LMFDB - Embedded newform 69.7.b.a.47.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [69,7,Mod(47,69)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(69, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("69.47");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 69 = 3 \cdot 23 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	69.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$15.8737317698$
Analytic rank:	$0$
Dimension:	$44$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			47.10
Character	$\chi$	$=$	69.47
Dual form			69.7.b.a.47.35

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-9.87745i q^{2} +(22.8275 + 14.4190i) q^{3} -33.5640 q^{4} -220.404i q^{5} +(142.423 - 225.477i) q^{6} +473.108 q^{7} -300.630i q^{8} +(313.187 + 658.297i) q^{9} +O(q^{10})$	\(q-9.87745i q^{2} +(22.8275 + 14.4190i) q^{3} -33.5640 q^{4} -220.404i q^{5} +(142.423 - 225.477i) q^{6} +473.108 q^{7} -300.630i q^{8} +(313.187 + 658.297i) q^{9} -2177.03 q^{10} +1895.42i q^{11} +(-766.181 - 483.958i) q^{12} +1951.15 q^{13} -4673.10i q^{14} +(3178.00 - 5031.27i) q^{15} -5117.55 q^{16} -7391.51i q^{17} +(6502.29 - 3093.49i) q^{18} -6144.18 q^{19} +7397.63i q^{20} +(10799.8 + 6821.72i) q^{21} +18722.0 q^{22} -2536.99i q^{23} +(4334.78 - 6862.63i) q^{24} -32952.9 q^{25} -19272.4i q^{26} +(-2342.70 + 19543.1i) q^{27} -15879.4 q^{28} -7966.70i q^{29} +(-49696.1 - 31390.5i) q^{30} +3070.52 q^{31} +31308.0i q^{32} +(-27330.1 + 43267.8i) q^{33} -73009.3 q^{34} -104275. i q^{35} +(-10511.8 - 22095.1i) q^{36} +17124.3 q^{37} +60688.8i q^{38} +(44539.8 + 28133.6i) q^{39} -66260.1 q^{40} -22873.7i q^{41} +(67381.2 - 106675. i) q^{42} -3573.42 q^{43} -63618.0i q^{44} +(145091. - 69027.6i) q^{45} -25059.0 q^{46} +183847. i q^{47} +(-116821. - 73789.8i) q^{48} +106182. q^{49} +325491. i q^{50} +(106578. - 168730. i) q^{51} -65488.3 q^{52} +133018. i q^{53} +(193036. + 23139.9i) q^{54} +417759. q^{55} -142230. i q^{56} +(-140256. - 88592.7i) q^{57} -78690.7 q^{58} +153966. i q^{59} +(-106666. + 168869. i) q^{60} -232527. q^{61} -30328.9i q^{62} +(148171. + 311445. i) q^{63} -18279.9 q^{64} -430041. i q^{65} +(427375. + 269951. i) q^{66} +475022. q^{67} +248089. i q^{68} +(36580.8 - 57913.2i) q^{69} -1.02997e6 q^{70} -56456.9i q^{71} +(197904. - 94153.4i) q^{72} +170962. q^{73} -169144. i q^{74} +(-752232. - 475147. i) q^{75} +206223. q^{76} +896740. i q^{77} +(277888. - 439940. i) q^{78} +290536. q^{79} +1.12793e6i q^{80} +(-335269. + 412340. i) q^{81} -225934. q^{82} -121214. i q^{83} +(-362486. - 228964. i) q^{84} -1.62912e6 q^{85} +35296.2i q^{86} +(114872. - 181860. i) q^{87} +569822. q^{88} -123578. i q^{89} +(-681817. - 1.43313e6i) q^{90} +923104. q^{91} +85151.6i q^{92} +(70092.2 + 44273.7i) q^{93} +1.81594e6 q^{94} +1.35420e6i q^{95} +(-451430. + 714683. i) q^{96} +222586. q^{97} -1.04881e6i q^{98} +(-1.24775e6 + 593622. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 20 q^{3} - 1408 q^{4} + 95 q^{6} + 568 q^{7} - 548 q^{9}+O(q^{10}) $ 44 * q + 20 * q^3 - 1408 * q^4 + 95 * q^6 + 568 * q^7 - 548 * q^9	$ 44 q + 20 q^{3} - 1408 q^{4} + 95 q^{6} + 568 q^{7} - 548 q^{9} + 1752 q^{10} + 4075 q^{12} + 808 q^{13} + 7696 q^{15} + 36776 q^{16} + 12149 q^{18} + 28936 q^{19} - 6416 q^{21} - 7764 q^{22} - 11792 q^{24} - 129172 q^{25} - 27172 q^{27} - 25988 q^{28} - 54658 q^{30} - 72248 q^{31} + 25968 q^{33} - 32100 q^{34} - 217125 q^{36} + 260968 q^{37} + 133440 q^{39} - 227880 q^{40} + 63332 q^{42} - 187304 q^{43} + 455472 q^{45} - 164849 q^{48} + 959652 q^{49} - 218832 q^{51} - 410102 q^{52} + 882504 q^{54} + 517392 q^{55} - 572600 q^{57} - 197334 q^{58} - 854196 q^{60} + 914248 q^{61} + 885136 q^{63} - 312634 q^{64} - 816874 q^{66} - 310856 q^{67} - 395040 q^{70} + 205764 q^{72} - 227912 q^{73} + 1167580 q^{75} - 1438412 q^{76} - 6065 q^{78} + 841384 q^{79} + 1019636 q^{81} - 291126 q^{82} - 2787738 q^{84} - 2823120 q^{85} - 2899120 q^{87} - 2657340 q^{88} + 1478966 q^{90} - 2848288 q^{91} - 1992952 q^{93} + 6985482 q^{94} + 1309665 q^{96} + 1079608 q^{97} + 3251880 q^{99}+O(q^{100}) $ 44 * q + 20 * q^3 - 1408 * q^4 + 95 * q^6 + 568 * q^7 - 548 * q^9 + 1752 * q^10 + 4075 * q^12 + 808 * q^13 + 7696 * q^15 + 36776 * q^16 + 12149 * q^18 + 28936 * q^19 - 6416 * q^21 - 7764 * q^22 - 11792 * q^24 - 129172 * q^25 - 27172 * q^27 - 25988 * q^28 - 54658 * q^30 - 72248 * q^31 + 25968 * q^33 - 32100 * q^34 - 217125 * q^36 + 260968 * q^37 + 133440 * q^39 - 227880 * q^40 + 63332 * q^42 - 187304 * q^43 + 455472 * q^45 - 164849 * q^48 + 959652 * q^49 - 218832 * q^51 - 410102 * q^52 + 882504 * q^54 + 517392 * q^55 - 572600 * q^57 - 197334 * q^58 - 854196 * q^60 + 914248 * q^61 + 885136 * q^63 - 312634 * q^64 - 816874 * q^66 - 310856 * q^67 - 395040 * q^70 + 205764 * q^72 - 227912 * q^73 + 1167580 * q^75 - 1438412 * q^76 - 6065 * q^78 + 841384 * q^79 + 1019636 * q^81 - 291126 * q^82 - 2787738 * q^84 - 2823120 * q^85 - 2899120 * q^87 - 2657340 * q^88 + 1478966 * q^90 - 2848288 * q^91 - 1992952 * q^93 + 6985482 * q^94 + 1309665 * q^96 + 1079608 * q^97 + 3251880 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/69\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$1$	$-1$

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 $

$2$		−	9.87745i		−	1.23468i	−0.786696	−	0.617340i	$-0.788210\pi$
$2$		−	9.87745i		−	1.23468i	0.786696	−	0.617340i	$-0.211790\pi$
$3$	22.8275	+	14.4190i	0.845462	+	0.534036i
$3$	22.8275	+	14.4190i	0.845462	+	0.534036i
$4$	−33.5640			−0.524437
$5$		−	220.404i		−	1.76323i	−0.471968	−	0.881616i	$-0.656456\pi$
$5$		−	220.404i		−	1.76323i	0.471968	−	0.881616i	$-0.343544\pi$
$6$	142.423	−	225.477i	0.659364	−	1.04388i
$7$	473.108			1.37932			0.689661	−	0.724132i	$-0.257759\pi$
$7$	473.108			1.37932			0.689661	+	0.724132i	$0.257759\pi$
$8$		−	300.630i		−	0.587168i
$9$	313.187	+	658.297i	0.429612	+	0.903014i
$10$	−2177.03			−2.17703
$11$			1895.42i			1.42406i	0.702149	+	0.712030i	$0.252224\pi$
$11$			1895.42i			1.42406i	−0.702149	+	0.712030i	$0.747776\pi$
$12$	−766.181	−	483.958i	−0.443392	−	0.280068i
$13$	1951.15			0.888097			0.444049	−	0.896003i	$-0.353542\pi$
$13$	1951.15			0.888097			0.444049	+	0.896003i	$0.353542\pi$
$14$		−	4673.10i		−	1.70302i
$15$	3178.00	−	5031.27i	0.941629	−	1.49075i
$16$	−5117.55			−1.24940
$17$		−	7391.51i		−	1.50448i	−0.658889	−	0.752240i	$-0.728973\pi$
$17$		−	7391.51i		−	1.50448i	0.658889	−	0.752240i	$-0.271027\pi$
$18$	6502.29	−	3093.49i	1.11493	−	0.530433i
$19$	−6144.18			−0.895783			−0.447892	−	0.894088i	$-0.647825\pi$
$19$	−6144.18			−0.895783			−0.447892	+	0.894088i	$0.647825\pi$
$20$			7397.63i			0.924704i
$21$	10799.8	+	6821.72i	1.16616	+	0.736608i
$22$	18722.0			1.75826
$23$		−	2536.99i		−	0.208514i
$23$		−	2536.99i		−	0.208514i
$24$	4334.78	−	6862.63i	0.313569	−	0.496429i
$25$	−32952.9			−2.10899
$26$		−	19272.4i		−	1.09652i
$27$	−2342.70	+	19543.1i	−0.119021	+	0.992892i
$28$	−15879.4			−0.723368
$29$		−	7966.70i		−	0.326651i	−0.986572	−	0.163326i	$-0.947778\pi$
$29$		−	7966.70i		−	0.326651i	0.986572	−	0.163326i	$-0.0522221\pi$
$30$	−49696.1	−	31390.5i	−1.84059	−	1.16261i
$31$	3070.52			0.103069			0.0515343	−	0.998671i	$-0.483589\pi$
$31$	3070.52			0.103069			0.0515343	+	0.998671i	$0.483589\pi$
$32$			31308.0i			0.955446i
$33$	−27330.1	+	43267.8i	−0.760499	+	1.20399i
$34$	−73009.3			−1.85755
$35$		−	104275.i		−	2.43207i
$36$	−10511.8	−	22095.1i	−0.225304	−	0.473574i
$37$	17124.3			0.338070			0.169035	−	0.985610i	$-0.445935\pi$
$37$	17124.3			0.338070			0.169035	+	0.985610i	$0.445935\pi$
$38$			60688.8i			1.10601i
$39$	44539.8	+	28133.6i	0.750852	+	0.474276i
$40$	−66260.1			−1.03531
$41$		−	22873.7i		−	0.331883i	−0.986136	−	0.165941i	$-0.946934\pi$
$41$		−	22873.7i		−	0.331883i	0.986136	−	0.165941i	$-0.0530663\pi$
$42$	67381.2	−	106675.i	0.909475	−	1.43984i
$43$	−3573.42			−0.0449447			−0.0224723	−	0.999747i	$-0.507154\pi$
$43$	−3573.42			−0.0449447			−0.0224723	+	0.999747i	$0.507154\pi$
$44$		−	63618.0i		−	0.746830i
$45$	145091.	−	69027.6i	1.59222	−	0.757505i
