950.			−0.585736			−0.292868	−	0.956153i	$-0.594610\pi$
$443$	−114950.			−0.585736			−0.292868	+	0.956153i	$0.594610\pi$
$444$	−28336.3	−	105753.i	−0.143740	−	0.536444i
$445$	−21303.2	+	36898.2i	−0.107578	+	0.186331i
$446$	−109476.	+	63206.0i	−0.550363	+	0.317752i
$447$	−49244.0	+	49244.0i	−0.246455	+	0.246455i
$448$	−7916.12	−	2121.12i	−0.0394418	−	0.0105684i
$449$	51856.6	−	193531.i	0.257224	−	0.959973i	−0.709616	−	0.704589i	$-0.751131\pi$
$449$	51856.6	−	193531.i	0.257224	−	0.959973i	0.966840	−	0.255384i	$-0.0822019\pi$
$450$	−27366.7	−	27366.7i	−0.135144	−	0.135144i
$451$	−97292.7	−	168516.i	−0.478330	−	0.828491i
$452$	−18653.6	−	10769.7i	−0.0913031	−	0.0527139i
$453$	89589.2	−	24005.4i	0.436576	−	0.116980i
$454$			47368.2i			0.229814i
$455$	−571.997	−	41286.6i	−0.00276294	−	0.199428i
$456$	−966.794			−0.00464948
$457$	100852.	+	376385.i	0.482895	+	1.80219i	0.589360	+	0.807871i	$0.299380\pi$
$457$	100852.	+	376385.i	0.482895	+	1.80219i	−0.106465	+	0.994316i	$0.533953\pi$
$458$	−29670.7	+	51391.1i	−0.141448	+	0.244995i
$459$	−204922.	+	118312.i	−0.972665	+	0.561568i
$460$	−33576.7	+	33576.7i	−0.158680	+	0.158680i
$461$	−194109.	−	52011.4i	−0.913364	−	0.244735i	−0.228618	−	0.973516i	$-0.573421\pi$
$461$	−194109.	−	52011.4i	−0.913364	−	0.244735i	−0.684747	+	0.728781i	$0.740087\pi$
$462$	5221.95	−	19488.6i	0.0244652	−	0.0913054i
$463$	4780.78	+	4780.78i	0.0223016	+	0.0223016i	0.718170	−	0.695868i	$-0.244980\pi$
$463$	4780.78	+	4780.78i	0.0223016	+	0.0223016i	−0.695868	+	0.718170i	$0.744980\pi$
$464$	4668.73	+	8086.48i	0.0216852	+	0.0375598i
$465$	79658.4	+	45990.8i	0.368405	+	0.212699i
$466$	125955.	−	33749.6i	0.580022	−	0.155416i
$467$		−	94457.6i		−	0.433115i	−0.976270	−	0.216558i	$-0.930517\pi$
$467$		−	94457.6i		−	0.433115i	0.976270	−	0.216558i	$-0.0694829\pi$
$468$	−24159.8	−	40538.6i	−0.110307	−	0.185087i
$469$	91884.6			0.417731
$470$	15037.4	+	56120.3i	0.0680733	+	0.254053i
$471$	106482.	−	184433.i	0.479993	−	0.831373i
$472$	86154.7	−	49741.4i	0.386719	−	0.223272i
$473$	110872.	−	110872.i	0.495564	−	0.495564i
$474$	−146905.	−	39363.2i	−0.653854	−	0.175200i
$475$	638.515	−	2382.97i	0.00282998	−	0.0105616i
$476$	−27227.2	−	27227.2i	−0.120168	−	0.120168i
$477$	46096.9	+	79842.2i	0.202598	+	0.350910i
$478$	−234531.	−	135406.i	−1.02647	−	0.592630i
$479$	−1628.86	+	436.452i	−0.00709927	+	0.00190224i	−0.262367	−	0.964968i	$-0.584503\pi$
$479$	−1628.86	+	436.452i	−0.00709927	+	0.00190224i	0.255268	+	0.966870i	$0.417836\pi$
$480$		−	18759.3i		−	0.0814204i
$481$	330240.	+	83601.8i	1.42738	+	0.361348i
$482$	84061.1			0.361827
$483$	10937.5	+	40819.3i	0.0468840	+	0.174973i
$484$	41329.7	−	71585.1i	0.176430	−	0.305585i
$485$	178658.	−	103148.i	0.759518	−	0.438508i
$486$	93326.2	−	93326.2i	0.395122	−	0.395122i
$487$	349560.	+	93664.5i	1.47389	+	0.394927i	0.904262	−	0.426977i	$-0.140422\pi$
$487$	349560.	+	93664.5i	1.47389	+	0.394927i	0.569625	+	0.821904i	$0.307088\pi$
$488$	29740.1	−	110991.i	0.124883	−	0.466069i
$489$	61685.1	+	61685.1i	0.257966	+	0.257966i
$490$	−46298.2	−	80190.9i	−0.192829	−	0.333990i
$491$	218904.	+	126384.i	0.908011	+	0.524240i	0.879791	−	0.475361i	$-0.157683\pi$
$491$	218904.	+	126384.i	0.908011	+	0.524240i	0.0282204	+	0.999602i	$0.491016\pi$
$492$	−155526.	+	41673.1i	−0.642499	+	0.172157i
$493$			43871.1i			0.180503i
$494$	1467.86	−	2625.75i	0.00601493	−	0.0107597i
$495$	−34972.2			−0.142729
$496$	14702.3	+	54869.9i	0.0597617	+	0.223034i
$497$	61607.6	−	106708.i	0.249414	−	0.431998i
$498$	−109061.	+	62966.2i	−0.439754	+	0.253892i
$499$	−247858.	+	247858.i	−0.995410	+	0.995410i	−0.999990	−	0.00457911i	$-0.998542\pi$
$499$	−247858.	+	247858.i	−0.995410	+	0.995410i	0.00457911	+	0.999990i	$0.498542\pi$
$500$	119957.	+	32142.4i	0.479828	+	0.128570i
$501$	53005.5	−	197819.i	0.211176	−	0.788121i
$502$	−112257.	−	112257.i	−0.445457	−	0.445457i
$503$	−78721.7	−	136350.i	−0.311142	−	0.538914i	0.667468	−	0.744639i	$-0.267378\pi$
$503$	−78721.7	−	136350.i	−0.311142	−	0.538914i	−0.978610	+	0.205725i	$0.934045\pi$
$504$	10948.5	+	6321.12i	0.0431016	+	0.0248847i
$505$	131540.	−	35246.0i	0.515792	−	0.138206i
$506$		−	72195.4i		−	0.281974i
$507$	−193835.	+	5371.94i	−0.754079	+	0.0208985i
$508$	98169.1			0.380406
$509$	84265.4	+	314483.i	0.325247	+	1.21384i	0.914063	+	0.405572i	$0.132928\pi$
$509$	84265.4	+	314483.i	0.325247	+	1.21384i	−0.588816	+	0.808267i	$0.700406\pi$
$510$	44069.2	−	76330.0i	0.169432	−	0.293464i
$511$	452.584	−	261.300i	0.00173324	−	0.00100068i
$512$	8192.00	−	8192.00i	0.0312500	−	0.0312500i
$513$	4783.50	+	1281.73i	0.0181765	+	0.00487039i
$514$	−18357.4	+	68510.8i	−0.0694840	+	0.259318i
$515$	−140396.	−	140396.i	−0.529348	−	0.529348i
$516$	−64871.8	−	112361.i	−0.243645	−	0.422005i
$517$	−76500.4	−	44167.5i	−0.286209	−	0.165243i
$518$	−88149.2	+	23619.5i	−0.328518	+	0.0880261i
$519$		−	239674.i		−	0.889789i
$520$	50949.0	+	28481.7i	0.188421	+	0.105332i
$521$	−65455.8			−0.241142			−0.120571	−	0.992705i	$-0.538473\pi$
$521$	−65455.8			−0.241142			−0.120571	+	0.992705i	$0.538473\pi$
$522$	−3728.04	−	13913.2i	−0.0136817	−	0.0510608i
$523$	6183.37	−	10709.9i	0.0226059	−	0.0391546i	−0.854501	−	0.519450i	$-0.826137\pi$
