LMFDB - Embedded newform 69.7.b.a.47.19

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			47.19
Character	$\chi$	$=$	69.47
Dual form			69.7.b.a.47.26

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.95357i q^{2} +(2.97092 - 26.8361i) q^{3} +55.2764 q^{4} -175.802i q^{5} +(-79.2621 - 8.77482i) q^{6} -435.351 q^{7} -352.291i q^{8} +(-711.347 - 159.456i) q^{9} +O(q^{10})$	\(q-2.95357i q^{2} +(2.97092 - 26.8361i) q^{3} +55.2764 q^{4} -175.802i q^{5} +(-79.2621 - 8.77482i) q^{6} -435.351 q^{7} -352.291i q^{8} +(-711.347 - 159.456i) q^{9} -519.242 q^{10} +467.266i q^{11} +(164.222 - 1483.40i) q^{12} +3432.36 q^{13} +1285.84i q^{14} +(-4717.82 - 522.293i) q^{15} +2497.18 q^{16} +38.8474i q^{17} +(-470.963 + 2101.01i) q^{18} -6960.90 q^{19} -9717.69i q^{20} +(-1293.39 + 11683.1i) q^{21} +1380.10 q^{22} +2536.99i q^{23} +(-9454.10 - 1046.63i) q^{24} -15281.2 q^{25} -10137.7i q^{26} +(-6392.52 + 18616.0i) q^{27} -24064.7 q^{28} +4962.99i q^{29} +(-1542.63 + 13934.4i) q^{30} -26104.3 q^{31} -29922.2i q^{32} +(12539.6 + 1388.21i) q^{33} +114.738 q^{34} +76535.5i q^{35} +(-39320.7 - 8814.14i) q^{36} +86907.3 q^{37} +20559.5i q^{38} +(10197.3 - 92111.0i) q^{39} -61933.4 q^{40} -112871. i q^{41} +(34506.9 + 3820.13i) q^{42} -114313. q^{43} +25828.8i q^{44} +(-28032.6 + 125056. i) q^{45} +7493.19 q^{46} -140262. i q^{47} +(7418.92 - 67014.3i) q^{48} +71881.7 q^{49} +45134.1i q^{50} +(1042.51 + 115.413i) q^{51} +189729. q^{52} +201347. i q^{53} +(54983.7 + 18880.7i) q^{54} +82146.2 q^{55} +153370. i q^{56} +(-20680.3 + 186803. i) q^{57} +14658.5 q^{58} -226492. i q^{59} +(-260784. - 28870.5i) q^{60} -15825.1 q^{61} +77100.9i q^{62} +(309686. + 69419.2i) q^{63} +71441.9 q^{64} -603415. i q^{65} +(4100.18 - 37036.5i) q^{66} +335370. q^{67} +2147.34i q^{68} +(68082.9 + 7537.22i) q^{69} +226053. q^{70} -347002. i q^{71} +(-56174.8 + 250601. i) q^{72} +93015.5 q^{73} -256687. i q^{74} +(-45399.3 + 410088. i) q^{75} -384774. q^{76} -203425. i q^{77} +(-272056. - 30118.4i) q^{78} +757584. q^{79} -439008. i q^{80} +(480589. + 226857. i) q^{81} -333372. q^{82} -508669. i q^{83} +(-71494.3 + 645801. i) q^{84} +6829.43 q^{85} +337630. i q^{86} +(133187. + 14744.7i) q^{87} +164614. q^{88} +739130. i q^{89} +(369362. + 82796.1i) q^{90} -1.49428e6 q^{91} +140236. i q^{92} +(-77553.9 + 700537. i) q^{93} -414272. q^{94} +1.22374e6i q^{95} +(-802994. - 88896.6i) q^{96} -719013. q^{97} -212307. i q^{98} +(74508.3 - 332389. 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 $

$2$		−	2.95357i		−	0.369196i	−0.982814	−	0.184598i	$-0.940902\pi$
$2$		−	2.95357i		−	0.369196i	0.982814	−	0.184598i	$-0.0590983\pi$
$3$	2.97092	−	26.8361i	0.110034	−	0.993928i
$3$	2.97092	−	26.8361i	0.110034	−	0.993928i
$4$	55.2764			0.863694
$5$		−	175.802i		−	1.40641i	−0.710986	−	0.703207i	$-0.751751\pi$
$5$		−	175.802i		−	1.40641i	0.710986	−	0.703207i	$-0.248249\pi$
$6$	−79.2621	−	8.77482i	−0.366954	−	0.0406242i
$7$	−435.351			−1.26925			−0.634623	−	0.772822i	$-0.718845\pi$
$7$	−435.351			−1.26925			−0.634623	+	0.772822i	$0.718845\pi$
$8$		−	352.291i		−	0.688069i
$9$	−711.347	−	159.456i	−0.975785	−	0.218732i
$10$	−519.242			−0.519242
$11$			467.266i			0.351064i	0.984474	+	0.175532i	$0.0561646\pi$
$11$			467.266i			0.351064i	−0.984474	+	0.175532i	$0.943835\pi$
$12$	164.222	−	1483.40i	0.0950359	−	0.858450i
$13$	3432.36			1.56229			0.781147	−	0.624347i	$-0.214635\pi$
$13$	3432.36			1.56229			0.781147	+	0.624347i	$0.214635\pi$
$14$			1285.84i			0.468600i
$15$	−4717.82	−	522.293i	−1.39787	−	0.154754i
$16$	2497.18			0.609662
$17$			38.8474i			0.00790706i	0.999992	+	0.00395353i	$0.00125845\pi$
$17$			38.8474i			0.00790706i	−0.999992	+	0.00395353i	$0.998742\pi$
$18$	−470.963	+	2101.01i	−0.0807550	+	0.360256i
$19$	−6960.90			−1.01486			−0.507428	−	0.861694i	$-0.669404\pi$
$19$	−6960.90			−1.01486			−0.507428	+	0.861694i	$0.669404\pi$
$20$		−	9717.69i		−	1.21471i
$21$	−1293.39	+	11683.1i	−0.139660	+	1.26154i
$22$	1380.10			0.129611
$23$			2536.99i			0.208514i
$23$			2536.99i			0.208514i
$24$	−9454.10	−	1046.63i	−0.683891	−	0.0757111i
$25$	−15281.2			−0.977998
$26$		−	10137.7i		−	0.576793i
$27$	−6392.52	+	18616.0i	−0.324774	+	0.945792i
$28$	−24064.7			−1.09624
$29$			4962.99i			0.203493i	0.994810	+	0.101746i	$0.0324431\pi$
$29$			4962.99i			0.203493i	−0.994810	+	0.101746i	$0.967557\pi$
$30$	−1542.63	+	13934.4i	−0.0571344	+	0.516089i
$31$	−26104.3			−0.876248			−0.438124	−	0.898914i	$-0.644357\pi$
$31$	−26104.3			−0.876248			−0.438124	+	0.898914i	$0.644357\pi$
$32$		−	29922.2i		−	0.913153i
$33$	12539.6	+	1388.21i	0.348932	+	0.0386290i
$34$	114.738			0.00291926
$35$			76535.5i			1.78508i
$36$	−39320.7	−	8814.14i	−0.842780	−	0.188918i
$37$	86907.3			1.71574			0.857869	−	0.513868i	$-0.171788\pi$
$37$	86907.3			1.71574			0.857869	+	0.513868i	$0.171788\pi$
$38$			20559.5i			0.374681i
$39$	10197.3	−	92111.0i	0.171906	−	1.55281i
$40$	−61933.4			−0.967709
$41$		−	112871.i		−	1.63768i	−0.574020	−	0.818842i	$-0.694617\pi$
$41$		−	112871.i		−	1.63768i	0.574020	−	0.818842i	$-0.305383\pi$
$42$	34506.9	+	3820.13i	0.465755	+	0.0515621i
$43$	−114313.			−1.43777			−0.718883	−	0.695131i	$-0.755346\pi$
$43$	−114313.			−1.43777			−0.718883	+	0.695131i	$0.755346\pi$
$44$			25828.8i			0.303212i
$45$	−28032.6	+	125056.i	−0.307628	+	1.37236i
$46$	7493.19			0.0769827
$47$		−	140262.i		−	1.35097i	−0.737375	−	0.675484i	$-0.763935\pi$
$47$		−	140262.i		−	1.35097i	0.737375	−	0.675484i	$-0.236065\pi$
$48$	7418.92	−	67014.3i	0.0670837	−	0.605960i
$49$	71881.7			0.610984
$50$			45134.1i			0.361073i
$51$	1042.51	+	115.413i	0.00785905	+	0.000870047i
$52$	189729.			1.34934
$53$			201347.i			1.35244i	0.736699	+	0.676221i	$0.236383\pi$
$53$			201347.i			1.35244i	−0.736699	+	0.676221i	$0.763617\pi$
$54$	54983.7	+	18880.7i	0.349183	+	0.119905i
$55$	82146.2			0.493741
$56$			153370.i			0.873328i
$57$	−20680.3	+	186803.i	−0.111669	+	1.00869i
$58$	14658.5			0.0751288
$59$		−	226492.i		−	1.10280i	−0.834241	−	0.551401i	$-0.814094\pi$
$59$		−	226492.i		−	1.10280i	0.834241	−	0.551401i	$-0.185906\pi$
$60$	−260784.	−	28870.5i	−1.20734	−	0.133660i
$61$	−15825.1			−0.0697197			−0.0348599	−	0.999392i	$-0.511098\pi$
$61$	−15825.1			−0.0697197			−0.0348599	+	0.999392i	$0.511098\pi$
$62$			77100.9i			0.323507i
$63$	309686.	+	69419.2i	1.23851	+	0.277625i
$64$	71441.9			0.272529
$65$		−	603415.i		−	2.19723i
$66$	4100.18	−	37036.5i	0.0142617	−	0.128824i
$67$	335370.			1.11506			0.557532	−	0.830155i	$-0.311748\pi$
$67$	335370.			1.11506			0.557532	+	0.830155i	$0.311748\pi$
$68$			2147.34i			0.00682928i
$69$	68082.9	+	7537.22i	0.207248	+	0.0229437i
$70$	226053.			0.659046
$71$		−	347002.i		−	0.969521i	−0.874647	−	0.484760i	$-0.838907\pi$
$71$		−	347002.i		−	0.969521i	0.874647	−	0.484760i	$-0.161093\pi$
$72$	−56174.8	+	250601.i	−0.150503	+	0.671407i
$73$	93015.5			0.239104			0.119552	−	0.992828i	$-0.461854\pi$
$73$	93015.5			0.239104			0.119552	+	0.992828i	$0.461854\pi$
$74$		−	256687.i		−	0.633444i
$75$	−45399.3	+	410088.i	−0.107613	+	0.972059i
$76$	−384774.			−0.876526
$77$		−	203425.i		−	0.445587i
$78$	−272056.	−	30118.4i	−0.573291	−	0.0634669i
$79$	757584.			1.53656			0.768280	−	0.640114i	$-0.221113\pi$
$79$	757584.			1.53656			0.768280	+	0.640114i	$0.221113\pi$
$80$		−	439008.i		−	0.857437i
$81$	480589.	+	226857.i	0.904313	+	0.426871i
$82$	−333372.			−0.604626
$83$		−	508669.i		−	0.889612i	−0.895627	−	0.444806i	$-0.853273\pi$
