LMFDB - Embedded newform 69.7.b.a.47.13

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			47.13
Character	$\chi$	$=$	69.47
Dual form			69.7.b.a.47.32

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-8.07729i q^{2} +(18.6168 + 19.5554i) q^{3} -1.24263 q^{4} +135.340i q^{5} +(157.955 - 150.374i) q^{6} -41.9690 q^{7} -506.910i q^{8} +(-35.8265 + 728.119i) q^{9} +O(q^{10})$	\(q-8.07729i q^{2} +(18.6168 + 19.5554i) q^{3} -1.24263 q^{4} +135.340i q^{5} +(157.955 - 150.374i) q^{6} -41.9690 q^{7} -506.910i q^{8} +(-35.8265 + 728.119i) q^{9} +1093.18 q^{10} +1280.75i q^{11} +(-23.1339 - 24.3002i) q^{12} -844.489 q^{13} +338.996i q^{14} +(-2646.63 + 2519.61i) q^{15} -4173.98 q^{16} +8234.44i q^{17} +(5881.23 + 289.381i) q^{18} +826.707 q^{19} -168.179i q^{20} +(-781.330 - 820.720i) q^{21} +10345.0 q^{22} +2536.99i q^{23} +(9912.81 - 9437.05i) q^{24} -2692.01 q^{25} +6821.18i q^{26} +(-14905.6 + 12854.7i) q^{27} +52.1521 q^{28} -19204.7i q^{29} +(20351.6 + 21377.6i) q^{30} +44052.6 q^{31} +1272.28i q^{32} +(-25045.6 + 23843.6i) q^{33} +66511.9 q^{34} -5680.10i q^{35} +(44.5192 - 904.786i) q^{36} +50025.4 q^{37} -6677.55i q^{38} +(-15721.7 - 16514.3i) q^{39} +68605.3 q^{40} +57195.8i q^{41} +(-6629.19 + 6311.03i) q^{42} +25350.4 q^{43} -1591.51i q^{44} +(-98543.9 - 4848.77i) q^{45} +20492.0 q^{46} -135933. i q^{47} +(-77706.4 - 81623.9i) q^{48} -115888. q^{49} +21744.1i q^{50} +(-161028. + 153299. i) q^{51} +1049.39 q^{52} -6064.93i q^{53} +(103831. + 120397. i) q^{54} -173337. q^{55} +21274.5i q^{56} +(15390.7 + 16166.6i) q^{57} -155122. q^{58} +65615.3i q^{59} +(3288.80 - 3130.95i) q^{60} -173042. q^{61} -355826. i q^{62} +(1503.60 - 30558.4i) q^{63} -256858. q^{64} -114293. i q^{65} +(192591. + 202301. i) q^{66} -77408.1 q^{67} -10232.4i q^{68} +(-49611.9 + 47230.8i) q^{69} -45879.8 q^{70} -579540. i q^{71} +(369091. + 18160.8i) q^{72} +654718. q^{73} -404070. i q^{74} +(-50116.7 - 52643.2i) q^{75} -1027.29 q^{76} -53751.9i q^{77} +(-133391. + 126989. i) q^{78} +503494. q^{79} -564908. i q^{80} +(-528874. - 52171.9i) q^{81} +461987. q^{82} +119119. i q^{83} +(970.908 + 1019.86i) q^{84} -1.11445e6 q^{85} -204763. i q^{86} +(375556. - 357531. i) q^{87} +649226. q^{88} +699816. i q^{89} +(-39164.9 + 795968. i) q^{90} +35442.3 q^{91} -3152.56i q^{92} +(820120. + 861466. i) q^{93} -1.09797e6 q^{94} +111887. i q^{95} +(-24879.9 + 23685.8i) q^{96} -1.08089e6 q^{97} +936058. i q^{98} +(-932540. - 45884.8i) 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 $

$2$		−	8.07729i		−	1.00966i	−0.863218	−	0.504831i	$-0.831555\pi$
$2$		−	8.07729i		−	1.00966i	0.863218	−	0.504831i	$-0.168445\pi$
$3$	18.6168	+	19.5554i	0.689513	+	0.724274i
$3$	18.6168	+	19.5554i	0.689513	+	0.724274i
$4$	−1.24263			−0.0194162
$5$			135.340i			1.08272i	0.840790	+	0.541361i	$0.182091\pi$
$5$			135.340i			1.08272i	−0.840790	+	0.541361i	$0.817909\pi$
$6$	157.955	−	150.374i	0.731271	−	0.696174i
$7$	−41.9690			−0.122359			−0.0611793	−	0.998127i	$-0.519486\pi$
$7$	−41.9690			−0.122359			−0.0611793	+	0.998127i	$0.519486\pi$
$8$		−	506.910i		−	0.990058i
$9$	−35.8265	+	728.119i	−0.0491447	+	0.998792i
$10$	1093.18			1.09318
$11$			1280.75i			0.962248i	0.876652	+	0.481124i	$0.159771\pi$
$11$			1280.75i			0.962248i	−0.876652	+	0.481124i	$0.840229\pi$
$12$	−23.1339	−	24.3002i	−0.0133877	−	0.0140626i
$13$	−844.489			−0.384383			−0.192191	−	0.981357i	$-0.561559\pi$
$13$	−844.489			−0.384383			−0.192191	+	0.981357i	$0.561559\pi$
$14$			338.996i			0.123541i
$15$	−2646.63	+	2519.61i	−0.784188	+	0.746551i
$16$	−4173.98			−1.01904
$17$			8234.44i			1.67605i	0.545631	+	0.838025i	$0.316290\pi$
$17$			8234.44i			1.67605i	−0.545631	+	0.838025i	$0.683710\pi$
$18$	5881.23	+	289.381i	1.00844	+	0.0496195i
$19$	826.707			0.120529			0.0602644	−	0.998182i	$-0.480806\pi$
$19$	826.707			0.120529			0.0602644	+	0.998182i	$0.480806\pi$
$20$		−	168.179i		−	0.0210223i
$21$	−781.330	−	820.720i	−0.0843678	−	0.0886211i
$22$	10345.0			0.971545
$23$			2536.99i			0.208514i
$23$			2536.99i			0.208514i
$24$	9912.81	−	9437.05i	0.717073	−	0.682657i
$25$	−2692.01			−0.172288
$26$			6821.18i			0.388096i
$27$	−14905.6	+	12854.7i	−0.757284	+	0.653085i
$28$	52.1521			0.00237573
$29$		−	19204.7i		−	0.787434i	−0.919232	−	0.393717i	$-0.871189\pi$
$29$		−	19204.7i		−	0.787434i	0.919232	−	0.393717i	$-0.128811\pi$
$30$	20351.6	+	21377.6i	0.753764	+	0.791764i
$31$	44052.6			1.47872			0.739361	−	0.673309i	$-0.235128\pi$
$31$	44052.6			1.47872			0.739361	+	0.673309i	$0.235128\pi$
$32$			1272.28i			0.0388269i
$33$	−25045.6	+	23843.6i	−0.696931	+	0.663482i
$34$	66511.9			1.69224
$35$		−	5680.10i		−	0.132480i
$36$	44.5192	−	904.786i	0.000954201	−	0.0193927i
$37$	50025.4			0.987611			0.493805	−	0.869572i	$-0.335606\pi$
$37$	50025.4			0.987611			0.493805	+	0.869572i	$0.335606\pi$
$38$		−	6677.55i		−	0.121693i
$39$	−15721.7	−	16514.3i	−0.265037	−	0.278398i
$40$	68605.3			1.07196
$41$			57195.8i			0.829875i	0.909850	+	0.414937i	$0.136197\pi$
$41$			57195.8i			0.829875i	−0.909850	+	0.414937i	$0.863803\pi$
$42$	−6629.19	+	6311.03i	−0.0894773	+	0.0851829i
$43$	25350.4			0.318845			0.159422	−	0.987210i	$-0.449037\pi$
$43$	25350.4			0.318845			0.159422	+	0.987210i	$0.449037\pi$
$44$		−	1591.51i		−	0.0186832i
$45$	−98543.9	−	4848.77i	−1.08141	−	0.0532100i
$46$	20492.0			0.210529
$47$		−	135933.i		−	1.30928i	−0.755941	−	0.654639i	$-0.772821\pi$
$47$		−	135933.i		−	1.30928i	0.755941	−	0.654639i	$-0.227179\pi$
$48$	−77706.4	−	81623.9i	−0.702640	−	0.738063i
$49$	−115888.			−0.985028
$50$			21744.1i			0.173953i
$51$	−161028.	+	153299.i	−1.21392	+	1.15566i
$52$	1049.39			0.00746324
$53$		−	6064.93i		−	0.0407379i	−0.999793	−	0.0203689i	$-0.993516\pi$
$53$		−	6064.93i		−	0.0407379i	0.999793	−	0.0203689i	$-0.00648408\pi$
$54$	103831.	+	120397.i	0.659395	+	0.764601i
$55$	−173337.			−1.04185
$56$			21274.5i			0.121142i
$57$	15390.7	+	16166.6i	0.0831061	+	0.0872958i
$58$	−155122.			−0.795042
$59$			65615.3i			0.319484i	0.987159	+	0.159742i	$0.0510663\pi$
$59$			65615.3i			0.319484i	−0.987159	+	0.159742i	$0.948934\pi$
$60$	3288.80	−	3130.95i	0.0152259	−	0.0144952i
$61$	−173042.			−0.762363			−0.381182	−	0.924500i	$-0.624483\pi$
$61$	−173042.			−0.762363			−0.381182	+	0.924500i	$0.624483\pi$
$62$		−	355826.i		−	1.49301i
$63$	1503.60	−	30558.4i	0.00601327	−	0.122211i
$64$	−256858.			−0.979837
$65$		−	114293.i		−	0.416180i
$66$	192591.	+	202301.i	0.669893	+	0.703664i
$67$	−77408.1			−0.257372			−0.128686	−	0.991685i	$-0.541076\pi$
$67$	−77408.1			−0.257372			−0.128686	+	0.991685i	$0.541076\pi$
$68$		−	10232.4i		−	0.0325425i
$69$	−49611.9	+	47230.8i	−0.151021	+	0.143773i
$70$	−45879.8			−0.133760
$71$		−	579540.i		−	1.61923i	−0.586962	−	0.809615i	$-0.699676\pi$
$71$		−	579540.i		−	1.61923i	0.586962	−	0.809615i	$-0.300324\pi$
$72$	369091.	+	18160.8i	0.988861	+	0.0486561i
$73$	654718.			1.68301			0.841503	−	0.540252i	$-0.181671\pi$
$73$	654718.			1.68301			0.841503	+	0.540252i	$0.181671\pi$
$74$		−	404070.i		−	0.997152i
$75$	−50116.7	−	52643.2i	−0.118795	−	0.124784i
$76$	−1027.29			−0.00234021
$77$		−	53751.9i		−	0.117739i
$78$	−133391.	+	126989.i	−0.281088	+	0.267597i
$79$	503494.			1.02121			0.510603	−	0.859817i	$-0.329422\pi$
$79$	503494.			1.02121			0.510603	+	0.859817i	$0.329422\pi$
$80$		−	564908.i		−	1.10334i
$81$	−528874.	−	52171.9i	−0.995170	−	0.0981706i
$82$	461987.			0.837893
$83$			119119.i			0.208327i	0.994560	+	0.104163i	$0.0332165\pi$
