LMFDB - Embedded newform 51.6.h.a.19.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [51,6,Mod(19,51)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(51, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([0, 7])) N = Newforms(chi, 6, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("51.19"); S:= CuspForms(chi, 6); N := Newforms(S);

Level:	$ N $	$=$	$ 51 = 3 \cdot 17 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	51.h (of order $8$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$8.17957481046$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			19.10
Character	$\chi$	$=$	51.19
Dual form			51.6.h.a.43.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(3.88932 + 3.88932i) q^{2} +(-8.31492 + 3.44415i) q^{3} -1.74633i q^{4} +(-17.4864 - 42.2159i) q^{5} +(-45.7348 - 18.9440i) q^{6} +(37.7648 - 91.1724i) q^{7} +(131.250 - 131.250i) q^{8} +(57.2756 - 57.2756i) q^{9} +(96.1811 - 232.202i) q^{10} +(27.0260 + 11.1945i) q^{11} +(6.01463 + 14.5206i) q^{12} -133.460i q^{13} +(501.479 - 207.719i) q^{14} +(290.796 + 290.796i) q^{15} +965.068 q^{16} +(-496.852 - 1083.05i) q^{17} +445.527 q^{18} +(358.264 + 358.264i) q^{19} +(-73.7230 + 30.5371i) q^{20} +888.159i q^{21} +(61.5736 + 148.652i) q^{22} +(-1660.81 - 687.931i) q^{23} +(-639.290 + 1543.38i) q^{24} +(733.298 - 733.298i) q^{25} +(519.069 - 519.069i) q^{26} +(-278.976 + 673.508i) q^{27} +(-159.217 - 65.9499i) q^{28} +(-527.990 - 1274.68i) q^{29} +2262.00i q^{30} +(1537.45 - 636.831i) q^{31} +(-446.552 - 446.552i) q^{32} -263.274 q^{33} +(2279.91 - 6144.75i) q^{34} -4509.30 q^{35} +(-100.022 - 100.022i) q^{36} +(-1436.34 + 594.951i) q^{37} +2786.81i q^{38} +(459.656 + 1109.71i) q^{39} +(-7835.96 - 3245.76i) q^{40} +(-6686.62 + 16142.9i) q^{41} +(-3454.34 + 3454.34i) q^{42} +(3819.54 - 3819.54i) q^{43} +(19.5494 - 47.1963i) q^{44} +(-3419.49 - 1416.40i) q^{45} +(-3783.85 - 9135.02i) q^{46} +22173.9i q^{47} +(-8024.46 + 3323.84i) q^{48} +(4998.12 + 4998.12i) q^{49} +5704.07 q^{50} +(7861.47 + 7294.23i) q^{51} -233.065 q^{52} +(13368.8 + 13368.8i) q^{53} +(-3704.52 + 1534.46i) q^{54} -1336.68i q^{55} +(-7009.76 - 16923.1i) q^{56} +(-4212.86 - 1745.02i) q^{57} +(2904.12 - 7011.16i) q^{58} +(27.6248 - 27.6248i) q^{59} +(507.826 - 507.826i) q^{60} +(14164.6 - 34196.5i) q^{61} +(8456.46 + 3502.78i) q^{62} +(-3058.95 - 7384.96i) q^{63} -34355.7i q^{64} +(-5634.14 + 2333.74i) q^{65} +(-1023.96 - 1023.96i) q^{66} +69182.8 q^{67} +(-1891.36 + 867.669i) q^{68} +16178.8 q^{69} +(-17538.1 - 17538.1i) q^{70} +(22969.2 - 9514.14i) q^{71} -15034.9i q^{72} +(-12819.1 - 30947.9i) q^{73} +(-7900.34 - 3272.43i) q^{74} +(-3571.72 + 8622.90i) q^{75} +(625.648 - 625.648i) q^{76} +(2041.26 - 2041.26i) q^{77} +(-2528.26 + 6103.77i) q^{78} +(41630.6 + 17244.0i) q^{79} +(-16875.6 - 40741.2i) q^{80} -6561.00i q^{81} +(-88791.5 + 36778.6i) q^{82} +(9473.65 + 9473.65i) q^{83} +1551.02 q^{84} +(-37033.8 + 39913.7i) q^{85} +29710.8 q^{86} +(8780.38 + 8780.38i) q^{87} +(5016.46 - 2077.88i) q^{88} +35980.1i q^{89} +(-7790.67 - 18808.3i) q^{90} +(-12167.9 - 5040.09i) q^{91} +(-1201.35 + 2900.33i) q^{92} +(-10590.4 + 10590.4i) q^{93} +(-86241.4 + 86241.4i) q^{94} +(8859.71 - 21389.2i) q^{95} +(5251.04 + 2175.05i) q^{96} +(45083.5 + 108841. i) q^{97} +38878.6i q^{98} +(2189.10 - 906.757i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 88 q^{5} + 360 q^{6} + 1280 q^{10} - 632 q^{11} - 4256 q^{14} - 8192 q^{16} + 6248 q^{17} + 4152 q^{19} - 16384 q^{20} - 19592 q^{22} - 3608 q^{23} + 10440 q^{24} + 30384 q^{25} - 19936 q^{26} + 13624 q^{28}+ \cdots - 51192 q^{99}+O(q^{100}) $ 56 * q - 88 * q^5 + 360 * q^6 + 1280 * q^10 - 632 * q^11 - 4256 * q^14 - 8192 * q^16 + 6248 * q^17 + 4152 * q^19 - 16384 * q^20 - 19592 * q^22 - 3608 * q^23 + 10440 * q^24 + 30384 * q^25 - 19936 * q^26 + 13624 * q^28 - 23424 * q^29 + 2728 * q^31 + 67200 * q^32 + 20376 * q^33 + 11960 * q^34 + 26272 * q^35 + 3240 * q^36 + 32296 * q^37 - 22320 * q^39 - 100184 * q^40 + 6552 * q^41 - 21528 * q^42 - 38152 * q^43 - 26208 * q^44 + 31752 * q^45 + 106368 * q^46 + 9768 * q^49 + 96128 * q^50 - 62720 * q^52 + 65984 * q^53 + 29160 * q^54 - 268304 * q^56 - 28656 * q^57 - 139352 * q^58 - 67312 * q^59 - 109800 * q^60 - 307184 * q^61 + 150704 * q^62 - 696 * q^65 + 54720 * q^66 + 364272 * q^67 + 558960 * q^68 - 81864 * q^69 + 313960 * q^70 + 309808 * q^71 - 268752 * q^73 - 393712 * q^74 - 96624 * q^75 - 228552 * q^76 - 841536 * q^77 - 130824 * q^78 - 57216 * q^79 + 658528 * q^80 - 335992 * q^82 + 406240 * q^83 + 664848 * q^84 + 686840 * q^85 - 842560 * q^86 + 127224 * q^87 + 538248 * q^88 - 103680 * q^90 - 368592 * q^91 + 96752 * q^92 - 113472 * q^93 - 622576 * q^94 - 1143560 * q^95 - 375552 * q^96 - 40424 * q^97 - 51192 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/51\mathbb{Z}\right)^\times$.

$n$	$35$	$37$
$\chi(n)$	$1$	$e\left(\frac{7}{8}\right)$

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 $

$2$	3.88932	+	3.88932i	0.687542	+	0.687542i	0.961688	−	0.274146i	$-0.0883953\pi$
$2$	3.88932	+	3.88932i	0.687542	+	0.687542i	−0.274146	+	0.961688i	$0.588395\pi$
$3$	−8.31492	+	3.44415i	−0.533402	+	0.220942i
$3$	−8.31492	+	3.44415i	−0.533402	+	0.220942i
$4$		−	1.74633i		−	0.0545728i
$5$	−17.4864	−	42.2159i	−0.312806	−	0.755182i	−0.999599	−	0.0283278i	$-0.990982\pi$
$5$	−17.4864	−	42.2159i	−0.312806	−	0.755182i	0.686792	−	0.726854i	$-0.259018\pi$
$6$	−45.7348	−	18.9440i	−0.518643	−	0.214829i
$7$	37.7648	−	91.1724i	0.291301	−	0.703264i	−0.708696	−	0.705514i	$-0.750716\pi$
$7$	37.7648	−	91.1724i	0.291301	−	0.703264i	0.999997	+	0.00225012i	$0.000716237\pi$
$8$	131.250	−	131.250i	0.725063	−	0.725063i
$9$	57.2756	−	57.2756i	0.235702	−	0.235702i
$10$	96.1811	−	232.202i	0.304151	−	0.734286i
$11$	27.0260	+	11.1945i	0.0673441	+	0.0278949i	0.416101	−	0.909318i	$-0.363396\pi$
$11$	27.0260	+	11.1945i	0.0673441	+	0.0278949i	−0.348757	+	0.937213i	$0.613396\pi$
$12$	6.01463	+	14.5206i	0.0120575	+	0.0291093i
$13$		−	133.460i		−	0.219024i	−0.993985	−	0.109512i	$-0.965071\pi$
$13$		−	133.460i		−	0.219024i	0.993985	−	0.109512i	$-0.0349289\pi$
$14$	501.479	−	207.719i	0.683805	−	0.283241i
$15$	290.796	+	290.796i	0.333703	+	0.333703i
$16$	965.068			0.942449
$17$	−496.852	−	1083.05i	−0.416970	−	0.908920i
$17$	−496.852	−	1083.05i	−0.416970	−	0.908920i
$18$	445.527			0.324110
$19$	358.264	+	358.264i	0.227677	+	0.227677i	0.811722	−	0.584044i	$-0.198531\pi$
$19$	358.264	+	358.264i	0.227677	+	0.227677i	−0.584044	+	0.811722i	$0.698531\pi$
$20$	−73.7230	+	30.5371i	−0.0412124	+	0.0170707i
$21$			888.159i			0.439483i
$22$	61.5736	+	148.652i	0.0271230	+	0.0654808i
$23$	−1660.81	−	687.931i	−0.654637	−	0.271160i	0.0305426	−	0.999533i	$-0.490276\pi$
$23$	−1660.81	−	687.931i	−0.654637	−	0.271160i	−0.685180	+	0.728374i	$0.740276\pi$
$24$	−639.290	+	1543.38i	−0.226553	+	0.546947i
$25$	733.298	−	733.298i	0.234655	−	0.234655i
$26$	519.069	−	519.069i	0.150588	−	0.150588i
$27$	−278.976	+	673.508i	−0.0736475	+	0.177801i
$28$	−159.217	−	65.9499i	−0.0383791	−	0.0158971i
$29$	−527.990	−	1274.68i	−0.116582	−	0.281453i	0.854808	−	0.518944i	$-0.173675\pi$
$29$	−527.990	−	1274.68i	−0.116582	−	0.281453i	−0.971390	+	0.237491i	$0.923675\pi$
$30$			2262.00i			0.458870i
$31$	1537.45	−	636.831i	0.287340	−	0.119020i	−0.234358	−	0.972150i	$-0.575299\pi$
$31$	1537.45	−	636.831i	0.287340	−	0.119020i	0.521698	+	0.853130i	$0.325299\pi$
$32$	−446.552	−	446.552i	−0.0770898	−	0.0770898i
$33$	−263.274			−0.0420847
$34$	2279.91	−	6144.75i	0.338236	−	0.911605i
$35$	−4509.30			−0.622213
$36$	−100.022	−	100.022i	−0.0128629	−	0.0128629i
$37$	−1436.34	+	594.951i	−0.172486	+	0.0714458i	−0.467255	−	0.884122i	$-0.654757\pi$
$37$	−1436.34	+	594.951i	−0.172486	+	0.0714458i	0.294770	+	0.955568i	$0.404757\pi$
$38$			2786.81i			0.313075i
$39$	459.656	+	1109.71i	0.0483918	+	0.116828i
$40$	−7835.96	−	3245.76i	−0.774358	−	0.320750i
$41$	−6686.62	+	16142.9i	−0.621222	+	1.49976i	0.229048	+	0.973415i	$0.426439\pi$
$41$	−6686.62	+	16142.9i	−0.621222	+	1.49976i	−0.850270	+	0.526347i	$0.823561\pi$
$42$	−3454.34	+	3454.34i	−0.302163	+	0.302163i
$43$	3819.54	−	3819.54i	0.315021	−	0.315021i	−0.531830	−	0.846851i	$-0.678495\pi$
$43$	3819.54	−	3819.54i	0.315021	−	0.315021i	0.846851	+	0.531830i	$0.178495\pi$
$44$	19.5494	−	47.1963i	0.00152230	−	0.00367516i
$45$	−3419.49	−	1416.40i	−0.251727	−	0.104269i
$46$	−3783.85	−	9135.02i	−0.263657	−	0.636524i
$47$			22173.9i			1.46419i	0.681203	+	0.732094i	$0.261457\pi$
$47$			22173.9i			1.46419i	−0.681203	+	0.732094i	$0.738543\pi$
$48$	−8024.46	+	3323.84i	−0.502704	+	0.208227i
$49$	4998.12	+	4998.12i	0.297383	+	0.297383i
$50$	5704.07			0.322671
$51$	7861.47	+	7294.23i	0.423232	+	0.392694i
$52$	−233.065			−0.0119528
$53$	13368.8	+	13368.8i	0.653735	+	0.653735i	0.953890	−	0.300155i	$-0.0970385\pi$
$53$	13368.8	+	13368.8i	0.653735	+	0.653735i	−0.300155	+	0.953890i	$0.597039\pi$
$54$	−3704.52	+	1534.46i	−0.172881	+	0.0716097i
$55$		−	1336.68i		−	0.0595827i
$56$	−7009.76	−	16923.1i	−0.298699	−	0.721122i
$57$	−4212.86	−	1745.02i	−0.171747	−	0.0711400i
$58$	2904.12	−	7011.16i	0.113356	−	0.273665i
$59$	27.6248	−	27.6248i	0.00103316	−	0.00103316i	−0.706590	−	0.707623i	$-0.749767\pi$
$59$	27.6248	−	27.6248i	0.00103316	−	0.00103316i	0.707623	+	0.706590i	$0.249767\pi$