$46$	−25059.0			−0.257449
$47$			183847.i			1.77078i	0.464852	+	0.885388i	$0.346108\pi$
$47$			183847.i			1.77078i	−0.464852	+	0.885388i	$0.653892\pi$
$48$	−116821.	−	73789.8i	−1.05632	−	0.667226i
$49$	106182.			0.902530
$50$			325491.i			2.60393i
$51$	106578.	−	168730.i	0.803446	−	1.27198i
$52$	−65488.3			−0.465751
$53$			133018.i			0.893473i	0.894666	+	0.446737i	$0.147414\pi$
$53$			133018.i			0.893473i	−0.894666	+	0.446737i	$0.852586\pi$
$54$	193036.	+	23139.9i	1.22590	+	0.146953i
$55$	417759.			2.51095
$56$		−	142230.i		−	0.809895i
$57$	−140256.	−	88592.7i	−0.757351	−	0.478380i
$58$	−78690.7			−0.403310
$59$			153966.i			0.749668i	0.927092	+	0.374834i	$0.122300\pi$
$59$			153966.i			0.749668i	−0.927092	+	0.374834i	$0.877700\pi$
$60$	−106666.	+	168869.i	−0.493825	+	0.781802i
$61$	−232527.			−1.02443			−0.512216	−	0.858857i	$-0.671175\pi$
$61$	−232527.			−1.02443			−0.512216	+	0.858857i	$0.671175\pi$
$62$		−	30328.9i		−	0.127257i
$63$	148171.	+	311445.i	0.592573	+	1.24555i
$64$	−18279.9			−0.0697324
$65$		−	430041.i		−	1.56592i
$66$	427375.	+	269951.i	1.48654	+	0.938974i
$67$	475022.			1.57939			0.789695	−	0.613499i	$-0.210239\pi$
$67$	475022.			1.57939			0.789695	+	0.613499i	$0.210239\pi$
$68$			248089.i			0.789005i
$69$	36580.8	−	57913.2i	0.111354	−	0.176291i
$70$	−1.02997e6			−3.00282
$71$		−	56456.9i		−	0.157740i	−0.996885	−	0.0788700i	$-0.974869\pi$
$71$		−	56456.9i		−	0.157740i	0.996885	−	0.0788700i	$-0.0251312\pi$
$72$	197904.	−	94153.4i	0.530221	−	0.252254i
$73$	170962.			0.439472			0.219736	−	0.975559i	$-0.429480\pi$
$73$	170962.			0.439472			0.219736	+	0.975559i	$0.429480\pi$
$74$		−	169144.i		−	0.417409i
$75$	−752232.	−	475147.i	−1.78307	−	1.12627i
$76$	206223.			0.469782
$77$			896740.i			1.96424i
$78$	277888.	−	439940.i	0.585579	−	0.927063i
$79$	290536.			0.589276			0.294638	−	0.955609i	$-0.404801\pi$
$79$	290536.			0.589276			0.294638	+	0.955609i	$0.404801\pi$
$80$			1.12793e6i			2.20299i
$81$	−335269.	+	412340.i	−0.630868	+	0.775890i
$82$	−225934.			−0.409770
$83$		−	121214.i		−	0.211992i	−0.994367	−	0.105996i	$-0.966197\pi$
$83$		−	121214.i		−	0.211992i	0.994367	−	0.105996i	$-0.0338030\pi$
$84$	−362486.	−	228964.i	−0.611580	−	0.386304i
$85$	−1.62912e6			−2.65275
$86$			35296.2i			0.0554923i
$87$	114872.	−	181860.i	0.174443	−	0.276171i
$88$	569822.			0.836164
$89$		−	123578.i		−	0.175296i	−0.996152	−	0.0876481i	$-0.972065\pi$
$89$		−	123578.i		−	0.175296i	0.996152	−	0.0876481i	$-0.0279351\pi$
$90$	−681817.	−	1.43313e6i	−0.935277	−	1.96589i
$91$	923104.			1.22497
$92$			85151.6i			0.109353i
$93$	70092.2	+	44273.7i	0.0871406	+	0.0550424i
$94$	1.81594e6			2.18634
$95$			1.35420e6i			1.57947i
$96$	−451430.	+	714683.i	−0.510242	+	0.807793i
$97$	222586.			0.243883			0.121942	−	0.992537i	$-0.461088\pi$
$97$	222586.			0.243883			0.121942	+	0.992537i	$0.461088\pi$
$98$		−	1.04881e6i		−	1.11434i
$99$	−1.24775e6	+	593622.i	−1.28595	+	0.611793i
$100$	1.10603e6			1.10603
$101$			1.14535e6i			1.11166i	0.831295	+	0.555831i	$0.187600\pi$
$101$			1.14535e6i			1.11166i	−0.831295	+	0.555831i	$0.812400\pi$
$102$	−1.66662e6	−	1.05272e6i	−1.57049	−	0.992000i
$103$	1.68535e6			1.54234			0.771168	−	0.636632i	$-0.219673\pi$
$103$	1.68535e6			1.54234			0.771168	+	0.636632i	$0.219673\pi$
$104$		−	586574.i		−	0.521463i
$105$	1.50353e6	−	2.38033e6i	1.29881	−	2.05622i
$106$	1.31387e6			1.10315
$107$			425048.i			0.346966i	0.984837	+	0.173483i	$0.0555022\pi$
$107$			425048.i			0.346966i	−0.984837	+	0.173483i	$0.944498\pi$
$108$	78630.3	−	655944.i	0.0624193	−	0.520709i
$109$	−1.84320e6			−1.42329			−0.711643	−	0.702542i	$-0.752048\pi$
$109$	−1.84320e6			−1.42329			−0.711643	+	0.702542i	$0.752048\pi$
$110$		−	4.12639e6i		−	3.10022i
$111$	390904.	+	246914.i	0.285825	+	0.180542i
$112$	−2.42115e6			−1.72333
$113$		−	1.57428e6i		−	1.09105i	−0.838094	−	0.545526i	$-0.816330\pi$
$113$		−	1.57428e6i		−	1.09105i	0.838094	−	0.545526i	$-0.183670\pi$
$114$	−875070.	+	1.38537e6i	−0.590647	+	0.935086i
$115$	−559164.			−0.367659
$116$			267394.i			0.171308i
$117$	611074.	+	1.28444e6i	0.381537	+	0.801964i
$118$	1.52079e6			0.925601
$119$		−	3.49698e6i		−	2.07516i
$120$	−1.51255e6	−	955402.i	−0.875319	−	0.552895i
$121$	−1.82107e6			−1.02795
$122$			2.29677e6i			1.26485i
$123$	329815.	−	522149.i	0.177237	−	0.280594i
$124$	−103059.			−0.0540530
$125$			3.81914e6i			1.95540i
$126$	3.07628e6	−	1.46355e6i	1.53785	−	0.731639i
$127$	1.32181e6			0.645292			0.322646	−	0.946520i	$-0.395428\pi$
$127$	1.32181e6			0.645292			0.322646	+	0.946520i	$0.395428\pi$
$128$			2.18427e6i			1.04154i
$129$	−81572.1	−	51525.0i	−0.0379990	−	0.0240021i
$130$	−4.24771e6			−1.93341
$131$			1.46462e6i			0.651494i	0.945457	+	0.325747i	$0.105616\pi$
$131$			1.46462e6i			0.651494i	−0.945457	+	0.325747i	$0.894384\pi$
$132$	917306.	−	1.45224e6i	0.398834	−	0.631417i
$133$	−2.90686e6			−1.23557
$134$		−	4.69201e6i		−	1.95004i
$135$	4.30737e6	+	516340.i	1.75070	+	0.209862i
$136$	−2.22211e6			−0.883383
$137$			3.52509e6i			1.37091i	0.728116	+	0.685454i	$0.240396\pi$
$137$			3.52509e6i			1.37091i	−0.728116	+	0.685454i	$0.759604\pi$
$138$	−572034.	−	361325.i	−0.217663	−	0.137487i
$139$	3.65644e6			1.36149			0.680744	−	0.732522i	$-0.261657\pi$
$139$	3.65644e6			1.36149			0.680744	+	0.732522i	$0.261657\pi$
$140$			3.49988e6i			1.27547i
$141$	−2.65089e6	+	4.19677e6i	−0.945658	+	1.49712i
$142$	−557650.			−0.194759
$143$			3.69826e6i			1.26470i
$144$	−1.60275e6	−	3.36887e6i	−0.536758	−	1.12823i
$145$	−1.75589e6			−0.575962
$146$		−	1.68867e6i		−	0.542608i
$147$	2.42386e6	+	1.53103e6i	0.763055	+	0.481983i
$148$	−574759.			−0.177297
$149$		−	3.84703e6i		−	1.16296i	−0.813559	−	0.581482i	$-0.802473\pi$
$149$		−	3.84703e6i		−	1.16296i	0.813559	−	0.581482i	$-0.197527\pi$
$150$	−4.69324e6	+	7.43013e6i	−1.39059	+	2.20152i
$151$	−5.48321e6			−1.59259			−0.796295	−	0.604908i	$-0.793210\pi$
$151$	−5.48321e6			−1.59259			−0.796295	+	0.604908i	$0.793210\pi$
$152$			1.84713e6i			0.525976i
$153$	4.86581e6	−	2.31492e6i	1.35857	−	0.646342i
$154$	8.85750e6			2.42521
$155$		−	676755.i		−	0.181734i
$156$	−1.49493e6	−	944274.i	−0.393775	−	0.248728i
$157$	5.32717e6			1.37657			0.688284	−	0.725442i	$-0.258364\pi$
$157$	5.32717e6			1.37657			0.688284	+	0.725442i	$0.258364\pi$
$158$		−	2.86975e6i		−	0.727568i
$159$	−1.91798e6	+	3.03646e6i	−0.477147	+	0.755397i
$160$	6.90042e6			1.68467
$161$		−	1.20027e6i		−	0.287609i
$162$	4.07287e6	+	3.31160e6i	0.957977	+	0.778920i
$163$	−477795.			−0.110326			−0.0551631	−	0.998477i	$-0.517568\pi$
$163$	−477795.			−0.110326			−0.0551631	+	0.998477i	$0.517568\pi$
$164$			767733.i			0.174052i
$165$	9.53639e6	+	6.02366e6i	2.12291	+	1.34094i
$166$	−1.19729e6			−0.261742
$167$		−	5.54517e6i		−	1.19060i	−0.803504	−	0.595299i	$-0.797034\pi$
$167$		−	5.54517e6i		−	1.19060i	0.803504	−	0.595299i	$-0.202966\pi$
$168$	2.05082e6	−	3.24676e6i	0.432513	−	0.684735i
$169$	−1.01983e6			−0.211284
$170$			1.60915e7i			3.27530i
$171$	−1.92428e6	−	4.04469e6i	−0.384839	−	0.808905i
$172$	119938.			0.0235707
$173$		−	3.93887e6i		−	0.760734i	−0.924836	−	0.380367i	$-0.875798\pi$
$173$		−	3.93887e6i		−	0.760734i	0.924836	−	0.380367i	$-0.124202\pi$
$174$	−1.79631e6	−	1.13464e6i	−0.340983	−	0.215382i
$175$	−1.55903e7			−2.90897
$176$		−	9.69994e6i		−	1.77923i
$177$	−2.22003e6	+	3.51466e6i	−0.400350	+	0.633816i
$178$	−1.22064e6			−0.216435
$179$			2.72312e6i			0.474797i	0.971412	+	0.237398i	$0.0762947\pi$
$179$			2.72312e6i			0.474797i	−0.971412	+	0.237398i	$0.923705\pi$
$180$	−4.86984e6	+	2.31684e6i	−0.835021	+	0.397264i
$181$	−7.40365e6			−1.24856			−0.624281	−	0.781200i	$-0.714608\pi$
$181$	−7.40365e6			−1.24856			−0.624281	+	0.781200i	$0.714608\pi$
$182$		−	9.11791e6i		−	1.51245i
$183$	−5.30799e6	−	3.35279e6i	−0.866118	−	0.547083i
$184$	−762697.			−0.122433
$185$		−	3.77426e6i		−	0.596096i
$186$	437311.	−	692332.i	0.0679598	−	0.107591i
$187$	1.40101e7			2.14247
$188$		−	6.17065e6i		−	0.928661i
$189$	−1.10835e6	+	9.24598e6i	−0.164169	+	1.36952i
$190$	1.33761e7			1.95015
