LMFDB - Embedded newform 3750.2.a.v.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3750,2,Mod(1,3750)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3750, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("3750.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3750 = 2 \cdot 3 \cdot 5^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3750.a (trivial)

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:	yes
Analytic conductor:	$29.9439007580$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.8.71684000000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} - 18x^{6} + 10x^{5} + 101x^{4} + 40x^{3} - 132x^{2} - 96x - 4 $ x^8 - 2x^7 - 18x^6 + 10x^5 + 101x^4 + 40x^3 - 132x^2 - 96*x - 4
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 5^{2} $
Twist minimal:	no (minimal twist has level 150)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$1.37243$ of defining polynomial
Character	$\chi$	$=$	3750.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} -0.329315 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} -0.329315 q^{7} +1.00000 q^{8} +1.00000 q^{9} -5.03339 q^{11} +1.00000 q^{12} -0.482152 q^{13} -0.329315 q^{14} +1.00000 q^{16} +6.78610 q^{17} +1.00000 q^{18} +5.44012 q^{19} -0.329315 q^{21} -5.03339 q^{22} +6.50055 q^{23} +1.00000 q^{24} -0.482152 q^{26} +1.00000 q^{27} -0.329315 q^{28} -6.02216 q^{29} +1.31869 q^{31} +1.00000 q^{32} -5.03339 q^{33} +6.78610 q^{34} +1.00000 q^{36} +0.780139 q^{37} +5.44012 q^{38} -0.482152 q^{39} +12.5205 q^{41} -0.329315 q^{42} -2.47582 q^{43} -5.03339 q^{44} +6.50055 q^{46} -4.38040 q^{47} +1.00000 q^{48} -6.89155 q^{49} +6.78610 q^{51} -0.482152 q^{52} -1.68591 q^{53} +1.00000 q^{54} -0.329315 q^{56} +5.44012 q^{57} -6.02216 q^{58} +1.01583 q^{59} +4.18808 q^{61} +1.31869 q^{62} -0.329315 q^{63} +1.00000 q^{64} -5.03339 q^{66} +3.14433 q^{67} +6.78610 q^{68} +6.50055 q^{69} +5.71189 q^{71} +1.00000 q^{72} +2.94269 q^{73} +0.780139 q^{74} +5.44012 q^{76} +1.65757 q^{77} -0.482152 q^{78} +8.48510 q^{79} +1.00000 q^{81} +12.5205 q^{82} +17.1955 q^{83} -0.329315 q^{84} -2.47582 q^{86} -6.02216 q^{87} -5.03339 q^{88} +3.45233 q^{89} +0.158780 q^{91} +6.50055 q^{92} +1.31869 q^{93} -4.38040 q^{94} +1.00000 q^{96} -9.51004 q^{97} -6.89155 q^{98} -5.03339 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} + 8 q^{3} + 8 q^{4} + 8 q^{6} + 4 q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 + 8 * q^6 + 4 * q^7 + 8 * q^8 + 8 * q^9	$ 8 q + 8 q^{2} + 8 q^{3} + 8 q^{4} + 8 q^{6} + 4 q^{7} + 8 q^{8} + 8 q^{9} + 6 q^{11} + 8 q^{12} + 2 q^{13} + 4 q^{14} + 8 q^{16} + 14 q^{17} + 8 q^{18} + 10 q^{19} + 4 q^{21} + 6 q^{22} + 12 q^{23} + 8 q^{24} + 2 q^{26} + 8 q^{27} + 4 q^{28} + 10 q^{29} + 16 q^{31} + 8 q^{32} + 6 q^{33} + 14 q^{34} + 8 q^{36} - 6 q^{37} + 10 q^{38} + 2 q^{39} + 6 q^{41} + 4 q^{42} + 2 q^{43} + 6 q^{44} + 12 q^{46} + 14 q^{47} + 8 q^{48} + 26 q^{49} + 14 q^{51} + 2 q^{52} + 12 q^{53} + 8 q^{54} + 4 q^{56} + 10 q^{57} + 10 q^{58} + 16 q^{61} + 16 q^{62} + 4 q^{63} + 8 q^{64} + 6 q^{66} - 6 q^{67} + 14 q^{68} + 12 q^{69} + 6 q^{71} + 8 q^{72} - 8 q^{73} - 6 q^{74} + 10 q^{76} + 8 q^{77} + 2 q^{78} + 10 q^{79} + 8 q^{81} + 6 q^{82} + 22 q^{83} + 4 q^{84} + 2 q^{86} + 10 q^{87} + 6 q^{88} + 20 q^{89} + 6 q^{91} + 12 q^{92} + 16 q^{93} + 14 q^{94} + 8 q^{96} - 16 q^{97} + 26 q^{98} + 6 q^{99}+O(q^{100}) $ 8 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 + 8 * q^6 + 4 * q^7 + 8 * q^8 + 8 * q^9 + 6 * q^11 + 8 * q^12 + 2 * q^13 + 4 * q^14 + 8 * q^16 + 14 * q^17 + 8 * q^18 + 10 * q^19 + 4 * q^21 + 6 * q^22 + 12 * q^23 + 8 * q^24 + 2 * q^26 + 8 * q^27 + 4 * q^28 + 10 * q^29 + 16 * q^31 + 8 * q^32 + 6 * q^33 + 14 * q^34 + 8 * q^36 - 6 * q^37 + 10 * q^38 + 2 * q^39 + 6 * q^41 + 4 * q^42 + 2 * q^43 + 6 * q^44 + 12 * q^46 + 14 * q^47 + 8 * q^48 + 26 * q^49 + 14 * q^51 + 2 * q^52 + 12 * q^53 + 8 * q^54 + 4 * q^56 + 10 * q^57 + 10 * q^58 + 16 * q^61 + 16 * q^62 + 4 * q^63 + 8 * q^64 + 6 * q^66 - 6 * q^67 + 14 * q^68 + 12 * q^69 + 6 * q^71 + 8 * q^72 - 8 * q^73 - 6 * q^74 + 10 * q^76 + 8 * q^77 + 2 * q^78 + 10 * q^79 + 8 * q^81 + 6 * q^82 + 22 * q^83 + 4 * q^84 + 2 * q^86 + 10 * q^87 + 6 * q^88 + 20 * q^89 + 6 * q^91 + 12 * q^92 + 16 * q^93 + 14 * q^94 + 8 * q^96 - 16 * q^97 + 26 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	1.00000	0.408248
$7$	−0.329315	−0.124469	−0.0622347	−	0.998062i	$-0.519823\pi$
$7$	−0.329315	−0.124469	−0.0622347	+	0.998062i	$0.519823\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	0	0
$11$	−5.03339	−1.51762	−0.758812	−	0.651309i	$-0.774220\pi$
$11$	−5.03339	−1.51762	−0.758812	+	0.651309i	$0.774220\pi$
$12$	1.00000	0.288675
$13$	−0.482152	−0.133725	−0.0668625	−	0.997762i	$-0.521299\pi$
$13$	−0.482152	−0.133725	−0.0668625	+	0.997762i	$0.521299\pi$
$14$	−0.329315	−0.0880131
$15$	0	0
$16$	1.00000	0.250000
$17$	6.78610	1.64587	0.822935	−	0.568135i	$-0.192335\pi$
$17$	6.78610	1.64587	0.822935	+	0.568135i	$0.192335\pi$
$18$	1.00000	0.235702
$19$	5.44012	1.24805	0.624025	−	0.781404i	$-0.285496\pi$
$19$	5.44012	1.24805	0.624025	+	0.781404i	$0.285496\pi$
$20$	0	0
$21$	−0.329315	−0.0718624
$22$	−5.03339	−1.07312
$23$	6.50055	1.35546	0.677729	−	0.735312i	$-0.262964\pi$
$23$	6.50055	1.35546	0.677729	+	0.735312i	$0.262964\pi$
$24$	1.00000	0.204124
$25$	0	0
$26$	−0.482152	−0.0945578
$27$	1.00000	0.192450
$28$	−0.329315	−0.0622347
$29$	−6.02216	−1.11829	−0.559144	−	0.829071i	$-0.688870\pi$
$29$	−6.02216	−1.11829	−0.559144	+	0.829071i	$0.688870\pi$
$30$	0	0
$31$	1.31869	0.236844	0.118422	−	0.992963i	$-0.462216\pi$
$31$	1.31869	0.236844	0.118422	+	0.992963i	$0.462216\pi$
$32$	1.00000	0.176777
$33$	−5.03339	−0.876201
$34$	6.78610	1.16381
$35$	0	0
$36$	1.00000	0.166667
$37$	0.780139	0.128254	0.0641270	−	0.997942i	$-0.479574\pi$