$60$	507.826	−	507.826i	0.0182111	−	0.0182111i
$61$	14164.6	−	34196.5i	0.487395	−	1.17667i	−0.468632	−	0.883394i	$-0.655253\pi$
$61$	14164.6	−	34196.5i	0.487395	−	1.17667i	0.956026	−	0.293281i	$-0.0947472\pi$
$62$	8456.46	+	3502.78i	0.279389	+	0.115727i
$63$	−3058.95	−	7384.96i	−0.0971005	−	0.234421i
$64$		−	34355.7i		−	1.04845i
$65$	−5634.14	+	2333.74i	−0.165403	+	0.0685123i
$66$	−1023.96	−	1023.96i	−0.0289350	−	0.0289350i
$67$	69182.8			1.88283			0.941414	−	0.337252i	$-0.109497\pi$
$67$	69182.8			1.88283			0.941414	+	0.337252i	$0.109497\pi$
$68$	−1891.36	+	867.669i	−0.0496024	+	0.0227553i
$69$	16178.8			0.409096
$70$	−17538.1	−	17538.1i	−0.427797	−	0.427797i
$71$	22969.2	−	9514.14i	0.540753	−	0.223987i	−0.0955524	−	0.995424i	$-0.530462\pi$
$71$	22969.2	−	9514.14i	0.540753	−	0.223987i	0.636306	+	0.771437i	$0.280462\pi$
$72$		−	15034.9i		−	0.341798i
$73$	−12819.1	−	30947.9i	−0.281546	−	0.679711i	0.718326	−	0.695706i	$-0.244908\pi$
$73$	−12819.1	−	30947.9i	−0.281546	−	0.679711i	−0.999872	+	0.0159949i	$0.994908\pi$
$74$	−7900.34	−	3272.43i	−0.167713	−	0.0694690i
$75$	−3571.72	+	8622.90i	−0.0733203	+	0.177011i
$76$	625.648	−	625.648i	0.0124250	−	0.0124250i
$77$	2041.26	−	2041.26i	0.0392349	−	0.0392349i
$78$	−2528.26	+	6103.77i	−0.0470528	+	0.113596i
$79$	41630.6	+	17244.0i	0.750490	+	0.310863i	0.724942	−	0.688810i	$-0.241867\pi$
$79$	41630.6	+	17244.0i	0.750490	+	0.310863i	0.0255487	+	0.999674i	$0.491867\pi$
$80$	−16875.6	−	40741.2i	−0.294804	−	0.711720i
$81$		−	6561.00i		−	0.111111i
$82$	−88791.5	+	36778.6i	−1.45827	+	0.604033i
$83$	9473.65	+	9473.65i	0.150946	+	0.150946i	0.778540	−	0.627594i	$-0.215960\pi$
$83$	9473.65	+	9473.65i	0.150946	+	0.150946i	−0.627594	+	0.778540i	$0.715960\pi$
$84$	1551.02			0.0239838
$85$	−37033.8	+	39913.7i	−0.555969	+	0.599204i
$86$	29710.8			0.433180
$87$	8780.38	+	8780.38i	0.124370	+	0.124370i
$88$	5016.46	−	2077.88i	0.0690542	−	0.0286032i
$89$			35980.1i			0.481490i	0.970588	+	0.240745i	$0.0773918\pi$
$89$			35980.1i			0.481490i	−0.970588	+	0.240745i	$0.922608\pi$
$90$	−7790.67	−	18808.3i	−0.101384	−	0.244762i
$91$	−12167.9	−	5040.09i	−0.154032	−	0.0638021i
$92$	−1201.35	+	2900.33i	−0.0147980	+	0.0357254i
$93$	−10590.4	+	10590.4i	−0.126971	+	0.126971i
$94$	−86241.4	+	86241.4i	−1.00669	+	1.00669i
$95$	8859.71	−	21389.2i	0.100719	−	0.243157i
$96$	5251.04	+	2175.05i	0.0581523	+	0.0240875i
$97$	45083.5	+	108841.i	0.486506	+	1.17453i	0.956467	+	0.291842i	$0.0942681\pi$
$97$	45083.5	+	108841.i	0.486506	+	1.17453i	−0.469961	+	0.882687i	$0.655732\pi$
$98$			38878.6i			0.408927i
$99$	2189.10	−	906.757i	0.0224480	−	0.00929828i
$100$	−1280.58	−	1280.58i	−0.0128058	−	0.0128058i
$101$	−79029.5			−0.770878			−0.385439	−	0.922733i	$-0.625950\pi$
$101$	−79029.5			−0.770878			−0.385439	+	0.922733i	$0.625950\pi$
$102$	2206.19	+	58945.4i	0.0209963	+	0.560983i
$103$	98906.5			0.918611			0.459305	−	0.888278i	$-0.348098\pi$
$103$	98906.5			0.918611			0.459305	+	0.888278i	$0.348098\pi$
$104$	−17516.7	−	17516.7i	−0.158806	−	0.158806i
$105$	37494.4	−	15530.7i	0.331890	−	0.137473i
$106$			103991.i			0.898940i
$107$	−75589.5	−	182489.i	−0.638266	−	1.54091i	−0.828988	−	0.559267i	$-0.811083\pi$
$107$	−75589.5	−	182489.i	−0.638266	−	1.54091i	0.190722	−	0.981644i	$-0.438917\pi$
$108$	1176.17	+	487.185i	0.00970309	+	0.00401915i
$109$	−76644.8	+	185037.i	−0.617898	+	1.49174i	0.236242	+	0.971694i	$0.424084\pi$
$109$	−76644.8	+	185037.i	−0.617898	+	1.49174i	−0.854140	+	0.520043i	$0.825916\pi$
$110$	5198.78	−	5198.78i	0.0409656	−	0.0409656i
$111$	9893.94	−	9893.94i	0.0762187	−	0.0762187i
$112$	36445.6	−	87987.5i	0.274537	−	0.662790i
$113$	−49291.8	−	20417.3i	−0.363143	−	0.150419i	0.193648	−	0.981071i	$-0.437968\pi$
$113$	−49291.8	−	20417.3i	−0.363143	−	0.150419i	−0.556792	+	0.830652i	$0.687968\pi$
$114$	−9598.20	−	23172.1i	−0.0691716	−	0.166995i
$115$			82142.2i			0.579191i
$116$	−2226.01	+	922.045i	−0.0153597	+	0.00636219i
$117$	−7644.01	−	7644.01i	−0.0516246	−	0.0516246i
$118$	214.883			0.00142068
$119$	−117508.	+	4398.05i	−0.760675	+	0.0284703i
$120$	76334.2			0.483912
$121$	−113275.	−	113275.i	−0.703350	−	0.703350i
$122$	188092.	−	77910.2i	1.14412	−	0.473909i
$123$		−	157257.i		−	0.937231i
$124$	−1112.12	−	2684.89i	−0.00649526	−	0.0156809i
$125$	−175704.	−	72779.2i	−1.00579	−	0.416612i
$126$	16825.3	−	40619.8i	0.0944138	−	0.227935i
$127$	−56472.2	+	56472.2i	−0.310689	+	0.310689i	−0.845176	−	0.534488i	$-0.820505\pi$
$127$	−56472.2	+	56472.2i	−0.310689	+	0.310689i	0.534488	+	0.845176i	$0.320505\pi$
$128$	119331.	−	119331.i	0.643766	−	0.643766i
$129$	−18604.1	+	44914.2i	−0.0984314	+	0.237634i
$130$	−30989.6	−	12836.3i	−0.160827	−	0.0666166i
$131$	−35723.3	−	86243.7i	−0.181875	−	0.439085i	0.806478	−	0.591264i	$-0.201371\pi$
$131$	−35723.3	−	86243.7i	−0.181875	−	0.439085i	−0.988353	+	0.152179i	$0.951371\pi$
$132$			459.764i			0.00229668i
$133$	46193.6	−	19134.0i	0.226440	−	0.0937945i
$134$	269074.	+	269074.i	1.29452	+	1.29452i
$135$	33311.1			0.157309
$136$	−207363.	−	76938.5i	−0.961354	−	0.356695i
$137$	328537.			1.49549			0.747745	−	0.663986i	$-0.231137\pi$
$137$	328537.			1.49549			0.747745	+	0.663986i	$0.231137\pi$
$138$	62924.8	+	62924.8i	0.281270	+	0.281270i
$139$	174276.	−	72187.3i	0.765067	−	0.316901i	0.0341946	−	0.999415i	$-0.489113\pi$
$139$	174276.	−	72187.3i	0.765067	−	0.316901i	0.730872	+	0.682514i	$0.239113\pi$
$140$			7874.73i			0.0339559i
$141$	−76370.2	−	184374.i	−0.323501	−	0.781001i
$142$	126338.	+	52330.9i	0.525791	+	0.217790i
$143$	1494.02	−	3606.89i	0.00610965	−	0.0147500i
$144$	55274.9	−	55274.9i	0.222137	−	0.222137i
$145$	−44579.1	+	44579.1i	−0.176081	+	0.176081i
$146$	70509.1	−	170224.i	0.273756	−	0.660904i
$147$	−58773.2	−	24344.7i	−0.224329	−	0.0929203i
$148$	1038.98	+	2508.32i	0.00389900	+	0.00941303i
$149$			371879.i			1.37226i	0.727479	+	0.686130i	$0.240692\pi$
$149$			371879.i			1.37226i	−0.727479	+	0.686130i	$0.759308\pi$
$150$	−47428.8	+	19645.7i	−0.172113	+	0.0712916i
$151$	27279.7	+	27279.7i	0.0973639	+	0.0973639i	0.754111	−	0.656747i	$-0.228068\pi$
$151$	27279.7	+	27279.7i	0.0973639	+	0.0973639i	−0.656747	+	0.754111i	$0.728068\pi$
$152$	94044.7			0.330161
$153$	−90489.9	−	33574.8i	−0.312515	−	0.115954i
$154$	15878.3			0.0539512
$155$	−53768.8	−	53768.8i	−0.179763	−	0.179763i
$156$	1937.92	−	802.712i	0.00637564	−	0.00264088i
$157$		−	66569.3i		−	0.215539i	−0.994176	−	0.107769i	$-0.965629\pi$
$157$		−	66569.3i		−	0.215539i	0.994176	−	0.107769i	$-0.0343708\pi$
$158$	94847.6	+	228982.i	0.302262	+	0.729725i
$159$	−157204.	−	65116.1i	−0.493141	−	0.204266i
$160$	−11043.0	+	26660.2i	−0.0341026	+	0.0823310i
$161$	−125441.	+	125441.i	−0.381394	+	0.381394i
$162$	25517.8	−	25517.8i	0.0763935	−	0.0763935i
$163$	213085.	−	514432.i	0.628179	−	1.51656i	−0.213703	−	0.976899i	$-0.568553\pi$
$163$	213085.	−	514432.i	0.628179	−	1.51656i	0.841883	−	0.539661i	$-0.181447\pi$
$164$	28190.9	+	11677.0i	0.0818463	+	0.0339019i
$165$	4603.72	+	11114.4i	0.0131644	+	0.0317816i
$166$			73692.1i			0.207563i
$167$	−124794.	+	51691.4i	−0.346260	+	0.143426i	−0.549034	−	0.835800i	$-0.685004\pi$
$167$	−124794.	+	51691.4i	−0.346260	+	0.143426i	0.202774	+	0.979226i	$0.435004\pi$
$168$	116571.	+	116571.i	0.318653	+	0.318653i
$169$	353481.			0.952028
$170$	−299274.	+	11201.1i	−0.794230	+	0.0297262i
$171$	41039.7			0.107328
$172$	−6670.18	−	6670.18i	−0.0171916	−	0.0171916i
$173$	−319209.	+	132221.i	−0.810885	+	0.335880i	−0.749307	−	0.662223i	$-0.769613\pi$
$173$	−319209.	+	132221.i	−0.810885	+	0.335880i	−0.0615779	+	0.998102i	$0.519613\pi$
$174$			68299.4i			0.171019i
$175$	−39163.7	−	94549.4i	−0.0966692	−	0.233380i
$176$	26081.9	+	10803.5i	0.0634684	+	0.0262895i
$177$	−134.554	+	324.841i	−0.000322821	+	0.000779360i
$178$	−139938.	+	139938.i	−0.331045	+	0.331045i
$179$	−65964.2	+	65964.2i	−0.153878	+	0.153878i	−0.779847	−	0.625970i	$-0.784703\pi$
$179$	−65964.2	+	65964.2i	−0.153878	+	0.153878i	0.625970	+	0.779847i	$0.284703\pi$
$180$	−2473.50	+	5971.56i	−0.00569025	+	0.0137375i
$181$	−573652.	−	237615.i	−1.30152	−	0.539109i	−0.379125	−	0.925346i	$-0.623775\pi$
$181$	−573652.	−	237615.i	−1.30152	−	0.539109i	−0.922400	+	0.386236i	$0.873775\pi$
$182$	−27722.2	−	66927.3i	−0.0620368	−	0.149770i
$183$			333126.i			0.735327i
$184$	−308273.	+	127691.i	−0.671261	+	0.278045i
$185$	50232.8	+	50232.8i	0.107909	+	0.107909i
$186$	−82378.9			−0.174596
$187$	−1303.70	−	34832.5i	−0.00272630	−	0.0728418i
$188$	38722.9			0.0799049
$189$	50869.9	+	50869.9i	0.103587	+	0.103587i
$190$	117648.	−	48731.4i	0.236429	−	0.0979320i
$191$		−	745501.i		−	1.47865i	−0.673350	−	0.739324i	$-0.735145\pi$
$191$		−	745501.i		−	1.47865i	0.673350	−	0.739324i	$-0.264855\pi$
$192$	118326.	+	285665.i	0.231648	+	0.559248i
$193$	106795.	+	44235.7i	0.206374	+	0.0854831i	0.483476	−	0.875357i	$-0.339374\pi$
$193$	106795.	+	44235.7i	0.206374	+	0.0854831i	−0.277102	+	0.960841i	$0.589374\pi$
$194$	−247974.	+	598663.i	−0.473045	+	1.14203i
$195$	38809.6	−	38809.6i	0.0730892	−	0.0730892i
$196$	8728.38	−	8728.38i	0.0162291	−	0.0162291i
$197$	96902.8	−	233944.i	0.177898	−	0.429483i	−0.809627	−	0.586944i	$-0.800331\pi$
$197$	96902.8	−	233944.i	0.177898	−	0.429483i	0.987525	+	0.157461i	$0.0503308\pi$
$198$	12040.8	+	4987.46i	0.0218269	+	0.00904101i
$199$	70596.7	+	170435.i	0.126372	+	0.305090i	0.974385	−	0.224886i	$-0.0722010\pi$
