LMFDB - Embedded newform 51.6.h.a.19.1

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			19.1
Character	$\chi$	$=$	51.19
Dual form			51.6.h.a.43.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-7.76922 - 7.76922i) q^{2} +(-8.31492 + 3.44415i) q^{3} +88.7215i q^{4} +(1.79786 + 4.34041i) q^{5} +(91.3588 + 37.8420i) q^{6} +(-2.94505 + 7.10998i) q^{7} +(440.682 - 440.682i) q^{8} +(57.2756 - 57.2756i) q^{9} +(19.7537 - 47.6896i) q^{10} +(-64.7337 - 26.8136i) q^{11} +(-305.570 - 737.712i) q^{12} +695.082i q^{13} +(78.1197 - 32.3583i) q^{14} +(-29.8981 - 29.8981i) q^{15} -4008.42 q^{16} +(1030.24 - 598.709i) q^{17} -889.974 q^{18} +(-1748.35 - 1748.35i) q^{19} +(-385.088 + 159.509i) q^{20} -69.2621i q^{21} +(294.610 + 711.251i) q^{22} +(-504.809 - 209.099i) q^{23} +(-2146.46 + 5182.01i) q^{24} +(2194.10 - 2194.10i) q^{25} +(5400.24 - 5400.24i) q^{26} +(-278.976 + 673.508i) q^{27} +(-630.808 - 261.289i) q^{28} +(-2289.94 - 5528.41i) q^{29} +464.569i q^{30} +(9063.24 - 3754.12i) q^{31} +(17040.5 + 17040.5i) q^{32} +630.606 q^{33} +(-12655.7 - 3352.69i) q^{34} -36.1550 q^{35} +(5081.58 + 5081.58i) q^{36} +(-7921.74 + 3281.29i) q^{37} +27166.7i q^{38} +(-2393.97 - 5779.55i) q^{39} +(2705.03 + 1120.46i) q^{40} +(3706.65 - 8948.63i) q^{41} +(-538.112 + 538.112i) q^{42} +(4656.35 - 4656.35i) q^{43} +(2378.94 - 5743.28i) q^{44} +(351.573 + 145.626i) q^{45} +(2297.44 + 5546.51i) q^{46} -22481.8i q^{47} +(33329.7 - 13805.6i) q^{48} +(11842.5 + 11842.5i) q^{49} -34092.9 q^{50} +(-6504.35 + 8526.54i) q^{51} -61668.7 q^{52} +(3500.04 + 3500.04i) q^{53} +(7400.06 - 3065.21i) q^{54} -329.178i q^{55} +(1835.41 + 4431.07i) q^{56} +(20559.0 + 8515.81i) q^{57} +(-25160.4 + 60742.5i) q^{58} +(-897.389 + 897.389i) q^{59} +(2652.60 - 2652.60i) q^{60} +(6754.33 - 16306.4i) q^{61} +(-99580.9 - 41247.8i) q^{62} +(238.549 + 575.908i) q^{63} -136513. i q^{64} +(-3016.94 + 1249.66i) q^{65} +(-4899.31 - 4899.31i) q^{66} +38183.2 q^{67} +(53118.4 + 91404.9i) q^{68} +4917.61 q^{69} +(280.896 + 280.896i) q^{70} +(-899.529 + 372.597i) q^{71} -50480.7i q^{72} +(19028.4 + 45938.6i) q^{73} +(87038.9 + 36052.7i) q^{74} +(-10687.0 + 25800.6i) q^{75} +(155117. - 155117. i) q^{76} +(381.288 - 381.288i) q^{77} +(-26303.3 + 63501.8i) q^{78} +(-31658.4 - 13113.3i) q^{79} +(-7206.57 - 17398.2i) q^{80} -6561.00i q^{81} +(-98321.6 + 40726.2i) q^{82} +(-11057.0 - 11057.0i) q^{83} +6145.04 q^{84} +(4450.88 + 3395.29i) q^{85} -72352.4 q^{86} +(38081.4 + 38081.4i) q^{87} +(-40343.3 + 16710.7i) q^{88} -48039.9i q^{89} +(-1600.05 - 3862.85i) q^{90} +(-4942.02 - 2047.05i) q^{91} +(18551.6 - 44787.5i) q^{92} +(-62430.4 + 62430.4i) q^{93} +(-174666. + 174666. i) q^{94} +(4445.28 - 10731.9i) q^{95} +(-200380. - 83000.2i) q^{96} +(65899.8 + 159096. i) q^{97} -184013. i q^{98} +(-5243.43 + 2171.90i) 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 $

$2$	−7.76922	−	7.76922i	−1.37342	−	1.37342i	−0.855325	−	0.518092i	$-0.826642\pi$
$2$	−7.76922	−	7.76922i	−1.37342	−	1.37342i	−0.518092	−	0.855325i	$-0.673358\pi$
$3$	−8.31492	+	3.44415i	−0.533402	+	0.220942i
$3$	−8.31492	+	3.44415i	−0.533402	+	0.220942i
$4$			88.7215i			2.77255i
$5$	1.79786	+	4.34041i	0.0321611	+	0.0776437i	0.939144	−	0.343524i	$-0.111621\pi$
$5$	1.79786	+	4.34041i	0.0321611	+	0.0776437i	−0.906983	+	0.421167i	$0.861621\pi$
$6$	91.3588	+	37.8420i	1.03603	+	0.429137i
$7$	−2.94505	+	7.10998i	−0.0227168	+	0.0548433i	−0.934831	−	0.355093i	$-0.884449\pi$
$7$	−2.94505	+	7.10998i	−0.0227168	+	0.0548433i	0.912114	+	0.409936i	$0.134449\pi$
$8$	440.682	−	440.682i	2.43445	−	2.43445i
$9$	57.2756	−	57.2756i	0.235702	−	0.235702i
$10$	19.7537	−	47.6896i	0.0624666	−	0.150808i
$11$	−64.7337	−	26.8136i	−0.161305	−	0.0668149i	0.300570	−	0.953760i	$-0.402823\pi$
$11$	−64.7337	−	26.8136i	−0.161305	−	0.0668149i	−0.461875	+	0.886945i	$0.652823\pi$
$12$	−305.570	−	737.712i	−0.612573	−	1.47888i
$13$			695.082i			1.14072i	0.821396	+	0.570358i	$0.193196\pi$
$13$			695.082i			1.14072i	−0.821396	+	0.570358i	$0.806804\pi$
$14$	78.1197	−	32.3583i	0.106522	−	0.0441230i
$15$	−29.8981	−	29.8981i	−0.0343095	−	0.0343095i
$16$	−4008.42			−3.91447
$17$	1030.24	−	598.709i	0.864606	−	0.502451i
$17$	1030.24	−	598.709i	0.864606	−	0.502451i
$18$	−889.974			−0.647435
$19$	−1748.35	−	1748.35i	−1.11108	−	1.11108i	−0.993005	−	0.118074i	$-0.962328\pi$
$19$	−1748.35	−	1748.35i	−1.11108	−	1.11108i	−0.118074	−	0.993005i	$-0.537672\pi$
$20$	−385.088	+	159.509i	−0.215271	+	0.0891681i
$21$		−	69.2621i		−	0.0342726i
$22$	294.610	+	711.251i	0.129775	+	0.313304i
$23$	−504.809	−	209.099i	−0.198979	−	0.0824199i	0.280968	−	0.959717i	$-0.409344\pi$
$23$	−504.809	−	209.099i	−0.198979	−	0.0824199i	−0.479948	+	0.877297i	$0.659344\pi$
$24$	−2146.46	+	5182.01i	−0.760667	+	1.83641i
$25$	2194.10	−	2194.10i	0.702113	−	0.702113i
$26$	5400.24	−	5400.24i	1.56668	−	1.56668i
$27$	−278.976	+	673.508i	−0.0736475	+	0.177801i
$28$	−630.808	−	261.289i	−0.152056	−	0.0629835i
$29$	−2289.94	−	5528.41i	−0.505626	−	1.22069i	−0.946378	−	0.323061i	$-0.895288\pi$
$29$	−2289.94	−	5528.41i	−0.505626	−	1.22069i	0.440752	−	0.897629i	$-0.354712\pi$
$30$			464.569i			0.0942426i
$31$	9063.24	−	3754.12i	1.69387	−	0.701623i	0.694035	−	0.719941i	$-0.255831\pi$
$31$	9063.24	−	3754.12i	1.69387	−	0.701623i	0.999832	+	0.0183183i	$0.00583122\pi$
$32$	17040.5	+	17040.5i	2.94176	+	2.94176i
$33$	630.606			0.100803
$34$	−12655.7	−	3352.69i	−1.87754	−	0.497389i
$35$	−36.1550			−0.00498883
$36$	5081.58	+	5081.58i	0.653496	+	0.653496i
$37$	−7921.74	+	3281.29i	−0.951298	+	0.394040i	−0.803718	−	0.595010i	$-0.797148\pi$
$37$	−7921.74	+	3281.29i	−0.951298	+	0.394040i	−0.147579	+	0.989050i	$0.547148\pi$
$38$			27166.7i			3.05195i
$39$	−2393.97	−	5779.55i	−0.252033	−	0.608460i
$40$	2705.03	+	1120.46i	0.267314	+	0.110725i
$41$	3706.65	−	8948.63i	0.344367	−	0.831375i	−0.652897	−	0.757447i	$-0.726446\pi$
$41$	3706.65	−	8948.63i	0.344367	−	0.831375i	0.997264	−	0.0739283i	$-0.0235536\pi$
$42$	−538.112	+	538.112i	−0.0470706	+	0.0470706i
$43$	4656.35	−	4656.35i	0.384038	−	0.384038i	−0.488516	−	0.872555i	$-0.662462\pi$
$43$	4656.35	−	4656.35i	0.384038	−	0.384038i	0.872555	+	0.488516i	$0.162462\pi$
$44$	2378.94	−	5743.28i	0.185248	−	0.447227i
$45$	351.573	+	145.626i	0.0258812	+	0.0107204i
$46$	2297.44	+	5546.51i	0.160085	+	0.386478i
$47$		−	22481.8i		−	1.48452i	−0.670111	−	0.742261i	$-0.733753\pi$
$47$		−	22481.8i		−	1.48452i	0.670111	−	0.742261i	$-0.266247\pi$
$48$	33329.7	−	13805.6i	2.08799	−	0.864873i
$49$	11842.5	+	11842.5i	0.704615	+	0.704615i
$50$	−34092.9			−1.92859
$51$	−6504.35	+	8526.54i	−0.350170	+	0.459036i
$52$	−61668.7			−3.16269
$53$	3500.04	+	3500.04i	0.171152	+	0.171152i	0.787485	−	0.616333i	$-0.211383\pi$
$53$	3500.04	+	3500.04i	0.171152	+	0.171152i	−0.616333	+	0.787485i	$0.711383\pi$
$54$	7400.06	−	3065.21i	0.345343	−	0.143046i
$55$		−	329.178i		−	0.0146732i
$56$	1835.41	+	4431.07i	0.0782101	+	0.188816i
$57$	20559.0	+	8515.81i	0.838136	+	0.347167i
$58$	−25160.4	+	60742.5i	−0.982081	+	2.37095i
$59$	−897.389	+	897.389i	−0.0335622	+	0.0335622i	−0.723689	−	0.690127i	$-0.757555\pi$
$59$	−897.389	+	897.389i	−0.0335622	+	0.0335622i	0.690127	+	0.723689i	$0.257555\pi$
$60$	2652.60	−	2652.60i	0.0951249	−	0.0951249i
$61$	6754.33	−	16306.4i	0.232412	−	0.561091i	−0.764048	−	0.645159i	$-0.776791\pi$
$61$	6754.33	−	16306.4i	0.232412	−	0.561091i	0.996460	+	0.0840676i	$0.0267912\pi$
$62$	−99580.9	−	41247.8i	−3.29001	−	1.36277i
$63$	238.549	+	575.908i	0.00757227	+	0.0182811i
$64$		−	136513.i		−	4.16605i
$65$	−3016.94	+	1249.66i	−0.0885694	+	0.0366866i
$66$	−4899.31	−	4899.31i	−0.138444	−	0.138444i
$67$	38183.2			1.03917			0.519584	−	0.854420i	$-0.326087\pi$
$67$	38183.2			1.03917			0.519584	+	0.854420i	$0.326087\pi$
$68$	53118.4	+	91404.9i	1.39307	+	2.39716i
$69$	4917.61			0.124346
$70$	280.896	+	280.896i	0.00685174	+	0.00685174i
$71$	−899.529	+	372.597i	−0.0211772	+	0.00877190i	−0.393247	−	0.919433i	$-0.628648\pi$
$71$	−899.529	+	372.597i	−0.0211772	+	0.00877190i	0.372070	+	0.928205i	$0.378648\pi$
$72$		−	50480.7i		−	1.14761i
$73$	19028.4	+	45938.6i	0.417922	+	1.00895i	0.982949	+	0.183880i	$0.0588659\pi$
$73$	19028.4	+	45938.6i	0.417922	+	1.00895i	−0.565026	+	0.825073i	$0.691134\pi$
$74$	87038.9	+	36052.7i	1.84771	+	0.765347i
$75$	−10687.0	+	25800.6i	−0.219382	+	0.529635i
$76$	155117.	−	155117.i	3.08052	−	3.08052i
$77$	381.288	−	381.288i	0.00732869	−	0.00732869i
$78$	−26303.3	+	63501.8i	−0.489524	+	1.18182i
$79$	−31658.4	−	13113.3i	−0.570717	−	0.236399i	0.0786132	−	0.996905i	$-0.474951\pi$
$79$	−31658.4	−	13113.3i	−0.570717	−	0.236399i	−0.649331	+	0.760506i	$0.724951\pi$
$80$	−7206.57	−	17398.2i	−0.125894	−	0.303934i
$81$		−	6561.00i		−	0.111111i
$82$	−98321.6	+	40726.2i	−1.61478	+	0.668866i
$83$	−11057.0	−	11057.0i	−0.176174	−	0.176174i	0.613512	−	0.789686i	$-0.289756\pi$
