LMFDB - Embedded newform 102.5.g.d.59.9

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			59.9
Character	$\chi$	$=$	102.59
Dual form			102.5.g.d.83.9

$q$-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 $\left(\mathbb{Z}/102\mathbb{Z}\right)^\times$.

$n$	$35$	$37$
$\chi(n)$	$-1$	$e\left(\frac{5}{8}\right)$

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	−0.290442	−	0.956893i	$-0.593802\pi$
$5$	14.7889	−	35.7036i	0.591557	−	1.42814i	0.881999	−	0.471252i	$-0.156198\pi$
$6$	4.78274	+	25.0025i	0.132854	+	0.694514i
$7$	33.4426	−	13.8524i	0.682501	−	0.282701i	−0.0143707	−	0.999897i	$-0.504575\pi$
$7$	33.4426	−	13.8524i	0.682501	−	0.282701i	0.696872	+	0.717195i	$0.254575\pi$
$8$	−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	0.196541	−	0.980496i	$-0.437029\pi$
$11$	124.489	−	51.5649i	1.02883	−	0.426156i	0.832291	+	0.554339i	$0.187029\pi$
$12$	−40.4395	+	59.5705i	−0.280830	+	0.413684i
$13$		−	150.152i		−	0.888473i	−0.895910	−	0.444236i	$-0.853475\pi$
$13$		−	150.152i		−	0.888473i	0.895910	−	0.444236i	$-0.146525\pi$
$14$	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	−0.280198	+	0.959942i	$0.590400\pi$
$19$	−447.691	+	447.691i	−1.24014	+	1.24014i	−0.959942	+	0.280198i	$0.909600\pi$
$20$	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	−0.272147	−	0.962256i	$-0.587734\pi$
$23$	114.176	−	47.2931i	0.215833	−	0.0894009i	0.487980	+	0.872855i	$0.337734\pi$
$24$	−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	0.328433	+	0.944527i	$0.393479\pi$
$29$	−480.788	+	1160.72i	−0.571686	+	1.38017i	−0.900119	+	0.435644i	$0.856521\pi$
$30$	963.411	+	198.999i	1.07046	+	0.221110i
$31$	572.928	−	1383.17i	0.596179	−	1.43930i	−0.281269	−	0.959629i	$-0.590755\pi$
$31$	572.928	−	1383.17i	0.596179	−	1.43930i	0.877447	−	0.479673i	$-0.159245\pi$
$32$	−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	−0.660683	−	0.750665i	$-0.729733\pi$
$37$	461.751	−	1114.77i	0.337291	−	0.814292i	0.997974	−	0.0636269i	$-0.0202668\pi$
$38$	−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	0.883112	+	0.469163i	$0.155444\pi$
$41$	992.472	+	2396.04i	0.590406	+	1.42537i	−0.292706	+	0.956202i	$0.594556\pi$
$42$	506.291	+	769.896i	0.287013	+	0.436449i
$43$	−574.440	−	574.440i	−0.310676	−	0.310676i	0.534495	−	0.845171i	$-0.320502\pi$
$43$	−574.440	−	574.440i	−0.310676	−	0.310676i	−0.845171	+	0.534495i	$0.820502\pi$
$44$	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	0.127961	−	0.991779i	$-0.459157\pi$
$53$	−2426.46	−	2426.46i	−0.863818	−	0.863818i	−0.991779	+	0.127961i	$0.959157\pi$
$54$	−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	−0.228300	−	0.973591i	$-0.573317\pi$
$59$	2594.36	−	2594.36i	0.745291	−	0.745291i	0.973591	+	0.228300i	$0.0733167\pi$
$60$	1528.82	+	2324.82i	0.424673	+	0.645783i
$61$	2456.03	−	1017.32i	0.660045	−	0.273400i	−0.0274124	−	0.999624i	$-0.508727\pi$
$61$	2456.03	−	1017.32i	0.660045	−	0.273400i	0.687458	+	0.726225i	$0.258727\pi$
$62$	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	0.468809	−	0.883299i	$-0.344683\pi$
$71$	885.807	+	366.913i	0.175721	+	0.0727858i	−0.293089	+	0.956085i	$0.594683\pi$
$72$	−1682.82	−	726.180i	−0.324619	−	0.140081i
$73$	−3055.41	−	1265.59i	−0.573355	−	0.237491i	0.0771166	−	0.997022i	$-0.475429\pi$
$73$	−3055.41	−	1265.59i	−0.573355	−	0.237491i	−0.650471	+	0.759531i	$0.725429\pi$