$83$		−	508669.i		−	0.889612i	0.895627	−	0.444806i	$-0.146727\pi$
$84$	−71494.3	+	645801.i	−0.120624	+	1.08958i
$85$	6829.43			0.0111206
$86$			337630.i			0.530818i
$87$	133187.	+	14744.7i	0.202257	+	0.0223912i
$88$	164614.			0.241556
$89$			739130.i			1.04846i	0.851578	+	0.524228i	$0.175646\pi$
$89$			739130.i			1.04846i	−0.851578	+	0.524228i	$0.824354\pi$
$90$	369362.	+	82796.1i	0.506669	+	0.113575i
$91$	−1.49428e6			−1.98294
$92$			140236.i			0.180093i
$93$	−77553.9	+	700537.i	−0.0964173	+	0.870928i
$94$	−414272.			−0.498772
$95$			1.22374e6i			1.42731i
$96$	−802994.	−	88896.6i	−0.907609	−	0.100478i
$97$	−719013.			−0.787810			−0.393905	−	0.919151i	$-0.628876\pi$
$97$	−719013.			−0.787810			−0.393905	+	0.919151i	$0.628876\pi$
$98$		−	212307.i		−	0.225573i
$99$	74508.3	−	332389.i	0.0767890	−	0.342563i
$100$	−844691.			−0.844691
$101$		−	1.50284e6i		−	1.45864i	−0.684171	−	0.729322i	$-0.739836\pi$
$101$		−	1.50284e6i		−	1.45864i	0.684171	−	0.729322i	$-0.260164\pi$
$102$	340.879	−	3079.13i	0.000321218	−	0.00290153i
$103$	−1.14232e6			−1.04539			−0.522694	−	0.852521i	$-0.675073\pi$
$103$	−1.14232e6			−1.04539			−0.522694	+	0.852521i	$0.675073\pi$
$104$		−	1.20919e6i		−	1.07497i
$105$	2.05391e6	+	227381.i	1.77424	+	0.196420i
$106$	594693.			0.499316
$107$			952859.i			0.777816i	0.921276	+	0.388908i	$0.127148\pi$
$107$			952859.i			0.777816i	−0.921276	+	0.388908i	$0.872852\pi$
$108$	−353356.	+	1.02903e6i	−0.280505	+	0.816875i
$109$	1.01929e6			0.787077			0.393538	−	0.919308i	$-0.371251\pi$
$109$	1.01929e6			0.787077			0.393538	+	0.919308i	$0.371251\pi$
$110$		−	242624.i		−	0.182287i
$111$	258195.	−	2.33225e6i	0.188790	−	1.70532i
$112$	−1.08715e6			−0.773811
$113$		−	1.27107e6i		−	0.880915i	−0.897773	−	0.440458i	$-0.854816\pi$
$113$		−	1.27107e6i		−	0.880915i	0.897773	−	0.440458i	$-0.145184\pi$
$114$	551736.	+	61080.7i	0.372406	+	0.0412277i
$115$	446008.			0.293257
$116$			274336.i			0.175756i
$117$	−2.44160e6	−	547309.i	−1.52446	−	0.341724i
$118$	−668960.			−0.407150
$119$		−	16912.3i		−	0.0100360i
$120$	−183999.	+	1.66205e6i	−0.106481	+	0.961833i
$121$	1.55322e6			0.876754
$122$			46740.4i			0.0257403i
$123$	−3.02901e6	−	335330.i	−1.62774	−	0.180201i
$124$	−1.44295e6			−0.756811
$125$		−	60437.3i		−	0.0309439i
$126$	205034.	−	914679.i	0.102498	−	0.457253i
$127$	−310553.			−0.151609			−0.0758045	−	0.997123i	$-0.524153\pi$
$127$	−310553.			−0.151609			−0.0758045	+	0.997123i	$0.524153\pi$
$128$		−	2.12603e6i		−	1.01377i
$129$	−339614.	+	3.06770e6i	−0.158203	+	1.42904i
$130$	−1.78223e6			−0.811209
$131$			1.59754e6i			0.710619i	0.934749	+	0.355309i	$0.115624\pi$
$131$			1.59754e6i			0.710619i	−0.934749	+	0.355309i	$0.884376\pi$
$132$	693143.	+	76735.4i	0.301371	+	0.0333637i
$133$	3.03044e6			1.28810
$134$		−	990539.i		−	0.411677i
$135$	3.27273e6	+	1.12382e6i	1.33017	+	0.456766i
$136$	13685.6			0.00544060
$137$		−	1.80210e6i		−	0.700839i	−0.936593	−	0.350419i	$-0.886039\pi$
$137$		−	1.80210e6i		−	0.700839i	0.936593	−	0.350419i	$-0.113961\pi$
$138$	22261.7	−	201088.i	0.00847073	−	0.0765152i
$139$	3.35663e6			1.24985			0.624927	−	0.780683i	$-0.285129\pi$
$139$	3.35663e6			1.24985			0.624927	+	0.780683i	$0.285129\pi$
$140$			4.23061e6i			1.54177i
$141$	−3.76407e6	−	416706.i	−1.34276	−	0.148653i
$142$	−1.02489e6			−0.357943
$143$			1.60383e6i			0.548466i
$144$	−1.77636e6	−	398189.i	−0.594899	−	0.133353i
$145$	872502.			0.286195
$146$		−	274728.i		−	0.0882763i
$147$	213555.	−	1.92902e6i	0.0672291	−	0.607274i
$148$	4.80392e6			1.48187
$149$			891192.i			0.269409i	0.990886	+	0.134705i	$0.0430086\pi$
$149$			891192.i			0.269409i	−0.990886	+	0.134705i	$0.956991\pi$
$150$	1.21122e6	+	134090.i	0.358881	+	0.0397304i
$151$	3.23213e6			0.938767			0.469384	−	0.882994i	$-0.344476\pi$
$151$	3.23213e6			0.938767			0.469384	+	0.882994i	$0.344476\pi$
$152$			2.45226e6i			0.698291i
$153$	6194.44	−	27634.0i	0.00172953	−	0.00771559i
$154$	−600830.			−0.164509
$155$			4.58918e6i			1.23237i
$156$	563669.	−	5.09157e6i	0.148474	−	1.34115i
$157$	3.04528e6			0.786917			0.393458	−	0.919342i	$-0.371279\pi$
$157$	3.04528e6			0.786917			0.393458	+	0.919342i	$0.371279\pi$
$158$		−	2.23758e6i		−	0.567292i
$159$	5.40337e6	+	598187.i	1.34423	+	0.148815i
$160$	−5.26037e6			−1.28427
$161$		−	1.10448e6i		−	0.264656i
$162$	670037.	−	1.41945e6i	0.157599	−	0.333869i
$163$	−2.73916e6			−0.632492			−0.316246	−	0.948677i	$-0.602423\pi$
$163$	−2.73916e6			−0.632492			−0.316246	+	0.948677i	$0.602423\pi$
$164$		−	6.23909e6i		−	1.41446i
$165$	244050.	−	2.20448e6i	0.0543284	−	0.490743i
$166$	−1.50239e6			−0.328441
$167$			4.11211e6i			0.882909i	0.897284	+	0.441454i	$0.145537\pi$
$167$			4.11211e6i			0.882909i	−0.897284	+	0.441454i	$0.854463\pi$
$168$	4.11586e6	+	455652.i	0.868025	+	0.0960959i
$169$	6.95429e6			1.44076
$170$		−	20171.2i		−	0.00410568i
$171$	4.95162e6	+	1.10996e6i	0.990282	+	0.221982i
$172$	−6.31879e6			−1.24179
$173$			3.76144e6i			0.726467i	0.931698	+	0.363233i	$0.118327\pi$
$173$			3.76144e6i			0.726467i	−0.931698	+	0.363233i	$0.881673\pi$
$174$	43549.4	−	393377.i	0.00826674	−	0.0746726i
$175$	6.65270e6			1.24132
$176$			1.16685e6i			0.214030i
$177$	−6.07816e6	−	672891.i	−1.09610	−	0.121346i
$178$	2.18307e6			0.387086
$179$		−	368386.i		−	0.0642308i	−0.999484	−	0.0321154i	$-0.989776\pi$
$179$		−	368386.i		−	0.0642308i	0.999484	−	0.0321154i	$-0.0102244\pi$
$180$	−1.54954e6	+	6.91265e6i	−0.265696	+	1.18530i
$181$	−8.38958e6			−1.41483			−0.707416	−	0.706798i	$-0.750139\pi$
$181$	−8.38958e6			−1.41483			−0.707416	+	0.706798i	$0.750139\pi$
$182$			4.41347e6i			0.732092i
$183$	−47015.0	+	424682.i	−0.00767155	+	0.0692964i
$184$	893761.			0.143472
$185$		−	1.52784e7i		−	2.41304i
$186$	2.06908e6	+	229061.i	0.321543	+	0.0355969i
$187$	−18152.1			−0.00277588
$188$		−	7.75316e6i		−	1.16682i
$189$	2.78299e6	−	8.10451e6i	0.412217	−	1.20044i
$190$	3.61439e6			0.526957
$191$			1.29577e6i			0.185964i	0.995668	+	0.0929820i	$0.0296399\pi$
$191$			1.29577e6i			0.185964i	−0.995668	+	0.0929820i	$0.970360\pi$
$192$	212248.	−	1.91722e6i	0.0299875	−	0.270875i
$193$	−1.92278e6			−0.267459			−0.133730	−	0.991018i	$-0.542695\pi$
$193$	−1.92278e6			−0.267459			−0.133730	+	0.991018i	$0.542695\pi$
$194$			2.12365e6i			0.290856i
$195$	−1.61933e7	−	1.79270e6i	−2.18389	−	0.241771i
$196$	3.97336e6			0.527704
$197$			1.22320e7i			1.59993i	0.600048	+	0.799964i	$0.295148\pi$
$197$			1.22320e7i			1.59993i	−0.600048	+	0.799964i	$0.704852\pi$
$198$	−981732.	−	220065.i	−0.126473	−	0.0283502i
$199$	−5.04313e6			−0.639942			−0.319971	−	0.947427i	$-0.603673\pi$
$199$	−5.04313e6			−0.639942			−0.319971	+	0.947427i	$0.603673\pi$
$200$			5.38344e6i			0.672930i
$201$	996359.	−	9.00001e6i	0.122695	−	1.10829i
$202$	−4.43875e6			−0.538525
$203$		−	2.16064e6i		−	0.258283i
$204$	57626.3	+	6379.60i	0.00678781	+	0.000751454i
$205$	−1.98429e7			−2.30326
$206$			3.37393e6i			0.385953i
$207$	404538.	−	1.80468e6i	0.0456088	−	0.203465i
$208$	8.57121e6			0.952472
$209$		−	3.25260e6i		−	0.356280i
$210$	671585.	−	6.06636e6i	0.0725176	−	0.655044i
$211$	−5.43898e6			−0.578989			−0.289494	−	0.957180i	$-0.593487\pi$
$211$	−5.43898e6			−0.578989			−0.289494	+	0.957180i	$0.593487\pi$
$212$			1.11298e7i			1.16810i
$213$	−9.31217e6	−	1.03092e6i	−0.963633	−	0.106680i
$214$	2.81433e6			0.287167
$215$			2.00963e7i			2.02209i
$216$	6.55826e6	+	2.25203e6i	0.650770	+	0.223466i
$217$	1.13645e7			1.11217
$218$		−	3.01053e6i		−	0.290586i