$37$	0.780139	0.128254	0.0641270	+	0.997942i	$0.479574\pi$
$38$	5.44012	0.882504
$39$	−0.482152	−0.0772061
$40$	0	0
$41$	12.5205	1.95538	0.977689	−	0.210059i	$-0.0673657\pi$
$41$	12.5205	1.95538	0.977689	+	0.210059i	$0.0673657\pi$
$42$	−0.329315	−0.0508144
$43$	−2.47582	−0.377559	−0.188779	−	0.982020i	$-0.560453\pi$
$43$	−2.47582	−0.377559	−0.188779	+	0.982020i	$0.560453\pi$
$44$	−5.03339	−0.758812
$45$	0	0
$46$	6.50055	0.958454
$47$	−4.38040	−0.638946	−0.319473	−	0.947595i	$-0.603506\pi$
$47$	−4.38040	−0.638946	−0.319473	+	0.947595i	$0.603506\pi$
$48$	1.00000	0.144338
$49$	−6.89155	−0.984507
$50$	0	0
$51$	6.78610	0.950244
$52$	−0.482152	−0.0668625
$53$	−1.68591	−0.231578	−0.115789	−	0.993274i	$-0.536940\pi$
$53$	−1.68591	−0.231578	−0.115789	+	0.993274i	$0.536940\pi$
$54$	1.00000	0.136083
$55$	0	0
$56$	−0.329315	−0.0440066
$57$	5.44012	0.720562
$58$	−6.02216	−0.790749
$59$	1.01583	0.132250	0.0661250	−	0.997811i	$-0.478936\pi$
$59$	1.01583	0.132250	0.0661250	+	0.997811i	$0.478936\pi$
$60$	0	0
$61$	4.18808	0.536229	0.268114	−	0.963387i	$-0.413599\pi$
$61$	4.18808	0.536229	0.268114	+	0.963387i	$0.413599\pi$
$62$	1.31869	0.167474
$63$	−0.329315	−0.0414898
$64$	1.00000	0.125000
$65$	0	0
$66$	−5.03339	−0.619568
$67$	3.14433	0.384141	0.192070	−	0.981381i	$-0.438480\pi$
$67$	3.14433	0.384141	0.192070	+	0.981381i	$0.438480\pi$
$68$	6.78610	0.822935
$69$	6.50055	0.782574
$70$	0	0
$71$	5.71189	0.677876	0.338938	−	0.940809i	$-0.389932\pi$
$71$	5.71189	0.677876	0.338938	+	0.940809i	$0.389932\pi$
$72$	1.00000	0.117851
$73$	2.94269	0.344415	0.172208	−	0.985061i	$-0.444910\pi$
$73$	2.94269	0.344415	0.172208	+	0.985061i	$0.444910\pi$
$74$	0.780139	0.0906893
$75$	0	0
$76$	5.44012	0.624025
$77$	1.65757	0.188898
$78$	−0.482152	−0.0545930
$79$	8.48510	0.954648	0.477324	−	0.878727i	$-0.341607\pi$
$79$	8.48510	0.954648	0.477324	+	0.878727i	$0.341607\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	12.5205	1.38266
$83$	17.1955	1.88745	0.943725	−	0.330730i	$-0.107295\pi$
$83$	17.1955	1.88745	0.943725	+	0.330730i	$0.107295\pi$
$84$	−0.329315	−0.0359312
$85$	0	0
$86$	−2.47582	−0.266974
$87$	−6.02216	−0.645644
$88$	−5.03339	−0.536561
$89$	3.45233	0.365946	0.182973	−	0.983118i	$-0.441428\pi$
$89$	3.45233	0.365946	0.182973	+	0.983118i	$0.441428\pi$
$90$	0	0
$91$	0.158780	0.0166447
$92$	6.50055	0.677729
$93$	1.31869	0.136742
$94$	−4.38040	−0.451803
$95$	0	0
$96$	1.00000	0.102062
$97$	−9.51004	−0.965598	−0.482799	−	0.875731i	$-0.660380\pi$
$97$	−9.51004	−0.965598	−0.482799	+	0.875731i	$0.660380\pi$
$98$	−6.89155	−0.696152
$99$	−5.03339	−0.505875
$100$	0	0
$101$	19.2435	1.91480	0.957400	−	0.288765i	$-0.0932447\pi$
$101$	19.2435	1.91480	0.957400	+	0.288765i	$0.0932447\pi$
$102$	6.78610	0.671924
$103$	5.10689	0.503196	0.251598	−	0.967832i	$-0.419044\pi$
$103$	5.10689	0.503196	0.251598	+	0.967832i	$0.419044\pi$
$104$	−0.482152	−0.0472789
$105$	0	0
$106$	−1.68591	−0.163750
$107$	−15.3340	−1.48239	−0.741194	−	0.671290i	$-0.765740\pi$
$107$	−15.3340	−1.48239	−0.741194	+	0.671290i	$0.765740\pi$
$108$	1.00000	0.0962250
$109$	−9.76027	−0.934865	−0.467432	−	0.884029i	$-0.654821\pi$
$109$	−9.76027	−0.934865	−0.467432	+	0.884029i	$0.654821\pi$
$110$	0	0
$111$	0.780139	0.0740475
$112$	−0.329315	−0.0311173
$113$	1.51566	0.142581	0.0712905	−	0.997456i	$-0.477288\pi$
$113$	1.51566	0.142581	0.0712905	+	0.997456i	$0.477288\pi$
$114$	5.44012	0.509514
$115$	0	0
$116$	−6.02216	−0.559144
$117$	−0.482152	−0.0445750
$118$	1.01583	0.0935149
$119$	−2.23476	−0.204860
$120$	0	0
$121$	14.3350	1.30319
$122$	4.18808	0.379171
$123$	12.5205	1.12894
$124$	1.31869	0.118422
$125$	0	0
$126$	−0.329315	−0.0293377
$127$	12.6056	1.11856	0.559282	−	0.828977i	$-0.311077\pi$
$127$	12.6056	1.11856	0.559282	+	0.828977i	$0.311077\pi$
$128$	1.00000	0.0883883
$129$	−2.47582	−0.217984
$130$	0	0
$131$	14.0559	1.22807	0.614036	−	0.789278i	$-0.289545\pi$
$131$	14.0559	1.22807	0.614036	+	0.789278i	$0.289545\pi$
$132$	−5.03339	−0.438101
$133$	−1.79151	−0.155344
$134$	3.14433	0.271629
$135$	0	0
$136$	6.78610	0.581903
$137$	−6.68863	−0.571448	−0.285724	−	0.958312i	$-0.592234\pi$
$137$	−6.68863	−0.571448	−0.285724	+	0.958312i	$0.592234\pi$
$138$	6.50055	0.553364
$139$	−3.07799	−0.261072	−0.130536	−	0.991444i	$-0.541670\pi$
$139$	−3.07799	−0.261072	−0.130536	+	0.991444i	$0.541670\pi$
$140$	0	0
$141$	−4.38040	−0.368896
$142$	5.71189	0.479331
$143$	2.42686	0.202944
$144$	1.00000	0.0833333
$145$	0	0
$146$	2.94269	0.243538
$147$	−6.89155	−0.568406
$148$	0.780139	0.0641270
$149$	5.06465	0.414912	0.207456	−	0.978244i	$-0.433482\pi$
$149$	5.06465	0.414912	0.207456	+	0.978244i	$0.433482\pi$
$150$	0	0
$151$	−16.9581	−1.38003	−0.690015	−	0.723795i	$-0.742396\pi$
$151$	−16.9581	−1.38003	−0.690015	+	0.723795i	$0.742396\pi$
$152$	5.44012	0.441252
$153$	6.78610	0.548623
$154$	1.65757	0.133571
$155$	0	0
$156$	−0.482152	−0.0386031
$157$	−22.8284	−1.82190	−0.910952	−	0.412513i	$-0.864651\pi$
$157$	−22.8284	−1.82190	−0.910952	+	0.412513i	$0.864651\pi$
$158$	8.48510	0.675038
$159$	−1.68591	−0.133701
$160$	0	0
$161$	−2.14073	−0.168713
$162$	1.00000	0.0785674
$163$	7.95823	0.623337	0.311668	−	0.950191i	$-0.399112\pi$
$163$	7.95823	0.623337	0.311668	+	0.950191i	$0.399112\pi$
$164$	12.5205	0.977689
$165$	0	0
$166$	17.1955	1.33463
$167$	13.9503	1.07951	0.539754	−	0.841823i	$-0.318517\pi$
$167$	13.9503	1.07951	0.539754	+	0.841823i	$0.318517\pi$
$168$	−0.329315	−0.0254072
$169$	−12.7675	−0.982118
$170$	0	0
$171$	5.44012	0.416017
$172$	−2.47582	−0.188779
$173$	−19.5009	−1.48262	−0.741312	−	0.671161i	$-0.765796\pi$
$173$	−19.5009	−1.48262	−0.741312	+	0.671161i	$0.765796\pi$
$174$	−6.02216	−0.456539
$175$	0	0
$176$	−5.03339	−0.379406
$177$	1.01583	0.0763546
$178$	3.45233	0.258763
$179$	−18.9911	−1.41946	−0.709731	−	0.704473i	$-0.751183\pi$
