LMFDB - Embedded newform 6027.2.a.bb.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:	$8$
Coefficient field:	8.8.7457527933.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} - 6x^{6} + 23x^{5} - 4x^{4} - 27x^{3} + 8x^{2} + 8x + 1 $ x^8 - 3x^7 - 6x^6 + 23x^5 - 4x^4 - 27x^3 + 8x^2 + 8*x + 1
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			$-0.314356$ 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)

$f(q)$	$=$	$q+2.55413 q^{2} -1.00000 q^{3} +4.52358 q^{4} -2.03983 q^{5} -2.55413 q^{6} +6.44554 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.55413 q^{2} -1.00000 q^{3} +4.52358 q^{4} -2.03983 q^{5} -2.55413 q^{6} +6.44554 q^{8} +1.00000 q^{9} -5.20999 q^{10} +2.19710 q^{11} -4.52358 q^{12} -4.05386 q^{13} +2.03983 q^{15} +7.41559 q^{16} +4.84721 q^{17} +2.55413 q^{18} -7.41918 q^{19} -9.22734 q^{20} +5.61167 q^{22} -4.70245 q^{23} -6.44554 q^{24} -0.839085 q^{25} -10.3541 q^{26} -1.00000 q^{27} -10.1020 q^{29} +5.20999 q^{30} +3.76089 q^{31} +6.04930 q^{32} -2.19710 q^{33} +12.3804 q^{34} +4.52358 q^{36} -6.51492 q^{37} -18.9495 q^{38} +4.05386 q^{39} -13.1478 q^{40} -1.00000 q^{41} +10.7302 q^{43} +9.93873 q^{44} -2.03983 q^{45} -12.0107 q^{46} -0.528264 q^{47} -7.41559 q^{48} -2.14313 q^{50} -4.84721 q^{51} -18.3379 q^{52} +7.25162 q^{53} -2.55413 q^{54} -4.48171 q^{55} +7.41918 q^{57} -25.8019 q^{58} -7.53546 q^{59} +9.22734 q^{60} -1.26730 q^{61} +9.60579 q^{62} +0.619503 q^{64} +8.26919 q^{65} -5.61167 q^{66} -8.72784 q^{67} +21.9267 q^{68} +4.70245 q^{69} -1.95591 q^{71} +6.44554 q^{72} +13.1873 q^{73} -16.6399 q^{74} +0.839085 q^{75} -33.5612 q^{76} +10.3541 q^{78} -2.93987 q^{79} -15.1266 q^{80} +1.00000 q^{81} -2.55413 q^{82} -12.0571 q^{83} -9.88750 q^{85} +27.4064 q^{86} +10.1020 q^{87} +14.1615 q^{88} +4.93696 q^{89} -5.20999 q^{90} -21.2719 q^{92} -3.76089 q^{93} -1.34925 q^{94} +15.1339 q^{95} -6.04930 q^{96} +4.56808 q^{97} +2.19710 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} - 8 q^{3} + 13 q^{4} - 7 q^{5} - q^{6} + 6 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q + q^2 - 8 * q^3 + 13 * q^4 - 7 * q^5 - q^6 + 6 * q^8 + 8 * q^9	$ 8 q + q^{2} - 8 q^{3} + 13 q^{4} - 7 q^{5} - q^{6} + 6 q^{8} + 8 q^{9} - 8 q^{10} + 11 q^{11} - 13 q^{12} - 10 q^{13} + 7 q^{15} - 17 q^{16} - 3 q^{17} + q^{18} - 6 q^{19} - 11 q^{20} + 15 q^{22} + 14 q^{23} - 6 q^{24} + 25 q^{25} - 24 q^{26} - 8 q^{27} + 2 q^{29} + 8 q^{30} - 16 q^{31} + 3 q^{32} - 11 q^{33} + 4 q^{34} + 13 q^{36} - 20 q^{37} - 10 q^{38} + 10 q^{39} + 3 q^{40} - 8 q^{41} + 7 q^{43} - 7 q^{45} - 5 q^{46} - 14 q^{47} + 17 q^{48} - 5 q^{50} + 3 q^{51} - 23 q^{52} + 7 q^{53} - q^{54} - 48 q^{55} + 6 q^{57} - 20 q^{58} - 22 q^{59} + 11 q^{60} + 33 q^{62} - 10 q^{64} - 14 q^{65} - 15 q^{66} + 12 q^{67} + 27 q^{68} - 14 q^{69} - 5 q^{71} + 6 q^{72} - 2 q^{73} + 6 q^{74} - 25 q^{75} - 43 q^{76} + 24 q^{78} - 15 q^{79} + 7 q^{80} + 8 q^{81} - q^{82} - 15 q^{83} - 43 q^{85} + 31 q^{86} - 2 q^{87} + 17 q^{88} - 29 q^{89} - 8 q^{90} + 19 q^{92} + 16 q^{93} - 20 q^{94} + 14 q^{95} - 3 q^{96} - 19 q^{97} + 11 q^{99}+O(q^{100}) $ 8 * q + q^2 - 8 * q^3 + 13 * q^4 - 7 * q^5 - q^6 + 6 * q^8 + 8 * q^9 - 8 * q^10 + 11 * q^11 - 13 * q^12 - 10 * q^13 + 7 * q^15 - 17 * q^16 - 3 * q^17 + q^18 - 6 * q^19 - 11 * q^20 + 15 * q^22 + 14 * q^23 - 6 * q^24 + 25 * q^25 - 24 * q^26 - 8 * q^27 + 2 * q^29 + 8 * q^30 - 16 * q^31 + 3 * q^32 - 11 * q^33 + 4 * q^34 + 13 * q^36 - 20 * q^37 - 10 * q^38 + 10 * q^39 + 3 * q^40 - 8 * q^41 + 7 * q^43 - 7 * q^45 - 5 * q^46 - 14 * q^47 + 17 * q^48 - 5 * q^50 + 3 * q^51 - 23 * q^52 + 7 * q^53 - q^54 - 48 * q^55 + 6 * q^57 - 20 * q^58 - 22 * q^59 + 11 * q^60 + 33 * q^62 - 10 * q^64 - 14 * q^65 - 15 * q^66 + 12 * q^67 + 27 * q^68 - 14 * q^69 - 5 * q^71 + 6 * q^72 - 2 * q^73 + 6 * q^74 - 25 * q^75 - 43 * q^76 + 24 * q^78 - 15 * q^79 + 7 * q^80 + 8 * q^81 - q^82 - 15 * q^83 - 43 * q^85 + 31 * q^86 - 2 * q^87 + 17 * q^88 - 29 * q^89 - 8 * q^90 + 19 * q^92 + 16 * q^93 - 20 * q^94 + 14 * q^95 - 3 * q^96 - 19 * q^97 + 11 * 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 $

$2$	2.55413	1.80604	0.903021	−	0.429596i	$-0.141344\pi$
$2$	2.55413	1.80604	0.903021	+	0.429596i	$0.141344\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	4.52358	2.26179
$5$	−2.03983	−0.912241	−0.456120	−	0.889918i	$-0.650761\pi$
$5$	−2.03983	−0.912241	−0.456120	+	0.889918i	$0.650761\pi$
$6$	−2.55413	−1.04272
$7$	0	0
$7$	0	0
$8$	6.44554	2.27884
$9$	1.00000	0.333333
$10$	−5.20999	−1.64755
$11$	2.19710	0.662449	0.331225	−	0.943552i	$-0.392538\pi$
$11$	2.19710	0.662449	0.331225	+	0.943552i	$0.392538\pi$
$12$	−4.52358	−1.30584
$13$	−4.05386	−1.12434	−0.562169	−	0.827022i	$-0.690033\pi$
$13$	−4.05386	−1.12434	−0.562169	+	0.827022i	$0.690033\pi$
$14$	0	0
$15$	2.03983	0.526682
$16$	7.41559	1.85390
$17$	4.84721	1.17562	0.587811	−	0.808999i	$-0.299990\pi$
$17$	4.84721	1.17562	0.587811	+	0.808999i	$0.299990\pi$
$18$	2.55413	0.602014
$19$	−7.41918	−1.70208	−0.851038	−	0.525104i	$-0.824026\pi$
$19$	−7.41918	−1.70208	−0.851038	+	0.525104i	$0.824026\pi$
$20$	−9.22734	−2.06330
$21$	0	0
$22$	5.61167	1.19641
$23$	−4.70245	−0.980529	−0.490264	−	0.871574i	$-0.663100\pi$
$23$	−4.70245	−0.980529	−0.490264	+	0.871574i	$0.663100\pi$
$24$	−6.44554	−1.31569
$25$	−0.839085	−0.167817
$26$	−10.3541	−2.03060
$27$	−1.00000	−0.192450
$28$	0	0
$29$	−10.1020	−1.87590	−0.937950	−	0.346769i	$-0.887279\pi$
$29$	−10.1020	−1.87590	−0.937950	+	0.346769i	$0.887279\pi$
$30$	5.20999	0.951211
$31$	3.76089	0.675475	0.337738	−	0.941240i	$-0.390338\pi$
$31$	3.76089	0.675475	0.337738	+	0.941240i	$0.390338\pi$
$32$	6.04930	1.06937
$33$	−2.19710	−0.382465
$34$	12.3804	2.12322
$35$	0	0
$36$	4.52358	0.753929
$37$	−6.51492	−1.07105	−0.535523	−	0.844521i	$-0.679885\pi$