$74$	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	0.750777	−	0.660555i	$-0.229679\pi$
$79$	−1542.68	−	3724.37i	−0.247186	−	0.596759i	−0.997963	+	0.0637966i	$0.979679\pi$
$80$	−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	0.957671	−	0.287863i	$-0.0929449\pi$
$83$	4614.31	+	4614.31i	0.669808	+	0.669808i	−0.287863	+	0.957671i	$0.592945\pi$
$84$	−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	0.407776	−	0.913082i	$-0.366304\pi$
$97$	474.885	+	196.704i	0.0504714	+	0.0209059i	−0.357305	+	0.933988i	$0.616304\pi$
$98$	−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	$0.0784801\pi$
$101$			4979.36i			0.488124i	−0.969760	+	0.244062i	$0.921520\pi$
$102$	−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	−0.995070	−	0.0991780i	$-0.968379\pi$
$107$	−2533.89	+	6117.35i	−0.221320	+	0.534313i	0.773750	+	0.633491i	$0.218379\pi$
$108$	−5693.49	−	1263.48i	−0.488125	−	0.108323i
$109$	5292.30	−	2192.14i	0.445442	−	0.184508i	−0.148676	−	0.988886i	$-0.547501\pi$
$109$	5292.30	−	2192.14i	0.445442	−	0.184508i	0.594118	+	0.804378i	$0.297501\pi$
$110$	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	0.361270	−	0.932461i	$-0.382343\pi$
$113$	16294.2	−	6749.28i	1.27608	−	0.528568i	0.914806	+	0.403893i	$0.132343\pi$
$114$	−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	0.859990	−	0.510312i	$-0.170470\pi$
$127$	5639.96	+	5639.96i	0.349678	+	0.349678i	−0.510312	+	0.859990i	$0.670470\pi$
$128$	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	−0.921715	−	0.387868i	$-0.873212\pi$
$131$	73.7878	−	178.139i	0.00429974	−	0.0103805i	0.926015	+	0.377487i	$0.123212\pi$
$132$	−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	$0.196760\pi$
$137$			21754.0i			1.15904i	−0.814958	+	0.579520i	$0.803240\pi$
$138$	1728.52	+	2628.48i	0.0907644	+	0.138022i
$139$	452.907	−	1093.41i	0.0234412	−	0.0565920i	−0.911726	−	0.410800i	$-0.865249\pi$
$139$	452.907	−	1093.41i	0.0234412	−	0.0565920i	0.935167	+	0.354208i	$0.115249\pi$
$140$	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	−0.987169	−	0.159679i	$-0.948954\pi$
$151$	−18867.6	+	18867.6i	−0.827490	+	0.827490i	0.159679	+	0.987169i	$0.448954\pi$
$152$		−	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	$-0.914735\pi$
$157$		−	13047.9i		−	0.529349i	0.964338	−	0.264675i	$-0.0852645\pi$
$158$	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	−0.589186	−	0.807997i	$-0.700552\pi$
$163$	−11543.3	+	4781.38i	−0.434464	+	0.179961i	0.154723	+	0.987958i	$0.450552\pi$
$164$	−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	−0.0385561	−	0.999256i	$-0.512276\pi$
$167$	−21541.5	−	8922.77i	−0.772400	−	0.319939i	−0.733844	+	0.679318i	$0.762276\pi$
$168$	−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	0.670619	−	0.741802i	$-0.266028\pi$
$173$	18564.5	+	7689.69i	0.620286	+	0.256931i	−0.0503333	+	0.998732i	$0.516028\pi$
$174$	−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	−0.979678	−	0.200575i	$-0.935719\pi$
$179$	−24963.3	+	24963.3i	−0.779104	+	0.779104i	0.200575	+	0.979678i	$0.435719\pi$
$180$	−367.731	+	25039.5i	−0.0113497	+	0.772823i
$181$	−15308.0	−	36956.7i	−0.467262	−	1.12807i	−0.965354	−	0.260945i	$-0.915966\pi$
$181$	−15308.0	−	36956.7i	−0.467262	−	1.12807i	0.498092	−	0.867124i	$-0.334034\pi$
$182$	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	0.899969	+	0.435954i	$0.143589\pi$