$219$	276342.	−	2.49617e6i	0.0263096	−	0.237652i
$220$	4.54075e6			0.426441
$221$			133338.i			0.0123532i
$222$	−6.88846e6	−	762596.i	−0.629597	−	0.0697005i
$223$	5.72093e6			0.515884			0.257942	−	0.966160i	$-0.416956\pi$
$223$	5.72093e6			0.515884			0.257942	+	0.966160i	$0.416956\pi$
$224$			1.30267e7i			1.15902i
$225$	1.08703e7	+	2.43668e6i	0.954316	+	0.213920i
$226$	−3.75419e6			−0.325230
$227$			3.86980e6i			0.330834i	0.986224	+	0.165417i	$0.0528971\pi$
$227$			3.86980e6i			0.330834i	−0.986224	+	0.165417i	$0.947103\pi$
$228$	−1.14313e6	+	1.03258e7i	−0.0964478	+	0.871204i
$229$	3.26380e6			0.271780			0.135890	−	0.990724i	$-0.456611\pi$
$229$	3.26380e6			0.271780			0.135890	+	0.990724i	$0.456611\pi$
$230$		−	1.31731e6i		−	0.108269i
$231$	−5.45912e6	−	604360.i	−0.442881	−	0.0490297i
$232$	1.74842e6			0.140017
$233$			1.55764e7i			1.23140i	0.787981	+	0.615700i	$0.211127\pi$
$233$			1.55764e7i			1.23140i	−0.787981	+	0.615700i	$0.788873\pi$
$234$	−1.61652e6	+	7.21144e6i	−0.126163	+	0.562826i
$235$	−2.46582e7			−1.90002
$236$		−	1.25197e7i		−	0.952483i
$237$	2.25072e6	−	2.03306e7i	0.169074	−	1.52723i
$238$	−49951.5			−0.00370525
$239$			1.08172e6i			0.0792359i	0.999215	+	0.0396179i	$0.0126141\pi$
$239$			1.08172e6i			0.0792359i	−0.999215	+	0.0396179i	$0.987386\pi$
$240$	−1.17812e7	−	1.30426e6i	−0.852230	−	0.0943473i
$241$	7.54932e6			0.539333			0.269666	−	0.962954i	$-0.413087\pi$
$241$	7.54932e6			0.539333			0.269666	+	0.962954i	$0.413087\pi$
$242$		−	4.58755e6i		−	0.323694i
$243$	7.51573e6	−	1.22231e7i	0.523784	−	0.851851i
$244$	−874753.			−0.0602165
$245$		−	1.26369e7i		−	0.859296i
$246$	−990421.	+	8.94638e6i	−0.0665295	+	0.600955i
$247$	−2.38923e7			−1.58551
$248$			9.19632e6i			0.602919i
$249$	−1.36507e7	−	1.51122e6i	−0.884210	−	0.0978877i
$250$	−178506.			−0.0114244
$251$		−	1.41014e7i		−	0.891745i	−0.895096	−	0.445873i	$-0.852893\pi$
$251$		−	1.41014e7i		−	0.891745i	0.895096	−	0.445873i	$-0.147107\pi$
$252$	1.71183e7	+	3.83725e6i	1.06969	+	0.239783i
$253$	−1.18545e6			−0.0732019
$254$			917241.i			0.0559735i
$255$	20289.7	−	183275.i	0.00122365	−	0.0110531i
$256$	−1.70709e6			−0.101751
$257$		−	4.95651e6i		−	0.291996i	−0.989285	−	0.145998i	$-0.953361\pi$
$257$		−	4.95651e6i		−	0.291996i	0.989285	−	0.145998i	$-0.0466392\pi$
$258$	9.06065e6	+	1.00307e6i	0.527595	+	0.0584081i
$259$	−3.78352e7			−2.17769
$260$		−	3.33546e7i		−	1.89774i
$261$	791377.	−	3.53041e6i	0.0445104	−	0.198565i
$262$	4.71843e6			0.262358
$263$			1.17154e7i			0.644007i	0.946738	+	0.322004i	$0.104356\pi$
$263$			1.17154e7i			0.644007i	−0.946738	+	0.322004i	$0.895644\pi$
$264$	489055.	−	4.41758e6i	0.0265794	−	0.240089i
$265$	3.53972e7			1.90209
$266$		−	8.95061e6i		−	0.475562i
$267$	1.98353e7	+	2.19590e6i	1.04209	+	0.115366i
$268$	1.85381e7			0.963075
$269$		−	1.65029e7i		−	0.847818i	−0.905705	−	0.423909i	$-0.860658\pi$
$269$		−	1.65029e7i		−	0.847818i	0.905705	−	0.423909i	$-0.139342\pi$
$270$	3.31927e6	−	9.66622e6i	0.168636	−	0.491095i
$271$	−1.22986e7			−0.617944			−0.308972	−	0.951071i	$-0.599985\pi$
$271$	−1.22986e7			−0.617944			−0.308972	+	0.951071i	$0.599985\pi$
$272$			97008.7i			0.00482063i
$273$	−4.43940e6	+	4.01006e7i	−0.218191	+	1.97089i
$274$	−5.32264e6			−0.258747
$275$		−	7.14040e6i		−	0.343340i
$276$	3.76338e6	+	416630.i	0.178999	+	0.0198164i
$277$	1.75652e7			0.826444			0.413222	−	0.910630i	$-0.364403\pi$
$277$	1.75652e7			0.826444			0.413222	+	0.910630i	$0.364403\pi$
$278$		−	9.91404e6i		−	0.461441i
$279$	1.85692e7	+	4.16248e6i	0.855030	+	0.191664i
$280$	2.69628e7			1.22826
$281$		−	3.42408e6i		−	0.154321i	−0.997019	−	0.0771605i	$-0.975415\pi$
$281$		−	3.42408e6i		−	0.154321i	0.997019	−	0.0771605i	$-0.0245854\pi$
$282$	−1.23077e6	+	1.11174e7i	−0.0548820	+	0.495743i
$283$	−1.11124e6			−0.0490284			−0.0245142	−	0.999699i	$-0.507804\pi$
$283$	−1.11124e6			−0.0490284			−0.0245142	+	0.999699i	$0.507804\pi$
$284$		−	1.91810e7i		−	0.837369i
$285$	3.28403e7	+	3.63563e6i	1.41864	+	0.157053i
$286$	4.73701e6			0.202491
$287$			4.91384e7i			2.07862i
$288$	−4.77127e6	+	2.12851e7i	−0.199736	+	0.891041i
$289$	2.41361e7			0.999937
$290$		−	2.57699e6i		−	0.105662i
$291$	−2.13613e6	+	1.92955e7i	−0.0866860	+	0.783026i
$292$	5.14157e6			0.206513
$293$			1.24286e7i			0.494107i	0.969002	+	0.247053i	$0.0794623\pi$
$293$			1.24286e7i			0.494107i	−0.969002	+	0.247053i	$0.920538\pi$
$294$	−5.69749e6	−	630749.i	−0.224203	−	0.0248207i
$295$	−3.98177e7			−1.55099
$296$		−	3.06167e7i		−	1.18055i
$297$	−8.69864e6	−	2.98701e6i	−0.332034	−	0.114016i
$298$	2.63220e6			0.0994649
$299$			8.70788e6i			0.325761i
$300$	−2.50951e6	+	2.26682e7i	−0.0929449	+	0.839562i
$301$	4.97661e7			1.82488
$302$		−	9.54632e6i		−	0.346589i
$303$	−4.03303e7	−	4.46483e6i	−1.44979	−	0.160501i
$304$	−1.73826e7			−0.618720
$305$			2.78207e6i			0.0980548i
$306$	−81618.9	−	18295.7i	−0.00284857	−	0.000638535i
$307$	4.34142e7			1.50043			0.750217	−	0.661192i	$-0.229949\pi$
$307$	4.34142e7			1.50043			0.750217	+	0.661192i	$0.229949\pi$
$308$		−	1.12446e7i		−	0.384851i
$309$	−3.39375e6	+	3.06554e7i	−0.115028	+	1.03904i
$310$	1.35545e7			0.454985
$311$		−	4.48670e7i		−	1.49158i	−0.666182	−	0.745789i	$-0.732073\pi$
$311$		−	4.48670e7i		−	1.49158i	0.666182	−	0.745789i	$-0.267927\pi$
$312$	−3.24499e7	−	3.59241e6i	−1.06844	−	0.118283i
$313$	−3.33369e7			−1.08716			−0.543579	−	0.839358i	$-0.682931\pi$
$313$	−3.33369e7			−1.08716			−0.543579	+	0.839358i	$0.682931\pi$
$314$		−	8.99446e6i		−	0.290527i
$315$	1.22040e7	−	5.44433e7i	0.390455	−	1.74186i
$316$	4.18765e7			1.32712
$317$			6.15537e7i			1.93231i	0.257966	+	0.966154i	$0.416948\pi$
$317$			6.15537e7i			1.93231i	−0.257966	+	0.966154i	$0.583052\pi$
$318$	1.76679e6	−	1.59592e7i	0.0549418	−	0.496284i
$319$	−2.31904e6			−0.0714391
$320$		−	1.25596e7i		−	0.383289i
$321$	2.55710e7	+	2.83087e6i	0.773093	+	0.0855864i
$322$	−3.26217e6			−0.0977100
$323$		−	270413.i		−	0.00802453i
$324$	2.65652e7	+	1.25398e7i	0.781050	+	0.368686i
$325$	−5.24507e7			−1.52792
$326$			8.09031e6i			0.233514i
$327$	3.02822e6	−	2.73536e7i	0.0866053	−	0.782297i
$328$	−3.97634e7			−1.12684
$329$			6.10630e7i			1.71471i
$330$	−6.51108e6	−	720818.i	−0.181180	−	0.0200578i
$331$	−6.22918e6			−0.171770			−0.0858849	−	0.996305i	$-0.527372\pi$
$331$	−6.22918e6			−0.171770			−0.0858849	+	0.996305i	$0.527372\pi$
$332$		−	2.81174e7i		−	0.768353i
$333$	−6.18213e7	−	1.38579e7i	−1.67419	−	0.375287i
$334$	1.21454e7			0.325966
$335$		−	5.89586e7i		−	1.56824i
$336$	−3.22983e6	+	2.91748e7i	−0.0851456	+	0.769112i
$337$	−3.68326e6			−0.0962372			−0.0481186	−	0.998842i	$-0.515323\pi$
$337$	−3.68326e6			−0.0962372			−0.0481186	+	0.998842i	$0.515323\pi$
$338$		−	2.05400e7i		−	0.531925i
$339$	−3.41105e7	−	3.77625e6i	−0.875566	−	0.0969308i
$340$	377507.			0.00960479
$341$		−	1.21977e7i		−	0.307619i
$342$	3.27833e6	−	1.46249e7i	0.0819548	−	0.365608i
$343$	1.99249e7			0.493756
$344$			4.02713e7i			0.989282i
$345$	1.32505e6	−	1.19691e7i	0.0322683	−	0.291477i
$346$	1.11097e7			0.268209
$347$			1.93262e7i			0.462550i	0.972888	+	0.231275i	$0.0742897\pi$
$347$			1.93262e7i			0.462550i	−0.972888	+	0.231275i	$0.925710\pi$
$348$	7.36210e6	+	815032.i	0.174688	+	0.0193391i
$349$	4.89202e7			1.15083			0.575416	−	0.817861i	$-0.304840\pi$
$349$	4.89202e7			1.15083			0.575416	+	0.817861i	$0.304840\pi$
$350$		−	1.96492e7i		−	0.458290i
$351$	−2.19414e7	+	6.38969e7i	−0.507392	+	1.47761i
$352$	1.39816e7			0.320575
