LMFDB - Embedded newform 69.7.b.a.47.18

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			47.18
Character	$\chi$	$=$	69.47
Dual form			69.7.b.a.47.27

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.32001i q^{2} +(-14.6931 + 22.6520i) q^{3} +45.3375 q^{4} -48.7369i q^{5} +(97.8569 + 63.4743i) q^{6} -61.9430 q^{7} -472.339i q^{8} +(-297.226 - 665.656i) q^{9} +O(q^{10})$	\(q-4.32001i q^{2} +(-14.6931 + 22.6520i) q^{3} +45.3375 q^{4} -48.7369i q^{5} +(97.8569 + 63.4743i) q^{6} -61.9430 q^{7} -472.339i q^{8} +(-297.226 - 665.656i) q^{9} -210.544 q^{10} +1348.22i q^{11} +(-666.148 + 1026.99i) q^{12} +1847.54 q^{13} +267.594i q^{14} +(1103.99 + 716.096i) q^{15} +861.091 q^{16} -5403.33i q^{17} +(-2875.64 + 1284.02i) q^{18} +10415.3 q^{19} -2209.61i q^{20} +(910.135 - 1403.13i) q^{21} +5824.34 q^{22} +2536.99i q^{23} +(10699.4 + 6940.12i) q^{24} +13249.7 q^{25} -7981.39i q^{26} +(19445.6 + 3047.78i) q^{27} -2808.34 q^{28} -30077.9i q^{29} +(3093.54 - 4769.24i) q^{30} -537.061 q^{31} -33949.6i q^{32} +(-30539.9 - 19809.6i) q^{33} -23342.4 q^{34} +3018.91i q^{35} +(-13475.5 - 30179.2i) q^{36} +59878.0 q^{37} -44994.2i q^{38} +(-27146.1 + 41850.5i) q^{39} -23020.3 q^{40} +39712.5i q^{41} +(-6061.55 - 3931.79i) q^{42} +103609. q^{43} +61125.1i q^{44} +(-32442.0 + 14485.9i) q^{45} +10959.8 q^{46} +47340.7i q^{47} +(-12652.1 + 19505.4i) q^{48} -113812. q^{49} -57238.9i q^{50} +(122396. + 79391.6i) q^{51} +83762.9 q^{52} -77383.7i q^{53} +(13166.4 - 84005.2i) q^{54} +65708.2 q^{55} +29258.1i q^{56} +(-153033. + 235927. i) q^{57} -129937. q^{58} +117701. i q^{59} +(50052.1 + 32466.0i) q^{60} +111988. q^{61} +2320.11i q^{62} +(18411.1 + 41232.7i) q^{63} -91552.9 q^{64} -90043.3i q^{65} +(-85577.5 + 131933. i) q^{66} -540176. q^{67} -244973. i q^{68} +(-57468.0 - 37276.3i) q^{69} +13041.7 q^{70} +246829. i q^{71} +(-314415. + 140391. i) q^{72} -427677. q^{73} -258673. i q^{74} +(-194679. + 300133. i) q^{75} +472204. q^{76} -83513.0i q^{77} +(180794. + 117271. i) q^{78} -473538. q^{79} -41966.9i q^{80} +(-354754. + 395700. i) q^{81} +171559. q^{82} -951641. i q^{83} +(41263.2 - 63614.6i) q^{84} -263341. q^{85} -447594. i q^{86} +(681325. + 441938. i) q^{87} +636819. q^{88} -624779. i q^{89} +(62579.1 + 140150. i) q^{90} -114442. q^{91} +115021. i q^{92} +(7891.09 - 12165.5i) q^{93} +204512. q^{94} -507609. i q^{95} +(769027. + 498825. i) q^{96} +903441. q^{97} +491669. i q^{98} +(897453. - 400727. 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 $

$2$		−	4.32001i		−	0.540001i	−0.962860	−	0.270001i	$-0.912976\pi$
$2$		−	4.32001i		−	0.540001i	0.962860	−	0.270001i	$-0.0870239\pi$
$3$	−14.6931	+	22.6520i	−0.544189	+	0.838963i
$3$	−14.6931	+	22.6520i	−0.544189	+	0.838963i
$4$	45.3375			0.708399
$5$		−	48.7369i		−	0.389895i	−0.980814	−	0.194948i	$-0.937546\pi$
$5$		−	48.7369i		−	0.389895i	0.980814	−	0.194948i	$-0.0624537\pi$
$6$	97.8569	+	63.4743i	0.453041	+	0.293863i
$7$	−61.9430			−0.180592			−0.0902959	−	0.995915i	$-0.528781\pi$
$7$	−61.9430			−0.180592			−0.0902959	+	0.995915i	$0.528781\pi$
$8$		−	472.339i		−	0.922537i
$9$	−297.226	−	665.656i	−0.407717	−	0.913108i
$10$	−210.544			−0.210544
$11$			1348.22i			1.01294i	0.862258	+	0.506470i	$0.169050\pi$
$11$			1348.22i			1.01294i	−0.862258	+	0.506470i	$0.830950\pi$
$12$	−666.148	+	1026.99i	−0.385502	+	0.594320i
$13$	1847.54			0.840938			0.420469	−	0.907307i	$-0.361866\pi$
$13$	1847.54			0.840938			0.420469	+	0.907307i	$0.361866\pi$
$14$			267.594i			0.0975198i
$15$	1103.99	+	716.096i	0.327108	+	0.212176i
$16$	861.091			0.210227
$17$		−	5403.33i		−	1.09980i	−0.835230	−	0.549901i	$-0.814665\pi$
$17$		−	5403.33i		−	1.09980i	0.835230	−	0.549901i	$-0.185335\pi$
$18$	−2875.64	+	1284.02i	−0.493080	+	0.220168i
$19$	10415.3			1.51849			0.759243	−	0.650807i	$-0.225569\pi$
$19$	10415.3			1.51849			0.759243	+	0.650807i	$0.225569\pi$
$20$		−	2209.61i		−	0.276201i
$21$	910.135	−	1403.13i	0.0982761	−	0.151510i
$22$	5824.34			0.546989
$23$			2536.99i			0.208514i
$23$			2536.99i			0.208514i
$24$	10699.4	+	6940.12i	0.773975	+	0.502034i
$25$	13249.7			0.847982
$26$		−	7981.39i		−	0.454107i
$27$	19445.6	+	3047.78i	0.987939	+	0.154843i
$28$	−2808.34			−0.127931
$29$		−	30077.9i		−	1.23326i	−0.787254	−	0.616629i	$-0.788498\pi$
$29$		−	30077.9i		−	1.23326i	0.787254	−	0.616629i	$-0.211502\pi$
$30$	3093.54	−	4769.24i	0.114576	−	0.176638i
$31$	−537.061			−0.0180276			−0.00901381	−	0.999959i	$-0.502869\pi$
$31$	−537.061			−0.0180276			−0.00901381	+	0.999959i	$0.502869\pi$
$32$		−	33949.6i		−	1.03606i
$33$	−30539.9	−	19809.6i	−0.849819	−	0.551230i
$34$	−23342.4			−0.593894
$35$			3018.91i			0.0704119i
$36$	−13475.5	−	30179.2i	−0.288826	−	0.646845i
$37$	59878.0			1.18212			0.591060	−	0.806627i	$-0.298709\pi$
$37$	59878.0			1.18212			0.591060	+	0.806627i	$0.298709\pi$
$38$		−	44994.2i		−	0.819985i
$39$	−27146.1	+	41850.5i	−0.457629	+	0.705515i
$40$	−23020.3			−0.359693
$41$			39712.5i			0.576204i	0.957600	+	0.288102i	$0.0930241\pi$
$41$			39712.5i			0.576204i	−0.957600	+	0.288102i	$0.906976\pi$
$42$	−6061.55	−	3931.79i	−0.0818155	−	0.0530692i
$43$	103609.			1.30315			0.651574	−	0.758585i	$-0.274109\pi$
$43$	103609.			1.30315			0.651574	+	0.758585i	$0.274109\pi$
$44$			61125.1i			0.717565i
$45$	−32442.0	+	14485.9i	−0.356016	+	0.158967i
$46$	10959.8			0.112598
$47$			47340.7i			0.455975i	0.973664	+	0.227988i	$0.0732146\pi$
$47$			47340.7i			0.455975i	−0.973664	+	0.227988i	$0.926785\pi$
$48$	−12652.1	+	19505.4i	−0.114403	+	0.176373i
$49$	−113812.			−0.967387
$50$		−	57238.9i		−	0.457911i
$51$	122396.	+	79391.6i	0.922693	+	0.598500i
$52$	83762.9			0.595719
$53$		−	77383.7i		−	0.519783i	−0.965638	−	0.259891i	$-0.916313\pi$
$53$		−	77383.7i		−	0.519783i	0.965638	−	0.259891i	$-0.0836867\pi$
$54$	13166.4	−	84005.2i	0.0836156	−	0.533488i
$55$	65708.2			0.394940
$56$			29258.1i			0.166603i
$57$	−153033.	+	235927.i	−0.826343	+	1.27395i
$58$	−129937.			−0.665961
$59$			117701.i			0.573090i	0.958067	+	0.286545i	$0.0925068\pi$
$59$			117701.i			0.573090i	−0.958067	+	0.286545i	$0.907493\pi$
$60$	50052.1	+	32466.0i	0.231723	+	0.150306i
$61$	111988.			0.493381			0.246690	−	0.969094i	$-0.420657\pi$
$61$	111988.			0.493381			0.246690	+	0.969094i	$0.420657\pi$
$62$			2320.11i			0.00973494i
$63$	18411.1	+	41232.7i	0.0736305	+	0.164900i
$64$	−91552.9			−0.349247
$65$		−	90043.3i		−	0.327877i
$66$	−85577.5	+	131933.i	−0.297665	+	0.458903i
$67$	−540176.			−1.79602			−0.898009	−	0.439976i	$-0.854987\pi$
$67$	−540176.			−1.79602			−0.898009	+	0.439976i	$0.854987\pi$
$68$		−	244973.i		−	0.779098i
$69$	−57468.0	−	37276.3i	−0.174936	−	0.113471i
$70$	13041.7			0.0380225
$71$			246829.i			0.689637i	0.938669	+	0.344818i	$0.112059\pi$
$71$			246829.i			0.689637i	−0.938669	+	0.344818i	$0.887941\pi$
$72$	−314415.	+	140391.i	−0.842376	+	0.376135i
$73$	−427677.			−1.09938			−0.549689	−	0.835369i	$-0.685254\pi$
$73$	−427677.			−1.09938			−0.549689	+	0.835369i	$0.685254\pi$
$74$		−	258673.i		−	0.638347i
$75$	−194679.	+	300133.i	−0.461462	+	0.711425i
$76$	472204.			1.07569
$77$		−	83513.0i		−	0.182929i
$78$	180794.	+	117271.i	0.380979	+	0.247120i
$79$	−473538.			−0.960448			−0.480224	−	0.877146i	$-0.659445\pi$
$79$	−473538.			−0.960448			−0.480224	+	0.877146i	$0.659445\pi$
$80$		−	41966.9i		−	0.0819666i
$81$	−354754.	+	395700.i	−0.667533	+	0.744580i
$82$	171559.			0.311151
$83$		−	951641.i		−	1.66433i	−0.554530	−	0.832164i	$-0.687102\pi$