$191$			8.24560e6i			1.18337i	0.806168	+	0.591687i	$0.201538\pi$
$191$			8.24560e6i			1.18337i	−0.806168	+	0.591687i	$0.798462\pi$
$192$	−417285.	−	263578.i	−0.0589561	−	0.0372396i
$193$	−7911.55			−0.00110050			−0.000550250	−	1.00000i	$-0.500175\pi$
$193$	−7911.55			−0.00110050			−0.000550250		1.00000i	$0.500175\pi$
$194$		−	2.19858e6i		−	0.301118i
$195$	6.20075e6	−	9.81675e6i	0.836258	−	1.32393i
$196$	−3.56388e6			−0.473320
$197$		−	5.56905e6i		−	0.728421i	−0.931317	−	0.364210i	$-0.881339\pi$
$197$		−	5.56905e6i		−	0.728421i	0.931317	−	0.364210i	$-0.118661\pi$
$198$	5.86347e6	+	1.23246e7i	0.755369	+	1.58773i
$199$	8.28350e6			1.05113			0.525563	−	0.850755i	$-0.323855\pi$
$199$	8.28350e6			1.05113			0.525563	+	0.850755i	$0.323855\pi$
$200$			9.90664e6i			1.23833i
$201$	1.08436e7	+	6.84933e6i	1.33531	+	0.843451i
$202$	1.13131e7			1.37255
$203$		−	3.76911e6i		−	0.450557i
$204$	−3.57718e6	+	5.66323e6i	−0.421357	+	0.667074i
$205$	−5.04146e6			−0.585187
$206$		−	1.66470e7i		−	1.90429i
$207$	1.67010e6	−	794553.i	0.188291	−	0.0895802i
$208$	−9.98511e6			−1.10959
$209$		−	1.16458e7i		−	1.27565i
$210$	−2.35116e7	−	1.48511e7i	−2.53877	−	1.60362i
$211$	−1.47798e7			−1.57334			−0.786669	−	0.617375i	$-0.788196\pi$
$211$	−1.47798e7			−1.57334			−0.786669	+	0.617375i	$0.788196\pi$
$212$		−	4.46460e6i		−	0.468570i
$213$	814050.	−	1.28877e6i	0.0842388	−	0.133363i
$214$	4.19839e6			0.428392
$215$			787595.i			0.0792479i
$216$	5.87524e6	+	704286.i	0.582995	+	0.0698856i
$217$	1.45269e6			0.142165
$218$			1.82061e7i			1.75730i
$219$	3.90264e6	+	2.46510e6i	0.371557	+	0.234694i
$220$	−1.40217e7			−1.31684
$221$		−	1.44219e7i		−	1.33612i
$222$	2.43888e6	−	3.86113e6i	0.222911	−	0.352903i
$223$	−1.81123e7			−1.63327			−0.816636	−	0.577153i	$-0.804163\pi$
$223$	−1.81123e7			−1.63327			−0.816636	+	0.577153i	$0.804163\pi$
$224$			1.48121e7i			1.31787i
$225$	−1.03204e7	−	2.16928e7i	−0.906045	−	1.90444i
$226$	−1.55498e7			−1.34710
$227$			8.39022e6i			0.717292i	0.933474	+	0.358646i	$0.116761\pi$
$227$			8.39022e6i			0.717292i	−0.933474	+	0.358646i	$0.883239\pi$
$228$	4.70755e6	+	2.97352e6i	0.397183	+	0.250880i
$229$	4.79089e6			0.398942			0.199471	−	0.979904i	$-0.436078\pi$
$229$	4.79089e6			0.398942			0.199471	+	0.979904i	$0.436078\pi$
$230$			5.52311e6i			0.453942i
$231$	−1.29301e7	+	2.04703e7i	−1.04897	+	1.66069i
$232$	−2.39503e6			−0.191799
$233$		−	1.45637e7i		−	1.15134i	−0.817681	−	0.575671i	$-0.804741\pi$
$233$		−	1.45637e7i		−	1.15134i	0.817681	−	0.575671i	$-0.195259\pi$
$234$	1.26869e7	−	6.03585e6i	0.990170	−	0.471076i
$235$	4.05207e7			3.12229
$236$		−	5.16772e6i		−	0.393154i
$237$	6.63220e6	+	4.18923e6i	0.498210	+	0.314694i
$238$	−3.45412e7			−2.56217
$239$			1.28301e6i			0.0939803i	0.998895	+	0.0469902i	$0.0149629\pi$
$239$			1.28301e6i			0.0939803i	−0.998895	+	0.0469902i	$0.985037\pi$
$240$	−1.62636e7	+	2.57478e7i	−1.17647	+	1.86254i
$241$	2.38638e6			0.170486			0.0852428	−	0.996360i	$-0.472833\pi$
$241$	2.38638e6			0.170486			0.0852428	+	0.996360i	$0.472833\pi$
$242$			1.79876e7i			1.26919i
$243$	−1.35989e7	+	4.57845e6i	−0.947728	+	0.319080i
$244$	7.80452e6			0.537250
$245$		−	2.34029e7i		−	1.59137i
$246$	−5.15750e6	−	3.25773e6i	−0.346445	−	0.218832i
$247$	−1.19882e7			−0.795543
$248$		−	923091.i		−	0.0605187i
$249$	1.74778e6	−	2.76701e6i	0.113211	−	0.179231i
$250$	3.77234e7			2.41429
$251$		−	1.30789e7i		−	0.827082i	−0.910485	−	0.413541i	$-0.864292\pi$
$251$		−	1.30789e7i		−	0.827082i	0.910485	−	0.413541i	$-0.135708\pi$
$252$	−4.97321e6	−	1.04533e7i	−0.310767	−	0.653211i
$253$	4.80868e6			0.296937
$254$		−	1.30561e7i		−	0.796730i
$255$	−3.71887e7	−	2.34902e7i	−2.24280	−	1.41666i
$256$	2.04051e7			1.21624
$257$			5.17721e6i			0.304997i	0.988304	+	0.152499i	$0.0487320\pi$
$257$			5.17721e6i			0.304997i	−0.988304	+	0.152499i	$0.951268\pi$
$258$	−508935.	+	805724.i	−0.0296349	+	0.0469167i
$259$	8.10162e6			0.466308
$260$			1.44339e7i			0.821227i
$261$	5.24445e6	−	2.49507e6i	0.294971	−	0.140333i
$262$	1.44667e7			0.804388
$263$			1.92205e7i			1.05657i	0.849068	+	0.528283i	$0.177164\pi$
$263$			1.92205e7i			1.05657i	−0.849068	+	0.528283i	$0.822836\pi$
$264$	1.30076e7	+	8.21624e6i	0.706944	+	0.446541i
$265$	2.93176e7			1.57540
$266$			2.87123e7i			1.52554i
$267$	1.78187e6	−	2.82098e6i	0.0936144	−	0.148206i
$268$	−1.59436e7			−0.828291
$269$		−	291998.i		−	0.0150011i	−0.999972	−	0.00750055i	$-0.997612\pi$
$269$		−	291998.i		−	0.0150011i	0.999972	−	0.00750055i	$-0.00238752\pi$
$270$	5.10012e6	−	4.25459e7i	0.259113	−	2.16155i
$271$	−4.66263e6			−0.234273			−0.117137	−	0.993116i	$-0.537372\pi$
$271$	−4.66263e6			−0.234273			−0.117137	+	0.993116i	$0.537372\pi$
$272$			3.78265e7i			1.87970i
$273$	2.10721e7	+	1.33102e7i	1.03567	+	0.654179i
$274$	3.48189e7			1.69263
$275$		−	6.24598e7i		−	3.00332i
$276$	−1.22780e6	+	1.94380e6i	−0.0583983	+	0.0924535i
$277$	2.89114e6			0.136029			0.0680143	−	0.997684i	$-0.478334\pi$
$277$	2.89114e6			0.136029			0.0680143	+	0.997684i	$0.478334\pi$
$278$		−	3.61163e7i		−	1.68100i
$279$	961646.	+	2.02131e6i	0.0442795	+	0.0930724i
$280$	−3.13482e7			−1.42803
$281$			1.35346e7i			0.609995i	0.952353	+	0.304998i	$0.0986557\pi$
$281$			1.35346e7i			0.609995i	−0.952353	+	0.304998i	$0.901344\pi$
$282$	4.14534e7	+	2.61840e7i	1.84847	+	1.16759i
$283$	−1.14649e7			−0.505836			−0.252918	−	0.967488i	$-0.581390\pi$
$283$	−1.14649e7			−0.505836			−0.252918	+	0.967488i	$0.581390\pi$
$284$			1.89492e6i			0.0827247i
$285$	−1.95262e7	+	3.09130e7i	−0.843495	+	1.33538i
$286$	3.65293e7			1.56151
$287$		−	1.08217e7i		−	0.457774i
$288$	−2.06100e7	+	9.80527e6i	−0.862780	+	0.410470i
$289$	−3.04969e7			−1.26346
$290$			1.73437e7i			0.711129i
$291$	5.08107e6	+	3.20946e6i	0.206194	+	0.130242i
$292$	−5.73817e6			−0.230476
$293$			4.89612e7i			1.94648i	0.229801	+	0.973238i	$0.426192\pi$
$293$			4.89612e7i			1.94648i	−0.229801	+	0.973238i	$0.573808\pi$
$294$	1.51227e7	−	2.39416e7i	0.595096	−	0.942129i
$295$	3.39347e7			1.32184
$296$		−	5.14807e6i		−	0.198504i
$297$	−3.70425e7	−	4.44041e6i	−1.41394	−	0.169494i
$298$	−3.79988e7			−1.43589
$299$		−	4.95006e6i		−	0.185181i
$300$	2.52479e7	+	1.59478e7i	0.935107	+	0.590660i
$301$	−1.69061e6			−0.0619932
$302$			5.41601e7i			1.96634i
$303$	−1.65147e7	+	2.61454e7i	−0.593667	+	0.939868i
$304$	3.14432e7			1.11919
$305$			5.12498e7i			1.80631i
$306$	−2.28655e7	−	4.80618e7i	−0.798027	−	1.67740i
$307$	−2.71405e7			−0.938000			−0.469000	−	0.883198i	$-0.655386\pi$
$307$	−2.71405e7			−0.938000			−0.469000	+	0.883198i	$0.655386\pi$
$308$		−	3.00982e7i		−	1.03012i
$309$	3.84723e7	+	2.43010e7i	1.30399	+	0.823662i
$310$	−6.68461e6			−0.224383
$311$			1.36475e7i			0.453704i	0.973929	+	0.226852i	$0.0728433\pi$
$311$			1.36475e7i			0.453704i	−0.973929	+	0.226852i	$0.927157\pi$
$312$	8.45780e6	−	1.33900e7i	0.278480	−	0.440877i
$313$	−4.15500e6			−0.135499			−0.0677497	−	0.997702i	$-0.521582\pi$
$313$	−4.15500e6			−0.135499			−0.0677497	+	0.997702i	$0.521582\pi$
$314$		−	5.26188e7i		−	1.69962i
$315$	6.86438e7	−	3.26575e7i	2.19619	−	1.04484i
$316$	−9.75154e6			−0.309038
$317$			1.91156e7i			0.600081i	0.953926	+	0.300040i	$0.0970002\pi$
$317$			1.91156e7i			0.600081i	−0.953926	+	0.300040i	$0.903000\pi$
$318$	2.99924e7	+	1.89447e7i	0.932675	+	0.589124i
$319$	1.51003e7			0.465171
$320$			4.02897e6i			0.122954i
$321$	−6.12876e6	+	9.70278e6i	−0.185292	+	0.293347i
$322$	−1.18556e7			−0.355105
$323$			4.54148e7i			1.34769i
$324$	1.12530e7	−	1.38398e7i	0.330850	−	0.406906i
$325$	−6.42960e7			−1.87298
$326$			4.71939e6i			0.136218i
$327$	−4.20755e7	−	2.65770e7i	−1.20333	−	0.760085i
$328$	−6.87653e6			−0.194871
$329$			8.69796e7i			2.44247i
$330$	5.94983e7	−	9.41952e7i	1.65563	−	2.62112i
$331$	−3.79094e7			−1.04535			−0.522677	−	0.852531i	$-0.675067\pi$
$331$	−3.79094e7			−1.04535			−0.522677	+	0.852531i	$0.675067\pi$
$332$			4.06842e6i			0.111176i
$333$	5.36310e6	+	1.12729e7i	0.145239	+	0.305282i
$334$	−5.47721e7			−1.47001
$335$		−	1.04697e8i		−	2.78483i
$336$	−5.52688e7	−	3.49105e7i	−1.45701	−	0.920319i