$199$	70596.7	+	170435.i	0.126372	+	0.305090i	−0.848013	+	0.529976i	$0.822201\pi$
$200$		−	192491.i		−	0.340280i
$201$	−575249.	+	238276.i	−1.00430	+	0.415997i
$202$	−307371.	−	307371.i	−0.530011	−	0.530011i
$203$	−136155.			−0.231896
$204$	12738.1	−	13728.7i	0.0214304	−	0.0230970i
$205$	798414.			1.32692
$206$	384679.	+	384679.i	0.631583	+	0.631583i
$207$	−134526.	+	55722.4i	−0.218212	+	0.0903866i
$208$		−	128798.i		−	0.206419i
$209$	5671.85	+	13693.0i	0.00898170	+	0.0216838i
$210$	206232.	+	85424.1i	0.322707	+	0.133669i
$211$	−73432.8	+	177282.i	−0.113549	+	0.274132i	−0.970430	−	0.241383i	$-0.922399\pi$
$211$	−73432.8	+	177282.i	−0.113549	+	0.274132i	0.856881	+	0.515514i	$0.172399\pi$
$212$	23346.3	−	23346.3i	0.0356762	−	0.0356762i
$213$	−158218.	+	158218.i	−0.238951	+	0.238951i
$214$	415767.	−	1.00375e6i	0.620606	−	1.49827i
$215$	−228035.	−	94455.3i	−0.336439	−	0.139358i
$216$	51782.5	+	125014.i	0.0755176	+	0.182316i
$217$		−	164222.i		−	0.236746i
$218$	−1.01777e6	+	421572.i	−1.45046	+	0.600801i
$219$	213179.	+	213179.i	0.300354	+	0.300354i
$220$	−2334.28			−0.00325160
$221$	−144544.	+	66309.9i	−0.199076	+	0.0913267i
$222$	76961.4			0.104807
$223$	1.01397e6	+	1.01397e6i	1.36541	+	1.36541i	0.866868	+	0.498538i	$0.166130\pi$
$223$	1.01397e6	+	1.01397e6i	1.36541	+	1.36541i	0.498538	+	0.866868i	$0.333870\pi$
$224$	−57577.2	+	23849.3i	−0.0766709	+	0.0317581i
$225$		−	84000.2i		−	0.110618i
$226$	−112302.	−	271121.i	−0.146257	−	0.353096i
$227$	625645.	+	259151.i	0.805867	+	0.333801i	0.747304	−	0.664483i	$-0.231348\pi$
$227$	625645.	+	259151.i	0.805867	+	0.333801i	0.0585632	+	0.998284i	$0.481348\pi$
$228$	−3047.39	+	7357.04i	−0.00388231	+	0.00937273i
$229$	−839814.	+	839814.i	−1.05827	+	1.05827i	−0.0600713	+	0.998194i	$0.519133\pi$
$229$	−839814.	+	839814.i	−1.05827	+	1.05827i	−0.998194	+	0.0600713i	$0.980867\pi$
$230$	−319477.	+	319477.i	−0.398218	+	0.398218i
$231$	−9942.52	+	24003.4i	−0.0122593	+	0.0295966i
$232$	−236601.	−	98003.3i	−0.288600	−	0.119542i
$233$	−79735.9	−	192499.i	−0.0962197	−	0.232295i	0.868440	−	0.495795i	$-0.165123\pi$
$233$	−79735.9	−	192499.i	−0.0962197	−	0.232295i	−0.964659	+	0.263500i	$0.915123\pi$
$234$		−	59460.0i		−	0.0709881i
$235$	936091.	−	387742.i	1.10573	−	0.458008i
$236$	−48.2420	−	48.2420i	−5.63826e−5	−	5.63826e-5i
$237$	−405546.			−0.468996
$238$	−474131.	−	439920.i	−0.542570	−	0.503421i
$239$	1.40431e6			1.59026			0.795132	−	0.606436i	$-0.207401\pi$
$239$	1.40431e6			1.59026			0.795132	+	0.606436i	$0.207401\pi$
$240$	280638.	+	280638.i	0.314498	+	0.314498i
$241$	465781.	−	192933.i	0.516582	−	0.213975i	−0.109133	−	0.994027i	$-0.534807\pi$
$241$	465781.	−	192933.i	0.516582	−	0.213975i	0.625715	+	0.780052i	$0.284807\pi$
$242$		−	881127.i		−	0.967164i
$243$	22597.1	+	54554.2i	0.0245492	+	0.0592669i
$244$	−59718.3	−	24736.1i	−0.0642145	−	0.0265985i
$245$	123601.	−	298400.i	0.131555	−	0.317602i
$246$	611622.	−	611622.i	0.644385	−	0.644385i
$247$	47814.0	−	47814.0i	0.0498669	−	0.0498669i
$248$	118206.	−	285375.i	0.122042	−	0.294636i
$249$	−111401.	−	46143.9i	−0.113865	−	0.0471646i
$250$	−400310.	−	966433.i	−0.405085	−	0.977961i
$251$		−	1.32807e6i		−	1.33056i	−0.746592	−	0.665282i	$-0.768311\pi$
$251$		−	1.32807e6i		−	1.33056i	0.746592	−	0.665282i	$-0.231689\pi$
$252$	−12896.6	+	5341.94i	−0.0127930	+	0.00529905i
$253$	−37184.0	−	37184.0i	−0.0365220	−	0.0365220i
$254$	−439277.			−0.427223
$255$	170464.	−	459429.i	0.164165	−	0.442454i
$256$	−171151.			−0.163222
$257$	618382.	+	618382.i	0.584015	+	0.584015i	0.936004	−	0.351989i	$-0.114495\pi$
$257$	618382.	+	618382.i	0.584015	+	0.584015i	−0.351989	+	0.936004i	$0.614495\pi$
$258$	−247043.	+	102329.i	−0.231059	+	0.0957079i
$259$			153423.i			0.142115i
$260$	4075.48	+	9839.07i	0.00373891	+	0.00902652i
$261$	−103249.	−	42767.2i	−0.0938177	−	0.0388606i
$262$	196490.	−	474369.i	0.176843	−	0.426936i
$263$	418227.	−	418227.i	0.372840	−	0.372840i	−0.495670	−	0.868511i	$-0.665078\pi$
$263$	418227.	−	418227.i	0.372840	−	0.372840i	0.868511	+	0.495670i	$0.165078\pi$
$264$	−34554.9	+	34554.9i	−0.0305140	+	0.0305140i
$265$	330603.	−	798147.i	0.289196	−	0.698181i
$266$	254080.	+	105244.i	0.220174	+	0.0911993i
$267$	−123921.	−	299172.i	−0.106382	−	0.256828i
$268$		−	120816.i		−	0.102751i
$269$	−343011.	+	142080.i	−0.289020	+	0.119716i	−0.522483	−	0.852650i	$-0.674994\pi$
$269$	−343011.	+	142080.i	−0.289020	+	0.119716i	0.233463	+	0.972366i	$0.424994\pi$
$270$	129558.	+	129558.i	0.108157	+	0.108157i
$271$	−1.26520e6			−1.04649			−0.523247	−	0.852181i	$-0.675279\pi$
$271$	−1.26520e6			−1.04649			−0.523247	+	0.852181i	$0.675279\pi$
$272$	−479496.	−	1.04522e6i	−0.392973	−	0.856611i
$273$	118534.			0.0962576
$274$	1.27779e6	+	1.27779e6i	1.02821	+	1.02821i
$275$	28027.0	−	11609.2i	0.0223483	−	0.00925698i
$276$		−	28253.6i		−	0.0223255i
$277$	779697.	+	1.88235e6i	0.610557	+	1.47401i	0.862390	+	0.506244i	$0.168967\pi$
$277$	779697.	+	1.88235e6i	0.610557	+	1.47401i	−0.251833	+	0.967771i	$0.581033\pi$
$278$	958574.	+	397054.i	0.743898	+	0.308133i
$279$	51583.3	−	124533.i	0.0396733	−	0.0957798i
$280$	−591847.	+	591847.i	−0.451143	+	0.451143i
$281$	−1.29662e6	+	1.29662e6i	−0.979594	+	0.979594i	−0.999796	−	0.0202019i	$-0.993569\pi$
$281$	−1.29662e6	+	1.29662e6i	−0.979594	+	0.979594i	0.0202019	+	0.999796i	$0.493569\pi$
$282$	420061.	−	1.01412e6i	0.314550	−	0.759392i
$283$	−850975.	−	352485.i	−0.631612	−	0.261622i	0.0438257	−	0.999039i	$-0.486045\pi$
$283$	−850975.	−	352485.i	−0.631612	−	0.261622i	−0.675438	+	0.737417i	$0.736045\pi$
$284$	−16614.8	−	40111.7i	−0.0122236	−	0.0295104i
$285$			208364.i			0.151953i
$286$	19839.1	−	8217.61i	0.0143419	−	0.00594060i
$287$	1.21927e6	+	1.21927e6i	0.873766	+	0.873766i
$288$	−51153.1			−0.0363405
$289$	−926133.	+	1.07623e6i	−0.652272	+	0.757985i
$290$	−346765.			−0.242126
$291$	−749731.	−	749731.i	−0.519007	−	0.519007i
$292$	−54045.3	+	22386.3i	−0.0370938	+	0.0153647i
$293$			730721.i			0.497259i	0.968599	+	0.248629i	$0.0799801\pi$
$293$			730721.i			0.497259i	−0.968599	+	0.248629i	$0.920020\pi$
$294$	−133904.	−	323272.i	−0.0903493	−	0.218122i
$295$	−1649.26	−	683.147i	−0.00110340	−	0.000457045i
$296$	−110432.	+	266608.i	−0.0732601	+	0.176866i
$297$	−15079.2	+	15079.2i	−0.00991945	+	0.00991945i
$298$	−1.44636e6	+	1.44636e6i	−0.943486	+	0.943486i
$299$	−91811.2	+	221652.i	−0.0593906	+	0.143382i
$300$	15058.4	+	6237.41i	0.00965999	+	0.00400130i
$301$	−203992.	−	492481.i	−0.129777	−	0.313309i
$302$			212199.i			0.133883i
$303$	657123.	−	272189.i	0.411188	−	0.170320i
$304$	345749.	+	345749.i	0.214574	+	0.214574i
$305$	−1.69132e6			−1.04106
$306$	−221361.	−	482528.i	−0.135144	−	0.294590i
$307$	−1.00230e6			−0.606946			−0.303473	−	0.952840i	$-0.598146\pi$
$307$	−1.00230e6			−0.606946			−0.303473	+	0.952840i	$0.598146\pi$
$308$	−3564.72	−	3564.72i	−0.00214116	−	0.00214116i
$309$	−822399.	+	340649.i	−0.489989	+	0.202960i
$310$		−	418249.i		−	0.247190i
$311$	884908.	+	2.13636e6i	0.518796	+	1.25249i	0.938643	+	0.344890i	$0.112084\pi$
$311$	884908.	+	2.13636e6i	0.518796	+	1.25249i	−0.419846	+	0.907595i	$0.637916\pi$
$312$	205980.	+	85319.6i	0.119795	+	0.0496206i
$313$	−853496.	+	2.06052e6i	−0.492426	+	1.18882i	0.461056	+	0.887371i	$0.347471\pi$
$313$	−853496.	+	2.06052e6i	−0.492426	+	1.18882i	−0.953482	+	0.301450i	$0.902529\pi$
$314$	258910.	−	258910.i	0.148192	−	0.148192i
$315$	−258273.	+	258273.i	−0.146657	+	0.146657i
$316$	30113.7	−	72700.8i	0.0169647	−	0.0409564i
$317$	−1.78339e6	−	738703.i	−0.996776	−	0.412878i	−0.176162	−	0.984361i	$-0.556368\pi$
$317$	−1.78339e6	−	738703.i	−0.996776	−	0.412878i	−0.820614	+	0.571483i	$0.806368\pi$
$318$	−358160.	−	864676.i	−0.198614	−	0.479497i
$319$		−	40360.1i		−	0.0222062i
$320$	−1.45036e6	+	600759.i	−0.791773	+	0.327963i
$321$	1.25704e6	+	1.25704e6i	0.680905	+	0.680905i
$322$	−975758.			−0.524448
$323$	210013.	−	566022.i	0.112006	−	0.301875i
$324$	−11457.7			−0.00606365
$325$	−97865.9	−	97865.9i	−0.0513953	−	0.0513953i
$326$	2.82955e6	−	1.17204e6i	1.47460	−	0.610798i
$327$		−	1.80254e6i		−	0.932215i
$328$	1.24114e6	+	2.99639e6i	0.636997	+	1.53785i
$329$	2.02165e6	+	837393.i	1.02971	+	0.426520i
$330$	−25322.0	+	61132.8i	−0.0128001	+	0.0309022i
$331$	−390377.	+	390377.i	−0.195846	+	0.195846i	−0.798217	−	0.602371i	$-0.794223\pi$
$331$	−390377.	+	390377.i	−0.195846	+	0.195846i	0.602371	+	0.798217i	$0.294223\pi$
$332$	16544.1	−	16544.1i	0.00823756	−	0.00823756i
$333$	−48191.0	+	116343.i	−0.0238153	+	0.0574952i
$334$	−686409.	−	284320.i	−0.336680	−	0.139457i
$335$	−1.20976e6	−	2.92061e6i	−0.588961	−	1.42188i
$336$			857133.i			0.414190i
$337$	2.63340e6	−	1.09079e6i	1.26311	−	0.523198i	0.352248	−	0.935907i	$-0.385417\pi$
$337$	2.63340e6	−	1.09079e6i	1.26311	−	0.523198i	0.910863	+	0.412709i	$0.135417\pi$
$338$	1.37480e6	+	1.37480e6i	0.654559	+	0.654559i
$339$	480177.			0.226935
$340$	69702.6	+	64673.2i	0.0327003	+	0.0303408i
$341$	48680.0			0.0226707
$342$	159616.	+	159616.i	0.0737925	+	0.0737925i
$343$	2.17678e6	−	901651.i	0.999031	−	0.413812i
$344$		−	1.00263e6i		−	0.456820i
$345$	−282910.	−	683005.i	−0.127968	−	0.308942i
$346$	−1.75575e6	−	727257.i	−0.788448	−	0.326586i
$347$	908124.	−	2.19241e6i	0.404876	−	0.977456i	−0.581589	−	0.813483i	$-0.697569\pi$
