LMFDB - Embedded newform 72.5.p.b.67.39

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [72,5,Mod(43,72)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(72, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 4])) N = Newforms(chi, 5, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("72.43"); S:= CuspForms(chi, 5); N := Newforms(S);

Level:	$N$	$=$	$72 = 2^{3} \cdot 3^{2}$
Weight:	$k$	$=$	$5$
Character orbit:	$[\chi]$	$=$	72.p (of order $6$ , degree $2$ , minimal)

Newform invariants

comment:select newform

sage:traces = [88] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$7.44263734204$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$44$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			67.39
Character	$\chi$	$=$	72.67
Dual form			72.5.p.b.43.39

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.60691 - 1.72923i) q^{2} +(4.44945 + 7.82320i) q^{3} +(10.0195 - 12.4743i) q^{4} +(2.53773 + 1.46516i) q^{5} +(29.5768 + 20.5234i) q^{6} +(39.8426 - 23.0032i) q^{7} +(14.5686 - 62.3198i) q^{8} +(-41.4048 + 69.6178i) q^{9} +(11.6869 + 0.896378i) q^{10} +(27.1224 + 46.9774i) q^{11} +(142.171 + 22.8810i) q^{12} +(174.611 + 100.811i) q^{13} +(103.931 - 151.867i) q^{14} +(-0.170730 + 26.3723i) q^{15} +(-55.2175 - 249.974i) q^{16} -88.7146 q^{17} +(-28.9582 + 322.703i) q^{18} -357.083 q^{19} +(43.7038 - 16.9762i) q^{20} +(357.236 + 209.345i) q^{21} +(179.063 + 122.542i) q^{22} +(-214.383 - 123.774i) q^{23} +(552.362 - 163.316i) q^{24} +(-308.207 - 533.830i) q^{25} +(804.130 + 61.6760i) q^{26} +(-728.863 - 14.1572i) q^{27} +(112.256 - 727.491i) q^{28} +(-18.7746 + 10.8395i) q^{29} +(44.9879 + 95.4177i) q^{30} +(-349.016 - 201.504i) q^{31} +(-631.426 - 806.149i) q^{32} +(-246.834 + 421.207i) q^{33} +(-319.985 + 153.408i) q^{34} +134.813 q^{35} +(453.578 + 1214.04i) q^{36} -1263.37i q^{37} +(-1287.96 + 617.478i) q^{38} +(-11.7472 + 1814.57i) q^{39} +(128.280 - 136.805i) q^{40} +(-1106.42 + 1916.37i) q^{41} +(1650.52 + 137.347i) q^{42} +(678.384 + 1175.00i) q^{43} +(857.765 + 132.358i) q^{44} +(-207.075 + 116.007i) q^{45} +(-987.293 - 75.7244i) q^{46} +(-3120.48 + 1801.61i) q^{47} +(1709.91 - 1544.22i) q^{48} +(-142.209 + 246.314i) q^{49} +(-2034.79 - 1392.51i) q^{50} +(-394.731 - 694.032i) q^{51} +(3007.07 - 1168.06i) q^{52} -4122.82i q^{53} +(-2653.42 + 1209.31i) q^{54} +158.955i q^{55} +(-853.100 - 2818.11i) q^{56} +(-1588.82 - 2793.53i) q^{57} +(-48.9743 + 71.5628i) q^{58} +(-2643.76 + 4579.12i) q^{59} +(327.266 + 266.368i) q^{60} +(4778.25 - 2758.72i) q^{61} +(-1607.31 - 123.280i) q^{62} +(-48.2476 + 3726.20i) q^{63} +(-3671.51 - 1815.82i) q^{64} +(295.410 + 511.664i) q^{65} +(-161.942 + 1946.09i) q^{66} +(3090.68 - 5353.21i) q^{67} +(-888.880 + 1106.65i) q^{68} +(14.4230 - 2227.89i) q^{69} +(486.258 - 233.123i) q^{70} +4832.30i q^{71} +(3735.36 + 3594.57i) q^{72} +9435.38 q^{73} +(-2184.65 - 4556.84i) q^{74} +(2804.90 - 4786.41i) q^{75} +(-3577.81 + 4454.37i) q^{76} +(2161.26 + 1247.80i) q^{77} +(3095.43 + 6565.29i) q^{78} +(1099.86 - 635.004i) q^{79} +(226.125 - 715.269i) q^{80} +(-3132.28 - 5765.03i) q^{81} +(-676.901 + 8825.41i) q^{82} +(1266.75 + 2194.08i) q^{83} +(6190.78 - 2358.73i) q^{84} +(-225.134 - 129.981i) q^{85} +(4478.70 + 3065.02i) q^{86} +(-168.337 - 98.6477i) q^{87} +(3322.76 - 1005.87i) q^{88} +5907.27 q^{89} +(-546.300 + 776.505i) q^{90} +9275.93 q^{91} +(-3692.02 + 1434.12i) q^{92} +(23.4806 - 3627.00i) q^{93} +(-8139.88 + 11894.2i) q^{94} +(-906.180 - 523.183i) q^{95} +(3497.16 - 8526.69i) q^{96} +(-928.999 - 1609.07i) q^{97} +(-87.0031 + 1134.34i) q^{98} +(-4393.46 - 56.8874i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$88 q + 7 q^{2} - 18 q^{3} + 31 q^{4} - 9 q^{6} - 386 q^{8} + 30 q^{9} - 36 q^{10} + 44 q^{11} + 612 q^{12} - 318 q^{14} + 511 q^{16} - 1156 q^{17} + 234 q^{18} + 860 q^{19} - 1164 q^{20} + 215 q^{22} - 561 q^{24}+ \cdots - 11742 q^{99}+O(q^{100})$ 88 * q + 7 * q^2 - 18 * q^3 + 31 * q^4 - 9 * q^6 - 386 * q^8 + 30 * q^9 - 36 * q^10 + 44 * q^11 + 612 * q^12 - 318 * q^14 + 511 * q^16 - 1156 * q^17 + 234 * q^18 + 860 * q^19 - 1164 * q^20 + 215 * q^22 - 561 * q^24 + 5998 * q^25 - 5232 * q^26 + 504 * q^27 - 516 * q^28 + 2046 * q^30 + 5227 * q^32 - 3204 * q^33 + 1877 * q^34 - 2508 * q^35 - 5877 * q^36 - 4393 * q^38 + 2274 * q^40 + 2348 * q^41 - 8166 * q^42 + 3500 * q^43 + 2234 * q^44 + 3576 * q^46 - 1641 * q^48 + 16462 * q^49 + 5785 * q^50 - 12378 * q^51 - 1440 * q^52 - 7467 * q^54 + 1146 * q^56 - 6522 * q^57 - 4128 * q^58 - 3508 * q^59 + 11934 * q^60 + 2376 * q^62 - 5510 * q^64 - 2502 * q^65 + 834 * q^66 + 5132 * q^67 + 10169 * q^68 + 1134 * q^70 + 9663 * q^72 + 19004 * q^73 - 2946 * q^74 - 39858 * q^75 - 5875 * q^76 - 3330 * q^78 + 8592 * q^80 - 11346 * q^81 - 18454 * q^82 + 17090 * q^83 + 12360 * q^84 + 18581 * q^86 - 3253 * q^88 - 8272 * q^89 - 9408 * q^90 - 9612 * q^91 + 9318 * q^92 - 7590 * q^94 + 52650 * q^96 + 9980 * q^97 + 6826 * q^98 - 11742 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/72\mathbb{Z}\right)^\times$ .

$n$	$37$	$55$	$65$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$ -expansion $a_n$ , the Satake parameters $\alpha_p$ , and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$ .

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$\alpha_n$			$\theta_n$
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$\alpha_p$			$\theta_p$

$2$	3.60691	−	1.72923i	0.901727	−	0.432307i
$2$	3.60691	−	1.72923i	0.901727	−	0.432307i
$3$	4.44945	+	7.82320i	0.494383	+	0.869244i
$3$	4.44945	+	7.82320i	0.494383	+	0.869244i
$4$	10.0195	−	12.4743i	0.626221	−	0.779645i
$5$	2.53773	+	1.46516i	0.101509	+	0.0586064i	0.549895	−	0.835234i	$-0.314668\pi$
$5$	2.53773	+	1.46516i	0.101509	+	0.0586064i	−0.448386	+	0.893840i	$0.648001\pi$
$6$	29.5768	+	20.5234i	0.821579	+	0.570095i
$7$	39.8426	−	23.0032i	0.813115	−	0.469452i	−0.0349214	−	0.999390i	$-0.511118\pi$
$7$	39.8426	−	23.0032i	0.813115	−	0.469452i	0.848036	+	0.529938i	$0.177785\pi$
$8$	14.5686	−	62.3198i	0.227634	−	0.973747i
$9$	−41.4048	+	69.6178i	−0.511171	+	0.859479i
$10$	11.6869	+	0.896378i	0.116869	+	0.00896378i
$11$	27.1224	+	46.9774i	0.224152	+	0.388243i	0.956065	−	0.293156i	$-0.0947054\pi$
$11$	27.1224	+	46.9774i	0.224152	+	0.388243i	−0.731913	+	0.681398i	$0.761372\pi$
$12$	142.171	+	22.8810i	0.987295	+	0.158896i
$13$	174.611	+	100.811i	1.03320	+	0.596517i	0.917899	−	0.396813i	$-0.129884\pi$
$13$	174.611	+	100.811i	1.03320	+	0.596517i	0.115299	+	0.993331i	$0.463217\pi$
$14$	103.931	−	151.867i	0.530260	−	0.774833i
$15$	−0.170730	+	26.3723i	−0.000758800	+	0.117210i
$16$	−55.2175	−	249.974i	−0.215693	−	0.976461i
$17$	−88.7146			−0.306971			−0.153485	−	0.988151i	$-0.549050\pi$
$17$	−88.7146			−0.306971			−0.153485	+	0.988151i	$0.549050\pi$
$18$	−28.9582	+	322.703i	−0.0893773	+	0.995998i
$19$	−357.083			−0.989149			−0.494575	−	0.869135i	$-0.664676\pi$
$19$	−357.083			−0.989149			−0.494575	+	0.869135i	$0.664676\pi$
$20$	43.7038	−	16.9762i	0.109259	−	0.0424406i
$21$	357.236	+	209.345i	0.810059	+	0.474706i
$22$	179.063	+	122.542i	0.369964	+	0.253186i
$23$	−214.383	−	123.774i	−0.405261	−	0.233977i	0.283491	−	0.958975i	$-0.408508\pi$
$23$	−214.383	−	123.774i	−0.405261	−	0.233977i	−0.688751	+	0.724998i	$0.741841\pi$
$24$	552.362	−	163.316i	0.958962	−	0.283534i
$25$	−308.207	−	533.830i	−0.493131	−	0.854127i
$26$	804.130	+	61.6760i	1.18954	+	0.0912367i
$27$	−728.863	−	14.1572i	−0.999811	−	0.0194200i
$28$	112.256	−	727.491i	0.143184	−	0.927922i
$29$	−18.7746	+	10.8395i	−0.0223242	+	0.0128889i	−0.511121	−	0.859509i	$-0.670769\pi$
$29$	−18.7746	+	10.8395i	−0.0223242	+	0.0128889i	0.488796	+	0.872398i	$0.337436\pi$
$30$	44.9879	+	95.4177i	0.0499866	+	0.106020i
$31$	−349.016	−	201.504i	−0.363180	−	0.209682i	0.307295	−	0.951614i	$-0.400576\pi$
$31$	−349.016	−	201.504i	−0.363180	−	0.209682i	−0.670475	+	0.741932i	$0.733910\pi$
$32$	−631.426	−	806.149i	−0.616627	−	0.787255i
$33$	−246.834	+	421.207i	−0.226661	+	0.386784i
$34$	−319.985	+	153.408i	−0.276804	+	0.132706i
$35$	134.813			0.110052
$36$	453.578	+	1214.04i	0.349983	+	0.936756i
$37$		−	1263.37i		−	0.922839i	−0.887182	−	0.461419i	$-0.847340\pi$
$37$		−	1263.37i		−	0.922839i	0.887182	−	0.461419i	$-0.152660\pi$
$38$	−1287.96	+	617.478i	−0.891942	+	0.427616i
$39$	−11.7472	+	1814.57i	−0.00772334	+	1.19301i
$40$	128.280	−	136.805i	0.0801747	−	0.0855034i
$41$	−1106.42	+	1916.37i	−0.658189	+	1.14002i	0.322895	+	0.946435i	$0.395344\pi$
$41$	−1106.42	+	1916.37i	−0.658189	+	1.14002i	−0.981084	+	0.193582i	$0.937989\pi$
$42$	1650.52	+	137.347i	0.935670	+	0.0778611i
$43$	678.384	+	1175.00i	0.366892	+	0.635476i	0.989078	−	0.147393i	$-0.0470884\pi$
$43$	678.384	+	1175.00i	0.366892	+	0.635476i	−0.622185	+	0.782870i	$0.713755\pi$
$44$	857.765	+	132.358i	0.443060	+	0.0683668i
$45$	−207.075	+	116.007i	−0.102259	+	0.0572872i
$46$	−987.293	−	75.7244i	−0.466584	−	0.0357866i
$47$	−3120.48	+	1801.61i	−1.41262	+	0.815577i	−0.995635	−	0.0933366i	$-0.970247\pi$
