LMFDB - Embedded newform 2842.2.a.i.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2842,2,Mod(1,2842)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2842, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2842.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2842 = 2 \cdot 7^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2842.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:	$22.6934842544$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{12})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 3 $ x^2 - 3
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 406)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1.73205$ of defining polynomial
Character	$\chi$	$=$	2842.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.00000 q^{3} +1.00000 q^{4} +0.732051 q^{5} -2.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.00000 q^{3} +1.00000 q^{4} +0.732051 q^{5} -2.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +0.732051 q^{10} +3.46410 q^{11} -2.00000 q^{12} -0.732051 q^{13} -1.46410 q^{15} +1.00000 q^{16} -4.19615 q^{17} +1.00000 q^{18} -3.46410 q^{19} +0.732051 q^{20} +3.46410 q^{22} -8.92820 q^{23} -2.00000 q^{24} -4.46410 q^{25} -0.732051 q^{26} +4.00000 q^{27} -1.00000 q^{29} -1.46410 q^{30} +2.19615 q^{31} +1.00000 q^{32} -6.92820 q^{33} -4.19615 q^{34} +1.00000 q^{36} -4.00000 q^{37} -3.46410 q^{38} +1.46410 q^{39} +0.732051 q^{40} +9.66025 q^{41} -2.92820 q^{43} +3.46410 q^{44} +0.732051 q^{45} -8.92820 q^{46} +7.66025 q^{47} -2.00000 q^{48} -4.46410 q^{50} +8.39230 q^{51} -0.732051 q^{52} +4.92820 q^{53} +4.00000 q^{54} +2.53590 q^{55} +6.92820 q^{57} -1.00000 q^{58} -10.7321 q^{59} -1.46410 q^{60} -4.00000 q^{61} +2.19615 q^{62} +1.00000 q^{64} -0.535898 q^{65} -6.92820 q^{66} -6.92820 q^{67} -4.19615 q^{68} +17.8564 q^{69} +8.92820 q^{71} +1.00000 q^{72} -5.26795 q^{73} -4.00000 q^{74} +8.92820 q^{75} -3.46410 q^{76} +1.46410 q^{78} -2.53590 q^{79} +0.732051 q^{80} -11.0000 q^{81} +9.66025 q^{82} -16.5885 q^{83} -3.07180 q^{85} -2.92820 q^{86} +2.00000 q^{87} +3.46410 q^{88} -16.1962 q^{89} +0.732051 q^{90} -8.92820 q^{92} -4.39230 q^{93} +7.66025 q^{94} -2.53590 q^{95} -2.00000 q^{96} +6.73205 q^{97} +3.46410 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 4 q^{3} + 2 q^{4} - 2 q^{5} - 4 q^{6} + 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 - 4 * q^3 + 2 * q^4 - 2 * q^5 - 4 * q^6 + 2 * q^8 + 2 * q^9	$ 2 q + 2 q^{2} - 4 q^{3} + 2 q^{4} - 2 q^{5} - 4 q^{6} + 2 q^{8} + 2 q^{9} - 2 q^{10} - 4 q^{12} + 2 q^{13} + 4 q^{15} + 2 q^{16} + 2 q^{17} + 2 q^{18} - 2 q^{20} - 4 q^{23} - 4 q^{24} - 2 q^{25} + 2 q^{26} + 8 q^{27} - 2 q^{29} + 4 q^{30} - 6 q^{31} + 2 q^{32} + 2 q^{34} + 2 q^{36} - 8 q^{37} - 4 q^{39} - 2 q^{40} + 2 q^{41} + 8 q^{43} - 2 q^{45} - 4 q^{46} - 2 q^{47} - 4 q^{48} - 2 q^{50} - 4 q^{51} + 2 q^{52} - 4 q^{53} + 8 q^{54} + 12 q^{55} - 2 q^{58} - 18 q^{59} + 4 q^{60} - 8 q^{61} - 6 q^{62} + 2 q^{64} - 8 q^{65} + 2 q^{68} + 8 q^{69} + 4 q^{71} + 2 q^{72} - 14 q^{73} - 8 q^{74} + 4 q^{75} - 4 q^{78} - 12 q^{79} - 2 q^{80} - 22 q^{81} + 2 q^{82} - 2 q^{83} - 20 q^{85} + 8 q^{86} + 4 q^{87} - 22 q^{89} - 2 q^{90} - 4 q^{92} + 12 q^{93} - 2 q^{94} - 12 q^{95} - 4 q^{96} + 10 q^{97}+O(q^{100}) $ 2 * q + 2 * q^2 - 4 * q^3 + 2 * q^4 - 2 * q^5 - 4 * q^6 + 2 * q^8 + 2 * q^9 - 2 * q^10 - 4 * q^12 + 2 * q^13 + 4 * q^15 + 2 * q^16 + 2 * q^17 + 2 * q^18 - 2 * q^20 - 4 * q^23 - 4 * q^24 - 2 * q^25 + 2 * q^26 + 8 * q^27 - 2 * q^29 + 4 * q^30 - 6 * q^31 + 2 * q^32 + 2 * q^34 + 2 * q^36 - 8 * q^37 - 4 * q^39 - 2 * q^40 + 2 * q^41 + 8 * q^43 - 2 * q^45 - 4 * q^46 - 2 * q^47 - 4 * q^48 - 2 * q^50 - 4 * q^51 + 2 * q^52 - 4 * q^53 + 8 * q^54 + 12 * q^55 - 2 * q^58 - 18 * q^59 + 4 * q^60 - 8 * q^61 - 6 * q^62 + 2 * q^64 - 8 * q^65 + 2 * q^68 + 8 * q^69 + 4 * q^71 + 2 * q^72 - 14 * q^73 - 8 * q^74 + 4 * q^75 - 4 * q^78 - 12 * q^79 - 2 * q^80 - 22 * q^81 + 2 * q^82 - 2 * q^83 - 20 * q^85 + 8 * q^86 + 4 * q^87 - 22 * q^89 - 2 * q^90 - 4 * q^92 + 12 * q^93 - 2 * q^94 - 12 * q^95 - 4 * q^96 + 10 * q^97

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−2.00000	−1.15470	−0.577350	−	0.816497i	$-0.695913\pi$
$3$	−2.00000	−1.15470	−0.577350	+	0.816497i	$0.695913\pi$
$4$	1.00000	0.500000
$5$	0.732051	0.327383	0.163692	−	0.986512i	$-0.447660\pi$
$5$	0.732051	0.327383	0.163692	+	0.986512i	$0.447660\pi$
$6$	−2.00000	−0.816497
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	0.732051	0.231495
$11$	3.46410	1.04447	0.522233	−	0.852803i	$-0.325099\pi$
$11$	3.46410	1.04447	0.522233	+	0.852803i	$0.325099\pi$
$12$	−2.00000	−0.577350
$13$	−0.732051	−0.203034	−0.101517	−	0.994834i	$-0.532370\pi$
$13$	−0.732051	−0.203034	−0.101517	+	0.994834i	$0.532370\pi$
$14$	0	0
$15$	−1.46410	−0.378029
$16$	1.00000	0.250000
$17$	−4.19615	−1.01772	−0.508858	−	0.860850i	$-0.669932\pi$
$17$	−4.19615	−1.01772	−0.508858	+	0.860850i	$0.669932\pi$
$18$	1.00000	0.235702
$19$	−3.46410	−0.794719	−0.397360	−	0.917663i	$-0.630073\pi$
$19$	−3.46410	−0.794719	−0.397360	+	0.917663i	$0.630073\pi$
$20$	0.732051	0.163692
$21$	0	0
$22$	3.46410	0.738549
$23$	−8.92820	−1.86166	−0.930830	−	0.365454i	$-0.880914\pi$
$23$	−8.92820	−1.86166	−0.930830	+	0.365454i	$0.880914\pi$
$24$	−2.00000	−0.408248
$25$	−4.46410	−0.892820
$26$	−0.732051	−0.143567
$27$	4.00000	0.769800
$28$	0	0
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	−1.46410	−0.267307
$31$	2.19615	0.394441	0.197220	−	0.980359i	$-0.436809\pi$
$31$	2.19615	0.394441	0.197220	+	0.980359i	$0.436809\pi$
$32$	1.00000	0.176777
$33$	−6.92820	−1.20605
$34$	−4.19615	−0.719634
$35$	0	0
$36$	1.00000	0.166667
$37$	−4.00000	−0.657596	−0.328798	−	0.944400i	$-0.606644\pi$
$37$	−4.00000	−0.657596	−0.328798	+	0.944400i	$0.606644\pi$
$38$	−3.46410	−0.561951