$353$		−	8.50053e6i		−	0.193251i	−0.995321	−	0.0966255i	$-0.969195\pi$
$353$		−	8.50053e6i		−	0.193251i	0.995321	−	0.0966255i	$-0.0308049\pi$
$354$	−1.98743e6	+	1.79522e7i	−0.0448004	+	0.404678i
$355$	−6.10035e7			−1.36355
$356$			4.08564e7i			0.905546i
$357$	−453858.	−	50245.0i	−0.00997506	−	0.00110430i
$358$	−1.08805e6			−0.0237138
$359$		−	6.39874e7i		−	1.38297i	−0.722393	−	0.691483i	$-0.756958\pi$
$359$		−	6.39874e7i		−	1.38297i	0.722393	−	0.691483i	$-0.243042\pi$
$360$	4.40561e7	+	9.87563e6i	0.944276	+	0.211669i
$361$	1.40829e6			0.0299343
$362$			2.47792e7i			0.522350i
$363$	4.61451e6	−	4.16824e7i	0.0964729	−	0.871430i
$364$	−8.25986e7			−1.71265
$365$		−	1.63523e7i		−	0.336279i
$366$	1.25433e6	+	138862.i	0.0255840	+	0.00283231i
$367$	1.17470e7			0.237645			0.118823	−	0.992915i	$-0.462088\pi$
$367$	1.17470e7			0.237645			0.118823	+	0.992915i	$0.462088\pi$
$368$			6.33532e6i			0.127123i
$369$	−1.79979e7	+	8.02903e7i	−0.358214	+	1.59803i
$370$	−4.51259e7			−0.890884
$371$		−	8.76568e7i		−	1.71658i
$372$	−4.28690e6	+	3.87232e7i	−0.0832750	+	0.752215i
$373$	−3.41647e7			−0.658342			−0.329171	−	0.944270i	$-0.606769\pi$
$373$	−3.41647e7			−0.658342			−0.329171	+	0.944270i	$0.606769\pi$
$374$			53613.4i			0.00102485i
$375$	−1.62190e6	−	179554.i	−0.0307560	−	0.00340488i
$376$	−4.94129e7			−0.929559
$377$			1.70348e7i			0.317916i
$378$	−2.39372e7	−	8.21975e6i	−0.443198	−	0.152189i
$379$	8.65898e7			1.59056			0.795278	−	0.606245i	$-0.207325\pi$
$379$	8.65898e7			1.59056			0.795278	+	0.606245i	$0.207325\pi$
$380$			6.76439e7i			1.23276i
$381$	−922630.	+	8.33403e6i	−0.0166822	+	0.150688i
$382$	3.82715e6			0.0686572
$383$			9.35875e7i			1.66579i	0.553428	+	0.832897i	$0.313319\pi$
$383$			9.35875e7i			1.66579i	−0.553428	+	0.832897i	$0.686681\pi$
$384$	−5.70543e7	−	6.31627e6i	−1.00761	−	0.111549i
$385$	−3.57624e7			−0.626679
$386$			5.67906e6i			0.0987449i
$387$	8.13159e7	+	1.82278e7i	1.40295	+	0.314486i
$388$	−3.97445e7			−0.680427
$389$		−	1.14241e8i		−	1.94076i	−0.241583	−	0.970380i	$-0.577667\pi$
$389$		−	1.14241e8i		−	1.94076i	0.241583	−	0.970380i	$-0.422333\pi$
$390$	−5.29486e6	+	4.78279e7i	−0.0892607	+	0.806284i
$391$	−98555.6			−0.00164874
$392$		−	2.53233e7i		−	0.420399i
$393$	4.28715e7	+	4.74615e6i	0.706304	+	0.0781923i
$394$	3.61282e7			0.590687
$395$		−	1.33184e8i		−	2.16104i
$396$	4.11855e6	−	1.83733e7i	0.0663222	−	0.295870i
$397$	9.85589e7			1.57516			0.787579	−	0.616213i	$-0.211334\pi$
$397$	9.85589e7			1.57516			0.787579	+	0.616213i	$0.211334\pi$
$398$			1.48952e7i			0.236264i
$399$	9.00320e6	−	8.13250e7i	0.141735	−	1.28028i
$400$	−3.81599e7			−0.596248
$401$			7.05092e7i			1.09349i	0.837301	+	0.546743i	$0.184132\pi$
$401$			7.05092e7i			1.09349i	−0.837301	+	0.546743i	$0.815868\pi$
$402$	−2.65822e7	−	2.94281e6i	−0.409178	−	0.0452986i
$403$	−8.95994e7			−1.36896
$404$		−	8.30717e7i		−	1.25982i
$405$	3.98818e7	−	8.44883e7i	0.600357	−	1.27184i
$406$	−6.38161e6			−0.0953569
$407$			4.06088e7i			0.602334i
$408$	40658.8	−	367267.i	0.000598652	−	0.00540756i
$409$	1.00142e8			1.46368			0.731839	−	0.681477i	$-0.238662\pi$
$409$	1.00142e8			1.46368			0.731839	+	0.681477i	$0.238662\pi$
$410$			5.86073e7i			0.850354i
$411$	−4.83613e7	−	5.35391e6i	−0.696583	−	0.0771162i
$412$	−6.31435e7			−0.902895
$413$			9.86036e7i			1.39973i
$414$	−5.33026e6	−	1.19483e6i	−0.0751186	−	0.0168386i
$415$	−8.94248e7			−1.25116
$416$		−	1.02704e8i		−	1.42661i
$417$	9.97229e6	−	9.00787e7i	0.137527	−	1.24226i
$418$	−9.60676e6			−0.131537
$419$			7.43851e7i			1.01122i	0.862763	+	0.505608i	$0.168732\pi$
$419$			7.43851e7i			1.01122i	−0.862763	+	0.505608i	$0.831268\pi$
$420$	1.13533e8	+	1.25688e7i	1.53240	+	0.169647i
$421$	−9.93925e7			−1.33201			−0.666005	−	0.745948i	$-0.731997\pi$
$421$	−9.93925e7			−1.33201			−0.666005	+	0.745948i	$0.731997\pi$
$422$			1.60644e7i			0.213760i
$423$	−2.23655e7	+	9.97747e7i	−0.295500	+	1.31825i
$424$	7.09329e7			0.930572
$425$		−	593635.i		−	0.00773309i
$426$	−3.04488e6	+	2.75041e7i	−0.0393860	+	0.355770i
$427$	6.88946e6			0.0884915
$428$			5.26706e7i			0.671796i
$429$	4.30404e7	+	4.76485e6i	0.545135	+	0.0603500i
$430$	5.93559e7			0.746549
$431$			1.28630e8i			1.60662i	0.595564	+	0.803308i	$0.296928\pi$
$431$			1.28630e8i			1.60662i	−0.595564	+	0.803308i	$0.703072\pi$
$432$	−1.59632e7	+	4.64875e7i	−0.198002	+	0.576613i
$433$	1.39833e8			1.72245			0.861225	−	0.508225i	$-0.169698\pi$
$433$	1.39833e8			1.72245			0.861225	+	0.508225i	$0.169698\pi$
$434$		−	3.35660e7i		−	0.410610i
$435$	2.59214e6	−	2.34145e7i	0.0314912	−	0.284457i
$436$	5.63426e7			0.679794
$437$		−	1.76598e7i		−	0.211612i
$438$	−7.37261e6	−	816195.i	−0.0877402	−	0.00971340i
$439$	−7.41824e7			−0.876813			−0.438407	−	0.898777i	$-0.644457\pi$
$439$	−7.41824e7			−0.876813			−0.438407	+	0.898777i	$0.644457\pi$
$440$		−	2.89394e7i		−	0.339728i
$441$	−5.11328e7	−	1.14619e7i	−0.596189	−	0.133642i
$442$	393824.			0.00456074
$443$		−	7.12303e7i		−	0.819320i	−0.912238	−	0.409660i	$-0.865647\pi$
$443$		−	7.12303e7i		−	0.819320i	0.912238	−	0.409660i	$-0.134353\pi$
$444$	1.42721e7	−	1.28918e8i	0.163057	−	1.47288i
$445$	1.29940e8			1.47456
$446$		−	1.68971e7i		−	0.190462i
$447$	2.39161e7	+	2.64766e6i	0.267773	+	0.0296442i
$448$	−3.11023e7			−0.345907
$449$		−	2.74987e7i		−	0.303789i	−0.988397	−	0.151895i	$-0.951463\pi$
$449$		−	2.74987e7i		−	0.303789i	0.988397	−	0.151895i	$-0.0485374\pi$
$450$	7.19689e6	−	3.21060e7i	0.0789782	−	0.352330i
$451$	5.27407e7			0.574932
$452$		−	7.02602e7i		−	0.760841i
$453$	9.60241e6	−	8.67376e7i	0.103296	−	0.933067i
$454$	1.14297e7			0.122143
$455$			2.62697e8i			2.78883i
$456$	6.58091e7	+	7.28549e6i	0.694051	+	0.0768359i
$457$	1.47897e8			1.54956			0.774782	−	0.632229i	$-0.217860\pi$
$457$	1.47897e8			1.54956			0.774782	+	0.632229i	$0.217860\pi$
$458$		−	9.63987e6i		−	0.100340i
$459$	−723184.	−	248333.i	−0.00747843	−	0.00256800i
$460$	2.46537e7			0.253285
$461$			9.39857e7i			0.959310i	0.877457	+	0.479655i	$0.159238\pi$
$461$			9.39857e7i			0.959310i	−0.877457	+	0.479655i	$0.840762\pi$
$462$	−1.78502e6	+	1.61239e7i	−0.0181016	+	0.163510i
$463$	−2.83470e7			−0.285604			−0.142802	−	0.989751i	$-0.545611\pi$
$463$	−2.83470e7			−0.285604			−0.142802	+	0.989751i	$0.545611\pi$
$464$			1.23935e7i			0.124062i
$465$	1.23155e8	+	1.36341e7i	1.22488	+	0.135602i
$466$	4.60059e7			0.454628
$467$		−	1.42853e8i		−	1.40261i	−0.712861	−	0.701306i	$-0.752601\pi$
$467$		−	1.42853e8i		−	1.40261i	0.712861	−	0.701306i	$-0.247399\pi$
$468$	−1.34963e8	−	3.02533e7i	−1.31667	−	0.295145i
$469$	−1.46004e8			−1.41529
$470$			7.28297e7i			0.701480i
$471$	9.04730e6	−	8.17234e7i	0.0865878	−	0.782139i
$472$	−7.97912e7			−0.758803
$473$		−	5.34144e7i		−	0.504748i
$474$	−6.00477e7	−	6.64766e6i	−0.563847	−	0.0624215i
$475$	1.06371e8			0.992528
$476$		−	934849.i		−	0.00866804i
$477$	3.21060e7	−	1.43228e8i	0.295822	−	1.31969i
$478$	3.19494e6			0.0292536
$479$		−	8.53022e7i		−	0.776164i	−0.921625	−	0.388082i	$-0.873138\pi$
$479$		−	8.53022e7i		−	0.776164i	0.921625	−	0.388082i	$-0.126862\pi$
$480$	−1.56282e7	+	1.41168e8i	−0.141314	+	1.27647i
$481$	2.98297e8			2.68049
$482$		−	2.22974e7i		−	0.199119i
$483$	−2.96400e7	−	3.28134e6i	−0.263049	−	0.0291212i
$484$	8.58566e7			0.757247
$485$			1.26404e8i			1.10799i
$486$	−3.61019e7	−	2.21982e7i	−0.314500	−	0.193379i
$487$	−4.23635e7			−0.366779			−0.183390	−	0.983040i	$-0.558707\pi$
$487$	−4.23635e7			−0.366779			−0.183390	+	0.983040i	$0.558707\pi$
$488$			5.57503e6i			0.0479720i
