LMFDB - Embedded newform 528.6.d.b.287.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [528,6,Mod(287,528)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(528, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("528.287");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 528 = 2^{4} \cdot 3 \cdot 11 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	528.d (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:	$84.6826568613$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{15} + 15 x^{14} + 440 x^{13} - 30788 x^{12} + 421206 x^{11} + 3494011 x^{10} + \cdots + 94\!\cdots\!91 $ x^16 - x^15 + 15x^14 + 440x^13 - 30788x^12 + 421206x^11 + 3494011x^10 + 20989805x^9 + 954917352x^8 + 10008088435x^7 + 94336579421x^6 - 2750414715894x^5 + 58245323176592x^4 + 3790123391809000x^3 + 71789557238409705x^2 + 1216670726903935009x + 9405993299160733691
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{31}\cdot 3^{10}\cdot 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			287.7
Root			$-0.415167 - 15.4002i$ of defining polynomial
Character	$\chi$	$=$	528.287
Dual form			528.6.d.b.287.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.41517 - 15.4002i) q^{3} -109.050i q^{5} -143.992i q^{7} +(-231.334 - 74.3882i) q^{9} +O(q^{10})$	\(q+(2.41517 - 15.4002i) q^{3} -109.050i q^{5} -143.992i q^{7} +(-231.334 - 74.3882i) q^{9} -121.000 q^{11} +98.5701 q^{13} +(-1679.39 - 263.373i) q^{15} +888.453i q^{17} -28.3295i q^{19} +(-2217.51 - 347.764i) q^{21} +474.055 q^{23} -8766.85 q^{25} +(-1704.31 + 3382.94i) q^{27} -5234.41i q^{29} +7437.67i q^{31} +(-292.235 + 1863.43i) q^{33} -15702.3 q^{35} -1734.45 q^{37} +(238.063 - 1518.00i) q^{39} +15104.1i q^{41} -18854.9i q^{43} +(-8112.02 + 25226.9i) q^{45} -1767.95 q^{47} -3926.66 q^{49} +(13682.4 + 2145.76i) q^{51} -17228.9i q^{53} +13195.0i q^{55} +(-436.281 - 68.4206i) q^{57} -30697.7 q^{59} +38030.9 q^{61} +(-10711.3 + 33310.2i) q^{63} -10749.0i q^{65} -47544.4i q^{67} +(1144.92 - 7300.55i) q^{69} +35948.9 q^{71} +20879.3 q^{73} +(-21173.4 + 135011. i) q^{75} +17423.0i q^{77} -77783.9i q^{79} +(47981.8 + 34417.0i) q^{81} -486.339 q^{83} +96885.6 q^{85} +(-80611.1 - 12642.0i) q^{87} +53921.3i q^{89} -14193.3i q^{91} +(114542. + 17963.2i) q^{93} -3089.33 q^{95} -85992.5 q^{97} +(27991.4 + 9000.97i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 31 q^{3} + 31 q^{9}+O(q^{10}) $ 16 * q + 31 * q^3 + 31 * q^9	$ 16 q + 31 q^{3} + 31 q^{9} - 1936 q^{11} + 444 q^{13} - 979 q^{15} - 3874 q^{21} + 4246 q^{23} - 4194 q^{25} + 1306 q^{27} - 3751 q^{33} - 13964 q^{35} + 35094 q^{37} - 7848 q^{39} - 43369 q^{45} + 18476 q^{47} - 6172 q^{49} + 40886 q^{51} - 27316 q^{57} - 59134 q^{59} + 93580 q^{61} + 52286 q^{63} + 23881 q^{69} + 129154 q^{71} + 63188 q^{73} - 30048 q^{75} + 132223 q^{81} - 46276 q^{83} + 141316 q^{85} - 86304 q^{87} + 228139 q^{93} - 238328 q^{95} - 244198 q^{97} - 3751 q^{99}+O(q^{100}) $ 16 * q + 31 * q^3 + 31 * q^9 - 1936 * q^11 + 444 * q^13 - 979 * q^15 - 3874 * q^21 + 4246 * q^23 - 4194 * q^25 + 1306 * q^27 - 3751 * q^33 - 13964 * q^35 + 35094 * q^37 - 7848 * q^39 - 43369 * q^45 + 18476 * q^47 - 6172 * q^49 + 40886 * q^51 - 27316 * q^57 - 59134 * q^59 + 93580 * q^61 + 52286 * q^63 + 23881 * q^69 + 129154 * q^71 + 63188 * q^73 - 30048 * q^75 + 132223 * q^81 - 46276 * q^83 + 141316 * q^85 - 86304 * q^87 + 228139 * q^93 - 238328 * q^95 - 244198 * q^97 - 3751 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/528\mathbb{Z}\right)^\times$.

$n$	$133$	$145$	$353$	$463$
$\chi(n)$	$1$	$1$	$-1$	$-1$

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 $

$2$		0			0
$2$		0			0
$3$	2.41517	−	15.4002i	0.154933	−	0.987925i
$3$	2.41517	−	15.4002i	0.154933	−	0.987925i
$4$		0			0
$5$		−	109.050i		−	1.95074i	−0.220572	−	0.975371i	$-0.570792\pi$
$5$		−	109.050i		−	1.95074i	0.220572	−	0.975371i	$-0.429208\pi$
$6$		0			0
$7$		−	143.992i		−	1.11069i	−0.831620	−	0.555345i	$-0.812586\pi$
$7$		−	143.992i		−	1.11069i	0.831620	−	0.555345i	$-0.187414\pi$
$8$		0			0
$9$	−231.334	−	74.3882i	−0.951992	−	0.306124i
$10$		0			0
$11$	−121.000			−0.301511
$11$	−121.000			−0.301511
$12$		0			0
$13$	98.5701			0.161766			0.0808829	−	0.996724i	$-0.474226\pi$
$13$	98.5701			0.161766			0.0808829	+	0.996724i	$0.474226\pi$
$14$		0			0
$15$	−1679.39	−	263.373i	−1.92719	−	0.302234i
$16$		0			0
$17$			888.453i			0.745611i	0.927910	+	0.372806i	$0.121604\pi$
$17$			888.453i			0.745611i	−0.927910	+	0.372806i	$0.878396\pi$
$18$		0			0
$19$		−	28.3295i		−	0.0180034i	−0.999959	−	0.00900172i	$-0.997135\pi$
$19$		−	28.3295i		−	0.0180034i	0.999959	−	0.00900172i	$-0.00286538\pi$
$20$		0			0
$21$	−2217.51	−	347.764i	−1.09728	−	0.172083i
$22$		0			0
$23$	474.055			0.186857			0.0934284	−	0.995626i	$-0.470217\pi$
$23$	474.055			0.186857			0.0934284	+	0.995626i	$0.470217\pi$
$24$		0			0
$25$	−8766.85			−2.80539
$26$		0			0
$27$	−1704.31	+	3382.94i	−0.449923	+	0.893067i
$28$		0			0
$29$		−	5234.41i		−	1.15577i	−0.816117	−	0.577887i	$-0.803877\pi$
$29$		−	5234.41i		−	1.15577i	0.816117	−	0.577887i	$-0.196123\pi$
$30$		0			0
$31$			7437.67i			1.39006i	0.718982	+	0.695029i	$0.244608\pi$
$31$			7437.67i			1.39006i	−0.718982	+	0.695029i	$0.755392\pi$
$32$		0			0
$33$	−292.235	+	1863.43i	−0.0467141	+	0.297871i
$34$		0			0
$35$	−15702.3			−2.16667
$36$		0			0
$37$	−1734.45			−0.208285			−0.104143	−	0.994562i	$-0.533210\pi$
$37$	−1734.45			−0.208285			−0.104143	+	0.994562i	$0.533210\pi$
$38$		0			0
$39$	238.063	−	1518.00i	0.0250629	−	0.159813i
$40$		0			0
$41$			15104.1i			1.40325i	0.712544	+	0.701627i	$0.247543\pi$
$41$			15104.1i			1.40325i	−0.712544	+	0.701627i	$0.752457\pi$
$42$		0			0
$43$		−	18854.9i		−	1.55508i	−0.628833	−	0.777540i	$-0.716467\pi$
$43$		−	18854.9i		−	1.55508i	0.628833	−	0.777540i	$-0.283533\pi$
$44$		0			0
$45$	−8112.02	+	25226.9i	−0.597170	+	1.85709i
$46$		0			0
$47$	−1767.95			−0.116741			−0.0583707	−	0.998295i	$-0.518591\pi$
$47$	−1767.95			−0.116741			−0.0583707	+	0.998295i	$0.518591\pi$
$48$		0			0
$49$	−3926.66			−0.233633
$50$		0			0