$47$	−3120.48	+	1801.61i	−1.41262	+	0.815577i	−0.416985	+	0.908913i	$0.636913\pi$
$48$	1709.91	−	1544.22i	0.742148	−	0.670236i
$49$	−142.209	+	246.314i	−0.0592292	+	0.102588i
$50$	−2034.79	−	1392.51i	−0.813914	−	0.557005i
$51$	−394.731	−	694.032i	−0.151761	−	0.266833i
$52$	3007.07	−	1168.06i	1.11208	−	0.431976i
$53$		−	4122.82i		−	1.46772i	−0.679303	−	0.733858i	$-0.737718\pi$
$53$		−	4122.82i		−	1.46772i	0.679303	−	0.733858i	$-0.262282\pi$
$54$	−2653.42	+	1209.31i	−0.909952	+	0.414714i
$55$			158.955i			0.0525469i
$56$	−853.100	−	2818.11i	−0.272035	−	0.898632i
$57$	−1588.82	−	2793.53i	−0.489019	−	0.859812i
$58$	−48.9743	+	71.5628i	−0.0145584	+	0.0212731i
$59$	−2643.76	+	4579.12i	−0.759482	+	1.31546i	0.183634	+	0.982995i	$0.441214\pi$
$59$	−2643.76	+	4579.12i	−0.759482	+	1.31546i	−0.943115	+	0.332466i	$0.892119\pi$
$60$	327.266	+	266.368i	0.0909072	+	0.0739912i
$61$	4778.25	−	2758.72i	1.28413	−	0.741393i	0.306530	−	0.951861i	$-0.400832\pi$
$61$	4778.25	−	2758.72i	1.28413	−	0.741393i	0.977601	+	0.210468i	$0.0674987\pi$
$62$	−1607.31	−	123.280i	−0.418136	−	0.0320706i
$63$	−48.2476	+	3726.20i	−0.0121561	+	0.938826i
$64$	−3671.51	−	1815.82i	−0.896365	−	0.443317i
$65$	295.410	+	511.664i	0.0699194	+	0.121104i
$66$	−161.942	+	1946.09i	−0.0371768	+	0.446760i
$67$	3090.68	−	5353.21i	0.688500	−	1.19252i	−0.283822	−	0.958877i	$-0.591603\pi$
$67$	3090.68	−	5353.21i	0.688500	−	1.19252i	0.972323	−	0.233641i	$-0.0750640\pi$
$68$	−888.880	+	1106.65i	−0.192232	+	0.239328i
$69$	14.4230	−	2227.89i	0.00302940	−	0.467945i
$70$	486.258	−	233.123i	0.0992364	−	0.0475760i
$71$			4832.30i			0.958600i	0.877651	+	0.479300i	$0.159109\pi$
$71$			4832.30i			0.958600i	−0.877651	+	0.479300i	$0.840891\pi$
$72$	3735.36	+	3594.57i	0.720555	+	0.693398i
$73$	9435.38			1.77057			0.885286	−	0.465047i	$-0.153963\pi$
$73$	9435.38			1.77057			0.885286	+	0.465047i	$0.153963\pi$
$74$	−2184.65	−	4556.84i	−0.398949	−	0.832148i
$75$	2804.90	−	4786.41i	0.498650	−	0.850917i
$76$	−3577.81	+	4454.37i	−0.619426	+	0.771185i
$77$	2161.26	+	1247.80i	0.364523	+	0.210457i
$78$	3095.43	+	6565.29i	0.508782	+	1.07911i
$79$	1099.86	−	635.004i	0.176231	−	0.101747i	−0.409290	−	0.912405i	$-0.634223\pi$
$79$	1099.86	−	635.004i	0.176231	−	0.101747i	0.585521	+	0.810657i	$0.300890\pi$
$80$	226.125	−	715.269i	0.0353320	−	0.111761i
$81$	−3132.28	−	5765.03i	−0.477409	−	0.878681i
$82$	−676.901	+	8825.41i	−0.100669	+	1.31252i
$83$	1266.75	+	2194.08i	0.183881	+	0.318490i	0.943199	−	0.332229i	$-0.107801\pi$
$83$	1266.75	+	2194.08i	0.183881	+	0.318490i	−0.759318	+	0.650720i	$0.774467\pi$
$84$	6190.78	−	2358.73i	0.877379	−	0.334287i
$85$	−225.134	−	129.981i	−0.0311604	−	0.0179904i
$86$	4478.70	+	3065.02i	0.605557	+	0.414416i
$87$	−168.337	−	98.6477i	−0.0222403	−	0.0130331i
$88$	3322.76	−	1005.87i	0.429075	−	0.129890i
$89$	5907.27			0.745773			0.372887	−	0.927877i	$-0.378368\pi$
$89$	5907.27			0.745773			0.372887	+	0.927877i	$0.378368\pi$
$90$	−546.300	+	776.505i	−0.0674444	+	0.0958649i
$91$	9275.93			1.12015
$92$	−3692.02	+	1434.12i	−0.436202	+	0.169438i
$93$	23.4806	−	3627.00i	0.00271484	−	0.419355i
$94$	−8139.88	+	11894.2i	−0.921218	+	1.34611i
$95$	−906.180	−	523.183i	−0.100408	−	0.0579704i
$96$	3497.16	−	8526.69i	0.379467	−	0.925205i
$97$	−928.999	−	1609.07i	−0.0987351	−	0.171014i	0.812426	−	0.583064i	$-0.198146\pi$
$97$	−928.999	−	1609.07i	−0.0987351	−	0.171014i	−0.911161	+	0.412050i	$0.864813\pi$
$98$	−87.0031	+	1134.34i	−0.00905905	+	0.118112i
$99$	−4393.46	−	56.8874i	−0.448267	−	0.00580425i
$100$	−9747.25	−	1504.06i	−0.974725	−	0.150406i
$101$	13841.8	−	7991.56i	1.35690	−	0.783409i	0.367699	−	0.929945i	$-0.380146\pi$
$101$	13841.8	−	7991.56i	1.35690	−	0.783409i	0.989205	+	0.146536i	$0.0468123\pi$
$102$	−2623.90	−	1820.73i	−0.252201	−	0.175003i
$103$	−17094.2	−	9869.37i	−1.61130	−	0.930283i	−0.989070	−	0.147445i	$-0.952895\pi$
$103$	−17094.2	−	9869.37i	−1.61130	−	0.930283i	−0.622227	−	0.782837i	$-0.713772\pi$
$104$	8826.38	−	9413.01i	0.816048	−	0.870286i
$105$	599.844	+	1054.67i	0.0544076	+	0.0956617i
$106$	−7129.29	−	14870.6i	−0.634504	−	1.32348i
$107$	8611.81			0.752189			0.376095	−	0.926581i	$-0.377267\pi$
$107$	8611.81			0.752189			0.376095	+	0.926581i	$0.377267\pi$
$108$	−7479.47	+	8950.22i	−0.641244	+	0.767337i
$109$			19759.0i			1.66307i	0.555470	+	0.831537i	$0.312539\pi$
$109$			19759.0i			1.66307i	−0.555470	+	0.831537i	$0.687461\pi$
$110$	274.869	+	573.334i	0.0227164	+	0.0473830i
$111$	9883.56	−	5621.28i	0.802172	−	0.456236i
$112$	−7950.20	−	8689.45i	−0.633785	−	0.692718i
$113$	−8203.89	+	14209.6i	−0.642485	+	1.11282i	0.342392	+	0.939557i	$0.388763\pi$
$113$	−8203.89	+	14209.6i	−0.642485	+	1.11282i	−0.984876	+	0.173259i	$0.944570\pi$
$114$	−10561.4	−	7328.56i	−0.812664	−	0.563909i
$115$	−362.697	−	628.210i	−0.0274251	−	0.0475017i
$116$	−52.8973	+	342.808i	−0.00393113	+	0.0254762i
$117$	−14248.0	+	7981.92i	−1.04083	+	0.583090i
$118$	−1617.44	+	21088.1i	−0.116162	+	1.51451i
$119$	−3534.62	+	2040.72i	−0.249603	+	0.144108i
$120$	1641.03	+	394.848i	0.113960	+	0.0274200i
$121$	5849.25	−	10131.2i	0.399512	−	0.691975i
$122$	12464.2	−	18213.1i	0.837425	−	1.22367i
$123$	−19915.1	−	128.927i	−1.31635	−	0.00852183i
$124$	−6010.61	+	2334.76i	−0.390909	+	0.151844i
$125$		−	3637.74i		−	0.232815i
$126$	6269.42	+	13523.5i	0.394899	+	0.851819i
$127$			190.402i			0.0118049i	0.999983	+	0.00590247i	$0.00187883\pi$
$127$			190.402i			0.0118049i	−0.999983	+	0.00590247i	$0.998121\pi$
$128$	−16382.8	−	200.628i	−0.999925	−	0.0122454i
$129$	−6173.79	+	10535.2i	−0.370999	+	0.633088i
$130$	1950.30	+	1334.69i	0.115402	+	0.0789760i
$131$	−5339.62	+	9248.49i	−0.311148	+	0.538925i	−0.978611	−	0.205718i	$-0.934047\pi$
$131$	−5339.62	+	9248.49i	−0.311148	+	0.538925i	0.667463	+	0.744643i	$0.267380\pi$
$132$	2781.12	+	7299.39i	0.159614	+	0.418927i
$133$	−14227.1	+	8214.03i	−0.804292	+	0.464358i
$134$	1890.86	−	24653.0i	0.105305	−	1.37297i
$135$	−1828.91	−	1103.83i	−0.100352	−	0.0605666i
$136$	−1292.45	+	5528.67i	−0.0698771	+	0.298912i
$137$	−2673.96	−	4631.43i	−0.142467	−	0.246759i	0.785958	−	0.618280i	$-0.212170\pi$
$137$	−2673.96	−	4631.43i	−0.142467	−	0.246759i	−0.928425	+	0.371520i	$0.878837\pi$
$138$	−3800.50	−	8060.72i	−0.199564	−	0.423268i
$139$	−4160.16	+	7205.61i	−0.215318	+	0.372942i	−0.953371	−	0.301801i	$-0.902412\pi$
$139$	−4160.16	+	7205.61i	−0.215318	+	0.372942i	0.738053	+	0.674743i	$0.235746\pi$
$140$	1350.77	−	1681.70i	0.0689166	−	0.0858012i
$141$	−27978.7	−	16395.9i	−1.40731	−	0.824704i
$142$	8356.15	+	17429.7i	0.414409	+	0.864395i
$143$			10937.0i			0.534842i
$144$	19688.9	+	6506.01i	0.949504	+	0.313754i
$145$	−63.5266			−0.00302148
$146$	34032.5	−	16315.9i	1.59657	−	0.765431i
$147$	−2559.72	−	16.5712i	−0.118456	−	0.000766864i
$148$	−15759.6	−	12658.3i	−0.719487	−	0.577901i
$149$	8232.13	+	4752.82i	0.370800	+	0.214082i	0.673808	−	0.738907i	$-0.264658\pi$
$149$	8232.13	+	4752.82i	0.370800	+	0.214082i	−0.303008	+	0.952988i	$0.597991\pi$
$150$	1840.24	−	22114.4i	0.0817883	−	0.982864i
$151$	23033.8	−	13298.5i	1.01021	−	0.583244i	0.0989556	−	0.995092i	$-0.468450\pi$
$151$	23033.8	−	13298.5i	1.01021	−	0.583244i	0.911253	+	0.411848i	$0.135116\pi$
$152$	−5202.20	+	22253.3i	−0.225164	+	0.963181i
$153$	3673.21	−	6176.12i	0.156914	−	0.263835i
$154$	9953.18	+	763.400i	0.419682	+	0.0321892i
$155$	−590.472	−	1022.73i	−0.0245774	−	0.0425693i
$156$	22517.8	+	18327.7i	0.925288	+	0.753110i
$157$	14257.2	+	8231.41i	0.578410	+	0.333945i	0.760501	−	0.649336i	$-0.224953\pi$
$157$	14257.2	+	8231.41i	0.578410	+	0.333945i	−0.182091	+	0.983282i	$0.558287\pi$
$158$	2869.02	−	4192.30i	0.114926	−	0.167934i
$159$	32253.6	−	18344.3i	1.27580	−	0.725614i
$160$	−421.253	−	2970.93i	−0.0164552	−	0.116052i
$161$	−11388.8			−0.439365
$162$	−21266.9	−	15377.5i	−0.810352	−	0.585943i
$163$	−6664.66			−0.250843			−0.125422	−	0.992104i	$-0.540028\pi$
$163$	−6664.66			−0.250843			−0.125422	+	0.992104i	$0.540028\pi$
$164$	12819.6	+	33002.9i	0.476637	+	1.22706i
$165$	−1243.53	+	707.260i	−0.0456761	+	0.0259783i
$166$	8363.13	+	5723.34i	0.303496	+	0.207698i
$167$	19196.1	+	11082.8i	0.688302	+	0.397391i	0.802976	−	0.596012i	$-0.203249\pi$
$167$	19196.1	+	11082.8i	0.688302	+	0.397391i	−0.114674	+	0.993403i	$0.536582\pi$
$168$	18250.8	−	19213.0i	0.646641	−	0.680733i
$169$	6045.39	+	10470.9i	0.211666	+	0.366616i
$170$	−1036.80	−	79.5218i	−0.0358755	−	0.00275162i
$171$	14785.0	−	24859.3i	0.505624	−	0.850153i
$172$	21454.4	+	3310.54i	0.725202	+	0.111903i
$173$	9709.71	−	5605.90i	0.324425	−	0.187307i	−0.328938	−	0.944351i	$-0.606691\pi$
$173$	9709.71	−	5605.90i	0.324425	−	0.187307i	0.653363	+	0.757045i	$0.273357\pi$
$174$	−777.759	−	64.7206i	−0.0256890	−	0.00213769i
$175$	−24559.5	−	14179.5i	−0.801944	−	0.463002i
$176$	10245.5	−	9373.87i	0.330756	−	0.302617i
$177$	−47586.6	−	308.068i	−1.51893	−	0.00983331i
$178$	21307.0	−	10215.0i	0.672483	−	0.322403i
$179$	−16987.5			−0.530179			−0.265090	−	0.964224i	$-0.585402\pi$
