LMFDB - Embedded newform 6762.2.a.cl.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("6762.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$53.9948418468$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.473376.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 13x^{2} + 8x + 30 $ x^4 - 2x^3 - 13x^2 + 8*x + 30
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 966)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-1.52852$ of defining polynomial
Character	$\chi$	$=$	6762.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.52852 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.52852 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +2.52852 q^{10} +4.29540 q^{11} -1.00000 q^{12} +0.393417 q^{13} -2.52852 q^{15} +1.00000 q^{16} +6.82392 q^{17} +1.00000 q^{18} -2.00000 q^{19} +2.52852 q^{20} +4.29540 q^{22} -1.00000 q^{23} -1.00000 q^{24} +1.39342 q^{25} +0.393417 q^{26} -1.00000 q^{27} +4.60658 q^{29} -2.52852 q^{30} -2.00000 q^{31} +1.00000 q^{32} -4.29540 q^{33} +6.82392 q^{34} +1.00000 q^{36} +9.05704 q^{37} -2.00000 q^{38} -0.393417 q^{39} +2.52852 q^{40} -3.05704 q^{41} +2.00000 q^{43} +4.29540 q^{44} +2.52852 q^{45} -1.00000 q^{46} -9.59080 q^{47} -1.00000 q^{48} +1.39342 q^{50} -6.82392 q^{51} +0.393417 q^{52} +0.258313 q^{53} -1.00000 q^{54} +10.8610 q^{55} +2.00000 q^{57} +4.60658 q^{58} +10.1141 q^{59} -2.52852 q^{60} +3.21317 q^{61} -2.00000 q^{62} +1.00000 q^{64} +0.994763 q^{65} -4.29540 q^{66} +3.74169 q^{67} +6.82392 q^{68} +1.00000 q^{69} -13.8610 q^{71} +1.00000 q^{72} +4.21317 q^{73} +9.05704 q^{74} -1.39342 q^{75} -2.00000 q^{76} -0.393417 q^{78} +3.70460 q^{79} +2.52852 q^{80} +1.00000 q^{81} -3.05704 q^{82} -13.6478 q^{83} +17.2544 q^{85} +2.00000 q^{86} -4.60658 q^{87} +4.29540 q^{88} -8.27021 q^{89} +2.52852 q^{90} -1.00000 q^{92} +2.00000 q^{93} -9.59080 q^{94} -5.05704 q^{95} -1.00000 q^{96} -8.00000 q^{97} +4.29540 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} + 2 q^{5} - 4 q^{6} + 4 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 + 2 * q^5 - 4 * q^6 + 4 * q^8 + 4 * q^9	$ 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} + 2 q^{5} - 4 q^{6} + 4 q^{8} + 4 q^{9} + 2 q^{10} - 4 q^{12} + 6 q^{13} - 2 q^{15} + 4 q^{16} + 2 q^{17} + 4 q^{18} - 8 q^{19} + 2 q^{20} - 4 q^{23} - 4 q^{24} + 10 q^{25} + 6 q^{26} - 4 q^{27} + 14 q^{29} - 2 q^{30} - 8 q^{31} + 4 q^{32} + 2 q^{34} + 4 q^{36} + 20 q^{37} - 8 q^{38} - 6 q^{39} + 2 q^{40} + 4 q^{41} + 8 q^{43} + 2 q^{45} - 4 q^{46} - 4 q^{47} - 4 q^{48} + 10 q^{50} - 2 q^{51} + 6 q^{52} + 18 q^{53} - 4 q^{54} - 16 q^{55} + 8 q^{57} + 14 q^{58} + 8 q^{59} - 2 q^{60} + 4 q^{61} - 8 q^{62} + 4 q^{64} + 14 q^{65} - 2 q^{67} + 2 q^{68} + 4 q^{69} + 4 q^{71} + 4 q^{72} + 8 q^{73} + 20 q^{74} - 10 q^{75} - 8 q^{76} - 6 q^{78} + 32 q^{79} + 2 q^{80} + 4 q^{81} + 4 q^{82} - 4 q^{83} + 14 q^{85} + 8 q^{86} - 14 q^{87} - 8 q^{89} + 2 q^{90} - 4 q^{92} + 8 q^{93} - 4 q^{94} - 4 q^{95} - 4 q^{96} - 32 q^{97}+O(q^{100}) $ 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 + 2 * q^5 - 4 * q^6 + 4 * q^8 + 4 * q^9 + 2 * q^10 - 4 * q^12 + 6 * q^13 - 2 * q^15 + 4 * q^16 + 2 * q^17 + 4 * q^18 - 8 * q^19 + 2 * q^20 - 4 * q^23 - 4 * q^24 + 10 * q^25 + 6 * q^26 - 4 * q^27 + 14 * q^29 - 2 * q^30 - 8 * q^31 + 4 * q^32 + 2 * q^34 + 4 * q^36 + 20 * q^37 - 8 * q^38 - 6 * q^39 + 2 * q^40 + 4 * q^41 + 8 * q^43 + 2 * q^45 - 4 * q^46 - 4 * q^47 - 4 * q^48 + 10 * q^50 - 2 * q^51 + 6 * q^52 + 18 * q^53 - 4 * q^54 - 16 * q^55 + 8 * q^57 + 14 * q^58 + 8 * q^59 - 2 * q^60 + 4 * q^61 - 8 * q^62 + 4 * q^64 + 14 * q^65 - 2 * q^67 + 2 * q^68 + 4 * q^69 + 4 * q^71 + 4 * q^72 + 8 * q^73 + 20 * q^74 - 10 * q^75 - 8 * q^76 - 6 * q^78 + 32 * q^79 + 2 * q^80 + 4 * q^81 + 4 * q^82 - 4 * q^83 + 14 * q^85 + 8 * q^86 - 14 * q^87 - 8 * q^89 + 2 * q^90 - 4 * q^92 + 8 * q^93 - 4 * q^94 - 4 * q^95 - 4 * q^96 - 32 * 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