$83$		−	951641.i		−	1.66433i	0.554530	−	0.832164i	$-0.312898\pi$
$84$	41263.2	−	63614.6i	0.0696186	−	0.107329i
$85$	−263341.			−0.428807
$86$		−	447594.i		−	0.703702i
$87$	681325.	+	441938.i	1.03466	+	0.671125i
$88$	636819.			0.934475
$89$		−	624779.i		−	0.886250i	−0.896460	−	0.443125i	$-0.853870\pi$
$89$		−	624779.i		−	0.886250i	0.896460	−	0.443125i	$-0.146130\pi$
$90$	62579.1	+	140150.i	0.0858424	+	0.192249i
$91$	−114442.			−0.151866
$92$			115021.i			0.147711i
$93$	7891.09	−	12165.5i	0.00981043	−	0.0151245i
$94$	204512.			0.246227
$95$		−	507609.i		−	0.592050i
$96$	769027.	+	498825.i	0.869216	+	0.563812i
$97$	903441.			0.989885			0.494942	−	0.868926i	$-0.335189\pi$
$97$	903441.			0.989885			0.494942	+	0.868926i	$0.335189\pi$
$98$			491669.i			0.522390i
$99$	897453.	−	400727.i	0.924924	−	0.412993i
$100$	600709.			0.600709
$101$			358055.i			0.347525i	0.984788	+	0.173762i	$0.0555924\pi$
$101$			358055.i			0.347525i	−0.984788	+	0.173762i	$0.944408\pi$
$102$	342972.	−	528753.i	0.323191	−	0.498255i
$103$	−215028.			−0.196781			−0.0983903	−	0.995148i	$-0.531369\pi$
$103$	−215028.			−0.196781			−0.0983903	+	0.995148i	$0.531369\pi$
$104$		−	872665.i		−	0.775796i
$105$	−68384.3	−	44357.1i	−0.0590730	−	0.0383174i
$106$	−334298.			−0.280683
$107$			1.07379e6i			0.876530i	0.898846	+	0.438265i	$0.144407\pi$
$107$			1.07379e6i			0.876530i	−0.898846	+	0.438265i	$0.855593\pi$
$108$	881615.	+	138179.i	0.699855	+	0.109691i
$109$	−1.27280e6			−0.982833			−0.491417	−	0.870925i	$-0.663521\pi$
$109$	−1.27280e6			−0.982833			−0.491417	+	0.870925i	$0.663521\pi$
$110$		−	283860.i		−	0.213268i
$111$	−879793.	+	1.35636e6i	−0.643297	+	0.991756i
$112$	−53338.6			−0.0379653
$113$			566030.i			0.392287i	0.980575	+	0.196144i	$0.0628419\pi$
$113$			566030.i			0.392287i	−0.980575	+	0.196144i	$0.937158\pi$
$114$	1.01921e6	+	661104.i	0.687937	+	0.446226i
$115$	123645.			0.0812987
$116$		−	1.36366e6i		−	0.873639i
$117$	−549137.	−	1.22983e6i	−0.342865	−	0.767867i
$118$	508468.			0.309469
$119$			334698.i			0.198615i
$120$	338240.	−	521457.i	0.195741	−	0.301769i
$121$	−46144.6			−0.0260474
$122$		−	483789.i		−	0.266426i
$123$	−899568.	−	583500.i	−0.483413	−	0.313563i
$124$	−24349.0			−0.0127707
$125$		−	1.40726e6i		−	0.720519i
$126$	178126.	−	79536.0i	0.0890462	−	0.0397605i
$127$	3.66735e6			1.79036			0.895182	−	0.445701i	$-0.147046\pi$
$127$	3.66735e6			1.79036			0.895182	+	0.445701i	$0.147046\pi$
$128$		−	1.77727e6i		−	0.847467i
$129$	−1.52234e6	+	2.34696e6i	−0.709158	+	1.09329i
$130$	−388988.			−0.177054
$131$		−	1.13571e6i		−	0.505187i	−0.967572	−	0.252593i	$-0.918716\pi$
$131$		−	1.13571e6i		−	0.505187i	0.967572	−	0.252593i	$-0.0812835\pi$
$132$	−1.38461e6	−	898117.i	−0.602011	−	0.390491i
$133$	−645155.			−0.274226
$134$			2.33357e6i			0.969853i
$135$	148539.	−	947718.i	0.0603727	−	0.385193i
$136$	−2.55220e6			−1.01461
$137$			117499.i			0.0456956i	0.999739	+	0.0228478i	$0.00727331\pi$
$137$			117499.i			0.0456956i	−0.999739	+	0.0228478i	$0.992727\pi$
$138$	−161034.	+	248262.i	−0.0612746	+	0.0944656i
$139$	1.48730e6			0.553800			0.276900	−	0.960899i	$-0.410693\pi$
$139$	1.48730e6			0.553800			0.276900	+	0.960899i	$0.410693\pi$
$140$			136870.i			0.0498797i
$141$	−1.07236e6	−	695582.i	−0.382546	−	0.248137i
$142$	1.06630e6			0.372405
$143$			2.49090e6i			0.851819i
$144$	−255939.	−	573190.i	−0.0857133	−	0.191960i
$145$	−1.46591e6			−0.480841
$146$			1.84757e6i			0.593666i
$147$	1.67225e6	−	2.57807e6i	0.526441	−	0.811601i
$148$	2.71472e6			0.837413
$149$			4.14379e6i			1.25268i	0.779552	+	0.626338i	$0.215447\pi$
$149$			4.14379e6i			1.25268i	−0.779552	+	0.626338i	$0.784553\pi$
$150$	1.29658e6	+	841017.i	0.384171	+	0.249190i
$151$	−3.24600e6			−0.942795			−0.471397	−	0.881921i	$-0.656250\pi$
$151$	−3.24600e6			−0.942795			−0.471397	+	0.881921i	$0.656250\pi$
$152$		−	4.91955e6i		−	1.40086i
$153$	−3.59676e6	+	1.60601e6i	−1.00424	+	0.448408i
$154$	−360777.			−0.0987818
$155$			26174.7i			0.00702888i
$156$	−1.23074e6	+	1.89740e6i	−0.324184	+	0.499786i
$157$	−1.80543e6			−0.466532			−0.233266	−	0.972413i	$-0.574941\pi$
$157$	−1.80543e6			−0.466532			−0.233266	+	0.972413i	$0.574941\pi$
$158$			2.04569e6i			0.518643i
$159$	1.75289e6	+	1.13701e6i	0.436078	+	0.282860i
$160$	−1.65460e6			−0.403955
$161$		−	157149.i		−	0.0376560i
$162$	1.70943e6	+	1.53254e6i	0.402074	+	0.360469i
$163$	138447.			0.0319684			0.0159842	−	0.999872i	$-0.494912\pi$
$163$	138447.			0.0319684			0.0159842	+	0.999872i	$0.494912\pi$
$164$			1.80047e6i			0.408182i
$165$	−965457.	+	1.48842e6i	−0.214922	+	0.331340i
$166$	−4.11110e6			−0.898739
$167$			7.71246e6i			1.65594i	0.560775	+	0.827968i	$0.310503\pi$
$167$			7.71246e6i			1.65594i	−0.560775	+	0.827968i	$0.689497\pi$
$168$	−662755.	−	429892.i	−0.139774	−	0.0906633i
$169$	−1.41341e6			−0.292824
$170$			1.13764e6i			0.231557i
$171$	−3.09570e6	−	6.93300e6i	−0.619113	−	1.38654i
$172$	4.69739e6			0.923148
$173$		−	9.67850e6i		−	1.86926i	−0.355621	−	0.934630i	$-0.615731\pi$
$173$		−	9.67850e6i		−	1.86926i	0.355621	−	0.934630i	$-0.384269\pi$
$174$	1.90918e6	−	2.94333e6i	0.362409	−	0.558717i
$175$	−820727.			−0.153139
$176$			1.16094e6i			0.212948i
$177$	−2.66616e6	−	1.72939e6i	−0.480801	−	0.311869i
$178$	−2.69905e6			−0.478576
$179$			7.60489e6i			1.32597i	0.748632	+	0.662986i	$0.230711\pi$
$179$			7.60489e6i			1.32597i	−0.748632	+	0.662986i	$0.769289\pi$
$180$	−1.47084e6	+	656753.i	−0.252202	+	0.112612i
$181$	−4.06065e6			−0.684794			−0.342397	−	0.939555i	$-0.611239\pi$
$181$	−4.06065e6			−0.684794			−0.342397	+	0.939555i	$0.611239\pi$
$182$			494391.i			0.0820081i
$183$	−1.64545e6	+	2.53675e6i	−0.268492	+	0.413928i
$184$	1.19832e6			0.192362
$185$		−	2.91827e6i		−	0.460903i
$186$	−52555.1	−	34089.6i	−0.00816725	−	0.00529764i
$187$	7.28489e6			1.11403
$188$			2.14631e6i			0.323012i
$189$	−1.20452e6	−	188789.i	−0.178414	−	0.0279635i
$190$	−2.19288e6			−0.319708
$191$			2.35527e6i			0.338019i	0.985614	+	0.169009i	$0.0540569\pi$
$191$			2.35527e6i			0.338019i	−0.985614	+	0.169009i	$0.945943\pi$
$192$	1.34520e6	−	2.07386e6i	0.190056	−	0.293005i
$193$	1.40298e7			1.95155			0.975775	−	0.218778i	$-0.0702071\pi$
$193$	1.40298e7			1.95155			0.975775	+	0.218778i	$0.0702071\pi$
$194$		−	3.90287e6i		−	0.534539i
$195$	2.03966e6	+	1.32302e6i	0.275077	+	0.178427i
$196$	−5.15996e6			−0.685295
$197$			1.02080e7i			1.33519i	0.744525	+	0.667595i	$0.232676\pi$
$197$			1.02080e7i			1.33519i	−0.744525	+	0.667595i	$0.767324\pi$
$198$	−1.73114e6	−	3.87700e6i	−0.223017	−	0.499460i
$199$	−5.06554e6			−0.642786			−0.321393	−	0.946946i	$-0.604151\pi$
$199$	−5.06554e6			−0.642786			−0.321393	+	0.946946i	$0.604151\pi$
$200$		−	6.25836e6i		−	0.782295i
$201$	7.93686e6	−	1.22361e7i	0.977373	−	1.50679i
$202$	1.54680e6			0.187664
$203$			1.86312e6i			0.222716i
$204$	5.54914e6	+	3.59942e6i	0.653634	+	0.423976i
$205$	1.93546e6			0.224659
$206$			928921.i			0.106262i
$207$	1.68877e6	−	754061.i	0.190396	−	0.0850150i
$208$	1.59090e6			0.176788
$209$			1.40421e7i			1.53814i
$210$	−191623.	+	295421.i	−0.0206914	+	0.0318995i
$211$	6.96636e6			0.741581			0.370791	−	0.928717i	$-0.379087\pi$
$211$	6.96636e6			0.741581			0.370791	+	0.928717i	$0.379087\pi$
$212$		−	3.50838e6i		−	0.368213i
$213$	−5.59116e6	−	3.62667e6i	−0.578580	−	0.375292i
$214$	4.63877e6			0.473327
$215$		−	5.04960e6i		−	0.508091i
$216$	1.43959e6	−	9.18492e6i	0.142849	−	0.911411i
$217$	33267.2			0.00325564