$51$	13682.4	+	2145.76i	0.736608	+	0.115520i
$52$		0			0
$53$		−	17228.9i		−	0.842494i	−0.906946	−	0.421247i	$-0.861593\pi$
$53$		−	17228.9i		−	0.842494i	0.906946	−	0.421247i	$-0.138407\pi$
$54$		0			0
$55$			13195.0i			0.588171i
$56$		0			0
$57$	−436.281	−	68.4206i	−0.0177861	−	0.00278933i
$58$		0			0
$59$	−30697.7			−1.14809			−0.574045	−	0.818824i	$-0.694626\pi$
$59$	−30697.7			−1.14809			−0.574045	+	0.818824i	$0.694626\pi$
$60$		0			0
$61$	38030.9			1.30862			0.654308	−	0.756228i	$-0.272960\pi$
$61$	38030.9			1.30862			0.654308	+	0.756228i	$0.272960\pi$
$62$		0			0
$63$	−10711.3	+	33310.2i	−0.340009	+	1.05737i
$64$		0			0
$65$		−	10749.0i		−	0.315563i
$66$		0			0
$67$		−	47544.4i		−	1.29393i	−0.762518	−	0.646967i	$-0.776037\pi$
$67$		−	47544.4i		−	1.29393i	0.762518	−	0.646967i	$-0.223963\pi$
$68$		0			0
$69$	1144.92	−	7300.55i	0.0289503	−	0.184601i
$70$		0			0
$71$	35948.9			0.846329			0.423165	−	0.906053i	$-0.360919\pi$
$71$	35948.9			0.846329			0.423165	+	0.906053i	$0.360919\pi$
$72$		0			0
$73$	20879.3			0.458573			0.229287	−	0.973359i	$-0.426361\pi$
$73$	20879.3			0.458573			0.229287	+	0.973359i	$0.426361\pi$
$74$		0			0
$75$	−21173.4	+	135011.i	−0.434648	+	2.77152i
$76$		0			0
$77$			17423.0i			0.334886i
$78$		0			0
$79$		−	77783.9i		−	1.40224i	−0.713044	−	0.701119i	$-0.752684\pi$
$79$		−	77783.9i		−	1.40224i	0.713044	−	0.701119i	$-0.247316\pi$
$80$		0			0
$81$	47981.8	+	34417.0i	0.812576	+	0.582856i
$82$		0			0
$83$	−486.339			−0.00774897			−0.00387449	−	0.999992i	$-0.501233\pi$
$83$	−486.339			−0.00774897			−0.00387449	+	0.999992i	$0.501233\pi$
$84$		0			0
$85$	96885.6			1.45449
$86$		0			0
$87$	−80611.1	−	12642.0i	−1.14182	−	0.179067i
$88$		0			0
$89$			53921.3i			0.721582i	0.932647	+	0.360791i	$0.117493\pi$
$89$			53921.3i			0.721582i	−0.932647	+	0.360791i	$0.882507\pi$
$90$		0			0
$91$		−	14193.3i		−	0.179672i
$92$		0			0
$93$	114542.	+	17963.2i	1.37327	+	0.215366i
$94$		0			0
$95$	−3089.33			−0.0351201
$96$		0			0
$97$	−85992.5			−0.927965			−0.463982	−	0.885844i	$-0.653580\pi$
$97$	−85992.5			−0.927965			−0.463982	+	0.885844i	$0.653580\pi$
$98$		0			0
$99$	27991.4	+	9000.97i	0.287036	+	0.0923000i
$100$		0			0
$101$		−	137216.i		−	1.33845i	−0.743060	−	0.669225i	$-0.766626\pi$
$101$		−	137216.i		−	1.33845i	0.743060	−	0.669225i	$-0.233374\pi$
$102$		0			0
$103$		−	108768.i		−	1.01021i	−0.863059	−	0.505103i	$-0.831455\pi$
$103$		−	108768.i		−	1.01021i	0.863059	−	0.505103i	$-0.168545\pi$
$104$		0			0
$105$	−37923.6	+	241819.i	−0.335689	+	2.14051i
$106$		0			0
$107$	−109925.			−0.928193			−0.464096	−	0.885785i	$-0.653621\pi$
$107$	−109925.			−0.928193			−0.464096	+	0.885785i	$0.653621\pi$
$108$		0			0
$109$	7630.23			0.0615136			0.0307568	−	0.999527i	$-0.490208\pi$
$109$	7630.23			0.0615136			0.0307568	+	0.999527i	$0.490208\pi$
$110$		0			0
$111$	−4188.99	+	26711.0i	−0.0322702	+	0.205770i
$112$		0			0
$113$			127210.i			0.937184i	0.883415	+	0.468592i	$0.155239\pi$
$113$			127210.i			0.937184i	−0.883415	+	0.468592i	$0.844761\pi$
$114$		0			0
$115$		−	51695.6i		−	0.364509i
$116$		0			0
$117$	−22802.6	−	7332.46i	−0.154000	−	0.0495205i
$118$		0			0
$119$	127930.			0.828143
$120$		0			0
$121$	14641.0			0.0909091
$122$		0			0
$123$	232607.	+	36479.0i	1.38631	+	0.217410i
$124$		0			0
$125$			615243.i			3.52185i
$126$		0			0
$127$			111494.i			0.613400i	0.951806	+	0.306700i	$0.0992248\pi$
$127$			111494.i			0.613400i	−0.951806	+	0.306700i	$0.900775\pi$
$128$		0			0
$129$	−290370.	−	45537.7i	−1.53630	−	0.240933i
$130$		0			0
$131$	−9697.72			−0.0493732			−0.0246866	−	0.999695i	$-0.507859\pi$
$131$	−9697.72			−0.0493732			−0.0246866	+	0.999695i	$0.507859\pi$
$132$		0			0
$133$	−4079.22			−0.0199962
$134$		0			0
$135$	368908.	+	185854.i	1.74214	+	0.877683i
$136$		0			0
$137$			178397.i			0.812057i	0.913860	+	0.406028i	$0.133087\pi$
$137$			178397.i			0.812057i	−0.913860	+	0.406028i	$0.866913\pi$
$138$		0			0
$139$		−	88316.5i		−	0.387708i	−0.981030	−	0.193854i	$-0.937901\pi$
$139$		−	88316.5i		−	0.387708i	0.981030	−	0.193854i	$-0.0620988\pi$
$140$		0			0
$141$	−4269.89	+	27226.8i	−0.0180871	+	0.115332i
$142$		0			0
$143$	−11927.0			−0.0487742
$144$		0			0
$145$	−570811.			−2.25462
$146$		0			0
$147$	−9483.54	+	60471.5i	−0.0361974	+	0.230811i
$148$		0			0
$149$			265854.i			0.981020i	0.871435	+	0.490510i	$0.163190\pi$
$149$			265854.i			0.981020i	−0.871435	+	0.490510i	$0.836810\pi$
$150$		0			0
$151$		−	540037.i		−	1.92744i	−0.266912	−	0.963721i	$-0.586003\pi$
$151$		−	540037.i		−	1.92744i	0.266912	−	0.963721i	$-0.413997\pi$
$152$		0			0
$153$	66090.5	−	205529.i	0.228250	−	0.709815i
$154$		0			0
$155$	811076.			2.71164
$156$		0			0
$157$	438254.			1.41898			0.709491	−	0.704714i	$-0.248925\pi$
$157$	438254.			1.41898			0.709491	+	0.704714i	$0.248925\pi$
$158$		0			0
$159$	−265328.	−	41610.6i	−0.832321	−	0.130530i
$160$		0			0
$161$		−	68260.0i		−	0.207540i
$162$		0			0
$163$		−	535551.i		−	1.57882i	−0.613869	−	0.789408i	$-0.710388\pi$
$163$		−	535551.i		−	1.57882i	0.613869	−	0.789408i	$-0.289612\pi$
$164$		0			0
$165$	203206.	+	31868.2i	0.581069	+	0.0911271i
$166$		0			0
$167$	−528334.			−1.46594			−0.732972	−	0.680259i	$-0.761867\pi$
$167$	−528334.			−1.46594			−0.732972	+	0.680259i	$0.761867\pi$
$168$		0			0
$169$	−361577.			−0.973832
$170$		0			0
$171$	−2107.38	+	6553.59i	−0.00551129	+	0.0171391i
$172$		0			0
$173$			418360.i			1.06276i	0.847134	+	0.531380i	$0.178326\pi$
$173$			418360.i			1.06276i	−0.847134	+	0.531380i	$0.821674\pi$
$174$		0			0
$175$			1.26236e6i			3.11592i
$176$		0			0
$177$	−74140.0	+	472751.i	−0.177877	+	1.13423i
$178$		0			0
$179$	106176.			0.247681			0.123840	−	0.992302i	$-0.460479\pi$
$179$	106176.			0.247681			0.123840	+	0.992302i	$0.460479\pi$
$180$		0			0
$181$	−198510.			−0.450388			−0.225194	−	0.974314i	$-0.572302\pi$
$181$	−198510.			−0.450388			−0.225194	+	0.974314i	$0.572302\pi$
$182$		0			0
$183$	91851.0	−	585685.i	0.202748	−	1.29281i
$184$		0			0
$185$			189142.i			0.406311i
$186$		0			0
$187$		−	107503.i		−	0.224810i
$188$		0			0