$39$	1.46410	0.234444
$40$	0.732051	0.115747
$41$	9.66025	1.50868	0.754339	−	0.656485i	$-0.227957\pi$
$41$	9.66025	1.50868	0.754339	+	0.656485i	$0.227957\pi$
$42$	0	0
$43$	−2.92820	−0.446547	−0.223273	−	0.974756i	$-0.571674\pi$
$43$	−2.92820	−0.446547	−0.223273	+	0.974756i	$0.571674\pi$
$44$	3.46410	0.522233
$45$	0.732051	0.109128
$46$	−8.92820	−1.31639
$47$	7.66025	1.11736	0.558681	−	0.829382i	$-0.311307\pi$
$47$	7.66025	1.11736	0.558681	+	0.829382i	$0.311307\pi$
$48$	−2.00000	−0.288675
$49$	0	0
$50$	−4.46410	−0.631319
$51$	8.39230	1.17516
$52$	−0.732051	−0.101517
$53$	4.92820	0.676941	0.338470	−	0.940977i	$-0.390091\pi$
$53$	4.92820	0.676941	0.338470	+	0.940977i	$0.390091\pi$
$54$	4.00000	0.544331
$55$	2.53590	0.341940
$56$	0	0
$57$	6.92820	0.917663
$58$	−1.00000	−0.131306
$59$	−10.7321	−1.39719	−0.698597	−	0.715515i	$-0.746192\pi$
$59$	−10.7321	−1.39719	−0.698597	+	0.715515i	$0.746192\pi$
$60$	−1.46410	−0.189015
$61$	−4.00000	−0.512148	−0.256074	−	0.966657i	$-0.582429\pi$
$61$	−4.00000	−0.512148	−0.256074	+	0.966657i	$0.582429\pi$
$62$	2.19615	0.278912
$63$	0	0
$64$	1.00000	0.125000
$65$	−0.535898	−0.0664700
$66$	−6.92820	−0.852803
$67$	−6.92820	−0.846415	−0.423207	−	0.906033i	$-0.639096\pi$
$67$	−6.92820	−0.846415	−0.423207	+	0.906033i	$0.639096\pi$
$68$	−4.19615	−0.508858
$69$	17.8564	2.14966
$70$	0	0
$71$	8.92820	1.05958	0.529791	−	0.848128i	$-0.322270\pi$
$71$	8.92820	1.05958	0.529791	+	0.848128i	$0.322270\pi$
$72$	1.00000	0.117851
$73$	−5.26795	−0.616567	−0.308283	−	0.951295i	$-0.599755\pi$
$73$	−5.26795	−0.616567	−0.308283	+	0.951295i	$0.599755\pi$
$74$	−4.00000	−0.464991
$75$	8.92820	1.03094
$76$	−3.46410	−0.397360
$77$	0	0
$78$	1.46410	0.165777
$79$	−2.53590	−0.285311	−0.142655	−	0.989772i	$-0.545564\pi$
$79$	−2.53590	−0.285311	−0.142655	+	0.989772i	$0.545564\pi$
$80$	0.732051	0.0818458
$81$	−11.0000	−1.22222
$82$	9.66025	1.06680
$83$	−16.5885	−1.82082	−0.910410	−	0.413707i	$-0.864234\pi$
$83$	−16.5885	−1.82082	−0.910410	+	0.413707i	$0.864234\pi$
$84$	0	0
$85$	−3.07180	−0.333183
$86$	−2.92820	−0.315756
$87$	2.00000	0.214423
$88$	3.46410	0.369274
$89$	−16.1962	−1.71679	−0.858394	−	0.512990i	$-0.828538\pi$
$89$	−16.1962	−1.71679	−0.858394	+	0.512990i	$0.828538\pi$
$90$	0.732051	0.0771649
$91$	0	0
$92$	−8.92820	−0.930830
$93$	−4.39230	−0.455461
$94$	7.66025	0.790095
$95$	−2.53590	−0.260178
$96$	−2.00000	−0.204124
$97$	6.73205	0.683536	0.341768	−	0.939784i	$-0.388974\pi$
$97$	6.73205	0.683536	0.341768	+	0.939784i	$0.388974\pi$
$98$	0	0
$99$	3.46410	0.348155
$100$	−4.46410	−0.446410
$101$	−4.00000	−0.398015	−0.199007	−	0.979998i	$-0.563772\pi$
$101$	−4.00000	−0.398015	−0.199007	+	0.979998i	$0.563772\pi$
$102$	8.39230	0.830962
$103$	−5.46410	−0.538394	−0.269197	−	0.963085i	$-0.586758\pi$
$103$	−5.46410	−0.538394	−0.269197	+	0.963085i	$0.586758\pi$
$104$	−0.732051	−0.0717835
$105$	0	0
$106$	4.92820	0.478669
$107$	4.00000	0.386695	0.193347	−	0.981130i	$-0.438066\pi$
$107$	4.00000	0.386695	0.193347	+	0.981130i	$0.438066\pi$
$108$	4.00000	0.384900
$109$	−10.0000	−0.957826	−0.478913	−	0.877862i	$-0.658969\pi$
$109$	−10.0000	−0.957826	−0.478913	+	0.877862i	$0.658969\pi$
$110$	2.53590	0.241788
$111$	8.00000	0.759326
$112$	0	0
$113$	−3.46410	−0.325875	−0.162938	−	0.986636i	$-0.552097\pi$
$113$	−3.46410	−0.325875	−0.162938	+	0.986636i	$0.552097\pi$
$114$	6.92820	0.648886
$115$	−6.53590	−0.609476
$116$	−1.00000	−0.0928477
$117$	−0.732051	−0.0676781
$118$	−10.7321	−0.987965
$119$	0	0
$120$	−1.46410	−0.133654
$121$	1.00000	0.0909091
$122$	−4.00000	−0.362143
$123$	−19.3205	−1.74207
$124$	2.19615	0.197220
$125$	−6.92820	−0.619677
$126$	0	0
$127$	−6.53590	−0.579967	−0.289984	−	0.957032i	$-0.593650\pi$
$127$	−6.53590	−0.579967	−0.289984	+	0.957032i	$0.593650\pi$
$128$	1.00000	0.0883883
$129$	5.85641	0.515628
$130$	−0.535898	−0.0470014
$131$	−8.53590	−0.745785	−0.372892	−	0.927875i	$-0.621634\pi$
$131$	−8.53590	−0.745785	−0.372892	+	0.927875i	$0.621634\pi$
$132$	−6.92820	−0.603023
$133$	0	0
$134$	−6.92820	−0.598506
$135$	2.92820	0.252020
$136$	−4.19615	−0.359817
$137$	−15.4641	−1.32119	−0.660594	−	0.750744i	$-0.729695\pi$
$137$	−15.4641	−1.32119	−0.660594	+	0.750744i	$0.729695\pi$
$138$	17.8564	1.52004
$139$	9.26795	0.786097	0.393049	−	0.919518i	$-0.371420\pi$
$139$	9.26795	0.786097	0.393049	+	0.919518i	$0.371420\pi$
$140$	0	0
$141$	−15.3205	−1.29022
$142$	8.92820	0.749238
$143$	−2.53590	−0.212062
$144$	1.00000	0.0833333
$145$	−0.732051	−0.0607935
$146$	−5.26795	−0.435979
$147$	0	0
$148$	−4.00000	−0.328798
$149$	−3.46410	−0.283790	−0.141895	−	0.989882i	$-0.545320\pi$
$149$	−3.46410	−0.283790	−0.141895	+	0.989882i	$0.545320\pi$
$150$	8.92820	0.728985
$151$	15.8564	1.29038	0.645188	−	0.764024i	$-0.276779\pi$
$151$	15.8564	1.29038	0.645188	+	0.764024i	$0.276779\pi$
$152$	−3.46410	−0.280976
$153$	−4.19615	−0.339239
$154$	0	0
$155$	1.60770	0.129133
$156$	1.46410	0.117222
$157$	−11.3205	−0.903475	−0.451737	−	0.892151i	$-0.649196\pi$
$157$	−11.3205	−0.903475	−0.451737	+	0.892151i	$0.649196\pi$
$158$	−2.53590	−0.201745
$159$	−9.85641	−0.781664
$160$	0.732051	0.0578737
$161$	0	0
$162$	−11.0000	−0.864242
$163$	15.4641	1.21124	0.605621	−	0.795753i	$-0.292925\pi$
$163$	15.4641	1.21124	0.605621	+	0.795753i	$0.292925\pi$
$164$	9.66025	0.754339
$165$	−5.07180	−0.394839
$166$	−16.5885	−1.28751
$167$	2.92820	0.226591	0.113296	−	0.993561i	$-0.463859\pi$
$167$	2.92820	0.226591	0.113296	+	0.993561i	$0.463859\pi$
$168$	0	0
$169$	−12.4641	−0.958777
$170$	−3.07180	−0.235596
$171$	−3.46410	−0.264906
$172$	−2.92820	−0.223273
$173$	−16.7321	−1.27211	−0.636057	−	0.771642i	$-0.719436\pi$
$173$	−16.7321	−1.27211	−0.636057	+	0.771642i	$0.719436\pi$
$174$	2.00000	0.151620
$175$	0	0
$176$	3.46410	0.261116
$177$	21.4641	1.61334
