LMFDB - Embedded newform 63.6.e.f.37.1

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			37.1
Root			$-5.31117 + 9.19921i$ of defining polynomial
Character	$\chi$	$=$	63.37
Dual form			63.6.e.f.46.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.31117 + 9.19921i) q^{2} +(-40.4170 - 70.0043i) q^{4} +(33.7376 - 58.4352i) q^{5} +(-120.281 + 48.3679i) q^{7} +518.731 q^{8} +O(q^{10})$	\(q+(-5.31117 + 9.19921i) q^{2} +(-40.4170 - 70.0043i) q^{4} +(33.7376 - 58.4352i) q^{5} +(-120.281 + 48.3679i) q^{7} +518.731 q^{8} +(358.372 + 620.718i) q^{10} +(261.323 + 452.625i) q^{11} +76.6331 q^{13} +(193.887 - 1363.38i) q^{14} +(-1461.72 + 2531.78i) q^{16} +(634.801 + 1099.51i) q^{17} +(946.362 - 1639.15i) q^{19} -5454.28 q^{20} -5551.73 q^{22} +(-575.022 + 995.967i) q^{23} +(-713.945 - 1236.59i) q^{25} +(-407.011 + 704.964i) q^{26} +(8247.36 + 6465.31i) q^{28} +3850.03 q^{29} +(5206.86 + 9018.55i) q^{31} +(-7227.21 - 12517.9i) q^{32} -13486.1 q^{34} +(-1231.60 + 8660.46i) q^{35} +(2801.14 - 4851.71i) q^{37} +(10052.6 + 17411.6i) q^{38} +(17500.7 - 30312.1i) q^{40} +14232.7 q^{41} -14827.9 q^{43} +(21123.8 - 36587.5i) q^{44} +(-6108.08 - 10579.5i) q^{46} +(-5774.88 + 10002.4i) q^{47} +(12128.1 - 11635.5i) q^{49} +15167.5 q^{50} +(-3097.28 - 5364.64i) q^{52} +(-2338.86 - 4051.02i) q^{53} +35265.6 q^{55} +(-62393.5 + 25089.9i) q^{56} +(-20448.2 + 35417.3i) q^{58} +(14551.0 + 25203.0i) q^{59} +(-5921.45 + 10256.2i) q^{61} -110618. q^{62} +59989.5 q^{64} +(2585.41 - 4478.06i) q^{65} +(18106.3 + 31361.0i) q^{67} +(51313.5 - 88877.6i) q^{68} +(-73128.1 - 57326.9i) q^{70} +13477.6 q^{71} +(-1304.23 - 2258.98i) q^{73} +(29754.6 + 51536.5i) q^{74} -152996. q^{76} +(-53324.8 - 41802.6i) q^{77} +(39160.2 - 67827.4i) q^{79} +(98629.9 + 170832. i) q^{80} +(-75592.3 + 130930. i) q^{82} -16746.0 q^{83} +85666.5 q^{85} +(78753.5 - 136405. i) q^{86} +(135557. + 234791. i) q^{88} +(18384.2 - 31842.4i) q^{89} +(-9217.51 + 3706.58i) q^{91} +92962.7 q^{92} +(-61342.7 - 106249. i) q^{94} +(-63855.9 - 110602. i) q^{95} +36133.4 q^{97} +(42623.0 + 173367. i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

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

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 $

$2$	−5.31117	+	9.19921i	−0.938891	+	1.62621i	−0.171346	+	0.985211i	$0.554811\pi$
$2$	−5.31117	+	9.19921i	−0.938891	+	1.62621i	−0.767545	+	0.640995i	$0.778522\pi$
$3$		0			0
$3$		0			0
$4$	−40.4170	−	70.0043i	−1.26303	−	2.18763i
$5$	33.7376	−	58.4352i	0.603516	−	1.04532i	−0.388769	−	0.921335i	$-0.627099\pi$
$5$	33.7376	−	58.4352i	0.603516	−	1.04532i	0.992284	−	0.123984i	$-0.0395673\pi$
$6$		0			0
$7$	−120.281	+	48.3679i	−0.927796	+	0.373089i
$7$	−120.281	+	48.3679i	−0.927796	+	0.373089i
$8$	518.731			2.86561
$9$		0			0
$10$	358.372	+	620.718i	1.13327	+	1.96288i
$11$	261.323	+	452.625i	0.651173	+	1.12787i	0.982839	+	0.184468i	$0.0590562\pi$
$11$	261.323	+	452.625i	0.651173	+	1.12787i	−0.331665	+	0.943397i	$0.607610\pi$
$12$		0			0
$13$	76.6331			0.125764			0.0628822	−	0.998021i	$-0.479971\pi$
$13$	76.6331			0.125764			0.0628822	+	0.998021i	$0.479971\pi$
$14$	193.887	−	1363.38i	0.264379	−	1.85908i
$15$		0			0
$16$	−1461.72	+	2531.78i	−1.42746	+	2.47244i
$17$	634.801	+	1099.51i	0.532740	+	0.922733i	0.999269	+	0.0382267i	$0.0121709\pi$
$17$	634.801	+	1099.51i	0.532740	+	0.922733i	−0.466529	+	0.884506i	$0.654496\pi$
$18$		0			0
$19$	946.362	−	1639.15i	0.601414	−	1.04168i	−0.391193	−	0.920309i	$-0.627938\pi$
$19$	946.362	−	1639.15i	0.601414	−	1.04168i	0.992607	−	0.121371i	$-0.0387290\pi$
$20$	−5454.28			−3.04904
$21$		0			0
$22$	−5551.73			−2.44552
$23$	−575.022	+	995.967i	−0.226655	+	0.392578i	−0.956815	−	0.290699i	$-0.906112\pi$
$23$	−575.022	+	995.967i	−0.226655	+	0.392578i	0.730160	+	0.683276i	$0.239446\pi$
$24$		0			0
$25$	−713.945	−	1236.59i	−0.228462	−	0.395708i
$26$	−407.011	+	704.964i	−0.118079	+	0.204519i
$27$		0			0
$28$	8247.36	+	6465.31i	1.98802	+	1.55845i
$29$	3850.03			0.850099			0.425049	−	0.905170i	$-0.360257\pi$
$29$	3850.03			0.850099			0.425049	+	0.905170i	$0.360257\pi$
$30$		0			0
$31$	5206.86	+	9018.55i	0.973132	+	1.68551i	0.685967	+	0.727633i	$0.259379\pi$
$31$	5206.86	+	9018.55i	0.973132	+	1.68551i	0.287165	+	0.957881i	$0.407287\pi$
$32$	−7227.21	−	12517.9i	−1.24766	−	2.16101i
$33$		0			0
$34$	−13486.1			−2.00074
$35$	−1231.60	+	8660.46i	−0.169942	+	1.19501i
$36$		0			0
$37$	2801.14	−	4851.71i	0.336380	−	0.582627i	−0.647369	−	0.762177i	$-0.724131\pi$
$37$	2801.14	−	4851.71i	0.336380	−	0.582627i	0.983749	+	0.179550i	$0.0574641\pi$
$38$	10052.6	+	17411.6i	1.12932	+	1.95605i
$39$		0			0
$40$	17500.7	−	30312.1i	1.72944	−	2.99548i
$41$	14232.7			1.32229			0.661147	−	0.750256i	$-0.270070\pi$
$41$	14232.7			1.32229			0.661147	+	0.750256i	$0.270070\pi$
$42$		0			0
$43$	−14827.9			−1.22295			−0.611475	−	0.791264i	$-0.709424\pi$
$43$	−14827.9			−1.22295			−0.611475	+	0.791264i	$0.709424\pi$
$44$	21123.8	−	36587.5i	1.64490	−	2.84906i
$45$		0			0
$46$	−6108.08	−	10579.5i	−0.425608	−	0.737175i
$47$	−5774.88	+	10002.4i	−0.381328	+	0.660479i	−0.991252	−	0.131981i	$-0.957866\pi$
$47$	−5774.88	+	10002.4i	−0.381328	+	0.660479i	0.609925	+	0.792459i	$0.291200\pi$
$48$		0			0
$49$	12128.1	−	11635.5i	0.721610	−	0.692300i
$50$	15167.5			0.858004
$51$		0			0
$52$	−3097.28	−	5364.64i	−0.158844	−	0.275127i
$53$	−2338.86	−	4051.02i	−0.114371	−	0.198096i	0.803157	−	0.595767i	$-0.203152\pi$
$53$	−2338.86	−	4051.02i	−0.114371	−	0.198096i	−0.917528	+	0.397671i	$0.869818\pi$
$54$		0			0
$55$	35265.6			1.57197
$56$	−62393.5	+	25089.9i	−2.65870	+	1.06913i
$57$		0			0
$58$	−20448.2	+	35417.3i	−0.798150	+	1.38244i
$59$	14551.0	+	25203.0i	0.544205	+	0.942590i	0.998656	+	0.0518189i	$0.0165019\pi$