$189$	487115.	+	245406.i	0.991921	+	0.499725i
$190$		0			0
$191$	74922.4			0.148603			0.0743016	−	0.997236i	$-0.476327\pi$
$191$	74922.4			0.148603			0.0743016	+	0.997236i	$0.476327\pi$
$192$		0			0
$193$	602862.			1.16500			0.582499	−	0.812832i	$-0.302075\pi$
$193$	602862.			1.16500			0.582499	+	0.812832i	$0.302075\pi$
$194$		0			0
$195$	−165538.	−	25960.7i	−0.311753	−	0.0488912i
$196$		0			0
$197$			869863.i			1.59693i	0.602042	+	0.798464i	$0.294354\pi$
$197$			869863.i			1.59693i	−0.602042	+	0.798464i	$0.705646\pi$
$198$		0			0
$199$			440528.i			0.788571i	0.918988	+	0.394286i	$0.129008\pi$
$199$			440528.i			0.788571i	−0.918988	+	0.394286i	$0.870992\pi$
$200$		0			0
$201$	−732195.	−	114828.i	−1.27831	−	0.200473i
$202$		0			0
$203$	−753713.			−1.28371
$204$		0			0
$205$	1.64710e6			2.73739
$206$		0			0
$207$	−109665.	−	35264.1i	−0.177886	−	0.0572014i
$208$		0			0
$209$			3427.87i			0.00542824i
$210$		0			0
$211$			326194.i			0.504394i	0.967676	+	0.252197i	$0.0811532\pi$
$211$			326194.i			0.504394i	−0.967676	+	0.252197i	$0.918847\pi$
$212$		0			0
$213$	86822.5	−	553621.i	0.131124	−	0.836110i
$214$		0			0
$215$	−2.05612e6			−3.03356
$216$		0			0
$217$	1.07096e6			1.54392
$218$		0			0
$219$	50427.0	−	321546.i	0.0710481	−	0.453036i
$220$		0			0
$221$			87574.9i			0.120614i
$222$		0			0
$223$			1.24289e6i			1.67367i	0.547457	+	0.836834i	$0.315596\pi$
$223$			1.24289e6i			1.67367i	−0.547457	+	0.836834i	$0.684404\pi$
$224$		0			0
$225$	2.02807e6	+	652150.i	2.67071	+	0.858799i
$226$		0			0
$227$	1.13099e6			1.45678			0.728389	−	0.685164i	$-0.240270\pi$
$227$	1.13099e6			1.45678			0.728389	+	0.685164i	$0.240270\pi$
$228$		0			0
$229$	−621722.			−0.783443			−0.391722	−	0.920084i	$-0.628120\pi$
$229$	−621722.			−0.783443			−0.391722	+	0.920084i	$0.628120\pi$
$230$		0			0
$231$	268318.	+	42079.5i	0.330842	+	0.0518848i
$232$		0			0
$233$			1.13898e6i			1.37444i	0.726447	+	0.687222i	$0.241170\pi$
$233$			1.13898e6i			1.37444i	−0.726447	+	0.687222i	$0.758830\pi$
$234$		0			0
$235$			192794.i			0.227732i
$236$		0			0
$237$	−1.19789e6	−	187861.i	−1.38531	−	0.217253i
$238$		0			0
$239$	−1.59756e6			−1.80910			−0.904551	−	0.426366i	$-0.859794\pi$
$239$	−1.59756e6			−1.80910			−0.904551	+	0.426366i	$0.859794\pi$
$240$		0			0
$241$	44929.5			0.0498297			0.0249149	−	0.999690i	$-0.492069\pi$
$241$	44929.5			0.0498297			0.0249149	+	0.999690i	$0.492069\pi$
$242$		0			0
$243$	645914.	−	655807.i	0.701712	−	0.712460i
$244$		0			0
$245$			428202.i			0.455757i
$246$		0			0
$247$		−	2792.45i		−	0.00291234i
$248$		0			0
$249$	−1174.59	+	7489.74i	−0.00120057	+	0.00765541i
$250$		0			0
$251$	−1.00436e6			−1.00625			−0.503126	−	0.864213i	$-0.667817\pi$
$251$	−1.00436e6			−1.00625			−0.503126	+	0.864213i	$0.667817\pi$
$252$		0			0
$253$	−57360.6			−0.0563395
$254$		0			0
$255$	233995.	−	1.49206e6i	0.225349	−	1.43693i
$256$		0			0
$257$		−	886645.i		−	0.837369i	−0.908132	−	0.418685i	$-0.862491\pi$
$257$		−	886645.i		−	0.837369i	0.908132	−	0.418685i	$-0.137509\pi$
$258$		0			0
$259$			249747.i			0.231340i
$260$		0			0
$261$	−389379.	+	1.21090e6i	−0.353810	+	1.10029i
$262$		0			0
$263$	−1.32047e6			−1.17717			−0.588586	−	0.808434i	$-0.700315\pi$
$263$	−1.32047e6			−1.17717			−0.588586	+	0.808434i	$0.700315\pi$
$264$		0			0
$265$	−1.87880e6			−1.64349
$266$		0			0
$267$	830400.	+	130229.i	0.712869	+	0.111797i
$268$		0			0
$269$		−	1.78258e6i		−	1.50200i	−0.660304	−	0.750999i	$-0.729572\pi$
$269$		−	1.78258e6i		−	1.50200i	0.660304	−	0.750999i	$-0.270428\pi$
$270$		0			0
$271$		−	1.40204e6i		−	1.15967i	−0.814733	−	0.579837i	$-0.803116\pi$
$271$		−	1.40204e6i		−	1.15967i	0.814733	−	0.579837i	$-0.196884\pi$
$272$		0			0
$273$	−218580.	−	34279.2i	−0.177502	−	0.0278371i
$274$		0			0
$275$	1.06079e6			0.845858
$276$		0			0
$277$	−2.07290e6			−1.62322			−0.811611	−	0.584198i	$-0.801409\pi$
$277$	−2.07290e6			−1.62322			−0.811611	+	0.584198i	$0.801409\pi$
$278$		0			0
$279$	553275.	−	1.72059e6i	0.425531	−	1.32332i
$280$		0			0
$281$		−	1.49088e6i		−	1.12636i	−0.826335	−	0.563179i	$-0.809578\pi$
$281$		−	1.49088e6i		−	1.12636i	0.826335	−	0.563179i	$-0.190422\pi$
$282$		0			0
$283$			2.13203e6i			1.58244i	0.611531	+	0.791220i	$0.290554\pi$
$283$			2.13203e6i			1.58244i	−0.611531	+	0.791220i	$0.709446\pi$
$284$		0			0
$285$	−7461.25	+	47576.4i	−0.00544126	+	0.0346960i
$286$		0			0
$287$	2.17487e6			1.55858
$288$		0			0
$289$	630508.			0.444064
$290$		0			0
$291$	−207686.	+	1.32430e6i	−0.143772	+	0.916759i
$292$		0			0
$293$			1.54771e6i			1.05322i	0.850107	+	0.526611i	$0.176537\pi$
$293$			1.54771e6i			1.05322i	−0.850107	+	0.526611i	$0.823463\pi$
$294$		0			0
$295$			3.34758e6i			2.23963i
$296$		0			0
$297$	206221.	−	409335.i	0.135657	−	0.269270i
$298$		0			0
$299$	46727.6			0.0302271
$300$		0			0
$301$	−2.71495e6			−1.72721
$302$		0			0
$303$	−2.11316e6	−	331400.i	−1.32229	−	0.207370i
$304$		0			0
$305$		−	4.14726e6i		−	2.55277i
$306$		0			0
$307$		−	1.77895e6i		−	1.07725i	−0.842545	−	0.538626i	$-0.818944\pi$
$307$		−	1.77895e6i		−	1.07725i	0.842545	−	0.538626i	$-0.181056\pi$
$308$		0			0
$309$	−1.67506e6	−	262694.i	−0.998007	−	0.156514i
$310$		0			0
$311$	2.61880e6			1.53533			0.767663	−	0.640853i	$-0.221419\pi$
$311$	2.61880e6			1.53533			0.767663	+	0.640853i	$0.221419\pi$
$312$		0			0
$313$	755063.			0.435635			0.217817	−	0.975990i	$-0.430106\pi$
$313$	755063.			0.435635			0.217817	+	0.975990i	$0.430106\pi$
$314$		0			0
$315$	3.63247e6	+	1.16806e6i	2.06265	+	0.663270i
$316$		0			0
$317$			2.08315e6i			1.16432i	0.813075	+	0.582159i	$0.197792\pi$
$317$			2.08315e6i			1.16432i	−0.813075	+	0.582159i	$0.802208\pi$
$318$		0			0
$319$			633364.i			0.348479i
$320$		0			0
$321$	−265488.	+	1.69287e6i	−0.143808	+	0.916985i
$322$		0			0
$323$	25169.5			0.0134236
$324$		0			0
$325$	−864150.			−0.453817
$326$		0			0
$327$	18428.3	−	117507.i	0.00953049	−	0.0607708i
$328$		0			0
$329$			254570.i			0.129664i
$330$		0			0
$331$		−	2.91256e6i		−	1.46119i	−0.682813	−	0.730593i	$-0.739244\pi$
$331$		−	2.91256e6i		−	1.46119i	0.682813	−	0.730593i	$-0.260756\pi$