$83$			119119.i			0.208327i	−0.994560	+	0.104163i	$0.966783\pi$
$84$	970.908	+	1019.86i	0.00163810	+	0.00172068i
$85$	−1.11445e6			−1.81470
$86$		−	204763.i		−	0.321925i
$87$	375556.	−	357531.i	0.570318	−	0.542946i
$88$	649226.			0.952681
$89$			699816.i			0.992691i	0.868125	+	0.496345i	$0.165325\pi$
$89$			699816.i			0.992691i	−0.868125	+	0.496345i	$0.834675\pi$
$90$	−39164.9	+	795968.i	−0.0537241	+	1.09186i
$91$	35442.3			0.0470325
$92$		−	3152.56i		−	0.00404855i
$93$	820120.	+	861466.i	1.01960	+	1.07100i
$94$	−1.09797e6			−1.32193
$95$			111887.i			0.130499i
$96$	−24879.9	+	23685.8i	−0.0281213	+	0.0267716i
$97$	−1.08089e6			−1.18431			−0.592156	−	0.805824i	$-0.701723\pi$
$97$	−1.08089e6			−1.18431			−0.592156	+	0.805824i	$0.701723\pi$
$98$			936058.i			0.994545i
$99$	−932540.	−	45884.8i	−0.961086	−	0.0472894i
$100$	3345.18			0.00334518
$101$		−	506355.i		−	0.491463i	−0.969338	−	0.245732i	$-0.920972\pi$
$101$		−	506355.i		−	0.491463i	0.969338	−	0.245732i	$-0.0790282\pi$
$102$	1.23824e6	+	1.30067e6i	1.16682	+	1.22565i
$103$	115936.			0.106098			0.0530489	−	0.998592i	$-0.483106\pi$
$103$	115936.			0.106098			0.0530489	+	0.998592i	$0.483106\pi$
$104$			428079.i			0.380561i
$105$	111077.	−	105745.i	0.0959521	−	0.0913469i
$106$	−48988.2			−0.0411314
$107$		−	1.93721e6i		−	1.58134i	−0.612242	−	0.790671i	$-0.709732\pi$
$107$		−	1.93721e6i		−	1.58134i	0.612242	−	0.790671i	$-0.290268\pi$
$108$	18522.3	−	15973.7i	0.0147036	−	0.0126804i
$109$	1.75338e6			1.35393			0.676964	−	0.736016i	$-0.263295\pi$
$109$	1.75338e6			1.35393			0.676964	+	0.736016i	$0.263295\pi$
$110$			1.40010e6i			1.05191i
$111$	931316.	+	978267.i	0.680970	+	0.715300i
$112$	175178.			0.124688
$113$		−	1.71971e6i		−	1.19185i	−0.803042	−	0.595923i	$-0.796786\pi$
$113$		−	1.71971e6i		−	1.19185i	0.803042	−	0.595923i	$-0.203214\pi$
$114$	130582.	−	124315.i	0.0881392	−	0.0839090i
$115$	−343358.			−0.225763
$116$			23864.5i			0.0152890i
$117$	30255.1	−	614889.i	0.0188904	−	0.383918i
$118$	529994.			0.322571
$119$		−	345591.i		−	0.205079i
$120$	1.27721e6	+	1.34160e6i	0.739129	+	0.776391i
$121$	131234.			0.0740781
$122$			1.39771e6i			0.769729i
$123$	−1.11849e6	+	1.06481e6i	−0.601057	+	0.572209i
$124$	−54741.3			−0.0287111
$125$			1.75036e6i			0.896182i
$126$	−246829.	−	12145.0i	−0.123391	−	0.00607137i
$127$	−689254.			−0.336487			−0.168243	−	0.985745i	$-0.553809\pi$
$127$	−689254.			−0.336487			−0.168243	+	0.985745i	$0.553809\pi$
$128$			2.15615e6i			1.02813i
$129$	471944.	+	495737.i	0.219848	+	0.230931i
$130$	−923181.			−0.420201
$131$			576153.i			0.256285i	0.991756	+	0.128143i	$0.0409015\pi$
$131$			576153.i			0.256285i	−0.991756	+	0.128143i	$0.959098\pi$
$132$	31122.6	−	29628.8i	0.0135317	−	0.0128823i
$133$	−34696.0			−0.0147477
$134$			625248.i			0.259859i
$135$	−1.73976e6	−	2.01733e6i	−0.707110	−	0.819929i
$136$	4.17411e6			1.65939
$137$		−	4.90507e6i		−	1.90758i	−0.300469	−	0.953791i	$-0.597143\pi$
$137$		−	4.90507e6i		−	1.90758i	0.300469	−	0.953791i	$-0.402857\pi$
$138$	381497.	+	400730.i	0.145162	+	0.152481i
$139$	−659388.			−0.245526			−0.122763	−	0.992436i	$-0.539175\pi$
$139$	−659388.			−0.245526			−0.122763	+	0.992436i	$0.539175\pi$
$140$			7058.29i			0.00257226i
$141$	2.65823e6	−	2.53065e6i	0.948276	−	0.902764i
$142$	−4.68111e6			−1.63487
$143$		−	1.08158e6i		−	0.369872i
$144$	149539.	−	3.03916e6i	0.0500803	−	1.01781i
$145$	2.59917e6			0.852573
$146$		−	5.28835e6i		−	1.69927i
$147$	−2.15746e6	−	2.26623e6i	−0.679190	−	0.713430i
$148$	−62163.4			−0.0191756
$149$		−	1.17188e6i		−	0.354261i	−0.984187	−	0.177130i	$-0.943319\pi$
$149$		−	1.17188e6i		−	0.354261i	0.984187	−	0.177130i	$-0.0566814\pi$
$150$	−425215.	+	404807.i	−0.125990	+	0.119943i
$151$	−1.54232e6			−0.447963			−0.223982	−	0.974593i	$-0.571906\pi$
$151$	−1.54232e6			−0.447963			−0.223982	+	0.974593i	$0.571906\pi$
$152$		−	419065.i		−	0.119330i
$153$	−5.99565e6	−	295011.i	−1.67403	−	0.0823689i
$154$	−434170.			−0.118877
$155$			5.96209e6i			1.60105i
$156$	19536.4	+	20521.3i	0.00514600	+	0.00540543i
$157$	4.73270e6			1.22295			0.611477	−	0.791262i	$-0.290576\pi$
$157$	4.73270e6			1.22295			0.611477	+	0.791262i	$0.290576\pi$
$158$		−	4.06687e6i		−	1.03107i
$159$	118602.	−	112910.i	0.0295054	−	0.0280893i
$160$	−172191.			−0.0420387
$161$		−	106475.i		−	0.0255135i
$162$	−421407.	+	4.27187e6i	−0.0991190	+	1.00478i
$163$	−3.37677e6			−0.779721			−0.389860	−	0.920874i	$-0.627477\pi$
$163$	−3.37677e6			−0.779721			−0.389860	+	0.920874i	$0.627477\pi$
$164$		−	71073.5i		−	0.0161130i
$165$	−3.22700e6	−	3.38968e6i	−0.718367	−	0.754583i
$166$	962156.			0.210340
$167$			1.99709e6i			0.428794i	0.976747	+	0.214397i	$0.0687786\pi$
$167$			1.99709e6i			0.428794i	−0.976747	+	0.214397i	$0.931221\pi$
$168$	−416031.	+	396064.i	−0.0877400	+	0.0835290i
$169$	−4.11365e6			−0.852250
$170$			9.00175e6i			1.83223i
$171$	−29618.0	+	601941.i	−0.00592334	+	0.120383i
$172$	−31501.3			−0.00619074
$173$			4.39409e6i			0.848654i	0.905509	+	0.424327i	$0.139489\pi$
$173$			4.39409e6i			0.848654i	−0.905509	+	0.424327i	$0.860511\pi$
$174$	−2.88788e6	−	3.03347e6i	−0.548191	−	0.575828i
$175$	112981.			0.0210810
$176$		−	5.34584e6i		−	0.980569i
$177$	−1.28313e6	+	1.22155e6i	−0.231394	+	0.220288i
$178$	5.65262e6			1.00228
$179$		−	6.10829e6i		−	1.06503i	−0.846421	−	0.532514i	$-0.821248\pi$
$179$		−	6.10829e6i		−	1.06503i	0.846421	−	0.532514i	$-0.178752\pi$
$180$	122454.	+	6025.24i	0.0209969	+	0.00103314i
$181$	3.71549e6			0.626586			0.313293	−	0.949656i	$-0.398568\pi$
$181$	3.71549e6			0.626586			0.313293	+	0.949656i	$0.398568\pi$
$182$		−	286278.i		−	0.0474869i
$183$	−3.22149e6	−	3.38390e6i	−0.525659	−	0.552159i
$184$	1.28603e6			0.206441
$185$			6.77046e6i			1.06931i
$186$	6.95831e6	−	6.62435e6i	1.08135	−	1.02945i
$187$	−1.05463e7			−1.61278
$188$			168915.i			0.0254212i
$189$	625574.	−	539498.i	0.0926602	−	0.0799106i
$190$	903742.			0.131760
$191$			5.64958e6i			0.810804i	0.914139	+	0.405402i	$0.132868\pi$
$191$			5.64958e6i			0.810804i	−0.914139	+	0.405402i	$0.867132\pi$
$192$	−4.78189e6	−	5.02297e6i	−0.675610	−	0.709670i
$193$	1.21486e7			1.68987			0.844936	−	0.534867i	$-0.179638\pi$
$193$	1.21486e7			1.68987			0.844936	+	0.534867i	$0.179638\pi$
$194$			8.73066e6i			1.19575i
$195$	2.23505e6	−	2.12778e6i	0.301428	−	0.286961i
$196$	144006.			0.0191255
$197$			7.07750e6i			0.925724i	0.886430	+	0.462862i	$0.153177\pi$
$197$			7.07750e6i			0.925724i	−0.886430	+	0.462862i	$0.846823\pi$
$198$	−370625.	+	7.53240e6i	−0.0477463	+	0.970371i
$199$	2.84995e6			0.361642			0.180821	−	0.983516i	$-0.442125\pi$
$199$	2.84995e6			0.361642			0.180821	+	0.983516i	$0.442125\pi$
$200$			1.36460e6i			0.170575i
$201$	−1.44109e6	−	1.51375e6i	−0.177462	−	0.186408i
$202$	−4.08998e6			−0.496212
$203$			806003.i			0.0963493i
$204$	200098.	−	190495.i	0.0235697	−	0.0224384i
$205$	−7.74090e6			−0.898524
$206$		−	936448.i		−	0.107123i
$207$	−1.84723e6	−	90891.5i	−0.208262	−	0.0102474i
$208$	3.52488e6			0.391701
$209$			1.05881e6i			0.115979i
$210$	−854137.	−	897197.i	−0.0922294	−	0.0968791i
$211$	1.59423e7			1.69708			0.848542	−	0.529128i	$-0.177481\pi$
$211$	1.59423e7			1.69708			0.848542	+	0.529128i	$0.177481\pi$
$212$			7536.49i			0.000790973i
$213$	1.13331e7	−	1.07892e7i	1.17276	−	1.11648i
$214$	−1.56474e7			−1.59662
$215$			3.43093e6i			0.345221i
$216$	6.51616e6	+	7.55580e6i	0.646592	+	0.749755i
$217$	−1.84884e6			−0.180934
$218$		−	1.41625e7i		−	1.36701i
$219$	1.21888e7	+	1.28033e7i	1.16045	+	1.21896i