$59$	14551.0	+	25203.0i	0.544205	+	0.942590i	−0.454452	+	0.890771i	$0.650165\pi$
$60$		0			0
$61$	−5921.45	+	10256.2i	−0.203753	+	0.352910i	−0.949735	−	0.313056i	$-0.898647\pi$
$61$	−5921.45	+	10256.2i	−0.203753	+	0.352910i	0.745982	+	0.665966i	$0.231980\pi$
$62$	−110618.			−3.65466
$63$		0			0
$64$	59989.5			1.83073
$65$	2585.41	−	4478.06i	0.0759008	−	0.131464i
$66$		0			0
$67$	18106.3	+	31361.0i	0.492768	+	0.853499i	0.999965	−	0.00833093i	$-0.00265185\pi$
$67$	18106.3	+	31361.0i	0.492768	+	0.853499i	−0.507197	+	0.861830i	$0.669319\pi$
$68$	51313.5	−	88877.6i	1.34573	−	2.33088i
$69$		0			0
$70$	−73128.1	−	57326.9i	−1.78377	−	1.39834i
$71$	13477.6			0.317298			0.158649	−	0.987335i	$-0.449286\pi$
$71$	13477.6			0.317298			0.158649	+	0.987335i	$0.449286\pi$
$72$		0			0
$73$	−1304.23	−	2258.98i	−0.0286448	−	0.0496142i	0.851348	−	0.524602i	$-0.175786\pi$
$73$	−1304.23	−	2258.98i	−0.0286448	−	0.0496142i	−0.879992	+	0.474988i	$0.842452\pi$
$74$	29754.6	+	51536.5i	0.631648	+	1.09405i
$75$		0			0
$76$	−152996.			−3.03842
$77$	−53324.8	−	41802.6i	−1.02495	−	0.803483i
$78$		0			0
$79$	39160.2	−	67827.4i	0.705955	−	1.22275i	−0.260391	−	0.965503i	$-0.583852\pi$
$79$	39160.2	−	67827.4i	0.705955	−	1.22275i	0.966346	−	0.257246i	$-0.0828151\pi$
$80$	98629.9	+	170832.i	1.72299	+	2.98431i
$81$		0			0
$82$	−75592.3	+	130930.i	−1.24149	+	2.15032i
$83$	−16746.0			−0.266819			−0.133410	−	0.991061i	$-0.542593\pi$
$83$	−16746.0			−0.266819			−0.133410	+	0.991061i	$0.542593\pi$
$84$		0			0
$85$	85666.5			1.28607
$86$	78753.5	−	136405.i	1.14822	−	1.98877i
$87$		0			0
$88$	135557.	+	234791.i	1.86601	+	3.23202i
$89$	18384.2	−	31842.4i	0.246020	−	0.426119i	−0.716398	−	0.697692i	$-0.754210\pi$
$89$	18384.2	−	31842.4i	0.246020	−	0.426119i	0.962418	+	0.271573i	$0.0875437\pi$
$90$		0			0
$91$	−9217.51	+	3706.58i	−0.116684	+	0.0469213i
$92$	92962.7			1.14509
$93$		0			0
$94$	−61342.7	−	106249.i	−0.716050	−	1.24023i
$95$	−63855.9	−	110602.i	−0.725925	−	1.25734i
$96$		0			0
$97$	36133.4			0.389924			0.194962	−	0.980811i	$-0.437542\pi$
$97$	36133.4			0.389924			0.194962	+	0.980811i	$0.437542\pi$
$98$	42623.0	+	173367.i	0.448310	+	1.82348i
$99$		0			0
$100$	−57711.0	+	99958.4i	−0.577110	+	0.999584i
$101$	−49337.6	−	85455.2i	−0.481254	−	0.833557i	0.518514	−	0.855069i	$-0.326485\pi$
$101$	−49337.6	−	85455.2i	−0.481254	−	0.833557i	−0.999769	+	0.0215120i	$0.993152\pi$
$102$		0			0
$103$	−3636.75	+	6299.03i	−0.0337769	+	0.0585034i	−0.882420	−	0.470463i	$-0.844087\pi$
$103$	−3636.75	+	6299.03i	−0.0337769	+	0.0585034i	0.848643	+	0.528966i	$0.177420\pi$
$104$	39751.9			0.360392
$105$		0			0
$106$	49688.3			0.429526
$107$	−15476.8	+	26806.5i	−0.130683	+	0.226350i	−0.923940	−	0.382537i	$-0.875050\pi$
$107$	−15476.8	+	26806.5i	−0.130683	+	0.226350i	0.793257	+	0.608887i	$0.208384\pi$
$108$		0			0
$109$	−56915.6	−	98580.8i	−0.458844	−	0.794742i	0.540056	−	0.841629i	$-0.318403\pi$
$109$	−56915.6	−	98580.8i	−0.458844	−	0.794742i	−0.998900	+	0.0468875i	$0.985070\pi$
$110$	−187302.	+	324416.i	−1.47591	+	2.55635i
$111$		0			0
$112$	53360.9	−	375226.i	0.401955	−	2.82649i
$113$	894.559			0.00659041			0.00329521	−	0.999995i	$-0.498951\pi$
$113$	894.559			0.00659041			0.00329521	+	0.999995i	$0.498951\pi$
$114$		0			0
$115$	38799.7	+	67203.0i	0.273579	+	0.473854i
$116$	−155607.	−	269519.i	−1.07370	−	1.85970i
$117$		0			0
$118$	−309131.			−2.04379
$119$	−129535.	−	101546.i	−0.838535	−	0.657348i
$120$		0			0
$121$	−56054.3	+	97088.9i	−0.348053	+	0.602846i
$122$	−62899.6	−	108945.i	−0.382603	−	0.662687i
$123$		0			0
$124$	420891.	−	729005.i	2.45819	−	4.25771i
$125$	114513.			0.655509
$126$		0			0
$127$	72325.9			0.397910			0.198955	−	0.980009i	$-0.436245\pi$
$127$	72325.9			0.397910			0.198955	+	0.980009i	$0.436245\pi$
$128$	−87343.4	+	151283.i	−0.471200	+	0.816142i
$129$		0			0
$130$	27463.1	+	47567.5i	0.142525	+	0.246861i
$131$	−35084.0	+	60767.3i	−0.178620	+	0.309380i	−0.941408	−	0.337269i	$-0.890497\pi$
$131$	−35084.0	+	60767.3i	−0.178620	+	0.309380i	0.762788	+	0.646649i	$0.223830\pi$
$132$		0			0
$133$	−34547.4	+	242932.i	−0.169350	+	1.19085i
$134$	−384662.			−1.85062
$135$		0			0
$136$	329291.	+	570348.i	1.52662	+	2.64419i
$137$	186004.	+	322169.i	0.846685	+	1.46650i	0.884150	+	0.467203i	$0.154738\pi$
$137$	186004.	+	322169.i	0.846685	+	1.46650i	−0.0374656	+	0.999298i	$0.511928\pi$
$138$		0			0
$139$	5566.26			0.0244358			0.0122179	−	0.999925i	$-0.496111\pi$
$139$	5566.26			0.0244358			0.0122179	+	0.999925i	$0.496111\pi$
$140$	656047.	−	263812.i	2.82888	−	1.13756i
$141$		0			0
$142$	−71581.9	+	123984.i	−0.297908	+	0.515992i
$143$	20026.0	+	34686.1i	0.0818944	+	0.141845i
$144$		0			0
$145$	129891.	−	224977.i	0.513048	−	0.888625i
$146$	27707.8			0.107577
$147$		0			0
$148$	−452854.			−1.69943
$149$	−166957.	+	289178.i	−0.616083	+	1.06709i	0.374110	+	0.927384i	$0.377948\pi$
$149$	−166957.	+	289178.i	−0.616083	+	1.06709i	−0.990193	+	0.139703i	$0.955385\pi$
$150$		0			0
$151$	−37578.6	−	65088.1i	−0.134122	−	0.232305i	0.791140	−	0.611635i	$-0.209488\pi$
$151$	−37578.6	−	65088.1i	−0.134122	−	0.232305i	−0.925262	+	0.379330i	$0.876155\pi$
$152$	490907.	−	850277.i	1.72342	−	2.98505i
$153$		0			0
$154$	667768.	−	268525.i	2.26894	−	0.912396i
$155$	702667.			2.34920
$156$		0			0
$157$	−237792.	−	411868.i	−0.769926	−	1.33355i	−0.937603	−	0.347708i	$-0.886960\pi$
$157$	−237792.	−	411868.i	−0.769926	−	1.33355i	0.167677	−	0.985842i	$-0.446373\pi$
$158$	415972.	+	720485.i	1.32563	+	2.29606i
$159$		0			0
$160$	−975314.			−3.01193
$161$	20991.4	−	147609.i	0.0638231	−	0.448794i
$162$		0			0
$163$	−119611.	+	207173.i	−0.352617	+	0.610751i	−0.986707	−	0.162508i	$-0.948042\pi$