$332$		0			0
$333$	401238.	+	129023.i	0.198286	+	0.0637612i
$334$		0			0
$335$	−5.18471e6			−2.52413
$336$		0			0
$337$	1.42230e6			0.682206			0.341103	−	0.940026i	$-0.389200\pi$
$337$	1.42230e6			0.682206			0.341103	+	0.940026i	$0.389200\pi$
$338$		0			0
$339$	1.95906e6	+	307233.i	0.925868	+	0.145201i
$340$		0			0
$341$		−	899958.i		−	0.419118i
$342$		0			0
$343$		−	1.85466e6i		−	0.851197i
$344$		0			0
$345$	−796123.	−	124853.i	−0.360108	−	0.0564745i
$346$		0			0
$347$	−3.16764e6			−1.41225			−0.706126	−	0.708086i	$-0.749559\pi$
$347$	−3.16764e6			−1.41225			−0.706126	+	0.708086i	$0.749559\pi$
$348$		0			0
$349$	1.84363e6			0.810232			0.405116	−	0.914265i	$-0.367231\pi$
$349$	1.84363e6			0.810232			0.405116	+	0.914265i	$0.367231\pi$
$350$		0			0
$351$	−167994.	+	333456.i	−0.0727822	+	0.144468i
$352$		0			0
$353$		−	3.21177e6i		−	1.37186i	−0.727670	−	0.685928i	$-0.759397\pi$
$353$		−	3.21177e6i		−	1.37186i	0.727670	−	0.685928i	$-0.240603\pi$
$354$		0			0
$355$		−	3.92022e6i		−	1.65097i
$356$		0			0
$357$	308972.	−	1.97015e6i	0.128307	−	0.818143i
$358$		0			0
$359$	3.32840e6			1.36301			0.681506	−	0.731813i	$-0.261325\pi$
$359$	3.32840e6			1.36301			0.681506	+	0.731813i	$0.261325\pi$
$360$		0			0
$361$	2.47530e6			0.999676
$362$		0			0
$363$	35360.5	−	225475.i	0.0140848	−	0.0898114i
$364$		0			0
$365$		−	2.27688e6i		−	0.894557i
$366$		0			0
$367$			332465.i			0.128849i	0.997923	+	0.0644244i	$0.0205211\pi$
$367$			332465.i			0.128849i	−0.997923	+	0.0644244i	$0.979479\pi$
$368$		0			0
$369$	1.12357e6	−	3.49410e6i	0.429570	−	1.33589i
$370$		0			0
$371$	−2.48082e6			−0.935750
$372$		0			0
$373$	−1.47610e6			−0.549345			−0.274672	−	0.961538i	$-0.588569\pi$
$373$	−1.47610e6			−0.549345			−0.274672	+	0.961538i	$0.588569\pi$
$374$		0			0
$375$	9.47487e6	+	1.48591e6i	3.47933	+	0.545651i
$376$		0			0
$377$		−	515956.i		−	0.186965i
$378$		0			0
$379$		−	2.39225e6i		−	0.855476i	−0.903903	−	0.427738i	$-0.859311\pi$
$379$		−	2.39225e6i		−	0.855476i	0.903903	−	0.427738i	$-0.140689\pi$
$380$		0			0
$381$	1.71704e6	+	269277.i	0.605993	+	0.0950359i
$382$		0			0
$383$	−1.22028e6			−0.425071			−0.212535	−	0.977153i	$-0.568172\pi$
$383$	−1.22028e6			−0.425071			−0.212535	+	0.977153i	$0.568172\pi$
$384$		0			0
$385$	1.89998e6			0.653275
$386$		0			0
$387$	−1.40258e6	+	4.36178e6i	−0.476048	+	1.48042i
$388$		0			0
$389$		−	2.89584e6i		−	0.970287i	−0.874434	−	0.485144i	$-0.838767\pi$
$389$		−	2.89584e6i		−	0.970287i	0.874434	−	0.485144i	$-0.161233\pi$
$390$		0			0
$391$			421176.i			0.139323i
$392$		0			0
$393$	−23421.6	+	149347.i	−0.00764954	+	0.0487770i
$394$		0			0
$395$	−8.48231e6			−2.73540
$396$		0			0
$397$	−441097.			−0.140462			−0.0702309	−	0.997531i	$-0.522374\pi$
$397$	−441097.			−0.140462			−0.0702309	+	0.997531i	$0.522374\pi$
$398$		0			0
$399$	−9852.01	+	62821.0i	−0.00309808	+	0.0197548i
$400$		0			0
$401$			606082.i			0.188222i	0.995562	+	0.0941110i	$0.0300009\pi$
$401$			606082.i			0.188222i	−0.995562	+	0.0941110i	$0.969999\pi$
$402$		0			0
$403$			733132.i			0.224864i
$404$		0			0
$405$	3.75317e6	−	5.23240e6i	1.13700	−	1.58513i
$406$		0			0
$407$	209869.			0.0628003
$408$		0			0
$409$	99950.0			0.0295444			0.0147722	−	0.999891i	$-0.495298\pi$
$409$	99950.0			0.0295444			0.0147722	+	0.999891i	$0.495298\pi$
$410$		0			0
$411$	2.74736e6	+	430859.i	0.802251	+	0.125814i
$412$		0			0
$413$			4.42022e6i			1.27517i
$414$		0			0
$415$			53035.2i			0.0151162i
$416$		0			0
$417$	−1.36009e6	−	213299.i	−0.383026	−	0.0600688i
$418$		0			0
$419$	4.61607e6			1.28451			0.642254	−	0.766492i	$-0.277999\pi$
$419$	4.61607e6			1.28451			0.642254	+	0.766492i	$0.277999\pi$
$420$		0			0
$421$	613373.			0.168663			0.0843315	−	0.996438i	$-0.473125\pi$
$421$	613373.			0.168663			0.0843315	+	0.996438i	$0.473125\pi$
$422$		0			0
$423$	408987.	+	131515.i	0.111137	+	0.0357374i
$424$		0			0
$425$		−	7.78894e6i		−	2.09173i
$426$		0			0
$427$		−	5.47614e6i		−	1.45347i
$428$		0			0
$429$	−28805.7	+	183678.i	−0.00755674	+	0.0481853i
$430$		0			0
$431$	3.52669e6			0.914479			0.457240	−	0.889344i	$-0.348838\pi$
$431$	3.52669e6			0.914479			0.457240	+	0.889344i	$0.348838\pi$
$432$		0			0
$433$	2.51717e6			0.645197			0.322599	−	0.946536i	$-0.395444\pi$
$433$	2.51717e6			0.645197			0.322599	+	0.946536i	$0.395444\pi$
$434$		0			0
$435$	−1.37860e6	+	8.79062e6i	−0.349314	+	2.22739i
$436$		0			0
$437$		−	13429.8i		−	0.00336407i
$438$		0			0
$439$			3.34610e6i			0.828662i	0.910126	+	0.414331i	$0.135984\pi$
$439$			3.34610e6i			0.828662i	−0.910126	+	0.414331i	$0.864016\pi$
$440$		0			0
$441$	908370.	+	292097.i	0.222416	+	0.0715206i
$442$		0			0
$443$	−232049.			−0.0561785			−0.0280893	−	0.999605i	$-0.508942\pi$
$443$	−232049.			−0.0561785			−0.0280893	+	0.999605i	$0.508942\pi$
$444$		0			0
$445$	5.88011e6			1.40762
$446$		0			0
$447$	4.09422e6	+	642082.i	0.969175	+	0.151992i
$448$		0			0
$449$		−	6.83019e6i		−	1.59888i	−0.600743	−	0.799442i	$-0.705129\pi$
$449$		−	6.83019e6i		−	1.59888i	0.600743	−	0.799442i	$-0.294871\pi$
$450$		0			0
$451$		−	1.82760e6i		−	0.423097i
$452$		0			0
$453$	−8.31670e6	−	1.30428e6i	−1.90417	−	0.298624i
$454$		0			0
$455$	−1.54778e6			−0.350493
$456$		0			0
$457$	−7.40729e6			−1.65909			−0.829543	−	0.558443i	$-0.811399\pi$
$457$	−7.40729e6			−1.65909			−0.829543	+	0.558443i	$0.811399\pi$
$458$		0			0
$459$	−3.00558e6	−	1.51420e6i	−0.665881	−	0.335467i
$460$		0			0
$461$		−	2.35773e6i		−	0.516705i	−0.966051	−	0.258352i	$-0.916820\pi$
$461$		−	2.35773e6i		−	0.516705i	0.966051	−	0.258352i	$-0.0831796\pi$
$462$		0			0
$463$		−	180103.i		−	0.0390453i	−0.999809	−	0.0195227i	$-0.993785\pi$
$463$		−	180103.i		−	0.0390453i	0.999809	−	0.0195227i	$-0.00621465\pi$
$464$		0			0
$465$	1.95888e6	−	1.24908e7i	0.420123	−	2.67890i
$466$		0			0
$467$	−3.12265e6			−0.662569			−0.331285	−	0.943531i	$-0.607482\pi$
$467$	−3.12265e6			−0.662569			−0.331285	+	0.943531i	$0.607482\pi$
$468$		0			0
$469$	−6.84601e6			−1.43716
$470$		0			0
$471$	1.05846e6	−	6.74921e6i	0.219847	−	1.40185i
$472$		0			0
$473$			2.28144e6i			0.468874i