$179$	−18.9911	−1.41946	−0.709731	+	0.704473i	$0.751183\pi$
$180$	0	0
$181$	−18.9484	−1.40842	−0.704211	−	0.709991i	$-0.748699\pi$
$181$	−18.9484	−1.40842	−0.704211	+	0.709991i	$0.748699\pi$
$182$	0.158780	0.0117695
$183$	4.18808	0.309592
$184$	6.50055	0.479227
$185$	0	0
$186$	1.31869	0.0966913
$187$	−34.1571	−2.49781
$188$	−4.38040	−0.319473
$189$	−0.329315	−0.0239541
$190$	0	0
$191$	−12.0933	−0.875040	−0.437520	−	0.899209i	$-0.644143\pi$
$191$	−12.0933	−0.875040	−0.437520	+	0.899209i	$0.644143\pi$
$192$	1.00000	0.0721688
$193$	−11.0357	−0.794368	−0.397184	−	0.917739i	$-0.630013\pi$
$193$	−11.0357	−0.794368	−0.397184	+	0.917739i	$0.630013\pi$
$194$	−9.51004	−0.682781
$195$	0	0
$196$	−6.89155	−0.492254
$197$	−20.6212	−1.46920	−0.734599	−	0.678502i	$-0.762630\pi$
$197$	−20.6212	−1.46920	−0.734599	+	0.678502i	$0.762630\pi$
$198$	−5.03339	−0.357708
$199$	18.5313	1.31365	0.656826	−	0.754042i	$-0.271899\pi$
$199$	18.5313	1.31365	0.656826	+	0.754042i	$0.271899\pi$
$200$	0	0
$201$	3.14433	0.221784
$202$	19.2435	1.35397
$203$	1.98319	0.139193
$204$	6.78610	0.475122
$205$	0	0
$206$	5.10689	0.355814
$207$	6.50055	0.451819
$208$	−0.482152	−0.0334312
$209$	−27.3823	−1.89407
$210$	0	0
$211$	15.7638	1.08523	0.542613	−	0.839983i	$-0.317435\pi$
$211$	15.7638	1.08523	0.542613	+	0.839983i	$0.317435\pi$
$212$	−1.68591	−0.115789
$213$	5.71189	0.391372
$214$	−15.3340	−1.04821
$215$	0	0
$216$	1.00000	0.0680414
$217$	−0.434265	−0.0294799
$218$	−9.76027	−0.661049
$219$	2.94269	0.198848
$220$	0	0
$221$	−3.27193	−0.220094
$222$	0.780139	0.0523595
$223$	−22.1782	−1.48516	−0.742582	−	0.669755i	$-0.766399\pi$
$223$	−22.1782	−1.48516	−0.742582	+	0.669755i	$0.766399\pi$
$224$	−0.329315	−0.0220033
$225$	0	0
$226$	1.51566	0.100820
$227$	11.0969	0.736528	0.368264	−	0.929721i	$-0.379952\pi$
$227$	11.0969	0.736528	0.368264	+	0.929721i	$0.379952\pi$
$228$	5.44012	0.360281
$229$	1.79879	0.118867	0.0594337	−	0.998232i	$-0.481071\pi$
$229$	1.79879	0.118867	0.0594337	+	0.998232i	$0.481071\pi$
$230$	0	0
$231$	1.65757	0.109060
$232$	−6.02216	−0.395374
$233$	3.70579	0.242774	0.121387	−	0.992605i	$-0.461266\pi$
$233$	3.70579	0.242774	0.121387	+	0.992605i	$0.461266\pi$
$234$	−0.482152	−0.0315193
$235$	0	0
$236$	1.01583	0.0661250
$237$	8.48510	0.551167
$238$	−2.23476	−0.144858
$239$	−16.8733	−1.09145	−0.545723	−	0.837966i	$-0.683745\pi$
$239$	−16.8733	−1.09145	−0.545723	+	0.837966i	$0.683745\pi$
$240$	0	0
$241$	20.6256	1.32861	0.664306	−	0.747461i	$-0.268727\pi$
$241$	20.6256	1.32861	0.664306	+	0.747461i	$0.268727\pi$
$242$	14.3350	0.921491
$243$	1.00000	0.0641500
$244$	4.18808	0.268114
$245$	0	0
$246$	12.5205	0.798279
$247$	−2.62297	−0.166895
$248$	1.31869	0.0837371
$249$	17.1955	1.08972
$250$	0	0
$251$	8.69615	0.548896	0.274448	−	0.961602i	$-0.411505\pi$
$251$	8.69615	0.548896	0.274448	+	0.961602i	$0.411505\pi$
$252$	−0.329315	−0.0207449
$253$	−32.7198	−2.05708
$254$	12.6056	0.790945
$255$	0	0
$256$	1.00000	0.0625000
$257$	7.10714	0.443331	0.221666	−	0.975123i	$-0.428851\pi$
$257$	7.10714	0.443331	0.221666	+	0.975123i	$0.428851\pi$
$258$	−2.47582	−0.154138
$259$	−0.256911	−0.0159637
$260$	0	0
$261$	−6.02216	−0.372763
$262$	14.0559	0.868378
$263$	−15.8609	−0.978028	−0.489014	−	0.872276i	$-0.662643\pi$
$263$	−15.8609	−0.978028	−0.489014	+	0.872276i	$0.662643\pi$
$264$	−5.03339	−0.309784
$265$	0	0
$266$	−1.79151	−0.109845
$267$	3.45233	0.211279
$268$	3.14433	0.192070
$269$	4.51935	0.275550	0.137775	−	0.990464i	$-0.456005\pi$
$269$	4.51935	0.275550	0.137775	+	0.990464i	$0.456005\pi$
$270$	0	0
$271$	11.1314	0.676186	0.338093	−	0.941113i	$-0.390218\pi$
$271$	11.1314	0.676186	0.338093	+	0.941113i	$0.390218\pi$
$272$	6.78610	0.411468
$273$	0.158780	0.00960980
$274$	−6.68863	−0.404075
$275$	0	0
$276$	6.50055	0.391287
$277$	−22.8338	−1.37195	−0.685975	−	0.727625i	$-0.740624\pi$
$277$	−22.8338	−1.37195	−0.685975	+	0.727625i	$0.740624\pi$
$278$	−3.07799	−0.184605
$279$	1.31869	0.0789481
$280$	0	0
$281$	28.7548	1.71537	0.857683	−	0.514179i	$-0.171903\pi$
$281$	28.7548	1.71537	0.857683	+	0.514179i	$0.171903\pi$
$282$	−4.38040	−0.260849
$283$	−19.3471	−1.15007	−0.575034	−	0.818130i	$-0.695011\pi$
$283$	−19.3471	−1.15007	−0.575034	+	0.818130i	$0.695011\pi$
$284$	5.71189	0.338938
$285$	0	0
$286$	2.42686	0.143503
$287$	−4.12320	−0.243385
$288$	1.00000	0.0589256
$289$	29.0511	1.70889
$290$	0	0
$291$	−9.51004	−0.557488
$292$	2.94269	0.172208
$293$	15.0301	0.878069	0.439035	−	0.898470i	$-0.355321\pi$
$293$	15.0301	0.878069	0.439035	+	0.898470i	$0.355321\pi$
$294$	−6.89155	−0.401923
$295$	0	0
$296$	0.780139	0.0453446
$297$	−5.03339	−0.292067
$298$	5.06465	0.293387
$299$	−3.13425	−0.181259
$300$	0	0
$301$	0.815324	0.0469945
$302$	−16.9581	−0.975829
$303$	19.2435	1.10551
$304$	5.44012	0.312012
$305$	0	0
$306$	6.78610	0.387935
$307$	19.7061	1.12468	0.562342	−	0.826905i	$-0.309900\pi$
$307$	19.7061	1.12468	0.562342	+	0.826905i	$0.309900\pi$
$308$	1.65757	0.0944489
$309$	5.10689	0.290521
$310$	0	0
$311$	28.2393	1.60130	0.800651	−	0.599130i	$-0.204487\pi$
$311$	28.2393	1.60130	0.800651	+	0.599130i	$0.204487\pi$
$312$	−0.482152	−0.0272965
$313$	−11.2478	−0.635764	−0.317882	−	0.948130i	$-0.602972\pi$
$313$	−11.2478	−0.635764	−0.317882	+	0.948130i	$0.602972\pi$
$314$	−22.8284	−1.28828
$315$	0	0
$316$	8.48510	0.477324
$317$	−23.2917	−1.30819	−0.654095	−	0.756412i	$-0.726950\pi$
$317$	−23.2917	−1.30819	−0.654095	+	0.756412i	$0.726950\pi$
$318$	−1.68591	−0.0945412
$319$	30.3119	1.69714
$320$	0	0
$321$	−15.3340	−0.855858
$322$	−2.14073	−0.119298
$323$	36.9172	2.05413
$324$	1.00000	0.0555556
$325$	0	0
$326$	7.95823	0.440766
$327$	−9.76027	−0.539744
$328$	12.5205	0.691330
$329$	1.44253	0.0795292
$330$	0	0
$331$	0.129334	0.00710883	0.00355441	−	0.999994i	$-0.498869\pi$
