LMFDB - Embedded newform 6027.2.a.bf.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6027,2,Mod(1,6027)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6027, 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("6027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6027 = 3 \cdot 7^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6027.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:	$48.1258372982$
Analytic rank:	$1$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} - 15 x^{10} + 30 x^{9} + 74 x^{8} - 149 x^{7} - 140 x^{6} + 278 x^{5} + 126 x^{4} + \cdots + 18 $ x^12 - 2x^11 - 15x^10 + 30x^9 + 74x^8 - 149x^7 - 140x^6 + 278x^5 + 126x^4 - 211x^3 - 64x^2 + 53*x + 18
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 861)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$-0.467496$ of defining polynomial
Character	$\chi$	$=$	6027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.467496 q^{2} -1.00000 q^{3} -1.78145 q^{4} -2.48991 q^{5} -0.467496 q^{6} -1.76781 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.467496 q^{2} -1.00000 q^{3} -1.78145 q^{4} -2.48991 q^{5} -0.467496 q^{6} -1.76781 q^{8} +1.00000 q^{9} -1.16402 q^{10} +5.31632 q^{11} +1.78145 q^{12} -3.14130 q^{13} +2.48991 q^{15} +2.73645 q^{16} -5.72132 q^{17} +0.467496 q^{18} +1.29973 q^{19} +4.43565 q^{20} +2.48536 q^{22} -7.14975 q^{23} +1.76781 q^{24} +1.19967 q^{25} -1.46854 q^{26} -1.00000 q^{27} +6.64170 q^{29} +1.16402 q^{30} +3.31751 q^{31} +4.81490 q^{32} -5.31632 q^{33} -2.67469 q^{34} -1.78145 q^{36} +0.130411 q^{37} +0.607620 q^{38} +3.14130 q^{39} +4.40170 q^{40} +1.00000 q^{41} +6.82425 q^{43} -9.47075 q^{44} -2.48991 q^{45} -3.34248 q^{46} +0.120892 q^{47} -2.73645 q^{48} +0.560843 q^{50} +5.72132 q^{51} +5.59606 q^{52} +9.92571 q^{53} -0.467496 q^{54} -13.2372 q^{55} -1.29973 q^{57} +3.10496 q^{58} +12.4957 q^{59} -4.43565 q^{60} +2.10795 q^{61} +1.55092 q^{62} -3.22196 q^{64} +7.82157 q^{65} -2.48536 q^{66} +6.29580 q^{67} +10.1922 q^{68} +7.14975 q^{69} -1.99477 q^{71} -1.76781 q^{72} -13.8293 q^{73} +0.0609666 q^{74} -1.19967 q^{75} -2.31541 q^{76} +1.46854 q^{78} -17.0137 q^{79} -6.81353 q^{80} +1.00000 q^{81} +0.467496 q^{82} +10.1178 q^{83} +14.2456 q^{85} +3.19031 q^{86} -6.64170 q^{87} -9.39825 q^{88} -0.414652 q^{89} -1.16402 q^{90} +12.7369 q^{92} -3.31751 q^{93} +0.0565166 q^{94} -3.23623 q^{95} -4.81490 q^{96} +7.26249 q^{97} +5.31632 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{2} - 12 q^{3} + 10 q^{4} - 12 q^{5} + 2 q^{6} + 12 q^{9}+O(q^{10}) $ 12 * q - 2 * q^2 - 12 * q^3 + 10 * q^4 - 12 * q^5 + 2 * q^6 + 12 * q^9	$ 12 q - 2 q^{2} - 12 q^{3} + 10 q^{4} - 12 q^{5} + 2 q^{6} + 12 q^{9} - 11 q^{10} + 10 q^{11} - 10 q^{12} - 15 q^{13} + 12 q^{15} + 14 q^{16} - 8 q^{17} - 2 q^{18} - 2 q^{19} - 16 q^{20} - 7 q^{22} + 5 q^{23} + 20 q^{25} - 12 q^{27} + 20 q^{29} + 11 q^{30} - 10 q^{31} + 3 q^{32} - 10 q^{33} + 23 q^{34} + 10 q^{36} - 17 q^{37} - 6 q^{38} + 15 q^{39} - 39 q^{40} + 12 q^{41} + 12 q^{43} + 20 q^{44} - 12 q^{45} - 36 q^{46} - 34 q^{47} - 14 q^{48} + 59 q^{50} + 8 q^{51} - 26 q^{52} + 6 q^{53} + 2 q^{54} + q^{55} + 2 q^{57} - 11 q^{58} - 27 q^{59} + 16 q^{60} - 22 q^{61} + 45 q^{62} + 26 q^{64} + 7 q^{66} - 26 q^{67} - 33 q^{68} - 5 q^{69} + 50 q^{71} - 21 q^{73} - 35 q^{74} - 20 q^{75} + 24 q^{76} - 10 q^{79} - 22 q^{80} + 12 q^{81} - 2 q^{82} - 8 q^{83} + 8 q^{85} - 17 q^{86} - 20 q^{87} - 46 q^{88} - 11 q^{89} - 11 q^{90} + 63 q^{92} + 10 q^{93} - 10 q^{94} + 35 q^{95} - 3 q^{96} - 32 q^{97} + 10 q^{99}+O(q^{100}) $ 12 * q - 2 * q^2 - 12 * q^3 + 10 * q^4 - 12 * q^5 + 2 * q^6 + 12 * q^9 - 11 * q^10 + 10 * q^11 - 10 * q^12 - 15 * q^13 + 12 * q^15 + 14 * q^16 - 8 * q^17 - 2 * q^18 - 2 * q^19 - 16 * q^20 - 7 * q^22 + 5 * q^23 + 20 * q^25 - 12 * q^27 + 20 * q^29 + 11 * q^30 - 10 * q^31 + 3 * q^32 - 10 * q^33 + 23 * q^34 + 10 * q^36 - 17 * q^37 - 6 * q^38 + 15 * q^39 - 39 * q^40 + 12 * q^41 + 12 * q^43 + 20 * q^44 - 12 * q^45 - 36 * q^46 - 34 * q^47 - 14 * q^48 + 59 * q^50 + 8 * q^51 - 26 * q^52 + 6 * q^53 + 2 * q^54 + q^55 + 2 * q^57 - 11 * q^58 - 27 * q^59 + 16 * q^60 - 22 * q^61 + 45 * q^62 + 26 * q^64 + 7 * q^66 - 26 * q^67 - 33 * q^68 - 5 * q^69 + 50 * q^71 - 21 * q^73 - 35 * q^74 - 20 * q^75 + 24 * q^76 - 10 * q^79 - 22 * q^80 + 12 * q^81 - 2 * q^82 - 8 * q^83 + 8 * q^85 - 17 * q^86 - 20 * q^87 - 46 * q^88 - 11 * q^89 - 11 * q^90 + 63 * q^92 + 10 * q^93 - 10 * q^94 + 35 * q^95 - 3 * q^96 - 32 * q^97 + 10 * 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 $

$2$	0.467496	0.330569	0.165285	−	0.986246i	$-0.447146\pi$
$2$	0.467496	0.330569	0.165285	+	0.986246i	$0.447146\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.78145	−0.890724
$5$	−2.48991	−1.11352	−0.556762	−	0.830672i	$-0.687956\pi$
$5$	−2.48991	−1.11352	−0.556762	+	0.830672i	$0.687956\pi$
$6$	−0.467496	−0.190854
$7$	0	0
$7$	0	0
$8$	−1.76781	−0.625016
$9$	1.00000	0.333333
$10$	−1.16402	−0.368097
$11$	5.31632	1.60293	0.801466	−	0.598041i	$-0.204054\pi$
$11$	5.31632	1.60293	0.801466	+	0.598041i	$0.204054\pi$
$12$	1.78145	0.514260
$13$	−3.14130	−0.871240	−0.435620	−	0.900131i	$-0.643471\pi$
$13$	−3.14130	−0.871240	−0.435620	+	0.900131i	$0.643471\pi$
$14$	0	0
$15$	2.48991	0.642893
$16$	2.73645	0.684113
$17$	−5.72132	−1.38762	−0.693812	−	0.720156i	$-0.744070\pi$
$17$	−5.72132	−1.38762	−0.693812	+	0.720156i	$0.744070\pi$
$18$	0.467496	0.110190
$19$	1.29973	0.298179	0.149090	−	0.988824i	$-0.452366\pi$
$19$	1.29973	0.298179	0.149090	+	0.988824i	$0.452366\pi$
$20$	4.43565	0.991842
$21$	0	0
$22$	2.48536	0.529880
$23$	−7.14975	−1.49083	−0.745413	−	0.666603i	$-0.767748\pi$
$23$	−7.14975	−1.49083	−0.745413	+	0.666603i	$0.767748\pi$
$24$	1.76781	0.360853
$25$	1.19967	0.239935
$26$	−1.46854	−0.288005
$27$	−1.00000	−0.192450
$28$	0	0
$29$	6.64170	1.23333	0.616666	−	0.787225i	$-0.288483\pi$