$474$		0			0
$475$			248361.i			0.0505067i
$476$		0			0
$477$	−1.28162e6	+	3.98562e6i	−0.257908	+	0.802047i
$478$		0			0
$479$	−9.21972e6			−1.83603			−0.918014	−	0.396549i	$-0.870208\pi$
$479$	−9.21972e6			−1.83603			−0.918014	+	0.396549i	$0.870208\pi$
$480$		0			0
$481$	−170965.			−0.0336934
$482$		0			0
$483$	−1.05122e6	−	164859.i	−0.205034	−	0.0321548i
$484$		0			0
$485$			9.37746e6i			1.81022i
$486$		0			0
$487$		−	4.23480e6i		−	0.809115i	−0.914513	−	0.404557i	$-0.867426\pi$
$487$		−	4.23480e6i		−	0.809115i	0.914513	−	0.404557i	$-0.132574\pi$
$488$		0			0
$489$	−8.24760e6	−	1.29344e6i	−1.55975	−	0.244611i
$490$		0			0
$491$	2.74363e6			0.513595			0.256798	−	0.966465i	$-0.417333\pi$
$491$	2.74363e6			0.513595			0.256798	+	0.966465i	$0.417333\pi$
$492$		0			0
$493$	4.65053e6			0.861758
$494$		0			0
$495$	981554.	−	3.05246e6i	0.180053	−	0.559934i
$496$		0			0
$497$		−	5.17634e6i		−	0.940009i
$498$		0			0
$499$			2.95694e6i			0.531607i	0.964027	+	0.265804i	$0.0856373\pi$
$499$			2.95694e6i			0.531607i	−0.964027	+	0.265804i	$0.914363\pi$
$500$		0			0
$501$	−1.27601e6	+	8.13646e6i	−0.227123	+	1.44824i
$502$		0			0
$503$	−7.97222e6			−1.40494			−0.702472	−	0.711711i	$-0.747920\pi$
$503$	−7.97222e6			−1.40494			−0.702472	+	0.711711i	$0.747920\pi$
$504$		0			0
$505$	−1.49634e7			−2.61097
$506$		0			0
$507$	−873269.	+	5.56837e6i	−0.150879	+	0.962073i
$508$		0			0
$509$			9.40478e6i			1.60899i	0.593957	+	0.804497i	$0.297565\pi$
$509$			9.40478e6i			1.60899i	−0.593957	+	0.804497i	$0.702435\pi$
$510$		0			0
$511$		−	3.00645e6i		−	0.509333i
$512$		0			0
$513$	95837.0	+	48282.2i	0.0160783	+	0.00810016i
$514$		0			0
$515$	−1.18612e7			−1.97065
$516$		0			0
$517$	213922.			0.0351989
$518$		0			0
$519$	6.44284e6	+	1.01041e6i	1.04993	+	0.164657i
$520$		0			0
$521$			5.42774e6i			0.876041i	0.898965	+	0.438021i	$0.144320\pi$
$521$			5.42774e6i			0.876041i	−0.898965	+	0.438021i	$0.855680\pi$
$522$		0			0
$523$		−	4.60412e6i		−	0.736025i	−0.929821	−	0.368013i	$-0.880038\pi$
$523$		−	4.60412e6i		−	0.736025i	0.929821	−	0.368013i	$-0.119962\pi$
$524$		0			0
$525$	1.94406e7	+	3.04880e6i	3.07830	+	0.482759i
$526$		0			0
$527$	−6.60803e6			−1.03644
$528$		0			0
$529$	−6.21162e6			−0.965085
$530$		0			0
$531$	7.10142e6	+	2.28355e6i	1.09297	+	0.351458i
$532$		0			0
$533$			1.48882e6i			0.226999i
$534$		0			0
$535$			1.19873e7i			1.81066i
$536$		0			0
$537$	256432.	−	1.63513e6i	0.0383739	−	0.244690i
$538$		0			0
$539$	475126.			0.0704429
$540$		0			0
$541$	4.83628e6			0.710425			0.355212	−	0.934786i	$-0.384409\pi$
$541$	4.83628e6			0.710425			0.355212	+	0.934786i	$0.384409\pi$
$542$		0			0
$543$	−479435.	+	3.05710e6i	−0.0697799	+	0.444949i
$544$		0			0
$545$		−	832075.i		−	0.119997i
$546$		0			0
$547$			1.17555e7i			1.67986i	0.542695	+	0.839930i	$0.317404\pi$
$547$			1.17555e7i			1.67986i	−0.542695	+	0.839930i	$0.682596\pi$
$548$		0			0
$549$	−8.79784e6	−	2.82905e6i	−1.24579	−	0.400599i
$550$		0			0
$551$	−148288.			−0.0208079
$552$		0			0
$553$	−1.12002e7			−1.55745
$554$		0			0
$555$	2.91283e6	+	456809.i	0.401404	+	0.0629509i
$556$		0			0
$557$		−	5.12536e6i		−	0.699981i	−0.936753	−	0.349991i	$-0.886185\pi$
$557$		−	5.12536e6i		−	0.699981i	0.936753	−	0.349991i	$-0.113815\pi$
$558$		0			0
$559$		−	1.85853e6i		−	0.251559i
$560$		0			0
$561$	−1.65557e6	−	259637.i	−0.222096	−	0.0348305i
$562$		0			0
$563$	−1.12501e7			−1.49585			−0.747923	−	0.663785i	$-0.768949\pi$
$563$	−1.12501e7			−1.49585			−0.747923	+	0.663785i	$0.768949\pi$
$564$		0			0
$565$	1.38722e7			1.82820
$566$		0			0
$567$	4.95577e6	−	6.90899e6i	0.647372	−	0.902520i
$568$		0			0
$569$		−	1.27257e7i		−	1.64778i	−0.566749	−	0.823890i	$-0.691799\pi$
$569$		−	1.27257e7i		−	1.64778i	0.566749	−	0.823890i	$-0.308201\pi$
$570$		0			0
$571$			5.15696e6i			0.661917i	0.943645	+	0.330959i	$0.107372\pi$
$571$			5.15696e6i			0.661917i	−0.943645	+	0.330959i	$0.892628\pi$
$572$		0			0
$573$	180950.	−	1.15382e6i	0.0230235	−	0.146809i
$574$		0			0
$575$	−4.15597e6			−0.524207
$576$		0			0
$577$	7.46314e6			0.933216			0.466608	−	0.884464i	$-0.345476\pi$
$577$	7.46314e6			0.933216			0.466608	+	0.884464i	$0.345476\pi$
$578$		0			0
$579$	1.45601e6	−	9.28422e6i	0.180497	−	1.15093i
$580$		0			0
$581$			70028.9i			0.00860671i
$582$		0			0
$583$			2.08469e6i			0.254022i
$584$		0			0
$585$	−799603.	+	2.48662e6i	−0.0966016	+	0.300414i
$586$		0			0
$587$	−2.05257e6			−0.245868			−0.122934	−	0.992415i	$-0.539230\pi$
$587$	−2.05257e6			−0.245868			−0.122934	+	0.992415i	$0.539230\pi$
$588$		0			0
$589$	210706.			0.0250258
$590$		0			0
$591$	1.33961e7	+	2.10086e6i	1.57765	+	0.247417i
$592$		0			0
$593$			1.30868e7i			1.52826i	0.645061	+	0.764131i	$0.276832\pi$
$593$			1.30868e7i			1.52826i	−0.645061	+	0.764131i	$0.723168\pi$
$594$		0			0
$595$		−	1.39507e7i		−	1.61549i
$596$		0			0
$597$	6.78423e6	+	1.06395e6i	0.779049	+	0.122176i
$598$		0			0
$599$	−3.19525e6			−0.363862			−0.181931	−	0.983311i	$-0.558235\pi$
$599$	−3.19525e6			−0.363862			−0.181931	+	0.983311i	$0.558235\pi$
$600$		0			0
$601$	−8.42062e6			−0.950950			−0.475475	−	0.879729i	$-0.657724\pi$
$601$	−8.42062e6			−0.950950			−0.475475	+	0.879729i	$0.657724\pi$
$602$		0			0
$603$	−3.53674e6	+	1.09986e7i	−0.396105	+	1.23182i
$604$		0			0
$605$		−	1.59660e6i		−	0.177340i
$606$		0			0
$607$		−	2.17792e6i		−	0.239922i	−0.992779	−	0.119961i	$-0.961723\pi$
$607$		−	2.17792e6i		−	0.239922i	0.992779	−	0.119961i	$-0.0382770\pi$
$608$		0			0
$609$	−1.82034e6	+	1.16073e7i	−0.198888	+	1.26821i
$610$		0			0
$611$	−174267.			−0.0188848
$612$		0			0
$613$	1.94928e6			0.209519			0.104759	−	0.994498i	$-0.466593\pi$
$613$	1.94928e6			0.209519			0.104759	+	0.994498i	$0.466593\pi$
$614$		0			0
$615$	3.97803e6	−	2.53658e7i	0.424111	−	2.70433i
$616$		0			0
$617$		−	1.53443e6i		−	0.162269i	−0.996703	−	0.0811343i	$-0.974146\pi$
$617$		−	1.53443e6i		−	0.162269i	0.996703	−	0.0811343i	$-0.0258543\pi$
$618$		0			0
$619$			8.76572e6i			0.919520i	0.888043	+	0.459760i	$0.152065\pi$
$619$			8.76572e6i			0.919520i	−0.888043	+	0.459760i	$0.847935\pi$
