LMFDB - Embedded newform 102.5.g.d.83.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [102,5,Mod(53,102)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(102, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 7]))

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

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

chi := DirichletCharacter("102.53");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 102 = 2 \cdot 3 \cdot 17 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	102.g (of order $8$, 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:	$10.5437362346$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$11$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			83.9
Character	$\chi$	$=$	102.83
Dual form			102.5.g.d.59.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.00000 - 2.00000i) q^{2} +(7.44631 - 5.05494i) q^{3} -8.00000i q^{4} +(14.7889 + 35.7036i) q^{5} +(4.78274 - 25.0025i) q^{6} +(33.4426 + 13.8524i) q^{7} +(-16.0000 - 16.0000i) q^{8} +(29.8951 - 75.2814i) q^{9} +(100.985 + 41.8294i) q^{10} +(124.489 + 51.5649i) q^{11} +(-40.4395 - 59.5705i) q^{12} +150.152i q^{13} +(94.5899 - 39.1804i) q^{14} +(290.603 + 191.103i) q^{15} -64.0000 q^{16} +(-136.449 - 254.760i) q^{17} +(-90.7725 - 210.353i) q^{18} +(-447.691 - 447.691i) q^{19} +(285.629 - 118.311i) q^{20} +(319.047 - 65.9012i) q^{21} +(352.107 - 145.848i) q^{22} +(114.176 + 47.2931i) q^{23} +(-200.020 - 38.2619i) q^{24} +(-614.093 + 614.093i) q^{25} +(300.304 + 300.304i) q^{26} +(-157.935 - 711.686i) q^{27} +(110.819 - 267.541i) q^{28} +(-480.788 - 1160.72i) q^{29} +(963.411 - 198.999i) q^{30} +(572.928 + 1383.17i) q^{31} +(-128.000 + 128.000i) q^{32} +(1187.64 - 245.315i) q^{33} +(-782.418 - 236.621i) q^{34} +1398.88i q^{35} +(-602.251 - 239.161i) q^{36} +(461.751 + 1114.77i) q^{37} -1790.76 q^{38} +(759.009 + 1118.08i) q^{39} +(334.635 - 807.880i) q^{40} +(992.472 - 2396.04i) q^{41} +(506.291 - 769.896i) q^{42} +(-574.440 + 574.440i) q^{43} +(412.519 - 995.909i) q^{44} +(3129.93 - 45.9663i) q^{45} +(322.937 - 133.765i) q^{46} -2683.82 q^{47} +(-476.564 + 323.516i) q^{48} +(-771.246 - 771.246i) q^{49} +2456.37i q^{50} +(-2303.84 - 1207.28i) q^{51} +1201.22 q^{52} +(-2426.46 + 2426.46i) q^{53} +(-1739.24 - 1107.50i) q^{54} +5207.28i q^{55} +(-313.443 - 756.719i) q^{56} +(-5596.70 - 1070.59i) q^{57} +(-3283.02 - 1359.87i) q^{58} +(2594.36 + 2594.36i) q^{59} +(1528.82 - 2324.82i) q^{60} +(2456.03 + 1017.32i) q^{61} +(3912.19 + 1620.48i) q^{62} +(2042.59 - 2103.48i) q^{63} +512.000i q^{64} +(-5360.96 + 2220.58i) q^{65} +(1884.65 - 2865.91i) q^{66} -3436.87 q^{67} +(-2038.08 + 1091.60i) q^{68} +(1089.25 - 224.992i) q^{69} +(2797.76 + 2797.76i) q^{70} +(885.807 - 366.913i) q^{71} +(-1682.82 + 726.180i) q^{72} +(-3055.41 + 1265.59i) q^{73} +(3153.03 + 1306.03i) q^{74} +(-1468.52 + 7676.94i) q^{75} +(-3581.53 + 3581.53i) q^{76} +(3448.93 + 3448.93i) q^{77} +(3754.17 + 718.137i) q^{78} +(-1542.68 + 3724.37i) q^{79} +(-946.491 - 2285.03i) q^{80} +(-4773.56 - 4501.09i) q^{81} +(-2807.13 - 6777.02i) q^{82} +(4614.31 - 4614.31i) q^{83} +(-527.210 - 2552.37i) q^{84} +(7077.90 - 8639.36i) q^{85} +2297.76i q^{86} +(-9447.49 - 6212.76i) q^{87} +(-1166.78 - 2816.86i) q^{88} -8112.87 q^{89} +(6167.93 - 6351.80i) q^{90} +(-2079.96 + 5021.47i) q^{91} +(378.344 - 913.404i) q^{92} +(11258.0 + 7403.40i) q^{93} +(-5367.64 + 5367.64i) q^{94} +(9363.31 - 22605.0i) q^{95} +(-306.095 + 1600.16i) q^{96} +(474.885 - 196.704i) q^{97} -3084.98 q^{98} +(7603.48 - 7830.14i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 88 q^{2} - 4 q^{3} + 72 q^{5} - 40 q^{6} + 132 q^{7} - 704 q^{8} + 324 q^{9} + 384 q^{10} - 616 q^{11} - 128 q^{12} + 416 q^{14} - 908 q^{15} - 2816 q^{16} + 424 q^{17} + 1016 q^{18} + 568 q^{19}+ \cdots + 91704 q^{99}+O(q^{100}) $ 44 * q + 88 * q^2 - 4 * q^3 + 72 * q^5 - 40 * q^6 + 132 * q^7 - 704 * q^8 + 324 * q^9 + 384 * q^10 - 616 * q^11 - 128 * q^12 + 416 * q^14 - 908 * q^15 - 2816 * q^16 + 424 * q^17 + 1016 * q^18 + 568 * q^19 + 960 * q^20 + 1020 * q^21 + 424 * q^22 + 332 * q^23 - 192 * q^24 + 1888 * q^25 - 1008 * q^26 - 436 * q^27 + 608 * q^28 - 6688 * q^29 - 2000 * q^30 - 1428 * q^31 - 5632 * q^32 + 2224 * q^33 + 512 * q^34 + 1472 * q^36 + 296 * q^37 + 2272 * q^38 - 3720 * q^39 + 768 * q^40 + 4592 * q^41 + 3328 * q^42 - 228 * q^43 + 6624 * q^44 + 8228 * q^45 + 1872 * q^46 + 10712 * q^47 + 256 * q^48 + 5304 * q^49 - 3984 * q^51 - 4032 * q^52 - 5656 * q^53 - 9288 * q^54 - 896 * q^56 - 13364 * q^57 - 11472 * q^58 + 3620 * q^59 - 736 * q^60 - 10448 * q^61 - 3536 * q^62 + 28248 * q^63 - 13760 * q^65 + 12952 * q^66 - 18584 * q^67 - 1344 * q^68 + 6500 * q^69 - 9664 * q^70 + 36660 * q^71 - 2240 * q^72 + 18008 * q^73 - 144 * q^74 + 30268 * q^75 + 4544 * q^76 - 5704 * q^77 - 22576 * q^78 - 7324 * q^79 - 4608 * q^80 - 33668 * q^81 + 11160 * q^82 - 12620 * q^83 + 5152 * q^84 - 10896 * q^85 + 23860 * q^87 + 23104 * q^88 - 5040 * q^89 - 8784 * q^90 + 52368 * q^91 + 4832 * q^92 - 1304 * q^93 + 21424 * q^94 + 16032 * q^95 + 2560 * q^96 - 40164 * q^97 + 21216 * q^98 + 91704 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/102\mathbb{Z}\right)^\times$.

$n$	$35$	$37$
$\chi(n)$	$-1$	$e\left(\frac{3}{8}\right)$

Coefficient data

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

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	2.00000	−	2.00000i	0.500000	−	0.500000i
$2$	2.00000	−	2.00000i	0.500000	−	0.500000i
$3$	7.44631	−	5.05494i	0.827368	−	0.561660i
$3$	7.44631	−	5.05494i	0.827368	−	0.561660i
$4$		−	8.00000i		−	0.500000i
$5$	14.7889	+	35.7036i	0.591557	+	1.42814i	0.881999	+	0.471252i	$0.156198\pi$
$5$	14.7889	+	35.7036i	0.591557	+	1.42814i	−0.290442	+	0.956893i	$0.593802\pi$
$6$	4.78274	−	25.0025i	0.132854	−	0.694514i
$7$	33.4426	+	13.8524i	0.682501	+	0.282701i	0.696872	−	0.717195i	$-0.254575\pi$
$7$	33.4426	+	13.8524i	0.682501	+	0.282701i	−0.0143707	+	0.999897i	$0.504575\pi$
$8$	−16.0000	−	16.0000i	−0.250000	−	0.250000i
$9$	29.8951	−	75.2814i	0.369075	−	0.929399i
$10$	100.985	+	41.8294i	1.00985	+	0.418294i
$11$	124.489	+	51.5649i	1.02883	+	0.426156i	0.832291	−	0.554339i	$-0.187029\pi$
$11$	124.489	+	51.5649i	1.02883	+	0.426156i	0.196541	+	0.980496i	$0.437029\pi$
$12$	−40.4395	−	59.5705i	−0.280830	−	0.413684i
$13$			150.152i			0.888473i	0.895910	+	0.444236i	$0.146525\pi$
$13$			150.152i			0.888473i	−0.895910	+	0.444236i	$0.853475\pi$
$14$	94.5899	−	39.1804i	0.482601	−	0.199900i
$15$	290.603	+	191.103i	1.29157	+	0.849347i
$16$	−64.0000			−0.250000
$17$	−136.449	−	254.760i	−0.472144	−	0.881522i
$17$	−136.449	−	254.760i	−0.472144	−	0.881522i
$18$	−90.7725	−	210.353i	−0.280162	−	0.649237i
$19$	−447.691	−	447.691i	−1.24014	−	1.24014i	−0.959942	−	0.280198i	$-0.909600\pi$
$19$	−447.691	−	447.691i	−1.24014	−	1.24014i	−0.280198	−	0.959942i	$-0.590400\pi$
$20$	285.629	−	118.311i	0.714072	−	0.295778i
$21$	319.047	−	65.9012i	0.723462	−	0.149436i
$22$	352.107	−	145.848i	0.727494	−	0.301338i
$23$	114.176	+	47.2931i	0.215833	+	0.0894009i	0.487980	−	0.872855i	$-0.337734\pi$
$23$	114.176	+	47.2931i	0.215833	+	0.0894009i	−0.272147	+	0.962256i	$0.587734\pi$
$24$	−200.020	−	38.2619i	−0.347257	−	0.0664269i
$25$	−614.093	+	614.093i	−0.982549	+	0.982549i
$26$	300.304	+	300.304i	0.444236	+	0.444236i
$27$	−157.935	−	711.686i	−0.216645	−	0.976250i
$28$	110.819	−	267.541i	0.141351	−	0.341251i
$29$	−480.788	−	1160.72i	−0.571686	−	1.38017i	−0.900119	−	0.435644i	$-0.856521\pi$
$29$	−480.788	−	1160.72i	−0.571686	−	1.38017i	0.328433	−	0.944527i	$-0.393479\pi$
$30$	963.411	−	198.999i	1.07046	−	0.221110i
$31$	572.928	+	1383.17i	0.596179	+	1.43930i	0.877447	+	0.479673i	$0.159245\pi$
$31$	572.928	+	1383.17i	0.596179	+	1.43930i	−0.281269	+	0.959629i	$0.590755\pi$
$32$	−128.000	+	128.000i	−0.125000	+	0.125000i
$33$	1187.64	−	245.315i	1.09058	−	0.225266i
$34$	−782.418	−	236.621i	−0.676833	−	0.204689i
$35$			1398.88i			1.14194i
$36$	−602.251	−	239.161i	−0.464700	−	0.184538i
$37$	461.751	+	1114.77i	0.337291	+	0.814292i	0.997974	+	0.0636269i	$0.0202668\pi$
$37$	461.751	+	1114.77i	0.337291	+	0.814292i	−0.660683	+	0.750665i	$0.729733\pi$
$38$	−1790.76			−1.24014
$39$	759.009	+	1118.08i	0.499020	+	0.735094i
$40$	334.635	−	807.880i	0.209147	−	0.504925i
$41$	992.472	−	2396.04i	0.590406	−	1.42537i	−0.292706	−	0.956202i	$-0.594556\pi$
$41$	992.472	−	2396.04i	0.590406	−	1.42537i	0.883112	−	0.469163i	$-0.155444\pi$
$42$	506.291	−	769.896i	0.287013	−	0.436449i
$43$	−574.440	+	574.440i	−0.310676	+	0.310676i	−0.845171	−	0.534495i	$-0.820502\pi$
$43$	−574.440	+	574.440i	−0.310676	+	0.310676i	0.534495	+	0.845171i	$0.320502\pi$
$44$	412.519	−	995.909i	0.213078	−	0.514416i
$45$	3129.93	−	45.9663i	1.54565	−	0.0226994i
$46$	322.937	−	133.765i	0.152617	−	0.0632160i
$47$	−2683.82			−1.21495			−0.607474	−	0.794340i	$-0.707817\pi$
$47$	−2683.82			−1.21495			−0.607474	+	0.794340i	$0.707817\pi$
$48$	−476.564	+	323.516i	−0.206842	+	0.140415i
$49$	−771.246	−	771.246i	−0.321219	−	0.321219i
$50$			2456.37i			0.982549i
$51$	−2303.84	−	1207.28i	−0.885752	−	0.464159i
$52$	1201.22			0.444236
$53$	−2426.46	+	2426.46i	−0.863818	+	0.863818i	−0.991779	−	0.127961i	$-0.959157\pi$
$53$	−2426.46	+	2426.46i	−0.863818	+	0.863818i	0.127961	+	0.991779i	$0.459157\pi$
