LMFDB - Embedded newform 63.6.e.f.46.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,6,Mod(37,63)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(63, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("63.37");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	63.e (of order $3$, degree $2$, 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:	$10.1041806482$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 187x^{10} + 25399x^{8} + 1518438x^{6} + 66232188x^{4} + 1297462320x^{2} + 18380851776 $ x^12 + 187x^10 + 25399x^8 + 1518438x^6 + 66232188x^4 + 1297462320*x^2 + 18380851776
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			46.2
Root			$-3.54467 - 6.13954i$ of defining polynomial
Character	$\chi$	$=$	63.46
Dual form			63.6.e.f.37.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.54467 - 6.13954i) q^{2} +(-9.12931 + 15.8124i) q^{4} +(-41.1020 - 71.1908i) q^{5} +(112.556 - 64.3292i) q^{7} -97.4172 q^{8} +O(q^{10})$	\(q+(-3.54467 - 6.13954i) q^{2} +(-9.12931 + 15.8124i) q^{4} +(-41.1020 - 71.1908i) q^{5} +(112.556 - 64.3292i) q^{7} -97.4172 q^{8} +(-291.386 + 504.695i) q^{10} +(176.118 - 305.046i) q^{11} -885.257 q^{13} +(-793.924 - 463.014i) q^{14} +(637.449 + 1104.09i) q^{16} +(-212.519 + 368.094i) q^{17} +(781.192 + 1353.06i) q^{19} +1500.93 q^{20} -2497.12 q^{22} +(1394.12 + 2414.69i) q^{23} +(-1816.26 + 3145.85i) q^{25} +(3137.94 + 5435.07i) q^{26} +(-10.3538 + 2367.06i) q^{28} -3678.79 q^{29} +(1795.76 - 3110.34i) q^{31} +(2960.41 - 5127.59i) q^{32} +3013.24 q^{34} +(-9205.91 - 5368.86i) q^{35} +(-7144.58 - 12374.8i) q^{37} +(5538.13 - 9592.31i) q^{38} +(4004.05 + 6935.21i) q^{40} -14325.8 q^{41} +7589.72 q^{43} +(3215.68 + 5569.72i) q^{44} +(9883.41 - 17118.6i) q^{46} +(-2884.17 - 4995.54i) q^{47} +(8530.51 - 14481.2i) q^{49} +25752.1 q^{50} +(8081.78 - 13998.1i) q^{52} +(-12694.2 + 21987.0i) q^{53} -28955.3 q^{55} +(-10964.9 + 6266.77i) q^{56} +(13040.1 + 22586.1i) q^{58} +(21611.7 - 37432.5i) q^{59} +(-9723.73 - 16842.0i) q^{61} -25461.4 q^{62} -1177.95 q^{64} +(36385.9 + 63022.2i) q^{65} +(14720.6 - 25496.7i) q^{67} +(-3880.31 - 6720.89i) q^{68} +(-330.470 + 75550.9i) q^{70} +51664.4 q^{71} +(-18972.8 + 32861.8i) q^{73} +(-50650.3 + 87728.9i) q^{74} -28527.0 q^{76} +(199.741 - 45664.2i) q^{77} +(-26899.7 - 46591.7i) q^{79} +(52400.9 - 90761.1i) q^{80} +(50780.1 + 87953.8i) q^{82} -85967.6 q^{83} +34939.9 q^{85} +(-26903.0 - 46597.4i) q^{86} +(-17157.0 + 29716.7i) q^{88} +(-10409.9 - 18030.5i) q^{89} +(-99640.6 + 56947.8i) q^{91} -50909.6 q^{92} +(-20446.9 + 35415.0i) q^{94} +(64217.1 - 111227. i) q^{95} -97587.2 q^{97} +(-119146. - 1042.34i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 182 q^{4} + 142 q^{7}+O(q^{10}) $ 12 * q - 182 * q^4 + 142 * q^7	$ 12 q - 182 q^{4} + 142 q^{7} + 686 q^{10} + 308 q^{13} - 1898 q^{16} + 9422 q^{19} - 18292 q^{22} - 7526 q^{25} + 37074 q^{28} + 23422 q^{31} - 55608 q^{34} - 18182 q^{37} + 69258 q^{40} - 87372 q^{43} + 25332 q^{46} + 30354 q^{49} + 34272 q^{52} - 96320 q^{55} - 89782 q^{58} - 16156 q^{61} + 380580 q^{64} + 144650 q^{67} - 187262 q^{70} - 100058 q^{73} - 685440 q^{76} + 101994 q^{79} + 75712 q^{82} + 602352 q^{85} + 752310 q^{88} - 282306 q^{91} - 120456 q^{94} - 866096 q^{97}+O(q^{100}) $ 12 * q - 182 * q^4 + 142 * q^7 + 686 * q^10 + 308 * q^13 - 1898 * q^16 + 9422 * q^19 - 18292 * q^22 - 7526 * q^25 + 37074 * q^28 + 23422 * q^31 - 55608 * q^34 - 18182 * q^37 + 69258 * q^40 - 87372 * q^43 + 25332 * q^46 + 30354 * q^49 + 34272 * q^52 - 96320 * q^55 - 89782 * q^58 - 16156 * q^61 + 380580 * q^64 + 144650 * q^67 - 187262 * q^70 - 100058 * q^73 - 685440 * q^76 + 101994 * q^79 + 75712 * q^82 + 602352 * q^85 + 752310 * q^88 - 282306 * q^91 - 120456 * q^94 - 866096 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

$n$	$10$	$29$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−3.54467	−	6.13954i	−0.626614	−	1.08533i	−0.988226	−	0.152999i	$-0.951107\pi$
$2$	−3.54467	−	6.13954i	−0.626614	−	1.08533i	0.361612	−	0.932329i	$-0.382226\pi$
$3$		0			0
$3$		0			0
$4$	−9.12931	+	15.8124i	−0.285291	+	0.494138i
$5$	−41.1020	−	71.1908i	−0.735256	−	1.27350i	−0.954611	−	0.297855i	$-0.903729\pi$
$5$	−41.1020	−	71.1908i	−0.735256	−	1.27350i	0.219355	−	0.975645i	$-0.429605\pi$
$6$		0			0
$7$	112.556	−	64.3292i	0.868204	−	0.496207i
$7$	112.556	−	64.3292i	0.868204	−	0.496207i
$8$	−97.4172			−0.538159
$9$		0			0
$10$	−291.386	+	504.695i	−0.921444	+	1.59599i
$11$	176.118	−	305.046i	0.438857	−	0.760123i	−0.558745	−	0.829340i	$-0.688717\pi$
$11$	176.118	−	305.046i	0.438857	−	0.760123i	0.997602	+	0.0692170i	$0.0220501\pi$
$12$		0			0
$13$	−885.257			−1.45282			−0.726408	−	0.687263i	$-0.758812\pi$
$13$	−885.257			−1.45282			−0.726408	+	0.687263i	$0.758812\pi$
$14$	−793.924	−	463.014i	−1.08258	−	0.631356i
$15$		0			0
$16$	637.449	+	1104.09i	0.622509	+	1.07822i
$17$	−212.519	+	368.094i	−0.178351	+	0.308913i	−0.941316	−	0.337527i	$-0.890410\pi$
$17$	−212.519	+	368.094i	−0.178351	+	0.308913i	0.762965	+	0.646440i	$0.223743\pi$
$18$		0			0
$19$	781.192	+	1353.06i	0.496448	+	0.859873i	0.999992	−	0.00409696i	$-0.00130411\pi$
$19$	781.192	+	1353.06i	0.496448	+	0.859873i	−0.503544	+	0.863970i	$0.667971\pi$
$20$	1500.93			0.839047
$21$		0			0
$22$	−2497.12			−1.09998
$23$	1394.12	+	2414.69i	0.549518	+	0.951793i	0.998308	+	0.0581556i	$0.0185219\pi$
$23$	1394.12	+	2414.69i	0.549518	+	0.951793i	−0.448790	+	0.893637i	$0.648145\pi$
$24$		0			0
$25$	−1816.26	+	3145.85i	−0.581202	+	1.00667i
$26$	3137.94	+	5435.07i	0.910356	+	1.57678i
$27$		0			0
$28$	−10.3538	+	2367.06i	−0.00249578	+	0.570576i
$29$	−3678.79			−0.812289			−0.406144	−	0.913809i	$-0.633127\pi$
$29$	−3678.79			−0.812289			−0.406144	+	0.913809i	$0.633127\pi$
$30$		0			0
$31$	1795.76	−	3110.34i	0.335617	−	0.581305i	−0.647986	−	0.761652i	$-0.724389\pi$
$31$	1795.76	−	3110.34i	0.335617	−	0.581305i	0.983603	+	0.180347i	$0.0577220\pi$
$32$	2960.41	−	5127.59i	0.511067	−	0.885193i
$33$		0			0
$34$	3013.24			0.447029
$35$	−9205.91	−	5368.86i	−1.27027	−	0.740819i