$178$	−16.1962	−1.21395
$179$	20.0000	1.49487	0.747435	−	0.664335i	$-0.231285\pi$
$179$	20.0000	1.49487	0.747435	+	0.664335i	$0.231285\pi$
$180$	0.732051	0.0545638
$181$	15.2679	1.13486	0.567429	−	0.823422i	$-0.307938\pi$
$181$	15.2679	1.13486	0.567429	+	0.823422i	$0.307938\pi$
$182$	0	0
$183$	8.00000	0.591377
$184$	−8.92820	−0.658196
$185$	−2.92820	−0.215286
$186$	−4.39230	−0.322059
$187$	−14.5359	−1.06297
$188$	7.66025	0.558681
$189$	0	0
$190$	−2.53590	−0.183973
$191$	−0.392305	−0.0283862	−0.0141931	−	0.999899i	$-0.504518\pi$
$191$	−0.392305	−0.0283862	−0.0141931	+	0.999899i	$0.504518\pi$
$192$	−2.00000	−0.144338
$193$	−14.3923	−1.03598	−0.517990	−	0.855386i	$-0.673320\pi$
$193$	−14.3923	−1.03598	−0.517990	+	0.855386i	$0.673320\pi$
$194$	6.73205	0.483333
$195$	1.07180	0.0767530
$196$	0	0
$197$	−20.5359	−1.46312	−0.731561	−	0.681776i	$-0.761208\pi$
$197$	−20.5359	−1.46312	−0.731561	+	0.681776i	$0.761208\pi$
$198$	3.46410	0.246183
$199$	−17.4641	−1.23800	−0.618999	−	0.785392i	$-0.712461\pi$
$199$	−17.4641	−1.23800	−0.618999	+	0.785392i	$0.712461\pi$
$200$	−4.46410	−0.315660
$201$	13.8564	0.977356
$202$	−4.00000	−0.281439
$203$	0	0
$204$	8.39230	0.587579
$205$	7.07180	0.493916
$206$	−5.46410	−0.380702
$207$	−8.92820	−0.620553
$208$	−0.732051	−0.0507586
$209$	−12.0000	−0.830057
$210$	0	0
$211$	6.92820	0.476957	0.238479	−	0.971148i	$-0.423351\pi$
$211$	6.92820	0.476957	0.238479	+	0.971148i	$0.423351\pi$
$212$	4.92820	0.338470
$213$	−17.8564	−1.22350
$214$	4.00000	0.273434
$215$	−2.14359	−0.146192
$216$	4.00000	0.272166
$217$	0	0
$218$	−10.0000	−0.677285
$219$	10.5359	0.711950
$220$	2.53590	0.170970
$221$	3.07180	0.206631
$222$	8.00000	0.536925
$223$	0.392305	0.0262707	0.0131353	−	0.999914i	$-0.495819\pi$
$223$	0.392305	0.0262707	0.0131353	+	0.999914i	$0.495819\pi$
$224$	0	0
$225$	−4.46410	−0.297607
$226$	−3.46410	−0.230429
$227$	12.5885	0.835525	0.417763	−	0.908556i	$-0.362814\pi$
$227$	12.5885	0.835525	0.417763	+	0.908556i	$0.362814\pi$
$228$	6.92820	0.458831
$229$	12.3923	0.818907	0.409453	−	0.912331i	$-0.365719\pi$
$229$	12.3923	0.818907	0.409453	+	0.912331i	$0.365719\pi$
$230$	−6.53590	−0.430964
$231$	0	0
$232$	−1.00000	−0.0656532
$233$	27.8564	1.82493	0.912467	−	0.409150i	$-0.134175\pi$
$233$	27.8564	1.82493	0.912467	+	0.409150i	$0.134175\pi$
$234$	−0.732051	−0.0478557
$235$	5.60770	0.365806
$236$	−10.7321	−0.698597
$237$	5.07180	0.329449
$238$	0	0
$239$	27.7128	1.79259	0.896296	−	0.443455i	$-0.146248\pi$
$239$	27.7128	1.79259	0.896296	+	0.443455i	$0.146248\pi$
$240$	−1.46410	−0.0945074
$241$	16.9282	1.09044	0.545221	−	0.838293i	$-0.316446\pi$
$241$	16.9282	1.09044	0.545221	+	0.838293i	$0.316446\pi$
$242$	1.00000	0.0642824
$243$	10.0000	0.641500
$244$	−4.00000	−0.256074
$245$	0	0
$246$	−19.3205	−1.23183
$247$	2.53590	0.161355
$248$	2.19615	0.139456
$249$	33.1769	2.10250
$250$	−6.92820	−0.438178
$251$	10.3923	0.655956	0.327978	−	0.944685i	$-0.393633\pi$
$251$	10.3923	0.655956	0.327978	+	0.944685i	$0.393633\pi$
$252$	0	0
$253$	−30.9282	−1.94444
$254$	−6.53590	−0.410099
$255$	6.14359	0.384727
$256$	1.00000	0.0625000
$257$	−19.4641	−1.21414	−0.607069	−	0.794649i	$-0.707655\pi$
$257$	−19.4641	−1.21414	−0.607069	+	0.794649i	$0.707655\pi$
$258$	5.85641	0.364604
$259$	0	0
$260$	−0.535898	−0.0332350
$261$	−1.00000	−0.0618984
$262$	−8.53590	−0.527350
$263$	16.3923	1.01079	0.505396	−	0.862887i	$-0.331346\pi$
$263$	16.3923	1.01079	0.505396	+	0.862887i	$0.331346\pi$
$264$	−6.92820	−0.426401
$265$	3.60770	0.221619
$266$	0	0
$267$	32.3923	1.98238
$268$	−6.92820	−0.423207
$269$	1.85641	0.113187	0.0565935	−	0.998397i	$-0.481976\pi$
$269$	1.85641	0.113187	0.0565935	+	0.998397i	$0.481976\pi$
$270$	2.92820	0.178205
$271$	−14.5885	−0.886186	−0.443093	−	0.896476i	$-0.646119\pi$
$271$	−14.5885	−0.886186	−0.443093	+	0.896476i	$0.646119\pi$
$272$	−4.19615	−0.254429
$273$	0	0
$274$	−15.4641	−0.934221
$275$	−15.4641	−0.932520
$276$	17.8564	1.07483
$277$	−18.3923	−1.10509	−0.552543	−	0.833484i	$-0.686343\pi$
$277$	−18.3923	−1.10509	−0.552543	+	0.833484i	$0.686343\pi$
$278$	9.26795	0.555855
$279$	2.19615	0.131480
$280$	0	0
$281$	−14.5359	−0.867139	−0.433569	−	0.901120i	$-0.642746\pi$
$281$	−14.5359	−0.867139	−0.433569	+	0.901120i	$0.642746\pi$
$282$	−15.3205	−0.912323
$283$	−16.5885	−0.986081	−0.493041	−	0.870006i	$-0.664115\pi$
$283$	−16.5885	−0.986081	−0.493041	+	0.870006i	$0.664115\pi$
$284$	8.92820	0.529791
$285$	5.07180	0.300427
$286$	−2.53590	−0.149951
$287$	0	0
$288$	1.00000	0.0589256
$289$	0.607695	0.0357468
$290$	−0.732051	−0.0429875
$291$	−13.4641	−0.789280
$292$	−5.26795	−0.308283
$293$	−3.60770	−0.210764	−0.105382	−	0.994432i	$-0.533606\pi$
$293$	−3.60770	−0.210764	−0.105382	+	0.994432i	$0.533606\pi$
$294$	0	0
$295$	−7.85641	−0.457418
$296$	−4.00000	−0.232495
$297$	13.8564	0.804030
$298$	−3.46410	−0.200670
$299$	6.53590	0.377981
$300$	8.92820	0.515470
$301$	0	0
$302$	15.8564	0.912434
$303$	8.00000	0.459588
$304$	−3.46410	−0.198680
$305$	−2.92820	−0.167668
$306$	−4.19615	−0.239878
$307$	3.07180	0.175317	0.0876584	−	0.996151i	$-0.472062\pi$
$307$	3.07180	0.175317	0.0876584	+	0.996151i	$0.472062\pi$
$308$	0	0
$309$	10.9282	0.621684
$310$	1.60770	0.0913109
$311$	29.1244	1.65149	0.825745	−	0.564043i	$-0.190755\pi$
$311$	29.1244	1.65149	0.825745	+	0.564043i	$0.190755\pi$
$312$	1.46410	0.0828884
$313$	19.8564	1.12235	0.561175	−	0.827697i	$-0.310349\pi$
$313$	19.8564	1.12235	0.561175	+	0.827697i	$0.310349\pi$
$314$	−11.3205	−0.638853
$315$	0	0
$316$	−2.53590	−0.142655
$317$	0.928203	0.0521331	0.0260665	−	0.999660i	$-0.491702\pi$
$317$	0.928203	0.0521331	0.0260665	+	0.999660i	$0.491702\pi$
$318$	−9.85641	−0.552720
$319$	−3.46410	−0.193952
$320$	0.732051	0.0409229
$321$	−8.00000	−0.446516
$322$	0	0
$323$	14.5359	0.808799