$347$	908124.	−	2.19241e6i	0.404876	−	0.977456i	0.986465	−	0.163973i	$-0.0524312\pi$
$348$	15333.4	−	15333.4i	0.00678722	−	0.00678722i
$349$	−1.20880e6	+	1.20880e6i	−0.531242	+	0.531242i	−0.920942	−	0.389700i	$-0.872579\pi$
$349$	−1.20880e6	+	1.20880e6i	−0.531242	+	0.531242i	0.389700	+	0.920942i	$0.372579\pi$
$350$	215413.	−	520053.i	0.0939944	−	0.226923i
$351$	89886.4	+	37232.2i	0.0389427	+	0.0161306i
$352$	−7069.57	−	17067.4i	−0.00304114	−	0.00734196i
$353$		−	2.97633e6i		−	1.27129i	−0.771982	−	0.635644i	$-0.780735\pi$
$353$		−	2.97633e6i		−	1.27129i	0.771982	−	0.635644i	$-0.219265\pi$
$354$	−1786.74	+	740.090i	−0.000757796	+	0.000313889i
$355$	−803296.	−	803296.i	−0.338302	−	0.338302i
$356$	62833.2			0.0262763
$357$	961919.	−	441284.i	0.399455	−	0.183251i
$358$	−513112.			−0.211595
$359$	−1.02877e6	−	1.02877e6i	−0.421289	−	0.421289i	0.464358	−	0.885647i	$-0.346285\pi$
$359$	−1.02877e6	−	1.02877e6i	−0.421289	−	0.421289i	−0.885647	+	0.464358i	$0.846285\pi$
$360$	−634712.	+	262907.i	−0.258119	+	0.106917i
$361$		−	2.21939e6i		−	0.896326i
$362$	−1.30696e6	−	3.15528e6i	−0.524192	−	1.26551i
$363$	1.33201e6	+	551737.i	0.530568	+	0.219768i
$364$	−8801.67	+	21249.1i	−0.00348186	+	0.00840596i
$365$	−1.08234e6	+	1.08234e6i	−0.425236	+	0.425236i
$366$	−1.29563e6	+	1.29563e6i	−0.505568	+	0.505568i
$367$	1.73899e6	−	4.19829e6i	0.673956	−	1.62707i	−0.100871	−	0.994899i	$-0.532163\pi$
$367$	1.73899e6	−	4.19829e6i	0.673956	−	1.62707i	0.774827	−	0.632173i	$-0.217837\pi$
$368$	−1.60280e6	−	663900.i	−0.616962	−	0.255554i
$369$	541616.	+	1.30758e6i	0.207074	+	0.499921i
$370$			390743.i			0.148384i
$371$	1.72373e6	−	713993.i	0.650182	−	0.269314i
$372$	18494.3	+	18494.3i	0.00692917	+	0.00692917i
$373$	675381.			0.251349			0.125674	−	0.992072i	$-0.459891\pi$
$373$	675381.			0.251349			0.125674	+	0.992072i	$0.459891\pi$
$374$	130404.	−	140545.i	0.0482073	−	0.0519562i
$375$	1.71163e6			0.628538
$376$	2.91033e6	+	2.91033e6i	1.06163	+	1.06163i
$377$	−170119.	+	70465.5i	−0.0616451	+	0.0255342i
$378$			395699.i			0.142441i
$379$	1.44064e6	+	3.47802e6i	0.515179	+	1.24375i	0.940834	+	0.338867i	$0.110044\pi$
$379$	1.44064e6	+	3.47802e6i	0.515179	+	1.24375i	−0.425655	+	0.904886i	$0.639956\pi$
$380$	−37352.7	−	15472.0i	−0.0132697	−	0.00549651i
$381$	275063.	−	664060.i	0.0970777	−	0.234366i
$382$	2.89949e6	−	2.89949e6i	1.01663	−	1.01663i
$383$	−3.34461e6	+	3.34461e6i	−1.16506	+	1.16506i	−0.181706	+	0.983353i	$0.558162\pi$
$383$	−3.34461e6	+	3.34461e6i	−1.16506	+	1.16506i	−0.983353	+	0.181706i	$0.941838\pi$
$384$	−581233.	+	1.40322e6i	−0.201151	+	0.485621i
$385$	−121868.	−	50479.5i	−0.0419024	−	0.0173565i
$386$	243311.	+	587406.i	0.0831178	+	0.200664i
$387$		−	437533.i		−	0.148502i
$388$	190073.	−	78730.7i	0.0640974	−	0.0265500i
$389$	798176.	+	798176.i	0.267439	+	0.267439i	0.828067	−	0.560628i	$-0.189440\pi$
$389$	798176.	+	798176.i	0.267439	+	0.267439i	−0.560628	+	0.828067i	$0.689440\pi$
$390$	301886.			0.100504
$391$	80115.6	+	2.14054e6i	0.0265018	+	0.708079i
$392$	1.31201e6			0.431243
$393$	594072.	+	594072.i	0.194025	+	0.194025i
$394$	1.28677e6	−	532997.i	0.417600	−	0.172976i
$395$		−	2.05901e6i		−	0.663997i
$396$	−1583.50	−	3822.90i	−0.000507434	−	0.00122505i
$397$	−3.86377e6	−	1.60043e6i	−1.23037	−	0.509635i	−0.329676	−	0.944094i	$-0.606940\pi$
$397$	−3.86377e6	−	1.60043e6i	−1.23037	−	0.509635i	−0.900692	+	0.434459i	$0.856940\pi$
$398$	−388305.	+	937452.i	−0.122876	+	0.296648i
$399$	−318196.	+	318196.i	−0.100060	+	0.100060i
$400$	707682.	−	707682.i	0.221151	−	0.221151i
$401$	−1.67885e6	+	4.05311e6i	−0.521377	+	1.25872i	0.415671	+	0.909515i	$0.363547\pi$
$401$	−1.67885e6	+	4.05311e6i	−0.521377	+	1.25872i	−0.937048	+	0.349201i	$0.886453\pi$
$402$	−3.16406e6	−	1.31060e6i	−0.976517	−	0.404486i
$403$	−84991.4	−	205187.i	−0.0260683	−	0.0629344i
$404$			138012.i			0.0420690i
$405$	−276979.	+	114728.i	−0.0839091	+	0.0347563i
$406$	−529551.	−	529551.i	−0.159438	−	0.159438i
$407$	−45478.7			−0.0136089
$408$	1.98919e6	−	74450.9i	0.591597	−	0.0221421i
$409$	−1.10868e6			−0.327716			−0.163858	−	0.986484i	$-0.552394\pi$
$409$	−1.10868e6			−0.327716			−0.163858	+	0.986484i	$0.552394\pi$
$410$	3.10529e6	+	3.10529e6i	0.912310	+	0.912310i
$411$	−2.73176e6	+	1.13153e6i	−0.797697	+	0.330417i
$412$		−	172723.i		−	0.0501312i
$413$	−1475.37	−	3561.86i	−0.000425624	−	0.00102755i
$414$	−739936.	−	306492.i	−0.212175	−	0.0878856i
$415$	234279.	−	565599.i	0.0667748	−	0.161209i
$416$	−59596.8	+	59596.8i	−0.0168846	+	0.0168846i
$417$	−1.20046e6	+	1.20046e6i	−0.338071	+	0.338071i
$418$	−31197.0	+	75316.3i	−0.00873319	+	0.0210838i
$419$	1.84109e6	+	762606.i	0.512319	+	0.212210i	0.623839	−	0.781553i	$-0.285572\pi$
$419$	1.84109e6	+	762606.i	0.512319	+	0.212210i	−0.111520	+	0.993762i	$0.535572\pi$
$420$	−27121.8	−	65477.7i	−0.00750230	−	0.0181122i
$421$		−	3.74530e6i		−	1.02987i	−0.857230	−	0.514933i	$-0.827817\pi$
$421$		−	3.74530e6i		−	1.02987i	0.857230	−	0.514933i	$-0.172183\pi$
$422$	−975113.	+	403905.i	−0.266547	+	0.110407i
$423$	1.27002e6	+	1.27002e6i	0.345113	+	0.345113i
$424$	3.50931e6			0.947998
$425$	−1.15854e6	−	429857.i	−0.311127	−	0.115439i
$426$	−1.23073e6			−0.328577
$427$	−2.58285e6	−	2.58285e6i	−0.685534	−	0.685534i
$428$	−318686.	+	132004.i	−0.0840919	+	0.0348320i
$429$			35136.6i			0.00921757i
$430$	−519536.	−	1.25427e6i	−0.135502	−	0.327130i
$431$	4.08329e6	+	1.69136e6i	1.05881	+	0.438573i	0.843028	−	0.537869i	$-0.180771\pi$
$431$	4.08329e6	+	1.69136e6i	1.05881	+	0.438573i	0.215780	+	0.976442i	$0.430771\pi$
$432$	−269231.	+	649981.i	−0.0694090	+	0.167568i
$433$	991034.	−	991034.i	0.254020	−	0.254020i	−0.568596	−	0.822617i	$-0.692513\pi$
$433$	991034.	−	991034.i	0.254020	−	0.254020i	0.822617	+	0.568596i	$0.192513\pi$
$434$	638714.	−	638714.i	0.162773	−	0.162773i
$435$	217135.	−	524209.i	0.0550181	−	0.132825i
$436$	323136.	+	133847.i	0.0814083	+	0.0337204i
$437$	−348549.	−	841471.i	−0.0873092	−	0.210783i
$438$			1.65824e6i			0.413012i
$439$	−4.37485e6	+	1.81212e6i	−1.08343	+	0.448772i	−0.851712	−	0.524010i	$-0.824435\pi$
$439$	−4.37485e6	+	1.81212e6i	−1.08343	+	0.448772i	−0.231720	+	0.972782i	$0.574435\pi$
$440$	−175440.	−	175440.i	−0.0432012	−	0.0432012i
$441$	572541.			0.140188
$442$	−820077.	−	304276.i	−0.199664	−	0.0740820i
$443$	−688217.			−0.166616			−0.0833078	−	0.996524i	$-0.526548\pi$
$443$	−688217.			−0.166616			−0.0833078	+	0.996524i	$0.526548\pi$
$444$	−17278.1	−	17278.1i	−0.00415947	−	0.00415947i
$445$	1.51893e6	−	629163.i	0.363613	−	0.150613i
$446$			7.88729e6i			1.87755i
$447$	−1.28081e6	−	3.09215e6i	−0.303190	−	0.731966i
$448$	−3.13229e6	−	1.29744e6i	−0.737340	−	0.305416i
$449$	−1.90839e6	+	4.60726e6i	−0.446736	+	1.07852i	0.526802	+	0.849988i	$0.323391\pi$
$449$	−1.90839e6	+	4.60726e6i	−0.446736	+	1.07852i	−0.973537	+	0.228528i	$0.926609\pi$
$450$	326704.	−	326704.i	0.0760542	−	0.0760542i
$451$	−361425.	+	361425.i	−0.0836713	+	0.0836713i
$452$	−35655.4	+	86079.7i	−0.00820879	+	0.0198178i
$453$	−320784.	−	132873.i	−0.0734459	−	0.0304223i
$454$	1.42541e6	+	3.44126e6i	0.324565	+	0.783569i
$455$			601811.i			0.136280i
$456$	−781974.	+	323904.i	−0.176108	+	0.0729465i
$457$	−6.02373e6	−	6.02373e6i	−1.34920	−	1.34920i	−0.886536	−	0.462660i	$-0.846895\pi$
$457$	−6.02373e6	−	6.02373e6i	−1.34920	−	1.34920i	−0.462660	−	0.886536i	$-0.653105\pi$
$458$	−6.53262e6			−1.45520
$459$	868052.	−	32489.2i	0.192315	−	0.00719793i
$460$	143447.			0.0316081
$461$	−3.63732e6	−	3.63732e6i	−0.797131	−	0.797131i	0.185511	−	0.982642i	$-0.440606\pi$
$461$	−3.63732e6	−	3.63732e6i	−0.797131	−	0.797131i	−0.982642	+	0.185511i	$0.940606\pi$
$462$	−132026.	+	54687.2i	−0.0287777	+	0.0119201i
$463$			1.94076e6i			0.420745i	0.977621	+	0.210373i	$0.0674677\pi$
$463$			1.94076e6i			0.420745i	−0.977621	+	0.210373i	$0.932532\pi$
$464$	−509546.	−	1.23015e6i	−0.109872	−	0.265255i
$465$	632271.	+	261895.i	0.135603	+	0.0561688i
$466$	438574.	−	1.05881e6i	0.0935573	−	0.225867i
$467$	−1.24560e6	+	1.24560e6i	−0.264293	+	0.264293i	−0.826796	−	0.562502i	$-0.809839\pi$
$467$	−1.24560e6	+	1.24560e6i	−0.264293	+	0.264293i	0.562502	+	0.826796i	$0.309839\pi$
$468$	−13349.0	+	13349.0i	−0.00281730	+	0.00281730i
$469$	2.61268e6	−	6.30756e6i	0.548471	−	1.32413i
$470$	5.14881e6	+	2.13271e6i	1.07513	+	0.445335i
$471$	229275.	+	553518.i	0.0476216	+	0.114969i
$472$		−	7251.52i		−	0.00149821i
$473$	145985.	−	60468.8i	0.0300023	−	0.0124274i
$474$	−1.57730e6	−	1.57730e6i	−0.322454	−	0.322454i
$475$	525429.			0.106851
$476$	7680.45	+	205207.i	0.00155371	+	0.0415122i
$477$	1.53141e6			0.308174
$478$	5.46183e6	+	5.46183e6i	1.09337	+	1.09337i
$479$	−5.50089e6	+	2.27854e6i	−1.09545	+	0.453752i	−0.855905	−	0.517132i	$-0.827000\pi$
$479$	−5.50089e6	+	2.27854e6i	−1.09545	+	0.453752i	−0.239549	+	0.970884i	$0.577000\pi$
$480$		−	259711.i		−	0.0514503i
$481$	79402.1	+	191694.i	0.0156484	+	0.0377785i
$482$	2.56195e6	+	1.06120e6i	0.502289	+	0.208055i
$483$	610992.	−	1.47506e6i	0.119170	−	0.287702i
$484$	−197816.	+	197816.i	−0.0383838	+	0.0383838i
$485$	3.80648e6	−	3.80648e6i	0.734801	−	0.734801i
$486$	−124291.	+	300066.i	−0.0238699	+	0.0576270i
$487$	3.30369e6	+	1.36843e6i	0.631214	+	0.261457i	0.675269	−	0.737572i	$-0.264028\pi$
$487$	3.30369e6	+	1.36843e6i	0.631214	+	0.261457i	−0.0440549	+	0.999029i	$0.514028\pi$
$488$	−2.62918e6	−	6.34741e6i	−0.499771	−	1.20655i