$83$	−11057.0	−	11057.0i	−0.176174	−	0.176174i	−0.789686	+	0.613512i	$0.789756\pi$
$84$	6145.04			0.0950225
$85$	4450.88	+	3395.29i	0.0668188	+	0.0509718i
$86$	−72352.4			−1.05489
$87$	38081.4	+	38081.4i	0.539404	+	0.539404i
$88$	−40343.3	+	16710.7i	−0.555347	+	0.230032i
$89$		−	48039.9i		−	0.642875i	−0.946931	−	0.321438i	$-0.895834\pi$
$89$		−	48039.9i		−	0.642875i	0.946931	−	0.321438i	$-0.104166\pi$
$90$	−1600.05	−	3862.85i	−0.0208222	−	0.0502692i
$91$	−4942.02	−	2047.05i	−0.0625606	−	0.0259135i
$92$	18551.6	−	44787.5i	0.228513	−	0.551679i
$93$	−62430.4	+	62430.4i	−0.748494	+	0.748494i
$94$	−174666.	+	174666.i	−2.03887	+	2.03887i
$95$	4445.28	−	10731.9i	0.0505348	−	0.122002i
$96$	−200380.	−	83000.2i	−2.21910	−	0.919181i
$97$	65899.8	+	159096.i	0.711140	+	1.71684i	0.697133	+	0.716941i	$0.254459\pi$
$97$	65899.8	+	159096.i	0.711140	+	1.71684i	0.0140063	+	0.999902i	$0.495541\pi$
$98$		−	184013.i		−	1.93546i
$99$	−5243.43	+	2171.90i	−0.0537685	+	0.0222716i
$100$	194664.	+	194664.i	1.94664	+	1.94664i
$101$	−75647.5			−0.737889			−0.368945	−	0.929451i	$-0.620281\pi$
$101$	−75647.5			−0.737889			−0.368945	+	0.929451i	$0.620281\pi$
$102$	116778.	−	15710.8i	1.11138	−	0.149519i
$103$	−127981.			−1.18865			−0.594325	−	0.804225i	$-0.702581\pi$
$103$	−127981.			−1.18865			−0.594325	+	0.804225i	$0.702581\pi$
$104$	306310.	+	306310.i	2.77701	+	2.77701i
$105$	300.626	−	124.523i	0.00266105	−	0.00110224i
$106$		−	54385.1i		−	0.470127i
$107$	−65512.3	−	158161.i	−0.553176	−	1.33549i	−0.915081	−	0.403270i	$-0.867873\pi$
$107$	−65512.3	−	158161.i	−0.553176	−	1.33549i	0.361905	−	0.932215i	$-0.382127\pi$
$108$	−59754.7	−	24751.2i	−0.492961	−	0.204191i
$109$	71136.7	−	171739.i	0.573492	−	1.38453i	−0.325071	−	0.945690i	$-0.605388\pi$
$109$	71136.7	−	171739.i	0.573492	−	1.38453i	0.898563	−	0.438844i	$-0.144612\pi$
$110$	−2557.46	+	2557.46i	−0.0201524	+	0.0201524i
$111$	54567.4	−	54567.4i	0.420364	−	0.420364i
$112$	11805.0	−	28499.8i	0.0889244	−	0.214683i
$113$	144799.	+	59977.6i	1.06677	+	0.441869i	0.845848	−	0.533424i	$-0.179095\pi$
$113$	144799.	+	59977.6i	1.06677	+	0.441869i	0.220917	+	0.975293i	$0.429095\pi$
$114$	−93566.1	−	225889.i	−0.674305	−	1.62792i
$115$		−	2567.01i		−	0.0181002i
$116$	490489.	−	203167.i	3.38442	−	1.40187i
$117$	39811.3	+	39811.3i	0.268869	+	0.268869i
$118$	13944.0			0.0921899
$119$	1222.69	+	9088.25i	0.00791496	+	0.0588319i
$120$	−26351.1			−0.167050
$121$	−110409.	−	110409.i	−0.685552	−	0.685552i
$122$	−179164.	+	74212.1i	−1.08981	+	0.451414i
$123$			87173.4i			0.519543i
$124$	333071.	+	804105.i	1.94528	+	4.69633i
$125$	27031.8	+	11196.9i	0.154739	+	0.0640950i
$126$	2621.02	−	6327.70i	0.0147077	−	0.0355074i
$127$	98759.3	−	98759.3i	0.543336	−	0.543336i	−0.381169	−	0.924505i	$-0.624478\pi$
$127$	98759.3	−	98759.3i	0.543336	−	0.543336i	0.924505	+	0.381169i	$0.124478\pi$
$128$	−515304.	+	515304.i	−2.77996	+	2.77996i
$129$	−22680.0	+	54754.3i	−0.119996	+	0.289697i
$130$	33148.2	+	13730.4i	0.172029	+	0.0712566i
$131$	−103483.	−	249830.i	−0.526854	−	1.27194i	−0.933574	−	0.358386i	$-0.883327\pi$
$131$	−103483.	−	249830.i	−0.526854	−	1.27194i	0.406719	−	0.913553i	$-0.366673\pi$
$132$			55948.3i			0.279481i
$133$	17579.7	−	7281.76i	0.0861754	−	0.0356950i
$134$	−296654.	−	296654.i	−1.42721	−	1.42721i
$135$	−3424.86			−0.0161737
$136$	190170.	−	717851.i	0.881647	−	3.32803i
$137$	−168902.			−0.768835			−0.384418	−	0.923159i	$-0.625598\pi$
$137$	−168902.			−0.768835			−0.384418	+	0.923159i	$0.625598\pi$
$138$	−38206.0	−	38206.0i	−0.170779	−	0.170779i
$139$	104801.	−	43409.9i	0.460074	−	0.190569i	−0.140594	−	0.990067i	$-0.544901\pi$
$139$	104801.	−	43409.9i	0.460074	−	0.190569i	0.600668	+	0.799498i	$0.294901\pi$
$140$		−	3207.73i		−	0.0138318i
$141$	77430.7	+	186934.i	0.327994	+	0.791847i
$142$	9883.42	+	4093.85i	0.0411326	+	0.0170377i
$143$	18637.6	−	44995.3i	0.0762169	−	0.184004i
$144$	−229585.	+	229585.i	−0.922651	+	0.922651i
$145$	19878.6	−	19878.6i	0.0785174	−	0.0785174i
$146$	209072.	−	504743.i	0.811732	−	1.95969i
$147$	−139256.	−	57681.9i	−0.531522	−	0.220164i
$148$	−291121.	−	702829.i	−1.09250	−	2.63752i
$149$			360642.i			1.33079i	0.746490	+	0.665397i	$0.231738\pi$
$149$			360642.i			1.33079i	−0.746490	+	0.665397i	$0.768262\pi$
$150$	283480.	−	117421.i	1.02871	−	0.426107i
$151$	−47862.7	−	47862.7i	−0.170826	−	0.170826i	0.616516	−	0.787342i	$-0.288544\pi$
$151$	−47862.7	−	47862.7i	−0.170826	−	0.170826i	−0.787342	+	0.616516i	$0.788544\pi$
$152$	−1.54094e6			−5.40973
$153$	24716.5	−	93299.4i	0.0853607	−	0.322218i
$154$	−5924.62			−0.0201307
$155$	32588.8	+	32588.8i	0.108953	+	0.108953i
$156$	512770.	−	212396.i	1.68699	−	0.698772i
$157$		−	79986.4i		−	0.258980i	−0.991581	−	0.129490i	$-0.958666\pi$
$157$		−	79986.4i		−	0.258980i	0.991581	−	0.129490i	$-0.0413341\pi$
$158$	144081.	+	347841.i	0.459159	+	1.10851i
$159$	−41157.1	−	17047.8i	−0.129108	−	0.0534782i
$160$	−43326.4	+	104599.i	−0.133799	+	0.323019i
$161$	2973.38	−	2973.38i	0.00904035	−	0.00904035i
$162$	−50973.8	+	50973.8i	−0.152602	+	0.152602i
$163$	−56708.7	+	136907.i	−0.167179	+	0.403605i	−0.985160	−	0.171640i	$-0.945093\pi$
$163$	−56708.7	+	136907.i	−0.167179	+	0.403605i	0.817981	+	0.575245i	$0.195093\pi$
$164$	793937.	+	328859.i	2.30503	+	0.954774i
$165$	1133.74	+	2737.09i	0.00324193	+	0.00782671i
$166$			171808.i			0.483920i
$167$	−125644.	+	52043.6i	−0.348620	+	0.144403i	−0.550120	−	0.835085i	$-0.685418\pi$
$167$	−125644.	+	52043.6i	−0.348620	+	0.144403i	0.201501	+	0.979488i	$0.435418\pi$
$168$	−30522.6	−	30522.6i	−0.0834349	−	0.0834349i
$169$	−111846.			−0.301234
$170$	−8201.08	−	60958.6i	−0.0217645	−	0.161776i
$171$	−200276.			−0.523768
$172$	413119.	+	413119.i	1.06476	+	1.06476i
$173$	59375.0	−	24593.9i	0.150830	−	0.0624760i	−0.305991	−	0.952034i	$-0.598988\pi$
$173$	59375.0	−	24593.9i	0.150830	−	0.0624760i	0.456821	+	0.889558i	$0.348988\pi$
$174$		−	591725.i		−	1.48165i
$175$	9138.28	+	22061.8i	0.0225564	+	0.0544559i
$176$	259480.	+	107480.i	0.631426	+	0.261545i
$177$	4370.97	−	10552.5i	0.0104868	−	0.0253175i
$178$	−373232.	+	373232.i	−0.882936	+	0.882936i
$179$	−463094.	+	463094.i	−1.08028	+	1.08028i	−0.0837981	+	0.996483i	$0.526705\pi$
$179$	−463094.	+	463094.i	−1.08028	+	1.08028i	−0.996483	+	0.0837981i	$0.973295\pi$
$180$	−12920.2	+	31192.1i	−0.0297227	+	0.0717569i
$181$	139687.	+	57860.1i	0.316927	+	0.131275i	0.535476	−	0.844551i	$-0.320132\pi$
$181$	139687.	+	57860.1i	0.316927	+	0.131275i	−0.218549	+	0.975826i	$0.570132\pi$
$182$	22491.6	+	54299.6i	0.0503318	+	0.121512i
$183$			158849.i			0.350637i
$184$	−314607.	+	130314.i	−0.685051	+	0.283758i
$185$	−28484.3	−	28484.3i	−0.0611895	−	0.0611895i
$186$	970070.			2.05599
$187$	−82745.2	+	11132.1i	−0.173037	+	0.0232795i
$188$	1.99462e6			4.11591
$189$	−3967.03	−	3967.03i	−0.00807813	−	0.00807813i
$190$	−117915.	+	48841.8i	−0.236965	+	0.0981539i
$191$			572028.i			1.13458i	0.823520	+	0.567288i	$0.192007\pi$
$191$			572028.i			1.13458i	−0.823520	+	0.567288i	$0.807993\pi$
$192$	470171.	+	1.13509e6i	0.920456	+	2.22218i
$193$	428127.	+	177336.i	0.827330	+	0.342691i	0.755845	−	0.654750i	$-0.227226\pi$
$193$	428127.	+	177336.i	0.827330	+	0.342691i	0.0714849	+	0.997442i	$0.477226\pi$
$194$	724064.	−	1.74804e6i	1.38125	−	3.33463i
$195$	20781.6	−	20781.6i	0.0391375	−	0.0391375i
$196$	−1.05068e6	+	1.05068e6i	−1.95358	+	1.95358i
$197$	−20763.8	+	50128.2i	−0.0381189	+	0.0920273i	−0.941792	−	0.336195i	$-0.890860\pi$
$197$	−20763.8	+	50128.2i	−0.0381189	+	0.0920273i	0.903673	+	0.428222i	$0.140860\pi$
$198$	57611.4	+	23863.4i	0.104435	+	0.0432583i
$199$	−235082.	−	567538.i	−0.420811	−	1.01593i	−0.982109	−	0.188313i	$-0.939698\pi$
$199$	−235082.	−	567538.i	−0.420811	−	1.01593i	0.561298	−	0.827614i	$-0.310302\pi$
$200$		−	1.93380e6i		−	3.41851i
$201$	−317490.	+	131509.i	−0.554294	+	0.229596i
$202$	587722.	+	587722.i	1.01343	+	1.01343i
$203$	46050.9			0.0784329
$204$	−756487.	−	577076.i	−1.27270	−	0.970863i
$205$	45504.8			0.0756262
$206$	994315.	+	994315.i	1.63251	+	1.63251i
$207$	−40889.6	+	16937.0i	−0.0663264	+	0.0274733i
$208$		−	2.78618e6i		−	4.46531i
$209$	66297.8	+	160057.i	0.104986	+	0.253460i
$210$	−3303.08	−	1368.18i	−0.00516857	−	0.00214089i
$211$	132853.	−	320735.i	0.205430	−	0.495952i	−0.787263	−	0.616617i	$-0.788503\pi$
$211$	132853.	−	320735.i	0.205430	−	0.495952i	0.992693	+	0.120665i	$0.0385026\pi$
$212$	−310528.	+	310528.i	−0.474528	+	0.474528i
$213$	6196.22	−	6196.22i	0.00935789	−	0.00935789i
$214$	−719806.	+	1.73776e6i	−1.07444	+	2.59392i
$215$	28581.9	+	11839.0i	0.0421692	+	0.0174671i
$216$	173863.	+	419743.i	0.253556	+	0.612137i
$217$			75495.5i			0.108836i
$218$	−1.88696e6	+	781603.i	−2.68919	+	1.11390i
$219$	−316439.	−	316439.i	−0.445841	−	0.445841i
$220$	29205.2			0.0406821
$221$	416152.	+	716105.i	0.573154	+	0.986270i