$193$	21301.2	+	51425.7i	0.571861	+	1.38059i	−0.328108	+	0.944640i	$0.606411\pi$
$194$	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	−0.994891	−	0.100951i	$-0.967812\pi$
$197$	−14079.1	−	33990.0i	−0.362780	−	0.875828i	0.632111	−	0.774877i	$-0.282188\pi$
$198$	−453.318	+	30867.2i	−0.0115630	+	0.787349i
$199$	−38206.0	−	15825.4i	−0.964773	−	0.399622i	−0.156009	−	0.987756i	$-0.549863\pi$
$199$	−38206.0	−	15825.4i	−0.964773	−	0.399622i	−0.808764	+	0.588133i	$0.799863\pi$
$200$	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	0.130583	−	0.991437i	$-0.458315\pi$
$211$	41136.1	−	17039.1i	0.923972	−	0.382722i	0.793388	+	0.608716i	$0.208315\pi$
$212$	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	−0.261977	−	0.965074i	$-0.584375\pi$
$223$	34964.3	−	34964.3i	0.703097	−	0.703097i	0.965074	+	0.261977i	$0.0843745\pi$
$224$	−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	0.239217	−	0.970966i	$-0.423109\pi$
$227$	56421.4	−	23370.5i	1.09495	−	0.453541i	0.855729	+	0.517425i	$0.173109\pi$
$228$	−8564.75	−	44773.6i	−0.164757	−	0.861295i
$229$	−5351.96	−	5351.96i	−0.102057	−	0.102057i	0.654235	−	0.756292i	$-0.272991\pi$
$229$	−5351.96	−	5351.96i	−0.102057	−	0.102057i	−0.756292	+	0.654235i	$0.772991\pi$
$230$	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	−0.734635	−	0.678462i	$-0.762647\pi$
$233$	14363.5	−	34676.6i	0.264575	−	0.638741i	0.999211	+	0.0397206i	$0.0126468\pi$
$234$	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	$0.0850300\pi$
$239$			30155.8i			0.527928i	−0.964533	+	0.263964i	$0.914970\pi$
$240$	−18598.6	+	12230.6i	−0.322892	+	0.212337i
$241$	29531.5	−	71295.3i	0.508454	−	1.22752i	−0.436320	−	0.899792i	$-0.643718\pi$
$241$	29531.5	−	71295.3i	0.508454	−	1.22752i	0.944774	−	0.327724i	$-0.106282\pi$
$242$	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	0.897117	−	0.441793i	$-0.145658\pi$
$257$	30073.7	+	30073.7i	0.455324	+	0.455324i	−0.441793	+	0.897117i	$0.645658\pi$
$258$	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	−0.348529	−	0.937298i	$-0.613319\pi$
$263$	40724.6	−	40724.6i	0.588769	−	0.588769i	0.937298	+	0.348529i	$0.113319\pi$
$264$	−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	0.649593	−	0.760282i	$-0.274939\pi$
$269$	41341.6	+	17124.3i	0.571325	+	0.236650i	−0.0782686	+	0.996932i	$0.524939\pi$
$270$	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	0.579499	−	0.814973i	$-0.303248\pi$
$277$	31688.5	+	13125.8i	0.412993	+	0.171067i	−0.166506	+	0.986041i	$0.553248\pi$
$278$	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	0.0995708	−	0.995030i	$-0.468253\pi$
$281$	86430.8	−	86430.8i	1.09460	−	1.09460i	0.995030	−	0.0995708i	$-0.0317470\pi$
$282$	−12836.0	−	67102.2i	−0.161410	−	0.843798i
$283$	−53178.6	−	128384.i	−0.663993	−	1.60302i	−0.791489	−	0.611183i	$-0.790694\pi$
$283$	−53178.6	−	128384.i	−0.663993	−	1.60302i	0.127496	−	0.991839i	$-0.459306\pi$
$284$	−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	−0.921076	−	0.389383i	$-0.872688\pi$
$311$	537.647	−	1298.00i	0.00555874	−	0.0134200i	0.926635	+	0.375963i	$0.122688\pi$
$312$	5745.10	+	30033.4i	0.0590185	+	0.308528i
$313$	108459.	−	44925.1i	1.10707	−	0.458564i	0.247143	−	0.968979i	$-0.420508\pi$
$313$	108459.	−	44925.1i	1.10707	−	0.458564i	0.859928	+	0.510415i	$0.170508\pi$
$314$	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	−0.892306	−	0.451432i	$-0.850914\pi$