$36$		0			0
$37$	−7144.58	−	12374.8i	−0.857971	−	1.48605i	−0.873861	−	0.486175i	$-0.838392\pi$
$37$	−7144.58	−	12374.8i	−0.857971	−	1.48605i	0.0158904	−	0.999874i	$-0.494942\pi$
$38$	5538.13	−	9592.31i	0.622162	−	1.07762i
$39$		0			0
$40$	4004.05	+	6935.21i	0.395685	+	0.685346i
$41$	−14325.8			−1.33094			−0.665471	−	0.746424i	$-0.731769\pi$
$41$	−14325.8			−1.33094			−0.665471	+	0.746424i	$0.731769\pi$
$42$		0			0
$43$	7589.72			0.625972			0.312986	−	0.949758i	$-0.398671\pi$
$43$	7589.72			0.625972			0.312986	+	0.949758i	$0.398671\pi$
$44$	3215.68	+	5569.72i	0.250404	+	0.433712i
$45$		0			0
$46$	9883.41	−	17118.6i	0.688672	−	1.19281i
$47$	−2884.17	−	4995.54i	−0.190448	−	0.329866i	0.754951	−	0.655782i	$-0.227661\pi$
$47$	−2884.17	−	4995.54i	−0.190448	−	0.329866i	−0.945399	+	0.325916i	$0.894327\pi$
$48$		0			0
$49$	8530.51	−	14481.2i	0.507557	−	0.861618i
$50$	25752.1			1.45676
$51$		0			0
$52$	8081.78	−	13998.1i	0.414475	−	0.717892i
$53$	−12694.2	+	21987.0i	−0.620747	+	1.07517i	0.368599	+	0.929588i	$0.379837\pi$
$53$	−12694.2	+	21987.0i	−0.620747	+	1.07517i	−0.989347	+	0.145578i	$0.953496\pi$
$54$		0			0
$55$	−28955.3			−1.29069
$56$	−10964.9	+	6266.77i	−0.467232	+	0.267038i
$57$		0			0
$58$	13040.1	+	22586.1i	0.508992	+	0.881600i
$59$	21611.7	−	37432.5i	0.808273	−	1.39997i	−0.105786	−	0.994389i	$-0.533736\pi$
$59$	21611.7	−	37432.5i	0.808273	−	1.39997i	0.914059	−	0.405582i	$-0.132931\pi$
$60$		0			0
$61$	−9723.73	−	16842.0i	−0.334586	−	0.579521i	0.648819	−	0.760943i	$-0.275263\pi$
$61$	−9723.73	−	16842.0i	−0.334586	−	0.579521i	−0.983405	+	0.181422i	$0.941930\pi$
$62$	−25461.4			−0.841209
$63$		0			0
$64$	−1177.95			−0.0359481
$65$	36385.9	+	63022.2i	1.06819	+	1.85016i
$66$		0			0
$67$	14720.6	−	25496.7i	0.400624	−	0.693901i	−0.593177	−	0.805072i	$-0.702127\pi$
$67$	14720.6	−	25496.7i	0.400624	−	0.693901i	0.993801	+	0.111171i	$0.0354600\pi$
$68$	−3880.31	−	6720.89i	−0.101764	−	0.176260i
$69$		0			0
$70$	−330.470	+	75550.9i	−0.00806096	+	1.84287i
$71$	51664.4			1.21631			0.608157	−	0.793817i	$-0.291909\pi$
$71$	51664.4			1.21631			0.608157	+	0.793817i	$0.291909\pi$
$72$		0			0
$73$	−18972.8	+	32861.8i	−0.416701	+	0.721746i	−0.995605	−	0.0936487i	$-0.970147\pi$
$73$	−18972.8	+	32861.8i	−0.416701	+	0.721746i	0.578905	+	0.815395i	$0.303480\pi$
$74$	−50650.3	+	87728.9i	−1.07523	+	1.86236i
$75$		0			0
$76$	−28527.0			−0.566528
$77$	199.741	−	45664.2i	0.00383920	−	0.877706i
$78$		0			0
$79$	−26899.7	−	46591.7i	−0.484931	−	0.839926i	0.514919	−	0.857239i	$-0.327822\pi$
$79$	−26899.7	−	46591.7i	−0.484931	−	0.839926i	−0.999850	+	0.0173134i	$0.994489\pi$
$80$	52400.9	−	90761.1i	0.915407	−	1.58553i
$81$		0			0
$82$	50780.1	+	87953.8i	0.833987	+	1.44451i
$83$	−85967.6			−1.36974			−0.684872	−	0.728663i	$-0.740142\pi$
$83$	−85967.6			−1.36974			−0.684872	+	0.728663i	$0.740142\pi$
$84$		0			0
$85$	34939.9			0.524535
$86$	−26903.0	−	46597.4i	−0.392243	−	0.679385i
$87$		0			0
$88$	−17157.0	+	29716.7i	−0.236175	+	0.409067i
$89$	−10409.9	−	18030.5i	−0.139307	−	0.241287i	0.787927	−	0.615768i	$-0.211154\pi$
$89$	−10409.9	−	18030.5i	−0.139307	−	0.241287i	−0.927235	+	0.374481i	$0.877821\pi$
$90$		0			0
$91$	−99640.6	+	56947.8i	−1.26134	+	0.720898i
$92$	−50909.6			−0.627090
$93$		0			0
$94$	−20446.9	+	35415.0i	−0.238675	+	0.413397i
$95$	64217.1	−	111227.i	0.730032	−	1.26445i
$96$		0			0
$97$	−97587.2			−1.05309			−0.526543	−	0.850149i	$-0.676512\pi$
$97$	−97587.2			−1.05309			−0.526543	+	0.850149i	$0.676512\pi$
$98$	−119146.	−	1042.34i	−1.25318	−	0.0109634i
$99$		0			0
$100$	−33162.3	−	57438.8i	−0.331623	−	0.574388i
$101$	−19601.1	+	33950.0i	−0.191195	+	0.331159i	−0.945646	−	0.325197i	$-0.894570\pi$
$101$	−19601.1	+	33950.0i	−0.191195	+	0.331159i	0.754452	+	0.656356i	$0.227903\pi$
$102$		0			0
$103$	9614.12	+	16652.1i	0.0892928	+	0.154660i	0.907212	−	0.420673i	$-0.138206\pi$
$103$	9614.12	+	16652.1i	0.0892928	+	0.154660i	−0.817920	+	0.575333i	$0.804873\pi$
$104$	86239.2			0.781847
$105$		0			0
$106$	179986.			1.55588
$107$	94910.6	+	164390.i	0.801411	+	1.38808i	0.918688	+	0.394985i	$0.129250\pi$
$107$	94910.6	+	164390.i	0.801411	+	1.38808i	−0.117277	+	0.993099i	$0.537417\pi$
$108$		0			0
$109$	114021.	−	197491.i	0.919222	−	1.59214i	0.118622	−	0.992939i	$-0.462152\pi$
$109$	114021.	−	197491.i	0.919222	−	1.59214i	0.800600	−	0.599200i	$-0.204514\pi$
$110$	102637.	+	177772.i	0.808764	+	1.40082i
$111$		0			0
$112$	142774.	+	83265.4i	1.07548	+	0.627219i
$113$	50309.6			0.370642			0.185321	−	0.982678i	$-0.440668\pi$
$113$	50309.6			0.370642			0.185321	+	0.982678i	$0.440668\pi$
$114$		0			0
$115$	114603.	−	198498.i	0.808073	−	1.39962i
$116$	33584.8	−	58170.7i	0.231739	−	0.401383i
$117$		0			0
$118$	−306425.			−2.02590
$119$	−241.025	+	55102.2i	−0.00156025	+	0.356699i
$120$		0			0
$121$	18490.1	+	32025.8i	0.114809	+	0.198855i
$122$	−68934.7	+	119398.i	−0.419313	+	0.726272i
$123$		0			0
$124$	32788.1	+	56790.6i	0.191497	+	0.331682i
$125$	41719.7			0.238817
$126$		0			0
$127$	−235054.			−1.29318			−0.646588	−	0.762839i	$-0.723805\pi$
$127$	−235054.			−1.29318			−0.646588	+	0.762839i	$0.723805\pi$
$128$	−90557.8	−	156851.i	−0.488541	−	0.846178i
$129$		0			0
$130$	257951.	−	446785.i	1.33869	−	2.31868i
$131$	−28690.0	−	49692.5i	−0.146067	−	0.252995i	0.783704	−	0.621135i	$-0.213328\pi$
$131$	−28690.0	−	49692.5i	−0.146067	−	0.252995i	−0.929770	+	0.368140i	$0.879995\pi$
$132$		0			0
$133$	174969.	+	102041.i	0.857693	+	0.500204i
$134$	−208718.			−1.00415
$135$		0			0
$136$	20703.0	−	35858.7i	0.0959813	−	0.166245i
$137$	109484.	−	189632.i	0.498367	−	0.863196i	−0.501632	−	0.865081i	$-0.667267\pi$
$137$	109484.	−	189632.i	0.498367	−	0.863196i	0.999998	+	0.00188499i	$0.000600011\pi$
$138$		0			0
$139$	−37298.9			−0.163742			−0.0818708	−	0.996643i	$-0.526089\pi$
$139$	−37298.9			−0.163742			−0.0818708	+	0.996643i	$0.526089\pi$
$140$	168938.	−	96553.8i	0.728464	−	0.416341i
$141$		0			0
$142$	−183133.	−	317196.i	−0.762159	−	1.32010i
$143$	−155910.	+	270044.i	−0.637579	+	1.10432i
$144$		0			0
$145$	151206.	+	261896.i	0.597240	+	1.03445i