$523$	6183.37	−	10709.9i	0.0226059	−	0.0391546i	0.877107	+	0.480295i	$0.159470\pi$
$524$	−202963.	+	117181.i	−0.739186	+	0.426769i
$525$	30123.9	−	30123.9i	0.109293	−	0.109293i
$526$	150219.	+	40251.2i	0.542943	+	0.145481i
$527$	−69077.4	+	257800.i	−0.248722	+	0.928244i
$528$	20167.8	+	20167.8i	0.0723419	+	0.0723419i
$529$	−64312.9	−	111393.i	−0.229819	−	0.398059i
$530$	−98753.3	−	57015.2i	−0.351560	−	0.202973i
$531$	−148234.	+	39719.2i	−0.525725	+	0.140868i
$532$			805.864i			0.00284733i
$533$	122950.	−	485670.i	0.432786	−	1.70957i
$534$	−53601.9			−0.187974
$535$	57509.3	+	214628.i	0.200923	+	0.749856i
$536$	−64945.5	+	112489.i	−0.226058	+	0.391543i
$537$	−249068.	+	143799.i	−0.863711	+	0.498664i
$538$	−29051.4	+	29051.4i	−0.100370	+	0.100370i
$539$	135986.	+	36437.4i	0.468078	+	0.125421i
$540$	−24870.2	+	92817.0i	−0.0852889	+	0.318302i
$541$	30488.1	+	30488.1i	0.104168	+	0.104168i	0.757270	−	0.653102i	$-0.226533\pi$
$541$	30488.1	+	30488.1i	0.104168	+	0.104168i	−0.653102	+	0.757270i	$0.726533\pi$
$542$	51191.2	+	88665.7i	0.174259	+	0.301826i
$543$	45682.0	+	26374.5i	0.154934	+	0.0894510i
$544$	52577.2	−	14088.0i	0.177664	−	0.0476050i
$545$		−	55309.6i		−	0.186212i
$546$	44622.9	−	26594.0i	0.149683	−	0.0892067i
$547$	−300886.			−1.00560			−0.502802	−	0.864401i	$-0.667698\pi$
$547$	−300886.			−1.00560			−0.502802	+	0.864401i	$0.667698\pi$
$548$	35703.3	+	133247.i	0.118891	+	0.443705i
$549$	−88628.1	+	153508.i	−0.294054	+	0.509316i
$550$	−63029.5	+	36390.1i	−0.208362	+	0.120298i
$551$	649.243	−	649.243i	0.00213847	−	0.00213847i
$552$	−57703.5	−	15461.6i	−0.189376	−	0.0507431i
$553$	−32810.9	+	122452.i	−0.107292	+	0.400420i
$554$	301196.	+	301196.i	0.981363	+	0.981363i
$555$	−104446.	−	180906.i	−0.339083	−	0.587309i
$556$	57647.3	+	33282.7i	0.186479	+	0.107664i
$557$	−526651.	+	141116.i	−1.69751	+	0.454847i	−0.972311	−	0.233690i	$-0.924920\pi$
$557$	−526651.	+	141116.i	−1.69751	+	0.454847i	−0.725201	+	0.688537i	$0.758253\pi$
$558$		−	87628.6i		−	0.281435i
$559$	403660.	−	5592.43i	1.29179	−	0.0178969i
$560$	−15636.6			−0.0498617
$561$	34683.1	+	129439.i	0.110203	+	0.411282i
$562$	89847.4	−	155620.i	0.284468	−	0.492712i
$563$	−400645.	+	231313.i	−1.26399	+	0.729764i	−0.973844	−	0.227219i	$-0.927037\pi$
$563$	−400645.	+	231313.i	−1.26399	+	0.729764i	−0.290145	+	0.956983i	$0.593703\pi$
$564$	−51685.3	+	51685.3i	−0.162483	+	0.162483i
$565$	−39696.3	−	10636.6i	−0.124352	−	0.0333201i
$566$	71192.8	−	265695.i	0.222230	−	0.829374i
$567$	28469.1	+	28469.1i	0.0885538	+	0.0885538i
$568$	87090.5	+	150845.i	0.269944	+	0.467557i
$569$	68140.5	+	39340.9i	0.210465	+	0.121512i	0.601528	−	0.798852i	$-0.294559\pi$
$569$	68140.5	+	39340.9i	0.210465	+	0.121512i	−0.391062	+	0.920364i	$0.627892\pi$
$570$	−1781.77	+	477.425i	−0.00548407	+	0.00146945i
$571$			174601.i			0.535517i	0.963486	+	0.267759i	$0.0862829\pi$
$571$			174601.i			0.535517i	−0.963486	+	0.267759i	$0.913717\pi$
$572$	−85394.6	+	24154.2i	−0.260999	+	0.0738244i
$573$	122740.			0.373831
$574$	34736.3	+	129638.i	0.105429	+	0.393466i
$575$	76220.1	−	132017.i	0.230533	−	0.399295i
$576$	−15477.2	+	8935.74i	−0.0466494	+	0.0269331i
$577$	333145.	−	333145.i	1.00065	−	1.00065i	0.000648117	−	1.00000i	$-0.499794\pi$
$577$	333145.	−	333145.i	1.00065	−	1.00065i	1.00000		0.000648117i	$-0.000206302\pi$
$578$	18844.8	+	5049.45i	0.0564073	+	0.0151143i
$579$	−85532.1	+	319210.i	−0.255136	+	0.952182i
$580$	12597.6	+	12597.6i	0.0374484	+	0.0374484i
$581$	52485.1	+	90906.8i	0.155483	+	0.269305i
$582$	224764.	+	129768.i	0.663562	+	0.383108i
$583$	167464.	−	44871.9i	0.492702	−	0.132019i
$584$			738.763i			0.00216611i
$585$	−64544.8	−	62780.8i	−0.188603	−	0.183449i
$586$	−11245.1			−0.0327467
$587$	−39644.6	−	147956.i	−0.115056	−	0.429394i	0.884235	−	0.467041i	$-0.154680\pi$
$587$	−39644.6	−	147956.i	−0.115056	−	0.429394i	−0.999291	+	0.0376479i	$0.988013\pi$
$588$	58246.6	−	100886.i	0.168467	−	0.291794i
$589$	4837.42	−	2792.89i	0.0139439	−	0.00805050i
$590$	134217.	−	134217.i	0.385571	−	0.385571i
$591$	86854.0	+	23272.5i	0.248665	+	0.0666296i
$592$	33389.3	−	124611.i	0.0952717	−	0.355559i
$593$	−308290.	−	308290.i	−0.876698	−	0.876698i	0.116493	−	0.993191i	$-0.462835\pi$
$593$	−308290.	−	308290.i	−0.876698	−	0.876698i	−0.993191	+	0.116493i	$0.962835\pi$
$594$	−73048.4	−	126524.i	−0.207032	−	0.358590i
$595$	−63624.3	−	36733.5i	−0.179717	−	0.103760i
$596$	−79264.0	+	21238.7i	−0.223143	+	0.0597910i
$597$		−	416614.i		−	1.16892i
$598$	129603.	−	133244.i	0.362419	−	0.372603i
$599$	120290.			0.335254			0.167627	−	0.985850i	$-0.446389\pi$
$599$	120290.			0.335254			0.167627	+	0.985850i	$0.446389\pi$
$600$	15586.9	+	58170.9i	0.0432968	+	0.161586i
$601$	−7610.64	+	13182.0i	−0.0210704	+	0.0364949i	−0.876368	−	0.481642i	$-0.840041\pi$
$601$	−7610.64	+	13182.0i	−0.0210704	+	0.0364949i	0.855298	+	0.518136i	$0.173374\pi$
$602$	−93658.0	+	54073.4i	−0.258435	+	0.149208i
$603$	141684.	−	141684.i	0.389659	−	0.389659i
$604$	105565.	+	28286.1i	0.289365	+	0.0775352i
$605$	40819.1	−	152339.i	0.111520	−	0.416198i
$606$	121145.	+	121145.i	0.329882	+	0.329882i
$607$	−286153.	−	495632.i	−0.776643	−	1.34519i	−0.933866	−	0.357622i	$-0.883587\pi$