$37$	−6.51492	−1.07105	−0.535523	+	0.844521i	$0.679885\pi$
$38$	−18.9495	−3.07402
$39$	4.05386	0.649137
$40$	−13.1478	−2.07885
$41$	−1.00000	−0.156174
$41$	−1.00000	−0.156174
$42$	0	0
$43$	10.7302	1.63635	0.818173	−	0.574972i	$-0.194987\pi$
$43$	10.7302	1.63635	0.818173	+	0.574972i	$0.194987\pi$
$44$	9.93873	1.49832
$45$	−2.03983	−0.304080
$46$	−12.0107	−1.77088
$47$	−0.528264	−0.0770552	−0.0385276	−	0.999258i	$-0.512267\pi$
$47$	−0.528264	−0.0770552	−0.0385276	+	0.999258i	$0.512267\pi$
$48$	−7.41559	−1.07035
$49$	0	0
$50$	−2.14313	−0.303085
$51$	−4.84721	−0.678745
$52$	−18.3379	−2.54301
$53$	7.25162	0.996086	0.498043	−	0.867152i	$-0.334052\pi$
$53$	7.25162	0.996086	0.498043	+	0.867152i	$0.334052\pi$
$54$	−2.55413	−0.347573
$55$	−4.48171	−0.604313
$56$	0	0
$57$	7.41918	0.982694
$58$	−25.8019	−3.38796
$59$	−7.53546	−0.981033	−0.490516	−	0.871432i	$-0.663192\pi$
$59$	−7.53546	−0.981033	−0.490516	+	0.871432i	$0.663192\pi$
$60$	9.22734	1.19124
$61$	−1.26730	−0.162261	−0.0811304	−	0.996703i	$-0.525853\pi$
$61$	−1.26730	−0.162261	−0.0811304	+	0.996703i	$0.525853\pi$
$62$	9.60579	1.21994
$63$	0	0
$64$	0.619503	0.0774378
$65$	8.26919	1.02567
$66$	−5.61167	−0.690748
$67$	−8.72784	−1.06628	−0.533138	−	0.846029i	$-0.678987\pi$
$67$	−8.72784	−1.06628	−0.533138	+	0.846029i	$0.678987\pi$
$68$	21.9267	2.65901
$69$	4.70245	0.566109
$70$	0	0
$71$	−1.95591	−0.232123	−0.116062	−	0.993242i	$-0.537027\pi$
$71$	−1.95591	−0.232123	−0.116062	+	0.993242i	$0.537027\pi$
$72$	6.44554	0.759614
$73$	13.1873	1.54346	0.771731	−	0.635949i	$-0.219391\pi$
$73$	13.1873	1.54346	0.771731	+	0.635949i	$0.219391\pi$
$74$	−16.6399	−1.93435
$75$	0.839085	0.0968892
$76$	−33.5612	−3.84974
$77$	0	0
$78$	10.3541	1.17237
$79$	−2.93987	−0.330761	−0.165380	−	0.986230i	$-0.552885\pi$
$79$	−2.93987	−0.330761	−0.165380	+	0.986230i	$0.552885\pi$
$80$	−15.1266	−1.69120
$81$	1.00000	0.111111
$82$	−2.55413	−0.282056
$83$	−12.0571	−1.32344	−0.661722	−	0.749750i	$-0.730174\pi$
$83$	−12.0571	−1.32344	−0.661722	+	0.749750i	$0.730174\pi$
$84$	0	0
$85$	−9.88750	−1.07245
$86$	27.4064	2.95531
$87$	10.1020	1.08305
$88$	14.1615	1.50962
$89$	4.93696	0.523317	0.261658	−	0.965161i	$-0.415731\pi$
$89$	4.93696	0.523317	0.261658	+	0.965161i	$0.415731\pi$
$90$	−5.20999	−0.549182
$91$	0	0
$92$	−21.2719	−2.21775
$93$	−3.76089	−0.389986
$94$	−1.34925	−0.139165
$95$	15.1339	1.55270
$96$	−6.04930	−0.617404
$97$	4.56808	0.463818	0.231909	−	0.972737i	$-0.425503\pi$
$97$	4.56808	0.463818	0.231909	+	0.972737i	$0.425503\pi$
$98$	0	0
$99$	2.19710	0.220816
$100$	−3.79567	−0.379567
$101$	−14.8399	−1.47663	−0.738313	−	0.674459i	$-0.764377\pi$
$101$	−14.8399	−1.47663	−0.738313	+	0.674459i	$0.764377\pi$
$102$	−12.3804	−1.22584
$103$	15.1660	1.49435	0.747174	−	0.664629i	$-0.231410\pi$
$103$	15.1660	1.49435	0.747174	+	0.664629i	$0.231410\pi$
$104$	−26.1293	−2.56219
$105$	0	0
$106$	18.5216	1.79897
$107$	−10.5325	−1.01822	−0.509109	−	0.860702i	$-0.670025\pi$
$107$	−10.5325	−1.01822	−0.509109	+	0.860702i	$0.670025\pi$
$108$	−4.52358	−0.435281
$109$	−20.4788	−1.96151	−0.980757	−	0.195234i	$-0.937453\pi$
$109$	−20.4788	−1.96151	−0.980757	+	0.195234i	$0.937453\pi$
$110$	−11.4469	−1.09141
$111$	6.51492	0.618369
$112$	0	0
$113$	3.99357	0.375683	0.187842	−	0.982199i	$-0.439851\pi$
$113$	3.99357	0.375683	0.187842	+	0.982199i	$0.439851\pi$
$114$	18.9495	1.77479
$115$	9.59221	0.894478
$116$	−45.6973	−4.24289
$117$	−4.05386	−0.374779
$118$	−19.2465	−1.77179
$119$	0	0
$120$	13.1478	1.20023
$121$	−6.17277	−0.561161
$122$	−3.23684	−0.293050
$123$	1.00000	0.0901670
$124$	17.0127	1.52778
$125$	11.9108	1.06533
$126$	0	0
$127$	1.59918	0.141905	0.0709523	−	0.997480i	$-0.477396\pi$
$127$	1.59918	0.141905	0.0709523	+	0.997480i	$0.477396\pi$
$128$	−10.5163	−0.929519
$129$	−10.7302	−0.944745
$130$	21.1206	1.85240
$131$	−9.63387	−0.841715	−0.420858	−	0.907127i	$-0.638271\pi$
$131$	−9.63387	−0.841715	−0.420858	+	0.907127i	$0.638271\pi$
$132$	−9.93873	−0.865055
$133$	0	0
$134$	−22.2920	−1.92574
$135$	2.03983	0.175561
$136$	31.2429	2.67906
$137$	−7.92292	−0.676900	−0.338450	−	0.940984i	$-0.609903\pi$
$137$	−7.92292	−0.676900	−0.338450	+	0.940984i	$0.609903\pi$
$138$	12.0107	1.02242
$139$	3.47465	0.294716	0.147358	−	0.989083i	$-0.452923\pi$
$139$	3.47465	0.294716	0.147358	+	0.989083i	$0.452923\pi$
$140$	0	0
$141$	0.528264	0.0444878
$142$	−4.99564	−0.419225
$143$	−8.90671	−0.744817
$144$	7.41559	0.617966
$145$	20.6065	1.71127
$146$	33.6822	2.78756
$147$	0	0
$148$	−29.4707	−2.42248
$149$	4.81236	0.394244	0.197122	−	0.980379i	$-0.436840\pi$
$149$	4.81236	0.394244	0.197122	+	0.980379i	$0.436840\pi$
$150$	2.14313	0.174986
$151$	−6.30410	−0.513021	−0.256510	−	0.966542i	$-0.582573\pi$
$151$	−6.30410	−0.513021	−0.256510	+	0.966542i	$0.582573\pi$
$152$	−47.8206	−3.87876
$153$	4.84721	0.391874
$154$	0	0
$155$	−7.67158	−0.616196
$156$	18.3379	1.46821
$157$	−4.07061	−0.324870	−0.162435	−	0.986719i	$-0.551935\pi$
$157$	−4.07061	−0.324870	−0.162435	+	0.986719i	$0.551935\pi$
$158$	−7.50880	−0.597368
$159$	−7.25162	−0.575090
$160$	−12.3395	−0.975527
$161$	0	0
$162$	2.55413	0.200671
$163$	9.43025	0.738634	0.369317	−	0.929303i	$-0.379592\pi$
$163$	9.43025	0.738634	0.369317	+	0.929303i	$0.379592\pi$
$164$	−4.52358	−0.353232
$165$	4.48171	0.348900
$166$	−30.7955	−2.39019
$167$	−12.2859	−0.950715	−0.475357	−	0.879793i	$-0.657681\pi$
$167$	−12.2859	−0.950715	−0.475357	+	0.879793i	$0.657681\pi$
$168$	0	0
$169$	3.43376	0.264135
$170$	−25.2539	−1.93689
$171$	−7.41918	−0.567359
$172$	48.5390	3.70107
$173$	−21.7797	−1.65588	−0.827940	−	0.560817i	$-0.810487\pi$
$173$	−21.7797	−1.65588	−0.827940	+	0.560817i	$0.810487\pi$
$174$	25.8019	1.95604
$175$	0	0
$176$	16.2928	1.22811
$177$	7.53546	0.566400
$178$	12.6096	0.945133