$324$	−11.0000	−0.611111
$325$	3.26795	0.181273
$326$	15.4641	0.856477
$327$	20.0000	1.10600
$328$	9.66025	0.533398
$329$	0	0
$330$	−5.07180	−0.279193
$331$	24.7846	1.36229	0.681143	−	0.732151i	$-0.261483\pi$
$331$	24.7846	1.36229	0.681143	+	0.732151i	$0.261483\pi$
$332$	−16.5885	−0.910410
$333$	−4.00000	−0.219199
$334$	2.92820	0.160224
$335$	−5.07180	−0.277102
$336$	0	0
$337$	−14.0000	−0.762629	−0.381314	−	0.924445i	$-0.624528\pi$
$337$	−14.0000	−0.762629	−0.381314	+	0.924445i	$0.624528\pi$
$338$	−12.4641	−0.677958
$339$	6.92820	0.376288
$340$	−3.07180	−0.166592
$341$	7.60770	0.411980
$342$	−3.46410	−0.187317
$343$	0	0
$344$	−2.92820	−0.157878
$345$	13.0718	0.703762
$346$	−16.7321	−0.899521
$347$	20.3923	1.09472	0.547358	−	0.836898i	$-0.315634\pi$
$347$	20.3923	1.09472	0.547358	+	0.836898i	$0.315634\pi$
$348$	2.00000	0.107211
$349$	14.1962	0.759903	0.379951	−	0.925006i	$-0.375941\pi$
$349$	14.1962	0.759903	0.379951	+	0.925006i	$0.375941\pi$
$350$	0	0
$351$	−2.92820	−0.156296
$352$	3.46410	0.184637
$353$	−11.8564	−0.631053	−0.315526	−	0.948917i	$-0.602181\pi$
$353$	−11.8564	−0.631053	−0.315526	+	0.948917i	$0.602181\pi$
$354$	21.4641	1.14080
$355$	6.53590	0.346889
$356$	−16.1962	−0.858394
$357$	0	0
$358$	20.0000	1.05703
$359$	−34.2487	−1.80758	−0.903789	−	0.427978i	$-0.859226\pi$
$359$	−34.2487	−1.80758	−0.903789	+	0.427978i	$0.859226\pi$
$360$	0.732051	0.0385825
$361$	−7.00000	−0.368421
$362$	15.2679	0.802466
$363$	−2.00000	−0.104973
$364$	0	0
$365$	−3.85641	−0.201854
$366$	8.00000	0.418167
$367$	−3.66025	−0.191064	−0.0955319	−	0.995426i	$-0.530455\pi$
$367$	−3.66025	−0.191064	−0.0955319	+	0.995426i	$0.530455\pi$
$368$	−8.92820	−0.465415
$369$	9.66025	0.502893
$370$	−2.92820	−0.152230
$371$	0	0
$372$	−4.39230	−0.227730
$373$	3.46410	0.179364	0.0896822	−	0.995970i	$-0.471415\pi$
$373$	3.46410	0.179364	0.0896822	+	0.995970i	$0.471415\pi$
$374$	−14.5359	−0.751633
$375$	13.8564	0.715542
$376$	7.66025	0.395047
$377$	0.732051	0.0377025
$378$	0	0
$379$	−24.7846	−1.27310	−0.636550	−	0.771235i	$-0.719639\pi$
$379$	−24.7846	−1.27310	−0.636550	+	0.771235i	$0.719639\pi$
$380$	−2.53590	−0.130089
$381$	13.0718	0.669688
$382$	−0.392305	−0.0200721
$383$	16.0000	0.817562	0.408781	−	0.912633i	$-0.365954\pi$
$383$	16.0000	0.817562	0.408781	+	0.912633i	$0.365954\pi$
$384$	−2.00000	−0.102062
$385$	0	0
$386$	−14.3923	−0.732549
$387$	−2.92820	−0.148849
$388$	6.73205	0.341768
$389$	5.07180	0.257150	0.128575	−	0.991700i	$-0.458960\pi$
$389$	5.07180	0.257150	0.128575	+	0.991700i	$0.458960\pi$
$390$	1.07180	0.0542725
$391$	37.4641	1.89464
$392$	0	0
$393$	17.0718	0.861158
$394$	−20.5359	−1.03458
$395$	−1.85641	−0.0934059
$396$	3.46410	0.174078
$397$	−1.12436	−0.0564298	−0.0282149	−	0.999602i	$-0.508982\pi$
$397$	−1.12436	−0.0564298	−0.0282149	+	0.999602i	$0.508982\pi$
$398$	−17.4641	−0.875396
$399$	0	0
$400$	−4.46410	−0.223205
$401$	7.85641	0.392330	0.196165	−	0.980571i	$-0.437151\pi$
$401$	7.85641	0.392330	0.196165	+	0.980571i	$0.437151\pi$
$402$	13.8564	0.691095
$403$	−1.60770	−0.0800850
$404$	−4.00000	−0.199007
$405$	−8.05256	−0.400135
$406$	0	0
$407$	−13.8564	−0.686837
$408$	8.39230	0.415481
$409$	−15.1244	−0.747851	−0.373926	−	0.927459i	$-0.621988\pi$
$409$	−15.1244	−0.747851	−0.373926	+	0.927459i	$0.621988\pi$
$410$	7.07180	0.349251
$411$	30.9282	1.52558
$412$	−5.46410	−0.269197
$413$	0	0
$414$	−8.92820	−0.438797
$415$	−12.1436	−0.596106
$416$	−0.732051	−0.0358917
$417$	−18.5359	−0.907707
$418$	−12.0000	−0.586939
$419$	−16.1962	−0.791234	−0.395617	−	0.918416i	$-0.629469\pi$
$419$	−16.1962	−0.791234	−0.395617	+	0.918416i	$0.629469\pi$
$420$	0	0
$421$	4.78461	0.233188	0.116594	−	0.993180i	$-0.462802\pi$
$421$	4.78461	0.233188	0.116594	+	0.993180i	$0.462802\pi$
$422$	6.92820	0.337260
$423$	7.66025	0.372454
$424$	4.92820	0.239335
$425$	18.7321	0.908638
$426$	−17.8564	−0.865146
$427$	0	0
$428$	4.00000	0.193347
$429$	5.07180	0.244869
$430$	−2.14359	−0.103373
$431$	−19.7128	−0.949533	−0.474766	−	0.880112i	$-0.657467\pi$
$431$	−19.7128	−0.949533	−0.474766	+	0.880112i	$0.657467\pi$
$432$	4.00000	0.192450
$433$	−9.26795	−0.445389	−0.222695	−	0.974888i	$-0.571485\pi$
$433$	−9.26795	−0.445389	−0.222695	+	0.974888i	$0.571485\pi$
$434$	0	0
$435$	1.46410	0.0701983
$436$	−10.0000	−0.478913
$437$	30.9282	1.47950
$438$	10.5359	0.503425
$439$	31.7128	1.51357	0.756785	−	0.653664i	$-0.226769\pi$
$439$	31.7128	1.51357	0.756785	+	0.653664i	$0.226769\pi$
$440$	2.53590	0.120894
$441$	0	0
$442$	3.07180	0.146110
$443$	−28.5359	−1.35578	−0.677891	−	0.735163i	$-0.737106\pi$
$443$	−28.5359	−1.35578	−0.677891	+	0.735163i	$0.737106\pi$
$444$	8.00000	0.379663
$445$	−11.8564	−0.562048
$446$	0.392305	0.0185762
$447$	6.92820	0.327693
$448$	0	0
$449$	41.7128	1.96855	0.984275	−	0.176645i	$-0.0565244\pi$
$449$	41.7128	1.96855	0.984275	+	0.176645i	$0.0565244\pi$
$450$	−4.46410	−0.210440
$451$	33.4641	1.57576
$452$	−3.46410	−0.162938
$453$	−31.7128	−1.49000
$454$	12.5885	0.590806
$455$	0	0
$456$	6.92820	0.324443
$457$	−33.1769	−1.55195	−0.775975	−	0.630763i	$-0.782742\pi$
$457$	−33.1769	−1.55195	−0.775975	+	0.630763i	$0.782742\pi$
$458$	12.3923	0.579054
$459$	−16.7846	−0.783438
$460$	−6.53590	−0.304738
$461$	−9.85641	−0.459059	−0.229529	−	0.973302i	$-0.573719\pi$
$461$	−9.85641	−0.459059	−0.229529	+	0.973302i	$0.573719\pi$
$462$	0	0
$463$	22.0000	1.02243	0.511213	−	0.859454i	$-0.329196\pi$
$463$	22.0000	1.02243	0.511213	+	0.859454i	$0.329196\pi$
$464$	−1.00000	−0.0464238
$465$	−3.21539	−0.149110
$466$	27.8564	1.29042
$467$	−17.3205	−0.801498	−0.400749	−	0.916188i	$-0.631250\pi$
$467$	−17.3205	−0.801498	−0.400749	+	0.916188i	$0.631250\pi$
$468$	−0.732051	−0.0338391
$469$	0	0
$470$	5.60770	0.258664
$471$	22.6410	1.04324
$472$	−10.7321	−0.493983