$607$	−286153.	−	495632.i	−0.776643	−	1.34519i	0.157223	−	0.987563i	$-0.449746\pi$
$608$	−986.572	−	569.598i	−0.00266883	−	0.00154085i
$609$	15315.0	−	4103.65i	0.0412936	−	0.0110646i
$610$		−	219240.i		−	0.589198i
$611$	−61901.5	−	218847.i	−0.165813	−	0.586216i
$612$	−83967.2			−0.224185
$613$	140865.	+	525716.i	0.374871	+	1.39904i	0.853533	+	0.521039i	$0.174456\pi$
$613$	140865.	+	525716.i	0.374871	+	1.39904i	−0.478661	+	0.878000i	$0.658878\pi$
$614$	−121158.	+	209851.i	−0.321376	+	0.556640i
$615$	−266051.	+	153605.i	−0.703420	+	0.406120i
$616$	16810.7	−	16810.7i	0.0443021	−	0.0443021i
$617$	−413208.	−	110719.i	−1.08542	−	0.290838i	−0.328606	−	0.944467i	$-0.606579\pi$
$617$	−413208.	−	110719.i	−1.08542	−	0.290838i	−0.756815	+	0.653629i	$0.773246\pi$
$618$	64650.7	−	241280.i	0.169276	−	0.631748i
$619$	73376.4	+	73376.4i	0.191503	+	0.191503i	0.796345	−	0.604842i	$-0.206764\pi$
$619$	73376.4	+	73376.4i	0.191503	+	0.191503i	−0.604842	+	0.796345i	$0.706764\pi$
$620$	54192.0	+	93863.3i	0.140978	+	0.244181i
$621$	265007.	+	153002.i	0.687186	+	0.396747i
$622$	−217469.	+	58270.7i	−0.562104	+	0.150615i
$623$			44679.5i			0.115115i
$624$	1017.27	+	73426.2i	0.00261256	+	0.188574i
$625$	−8058.73			−0.0206303
$626$	20234.5	+	75516.2i	0.0516350	+	0.192704i
$627$	1402.28	−	2428.83i	0.00356698	−	0.00617819i
$628$	217321.	−	125470.i	0.551039	−	0.318143i
$629$	428593.	−	428593.i	1.08329	−	1.08329i
$630$	23299.3	+	6243.03i	0.0587032	+	0.0157295i
$631$	147588.	−	550805.i	0.370674	−	1.38337i	−0.488891	−	0.872345i	$-0.662598\pi$
$631$	147588.	−	550805.i	0.370674	−	1.38337i	0.859564	−	0.511027i	$-0.170735\pi$
$632$	−126719.	−	126719.i	−0.317255	−	0.317255i
$633$	173999.	+	301376.i	0.434251	+	0.752144i
$634$	−50641.5	−	29237.9i	−0.125988	−	0.0727390i
$635$	180923.	−	48478.2i	0.448690	−	0.120226i
$636$		−	143459.i		−	0.354660i
$637$	185566.	+	311367.i	0.457319	+	0.767350i
$638$	−27087.0			−0.0665457
$639$	−69542.9	−	259537.i	−0.170314	−	0.635621i
$640$	11052.2	−	19143.0i	0.0269830	−	0.0467359i
$641$	−372636.	+	215141.i	−0.906919	+	0.523610i	−0.879439	−	0.476012i	$-0.842082\pi$
$641$	−372636.	+	215141.i	−0.906919	+	0.523610i	−0.0274805	+	0.999622i	$0.508748\pi$
$642$	−197666.	+	197666.i	−0.479582	+	0.479582i
$643$	737369.	+	197577.i	1.78346	+	0.477876i	0.991207	−	0.132319i	$-0.0422422\pi$
$643$	737369.	+	197577.i	1.78346	+	0.477876i	0.792251	+	0.610195i	$0.208909\pi$
$644$	−12887.9	+	48098.4i	−0.0310750	+	0.115973i
$645$	−175044.	−	175044.i	−0.420752	−	0.420752i
$646$	−2676.19	−	4635.30i	−0.00641287	−	0.0111074i
$647$	536098.	+	309516.i	1.28066	+	0.739392i	0.976970	−	0.213377i	$-0.0684464\pi$
$647$	536098.	+	309516.i	1.28066	+	0.739392i	0.303695	+	0.952769i	$0.401780\pi$
$648$	−54975.4	+	14730.6i	−0.130924	+	0.0350809i
$649$			288589.i			0.685158i
$650$	−181654.	−	45986.6i	−0.429950	−	0.108844i
$651$	96457.2			0.227600
$652$	26604.6	+	99289.6i	0.0625836	+	0.233565i
$653$	−371271.	+	643061.i	−0.870693	+	1.50808i	−0.00941110	+	0.999956i	$0.502996\pi$
$653$	−371271.	+	643061.i	−0.870693	+	1.50808i	−0.861282	+	0.508128i	$0.830338\pi$
$654$	60261.1	−	34791.7i	0.140890	−	0.0813431i
$655$	−316188.	+	316188.i	−0.736993	+	0.736993i
$656$	−183260.	−	49104.3i	−0.425853	−	0.114107i
$657$	294.956	−	1100.79i	0.000683324	−	0.00255020i
$658$	43081.9	+	43081.9i	0.0995046	+	0.0995046i
$659$	−91599.7	−	158655.i	−0.210923	−	0.365329i	0.741081	−	0.671416i	$-0.234313\pi$
$659$	−91599.7	−	158655.i	−0.210923	−	0.365329i	−0.952004	+	0.306087i	$0.900980\pi$
$660$	47127.9	+	27209.3i	0.108191	+	0.0624640i
$661$	151719.	−	40652.9i	0.347246	−	0.0930442i	−0.0809808	−	0.996716i	$-0.525805\pi$
$661$	151719.	−	40652.9i	0.347246	−	0.0930442i	0.428226	+	0.903672i	$0.359139\pi$
$662$			47720.8i			0.108891i
$663$	−168353.	+	301155.i	−0.382996	+	0.685115i
$664$	−148389.			−0.336563
$665$	397.954	+	1485.18i	0.000899890	+	0.00335844i
$666$	−99503.1	+	172344.i	−0.224330	+	0.388552i
$667$	49133.5	−	28367.2i	0.110440	−	0.0637625i
$668$	170637.	−	170637.i	0.382402	−	0.382402i
$669$	−293098.	−	78535.4i	−0.654878	−	0.175474i
$670$	−64143.1	+	239385.i	−0.142890	+	0.533271i
$671$	235702.	+	235702.i	0.523501	+	0.523501i
$672$	−9836.02	−	17036.5i	−0.0217812	−	0.0377261i
$673$	−516154.	−	298002.i	−1.13959	−	0.657943i	−0.193262	−	0.981147i	$-0.561907\pi$
$673$	−516154.	−	298002.i	−1.13959	−	0.657943i	−0.946329	+	0.323204i	$0.895240\pi$
$674$	−194342.	+	52073.8i	−0.427806	+	0.114630i
$675$		−	308482.i		−	0.677053i
$676$	−200965.	−	108718.i	−0.439772	−	0.237908i
$677$	−125593.			−0.274023			−0.137012	−	0.990569i	$-0.543750\pi$
$677$	−125593.			−0.274023			−0.137012	+	0.990569i	$0.543750\pi$
$678$	−13381.6	−	49940.9i	−0.0291105	−	0.108642i
$679$	108167.	−	187351.i	0.234615	−	0.406365i
$680$	89941.4	−	51927.7i	0.194510	−	0.112300i
$681$	−80399.5	+	80399.5i	−0.173364	+	0.173364i
$682$	−159172.	−	42650.0i	−0.342214	−	0.0916959i
$683$	−148906.	+	555724.i	−0.319206	+	1.19129i	0.600804	+	0.799396i	$0.294847\pi$
$683$	−148906.	+	555724.i	−0.319206	+	1.19129i	−0.920010	+	0.391895i	$0.871820\pi$
$684$	1242.62	+	1242.62i	0.00265599	+	0.00265599i
$685$	131600.	+	227938.i	0.280463	+	0.485776i