$54$	−1739.24	−	1107.50i	−0.596448	−	0.379802i
$55$			5207.28i			1.72142i
$56$	−313.443	−	756.719i	−0.0999500	−	0.241301i
$57$	−5596.70	−	1070.59i	−1.72259	−	0.329515i
$58$	−3283.02	−	1359.87i	−0.975928	−	0.404243i
$59$	2594.36	+	2594.36i	0.745291	+	0.745291i	0.973591	−	0.228300i	$-0.0733167\pi$
$59$	2594.36	+	2594.36i	0.745291	+	0.745291i	−0.228300	+	0.973591i	$0.573317\pi$
$60$	1528.82	−	2324.82i	0.424673	−	0.645783i
$61$	2456.03	+	1017.32i	0.660045	+	0.273400i	0.687458	−	0.726225i	$-0.258727\pi$
$61$	2456.03	+	1017.32i	0.660045	+	0.273400i	−0.0274124	+	0.999624i	$0.508727\pi$
$62$	3912.19	+	1620.48i	1.01774	+	0.421562i
$63$	2042.59	−	2103.48i	0.514637	−	0.529978i
$64$			512.000i			0.125000i
$65$	−5360.96	+	2220.58i	−1.26887	+	0.525582i
$66$	1884.65	−	2865.91i	0.432656	−	0.657922i
$67$	−3436.87			−0.765621			−0.382810	−	0.923827i	$-0.625044\pi$
$67$	−3436.87			−0.765621			−0.382810	+	0.923827i	$0.625044\pi$
$68$	−2038.08	+	1091.60i	−0.440761	+	0.236072i
$69$	1089.25	−	224.992i	0.228786	−	0.0472573i
$70$	2797.76	+	2797.76i	0.570972	+	0.570972i
$71$	885.807	−	366.913i	0.175721	−	0.0727858i	−0.293089	−	0.956085i	$-0.594683\pi$
$71$	885.807	−	366.913i	0.175721	−	0.0727858i	0.468809	+	0.883299i	$0.344683\pi$
$72$	−1682.82	+	726.180i	−0.324619	+	0.140081i
$73$	−3055.41	+	1265.59i	−0.573355	+	0.237491i	−0.650471	−	0.759531i	$-0.725429\pi$
$73$	−3055.41	+	1265.59i	−0.573355	+	0.237491i	0.0771166	+	0.997022i	$0.475429\pi$
$74$	3153.03	+	1306.03i	0.575791	+	0.238501i
$75$	−1468.52	+	7676.94i	−0.261071	+	1.36479i
$76$	−3581.53	+	3581.53i	−0.620070	+	0.620070i
$77$	3448.93	+	3448.93i	0.581704	+	0.581704i
$78$	3754.17	+	718.137i	0.617057	+	0.118037i
$79$	−1542.68	+	3724.37i	−0.247186	+	0.596759i	−0.997963	−	0.0637966i	$-0.979679\pi$
$79$	−1542.68	+	3724.37i	−0.247186	+	0.596759i	0.750777	+	0.660555i	$0.229679\pi$
$80$	−946.491	−	2285.03i	−0.147889	−	0.357036i
$81$	−4773.56	−	4501.09i	−0.727567	−	0.686037i
$82$	−2807.13	−	6777.02i	−0.417480	−	1.00789i
$83$	4614.31	−	4614.31i	0.669808	−	0.669808i	−0.287863	−	0.957671i	$-0.592945\pi$
$83$	4614.31	−	4614.31i	0.669808	−	0.669808i	0.957671	+	0.287863i	$0.0929449\pi$
$84$	−527.210	−	2552.37i	−0.0747179	−	0.361731i
$85$	7077.90	−	8639.36i	0.979640	−	1.19576i
$86$			2297.76i			0.310676i
$87$	−9447.49	−	6212.76i	−1.24818	−	0.820816i
$88$	−1166.78	−	2816.86i	−0.150669	−	0.363747i
$89$	−8112.87			−1.02422			−0.512111	−	0.858919i	$-0.671136\pi$
$89$	−8112.87			−1.02422			−0.512111	+	0.858919i	$0.671136\pi$
$90$	6167.93	−	6351.80i	0.761473	−	0.784172i
$91$	−2079.96	+	5021.47i	−0.251172	+	0.606384i
$92$	378.344	−	913.404i	0.0447004	−	0.107916i
$93$	11258.0	+	7403.40i	1.30166	+	0.855983i
$94$	−5367.64	+	5367.64i	−0.607474	+	0.607474i
$95$	9363.31	−	22605.0i	1.03749	−	2.50471i
$96$	−306.095	+	1600.16i	−0.0332135	+	0.173629i
$97$	474.885	−	196.704i	0.0504714	−	0.0209059i	−0.357305	−	0.933988i	$-0.616304\pi$
$97$	474.885	−	196.704i	0.0504714	−	0.0209059i	0.407776	+	0.913082i	$0.366304\pi$
$98$	−3084.98			−0.321219
$99$	7603.48	−	7830.14i	0.775786	−	0.798912i
$100$	4912.75	+	4912.75i	0.491275	+	0.491275i
$101$		−	4979.36i		−	0.488124i	−0.969760	−	0.244062i	$-0.921520\pi$
$101$		−	4979.36i		−	0.488124i	0.969760	−	0.244062i	$-0.0784801\pi$
$102$	−7022.24	+	2193.13i	−0.674955	+	0.210797i
$103$	−9976.88			−0.940417			−0.470208	−	0.882555i	$-0.655821\pi$
$103$	−9976.88			−0.940417			−0.470208	+	0.882555i	$0.655821\pi$
$104$	2402.43	−	2402.43i	0.222118	−	0.222118i
$105$	7071.27	+	10416.5i	0.641385	+	0.944808i
$106$			9705.85i			0.863818i
$107$	−2533.89	−	6117.35i	−0.221320	−	0.534313i	0.773750	−	0.633491i	$-0.218379\pi$
$107$	−2533.89	−	6117.35i	−0.221320	−	0.534313i	−0.995070	+	0.0991780i	$0.968379\pi$
$108$	−5693.49	+	1263.48i	−0.488125	+	0.108323i
$109$	5292.30	+	2192.14i	0.445442	+	0.184508i	0.594118	−	0.804378i	$-0.297501\pi$
$109$	5292.30	+	2192.14i	0.445442	+	0.184508i	−0.148676	+	0.988886i	$0.547501\pi$
$110$	10414.6	+	10414.6i	0.860708	+	0.860708i
$111$	9073.42	+	5966.77i	0.736419	+	0.484276i
$112$	−2140.32	−	886.551i	−0.170625	−	0.0706753i
$113$	16294.2	+	6749.28i	1.27608	+	0.528568i	0.914806	−	0.403893i	$-0.132343\pi$
$113$	16294.2	+	6749.28i	1.27608	+	0.528568i	0.361270	+	0.932461i	$0.382343\pi$
$114$	−13334.6	+	9052.20i	−1.02605	+	0.696538i
$115$			4775.89i			0.361126i
$116$	−9285.79	+	3846.30i	−0.690086	+	0.285843i
$117$	11303.6	+	4488.81i	0.825746	+	0.327914i
$118$	10377.4			0.745291
$119$	−1034.20	−	10410.0i	−0.0730313	−	0.735115i
$120$	−1591.99	−	7707.29i	−0.110555	−	0.535228i
$121$	2485.74	+	2485.74i	0.169780	+	0.169780i
$122$	6946.70	−	2877.42i	0.466722	−	0.193323i
$123$	−4721.58	−	22858.5i	−0.312088	−	1.51091i
$124$	11065.4	−	4583.42i	0.719651	−	0.298089i
$125$	−8692.37	−	3600.50i	−0.556312	−	0.230432i
$126$	−121.779	−	8292.16i	−0.00767064	−	0.522308i
$127$	5639.96	−	5639.96i	0.349678	−	0.349678i	−0.510312	−	0.859990i	$-0.670470\pi$
$127$	5639.96	−	5639.96i	0.349678	−	0.349678i	0.859990	+	0.510312i	$0.170470\pi$
$128$	1024.00	+	1024.00i	0.0625000	+	0.0625000i
$129$	−1373.70	+	7181.22i	−0.0825490	+	0.431538i
$130$	−6280.76	+	15163.1i	−0.371643	+	0.897225i
$131$	73.7878	+	178.139i	0.00429974	+	0.0103805i	0.926015	−	0.377487i	$-0.123212\pi$
$131$	73.7878	+	178.139i	0.00429974	+	0.0103805i	−0.921715	+	0.387868i	$0.873212\pi$
$132$	−1962.52	−	9501.11i	−0.112633	−	0.545289i
$133$	−8770.35	−	21173.5i	−0.495808	−	1.19699i
$134$	−6873.74	+	6873.74i	−0.382810	+	0.382810i
$135$	23074.1	−	16163.9i	1.26607	−	0.886908i
$136$	−1892.96	+	6259.35i	−0.102345	+	0.338416i
$137$		−	21754.0i		−	1.15904i	−0.814958	−	0.579520i	$-0.803240\pi$
$137$		−	21754.0i		−	1.15904i	0.814958	−	0.579520i	$-0.196760\pi$
$138$	1728.52	−	2628.48i	0.0907644	−	0.138022i
$139$	452.907	+	1093.41i	0.0234412	+	0.0565920i	0.935167	−	0.354208i	$-0.115249\pi$
$139$	452.907	+	1093.41i	0.0234412	+	0.0565920i	−0.911726	+	0.410800i	$0.865249\pi$
$140$	11191.1			0.570972
$141$	−19984.5	+	13566.5i	−1.00521	+	0.682388i
$142$	1037.79	−	2505.44i	0.0514674	−	0.124253i
$143$	−7742.57	+	18692.2i	−0.378628	+	0.914089i
$144$	−1913.29	+	4818.01i	−0.0922689	+	0.232350i
$145$	34331.7	−	34331.7i	1.63290	−	1.63290i
$146$	−3579.63	+	8642.00i	−0.167932	+	0.405423i
$147$	−9641.54	−	1844.33i	−0.446182	−	0.0853503i
$148$	8918.13	−	3694.01i	0.407146	−	0.168645i
$149$	30407.0			1.36962			0.684811	−	0.728721i	$-0.259885\pi$
$149$	30407.0			1.36962			0.684811	+	0.728721i	$0.259885\pi$
$150$	12416.8	+	18290.9i	0.551859	+	0.812930i
$151$	−18867.6	−	18867.6i	−0.827490	−	0.827490i	0.159679	−	0.987169i	$-0.448954\pi$
$151$	−18867.6	−	18867.6i	−0.827490	−	0.827490i	−0.987169	+	0.159679i	$0.948954\pi$
$152$			14326.1i			0.620070i
$153$	−23257.8	+	2656.03i	−0.993542	+	0.113462i
$154$	13795.7			0.581704
$155$	−40911.2	+	40911.2i	−1.70286	+	1.70286i
$156$	8944.62	−	6072.07i	0.367547	−	0.249510i
$157$			13047.9i			0.529349i	0.964338	+	0.264675i	$0.0852645\pi$
$157$			13047.9i			0.529349i	−0.964338	+	0.264675i	$0.914735\pi$
$158$	4363.37	+	10534.1i	0.174787	+	0.421972i
$159$	−5802.57	+	30333.8i	−0.229523	+	1.19987i
$160$	−6463.04	−	2677.08i	−0.252463	−	0.104573i
$161$	3163.20	+	3163.20i	0.122032	+	0.122032i
$162$	−18549.3	+	544.950i	−0.706802	+	0.0207647i
$163$	−11543.3	−	4781.38i	−0.434464	−	0.179961i	0.154723	−	0.987958i	$-0.450552\pi$
$163$	−11543.3	−	4781.38i	−0.434464	−	0.179961i	−0.589186	+	0.807997i	$0.700552\pi$
$164$	−19168.3	−	7939.77i	−0.712683	−	0.295203i
$165$	26322.5	+	38775.1i	0.966851	+	1.42424i
$166$		−	18457.2i		−	0.669808i
$167$	−21541.5	+	8922.77i	−0.772400	+	0.319939i	−0.733844	−	0.679318i	$-0.762276\pi$
$167$	−21541.5	+	8922.77i	−0.772400	+	0.319939i	−0.0385561	+	0.999256i	$0.512276\pi$
$168$	−6159.17	−	4050.33i	−0.218224	−	0.143506i
$169$	6015.40			0.210616
$170$	−3122.91	−	31434.5i	−0.108059	−	1.08770i
$171$	−47086.5	+	20319.0i	−1.61029	+	0.694880i
$172$	4595.52	+	4595.52i	0.155338	+	0.155338i
$173$	18564.5	−	7689.69i	0.620286	−	0.256931i	−0.0503333	−	0.998732i	$-0.516028\pi$
$173$	18564.5	−	7689.69i	0.620286	−	0.256931i	0.670619	+	0.741802i	$0.266028\pi$
$174$	−31320.5	+	6469.46i	−1.03450	+	0.213683i
$175$	−29043.5	+	12030.2i	−0.948359	+	0.392823i
$176$	−7967.28	−	3300.15i	−0.257208	−	0.106539i
$177$	32432.7	+	6204.07i	1.03523	+	0.198030i
$178$	−16225.7	+	16225.7i	−0.512111	+	0.512111i
$179$	−24963.3	−	24963.3i	−0.779104	−	0.779104i	0.200575	−	0.979678i	$-0.435719\pi$
$179$	−24963.3	−	24963.3i	−0.779104	−	0.779104i	−0.979678	+	0.200575i	$0.935719\pi$
$180$	−367.731	−	25039.5i	−0.0113497	−	0.772823i
$181$	−15308.0	+	36956.7i	−0.467262	+	1.12807i	0.498092	+	0.867124i	$0.334034\pi$
$181$	−15308.0	+	36956.7i	−0.467262	+	1.12807i	−0.965354	+	0.260945i	$0.915966\pi$
$182$	5883.01	+	14202.9i	0.177606	+	0.428778i
$183$	23430.8	−	4839.80i	0.699658	−	0.144519i
$184$	−1070.12	−	2583.50i	−0.0316080	−	0.0763084i
$185$	−32972.4	+	32972.4i	−0.963400	+	0.963400i
$186$	37322.9	−	7709.29i	1.07882	−	0.222838i
$187$	−3849.75	−	38750.7i	−0.110090	−	1.10814i
$188$			21470.5i			0.607474i
$189$	4576.80	−	25988.4i	0.128126	−	0.727538i
$190$	−26483.4	−	63936.7i	−0.733613	−	1.77110i
$191$	−5156.02			−0.141334			−0.0706672	−	0.997500i	$-0.522513\pi$
$191$	−5156.02			−0.141334			−0.0706672	+	0.997500i	$0.522513\pi$