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	2.52852	1.13079	0.565394	−	0.824821i	$-0.308724\pi$
$5$	2.52852	1.13079	0.565394	+	0.824821i	$0.308724\pi$
$6$	−1.00000	−0.408248
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	2.52852	0.799588
$11$	4.29540	1.29511	0.647556	−	0.762018i	$-0.275791\pi$
$11$	4.29540	1.29511	0.647556	+	0.762018i	$0.275791\pi$
$12$	−1.00000	−0.288675
$13$	0.393417	0.109114	0.0545571	−	0.998511i	$-0.482625\pi$
$13$	0.393417	0.109114	0.0545571	+	0.998511i	$0.482625\pi$
$14$	0	0
$15$	−2.52852	−0.652861
$16$	1.00000	0.250000
$17$	6.82392	1.65504	0.827522	−	0.561433i	$-0.189750\pi$
$17$	6.82392	1.65504	0.827522	+	0.561433i	$0.189750\pi$
$18$	1.00000	0.235702
$19$	−2.00000	−0.458831	−0.229416	−	0.973329i	$-0.573682\pi$
$19$	−2.00000	−0.458831	−0.229416	+	0.973329i	$0.573682\pi$
$20$	2.52852	0.565394
$21$	0	0
$22$	4.29540	0.915782
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−1.00000	−0.204124
$25$	1.39342	0.278683
$26$	0.393417	0.0771554
$27$	−1.00000	−0.192450
$28$	0	0
$29$	4.60658	0.855421	0.427711	−	0.903916i	$-0.359320\pi$
$29$	4.60658	0.855421	0.427711	+	0.903916i	$0.359320\pi$
$30$	−2.52852	−0.461643
$31$	−2.00000	−0.359211	−0.179605	−	0.983739i	$-0.557482\pi$
$31$	−2.00000	−0.359211	−0.179605	+	0.983739i	$0.557482\pi$
$32$	1.00000	0.176777
$33$	−4.29540	−0.747733
$34$	6.82392	1.17029
$35$	0	0
$36$	1.00000	0.166667
$37$	9.05704	1.48897	0.744484	−	0.667640i	$-0.232695\pi$
$37$	9.05704	1.48897	0.744484	+	0.667640i	$0.232695\pi$
$38$	−2.00000	−0.324443
$39$	−0.393417	−0.0629971
$40$	2.52852	0.399794
$41$	−3.05704	−0.477430	−0.238715	−	0.971090i	$-0.576726\pi$
$41$	−3.05704	−0.477430	−0.238715	+	0.971090i	$0.576726\pi$
$42$	0	0
$43$	2.00000	0.304997	0.152499	−	0.988304i	$-0.451268\pi$
$43$	2.00000	0.304997	0.152499	+	0.988304i	$0.451268\pi$
$44$	4.29540	0.647556
$45$	2.52852	0.376930
$46$	−1.00000	−0.147442
$47$	−9.59080	−1.39896	−0.699481	−	0.714651i	$-0.746585\pi$
$47$	−9.59080	−1.39896	−0.699481	+	0.714651i	$0.746585\pi$
$48$	−1.00000	−0.144338
$49$	0	0
$50$	1.39342	0.197059
$51$	−6.82392	−0.955540
$52$	0.393417	0.0545571
$53$	0.258313	0.0354820	0.0177410	−	0.999843i	$-0.494353\pi$
$53$	0.258313	0.0354820	0.0177410	+	0.999843i	$0.494353\pi$
$54$	−1.00000	−0.136083
$55$	10.8610	1.46450
$56$	0	0
$57$	2.00000	0.264906
$58$	4.60658	0.604874
$59$	10.1141	1.31674	0.658371	−	0.752694i	$-0.271246\pi$
$59$	10.1141	1.31674	0.658371	+	0.752694i	$0.271246\pi$
$60$	−2.52852	−0.326431
$61$	3.21317	0.411404	0.205702	−	0.978615i	$-0.434052\pi$
$61$	3.21317	0.411404	0.205702	+	0.978615i	$0.434052\pi$
$62$	−2.00000	−0.254000
$63$	0	0
$64$	1.00000	0.125000
$65$	0.994763	0.123385
$66$	−4.29540	−0.528727
$67$	3.74169	0.457120	0.228560	−	0.973530i	$-0.426598\pi$
$67$	3.74169	0.457120	0.228560	+	0.973530i	$0.426598\pi$
$68$	6.82392	0.827522
$69$	1.00000	0.120386
$70$	0	0
$71$	−13.8610	−1.64500	−0.822499	−	0.568766i	$-0.807421\pi$
$71$	−13.8610	−1.64500	−0.822499	+	0.568766i	$0.807421\pi$
$72$	1.00000	0.117851
$73$	4.21317	0.493114	0.246557	−	0.969128i	$-0.420701\pi$
$73$	4.21317	0.493114	0.246557	+	0.969128i	$0.420701\pi$
$74$	9.05704	1.05286
$75$	−1.39342	−0.160898
$76$	−2.00000	−0.229416
$77$	0	0