$163$	−119611.	+	207173.i	−0.352617	+	0.610751i	0.634090	+	0.773259i	$0.281375\pi$
$164$	−575243.	−	996351.i	−1.67010	−	2.89270i
$165$		0			0
$166$	88941.0	−	154050.i	0.250514	−	0.433903i
$167$	111308.			0.308842			0.154421	−	0.988005i	$-0.450649\pi$
$167$	111308.			0.308842			0.154421	+	0.988005i	$0.450649\pi$
$168$		0			0
$169$	−365420.			−0.984183
$170$	−454989.	+	788064.i	−1.20748	+	2.09141i
$171$		0			0
$172$	599299.	+	1.03802e6i	1.54462	+	2.67537i
$173$	−349497.	+	605346.i	−0.887826	+	1.53776i	−0.0453864	+	0.998970i	$0.514452\pi$
$173$	−349497.	+	605346.i	−0.887826	+	1.53776i	−0.842440	+	0.538791i	$0.818881\pi$
$174$		0			0
$175$	145685.	+	114206.i	0.359601	+	0.281900i
$176$	−1.52793e6			−3.71810
$177$		0			0
$178$	195284.	+	338241.i	0.461972	+	0.800159i
$179$	51954.4	+	89987.7i	0.121196	+	0.209918i	0.920240	−	0.391355i	$-0.127994\pi$
$179$	51954.4	+	89987.7i	0.121196	+	0.209918i	−0.799043	+	0.601273i	$0.794660\pi$
$180$		0			0
$181$	−415260.			−0.942159			−0.471079	−	0.882091i	$-0.656135\pi$
$181$	−415260.			−0.942159			−0.471079	+	0.882091i	$0.656135\pi$
$182$	14858.1	−	104480.i	0.0332495	−	0.233806i
$183$		0			0
$184$	−298282.	+	516639.i	−0.649504	+	1.12497i
$185$	−189007.	−	327370.i	−0.406021	−	0.703249i
$186$		0			0
$187$	−331777.	+	574654.i	−0.693812	+	1.20172i
$188$	933613.			1.92651
$189$		0			0
$190$	1.35660e6			2.72626
$191$	285058.	−	493735.i	0.565392	−	0.979287i	−0.431621	−	0.902055i	$-0.642058\pi$
$191$	285058.	−	493735.i	0.565392	−	0.979287i	0.997013	−	0.0772324i	$-0.0246083\pi$
$192$		0			0
$193$	−148854.	−	257823.i	−0.287653	−	0.498229i	0.685596	−	0.727982i	$-0.259542\pi$
$193$	−148854.	−	257823.i	−0.287653	−	0.498229i	−0.973249	+	0.229753i	$0.926208\pi$
$194$	−191911.	+	332399.i	−0.366096	+	0.634097i
$195$		0			0
$196$	−1.30472e6	−	378747.i	−2.42591	−	0.704221i
$197$	−410678.			−0.753938			−0.376969	−	0.926226i	$-0.623034\pi$
$197$	−410678.			−0.753938			−0.376969	+	0.926226i	$0.623034\pi$
$198$		0			0
$199$	349672.	+	605650.i	0.625934	+	1.08415i	0.988359	+	0.152137i	$0.0486155\pi$
$199$	349672.	+	605650.i	0.625934	+	1.08415i	−0.362425	+	0.932013i	$0.618051\pi$
$200$	−370345.	−	641457.i	−0.654684	−	1.13395i
$201$		0			0
$202$	1.04816e6			1.80738
$203$	−463086.	+	186218.i	−0.788718	+	0.317162i
$204$		0			0
$205$	480177.	−	831691.i	0.798025	−	1.38222i
$206$	−38630.8	−	66910.4i	−0.0634257	−	0.109857i
$207$		0			0
$208$	−112016.	+	194018.i	−0.179524	+	0.310945i
$209$	989226.			1.56650
$210$		0			0
$211$	−58292.9			−0.0901384			−0.0450692	−	0.998984i	$-0.514351\pi$
$211$	−58292.9			−0.0901384			−0.0450692	+	0.998984i	$0.514351\pi$
$212$	−189059.	+	327460.i	−0.288907	+	0.500402i
$213$		0			0
$214$	−164399.	−	284748.i	−0.245395	−	0.425036i
$215$	−500257.	+	866471.i	−0.738069	+	1.27837i
$216$		0			0
$217$	−1.06250e6	−	832916.i	−1.53171	−	1.20075i
$218$	1.20915e6			1.72322
$219$		0			0
$220$	−1.42533e6	−	2.46875e6i	−1.98545	−	3.43890i
$221$	48646.7	+	84258.6i	0.0669997	+	0.116047i
$222$		0			0
$223$	25758.5			0.0346864			0.0173432	−	0.999850i	$-0.494479\pi$
$223$	25758.5			0.0346864			0.0173432	+	0.999850i	$0.494479\pi$
$224$	1.47476e6	+	1.15610e6i	1.96382	+	1.53949i
$225$		0			0
$226$	−4751.15	+	8229.23i	−0.00618768	+	0.0107174i
$227$	−491123.	−	850649.i	−0.632594	−	1.09569i	−0.987019	−	0.160601i	$-0.948657\pi$
$227$	−491123.	−	850649.i	−0.632594	−	1.09569i	0.354425	−	0.935084i	$-0.384677\pi$
$228$		0			0
$229$	−259982.	+	450301.i	−0.327607	+	0.567433i	−0.982037	−	0.188691i	$-0.939576\pi$
$229$	−259982.	+	450301.i	−0.327607	+	0.567433i	0.654429	+	0.756123i	$0.272909\pi$
$230$	−824286.			−1.02744
$231$		0			0
$232$	1.99713e6			2.43605
$233$	609703.	−	1.05604e6i	0.735747	−	1.27435i	−0.218648	−	0.975804i	$-0.570165\pi$
$233$	609703.	−	1.05604e6i	0.735747	−	1.27435i	0.954395	−	0.298547i	$-0.0965020\pi$
$234$		0			0
$235$	389660.	+	674912.i	0.460274	+	0.797218i
$236$	1.17621e6	−	2.03726e6i	1.37469	−	2.38104i
$237$		0			0
$238$	1.62213e6	−	652296.i	1.85628	−	0.746453i
$239$	909357.			1.02977			0.514884	−	0.857260i	$-0.327835\pi$
$239$	909357.			1.02977			0.514884	+	0.857260i	$0.327835\pi$
$240$		0			0
$241$	320798.	+	555638.i	0.355786	+	0.616240i	0.987252	−	0.159164i	$-0.0508798\pi$
$241$	320798.	+	555638.i	0.355786	+	0.616240i	−0.631466	+	0.775404i	$0.717546\pi$
$242$	−595428.	−	1.03131e6i	−0.653568	−	1.13201i
$243$		0			0
$244$	957308.			1.02938
$245$	−270749.	−	1.10126e6i	−0.288172	−	1.17213i
$246$		0			0
$247$	72522.6	−	125613.i	0.0756365	−	0.131006i
$248$	2.70096e6	+	4.67820e6i	2.78862	+	4.83003i
$249$		0			0
$250$	−608196.	+	1.05343e6i	−0.615451	+	1.06599i
$251$	−1.92052e6			−1.92413			−0.962066	−	0.272816i	$-0.912045\pi$
$251$	−1.92052e6			−1.92413			−0.962066	+	0.272816i	$0.912045\pi$
$252$		0			0
$253$	−601067.			−0.590366
$254$	−384135.	+	665342.i	−0.373594	+	0.647084i
$255$		0			0
$256$	32041.3	+	55497.2i	0.0305570	+	0.0529263i
$257$	−493184.	+	854221.i	−0.465775	+	0.806747i	−0.999236	−	0.0390781i	$-0.987558\pi$
$257$	−493184.	+	854221.i	−0.465775	+	0.806747i	0.533461	+	0.845825i	$0.320891\pi$
$258$		0			0
$259$	−102257.	+	719054.i	−0.0947202	+	0.666058i
$260$	−417978.			−0.383460
$261$		0			0
$262$	−372674.	−	645491.i	−0.335410	−	0.580948i
$263$	424509.	+	735272.i	0.378441	+	0.655479i	0.990836	−	0.135073i	$-0.0431270\pi$
$263$	424509.	+	735272.i	0.378441	+	0.655479i	−0.612395	+	0.790552i	$0.709794\pi$
$264$		0			0
$265$	−315630.			−0.276098
$266$	−2.05130e6	−	1.60806e6i	−1.77756	−	1.39347i
$267$		0			0
$268$	1.46360e6	−	2.53504e6i	1.24476	−	2.15599i
$269$	−866792.	−	1.50133e6i	−0.730355	−	1.26501i	−0.956732	−	0.290972i	$-0.906021\pi$
$269$	−866792.	−	1.50133e6i	−0.730355	−	1.26501i	0.226377	−	0.974040i	$-0.427312\pi$