$220$	215395.			0.0202287
$221$		−	6.95389e6i		−	0.644245i
$222$	7.90175e6	−	7.52251e6i	0.722211	−	0.687549i
$223$	1.17218e7			1.05702			0.528508	−	0.848928i	$-0.322752\pi$
$223$	1.17218e7			1.05702			0.528508	+	0.848928i	$0.322752\pi$
$224$		−	53396.3i		−	0.00475080i
$225$	96445.1	−	1.96010e6i	0.00846706	−	0.172080i
$226$	−1.38906e7			−1.20336
$227$			2.17449e7i			1.85900i	0.368823	+	0.929500i	$0.379761\pi$
$227$			2.17449e7i			1.85900i	−0.368823	+	0.929500i	$0.620239\pi$
$228$	−19125.0	−	20089.1i	−0.00161360	−	0.00169495i
$229$	−1.34348e7			−1.11873			−0.559365	−	0.828922i	$-0.688955\pi$
$229$	−1.34348e7			−1.11873			−0.559365	+	0.828922i	$0.688955\pi$
$230$			2.77340e6i			0.227944i
$231$	1.05114e6	−	1.00069e6i	0.0852755	−	0.0811828i
$232$	−9.73506e6			−0.779605
$233$			750459.i			0.0593280i	0.999560	+	0.0296640i	$0.00944372\pi$
$233$			750459.i			0.0593280i	−0.999560	+	0.0296640i	$0.990556\pi$
$234$	−4.96663e6	−	244379.i	−0.387628	−	0.0190729i
$235$	1.83972e7			1.41759
$236$		−	81535.9i		−	0.00620316i
$237$	9.37347e6	+	9.84602e6i	0.704134	+	0.739632i
$238$	−2.79144e6			−0.207060
$239$			2.65640e7i			1.94581i	0.231212	+	0.972903i	$0.425731\pi$
$239$			2.65640e7i			1.94581i	−0.231212	+	0.972903i	$0.574269\pi$
$240$	1.10470e7	−	1.05168e7i	0.799118	−	0.760765i
$241$	4.47072e6			0.319393			0.159697	−	0.987166i	$-0.448948\pi$
$241$	4.47072e6			0.319393			0.159697	+	0.987166i	$0.448948\pi$
$242$		−	1.06001e6i		−	0.0747938i
$243$	−8.82572e6	−	1.13136e7i	−0.615080	−	0.788465i
$244$	215028.			0.0148022
$245$		−	1.56843e7i		−	1.06651i
$246$	8.60074e6	+	9.03434e6i	0.577738	+	0.606864i
$247$	−698145.			−0.0463292
$248$		−	2.23307e7i		−	1.46402i
$249$	−2.32941e6	+	2.21761e6i	−0.150886	+	0.143644i
$250$	1.41381e7			0.904840
$251$		−	1.30163e7i		−	0.823128i	−0.911381	−	0.411564i	$-0.864983\pi$
$251$		−	1.30163e7i		−	0.823128i	0.911381	−	0.411564i	$-0.135017\pi$
$252$	−1868.43	+	37973.0i	−0.000116755	+	0.00237286i
$253$	−3.24926e6			−0.200643
$254$			5.56730e6i			0.339738i
$255$	−2.07476e7	−	2.17935e7i	−1.25126	−	1.31434i
$256$	976882.			0.0582267
$257$			1.23529e7i			0.727729i	0.931452	+	0.363864i	$0.118543\pi$
$257$			1.23529e7i			0.727729i	−0.931452	+	0.363864i	$0.881457\pi$
$258$	4.00421e6	−	3.81203e6i	0.233162	−	0.221972i
$259$	−2.09952e6			−0.120843
$260$			142025.i			0.00808062i
$261$	1.39833e7	+	688037.i	0.786483	+	0.0386982i
$262$	4.65375e6			0.258761
$263$			1.68055e7i			0.923813i	0.886929	+	0.461907i	$0.152834\pi$
$263$			1.68055e7i			0.923813i	−0.886929	+	0.461907i	$0.847166\pi$
$264$	1.20865e7	+	1.26959e7i	0.656886	+	0.690002i
$265$	820830.			0.0441078
$266$			280250.i			0.0148902i
$267$	−1.36852e7	+	1.30284e7i	−0.718980	+	0.684473i
$268$	96190.0			0.00499719
$269$		−	1.40706e7i		−	0.722863i	−0.932399	−	0.361432i	$-0.882288\pi$
$269$		−	1.40706e7i		−	0.722863i	0.932399	−	0.361432i	$-0.117712\pi$
$270$	−1.62946e7	+	1.40525e7i	−0.827851	+	0.713942i
$271$	−2.48407e6			−0.124812			−0.0624060	−	0.998051i	$-0.519877\pi$
$271$	−2.48407e6			−0.124812			−0.0624060	+	0.998051i	$0.519877\pi$
$272$		−	3.43704e7i		−	1.70796i
$273$	659825.	+	693089.i	0.0324295	+	0.0340644i
$274$	−3.96197e7			−1.92601
$275$		−	3.44779e6i		−	0.165784i
$276$	61649.5	−	58690.7i	0.00293226	−	0.00279153i
$277$	−1.13718e7			−0.535046			−0.267523	−	0.963551i	$-0.586205\pi$
$277$	−1.13718e7			−0.535046			−0.267523	+	0.963551i	$0.586205\pi$
$278$			5.32607e6i			0.247898i
$279$	−1.57825e6	+	3.20755e7i	−0.0726713	+	1.47694i
$280$	−2.87930e6			−0.131163
$281$			3.18582e7i			1.43583i	0.696132	+	0.717914i	$0.254903\pi$
$281$			3.18582e7i			1.43583i	−0.696132	+	0.717914i	$0.745097\pi$
$282$	−2.04408e7	−	2.14713e7i	−0.911486	−	0.957438i
$283$	2.57674e7			1.13687			0.568436	−	0.822728i	$-0.307549\pi$
$283$	2.57674e7			1.13687			0.568436	+	0.822728i	$0.307549\pi$
$284$			720156.i			0.0314392i
$285$	−2.18799e6	+	2.08298e6i	−0.0945171	+	0.0899808i
$286$	−8.73625e6			−0.373445
$287$		−	2.40045e6i		−	0.101542i
$288$	−926371.	−	45581.3i	−0.0387800	−	0.00190813i
$289$	−4.36684e7			−1.80915
$290$		−	2.09943e7i		−	0.860810i
$291$	−2.01227e7	−	2.11372e7i	−0.816598	−	0.857766i
$292$	−813576.			−0.0326775
$293$		−	1.55197e7i		−	0.616995i	−0.951225	−	0.308497i	$-0.900174\pi$
$293$		−	1.55197e7i		−	0.616995i	0.951225	−	0.308497i	$-0.0998261\pi$
$294$	−1.83050e7	+	1.74264e7i	−0.720323	+	0.685751i
$295$	−8.88040e6			−0.345913
$296$		−	2.53584e7i		−	0.977792i
$297$	−1.64637e7	−	1.90904e7i	−0.628430	−	0.728696i
$298$	−9.46558e6			−0.357683
$299$		−	2.14246e6i		−	0.0801493i
$300$	62276.7	+	65416.3i	0.00230654	+	0.00242283i
$301$	−1.06393e6			−0.0390134
$302$			1.24577e7i			0.452291i
$303$	9.90197e6	−	9.42673e6i	0.355954	−	0.338870i
$304$	−3.45066e6			−0.122824
$305$		−	2.34196e7i		−	0.825428i
$306$	−2.38289e6	+	4.84286e7i	−0.0831647	+	1.69020i
$307$	3.33621e7			1.15302			0.576512	−	0.817088i	$-0.304413\pi$
$307$	3.33621e7			1.15302			0.576512	+	0.817088i	$0.304413\pi$
$308$			66794.0i			0.00228605i
$309$	2.15836e6	+	2.26717e6i	0.0731557	+	0.0768438i
$310$	4.81576e7			1.61651
$311$			5.50676e6i			0.183069i	0.995802	+	0.0915345i	$0.0291772\pi$
$311$			5.50676e6i			0.183069i	−0.995802	+	0.0915345i	$0.970823\pi$
$312$	−8.37126e6	+	7.96949e6i	−0.275630	+	0.262402i
$313$	−450526.			−0.0146922			−0.00734609	−	0.999973i	$-0.502338\pi$
$313$	−450526.			−0.0146922			−0.00734609	+	0.999973i	$0.502338\pi$
$314$		−	3.82274e7i		−	1.23477i
$315$	4.13579e6	+	203498.i	0.132320	+	0.00651070i
$316$	−625659.			−0.0198279
$317$		−	5.85735e7i		−	1.83875i	−0.393378	−	0.919377i	$-0.628694\pi$
$317$		−	5.85735e7i		−	1.83875i	0.393378	−	0.919377i	$-0.371306\pi$
$318$	−912005.	−	957983.i	−0.0283606	−	0.0297904i
$319$	2.45965e7			0.757707
$320$		−	3.47633e7i		−	1.06089i
$321$	3.78829e7	−	3.60648e7i	1.14532	−	1.09035i
$322$	−860030.			−0.0257600
$323$			6.80746e6i			0.202012i
$324$	657197.	+	64830.6i	0.0193224	+	0.00190610i
$325$	2.27337e6			0.0662247
$326$			2.72752e7i			0.787254i
$327$	3.26423e7	+	3.42879e7i	0.933550	+	0.980614i
$328$	2.89931e7			0.821624
$329$			5.70498e6i			0.160201i
$330$	−2.73794e7	+	2.60654e7i	−0.761873	+	0.725308i
$331$	3.92362e7			1.08194			0.540970	−	0.841042i	$-0.318057\pi$
$331$	3.92362e7			1.08194			0.540970	+	0.841042i	$0.318057\pi$
$332$		−	148021.i		−	0.00404491i
$333$	−1.79223e6	+	3.64245e7i	−0.0485358	+	0.986417i
$334$	1.61311e7			0.432937
$335$		−	1.04764e7i		−	0.278663i
$336$	3.26126e6	+	3.42567e6i	0.0859741	+	0.0903084i
$337$	−5.66230e7			−1.47946			−0.739731	−	0.672903i	$-0.765047\pi$
$337$	−5.66230e7			−1.47946			−0.739731	+	0.672903i	$0.765047\pi$
$338$			3.32271e7i			0.860484i
$339$	3.36296e7	−	3.20156e7i	0.863222	−	0.821793i
$340$	1.38486e6			0.0352345
$341$			5.64205e7i			1.42290i
$342$	4.86205e6	+	239233.i	0.121546	+	0.00598057i
$343$	9.80129e6			0.242885
$344$		−	1.28504e7i		−	0.315675i
$345$	−6.39224e6	−	6.71449e6i	−0.155667	−	0.163514i
$346$	3.54923e7			0.856853
$347$		−	1.82136e7i		−	0.435920i	−0.975958	−	0.217960i	$-0.930060\pi$
$347$		−	1.82136e7i		−	0.435920i	0.975958	−	0.217960i	$-0.0699402\pi$
$348$	−466679.	+	444281.i	−0.0110734	+	0.0105419i
$349$	−6.76943e7			−1.59249			−0.796244	−	0.604976i	$-0.793183\pi$
$349$	−6.76943e7			−1.59249			−0.796244	+	0.604976i	$0.793183\pi$
$350$		−	912579.i		−	0.0212846i
$351$	1.25876e7	−	1.08556e7i	0.291087	−	0.251035i
$352$	−1.62947e6			−0.0373611
$353$		−	2.49672e7i		−	0.567605i	−0.958883	−	0.283803i	$-0.908404\pi$