$29$	6.64170	1.23333	0.616666	+	0.787225i	$0.288483\pi$
$30$	1.16402	0.212521
$31$	3.31751	0.595842	0.297921	−	0.954591i	$-0.403707\pi$
$31$	3.31751	0.595842	0.297921	+	0.954591i	$0.403707\pi$
$32$	4.81490	0.851162
$33$	−5.31632	−0.925453
$34$	−2.67469	−0.458706
$35$	0	0
$36$	−1.78145	−0.296908
$37$	0.130411	0.0214394	0.0107197	−	0.999943i	$-0.496588\pi$
$37$	0.130411	0.0214394	0.0107197	+	0.999943i	$0.496588\pi$
$38$	0.607620	0.0985690
$39$	3.14130	0.503011
$40$	4.40170	0.695970
$41$	1.00000	0.156174
$41$	1.00000	0.156174
$42$	0	0
$43$	6.82425	1.04069	0.520344	−	0.853957i	$-0.325804\pi$
$43$	6.82425	1.04069	0.520344	+	0.853957i	$0.325804\pi$
$44$	−9.47075	−1.42777
$45$	−2.48991	−0.371175
$46$	−3.34248	−0.492822
$47$	0.120892	0.0176339	0.00881697	−	0.999961i	$-0.497193\pi$
$47$	0.120892	0.0176339	0.00881697	+	0.999961i	$0.497193\pi$
$48$	−2.73645	−0.394973
$49$	0	0
$50$	0.560843	0.0793152
$51$	5.72132	0.801145
$52$	5.59606	0.776034
$53$	9.92571	1.36340	0.681701	−	0.731631i	$-0.261241\pi$
$53$	9.92571	1.36340	0.681701	+	0.731631i	$0.261241\pi$
$54$	−0.467496	−0.0636181
$55$	−13.2372	−1.78490
$56$	0	0
$57$	−1.29973	−0.172154
$58$	3.10496	0.407702
$59$	12.4957	1.62680	0.813400	−	0.581705i	$-0.197614\pi$
$59$	12.4957	1.62680	0.813400	+	0.581705i	$0.197614\pi$
$60$	−4.43565	−0.572640
$61$	2.10795	0.269896	0.134948	−	0.990853i	$-0.456913\pi$
$61$	2.10795	0.269896	0.134948	+	0.990853i	$0.456913\pi$
$62$	1.55092	0.196967
$63$	0	0
$64$	−3.22196	−0.402744
$65$	7.82157	0.970146
$66$	−2.48536	−0.305927
$67$	6.29580	0.769154	0.384577	−	0.923093i	$-0.374347\pi$
$67$	6.29580	0.769154	0.384577	+	0.923093i	$0.374347\pi$
$68$	10.1922	1.23599
$69$	7.14975	0.860729
$70$	0	0
$71$	−1.99477	−0.236735	−0.118368	−	0.992970i	$-0.537766\pi$
$71$	−1.99477	−0.236735	−0.118368	+	0.992970i	$0.537766\pi$
$72$	−1.76781	−0.208339
$73$	−13.8293	−1.61860	−0.809298	−	0.587398i	$-0.800152\pi$
$73$	−13.8293	−1.61860	−0.809298	+	0.587398i	$0.800152\pi$
$74$	0.0609666	0.00708722
$75$	−1.19967	−0.138526
$76$	−2.31541	−0.265596
$77$	0	0
$78$	1.46854	0.166280
$79$	−17.0137	−1.91419	−0.957095	−	0.289774i	$-0.906420\pi$
$79$	−17.0137	−1.91419	−0.957095	+	0.289774i	$0.906420\pi$
$80$	−6.81353	−0.761776
$81$	1.00000	0.111111
$82$	0.467496	0.0516263
$83$	10.1178	1.11057	0.555286	−	0.831660i	$-0.312609\pi$
$83$	10.1178	1.11057	0.555286	+	0.831660i	$0.312609\pi$
$84$	0	0
$85$	14.2456	1.54515
$86$	3.19031	0.344020
$87$	−6.64170	−0.712064
$88$	−9.39825	−1.00186
$89$	−0.414652	−0.0439530	−0.0219765	−	0.999758i	$-0.506996\pi$
$89$	−0.414652	−0.0439530	−0.0219765	+	0.999758i	$0.506996\pi$
$90$	−1.16402	−0.122699
$91$	0	0
$92$	12.7369	1.32791
$93$	−3.31751	−0.344009
$94$	0.0565166	0.00582924
$95$	−3.23623	−0.332030
$96$	−4.81490	−0.491419
$97$	7.26249	0.737394	0.368697	−	0.929550i	$-0.379804\pi$
$97$	7.26249	0.737394	0.368697	+	0.929550i	$0.379804\pi$
$98$	0	0
$99$	5.31632	0.534311
$100$	−2.13716	−0.213716
$101$	−8.23179	−0.819094	−0.409547	−	0.912289i	$-0.634313\pi$
$101$	−8.23179	−0.819094	−0.409547	+	0.912289i	$0.634313\pi$
$102$	2.67469	0.264834
$103$	1.06395	0.104834	0.0524168	−	0.998625i	$-0.483308\pi$
$103$	1.06395	0.104834	0.0524168	+	0.998625i	$0.483308\pi$
$104$	5.55322	0.544538
$105$	0	0
$106$	4.64023	0.450699
$107$	−13.9713	−1.35066	−0.675329	−	0.737517i	$-0.735998\pi$
$107$	−13.9713	−1.35066	−0.675329	+	0.737517i	$0.735998\pi$
$108$	1.78145	0.171420
$109$	13.7027	1.31248	0.656241	−	0.754552i	$-0.272146\pi$
$109$	13.7027	1.31248	0.656241	+	0.754552i	$0.272146\pi$
$110$	−6.18833	−0.590034
$111$	−0.130411	−0.0123781
$112$	0	0
$113$	6.05734	0.569827	0.284914	−	0.958553i	$-0.408035\pi$
$113$	6.05734	0.569827	0.284914	+	0.958553i	$0.408035\pi$
$114$	−0.607620	−0.0569088
$115$	17.8023	1.66007
$116$	−11.8318	−1.09856
$117$	−3.14130	−0.290413
$118$	5.84168	0.537770
$119$	0	0
$120$	−4.40170	−0.401818
$121$	17.2633	1.56939
$122$	0.985458	0.0892192
$123$	−1.00000	−0.0901670
$124$	−5.90996	−0.530730
$125$	9.46249	0.846350
$126$	0	0
$127$	−3.27309	−0.290439	−0.145220	−	0.989399i	$-0.546389\pi$
$127$	−3.27309	−0.290439	−0.145220	+	0.989399i	$0.546389\pi$
$128$	−11.1361	−0.984297
$129$	−6.82425	−0.600842
$130$	3.65655	0.320701
$131$	−12.9751	−1.13364	−0.566821	−	0.823841i	$-0.691827\pi$
$131$	−12.9751	−1.13364	−0.566821	+	0.823841i	$0.691827\pi$
$132$	9.47075	0.824323
$133$	0	0
$134$	2.94326	0.254259
$135$	2.48991	0.214298
$136$	10.1142	0.867286
$137$	−19.3260	−1.65113	−0.825566	−	0.564306i	$-0.809144\pi$
$137$	−19.3260	−1.65113	−0.825566	+	0.564306i	$0.809144\pi$
$138$	3.34248	0.284531
$139$	−5.34559	−0.453407	−0.226703	−	0.973964i	$-0.572795\pi$
$139$	−5.34559	−0.453407	−0.226703	+	0.973964i	$0.572795\pi$
$140$	0	0
$141$	−0.120892	−0.0101810
$142$	−0.932545	−0.0782574
$143$	−16.7002	−1.39654
$144$	2.73645	0.228038
$145$	−16.5373	−1.37334
$146$	−6.46514	−0.535058
$147$	0	0
$148$	−0.232320	−0.0190966
$149$	0.427636	0.0350333	0.0175166	−	0.999847i	$-0.494424\pi$
$149$	0.427636	0.0350333	0.0175166	+	0.999847i	$0.494424\pi$
$150$	−0.560843	−0.0457926
$151$	−4.05095	−0.329662	−0.164831	−	0.986322i	$-0.552708\pi$
$151$	−4.05095	−0.329662	−0.164831	+	0.986322i	$0.552708\pi$
$152$	−2.29768	−0.186367
$153$	−5.72132	−0.462541
$154$	0	0
$155$	−8.26031	−0.663484
$156$	−5.59606	−0.448043
$157$	19.7473	1.57601	0.788005	−	0.615669i	$-0.211114\pi$
$157$	19.7473	1.57601	0.788005	+	0.615669i	$0.211114\pi$
$158$	−7.95383	−0.632773
$159$	−9.92571	−0.787160
$160$	−11.9887	−0.947789
$161$	0	0
$162$	0.467496	0.0367299
$163$	−3.41869	−0.267772	−0.133886	−	0.990997i	$-0.542746\pi$
$163$	−3.41869	−0.267772	−0.133886	+	0.990997i	$0.542746\pi$
$164$	−1.78145	−0.139108
$165$	13.2372	1.03051
$166$	4.73002	0.367121
$167$	5.10863	0.395318	0.197659	−	0.980271i	$-0.436666\pi$
$167$	5.10863	0.395318	0.197659	+	0.980271i	$0.436666\pi$
$168$	0	0
$169$	−3.13223	−0.240941
$170$	6.65976	0.510780