$270$		0			0
$271$	527825.	−	914221.i	0.436583	−	0.756184i	−0.560840	−	0.827924i	$-0.689522\pi$
$271$	527825.	−	914221.i	0.436583	−	0.756184i	0.997423	+	0.0717397i	$0.0228551\pi$
$272$	−3.71161e6			−3.04187
$273$		0			0
$274$	−3.95160e6			−3.17978
$275$	373141.	−	646299.i	0.297537	−	0.515349i
$276$		0			0
$277$	−812463.	−	1.40723e6i	−0.636216	−	1.10196i	−0.986256	−	0.165223i	$-0.947166\pi$
$277$	−812463.	−	1.40723e6i	−0.636216	−	1.10196i	0.350041	−	0.936735i	$-0.386168\pi$
$278$	−29563.3	+	51205.2i	−0.0229425	+	0.0397377i
$279$		0			0
$280$	−638872.	+	4.49245e6i	−0.486988	+	3.42443i
$281$	1.56484e6			1.18224			0.591118	−	0.806585i	$-0.298687\pi$
$281$	1.56484e6			1.18224			0.591118	+	0.806585i	$0.298687\pi$
$282$		0			0
$283$	347107.	+	601206.i	0.257630	+	0.446229i	0.965607	−	0.260007i	$-0.0837250\pi$
$283$	347107.	+	601206.i	0.257630	+	0.446229i	−0.707976	+	0.706236i	$0.750392\pi$
$284$	−544725.	−	943491.i	−0.400757	−	0.694132i
$285$		0			0
$286$	−425446.			−0.307560
$287$	−1.71193e6	+	688406.i	−1.22682	+	0.493333i
$288$		0			0
$289$	−96015.8	+	166304.i	−0.0676236	+	0.117127i
$290$	1.37974e6	+	2.38978e6i	0.963392	+	1.66864i
$291$		0			0
$292$	−105426.	+	182603.i	−0.0723585	+	0.125329i
$293$	−999262.			−0.680002			−0.340001	−	0.940425i	$-0.610427\pi$
$293$	−999262.			−0.680002			−0.340001	+	0.940425i	$0.610427\pi$
$294$		0			0
$295$	1.96366e6			1.31374
$296$	1.45304e6	−	2.51673e6i	0.963934	−	1.66958i
$297$		0			0
$298$	−1.77347e6	−	3.07175e6i	−1.15687	−	2.00376i
$299$	−44065.7	+	76324.0i	−0.0285051	+	0.0493723i
$300$		0			0
$301$	1.78352e6	−	717195.i	1.13465	−	0.456269i
$302$	798346.			0.503702
$303$		0			0
$304$	2.76664e6	+	4.79196e6i	1.71699	+	2.97392i
$305$	399550.	+	692041.i	0.245936	+	0.425973i
$306$		0			0
$307$	800764.			0.484907			0.242453	−	0.970163i	$-0.422048\pi$
$307$	800764.			0.484907			0.242453	+	0.970163i	$0.422048\pi$
$308$	−771134.	+	5.42250e6i	−0.463184	+	3.25704i
$309$		0			0
$310$	−3.73198e6	+	6.46398e6i	−2.20564	+	3.82029i
$311$	−291472.	−	504844.i	−0.170882	−	0.295976i	0.767847	−	0.640634i	$-0.221328\pi$
$311$	−291472.	−	504844.i	−0.170882	−	0.295976i	−0.938728	+	0.344658i	$0.887995\pi$
$312$		0			0
$313$	999546.	−	1.73126e6i	0.576689	−	0.998855i	−0.419166	−	0.907909i	$-0.637678\pi$
$313$	999546.	−	1.73126e6i	0.576689	−	0.998855i	0.995856	−	0.0909459i	$-0.0289890\pi$
$314$	5.05182e6			2.89150
$315$		0			0
$316$	−6.33095e6			−3.56657
$317$	901038.	−	1.56064e6i	0.503610	−	0.872279i	−0.496381	−	0.868105i	$-0.665338\pi$
$317$	901038.	−	1.56064e6i	0.503610	−	0.872279i	0.999991	−	0.00417407i	$-0.00132865\pi$
$318$		0			0
$319$	1.00610e6	+	1.74262e6i	0.553561	+	0.958797i
$320$	2.02390e6	−	3.50549e6i	1.10488	−	1.91370i
$321$		0			0
$322$	1.24639e6	+	977079.i	0.669909	+	0.525158i
$323$	2.40301e6			1.28159
$324$		0			0
$325$	−54711.8	−	94763.6i	−0.0287324	−	0.0497660i
$326$	−1.27055e6	−	2.20066e6i	−0.662138	−	1.14686i
$327$		0			0
$328$	7.38295e6			3.78918
$329$	210815.	−	1.48242e6i	0.107377	−	0.755058i
$330$		0			0
$331$	−51885.5	+	89868.4i	−0.0260301	+	0.0450855i	−0.878747	−	0.477288i	$-0.841620\pi$
$331$	−51885.5	+	89868.4i	−0.0260301	+	0.0450855i	0.852717	+	0.522373i	$0.174953\pi$
$332$	676824.	+	1.17229e6i	0.337001	+	0.583702i
$333$		0			0
$334$	−591176.	+	1.02395e6i	−0.289969	+	0.502240i
$335$	2.44345e6			1.18957
$336$		0			0
$337$	961978.			0.461414			0.230707	−	0.973023i	$-0.425896\pi$
$337$	961978.			0.461414			0.230707	+	0.973023i	$0.425896\pi$
$338$	1.94081e6	−	3.36158e6i	0.924040	−	1.60048i
$339$		0			0
$340$	−3.46238e6	−	5.99702e6i	−1.62434	−	2.81344i
$341$	−2.72135e6	+	4.71351e6i	−1.26735	+	2.19512i
$342$		0			0
$343$	−895997.	+	1.98614e6i	−0.411217	+	0.911537i
$344$	−7.69169e6			−3.50450
$345$		0			0
$346$	−3.71247e6	−	6.43019e6i	−1.66714	−	2.88758i
$347$	1.21674e6	+	2.10746e6i	0.542468	+	0.939582i	0.998762	+	0.0497528i	$0.0158433\pi$
$347$	1.21674e6	+	2.10746e6i	0.542468	+	0.939582i	−0.456294	+	0.889829i	$0.650823\pi$
$348$		0			0
$349$	−3.42269e6			−1.50419			−0.752096	−	0.659053i	$-0.770957\pi$
$349$	−3.42269e6			−1.50419			−0.752096	+	0.659053i	$0.770957\pi$
$350$	−1.82437e6	+	733621.i	−0.796053	+	0.320112i
$351$		0			0
$352$	3.77728e6	−	6.54244e6i	1.62488	−	2.81438i
$353$	1.92748e6	+	3.33850e6i	0.823292	+	1.42598i	0.903218	+	0.429183i	$0.141198\pi$
$353$	1.92748e6	+	3.33850e6i	0.823292	+	1.42598i	−0.0799253	+	0.996801i	$0.525468\pi$
$354$		0			0
$355$	454702.	−	787567.i	0.191494	−	0.331678i
$356$	−2.97214e6			−1.24292
$357$		0			0
$358$	−1.10375e6			−0.455161
$359$	−1.24184e6	+	2.15094e6i	−0.508547	+	0.880829i	0.491404	+	0.870932i	$0.336484\pi$
$359$	−1.24184e6	+	2.15094e6i	−0.508547	+	0.880829i	−0.999951	+	0.00989749i	$0.996849\pi$
$360$		0			0
$361$	−553154.	−	958091.i	−0.223397	−	0.386936i
$362$	2.20552e6	−	3.82007e6i	0.884584	−	1.53214i
$363$		0			0
$364$	632020.	+	495456.i	0.250022	+	0.195998i
$365$	−176005.			−0.0691503
$366$		0			0
$367$	2.03612e6	+	3.52666e6i	0.789111	+	1.36678i	0.926512	+	0.376265i	$0.122792\pi$
$367$	2.03612e6	+	3.52666e6i	0.789111	+	1.36678i	−0.137401	+	0.990516i	$0.543875\pi$
$368$	−1.68105e6	−	2.91166e6i	−0.647083	−	1.12078i
$369$		0			0
$370$	4.01539e6			1.52484
$371$	477260.	+	374136.i	0.180020	+	0.141122i
$372$		0			0
$373$	2.34636e6	−	4.06402e6i	0.873218	−	1.51246i	0.0145699	−	0.999894i	$-0.495362\pi$
$373$	2.34636e6	−	4.06402e6i	0.873218	−	1.51246i	0.858649	−	0.512565i	$-0.171305\pi$
$374$	−3.52424e6	−	6.10417e6i	−1.30283	−	2.25656i
$375$		0			0
$376$	−2.99561e6	+	5.18854e6i	−1.09274	+	1.89267i
$377$	295040.			0.106912
$378$		0			0
$379$	5.04599e6			1.80446			0.902232	−	0.431251i	$-0.141928\pi$
$379$	5.04599e6			1.80446			0.902232	+	0.431251i	$0.141928\pi$
