LMFDB - Embedded newform 6762.2.a.bw.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6762,2,Mod(1,6762)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6762, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("6762.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6762 = 2 \cdot 3 \cdot 7^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6762.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:	$53.9948418468$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{17}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 4 $ x^2 - x - 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 966)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1.56155$ of defining polynomial
Character	$\chi$	$=$	6762.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.56155 q^{5} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.56155 q^{5} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} -1.56155 q^{10} +5.12311 q^{11} +1.00000 q^{12} +3.56155 q^{13} +1.56155 q^{15} +1.00000 q^{16} +1.12311 q^{17} -1.00000 q^{18} +5.12311 q^{19} +1.56155 q^{20} -5.12311 q^{22} +1.00000 q^{23} -1.00000 q^{24} -2.56155 q^{25} -3.56155 q^{26} +1.00000 q^{27} +7.56155 q^{29} -1.56155 q^{30} -3.12311 q^{31} -1.00000 q^{32} +5.12311 q^{33} -1.12311 q^{34} +1.00000 q^{36} -1.56155 q^{37} -5.12311 q^{38} +3.56155 q^{39} -1.56155 q^{40} -3.56155 q^{41} +6.68466 q^{43} +5.12311 q^{44} +1.56155 q^{45} -1.00000 q^{46} -2.43845 q^{47} +1.00000 q^{48} +2.56155 q^{50} +1.12311 q^{51} +3.56155 q^{52} +14.2462 q^{53} -1.00000 q^{54} +8.00000 q^{55} +5.12311 q^{57} -7.56155 q^{58} -4.87689 q^{59} +1.56155 q^{60} -0.876894 q^{61} +3.12311 q^{62} +1.00000 q^{64} +5.56155 q^{65} -5.12311 q^{66} -1.12311 q^{67} +1.12311 q^{68} +1.00000 q^{69} -9.36932 q^{71} -1.00000 q^{72} -9.12311 q^{73} +1.56155 q^{74} -2.56155 q^{75} +5.12311 q^{76} -3.56155 q^{78} +14.2462 q^{79} +1.56155 q^{80} +1.00000 q^{81} +3.56155 q^{82} +9.12311 q^{83} +1.75379 q^{85} -6.68466 q^{86} +7.56155 q^{87} -5.12311 q^{88} -14.0000 q^{89} -1.56155 q^{90} +1.00000 q^{92} -3.12311 q^{93} +2.43845 q^{94} +8.00000 q^{95} -1.00000 q^{96} +12.4384 q^{97} +5.12311 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - q^{5} - 2 q^{6} - 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - q^5 - 2 * q^6 - 2 * q^8 + 2 * q^9	$ 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - q^{5} - 2 q^{6} - 2 q^{8} + 2 q^{9} + q^{10} + 2 q^{11} + 2 q^{12} + 3 q^{13} - q^{15} + 2 q^{16} - 6 q^{17} - 2 q^{18} + 2 q^{19} - q^{20} - 2 q^{22} + 2 q^{23} - 2 q^{24} - q^{25} - 3 q^{26} + 2 q^{27} + 11 q^{29} + q^{30} + 2 q^{31} - 2 q^{32} + 2 q^{33} + 6 q^{34} + 2 q^{36} + q^{37} - 2 q^{38} + 3 q^{39} + q^{40} - 3 q^{41} + q^{43} + 2 q^{44} - q^{45} - 2 q^{46} - 9 q^{47} + 2 q^{48} + q^{50} - 6 q^{51} + 3 q^{52} + 12 q^{53} - 2 q^{54} + 16 q^{55} + 2 q^{57} - 11 q^{58} - 18 q^{59} - q^{60} - 10 q^{61} - 2 q^{62} + 2 q^{64} + 7 q^{65} - 2 q^{66} + 6 q^{67} - 6 q^{68} + 2 q^{69} + 6 q^{71} - 2 q^{72} - 10 q^{73} - q^{74} - q^{75} + 2 q^{76} - 3 q^{78} + 12 q^{79} - q^{80} + 2 q^{81} + 3 q^{82} + 10 q^{83} + 20 q^{85} - q^{86} + 11 q^{87} - 2 q^{88} - 28 q^{89} + q^{90} + 2 q^{92} + 2 q^{93} + 9 q^{94} + 16 q^{95} - 2 q^{96} + 29 q^{97} + 2 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - q^5 - 2 * q^6 - 2 * q^8 + 2 * q^9 + q^10 + 2 * q^11 + 2 * q^12 + 3 * q^13 - q^15 + 2 * q^16 - 6 * q^17 - 2 * q^18 + 2 * q^19 - q^20 - 2 * q^22 + 2 * q^23 - 2 * q^24 - q^25 - 3 * q^26 + 2 * q^27 + 11 * q^29 + q^30 + 2 * q^31 - 2 * q^32 + 2 * q^33 + 6 * q^34 + 2 * q^36 + q^37 - 2 * q^38 + 3 * q^39 + q^40 - 3 * q^41 + q^43 + 2 * q^44 - q^45 - 2 * q^46 - 9 * q^47 + 2 * q^48 + q^50 - 6 * q^51 + 3 * q^52 + 12 * q^53 - 2 * q^54 + 16 * q^55 + 2 * q^57 - 11 * q^58 - 18 * q^59 - q^60 - 10 * q^61 - 2 * q^62 + 2 * q^64 + 7 * q^65 - 2 * q^66 + 6 * q^67 - 6 * q^68 + 2 * q^69 + 6 * q^71 - 2 * q^72 - 10 * q^73 - q^74 - q^75 + 2 * q^76 - 3 * q^78 + 12 * q^79 - q^80 + 2 * q^81 + 3 * q^82 + 10 * q^83 + 20 * q^85 - q^86 + 11 * q^87 - 2 * q^88 - 28 * q^89 + q^90 + 2 * q^92 + 2 * q^93 + 9 * q^94 + 16 * q^95 - 2 * q^96 + 29 * q^97 + 2 * 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
$5$	1.56155	0.698348	0.349174	−	0.937058i	$-0.386462\pi$
$5$	1.56155	0.698348	0.349174	+	0.937058i	$0.386462\pi$
$6$	−1.00000	−0.408248
$7$	0	0
$7$	0	0
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−1.56155	−0.493806
$11$	5.12311	1.54467	0.772337	−	0.635213i	$-0.219088\pi$
$11$	5.12311	1.54467	0.772337	+	0.635213i	$0.219088\pi$
$12$	1.00000	0.288675
$13$	3.56155	0.987797	0.493899	−	0.869520i	$-0.335571\pi$
$13$	3.56155	0.987797	0.493899	+	0.869520i	$0.335571\pi$
$14$	0	0
$15$	1.56155	0.403191
$16$	1.00000	0.250000
$17$	1.12311	0.272393	0.136197	−	0.990682i	$-0.456512\pi$
$17$	1.12311	0.272393	0.136197	+	0.990682i	$0.456512\pi$
$18$	−1.00000	−0.235702
$19$	5.12311	1.17532	0.587661	−	0.809108i	$-0.300049\pi$
$19$	5.12311	1.17532	0.587661	+	0.809108i	$0.300049\pi$
$20$	1.56155	0.349174
$21$	0	0
$22$	−5.12311	−1.09225
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−1.00000	−0.204124
$25$	−2.56155	−0.512311
$26$	−3.56155	−0.698478
$27$	1.00000	0.192450
$28$	0	0
$29$	7.56155	1.40415	0.702073	−	0.712105i	$-0.252258\pi$
$29$	7.56155	1.40415	0.702073	+	0.712105i	$0.252258\pi$
$30$	−1.56155	−0.285099
$31$	−3.12311	−0.560926	−0.280463	−	0.959865i	$-0.590488\pi$
$31$	−3.12311	−0.560926	−0.280463	+	0.959865i	$0.590488\pi$
$32$	−1.00000	−0.176777
$33$	5.12311	0.891818
$34$	−1.12311	−0.192611
$35$	0	0
$36$	1.00000	0.166667
$37$	−1.56155	−0.256718	−0.128359	−	0.991728i	$-0.540971\pi$
$37$	−1.56155	−0.256718	−0.128359	+	0.991728i	$0.540971\pi$
$38$	−5.12311	−0.831077
$39$	3.56155	0.570305
$40$	−1.56155	−0.246903
$41$	−3.56155	−0.556221	−0.278111	−	0.960549i	$-0.589708\pi$