$686$	−178231.	−	102902.i	−0.378735	−	0.218663i
$687$	−137588.	+	36866.7i	−0.291520	+	0.0781126i
$688$		−	152880.i		−	0.322978i
$689$	389625.	+	217810.i	0.820745	+	0.458817i
$690$	−113981.			−0.239406
$691$	−48982.1	−	182804.i	−0.102584	−	0.382850i	0.895475	−	0.445111i	$-0.146836\pi$
$691$	−48982.1	−	182804.i	−0.102584	−	0.382850i	−0.998060	+	0.0622604i	$0.980169\pi$
$692$	141207.	−	244578.i	0.294879	−	0.510745i
$693$	−31760.5	+	18336.9i	−0.0661333	+	0.0381821i
$694$	−457584.	+	457584.i	−0.950061	+	0.950061i
$695$	122678.	+	32871.5i	0.253979	+	0.0680535i
$696$	−5801.04	+	21649.8i	−0.0119753	+	0.0446926i
$697$	−630315.	−	630315.i	−1.29745	−	1.29745i
$698$	−127769.	−	221303.i	−0.262250	−	0.454231i
$699$	271072.	+	156503.i	0.554791	+	0.320309i
$700$	48488.0	−	12992.3i	0.0989550	−	0.0265149i
$701$			662975.i			1.34915i	0.738205	+	0.674576i	$0.235674\pi$
$701$			662975.i			1.34915i	−0.738205	+	0.674576i	$0.764326\pi$
$702$	92312.1	−	364646.i	0.187320	−	0.739942i
$703$	−12685.4			−0.0256681
$704$	8698.28	+	32462.4i	0.0175504	+	0.0654991i
$705$	−69731.2	+	120778.i	−0.140297	+	0.243002i
$706$	510661.	−	294830.i	1.02453	−	0.591511i
$707$	100979.	−	100979.i	0.202020	−	0.202020i
$708$	230660.	+	61805.2i	0.460157	+	0.123299i
$709$	176526.	−	658803.i	0.351168	−	1.31058i	−0.534070	−	0.845440i	$-0.679338\pi$
$709$	176526.	−	658803.i	0.351168	−	1.31058i	0.885238	−	0.465138i	$-0.153995\pi$
$710$	234996.	+	234996.i	0.466170	+	0.466170i
$711$	138224.	+	239411.i	0.273429	+	0.473593i
$712$	−54698.4	−	31580.1i	−0.107898	−	0.0622951i
$713$	333390.	−	89331.5i	0.655802	−	0.175722i
$714$		−	92426.9i		−	0.181302i
$715$	−145452.	+	86685.3i	−0.284517	+	0.169564i
$716$	−338884.			−0.661035
$717$	−168247.	−	627905.i	−0.327272	−	1.22139i
$718$	−267555.	+	463419.i	−0.518996	+	0.898927i
$719$	214139.	−	123633.i	0.414227	−	0.239154i	−0.278377	−	0.960472i	$-0.589797\pi$
$719$	214139.	−	123633.i	0.414227	−	0.239154i	0.692604	+	0.721318i	$0.256463\pi$
$720$	−24111.3	+	24111.3i	−0.0465110	+	0.0465110i
$721$	−201117.	−	53889.1i	−0.386882	−	0.103665i
$722$	95372.6	−	355935.i	0.182957	−	0.682805i
$723$	142679.	+	142679.i	0.272951	+	0.272951i
$724$	31077.7	+	53828.2i	0.0592887	+	0.102691i
$725$	−49531.5	−	28597.0i	−0.0942335	−	0.0544057i
$726$	191653.	−	51353.4i	0.363616	−	0.0974307i
$727$			551704.i			1.04385i	0.852992	+	0.521924i	$0.174785\pi$
$727$			551704.i			1.04385i	−0.852992	+	0.521924i	$0.825215\pi$
$728$	61203.8	−	847.938i	0.115482	−	0.00159993i
$729$	520550.			0.979506
$730$	364.818	+	1361.52i	0.000684590	+	0.00255493i
$731$	359145.	−	622057.i	0.672101	−	1.16411i
$732$	238868.	−	137910.i	0.445795	−	0.257380i
$733$	−636870.	+	636870.i	−1.18534	+	1.18534i	−0.206997	+	0.978341i	$0.566369\pi$
$733$	−636870.	+	636870.i	−1.18534	+	1.18534i	−0.978341	+	0.206997i	$0.933631\pi$
$734$	536396.	+	143727.i	0.995619	+	0.266775i
$735$	57527.0	−	214694.i	0.106487	−	0.397415i
$736$	−49774.6	−	49774.6i	−0.0918866	−	0.0918866i
$737$	−188400.	−	326318.i	−0.346853	−	0.600768i
$738$	253460.	+	146335.i	0.465368	+	0.268681i
$739$	660514.	−	176984.i	1.20946	−	0.324075i	0.402913	−	0.915238i	$-0.367998\pi$
$739$	660514.	−	176984.i	1.20946	−	0.324075i	0.806552	+	0.591164i	$0.201331\pi$
$740$		−	246142.i		−	0.449493i
$741$	6948.20	−	1965.32i	0.0126542	−	0.00357930i
$742$	−119579.			−0.217194
$743$	−108517.	−	404990.i	−0.196571	−	0.733613i	−0.991855	−	0.127375i	$-0.959345\pi$
$743$	−108517.	−	404990.i	−0.196571	−	0.733613i	0.795284	−	0.606238i	$-0.207322\pi$
$744$	−68177.5	+	118087.i	−0.123167	+	0.213332i
$745$	−135593.	+	78284.7i	−0.244301	+	0.141047i
$746$	−91893.1	+	91893.1i	−0.165122	+	0.165122i
$747$	221106.	+	59245.3i	0.396242	+	0.106173i
$748$	−40867.9	+	152521.i	−0.0730431	+	0.272600i
$749$	164763.	+	164763.i	0.293695	+	0.293695i
$750$	149050.	+	258163.i	0.264978	+	0.458956i
$751$	−671832.	−	387882.i	−1.19119	−	0.687734i	−0.232613	−	0.972569i	$-0.574728\pi$
$751$	−671832.	−	387882.i	−1.19119	−	0.687734i	−0.958576	+	0.284836i	$0.908061\pi$
$752$	−83193.6	+	22291.7i	−0.147114	+	0.0394191i
$753$		−	381074.i		−	0.672077i
$754$	−49991.9	−	48625.6i	−0.0879340	−	0.0855308i
$755$	208522.			0.365811
$756$	26080.4	+	97333.3i	0.0456321	+	0.170301i
$757$	347108.	−	601209.i	0.605722	−	1.04914i	−0.386215	−	0.922409i	$-0.626218\pi$
$757$	347108.	−	601209.i	0.605722	−	1.04914i	0.991937	−	0.126732i	$-0.0404489\pi$
$758$	444335.	−	256537.i	0.773342	−	0.446489i
$759$	122539.	−	122539.i	0.212712	−	0.212712i
$760$	−2099.50	−	562.561i	−0.00363488	−	0.000973962i
$761$	−154247.	+	575658.i	−0.266347	+	0.994021i	0.695074	+	0.718939i	$0.255372\pi$
$761$	−154247.	+	575658.i	−0.266347	+	0.994021i	−0.961421	+	0.275082i	$0.911295\pi$
$762$	166625.	+	166625.i	0.286966	+	0.286966i
$763$	−29000.4	−	50230.2i	−0.0498144	−	0.0862811i
$764$	125250.	+	72313.4i	0.214582	+	0.123889i
$765$	−154749.	+	41464.9i	−0.264427	+	0.0708529i
$766$			551709.i			0.940271i
$767$	−518065.	+	532622.i	−0.880630	+	0.905374i
$768$	27809.0			0.0471480
$769$	−164062.	−	612288.i	−0.277432	−	1.03539i	−0.954194	−	0.299187i	$-0.903284\pi$
$769$	−164062.	−	612288.i	−0.277432	−	1.03539i	0.676763	−	0.736201i	$-0.263382\pi$