$78$	−0.393417	−0.0445457
$79$	3.70460	0.416800	0.208400	−	0.978044i	$-0.433174\pi$
$79$	3.70460	0.416800	0.208400	+	0.978044i	$0.433174\pi$
$80$	2.52852	0.282697
$81$	1.00000	0.111111
$82$	−3.05704	−0.337594
$83$	−13.6478	−1.49805	−0.749023	−	0.662544i	$-0.769477\pi$
$83$	−13.6478	−1.49805	−0.749023	+	0.662544i	$0.769477\pi$
$84$	0	0
$85$	17.2544	1.87151
$86$	2.00000	0.215666
$87$	−4.60658	−0.493878
$88$	4.29540	0.457891
$89$	−8.27021	−0.876640	−0.438320	−	0.898819i	$-0.644426\pi$
$89$	−8.27021	−0.876640	−0.438320	+	0.898819i	$0.644426\pi$
$90$	2.52852	0.266529
$91$	0	0
$92$	−1.00000	−0.104257
$93$	2.00000	0.207390
$94$	−9.59080	−0.989215
$95$	−5.05704	−0.518841
$96$	−1.00000	−0.102062
$97$	−8.00000	−0.812277	−0.406138	−	0.913812i	$-0.633125\pi$
$97$	−8.00000	−0.812277	−0.406138	+	0.913812i	$0.633125\pi$
$98$	0	0
$99$	4.29540	0.431704
$100$	1.39342	0.139342
$101$	5.39342	0.536665	0.268333	−	0.963326i	$-0.413527\pi$
$101$	5.39342	0.536665	0.268333	+	0.963326i	$0.413527\pi$
$102$	−6.82392	−0.675669
$103$	−18.1512	−1.78849	−0.894244	−	0.447580i	$-0.852286\pi$
$103$	−18.1512	−1.78849	−0.894244	+	0.447580i	$0.852286\pi$
$104$	0.393417	0.0385777
$105$	0	0
$106$	0.258313	0.0250896
$107$	16.5908	1.60389	0.801947	−	0.597396i	$-0.203798\pi$
$107$	16.5908	1.60389	0.801947	+	0.597396i	$0.203798\pi$
$108$	−1.00000	−0.0962250
$109$	14.5656	1.39513	0.697566	−	0.716520i	$-0.254266\pi$
$109$	14.5656	1.39513	0.697566	+	0.716520i	$0.254266\pi$
$110$	10.8610	1.03556
$111$	−9.05704	−0.859656
$112$	0	0
$113$	−9.11932	−0.857873	−0.428937	−	0.903335i	$-0.641112\pi$
$113$	−9.11932	−0.857873	−0.428937	+	0.903335i	$0.641112\pi$
$114$	2.00000	0.187317
$115$	−2.52852	−0.235786
$116$	4.60658	0.427711
$117$	0.393417	0.0363714
$118$	10.1141	0.931077
$119$	0	0
$120$	−2.52852	−0.230821
$121$	7.45046	0.677314
$122$	3.21317	0.290906
$123$	3.05704	0.275644
$124$	−2.00000	−0.179605
$125$	−9.11932	−0.815657
$126$	0	0
$127$	6.27021	0.556391	0.278195	−	0.960524i	$-0.410264\pi$
$127$	6.27021	0.556391	0.278195	+	0.960524i	$0.410264\pi$
$128$	1.00000	0.0883883
$129$	−2.00000	−0.176090
$130$	0.994763	0.0872465
$131$	−19.0983	−1.66863	−0.834313	−	0.551291i	$-0.814135\pi$
$131$	−19.0983	−1.66863	−0.834313	+	0.551291i	$0.814135\pi$
$132$	−4.29540	−0.373867
$133$	0	0
$134$	3.74169	0.323233
$135$	−2.52852	−0.217620
$136$	6.82392	0.585146
$137$	−17.5288	−1.49759	−0.748793	−	0.662804i	$-0.769366\pi$
$137$	−17.5288	−1.49759	−0.748793	+	0.662804i	$0.769366\pi$
$138$	1.00000	0.0851257
$139$	13.0413	1.10615	0.553073	−	0.833133i	$-0.313455\pi$
$139$	13.0413	1.10615	0.553073	+	0.833133i	$0.313455\pi$
$140$	0	0
$141$	9.59080	0.807691
$142$	−13.8610	−1.16319
$143$	1.68988	0.141315
$144$	1.00000	0.0833333
$145$	11.6478	0.967301
$146$	4.21317	0.348684
$147$	0	0
$148$	9.05704	0.744484
$149$	−0.0622786	−0.00510206	−0.00255103	−	0.999997i	$-0.500812\pi$
$149$	−0.0622786	−0.00510206	−0.00255103	+	0.999997i	$0.500812\pi$
$150$	−1.39342	−0.113772
$151$	−2.15612	−0.175463	−0.0877315	−	0.996144i	$-0.527962\pi$
$151$	−2.15612	−0.175463	−0.0877315	+	0.996144i	$0.527962\pi$
$152$	−2.00000	−0.162221
$153$	6.82392	0.551681
$154$	0	0
$155$	−5.05704	−0.406191
$156$	−0.393417	−0.0314986
$157$	11.0822	0.884459	0.442229	−	0.896902i	$-0.354188\pi$
$157$	11.0822	0.884459	0.442229	+	0.896902i	$0.354188\pi$
$158$	3.70460	0.294722
$159$	−0.258313	−0.0204856
$160$	2.52852	0.199897
$161$	0	0
$162$	1.00000	0.0785674
$163$	12.2544	0.959841	0.479920	−	0.877312i	$-0.340666\pi$
$163$	12.2544	0.959841	0.479920	+	0.877312i	$0.340666\pi$
$164$	−3.05704	−0.238715
$165$	−10.8610	−0.845528