$222$	−847892.			−1.15467
$223$	−366464.	−	366464.i	−0.493480	−	0.493480i	0.415921	−	0.909401i	$-0.363459\pi$
$223$	−366464.	−	366464.i	−0.493480	−	0.493480i	−0.909401	+	0.415921i	$0.863459\pi$
$224$	−171343.	+	70972.4i	−0.228163	+	0.0945082i
$225$		−	251337.i		−	0.330979i
$226$	−658994.	−	1.59095e6i	−0.858244	−	2.07198i
$227$	491408.	+	203548.i	0.632961	+	0.262181i	0.676011	−	0.736892i	$-0.263707\pi$
$227$	491408.	+	203548.i	0.632961	+	0.262181i	−0.0430494	+	0.999073i	$0.513707\pi$
$228$	−755536.	+	1.82403e6i	−0.962538	+	2.32377i
$229$	−370390.	+	370390.i	−0.466735	+	0.466735i	−0.900855	−	0.434120i	$-0.857059\pi$
$229$	−370390.	+	370390.i	−0.466735	+	0.466735i	0.434120	+	0.900855i	$0.357059\pi$
$230$	−19943.7	+	19943.7i	−0.0248591	+	0.0248591i
$231$	−1857.17	+	4483.59i	−0.00228992	+	0.00552836i
$232$	−3.44541e6	−	1.42714e6i	−4.20263	−	1.74079i
$233$	530708.	+	1.28124e6i	0.640421	+	1.54611i	0.826113	+	0.563505i	$0.190547\pi$
$233$	530708.	+	1.28124e6i	0.640421	+	1.54611i	−0.185692	+	0.982608i	$0.559453\pi$
$234$		−	618605.i		−	0.738540i
$235$	97580.3	−	40419.1i	0.115264	−	0.0477438i
$236$	−79617.7	−	79617.7i	−0.0930529	−	0.0930529i
$237$	308401.			0.356652
$238$	61109.3	−	80107.9i	0.0699302	−	0.0916712i
$239$	−1.03986e6			−1.17755			−0.588774	−	0.808298i	$-0.700389\pi$
$239$	−1.03986e6			−1.17755			−0.588774	+	0.808298i	$0.700389\pi$
$240$	119844.	+	119844.i	0.134304	+	0.134304i
$241$	968591.	−	401203.i	1.07423	−	0.444961i	0.225749	−	0.974185i	$-0.427517\pi$
$241$	968591.	−	401203.i	1.07423	−	0.444961i	0.848482	+	0.529224i	$0.177517\pi$
$242$			1.71558e6i			1.88310i
$243$	22597.1	+	54554.2i	0.0245492	+	0.0592669i
$244$	1.44673e6	+	599255.i	1.55565	+	0.644372i
$245$	−30110.1	+	72692.2i	−0.0320477	+	0.0773700i
$246$	677269.	−	677269.i	0.713549	−	0.713549i
$247$	1.21525e6	−	1.21525e6i	1.26743	−	1.26743i
$248$	2.33964e6	−	5.64838e6i	2.41557	−	5.83169i
$249$	130020.	+	53856.0i	0.132896	+	0.0550472i
$250$	−123024.	−	297007.i	−0.124492	−	0.300550i
$251$		−	109868.i		−	0.110075i	−0.998484	−	0.0550375i	$-0.982472\pi$
$251$		−	109868.i		−	0.110075i	0.998484	−	0.0550375i	$-0.0175278\pi$
$252$	−51095.5	+	21164.4i	−0.0506852	+	0.0209945i
$253$	27071.5	+	27071.5i	0.0265896	+	0.0265896i
$254$	−1.53457e6			−1.49245
$255$	−48702.6	−	12902.1i	−0.0469031	−	0.0124254i
$256$	3.63860e6			3.47004
$257$	−227692.	−	227692.i	−0.215038	−	0.215038i	0.591366	−	0.806403i	$-0.298589\pi$
$257$	−227692.	−	227692.i	−0.215038	−	0.215038i	−0.806403	+	0.591366i	$0.798589\pi$
$258$	601604.	−	249193.i	0.562680	−	0.233070i
$259$		−	65987.0i		−	0.0611236i
$260$	−110872.	−	267668.i	−0.101715	−	0.245563i
$261$	−447801.	−	185485.i	−0.406897	−	0.168542i
$262$	−1.13700e6	+	2.74497e6i	−1.02331	+	2.47049i
$263$	1.02449e6	−	1.02449e6i	0.913308	−	0.913308i	−0.0832232	−	0.996531i	$-0.526521\pi$
$263$	1.02449e6	−	1.02449e6i	0.913308	−	0.913308i	0.996531	+	0.0832232i	$0.0265214\pi$
$264$	277897.	−	277897.i	0.245399	−	0.245399i
$265$	−8899.03	+	21484.2i	−0.00778445	+	0.0187933i
$266$	−193154.	−	80007.2i	−0.167379	−	0.0693306i
$267$	165457.	+	399448.i	0.142038	+	0.342911i
$268$			3.38767e6i			2.88114i
$269$	1.26840e6	−	525389.i	1.06875	−	0.442691i	0.222201	−	0.975001i	$-0.428676\pi$
$269$	1.26840e6	−	525389.i	1.06875	−	0.442691i	0.846549	+	0.532310i	$0.178676\pi$
$270$	26608.5	+	26608.5i	0.0222132	+	0.0222132i
$271$	437145.			0.361578			0.180789	−	0.983522i	$-0.442135\pi$
$271$	437145.			0.361578			0.180789	+	0.983522i	$0.442135\pi$
$272$	−4.12966e6	+	2.39988e6i	−3.38448	+	1.96683i
$273$	48142.8			0.0390953
$274$	1.31224e6	+	1.31224e6i	1.05593	+	1.05593i
$275$	−200864.	+	83200.7i	−0.160166	+	0.0663430i
$276$			436298.i			0.344755i
$277$	−534180.	−	1.28963e6i	−0.418301	−	1.00987i	−0.982840	−	0.184461i	$-0.940946\pi$
$277$	−534180.	−	1.28963e6i	−0.418301	−	1.00987i	0.564539	−	0.825406i	$-0.309054\pi$
$278$	−1.15148e6	−	476959.i	−0.893604	−	0.370143i
$279$	304084.	−	734123.i	0.233874	−	0.564622i
$280$	−15932.9	+	15932.9i	−0.0121450	+	0.0121450i
$281$	294719.	−	294719.i	0.222660	−	0.222660i	−0.586957	−	0.809618i	$-0.699674\pi$
$281$	294719.	−	294719.i	0.222660	−	0.222660i	0.809618	+	0.586957i	$0.199674\pi$
$282$	850758.	−	2.05391e6i	0.637064	−	1.53801i
$283$	−1.73195e6	−	717397.i	−1.28549	−	0.532468i	−0.367853	−	0.929884i	$-0.619907\pi$
$283$	−1.73195e6	−	717397.i	−1.28549	−	0.532468i	−0.917639	+	0.397416i	$0.869907\pi$
$284$	−33057.4	−	79807.6i	−0.0243205	−	0.0587149i
$285$			104545.i			0.0762412i
$286$	−494378.	+	204778.i	−0.357391	+	0.148036i
$287$	52708.3	+	52708.3i	0.0377724	+	0.0377724i
$288$	1.95201e6			1.38676
$289$	702951.	−	1.23363e6i	0.495086	−	0.868844i
$290$	−308882.			−0.215674
$291$	−1.09590e6	−	1.09590e6i	−0.758647	−	0.758647i
$292$	−4.07575e6	+	1.68823e6i	−2.79737	+	1.15871i
$293$			873748.i			0.594589i	0.954786	+	0.297295i	$0.0960844\pi$
$293$			873748.i			0.594589i	−0.954786	+	0.297295i	$0.903916\pi$
$294$	633770.	+	1.53006e6i	0.427625	+	1.03238i
$295$	−5508.42	−	2281.66i	−0.00368529	−	0.00152650i
$296$	−2.04496e6	+	4.93698e6i	−1.35661	+	3.27516i
$297$	36118.4	−	36118.4i	0.0237595	−	0.0237595i
$298$	2.80191e6	−	2.80191e6i	1.82773	−	1.82773i
$299$	145341.	−	350884.i	0.0940177	−	0.226979i
$300$	−2.28907e6	−	948163.i	−1.46844	−	0.608247i
$301$	19393.4	+	46819.7i	0.0123378	+	0.0297860i
$302$			743712.i			0.469232i
$303$	629003.	−	260541.i	0.393592	−	0.163031i
$304$	7.00813e6	+	7.00813e6i	4.34929	+	4.34929i
$305$	82919.8			0.0510398
$306$	−916891.	+	532836.i	−0.559776	+	0.325304i
$307$	−466237.			−0.282332			−0.141166	−	0.989986i	$-0.545085\pi$
$307$	−466237.			−0.282332			−0.141166	+	0.989986i	$0.545085\pi$
$308$	33828.5	+	33828.5i	0.0203192	+	0.0203192i
$309$	1.06415e6	−	440787.i	0.634028	−	0.262623i
$310$		−	506380.i		−	0.299276i
$311$	−835868.	−	2.01796e6i	−0.490046	−	1.18308i	−0.954696	−	0.297581i	$-0.903820\pi$
$311$	−835868.	−	2.01796e6i	−0.490046	−	1.18308i	0.464650	−	0.885494i	$-0.346180\pi$
$312$	−3.60192e6	−	1.49196e6i	−2.09483	−	0.867705i
$313$	458341.	−	1.10653e6i	0.264441	−	0.638416i	−0.734763	−	0.678324i	$-0.762707\pi$
$313$	458341.	−	1.10653e6i	0.264441	−	0.638416i	0.999203	+	0.0399082i	$0.0127065\pi$
$314$	−621432.	+	621432.i	−0.355688	+	0.355688i
$315$	−2070.80	+	2070.80i	−0.00117588	+	0.00117588i
$316$	1.16344e6	−	2.80878e6i	0.655427	−	1.58234i
$317$	803962.	+	333012.i	0.449353	+	0.186128i	0.595871	−	0.803080i	$-0.296807\pi$
$317$	803962.	+	333012.i	0.449353	+	0.186128i	−0.146518	+	0.989208i	$0.546807\pi$
$318$	187310.	+	452207.i	0.103871	+	0.250767i
$319$			419276.i			0.230687i
$320$	592523.	−	245431.i	0.323467	−	0.133984i
$321$	1.08946e6	+	1.08946e6i	0.590131	+	0.590131i
$322$	−46201.6			−0.0248323
$323$	−2.84799e6	−	754476.i	−1.51891	−	0.402383i
$324$	582102.			0.308061
$325$	1.52508e6	+	1.52508e6i	0.800911	+	0.800911i
$326$	1.50424e6	−	623078.i	0.783924	−	0.324712i
$327$			1.67300e6i			0.865222i
$328$	−2.31005e6	−	5.57695e6i	−1.18560	−	2.86228i
$329$	159845.	+	66210.1i	0.0814160	+	0.0337236i
$330$	12456.8	−	30073.3i	0.00629681	−	0.0152018i
$331$	1.29646e6	−	1.29646e6i	0.650410	−	0.650410i	−0.302681	−	0.953092i	$-0.597882\pi$
$331$	1.29646e6	−	1.29646e6i	0.650410	−	0.650410i	0.953092	+	0.302681i	$0.0978818\pi$
$332$	980993.	−	980993.i	0.488451	−	0.488451i
$333$	−265785.	+	641661.i	−0.131347	+	0.317099i
$334$	1.38050e6	+	571821.i	0.677126	+	0.280475i
$335$	68648.0	+	165731.i	0.0334207	+	0.0806847i
$336$			277632.i			0.134159i
$337$	−2.04150e6	+	845617.i	−0.979207	+	0.405601i	−0.814132	−	0.580680i	$-0.802787\pi$
$337$	−2.04150e6	+	845617.i	−0.979207	+	0.405601i	−0.165075	+	0.986281i	$0.552787\pi$
$338$	868956.	+	868956.i	0.413720	+	0.413720i
$339$	−1.41056e6			−0.666642
$340$	−301236.	+	394889.i	−0.141322	+	0.185258i
$341$	−687359.			−0.320109
$342$	1.55599e6	+	1.55599e6i	0.719351	+	0.719351i
$343$	−238574.	+	98820.5i	−0.109493	+	0.0453536i
$344$		−	4.10394e6i		−	1.86984i
$345$	8841.17	+	21344.5i	0.00399910	+	0.00965468i
$346$	−652373.	−	270222.i	−0.292958	−	0.121347i
$347$	413864.	−	999155.i	0.184516	−	0.445461i	−0.804372	−	0.594126i	$-0.797498\pi$
$347$	413864.	−	999155.i	0.184516	−	0.445461i	0.988887	+	0.148666i	$0.0474979\pi$
$348$	−3.37864e6	+	3.37864e6i	−1.49552	+	1.49552i
$349$	−2.56248e6	+	2.56248e6i	−1.12615	+	1.12615i	−0.135352	+	0.990798i	$0.543217\pi$
$349$	−2.56248e6	+	2.56248e6i	−1.12615	+	1.12615i	−0.990798	+	0.135352i	$0.956783\pi$
$350$	100405.	−	242400.i	0.0438114	−	0.105770i
$351$	−468143.	−	193911.i	−0.202820	−	0.0840109i
$352$	−646178.	−	1.56001e6i	−0.277968	−	0.671075i
$353$			2.84085e6i			1.21342i	0.794923	+	0.606710i	$0.207511\pi$
$353$			2.84085e6i			1.21342i	−0.794923	+	0.606710i	$0.792489\pi$
$354$	−115943.	+	48025.3i	−0.0491743	+	0.0203686i
$355$	−3234.45	−	3234.45i	−0.00136216	−	0.00136216i
$356$	4.26217e6			1.78240
$357$	−41467.9	−	71356.9i	−0.0172203	−	0.0296323i