$489$			5.01136e6i			0.947727i
$490$	1.64130e6	−	679848.i	0.308814	−	0.127915i
$491$	5.69566e6	+	5.69566e6i	1.06620	+	1.06620i	0.997647	+	0.0685572i	$0.0218396\pi$
$491$	5.69566e6	+	5.69566e6i	1.06620	+	1.06620i	0.0685572	+	0.997647i	$0.478160\pi$
$492$	−274622.			−0.0511473
$493$	−1.11821e6	+	1.20517e6i	−0.207207	+	0.223321i
$494$	371928.			0.0685711
$495$	−76559.2	−	76559.2i	−0.0140438	−	0.0140438i
$496$	1.48374e6	−	614585.i	0.270803	−	0.112170i
$497$		−	2.45345e6i		−	0.445540i
$498$	−253807.	−	612744.i	−0.0458596	−	0.110715i
$499$	−3.35144e6	−	1.38821e6i	−0.602532	−	0.249577i	0.0604997	−	0.998168i	$-0.480731\pi$
$499$	−3.35144e6	−	1.38821e6i	−0.602532	−	0.249577i	−0.663032	+	0.748591i	$0.730731\pi$
$500$	−127096.	+	306838.i	−0.0227357	+	0.0548889i
$501$	859619.	−	859619.i	0.153007	−	0.153007i
$502$	5.16528e6	−	5.16528e6i	0.914818	−	0.914818i
$503$	−103993.	+	251062.i	−0.0183267	+	0.0442446i	−0.932778	−	0.360451i	$-0.882623\pi$
$503$	−103993.	+	251062.i	−0.0183267	+	0.0442446i	0.914451	+	0.404696i	$0.132623\pi$
$504$	−1.37077e6	−	567791.i	−0.240374	−	0.0995662i
$505$	1.38194e6	+	3.33630e6i	0.241136	+	0.582153i
$506$		−	289241.i		−	0.0502208i
$507$	−2.93917e6	+	1.21744e6i	−0.507814	+	0.210343i
$508$	98619.2	+	98619.2i	0.0169552	+	0.0169552i
$509$	1.99471e6			0.341260			0.170630	−	0.985335i	$-0.445420\pi$
$509$	1.99471e6			0.341260			0.170630	+	0.985335i	$0.445420\pi$
$510$	2.44986e6	−	1.12388e6i	0.417076	−	0.191335i
$511$	−3.30571e6			−0.560031
$512$	−4.48425e6	−	4.48425e6i	−0.755988	−	0.755988i
$513$	−341241.	+	141347.i	−0.0572490	+	0.0237133i
$514$			4.81017e6i			0.803069i
$515$	−1.72952e6	−	4.17543e6i	−0.287347	−	0.693718i
$516$	78435.1	+	32488.9i	0.0129684	+	0.00537168i
$517$	−248226.	+	599271.i	−0.0408433	+	0.0986045i
$518$	−596710.	+	596710.i	−0.0977101	+	0.0977101i
$519$	2.19880e6	−	2.19880e6i	0.358318	−	0.358318i
$520$	−433179.	+	1.04579e6i	−0.0702520	+	0.169603i
$521$	8.81731e6	+	3.65225e6i	1.42312	+	0.589476i	0.955643	−	0.294529i	$-0.0951627\pi$
$521$	8.81731e6	+	3.65225e6i	1.42312	+	0.589476i	0.467478	+	0.884005i	$0.345163\pi$
$522$	−235234.	−	567904.i	−0.0377853	−	0.0912218i
$523$			5.41741e6i			0.866039i	0.901385	+	0.433019i	$0.142552\pi$
$523$			5.41741e6i			0.866039i	−0.901385	+	0.433019i	$0.857448\pi$
$524$	−150610.	+	62384.7i	−0.0239621	+	0.00992544i
$525$	651285.	+	651285.i	0.103127	+	0.103127i
$526$	3.25324e6			0.512687
$527$	−1.45360e6	−	1.34872e6i	−0.227992	−	0.211541i
$528$	−254078.			−0.0396626
$529$	−2.26613e6	−	2.26613e6i	−0.352084	−	0.352084i
$530$	4.39007e6	−	1.81843e6i	0.678863	−	0.281194i
$531$		−	3164.45i		−	0.000487037i
$532$	−33414.3	−	80669.4i	−0.00511863	−	0.0123575i
$533$	2.15443e6	+	892396.i	0.328485	+	0.136063i
$534$	681606.	−	1.64554e6i	0.103438	−	0.249722i
$535$	−6.38216e6	+	6.38216e6i	−0.964014	+	0.964014i
$536$	9.08026e6	−	9.08026e6i	1.36517	−	1.36517i
$537$	321296.	−	775677.i	0.0480806	−	0.116077i
$538$	−1.88668e6	−	781487.i	−0.281023	−	0.116404i
$539$	79127.5	+	191031.i	0.0117316	+	0.0283225i
$540$		−	58172.2i		−	0.00858481i
$541$	6.40533e6	−	2.65317e6i	0.940910	−	0.389738i	0.141103	−	0.989995i	$-0.454935\pi$
$541$	6.40533e6	−	2.65317e6i	0.940910	−	0.389738i	0.799807	+	0.600257i	$0.204935\pi$
$542$	−4.92078e6	−	4.92078e6i	−0.719508	−	0.719508i
$543$	5.58825e6			0.813348
$544$	−261767.	+	705508.i	−0.0379243	+	0.102213i
$545$	9.15175e6			1.31981
$546$	461015.	+	461015.i	0.0661811	+	0.0661811i
$547$	−6.95431e6	+	2.88057e6i	−0.993770	+	0.411633i	−0.819509	−	0.573067i	$-0.805754\pi$
$547$	−6.95431e6	+	2.88057e6i	−0.993770	+	0.411633i	−0.174261	+	0.984700i	$0.555754\pi$
$548$		−	573735.i		−	0.0816131i
$549$	−1.14734e6	−	2.76991e6i	−0.162465	−	0.392225i
$550$	154158.	+	63854.3i	0.0217300	+	0.00900085i
$551$	267512.	−	645832.i	0.0375375	−	0.0906235i
$552$	2.12348e6	−	2.12348e6i	0.296620	−	0.296620i
$553$	3.14435e6	−	3.14435e6i	0.437238	−	0.437238i
$554$	−4.28859e6	+	1.03536e7i	−0.593663	+	1.43323i
$555$	−590691.	−	244672.i	−0.0814007	−	0.0337173i
$556$	−126063.	−	304343.i	−0.0172942	−	0.0417519i
$557$		−	9.43243e6i		−	1.28821i	−0.764939	−	0.644103i	$-0.777231\pi$
$557$		−	9.43243e6i		−	1.28821i	0.764939	−	0.644103i	$-0.222769\pi$
$558$	684973.	−	283725.i	0.0931297	−	0.0385756i
$559$	−509755.	−	509755.i	−0.0689973	−	0.0689973i
$560$	−4.35178e6			−0.586404
$561$	130808.	+	285139.i	0.0175480	+	0.0382516i
$562$	−1.00859e7			−1.34702
$563$	−9.35925e6	−	9.35925e6i	−1.24443	−	1.24443i	−0.958145	−	0.286284i	$-0.907580\pi$
$563$	−9.35925e6	−	9.35925e6i	−1.24443	−	1.24443i	−0.286284	−	0.958145i	$-0.592420\pi$
$564$	−321978.	+	133368.i	−0.0426215	+	0.0176544i
$565$			2.43792e6i			0.321291i
$566$	−1.93879e6	−	4.68064e6i	−0.254383	−	0.614136i
$567$	−598182.	−	247775.i	−0.0781404	−	0.0323668i
$568$	1.76598e6	−	4.26344e6i	0.229675	−	0.554485i
$569$	−1.71513e6	+	1.71513e6i	−0.222084	+	0.222084i	−0.809375	−	0.587292i	$-0.800194\pi$
$569$	−1.71513e6	+	1.71513e6i	−0.222084	+	0.222084i	0.587292	+	0.809375i	$0.300194\pi$
$570$	−810394.	+	810394.i	−0.104474	+	0.104474i
$571$	−2.26380e6	+	5.46530e6i	−0.290568	+	0.701494i	−0.999995	−	0.00328552i	$-0.998954\pi$
$571$	−2.26380e6	+	5.46530e6i	−0.290568	+	0.701494i	0.709426	+	0.704780i	$0.248954\pi$
$572$	−6298.82	−	2609.06i	−0.000804950	−	0.000333421i
$573$	2.56762e6	+	6.19878e6i	0.326696	+	0.788714i
$574$			9.48427e6i			1.20150i
$575$	−1.72233e6	+	713412.i	−0.217243	+	0.0899851i
$576$	−1.96775e6	−	1.96775e6i	−0.247123	−	0.247123i
$577$	9.31578e6			1.16488			0.582438	−	0.812875i	$-0.302099\pi$
$577$	9.31578e6			1.16488			0.582438	+	0.812875i	$0.302099\pi$
$578$	−7.78784e6	+	583780.i	−0.969610	+	0.0726825i
$579$	−1.04034e6			−0.128967
$580$	77849.9	+	77849.9i	0.00960922	+	0.00960922i
$581$	1.22151e6	−	505964.i	0.150126	−	0.0621841i
$582$		−	5.83189e6i		−	0.713677i
$583$	211647.	+	510961.i	0.0257894	+	0.0622611i
$584$	−5.74443e6	−	2.37942e6i	−0.696972	−	0.288695i
$585$	−189033.	+	456365.i	−0.0228374	+	0.0551344i
$586$	−2.84201e6	+	2.84201e6i	−0.341886	+	0.341886i
$587$	7.26101e6	−	7.26101e6i	0.869764	−	0.869764i	−0.122682	−	0.992446i	$-0.539149\pi$
$587$	7.26101e6	−	7.26101e6i	0.869764	−	0.869764i	0.992446	+	0.122682i	$0.0391495\pi$
$588$	−42513.9	+	102638.i	−0.00507093	+	0.0122423i
$589$	778966.	+	322658.i	0.0925188	+	0.0383226i
$590$	−3757.54	−	9071.49i	−0.000444399	−	0.00107287i
$591$			2.27897e6i			0.268392i
$592$	−1.38616e6	+	574168.i	−0.162559	+	0.0673341i
$593$	730078.	+	730078.i	0.0852574	+	0.0852574i	0.748449	−	0.663192i	$-0.230799\pi$
$593$	730078.	+	730078.i	0.0852574	+	0.0852574i	−0.663192	+	0.748449i	$0.730799\pi$
$594$	−117296.			−0.0136401
$595$	2.24046e6	+	4.88379e6i	0.259444	+	0.565542i
$596$	649425.			0.0748881
$597$	−1.17401e6	−	1.17401e6i	−0.134814	−	0.134814i
$598$	−1.21916e6	+	504992.i	−0.139414	+	0.0577473i
$599$			1.13080e7i			1.28771i	0.765147	+	0.643856i	$0.222666\pi$
$599$			1.13080e7i			1.28771i	−0.765147	+	0.643856i	$0.777334\pi$
$600$	662969.	+	1.60055e6i	0.0751822	+	0.181506i
$601$	−277194.	−	114817.i	−0.0313038	−	0.0129665i	0.366977	−	0.930230i	$-0.380393\pi$
$601$	−277194.	−	114817.i	−0.0313038	−	0.0129665i	−0.398280	+	0.917264i	$0.630393\pi$
$602$	1.12202e6	−	2.70881e6i	0.126186	−	0.304640i
$603$	3.96249e6	−	3.96249e6i	0.443787	−	0.443787i
$604$	47639.5	−	47639.5i	0.00531342	−	0.00531342i
$605$	−2.80124e6	+	6.76279e6i	−0.311144	+	0.751169i
$606$	3.61440e6	+	1.49713e6i	0.399811	+	0.165607i
$607$	5.09657e6	+	1.23042e7i	0.561444	+	1.35545i	0.908612	+	0.417642i	$0.137143\pi$
$607$	5.09657e6	+	1.23042e7i	0.561444	+	1.35545i	−0.347168	+	0.937803i	$0.612857\pi$
$608$		−	319967.i		−	0.0351032i
$609$	1.13212e6	−	468938.i	0.123694	−	0.0512357i
$610$	−6.57811e6	−	6.57811e6i	−0.715775	−	0.715775i
$611$	2.95932e6			0.320693
$612$	−58632.7	+	158025.i	−0.00632792	+	0.0170549i
$613$	9.62269e6			1.03430			0.517149	−	0.855896i	$-0.326993\pi$
$613$	9.62269e6			1.03430			0.517149	+	0.855896i	$0.326993\pi$
$614$	−3.89826e6	−	3.89826e6i	−0.417301	−	0.417301i
$615$	−6.63874e6	+	2.74986e6i	−0.707779	+	0.293172i
$616$		−	535833.i		−	0.0568955i
$617$	2.89542e6	+	6.99017e6i	0.306196	+	0.739222i	0.999822	+	0.0188864i	$0.00601210\pi$
$617$	2.89542e6	+	6.99017e6i	0.306196	+	0.739222i	−0.693626	+	0.720335i	$0.743988\pi$
$618$	−4.52347e6	−	1.87368e6i	−0.476431	−	0.197344i
$619$	−6.33958e6	+	1.53051e7i	−0.665019	+	1.60550i	0.124816	+	0.992180i	$0.460166\pi$
$619$	−6.33958e6	+	1.53051e7i	−0.665019	+	1.60550i	−0.789836	+	0.613319i	$0.789834\pi$
$620$	−93898.1	+	93898.1i	−0.00981020	+	0.00981020i
$621$	926654.	−	926654.i	0.0964248	−	0.0964248i
$622$	−4.86729e6	+	1.17507e7i	−0.504442	+	1.21783i
$623$	3.28039e6	+	1.35878e6i	0.338615	+	0.140259i
$624$	443599.	+	1.07094e6i	0.0456068	+	0.110105i
$625$			5.44942e6i			0.558021i
$626$	−1.13336e7	+	4.69451e6i	−1.15593	+	0.478801i
$627$	−94321.9	−	94321.9i	−0.00958172	−	0.00958172i
$628$	−116252.			−0.0117626
$629$	1.35801e6	+	1.26002e6i	0.136860	+	0.126985i
$630$	−2.00901e6			−0.201666
$631$	−1.24230e7	−	1.24230e7i	−1.24209	−	1.24209i	−0.959133	−	0.282955i	$-0.908685\pi$
$631$	−1.24230e7	−	1.24230e7i	−1.24209	−	1.24209i	−0.282955	−	0.959133i	$-0.591315\pi$
$632$	7.72731e6	−	3.20076e6i	0.769548	−	0.318757i
$633$		−	1.72700e6i		−	0.171310i
$634$	−4.06311e6	−	9.80922e6i	−0.401454	−	0.969196i
$635$	3.37152e6	+	1.39653e6i	0.331812	+	0.137441i