$179$	−16987.5			−0.530179			−0.265090	+	0.964224i	$0.585402\pi$
$180$	−627.697	+	3745.46i	−0.0193734	+	0.115601i
$181$			48494.7i			1.48026i	0.672465	+	0.740129i	$0.265236\pi$
$181$			48494.7i			1.48026i	−0.672465	+	0.740129i	$0.734764\pi$
$182$	33457.4	−	16040.2i	1.01006	−	0.484247i
$183$	42842.6	+	25106.4i	1.27930	+	0.749691i
$184$	−10836.8	+	11557.1i	−0.320086	+	0.341360i
$185$	1851.03	−	3206.08i	0.0540842	−	0.0936766i
$186$	−6187.22	−	13122.9i	−0.178842	−	0.379317i
$187$	−2406.15	−	4167.58i	−0.0688082	−	0.119179i
$188$	−8791.91	+	56977.1i	−0.248753	+	1.61207i
$189$	−29365.5	+	16202.1i	−0.822079	+	0.453573i
$190$	−4173.21	−	320.081i	−0.115601	−	0.00886652i
$191$	−31625.9	+	18259.2i	−0.866915	+	0.500514i	−0.866322	−	0.499486i	$-0.833522\pi$
$191$	−31625.9	+	18259.2i	−0.866915	+	0.500514i	−0.000593302		1.00000i	$0.500189\pi$
$192$	−2130.65	−	36802.4i	−0.0577976	−	0.998328i
$193$	−12557.9	+	21750.9i	−0.337133	+	0.583932i	−0.983892	−	0.178762i	$-0.942791\pi$
$193$	−12557.9	+	21750.9i	−0.337133	+	0.583932i	0.646759	+	0.762694i	$0.276124\pi$
$194$	−6133.26	−	4197.32i	−0.162963	−	0.111524i
$195$	−2688.44	+	4587.67i	−0.0707019	+	0.120649i
$196$	1647.73	+	4241.92i	0.0428917	+	0.110421i
$197$		−	28539.7i		−	0.735388i	−0.929947	−	0.367694i	$-0.880147\pi$
$197$		−	28539.7i		−	0.735388i	0.929947	−	0.367694i	$-0.119853\pi$
$198$	−15945.2	+	7392.11i	−0.406723	+	0.188555i
$199$		−	63914.2i		−	1.61395i	−0.590583	−	0.806977i	$-0.701102\pi$
$199$		−	63914.2i		−	1.61395i	0.590583	−	0.806977i	$-0.298898\pi$
$200$	−37758.3	+	11430.2i	−0.943957	+	0.285756i
$201$	55631.0	+	360.146i	1.37697	+	0.00891429i
$202$	36106.8	−	52760.4i	0.884883	−	1.29302i
$203$	−498.687	+	863.752i	−0.0121014	+	0.0209603i
$204$	−12612.6	−	2029.88i	−0.303071	−	0.0487764i
$205$	−5615.57	+	3242.15i	−0.133624	+	0.0771481i
$206$	−78723.7	−	6038.04i	−1.85512	−	0.142286i
$207$	17493.4	−	9800.03i	0.408256	−	0.228711i
$208$	15558.7	−	49214.7i	0.359622	−	1.13754i
$209$	−9684.94	−	16774.8i	−0.221720	−	0.384030i
$210$	3987.35	+	2766.83i	0.0904160	+	0.0627399i
$211$	−7822.71	+	13549.3i	−0.175708	+	0.304336i	−0.940406	−	0.340053i	$-0.889555\pi$
$211$	−7822.71	+	13549.3i	−0.175708	+	0.304336i	0.764698	+	0.644389i	$0.222888\pi$
$212$	−51429.3	−	41308.7i	−1.14430	−	0.919116i
$213$	−37804.0	+	21501.1i	−0.833257	+	0.473916i
$214$	31062.0	−	14891.8i	0.678269	−	0.325177i
$215$			3975.76i			0.0860089i
$216$	−11500.8	+	45216.3i	−0.246502	+	0.969142i
$217$	−18541.0			−0.393743
$218$	34167.8	+	71268.8i	0.718958	+	1.49964i
$219$	41982.2	+	73814.8i	0.875341	+	1.53906i
$220$	1982.85	+	1592.65i	0.0409680	+	0.0329060i
$221$	−15490.5	−	8943.44i	−0.317162	−	0.183113i
$222$	25928.6	−	37366.4i	0.526106	−	0.758184i
$223$	44835.1	−	25885.6i	0.901589	−	0.520532i	0.0238733	−	0.999715i	$-0.492400\pi$
$223$	44835.1	−	25885.6i	0.901589	−	0.520532i	0.877715	+	0.479183i	$0.159067\pi$
$224$	−43701.7	−	17594.3i	−0.870968	−	0.350652i
$225$	49925.3	+	646.443i	0.986179	+	0.0127692i
$226$	−5019.10	+	65438.9i	−0.0982674	+	1.28121i
$227$	−28229.2	−	48894.4i	−0.547831	−	0.948871i	−0.998423	−	0.0561410i	$-0.982120\pi$
$227$	−28229.2	−	48894.4i	−0.547831	−	0.948871i	0.450592	−	0.892730i	$-0.351213\pi$
$228$	−50766.7	−	8170.41i	−0.976582	−	0.157172i
$229$	48956.6	+	28265.1i	0.933556	+	0.538989i	0.887935	−	0.459970i	$-0.152140\pi$
$229$	48956.6	+	28265.1i	0.933556	+	0.538989i	0.0456218	+	0.998959i	$0.485473\pi$
$230$	−2394.53	−	1638.71i	−0.0452653	−	0.0309775i
$231$	−145.402	+	22460.0i	−0.00272487	+	0.420906i
$232$	401.998	+	1327.95i	0.00746874	+	0.0246720i
$233$	72322.4			1.33217			0.666087	−	0.745874i	$-0.267968\pi$
$233$	72322.4			1.33217			0.666087	+	0.745874i	$0.267968\pi$
$234$	−37588.6	+	53428.1i	−0.686474	+	0.975748i
$235$	−10558.6			−0.191192
$236$	30632.2	+	78859.7i	0.549989	+	1.41590i
$237$	9861.52	+	5778.99i	0.175569	+	0.102886i
$238$	−9220.19	+	13472.8i	−0.162774	+	0.237851i
$239$	−86456.7	−	49915.8i	−1.51357	−	0.873861i	−0.999874	−	0.0158894i	$-0.994942\pi$
$239$	−86456.7	−	49915.8i	−1.51357	−	0.873861i	−0.513698	−	0.857971i	$-0.671725\pi$
$240$	6601.82	−	1413.54i	0.114615	−	0.0245405i
$241$	−13108.7	−	22704.9i	−0.225697	−	0.390918i	0.730832	−	0.682558i	$-0.239132\pi$
$241$	−13108.7	−	22704.9i	−0.225697	−	0.390918i	−0.956528	+	0.291640i	$0.905799\pi$
$242$	3578.55	−	46657.0i	0.0611049	−	0.796684i
$243$	31164.0	−	50155.6i	0.527765	−	0.849390i
$244$	13462.7	−	87246.6i	0.226127	−	1.46544i
$245$	−721.778	+	416.719i	−0.0120246	+	0.00694242i
$246$	−72054.7	+	33972.7i	−1.19067	+	0.561383i
$247$	−62350.4	−	35998.0i	−1.02199	−	0.590045i
$248$	−17642.4	+	18815.0i	−0.286849	+	0.305914i
$249$	−11528.4	+	19672.5i	−0.185939	+	0.317293i
$250$	−6290.47	−	13121.0i	−0.100648	−	0.209936i
$251$	110168.			1.74866			0.874332	−	0.485328i	$-0.161300\pi$
$251$	110168.			1.74866			0.874332	+	0.485328i	$0.161300\pi$
$252$	45998.4	+	37936.7i	0.724339	+	0.597390i
$253$		−	13428.2i		−	0.209786i
$254$	329.248	+	686.762i	0.00510336	+	0.0106448i
$255$	15.1462	−	2339.61i	0.000232929	−	0.0359801i
$256$	−59438.1	+	27605.9i	−0.906953	+	0.421233i
$257$	21395.2	−	37057.7i	0.323930	−	0.561063i	−0.657365	−	0.753572i	$-0.728329\pi$
$257$	21395.2	−	37057.7i	0.323930	−	0.561063i	0.981295	+	0.192509i	$0.0616625\pi$
$258$	−4050.49	+	48675.4i	−0.0608510	+	0.731257i
$259$	−29061.4	−	50335.8i	−0.433229	−	0.750374i
$260$	9342.54	+	1441.61i	0.138203	+	0.0213256i
$261$	22.7352	−	1755.86i	0.000333748	−	0.0257756i
$262$	−3266.76	+	42591.9i	−0.0475898	+	0.620475i
$263$	−70761.8	+	40854.3i	−1.02303	+	0.590645i	−0.914979	−	0.403501i	$-0.867793\pi$
$263$	−70761.8	+	40854.3i	−1.02303	+	0.590645i	−0.108048	+	0.994146i	$0.534460\pi$
$264$	22653.5	+	21519.0i	0.325033	+	0.308755i
$265$	6040.58	−	10462.6i	0.0860175	−	0.148987i
$266$	−37112.0	+	54229.2i	−0.524506	+	0.766425i
$267$	26284.1	+	46213.7i	0.368698	+	0.648259i
$268$	−35810.5	−	92190.9i	−0.498587	−	1.28357i
$269$		−	71867.3i		−	0.993177i	−0.867986	−	0.496589i	$-0.834586\pi$
$269$		−	71867.3i		−	0.993177i	0.867986	−	0.496589i	$-0.165414\pi$
$270$	−8505.49	−	818.791i	−0.116673	−	0.0112317i
$271$			57719.4i			0.785929i	0.919554	+	0.392964i	$0.128550\pi$
$271$			57719.4i			0.785929i	−0.919554	+	0.392964i	$0.871450\pi$
$272$	4898.60	+	22176.3i	0.0662116	+	0.299745i
$273$	41272.8	+	72567.4i	0.553781	+	0.973680i
$274$	−17653.5	−	12081.2i	−0.235142	−	0.160920i
$275$	16718.6	−	28957.5i	0.221072	−	0.382909i
$276$	−27646.9	−	22502.3i	−0.362934	−	0.295399i
$277$	17169.2	−	9912.65i	0.223764	−	0.129190i	−0.383928	−	0.923363i	$-0.625429\pi$
$277$	17169.2	−	9912.65i	0.223764	−	0.129190i	0.607692	+	0.794173i	$0.292095\pi$
$278$	−2545.17	+	33183.8i	−0.0329327	+	0.429375i
$279$	28479.2	−	15954.5i	0.365864	−	0.204962i
$280$	1964.04	−	8401.53i	0.0250515	−	0.107162i
$281$	−62271.1	−	107857.i	−0.788631	−	1.36595i	−0.926806	−	0.375541i	$-0.877457\pi$
$281$	−62271.1	−	107857.i	−0.788631	−	1.36595i	0.138175	−	0.990408i	$-0.455876\pi$
$282$	−129269.	−	10757.0i	−1.62553	−	0.135268i
$283$	−28575.7	+	49494.6i	−0.356799	+	0.617995i	−0.987424	−	0.158093i	$-0.949465\pi$
$283$	−28575.7	+	49494.6i	−0.356799	+	0.617995i	0.630625	+	0.776088i	$0.282799\pi$
$284$	60279.7	+	48417.5i	0.747368	+	0.600296i
$285$	60.9647	−	9417.10i	0.000750566	−	0.115938i
$286$	18912.5	+	39448.7i	0.231216	+	0.482282i
$287$			101804.i			1.23595i
$288$	82266.5	−	10580.1i	0.991831	−	0.127557i
$289$	−75650.7			−0.905769
$290$	−229.134	+	109.852i	−0.00272455	+	0.00130621i
$291$	8454.56	−	14427.2i	0.0998401	−	0.170371i
$292$	94538.2	−	117700.i	1.10877	−	1.38042i
$293$	25459.0	+	14698.8i	0.296555	+	0.171216i	0.640894	−	0.767629i	$-0.278564\pi$
$293$	25459.0	+	14698.8i	0.296555	+	0.171216i	−0.344339	+	0.938845i	$0.611897\pi$
$294$	−9261.31	+	4366.56i	−0.107146	+	0.0505178i
$295$	−13418.3	+	7747.04i	−0.154189	+	0.0890209i
$296$	−78732.7	−	18405.5i	−0.898611	−	0.210070i
$297$	−19103.4	−	34624.0i	−0.216570	−	0.392523i
$298$	37911.2	+	2907.76i	0.426909	+	0.0327435i
$299$	−24955.7	−	43224.5i	−0.279143	−	0.483490i
$300$	−31603.3	−	82946.9i	−0.351148	−	0.921632i
$301$	54057.2	+	31210.0i	0.596652	+	0.344477i
$302$	60084.4	−	87797.2i	0.658791	−	0.962647i
$303$	124108.	+	72729.0i	1.35180	+	0.792177i
$304$	19717.2	+	89261.5i	0.213353	+	0.965866i
$305$	16167.9			0.173801
$306$	2569.02	−	28628.5i	0.0274362	−	0.305742i
$307$	−77280.8			−0.819964			−0.409982	−	0.912094i	$-0.634465\pi$
$307$	−77280.8			−0.819964			−0.409982	+	0.912094i	$0.634465\pi$
$308$	37220.3	−	14457.8i	0.392354	−	0.152406i
$309$	1150.04	−	177645.i	0.0120447	−	1.86053i
$310$	−3898.31	−	2667.82i	−0.0405651	−	0.0277609i
$311$	88843.4	+	51293.7i	0.918553	+	0.530327i	0.883173	−	0.469047i	$-0.155403\pi$
$311$	88843.4	+	51293.7i	0.918553	+	0.530327i	0.0353799	+	0.999374i	$0.488736\pi$
$312$	112912.	+	27167.8i	1.15993	+	0.279091i
$313$	20566.6	+	35622.4i	0.209930	+	0.363609i	0.951692	−	0.307054i	$-0.0993431\pi$
$313$	20566.6	+	35622.4i	0.209930	+	0.363609i	−0.741762	+	0.670663i	$0.766010\pi$