$358$	7.19576e6			2.96735
$359$	812185.	+	812185.i	0.332597	+	0.332597i	0.853572	−	0.520975i	$-0.174431\pi$
$359$	812185.	+	812185.i	0.332597	+	0.332597i	−0.520975	+	0.853572i	$0.674431\pi$
$360$	219107.	−	90757.1i	0.0891046	−	0.0369083i
$361$			3.63737e6i			1.46899i
$362$	−635729.	−	1.53478e6i	−0.254977	−	0.615568i
$363$	1.29830e6	+	537775.i	0.517142	+	0.214207i
$364$	181618.	−	438464.i	0.0718463	−	0.173452i
$365$	−165182.	+	165182.i	−0.0648980	+	0.0648980i
$366$	1.23414e6	−	1.23414e6i	0.481571	−	0.481571i
$367$	−914816.	+	2.20856e6i	−0.354543	+	0.855942i	0.641505	+	0.767119i	$0.278311\pi$
$367$	−914816.	+	2.20856e6i	−0.354543	+	0.855942i	−0.996047	+	0.0888229i	$0.971689\pi$
$368$	2.02349e6	+	838156.i	0.778899	+	0.322631i
$369$	−300238.	−	724839.i	−0.114789	−	0.277125i
$370$			442602.i			0.168077i
$371$	−35193.0	+	14577.4i	−0.0132746	+	0.00549851i
$372$	−5.53892e6	−	5.53892e6i	−2.07524	−	2.07524i
$373$	267022.			0.0993746			0.0496873	−	0.998765i	$-0.484178\pi$
$373$	267022.			0.0993746			0.0496873	+	0.998765i	$0.484178\pi$
$374$	729353.	+	556377.i	0.269624	+	0.205679i
$375$	−263331.			−0.0966994
$376$	−9.90733e6	−	9.90733e6i	−3.61399	−	3.61399i
$377$	3.84270e6	−	1.59170e6i	1.39246	−	0.576776i
$378$			61641.5i			0.0221893i
$379$	225568.	+	544570.i	0.0806640	+	0.194740i	0.959066	−	0.283182i	$-0.0913901\pi$
$379$	225568.	+	544570.i	0.0806640	+	0.194740i	−0.878402	+	0.477922i	$0.841390\pi$
$380$	952147.	+	394392.i	0.338256	+	0.140110i
$381$	−481033.	+	1.16132e6i	−0.169771	+	0.409863i
$382$	4.44421e6	−	4.44421e6i	1.55825	−	1.55825i
$383$	522549.	−	522549.i	0.182025	−	0.182025i	−0.610213	−	0.792237i	$-0.708916\pi$
$383$	522549.	−	522549.i	0.182025	−	0.182025i	0.792237	+	0.610213i	$0.208916\pi$
$384$	2.50992e6	−	6.05949e6i	0.868626	−	2.09705i
$385$	2340.45	+	969.446i	0.000804725	+	0.000333328i
$386$	−1.94845e6	−	4.70397e6i	−0.665611	−	1.60693i
$387$		−	533391.i		−	0.181037i
$388$	−1.41153e7	+	5.84673e6i	−4.76003	+	1.97167i
$389$	−3.99934e6	−	3.99934e6i	−1.34003	−	1.34003i	−0.896024	−	0.444006i	$-0.853557\pi$
$389$	−3.99934e6	−	3.99934e6i	−1.34003	−	1.34003i	−0.444006	−	0.896024i	$-0.646443\pi$
$390$	−322914.			−0.107504
$391$	−645267.	+	86811.0i	−0.213451	+	0.0287166i
$392$	1.04375e7			3.43070
$393$	1.72090e6	+	1.72090e6i	0.562051	+	0.562051i
$394$	550775.	−	228139.i	0.178745	−	0.0740386i
$395$		−	160986.i		−	0.0519154i
$396$	−192694.	−	465205.i	−0.0617492	−	0.149076i
$397$	903742.	+	374342.i	0.287785	+	0.119204i	0.521906	−	0.853003i	$-0.325221\pi$
$397$	903742.	+	374342.i	0.287785	+	0.119204i	−0.234121	+	0.972207i	$0.575221\pi$
$398$	−2.58293e6	+	6.23573e6i	−0.817343	+	1.97324i
$399$	−121095.	+	121095.i	−0.0380796	+	0.0380796i
$400$	−8.79489e6	+	8.79489e6i	−2.74840	+	2.74840i
$401$	−1.63058e6	+	3.93657e6i	−0.506386	+	1.22252i	0.439564	+	0.898211i	$0.355133\pi$
$401$	−1.63058e6	+	3.93657e6i	−0.506386	+	1.22252i	−0.945950	+	0.324313i	$0.894867\pi$
$402$	3.48837e6	+	1.44493e6i	1.07661	+	0.445945i
$403$	2.60942e6	+	6.29970e6i	0.800353	+	1.93222i
$404$		−	6.71156e6i		−	2.04583i
$405$	28477.4	−	11795.7i	0.00862707	−	0.00357345i
$406$	−357780.	−	357780.i	−0.107721	−	0.107721i
$407$	600787.			0.179777
$408$	891140.	+	6.62384e6i	0.265030	+	1.96997i
$409$	−2.83104e6			−0.836830			−0.418415	−	0.908256i	$-0.637414\pi$
$409$	−2.83104e6			−0.836830			−0.418415	+	0.908256i	$0.637414\pi$
$410$	−353537.	−	353537.i	−0.103866	−	0.103866i
$411$	1.40441e6	−	581724.i	0.410098	−	0.169868i
$412$		−	1.13547e7i		−	3.29559i
$413$	−3737.56	−	9023.27i	−0.00107823	−	0.00260309i
$414$	449267.	+	186093.i	0.128826	+	0.0533615i
$415$	28113.0	−	67870.8i	0.00801285	−	0.0193447i
$416$	−1.18445e7	+	1.18445e7i	−3.35571	+	3.35571i
$417$	−721900.	+	721900.i	−0.203300	+	0.203300i
$418$	728436.	−	1.75860e6i	0.203916	−	0.492296i
$419$	−6.23027e6	−	2.58066e6i	−1.73369	−	0.718119i	−0.999220	−	0.0394803i	$-0.987430\pi$
$419$	−6.23027e6	−	2.58066e6i	−1.73369	−	0.718119i	−0.734472	−	0.678639i	$-0.762570\pi$
$420$	11047.9	+	26672.0i	0.00305602	+	0.00737789i
$421$			3.34684e6i			0.920301i	0.887841	+	0.460150i	$0.152205\pi$
$421$			3.34684e6i			0.920301i	−0.887841	+	0.460150i	$0.847795\pi$
$422$	−3.52402e6	+	1.45970e6i	−0.963291	+	0.399008i
$423$	−1.28766e6	−	1.28766e6i	−0.349905	−	0.349905i
$424$	3.08481e6			0.833323
$425$	946833.	−	3.57409e6i	0.254273	−	0.959828i
$426$	−96279.7			−0.0257046
$427$	96046.3	+	96046.3i	0.0254924	+	0.0254924i
$428$	1.40323e7	−	5.81235e6i	3.70270	−	1.53371i
$429$			438323.i			0.114988i
$430$	−130079.	−	314039.i	−0.0339264	−	0.0819055i
$431$	−2.20834e6	−	914725.i	−0.572629	−	0.237191i	0.0775286	−	0.996990i	$-0.475297\pi$
$431$	−2.20834e6	−	914725.i	−0.572629	−	0.237191i	−0.650157	+	0.759799i	$0.725297\pi$
$432$	1.11825e6	−	2.69970e6i	0.288291	−	0.695996i
$433$	1.20482e6	−	1.20482e6i	0.308818	−	0.308818i	−0.535633	−	0.844451i	$-0.679927\pi$
$433$	1.20482e6	−	1.20482e6i	0.308818	−	0.308818i	0.844451	+	0.535633i	$0.179927\pi$
$434$	586541.	−	586541.i	0.149477	−	0.149477i
$435$	−96824.0	+	233754.i	−0.0245335	+	0.0592291i
$436$	1.52370e7	+	6.31136e6i	3.83869	+	1.59004i
$437$	517006.	+	1.24816e6i	0.129507	+	0.312657i
$438$			4.91697e6i			1.22465i
$439$	1.84472e6	−	764107.i	0.456845	−	0.189231i	−0.142380	−	0.989812i	$-0.545476\pi$
$439$	1.84472e6	−	764107.i	0.456845	−	0.189231i	0.599225	+	0.800581i	$0.295476\pi$
$440$	−145063.	−	145063.i	−0.0357211	−	0.0357211i
$441$	1.35657e6			0.332159
$442$	2.33040e6	−	8.79675e6i	0.567380	−	2.14174i
$443$	93911.4			0.0227357			0.0113679	−	0.999935i	$-0.496381\pi$
$443$	93911.4			0.0227357			0.0113679	+	0.999935i	$0.496381\pi$
$444$	4.84130e6	+	4.84130e6i	1.16548	+	1.16548i
$445$	208513.	−	86368.9i	0.0499152	−	0.0206756i
$446$			5.69428e6i			1.35551i
$447$	−1.24211e6	−	2.99871e6i	−0.294029	−	0.709848i
$448$	970605.	+	402038.i	0.228480	+	0.0946393i
$449$	2.63151e6	−	6.35302e6i	0.616011	−	1.48718i	−0.240288	−	0.970702i	$-0.577242\pi$
$449$	2.63151e6	−	6.35302e6i	0.616011	−	1.48718i	0.856299	−	0.516480i	$-0.172758\pi$
$450$	−1.95269e6	+	1.95269e6i	−0.454572	+	0.454572i
$451$	−479890.	+	479890.i	−0.111097	+	0.111097i
$452$	−5.32131e6	+	1.28468e7i	−1.22510	+	2.95766i
$453$	562821.	+	233128.i	0.128862	+	0.0533763i
$454$	−2.23645e6	−	5.39926e6i	−0.509236	−	1.22940i
$455$		−	25130.7i		−	0.00569084i
$456$	1.28127e7	−	5.30721e6i	2.88556	−	1.19524i
$457$	−1.66464e6	−	1.66464e6i	−0.372847	−	0.372847i	0.495666	−	0.868513i	$-0.334924\pi$
$457$	−1.66464e6	−	1.66464e6i	−0.372847	−	0.372847i	−0.868513	+	0.495666i	$0.834924\pi$
$458$	5.75528e6			1.28204
$459$	115822.	+	860904.i	0.0256601	+	0.190732i
$460$	227749.			0.0501836
$461$	−258349.	−	258349.i	−0.0566181	−	0.0566181i	0.678231	−	0.734849i	$-0.262747\pi$
$461$	−258349.	−	258349.i	−0.0566181	−	0.0566181i	−0.734849	+	0.678231i	$0.762747\pi$
$462$	49262.8	−	20405.3i	0.0107378	−	0.00444773i
$463$			3.78767e6i			0.821146i	0.911828	+	0.410573i	$0.134671\pi$
$463$			3.78767e6i			0.821146i	−0.911828	+	0.410573i	$0.865329\pi$
$464$	9.17906e6	+	2.21602e7i	1.97926	+	4.77836i
$465$	−383214.	−	158733.i	−0.0821882	−	0.0340435i
$466$	5.83106e6	−	1.40774e7i	1.24389	−	3.00302i
$467$	−2.10136e6	+	2.10136e6i	−0.445870	+	0.445870i	−0.893979	−	0.448109i	$-0.852098\pi$
$467$	−2.10136e6	+	2.10136e6i	−0.445870	+	0.445870i	0.448109	+	0.893979i	$0.352098\pi$
$468$	−3.53212e6	+	3.53212e6i	−0.745453	+	0.745453i
$469$	−112451.	+	271482.i	−0.0236066	+	0.0569913i
$470$	−1.07215e6	−	444098.i	−0.223877	−	0.0927330i
$471$	275485.	+	665080.i	0.0572197	+	0.138141i
$472$			790927.i			0.163411i
$473$	−426276.	+	176570.i	−0.0876069	+	0.0362880i
$474$	−2.39604e6	−	2.39604e6i	−0.489832	−	0.489832i
$475$	−7.67213e6			−1.56021
$476$	−806323.	+	108479.i	−0.163114	+	0.0219446i
$477$	400934.			0.0806820
$478$	8.07887e6	+	8.07887e6i	1.61726	+	1.61726i
$479$	3.74326e6	−	1.55051e6i	0.745437	−	0.308770i	0.0225586	−	0.999746i	$-0.492819\pi$
$479$	3.74326e6	−	1.55051e6i	0.745437	−	0.308770i	0.722878	+	0.690976i	$0.242819\pi$
$480$		−	1.01896e6i		−	0.201861i
$481$	−2.28077e6	−	5.50626e6i	−0.449488	−	1.08516i
$482$	−1.06422e7	−	4.40816e6i	−2.08648	−	0.864250i
$483$	−14482.6	+	34964.1i	−0.00282475	+	0.00681954i
$484$	9.79564e6	−	9.79564e6i	1.90072	−	1.90072i
$485$	−572065.	+	572065.i	−0.110431	+	0.110431i
$486$	248282.	−	599405.i	0.0476819	−	0.115114i
$487$	6.32376e6	+	2.61939e6i	1.20824	+	0.500469i	0.893652	−	0.448760i	$-0.148134\pi$
$487$	6.32376e6	+	2.61939e6i	1.20824	+	0.500469i	0.314586	+	0.949229i	$0.398134\pi$
$488$	−4.20943e6	−	1.01625e7i	−0.800153	−	1.93174i
$489$		−	1.33368e6i		−	0.252221i
$490$	798694.	−	330830.i	0.150276	−	0.0622464i
$491$	2.59367e6	+	2.59367e6i	0.485525	+	0.485525i	0.906891	−	0.421366i	$-0.138449\pi$
$491$	2.59367e6	+	2.59367e6i	0.485525	+	0.485525i	−0.421366	+	0.906891i	$0.638449\pi$
$492$	−7.73416e6			−1.44046
$493$	−5.66911e6	−	4.32461e6i	−1.05050	−	0.801363i