$218$			5.49850e6i			0.530731i
$219$	6.28390e6	−	9.68774e6i	0.598270	−	0.922338i
$220$	2.97905e6			0.279775
$221$		−	9.98286e6i		−	0.924865i
$222$	5.85947e6	+	3.80071e6i	0.535549	+	0.347381i
$223$	8.43280e6			0.760427			0.380213	−	0.924899i	$-0.375851\pi$
$223$	8.43280e6			0.760427			0.380213	+	0.924899i	$0.375851\pi$
$224$			2.10294e6i			0.187104i
$225$	−3.93816e6	−	8.81975e6i	−0.345737	−	0.774299i
$226$	2.44526e6			0.211836
$227$		−	4.98087e6i		−	0.425821i	−0.977072	−	0.212911i	$-0.931706\pi$
$227$		−	4.98087e6i		−	0.425821i	0.977072	−	0.212911i	$-0.0682943\pi$
$228$	−6.93813e6	+	1.06964e7i	−0.585380	+	0.902467i
$229$	−1.03695e7			−0.863481			−0.431740	−	0.901998i	$-0.642100\pi$
$229$	−1.03695e7			−0.863481			−0.431740	+	0.901998i	$0.642100\pi$
$230$		−	534149.i		−	0.0439014i
$231$	1.89174e6	+	1.22706e6i	0.153470	+	0.0995477i
$232$	−1.42070e7			−1.13773
$233$			1.04446e7i			0.825705i	0.910798	+	0.412853i	$0.135468\pi$
$233$			1.04446e7i			0.825705i	−0.910798	+	0.412853i	$0.864532\pi$
$234$	−5.31286e6	+	2.37228e6i	−0.414649	+	0.185147i
$235$	2.30724e6			0.177783
$236$			5.33626e6i			0.405976i
$237$	6.95774e6	−	1.07266e7i	0.522665	−	0.805780i
$238$	1.44590e6			0.107253
$239$		−	1.91572e7i		−	1.40326i	−0.712542	−	0.701630i	$-0.752456\pi$
$239$		−	1.91572e7i		−	1.40326i	0.712542	−	0.701630i	$-0.247544\pi$
$240$	950634.	+	616623.i	0.0687669	+	0.0446053i
$241$	−9.28117e6			−0.663058			−0.331529	−	0.943445i	$-0.607564\pi$
$241$	−9.28117e6			−0.663058			−0.331529	+	0.943445i	$0.607564\pi$
$242$			199345.i			0.0140656i
$243$	−3.75097e6	−	1.38500e7i	−0.261411	−	0.965228i
$244$	5.07726e6			0.349510
$245$			5.54685e6i			0.377179i
$246$	−2.52073e6	+	3.88614e6i	−0.169325	+	0.261044i
$247$	1.92427e7			1.27695
$248$			253675.i			0.0166312i
$249$	2.15566e7	+	1.39825e7i	1.39631	+	0.905708i
$250$	−6.07939e6			−0.389081
$251$			619818.i			0.0391961i	0.999808	+	0.0195981i	$0.00623866\pi$
$251$			619818.i			0.0391961i	−0.999808	+	0.0195981i	$0.993761\pi$
$252$	834712.	+	1.86939e6i	0.0521597	+	0.116815i
$253$	−3.42044e6			−0.211213
$254$		−	1.58430e7i		−	0.966799i
$255$	3.86930e6	−	5.96521e6i	0.233352	−	0.359753i
$256$	−1.35372e7			−0.806880
$257$			1.51755e7i			0.894011i	0.894531	+	0.447006i	$0.147510\pi$
$257$			1.51755e7i			0.894011i	−0.894531	+	0.447006i	$0.852490\pi$
$258$	1.01389e7	+	6.57654e6i	0.590380	+	0.382946i
$259$	−3.70902e6			−0.213481
$260$		−	4.08234e6i		−	0.232268i
$261$	−2.00216e7	+	8.93995e6i	−1.12610	+	0.502821i
$262$	−4.90626e6			−0.272802
$263$		−	2.39966e7i		−	1.31912i	−0.751653	−	0.659559i	$-0.770743\pi$
$263$		−	2.39966e7i		−	1.31912i	0.751653	−	0.659559i	$-0.229257\pi$
$264$	−9.35684e6	+	1.44252e7i	−0.508531	+	0.783990i
$265$	−3.77144e6			−0.202661
$266$			2.78708e6i			0.148083i
$267$	1.41525e7	+	9.17993e6i	0.743531	+	0.482287i
$268$	−2.44902e7			−1.27230
$269$			1.93942e7i			0.996356i	0.867075	+	0.498178i	$0.165997\pi$
$269$			1.93942e7i			0.996356i	−0.867075	+	0.498178i	$0.834003\pi$
$270$	−4.09415e6	−	641692.i	−0.208004	−	0.0326013i
$271$	−2.06201e7			−1.03606			−0.518028	−	0.855364i	$-0.673334\pi$
$271$	−2.06201e7			−1.03606			−0.518028	+	0.855364i	$0.673334\pi$
$272$		−	4.65275e6i		−	0.231208i
$273$	1.68151e6	−	2.59234e6i	0.0826440	−	0.127410i
$274$	507599.			0.0246757
$275$			1.78636e7i			0.858955i
$276$	−2.60546e6	−	1.69001e6i	−0.123924	−	0.0803828i
$277$	2.60702e7			1.22661			0.613303	−	0.789848i	$-0.289840\pi$
$277$	2.60702e7			1.22661			0.613303	+	0.789848i	$0.289840\pi$
$278$		−	6.42514e6i		−	0.299053i
$279$	159628.	+	357498.i	0.00735018	+	0.0164612i
$280$	1.42595e6			0.0649576
$281$		−	3.32777e6i		−	0.149981i	−0.997184	−	0.0749903i	$-0.976107\pi$
$281$		−	3.32777e6i		−	0.149981i	0.997184	−	0.0749903i	$-0.0238926\pi$
$282$	−3.00492e6	+	4.63262e6i	−0.133994	+	0.206576i
$283$	7.58146e6			0.334498			0.167249	−	0.985915i	$-0.446512\pi$
$283$	7.58146e6			0.334498			0.167249	+	0.985915i	$0.446512\pi$
$284$			1.11906e7i			0.488538i
$285$	1.14984e7	+	7.45835e6i	0.496708	+	0.322187i
$286$	1.07607e7			0.459983
$287$		−	2.45991e6i		−	0.104058i
$288$	−2.25988e7	+	1.00907e7i	−0.946035	+	0.422420i
$289$	−5.05837e6			−0.209564
$290$			6.33273e6i			0.259655i
$291$	−1.32743e7	+	2.04647e7i	−0.538684	+	0.830477i
$292$	−1.93898e7			−0.778799
$293$		−	1.64984e6i		−	0.0655903i	−0.999462	−	0.0327951i	$-0.989559\pi$
$293$		−	1.64984e6i		−	0.0655903i	0.999462	−	0.0327951i	$-0.0104409\pi$
$294$	−1.11373e7	−	7.22414e6i	−0.438266	−	0.284279i
$295$	5.73637e6			0.223445
$296$		−	2.82827e7i		−	1.09055i
$297$	−4.10909e6	+	2.62170e7i	−0.156847	+	1.00072i
$298$	1.79012e7			0.676446
$299$			4.68720e6i			0.175348i
$300$	−8.82628e6	+	1.36073e7i	−0.326899	+	0.503973i
$301$	−6.41788e6			−0.235338
$302$			1.40227e7i			0.509110i
$303$	−8.11066e6	−	5.26093e6i	−0.291560	−	0.189119i
$304$	8.96852e6			0.319227
$305$		−	5.45795e6i		−	0.192367i
$306$	6.93798e6	+	1.55380e7i	0.242141	+	0.542290i
$307$	−8.04212e6			−0.277943			−0.138971	−	0.990296i	$-0.544380\pi$
$307$	−8.04212e6			−0.277943			−0.138971	+	0.990296i	$0.544380\pi$
$308$		−	3.78627e6i		−	0.129586i
$309$	3.15942e6	−	4.87080e6i	0.107086	−	0.165092i
$310$	113075.			0.00379561
$311$		−	1.33942e7i		−	0.445282i	−0.974900	−	0.222641i	$-0.928532\pi$
$311$		−	1.33942e7i		−	0.445282i	0.974900	−	0.222641i	$-0.0714678\pi$
$312$	1.97676e7	+	1.28222e7i	0.650864	+	0.422180i
$313$	−2.56635e7			−0.836917			−0.418458	−	0.908236i	$-0.637429\pi$
$313$	−2.56635e7			−0.836917			−0.418458	+	0.908236i	$0.637429\pi$
$314$			7.79948e6i			0.251928i
$315$	2.00955e6	−	897298.i	0.0642937	−	0.0287082i
$316$	−2.14691e7			−0.680380
$317$		−	1.40072e7i		−	0.439718i	−0.975532	−	0.219859i	$-0.929440\pi$
$317$		−	1.40072e7i		−	0.439718i	0.975532	−	0.219859i	$-0.0705597\pi$
$318$	4.91188e6	−	7.57252e6i	0.152745	−	0.235483i
$319$	4.05518e7			1.24922
$320$			4.46201e6i			0.136170i
$321$	−2.43234e7	−	1.57772e7i	−0.735376	−	0.476997i
$322$	−678886.			−0.0203343
$323$		−	5.62773e7i		−	1.67003i
$324$	−1.60837e7	+	1.79401e7i	−0.472879	+	0.527460i
$325$	2.44794e7			0.713100
$326$		−	598093.i		−	0.0172630i
$327$	1.87013e7	−	2.88314e7i	0.534847	−	0.824560i
$328$	1.87578e7			0.531569
$329$		−	2.93243e6i		−	0.0823455i
$330$	6.43000e6	+	4.17078e6i	0.178924	+	0.116058i
$331$	−3.52750e7			−0.972708			−0.486354	−	0.873762i	$-0.661674\pi$
$331$	−3.52750e7			−0.972708			−0.486354	+	0.873762i	$0.661674\pi$
$332$		−	4.31450e7i		−	1.17901i
$333$	−1.77973e7	−	3.98581e7i	−0.481971	−	1.07940i
$334$	3.33179e7			0.894208
$335$			2.63265e7i			0.700259i
$336$	783708.	−	1.20822e6i	0.0206603	−	0.0318515i
$337$	−2.65892e7			−0.694730			−0.347365	−	0.937730i	$-0.612924\pi$
$337$	−2.65892e7			−0.694730			−0.347365	+	0.937730i	$0.612924\pi$
$338$			6.10593e6i			0.158125i
$339$	−1.28217e7	−	8.31673e6i	−0.329114	−	0.213478i
$340$	−1.19392e7			−0.303767
$341$		−	724078.i		−	0.0182609i
$342$	−2.99507e7	+	1.33734e7i	−0.748735	+	0.334322i
$343$	1.43374e7			0.355294
$344$		−	4.89388e7i		−	1.20220i
$345$	−1.81673e6	+	2.80081e6i	−0.0442419	+	0.0682066i
$346$	−4.18112e7			−1.00940
$347$			3.05731e7i			0.731730i	0.930668	+	0.365865i	$0.119227\pi$
$347$			3.05731e7i			0.731730i	−0.930668	+	0.365865i	$0.880773\pi$
$348$	3.08896e7	+	2.00364e7i	0.732950	+	0.475424i
$349$	4.03285e6			0.0948714			0.0474357	−	0.998874i	$-0.484895\pi$
$349$	4.03285e6			0.0948714			0.0474357	+	0.998874i	$0.484895\pi$
$350$			3.54555e6i			0.0826951i
$351$	3.59265e7	+	5.63090e6i	0.830795	+	0.130214i
