LMFDB - Embedded newform 6027.2.a.bn.1.22

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:	$0$
Dimension:	$24$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.22
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)

$f(q)$	$=$	$q+2.56249 q^{2} -1.00000 q^{3} +4.56633 q^{4} +3.89232 q^{5} -2.56249 q^{6} +6.57620 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.56249 q^{2} -1.00000 q^{3} +4.56633 q^{4} +3.89232 q^{5} -2.56249 q^{6} +6.57620 q^{8} +1.00000 q^{9} +9.97400 q^{10} +3.81355 q^{11} -4.56633 q^{12} -6.39406 q^{13} -3.89232 q^{15} +7.71874 q^{16} -1.70351 q^{17} +2.56249 q^{18} +6.47548 q^{19} +17.7736 q^{20} +9.77216 q^{22} +3.51424 q^{23} -6.57620 q^{24} +10.1501 q^{25} -16.3847 q^{26} -1.00000 q^{27} -8.65494 q^{29} -9.97400 q^{30} -0.432523 q^{31} +6.62678 q^{32} -3.81355 q^{33} -4.36521 q^{34} +4.56633 q^{36} +7.97403 q^{37} +16.5933 q^{38} +6.39406 q^{39} +25.5966 q^{40} +1.00000 q^{41} -6.41643 q^{43} +17.4139 q^{44} +3.89232 q^{45} +9.00520 q^{46} -3.72691 q^{47} -7.71874 q^{48} +26.0095 q^{50} +1.70351 q^{51} -29.1974 q^{52} +14.2446 q^{53} -2.56249 q^{54} +14.8435 q^{55} -6.47548 q^{57} -22.1782 q^{58} -3.38894 q^{59} -17.7736 q^{60} +4.40630 q^{61} -1.10833 q^{62} +1.54354 q^{64} -24.8877 q^{65} -9.77216 q^{66} +3.61186 q^{67} -7.77878 q^{68} -3.51424 q^{69} -0.619870 q^{71} +6.57620 q^{72} -2.71814 q^{73} +20.4334 q^{74} -10.1501 q^{75} +29.5692 q^{76} +16.3847 q^{78} +11.5546 q^{79} +30.0438 q^{80} +1.00000 q^{81} +2.56249 q^{82} -5.74873 q^{83} -6.63058 q^{85} -16.4420 q^{86} +8.65494 q^{87} +25.0786 q^{88} -16.4936 q^{89} +9.97400 q^{90} +16.0472 q^{92} +0.432523 q^{93} -9.55015 q^{94} +25.2046 q^{95} -6.62678 q^{96} -2.81728 q^{97} +3.81355 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 8 q^{2} - 24 q^{3} + 32 q^{4} - 4 q^{5} - 8 q^{6} + 24 q^{8} + 24 q^{9}+O(q^{10}) $ 24 * q + 8 * q^2 - 24 * q^3 + 32 * q^4 - 4 * q^5 - 8 * q^6 + 24 * q^8 + 24 * q^9	$ 24 q + 8 q^{2} - 24 q^{3} + 32 q^{4} - 4 q^{5} - 8 q^{6} + 24 q^{8} + 24 q^{9} + 4 q^{10} + 12 q^{11} - 32 q^{12} + 4 q^{15} + 44 q^{16} - 8 q^{17} + 8 q^{18} + 4 q^{19} - 28 q^{20} + 16 q^{22} + 20 q^{23} - 24 q^{24} + 48 q^{25} - 32 q^{26} - 24 q^{27} + 24 q^{29} - 4 q^{30} + 4 q^{31} + 36 q^{32} - 12 q^{33} - 16 q^{34} + 32 q^{36} + 64 q^{37} - 20 q^{38} + 48 q^{40} + 24 q^{41} + 20 q^{43} + 48 q^{44} - 4 q^{45} + 28 q^{46} - 32 q^{47} - 44 q^{48} - 20 q^{50} + 8 q^{51} + 76 q^{53} - 8 q^{54} + 24 q^{55} - 4 q^{57} + 28 q^{58} - 28 q^{59} + 28 q^{60} + 28 q^{61} + 4 q^{62} + 48 q^{64} + 28 q^{65} - 16 q^{66} + 44 q^{67} + 32 q^{68} - 20 q^{69} + 20 q^{71} + 24 q^{72} + 16 q^{73} + 44 q^{74} - 48 q^{75} + 16 q^{76} + 32 q^{78} + 4 q^{79} - 44 q^{80} + 24 q^{81} + 8 q^{82} - 8 q^{83} + 28 q^{85} + 56 q^{86} - 24 q^{87} + 60 q^{88} - 60 q^{89} + 4 q^{90} + 60 q^{92} - 4 q^{93} - 24 q^{94} + 28 q^{95} - 36 q^{96} + 48 q^{97} + 12 q^{99}+O(q^{100}) $ 24 * q + 8 * q^2 - 24 * q^3 + 32 * q^4 - 4 * q^5 - 8 * q^6 + 24 * q^8 + 24 * q^9 + 4 * q^10 + 12 * q^11 - 32 * q^12 + 4 * q^15 + 44 * q^16 - 8 * q^17 + 8 * q^18 + 4 * q^19 - 28 * q^20 + 16 * q^22 + 20 * q^23 - 24 * q^24 + 48 * q^25 - 32 * q^26 - 24 * q^27 + 24 * q^29 - 4 * q^30 + 4 * q^31 + 36 * q^32 - 12 * q^33 - 16 * q^34 + 32 * q^36 + 64 * q^37 - 20 * q^38 + 48 * q^40 + 24 * q^41 + 20 * q^43 + 48 * q^44 - 4 * q^45 + 28 * q^46 - 32 * q^47 - 44 * q^48 - 20 * q^50 + 8 * q^51 + 76 * q^53 - 8 * q^54 + 24 * q^55 - 4 * q^57 + 28 * q^58 - 28 * q^59 + 28 * q^60 + 28 * q^61 + 4 * q^62 + 48 * q^64 + 28 * q^65 - 16 * q^66 + 44 * q^67 + 32 * q^68 - 20 * q^69 + 20 * q^71 + 24 * q^72 + 16 * q^73 + 44 * q^74 - 48 * q^75 + 16 * q^76 + 32 * q^78 + 4 * q^79 - 44 * q^80 + 24 * q^81 + 8 * q^82 - 8 * q^83 + 28 * q^85 + 56 * q^86 - 24 * q^87 + 60 * q^88 - 60 * q^89 + 4 * q^90 + 60 * q^92 - 4 * q^93 - 24 * q^94 + 28 * q^95 - 36 * q^96 + 48 * q^97 + 12 * 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 $

$2$	2.56249	1.81195	0.905976	−	0.423330i	$-0.139139\pi$
$2$	2.56249	1.81195	0.905976	+	0.423330i	$0.139139\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	4.56633	2.28317
$5$	3.89232	1.74070	0.870348	−	0.492437i	$-0.163894\pi$
$5$	3.89232	1.74070	0.870348	+	0.492437i	$0.163894\pi$
$6$	−2.56249	−1.04613
$7$	0	0
$7$	0	0
$8$	6.57620	2.32504
$9$	1.00000	0.333333
$10$	9.97400	3.15406
$11$	3.81355	1.14983	0.574914	−	0.818214i	$-0.305035\pi$
$11$	3.81355	1.14983	0.574914	+	0.818214i	$0.305035\pi$
$12$	−4.56633	−1.31819
$13$	−6.39406	−1.77339	−0.886697	−	0.462351i	$-0.847006\pi$
$13$	−6.39406	−1.77339	−0.886697	+	0.462351i	$0.847006\pi$
$14$	0	0
$15$	−3.89232	−1.00499
$16$	7.71874	1.92969
$17$	−1.70351	−0.413161	−0.206580	−	0.978430i	$-0.566233\pi$
$17$	−1.70351	−0.413161	−0.206580	+	0.978430i	$0.566233\pi$
$18$	2.56249	0.603984
$19$	6.47548	1.48558	0.742789	−	0.669526i	$-0.233503\pi$
$19$	6.47548	1.48558	0.742789	+	0.669526i	$0.233503\pi$
$20$	17.7736	3.97430
$21$	0	0
$22$	9.77216	2.08343
$23$	3.51424	0.732771	0.366385	−	0.930463i	$-0.380595\pi$
$23$	3.51424	0.732771	0.366385	+	0.930463i	$0.380595\pi$
$24$	−6.57620	−1.34236
$25$	10.1501	2.03002
$26$	−16.3847	−3.21330
$27$	−1.00000	−0.192450
$28$	0	0
$29$	−8.65494	−1.60718	−0.803591	−	0.595182i	$-0.797080\pi$
$29$	−8.65494	−1.60718	−0.803591	+	0.595182i	$0.797080\pi$
$30$	−9.97400	−1.82100
$31$	−0.432523	−0.0776834	−0.0388417	−	0.999245i	$-0.512367\pi$
$31$	−0.432523	−0.0776834	−0.0388417	+	0.999245i	$0.512367\pi$
$32$	6.62678	1.17146
$33$	−3.81355	−0.663854
$34$	−4.36521	−0.748627
$35$	0	0
$36$	4.56633	0.761056
$37$	7.97403	1.31092	0.655462	−	0.755229i	$-0.272474\pi$
$37$	7.97403	1.31092	0.655462	+	0.755229i	$0.272474\pi$
$38$	16.5933	2.69179
$39$	6.39406	1.02387
$40$	25.5966	4.04718