$166$	−13.6478	−1.05928
$167$	4.81975	0.372963	0.186482	−	0.982458i	$-0.440291\pi$
$167$	4.81975	0.372963	0.186482	+	0.982458i	$0.440291\pi$
$168$	0	0
$169$	−12.8452	−0.988094
$170$	17.2544	1.32335
$171$	−2.00000	−0.152944
$172$	2.00000	0.152499
$173$	22.9593	1.74556	0.872782	−	0.488110i	$-0.162314\pi$
$173$	22.9593	1.74556	0.872782	+	0.488110i	$0.162314\pi$
$174$	−4.60658	−0.349224
$175$	0	0
$176$	4.29540	0.323778
$177$	−10.1141	−0.760221
$178$	−8.27021	−0.619878
$179$	21.8452	1.63279	0.816394	−	0.577495i	$-0.195970\pi$
$179$	21.8452	1.63279	0.816394	+	0.577495i	$0.195970\pi$
$180$	2.52852	0.188465
$181$	−22.0994	−1.64263	−0.821316	−	0.570473i	$-0.806760\pi$
$181$	−22.0994	−1.64263	−0.821316	+	0.570473i	$0.806760\pi$
$182$	0	0
$183$	−3.21317	−0.237524
$184$	−1.00000	−0.0737210
$185$	22.9009	1.68371
$186$	2.00000	0.146647
$187$	29.3115	2.14347
$188$	−9.59080	−0.699481
$189$	0	0
$190$	−5.05704	−0.366876
$191$	−8.27021	−0.598411	−0.299206	−	0.954189i	$-0.596722\pi$
$191$	−8.27021	−0.598411	−0.299206	+	0.954189i	$0.596722\pi$
$192$	−1.00000	−0.0721688
$193$	−6.50750	−0.468420	−0.234210	−	0.972186i	$-0.575250\pi$
$193$	−6.50750	−0.468420	−0.234210	+	0.972186i	$0.575250\pi$
$194$	−8.00000	−0.574367
$195$	−0.994763	−0.0712364
$196$	0	0
$197$	8.18025	0.582819	0.291409	−	0.956598i	$-0.405876\pi$
$197$	8.18025	0.582819	0.291409	+	0.956598i	$0.405876\pi$
$198$	4.29540	0.305261
$199$	−14.4095	−1.02146	−0.510731	−	0.859741i	$-0.670625\pi$
$199$	−14.4095	−1.02146	−0.510731	+	0.859741i	$0.670625\pi$
$200$	1.39342	0.0985295
$201$	−3.74169	−0.263918
$202$	5.39342	0.379479
$203$	0	0
$204$	−6.82392	−0.477770
$205$	−7.72979	−0.539872
$206$	−18.1512	−1.26465
$207$	−1.00000	−0.0695048
$208$	0.393417	0.0272786
$209$	−8.59080	−0.594238
$210$	0	0
$211$	15.1974	1.04623	0.523115	−	0.852262i	$-0.324770\pi$
$211$	15.1974	1.04623	0.523115	+	0.852262i	$0.324770\pi$
$212$	0.258313	0.0177410
$213$	13.8610	0.949741
$214$	16.5908	1.13412
$215$	5.05704	0.344887
$216$	−1.00000	−0.0680414
$217$	0	0
$218$	14.5656	0.986507
$219$	−4.21317	−0.284699
$220$	10.8610	0.732249
$221$	2.68465	0.180589
$222$	−9.05704	−0.607869
$223$	−21.1711	−1.41772	−0.708862	−	0.705348i	$-0.750791\pi$
$223$	−21.1711	−1.41772	−0.708862	+	0.705348i	$0.750791\pi$
$224$	0	0
$225$	1.39342	0.0928945
$226$	−9.11932	−0.606608
$227$	−2.40948	−0.159923	−0.0799615	−	0.996798i	$-0.525480\pi$
$227$	−2.40948	−0.159923	−0.0799615	+	0.996798i	$0.525480\pi$
$228$	2.00000	0.132453
$229$	10.6160	0.701524	0.350762	−	0.936465i	$-0.385923\pi$
$229$	10.6160	0.701524	0.350762	+	0.936465i	$0.385923\pi$
$230$	−2.52852	−0.166726
$231$	0	0
$232$	4.60658	0.302437
$233$	13.1816	0.863555	0.431778	−	0.901980i	$-0.357887\pi$
$233$	13.1816	0.863555	0.431778	+	0.901980i	$0.357887\pi$
$234$	0.393417	0.0257185
$235$	−24.2505	−1.58193
$236$	10.1141	0.658371
$237$	−3.70460	−0.240640
$238$	0	0
$239$	4.25442	0.275196	0.137598	−	0.990488i	$-0.456062\pi$
$239$	4.25442	0.275196	0.137598	+	0.990488i	$0.456062\pi$
$240$	−2.52852	−0.163215
$241$	15.5338	1.00062	0.500309	−	0.865847i	$-0.333220\pi$
$241$	15.5338	1.00062	0.500309	+	0.865847i	$0.333220\pi$
$242$	7.45046	0.478934
$243$	−1.00000	−0.0641500
$244$	3.21317	0.205702
$245$	0	0
$246$	3.05704	0.194910
$247$	−0.786834	−0.0500650
$248$	−2.00000	−0.127000
$249$	13.6478	0.864897
$250$	−9.11932	−0.576756
$251$	−21.4266	−1.35244	−0.676218	−	0.736702i	$-0.736382\pi$
$251$	−21.4266	−1.35244	−0.676218	+	0.736702i	$0.736382\pi$
$252$	0	0
$253$	−4.29540	−0.270049
$254$	6.27021	0.393428
$255$	−17.2544	−1.08051
$256$	1.00000	0.0625000