$171$	1.29973	0.0993931
$172$	−12.1570	−0.926966
$173$	−10.7996	−0.821075	−0.410537	−	0.911844i	$-0.634659\pi$
$173$	−10.7996	−0.821075	−0.410537	+	0.911844i	$0.634659\pi$
$174$	−3.10496	−0.235387
$175$	0	0
$176$	14.5479	1.09659
$177$	−12.4957	−0.939233
$178$	−0.193848	−0.0145295
$179$	0.632276	0.0472585	0.0236293	−	0.999721i	$-0.492478\pi$
$179$	0.632276	0.0472585	0.0236293	+	0.999721i	$0.492478\pi$
$180$	4.43565	0.330614
$181$	3.24632	0.241297	0.120649	−	0.992695i	$-0.461503\pi$
$181$	3.24632	0.241297	0.120649	+	0.992695i	$0.461503\pi$
$182$	0	0
$183$	−2.10795	−0.155824
$184$	12.6394	0.931790
$185$	−0.324712	−0.0238733
$186$	−1.55092	−0.113719
$187$	−30.4164	−2.22427
$188$	−0.215363	−0.0157070
$189$	0	0
$190$	−1.51292	−0.109759
$191$	−2.69791	−0.195214	−0.0976071	−	0.995225i	$-0.531119\pi$
$191$	−2.69791	−0.195214	−0.0976071	+	0.995225i	$0.531119\pi$
$192$	3.22196	0.232525
$193$	−1.09647	−0.0789256	−0.0394628	−	0.999221i	$-0.512565\pi$
$193$	−1.09647	−0.0789256	−0.0394628	+	0.999221i	$0.512565\pi$
$194$	3.39518	0.243760
$195$	−7.82157	−0.560114
$196$	0	0
$197$	12.0471	0.858317	0.429158	−	0.903229i	$-0.358810\pi$
$197$	12.0471	0.858317	0.429158	+	0.903229i	$0.358810\pi$
$198$	2.48536	0.176627
$199$	−18.7422	−1.32860	−0.664298	−	0.747468i	$-0.731269\pi$
$199$	−18.7422	−1.32860	−0.664298	+	0.747468i	$0.731269\pi$
$200$	−2.12080	−0.149963
$201$	−6.29580	−0.444071
$202$	−3.84833	−0.270767
$203$	0	0
$204$	−10.1922	−0.713599
$205$	−2.48991	−0.173903
$206$	0.497390	0.0346548
$207$	−7.14975	−0.496942
$208$	−8.59601	−0.596026
$209$	6.90981	0.477961
$210$	0	0
$211$	21.3366	1.46887	0.734435	−	0.678679i	$-0.237447\pi$
$211$	21.3366	1.46887	0.734435	+	0.678679i	$0.237447\pi$
$212$	−17.6821	−1.21441
$213$	1.99477	0.136679
$214$	−6.53153	−0.446486
$215$	−16.9918	−1.15883
$216$	1.76781	0.120284
$217$	0	0
$218$	6.40596	0.433866
$219$	13.8293	0.934497
$220$	23.5814	1.58986
$221$	17.9724	1.20895
$222$	−0.0609666	−0.00409181
$223$	−19.7146	−1.32019	−0.660093	−	0.751184i	$-0.729483\pi$
$223$	−19.7146	−1.32019	−0.660093	+	0.751184i	$0.729483\pi$
$224$	0	0
$225$	1.19967	0.0799783
$226$	2.83178	0.188367
$227$	15.8988	1.05524	0.527621	−	0.849480i	$-0.323084\pi$
$227$	15.8988	1.05524	0.527621	+	0.849480i	$0.323084\pi$
$228$	2.31541	0.153342
$229$	−26.3058	−1.73833	−0.869167	−	0.494518i	$-0.835345\pi$
$229$	−26.3058	−1.73833	−0.869167	+	0.494518i	$0.835345\pi$
$230$	8.32249	0.548769
$231$	0	0
$232$	−11.7413	−0.770852
$233$	13.3645	0.875538	0.437769	−	0.899087i	$-0.355769\pi$
$233$	13.3645	0.875538	0.437769	+	0.899087i	$0.355769\pi$
$234$	−1.46854	−0.0960018
$235$	−0.301011	−0.0196358
$236$	−22.2604	−1.44903
$237$	17.0137	1.10516
$238$	0	0
$239$	−7.72975	−0.499996	−0.249998	−	0.968246i	$-0.580430\pi$
$239$	−7.72975	−0.499996	−0.249998	+	0.968246i	$0.580430\pi$
$240$	6.81353	0.439811
$241$	−18.1506	−1.16918	−0.584590	−	0.811329i	$-0.698745\pi$
$241$	−18.1506	−1.16918	−0.584590	+	0.811329i	$0.698745\pi$
$242$	8.07052	0.518792
$243$	−1.00000	−0.0641500
$244$	−3.75520	−0.240402
$245$	0	0
$246$	−0.467496	−0.0298064
$247$	−4.08285	−0.259786
$248$	−5.86472	−0.372410
$249$	−10.1178	−0.641189
$250$	4.42367	0.279778
$251$	2.70780	0.170915	0.0854575	−	0.996342i	$-0.472765\pi$
$251$	2.70780	0.170915	0.0854575	+	0.996342i	$0.472765\pi$
$252$	0	0
$253$	−38.0104	−2.38969
$254$	−1.53015	−0.0960104
$255$	−14.2456	−0.892094
$256$	1.23785	0.0773658
$257$	4.77854	0.298077	0.149039	−	0.988831i	$-0.452382\pi$
$257$	4.77854	0.298077	0.149039	+	0.988831i	$0.452382\pi$
$258$	−3.19031	−0.198620
$259$	0	0
$260$	−13.9337	−0.864132
$261$	6.64170	0.411111
$262$	−6.06582	−0.374747
$263$	−14.7301	−0.908299	−0.454150	−	0.890925i	$-0.650057\pi$
$263$	−14.7301	−0.908299	−0.454150	+	0.890925i	$0.650057\pi$
$264$	9.39825	0.578423
$265$	−24.7142	−1.51818
$266$	0	0
$267$	0.414652	0.0253763
$268$	−11.2156	−0.685104
$269$	−12.5726	−0.766563	−0.383282	−	0.923631i	$-0.625206\pi$
$269$	−12.5726	−0.766563	−0.383282	+	0.923631i	$0.625206\pi$
$270$	1.16402	0.0708403
$271$	−16.3050	−0.990461	−0.495230	−	0.868762i	$-0.664916\pi$
$271$	−16.3050	−0.990461	−0.495230	+	0.868762i	$0.664916\pi$
$272$	−15.6561	−0.949291
$273$	0	0
$274$	−9.03482	−0.545814
$275$	6.37786	0.384599
$276$	−12.7369	−0.766672
$277$	19.0119	1.14232	0.571158	−	0.820840i	$-0.306495\pi$
$277$	19.0119	1.14232	0.571158	+	0.820840i	$0.306495\pi$
$278$	−2.49904	−0.149883
$279$	3.31751	0.198614
$280$	0	0
$281$	−12.3779	−0.738404	−0.369202	−	0.929349i	$-0.620369\pi$
$281$	−12.3779	−0.738404	−0.369202	+	0.929349i	$0.620369\pi$
$282$	−0.0565166	−0.00336552
$283$	−25.5514	−1.51888	−0.759438	−	0.650580i	$-0.774526\pi$
$283$	−25.5514	−1.51888	−0.759438	+	0.650580i	$0.774526\pi$
$284$	3.55357	0.210866
$285$	3.23623	0.191698
$286$	−7.80726	−0.461653
$287$	0	0
$288$	4.81490	0.283721
$289$	15.7335	0.925499
$290$	−7.73110	−0.453986
$291$	−7.26249	−0.425735
$292$	24.6362	1.44172
$293$	−34.1011	−1.99221	−0.996104	−	0.0881812i	$-0.971895\pi$
$293$	−34.1011	−1.99221	−0.996104	+	0.0881812i	$0.971895\pi$
$294$	0	0
$295$	−31.1132	−1.81148
$296$	−0.230542	−0.0134000
$297$	−5.31632	−0.308484
$298$	0.199918	0.0115809
$299$	22.4595	1.29887
$300$	2.13716	0.123389
$301$	0	0
$302$	−1.89380	−0.108976
$303$	8.23179	0.472904
$304$	3.55666	0.203988
$305$	−5.24862	−0.300535
$306$	−2.67469	−0.152902
$307$	−16.5266	−0.943223	−0.471611	−	0.881806i	$-0.656328\pi$
$307$	−16.5266	−0.943223	−0.471611	+	0.881806i	$0.656328\pi$
$308$	0	0
$309$	−1.06395	−0.0605258
$310$	−3.86166	−0.219327
$311$	−7.64063	−0.433260	−0.216630	−	0.976254i	$-0.569507\pi$
$311$	−7.64063	−0.433260	−0.216630	+	0.976254i	$0.569507\pi$
$312$	−5.55322	−0.314389
$313$	−19.2853	−1.09007	−0.545034	−	0.838414i	$-0.683483\pi$
$313$	−19.2853	−1.09007	−0.545034	+	0.838414i	$0.683483\pi$
$314$	9.23180	0.520981
$315$	0	0
$316$	30.3090	1.70501
$317$	4.94086	0.277506	0.138753	−	0.990327i	$-0.455691\pi$