$353$		−	2.49672e7i		−	0.567605i	0.958883	−	0.283803i	$-0.0915961\pi$
$354$	9.86682e6	+	1.03642e7i	0.222417	+	0.233630i
$355$	7.84351e7			1.75318
$356$		−	869616.i		−	0.0192742i
$357$	6.75817e6	−	6.43381e6i	0.148533	−	0.141405i
$358$	−4.93385e7			−1.07532
$359$			1.53007e7i			0.330695i	0.986235	+	0.165347i	$0.0528745\pi$
$359$			1.53007e7i			0.330695i	−0.986235	+	0.165347i	$0.947125\pi$
$360$	−2.45789e6	+	4.99528e7i	−0.0526810	+	1.07066i
$361$	−4.63624e7			−0.985473
$362$		−	3.00111e7i		−	0.632640i
$363$	2.44316e6	+	2.56633e6i	0.0510778	+	0.0536528i
$364$	−44041.9			−0.000913191
$365$			8.86098e7i			1.82223i
$366$	−2.73328e7	+	2.60209e7i	−0.557494	+	0.530738i
$367$	5.32878e7			1.07803			0.539013	−	0.842297i	$-0.318797\pi$
$367$	5.32878e7			1.07803			0.539013	+	0.842297i	$0.318797\pi$
$368$		−	1.05894e7i		−	0.212484i
$369$	−4.16454e7	−	2.04912e6i	−0.828872	−	0.0407839i
$370$	5.46870e7			1.07964
$371$			254539.i			0.00498463i
$372$	−1.01911e6	−	1.07049e6i	−0.0197967	−	0.0207947i
$373$	4.98098e7			0.959816			0.479908	−	0.877319i	$-0.340670\pi$
$373$	4.98098e7			0.959816			0.479908	+	0.877319i	$0.340670\pi$
$374$			8.51853e7i			1.62836i
$375$	−3.42289e7	+	3.25861e7i	−0.649081	+	0.617929i
$376$	−6.89059e7			−1.29626
$377$			1.62182e7i			0.302676i
$378$	−4.35768e6	−	5.05294e6i	−0.0806826	−	0.0935555i
$379$	−1.46614e6			−0.0269314			−0.0134657	−	0.999909i	$-0.504286\pi$
$379$	−1.46614e6			−0.0269314			−0.0134657	+	0.999909i	$0.504286\pi$
$380$		−	139034.i		−	0.00253379i
$381$	−1.28317e7	−	1.34786e7i	−0.232012	−	0.243708i
$382$	4.56333e7			0.818637
$383$		−	4.67224e7i		−	0.831627i	−0.909450	−	0.415814i	$-0.863497\pi$
$383$		−	4.67224e7i		−	0.831627i	0.909450	−	0.415814i	$-0.136503\pi$
$384$	−4.21643e7	+	4.01406e7i	−0.744648	+	0.708909i
$385$	7.27480e6			0.127479
$386$		−	9.81277e7i		−	1.70620i
$387$	−908215.	+	1.84581e7i	−0.0156695	+	0.318460i
$388$	1.34315e6			0.0229948
$389$			3.48480e7i			0.592010i	0.955186	+	0.296005i	$0.0956544\pi$
$389$			3.48480e7i			0.592010i	−0.955186	+	0.296005i	$0.904346\pi$
$390$	−1.71867e7	−	1.80532e7i	−0.289734	−	0.304340i
$391$	−2.08907e7			−0.349481
$392$			5.87445e7i			0.975235i
$393$	−1.12669e7	+	1.07261e7i	−0.185621	+	0.176712i
$394$	5.71671e7			0.934668
$395$			6.81430e7i			1.10568i
$396$	1.15881e6	+	57018.1i	0.0186606	+	0.000918178i
$397$	−3.44010e7			−0.549793			−0.274897	−	0.961474i	$-0.588644\pi$
$397$	−3.44010e7			−0.549793			−0.274897	+	0.961474i	$0.588644\pi$
$398$		−	2.30199e7i		−	0.365136i
$399$	−645931.	−	678495.i	−0.0101687	−	0.0106814i
$400$	1.12364e7			0.175569
$401$		−	1.22590e8i		−	1.90118i	−0.310452	−	0.950589i	$-0.600480\pi$
$401$		−	1.22590e8i		−	1.90118i	0.310452	−	0.950589i	$-0.399520\pi$
$402$	−1.22270e7	+	1.16401e7i	−0.188209	+	0.179176i
$403$	−3.72019e7			−0.568395
$404$			629214.i			0.00954233i
$405$	7.06096e6	−	7.15780e7i	0.106291	−	1.07749i
$406$	6.51032e6			0.0972802
$407$			6.40702e7i			0.950327i
$408$	7.77088e7	+	8.16264e7i	1.14417	+	1.20185i
$409$	−1.09719e8			−1.60366			−0.801832	−	0.597550i	$-0.796141\pi$
$409$	−1.09719e8			−1.60366			−0.801832	+	0.597550i	$0.796141\pi$
$410$			6.25255e7i			0.907205i
$411$	9.59205e7	−	9.13169e7i	1.38161	−	1.31530i
$412$	−144066.			−0.00206001
$413$		−	2.75381e6i		−	0.0390916i
$414$	−734158.	+	1.49207e7i	−0.0103464	+	0.210275i
$415$	−1.61216e7			−0.225560
$416$		−	1.07443e6i		−	0.0149244i
$417$	−1.22757e7	−	1.28946e7i	−0.169293	−	0.177828i
$418$	8.55229e6			0.117099
$419$			1.87312e6i			0.0254638i	0.999919	+	0.0127319i	$0.00405281\pi$
$419$			1.87312e6i			0.0254638i	−0.999919	+	0.0127319i	$0.995947\pi$
$420$	−138028.	+	131403.i	−0.00186302	+	0.00177361i
$421$	−9.91465e7			−1.32871			−0.664356	−	0.747416i	$-0.731294\pi$
$421$	−9.91465e7			−1.32871			−0.664356	+	0.747416i	$0.731294\pi$
$422$		−	1.28770e8i		−	1.71348i
$423$	9.89756e7	+	4.87001e6i	1.30770	+	0.0643441i
$424$	−3.07437e6			−0.0403328
$425$		−	2.21672e7i		−	0.288764i
$426$	−8.71475e7	−	9.15410e7i	−1.12727	−	1.18410i
$427$	7.26239e6			0.0932816
$428$			2.40725e6i			0.0307036i
$429$	2.11507e7	−	2.01356e7i	0.267888	−	0.255031i
$430$	2.77126e7			0.348556
$431$		−	1.32859e7i		−	0.165943i	−0.996552	−	0.0829714i	$-0.973559\pi$
$431$		−	1.32859e7i		−	0.165943i	0.996552	−	0.0829714i	$-0.0264410\pi$
$432$	6.22159e7	−	5.36552e7i	0.771702	−	0.665519i
$433$	1.48701e8			1.83168			0.915840	−	0.401544i	$-0.131526\pi$
$433$	1.48701e8			1.83168			0.915840	+	0.401544i	$0.131526\pi$
$434$			1.49336e7i			0.182682i
$435$	4.83884e7	+	5.08279e7i	0.587860	+	0.617496i
$436$	−2.17881e6			−0.0262881
$437$			2.09735e6i			0.0251320i
$438$	1.03416e8	−	9.84524e7i	1.23073	−	1.17167i
$439$	−1.27974e8			−1.51261			−0.756305	−	0.654219i	$-0.772998\pi$
$439$	−1.27974e8			−1.51261			−0.756305	+	0.654219i	$0.772998\pi$
$440$			8.78664e7i			1.03149i
$441$	4.15184e6	−	8.43800e7i	0.0484089	−	0.983838i
$442$	−5.61686e7			−0.650469
$443$			7.75444e7i			0.891947i	0.895046	+	0.445973i	$0.147142\pi$
$443$			7.75444e7i			0.891947i	−0.895046	+	0.445973i	$0.852858\pi$
$444$	−1.15729e6	−	1.21563e6i	−0.0132218	−	0.0138884i
$445$	−9.47134e7			−1.07481
$446$		−	9.46808e7i		−	1.06723i
$447$	2.29165e7	−	2.18166e7i	0.256582	−	0.244267i
$448$	1.07801e7			0.119891
$449$		−	2.37884e7i		−	0.262800i	−0.991329	−	0.131400i	$-0.958053\pi$
$449$		−	2.37884e7i		−	0.262800i	0.991329	−	0.131400i	$-0.0419472\pi$
$450$	−1.58323e7	−	779015.i	−0.173743	−	0.00854886i
$451$	−7.32537e7			−0.798546
$452$			2.13697e6i			0.0231411i
$453$	−2.87130e7	−	3.01606e7i	−0.308876	−	0.324448i
$454$	1.75640e8			1.87696
$455$			4.79678e6i			0.0509232i
$456$	8.19499e6	−	7.80167e6i	0.0864279	−	0.0822798i
$457$	−1.44723e8			−1.51631			−0.758157	−	0.652073i	$-0.773900\pi$
$457$	−1.44723e8			−1.51631			−0.758157	+	0.652073i	$0.773900\pi$
$458$			1.08517e8i			1.12954i
$459$	−1.05851e8	−	1.22739e8i	−1.09460	−	1.26925i
$460$	426668.			0.00438346
$461$		−	9.28926e7i		−	0.948153i	−0.880484	−	0.474076i	$-0.842782\pi$
$461$		−	9.28926e7i		−	0.948153i	0.880484	−	0.474076i	$-0.157218\pi$
$462$	−8.08287e6	−	8.49036e6i	−0.0819671	−	0.0860994i
$463$	−1.55998e8			−1.57173			−0.785863	−	0.618401i	$-0.787781\pi$
$463$	−1.55998e8			−1.57173			−0.785863	+	0.618401i	$0.787781\pi$
$464$			8.01602e7i			0.802426i
$465$	−1.16591e8	+	1.10995e8i	−1.15960	+	1.10394i
$466$	6.06168e6			0.0599012
$467$		−	1.13830e7i		−	0.111765i	−0.998437	−	0.0558825i	$-0.982203\pi$
$467$		−	1.13830e7i		−	0.111765i	0.998437	−	0.0558825i	$-0.0177972\pi$
$468$	−37596.0	+	764082.i	−0.000366778	+	0.00745422i
$469$	3.24874e6			0.0314917
$470$		−	1.48600e8i		−	1.43128i
$471$	8.81079e7	+	9.25498e7i	0.843242	+	0.885753i
$472$	3.32610e7			0.316308
$473$			3.24676e7i			0.306808i
$474$	7.95292e7	−	7.57122e7i	0.746778	−	0.710937i
$475$	−2.22550e6			−0.0207657
$476$			429443.i			0.00398185i
$477$	4.41599e6	+	217285.i	0.0406886	+	0.00200205i
$478$	2.14565e8			1.96461
$479$			1.12502e8i			1.02366i	0.859088	+	0.511828i	$0.171031\pi$
$479$			1.12502e8i			1.02366i	−0.859088	+	0.511828i	$0.828969\pi$
$480$	−3.20565e6	−	3.36726e6i	−0.0289862	−	0.0304476i
$481$	−4.22459e7			−0.379621
$482$		−	3.61113e7i		−	0.322479i
$483$	2.08216e6	−	1.98223e6i	0.0184788	−	0.0175919i
$484$	−163076.			−0.00143831
$485$		−	1.46288e8i		−	1.28228i
$486$	−9.13833e7	+	7.12879e7i	−0.796083	+	0.621022i
$487$	−9.47084e7			−0.819977			−0.409988	−	0.912091i	$-0.634467\pi$
$487$	−9.47084e7			−0.819977			−0.409988	+	0.912091i	$0.634467\pi$
$488$			8.77166e7i			0.754783i