$257$	19.5338	1.21848	0.609241	−	0.792985i	$-0.291474\pi$
$257$	19.5338	1.21848	0.609241	+	0.792985i	$0.291474\pi$
$258$	−2.00000	−0.124515
$259$	0	0
$260$	0.994763	0.0616926
$261$	4.60658	0.285140
$262$	−19.0983	−1.17990
$263$	17.8040	1.09784	0.548920	−	0.835875i	$-0.315039\pi$
$263$	17.8040	1.09784	0.548920	+	0.835875i	$0.315039\pi$
$264$	−4.29540	−0.264364
$265$	0.653150	0.0401227
$266$	0	0
$267$	8.27021	0.506128
$268$	3.74169	0.228560
$269$	−19.6321	−1.19699	−0.598494	−	0.801127i	$-0.704234\pi$
$269$	−19.6321	−1.19699	−0.598494	+	0.801127i	$0.704234\pi$
$270$	−2.52852	−0.153881
$271$	9.37763	0.569651	0.284825	−	0.958579i	$-0.408064\pi$
$271$	9.37763	0.569651	0.284825	+	0.958579i	$0.408064\pi$
$272$	6.82392	0.413761
$273$	0	0
$274$	−17.5288	−1.05895
$275$	5.98528	0.360926
$276$	1.00000	0.0601929
$277$	−11.9272	−0.716634	−0.358317	−	0.933600i	$-0.616649\pi$
$277$	−11.9272	−0.716634	−0.358317	+	0.933600i	$0.616649\pi$
$278$	13.0413	0.782163
$279$	−2.00000	−0.119737
$280$	0	0
$281$	−10.6783	−0.637012	−0.318506	−	0.947921i	$-0.603181\pi$
$281$	−10.6783	−0.637012	−0.318506	+	0.947921i	$0.603181\pi$
$282$	9.59080	0.571124
$283$	−11.2334	−0.667756	−0.333878	−	0.942616i	$-0.608357\pi$
$283$	−11.2334	−0.667756	−0.333878	+	0.942616i	$0.608357\pi$
$284$	−13.8610	−0.822499
$285$	5.05704	0.299553
$286$	1.68988	0.0999249
$287$	0	0
$288$	1.00000	0.0589256
$289$	29.5659	1.73917
$290$	11.6478	0.683985
$291$	8.00000	0.468968
$292$	4.21317	0.246557
$293$	22.1764	1.29556	0.647778	−	0.761829i	$-0.275698\pi$
$293$	22.1764	1.29556	0.647778	+	0.761829i	$0.275698\pi$
$294$	0	0
$295$	25.5737	1.48896
$296$	9.05704	0.526430
$297$	−4.29540	−0.249244
$298$	−0.0622786	−0.00360770
$299$	−0.393417	−0.0227519
$300$	−1.39342	−0.0804490
$301$	0	0
$302$	−2.15612	−0.124071
$303$	−5.39342	−0.309844
$304$	−2.00000	−0.114708
$305$	8.12456	0.465211
$306$	6.82392	0.390098
$307$	−8.01578	−0.457485	−0.228742	−	0.973487i	$-0.573461\pi$
$307$	−8.01578	−0.457485	−0.228742	+	0.973487i	$0.573461\pi$
$308$	0	0
$309$	18.1512	1.03258
$310$	−5.05704	−0.287221
$311$	21.5908	1.22430	0.612151	−	0.790741i	$-0.290304\pi$
$311$	21.5908	1.22430	0.612151	+	0.790741i	$0.290304\pi$
$312$	−0.393417	−0.0222728
$313$	13.1816	0.745068	0.372534	−	0.928019i	$-0.378489\pi$
$313$	13.1816	0.745068	0.372534	+	0.928019i	$0.378489\pi$
$314$	11.0822	0.625407
$315$	0	0
$316$	3.70460	0.208400
$317$	−14.2282	−0.799133	−0.399567	−	0.916704i	$-0.630839\pi$
$317$	−14.2282	−0.799133	−0.399567	+	0.916704i	$0.630839\pi$
$318$	−0.258313	−0.0144855
$319$	19.7871	1.10787
$320$	2.52852	0.141349
$321$	−16.5908	−0.926008
$322$	0	0
$323$	−13.6478	−0.759386
$324$	1.00000	0.0555556
$325$	0.548194	0.0304083
$326$	12.2544	0.678710
$327$	−14.5656	−0.805480
$328$	−3.05704	−0.168797
$329$	0	0
$330$	−10.8610	−0.597879
$331$	−21.5975	−1.18710	−0.593552	−	0.804796i	$-0.702275\pi$
$331$	−21.5975	−1.18710	−0.593552	+	0.804796i	$0.702275\pi$
$332$	−13.6478	−0.749023
$333$	9.05704	0.496323
$334$	4.81975	0.263725
$335$	9.46093	0.516906
$336$	0	0
$337$	13.2132	0.719767	0.359884	−	0.932997i	$-0.382816\pi$
$337$	13.2132	0.719767	0.359884	+	0.932997i	$0.382816\pi$
$338$	−12.8452	−0.698688
$339$	9.11932	0.495293
$340$	17.2544	0.935753
$341$	−8.59080	−0.465218
$342$	−2.00000	−0.108148
$343$	0	0
$344$	2.00000	0.107833
$345$	2.52852	0.136131
$346$	22.9593	1.23430
$347$	−19.4189	−1.04246	−0.521230	−	0.853416i	$-0.674527\pi$
$347$	−19.4189	−1.04246	−0.521230	+	0.853416i	$0.674527\pi$
$348$	−4.60658	−0.246939
$349$	−5.80262	−0.310607	−0.155303	−	0.987867i	$-0.549636\pi$