$380$	−5.16173e6	+	8.94037e6i	−1.83373	+	3.17612i
$381$		0			0
$382$	3.02798e6	+	5.24461e6i	1.06168	+	1.83889i
$383$	826418.	−	1.43140e6i	0.287874	−	0.498613i	−0.685428	−	0.728141i	$-0.740385\pi$
$383$	826418.	−	1.43140e6i	0.287874	−	0.498613i	0.973302	+	0.229528i	$0.0737181\pi$
$384$		0			0
$385$	−4.24179e6	+	1.70572e6i	−1.45847	+	0.586485i
$386$	3.16236e6			1.08030
$387$		0			0
$388$	−1.46040e6	−	2.52950e6i	−0.492486	−	0.853011i
$389$	1.45727e6	+	2.52407e6i	0.488278	+	0.845722i	0.999909	−	0.0134832i	$-0.00429195\pi$
$389$	1.45727e6	+	2.52407e6i	0.488278	+	0.845722i	−0.511631	+	0.859205i	$0.670959\pi$
$390$		0			0
$391$	−1.46010e6			−0.482992
$392$	6.29122e6	−	6.03569e6i	2.06785	−	1.98386i
$393$		0			0
$394$	2.18118e6	−	3.77791e6i	0.707865	−	1.22606i
$395$	−2.64234e6	−	4.57666e6i	−0.852109	−	1.47590i
$396$		0			0
$397$	237471.	−	411312.i	0.0756197	−	0.130977i	−0.825736	−	0.564057i	$-0.809240\pi$
$397$	237471.	−	411312.i	0.0756197	−	0.130977i	0.901356	+	0.433080i	$0.142573\pi$
$398$	−7.42867e6			−2.35073
$399$		0			0
$400$	4.17436e6			1.30449
$401$	24440.9	−	42332.8i	0.00759025	−	0.0131467i	−0.862205	−	0.506559i	$-0.830917\pi$
$401$	24440.9	−	42332.8i	0.00759025	−	0.0131467i	0.869796	+	0.493412i	$0.164251\pi$
$402$		0			0
$403$	399018.	+	691119.i	0.122385	+	0.211978i
$404$	−3.98816e6	+	6.90769e6i	−1.21568	+	2.10562i
$405$		0			0
$406$	746470.	−	5.24906e6i	0.224749	−	1.58040i
$407$	2.92801e6			0.876166
$408$		0			0
$409$	−1.86947e6	−	3.23802e6i	−0.552599	−	0.957130i	−0.998086	−	0.0618416i	$-0.980303\pi$
$409$	−1.86947e6	−	3.23802e6i	−0.552599	−	0.957130i	0.445487	−	0.895289i	$-0.353031\pi$
$410$	5.10060e6	+	8.83450e6i	1.49852	+	2.59551i
$411$		0			0
$412$	587946.			0.170645
$413$	−2.96923e6	−	2.32765e6i	−0.856581	−	0.671495i
$414$		0			0
$415$	−564970.	+	978557.i	−0.161029	+	0.278911i
$416$	−553843.	−	959285.i	−0.156911	−	0.271778i
$417$		0			0
$418$	−5.25395e6	+	9.10010e6i	−1.47077	+	2.54745i
$419$	681425.			0.189619			0.0948097	−	0.995495i	$-0.469776\pi$
$419$	681425.			0.189619			0.0948097	+	0.995495i	$0.469776\pi$
$420$		0			0
$421$	1.54803e6			0.425670			0.212835	−	0.977088i	$-0.431730\pi$
$421$	1.54803e6			0.425670			0.212835	+	0.977088i	$0.431730\pi$
$422$	309604.	−	536249.i	0.0846301	−	0.146584i
$423$		0			0
$424$	−1.21324e6	−	2.10139e6i	−0.327742	−	0.567665i
$425$	906425.	−	1.56997e6i	0.243422	−	0.421619i
$426$		0			0
$427$	216165.	−	1.52004e6i	0.0573741	−	0.403446i
$428$	2.50210e6			0.660229
$429$		0			0
$430$	−5.31390e6	−	9.20394e6i	−1.38593	−	2.40051i
$431$	−3.18855e6	−	5.52273e6i	−0.826799	−	1.43206i	−0.900536	−	0.434781i	$-0.856826\pi$
$431$	−3.18855e6	−	5.52273e6i	−0.826799	−	1.43206i	0.0737367	−	0.997278i	$-0.476508\pi$
$432$		0			0
$433$	1.32669e6			0.340056			0.170028	−	0.985439i	$-0.445614\pi$
$433$	1.32669e6			0.340056			0.170028	+	0.985439i	$0.445614\pi$
$434$	1.33053e7	−	5.35036e6i	3.39078	−	1.36351i
$435$		0			0
$436$	−4.60072e6	+	7.96868e6i	−1.15907	+	2.00757i
$437$	1.08836e6	+	1.88509e6i	0.272627	+	0.472203i
$438$		0			0
$439$	−1.92664e6	+	3.33704e6i	−0.477133	+	0.826419i	−0.999657	−	0.0262059i	$-0.991657\pi$
$439$	−1.92664e6	+	3.33704e6i	−0.477133	+	0.826419i	0.522523	+	0.852625i	$0.324991\pi$
$440$	1.82934e7			4.50466
$441$		0			0
$442$	−1.03348e6			−0.251622
$443$	−645522.	+	1.11808e6i	−0.156279	+	0.270684i	−0.933524	−	0.358515i	$-0.883283\pi$
$443$	−645522.	+	1.11808e6i	−0.156279	+	0.270684i	0.777245	+	0.629198i	$0.216617\pi$
$444$		0			0
$445$	−1.24048e6	−	2.14857e6i	−0.296954	−	0.514339i
$446$	−136808.	+	236958.i	−0.0325667	+	0.0564072i
$447$		0			0
$448$	−7.21560e6	+	2.90156e6i	−1.69855	+	0.683026i
$449$	−7.49006e6			−1.75335			−0.876677	−	0.481080i	$-0.840245\pi$
$449$	−7.49006e6			−1.75335			−0.876677	+	0.481080i	$0.840245\pi$
$450$		0			0
$451$	3.71934e6	+	6.44209e6i	0.861042	+	1.49137i
$452$	−36155.4	−	62622.9i	−0.00832390	−	0.0144174i
$453$		0			0
$454$	1.04337e7			2.37575
$455$	−94381.7	+	663678.i	−0.0213727	+	0.150289i
$456$		0			0
$457$	−249662.	+	432427.i	−0.0559193	+	0.0968550i	−0.892630	−	0.450790i	$-0.851142\pi$
$457$	−249662.	+	432427.i	−0.0559193	+	0.0968550i	0.836711	+	0.547645i	$0.184476\pi$
$458$	−2.76161e6	−	4.78325e6i	−0.615175	−	1.06551i
$459$		0			0
$460$	3.13633e6	−	5.43229e6i	0.691079	−	1.19698i
$461$	5.34926e6			1.17231			0.586153	−	0.810200i	$-0.300642\pi$
$461$	5.34926e6			1.17231			0.586153	+	0.810200i	$0.300642\pi$
$462$		0			0
$463$	−6.52516e6			−1.41462			−0.707308	−	0.706906i	$-0.750091\pi$
$463$	−6.52516e6			−1.41462			−0.707308	+	0.706906i	$0.750091\pi$
$464$	−5.62768e6	+	9.74743e6i	−1.21348	+	2.10182i
$465$		0			0
$466$	6.47647e6	+	1.12176e7i	1.38157	+	2.39295i
$467$	−1.60324e6	+	2.77690e6i	−0.340179	+	0.589207i	−0.984466	−	0.175577i	$-0.943821\pi$
$467$	−1.60324e6	+	2.77690e6i	−0.340179	+	0.589207i	0.644287	+	0.764784i	$0.277154\pi$
$468$		0			0
$469$	−3.69471e6	−	2.89637e6i	−0.775619	−	0.608027i
$470$	−8.27821e6			−1.72859
$471$		0			0
$472$	7.54804e6	+	1.30736e7i	1.55948	+	2.70110i
$473$	−3.87488e6	−	6.71149e6i	−0.796352	−	1.37932i
$474$		0			0
$475$	−2.70260e6			−0.549602
$476$	−1.87322e6	+	1.31722e7i	−0.378941	+	2.66466i
$477$		0			0
$478$	−4.82975e6	+	8.36536e6i	−0.966840	+	1.67462i
$479$	−4.43405e6	−	7.68001e6i	−0.883003	−	1.52941i	−0.847985	−	0.530019i	$-0.822185\pi$
$479$	−4.43405e6	−	7.68001e6i	−0.883003	−	1.52941i	−0.0350175	−	0.999387i	$-0.511149\pi$
$480$		0			0
$481$	214660.	−	371801.i	0.0423046	−	0.0732737i
$482$	−6.81525e6			−1.33618
$483$		0			0
$484$	9.06218e6			1.75841
$485$	1.21905e6	−	2.11146e6i	0.235325	−	0.407595i
$486$		0			0
$487$	−2.92361e6	−	5.06384e6i	−0.558595	−	0.967515i	−0.997614	−	0.0690371i	$-0.978007\pi$