$192$	2588.13	+	3812.51i	0.0702075	+	0.103421i
$193$	21301.2	−	51425.7i	0.571861	−	1.38059i	−0.328108	−	0.944640i	$-0.606411\pi$
$193$	21301.2	−	51425.7i	0.571861	−	1.38059i	0.899969	−	0.435954i	$-0.143589\pi$
$194$	556.363	−	1343.18i	0.0147827	−	0.0356887i
$195$	−28694.5	+	43634.5i	−0.754622	+	1.14752i
$196$	−6169.97	+	6169.97i	−0.160609	+	0.160609i
$197$	−14079.1	+	33990.0i	−0.362780	+	0.875828i	0.632111	+	0.774877i	$0.282188\pi$
$197$	−14079.1	+	33990.0i	−0.362780	+	0.875828i	−0.994891	+	0.100951i	$0.967812\pi$
$198$	−453.318	−	30867.2i	−0.0115630	−	0.787349i
$199$	−38206.0	+	15825.4i	−0.964773	+	0.399622i	−0.808764	−	0.588133i	$-0.799863\pi$
$199$	−38206.0	+	15825.4i	−0.964773	+	0.399622i	−0.156009	+	0.987756i	$0.549863\pi$
$200$	19651.0			0.491275
$201$	−25592.0	+	17373.2i	−0.633450	+	0.430019i
$202$	−9958.71	−	9958.71i	−0.244062	−	0.244062i
$203$		−	45477.6i		−	1.10359i
$204$	−9658.21	+	18430.7i	−0.232079	+	0.442876i
$205$	100225.			2.38488
$206$	−19953.8	+	19953.8i	−0.470208	+	0.470208i
$207$	6973.58	−	7181.46i	0.162748	−	0.167599i
$208$		−	9609.72i		−	0.222118i
$209$	−32647.3	−	78817.6i	−0.747403	−	1.80439i
$210$	34975.5	+	6690.48i	0.793096	+	0.151712i
$211$	41136.1	+	17039.1i	0.923972	+	0.382722i	0.793388	−	0.608716i	$-0.208315\pi$
$211$	41136.1	+	17039.1i	0.923972	+	0.382722i	0.130583	+	0.991437i	$0.458315\pi$
$212$	19411.7	+	19411.7i	0.431909	+	0.431909i
$213$	4741.27	−	7209.86i	0.104505	−	0.158916i
$214$	−17302.5	−	7166.92i	−0.377816	−	0.156497i
$215$	−29004.9	−	12014.2i	−0.627473	−	0.259908i
$216$	−8860.03	+	13913.9i	−0.189901	+	0.298224i
$217$			54193.1i			1.15087i
$218$	14968.9	−	6200.32i	0.314975	−	0.130467i
$219$	−16354.0	+	24868.9i	−0.340986	+	0.518523i
$220$	41658.3			0.860708
$221$	38252.7	−	20488.2i	0.783208	−	0.419487i
$222$	30080.4	−	6213.30i	0.610348	−	0.126071i
$223$	34964.3	+	34964.3i	0.703097	+	0.703097i	0.965074	−	0.261977i	$-0.0843745\pi$
$223$	34964.3	+	34964.3i	0.703097	+	0.703097i	−0.261977	+	0.965074i	$0.584375\pi$
$224$	−6053.75	+	2507.55i	−0.120650	+	0.0499750i
$225$	27871.4	+	64588.2i	0.550546	+	1.27582i
$226$	46087.0	−	19089.9i	0.902322	−	0.373754i
$227$	56421.4	+	23370.5i	1.09495	+	0.453541i	0.855729	−	0.517425i	$-0.173109\pi$
$227$	56421.4	+	23370.5i	1.09495	+	0.453541i	0.239217	+	0.970966i	$0.423109\pi$
$228$	−8564.75	+	44773.6i	−0.164757	+	0.861295i
$229$	−5351.96	+	5351.96i	−0.102057	+	0.102057i	−0.756292	−	0.654235i	$-0.772991\pi$
$229$	−5351.96	+	5351.96i	−0.102057	+	0.102057i	0.654235	+	0.756292i	$0.272991\pi$
$230$	9551.78	+	9551.78i	0.180563	+	0.180563i
$231$	43115.9	+	8247.65i	0.808004	+	0.154563i
$232$	−10879.0	+	26264.2i	−0.202121	+	0.487964i
$233$	14363.5	+	34676.6i	0.264575	+	0.638741i	0.999211	−	0.0397206i	$-0.0126468\pi$
$233$	14363.5	+	34676.6i	0.264575	+	0.638741i	−0.734635	+	0.678462i	$0.762647\pi$
$234$	31584.9	−	13629.7i	0.576830	−	0.248916i
$235$	−39690.8	−	95822.0i	−0.718710	−	1.73512i
$236$	20754.9	−	20754.9i	0.372645	−	0.372645i
$237$	7339.17	+	35531.0i	0.130662	+	0.632573i
$238$	−22888.3	−	18751.5i	−0.404073	−	0.331042i
$239$		−	30155.8i		−	0.527928i	−0.964533	−	0.263964i	$-0.914970\pi$
$239$		−	30155.8i		−	0.527928i	0.964533	−	0.263964i	$-0.0850300\pi$
$240$	−18598.6	−	12230.6i	−0.322892	−	0.212337i
$241$	29531.5	+	71295.3i	0.508454	+	1.22752i	0.944774	+	0.327724i	$0.106282\pi$
$241$	29531.5	+	71295.3i	0.508454	+	1.22752i	−0.436320	+	0.899792i	$0.643718\pi$
$242$	9942.97			0.169780
$243$	−58298.2	−	9386.42i	−0.987285	−	0.158960i
$244$	8138.56	−	19648.2i	0.136700	−	0.330023i
$245$	16130.4	−	38942.2i	0.268728	−	0.648766i
$246$	−55160.2	−	36273.9i	−0.911499	−	0.599410i
$247$	67221.6	−	67221.6i	1.10183	−	1.10183i
$248$	12963.9	−	31297.6i	0.210781	−	0.508870i
$249$	11034.5	−	57684.6i	0.177973	−	0.930382i
$250$	−24585.7	+	10183.7i	−0.393372	+	0.162940i
$251$	88350.7			1.40237			0.701185	−	0.712979i	$-0.252655\pi$
$251$	88350.7			1.40237			0.701185	+	0.712979i	$0.252655\pi$
$252$	−16827.9	−	16340.8i	−0.264989	−	0.257318i
$253$	11774.9	+	11774.9i	0.183957	+	0.183957i
$254$		−	22559.8i		−	0.349678i
$255$	9032.80	−	100110.i	0.138913	−	1.53956i
$256$	4096.00			0.0625000
$257$	30073.7	−	30073.7i	0.455324	−	0.455324i	−0.441793	−	0.897117i	$-0.645658\pi$
$257$	30073.7	−	30073.7i	0.455324	−	0.455324i	0.897117	+	0.441793i	$0.145658\pi$
$258$	11615.0	+	17109.8i	0.174494	+	0.257043i
$259$			43677.0i			0.651108i
$260$	17764.7	+	42887.7i	0.262791	+	0.634434i
$261$	−101754.	+	1494.37i	−1.49373	+	0.0219369i
$262$	503.855	+	208.703i	0.00734011	+	0.00304037i
$263$	40724.6	+	40724.6i	0.588769	+	0.588769i	0.937298	−	0.348529i	$-0.113319\pi$
$263$	40724.6	+	40724.6i	0.588769	+	0.588769i	−0.348529	+	0.937298i	$0.613319\pi$
$264$	−22927.3	−	15077.2i	−0.328961	−	0.216328i
$265$	−122518.	−	50748.7i	−1.74465	−	0.722659i
$266$	−59887.7	−	24806.3i	−0.846398	−	0.350589i
$267$	−60410.9	+	41010.1i	−0.847409	+	0.575265i
$268$			27495.0i			0.382810i
$269$	41341.6	−	17124.3i	0.571325	−	0.236650i	−0.0782686	−	0.996932i	$-0.524939\pi$
$269$	41341.6	−	17124.3i	0.571325	−	0.236650i	0.649593	+	0.760282i	$0.274939\pi$
$270$	13820.4	−	78476.0i	0.189580	−	1.07649i
$271$	−113469.			−1.54504			−0.772518	−	0.634993i	$-0.781003\pi$
$271$	−113469.			−1.54504			−0.772518	+	0.634993i	$0.781003\pi$
$272$	8732.77	+	16304.6i	0.118036	+	0.220380i
$273$	9895.20	+	47905.5i	0.132770	+	0.642776i
$274$	−43508.1	−	43508.1i	−0.579520	−	0.579520i
$275$	−108113.	+	44782.0i	−1.42960	+	0.592159i
$276$	−1799.94	−	8714.00i	−0.0236286	−	0.114393i
$277$	31688.5	−	13125.8i	0.412993	−	0.171067i	−0.166506	−	0.986041i	$-0.553248\pi$
$277$	31688.5	−	13125.8i	0.412993	−	0.171067i	0.579499	+	0.814973i	$0.303248\pi$
$278$	3092.64	+	1281.01i	0.0400166	+	0.0165754i
$279$	121255.	−	1780.75i	1.55772	−	0.0228768i
$280$	22382.1	−	22382.1i	0.285486	−	0.285486i
$281$	86430.8	+	86430.8i	1.09460	+	1.09460i	0.995030	+	0.0995708i	$0.0317470\pi$
$281$	86430.8	+	86430.8i	1.09460	+	1.09460i	0.0995708	+	0.995030i	$0.468253\pi$
$282$	−12836.0	+	67102.2i	−0.161410	+	0.843798i
$283$	−53178.6	+	128384.i	−0.663993	+	1.60302i	0.127496	+	0.991839i	$0.459306\pi$
$283$	−53178.6	+	128384.i	−0.663993	+	1.60302i	−0.791489	+	0.611183i	$0.790694\pi$
$284$	−2935.31	−	7086.46i	−0.0363929	−	0.0878603i
$285$	−44545.0	−	215655.i	−0.548415	−	2.65503i
$286$	21899.3	+	52869.6i	0.267731	+	0.646359i
$287$	66381.6	−	66381.6i	0.805905	−	0.805905i
$288$	5809.44	+	13462.6i	0.0700405	+	0.162309i
$289$	−46284.1	+	69523.7i	−0.554161	+	0.832410i
$290$		−	137327.i		−	1.63290i
$291$	2541.82	−	3865.24i	0.0300164	−	0.0456447i
$292$	10124.7	+	24443.3i	0.118746	+	0.286677i
$293$	−53715.6			−0.625699			−0.312849	−	0.949803i	$-0.601284\pi$
$293$	−53715.6			−0.625699			−0.312849	+	0.949803i	$0.601284\pi$
$294$	−22971.8	+	15594.4i	−0.265766	+	0.180416i
$295$	−54260.2	+	130996.i	−0.623501	+	1.50526i
$296$	10448.2	−	25224.3i	0.119250	−	0.287896i
$297$	17037.0	−	96740.8i	0.193143	−	1.09672i
$298$	60813.9	−	60813.9i	0.684811	−	0.684811i
$299$	−7101.14	+	17143.7i	−0.0794302	+	0.191762i
$300$	61415.5	+	11748.2i	0.682394	+	0.130535i
$301$	−27168.1	+	11253.4i	−0.299865	+	0.124208i
$302$	−75470.4			−0.827490
$303$	−25170.4	−	37077.8i	−0.274160	−	0.403858i
$304$	28652.2	+	28652.2i	0.310035	+	0.310035i
$305$			102734.i			1.10437i
$306$	−41203.6	+	51827.7i	−0.440040	+	0.553502i
$307$	90785.3			0.963249			0.481625	−	0.876378i	$-0.340047\pi$
$307$	90785.3			0.963249			0.481625	+	0.876378i	$0.340047\pi$
$308$	27591.4	−	27591.4i	0.290852	−	0.290852i
$309$	−74291.0	+	50432.6i	−0.778071	+	0.528195i
$310$			163645.i			1.70286i
$311$	537.647	+	1298.00i	0.00555874	+	0.0134200i	0.926635	−	0.375963i	$-0.122688\pi$
$311$	537.647	+	1298.00i	0.00555874	+	0.0134200i	−0.921076	+	0.389383i	$0.872688\pi$
$312$	5745.10	−	30033.4i	0.0590185	−	0.308528i
$313$	108459.	+	44925.1i	1.10707	+	0.458564i	0.859928	−	0.510415i	$-0.170508\pi$
$313$	108459.	+	44925.1i	1.10707	+	0.458564i	0.247143	+	0.968979i	$0.420508\pi$
$314$	26095.9	+	26095.9i	0.264675	+	0.264675i
$315$	105310.	+	41819.7i	1.06132	+	0.421464i
$316$	29795.0	+	12341.5i	0.298379	+	0.123593i
$317$	−120994.	−	50117.3i	−1.20405	−	0.498734i	−0.311745	−	0.950166i	$-0.600914\pi$
$317$	−120994.	−	50117.3i	−1.20405	−	0.498734i	−0.892306	+	0.451432i	$0.850914\pi$
$318$	49062.5	+	72272.8i	0.485172	+	0.714695i
$319$		−	169289.i		−	1.66359i
$320$	−18280.2	+	7571.92i	−0.178518	+	0.0739446i
$321$	−49791.0	−	32743.0i	−0.483215	−	0.317767i
$322$	12652.8			0.122032
$323$	−52966.4	+	175141.i	−0.507686	+	1.67874i
$324$	−36008.7	+	38188.5i	−0.343019	+	0.363783i
$325$	−92207.3	−	92207.3i	−0.872968	−	0.872968i
$326$	−32649.3	+	13523.8i	−0.307212	+	0.127251i
$327$	50489.3	−	10428.9i	0.472176	−	0.0975311i
$328$	−54216.2	+	22457.1i	−0.503943	+	0.208740i
$329$	−89753.8	−	37177.2i	−0.829203	−	0.343467i
$330$	130195.	+	24905.1i	1.19555	+	0.228697i
$331$	103811.	−	103811.i	0.947521	−	0.947521i	−0.0511687	−	0.998690i	$-0.516295\pi$
$331$	103811.	−	103811.i	0.947521	−	0.947521i	0.998690	+	0.0511687i	$0.0162946\pi$
$332$	−36914.5	−	36914.5i	−0.334904	−	0.334904i
$333$	97725.2	−	1435.20i	0.881288	−	0.0129426i
$334$	−25237.4	+	60928.5i	−0.226231	+	0.546170i
$335$	−50827.6	−	122709.i	−0.452908	−	1.09342i
$336$	−20419.0	+	4217.68i	−0.180865	+	0.0373590i