$179$	−8.27123	−0.618221	−0.309110	−	0.951026i	$-0.600031\pi$
$179$	−8.27123	−0.618221	−0.309110	+	0.951026i	$0.600031\pi$
$180$	−9.22734	−0.687765
$181$	−2.34065	−0.173979	−0.0869894	−	0.996209i	$-0.527725\pi$
$181$	−2.34065	−0.173979	−0.0869894	+	0.996209i	$0.527725\pi$
$182$	0	0
$183$	1.26730	0.0936813
$184$	−30.3098	−2.23447
$185$	13.2893	0.977052
$186$	−9.60579	−0.704331
$187$	10.6498	0.778789
$188$	−2.38964	−0.174282
$189$	0	0
$190$	38.6539	2.80425
$191$	14.5214	1.05073	0.525367	−	0.850876i	$-0.323928\pi$
$191$	14.5214	1.05073	0.525367	+	0.850876i	$0.323928\pi$
$192$	−0.619503	−0.0447087
$193$	18.0211	1.29719	0.648593	−	0.761136i	$-0.275358\pi$
$193$	18.0211	1.29719	0.648593	+	0.761136i	$0.275358\pi$
$194$	11.6675	0.837676
$195$	−8.26919	−0.592169
$196$	0	0
$197$	25.2224	1.79702	0.898510	−	0.438953i	$-0.144650\pi$
$197$	25.2224	1.79702	0.898510	+	0.438953i	$0.144650\pi$
$198$	5.61167	0.398804
$199$	−2.07686	−0.147225	−0.0736125	−	0.997287i	$-0.523453\pi$
$199$	−2.07686	−0.147225	−0.0736125	+	0.997287i	$0.523453\pi$
$200$	−5.40836	−0.382429
$201$	8.72784	0.615614
$202$	−37.9030	−2.66685
$203$	0	0
$204$	−21.9267	−1.53518
$205$	2.03983	0.142468
$206$	38.7358	2.69885
$207$	−4.70245	−0.326843
$208$	−30.0617	−2.08441
$209$	−16.3006	−1.12754
$210$	0	0
$211$	9.20520	0.633712	0.316856	−	0.948474i	$-0.397373\pi$
$211$	9.20520	0.633712	0.316856	+	0.948474i	$0.397373\pi$
$212$	32.8032	2.25294
$213$	1.95591	0.134017
$214$	−26.9014	−1.83894
$215$	−21.8879	−1.49274
$216$	−6.44554	−0.438563
$217$	0	0
$218$	−52.3055	−3.54258
$219$	−13.1873	−0.891118
$220$	−20.2733	−1.36683
$221$	−19.6499	−1.32180
$222$	16.6399	1.11680
$223$	−23.2274	−1.55542	−0.777710	−	0.628624i	$-0.783619\pi$
$223$	−23.2274	−1.55542	−0.777710	+	0.628624i	$0.783619\pi$
$224$	0	0
$225$	−0.839085	−0.0559390
$226$	10.2001	0.678500
$227$	4.57677	0.303771	0.151885	−	0.988398i	$-0.451466\pi$
$227$	4.57677	0.303771	0.151885	+	0.988398i	$0.451466\pi$
$228$	33.5612	2.22265
$229$	−10.8001	−0.713688	−0.356844	−	0.934164i	$-0.616147\pi$
$229$	−10.8001	−0.713688	−0.356844	+	0.934164i	$0.616147\pi$
$230$	24.4997	1.61547
$231$	0	0
$232$	−65.1131	−4.27488
$233$	−19.0904	−1.25065	−0.625325	−	0.780364i	$-0.715034\pi$
$233$	−19.0904	−1.25065	−0.625325	+	0.780364i	$0.715034\pi$
$234$	−10.3541	−0.676867
$235$	1.07757	0.0702929
$236$	−34.0872	−2.21889
$237$	2.93987	0.190965
$238$	0	0
$239$	−7.39421	−0.478291	−0.239146	−	0.970984i	$-0.576867\pi$
$239$	−7.39421	−0.478291	−0.239146	+	0.970984i	$0.576867\pi$
$240$	15.1266	0.976415
$241$	−8.85999	−0.570722	−0.285361	−	0.958420i	$-0.592113\pi$
$241$	−8.85999	−0.570722	−0.285361	+	0.958420i	$0.592113\pi$
$242$	−15.7661	−1.01348
$243$	−1.00000	−0.0641500
$244$	−5.73271	−0.366999
$245$	0	0
$246$	2.55413	0.162845
$247$	30.0763	1.91371
$248$	24.2410	1.53930
$249$	12.0571	0.764090
$250$	30.4216	1.92403
$251$	2.14037	0.135099	0.0675495	−	0.997716i	$-0.478482\pi$
$251$	2.14037	0.135099	0.0675495	+	0.997716i	$0.478482\pi$
$252$	0	0
$253$	−10.3317	−0.649550
$254$	4.08452	0.256286
$255$	9.88750	0.619179
$256$	−28.0990	−1.75619
$257$	14.2797	0.890744	0.445372	−	0.895346i	$-0.353071\pi$
$257$	14.2797	0.890744	0.445372	+	0.895346i	$0.353071\pi$
$258$	−27.4064	−1.70625
$259$	0	0
$260$	37.4063	2.31984
$261$	−10.1020	−0.625300
$262$	−24.6061	−1.52017
$263$	16.4154	1.01222	0.506109	−	0.862469i	$-0.331083\pi$
$263$	16.4154	1.01222	0.506109	+	0.862469i	$0.331083\pi$
$264$	−14.1615	−0.871578
$265$	−14.7921	−0.908670
$266$	0	0
$267$	−4.93696	−0.302137
$268$	−39.4810	−2.41169
$269$	5.20640	0.317440	0.158720	−	0.987324i	$-0.449263\pi$
$269$	5.20640	0.317440	0.158720	+	0.987324i	$0.449263\pi$
$270$	5.20999	0.317070
$271$	−30.7434	−1.86753	−0.933765	−	0.357888i	$-0.883497\pi$
$271$	−30.7434	−1.86753	−0.933765	+	0.357888i	$0.883497\pi$
$272$	35.9449	2.17948
$273$	0	0
$274$	−20.2362	−1.22251
$275$	−1.84355	−0.111170
$276$	21.2719	1.28042
$277$	−11.4285	−0.686669	−0.343335	−	0.939213i	$-0.611556\pi$
$277$	−11.4285	−0.686669	−0.343335	+	0.939213i	$0.611556\pi$
$278$	8.87472	0.532270
$279$	3.76089	0.225158
$280$	0	0
$281$	1.76574	0.105335	0.0526677	−	0.998612i	$-0.483228\pi$
$281$	1.76574	0.105335	0.0526677	+	0.998612i	$0.483228\pi$
$282$	1.34925	0.0803469
$283$	9.61324	0.571448	0.285724	−	0.958312i	$-0.407766\pi$
$283$	9.61324	0.571448	0.285724	+	0.958312i	$0.407766\pi$
$284$	−8.84770	−0.525014
$285$	−15.1339	−0.896454
$286$	−22.7489	−1.34517
$287$	0	0
$288$	6.04930	0.356458
$289$	6.49545	0.382086
$290$	52.6316	3.09063
$291$	−4.56808	−0.267786
$292$	59.6540	3.49098
$293$	0.406494	0.0237476	0.0118738	−	0.999930i	$-0.496220\pi$
$293$	0.406494	0.0237476	0.0118738	+	0.999930i	$0.496220\pi$
$294$	0	0
$295$	15.3711	0.894938
$296$	−41.9922	−2.44075
$297$	−2.19710	−0.127488
$298$	12.2914	0.712021
$299$	19.0631	1.10245
$300$	3.79567	0.219143
$301$	0	0
$302$	−16.1015	−0.926537
$303$	14.8399	0.852530
$304$	−55.0176	−3.15547
$305$	2.58507	0.148021
$306$	12.3804	0.707741
$307$	1.20072	0.0685287	0.0342644	−	0.999413i	$-0.489091\pi$
$307$	1.20072	0.0685287	0.0342644	+	0.999413i	$0.489091\pi$
$308$	0	0
$309$	−15.1660	−0.862762
$310$	−19.5942	−1.11288
$311$	28.8728	1.63722	0.818612	−	0.574346i	$-0.194744\pi$
$311$	28.8728	1.63722	0.818612	+	0.574346i	$0.194744\pi$
$312$	26.1293	1.47928
$313$	15.2516	0.862073	0.431037	−	0.902334i	$-0.358148\pi$
$313$	15.2516	0.862073	0.431037	+	0.902334i	$0.358148\pi$
$314$	−10.3969	−0.586729
$315$	0	0
$316$	−13.2987	−0.748111
$317$	19.2570	1.08158	0.540790	−	0.841158i	$-0.318125\pi$
$317$	19.2570	1.08158	0.540790	+	0.841158i	$0.318125\pi$
$318$	−18.5216	−1.03864
$319$	−22.1951	−1.24269
$320$	−1.26368	−0.0706419
$321$	10.5325	0.587868
$322$	0	0
$323$	−35.9623	−2.00100
$324$	4.52358	0.251310
$325$	3.40153	0.188683