$41$	1.00000	0.156174
$41$	1.00000	0.156174
$42$	0	0
$43$	−6.41643	−0.978496	−0.489248	−	0.872145i	$-0.662729\pi$
$43$	−6.41643	−0.978496	−0.489248	+	0.872145i	$0.662729\pi$
$44$	17.4139	2.62525
$45$	3.89232	0.580232
$46$	9.00520	1.32774
$47$	−3.72691	−0.543625	−0.271813	−	0.962350i	$-0.587623\pi$
$47$	−3.72691	−0.543625	−0.271813	+	0.962350i	$0.587623\pi$
$48$	−7.71874	−1.11410
$49$	0	0
$50$	26.0095	3.67830
$51$	1.70351	0.238538
$52$	−29.1974	−4.04896
$53$	14.2446	1.95665	0.978323	−	0.207085i	$-0.0663977\pi$
$53$	14.2446	1.95665	0.978323	+	0.207085i	$0.0663977\pi$
$54$	−2.56249	−0.348710
$55$	14.8435	2.00150
$56$	0	0
$57$	−6.47548	−0.857699
$58$	−22.1782	−2.91213
$59$	−3.38894	−0.441203	−0.220601	−	0.975364i	$-0.570802\pi$
$59$	−3.38894	−0.441203	−0.220601	+	0.975364i	$0.570802\pi$
$60$	−17.7736	−2.29456
$61$	4.40630	0.564169	0.282084	−	0.959390i	$-0.408974\pi$
$61$	4.40630	0.564169	0.282084	+	0.959390i	$0.408974\pi$
$62$	−1.10833	−0.140759
$63$	0	0
$64$	1.54354	0.192943
$65$	−24.8877	−3.08694
$66$	−9.77216	−1.20287
$67$	3.61186	0.441259	0.220630	−	0.975358i	$-0.429189\pi$
$67$	3.61186	0.441259	0.220630	+	0.975358i	$0.429189\pi$
$68$	−7.77878	−0.943315
$69$	−3.51424	−0.423065
$70$	0	0
$71$	−0.619870	−0.0735650	−0.0367825	−	0.999323i	$-0.511711\pi$
$71$	−0.619870	−0.0735650	−0.0367825	+	0.999323i	$0.511711\pi$
$72$	6.57620	0.775012
$73$	−2.71814	−0.318134	−0.159067	−	0.987268i	$-0.550849\pi$
$73$	−2.71814	−0.318134	−0.159067	+	0.987268i	$0.550849\pi$
$74$	20.4334	2.37533
$75$	−10.1501	−1.17204
$76$	29.5692	3.39182
$77$	0	0
$78$	16.3847	1.85520
$79$	11.5546	1.29999	0.649995	−	0.759939i	$-0.274771\pi$
$79$	11.5546	1.29999	0.649995	+	0.759939i	$0.274771\pi$
$80$	30.0438	3.35900
$81$	1.00000	0.111111
$82$	2.56249	0.282979
$83$	−5.74873	−0.631005	−0.315502	−	0.948925i	$-0.602173\pi$
$83$	−5.74873	−0.631005	−0.315502	+	0.948925i	$0.602173\pi$
$84$	0	0
$85$	−6.63058	−0.719188
$86$	−16.4420	−1.77299
$87$	8.65494	0.927907
$88$	25.0786	2.67339
$89$	−16.4936	−1.74831	−0.874157	−	0.485644i	$-0.838585\pi$
$89$	−16.4936	−1.74831	−0.874157	+	0.485644i	$0.838585\pi$
$90$	9.97400	1.05135
$91$	0	0
$92$	16.0472	1.67304
$93$	0.432523	0.0448505
$94$	−9.55015	−0.985022
$95$	25.2046	2.58594
$96$	−6.62678	−0.676343
$97$	−2.81728	−0.286051	−0.143026	−	0.989719i	$-0.545683\pi$
$97$	−2.81728	−0.286051	−0.143026	+	0.989719i	$0.545683\pi$
$98$	0	0
$99$	3.81355	0.383276
$100$	46.3489	4.63489
$101$	−9.17978	−0.913422	−0.456711	−	0.889615i	$-0.650973\pi$
$101$	−9.17978	−0.913422	−0.456711	+	0.889615i	$0.650973\pi$
$102$	4.36521	0.432220
$103$	12.7010	1.25147	0.625734	−	0.780036i	$-0.284799\pi$
$103$	12.7010	1.25147	0.625734	+	0.780036i	$0.284799\pi$
$104$	−42.0486	−4.12321
$105$	0	0
$106$	36.5016	3.54535
$107$	9.75066	0.942632	0.471316	−	0.881964i	$-0.343779\pi$
$107$	9.75066	0.942632	0.471316	+	0.881964i	$0.343779\pi$
$108$	−4.56633	−0.439396
$109$	−15.4367	−1.47856	−0.739282	−	0.673396i	$-0.764835\pi$
$109$	−15.4367	−1.47856	−0.739282	+	0.673396i	$0.764835\pi$
$110$	38.0363	3.62662
$111$	−7.97403	−0.756862
$112$	0	0
$113$	16.0865	1.51329	0.756646	−	0.653825i	$-0.226837\pi$
$113$	16.0865	1.51329	0.756646	+	0.653825i	$0.226837\pi$
$114$	−16.5933	−1.55411
$115$	13.6786	1.27553
$116$	−39.5213	−3.66946
$117$	−6.39406	−0.591131
$118$	−8.68412	−0.799438
$119$	0	0
$120$	−25.5966	−2.33664
$121$	3.54315	0.322105
$122$	11.2911	1.02225
$123$	−1.00000	−0.0901670
$124$	−1.97504	−0.177364
$125$	20.0459	1.79296
$126$	0	0
$127$	−13.4222	−1.19103	−0.595515	−	0.803344i	$-0.703052\pi$
$127$	−13.4222	−1.19103	−0.595515	+	0.803344i	$0.703052\pi$
$128$	−9.29825	−0.821857
$129$	6.41643	0.564935
$130$	−63.7744	−5.59339
$131$	3.10894	0.271630	0.135815	−	0.990734i	$-0.456635\pi$
$131$	3.10894	0.271630	0.135815	+	0.990734i	$0.456635\pi$
$132$	−17.4139	−1.51569
$133$	0	0
$134$	9.25535	0.799540
$135$	−3.89232	−0.334997
$136$	−11.2026	−0.960614
$137$	−12.3063	−1.05140	−0.525700	−	0.850670i	$-0.676196\pi$
$137$	−12.3063	−1.05140	−0.525700	+	0.850670i	$0.676196\pi$
$138$	−9.00520	−0.766574
$139$	−10.9403	−0.927944	−0.463972	−	0.885850i	$-0.653576\pi$
$139$	−10.9403	−0.927944	−0.463972	+	0.885850i	$0.653576\pi$
$140$	0	0
$141$	3.72691	0.313862
$142$	−1.58841	−0.133296
$143$	−24.3841	−2.03910
$144$	7.71874	0.643229
$145$	−33.6877	−2.79762
$146$	−6.96519	−0.576443
$147$	0	0
$148$	36.4121	2.99306
$149$	10.0711	0.825057	0.412529	−	0.910945i	$-0.364646\pi$
$149$	10.0711	0.825057	0.412529	+	0.910945i	$0.364646\pi$
$150$	−26.0095	−2.12367
$151$	−17.6807	−1.43883	−0.719416	−	0.694579i	$-0.755590\pi$
$151$	−17.6807	−1.43883	−0.719416	+	0.694579i	$0.755590\pi$
$152$	42.5841	3.45402
$153$	−1.70351	−0.137720
$154$	0	0
$155$	−1.68352	−0.135223
$156$	29.1974	2.33767
$157$	−9.27189	−0.739977	−0.369989	−	0.929036i	$-0.620638\pi$
$157$	−9.27189	−0.739977	−0.369989	+	0.929036i	$0.620638\pi$
$158$	29.6084	2.35552
$159$	−14.2446	−1.12967
$160$	25.7935	2.03916
$161$	0	0
$162$	2.56249	0.201328
$163$	−21.2183	−1.66195	−0.830974	−	0.556312i	$-0.812216\pi$
$163$	−21.2183	−1.66195	−0.830974	+	0.556312i	$0.812216\pi$
$164$	4.56633	0.356571
$165$	−14.8435	−1.15557
$166$	−14.7310	−1.14335
$167$	15.0869	1.16746	0.583731	−	0.811947i	$-0.301592\pi$
$167$	15.0869	1.16746	0.583731	+	0.811947i	$0.301592\pi$
$168$	0	0
$169$	27.8841	2.14493
$170$	−16.9908	−1.30313
$171$	6.47548	0.495193
$172$	−29.2996	−2.23407
$173$	3.21775	0.244641	0.122320	−	0.992491i	$-0.460966\pi$
$173$	3.21775	0.244641	0.122320	+	0.992491i	$0.460966\pi$
$174$	22.1782	1.68132
$175$	0	0
$176$	29.4358	2.21881
$177$	3.38894	0.254729
$178$	−42.2645	−3.16786
$179$	−3.09693	−0.231475	−0.115738	−	0.993280i	$-0.536923\pi$
$179$	−3.09693	−0.231475	−0.115738	+	0.993280i	$0.536923\pi$