$489$	−8.13784e6	+	7.35083e7i	−0.0695958	+	0.628652i
$490$	−3.73240e7			−0.317249
$491$			1.58199e8i			1.33647i	0.743951	+	0.668234i	$0.232950\pi$
$491$			1.58199e8i			1.33647i	−0.743951	+	0.668234i	$0.767050\pi$
$492$	−1.67433e8	−	1.85359e7i	−1.40587	−	0.155639i
$493$	−192799.			−0.00160903
$494$			7.05676e7i			0.585362i
$495$	−5.84345e7	−	1.30987e7i	−0.481785	−	0.107997i
$496$	−6.51871e7			−0.534215
$497$			1.51068e8i			1.23056i
$498$	−4.46348e6	+	4.03182e7i	−0.0361398	+	0.326447i
$499$	−2.21245e8			−1.78062			−0.890312	−	0.455350i	$-0.849514\pi$
$499$	−2.21245e8			−1.78062			−0.890312	+	0.455350i	$0.849514\pi$
$500$		−	3.34076e6i		−	0.0267260i
$501$	1.10353e8	+	1.22168e7i	0.877547	+	0.0971501i
$502$	−4.16494e7			−0.329229
$503$			8.07925e7i			0.634844i	0.948284	+	0.317422i	$0.102817\pi$
$503$			8.07925e7i			0.634844i	−0.948284	+	0.317422i	$0.897183\pi$
$504$	2.44558e7	−	1.09100e8i	0.191025	−	0.852180i
$505$	−2.64202e8			−2.05145
$506$			3.50131e6i			0.0270259i
$507$	2.06607e7	−	1.86626e8i	0.158533	−	1.43202i
$508$	−1.71663e7			−0.130944
$509$		−	6.68069e7i		−	0.506603i	−0.967387	−	0.253302i	$-0.918484\pi$
$509$		−	6.68069e7i		−	0.506603i	0.967387	−	0.253302i	$-0.0815165\pi$
$510$	−541315.	−	59927.1i	−0.00408075	−	0.000451765i
$511$	−4.04944e7			−0.303482
$512$		−	1.31024e8i		−	0.976204i
$513$	4.44977e7	−	1.29584e8i	0.329599	−	0.959843i
$514$	−1.46394e7			−0.107804
$515$			2.00822e8i			1.47025i
$516$	−1.87726e7	+	1.69571e8i	−0.136639	+	1.23425i
$517$	6.55395e7			0.474276
$518$			1.11749e8i			0.803996i
$519$	1.00942e8	+	1.11749e7i	0.722056	+	0.0799362i
$520$	−2.12578e8			−1.51185
$521$		−	7.76448e7i		−	0.549034i	−0.961582	−	0.274517i	$-0.911482\pi$
$521$		−	7.76448e7i		−	0.549034i	0.961582	−	0.274517i	$-0.0885179\pi$
$522$	−1.04273e7	−	2.33739e6i	−0.0733096	−	0.0164331i
$523$	−7.65480e7			−0.535093			−0.267546	−	0.963545i	$-0.586213\pi$
$523$	−7.65480e7			−0.535093			−0.267546	+	0.963545i	$0.586213\pi$
$524$			8.83061e7i			0.613757i
$525$	1.97646e7	−	1.78532e8i	0.136588	−	1.23378i
$526$	3.46023e7			0.237765
$527$		−	1.01408e6i		−	0.00692855i
$528$	3.13135e7	+	3.46661e6i	0.212731	+	0.0235507i
$529$	−6.43634e6			−0.0434783
$530$		−	1.04548e8i		−	0.702245i
$531$	−3.61155e7	+	1.61115e8i	−0.241218	+	1.07610i
$532$	1.67512e8			1.11253
$533$		−	3.87413e8i		−	2.55854i
$534$	6.48573e6	−	5.85850e7i	0.0425927	−	0.384736i
$535$	1.67514e8			1.09393
$536$		−	1.18148e8i		−	0.767241i
$537$	−9.88601e6	−	1.09445e6i	−0.0638408	−	0.00706759i
$538$	−4.87424e7			−0.313011
$539$			3.35879e7i			0.214495i
$540$	1.80905e8	+	6.21205e7i	1.14886	+	0.394506i
$541$	1.39110e8			0.878549			0.439274	−	0.898353i	$-0.355236\pi$
$541$	1.39110e8			0.878549			0.439274	+	0.898353i	$0.355236\pi$
$542$			3.63249e7i			0.228142i
$543$	−2.49248e7	+	2.25143e8i	−0.155680	+	1.40624i
$544$	1.16240e6			0.00722036
$545$		−	1.79192e8i		−	1.10695i
$546$	1.18440e8	+	1.31121e7i	0.727647	+	0.0805551i
$547$	3.79215e7			0.231699			0.115849	−	0.993267i	$-0.463041\pi$
$547$	3.79215e7			0.231699			0.115849	+	0.993267i	$0.463041\pi$
$548$		−	9.96138e7i		−	0.605310i
$549$	1.12571e7	+	2.52339e6i	0.0680315	+	0.0152499i
$550$	−2.10897e7			−0.126760
$551$		−	3.45469e7i		−	0.206516i
$552$	2.65529e6	−	2.39850e7i	0.0157868	−	0.142601i
$553$	−3.29815e8			−1.95027
$554$		−	5.18800e7i		−	0.305120i
$555$	−4.10013e8	−	4.53911e7i	−2.39838	−	0.265517i
$556$	1.85543e8			1.07949
$557$		−	1.45153e8i		−	0.839961i	−0.907533	−	0.419980i	$-0.862037\pi$
$557$		−	1.45153e8i		−	0.839961i	0.907533	−	0.419980i	$-0.137963\pi$
$558$	1.22942e7	−	5.48455e7i	0.0707614	−	0.315674i
$559$	−3.92362e8			−2.24622
$560$			1.91122e8i			1.08830i
$561$	−53928.4	+	487130.i	−0.000305442	+	0.00275903i
$562$	−1.01133e7			−0.0569747
$563$			2.89267e8i			1.62097i	0.585762	+	0.810483i	$0.300796\pi$
$563$			2.89267e8i			1.62097i	−0.585762	+	0.810483i	$0.699204\pi$
$564$	−2.08064e8	−	2.30340e7i	−1.15974	−	0.128390i
$565$	−2.23456e8			−1.23893
$566$			3.28212e6i			0.0181011i
$567$	−2.09225e8	−	9.87623e7i	−1.14779	−	0.541804i
$568$	−1.22246e8			−0.667097
$569$			1.82902e8i			0.992848i	0.868080	+	0.496424i	$0.165354\pi$
$569$			1.82902e8i			0.992848i	−0.868080	+	0.496424i	$0.834646\pi$
$570$	1.07381e7	−	9.69961e7i	0.0579832	−	0.523757i
$571$	1.21574e8			0.653031			0.326516	−	0.945192i	$-0.394125\pi$
$571$	1.21574e8			0.653031			0.326516	+	0.945192i	$0.394125\pi$
$572$			8.86538e7i			0.473707i
$573$	3.47734e7	+	3.84964e6i	0.184835	+	0.0204624i
$574$	1.45134e8			0.767419
$575$		−	3.87684e7i		−	0.203927i
$576$	−5.08200e7	−	1.13918e7i	−0.265930	−	0.0596109i
$577$	−1.54816e8			−0.805912			−0.402956	−	0.915219i	$-0.632017\pi$
$577$	−1.54816e8			−0.805912			−0.402956	+	0.915219i	$0.632017\pi$
$578$		−	7.12875e7i		−	0.369173i
$579$	−5.71243e6	+	5.15998e7i	−0.0294297	+	0.265835i
$580$	4.82288e7			0.247185
$581$			2.21450e8i			1.12914i
$582$	5.69905e7	+	6.30921e6i	0.289090	+	0.0320041i
$583$	−9.40828e7			−0.474794
$584$		−	3.27685e7i		−	0.164520i
$585$	−9.62179e7	+	4.29237e8i	−0.480605	+	2.14403i
$586$	3.67088e7			0.182422
$587$			2.47469e8i			1.22351i	0.791048	+	0.611754i	$0.209536\pi$
$587$			2.47469e8i			1.22351i	−0.791048	+	0.611754i	$0.790464\pi$
$588$	1.18046e7	−	1.06629e8i	0.0580654	−	0.524499i
$589$	1.81710e8			0.889267
$590$			1.17604e8i			0.572621i
$591$	3.28260e8	+	3.63405e7i	1.59021	+	0.176047i
$592$	2.17023e8			1.04602
$593$		−	7.97730e6i		−	0.0382553i	−0.999817	−	0.0191277i	$-0.993911\pi$
$593$		−	7.97730e6i		−	0.0382553i	0.999817	−	0.0191277i	$-0.00608890\pi$
$594$	−8.82233e6	+	2.56920e7i	−0.0420944	+	0.122585i
$595$	−2.97320e6			−0.0141148
$596$			4.92619e7i			0.232687i
$597$	−1.49827e7	+	1.35338e8i	−0.0704155	+	0.636056i
$598$	2.57193e7			0.120270
$599$		−	1.49273e8i		−	0.694543i	−0.937765	−	0.347272i	$-0.887108\pi$
$599$		−	1.49273e8i		−	0.694543i	0.937765	−	0.347272i	$-0.112892\pi$
$600$	1.44470e8	+	1.59938e7i	0.668844	+	0.0740453i
$601$	3.30496e8			1.52245			0.761225	−	0.648488i	$-0.224598\pi$
$601$	3.30496e8			1.52245			0.761225	+	0.648488i	$0.224598\pi$
$602$		−	1.46988e8i		−	0.673738i
$603$	−2.38565e8	−	5.34767e7i	−1.08806	−	0.243900i
$604$	1.78661e8			0.810808
$605$		−	2.73059e8i		−	1.23308i
$606$	−1.31872e7	+	1.19118e8i	−0.0592562	+	0.535255i
$607$	3.45722e8			1.54583			0.772913	−	0.634512i	$-0.218799\pi$
$607$	3.45722e8			1.54583			0.772913	+	0.634512i	$0.218799\pi$
$608$			2.08286e8i			0.926720i
$609$	−5.79831e7	−	6.41911e6i	−0.256714	−	0.0284199i
$610$	8.21704e6			0.0362014
$611$		−	4.81428e8i		−	2.11061i
$612$	342406.	−	1.52751e6i	0.00149378	−	0.00666391i
$613$	−1.24450e7			−0.0540271			−0.0270136	−	0.999635i	$-0.508600\pi$
$613$	−1.24450e7			−0.0540271			−0.0270136	+	0.999635i	$0.508600\pi$
$614$		−	1.28227e8i		−	0.553954i
$615$	−5.89516e7	+	5.32504e8i	−0.253437	+	2.28927i
$616$	−7.16648e7			−0.306594
$617$		−	1.53667e8i		−	0.654224i	−0.944986	−	0.327112i	$-0.893925\pi$
$617$		−	1.53667e8i		−	0.654224i	0.944986	−	0.327112i	$-0.106075\pi$
$618$	9.05429e7	+	1.00237e7i	0.383609	+	0.0424680i
$619$	5.18448e7			0.218591			0.109296	−	0.994009i	$-0.465140\pi$
$619$	5.18448e7			0.218591			0.109296	+	0.994009i	$0.465140\pi$
$620$			2.53674e8i			1.06439i
$621$	−4.72287e7	−	1.62178e7i	−0.197211	−	0.0677200i
$622$	−1.32518e8			−0.550685
$623$		−	3.21781e8i		−	1.33075i
$624$	2.54644e7	−	2.30017e8i	0.104804	−	0.946688i
$625$	−2.49394e8			−1.02152
$626$			9.84629e7i			0.401374i
$627$	−8.72868e7	−	9.66321e6i	−0.354116	−	0.0392030i