$146$	269009.			1.04444
$147$		0			0
$148$	260900.			0.979085
$149$	−198204.	−	343300.i	−0.731387	−	1.26680i	−0.956291	−	0.292418i	$-0.905540\pi$
$149$	−198204.	−	343300.i	−0.731387	−	1.26680i	0.224904	−	0.974381i	$-0.427793\pi$
$150$		0			0
$151$	−138220.	+	239405.i	−0.493321	+	0.854458i	−0.999970	−	0.00769465i	$-0.997551\pi$
$151$	−138220.	+	239405.i	−0.493321	+	0.854458i	0.506649	+	0.862152i	$0.330884\pi$
$152$	−76101.5	−	131812.i	−0.267168	−	0.462748i
$153$		0			0
$154$	−281065.	+	160638.i	−0.955004	+	0.545816i
$155$	−295237.			−0.987057
$156$		0			0
$157$	54401.7	−	94226.6i	0.176142	−	0.305087i	−0.764414	−	0.644726i	$-0.776971\pi$
$157$	54401.7	−	94226.6i	0.176142	−	0.305087i	0.940556	+	0.339639i	$0.110305\pi$
$158$	−190701.	+	330304.i	−0.607730	+	1.05262i
$159$		0			0
$160$	−486716.			−1.50306
$161$	312252.	+	182104.i	0.949380	+	0.553676i
$162$		0			0
$163$	−65806.5	−	113980.i	−0.193999	−	0.336016i	0.752573	−	0.658509i	$-0.228813\pi$
$163$	−65806.5	−	113980.i	−0.193999	−	0.336016i	−0.946572	+	0.322493i	$0.895479\pi$
$164$	130785.	−	226526.i	0.379705	−	0.657669i
$165$		0			0
$166$	304726.	+	527802.i	0.858302	+	1.48662i
$167$	−14833.5			−0.0411580			−0.0205790	−	0.999788i	$-0.506551\pi$
$167$	−14833.5			−0.0411580			−0.0205790	+	0.999788i	$0.506551\pi$
$168$		0			0
$169$	412386.			1.11068
$170$	−123850.	−	214515.i	−0.328681	−	0.569292i
$171$		0			0
$172$	−69288.9	+	120012.i	−0.178584	+	0.309317i
$173$	−359079.	−	621944.i	−0.912169	−	1.57992i	−0.810994	−	0.585054i	$-0.801073\pi$
$173$	−359079.	−	621944.i	−0.912169	−	1.57992i	−0.101175	−	0.994869i	$-0.532260\pi$
$174$		0			0
$175$	−2059.87	+	470921.i	−0.00508446	+	1.16239i
$176$	449066.			1.09277
$177$		0			0
$178$	−73799.5	+	127824.i	−0.174584	+	0.302388i
$179$	−81946.5	+	141936.i	−0.191160	+	0.331100i	−0.945635	−	0.325230i	$-0.894558\pi$
$179$	−81946.5	+	141936.i	−0.191160	+	0.331100i	0.754475	+	0.656329i	$0.227892\pi$
$180$		0			0
$181$	−414321.			−0.940027			−0.470013	−	0.882659i	$-0.655751\pi$
$181$	−414321.			−0.940027			−0.470013	+	0.882659i	$0.655751\pi$
$182$	702826.	+	409886.i	1.57279	+	0.917244i
$183$		0			0
$184$	−135812.	−	235233.i	−0.295728	−	0.512216i
$185$	−587314.	+	1.01726e6i	−1.26166	+	2.18525i
$186$		0			0
$187$	74857.1	+	129656.i	0.156541	+	0.271138i
$188$	105322.			0.217333
$189$		0			0
$190$	−910513.			−1.82979
$191$	51316.9	+	88883.5i	0.101783	+	0.176294i	0.912419	−	0.409256i	$-0.134212\pi$
$191$	51316.9	+	88883.5i	0.101783	+	0.176294i	−0.810636	+	0.585550i	$0.800878\pi$
$192$		0			0
$193$	160154.	−	277395.i	0.309488	−	0.536049i	−0.668762	−	0.743476i	$-0.733176\pi$
$193$	160154.	−	277395.i	0.309488	−	0.536049i	0.978250	+	0.207427i	$0.0665090\pi$
$194$	345914.	+	599141.i	0.659878	+	1.14294i
$195$		0			0
$196$	151106.	+	267092.i	0.280957	+	0.496615i
$197$	495759.			0.910134			0.455067	−	0.890457i	$-0.349615\pi$
$197$	495759.			0.910134			0.455067	+	0.890457i	$0.349615\pi$
$198$		0			0
$199$	−260356.	+	450950.i	−0.466052	+	0.807226i	−0.999248	−	0.0387653i	$-0.987658\pi$
$199$	−260356.	+	450950.i	−0.466052	+	0.807226i	0.533196	+	0.845992i	$0.320991\pi$
$200$	176935.	−	306460.i	0.312779	−	0.541750i
$201$		0			0
$202$	277917.			0.479221
$203$	−414069.	+	236654.i	−0.705233	+	0.403064i
$204$		0			0
$205$	588819.	+	1.01987e6i	0.978583	+	1.69495i
$206$	68157.7	−	118053.i	0.111904	−	0.193824i
$207$		0			0
$208$	−564306.	−	977407.i	−0.904392	−	1.56645i
$209$	550329.			0.871478
$210$		0			0
$211$	759493.			1.17440			0.587202	−	0.809440i	$-0.300229\pi$
$211$	759493.			1.17440			0.587202	+	0.809440i	$0.300229\pi$
$212$	−231778.	−	401452.i	−0.354187	−	0.613470i
$213$		0			0
$214$	672852.	−	1.16541e6i	1.00435	−	1.73959i
$215$	−311953.	−	540319.i	−0.460249	−	0.797175i
$216$		0			0
$217$	2036.62	−	465606.i	0.00293604	−	0.671227i
$218$	−1.61667e6			−2.30399
$219$		0			0
$220$	264342.	−	457854.i	0.368222	−	0.637779i
$221$	188134.	−	325858.i	0.259111	−	0.448794i
$222$		0			0
$223$	−352354.			−0.474479			−0.237240	−	0.971451i	$-0.576243\pi$
$223$	−352354.			−0.474479			−0.237240	+	0.971451i	$0.576243\pi$
$224$	3357.50	−	767579.i	0.00447091	−	1.02212i
$225$		0			0
$226$	−178331.	−	308878.i	−0.232250	−	0.402268i
$227$	587661.	−	1.01786e6i	0.756941	−	1.31106i	−0.187463	−	0.982272i	$-0.560026\pi$
$227$	587661.	−	1.01786e6i	0.756941	−	1.31106i	0.944404	−	0.328788i	$-0.106640\pi$
$228$		0			0
$229$	17343.0	+	30039.0i	0.0218542	+	0.0378526i	0.876746	−	0.480954i	$-0.159710\pi$
$229$	17343.0	+	30039.0i	0.0218542	+	0.0378526i	−0.854891	+	0.518807i	$0.826376\pi$
$230$	−1.62491e6			−2.02540
$231$		0			0
$232$	358378.			0.437141
$233$	−33247.7	−	57586.7i	−0.0401210	−	0.0694917i	0.845268	−	0.534343i	$-0.179441\pi$
$233$	−33247.7	−	57586.7i	−0.0401210	−	0.0694917i	−0.885389	+	0.464852i	$0.846108\pi$
$234$		0			0
$235$	−237091.	+	410654.i	−0.280056	+	0.485072i
$236$	394599.	+	683466.i	0.461186	+	0.798798i
$237$		0			0
$238$	339157.	−	193839.i	0.388113	−	0.221819i
$239$	968532.			1.09678			0.548390	−	0.836223i	$-0.315241\pi$
$239$	968532.			1.09678			0.548390	+	0.836223i	$0.315241\pi$
$240$		0			0
$241$	317055.	−	549155.i	0.351635	−	0.609049i	−0.634901	−	0.772593i	$-0.718959\pi$
$241$	317055.	−	549155.i	0.351635	−	0.609049i	0.986536	+	0.163544i	$0.0522926\pi$
$242$	131082.	−	227041.i	0.143882	−	0.249211i
$243$		0			0
$244$	355084.			0.381818
$245$	−1.38155e6	−	12086.4i	−1.47046	−	0.0128642i
$246$		0			0
$247$	−691555.	−	1.19781e6i	−0.721248	−	1.24924i
$248$	−174938.	+	303001.i	−0.180615	+	0.312835i
$249$		0			0
$250$	−147882.	−	256140.i	−0.149646	−	0.259195i
$251$	1.77716e6			1.78050			0.890249	−	0.455474i	$-0.150530\pi$
$251$	1.77716e6			1.78050			0.890249	+	0.455474i	$0.150530\pi$
$252$		0			0
$253$	982124.			0.964639
$254$	833186.	+	1.44312e6i	0.810322	+	1.40352i
$255$		0			0
$256$	−660841.	+	1.14461e6i	−0.630228	+	1.09159i
$257$	720322.	+	1.24764e6i	0.680290	+	1.17830i	0.974892	+	0.222677i	$0.0714795\pi$
$257$	720322.	+	1.24764e6i	0.680290	+	1.17830i	−0.294602	+	0.955620i	$0.595187\pi$
$258$		0			0