$489$	−6.28648e7	−	6.60341e7i	−0.537627	−	0.564731i
$490$	−1.26686e8			−1.07682
$491$			6.48474e7i			0.547833i	0.961753	+	0.273917i	$0.0883192\pi$
$491$			6.48474e7i			0.547833i	−0.961753	+	0.273917i	$0.911681\pi$
$492$	1.38987e6	−	1.32316e6i	0.0116702	−	0.0111101i
$493$	1.58140e8			1.31978
$494$			5.63912e6i			0.0467768i
$495$	6.21007e6	−	1.26210e8i	0.0512013	−	1.04059i
$496$	−1.83875e8			−1.50688
$497$			2.43227e7i			0.198127i
$498$	1.79123e7	+	1.88153e7i	0.145032	+	0.152343i
$499$	7.67433e7			0.617645			0.308823	−	0.951120i	$-0.400065\pi$
$499$	7.67433e7			0.617645			0.308823	+	0.951120i	$0.400065\pi$
$500$		−	2.17505e6i		−	0.0174004i
$501$	−3.90539e7	+	3.71795e7i	−0.310564	+	0.295659i
$502$	−1.05137e8			−0.831081
$503$			8.77270e7i			0.689333i	0.938725	+	0.344667i	$0.112008\pi$
$503$			8.77270e7i			0.689333i	−0.938725	+	0.344667i	$0.887992\pi$
$504$	−1.54904e7	−	762189.i	−0.120996	−	0.00595348i
$505$	6.85303e7			0.532118
$506$			2.62452e7i			0.202581i
$507$	−7.65831e7	−	8.04440e7i	−0.587637	−	0.617262i
$508$	856491.			0.00653328
$509$			4.31930e7i			0.327536i	0.986499	+	0.163768i	$0.0523649\pi$
$509$			4.31930e7i			0.327536i	−0.986499	+	0.163768i	$0.947635\pi$
$510$	−1.76033e8	+	1.67584e8i	−1.32704	+	1.26335i
$511$	−2.74779e7			−0.205930
$512$			1.30103e8i			0.969341i
$513$	−1.23226e7	+	1.06270e7i	−0.0912745	+	0.0787155i
$514$	9.97780e7			0.734760
$515$			1.56908e7i			0.114874i
$516$	−586454.	−	616020.i	−0.00426860	−	0.00448379i
$517$	1.74097e8			1.25985
$518$			1.69584e7i			0.122010i
$519$	−8.59281e7	+	8.18041e7i	−0.614658	+	0.585158i
$520$	−5.79364e7			−0.412042
$521$			5.23664e7i			0.370288i	0.982711	+	0.185144i	$0.0592751\pi$
$521$			5.23664e7i			0.370288i	−0.982711	+	0.185144i	$0.940725\pi$
$522$	5.55748e6	−	1.12947e8i	0.0390721	−	0.794081i
$523$	8.43046e7			0.589313			0.294657	−	0.955603i	$-0.404795\pi$
$523$	8.43046e7			0.589313			0.294657	+	0.955603i	$0.404795\pi$
$524$		−	715947.i		−	0.00497608i
$525$	2.10335e6	+	2.20938e6i	0.0145356	+	0.0152684i
$526$	1.35743e8			0.932738
$527$			3.62748e8i			2.47841i
$528$	1.04540e8	−	9.95227e7i	0.710200	−	0.676115i
$529$	−6.43634e6			−0.0434783
$530$		−	6.63008e6i		−	0.0445339i
$531$	−4.77758e7	−	2.35077e6i	−0.319098	−	0.0157009i
$532$	43114.5			0.000286344
$533$		−	4.83012e7i		−	0.318990i
$534$	1.05234e8	+	1.10539e8i	0.691086	+	0.725926i
$535$	2.62183e8			1.71215
$536$			3.92389e7i			0.254814i
$537$	1.19450e8	−	1.13717e8i	0.771371	−	0.734350i
$538$	−1.13652e8			−0.729847
$539$		−	1.48423e8i		−	0.947842i
$540$	2.16188e6	+	2.50681e6i	0.0137294	+	0.0159199i
$541$	2.75534e8			1.74014			0.870069	−	0.492929i	$-0.164074\pi$
$541$	2.75534e8			1.74014			0.870069	+	0.492929i	$0.164074\pi$
$542$			2.00646e7i			0.126018i
$543$	6.91708e7	+	7.26579e7i	0.432039	+	0.453820i
$544$	−1.04765e7			−0.0650758
$545$			2.37302e8i			1.46593i
$546$	5.59828e6	−	5.32960e6i	0.0343935	−	0.0327428i
$547$	1.91240e8			1.16847			0.584234	−	0.811586i	$-0.301395\pi$
$547$	1.91240e8			1.16847			0.584234	+	0.811586i	$0.301395\pi$
$548$			6.09521e6i			0.0370380i
$549$	6.19948e6	−	1.25995e8i	0.0374661	−	0.761442i
$550$	−2.78488e7			−0.167386
$551$		−	1.58767e7i		−	0.0949084i
$552$	2.39418e7	+	2.51488e7i	0.142344	+	0.149520i
$553$	−2.11311e7			−0.124953
$554$			9.18536e7i			0.540215i
$555$	−1.32399e8	+	1.26045e8i	−0.774472	+	0.737302i
$556$	819379.			0.00476717
$557$		−	2.86029e8i		−	1.65518i	−0.561333	−	0.827590i	$-0.689711\pi$
$557$		−	2.86029e8i		−	1.65518i	0.561333	−	0.827590i	$-0.310289\pi$
$558$	2.59083e8	+	1.27480e7i	1.49120	+	0.0733734i
$559$	−2.14081e7			−0.122558
$560$			2.37086e7i			0.135003i
$561$	−1.96338e8	−	2.06237e8i	−1.11203	−	1.16809i
$562$	2.57328e8			1.44970
$563$			1.04945e7i			0.0588079i	0.999568	+	0.0294040i	$0.00936092\pi$
$563$			1.04945e7i			0.0588079i	−0.999568	+	0.0294040i	$0.990639\pi$
$564$	−3.30321e6	+	3.14467e6i	−0.0184119	+	0.0175282i
$565$	2.32746e8			1.29044
$566$		−	2.08131e8i		−	1.14786i
$567$	2.21963e7	+	2.18960e6i	0.121768	+	0.0120120i
$568$	−2.93774e8			−1.60313
$569$		−	3.45218e8i		−	1.87394i	−0.349404	−	0.936972i	$-0.613616\pi$
$569$		−	3.45218e8i		−	1.87394i	0.349404	−	0.936972i	$-0.386384\pi$
$570$	1.68248e7	+	1.76730e7i	0.0908502	+	0.0954303i
$571$	−1.24158e8			−0.666907			−0.333453	−	0.942767i	$-0.608214\pi$
$571$	−1.24158e8			−0.666907			−0.333453	+	0.942767i	$0.608214\pi$
$572$			1.34401e6i			0.00718149i
$573$	−1.10480e8	+	1.05177e8i	−0.587244	+	0.559059i
$574$	−1.93891e7			−0.102523
$575$		−	6.82961e6i		−	0.0359246i
$576$	9.20233e6	−	1.87024e8i	0.0481538	−	0.978653i
$577$	1.52305e8			0.792842			0.396421	−	0.918069i	$-0.370252\pi$
$577$	1.52305e8			0.792842			0.396421	+	0.918069i	$0.370252\pi$
$578$			3.52722e8i			1.82662i
$579$	2.26168e8	+	2.37570e8i	1.16519	+	1.22393i
$580$	−3.22982e6			−0.0165537
$581$		−	4.99929e6i		−	0.0254906i
$582$	−1.70731e8	+	1.62537e8i	−0.866053	+	0.824487i
$583$	7.76767e6			0.0391999
$584$		−	3.31883e8i		−	1.66627i
$585$	8.32192e7	+	4.09473e6i	0.415677	+	0.0204530i
$586$	−1.25357e8			−0.622956
$587$		−	2.15931e8i		−	1.06758i	−0.845618	−	0.533789i	$-0.820768\pi$
$587$		−	2.15931e8i		−	1.06758i	0.845618	−	0.533789i	$-0.179232\pi$
$588$	2.68094e6	+	2.81609e6i	0.0131873	+	0.0138521i
$589$	3.64186e7			0.178228
$590$			7.17296e7i			0.349255i
$591$	−1.38403e8	+	1.31761e8i	−0.670477	+	0.638298i
$592$	−2.08805e8			−1.00641
$593$		−	2.58924e8i		−	1.24167i	−0.783939	−	0.620837i	$-0.786793\pi$
$593$		−	2.58924e8i		−	1.24167i	0.783939	−	0.620837i	$-0.213207\pi$
$594$	−1.54199e8	+	1.32982e8i	−0.735736	+	0.634502i
$595$	4.67724e7			0.222044
$596$			1.45621e6i			0.00687838i
$597$	5.30571e7	+	5.57320e7i	0.249357	+	0.261928i
$598$	−1.73053e7			−0.0809237
$599$			3.12926e8i			1.45600i	0.685576	+	0.728001i	$0.259550\pi$
$599$			3.12926e8i			1.45600i	−0.685576	+	0.728001i	$0.740450\pi$
$600$	−2.66854e7	+	2.54046e7i	−0.123543	+	0.117614i
$601$	−2.74362e8			−1.26387			−0.631933	−	0.775023i	$-0.717738\pi$
$601$	−2.74362e8			−1.26387			−0.631933	+	0.775023i	$0.717738\pi$
$602$			8.59368e6i			0.0393903i
$603$	2.77326e6	−	5.63623e7i	0.0126485	−	0.257061i
$604$	1.91654e6			0.00869773
$605$			1.77612e7i			0.0802061i
$606$	−7.61425e7	−	7.99811e7i	−0.342144	−	0.359393i
$607$	1.28653e8			0.575246			0.287623	−	0.957744i	$-0.407135\pi$
$607$	1.28653e8			0.575246			0.287623	+	0.957744i	$0.407135\pi$
$608$			1.05180e6i			0.00467975i
$609$	−1.57617e7	+	1.50052e7i	−0.0697833	+	0.0664341i
$610$	−1.89167e8			−0.833403
$611$			1.14794e8i			0.503264i
$612$	7.45040e6	+	366591.i	0.0325032	+	0.00159929i
$613$	2.42123e8			1.05113			0.525563	−	0.850755i	$-0.323855\pi$
$613$	2.42123e8			1.05113			0.525563	+	0.850755i	$0.323855\pi$
$614$		−	2.69476e8i		−	1.16416i
$615$	−1.44111e8	−	1.51376e8i	−0.619544	−	0.650778i
$616$	−2.72473e7			−0.116569
$617$			7.02546e7i			0.299102i	0.988754	+	0.149551i	$0.0477828\pi$
$617$			7.02546e7i			0.299102i	−0.988754	+	0.149551i	$0.952217\pi$
$618$	1.83126e7	−	1.74337e7i	0.0775862	−	0.0738625i
$619$	8.45389e6			0.0356438			0.0178219	−	0.999841i	$-0.494327\pi$
$619$	8.45389e6			0.0356438			0.0178219	+	0.999841i	$0.494327\pi$
$620$		−	7.40871e6i		−	0.0310862i
$621$	−3.26123e7	−	3.78155e7i	−0.136178	−	0.157905i
$622$	4.44797e7			0.184838
$623$		−	2.93706e7i		−	0.121464i
$624$	6.56222e7	+	6.89305e7i	0.270083	+	0.283699i
$625$	−2.78956e8			−1.14261
$626$			3.63903e6i			0.0148341i
$627$	−2.07054e7	+	1.97116e7i	−0.0840002	+	0.0799687i
$628$	−5.88102e6			−0.0237451