$317$	−120994.	+	50117.3i	−1.20405	+	0.498734i	−0.311745	+	0.950166i	$0.600914\pi$
$318$	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	0.998690	−	0.0511687i	$-0.0162946\pi$
$331$	103811.	+	103811.i	0.947521	+	0.947521i	−0.0511687	+	0.998690i	$0.516295\pi$
$332$	−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	0.404033	+	0.914745i	$0.367608\pi$
$337$	−60019.4	+	144900.i	−0.528484	+	1.27587i	−0.932516	+	0.361128i	$0.882392\pi$
$338$	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	0.884860	−	0.465858i	$-0.154254\pi$
$347$	−8457.76	−	20418.8i	−0.0702419	−	0.169579i	−0.955101	+	0.296279i	$0.904254\pi$
$348$	−49702.1	−	75579.9i	−0.410408	−	0.624091i
$349$	−63304.9	−	63304.9i	−0.519740	−	0.519740i	0.397752	−	0.917493i	$-0.369790\pi$
$349$	−63304.9	−	63304.9i	−0.519740	−	0.519740i	−0.917493	+	0.397752i	$0.869790\pi$
$350$	−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	0.521121	−	0.853483i	$-0.325514\pi$
$359$	−42835.1	−	42835.1i	−0.332362	−	0.332362i	−0.853483	+	0.521121i	$0.825514\pi$
$360$	−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	−0.370946	−	0.928654i	$-0.620967\pi$
$367$	3153.46	−	1306.21i	0.0234129	−	0.00969794i	0.394359	+	0.918956i	$0.370967\pi$
$368$	−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	−0.0990415	−	0.995083i	$-0.531578\pi$
$379$	−125356.	−	51924.2i	−0.872704	−	0.361486i	−0.773663	+	0.633597i	$0.781578\pi$
$380$	−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	−0.522500	−	0.852639i	$-0.675001\pi$
$383$	48427.8	−	48427.8i	0.330139	−	0.330139i	0.852639	+	0.522500i	$0.175001\pi$
$384$	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	0.928886	+	0.370367i	$0.120768\pi$
$389$	196604.	+	196604.i	1.29925	+	1.29925i	0.370367	+	0.928886i	$0.379232\pi$
$390$	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	0.977723	+	0.209898i	$0.0673132\pi$
$397$	68526.6	+	165438.i	0.434789	+	1.04967i	−0.542934	+	0.839775i	$0.682687\pi$
$398$	−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	0.850521	−	0.525941i	$-0.176287\pi$
$401$	−19743.9	−	47666.0i	−0.122785	−	0.296429i	−0.973306	+	0.229513i	$0.926287\pi$
$402$	−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	0.682769	−	0.730635i	$-0.260776\pi$
$419$	295328.	−	122329.i	1.68220	−	0.696788i	0.999427	+	0.0338463i	$0.0107757\pi$
$420$	83332.1	+	56570.1i	0.472404	+	0.320692i
$421$			272885.i			1.53963i	0.638268	+	0.769814i	$0.279651\pi$
$421$			272885.i			1.53963i	−0.638268	+	0.769814i	$0.720349\pi$
$422$	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	−0.497230	−	0.867619i	$-0.665649\pi$
$431$	−43714.1	+	18107.0i	−0.235325	+	0.0974746i	0.261905	+	0.965094i	$0.415649\pi$
$432$	10107.8	−	45547.9i	0.0541614	−	0.244063i
$433$	−136181.	−	136181.i	−0.726343	−	0.726343i	0.243546	−	0.969889i	$-0.421689\pi$
$433$	−136181.	−	136181.i	−0.726343	−	0.726343i	−0.969889	+	0.243546i	$0.921689\pi$
$434$	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	−0.620870	−	0.783914i	$-0.713220\pi$
$439$	71781.3	−	173295.i	0.372462	−	0.899203i	0.993332	−	0.115289i	$-0.0367796\pi$
$440$	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	$0.0530483\pi$
$443$			65109.8i			0.331772i	−0.986145	+	0.165886i	$0.946952\pi$
$444$	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	0.975926	+	0.218103i	$0.0699867\pi$
$449$	88717.3	+	214183.i	0.440064	+	1.06241i	−0.535862	+	0.844306i	$0.680013\pi$