$41$	−3.56155	−0.556221	−0.278111	+	0.960549i	$0.589708\pi$
$42$	0	0
$43$	6.68466	1.01940	0.509700	−	0.860352i	$-0.329756\pi$
$43$	6.68466	1.01940	0.509700	+	0.860352i	$0.329756\pi$
$44$	5.12311	0.772337
$45$	1.56155	0.232783
$46$	−1.00000	−0.147442
$47$	−2.43845	−0.355684	−0.177842	−	0.984059i	$-0.556912\pi$
$47$	−2.43845	−0.355684	−0.177842	+	0.984059i	$0.556912\pi$
$48$	1.00000	0.144338
$49$	0	0
$50$	2.56155	0.362258
$51$	1.12311	0.157266
$52$	3.56155	0.493899
$53$	14.2462	1.95687	0.978434	−	0.206561i	$-0.0662271\pi$
$53$	14.2462	1.95687	0.978434	+	0.206561i	$0.0662271\pi$
$54$	−1.00000	−0.136083
$55$	8.00000	1.07872
$56$	0	0
$57$	5.12311	0.678572
$58$	−7.56155	−0.992881
$59$	−4.87689	−0.634918	−0.317459	−	0.948272i	$-0.602830\pi$
$59$	−4.87689	−0.634918	−0.317459	+	0.948272i	$0.602830\pi$
$60$	1.56155	0.201596
$61$	−0.876894	−0.112275	−0.0561374	−	0.998423i	$-0.517878\pi$
$61$	−0.876894	−0.112275	−0.0561374	+	0.998423i	$0.517878\pi$
$62$	3.12311	0.396635
$63$	0	0
$64$	1.00000	0.125000
$65$	5.56155	0.689826
$66$	−5.12311	−0.630611
$67$	−1.12311	−0.137209	−0.0686046	−	0.997644i	$-0.521855\pi$
$67$	−1.12311	−0.137209	−0.0686046	+	0.997644i	$0.521855\pi$
$68$	1.12311	0.136197
$69$	1.00000	0.120386
$70$	0	0
$71$	−9.36932	−1.11193	−0.555967	−	0.831205i	$-0.687652\pi$
$71$	−9.36932	−1.11193	−0.555967	+	0.831205i	$0.687652\pi$
$72$	−1.00000	−0.117851
$73$	−9.12311	−1.06778	−0.533889	−	0.845554i	$-0.679270\pi$
$73$	−9.12311	−1.06778	−0.533889	+	0.845554i	$0.679270\pi$
$74$	1.56155	0.181527
$75$	−2.56155	−0.295783
$76$	5.12311	0.587661
$77$	0	0
$78$	−3.56155	−0.403266
$79$	14.2462	1.60282	0.801412	−	0.598113i	$-0.204082\pi$
$79$	14.2462	1.60282	0.801412	+	0.598113i	$0.204082\pi$
$80$	1.56155	0.174587
$81$	1.00000	0.111111
$82$	3.56155	0.393308
$83$	9.12311	1.00139	0.500695	−	0.865624i	$-0.333078\pi$
$83$	9.12311	1.00139	0.500695	+	0.865624i	$0.333078\pi$
$84$	0	0
$85$	1.75379	0.190225
$86$	−6.68466	−0.720825
$87$	7.56155	0.810684
$88$	−5.12311	−0.546125
$89$	−14.0000	−1.48400	−0.741999	−	0.670402i	$-0.766122\pi$
$89$	−14.0000	−1.48400	−0.741999	+	0.670402i	$0.766122\pi$
$90$	−1.56155	−0.164602
$91$	0	0
$92$	1.00000	0.104257
$93$	−3.12311	−0.323851
$94$	2.43845	0.251507
$95$	8.00000	0.820783
$96$	−1.00000	−0.102062
$97$	12.4384	1.26293	0.631466	−	0.775403i	$-0.282453\pi$
$97$	12.4384	1.26293	0.631466	+	0.775403i	$0.282453\pi$
$98$	0	0
$99$	5.12311	0.514891
$100$	−2.56155	−0.256155
$101$	−16.2462	−1.61656	−0.808279	−	0.588799i	$-0.799601\pi$
$101$	−16.2462	−1.61656	−0.808279	+	0.588799i	$0.799601\pi$
$102$	−1.12311	−0.111204
$103$	−18.9309	−1.86531	−0.932657	−	0.360764i	$-0.882516\pi$
$103$	−18.9309	−1.86531	−0.932657	+	0.360764i	$0.882516\pi$
$104$	−3.56155	−0.349239
$105$	0	0
$106$	−14.2462	−1.38371
$107$	−5.12311	−0.495269	−0.247635	−	0.968853i	$-0.579653\pi$
$107$	−5.12311	−0.495269	−0.247635	+	0.968853i	$0.579653\pi$
$108$	1.00000	0.0962250
$109$	10.4384	0.999822	0.499911	−	0.866077i	$-0.333366\pi$
$109$	10.4384	0.999822	0.499911	+	0.866077i	$0.333366\pi$
$110$	−8.00000	−0.762770
$111$	−1.56155	−0.148216
$112$	0	0
$113$	−2.68466	−0.252551	−0.126276	−	0.991995i	$-0.540302\pi$
$113$	−2.68466	−0.252551	−0.126276	+	0.991995i	$0.540302\pi$
$114$	−5.12311	−0.479823
$115$	1.56155	0.145616
$116$	7.56155	0.702073
$117$	3.56155	0.329266
$118$	4.87689	0.448955
$119$	0	0
$120$	−1.56155	−0.142550
$121$	15.2462	1.38602
$122$	0.876894	0.0793903
$123$	−3.56155	−0.321134
$124$	−3.12311	−0.280463
$125$	−11.8078	−1.05612
$126$	0	0
$127$	−16.6847	−1.48052	−0.740262	−	0.672318i	$-0.765299\pi$
$127$	−16.6847	−1.48052	−0.740262	+	0.672318i	$0.765299\pi$
$128$	−1.00000	−0.0883883
$129$	6.68466	0.588551
$130$	−5.56155	−0.487780
$131$	−4.87689	−0.426096	−0.213048	−	0.977042i	$-0.568339\pi$
$131$	−4.87689	−0.426096	−0.213048	+	0.977042i	$0.568339\pi$
$132$	5.12311	0.445909
$133$	0	0
$134$	1.12311	0.0970215
$135$	1.56155	0.134397
$136$	−1.12311	−0.0963055
$137$	−0.438447	−0.0374591	−0.0187295	−	0.999825i	$-0.505962\pi$
$137$	−0.438447	−0.0374591	−0.0187295	+	0.999825i	$0.505962\pi$
$138$	−1.00000	−0.0851257
$139$	−3.80776	−0.322970	−0.161485	−	0.986875i	$-0.551628\pi$
$139$	−3.80776	−0.322970	−0.161485	+	0.986875i	$0.551628\pi$
$140$	0	0
$141$	−2.43845	−0.205354
$142$	9.36932	0.786256
$143$	18.2462	1.52582
$144$	1.00000	0.0833333
$145$	11.8078	0.980581
$146$	9.12311	0.755034
$147$	0	0
$148$	−1.56155	−0.128359
$149$	−6.24621	−0.511710	−0.255855	−	0.966715i	$-0.582357\pi$
$149$	−6.24621	−0.511710	−0.255855	+	0.966715i	$0.582357\pi$
$150$	2.56155	0.209150
$151$	7.31534	0.595314	0.297657	−	0.954673i	$-0.403795\pi$
$151$	7.31534	0.595314	0.297657	+	0.954673i	$0.403795\pi$
$152$	−5.12311	−0.415539
$153$	1.12311	0.0907977
$154$	0	0
$155$	−4.87689	−0.391722
$156$	3.56155	0.285152
$157$	−14.2462	−1.13697	−0.568486	−	0.822693i	$-0.692471\pi$
$157$	−14.2462	−1.13697	−0.568486	+	0.822693i	$0.692471\pi$
$158$	−14.2462	−1.13337
$159$	14.2462	1.12980
$160$	−1.56155	−0.123452
$161$	0	0
$162$	−1.00000	−0.0785674
$163$	−8.00000	−0.626608	−0.313304	−	0.949653i	$-0.601436\pi$
$163$	−8.00000	−0.626608	−0.313304	+	0.949653i	$0.601436\pi$
$164$	−3.56155	−0.278111
$165$	8.00000	0.622799
$166$	−9.12311	−0.708090
$167$	14.2462	1.10240	0.551202	−	0.834372i	$-0.314169\pi$
$167$	14.2462	1.10240	0.551202	+	0.834372i	$0.314169\pi$
$168$	0	0
$169$	−0.315342	−0.0242570
$170$	−1.75379	−0.134509
$171$	5.12311	0.391774
$172$	6.68466	0.509700
$173$	−18.4924	−1.40595	−0.702976	−	0.711213i	$-0.748146\pi$
$173$	−18.4924	−1.40595	−0.702976	+	0.711213i	$0.748146\pi$
$174$	−7.56155	−0.573240
$175$	0	0
$176$	5.12311	0.386169
$177$	−4.87689	−0.366570
$178$	14.0000	1.04934
$179$	−3.80776	−0.284606	−0.142303	−	0.989823i	$-0.545451\pi$