$629$			4.11931e8i			1.65529i
$630$	1.64371e6	−	3.34060e7i	0.00657361	−	0.133599i
$631$	−1.94463e8			−0.774012			−0.387006	−	0.922077i	$-0.626491\pi$
$631$	−1.94463e8			−0.774012			−0.387006	+	0.922077i	$0.626491\pi$
$632$		−	2.55226e8i		−	1.01105i
$633$	2.96795e8	+	3.11758e8i	1.17016	+	1.22915i
$634$	−4.73115e8			−1.85652
$635$		−	9.32838e7i		−	0.364322i
$636$	−147379.	+	140306.i	−0.000572881	+	0.000545386i
$637$	9.78658e7			0.378628
$638$		−	1.98673e8i		−	0.765028i
$639$	4.21974e8	+	2.07629e7i	1.61727	+	0.0795765i
$640$	−2.91814e8			−1.11318
$641$			1.17229e8i			0.445104i	0.974921	+	0.222552i	$0.0714387\pi$
$641$			1.17229e8i			0.445104i	−0.974921	+	0.222552i	$0.928561\pi$
$642$	−2.91306e8	−	3.05991e8i	−1.10089	−	1.15639i
$643$	1.96652e8			0.739716			0.369858	−	0.929088i	$-0.379406\pi$
$643$	1.96652e8			0.739716			0.369858	+	0.929088i	$0.379406\pi$
$644$			132310.i			0.000495375i
$645$	−6.70932e7	+	6.38731e7i	−0.250034	+	0.238034i
$646$	5.49859e7			0.203964
$647$		−	2.94415e8i		−	1.08704i	−0.839395	−	0.543522i	$-0.817090\pi$
$647$		−	2.94415e8i		−	1.08704i	0.839395	−	0.543522i	$-0.182910\pi$
$648$	−2.64464e7	+	2.68091e8i	−0.0971945	+	0.985275i
$649$	−8.40370e7			−0.307423
$650$		−	1.83627e7i		−	0.0668645i
$651$	−3.44196e7	−	3.61548e7i	−0.124756	−	0.131046i
$652$	4.19610e6			0.0151392
$653$		−	1.74241e8i		−	0.625763i	−0.949792	−	0.312881i	$-0.898706\pi$
$653$		−	1.74241e8i		−	0.625763i	0.949792	−	0.312881i	$-0.101294\pi$
$654$	2.76954e8	−	2.63661e8i	0.990088	−	0.942569i
$655$	−7.79767e7			−0.277486
$656$		−	2.38734e8i		−	0.845675i
$657$	−2.34562e7	+	4.76713e8i	−0.0827108	+	1.68097i
$658$	4.60808e7			0.161749
$659$		−	3.31026e8i		−	1.15666i	−0.815802	−	0.578331i	$-0.803704\pi$
$659$		−	3.31026e8i		−	1.15666i	0.815802	−	0.578331i	$-0.196296\pi$
$660$	4.00998e6	+	4.21214e6i	0.0139479	+	0.0146511i
$661$	−3.73169e8			−1.29211			−0.646057	−	0.763289i	$-0.723583\pi$
$661$	−3.73169e8			−1.29211			−0.646057	+	0.763289i	$0.723583\pi$
$662$		−	3.16922e8i		−	1.09239i
$663$	1.35986e8	−	1.29459e8i	0.466610	−	0.444215i
$664$	6.03824e7			0.206256
$665$		−	4.69577e6i		−	0.0159677i
$666$	2.94211e8	+	1.44764e7i	0.995947	+	0.0490047i
$667$	4.87223e7			0.164191
$668$		−	2.48166e6i		−	0.00832553i
$669$	2.18224e8	+	2.29225e8i	0.728826	+	0.765569i
$670$	−8.46212e7			−0.281355
$671$		−	2.21624e8i		−	0.733583i
$672$	1.04418e6	−	994070.i	0.00344088	−	0.00327574i
$673$	−3.67836e8			−1.20673			−0.603363	−	0.797467i	$-0.706173\pi$
$673$	−3.67836e8			−1.20673			−0.603363	+	0.797467i	$0.706173\pi$
$674$			4.57361e8i			1.49375i
$675$	4.01261e7	−	3.46049e7i	0.130471	−	0.112519i
$676$	5.11176e6			0.0165474
$677$		−	4.77191e8i		−	1.53789i	−0.639314	−	0.768946i	$-0.720781\pi$
$677$		−	4.77191e8i		−	1.53789i	0.639314	−	0.768946i	$-0.279219\pi$
$678$	−2.58599e8	−	2.71636e8i	−0.829732	−	0.871562i
$679$	4.53638e7			0.144911
$680$			5.64926e8i			1.79666i
$681$	−4.25229e8	+	4.04821e8i	−1.34642	+	1.28180i
$682$	4.55725e8			1.43664
$683$			5.17747e8i			1.62501i	0.582956	+	0.812504i	$0.301896\pi$
$683$			5.17747e8i			1.62501i	−0.582956	+	0.812504i	$0.698104\pi$
$684$	36804.3	−	747993.i	0.000115009	−	0.00233738i
$685$	6.63854e8			2.06538
$686$		−	7.91679e7i		−	0.245232i
$687$	−2.50114e8	−	2.62723e8i	−0.771378	−	0.810266i
$688$	−1.05812e8			−0.324915
$689$			5.12177e6i			0.0156589i
$690$	−5.42349e7	+	5.16320e7i	−0.165094	+	0.157171i
$691$	−1.79348e8			−0.543579			−0.271790	−	0.962357i	$-0.587616\pi$
$691$	−1.79348e8			−0.543579			−0.271790	+	0.962357i	$0.587616\pi$
$692$		−	5.46025e6i		−	0.0164776i
$693$	3.91378e7	+	1.92574e6i	0.117597	+	0.00578626i
$694$	−1.47116e8			−0.440131
$695$		−	8.92418e7i		−	0.265836i
$696$	−1.81236e8	−	1.90373e8i	−0.537548	−	0.564647i
$697$	−4.70975e8			−1.39091
$698$			5.46787e8i			1.60787i
$699$	−1.46755e7	+	1.39712e7i	−0.0429697	+	0.0409074i
$700$	−140394.			−0.000409312
$701$		−	3.05804e8i		−	0.887748i	−0.896089	−	0.443874i	$-0.853604\pi$
$701$		−	3.05804e8i		−	0.887748i	0.896089	−	0.443874i	$-0.146396\pi$
$702$	−8.76841e7	−	1.01674e8i	−0.253460	−	0.293899i
$703$	4.13564e7			0.119035
$704$		−	3.28972e8i		−	0.942847i
$705$	3.42499e8	+	3.59765e8i	0.977443	+	1.02672i
$706$	−2.01668e8			−0.573089
$707$			2.12512e7i			0.0601347i
$708$	1.59447e6	−	1.51794e6i	0.00449278	−	0.00427716i
$709$	−3.69469e8			−1.03667			−0.518334	−	0.855178i	$-0.673448\pi$
$709$	−3.69469e8			−1.03667			−0.518334	+	0.855178i	$0.673448\pi$
$710$		−	6.33543e8i		−	1.77011i
$711$	−1.80384e7	+	3.66604e8i	−0.0501868	+	1.01997i
$712$	3.54743e8			0.982821
$713$			1.11761e8i			0.308335i
$714$	−5.19678e7	−	5.45877e7i	−0.142771	−	0.149968i
$715$	1.46382e8			0.400468
$716$			7.59038e6i			0.0206787i
$717$	−5.19469e8	+	4.94538e8i	−1.40930	+	1.34166i
$718$	1.23588e8			0.333890
$719$		−	5.19517e8i		−	1.39770i	−0.715270	−	0.698849i	$-0.753696\pi$
$719$		−	5.19517e8i		−	1.39770i	0.715270	−	0.698849i	$-0.246304\pi$
$720$	4.11321e8	+	2.02387e7i	1.10200	+	0.0542231i
$721$	−4.86571e6			−0.0129820
$722$			3.74483e8i			0.994994i
$723$	8.32306e7	+	8.74266e7i	0.220226	+	0.231328i
$724$	−4.61700e6			−0.0121659
$725$			5.16993e7i			0.135666i
$726$	2.07290e7	−	1.97341e7i	0.0541712	−	0.0515713i
$727$	7.05611e8			1.83638			0.918189	−	0.396143i	$-0.129652\pi$
$727$	7.05611e8			1.83638			0.918189	+	0.396143i	$0.129652\pi$
$728$		−	1.79661e7i		−	0.0465649i
$729$	5.69350e7	−	3.83214e8i	0.146959	−	0.989143i
$730$	7.15727e8			1.83984
$731$			2.08746e8i			0.534400i
$732$	4.00314e6	+	4.20495e6i	0.0102063	+	0.0107208i
$733$	3.25004e8			0.825234			0.412617	−	0.910905i	$-0.364615\pi$
$733$	3.25004e8			0.825234			0.412617	+	0.910905i	$0.364615\pi$
$734$		−	4.30421e8i		−	1.08844i
$735$	3.06712e8	−	2.91992e8i	0.772447	−	0.735374i
$736$	−3.22777e6			−0.00809596
$737$		−	9.91406e7i		−	0.247656i
$738$	−1.65514e7	+	3.36382e8i	−0.0411780	+	0.836880i
$739$	−5.39968e8			−1.33793			−0.668967	−	0.743292i	$-0.733263\pi$
$739$	−5.39968e8			−1.33793			−0.668967	+	0.743292i	$0.733263\pi$
$740$		−	8.41321e6i		−	0.0207619i
$741$	−1.29972e7	−	1.36525e7i	−0.0319445	−	0.0335550i
$742$	2.05599e6			0.00503278
$743$			6.45572e8i			1.57390i	0.617014	+	0.786952i	$0.288342\pi$
$743$			6.45572e8i			1.57390i	−0.617014	+	0.786952i	$0.711658\pi$
$744$	4.36685e8	−	4.15727e8i	1.06035	−	1.00946i
$745$	1.58602e8			0.383566
$746$		−	4.02328e8i		−	0.969089i
$747$	−8.67325e7	−	4.26760e6i	−0.208075	−	0.0102382i
$748$	1.31052e7			0.0313139
$749$			8.13028e7i			0.193491i
$750$	2.63207e8	+	2.76477e8i	0.623899	+	0.655352i
$751$	1.70749e8			0.403123			0.201562	−	0.979476i	$-0.435398\pi$
$751$	1.70749e8			0.403123			0.201562	+	0.979476i	$0.435398\pi$
$752$			5.67383e8i			1.33421i
$753$	2.54539e8	−	2.42323e8i	0.596170	−	0.567557i
$754$	1.30999e8			0.305600
$755$		−	2.08738e8i		−	0.485020i
$756$	−777360.	+	670399.i	−0.00179911	+	0.00155156i
$757$	−3.18707e8			−0.734690			−0.367345	−	0.930085i	$-0.619733\pi$
$757$	−3.18707e8			−0.734690			−0.367345	+	0.930085i	$0.619733\pi$
$758$			1.18425e7i			0.0271916i
$759$	−6.04910e7	−	6.35406e7i	−0.138346	−	0.145320i
$760$	5.67165e7			0.129202
$761$			4.04851e8i			0.918631i	0.888273	+	0.459316i	$0.151905\pi$
$761$			4.04851e8i			0.918631i	−0.888273	+	0.459316i	$0.848095\pi$
$762$	−1.08871e8	+	1.03646e8i	−0.246063	+	0.234253i
$763$	−7.35874e7			−0.165665
$764$		−	7.02036e6i		−	0.0157427i
$765$	3.99268e7	−	8.11453e8i	0.0891827	−	1.81251i
$766$	−3.77390e8			−0.839662
$767$		−	5.54114e7i		−	0.122804i
$768$	1.81865e7	+	1.91033e7i	0.0401480	+	0.0421721i