$259$	−1.60022e6	−	933245.i	−1.48228	−	0.864463i
$260$	−1.32871e6			−1.21898
$261$		0			0
$262$	−203393.	+	352286.i	−0.183055	+	0.317061i
$263$	49484.0	−	85708.8i	0.0441139	−	0.0764075i	−0.843125	−	0.537717i	$-0.819287\pi$
$263$	49484.0	−	85708.8i	0.0441139	−	0.0764075i	0.887239	+	0.461310i	$0.152620\pi$
$264$		0			0
$265$	2.08703e6			1.82563
$266$	6280.96	−	1.43593e6i	0.00544279	−	1.24431i
$267$		0			0
$268$	268777.	+	465535.i	0.228589	+	0.395927i
$269$	37927.9	−	65693.0i	0.0319579	−	0.0553526i	−0.849604	−	0.527421i	$-0.823159\pi$
$269$	37927.9	−	65693.0i	0.0319579	−	0.0553526i	0.881562	+	0.472068i	$0.156492\pi$
$270$		0			0
$271$	97239.3	+	168423.i	0.0804301	+	0.139309i	0.903435	−	0.428726i	$-0.141037\pi$
$271$	97239.3	+	168423.i	0.0804301	+	0.139309i	−0.823005	+	0.568035i	$0.807704\pi$
$272$	−541881.			−0.444101
$273$		0			0
$274$	−1.55234e6			−1.24913
$275$	639753.	+	1.10808e6i	0.510129	+	0.883570i
$276$		0			0
$277$	−162678.	+	281766.i	−0.127388	+	0.220643i	−0.922664	−	0.385605i	$-0.873993\pi$
$277$	−162678.	+	281766.i	−0.127388	+	0.220643i	0.795276	+	0.606248i	$0.207326\pi$
$278$	132212.	+	228998.i	0.102603	+	0.177713i
$279$		0			0
$280$	896815.	+	523020.i	0.683609	+	0.398679i
$281$	2.17543e6			1.64353			0.821767	−	0.569824i	$-0.192989\pi$
$281$	2.17543e6			1.64353			0.821767	+	0.569824i	$0.192989\pi$
$282$		0			0
$283$	−285752.	+	494936.i	−0.212091	+	0.367353i	−0.952369	−	0.304949i	$-0.901361\pi$
$283$	−285752.	+	494936.i	−0.212091	+	0.367353i	0.740278	+	0.672301i	$0.234694\pi$
$284$	−471660.	+	816939.i	−0.347003	+	0.601027i
$285$		0			0
$286$	2.21060e6			1.59806
$287$	−1.61245e6	+	921567.i	−1.15553	+	0.660423i
$288$		0			0
$289$	619600.	+	1.07318e6i	0.436382	+	0.755835i
$290$	1.07195e6	−	1.85667e6i	0.748478	−	1.29640i
$291$		0			0
$292$	−346417.	−	600012.i	−0.237762	−	0.411815i
$293$	−2.15439e6			−1.46607			−0.733037	−	0.680189i	$-0.761898\pi$
$293$	−2.15439e6			−1.46607			−0.733037	+	0.680189i	$0.761898\pi$
$294$		0			0
$295$	−3.55314e6			−2.37715
$296$	696005.	+	1.20552e6i	0.461725	+	0.799731i
$297$		0			0
$298$	−1.40514e6	+	2.43377e6i	−0.916595	+	1.58759i
$299$	−1.23416e6	−	2.13762e6i	−0.798349	−	1.38278i
$300$		0			0
$301$	854266.	−	488241.i	0.543471	−	0.310612i
$302$	1.95978e6			1.23649
$303$		0			0
$304$	−995940.	+	1.72502e6i	−0.618086	+	1.07056i
$305$	−799330.	+	1.38448e6i	−0.492013	+	0.852192i
$306$		0			0
$307$	−2.86577e6			−1.73539			−0.867693	−	0.497101i	$-0.834398\pi$
$307$	−2.86577e6			−1.73539			−0.867693	+	0.497101i	$0.834398\pi$
$308$	720238.	+	420041.i	0.432613	+	0.252299i
$309$		0			0
$310$	1.04652e6	+	1.81262e6i	0.618504	+	1.07128i
$311$	1.07116e6	−	1.85531e6i	0.627992	−	1.08771i	−0.359962	−	0.932967i	$-0.617210\pi$
$311$	1.07116e6	−	1.85531e6i	0.627992	−	1.08771i	0.987954	−	0.154747i	$-0.0494563\pi$
$312$		0			0
$313$	−124864.	−	216271.i	−0.0720405	−	0.124778i	0.827755	−	0.561090i	$-0.189618\pi$
$313$	−124864.	−	216271.i	−0.0720405	−	0.124778i	−0.899795	+	0.436312i	$0.856284\pi$
$314$	−771344.			−0.441493
$315$		0			0
$316$	982304.			0.553386
$317$	−429015.	−	743077.i	−0.239787	−	0.415322i	0.720866	−	0.693074i	$-0.243744\pi$
$317$	−429015.	−	743077.i	−0.239787	−	0.415322i	−0.960653	+	0.277752i	$0.910411\pi$
$318$		0			0
$319$	−647903.	+	1.12220e6i	−0.356479	+	0.617439i
$320$	48416.1	+	83859.2i	0.0264311	+	0.0457800i
$321$		0			0
$322$	11209.1	−	2.56258e6i	0.00602463	−	1.37733i
$323$	−664073.			−0.354168
$324$		0			0
$325$	1.60785e6	−	2.78488e6i	0.844380	−	1.46251i
$326$	−466524.	+	808043.i	−0.243125	+	0.421105i
$327$		0			0
$328$	1.39558e6			0.716259
$329$	−645989.	−	376739.i	−0.329030	−	0.191889i
$330$		0			0
$331$	1.16446e6	+	2.01690e6i	0.584189	+	1.01185i	0.994976	+	0.100114i	$0.0319208\pi$
$331$	1.16446e6	+	2.01690e6i	0.584189	+	1.01185i	−0.410786	+	0.911732i	$0.634746\pi$
$332$	784825.	−	1.35936e6i	0.390776	−	0.676843i
$333$		0			0
$334$	52580.0	+	91071.2i	0.0257902	+	0.0446699i
$335$	−2.42018e6			−1.17824
$336$		0			0
$337$	−384940.			−0.184637			−0.0923185	−	0.995730i	$-0.529428\pi$
$337$	−384940.			−0.184637			−0.0923185	+	0.995730i	$0.529428\pi$
$338$	−1.46177e6	−	2.53186e6i	−0.695966	−	1.20545i
$339$		0			0
$340$	−318977.	+	552484.i	−0.149645	+	0.259193i
$341$	−632532.	−	1.09558e6i	−0.294576	−	0.510220i
$342$		0			0
$343$	28591.3	−	2.17870e6i	0.0131219	−	0.999914i
$344$	−739370.			−0.336873
$345$		0			0
$346$	−2.54563e6	+	4.40917e6i	−1.14316	+	1.98000i
$347$	546073.	−	945826.i	0.243460	−	0.421685i	−0.718238	−	0.695798i	$-0.755051\pi$
$347$	546073.	−	945826.i	0.243460	−	0.421685i	0.961697	+	0.274113i	$0.0883843\pi$
$348$		0			0
$349$	1.96544e6			0.863765			0.431883	−	0.901930i	$-0.357849\pi$
$349$	1.96544e6			0.863765			0.431883	+	0.901930i	$0.357849\pi$
$350$	2.89854e6	−	1.65661e6i	1.26476	−	0.722854i
$351$		0			0
$352$	−1.04277e6	−	1.80613e6i	−0.448570	−	0.776947i
$353$	−1.29884e6	+	2.24966e6i	−0.554779	+	0.960905i	0.443142	+	0.896451i	$0.353864\pi$
$353$	−1.29884e6	+	2.24966e6i	−0.554779	+	0.960905i	−0.997921	+	0.0644536i	$0.979470\pi$
$354$		0			0
$355$	−2.12351e6	−	3.67803e6i	−0.894301	−	1.54898i
$356$	380142.			0.158972
$357$		0			0
$358$	1.16189e6			0.479135
$359$	1.24594e6	+	2.15803e6i	0.510225	+	0.883735i	0.999930	+	0.0118470i	$0.00377109\pi$
$359$	1.24594e6	+	2.15803e6i	0.510225	+	0.883735i	−0.489705	+	0.871888i	$0.662896\pi$
$360$		0			0
$361$	17529.0	−	30361.2i	0.00707929	−	0.0122617i
$362$	1.46863e6	+	2.54374e6i	0.589034	+	1.02024i
$363$		0			0
$364$	9165.80	−	2.09545e6i	0.00362591	−	0.828943i
$365$	3.11928e6			1.22553
$366$		0			0
$367$	1.80000e6	−	3.11769e6i	0.697602	−	1.20828i	−0.271694	−	0.962384i	$-0.587584\pi$
$367$	1.80000e6	−	3.11769e6i	0.697602	−	1.20828i	0.969296	−	0.245898i	$-0.0790827\pi$
$368$	−1.77737e6	+	3.07849e6i	−0.684160	+	1.18500i
$369$		0			0
$370$	8.32733e6			3.16229
$371$	−14396.9	+	3.29136e6i	−0.00543041	+	1.24148i
$372$		0			0
$373$	−943797.	−	1.63470e6i	−0.351242	−	0.608369i	0.635225	−	0.772327i	$-0.280907\pi$
$373$	−943797.	−	1.63470e6i	−0.351242	−	0.608369i	−0.986467	+	0.163958i	$0.947574\pi$