$180$	17.7736	1.32477
$181$	0.106111	0.00788716	0.00394358	−	0.999992i	$-0.498745\pi$
$181$	0.106111	0.00788716	0.00394358	+	0.999992i	$0.498745\pi$
$182$	0	0
$183$	−4.40630	−0.325723
$184$	23.1104	1.70372
$185$	31.0375	2.28192
$186$	1.10833	0.0812670
$187$	−6.49640	−0.475064
$188$	−17.0183	−1.24119
$189$	0	0
$190$	64.5865	4.68560
$191$	−11.2353	−0.812957	−0.406478	−	0.913660i	$-0.633243\pi$
$191$	−11.2353	−0.812957	−0.406478	+	0.913660i	$0.633243\pi$
$192$	−1.54354	−0.111396
$193$	−8.99177	−0.647242	−0.323621	−	0.946187i	$-0.604900\pi$
$193$	−8.99177	−0.647242	−0.323621	+	0.946187i	$0.604900\pi$
$194$	−7.21924	−0.518311
$195$	24.8877	1.78225
$196$	0	0
$197$	0.416020	0.0296402	0.0148201	−	0.999890i	$-0.495282\pi$
$197$	0.416020	0.0296402	0.0148201	+	0.999890i	$0.495282\pi$
$198$	9.77216	0.694477
$199$	7.21407	0.511392	0.255696	−	0.966757i	$-0.417695\pi$
$199$	7.21407	0.511392	0.255696	+	0.966757i	$0.417695\pi$
$200$	66.7492	4.71988
$201$	−3.61186	−0.254761
$202$	−23.5231	−1.65508
$203$	0	0
$204$	7.77878	0.544623
$205$	3.89232	0.271851
$206$	32.5462	2.26760
$207$	3.51424	0.244257
$208$	−49.3541	−3.42209
$209$	24.6946	1.70816
$210$	0	0
$211$	−11.7020	−0.805599	−0.402800	−	0.915288i	$-0.631963\pi$
$211$	−11.7020	−0.805599	−0.402800	+	0.915288i	$0.631963\pi$
$212$	65.0456	4.46735
$213$	0.619870	0.0424728
$214$	24.9859	1.70800
$215$	−24.9748	−1.70327
$216$	−6.57620	−0.447454
$217$	0	0
$218$	−39.5562	−2.67909
$219$	2.71814	0.183675
$220$	67.7805	4.56976
$221$	10.8923	0.732697
$222$	−20.4334	−1.37140
$223$	8.90948	0.596623	0.298311	−	0.954469i	$-0.403577\pi$
$223$	8.90948	0.596623	0.298311	+	0.954469i	$0.403577\pi$
$224$	0	0
$225$	10.1501	0.676675
$226$	41.2215	2.74201
$227$	14.3864	0.954861	0.477431	−	0.878669i	$-0.341568\pi$
$227$	14.3864	0.954861	0.477431	+	0.878669i	$0.341568\pi$
$228$	−29.5692	−1.95827
$229$	4.19714	0.277355	0.138677	−	0.990338i	$-0.455715\pi$
$229$	4.19714	0.277355	0.138677	+	0.990338i	$0.455715\pi$
$230$	35.0511	2.31120
$231$	0	0
$232$	−56.9166	−3.73676
$233$	−4.56437	−0.299022	−0.149511	−	0.988760i	$-0.547770\pi$
$233$	−4.56437	−0.299022	−0.149511	+	0.988760i	$0.547770\pi$
$234$	−16.3847	−1.07110
$235$	−14.5063	−0.946287
$236$	−15.4750	−1.00734
$237$	−11.5546	−0.750549
$238$	0	0
$239$	−26.7068	−1.72752	−0.863761	−	0.503902i	$-0.831897\pi$
$239$	−26.7068	−1.72752	−0.863761	+	0.503902i	$0.831897\pi$
$240$	−30.0438	−1.93932
$241$	−10.9960	−0.708316	−0.354158	−	0.935186i	$-0.615233\pi$
$241$	−10.9960	−0.708316	−0.354158	+	0.935186i	$0.615233\pi$
$242$	9.07927	0.583638
$243$	−1.00000	−0.0641500
$244$	20.1206	1.28809
$245$	0	0
$246$	−2.56249	−0.163378
$247$	−41.4047	−2.63452
$248$	−2.84436	−0.180617
$249$	5.74873	0.364311
$250$	51.3673	3.24876
$251$	19.7095	1.24405	0.622026	−	0.782997i	$-0.286310\pi$
$251$	19.7095	1.24405	0.622026	+	0.782997i	$0.286310\pi$
$252$	0	0
$253$	13.4017	0.842560
$254$	−34.3943	−2.15809
$255$	6.63058	0.415223
$256$	−26.9137	−1.68211
$257$	31.9263	1.99151	0.995754	−	0.0920522i	$-0.0293427\pi$
$257$	31.9263	1.99151	0.995754	+	0.0920522i	$0.0293427\pi$
$258$	16.4420	1.02363
$259$	0	0
$260$	−113.646	−7.04800
$261$	−8.65494	−0.535727
$262$	7.96662	0.492180
$263$	17.2241	1.06208	0.531042	−	0.847345i	$-0.321801\pi$
$263$	17.2241	1.06208	0.531042	+	0.847345i	$0.321801\pi$
$264$	−25.0786	−1.54348
$265$	55.4445	3.40593
$266$	0	0
$267$	16.4936	1.00939
$268$	16.4930	1.00747
$269$	−10.3538	−0.631282	−0.315641	−	0.948879i	$-0.602220\pi$
$269$	−10.3538	−0.631282	−0.315641	+	0.948879i	$0.602220\pi$
$270$	−9.97400	−0.606999
$271$	−27.4283	−1.66615	−0.833076	−	0.553158i	$-0.813423\pi$
$271$	−27.4283	−1.66615	−0.833076	+	0.553158i	$0.813423\pi$
$272$	−13.1489	−0.797271
$273$	0	0
$274$	−31.5348	−1.90508
$275$	38.7080	2.33418
$276$	−16.0472	−0.965929
$277$	11.9690	0.719149	0.359574	−	0.933116i	$-0.382922\pi$
$277$	11.9690	0.719149	0.359574	+	0.933116i	$0.382922\pi$
$278$	−28.0344	−1.68139
$279$	−0.432523	−0.0258945
$280$	0	0
$281$	10.1762	0.607063	0.303531	−	0.952821i	$-0.401834\pi$
$281$	10.1762	0.607063	0.303531	+	0.952821i	$0.401834\pi$
$282$	9.55015	0.568703
$283$	6.37817	0.379143	0.189572	−	0.981867i	$-0.439290\pi$
$283$	6.37817	0.379143	0.189572	+	0.981867i	$0.439290\pi$
$284$	−2.83053	−0.167961
$285$	−25.2046	−1.49299
$286$	−62.4838	−3.69475
$287$	0	0
$288$	6.62678	0.390487
$289$	−14.0981	−0.829298
$290$	−86.3244	−5.06914
$291$	2.81728	0.165152
$292$	−12.4119	−0.726353
$293$	−31.5877	−1.84537	−0.922687	−	0.385550i	$-0.874012\pi$
$293$	−31.5877	−1.84537	−0.922687	+	0.385550i	$0.874012\pi$
$294$	0	0
$295$	−13.1908	−0.768000
$296$	52.4388	3.04794
$297$	−3.81355	−0.221285
$298$	25.8071	1.49496
$299$	−22.4703	−1.29949
$300$	−46.3489	−2.67595
$301$	0	0
$302$	−45.3065	−2.60709
$303$	9.17978	0.527364
$304$	49.9826	2.86670
$305$	17.1507	0.982046
$306$	−4.36521	−0.249542
$307$	4.13968	0.236264	0.118132	−	0.992998i	$-0.462309\pi$
$307$	4.13968	0.236264	0.118132	+	0.992998i	$0.462309\pi$
$308$	0	0
$309$	−12.7010	−0.722536
$310$	−4.31398	−0.245018
$311$	−14.6828	−0.832587	−0.416293	−	0.909230i	$-0.636671\pi$
$311$	−14.6828	−0.832587	−0.416293	+	0.909230i	$0.636671\pi$
$312$	42.0486	2.38053
$313$	32.5963	1.84245	0.921225	−	0.389031i	$-0.127190\pi$
$313$	32.5963	1.84245	0.921225	+	0.389031i	$0.127190\pi$
$314$	−23.7591	−1.34080
$315$	0	0
$316$	52.7620	2.96809
$317$	−0.374845	−0.0210534	−0.0105267	−	0.999945i	$-0.503351\pi$
$317$	−0.374845	−0.0210534	−0.0105267	+	0.999945i	$0.503351\pi$
$318$	−36.5016	−2.04691
$319$	−33.0060	−1.84798
$320$	6.00795	0.335855
$321$	−9.75066	−0.544229
$322$	0	0
$323$	−11.0310	−0.613782
$324$	4.56633	0.253685
$325$	−64.9005	−3.60003
$326$	−54.3717	−3.01137
$327$	15.4367	0.853650
$328$	6.57620	0.363110
$329$	0	0