$337$	−60019.4	−	144900.i	−0.528484	−	1.27587i	−0.932516	−	0.361128i	$-0.882392\pi$
$337$	−60019.4	−	144900.i	−0.528484	−	1.27587i	0.404033	−	0.914745i	$-0.367608\pi$
$338$	12030.8	−	12030.8i	0.105308	−	0.105308i
$339$	155449.	−	32109.0i	1.35266	−	0.279401i
$340$	−69114.9	−	56623.2i	−0.597879	−	0.489820i
$341$			201732.i			1.73487i
$342$	−53535.1	+	134811.i	−0.457705	+	1.15259i
$343$	−48368.4	−	116772.i	−0.411125	−	0.992543i
$344$	18382.1			0.155338
$345$	24141.9	+	35562.8i	0.202830	+	0.298784i
$346$	21749.7	−	52508.5i	0.181678	−	0.438609i
$347$	−8457.76	+	20418.8i	−0.0702419	+	0.169579i	−0.955101	−	0.296279i	$-0.904254\pi$
$347$	−8457.76	+	20418.8i	−0.0702419	+	0.169579i	0.884860	+	0.465858i	$0.154254\pi$
$348$	−49702.1	+	75579.9i	−0.410408	+	0.624091i
$349$	−63304.9	+	63304.9i	−0.519740	+	0.519740i	−0.917493	−	0.397752i	$-0.869790\pi$
$349$	−63304.9	+	63304.9i	−0.519740	+	0.519740i	0.397752	+	0.917493i	$0.369790\pi$
$350$	−34026.6	+	82147.4i	−0.277768	+	0.670591i
$351$	106861.	−	23714.2i	0.867372	−	0.192484i
$352$	−22534.9	+	9334.24i	−0.181874	+	0.0753345i
$353$	79496.6			0.637969			0.318984	−	0.947760i	$-0.396658\pi$
$353$	79496.6			0.637969			0.318984	+	0.947760i	$0.396658\pi$
$354$	77273.6	−	52457.3i	0.616630	−	0.418600i
$355$	26200.3	+	26200.3i	0.207897	+	0.207897i
$356$			64902.9i			0.512111i
$357$	−60322.7	−	72288.1i	−0.473309	−	0.567192i
$358$	−99853.1			−0.779104
$359$	−42835.1	+	42835.1i	−0.332362	+	0.332362i	−0.853483	−	0.521121i	$-0.825514\pi$
$359$	−42835.1	+	42835.1i	−0.332362	+	0.332362i	0.521121	+	0.853483i	$0.325514\pi$
$360$	−50814.4	−	49343.4i	−0.392086	−	0.380736i
$361$			270533.i			2.07590i
$362$	43297.5	+	104529.i	0.330404	+	0.797666i
$363$	31074.9	+	5944.33i	0.235829	+	0.0451117i
$364$	40171.7	+	16639.7i	0.303192	+	0.125586i
$365$	−90372.3	−	90372.3i	−0.678344	−	0.678344i
$366$	37182.1	−	56541.3i	0.277569	−	0.422088i
$367$	3153.46	+	1306.21i	0.0234129	+	0.00969794i	0.394359	−	0.918956i	$-0.370967\pi$
$367$	3153.46	+	1306.21i	0.0234129	+	0.00969794i	−0.370946	+	0.928654i	$0.620967\pi$
$368$	−7307.23	−	3026.76i	−0.0539582	−	0.0223502i
$369$	−150707.	−	146344.i	−1.10683	−	1.07479i
$370$			131889.i			0.963400i
$371$	−114759.	+	47534.9i	−0.833759	+	0.345354i
$372$	59227.2	−	90064.3i	0.427991	−	0.650829i
$373$	160603.			1.15434			0.577171	−	0.816623i	$-0.304156\pi$
$373$	160603.			1.15434			0.577171	+	0.816623i	$0.304156\pi$
$374$	−85200.9	−	69801.9i	−0.609118	−	0.499027i
$375$	−82926.4	+	17129.0i	−0.589699	+	0.121806i
$376$	42941.1	+	42941.1i	0.303737	+	0.303737i
$377$	174285.	−	72191.2i	1.22624	−	0.507927i
$378$	−42823.2	−	61130.4i	−0.299706	−	0.427832i
$379$	−125356.	+	51924.2i	−0.872704	+	0.361486i	−0.773663	−	0.633597i	$-0.781578\pi$
$379$	−125356.	+	51924.2i	−0.872704	+	0.361486i	−0.0990415	+	0.995083i	$0.531578\pi$
$380$	−180840.	−	74906.5i	−1.25236	−	0.518743i
$381$	13487.2	−	70506.5i	0.0929121	−	0.485713i
$382$	−10312.0	+	10312.0i	−0.0706672	+	0.0706672i
$383$	48427.8	+	48427.8i	0.330139	+	0.330139i	0.852639	−	0.522500i	$-0.175001\pi$
$383$	48427.8	+	48427.8i	0.330139	+	0.330139i	−0.522500	+	0.852639i	$0.675001\pi$
$384$	12801.3	+	2448.76i	0.0868143	+	0.0166067i
$385$	−72133.2	+	174145.i	−0.486647	+	1.17487i
$386$	−60249.0	−	145454.i	−0.404367	−	0.976227i
$387$	26071.7	+	60417.6i	0.174079	+	0.403405i
$388$	−1573.63	−	3799.08i	−0.0104530	−	0.0252357i
$389$	196604.	−	196604.i	1.29925	−	1.29925i	0.370367	−	0.928886i	$-0.379232\pi$
$389$	196604.	−	196604.i	1.29925	−	1.29925i	0.928886	−	0.370367i	$-0.120768\pi$
$390$	29880.1	+	144658.i	0.196450	+	0.951072i
$391$	−3530.83	−	35540.4i	−0.0230953	−	0.232471i
$392$			24679.9i			0.160609i
$393$	1449.93	+	953.489i	0.00938777	+	0.00617349i
$394$	39821.8	+	96138.3i	0.256524	+	0.619304i
$395$	−155788.			−0.998482
$396$	−62641.1	−	60827.8i	−0.399456	−	0.387893i
$397$	68526.6	−	165438.i	0.434789	−	1.04967i	−0.542934	−	0.839775i	$-0.682687\pi$
$397$	68526.6	−	165438.i	0.434789	−	1.04967i	0.977723	−	0.209898i	$-0.0673132\pi$
$398$	−44761.1	+	108063.i	−0.282575	+	0.682198i
$399$	−172338.	−	113331.i	−1.08252	−	0.711873i
$400$	39302.0	−	39302.0i	0.245637	−	0.245637i
$401$	−19743.9	+	47666.0i	−0.122785	+	0.296429i	−0.973306	−	0.229513i	$-0.926287\pi$
$401$	−19743.9	+	47666.0i	−0.122785	+	0.296429i	0.850521	+	0.525941i	$0.176287\pi$
$402$	−16437.7	+	85930.4i	−0.101716	+	0.531734i
$403$	−207686.	+	86026.2i	−1.27878	+	0.529688i
$404$	−39834.8			−0.244062
$405$	90109.3	−	237000.i	0.549363	−	1.44490i
$406$	−90955.3	−	90955.3i	−0.551793	−	0.551793i
$407$			162586.i			0.981508i
$408$	17545.0	+	56177.9i	0.105398	+	0.337478i
$409$	102575.			0.613189			0.306595	−	0.951840i	$-0.400810\pi$
$409$	102575.			0.613189			0.306595	+	0.951840i	$0.400810\pi$
$410$	200450.	−	200450.i	1.19244	−	1.19244i
$411$	−109965.	−	161987.i	−0.650987	−	0.958953i
$412$			79815.0i			0.470208i
$413$	50824.0	+	122700.i	0.297967	+	0.719357i
$414$	−415.763	−	28310.1i	−0.00242575	−	0.165173i
$415$	232988.	+	96506.8i	1.35281	+	0.560353i
$416$	−19219.4	−	19219.4i	−0.111059	−	0.111059i
$417$	8899.63	+	5852.48i	0.0511799	+	0.0336564i
$418$	−222930.	−	92340.5i	−1.27590	−	0.528494i
$419$	295328.	+	122329.i	1.68220	+	0.696788i	0.999427	−	0.0338463i	$-0.0107757\pi$
$419$	295328.	+	122329.i	1.68220	+	0.696788i	0.682769	+	0.730635i	$0.260776\pi$
$420$	83332.1	−	56570.1i	0.472404	−	0.320692i
$421$		−	272885.i		−	1.53963i	−0.638268	−	0.769814i	$-0.720349\pi$
$421$		−	272885.i		−	1.53963i	0.638268	−	0.769814i	$-0.279651\pi$
$422$	116351.	−	48194.0i	0.653347	−	0.270625i
$423$	−80233.1	+	202041.i	−0.448407	+	1.12917i
$424$	77646.8			0.431909
$425$	240239.	+	72653.6i	1.33004	+	0.402234i
$426$	−4937.17	−	23902.3i	−0.0272056	−	0.131710i
$427$	68043.6	+	68043.6i	0.373191	+	0.373191i
$428$	−48938.8	+	20271.1i	−0.267157	+	0.110660i
$429$	36834.5	+	178326.i	0.200143	+	0.968949i
$430$	−82038.3	+	33981.4i	−0.443690	+	0.183783i
$431$	−43714.1	−	18107.0i	−0.235325	−	0.0974746i	0.261905	−	0.965094i	$-0.415649\pi$
$431$	−43714.1	−	18107.0i	−0.235325	−	0.0974746i	−0.497230	+	0.867619i	$0.665649\pi$
$432$	10107.8	+	45547.9i	0.0541614	+	0.244063i
$433$	−136181.	+	136181.i	−0.726343	+	0.726343i	−0.969889	−	0.243546i	$-0.921689\pi$
$433$	−136181.	+	136181.i	−0.726343	+	0.726343i	0.243546	+	0.969889i	$0.421689\pi$
$434$	108386.	+	108386.i	0.575433	+	0.575433i
$435$	82099.8	−	429189.i	0.433874	−	2.26814i
$436$	17537.1	−	42338.4i	0.0922542	−	0.222721i
$437$	−29942.7	−	72288.0i	−0.156793	−	0.378533i
$438$	17029.7	+	82445.8i	0.0887687	+	0.429755i
$439$	71781.3	+	173295.i	0.372462	+	0.899203i	0.993332	+	0.115289i	$0.0367796\pi$
$439$	71781.3	+	173295.i	0.372462	+	0.899203i	−0.620870	+	0.783914i	$0.713220\pi$
$440$	83316.5	−	83316.5i	0.430354	−	0.430354i
$441$	−81116.9	+	35004.0i	−0.417094	+	0.179987i
$442$	35529.0	−	117482.i	0.181861	−	0.601347i
$443$		−	65109.8i		−	0.331772i	−0.986145	−	0.165886i	$-0.946952\pi$
$443$		−	65109.8i		−	0.331772i	0.986145	−	0.165886i	$-0.0530483\pi$
$444$	47734.1	−	72587.3i	0.242138	−	0.368209i
$445$	−119981.	−	289659.i	−0.605886	−	1.46274i
$446$	139857.			0.703097
$447$	226420.	−	153705.i	1.13318	−	0.769262i
$448$	−7092.41	+	17122.6i	−0.0353377	+	0.0853127i
$449$	88717.3	−	214183.i	0.440064	−	1.06241i	−0.535862	−	0.844306i	$-0.680013\pi$
$449$	88717.3	−	214183.i	0.440064	−	1.06241i	0.975926	−	0.218103i	$-0.0699867\pi$
$450$	184919.	+	73433.6i	0.913181	+	0.362635i
$451$	247103.	−	247103.i	1.21486	−	1.21486i
$452$	53994.3	−	130354.i	0.264284	−	0.638038i
$453$	−235869.	−	45119.4i	−1.14941	−	0.219871i
$454$	159584.	−	66101.8i	0.774243	−	0.320702i
$455$	−210045.			−1.01459
$456$	72417.6	+	106677.i	0.348269	+	0.513026i
$457$	80749.8	+	80749.8i	0.386642	+	0.386642i	0.873488	−	0.486846i	$-0.161853\pi$
$457$	80749.8	+	80749.8i	0.386642	+	0.386642i	−0.486846	+	0.873488i	$0.661853\pi$
$458$			21407.8i			0.102057i
$459$	−159759.	+	137345.i	−0.758298	+	0.651908i
$460$	38207.1			0.180563
$461$	−61867.1	+	61867.1i	−0.291110	+	0.291110i	−0.837519	−	0.546408i	$-0.815995\pi$
$461$	−61867.1	+	61867.1i	−0.291110	+	0.291110i	0.546408	+	0.837519i	$0.315995\pi$
$462$	102727.	−	69736.5i	0.481284	−	0.326720i
$463$			4892.43i			0.0228225i	0.999935	+	0.0114112i	$0.00363239\pi$
$463$			4892.43i			0.0228225i	−0.999935	+	0.0114112i	$0.996368\pi$
$464$	30770.4	+	74286.3i	0.142921	+	0.345043i
$465$	−97833.7	+	511441.i	−0.452462	+	2.36532i
$466$	98080.3	+	40626.2i	0.451658	+	0.187083i
$467$	−205407.	−	205407.i	−0.941851	−	0.941851i	0.0565485	−	0.998400i	$-0.481990\pi$
$467$	−205407.	−	205407.i	−0.941851	−	0.941851i	−0.998400	+	0.0565485i	$0.981990\pi$
$468$	35910.5	−	90429.1i	0.163957	−	0.412873i
$469$	−114938.	−	47608.8i	−0.522537	−	0.216442i
$470$	−271025.	−	112262.i	−1.22691	−	0.508205i
$471$	65956.5	+	97158.9i	0.297314	+	0.437967i
$472$		−	83019.5i		−	0.372645i
$473$	−101132.	+	41890.3i	−0.452030	+	0.187237i
$474$	85740.4	+	56383.7i	0.381618	+	0.250956i
$475$	549848.			2.43700
$476$	−83279.8	+	8273.57i	−0.367558	+	0.0365156i
$477$	110128.	+	255207.i	0.484018	+	1.12165i
$478$	−60311.6	−	60311.6i	−0.263964	−	0.263964i
$479$	314561.	−	130296.i	1.37099	−	0.567883i	0.428934	−	0.903336i	$-0.358889\pi$
$479$	314561.	−	130296.i	1.37099	−	0.567883i	0.942057	+	0.335453i	$0.108889\pi$
$480$	−61658.3	+	12735.9i	−0.267614	+	0.0552775i