$636$	−113714.	+	274531.i	−0.0111474	+	0.0269121i
$637$	667049.	−	667049.i	0.0651342	−	0.0651342i
$638$	156973.	−	156973.i	0.0152677	−	0.0152677i
$639$	770645.	−	1.86050e6i	0.0746624	−	0.180251i
$640$	−7.12434e6	−	2.95100e6i	−0.687534	−	0.284786i
$641$	5.29438e6	+	1.27818e7i	0.508944	+	1.22870i	0.944492	+	0.328533i	$0.106554\pi$
$641$	5.29438e6	+	1.27818e7i	0.508944	+	1.22870i	−0.435549	+	0.900165i	$0.643446\pi$
$642$			9.77807e6i			0.936301i
$643$	3.96277e6	−	1.64143e6i	0.377982	−	0.156565i	−0.185600	−	0.982625i	$-0.559423\pi$
$643$	3.96277e6	−	1.64143e6i	0.377982	−	0.156565i	0.563582	+	0.826060i	$0.309423\pi$
$644$	219061.	+	219061.i	0.0208137	+	0.0208137i
$645$	2.22141e6			0.210247
$646$	3.01825e6	−	1.38463e6i	0.284560	−	0.130543i
$647$	−2.92855e6			−0.275038			−0.137519	−	0.990499i	$-0.543913\pi$
$647$	−2.92855e6			−0.275038			−0.137519	+	0.990499i	$0.543913\pi$
$648$	−861134.	−	861134.i	−0.0805625	−	0.0805625i
$649$	1055.83	−	437.340i	9.83973e−5	−	4.07575e-5i
$650$		−	761264.i		−	0.0706728i
$651$	565607.	+	1.36550e6i	0.0523073	+	0.126281i
$652$	−898369.	−	372117.i	−0.0827629	−	0.0342815i
$653$	1.92377e6	−	4.64440e6i	0.176551	−	0.426232i	−0.810688	−	0.585479i	$-0.800906\pi$
$653$	1.92377e6	−	4.64440e6i	0.176551	−	0.426232i	0.987239	+	0.159247i	$0.0509065\pi$
$654$	7.01067e6	−	7.01067e6i	0.640937	−	0.640937i
$655$	−3.01619e6	+	3.01619e6i	−0.274698	+	0.274698i
$656$	−6.45304e6	+	1.55790e7i	−0.585470	+	1.41345i
$657$	−2.50678e6	−	1.03834e6i	−0.226570	−	0.0938486i
$658$	4.60594e6	+	1.11197e7i	0.414719	+	1.00122i
$659$		−	8.90743e6i		−	0.798985i	−0.916736	−	0.399493i	$-0.869186\pi$
$659$		−	8.90743e6i		−	0.798985i	0.916736	−	0.399493i	$-0.130814\pi$
$660$	19409.4	−	8039.63i	0.00173441	−	0.000718416i
$661$	−1.45626e7	−	1.45626e7i	−1.29639	−	1.29639i	−0.930760	−	0.365631i	$-0.880853\pi$
$661$	−1.45626e7	−	1.45626e7i	−1.29639	−	1.29639i	−0.365631	−	0.930760i	$-0.619147\pi$
$662$	−3.03661e6			−0.269304
$663$	973487.	−	1.04919e6i	0.0860095	−	0.0926981i
$664$	2.48684e6			0.218891
$665$	−1.61552e6	−	1.61552e6i	−0.141664	−	0.141664i
$666$	−639928.	+	265067.i	−0.0559043	+	0.0231563i
$667$			2.48022e6i			0.215862i
$668$	90270.3	+	217932.i	0.00782715	+	0.0188964i
$669$	−1.19233e7	−	4.93880e6i	−1.02999	−	0.426634i
$670$	6.65407e6	−	1.60644e7i	0.572665	−	1.38254i
$671$	765626.	−	765626.i	0.0656463	−	0.0656463i
$672$	396609.	−	396609.i	0.0338797	−	0.0338797i
$673$	6.79776e6	−	1.64112e7i	0.578533	−	1.39670i	−0.315596	−	0.948894i	$-0.602204\pi$
$673$	6.79776e6	−	1.64112e7i	0.578533	−	1.39670i	0.894129	−	0.447809i	$-0.147796\pi$
$674$	1.44846e7	+	5.99970e6i	1.22816	+	0.508721i
$675$	289310.	+	698455.i	0.0244401	+	0.0590037i
$676$		−	617296.i		−	0.0519549i
$677$	5.41540e6	−	2.24313e6i	0.454107	−	0.188097i	−0.143893	−	0.989593i	$-0.545962\pi$
$677$	5.41540e6	−	2.24313e6i	0.454107	−	0.188097i	0.598000	+	0.801496i	$0.295962\pi$
$678$	1.86756e6	+	1.86756e6i	0.156028	+	0.156028i
$679$	1.16259e7			0.967724
$680$	377997.	+	1.00994e7i	0.0313485	+	0.837573i
$681$	−6.09474e6			−0.503602
$682$	189332.	+	189332.i	0.0155870	+	0.0155870i
$683$	912337.	−	377902.i	0.0748348	−	0.0309976i	−0.344952	−	0.938620i	$-0.612105\pi$
$683$	912337.	−	377902.i	0.0748348	−	0.0309976i	0.419787	+	0.907623i	$0.362105\pi$
$684$		−	71668.8i		−	0.00585720i
$685$	−5.74494e6	−	1.38695e7i	−0.467799	−	1.12937i
$686$	1.19730e7	+	4.95938e6i	0.971388	+	0.402362i
$687$	4.09054e6	−	9.87543e6i	0.330665	−	0.798297i
$688$	3.68611e6	−	3.68611e6i	0.296891	−	0.296891i
$689$	1.78420e6	−	1.78420e6i	0.143184	−	0.143184i
$690$	1.55610e6	−	3.75676e6i	0.124427	−	0.300393i
$691$	−4.69119e6	−	1.94316e6i	−0.373756	−	0.154815i	0.187895	−	0.982189i	$-0.439834\pi$
$691$	−4.69119e6	−	1.94316e6i	−0.373756	−	0.154815i	−0.561651	+	0.827374i	$0.689834\pi$
$692$	230901.	+	557444.i	0.0183299	+	0.0442523i
$693$		−	233829.i		−	0.0184955i
$694$	1.20590e7	−	4.99499e6i	0.950411	−	0.393673i
$695$	−6.09491e6	−	6.09491e6i	−0.478636	−	0.478636i
$696$	2.30486e6			0.180352
$697$	2.08058e7	−	778715.i	1.62220	−	0.0607151i
$698$	−9.40286e6			−0.730502
$699$	1.32599e6	+	1.32599e6i	0.102648	+	0.102648i
$700$	−165115.	+	68392.7i	−0.0127362	+	0.00527551i
$701$			2.27457e6i			0.174826i	0.996172	+	0.0874128i	$0.0278599\pi$
$701$			2.27457e6i			0.174826i	−0.996172	+	0.0874128i	$0.972140\pi$
$702$	204789.	+	494405.i	0.0156843	+	0.0378652i
$703$	−727739.	−	301439.i	−0.0555376	−	0.0230044i
$704$	384596.	−	928498.i	0.0292465	−	0.0706072i
$705$	−6.44808e6	+	6.44808e6i	−0.488604	+	0.488604i
$706$	1.15759e7	−	1.15759e7i	0.874063	−	0.874063i
$707$	−2.98454e6	+	7.20531e6i	−0.224558	+	0.542131i
$708$	567.280	+	234.975i	4.25319e−5	+	1.76173e-5i
$709$	−4.70040e6	−	1.13478e7i	−0.351171	−	0.847803i	−0.996476	−	0.0838775i	$-0.973270\pi$
$709$	−4.70040e6	−	1.13478e7i	−0.351171	−	0.847803i	0.645305	−	0.763925i	$-0.276730\pi$
$710$		−	6.24856e6i		−	0.465194i
$711$	3.37208e6	−	1.39676e6i	0.250163	−	0.103621i
$712$	4.72240e6	+	4.72240e6i	0.349111	+	0.349111i
$713$	−2.99150e6			−0.220377
$714$	5.45751e6	+	2.02492e6i	0.400635	+	0.148649i
$715$	−178393.			−0.0130501
$716$	115195.	+	115195.i	0.00839754	+	0.00839754i
$717$	−1.16767e7	+	4.83667e6i	−0.848250	+	0.351357i
$718$		−	8.00240e6i		−	0.579308i
$719$	−3.55467e6	−	8.58173e6i	−0.256435	−	0.619089i	0.742263	−	0.670109i	$-0.233753\pi$
$719$	−3.55467e6	−	8.58173e6i	−0.256435	−	0.619089i	−0.998698	+	0.0510204i	$0.983753\pi$
$720$	−3.30004e6	−	1.36692e6i	−0.237240	−	0.0982680i
$721$	3.73519e6	−	9.01754e6i	0.267593	−	0.646026i
$722$	8.63193e6	−	8.63193e6i	0.616262	−	0.616262i
$723$	−3.20844e6	+	3.20844e6i	−0.228270	+	0.228270i
$724$	−414954.	+	1.00179e6i	−0.0294207	+	0.0710279i
$725$	−1.32189e6	−	547546.i	−0.0934010	−	0.0386880i
$726$	3.03474e6	+	7.32650e6i	0.213688	+	0.515888i
$727$			1.29728e7i			0.910326i	0.890408	+	0.455163i	$0.150419\pi$
$727$			1.29728e7i			0.910326i	−0.890408	+	0.455163i	$0.849581\pi$
$728$	−2.25855e6	+	935522.i	−0.157943	+	0.0654223i
$729$	−375786.	−	375786.i	−0.0261891	−	0.0261891i
$730$	−8.41912e6			−0.584735
$731$	−6.03449e6	−	2.23900e6i	−0.417683	−	0.154975i
$732$	581748.			0.0401289
$733$	−6.88407e6	−	6.88407e6i	−0.473244	−	0.473244i	0.429719	−	0.902963i	$-0.358613\pi$
$733$	−6.88407e6	−	6.88407e6i	−0.473244	−	0.473244i	−0.902963	+	0.429719i	$0.858613\pi$
$734$	2.30920e7	−	9.56501e6i	1.58205	−	0.655308i
$735$			2.90687e6i			0.198476i
$736$	434442.	+	1.04884e6i	0.0295622	+	0.0713696i
$737$	1.86973e6	+	774468.i	0.126797	+	0.0525212i
$738$	−2.97907e6	+	7.19211e6i	−0.201344	+	0.486088i
$739$	927244.	−	927244.i	0.0624573	−	0.0624573i	−0.675188	−	0.737645i	$-0.735938\pi$
$739$	927244.	−	927244.i	0.0624573	−	0.0624573i	0.737645	+	0.675188i	$0.235938\pi$
$740$	87723.2	−	87723.2i	0.00588891	−	0.00588891i
$741$	−232891.	+	562247.i	−0.0155814	+	0.0376168i
$742$	9.48110e6	+	3.92720e6i	0.632192	+	0.261863i
$743$	−2.87705e6	−	6.94582e6i	−0.191195	−	0.461585i	0.798991	−	0.601343i	$-0.205367\pi$
$743$	−2.87705e6	−	6.94582e6i	−0.191195	−	0.461585i	−0.990186	+	0.139758i	$0.955367\pi$
$744$			2.77998e6i			0.184124i
$745$	1.56992e7	−	6.50284e6i	1.03631	−	0.429252i
$746$	2.62677e6	+	2.62677e6i	0.172813	+	0.172813i
$747$	1.08522e6			0.0711567
$748$	−60829.0	+	2276.69i	−0.00397518	+	0.000148782i
$749$	−1.94926e7			−1.26959
$750$	6.65708e6	+	6.65708e6i	0.432146	+	0.432146i
$751$	−2.40176e7	+	9.94841e6i	−1.55392	+	0.643656i	−0.984020	−	0.178056i	$-0.943019\pi$
$751$	−2.40176e7	+	9.94841e6i	−1.55392	+	0.643656i	−0.569903	+	0.821712i	$0.693019\pi$
$752$			2.13993e7i			1.37992i
$753$	4.57406e6	+	1.10428e7i	0.293978	+	0.709725i
$754$	−935709.	−	387583.i	−0.0599394	−	0.0248277i
$755$	674615.	−	1.62866e6i	0.0430714	−	0.103983i
$756$	88835.6	−	88835.6i	0.00565305	−	0.00565305i
$757$	−3.18761e6	+	3.18761e6i	−0.202174	+	0.202174i	−0.800931	−	0.598757i	$-0.795662\pi$
$757$	−3.18761e6	+	3.18761e6i	−0.202174	+	0.202174i	0.598757	+	0.800931i	$0.295662\pi$
$758$	−7.92402e6	+	1.91303e7i	−0.500925	+	1.20934i
$759$	437249.	+	181115.i	0.0275502	+	0.0114117i
$760$	−1.64450e6	−	3.97018e6i	−0.103276	−	0.249331i
$761$		−	2.40761e7i		−	1.50704i	−0.657425	−	0.753520i	$-0.728354\pi$
$761$		−	2.40761e7i		−	1.50704i	0.657425	−	0.753520i	$-0.271646\pi$
$762$	3.65255e6	−	1.51294e6i	0.227882	−	0.0943916i
$763$	1.39758e7	+	1.39758e7i	0.869090	+	0.869090i
$764$	−1.30189e6			−0.0806940
$765$	164952.	+	4.40722e6i	0.0101907	+	0.272277i
$766$	−2.60165e7			−1.60205
$767$	−3686.80	−	3686.80i	−0.000226288	−	0.000226288i
$768$	1.42310e6	−	589469.i	0.0870630	−	0.0360627i
$769$			1.99622e7i			1.21729i	0.793443	+	0.608644i	$0.208286\pi$
$769$			1.99622e7i			1.21729i	−0.793443	+	0.608644i	$0.791714\pi$
$770$	−277654.	−	670316.i	−0.0168763	−	0.0407430i
$771$	−7.27159e6	−	3.01199e6i	−0.440548	−	0.182481i
$772$	77250.2	−	186499.i	0.00466505	−	0.0112624i
$773$	−2.03805e7	+	2.03805e7i	−1.22678	+	1.22678i	−0.261605	+	0.965175i	$0.584252\pi$
$773$	−2.03805e7	+	2.03805e7i	−1.22678	+	1.22678i	−0.965175	+	0.261605i	$0.915748\pi$
$774$	1.70171e6	−	1.70171e6i	0.102102	−	0.102102i
$775$	660419.	−	1.59439e6i	0.0394971	−	0.0953544i
$776$	2.02027e7	+	8.36822e6i	1.20435	+	0.498860i
$777$	−528411.	−	1.27570e6i	−0.0313992	−	0.0758045i
$778$			6.20873e6i			0.367751i
$779$	−8.17901e6	+	3.38786e6i	−0.482900	+	0.200024i
$780$	−67774.5	−	67774.5i	−0.00398868	−	0.00398868i