$179$	−3.80776	−0.284606	−0.142303	+	0.989823i	$0.545451\pi$
$180$	1.56155	0.116391
$181$	15.1231	1.12409	0.562046	−	0.827106i	$-0.310014\pi$
$181$	15.1231	1.12409	0.562046	+	0.827106i	$0.310014\pi$
$182$	0	0
$183$	−0.876894	−0.0648219
$184$	−1.00000	−0.0737210
$185$	−2.43845	−0.179278
$186$	3.12311	0.228997
$187$	5.75379	0.420759
$188$	−2.43845	−0.177842
$189$	0	0
$190$	−8.00000	−0.580381
$191$	−20.0000	−1.44715	−0.723575	−	0.690246i	$-0.757502\pi$
$191$	−20.0000	−1.44715	−0.723575	+	0.690246i	$0.757502\pi$
$192$	1.00000	0.0721688
$193$	2.68466	0.193246	0.0966230	−	0.995321i	$-0.469196\pi$
$193$	2.68466	0.193246	0.0966230	+	0.995321i	$0.469196\pi$
$194$	−12.4384	−0.893028
$195$	5.56155	0.398271
$196$	0	0
$197$	24.9309	1.77625	0.888125	−	0.459601i	$-0.152008\pi$
$197$	24.9309	1.77625	0.888125	+	0.459601i	$0.152008\pi$
$198$	−5.12311	−0.364083
$199$	21.1771	1.50120	0.750602	−	0.660755i	$-0.229764\pi$
$199$	21.1771	1.50120	0.750602	+	0.660755i	$0.229764\pi$
$200$	2.56155	0.181129
$201$	−1.12311	−0.0792178
$202$	16.2462	1.14308
$203$	0	0
$204$	1.12311	0.0786331
$205$	−5.56155	−0.388436
$206$	18.9309	1.31898
$207$	1.00000	0.0695048
$208$	3.56155	0.246949
$209$	26.2462	1.81549
$210$	0	0
$211$	−16.4924	−1.13539	−0.567693	−	0.823241i	$-0.692164\pi$
$211$	−16.4924	−1.13539	−0.567693	+	0.823241i	$0.692164\pi$
$212$	14.2462	0.978434
$213$	−9.36932	−0.641975
$214$	5.12311	0.350208
$215$	10.4384	0.711896
$216$	−1.00000	−0.0680414
$217$	0	0
$218$	−10.4384	−0.706981
$219$	−9.12311	−0.616482
$220$	8.00000	0.539360
$221$	4.00000	0.269069
$222$	1.56155	0.104805
$223$	−3.12311	−0.209139	−0.104569	−	0.994518i	$-0.533346\pi$
$223$	−3.12311	−0.209139	−0.104569	+	0.994518i	$0.533346\pi$
$224$	0	0
$225$	−2.56155	−0.170770
$226$	2.68466	0.178581
$227$	6.19224	0.410993	0.205497	−	0.978658i	$-0.434119\pi$
$227$	6.19224	0.410993	0.205497	+	0.978658i	$0.434119\pi$
$228$	5.12311	0.339286
$229$	−2.24621	−0.148434	−0.0742169	−	0.997242i	$-0.523646\pi$
$229$	−2.24621	−0.148434	−0.0742169	+	0.997242i	$0.523646\pi$
$230$	−1.56155	−0.102966
$231$	0	0
$232$	−7.56155	−0.496440
$233$	−18.4924	−1.21148	−0.605739	−	0.795663i	$-0.707123\pi$
$233$	−18.4924	−1.21148	−0.605739	+	0.795663i	$0.707123\pi$
$234$	−3.56155	−0.232826
$235$	−3.80776	−0.248391
$236$	−4.87689	−0.317459
$237$	14.2462	0.925391
$238$	0	0
$239$	4.49242	0.290591	0.145295	−	0.989388i	$-0.453587\pi$
$239$	4.49242	0.290591	0.145295	+	0.989388i	$0.453587\pi$
$240$	1.56155	0.100798
$241$	20.0540	1.29179	0.645895	−	0.763426i	$-0.276484\pi$
$241$	20.0540	1.29179	0.645895	+	0.763426i	$0.276484\pi$
$242$	−15.2462	−0.980064
$243$	1.00000	0.0641500
$244$	−0.876894	−0.0561374
$245$	0	0
$246$	3.56155	0.227076
$247$	18.2462	1.16098
$248$	3.12311	0.198317
$249$	9.12311	0.578153
$250$	11.8078	0.746789
$251$	0.438447	0.0276745	0.0138373	−	0.999904i	$-0.495595\pi$
$251$	0.438447	0.0276745	0.0138373	+	0.999904i	$0.495595\pi$
$252$	0	0
$253$	5.12311	0.322087
$254$	16.6847	1.04689
$255$	1.75379	0.109827
$256$	1.00000	0.0625000
$257$	2.00000	0.124757	0.0623783	−	0.998053i	$-0.480131\pi$
$257$	2.00000	0.124757	0.0623783	+	0.998053i	$0.480131\pi$
$258$	−6.68466	−0.416169
$259$	0	0
$260$	5.56155	0.344913
$261$	7.56155	0.468048
$262$	4.87689	0.301296
$263$	22.9309	1.41398	0.706989	−	0.707225i	$-0.250053\pi$
$263$	22.9309	1.41398	0.706989	+	0.707225i	$0.250053\pi$
$264$	−5.12311	−0.315305
$265$	22.2462	1.36657
$266$	0	0
$267$	−14.0000	−0.856786
$268$	−1.12311	−0.0686046
$269$	−12.2462	−0.746665	−0.373332	−	0.927698i	$-0.621785\pi$
$269$	−12.2462	−0.746665	−0.373332	+	0.927698i	$0.621785\pi$
$270$	−1.56155	−0.0950331
$271$	−14.2462	−0.865396	−0.432698	−	0.901539i	$-0.642438\pi$
$271$	−14.2462	−0.865396	−0.432698	+	0.901539i	$0.642438\pi$
$272$	1.12311	0.0680983
$273$	0	0
$274$	0.438447	0.0264876
$275$	−13.1231	−0.791353
$276$	1.00000	0.0601929
$277$	13.1231	0.788491	0.394245	−	0.919005i	$-0.371006\pi$
$277$	13.1231	0.788491	0.394245	+	0.919005i	$0.371006\pi$
$278$	3.80776	0.228375
$279$	−3.12311	−0.186975
$280$	0	0
$281$	4.93087	0.294151	0.147076	−	0.989125i	$-0.453014\pi$
$281$	4.93087	0.294151	0.147076	+	0.989125i	$0.453014\pi$
$282$	2.43845	0.145207
$283$	10.4924	0.623710	0.311855	−	0.950130i	$-0.399050\pi$
$283$	10.4924	0.623710	0.311855	+	0.950130i	$0.399050\pi$
$284$	−9.36932	−0.555967
$285$	8.00000	0.473879
$286$	−18.2462	−1.07892
$287$	0	0
$288$	−1.00000	−0.0589256
$289$	−15.7386	−0.925802
$290$	−11.8078	−0.693376
$291$	12.4384	0.729155
$292$	−9.12311	−0.533889
$293$	−27.6155	−1.61332	−0.806658	−	0.591018i	$-0.798726\pi$
$293$	−27.6155	−1.61332	−0.806658	+	0.591018i	$0.798726\pi$
$294$	0	0
$295$	−7.61553	−0.443393
$296$	1.56155	0.0907634
$297$	5.12311	0.297273
$298$	6.24621	0.361833
$299$	3.56155	0.205970
$300$	−2.56155	−0.147891
$301$	0	0
$302$	−7.31534	−0.420951
$303$	−16.2462	−0.933320
$304$	5.12311	0.293830
$305$	−1.36932	−0.0784069
$306$	−1.12311	−0.0642037
$307$	−2.93087	−0.167274	−0.0836368	−	0.996496i	$-0.526654\pi$
$307$	−2.93087	−0.167274	−0.0836368	+	0.996496i	$0.526654\pi$
$308$	0	0
$309$	−18.9309	−1.07694
$310$	4.87689	0.276989
$311$	−18.7386	−1.06257	−0.531285	−	0.847193i	$-0.678291\pi$
$311$	−18.7386	−1.06257	−0.531285	+	0.847193i	$0.678291\pi$
$312$	−3.56155	−0.201633
$313$	−4.24621	−0.240010	−0.120005	−	0.992773i	$-0.538291\pi$
$313$	−4.24621	−0.240010	−0.120005	+	0.992773i	$0.538291\pi$
$314$	14.2462	0.803960
$315$	0	0
$316$	14.2462	0.801412
$317$	−17.8078	−1.00018	−0.500092	−	0.865972i	$-0.666700\pi$
$317$	−17.8078	−1.00018	−0.500092	+	0.865972i	$0.666700\pi$
$318$	−14.2462	−0.798888
$319$	38.7386	2.16895
$320$	1.56155	0.0872935
$321$	−5.12311	−0.285944
$322$	0	0
$323$	5.75379	0.320149
$324$	1.00000	0.0555556
$325$	−9.12311	−0.506059
$326$	8.00000	0.443079
$327$	10.4384	0.577247
$328$	3.56155	0.196654