$374$	530687.	−	919176.i	0.196182	−	0.339797i
$375$		0			0
$376$	280968.	+	486651.i	0.102491	+	0.177520i
$377$	3.25668e6			1.18011
$378$		0			0
$379$	753126.			0.269321			0.134660	−	0.990892i	$-0.457006\pi$
$379$	753126.			0.269321			0.134660	+	0.990892i	$0.457006\pi$
$380$	1.17252e6	+	2.03086e6i	0.416543	+	0.721474i
$381$		0			0
$382$	363803.	−	630125.i	0.127558	−	0.220937i
$383$	−149129.	−	258299.i	−0.0519475	−	0.0899757i	0.838882	−	0.544313i	$-0.183210\pi$
$383$	−149129.	−	258299.i	−0.0519475	−	0.0899757i	−0.890830	+	0.454337i	$0.849876\pi$
$384$		0			0
$385$	−3.25908e6	+	1.86267e6i	−1.12058	+	0.640449i
$386$	−2.27077e6			−0.775719
$387$		0			0
$388$	890904.	−	1.54309e6i	0.300436	−	0.520370i
$389$	912091.	−	1.57979e6i	0.305608	−	0.529328i	−0.671789	−	0.740743i	$-0.734474\pi$
$389$	912091.	−	1.57979e6i	0.305608	−	0.529328i	0.977396	+	0.211415i	$0.0678071\pi$
$390$		0			0
$391$	−1.18511e6			−0.392029
$392$	−831019.	+	1.41072e6i	−0.273146	+	0.463688i
$393$		0			0
$394$	−1.75730e6	−	3.04373e6i	−0.570303	−	0.987793i
$395$	−2.21127e6	+	3.83003e6i	−0.713097	+	1.23512i
$396$		0			0
$397$	−807950.	−	1.39941e6i	−0.257281	−	0.445625i	0.708231	−	0.705981i	$-0.249493\pi$
$397$	−807950.	−	1.39941e6i	−0.257281	−	0.445625i	−0.965513	+	0.260356i	$0.916160\pi$
$398$	3.69150e6			1.16814
$399$		0			0
$400$	−4.63109e6			−1.44721
$401$	−1.72790e6	−	2.99280e6i	−0.536608	−	0.929431i	−0.999084	−	0.0427998i	$-0.986372\pi$
$401$	−1.72790e6	−	2.99280e6i	−0.536608	−	0.929431i	0.462476	−	0.886632i	$-0.346961\pi$
$402$		0			0
$403$	−1.58971e6	+	2.75345e6i	−0.487590	+	0.844530i
$404$	−357888.	−	619880.i	−0.109092	−	0.188953i
$405$		0			0
$406$	2.92068e6	+	1.70333e6i	0.879365	+	0.512843i
$407$	−5.03317e6			−1.50611
$408$		0			0
$409$	714625.	−	1.23777e6i	0.211237	−	0.365873i	−0.740865	−	0.671654i	$-0.765584\pi$
$409$	714625.	−	1.23777e6i	0.211237	−	0.365873i	0.952102	+	0.305781i	$0.0989175\pi$
$410$	4.17434e6	−	7.23016e6i	1.22639	−	2.12417i
$411$		0			0
$412$	−351081.			−0.101898
$413$	24510.5	−	5.60350e6i	0.00707093	−	1.61653i
$414$		0			0
$415$	3.53344e6	+	6.12011e6i	1.00711	+	1.74437i
$416$	−2.62073e6	+	4.53923e6i	−0.742486	+	1.28602i
$417$		0			0
$418$	−1.95073e6	−	3.37877e6i	−0.546081	−	0.945840i
$419$	2.27839e6			0.634006			0.317003	−	0.948425i	$-0.397323\pi$
$419$	2.27839e6			0.634006			0.317003	+	0.948425i	$0.397323\pi$
$420$		0			0
$421$	6.36256e6			1.74955			0.874775	−	0.484529i	$-0.161009\pi$
$421$	6.36256e6			1.74955			0.874775	+	0.484529i	$0.161009\pi$
$422$	−2.69215e6	−	4.66294e6i	−0.735899	−	1.27461i
$423$		0			0
$424$	1.23663e6	−	2.14191e6i	0.334061	−	0.578611i
$425$	−771979.	−	1.33711e6i	−0.207316	−	0.359082i
$426$		0			0
$427$	−2.17789e6	−	1.27014e6i	−0.578052	−	0.337118i
$428$	−3.46587e6			−0.914541
$429$		0			0
$430$	−2.21154e6	+	3.83050e6i	−0.576798	+	0.999043i
$431$	1.32575e6	−	2.29626e6i	0.343770	−	0.595427i	−0.641360	−	0.767240i	$-0.721629\pi$
$431$	1.32575e6	−	2.29626e6i	0.343770	−	0.595427i	0.985129	+	0.171814i	$0.0549627\pi$
$432$		0			0
$433$	688738.			0.176536			0.0882682	−	0.996097i	$-0.471867\pi$
$433$	688738.			0.176536			0.0882682	+	0.996097i	$0.471867\pi$
$434$	−2.86583e6	+	1.63791e6i	−0.730341	+	0.417414i
$435$		0			0
$436$	2.08187e6	+	3.60591e6i	0.524491	+	0.908445i
$437$	−2.17816e6	+	3.77268e6i	−0.545614	+	0.945031i
$438$		0			0
$439$	116398.	+	201608.i	0.0288261	+	0.0499282i	0.880079	−	0.474828i	$-0.157490\pi$
$439$	116398.	+	201608.i	0.0288261	+	0.0499282i	−0.851252	+	0.524756i	$0.824156\pi$
$440$	2.82075e6			0.694596
$441$		0			0
$442$	−2.66749e6			−0.649452
$443$	−718741.	−	1.24490e6i	−0.174006	−	0.301386i	0.765811	−	0.643066i	$-0.222338\pi$
$443$	−718741.	−	1.24490e6i	−0.174006	−	0.301386i	−0.939817	+	0.341679i	$0.889004\pi$
$444$		0			0
$445$	−855739.	+	1.48218e6i	−0.204853	+	0.354815i
$446$	1.24898e6	+	2.16329e6i	0.297315	+	0.514965i
$447$		0			0
$448$	−132585.	+	75776.5i	−0.0312103	+	0.0178377i
$449$	−333630.			−0.0780997			−0.0390499	−	0.999237i	$-0.512433\pi$
$449$	−333630.			−0.0780997			−0.0390499	+	0.999237i	$0.512433\pi$
$450$		0			0
$451$	−2.52304e6	+	4.37003e6i	−0.584093	+	1.01168i
$452$	−459292.	+	795516.i	−0.105741	+	0.183148i
$453$		0			0
$454$	−8.33224e6			−1.89724
$455$	8.14960e6	+	4.75282e6i	1.84547	+	1.07627i
$456$		0			0
$457$	1.27431e6	+	2.20717e6i	0.285421	+	0.494363i	0.972711	−	0.232020i	$-0.0745334\pi$
$457$	1.27431e6	+	2.20717e6i	0.285421	+	0.494363i	−0.687290	+	0.726383i	$0.741200\pi$
$458$	122950.	−	212956.i	0.0273883	−	0.0474380i
$459$		0			0
$460$	2.09249e6	+	3.62429e6i	0.461071	+	0.798599i
$461$	−1.54182e6			−0.337894			−0.168947	−	0.985625i	$-0.554037\pi$
$461$	−1.54182e6			−0.337894			−0.168947	+	0.985625i	$0.554037\pi$
$462$		0			0
$463$	−1.05753e6			−0.229266			−0.114633	−	0.993408i	$-0.536569\pi$
$463$	−1.05753e6			−0.229266			−0.114633	+	0.993408i	$0.536569\pi$
$464$	−2.34504e6	−	4.06174e6i	−0.505657	−	0.875824i
$465$		0			0
$466$	−235704.	+	408251.i	−0.0502808	+	0.0870889i
$467$	−411966.	−	713545.i	−0.0874115	−	0.151401i	0.819005	−	0.573787i	$-0.194526\pi$
$467$	−411966.	−	713545.i	−0.0874115	−	0.151401i	−0.906416	+	0.422386i	$0.861193\pi$
$468$		0			0
$469$	16695.0	−	3.81676e6i	0.00350474	−	0.801241i
$470$	3.36163e6			0.701949
$471$		0			0
$472$	−2.10535e6	+	3.64657e6i	−0.434980	+	0.753407i
$473$	1.33669e6	−	2.31522e6i	0.274712	−	0.475815i
$474$		0			0
$475$	−5.67538e6			−1.15415
$476$	−869099.	−	506856.i	−0.175813	−	0.102534i
$477$		0			0
$478$	−3.43312e6	−	5.94634e6i	−0.687258	−	1.19037i
$479$	613204.	−	1.06210e6i	0.122114	−	0.211508i	−0.798487	−	0.602012i	$-0.794366\pi$
$479$	613204.	−	1.06210e6i	0.122114	−	0.211508i	0.920601	+	0.390504i	$0.127699\pi$
$480$		0			0
$481$	6.32479e6	+	1.09549e7i	1.24647	+	2.15896i
$482$	−4.49541e6			−0.881358
$483$		0			0
$484$	−675207.			−0.131016
$485$	4.01103e6	+	6.94732e6i	0.774287	+	1.34110i
$486$		0			0
$487$	1.36094e6	−	2.35722e6i	0.260027	−	0.450379i	−0.706222	−	0.707990i	$-0.749602\pi$
$487$	1.36094e6	−	2.35722e6i	0.260027	−	0.450379i	0.966249	+	0.257611i	$0.0829353\pi$