$337$	−4.89785e7			−1.27972			−0.639862	−	0.768490i	$-0.721008\pi$
$337$	−4.89785e7			−1.27972			−0.639862	+	0.768490i	$0.721008\pi$
$338$			1.00733e7i			0.260868i
$339$	2.26994e7	−	3.59368e7i	0.582661	−	0.922444i
$340$	5.46797e7			1.39120
$341$			5.81994e6i			0.146776i
$342$	−3.99513e7	+	1.90069e7i	−0.998739	+	0.475153i
$343$	−5.42522e6			−0.134442
$344$			1.07428e6i			0.0263901i
$345$	−1.27643e7	−	8.06256e6i	−0.310842	−	0.196343i
$346$	−3.89060e7			−0.939264
$347$		−	8.08637e7i		−	1.93538i	−0.252151	−	0.967688i	$-0.581138\pi$
$347$		−	8.08637e7i		−	1.93538i	0.252151	−	0.967688i	$-0.418862\pi$
$348$	−3.85555e6	+	6.10393e6i	−0.0914846	+	0.144834i
$349$	3.12469e7			0.735074			0.367537	−	0.930009i	$-0.380201\pi$
$349$	3.12469e7			0.735074			0.367537	+	0.930009i	$0.380201\pi$
$350$			1.53992e8i			3.59165i
$351$	−4.57095e6	+	3.81315e7i	−0.105703	+	0.881784i
$352$	−5.93420e7			−1.36061
$353$		−	3.73923e7i		−	0.850076i	−0.905176	−	0.425038i	$-0.860261\pi$
$353$		−	3.73923e7i		−	0.850076i	0.905176	−	0.425038i	$-0.139739\pi$
$354$	3.47158e7	+	2.19283e7i	0.782561	+	0.494304i
$355$	−1.24433e7			−0.278132
$356$			4.14778e6i			0.0919318i
$357$	5.04228e7	−	7.98272e7i	1.10821	−	1.75447i
$358$	2.68975e7			0.586223
$359$		−	6.00644e7i		−	1.29818i	−0.760713	−	0.649089i	$-0.775150\pi$
$359$		−	6.00644e7i		−	1.29818i	0.760713	−	0.649089i	$-0.224850\pi$
$360$	−2.07518e7	−	4.36188e7i	−0.444783	−	0.934903i
$361$	−9.29496e6			−0.197572
$362$			7.31291e7i			1.54157i
$363$	−4.15705e7	−	2.62580e7i	−0.869092	−	0.548962i
$364$	−3.09830e7			−0.642421
$365$		−	3.76808e7i		−	0.774892i
$366$	−3.31170e7	+	5.24294e7i	−0.675473	+	1.06938i
$367$	4.28602e7			0.867074			0.433537	−	0.901136i	$-0.357265\pi$
$367$	4.28602e7			0.867074			0.433537	+	0.901136i	$0.357265\pi$
$368$			1.29832e7i			0.260518i
$369$	1.50577e7	−	7.16374e6i	0.299695	−	0.142581i
$370$	−3.72800e7			−0.735988
$371$			6.29316e7i			1.23239i
$372$	−2.35257e6	−	1.48600e6i	−0.0456998	−	0.0288663i
$373$	9.68236e6			0.186576			0.0932878	−	0.995639i	$-0.470262\pi$
$373$	9.68236e6			0.186576			0.0932878	+	0.995639i	$0.470262\pi$
$374$		−	1.38384e8i		−	2.64527i
$375$	−5.50680e7	+	8.71813e7i	−1.04425	+	1.65322i
$376$	5.52701e7			1.03974
$377$		−	1.55442e7i		−	0.290098i
$378$	9.13267e7	+	1.09477e7i	1.69092	+	0.202696i
$379$	5.16732e7			0.949179			0.474589	−	0.880207i	$-0.342597\pi$
$379$	5.16732e7			0.949179			0.474589	+	0.880207i	$0.342597\pi$
$380$		−	4.54524e7i		−	0.828335i
$381$	3.01735e7	+	1.90591e7i	0.545570	+	0.344609i
$382$	8.14455e7			1.46109
$383$		−	7.52238e7i		−	1.33893i	−0.742842	−	0.669467i	$-0.766523\pi$
$383$		−	7.52238e7i		−	1.33893i	0.742842	−	0.669467i	$-0.233477\pi$
$384$	−3.14950e7	+	4.98614e7i	−0.556221	+	0.880585i
$385$	1.97645e8			3.46341
$386$			78145.9i			0.00135877i
$387$	−1.11915e6	−	2.35237e6i	−0.0193088	−	0.0405857i
$388$	−7.47086e6			−0.127902
$389$			3.15035e7i			0.535192i	0.963531	+	0.267596i	$0.0862292\pi$
$389$			3.15035e7i			0.535192i	−0.963531	+	0.267596i	$0.913771\pi$
$390$	−9.69644e7	−	6.12476e7i	−1.63463	−	1.03251i
$391$	−1.87522e7			−0.313706
$392$		−	3.19215e7i		−	0.529937i
$393$	−2.11183e7	+	3.34335e7i	−0.347921	+	0.550814i
$394$	−5.50080e7			−0.899367
$395$		−	6.40353e7i		−	1.03903i
$396$	4.18795e7	−	1.99243e7i	0.674398	−	0.320847i
$397$	8.80638e6			0.140743			0.0703714	−	0.997521i	$-0.477582\pi$
$397$	8.80638e6			0.140743			0.0703714	+	0.997521i	$0.477582\pi$
$398$		−	8.18198e7i		−	1.29780i
$399$	−6.63562e7	−	4.19139e7i	−1.04463	−	0.659841i
$400$	1.68638e8			2.63497
$401$		−	8.58838e7i		−	1.33192i	−0.745987	−	0.665960i	$-0.768022\pi$
$401$		−	8.58838e7i		−	1.33192i	0.745987	−	0.665960i	$-0.231978\pi$
$402$	6.76539e7	−	1.07107e8i	1.04139	−	1.64869i
$403$	5.99104e6			0.0915350
$404$		−	3.84424e7i		−	0.582997i
$405$	9.08814e7	+	7.38946e7i	1.36807	+	1.11237i
$406$	−3.72291e7			−0.556295
$407$			3.24578e7i			0.481433i
$408$	−5.07252e7	−	3.20406e7i	−0.746867	−	0.471758i
$409$	−1.25331e8			−1.83184			−0.915920	−	0.401360i	$-0.868538\pi$
$409$	−1.25331e8			−1.83184			−0.915920	+	0.401360i	$0.868538\pi$
$410$			4.97967e7i			0.722519i
$411$	−5.08281e7	+	8.04689e7i	−0.732114	+	1.15905i
$412$	−5.65671e7			−0.808858
$413$			7.28425e7i			1.03403i
$414$	−7.84816e6	−	1.64963e7i	−0.110603	−	0.232480i
$415$	−2.67161e7			−0.373790
$416$			6.10867e7i			0.848528i
$417$	8.34672e7	+	5.27220e7i	1.15109	+	0.727083i
$418$	−1.15031e8			−1.57502
$419$			1.23815e7i			0.168319i	0.996452	+	0.0841593i	$0.0268205\pi$
$419$			1.23815e7i			0.168319i	−0.996452	+	0.0841593i	$0.973180\pi$
$420$	−5.04646e7	+	7.98933e7i	−0.681144	+	1.07836i
$421$	1.23587e8			1.65625			0.828124	−	0.560545i	$-0.189408\pi$
$421$	1.23587e8			1.65625			0.828124	+	0.560545i	$0.189408\pi$
$422$			1.45987e8i			1.94257i
$423$	−1.21026e8	+	5.75786e7i	−1.59904	+	0.760746i
$424$	3.99891e7			0.524619
$425$			2.43572e8i			3.17293i
$426$	−1.27297e7	−	8.04074e6i	−0.164661	−	0.104008i
$427$	−1.10010e8			−1.41302
$428$		−	1.42663e7i		−	0.181962i
$429$	−5.33250e7	+	8.44219e7i	−0.675397	+	1.06926i
$430$	7.77943e6			0.0978459
$431$			1.54799e7i			0.193346i	0.995316	+	0.0966732i	$0.0308202\pi$
$431$			1.54799e7i			0.193346i	−0.995316	+	0.0966732i	$0.969180\pi$
$432$	1.19889e7	−	1.00013e8i	0.148706	−	1.24052i
$433$	5.31238e7			0.654374			0.327187	−	0.944960i	$-0.393899\pi$
$433$	5.31238e7			0.654374			0.327187	+	0.944960i	$0.393899\pi$
$434$		−	1.43488e7i		−	0.175528i
$435$	−4.00826e7	−	2.53181e7i	−0.486954	−	0.307584i
$436$	6.18650e7			0.746424
$437$			1.55877e7i			0.186784i
$438$	2.43489e7	−	3.85481e7i	0.289772	−	0.458755i
$439$	−8.72723e6			−0.103153			−0.0515766	−	0.998669i	$-0.516425\pi$
$439$	−8.72723e6			−0.103153			−0.0515766	+	0.998669i	$0.516425\pi$
$440$		−	1.25591e8i		−	1.47435i
$441$	3.32547e7	+	6.98992e7i	0.387738	+	0.814997i
$442$	−1.42452e8			−1.64969
$443$		−	1.77158e7i		−	0.203774i	−0.994796	−	0.101887i	$-0.967512\pi$
$443$		−	1.77158e7i		−	0.203774i	0.994796	−	0.101887i	$-0.0324881\pi$
$444$	−1.31203e7	−	8.28742e6i	−0.149897	−	0.0946827i
$445$	−2.72372e7			−0.309088
$446$			1.78903e8i			2.01657i
$447$	5.54701e7	−	8.78179e7i	0.621064	−	0.983242i
$448$	−8.64838e6			−0.0961835
$449$		−	1.08410e8i		−	1.19765i	−0.800881	−	0.598824i	$-0.795635\pi$
$449$		−	1.08410e8i		−	1.19765i	0.800881	−	0.598824i	$-0.204365\pi$
$450$	−2.14270e8	+	1.01939e8i	−2.35138	+	1.11868i
$451$	4.33554e7			0.472622
$452$			5.28390e7i			0.572189i
$453$	−1.25168e8	−	7.90622e7i	−1.34647	−	0.850500i
$454$	8.28740e7			0.885626
$455$		−	2.03456e8i		−	2.15991i
$456$	−2.66336e7	+	4.21652e7i	−0.280890	+	0.444692i
$457$	1.18728e8			1.24395			0.621977	−	0.783036i	$-0.286330\pi$
$457$	1.18728e8			1.24395			0.621977	+	0.783036i	$0.286330\pi$
$458$		−	4.73218e7i		−	0.492566i
$459$	1.44453e8	+	1.73161e7i	1.49379	+	0.179065i
$460$	1.87678e7			0.192814
$461$			1.39900e6i			0.0142795i	0.999975	+	0.00713977i	$0.00227268\pi$
$461$			1.39900e6i			0.0142795i	−0.999975	+	0.00713977i	$0.997727\pi$
$462$	2.02194e8	+	1.27716e8i	2.05042	+	1.29515i
$463$	−1.36009e8			−1.37032			−0.685162	−	0.728391i	$-0.740268\pi$
$463$	−1.36009e8			−1.37032			−0.685162	+	0.728391i	$0.740268\pi$
$464$			4.07700e7i			0.408119i
$465$	9.75810e6	−	1.54486e7i	0.0970524	−	0.153649i
$466$	−1.43852e8			−1.42154
$467$			1.23714e8i			1.21470i	0.794435	+	0.607349i	$0.207767\pi$
$467$			1.23714e8i			1.21470i	−0.794435	+	0.607349i	$0.792233\pi$
$468$	−2.05101e7	−	4.31108e7i	−0.200092	−	0.420580i
$469$	2.24737e8			2.17849
$470$		−	4.00241e8i		−	3.85503i
$471$	1.21606e8	+	7.68123e7i	1.16384	+	0.735136i
$472$	4.62869e7			0.440182
$473$		−	6.77314e6i		−	0.0640040i
$474$	4.13789e7	−	6.55092e7i	0.388547	−	0.615131i
$475$	2.02469e8			1.88919
$476$			1.17373e8i			1.08829i
$477$	−8.75651e7	+	4.16594e7i	−0.806818	+	0.383846i
$478$	1.26729e7			0.116036
$479$			1.22175e8i			1.11167i	0.831292	+	0.555836i	$0.187602\pi$
$479$			1.22175e8i			1.11167i	−0.831292	+	0.555836i	$0.812398\pi$
$480$	1.57519e8	+	9.94969e7i	1.42433	+	0.899675i
$481$	3.34120e7			0.300239
$482$		−	2.35713e7i		−	0.210495i