$329$	0	0
$330$	−8.00000	−0.440386
$331$	−24.4924	−1.34623	−0.673113	−	0.739540i	$-0.735043\pi$
$331$	−24.4924	−1.34623	−0.673113	+	0.739540i	$0.735043\pi$
$332$	9.12311	0.500695
$333$	−1.56155	−0.0855726
$334$	−14.2462	−0.779518
$335$	−1.75379	−0.0958197
$336$	0	0
$337$	27.3693	1.49090	0.745451	−	0.666561i	$-0.232234\pi$
$337$	27.3693	1.49090	0.745451	+	0.666561i	$0.232234\pi$
$338$	0.315342	0.0171523
$339$	−2.68466	−0.145811
$340$	1.75379	0.0951125
$341$	−16.0000	−0.866449
$342$	−5.12311	−0.277026
$343$	0	0
$344$	−6.68466	−0.360413
$345$	1.56155	0.0840712
$346$	18.4924	0.994159
$347$	14.9309	0.801531	0.400766	−	0.916181i	$-0.368744\pi$
$347$	14.9309	0.801531	0.400766	+	0.916181i	$0.368744\pi$
$348$	7.56155	0.405342
$349$	16.2462	0.869640	0.434820	−	0.900517i	$-0.356812\pi$
$349$	16.2462	0.869640	0.434820	+	0.900517i	$0.356812\pi$
$350$	0	0
$351$	3.56155	0.190102
$352$	−5.12311	−0.273062
$353$	33.8078	1.79941	0.899703	−	0.436503i	$-0.143783\pi$
$353$	33.8078	1.79941	0.899703	+	0.436503i	$0.143783\pi$
$354$	4.87689	0.259204
$355$	−14.6307	−0.776516
$356$	−14.0000	−0.741999
$357$	0	0
$358$	3.80776	0.201247
$359$	−6.43845	−0.339808	−0.169904	−	0.985461i	$-0.554346\pi$
$359$	−6.43845	−0.339808	−0.169904	+	0.985461i	$0.554346\pi$
$360$	−1.56155	−0.0823011
$361$	7.24621	0.381380
$362$	−15.1231	−0.794853
$363$	15.2462	0.800219
$364$	0	0
$365$	−14.2462	−0.745681
$366$	0.876894	0.0458360
$367$	18.4384	0.962479	0.481240	−	0.876589i	$-0.340187\pi$
$367$	18.4384	0.962479	0.481240	+	0.876589i	$0.340187\pi$
$368$	1.00000	0.0521286
$369$	−3.56155	−0.185407
$370$	2.43845	0.126769
$371$	0	0
$372$	−3.12311	−0.161925
$373$	15.1231	0.783045	0.391522	−	0.920169i	$-0.371949\pi$
$373$	15.1231	0.783045	0.391522	+	0.920169i	$0.371949\pi$
$374$	−5.75379	−0.297521
$375$	−11.8078	−0.609750
$376$	2.43845	0.125753
$377$	26.9309	1.38701
$378$	0	0
$379$	20.0540	1.03010	0.515052	−	0.857159i	$-0.327773\pi$
$379$	20.0540	1.03010	0.515052	+	0.857159i	$0.327773\pi$
$380$	8.00000	0.410391
$381$	−16.6847	−0.854781
$382$	20.0000	1.02329
$383$	6.24621	0.319166	0.159583	−	0.987184i	$-0.448985\pi$
$383$	6.24621	0.319166	0.159583	+	0.987184i	$0.448985\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	−2.68466	−0.136646
$387$	6.68466	0.339800
$388$	12.4384	0.631466
$389$	−29.3693	−1.48908	−0.744542	−	0.667576i	$-0.767332\pi$
$389$	−29.3693	−1.48908	−0.744542	+	0.667576i	$0.767332\pi$
$390$	−5.56155	−0.281620
$391$	1.12311	0.0567979
$392$	0	0
$393$	−4.87689	−0.246007
$394$	−24.9309	−1.25600
$395$	22.2462	1.11933
$396$	5.12311	0.257446
$397$	7.75379	0.389152	0.194576	−	0.980887i	$-0.437667\pi$
$397$	7.75379	0.389152	0.194576	+	0.980887i	$0.437667\pi$
$398$	−21.1771	−1.06151
$399$	0	0
$400$	−2.56155	−0.128078
$401$	16.2462	0.811297	0.405649	−	0.914029i	$-0.367046\pi$
$401$	16.2462	0.811297	0.405649	+	0.914029i	$0.367046\pi$
$402$	1.12311	0.0560154
$403$	−11.1231	−0.554081
$404$	−16.2462	−0.808279
$405$	1.56155	0.0775942
$406$	0	0
$407$	−8.00000	−0.396545
$408$	−1.12311	−0.0556020
$409$	−33.6155	−1.66218	−0.831090	−	0.556137i	$-0.812283\pi$
$409$	−33.6155	−1.66218	−0.831090	+	0.556137i	$0.812283\pi$
$410$	5.56155	0.274666
$411$	−0.438447	−0.0216270
$412$	−18.9309	−0.932657
$413$	0	0
$414$	−1.00000	−0.0491473
$415$	14.2462	0.699319
$416$	−3.56155	−0.174619
$417$	−3.80776	−0.186467
$418$	−26.2462	−1.28374
$419$	−23.8617	−1.16572	−0.582861	−	0.812572i	$-0.698067\pi$
$419$	−23.8617	−1.16572	−0.582861	+	0.812572i	$0.698067\pi$
$420$	0	0
$421$	33.1771	1.61695	0.808476	−	0.588529i	$-0.200293\pi$
$421$	33.1771	1.61695	0.808476	+	0.588529i	$0.200293\pi$
$422$	16.4924	0.802839
$423$	−2.43845	−0.118561
$424$	−14.2462	−0.691857
$425$	−2.87689	−0.139550
$426$	9.36932	0.453945
$427$	0	0
$428$	−5.12311	−0.247635
$429$	18.2462	0.880935
$430$	−10.4384	−0.503387
$431$	−3.31534	−0.159694	−0.0798472	−	0.996807i	$-0.525443\pi$
$431$	−3.31534	−0.159694	−0.0798472	+	0.996807i	$0.525443\pi$
$432$	1.00000	0.0481125
$433$	−14.6847	−0.705700	−0.352850	−	0.935680i	$-0.614787\pi$
$433$	−14.6847	−0.705700	−0.352850	+	0.935680i	$0.614787\pi$
$434$	0	0
$435$	11.8078	0.566139
$436$	10.4384	0.499911
$437$	5.12311	0.245071
$438$	9.12311	0.435919
$439$	23.6155	1.12711	0.563554	−	0.826079i	$-0.309434\pi$
$439$	23.6155	1.12711	0.563554	+	0.826079i	$0.309434\pi$
$440$	−8.00000	−0.381385
$441$	0	0
$442$	−4.00000	−0.190261
$443$	9.06913	0.430887	0.215444	−	0.976516i	$-0.430880\pi$
$443$	9.06913	0.430887	0.215444	+	0.976516i	$0.430880\pi$
$444$	−1.56155	−0.0741080
$445$	−21.8617	−1.03635
$446$	3.12311	0.147883
$447$	−6.24621	−0.295436
$448$	0	0
$449$	−0.246211	−0.0116194	−0.00580971	−	0.999983i	$-0.501849\pi$
$449$	−0.246211	−0.0116194	−0.00580971	+	0.999983i	$0.501849\pi$
$450$	2.56155	0.120753
$451$	−18.2462	−0.859181
$452$	−2.68466	−0.126276
$453$	7.31534	0.343705
$454$	−6.19224	−0.290616
$455$	0	0
$456$	−5.12311	−0.239911
$457$	7.36932	0.344722	0.172361	−	0.985034i	$-0.444860\pi$
$457$	7.36932	0.344722	0.172361	+	0.985034i	$0.444860\pi$
$458$	2.24621	0.104959
$459$	1.12311	0.0524221
$460$	1.56155	0.0728078
$461$	−40.7386	−1.89739	−0.948694	−	0.316197i	$-0.897594\pi$
$461$	−40.7386	−1.89739	−0.948694	+	0.316197i	$0.897594\pi$
$462$	0	0
$463$	−13.5616	−0.630259	−0.315129	−	0.949049i	$-0.602048\pi$
$463$	−13.5616	−0.630259	−0.315129	+	0.949049i	$0.602048\pi$
$464$	7.56155	0.351036
$465$	−4.87689	−0.226161
$466$	18.4924	0.856645
$467$	−2.68466	−0.124231	−0.0621156	−	0.998069i	$-0.519785\pi$
$467$	−2.68466	−0.124231	−0.0621156	+	0.998069i	$0.519785\pi$
$468$	3.56155	0.164633
$469$	0	0
$470$	3.80776	0.175639
$471$	−14.2462	−0.656431
$472$	4.87689	0.224477
$473$	34.2462	1.57464
$474$	−14.2462	−0.654350
$475$	−13.1231	−0.602129
$476$	0	0
$477$	14.2462	0.652289
$478$	−4.49242	−0.205479