$488$	947259.	+	1.64070e6i	0.180061	+	0.311874i
$489$		0			0
$490$	4.82293e6	+	8.52493e6i	0.907446	+	1.60399i
$491$	−5.69198e6			−1.06552			−0.532758	−	0.846268i	$-0.678844\pi$
$491$	−5.69198e6			−1.06552			−0.532758	+	0.846268i	$0.678844\pi$
$492$		0			0
$493$	781814.	−	1.35414e6i	0.144873	−	0.250927i
$494$	−4.90266e6	+	8.49166e6i	−0.903888	+	1.56558i
$495$		0			0
$496$	4.57882e6			0.835698
$497$	5.81511e6	−	3.32353e6i	1.05601	−	0.603543i
$498$		0			0
$499$	−2.43358e6	−	4.21509e6i	−0.437517	−	0.757802i	0.559980	−	0.828506i	$-0.310809\pi$
$499$	−2.43358e6	−	4.21509e6i	−0.437517	−	0.757802i	−0.997497	+	0.0707042i	$0.977475\pi$
$500$	−380872.	+	659689.i	−0.0681324	+	0.118009i
$501$		0			0
$502$	−6.29943e6	−	1.09109e7i	−1.11569	−	1.93242i
$503$	8.13233e6			1.43316			0.716581	−	0.697504i	$-0.245706\pi$
$503$	8.13233e6			1.43316			0.716581	+	0.697504i	$0.245706\pi$
$504$		0			0
$505$	3.22257e6			0.562308
$506$	−3.48130e6	−	6.02979e6i	−0.604457	−	1.04695i
$507$		0			0
$508$	2.14588e6	−	3.71677e6i	0.368931	−	0.639008i
$509$	2.30125e6	+	3.98589e6i	0.393704	+	0.681915i	0.992935	−	0.118661i	$-0.0378602\pi$
$509$	2.30125e6	+	3.98589e6i	0.393704	+	0.681915i	−0.599231	+	0.800576i	$0.704527\pi$
$510$		0			0
$511$	−21517.6	+	4.91929e6i	−0.00364537	+	0.833393i
$512$	3.57415e6			0.602556
$513$		0			0
$514$	5.10660e6	−	8.84490e6i	0.852559	−	1.47668i
$515$	790320.	−	1.36887e6i	0.131306	−	0.227429i
$516$		0			0
$517$	−2.03183e6			−0.334318
$518$	−57444.1	+	1.31327e7i	−0.00940634	+	2.15045i
$519$		0			0
$520$	−3.54461e6	−	6.13944e6i	−0.574857	−	0.995682i
$521$	−234824.	+	406727.i	−0.0379008	+	0.0656461i	−0.884354	−	0.466818i	$-0.845400\pi$
$521$	−234824.	+	406727.i	−0.0379008	+	0.0656461i	0.846453	+	0.532464i	$0.178734\pi$
$522$		0			0
$523$	6.02078e6	+	1.04283e7i	0.962495	+	1.66709i	0.716200	+	0.697895i	$0.245880\pi$
$523$	6.02078e6	+	1.04283e7i	0.962495	+	1.66709i	0.246295	+	0.969195i	$0.420787\pi$
$524$	1.04768e6			0.166686
$525$		0			0
$526$	−701617.			−0.110570
$527$	763266.	+	1.32202e6i	0.119715	+	0.207353i
$528$		0			0
$529$	−668993.	+	1.15873e6i	−0.103940	+	0.180029i
$530$	−7.39781e6	−	1.28134e7i	−1.14397	−	1.98141i
$531$		0			0
$532$	−3.21087e6	+	1.83512e6i	−0.491862	+	0.281115i
$533$	1.26820e7			1.93361
$534$		0			0
$535$	7.80204e6	−	1.35135e7i	1.17848	−	2.04119i
$536$	−1.43404e6	+	2.48382e6i	−0.215600	+	0.373429i
$537$		0			0
$538$	−537766.			−0.0801010
$539$	−2.91506e6	−	5.15261e6i	−0.432191	−	0.763933i
$540$		0			0
$541$	2.43174e6	+	4.21190e6i	0.357211	+	0.618707i	0.987494	−	0.157659i	$-0.0503945\pi$
$541$	2.43174e6	+	4.21190e6i	0.357211	+	0.618707i	−0.630283	+	0.776365i	$0.717061\pi$
$542$	689361.	−	1.19401e6i	0.100797	−	0.174586i
$543$		0			0
$544$	1.25829e6	+	2.17942e6i	0.182299	+	0.315750i
$545$	−1.87461e7			−2.70345
$546$		0			0
$547$	5.47821e6			0.782836			0.391418	−	0.920213i	$-0.371985\pi$
$547$	5.47821e6			0.782836			0.391418	+	0.920213i	$0.371985\pi$
$548$	1.99903e6	+	3.46241e6i	0.284359	+	0.492524i
$549$		0			0
$550$	4.53542e6	−	7.85557e6i	0.639309	−	1.10732i
$551$	−2.87384e6	−	4.97764e6i	−0.403259	−	0.698465i
$552$		0			0
$553$	−6.02492e6	−	3.51372e6i	−0.837796	−	0.488601i
$554$	2.30656e6			0.319293
$555$		0			0
$556$	340513.	−	589786.i	0.0467140	−	0.0809110i
$557$	−6.18341e6	+	1.07100e7i	−0.844481	+	1.46268i	0.0415907	+	0.999135i	$0.486757\pi$
$557$	−6.18341e6	+	1.07100e7i	−0.844481	+	1.46268i	−0.886071	+	0.463549i	$0.846576\pi$
$558$		0			0
$559$	−6.71885e6			−0.909422
$560$	59429.5	−	1.35866e7i	0.00800815	−	1.83080i
$561$		0			0
$562$	−7.71116e6	−	1.33561e7i	−1.02986	−	1.78377i
$563$	7.15837e6	−	1.23987e7i	0.951794	−	1.64856i	0.210255	−	0.977647i	$-0.432571\pi$
$563$	7.15837e6	−	1.23987e7i	0.951794	−	1.64856i	0.741539	−	0.670909i	$-0.234096\pi$
$564$		0			0
$565$	−2.06783e6	−	3.58158e6i	−0.272517	−	0.472013i
$566$	4.05158e6			0.531597
$567$		0			0
$568$	−5.03300e6			−0.654570
$569$	−4.55772e6	−	7.89420e6i	−0.590156	−	1.02218i	−0.994211	−	0.107445i	$-0.965733\pi$
$569$	−4.55772e6	−	7.89420e6i	−0.590156	−	1.02218i	0.404055	−	0.914735i	$-0.367600\pi$
$570$		0			0
$571$	2.54771e6	−	4.41277e6i	0.327009	−	0.566397i	−0.654908	−	0.755709i	$-0.727292\pi$
$571$	2.54771e6	−	4.41277e6i	0.327009	−	0.566397i	0.981917	+	0.189312i	$0.0606258\pi$
$572$	−2.84670e6	−	4.93063e6i	−0.363791	−	0.630104i
$573$		0			0
$574$	1.13736e7	+	6.63304e6i	1.44085	+	0.840297i
$575$	−1.01283e7			−1.27752
$576$		0			0
$577$	87796.6	−	152068.i	0.0109784	−	0.0190151i	−0.860484	−	0.509477i	$-0.829839\pi$
$577$	87796.6	−	152068.i	0.0109784	−	0.0190151i	0.871462	+	0.490462i	$0.163172\pi$
$578$	4.39255e6	−	7.60812e6i	0.546886	−	0.947234i
$579$		0			0
$580$	−5.52162e6			−0.681549
$581$	−9.67613e6	+	5.53023e6i	−1.18922	+	0.679677i
$582$		0			0
$583$	4.47136e6	+	7.74462e6i	0.544839	+	0.943689i
$584$	1.84828e6	−	3.20131e6i	0.224251	−	0.388415i
$585$		0			0
$586$	7.63660e6	+	1.32270e7i	0.918663	+	1.59117i
$587$	−6.35775e6			−0.761567			−0.380784	−	0.924664i	$-0.624346\pi$
$587$	−6.35775e6			−0.761567			−0.380784	+	0.924664i	$0.624346\pi$
$588$		0			0
$589$	5.61132e6			0.666465
$590$	1.25947e7	+	2.18146e7i	1.48956	+	2.57999i
$591$		0			0
$592$	9.10862e6	−	1.57766e7i	1.06819	−	1.85016i
$593$	5.59393e6	+	9.68897e6i	0.653251	+	1.13146i	0.982329	+	0.187162i	$0.0599289\pi$
$593$	5.59393e6	+	9.68897e6i	0.653251	+	1.13146i	−0.329078	+	0.944303i	$0.606738\pi$
$594$		0			0
$595$	3.93268e6	−	2.24766e6i	0.455403	−	0.260278i
$596$	7.23787e6			0.834632
$597$		0			0
$598$	−8.74935e6	+	1.51543e7i	−1.00051	+	1.73294i
$599$	−227851.	+	394650.i	−0.0259468	+	0.0449412i	−0.878707	−	0.477361i	$-0.841593\pi$
$599$	−227851.	+	394650.i	−0.0259468	+	0.0449412i	0.852760	+	0.522302i	$0.174927\pi$
$600$		0			0
$601$	−1.72814e7			−1.95161			−0.975804	−	0.218649i	$-0.929835\pi$
$601$	−1.72814e7			−1.95161			−0.975804	+	0.218649i	$0.929835\pi$
$602$	−6.02566e6	−	3.51415e6i	−0.677662	−	0.395211i
$603$		0			0
$604$	−2.52371e6	−	4.37120e6i	−0.281480	−	0.487538i
$605$	1.51996e6	−	2.63265e6i	0.168828	−	0.292418i
$606$		0			0