$352$	4.57717e7			1.04947
$353$			1.48882e7i			0.338469i	0.985576	+	0.169235i	$0.0541296\pi$
$353$			1.48882e7i			0.338469i	−0.985576	+	0.169235i	$0.945870\pi$
$354$	−7.47097e6	+	1.15178e7i	−0.168410	+	0.259633i
$355$	1.20297e7			0.268886
$356$		−	2.83259e7i		−	0.627818i
$357$	−7.58159e6	−	4.91775e6i	−0.166631	−	0.108084i
$358$	3.28532e7			0.716026
$359$			1.41898e6i			0.0306686i	0.999882	+	0.0153343i	$0.00488125\pi$
$359$			1.41898e6i			0.0306686i	−0.999882	+	0.0153343i	$0.995119\pi$
$360$	6.84224e6	+	1.53236e7i	0.146653	+	0.328438i
$361$	6.14326e7			1.30580
$362$			1.75420e7i			0.369789i
$363$	678007.	−	1.04527e6i	0.0141747	−	0.0218528i
$364$	−5.18852e6			−0.107582
$365$			2.08436e7i			0.428642i
$366$	1.09588e7	+	7.10836e6i	0.223522	+	0.144986i
$367$	−9.46597e7			−1.91499			−0.957496	−	0.288445i	$-0.906862\pi$
$367$	−9.46597e7			−1.91499			−0.957496	+	0.288445i	$0.906862\pi$
$368$			2.18458e6i			0.0438354i
$369$	2.64349e7	−	1.18036e7i	0.526136	−	0.234928i
$370$	−1.26069e7			−0.248888
$371$			4.79338e6i			0.0938685i
$372$	357762.	−	551554.i	0.00694969	−	0.0107142i
$373$	2.71019e7			0.522244			0.261122	−	0.965306i	$-0.415908\pi$
$373$	2.71019e7			0.522244			0.261122	+	0.965306i	$0.415908\pi$
$374$		−	3.14708e7i		−	0.601579i
$375$	3.18773e7	+	2.06771e7i	0.604489	+	0.392098i
$376$	2.23609e7			0.420654
$377$		−	5.55702e7i		−	1.03709i
$378$	−815569.	+	5.20354e6i	−0.0151003	+	0.0963437i
$379$	1.06346e8			1.95346			0.976730	−	0.214471i	$-0.0688027\pi$
$379$	1.06346e8			1.95346			0.976730	+	0.214471i	$0.0688027\pi$
$380$		−	2.30137e7i		−	0.419408i
$381$	−5.38847e7	+	8.30728e7i	−0.974296	+	1.50205i
$382$	1.01748e7			0.182531
$383$		−	6.38467e7i		−	1.13643i	−0.822880	−	0.568215i	$-0.807634\pi$
$383$		−	6.38467e7i		−	1.13643i	0.822880	−	0.568215i	$-0.192366\pi$
$384$	4.02586e7	+	2.61135e7i	0.710993	+	0.461182i
$385$	−4.07016e6			−0.0713230
$386$		−	6.06089e7i		−	1.05384i
$387$	−3.07954e7	−	6.89682e7i	−0.531316	−	1.18992i
$388$	4.09598e7			0.701233
$389$			3.66826e7i			0.623177i	0.950217	+	0.311588i	$0.100861\pi$
$389$			3.66826e7i			0.623177i	−0.950217	+	0.311588i	$0.899139\pi$
$390$	5.71544e6	−	8.81136e6i	0.0963509	−	0.148542i
$391$	1.37082e7			0.229325
$392$			5.37579e7i			0.892450i
$393$	2.57260e7	+	1.66870e7i	0.423833	+	0.274917i
$394$	4.40988e7			0.721004
$395$			2.30788e7i			0.374474i
$396$	4.06883e7	−	1.81680e7i	0.655215	−	0.292564i
$397$	−5.34559e7			−0.854327			−0.427164	−	0.904174i	$-0.640487\pi$
$397$	−5.34559e7			−0.854327			−0.427164	+	0.904174i	$0.640487\pi$
$398$			2.18832e7i			0.347105i
$399$	9.47932e6	−	1.46141e7i	0.149231	−	0.230066i
$400$	1.14092e7			0.178269
$401$			5.54961e7i			0.860655i	0.902673	+	0.430328i	$0.141602\pi$
$401$			5.54961e7i			0.860655i	−0.902673	+	0.430328i	$0.858398\pi$
$402$	−5.28599e7	−	3.42873e7i	−0.813670	−	0.527783i
$403$	−992241.			−0.0151601
$404$			1.62333e7i			0.246186i
$405$	1.92852e7	+	1.72896e7i	0.290308	+	0.260268i
$406$	8.04869e6			0.120267
$407$			8.07289e7i			1.19742i
$408$	3.74998e7	−	5.78125e7i	0.552138	−	0.851219i
$409$	−7.66483e7			−1.12030			−0.560148	−	0.828393i	$-0.689256\pi$
$409$	−7.66483e7			−1.12030			−0.560148	+	0.828393i	$0.689256\pi$
$410$		−	8.36123e6i		−	0.121316i
$411$	−2.66160e6	−	1.72643e6i	−0.0383369	−	0.0248670i
$412$	−9.74881e6			−0.139399
$413$		−	7.29074e6i		−	0.103495i
$414$	−3.25755e6	−	7.29548e6i	−0.0459082	−	0.102814i
$415$	−4.63800e7			−0.648913
$416$		−	6.27233e7i		−	0.871262i
$417$	−2.18530e7	+	3.36902e7i	−0.301372	+	0.464618i
$418$	6.06622e7			0.830595
$419$			1.04857e8i			1.42546i	0.701438	+	0.712730i	$0.252542\pi$
$419$			1.04857e8i			1.42546i	−0.701438	+	0.712730i	$0.747458\pi$
$420$	−3.10038e6	−	2.01104e6i	−0.0418472	−	0.0271440i
$421$	−1.05549e8			−1.41452			−0.707259	−	0.706955i	$-0.750068\pi$
$421$	−1.05549e8			−1.41452			−0.707259	+	0.706955i	$0.750068\pi$
$422$		−	3.00948e7i		−	0.400455i
$423$	3.15126e7	−	1.40709e7i	0.416355	−	0.185909i
$424$	−3.65513e7			−0.479519
$425$		−	7.15925e7i		−	0.932612i
$426$	−1.56673e7	+	2.41539e7i	−0.202658	+	0.312434i
$427$	−6.93688e6			−0.0891005
$428$			4.86828e7i			0.620932i
$429$	−5.64238e7	−	3.65990e7i	−0.714645	−	0.463550i
$430$	−2.18143e7			−0.274370
$431$		−	4.71907e7i		−	0.589420i	−0.955587	−	0.294710i	$-0.904777\pi$
$431$		−	4.71907e7i		−	0.589420i	0.955587	−	0.294710i	$-0.0952230\pi$
$432$	1.67444e7	+	2.62442e6i	0.207692	+	0.0325523i
$433$	−8.99217e7			−1.10765			−0.553823	−	0.832635i	$-0.686832\pi$
$433$	−8.99217e7			−1.10765			−0.553823	+	0.832635i	$0.686832\pi$
$434$		−	143715.i		−	0.00175805i
$435$	2.15387e7	−	3.32057e7i	0.261668	−	0.403408i
$436$	−5.77055e7			−0.696238
$437$			2.64236e7i			0.316626i
$438$	−4.18511e7	−	2.71465e7i	−0.498064	−	0.323066i
$439$	−1.43206e8			−1.69265			−0.846325	−	0.532667i	$-0.821190\pi$
$439$	−1.43206e8			−1.69265			−0.846325	+	0.532667i	$0.821190\pi$
$440$		−	3.10366e7i		−	0.364347i
$441$	3.38279e7	+	7.57597e7i	0.394420	+	0.883329i
$442$	−4.31261e7			−0.499428
$443$		−	1.20631e8i		−	1.38754i	−0.720195	−	0.693772i	$-0.755948\pi$
$443$		−	1.20631e8i		−	1.38754i	0.720195	−	0.693772i	$-0.244052\pi$
$444$	−3.98876e7	+	6.14938e7i	−0.455711	+	0.702558i
$445$	−3.04498e7			−0.345544
$446$		−	3.64298e7i		−	0.410631i
$447$	−9.38650e7	−	6.08850e7i	−1.05095	−	0.681692i
$448$	5.67106e6			0.0630711
$449$			1.29753e8i			1.43344i	0.697360	+	0.716721i	$0.254358\pi$
$449$			1.29753e8i			1.43344i	−0.697360	+	0.716721i	$0.745642\pi$
$450$	−3.81014e7	+	1.70129e7i	−0.418123	+	0.186698i
$451$	−5.35413e7			−0.583660
$452$			2.56624e7i			0.277896i
$453$	4.76937e7	−	7.35283e7i	0.513058	−	0.790970i
$454$	−2.15174e7			−0.229944
$455$			5.57756e6i			0.0592120i
$456$	1.11438e8	+	7.22835e7i	1.17527	+	0.762333i
$457$	−1.56109e7			−0.163560			−0.0817802	−	0.996650i	$-0.526061\pi$
$457$	−1.56109e7			−0.163560			−0.0817802	+	0.996650i	$0.526061\pi$
$458$			4.47965e7i			0.466281i
$459$	1.64682e7	−	1.05071e8i	0.170297	−	1.08654i
$460$	5.60577e6			0.0575919
$461$			1.73397e8i			1.76986i	0.465725	+	0.884930i	$0.345794\pi$
$461$			1.73397e8i			1.76986i	−0.465725	+	0.884930i	$0.654206\pi$
$462$	5.30093e6	−	8.17232e6i	0.0537559	−	0.0828742i
$463$	1.09977e8			1.10805			0.554023	−	0.832502i	$-0.313092\pi$
$463$	1.09977e8			1.10805			0.554023	+	0.832502i	$0.313092\pi$
$464$		−	2.58998e7i		−	0.259265i
$465$	−592909.	−	384587.i	−0.00589697	−	0.00382504i
$466$	4.51209e7			0.445882
$467$			1.83183e8i			1.79860i	0.437331	+	0.899301i	$0.355924\pi$
$467$			1.83183e8i			1.79860i	−0.437331	+	0.899301i	$0.644076\pi$
$468$	−2.48965e7	−	5.57572e7i	−0.242885	−	0.543956i
$469$	3.34601e7			0.324346
$470$		−	9.96730e6i		−	0.0960028i
$471$	2.65274e7	−	4.08966e7i	0.253882	−	0.391403i
$472$	5.55946e7			0.528697
$473$			1.39689e8i			1.32001i
$474$	−4.63390e7	−	3.00575e7i	−0.435122	−	0.282240i
$475$	1.38000e8			1.28765
$476$			1.51744e7i			0.140699i
$477$	−5.15109e7	+	2.30004e7i	−0.474618	+	0.211924i
$478$	−8.27592e7			−0.757762
$479$			5.76977e7i			0.524991i	0.964933	+	0.262495i	$0.0845455\pi$
$479$			5.76977e7i			0.524991i	−0.964933	+	0.262495i	$0.915455\pi$
$480$	2.43112e7	−	3.74800e7i	0.219828	−	0.338903i
$481$	1.10627e8			0.994090
$482$			4.00947e7i			0.358052i
$483$	3.55974e6	+	2.30901e6i	0.0315920	+	0.0204920i
$484$	−2.09208e6			−0.0184519
$485$		−	4.40309e7i		−	0.385951i
$486$	−5.98320e7	+	1.62042e7i	−0.521224	+	0.141162i
$487$	1.27288e8			1.10205			0.551026	−	0.834488i	$-0.314236\pi$