$330$	−38.0363	−2.09383
$331$	−2.42663	−0.133379	−0.0666897	−	0.997774i	$-0.521244\pi$
$331$	−2.42663	−0.133379	−0.0666897	+	0.997774i	$0.521244\pi$
$332$	−26.2506	−1.44069
$333$	7.97403	0.436974
$334$	38.6601	2.11539
$335$	14.0585	0.768098
$336$	0	0
$337$	−22.6106	−1.23168	−0.615840	−	0.787871i	$-0.711183\pi$
$337$	−22.6106	−1.23168	−0.615840	+	0.787871i	$0.711183\pi$
$338$	71.4525	3.88650
$339$	−16.0865	−0.873699
$340$	−30.2775	−1.64203
$341$	−1.64945	−0.0893225
$342$	16.5933	0.897265
$343$	0	0
$344$	−42.1957	−2.27504
$345$	−13.6786	−0.736428
$346$	8.24544	0.443277
$347$	−32.2232	−1.72983	−0.864916	−	0.501916i	$-0.832629\pi$
$347$	−32.2232	−1.72983	−0.864916	+	0.501916i	$0.832629\pi$
$348$	39.5213	2.11857
$349$	−9.93257	−0.531678	−0.265839	−	0.964017i	$-0.585649\pi$
$349$	−9.93257	−0.531678	−0.265839	+	0.964017i	$0.585649\pi$
$350$	0	0
$351$	6.39406	0.341290
$352$	25.2715	1.34698
$353$	−0.470477	−0.0250410	−0.0125205	−	0.999922i	$-0.503985\pi$
$353$	−0.470477	−0.0250410	−0.0125205	+	0.999922i	$0.503985\pi$
$354$	8.68412	0.461556
$355$	−2.41273	−0.128054
$356$	−75.3151	−3.99169
$357$	0	0
$358$	−7.93584	−0.419422
$359$	−3.78654	−0.199846	−0.0999230	−	0.994995i	$-0.531860\pi$
$359$	−3.78654	−0.199846	−0.0999230	+	0.994995i	$0.531860\pi$
$360$	25.5966	1.34906
$361$	22.9319	1.20694
$362$	0.271908	0.0142912
$363$	−3.54315	−0.185967
$364$	0	0
$365$	−10.5799	−0.553775
$366$	−11.2911	−0.590194
$367$	5.50525	0.287372	0.143686	−	0.989623i	$-0.454105\pi$
$367$	5.50525	0.287372	0.143686	+	0.989623i	$0.454105\pi$
$368$	27.1256	1.41402
$369$	1.00000	0.0520579
$370$	79.5331	4.13473
$371$	0	0
$372$	1.97504	0.102401
$373$	18.8594	0.976505	0.488252	−	0.872703i	$-0.337635\pi$
$373$	18.8594	0.976505	0.488252	+	0.872703i	$0.337635\pi$
$374$	−16.6469	−0.860793
$375$	−20.0459	−1.03517
$376$	−24.5089	−1.26395
$377$	55.3402	2.85017
$378$	0	0
$379$	4.70498	0.241678	0.120839	−	0.992672i	$-0.461441\pi$
$379$	4.70498	0.241678	0.120839	+	0.992672i	$0.461441\pi$
$380$	115.093	5.90413
$381$	13.4222	0.687642
$382$	−28.7903	−1.47304
$383$	−9.31366	−0.475906	−0.237953	−	0.971277i	$-0.576476\pi$
$383$	−9.31366	−0.475906	−0.237953	+	0.971277i	$0.576476\pi$
$384$	9.29825	0.474500
$385$	0	0
$386$	−23.0413	−1.17277
$387$	−6.41643	−0.326165
$388$	−12.8646	−0.653103
$389$	11.8547	0.601056	0.300528	−	0.953773i	$-0.402837\pi$
$389$	11.8547	0.601056	0.300528	+	0.953773i	$0.402837\pi$
$390$	63.7744	3.22934
$391$	−5.98654	−0.302752
$392$	0	0
$393$	−3.10894	−0.156825
$394$	1.06605	0.0537066
$395$	44.9740	2.26289
$396$	17.4139	0.875083
$397$	24.0952	1.20930	0.604652	−	0.796490i	$-0.293312\pi$
$397$	24.0952	1.20930	0.604652	+	0.796490i	$0.293312\pi$
$398$	18.4860	0.926617
$399$	0	0
$400$	78.3462	3.91731
$401$	28.0444	1.40047	0.700234	−	0.713913i	$-0.253079\pi$
$401$	28.0444	1.40047	0.700234	+	0.713913i	$0.253079\pi$
$402$	−9.25535	−0.461615
$403$	2.76558	0.137763
$404$	−41.9179	−2.08550
$405$	3.89232	0.193411
$406$	0	0
$407$	30.4094	1.50734
$408$	11.2026	0.554611
$409$	17.0017	0.840682	0.420341	−	0.907366i	$-0.361911\pi$
$409$	17.0017	0.840682	0.420341	+	0.907366i	$0.361911\pi$
$410$	9.97400	0.492581
$411$	12.3063	0.607026
$412$	57.9971	2.85731
$413$	0	0
$414$	9.00520	0.442582
$415$	−22.3759	−1.09839
$416$	−42.3721	−2.07746
$417$	10.9403	0.535749
$418$	63.2795	3.09510
$419$	34.5411	1.68744	0.843722	−	0.536781i	$-0.180360\pi$
$419$	34.5411	1.68744	0.843722	+	0.536781i	$0.180360\pi$
$420$	0	0
$421$	−7.26526	−0.354087	−0.177044	−	0.984203i	$-0.556653\pi$
$421$	−7.26526	−0.354087	−0.177044	+	0.984203i	$0.556653\pi$
$422$	−29.9862	−1.45971
$423$	−3.72691	−0.181208
$424$	93.6753	4.54927
$425$	−17.2908	−0.838726
$426$	1.58841	0.0769586
$427$	0	0
$428$	44.5248	2.15219
$429$	24.3841	1.17727
$430$	−63.9975	−3.08623
$431$	−8.73640	−0.420818	−0.210409	−	0.977613i	$-0.567480\pi$
$431$	−8.73640	−0.420818	−0.210409	+	0.977613i	$0.567480\pi$
$432$	−7.71874	−0.371368
$433$	−25.5753	−1.22907	−0.614534	−	0.788890i	$-0.710656\pi$
$433$	−25.5753	−1.22907	−0.614534	+	0.788890i	$0.710656\pi$
$434$	0	0
$435$	33.6877	1.61520
$436$	−70.4890	−3.37581
$437$	22.7564	1.08859
$438$	6.96519	0.332810
$439$	30.0329	1.43339	0.716697	−	0.697385i	$-0.245653\pi$
$439$	30.0329	1.43339	0.716697	+	0.697385i	$0.245653\pi$
$440$	97.6140	4.65357
$441$	0	0
$442$	27.9114	1.32761
$443$	11.8190	0.561538	0.280769	−	0.959775i	$-0.409411\pi$
$443$	11.8190	0.561538	0.280769	+	0.959775i	$0.409411\pi$
$444$	−36.4121	−1.72804
$445$	−64.1981	−3.04328
$446$	22.8304	1.08105
$447$	−10.0711	−0.476347
$448$	0	0
$449$	4.74219	0.223798	0.111899	−	0.993720i	$-0.464307\pi$
$449$	4.74219	0.223798	0.111899	+	0.993720i	$0.464307\pi$
$450$	26.0095	1.22610
$451$	3.81355	0.179573
$452$	73.4564	3.45510
$453$	17.6807	0.830710
$454$	36.8650	1.73016
$455$	0	0
$456$	−42.5841	−1.99418
$457$	−4.79322	−0.224217	−0.112109	−	0.993696i	$-0.535760\pi$
$457$	−4.79322	−0.224217	−0.112109	+	0.993696i	$0.535760\pi$
$458$	10.7551	0.502553
$459$	1.70351	0.0795128
$460$	62.4608	2.91225
$461$	−0.478050	−0.0222650	−0.0111325	−	0.999938i	$-0.503544\pi$
$461$	−0.478050	−0.0222650	−0.0111325	+	0.999938i	$0.503544\pi$
$462$	0	0
$463$	−4.36341	−0.202785	−0.101392	−	0.994847i	$-0.532330\pi$
$463$	−4.36341	−0.202785	−0.101392	+	0.994847i	$0.532330\pi$
$464$	−66.8052	−3.10136
$465$	1.68352	0.0780711
$466$	−11.6961	−0.541813
$467$	−34.5418	−1.59841	−0.799203	−	0.601062i	$-0.794745\pi$
$467$	−34.5418	−1.59841	−0.799203	+	0.601062i	$0.794745\pi$
$468$	−29.1974	−1.34965
$469$	0	0
$470$	−37.1722	−1.71463
$471$	9.27189	0.427226
$472$	−22.2864	−1.02581
$473$	−24.4694	−1.12510
$474$	−29.6084	−1.35996
$475$	65.7269	3.01576
$476$	0	0
$477$	14.2446	0.652215
$478$	−68.4359	−3.13018
$479$	−41.9564	−1.91704	−0.958518	−	0.285032i	$-0.907996\pi$