$481$	−167384.	+	69332.8i	−0.723476	+	0.299674i
$482$	201654.	+	83527.7i	0.867984	+	0.359531i
$483$	39544.0	+	7564.39i	0.169506	+	0.0324250i
$484$	19885.9	−	19885.9i	0.0848898	−	0.0848898i
$485$	14046.1	+	14046.1i	0.0597134	+	0.0597134i
$486$	−135369.	+	97823.5i	−0.573122	+	0.414163i
$487$	−135271.	+	326573.i	−0.570357	+	1.37696i	0.330894	+	0.943668i	$0.392650\pi$
$487$	−135271.	+	326573.i	−0.570357	+	1.37696i	−0.901252	+	0.433296i	$0.857350\pi$
$488$	−23019.3	−	55573.6i	−0.0966614	−	0.233361i
$489$	−110124.	+	22746.9i	−0.460538	+	0.0951272i
$490$	−45623.6	−	110145.i	−0.190019	−	0.458747i
$491$	−290903.	+	290903.i	−1.20666	+	1.20666i	−0.234557	+	0.972102i	$0.575364\pi$
$491$	−290903.	+	290903.i	−1.20666	+	1.20666i	−0.972102	+	0.234557i	$0.924636\pi$
$492$	−182868.	+	37772.7i	−0.755454	+	0.156044i
$493$	−230103.	+	280866.i	−0.946733	+	1.15559i
$494$		−	268886.i		−	1.10183i
$495$	392011.	+	155672.i	1.59988	+	0.635332i
$496$	−36667.4	−	88522.8i	−0.149045	−	0.359826i
$497$	34706.3			0.140506
$498$	−93300.2	−	137438.i	−0.376205	−	0.554178i
$499$	20653.3	−	49861.5i	0.0829447	−	0.200246i	−0.876966	−	0.480553i	$-0.840436\pi$
$499$	20653.3	−	49861.5i	0.0829447	−	0.200246i	0.959911	+	0.280307i	$0.0904361\pi$
$500$	−28804.0	+	69538.9i	−0.115216	+	0.278156i
$501$	−115300.	+	175333.i	−0.459362	+	0.698534i
$502$	176701.	−	176701.i	0.701185	−	0.701185i
$503$	−131543.	+	317573.i	−0.519914	+	1.25518i	0.418041	+	0.908428i	$0.362717\pi$
$503$	−131543.	+	317573.i	−0.519914	+	1.25518i	−0.937955	+	0.346756i	$0.887283\pi$
$504$	−66337.2	+	974.232i	−0.261154	+	0.00383532i
$505$	177781.	−	73639.3i	0.697112	−	0.288753i
$506$	47099.6			0.183957
$507$	44792.5	−	30407.5i	0.174257	−	0.118295i
$508$	−45119.7	−	45119.7i	−0.174839	−	0.174839i
$509$		−	420292.i		−	1.62224i	−0.584878	−	0.811121i	$-0.698858\pi$
$509$		−	420292.i		−	1.62224i	0.584878	−	0.811121i	$-0.301142\pi$
$510$	−182154.	−	218285.i	−0.700322	−	0.839235i
$511$	−119712.			−0.458455
$512$	8192.00	−	8192.00i	0.0312500	−	0.0312500i
$513$	−247910.	+	389321.i	−0.942017	+	1.47936i
$514$		−	120295.i		−	0.455324i
$515$	−147547.	−	356211.i	−0.556310	−	1.34305i
$516$	57449.8	+	10989.6i	0.215769	+	0.0412745i
$517$	−334105.	−	138391.i	−1.24998	−	0.517757i
$518$	87353.9	+	87353.9i	0.325554	+	0.325554i
$519$	99366.5	−	151103.i	0.368897	−	0.560967i
$520$	121305.	+	50246.1i	0.448612	+	0.185821i
$521$	314223.	+	130156.i	1.15761	+	0.479498i	0.877079	−	0.480346i	$-0.159489\pi$
$521$	314223.	+	130156.i	1.15761	+	0.479498i	0.280533	+	0.959844i	$0.409489\pi$
$522$	−200519.	+	206497.i	−0.735894	+	0.757831i
$523$		−	306864.i		−	1.12187i	−0.827860	−	0.560935i	$-0.810442\pi$
$523$		−	306864.i		−	1.12187i	0.827860	−	0.560935i	$-0.189558\pi$
$524$	1425.12	−	590.302i	0.00519024	−	0.00214987i
$525$	−155455.	+	236394.i	−0.564009	+	0.857665i
$526$	162898.			0.588769
$527$	274200.	−	334692.i	0.987294	−	1.20510i
$528$	−76008.9	+	15700.1i	−0.272644	+	0.0563165i
$529$	−187078.	−	187078.i	−0.668516	−	0.668516i
$530$	−346534.	+	143539.i	−1.23366	+	0.510997i
$531$	272865.	−	117748.i	0.967742	−	0.417604i
$532$	−169388.	+	70162.8i	−0.598493	+	0.247904i
$533$	359770.	+	149022.i	1.26640	+	0.524559i
$534$	−38801.7	+	202842.i	−0.136072	+	0.711337i
$535$	180938.	−	180938.i	0.632153	−	0.632153i
$536$	54989.9	+	54989.9i	0.191405	+	0.191405i
$537$	−312072.	−	59696.4i	−1.08220	−	0.207014i
$538$	48434.7	−	116932.i	0.167337	−	0.403988i
$539$	−56242.2	−	135781.i	−0.193591	−	0.467369i
$540$	−129311.	−	184593.i	−0.443454	−	0.633034i
$541$	−194320.	−	469130.i	−0.663931	−	1.60287i	−0.791589	−	0.611054i	$-0.790746\pi$
$541$	−194320.	−	469130.i	−0.663931	−	1.60287i	0.127658	−	0.991818i	$-0.459254\pi$
$542$	−226938.	+	226938.i	−0.772518	+	0.772518i
$543$	72826.1	+	352572.i	0.246995	+	1.19577i
$544$	50074.8	+	15143.7i	0.169208	+	0.0511723i
$545$			221374.i			0.745303i
$546$	115601.	+	76020.6i	0.387773	+	0.255003i
$547$	86830.8	+	209628.i	0.290201	+	0.700607i	0.999993	−	0.00380432i	$-0.00121095\pi$
$547$	86830.8	+	209628.i	0.290201	+	0.700607i	−0.709792	+	0.704412i	$0.751211\pi$
$548$	−174032.			−0.579520
$549$	150008.	−	154480.i	0.497704	−	0.512540i
$550$	−126663.	+	305791.i	−0.418719	+	1.01088i
$551$	−304401.	+	734890.i	−1.00264	+	2.42058i
$552$	−21027.9	−	13828.1i	−0.0690108	−	0.0453822i
$553$	−103183.	+	103183.i	−0.337409	+	0.337409i
$554$	37125.4	−	89628.8i	0.120963	−	0.292030i
$555$	−78849.1	+	412196.i	−0.255983	+	1.33819i
$556$	8747.31	−	3623.25i	0.0282960	−	0.0117206i
$557$	−61251.2			−0.197426			−0.0987129	−	0.995116i	$-0.531473\pi$
$557$	−61251.2			−0.197426			−0.0987129	+	0.995116i	$0.531473\pi$
$558$	238948.	−	246071.i	0.767422	−	0.790299i
$559$	−86253.3	−	86253.3i	−0.276027	−	0.276027i
$560$		−	89528.4i		−	0.285486i
$561$	−224549.	−	269090.i	−0.713486	−	0.855010i
$562$	345723.			1.09460
$563$	51959.2	−	51959.2i	0.163925	−	0.163925i	−0.620378	−	0.784303i	$-0.713021\pi$
$563$	51959.2	−	51959.2i	0.163925	−	0.163925i	0.784303	+	0.620378i	$0.213021\pi$
$564$	108532.	+	159876.i	0.341194	+	0.502604i
$565$			681577.i			2.13510i
$566$	150412.	+	363126.i	0.469514	+	1.13351i
$567$	−97289.5	−	216653.i	−0.302622	−	0.673905i
$568$	−20043.5	−	8302.30i	−0.0621266	−	0.0257337i
$569$	−203675.	−	203675.i	−0.629091	−	0.629091i	0.318749	−	0.947839i	$-0.396737\pi$
$569$	−203675.	−	203675.i	−0.629091	−	0.629091i	−0.947839	+	0.318749i	$0.896737\pi$
$570$	−520400.	−	342220.i	−1.60172	−	1.05331i
$571$	321821.	+	133303.i	0.987056	+	0.408852i	0.817035	−	0.576588i	$-0.195616\pi$
$571$	321821.	+	133303.i	0.987056	+	0.408852i	0.170021	+	0.985440i	$0.445616\pi$
$572$	149538.	+	61940.5i	0.457045	+	0.189314i
$573$	−38393.3	+	26063.4i	−0.116936	+	0.0793819i
$574$		−	265526.i		−	0.805905i
$575$	−99156.8	+	41072.1i	−0.299907	+	0.124226i
$576$	38544.1	+	15306.3i	0.116175	+	0.0461344i
$577$	175255.			0.526403			0.263201	−	0.964741i	$-0.415222\pi$
$577$	175255.			0.526403			0.263201	+	0.964741i	$0.415222\pi$
$578$	46479.2	+	231616.i	0.139124	+	0.693285i
$579$	−101338.	−	490609.i	−0.302286	−	1.46345i
$580$	−274654.	−	274654.i	−0.816449	−	0.816449i
$581$	218233.	−	90395.2i	0.646501	−	0.267789i
$582$	−2646.84	−	12814.1i	−0.00781415	−	0.0378305i
$583$	−427188.	+	176947.i	−1.25684	+	0.520602i
$584$	69136.0	+	28637.1i	0.202712	+	0.0839659i
$585$	6901.93	+	469965.i	0.0201678	+	1.37326i
$586$	−107431.	+	107431.i	−0.312849	+	0.312849i
$587$	−30034.5	−	30034.5i	−0.0871655	−	0.0871655i	0.662180	−	0.749345i	$-0.269632\pi$
$587$	−30034.5	−	30034.5i	−0.0871655	−	0.0871655i	−0.749345	+	0.662180i	$0.769632\pi$
$588$	−14754.7	+	77132.3i	−0.0426751	+	0.223091i
$589$	362738.	−	875727.i	1.04559	−	2.52428i
$590$	153471.	+	370512.i	0.440882	+	1.06438i
$591$	66980.0	+	324269.i	0.191765	+	0.928391i
$592$	−29552.1	−	71345.0i	−0.0843227	−	0.203573i
$593$	−345205.	+	345205.i	−0.981675	+	0.981675i	−0.999835	−	0.0181605i	$-0.994219\pi$
$593$	−345205.	+	345205.i	−0.981675	+	0.981675i	0.0181605	+	0.999835i	$0.494219\pi$
$594$	−159408.	−	227556.i	−0.451790	−	0.644933i
$595$	356379.	−	190877.i	1.00665	−	0.539162i
$596$		−	243256.i		−	0.684811i
$597$	−204497.	+	310970.i	−0.573770	+	0.872509i
$598$	20085.1	+	48489.6i	0.0561657	+	0.135596i
$599$	−533402.			−1.48662			−0.743311	−	0.668946i	$-0.766746\pi$
$599$	−533402.			−1.48662			−0.743311	+	0.668946i	$0.766746\pi$
$600$	146327.	−	99334.6i	0.406465	−	0.275929i
$601$	−17091.2	+	41261.9i	−0.0473178	+	0.114235i	−0.945771	−	0.324834i	$-0.894692\pi$
$601$	−17091.2	+	41261.9i	−0.0473178	+	0.114235i	0.898453	+	0.439069i	$0.144692\pi$
$602$	−31829.4	+	76843.0i	−0.0878286	+	0.212037i
$603$	−102746.	+	258732.i	−0.282572	+	0.711567i
$604$	−150941.	+	150941.i	−0.413745	+	0.413745i
$605$	−51988.5	+	125511.i	−0.142035	+	0.342904i
$606$	−124496.	−	23815.0i	−0.339009	−	0.0648492i
$607$	−128696.	+	53307.6i	−0.349291	+	0.144681i	−0.550429	−	0.834882i	$-0.685536\pi$
$607$	−128696.	+	53307.6i	−0.349291	+	0.144681i	0.201138	+	0.979563i	$0.435536\pi$
$608$	114609.			0.310035
$609$	−229887.	−	338641.i	−0.619840	−	0.913071i
$610$	205468.	+	205468.i	0.552185	+	0.552185i
$611$		−	402980.i		−	1.07945i
$612$	21248.2	+	186063.i	0.0567309	+	0.496771i
$613$	33190.1			0.0883258			0.0441629	−	0.999024i	$-0.485938\pi$
$613$	33190.1			0.0883258			0.0441629	+	0.999024i	$0.485938\pi$
$614$	181571.	−	181571.i	0.481625	−	0.481625i
$615$	746305.	−	506631.i	1.97318	−	1.33950i
$616$		−	110366.i		−	0.290852i
$617$	−50786.5	−	122610.i	−0.133407	−	0.322073i	0.843033	−	0.537862i	$-0.180768\pi$
$617$	−50786.5	−	122610.i	−0.133407	−	0.322073i	−0.976440	+	0.215789i	$0.930768\pi$
$618$	−47716.8	+	249447.i	−0.124938	+	0.653133i
$619$	256908.	+	106415.i	0.670495	+	0.277728i	0.691847	−	0.722044i	$-0.256797\pi$
$619$	256908.	+	106415.i	0.670495	+	0.277728i	−0.0213522	+	0.999772i	$0.506797\pi$
$620$	327289.	+	327289.i	0.851429	+	0.851429i
$621$	15625.6	−	88726.4i	0.0405184	−	0.230075i
$622$	3671.28	+	1520.70i	0.00948937	+	0.00393062i
$623$	−271315.	−	112382.i	−0.699033	−	0.289549i
$624$	−48576.6	−	71557.0i	−0.124755	−	0.183774i
$625$			179191.i			0.458728i
$626$	306767.	−	127067.i	0.782818	−	0.324254i
$627$	−641520.	−	421870.i	−1.63183	−	1.07311i
$628$	104383.			0.264675
$629$	220992.	−	269745.i	0.558566	−	0.681792i
$630$	294259.	−	126980.i	0.741393	−	0.319929i