$494$	−1.88831e7			−3.48141
$495$	−18853.9	−	18853.9i	−0.00345850	−	0.00345850i
$496$	−3.63293e7	+	1.50481e7i	−6.63060	+	2.74648i
$497$		−	7492.95i		−	0.00136070i
$498$	−591734.	−	1.42857e6i	−0.106919	−	0.258124i
$499$	4.52323e6	+	1.87358e6i	0.813199	+	0.336838i	0.750230	−	0.661177i	$-0.229943\pi$
$499$	4.52323e6	+	1.87358e6i	0.813199	+	0.336838i	0.0629695	+	0.998015i	$0.479943\pi$
$500$	−993409.	+	2.39830e6i	−0.177706	+	0.429021i
$501$	865477.	−	865477.i	0.154050	−	0.154050i
$502$	−853592.	+	853592.i	−0.151179	+	0.151179i
$503$	2.67224e6	−	6.45136e6i	0.470930	−	1.13692i	−0.492824	−	0.870129i	$-0.664035\pi$
$503$	2.67224e6	−	6.45136e6i	0.470930	−	1.13692i	0.963753	−	0.266795i	$-0.0859648\pi$
$504$	358917.	+	148668.i	0.0629386	+	0.0260700i
$505$	−136003.	−	328341.i	−0.0237313	−	0.0572924i
$506$		−	420649.i		−	0.0730371i
$507$	929990.	−	385214.i	0.160679	−	0.0665553i
$508$	8.76208e6	+	8.76208e6i	1.50643	+	1.50643i
$509$	−2.73707e6			−0.468265			−0.234132	−	0.972205i	$-0.575225\pi$
$509$	−2.73707e6			−0.468265			−0.234132	+	0.972205i	$0.575225\pi$
$510$	278142.	+	478620.i	0.0473523	+	0.0814827i
$511$	−382662.			−0.0648281
$512$	−1.17794e7	−	1.17794e7i	−1.98585	−	1.98585i
$513$	1.66528e6	−	689781.i	0.279379	−	0.115722i
$514$			3.53798e6i			0.590673i
$515$	−230092.	−	555492.i	−0.0382282	−	0.0922911i
$516$	−4.85789e6	−	2.01220e6i	−0.803199	−	0.332696i
$517$	−602818.	+	1.45533e6i	−0.0991882	+	0.239461i
$518$	−512668.	+	512668.i	−0.0839482	+	0.0839482i
$519$	−408993.	+	408993.i	−0.0666496	+	0.0666496i
$520$	−778810.	+	1.88021e6i	−0.126306	+	0.304929i
$521$	−4.57157e6	−	1.89361e6i	−0.737855	−	0.305629i	−0.0180795	−	0.999837i	$-0.505755\pi$
$521$	−4.57157e6	−	1.89361e6i	−0.737855	−	0.305629i	−0.719775	+	0.694207i	$0.755755\pi$
$522$	2.03799e6	+	4.92014e6i	0.327360	+	0.790317i
$523$			2.82849e6i			0.452168i	0.974108	+	0.226084i	$0.0725924\pi$
$523$			2.82849e6i			0.452168i	−0.974108	+	0.226084i	$0.927408\pi$
$524$	2.21653e7	−	9.18117e6i	3.52651	−	1.46073i
$525$	−151968.	−	151968.i	−0.0240632	−	0.0240632i
$526$	−1.59189e7			−2.50870
$527$	7.08973e6	−	9.29391e6i	1.11200	−	1.45771i
$528$	−2.52773e6			−0.394590
$529$	−4.34007e6	−	4.34007e6i	−0.674307	−	0.674307i
$530$	236054.	−	97776.6i	0.0365024	−	0.0151198i
$531$			102797.i			0.0158214i
$532$	646049.	+	1.55970e6i	0.0989661	+	0.238925i
$533$	6.22003e6	+	2.57642e6i	0.948363	+	0.392825i
$534$	1.81793e6	−	4.38886e6i	0.275882	−	0.666038i
$535$	568701.	−	568701.i	0.0859012	−	0.0859012i
$536$	1.68267e7	−	1.68267e7i	2.52980	−	2.52980i
$537$	2.25562e6	−	5.44555e6i	0.337544	−	0.814904i
$538$	−1.39364e7	−	5.77263e6i	−2.07584	−	0.859840i
$539$	−449068.	−	1.08415e6i	−0.0665795	−	0.160737i
$540$		−	303859.i		−	0.0448423i
$541$	−860627.	+	356483.i	−0.126422	+	0.0523656i	−0.444998	−	0.895532i	$-0.646795\pi$
$541$	−860627.	+	356483.i	−0.126422	+	0.0523656i	0.318576	+	0.947897i	$0.396795\pi$
$542$	−3.39628e6	−	3.39628e6i	−0.496598	−	0.496598i
$543$	−1.36076e6			−0.198054
$544$	2.77582e7	+	7.35357e6i	4.02155	+	1.06537i
$545$	873313.			0.125944
$546$	−374032.	−	374032.i	−0.0536942	−	0.0536942i
$547$	1.22491e7	−	5.07373e6i	1.75039	−	0.725035i	0.752607	−	0.658470i	$-0.228796\pi$
$547$	1.22491e7	−	5.07373e6i	1.75039	−	0.725035i	0.997782	−	0.0665649i	$-0.0212039\pi$
$548$		−	1.49852e7i		−	2.13163i
$549$	−547101.	−	1.32082e6i	−0.0774705	−	0.187030i
$550$	2.20696e6	+	914154.i	0.311092	+	0.128858i
$551$	−5.66198e6	+	1.36692e7i	−0.794492	+	1.91807i
$552$	2.16710e6	−	2.16710e6i	0.302714	−	0.302714i
$553$	186471.	−	186471.i	0.0259298	−	0.0259298i
$554$	−5.86922e6	+	1.41696e7i	−0.812467	+	1.96147i
$555$	334949.	+	138740.i	0.0461579	+	0.0191192i
$556$	3.85139e6	+	9.29809e6i	0.528361	+	1.27558i
$557$			6.43167e6i			0.878386i	0.898393	+	0.439193i	$0.144736\pi$
$557$			6.43167e6i			0.878386i	−0.898393	+	0.439193i	$0.855264\pi$
$558$	−8.06605e6	+	3.34107e6i	−1.09667	+	0.454255i
$559$	3.23655e6	+	3.23655e6i	0.438079	+	0.438079i
$560$	144925.			0.0195286
$561$	649678.	−	377550.i	0.0871548	−	0.0506485i
$562$	−4.57948e6			−0.611611
$563$	5.64530e6	+	5.64530e6i	0.750614	+	0.750614i	0.974594	−	0.223980i	$-0.0719051\pi$
$563$	5.64530e6	+	5.64530e6i	0.750614	+	0.750614i	−0.223980	+	0.974594i	$0.571905\pi$
$564$	−1.65851e7	+	6.86977e6i	−2.19543	+	0.909379i
$565$			736318.i			0.0970385i
$566$	7.88228e6	+	1.90295e7i	1.03422	+	2.49682i
$567$	46648.6	+	19322.5i	0.00609370	+	0.00252409i
$568$	−232209.	+	560603.i	−0.0302001	+	0.0729096i
$569$	1.01961e7	−	1.01961e7i	1.32024	−	1.32024i	0.406666	−	0.913577i	$-0.366691\pi$
$569$	1.01961e7	−	1.01961e7i	1.32024	−	1.32024i	0.913577	−	0.406666i	$-0.133309\pi$
$570$	812231.	−	812231.i	0.104711	−	0.104711i
$571$	−1.77698e6	+	4.29001e6i	−0.228083	+	0.550640i	−0.995944	−	0.0899759i	$-0.971321\pi$
$571$	−1.77698e6	+	4.29001e6i	−0.228083	+	0.550640i	0.767861	+	0.640616i	$0.221321\pi$
$572$	3.99205e6	+	1.65356e6i	0.510159	+	0.211315i
$573$	−1.97015e6	−	4.75636e6i	−0.250676	−	0.605185i
$574$		−	819005.i		−	0.103755i
$575$	−1.56639e6	+	648819.i	−0.197574	+	0.0818378i
$576$	−7.81887e6	−	7.81887e6i	−0.981947	−	0.981947i
$577$	1.32328e6			0.165467			0.0827335	−	0.996572i	$-0.473635\pi$
$577$	1.32328e6			0.165467			0.0827335	+	0.996572i	$0.473635\pi$
$578$	−1.50458e7	+	4.12299e6i	−1.87324	+	0.513325i
$579$	−4.17061e6			−0.517015
$580$	1.76366e6	+	1.76366e6i	0.217693	+	0.217693i
$581$	111178.	−	46051.6i	0.0136641	−	0.00565984i
$582$			1.70286e7i			2.08388i
$583$	−132722.	−	320419.i	−0.0161723	−	0.0390433i
$584$	2.86298e7	+	1.18589e7i	3.47365	+	1.43883i
$585$	−101222.	+	244372.i	−0.0122289	+	0.0295231i
$586$	6.78834e6	−	6.78834e6i	0.816619	−	0.816619i
$587$	−6.40236e6	+	6.40236e6i	−0.766911	+	0.766911i	−0.977561	−	0.210651i	$-0.932442\pi$
$587$	−6.40236e6	+	6.40236e6i	−0.766911	+	0.766911i	0.210651	+	0.977561i	$0.432442\pi$
$588$	5.11762e6	−	1.23550e7i	0.610415	−	1.47367i
$589$	−2.24093e7	−	9.28222e6i	−2.66158	−	1.10246i
$590$	25069.4	+	60522.8i	0.00296492	+	0.00715796i
$591$		−	488325.i		−	0.0575096i
$592$	3.17537e7	−	1.31528e7i	3.72383	−	1.54246i
$593$	1.30065e6	+	1.30065e6i	0.151888	+	0.151888i	0.778961	−	0.627073i	$-0.215747\pi$
$593$	1.30065e6	+	1.30065e6i	0.151888	+	0.151888i	−0.627073	+	0.778961i	$0.715747\pi$
$594$	−561223.			−0.0652633
$595$	−37248.5	+	21646.3i	−0.00431337	+	0.00250664i
$596$	−3.19967e7			−3.68969
$597$	3.90938e6	+	3.90938e6i	0.448923	+	0.448923i
$598$	−3.85528e6	+	1.59691e6i	−0.440862	+	0.182611i
$599$			1.50508e7i			1.71392i	0.515380	+	0.856962i	$0.327651\pi$
$599$			1.50508e7i			1.71392i	−0.515380	+	0.856962i	$0.672349\pi$
$600$	6.66031e6	+	1.60794e7i	0.755294	+	1.82344i
$601$	8.39465e6	+	3.47718e6i	0.948018	+	0.392682i	0.802485	−	0.596672i	$-0.203511\pi$
$601$	8.39465e6	+	3.47718e6i	0.948018	+	0.392682i	0.145532	+	0.989354i	$0.453511\pi$
$602$	213081.	−	514424.i	0.0239637	−	0.0578536i
$603$	2.18697e6	−	2.18697e6i	0.244934	−	0.244934i
$604$	4.24645e6	−	4.24645e6i	0.473624	−	0.473624i
$605$	280720.	−	677719.i	0.0311807	−	0.0752768i
$606$	−6.91106e6	−	2.86266e6i	−0.764475	−	0.316656i
$607$	1.32096e6	+	3.18908e6i	0.145518	+	0.351313i	0.979786	−	0.200047i	$-0.0641094\pi$
$607$	1.32096e6	+	3.18908e6i	0.145518	+	0.351313i	−0.834268	+	0.551359i	$0.814109\pi$
$608$		−	5.95855e7i		−	6.53705i
$609$	−382909.	+	158606.i	−0.0418362	+	0.0173291i
$610$	−644222.	−	644222.i	−0.0700989	−	0.0700989i
$611$	1.56267e7			1.69342
$612$	8.27767e6	+	2.19288e6i	0.893366	+	0.236667i
$613$	−1.38232e6			−0.148579			−0.0742897	−	0.997237i	$-0.523669\pi$
$613$	−1.38232e6			−0.148579			−0.0742897	+	0.997237i	$0.523669\pi$
$614$	3.62230e6	+	3.62230e6i	0.387760	+	0.387760i
$615$	−378368.	+	156725.i	−0.0403392	+	0.0167090i
$616$		−	336054.i		−	0.0356826i
$617$	−2.83562e6	−	6.84580e6i	−0.299872	−	0.723954i	−0.999951	−	0.00988915i	$-0.996852\pi$
$617$	−2.83562e6	−	6.84580e6i	−0.299872	−	0.723954i	0.700080	−	0.714065i	$-0.253148\pi$
$618$	−1.16922e7	−	4.84308e6i	−1.23148	−	0.510094i
$619$	5.16300e6	−	1.24646e7i	0.541596	−	1.30753i	−0.382001	−	0.924162i	$-0.624765\pi$
$619$	5.16300e6	−	1.24646e7i	0.541596	−	1.30753i	0.923597	−	0.383365i	$-0.125235\pi$
$620$	−2.89133e6	+	2.89133e6i	−0.302078	+	0.302078i
$621$	281660.	−	281660.i	0.0293086	−	0.0293086i
$622$	−9.18396e6	+	2.21721e7i	−0.951819	+	2.29789i
$623$	341563.	+	141480.i	0.0352574	+	0.0146041i
$624$	9.59603e6	+	2.31669e7i	0.986575	+	2.38180i
$625$		−	9.55919e6i		−	0.978861i
$626$	−1.21579e7	+	5.03595e6i	−1.24000	+	0.513624i
$627$	−1.10252e6	−	1.10252e6i	−0.112000	−	0.112000i
$628$	7.09651e6			0.718036
$629$	−6.19679e6	+	8.12336e6i	−0.624511	+	0.818670i
$630$	32177.0			0.00322994
$631$	1.08363e7	+	1.08363e7i	1.08345	+	1.08345i	0.996185	+	0.0872618i	$0.0278117\pi$
$631$	1.08363e7	+	1.08363e7i	1.08345	+	1.08345i	0.0872618	+	0.996185i	$0.472188\pi$
$632$	−1.97301e7	+	8.17247e6i	−1.96488	+	0.813881i