$317$	4.94086	0.277506	0.138753	+	0.990327i	$0.455691\pi$
$318$	−4.64023	−0.260211
$319$	35.3094	1.97695
$320$	8.02239	0.448465
$321$	13.9713	0.779802
$322$	0	0
$323$	−7.43619	−0.413761
$324$	−1.78145	−0.0989693
$325$	−3.76854	−0.209041
$326$	−1.59822	−0.0885174
$327$	−13.7027	−0.757761
$328$	−1.76781	−0.0976110
$329$	0	0
$330$	6.18833	0.340656
$331$	−28.0809	−1.54347	−0.771734	−	0.635946i	$-0.780610\pi$
$331$	−28.0809	−1.54347	−0.771734	+	0.635946i	$0.780610\pi$
$332$	−18.0243	−0.989213
$333$	0.130411	0.00714647
$334$	2.38826	0.130680
$335$	−15.6760	−0.856472
$336$	0	0
$337$	17.2575	0.940074	0.470037	−	0.882647i	$-0.344241\pi$
$337$	17.2575	0.940074	0.470037	+	0.882647i	$0.344241\pi$
$338$	−1.46431	−0.0796478
$339$	−6.05734	−0.328990
$340$	−25.3778	−1.37630
$341$	17.6369	0.955093
$342$	0.607620	0.0328563
$343$	0	0
$344$	−12.0640	−0.650446
$345$	−17.8023	−0.958442
$346$	−5.04875	−0.271422
$347$	−22.6422	−1.21550	−0.607749	−	0.794129i	$-0.707927\pi$
$347$	−22.6422	−1.21550	−0.607749	+	0.794129i	$0.707927\pi$
$348$	11.8318	0.634253
$349$	−10.6177	−0.568351	−0.284175	−	0.958772i	$-0.591720\pi$
$349$	−10.6177	−0.568351	−0.284175	+	0.958772i	$0.591720\pi$
$350$	0	0
$351$	3.14130	0.167670
$352$	25.5976	1.36436
$353$	26.6357	1.41767	0.708837	−	0.705372i	$-0.249220\pi$
$353$	26.6357	1.41767	0.708837	+	0.705372i	$0.249220\pi$
$354$	−5.84168	−0.310482
$355$	4.96680	0.263610
$356$	0.738681	0.0391500
$357$	0	0
$358$	0.295586	0.0156222
$359$	14.2091	0.749927	0.374964	−	0.927040i	$-0.377655\pi$
$359$	14.2091	0.749927	0.374964	+	0.927040i	$0.377655\pi$
$360$	4.40170	0.231990
$361$	−17.3107	−0.911089
$362$	1.51764	0.0797655
$363$	−17.2633	−0.906088
$364$	0	0
$365$	34.4338	1.80234
$366$	−0.985458	−0.0515107
$367$	3.29888	0.172200	0.0861000	−	0.996286i	$-0.472560\pi$
$367$	3.29888	0.172200	0.0861000	+	0.996286i	$0.472560\pi$
$368$	−19.5649	−1.01989
$369$	1.00000	0.0520579
$370$	−0.151802	−0.00789179
$371$	0	0
$372$	5.90996	0.306417
$373$	−31.7746	−1.64523	−0.822614	−	0.568600i	$-0.807485\pi$
$373$	−31.7746	−1.64523	−0.822614	+	0.568600i	$0.807485\pi$
$374$	−14.2195	−0.735274
$375$	−9.46249	−0.488641
$376$	−0.213715	−0.0110215
$377$	−20.8636	−1.07453
$378$	0	0
$379$	−4.74760	−0.243868	−0.121934	−	0.992538i	$-0.538910\pi$
$379$	−4.74760	−0.243868	−0.121934	+	0.992538i	$0.538910\pi$
$380$	5.76517	0.295747
$381$	3.27309	0.167685
$382$	−1.26126	−0.0645319
$383$	−22.2893	−1.13893	−0.569464	−	0.822016i	$-0.692849\pi$
$383$	−22.2893	−1.13893	−0.569464	+	0.822016i	$0.692849\pi$
$384$	11.1361	0.568284
$385$	0	0
$386$	−0.512595	−0.0260904
$387$	6.82425	0.346896
$388$	−12.9377	−0.656814
$389$	−26.7971	−1.35867	−0.679334	−	0.733830i	$-0.737731\pi$
$389$	−26.7971	−1.35867	−0.679334	+	0.733830i	$0.737731\pi$
$390$	−3.65655	−0.185157
$391$	40.9060	2.06871
$392$	0	0
$393$	12.9751	0.654508
$394$	5.63195	0.283733
$395$	42.3626	2.13150
$396$	−9.47075	−0.475923
$397$	20.5329	1.03052	0.515258	−	0.857035i	$-0.327696\pi$
$397$	20.5329	1.03052	0.515258	+	0.857035i	$0.327696\pi$
$398$	−8.76188	−0.439193
$399$	0	0
$400$	3.28285	0.164143
$401$	4.04841	0.202168	0.101084	−	0.994878i	$-0.467769\pi$
$401$	4.04841	0.202168	0.101084	+	0.994878i	$0.467769\pi$
$402$	−2.94326	−0.146796
$403$	−10.4213	−0.519121
$404$	14.6645	0.729586
$405$	−2.48991	−0.123725
$406$	0	0
$407$	0.693307	0.0343659
$408$	−10.1142	−0.500728
$409$	31.2232	1.54389	0.771943	−	0.635691i	$-0.219285\pi$
$409$	31.2232	1.54389	0.771943	+	0.635691i	$0.219285\pi$
$410$	−1.16402	−0.0574871
$411$	19.3260	0.953281
$412$	−1.89536	−0.0933779
$413$	0	0
$414$	−3.34248	−0.164274
$415$	−25.1924	−1.23665
$416$	−15.1250	−0.741567
$417$	5.34559	0.261775
$418$	3.23031	0.157999
$419$	5.92612	0.289510	0.144755	−	0.989468i	$-0.453761\pi$
$419$	5.92612	0.289510	0.144755	+	0.989468i	$0.453761\pi$
$420$	0	0
$421$	−4.82299	−0.235058	−0.117529	−	0.993069i	$-0.537497\pi$
$421$	−4.82299	−0.235058	−0.117529	+	0.993069i	$0.537497\pi$
$422$	9.97475	0.485563
$423$	0.120892	0.00587798
$424$	−17.5468	−0.852147
$425$	−6.86372	−0.332939
$426$	0.932545	0.0451819
$427$	0	0
$428$	24.8891	1.20306
$429$	16.7002	0.806292
$430$	−7.94359	−0.383074
$431$	32.8146	1.58062	0.790311	−	0.612706i	$-0.209919\pi$
$431$	32.8146	1.58062	0.790311	+	0.612706i	$0.209919\pi$
$432$	−2.73645	−0.131658
$433$	24.1095	1.15863	0.579315	−	0.815103i	$-0.303320\pi$
$433$	24.1095	1.15863	0.579315	+	0.815103i	$0.303320\pi$
$434$	0	0
$435$	16.5373	0.792901
$436$	−24.4107	−1.16906
$437$	−9.29278	−0.444534
$438$	6.46514	0.308916
$439$	10.4952	0.500910	0.250455	−	0.968128i	$-0.419420\pi$
$439$	10.4952	0.500910	0.250455	+	0.968128i	$0.419420\pi$
$440$	23.4008	1.11559
$441$	0	0
$442$	8.40201	0.399643
$443$	−25.9121	−1.23112	−0.615561	−	0.788089i	$-0.711070\pi$
$443$	−25.9121	−1.23112	−0.615561	+	0.788089i	$0.711070\pi$
$444$	0.232320	0.0110254
$445$	1.03245	0.0489427
$446$	−9.21648	−0.436413
$447$	−0.427636	−0.0202265
$448$	0	0
$449$	−15.5623	−0.734432	−0.367216	−	0.930136i	$-0.619689\pi$
$449$	−15.5623	−0.734432	−0.367216	+	0.930136i	$0.619689\pi$
$450$	0.560843	0.0264384
$451$	5.31632	0.250336
$452$	−10.7908	−0.507558
$453$	4.05095	0.190330
$454$	7.43264	0.348831
$455$	0	0
$456$	2.29768	0.107599
$457$	−25.3788	−1.18717	−0.593584	−	0.804772i	$-0.702288\pi$
$457$	−25.3788	−1.18717	−0.593584	+	0.804772i	$0.702288\pi$
$458$	−12.2978	−0.574640
$459$	5.72132	0.267048
$460$	−31.7138	−1.47866
$461$	−2.41621	−0.112534	−0.0562671	−	0.998416i	$-0.517920\pi$
$461$	−2.41621	−0.112534	−0.0562671	+	0.998416i	$0.517920\pi$
$462$	0	0
$463$	−36.9928	−1.71920	−0.859600	−	0.510968i	$-0.829287\pi$
$463$	−36.9928	−1.71920	−0.859600	+	0.510968i	$0.829287\pi$
$464$	18.1747	0.843738
$465$	8.26031	0.383063
$466$	6.24785	0.289426
$467$	13.9352	0.644845	0.322422	−	0.946596i	$-0.395503\pi$
$467$	13.9352	0.644845	0.322422	+	0.946596i	$0.395503\pi$