$331$	0.129334	0.00710883	0.00355441	+	0.999994i	$0.498869\pi$
$332$	17.1955	0.943725
$333$	0.780139	0.0427513
$334$	13.9503	0.763327
$335$	0	0
$336$	−0.329315	−0.0179656
$337$	0.538069	0.0293105	0.0146552	−	0.999893i	$-0.495335\pi$
$337$	0.538069	0.0293105	0.0146552	+	0.999893i	$0.495335\pi$
$338$	−12.7675	−0.694462
$339$	1.51566	0.0823192
$340$	0	0
$341$	−6.63750	−0.359441
$342$	5.44012	0.294168
$343$	4.57470	0.247010
$344$	−2.47582	−0.133487
$345$	0	0
$346$	−19.5009	−1.04837
$347$	−22.7156	−1.21944	−0.609719	−	0.792618i	$-0.708718\pi$
$347$	−22.7156	−1.21944	−0.609719	+	0.792618i	$0.708718\pi$
$348$	−6.02216	−0.322822
$349$	6.84350	0.366324	0.183162	−	0.983083i	$-0.441367\pi$
$349$	6.84350	0.366324	0.183162	+	0.983083i	$0.441367\pi$
$350$	0	0
$351$	−0.482152	−0.0257354
$352$	−5.03339	−0.268281
$353$	−16.7789	−0.893049	−0.446524	−	0.894771i	$-0.647338\pi$
$353$	−16.7789	−0.893049	−0.446524	+	0.894771i	$0.647338\pi$
$354$	1.01583	0.0539909
$355$	0	0
$356$	3.45233	0.182973
$357$	−2.23476	−0.118276
$358$	−18.9911	−1.00371
$359$	−7.46364	−0.393916	−0.196958	−	0.980412i	$-0.563106\pi$
$359$	−7.46364	−0.393916	−0.196958	+	0.980412i	$0.563106\pi$
$360$	0	0
$361$	10.5949	0.557628
$362$	−18.9484	−0.995905
$363$	14.3350	0.752395
$364$	0.158780	0.00832233
$365$	0	0
$366$	4.18808	0.218914
$367$	6.15474	0.321275	0.160637	−	0.987013i	$-0.448645\pi$
$367$	6.15474	0.321275	0.160637	+	0.987013i	$0.448645\pi$
$368$	6.50055	0.338865
$369$	12.5205	0.651792
$370$	0	0
$371$	0.555196	0.0288243
$372$	1.31869	0.0683711
$373$	−9.16928	−0.474767	−0.237384	−	0.971416i	$-0.576290\pi$
$373$	−9.16928	−0.474767	−0.237384	+	0.971416i	$0.576290\pi$
$374$	−34.1571	−1.76622
$375$	0	0
$376$	−4.38040	−0.225902
$377$	2.90360	0.149543
$378$	−0.329315	−0.0169381
$379$	−34.6321	−1.77893	−0.889465	−	0.457004i	$-0.848923\pi$
$379$	−34.6321	−1.77893	−0.889465	+	0.457004i	$0.848923\pi$
$380$	0	0
$381$	12.6056	0.645804
$382$	−12.0933	−0.618746
$383$	−9.52044	−0.486472	−0.243236	−	0.969967i	$-0.578209\pi$
$383$	−9.52044	−0.486472	−0.243236	+	0.969967i	$0.578209\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	−11.0357	−0.561703
$387$	−2.47582	−0.125853
$388$	−9.51004	−0.482799
$389$	−17.4454	−0.884515	−0.442258	−	0.896888i	$-0.645822\pi$
$389$	−17.4454	−0.884515	−0.442258	+	0.896888i	$0.645822\pi$
$390$	0	0
$391$	44.1134	2.23091
$392$	−6.89155	−0.348076
$393$	14.0559	0.709028
$394$	−20.6212	−1.03888
$395$	0	0
$396$	−5.03339	−0.252937
$397$	−13.5551	−0.680313	−0.340157	−	0.940369i	$-0.610480\pi$
$397$	−13.5551	−0.680313	−0.340157	+	0.940369i	$0.610480\pi$
$398$	18.5313	0.928892
$399$	−1.79151	−0.0896879
$400$	0	0
$401$	14.1105	0.704642	0.352321	−	0.935879i	$-0.385392\pi$
$401$	14.1105	0.704642	0.352321	+	0.935879i	$0.385392\pi$
$402$	3.14433	0.156825
$403$	−0.635811	−0.0316720
$404$	19.2435	0.957400
$405$	0	0
$406$	1.98319	0.0984240
$407$	−3.92674	−0.194641
$408$	6.78610	0.335962
$409$	−16.5637	−0.819024	−0.409512	−	0.912305i	$-0.634301\pi$
$409$	−16.5637	−0.819024	−0.409512	+	0.912305i	$0.634301\pi$
$410$	0	0
$411$	−6.68863	−0.329926
$412$	5.10689	0.251598
$413$	−0.334529	−0.0164611
$414$	6.50055	0.319485
$415$	0	0
$416$	−0.482152	−0.0236395
$417$	−3.07799	−0.150730
$418$	−27.3823	−1.33931
$419$	16.9705	0.829062	0.414531	−	0.910035i	$-0.363946\pi$
$419$	16.9705	0.829062	0.414531	+	0.910035i	$0.363946\pi$
$420$	0	0
$421$	−7.06240	−0.344200	−0.172100	−	0.985079i	$-0.555055\pi$
$421$	−7.06240	−0.344200	−0.172100	+	0.985079i	$0.555055\pi$
$422$	15.7638	0.767371
$423$	−4.38040	−0.212982
$424$	−1.68591	−0.0818751
$425$	0	0
$426$	5.71189	0.276742
$427$	−1.37920	−0.0667440
$428$	−15.3340	−0.741194
$429$	2.42686	0.117170
$430$	0	0
$431$	−17.8582	−0.860199	−0.430099	−	0.902782i	$-0.641521\pi$
$431$	−17.8582	−0.860199	−0.430099	+	0.902782i	$0.641521\pi$
$432$	1.00000	0.0481125
$433$	−24.1797	−1.16200	−0.581000	−	0.813903i	$-0.697339\pi$
$433$	−24.1797	−1.16200	−0.581000	+	0.813903i	$0.697339\pi$
$434$	−0.434265	−0.0208454
$435$	0	0
$436$	−9.76027	−0.467432
$437$	35.3638	1.69168
$438$	2.94269	0.140607
$439$	−18.9103	−0.902537	−0.451269	−	0.892388i	$-0.649028\pi$
$439$	−18.9103	−0.902537	−0.451269	+	0.892388i	$0.649028\pi$
$440$	0	0
$441$	−6.89155	−0.328169
$442$	−3.27193	−0.155630
$443$	4.05769	0.192787	0.0963933	−	0.995343i	$-0.469269\pi$
$443$	4.05769	0.192787	0.0963933	+	0.995343i	$0.469269\pi$
$444$	0.780139	0.0370237
$445$	0	0
$446$	−22.1782	−1.05017
$447$	5.06465	0.239550
$448$	−0.329315	−0.0155587
$449$	−6.26150	−0.295498	−0.147749	−	0.989025i	$-0.547203\pi$
$449$	−6.26150	−0.295498	−0.147749	+	0.989025i	$0.547203\pi$
$450$	0	0
$451$	−63.0207	−2.96753
$452$	1.51566	0.0712905
$453$	−16.9581	−0.796761
$454$	11.0969	0.520804
$455$	0	0
$456$	5.44012	0.254757
$457$	1.94229	0.0908564	0.0454282	−	0.998968i	$-0.485535\pi$
$457$	1.94229	0.0908564	0.0454282	+	0.998968i	$0.485535\pi$
$458$	1.79879	0.0840520
$459$	6.78610	0.316748
$460$	0	0
$461$	3.12391	0.145495	0.0727475	−	0.997350i	$-0.476823\pi$
$461$	3.12391	0.145495	0.0727475	+	0.997350i	$0.476823\pi$
$462$	1.65757	0.0771172
$463$	−8.26641	−0.384173	−0.192086	−	0.981378i	$-0.561525\pi$
$463$	−8.26641	−0.384173	−0.192086	+	0.981378i	$0.561525\pi$
$464$	−6.02216	−0.279572
$465$	0	0
$466$	3.70579	0.171667
$467$	−30.6192	−1.41689	−0.708445	−	0.705766i	$-0.750603\pi$
$467$	−30.6192	−1.41689	−0.708445	+	0.705766i	$0.750603\pi$
$468$	−0.482152	−0.0222875
$469$	−1.03547	−0.0478137
$470$	0	0
$471$	−22.8284	−1.05188
$472$	1.01583	0.0467575
$473$	12.4618	0.572993
$474$	8.48510	0.389734
$475$	0	0
$476$	−2.23476	−0.102430
$477$	−1.68591	−0.0771925
$478$	−16.8733	−0.771769
$479$	−1.17289	−0.0535907	−0.0267953	−	0.999641i	$-0.508530\pi$
$479$	−1.17289	−0.0535907	−0.0267953	+	0.999641i	$0.508530\pi$
$480$	0	0
$481$	−0.376146	−0.0171508
$482$	20.6256	0.939471