$326$	24.0861	1.33400
$327$	20.4788	1.13248
$328$	−6.44554	−0.355895
$329$	0	0
$330$	11.4469	0.630129
$331$	2.31034	0.126988	0.0634939	−	0.997982i	$-0.479776\pi$
$331$	2.31034	0.126988	0.0634939	+	0.997982i	$0.479776\pi$
$332$	−54.5414	−2.99335
$333$	−6.51492	−0.357015
$334$	−31.3799	−1.71703
$335$	17.8033	0.972700
$336$	0	0
$337$	−6.37449	−0.347240	−0.173620	−	0.984813i	$-0.555547\pi$
$337$	−6.37449	−0.347240	−0.173620	+	0.984813i	$0.555547\pi$
$338$	8.77026	0.477039
$339$	−3.99357	−0.216901
$340$	−44.7268	−2.42565
$341$	8.26303	0.447468
$342$	−18.9495	−1.02467
$343$	0	0
$344$	69.1622	3.72897
$345$	−9.59221	−0.516427
$346$	−55.6282	−2.99059
$347$	−3.75901	−0.201794	−0.100897	−	0.994897i	$-0.532171\pi$
$347$	−3.75901	−0.201794	−0.100897	+	0.994897i	$0.532171\pi$
$348$	45.6973	2.44963
$349$	16.7097	0.894451	0.447225	−	0.894421i	$-0.352412\pi$
$349$	16.7097	0.894451	0.447225	+	0.894421i	$0.352412\pi$
$350$	0	0
$351$	4.05386	0.216379
$352$	13.2909	0.708406
$353$	2.05629	0.109445	0.0547226	−	0.998502i	$-0.482573\pi$
$353$	2.05629	0.109445	0.0547226	+	0.998502i	$0.482573\pi$
$354$	19.2465	1.02294
$355$	3.98972	0.211752
$356$	22.3327	1.18363
$357$	0	0
$358$	−21.1258	−1.11653
$359$	35.2054	1.85807	0.929036	−	0.369989i	$-0.120639\pi$
$359$	35.2054	1.85807	0.929036	+	0.369989i	$0.120639\pi$
$360$	−13.1478	−0.692951
$361$	36.0442	1.89706
$362$	−5.97831	−0.314213
$363$	6.17277	0.323986
$364$	0	0
$365$	−26.9000	−1.40801
$366$	3.23684	0.169192
$367$	13.9271	0.726989	0.363494	−	0.931596i	$-0.381584\pi$
$367$	13.9271	0.726989	0.363494	+	0.931596i	$0.381584\pi$
$368$	−34.8714	−1.81780
$369$	−1.00000	−0.0520579
$370$	33.9427	1.76460
$371$	0	0
$372$	−17.0127	−0.882065
$373$	20.9602	1.08528	0.542639	−	0.839966i	$-0.317425\pi$
$373$	20.9602	1.08528	0.542639	+	0.839966i	$0.317425\pi$
$374$	27.2009	1.40653
$375$	−11.9108	−0.615069
$376$	−3.40494	−0.175597
$377$	40.9522	2.10915
$378$	0	0
$379$	−26.2526	−1.34851	−0.674253	−	0.738501i	$-0.735534\pi$
$379$	−26.2526	−1.34851	−0.674253	+	0.738501i	$0.735534\pi$
$380$	68.4593	3.51189
$381$	−1.59918	−0.0819287
$382$	37.0896	1.89767
$383$	−18.8996	−0.965723	−0.482861	−	0.875697i	$-0.660402\pi$
$383$	−18.8996	−0.965723	−0.482861	+	0.875697i	$0.660402\pi$
$384$	10.5163	0.536658
$385$	0	0
$386$	46.0282	2.34277
$387$	10.7302	0.545449
$388$	20.6641	1.04906
$389$	14.4255	0.731400	0.365700	−	0.930733i	$-0.380830\pi$
$389$	14.4255	0.731400	0.365700	+	0.930733i	$0.380830\pi$
$390$	−21.1206	−1.06948
$391$	−22.7938	−1.15273
$392$	0	0
$393$	9.63387	0.485964
$394$	64.4212	3.24549
$395$	5.99683	0.301733
$396$	9.93873	0.499440
$397$	−11.9969	−0.602109	−0.301055	−	0.953607i	$-0.597339\pi$
$397$	−11.9969	−0.602109	−0.301055	+	0.953607i	$0.597339\pi$
$398$	−5.30458	−0.265895
$399$	0	0
$400$	−6.22231	−0.311116
$401$	29.7872	1.48750	0.743751	−	0.668457i	$-0.233045\pi$
$401$	29.7872	1.48750	0.743751	+	0.668457i	$0.233045\pi$
$402$	22.2920	1.11183
$403$	−15.2461	−0.759462
$404$	−67.1294	−3.33981
$405$	−2.03983	−0.101360
$406$	0	0
$407$	−14.3139	−0.709514
$408$	−31.2429	−1.54675
$409$	17.3151	0.856175	0.428087	−	0.903737i	$-0.359188\pi$
$409$	17.3151	0.856175	0.428087	+	0.903737i	$0.359188\pi$
$410$	5.20999	0.257303
$411$	7.92292	0.390809
$412$	68.6044	3.37990
$413$	0	0
$414$	−12.0107	−0.590292
$415$	24.5945	1.20730
$416$	−24.5230	−1.20234
$417$	−3.47465	−0.170155
$418$	−41.6339	−2.03638
$419$	39.3854	1.92410	0.962051	−	0.272869i	$-0.0879726\pi$
$419$	39.3854	1.92410	0.962051	+	0.272869i	$0.0879726\pi$
$420$	0	0
$421$	−3.88794	−0.189486	−0.0947432	−	0.995502i	$-0.530203\pi$
$421$	−3.88794	−0.189486	−0.0947432	+	0.995502i	$0.530203\pi$
$422$	23.5113	1.14451
$423$	−0.528264	−0.0256851
$424$	46.7406	2.26992
$425$	−4.06722	−0.197289
$426$	4.99564	0.242040
$427$	0	0
$428$	−47.6447	−2.30299
$429$	8.90671	0.430020
$430$	−55.9045	−2.69595
$431$	18.5771	0.894827	0.447414	−	0.894327i	$-0.352345\pi$
$431$	18.5771	0.894827	0.447414	+	0.894327i	$0.352345\pi$
$432$	−7.41559	−0.356783
$433$	17.0462	0.819187	0.409593	−	0.912268i	$-0.365671\pi$
$433$	17.0462	0.819187	0.409593	+	0.912268i	$0.365671\pi$
$434$	0	0
$435$	−20.6065	−0.988004
$436$	−92.6374	−4.43653
$437$	34.8883	1.66893
$438$	−33.6822	−1.60940
$439$	32.6415	1.55789	0.778947	−	0.627090i	$-0.215754\pi$
$439$	32.6415	1.55789	0.778947	+	0.627090i	$0.215754\pi$
$440$	−28.8870	−1.37713
$441$	0	0
$442$	−50.1884	−2.38722
$443$	8.03404	0.381709	0.190854	−	0.981618i	$-0.438874\pi$
$443$	8.03404	0.381709	0.190854	+	0.981618i	$0.438874\pi$
$444$	29.4707	1.39862
$445$	−10.0706	−0.477391
$446$	−59.3257	−2.80915
$447$	−4.81236	−0.227617
$448$	0	0
$449$	−13.9945	−0.660444	−0.330222	−	0.943903i	$-0.607124\pi$
$449$	−13.9945	−0.660444	−0.330222	+	0.943903i	$0.607124\pi$
$450$	−2.14313	−0.101028
$451$	−2.19710	−0.103457
$452$	18.0652	0.849716
$453$	6.30410	0.296193
$454$	11.6897	0.548623
$455$	0	0
$456$	47.8206	2.23941
$457$	−25.8840	−1.21080	−0.605401	−	0.795920i	$-0.706987\pi$
$457$	−25.8840	−1.21080	−0.605401	+	0.795920i	$0.706987\pi$
$458$	−27.5848	−1.28895
$459$	−4.84721	−0.226248
$460$	43.3911	2.02312
$461$	11.8265	0.550817	0.275408	−	0.961327i	$-0.411187\pi$
$461$	11.8265	0.550817	0.275408	+	0.961327i	$0.411187\pi$
$462$	0	0
$463$	−1.25951	−0.0585345	−0.0292672	−	0.999572i	$-0.509317\pi$
$463$	−1.25951	−0.0585345	−0.0292672	+	0.999572i	$0.509317\pi$
$464$	−74.9126	−3.47773
$465$	7.67158	0.355761
$466$	−48.7592	−2.25873
$467$	5.15600	0.238591	0.119296	−	0.992859i	$-0.461936\pi$
$467$	5.15600	0.238591	0.119296	+	0.992859i	$0.461936\pi$
$468$	−18.3379	−0.847671
$469$	0	0
$470$	2.75225	0.126952
$471$	4.07061	0.187564
$472$	−48.5701	−2.23562
$473$	23.5754	1.08400
$474$	7.50880	0.344890
$475$	6.22532	0.285637
$476$	0	0
$477$	7.25162	0.332029
$478$	−18.8858	−0.863815