$628$	1.68332e8			0.679656
$629$			3.37612e6i			0.0135664i
$630$	−1.60802e8	−	3.60454e7i	−0.643087	−	0.144154i
$631$	2.20966e7			0.0879504			0.0439752	−	0.999033i	$-0.485998\pi$
$631$	2.20966e7			0.0879504			0.0439752	+	0.999033i	$0.485998\pi$
$632$		−	2.66890e8i		−	1.05726i
$633$	−1.61588e7	+	1.45961e8i	−0.0637086	+	0.575473i
$634$	1.81803e8			0.713401
$635$			5.45958e7i			0.213225i
$636$	2.98679e8	+	3.30657e7i	1.16100	+	0.128530i
$637$	2.46724e8			0.954537
$638$			6.84944e6i			0.0263750i
$639$	−5.53314e7	+	2.46839e8i	−0.212065	+	0.946044i
$640$	−3.73760e8			−1.42578
$641$		−	3.93694e7i		−	0.149481i	−0.997203	−	0.0747403i	$-0.976187\pi$
$641$		−	3.93694e7i		−	0.149481i	0.997203	−	0.0747403i	$-0.0238128\pi$
$642$	8.36117e6	−	7.55256e7i	0.0315982	−	0.285423i
$643$	1.54289e8			0.580366			0.290183	−	0.956971i	$-0.406284\pi$
$643$	1.54289e8			0.580366			0.290183	+	0.956971i	$0.406284\pi$
$644$		−	6.10519e7i		−	0.228582i
$645$	5.39306e8	+	5.97046e7i	2.00982	+	0.222499i
$646$	−798683.			−0.00296263
$647$		−	3.99669e8i		−	1.47566i	−0.674985	−	0.737831i	$-0.735850\pi$
$647$		−	3.99669e8i		−	1.47566i	0.674985	−	0.737831i	$-0.264150\pi$
$648$	7.99196e7	−	1.69307e8i	0.293716	−	0.622229i
$649$	1.05832e8			0.387154
$650$			1.54917e8i			0.564102i
$651$	3.37632e7	−	3.04979e8i	0.122377	−	1.10542i
$652$	−1.51411e8			−0.546280
$653$		−	4.13532e8i		−	1.48515i	−0.669765	−	0.742574i	$-0.733605\pi$
$653$		−	4.13532e8i		−	1.48515i	0.669765	−	0.742574i	$-0.266395\pi$
$654$	−8.07909e7	−	8.94406e6i	−0.288821	−	0.0319743i
$655$	2.80849e8			0.999424
$656$		−	2.81858e8i		−	0.998433i
$657$	−6.61663e7	−	1.48319e7i	−0.233314	−	0.0522997i
$658$	1.80354e8			0.633064
$659$			1.89847e8i			0.663356i	0.943393	+	0.331678i	$0.107615\pi$
$659$			1.89847e8i			0.663356i	−0.943393	+	0.331678i	$0.892385\pi$
$660$	1.34902e7	−	1.21856e8i	0.0469231	−	0.423852i
$661$	−2.15284e8			−0.745430			−0.372715	−	0.927946i	$-0.621573\pi$
$661$	−2.15284e8			−0.745430			−0.372715	+	0.927946i	$0.621573\pi$
$662$			1.83983e7i			0.0634167i
$663$	3.57827e6	+	396138.i	0.0122781	+	0.00135927i
$664$	−1.79199e8			−0.612114
$665$		−	5.32756e8i		−	1.81160i
$666$	−4.09301e7	+	1.82593e8i	−0.138554	+	0.618105i
$667$	−1.25911e7			−0.0424312
$668$			2.27303e8i			0.762563i
$669$	1.69964e7	−	1.53527e8i	0.0567648	−	0.512751i
$670$	−1.74138e8			−0.578989
$671$		−	7.39452e6i		−	0.0244761i
$672$	3.49584e8	+	3.87012e7i	1.15198	+	0.127531i
$673$	−5.36596e8			−1.76036			−0.880181	−	0.474638i	$-0.842579\pi$
$673$	−5.36596e8			−1.76036			−0.880181	+	0.474638i	$0.842579\pi$
$674$			1.08788e7i			0.0355304i
$675$	9.76855e7	−	2.84475e8i	0.317628	−	0.924983i
$676$	3.84409e8			1.24438
$677$			4.72953e8i			1.52423i	0.647439	+	0.762117i	$0.275840\pi$
$677$			4.72953e8i			1.52423i	−0.647439	+	0.762117i	$0.724160\pi$
$678$	−1.11534e7	+	1.00748e8i	−0.0357865	+	0.323256i
$679$	3.13023e8			0.999924
$680$		−	2.40595e6i		−	0.00765173i
$681$	1.03850e8	+	1.14969e7i	0.328825	+	0.0364031i
$682$	−3.60266e7			−0.113572
$683$			4.82871e8i			1.51555i	0.652518	+	0.757773i	$0.273713\pi$
$683$			4.82871e8i			1.51555i	−0.652518	+	0.757773i	$0.726287\pi$
$684$	2.73708e8	+	6.13544e7i	0.855301	+	0.191724i
$685$	−3.16813e8			−0.985669
$686$		−	5.88494e7i		−	0.182293i
$687$	9.69651e6	−	8.75876e7i	0.0299051	−	0.270130i
$688$	−2.85458e8			−0.876552
$689$			6.91097e8i			2.11291i
$690$	−3.53515e7	−	3.91364e6i	−0.107612	−	0.0119133i
$691$	−1.78124e8			−0.539869			−0.269934	−	0.962879i	$-0.587002\pi$
$691$	−1.78124e8			−0.539869			−0.269934	+	0.962879i	$0.587002\pi$
$692$			2.07919e8i			0.627445i
$693$	−3.24373e7	+	1.44706e8i	−0.0974641	+	0.434797i
$694$	5.70813e7			0.170772
$695$		−	5.90101e8i		−	1.75781i
$696$	5.19441e6	−	4.69206e7i	0.0154067	−	0.139167i
$697$	4.38473e6			0.0129493
$698$		−	1.44489e8i		−	0.424883i
$699$	4.18009e8	+	4.62762e7i	1.22392	+	0.135496i
$700$	3.67737e8			1.07212
$701$		−	2.17172e8i		−	0.630449i	−0.949017	−	0.315225i	$-0.897920\pi$
$701$		−	2.17172e8i		−	0.630449i	0.949017	−	0.315225i	$-0.102080\pi$
$702$	1.88724e8	+	6.48055e7i	0.545526	+	0.187327i
$703$	−6.04953e8			−1.74123
$704$			3.33824e7i			0.0956753i
$705$	−7.32576e7	+	6.61729e8i	−0.209067	+	1.88848i
$706$	−2.51069e7			−0.0713475
$707$			6.54264e8i			1.85138i
$708$	−3.35979e8	−	3.71950e7i	−0.946699	−	0.104806i
$709$	−8.29262e6			−0.0232677			−0.0116338	−	0.999932i	$-0.503703\pi$
$709$	−8.29262e6			−0.0232677			−0.0116338	+	0.999932i	$0.503703\pi$
$710$			1.80178e8i			0.503416i
$711$	−5.38905e8	−	1.20801e8i	−1.49935	−	0.336095i
$712$	2.60389e8			0.721410
$713$		−	6.62265e7i		−	0.182710i
$714$	−148402.	+	1.34050e6i	−0.000407704	+	0.00368275i
$715$	2.81955e8			0.771369
$716$		−	2.03630e7i		−	0.0554758i
$717$	2.90291e7	+	3.21371e6i	0.0787547	+	0.00871865i
$718$	−1.88991e8			−0.510585
$719$		−	1.60702e7i		−	0.0432349i	−0.999766	−	0.0216174i	$-0.993118\pi$
$719$		−	1.60702e7i		−	0.0432349i	0.999766	−	0.0216174i	$-0.00688158\pi$
$720$	−7.00022e7	+	3.12287e8i	−0.187549	+	0.836674i
$721$	4.97312e8			1.32685
$722$		−	4.15947e6i		−	0.0110516i
$723$	2.24284e7	−	2.02594e8i	0.0593450	−	0.536058i
$724$	−4.63746e8			−1.22198
$725$		−	7.58405e7i		−	0.199016i
$726$	−1.23112e8	−	1.36293e7i	−0.321729	−	0.0356174i
$727$	−4.73951e8			−1.23347			−0.616737	−	0.787169i	$-0.711546\pi$
$727$	−4.73951e8			−1.23347			−0.616737	+	0.787169i	$0.711546\pi$
$728$			5.26423e8i			1.36440i
$729$	−3.05692e8	−	2.38006e8i	−0.789044	−	0.614336i
$730$	−4.82976e7			−0.124153
$731$		−	4.44074e6i		−	0.0113685i
$732$	−2.59882e6	+	2.34749e7i	−0.00662588	+	0.0598509i
$733$	−1.35589e8			−0.344280			−0.172140	−	0.985072i	$-0.555068\pi$
$733$	−1.35589e8			−0.344280			−0.172140	+	0.985072i	$0.555068\pi$
$734$		−	3.46956e7i		−	0.0877378i
$735$	−3.39125e8	−	3.75433e7i	−0.854079	−	0.0945520i
$736$	7.59125e7			0.190406
$737$			1.56707e8i			0.391459i
$738$	2.37143e8	+	5.31580e7i	0.589985	+	0.132251i
$739$	5.69380e8			1.41081			0.705406	−	0.708804i	$-0.250765\pi$
$739$	5.69380e8			1.41081			0.705406	+	0.708804i	$0.250765\pi$
$740$		−	8.44538e8i		−	2.08413i
$741$	−7.09823e7	+	6.41176e8i	−0.174460	+	1.57588i
$742$	−2.58900e8			−0.633755
$743$		−	5.41776e8i		−	1.32085i	−0.750892	−	0.660425i	$-0.770376\pi$
$743$		−	5.41776e8i		−	1.32085i	0.750892	−	0.660425i	$-0.229624\pi$
$744$	2.46793e8	+	2.73215e7i	0.599258	+	0.0663417i
$745$	1.56673e8			0.378901
$746$			1.00908e8i			0.243057i
$747$	−8.11101e7	+	3.61840e8i	−0.194587	+	0.868070i
$748$	−1.00338e6			−0.00239752
$749$		−	4.14828e8i		−	0.987240i
$750$	−530326.	+	4.79038e6i	−0.00125707	+	0.0113550i
$751$	−1.74986e8			−0.413127			−0.206564	−	0.978433i	$-0.566228\pi$
$751$	−1.74986e8			−0.413127			−0.206564	+	0.978433i	$0.566228\pi$
$752$		−	3.50258e8i		−	0.823634i
$753$	−3.78426e8	−	4.18941e7i	−0.886330	−	0.0981225i
$754$	5.03134e7			0.117373
$755$		−	5.68214e8i		−	1.32029i
$756$	1.53834e8	−	4.47988e8i	0.356030	−	1.03681i
$757$	−1.52552e8			−0.351666			−0.175833	−	0.984420i	$-0.556262\pi$
$757$	−1.52552e8			−0.351666			−0.175833	+	0.984420i	$0.556262\pi$
$758$		−	2.55749e8i		−	0.587227i
$759$	−3.52189e6	+	3.18129e7i	−0.00805471	+	0.0727574i
$760$	4.31112e8			0.982086
$761$			5.23117e8i			1.18699i	0.804840	+	0.593493i	$0.202251\pi$
$761$			5.23117e8i			1.18699i	−0.804840	+	0.593493i	$0.797749\pi$
$762$	2.46151e7	+	2.72505e6i	0.0556336	+	0.00615900i
$763$	−4.43748e8			−0.998994
$764$			7.16257e7i			0.160616i
$765$	−4.85810e6	−	1.08899e6i	−0.0108513	−	0.00243243i