$479$	−31.6155	−1.44455	−0.722275	−	0.691606i	$-0.756904\pi$
$479$	−31.6155	−1.44455	−0.722275	+	0.691606i	$0.756904\pi$
$480$	−1.56155	−0.0712748
$481$	−5.56155	−0.253585
$482$	−20.0540	−0.913434
$483$	0	0
$484$	15.2462	0.693010
$485$	19.4233	0.881966
$486$	−1.00000	−0.0453609
$487$	−5.56155	−0.252018	−0.126009	−	0.992029i	$-0.540217\pi$
$487$	−5.56155	−0.252018	−0.126009	+	0.992029i	$0.540217\pi$
$488$	0.876894	0.0396951
$489$	−8.00000	−0.361773
$490$	0	0
$491$	−26.7386	−1.20670	−0.603349	−	0.797477i	$-0.706167\pi$
$491$	−26.7386	−1.20670	−0.603349	+	0.797477i	$0.706167\pi$
$492$	−3.56155	−0.160567
$493$	8.49242	0.382479
$494$	−18.2462	−0.820936
$495$	8.00000	0.359573
$496$	−3.12311	−0.140232
$497$	0	0
$498$	−9.12311	−0.408816
$499$	41.3693	1.85194	0.925972	−	0.377591i	$-0.123247\pi$
$499$	41.3693	1.85194	0.925972	+	0.377591i	$0.123247\pi$
$500$	−11.8078	−0.528059
$501$	14.2462	0.636474
$502$	−0.438447	−0.0195689
$503$	32.1080	1.43162	0.715811	−	0.698294i	$-0.246057\pi$
$503$	32.1080	1.43162	0.715811	+	0.698294i	$0.246057\pi$
$504$	0	0
$505$	−25.3693	−1.12892
$506$	−5.12311	−0.227750
$507$	−0.315342	−0.0140048
$508$	−16.6847	−0.740262
$509$	3.36932	0.149342	0.0746712	−	0.997208i	$-0.476209\pi$
$509$	3.36932	0.149342	0.0746712	+	0.997208i	$0.476209\pi$
$510$	−1.75379	−0.0776591
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	5.12311	0.226191
$514$	−2.00000	−0.0882162
$515$	−29.5616	−1.30264
$516$	6.68466	0.294276
$517$	−12.4924	−0.549416
$518$	0	0
$519$	−18.4924	−0.811727
$520$	−5.56155	−0.243890
$521$	−0.246211	−0.0107867	−0.00539336	−	0.999985i	$-0.501717\pi$
$521$	−0.246211	−0.0107867	−0.00539336	+	0.999985i	$0.501717\pi$
$522$	−7.56155	−0.330960
$523$	−14.0000	−0.612177	−0.306089	−	0.952003i	$-0.599020\pi$
$523$	−14.0000	−0.612177	−0.306089	+	0.952003i	$0.599020\pi$
$524$	−4.87689	−0.213048
$525$	0	0
$526$	−22.9309	−0.999833
$527$	−3.50758	−0.152792
$528$	5.12311	0.222955
$529$	1.00000	0.0434783
$530$	−22.2462	−0.966314
$531$	−4.87689	−0.211639
$532$	0	0
$533$	−12.6847	−0.549434
$534$	14.0000	0.605839
$535$	−8.00000	−0.345870
$536$	1.12311	0.0485108
$537$	−3.80776	−0.164317
$538$	12.2462	0.527972
$539$	0	0
$540$	1.56155	0.0671985
$541$	−15.3693	−0.660779	−0.330389	−	0.943845i	$-0.607180\pi$
$541$	−15.3693	−0.660779	−0.330389	+	0.943845i	$0.607180\pi$
$542$	14.2462	0.611927
$543$	15.1231	0.648995
$544$	−1.12311	−0.0481528
$545$	16.3002	0.698223
$546$	0	0
$547$	−3.61553	−0.154589	−0.0772944	−	0.997008i	$-0.524628\pi$
$547$	−3.61553	−0.154589	−0.0772944	+	0.997008i	$0.524628\pi$
$548$	−0.438447	−0.0187295
$549$	−0.876894	−0.0374249
$550$	13.1231	0.559571
$551$	38.7386	1.65032
$552$	−1.00000	−0.0425628
$553$	0	0
$554$	−13.1231	−0.557547
$555$	−2.43845	−0.103506
$556$	−3.80776	−0.161485
$557$	−28.9848	−1.22813	−0.614064	−	0.789257i	$-0.710466\pi$
$557$	−28.9848	−1.22813	−0.614064	+	0.789257i	$0.710466\pi$
$558$	3.12311	0.132212
$559$	23.8078	1.00696
$560$	0	0
$561$	5.75379	0.242925
$562$	−4.93087	−0.207996
$563$	−19.5616	−0.824421	−0.412211	−	0.911089i	$-0.635243\pi$
$563$	−19.5616	−0.824421	−0.412211	+	0.911089i	$0.635243\pi$
$564$	−2.43845	−0.102677
$565$	−4.19224	−0.176369
$566$	−10.4924	−0.441029
$567$	0	0
$568$	9.36932	0.393128
$569$	−44.5464	−1.86748	−0.933741	−	0.357949i	$-0.883476\pi$
$569$	−44.5464	−1.86748	−0.933741	+	0.357949i	$0.883476\pi$
$570$	−8.00000	−0.335083
$571$	43.3693	1.81495	0.907475	−	0.420107i	$-0.138007\pi$
$571$	43.3693	1.81495	0.907475	+	0.420107i	$0.138007\pi$
$572$	18.2462	0.762912
$573$	−20.0000	−0.835512
$574$	0	0
$575$	−2.56155	−0.106824
$576$	1.00000	0.0416667
$577$	19.7538	0.822361	0.411180	−	0.911554i	$-0.365117\pi$
$577$	19.7538	0.822361	0.411180	+	0.911554i	$0.365117\pi$
$578$	15.7386	0.654641
$579$	2.68466	0.111571
$580$	11.8078	0.490291
$581$	0	0
$582$	−12.4384	−0.515590
$583$	72.9848	3.02272
$584$	9.12311	0.377517
$585$	5.56155	0.229942
$586$	27.6155	1.14079
$587$	24.9848	1.03123	0.515617	−	0.856819i	$-0.327563\pi$
$587$	24.9848	1.03123	0.515617	+	0.856819i	$0.327563\pi$
$588$	0	0
$589$	−16.0000	−0.659269
$590$	7.61553	0.313526
$591$	24.9309	1.02552
$592$	−1.56155	−0.0641794
$593$	−30.3002	−1.24428	−0.622140	−	0.782906i	$-0.713736\pi$
$593$	−30.3002	−1.24428	−0.622140	+	0.782906i	$0.713736\pi$
$594$	−5.12311	−0.210204
$595$	0	0
$596$	−6.24621	−0.255855
$597$	21.1771	0.866720
$598$	−3.56155	−0.145643
$599$	−10.7386	−0.438769	−0.219384	−	0.975639i	$-0.570405\pi$
$599$	−10.7386	−0.438769	−0.219384	+	0.975639i	$0.570405\pi$
$600$	2.56155	0.104575
$601$	3.36932	0.137437	0.0687187	−	0.997636i	$-0.478109\pi$
$601$	3.36932	0.137437	0.0687187	+	0.997636i	$0.478109\pi$
$602$	0	0
$603$	−1.12311	−0.0457364
$604$	7.31534	0.297657
$605$	23.8078	0.967923
$606$	16.2462	0.659957
$607$	47.6155	1.93265	0.966327	−	0.257316i	$-0.0828381\pi$
$607$	47.6155	1.93265	0.966327	+	0.257316i	$0.0828381\pi$
$608$	−5.12311	−0.207769
$609$	0	0
$610$	1.36932	0.0554420
$611$	−8.68466	−0.351344
$612$	1.12311	0.0453989
$613$	3.80776	0.153794	0.0768971	−	0.997039i	$-0.475499\pi$
$613$	3.80776	0.153794	0.0768971	+	0.997039i	$0.475499\pi$
$614$	2.93087	0.118280
$615$	−5.56155	−0.224263
$616$	0	0
$617$	31.7538	1.27836	0.639180	−	0.769057i	$-0.279274\pi$
$617$	31.7538	1.27836	0.639180	+	0.769057i	$0.279274\pi$
$618$	18.9309	0.761511
$619$	−8.24621	−0.331443	−0.165722	−	0.986173i	$-0.552995\pi$
$619$	−8.24621	−0.331443	−0.165722	+	0.986173i	$0.552995\pi$
$620$	−4.87689	−0.195861
$621$	1.00000	0.0401286
$622$	18.7386	0.751351
$623$	0	0
$624$	3.56155	0.142576
$625$	−5.63068	−0.225227
$626$	4.24621	0.169713
$627$	26.2462	1.04817
$628$	−14.2462	−0.568486
$629$	−1.75379	−0.0699281
$630$	0	0
$631$	8.49242	0.338078	0.169039	−	0.985609i	$-0.445934\pi$
$631$	8.49242	0.338078	0.169039	+	0.985609i	$0.445934\pi$
$632$	−14.2462	−0.566684