$770$	22680.1	−	39283.1i	0.0382529	−	0.0662559i
$771$	−147444.	+	85126.7i	−0.248038	+	0.143205i
$772$	−275348.	+	275348.i	−0.462006	+	0.462006i
$773$	−216990.	−	58142.3i	−0.363146	−	0.0973046i	0.0726322	−	0.997359i	$-0.476860\pi$
$773$	−216990.	−	58142.3i	−0.363146	−	0.0973046i	−0.435778	+	0.900054i	$0.643527\pi$
$774$	−61038.3	+	227798.i	−0.101887	+	0.380249i
$775$	−246035.	−	246035.i	−0.409632	−	0.409632i
$776$	152908.	+	264845.i	0.253926	+	0.439813i
$777$	−189708.	−	109528.i	−0.314227	−	0.181419i
$778$	622089.	−	166688.i	1.02776	−	0.275389i
$779$			18655.9i			0.0307427i
$780$	38134.3	+	134820.i	0.0626797	+	0.221598i
$781$	−505281.			−0.828382
$782$	−85598.9	−	319459.i	−0.139976	−	0.522399i
$783$	57404.8	−	99428.0i	0.0936320	−	0.162175i
$784$	118876.	−	68633.3i	0.193403	−	0.111661i
$785$	338556.	−	338556.i	0.549404	−	0.549404i
$786$	−543389.	−	145601.i	−0.879560	−	0.235677i
$787$	−139241.	+	519655.i	−0.224811	+	0.839007i	0.757669	+	0.652639i	$0.226338\pi$
$787$	−139241.	+	519655.i	−0.224811	+	0.839007i	−0.982480	+	0.186368i	$0.940328\pi$
$788$	74919.5	+	74919.5i	0.120654	+	0.120654i
$789$	186652.	+	323291.i	0.299833	+	0.519325i
$790$	−296117.	−	170963.i	−0.474471	−	0.273936i
$791$	−41627.9	+	11154.2i	−0.0665321	+	0.0178272i
$792$		−	51843.3i		−	0.0826499i
$793$	11888.9	+	858135.i	0.0189058	+	1.36461i
$794$	186079.			0.295159
$795$	−70843.2	−	264390.i	−0.112089	−	0.418323i
$796$	245453.	−	425137.i	0.387384	−	0.670969i
$797$	852147.	−	491987.i	1.34152	−	0.774528i	0.354492	−	0.935059i	$-0.384654\pi$
$797$	852147.	−	491987.i	1.34152	−	0.774528i	0.987031	+	0.160531i	$0.0513206\pi$
$798$	−1367.82	+	1367.82i	−0.00214794	+	0.00214794i
$799$	−390876.	−	104735.i	−0.612274	−	0.164058i
$800$	−18366.3	+	68544.1i	−0.0286974	+	0.107100i
$801$	68894.5	+	68894.5i	0.107379	+	0.107379i
$802$	−59674.2	−	103359.i	−0.0927765	−	0.160694i
$803$	−1855.96	−	1071.54i	−0.00287831	−	0.00166179i
$804$	−301164.	+	80696.7i	−0.465899	+	0.124837i
$805$			95008.3i			0.146612i
$806$	−217205.	−	364454.i	−0.334348	−	0.561013i
$807$	−98619.5			−0.151431
$808$	52249.2	+	194997.i	0.0800308	+	0.298679i
$809$	−405227.	+	701874.i	−0.619158	+	1.07241i	0.370481	+	0.928840i	$0.379193\pi$
$809$	−405227.	+	701874.i	−0.619158	+	1.07241i	−0.989640	+	0.143574i	$0.954141\pi$
$810$	−94043.9	+	54296.2i	−0.143338	+	0.0827560i
$811$	−145932.	+	145932.i	−0.221875	+	0.221875i	−0.809288	−	0.587413i	$-0.800147\pi$
$811$	−145932.	+	145932.i	−0.221875	+	0.221875i	0.587413	+	0.809288i	$0.300147\pi$
$812$	18046.0	+	4835.42i	0.0273697	+	0.00733368i
$813$	−63606.6	+	237383.i	−0.0962323	+	0.359144i
$814$	264623.	+	264623.i	0.399374	+	0.399374i
$815$	98062.9	+	169850.i	0.147635	+	0.255711i
$816$	113153.	+	65328.8i	0.169936	+	0.0981125i
$817$	−14520.7	+	3890.81i	−0.0217542	+	0.00582902i
$818$		−	590984.i		−	0.883221i
$819$	−91535.0	−	23172.6i	−0.136464	−	0.0345467i
$820$	−361991.			−0.538357
$821$	28084.8	+	104814.i	0.0416663	+	0.155501i	0.983625	−	0.180229i	$-0.0576838\pi$
$821$	28084.8	+	104814.i	0.0416663	+	0.155501i	−0.941958	+	0.335730i	$0.891017\pi$
$822$	−165563.	+	286763.i	−0.245030	+	0.424404i
$823$	−597087.	+	344728.i	−0.881531	+	0.508952i	−0.871163	−	0.490994i	$-0.836634\pi$
$823$	−597087.	+	344728.i	−0.881531	+	0.508952i	−0.0103684	+	0.999946i	$0.503300\pi$
$824$	208126.	−	208126.i	0.306529	−	0.306529i
$825$	−168748.	−	45215.8i	−0.247931	−	0.0664328i
$826$	51517.3	−	192265.i	0.0755080	−	0.281800i
$827$	−139294.	−	139294.i	−0.203668	−	0.203668i	0.597902	−	0.801569i	$-0.296001\pi$
$827$	−139294.	−	139294.i	−0.203668	−	0.203668i	−0.801569	+	0.597902i	$0.796001\pi$
$828$	54293.6	+	94039.2i	0.0791932	+	0.137167i
$829$	−650628.	−	375640.i	−0.946725	−	0.546592i	−0.0546626	−	0.998505i	$-0.517408\pi$
$829$	−650628.	−	375640.i	−0.946725	−	0.546592i	−0.892062	+	0.451913i	$0.850742\pi$
$830$	−273477.	+	73277.9i	−0.396976	+	0.106369i
$831$			1.02246e6i			1.48062i
$832$	−42221.8	+	75527.6i	−0.0609944	+	0.109109i
$833$	644932.			0.929445
$834$	41354.8	+	154338.i	0.0594557	+	0.221892i
$835$	230215.	−	398744.i	0.330187	−	0.571901i
$836$	2861.94	−	1652.34i	0.00409495	−	0.00236422i
$837$	493883.	−	493883.i	0.704974	−	0.704974i
$838$	−476837.	−	127768.i	−0.679020	−	0.181943i
$839$	−212762.	+	794040.i	−0.302253	+	1.12802i	0.633031	+	0.774126i	$0.281810\pi$
$839$	−212762.	+	794040.i	−0.302253	+	1.12802i	−0.935284	+	0.353897i	$0.884856\pi$
$840$	−26540.5	−	26540.5i	−0.0376141	−	0.0376141i
$841$	342997.	+	594089.i	0.484952	+	0.839962i
$842$	−366836.	−	211793.i	−0.517426	−	0.298736i
$843$	416639.	−	111638.i	0.586280	−	0.157093i
$844$			410055.i			0.575648i
$845$	−424061.	−	101123.i	−0.593902	−	0.141625i
$846$	132862.			0.185636
$847$	−42805.3	−	159751.i	−0.0596665	−	0.222678i
$848$	84520.3	−	146393.i	0.117536	−	0.203578i
$849$	571809.	−	330134.i	0.793297	−	0.458010i
$850$	−235755.	+	235755.i	−0.326304	+	0.326304i
$851$	−757134.	−	202873.i	−1.04547	−	0.280134i
$852$	−108213.	+	403855.i	−0.149073	+	0.556347i
$853$	175083.	+	175083.i	0.240628	+	0.240628i	0.817110	−	0.576482i	$-0.195575\pi$
$853$	175083.	+	175083.i	0.240628	+	0.240628i	−0.576482	+	0.817110i	$0.695575\pi$
$854$	−114954.	−	199106.i	−0.157619	−	0.273004i