$479$	−24.6671	−1.12707	−0.563534	−	0.826093i	$-0.690558\pi$
$479$	−24.6671	−1.12707	−0.563534	+	0.826093i	$0.690558\pi$
$480$	12.3395	0.563221
$481$	26.4105	1.20422
$482$	−22.6296	−1.03075
$483$	0	0
$484$	−27.9230	−1.26923
$485$	−9.31812	−0.423114
$486$	−2.55413	−0.115858
$487$	−36.9281	−1.67337	−0.836685	−	0.547684i	$-0.815510\pi$
$487$	−36.9281	−1.67337	−0.836685	+	0.547684i	$0.815510\pi$
$488$	−8.16841	−0.369767
$489$	−9.43025	−0.426451
$490$	0	0
$491$	38.8273	1.75225	0.876125	−	0.482085i	$-0.160120\pi$
$491$	38.8273	1.75225	0.876125	+	0.482085i	$0.160120\pi$
$492$	4.52358	0.203939
$493$	−48.9667	−2.20535
$494$	76.8187	3.45624
$495$	−4.48171	−0.201438
$496$	27.8892	1.25226
$497$	0	0
$498$	30.7955	1.37998
$499$	−11.8209	−0.529175	−0.264587	−	0.964362i	$-0.585236\pi$
$499$	−11.8209	−0.529175	−0.264587	+	0.964362i	$0.585236\pi$
$500$	53.8792	2.40955
$501$	12.2859	0.548895
$502$	5.46679	0.243995
$503$	28.3846	1.26561	0.632803	−	0.774312i	$-0.281904\pi$
$503$	28.3846	1.26561	0.632803	+	0.774312i	$0.281904\pi$
$504$	0	0
$505$	30.2709	1.34704
$506$	−26.3886	−1.17312
$507$	−3.43376	−0.152499
$508$	7.23403	0.320958
$509$	−7.66798	−0.339877	−0.169939	−	0.985455i	$-0.554357\pi$
$509$	−7.66798	−0.339877	−0.169939	+	0.985455i	$0.554357\pi$
$510$	25.2539	1.11826
$511$	0	0
$512$	−50.7359	−2.24223
$513$	7.41918	0.327565
$514$	36.4722	1.60872
$515$	−30.9360	−1.36320
$516$	−48.5390	−2.13681
$517$	−1.16065	−0.0510451
$518$	0	0
$519$	21.7797	0.956023
$520$	53.2994	2.33733
$521$	−9.40056	−0.411846	−0.205923	−	0.978568i	$-0.566020\pi$
$521$	−9.40056	−0.411846	−0.205923	+	0.978568i	$0.566020\pi$
$522$	−25.8019	−1.12932
$523$	−35.7553	−1.56347	−0.781735	−	0.623610i	$-0.785665\pi$
$523$	−35.7553	−1.56347	−0.781735	+	0.623610i	$0.785665\pi$
$524$	−43.5795	−1.90378
$525$	0	0
$526$	41.9271	1.82811
$527$	18.2298	0.794103
$528$	−16.2928	−0.709051
$529$	−0.886957	−0.0385634
$530$	−37.7809	−1.64110
$531$	−7.53546	−0.327011
$532$	0	0
$533$	4.05386	0.175592
$534$	−12.6096	−0.545673
$535$	21.4846	0.928860
$536$	−56.2556	−2.42987
$537$	8.27123	0.356930
$538$	13.2978	0.573309
$539$	0	0
$540$	9.22734	0.397081
$541$	20.1520	0.866401	0.433201	−	0.901298i	$-0.357384\pi$
$541$	20.1520	0.866401	0.433201	+	0.901298i	$0.357384\pi$
$542$	−78.5226	−3.37284
$543$	2.34065	0.100447
$544$	29.3222	1.25718
$545$	41.7733	1.78937
$546$	0	0
$547$	−15.9234	−0.680837	−0.340419	−	0.940274i	$-0.610569\pi$
$547$	−15.9234	−0.680837	−0.340419	+	0.940274i	$0.610569\pi$
$548$	−35.8399	−1.53101
$549$	−1.26730	−0.0540869
$550$	−4.70866	−0.200778
$551$	74.9488	3.19293
$552$	30.3098	1.29007
$553$	0	0
$554$	−29.1898	−1.24015
$555$	−13.2893	−0.564101
$556$	15.7179	0.666586
$557$	−23.1311	−0.980095	−0.490047	−	0.871696i	$-0.663020\pi$
$557$	−23.1311	−0.980095	−0.490047	+	0.871696i	$0.663020\pi$
$558$	9.60579	0.406646
$559$	−43.4988	−1.83981
$560$	0	0
$561$	−10.6498	−0.449634
$562$	4.50993	0.190240
$563$	30.7087	1.29422	0.647109	−	0.762398i	$-0.275978\pi$
$563$	30.7087	1.29422	0.647109	+	0.762398i	$0.275978\pi$
$564$	2.38964	0.100622
$565$	−8.14621	−0.342714
$566$	24.5534	1.03206
$567$	0	0
$568$	−12.6069	−0.528973
$569$	3.03214	0.127114	0.0635570	−	0.997978i	$-0.479756\pi$
$569$	3.03214	0.127114	0.0635570	+	0.997978i	$0.479756\pi$
$570$	−38.6539	−1.61903
$571$	−1.79836	−0.0752589	−0.0376294	−	0.999292i	$-0.511981\pi$
$571$	−1.79836	−0.0752589	−0.0376294	+	0.999292i	$0.511981\pi$
$572$	−40.2902	−1.68462
$573$	−14.5214	−0.606642
$574$	0	0
$575$	3.94576	0.164549
$576$	0.619503	0.0258126
$577$	−26.4404	−1.10073	−0.550365	−	0.834924i	$-0.685511\pi$
$577$	−26.4404	−1.10073	−0.550365	+	0.834924i	$0.685511\pi$
$578$	16.5902	0.690063
$579$	−18.0211	−0.748930
$580$	93.2149	3.87054
$581$	0	0
$582$	−11.6675	−0.483632
$583$	15.9325	0.659856
$584$	84.9996	3.51731
$585$	8.26919	0.341889
$586$	1.03824	0.0428892
$587$	−3.24299	−0.133853	−0.0669263	−	0.997758i	$-0.521319\pi$
$587$	−3.24299	−0.133853	−0.0669263	+	0.997758i	$0.521319\pi$
$588$	0	0
$589$	−27.9027	−1.14971
$590$	39.2597	1.61630
$591$	−25.2224	−1.03751
$592$	−48.3120	−1.98561
$593$	25.9252	1.06462	0.532311	−	0.846549i	$-0.321324\pi$
$593$	25.9252	1.06462	0.532311	+	0.846549i	$0.321324\pi$
$594$	−5.61167	−0.230249
$595$	0	0
$596$	21.7691	0.891697
$597$	2.07686	0.0850004
$598$	48.6895	1.99106
$599$	−16.7618	−0.684867	−0.342433	−	0.939542i	$-0.611251\pi$
$599$	−16.7618	−0.684867	−0.342433	+	0.939542i	$0.611251\pi$
$600$	5.40836	0.220795
$601$	9.35320	0.381525	0.190762	−	0.981636i	$-0.438904\pi$
$601$	9.35320	0.381525	0.190762	+	0.981636i	$0.438904\pi$
$602$	0	0
$603$	−8.72784	−0.355425
$604$	−28.5171	−1.16034
$605$	12.5914	0.511914
$606$	37.9030	1.53970
$607$	−5.62356	−0.228253	−0.114127	−	0.993466i	$-0.536407\pi$
$607$	−5.62356	−0.228253	−0.114127	+	0.993466i	$0.536407\pi$
$608$	−44.8808	−1.82016
$609$	0	0
$610$	6.60261	0.267332
$611$	2.14151	0.0866360
$612$	21.9267	0.886335
$613$	13.6259	0.550346	0.275173	−	0.961395i	$-0.411265\pi$
$613$	13.6259	0.550346	0.275173	+	0.961395i	$0.411265\pi$
$614$	3.06679	0.123766
$615$	−2.03983	−0.0822540
$616$	0	0
$617$	45.9830	1.85121	0.925604	−	0.378494i	$-0.123558\pi$
$617$	45.9830	1.85121	0.925604	+	0.378494i	$0.123558\pi$
$618$	−38.7358	−1.55818
$619$	12.0863	0.485791	0.242895	−	0.970052i	$-0.421903\pi$
$619$	12.0863	0.485791	0.242895	+	0.970052i	$0.421903\pi$
$620$	−34.7030	−1.39371
$621$	4.70245	0.188703
$622$	73.7448	2.95690
$623$	0	0
$624$	30.0617	1.20343
$625$	−20.1005	−0.804020
$626$	38.9546	1.55694
$627$	16.3006	0.650985
$628$	−18.4137	−0.734787
$629$	−31.5792	−1.25914
$630$	0	0
$631$	−45.2956	−1.80319	−0.901596	−	0.432580i	$-0.857603\pi$
$631$	−45.2956	−1.80319	−0.901596	+	0.432580i	$0.857603\pi$
$632$	−18.9490	−0.753752
$633$	−9.20520	−0.365874
$634$	49.1848	1.95338