$633$	−16.4924	−0.655515
$634$	17.8078	0.707237
$635$	−26.0540	−1.03392
$636$	14.2462	0.564899
$637$	0	0
$638$	−38.7386	−1.53368
$639$	−9.36932	−0.370644
$640$	−1.56155	−0.0617258
$641$	−13.3153	−0.525924	−0.262962	−	0.964806i	$-0.584699\pi$
$641$	−13.3153	−0.525924	−0.262962	+	0.964806i	$0.584699\pi$
$642$	5.12311	0.202193
$643$	38.0000	1.49857	0.749287	−	0.662246i	$-0.230396\pi$
$643$	38.0000	1.49857	0.749287	+	0.662246i	$0.230396\pi$
$644$	0	0
$645$	10.4384	0.411013
$646$	−5.75379	−0.226380
$647$	3.50758	0.137897	0.0689486	−	0.997620i	$-0.478036\pi$
$647$	3.50758	0.137897	0.0689486	+	0.997620i	$0.478036\pi$
$648$	−1.00000	−0.0392837
$649$	−24.9848	−0.980741
$650$	9.12311	0.357838
$651$	0	0
$652$	−8.00000	−0.313304
$653$	36.5464	1.43017	0.715086	−	0.699037i	$-0.246388\pi$
$653$	36.5464	1.43017	0.715086	+	0.699037i	$0.246388\pi$
$654$	−10.4384	−0.408176
$655$	−7.61553	−0.297563
$656$	−3.56155	−0.139055
$657$	−9.12311	−0.355926
$658$	0	0
$659$	5.61553	0.218750	0.109375	−	0.994001i	$-0.465115\pi$
$659$	5.61553	0.218750	0.109375	+	0.994001i	$0.465115\pi$
$660$	8.00000	0.311400
$661$	−32.8769	−1.27876	−0.639381	−	0.768890i	$-0.720810\pi$
$661$	−32.8769	−1.27876	−0.639381	+	0.768890i	$0.720810\pi$
$662$	24.4924	0.951925
$663$	4.00000	0.155347
$664$	−9.12311	−0.354045
$665$	0	0
$666$	1.56155	0.0605089
$667$	7.56155	0.292784
$668$	14.2462	0.551202
$669$	−3.12311	−0.120746
$670$	1.75379	0.0677548
$671$	−4.49242	−0.173428
$672$	0	0
$673$	22.6847	0.874429	0.437215	−	0.899357i	$-0.355965\pi$
$673$	22.6847	0.874429	0.437215	+	0.899357i	$0.355965\pi$
$674$	−27.3693	−1.05423
$675$	−2.56155	−0.0985942
$676$	−0.315342	−0.0121285
$677$	−2.63068	−0.101105	−0.0505527	−	0.998721i	$-0.516098\pi$
$677$	−2.63068	−0.101105	−0.0505527	+	0.998721i	$0.516098\pi$
$678$	2.68466	0.103104
$679$	0	0
$680$	−1.75379	−0.0672547
$681$	6.19224	0.237287
$682$	16.0000	0.612672
$683$	−7.50758	−0.287269	−0.143635	−	0.989631i	$-0.545879\pi$
$683$	−7.50758	−0.287269	−0.143635	+	0.989631i	$0.545879\pi$
$684$	5.12311	0.195887
$685$	−0.684658	−0.0261595
$686$	0	0
$687$	−2.24621	−0.0856983
$688$	6.68466	0.254850
$689$	50.7386	1.93299
$690$	−1.56155	−0.0594473
$691$	50.0540	1.90414	0.952071	−	0.305876i	$-0.0989492\pi$
$691$	50.0540	1.90414	0.952071	+	0.305876i	$0.0989492\pi$
$692$	−18.4924	−0.702976
$693$	0	0
$694$	−14.9309	−0.566768
$695$	−5.94602	−0.225546
$696$	−7.56155	−0.286620
$697$	−4.00000	−0.151511
$698$	−16.2462	−0.614928
$699$	−18.4924	−0.699448
$700$	0	0
$701$	34.2462	1.29346	0.646731	−	0.762718i	$-0.276136\pi$
$701$	34.2462	1.29346	0.646731	+	0.762718i	$0.276136\pi$
$702$	−3.56155	−0.134422
$703$	−8.00000	−0.301726
$704$	5.12311	0.193084
$705$	−3.80776	−0.143409
$706$	−33.8078	−1.27237
$707$	0	0
$708$	−4.87689	−0.183285
$709$	10.6307	0.399244	0.199622	−	0.979873i	$-0.436029\pi$
$709$	10.6307	0.399244	0.199622	+	0.979873i	$0.436029\pi$
$710$	14.6307	0.549080
$711$	14.2462	0.534275
$712$	14.0000	0.524672
$713$	−3.12311	−0.116961
$714$	0	0
$715$	28.4924	1.06556
$716$	−3.80776	−0.142303
$717$	4.49242	0.167773
$718$	6.43845	0.240281
$719$	−10.4384	−0.389288	−0.194644	−	0.980874i	$-0.562355\pi$
$719$	−10.4384	−0.389288	−0.194644	+	0.980874i	$0.562355\pi$
$720$	1.56155	0.0581956
$721$	0	0
$722$	−7.24621	−0.269676
$723$	20.0540	0.745815
$724$	15.1231	0.562046
$725$	−19.3693	−0.719358
$726$	−15.2462	−0.565840
$727$	1.75379	0.0650444	0.0325222	−	0.999471i	$-0.489646\pi$
$727$	1.75379	0.0650444	0.0325222	+	0.999471i	$0.489646\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	14.2462	0.527276
$731$	7.50758	0.277678
$732$	−0.876894	−0.0324109
$733$	−25.7538	−0.951238	−0.475619	−	0.879651i	$-0.657776\pi$
$733$	−25.7538	−0.951238	−0.475619	+	0.879651i	$0.657776\pi$
$734$	−18.4384	−0.680576
$735$	0	0
$736$	−1.00000	−0.0368605
$737$	−5.75379	−0.211944
$738$	3.56155	0.131103
$739$	23.6155	0.868711	0.434356	−	0.900741i	$-0.356976\pi$
$739$	23.6155	0.868711	0.434356	+	0.900741i	$0.356976\pi$
$740$	−2.43845	−0.0896391
$741$	18.2462	0.670291
$742$	0	0
$743$	−24.9848	−0.916605	−0.458303	−	0.888796i	$-0.651542\pi$
$743$	−24.9848	−0.916605	−0.458303	+	0.888796i	$0.651542\pi$
$744$	3.12311	0.114499
$745$	−9.75379	−0.357351
$746$	−15.1231	−0.553696
$747$	9.12311	0.333797
$748$	5.75379	0.210379
$749$	0	0
$750$	11.8078	0.431159
$751$	24.4924	0.893741	0.446871	−	0.894599i	$-0.352538\pi$
$751$	24.4924	0.893741	0.446871	+	0.894599i	$0.352538\pi$
$752$	−2.43845	−0.0889210
$753$	0.438447	0.0159779
$754$	−26.9309	−0.980764
$755$	11.4233	0.415736
$756$	0	0
$757$	−25.3693	−0.922064	−0.461032	−	0.887384i	$-0.652521\pi$
$757$	−25.3693	−0.922064	−0.461032	+	0.887384i	$0.652521\pi$
$758$	−20.0540	−0.728393
$759$	5.12311	0.185957
$760$	−8.00000	−0.290191
$761$	3.26137	0.118224	0.0591122	−	0.998251i	$-0.481173\pi$
$761$	3.26137	0.118224	0.0591122	+	0.998251i	$0.481173\pi$
$762$	16.6847	0.604421
$763$	0	0
$764$	−20.0000	−0.723575
$765$	1.75379	0.0634084
$766$	−6.24621	−0.225685
$767$	−17.3693	−0.627170
$768$	1.00000	0.0360844
$769$	47.1771	1.70125	0.850625	−	0.525774i	$-0.176224\pi$
$769$	47.1771	1.70125	0.850625	+	0.525774i	$0.176224\pi$
$770$	0	0
$771$	2.00000	0.0720282
$772$	2.68466	0.0966230
$773$	32.3002	1.16176	0.580878	−	0.813990i	$-0.302709\pi$
$773$	32.3002	1.16176	0.580878	+	0.813990i	$0.302709\pi$
$774$	−6.68466	−0.240275
$775$	8.00000	0.287368
$776$	−12.4384	−0.446514
$777$	0	0
$778$	29.3693	1.05294
$779$	−18.2462	−0.653738
$780$	5.56155	0.199136
$781$	−48.0000	−1.71758
$782$	−1.12311	−0.0401622
$783$	7.56155	0.270228
$784$	0	0
$785$	−22.2462	−0.794001
$786$	4.87689	0.173953
$787$	10.8769	0.387719	0.193860	−	0.981029i	$-0.437899\pi$
$787$	10.8769	0.387719	0.193860	+	0.981029i	$0.437899\pi$
$788$	24.9309	0.888125
$789$	22.9309	0.816361
$790$	−22.2462	−0.791485