$349$	−5.80262	−0.310607	−0.155303	+	0.987867i	$0.549636\pi$
$350$	0	0
$351$	−0.393417	−0.0209990
$352$	4.29540	0.228946
$353$	20.9430	1.11468	0.557341	−	0.830284i	$-0.311822\pi$
$353$	20.9430	1.11468	0.557341	+	0.830284i	$0.311822\pi$
$354$	−10.1141	−0.537557
$355$	−35.0478	−1.86015
$356$	−8.27021	−0.438320
$357$	0	0
$358$	21.8452	1.15456
$359$	−4.70488	−0.248314	−0.124157	−	0.992263i	$-0.539623\pi$
$359$	−4.70488	−0.248314	−0.124157	+	0.992263i	$0.539623\pi$
$360$	2.52852	0.133265
$361$	−15.0000	−0.789474
$362$	−22.0994	−1.16152
$363$	−7.45046	−0.391048
$364$	0	0
$365$	10.6531	0.557608
$366$	−3.21317	−0.167955
$367$	−9.43991	−0.492759	−0.246380	−	0.969173i	$-0.579241\pi$
$367$	−9.43991	−0.492759	−0.246380	+	0.969173i	$0.579241\pi$
$368$	−1.00000	−0.0521286
$369$	−3.05704	−0.159143
$370$	22.9009	1.19056
$371$	0	0
$372$	2.00000	0.103695
$373$	11.6730	0.604407	0.302203	−	0.953243i	$-0.402278\pi$
$373$	11.6730	0.604407	0.302203	+	0.953243i	$0.402278\pi$
$374$	29.3115	1.51566
$375$	9.11932	0.470920
$376$	−9.59080	−0.494608
$377$	1.81231	0.0933386
$378$	0	0
$379$	9.42944	0.484358	0.242179	−	0.970232i	$-0.422138\pi$
$379$	9.42944	0.484358	0.242179	+	0.970232i	$0.422138\pi$
$380$	−5.05704	−0.259421
$381$	−6.27021	−0.321232
$382$	−8.27021	−0.423141
$383$	−23.4098	−1.19618	−0.598092	−	0.801428i	$-0.704074\pi$
$383$	−23.4098	−1.19618	−0.598092	+	0.801428i	$0.704074\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	−6.50750	−0.331223
$387$	2.00000	0.101666
$388$	−8.00000	−0.406138
$389$	−22.0742	−1.11921	−0.559603	−	0.828761i	$-0.689046\pi$
$389$	−22.0742	−1.11921	−0.559603	+	0.828761i	$0.689046\pi$
$390$	−0.994763	−0.0503718
$391$	−6.82392	−0.345100
$392$	0	0
$393$	19.0983	0.963382
$394$	8.18025	0.412115
$395$	9.36716	0.471313
$396$	4.29540	0.215852
$397$	−16.8281	−0.844578	−0.422289	−	0.906461i	$-0.638773\pi$
$397$	−16.8281	−0.844578	−0.422289	+	0.906461i	$0.638773\pi$
$398$	−14.4095	−0.722282
$399$	0	0
$400$	1.39342	0.0696708
$401$	6.23312	0.311267	0.155634	−	0.987815i	$-0.450258\pi$
$401$	6.23312	0.311267	0.155634	+	0.987815i	$0.450258\pi$
$402$	−3.74169	−0.186618
$403$	−0.786834	−0.0391950
$404$	5.39342	0.268333
$405$	2.52852	0.125643
$406$	0	0
$407$	38.9036	1.92838
$408$	−6.82392	−0.337834
$409$	0.369291	0.0182603	0.00913013	−	0.999958i	$-0.497094\pi$
$409$	0.369291	0.0182603	0.00913013	+	0.999958i	$0.497094\pi$
$410$	−7.72979	−0.381747
$411$	17.5288	0.864632
$412$	−18.1512	−0.894244
$413$	0	0
$414$	−1.00000	−0.0491473
$415$	−34.5088	−1.69397
$416$	0.393417	0.0192889
$417$	−13.0413	−0.638633
$418$	−8.59080	−0.420190
$419$	30.4837	1.48922	0.744612	−	0.667498i	$-0.232635\pi$
$419$	30.4837	1.48922	0.744612	+	0.667498i	$0.232635\pi$
$420$	0	0
$421$	34.2954	1.67146	0.835728	−	0.549144i	$-0.185046\pi$
$421$	34.2954	1.67146	0.835728	+	0.549144i	$0.185046\pi$
$422$	15.1974	0.739797
$423$	−9.59080	−0.466321
$424$	0.258313	0.0125448
$425$	9.50857	0.461233
$426$	13.8610	0.671568
$427$	0	0
$428$	16.5908	0.801947
$429$	−1.68988	−0.0815883
$430$	5.05704	0.243872
$431$	32.1966	1.55086	0.775428	−	0.631436i	$-0.217534\pi$
$431$	32.1966	1.55086	0.775428	+	0.631436i	$0.217534\pi$
$432$	−1.00000	−0.0481125
$433$	−22.5592	−1.08413	−0.542064	−	0.840337i	$-0.682357\pi$
$433$	−22.5592	−1.08413	−0.542064	+	0.840337i	$0.682357\pi$
$434$	0	0
$435$	−11.6478	−0.558471
$436$	14.5656	0.697566
$437$	2.00000	0.0956730
$438$	−4.21317	−0.201313
$439$	5.94962	0.283960	0.141980	−	0.989870i	$-0.454653\pi$
$439$	5.94962	0.283960	0.141980	+	0.989870i	$0.454653\pi$
$440$	10.8610	0.517778
$441$	0	0
$442$	2.68465	0.127696