$479$	−41.9564	−1.91704	−0.958518	+	0.285032i	$0.907996\pi$
$480$	−25.7935	−1.17731
$481$	−50.9865	−2.32478
$482$	−28.1772	−1.28343
$483$	0	0
$484$	16.1792	0.735419
$485$	−10.9657	−0.497929
$486$	−2.56249	−0.116237
$487$	12.9603	0.587287	0.293644	−	0.955915i	$-0.405132\pi$
$487$	12.9603	0.587287	0.293644	+	0.955915i	$0.405132\pi$
$488$	28.9767	1.31171
$489$	21.2183	0.959526
$490$	0	0
$491$	−29.3306	−1.32367	−0.661835	−	0.749650i	$-0.730222\pi$
$491$	−29.3306	−1.32367	−0.661835	+	0.749650i	$0.730222\pi$
$492$	−4.56633	−0.205866
$493$	14.7437	0.664024
$494$	−106.099	−4.77361
$495$	14.8435	0.667167
$496$	−3.33853	−0.149905
$497$	0	0
$498$	14.7310	0.660114
$499$	29.3644	1.31453	0.657265	−	0.753659i	$-0.271713\pi$
$499$	29.3644	1.31453	0.657265	+	0.753659i	$0.271713\pi$
$500$	91.5363	4.09363
$501$	−15.0869	−0.674035
$502$	50.5053	2.25416
$503$	14.3799	0.641166	0.320583	−	0.947220i	$-0.396121\pi$
$503$	14.3799	0.641166	0.320583	+	0.947220i	$0.396121\pi$
$504$	0	0
$505$	−35.7306	−1.58999
$506$	34.3418	1.52668
$507$	−27.8841	−1.23837
$508$	−61.2904	−2.71932
$509$	22.5208	0.998216	0.499108	−	0.866540i	$-0.333661\pi$
$509$	22.5208	0.998216	0.499108	+	0.866540i	$0.333661\pi$
$510$	16.9908	0.752364
$511$	0	0
$512$	−50.3696	−2.22604
$513$	−6.47548	−0.285900
$514$	81.8107	3.60852
$515$	49.4364	2.17843
$516$	29.2996	1.28984
$517$	−14.2127	−0.625076
$518$	0	0
$519$	−3.21775	−0.141243
$520$	−163.667	−7.17725
$521$	19.3136	0.846144	0.423072	−	0.906096i	$-0.360952\pi$
$521$	19.3136	0.846144	0.423072	+	0.906096i	$0.360952\pi$
$522$	−22.1782	−0.970712
$523$	2.22956	0.0974918	0.0487459	−	0.998811i	$-0.484478\pi$
$523$	2.22956	0.0974918	0.0487459	+	0.998811i	$0.484478\pi$
$524$	14.1965	0.620176
$525$	0	0
$526$	44.1366	1.92445
$527$	0.736805	0.0320957
$528$	−29.4358	−1.28103
$529$	−10.6501	−0.463047
$530$	142.076	6.17137
$531$	−3.38894	−0.147068
$532$	0	0
$533$	−6.39406	−0.276958
$534$	42.2645	1.82896
$535$	37.9527	1.64084
$536$	23.7523	1.02594
$537$	3.09693	0.133642
$538$	−26.5315	−1.14385
$539$	0	0
$540$	−17.7736	−0.764855
$541$	−22.6192	−0.972473	−0.486237	−	0.873827i	$-0.661631\pi$
$541$	−22.6192	−0.972473	−0.486237	+	0.873827i	$0.661631\pi$
$542$	−70.2847	−3.01899
$543$	−0.106111	−0.00455366
$544$	−11.2888	−0.484001
$545$	−60.0844	−2.57373
$546$	0	0
$547$	−30.0174	−1.28345	−0.641725	−	0.766935i	$-0.721781\pi$
$547$	−30.0174	−1.28345	−0.641725	+	0.766935i	$0.721781\pi$
$548$	−56.1947	−2.40052
$549$	4.40630	0.188056
$550$	99.1887	4.22942
$551$	−56.0449	−2.38759
$552$	−23.1104	−0.983643
$553$	0	0
$554$	30.6705	1.30306
$555$	−31.0375	−1.31747
$556$	−49.9571	−2.11865
$557$	7.24842	0.307125	0.153563	−	0.988139i	$-0.450925\pi$
$557$	7.24842	0.307125	0.153563	+	0.988139i	$0.450925\pi$
$558$	−1.10833	−0.0469195
$559$	41.0271	1.73526
$560$	0	0
$561$	6.49640	0.274278
$562$	26.0764	1.09997
$563$	−22.1704	−0.934372	−0.467186	−	0.884159i	$-0.654732\pi$
$563$	−22.1704	−0.934372	−0.467186	+	0.884159i	$0.654732\pi$
$564$	17.0183	0.716600
$565$	62.6138	2.63418
$566$	16.3440	0.686989
$567$	0	0
$568$	−4.07639	−0.171041
$569$	−31.1263	−1.30488	−0.652440	−	0.757840i	$-0.726255\pi$
$569$	−31.1263	−1.30488	−0.652440	+	0.757840i	$0.726255\pi$
$570$	−64.5865	−2.70523
$571$	−18.3057	−0.766068	−0.383034	−	0.923734i	$-0.625121\pi$
$571$	−18.3057	−0.766068	−0.383034	+	0.923734i	$0.625121\pi$
$572$	−111.346	−4.65560
$573$	11.2353	0.469361
$574$	0	0
$575$	35.6700	1.48754
$576$	1.54354	0.0643143
$577$	4.86103	0.202367	0.101184	−	0.994868i	$-0.467737\pi$
$577$	4.86103	0.202367	0.101184	+	0.994868i	$0.467737\pi$
$578$	−36.1261	−1.50265
$579$	8.99177	0.373685
$580$	−153.830	−6.38742
$581$	0	0
$582$	7.21924	0.299247
$583$	54.3225	2.24981
$584$	−17.8750	−0.739673
$585$	−24.8877	−1.02898
$586$	−80.9431	−3.34373
$587$	28.6682	1.18326	0.591632	−	0.806208i	$-0.298484\pi$
$587$	28.6682	1.18326	0.591632	+	0.806208i	$0.298484\pi$
$588$	0	0
$589$	−2.80079	−0.115405
$590$	−33.8013	−1.39158
$591$	−0.416020	−0.0171128
$592$	61.5495	2.52967
$593$	21.9738	0.902354	0.451177	−	0.892434i	$-0.351004\pi$
$593$	21.9738	0.902354	0.451177	+	0.892434i	$0.351004\pi$
$594$	−9.77216	−0.400957
$595$	0	0
$596$	45.9881	1.88374
$597$	−7.21407	−0.295252
$598$	−57.5799	−2.35462
$599$	31.3230	1.27982	0.639911	−	0.768449i	$-0.278971\pi$
$599$	31.3230	1.27982	0.639911	+	0.768449i	$0.278971\pi$
$600$	−66.7492	−2.72502
$601$	6.15788	0.251185	0.125593	−	0.992082i	$-0.459917\pi$
$601$	6.15788	0.251185	0.125593	+	0.992082i	$0.459917\pi$
$602$	0	0
$603$	3.61186	0.147086
$604$	−80.7358	−3.28509
$605$	13.7911	0.560686
$606$	23.5231	0.955559
$607$	12.7567	0.517779	0.258889	−	0.965907i	$-0.416643\pi$
$607$	12.7567	0.517779	0.258889	+	0.965907i	$0.416643\pi$
$608$	42.9116	1.74029
$609$	0	0
$610$	43.9484	1.77942
$611$	23.8301	0.964062
$612$	−7.77878	−0.314438
$613$	−43.0140	−1.73732	−0.868659	−	0.495410i	$-0.835018\pi$
$613$	−43.0140	−1.73732	−0.868659	+	0.495410i	$0.835018\pi$
$614$	10.6079	0.428099
$615$	−3.89232	−0.156953
$616$	0	0
$617$	−34.6914	−1.39662	−0.698312	−	0.715793i	$-0.746065\pi$
$617$	−34.6914	−1.39662	−0.698312	+	0.715793i	$0.746065\pi$
$618$	−32.5462	−1.30920
$619$	−3.93932	−0.158335	−0.0791673	−	0.996861i	$-0.525226\pi$
$619$	−3.93932	−0.158335	−0.0791673	+	0.996861i	$0.525226\pi$
$620$	−7.68749	−0.308737
$621$	−3.51424	−0.141022
$622$	−37.6246	−1.50861
$623$	0	0
$624$	49.3541	1.97575
$625$	27.2744	1.09097
$626$	83.5275	3.33843
$627$	−24.6946	−0.986206
$628$	−42.3385	−1.68949
$629$	−13.5838	−0.541622
$630$	0	0
$631$	1.68087	0.0669144	0.0334572	−	0.999440i	$-0.489348\pi$
$631$	1.68087	0.0669144	0.0334572	+	0.999440i	$0.489348\pi$
$632$	75.9850	3.02252
$633$	11.7020	0.465113
$634$	−0.960534	−0.0381477