$450$	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	−0.486846	−	0.873488i	$-0.661853\pi$
$457$	80749.8	−	80749.8i	0.386642	−	0.386642i	0.873488	+	0.486846i	$0.161853\pi$
$458$		−	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	0.546408	−	0.837519i	$-0.315995\pi$
$461$	−61867.1	−	61867.1i	−0.291110	−	0.291110i	−0.837519	+	0.546408i	$0.815995\pi$
$462$	102727.	+	69736.5i	0.481284	+	0.326720i
$463$		−	4892.43i		−	0.0228225i	−0.999935	−	0.0114112i	$-0.996368\pi$
$463$		−	4892.43i		−	0.0228225i	0.999935	−	0.0114112i	$-0.00363239\pi$
$464$	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	−0.998400	−	0.0565485i	$-0.981990\pi$
$467$	−205407.	+	205407.i	−0.941851	+	0.941851i	0.0565485	+	0.998400i	$0.481990\pi$
$468$	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	0.942057	−	0.335453i	$-0.108889\pi$
$479$	314561.	+	130296.i	1.37099	+	0.567883i	0.428934	+	0.903336i	$0.358889\pi$
$480$	−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	−0.901252	−	0.433296i	$-0.857350\pi$
$487$	−135271.	−	326573.i	−0.570357	−	1.37696i	0.330894	−	0.943668i	$-0.392650\pi$
$488$	−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	−0.972102	−	0.234557i	$-0.924636\pi$
$491$	−290903.	−	290903.i	−1.20666	−	1.20666i	−0.234557	−	0.972102i	$-0.575364\pi$
$492$	−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	0.959911	−	0.280307i	$-0.0904361\pi$
$499$	20653.3	+	49861.5i	0.0829447	+	0.200246i	−0.876966	+	0.480553i	$0.840436\pi$
$500$	−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	−0.937955	−	0.346756i	$-0.887283\pi$
$503$	−131543.	−	317573.i	−0.519914	−	1.25518i	0.418041	−	0.908428i	$-0.362717\pi$
$504$	−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	$0.301142\pi$
$509$			420292.i			1.62224i	−0.584878	+	0.811121i	$0.698858\pi$
$510$	−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	0.280533	−	0.959844i	$-0.409489\pi$
$521$	314223.	−	130156.i	1.15761	−	0.479498i	0.877079	+	0.480346i	$0.159489\pi$
$522$	−200519.	−	206497.i	−0.735894	−	0.757831i
$523$			306864.i			1.12187i	0.827860	+	0.560935i	$0.189558\pi$
$523$			306864.i			1.12187i	−0.827860	+	0.560935i	$0.810442\pi$
$524$	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	0.127658	+	0.991818i	$0.459254\pi$
$541$	−194320.	+	469130.i	−0.663931	+	1.60287i	−0.791589	+	0.611054i	$0.790746\pi$
$542$	−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	−0.709792	−	0.704412i	$-0.751211\pi$
$547$	86830.8	−	209628.i	0.290201	−	0.700607i	0.999993	+	0.00380432i	$0.00121095\pi$
$548$	−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	0.784303	−	0.620378i	$-0.213021\pi$
$563$	51959.2	+	51959.2i	0.163925	+	0.163925i	−0.620378	+	0.784303i	$0.713021\pi$
$564$	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	−0.947839	−	0.318749i	$-0.896737\pi$
$569$	−203675.	+	203675.i	−0.629091	+	0.629091i	0.318749	+	0.947839i	$0.396737\pi$
$570$	−520400.	+	342220.i	−1.60172	+	1.05331i
$571$	321821.	−	133303.i	0.987056	−	0.408852i	0.170021	−	0.985440i	$-0.445616\pi$
$571$	321821.	−	133303.i	0.987056	−	0.408852i	0.817035	+	0.576588i	$0.195616\pi$
$572$	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	−0.749345	−	0.662180i	$-0.769632\pi$
$587$	−30034.5	+	30034.5i	−0.0871655	+	0.0871655i	0.662180	+	0.749345i	$0.269632\pi$
$588$	−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	0.0181605	−	0.999835i	$-0.494219\pi$