$635$	−3.26207	−0.129451
$636$	−32.8032	−1.30073
$637$	0	0
$638$	−56.6892	−2.24435
$639$	−1.95591	−0.0773745
$640$	21.4515	0.847945
$641$	−14.8236	−0.585495	−0.292748	−	0.956190i	$-0.594570\pi$
$641$	−14.8236	−0.585495	−0.292748	+	0.956190i	$0.594570\pi$
$642$	26.9014	1.06171
$643$	10.4299	0.411314	0.205657	−	0.978624i	$-0.434067\pi$
$643$	10.4299	0.411314	0.205657	+	0.978624i	$0.434067\pi$
$644$	0	0
$645$	21.8879	0.861834
$646$	−91.8524	−3.61389
$647$	−17.4261	−0.685093	−0.342546	−	0.939501i	$-0.611289\pi$
$647$	−17.4261	−0.685093	−0.342546	+	0.939501i	$0.611289\pi$
$648$	6.44554	0.253205
$649$	−16.5561	−0.649884
$650$	8.68795	0.340769
$651$	0	0
$652$	42.6584	1.67063
$653$	15.0102	0.587394	0.293697	−	0.955899i	$-0.405114\pi$
$653$	15.0102	0.587394	0.293697	+	0.955899i	$0.405114\pi$
$654$	52.3055	2.04531
$655$	19.6515	0.767847
$656$	−7.41559	−0.289530
$657$	13.1873	0.514487
$658$	0	0
$659$	32.1433	1.25212	0.626062	−	0.779774i	$-0.284666\pi$
$659$	32.1433	1.25212	0.626062	+	0.779774i	$0.284666\pi$
$660$	20.2733	0.789139
$661$	2.34987	0.0913992	0.0456996	−	0.998955i	$-0.485448\pi$
$661$	2.34987	0.0913992	0.0456996	+	0.998955i	$0.485448\pi$
$662$	5.90091	0.229345
$663$	19.6499	0.763139
$664$	−77.7148	−3.01592
$665$	0	0
$666$	−16.6399	−0.644785
$667$	47.5043	1.83937
$668$	−55.5764	−2.15032
$669$	23.2274	0.898022
$670$	45.4720	1.75674
$671$	−2.78437	−0.107489
$672$	0	0
$673$	−29.7768	−1.14781	−0.573906	−	0.818921i	$-0.694573\pi$
$673$	−29.7768	−1.14781	−0.573906	+	0.818921i	$0.694573\pi$
$674$	−16.2813	−0.627131
$675$	0.839085	0.0322964
$676$	15.5329	0.597418
$677$	−27.9673	−1.07487	−0.537435	−	0.843305i	$-0.680607\pi$
$677$	−27.9673	−1.07487	−0.537435	+	0.843305i	$0.680607\pi$
$678$	−10.2001	−0.391732
$679$	0	0
$680$	−63.7303	−2.44394
$681$	−4.57677	−0.175382
$682$	21.1048	0.808146
$683$	−26.5644	−1.01646	−0.508230	−	0.861221i	$-0.669700\pi$
$683$	−26.5644	−1.01646	−0.508230	+	0.861221i	$0.669700\pi$
$684$	−33.5612	−1.28325
$685$	16.1614	0.617496
$686$	0	0
$687$	10.8001	0.412048
$688$	79.5710	3.03362
$689$	−29.3970	−1.11994
$690$	−24.4997	−0.932689
$691$	1.69085	0.0643229	0.0321614	−	0.999483i	$-0.489761\pi$
$691$	1.69085	0.0643229	0.0321614	+	0.999483i	$0.489761\pi$
$692$	−98.5221	−3.74525
$693$	0	0
$694$	−9.60100	−0.364449
$695$	−7.08771	−0.268852
$696$	65.1131	2.46810
$697$	−4.84721	−0.183601
$698$	42.6788	1.61542
$699$	19.0904	0.722064
$700$	0	0
$701$	3.65407	0.138012	0.0690062	−	0.997616i	$-0.478017\pi$
$701$	3.65407	0.138012	0.0690062	+	0.997616i	$0.478017\pi$
$702$	10.3541	0.390789
$703$	48.3353	1.82300
$704$	1.36111	0.0512986
$705$	−1.07757	−0.0405836
$706$	5.25203	0.197663
$707$	0	0
$708$	34.0872	1.28108
$709$	−29.8396	−1.12065	−0.560324	−	0.828273i	$-0.689323\pi$
$709$	−29.8396	−1.12065	−0.560324	+	0.828273i	$0.689323\pi$
$710$	10.1903	0.382434
$711$	−2.93987	−0.110254
$712$	31.8214	1.19256
$713$	−17.6854	−0.662323
$714$	0	0
$715$	18.1682	0.679452
$716$	−37.4155	−1.39828
$717$	7.39421	0.276142
$718$	89.9193	3.35576
$719$	21.2360	0.791970	0.395985	−	0.918257i	$-0.370403\pi$
$719$	21.2360	0.791970	0.395985	+	0.918257i	$0.370403\pi$
$720$	−15.1266	−0.563734
$721$	0	0
$722$	92.0616	3.42618
$723$	8.85999	0.329506
$724$	−10.5881	−0.393503
$725$	8.47647	0.314808
$726$	15.7661	0.585133
$727$	−48.4942	−1.79855	−0.899275	−	0.437383i	$-0.855905\pi$
$727$	−48.4942	−1.79855	−0.899275	+	0.437383i	$0.855905\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−68.7060	−2.54292
$731$	52.0117	1.92372
$732$	5.73271	0.211887
$733$	−27.3083	−1.00866	−0.504328	−	0.863512i	$-0.668260\pi$
$733$	−27.3083	−1.00866	−0.504328	+	0.863512i	$0.668260\pi$
$734$	35.5716	1.31297
$735$	0	0
$736$	−28.4465	−1.04855
$737$	−19.1759	−0.706353
$738$	−2.55413	−0.0940188
$739$	−13.4819	−0.495940	−0.247970	−	0.968768i	$-0.579763\pi$
$739$	−13.4819	−0.495940	−0.247970	+	0.968768i	$0.579763\pi$
$740$	60.1153	2.20988
$741$	−30.0763	−1.10488
$742$	0	0
$743$	46.0019	1.68765	0.843823	−	0.536622i	$-0.180300\pi$
$743$	46.0019	1.68765	0.843823	+	0.536622i	$0.180300\pi$
$744$	−24.2410	−0.888716
$745$	−9.81641	−0.359645
$746$	53.5350	1.96006
$747$	−12.0571	−0.441148
$748$	48.1751	1.76146
$749$	0	0
$750$	−30.4216	−1.11084
$751$	21.8979	0.799066	0.399533	−	0.916719i	$-0.369172\pi$
$751$	21.8979	0.799066	0.399533	+	0.916719i	$0.369172\pi$
$752$	−3.91739	−0.142852
$753$	−2.14037	−0.0779995
$754$	104.597	3.80921
$755$	12.8593	0.467998
$756$	0	0
$757$	−42.5655	−1.54707	−0.773535	−	0.633754i	$-0.781513\pi$
$757$	−42.5655	−1.54707	−0.773535	+	0.633754i	$0.781513\pi$
$758$	−67.0525	−2.43546
$759$	10.3317	0.375018
$760$	97.5460	3.53837
$761$	−18.1190	−0.656812	−0.328406	−	0.944537i	$-0.606511\pi$
$761$	−18.1190	−0.656812	−0.328406	+	0.944537i	$0.606511\pi$
$762$	−4.08452	−0.147967
$763$	0	0
$764$	65.6888	2.37654
$765$	−9.88750	−0.357483
$766$	−48.2719	−1.74414
$767$	30.5477	1.10301
$768$	28.0990	1.01394
$769$	0.938954	0.0338596	0.0169298	−	0.999857i	$-0.494611\pi$
$769$	0.938954	0.0338596	0.0169298	+	0.999857i	$0.494611\pi$
$770$	0	0
$771$	−14.2797	−0.514271
$772$	81.5197	2.93396
$773$	−19.5127	−0.701821	−0.350911	−	0.936409i	$-0.614128\pi$
$773$	−19.5127	−0.701821	−0.350911	+	0.936409i	$0.614128\pi$
$774$	27.4064	0.985103
$775$	−3.15570	−0.113356
$776$	29.4438	1.05697
$777$	0	0
$778$	36.8445	1.32094
$779$	7.41918	0.265820
$780$	−37.4063	−1.33936
$781$	−4.29732	−0.153770
$782$	−58.2182	−2.08188
$783$	10.1020	0.361017
$784$	0	0
$785$	8.30336	0.296360
$786$	24.6061	0.877672
$787$	46.1884	1.64644	0.823219	−	0.567724i	$-0.192176\pi$
$787$	46.1884	1.64644	0.823219	+	0.567724i	$0.192176\pi$
$788$	114.095	4.06448
$789$	−16.4154	−0.584404
$790$	15.3167	0.544943
$791$	0	0
$792$	14.1615	0.503206
$793$	5.13744	0.182436
$794$	−30.6417	−1.08743
$795$	14.7921	0.524621