$635$	−52.2436	−2.07322
$636$	−65.0456	−2.57923
$637$	0	0
$638$	−84.5775	−3.34845
$639$	−0.619870	−0.0245217
$640$	−36.1917	−1.43060
$641$	21.8935	0.864740	0.432370	−	0.901696i	$-0.357678\pi$
$641$	21.8935	0.864740	0.432370	+	0.901696i	$0.357678\pi$
$642$	−24.9859	−0.986116
$643$	−47.8257	−1.88606	−0.943031	−	0.332705i	$-0.892039\pi$
$643$	−47.8257	−1.88606	−0.943031	+	0.332705i	$0.892039\pi$
$644$	0	0
$645$	24.9748	0.983381
$646$	−28.2668	−1.11214
$647$	−13.4095	−0.527181	−0.263591	−	0.964635i	$-0.584907\pi$
$647$	−13.4095	−0.527181	−0.263591	+	0.964635i	$0.584907\pi$
$648$	6.57620	0.258337
$649$	−12.9239	−0.507307
$650$	−166.307	−6.52309
$651$	0	0
$652$	−96.8900	−3.79450
$653$	4.31746	0.168955	0.0844775	−	0.996425i	$-0.473078\pi$
$653$	4.31746	0.168955	0.0844775	+	0.996425i	$0.473078\pi$
$654$	39.5562	1.54677
$655$	12.1010	0.472825
$656$	7.71874	0.301366
$657$	−2.71814	−0.106045
$658$	0	0
$659$	27.7187	1.07977	0.539883	−	0.841740i	$-0.318468\pi$
$659$	27.7187	1.07977	0.539883	+	0.841740i	$0.318468\pi$
$660$	−67.7805	−2.63835
$661$	24.2825	0.944481	0.472241	−	0.881470i	$-0.343445\pi$
$661$	24.2825	0.944481	0.472241	+	0.881470i	$0.343445\pi$
$662$	−6.21820	−0.241677
$663$	−10.8923	−0.423023
$664$	−37.8048	−1.46711
$665$	0	0
$666$	20.4334	0.791776
$667$	−30.4156	−1.17770
$668$	68.8920	2.66551
$669$	−8.90948	−0.344460
$670$	36.0247	1.39176
$671$	16.8036	0.648697
$672$	0	0
$673$	16.8664	0.650152	0.325076	−	0.945688i	$-0.394610\pi$
$673$	16.8664	0.650152	0.325076	+	0.945688i	$0.394610\pi$
$674$	−57.9395	−2.23174
$675$	−10.1501	−0.390678
$676$	127.328	4.89723
$677$	36.5414	1.40440	0.702200	−	0.711980i	$-0.252201\pi$
$677$	36.5414	1.40440	0.702200	+	0.711980i	$0.252201\pi$
$678$	−41.2215	−1.58310
$679$	0	0
$680$	−43.6040	−1.67214
$681$	−14.3864	−0.551289
$682$	−4.22668	−0.161848
$683$	−19.6855	−0.753244	−0.376622	−	0.926367i	$-0.622914\pi$
$683$	−19.6855	−0.753244	−0.376622	+	0.926367i	$0.622914\pi$
$684$	29.5692	1.13061
$685$	−47.9001	−1.83017
$686$	0	0
$687$	−4.19714	−0.160131
$688$	−49.5268	−1.88819
$689$	−91.0809	−3.46990
$690$	−35.0511	−1.33437
$691$	11.0941	0.422041	0.211020	−	0.977482i	$-0.432321\pi$
$691$	11.0941	0.422041	0.211020	+	0.977482i	$0.432321\pi$
$692$	14.6933	0.558556
$693$	0	0
$694$	−82.5715	−3.13437
$695$	−42.5831	−1.61527
$696$	56.9166	2.15742
$697$	−1.70351	−0.0645249
$698$	−25.4521	−0.963375
$699$	4.56437	0.172640
$700$	0	0
$701$	29.7923	1.12524	0.562620	−	0.826716i	$-0.309794\pi$
$701$	29.7923	1.12524	0.562620	+	0.826716i	$0.309794\pi$
$702$	16.3847	0.618401
$703$	51.6357	1.94748
$704$	5.88637	0.221851
$705$	14.5063	0.546339
$706$	−1.20559	−0.0453730
$707$	0	0
$708$	15.4750	0.581588
$709$	36.5747	1.37359	0.686795	−	0.726851i	$-0.259017\pi$
$709$	36.5747	1.37359	0.686795	+	0.726851i	$0.259017\pi$
$710$	−6.18258	−0.232028
$711$	11.5546	0.433330
$712$	−108.465	−4.06489
$713$	−1.51999	−0.0569241
$714$	0	0
$715$	−94.9105	−3.54945
$716$	−14.1416	−0.528497
$717$	26.7068	0.997385
$718$	−9.70296	−0.362111
$719$	−34.8891	−1.30114	−0.650572	−	0.759444i	$-0.725471\pi$
$719$	−34.8891	−1.30114	−0.650572	+	0.759444i	$0.725471\pi$
$720$	30.0438	1.11967
$721$	0	0
$722$	58.7626	2.18692
$723$	10.9960	0.408947
$724$	0.484538	0.0180077
$725$	−87.8487	−3.26262
$726$	−9.07927	−0.336963
$727$	5.29173	0.196259	0.0981296	−	0.995174i	$-0.468714\pi$
$727$	5.29173	0.196259	0.0981296	+	0.995174i	$0.468714\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−27.1107	−1.00341
$731$	10.9304	0.404276
$732$	−20.1206	−0.743680
$733$	−10.9375	−0.403986	−0.201993	−	0.979387i	$-0.564742\pi$
$733$	−10.9375	−0.403986	−0.201993	+	0.979387i	$0.564742\pi$
$734$	14.1071	0.520703
$735$	0	0
$736$	23.2881	0.858412
$737$	13.7740	0.507372
$738$	2.56249	0.0943264
$739$	14.0490	0.516802	0.258401	−	0.966038i	$-0.416805\pi$
$739$	14.0490	0.516802	0.258401	+	0.966038i	$0.416805\pi$
$740$	141.727	5.21000
$741$	41.4047	1.52104
$742$	0	0
$743$	−47.8936	−1.75704	−0.878522	−	0.477701i	$-0.841470\pi$
$743$	−47.8936	−1.75704	−0.878522	+	0.477701i	$0.841470\pi$
$744$	2.84436	0.104279
$745$	39.1999	1.43617
$746$	48.3270	1.76938
$747$	−5.74873	−0.210335
$748$	−29.6647	−1.08465
$749$	0	0
$750$	−51.3673	−1.87567
$751$	−30.9737	−1.13025	−0.565124	−	0.825006i	$-0.691172\pi$
$751$	−30.9737	−1.13025	−0.565124	+	0.825006i	$0.691172\pi$
$752$	−28.7670	−1.04903
$753$	−19.7095	−0.718254
$754$	141.809	5.16436
$755$	−68.8187	−2.50457
$756$	0	0
$757$	20.1123	0.730995	0.365497	−	0.930812i	$-0.380899\pi$
$757$	20.1123	0.730995	0.365497	+	0.930812i	$0.380899\pi$
$758$	12.0564	0.437909
$759$	−13.4017	−0.486452
$760$	165.751	6.01240
$761$	−13.6838	−0.496038	−0.248019	−	0.968755i	$-0.579780\pi$
$761$	−13.6838	−0.496038	−0.248019	+	0.968755i	$0.579780\pi$
$762$	34.3943	1.24597
$763$	0	0
$764$	−51.3041	−1.85612
$765$	−6.63058	−0.239729
$766$	−23.8661	−0.862318
$767$	21.6691	0.782427
$768$	26.9137	0.971166
$769$	1.06746	0.0384937	0.0192468	−	0.999815i	$-0.493873\pi$
$769$	1.06746	0.0384937	0.0192468	+	0.999815i	$0.493873\pi$
$770$	0	0
$771$	−31.9263	−1.14980
$772$	−41.0594	−1.47776
$773$	2.94940	0.106082	0.0530412	−	0.998592i	$-0.483109\pi$
$773$	2.94940	0.106082	0.0530412	+	0.998592i	$0.483109\pi$
$774$	−16.4420	−0.590996
$775$	−4.39016	−0.157699
$776$	−18.5270	−0.665080
$777$	0	0
$778$	30.3774	1.08908
$779$	6.47548	0.232008
$780$	113.646	4.06917
$781$	−2.36390	−0.0845871
$782$	−15.3404	−0.548572
$783$	8.65494	0.309302
$784$	0	0
$785$	−36.0891	−1.28808
$786$	−7.96662	−0.284160
$787$	0.0995646	0.00354910	0.00177455	−	0.999998i	$-0.499435\pi$
$787$	0.0995646	0.00354910	0.00177455	+	0.999998i	$0.499435\pi$
$788$	1.89969	0.0676735
$789$	−17.2241	−0.613195
$790$	115.245	4.10024
$791$	0	0
$792$	25.0786	0.891131
$793$	−28.1741	−1.00049