$855$	2903.75	+	1676.48i	0.00397216	+	0.00229333i
$856$	−318167.	+	85252.7i	−0.434218	+	0.116348i
$857$			305115.i			0.415434i	0.978189	+	0.207717i	$0.0666033\pi$
$857$			305115.i			0.415434i	−0.978189	+	0.207717i	$0.933397\pi$
$858$	−185940.	−	103945.i	−0.252580	−	0.141198i
$859$	893826.			1.21134			0.605671	−	0.795715i	$-0.292905\pi$
$859$	893826.			1.21134			0.605671	+	0.795715i	$0.292905\pi$
$860$	−75495.6	−	281753.i	−0.102076	−	0.380954i
$861$	−161079.	+	278996.i	−0.217286	+	0.376350i
$862$	564184.	−	325732.i	0.759287	−	0.438375i
$863$	222444.	−	222444.i	0.298675	−	0.298675i	−0.541820	−	0.840495i	$-0.682265\pi$
$863$	222444.	−	222444.i	0.298675	−	0.298675i	0.840495	+	0.541820i	$0.182265\pi$
$864$	−137593.	−	36868.0i	−0.184319	−	0.0493881i
$865$	139462.	−	520481.i	0.186391	−	0.695621i
$866$	418810.	+	418810.i	0.558447	+	0.558447i
$867$	23415.2	+	40556.4i	0.0311502	+	0.0539536i
$868$	98430.5	+	56828.9i	0.130644	+	0.0754275i
$869$	502151.	−	134551.i	0.664958	−	0.178175i
$870$			42764.6i			0.0564997i
$871$	238083.	−	940464.i	0.313828	−	1.23967i
$872$	81991.8			0.107829
$873$	−122099.	−	455680.i	−0.160208	−	0.597905i
$874$	−3460.87	+	5994.41i	−0.00453068	+	0.00784736i
$875$	215190.	−	124240.i	0.281064	−	0.162272i
$876$	−1253.92	+	1253.92i	−0.00163404	+	0.00163404i
$877$	205293.	+	55008.1i	0.266916	+	0.0715200i	0.389795	−	0.920902i	$-0.372546\pi$
$877$	205293.	+	55008.1i	0.266916	+	0.0715200i	−0.122879	+	0.992422i	$0.539213\pi$
$878$	131370.	−	490280.i	0.170415	−	0.635997i
$879$	−19086.6	−	19086.6i	−0.0247031	−	0.0247031i
$880$	32061.4	+	55531.9i	0.0414015	+	0.0717096i
$881$	1.16939e6	+	675146.i	1.50663	+	0.869853i	0.999970	+	0.00770764i	$0.00245344\pi$
$881$	1.16939e6	+	675146.i	1.50663	+	0.869853i	0.506660	+	0.862146i	$0.330880\pi$
$882$	−204533.	+	54804.5i	−0.262922	+	0.0704497i
$883$		−	125452.i		−	0.160901i	−0.996759	−	0.0804503i	$-0.974364\pi$
$883$		−	125452.i		−	0.160901i	0.996759	−	0.0804503i	$-0.0256358\pi$
$884$	−349226.	+	208129.i	−0.446892	+	0.266335i
$885$	455621.			0.581725
$886$	−84149.3	−	314049.i	−0.107197	−	0.400065i
$887$	−123930.	+	214653.i	−0.157517	+	0.272828i	−0.933973	−	0.357344i	$-0.883682\pi$
$887$	−123930.	+	214653.i	−0.157517	+	0.272828i	0.776455	+	0.630172i	$0.217016\pi$
$888$	268178.	−	154832.i	0.340092	−	0.196352i
$889$	138889.	−	138889.i	0.175738	−	0.175738i
$890$	−116403.	−	31190.0i	−0.146954	−	0.0393763i
$891$	42732.0	−	159478.i	0.0538267	−	0.200884i
$892$	−252824.	−	252824.i	−0.317752	−	0.317752i
$893$	4234.57	+	7334.49i	0.00531015	+	0.00919744i
$894$	−170586.	−	98487.9i	−0.213436	−	0.123228i
$895$	−624553.	+	167348.i	−0.779692	+	0.208918i
$896$		−	23180.0i		−	0.0288734i
$897$	446137.	−	6180.93i	0.554477	−	0.00768191i
$898$	566700.			0.702749
$899$	−33516.3	−	125084.i	−0.0414702	−	0.154769i
$900$	54733.4	−	94801.0i	0.0675721	−	0.117038i
$901$	687814.	−	397109.i	0.847269	−	0.489171i
$902$	389171.	−	389171.i	0.478330	−	0.478330i
$903$	−250749.	−	67187.9i	−0.307513	−	0.0823978i
$904$	15767.9	−	58846.5i	0.0192946	−	0.0720085i
$905$	83856.9	+	83856.9i	0.102386	+	0.102386i
$906$	131168.	+	227189.i	0.159798	+	0.276778i
$907$	−335161.	−	193505.i	−0.407416	−	0.235222i	0.282263	−	0.959337i	$-0.408915\pi$
$907$	−335161.	−	193505.i	−0.407416	−	0.235222i	−0.689679	+	0.724115i	$0.742248\pi$
$908$	−129412.	+	34676.0i	−0.156966	+	0.0420588i
$909$		−	311415.i		−	0.376887i
$910$	112378.	−	31786.6i	0.135706	−	0.0383850i
$911$	−573731.			−0.691308			−0.345654	−	0.938362i	$-0.612343\pi$
$911$	−573731.			−0.691308			−0.345654	+	0.938362i	$0.612343\pi$
$912$	−707.742	−	2641.33i	−0.000850914	−	0.00317565i
$913$	215231.	−	372790.i	0.258204	−	0.447222i
$914$	−954474.	+	551066.i	−1.14254	+	0.659646i
$915$	372123.	−	372123.i	0.444472	−	0.444472i
$916$	−162124.	−	43440.9i	−0.193221	−	0.0517735i
$917$	−121364.	+	452938.i	−0.144329	+	0.538641i
$918$	−473247.	−	473247.i	−0.561568	−	0.561568i
$919$	78636.0	+	136202.i	0.0931087	+	0.161269i	0.908818	−	0.417193i	$-0.136986\pi$
$919$	78636.0	+	136202.i	0.0931087	+	0.161269i	−0.815709	+	0.578463i	$0.803653\pi$
$920$	−116313.	−	67153.4i	−0.137421	−	0.0793400i
$921$	−561830.	+	150542.i	−0.662348	+	0.177475i
$922$		−	568391.i		−	0.668629i
$923$	−932548.	−	907062.i	−1.09463	−	1.06472i
$924$	57066.5			0.0668402
$925$	204517.	+	763267.i	0.239026	+	0.892058i
$926$	−9561.56	+	16561.1i	−0.0111508	+	0.0193138i
$927$	−393213.	+	227021.i	−0.457581	+	0.264184i
$928$	−18674.9	+	18674.9i	−0.0216852	+	0.0216852i
$929$	−444772.	−	119176.i	−0.515354	−	0.138089i	−0.00823734	−	0.999966i	$-0.502622\pi$
$929$	−444772.	−	119176.i	−0.515354	−	0.138089i	−0.507117	+	0.861877i	$0.669289\pi$
$930$	−67335.2	+	251298.i	−0.0778532	+	0.290552i
$931$	−9544.27	−	9544.27i	−0.0110114	−	0.0110114i
$932$	184411.	+	319410.i	0.212303	+	0.367719i
$933$	−468021.	−	270212.i	−0.537653	−	0.310414i
$934$	258063.	−	69147.8i	0.295823	−	0.0792656i
$935$			301274.i			0.344618i
$936$	93067.2	−	95682.2i	0.106229	−	0.109214i
$937$	664201.			0.756520			0.378260	−	0.925699i	$-0.376523\pi$
$937$	664201.			0.756520			0.378260	+	0.925699i	$0.376523\pi$
$938$	67264.2	+	251033.i	0.0764501	+	0.285316i