$483$	−2.14073	−0.0974065
$484$	14.3350	0.651593
$485$	0	0
$486$	1.00000	0.0453609
$487$	11.7556	0.532695	0.266348	−	0.963877i	$-0.414183\pi$
$487$	11.7556	0.532695	0.266348	+	0.963877i	$0.414183\pi$
$488$	4.18808	0.189585
$489$	7.95823	0.359884
$490$	0	0
$491$	4.13052	0.186408	0.0932038	−	0.995647i	$-0.470289\pi$
$491$	4.13052	0.186408	0.0932038	+	0.995647i	$0.470289\pi$
$492$	12.5205	0.564469
$493$	−40.8670	−1.84056
$494$	−2.62297	−0.118013
$495$	0	0
$496$	1.31869	0.0592111
$497$	−1.88101	−0.0843748
$498$	17.1955	0.770549
$499$	9.59154	0.429376	0.214688	−	0.976683i	$-0.431127\pi$
$499$	9.59154	0.429376	0.214688	+	0.976683i	$0.431127\pi$
$500$	0	0
$501$	13.9503	0.623254
$502$	8.69615	0.388128
$503$	16.9453	0.755555	0.377777	−	0.925896i	$-0.376688\pi$
$503$	16.9453	0.755555	0.377777	+	0.925896i	$0.376688\pi$
$504$	−0.329315	−0.0146689
$505$	0	0
$506$	−32.7198	−1.45457
$507$	−12.7675	−0.567026
$508$	12.6056	0.559282
$509$	34.3000	1.52032	0.760161	−	0.649735i	$-0.225120\pi$
$509$	34.3000	1.52032	0.760161	+	0.649735i	$0.225120\pi$
$510$	0	0
$511$	−0.969070	−0.0428691
$512$	1.00000	0.0441942
$513$	5.44012	0.240187
$514$	7.10714	0.313483
$515$	0	0
$516$	−2.47582	−0.108992
$517$	22.0482	0.969681
$518$	−0.256911	−0.0112880
$519$	−19.5009	−0.855993
$520$	0	0
$521$	21.2832	0.932436	0.466218	−	0.884670i	$-0.345616\pi$
$521$	21.2832	0.932436	0.466218	+	0.884670i	$0.345616\pi$
$522$	−6.02216	−0.263583
$523$	−41.3492	−1.80807	−0.904037	−	0.427454i	$-0.859411\pi$
$523$	−41.3492	−1.80807	−0.904037	+	0.427454i	$0.859411\pi$
$524$	14.0559	0.614036
$525$	0	0
$526$	−15.8609	−0.691570
$527$	8.94878	0.389815
$528$	−5.03339	−0.219050
$529$	19.2571	0.837267
$530$	0	0
$531$	1.01583	0.0440833
$532$	−1.79151	−0.0776720
$533$	−6.03680	−0.261483
$534$	3.45233	0.149397
$535$	0	0
$536$	3.14433	0.135814
$537$	−18.9911	−0.819526
$538$	4.51935	0.194843
$539$	34.6879	1.49411
$540$	0	0
$541$	−35.8217	−1.54010	−0.770048	−	0.637987i	$-0.779768\pi$
$541$	−35.8217	−1.54010	−0.770048	+	0.637987i	$0.779768\pi$
$542$	11.1314	0.478136
$543$	−18.9484	−0.813153
$544$	6.78610	0.290951
$545$	0	0
$546$	0.158780	0.00679515
$547$	8.36253	0.357556	0.178778	−	0.983889i	$-0.442786\pi$
$547$	8.36253	0.357556	0.178778	+	0.983889i	$0.442786\pi$
$548$	−6.68863	−0.285724
$549$	4.18808	0.178743
$550$	0	0
$551$	−32.7613	−1.39568
$552$	6.50055	0.276682
$553$	−2.79427	−0.118824
$554$	−22.8338	−0.970115
$555$	0	0
$556$	−3.07799	−0.130536
$557$	−28.1467	−1.19262	−0.596308	−	0.802756i	$-0.703366\pi$
$557$	−28.1467	−1.19262	−0.596308	+	0.802756i	$0.703366\pi$
$558$	1.31869	0.0558247
$559$	1.19372	0.0504890
$560$	0	0
$561$	−34.1571	−1.44211
$562$	28.7548	1.21295
$563$	−3.45072	−0.145431	−0.0727153	−	0.997353i	$-0.523166\pi$
$563$	−3.45072	−0.145431	−0.0727153	+	0.997353i	$0.523166\pi$
$564$	−4.38040	−0.184448
$565$	0	0
$566$	−19.3471	−0.813220
$567$	−0.329315	−0.0138299
$568$	5.71189	0.239665
$569$	17.4040	0.729614	0.364807	−	0.931083i	$-0.381135\pi$
$569$	17.4040	0.729614	0.364807	+	0.931083i	$0.381135\pi$
$570$	0	0
$571$	−37.2213	−1.55766	−0.778831	−	0.627234i	$-0.784187\pi$
$571$	−37.2213	−1.55766	−0.778831	+	0.627234i	$0.784187\pi$
$572$	2.42686	0.101472
$573$	−12.0933	−0.505204
$574$	−4.12320	−0.172099
$575$	0	0
$576$	1.00000	0.0416667
$577$	−20.1041	−0.836943	−0.418472	−	0.908230i	$-0.637434\pi$
$577$	−20.1041	−0.836943	−0.418472	+	0.908230i	$0.637434\pi$
$578$	29.0511	1.20837
$579$	−11.0357	−0.458629
$580$	0	0
$581$	−5.66273	−0.234930
$582$	−9.51004	−0.394204
$583$	8.48585	0.351448
$584$	2.94269	0.121769
$585$	0	0
$586$	15.0301	0.620889
$587$	−6.11838	−0.252533	−0.126266	−	0.991996i	$-0.540299\pi$
$587$	−6.11838	−0.252533	−0.126266	+	0.991996i	$0.540299\pi$
$588$	−6.89155	−0.284203
$589$	7.17385	0.295593
$590$	0	0
$591$	−20.6212	−0.848242
$592$	0.780139	0.0320635
$593$	24.9458	1.02440	0.512201	−	0.858866i	$-0.328830\pi$
$593$	24.9458	1.02440	0.512201	+	0.858866i	$0.328830\pi$
$594$	−5.03339	−0.206523
$595$	0	0
$596$	5.06465	0.207456
$597$	18.5313	0.758437
$598$	−3.13425	−0.128169
$599$	−0.941228	−0.0384575	−0.0192288	−	0.999815i	$-0.506121\pi$
$599$	−0.941228	−0.0384575	−0.0192288	+	0.999815i	$0.506121\pi$
$600$	0	0
$601$	10.2333	0.417426	0.208713	−	0.977977i	$-0.433073\pi$
$601$	10.2333	0.417426	0.208713	+	0.977977i	$0.433073\pi$
$602$	0.815324	0.0332301
$603$	3.14433	0.128047
$604$	−16.9581	−0.690015
$605$	0	0
$606$	19.2435	0.781714
$607$	6.80623	0.276256	0.138128	−	0.990414i	$-0.455891\pi$
$607$	6.80623	0.276256	0.138128	+	0.990414i	$0.455891\pi$
$608$	5.44012	0.220626
$609$	1.98319	0.0803629
$610$	0	0
$611$	2.11202	0.0854431
$612$	6.78610	0.274312
$613$	−1.13944	−0.0460215	−0.0230107	−	0.999735i	$-0.507325\pi$
$613$	−1.13944	−0.0460215	−0.0230107	+	0.999735i	$0.507325\pi$
$614$	19.7061	0.795272
$615$	0	0
$616$	1.65757	0.0667854
$617$	−14.3577	−0.578020	−0.289010	−	0.957326i	$-0.593326\pi$
$617$	−14.3577	−0.578020	−0.289010	+	0.957326i	$0.593326\pi$
$618$	5.10689	0.205429
$619$	0.476518	0.0191529	0.00957644	−	0.999954i	$-0.496952\pi$
$619$	0.476518	0.0191529	0.00957644	+	0.999954i	$0.496952\pi$
$620$	0	0
$621$	6.50055	0.260858
$622$	28.2393	1.13229
$623$	−1.13690	−0.0455491
$624$	−0.482152	−0.0193015
$625$	0	0
$626$	−11.2478	−0.449553
$627$	−27.3823	−1.09354
$628$	−22.8284	−0.910952
$629$	5.29410	0.211089
$630$	0	0
$631$	−17.0525	−0.678850	−0.339425	−	0.940633i	$-0.610232\pi$
$631$	−17.0525	−0.678850	−0.339425	+	0.940633i	$0.610232\pi$
$632$	8.48510	0.337519
$633$	15.7638	0.626556
$634$	−23.2917	−0.925030
$635$	0	0
$636$	−1.68591	−0.0668507
$637$	3.32278	0.131653
$638$	30.3119	1.20006
$639$	5.71189	0.225959
$640$	0	0
$641$	−32.7254	−1.29258	−0.646288	−	0.763094i	$-0.723680\pi$
$641$	−32.7254	−1.29258	−0.646288	+	0.763094i	$0.723680\pi$
$642$	−15.3340	−0.605183