$794$	61.7437	2.19120
$795$	−55.4445	−1.96641
$796$	32.9419	1.16759
$797$	18.5859	0.658346	0.329173	−	0.944270i	$-0.393230\pi$
$797$	18.5859	0.658346	0.329173	+	0.944270i	$0.393230\pi$
$798$	0	0
$799$	6.34881	0.224605
$800$	67.2626	2.37809
$801$	−16.4936	−0.582771
$802$	71.8633	2.53758
$803$	−10.3657	−0.365799
$804$	−16.4930	−0.581662
$805$	0	0
$806$	7.08676	0.249620
$807$	10.3538	0.364471
$808$	−60.3680	−2.12374
$809$	−37.1832	−1.30729	−0.653645	−	0.756801i	$-0.726761\pi$
$809$	−37.1832	−1.30729	−0.653645	+	0.756801i	$0.726761\pi$
$810$	9.97400	0.350451
$811$	−15.1429	−0.531738	−0.265869	−	0.964009i	$-0.585659\pi$
$811$	−15.1429	−0.531738	−0.265869	+	0.964009i	$0.585659\pi$
$812$	0	0
$813$	27.4283	0.961954
$814$	77.9236	2.73122
$815$	−82.5884	−2.89295
$816$	13.1489	0.460304
$817$	−41.5495	−1.45363
$818$	43.5667	1.52327
$819$	0	0
$820$	17.7736	0.620682
$821$	−9.35104	−0.326354	−0.163177	−	0.986597i	$-0.552174\pi$
$821$	−9.35104	−0.326354	−0.163177	+	0.986597i	$0.552174\pi$
$822$	31.5348	1.09990
$823$	4.99218	0.174017	0.0870083	−	0.996208i	$-0.472269\pi$
$823$	4.99218	0.174017	0.0870083	+	0.996208i	$0.472269\pi$
$824$	83.5244	2.90971
$825$	−38.7080	−1.34764
$826$	0	0
$827$	6.42913	0.223563	0.111781	−	0.993733i	$-0.464344\pi$
$827$	6.42913	0.223563	0.111781	+	0.993733i	$0.464344\pi$
$828$	16.0472	0.557679
$829$	−18.3653	−0.637853	−0.318926	−	0.947779i	$-0.603322\pi$
$829$	−18.3653	−0.637853	−0.318926	+	0.947779i	$0.603322\pi$
$830$	−57.3378	−1.99023
$831$	−11.9690	−0.415201
$832$	−9.86951	−0.342164
$833$	0	0
$834$	28.0344	0.970750
$835$	58.7231	2.03220
$836$	112.764	3.90001
$837$	0.432523	0.0149502
$838$	88.5111	3.05756
$839$	−54.3366	−1.87591	−0.937954	−	0.346760i	$-0.887282\pi$
$839$	−54.3366	−1.87591	−0.937954	+	0.346760i	$0.887282\pi$
$840$	0	0
$841$	45.9079	1.58303
$842$	−18.6171	−0.641589
$843$	−10.1762	−0.350488
$844$	−53.4353	−1.83932
$845$	108.534	3.73367
$846$	−9.55015	−0.328341
$847$	0	0
$848$	109.950	3.77571
$849$	−6.37817	−0.218898
$850$	−44.3074	−1.51973
$851$	28.0227	0.960606
$852$	2.83053	0.0969725
$853$	23.5896	0.807692	0.403846	−	0.914827i	$-0.367673\pi$
$853$	23.5896	0.807692	0.403846	+	0.914827i	$0.367673\pi$
$854$	0	0
$855$	25.2046	0.861980
$856$	64.1223	2.19165
$857$	45.5365	1.55550	0.777749	−	0.628575i	$-0.216362\pi$
$857$	45.5365	1.55550	0.777749	+	0.628575i	$0.216362\pi$
$858$	62.4838	2.13316
$859$	−46.3999	−1.58314	−0.791572	−	0.611075i	$-0.790737\pi$
$859$	−46.3999	−1.58314	−0.791572	+	0.611075i	$0.790737\pi$
$860$	−114.043	−3.88884
$861$	0	0
$862$	−22.3869	−0.762501
$863$	−28.2733	−0.962433	−0.481217	−	0.876602i	$-0.659805\pi$
$863$	−28.2733	−0.962433	−0.481217	+	0.876602i	$0.659805\pi$
$864$	−6.62678	−0.225448
$865$	12.5245	0.425846
$866$	−65.5362	−2.22701
$867$	14.0981	0.478796
$868$	0	0
$869$	44.0639	1.49476
$870$	86.3244	2.92667
$871$	−23.0945	−0.782527
$872$	−101.515	−3.43772
$873$	−2.81728	−0.0953504
$874$	58.3130	1.97247
$875$	0	0
$876$	12.4119	0.419360
$877$	25.1433	0.849030	0.424515	−	0.905421i	$-0.360445\pi$
$877$	25.1433	0.849030	0.424515	+	0.905421i	$0.360445\pi$
$878$	76.9590	2.59724
$879$	31.5877	1.06543
$880$	114.573	3.86227
$881$	−25.6604	−0.864519	−0.432260	−	0.901749i	$-0.642284\pi$
$881$	−25.6604	−0.864519	−0.432260	+	0.901749i	$0.642284\pi$
$882$	0	0
$883$	−50.6683	−1.70512	−0.852562	−	0.522627i	$-0.824952\pi$
$883$	−50.6683	−1.70512	−0.852562	+	0.522627i	$0.824952\pi$
$884$	49.7380	1.67287
$885$	13.1908	0.443405
$886$	30.2860	1.01748
$887$	23.1852	0.778483	0.389242	−	0.921136i	$-0.372737\pi$
$887$	23.1852	0.778483	0.389242	+	0.921136i	$0.372737\pi$
$888$	−52.4388	−1.75973
$889$	0	0
$890$	−164.507	−5.51428
$891$	3.81355	0.127759
$892$	40.6836	1.36219
$893$	−24.1335	−0.807598
$894$	−25.8071	−0.863118
$895$	−12.0542	−0.402928
$896$	0	0
$897$	22.4703	0.750262
$898$	12.1518	0.405511
$899$	3.74346	0.124851
$900$	46.3489	1.54496
$901$	−24.2658	−0.808409
$902$	9.77216	0.325377
$903$	0	0
$904$	105.788	3.51846
$905$	0.413017	0.0137292
$906$	45.3065	1.50521
$907$	33.2474	1.10396	0.551981	−	0.833856i	$-0.313872\pi$
$907$	33.2474	1.10396	0.551981	+	0.833856i	$0.313872\pi$
$908$	65.6933	2.18011
$909$	−9.17978	−0.304474
$910$	0	0
$911$	15.5992	0.516825	0.258412	−	0.966035i	$-0.416801\pi$
$911$	15.5992	0.516825	0.258412	+	0.966035i	$0.416801\pi$
$912$	−49.9826	−1.65509
$913$	−21.9231	−0.725547
$914$	−12.2826	−0.406271
$915$	−17.1507	−0.566985
$916$	19.1655	0.633247
$917$	0	0
$918$	4.36521	0.144073
$919$	−4.50305	−0.148542	−0.0742709	−	0.997238i	$-0.523663\pi$
$919$	−4.50305	−0.148542	−0.0742709	+	0.997238i	$0.523663\pi$
$920$	89.9528	2.96566
$921$	−4.13968	−0.136407
$922$	−1.22500	−0.0403431
$923$	3.96349	0.130460
$924$	0	0
$925$	80.9374	2.66121
$926$	−11.1812	−0.367437
$927$	12.7010	0.417156
$928$	−57.3544	−1.88275
$929$	4.26219	0.139838	0.0699190	−	0.997553i	$-0.477726\pi$
$929$	4.26219	0.139838	0.0699190	+	0.997553i	$0.477726\pi$
$930$	4.31398	0.141461
$931$	0	0
$932$	−20.8424	−0.682717
$933$	14.6828	0.480694
$934$	−88.5130	−2.89623
$935$	−25.2860	−0.826942
$936$	−42.0486	−1.37440
$937$	25.6728	0.838695	0.419347	−	0.907826i	$-0.362259\pi$
$937$	25.6728	0.838695	0.419347	+	0.907826i	$0.362259\pi$
$938$	0	0
$939$	−32.5963	−1.06374
$940$	−66.2406	−2.16053
$941$	−25.1298	−0.819210	−0.409605	−	0.912263i	$-0.634333\pi$
$941$	−25.1298	−0.819210	−0.409605	+	0.912263i	$0.634333\pi$
$942$	23.7591	0.774113
$943$	3.51424	0.114440
$944$	−26.1584	−0.851383
$945$	0	0
$946$	−62.7024	−2.03863
$947$	1.84065	0.0598131	0.0299065	−	0.999553i	$-0.490479\pi$
$947$	1.84065	0.0598131	0.0299065	+	0.999553i	$0.490479\pi$
$948$	−52.7620	−1.71363
$949$	17.3799	0.564177
$950$	168.424	5.46441
$951$	0.374845	0.0121552
$952$	0	0