$487$	−2.92361e6	−	5.06384e6i	−0.558595	−	0.967515i	0.439019	−	0.898478i	$-0.355326\pi$
$488$	−3.07164e6	+	5.32023e6i	−0.583876	+	1.01130i
$489$		0			0
$490$	1.15687e7	+	3.35829e6i	2.17668	+	0.631871i
$491$	114241.			0.0213854			0.0106927	−	0.999943i	$-0.496596\pi$
$491$	114241.			0.0213854			0.0106927	+	0.999943i	$0.496596\pi$
$492$		0			0
$493$	2.44400e6	+	4.23314e6i	0.452881	+	0.784414i
$494$	770360.	+	1.33430e6i	0.142029	+	0.246001i
$495$		0			0
$496$	−3.04439e7			−5.55644
$497$	−1.62110e6	+	651884.i	−0.294388	+	0.118380i
$498$		0			0
$499$	4.67241e6	−	8.09285e6i	0.840020	−	1.45496i	−0.0498573	−	0.998756i	$-0.515877\pi$
$499$	4.67241e6	−	8.09285e6i	0.840020	−	1.45496i	0.889877	−	0.456200i	$-0.150790\pi$
$500$	−4.62826e6	−	8.01638e6i	−0.827928	−	1.43401i
$501$		0			0
$502$	1.02002e7	−	1.76673e7i	1.80655	−	3.12904i
$503$	892118.			0.157218			0.0786091	−	0.996906i	$-0.474952\pi$
$503$	892118.			0.157218			0.0786091	+	0.996906i	$0.474952\pi$
$504$		0			0
$505$	−6.65812e6			−1.16178
$506$	3.19237e6	−	5.52934e6i	0.554289	−	0.960057i
$507$		0			0
$508$	−2.92320e6	−	5.06313e6i	−0.502573	−	0.870481i
$509$	3.42011e6	−	5.92381e6i	0.585122	−	1.01346i	−0.409739	−	0.912203i	$-0.634380\pi$
$509$	3.42011e6	−	5.92381e6i	0.585122	−	1.01346i	0.994860	−	0.101257i	$-0.0322865\pi$
$510$		0			0
$511$	266136.	+	208631.i	0.0450870	+	0.0353448i
$512$	−6.27068e6			−1.05716
$513$		0			0
$514$	−5.23877e6	−	9.07382e6i	−0.874624	−	1.51489i
$515$	245390.	+	425028.i	0.0407698	+	0.0706154i
$516$		0			0
$517$	−6.03644e6			−0.993241
$518$	−6.07163e6	−	4.75970e6i	−0.994216	−	0.779391i
$519$		0			0
$520$	1.34113e6	−	2.32291e6i	0.217502	−	0.376725i
$521$	4.45943e6	+	7.72397e6i	0.719756	+	1.24665i	0.961096	+	0.276214i	$0.0890798\pi$
$521$	4.45943e6	+	7.72397e6i	0.719756	+	1.24665i	−0.241340	+	0.970441i	$0.577587\pi$
$522$		0			0
$523$	−305911.	+	529854.i	−0.0489037	+	0.0847036i	−0.889441	−	0.457050i	$-0.848906\pi$
$523$	−305911.	+	529854.i	−0.0489037	+	0.0847036i	0.840537	+	0.541754i	$0.182239\pi$
$524$	5.67196e6			0.902413
$525$		0			0
$526$	−9.01856e6			−1.42126
$527$	−6.61064e6	+	1.14500e7i	−1.03685	+	1.79588i
$528$		0			0
$529$	2.55687e6	+	4.42863e6i	0.397255	+	0.688066i
$530$	1.67636e6	−	2.90354e6i	0.259226	−	0.448992i
$531$		0			0
$532$	1.84026e7	−	7.40012e6i	2.81903	−	1.13360i
$533$	1.09070e6			0.166298
$534$		0			0
$535$	1.04430e6	+	1.80877e6i	0.157739	+	0.273212i
$536$	9.39229e6	+	1.62679e7i	1.41208	+	2.44580i
$537$		0			0
$538$	1.84147e7			2.74289
$539$	8.43587e6	+	2.44886e6i	1.25071	+	0.363071i
$540$		0			0
$541$	122172.	−	211607.i	0.0179464	−	0.0310840i	−0.856913	−	0.515461i	$-0.827621\pi$
$541$	122172.	−	211607.i	0.0179464	−	0.0310840i	0.874859	+	0.484377i	$0.160954\pi$
$542$	5.60674e6	+	9.71116e6i	0.819808	+	1.41995i
$543$		0			0
$544$	9.17568e6	−	1.58927e7i	1.32936	−	2.30251i
$545$	−7.68078e6			−1.10768
$546$		0			0
$547$	−7.55551e6			−1.07968			−0.539840	−	0.841767i	$-0.681515\pi$
$547$	−7.55551e6			−1.07968			−0.539840	+	0.841767i	$0.681515\pi$
$548$	1.50355e7	−	2.60422e7i	2.13878	−	3.70447i
$549$		0			0
$550$	3.96363e6	+	6.86520e6i	0.558709	+	0.967713i
$551$	3.64353e6	−	6.31077e6i	0.511261	−	0.885530i
$552$		0			0
$553$	−1.42956e6	+	1.00525e7i	−0.198788	+	1.39785i
$554$	1.72605e7			2.38935
$555$		0			0
$556$	−224972.	−	389662.i	−0.0308632	−	0.0534566i
$557$	1.28638e6	+	2.22808e6i	0.175684	+	0.304293i	0.940398	−	0.340077i	$-0.110453\pi$
$557$	1.28638e6	+	2.22808e6i	0.175684	+	0.304293i	−0.764714	+	0.644370i	$0.777120\pi$
$558$		0			0
$559$	−1.13631e6			−0.153804
$560$	−2.01261e7	−	1.57773e7i	−2.71200	−	2.12600i
$561$		0			0
$562$	−8.31113e6	+	1.43953e7i	−1.10999	+	1.92256i
$563$	5.53466e6	+	9.58632e6i	0.735903	+	1.27462i	0.954326	+	0.298767i	$0.0965752\pi$
$563$	5.53466e6	+	9.58632e6i	0.735903	+	1.27462i	−0.218424	+	0.975854i	$0.570091\pi$
$564$		0			0
$565$	30180.2	−	52273.7i	0.00397742	−	0.00688909i
$566$	−7.37416e6			−0.967546
$567$		0			0
$568$	6.99126e6			0.909253
$569$	1.55605e6	−	2.69515e6i	0.201485	−	0.348982i	−0.747522	−	0.664237i	$-0.768757\pi$
$569$	1.55605e6	−	2.69515e6i	0.201485	−	0.348982i	0.949007	+	0.315255i	$0.102090\pi$
$570$		0			0
$571$	−2.86862e6	−	4.96859e6i	−0.368199	−	0.637739i	0.621085	−	0.783743i	$-0.286692\pi$
$571$	−2.86862e6	−	4.96859e6i	−0.368199	−	0.637739i	−0.989284	+	0.146004i	$0.953359\pi$
$572$	1.61878e6	−	2.80381e6i	0.206870	−	0.358310i
$573$		0			0
$574$	2.75953e6	−	1.94046e7i	0.349587	−	2.45825i
$575$	1.64214e6			0.207128
$576$		0			0
$577$	5.56528e6	+	9.63935e6i	0.695901	+	1.20534i	0.969876	+	0.243599i	$0.0783282\pi$
$577$	5.56528e6	+	9.63935e6i	0.695901	+	1.20534i	−0.273975	+	0.961737i	$0.588338\pi$
$578$	−1.01991e6	−	1.76654e6i	−0.126982	−	0.219940i
$579$		0			0
$580$	−2.09992e7			−2.59198
$581$	2.01423e6	−	809970.i	0.247554	−	0.0995472i
$582$		0			0
$583$	1.22240e6	−	2.11725e6i	0.148950	−	0.257989i
$584$	−676542.	−	1.17180e6i	−0.0820848	−	0.142175i
$585$		0			0
$586$	5.30725e6	−	9.19242e6i	0.638448	−	1.10582i
$587$	−7.71211e6			−0.923800			−0.461900	−	0.886932i	$-0.652832\pi$
$587$	−7.71211e6			−0.923800			−0.461900	+	0.886932i	$0.652832\pi$
$588$		0			0
$589$	1.97103e7			2.34102
$590$	−1.04293e7	+	1.80641e7i	−1.23346	+	2.13642i
$591$		0			0
$592$	8.18897e6	+	1.41837e7i	0.960340	+	1.66336i
$593$	4.16650e6	−	7.21660e6i	0.486558	−	0.842744i	−0.513322	−	0.858196i	$-0.671585\pi$
$593$	4.16650e6	−	7.21660e6i	0.486558	−	0.842744i	0.999881	+	0.0154520i	$0.00491872\pi$
$594$		0			0
$595$	−1.03041e7	+	4.14351e6i	−1.19321	+	0.479817i
$596$	2.69916e7			3.11253
$597$		0			0
$598$	−468081.	−	810739.i	−0.0535264	−	0.0927104i
$599$	2.66790e6	+	4.62094e6i	0.303811	+	0.526216i	0.976996	−	0.213258i	$-0.0684076\pi$