$620$		0			0
$621$	−807934.	+	1.60370e6i	−0.0840711	+	0.166876i
$622$		0			0
$623$	7.76423e6			0.801454
$624$		0			0
$625$	3.96956e7			4.06483
$626$		0			0
$627$	52790.0	+	8278.89i	0.00536270	+	0.000841014i
$628$		0			0
$629$		−	1.54098e6i		−	0.155300i
$630$		0			0
$631$			9.22876e6i			0.922720i	0.887213	+	0.461360i	$0.152638\pi$
$631$			9.22876e6i			0.922720i	−0.887213	+	0.461360i	$0.847362\pi$
$632$		0			0
$633$	5.02347e6	+	787814.i	0.498304	+	0.0781473i
$634$		0			0
$635$	1.21584e7			1.19658
$636$		0			0
$637$	−387052.			−0.0377938
$638$		0			0
$639$	−8.31619e6	−	2.67417e6i	−0.805698	−	0.259082i
$640$		0			0
$641$			1.20197e7i			1.15544i	0.816236	+	0.577719i	$0.196057\pi$
$641$			1.20197e7i			1.15544i	−0.816236	+	0.577719i	$0.803943\pi$
$642$		0			0
$643$			66431.6i			0.00633647i	0.999995	+	0.00316823i	$0.00100848\pi$
$643$			66431.6i			0.00633647i	−0.999995	+	0.00316823i	$0.998992\pi$
$644$		0			0
$645$	−4.96588e6	+	3.16647e7i	−0.469999	+	2.99693i
$646$		0			0
$647$	2.06348e7			1.93793			0.968967	−	0.247191i	$-0.0795075\pi$
$647$	2.06348e7			1.93793			0.968967	+	0.247191i	$0.0795075\pi$
$648$		0			0
$649$	3.71442e6			0.346162
$650$		0			0
$651$	2.58656e6	−	1.64931e7i	0.239205	−	1.52528i
$652$		0			0
$653$		−	5.04353e6i		−	0.462862i	−0.972851	−	0.231431i	$-0.925659\pi$
$653$		−	5.04353e6i		−	0.462862i	0.972851	−	0.231431i	$-0.0743408\pi$
$654$		0			0
$655$			1.05753e6i			0.0963144i
$656$		0			0
$657$	−4.83009e6	−	1.55317e6i	−0.436558	−	0.140380i
$658$		0			0
$659$	2.03058e7			1.82140			0.910702	−	0.413064i	$-0.135541\pi$
$659$	2.03058e7			1.82140			0.910702	+	0.413064i	$0.135541\pi$
$660$		0			0
$661$	−3.46379e6			−0.308352			−0.154176	−	0.988043i	$-0.549272\pi$
$661$	−3.46379e6			−0.308352			−0.154176	+	0.988043i	$0.549272\pi$
$662$		0			0
$663$	1.34867e6	+	211508.i	0.119158	+	0.0186872i
$664$		0			0
$665$			444838.i			0.0390075i
$666$		0			0
$667$		−	2.48140e6i		−	0.215964i
$668$		0			0
$669$	1.91407e7	+	3.00178e6i	1.65346	+	0.259306i
$670$		0			0
$671$	−4.60174e6			−0.394562
$672$		0			0
$673$	−4.20955e6			−0.358260			−0.179130	−	0.983825i	$-0.557328\pi$
$673$	−4.20955e6			−0.358260			−0.179130	+	0.983825i	$0.557328\pi$
$674$		0			0
$675$	1.49414e7	−	2.96577e7i	1.26221	−	2.50540i
$676$		0			0
$677$			7.08131e6i			0.593802i	0.954908	+	0.296901i	$0.0959532\pi$
$677$			7.08131e6i			0.593802i	−0.954908	+	0.296901i	$0.904047\pi$
$678$		0			0
$679$			1.23822e7i			1.03068i
$680$		0			0
$681$	2.73152e6	−	1.74175e7i	0.225703	−	1.43919i
$682$		0			0
$683$	−2.99438e6			−0.245615			−0.122808	−	0.992430i	$-0.539190\pi$
$683$	−2.99438e6			−0.245615			−0.122808	+	0.992430i	$0.539190\pi$
$684$		0			0
$685$	1.94542e7			1.58411
$686$		0			0
$687$	−1.50156e6	+	9.57466e6i	−0.121381	+	0.773983i
$688$		0			0
$689$		−	1.69825e6i		−	0.136287i
$690$		0			0
$691$			1.50320e7i			1.19763i	0.800889	+	0.598813i	$0.204361\pi$
$691$			1.50320e7i			1.19763i	−0.800889	+	0.598813i	$0.795639\pi$
$692$		0			0
$693$	1.29607e6	−	4.03054e6i	0.102517	−	0.318808i
$694$		0			0
$695$	−9.63089e6			−0.756318
$696$		0			0
$697$	−1.34193e7			−1.04628
$698$		0			0
$699$	1.75406e7	+	2.75083e6i	1.35785	+	0.212947i
$700$		0			0
$701$			8.56740e6i			0.658498i	0.944243	+	0.329249i	$0.106795\pi$
$701$			8.56740e6i			0.658498i	−0.944243	+	0.329249i	$0.893205\pi$
$702$		0			0
$703$			49136.3i			0.00374985i
$704$		0			0
$705$	2.96908e6	+	465631.i	0.224983	+	0.0352833i
$706$		0			0
$707$	−1.97580e7			−1.48660
$708$		0			0
$709$	−1.07577e7			−0.803716			−0.401858	−	0.915702i	$-0.631635\pi$
$709$	−1.07577e7			−0.803716			−0.401858	+	0.915702i	$0.631635\pi$
$710$		0			0
$711$	−5.78620e6	+	1.79941e7i	−0.429259	+	1.33492i
$712$		0			0
$713$			3.52586e6i			0.259742i
$714$		0			0
$715$			1.30063e6i			0.0951459i
$716$		0			0
$717$	−3.85838e6	+	2.46028e7i	−0.280290	+	1.78726i
$718$		0			0
$719$	−3.77766e6			−0.272522			−0.136261	−	0.990673i	$-0.543509\pi$
$719$	−3.77766e6			−0.272522			−0.136261	+	0.990673i	$0.543509\pi$
$720$		0			0
$721$	−1.56618e7			−1.12202
$722$		0			0
$723$	108512.	−	691924.i	0.00772027	−	0.0492280i
$724$		0			0
$725$			4.58893e7i			3.24240i
$726$		0			0
$727$			1.81386e7i			1.27282i	0.771349	+	0.636412i	$0.219582\pi$
$727$			1.81386e7i			1.27282i	−0.771349	+	0.636412i	$0.780418\pi$
$728$		0			0
$729$	−8.53959e6	−	1.15311e7i	−0.595139	−	0.803623i
$730$		0			0
$731$	1.67517e7			1.15949
$732$		0			0
$733$	−1.48710e7			−1.02230			−0.511151	−	0.859491i	$-0.670781\pi$
$733$	−1.48710e7			−1.02230			−0.511151	+	0.859491i	$0.670781\pi$
$734$		0			0
$735$	6.59440e6	+	1.03418e6i	0.450253	+	0.0706118i
$736$		0			0
$737$			5.75287e6i			0.390136i
$738$		0			0
$739$		−	1.74778e7i		−	1.17727i	−0.808400	−	0.588633i	$-0.799666\pi$
$739$		−	1.74778e7i		−	1.17727i	0.808400	−	0.588633i	$-0.200334\pi$
$740$		0			0
$741$	−43004.3	−	6744.22i	−0.00287718	−	0.000451218i
$742$		0			0
$743$	7.33415e6			0.487391			0.243696	−	0.969852i	$-0.421640\pi$
$743$	7.33415e6			0.487391			0.243696	+	0.969852i	$0.421640\pi$
$744$		0			0
$745$	2.89914e7			1.91372
$746$		0			0
$747$	112507.	+	36177.9i	0.00737696	+	0.00237215i
$748$		0			0
$749$			1.58283e7i			1.03093i
$750$		0			0
$751$			1.17761e6i			0.0761908i	0.999274	+	0.0380954i	$0.0121291\pi$
$751$			1.17761e6i			0.0761908i	−0.999274	+	0.0380954i	$0.987871\pi$
$752$		0			0
$753$	−2.42571e6	+	1.54674e7i	−0.155902	+	0.994101i
$754$		0			0
$755$	−5.88909e7			−3.75994
$756$		0			0
$757$	−1.27420e7			−0.808159			−0.404079	−	0.914724i	$-0.632408\pi$
$757$	−1.27420e7			−0.808159			−0.404079	+	0.914724i	$0.632408\pi$
$758$		0			0
$759$	−138535.	+	883367.i	−0.00872884	+	0.0556592i
$760$		0			0
$761$			1.90074e7i			1.18976i	0.803814	+	0.594881i	$0.202801\pi$
$761$			1.90074e7i			1.18976i	−0.803814	+	0.594881i	$0.797199\pi$
$762$		0			0
$763$		−	1.09869e6i		−	0.0683226i
$764$		0			0
$765$	−2.24129e7	−	7.20715e6i	−1.38467	−	0.445256i
$766$		0			0
$767$	−3.02588e6			−0.185722
$768$		0			0
$769$	−2.30638e7			−1.40642			−0.703210	−	0.710982i	$-0.748251\pi$