$483$	1.73067e7	−	2.73992e7i	0.153593	−	0.243162i
$484$	6.11225e7			0.539095
$485$		−	4.90588e7i		−	0.430023i
$486$	4.52234e7	+	1.34322e8i	0.393962	+	1.17014i
$487$	−2.03442e7			−0.176138			−0.0880691	−	0.996114i	$-0.528070\pi$
$487$	−2.03442e7			−0.176138			−0.0880691	+	0.996114i	$0.528070\pi$
$488$			6.99045e7i			0.601514i
$489$	−1.09068e7	−	6.88931e6i	−0.0932766	−	0.0589181i
$490$	−2.31161e8			−1.96483
$491$		−	9.82534e7i		−	0.830048i	−0.909811	−	0.415024i	$-0.863773\pi$
$491$		−	9.82534e7i		−	0.830048i	0.909811	−	0.415024i	$-0.136227\pi$
$492$	−1.10699e7	+	1.75254e7i	−0.0929499	+	0.147154i
$493$	−5.88860e7			−0.491441
$494$			1.18413e8i			0.982241i
$495$	1.30837e8	+	2.75010e8i	1.07873	+	2.26742i
$496$	−1.57135e7			−0.128774
$497$		−	2.67102e7i		−	0.217574i
$498$	−2.73310e7	−	1.72636e7i	−0.221293	−	0.139780i
$499$	−9.72751e7			−0.782889			−0.391445	−	0.920202i	$-0.628025\pi$
$499$	−9.72751e7			−0.782889			−0.391445	+	0.920202i	$0.628025\pi$
$500$		−	1.28186e8i		−	1.02548i
$501$	7.99556e7	−	1.26582e8i	0.635822	−	1.00661i
$502$	−1.29186e8			−1.02118
$503$			1.01295e7i			0.0795945i	0.999208	+	0.0397972i	$0.0126712\pi$
$503$			1.01295e7i			0.0795945i	−0.999208	+	0.0397972i	$0.987329\pi$
$504$	9.36299e7	−	4.45447e7i	0.731346	−	0.347940i
$505$	2.52439e8			1.96012
$506$		−	4.74975e7i		−	0.366623i
$507$	−2.32800e7	−	1.47048e7i	−0.178632	−	0.112833i
$508$	−4.43650e7			−0.338415
$509$			1.21214e8i			0.919178i	0.888132	+	0.459589i	$0.152003\pi$
$509$			1.21214e8i			0.919178i	−0.888132	+	0.459589i	$0.847997\pi$
$510$	−2.32023e8	+	3.67329e8i	−1.74913	+	2.76914i
$511$	8.08835e7			0.606174
$512$		−	6.17571e7i		−	0.460126i
$513$	1.43940e7	−	1.20076e8i	0.106617	−	0.889416i
$514$	5.11376e7			0.376574
$515$		−	3.71458e8i		−	2.71950i
$516$	2.73788e6	+	1.72938e6i	0.0199281	+	0.0125876i
$517$	−3.48469e8			−2.52169
$518$		−	8.00233e7i		−	0.575741i
$519$	5.67944e7	−	8.99144e7i	0.406259	−	0.643172i
$520$	−1.29283e8			−0.919459
$521$			9.71767e7i			0.687146i	0.939126	+	0.343573i	$0.111637\pi$
$521$			9.71767e7i			0.687146i	−0.939126	+	0.343573i	$0.888363\pi$
$522$	−2.46449e7	−	5.18018e7i	−0.173267	−	0.364195i
$523$	8.16054e7			0.570445			0.285223	−	0.958461i	$-0.407932\pi$
$523$	8.16054e7			0.570445			0.285223	+	0.958461i	$0.407932\pi$
$524$		−	4.91584e7i		−	0.341668i
$525$	−3.55886e8	−	2.24796e8i	−2.45942	−	1.55349i
$526$	1.89849e8			1.30452
$527$		−	2.26958e7i		−	0.155065i
$528$	1.39863e8	−	2.21425e8i	0.950170	−	1.50427i
$529$	−6.43634e6			−0.0434783
$530$		−	2.89583e8i		−	1.94512i
$531$	−1.01355e8	+	4.82202e7i	−0.676961	+	0.322066i
$532$	9.75657e7			0.647981
$533$		−	4.46300e7i		−	0.294744i
$534$	−2.78641e7	−	1.76003e7i	−0.182987	−	0.115584i
$535$	9.36823e7			0.611782
$536$		−	1.42806e8i		−	0.927368i
$537$	−3.92646e7	+	6.21620e7i	−0.253559	+	0.401423i
$538$	−2.88420e6			−0.0185216
$539$			2.01260e8i			1.28526i
$540$	−1.44573e8	−	1.73304e7i	−0.918131	−	0.110060i
$541$	−1.48851e8			−0.940067			−0.470034	−	0.882648i	$-0.655758\pi$
$541$	−1.48851e8			−0.940067			−0.470034	+	0.882648i	$0.655758\pi$
$542$			4.60548e7i			0.289253i
$543$	−1.69006e8	−	1.06753e8i	−1.05561	−	0.666776i
$544$	2.31414e8			1.43745
$545$			4.06248e8i			2.50958i
$546$	1.31471e8	−	2.08139e8i	0.807702	−	1.27872i
$547$	1.57545e8			0.962594			0.481297	−	0.876558i	$-0.340166\pi$
$547$	1.57545e8			0.962594			0.481297	+	0.876558i	$0.340166\pi$
$548$		−	1.18316e8i		−	0.718955i
$549$	−7.28243e7	−	1.53072e8i	−0.440108	−	0.925076i
$550$	−6.16943e8			−3.70815
$551$			4.89488e7i			0.292609i
$552$	−1.74105e7	−	1.09973e7i	−0.103513	−	0.0653836i
$553$	1.37455e8			0.812801
$554$		−	2.85571e7i		−	0.167952i
$555$	5.44209e7	−	8.61567e7i	0.318337	−	0.503977i
$556$	−1.22725e8			−0.714014
$557$		−	2.01341e8i		−	1.16511i	−0.812791	−	0.582556i	$-0.802053\pi$
$557$		−	2.01341e8i		−	1.16511i	0.812791	−	0.582556i	$-0.197947\pi$
$558$	1.99654e7	−	9.49861e6i	0.114915	−	0.0546711i
$559$	−6.97227e6			−0.0399152
$560$			5.33632e8i			3.03863i
$561$	3.19814e8	+	2.02011e8i	1.81138	+	1.14416i
$562$	1.33687e8			0.753150
$563$		−	1.86976e8i		−	1.04776i	−0.851793	−	0.523879i	$-0.824484\pi$
$563$		−	1.86976e8i		−	1.04776i	0.851793	−	0.523879i	$-0.175516\pi$
$564$	8.89744e7	−	1.40860e8i	0.495938	−	0.785148i
$565$	−3.46977e8			−1.92378
$566$			1.13244e8i			0.624547i
$567$	−1.58618e8	+	1.95081e8i	−0.870170	+	1.07020i
$568$	−1.69727e7			−0.0926200
$569$		−	2.76501e8i		−	1.50093i	−0.660910	−	0.750465i	$-0.729830\pi$
$569$		−	2.76501e8i		−	1.50093i	0.660910	−	0.750465i	$-0.270170\pi$
$570$	3.05341e8	+	1.92869e8i	1.64877	+	1.04145i
$571$	−2.19400e8			−1.17850			−0.589250	−	0.807951i	$-0.700577\pi$
$571$	−2.19400e8			−1.17850			−0.589250	+	0.807951i	$0.700577\pi$
$572$		−	1.24128e8i		−	0.663258i
$573$	−1.18893e8	+	1.88226e8i	−0.631964	+	1.00050i
$574$	−1.06891e8			−0.565204
$575$			8.36014e7i			0.439754i
$576$	−5.72504e6	−	1.20336e7i	−0.0299579	−	0.0629693i
$577$	7.62795e7			0.397082			0.198541	−	0.980093i	$-0.436380\pi$
$577$	7.62795e7			0.397082			0.198541	+	0.980093i	$0.436380\pi$
$578$			3.01231e8i			1.55997i
$579$	−180601.	−	114076.i	−0.000930430	−	0.000587706i
$580$	5.89347e7			0.302056
$581$		−	5.73473e7i		−	0.292405i
$582$	3.17012e7	−	5.01880e7i	0.160808	−	0.254584i
$583$	−2.52125e8			−1.27236
$584$		−	5.13964e7i		−	0.258044i
$585$	2.83095e8	−	1.34683e8i	1.41405	−	0.672738i
$586$	4.83611e8			2.40328
$587$		−	7.61077e7i		−	0.376283i	−0.982142	−	0.188141i	$-0.939754\pi$
$587$		−	7.61077e7i		−	0.376283i	0.982142	−	0.188141i	$-0.0602463\pi$
$588$	−8.13544e7	−	5.13875e7i	−0.400174	−	0.252770i
$589$	−1.88658e7			−0.0923272
$590$		−	3.35189e8i		−	1.63205i
$591$	8.02999e7	−	1.27127e8i	0.389003	−	0.615852i
$592$	−8.76344e7			−0.422386
$593$			9.58277e7i			0.459544i	0.973245	+	0.229772i	$0.0737980\pi$
$593$			9.58277e7i			0.459544i	−0.973245	+	0.229772i	$0.926202\pi$
$594$	−4.38599e7	+	3.65885e8i	−0.209271	+	1.74576i
$595$	−7.70748e8			−3.65899
$596$			1.29121e8i			0.609902i
$597$	1.89091e8	+	1.19439e8i	0.888686	+	0.561338i
$598$	−4.88939e7			−0.228640
$599$			1.47975e7i			0.0688508i	0.999407	+	0.0344254i	$0.0109601\pi$
$599$			1.47975e7i			0.0688508i	−0.999407	+	0.0344254i	$0.989040\pi$
$600$	−1.42844e8	+	2.26144e8i	−0.661313	+	1.04696i
$601$	−3.94368e8			−1.81668			−0.908339	−	0.418235i	$-0.862649\pi$
$601$	−3.94368e8			−1.81668			−0.908339	+	0.418235i	$0.862649\pi$
$602$			1.66989e7i			0.0765418i
$603$	1.48771e8	+	3.12706e8i	0.678525	+	1.42621i
$604$	1.84038e8			0.835213
$605$			4.01372e8i			1.81251i
$606$	2.58249e8	+	1.63123e8i	1.16044	+	0.732989i
$607$	−3.16693e8			−1.41603			−0.708014	−	0.706198i	$-0.750409\pi$
$607$	−3.16693e8			−1.41603			−0.708014	+	0.706198i	$0.750409\pi$
$608$		−	1.92362e8i		−	0.855872i
$609$	5.43466e7	−	8.60392e7i	0.240614	−	0.380929i
$610$	5.06217e8			2.23022
$611$			3.58714e8i			1.57262i
$612$	−1.63316e8	+	7.76981e7i	−0.712483	+	0.338966i
$613$	1.13717e8			0.493679			0.246839	−	0.969056i	$-0.420608\pi$
$613$	1.13717e8			0.493679			0.246839	+	0.969056i	$0.420608\pi$
$614$			2.68079e8i			1.15813i
$615$	−1.15084e8	−	7.26926e7i	−0.494753	−	0.312511i
$616$	2.69587e8			1.15334
$617$		−	2.88313e8i		−	1.22746i	−0.789515	−	0.613732i	$-0.789668\pi$
$617$		−	2.88313e8i		−	1.22746i	0.789515	−	0.613732i	$-0.210332\pi$
$618$	2.40032e8	−	3.80008e8i	1.01696	−	1.61001i
$619$	−2.79990e7			−0.118051			−0.0590256	−	0.998256i	$-0.518799\pi$
$619$	−2.79990e7			−0.118051			−0.0590256	+	0.998256i	$0.518799\pi$
$620$			2.27146e7i			0.0953080i
$621$	4.95807e7	+	5.94341e6i	0.207032	+	0.0248177i
$622$	1.34803e8			0.560179
$623$		−	5.84658e7i		−	0.241790i
$624$	−2.27935e8	−	1.43975e8i	−0.938117	−	0.592561i
$625$	3.26864e8			1.33884
$626$			4.10408e7i			0.167299i
$627$	1.67921e8	−	2.65845e8i	0.681243	−	1.07851i
$628$	−1.78801e8			−0.721923
$629$		−	1.26574e8i		−	0.508620i
$630$	−3.22573e8	−	6.78025e8i	−1.29005	−	2.71159i
$631$	2.98586e8			1.18845			0.594225	−	0.804299i	$-0.297459\pi$
$631$	2.98586e8			1.18845			0.594225	+	0.804299i	$0.297459\pi$
$632$		−	8.73439e7i		−	0.346004i
$633$	−3.37386e8	−	2.13110e8i	−1.33020	−	0.840219i