$599$	2.66790e6	+	4.62094e6i	0.303811	+	0.526216i	−0.673185	+	0.739474i	$0.735074\pi$
$600$		0			0
$601$	−7.53972e6			−0.851470			−0.425735	−	0.904848i	$-0.639984\pi$
$601$	−7.53972e6			−0.851470			−0.425735	+	0.904848i	$0.639984\pi$
$602$	−2.87493e6	+	2.02161e7i	−0.323323	+	2.27356i
$603$		0			0
$604$	−3.03763e6	+	5.26133e6i	−0.338799	+	0.586818i
$605$	3.78227e6	+	6.55108e6i	0.420111	+	0.727654i
$606$		0			0
$607$	4.84283e6	−	8.38802e6i	0.533491	−	0.924034i	−0.465744	−	0.884920i	$-0.654213\pi$
$607$	4.84283e6	−	8.38802e6i	0.533491	−	0.924034i	0.999235	−	0.0391140i	$-0.0124536\pi$
$608$	−2.73582e7			−3.00144
$609$		0			0
$610$	−8.48831e6			−0.923627
$611$	−442547.	+	766513.i	−0.0479574	+	0.0830647i
$612$		0			0
$613$	−6.83805e6	−	1.18438e7i	−0.734989	−	1.27304i	−0.954728	−	0.297480i	$-0.903854\pi$
$613$	−6.83805e6	−	1.18438e7i	−0.734989	−	1.27304i	0.219739	−	0.975559i	$-0.429479\pi$
$614$	−4.25299e6	+	7.36639e6i	−0.455275	+	0.788559i
$615$		0			0
$616$	−2.76612e7	−	2.16843e7i	−2.93711	−	2.30247i
$617$	−1.53796e7			−1.62642			−0.813211	−	0.581969i	$-0.802283\pi$
$617$	−1.53796e7			−1.62642			−0.813211	+	0.581969i	$0.802283\pi$
$618$		0			0
$619$	−2.70804e6	−	4.69046e6i	−0.284072	−	0.492027i	0.688312	−	0.725415i	$-0.258352\pi$
$619$	−2.70804e6	−	4.69046e6i	−0.284072	−	0.492027i	−0.972384	+	0.233388i	$0.925019\pi$
$620$	−2.83997e7	−	4.91897e7i	−2.96711	−	5.13919i
$621$		0			0
$622$	6.19223e6			0.641757
$623$	−671125.	+	4.71925e6i	−0.0692761	+	0.487139i
$624$		0			0
$625$	6.09446e6	−	1.05559e7i	0.624072	−	1.08092i
$626$	1.06175e7	+	1.83901e7i	1.08290	+	1.87563i
$627$		0			0
$628$	−1.92217e7	+	3.32930e7i	−1.94488	+	3.36863i
$629$	7.11266e6			0.716812
$630$		0			0
$631$	1.44178e7			1.44154			0.720770	−	0.693174i	$-0.243788\pi$
$631$	1.44178e7			1.44154			0.720770	+	0.693174i	$0.243788\pi$
$632$	2.03136e7	−	3.51842e7i	2.02299	−	3.50392i
$633$		0			0
$634$	9.57112e6	+	1.65777e7i	0.945670	+	1.63795i
$635$	2.44010e6	−	4.22638e6i	0.240145	−	0.415943i
$636$		0			0
$637$	929413.	−	891663.i	0.0907528	−	0.0870667i
$638$	−2.13743e7			−2.07893
$639$		0			0
$640$	5.89350e6	+	1.02078e7i	0.568753	+	0.985109i
$641$	3.06909e6	+	5.31582e6i	0.295029	+	0.511005i	0.974992	−	0.222242i	$-0.0713375\pi$
$641$	3.06909e6	+	5.31582e6i	0.295029	+	0.511005i	−0.679963	+	0.733247i	$0.738004\pi$
$642$		0			0
$643$	−402177.			−0.0383610			−0.0191805	−	0.999816i	$-0.506106\pi$
$643$	−402177.			−0.0383610			−0.0191805	+	0.999816i	$0.506106\pi$
$644$	−1.11817e7	+	4.49641e6i	−1.06241	+	0.427219i
$645$		0			0
$646$	−1.27628e7	+	2.21058e7i	−1.20327	+	2.08413i
$647$	6.64081e6	+	1.15022e7i	0.623678	+	1.08024i	0.988795	+	0.149280i	$0.0476955\pi$
$647$	6.64081e6	+	1.15022e7i	0.623678	+	1.08024i	−0.365117	+	0.930961i	$0.618971\pi$
$648$		0			0
$649$	−7.60502e6	+	1.31723e7i	−0.708743	+	1.22758i
$650$	1.16233e6			0.107906
$651$		0			0
$652$	1.93373e7			1.78147
$653$	5.63657e6	−	9.76282e6i	0.517287	−	0.895968i	−0.482511	−	0.875890i	$-0.660275\pi$
$653$	5.63657e6	−	9.76282e6i	0.517287	−	0.895968i	0.999798	−	0.0200780i	$-0.00639144\pi$
$654$		0			0
$655$	2.36730e6	+	4.10028e6i	0.215601	+	0.373431i
$656$	−2.08043e7	+	3.60341e7i	−1.88753	+	3.26929i
$657$		0			0
$658$	1.25174e7	+	9.81269e6i	1.12707	+	0.883534i
$659$	−9.29624e6			−0.833861			−0.416930	−	0.908938i	$-0.636894\pi$
$659$	−9.29624e6			−0.833861			−0.416930	+	0.908938i	$0.636894\pi$
$660$		0			0
$661$	314386.	+	544533.i	0.0279872	+	0.0484753i	0.879680	−	0.475566i	$-0.157757\pi$
$661$	314386.	+	544533.i	0.0279872	+	0.0484753i	−0.851693	+	0.524042i	$0.824424\pi$
$662$	−551146.	−	954612.i	−0.0488789	−	0.0846607i
$663$		0			0
$664$	−8.68669e6			−0.764599
$665$	1.30302e7	+	1.02147e7i	1.14261	+	0.895720i
$666$		0			0
$667$	−2.21385e6	+	3.83451e6i	−0.192679	+	0.333730i
$668$	−4.49874e6	−	7.79205e6i	−0.390077	−	0.675633i
$669$		0			0
$670$	−1.29776e7	+	2.24778e7i	−1.11688	+	1.93449i
$671$	−6.18965e6			−0.530713
$672$		0			0
$673$	5.15635e6			0.438838			0.219419	−	0.975631i	$-0.429584\pi$
$673$	5.15635e6			0.438838			0.219419	+	0.975631i	$0.429584\pi$
$674$	−5.10923e6	+	8.84944e6i	−0.433217	+	0.750354i
$675$		0			0
$676$	1.47692e7	+	2.55810e7i	1.24305	+	2.15303i
$677$	−3.28149e6	+	5.68370e6i	−0.275169	+	0.476606i	−0.970178	−	0.242395i	$-0.922067\pi$
$677$	−3.28149e6	+	5.68370e6i	−0.275169	+	0.476606i	0.695009	+	0.719001i	$0.255400\pi$
$678$		0			0
$679$	−4.34617e6	+	1.74770e6i	−0.361770	+	0.145476i
$680$	4.44379e7			3.68537
$681$		0			0
$682$	−2.89071e7	−	5.00685e7i	−2.37982	−	4.12196i
$683$	−1.00766e7	−	1.74532e7i	−0.826540	−	1.43161i	−0.900737	−	0.434365i	$-0.856973\pi$
$683$	−1.00766e7	−	1.74532e7i	−0.826540	−	1.43161i	0.0741975	−	0.997244i	$-0.476360\pi$
$684$		0			0
$685$	2.51013e7			2.04395
$686$	−1.35121e7	−	1.87912e7i	−1.09626	−	1.52456i
$687$		0			0
$688$	2.16743e7	−	3.75410e7i	1.74572	−	3.02367i
$689$	−179234.	−	310442.i	−0.0143838	−	0.0249134i
$690$		0			0
$691$	5.05979e6	−	8.76382e6i	0.403123	−	0.698229i	−0.590978	−	0.806688i	$-0.701258\pi$
$691$	5.05979e6	−	8.76382e6i	0.403123	−	0.698229i	0.994101	+	0.108458i	$0.0345914\pi$
$692$	5.65024e7			4.48541
$693$		0			0
$694$	−2.58492e7			−2.03727
$695$	187792.	−	325265.i	0.0147474	−	0.0255432i
$696$		0			0
$697$	9.03494e6	+	1.56490e7i	0.704439	+	1.22012i
$698$	1.81785e7	−	3.14860e7i	1.41227	−	2.44613i
$699$		0			0
$700$	2.10677e6	−	1.48145e7i	0.162507	−	1.14272i
$701$	3.27446e6			0.251678			0.125839	−	0.992051i	$-0.459838\pi$
$701$	3.27446e6			0.251678			0.125839	+	0.992051i	$0.459838\pi$
$702$		0			0
$703$	−5.30178e6	−	9.18295e6i	−0.404607	−	0.700800i
$704$	1.56767e7	+	2.71528e7i	1.19212	+	2.06482i
$705$		0			0
$706$	−4.09488e7			−3.09193
$707$	1.00677e7	+	7.89230e6i	0.757496	+	0.593820i
$708$		0			0