$631$	−448579.	−	448579.i	−1.12663	−	1.12663i	−0.990722	−	0.135906i	$-0.956606\pi$
$631$	−448579.	−	448579.i	−1.12663	−	1.12663i	−0.135906	−	0.990722i	$-0.543394\pi$
$632$	84272.9	−	34907.0i	0.210986	−	0.0873933i
$633$	392444.	−	81062.0i	0.979424	−	0.202307i
$634$	−342222.	+	141753.i	−0.851393	+	0.352658i
$635$	284776.	+	117958.i	0.706245	+	0.292536i
$636$	242671.	+	46420.6i	0.599934	+	0.114761i
$637$	115804.	−	115804.i	0.285394	−	0.285394i
$638$	−338578.	−	338578.i	−0.831796	−	0.831796i
$639$	−1140.43	−	77653.7i	−0.00279296	−	0.190178i
$640$	−21416.6	+	51704.3i	−0.0522867	+	0.126231i
$641$	−206632.	−	498855.i	−0.502901	−	1.21411i	−0.947897	−	0.318578i	$-0.896795\pi$
$641$	−206632.	−	498855.i	−0.502901	−	1.21411i	0.444996	−	0.895533i	$-0.353205\pi$
$642$	−165068.	+	34095.9i	−0.400491	+	0.0827241i
$643$	169063.	+	408153.i	0.408908	+	0.987191i	0.985426	+	0.170107i	$0.0544112\pi$
$643$	169063.	+	408153.i	0.408908	+	0.987191i	−0.576518	+	0.817085i	$0.695589\pi$
$644$	25305.6	−	25305.6i	0.0610162	−	0.0610162i
$645$	−276711.	+	57156.5i	−0.665131	+	0.137387i
$646$	244349.	+	456214.i	0.585524	+	1.09321i
$647$			529176.i			1.26413i	0.774916	+	0.632065i	$0.217792\pi$
$647$			529176.i			1.26413i	−0.774916	+	0.632065i	$0.782208\pi$
$648$	4359.60	+	148394.i	0.0103824	+	0.353401i
$649$	189190.	+	456746.i	0.449169	+	1.08439i
$650$	−368829.			−0.872968
$651$	273943.	+	403539.i	0.646396	+	0.952190i
$652$	−38251.0	+	92346.1i	−0.0899803	+	0.217232i
$653$	115103.	−	277884.i	0.269936	−	0.651684i	−0.729543	−	0.683934i	$-0.760267\pi$
$653$	115103.	−	277884.i	0.269936	−	0.651684i	0.999480	+	0.0322505i	$0.0102674\pi$
$654$	80120.8	−	121836.i	0.187322	−	0.284853i
$655$	−5268.98	+	5268.98i	−0.0122813	+	0.0122813i
$656$	−63518.2	+	153346.i	−0.147601	+	0.356341i
$657$	3933.66	+	267850.i	0.00911310	+	0.620528i
$658$	−253862.	+	105153.i	−0.586335	+	0.242868i
$659$	333013.			0.766814			0.383407	−	0.923579i	$-0.374751\pi$
$659$	333013.			0.766814			0.383407	+	0.923579i	$0.374751\pi$
$660$	310200.	−	210580.i	0.712122	−	0.483425i
$661$	−479228.	−	479228.i	−1.09683	−	1.09683i	−0.994779	−	0.102051i	$-0.967460\pi$
$661$	−479228.	−	479228.i	−1.09683	−	1.09683i	−0.102051	−	0.994779i	$-0.532540\pi$
$662$		−	415246.i		−	0.947521i
$663$	181275.	−	345926.i	0.412392	−	0.786967i
$664$	−147658.			−0.334904
$665$	626266.	−	626266.i	1.41617	−	1.41617i
$666$	192580.	−	198321.i	0.434173	−	0.447115i
$667$		−	155264.i		−	0.348995i
$668$	71382.2	+	172332.i	0.159969	+	0.386200i
$669$	437098.	+	83612.6i	0.976621	+	0.186818i
$670$	−347073.	−	143762.i	−0.773162	−	0.320254i
$671$	253290.	+	253290.i	0.562565	+	0.562565i
$672$	−32402.6	+	49273.3i	−0.0717532	+	0.109112i
$673$	543720.	+	225216.i	1.20045	+	0.497244i	0.891145	−	0.453718i	$-0.149903\pi$
$673$	543720.	+	225216.i	1.20045	+	0.497244i	0.309307	+	0.950962i	$0.399903\pi$
$674$	−409838.	−	169760.i	−0.902178	−	0.373694i
$675$	534028.	+	340055.i	1.17208	+	0.746349i
$676$		−	48123.2i		−	0.105308i
$677$	−316065.	+	130918.i	−0.689603	+	0.285643i	−0.699835	−	0.714305i	$-0.746743\pi$
$677$	−316065.	+	130918.i	−0.689603	+	0.285643i	0.0102318	+	0.999948i	$0.496743\pi$
$678$	246680.	−	375116.i	0.536630	−	0.816031i
$679$	18606.2			0.0403569
$680$	−251476.	+	24983.3i	−0.543850	+	0.0540297i
$681$	538268.	−	111183.i	1.16066	−	0.239742i
$682$	403464.	+	403464.i	0.867433	+	0.867433i
$683$	−67726.1	+	28053.1i	−0.145183	+	0.0601366i	−0.454092	−	0.890955i	$-0.650036\pi$
$683$	−67726.1	+	28053.1i	−0.145183	+	0.0601366i	0.308909	+	0.951092i	$0.400036\pi$
$684$	162552.	+	376692.i	0.347440	+	0.805146i
$685$	776697.	−	321719.i	1.65528	−	0.685638i
$686$	−330280.	−	136806.i	−0.701834	−	0.290709i
$687$	−12798.5	+	66906.2i	−0.0271173	+	0.141760i
$688$	36764.2	−	36764.2i	0.0776690	−	0.0776690i
$689$	−364338.	−	364338.i	−0.767479	−	0.767479i
$690$	119409.	+	22841.8i	0.250807	+	0.0479770i
$691$	−248749.	+	600533.i	−0.520961	+	1.25771i	0.416346	+	0.909206i	$0.363310\pi$
$691$	−248749.	+	600533.i	−0.520961	+	1.25771i	−0.937307	+	0.348504i	$0.886690\pi$
$692$	−61517.5	−	148516.i	−0.128465	−	0.310143i
$693$	362746.	−	156534.i	0.755329	−	0.325943i
$694$	23922.1	+	57753.2i	0.0496685	+	0.119910i
$695$	−32340.8	+	32340.8i	−0.0669547	+	0.0669547i
$696$	51755.7	+	250564.i	0.106841	+	0.517250i
$697$	−745837.	+	74096.4i	−1.53525	+	0.152522i
$698$			253220.i			0.519740i
$699$	282244.	+	185606.i	0.577657	+	0.379873i
$700$	96241.7	+	232348.i	0.196412	+	0.474180i
$701$	−144429.			−0.293913			−0.146957	−	0.989143i	$-0.546948\pi$
$701$	−144429.			−0.293913			−0.146957	+	0.989143i	$0.546948\pi$
$702$	166294.	−	261151.i	0.337444	−	0.529928i
$703$	292349.	−	705792.i	0.591548	−	1.42812i
$704$	−26401.2	+	63738.2i	−0.0532695	+	0.128604i
$705$	−779924.	−	512886.i	−1.56919	−	1.03191i
$706$	158993.	−	158993.i	0.318984	−	0.318984i
$707$	68975.9	−	166522.i	0.137993	−	0.333146i
$708$	49632.5	−	259462.i	0.0990148	−	0.517615i
$709$	198380.	−	82171.6i	0.394643	−	0.163467i	−0.176532	−	0.984295i	$-0.556488\pi$
$709$	198380.	−	82171.6i	0.394643	−	0.163467i	0.571175	+	0.820828i	$0.306488\pi$
$710$	104801.			0.207897
$711$	234257.	+	227476.i	0.463397	+	0.449983i
$712$	129806.	+	129806.i	0.256056	+	0.256056i
$713$			185020.i			0.363947i
$714$	−265222.	−	23930.7i	−0.520250	−	0.0469417i
$715$	−781884.			−1.52943
$716$	−199706.	+	199706.i	−0.389552	+	0.389552i
$717$	−152436.	−	224549.i	−0.296516	−	0.436791i
$718$			171340.i			0.332362i
$719$	−150826.	−	364127.i	−0.291755	−	0.704360i	0.708243	−	0.705968i	$-0.249488\pi$
$719$	−150826.	−	364127.i	−0.291755	−	0.704360i	−0.999999	+	0.00160856i	$0.999488\pi$
$720$	−200316.	+	2941.85i	−0.386411	+	0.00567486i
$721$	−333652.	−	138203.i	−0.641836	−	0.265857i
$722$	541066.	+	541066.i	1.03795	+	1.03795i
$723$	580294.	+	381607.i	1.11012	+	0.730029i
$724$	295654.	+	122464.i	0.564035	+	0.233631i
$725$	1.00804e6	+	417544.i	1.91780	+	0.794377i
$726$	74038.4	−	50261.1i	0.140470	−	0.0953584i
$727$			814406.i			1.54089i	0.637506	+	0.770445i	$0.279966\pi$
$727$			814406.i			1.54089i	−0.637506	+	0.770445i	$0.720034\pi$
$728$	113623.	−	47064.1i	0.214389	−	0.0888029i
$729$	−481554.	+	224800.i	−0.906129	+	0.423000i
$730$	−361489.			−0.678344
$731$	224726.	+	67962.2i	0.420551	+	0.127184i
$732$	−38718.4	−	187447.i	−0.0722595	−	0.349829i
$733$	−136189.	−	136189.i	−0.253474	−	0.253474i	0.568919	−	0.822393i	$-0.307362\pi$
$733$	−136189.	−	136189.i	−0.253474	−	0.253474i	−0.822393	+	0.568919i	$0.807362\pi$
$734$	8919.33	−	3694.51i	0.0165554	−	0.00685748i
$735$	−76738.6	−	371514.i	−0.142049	−	0.687701i
$736$	−20668.0	+	8560.96i	−0.0381542	+	0.0158040i
$737$	−427852.	−	177222.i	−0.787695	−	0.326274i
$738$	−594103.	+	8725.03i	−1.09081	+	0.0160197i
$739$	358602.	−	358602.i	0.656635	−	0.656635i	−0.297947	−	0.954582i	$-0.596302\pi$
$739$	358602.	−	358602.i	0.656635	−	0.656635i	0.954582	+	0.297947i	$0.0963020\pi$
$740$	263779.	+	263779.i	0.481700	+	0.481700i
$741$	160752.	−	840355.i	0.292765	−	1.53047i
$742$	−134449.	+	324589.i	−0.244202	+	0.589557i
$743$	−123085.	−	297154.i	−0.222960	−	0.538274i	0.772329	−	0.635223i	$-0.219092\pi$
$743$	−123085.	−	297154.i	−0.222960	−	0.538274i	−0.995289	+	0.0969488i	$0.969092\pi$
$744$	−61674.3	−	298583.i	−0.111419	−	0.539410i
$745$	449686.	+	1.08564e6i	0.810209	+	1.95602i
$746$	321205.	−	321205.i	0.577171	−	0.577171i
$747$	−209426.	−	485317.i	−0.375309	−	0.869729i
$748$	−310006.	+	30798.0i	−0.554072	+	0.0550452i
$749$		−	239680.i		−	0.427237i
$750$	−131595.	+	200111.i	−0.233946	+	0.355752i
$751$	−24973.8	−	60292.2i	−0.0442798	−	0.106901i	0.900192	−	0.435493i	$-0.143426\pi$
$751$	−24973.8	−	60292.2i	−0.0442798	−	0.106901i	−0.944472	+	0.328592i	$0.893426\pi$
$752$	171764.			0.303737
$753$	657887.	−	446608.i	1.16028	−	0.787656i
$754$	204188.	−	492952.i	0.359159	−	0.867086i
$755$	394610.	−	952673.i	0.692268	−	1.67128i
$756$	−207907.	−	36614.4i	−0.363769	−	0.0640632i
$757$	−245975.	+	245975.i	−0.429238	+	0.429238i	−0.888369	−	0.459130i	$-0.848161\pi$
$757$	−245975.	+	245975.i	−0.429238	+	0.429238i	0.459130	+	0.888369i	$0.348161\pi$
$758$	−146864.	+	354561.i	−0.255609	+	0.617095i
$759$	147201.	+	28158.1i	0.255521	+	0.0488788i
$760$	−511493.	+	211868.i	−0.885550	+	0.366807i
$761$	23513.2			0.0406015			0.0203008	−	0.999794i	$-0.493538\pi$
$761$	23513.2			0.0406015			0.0203008	+	0.999794i	$0.493538\pi$
$762$	−114039.	−	167988.i	−0.196400	−	0.289312i
$763$	146622.	+	146622.i	0.251854	+	0.251854i
$764$			41248.2i			0.0706672i
$765$	−438788.	−	791109.i	−0.749776	−	1.35180i
$766$	193711.			0.330139
$767$	−389548.	+	389548.i	−0.662171	+	0.662171i
$768$	30500.1	−	20705.0i	0.0517105	−	0.0351038i
$769$		−	592409.i		−	1.00177i	−0.865513	−	0.500886i	$-0.833007\pi$
$769$		−	592409.i		−	1.00177i	0.865513	−	0.500886i	$-0.166993\pi$
$770$	204023.	+	492556.i	0.344111	+	0.830758i
$771$	71917.3	−	375959.i	0.120983	−	0.632457i
$772$	−411406.	−	170410.i	−0.690297	−	0.285930i
$773$	296925.	+	296925.i	0.496921	+	0.496921i	0.910478	−	0.413557i	$-0.135714\pi$
$773$	296925.	+	296925.i	0.496921	+	0.496921i	−0.413557	+	0.910478i	$0.635714\pi$
$774$	172979.	+	68691.8i	0.288742	+	0.114663i
$775$	−1.20123e6	−	497564.i	−1.99996	−	0.828411i
$776$	−10745.4	−	4450.90i	−0.0178443	−	0.00739137i
$777$	220785.	+	325232.i	0.365701	+	0.538706i
$778$		−	786417.i		−	1.29925i