$633$			3.12445e6i			0.309930i
$634$	−3.65892e6	−	8.83341e6i	−0.361518	−	0.872780i
$635$	606211.	+	251101.i	0.0596609	+	0.0247124i
$636$	1.51251e6	−	3.65153e6i	0.148271	−	0.357958i
$637$	−8.23148e6	+	8.23148e6i	−0.803766	+	0.803766i
$638$	3.25745e6	−	3.25745e6i	0.316830	−	0.316830i
$639$	−30180.4	+	72861.8i	−0.00292397	+	0.00705908i
$640$	−3.16307e6	−	1.31019e6i	−0.305253	−	0.126440i
$641$	5.84340e6	+	1.41072e7i	0.561720	+	1.35611i	0.908389	+	0.418126i	$0.137313\pi$
$641$	5.84340e6	+	1.41072e7i	0.561720	+	1.35611i	−0.346669	+	0.937988i	$0.612687\pi$
$642$		−	1.69285e7i		−	1.62099i
$643$	−2.21472e6	+	917367.i	−0.211247	+	0.0875015i	−0.485798	−	0.874071i	$-0.661471\pi$
$643$	−2.21472e6	+	917367.i	−0.211247	+	0.0875015i	0.274551	+	0.961573i	$0.411471\pi$
$644$	263803.	+	263803.i	0.0250648	+	0.0250648i
$645$	−278432.			−0.0263524
$646$	1.62649e7	+	2.79883e7i	1.53346	+	2.63873i
$647$	−1.88179e7			−1.76730			−0.883649	−	0.468150i	$-0.844921\pi$
$647$	−1.88179e7			−1.76730			−0.883649	+	0.468150i	$0.844921\pi$
$648$	−2.89132e6	−	2.89132e6i	−0.270494	−	0.270494i
$649$	82153.6	−	34029.1i	0.00765623	−	0.00317131i
$650$		−	2.36974e7i		−	2.19997i
$651$	−260018.	−	627739.i	−0.0240465	−	0.0580533i
$652$	−1.21466e7	−	5.03128e6i	−1.11901	−	0.463511i
$653$	4.03152e6	−	9.73294e6i	0.369986	−	0.893226i	−0.623765	−	0.781612i	$-0.714398\pi$
$653$	4.03152e6	−	9.73294e6i	0.369986	−	0.893226i	0.993752	−	0.111614i	$-0.0356021\pi$
$654$	1.29979e7	−	1.29979e7i	1.18831	−	1.18831i
$655$	898317.	−	898317.i	0.0818138	−	0.0818138i
$656$	−1.48578e7	+	3.58699e7i	−1.34802	+	3.25440i
$657$	3.72103e6	+	1.54130e6i	0.336318	+	0.139307i
$658$	−727472.	−	1.75627e6i	−0.0655016	−	0.158135i
$659$			4.59505e6i			0.412170i	0.978534	+	0.206085i	$0.0660724\pi$
$659$			4.59505e6i			0.412170i	−0.978534	+	0.206085i	$0.933928\pi$
$660$	−242839.	+	100587.i	−0.0216999	+	0.00898840i
$661$	−1.11170e7	−	1.11170e7i	−0.989657	−	0.989657i	0.0102897	−	0.999947i	$-0.496725\pi$
$661$	−1.11170e7	−	1.11170e7i	−0.989657	−	0.989657i	−0.999947	+	0.0102897i	$0.996725\pi$
$662$	−2.01449e7			−1.78657
$663$	−5.92664e6	−	4.52106e6i	−0.523630	−	0.399444i
$664$	−9.74523e6			−0.857772
$665$	63211.7	+	63211.7i	0.00554298	+	0.00554298i
$666$	7.05015e6	−	2.92027e6i	0.615903	−	0.255116i
$667$			3.26962e6i			0.284566i
$668$	−4.61739e6	−	1.11474e7i	−0.400364	−	0.966565i
$669$	4.30928e6	+	1.78496e6i	0.372254	+	0.154193i
$670$	754258.	−	1.82094e6i	0.0649132	−	0.156714i
$671$	−874467.	+	874467.i	−0.0749785	+	0.0749785i
$672$	1.18026e6	−	1.18026e6i	0.100822	−	0.100822i
$673$	1.52483e6	−	3.68127e6i	0.129773	−	0.313300i	−0.845616	−	0.533792i	$-0.820766\pi$
$673$	1.52483e6	−	3.68127e6i	0.129773	−	0.313300i	0.975389	+	0.220492i	$0.0707664\pi$
$674$	2.24306e7	+	9.29108e6i	1.90192	+	0.787801i
$675$	865643.	+	2.08985e6i	0.0731273	+	0.176545i
$676$		−	9.92315e6i		−	0.835185i
$677$	1.13628e6	−	470662.i	0.0952825	−	0.0394673i	−0.334533	−	0.942384i	$-0.608579\pi$
$677$	1.13628e6	−	470662.i	0.0952825	−	0.0394673i	0.429816	+	0.902917i	$0.358579\pi$
$678$	1.09590e7	+	1.09590e7i	0.915578	+	0.915578i
$679$	−1.32525e6			−0.110312
$680$	3.45767e6	−	465178.i	0.286755	−	0.0385786i
$681$	−4.78706e6			−0.395550
$682$	5.34024e6	+	5.34024e6i	0.439643	+	0.439643i
$683$	1.29124e7	−	5.34851e6i	1.05915	−	0.438713i	0.215999	−	0.976394i	$-0.430699\pi$
$683$	1.29124e7	−	5.34851e6i	1.05915	−	0.438713i	0.843149	+	0.537680i	$0.180699\pi$
$684$		−	1.77688e7i		−	1.45217i
$685$	−303662.	−	733104.i	−0.0247265	−	0.0596952i
$686$	2.62129e6	+	1.08577e6i	0.212669	+	0.0880905i
$687$	1.80408e6	−	4.35544e6i	0.145836	−	0.352079i
$688$	−1.86646e7	+	1.86646e7i	−1.50331	+	1.50331i
$689$	−2.43281e6	+	2.43281e6i	−0.195236	+	0.195236i
$690$	97140.9	−	234519.i	0.00776747	−	0.0187523i
$691$	4.13263e6	+	1.71179e6i	0.329254	+	0.136381i	0.541186	−	0.840903i	$-0.317976\pi$
$691$	4.13263e6	+	1.71179e6i	0.329254	+	0.136381i	−0.211932	+	0.977284i	$0.567976\pi$
$692$	2.18201e6	+	5.26784e6i	0.173218	+	0.418184i
$693$		−	43677.1i		−	0.00345478i
$694$	−1.09781e7	+	4.54726e6i	−0.865220	+	0.358386i
$695$	376834.	+	376834.i	0.0295929	+	0.0295929i
$696$	3.35636e7			2.62630
$697$	−1.53888e6	−	1.14385e7i	−0.119984	−	0.891839i
$698$	3.98169e7			3.09335
$699$	−8.82558e6	−	8.82558e6i	−0.683204	−	0.683204i
$700$	−1.95735e6	+	810762.i	−0.150982	+	0.0625386i
$701$			1.65439e7i			1.27158i	0.771863	+	0.635789i	$0.219325\pi$
$701$			1.65439e7i			1.27158i	−0.771863	+	0.635789i	$0.780675\pi$
$702$	2.13057e6	+	5.14365e6i	0.163175	+	0.393939i
$703$	1.95869e7	+	8.11314e6i	1.49478	+	0.619157i
$704$	−3.66040e6	+	8.83700e6i	−0.278354	+	0.672006i
$705$	−672163.	+	672163.i	−0.0509333	+	0.0509333i
$706$	2.20712e7	−	2.20712e7i	1.66653	−	1.66653i
$707$	222786.	−	537852.i	0.0167625	−	0.0404683i
$708$	936230.	+	387799.i	0.0701939	+	0.0290753i
$709$	−7.20172e6	−	1.73865e7i	−0.538047	−	1.29896i	−0.926084	−	0.377317i	$-0.876847\pi$
$709$	−7.20172e6	−	1.73865e7i	−0.538047	−	1.29896i	0.388037	−	0.921644i	$-0.373153\pi$
$710$			50258.3i			0.00374164i
$711$	−2.56433e6	+	1.06218e6i	−0.190239	+	0.0787996i
$712$	−2.11703e7	−	2.11703e7i	−1.56505	−	1.56505i
$713$	−5.36019e6			−0.394872
$714$	−232215.	+	876560.i	−0.0170468	+	0.0643482i
$715$	228806.			0.0167379
$716$	−4.10864e7	−	4.10864e7i	−2.99513	−	2.99513i
$717$	8.64632e6	−	3.58142e6i	0.628107	−	0.260170i
$718$		−	1.26201e7i		−	0.913589i
$719$	−1.21868e6	−	2.94215e6i	−0.0879158	−	0.212248i	0.873806	−	0.486274i	$-0.161644\pi$
$719$	−1.21868e6	−	2.94215e6i	−0.0879158	−	0.212248i	−0.961722	+	0.274027i	$0.911644\pi$
$720$	−1.40925e6	−	583732.i	−0.101311	−	0.0419645i
$721$	376912.	−	909945.i	0.0270023	−	0.0651894i
$722$	2.82596e7	−	2.82596e7i	2.01754	−	2.01754i
$723$	−6.67194e6	+	6.67194e6i	−0.474686	+	0.474686i
$724$	−5.13344e6	+	1.23932e7i	−0.363967	+	0.878694i
$725$	−1.71543e7	−	7.10553e6i	−1.21207	−	0.502055i
$726$	−5.90872e6	−	1.42649e7i	−0.416056	−	1.00445i
$727$			2.01103e7i			1.41118i	0.708620	+	0.705591i	$0.249318\pi$
$727$			2.01103e7i			1.41118i	−0.708620	+	0.705591i	$0.750682\pi$
$728$	−3.07996e6	+	1.27576e6i	−0.215385	+	0.0892156i
$729$	−375786.	−	375786.i	−0.0261891	−	0.0261891i
$730$	2.56667e6			0.178264
$731$	2.00938e6	−	7.58498e6i	0.139081	−	0.525002i
$732$	−1.40934e7			−0.972158
$733$	6.86067e6	+	6.86067e6i	0.471635	+	0.471635i	0.902444	−	0.430808i	$-0.141771\pi$
$733$	6.86067e6	+	6.86067e6i	0.471635	+	0.471635i	−0.430808	+	0.902444i	$0.641771\pi$
$734$	2.42662e7	−	1.00514e7i	1.66250	−	0.688630i
$735$		−	708134.i		−	0.0483500i
$736$	−5.03905e6	−	1.21653e7i	−0.342889	−	0.827808i
$737$	−2.47174e6	−	1.02383e6i	−0.167623	−	0.0694318i
$738$	−3.29882e6	+	7.96405e6i	−0.222955	+	0.538261i
$739$	616078.	−	616078.i	0.0414978	−	0.0414978i	−0.686053	−	0.727551i	$-0.740658\pi$
$739$	616078.	−	616078.i	0.0414978	−	0.0414978i	0.727551	+	0.686053i	$0.240658\pi$
$740$	2.52717e6	−	2.52717e6i	0.169651	−	0.169651i
$741$	−5.91919e6	+	1.42902e7i	−0.396020	+	0.956076i
$742$	386677.	+	160167.i	0.0257833	+	0.0106798i
$743$	−7.57336e6	−	1.82837e7i	−0.503288	−	1.21504i	−0.947683	−	0.319213i	$-0.896581\pi$
$743$	−7.57336e6	−	1.82837e7i	−0.503288	−	1.21504i	0.444395	−	0.895831i	$-0.353419\pi$
$744$			5.50239e7i			3.64434i
$745$	−1.56533e6	+	648383.i	−0.103328	+	0.0427997i
$746$	−2.07455e6	−	2.07455e6i	−0.136483	−	0.136483i
$747$	−1.26659e6			−0.0830492
$748$	−987660.	−	7.34128e6i	−0.0645436	−	0.479753i
$749$	1.31746e6			0.0858088
$750$	2.04588e6	+	2.04588e6i	0.132809	+	0.132809i
$751$	−1.08893e7	+	4.51051e6i	−0.704533	+	0.291827i	−0.706040	−	0.708172i	$-0.749520\pi$
$751$	−1.08893e7	+	4.51051e6i	−0.704533	+	0.291827i	0.00150742	+	0.999999i	$0.499520\pi$
$752$			9.01166e7i			5.81112i
$753$	378404.	+	913547.i	0.0243202	+	0.0587142i
$754$	−4.22210e7	−	1.74885e7i	−2.70458	−	1.12028i
$755$	121694.	−	293794.i	0.00776962	−	0.0187575i
$756$	351961.	−	351961.i	0.0223970	−	0.0223970i
$757$	6.87932e6	−	6.87932e6i	0.436320	−	0.436320i	−0.454451	−	0.890772i	$-0.650165\pi$
$757$	6.87932e6	−	6.87932e6i	0.436320	−	0.436320i	0.890772	+	0.454451i	$0.150165\pi$
$758$	2.47839e6	−	5.98337e6i	0.156674	−	0.378245i
$759$	−318336.	−	131859.i	−0.0200577	−	0.00830817i
$760$	−2.77038e6	−	6.68829e6i	−0.173983	−	0.420031i
$761$		−	3.03683e6i		−	0.190090i	−0.995473	−	0.0950450i	$-0.969701\pi$
$761$		−	3.03683e6i		−	0.190090i	0.995473	−	0.0950450i	$-0.0302995\pi$
$762$	1.27598e7	−	5.28528e6i	0.796078	−	0.329747i
$763$	1.01156e6	+	1.01156e6i	0.0629044	+	0.0629044i
$764$	−5.07512e7			−3.14567
$765$	449395.	−	60459.4i	0.0277635	−	0.00373517i
$766$	−8.11960e6			−0.499991
$767$	−623759.	−	623759.i	−0.0382850	−	0.0382850i
$768$	−3.02547e7	+	1.25319e7i	−1.85093	+	0.766679i
$769$		−	9.70564e6i		−	0.591845i	−0.955212	−	0.295923i	$-0.904373\pi$
$769$		−	9.70564e6i		−	0.591845i	0.955212	−	0.295923i	$-0.0956271\pi$