$634$	1.88813e8			0.740908
$635$		−	2.91331e8i		−	1.13780i
$636$	6.43749e7	−	1.01916e8i	0.250233	−	0.396158i
$637$	2.07177e8			0.801535
$638$		−	1.49152e8i		−	0.574338i
$639$	3.71654e7	−	1.76816e7i	0.142441	−	0.0677670i
$640$	4.81423e8			1.83648
$641$			2.97510e8i			1.12961i	0.825225	+	0.564804i	$0.191048\pi$
$641$			2.97510e8i			1.12961i	−0.825225	+	0.564804i	$0.808952\pi$
$642$	9.58387e7	+	6.05365e7i	0.362189	+	0.228777i
$643$	−2.19517e8			−0.825724			−0.412862	−	0.910794i	$-0.635471\pi$
$643$	−2.19517e8			−0.825724			−0.412862	+	0.910794i	$0.635471\pi$
$644$			4.02859e7i			0.150833i
$645$	−1.13563e7	+	1.79788e7i	−0.0423212	+	0.0670011i
$646$	4.48582e8			1.66397
$647$			1.93742e8i			0.715337i	0.933849	+	0.357669i	$0.116428\pi$
$647$			1.93742e8i			0.715337i	−0.933849	+	0.357669i	$0.883572\pi$
$648$	1.23962e8	+	1.00792e8i	0.455578	+	0.370426i
$649$	−2.91831e8			−1.06757
$650$			6.35081e8i			2.31254i
$651$	3.31611e7	+	2.09462e7i	0.120195	+	0.0759212i
$652$	1.60367e7			0.0578592
$653$		−	1.43123e8i		−	0.514008i	−0.966410	−	0.257004i	$-0.917265\pi$
$653$		−	1.43123e8i		−	0.514008i	0.966410	−	0.257004i	$-0.0827353\pi$
$654$	−2.62513e8	+	4.15598e8i	−0.938463	+	1.48573i
$655$	3.22808e8			1.14874
$656$			1.17057e8i			0.414656i
$657$	5.35431e7	+	1.12544e8i	0.188802	+	0.396850i
$658$	8.59136e8			3.01567
$659$			2.25650e8i			0.788461i	0.919012	+	0.394230i	$0.128989\pi$
$659$			2.25650e8i			0.788461i	−0.919012	+	0.394230i	$0.871011\pi$
$660$	−3.20079e8	−	2.02178e8i	−1.11333	−	0.703237i
$661$	−9.08081e7			−0.314427			−0.157214	−	0.987565i	$-0.550251\pi$
$661$	−9.08081e7			−0.314427			−0.157214	+	0.987565i	$0.550251\pi$
$662$			3.74448e8i			1.29068i
$663$	2.07950e8	−	3.29217e8i	0.713538	−	1.12964i
$664$	−3.64406e7			−0.124475
$665$			6.40683e8i			2.17860i
$666$	1.11347e8	−	5.29737e7i	0.376926	−	0.179324i
$667$	−2.02115e7			−0.0681115
$668$			1.86118e8i			0.624394i
$669$	−4.13457e8	−	2.61160e8i	−1.38087	−	0.872225i
$670$	−1.03414e9			−3.43838
$671$		−	4.40737e8i		−	1.45885i
$672$	−2.13575e8	+	3.38122e8i	−0.703788	+	1.11421i
$673$	5.14703e7			0.168854			0.0844270	−	0.996430i	$-0.473094\pi$
$673$	5.14703e7			0.168854			0.0844270	+	0.996430i	$0.473094\pi$
$674$			4.83783e8i			1.58005i
$675$	7.71987e7	−	6.44002e8i	0.251015	−	2.09399i
$676$	3.42294e7			0.110805
$677$		−	5.59046e8i		−	1.80170i	−0.434134	−	0.900848i	$-0.642945\pi$
$677$		−	5.59046e8i		−	1.80170i	0.434134	−	0.900848i	$-0.357055\pi$
$678$	−3.54963e8	−	2.24213e8i	−1.13892	−	0.719401i
$679$	1.05307e8			0.336394
$680$			4.89762e8i			1.55761i
$681$	−1.20978e8	+	1.91528e8i	−0.383059	+	0.606443i
$682$	5.74861e7			0.181222
$683$		−	2.79518e8i		−	0.877300i	−0.898658	−	0.438650i	$-0.855457\pi$
$683$		−	2.79518e8i		−	0.877300i	0.898658	−	0.438650i	$-0.144543\pi$
$684$	6.45863e7	+	1.35756e8i	0.201824	+	0.424220i
$685$	7.76944e8			2.41723
$686$			5.35874e7i			0.165993i
$687$	1.09364e8	+	6.90797e7i	0.337290	+	0.213049i
$688$	1.82872e7			0.0561540
$689$			2.59537e8i			0.793491i
$690$	−7.96375e7	+	1.26079e8i	−0.242421	+	0.383791i
$691$	5.52797e7			0.167545			0.0837725	−	0.996485i	$-0.473303\pi$
$691$	5.52797e7			0.167545			0.0837725	+	0.996485i	$0.473303\pi$
$692$			1.32204e8i			0.398957i
$693$	−5.90321e8	+	2.80847e8i	−1.77373	+	0.843860i
$694$	−7.98727e8			−2.38957
$695$		−	8.05893e8i		−	2.40062i
$696$	−5.46725e7	−	3.45339e7i	−0.162159	−	0.102428i
$697$	−1.69071e8			−0.499311
$698$		−	3.08640e8i		−	0.907581i
$699$	2.09994e8	−	3.32453e8i	0.614858	−	0.973416i
$700$	5.23271e8			1.52557
$701$		−	5.59082e8i		−	1.62301i	−0.584346	−	0.811505i	$-0.698649\pi$
$701$		−	5.59082e8i		−	1.62301i	0.584346	−	0.811505i	$-0.301351\pi$
$702$	3.76642e8	+	4.51494e7i	1.08872	+	0.130509i
$703$	−1.05215e8			−0.302838
$704$		−	3.46483e7i		−	0.0993032i
$705$	9.24985e8	+	5.84266e8i	2.63978	+	1.66741i
$706$	−3.69340e8			−1.04957
$707$			5.41872e8i			1.53334i
$708$	7.45131e7	−	1.17966e8i	0.209958	−	0.332397i
$709$	−2.53001e8			−0.709879			−0.354939	−	0.934889i	$-0.615499\pi$
$709$	−2.53001e8			−0.709879			−0.354939	+	0.934889i	$0.615499\pi$
$710$			1.22908e8i			0.343405i
$711$	9.09920e7	+	1.91259e8i	0.253160	+	0.532124i
$712$	−3.71514e7			−0.102928
$713$		−	7.78989e6i		−	0.0214913i
$714$	−7.88489e8	−	4.98049e8i	−2.16621	−	1.36829i
$715$	8.15111e8			2.22997
$716$		−	9.13988e7i		−	0.249001i
$717$	−1.84997e7	+	2.92879e7i	−0.0501888	+	0.0794568i
$718$	−5.93283e8			−1.60283
$719$			3.63882e8i			0.978981i	0.872009	+	0.489491i	$0.162817\pi$
$719$			3.63882e8i			0.978981i	−0.872009	+	0.489491i	$0.837183\pi$
$720$	−7.42512e8	+	3.53253e8i	−1.98933	+	0.946429i
$721$	7.97353e8			2.12738
$722$			9.18105e7i			0.243939i
$723$	5.44749e7	+	3.44091e7i	0.144139	+	0.0910454i
$724$	2.48496e8			0.654792
$725$			2.62526e8i			0.688903i
$726$	−2.59362e8	+	4.10611e8i	−0.677793	+	1.07305i
$727$	−6.63578e8			−1.72699			−0.863493	−	0.504361i	$-0.831728\pi$
$727$	−6.63578e8			−1.72699			−0.863493	+	0.504361i	$0.831728\pi$
$728$		−	2.77513e8i		−	0.719265i
$729$	−3.76444e8	−	9.15671e7i	−0.971668	−	0.236351i
$730$	−3.72190e8			−0.956744
$731$			2.64130e7i			0.0676184i
$732$	1.78157e8	+	1.12533e8i	0.454225	+	0.286911i
$733$	4.59798e8			1.16750			0.583748	−	0.811935i	$-0.301586\pi$
$733$	4.59798e8			1.16750			0.583748	+	0.811935i	$0.301586\pi$
$734$		−	4.23350e8i		−	1.07056i
$735$	3.37445e8	−	5.34229e8i	0.849849	−	1.34544i
$736$	7.94283e7			0.199224
$737$			9.00369e8i			2.24915i
$738$	−7.07595e7	−	1.48732e8i	−0.176042	−	0.370028i
$739$	3.26721e8			0.809550			0.404775	−	0.914416i	$-0.367350\pi$
$739$	3.26721e8			0.809550			0.404775	+	0.914416i	$0.367350\pi$
$740$			1.26679e8i			0.312615i
$741$	−2.73660e8	−	1.72858e8i	−0.672601	−	0.424848i
$742$	6.21604e8			1.52161
$743$		−	7.49362e8i		−	1.82694i	−0.406902	−	0.913472i	$-0.633391\pi$
$743$		−	7.49362e8i		−	1.82694i	0.406902	−	0.913472i	$-0.366609\pi$
$744$	1.33100e7	−	2.10718e7i	0.0323191	−	0.0511662i
$745$	−8.47900e8			−2.05058
$746$		−	9.56370e7i		−	0.230361i
$747$	7.97948e7	−	3.79626e7i	0.191431	−	0.0910740i
$748$	−4.70233e8			−1.12359
$749$			2.01094e8i			0.478578i
$750$	8.61129e8	+	5.43932e8i	2.04119	+	1.28932i
$751$	−6.34036e8			−1.49690			−0.748452	−	0.663189i	$-0.769203\pi$
$751$	−6.34036e8			−1.49690			−0.748452	+	0.663189i	$0.769203\pi$
$752$		−	9.40849e8i		−	2.21241i
$753$	1.88584e8	−	2.98557e8i	0.441692	−	0.699267i
$754$	−1.53537e8			−0.358179
$755$			1.20852e9i			2.80811i
$756$	3.72006e7	−	3.10332e8i	0.0860963	−	0.718226i
$757$	1.94781e8			0.449013			0.224507	−	0.974473i	$-0.427923\pi$
$757$	1.94781e8			0.449013			0.224507	+	0.974473i	$0.427923\pi$
$758$		−	5.10400e8i		−	1.17193i
$759$	1.09770e8	+	6.93362e7i	0.251049	+	0.158575i
$760$	4.07114e8			0.927417
$761$			1.00617e8i			0.228305i	0.993463	+	0.114153i	$0.0364153\pi$
$761$			1.00617e8i			0.228305i	−0.993463	+	0.114153i	$0.963585\pi$
$762$	1.88255e8	−	2.98037e8i	0.425482	−	0.673605i
$763$	−8.72030e8			−1.96317
$764$		−	2.76755e8i		−	0.620605i
$765$	−5.10219e8	−	1.07244e9i	−1.13965	−	2.39547i
$766$	−7.43020e8			−1.65316
$767$			3.00411e8i			0.665778i
$768$	4.65798e8	+	2.94221e8i	1.02829	+	0.649516i
$769$	−2.96761e8			−0.652571			−0.326286	−	0.945271i	$-0.605797\pi$
$769$	−2.96761e8			−0.652571			−0.326286	+	0.945271i	$0.605797\pi$
$770$		−	1.95223e9i		−	4.27620i
$771$	−7.46499e7	+	1.18182e8i	−0.162879	+	0.257864i
$772$	265543.			0.000577143
$773$			1.77694e7i			0.0384710i	0.999815	+	0.0192355i	$0.00612323\pi$
$773$			1.77694e7i			0.0384710i	−0.999815	+	0.0192355i	$0.993877\pi$
$774$	−2.32354e7	+	1.10543e7i	−0.0501104	+	0.0238402i
$775$	−1.01183e8			−0.217370
$776$		−	6.69160e7i		−	0.143201i
$777$	1.84940e8	+	1.16817e8i	0.394245	+	0.249025i
$778$	3.11174e8			0.660791
$779$			1.40540e8i			0.297295i
$780$	−2.08122e8	+	3.29489e8i	−0.438565	+	0.694316i
$781$	1.07010e8			0.224631
$782$			1.85224e8i			0.387327i
$783$	1.55694e8	+	1.86636e7i	0.324329	+	0.0388785i
$784$	−5.43391e8			−1.12762
$785$		−	1.17413e9i		−	2.42721i
$786$	3.30238e8	+	2.08595e8i	0.680079	+	0.429572i
$787$	8.11498e7			0.166480			0.0832402	−	0.996530i	$-0.473473\pi$