$643$	−12.5844	−0.496281	−0.248141	−	0.968724i	$-0.579820\pi$
$643$	−12.5844	−0.496281	−0.248141	+	0.968724i	$0.579820\pi$
$644$	−2.14073	−0.0843565
$645$	0	0
$646$	36.9172	1.45249
$647$	25.6397	1.00800	0.504000	−	0.863703i	$-0.331861\pi$
$647$	25.6397	1.00800	0.504000	+	0.863703i	$0.331861\pi$
$648$	1.00000	0.0392837
$649$	−5.11308	−0.200706
$650$	0	0
$651$	−0.434265	−0.0170202
$652$	7.95823	0.311668
$653$	30.0568	1.17621	0.588107	−	0.808783i	$-0.299873\pi$
$653$	30.0568	1.17621	0.588107	+	0.808783i	$0.299873\pi$
$654$	−9.76027	−0.381657
$655$	0	0
$656$	12.5205	0.488844
$657$	2.94269	0.114805
$658$	1.44253	0.0562357
$659$	−8.04829	−0.313517	−0.156759	−	0.987637i	$-0.550104\pi$
$659$	−8.04829	−0.313517	−0.156759	+	0.987637i	$0.550104\pi$
$660$	0	0
$661$	−0.728568	−0.0283380	−0.0141690	−	0.999900i	$-0.504510\pi$
$661$	−0.728568	−0.0283380	−0.0141690	+	0.999900i	$0.504510\pi$
$662$	0.129334	0.00502670
$663$	−3.27193	−0.127071
$664$	17.1955	0.667315
$665$	0	0
$666$	0.780139	0.0302298
$667$	−39.1474	−1.51579
$668$	13.9503	0.539754
$669$	−22.1782	−0.857460
$670$	0	0
$671$	−21.0803	−0.813794
$672$	−0.329315	−0.0127036
$673$	7.40821	0.285566	0.142783	−	0.989754i	$-0.454395\pi$
$673$	7.40821	0.285566	0.142783	+	0.989754i	$0.454395\pi$
$674$	0.538069	0.0207256
$675$	0	0
$676$	−12.7675	−0.491059
$677$	9.79504	0.376454	0.188227	−	0.982126i	$-0.439726\pi$
$677$	9.79504	0.376454	0.188227	+	0.982126i	$0.439726\pi$
$678$	1.51566	0.0582084
$679$	3.13180	0.120187
$680$	0	0
$681$	11.0969	0.425235
$682$	−6.63750	−0.254163
$683$	33.5847	1.28508	0.642542	−	0.766250i	$-0.277880\pi$
$683$	33.5847	1.28508	0.642542	+	0.766250i	$0.277880\pi$
$684$	5.44012	0.208008
$685$	0	0
$686$	4.57470	0.174663
$687$	1.79879	0.0686281
$688$	−2.47582	−0.0943897
$689$	0.812865	0.0309677
$690$	0	0
$691$	26.1110	0.993309	0.496655	−	0.867948i	$-0.334562\pi$
$691$	26.1110	0.993309	0.496655	+	0.867948i	$0.334562\pi$
$692$	−19.5009	−0.741312
$693$	1.65757	0.0629659
$694$	−22.7156	−0.862273
$695$	0	0
$696$	−6.02216	−0.228270
$697$	84.9655	3.21830
$698$	6.84350	0.259030
$699$	3.70579	0.140166
$700$	0	0
$701$	41.8212	1.57956	0.789782	−	0.613388i	$-0.210194\pi$
$701$	41.8212	1.57956	0.789782	+	0.613388i	$0.210194\pi$
$702$	−0.482152	−0.0181977
$703$	4.24405	0.160067
$704$	−5.03339	−0.189703
$705$	0	0
$706$	−16.7789	−0.631481
$707$	−6.33717	−0.238334
$708$	1.01583	0.0381773
$709$	−8.86903	−0.333083	−0.166542	−	0.986034i	$-0.553260\pi$
$709$	−8.86903	−0.333083	−0.166542	+	0.986034i	$0.553260\pi$
$710$	0	0
$711$	8.48510	0.318216
$712$	3.45233	0.129382
$713$	8.57223	0.321033
$714$	−2.23476	−0.0836339
$715$	0	0
$716$	−18.9911	−0.709731
$717$	−16.8733	−0.630146
$718$	−7.46364	−0.278541
$719$	−2.65509	−0.0990182	−0.0495091	−	0.998774i	$-0.515766\pi$
$719$	−2.65509	−0.0990182	−0.0495091	+	0.998774i	$0.515766\pi$
$720$	0	0
$721$	−1.68177	−0.0626325
$722$	10.5949	0.394303
$723$	20.6256	0.767075
$724$	−18.9484	−0.704211
$725$	0	0
$726$	14.3350	0.532023
$727$	−7.03681	−0.260981	−0.130490	−	0.991450i	$-0.541655\pi$
$727$	−7.03681	−0.260981	−0.130490	+	0.991450i	$0.541655\pi$
$728$	0.158780	0.00588477
$729$	1.00000	0.0370370
$730$	0	0
$731$	−16.8011	−0.621413
$732$	4.18808	0.154796
$733$	20.2601	0.748324	0.374162	−	0.927363i	$-0.377930\pi$
$733$	20.2601	0.748324	0.374162	+	0.927363i	$0.377930\pi$
$734$	6.15474	0.227176
$735$	0	0
$736$	6.50055	0.239613
$737$	−15.8266	−0.582982
$738$	12.5205	0.460887
$739$	17.1512	0.630919	0.315459	−	0.948939i	$-0.397841\pi$
$739$	17.1512	0.630919	0.315459	+	0.948939i	$0.397841\pi$
$740$	0	0
$741$	−2.62297	−0.0963571
$742$	0.555196	0.0203819
$743$	−9.94252	−0.364756	−0.182378	−	0.983229i	$-0.558379\pi$
$743$	−9.94252	−0.364756	−0.182378	+	0.983229i	$0.558379\pi$
$744$	1.31869	0.0483456
$745$	0	0
$746$	−9.16928	−0.335711
$747$	17.1955	0.629150
$748$	−34.1571	−1.24891
$749$	5.04970	0.184512
$750$	0	0
$751$	−17.6941	−0.645667	−0.322833	−	0.946456i	$-0.604635\pi$
$751$	−17.6941	−0.645667	−0.322833	+	0.946456i	$0.604635\pi$
$752$	−4.38040	−0.159737
$753$	8.69615	0.316905
$754$	2.90360	0.105743
$755$	0	0
$756$	−0.329315	−0.0119771
$757$	37.1272	1.34941	0.674706	−	0.738087i	$-0.264271\pi$
$757$	37.1272	1.34941	0.674706	+	0.738087i	$0.264271\pi$
$758$	−34.6321	−1.25789
$759$	−32.7198	−1.18765
$760$	0	0
$761$	−49.5640	−1.79669	−0.898346	−	0.439289i	$-0.855230\pi$
$761$	−49.5640	−1.79669	−0.898346	+	0.439289i	$0.855230\pi$
$762$	12.6056	0.456652
$763$	3.21420	0.116362
$764$	−12.0933	−0.437520
$765$	0	0
$766$	−9.52044	−0.343987
$767$	−0.489786	−0.0176851
$768$	1.00000	0.0360844
$769$	34.3645	1.23922	0.619608	−	0.784911i	$-0.287291\pi$
$769$	34.3645	1.23922	0.619608	+	0.784911i	$0.287291\pi$
$770$	0	0
$771$	7.10714	0.255957
$772$	−11.0357	−0.397184
$773$	−22.9926	−0.826985	−0.413493	−	0.910507i	$-0.635691\pi$
$773$	−22.9926	−0.826985	−0.413493	+	0.910507i	$0.635691\pi$
$774$	−2.47582	−0.0889915
$775$	0	0
$776$	−9.51004	−0.341390
$777$	−0.256911	−0.00921664
$778$	−17.4454	−0.625447
$779$	68.1132	2.44041
$780$	0	0
$781$	−28.7502	−1.02876
$782$	44.1134	1.57749
$783$	−6.02216	−0.215215
$784$	−6.89155	−0.246127
$785$	0	0
$786$	14.0559	0.501358
$787$	−8.41183	−0.299849	−0.149925	−	0.988697i	$-0.547903\pi$
$787$	−8.41183	−0.299849	−0.149925	+	0.988697i	$0.547903\pi$
$788$	−20.6212	−0.734599
$789$	−15.8609	−0.564665
$790$	0	0
$791$	−0.499128	−0.0177470
$792$	−5.03339	−0.178854
$793$	−2.01929	−0.0717072
$794$	−13.5551	−0.481054
$795$	0	0
$796$	18.5313	0.656826
$797$	38.2745	1.35575	0.677875	−	0.735177i	$-0.262901\pi$
$797$	38.2745	1.35575	0.677875	+	0.735177i	$0.262901\pi$
$798$	−1.79151	−0.0634189
$799$	−29.7258	−1.05162
$800$	0	0
$801$	3.45233	0.121982
$802$	14.1105	0.498257
$803$	−14.8117	−0.522693
$804$	3.14433	0.110892
$805$	0	0
$806$	−0.635811	−0.0223955
$807$	4.51935	0.159089
$808$	19.2435	0.676984