$791$	0	0
$792$	−5.12311	−0.182042
$793$	−3.12311	−0.110905
$794$	−7.75379	−0.275172
$795$	22.2462	0.788992
$796$	21.1771	0.750602
$797$	−27.4233	−0.971383	−0.485691	−	0.874130i	$-0.661432\pi$
$797$	−27.4233	−0.971383	−0.485691	+	0.874130i	$0.661432\pi$
$798$	0	0
$799$	−2.73863	−0.0968859
$800$	2.56155	0.0905646
$801$	−14.0000	−0.494666
$802$	−16.2462	−0.573674
$803$	−46.7386	−1.64937
$804$	−1.12311	−0.0396089
$805$	0	0
$806$	11.1231	0.391795
$807$	−12.2462	−0.431087
$808$	16.2462	0.571540
$809$	23.8617	0.838934	0.419467	−	0.907771i	$-0.362217\pi$
$809$	23.8617	0.838934	0.419467	+	0.907771i	$0.362217\pi$
$810$	−1.56155	−0.0548674
$811$	24.6847	0.866796	0.433398	−	0.901203i	$-0.357315\pi$
$811$	24.6847	0.866796	0.433398	+	0.901203i	$0.357315\pi$
$812$	0	0
$813$	−14.2462	−0.499636
$814$	8.00000	0.280400
$815$	−12.4924	−0.437590
$816$	1.12311	0.0393166
$817$	34.2462	1.19812
$818$	33.6155	1.17534
$819$	0	0
$820$	−5.56155	−0.194218
$821$	−55.4773	−1.93617	−0.968085	−	0.250622i	$-0.919365\pi$
$821$	−55.4773	−1.93617	−0.968085	+	0.250622i	$0.919365\pi$
$822$	0.438447	0.0152926
$823$	23.3153	0.812722	0.406361	−	0.913713i	$-0.366798\pi$
$823$	23.3153	0.812722	0.406361	+	0.913713i	$0.366798\pi$
$824$	18.9309	0.659488
$825$	−13.1231	−0.456888
$826$	0	0
$827$	48.7386	1.69481	0.847404	−	0.530948i	$-0.178164\pi$
$827$	48.7386	1.69481	0.847404	+	0.530948i	$0.178164\pi$
$828$	1.00000	0.0347524
$829$	−24.7386	−0.859208	−0.429604	−	0.903017i	$-0.641347\pi$
$829$	−24.7386	−0.859208	−0.429604	+	0.903017i	$0.641347\pi$
$830$	−14.2462	−0.494493
$831$	13.1231	0.455235
$832$	3.56155	0.123475
$833$	0	0
$834$	3.80776	0.131852
$835$	22.2462	0.769862
$836$	26.2462	0.907744
$837$	−3.12311	−0.107950
$838$	23.8617	0.824290
$839$	−7.61553	−0.262917	−0.131459	−	0.991322i	$-0.541966\pi$
$839$	−7.61553	−0.262917	−0.131459	+	0.991322i	$0.541966\pi$
$840$	0	0
$841$	28.1771	0.971623
$842$	−33.1771	−1.14336
$843$	4.93087	0.169828
$844$	−16.4924	−0.567693
$845$	−0.492423	−0.0169398
$846$	2.43845	0.0838355
$847$	0	0
$848$	14.2462	0.489217
$849$	10.4924	0.360099
$850$	2.87689	0.0986767
$851$	−1.56155	−0.0535293
$852$	−9.36932	−0.320988
$853$	0.438447	0.0150121	0.00750607	−	0.999972i	$-0.497611\pi$
$853$	0.438447	0.0150121	0.00750607	+	0.999972i	$0.497611\pi$
$854$	0	0
$855$	8.00000	0.273594
$856$	5.12311	0.175104
$857$	−1.31534	−0.0449312	−0.0224656	−	0.999748i	$-0.507152\pi$
$857$	−1.31534	−0.0449312	−0.0224656	+	0.999748i	$0.507152\pi$
$858$	−18.2462	−0.622915
$859$	33.1771	1.13199	0.565994	−	0.824410i	$-0.308493\pi$
$859$	33.1771	1.13199	0.565994	+	0.824410i	$0.308493\pi$
$860$	10.4384	0.355948
$861$	0	0
$862$	3.31534	0.112921
$863$	10.7386	0.365547	0.182774	−	0.983155i	$-0.441492\pi$
$863$	10.7386	0.365547	0.182774	+	0.983155i	$0.441492\pi$
$864$	−1.00000	−0.0340207
$865$	−28.8769	−0.981844
$866$	14.6847	0.499005
$867$	−15.7386	−0.534512
$868$	0	0
$869$	72.9848	2.47584
$870$	−11.8078	−0.400321
$871$	−4.00000	−0.135535
$872$	−10.4384	−0.353490
$873$	12.4384	0.420978
$874$	−5.12311	−0.173292
$875$	0	0
$876$	−9.12311	−0.308241
$877$	−35.8617	−1.21096	−0.605482	−	0.795859i	$-0.707020\pi$
$877$	−35.8617	−1.21096	−0.605482	+	0.795859i	$0.707020\pi$
$878$	−23.6155	−0.796985
$879$	−27.6155	−0.931449
$880$	8.00000	0.269680
$881$	2.00000	0.0673817	0.0336909	−	0.999432i	$-0.489274\pi$
$881$	2.00000	0.0673817	0.0336909	+	0.999432i	$0.489274\pi$
$882$	0	0
$883$	−8.87689	−0.298731	−0.149366	−	0.988782i	$-0.547723\pi$
$883$	−8.87689	−0.298731	−0.149366	+	0.988782i	$0.547723\pi$
$884$	4.00000	0.134535
$885$	−7.61553	−0.255993
$886$	−9.06913	−0.304683
$887$	−24.0000	−0.805841	−0.402921	−	0.915235i	$-0.632005\pi$
$887$	−24.0000	−0.805841	−0.402921	+	0.915235i	$0.632005\pi$
$888$	1.56155	0.0524023
$889$	0	0
$890$	21.8617	0.732807
$891$	5.12311	0.171630
$892$	−3.12311	−0.104569
$893$	−12.4924	−0.418043
$894$	6.24621	0.208905
$895$	−5.94602	−0.198754
$896$	0	0
$897$	3.56155	0.118917
$898$	0.246211	0.00821618
$899$	−23.6155	−0.787622
$900$	−2.56155	−0.0853851
$901$	16.0000	0.533037
$902$	18.2462	0.607532
$903$	0	0
$904$	2.68466	0.0892904
$905$	23.6155	0.785007
$906$	−7.31534	−0.243036
$907$	52.5464	1.74477	0.872387	−	0.488815i	$-0.162571\pi$
$907$	52.5464	1.74477	0.872387	+	0.488815i	$0.162571\pi$
$908$	6.19224	0.205497
$909$	−16.2462	−0.538853
$910$	0	0
$911$	−1.94602	−0.0644747	−0.0322373	−	0.999480i	$-0.510263\pi$
$911$	−1.94602	−0.0644747	−0.0322373	+	0.999480i	$0.510263\pi$
$912$	5.12311	0.169643
$913$	46.7386	1.54682
$914$	−7.36932	−0.243755
$915$	−1.36932	−0.0452682
$916$	−2.24621	−0.0742169
$917$	0	0
$918$	−1.12311	−0.0370680
$919$	−50.7386	−1.67371	−0.836857	−	0.547422i	$-0.815609\pi$
$919$	−50.7386	−1.67371	−0.836857	+	0.547422i	$0.815609\pi$
$920$	−1.56155	−0.0514829
$921$	−2.93087	−0.0965754
$922$	40.7386	1.34166
$923$	−33.3693	−1.09836
$924$	0	0
$925$	4.00000	0.131519
$926$	13.5616	0.445660
$927$	−18.9309	−0.621771
$928$	−7.56155	−0.248220
$929$	36.4384	1.19551	0.597753	−	0.801680i	$-0.296060\pi$
$929$	36.4384	1.19551	0.597753	+	0.801680i	$0.296060\pi$
$930$	4.87689	0.159920
$931$	0	0
$932$	−18.4924	−0.605739
$933$	−18.7386	−0.613475
$934$	2.68466	0.0878447
$935$	8.98485	0.293836
$936$	−3.56155	−0.116413
$937$	27.1771	0.887837	0.443918	−	0.896067i	$-0.353588\pi$
$937$	27.1771	0.887837	0.443918	+	0.896067i	$0.353588\pi$
$938$	0	0
$939$	−4.24621	−0.138570
$940$	−3.80776	−0.124196
$941$	−1.94602	−0.0634386	−0.0317193	−	0.999497i	$-0.510098\pi$
$941$	−1.94602	−0.0634386	−0.0317193	+	0.999497i	$0.510098\pi$
$942$	14.2462	0.464167
$943$	−3.56155	−0.115980
$944$	−4.87689	−0.158729
$945$	0	0
$946$	−34.2462	−1.11344
$947$	−54.9309	−1.78501	−0.892507	−	0.451034i	$-0.851055\pi$
$947$	−54.9309	−1.78501	−0.892507	+	0.451034i	$0.851055\pi$
$948$	14.2462	0.462695