$487$	1.27288e8			1.10205			0.551026	+	0.834488i	$0.314236\pi$
$488$		−	5.28963e7i		−	0.455162i
$489$	−2.03422e6	+	3.13610e6i	−0.0173968	+	0.0268203i
$490$	2.39624e7			0.203677
$491$			2.00554e8i			1.69429i	0.531363	+	0.847144i	$0.321680\pi$
$491$			2.00554e8i			1.69429i	−0.531363	+	0.847144i	$0.678320\pi$
$492$	−4.07842e7	−	2.64544e7i	−0.342449	−	0.222128i
$493$	−1.62521e8			−1.35634
$494$		−	8.31286e7i		−	0.689556i
$495$	−1.95302e7	−	4.37390e7i	−0.161024	−	0.360623i
$496$	−462458.			−0.00378990
$497$		−	1.52893e7i		−	0.124543i
$498$	6.04048e7	−	9.31246e7i	0.489084	−	0.754009i
$499$	7.79986e7			0.627748			0.313874	−	0.949465i	$-0.398373\pi$
$499$	7.79986e7			0.627748			0.313874	+	0.949465i	$0.398373\pi$
$500$		−	6.38018e7i		−	0.510415i
$501$	−1.74703e8	−	1.13320e8i	−1.38927	−	0.901142i
$502$	2.67762e6			0.0211660
$503$		−	1.89658e8i		−	1.49028i	−0.666907	−	0.745141i	$-0.732382\pi$
$503$		−	1.89658e8i		−	1.49028i	0.666907	−	0.745141i	$-0.267618\pi$
$504$	1.94758e7	−	8.69627e6i	0.152126	−	0.0679268i
$505$	1.74505e7			0.135498
$506$			1.47763e7i			0.114055i
$507$	2.07673e7	−	3.20165e7i	0.159352	−	0.245669i
$508$	1.66269e8			1.26829
$509$			2.03629e8i			1.54414i	0.635537	+	0.772071i	$0.280779\pi$
$509$			2.03629e8i			1.54414i	−0.635537	+	0.772071i	$0.719221\pi$
$510$	−2.57698e7	−	1.67154e7i	−0.194267	−	0.126010i
$511$	2.64916e7			0.198539
$512$		−	5.52642e7i		−	0.411751i
$513$	2.02532e8	+	3.17436e7i	1.50017	+	0.235128i
$514$	6.55582e7			0.482767
$515$			1.04798e7i			0.0767238i
$516$	−6.90192e7	+	1.06405e8i	−0.502367	+	0.774487i
$517$	−6.38259e7			−0.461876
$518$			1.60230e7i			0.115280i
$519$	2.19237e8	+	1.42207e8i	1.56824	+	1.01723i
$520$	−4.25310e7			−0.302479
$521$		−	1.44246e8i		−	1.01998i	−0.860180	−	0.509990i	$-0.829649\pi$
$521$		−	1.44246e8i		−	1.01998i	0.860180	−	0.509990i	$-0.170351\pi$
$522$	3.86207e7	+	8.64933e7i	0.271524	+	0.608095i
$523$	−9.08079e7			−0.634773			−0.317387	−	0.948296i	$-0.602805\pi$
$523$	−9.08079e7			−0.634773			−0.317387	+	0.948296i	$0.602805\pi$
$524$		−	5.14901e7i		−	0.357874i
$525$	1.20590e7	−	1.85911e7i	0.0833363	−	0.128478i
$526$	−1.03666e8			−0.712325
$527$			2.90192e6i			0.0198268i
$528$	−2.62977e7	−	1.70578e7i	−0.178655	−	0.115884i
$529$	−6.43634e6			−0.0434783
$530$			1.62927e7i			0.109437i
$531$	7.83482e7	−	3.49837e7i	0.523293	−	0.233659i
$532$	−2.92497e7			−0.194262
$533$			7.33705e7i			0.484551i
$534$	3.96574e7	−	6.11389e7i	0.260436	−	0.401507i
$535$	5.23330e7			0.341755
$536$			2.55146e8i			1.65689i
$537$	−1.72266e8	−	1.11739e8i	−1.11244	−	0.721578i
$538$	8.37830e7			0.538033
$539$		−	1.53444e8i		−	0.979905i
$540$	6.73441e6	−	4.29672e7i	0.0427679	−	0.272870i
$541$	−2.05882e8			−1.30025			−0.650124	−	0.759828i	$-0.725283\pi$
$541$	−2.05882e8			−1.30025			−0.650124	+	0.759828i	$0.725283\pi$
$542$			8.90791e7i			0.559471i
$543$	5.96635e7	−	9.19818e7i	0.372657	−	0.574516i
$544$	−1.83441e8			−1.13946
$545$			6.20322e7i			0.383202i
$546$	−1.11990e7	−	7.26414e6i	−0.0688017	−	0.0446279i
$547$	6.21481e7			0.379722			0.189861	−	0.981811i	$-0.439196\pi$
$547$	6.21481e7			0.379722			0.189861	+	0.981811i	$0.439196\pi$
$548$			5.32713e6i			0.0323707i
$549$	−3.32858e7	−	7.45455e7i	−0.201160	−	0.450510i
$550$	7.71708e7			0.463837
$551$		−	3.13271e8i		−	1.87269i
$552$	−1.76071e7	+	2.71444e7i	−0.104681	+	0.161385i
$553$	2.93324e7			0.173449
$554$		−	1.12624e8i		−	0.662369i
$555$	6.61046e7	+	4.28784e7i	0.386681	+	0.250818i
$556$	6.74303e7			0.392311
$557$		−	2.72647e8i		−	1.57774i	−0.614561	−	0.788870i	$-0.710667\pi$
$557$		−	2.72647e8i		−	1.57774i	0.614561	−	0.788870i	$-0.289333\pi$
$558$	1.54439e6	−	689597.i	0.00888905	−	0.00396910i
$559$	1.91422e8			1.09587
$560$			2.59955e6i			0.0148025i
$561$	−1.07038e8	+	1.65017e8i	−0.606244	+	0.934633i
$562$	−1.43760e7			−0.0809897
$563$		−	1.40705e8i		−	0.788467i	−0.919010	−	0.394233i	$-0.871010\pi$
$563$		−	1.40705e8i		−	0.788467i	0.919010	−	0.394233i	$-0.128990\pi$
$564$	−4.86182e7	−	3.15360e7i	−0.270995	−	0.175780i
$565$	2.75865e7			0.152951
$566$		−	3.27520e7i		−	0.180629i
$567$	2.19746e7	−	2.45109e7i	0.120551	−	0.134465i
$568$	1.16587e8			0.636216
$569$		−	1.03800e8i		−	0.563457i	−0.959494	−	0.281729i	$-0.909092\pi$
$569$		−	1.03800e8i		−	0.563457i	0.959494	−	0.281729i	$-0.0909078\pi$
$570$	3.22202e7	−	4.96730e7i	0.173981	−	0.268223i
$571$	2.55241e8			1.37102			0.685508	−	0.728065i	$-0.259580\pi$
$571$	2.55241e8			1.37102			0.685508	+	0.728065i	$0.259580\pi$
$572$			1.12931e8i			0.603428i
$573$	−5.33516e7	−	3.46062e7i	−0.283585	−	0.183946i
$574$	−1.06269e7			−0.0561913
$575$			3.36145e7i			0.176816i
$576$	2.72119e7	+	6.09427e7i	0.142394	+	0.318900i
$577$	2.96904e7			0.154557			0.0772784	−	0.997010i	$-0.475377\pi$
$577$	2.96904e7			0.154557			0.0772784	+	0.997010i	$0.475377\pi$
$578$			2.18522e7i			0.113165i
$579$	−2.06141e8	+	3.17803e8i	−1.06201	+	1.63728i
$580$	−6.64605e7			−0.340627
$581$			5.89475e7i			0.300564i
$582$	8.84079e7	+	5.73453e7i	0.448458	+	0.290890i
$583$	1.04330e8			0.526509
$584$			2.02009e8i			1.01422i
$585$	−5.99379e7	+	2.67632e7i	−0.299388	+	0.133681i
$586$	−7.12733e6			−0.0354188
$587$		−	1.55896e8i		−	0.770763i	−0.922757	−	0.385381i	$-0.874070\pi$
$587$		−	1.55896e8i		−	0.770763i	0.922757	−	0.385381i	$-0.125930\pi$
$588$	7.58157e7	−	1.16883e8i	0.372930	−	0.574937i
$589$	−5.59365e6			−0.0273747
$590$		−	2.47812e7i		−	0.120661i
$591$	−2.31232e8	−	1.49987e8i	−1.12017	−	0.726595i
$592$	5.15604e7			0.248514
$593$		−	2.85683e8i		−	1.37000i	−0.728544	−	0.684999i	$-0.759803\pi$
$593$		−	2.85683e8i		−	1.37000i	0.728544	−	0.684999i	$-0.240197\pi$
$594$	1.13258e8	+	1.77513e7i	0.540392	+	0.0846976i
$595$	1.63122e7			0.0774391
$596$			1.87869e8i			0.887393i
$597$	7.44284e7	−	1.14745e8i	0.349797	−	0.539273i
$598$	2.02487e7			0.0946879
$599$			1.94295e7i			0.0904027i	0.998978	+	0.0452014i	$0.0143929\pi$
$599$			1.94295e7i			0.0904027i	−0.998978	+	0.0452014i	$0.985607\pi$
$600$	1.41764e8	+	9.19547e7i	0.656316	+	0.425716i
$601$	3.97241e8			1.82991			0.914957	−	0.403550i	$-0.132224\pi$
$601$	3.97241e8			1.82991			0.914957	+	0.403550i	$0.132224\pi$
$602$			2.77253e7i			0.127083i
$603$	1.60554e8	+	3.59571e8i	0.732268	+	1.63996i
$604$	−1.47165e8			−0.667875
$605$			2.24894e6i			0.0101558i
$606$	−2.27273e7	+	3.50381e7i	−0.102124	+	0.157443i
$607$	−3.06952e8			−1.37247			−0.686236	−	0.727379i	$-0.740738\pi$
$607$	−3.06952e8			−1.37247			−0.686236	+	0.727379i	$0.740738\pi$
$608$		−	3.53596e8i		−	1.57324i
$609$	−4.22034e7	−	2.73750e7i	−0.186851	−	0.121200i
$610$	−2.35784e7			−0.103878
$611$			8.74639e7i			0.383447i
$612$	−1.63068e8	+	7.28125e7i	−0.711401	+	0.317652i
$613$	−2.06330e8			−0.895738			−0.447869	−	0.894099i	$-0.647817\pi$
$613$	−2.06330e8			−0.895738			−0.447869	+	0.894099i	$0.647817\pi$
$614$			3.47421e7i			0.150090i
$615$	−2.84380e7	+	4.38421e7i	−0.122257	+	0.188481i
$616$	−3.94465e7			−0.168759
$617$			3.15294e8i			1.34233i	0.741307	+	0.671166i	$0.234206\pi$
$617$			3.15294e8i			1.34233i	−0.741307	+	0.671166i	$0.765794\pi$
$618$	−2.10419e7	−	1.36487e7i	−0.0891497	−	0.0578265i
$619$	8.23375e7			0.347157			0.173579	−	0.984820i	$-0.444467\pi$
$619$	8.23375e7			0.347157			0.173579	+	0.984820i	$0.444467\pi$
$620$			1.18669e6i			0.00497925i
$621$	−7.73221e6	+	4.93334e7i	−0.0322871	+	0.206000i
$622$	−5.78631e7			−0.240453
$623$			3.87007e7i			0.160050i
$624$	−2.33752e7	+	3.60370e7i	−0.0962060	+	0.148319i
$625$	1.38441e8			0.567055
$626$			1.10866e8i			0.451936i