$468$	5.59606	0.258678
$469$	0	0
$470$	−0.140722	−0.00649100
$471$	−19.7473	−0.909910
$472$	−22.0900	−1.01678
$473$	36.2799	1.66815
$474$	7.95383	0.365332
$475$	1.55926	0.0715437
$476$	0	0
$477$	9.92571	0.454467
$478$	−3.61362	−0.165283
$479$	35.5586	1.62471	0.812357	−	0.583160i	$-0.198184\pi$
$479$	35.5586	1.62471	0.812357	+	0.583160i	$0.198184\pi$
$480$	11.9887	0.547206
$481$	−0.409660	−0.0186789
$482$	−8.48532	−0.386496
$483$	0	0
$484$	−30.7536	−1.39789
$485$	−18.0830	−0.821106
$486$	−0.467496	−0.0212060
$487$	−37.2431	−1.68764	−0.843822	−	0.536623i	$-0.819700\pi$
$487$	−37.2431	−1.68764	−0.843822	+	0.536623i	$0.819700\pi$
$488$	−3.72646	−0.168689
$489$	3.41869	0.154598
$490$	0	0
$491$	19.7187	0.889892	0.444946	−	0.895557i	$-0.353223\pi$
$491$	19.7187	0.889892	0.444946	+	0.895557i	$0.353223\pi$
$492$	1.78145	0.0803139
$493$	−37.9993	−1.71140
$494$	−1.90872	−0.0858772
$495$	−13.2372	−0.594967
$496$	9.07819	0.407623
$497$	0	0
$498$	−4.73002	−0.211957
$499$	35.7234	1.59920	0.799599	−	0.600534i	$-0.205045\pi$
$499$	35.7234	1.59920	0.799599	+	0.600534i	$0.205045\pi$
$500$	−16.8569	−0.753864
$501$	−5.10863	−0.228237
$502$	1.26589	0.0564993
$503$	−32.8860	−1.46631	−0.733157	−	0.680059i	$-0.761954\pi$
$503$	−32.8860	−1.46631	−0.733157	+	0.680059i	$0.761954\pi$
$504$	0	0
$505$	20.4965	0.912080
$506$	−17.7697	−0.789960
$507$	3.13223	0.139107
$508$	5.83083	0.258701
$509$	25.7759	1.14250	0.571248	−	0.820778i	$-0.306460\pi$
$509$	25.7759	1.14250	0.571248	+	0.820778i	$0.306460\pi$
$510$	−6.65976	−0.294899
$511$	0	0
$512$	22.8508	1.00987
$513$	−1.29973	−0.0573847
$514$	2.23395	0.0985352
$515$	−2.64913	−0.116735
$516$	12.1570	0.535184
$517$	0.642702	0.0282660
$518$	0	0
$519$	10.7996	0.474048
$520$	−13.8271	−0.606356
$521$	4.35424	0.190763	0.0953813	−	0.995441i	$-0.469593\pi$
$521$	4.35424	0.190763	0.0953813	+	0.995441i	$0.469593\pi$
$522$	3.10496	0.135901
$523$	35.4249	1.54902	0.774511	−	0.632560i	$-0.217996\pi$
$523$	35.4249	1.54902	0.774511	+	0.632560i	$0.217996\pi$
$524$	23.1145	1.00976
$525$	0	0
$526$	−6.88628	−0.300256
$527$	−18.9805	−0.826804
$528$	−14.5479	−0.633114
$529$	28.1190	1.22256
$530$	−11.5538	−0.501864
$531$	12.4957	0.542267
$532$	0	0
$533$	−3.14130	−0.136065
$534$	0.193848	0.00838863
$535$	34.7874	1.50399
$536$	−11.1298	−0.480733
$537$	−0.632276	−0.0272847
$538$	−5.87763	−0.253402
$539$	0	0
$540$	−4.43565	−0.190880
$541$	9.81032	0.421779	0.210889	−	0.977510i	$-0.432364\pi$
$541$	9.81032	0.421779	0.210889	+	0.977510i	$0.432364\pi$
$542$	−7.62254	−0.327416
$543$	−3.24632	−0.139313
$544$	−27.5476	−1.18109
$545$	−34.1186	−1.46148
$546$	0	0
$547$	−7.28690	−0.311565	−0.155783	−	0.987791i	$-0.549790\pi$
$547$	−7.28690	−0.311565	−0.155783	+	0.987791i	$0.549790\pi$
$548$	34.4283	1.47070
$549$	2.10795	0.0899652
$550$	2.98162	0.127137
$551$	8.63244	0.367754
$552$	−12.6394	−0.537969
$553$	0	0
$554$	8.88799	0.377615
$555$	0.324712	0.0137833
$556$	9.52289	0.403860
$557$	35.4329	1.50134	0.750669	−	0.660678i	$-0.229731\pi$
$557$	35.4329	1.50134	0.750669	+	0.660678i	$0.229731\pi$
$558$	1.55092	0.0656557
$559$	−21.4370	−0.906689
$560$	0	0
$561$	30.4164	1.28418
$562$	−5.78662	−0.244094
$563$	−28.7535	−1.21181	−0.605907	−	0.795535i	$-0.707190\pi$
$563$	−28.7535	−1.21181	−0.605907	+	0.795535i	$0.707190\pi$
$564$	0.215363	0.00906843
$565$	−15.0823	−0.634516
$566$	−11.9452	−0.502094
$567$	0	0
$568$	3.52637	0.147963
$569$	29.3434	1.23014	0.615070	−	0.788473i	$-0.289128\pi$
$569$	29.3434	1.23014	0.615070	+	0.788473i	$0.289128\pi$
$570$	1.51292	0.0633693
$571$	5.28258	0.221069	0.110535	−	0.993872i	$-0.464744\pi$
$571$	5.28258	0.221069	0.110535	+	0.993872i	$0.464744\pi$
$572$	29.7505	1.24393
$573$	2.69791	0.112707
$574$	0	0
$575$	−8.57738	−0.357701
$576$	−3.22196	−0.134248
$577$	−14.4751	−0.602606	−0.301303	−	0.953528i	$-0.597422\pi$
$577$	−14.4751	−0.602606	−0.301303	+	0.953528i	$0.597422\pi$
$578$	7.35534	0.305942
$579$	1.09647	0.0455677
$580$	29.4603	1.22327
$581$	0	0
$582$	−3.39518	−0.140735
$583$	52.7683	2.18544
$584$	24.4476	1.01165
$585$	7.82157	0.323382
$586$	−15.9421	−0.658563
$587$	32.6688	1.34839	0.674193	−	0.738556i	$-0.264492\pi$
$587$	32.6688	1.34839	0.674193	+	0.738556i	$0.264492\pi$
$588$	0	0
$589$	4.31188	0.177668
$590$	−14.5453	−0.598820
$591$	−12.0471	−0.495549
$592$	0.356863	0.0146670
$593$	14.8785	0.610988	0.305494	−	0.952194i	$-0.401178\pi$
$593$	14.8785	0.610988	0.305494	+	0.952194i	$0.401178\pi$
$594$	−2.48536	−0.101976
$595$	0	0
$596$	−0.761811	−0.0312050
$597$	18.7422	0.767065
$598$	10.4997	0.429366
$599$	−8.72721	−0.356584	−0.178292	−	0.983978i	$-0.557057\pi$
$599$	−8.72721	−0.356584	−0.178292	+	0.983978i	$0.557057\pi$
$600$	2.12080	0.0865812
$601$	8.13308	0.331755	0.165878	−	0.986146i	$-0.446954\pi$
$601$	8.13308	0.331755	0.165878	+	0.986146i	$0.446954\pi$
$602$	0	0
$603$	6.29580	0.256385
$604$	7.21656	0.293638
$605$	−42.9841	−1.74755
$606$	3.84833	0.156328
$607$	−42.1210	−1.70964	−0.854820	−	0.518925i	$-0.826333\pi$
$607$	−42.1210	−1.70964	−0.854820	+	0.518925i	$0.826333\pi$
$608$	6.25809	0.253799
$609$	0	0
$610$	−2.45371	−0.0993477
$611$	−0.379759	−0.0153634
$612$	10.1922	0.411996
$613$	−37.0682	−1.49717	−0.748585	−	0.663039i	$-0.769266\pi$
$613$	−37.0682	−1.49717	−0.748585	+	0.663039i	$0.769266\pi$
$614$	−7.72612	−0.311801
$615$	2.48991	0.100403
$616$	0	0
$617$	40.4266	1.62751	0.813757	−	0.581205i	$-0.197418\pi$
$617$	40.4266	1.62751	0.813757	+	0.581205i	$0.197418\pi$
$618$	−0.497390	−0.0200080
$619$	−7.12931	−0.286551	−0.143276	−	0.989683i	$-0.545764\pi$
$619$	−7.12931	−0.286551	−0.143276	+	0.989683i	$0.545764\pi$
$620$	14.7153	0.590981
$621$	7.14975	0.286910
$622$	−3.57196	−0.143223
$623$	0	0
$624$	8.59601	0.344116
$625$	−29.5592	−1.18237
$626$	−9.01579	−0.360343
$627$	−6.90981	−0.275951
$628$	−35.1789	−1.40379
$629$	−0.746122	−0.0297498
$630$	0	0
$631$	20.9305	0.833230	0.416615	−	0.909083i	$-0.363216\pi$