$770$	−10651.6	−	25715.3i	−0.000647425	−	0.00156302i
$771$	2.67744e6	+	1.10903e6i	0.162213	+	0.0671906i
$772$	−1.57335e7	+	3.79840e7i	−0.950128	+	2.29381i
$773$	−1.20448e7	+	1.20448e7i	−0.725023	+	0.725023i	−0.969624	−	0.244601i	$-0.921343\pi$
$773$	−1.20448e7	+	1.20448e7i	−0.725023	+	0.725023i	0.244601	+	0.969624i	$0.421343\pi$
$774$	−4.14403e6	+	4.14403e6i	−0.248640	+	0.248640i
$775$	1.16488e7	−	2.81226e7i	0.696667	−	1.68190i
$776$	9.91517e7	+	4.10700e7i	5.91080	+	2.44833i
$777$	227269.	+	548676.i	0.0135048	+	0.0326035i
$778$			6.21435e7i			3.68084i
$779$	−2.21259e7	+	9.16484e6i	−1.30634	+	0.541105i
$780$	1.84378e6	+	1.84378e6i	0.108510	+	0.108510i
$781$	68220.5			0.00400210
$782$	5.68767e6	+	4.33876e6i	0.332596	+	0.253717i
$783$	4.36227e6			0.254278
$784$	−4.74696e7	−	4.74696e7i	−2.75820	−	2.75820i
$785$	347174.	−	143804.i	0.0201082	−	0.00832908i
$786$		−	2.67402e7i		−	1.54386i
$787$	−656465.	−	1.58485e6i	−0.0377811	−	0.0912117i	0.903863	−	0.427823i	$-0.140719\pi$
$787$	−656465.	−	1.58485e6i	−0.0377811	−	0.0912117i	−0.941644	+	0.336611i	$0.890719\pi$
$788$	−4.44745e6	−	1.84219e6i	−0.255150	−	0.105687i
$789$	−4.99004e6	+	1.20470e7i	−0.285372	+	0.688949i
$790$	−1.25074e6	+	1.25074e6i	−0.0713015	+	0.0713015i
$791$	−852880.	+	852880.i	−0.0484670	+	0.0484670i
$792$	−1.35357e6	+	3.26781e6i	−0.0766774	+	0.185116i
$793$	1.13343e7	+	4.69482e6i	0.640046	+	0.265116i
$794$	−4.11302e6	−	9.92971e6i	−0.231531	−	0.558966i
$795$		−	209289.i		−	0.0117443i
$796$	5.03529e7	−	2.08568e7i	2.81671	−	1.16672i
$797$	1.41801e7	+	1.41801e7i	0.790742	+	0.790742i	0.981615	−	0.190873i	$-0.0611318\pi$
$797$	1.41801e7	+	1.41801e7i	0.790742	+	0.790742i	−0.190873	+	0.981615i	$0.561132\pi$
$798$	1.88162e6			0.104598
$799$	−1.34601e7	−	2.31618e7i	−0.745900	−	1.28353i
$800$	7.47771e7			4.13089
$801$	−2.75152e6	−	2.75152e6i	−0.151527	−	0.151527i
$802$	4.32525e7	−	1.79158e7i	2.37451	−	0.983556i
$803$		−	3.48400e6i		−	0.190673i
$804$	−1.16677e7	−	2.81682e7i	−0.636566	−	1.53681i
$805$	18251.4	+	7559.97i	0.000992673	+	0.000411179i
$806$	2.86706e7	−	6.92169e7i	1.55453	−	3.75296i
$807$	−8.73713e6	+	8.73713e6i	−0.472264	+	0.472264i
$808$	−3.33365e7	+	3.33365e7i	−1.79635	+	1.79635i
$809$	1.13360e7	−	2.73675e7i	0.608959	−	1.47016i	−0.255175	−	0.966895i	$-0.582133\pi$
$809$	1.13360e7	−	2.73675e7i	0.608959	−	1.47016i	0.864134	−	0.503262i	$-0.167867\pi$
$810$	−312891.	−	129604.i	−0.0167564	−	0.00694073i
$811$	1.09382e7	+	2.64071e7i	0.583973	+	1.40984i	0.889183	+	0.457551i	$0.151273\pi$
$811$	1.09382e7	+	2.64071e7i	0.583973	+	1.40984i	−0.305210	+	0.952285i	$0.598727\pi$
$812$			4.08571e6i			0.217459i
$813$	−3.63482e6	+	1.50559e6i	−0.192867	+	0.0798880i
$814$	−4.66765e6	−	4.66765e6i	−0.246909	−	0.246909i
$815$	−696187.			−0.0367140
$816$	2.60722e7	−	3.41780e7i	1.37073	−	1.79689i
$817$	−1.62819e7			−0.853394
$818$	2.19949e7	+	2.19949e7i	1.14932	+	1.14932i
$819$	−400304.	+	165811.i	−0.0208535	+	0.00863782i
$820$			4.03725e6i			0.209677i
$821$	−8.07083e6	−	1.94847e7i	−0.417889	−	1.00887i	−0.982958	−	0.183829i	$-0.941151\pi$
$821$	−8.07083e6	−	1.94847e7i	−0.417889	−	1.00887i	0.565070	−	0.825043i	$-0.308849\pi$
$822$	−1.54307e7	−	6.39159e6i	−0.796536	−	0.329936i
$823$	2.53517e6	−	6.12045e6i	0.130469	−	0.314981i	−0.845123	−	0.534573i	$-0.820473\pi$
$823$	2.53517e6	−	6.12045e6i	0.130469	−	0.314981i	0.975592	+	0.219592i	$0.0704726\pi$
$824$	−5.63991e7	+	5.63991e7i	−2.89370	+	2.89370i
$825$	1.38361e6	−	1.38361e6i	0.0707750	−	0.0707750i
$826$	−41065.9	+	99141.7i	−0.00209426	+	0.00505599i
$827$	7.29137e6	+	3.02018e6i	0.370719	+	0.153557i	0.560262	−	0.828315i	$-0.310700\pi$
$827$	7.29137e6	+	3.02018e6i	0.370719	+	0.153557i	−0.189542	+	0.981873i	$0.560700\pi$
$828$	−1.50268e6	−	3.62778e6i	−0.0761710	−	0.183893i
$829$			9.09985e6i			0.459883i	0.973204	+	0.229942i	$0.0738536\pi$
$829$			9.09985e6i			0.459883i	−0.973204	+	0.229942i	$0.926146\pi$
$830$	−745719.	+	308887.i	−0.0375733	+	0.0155634i
$831$	8.88333e6	+	8.88333e6i	0.446245	+	0.446245i
$832$	9.48877e7			4.75228
$833$	1.92908e7	+	5.11044e6i	0.963249	+	0.255180i
$834$	1.12172e7			0.558430
$835$	−451781.	−	451781.i	−0.0224240	−	0.0224240i
$836$	−1.42005e7	+	5.88204e6i	−0.702729	+	0.291080i
$837$			7.15148e6i			0.352844i
$838$	2.83546e7	+	6.84541e7i	1.39481	+	3.36736i
$839$	−1.11972e7	−	4.63802e6i	−0.549166	−	0.227472i	0.0908083	−	0.995868i	$-0.471055\pi$
$839$	−1.11972e7	−	4.63802e6i	−0.549166	−	0.227472i	−0.639974	+	0.768396i	$0.721055\pi$
$840$	77605.3	−	187356.i	0.00379484	−	0.00916154i
$841$	−1.08159e7	+	1.08159e7i	−0.527319	+	0.527319i
$842$	2.60023e7	−	2.60023e7i	1.26396	−	1.26396i
$843$	−1.43551e6	+	3.46562e6i	−0.0695724	+	0.167963i
$844$	2.84561e7	+	1.17869e7i	1.37505	+	0.569565i
$845$	−201083.	−	485458.i	−0.00968800	−	0.0233889i
$846$			2.00082e7i			0.961131i
$847$	1.11016e6	−	459845.i	0.0531714	−	0.0220243i
$848$	−1.40296e7	−	1.40296e7i	−0.669971	−	0.669971i
$849$	1.68718e7			0.803329
$850$	−3.51240e7	+	2.04117e7i	−1.66747	+	0.969020i
$851$	4.68508e6			0.221765
$852$	549739.	+	549739.i	0.0259452	+	0.0259452i
$853$	−1.55576e7	+	6.44416e6i	−0.732098	+	0.303245i	−0.717414	−	0.696647i	$-0.754674\pi$
$853$	−1.55576e7	+	6.44416e6i	−0.732098	+	0.303245i	−0.0146843	+	0.999892i	$0.504674\pi$
$854$		−	1.49241e6i		−	0.0700235i
$855$	−360068.	−	869281.i	−0.0168449	−	0.0406672i
$856$	−9.85687e7	−	4.08285e7i	−4.59785	−	1.90449i
$857$	23659.3	−	57118.7i	0.00110040	−	0.00265660i	−0.923328	−	0.384011i	$-0.874542\pi$
$857$	23659.3	−	57118.7i	0.00110040	−	0.00265660i	0.924429	+	0.381355i	$0.124542\pi$
$858$	3.40543e6	−	3.40543e6i	0.157926	−	0.157926i
$859$	805088.	−	805088.i	0.0372272	−	0.0372272i	−0.688248	−	0.725475i	$-0.741620\pi$
$859$	805088.	−	805088.i	0.0372272	−	0.0372272i	0.725475	+	0.688248i	$0.241620\pi$
$860$	−1.05038e6	+	2.53583e6i	−0.0484283	+	0.116916i
$861$	−619801.	−	256730.i	−0.0284934	−	0.0118024i
$862$	1.00504e7	+	2.42638e7i	0.460697	+	1.11222i
$863$			1.53265e6i			0.0700513i	0.999386	+	0.0350257i	$0.0111513\pi$
$863$			1.53265e6i			0.0700513i	−0.999386	+	0.0350257i	$0.988849\pi$
$864$	−1.62308e7	+	6.72302e6i	−0.739700	+	0.306394i
$865$	213496.	+	213496.i	0.00970172	+	0.00970172i
$866$	−1.87210e7			−0.848272
$867$	−1.59616e6	+	1.26786e7i	−0.0721155	+	0.572829i
$868$	−6.69808e6			−0.301753
$869$	1.69775e6	+	1.69775e6i	0.0762648	+	0.0762648i
$870$	2.56833e6	−	1.06384e6i	0.115041	−	0.0476516i
$871$			2.65405e7i			1.18539i
$872$	−4.43337e7	−	1.07031e8i	−1.97444	−	4.76671i
$873$	1.28868e7	+	5.33789e6i	0.572281	+	0.237047i
$874$	5.68052e6	−	1.37140e7i	0.251541	−	0.607275i
$875$	−159220.	+	159220.i	−0.00703035	+	0.00703035i
$876$	2.80750e7	−	2.80750e7i	1.23612	−	1.23612i
$877$	−2.06846e6	+	4.99369e6i	−0.0908128	+	0.219242i	−0.962759	−	0.270359i	$-0.912857\pi$
$877$	−2.06846e6	+	4.99369e6i	−0.0908128	+	0.219242i	0.871947	+	0.489601i	$0.162857\pi$
$878$	−2.02685e7	−	8.39550e6i	−0.887332	−	0.367545i
$879$	−3.00932e6	−	7.26514e6i	−0.131370	−	0.317155i
$880$			1.31949e6i			0.0574378i
$881$	3.03489e7	−	1.25709e7i	1.31736	−	0.545667i	0.390335	−	0.920673i	$-0.372359\pi$
$881$	3.03489e7	−	1.25709e7i	1.31736	−	0.545667i	0.927023	+	0.375006i	$0.122359\pi$
$882$	−1.05395e7	−	1.05395e7i	−0.456192	−	0.456192i
$883$	3.44142e7			1.48537			0.742687	−	0.669639i	$-0.233551\pi$
$883$	3.44142e7			1.48537			0.742687	+	0.669639i	$0.233551\pi$
$884$	−6.35339e7	+	3.69216e7i	−2.73448	+	1.58910i
$885$	53660.4			0.00230301
$886$	−729618.	−	729618.i	−0.0312256	−	0.0312256i
$887$	−1.85265e7	+	7.67391e6i	−0.790649	+	0.327497i	−0.741204	−	0.671280i	$-0.765745\pi$
$887$	−1.85265e7	+	7.67391e6i	−0.790649	+	0.327497i	−0.0494443	+	0.998777i	$0.515745\pi$
$888$		−	4.80937e7i		−	2.04671i
$889$	411326.	+	993028.i	0.0174555	+	0.0421412i
$890$	−2.29100e6	−	948964.i	−0.0969505	−	0.0401582i
$891$	−175924.	+	424718.i	−0.00742388	+	0.0179228i
$892$	3.25133e7	−	3.25133e7i	1.36820	−	1.36820i
$893$	−3.93061e7	+	3.93061e7i	−1.64942	+	1.64942i
$894$	−1.36474e7	+	3.29478e7i	−0.571093	+	1.37874i
$895$	−2.84260e6	−	1.17744e6i	−0.118620	−	0.0491340i
$896$	−2.14620e6	−	5.18140e6i	−0.0893102	−	0.215614i
$897$			3.41815e6i			0.141843i
$898$	−6.98027e7	+	2.89132e7i	−2.88856	+	1.19648i
$899$	−4.15086e7	−	4.15086e7i	−1.71293	−	1.71293i
$900$	2.22990e7			0.917655
$901$	5.70140e6	+	1.51039e6i	0.233975	+	0.0619836i
$902$	7.45674e6			0.305164
$903$	−322508.	−	322508.i	−0.0131620	−	0.0131620i
$904$	9.02413e7	−	3.73792e7i	3.67269	−	1.52128i
$905$			710322.i			0.0288293i
$906$	−2.56145e6	−	6.18390e6i	−0.103673	−	0.250289i
$907$	2.91857e7	+	1.20891e7i	1.17802	+	0.487951i	0.883835	−	0.467798i	$-0.154953\pi$
$907$	2.91857e7	+	1.20891e7i	1.17802	+	0.487951i	0.294182	+	0.955749i	$0.404953\pi$
$908$	−1.80591e7	+	4.35984e7i	−0.726910	+	1.75492i
$909$	−4.33276e6	+	4.33276e6i	−0.173922	+	0.173922i
$910$	−195246.	+	195246.i	−0.00781589	+	0.00781589i