$314$	65658.5	+	5035.94i	0.665934	+	0.0510766i
$315$	−5581.91	+	9385.40i	−0.0562551	+	0.0945870i
$316$	3098.84	−	20082.4i	0.0310331	−	0.201114i
$317$	109026.	−	62945.9i	1.08495	−	0.626396i	0.152723	−	0.988269i	$-0.451196\pi$
$317$	109026.	−	62945.9i	1.08495	−	0.626396i	0.932227	+	0.361873i	$0.117863\pi$
$318$	84614.3	−	121940.i	0.836738	−	1.20584i
$319$	−1018.43	−	587.989i	−0.0100080	−	0.00577813i
$320$	−6656.83	−	9987.42i	−0.0650081	−	0.0975334i
$321$	38317.8	+	67371.9i	0.371870	+	0.653836i
$322$	−41078.2	+	19693.8i	−0.396187	+	0.189940i
$323$	31678.5			0.303640
$324$	−103299.	−	18689.8i	−0.984023	−	0.178039i
$325$		−	124283.i		−	1.17664i
$326$	−24038.8	+	11524.7i	−0.226192	+	0.108441i
$327$	−154578.	+	87916.6i	−1.44562	+	0.822196i
$328$	103309.	+	96870.4i	0.960261	+	0.900417i
$329$	−82885.4	+	143562.i	−0.765748	+	1.32632i
$330$	−3262.29	+	4701.37i	−0.0299568	+	0.0431714i
$331$	54232.0	+	93932.5i	0.494993	+	0.857354i	0.999983	−	0.00577154i	$-0.00183715\pi$
$331$	54232.0	+	93932.5i	0.494993	+	0.857354i	−0.504990	+	0.863125i	$0.668504\pi$
$332$	40062.0	+	6181.80i	0.363460	+	0.0560840i
$333$	87952.8	+	52309.4i	0.793161	+	0.471728i
$334$	88403.2	+	6780.44i	0.792455	+	0.0607806i
$335$	15686.6	−	9056.67i	0.139778	−	0.0807010i
$336$	32605.2	−	100859.i	0.288808	−	0.893382i
$337$	−1823.71	+	3158.77i	−0.0160582	+	0.0278136i	−0.873943	−	0.486029i	$-0.838445\pi$
$337$	−1823.71	+	3158.77i	−0.0160582	+	0.0278136i	0.857885	+	0.513842i	$0.171778\pi$
$338$	39911.8	+	27313.8i	0.349355	+	0.239083i
$339$	−147667.	−	955.971i	−1.28494	−	0.00831850i
$340$	−3877.16	+	1506.04i	−0.0335395	+	0.0130280i
$341$		−	21861.1i		−	0.188003i
$342$	10340.5	−	115232.i	0.0884075	−	0.985190i
$343$			123546.i			1.05013i
$344$	83108.6	−	25158.7i	0.702310	−	0.212604i
$345$	3300.81	−	5632.64i	0.0277321	−	0.0473232i
$346$	25328.1	−	37010.3i	0.211568	−	0.309151i
$347$	−86264.4	+	149414.i	−0.716428	+	1.24089i	0.245978	+	0.969275i	$0.420891\pi$
$347$	−86264.4	+	149414.i	−0.716428	+	1.24089i	−0.962406	+	0.271615i	$0.912442\pi$
$348$	−2917.22	+	1111.48i	−0.0240885	+	0.00917790i
$349$	−138147.	+	79759.0i	−1.13420	+	0.654831i	−0.944988	−	0.327106i	$-0.893927\pi$
$349$	−138147.	+	79759.0i	−1.13420	+	0.654831i	−0.189212	+	0.981936i	$0.560593\pi$
$350$	−113103.	−	8674.93i	−0.923293	−	0.0708157i
$351$	−125840.	−	75949.7i	−1.02142	−	0.616470i
$352$	20745.0	−	51527.5i	0.167428	−	0.415866i
$353$	−20555.4	−	35603.0i	−0.164959	−	0.285718i	0.771681	−	0.636009i	$-0.219416\pi$
$353$	−20555.4	−	35603.0i	−0.164959	−	0.285718i	−0.936641	+	0.350291i	$0.886083\pi$
$354$	−172173.	+	81176.9i	−1.37391	+	0.647778i
$355$	−7080.09	+	12263.1i	−0.0561800	+	0.0973067i
$356$	59188.1	−	73689.2i	0.467019	−	0.581438i
$357$	−31692.0	−	18572.0i	−0.248664	−	0.145721i
$358$	−61272.2	+	29375.2i	−0.478077	+	0.229200i
$359$		−	76360.8i		−	0.592491i	−0.955112	−	0.296245i	$-0.904265\pi$
$359$		−	76360.8i		−	0.592491i	0.955112	−	0.296245i	$-0.0957346\pi$
$360$	4212.71	+	14594.9i	0.0325054	+	0.112615i
$361$	−2812.82			−0.0215838
$362$	83858.4	+	174916.i	0.639926	+	1.33479i
$363$	105284.	+	681.593i	0.799007	+	0.00517263i
$364$	92940.5	−	115711.i	0.701459	−	0.873316i
$365$	23944.4	+	13824.3i	0.179729	+	0.103767i
$366$	197944.	+	16471.8i	1.47768	+	0.122964i
$367$	−102925.	+	59423.6i	−0.764165	+	0.441191i	−0.830789	−	0.556587i	$-0.812111\pi$
$367$	−102925.	+	59423.6i	−0.764165	+	0.441191i	0.0666239	+	0.997778i	$0.478777\pi$
$368$	−19102.6	+	60424.7i	−0.141058	+	0.446189i
$369$	−87602.4	−	156373.i	−0.643374	−	1.14844i
$370$	1132.45	−	14764.9i	0.00827212	−	0.107852i
$371$	−94837.8	−	164264.i	−0.689023	−	1.19342i
$372$	−45009.2	−	36633.8i	−0.325248	−	0.264726i
$373$	115434.	+	66645.9i	0.829691	+	0.479023i	0.853747	−	0.520688i	$-0.174325\pi$
$373$	115434.	+	66645.9i	0.829691	+	0.479023i	−0.0240556	+	0.999711i	$0.507658\pi$
$374$	−15885.5	−	10871.3i	−0.113568	−	0.0777208i
$375$	28458.7	−	16185.9i	0.202373	−	0.115100i
$376$	66814.9	+	220714.i	0.472604	+	1.56119i
$377$	−4371.00			−0.0307537
$378$	−77901.4	+	109219.i	−0.545207	+	0.764389i
$379$	141694.			0.986447			0.493224	−	0.869902i	$-0.335818\pi$
$379$	141694.			0.986447			0.493224	+	0.869902i	$0.335818\pi$
$380$	−15605.9	+	6061.92i	−0.108074	+	0.0419801i
$381$	−1489.55	+	847.183i	−0.0102614	+	0.00583616i
$382$	−82497.4	+	120548.i	−0.565345	+	0.826100i
$383$	43983.8	+	25394.1i	0.299844	+	0.173115i	0.642373	−	0.766392i	$-0.277950\pi$
$383$	43983.8	+	25394.1i	0.299844	+	0.173115i	−0.342529	+	0.939507i	$0.611283\pi$
$384$	−71324.7	−	129058.i	−0.483702	−	0.875233i
$385$	3656.46	+	6333.17i	0.0246683	+	0.0427267i
$386$	−7682.86	+	100169.i	−0.0515642	+	0.672292i
$387$	−109889.	−	1422.87i	−0.733723	−	0.00950040i
$388$	−29380.2	−	4533.54i	−0.195160	−	0.0301144i
$389$	−103180.	+	59570.8i	−0.681860	+	0.393672i	−0.800555	−	0.599259i	$-0.795462\pi$
$389$	−103180.	+	59570.8i	−0.681860	+	0.393672i	0.118696	+	0.992931i	$0.462129\pi$
$390$	−1763.83	+	21196.2i	−0.0115965	+	0.139357i
$391$	19018.9	+	10980.6i	0.124403	+	0.0718242i
$392$	13278.4	+	12450.9i	0.0864121	+	0.0810268i
$393$	−96111.1	−	622.207i	−0.622284	−	0.00402856i
$394$	−49351.6	−	102940.i	−0.317913	−	0.663119i
$395$	3721.53			0.0238521
$396$	−44730.1	+	54235.5i	−0.285239	+	0.345854i
$397$		−	200049.i		−	1.26927i	−0.772812	−	0.634635i	$-0.781150\pi$
$397$		−	200049.i		−	1.26927i	0.772812	−	0.634635i	$-0.218850\pi$
$398$	−110522.	−	230532.i	−0.697723	−	1.45534i
$399$	−127563.	−	74753.7i	−0.801269	−	0.469555i
$400$	−116425.	+	106520.i	−0.727657	+	0.665753i
$401$	−13977.6	+	24209.9i	−0.0869248	+	0.150558i	−0.906210	−	0.422828i	$-0.861037\pi$
$401$	−13977.6	+	24209.9i	−0.0869248	+	0.150558i	0.819285	+	0.573387i	$0.194371\pi$
$402$	201279.	−	94899.7i	1.24551	−	0.587236i
$403$	−40627.9	−	70369.6i	−0.250158	−	0.433286i
$404$	38999.1	−	252739.i	0.238941	−	1.54849i
$405$	497.796	−	19219.4i	0.00303488	−	0.117173i
$406$	−305.095	+	3977.82i	−0.00185090	+	0.0241320i
$407$	59349.6	−	34265.5i	0.358285	−	0.206856i
$408$	−49002.6	+	14488.5i	−0.294373	+	0.0870367i
$409$	−27650.2	+	47891.6i	−0.165292	+	0.286294i	−0.936759	−	0.349975i	$-0.886190\pi$
$409$	−27650.2	+	47891.6i	−0.165292	+	0.286294i	0.771467	+	0.636270i	$0.219523\pi$
$410$	−14648.4	+	21404.7i	−0.0871411	+	0.127333i
$411$	24334.9	−	41526.2i	0.144061	−	0.245832i
$412$	−294390.	+	114353.i	−1.73432	+	0.673677i
$413$			243259.i			1.42616i
$414$	46150.4	−	65597.8i	0.269262	−	0.382727i
$415$			7423.98i			0.0431063i
$416$	−28984.6	−	204417.i	−0.167487	−	1.18122i
$417$	−74881.3	−	484.769i	−0.430627	−	0.00278781i
$418$	−63940.2	−	43757.7i	−0.365950	−	0.250439i
$419$	−76753.4	+	132941.i	−0.437189	+	0.757234i	−0.997472	−	0.0710675i	$-0.977359\pi$
$419$	−76753.4	+	132941.i	−0.437189	+	0.757234i	0.560282	+	0.828302i	$0.310693\pi$
$420$	19166.5	+	3084.66i	0.108653	+	0.0174867i
$421$	−230275.	+	132949.i	−1.29922	+	0.750105i	−0.980269	−	0.197667i	$-0.936664\pi$
$421$	−230275.	+	132949.i	−1.29922	+	0.750105i	−0.318950	+	0.947771i	$0.603330\pi$
$422$	−4785.90	+	62398.4i	−0.0268744	+	0.350387i
$423$	3778.75	−	291836.i	0.0211187	−	1.63102i
$424$	−256933.	−	60063.7i	−1.42918	−	0.334103i
$425$	27342.4	+	47358.5i	0.151377	+	0.262192i
$426$	−99175.4	+	142924.i	−0.546493	+	0.787565i
$427$	126919.	−	219830.i	0.696097	−	1.20568i
$428$	86286.4	−	107427.i	0.471037	−	0.586441i
$429$	−85562.2	+	48663.6i	−0.464909	+	0.264417i
$430$	6875.00	+	14340.2i	0.0371823	+	0.0775565i
$431$		−	187074.i		−	1.00707i	−0.863976	−	0.503533i	$-0.832033\pi$
$431$		−	187074.i		−	1.00707i	0.863976	−	0.503533i	$-0.167967\pi$
$432$	36707.1	+	182978.i	0.196690	+	0.980466i
$433$	252526.			1.34688			0.673441	−	0.739241i	$-0.264815\pi$
$433$	252526.			1.34688			0.673441	+	0.739241i	$0.264815\pi$
$434$	−66875.5	+	32061.5i	−0.355048	+	0.170218i
$435$	−282.658	−	496.981i	−0.00149377	−	0.00262640i
$436$	246480.	+	197976.i	1.29661	+	1.04145i
$437$	76552.5	+	44197.6i	0.400863	+	0.231439i
$438$	279069.	+	193646.i	1.45466	+	1.00939i
$439$	138415.	−	79914.0i	0.718215	−	0.414662i	−0.0958801	−	0.995393i	$-0.530567\pi$
$439$	138415.	−	79914.0i	0.718215	−	0.414662i	0.814095	+	0.580731i	$0.197233\pi$
$440$	9906.01	+	2315.75i	0.0511674	+	0.0119615i
$441$	−11259.7	−	20098.9i	−0.0578960	−	0.103346i
$442$	−71338.0	−	5471.56i	−0.365154	−	0.0280070i
$443$	152813.	+	264680.i	0.778670	+	1.34870i	0.932708	+	0.360632i	$0.117439\pi$
$443$	152813.	+	264680.i	0.778670	+	1.34870i	−0.154038	+	0.988065i	$0.549228\pi$
$444$	28907.1	−	179613.i	0.146635	−	0.911114i
$445$	14991.1	+	8655.09i	0.0757028	+	0.0437070i
$446$	116954.	−	170897.i	0.587957	−	0.859141i
$447$	−553.830	+	85549.0i	−0.00277180	+	0.428154i
$448$	−188052.	+	12109.1i	−0.936964	+	0.0603333i
$449$	338152.			1.67733			0.838667	−	0.544645i	$-0.183336\pi$
$449$	338152.			1.67733			0.838667	+	0.544645i	$0.183336\pi$
$450$	181194.	−	84000.5i	0.894784	−	0.414817i
$451$	−120035.			−0.590138
$452$	95055.3	+	244711.i	0.465264	+	1.19778i