$607$	−963589.	−	1.66898e6i	−0.106150	−	0.183857i	0.808057	−	0.589104i	$-0.200519\pi$
$607$	−963589.	−	1.66898e6i	−0.106150	−	0.183857i	−0.914207	+	0.405246i	$0.867186\pi$
$608$	9.25060e6			1.01487
$609$		0			0
$610$	1.13334e7			1.23321
$611$	2.55323e6	+	4.42233e6i	0.276686	+	0.479235i
$612$		0			0
$613$	−963889.	+	1.66950e6i	−0.103604	+	0.179447i	−0.913167	−	0.407586i	$-0.866371\pi$
$613$	−963889.	+	1.66950e6i	−0.103604	+	0.179447i	0.809563	+	0.587033i	$0.199704\pi$
$614$	1.01582e7	+	1.75945e7i	1.08742	+	1.88346i
$615$		0			0
$616$	−19458.2	+	4.44848e6i	−0.00206610	+	0.472345i
$617$	−8.90588e6			−0.941812			−0.470906	−	0.882183i	$-0.656073\pi$
$617$	−8.90588e6			−0.941812			−0.470906	+	0.882183i	$0.656073\pi$
$618$		0			0
$619$	−1.18219e6	+	2.04762e6i	−0.124011	+	0.214794i	−0.921346	−	0.388743i	$-0.872909\pi$
$619$	−1.18219e6	+	2.04762e6i	−0.124011	+	0.214794i	0.797335	+	0.603537i	$0.206243\pi$
$620$	2.69531e6	−	4.66842e6i	0.281598	−	0.487742i
$621$		0			0
$622$	−1.51876e7			−1.57403
$623$	−2.33159e6	−	1.35977e6i	−0.240675	−	0.140361i
$624$		0			0
$625$	3.96104e6	+	6.86072e6i	0.405610	+	0.702538i
$626$	−885203.	+	1.53322e6i	−0.0902832	+	0.156375i
$627$		0			0
$628$	993301.	+	1.72045e6i	0.100504	+	0.174077i
$629$	6.07344e6			0.612080
$630$		0			0
$631$	−3.00892e6			−0.300841			−0.150420	−	0.988622i	$-0.548063\pi$
$631$	−3.00892e6			−0.300841			−0.150420	+	0.988622i	$0.548063\pi$
$632$	2.62050e6	+	4.53883e6i	0.260970	+	0.452014i
$633$		0			0
$634$	−3.04143e6	+	5.26792e6i	−0.300507	+	0.520494i
$635$	9.66118e6	+	1.67337e7i	0.950815	+	1.64686i
$636$		0			0
$637$	−7.55169e6	+	1.28196e7i	−0.737387	+	1.25177i
$638$	9.18640e6			0.893499
$639$		0			0
$640$	−7.44422e6	+	1.28938e7i	−0.718405	+	1.24431i
$641$	−3.53263e6	+	6.11869e6i	−0.339588	+	0.588184i	−0.984355	−	0.176195i	$-0.943621\pi$
$641$	−3.53263e6	+	6.11869e6i	−0.339588	+	0.588184i	0.644767	+	0.764379i	$0.276954\pi$
$642$		0			0
$643$	1.11768e7			1.06608			0.533038	−	0.846091i	$-0.321050\pi$
$643$	1.11768e7			1.06608			0.533038	+	0.846091i	$0.321050\pi$
$644$	−5.73015e6	+	3.27497e6i	−0.544442	+	0.311166i
$645$		0			0
$646$	2.35392e6	+	4.07710e6i	0.221927	+	0.384388i
$647$	3.56677e6	−	6.17783e6i	0.334977	−	0.580197i	−0.648504	−	0.761212i	$-0.724605\pi$
$647$	3.56677e6	−	6.17783e6i	0.334977	−	0.580197i	0.983480	+	0.181015i	$0.0579382\pi$
$648$		0			0
$649$	−7.61243e6	−	1.31851e7i	−0.709433	−	1.22877i
$650$	−2.27972e7			−2.11640
$651$		0			0
$652$	2.40307e6			0.221385
$653$	−3.09586e6	−	5.36218e6i	−0.284117	−	0.492106i	0.688277	−	0.725448i	$-0.258367\pi$
$653$	−3.09586e6	−	5.36218e6i	−0.284117	−	0.492106i	−0.972395	+	0.233342i	$0.925034\pi$
$654$		0			0
$655$	−2.35843e6	+	4.08493e6i	−0.214793	+	0.372033i
$656$	−9.13197e6	−	1.58170e7i	−0.828523	−	1.43504i
$657$		0			0
$658$	−23189.4	+	5.30149e6i	−0.00208797	+	0.477346i
$659$	747569.			0.0670560			0.0335280	−	0.999438i	$-0.489326\pi$
$659$	747569.			0.0670560			0.0335280	+	0.999438i	$0.489326\pi$
$660$		0			0
$661$	1.03881e7	−	1.79927e7i	0.924769	−	1.60175i	0.132836	−	0.991138i	$-0.457592\pi$
$661$	1.03881e7	−	1.79927e7i	0.924769	−	1.60175i	0.791933	−	0.610609i	$-0.209075\pi$
$662$	8.25523e6	−	1.42985e7i	0.732123	−	1.26807i
$663$		0			0
$664$	8.37473e6			0.737141
$665$	72830.6	−	1.66503e7i	0.00638646	−	1.46005i
$666$		0			0
$667$	−5.12870e6	−	8.88316e6i	−0.446367	−	0.773131i
$668$	135420.	−	234554.i	0.0117420	−	0.0203377i
$669$		0			0
$670$	8.57873e6	+	1.48588e7i	0.738305	+	1.27878i
$671$	−6.85011e6			−0.587343
$672$		0			0
$673$	−1.20681e7			−1.02707			−0.513536	−	0.858068i	$-0.671665\pi$
$673$	−1.20681e7			−1.02707			−0.513536	+	0.858068i	$0.671665\pi$
$674$	1.36449e6	+	2.36336e6i	0.115696	+	0.200392i
$675$		0			0
$676$	−3.76480e6	+	6.52083e6i	−0.316866	+	0.548828i
$677$	5.65866e6	+	9.80109e6i	0.474506	+	0.821869i	0.999574	−	0.0291915i	$-0.00929325\pi$
$677$	5.65866e6	+	9.80109e6i	0.474506	+	0.821869i	−0.525067	+	0.851061i	$0.675960\pi$
$678$		0			0
$679$	−1.09840e7	+	6.27771e6i	−0.914293	+	0.522549i
$680$	−3.40375e6			−0.282283
$681$		0			0
$682$	−4.48423e6	+	7.76692e6i	−0.369171	+	0.639422i
$683$	−2.84116e6	+	4.92103e6i	−0.233047	+	0.403650i	−0.958703	−	0.284408i	$-0.908203\pi$
$683$	−2.84116e6	+	4.92103e6i	−0.233047	+	0.403650i	0.725656	+	0.688058i	$0.241536\pi$
$684$		0			0
$685$	−1.80001e7			−1.46571
$686$	−1.34776e7	+	7.54723e6i	−1.09346	+	0.612319i
$687$		0			0
$688$	4.83806e6	+	8.37977e6i	0.389673	+	0.674934i
$689$	1.12376e7	−	1.94641e7i	0.901832	−	1.56202i
$690$		0			0
$691$	2.88281e6	+	4.99317e6i	0.229679	+	0.397815i	0.957713	−	0.287726i	$-0.0928991\pi$
$691$	2.88281e6	+	4.99317e6i	0.229679	+	0.397815i	−0.728034	+	0.685541i	$0.759566\pi$
$692$	1.31126e7			1.04093
$693$		0			0
$694$	−7.74258e6			−0.610221
$695$	1.53306e6	+	2.65534e6i	0.120392	+	0.208525i
$696$		0			0
$697$	3.04451e6	−	5.27324e6i	0.237375	−	0.411145i
$698$	−6.96682e6	−	1.20669e7i	−0.541248	−	0.937469i
$699$		0			0
$700$	−7.42760e6	−	4.33176e6i	−0.572932	−	0.334133i
$701$	−4.04459e6			−0.310870			−0.155435	−	0.987846i	$-0.549678\pi$
$701$	−4.04459e6			−0.310870			−0.155435	+	0.987846i	$0.549678\pi$
$702$		0			0
$703$	1.11626e7	−	1.93341e7i	0.851875	−	1.47549i
$704$	−207459.	+	359329.i	−0.0157761	+	0.0273250i
$705$		0			0
$706$	1.84159e7			1.39053
$707$	−22230.2	+	5.08218e6i	−0.00167261	+	0.382386i
$708$		0			0
$709$	−3.57921e6	−	6.19937e6i	−0.267406	−	0.463161i	0.700785	−	0.713372i	$-0.252833\pi$
$709$	−3.57921e6	−	6.19937e6i	−0.267406	−	0.463161i	−0.968191	+	0.250211i	$0.919500\pi$
$710$	−1.50543e7	+	2.60748e7i	−1.12076	+	1.94122i
$711$		0			0
$712$	1.01411e6	+	1.75648e6i	0.0749694	+	0.129851i
$713$	1.00140e7			0.737710
$714$		0			0
$715$	2.56329e7			1.87513
$716$	−1.49623e6	−	2.59155e6i	−0.109073	−	0.188919i
$717$		0			0
$718$	8.83289e6	−	1.52990e7i	0.639428	−	1.10752i
$719$	−4.91370e6	−	8.51077e6i	−0.354475	−	0.613969i	0.632553	−	0.774517i	$-0.282007\pi$
$719$	−4.91370e6	−	8.51077e6i	−0.354475	−	0.613969i	−0.987028	+	0.160548i	$0.948674\pi$
$720$		0			0
$721$	2.15334e6	+	1.25582e6i	0.154268	+	0.0899685i
$722$	−248538.			−0.0177439