$781$	727270.			0.0426647
$782$	−8.01366e6	+	8.63685e6i	−0.468612	+	0.505055i
$783$	1.00580e6			0.0586285
$784$	4.82353e6	+	4.82353e6i	0.280269	+	0.280269i
$785$	−2.81029e6	+	1.16406e6i	−0.162771	+	0.0674219i
$786$			4.62108e6i			0.266801i
$787$	1.92563e6	+	4.64889e6i	0.110825	+	0.267555i	0.969555	−	0.244873i	$-0.0787463\pi$
$787$	1.92563e6	+	4.64889e6i	0.110825	+	0.267555i	−0.858730	+	0.512428i	$0.828746\pi$
$788$	−408544.	−	169224.i	−0.0234381	−	0.00970839i
$789$	−2.03709e6	+	4.91796e6i	−0.116498	+	0.281250i
$790$	8.00816e6	−	8.00816e6i	0.456525	−	0.456525i
$791$	−3.72299e6	+	3.72299e6i	−0.211568	+	0.211568i
$792$	168309.	−	406333.i	0.00953440	−	0.0230181i
$793$	−4.56386e6	−	1.89041e6i	−0.257721	−	0.106751i
$794$	−8.80288e6	−	2.12520e7i	−0.495534	−	1.19632i
$795$			7.77517e6i			0.436307i
$796$	297637.	−	123285.i	0.0166496	−	0.00689649i
$797$	−1.42029e7	−	1.42029e7i	−0.792014	−	0.792014i	0.189808	−	0.981821i	$-0.439214\pi$
$797$	−1.42029e7	−	1.42029e7i	−0.792014	−	0.792014i	−0.981821	+	0.189808i	$0.939214\pi$
$798$	−2.47513e6			−0.137591
$799$	2.40154e7	−	1.10171e7i	1.33083	−	0.610523i
$800$	−654912.			−0.0361791
$801$	2.06078e6	+	2.06078e6i	0.113488	+	0.113488i
$802$	−2.22935e7	+	9.23426e6i	−1.22389	+	0.506951i
$803$		−	979902.i		−	0.0536282i
$804$	416109.	+	1.00457e6i	0.0227021	+	0.0548078i
$805$	7.48910e6	+	3.10209e6i	0.407324	+	0.168719i
$806$	467481.	−	1.12860e6i	0.0253470	−	0.0611930i
$807$	2.36277e6	−	2.36277e6i	0.127714	−	0.127714i
$808$	−1.03726e7	+	1.03726e7i	−0.558935	+	0.558935i
$809$	−3.15318e6	+	7.61245e6i	−0.169386	+	0.408934i	−0.985663	−	0.168727i	$-0.946034\pi$
$809$	−3.15318e6	+	7.61245e6i	−0.169386	+	0.408934i	0.816277	+	0.577661i	$0.196034\pi$
$810$	−1.52348e6	−	631044.i	−0.0815874	−	0.0337946i
$811$	−5.09389e6	−	1.22977e7i	−0.271955	−	0.656558i	0.727612	−	0.685989i	$-0.240630\pi$
$811$	−5.09389e6	−	1.22977e7i	−0.271955	−	0.656558i	−0.999567	+	0.0294313i	$0.990630\pi$
$812$			237772.i			0.0126552i
$813$	1.05200e7	−	4.35755e6i	0.558202	−	0.231215i
$814$	−176881.	−	176881.i	−0.00935666	−	0.00935666i
$815$	−2.54433e7			−1.34178
$816$	7.58685e6	+	7.03942e6i	0.398874	+	0.370094i
$817$	2.73681e6			0.143446
$818$	−4.31201e6	−	4.31201e6i	−0.225318	−	0.225318i
$819$	−985597.	+	408248.i	−0.0513440	+	0.0212674i
$820$		−	1.39429e6i		−	0.0724135i
$821$	−171223.	−	413369.i	−0.00886553	−	0.0214033i	0.919385	−	0.393359i	$-0.128687\pi$
$821$	−171223.	−	413369.i	−0.00886553	−	0.0214033i	−0.928250	+	0.371956i	$0.878687\pi$
$822$	−1.50256e7	−	6.22381e6i	−0.775626	−	0.321275i
$823$	−3.19789e6	+	7.72039e6i	−0.164575	+	0.397319i	−0.984556	−	0.175072i	$-0.943984\pi$
$823$	−3.19789e6	+	7.72039e6i	−0.164575	+	0.397319i	0.819981	+	0.572391i	$0.193984\pi$
$824$	1.29815e7	−	1.29815e7i	0.666051	−	0.666051i
$825$	−193059.	+	193059.i	−0.00987539	+	0.00987539i
$826$	8115.03	−	19591.4i	0.000413847	−	0.000999115i
$827$	2.10155e7	+	8.70491e6i	1.06850	+	0.442589i	0.846463	−	0.532448i	$-0.178728\pi$
$827$	2.10155e7	+	8.70491e6i	1.06850	+	0.442589i	0.222042	+	0.975037i	$0.428728\pi$
$828$	97309.7	+	234926.i	0.00493265	+	0.0119085i
$829$		−	2.34178e7i		−	1.18348i	−0.806129	−	0.591740i	$-0.798441\pi$
$829$		−	2.34178e7i		−	1.18348i	0.806129	−	0.591740i	$-0.201559\pi$
$830$	3.11098e6	−	1.28861e6i	0.156748	−	0.0649272i
$831$	−1.29662e7	−	1.29662e7i	−0.651345	−	0.651345i
$832$	−4.58511e6			−0.229637
$833$	2.92988e6	−	7.89654e6i	0.146298	−	0.394298i
$834$	−9.33797e6			−0.464876
$835$	4.36440e6	+	4.36440e6i	0.216625	+	0.216625i
$836$	23912.6	−	9904.92i	0.00118334	−	0.000490157i
$837$			1.21314e6i			0.0598547i
$838$	4.19459e6	+	1.01266e7i	0.206338	+	0.498144i
$839$	2.60900e7	+	1.08068e7i	1.27959	+	0.530022i	0.915865	−	0.401485i	$-0.131506\pi$
$839$	2.60900e7	+	1.08068e7i	1.27959	+	0.530022i	0.363722	+	0.931508i	$0.381506\pi$
$840$	2.88275e6	−	6.95957e6i	0.140964	−	0.340318i
$841$	1.31575e7	−	1.31575e7i	0.641482	−	0.641482i
$842$	1.45667e7	−	1.45667e7i	0.708076	−	0.708076i
$843$	6.31552e6	−	1.52470e7i	0.306084	−	0.738951i
$844$	309594.	+	128238.i	0.0149602	+	0.00619670i
$845$	−6.18112e6	−	1.49226e7i	−0.297801	−	0.718954i
$846$			9.87906e6i			0.474559i
$847$	−1.46054e7	+	6.04975e6i	−0.699527	+	0.289754i
$848$	1.29018e7	+	1.29018e7i	0.616112	+	0.616112i
$849$	8.28980e6			0.394707
$850$	−2.83408e6	−	6.17778e6i	−0.134544	−	0.293282i
$851$	2.79477e6			0.132289
$852$	276302.	+	276302.i	0.0130402	+	0.0130402i
$853$	1.36032e7	−	5.63465e6i	0.640132	−	0.265151i	−0.0389189	−	0.999242i	$-0.512391\pi$
$853$	1.36032e7	−	5.63465e6i	0.640132	−	0.265151i	0.679051	+	0.734091i	$0.262391\pi$
$854$		−	2.00911e7i		−	0.942666i
$855$	−717636.	−	1.73253e6i	−0.0335729	−	0.0810522i
$856$	−3.38729e7	−	1.40306e7i	−1.58004	−	0.654474i
$857$	−1.44914e7	+	3.49853e7i	−0.673996	+	1.62717i	0.100759	+	0.994911i	$0.467873\pi$
$857$	−1.44914e7	+	3.49853e7i	−0.673996	+	1.62717i	−0.774756	+	0.632261i	$0.782127\pi$
$858$	−136658.	+	136658.i	−0.00633746	+	0.00633746i
$859$	−1.92912e7	+	1.92912e7i	−0.892024	+	0.892024i	−0.994713	−	0.102690i	$-0.967255\pi$
$859$	−1.92912e7	+	1.92912e7i	−0.892024	+	0.892024i	0.102690	+	0.994713i	$0.467255\pi$
$860$	−164950.	+	398225.i	−0.00760514	+	0.0183604i
$861$	−1.43375e7	−	5.93878e6i	−0.659120	−	0.273017i
$862$	9.30302e6	+	2.24595e7i	0.426438	+	1.02951i
$863$		−	3.95227e7i		−	1.80642i	−0.429197	−	0.903211i	$-0.641203\pi$
$863$		−	3.95227e7i		−	1.80642i	0.429197	−	0.903211i	$-0.358797\pi$
$864$	425334.	−	176179.i	0.0193841	−	0.00802916i
$865$	1.11636e7	+	1.11636e7i	0.507300	+	0.507300i
$866$	7.70890e6			0.349299
$867$	3.99401e6	−	1.21385e7i	0.180452	−	0.548425i
$868$	−286787.			−0.0129199
$869$	932070.	+	932070.i	0.0418696	+	0.0418696i
$870$	2.88333e6	−	1.19431e6i	0.129150	−	0.0534958i
$871$		−	9.23313e6i		−	0.412386i
$872$	1.42265e7	+	3.43458e7i	0.633588	+	1.52962i
$873$	8.81613e6	+	3.65176e6i	0.391510	+	0.162169i
$874$	1.91713e6	−	4.62837e6i	0.0848934	−	0.204951i
$875$	−1.32709e7	+	1.32709e7i	−0.585977	+	0.585977i
$876$	372281.	−	372281.i	0.0163912	−	0.0163912i
$877$	−1.21571e7	+	2.93497e7i	−0.533740	+	1.28856i	0.395290	+	0.918556i	$0.370644\pi$
$877$	−1.21571e7	+	2.93497e7i	−0.533740	+	1.28856i	−0.929030	+	0.370005i	$0.879356\pi$
$878$	−2.40631e7	−	9.96727e6i	−1.05345	−	0.436355i
$879$	−2.51671e6	−	6.07588e6i	−0.109866	−	0.265239i
$880$		−	1.28999e6i		−	0.0561537i
$881$	2.54899e7	−	1.05583e7i	1.10644	−	0.458304i	0.246732	−	0.969084i	$-0.420643\pi$
$881$	2.54899e7	−	1.05583e7i	1.10644	−	0.458304i	0.859711	+	0.510780i	$0.170643\pi$
$882$	2.22680e6	+	2.22680e6i	0.0963850	+	0.0963850i
$883$	1.87410e7			0.808892			0.404446	−	0.914562i	$-0.367464\pi$
$883$	1.87410e7			0.808892			0.404446	+	0.914562i	$0.367464\pi$
$884$	115799.	+	252421.i	0.00498396	+	0.0108641i
$885$	16066.3			0.000689539
$886$	−2.67670e6	−	2.67670e6i	−0.114555	−	0.114555i
$887$	2.60028e7	−	1.07707e7i	1.10972	−	0.459659i	0.248876	−	0.968535i	$-0.419939\pi$
$887$	2.60028e7	−	1.07707e7i	1.10972	−	0.459659i	0.860840	+	0.508876i	$0.169939\pi$
$888$		−	2.59717e6i		−	0.110527i
$889$	3.01604e6	+	7.28137e6i	0.127992	+	0.309000i
$890$	8.35464e6	+	3.46061e6i	0.353552	+	0.146446i
$891$	73447.3	−	177317.i	0.00309943	−	0.00748268i
$892$	1.77072e6	−	1.77072e6i	0.0745141	−	0.0745141i
$893$	−7.94411e6	+	7.94411e6i	−0.333362	+	0.333362i
$894$	7.04488e6	−	1.70078e7i	0.294801	−	0.711713i
$895$	3.93822e6	+	1.63126e6i	0.164340	+	0.0680717i
$896$	−6.37317e6	−	1.53862e7i	−0.265207	−	0.640267i
$897$		−	2.15923e6i		−	0.0896019i
$898$	−2.53414e7	+	1.04968e7i	−1.04867	+	0.434375i
$899$	−1.62351e6	−	1.62351e6i	−0.0669971	−	0.0669971i
$900$	−146692.			−0.00603672
$901$	7.83673e6	−	2.11213e7i	0.321605	−	0.866781i
$902$	−2.81140e6			−0.115055
$903$	3.39236e6	+	3.39236e6i	0.138446	+	0.138446i
$904$	−9.14934e6	+	3.78978e6i	−0.372365	+	0.154239i
$905$			2.83723e7i			1.15152i
$906$	−730847.	−	1.76442e6i	−0.0295805	−	0.0714137i
$907$	4.10197e7	+	1.69909e7i	1.65567	+	0.685802i	0.997735	−	0.0672708i	$-0.0214292\pi$
$907$	4.10197e7	+	1.69909e7i	1.65567	+	0.685802i	0.657937	+	0.753073i	$0.271429\pi$
$908$	452563.	−	1.09258e6i	0.0182165	−	0.0439784i
$909$	−4.52646e6	+	4.52646e6i	−0.181698	+	0.181698i
$910$	−2.34064e6	+	2.34064e6i	−0.0936981	+	0.0936981i
$911$	−7.31986e6	+	1.76717e7i	−0.292218	+	0.705477i	−1.00000		0.000954724i	$-0.999696\pi$
$911$	−7.31986e6	+	1.76717e7i	−0.292218	+	0.705477i	0.707782	+	0.706431i	$0.249696\pi$
$912$	−4.06569e6	−	1.68406e6i	−0.161863	−	0.0670458i
$913$	149982.	+	362088.i	0.00595471	+	0.0143760i
$914$		−	4.68565e7i		−	1.85526i
$915$	1.40632e7	−	5.82517e6i	0.555305	−	0.230015i
$916$	1.46659e6	+	1.46659e6i	0.0577526	+	0.0577526i
$917$	−9.21213e6			−0.361773
$918$	3.50250e6	+	3.24977e6i	0.137174	+	0.127276i
$919$	−2.20971e7			−0.863071			−0.431535	−	0.902096i	$-0.642028\pi$
$919$	−2.20971e7			−0.863071			−0.431535	+	0.902096i	$0.642028\pi$
$920$	1.07812e7	+	1.07812e7i	0.419950	+	0.419950i
$921$	8.33401e6	−	3.45206e6i	0.323747	−	0.134100i
$922$		−	2.82935e7i		−	1.09612i
$923$	−1.26976e6	−	3.06546e6i	−0.0490587	−	0.118438i
$924$	41917.8	+	17362.9i	0.00161517	+	0.000669026i
$925$	−616988.	+	1.48954e6i	−0.0237095	+	0.0572398i
$926$	−7.54824e6	+	7.54824e6i	−0.289280	+	0.289280i
$927$	5.66493e6	−	5.66493e6i	0.216519	−	0.216519i
$928$	−333436.	+	804986.i	−0.0127099	+	0.0306844i