$453$	206525.	+	121026.i	1.00641	+	0.589772i
$454$	−186370.	−	127543.i	−0.904197	−	0.618791i
$455$	23539.8	+	13590.7i	0.113705	+	0.0656477i
$456$	−197239.	+	58317.2i	−0.948557	+	0.280457i
$457$	−1641.07	−	2842.42i	−0.00785770	−	0.0136099i	0.862070	−	0.506790i	$-0.169168\pi$
$457$	−1641.07	−	2842.42i	−0.00785770	−	0.0136099i	−0.869928	+	0.493180i	$0.835835\pi$
$458$	225459.	+	17292.5i	1.07482	+	0.0824378i
$459$	64660.7	+	1255.95i	0.306913	+	0.00596137i
$460$	−11470.6	−	1769.97i	−0.0542087	−	0.00836472i
$461$	−215070.	+	124171.i	−1.01199	+	0.584275i	−0.911775	−	0.410690i	$-0.865288\pi$
$461$	−215070.	+	124171.i	−1.01199	+	0.584275i	−0.100220	+	0.994965i	$0.531955\pi$
$462$	38313.9	+	81262.4i	0.179503	+	0.380720i
$463$	42958.9	+	24802.3i	0.200397	+	0.115699i	0.596841	−	0.802360i	$-0.296422\pi$
$463$	42958.9	+	24802.3i	0.200397	+	0.115699i	−0.396444	+	0.918059i	$0.629756\pi$
$464$	3746.29	+	4094.64i	0.0174007	+	0.0190186i
$465$	5373.72	−	9169.95i	0.0248525	−	0.0424093i
$466$	260860.	−	125062.i	1.20126	−	0.575908i
$467$	18727.6			0.0858712			0.0429356	−	0.999078i	$-0.486329\pi$
$467$	18727.6			0.0858712			0.0429356	+	0.999078i	$0.486329\pi$
$468$	−43189.2	+	257709.i	−0.197189	+	1.17663i
$469$		−	284381.i		−	1.29287i
$470$	−38083.8	+	18258.2i	−0.172403	+	0.0826536i
$471$	−959.178	+	148162.i	−0.00432372	+	0.667876i
$472$	246854.	+	231470.i	1.10804	+	1.03899i
$473$	−36798.8	+	63737.4i	−0.164479	+	0.284887i
$474$	45562.8	+	3791.47i	0.202793	+	0.0168753i
$475$	110055.	+	190621.i	0.487780	+	0.844859i
$476$	−9958.76	+	64539.1i	−0.0439533	+	0.284845i
$477$	287021.	+	170704.i	1.26147	+	0.750254i
$478$	−398157.	−	30538.3i	−1.74260	−	0.133656i
$479$	343234.	−	198166.i	1.49596	−	0.863691i	0.495967	−	0.868341i	$-0.334814\pi$
$479$	343234.	−	198166.i	1.49596	−	0.863691i	0.999989	+	0.00465021i	$0.00148021\pi$
$480$	21367.8	−	16514.5i	0.0927423	−	0.0716777i
$481$	127362.	−	220597.i	0.550489	−	0.953475i
$482$	−86543.8	−	59226.6i	−0.372513	−	0.254931i
$483$	−50673.8	−	89096.6i	−0.217215	−	0.381915i
$484$	−67773.0	−	174475.i	−0.289312	−	0.744807i
$485$		−	5444.52i		−	0.0231460i
$486$	25675.1	−	234796.i	0.108703	−	0.994074i
$487$			240262.i			1.01304i	0.862228	+	0.506520i	$0.169068\pi$
$487$			240262.i			1.01304i	−0.862228	+	0.506520i	$0.830932\pi$
$488$	−102311.	−	337970.i	−0.429617	−	1.41918i
$489$	−29654.0	−	52138.9i	−0.124013	−	0.218044i
$490$	−1882.78	+	2751.18i	−0.00784167	+	0.0114585i
$491$	98040.3	−	169811.i	0.406670	−	0.704372i	−0.587845	−	0.808974i	$-0.700023\pi$
$491$	98040.3	−	169811.i	0.406670	−	0.704372i	0.994514	+	0.104601i	$0.0333567\pi$
$492$	−201148.	+	247135.i	−0.830971	+	1.02095i
$493$	1665.58	−	961.625i	0.00685287	−	0.00395651i
$494$	−287141.	−	22023.4i	−1.17663	−	0.0902467i
$495$	−11066.1	−	6581.48i	−0.0451630	−	0.0268605i
$496$	−31099.1	+	98371.5i	−0.126411	+	0.399858i
$497$	111158.	+	192532.i	0.450017	+	0.779452i
$498$	−7563.51	+	90892.1i	−0.0304976	+	0.366494i
$499$	130948.	−	226808.i	0.525892	−	0.910871i	−0.473654	−	0.880711i	$-0.657065\pi$
$499$	130948.	−	226808.i	0.525892	−	0.910871i	0.999545	−	0.0301596i	$-0.00960157\pi$
$500$	−45378.3	−	36448.4i	−0.181513	−	0.145794i
$501$	−1291.45	+	199487.i	−0.00514518	+	0.794766i
$502$	397364.	−	190505.i	1.57682	−	0.755960i
$503$		−	311251.i		−	1.23020i	−0.788450	−	0.615099i	$-0.789116\pi$
$503$		−	311251.i		−	1.23020i	0.788450	−	0.615099i	$-0.210884\pi$
$504$	231513.	+	57292.3i	0.911411	+	0.225546i
$505$	46835.6			0.183651
$506$	−23220.4	−	48434.2i	−0.0906920	−	0.189170i
$507$	−55017.4	+	93884.1i	−0.214035	+	0.365238i
$508$	2375.13	+	1907.74i	0.00920366	+	0.00739251i
$509$	−317446.	−	183278.i	−1.22528	−	0.707415i	−0.259240	−	0.965813i	$-0.583472\pi$
$509$	−317446.	−	183278.i	−1.22528	−	0.707415i	−0.966039	+	0.258398i	$0.916805\pi$
$510$	−3991.08	−	8464.94i	−0.0153444	−	0.0325449i
$511$	375930.	−	217043.i	1.43968	−	0.831199i
$512$	−166651.	+	202354.i	−0.635722	+	0.771918i
$513$	260264.	+	5055.29i	0.988963	+	0.0192093i
$514$	13089.5	−	170661.i	0.0495447	−	0.645963i
$515$	−28920.4	−	50091.6i	−0.109041	−	0.188864i
$516$	69561.2	+	182572.i	0.261257	+	0.685701i
$517$	−169270.	−	97727.9i	−0.633283	−	0.365626i
$518$	−191864.	−	131303.i	−0.715046	−	0.489344i
$519$	87058.9	+	51017.8i	0.323205	+	0.189403i
$520$	36190.5	−	10955.6i	0.133841	−	0.0405164i
$521$	−526988.			−1.94145			−0.970723	−	0.240203i	$-0.922786\pi$
$521$	−526988.			−1.94145			−0.970723	+	0.240203i	$0.922786\pi$
$522$	−2954.28	−	6372.53i	−0.0108420	−	0.0233868i
$523$	311012.			1.13703			0.568517	−	0.822671i	$-0.307517\pi$
$523$	311012.			1.13703			0.568517	+	0.822671i	$0.307517\pi$
$524$	61868.1	+	159274.i	0.225322	+	0.580072i
$525$	1652.28	−	255225.i	0.00599467	−	0.925986i
$526$	−184585.	+	269721.i	−0.667151	+	0.974862i
$527$	30962.8	+	17876.4i	0.111486	+	0.0643663i
$528$	118920.	+	38444.0i	0.426568	+	0.137899i
$529$	−109280.	−	189279.i	−0.390509	−	0.676382i
$530$	3695.60	−	48183.1i	0.0131563	−	0.171531i
$531$	−209324.	−	373650.i	−0.742386	−	1.32518i
$532$	−40084.8	+	259775.i	−0.141630	+	0.917854i
$533$	−386384.	+	223079.i	−1.36008	+	0.785242i
$534$	174718.	+	121237.i	0.612711	+	0.425162i
$535$	21854.5	+	12617.7i	0.0763541	+	0.0440831i
$536$	−288584.	−	270599.i	−1.00448	−	0.941883i
$537$	−75584.9	−	132896.i	−0.262112	−	0.460855i
$538$	−124275.	−	259219.i	−0.429357	−	0.895574i
$539$	−15428.2			−0.0531054
$540$	−32094.4	+	11754.6i	−0.110063	+	0.0403108i
$541$		−	377631.i		−	1.29025i	−0.764078	−	0.645124i	$-0.776806\pi$
$541$		−	377631.i		−	1.29025i	0.764078	−	0.645124i	$-0.223194\pi$
$542$	99810.0	+	208188.i	0.339762	+	0.708693i
$543$	−379384.	+	215775.i	−1.28671	+	0.731815i
$544$	56016.7	+	71517.2i	0.189287	+	0.241664i
$545$	−28950.0	+	50143.0i	−0.0974667	+	0.168817i
$546$	274352.	+	190374.i	0.920288	+	0.638590i
$547$	−51766.7	−	89662.5i	−0.173012	−	0.299665i	0.766460	−	0.642292i	$-0.222017\pi$
$547$	−51766.7	−	89662.5i	−0.173012	−	0.299665i	−0.939471	+	0.342627i	$0.888683\pi$
$548$	−84565.8	−	13049.0i	−0.281601	−	0.0434526i
$549$	−5786.24	+	446876.i	−0.0191978	+	1.48266i
$550$	10228.4	−	133357.i	0.0338128	−	0.440850i
$551$	6704.10	−	3870.61i	0.0220819	−	0.0127490i
$552$	−138631.	−	33356.0i	−0.454970	−	0.109470i
$553$	29214.2	−	50600.4i	0.0955308	−	0.165464i
$554$	44786.5	−	65443.5i	0.145924	−	0.213229i
$555$	33317.9	+	215.694i	0.108166	+	0.000700249i
$556$	48202.2	+	124092.i	0.155926	+	0.401416i
$557$			321643.i			1.03673i	0.855161	+	0.518363i	$0.173458\pi$
$557$			321643.i			1.03673i	−0.855161	+	0.518363i	$0.826542\pi$
$558$	75133.0	−	106793.i	0.241303	−	0.342986i
$559$			273556.i			0.875431i
$560$	−7444.05	−	33699.8i	−0.0237374	−	0.107461i
$561$	21897.7	−	37367.2i	0.0695782	−	0.118731i
$562$	−411115.	−	281348.i	−1.30164	−	0.890781i
$563$	−15717.8	+	27224.0i	−0.0495878	+	0.0858885i	−0.889754	−	0.456441i	$-0.849124\pi$
$563$	−15717.8	+	27224.0i	−0.0495878	+	0.0858885i	0.840166	+	0.542329i	$0.182457\pi$
$564$	−484863.	+	184736.i	−1.52426	+	0.580756i
$565$	−41638.5	+	24040.0i	−0.130436	+	0.0753074i
$566$	−17482.5	+	227936.i	−0.0545721	+	0.711509i
$567$	−257412.	−	157642.i	−0.800687	−	0.490348i
$568$	301148.	+	70399.9i	0.933433	+	0.218210i
$569$	118855.	+	205862.i	0.367106	+	0.635846i	0.989112	−	0.147166i	$-0.0470153\pi$
$569$	118855.	+	205862.i	0.367106	+	0.635846i	−0.622006	+	0.783013i	$0.713682\pi$
$570$	−16064.4	−	34072.0i	−0.0494442	−	0.104869i
$571$	−259870.	+	450108.i	−0.797047	+	1.38053i	0.124484	+	0.992222i	$0.460272\pi$
$571$	−259870.	+	450108.i	−0.797047	+	1.38053i	−0.921531	+	0.388304i	$0.873061\pi$
$572$	136432.	+	109584.i	0.416987	+	0.334930i
$573$	−283564.	−	166172.i	−0.863657	−	0.506115i
$574$	176043.	+	367198.i	0.534311	+	1.11449i
$575$			152592.i			0.461526i
$576$	278432.	−	180419.i	0.839217	−	0.543797i
$577$	−150655.			−0.452513			−0.226257	−	0.974068i	$-0.572649\pi$
$577$	−150655.			−0.452513			−0.226257	+	0.974068i	$0.572649\pi$
$578$	−272865.	+	130817.i	−0.816756	+	0.391570i
$579$	−226037.	−	1463.33i	−0.674252	−	0.00436500i
$580$	−636.507	+	792.451i	−0.00189212	+	0.00235568i
$581$	100942.	+	58278.7i	0.299032	+	0.172646i
$582$	5546.85	−	66657.5i	0.0163757	−	0.196790i
$583$	193679.	−	111821.i	0.569830	−	0.328992i
$584$	137460.	−	588011.i	0.403043	−	1.72409i
$585$	−47852.3	−	619.602i	−0.139827	−	0.00181051i
$586$	117246.	+	8992.64i	0.341430	+	0.0261874i
$587$	222883.	+	386045.i	0.646846	+	1.12037i	0.983872	+	0.178875i	$0.0572458\pi$
$587$	222883.	+	386045.i	0.646846	+	1.12037i	−0.337025	+	0.941496i	$0.609421\pi$
$588$	−25853.9	+	31764.7i	−0.0747776	+	0.0918734i
$589$	124628.	+	71953.8i	0.359239	+	0.207407i
$590$	−35002.0	+	51146.1i	−0.100552	+	0.146929i
$591$	223272.	−	126986.i	0.639232	−	0.363563i
$592$	−315809.	+	69759.9i	−0.901116	+	0.199050i
$593$	−59064.6			−0.167965			−0.0839823	−	0.996467i	$-0.526764\pi$
$593$	−59064.6			−0.167965			−0.0839823	+	0.996467i	$0.526764\pi$
$594$	−128777.	−	91851.4i	−0.364977	−	0.260323i
$595$	−11959.9			−0.0337826