$473$	−10.1436	−0.466403
$474$	5.07180	0.232955
$475$	15.4641	0.709542
$476$	0	0
$477$	4.92820	0.225647
$478$	27.7128	1.26755
$479$	−17.5167	−0.800357	−0.400178	−	0.916437i	$-0.631052\pi$
$479$	−17.5167	−0.800357	−0.400178	+	0.916437i	$0.631052\pi$
$480$	−1.46410	−0.0668268
$481$	2.92820	0.133515
$482$	16.9282	0.771059
$483$	0	0
$484$	1.00000	0.0454545
$485$	4.92820	0.223778
$486$	10.0000	0.453609
$487$	2.92820	0.132690	0.0663448	−	0.997797i	$-0.478866\pi$
$487$	2.92820	0.132690	0.0663448	+	0.997797i	$0.478866\pi$
$488$	−4.00000	−0.181071
$489$	−30.9282	−1.39862
$490$	0	0
$491$	12.0000	0.541552	0.270776	−	0.962642i	$-0.412720\pi$
$491$	12.0000	0.541552	0.270776	+	0.962642i	$0.412720\pi$
$492$	−19.3205	−0.871036
$493$	4.19615	0.188985
$494$	2.53590	0.114095
$495$	2.53590	0.113980
$496$	2.19615	0.0986102
$497$	0	0
$498$	33.1769	1.48669
$499$	−16.7846	−0.751382	−0.375691	−	0.926745i	$-0.622595\pi$
$499$	−16.7846	−0.751382	−0.375691	+	0.926745i	$0.622595\pi$
$500$	−6.92820	−0.309839
$501$	−5.85641	−0.261645
$502$	10.3923	0.463831
$503$	−13.8038	−0.615483	−0.307742	−	0.951470i	$-0.599573\pi$
$503$	−13.8038	−0.615483	−0.307742	+	0.951470i	$0.599573\pi$
$504$	0	0
$505$	−2.92820	−0.130303
$506$	−30.9282	−1.37493
$507$	24.9282	1.10710
$508$	−6.53590	−0.289984
$509$	−12.3397	−0.546950	−0.273475	−	0.961879i	$-0.588173\pi$
$509$	−12.3397	−0.546950	−0.273475	+	0.961879i	$0.588173\pi$
$510$	6.14359	0.272043
$511$	0	0
$512$	1.00000	0.0441942
$513$	−13.8564	−0.611775
$514$	−19.4641	−0.858525
$515$	−4.00000	−0.176261
$516$	5.85641	0.257814
$517$	26.5359	1.16705
$518$	0	0
$519$	33.4641	1.46891
$520$	−0.535898	−0.0235007
$521$	−35.4641	−1.55371	−0.776855	−	0.629679i	$-0.783186\pi$
$521$	−35.4641	−1.55371	−0.776855	+	0.629679i	$0.783186\pi$
$522$	−1.00000	−0.0437688
$523$	37.2679	1.62961	0.814807	−	0.579733i	$-0.196843\pi$
$523$	37.2679	1.62961	0.814807	+	0.579733i	$0.196843\pi$
$524$	−8.53590	−0.372892
$525$	0	0
$526$	16.3923	0.714738
$527$	−9.21539	−0.401429
$528$	−6.92820	−0.301511
$529$	56.7128	2.46577
$530$	3.60770	0.156708
$531$	−10.7321	−0.465731
$532$	0	0
$533$	−7.07180	−0.306314
$534$	32.3923	1.40175
$535$	2.92820	0.126597
$536$	−6.92820	−0.299253
$537$	−40.0000	−1.72613
$538$	1.85641	0.0800354
$539$	0	0
$540$	2.92820	0.126010
$541$	−8.92820	−0.383853	−0.191927	−	0.981409i	$-0.561474\pi$
$541$	−8.92820	−0.383853	−0.191927	+	0.981409i	$0.561474\pi$
$542$	−14.5885	−0.626628
$543$	−30.5359	−1.31042
$544$	−4.19615	−0.179909
$545$	−7.32051	−0.313576
$546$	0	0
$547$	38.2487	1.63540	0.817698	−	0.575647i	$-0.195250\pi$
$547$	38.2487	1.63540	0.817698	+	0.575647i	$0.195250\pi$
$548$	−15.4641	−0.660594
$549$	−4.00000	−0.170716
$550$	−15.4641	−0.659392
$551$	3.46410	0.147576
$552$	17.8564	0.760019
$553$	0	0
$554$	−18.3923	−0.781414
$555$	5.85641	0.248591
$556$	9.26795	0.393049
$557$	−3.85641	−0.163401	−0.0817006	−	0.996657i	$-0.526035\pi$
$557$	−3.85641	−0.163401	−0.0817006	+	0.996657i	$0.526035\pi$
$558$	2.19615	0.0929705
$559$	2.14359	0.0906643
$560$	0	0
$561$	29.0718	1.22741
$562$	−14.5359	−0.613160
$563$	34.1051	1.43736	0.718680	−	0.695341i	$-0.244747\pi$
$563$	34.1051	1.43736	0.718680	+	0.695341i	$0.244747\pi$
$564$	−15.3205	−0.645110
$565$	−2.53590	−0.106686
$566$	−16.5885	−0.697265
$567$	0	0
$568$	8.92820	0.374619
$569$	−14.7846	−0.619803	−0.309902	−	0.950769i	$-0.600296\pi$
$569$	−14.7846	−0.619803	−0.309902	+	0.950769i	$0.600296\pi$
$570$	5.07180	0.212434
$571$	24.3923	1.02079	0.510393	−	0.859941i	$-0.329500\pi$
$571$	24.3923	1.02079	0.510393	+	0.859941i	$0.329500\pi$
$572$	−2.53590	−0.106031
$573$	0.784610	0.0327775
$574$	0	0
$575$	39.8564	1.66213
$576$	1.00000	0.0416667
$577$	11.5167	0.479445	0.239722	−	0.970841i	$-0.422944\pi$
$577$	11.5167	0.479445	0.239722	+	0.970841i	$0.422944\pi$
$578$	0.607695	0.0252768
$579$	28.7846	1.19625
$580$	−0.732051	−0.0303968
$581$	0	0
$582$	−13.4641	−0.558105
$583$	17.0718	0.707042
$584$	−5.26795	−0.217989
$585$	−0.535898	−0.0221567
$586$	−3.60770	−0.149033
$587$	36.9808	1.52636	0.763180	−	0.646186i	$-0.223637\pi$
$587$	36.9808	1.52636	0.763180	+	0.646186i	$0.223637\pi$
$588$	0	0
$589$	−7.60770	−0.313470
$590$	−7.85641	−0.323443
$591$	41.0718	1.68947
$592$	−4.00000	−0.164399
$593$	0.928203	0.0381167	0.0190584	−	0.999818i	$-0.493933\pi$
$593$	0.928203	0.0381167	0.0190584	+	0.999818i	$0.493933\pi$
$594$	13.8564	0.568535
$595$	0	0
$596$	−3.46410	−0.141895
$597$	34.9282	1.42952
$598$	6.53590	0.267273
$599$	39.3205	1.60659	0.803296	−	0.595580i	$-0.203078\pi$
$599$	39.3205	1.60659	0.803296	+	0.595580i	$0.203078\pi$
$600$	8.92820	0.364492
$601$	2.05256	0.0837256	0.0418628	−	0.999123i	$-0.486671\pi$
$601$	2.05256	0.0837256	0.0418628	+	0.999123i	$0.486671\pi$
$602$	0	0
$603$	−6.92820	−0.282138
$604$	15.8564	0.645188
$605$	0.732051	0.0297621
$606$	8.00000	0.324978
$607$	−19.2679	−0.782062	−0.391031	−	0.920378i	$-0.627881\pi$
$607$	−19.2679	−0.782062	−0.391031	+	0.920378i	$0.627881\pi$
$608$	−3.46410	−0.140488
$609$	0	0
$610$	−2.92820	−0.118559
$611$	−5.60770	−0.226863
$612$	−4.19615	−0.169619
$613$	20.2487	0.817838	0.408919	−	0.912571i	$-0.365906\pi$
$613$	20.2487	0.817838	0.408919	+	0.912571i	$0.365906\pi$
$614$	3.07180	0.123968
$615$	−14.1436	−0.570325
$616$	0	0
$617$	−33.7128	−1.35723	−0.678613	−	0.734496i	$-0.737419\pi$
$617$	−33.7128	−1.35723	−0.678613	+	0.734496i	$0.737419\pi$
$618$	10.9282	0.439597
$619$	−24.5359	−0.986181	−0.493091	−	0.869978i	$-0.664133\pi$
$619$	−24.5359	−0.986181	−0.493091	+	0.869978i	$0.664133\pi$
$620$	1.60770	0.0645666
$621$	−35.7128	−1.43311
$622$	29.1244	1.16778
$623$	0	0
$624$	1.46410	0.0586110
$625$	17.2487	0.689948
$626$	19.8564	0.793622
$627$	24.0000	0.958468
$628$	−11.3205	−0.451737
$629$	16.7846	0.669246
$630$	0	0
$631$	40.0000	1.59237	0.796187	−	0.605050i	$-0.206847\pi$