$627$	−3.18083e8	−	2.06323e8i	−1.29044	−	0.837036i
$628$	−8.18537e7			−0.330491
$629$		−	3.23540e8i		−	1.30010i
$630$	−3.87634e6	−	8.68130e6i	−0.0155024	−	0.0347187i
$631$	−1.28548e8			−0.511655			−0.255827	−	0.966723i	$-0.582348\pi$
$631$	−1.28548e8			−0.511655			−0.255827	+	0.966723i	$0.582348\pi$
$632$			2.23671e8i			0.886049i
$633$	−1.02357e8	+	1.57802e8i	−0.403560	+	0.622159i
$634$	−6.05113e7			−0.237448
$635$		−	1.78735e8i		−	0.698054i
$636$	7.94719e7	+	5.15490e7i	0.308917	+	0.200377i
$637$	−2.10272e8			−0.813512
$638$		−	1.75184e8i		−	0.674579i
$639$	1.64303e8	−	7.33639e7i	0.629713	−	0.281177i
$640$	−8.66184e7			−0.330423
$641$			8.54896e7i			0.324593i	0.986742	+	0.162297i	$0.0518901\pi$
$641$			8.54896e7i			0.324593i	−0.986742	+	0.162297i	$0.948110\pi$
$642$	−6.81579e7	+	1.05077e8i	−0.257579	+	0.397104i
$643$	1.12241e8			0.422202			0.211101	−	0.977464i	$-0.432295\pi$
$643$	1.12241e8			0.422202			0.211101	+	0.977464i	$0.432295\pi$
$644$		−	7.12475e6i		−	0.0266755i
$645$	1.14384e8	+	7.41942e7i	0.426270	+	0.276497i
$646$	−2.43118e8			−0.901821
$647$			3.23520e8i			1.19451i	0.802053	+	0.597253i	$0.203741\pi$
$647$			3.23520e8i			1.19451i	−0.802053	+	0.597253i	$0.796259\pi$
$648$	1.86905e8	+	1.67564e8i	0.686903	+	0.615824i
$649$	−1.58687e8			−0.580506
$650$		−	1.05751e8i		−	0.385075i
$651$	−488798.	+	753568.i	−0.00177168	+	0.00273136i
$652$	6.27684e6			0.0226464
$653$			6.57744e7i			0.236220i	0.993001	+	0.118110i	$0.0376836\pi$
$653$			6.57744e7i			0.236220i	−0.993001	+	0.118110i	$0.962316\pi$
$654$	−1.24552e8	−	8.07899e7i	−0.445264	−	0.288818i
$655$	−5.53508e7			−0.196970
$656$			3.41961e7i			0.121134i
$657$	1.27117e8	+	2.84686e8i	0.448236	+	1.00385i
$658$	−1.26681e7			−0.0444667
$659$		−	4.64344e8i		−	1.62250i	−0.584701	−	0.811249i	$-0.698788\pi$
$659$		−	4.64344e8i		−	1.62250i	0.584701	−	0.811249i	$-0.301212\pi$
$660$	−4.37714e7	+	6.74813e7i	−0.152250	+	0.234721i
$661$	−5.33344e8			−1.84673			−0.923364	−	0.383926i	$-0.874572\pi$
$661$	−5.33344e8			−1.84673			−0.923364	+	0.383926i	$0.874572\pi$
$662$			1.52388e8i			0.525264i
$663$	2.26132e8	+	1.46679e8i	0.775927	+	0.503301i
$664$	−4.49497e8			−1.53540
$665$			3.14428e7i			0.106920i
$666$	−1.72188e8	+	7.68845e7i	−0.582880	+	0.260265i
$667$	7.63076e7			0.257152
$668$			3.49664e8i			1.17306i
$669$	−1.23904e8	+	1.91020e8i	−0.413816	+	0.637970i
$670$	1.13731e8			0.378141
$671$			1.50985e8i			0.499765i
$672$	−4.76358e7	−	3.08987e7i	−0.156973	−	0.101820i
$673$	6.63575e7			0.217693			0.108847	−	0.994059i	$-0.465284\pi$
$673$	6.63575e7			0.217693			0.108847	+	0.994059i	$0.465284\pi$
$674$			1.14866e8i			0.375155i
$675$	2.57649e8	+	4.03822e7i	0.837754	+	0.131304i
$676$	−6.40803e7			−0.207436
$677$		−	5.55365e8i		−	1.78983i	−0.446234	−	0.894916i	$-0.647235\pi$
$677$		−	5.55365e8i		−	1.78983i	0.446234	−	0.894916i	$-0.352765\pi$
$678$	−3.59284e7	+	5.53899e7i	−0.115279	+	0.177722i
$679$	−5.59619e7			−0.178765
$680$			1.24386e8i			0.395591i
$681$	1.12827e8	+	7.31844e7i	0.357248	+	0.231727i
$682$	−3.12802e6			−0.00986091
$683$			3.50394e8i			1.09975i	0.835246	+	0.549876i	$0.185325\pi$
$683$			3.50394e8i			1.09975i	−0.835246	+	0.549876i	$0.814675\pi$
$684$	−1.40351e8	−	3.14325e8i	−0.438579	−	0.982225i
$685$	5.72656e6			0.0178165
$686$		−	6.19377e7i		−	0.191859i
$687$	1.52360e8	−	2.34891e8i	0.469896	−	0.724428i
$688$	8.92171e7			0.273957
$689$		−	1.42969e8i		−	0.437105i
$690$	1.20995e7	+	7.84830e6i	0.0368317	+	0.0238907i
$691$	1.70978e8			0.518210			0.259105	−	0.965849i	$-0.416573\pi$
$691$	1.70978e8			0.518210			0.259105	+	0.965849i	$0.416573\pi$
$692$		−	4.38799e8i		−	1.32418i
$693$	−5.55909e7	+	2.48222e7i	−0.167034	+	0.0745832i
$694$	1.32076e8			0.395135
$695$		−	7.24862e7i		−	0.215924i
$696$	2.08745e8	−	3.21817e8i	0.619138	−	0.954511i
$697$	2.14580e8			0.633710
$698$		−	1.74219e7i		−	0.0512307i
$699$	−2.36592e8	−	1.53464e8i	−0.692736	−	0.449340i
$700$	−3.72097e7			−0.108483
$701$		−	6.41950e7i		−	0.186358i	−0.995649	−	0.0931788i	$-0.970297\pi$
$701$		−	6.41950e7i		−	0.186358i	0.995649	−	0.0931788i	$-0.0297028\pi$
$702$	2.43255e7	−	1.55203e8i	0.0703155	−	0.448630i
$703$	6.23647e8			1.79503
$704$		−	1.23434e8i		−	0.353766i
$705$	−3.39005e7	+	5.22636e7i	−0.0967473	+	0.149153i
$706$	6.43173e7			0.182774
$707$		−	2.21790e7i		−	0.0627601i
$708$	−1.20877e8	−	7.84061e7i	−0.340599	−	0.220928i
$709$	−2.25037e8			−0.631414			−0.315707	−	0.948857i	$-0.602242\pi$
$709$	−2.25037e8			−0.631414			−0.315707	+	0.948857i	$0.602242\pi$
$710$		−	5.19682e7i		−	0.145199i
$711$	1.40748e8	+	3.15214e8i	0.391591	+	0.876993i
$712$	−2.95107e8			−0.817599
$713$		−	1.36252e6i		−	0.00375902i
$714$	−2.12447e7	+	3.27525e7i	−0.0583656	+	0.0899809i
$715$	1.21399e8			0.332120
$716$			3.44787e8i			0.939316i
$717$	4.33949e8	+	2.81478e8i	1.17728	+	0.763638i
$718$	6.13002e6			0.0165611
$719$			1.97612e8i			0.531650i	0.964021	+	0.265825i	$0.0856444\pi$
$719$			1.97612e8i			0.531650i	−0.964021	+	0.265825i	$0.914356\pi$
$720$	−2.79355e7	+	1.24736e7i	−0.0748443	+	0.0334192i
$721$	1.33195e7			0.0355370
$722$		−	2.65389e8i		−	0.705134i
$723$	1.36369e8	−	2.10237e8i	0.360829	−	0.556281i
$724$	−1.84100e8			−0.485107
$725$		−	3.98524e8i		−	1.04578i
$726$	−4.51556e6	−	2.92900e6i	−0.0118005	−	0.00765436i
$727$	−2.57795e7			−0.0670921			−0.0335461	−	0.999437i	$-0.510680\pi$
$727$	−2.57795e7			−0.0670921			−0.0335461	+	0.999437i	$0.510680\pi$
$728$			5.40555e7i			0.140103i
$729$	3.68843e8	+	1.18532e8i	0.952047	+	0.305952i
$730$	9.00448e7			0.231467
$731$		−	5.59835e8i		−	1.43320i
$732$	−7.46006e7	+	1.15010e8i	−0.190199	+	0.293226i
$733$	2.42048e8			0.614595			0.307298	−	0.951613i	$-0.400575\pi$
$733$	2.42048e8			0.614595			0.307298	+	0.951613i	$0.400575\pi$
$734$			4.08931e8i			1.03410i
$735$	−1.25647e8	−	8.15003e7i	−0.316439	−	0.205257i
$736$	8.61300e7			0.216034
$737$		−	7.28278e8i		−	1.81926i
$738$	−5.09916e7	−	1.14199e8i	−0.126862	−	0.284114i
$739$	−1.07133e8			−0.265454			−0.132727	−	0.991153i	$-0.542373\pi$
$739$	−1.07133e8			−0.265454			−0.132727	+	0.991153i	$0.542373\pi$
$740$		−	1.32307e8i		−	0.326503i
$741$	−2.82734e8	+	4.35885e8i	−0.694903	+	1.07132i
$742$	2.07074e7			0.0506891
$743$			5.66021e8i			1.37996i	0.723829	+	0.689980i	$0.242380\pi$
$743$			5.66021e8i			1.37996i	−0.723829	+	0.689980i	$0.757620\pi$
$744$	−5.74624e6	−	3.72727e6i	−0.0139529	−	0.00905049i
$745$	2.01955e8			0.488412
$746$		−	1.17080e8i		−	0.282012i
$747$	−6.33465e8	+	2.82852e8i	−1.51971	+	0.678575i
$748$	3.30279e8			0.789180
$749$		−	6.65136e7i		−	0.158294i
$750$	8.93251e7	−	1.37710e8i	0.211734	−	0.326425i
$751$	4.51672e8			1.06636			0.533179	−	0.846002i	$-0.320997\pi$
$751$	4.51672e8			1.06636			0.533179	+	0.846002i	$0.320997\pi$
$752$			4.07647e7i			0.0958584i
$753$	−1.40401e7	−	9.10705e6i	−0.0328841	−	0.0213301i
$754$	−2.40064e8			−0.560032
$755$			1.58200e8i			0.367591i
$756$	−5.46099e7	−	8.55921e6i	−0.126388	−	0.0198093i
$757$	5.69900e8			1.31374			0.656872	−	0.754002i	$-0.271879\pi$
$757$	5.69900e8			1.31374			0.656872	+	0.754002i	$0.271879\pi$
$758$		−	4.59417e8i		−	1.05487i
$759$	5.02568e7	−	7.74797e7i	0.114939	−	0.177200i
$760$	−2.39764e8			−0.546189
$761$			4.83020e8i			1.09600i	0.836478	+	0.548001i	$0.184611\pi$
$761$			4.83020e8i			1.09600i	−0.836478	+	0.548001i	$0.815389\pi$
$762$	3.58875e8	+	2.32783e8i	0.811108	+	0.526121i
$763$	7.88409e7			0.177492
$764$			1.06782e8i			0.239452i
$765$	7.82719e7	+	1.75295e8i	0.174832	+	0.391547i