$779$	−1.51700e6	+	628364.i	−2.49984	+	1.03547i
$780$	349076.	+	229556.i	0.573761	+	0.377311i
$781$	129193.			0.211805
$782$	−78142.5	−	64019.2i	−0.127783	−	0.104688i
$783$	−750139.	+	525489.i	−1.22354	+	0.857116i
$784$	49359.7	+	49359.7i	0.0803047	+	0.0803047i
$785$	−465858.	+	192965.i	−0.755987	+	0.313140i
$786$	4806.84	−	992.885i	0.00778063	−	0.00160714i
$787$	−968103.	+	401001.i	−1.56305	+	0.647435i	−0.985615	−	0.169004i	$-0.945945\pi$
$787$	−968103.	+	401001.i	−1.56305	+	0.647435i	−0.577431	+	0.816439i	$0.695945\pi$
$788$	271920.	+	112633.i	0.437914	+	0.181390i
$789$	509109.	+	97387.5i	0.817817	+	0.156441i
$790$	−311576.	+	311576.i	−0.499241	+	0.499241i
$791$	451427.	+	451427.i	0.721497	+	0.721497i
$792$	−246938.	+	3626.54i	−0.393675	+	0.00578152i
$793$	−152753.	+	368777.i	−0.242908	+	0.586432i
$794$	−193823.	−	467929.i	−0.307442	−	0.742231i
$795$	−1.16884e6	+	241432.i	−1.84936	+	0.381997i
$796$	126603.	+	305648.i	0.199811	+	0.482387i
$797$	299220.	−	299220.i	0.471057	−	0.471057i	−0.431200	−	0.902257i	$-0.641910\pi$
$797$	299220.	−	299220.i	0.471057	−	0.471057i	0.902257	+	0.431200i	$0.141910\pi$
$798$	−571337.	+	118013.i	−0.897194	+	0.185321i
$799$	366206.	+	683729.i	0.573629	+	1.07100i
$800$		−	157208.i		−	0.245637i
$801$	−242535.	+	610748.i	−0.378015	+	0.951912i
$802$	55844.2	+	134820.i	0.0868219	+	0.209607i
$803$	−445624.			−0.691094
$804$	138985.	+	204736.i	0.215009	+	0.316725i
$805$	−66157.4	+	159718.i	−0.102091	+	0.246469i
$806$	−243319.	+	587423.i	−0.374546	+	0.904235i
$807$	221280.	−	336492.i	0.339779	−	0.516687i
$808$	−79669.7	+	79669.7i	−0.122031	+	0.122031i
$809$	80546.1	−	194456.i	0.123069	−	0.297114i	−0.850323	−	0.526261i	$-0.823594\pi$
$809$	80546.1	−	194456.i	0.123069	−	0.297114i	0.973392	+	0.229147i	$0.0735935\pi$
$810$	−293781.	−	654218.i	−0.447768	−	0.997131i
$811$	−13170.0	+	5455.18i	−0.0200236	+	0.00829407i	−0.392673	−	0.919678i	$-0.628450\pi$
$811$	−13170.0	+	5455.18i	−0.0200236	+	0.00829407i	0.372649	+	0.927972i	$0.378450\pi$
$812$	−363821.			−0.551793
$813$	−844925.	+	573579.i	−1.27831	+	0.867785i
$814$	325172.	+	325172.i	0.490754	+	0.490754i
$815$		−	482847.i		−	0.726933i
$816$	147446.	+	77265.7i	0.221438	+	0.116040i
$817$	514343.			0.770564
$818$	205150.	−	205150.i	0.306595	−	0.306595i
$819$	315842.	+	306699.i	0.470871	+	0.457241i
$820$		−	801798.i		−	1.19244i
$821$	237362.	+	573042.i	0.352147	+	0.850158i	0.996355	+	0.0853076i	$0.0271873\pi$
$821$	237362.	+	573042.i	0.352147	+	0.850158i	−0.644208	+	0.764851i	$0.722813\pi$
$822$	−543905.	−	104044.i	−0.804970	−	0.153983i
$823$	476207.	+	197252.i	0.703067	+	0.291220i	0.705432	−	0.708777i	$-0.250753\pi$
$823$	476207.	+	197252.i	0.703067	+	0.291220i	−0.00236544	+	0.999997i	$0.500753\pi$
$824$	159630.	+	159630.i	0.235104	+	0.235104i
$825$	−578675.	+	879967.i	−0.850211	+	1.29288i
$826$	347048.	+	143752.i	0.508662	+	0.210695i
$827$	549453.	+	227591.i	0.803378	+	0.332770i	0.746308	−	0.665600i	$-0.231824\pi$
$827$	549453.	+	227591.i	0.803378	+	0.332770i	0.0570693	+	0.998370i	$0.481824\pi$
$828$	−57451.7	−	55788.6i	−0.0837996	−	0.0813739i
$829$			549105.i			0.798999i	0.916733	+	0.399500i	$0.130816\pi$
$829$			549105.i			0.798999i	−0.916733	+	0.399500i	$0.869184\pi$
$830$	658990.	−	272962.i	0.956582	−	0.396229i
$831$	169613.	−	257923.i	0.245616	−	0.373497i
$832$	−76877.8			−0.111059
$833$	−91246.3	+	301719.i	−0.131500	+	0.434823i
$834$	29504.2	−	6094.29i	0.0424182	−	0.00876176i
$835$	−637150.	−	637150.i	−0.913837	−	0.913837i
$836$	−630540.	+	261178.i	−0.902195	+	0.373701i
$837$	893898.	−	626195.i	1.27596	−	0.893838i
$838$	835314.	−	345998.i	1.18949	−	0.492704i
$839$	581462.	+	240849.i	0.826033	+	0.342154i	0.755331	−	0.655344i	$-0.227476\pi$
$839$	581462.	+	240849.i	0.826033	+	0.342154i	0.0707018	+	0.997497i	$0.477476\pi$
$840$	53523.9	−	279804.i	0.0758558	−	0.396548i
$841$	−616000.	+	616000.i	−0.870942	+	0.870942i
$842$	−545771.	−	545771.i	−0.769814	−	0.769814i
$843$	1.08049e6	+	206688.i	1.52043	+	0.290844i
$844$	136313.	−	329089.i	0.191361	−	0.461986i
$845$	88961.2	+	214771.i	0.124591	+	0.300790i
$846$	243617.	+	564549.i	0.340382	+	0.788789i
$847$	48696.2	+	117563.i	0.0678779	+	0.163872i
$848$	155294.	−	155294.i	0.215954	−	0.215954i
$849$	252992.	+	1.22481e6i	0.350987	+	1.69923i
$850$	625785.	−	335171.i	0.866139	−	0.463904i
$851$			149117.i			0.205905i
$852$	−57678.9	−	37930.2i	−0.0794580	−	0.0522523i
$853$	−45287.5	−	109334.i	−0.0622415	−	0.150264i	0.889699	−	0.456548i	$-0.150914\pi$
$853$	−45287.5	−	109334.i	−0.0622415	−	0.150264i	−0.951940	+	0.306284i	$0.900914\pi$
$854$	272174.			0.373191
$855$	−1.42182e6	−	1.38066e6i	−1.94497	−	1.88867i
$856$	−57335.4	+	138420.i	−0.0782483	+	0.188908i
$857$	185185.	−	447076.i	0.252141	−	0.608723i	−0.746235	−	0.665682i	$-0.768141\pi$
$857$	185185.	−	447076.i	0.252141	−	0.608723i	0.998376	+	0.0569596i	$0.0181406\pi$
$858$	430322.	+	282984.i	0.584546	+	0.384403i
$859$	423272.	−	423272.i	0.573632	−	0.573632i	−0.359509	−	0.933141i	$-0.617056\pi$
$859$	423272.	−	423272.i	0.573632	−	0.573632i	0.933141	+	0.359509i	$0.117056\pi$
$860$	−96113.9	+	232039.i	−0.129954	+	0.313736i
$861$	158743.	−	829853.i	0.214135	−	1.11943i
$862$	−123642.	+	51214.3i	−0.166400	+	0.0689250i
$863$	−673516.			−0.904329			−0.452165	−	0.891935i	$-0.649348\pi$
$863$	−673516.			−0.904329			−0.452165	+	0.891935i	$0.649348\pi$
$864$	111311.	+	70880.2i	0.149112	+	0.0949506i
$865$	549099.	+	549099.i	0.733869	+	0.733869i
$866$			544725.i			0.726343i
$867$	6792.51	+	751658.i	0.00903634	+	0.999959i
$868$	433545.			0.575433
$869$	−384094.	+	384094.i	−0.508625	+	0.508625i
$870$	−694179.	−	1.02258e6i	−0.917134	−	1.35101i
$871$		−	516053.i		−	0.680233i
$872$	−49602.5	−	119751.i	−0.0652335	−	0.157488i
$873$	−611.388	−	41630.5i	−0.000802210	−	0.0546240i
$874$	−204461.	−	84690.7i	−0.267663	−	0.110870i
$875$	−240820.	−	240820.i	−0.314540	−	0.314540i
$876$	198951.	+	130832.i	0.259262	+	0.170493i
$877$	610634.	+	252933.i	0.793930	+	0.328857i	0.742522	−	0.669821i	$-0.233629\pi$
$877$	610634.	+	252933.i	0.793930	+	0.328857i	0.0514075	+	0.998678i	$0.483629\pi$
$878$	490153.	+	203028.i	0.635833	+	0.263371i
$879$	−399983.	+	271529.i	−0.517683	+	0.351430i
$880$		−	333266.i		−	0.430354i
$881$	−33969.4	+	14070.6i	−0.0437659	+	0.0181284i	−0.404459	−	0.914556i	$-0.632540\pi$
$881$	−33969.4	+	14070.6i	−0.0437659	+	0.0181284i	0.360693	+	0.932685i	$0.382540\pi$
$882$	−92226.0	+	232242.i	−0.118554	+	0.298540i
$883$	−545012.			−0.699012			−0.349506	−	0.936934i	$-0.613651\pi$
$883$	−545012.			−0.699012			−0.349506	+	0.936934i	$0.613651\pi$
$884$	−163905.	−	306021.i	−0.209743	−	0.391604i
$885$	258137.	+	1.24972e6i	0.329583	+	1.59560i
$886$	−130220.	−	130220.i	−0.165886	−	0.165886i
$887$	−1.09505e6	+	453587.i	−1.39184	+	0.576518i	−0.947620	−	0.319401i	$-0.896518\pi$
$887$	−1.09505e6	+	453587.i	−1.39184	+	0.576518i	−0.444218	+	0.895919i	$0.646518\pi$
$888$	−49706.4	−	240643.i	−0.0630357	−	0.305174i
$889$	266741.	−	110488.i	0.337510	−	0.139801i
$890$	−819278.	−	339356.i	−1.03431	−	0.428426i
$891$	−362156.	−	806483.i	−0.456185	−	1.01587i
$892$	279714.	−	279714.i	0.351548	−	0.351548i
$893$	1.20152e6	+	1.20152e6i	1.50671	+	1.50671i
$894$	145429.	−	760251.i	0.181960	−	0.951222i
$895$	522099.	−	1.26046e6i	0.651788	−	1.57356i
$896$	20060.4	+	48430.0i	0.0249875	+	0.0603252i
$897$	33783.0	+	163553.i	0.0419868	+	0.203270i
$898$	−250930.	−	605800.i	−0.311172	−	0.751236i
$899$	1.33002e6	−	1.33002e6i	1.64566	−	1.64566i
$900$	516705.	−	222971.i	0.637908	−	0.275273i
$901$	949255.	+	287076.i	1.16932	+	0.353628i
$902$		−	988412.i		−	1.21486i
$903$	−145417.	+	221130.i	−0.178336	+	0.271189i
$904$	−152719.	−	368696.i	−0.186877	−	0.451161i
$905$	−1.54588e6			−1.88746
$906$	−561976.	+	381499.i	−0.684639	+	0.464768i
$907$	−167846.	+	405217.i	−0.204031	+	0.492575i	−0.992463	−	0.122548i	$-0.960894\pi$
$907$	−167846.	+	405217.i	−0.204031	+	0.492575i	0.788431	+	0.615123i	$0.210894\pi$
$908$	186964.	−	451372.i	0.226771	−	0.547473i
$909$	−374853.	−	148858.i	−0.453662	−	0.180155i
$910$	−420090.	+	420090.i	−0.507293	+	0.507293i
$911$	−118215.	+	285396.i	−0.142441	+	0.343883i	−0.978959	−	0.204056i	$-0.934587\pi$
$911$	−118215.	+	285396.i	−0.142441	+	0.343883i	0.836518	+	0.547939i	$0.184587\pi$
$912$	358189.	+	68518.0i	0.430648	+	0.0823787i
$913$	812365.	−	336493.i	0.974563	−	0.403677i
$914$	322999.			0.386642
$915$	519315.	+	764990.i	0.620281	+	0.913721i
$916$	42815.7	+	42815.7i	0.0510284	+	0.0510284i
$917$			6979.58i			0.00830024i
$918$	−44828.7	+	594207.i	−0.0531950	+	0.705103i
$919$	−1.30985e6			−1.55092			−0.775460	−	0.631397i	$-0.782482\pi$
$919$	−1.30985e6			−1.55092			−0.775460	+	0.631397i	$0.782482\pi$
$920$	76414.3	−	76414.3i	0.0902815	−	0.0902815i
$921$	676015.	−	458914.i	0.796962	−	0.541019i
$922$			247468.i			0.291110i
$923$	55092.8	+	133006.i	0.0646682	+	0.156123i
$924$	65981.2	−	344927.i	0.0772817	−	0.404002i
$925$	−968128.	−	401012.i	−1.13149	−	0.468677i
$926$	9784.87	+	9784.87i	0.0114112	+	0.0114112i
$927$	−298260.	+	751073.i	−0.347085	+	0.874023i
$928$	210113.	+	87031.9i	0.243982	+	0.101061i
$929$	−196242.	−	81286.2i	−0.227385	−	0.0941858i	0.266082	−	0.963950i	$-0.414271\pi$
$929$	−196242.	−	81286.2i	−0.227385	−	0.0941858i	−0.493467	+	0.869764i	$0.664271\pi$