$769$	−3.69184e8			−0.811827			−0.405914	−	0.913911i	$-0.633047\pi$
$769$	−3.69184e8			−0.811827			−0.405914	+	0.913911i	$0.633047\pi$
$770$		−	5.87607e7i		−	0.128711i
$771$	−2.41566e8	+	2.29972e8i	−0.527075	+	0.501778i
$772$	−1.50963e7			−0.0328108
$773$		−	3.67435e7i		−	0.0795503i	−0.999209	−	0.0397751i	$-0.987336\pi$
$773$		−	3.67435e7i		−	0.0795503i	0.999209	−	0.0397751i	$-0.0126642\pi$
$774$	1.49092e8	+	7.33592e6i	0.321536	+	0.0158209i
$775$	−1.18590e8			−0.254767
$776$			5.47913e8i			1.17254i
$777$	−3.90864e7	−	4.10569e7i	−0.0833225	−	0.0875231i
$778$	2.81477e8			0.597729
$779$			4.72842e7i			0.100024i
$780$	−2.77735e6	+	2.64406e6i	−0.00585258	+	0.00557169i
$781$	7.42247e8			1.55810
$782$			1.68740e8i			0.352857i
$783$	2.46871e8	+	2.86259e8i	0.514262	+	0.596311i
$784$	4.83713e8			1.00378
$785$			6.40525e8i			1.32412i
$786$	8.66382e7	+	9.10060e7i	0.178419	+	0.187414i
$787$	−8.35847e8			−1.71476			−0.857378	−	0.514687i	$-0.827908\pi$
$787$	−8.35847e8			−1.71476			−0.857378	+	0.514687i	$0.827908\pi$
$788$		−	8.79475e6i		−	0.0179740i
$789$	−3.28638e8	+	3.12865e8i	−0.669093	+	0.636981i
$790$	5.50411e8			1.11636
$791$			7.21745e7i			0.145833i
$792$	−2.32595e7	+	4.72714e8i	−0.0468192	+	0.951530i
$793$	1.46132e8			0.293039
$794$			2.77867e8i			0.555105i
$795$	1.52813e7	+	1.60516e7i	0.0304129	+	0.0319461i
$796$	−3.54145e6			−0.00702170
$797$			1.07337e8i			0.212019i	0.994365	+	0.106009i	$0.0338074\pi$
$797$			1.07337e8i			0.212019i	−0.994365	+	0.106009i	$0.966193\pi$
$798$	−5.48040e6	+	5.21737e6i	−0.0107846	+	0.0102670i
$799$	1.11933e9			2.19442
$800$		−	3.42498e6i		−	0.00668942i
$801$	−5.09550e8	−	2.50719e7i	−0.991491	−	0.0487855i
$802$	−9.90197e8			−1.91955
$803$			8.38532e8i			1.61947i
$804$	1.79075e6	+	1.88103e6i	0.00344562	+	0.00361933i
$805$	1.44104e7			0.0276241
$806$			3.00491e8i			0.573887i
$807$	2.75156e8	−	2.61950e8i	0.523551	−	0.498423i
$808$	−2.56676e8			−0.486577
$809$		−	5.81899e8i		−	1.09901i	−0.835490	−	0.549506i	$-0.814816\pi$
$809$		−	5.81899e8i		−	1.09901i	0.835490	−	0.549506i	$-0.185184\pi$
$810$	−5.78156e8	−	5.70334e7i	−1.08790	−	0.107318i
$811$	−3.66440e8			−0.686974			−0.343487	−	0.939157i	$-0.611608\pi$
$811$	−3.66440e8			−0.686974			−0.343487	+	0.939157i	$0.611608\pi$
$812$		−	1.00157e6i		−	0.00187073i
$813$	−4.62456e7	−	4.85770e7i	−0.0860595	−	0.0903981i
$814$	5.17514e8			0.959508
$815$		−	4.57014e8i		−	0.844221i
$816$	6.72127e8	−	6.39868e8i	1.23703	−	1.17766i
$817$	2.09573e7			0.0384300
$818$			8.86235e8i			1.61916i
$819$	−1.26977e6	+	2.58063e7i	−0.00231140	+	0.0469757i
$820$	9.61911e6			0.0174459
$821$		−	6.64408e7i		−	0.120062i	−0.998197	−	0.0600310i	$-0.980880\pi$
$821$		−	6.64408e7i		−	0.120062i	0.998197	−	0.0600310i	$-0.0191200\pi$
$822$	−7.37593e8	−	7.74778e8i	−1.32801	−	1.39496i
$823$	−4.85298e8			−0.870580			−0.435290	−	0.900290i	$-0.643354\pi$
$823$	−4.85298e8			−0.870580			−0.435290	+	0.900290i	$0.643354\pi$
$824$		−	5.87690e7i		−	0.105043i
$825$	6.74230e7	−	6.41870e7i	0.120073	−	0.114310i
$826$	−2.22433e7			−0.0394693
$827$			3.89827e8i			0.689216i	0.938747	+	0.344608i	$0.111988\pi$
$827$			3.89827e8i			0.689216i	−0.938747	+	0.344608i	$0.888012\pi$
$828$	2.29544e6	+	112945.i	0.00404366	+	0.000198965i
$829$	5.07379e7			0.0890571			0.0445286	−	0.999008i	$-0.485821\pi$
$829$	5.07379e7			0.0890571			0.0445286	+	0.999008i	$0.485821\pi$
$830$			1.30218e8i			0.227739i
$831$	−2.11708e8	−	2.22381e8i	−0.368921	−	0.387520i
$832$	2.16914e8			0.376633
$833$		−	9.54269e8i		−	1.65096i
$834$	−1.04153e8	+	9.91546e7i	−0.179546	+	0.170929i
$835$	−2.70287e8			−0.464265
$836$		−	1.31571e6i		−	0.00225186i
$837$	−6.56632e8	+	5.66282e8i	−1.11981	+	0.965731i
$838$	1.51298e7			0.0257099
$839$		−	1.08048e9i		−	1.82949i	−0.404026	−	0.914747i	$-0.632390\pi$
$839$		−	1.08048e9i		−	1.82949i	0.404026	−	0.914747i	$-0.367610\pi$
$840$	−5.36034e7	−	5.63057e7i	−0.0904387	−	0.0949981i
$841$	2.26002e8			0.379948
$842$			8.00835e8i			1.34155i
$843$	−6.23000e8	+	5.93099e8i	−1.03993	+	0.990021i
$844$	−1.98104e7			−0.0329509
$845$		−	5.56742e8i		−	0.922750i
$846$	3.93365e7	−	7.99455e8i	0.0649657	−	1.32033i
$847$	−5.50776e6			−0.00906409
$848$			2.53149e7i			0.0415135i
$849$	4.79708e8	+	5.03892e8i	0.783887	+	0.823406i
$850$	−1.79051e8			−0.291554
$851$			1.26914e8i			0.205931i
$852$	−1.40829e7	+	1.34070e7i	−0.0227706	+	0.0216777i
$853$	8.28377e8			1.33469			0.667346	−	0.744748i	$-0.267430\pi$
$853$	8.28377e8			1.33469			0.667346	+	0.744748i	$0.267430\pi$
$854$		−	5.86605e7i		−	0.0941829i
$855$	−8.14669e7	−	4.00851e6i	−0.130342	−	0.00641334i
$856$	−9.81991e8			−1.56562
$857$		−	7.86591e8i		−	1.24970i	−0.780744	−	0.624851i	$-0.785160\pi$
$857$		−	7.86591e8i		−	1.24970i	0.780744	−	0.624851i	$-0.214840\pi$
$858$	−1.62641e8	−	1.70841e8i	−0.257495	−	0.270476i
$859$	−5.10717e8			−0.805751			−0.402875	−	0.915255i	$-0.631989\pi$
$859$	−5.10717e8			−0.805751			−0.402875	+	0.915255i	$0.631989\pi$
$860$		−	4.26339e6i		−	0.00670286i
$861$	4.69417e7	−	4.46888e7i	0.0735444	−	0.0700147i
$862$	−1.07314e8			−0.167546
$863$			7.68698e8i			1.19598i	0.801504	+	0.597989i	$0.204033\pi$
$863$			7.68698e8i			1.19598i	−0.801504	+	0.597989i	$0.795967\pi$
$864$	−1.63547e7	−	1.89641e7i	−0.0253573	−	0.0294030i
$865$	−5.94698e8			−0.918857
$866$		−	1.20110e9i		−	1.84938i
$867$	−8.12967e8	−	8.53952e8i	−1.24743	−	1.31032i
$868$	2.29744e6			0.00351305
$869$			6.44851e8i			0.982653i
$870$	4.10551e8	−	3.90847e8i	0.623462	−	0.593539i
$871$	6.53703e7			0.0989295
$872$		−	8.88803e8i		−	1.34047i
$873$	3.87244e7	−	7.87016e8i	0.0582026	−	1.18288i
$874$	1.69409e7			0.0253748
$875$		−	7.34607e7i		−	0.109656i
$876$	−1.51462e7	−	1.59098e7i	−0.0225316	−	0.0236675i
$877$	4.23683e8			0.628120			0.314060	−	0.949403i	$-0.398311\pi$
$877$	4.23683e8			0.628120			0.314060	+	0.949403i	$0.398311\pi$
$878$			1.03368e9i			1.52722i
$879$	3.03494e8	−	2.88928e8i	0.446873	−	0.425426i
$880$	7.23508e8			1.06168
$881$		−	4.04706e7i		−	0.0591851i	−0.999562	−	0.0295925i	$-0.990579\pi$
$881$		−	4.04706e7i		−	0.0591851i	0.999562	−	0.0295925i	$-0.00942097\pi$
$882$	−6.81562e8	−	3.35356e7i	−0.993343	−	0.0488766i
$883$	−4.52758e7			−0.0657634			−0.0328817	−	0.999459i	$-0.510468\pi$
$883$	−4.52758e7			−0.0657634			−0.0328817	+	0.999459i	$0.510468\pi$
$884$			8.64115e6i			0.0125088i
$885$	−1.65325e8	−	1.73660e8i	−0.238511	−	0.250536i
$886$	6.26348e8			0.900564
$887$			5.04848e8i			0.723419i	0.932291	+	0.361710i	$0.117807\pi$
$887$			5.04848e8i			0.723419i	−0.932291	+	0.361710i	$0.882193\pi$
$888$	4.95893e8	−	4.72093e8i	0.708189	−	0.674200i
$889$	2.89273e7			0.0411720
$890$			7.65027e8i			1.08519i
$891$	6.68192e7	−	6.77357e8i	0.0944645	−	0.957600i
$892$	−1.45660e7			−0.0205232
$893$		−	1.12377e8i		−	0.157806i
$894$	−1.76219e8	−	1.85103e8i	−0.246627	−	0.259061i
$895$	8.26698e8			1.15313
$896$		−	9.04913e7i		−	0.125801i
$897$	4.18967e7	−	3.98859e7i	0.0580501	−	0.0552640i
$898$	−1.92145e8			−0.265339
$899$		−	8.46018e8i		−	1.16440i
$900$	−119846.	+	2.43569e6i	−0.000164398	+	0.00334114i
$901$	4.99413e7			0.0682787
$902$			5.91691e8i			0.806261i
$903$	−1.98070e7	−	2.08056e7i	−0.0269002	−	0.0282564i
$904$	−8.71738e8			−1.18000
$905$			5.02856e8i			0.678419i
$906$	−2.43616e8	+	2.31924e8i	−0.327583	+	0.311861i
$907$	1.24506e9			1.66866			0.834330	−	0.551265i	$-0.185855\pi$
$907$	1.24506e9			1.66866			0.834330	+	0.551265i	$0.185855\pi$
$908$		−	2.70209e7i		−	0.0360946i
$909$	3.68687e8	+	1.81409e7i	0.490869	+	0.0241528i