$723$		0			0
$724$	3.78246e6	−	6.55142e6i	0.268181	−	0.464503i
$725$	6.68163e6	−	1.15729e7i	0.472104	−	0.817708i
$726$		0			0
$727$	1.63233e7			1.14544			0.572720	−	0.819751i	$-0.305888\pi$
$727$	1.63233e7			1.14544			0.572720	+	0.819751i	$0.305888\pi$
$728$	9.70671e6	−	5.54770e6i	0.678803	−	0.387958i
$729$		0			0
$730$	−1.10568e7	−	1.91510e7i	−0.767932	−	1.33010i
$731$	−1.61296e6	+	2.79373e6i	−0.111643	+	0.193371i
$732$		0			0
$733$	−8.80166e6	−	1.52449e7i	−0.605069	−	1.04801i	−0.992041	−	0.125918i	$-0.959812\pi$
$733$	−8.80166e6	−	1.52449e7i	−0.605069	−	1.04801i	0.386972	−	0.922091i	$-0.373521\pi$
$734$	−2.55216e7			−1.74851
$735$		0			0
$736$	1.65087e7			1.12336
$737$	−5.18512e6	−	8.98090e6i	−0.351634	−	0.609047i
$738$		0			0
$739$	−3.46287e6	+	5.99787e6i	−0.233252	+	0.404004i	−0.958763	−	0.284206i	$-0.908270\pi$
$739$	−3.46287e6	+	5.99787e6i	−0.233252	+	0.404004i	0.725511	+	0.688210i	$0.241603\pi$
$740$	−1.07235e7	−	1.85737e7i	−0.719878	−	1.24687i
$741$		0			0
$742$	2.02585e7	−	1.15784e7i	1.35082	−	0.772037i
$743$	1.38786e7			0.922305			0.461153	−	0.887321i	$-0.347436\pi$
$743$	1.38786e7			0.922305			0.461153	+	0.887321i	$0.347436\pi$
$744$		0			0
$745$	−1.62932e7	+	2.82206e7i	−1.07551	+	1.86284i
$746$	−6.69089e6	+	1.15890e7i	−0.440187	+	0.762426i
$747$		0			0
$748$	−2.73357e6			−0.178639
$749$	2.12578e7	+	1.23975e7i	1.38457	+	0.807475i
$750$		0			0
$751$	2.42409e6	+	4.19864e6i	0.156837	+	0.271650i	0.933726	−	0.357987i	$-0.116537\pi$
$751$	2.42409e6	+	4.19864e6i	0.156837	+	0.271650i	−0.776889	+	0.629637i	$0.783204\pi$
$752$	3.67703e6	−	6.36880e6i	0.237112	−	0.410689i
$753$		0			0
$754$	−1.15438e7	−	1.99945e7i	−0.739472	−	1.28080i
$755$	2.27246e7			1.45087
$756$		0			0
$757$	−2.41206e7			−1.52985			−0.764926	−	0.644119i	$-0.777224\pi$
$757$	−2.41206e7			−1.52985			−0.764926	+	0.644119i	$0.777224\pi$
$758$	−2.66958e6	−	4.62385e6i	−0.168760	−	0.292301i
$759$		0			0
$760$	−6.25586e6	+	1.08355e7i	−0.392874	+	0.680477i
$761$	1.03215e6	+	1.78774e6i	0.0646074	+	0.111903i	0.896520	−	0.443004i	$-0.146087\pi$
$761$	1.03215e6	+	1.78774e6i	0.0646074	+	0.111903i	−0.831912	+	0.554907i	$0.812754\pi$
$762$		0			0
$763$	129315.	−	2.95636e7i	0.00804153	−	1.83843i
$764$	−1.87395e6			−0.116152
$765$		0			0
$766$	−1.05722e6	+	1.83117e6i	−0.0651021	+	0.112760i
$767$	−1.91319e7	+	3.31374e7i	−1.17427	+	2.03390i
$768$		0			0
$769$	−1.80825e7			−1.10266			−0.551331	−	0.834287i	$-0.685880\pi$
$769$	−1.80825e7			−1.10266			−0.551331	+	0.834287i	$0.685880\pi$
$770$	2.29883e7	+	1.34067e7i	1.39727	+	0.814884i
$771$		0			0
$772$	2.92419e6	+	5.06484e6i	0.176588	+	0.305860i
$773$	−6.87405e6	+	1.19062e7i	−0.413775	+	0.716679i	−0.995299	−	0.0968501i	$-0.969123\pi$
$773$	−6.87405e6	+	1.19062e7i	−0.413775	+	0.716679i	0.581524	+	0.813529i	$0.302457\pi$
$774$		0			0
$775$	6.52312e6	+	1.12984e7i	0.390122	+	0.675712i
$776$	9.50668e6			0.566728

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:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	63.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.54467 - 6.13954i) q^{2} +(-9.12931 + 15.8124i) q^{4} +(-41.1020 - 71.1908i) q^{5} +(112.556 - 64.3292i) q^{7} -97.4172 q^{8} +O(q^{10})\)	\(q+(-3.54467 - 6.13954i) q^{2} +(-9.12931 + 15.8124i) q^{4} +(-41.1020 - 71.1908i) q^{5} +(112.556 - 64.3292i) q^{7} -97.4172 q^{8} +(-291.386 + 504.695i) q^{10} +(176.118 - 305.046i) q^{11} -885.257 q^{13} +(-793.924 - 463.014i) q^{14} +(637.449 + 1104.09i) q^{16} +(-212.519 + 368.094i) q^{17} +(781.192 + 1353.06i) q^{19} +1500.93 q^{20} -2497.12 q^{22} +(1394.12 + 2414.69i) q^{23} +(-1816.26 + 3145.85i) q^{25} +(3137.94 + 5435.07i) q^{26} +(-10.3538 + 2367.06i) q^{28} -3678.79 q^{29} +(1795.76 - 3110.34i) q^{31} +(2960.41 - 5127.59i) q^{32} +3013.24 q^{34} +(-9205.91 - 5368.86i) q^{35} +(-7144.58 - 12374.8i) q^{37} +(5538.13 - 9592.31i) q^{38} +(4004.05 + 6935.21i) q^{40} -14325.8 q^{41} +7589.72 q^{43} +(3215.68 + 5569.72i) q^{44} +(9883.41 - 17118.6i) q^{46} +(-2884.17 - 4995.54i) q^{47} +(8530.51 - 14481.2i) q^{49} +25752.1 q^{50} +(8081.78 - 13998.1i) q^{52} +(-12694.2 + 21987.0i) q^{53} -28955.3 q^{55} +(-10964.9 + 6266.77i) q^{56} +(13040.1 + 22586.1i) q^{58} +(21611.7 - 37432.5i) q^{59} +(-9723.73 - 16842.0i) q^{61} -25461.4 q^{62} -1177.95 q^{64} +(36385.9 + 63022.2i) q^{65} +(14720.6 - 25496.7i) q^{67} +(-3880.31 - 6720.89i) q^{68} +(-330.470 + 75550.9i) q^{70} +51664.4 q^{71} +(-18972.8 + 32861.8i) q^{73} +(-50650.3 + 87728.9i) q^{74} -28527.0 q^{76} +(199.741 - 45664.2i) q^{77} +(-26899.7 - 46591.7i) q^{79} +(52400.9 - 90761.1i) q^{80} +(50780.1 + 87953.8i) q^{82} -85967.6 q^{83} +34939.9 q^{85} +(-26903.0 - 46597.4i) q^{86} +(-17157.0 + 29716.7i) q^{88} +(-10409.9 - 18030.5i) q^{89} +(-99640.6 + 56947.8i) q^{91} -50909.6 q^{92} +(-20446.9 + 35415.0i) q^{94} +(64217.1 - 111227. i) q^{95} -97587.2 q^{97} +(-119146. - 1042.34i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 182 q^{4} + 142 q^{7}+O(q^{10}) \) 12 * q - 182 * q^4 + 142 * q^7	\( 12 q - 182 q^{4} + 142 q^{7} + 686 q^{10} + 308 q^{13} - 1898 q^{16} + 9422 q^{19} - 18292 q^{22} - 7526 q^{25} + 37074 q^{28} + 23422 q^{31} - 55608 q^{34} - 18182 q^{37} + 69258 q^{40} - 87372 q^{43} + 25332 q^{46} + 30354 q^{49} + 34272 q^{52} - 96320 q^{55} - 89782 q^{58} - 16156 q^{61} + 380580 q^{64} + 144650 q^{67} - 187262 q^{70} - 100058 q^{73} - 685440 q^{76} + 101994 q^{79} + 75712 q^{82} + 602352 q^{85} + 752310 q^{88} - 282306 q^{91} - 120456 q^{94} - 866096 q^{97}+O(q^{100}) \) 12 * q - 182 * q^4 + 142 * q^7 + 686 * q^10 + 308 * q^13 - 1898 * q^16 + 9422 * q^19 - 18292 * q^22 - 7526 * q^25 + 37074 * q^28 + 23422 * q^31 - 55608 * q^34 - 18182 * q^37 + 69258 * q^40 - 87372 * q^43 + 25332 * q^46 + 30354 * q^49 + 34272 * q^52 - 96320 * q^55 - 89782 * q^58 - 16156 * q^61 + 380580 * q^64 + 144650 * q^67 - 187262 * q^70 - 100058 * q^73 - 685440 * q^76 + 101994 * q^79 + 75712 * q^82 + 602352 * q^85 + 752310 * q^88 - 282306 * q^91 - 120456 * q^94 - 866096 * q^97

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