$631$	20.9305	0.833230	0.416615	+	0.909083i	$0.363216\pi$
$632$	30.0770	1.19640
$633$	−21.3366	−0.848052
$634$	2.30983	0.0917351
$635$	8.14970	0.323411
$636$	17.6821	0.701142
$637$	0	0
$638$	16.5070	0.653518
$639$	−1.99477	−0.0789117
$640$	27.7278	1.09604
$641$	12.4115	0.490227	0.245113	−	0.969494i	$-0.421175\pi$
$641$	12.4115	0.490227	0.245113	+	0.969494i	$0.421175\pi$
$642$	6.53153	0.257779
$643$	−18.4629	−0.728107	−0.364053	−	0.931378i	$-0.618607\pi$
$643$	−18.4629	−0.728107	−0.364053	+	0.931378i	$0.618607\pi$
$644$	0	0
$645$	16.9918	0.669051
$646$	−3.47639	−0.136777
$647$	22.7620	0.894865	0.447433	−	0.894318i	$-0.352338\pi$
$647$	22.7620	0.894865	0.447433	+	0.894318i	$0.352338\pi$
$648$	−1.76781	−0.0694462
$649$	66.4311	2.60765
$650$	−1.76178	−0.0691025
$651$	0	0
$652$	6.09022	0.238511
$653$	−39.7604	−1.55594	−0.777972	−	0.628299i	$-0.783751\pi$
$653$	−39.7604	−1.55594	−0.777972	+	0.628299i	$0.783751\pi$
$654$	−6.40596	−0.250493
$655$	32.3070	1.26234
$656$	2.73645	0.106840
$657$	−13.8293	−0.539532
$658$	0	0
$659$	−11.6201	−0.452656	−0.226328	−	0.974051i	$-0.572672\pi$
$659$	−11.6201	−0.452656	−0.226328	+	0.974051i	$0.572672\pi$
$660$	−23.5814	−0.917903
$661$	42.6438	1.65865	0.829325	−	0.558766i	$-0.188725\pi$
$661$	42.6438	1.65865	0.829325	+	0.558766i	$0.188725\pi$
$662$	−13.1277	−0.510223
$663$	−17.9724	−0.697989
$664$	−17.8863	−0.694125
$665$	0	0
$666$	0.0609666	0.00236241
$667$	−47.4865	−1.83868
$668$	−9.10076	−0.352119
$669$	19.7146	0.762210
$670$	−7.32847	−0.283123
$671$	11.2065	0.432624
$672$	0	0
$673$	−46.0452	−1.77491	−0.887455	−	0.460894i	$-0.847529\pi$
$673$	−46.0452	−1.77491	−0.887455	+	0.460894i	$0.847529\pi$
$674$	8.06779	0.310760
$675$	−1.19967	−0.0461755
$676$	5.57991	0.214612
$677$	11.8928	0.457077	0.228538	−	0.973535i	$-0.426605\pi$
$677$	11.8928	0.457077	0.228538	+	0.973535i	$0.426605\pi$
$678$	−2.83178	−0.108754
$679$	0	0
$680$	−25.1835	−0.965744
$681$	−15.8988	−0.609244
$682$	8.24519	0.315725
$683$	−2.72867	−0.104410	−0.0522049	−	0.998636i	$-0.516625\pi$
$683$	−2.72867	−0.104410	−0.0522049	+	0.998636i	$0.516625\pi$
$684$	−2.31541	−0.0885318
$685$	48.1201	1.83857
$686$	0	0
$687$	26.3058	1.00363
$688$	18.6742	0.711948
$689$	−31.1796	−1.18785
$690$	−8.32249	−0.316832
$691$	34.2991	1.30480	0.652399	−	0.757876i	$-0.273763\pi$
$691$	34.2991	1.30480	0.652399	+	0.757876i	$0.273763\pi$
$692$	19.2388	0.731351
$693$	0	0
$694$	−10.5851	−0.401807
$695$	13.3101	0.504879
$696$	11.7413	0.445051
$697$	−5.72132	−0.216710
$698$	−4.96372	−0.187879
$699$	−13.3645	−0.505492
$700$	0	0
$701$	2.14489	0.0810113	0.0405057	−	0.999179i	$-0.487103\pi$
$701$	2.14489	0.0810113	0.0405057	+	0.999179i	$0.487103\pi$
$702$	1.46854	0.0554266
$703$	0.169500	0.00639279
$704$	−17.1290	−0.645572
$705$	0.301011	0.0113367
$706$	12.4521	0.468640
$707$	0	0
$708$	22.2604	0.836598
$709$	−14.7175	−0.552728	−0.276364	−	0.961053i	$-0.589130\pi$
$709$	−14.7175	−0.552728	−0.276364	+	0.961053i	$0.589130\pi$
$710$	2.32196	0.0871415
$711$	−17.0137	−0.638063
$712$	0.733026	0.0274713
$713$	−23.7193	−0.888297
$714$	0	0
$715$	41.5820	1.55508
$716$	−1.12637	−0.0420943
$717$	7.72975	0.288673
$718$	6.64269	0.247903
$719$	0.753231	0.0280908	0.0140454	−	0.999901i	$-0.495529\pi$
$719$	0.753231	0.0280908	0.0140454	+	0.999901i	$0.495529\pi$
$720$	−6.81353	−0.253925
$721$	0	0
$722$	−8.09268	−0.301178
$723$	18.1506	0.675027
$724$	−5.78315	−0.214929
$725$	7.96787	0.295919
$726$	−8.07052	−0.299525
$727$	−5.76563	−0.213835	−0.106918	−	0.994268i	$-0.534098\pi$
$727$	−5.76563	−0.213835	−0.106918	+	0.994268i	$0.534098\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	16.0976	0.595800
$731$	−39.0437	−1.44408
$732$	3.75520	0.138796
$733$	−46.2479	−1.70820	−0.854102	−	0.520106i	$-0.825893\pi$
$733$	−46.2479	−1.70820	−0.854102	+	0.520106i	$0.825893\pi$
$734$	1.54221	0.0569241
$735$	0	0
$736$	−34.4254	−1.26894
$737$	33.4705	1.23290
$738$	0.467496	0.0172088
$739$	−32.5856	−1.19868	−0.599340	−	0.800494i	$-0.704570\pi$
$739$	−32.5856	−1.19868	−0.599340	+	0.800494i	$0.704570\pi$
$740$	0.578458	0.0212645
$741$	4.08285	0.149987
$742$	0	0
$743$	4.01713	0.147374	0.0736871	−	0.997281i	$-0.476523\pi$
$743$	4.01713	0.147374	0.0736871	+	0.997281i	$0.476523\pi$
$744$	5.86472	0.215011
$745$	−1.06478	−0.0390104
$746$	−14.8545	−0.543862
$747$	10.1178	0.370191
$748$	54.1852	1.98121
$749$	0	0
$750$	−4.42367	−0.161530
$751$	33.4781	1.22163	0.610816	−	0.791772i	$-0.290841\pi$
$751$	33.4781	1.22163	0.610816	+	0.791772i	$0.290841\pi$
$752$	0.330816	0.0120636
$753$	−2.70780	−0.0986779
$754$	−9.75363	−0.355206
$755$	10.0865	0.367086
$756$	0	0
$757$	−47.4372	−1.72413	−0.862067	−	0.506794i	$-0.830831\pi$
$757$	−47.4372	−1.72413	−0.862067	+	0.506794i	$0.830831\pi$
$758$	−2.21949	−0.0806153
$759$	38.0104	1.37969
$760$	5.72104	0.207524
$761$	41.1769	1.49266	0.746331	−	0.665575i	$-0.231814\pi$
$761$	41.1769	1.49266	0.746331	+	0.665575i	$0.231814\pi$
$762$	1.53015	0.0554316
$763$	0	0
$764$	4.80619	0.173882
$765$	14.2456	0.515051
$766$	−10.4201	−0.376495
$767$	−39.2527	−1.41733
$768$	−1.23785	−0.0446672
$769$	26.5898	0.958853	0.479426	−	0.877582i	$-0.340845\pi$
$769$	26.5898	0.958853	0.479426	+	0.877582i	$0.340845\pi$
$770$	0	0
$771$	−4.77854	−0.172095
$772$	1.95330	0.0703009
$773$	20.9554	0.753712	0.376856	−	0.926272i	$-0.377005\pi$
$773$	20.9554	0.753712	0.376856	+	0.926272i	$0.377005\pi$
$774$	3.19031	0.114673
$775$	3.97993	0.142963
$776$	−12.8387	−0.460883
$777$	0	0
$778$	−12.5275	−0.449134
$779$	1.29973	0.0465678
$780$	13.9337	0.498907
$781$	−10.6048	−0.379470
$782$	19.1234	0.683851
$783$	−6.64170	−0.237355
$784$	0	0
$785$	−49.1692	−1.75492
$786$	6.06582	0.216361
$787$	16.9981	0.605917	0.302959	−	0.953004i	$-0.402026\pi$
$787$	16.9981	0.605917	0.302959	+	0.953004i	$0.402026\pi$
$788$	−21.4612	−0.764523
$789$	14.7301	0.524407
$790$	19.8044	0.704607