$787$	8.11498e7			0.166480			0.0832402	+	0.996530i	$0.473473\pi$
$788$			1.86919e8i			0.382011i
$789$	−2.77139e8	+	4.38755e8i	−0.564244	+	0.893286i
$790$	−6.32505e8			−1.28287
$791$		−	7.44802e8i		−	1.50491i
$792$	1.78461e8	+	3.75112e8i	0.359226	+	0.755067i
$793$	−4.53694e8			−0.909795
$794$		−	8.69846e7i		−	0.173772i
$795$	6.69247e8	+	4.22730e8i	1.33194	+	0.841320i
$796$	−2.78027e8			−0.551249
$797$			4.91313e8i			0.970473i	0.874383	+	0.485237i	$0.161267\pi$
$797$			4.91313e8i			0.970473i	−0.874383	+	0.485237i	$0.838733\pi$
$798$	−4.14002e8	+	6.55430e8i	−0.814693	+	1.28979i
$799$	1.35891e9			2.66410
$800$		−	1.03169e9i		−	2.01502i
$801$	8.13512e7	−	3.87031e7i	0.158295	−	0.0753092i
$802$	−8.48313e8			−1.64450
$803$			3.24046e8i			0.625835i
$804$	−3.63953e8	−	2.29891e8i	−0.700289	−	0.442337i
$805$	−2.64545e8			−0.507121
$806$		−	5.91762e7i		−	0.113017i
$807$	4.21031e6	−	6.66558e6i	0.00801112	−	0.0126829i
$808$	3.44326e8			0.652733
$809$			1.33882e8i			0.252858i	0.991976	+	0.126429i	$0.0403516\pi$
$809$			1.33882e8i			0.252858i	−0.991976	+	0.126429i	$0.959648\pi$
$810$	7.29890e8	−	8.97676e8i	1.37342	−	1.68914i
$811$	3.64376e8			0.683104			0.341552	−	0.939863i	$-0.389047\pi$
$811$	3.64376e8			0.683104			0.341552	+	0.939863i	$0.389047\pi$
$812$			1.26506e8i			0.236289i
$813$	−1.06436e8	−	6.72302e7i	−0.198069	−	0.125110i
$814$	3.20600e8			0.594416
$815$			1.05308e8i			0.194531i
$816$	−5.45418e8	+	8.63483e8i	−1.00383	+	1.58922i
$817$	2.19557e7			0.0402607
$818$			1.23795e9i			2.26174i
$819$	2.89104e8	+	6.07676e8i	0.526262	+	1.10617i
$820$	1.69211e8			0.306894
$821$			8.17431e8i			1.47714i	0.674177	+	0.738570i	$0.264499\pi$
$821$			8.17431e8i			1.47714i	−0.674177	+	0.738570i	$0.735501\pi$
$822$	7.94827e8	+	5.02052e8i	1.43106	+	0.903927i
$823$	6.47582e8			1.16170			0.580852	−	0.814009i	$-0.302720\pi$
$823$	6.47582e8			1.16170			0.580852	+	0.814009i	$0.302720\pi$
$824$		−	5.06668e8i		−	0.905611i
$825$	9.00605e8	−	1.42580e9i	1.60388	−	2.53920i
$826$	7.19498e8			1.27670
$827$			3.15443e8i			0.557705i	0.960334	+	0.278852i	$0.0899540\pi$
$827$			3.15443e8i			0.557705i	−0.960334	+	0.278852i	$0.910046\pi$
$828$	−5.60551e7	+	2.66684e7i	−0.0987470	+	0.0469792i
$829$	−5.48592e8			−0.962911			−0.481455	−	0.876471i	$-0.659892\pi$
$829$	−5.48592e8			−0.962911			−0.481455	+	0.876471i	$0.659892\pi$
$830$			2.63886e8i			0.461512i
$831$	6.59974e7	+	4.16873e7i	0.115007	+	0.0726441i
$832$	−3.56669e7			−0.0619292
$833$		−	7.84844e8i		−	1.35784i
$834$	5.20759e8	−	8.24443e8i	0.897715	−	1.42122i
$835$	−1.22218e9			−2.09930
$836$			3.90880e8i			0.668998i
$837$	−7.19330e6	+	6.00074e7i	−0.0122674	+	0.102336i
$838$	1.22298e8			0.207820
$839$			1.42520e8i			0.241318i	0.992694	+	0.120659i	$0.0385007\pi$
$839$			1.42520e8i			0.241318i	−0.992694	+	0.120659i	$0.961499\pi$
$840$	−7.15599e8	−	4.52008e8i	−1.20735	−	0.762620i
$841$	5.31355e8			0.893299
$842$		−	1.22072e9i		−	2.04494i
$843$	−1.95155e8	+	3.08961e8i	−0.325759	+	0.515728i
$844$	4.96070e8			0.825117
$845$			2.24774e8i			0.372542i
$846$	5.68729e8	+	1.19543e9i	0.939279	+	1.97430i
$847$	−8.61564e8			−1.41787
$848$		−	6.80725e8i		−	1.11631i
$849$	−2.61714e8	−	1.65312e8i	−0.427665	−	0.270135i
$850$	2.40587e9			3.91755
$851$		−	4.34442e7i		−	0.0704925i
$852$	−2.73228e7	+	4.32562e7i	−0.0441780	+	0.0699406i
$853$	1.86992e8			0.301284			0.150642	−	0.988588i	$-0.451866\pi$
$853$	1.86992e8			0.301284			0.150642	+	0.988588i	$0.451866\pi$
$854$			1.08662e9i			1.74463i
$855$	−8.91467e8	+	4.24118e8i	−1.42629	+	0.678560i
$856$	1.27782e8			0.203727
$857$		−	5.61726e8i		−	0.892446i	−0.894922	−	0.446223i	$-0.852769\pi$
$857$		−	5.61726e8i		−	0.892446i	0.894922	−	0.446223i	$-0.147231\pi$
$858$	8.33873e8	+	5.26715e8i	1.32019	+	0.833900i
$859$	−7.50145e8			−1.18349			−0.591746	−	0.806124i	$-0.701561\pi$
$859$	−7.50145e8			−1.18349			−0.591746	+	0.806124i	$0.701561\pi$
$860$		−	2.64348e7i		−	0.0415605i
$861$	1.56038e8	−	2.47033e8i	0.244467	−	0.387030i
$862$	1.52902e8			0.238721
$863$		−	1.34272e8i		−	0.208907i	−0.994530	−	0.104454i	$-0.966691\pi$
$863$		−	1.34272e8i		−	0.208907i	0.994530	−	0.104454i	$-0.0333094\pi$
$864$	−6.11856e8	−	7.33453e7i	−0.948654	−	0.113718i
$865$	−8.68142e8			−1.34135
$866$		−	5.24728e8i		−	0.807943i
$867$	−6.96167e8	−	4.39734e8i	−1.06821	−	0.674734i
$868$	−4.87579e7			−0.0745566
$869$			5.50689e8i			0.839164i
$870$	−2.50079e8	+	3.95914e8i	−0.379768	+	0.601233i
$871$	9.26839e8			1.40265
$872$			5.54120e8i			0.835708i
$873$	6.97109e7	+	1.46528e8i	0.104775	+	0.220230i
$874$	1.53967e8			0.230618
$875$			1.80686e9i			2.69713i
$876$	−1.30988e8	−	8.27385e7i	−0.194858	−	0.123082i
$877$	7.18367e8			1.06500			0.532498	−	0.846431i	$-0.321253\pi$
$877$	7.18367e8			1.06500			0.532498	+	0.846431i	$0.321253\pi$
$878$			8.62028e7i			0.127361i
$879$	−7.05969e8	+	1.11766e9i	−1.03949	+	1.64567i
$880$	−2.13791e9			−3.13719
$881$		−	3.31128e8i		−	0.484248i	−0.970245	−	0.242124i	$-0.922156\pi$
$881$		−	3.31128e8i		−	0.484248i	0.970245	−	0.242124i	$-0.0778442\pi$
$882$	6.90425e8	−	3.28472e8i	1.00626	−	0.478732i
$883$	4.62757e8			0.672157			0.336078	−	0.941834i	$-0.390899\pi$
$883$	4.62757e8			0.672157			0.336078	+	0.941834i	$0.390899\pi$
$884$			4.84058e8i			0.700713i
$885$	7.74644e8	+	4.89304e8i	1.11756	+	0.705909i
$886$	−1.74987e8			−0.251596
$887$		−	6.69384e8i		−	0.959189i	−0.877490	−	0.479595i	$-0.840784\pi$
$887$		−	6.69384e8i		−	0.959189i	0.877490	−	0.479595i	$-0.159216\pi$
$888$	7.42299e7	−	1.17517e8i	0.106008	−	0.167828i
$889$	6.25356e8			0.890066
$890$			2.69034e8i			0.381625i
$891$	−7.81559e8	−	6.35477e8i	−1.10492	−	0.898394i
$892$	6.07920e8			0.856548
$893$		−	1.12959e9i		−	1.58623i
$894$	−8.67417e8	−	5.47903e8i	−1.21399	−	0.766816i
$895$	6.00187e8			0.837177
$896$			1.03340e9i			1.43662i
$897$	7.13747e7	−	1.12997e8i	0.0988933	−	0.156564i
$898$	−1.07081e9			−1.47871
$899$		−	2.44619e7i		−	0.0336675i
$900$	3.46394e8	+	7.28097e8i	0.475164	+	0.998761i
$901$	9.83201e8			1.34421
$902$		−	4.28241e8i		−	0.583537i
$903$	−3.85924e7	−	2.43769e7i	−0.0524129	−	0.0331066i
$904$	−4.73275e8			−0.640632
$905$			1.63179e9i			2.20150i
$906$	−7.80933e8	+	1.23634e9i	−1.05010	+	1.66247i
$907$	5.61521e8			0.752565			0.376282	−	0.926505i	$-0.377202\pi$
$907$	5.61521e8			0.752565			0.376282	+	0.926505i	$0.377202\pi$
$908$		−	2.81609e8i		−	0.376174i
$909$	−7.53978e8	+	3.58707e8i	−1.00385	+	0.477583i
$910$	−2.00962e9			−2.66680
$911$			2.43328e8i			0.321837i	0.986968	+	0.160919i	$0.0514457\pi$
$911$			2.43328e8i			0.321837i	−0.986968	+	0.160919i	$0.948554\pi$
$912$	7.17768e8	+	4.53378e8i	0.946236	+	0.597690i
$913$	2.29752e8			0.301889
$914$		−	1.17273e9i		−	1.53589i
$915$	−7.38969e8	+	1.16990e9i	−0.964635	+	1.52717i
$916$	−1.60801e8			−0.209220
$917$			6.92922e8i			0.898621i
$918$	1.71039e8	−	1.42683e9i	0.221089	−	1.84435i
$919$	−1.53956e8			−0.198358			−0.0991791	−	0.995070i	$-0.531622\pi$
$919$	−1.53956e8			−0.198358			−0.0991791	+	0.995070i	$0.531622\pi$
$920$			1.68102e8i			0.215878i
$921$	−6.19549e8	−	3.91338e8i	−0.793043	−	0.500926i
$922$	1.38185e7			0.0176307
$923$		−	1.10156e8i		−	0.140088i
$924$	4.33984e8	−	6.87065e8i	0.550121	−	0.870927i
$925$	−5.64294e8			−0.712985
$926$			1.34342e9i			1.69191i
$927$	5.27830e8	+	1.10946e9i	0.662605	+	1.39275i
$928$	2.49422e8			0.312098
$929$			3.39359e8i			0.423265i	0.977349	+	0.211632i	$0.0678779\pi$
$929$			3.39359e8i			0.423265i	−0.977349	+	0.211632i	$0.932122\pi$
$930$	−1.52593e8	−	9.63851e7i	−0.189708	−	0.119829i
$931$	−6.52400e8			−0.808472
$932$			4.88816e8i			0.603806i
$933$	−1.96783e8	+	3.11538e8i	−0.242294	+	0.383589i
$934$	1.22198e9			1.49977
$935$		−	3.08787e9i		−	3.77767i
$936$	3.86140e8	−	1.83707e8i	0.470888	−	0.224026i
$937$	9.09042e7			0.110501			0.0552504	−	0.998473i	$-0.482404\pi$
$937$	9.09042e7			0.110501			0.0552504	+	0.998473i	$0.482404\pi$
$938$		−	2.21982e9i		−	2.68974i
$939$	−9.48481e7	−	5.99108e7i	−0.114560	−	0.0723616i
$940$	−1.36004e9			−1.63744
$941$		−	1.76812e8i		−	0.212198i	−0.994356	−	0.106099i	$-0.966164\pi$