$766$	−2.75819e8			−0.613673
$767$			2.17457e8i			0.481933i
$768$	1.98903e8	−	3.06645e8i	0.439095	−	0.676942i
$769$	−2.23478e8			−0.491423			−0.245712	−	0.969343i	$-0.579022\pi$
$769$	−2.23478e8			−0.491423			−0.245712	+	0.969343i	$0.579022\pi$
$770$			1.75831e7i			0.0385145i
$771$	−3.43755e8	−	2.22975e8i	−0.750042	−	0.486511i
$772$	6.36076e8			1.38247
$773$		−	8.28554e8i		−	1.79383i	−0.442199	−	0.896917i	$-0.645801\pi$
$773$		−	8.28554e8i		−	1.79383i	0.442199	−	0.896917i	$-0.354199\pi$
$774$	−2.97943e8	+	1.33036e8i	−0.642556	+	0.286911i
$775$	−7.11590e6			−0.0152871
$776$		−	4.26731e8i		−	0.913206i
$777$	5.44970e7	−	8.40168e7i	0.116174	−	0.179103i
$778$	1.58469e8			0.336516
$779$			4.13618e8i			0.874957i
$780$	9.24732e7	+	5.99822e7i	0.194864	+	0.126398i
$781$	−3.32780e8			−0.698561
$782$		−	5.92196e7i		−	0.123836i
$783$	9.16710e7	−	5.84884e8i	0.190962	−	1.21838i
$784$	−9.80025e7			−0.203371
$785$			8.79910e7i			0.181899i
$786$	7.20882e7	−	1.11137e8i	0.148456	−	0.228870i
$787$	−7.61978e8			−1.56321			−0.781607	−	0.623771i	$-0.785600\pi$
$787$	−7.61978e8			−1.56321			−0.781607	+	0.623771i	$0.785600\pi$
$788$			4.62806e8i			0.945846i
$789$	5.43572e8	+	3.52585e8i	1.10669	+	0.717849i
$790$	9.97006e7			0.202216
$791$		−	3.50616e7i		−	0.0708439i
$792$	−1.89279e8	−	4.23902e8i	−0.381002	−	0.853277i
$793$	2.06902e8			0.414902
$794$			2.30930e8i			0.461338i
$795$	5.54141e7	−	8.54306e7i	0.110286	−	0.170025i
$796$	−2.29659e8			−0.455349
$797$		−	1.69905e8i		−	0.335608i	−0.985820	−	0.167804i	$-0.946333\pi$
$797$		−	1.69905e8i		−	0.335608i	0.985820	−	0.167804i	$-0.0536675\pi$
$798$	−6.31328e7	−	4.09508e7i	−0.124236	−	0.0805849i
$799$	2.55797e8			0.501483
$800$		−	4.49823e8i		−	0.878560i
$801$	−4.15888e8	+	1.85700e8i	−0.809242	+	0.361339i
$802$	2.39744e8			0.464755
$803$		−	5.76604e8i		−	1.11360i
$804$	3.59837e8	−	5.54753e8i	0.692370	−	1.06741i
$805$	−7.65896e6			−0.0146819
$806$			4.28649e6i			0.00818648i
$807$	−4.39317e8	−	2.84960e8i	−0.835906	−	0.542206i
$808$	1.69123e8			0.320604
$809$			3.14882e8i			0.594706i	0.954768	+	0.297353i	$0.0961038\pi$
$809$			3.14882e8i			0.594706i	−0.954768	+	0.297353i	$0.903896\pi$
$810$	7.46914e7	−	8.33123e7i	0.140545	−	0.156767i
$811$	−6.75287e8			−1.26598			−0.632989	−	0.774161i	$-0.718172\pi$
$811$	−6.75287e8			−1.26598			−0.632989	+	0.774161i	$0.718172\pi$
$812$			8.44691e7i			0.157772i
$813$	3.02973e8	−	4.67087e8i	0.563810	−	0.869212i
$814$	3.48750e8			0.646607
$815$		−	6.74748e6i		−	0.0124643i
$816$	1.05394e8	+	6.83634e7i	0.193975	+	0.125821i
$817$	1.07912e9			1.97881
$818$			3.31121e8i			0.604961i
$819$	3.40152e7	+	7.61791e7i	0.0619186	+	0.138671i
$820$	8.77492e7			0.159148
$821$			7.03872e8i			1.27193i	0.771717	+	0.635967i	$0.219398\pi$
$821$			7.03872e8i			1.27193i	−0.771717	+	0.635967i	$0.780602\pi$
$822$	−7.45820e6	+	1.14981e7i	−0.0134282	+	0.0207020i
$823$	−1.86537e8			−0.334630			−0.167315	−	0.985903i	$-0.553510\pi$
$823$	−1.86537e8			−0.334630			−0.167315	+	0.985903i	$0.553510\pi$
$824$			1.01566e8i			0.181538i
$825$	−4.04646e8	−	2.62471e8i	−0.720631	−	0.467433i
$826$	−3.14961e7			−0.0558877
$827$			8.30638e8i			1.46857i	0.678840	+	0.734286i	$0.262483\pi$
$827$			8.30638e8i			1.46857i	−0.678840	+	0.734286i	$0.737517\pi$
$828$	7.65644e7	−	3.41872e7i	0.134876	−	0.0602245i
$829$	−1.69495e8			−0.297504			−0.148752	−	0.988875i	$-0.547526\pi$
$829$	−1.69495e8			−0.297504			−0.148752	+	0.988875i	$0.547526\pi$
$830$			2.00362e8i			0.350414i
$831$	−3.83052e8	+	5.90542e8i	−0.667505	+	1.02908i
$832$	−1.69148e8			−0.293695
$833$			6.14964e8i			1.06393i
$834$	1.45542e8	+	9.44051e7i	0.250894	+	0.162741i
$835$	3.75881e8			0.645641
$836$			6.36636e8i			1.08961i
$837$	−1.04435e7	−	1.63684e6i	−0.0178102	−	0.00279146i
$838$	4.52983e8			0.769750
$839$		−	1.29727e8i		−	0.219656i	−0.993951	−	0.109828i	$-0.964970\pi$
$839$		−	1.29727e8i		−	0.219656i	0.993951	−	0.109828i	$-0.0350301\pi$
$840$	−2.09516e7	+	3.23006e7i	−0.0353492	+	0.0544970i
$841$	−3.09859e8			−0.520927
$842$			4.55973e8i			0.763841i
$843$	7.53807e7	+	4.88953e7i	0.125828	+	0.0816177i
$844$	3.15837e8			0.525335
$845$			6.88850e7i			0.114171i
$846$	−6.07864e7	−	1.36135e8i	−0.100391	−	0.224832i
$847$	2.85833e6			0.00470395
$848$		−	6.66344e7i		−	0.109272i
$849$	−1.11395e8	+	1.71735e8i	−0.182030	+	0.280631i
$850$	−3.09281e8			−0.503612
$851$			1.51910e8i			0.246489i
$852$	−2.53489e8	−	1.64424e8i	−0.409865	−	0.265857i
$853$	5.31553e8			0.856444			0.428222	−	0.903673i	$-0.359140\pi$
$853$	5.31553e8			0.856444			0.428222	+	0.903673i	$0.359140\pi$
$854$			2.99674e7i			0.0481144i
$855$	−3.37893e8	+	1.50875e8i	−0.540606	+	0.241389i
$856$	5.07191e8			0.808631
$857$			8.99535e8i			1.42914i	0.699563	+	0.714571i	$0.253378\pi$
$857$			8.99535e8i			1.42914i	−0.699563	+	0.714571i	$0.746622\pi$
$858$	−1.58108e8	+	2.43751e8i	−0.250318	+	0.385909i
$859$	−8.46320e8			−1.33523			−0.667613	−	0.744508i	$-0.732684\pi$
$859$	−8.46320e8			−1.33523			−0.667613	+	0.744508i	$0.732684\pi$
$860$		−	2.28936e8i		−	0.359931i
$861$	5.57220e7	+	3.61437e7i	0.0873005	+	0.0566270i
$862$	−2.03864e8			−0.318287
$863$		−	1.10091e9i		−	1.71286i	−0.516265	−	0.856429i	$-0.672678\pi$
$863$		−	1.10091e9i		−	1.71286i	0.516265	−	0.856429i	$-0.327322\pi$
$864$	1.03471e8	−	6.60171e8i	0.160427	−	1.02356i
$865$	−4.71700e8			−0.728815
$866$			3.88463e8i			0.598130i
$867$	7.43231e7	−	1.14582e8i	0.114042	−	0.175816i
$868$	1.50825e6			0.00230629
$869$		−	6.38435e8i		−	0.972876i
$870$	−1.43449e8	−	9.30473e7i	−0.217841	−	0.141301i
$871$	−9.97997e8			−1.51034
$872$			6.01192e8i			0.906700i
$873$	−2.68526e8	−	6.01381e8i	−0.403593	−	0.903872i
$874$	1.14150e8			0.170979
$875$			8.71702e7i			0.130120i
$876$	2.84896e8	−	4.39218e8i	0.423813	−	0.653383i
$877$	−6.95555e8			−1.03118			−0.515588	−	0.856837i	$-0.672426\pi$
$877$	−6.95555e8			−1.03118			−0.515588	+	0.856837i	$0.672426\pi$
$878$			6.18651e8i			0.914033i
$879$	3.73722e7	+	2.42413e7i	0.0550278	+	0.0356935i
$880$	5.65807e7			0.0830272
$881$		−	8.42384e8i		−	1.23192i	−0.787778	−	0.615960i	$-0.788768\pi$
$881$		−	8.42384e8i		−	1.23192i	0.787778	−	0.615960i	$-0.211232\pi$
$882$	3.27283e8	−	1.46137e8i	0.476999	−	0.212987i
$883$	−1.16198e9			−1.68779			−0.843893	−	0.536512i	$-0.819742\pi$
$883$	−1.16198e9			−1.68779			−0.843893	+	0.536512i	$0.819742\pi$
$884$		−	4.52598e8i		−	0.655173i
$885$	−8.42850e7	+	1.29940e8i	−0.121596	+	0.187462i
$886$	−5.21126e8			−0.749275
$887$			7.56398e8i			1.08388i	0.840418	+	0.541938i	$0.182309\pi$
$887$			7.56398e8i			1.08388i	−0.840418	+	0.541938i	$0.817691\pi$
$888$	6.40660e8	+	4.15561e8i	0.914932	+	0.593465i
$889$	−2.27167e8			−0.323325
$890$			1.31543e8i			0.186594i
$891$	−5.33492e8	−	4.78288e8i	−0.754215	−	0.676171i
$892$	3.82322e8			0.538685
$893$			4.93068e8i			0.692393i
$894$	−2.63024e8	+	4.05498e8i	−0.368114	+	0.567513i
$895$	3.70639e8			0.516990
$896$			1.10089e8i			0.153046i
$897$	−1.06174e8	−	6.88695e7i	−0.147110	−	0.0954222i
$898$	5.60536e8			0.774060
$899$			1.61537e7i			0.0222327i
$900$	−1.78546e8	−	3.99866e8i	−0.244920	−	0.548512i
$901$	−4.18129e8			−0.571658
$902$			2.31299e8i			0.315177i
$903$	9.42985e7	−	1.45378e8i	0.128068	−	0.197440i
$904$	2.67358e8			0.361900
$905$			1.97903e8i			0.266998i
$906$	−3.17643e8	−	2.06037e8i	−0.427125	−	0.277052i
$907$	−1.42095e9			−1.90439			−0.952194	−	0.305493i	$-0.901179\pi$
$907$	−1.42095e9			−1.90439			−0.952194	+	0.305493i	$0.901179\pi$
$908$		−	2.25820e8i		−	0.301651i