$929$	−769312.	−	318660.i	−0.0292458	−	0.0121140i	0.368013	−	0.929821i	$-0.380038\pi$
$929$	−769312.	−	318660.i	−0.0292458	−	0.0121140i	−0.397258	+	0.917707i	$0.630038\pi$
$930$	1.44051e6	+	3.47770e6i	0.0546147	+	0.131851i
$931$			3.58130e6i			0.135415i
$932$	−336168.	+	139245.i	−0.0126770	+	0.00525098i
$933$	−1.47159e7	−	1.47159e7i	−0.553454	−	0.553454i
$934$	−9.68908e6			−0.363425
$935$	−1.44769e6	+	664132.i	−0.0541560	+	0.0248442i
$936$	−2.00656e6			−0.0748621
$937$	2.35120e7	+	2.35120e7i	0.874863	+	0.874863i	0.992998	−	0.118135i	$-0.0376915\pi$
$937$	2.35120e7	+	2.35120e7i	0.874863	+	0.874863i	−0.118135	+	0.992998i	$0.537692\pi$
$938$	3.46937e7	−	1.43706e7i	1.28749	−	0.533295i
$939$		−	2.00726e7i		−	0.742917i
$940$	−677125.	−	1.63472e6i	−0.0249948	−	0.0603427i
$941$	3.74916e6	+	1.55295e6i	0.138026	+	0.0571721i	0.450627	−	0.892712i	$-0.351200\pi$
$941$	3.74916e6	+	1.55295e6i	0.138026	+	0.0571721i	−0.312601	+	0.949884i	$0.601200\pi$
$942$	−1.26109e6	+	3.04454e6i	−0.0463040	+	0.111788i
$943$	2.22104e7	−	2.22104e7i	0.813350	−	0.813350i
$944$	26659.8	−	26659.8i	0.000973702	−	0.000973702i
$945$	1.25799e6	−	3.03705e6i	0.0458244	−	0.110630i
$946$	802964.	+	332599.i	0.0291721	+	0.0120835i
$947$	3.59823e6	+	8.68690e6i	0.130381	+	0.314767i	0.975566	−	0.219706i	$-0.0705099\pi$
$947$	3.59823e6	+	8.68690e6i	0.130381	+	0.314767i	−0.845185	+	0.534474i	$0.820510\pi$
$948$			708217.i			0.0255944i
$949$	−4.13031e6	+	1.71083e6i	−0.148873	+	0.0616654i
$950$	2.04356e6	+	2.04356e6i	0.0734648	+	0.0734648i
$951$	1.73729e7			0.622904
$952$	−1.48457e7	+	1.60002e7i	−0.530894	+	0.572180i
$953$	3.84672e7			1.37201			0.686007	−	0.727595i	$-0.259362\pi$
$953$	3.84672e7			1.37201			0.686007	+	0.727595i	$0.259362\pi$
$954$	5.95615e6	+	5.95615e6i	0.211882	+	0.211882i
$955$	−3.14720e7	+	1.30361e7i	−1.11665	+	0.462530i
$956$		−	2.45240e6i		−	0.0867853i
$957$	139006.	+	335590.i	0.00490630	+	0.0118449i
$958$	−3.02567e7	−	1.25327e7i	−1.06514	−	0.441197i
$959$	1.24072e7	−	2.99535e7i	0.435638	−	1.05172i
$960$	9.99052e6	−	9.99052e6i	0.349872	−	0.349872i
$961$	−1.82857e7	+	1.82857e7i	−0.638709	+	0.638709i
$962$	−436738.	+	1.05438e6i	−0.0152154	+	0.0367332i
$963$	−1.47816e7	−	6.12275e6i	−0.513637	−	0.212755i
$964$	−336925.	−	813409.i	−0.0116772	−	0.0281914i
$965$		−	5.28196e6i		−	0.182590i
$966$	8.11334e6	−	3.36066e6i	0.279742	−	0.115873i
$967$	3.04101e7	+	3.04101e7i	1.04581	+	1.04581i	0.998899	+	0.0469084i	$0.0149369\pi$
$967$	3.04101e7	+	3.04101e7i	1.04581	+	1.04581i	0.0469084	+	0.998899i	$0.485063\pi$
$968$	−2.97348e7			−1.01995
$969$	203223.	+	5.42975e6i	0.00695286	+	0.185768i
$970$	2.96093e7			1.01041
$971$	−1.09462e7	−	1.09462e7i	−0.372575	−	0.372575i	0.495839	−	0.868414i	$-0.334861\pi$
$971$	−1.09462e7	−	1.09462e7i	−0.372575	−	0.372575i	−0.868414	+	0.495839i	$0.834861\pi$
$972$	95269.6	−	39462.0i	0.00323436	−	0.00133972i
$973$		−	1.86153e7i		−	0.630358i
$974$	7.52683e6	+	1.81714e7i	0.254223	+	0.613749i
$975$	1.15081e6	+	476682.i	0.0387697	+	0.0160589i
$976$	1.36698e7	−	3.30019e7i	0.459345	−	1.10896i
$977$	−3.98054e7	+	3.98054e7i	−1.33415	+	1.33415i	−0.432538	+	0.901616i	$0.642382\pi$
$977$	−3.98054e7	+	3.98054e7i	−1.33415	+	1.33415i	−0.901616	+	0.432538i	$0.857618\pi$
$978$	−1.94908e7	+	1.94908e7i	−0.651602	+	0.651602i
$979$	−402780.	+	972398.i	−0.0134311	+	0.0324255i
$980$	−521105.	−	215849.i	−0.0173324	−	0.00717933i
$981$	6.20823e6	+	1.49880e7i	0.205966	+	0.497246i
$982$			4.43045e7i			1.46612i
$983$	4.57878e6	−	1.89659e6i	0.151135	−	0.0626023i	−0.305834	−	0.952085i	$-0.598935\pi$
$983$	4.57878e6	−	1.89659e6i	0.151135	−	0.0626023i	0.456969	+	0.889483i	$0.348935\pi$
$984$	−2.06400e7	−	2.06400e7i	−0.679551	−	0.679551i
$985$	−1.15706e7			−0.379985
$986$	−9.03635e6	+	338210.i	−0.296006	+	0.0110788i
$987$	−1.96939e7			−0.643486
$988$	−83499.0	−	83499.0i	−0.00272138	−	0.00272138i
$989$	−8.97111e6	+	3.71596e6i	−0.291646	+	0.120804i
$990$		−	595527.i		−	0.0193114i
$991$	−1.31535e7	−	3.17553e7i	−0.425457	−	1.02714i	−0.980711	−	0.195464i	$-0.937379\pi$
$991$	−1.31535e7	−	3.17553e7i	−0.425457	−	1.02714i	0.555254	−	0.831681i	$-0.312621\pi$
$992$	−970927.	−	402171.i	−0.0313262	−	0.0129757i
$993$	1.90144e6	−	4.59047e6i	0.0611939	−	0.147735i
$994$	9.54227e6	−	9.54227e6i	0.306327	−	0.306327i
$995$	5.96061e6	−	5.96061e6i	0.190868	−	0.190868i
$996$	−80582.5	+	194543.i	−0.00257391	+	0.00621396i
$997$	−3.29106e7	−	1.36320e7i	−1.04857	−	0.434332i	−0.209189	−	0.977875i	$-0.567082\pi$
$997$	−3.29106e7	−	1.36320e7i	−1.04857	−	0.434332i	−0.839381	+	0.543543i	$0.817082\pi$
$998$	−7.63563e6	−	1.84340e7i	−0.242671	−	0.585861i
$999$		−	1.13336e6i		−	0.0359299i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	51.6.h.a.19.10	✓	56
17.3	odd	16		867.6.a.t.1.20		28
17.9	even	8	inner	51.6.h.a.43.10	yes	56
17.14	odd	16		867.6.a.u.1.20		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.6.h.a.19.10	✓	56	1.1	even	1	trivial
51.6.h.a.43.10	yes	56	17.9	even	8	inner
867.6.a.t.1.20		28	17.3	odd	16
867.6.a.u.1.20		28	17.14	odd	16

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 51 = 3 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	51.h (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(3.88932 + 3.88932i) q^{2} +(-8.31492 + 3.44415i) q^{3} -1.74633i q^{4} +(-17.4864 - 42.2159i) q^{5} +(-45.7348 - 18.9440i) q^{6} +(37.7648 - 91.1724i) q^{7} +(131.250 - 131.250i) q^{8} +(57.2756 - 57.2756i) q^{9} +(96.1811 - 232.202i) q^{10} +(27.0260 + 11.1945i) q^{11} +(6.01463 + 14.5206i) q^{12} -133.460i q^{13} +(501.479 - 207.719i) q^{14} +(290.796 + 290.796i) q^{15} +965.068 q^{16} +(-496.852 - 1083.05i) q^{17} +445.527 q^{18} +(358.264 + 358.264i) q^{19} +(-73.7230 + 30.5371i) q^{20} +888.159i q^{21} +(61.5736 + 148.652i) q^{22} +(-1660.81 - 687.931i) q^{23} +(-639.290 + 1543.38i) q^{24} +(733.298 - 733.298i) q^{25} +(519.069 - 519.069i) q^{26} +(-278.976 + 673.508i) q^{27} +(-159.217 - 65.9499i) q^{28} +(-527.990 - 1274.68i) q^{29} +2262.00i q^{30} +(1537.45 - 636.831i) q^{31} +(-446.552 - 446.552i) q^{32} -263.274 q^{33} +(2279.91 - 6144.75i) q^{34} -4509.30 q^{35} +(-100.022 - 100.022i) q^{36} +(-1436.34 + 594.951i) q^{37} +2786.81i q^{38} +(459.656 + 1109.71i) q^{39} +(-7835.96 - 3245.76i) q^{40} +(-6686.62 + 16142.9i) q^{41} +(-3454.34 + 3454.34i) q^{42} +(3819.54 - 3819.54i) q^{43} +(19.5494 - 47.1963i) q^{44} +(-3419.49 - 1416.40i) q^{45} +(-3783.85 - 9135.02i) q^{46} +22173.9i q^{47} +(-8024.46 + 3323.84i) q^{48} +(4998.12 + 4998.12i) q^{49} +5704.07 q^{50} +(7861.47 + 7294.23i) q^{51} -233.065 q^{52} +(13368.8 + 13368.8i) q^{53} +(-3704.52 + 1534.46i) q^{54} -1336.68i q^{55} +(-7009.76 - 16923.1i) q^{56} +(-4212.86 - 1745.02i) q^{57} +(2904.12 - 7011.16i) q^{58} +(27.6248 - 27.6248i) q^{59} +(507.826 - 507.826i) q^{60} +(14164.6 - 34196.5i) q^{61} +(8456.46 + 3502.78i) q^{62} +(-3058.95 - 7384.96i) q^{63} -34355.7i q^{64} +(-5634.14 + 2333.74i) q^{65} +(-1023.96 - 1023.96i) q^{66} +69182.8 q^{67} +(-1891.36 + 867.669i) q^{68} +16178.8 q^{69} +(-17538.1 - 17538.1i) q^{70} +(22969.2 - 9514.14i) q^{71} -15034.9i q^{72} +(-12819.1 - 30947.9i) q^{73} +(-7900.34 - 3272.43i) q^{74} +(-3571.72 + 8622.90i) q^{75} +(625.648 - 625.648i) q^{76} +(2041.26 - 2041.26i) q^{77} +(-2528.26 + 6103.77i) q^{78} +(41630.6 + 17244.0i) q^{79} +(-16875.6 - 40741.2i) q^{80} -6561.00i q^{81} +(-88791.5 + 36778.6i) q^{82} +(9473.65 + 9473.65i) q^{83} +1551.02 q^{84} +(-37033.8 + 39913.7i) q^{85} +29710.8 q^{86} +(8780.38 + 8780.38i) q^{87} +(5016.46 - 2077.88i) q^{88} +35980.1i q^{89} +(-7790.67 - 18808.3i) q^{90} +(-12167.9 - 5040.09i) q^{91} +(-1201.35 + 2900.33i) q^{92} +(-10590.4 + 10590.4i) q^{93} +(-86241.4 + 86241.4i) q^{94} +(8859.71 - 21389.2i) q^{95} +(5251.04 + 2175.05i) q^{96} +(45083.5 + 108841. i) q^{97} +38878.6i q^{98} +(2189.10 - 906.757i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 88 q^{5} + 360 q^{6} + 1280 q^{10} - 632 q^{11} - 4256 q^{14} - 8192 q^{16} + 6248 q^{17} + 4152 q^{19} - 16384 q^{20} - 19592 q^{22} - 3608 q^{23} + 10440 q^{24} + 30384 q^{25} - 19936 q^{26} + 13624 q^{28}+ \cdots - 51192 q^{99}+O(q^{100}) \) 56 * q - 88 * q^5 + 360 * q^6 + 1280 * q^10 - 632 * q^11 - 4256 * q^14 - 8192 * q^16 + 6248 * q^17 + 4152 * q^19 - 16384 * q^20 - 19592 * q^22 - 3608 * q^23 + 10440 * q^24 + 30384 * q^25 - 19936 * q^26 + 13624 * q^28 - 23424 * q^29 + 2728 * q^31 + 67200 * q^32 + 20376 * q^33 + 11960 * q^34 + 26272 * q^35 + 3240 * q^36 + 32296 * q^37 - 22320 * q^39 - 100184 * q^40 + 6552 * q^41 - 21528 * q^42 - 38152 * q^43 - 26208 * q^44 + 31752 * q^45 + 106368 * q^46 + 9768 * q^49 + 96128 * q^50 - 62720 * q^52 + 65984 * q^53 + 29160 * q^54 - 268304 * q^56 - 28656 * q^57 - 139352 * q^58 - 67312 * q^59 - 109800 * q^60 - 307184 * q^61 + 150704 * q^62 - 696 * q^65 + 54720 * q^66 + 364272 * q^67 + 558960 * q^68 - 81864 * q^69 + 313960 * q^70 + 309808 * q^71 - 268752 * q^73 - 393712 * q^74 - 96624 * q^75 - 228552 * q^76 - 841536 * q^77 - 130824 * q^78 - 57216 * q^79 + 658528 * q^80 - 335992 * q^82 + 406240 * q^83 + 664848 * q^84 + 686840 * q^85 - 842560 * q^86 + 127224 * q^87 + 538248 * q^88 - 103680 * q^90 - 368592 * q^91 + 96752 * q^92 - 113472 * q^93 - 622576 * q^94 - 1143560 * q^95 - 375552 * q^96 - 40424 * q^97 - 51192 * q^99

Introduction

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