$796$	−9.39486	−0.332992
$797$	−4.04847	−0.143404	−0.0717020	−	0.997426i	$-0.522843\pi$
$797$	−4.04847	−0.143404	−0.0717020	+	0.997426i	$0.522843\pi$
$798$	0	0
$799$	−2.56060	−0.0905877
$800$	−5.07587	−0.179459
$801$	4.93696	0.174439
$802$	76.0804	2.68649
$803$	28.9739	1.02247
$804$	39.4810	1.39239
$805$	0	0
$806$	−38.9405	−1.37162
$807$	−5.20640	−0.183274
$808$	−95.6512	−3.36500
$809$	−21.5809	−0.758745	−0.379373	−	0.925244i	$-0.623860\pi$
$809$	−21.5809	−0.758745	−0.379373	+	0.925244i	$0.623860\pi$
$810$	−5.20999	−0.183061
$811$	0.609476	0.0214016	0.0107008	−	0.999943i	$-0.496594\pi$
$811$	0.609476	0.0214016	0.0107008	+	0.999943i	$0.496594\pi$
$812$	0	0
$813$	30.7434	1.07822
$814$	−36.5595	−1.28141
$815$	−19.2361	−0.673812
$816$	−35.9449	−1.25832
$817$	−79.6095	−2.78519
$818$	44.2249	1.54629
$819$	0	0
$820$	9.22734	0.322233
$821$	6.40281	0.223460	0.111730	−	0.993739i	$-0.464361\pi$
$821$	6.40281	0.223460	0.111730	+	0.993739i	$0.464361\pi$
$822$	20.2362	0.705817
$823$	−34.8973	−1.21644	−0.608221	−	0.793768i	$-0.708117\pi$
$823$	−34.8973	−1.21644	−0.608221	+	0.793768i	$0.708117\pi$
$824$	97.7529	3.40538
$825$	1.84355	0.0641842
$826$	0	0
$827$	19.4846	0.677545	0.338773	−	0.940868i	$-0.389988\pi$
$827$	19.4846	0.677545	0.338773	+	0.940868i	$0.389988\pi$
$828$	−21.2719	−0.739249
$829$	−49.9870	−1.73612	−0.868060	−	0.496460i	$-0.834633\pi$
$829$	−49.9870	−1.73612	−0.868060	+	0.496460i	$0.834633\pi$
$830$	62.8176	2.18043
$831$	11.4285	0.396449
$832$	−2.51137	−0.0870663
$833$	0	0
$834$	−8.87472	−0.307306
$835$	25.0613	0.867281
$836$	−73.7372	−2.55025
$837$	−3.76089	−0.129995
$838$	100.595	3.47501
$839$	33.9692	1.17275	0.586374	−	0.810040i	$-0.300555\pi$
$839$	33.9692	1.17275	0.586374	+	0.810040i	$0.300555\pi$
$840$	0	0
$841$	73.0511	2.51900
$842$	−9.93029	−0.342221
$843$	−1.76574	−0.0608154
$844$	41.6404	1.43332
$845$	−7.00429	−0.240955
$846$	−1.34925	−0.0463883
$847$	0	0
$848$	53.7750	1.84664
$849$	−9.61324	−0.329925
$850$	−10.3882	−0.356313
$851$	30.6361	1.05019
$852$	8.84770	0.303117
$853$	21.9694	0.752219	0.376109	−	0.926575i	$-0.377262\pi$
$853$	21.9694	0.752219	0.376109	+	0.926575i	$0.377262\pi$
$854$	0	0
$855$	15.1339	0.517568
$856$	−67.8878	−2.32036
$857$	29.0187	0.991261	0.495630	−	0.868534i	$-0.334937\pi$
$857$	29.0187	0.991261	0.495630	+	0.868534i	$0.334937\pi$
$858$	22.7489	0.776634
$859$	51.7596	1.76602	0.883008	−	0.469358i	$-0.155515\pi$
$859$	51.7596	1.76602	0.883008	+	0.469358i	$0.155515\pi$
$860$	−99.0115	−3.37626
$861$	0	0
$862$	47.4483	1.61610
$863$	2.65807	0.0904819	0.0452409	−	0.998976i	$-0.485594\pi$
$863$	2.65807	0.0904819	0.0452409	+	0.998976i	$0.485594\pi$
$864$	−6.04930	−0.205801
$865$	44.4269	1.51056
$866$	43.5381	1.47949
$867$	−6.49545	−0.220597
$868$	0	0
$869$	−6.45916	−0.219112
$870$	−52.6316	−1.78438
$871$	35.3814	1.19885
$872$	−131.997	−4.46998
$873$	4.56808	0.154606
$874$	89.1093	3.01417
$875$	0	0
$876$	−59.6540	−2.01552
$877$	36.3290	1.22674	0.613371	−	0.789795i	$-0.289813\pi$
$877$	36.3290	1.22674	0.613371	+	0.789795i	$0.289813\pi$
$878$	83.3706	2.81362
$879$	−0.406494	−0.0137107
$880$	−33.2345	−1.12033
$881$	−54.4117	−1.83318	−0.916588	−	0.399833i	$-0.869068\pi$
$881$	−54.4117	−1.83318	−0.916588	+	0.399833i	$0.869068\pi$
$882$	0	0
$883$	25.0694	0.843654	0.421827	−	0.906676i	$-0.361389\pi$
$883$	25.0694	0.843654	0.421827	+	0.906676i	$0.361389\pi$
$884$	−88.8878	−2.98962
$885$	−15.3711	−0.516693
$886$	20.5200	0.689382
$887$	−44.5935	−1.49730	−0.748651	−	0.662964i	$-0.769298\pi$
$887$	−44.5935	−1.49730	−0.748651	+	0.662964i	$0.769298\pi$
$888$	41.9922	1.40916
$889$	0	0
$890$	−25.7216	−0.862188
$891$	2.19710	0.0736055
$892$	−105.071	−3.51803
$893$	3.91928	0.131154
$894$	−12.2914	−0.411086
$895$	16.8719	0.563966
$896$	0	0
$897$	−19.0631	−0.636497
$898$	−35.7439	−1.19279
$899$	−37.9926	−1.26712
$900$	−3.79567	−0.126522
$901$	35.1501	1.17102
$902$	−5.61167	−0.186848
$903$	0	0
$904$	25.7407	0.856123
$905$	4.77452	0.158711
$906$	16.1015	0.534936
$907$	−51.9895	−1.72628	−0.863141	−	0.504962i	$-0.831506\pi$
$907$	−51.9895	−1.72628	−0.863141	+	0.504962i	$0.831506\pi$
$908$	20.7034	0.687065
$909$	−14.8399	−0.492208
$910$	0	0
$911$	−12.5978	−0.417383	−0.208692	−	0.977981i	$-0.566921\pi$
$911$	−12.5978	−0.417383	−0.208692	+	0.977981i	$0.566921\pi$
$912$	55.0176	1.82181
$913$	−26.4907	−0.876714
$914$	−66.1111	−2.18676
$915$	−2.58507	−0.0854599
$916$	−48.8549	−1.61421
$917$	0	0
$918$	−12.3804	−0.408614
$919$	−40.2751	−1.32855	−0.664277	−	0.747487i	$-0.731260\pi$
$919$	−40.2751	−1.32855	−0.664277	+	0.747487i	$0.731260\pi$
$920$	61.8270	2.03837
$921$	−1.20072	−0.0395651
$922$	30.2065	0.994799
$923$	7.92897	0.260985
$924$	0	0
$925$	5.46657	0.179740
$926$	−3.21696	−0.105716
$927$	15.1660	0.498116
$928$	−61.1102	−2.00604
$929$	−37.4105	−1.22740	−0.613700	−	0.789539i	$-0.710320\pi$
$929$	−37.4105	−1.22740	−0.613700	+	0.789539i	$0.710320\pi$
$930$	19.5942	0.642519
$931$	0	0
$932$	−86.3567	−2.82871
$933$	−28.8728	−0.945252
$934$	13.1691	0.430906
$935$	−21.7238	−0.710443
$936$	−26.1293	−0.854063
$937$	6.39519	0.208922	0.104461	−	0.994529i	$-0.466688\pi$
$937$	6.39519	0.208922	0.104461	+	0.994529i	$0.466688\pi$
$938$	0	0
$939$	−15.2516	−0.497718
$940$	4.87447	0.158988
$941$	28.2888	0.922189	0.461095	−	0.887351i	$-0.347457\pi$
$941$	28.2888	0.922189	0.461095	+	0.887351i	$0.347457\pi$
$942$	10.3969	0.338748
$943$	4.70245	0.153133
$944$	−55.8799	−1.81873
$945$	0	0
$946$	60.2145	1.95774
$947$	−11.5695	−0.375957	−0.187979	−	0.982173i	$-0.560194\pi$
$947$	−11.5695	−0.375957	−0.187979	+	0.982173i	$0.560194\pi$
$948$	13.2987	0.431922
$949$	−53.4596	−1.73537
$950$	15.9003	0.515873
$951$	−19.2570	−0.624450
$952$	0	0
$953$	−26.3771	−0.854437	−0.427219	−	0.904148i	$-0.640507\pi$