$593$	−345205.	−	345205.i	−0.981675	−	0.981675i	−0.999835	+	0.0181605i	$0.994219\pi$
$594$	−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	0.898453	−	0.439069i	$-0.144692\pi$
$601$	−17091.2	−	41261.9i	−0.0473178	−	0.114235i	−0.945771	+	0.324834i	$0.894692\pi$
$602$	−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	0.201138	−	0.979563i	$-0.435536\pi$
$607$	−128696.	−	53307.6i	−0.349291	−	0.144681i	−0.550429	+	0.834882i	$0.685536\pi$
$608$	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	−0.976440	−	0.215789i	$-0.930768\pi$
$617$	−50786.5	+	122610.i	−0.133407	+	0.322073i	0.843033	+	0.537862i	$0.180768\pi$
$618$	−47716.8	−	249447.i	−0.124938	−	0.653133i
$619$	256908.	−	106415.i	0.670495	−	0.277728i	−0.0213522	−	0.999772i	$-0.506797\pi$
$619$	256908.	−	106415.i	0.670495	−	0.277728i	0.691847	+	0.722044i	$0.256797\pi$
$620$	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	−0.135906	+	0.990722i	$0.543394\pi$
$631$	−448579.	+	448579.i	−1.12663	+	1.12663i	−0.990722	+	0.135906i	$0.956606\pi$
$632$	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	0.444996	+	0.895533i	$0.353205\pi$
$641$	−206632.	+	498855.i	−0.502901	+	1.21411i	−0.947897	+	0.318578i	$0.896795\pi$
$642$	−165068.	−	34095.9i	−0.400491	−	0.0827241i
$643$	169063.	−	408153.i	0.408908	−	0.987191i	−0.576518	−	0.817085i	$-0.695589\pi$
$643$	169063.	−	408153.i	0.408908	−	0.987191i	0.985426	−	0.170107i	$-0.0544112\pi$
$644$	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	$-0.782208\pi$
$647$		−	529176.i		−	1.26413i	0.774916	−	0.632065i	$-0.217792\pi$
$648$	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	0.999480	−	0.0322505i	$-0.0102674\pi$
$653$	115103.	+	277884.i	0.269936	+	0.651684i	−0.729543	+	0.683934i	$0.760267\pi$
$654$	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	−0.102051	+	0.994779i	$0.532540\pi$
$661$	−479228.	+	479228.i	−1.09683	+	1.09683i	−0.994779	+	0.102051i	$0.967460\pi$
$662$			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	0.309307	−	0.950962i	$-0.399903\pi$
$673$	543720.	−	225216.i	1.20045	−	0.497244i	0.891145	+	0.453718i	$0.149903\pi$
$674$	−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	0.0102318	−	0.999948i	$-0.496743\pi$
$677$	−316065.	−	130918.i	−0.689603	−	0.285643i	−0.699835	+	0.714305i	$0.746743\pi$
$678$	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	0.308909	−	0.951092i	$-0.400036\pi$
$683$	−67726.1	−	28053.1i	−0.145183	−	0.0601366i	−0.454092	+	0.890955i	$0.650036\pi$
$684$	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	−0.937307	−	0.348504i	$-0.886690\pi$
$691$	−248749.	−	600533.i	−0.520961	−	1.25771i	0.416346	−	0.909206i	$-0.363310\pi$
$692$	−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	0.571175	−	0.820828i	$-0.306488\pi$
$709$	198380.	+	82171.6i	0.394643	+	0.163467i	−0.176532	+	0.984295i	$0.556488\pi$
$710$	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	−0.999999	−	0.00160856i	$-0.999488\pi$
$719$	−150826.	+	364127.i	−0.291755	+	0.704360i	0.708243	+	0.705968i	$0.249488\pi$
$720$	−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	$-0.720034\pi$
$727$		−	814406.i		−	1.54089i	0.637506	−	0.770445i	$-0.279966\pi$
$728$	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	−0.822393	−	0.568919i	$-0.807362\pi$
$733$	−136189.	+	136189.i	−0.253474	+	0.253474i	0.568919	+	0.822393i	$0.307362\pi$