$941$		−	1.76812e8i		−	0.212198i	0.994356	−	0.106099i	$-0.0338361\pi$
$942$	7.58709e8	−	1.20115e9i	0.907659	−	1.43697i
$943$	−5.80305e7			−0.0692024
$944$		−	7.87930e8i		−	0.936638i
$945$	2.03785e9	+	2.44284e8i	2.41478	+	0.289468i
$946$	−6.69014e7			−0.0790245
$947$			1.14101e9i			1.34351i	0.740774	+	0.671754i	$0.234459\pi$
$947$			1.14101e9i			1.34351i	−0.740774	+	0.671754i	$0.765541\pi$
$948$	−2.22603e8	−	1.40607e8i	−0.261280	−	0.165037i
$949$	3.33573e8			0.390294
$950$		−	1.99987e9i		−	2.33255i
$951$	−2.75627e8	+	4.36360e8i	−0.320465	+	0.507345i
$952$	−1.05130e9			−1.21847
$953$		−	9.30672e8i		−	1.07527i	−0.843177	−	0.537635i	$-0.819318\pi$
$953$		−	9.30672e8i		−	1.07527i	0.843177	−	0.537635i	$-0.180682\pi$
$954$	4.11488e8	+	8.64920e8i	0.473928	+	0.996163i
$955$	1.81736e9			2.08656
$956$		−	4.30630e7i		−	0.0492868i
$957$	3.44701e8	+	2.17730e8i	0.393285	+	0.248418i
$958$	1.20678e9			1.37256
$959$			1.66775e9i			1.89092i
$960$	−5.80936e7	+	9.19712e7i	−0.0656621	+	0.103953i
$961$	−8.78076e8			−0.989377
$962$		−	3.30025e8i		−	0.370700i
$963$	−2.79808e8	+	1.33120e8i	−0.313315	+	0.149061i
$964$	−8.00963e7			−0.0894090
$965$			1.74374e6i			0.00194043i
$966$	−2.70634e8	−	1.70946e8i	−0.300228	−	0.189639i
$967$	1.00117e9			1.10720			0.553602	−	0.832782i	$-0.313253\pi$
$967$	1.00117e9			1.10720			0.553602	+	0.832782i	$0.313253\pi$
$968$			5.47470e8i			0.603579i
$969$	−6.54834e8	+	1.03670e9i	−0.719714	+	1.13942i
$970$	−4.84576e8			−0.530941
$971$		−	2.02767e8i		−	0.221482i	−0.993849	−	0.110741i	$-0.964678\pi$
$971$		−	2.02767e8i		−	0.221482i	0.993849	−	0.110741i	$-0.0353224\pi$
$972$	4.56432e8	−	1.53671e8i	0.497024	−	0.167337i
$973$	1.72989e9			1.87793
$974$			2.00949e8i			0.217474i
$975$	−1.46772e9	−	9.27082e8i	−1.58354	−	1.00024i
$976$	1.18997e9			1.27993
$977$		−	7.31277e8i		−	0.784149i	−0.919934	−	0.392074i	$-0.871758\pi$
$977$		−	7.31277e8i		−	0.784149i	0.919934	−	0.392074i	$-0.128242\pi$
$978$	−6.80488e7	+	1.07732e8i	−0.0727451	+	0.115167i
$979$	2.34233e8			0.249632
$980$			7.85494e8i			0.834574i
$981$	−5.77265e8	−	1.21337e9i	−0.611460	−	1.28525i
$982$	−9.70493e8			−1.02484
$983$		−	1.30850e9i		−	1.37756i	−0.724969	−	0.688782i	$-0.758146\pi$
$983$		−	1.30850e9i		−	1.37756i	0.724969	−	0.688782i	$-0.241854\pi$
$984$	−1.56974e8	−	9.91524e7i	−0.164756	−	0.104068i
$985$	−1.22744e9			−1.28437
$986$			5.81643e8i			0.606772i
$987$	−1.25416e9	+	1.98552e9i	−1.30437	+	2.06502i
$988$	4.02372e8			0.417212
$989$			9.06574e6i			0.00937161i
$990$	2.71639e9	−	1.29233e9i	2.79954	−	1.33189i
$991$	−3.09139e8			−0.317639			−0.158819	−	0.987308i	$-0.550769\pi$
$991$	−3.09139e8			−0.317639			−0.158819	+	0.987308i	$0.550769\pi$
$992$			9.61319e7i			0.0984765i
$993$	−8.65377e8	−	5.46615e8i	−0.883807	−	0.558256i
$994$	−2.63828e8			−0.268635
$995$		−	1.82572e9i		−	1.85338i
$996$	−5.86625e7	+	9.28718e7i	−0.0593721	+	0.0939953i
$997$	−1.52147e8			−0.153524			−0.0767620	−	0.997049i	$-0.524458\pi$
$997$	−1.52147e8			−0.153524			−0.0767620	+	0.997049i	$0.524458\pi$
$998$			9.60830e8i			0.966618i
$999$	−4.01170e7	+	3.34661e8i	−0.0402376	+	0.335667i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	69.7.b.a.47.10	✓	44
3.2	odd	2	inner	69.7.b.a.47.35	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.7.b.a.47.10	✓	44	1.1	even	1	trivial
69.7.b.a.47.35	yes	44	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 69 = 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	69.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-9.87745i q^{2} +(22.8275 + 14.4190i) q^{3} -33.5640 q^{4} -220.404i q^{5} +(142.423 - 225.477i) q^{6} +473.108 q^{7} -300.630i q^{8} +(313.187 + 658.297i) q^{9} +O(q^{10})\)	\(q-9.87745i q^{2} +(22.8275 + 14.4190i) q^{3} -33.5640 q^{4} -220.404i q^{5} +(142.423 - 225.477i) q^{6} +473.108 q^{7} -300.630i q^{8} +(313.187 + 658.297i) q^{9} -2177.03 q^{10} +1895.42i q^{11} +(-766.181 - 483.958i) q^{12} +1951.15 q^{13} -4673.10i q^{14} +(3178.00 - 5031.27i) q^{15} -5117.55 q^{16} -7391.51i q^{17} +(6502.29 - 3093.49i) q^{18} -6144.18 q^{19} +7397.63i q^{20} +(10799.8 + 6821.72i) q^{21} +18722.0 q^{22} -2536.99i q^{23} +(4334.78 - 6862.63i) q^{24} -32952.9 q^{25} -19272.4i q^{26} +(-2342.70 + 19543.1i) q^{27} -15879.4 q^{28} -7966.70i q^{29} +(-49696.1 - 31390.5i) q^{30} +3070.52 q^{31} +31308.0i q^{32} +(-27330.1 + 43267.8i) q^{33} -73009.3 q^{34} -104275. i q^{35} +(-10511.8 - 22095.1i) q^{36} +17124.3 q^{37} +60688.8i q^{38} +(44539.8 + 28133.6i) q^{39} -66260.1 q^{40} -22873.7i q^{41} +(67381.2 - 106675. i) q^{42} -3573.42 q^{43} -63618.0i q^{44} +(145091. - 69027.6i) q^{45} -25059.0 q^{46} +183847. i q^{47} +(-116821. - 73789.8i) q^{48} +106182. q^{49} +325491. i q^{50} +(106578. - 168730. i) q^{51} -65488.3 q^{52} +133018. i q^{53} +(193036. + 23139.9i) q^{54} +417759. q^{55} -142230. i q^{56} +(-140256. - 88592.7i) q^{57} -78690.7 q^{58} +153966. i q^{59} +(-106666. + 168869. i) q^{60} -232527. q^{61} -30328.9i q^{62} +(148171. + 311445. i) q^{63} -18279.9 q^{64} -430041. i q^{65} +(427375. + 269951. i) q^{66} +475022. q^{67} +248089. i q^{68} +(36580.8 - 57913.2i) q^{69} -1.02997e6 q^{70} -56456.9i q^{71} +(197904. - 94153.4i) q^{72} +170962. q^{73} -169144. i q^{74} +(-752232. - 475147. i) q^{75} +206223. q^{76} +896740. i q^{77} +(277888. - 439940. i) q^{78} +290536. q^{79} +1.12793e6i q^{80} +(-335269. + 412340. i) q^{81} -225934. q^{82} -121214. i q^{83} +(-362486. - 228964. i) q^{84} -1.62912e6 q^{85} +35296.2i q^{86} +(114872. - 181860. i) q^{87} +569822. q^{88} -123578. i q^{89} +(-681817. - 1.43313e6i) q^{90} +923104. q^{91} +85151.6i q^{92} +(70092.2 + 44273.7i) q^{93} +1.81594e6 q^{94} +1.35420e6i q^{95} +(-451430. + 714683. i) q^{96} +222586. q^{97} -1.04881e6i q^{98} +(-1.24775e6 + 593622. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 20 q^{3} - 1408 q^{4} + 95 q^{6} + 568 q^{7} - 548 q^{9}+O(q^{10}) \) 44 * q + 20 * q^3 - 1408 * q^4 + 95 * q^6 + 568 * q^7 - 548 * q^9	\( 44 q + 20 q^{3} - 1408 q^{4} + 95 q^{6} + 568 q^{7} - 548 q^{9} + 1752 q^{10} + 4075 q^{12} + 808 q^{13} + 7696 q^{15} + 36776 q^{16} + 12149 q^{18} + 28936 q^{19} - 6416 q^{21} - 7764 q^{22} - 11792 q^{24} - 129172 q^{25} - 27172 q^{27} - 25988 q^{28} - 54658 q^{30} - 72248 q^{31} + 25968 q^{33} - 32100 q^{34} - 217125 q^{36} + 260968 q^{37} + 133440 q^{39} - 227880 q^{40} + 63332 q^{42} - 187304 q^{43} + 455472 q^{45} - 164849 q^{48} + 959652 q^{49} - 218832 q^{51} - 410102 q^{52} + 882504 q^{54} + 517392 q^{55} - 572600 q^{57} - 197334 q^{58} - 854196 q^{60} + 914248 q^{61} + 885136 q^{63} - 312634 q^{64} - 816874 q^{66} - 310856 q^{67} - 395040 q^{70} + 205764 q^{72} - 227912 q^{73} + 1167580 q^{75} - 1438412 q^{76} - 6065 q^{78} + 841384 q^{79} + 1019636 q^{81} - 291126 q^{82} - 2787738 q^{84} - 2823120 q^{85} - 2899120 q^{87} - 2657340 q^{88} + 1478966 q^{90} - 2848288 q^{91} - 1992952 q^{93} + 6985482 q^{94} + 1309665 q^{96} + 1079608 q^{97} + 3251880 q^{99}+O(q^{100}) \) 44 * q + 20 * q^3 - 1408 * q^4 + 95 * q^6 + 568 * q^7 - 548 * q^9 + 1752 * q^10 + 4075 * q^12 + 808 * q^13 + 7696 * q^15 + 36776 * q^16 + 12149 * q^18 + 28936 * q^19 - 6416 * q^21 - 7764 * q^22 - 11792 * q^24 - 129172 * q^25 - 27172 * q^27 - 25988 * q^28 - 54658 * q^30 - 72248 * q^31 + 25968 * q^33 - 32100 * q^34 - 217125 * q^36 + 260968 * q^37 + 133440 * q^39 - 227880 * q^40 + 63332 * q^42 - 187304 * q^43 + 455472 * q^45 - 164849 * q^48 + 959652 * q^49 - 218832 * q^51 - 410102 * q^52 + 882504 * q^54 + 517392 * q^55 - 572600 * q^57 - 197334 * q^58 - 854196 * q^60 + 914248 * q^61 + 885136 * q^63 - 312634 * q^64 - 816874 * q^66 - 310856 * q^67 - 395040 * q^70 + 205764 * q^72 - 227912 * q^73 + 1167580 * q^75 - 1438412 * q^76 - 6065 * q^78 + 841384 * q^79 + 1019636 * q^81 - 291126 * q^82 - 2787738 * q^84 - 2823120 * q^85 - 2899120 * q^87 - 2657340 * q^88 + 1478966 * q^90 - 2848288 * q^91 - 1992952 * q^93 + 6985482 * q^94 + 1309665 * q^96 + 1079608 * q^97 + 3251880 * q^99

Introduction

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