$631$	40.0000	1.59237	0.796187	+	0.605050i	$0.206847\pi$
$632$	−2.53590	−0.100873
$633$	−13.8564	−0.550743
$634$	0.928203	0.0368637
$635$	−4.78461	−0.189871
$636$	−9.85641	−0.390832
$637$	0	0
$638$	−3.46410	−0.137145
$639$	8.92820	0.353194
$640$	0.732051	0.0289368
$641$	47.8564	1.89021	0.945107	−	0.326760i	$-0.105957\pi$
$641$	47.8564	1.89021	0.945107	+	0.326760i	$0.105957\pi$
$642$	−8.00000	−0.315735
$643$	14.3397	0.565504	0.282752	−	0.959193i	$-0.408753\pi$
$643$	14.3397	0.565504	0.282752	+	0.959193i	$0.408753\pi$
$644$	0	0
$645$	4.28719	0.168808
$646$	14.5359	0.571907
$647$	36.3923	1.43073	0.715365	−	0.698751i	$-0.246261\pi$
$647$	36.3923	1.43073	0.715365	+	0.698751i	$0.246261\pi$
$648$	−11.0000	−0.432121
$649$	−37.1769	−1.45932
$650$	3.26795	0.128180
$651$	0	0
$652$	15.4641	0.605621
$653$	22.0000	0.860927	0.430463	−	0.902608i	$-0.358350\pi$
$653$	22.0000	0.860927	0.430463	+	0.902608i	$0.358350\pi$
$654$	20.0000	0.782062
$655$	−6.24871	−0.244157
$656$	9.66025	0.377170
$657$	−5.26795	−0.205522
$658$	0	0
$659$	−13.6077	−0.530081	−0.265040	−	0.964237i	$-0.585385\pi$
$659$	−13.6077	−0.530081	−0.265040	+	0.964237i	$0.585385\pi$
$660$	−5.07180	−0.197419
$661$	16.7321	0.650801	0.325401	−	0.945576i	$-0.394501\pi$
$661$	16.7321	0.650801	0.325401	+	0.945576i	$0.394501\pi$
$662$	24.7846	0.963281
$663$	−6.14359	−0.238597
$664$	−16.5885	−0.643757
$665$	0	0
$666$	−4.00000	−0.154997
$667$	8.92820	0.345701
$668$	2.92820	0.113296
$669$	−0.784610	−0.0303348
$670$	−5.07180	−0.195941
$671$	−13.8564	−0.534921
$672$	0	0
$673$	38.5359	1.48545	0.742725	−	0.669597i	$-0.233533\pi$
$673$	38.5359	1.48545	0.742725	+	0.669597i	$0.233533\pi$
$674$	−14.0000	−0.539260
$675$	−17.8564	−0.687293
$676$	−12.4641	−0.479389
$677$	29.1769	1.12136	0.560680	−	0.828033i	$-0.310540\pi$
$677$	29.1769	1.12136	0.560680	+	0.828033i	$0.310540\pi$
$678$	6.92820	0.266076
$679$	0	0
$680$	−3.07180	−0.117798
$681$	−25.1769	−0.964781
$682$	7.60770	0.291314
$683$	1.85641	0.0710334	0.0355167	−	0.999369i	$-0.488692\pi$
$683$	1.85641	0.0710334	0.0355167	+	0.999369i	$0.488692\pi$
$684$	−3.46410	−0.132453
$685$	−11.3205	−0.432534
$686$	0	0
$687$	−24.7846	−0.945592
$688$	−2.92820	−0.111637
$689$	−3.60770	−0.137442
$690$	13.0718	0.497635
$691$	−18.0526	−0.686752	−0.343376	−	0.939198i	$-0.611570\pi$
$691$	−18.0526	−0.686752	−0.343376	+	0.939198i	$0.611570\pi$
$692$	−16.7321	−0.636057
$693$	0	0
$694$	20.3923	0.774081
$695$	6.78461	0.257355
$696$	2.00000	0.0758098
$697$	−40.5359	−1.53541
$698$	14.1962	0.537332
$699$	−55.7128	−2.10725
$700$	0	0
$701$	−31.1769	−1.17754	−0.588768	−	0.808302i	$-0.700387\pi$
$701$	−31.1769	−1.17754	−0.588768	+	0.808302i	$0.700387\pi$
$702$	−2.92820	−0.110518
$703$	13.8564	0.522604
$704$	3.46410	0.130558
$705$	−11.2154	−0.422396
$706$	−11.8564	−0.446222
$707$	0	0
$708$	21.4641	0.806670
$709$	47.5692	1.78650	0.893250	−	0.449561i	$-0.148419\pi$
$709$	47.5692	1.78650	0.893250	+	0.449561i	$0.148419\pi$
$710$	6.53590	0.245288
$711$	−2.53590	−0.0951036
$712$	−16.1962	−0.606976
$713$	−19.6077	−0.734314
$714$	0	0
$715$	−1.85641	−0.0694257
$716$	20.0000	0.747435
$717$	−55.4256	−2.06991
$718$	−34.2487	−1.27815
$719$	−27.3205	−1.01888	−0.509442	−	0.860505i	$-0.670148\pi$
$719$	−27.3205	−1.01888	−0.509442	+	0.860505i	$0.670148\pi$
$720$	0.732051	0.0272819
$721$	0	0
$722$	−7.00000	−0.260513
$723$	−33.8564	−1.25913
$724$	15.2679	0.567429
$725$	4.46410	0.165793
$726$	−2.00000	−0.0742270
$727$	−37.9090	−1.40597	−0.702983	−	0.711207i	$-0.748149\pi$
$727$	−37.9090	−1.40597	−0.702983	+	0.711207i	$0.748149\pi$
$728$	0	0
$729$	13.0000	0.481481
$730$	−3.85641	−0.142732
$731$	12.2872	0.454458
$732$	8.00000	0.295689
$733$	39.7128	1.46683	0.733413	−	0.679783i	$-0.237926\pi$
$733$	39.7128	1.46683	0.733413	+	0.679783i	$0.237926\pi$
$734$	−3.66025	−0.135102
$735$	0	0
$736$	−8.92820	−0.329098
$737$	−24.0000	−0.884051
$738$	9.66025	0.355599
$739$	7.21539	0.265422	0.132711	−	0.991155i	$-0.457632\pi$
$739$	7.21539	0.265422	0.132711	+	0.991155i	$0.457632\pi$
$740$	−2.92820	−0.107643
$741$	−5.07180	−0.186317
$742$	0	0
$743$	−21.0718	−0.773049	−0.386525	−	0.922279i	$-0.626325\pi$
$743$	−21.0718	−0.773049	−0.386525	+	0.922279i	$0.626325\pi$
$744$	−4.39230	−0.161030
$745$	−2.53590	−0.0929081
$746$	3.46410	0.126830
$747$	−16.5885	−0.606940
$748$	−14.5359	−0.531485
$749$	0	0
$750$	13.8564	0.505964
$751$	−33.5692	−1.22496	−0.612479	−	0.790487i	$-0.709828\pi$
$751$	−33.5692	−1.22496	−0.612479	+	0.790487i	$0.709828\pi$
$752$	7.66025	0.279341
$753$	−20.7846	−0.757433
$754$	0.732051	0.0266597
$755$	11.6077	0.422447
$756$	0	0
$757$	−33.0718	−1.20201	−0.601007	−	0.799243i	$-0.705234\pi$
$757$	−33.0718	−1.20201	−0.601007	+	0.799243i	$0.705234\pi$
$758$	−24.7846	−0.900218
$759$	61.8564	2.24525
$760$	−2.53590	−0.0919867
$761$	21.7128	0.787089	0.393544	−	0.919306i	$-0.371249\pi$
$761$	21.7128	0.787089	0.393544	+	0.919306i	$0.371249\pi$
$762$	13.0718	0.473541
$763$	0	0
$764$	−0.392305	−0.0141931
$765$	−3.07180	−0.111061
$766$	16.0000	0.578103
$767$	7.85641	0.283678
$768$	−2.00000	−0.0721688
$769$	−8.48334	−0.305917	−0.152959	−	0.988233i	$-0.548880\pi$
$769$	−8.48334	−0.305917	−0.152959	+	0.988233i	$0.548880\pi$
$770$	0	0
$771$	38.9282	1.40196
$772$	−14.3923	−0.517990
$773$	23.6077	0.849110	0.424555	−	0.905402i	$-0.360431\pi$
$773$	23.6077	0.849110	0.424555	+	0.905402i	$0.360431\pi$
$774$	−2.92820	−0.105252
$775$	−9.80385	−0.352165
$776$	6.73205	0.241667
$777$	0	0
$778$	5.07180	0.181833
$779$	−33.4641	−1.19898
$780$	1.07180	0.0383765
$781$	30.9282	1.10670
$782$	37.4641	1.33971
$783$	−4.00000	−0.142948
$784$	0	0
$785$	−8.28719	−0.295782
$786$	17.0718	0.608931
$787$	24.1962	0.862500	0.431250	−	0.902233i	$-0.358073\pi$
$787$	24.1962	0.862500	0.431250	+	0.902233i	$0.358073\pi$