$596$	141770.	−	55069.2i	0.399111	−	0.155030i
$597$	500013.	−	284383.i	1.40292	−	0.797911i
$598$	−164758.	−	112753.i	−0.460727	−	0.315300i
$599$	−354748.	−	204814.i	−0.988703	−	0.570828i	−0.0838164	−	0.996481i	$-0.526711\pi$
$599$	−354748.	−	204814.i	−0.988703	−	0.570828i	−0.904886	+	0.425653i	$0.860044\pi$
$600$	−257424.	−	244532.i	−0.715068	−	0.679256i
$601$	268772.	+	465527.i	0.744107	+	1.28883i	0.950611	+	0.310385i	$0.100458\pi$
$601$	268772.	+	465527.i	0.744107	+	1.28883i	−0.206505	+	0.978446i	$0.566209\pi$
$602$	248948.	+	19094.1i	0.686936	+	0.0526874i
$603$	244710.	+	436815.i	0.673003	+	1.20133i
$604$	64897.3	−	420576.i	0.177891	−	1.15284i
$605$	29687.6	−	17140.2i	0.0811082	−	0.0468279i
$606$	573410.	+	47715.9i	1.56142	+	0.129932i
$607$	−377551.	−	217979.i	−1.02470	−	0.591614i	−0.109242	−	0.994015i	$-0.534842\pi$
$607$	−377551.	−	217979.i	−1.02470	−	0.591614i	−0.915463	+	0.402402i	$0.868176\pi$
$608$	225472.	+	287862.i	0.609937	+	0.778713i
$609$	−8976.18	−	58.1103i	−0.0242023	−	0.000156682i
$610$	58316.0	−	27957.9i	0.156721	−	0.0751356i
$611$	−726491.			−1.94602
$612$	−40239.0	−	107703.i	−0.107435	−	0.287557i
$613$		−	184751.i		−	0.491662i	−0.969313	−	0.245831i	$-0.920939\pi$
$613$		−	184751.i		−	0.491662i	0.969313	−	0.245831i	$-0.0790608\pi$
$614$	−278745.	+	133636.i	−0.739383	+	0.354476i
$615$	−50350.2	−	29505.9i	−0.133122	−	0.0780116i
$616$	109249.	−	116510.i	0.287910	−	0.307046i
$617$	70628.6	−	122332.i	0.185528	−	0.321344i	−0.758226	−	0.651992i	$-0.773934\pi$
$617$	70628.6	−	122332.i	0.185528	−	0.321344i	0.943754	+	0.330647i	$0.107267\pi$
$618$	−303040.	−	642737.i	−0.793457	−	1.68289i
$619$	−132429.	−	229374.i	−0.345623	−	0.598637i	0.639844	−	0.768505i	$-0.278999\pi$
$619$	−132429.	−	229374.i	−0.345623	−	0.598637i	−0.985467	+	0.169868i	$0.945666\pi$
$620$	−18674.1	−	2881.52i	−0.0485799	−	0.00749616i
$621$	154503.	+	93249.3i	0.400640	+	0.241803i
$622$	409148.	+	31381.3i	1.05755	+	0.0811129i
$623$	235361.	−	135886.i	0.606399	−	0.350105i
$624$	454244.	−	97259.4i	1.16659	−	0.249783i
$625$	−187299.	+	324412.i	−0.479486	+	0.830494i
$626$	135781.	+	92922.4i	0.346490	+	0.237122i
$627$	88140.0	−	150406.i	0.224201	−	0.382587i
$628$	245532.	−	95374.3i	0.622571	−	0.241831i
$629$			112079.i			0.283285i
$630$	−3903.95	+	43504.6i	−0.00983611	+	0.109611i
$631$			699879.i			1.75778i	0.477026	+	0.878889i	$0.341715\pi$
$631$			699879.i			1.75778i	−0.477026	+	0.878889i	$0.658285\pi$
$632$	−23549.9	−	77794.1i	−0.0589596	−	0.194766i
$633$	−140806.	−	911.553i	−0.351409	−	0.00227496i
$634$	284397.	−	415570.i	0.707533	−	1.03387i
$635$	−278.969	+	483.188i	−0.000691844	+	0.00119831i
$636$	94334.1	−	586143.i	0.233214	−	1.44907i
$637$	−49662.5	+	28672.7i	−0.122391	+	0.0706625i
$638$	−4690.13	−	359.729i	−0.0115224	−	0.000883759i
$639$	−336414.	−	200081.i	−0.823897	−	0.490008i
$640$	−41281.1	−	24512.5i	−0.100784	−	0.0598450i
$641$	−159686.	−	276584.i	−0.388643	−	0.673149i	0.603625	−	0.797269i	$-0.293723\pi$
$641$	−159686.	−	276584.i	−0.388643	−	0.673149i	−0.992267	+	0.124120i	$0.960389\pi$
$642$	254710.	+	176744.i	0.617982	+	0.428819i
$643$	−120033.	+	207903.i	−0.290321	+	0.502850i	−0.973886	−	0.227040i	$-0.927095\pi$
$643$	−120033.	+	207903.i	−0.290321	+	0.502850i	0.683565	+	0.729890i	$0.260429\pi$
$644$	−114110.	+	142067.i	−0.275140	+	0.342549i
$645$	−31103.2	+	17689.9i	−0.0747627	+	0.0425214i
$646$	114261.	−	54779.3i	0.273800	−	0.131266i
$647$			160526.i			0.383475i	0.981446	+	0.191737i	$0.0614122\pi$
$647$			160526.i			0.383475i	−0.981446	+	0.191737i	$0.938588\pi$
$648$	−404908.	+	111215.i	−0.964288	+	0.264858i
$649$	−286820.			−0.680957
$650$	−214914.	−	448277.i	−0.508671	−	1.06101i
$651$	−82497.0	−	145050.i	−0.194660	−	0.342259i
$652$	−66776.8	+	83137.1i	−0.157083	+	0.195569i
$653$	23755.5	+	13715.3i	0.0557107	+	0.0321646i	0.527597	−	0.849495i	$-0.323093\pi$
$653$	23755.5	+	13715.3i	0.0557107	+	0.0321646i	−0.471886	+	0.881660i	$0.656427\pi$
$654$	−405522.	+	584408.i	−0.948110	+	1.36635i
$655$	−27101.0	+	15646.8i	−0.0631689	+	0.0364706i
$656$	540136.	+	170758.i	1.25515	+	0.396802i
$657$	−390670.	+	656870.i	−0.905064	+	1.52177i
$658$	−50708.9	+	661141.i	−0.117120	+	1.52701i
$659$	−215117.	−	372594.i	−0.495341	−	0.857957i	0.504644	−	0.863327i	$-0.331624\pi$
$659$	−215117.	−	372594.i	−0.495341	−	0.857957i	−0.999986	+	0.00537093i	$0.998290\pi$
$660$	−3637.04	+	22598.6i	−0.00834949	+	0.0518794i
$661$	122972.	+	70998.0i	0.281451	+	0.162496i	0.634080	−	0.773267i	$-0.281379\pi$
$661$	122972.	+	70998.0i	0.281451	+	0.162496i	−0.352629	+	0.935763i	$0.614712\pi$
$662$	358040.	+	245026.i	0.816989	+	0.559109i
$663$	1042.15	−	160979.i	0.00237084	−	0.366219i
$664$	155189.	−	46979.1i	0.351987	−	0.106554i
$665$	−48139.5			−0.108857
$666$	407692.	+	36584.8i	0.919145	+	0.0824808i
$667$	5366.61			0.0120628
$668$	330587.	−	128413.i	0.740854	−	0.287776i
$669$	401999.	+	235577.i	0.898200	+	0.526358i
$670$	40919.1	−	59792.3i	0.0911541	−	0.133197i
$671$	259195.	+	149646.i	0.575681	+	0.332370i
$672$	−56804.6	−	420172.i	−0.125790	−	0.930440i
$673$	−78759.2	−	136415.i	−0.173889	−	0.301184i	0.765887	−	0.642975i	$-0.222300\pi$
$673$	−78759.2	−	136415.i	−0.173889	−	0.301184i	−0.939776	+	0.341791i	$0.888967\pi$
$674$	−1115.74	+	14547.0i	−0.00245609	+	0.0320224i
$675$	217083.	+	393452.i	0.476450	+	0.863543i
$676$	191190.	+	29501.7i	0.418380	+	0.0645585i
$677$	606737.	−	350300.i	1.32380	−	0.764298i	0.339470	−	0.940617i	$-0.389752\pi$
$677$	606737.	−	350300.i	1.32380	−	0.764298i	0.984333	+	0.176319i	$0.0564190\pi$
$678$	−534274.	+	251902.i	−1.16226	+	0.547989i
$679$	−74027.5	−	42739.8i	−0.160566	−	0.0927028i
$680$	−11380.3	+	12136.6i	−0.0246113	+	0.0262471i
$681$	256906.	−	438395.i	0.553962	−	0.945305i
$682$	−37802.9	−	78851.1i	−0.0812748	−	0.169527i
$683$	408773.			0.876275			0.438137	−	0.898908i	$-0.355638\pi$
$683$	408773.			0.876275			0.438137	+	0.898908i	$0.355638\pi$
$684$	−161965.	−	433511.i	−0.346185	−	0.926592i
$685$		−	15671.1i		−	0.0333978i
$686$	213640.	+	445620.i	0.453977	+	0.946926i
$687$	−3293.64	+	508762.i	−0.00697850	+	1.07796i
$688$	256260.	−	234459.i	0.541382	−	0.495324i
$689$	415627.	−	719887.i	0.875518	−	1.51644i
$690$	2165.59	−	26024.3i	0.00454860	−	0.0546613i
$691$	−309805.	−	536598.i	−0.648832	−	1.12381i	−0.983402	−	0.181439i	$-0.941924\pi$
$691$	−309805.	−	536598.i	−0.648832	−	1.12381i	0.334570	−	0.942371i	$-0.391409\pi$
$692$	27357.0	−	177291.i	0.0571289	−	0.370232i
$693$	−176356.	+	98796.9i	−0.367217	+	0.205720i
$694$	−52776.2	+	688094.i	−0.109577	+	1.42866i
$695$	−21114.7	+	12190.6i	−0.0437135	+	0.0252380i
$696$	−8600.13	+	9053.54i	−0.0177536	+	0.0186896i
$697$	98155.2	−	170010.i	0.202045	−	0.349952i
$698$	−360361.	+	526570.i	−0.739650	+	1.08080i
$699$	321795.	+	565792.i	0.658604	+	1.15798i
$700$	−422954.	+	164292.i	−0.863172	+	0.335290i
$701$		−	98886.5i		−	0.201234i	−0.994925	−	0.100617i	$-0.967918\pi$
$701$		−	98886.5i		−	0.201234i	0.994925	−	0.100617i	$-0.0320816\pi$
$702$	−585227.	−	56337.5i	−1.18754	−	0.114320i
$703$			451126.i			0.912825i
$704$	−14277.5	−	221727.i	−0.0288077	−	0.447378i
$705$	−46979.8	−	82601.8i	−0.0945220	−	0.166192i
$706$	−135707.	−	92871.8i	−0.272266	−	0.186326i
$707$	367662.	−	636809.i	0.735546	−	1.27400i
$708$	−480639.	+	590524.i	−0.958854	+	1.17807i
$709$	−16701.3	+	9642.51i	−0.0332245	+	0.0191822i	−0.516520	−	0.856275i	$-0.672773\pi$
$709$	−16701.3	+	9642.51i	−0.0332245	+	0.0191822i	0.483296	+	0.875457i	$0.339440\pi$
$710$	−4331.57	+	56474.9i	−0.00859268	+	0.112031i
$711$	−1331.88	+	102862.i	−0.00263466	+	0.203477i
$712$	86060.7	−	368140.i	0.169764	−	0.726194i
$713$	49882.0	+	86398.2i	0.0981217	+	0.169952i
$714$	−146425.	−	12184.7i	−0.287224	−	0.0239011i
$715$	−16024.4	+	27755.1i	−0.0313452	+	0.0542914i
$716$	−170207.	+	211907.i	−0.332010	+	0.413352i
$717$	5816.52	−	898466.i	0.0113142	−	1.74768i
$718$	−132045.	−	275426.i	−0.256138	−	0.534265i
$719$		−	124940.i		−	0.241681i	−0.992672	−	0.120841i	$-0.961441\pi$
$719$		−	124940.i		−	0.241681i	0.992672	−	0.120841i	$-0.0385590\pi$
$720$	40432.8	+	45357.9i	0.0779954	+	0.0874959i
$721$	−908107.			−1.74689
$722$	−10145.6	+	4864.01i	−0.0194627	+	0.00933083i
$723$	119299.	−	203576.i	0.228223	−	0.389449i
$724$	604939.	+	485895.i	1.15408	+	0.926969i
$725$	11572.9	+	6681.64i	0.0220175	+	0.0127118i
$726$	380929.	−	179602.i	0.722722	−	0.340752i
$727$	−237638.	+	137200.i	−0.449621	+	0.259589i	−0.707670	−	0.706543i	$-0.750254\pi$
$727$	−237638.	+	137200.i	−0.449621	+	0.259589i	0.258049	+	0.966132i	$0.416920\pi$
$728$	135137.	−	578074.i	0.254984	−	1.09074i
$729$	531040.	+	20637.3i	0.999246	+	0.0388327i
$730$	110271.	+	8457.67i	0.206926	+	0.0158710i
$731$	−60182.6	−	104239.i	−0.112625	−	0.195073i
$732$	742449.	−	282878.i	1.38562	−	0.527931i
$733$	196395.	+	113389.i	0.365530	+	0.211039i	0.671504	−	0.741001i	$-0.265649\pi$
$733$	196395.	+	113389.i	0.365530	+	0.211039i	−0.305974	+	0.952040i	$0.598982\pi$
$734$	−268483.	+	392316.i	−0.498338	+	0.728188i