$769$	−2.30638e7			−1.40642			−0.703210	+	0.710982i	$0.748251\pi$
$770$		0			0
$771$	−1.36545e7	−	2.14140e6i	−0.827258	−	0.129736i
$772$		0			0
$773$			1.53098e7i			0.921556i	0.887515	+	0.460778i	$0.152430\pi$
$773$			1.53098e7i			0.921556i	−0.887515	+	0.460778i	$0.847570\pi$
$774$		0			0
$775$		−	6.52050e7i		−	3.89966i
$776$		0			0
$777$	3.84616e6	+	603181.i	0.228547	+	0.0358422i
$778$		0			0
$779$	427893.			0.0252634
$780$		0			0
$781$	−4.34981e6			−0.255178
$782$		0			0
$783$	1.77077e7	+	8.92103e6i	1.03218	+	0.520009i
$784$		0			0
$785$		−	4.77915e7i		−	2.76807i
$786$		0			0
$787$			1.77422e7i			1.02110i	0.859847	+	0.510551i	$0.170559\pi$
$787$			1.77422e7i			1.02110i	−0.859847	+	0.510551i	$0.829441\pi$
$788$		0			0
$789$	−3.18916e6	+	2.03356e7i	−0.182383	+	1.16296i
$790$		0			0
$791$	1.83172e7			1.04092
$792$		0			0
$793$	3.74871e6			0.211689
$794$		0			0
$795$	−4.53762e6	+	2.89340e7i	−0.254631	+	1.62364i
$796$		0			0
$797$		−	1.72164e7i		−	0.960058i	−0.877253	−	0.480029i	$-0.840626\pi$
$797$		−	1.72164e7i		−	0.960058i	0.877253	−	0.480029i	$-0.159374\pi$
$798$		0			0
$799$		−	1.57074e6i		−	0.0870437i
$800$		0			0
$801$	4.01111e6	−	1.24738e7i	0.220894	−	0.686940i
$802$		0			0
$803$	−2.52639e6			−0.138265
$804$		0			0
$805$	−7.44374e6			−0.404857
$806$		0			0
$807$	−2.74522e7	−	4.30524e6i	−1.48386	−	0.232709i
$808$		0			0
$809$		−	1.23019e7i		−	0.660848i	−0.943833	−	0.330424i	$-0.892808\pi$
$809$		−	1.23019e7i		−	0.660848i	0.943833	−	0.330424i	$-0.107192\pi$
$810$		0			0
$811$		−	2.24806e7i		−	1.20020i	−0.799923	−	0.600102i	$-0.795127\pi$
$811$		−	2.24806e7i		−	1.20020i	0.799923	−	0.600102i	$-0.204873\pi$
$812$		0			0
$813$	−2.15917e7	−	3.38615e6i	−1.14567	−	0.179672i
$814$		0			0
$815$	−5.84017e7			−3.07986
$816$		0			0
$817$	−534150.			−0.0279968
$818$		0			0
$819$	−1.05581e6	+	3.28339e6i	−0.0550019	+	0.171046i
$820$		0			0
$821$		−	1.36979e7i		−	0.709243i	−0.935010	−	0.354622i	$-0.884610\pi$
$821$		−	1.36979e7i		−	0.709243i	0.935010	−	0.354622i	$-0.115390\pi$
$822$		0			0
$823$		−	2.64253e7i		−	1.35994i	−0.733240	−	0.679970i	$-0.761993\pi$
$823$		−	2.64253e7i		−	1.35994i	0.733240	−	0.679970i	$-0.238007\pi$
$824$		0			0
$825$	2.56198e6	−	1.63364e7i	0.131051	−	0.835644i
$826$		0			0
$827$	3.44947e6			0.175384			0.0876918	−	0.996148i	$-0.472051\pi$
$827$	3.44947e6			0.175384			0.0876918	+	0.996148i	$0.472051\pi$
$828$		0			0
$829$	−3.04445e6			−0.153859			−0.0769295	−	0.997037i	$-0.524512\pi$
$829$	−3.04445e6			−0.153859			−0.0769295	+	0.997037i	$0.524512\pi$
$830$		0			0
$831$	−5.00639e6	+	3.19231e7i	−0.251491	+	1.60362i
$832$		0			0
$833$		−	3.48866e6i		−	0.174199i
$834$		0			0
$835$			5.76147e7i			2.85968i
$836$		0			0
$837$	−2.51612e7	−	1.26761e7i	−1.24142	−	0.625419i
$838$		0			0
$839$	5.08367e6			0.249329			0.124664	−	0.992199i	$-0.460215\pi$
$839$	5.08367e6			0.249329			0.124664	+	0.992199i	$0.460215\pi$
$840$		0			0
$841$	−6.88791e6			−0.335813
$842$		0			0
$843$	−2.29599e7	−	3.60072e6i	−1.11276	−	0.174510i
$844$		0			0
$845$			3.94299e7i			1.89969i
$846$		0			0
$847$		−	2.10819e6i		−	0.100972i
$848$		0			0
$849$	3.28338e7	+	5.14921e6i	1.56333	+	0.245172i
$850$		0			0
$851$	−822226.			−0.0389195
$852$		0			0
$853$	−1.16214e7			−0.546870			−0.273435	−	0.961890i	$-0.588160\pi$
$853$	−1.16214e7			−0.546870			−0.273435	+	0.961890i	$0.588160\pi$
$854$		0			0
$855$	714667.	+	229810.i	0.0334340	+	0.0107511i
$856$		0			0
$857$			2.28907e7i			1.06465i	0.846540	+	0.532325i	$0.178682\pi$
$857$			2.28907e7i			1.06465i	−0.846540	+	0.532325i	$0.821318\pi$
$858$		0			0
$859$			2.17393e7i			1.00522i	0.864513	+	0.502611i	$0.167627\pi$
$859$			2.17393e7i			1.00522i	−0.864513	+	0.502611i	$0.832373\pi$
$860$		0			0
$861$	5.25268e6	−	3.34935e7i	0.241476	−	1.53976i
$862$		0			0
$863$	3.21454e6			0.146924			0.0734618	−	0.997298i	$-0.476595\pi$
$863$	3.21454e6			0.146924			0.0734618	+	0.997298i	$0.476595\pi$
$864$		0			0
$865$	4.56221e7			2.07317
$866$		0			0
$867$	1.52278e6	−	9.70996e6i	0.0688002	−	0.438702i
$868$		0			0
$869$			9.41185e6i			0.422791i
$870$		0			0
$871$		−	4.68646e6i		−	0.209315i
$872$		0			0
$873$	1.98930e7	+	6.39683e6i	0.883414	+	0.284073i
$874$		0			0
$875$	8.85899e7			3.91169
$876$		0			0
$877$	2.01232e7			0.883484			0.441742	−	0.897142i	$-0.354361\pi$
$877$	2.01232e7			0.883484			0.441742	+	0.897142i	$0.354361\pi$
$878$		0			0
$879$	2.38350e7	+	3.73797e6i	1.04050	+	0.163179i
$880$		0			0
$881$		−	7.12664e6i		−	0.309347i	−0.987966	−	0.154673i	$-0.950568\pi$
$881$		−	7.12664e6i		−	0.309347i	0.987966	−	0.154673i	$-0.0494325\pi$
$882$		0			0
$883$		−	9.65529e6i		−	0.416739i	−0.978050	−	0.208369i	$-0.933184\pi$
$883$		−	9.65529e6i		−	0.416739i	0.978050	−	0.208369i	$-0.0668156\pi$
$884$		0			0
$885$	5.15534e7	+	8.08495e6i	2.21258	+	0.346992i
$886$		0			0
$887$	−3.06453e6			−0.130784			−0.0653919	−	0.997860i	$-0.520830\pi$
$887$	−3.06453e6			−0.130784			−0.0653919	+	0.997860i	$0.520830\pi$
$888$		0			0
$889$	1.60543e7			0.681297
$890$		0			0
$891$	−5.80580e6	−	4.16446e6i	−0.245001	−	0.175738i
$892$		0			0
$893$			50085.2i			0.00210175i
$894$		0			0
$895$		−	1.15784e7i		−	0.483161i
$896$		0			0
$897$	112855.	−	719616.i	0.00468317	−	0.0298621i
$898$		0			0
$899$	3.89318e7			1.60659
$900$		0			0
$901$	1.53070e7			0.628173
$902$		0			0
$903$	−6.55706e6	+	4.18109e7i	−0.267602	+	1.70636i
$904$		0			0
$905$			2.16475e7i			0.878590i
$906$		0			0
$907$		−	3.50388e7i		−	1.41426i	−0.707081	−	0.707132i	$-0.749988\pi$
$907$		−	3.50388e7i		−	1.41426i	0.707081	−	0.707132i	$-0.250012\pi$
$908$		0			0
$909$	−1.02073e7	+	3.17428e7i	−0.409732	+	1.27419i
$910$		0			0
$911$	−2.50005e7			−0.998051			−0.499025	−	0.866587i	$-0.666309\pi$
$911$	−2.50005e7			−0.998051			−0.499025	+	0.866587i	$0.666309\pi$
$912$		0			0
$913$	58847.1			0.00233640
$914$		0			0
$915$	−6.38688e7	−	1.00163e7i	−2.52195	−	0.395508i
$916$		0			0
$917$			1.39639e6i			0.0548383i
$918$		0			0
$919$		−	2.92789e7i		−	1.14358i	−0.820400	−	0.571790i	$-0.806249\pi$
$919$		−	2.92789e7i		−	1.14358i	0.820400	−	0.571790i	$-0.193751\pi$
$920$		0			0