$734$	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	0.954582	−	0.297947i	$-0.0963020\pi$
$739$	358602.	+	358602.i	0.656635	+	0.656635i	−0.297947	+	0.954582i	$0.596302\pi$
$740$	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	−0.995289	−	0.0969488i	$-0.969092\pi$
$743$	−123085.	+	297154.i	−0.222960	+	0.538274i	0.772329	+	0.635223i	$0.219092\pi$
$744$	−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	−0.944472	−	0.328592i	$-0.893426\pi$
$751$	−24973.8	+	60292.2i	−0.0442798	+	0.106901i	0.900192	+	0.435493i	$0.143426\pi$
$752$	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	0.459130	−	0.888369i	$-0.348161\pi$
$757$	−245975.	−	245975.i	−0.429238	−	0.429238i	−0.888369	+	0.459130i	$0.848161\pi$
$758$	−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	$0.166993\pi$
$769$			592409.i			1.00177i	−0.865513	+	0.500886i	$0.833007\pi$
$770$	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	−0.413557	−	0.910478i	$-0.635714\pi$
$773$	296925.	−	296925.i	0.496921	−	0.496921i	0.910478	+	0.413557i	$0.135714\pi$
$774$	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	−0.577431	−	0.816439i	$-0.695945\pi$
$787$	−968103.	−	401001.i	−1.56305	−	0.647435i	−0.985615	+	0.169004i	$0.945945\pi$
$788$	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	0.902257	−	0.431200i	$-0.141910\pi$
$797$	299220.	+	299220.i	0.471057	+	0.471057i	−0.431200	+	0.902257i	$0.641910\pi$
$798$	−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	0.973392	−	0.229147i	$-0.0735935\pi$
$809$	80546.1	+	194456.i	0.123069	+	0.297114i	−0.850323	+	0.526261i	$0.823594\pi$
$810$	−293781.	+	654218.i	−0.447768	+	0.997131i
$811$	−13170.0	−	5455.18i	−0.0200236	−	0.00829407i	0.372649	−	0.927972i	$-0.378450\pi$
$811$	−13170.0	−	5455.18i	−0.0200236	−	0.00829407i	−0.392673	+	0.919678i	$0.628450\pi$
$812$	−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	−0.644208	−	0.764851i	$-0.722813\pi$
$821$	237362.	−	573042.i	0.352147	−	0.850158i	0.996355	−	0.0853076i	$-0.0271873\pi$
$822$	−543905.	+	104044.i	−0.804970	+	0.153983i
$823$	476207.	−	197252.i	0.703067	−	0.291220i	−0.00236544	−	0.999997i	$-0.500753\pi$
$823$	476207.	−	197252.i	0.703067	−	0.291220i	0.705432	+	0.708777i	$0.250753\pi$
$824$	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	0.0570693	−	0.998370i	$-0.481824\pi$
$827$	549453.	−	227591.i	0.803378	−	0.332770i	0.746308	+	0.665600i	$0.231824\pi$
$828$	−57451.7	+	55788.6i	−0.0837996	+	0.0813739i
$829$		−	549105.i		−	0.798999i	−0.916733	−	0.399500i	$-0.869184\pi$
$829$		−	549105.i		−	0.798999i	0.916733	−	0.399500i	$-0.130816\pi$
$830$	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	0.0707018	−	0.997497i	$-0.477476\pi$
$839$	581462.	−	240849.i	0.826033	−	0.342154i	0.755331	+	0.655344i	$0.227476\pi$
$840$	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	−0.951940	−	0.306284i	$-0.900914\pi$
$853$	−45287.5	+	109334.i	−0.0622415	+	0.150264i	0.889699	+	0.456548i	$0.150914\pi$
$854$	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	0.998376	−	0.0569596i	$-0.0181406\pi$
$857$	185185.	+	447076.i	0.252141	+	0.608723i	−0.746235	+	0.665682i	$0.768141\pi$
$858$	430322.	−	282984.i	0.584546	−	0.384403i
$859$	423272.	+	423272.i	0.573632	+	0.573632i	0.933141	−	0.359509i	$-0.117056\pi$
$859$	423272.	+	423272.i	0.573632	+	0.573632i	−0.359509	+	0.933141i	$0.617056\pi$