$788$	−20.5359	−0.731561
$789$	−32.7846	−1.16716
$790$	−1.85641	−0.0660480
$791$	0	0
$792$	3.46410	0.123091
$793$	2.92820	0.103984
$794$	−1.12436	−0.0399019
$795$	−7.21539	−0.255904
$796$	−17.4641	−0.618999
$797$	15.6077	0.552853	0.276426	−	0.961035i	$-0.410850\pi$
$797$	15.6077	0.552853	0.276426	+	0.961035i	$0.410850\pi$
$798$	0	0
$799$	−32.1436	−1.13716
$800$	−4.46410	−0.157830
$801$	−16.1962	−0.572263
$802$	7.85641	0.277419
$803$	−18.2487	−0.643983
$804$	13.8564	0.488678
$805$	0	0
$806$	−1.60770	−0.0566286
$807$	−3.71281	−0.130697
$808$	−4.00000	−0.140720
$809$	−24.2487	−0.852539	−0.426270	−	0.904596i	$-0.640173\pi$
$809$	−24.2487	−0.852539	−0.426270	+	0.904596i	$0.640173\pi$
$810$	−8.05256	−0.282938
$811$	54.8372	1.92559	0.962797	−	0.270227i	$-0.0870987\pi$
$811$	54.8372	1.92559	0.962797	+	0.270227i	$0.0870987\pi$
$812$	0	0
$813$	29.1769	1.02328
$814$	−13.8564	−0.485667
$815$	11.3205	0.396540
$816$	8.39230	0.293789
$817$	10.1436	0.354879
$818$	−15.1244	−0.528811
$819$	0	0
$820$	7.07180	0.246958
$821$	−42.0000	−1.46581	−0.732905	−	0.680331i	$-0.761836\pi$
$821$	−42.0000	−1.46581	−0.732905	+	0.680331i	$0.761836\pi$
$822$	30.9282	1.07874
$823$	−22.9282	−0.799227	−0.399613	−	0.916684i	$-0.630856\pi$
$823$	−22.9282	−0.799227	−0.399613	+	0.916684i	$0.630856\pi$
$824$	−5.46410	−0.190351
$825$	30.9282	1.07678
$826$	0	0
$827$	−37.3205	−1.29776	−0.648881	−	0.760890i	$-0.724763\pi$
$827$	−37.3205	−1.29776	−0.648881	+	0.760890i	$0.724763\pi$
$828$	−8.92820	−0.310277
$829$	−22.9282	−0.796329	−0.398165	−	0.917314i	$-0.630353\pi$
$829$	−22.9282	−0.796329	−0.398165	+	0.917314i	$0.630353\pi$
$830$	−12.1436	−0.421510
$831$	36.7846	1.27604
$832$	−0.732051	−0.0253793
$833$	0	0
$834$	−18.5359	−0.641846
$835$	2.14359	0.0741821
$836$	−12.0000	−0.415029
$837$	8.78461	0.303641
$838$	−16.1962	−0.559487
$839$	−31.2679	−1.07949	−0.539745	−	0.841829i	$-0.681479\pi$
$839$	−31.2679	−1.07949	−0.539745	+	0.841829i	$0.681479\pi$
$840$	0	0
$841$	1.00000	0.0344828
$842$	4.78461	0.164889
$843$	29.0718	1.00129
$844$	6.92820	0.238479
$845$	−9.12436	−0.313887
$846$	7.66025	0.263365
$847$	0	0
$848$	4.92820	0.169235
$849$	33.1769	1.13863
$850$	18.7321	0.642504
$851$	35.7128	1.22422
$852$	−17.8564	−0.611750
$853$	21.0718	0.721485	0.360742	−	0.932666i	$-0.382523\pi$
$853$	21.0718	0.721485	0.360742	+	0.932666i	$0.382523\pi$
$854$	0	0
$855$	−2.53590	−0.0867259
$856$	4.00000	0.136717
$857$	16.1436	0.551455	0.275727	−	0.961236i	$-0.411081\pi$
$857$	16.1436	0.551455	0.275727	+	0.961236i	$0.411081\pi$
$858$	5.07180	0.173148
$859$	46.4974	1.58647	0.793236	−	0.608915i	$-0.208395\pi$
$859$	46.4974	1.58647	0.793236	+	0.608915i	$0.208395\pi$
$860$	−2.14359	−0.0730959
$861$	0	0
$862$	−19.7128	−0.671421
$863$	−47.8564	−1.62905	−0.814526	−	0.580128i	$-0.803003\pi$
$863$	−47.8564	−1.62905	−0.814526	+	0.580128i	$0.803003\pi$
$864$	4.00000	0.136083
$865$	−12.2487	−0.416469
$866$	−9.26795	−0.314938
$867$	−1.21539	−0.0412768
$868$	0	0
$869$	−8.78461	−0.297997
$870$	1.46410	0.0496377
$871$	5.07180	0.171851
$872$	−10.0000	−0.338643
$873$	6.73205	0.227845
$874$	30.9282	1.04616
$875$	0	0
$876$	10.5359	0.355975
$877$	23.1769	0.782629	0.391314	−	0.920257i	$-0.372021\pi$
$877$	23.1769	0.782629	0.391314	+	0.920257i	$0.372021\pi$
$878$	31.7128	1.07026
$879$	7.21539	0.243369
$880$	2.53590	0.0854851
$881$	−51.1244	−1.72242	−0.861212	−	0.508246i	$-0.830294\pi$
$881$	−51.1244	−1.72242	−0.861212	+	0.508246i	$0.830294\pi$
$882$	0	0
$883$	−23.7128	−0.798000	−0.399000	−	0.916951i	$-0.630643\pi$
$883$	−23.7128	−0.798000	−0.399000	+	0.916951i	$0.630643\pi$
$884$	3.07180	0.103316
$885$	15.7128	0.528180
$886$	−28.5359	−0.958682
$887$	−22.9808	−0.771618	−0.385809	−	0.922579i	$-0.626078\pi$
$887$	−22.9808	−0.771618	−0.385809	+	0.922579i	$0.626078\pi$
$888$	8.00000	0.268462
$889$	0	0
$890$	−11.8564	−0.397428
$891$	−38.1051	−1.27657
$892$	0.392305	0.0131353
$893$	−26.5359	−0.887990
$894$	6.92820	0.231714
$895$	14.6410	0.489395
$896$	0	0
$897$	−13.0718	−0.436455
$898$	41.7128	1.39197
$899$	−2.19615	−0.0732458
$900$	−4.46410	−0.148803
$901$	−20.6795	−0.688934
$902$	33.4641	1.11423
$903$	0	0
$904$	−3.46410	−0.115214
$905$	11.1769	0.371533
$906$	−31.7128	−1.05359
$907$	2.39230	0.0794352	0.0397176	−	0.999211i	$-0.487354\pi$
$907$	2.39230	0.0794352	0.0397176	+	0.999211i	$0.487354\pi$
$908$	12.5885	0.417763
$909$	−4.00000	−0.132672
$910$	0	0
$911$	−9.75129	−0.323075	−0.161537	−	0.986867i	$-0.551645\pi$
$911$	−9.75129	−0.323075	−0.161537	+	0.986867i	$0.551645\pi$
$912$	6.92820	0.229416
$913$	−57.4641	−1.90178
$914$	−33.1769	−1.09739
$915$	5.85641	0.193607
$916$	12.3923	0.409453
$917$	0	0
$918$	−16.7846	−0.553975
$919$	19.8564	0.655002	0.327501	−	0.944851i	$-0.393793\pi$
$919$	19.8564	0.655002	0.327501	+	0.944851i	$0.393793\pi$
$920$	−6.53590	−0.215482
$921$	−6.14359	−0.202438
$922$	−9.85641	−0.324603
$923$	−6.53590	−0.215132
$924$	0	0
$925$	17.8564	0.587115
$926$	22.0000	0.722965
$927$	−5.46410	−0.179465
$928$	−1.00000	−0.0328266
$929$	38.7846	1.27248	0.636241	−	0.771490i	$-0.280488\pi$
$929$	38.7846	1.27248	0.636241	+	0.771490i	$0.280488\pi$
$930$	−3.21539	−0.105437
$931$	0	0
$932$	27.8564	0.912467
$933$	−58.2487	−1.90698
$934$	−17.3205	−0.566744
$935$	−10.6410	−0.347998
$936$	−0.732051	−0.0239278
$937$	−39.5692	−1.29267	−0.646335	−	0.763054i	$-0.723699\pi$
$937$	−39.5692	−1.29267	−0.646335	+	0.763054i	$0.723699\pi$
$938$	0	0
$939$	−39.7128	−1.29598
$940$	5.60770	0.182903
$941$	22.1962	0.723574	0.361787	−	0.932261i	$-0.382167\pi$
$941$	22.1962	0.723574	0.361787	+	0.932261i	$0.382167\pi$
$942$	22.6410	0.737684
$943$	−86.2487	−2.80864
$944$	−10.7321	−0.349299
$945$	0	0
$946$	−10.1436	−0.329797
$947$	−32.7846	−1.06536	−0.532678	−	0.846318i	$-0.678814\pi$