$939$	−93831.2	+	162520.i	−0.106418	+	0.184322i
$940$	−142315.	+	82165.8i	−0.161063	+	0.0929898i
$941$	−342195.	+	342195.i	−0.386451	+	0.386451i	−0.873420	−	0.486968i	$-0.838103\pi$
$941$	−342195.	+	342195.i	−0.386451	+	0.386451i	0.486968	+	0.873420i	$0.338103\pi$
$942$	581830.	+	155901.i	0.655683	+	0.175690i
$943$	−298358.	+	1.11349e6i	−0.335517	+	1.25216i
$944$	198966.	+	198966.i	0.223272	+	0.223272i
$945$	96130.8	+	166503.i	0.107646	+	0.186449i
$946$	384072.	+	221744.i	0.429171	+	0.247782i
$947$	−321012.	+	86015.0i	−0.357950	+	0.0959123i	−0.433312	−	0.901244i	$-0.642655\pi$
$947$	−321012.	+	86015.0i	−0.357950	+	0.0959123i	0.0753626	+	0.997156i	$0.475989\pi$
$948$		−	430169.i		−	0.478655i
$949$	−1501.78	−	5309.38i	−0.00166753	−	0.00589538i
$950$	6977.82			0.00773166
$951$	−36329.0	−	135582.i	−0.0401691	−	0.149913i
$952$	54454.4	−	94317.7i	0.0600840	−	0.104069i
$953$	−259650.	+	149909.i	−0.285893	+	0.165060i	−0.636088	−	0.771616i	$-0.719449\pi$
$953$	−259650.	+	149909.i	−0.285893	+	0.165060i	0.350195	+	0.936677i	$0.386115\pi$
$954$	−184388.	+	184388.i	−0.202598	+	0.202598i
$955$	266543.	+	71420.0i	0.292254	+	0.0783093i
$956$	198249.	−	739875.i	0.216918	−	0.809548i
$957$	−45975.6	−	45975.6i	−0.0501999	−	0.0501999i
$958$	−2384.82	−	4130.63i	−0.00259851	−	0.00450075i
$959$	239029.	+	138004.i	0.259905	+	0.150056i
$960$	51251.2	−	13732.7i	0.0556112	−	0.0149010i
$961$			135712.i			0.146951i
$962$	13347.7	+	963432.i	0.0144230	+	1.04105i
$963$	508121.			0.547917
$964$	61537.0	+	229659.i	0.0662189	+	0.247132i
$965$	−371486.	+	643432.i	−0.398922	+	0.690953i
$966$	−103514.	+	59763.7i	−0.110929	+	0.0640447i
$967$	−776828.	+	776828.i	−0.830753	+	0.830753i	−0.987620	−	0.156867i	$-0.949861\pi$
$967$	−776828.	+	776828.i	−0.830753	+	0.830753i	0.156867	+	0.987620i	$0.449861\pi$
$968$	225830.	+	60510.9i	0.241007	+	0.0645777i
$969$	3325.25	−	12410.0i	0.00354141	−	0.0132167i
$970$	412592.	+	412592.i	0.438508	+	0.438508i
$971$	−240364.	−	416323.i	−0.254936	−	0.441563i	0.709942	−	0.704260i	$-0.248721\pi$
$971$	−240364.	−	416323.i	−0.254936	−	0.441563i	−0.964878	+	0.262698i	$0.915388\pi$
$972$	323291.	+	186652.i	0.342186	+	0.197561i
$973$	128647.	−	34471.0i	0.135886	−	0.0364106i
$974$			1.02358e6i			1.07896i
$975$	−230272.	−	386381.i	−0.242232	−	0.406449i
$976$	325006.			0.341186
$977$	−13221.5	−	49343.3i	−0.0138513	−	0.0516939i	0.958654	−	0.284573i	$-0.0918519\pi$
$977$	−13221.5	−	49343.3i	−0.0138513	−	0.0516939i	−0.972506	+	0.232879i	$0.925185\pi$
$978$	−123370.	+	213684.i	−0.128983	+	0.223405i
$979$	158674.	−	91610.7i	0.165555	−	0.0955830i
$980$	185193.	−	185193.i	0.192829	−	0.192829i
$981$	−122171.	−	32735.7i	−0.126950	−	0.0340161i
$982$	−185040.	+	690577.i	−0.191885	+	0.716126i
$983$	83088.3	+	83088.3i	0.0859870	+	0.0859870i	0.748792	−	0.662805i	$-0.230634\pi$
$983$	83088.3	+	83088.3i	0.0859870	+	0.0859870i	−0.662805	+	0.748792i	$0.730634\pi$
$984$	−227706.	−	394398.i	−0.235171	−	0.407328i
$985$	175072.	+	101078.i	0.180444	+	0.104180i
$986$	−119858.	+	32115.9i	−0.123286	+	0.0330343i
$987$			146248.i			0.150126i
$988$	8248.24	+	2088.08i	0.00844982	+	0.00213911i
$989$	−928898.			−0.949676
$990$	−25601.4	−	95545.7i	−0.0261212	−	0.0974857i
$991$	663444.	−	1.14912e6i	0.675549	−	1.17009i	−0.300759	−	0.953700i	$-0.597240\pi$
$991$	663444.	−	1.14912e6i	0.675549	−	1.17009i	0.976308	−	0.216385i	$-0.0694267\pi$
$992$	−139144.	+	80335.1i	−0.141398	+	0.0816361i
$993$	−80997.8	+	80997.8i	−0.0821438	+	0.0821438i
$994$	336630.	+	90199.8i	0.340706	+	0.0912920i
$995$	242420.	−	904725.i	0.244863	−	0.913841i
$996$	−251865.	−	251865.i	−0.253892	−	0.253892i
$997$	−344908.	−	597398.i	−0.346987	−	0.600998i	0.638726	−	0.769434i	$-0.279462\pi$
$997$	−344908.	−	597398.i	−0.346987	−	0.600998i	−0.985713	+	0.168436i	$0.946128\pi$
$998$	−858606.	−	495716.i	−0.862051	−	0.497705i
$999$	−1.53216e6	+	410541.i	−1.53523	+	0.411363i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	26.5.f.a.19.1	yes	8
3.2	odd	2		234.5.bb.c.19.2		8
13.4	even	6		338.5.d.e.239.4		8
13.6	odd	12		338.5.d.e.99.4		8
13.7	odd	12		338.5.d.h.99.4		8
13.9	even	3		338.5.d.h.239.4		8
13.11	odd	12	inner	26.5.f.a.11.1	✓	8
39.11	even	12		234.5.bb.c.37.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.5.f.a.11.1	✓	8	13.11	odd	12	inner
26.5.f.a.19.1	yes	8	1.1	even	1	trivial
234.5.bb.c.19.2		8	3.2	odd	2
234.5.bb.c.37.2		8	39.11	even	12
338.5.d.e.99.4		8	13.6	odd	12
338.5.d.e.239.4		8	13.4	even	6
338.5.d.h.99.4		8	13.7	odd	12