$809$	−30.8014	−1.08292	−0.541461	−	0.840726i	$-0.682128\pi$
$809$	−30.8014	−1.08292	−0.541461	+	0.840726i	$0.682128\pi$
$810$	0	0
$811$	−0.787233	−0.0276435	−0.0138217	−	0.999904i	$-0.504400\pi$
$811$	−0.787233	−0.0276435	−0.0138217	+	0.999904i	$0.504400\pi$
$812$	1.98319	0.0695963
$813$	11.1314	0.390396
$814$	−3.92674	−0.137632
$815$	0	0
$816$	6.78610	0.237561
$817$	−13.4688	−0.471212
$818$	−16.5637	−0.579138
$819$	0.158780	0.00554822
$820$	0	0
$821$	17.4710	0.609743	0.304872	−	0.952393i	$-0.401386\pi$
$821$	17.4710	0.609743	0.304872	+	0.952393i	$0.401386\pi$
$822$	−6.68863	−0.233293
$823$	37.4268	1.30462	0.652309	−	0.757953i	$-0.273801\pi$
$823$	37.4268	1.30462	0.652309	+	0.757953i	$0.273801\pi$
$824$	5.10689	0.177907
$825$	0	0
$826$	−0.334529	−0.0116397
$827$	−11.7918	−0.410041	−0.205020	−	0.978758i	$-0.565726\pi$
$827$	−11.7918	−0.410041	−0.205020	+	0.978758i	$0.565726\pi$
$828$	6.50055	0.225910
$829$	−35.0287	−1.21660	−0.608298	−	0.793708i	$-0.708148\pi$
$829$	−35.0287	−1.21660	−0.608298	+	0.793708i	$0.708148\pi$
$830$	0	0
$831$	−22.8338	−0.792096
$832$	−0.482152	−0.0167156
$833$	−46.7667	−1.62037
$834$	−3.07799	−0.106582
$835$	0	0
$836$	−27.3823	−0.947036
$837$	1.31869	0.0455807
$838$	16.9705	0.586235
$839$	0.498658	0.0172156	0.00860779	−	0.999963i	$-0.497260\pi$
$839$	0.498658	0.0172156	0.00860779	+	0.999963i	$0.497260\pi$
$840$	0	0
$841$	7.26647	0.250568
$842$	−7.06240	−0.243386
$843$	28.7548	0.990367
$844$	15.7638	0.542613
$845$	0	0
$846$	−4.38040	−0.150601
$847$	−4.72074	−0.162207
$848$	−1.68591	−0.0578944
$849$	−19.3471	−0.663992
$850$	0	0
$851$	5.07133	0.173843
$852$	5.71189	0.195686
$853$	21.3584	0.731298	0.365649	−	0.930753i	$-0.380847\pi$
$853$	21.3584	0.731298	0.365649	+	0.930753i	$0.380847\pi$
$854$	−1.37920	−0.0471952
$855$	0	0
$856$	−15.3340	−0.524104
$857$	−33.4831	−1.14376	−0.571880	−	0.820337i	$-0.693786\pi$
$857$	−33.4831	−1.14376	−0.571880	+	0.820337i	$0.693786\pi$
$858$	2.42686	0.0828517
$859$	45.4873	1.55201	0.776003	−	0.630729i	$-0.217244\pi$
$859$	45.4873	1.55201	0.776003	+	0.630729i	$0.217244\pi$
$860$	0	0
$861$	−4.12320	−0.140518
$862$	−17.8582	−0.608252
$863$	14.4689	0.492529	0.246264	−	0.969203i	$-0.420797\pi$
$863$	14.4689	0.492529	0.246264	+	0.969203i	$0.420797\pi$
$864$	1.00000	0.0340207
$865$	0	0
$866$	−24.1797	−0.821659
$867$	29.0511	0.986627
$868$	−0.434265	−0.0147399
$869$	−42.7088	−1.44880
$870$	0	0
$871$	−1.51604	−0.0513692
$872$	−9.76027	−0.330525
$873$	−9.51004	−0.321866
$874$	35.3638	1.19620
$875$	0	0
$876$	2.94269	0.0994241
$877$	−45.1991	−1.52626	−0.763132	−	0.646243i	$-0.776339\pi$
$877$	−45.1991	−1.52626	−0.763132	+	0.646243i	$0.776339\pi$
$878$	−18.9103	−0.638190
$879$	15.0301	0.506954
$880$	0	0
$881$	13.9752	0.470836	0.235418	−	0.971894i	$-0.424354\pi$
$881$	13.9752	0.470836	0.235418	+	0.971894i	$0.424354\pi$
$882$	−6.89155	−0.232051
$883$	−11.7349	−0.394911	−0.197455	−	0.980312i	$-0.563268\pi$
$883$	−11.7349	−0.394911	−0.197455	+	0.980312i	$0.563268\pi$
$884$	−3.27193	−0.110047
$885$	0	0
$886$	4.05769	0.136321
$887$	19.7512	0.663180	0.331590	−	0.943424i	$-0.392415\pi$
$887$	19.7512	0.663180	0.331590	+	0.943424i	$0.392415\pi$
$888$	0.780139	0.0261797
$889$	−4.15121	−0.139227
$890$	0	0
$891$	−5.03339	−0.168625
$892$	−22.1782	−0.742582
$893$	−23.8299	−0.797437
$894$	5.06465	0.169387
$895$	0	0
$896$	−0.329315	−0.0110016
$897$	−3.13425	−0.104650
$898$	−6.26150	−0.208949
$899$	−7.94139	−0.264860
$900$	0	0
$901$	−11.4408	−0.381147
$902$	−63.0207	−2.09836
$903$	0.815324	0.0271323
$904$	1.51566	0.0504100
$905$	0	0
$906$	−16.9581	−0.563395
$907$	−21.0111	−0.697661	−0.348831	−	0.937186i	$-0.613421\pi$
$907$	−21.0111	−0.697661	−0.348831	+	0.937186i	$0.613421\pi$
$908$	11.0969	0.368264
$909$	19.2435	0.638267
$910$	0	0
$911$	24.8288	0.822614	0.411307	−	0.911497i	$-0.365072\pi$
$911$	24.8288	0.822614	0.411307	+	0.911497i	$0.365072\pi$
$912$	5.44012	0.180140
$913$	−86.5517	−2.86444
$914$	1.94229	0.0642452
$915$	0	0
$916$	1.79879	0.0594337
$917$	−4.62883	−0.152857
$918$	6.78610	0.223975
$919$	−36.0292	−1.18849	−0.594247	−	0.804283i	$-0.702550\pi$
$919$	−36.0292	−1.18849	−0.594247	+	0.804283i	$0.702550\pi$
$920$	0	0
$921$	19.7061	0.649337
$922$	3.12391	0.102881
$923$	−2.75400	−0.0906490
$924$	1.65757	0.0545301
$925$	0	0
$926$	−8.26641	−0.271651
$927$	5.10689	0.167732
$928$	−6.02216	−0.197687
$929$	−56.9634	−1.86891	−0.934454	−	0.356084i	$-0.884112\pi$
$929$	−56.9634	−1.86891	−0.934454	+	0.356084i	$0.884112\pi$
$930$	0	0
$931$	−37.4909	−1.22871
$932$	3.70579	0.121387
$933$	28.2393	0.924513
$934$	−30.6192	−1.00189
$935$	0	0
$936$	−0.482152	−0.0157596
$937$	41.7570	1.36414	0.682071	−	0.731286i	$-0.261080\pi$
$937$	41.7570	1.36414	0.682071	+	0.731286i	$0.261080\pi$
$938$	−1.03547	−0.0338094
$939$	−11.2478	−0.367059
$940$	0	0
$941$	−22.8232	−0.744014	−0.372007	−	0.928230i	$-0.621330\pi$
$941$	−22.8232	−0.744014	−0.372007	+	0.928230i	$0.621330\pi$
$942$	−22.8284	−0.743789
$943$	81.3903	2.65043
$944$	1.01583	0.0330625
$945$	0	0
$946$	12.4618	0.405167
$947$	−8.46744	−0.275155	−0.137577	−	0.990491i	$-0.543932\pi$
$947$	−8.46744	−0.275155	−0.137577	+	0.990491i	$0.543932\pi$
$948$	8.48510	0.275583
$949$	−1.41882	−0.0460569
$950$	0	0
$951$	−23.2917	−0.755284
$952$	−2.23476	−0.0724291
$953$	24.8878	0.806195	0.403097	−	0.915157i	$-0.367934\pi$
$953$	24.8878	0.806195	0.403097	+	0.915157i	$0.367934\pi$
$954$	−1.68591	−0.0545834
$955$	0	0
$956$	−16.8733	−0.545723
$957$	30.3119	0.979845
$958$	−1.17289	−0.0378943
$959$	2.20267	0.0711278
$960$	0	0
$961$	−29.2610	−0.943905
$962$	−0.376146	−0.0121274
$963$	−15.3340	−0.494130
$964$	20.6256	0.664306
$965$	0	0
$966$	−2.14073	−0.0688768
$967$	−22.1247	−0.711483	−0.355742	−	0.934584i	$-0.615772\pi$
$967$	−22.1247	−0.711483	−0.355742	+	0.934584i	$0.615772\pi$