$791$	0	0
$792$	−9.39825	−0.333952
$793$	−6.62171	−0.235144
$794$	9.59905	0.340657
$795$	24.7142	0.876521
$796$	33.3882	1.18341
$797$	15.3946	0.545306	0.272653	−	0.962112i	$-0.412099\pi$
$797$	15.3946	0.545306	0.272653	+	0.962112i	$0.412099\pi$
$798$	0	0
$799$	−0.691663	−0.0244693
$800$	5.77632	0.204224
$801$	−0.414652	−0.0146510
$802$	1.89261	0.0668305
$803$	−73.5210	−2.59450
$804$	11.2156	0.395545
$805$	0	0
$806$	−4.87191	−0.171606
$807$	12.5726	0.442576
$808$	14.5523	0.511946
$809$	−35.4587	−1.24666	−0.623332	−	0.781958i	$-0.714221\pi$
$809$	−35.4587	−1.24666	−0.623332	+	0.781958i	$0.714221\pi$
$810$	−1.16402	−0.0408997
$811$	−18.1260	−0.636490	−0.318245	−	0.948009i	$-0.603093\pi$
$811$	−18.1260	−0.636490	−0.318245	+	0.948009i	$0.603093\pi$
$812$	0	0
$813$	16.3050	0.571843
$814$	0.324118	0.0113603
$815$	8.51225	0.298171
$816$	15.6561	0.548073
$817$	8.86971	0.310312
$818$	14.5967	0.510362
$819$	0	0
$820$	4.43565	0.154900
$821$	52.7592	1.84131	0.920654	−	0.390381i	$-0.127657\pi$
$821$	52.7592	1.84131	0.920654	+	0.390381i	$0.127657\pi$
$822$	9.03482	0.315126
$823$	25.4878	0.888448	0.444224	−	0.895916i	$-0.353479\pi$
$823$	25.4878	0.888448	0.444224	+	0.895916i	$0.353479\pi$
$824$	−1.88086	−0.0655227
$825$	−6.37786	−0.222049
$826$	0	0
$827$	34.2046	1.18941	0.594706	−	0.803943i	$-0.297269\pi$
$827$	34.2046	1.18941	0.594706	+	0.803943i	$0.297269\pi$
$828$	12.7369	0.442638
$829$	2.43288	0.0844973	0.0422487	−	0.999107i	$-0.486548\pi$
$829$	2.43288	0.0844973	0.0422487	+	0.999107i	$0.486548\pi$
$830$	−11.7774	−0.408798
$831$	−19.0119	−0.659516
$832$	10.1211	0.350887
$833$	0	0
$834$	2.49904	0.0865347
$835$	−12.7201	−0.440196
$836$	−12.3095	−0.425731
$837$	−3.31751	−0.114670
$838$	2.77044	0.0957032
$839$	3.85230	0.132996	0.0664981	−	0.997787i	$-0.478817\pi$
$839$	3.85230	0.132996	0.0664981	+	0.997787i	$0.478817\pi$
$840$	0	0
$841$	15.1121	0.521107
$842$	−2.25473	−0.0777031
$843$	12.3779	0.426317
$844$	−38.0100	−1.30836
$845$	7.79900	0.268294
$846$	0.0565166	0.00194308
$847$	0	0
$848$	27.1612	0.932720
$849$	25.5514	0.876923
$850$	−3.20876	−0.110060
$851$	−0.932406	−0.0319625
$852$	−3.55357	−0.121743
$853$	−34.7837	−1.19097	−0.595486	−	0.803366i	$-0.703040\pi$
$853$	−34.7837	−1.19097	−0.595486	+	0.803366i	$0.703040\pi$
$854$	0	0
$855$	−3.23623	−0.110677
$856$	24.6986	0.844182
$857$	−22.5815	−0.771369	−0.385685	−	0.922631i	$-0.626035\pi$
$857$	−22.5815	−0.771369	−0.385685	+	0.922631i	$0.626035\pi$
$858$	7.80726	0.266535
$859$	51.2667	1.74920	0.874599	−	0.484847i	$-0.161125\pi$
$859$	51.2667	1.74920	0.874599	+	0.484847i	$0.161125\pi$
$860$	30.2700	1.03220
$861$	0	0
$862$	15.3407	0.522505
$863$	37.0308	1.26054	0.630272	−	0.776374i	$-0.282943\pi$
$863$	37.0308	1.26054	0.630272	+	0.776374i	$0.282943\pi$
$864$	−4.81490	−0.163806
$865$	26.8900	0.914286
$866$	11.2711	0.383008
$867$	−15.7335	−0.534337
$868$	0	0
$869$	−90.4503	−3.06832
$870$	7.73110	0.262109
$871$	−19.7770	−0.670118
$872$	−24.2238	−0.820321
$873$	7.26249	0.245798
$874$	−4.34433	−0.146949
$875$	0	0
$876$	−24.6362	−0.832379
$877$	13.4630	0.454612	0.227306	−	0.973823i	$-0.427008\pi$
$877$	13.4630	0.454612	0.227306	+	0.973823i	$0.427008\pi$
$878$	4.90647	0.165585
$879$	34.1011	1.15020
$880$	−36.2229	−1.22107
$881$	−46.4466	−1.56482	−0.782412	−	0.622761i	$-0.786011\pi$
$881$	−46.4466	−1.56482	−0.782412	+	0.622761i	$0.786011\pi$
$882$	0	0
$883$	−24.4619	−0.823207	−0.411604	−	0.911363i	$-0.635031\pi$
$883$	−24.4619	−0.823207	−0.411604	+	0.911363i	$0.635031\pi$
$884$	−32.0168	−1.07684
$885$	31.1132	1.04586
$886$	−12.1138	−0.406971
$887$	−4.40051	−0.147755	−0.0738773	−	0.997267i	$-0.523537\pi$
$887$	−4.40051	−0.147755	−0.0738773	+	0.997267i	$0.523537\pi$
$888$	0.230542	0.00773648
$889$	0	0
$890$	0.482665	0.0161790
$891$	5.31632	0.178104
$892$	35.1205	1.17592
$893$	0.157128	0.00525808
$894$	−0.199918	−0.00668626
$895$	−1.57431	−0.0526235
$896$	0	0
$897$	−22.4595	−0.749902
$898$	−7.27533	−0.242781
$899$	22.0339	0.734871
$900$	−2.13716	−0.0712386
$901$	−56.7881	−1.89189
$902$	2.48536	0.0827534
$903$	0	0
$904$	−10.7082	−0.356151
$905$	−8.08307	−0.268690
$906$	1.89380	0.0629174
$907$	−26.4356	−0.877780	−0.438890	−	0.898541i	$-0.644628\pi$
$907$	−26.4356	−0.877780	−0.438890	+	0.898541i	$0.644628\pi$
$908$	−28.3229	−0.939929
$909$	−8.23179	−0.273031
$910$	0	0
$911$	31.5097	1.04396	0.521982	−	0.852957i	$-0.325193\pi$
$911$	31.5097	1.04396	0.521982	+	0.852957i	$0.325193\pi$
$912$	−3.55666	−0.117773
$913$	53.7894	1.78017
$914$	−11.8645	−0.392442
$915$	5.24862	0.173514
$916$	46.8624	1.54838
$917$	0	0
$918$	2.67469	0.0882780
$919$	−41.0251	−1.35329	−0.676647	−	0.736307i	$-0.736568\pi$
$919$	−41.0251	−1.35329	−0.676647	+	0.736307i	$0.736568\pi$
$920$	−31.4711	−1.03757
$921$	16.5266	0.544570
$922$	−1.12957	−0.0372004
$923$	6.26616	0.206253
$924$	0	0
$925$	0.156451	0.00514407
$926$	−17.2940	−0.568315
$927$	1.06395	0.0349446
$928$	31.9791	1.04977
$929$	19.3736	0.635627	0.317814	−	0.948153i	$-0.397051\pi$
$929$	19.3736	0.635627	0.317814	+	0.948153i	$0.397051\pi$
$930$	3.86166	0.126629
$931$	0	0
$932$	−23.8082	−0.779863
$933$	7.64063	0.250143
$934$	6.51465	0.213166
$935$	75.7342	2.47677
$936$	5.55322	0.181513
$937$	−9.08010	−0.296634	−0.148317	−	0.988940i	$-0.547386\pi$
$937$	−9.08010	−0.296634	−0.148317	+	0.988940i	$0.547386\pi$
$938$	0	0
$939$	19.2853	0.629351
$940$	0.536236	0.0174901
$941$	4.13494	0.134795	0.0673976	−	0.997726i	$-0.478530\pi$
$941$	4.13494	0.134795	0.0673976	+	0.997726i	$0.478530\pi$
$942$	−9.23180	−0.300788
$943$	−7.14975	−0.232828
$944$	34.1938	1.11291
$945$	0	0
$946$	16.9607	0.551440
$947$	−12.7363	−0.413875	−0.206937	−	0.978354i	$-0.566350\pi$
$947$	−12.7363	−0.413875	−0.206937	+	0.978354i	$0.566350\pi$
$948$	−30.3090	−0.984391
$949$	43.4419	1.41019
$950$	0.728947	0.0236501
$951$	−4.94086	−0.160218
$952$	0	0