$909$	2.38341e8	−	1.06423e8i	0.317328	−	0.141692i
$910$	2.40951e7			0.0319746
$911$		−	5.86429e7i		−	0.0775640i	−0.999248	−	0.0387820i	$-0.987652\pi$
$911$		−	5.86429e7i		−	0.0775640i	0.999248	−	0.0387820i	$-0.0123478\pi$
$912$	−1.31775e8	+	2.03155e8i	−0.173720	+	0.267820i
$913$	1.28302e9			1.68586
$914$			6.74391e7i			0.0883229i
$915$	1.23633e8	+	8.01941e7i	0.161389	+	0.104684i
$916$	−4.70129e8			−0.611689
$917$			7.03491e7i			0.0912327i
$918$	−4.53908e8	−	7.11426e7i	−0.586731	−	0.0919606i
$919$	−1.18772e8			−0.153027			−0.0765133	−	0.997069i	$-0.524379\pi$
$919$	−1.18772e8			−0.153027			−0.0765133	+	0.997069i	$0.524379\pi$
$920$		−	5.84025e7i		−	0.0750011i
$921$	1.18164e8	−	1.82170e8i	0.151253	−	0.233184i
$922$	7.49077e8			0.955726
$923$			4.56026e8i			0.579941i
$924$	8.57666e7	+	5.56320e7i	0.108718	+	0.0705195i
$925$	7.93366e8			1.00242
$926$		−	4.75100e8i		−	0.598346i
$927$	6.39118e7	+	1.43134e8i	0.0802309	+	0.179682i
$928$	−1.02113e9			−1.27773
$929$		−	1.32142e9i		−	1.64813i	−0.566492	−	0.824067i	$-0.691700\pi$
$929$		−	1.32142e9i		−	1.64813i	0.566492	−	0.824067i	$-0.308300\pi$
$930$	−1.66142e6	+	2.56137e6i	−0.00206553	+	0.00318437i
$931$	−1.18539e9			−1.46896
$932$			4.73533e8i			0.584929i
$933$	3.03405e8	+	1.96802e8i	0.373575	+	0.242318i
$934$	7.91353e8			0.971247
$935$		−	3.55043e8i		−	0.434356i
$936$	−5.80895e8	+	2.59379e8i	−0.708386	+	0.316306i
$937$	4.40599e8			0.535580			0.267790	−	0.963477i	$-0.413707\pi$
$937$	4.40599e8			0.535580			0.267790	+	0.963477i	$0.413707\pi$
$938$		−	1.44548e8i		−	0.175147i
$939$	3.77076e8	−	5.81329e8i	0.455440	−	0.702142i
$940$	1.04605e8			0.125941
$941$			9.42725e8i			1.13140i	0.824611	+	0.565700i	$0.191394\pi$
$941$			9.42725e8i			1.13140i	−0.824611	+	0.565700i	$0.808606\pi$
$942$	−1.76674e8	−	1.14598e8i	−0.211358	−	0.137096i
$943$	−1.00750e8			−0.120147
$944$			1.01351e8i			0.120479i
$945$	−9.20098e6	+	5.87045e7i	−0.0109028	+	0.0695627i
$946$	6.03456e8			0.712808
$947$			9.25332e8i			1.08955i	0.838582	+	0.544775i	$0.183385\pi$
$947$			9.25332e8i			1.08955i	−0.838582	+	0.544775i	$0.816615\pi$
$948$	3.15447e8	−	4.86317e8i	0.370255	−	0.570814i
$949$	−7.90150e8			−0.924509
$950$		−	5.96160e8i		−	0.695332i
$951$	3.17291e8	+	2.05809e8i	0.368907	+	0.239289i
$952$	1.58091e8			0.183230
$953$		−	6.06628e8i		−	0.700881i	−0.936585	−	0.350440i	$-0.886032\pi$
$953$		−	6.06628e8i		−	0.700881i	0.936585	−	0.350440i	$-0.113968\pi$
$954$	9.93621e7	+	2.22528e8i	0.114439	+	0.256294i
$955$	1.14789e8			0.131792
$956$		−	8.68539e8i		−	0.994067i
$957$	−5.95831e8	+	9.18579e8i	−0.679810	+	1.04805i
$958$	2.49255e8			0.283496
$959$		−	7.27827e6i		−	0.00825225i
$960$	−1.01073e8	−	6.55607e7i	−0.114241	−	0.0741019i
$961$	−8.87215e8			−0.999675
$962$		−	4.77910e8i		−	0.536810i
$963$	7.14772e8	−	3.19157e8i	0.800366	−	0.357376i
$964$	−4.20785e8			−0.469709
$965$		−	6.83769e8i		−	0.760899i
$966$	9.97493e6	−	1.53781e7i	0.0110657	−	0.0170597i
$967$	5.15943e8			0.570587			0.285294	−	0.958440i	$-0.407909\pi$
$967$	5.15943e8			0.570587			0.285294	+	0.958440i	$0.407909\pi$
$968$			2.17959e7i			0.0240297i
$969$	1.27479e9	+	8.26887e8i	1.40110	+	0.908814i
$970$	−1.90214e8			−0.208414
$971$			4.34215e8i			0.474293i	0.971474	+	0.237147i	$0.0762122\pi$
$971$			4.34215e8i			0.474293i	−0.971474	+	0.237147i	$0.923788\pi$
$972$	−1.70059e8	−	6.27923e8i	−0.185183	−	0.683766i
$973$	−9.21276e7			−0.100012
$974$		−	5.49888e8i		−	0.595110i
$975$	−3.59678e8	+	5.54507e8i	−0.388061	+	0.598264i
$976$	9.64319e7			0.103722
$977$		−	5.89971e8i		−	0.632626i	−0.948655	−	0.316313i	$-0.897555\pi$
$977$		−	5.89971e8i		−	0.632626i	0.948655	−	0.316313i	$-0.102445\pi$
$978$	1.35480e7	+	8.78783e6i	0.0144830	+	0.00939432i
$979$	8.42341e8			0.897718
$980$			2.51480e8i			0.267193i
$981$	3.78308e8	+	8.47245e8i	0.400718	+	0.897433i
$982$	8.66396e8			0.914918
$983$			1.53955e9i			1.62081i	0.585869	+	0.810406i	$0.300753\pi$
$983$			1.53955e9i			1.62081i	−0.585869	+	0.810406i	$0.699247\pi$
$984$	−2.75610e8	+	4.24901e8i	−0.289274	+	0.445967i
$985$	4.97507e8			0.520584
$986$			7.02092e8i			0.732425i
$987$	6.64254e7	+	4.30864e7i	0.0690848	+	0.0448115i
$988$	8.72415e8			0.904591
$989$			2.62857e8i			0.271725i
$990$	−1.88953e8	+	8.43706e7i	−0.194737	+	0.0869532i
$991$	3.91743e6			0.00402514			0.00201257	−	0.999998i	$-0.499359\pi$
$991$	3.91743e6			0.00402514			0.00201257	+	0.999998i	$0.499359\pi$
$992$			1.82330e7i			0.0186777i
$993$	5.18298e8	−	7.99049e8i	0.529337	−	0.816066i
$994$	−6.60499e7			−0.0672533
$995$			2.46879e8i			0.250619i
$996$	9.77321e8	+	6.33934e8i	0.989143	+	0.641602i
$997$	7.52794e8			0.759610			0.379805	−	0.925067i	$-0.375991\pi$
$997$	7.52794e8			0.759610			0.379805	+	0.925067i	$0.375991\pi$
$998$		−	3.36955e8i		−	0.338985i
$999$	1.16436e9	+	1.82495e8i	1.16786	+	0.183044i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	69.7.b.a.47.18	✓	44
3.2	odd	2	inner	69.7.b.a.47.27	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.7.b.a.47.18	✓	44	1.1	even	1	trivial
69.7.b.a.47.27	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)

\(f(q)\)	\(=\)	\(q-4.32001i q^{2} +(-14.6931 + 22.6520i) q^{3} +45.3375 q^{4} -48.7369i q^{5} +(97.8569 + 63.4743i) q^{6} -61.9430 q^{7} -472.339i q^{8} +(-297.226 - 665.656i) q^{9} +O(q^{10})\)	\(q-4.32001i q^{2} +(-14.6931 + 22.6520i) q^{3} +45.3375 q^{4} -48.7369i q^{5} +(97.8569 + 63.4743i) q^{6} -61.9430 q^{7} -472.339i q^{8} +(-297.226 - 665.656i) q^{9} -210.544 q^{10} +1348.22i q^{11} +(-666.148 + 1026.99i) q^{12} +1847.54 q^{13} +267.594i q^{14} +(1103.99 + 716.096i) q^{15} +861.091 q^{16} -5403.33i q^{17} +(-2875.64 + 1284.02i) q^{18} +10415.3 q^{19} -2209.61i q^{20} +(910.135 - 1403.13i) q^{21} +5824.34 q^{22} +2536.99i q^{23} +(10699.4 + 6940.12i) q^{24} +13249.7 q^{25} -7981.39i q^{26} +(19445.6 + 3047.78i) q^{27} -2808.34 q^{28} -30077.9i q^{29} +(3093.54 - 4769.24i) q^{30} -537.061 q^{31} -33949.6i q^{32} +(-30539.9 - 19809.6i) q^{33} -23342.4 q^{34} +3018.91i q^{35} +(-13475.5 - 30179.2i) q^{36} +59878.0 q^{37} -44994.2i q^{38} +(-27146.1 + 41850.5i) q^{39} -23020.3 q^{40} +39712.5i q^{41} +(-6061.55 - 3931.79i) q^{42} +103609. q^{43} +61125.1i q^{44} +(-32442.0 + 14485.9i) q^{45} +10959.8 q^{46} +47340.7i q^{47} +(-12652.1 + 19505.4i) q^{48} -113812. q^{49} -57238.9i q^{50} +(122396. + 79391.6i) q^{51} +83762.9 q^{52} -77383.7i q^{53} +(13166.4 - 84005.2i) q^{54} +65708.2 q^{55} +29258.1i q^{56} +(-153033. + 235927. i) q^{57} -129937. q^{58} +117701. i q^{59} +(50052.1 + 32466.0i) q^{60} +111988. q^{61} +2320.11i q^{62} +(18411.1 + 41232.7i) q^{63} -91552.9 q^{64} -90043.3i q^{65} +(-85577.5 + 131933. i) q^{66} -540176. q^{67} -244973. i q^{68} +(-57468.0 - 37276.3i) q^{69} +13041.7 q^{70} +246829. i q^{71} +(-314415. + 140391. i) q^{72} -427677. q^{73} -258673. i q^{74} +(-194679. + 300133. i) q^{75} +472204. q^{76} -83513.0i q^{77} +(180794. + 117271. i) q^{78} -473538. q^{79} -41966.9i q^{80} +(-354754. + 395700. i) q^{81} +171559. q^{82} -951641. i q^{83} +(41263.2 - 63614.6i) q^{84} -263341. q^{85} -447594. i q^{86} +(681325. + 441938. i) q^{87} +636819. q^{88} -624779. i q^{89} +(62579.1 + 140150. i) q^{90} -114442. q^{91} +115021. i q^{92} +(7891.09 - 12165.5i) q^{93} +204512. q^{94} -507609. i q^{95} +(769027. + 498825. i) q^{96} +903441. q^{97} +491669. i q^{98} +(897453. - 400727. 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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