$930$	827214.	+	1.21855e6i	0.956427	+	1.40889i
$931$			690559.i			0.796713i
$932$	277413.	−	114908.i	0.319371	−	0.132288i
$933$	10564.8	+	6947.50i	0.0121366	+	0.00798115i
$934$	−821630.			−0.941851
$935$	1.32661e6	−	710531.i	1.51747	−	0.812755i
$936$	−109037.	−	252679.i	−0.124458	−	0.288415i
$937$	1.06942e6	+	1.06942e6i	1.21806	+	1.21806i	0.968312	+	0.249746i	$0.0803470\pi$
$937$	1.06942e6	+	1.06942e6i	1.21806	+	1.21806i	0.249746	+	0.968312i	$0.419653\pi$
$938$	−325093.	+	134658.i	−0.369490	+	0.153048i
$939$	1.03471e6	−	213726.i	1.17351	−	0.242397i
$940$	−766576.	+	317526.i	−0.867560	+	0.359355i
$941$	−1.01065e6	−	418626.i	−1.14136	−	0.472766i	−0.269732	−	0.962935i	$-0.586935\pi$
$941$	−1.01065e6	−	418626.i	−1.14136	−	0.472766i	−0.871627	+	0.490169i	$0.836935\pi$
$942$	326231.	+	62404.8i	0.367640	+	0.0703261i
$943$	226632.	−	226632.i	0.254858	−	0.254858i
$944$	−166039.	−	166039.i	−0.186323	−	0.186323i
$945$	995565.	−	220932.i	1.11482	−	0.247397i
$946$	−118484.	+	286045.i	−0.132397	+	0.319634i
$947$	−250738.	−	605335.i	−0.279589	−	0.674988i	0.720235	−	0.693730i	$-0.244034\pi$
$947$	−250738.	−	605335.i	−0.279589	−	0.674988i	−0.999824	+	0.0187420i	$0.994034\pi$
$948$	284248.	−	58713.3i	0.316287	−	0.0653311i
$949$	−190031.	−	458775.i	−0.211005	−	0.509410i
$950$	1.09970e6	−	1.09970e6i	1.21850	−	1.21850i
$951$	−1.15430e6	+	238428.i	−1.27631	+	0.263631i
$952$	−150012.	+	183107.i	−0.165521	+	0.202037i
$953$		−	390739.i		−	0.430230i	−0.976589	−	0.215115i	$-0.930987\pi$
$953$		−	390739.i		−	0.430230i	0.976589	−	0.215115i	$-0.0690126\pi$
$954$	730670.	+	290158.i	0.802832	+	0.318814i
$955$	−76252.0	−	184089.i	−0.0836073	−	0.201846i
$956$	−241246.			−0.263964
$957$	−855745.	−	1.26058e6i	−0.934373	−	1.37640i
$958$	368532.	−	889714.i	0.401554	−	0.969437i
$959$	301345.	−	727511.i	0.327662	−	0.791047i
$960$	−97844.7	+	148788.i	−0.106168	+	0.161446i
$961$	−931884.	+	931884.i	−1.00906	+	1.00906i
$962$	−196103.	+	473434.i	−0.211901	+	0.511575i
$963$	−536273.	+	7875.74i	−0.578274	+	0.00849256i
$964$	570363.	−	236252.i	0.613758	−	0.254227i
$965$	2.15111e6			2.30998
$966$	94216.8	−	63959.2i	0.100966	−	0.0685408i
$967$	633030.	+	633030.i	0.676973	+	0.676973i	0.959314	−	0.282341i	$-0.0911110\pi$
$967$	633030.	+	633030.i	0.676973	+	0.676973i	−0.282341	+	0.959314i	$0.591111\pi$
$968$		−	79543.7i		−	0.0848898i
$969$	490922.	+	1.57189e6i	0.522835	+	1.67408i
$970$	56184.3			0.0597134
$971$	−662684.	+	662684.i	−0.702859	+	0.702859i	−0.965023	−	0.262164i	$-0.915564\pi$
$971$	−662684.	+	662684.i	−0.702859	+	0.702859i	0.262164	+	0.965023i	$0.415564\pi$
$972$	−75091.4	+	466386.i	−0.0794799	+	0.493643i
$973$			42840.4i			0.0452509i
$974$	382604.	+	923688.i	0.403303	+	0.973661i
$975$	−1.15271e6	−	220502.i	−1.21258	−	0.231954i
$976$	−157186.	−	65108.5i	−0.165011	−	0.0683499i
$977$	271115.	+	271115.i	0.284030	+	0.284030i	0.834714	−	0.550684i	$-0.185633\pi$
$977$	271115.	+	271115.i	0.284030	+	0.284030i	−0.550684	+	0.834714i	$0.685633\pi$
$978$	−174755.	+	265742.i	−0.182705	+	0.277833i
$979$	−1.00996e6	−	418339.i	−1.05375	−	0.436479i
$980$	−311537.	−	129043.i	−0.324383	−	0.134364i
$981$	323241.	−	332877.i	0.335884	−	0.345896i
$982$			1.16361e6i			1.20666i
$983$	−196231.	+	81281.7i	−0.203077	+	0.0841174i	−0.481904	−	0.876224i	$-0.660055\pi$
$983$	−196231.	+	81281.7i	−0.203077	+	0.0841174i	0.278826	+	0.960341i	$0.410055\pi$
$984$	−290191.	+	441282.i	−0.299705	+	0.455749i
$985$	−1.42178e6			−1.46541
$986$	101526.	+	1.02194e6i	0.104430	+	1.05116i
$987$	−856263.	+	176867.i	−0.878968	+	0.181557i
$988$	−537773.	−	537773.i	−0.550916	−	0.550916i
$989$	−92754.0	+	38420.0i	−0.0948288	+	0.0392794i
$990$	1.09537e6	−	472678.i	1.11761	−	0.482275i
$991$	644264.	−	266863.i	0.656019	−	0.271732i	−0.0297434	−	0.999558i	$-0.509469\pi$
$991$	644264.	−	266863.i	0.656019	−	0.271732i	0.685762	+	0.727826i	$0.259469\pi$
$992$	−250380.	−	103711.i	−0.254435	−	0.105390i
$993$	248251.	−	1.29777e6i	0.251764	−	1.31613i
$994$	69412.6	−	69412.6i	0.0702531	−	0.0702531i
$995$	−1.13005e6	−	1.13005e6i	−1.14144	−	1.14144i
$996$	−461477.	−	88276.1i	−0.465191	−	0.0889866i
$997$	489424.	−	1.18157e6i	0.492374	−	1.18870i	−0.461135	−	0.887330i	$-0.652557\pi$
$997$	489424.	−	1.18157e6i	0.492374	−	1.18870i	0.953509	−	0.301366i	$-0.0974425\pi$
$998$	−58416.4	−	141030.i	−0.0586507	−	0.141595i
$999$	720437.	−	504682.i	0.721880	−	0.505693i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	102.5.g.d.83.9	yes	44
3.2	odd	2		102.5.g.c.83.1	yes	44
17.8	even	8		102.5.g.c.59.1	✓	44
51.8	odd	8	inner	102.5.g.d.59.9	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
102.5.g.c.59.1	✓	44	17.8	even	8
102.5.g.c.83.1	yes	44	3.2	odd	2
102.5.g.d.59.9	yes	44	51.8	odd	8	inner
102.5.g.d.83.9	yes	44	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 102 = 2 \cdot 3 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	102.g (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.00000 - 2.00000i) q^{2} +(7.44631 - 5.05494i) q^{3} -8.00000i q^{4} +(14.7889 + 35.7036i) q^{5} +(4.78274 - 25.0025i) q^{6} +(33.4426 + 13.8524i) q^{7} +(-16.0000 - 16.0000i) q^{8} +(29.8951 - 75.2814i) q^{9} +(100.985 + 41.8294i) q^{10} +(124.489 + 51.5649i) q^{11} +(-40.4395 - 59.5705i) q^{12} +150.152i q^{13} +(94.5899 - 39.1804i) q^{14} +(290.603 + 191.103i) q^{15} -64.0000 q^{16} +(-136.449 - 254.760i) q^{17} +(-90.7725 - 210.353i) q^{18} +(-447.691 - 447.691i) q^{19} +(285.629 - 118.311i) q^{20} +(319.047 - 65.9012i) q^{21} +(352.107 - 145.848i) q^{22} +(114.176 + 47.2931i) q^{23} +(-200.020 - 38.2619i) q^{24} +(-614.093 + 614.093i) q^{25} +(300.304 + 300.304i) q^{26} +(-157.935 - 711.686i) q^{27} +(110.819 - 267.541i) q^{28} +(-480.788 - 1160.72i) q^{29} +(963.411 - 198.999i) q^{30} +(572.928 + 1383.17i) q^{31} +(-128.000 + 128.000i) q^{32} +(1187.64 - 245.315i) q^{33} +(-782.418 - 236.621i) q^{34} +1398.88i q^{35} +(-602.251 - 239.161i) q^{36} +(461.751 + 1114.77i) q^{37} -1790.76 q^{38} +(759.009 + 1118.08i) q^{39} +(334.635 - 807.880i) q^{40} +(992.472 - 2396.04i) q^{41} +(506.291 - 769.896i) q^{42} +(-574.440 + 574.440i) q^{43} +(412.519 - 995.909i) q^{44} +(3129.93 - 45.9663i) q^{45} +(322.937 - 133.765i) q^{46} -2683.82 q^{47} +(-476.564 + 323.516i) q^{48} +(-771.246 - 771.246i) q^{49} +2456.37i q^{50} +(-2303.84 - 1207.28i) q^{51} +1201.22 q^{52} +(-2426.46 + 2426.46i) q^{53} +(-1739.24 - 1107.50i) q^{54} +5207.28i q^{55} +(-313.443 - 756.719i) q^{56} +(-5596.70 - 1070.59i) q^{57} +(-3283.02 - 1359.87i) q^{58} +(2594.36 + 2594.36i) q^{59} +(1528.82 - 2324.82i) q^{60} +(2456.03 + 1017.32i) q^{61} +(3912.19 + 1620.48i) q^{62} +(2042.59 - 2103.48i) q^{63} +512.000i q^{64} +(-5360.96 + 2220.58i) q^{65} +(1884.65 - 2865.91i) q^{66} -3436.87 q^{67} +(-2038.08 + 1091.60i) q^{68} +(1089.25 - 224.992i) q^{69} +(2797.76 + 2797.76i) q^{70} +(885.807 - 366.913i) q^{71} +(-1682.82 + 726.180i) q^{72} +(-3055.41 + 1265.59i) q^{73} +(3153.03 + 1306.03i) q^{74} +(-1468.52 + 7676.94i) q^{75} +(-3581.53 + 3581.53i) q^{76} +(3448.93 + 3448.93i) q^{77} +(3754.17 + 718.137i) q^{78} +(-1542.68 + 3724.37i) q^{79} +(-946.491 - 2285.03i) q^{80} +(-4773.56 - 4501.09i) q^{81} +(-2807.13 - 6777.02i) q^{82} +(4614.31 - 4614.31i) q^{83} +(-527.210 - 2552.37i) q^{84} +(7077.90 - 8639.36i) q^{85} +2297.76i q^{86} +(-9447.49 - 6212.76i) q^{87} +(-1166.78 - 2816.86i) q^{88} -8112.87 q^{89} +(6167.93 - 6351.80i) q^{90} +(-2079.96 + 5021.47i) q^{91} +(378.344 - 913.404i) q^{92} +(11258.0 + 7403.40i) q^{93} +(-5367.64 + 5367.64i) q^{94} +(9363.31 - 22605.0i) q^{95} +(-306.095 + 1600.16i) q^{96} +(474.885 - 196.704i) q^{97} -3084.98 q^{98} +(7603.48 - 7830.14i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 88 q^{2} - 4 q^{3} + 72 q^{5} - 40 q^{6} + 132 q^{7} - 704 q^{8} + 324 q^{9} + 384 q^{10} - 616 q^{11} - 128 q^{12} + 416 q^{14} - 908 q^{15} - 2816 q^{16} + 424 q^{17} + 1016 q^{18} + 568 q^{19}+ \cdots + 91704 q^{99}+O(q^{100}) \) 44 * q + 88 * q^2 - 4 * q^3 + 72 * q^5 - 40 * q^6 + 132 * q^7 - 704 * q^8 + 324 * q^9 + 384 * q^10 - 616 * q^11 - 128 * q^12 + 416 * q^14 - 908 * q^15 - 2816 * q^16 + 424 * q^17 + 1016 * q^18 + 568 * q^19 + 960 * q^20 + 1020 * q^21 + 424 * q^22 + 332 * q^23 - 192 * q^24 + 1888 * q^25 - 1008 * q^26 - 436 * q^27 + 608 * q^28 - 6688 * q^29 - 2000 * q^30 - 1428 * q^31 - 5632 * q^32 + 2224 * q^33 + 512 * q^34 + 1472 * q^36 + 296 * q^37 + 2272 * q^38 - 3720 * q^39 + 768 * q^40 + 4592 * q^41 + 3328 * q^42 - 228 * q^43 + 6624 * q^44 + 8228 * q^45 + 1872 * q^46 + 10712 * q^47 + 256 * q^48 + 5304 * q^49 - 3984 * q^51 - 4032 * q^52 - 5656 * q^53 - 9288 * q^54 - 896 * q^56 - 13364 * q^57 - 11472 * q^58 + 3620 * q^59 - 736 * q^60 - 10448 * q^61 - 3536 * q^62 + 28248 * q^63 - 13760 * q^65 + 12952 * q^66 - 18584 * q^67 - 1344 * q^68 + 6500 * q^69 - 9664 * q^70 + 36660 * q^71 - 2240 * q^72 + 18008 * q^73 - 144 * q^74 + 30268 * q^75 + 4544 * q^76 - 5704 * q^77 - 22576 * q^78 - 7324 * q^79 - 4608 * q^80 - 33668 * q^81 + 11160 * q^82 - 12620 * q^83 + 5152 * q^84 - 10896 * q^85 + 23860 * q^87 + 23104 * q^88 - 5040 * q^89 - 8784 * q^90 + 52368 * q^91 + 4832 * q^92 - 1304 * q^93 + 21424 * q^94 + 16032 * q^95 + 2560 * q^96 - 40164 * q^97 + 21216 * q^98 + 91704 * q^99

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