$860$	−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	0.0514075	−	0.998678i	$-0.483629\pi$
$877$	610634.	−	252933.i	0.793930	−	0.328857i	0.742522	+	0.669821i	$0.233629\pi$
$878$	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	0.360693	−	0.932685i	$-0.382540\pi$
$881$	−33969.4	−	14070.6i	−0.0437659	−	0.0181284i	−0.404459	+	0.914556i	$0.632540\pi$
$882$	−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	−0.444218	−	0.895919i	$-0.646518\pi$
$887$	−1.09505e6	−	453587.i	−1.39184	−	0.576518i	−0.947620	+	0.319401i	$0.896518\pi$
$888$	−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	0.788431	−	0.615123i	$-0.210894\pi$
$907$	−167846.	−	405217.i	−0.204031	−	0.492575i	−0.992463	+	0.122548i	$0.960894\pi$
$908$	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	0.836518	−	0.547939i	$-0.184587\pi$
$911$	−118215.	−	285396.i	−0.142441	−	0.343883i	−0.978959	+	0.204056i	$0.934587\pi$
$912$	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	−0.493467	−	0.869764i	$-0.664271\pi$
$929$	−196242.	+	81286.2i	−0.227385	+	0.0941858i	0.266082	+	0.963950i	$0.414271\pi$
$930$	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	0.249746	−	0.968312i	$-0.419653\pi$
$937$	1.06942e6	−	1.06942e6i	1.21806	−	1.21806i	0.968312	−	0.249746i	$-0.0803470\pi$
$938$	−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	−0.871627	−	0.490169i	$-0.836935\pi$
$941$	−1.01065e6	+	418626.i	−1.14136	+	0.472766i	−0.269732	+	0.962935i	$0.586935\pi$
$942$	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	−0.999824	−	0.0187420i	$-0.994034\pi$
$947$	−250738.	+	605335.i	−0.279589	+	0.674988i	0.720235	+	0.693730i	$0.244034\pi$
$948$	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	$0.0690126\pi$
$953$			390739.i			0.430230i	−0.976589	+	0.215115i	$0.930987\pi$
$954$	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	−0.282341	−	0.959314i	$-0.591111\pi$
$967$	633030.	−	633030.i	0.676973	−	0.676973i	0.959314	+	0.282341i	$0.0911110\pi$
$968$			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	0.262164	−	0.965023i	$-0.415564\pi$
$971$	−662684.	−	662684.i	−0.702859	−	0.702859i	−0.965023	+	0.262164i	$0.915564\pi$
$972$	−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	−0.550684	−	0.834714i	$-0.685633\pi$
$977$	271115.	−	271115.i	0.284030	−	0.284030i	0.834714	+	0.550684i	$0.185633\pi$
$978$	−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	0.278826	−	0.960341i	$-0.410055\pi$
$983$	−196231.	−	81281.7i	−0.203077	−	0.0841174i	−0.481904	+	0.876224i	$0.660055\pi$
$984$	−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	0.685762	−	0.727826i	$-0.259469\pi$
$991$	644264.	+	266863.i	0.656019	+	0.271732i	−0.0297434	+	0.999558i	$0.509469\pi$
$992$	−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	0.953509	+	0.301366i	$0.0974425\pi$
$997$	489424.	+	1.18157e6i	0.492374	+	1.18870i	−0.461135	+	0.887330i	$0.652557\pi$
$998$	−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.59.9	yes	44
3.2	odd	2		102.5.g.c.59.1	✓	44
17.15	even	8		102.5.g.c.83.1	yes	44
51.32	odd	8	inner	102.5.g.d.83.9	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
102.5.g.c.59.1	✓	44	3.2	odd	2
102.5.g.c.83.1	yes	44	17.15	even	8
102.5.g.d.59.9	yes	44	1.1	even	1	trivial
102.5.g.d.83.9	yes	44	51.32	odd	8	inner

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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