$735$	−6471.59	−	3792.44i	−0.0119794	−	0.00702012i
$736$	35586.7	+	250979.i	0.0656950	+	0.463320i
$737$	335306.			0.617315
$738$	−586379.	−	412539.i	−1.07663	−	0.757447i
$739$	−173966.			−0.318549			−0.159274	−	0.987234i	$-0.550915\pi$
$739$	−173966.			−0.318549			−0.159274	+	0.987234i	$0.550915\pi$
$740$	−21447.2	−	55213.8i	−0.0391658	−	0.100829i
$741$	4194.73	−	647951.i	0.00763954	−	1.18006i
$742$	−626121.	−	428488.i	−1.13724	−	0.778271i
$743$	223552.	+	129068.i	0.404949	+	0.233797i	0.688617	−	0.725125i	$-0.258218\pi$
$743$	223552.	+	129068.i	0.404949	+	0.233797i	−0.283668	+	0.958923i	$0.591551\pi$
$744$	−225692.	−	54303.7i	−0.407728	−	0.0981032i
$745$	13927.3	+	24122.8i	0.0250931	+	0.0434625i
$746$	531606.	+	40773.7i	0.955239	+	0.0732660i
$747$	−205197.	−	2656.93i	−0.367730	−	0.00476145i
$748$	−76096.3	−	11742.1i	−0.136007	−	0.0209866i
$749$	343117.	−	198099.i	0.611616	−	0.353117i
$750$	74658.8	−	107593.i	0.132727	−	0.191276i
$751$	−439854.	−	253950.i	−0.779881	−	0.450264i	0.0565073	−	0.998402i	$-0.482004\pi$
$751$	−439854.	−	253950.i	−0.779881	−	0.450264i	−0.836388	+	0.548138i	$0.815337\pi$
$752$	622660.	+	680558.i	1.10107	+	1.20345i
$753$	490185.	+	861863.i	0.864510	+	1.52002i
$754$	−15765.8	+	7558.45i	−0.0277315	+	0.0132951i
$755$	77937.9			0.136727
$756$	−92118.5	+	528652.i	−0.161177	+	0.924967i
$757$			146756.i			0.256097i	0.991768	+	0.128048i	$0.0408713\pi$
$757$			146756.i			0.256097i	−0.991768	+	0.128048i	$0.959129\pi$
$758$	511078.	−	245022.i	0.889506	−	0.426448i
$759$	105051.	−	59748.1i	0.182355	−	0.103715i
$760$	−45806.4	+	48850.9i	−0.0793048	+	0.0845756i
$761$	106335.	−	184178.i	0.183615	−	0.318030i	−0.759494	−	0.650514i	$-0.774553\pi$
$761$	106335.	−	184178.i	0.183615	−	0.318030i	0.943109	+	0.332484i	$0.107887\pi$
$762$	−3907.70	+	5631.48i	−0.00672994	+	0.00969869i
$763$	454519.	+	787250.i	0.780734	+	1.35227i
$764$	−89105.7	+	577461.i	−0.152658	+	0.989319i
$765$	18370.6	−	10291.5i	0.0313907	−	0.0175855i
$766$	202558.	+	15536.0i	0.345216	+	0.0264778i
$767$	−923255.	+	533042.i	−1.56939	+	0.906088i
$768$	−480433.	−	342165.i	−0.814536	−	0.580113i
$769$	44021.9	−	76248.2i	0.0744417	−	0.128937i	−0.826402	−	0.563081i	$-0.809616\pi$
$769$	44021.9	−	76248.2i	0.0744417	−	0.128937i	0.900843	+	0.434144i	$0.142949\pi$
$770$	24140.0	+	16520.3i	0.0407151	+	0.0278635i
$771$	385106.	+	2493.11i	0.647846	+	0.00419405i
$772$	145503.	+	374585.i	0.244140	+	0.628515i
$773$		−	956337.i		−	1.60049i	−0.599675	−	0.800243i	$-0.704704\pi$
$773$		−	956337.i		−	1.60049i	0.599675	−	0.800243i	$-0.295296\pi$
$774$	−398820.	+	184891.i	−0.665725	+	0.308627i
$775$			248420.i			0.413602i
$776$	−113811.	+	34453.1i	−0.189000	+	0.0572143i
$777$	264480.	−	451320.i	0.438077	−	0.747554i
$778$	−269148.	+	393288.i	−0.444664	+	0.649757i
$779$	395082.	−	684302.i	0.651047	−	1.12765i
$780$	30291.1	+	79502.9i	0.0497882	+	0.130675i
$781$	−227009.	+	131064.i	−0.372169	+	0.214872i
$782$	87587.2	+	6717.86i	0.143228	+	0.0109854i
$783$	13837.6	−	7634.74i	0.0225703	−	0.0124529i
$784$	69424.5	+	21947.8i	0.112949	+	0.0357075i
$785$	24120.7	+	41778.2i	0.0391426	+	0.0677970i
$786$	−347740.	+	163954.i	−0.562871	+	0.265385i
$787$	−150134.	+	260040.i	−0.242398	+	0.419846i	−0.961397	−	0.275165i	$-0.911267\pi$
$787$	−150134.	+	260040.i	−0.242398	+	0.419846i	0.718999	+	0.695012i	$0.244601\pi$
$788$	−356013.	−	285955.i	−0.573342	−	0.460516i
$789$	−634462.	−	371804.i	−1.01918	−	0.597255i
$790$	13423.2	−	6435.36i	0.0215081	−	0.0103114i
$791$			754861.i			1.20646i
$792$	−67551.8	+	272971.i	−0.107693	+	0.435177i
$793$	1.11244e6			1.76902
$794$	−345929.	−	721556.i	−0.548715	−	1.14454i
$795$	108728.	+	703.888i	0.172031	+	0.00111370i
$796$	−797286.	−	640391.i	−1.25831	−	1.01069i
$797$	189436.	+	109371.i	0.298226	+	0.172181i	0.641646	−	0.767001i	$-0.278252\pi$
$797$	189436.	+	109371.i	0.298226	+	0.172181i	−0.343420	+	0.939182i	$0.611585\pi$
$798$	−589373.	−	49044.3i	−0.925518	−	0.0770162i
$799$	276832.	−	159829.i	0.433633	−	0.250358i
$800$	−235736.	+	585535.i	−0.368338	+	0.914898i
$801$	−244589.	+	411251.i	−0.381217	+	0.640977i
$802$	−8551.44	+	111493.i	−0.0132951	+	0.173341i
$803$	255910.	+	443249.i	0.396877	+	0.687412i
$804$	561890.	−	690351.i	0.869239	−	1.06797i
$805$	−28901.6	−	16686.4i	−0.0445996	−	0.0257496i
$806$	−268226.	−	183562.i	−0.412887	−	0.282561i
$807$	562232.	−	319770.i	0.863313	−	0.491010i
$808$	−296377.	−	979043.i	−0.453964	−	1.49961i
$809$	−373854.			−0.571223			−0.285611	−	0.958346i	$-0.592197\pi$
$809$	−373854.			−0.571223			−0.285611	+	0.958346i	$0.592197\pi$
$810$	−31439.2	−	70183.3i	−0.0479183	−	0.106970i
$811$	−389516.			−0.592220			−0.296110	−	0.955154i	$-0.595690\pi$
$811$	−389516.			−0.592220			−0.296110	+	0.955154i	$0.595690\pi$
$812$	5778.10	+	14875.2i	0.00876341	+	0.0225606i
$813$	−451550.	+	256819.i	−0.683164	+	0.388550i
$814$	154816.	−	226221.i	0.233650	−	0.341417i
$815$	−16913.1	−	9764.78i	−0.0254629	−	0.0147010i
$816$	−151694.	+	136995.i	−0.227818	+	0.205743i
$817$	−242239.	−	419571.i	−0.362911	−	0.628581i
$818$	−16916.3	+	220554.i	−0.0252813	+	0.329616i
$819$	−384068.	+	645770.i	−0.572586	+	0.962742i
$820$	−15821.8	+	102535.i	−0.0235303	+	0.152492i
$821$	−766580.	+	442585.i	−1.13729	+	0.656614i	−0.945758	−	0.324872i	$-0.894679\pi$
$821$	−766580.	+	442585.i	−1.13729	+	0.656614i	−0.191531	+	0.981486i	$0.561345\pi$
$822$	15965.6	−	191862.i	0.0236288	−	0.283952i
$823$	−556310.	−	321186.i	−0.821329	−	0.474195i	0.0295455	−	0.999563i	$-0.490594\pi$
$823$	−556310.	−	321186.i	−0.821329	−	0.474195i	−0.850875	+	0.525369i	$0.823927\pi$
$824$	−864096.	+	921527.i	−1.27265	+	1.35723i
$825$	300929.	+	1948.16i	0.442136	+	0.00286231i
$826$	420650.	+	877412.i	0.616539	+	1.28601i
$827$	−144563.			−0.211372			−0.105686	−	0.994400i	$-0.533704\pi$
$827$	−144563.			−0.211372			−0.105686	+	0.994400i	$0.533704\pi$
$828$	53026.8	−	316410.i	0.0773454	−	0.461519i
$829$			390583.i			0.568335i	0.958775	+	0.284167i	$0.0917171\pi$
$829$			390583.i			0.568335i	−0.958775	+	0.284167i	$0.908283\pi$
$830$	12837.8	+	26777.6i	0.0186351	+	0.0388701i
$831$	153942.	+	90212.3i	0.222923	+	0.130636i
$832$	−458029.	−	687192.i	−0.661677	−	0.992731i
$833$	12616.0	−	21851.6i	0.0181816	−	0.0314915i
$834$	−270928.	+	127738.i	−0.389513	+	0.183649i
$835$	32476.3	+	56250.6i	0.0465793	+	0.0806778i
$836$	−306293.	−	47262.8i	−0.438253	−	0.0676250i
$837$	251532.	+	151810.i	0.359039	+	0.216695i
$838$	−46957.4	+	612229.i	−0.0668677	+	0.871818i
$839$	21529.2	−	12429.9i	0.0305846	−	0.0176580i	−0.484630	−	0.874719i	$-0.661046\pi$
$839$	21529.2	−	12429.9i	0.0305846	−	0.0176580i	0.515214	+	0.857061i	$0.327712\pi$
$840$	74465.7	−	22017.1i	0.105535	−	0.0312034i
$841$	−353406.	+	612116.i	−0.499668	+	0.865450i
$842$	−600681.	+	877734.i	−0.847265	+	1.23805i
$843$	566712.	−	967062.i	0.797457	−	1.36081i
$844$	90638.7	+	233341.i	0.127242	+	0.327572i
$845$			35429.8i			0.0496199i
$846$	−491022.	−	1.05916e6i	−0.686056	−	1.47986i
$847$		−	538205.i		−	0.750207i
$848$	−1.03060e6	+	227652.i	−1.43317	+	0.316577i
$849$	−514352.	−	3329.83i	−0.713584	−	0.00461962i
$850$	180515.	+	123536.i	0.249848	+	0.170984i
$851$	−156372.	+	270844.i	−0.215923	+	0.373990i
$852$	−110568.	+	687011.i	−0.152317	+	0.946421i
$853$	264635.	−	152787.i	0.363705	−	0.209985i	−0.307000	−	0.951710i	$-0.599325\pi$
$853$	264635.	−	152787.i	0.363705	−	0.209985i	0.670705	+	0.741724i	$0.265992\pi$
$854$	77648.4	−	1.01238e6i	0.106467	−	1.38812i
$855$	73943.1	−	41424.0i	0.101150	−	0.0566656i
$856$	125462.	−	536686.i	0.171224	−	0.732442i
$857$	−221670.	−	383944.i	−0.301818	−	0.522764i	0.674730	−	0.738065i	$-0.264260\pi$
$857$	−221670.	−	383944.i	−0.301818	−	0.522764i	−0.976548	+	0.215301i	$0.930927\pi$
$858$	−224465.	+	323482.i	−0.304911	+	0.439415i
$859$	228055.	−	395003.i	0.309067	−	0.535320i	−0.669091	−	0.743180i	$-0.733317\pi$
$859$	228055.	−	395003.i	0.309067	−	0.535320i	0.978159	+	0.207860i	$0.0666498\pi$
$860$	49594.9	+	39835.3i	0.0670564	+	0.0538606i
$861$	−796435.	+	452973.i	−1.07435	+	0.611034i
$862$	−323493.	−	674757.i	−0.435362	−	0.908098i
$863$		−	432830.i		−	0.581160i	−0.956851	−	0.290580i	$-0.906152\pi$
$863$		−	432830.i		−	0.581160i	0.956851	−	0.290580i	$-0.0938483\pi$
$864$	448810.	+	596511.i	0.601223	+	0.799082i
$865$	32854.2			0.0439095
$866$	910836.	−	436674.i	1.21452	−	0.582267i
$867$	−336604.	−	591831.i	−0.447797	−	0.787334i
$868$	−185772.	+	231286.i	−0.246570	+	0.306980i
$869$	59661.6	+	34445.6i	0.0790052	+	0.0456136i
$870$	−1878.92	−	1303.78i	−0.00248238	−	0.00172253i
$871$	1.07933e6	−	623151.i	1.42272	−	0.821405i
$872$	1.23138e6	+	287861.i	1.61941	+	0.378573i
$873$	150485.	+	1948.51i	0.197454	+	0.00255667i
$874$	352545.	+	27039.9i	0.461522	+	0.0353983i
$875$	−83679.4	−	144937.i	−0.109296	−	0.189305i
$876$	1.34143e6	+	215891.i	1.74808	+	0.281336i
$877$	439842.	+	253943.i	0.571870	+	0.330169i	0.757896	−	0.652376i	$-0.226227\pi$
$877$	439842.	+	253943.i	0.571870	+	0.330169i	−0.186026	+	0.982545i	$0.559561\pi$