338.5.d.h.239.4		8	13.9	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 26 = 2 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	26.f (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.732051 + 2.73205i) q^{2} +(-3.39466 + 5.87972i) q^{3} +(-6.92820 + 4.00000i) q^{4} +(-10.7932 + 10.7932i) q^{5} +(-18.5487 - 4.97012i) q^{6} +(-4.14281 + 15.4612i) q^{7} +(-16.0000 - 16.0000i) q^{8} +(17.4526 + 30.2288i) q^{9} +O(q^{10})\)	\(q+(0.732051 + 2.73205i) q^{2} +(-3.39466 + 5.87972i) q^{3} +(-6.92820 + 4.00000i) q^{4} +(-10.7932 + 10.7932i) q^{5} +(-18.5487 - 4.97012i) q^{6} +(-4.14281 + 15.4612i) q^{7} +(-16.0000 - 16.0000i) q^{8} +(17.4526 + 30.2288i) q^{9} +(-37.3887 - 21.5864i) q^{10} +(63.4031 - 16.9888i) q^{11} -54.3145i q^{12} +(147.515 + 82.4644i) q^{13} -45.2735 q^{14} +(-26.8217 - 100.100i) q^{15} +(32.0000 - 55.4256i) q^{16} +(260.411 - 150.348i) q^{17} +(-69.8105 + 69.8105i) q^{18} +(-6.07879 - 1.62881i) q^{19} +(31.6047 - 117.950i) q^{20} +(-76.8439 - 76.8439i) q^{21} +(92.8286 + 160.784i) q^{22} +(-336.766 - 194.432i) q^{23} +(148.390 - 39.7610i) q^{24} +392.014i q^{25} +(-117.309 + 463.386i) q^{26} -786.917 q^{27} +(-33.1425 - 123.689i) q^{28} +(-72.9490 + 126.351i) q^{29} +(253.844 - 146.557i) q^{30} +(-627.618 + 627.618i) q^{31} +(174.851 + 46.8513i) q^{32} +(-115.342 + 430.464i) q^{33} +(601.394 + 601.394i) q^{34} +(-122.161 - 211.590i) q^{35} +(-241.831 - 139.621i) q^{36} +(1947.04 - 521.708i) q^{37} -17.7999i q^{38} +(-985.629 + 587.407i) q^{39} +345.382 q^{40} +(-767.255 - 2863.43i) q^{41} +(153.688 - 266.195i) q^{42} +(2068.72 - 1194.37i) q^{43} +(-371.315 + 371.315i) q^{44} +(-514.635 - 137.896i) q^{45} +(284.668 - 1062.40i) q^{46} +(-951.593 - 951.593i) q^{47} +(217.258 + 376.302i) q^{48} +(1857.44 + 1072.39i) q^{49} +(-1071.00 + 286.974i) q^{50} +2041.53i q^{51} +(-1351.87 + 18.7293i) q^{52} +2641.26 q^{53} +(-576.063 - 2149.90i) q^{54} +(-500.959 + 867.686i) q^{55} +(313.664 - 181.094i) q^{56} +(30.2123 - 30.2123i) q^{57} +(-398.601 - 106.805i) q^{58} +(-1137.91 + 4246.75i) q^{59} +(586.227 + 586.227i) q^{60} +(2539.11 + 4397.86i) q^{61} +(-2174.13 - 1255.24i) q^{62} +(-539.676 + 144.606i) q^{63} +512.000i q^{64} +(-2482.21 + 702.102i) q^{65} -1260.49 q^{66} +(-1485.73 - 5544.82i) q^{67} +(-1202.79 + 2083.29i) q^{68} +(2286.41 - 1320.06i) q^{69} +(488.645 - 488.645i) q^{70} +(-7435.49 - 1992.33i) q^{71} +(204.419 - 762.903i) q^{72} +(-23.0864 - 23.0864i) q^{73} +(2850.66 + 4937.50i) q^{74} +(-2304.93 - 1330.75i) q^{75} +(48.6303 - 13.0304i) q^{76} +1050.67i q^{77} +(-2326.36 - 2262.78i) q^{78} +7919.96 q^{79} +(252.837 + 943.602i) q^{80} +(1257.65 - 2178.31i) q^{81} +(7261.38 - 4192.36i) q^{82} +(4637.16 - 4637.16i) q^{83} +(839.766 + 225.015i) q^{84} +(-1187.93 + 4433.41i) q^{85} +(4777.50 + 4777.50i) q^{86} +(-495.273 - 857.839i) q^{87} +(-1286.27 - 742.629i) q^{88} +(2696.21 - 722.446i) q^{89} -1506.96i q^{90} +(-1886.12 + 1939.12i) q^{91} +3110.91 q^{92} +(-1559.67 - 5820.76i) q^{93} +(1903.19 - 3296.41i) q^{94} +(83.1895 - 48.0295i) q^{95} +(-869.032 + 869.032i) q^{96} +(-13054.8 - 3498.02i) q^{97} +(-1570.09 + 5859.67i) q^{98} +(1620.10 + 1620.10i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} + 30 q^{5} + 36 q^{6} - 92 q^{7} - 128 q^{8} + 90 q^{9}+O(q^{10}) \) 8 * q - 8 * q^2 + 30 * q^5 + 36 * q^6 - 92 * q^7 - 128 * q^8 + 90 * q^9	\( 8 q - 8 q^{2} + 30 q^{5} + 36 q^{6} - 92 q^{7} - 128 q^{8} + 90 q^{9} + 132 q^{10} + 192 q^{11} - 78 q^{13} - 344 q^{14} + 132 q^{15} + 256 q^{16} - 870 q^{17} - 360 q^{18} - 218 q^{19} - 144 q^{20} + 1914 q^{21} + 948 q^{22} + 264 q^{23} - 288 q^{24} - 520 q^{26} - 2268 q^{27} - 736 q^{28} - 252 q^{29} + 1728 q^{30} - 3376 q^{31} + 512 q^{32} + 1698 q^{33} + 1080 q^{34} + 6474 q^{35} + 2016 q^{36} + 2552 q^{37} - 5928 q^{39} - 960 q^{40} - 8472 q^{41} - 3828 q^{42} + 7290 q^{43} - 3792 q^{44} - 6282 q^{45} - 540 q^{46} + 4848 q^{47} + 9678 q^{49} + 2524 q^{50} - 832 q^{52} - 6840 q^{53} + 2268 q^{54} + 294 q^{55} + 4320 q^{56} - 4434 q^{57} - 7008 q^{58} - 4632 q^{59} + 9024 q^{60} + 8670 q^{61} + 3936 q^{62} + 8100 q^{63} - 2808 q^{65} - 984 q^{66} - 12446 q^{67} - 2160 q^{68} + 19206 q^{69} - 25896 q^{70} - 4554 q^{71} - 5472 q^{72} + 19294 q^{73} + 10112 q^{74} - 25992 q^{75} + 1744 q^{76} - 8580 q^{78} - 11328 q^{79} - 1152 q^{80} + 6048 q^{81} + 42672 q^{82} + 10344 q^{83} - 8592 q^{84} - 23178 q^{85} + 13536 q^{86} + 18372 q^{87} + 1440 q^{88} - 2538 q^{89} + 1456 q^{91} + 96 q^{92} - 162 q^{93} - 9696 q^{94} + 26568 q^{95} - 64282 q^{97} - 31676 q^{98} + 9504 q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 + 30 * q^5 + 36 * q^6 - 92 * q^7 - 128 * q^8 + 90 * q^9 + 132 * q^10 + 192 * q^11 - 78 * q^13 - 344 * q^14 + 132 * q^15 + 256 * q^16 - 870 * q^17 - 360 * q^18 - 218 * q^19 - 144 * q^20 + 1914 * q^21 + 948 * q^22 + 264 * q^23 - 288 * q^24 - 520 * q^26 - 2268 * q^27 - 736 * q^28 - 252 * q^29 + 1728 * q^30 - 3376 * q^31 + 512 * q^32 + 1698 * q^33 + 1080 * q^34 + 6474 * q^35 + 2016 * q^36 + 2552 * q^37 - 5928 * q^39 - 960 * q^40 - 8472 * q^41 - 3828 * q^42 + 7290 * q^43 - 3792 * q^44 - 6282 * q^45 - 540 * q^46 + 4848 * q^47 + 9678 * q^49 + 2524 * q^50 - 832 * q^52 - 6840 * q^53 + 2268 * q^54 + 294 * q^55 + 4320 * q^56 - 4434 * q^57 - 7008 * q^58 - 4632 * q^59 + 9024 * q^60 + 8670 * q^61 + 3936 * q^62 + 8100 * q^63 - 2808 * q^65 - 984 * q^66 - 12446 * q^67 - 2160 * q^68 + 19206 * q^69 - 25896 * q^70 - 4554 * q^71 - 5472 * q^72 + 19294 * q^73 + 10112 * q^74 - 25992 * q^75 + 1744 * q^76 - 8580 * q^78 - 11328 * q^79 - 1152 * q^80 + 6048 * q^81 + 42672 * q^82 + 10344 * q^83 - 8592 * q^84 - 23178 * q^85 + 13536 * q^86 + 18372 * q^87 + 1440 * q^88 - 2538 * q^89 + 1456 * q^91 + 96 * q^92 - 162 * q^93 - 9696 * q^94 + 26568 * q^95 - 64282 * q^97 - 31676 * q^98 + 9504 * q^99

Introduction

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