$766$	2.76417e8			0.615005
$767$		−	7.77403e8i		−	1.72290i
$768$	−5.07164e6	+	4.58116e7i	−0.0111960	+	0.101133i
$769$	−3.84461e8			−0.845422			−0.422711	−	0.906264i	$-0.638922\pi$
$769$	−3.84461e8			−0.845422			−0.422711	+	0.906264i	$0.638922\pi$
$770$			1.05627e8i			0.231367i
$771$	−1.33013e8	−	1.47254e7i	−0.290223	−	0.0321295i
$772$	−1.06284e8			−0.231003
$773$			3.75008e7i			0.0811899i	0.999176	+	0.0405950i	$0.0129253\pi$
$773$			3.75008e7i			0.0811899i	−0.999176	+	0.0405950i	$0.987075\pi$
$774$	5.38370e7	−	2.40172e8i	0.116107	−	0.517964i
$775$	3.98906e8			0.856969
$776$			2.53302e8i			0.542067i
$777$	−1.12405e8	+	1.01535e9i	−0.239621	+	2.16447i
$778$	−3.37418e8			−0.716521
$779$			7.85682e8i			1.66201i
$780$	−8.95106e8	−	9.90940e7i	−1.88621	−	0.208816i
$781$	1.62142e8			0.340364
$782$			291091.i			0.000608707i
$783$	−9.23911e7	−	3.17260e7i	−0.192462	−	0.0660891i
$784$	1.79501e8			0.372494
$785$		−	5.35366e8i		−	1.10673i
$786$	1.40181e7	−	1.26624e8i	0.0288683	−	0.260765i
$787$	4.01408e8			0.823496			0.411748	−	0.911298i	$-0.364918\pi$
$787$	4.01408e8			0.823496			0.411748	+	0.911298i	$0.364918\pi$
$788$			6.76144e8i			1.38185i
$789$	3.14396e8	+	3.48056e7i	0.640097	+	0.0708628i
$790$	−3.93369e8			−0.797846
$791$			5.53362e8i			1.11810i
$792$	−1.17098e8	−	2.62486e7i	−0.235707	−	0.0528361i
$793$	−5.43173e7			−0.108923
$794$		−	2.91100e8i		−	0.581542i
$795$	1.05162e8	−	9.49921e8i	0.209295	−	1.89054i
$796$	−2.78766e8			−0.552714
$797$		−	3.21652e8i		−	0.635348i	−0.948200	−	0.317674i	$-0.897098\pi$
$797$		−	3.21652e8i		−	0.635348i	0.948200	−	0.317674i	$-0.102902\pi$
$798$	−2.40199e8	−	2.65916e7i	−0.472675	−	0.0523281i
$799$	5.44879e6			0.0106822
$800$			4.57248e8i			0.893062i
$801$	1.17858e8	−	5.25778e8i	0.229331	−	1.02307i
$802$	2.08254e8			0.403710
$803$			4.34630e7i			0.0839408i
$804$	5.50752e7	−	4.97489e8i	0.105971	−	0.957227i
$805$	−1.94170e8			−0.372216
$806$			2.64638e8i			0.505414i
$807$	−4.42872e8	−	4.90288e7i	−0.842670	−	0.0932890i
$808$	−5.29438e8			−1.00365
$809$			3.36283e8i			0.635125i	0.948237	+	0.317562i	$0.102864\pi$
$809$			3.36283e8i			0.635125i	−0.948237	+	0.317562i	$0.897136\pi$
$810$	−2.49542e8	−	1.17794e8i	−0.469557	−	0.221649i
$811$	−5.16627e8			−0.968534			−0.484267	−	0.874920i	$-0.660914\pi$
$811$	−5.16627e8			−0.968534			−0.484267	+	0.874920i	$0.660914\pi$
$812$		−	1.19433e8i		−	0.223077i
$813$	−3.65383e7	+	3.30047e8i	−0.0679949	+	0.614191i
$814$	1.19941e8			0.222379
$815$			4.81550e8i			0.889545i
$816$	2.60333e6	+	288205.i	0.00479136	+	0.000530434i
$817$	7.95718e8			1.45913
$818$		−	2.95776e8i		−	0.540384i
$819$	1.06295e9	+	2.38272e8i	1.93492	+	0.433732i
$820$	−1.09684e9			−1.98931
$821$		−	7.49058e8i		−	1.35359i	−0.736173	−	0.676793i	$-0.763369\pi$
$821$		−	7.49058e8i		−	1.35359i	0.736173	−	0.676793i	$-0.236631\pi$
$822$	−1.58131e7	+	1.42839e8i	−0.0284710	+	0.257176i
$823$	6.18543e7			0.110961			0.0554805	−	0.998460i	$-0.482331\pi$
$823$	6.18543e7			0.110961			0.0554805	+	0.998460i	$0.482331\pi$
$824$			4.02430e8i			0.719298i
$825$	−1.91620e8	−	2.12136e7i	−0.341255	−	0.0377791i
$826$	2.91233e8			0.516773
$827$			6.30839e8i			1.11533i	0.830068	+	0.557663i	$0.188302\pi$
$827$			6.30839e8i			1.11533i	−0.830068	+	0.557663i	$0.811698\pi$
$828$	2.23614e7	−	9.97565e7i	0.0393920	−	0.175732i
$829$	8.05792e8			1.41436			0.707179	−	0.707035i	$-0.249968\pi$
$829$	8.05792e8			1.41436			0.707179	+	0.707035i	$0.249968\pi$
$830$			2.64122e8i			0.461924i
$831$	5.21848e7	−	4.71380e8i	0.0909370	−	0.821425i
$832$	2.45215e8			0.425771
$833$			2.79242e6i			0.00483109i
$834$	−2.66054e8	−	2.94538e7i	−0.458639	−	0.0507743i
$835$	7.22917e8			1.24173
$836$		−	1.79792e8i		−	0.307717i
$837$	1.66872e8	−	4.85958e8i	0.284582	−	0.828748i
$838$	2.19702e8			0.373337
$839$			3.20006e8i			0.541841i	0.962602	+	0.270921i	$0.0873281\pi$
$839$			3.20006e8i			0.541841i	−0.962602	+	0.270921i	$0.912672\pi$
$840$	8.01043e7	−	7.23574e8i	0.135151	−	1.22080i
$841$	5.70192e8			0.958591
$842$			2.93562e8i			0.491773i
$843$	−9.18888e7	−	1.01727e7i	−0.153384	−	0.0169806i
$844$	−3.00647e8			−0.500069
$845$		−	1.22258e9i		−	2.02631i
$846$	2.94691e8	+	6.60580e7i	0.486694	+	0.109097i
$847$	−6.76198e8			−1.11282
$848$			5.02800e8i			0.824532i
$849$	−3.30140e6	+	2.98212e7i	−0.00539480	+	0.0487307i
$850$	−1.75334e6			−0.00285503
$851$			2.20483e8i			0.357756i
$852$	−5.14743e8	−	5.69854e7i	−0.832285	−	0.0921392i
$853$	−5.02504e8			−0.809641			−0.404820	−	0.914396i	$-0.632666\pi$
$853$	−5.02504e8			−0.809641			−0.404820	+	0.914396i	$0.632666\pi$
$854$		−	2.03485e7i		−	0.0326707i
$855$	1.95132e8	−	8.70503e8i	0.312198	−	1.39275i
$856$	3.35684e8			0.535191
$857$			9.15923e8i			1.45518i	0.686013	+	0.727590i	$0.259359\pi$
$857$			9.15923e8i			1.45518i	−0.686013	+	0.727590i	$0.740641\pi$
$858$	1.40733e7	−	1.27123e8i	0.0222810	−	0.201262i
$859$	−6.80403e8			−1.07346			−0.536731	−	0.843754i	$-0.680341\pi$
$859$	−6.80403e8			−1.07346			−0.536731	+	0.843754i	$0.680341\pi$
$860$			1.11085e9i			1.74647i
$861$	1.31868e9	+	1.45986e8i	2.06600	+	0.228719i
$862$	3.79919e8			0.593156
$863$			8.80979e8i			1.37067i	0.728227	+	0.685336i	$0.240345\pi$
$863$			8.80979e8i			1.37067i	−0.728227	+	0.685336i	$0.759655\pi$
$864$	5.57032e8	+	1.91278e8i	0.863653	+	0.296568i
$865$	6.61267e8			1.02171
$866$		−	4.13007e8i		−	0.635921i
$867$	7.17064e7	−	6.47717e8i	0.110027	−	0.993866i
$868$	6.28191e8			0.960578
$869$			3.53993e8i			0.539431i
$870$	−6.91563e7	−	7.65605e6i	−0.105021	−	0.0116264i
$871$	1.15111e9			1.74206
$872$		−	3.59086e8i		−	0.541563i
$873$	5.11468e8	+	1.14651e8i	0.768733	+	0.172319i
$874$	−5.21594e7			−0.0781264
$875$			2.63114e7i			0.0392754i
$876$	1.52752e7	−	1.37979e8i	0.0227235	−	0.205259i
$877$	−1.09685e9			−1.62611			−0.813055	−	0.582187i	$-0.802197\pi$
$877$	−1.09685e9			−1.62611			−0.813055	+	0.582187i	$0.802197\pi$
$878$			2.19103e8i			0.323716i
$879$	3.33536e8	+	3.69245e7i	0.491106	+	0.0543686i
$880$	2.05133e8			0.301015
$881$		−	1.35200e9i		−	1.97719i	−0.150587	−	0.988597i	$-0.548116\pi$
$881$		−	1.35200e9i		−	1.97719i	0.150587	−	0.988597i	$-0.451884\pi$
$882$	−3.38536e7	+	1.51024e8i	−0.0493400	+	0.220111i
$883$	4.04857e8			0.588057			0.294028	−	0.955797i	$-0.405004\pi$
$883$	4.04857e8			0.588057			0.294028	+	0.955797i	$0.405004\pi$
$884$			7.37046e6i			0.0106694i
$885$	−1.18295e8	+	1.06855e9i	−0.170662	+	1.54158i
$886$	−2.10383e8			−0.302490
$887$			4.66825e7i			0.0668934i	0.999441	+	0.0334467i	$0.0106484\pi$
$887$			4.66825e7i			0.0668934i	−0.999441	+	0.0334467i	$0.989352\pi$
$888$	−8.21630e8	−	9.09597e7i	−1.17338	−	0.129900i
$889$	1.35200e8			0.192429
$890$		−	3.83787e8i		−	0.544403i
$891$	−1.06002e8	+	2.24563e8i	−0.149859	+	0.317472i
$892$	3.16232e8			0.445566
$893$			9.76347e8i			1.37104i
$894$	7.82006e6	−	7.06378e7i	0.0109445	−	0.0988609i
$895$	−6.47628e7			−0.0903351
$896$			9.25570e8i			1.28672i
$897$	2.33685e8	+	2.58704e7i	0.323783	+	0.0358448i
$898$	−8.12192e7			−0.112158
$899$		−	1.29555e8i		−	0.178310i
$900$	6.00869e8	+	1.34691e8i	0.824237	+	0.184761i
$901$	−7.82182e6			−0.0106938
$902$		−	1.55773e8i		−	0.212263i
$903$	1.47851e8	−	1.33553e9i	0.200799	−	1.81380i
$904$	−4.47787e8			−0.606130
$905$			1.47490e9i			1.98984i
$906$	−2.56185e8	−	2.83614e7i	−0.344485	−	0.0381367i
$907$	5.79799e8			0.777062			0.388531	−	0.921436i	$-0.372983\pi$
$907$	5.79799e8			0.777062			0.388531	+	0.921436i	$0.372983\pi$
$908$			2.13909e8i			0.285740i
$909$	−2.39637e8	+	1.06904e9i	−0.319052	+	1.42332i