$910$	3.87450e7			0.0514152
$911$		−	1.14993e9i		−	1.52095i	−0.649366	−	0.760476i	$-0.724966\pi$
$911$		−	1.14993e9i		−	1.52095i	0.649366	−	0.760476i	$-0.275034\pi$
$912$	−6.42404e7	−	6.74790e7i	−0.0846884	−	0.0889578i
$913$	−1.52561e8			−0.200462
$914$			1.16897e9i			1.53096i
$915$	4.57978e8	−	4.35998e8i	0.597836	−	0.569143i
$916$	1.66946e7			0.0217214
$917$		−	2.41805e7i		−	0.0313587i
$918$	−9.91402e8	+	8.54990e8i	−1.28151	+	1.10518i
$919$	−6.27201e8			−0.808091			−0.404046	−	0.914739i	$-0.632396\pi$
$919$	−6.27201e8			−0.808091			−0.404046	+	0.914739i	$0.632396\pi$
$920$			1.74051e8i			0.223519i
$921$	6.21098e8	+	6.52409e8i	0.795025	+	0.835106i
$922$	−7.50321e8			−0.957313
$923$			4.89415e8i			0.622404i
$924$	−1.30618e6	+	1.24349e6i	−0.00165572	+	0.00157626i
$925$	−1.34669e8			−0.170154
$926$			1.26004e9i			1.58691i
$927$	−4.15357e6	+	8.44151e7i	−0.00521414	+	0.105970i
$928$	2.44338e7			0.0305736
$929$		−	1.25486e9i		−	1.56513i	−0.622571	−	0.782563i	$-0.713912\pi$
$929$		−	1.25486e9i		−	1.56513i	0.622571	−	0.782563i	$-0.286088\pi$
$930$	8.96542e8	+	9.41740e8i	1.11461	+	1.17080i
$931$	−9.58050e7			−0.118724
$932$		−	932547.i		−	0.00115192i
$933$	−1.07687e8	+	1.02518e8i	−0.132592	+	0.126228i
$934$	−9.19437e7			−0.112845
$935$		−	1.42734e9i		−	1.74619i
$936$	−3.11693e8	−	1.53366e7i	−0.380101	−	0.0187025i
$937$	−1.20465e9			−1.46434			−0.732170	−	0.681122i	$-0.761492\pi$
$937$	−1.20465e9			−1.46434			−0.732170	+	0.681122i	$0.761492\pi$
$938$		−	2.62410e7i		−	0.0317960i
$939$	−8.38736e6	−	8.81020e6i	−0.0101305	−	0.0106412i
$940$	−2.28611e7			−0.0275241
$941$		−	3.30050e8i		−	0.396106i	−0.980191	−	0.198053i	$-0.936538\pi$
$941$		−	3.30050e8i		−	0.396106i	0.980191	−	0.198053i	$-0.0634618\pi$
$942$	7.47552e8	−	7.11674e8i	0.894311	−	0.851389i
$943$	−1.45105e8			−0.173041
$944$		−	2.73877e8i		−	0.325567i
$945$	7.30158e7	+	8.46654e7i	0.0865210	+	0.100325i
$946$	2.62250e8			0.309772
$947$		−	1.22987e9i		−	1.44813i	−0.689731	−	0.724066i	$-0.742271\pi$
$947$		−	1.22987e9i		−	1.44813i	0.689731	−	0.724066i	$-0.257729\pi$
$948$	−1.16478e7	−	1.22350e7i	−0.0136716	−	0.0143608i
$949$	−5.52902e8			−0.646919
$950$			1.79760e7i			0.0209663i
$951$	1.14543e9	−	1.09045e9i	1.33176	−	1.26784i
$952$	−1.75183e8			−0.203040
$953$		−	3.37839e7i		−	0.0390330i	−0.999810	−	0.0195165i	$-0.993787\pi$
$953$		−	3.37839e7i		−	0.0390330i	0.999810	−	0.0195165i	$-0.00621268\pi$
$954$	1.75507e6	−	3.56692e7i	0.00202139	−	0.0410817i
$955$	−7.64616e8			−0.877876
$956$		−	3.30093e7i		−	0.0377801i
$957$	4.57909e8	+	4.80994e8i	0.522449	+	0.548787i
$958$	9.08712e8			1.03355
$959$			2.05861e8i			0.233409i
$960$	6.79810e8	−	6.47183e8i	0.768376	−	0.731498i
$961$	1.05313e9			1.18662
$962$			3.41233e8i			0.383288i
$963$	1.41052e9	+	6.94034e7i	1.57943	+	0.0777145i
$964$	−5.55547e6			−0.00620140
$965$			1.64419e9i			1.82966i
$966$	−1.60111e7	−	1.68182e7i	−0.0177619	−	0.0186573i
$967$	4.12084e7			0.0455729			0.0227864	−	0.999740i	$-0.492746\pi$
$967$	4.12084e7			0.0455729			0.0227864	+	0.999740i	$0.492746\pi$
$968$		−	6.65237e7i		−	0.0733416i
$969$	−1.33123e8	+	1.26733e8i	−0.146312	+	0.139290i
$970$	−1.18161e9			−1.29467
$971$		−	1.95181e8i		−	0.213196i	−0.994302	−	0.106598i	$-0.966004\pi$
$971$		−	1.95181e8i		−	0.213196i	0.994302	−	0.106598i	$-0.0339958\pi$
$972$	1.09671e7	+	1.40587e7i	0.0119425	+	0.0153090i
$973$	2.76739e7			0.0300422
$974$			7.64987e8i			0.827899i
$975$	4.23230e7	+	4.44566e7i	0.0456628	+	0.0479648i
$976$	7.22274e8			0.776878
$977$			1.05343e9i			1.12959i	0.825230	+	0.564797i	$0.191045\pi$
$977$			1.05343e9i			1.12959i	−0.825230	+	0.564797i	$0.808955\pi$
$978$	−5.33377e8	+	5.07778e8i	−0.570187	+	0.542821i
$979$	−8.96291e8			−0.955215
$980$			1.94898e7i			0.0207076i
$981$	−6.28172e7	+	1.27667e9i	−0.0665383	+	1.35229i
$982$	5.23792e8			0.553126
$983$			1.20906e9i			1.27288i	0.771326	+	0.636440i	$0.219594\pi$
$983$			1.20906e9i			1.27288i	−0.771326	+	0.636440i	$0.780406\pi$
$984$	5.39760e8	+	5.66971e8i	0.566520	+	0.595081i
$985$	−9.57872e8			−1.00230
$986$		−	1.27734e9i		−	1.33253i
$987$	−1.11563e8	+	1.06209e8i	−0.116030	+	0.110461i
$988$	867539.			0.000899535
$989$			6.43138e7i			0.0664837i
$990$	−1.01944e9	−	5.01605e7i	−1.05064	−	0.0516960i
$991$	−1.73083e9			−1.77841			−0.889206	−	0.457507i	$-0.848743\pi$
$991$	−1.73083e9			−1.77841			−0.889206	+	0.457507i	$0.848743\pi$
$992$			5.60472e7i			0.0574142i
$993$	7.30454e8	+	7.67279e8i	0.746011	+	0.783621i
$994$	1.96462e8			0.200041
$995$			3.85714e8i			0.391558i
$996$	2.89461e6	−	2.75568e6i	0.00292962	−	0.00278902i
$997$	−2.93281e8			−0.295936			−0.147968	−	0.988992i	$-0.547273\pi$
$997$	−2.93281e8			−0.295936			−0.147968	+	0.988992i	$0.547273\pi$
$998$		−	6.19878e8i		−	0.623612i
$999$	−7.45661e8	+	6.43061e8i	−0.747902	+	0.644994i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	69.7.b.a.47.13	✓	44
3.2	odd	2	inner	69.7.b.a.47.32	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.7.b.a.47.13	✓	44	1.1	even	1	trivial
69.7.b.a.47.32	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)

\(f(q)\)	\(=\)	\(q-8.07729i q^{2} +(18.6168 + 19.5554i) q^{3} -1.24263 q^{4} +135.340i q^{5} +(157.955 - 150.374i) q^{6} -41.9690 q^{7} -506.910i q^{8} +(-35.8265 + 728.119i) q^{9} +O(q^{10})\)	\(q-8.07729i q^{2} +(18.6168 + 19.5554i) q^{3} -1.24263 q^{4} +135.340i q^{5} +(157.955 - 150.374i) q^{6} -41.9690 q^{7} -506.910i q^{8} +(-35.8265 + 728.119i) q^{9} +1093.18 q^{10} +1280.75i q^{11} +(-23.1339 - 24.3002i) q^{12} -844.489 q^{13} +338.996i q^{14} +(-2646.63 + 2519.61i) q^{15} -4173.98 q^{16} +8234.44i q^{17} +(5881.23 + 289.381i) q^{18} +826.707 q^{19} -168.179i q^{20} +(-781.330 - 820.720i) q^{21} +10345.0 q^{22} +2536.99i q^{23} +(9912.81 - 9437.05i) q^{24} -2692.01 q^{25} +6821.18i q^{26} +(-14905.6 + 12854.7i) q^{27} +52.1521 q^{28} -19204.7i q^{29} +(20351.6 + 21377.6i) q^{30} +44052.6 q^{31} +1272.28i q^{32} +(-25045.6 + 23843.6i) q^{33} +66511.9 q^{34} -5680.10i q^{35} +(44.5192 - 904.786i) q^{36} +50025.4 q^{37} -6677.55i q^{38} +(-15721.7 - 16514.3i) q^{39} +68605.3 q^{40} +57195.8i q^{41} +(-6629.19 + 6311.03i) q^{42} +25350.4 q^{43} -1591.51i q^{44} +(-98543.9 - 4848.77i) q^{45} +20492.0 q^{46} -135933. i q^{47} +(-77706.4 - 81623.9i) q^{48} -115888. q^{49} +21744.1i q^{50} +(-161028. + 153299. i) q^{51} +1049.39 q^{52} -6064.93i q^{53} +(103831. + 120397. i) q^{54} -173337. q^{55} +21274.5i q^{56} +(15390.7 + 16166.6i) q^{57} -155122. q^{58} +65615.3i q^{59} +(3288.80 - 3130.95i) q^{60} -173042. q^{61} -355826. i q^{62} +(1503.60 - 30558.4i) q^{63} -256858. q^{64} -114293. i q^{65} +(192591. + 202301. i) q^{66} -77408.1 q^{67} -10232.4i q^{68} +(-49611.9 + 47230.8i) q^{69} -45879.8 q^{70} -579540. i q^{71} +(369091. + 18160.8i) q^{72} +654718. q^{73} -404070. i q^{74} +(-50116.7 - 52643.2i) q^{75} -1027.29 q^{76} -53751.9i q^{77} +(-133391. + 126989. i) q^{78} +503494. q^{79} -564908. i q^{80} +(-528874. - 52171.9i) q^{81} +461987. q^{82} +119119. i q^{83} +(970.908 + 1019.86i) q^{84} -1.11445e6 q^{85} -204763. i q^{86} +(375556. - 357531. i) q^{87} +649226. q^{88} +699816. i q^{89} +(-39164.9 + 795968. i) q^{90} +35442.3 q^{91} -3152.56i q^{92} +(820120. + 861466. i) q^{93} -1.09797e6 q^{94} +111887. i q^{95} +(-24879.9 + 23685.8i) q^{96} -1.08089e6 q^{97} +936058. i q^{98} +(-932540. - 45884.8i) 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

L-functions

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