$953$	−4.07352	−0.131954	−0.0659772	−	0.997821i	$-0.521016\pi$
$953$	−4.07352	−0.131954	−0.0659772	+	0.997821i	$0.521016\pi$
$954$	4.64023	0.150233
$955$	6.71758	0.217376
$956$	13.7701	0.445358
$957$	−35.3094	−1.14139
$958$	16.6235	0.537081
$959$	0	0
$960$	−8.02239	−0.258922
$961$	−19.9942	−0.644973
$962$	−0.191514	−0.00617467
$963$	−13.9713	−0.450219
$964$	32.3343	1.04142
$965$	2.73012	0.0878855
$966$	0	0
$967$	−13.6737	−0.439717	−0.219858	−	0.975532i	$-0.570560\pi$
$967$	−13.6737	−0.439717	−0.219858	+	0.975532i	$0.570560\pi$
$968$	−30.5182	−0.980893
$969$	7.43619	0.238885
$970$	−8.45371	−0.271432
$971$	−39.9822	−1.28309	−0.641545	−	0.767085i	$-0.721706\pi$
$971$	−39.9822	−1.28309	−0.641545	+	0.767085i	$0.721706\pi$
$972$	1.78145	0.0571400
$973$	0	0
$974$	−17.4110	−0.557884
$975$	3.76854	0.120690
$976$	5.76831	0.184639
$977$	−35.2159	−1.12666	−0.563329	−	0.826233i	$-0.690480\pi$
$977$	−35.2159	−1.12666	−0.563329	+	0.826233i	$0.690480\pi$
$978$	1.59822	0.0511055
$979$	−2.20442	−0.0704537
$980$	0	0
$981$	13.7027	0.437494
$982$	9.21841	0.294171
$983$	−43.1205	−1.37533	−0.687666	−	0.726027i	$-0.741365\pi$
$983$	−43.1205	−1.37533	−0.687666	+	0.726027i	$0.741365\pi$
$984$	1.76781	0.0563558
$985$	−29.9961	−0.955756
$986$	−17.7645	−0.565737
$987$	0	0
$988$	7.27339	0.231397
$989$	−48.7917	−1.55149
$990$	−6.18833	−0.196678
$991$	−57.1493	−1.81541	−0.907703	−	0.419613i	$-0.862166\pi$
$991$	−57.1493	−1.81541	−0.907703	+	0.419613i	$0.862166\pi$
$992$	15.9735	0.507158
$993$	28.0809	0.891121
$994$	0	0
$995$	46.6664	1.47942
$996$	18.0243	0.571122
$997$	46.4135	1.46993	0.734964	−	0.678106i	$-0.237199\pi$
$997$	46.4135	1.46993	0.734964	+	0.678106i	$0.237199\pi$
$998$	16.7005	0.528646
$999$	−0.130411	−0.00412602

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6027.2.a.bf.1.8		12
7.3	odd	6		861.2.i.e.247.5	✓	24
7.5	odd	6		861.2.i.e.739.5	yes	24
7.6	odd	2		6027.2.a.bg.1.8		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
861.2.i.e.247.5	✓	24	7.3	odd	6
861.2.i.e.739.5	yes	24	7.5	odd	6
6027.2.a.bf.1.8		12	1.1	even	1	trivial
6027.2.a.bg.1.8		12	7.6	odd	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:	\( N \)	\(=\)	\( 6027 = 3 \cdot 7^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6027.a (trivial)

\(f(q)\)	\(=\)	\(q+0.467496 q^{2} -1.00000 q^{3} -1.78145 q^{4} -2.48991 q^{5} -0.467496 q^{6} -1.76781 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.467496 q^{2} -1.00000 q^{3} -1.78145 q^{4} -2.48991 q^{5} -0.467496 q^{6} -1.76781 q^{8} +1.00000 q^{9} -1.16402 q^{10} +5.31632 q^{11} +1.78145 q^{12} -3.14130 q^{13} +2.48991 q^{15} +2.73645 q^{16} -5.72132 q^{17} +0.467496 q^{18} +1.29973 q^{19} +4.43565 q^{20} +2.48536 q^{22} -7.14975 q^{23} +1.76781 q^{24} +1.19967 q^{25} -1.46854 q^{26} -1.00000 q^{27} +6.64170 q^{29} +1.16402 q^{30} +3.31751 q^{31} +4.81490 q^{32} -5.31632 q^{33} -2.67469 q^{34} -1.78145 q^{36} +0.130411 q^{37} +0.607620 q^{38} +3.14130 q^{39} +4.40170 q^{40} +1.00000 q^{41} +6.82425 q^{43} -9.47075 q^{44} -2.48991 q^{45} -3.34248 q^{46} +0.120892 q^{47} -2.73645 q^{48} +0.560843 q^{50} +5.72132 q^{51} +5.59606 q^{52} +9.92571 q^{53} -0.467496 q^{54} -13.2372 q^{55} -1.29973 q^{57} +3.10496 q^{58} +12.4957 q^{59} -4.43565 q^{60} +2.10795 q^{61} +1.55092 q^{62} -3.22196 q^{64} +7.82157 q^{65} -2.48536 q^{66} +6.29580 q^{67} +10.1922 q^{68} +7.14975 q^{69} -1.99477 q^{71} -1.76781 q^{72} -13.8293 q^{73} +0.0609666 q^{74} -1.19967 q^{75} -2.31541 q^{76} +1.46854 q^{78} -17.0137 q^{79} -6.81353 q^{80} +1.00000 q^{81} +0.467496 q^{82} +10.1178 q^{83} +14.2456 q^{85} +3.19031 q^{86} -6.64170 q^{87} -9.39825 q^{88} -0.414652 q^{89} -1.16402 q^{90} +12.7369 q^{92} -3.31751 q^{93} +0.0565166 q^{94} -3.23623 q^{95} -4.81490 q^{96} +7.26249 q^{97} +5.31632 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{2} - 12 q^{3} + 10 q^{4} - 12 q^{5} + 2 q^{6} + 12 q^{9}+O(q^{10}) \) 12 * q - 2 * q^2 - 12 * q^3 + 10 * q^4 - 12 * q^5 + 2 * q^6 + 12 * q^9	\( 12 q - 2 q^{2} - 12 q^{3} + 10 q^{4} - 12 q^{5} + 2 q^{6} + 12 q^{9} - 11 q^{10} + 10 q^{11} - 10 q^{12} - 15 q^{13} + 12 q^{15} + 14 q^{16} - 8 q^{17} - 2 q^{18} - 2 q^{19} - 16 q^{20} - 7 q^{22} + 5 q^{23} + 20 q^{25} - 12 q^{27} + 20 q^{29} + 11 q^{30} - 10 q^{31} + 3 q^{32} - 10 q^{33} + 23 q^{34} + 10 q^{36} - 17 q^{37} - 6 q^{38} + 15 q^{39} - 39 q^{40} + 12 q^{41} + 12 q^{43} + 20 q^{44} - 12 q^{45} - 36 q^{46} - 34 q^{47} - 14 q^{48} + 59 q^{50} + 8 q^{51} - 26 q^{52} + 6 q^{53} + 2 q^{54} + q^{55} + 2 q^{57} - 11 q^{58} - 27 q^{59} + 16 q^{60} - 22 q^{61} + 45 q^{62} + 26 q^{64} + 7 q^{66} - 26 q^{67} - 33 q^{68} - 5 q^{69} + 50 q^{71} - 21 q^{73} - 35 q^{74} - 20 q^{75} + 24 q^{76} - 10 q^{79} - 22 q^{80} + 12 q^{81} - 2 q^{82} - 8 q^{83} + 8 q^{85} - 17 q^{86} - 20 q^{87} - 46 q^{88} - 11 q^{89} - 11 q^{90} + 63 q^{92} + 10 q^{93} - 10 q^{94} + 35 q^{95} - 3 q^{96} - 32 q^{97} + 10 q^{99}+O(q^{100}) \) 12 * q - 2 * q^2 - 12 * q^3 + 10 * q^4 - 12 * q^5 + 2 * q^6 + 12 * q^9 - 11 * q^10 + 10 * q^11 - 10 * q^12 - 15 * q^13 + 12 * q^15 + 14 * q^16 - 8 * q^17 - 2 * q^18 - 2 * q^19 - 16 * q^20 - 7 * q^22 + 5 * q^23 + 20 * q^25 - 12 * q^27 + 20 * q^29 + 11 * q^30 - 10 * q^31 + 3 * q^32 - 10 * q^33 + 23 * q^34 + 10 * q^36 - 17 * q^37 - 6 * q^38 + 15 * q^39 - 39 * q^40 + 12 * q^41 + 12 * q^43 + 20 * q^44 - 12 * q^45 - 36 * q^46 - 34 * q^47 - 14 * q^48 + 59 * q^50 + 8 * q^51 - 26 * q^52 + 6 * q^53 + 2 * q^54 + q^55 + 2 * q^57 - 11 * q^58 - 27 * q^59 + 16 * q^60 - 22 * q^61 + 45 * q^62 + 26 * q^64 + 7 * q^66 - 26 * q^67 - 33 * q^68 - 5 * q^69 + 50 * q^71 - 21 * q^73 - 35 * q^74 - 20 * q^75 + 24 * q^76 - 10 * q^79 - 22 * q^80 + 12 * q^81 - 2 * q^82 - 8 * q^83 + 8 * q^85 - 17 * q^86 - 20 * q^87 - 46 * q^88 - 11 * q^89 - 11 * q^90 + 63 * q^92 + 10 * q^93 - 10 * q^94 + 35 * q^95 - 3 * q^96 - 32 * q^97 + 10 * q^99

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