$947$	−32.7846	−1.06536	−0.532678	+	0.846318i	$0.678814\pi$
$948$	5.07180	0.164724
$949$	3.85641	0.125184
$950$	15.4641	0.501722
$951$	−1.85641	−0.0601981
$952$	0	0
$953$	−11.6077	−0.376010	−0.188005	−	0.982168i	$-0.560202\pi$
$953$	−11.6077	−0.376010	−0.188005	+	0.982168i	$0.560202\pi$
$954$	4.92820	0.159556
$955$	−0.287187	−0.00929316
$956$	27.7128	0.896296
$957$	6.92820	0.223957
$958$	−17.5167	−0.565938
$959$	0	0
$960$	−1.46410	−0.0472537
$961$	−26.1769	−0.844417
$962$	2.92820	0.0944091
$963$	4.00000	0.128898
$964$	16.9282	0.545221
$965$	−10.5359	−0.339163
$966$	0	0
$967$	41.8564	1.34601	0.673006	−	0.739637i	$-0.265003\pi$
$967$	41.8564	1.34601	0.673006	+	0.739637i	$0.265003\pi$
$968$	1.00000	0.0321412
$969$	−29.0718	−0.933921
$970$	4.92820	0.158235
$971$	−13.3205	−0.427475	−0.213738	−	0.976891i	$-0.568564\pi$
$971$	−13.3205	−0.427475	−0.213738	+	0.976891i	$0.568564\pi$
$972$	10.0000	0.320750
$973$	0	0
$974$	2.92820	0.0938257
$975$	−6.53590	−0.209316
$976$	−4.00000	−0.128037
$977$	−17.4641	−0.558726	−0.279363	−	0.960186i	$-0.590123\pi$
$977$	−17.4641	−0.558726	−0.279363	+	0.960186i	$0.590123\pi$
$978$	−30.9282	−0.988975
$979$	−56.1051	−1.79313
$980$	0	0
$981$	−10.0000	−0.319275
$982$	12.0000	0.382935
$983$	−54.6936	−1.74445	−0.872227	−	0.489101i	$-0.837325\pi$
$983$	−54.6936	−1.74445	−0.872227	+	0.489101i	$0.837325\pi$
$984$	−19.3205	−0.615915
$985$	−15.0333	−0.479001
$986$	4.19615	0.133633
$987$	0	0
$988$	2.53590	0.0806777
$989$	26.1436	0.831318
$990$	2.53590	0.0805961
$991$	43.7128	1.38858	0.694292	−	0.719694i	$-0.255718\pi$
$991$	43.7128	1.38858	0.694292	+	0.719694i	$0.255718\pi$
$992$	2.19615	0.0697279
$993$	−49.5692	−1.57303
$994$	0	0
$995$	−12.7846	−0.405299
$996$	33.1769	1.05125
$997$	43.7128	1.38440	0.692199	−	0.721706i	$-0.256642\pi$
$997$	43.7128	1.38440	0.692199	+	0.721706i	$0.256642\pi$
$998$	−16.7846	−0.531308
$999$	−16.0000	−0.506218

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2842.2.a.i.1.2		2
7.6	odd	2		406.2.a.e.1.1	✓	2
21.20	even	2		3654.2.a.y.1.2		2
28.27	even	2		3248.2.a.o.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
406.2.a.e.1.1	✓	2	7.6	odd	2
2842.2.a.i.1.2		2	1.1	even	1	trivial
3248.2.a.o.1.1		2	28.27	even	2
3654.2.a.y.1.2		2	21.20	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2842 = 2 \cdot 7^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2842.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.00000 q^{3} +1.00000 q^{4} +0.732051 q^{5} -2.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.00000 q^{3} +1.00000 q^{4} +0.732051 q^{5} -2.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +0.732051 q^{10} +3.46410 q^{11} -2.00000 q^{12} -0.732051 q^{13} -1.46410 q^{15} +1.00000 q^{16} -4.19615 q^{17} +1.00000 q^{18} -3.46410 q^{19} +0.732051 q^{20} +3.46410 q^{22} -8.92820 q^{23} -2.00000 q^{24} -4.46410 q^{25} -0.732051 q^{26} +4.00000 q^{27} -1.00000 q^{29} -1.46410 q^{30} +2.19615 q^{31} +1.00000 q^{32} -6.92820 q^{33} -4.19615 q^{34} +1.00000 q^{36} -4.00000 q^{37} -3.46410 q^{38} +1.46410 q^{39} +0.732051 q^{40} +9.66025 q^{41} -2.92820 q^{43} +3.46410 q^{44} +0.732051 q^{45} -8.92820 q^{46} +7.66025 q^{47} -2.00000 q^{48} -4.46410 q^{50} +8.39230 q^{51} -0.732051 q^{52} +4.92820 q^{53} +4.00000 q^{54} +2.53590 q^{55} +6.92820 q^{57} -1.00000 q^{58} -10.7321 q^{59} -1.46410 q^{60} -4.00000 q^{61} +2.19615 q^{62} +1.00000 q^{64} -0.535898 q^{65} -6.92820 q^{66} -6.92820 q^{67} -4.19615 q^{68} +17.8564 q^{69} +8.92820 q^{71} +1.00000 q^{72} -5.26795 q^{73} -4.00000 q^{74} +8.92820 q^{75} -3.46410 q^{76} +1.46410 q^{78} -2.53590 q^{79} +0.732051 q^{80} -11.0000 q^{81} +9.66025 q^{82} -16.5885 q^{83} -3.07180 q^{85} -2.92820 q^{86} +2.00000 q^{87} +3.46410 q^{88} -16.1962 q^{89} +0.732051 q^{90} -8.92820 q^{92} -4.39230 q^{93} +7.66025 q^{94} -2.53590 q^{95} -2.00000 q^{96} +6.73205 q^{97} +3.46410 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 4 q^{3} + 2 q^{4} - 2 q^{5} - 4 q^{6} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 - 4 * q^3 + 2 * q^4 - 2 * q^5 - 4 * q^6 + 2 * q^8 + 2 * q^9	\( 2 q + 2 q^{2} - 4 q^{3} + 2 q^{4} - 2 q^{5} - 4 q^{6} + 2 q^{8} + 2 q^{9} - 2 q^{10} - 4 q^{12} + 2 q^{13} + 4 q^{15} + 2 q^{16} + 2 q^{17} + 2 q^{18} - 2 q^{20} - 4 q^{23} - 4 q^{24} - 2 q^{25} + 2 q^{26} + 8 q^{27} - 2 q^{29} + 4 q^{30} - 6 q^{31} + 2 q^{32} + 2 q^{34} + 2 q^{36} - 8 q^{37} - 4 q^{39} - 2 q^{40} + 2 q^{41} + 8 q^{43} - 2 q^{45} - 4 q^{46} - 2 q^{47} - 4 q^{48} - 2 q^{50} - 4 q^{51} + 2 q^{52} - 4 q^{53} + 8 q^{54} + 12 q^{55} - 2 q^{58} - 18 q^{59} + 4 q^{60} - 8 q^{61} - 6 q^{62} + 2 q^{64} - 8 q^{65} + 2 q^{68} + 8 q^{69} + 4 q^{71} + 2 q^{72} - 14 q^{73} - 8 q^{74} + 4 q^{75} - 4 q^{78} - 12 q^{79} - 2 q^{80} - 22 q^{81} + 2 q^{82} - 2 q^{83} - 20 q^{85} + 8 q^{86} + 4 q^{87} - 22 q^{89} - 2 q^{90} - 4 q^{92} + 12 q^{93} - 2 q^{94} - 12 q^{95} - 4 q^{96} + 10 q^{97}+O(q^{100}) \) 2 * q + 2 * q^2 - 4 * q^3 + 2 * q^4 - 2 * q^5 - 4 * q^6 + 2 * q^8 + 2 * q^9 - 2 * q^10 - 4 * q^12 + 2 * q^13 + 4 * q^15 + 2 * q^16 + 2 * q^17 + 2 * q^18 - 2 * q^20 - 4 * q^23 - 4 * q^24 - 2 * q^25 + 2 * q^26 + 8 * q^27 - 2 * q^29 + 4 * q^30 - 6 * q^31 + 2 * q^32 + 2 * q^34 + 2 * q^36 - 8 * q^37 - 4 * q^39 - 2 * q^40 + 2 * q^41 + 8 * q^43 - 2 * q^45 - 4 * q^46 - 2 * q^47 - 4 * q^48 - 2 * q^50 - 4 * q^51 + 2 * q^52 - 4 * q^53 + 8 * q^54 + 12 * q^55 - 2 * q^58 - 18 * q^59 + 4 * q^60 - 8 * q^61 - 6 * q^62 + 2 * q^64 - 8 * q^65 + 2 * q^68 + 8 * q^69 + 4 * q^71 + 2 * q^72 - 14 * q^73 - 8 * q^74 + 4 * q^75 - 4 * q^78 - 12 * q^79 - 2 * q^80 - 22 * q^81 + 2 * q^82 - 2 * q^83 - 20 * q^85 + 8 * q^86 + 4 * q^87 - 22 * q^89 - 2 * q^90 - 4 * q^92 + 12 * q^93 - 2 * q^94 - 12 * q^95 - 4 * q^96 + 10 * q^97

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