$953$	−25.9038	−0.839107	−0.419554	−	0.907731i	$-0.637813\pi$
$953$	−25.9038	−0.839107	−0.419554	+	0.907731i	$0.637813\pi$
$954$	36.5016	1.18178
$955$	−43.7313	−1.41511
$956$	−121.952	−3.94422
$957$	33.0060	1.06693
$958$	−107.513	−3.47358
$959$	0	0
$960$	−6.00795	−0.193906
$961$	−30.8129	−0.993965
$962$	−130.652	−4.21240
$963$	9.75066	0.314211
$964$	−50.2115	−1.61720
$965$	−34.9988	−1.12665
$966$	0	0
$967$	−17.7879	−0.572019	−0.286009	−	0.958227i	$-0.592329\pi$
$967$	−17.7879	−0.572019	−0.286009	+	0.958227i	$0.592329\pi$
$968$	23.3005	0.748905
$969$	11.0310	0.354367
$970$	−28.0996	−0.902222
$971$	−53.5532	−1.71860	−0.859302	−	0.511468i	$-0.829102\pi$
$971$	−53.5532	−1.71860	−0.859302	+	0.511468i	$0.829102\pi$
$972$	−4.56633	−0.146465
$973$	0	0
$974$	33.2106	1.06414
$975$	64.9005	2.07848
$976$	34.0111	1.08867
$977$	31.9422	1.02192	0.510961	−	0.859604i	$-0.329290\pi$
$977$	31.9422	1.02192	0.510961	+	0.859604i	$0.329290\pi$
$978$	54.3717	1.73861
$979$	−62.8990	−2.01026
$980$	0	0
$981$	−15.4367	−0.492855
$982$	−75.1591	−2.39842
$983$	−26.2569	−0.837466	−0.418733	−	0.908109i	$-0.637526\pi$
$983$	−26.2569	−0.837466	−0.418733	+	0.908109i	$0.637526\pi$
$984$	−6.57620	−0.209642
$985$	1.61928	0.0515946
$986$	37.7806	1.20318
$987$	0	0
$988$	−189.068	−6.01504
$989$	−22.5489	−0.717014
$990$	38.0363	1.20887
$991$	−59.4449	−1.88833	−0.944164	−	0.329475i	$-0.893128\pi$
$991$	−59.4449	−1.88833	−0.944164	+	0.329475i	$0.893128\pi$
$992$	−2.86623	−0.0910030
$993$	2.42663	0.0770066
$994$	0	0
$995$	28.0794	0.890178
$996$	26.2506	0.831783
$997$	6.34221	0.200860	0.100430	−	0.994944i	$-0.467978\pi$
$997$	6.34221	0.200860	0.100430	+	0.994944i	$0.467978\pi$
$998$	75.2458	2.38187
$999$	−7.97403	−0.252287

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6027.2.a.bn.1.22	✓	24
7.6	odd	2		6027.2.a.bo.1.22	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6027.2.a.bn.1.22	✓	24	1.1	even	1	trivial
6027.2.a.bo.1.22	yes	24	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)

\(f(q)\)	\(=\)	\(q+2.56249 q^{2} -1.00000 q^{3} +4.56633 q^{4} +3.89232 q^{5} -2.56249 q^{6} +6.57620 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.56249 q^{2} -1.00000 q^{3} +4.56633 q^{4} +3.89232 q^{5} -2.56249 q^{6} +6.57620 q^{8} +1.00000 q^{9} +9.97400 q^{10} +3.81355 q^{11} -4.56633 q^{12} -6.39406 q^{13} -3.89232 q^{15} +7.71874 q^{16} -1.70351 q^{17} +2.56249 q^{18} +6.47548 q^{19} +17.7736 q^{20} +9.77216 q^{22} +3.51424 q^{23} -6.57620 q^{24} +10.1501 q^{25} -16.3847 q^{26} -1.00000 q^{27} -8.65494 q^{29} -9.97400 q^{30} -0.432523 q^{31} +6.62678 q^{32} -3.81355 q^{33} -4.36521 q^{34} +4.56633 q^{36} +7.97403 q^{37} +16.5933 q^{38} +6.39406 q^{39} +25.5966 q^{40} +1.00000 q^{41} -6.41643 q^{43} +17.4139 q^{44} +3.89232 q^{45} +9.00520 q^{46} -3.72691 q^{47} -7.71874 q^{48} +26.0095 q^{50} +1.70351 q^{51} -29.1974 q^{52} +14.2446 q^{53} -2.56249 q^{54} +14.8435 q^{55} -6.47548 q^{57} -22.1782 q^{58} -3.38894 q^{59} -17.7736 q^{60} +4.40630 q^{61} -1.10833 q^{62} +1.54354 q^{64} -24.8877 q^{65} -9.77216 q^{66} +3.61186 q^{67} -7.77878 q^{68} -3.51424 q^{69} -0.619870 q^{71} +6.57620 q^{72} -2.71814 q^{73} +20.4334 q^{74} -10.1501 q^{75} +29.5692 q^{76} +16.3847 q^{78} +11.5546 q^{79} +30.0438 q^{80} +1.00000 q^{81} +2.56249 q^{82} -5.74873 q^{83} -6.63058 q^{85} -16.4420 q^{86} +8.65494 q^{87} +25.0786 q^{88} -16.4936 q^{89} +9.97400 q^{90} +16.0472 q^{92} +0.432523 q^{93} -9.55015 q^{94} +25.2046 q^{95} -6.62678 q^{96} -2.81728 q^{97} +3.81355 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{2} - 24 q^{3} + 32 q^{4} - 4 q^{5} - 8 q^{6} + 24 q^{8} + 24 q^{9}+O(q^{10}) \) 24 * q + 8 * q^2 - 24 * q^3 + 32 * q^4 - 4 * q^5 - 8 * q^6 + 24 * q^8 + 24 * q^9	\( 24 q + 8 q^{2} - 24 q^{3} + 32 q^{4} - 4 q^{5} - 8 q^{6} + 24 q^{8} + 24 q^{9} + 4 q^{10} + 12 q^{11} - 32 q^{12} + 4 q^{15} + 44 q^{16} - 8 q^{17} + 8 q^{18} + 4 q^{19} - 28 q^{20} + 16 q^{22} + 20 q^{23} - 24 q^{24} + 48 q^{25} - 32 q^{26} - 24 q^{27} + 24 q^{29} - 4 q^{30} + 4 q^{31} + 36 q^{32} - 12 q^{33} - 16 q^{34} + 32 q^{36} + 64 q^{37} - 20 q^{38} + 48 q^{40} + 24 q^{41} + 20 q^{43} + 48 q^{44} - 4 q^{45} + 28 q^{46} - 32 q^{47} - 44 q^{48} - 20 q^{50} + 8 q^{51} + 76 q^{53} - 8 q^{54} + 24 q^{55} - 4 q^{57} + 28 q^{58} - 28 q^{59} + 28 q^{60} + 28 q^{61} + 4 q^{62} + 48 q^{64} + 28 q^{65} - 16 q^{66} + 44 q^{67} + 32 q^{68} - 20 q^{69} + 20 q^{71} + 24 q^{72} + 16 q^{73} + 44 q^{74} - 48 q^{75} + 16 q^{76} + 32 q^{78} + 4 q^{79} - 44 q^{80} + 24 q^{81} + 8 q^{82} - 8 q^{83} + 28 q^{85} + 56 q^{86} - 24 q^{87} + 60 q^{88} - 60 q^{89} + 4 q^{90} + 60 q^{92} - 4 q^{93} - 24 q^{94} + 28 q^{95} - 36 q^{96} + 48 q^{97} + 12 q^{99}+O(q^{100}) \) 24 * q + 8 * q^2 - 24 * q^3 + 32 * q^4 - 4 * q^5 - 8 * q^6 + 24 * q^8 + 24 * q^9 + 4 * q^10 + 12 * q^11 - 32 * q^12 + 4 * q^15 + 44 * q^16 - 8 * q^17 + 8 * q^18 + 4 * q^19 - 28 * q^20 + 16 * q^22 + 20 * q^23 - 24 * q^24 + 48 * q^25 - 32 * q^26 - 24 * q^27 + 24 * q^29 - 4 * q^30 + 4 * q^31 + 36 * q^32 - 12 * q^33 - 16 * q^34 + 32 * q^36 + 64 * q^37 - 20 * q^38 + 48 * q^40 + 24 * q^41 + 20 * q^43 + 48 * q^44 - 4 * q^45 + 28 * q^46 - 32 * q^47 - 44 * q^48 - 20 * q^50 + 8 * q^51 + 76 * q^53 - 8 * q^54 + 24 * q^55 - 4 * q^57 + 28 * q^58 - 28 * q^59 + 28 * q^60 + 28 * q^61 + 4 * q^62 + 48 * q^64 + 28 * q^65 - 16 * q^66 + 44 * q^67 + 32 * q^68 - 20 * q^69 + 20 * q^71 + 24 * q^72 + 16 * q^73 + 44 * q^74 - 48 * q^75 + 16 * q^76 + 32 * q^78 + 4 * q^79 - 44 * q^80 + 24 * q^81 + 8 * q^82 - 8 * q^83 + 28 * q^85 + 56 * q^86 - 24 * q^87 + 60 * q^88 - 60 * q^89 + 4 * q^90 + 60 * q^92 - 4 * q^93 - 24 * q^94 + 28 * q^95 - 36 * q^96 + 48 * q^97 + 12 * q^99

Introduction

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