$921$	−2.73962e7	−	4.29646e6i	−1.06424	−	0.166902i
$922$		0			0
$923$	3.54348e6			0.136907
$924$		0			0
$925$	1.52057e7			0.584322
$926$		0			0
$927$	−8.09109e6	+	2.51618e7i	−0.309248	+	0.961707i
$928$		0			0
$929$		−	1.50991e7i		−	0.574001i	−0.957930	−	0.287001i	$-0.907342\pi$
$929$		−	1.50991e7i		−	0.574001i	0.957930	−	0.287001i	$-0.0926582\pi$
$930$		0			0
$931$			111241.i			0.00420619i
$932$		0			0
$933$	6.32483e6	−	4.03301e7i	0.237873	−	1.51679i
$934$		0			0
$935$	−1.17232e7			−0.438547
$936$		0			0
$937$	−4.31896e7			−1.60705			−0.803526	−	0.595269i	$-0.797045\pi$
$937$	−4.31896e7			−1.60705			−0.803526	+	0.595269i	$0.797045\pi$
$938$		0			0
$939$	1.82360e6	−	1.16281e7i	0.0674942	−	0.430374i
$940$		0			0
$941$			6.27727e6i			0.231098i	0.993302	+	0.115549i	$0.0368628\pi$
$941$			6.27727e6i			0.231098i	−0.993302	+	0.115549i	$0.963137\pi$
$942$		0			0
$943$			7.16019e6i			0.262208i
$944$		0			0
$945$	2.67615e7	−	5.31198e7i	0.974834	−	1.93498i
$946$		0			0
$947$	−2.82883e7			−1.02502			−0.512510	−	0.858681i	$-0.671284\pi$
$947$	−2.82883e7			−1.02502			−0.512510	+	0.858681i	$0.671284\pi$
$948$		0			0
$949$	2.05807e6			0.0741815
$950$		0			0
$951$	3.20809e7	+	5.03115e6i	1.15026	+	0.180391i
$952$		0			0
$953$		−	4.56230e7i		−	1.62724i	−0.581397	−	0.813620i	$-0.697494\pi$
$953$		−	4.56230e7i		−	1.62724i	0.581397	−	0.813620i	$-0.302506\pi$
$954$		0			0
$955$		−	8.17027e6i		−	0.289886i
$956$		0			0
$957$	9.75394e6	+	1.52968e6i	0.344271	+	0.0539909i
$958$		0			0
$959$	2.56877e7			0.901943
$960$		0			0
$961$	−2.66898e7			−0.932261
$962$		0			0
$963$	2.54295e7	+	8.17715e6i	0.883632	+	0.284142i
$964$		0			0
$965$		−	6.57420e7i		−	2.27261i
$966$		0			0
$967$		−	6.93845e6i		−	0.238614i	−0.992857	−	0.119307i	$-0.961933\pi$
$967$		−	6.93845e6i		−	0.238614i	0.992857	−	0.119307i	$-0.0380673\pi$
$968$		0			0
$969$	60788.5	−	387616.i	0.00207975	−	0.0132615i
$970$		0			0
$971$	1.42833e7			0.486162			0.243081	−	0.970006i	$-0.421842\pi$
$971$	1.42833e7			0.486162			0.243081	+	0.970006i	$0.421842\pi$
$972$		0			0
$973$	−1.27169e7			−0.430623
$974$		0			0
$975$	−2.08706e6	+	1.33081e7i	−0.0703112	+	0.448337i
$976$		0			0
$977$		−	1.02610e7i		−	0.343918i	−0.985104	−	0.171959i	$-0.944990\pi$
$977$		−	1.02610e7i		−	0.343918i	0.985104	−	0.171959i	$-0.0550096\pi$
$978$		0			0
$979$		−	6.52448e6i		−	0.217565i
$980$		0			0
$981$	−1.76513e6	−	567599.i	−0.0585604	−	0.0188308i
$982$		0			0
$983$	−5.52793e7			−1.82465			−0.912323	−	0.409470i	$-0.865713\pi$
$983$	−5.52793e7			−1.82465			−0.912323	+	0.409470i	$0.865713\pi$
$984$		0			0
$985$	9.48584e7			3.11519
$986$		0			0
$987$	3.92044e6	+	614830.i	0.128098	+	0.0200892i
$988$		0			0
$989$		−	8.93825e6i		−	0.290577i
$990$		0			0
$991$		−	3.91872e7i		−	1.26754i	−0.773523	−	0.633768i	$-0.781507\pi$
$991$		−	3.91872e7i		−	1.26754i	0.773523	−	0.633768i	$-0.218493\pi$
$992$		0			0
$993$	−4.48541e7	−	7.03432e6i	−1.44354	−	0.226386i
$994$		0			0
$995$	4.80395e7			1.53830
$996$		0			0
$997$	2.96695e7			0.945305			0.472653	−	0.881249i	$-0.343297\pi$
$997$	2.96695e7			0.945305			0.472653	+	0.881249i	$0.343297\pi$
$998$		0			0
$999$	2.95604e6	−	5.86754e6i	0.0937123	−	0.186013i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	528.6.d.b.287.7	yes	16
3.2	odd	2		528.6.d.a.287.9	✓	16
4.3	odd	2		528.6.d.a.287.10	yes	16
12.11	even	2	inner	528.6.d.b.287.8	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
528.6.d.a.287.9	✓	16	3.2	odd	2
528.6.d.a.287.10	yes	16	4.3	odd	2
528.6.d.b.287.7	yes	16	1.1	even	1	trivial
528.6.d.b.287.8	yes	16	12.11	even	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:	\( N \)	\(=\)	\( 528 = 2^{4} \cdot 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	528.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(2.41517 - 15.4002i) q^{3} -109.050i q^{5} -143.992i q^{7} +(-231.334 - 74.3882i) q^{9} +O(q^{10})\)	\(q+(2.41517 - 15.4002i) q^{3} -109.050i q^{5} -143.992i q^{7} +(-231.334 - 74.3882i) q^{9} -121.000 q^{11} +98.5701 q^{13} +(-1679.39 - 263.373i) q^{15} +888.453i q^{17} -28.3295i q^{19} +(-2217.51 - 347.764i) q^{21} +474.055 q^{23} -8766.85 q^{25} +(-1704.31 + 3382.94i) q^{27} -5234.41i q^{29} +7437.67i q^{31} +(-292.235 + 1863.43i) q^{33} -15702.3 q^{35} -1734.45 q^{37} +(238.063 - 1518.00i) q^{39} +15104.1i q^{41} -18854.9i q^{43} +(-8112.02 + 25226.9i) q^{45} -1767.95 q^{47} -3926.66 q^{49} +(13682.4 + 2145.76i) q^{51} -17228.9i q^{53} +13195.0i q^{55} +(-436.281 - 68.4206i) q^{57} -30697.7 q^{59} +38030.9 q^{61} +(-10711.3 + 33310.2i) q^{63} -10749.0i q^{65} -47544.4i q^{67} +(1144.92 - 7300.55i) q^{69} +35948.9 q^{71} +20879.3 q^{73} +(-21173.4 + 135011. i) q^{75} +17423.0i q^{77} -77783.9i q^{79} +(47981.8 + 34417.0i) q^{81} -486.339 q^{83} +96885.6 q^{85} +(-80611.1 - 12642.0i) q^{87} +53921.3i q^{89} -14193.3i q^{91} +(114542. + 17963.2i) q^{93} -3089.33 q^{95} -85992.5 q^{97} +(27991.4 + 9000.97i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 31 q^{3} + 31 q^{9}+O(q^{10}) \) 16 * q + 31 * q^3 + 31 * q^9	\( 16 q + 31 q^{3} + 31 q^{9} - 1936 q^{11} + 444 q^{13} - 979 q^{15} - 3874 q^{21} + 4246 q^{23} - 4194 q^{25} + 1306 q^{27} - 3751 q^{33} - 13964 q^{35} + 35094 q^{37} - 7848 q^{39} - 43369 q^{45} + 18476 q^{47} - 6172 q^{49} + 40886 q^{51} - 27316 q^{57} - 59134 q^{59} + 93580 q^{61} + 52286 q^{63} + 23881 q^{69} + 129154 q^{71} + 63188 q^{73} - 30048 q^{75} + 132223 q^{81} - 46276 q^{83} + 141316 q^{85} - 86304 q^{87} + 228139 q^{93} - 238328 q^{95} - 244198 q^{97} - 3751 q^{99}+O(q^{100}) \) 16 * q + 31 * q^3 + 31 * q^9 - 1936 * q^11 + 444 * q^13 - 979 * q^15 - 3874 * q^21 + 4246 * q^23 - 4194 * q^25 + 1306 * q^27 - 3751 * q^33 - 13964 * q^35 + 35094 * q^37 - 7848 * q^39 - 43369 * q^45 + 18476 * q^47 - 6172 * q^49 + 40886 * q^51 - 27316 * q^57 - 59134 * q^59 + 93580 * q^61 + 52286 * q^63 + 23881 * q^69 + 129154 * q^71 + 63188 * q^73 - 30048 * q^75 + 132223 * q^81 - 46276 * q^83 + 141316 * q^85 - 86304 * q^87 + 228139 * q^93 - 238328 * q^95 - 244198 * q^97 - 3751 * q^99

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