$443$	15.2439	0.724262	0.362131	−	0.932127i	$-0.382049\pi$
$443$	15.2439	0.724262	0.362131	+	0.932127i	$0.382049\pi$
$444$	−9.05704	−0.429828
$445$	−20.9114	−0.991295
$446$	−21.1711	−1.00248
$447$	0.0622786	0.00294568
$448$	0	0
$449$	−22.5488	−1.06414	−0.532071	−	0.846700i	$-0.678586\pi$
$449$	−22.5488	−1.06414	−0.532071	+	0.846700i	$0.678586\pi$
$450$	1.39342	0.0656863
$451$	−13.1312	−0.618325
$452$	−9.11932	−0.428937
$453$	2.15612	0.101304
$454$	−2.40948	−0.113083
$455$	0	0
$456$	2.00000	0.0936586
$457$	2.11408	0.0988926	0.0494463	−	0.998777i	$-0.484254\pi$
$457$	2.11408	0.0988926	0.0494463	+	0.998777i	$0.484254\pi$
$458$	10.6160	0.496053
$459$	−6.82392	−0.318513
$460$	−2.52852	−0.117893
$461$	6.00000	0.279448	0.139724	−	0.990190i	$-0.455378\pi$
$461$	6.00000	0.279448	0.139724	+	0.990190i	$0.455378\pi$
$462$	0	0
$463$	−2.42633	−0.112761	−0.0563806	−	0.998409i	$-0.517956\pi$
$463$	−2.42633	−0.112761	−0.0563806	+	0.998409i	$0.517956\pi$
$464$	4.60658	0.213855
$465$	5.05704	0.234515
$466$	13.1816	0.610626
$467$	−19.7871	−0.915639	−0.457819	−	0.889045i	$-0.651369\pi$
$467$	−19.7871	−0.915639	−0.457819	+	0.889045i	$0.651369\pi$
$468$	0.393417	0.0181857
$469$	0	0
$470$	−24.2505	−1.11859
$471$	−11.0822	−0.510642
$472$	10.1141	0.465538
$473$	8.59080	0.395005
$474$	−3.70460	−0.170158
$475$	−2.78683	−0.127869
$476$	0	0
$477$	0.258313	0.0118273
$478$	4.25442	0.194593
$479$	22.1246	1.01090	0.505448	−	0.862857i	$-0.331327\pi$
$479$	22.1246	1.01090	0.505448	+	0.862857i	$0.331327\pi$
$480$	−2.52852	−0.115411
$481$	3.56319	0.162468
$482$	15.5338	0.707543
$483$	0	0
$484$	7.45046	0.338657
$485$	−20.2282	−0.918514
$486$	−1.00000	−0.0453609
$487$	8.54876	0.387381	0.193691	−	0.981063i	$-0.437954\pi$
$487$	8.54876	0.387381	0.193691	+	0.981063i	$0.437954\pi$
$488$	3.21317	0.145453
$489$	−12.2544	−0.554164
$490$	0	0
$491$	22.4360	1.01252	0.506262	−	0.862380i	$-0.331027\pi$
$491$	22.4360	1.01252	0.506262	+	0.862380i	$0.331027\pi$
$492$	3.05704	0.137822
$493$	31.4350	1.41576
$494$	−0.786834	−0.0354013
$495$	10.8610	0.488166
$496$	−2.00000	−0.0898027
$497$	0	0
$498$	13.6478	0.611574
$499$	−36.4931	−1.63365	−0.816827	−	0.576883i	$-0.804269\pi$
$499$	−36.4931	−1.63365	−0.816827	+	0.576883i	$0.804269\pi$
$500$	−9.11932	−0.407828
$501$	−4.81975	−0.215331
$502$	−21.4266	−0.956317
$503$	38.4585	1.71478	0.857389	−	0.514669i	$-0.172085\pi$
$503$	38.4585	1.71478	0.857389	+	0.514669i	$0.172085\pi$
$504$	0	0
$505$	13.6374	0.606855
$506$	−4.29540	−0.190954
$507$	12.8452	0.570476
$508$	6.27021	0.278195
$509$	22.5750	1.00062	0.500310	−	0.865846i	$-0.333219\pi$
$509$	22.5750	1.00062	0.500310	+	0.865846i	$0.333219\pi$
$510$	−17.2544	−0.764039
$511$	0	0
$512$	1.00000	0.0441942
$513$	2.00000	0.0883022
$514$	19.5338	0.861597
$515$	−45.8956	−2.02240
$516$	−2.00000	−0.0880451
$517$	−41.1963	−1.81181
$518$	0	0
$519$	−22.9593	−1.00780
$520$	0.994763	0.0436232
$521$	17.5352	0.768230	0.384115	−	0.923285i	$-0.374507\pi$
$521$	17.5352	0.768230	0.384115	+	0.923285i	$0.374507\pi$
$522$	4.60658	0.201625
$523$	20.3009	0.887697	0.443849	−	0.896102i	$-0.353613\pi$
$523$	20.3009	0.887697	0.443849	+	0.896102i	$0.353613\pi$
$524$	−19.0983	−0.834313
$525$	0	0
$526$	17.8040	0.776290
$527$	−13.6478	−0.594509
$528$	−4.29540	−0.186933
$529$	1.00000	0.0434783
$530$	0.653150	0.0283710
$531$	10.1141	0.438914
$532$	0	0
$533$	−1.20269	−0.0520944
$534$	8.27021	0.357887
$535$	41.9502	1.81366
$536$	3.74169	0.161616
$537$	−21.8452	−0.942691
$538$	−19.6321	−0.846398
$539$	0	0
$540$	−2.52852	−0.108810
$541$	31.8032	1.36733	0.683663	−	0.729798i	$-0.260386\pi$