$878$	361061.	−	527594.i	0.468373	−	0.684401i
$879$	−1712.79	+	264572.i	−0.00221681	+	0.342426i
$880$	39734.5	−	8777.07i	0.0513100	−	0.0113340i
$881$	−630033.			−0.811730			−0.405865	−	0.913933i	$-0.633030\pi$
$881$	−630033.			−0.811730			−0.405865	+	0.913933i	$0.633030\pi$
$882$	−75368.2	−	53024.3i	−0.0968837	−	0.0681612i
$883$	−111488.			−0.142990			−0.0714950	−	0.997441i	$-0.522777\pi$
$883$	−111488.			−0.142990			−0.0714950	+	0.997441i	$0.522777\pi$
$884$	−266771.	+	103624.i	−0.341377	+	0.132604i
$885$	−120311.	−	70503.7i	−0.153609	−	0.0900172i
$886$	1.00888e6	+	690428.i	1.28520	+	0.879531i
$887$	−642963.	−	371215.i	−0.817220	−	0.471822i	0.0322369	−	0.999480i	$-0.489737\pi$
$887$	−642963.	−	371215.i	−0.817220	−	0.471822i	−0.849457	+	0.527658i	$0.823070\pi$
$888$	−206327.	−	697836.i	−0.261656	−	0.884967i
$889$	4379.84	+	7586.11i	0.00554185	+	0.00959877i
$890$	69037.9	+	5295.15i	0.0871581	+	0.00668495i
$891$	185871.	−	303508.i	0.234129	−	0.382309i
$892$	126322.	−	818649.i	0.158763	−	1.02889i
$893$	1.11427e6	−	643324.i	1.39729	−	0.806727i
$894$	145936.	+	309525.i	0.182595	+	0.387276i
$895$	−43109.6	−	24889.4i	−0.0538181	−	0.0310719i
$896$	−657348.	+	368862.i	−0.818803	+	0.459460i
$897$	227115.	−	387558.i	0.282267	−	0.481673i
$898$	1.21968e6	−	584742.i	1.51250	−	0.725123i
$899$	8736.86			0.0108103
$900$	508292.	−	616307.i	0.627522	−	0.760873i
$901$			365754.i			0.450546i
$902$	−432954.	+	207567.i	−0.532143	+	0.255121i
$903$	−3636.79	+	561767.i	−0.00446008	+	0.688939i
$904$	766017.	+	718278.i	0.937349	+	0.878933i
$905$	−71052.5	+	123067.i	−0.0867525	+	0.150260i
$906$	954197.	+	79402.8i	1.16247	+	0.0967341i
$907$	−120922.	−	209443.i	−0.146991	−	0.254596i	0.783123	−	0.621867i	$-0.213626\pi$
$907$	−120922.	−	209443.i	−0.146991	−	0.254596i	−0.930114	+	0.367271i	$0.880292\pi$
$908$	−892768.	−	137759.i	−1.08285	−	0.167090i
$909$	−16761.8	+	1.29452e6i	−0.0202858	+	1.56669i
$910$	108407.	+	8314.74i	0.130911	+	0.0100407i
$911$	−276542.	+	159661.i	−0.333214	+	0.192381i	−0.657267	−	0.753658i	$-0.728288\pi$
$911$	−276542.	+	159661.i	−0.333214	+	0.192381i	0.324053	+	0.946039i	$0.394954\pi$
$912$	−610579.	+	551416.i	−0.734095	+	0.662964i
$913$	−68714.8	+	119017.i	−0.0824344	+	0.142781i
$914$	−10834.4	−	7414.56i	−0.0129692	−	0.00887550i
$915$	71938.1	+	126485.i	0.0859245	+	0.151076i
$916$	843111.	−	327497.i	1.00483	−	0.390316i
$917$			491312.i			0.584277i
$918$	235397.	−	107283.i	0.279329	−	0.127305i
$919$		−	1.48790e6i		−	1.76175i	−0.473350	−	0.880875i	$-0.656955\pi$
$919$		−	1.48790e6i		−	1.76175i	0.473350	−	0.880875i	$-0.343045\pi$
$920$	−44433.9	+	13451.1i	−0.0524975	+	0.0158921i
$921$	−343857.	−	604583.i	−0.405376	−	0.712749i
$922$	−561018.	+	819778.i	−0.659956	+	0.964349i
$923$	−487151.	+	843771.i	−0.571821	+	0.990424i
$924$	278716.	+	226852.i	0.326451	+	0.265705i
$925$	−674422.	+	389378.i	−0.788222	+	0.455080i
$926$	197837.	+	15173.9i	0.230721	+	0.0176961i
$927$	1.39487e6	−	781425.i	1.62321	−	0.909343i
$928$	20593.1	+	8290.78i	0.0239125	+	0.00962719i
$929$	588618.	+	1.01952e6i	0.682028	+	1.18131i	0.974361	+	0.224991i	$0.0722352\pi$
$929$	588618.	+	1.01952e6i	0.682028	+	1.18131i	−0.292333	+	0.956317i	$0.594431\pi$
$930$	3525.58	−	42367.5i	0.00407629	−	0.0489855i
$931$	50780.5	−	87954.5i	0.0585865	−	0.101475i
$932$	724637.	−	902173.i	0.834236	−	1.03862i
$933$	−5977.08	+	923268.i	−0.00686635	+	1.06063i
$934$	67548.6	−	32384.2i	0.0774324	−	0.0371227i
$935$		−	14101.6i		−	0.0161304i
$936$	289859.	+	1.00422e6i	0.330852	+	1.14624i
$937$	904036.			1.02969			0.514845	−	0.857283i	$-0.327849\pi$
$937$	904036.			1.02969			0.514845	+	0.857283i	$0.327849\pi$
$938$	−491760.	−	1.02574e6i	−0.558918	−	1.16582i
$939$	−187171.	+	319397.i	−0.212279	+	0.362243i
$940$	−105792.	+	131711.i	−0.119728	+	0.149062i
$941$	−569128.	−	328586.i	−0.642733	−	0.371082i	0.142934	−	0.989732i	$-0.454346\pi$
$941$	−569128.	−	328586.i	−0.642733	−	0.371082i	−0.785666	+	0.618650i	$0.787680\pi$
$942$	252747.	+	536066.i	0.284829	+	0.604111i
$943$	474393.	−	273891.i	0.533476	−	0.308003i
$944$	1.29064e6	+	408023.i	1.44831	+	0.457868i
$945$	−98260.2	−	1908.57i	−0.110031	−	0.00213720i
$946$	−22513.4	+	293528.i	−0.0251570	+	0.327995i
$947$	100820.	+	174625.i	0.112420	+	0.194718i	0.916746	−	0.399471i	$-0.130806\pi$
$947$	100820.	+	174625.i	0.112420	+	0.194718i	−0.804325	+	0.594189i	$0.797473\pi$
$948$	170897.	−	65112.9i	0.190159	−	0.0724521i
$949$	1.64752e6	+	951194.i	1.82935	+	1.05618i
$950$	726587.	+	497243.i	0.805082	+	0.550961i
$951$	977542.	+	572854.i	1.08087	+	0.633407i
$952$	75682.4	+	250007.i	0.0835067	+	0.275854i
$953$	−638389.			−0.702910			−0.351455	−	0.936205i	$-0.614313\pi$
$953$	−638389.			−0.702910			−0.351455	+	0.936205i	$0.614313\pi$
$954$	1.33045e6	+	119389.i	1.46184	+	0.131181i
$955$	−107011.			−0.117333
$956$	−1.48892e6	+	578355.i	−1.62913	+	0.632818i
$957$	68.5163	−	10583.6i	7.48118e−5	−	0.0115560i
$958$	895338.	−	1.30830e6i	0.975564	−	1.42553i
$959$	−213075.	−	123019.i	−0.231684	−	0.133763i
$960$	48514.3	−	96516.2i	0.0526414	−	0.104727i
$961$	−380552.	−	659136.i	−0.412067	−	0.713721i
$962$	77919.4	−	1.01591e6i	0.0841967	−	1.09775i
$963$	−356571.	+	599536.i	−0.384497	+	0.646491i
$964$	−414571.	−	63970.8i	−0.446113	−	0.0688379i
$965$	−63737.0	+	36798.6i	−0.0684443	+	0.0395163i
$966$	−336844.	−	233737.i	−0.360973	−	0.250480i
$967$	−961591.	−	555175.i	−1.02834	−	0.593714i	−0.111833	−	0.993727i	$-0.535672\pi$
$967$	−961591.	−	555175.i	−1.02834	−	0.593714i	−0.916509	+	0.400013i	$0.869005\pi$
$968$	−546159.	−	512121.i	−0.582865	−	0.546540i
$969$	140952.	+	247827.i	0.150114	+	0.263937i
$970$	−9414.82	−	19637.9i	−0.0100062	−	0.0208714i
$971$	−1.25193e6			−1.32783			−0.663913	−	0.747810i	$-0.731105\pi$
$971$	−1.25193e6			−1.32783			−0.663913	+	0.747810i	$0.731105\pi$
$972$	−313409.	−	891287.i	−0.331725	−	0.943376i
$973$			382787.i			0.404326i
$974$	415467.	+	866601.i	0.437944	+	0.913485i
$975$	972290.	−	552991.i	1.02279	−	0.581713i
$976$	−953453.	−	1.04211e6i	−1.00092	−	1.09399i
$977$	33214.5	−	57529.3i	0.0347968	−	0.0602698i	−0.848103	−	0.529832i	$-0.822255\pi$
$977$	33214.5	−	57529.3i	0.0347968	−	0.0602698i	0.882899	+	0.469562i	$0.155588\pi$
$978$	−197119.	−	136782.i	−0.206088	−	0.143005i
$979$	160219.	+	277508.i	0.167167	+	0.289541i
$980$	−2033.60	+	13179.0i	−0.00211745	+	0.0137224i
$981$	−1.37558e6	−	818117.i	−1.42938	−	0.850114i
$982$	59980.7	−	782026.i	0.0621997	−	0.810957i
$983$	130314.	−	75236.9i	0.134860	−	0.0778617i	−0.431052	−	0.902327i	$-0.641857\pi$
$983$	130314.	−	75236.9i	0.134860	−	0.0778617i	0.565912	+	0.824465i	$0.308524\pi$
$984$	−298169.	+	1.23922e6i	−0.307945	+	1.27985i
$985$	41815.2	−	72426.0i	0.0430984	−	0.0746487i
$986$	4344.74	−	6348.67i	0.00446899	−	0.00653023i
$987$	−1.49191e6	−	9658.35i	−1.53146	−	0.00991445i
$988$	−1.07377e6	+	417096.i	−1.10002	+	0.427289i
$989$		−	335865.i		−	0.343378i
$990$	−51295.1	−	4603.04i	−0.0523366	−	0.00469650i
$991$		−	795870.i		−	0.810391i	−0.914230	−	0.405196i	$-0.867203\pi$
$991$		−	795870.i		−	0.810391i	0.914230	−	0.405196i	$-0.132797\pi$
$992$	57935.2	+	408594.i	0.0588734	+	0.415211i
$993$	−493550.	+	842215.i	−0.500533	+	0.854131i
$994$	733868.	+	502226.i	0.742755	+	0.508307i
$995$	93644.4	−	162197.i	0.0945879	−	0.163831i
$996$	129892.	+	340918.i	0.130938	+	0.343662i
$997$	−674456.	+	389398.i	−0.678521	+	0.391745i	−0.799298	−	0.600935i	$-0.794795\pi$
$997$	−674456.	+	389398.i	−0.678521	+	0.391745i	0.120776	+	0.992680i	$0.461462\pi$
$998$	80113.1	−	1.04451e6i	0.0804346	−	1.04870i
$999$	−17885.7	+	920820.i	−0.0179215	+	0.922664i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	72.5.p.b.67.39	yes	88
3.2	odd	2		216.5.p.b.91.6		88
4.3	odd	2		288.5.t.b.175.16		88
8.3	odd	2	inner	72.5.p.b.67.10	yes	88
8.5	even	2		288.5.t.b.175.15		88
9.2	odd	6		216.5.p.b.19.35		88
9.7	even	3	inner	72.5.p.b.43.10	✓	88
12.11	even	2		864.5.t.b.847.20		88
24.5	odd	2		864.5.t.b.847.25		88
24.11	even	2		216.5.p.b.91.35		88
36.7	odd	6		288.5.t.b.79.15		88
36.11	even	6		864.5.t.b.559.25		88
72.11	even	6		216.5.p.b.19.6		88
72.29	odd	6		864.5.t.b.559.20		88
72.43	odd	6	inner	72.5.p.b.43.39	yes	88
72.61	even	6		288.5.t.b.79.16		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.5.p.b.43.10	✓	88	9.7	even	3	inner
72.5.p.b.43.39	yes	88	72.43	odd	6	inner
72.5.p.b.67.10	yes	88	8.3	odd	2	inner
72.5.p.b.67.39	yes	88	1.1	even	1	trivial
216.5.p.b.19.6		88	72.11	even	6
216.5.p.b.19.35		88	9.2	odd	6
216.5.p.b.91.6		88	3.2	odd	2
216.5.p.b.91.35		88	24.11	even	2
288.5.t.b.79.15		88	36.7	odd	6
288.5.t.b.79.16		88	72.61	even	6
288.5.t.b.175.15		88	8.5	even	2
288.5.t.b.175.16		88	4.3	odd	2
864.5.t.b.559.20		88	72.29	odd	6
864.5.t.b.559.25		88	36.11	even	6
864.5.t.b.847.20		88	12.11	even	2
864.5.t.b.847.25		88	24.5	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	72.5.p.b.67.39

Level	$72$
Weight	$5$
Character	72.67
Analytic conductor	$7.443$
Analytic rank	$0$
Dimension	$88$
Inner twists	$4$