$968$	14.3350	0.460746
$969$	36.9172	1.18595
$970$	0	0
$971$	−17.0050	−0.545716	−0.272858	−	0.962054i	$-0.587969\pi$
$971$	−17.0050	−0.545716	−0.272858	+	0.962054i	$0.587969\pi$
$972$	1.00000	0.0320750
$973$	1.01363	0.0324954
$974$	11.7556	0.376672
$975$	0	0
$976$	4.18808	0.134057
$977$	41.3030	1.32140	0.660701	−	0.750650i	$-0.270259\pi$
$977$	41.3030	1.32140	0.660701	+	0.750650i	$0.270259\pi$
$978$	7.95823	0.254476
$979$	−17.3769	−0.555369
$980$	0	0
$981$	−9.76027	−0.311622
$982$	4.13052	0.131810
$983$	61.9160	1.97481	0.987407	−	0.158199i	$-0.0505687\pi$
$983$	61.9160	1.97481	0.987407	+	0.158199i	$0.0505687\pi$
$984$	12.5205	0.399140
$985$	0	0
$986$	−40.8670	−1.30147
$987$	1.44253	0.0459162
$988$	−2.62297	−0.0834477
$989$	−16.0942	−0.511765
$990$	0	0
$991$	4.93098	0.156638	0.0783188	−	0.996928i	$-0.475045\pi$
$991$	4.93098	0.156638	0.0783188	+	0.996928i	$0.475045\pi$
$992$	1.31869	0.0418686
$993$	0.129334	0.00410428
$994$	−1.88101	−0.0596620
$995$	0	0
$996$	17.1955	0.544860
$997$	−49.5596	−1.56957	−0.784784	−	0.619769i	$-0.787226\pi$
$997$	−49.5596	−1.56957	−0.784784	+	0.619769i	$0.787226\pi$
$998$	9.59154	0.303615
$999$	0.780139	0.0246825

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3750.2.a.v.1.4		8
5.2	odd	4		3750.2.c.k.1249.12		16
5.3	odd	4		3750.2.c.k.1249.5		16
5.4	even	2		3750.2.a.u.1.5		8
25.2	odd	20		150.2.h.b.79.4	yes	16
25.9	even	10		750.2.g.g.151.3		16
25.11	even	5		750.2.g.f.601.2		16
25.12	odd	20		750.2.h.d.349.1		16
25.13	odd	20		150.2.h.b.19.4	✓	16
25.14	even	10		750.2.g.g.601.3		16
25.16	even	5		750.2.g.f.151.2		16
25.23	odd	20		750.2.h.d.649.2		16
75.2	even	20		450.2.l.c.379.1		16
75.38	even	20		450.2.l.c.19.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.h.b.19.4	✓	16	25.13	odd	20
150.2.h.b.79.4	yes	16	25.2	odd	20
450.2.l.c.19.1		16	75.38	even	20
450.2.l.c.379.1		16	75.2	even	20
750.2.g.f.151.2		16	25.16	even	5
750.2.g.f.601.2		16	25.11	even	5
750.2.g.g.151.3		16	25.9	even	10
750.2.g.g.601.3		16	25.14	even	10
750.2.h.d.349.1		16	25.12	odd	20
750.2.h.d.649.2		16	25.23	odd	20
3750.2.a.u.1.5		8	5.4	even	2
3750.2.a.v.1.4		8	1.1	even	1	trivial
3750.2.c.k.1249.5		16	5.3	odd	4
3750.2.c.k.1249.12		16	5.2	odd	4

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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:	\( N \)	\(=\)	\( 3750 = 2 \cdot 3 \cdot 5^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3750.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} -0.329315 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} -0.329315 q^{7} +1.00000 q^{8} +1.00000 q^{9} -5.03339 q^{11} +1.00000 q^{12} -0.482152 q^{13} -0.329315 q^{14} +1.00000 q^{16} +6.78610 q^{17} +1.00000 q^{18} +5.44012 q^{19} -0.329315 q^{21} -5.03339 q^{22} +6.50055 q^{23} +1.00000 q^{24} -0.482152 q^{26} +1.00000 q^{27} -0.329315 q^{28} -6.02216 q^{29} +1.31869 q^{31} +1.00000 q^{32} -5.03339 q^{33} +6.78610 q^{34} +1.00000 q^{36} +0.780139 q^{37} +5.44012 q^{38} -0.482152 q^{39} +12.5205 q^{41} -0.329315 q^{42} -2.47582 q^{43} -5.03339 q^{44} +6.50055 q^{46} -4.38040 q^{47} +1.00000 q^{48} -6.89155 q^{49} +6.78610 q^{51} -0.482152 q^{52} -1.68591 q^{53} +1.00000 q^{54} -0.329315 q^{56} +5.44012 q^{57} -6.02216 q^{58} +1.01583 q^{59} +4.18808 q^{61} +1.31869 q^{62} -0.329315 q^{63} +1.00000 q^{64} -5.03339 q^{66} +3.14433 q^{67} +6.78610 q^{68} +6.50055 q^{69} +5.71189 q^{71} +1.00000 q^{72} +2.94269 q^{73} +0.780139 q^{74} +5.44012 q^{76} +1.65757 q^{77} -0.482152 q^{78} +8.48510 q^{79} +1.00000 q^{81} +12.5205 q^{82} +17.1955 q^{83} -0.329315 q^{84} -2.47582 q^{86} -6.02216 q^{87} -5.03339 q^{88} +3.45233 q^{89} +0.158780 q^{91} +6.50055 q^{92} +1.31869 q^{93} -4.38040 q^{94} +1.00000 q^{96} -9.51004 q^{97} -6.89155 q^{98} -5.03339 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} + 8 q^{3} + 8 q^{4} + 8 q^{6} + 4 q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 + 8 * q^6 + 4 * q^7 + 8 * q^8 + 8 * q^9	\( 8 q + 8 q^{2} + 8 q^{3} + 8 q^{4} + 8 q^{6} + 4 q^{7} + 8 q^{8} + 8 q^{9} + 6 q^{11} + 8 q^{12} + 2 q^{13} + 4 q^{14} + 8 q^{16} + 14 q^{17} + 8 q^{18} + 10 q^{19} + 4 q^{21} + 6 q^{22} + 12 q^{23} + 8 q^{24} + 2 q^{26} + 8 q^{27} + 4 q^{28} + 10 q^{29} + 16 q^{31} + 8 q^{32} + 6 q^{33} + 14 q^{34} + 8 q^{36} - 6 q^{37} + 10 q^{38} + 2 q^{39} + 6 q^{41} + 4 q^{42} + 2 q^{43} + 6 q^{44} + 12 q^{46} + 14 q^{47} + 8 q^{48} + 26 q^{49} + 14 q^{51} + 2 q^{52} + 12 q^{53} + 8 q^{54} + 4 q^{56} + 10 q^{57} + 10 q^{58} + 16 q^{61} + 16 q^{62} + 4 q^{63} + 8 q^{64} + 6 q^{66} - 6 q^{67} + 14 q^{68} + 12 q^{69} + 6 q^{71} + 8 q^{72} - 8 q^{73} - 6 q^{74} + 10 q^{76} + 8 q^{77} + 2 q^{78} + 10 q^{79} + 8 q^{81} + 6 q^{82} + 22 q^{83} + 4 q^{84} + 2 q^{86} + 10 q^{87} + 6 q^{88} + 20 q^{89} + 6 q^{91} + 12 q^{92} + 16 q^{93} + 14 q^{94} + 8 q^{96} - 16 q^{97} + 26 q^{98} + 6 q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 + 8 * q^6 + 4 * q^7 + 8 * q^8 + 8 * q^9 + 6 * q^11 + 8 * q^12 + 2 * q^13 + 4 * q^14 + 8 * q^16 + 14 * q^17 + 8 * q^18 + 10 * q^19 + 4 * q^21 + 6 * q^22 + 12 * q^23 + 8 * q^24 + 2 * q^26 + 8 * q^27 + 4 * q^28 + 10 * q^29 + 16 * q^31 + 8 * q^32 + 6 * q^33 + 14 * q^34 + 8 * q^36 - 6 * q^37 + 10 * q^38 + 2 * q^39 + 6 * q^41 + 4 * q^42 + 2 * q^43 + 6 * q^44 + 12 * q^46 + 14 * q^47 + 8 * q^48 + 26 * q^49 + 14 * q^51 + 2 * q^52 + 12 * q^53 + 8 * q^54 + 4 * q^56 + 10 * q^57 + 10 * q^58 + 16 * q^61 + 16 * q^62 + 4 * q^63 + 8 * q^64 + 6 * q^66 - 6 * q^67 + 14 * q^68 + 12 * q^69 + 6 * q^71 + 8 * q^72 - 8 * q^73 - 6 * q^74 + 10 * q^76 + 8 * q^77 + 2 * q^78 + 10 * q^79 + 8 * q^81 + 6 * q^82 + 22 * q^83 + 4 * q^84 + 2 * q^86 + 10 * q^87 + 6 * q^88 + 20 * q^89 + 6 * q^91 + 12 * q^92 + 16 * q^93 + 14 * q^94 + 8 * q^96 - 16 * q^97 + 26 * q^98 + 6 * q^99

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