$949$	−32.4924	−1.05475
$950$	13.1231	0.425770
$951$	−17.8078	−0.577456
$952$	0	0
$953$	50.0000	1.61966	0.809829	−	0.586665i	$-0.199560\pi$
$953$	50.0000	1.61966	0.809829	+	0.586665i	$0.199560\pi$
$954$	−14.2462	−0.461238
$955$	−31.2311	−1.01061
$956$	4.49242	0.145295
$957$	38.7386	1.25224
$958$	31.6155	1.02145
$959$	0	0
$960$	1.56155	0.0503989
$961$	−21.2462	−0.685362
$962$	5.56155	0.179312
$963$	−5.12311	−0.165090
$964$	20.0540	0.645895
$965$	4.19224	0.134953
$966$	0	0
$967$	−9.75379	−0.313661	−0.156830	−	0.987626i	$-0.550128\pi$
$967$	−9.75379	−0.313661	−0.156830	+	0.987626i	$0.550128\pi$
$968$	−15.2462	−0.490032
$969$	5.75379	0.184838
$970$	−19.4233	−0.623644
$971$	1.61553	0.0518448	0.0259224	−	0.999664i	$-0.491748\pi$
$971$	1.61553	0.0518448	0.0259224	+	0.999664i	$0.491748\pi$
$972$	1.00000	0.0320750
$973$	0	0
$974$	5.56155	0.178204
$975$	−9.12311	−0.292173
$976$	−0.876894	−0.0280687
$977$	−26.1922	−0.837964	−0.418982	−	0.907995i	$-0.637613\pi$
$977$	−26.1922	−0.837964	−0.418982	+	0.907995i	$0.637613\pi$
$978$	8.00000	0.255812
$979$	−71.7235	−2.29229
$980$	0	0
$981$	10.4384	0.333274
$982$	26.7386	0.853264
$983$	−33.8617	−1.08002	−0.540011	−	0.841658i	$-0.681580\pi$
$983$	−33.8617	−1.08002	−0.540011	+	0.841658i	$0.681580\pi$
$984$	3.56155	0.113538
$985$	38.9309	1.24044
$986$	−8.49242	−0.270454
$987$	0	0
$988$	18.2462	0.580489
$989$	6.68466	0.212560
$990$	−8.00000	−0.254257
$991$	−6.24621	−0.198417	−0.0992087	−	0.995067i	$-0.531631\pi$
$991$	−6.24621	−0.198417	−0.0992087	+	0.995067i	$0.531631\pi$
$992$	3.12311	0.0991587
$993$	−24.4924	−0.777244
$994$	0	0
$995$	33.0691	1.04836
$996$	9.12311	0.289077
$997$	−51.4773	−1.63030	−0.815151	−	0.579249i	$-0.803346\pi$
$997$	−51.4773	−1.63030	−0.815151	+	0.579249i	$0.803346\pi$
$998$	−41.3693	−1.30952
$999$	−1.56155	−0.0494053

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6762.2.a.bw.1.2		2
7.6	odd	2		966.2.a.l.1.1	✓	2
21.20	even	2		2898.2.a.ba.1.2		2
28.27	even	2		7728.2.a.bm.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.a.l.1.1	✓	2	7.6	odd	2
2898.2.a.ba.1.2		2	21.20	even	2
6762.2.a.bw.1.2		2	1.1	even	1	trivial
7728.2.a.bm.1.1		2	28.27	even	2

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:	\( N \)	\(=\)	\( 6762 = 2 \cdot 3 \cdot 7^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6762.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.56155 q^{5} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.56155 q^{5} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} -1.56155 q^{10} +5.12311 q^{11} +1.00000 q^{12} +3.56155 q^{13} +1.56155 q^{15} +1.00000 q^{16} +1.12311 q^{17} -1.00000 q^{18} +5.12311 q^{19} +1.56155 q^{20} -5.12311 q^{22} +1.00000 q^{23} -1.00000 q^{24} -2.56155 q^{25} -3.56155 q^{26} +1.00000 q^{27} +7.56155 q^{29} -1.56155 q^{30} -3.12311 q^{31} -1.00000 q^{32} +5.12311 q^{33} -1.12311 q^{34} +1.00000 q^{36} -1.56155 q^{37} -5.12311 q^{38} +3.56155 q^{39} -1.56155 q^{40} -3.56155 q^{41} +6.68466 q^{43} +5.12311 q^{44} +1.56155 q^{45} -1.00000 q^{46} -2.43845 q^{47} +1.00000 q^{48} +2.56155 q^{50} +1.12311 q^{51} +3.56155 q^{52} +14.2462 q^{53} -1.00000 q^{54} +8.00000 q^{55} +5.12311 q^{57} -7.56155 q^{58} -4.87689 q^{59} +1.56155 q^{60} -0.876894 q^{61} +3.12311 q^{62} +1.00000 q^{64} +5.56155 q^{65} -5.12311 q^{66} -1.12311 q^{67} +1.12311 q^{68} +1.00000 q^{69} -9.36932 q^{71} -1.00000 q^{72} -9.12311 q^{73} +1.56155 q^{74} -2.56155 q^{75} +5.12311 q^{76} -3.56155 q^{78} +14.2462 q^{79} +1.56155 q^{80} +1.00000 q^{81} +3.56155 q^{82} +9.12311 q^{83} +1.75379 q^{85} -6.68466 q^{86} +7.56155 q^{87} -5.12311 q^{88} -14.0000 q^{89} -1.56155 q^{90} +1.00000 q^{92} -3.12311 q^{93} +2.43845 q^{94} +8.00000 q^{95} -1.00000 q^{96} +12.4384 q^{97} +5.12311 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - q^{5} - 2 q^{6} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - q^5 - 2 * q^6 - 2 * q^8 + 2 * q^9	\( 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - q^{5} - 2 q^{6} - 2 q^{8} + 2 q^{9} + q^{10} + 2 q^{11} + 2 q^{12} + 3 q^{13} - q^{15} + 2 q^{16} - 6 q^{17} - 2 q^{18} + 2 q^{19} - q^{20} - 2 q^{22} + 2 q^{23} - 2 q^{24} - q^{25} - 3 q^{26} + 2 q^{27} + 11 q^{29} + q^{30} + 2 q^{31} - 2 q^{32} + 2 q^{33} + 6 q^{34} + 2 q^{36} + q^{37} - 2 q^{38} + 3 q^{39} + q^{40} - 3 q^{41} + q^{43} + 2 q^{44} - q^{45} - 2 q^{46} - 9 q^{47} + 2 q^{48} + q^{50} - 6 q^{51} + 3 q^{52} + 12 q^{53} - 2 q^{54} + 16 q^{55} + 2 q^{57} - 11 q^{58} - 18 q^{59} - q^{60} - 10 q^{61} - 2 q^{62} + 2 q^{64} + 7 q^{65} - 2 q^{66} + 6 q^{67} - 6 q^{68} + 2 q^{69} + 6 q^{71} - 2 q^{72} - 10 q^{73} - q^{74} - q^{75} + 2 q^{76} - 3 q^{78} + 12 q^{79} - q^{80} + 2 q^{81} + 3 q^{82} + 10 q^{83} + 20 q^{85} - q^{86} + 11 q^{87} - 2 q^{88} - 28 q^{89} + q^{90} + 2 q^{92} + 2 q^{93} + 9 q^{94} + 16 q^{95} - 2 q^{96} + 29 q^{97} + 2 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - q^5 - 2 * q^6 - 2 * q^8 + 2 * q^9 + q^10 + 2 * q^11 + 2 * q^12 + 3 * q^13 - q^15 + 2 * q^16 - 6 * q^17 - 2 * q^18 + 2 * q^19 - q^20 - 2 * q^22 + 2 * q^23 - 2 * q^24 - q^25 - 3 * q^26 + 2 * q^27 + 11 * q^29 + q^30 + 2 * q^31 - 2 * q^32 + 2 * q^33 + 6 * q^34 + 2 * q^36 + q^37 - 2 * q^38 + 3 * q^39 + q^40 - 3 * q^41 + q^43 + 2 * q^44 - q^45 - 2 * q^46 - 9 * q^47 + 2 * q^48 + q^50 - 6 * q^51 + 3 * q^52 + 12 * q^53 - 2 * q^54 + 16 * q^55 + 2 * q^57 - 11 * q^58 - 18 * q^59 - q^60 - 10 * q^61 - 2 * q^62 + 2 * q^64 + 7 * q^65 - 2 * q^66 + 6 * q^67 - 6 * q^68 + 2 * q^69 + 6 * q^71 - 2 * q^72 - 10 * q^73 - q^74 - q^75 + 2 * q^76 - 3 * q^78 + 12 * q^79 - q^80 + 2 * q^81 + 3 * q^82 + 10 * q^83 + 20 * q^85 - q^86 + 11 * q^87 - 2 * q^88 - 28 * q^89 + q^90 + 2 * q^92 + 2 * q^93 + 9 * q^94 + 16 * q^95 - 2 * q^96 + 29 * q^97 + 2 * q^99

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