$953$	−26.3771	−0.854437	−0.427219	+	0.904148i	$0.640507\pi$
$954$	18.5216	0.599658
$955$	−29.6213	−0.958522
$956$	−33.4483	−1.08179
$957$	22.1951	0.717467
$958$	−63.0029	−2.03553
$959$	0	0
$960$	1.26368	0.0407851
$961$	−16.8557	−0.543733
$962$	67.4560	2.17487
$963$	−10.5325	−0.339406
$964$	−40.0788	−1.29085
$965$	−36.7600	−1.18335
$966$	0	0
$967$	−33.1048	−1.06458	−0.532290	−	0.846562i	$-0.678668\pi$
$967$	−33.1048	−1.06458	−0.532290	+	0.846562i	$0.678668\pi$
$968$	−39.7868	−1.27880
$969$	35.9623	1.15528
$970$	−23.7997	−0.764162
$971$	−13.5891	−0.436095	−0.218047	−	0.975938i	$-0.569969\pi$
$971$	−13.5891	−0.436095	−0.218047	+	0.975938i	$0.569969\pi$
$972$	−4.52358	−0.145094
$973$	0	0
$974$	−94.3191	−3.02218
$975$	−3.40153	−0.108936
$976$	−9.39775	−0.300815
$977$	−58.3154	−1.86567	−0.932837	−	0.360299i	$-0.882675\pi$
$977$	−58.3154	−1.86567	−0.932837	+	0.360299i	$0.882675\pi$
$978$	−24.0861	−0.770188
$979$	10.8470	0.346671
$980$	0	0
$981$	−20.4788	−0.653838
$982$	99.1698	3.16464
$983$	−16.9974	−0.542132	−0.271066	−	0.962561i	$-0.587376\pi$
$983$	−16.9974	−0.542132	−0.271066	+	0.962561i	$0.587376\pi$
$984$	6.44554	0.205476
$985$	−51.4494	−1.63932
$986$	−125.067	−3.98295
$987$	0	0
$988$	136.052	4.32840
$989$	−50.4584	−1.60448
$990$	−11.4469	−0.363805
$991$	−9.52580	−0.302597	−0.151299	−	0.988488i	$-0.548345\pi$
$991$	−9.52580	−0.302597	−0.151299	+	0.988488i	$0.548345\pi$
$992$	22.7507	0.722336
$993$	−2.31034	−0.0733164
$994$	0	0
$995$	4.23646	0.134305
$996$	54.5414	1.72821
$997$	−43.2360	−1.36930	−0.684648	−	0.728874i	$-0.740044\pi$
$997$	−43.2360	−1.36930	−0.684648	+	0.728874i	$0.740044\pi$
$998$	−30.1920	−0.955712
$999$	6.51492	0.206123

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6027.2.a.bb.1.8		8
7.2	even	3		861.2.i.d.739.1	yes	16
7.4	even	3		861.2.i.d.247.1	✓	16
7.6	odd	2		6027.2.a.bc.1.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
861.2.i.d.247.1	✓	16	7.4	even	3
861.2.i.d.739.1	yes	16	7.2	even	3
6027.2.a.bb.1.8		8	1.1	even	1	trivial
6027.2.a.bc.1.8		8	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)

\(f(q)\)	\(=\)	\(q+2.55413 q^{2} -1.00000 q^{3} +4.52358 q^{4} -2.03983 q^{5} -2.55413 q^{6} +6.44554 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.55413 q^{2} -1.00000 q^{3} +4.52358 q^{4} -2.03983 q^{5} -2.55413 q^{6} +6.44554 q^{8} +1.00000 q^{9} -5.20999 q^{10} +2.19710 q^{11} -4.52358 q^{12} -4.05386 q^{13} +2.03983 q^{15} +7.41559 q^{16} +4.84721 q^{17} +2.55413 q^{18} -7.41918 q^{19} -9.22734 q^{20} +5.61167 q^{22} -4.70245 q^{23} -6.44554 q^{24} -0.839085 q^{25} -10.3541 q^{26} -1.00000 q^{27} -10.1020 q^{29} +5.20999 q^{30} +3.76089 q^{31} +6.04930 q^{32} -2.19710 q^{33} +12.3804 q^{34} +4.52358 q^{36} -6.51492 q^{37} -18.9495 q^{38} +4.05386 q^{39} -13.1478 q^{40} -1.00000 q^{41} +10.7302 q^{43} +9.93873 q^{44} -2.03983 q^{45} -12.0107 q^{46} -0.528264 q^{47} -7.41559 q^{48} -2.14313 q^{50} -4.84721 q^{51} -18.3379 q^{52} +7.25162 q^{53} -2.55413 q^{54} -4.48171 q^{55} +7.41918 q^{57} -25.8019 q^{58} -7.53546 q^{59} +9.22734 q^{60} -1.26730 q^{61} +9.60579 q^{62} +0.619503 q^{64} +8.26919 q^{65} -5.61167 q^{66} -8.72784 q^{67} +21.9267 q^{68} +4.70245 q^{69} -1.95591 q^{71} +6.44554 q^{72} +13.1873 q^{73} -16.6399 q^{74} +0.839085 q^{75} -33.5612 q^{76} +10.3541 q^{78} -2.93987 q^{79} -15.1266 q^{80} +1.00000 q^{81} -2.55413 q^{82} -12.0571 q^{83} -9.88750 q^{85} +27.4064 q^{86} +10.1020 q^{87} +14.1615 q^{88} +4.93696 q^{89} -5.20999 q^{90} -21.2719 q^{92} -3.76089 q^{93} -1.34925 q^{94} +15.1339 q^{95} -6.04930 q^{96} +4.56808 q^{97} +2.19710 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} - 8 q^{3} + 13 q^{4} - 7 q^{5} - q^{6} + 6 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q + q^2 - 8 * q^3 + 13 * q^4 - 7 * q^5 - q^6 + 6 * q^8 + 8 * q^9	\( 8 q + q^{2} - 8 q^{3} + 13 q^{4} - 7 q^{5} - q^{6} + 6 q^{8} + 8 q^{9} - 8 q^{10} + 11 q^{11} - 13 q^{12} - 10 q^{13} + 7 q^{15} - 17 q^{16} - 3 q^{17} + q^{18} - 6 q^{19} - 11 q^{20} + 15 q^{22} + 14 q^{23} - 6 q^{24} + 25 q^{25} - 24 q^{26} - 8 q^{27} + 2 q^{29} + 8 q^{30} - 16 q^{31} + 3 q^{32} - 11 q^{33} + 4 q^{34} + 13 q^{36} - 20 q^{37} - 10 q^{38} + 10 q^{39} + 3 q^{40} - 8 q^{41} + 7 q^{43} - 7 q^{45} - 5 q^{46} - 14 q^{47} + 17 q^{48} - 5 q^{50} + 3 q^{51} - 23 q^{52} + 7 q^{53} - q^{54} - 48 q^{55} + 6 q^{57} - 20 q^{58} - 22 q^{59} + 11 q^{60} + 33 q^{62} - 10 q^{64} - 14 q^{65} - 15 q^{66} + 12 q^{67} + 27 q^{68} - 14 q^{69} - 5 q^{71} + 6 q^{72} - 2 q^{73} + 6 q^{74} - 25 q^{75} - 43 q^{76} + 24 q^{78} - 15 q^{79} + 7 q^{80} + 8 q^{81} - q^{82} - 15 q^{83} - 43 q^{85} + 31 q^{86} - 2 q^{87} + 17 q^{88} - 29 q^{89} - 8 q^{90} + 19 q^{92} + 16 q^{93} - 20 q^{94} + 14 q^{95} - 3 q^{96} - 19 q^{97} + 11 q^{99}+O(q^{100}) \) 8 * q + q^2 - 8 * q^3 + 13 * q^4 - 7 * q^5 - q^6 + 6 * q^8 + 8 * q^9 - 8 * q^10 + 11 * q^11 - 13 * q^12 - 10 * q^13 + 7 * q^15 - 17 * q^16 - 3 * q^17 + q^18 - 6 * q^19 - 11 * q^20 + 15 * q^22 + 14 * q^23 - 6 * q^24 + 25 * q^25 - 24 * q^26 - 8 * q^27 + 2 * q^29 + 8 * q^30 - 16 * q^31 + 3 * q^32 - 11 * q^33 + 4 * q^34 + 13 * q^36 - 20 * q^37 - 10 * q^38 + 10 * q^39 + 3 * q^40 - 8 * q^41 + 7 * q^43 - 7 * q^45 - 5 * q^46 - 14 * q^47 + 17 * q^48 - 5 * q^50 + 3 * q^51 - 23 * q^52 + 7 * q^53 - q^54 - 48 * q^55 + 6 * q^57 - 20 * q^58 - 22 * q^59 + 11 * q^60 + 33 * q^62 - 10 * q^64 - 14 * q^65 - 15 * q^66 + 12 * q^67 + 27 * q^68 - 14 * q^69 - 5 * q^71 + 6 * q^72 - 2 * q^73 + 6 * q^74 - 25 * q^75 - 43 * q^76 + 24 * q^78 - 15 * q^79 + 7 * q^80 + 8 * q^81 - q^82 - 15 * q^83 - 43 * q^85 + 31 * q^86 - 2 * q^87 + 17 * q^88 - 29 * q^89 - 8 * q^90 + 19 * q^92 + 16 * q^93 - 20 * q^94 + 14 * q^95 - 3 * q^96 - 19 * q^97 + 11 * q^99

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