$910$	7.75895e8			1.02962
$911$		−	1.34185e9i		−	1.77479i	−0.461007	−	0.887396i	$-0.652512\pi$
$911$		−	1.34185e9i		−	1.77479i	0.461007	−	0.887396i	$-0.347488\pi$
$912$	−5.16424e7	+	4.66480e8i	−0.0680803	+	0.614963i
$913$	2.37684e8			0.312311
$914$		−	4.36823e8i		−	0.572093i
$915$	7.46598e7	+	8.26532e6i	0.0974594	+	0.0107894i
$916$	1.80411e8			0.234735
$917$		−	6.95489e8i		−	0.901950i
$918$	−733467.	+	2.13597e6i	−0.000948097	+	0.00276101i
$919$	−7.17226e8			−0.924080			−0.462040	−	0.886859i	$-0.652882\pi$
$919$	−7.17226e8			−0.924080			−0.462040	+	0.886859i	$0.652882\pi$
$920$		−	1.57125e8i		−	0.201781i
$921$	1.28980e8	−	1.16507e9i	0.165099	−	1.49132i
$922$	2.77593e8			0.354173
$923$		−	1.19104e9i		−	1.51468i
$924$	−3.01761e8	−	3.34069e7i	−0.382514	−	0.0423467i
$925$	−1.32805e9			−1.67799
$926$			8.37248e7i			0.105444i
$927$	8.12588e8	+	1.82150e8i	1.02007	+	0.228660i
$928$	1.48504e8			0.185820
$929$		−	7.25116e8i		−	0.904399i	−0.891917	−	0.452200i	$-0.850639\pi$
$929$		−	7.25116e8i		−	0.904399i	0.891917	−	0.452200i	$-0.149361\pi$
$930$	4.02693e7	−	3.63748e8i	0.0500639	−	0.452222i
$931$	−5.00361e8			−0.620062
$932$			8.61007e8i			1.06355i
$933$	−1.20405e9	−	1.33296e8i	−1.48252	−	0.164125i
$934$	−4.21925e8			−0.517839
$935$			3.19116e6i			0.00390404i
$936$	−1.92812e8	+	8.60154e8i	−0.235129	+	1.04894i
$937$	2.43410e8			0.295882			0.147941	−	0.988996i	$-0.452735\pi$
$937$	2.43410e8			0.295882			0.147941	+	0.988996i	$0.452735\pi$
$938$			4.31232e8i			0.522520i
$939$	−9.90415e7	+	8.94632e8i	−0.119625	+	1.08056i
$940$	−1.36302e9			−1.64104
$941$		−	5.45355e8i		−	0.654501i	−0.944938	−	0.327251i	$-0.893878\pi$
$941$		−	5.45355e8i		−	0.654501i	0.944938	−	0.327251i	$-0.106122\pi$
$942$	−2.41376e8	−	2.67218e7i	−0.288763	−	0.0319679i
$943$	2.86353e8			0.341481
$944$		−	5.65591e8i		−	0.672336i
$945$	−1.42479e9	−	4.89254e8i	−1.68832	−	0.579748i
$946$	−1.57763e8			−0.186351
$947$			1.50322e9i			1.77000i	0.465593	+	0.884999i	$0.345841\pi$
$947$			1.50322e9i			1.77000i	−0.465593	+	0.884999i	$0.654159\pi$
$948$	1.24412e8	−	1.12380e9i	0.146028	−	1.31906i
$949$	3.19263e8			0.373551
$950$		−	3.14174e8i		−	0.366437i
$951$	1.65186e9	+	1.82871e8i	1.92057	+	0.212620i
$952$	−5.95804e6			−0.00690546
$953$		−	8.89049e8i		−	1.02718i	−0.858035	−	0.513591i	$-0.828315\pi$
$953$		−	8.89049e8i		−	1.02718i	0.858035	−	0.513591i	$-0.171685\pi$
$954$	−4.23033e8	−	9.48272e7i	−0.487225	−	0.109216i
$955$	2.27799e8			0.261542
$956$			5.97937e7i			0.0684356i
$957$	−6.88968e6	+	6.22338e7i	−0.00786074	+	0.0710053i
$958$	−2.51946e8			−0.286557
$959$			7.84548e8i			0.889536i
$960$	−3.37050e8	−	3.73136e7i	−0.380961	−	0.0421749i
$961$	−2.06069e8			−0.232189
$962$		−	8.81041e8i		−	0.989626i
$963$	1.51939e8	−	6.77813e8i	0.170133	−	0.758982i
$964$	4.17299e8			0.465818
$965$			3.38028e8i			0.376158i
$966$	−9.69165e6	+	8.75437e7i	−0.0107514	+	0.0971166i
$967$	1.61146e9			1.78213			0.891065	−	0.453877i	$-0.149959\pi$
$967$	1.61146e9			1.78213			0.891065	+	0.453877i	$0.149959\pi$
$968$		−	5.47187e8i		−	0.603267i
$969$	−7.25681e6	−	803376.i	−0.00797581	−	0.000882973i
$970$	3.73342e8			0.409064
$971$			4.99661e8i			0.545780i	0.962045	+	0.272890i	$0.0879795\pi$
$971$			4.99661e8i			0.545780i	−0.962045	+	0.272890i	$0.912021\pi$
$972$	4.15443e8	−	6.75651e8i	0.452389	−	0.735739i
$973$	−1.46131e9			−1.58637
$974$			1.25123e8i			0.135413i
$975$	−1.55827e8	+	1.40757e9i	−0.168124	+	1.51864i
$976$	−3.95179e7			−0.0425055
$977$		−	6.97375e8i		−	0.747795i	−0.927470	−	0.373897i	$-0.878021\pi$
$977$		−	6.97375e8i		−	0.747795i	0.927470	−	0.373897i	$-0.121979\pi$
$978$	2.17112e8	+	2.40357e7i	0.232096	+	0.0256945i
$979$	−3.45370e8			−0.368076
$980$		−	6.98524e8i		−	0.742169i
$981$	−7.25067e8	−	1.62531e8i	−0.768018	−	0.172159i
$982$	4.67251e8			0.493419
$983$		−	2.53195e8i		−	0.266560i	−0.991078	−	0.133280i	$-0.957449\pi$
$983$		−	2.53195e8i		−	0.266560i	0.991078	−	0.133280i	$-0.0425510\pi$
$984$	−1.18134e8	+	1.06709e9i	−0.123991	+	1.12000i
$985$	2.15041e9			2.25016
$986$			569446.i			0.000594048i
$987$	1.63869e9	+	1.81414e8i	1.70430	+	0.188677i
$988$	−1.32068e9			−1.36939
$989$		−	2.90010e8i		−	0.299795i
$990$	−3.86878e7	+	1.72590e8i	−0.0398721	+	0.177873i
$991$	−5.86507e8			−0.602632			−0.301316	−	0.953524i	$-0.597426\pi$
$991$	−5.86507e8			−0.602632			−0.301316	+	0.953524i	$0.597426\pi$
$992$			7.81099e8i			0.800149i
$993$	−1.85064e7	+	1.67166e8i	−0.0189005	+	0.170727i
$994$	4.46189e8			0.454318
$995$			8.86590e8i			0.900023i
$996$	−7.54560e8	−	8.35346e7i	−0.763687	−	0.0845451i
$997$	−1.47482e9			−1.48817			−0.744084	−	0.668086i	$-0.767114\pi$
$997$	−1.47482e9			−1.48817			−0.744084	+	0.668086i	$0.767114\pi$
$998$			6.53463e8i			0.657400i
$999$	−5.55556e8	+	1.61787e9i	−0.557226	+	1.62273i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	69.7.b.a.47.19	✓	44
3.2	odd	2	inner	69.7.b.a.47.26	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.7.b.a.47.19	✓	44	1.1	even	1	trivial
69.7.b.a.47.26	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)

\(f(q)\)	\(=\)	\(q-2.95357i q^{2} +(2.97092 - 26.8361i) q^{3} +55.2764 q^{4} -175.802i q^{5} +(-79.2621 - 8.77482i) q^{6} -435.351 q^{7} -352.291i q^{8} +(-711.347 - 159.456i) q^{9} +O(q^{10})\)	\(q-2.95357i q^{2} +(2.97092 - 26.8361i) q^{3} +55.2764 q^{4} -175.802i q^{5} +(-79.2621 - 8.77482i) q^{6} -435.351 q^{7} -352.291i q^{8} +(-711.347 - 159.456i) q^{9} -519.242 q^{10} +467.266i q^{11} +(164.222 - 1483.40i) q^{12} +3432.36 q^{13} +1285.84i q^{14} +(-4717.82 - 522.293i) q^{15} +2497.18 q^{16} +38.8474i q^{17} +(-470.963 + 2101.01i) q^{18} -6960.90 q^{19} -9717.69i q^{20} +(-1293.39 + 11683.1i) q^{21} +1380.10 q^{22} +2536.99i q^{23} +(-9454.10 - 1046.63i) q^{24} -15281.2 q^{25} -10137.7i q^{26} +(-6392.52 + 18616.0i) q^{27} -24064.7 q^{28} +4962.99i q^{29} +(-1542.63 + 13934.4i) q^{30} -26104.3 q^{31} -29922.2i q^{32} +(12539.6 + 1388.21i) q^{33} +114.738 q^{34} +76535.5i q^{35} +(-39320.7 - 8814.14i) q^{36} +86907.3 q^{37} +20559.5i q^{38} +(10197.3 - 92111.0i) q^{39} -61933.4 q^{40} -112871. i q^{41} +(34506.9 + 3820.13i) q^{42} -114313. q^{43} +25828.8i q^{44} +(-28032.6 + 125056. i) q^{45} +7493.19 q^{46} -140262. i q^{47} +(7418.92 - 67014.3i) q^{48} +71881.7 q^{49} +45134.1i q^{50} +(1042.51 + 115.413i) q^{51} +189729. q^{52} +201347. i q^{53} +(54983.7 + 18880.7i) q^{54} +82146.2 q^{55} +153370. i q^{56} +(-20680.3 + 186803. i) q^{57} +14658.5 q^{58} -226492. i q^{59} +(-260784. - 28870.5i) q^{60} -15825.1 q^{61} +77100.9i q^{62} +(309686. + 69419.2i) q^{63} +71441.9 q^{64} -603415. i q^{65} +(4100.18 - 37036.5i) q^{66} +335370. q^{67} +2147.34i q^{68} +(68082.9 + 7537.22i) q^{69} +226053. q^{70} -347002. i q^{71} +(-56174.8 + 250601. i) q^{72} +93015.5 q^{73} -256687. i q^{74} +(-45399.3 + 410088. i) q^{75} -384774. q^{76} -203425. i q^{77} +(-272056. - 30118.4i) q^{78} +757584. q^{79} -439008. i q^{80} +(480589. + 226857. i) q^{81} -333372. q^{82} -508669. i q^{83} +(-71494.3 + 645801. i) q^{84} +6829.43 q^{85} +337630. i q^{86} +(133187. + 14744.7i) q^{87} +164614. q^{88} +739130. i q^{89} +(369362. + 82796.1i) q^{90} -1.49428e6 q^{91} +140236. i q^{92} +(-77553.9 + 700537. i) q^{93} -414272. q^{94} +1.22374e6i q^{95} +(-802994. - 88896.6i) q^{96} -719013. q^{97} -212307. i q^{98} +(74508.3 - 332389. 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

L-functions

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