$709$	−2.99723e6	+	5.19136e6i	−0.223926	+	0.387851i	−0.955997	−	0.293377i	$-0.905221\pi$
$709$	−2.99723e6	+	5.19136e6i	−0.223926	+	0.387851i	0.732071	+	0.681229i	$0.238554\pi$
$710$	4.83000e6	+	8.36580e6i	0.359585	+	0.622819i
$711$		0			0
$712$	9.53647e6	−	1.65177e7i	0.704998	−	1.22109i
$713$	−1.19762e7			−0.882260
$714$		0			0
$715$	2.70251e6			0.197698
$716$	4.19968e6	−	7.27406e6i	0.306150	−	0.530267i
$717$		0			0
$718$	−1.31913e7	−	2.28480e7i	−0.954940	−	1.65400i
$719$	1.23868e7	−	2.14546e7i	0.893590	−	1.54774i	0.0580490	−	0.998314i	$-0.481512\pi$
$719$	1.23868e7	−	2.14546e7i	0.893590	−	1.54774i	0.835541	−	0.549429i	$-0.185155\pi$
$720$		0			0
$721$	132761.	−	933557.i	0.00951115	−	0.0668810i
$722$	1.17516e7			0.838983
$723$		0			0
$724$	1.67836e7	+	2.90700e7i	1.18998	+	2.06110i
$725$	−2.74871e6	−	4.76091e6i	−0.194215	−	0.336391i
$726$		0			0
$727$	−1.16194e7			−0.815357			−0.407678	−	0.913126i	$-0.633662\pi$
$727$	−1.16194e7			−0.815357			−0.407678	+	0.913126i	$0.633662\pi$
$728$	−4.78141e6	+	1.92272e6i	−0.334370	+	0.134458i
$729$		0			0
$730$	934794.	−	1.61911e6i	0.0649245	−	0.112453i
$731$	−9.41277e6	−	1.63034e7i	−0.651514	−	1.12846i
$732$		0			0
$733$	6.37168e6	−	1.10361e7i	0.438020	−	0.758674i	−0.559516	−	0.828819i	$-0.689013\pi$
$733$	6.37168e6	−	1.10361e7i	0.438020	−	0.758674i	0.997537	+	0.0701457i	$0.0223464\pi$
$734$	−4.32567e7			−2.96356
$735$		0			0
$736$	1.66232e7			1.13115
$737$	−9.46319e6	+	1.63907e7i	−0.641754	+	1.11155i
$738$		0			0
$739$	−6.04589e6	−	1.04718e7i	−0.407238	−	0.705358i	0.587341	−	0.809340i	$-0.300175\pi$
$739$	−6.04589e6	−	1.04718e7i	−0.407238	−	0.705358i	−0.994579	+	0.103982i	$0.966842\pi$
$740$	−1.52782e7	+	2.64626e7i	−1.02563	+	1.77645i
$741$		0			0
$742$	−5.97656e6	+	2.40332e6i	−0.398512	+	0.160251i
$743$	−9.79136e6			−0.650685			−0.325343	−	0.945596i	$-0.605480\pi$
$743$	−9.79136e6			−0.650685			−0.325343	+	0.945596i	$0.605480\pi$
$744$		0			0
$745$	1.12654e7	+	1.95123e7i	0.743632	+	1.28801i
$746$	2.49238e7	+	4.31694e7i	1.63971	+	2.84007i
$747$		0			0
$748$	5.36376e7			3.50522
$749$	564986.	−	3.97290e6i	0.0367988	−	0.258763i
$750$		0			0
$751$	8.76513e6	−	1.51816e7i	0.567098	−	0.982243i	−0.429753	−	0.902947i	$-0.641399\pi$
$751$	8.76513e6	−	1.51816e7i	0.567098	−	0.982243i	0.996851	−	0.0792967i	$-0.0252674\pi$
$752$	−1.68825e7	−	2.92414e7i	−1.08866	−	1.88562i
$753$		0			0
$754$	−1.56701e6	+	2.71413e6i	−0.100379	+	0.173861i
$755$	−5.07125e6			−0.323778
$756$		0			0
$757$	6.01558e6			0.381538			0.190769	−	0.981635i	$-0.438902\pi$
$757$	6.01558e6			0.381538			0.190769	+	0.981635i	$0.438902\pi$
$758$	−2.68001e7	+	4.64191e7i	−1.69419	+	2.93443i
$759$		0			0
$760$	−3.31240e7	−	5.73725e7i	−2.08022	−	3.60305i
$761$	6.38402e6	−	1.10575e7i	0.399607	−	0.692139i	−0.594071	−	0.804413i	$-0.702480\pi$
$761$	6.38402e6	−	1.10575e7i	0.399607	−	0.692139i	0.993677	+	0.112274i	$0.0358133\pi$
$762$		0			0
$763$	1.16140e7	+	9.10452e6i	0.722223	+	0.566168i
$764$	−4.60847e7			−2.85643
$765$		0			0
$766$	8.77849e6	+	1.52048e7i	0.540565	+	0.936286i
$767$	1.11509e6	+	1.93139e6i	0.0684416	+	0.118544i
$768$		0			0
$769$	−6.32718e6			−0.385829			−0.192914	−	0.981216i	$-0.561794\pi$
$769$	−6.32718e6			−0.385829			−0.192914	+	0.981216i	$0.561794\pi$
$770$	6.83754e6	−	4.80805e7i	0.415597	−	2.92242i
$771$		0			0
$772$	−1.20325e7	+	2.08409e7i	−0.726628	+	1.25856i
$773$	−8.10085e6	−	1.40311e7i	−0.487620	−	0.844583i	0.512279	−	0.858819i	$-0.328802\pi$
$773$	−8.10085e6	−	1.40311e7i	−0.487620	−	0.844583i	−0.999899	+	0.0142365i	$0.995468\pi$
$774$		0			0
$775$	7.43482e6	−	1.28775e7i	0.444648

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)

\(f(q)\)	\(=\)	\(q+(-5.31117 + 9.19921i) q^{2} +(-40.4170 - 70.0043i) q^{4} +(33.7376 - 58.4352i) q^{5} +(-120.281 + 48.3679i) q^{7} +518.731 q^{8} +O(q^{10})\)	\(q+(-5.31117 + 9.19921i) q^{2} +(-40.4170 - 70.0043i) q^{4} +(33.7376 - 58.4352i) q^{5} +(-120.281 + 48.3679i) q^{7} +518.731 q^{8} +(358.372 + 620.718i) q^{10} +(261.323 + 452.625i) q^{11} +76.6331 q^{13} +(193.887 - 1363.38i) q^{14} +(-1461.72 + 2531.78i) q^{16} +(634.801 + 1099.51i) q^{17} +(946.362 - 1639.15i) q^{19} -5454.28 q^{20} -5551.73 q^{22} +(-575.022 + 995.967i) q^{23} +(-713.945 - 1236.59i) q^{25} +(-407.011 + 704.964i) q^{26} +(8247.36 + 6465.31i) q^{28} +3850.03 q^{29} +(5206.86 + 9018.55i) q^{31} +(-7227.21 - 12517.9i) q^{32} -13486.1 q^{34} +(-1231.60 + 8660.46i) q^{35} +(2801.14 - 4851.71i) q^{37} +(10052.6 + 17411.6i) q^{38} +(17500.7 - 30312.1i) q^{40} +14232.7 q^{41} -14827.9 q^{43} +(21123.8 - 36587.5i) q^{44} +(-6108.08 - 10579.5i) q^{46} +(-5774.88 + 10002.4i) q^{47} +(12128.1 - 11635.5i) q^{49} +15167.5 q^{50} +(-3097.28 - 5364.64i) q^{52} +(-2338.86 - 4051.02i) q^{53} +35265.6 q^{55} +(-62393.5 + 25089.9i) q^{56} +(-20448.2 + 35417.3i) q^{58} +(14551.0 + 25203.0i) q^{59} +(-5921.45 + 10256.2i) q^{61} -110618. q^{62} +59989.5 q^{64} +(2585.41 - 4478.06i) q^{65} +(18106.3 + 31361.0i) q^{67} +(51313.5 - 88877.6i) q^{68} +(-73128.1 - 57326.9i) q^{70} +13477.6 q^{71} +(-1304.23 - 2258.98i) q^{73} +(29754.6 + 51536.5i) q^{74} -152996. q^{76} +(-53324.8 - 41802.6i) q^{77} +(39160.2 - 67827.4i) q^{79} +(98629.9 + 170832. i) q^{80} +(-75592.3 + 130930. i) q^{82} -16746.0 q^{83} +85666.5 q^{85} +(78753.5 - 136405. i) q^{86} +(135557. + 234791. i) q^{88} +(18384.2 - 31842.4i) q^{89} +(-9217.51 + 3706.58i) q^{91} +92962.7 q^{92} +(-61342.7 - 106249. i) q^{94} +(-63855.9 - 110602. i) q^{95} +36133.4 q^{97} +(42623.0 + 173367. i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 182 q^{4} + 142 q^{7}+O(q^{10}) \) 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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