$911$	−5.55893e6	+	1.34204e7i	−0.221919	+	0.535761i	−0.995151	−	0.0983634i	$-0.968639\pi$
$911$	−5.55893e6	+	1.34204e7i	−0.221919	+	0.535761i	0.773231	+	0.634124i	$0.218639\pi$
$912$	−8.24091e7	−	3.41350e7i	−3.28086	−	1.35898i
$913$	419283.	+	1.01224e6i	0.0166468	+	0.0401889i
$914$			2.58660e7i			1.02415i
$915$	−689471.	+	285588.i	−0.0272247	+	0.0112769i
$916$	−3.28616e7	−	3.28616e7i	−1.29405	−	1.29405i
$917$	2.08105e6			0.0817257
$918$	5.78871e6	−	7.58840e6i	0.226712	−	0.297196i
$919$	2.21902e7			0.866708			0.433354	−	0.901224i	$-0.357330\pi$
$919$	2.21902e7			0.866708			0.433354	+	0.901224i	$0.357330\pi$
$920$	−1.13124e6	−	1.13124e6i	−0.0440639	−	0.0440639i
$921$	3.87672e6	−	1.60579e6i	0.150597	−	0.0623792i
$922$			4.01435e6i			0.155520i
$923$	−258985.	−	625246.i	−0.0100062	−	0.0241572i
$924$	−397791.	−	164771.i	−0.0153276	−	0.00634892i
$925$	−1.01816e7	+	2.45806e7i	−0.391257	+	0.944579i
$926$	2.94273e7	−	2.94273e7i	1.12778	−	1.12778i
$927$	−7.33022e6	+	7.33022e6i	−0.280167	+	0.280167i
$928$	5.51851e7	−	1.33229e8i	2.10354	−	5.07841i
$929$	2.45604e7	+	1.01733e7i	0.933677	+	0.386742i	0.797072	−	0.603884i	$-0.206381\pi$
$929$	2.45604e7	+	1.01733e7i	0.933677	+	0.386742i	0.136605	+	0.990626i	$0.456381\pi$
$930$	1.74405e6	+	4.21050e6i	0.0661228	+	0.159635i
$931$		−	4.14096e7i		−	1.56577i
$932$	−1.13674e8	+	4.70852e7i	−4.28667	+	1.77560i
$933$	1.39003e7	+	1.39003e7i	0.522783	+	0.522783i
$934$	3.26519e7			1.22473
$935$	−197082.	−	339134.i	−0.00737255	−	0.0126865i
$936$	3.50882e7			1.30910
$937$	−2.45436e7	−	2.45436e7i	−0.913251	−	0.913251i	0.0832759	−	0.996527i	$-0.473462\pi$
$937$	−2.45436e7	−	2.45436e7i	−0.913251	−	0.913251i	−0.996527	+	0.0832759i	$0.973462\pi$
$938$	2.98286e6	−	1.23554e6i	0.110694	−	0.0458512i
$939$			1.07793e7i			0.398959i
$940$	3.58604e6	+	8.65748e6i	0.132372	+	0.319574i
$941$	2.45368e7	+	1.01635e7i	0.903326	+	0.374170i	0.785498	−	0.618864i	$-0.212407\pi$
$941$	2.45368e7	+	1.01635e7i	0.903326	+	0.374170i	0.117828	+	0.993034i	$0.462407\pi$
$942$	3.02685e6	−	7.30746e6i	0.111138	−	0.268311i
$943$	−3.74230e6	+	3.74230e6i	−0.137044	+	0.137044i
$944$	3.59711e6	−	3.59711e6i	0.131378	−	0.131378i
$945$	10086.4	−	24350.7i	0.000367415	−	0.000887017i
$946$	4.68364e6	+	1.94003e6i	0.170159	+	0.0704823i
$947$	5.21039e6	+	1.25790e7i	0.188797	+	0.455797i	0.989729	−	0.142960i	$-0.0456619\pi$
$947$	5.21039e6	+	1.25790e7i	0.188797	+	0.455797i	−0.800931	+	0.598756i	$0.795662\pi$
$948$			2.73618e7i			0.988836i
$949$	−3.19311e7	+	1.32263e7i	−1.15093	+	0.476731i
$950$	5.96064e7	+	5.96064e7i	2.14281	+	2.14281i
$951$	−7.83182e6			−0.280809
$952$	4.54384e6	+	3.46621e6i	0.162492	+	0.123955i
$953$	2.58794e6			0.0923043			0.0461521	−	0.998934i	$-0.485304\pi$
$953$	2.58794e6			0.0923043			0.0461521	+	0.998934i	$0.485304\pi$
$954$	−3.11494e6	−	3.11494e6i	−0.110810	−	0.110810i
$955$	−2.48284e6	+	1.02842e6i	−0.0880926	+	0.0364892i
$956$		−	9.22577e7i		−	3.26481i
$957$	−1.44405e6	−	3.48625e6i	−0.0509686	−	0.123049i
$958$	−4.11284e7	−	1.70359e7i	−1.44787	−	0.599725i
$959$	497425.	−	1.20089e6i	0.0174655	−	0.0421654i
$960$	−4.08148e6	+	4.08148e6i	−0.142935	+	0.142935i
$961$	4.78051e7	−	4.78051e7i	1.66981	−	1.66981i
$962$	−2.50596e7	+	6.04991e7i	−0.873043	+	2.10771i
$963$	−1.28110e7	−	5.30650e6i	−0.445162	−	0.184392i
$964$	3.55954e7	+	8.59348e7i	1.23368	+	2.97836i
$965$			2.17707e6i			0.0752583i
$966$	384163.	−	159125.i	0.0132456	−	0.00548652i
$967$	−2.47037e7	−	2.47037e7i	−0.849563	−	0.849563i	0.140515	−	0.990078i	$-0.455124\pi$
$967$	−2.47037e7	−	2.47037e7i	−0.849563	−	0.849563i	−0.990078	+	0.140515i	$0.955124\pi$
$968$	−9.73103e7			−3.33788
$969$	2.62793e7	−	3.53549e6i	0.899092	−	0.120959i
$970$	8.88899e6			0.303336
$971$	−2.47269e7	−	2.47269e7i	−0.841631	−	0.841631i	0.147440	−	0.989071i	$-0.452897\pi$
$971$	−2.47269e7	−	2.47269e7i	−0.841631	−	0.841631i	−0.989071	+	0.147440i	$0.952897\pi$
$972$	−4.84013e6	+	2.00485e6i	−0.164320	+	0.0680637i
$973$			872976.i			0.0295611i
$974$	−2.87801e7	−	6.94812e7i	−0.972063	−	2.34677i
$975$	−1.79335e7	−	7.42831e6i	−0.604163	−	0.250253i
$976$	−2.70742e7	+	6.53629e7i	−0.909769	+	2.19638i
$977$	4.67753e6	−	4.67753e6i	0.156776	−	0.156776i	−0.624360	−	0.781136i	$-0.714640\pi$
$977$	4.67753e6	−	4.67753e6i	0.156776	−	0.156776i	0.781136	+	0.624360i	$0.214640\pi$
$978$	−1.03617e7	+	1.03617e7i	−0.346404	+	0.346404i
$979$	−1.28812e6	+	3.10980e6i	−0.0429537	+	0.103699i
$980$	−6.44937e6	−	2.67142e6i	−0.214512	−	0.0888539i
$981$	−5.76208e6	−	1.39109e7i	−0.191164	−	0.461511i
$982$		−	4.03016e7i		−	1.33366i
$983$	4.04550e7	−	1.67570e7i	1.33533	−	0.553112i	0.403159	−	0.915130i	$-0.367912\pi$
$983$	4.04550e7	−	1.67570e7i	1.33533	−	0.553112i	0.932171	+	0.362018i	$0.117912\pi$
$984$	3.84157e7	+	3.84157e7i	1.26480	+	1.26480i
$985$	−254907.			−0.00837128
$986$	1.04458e7	+	7.76434e7i	0.342175	+	2.54339i
$987$	−1.55714e6			−0.0508785
$988$	1.07819e8	+	1.07819e8i	3.51400	+	3.51400i
$989$	−3.32421e6	+	1.37693e6i	−0.108068	+	0.0447632i
$990$			292960.i			0.00949993i
$991$	1.80503e7	+	4.35772e7i	0.583848	+	1.40953i	0.889299	+	0.457325i	$0.151193\pi$
$991$	1.80503e7	+	4.35772e7i	0.583848	+	1.40953i	−0.305452	+	0.952208i	$0.598807\pi$
$992$	2.18414e8	+	9.04701e7i	7.04695	+	2.91894i
$993$	−6.31473e6	+	1.52451e7i	−0.203227	+	0.490634i
$994$	−58214.3	+	58214.3i	−0.00186881	+	0.00186881i
$995$	2.04071e6	−	2.04071e6i	0.0653466	−	0.0653466i
$996$	−4.77819e6	+	1.15356e7i	−0.152621	+	0.368460i
$997$	−1.81960e7	−	7.53703e6i	−0.579746	−	0.240139i	0.0734862	−	0.997296i	$-0.476588\pi$
$997$	−1.81960e7	−	7.53703e6i	−0.579746	−	0.240139i	−0.653232	+	0.757158i	$0.726588\pi$
$998$	−2.05857e7	−	4.96982e7i	−0.654242	−	1.57948i
$999$		−	6.25076e6i		−	0.198161i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	51.6.h.a.19.1	✓	56
17.3	odd	16		867.6.a.t.1.1		28
17.9	even	8	inner	51.6.h.a.43.1	yes	56
17.14	odd	16		867.6.a.u.1.1		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.6.h.a.19.1	✓	56	1.1	even	1	trivial
51.6.h.a.43.1	yes	56	17.9	even	8	inner
867.6.a.t.1.1		28	17.3	odd	16
867.6.a.u.1.1		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+(-7.76922 - 7.76922i) q^{2} +(-8.31492 + 3.44415i) q^{3} +88.7215i q^{4} +(1.79786 + 4.34041i) q^{5} +(91.3588 + 37.8420i) q^{6} +(-2.94505 + 7.10998i) q^{7} +(440.682 - 440.682i) q^{8} +(57.2756 - 57.2756i) q^{9} +(19.7537 - 47.6896i) q^{10} +(-64.7337 - 26.8136i) q^{11} +(-305.570 - 737.712i) q^{12} +695.082i q^{13} +(78.1197 - 32.3583i) q^{14} +(-29.8981 - 29.8981i) q^{15} -4008.42 q^{16} +(1030.24 - 598.709i) q^{17} -889.974 q^{18} +(-1748.35 - 1748.35i) q^{19} +(-385.088 + 159.509i) q^{20} -69.2621i q^{21} +(294.610 + 711.251i) q^{22} +(-504.809 - 209.099i) q^{23} +(-2146.46 + 5182.01i) q^{24} +(2194.10 - 2194.10i) q^{25} +(5400.24 - 5400.24i) q^{26} +(-278.976 + 673.508i) q^{27} +(-630.808 - 261.289i) q^{28} +(-2289.94 - 5528.41i) q^{29} +464.569i q^{30} +(9063.24 - 3754.12i) q^{31} +(17040.5 + 17040.5i) q^{32} +630.606 q^{33} +(-12655.7 - 3352.69i) q^{34} -36.1550 q^{35} +(5081.58 + 5081.58i) q^{36} +(-7921.74 + 3281.29i) q^{37} +27166.7i q^{38} +(-2393.97 - 5779.55i) q^{39} +(2705.03 + 1120.46i) q^{40} +(3706.65 - 8948.63i) q^{41} +(-538.112 + 538.112i) q^{42} +(4656.35 - 4656.35i) q^{43} +(2378.94 - 5743.28i) q^{44} +(351.573 + 145.626i) q^{45} +(2297.44 + 5546.51i) q^{46} -22481.8i q^{47} +(33329.7 - 13805.6i) q^{48} +(11842.5 + 11842.5i) q^{49} -34092.9 q^{50} +(-6504.35 + 8526.54i) q^{51} -61668.7 q^{52} +(3500.04 + 3500.04i) q^{53} +(7400.06 - 3065.21i) q^{54} -329.178i q^{55} +(1835.41 + 4431.07i) q^{56} +(20559.0 + 8515.81i) q^{57} +(-25160.4 + 60742.5i) q^{58} +(-897.389 + 897.389i) q^{59} +(2652.60 - 2652.60i) q^{60} +(6754.33 - 16306.4i) q^{61} +(-99580.9 - 41247.8i) q^{62} +(238.549 + 575.908i) q^{63} -136513. i q^{64} +(-3016.94 + 1249.66i) q^{65} +(-4899.31 - 4899.31i) q^{66} +38183.2 q^{67} +(53118.4 + 91404.9i) q^{68} +4917.61 q^{69} +(280.896 + 280.896i) q^{70} +(-899.529 + 372.597i) q^{71} -50480.7i q^{72} +(19028.4 + 45938.6i) q^{73} +(87038.9 + 36052.7i) q^{74} +(-10687.0 + 25800.6i) q^{75} +(155117. - 155117. i) q^{76} +(381.288 - 381.288i) q^{77} +(-26303.3 + 63501.8i) q^{78} +(-31658.4 - 13113.3i) q^{79} +(-7206.57 - 17398.2i) q^{80} -6561.00i q^{81} +(-98321.6 + 40726.2i) q^{82} +(-11057.0 - 11057.0i) q^{83} +6145.04 q^{84} +(4450.88 + 3395.29i) q^{85} -72352.4 q^{86} +(38081.4 + 38081.4i) q^{87} +(-40343.3 + 16710.7i) q^{88} -48039.9i q^{89} +(-1600.05 - 3862.85i) q^{90} +(-4942.02 - 2047.05i) q^{91} +(18551.6 - 44787.5i) q^{92} +(-62430.4 + 62430.4i) q^{93} +(-174666. + 174666. i) q^{94} +(4445.28 - 10731.9i) q^{95} +(-200380. - 83000.2i) q^{96} +(65899.8 + 159096. i) q^{97} -184013. i q^{98} +(-5243.43 + 2171.90i) 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

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