$541$	31.8032	1.36733	0.683663	+	0.729798i	$0.260386\pi$
$542$	9.37763	0.402804
$543$	22.0994	0.948375
$544$	6.82392	0.292573
$545$	36.8294	1.57760
$546$	0	0
$547$	29.5817	1.26482	0.632410	−	0.774633i	$-0.282066\pi$
$547$	29.5817	1.26482	0.632410	+	0.774633i	$0.282066\pi$
$548$	−17.5288	−0.748793
$549$	3.21317	0.137135
$550$	5.98528	0.255213
$551$	−9.21317	−0.392494
$552$	1.00000	0.0425628
$553$	0	0
$554$	−11.9272	−0.506737
$555$	−22.9009	−0.972090
$556$	13.0413	0.553073
$557$	−21.5022	−0.911077	−0.455539	−	0.890216i	$-0.650553\pi$
$557$	−21.5022	−0.911077	−0.455539	+	0.890216i	$0.650553\pi$
$558$	−2.00000	−0.0846668
$559$	0.786834	0.0332795
$560$	0	0
$561$	−29.3115	−1.23753
$562$	−10.6783	−0.450436
$563$	−31.4665	−1.32616	−0.663078	−	0.748550i	$-0.730750\pi$
$563$	−31.4665	−1.32616	−0.663078	+	0.748550i	$0.730750\pi$
$564$	9.59080	0.403846
$565$	−23.0584	−0.970074
$566$	−11.2334	−0.472175
$567$	0	0
$568$	−13.8610	−0.581595
$569$	−37.4720	−1.57091	−0.785455	−	0.618919i	$-0.787571\pi$
$569$	−37.4720	−1.57091	−0.785455	+	0.618919i	$0.787571\pi$
$570$	5.05704	0.211816
$571$	28.2085	1.18049	0.590244	−	0.807225i	$-0.299031\pi$
$571$	28.2085	1.18049	0.590244	+	0.807225i	$0.299031\pi$
$572$	1.68988	0.0706575
$573$	8.27021	0.345493
$574$	0	0
$575$	−1.39342	−0.0581095
$576$	1.00000	0.0416667
$577$	2.87679	0.119762	0.0598812	−	0.998206i	$-0.480928\pi$
$577$	2.87679	0.119762	0.0598812	+	0.998206i	$0.480928\pi$
$578$	29.5659	1.22978
$579$	6.50750	0.270442
$580$	11.6478	0.483650
$581$	0	0
$582$	8.00000	0.331611
$583$	1.10956	0.0459532
$584$	4.21317	0.174342
$585$	0.994763	0.0411284
$586$	22.1764	0.916097
$587$	−19.8873	−0.820835	−0.410418	−	0.911898i	$-0.634617\pi$
$587$	−19.8873	−0.820835	−0.410418	+	0.911898i	$0.634617\pi$
$588$	0	0
$589$	4.00000	0.164817
$590$	25.5737	1.05285
$591$	−8.18025	−0.336491
$592$	9.05704	0.372242
$593$	−1.10743	−0.0454765	−0.0227383	−	0.999741i	$-0.507238\pi$
$593$	−1.10743	−0.0454765	−0.0227383	+	0.999741i	$0.507238\pi$
$594$	−4.29540	−0.176242
$595$	0	0
$596$	−0.0622786	−0.00255103
$597$	14.4095	0.589741
$598$	−0.393417	−0.0160880
$599$	−29.7469	−1.21543	−0.607713	−	0.794157i	$-0.707913\pi$
$599$	−29.7469	−1.21543	−0.607713	+	0.794157i	$0.707913\pi$
$600$	−1.39342	−0.0568860
$601$	−3.88592	−0.158510	−0.0792549	−	0.996854i	$-0.525254\pi$
$601$	−3.88592	−0.158510	−0.0792549	+	0.996854i	$0.525254\pi$
$602$	0	0
$603$	3.74169	0.152373
$604$	−2.15612	−0.0877315
$605$	18.8386	0.765900
$606$	−5.39342	−0.219093
$607$	−1.95796	−0.0794711	−0.0397355	−	0.999210i	$-0.512652\pi$
$607$	−1.95796	−0.0794711	−0.0397355	+	0.999210i	$0.512652\pi$
$608$	−2.00000	−0.0811107
$609$	0	0
$610$	8.12456	0.328954
$611$	−3.77318	−0.152647
$612$	6.82392	0.275841
$613$	−3.94324	−0.159266	−0.0796330	−	0.996824i	$-0.525375\pi$
$613$	−3.94324	−0.159266	−0.0796330	+	0.996824i	$0.525375\pi$
$614$	−8.01578	−0.323491
$615$	7.72979	0.311695
$616$	0	0
$617$	−20.8876	−0.840904	−0.420452	−	0.907315i	$-0.638128\pi$
$617$	−20.8876	−0.840904	−0.420452	+	0.907315i	$0.638128\pi$
$618$	18.1512	0.730147
$619$	29.2018	1.17372	0.586860	−	0.809688i	$-0.300364\pi$
$619$	29.2018	1.17372	0.586860	+	0.809688i	$0.300364\pi$
$620$	−5.05704	−0.203096
$621$	1.00000	0.0401286
$622$	21.5908	0.865712
$623$	0	0
$624$	−0.393417	−0.0157493
$625$	−30.0255	−1.20102
$626$	13.1816	0.526843
$627$	8.59080	0.343083
$628$	11.0822	0.442229
$629$	61.8045	2.46431
$630$	0	0
$631$	−16.2653	−0.647509	−0.323755	−	0.946141i	$-0.604945\pi$
$631$	−16.2653	−0.647509	−0.323755	+	0.946141i	$0.604945\pi$
$632$	3.70460	0.147361
$633$	−15.1974	−0.604042
$634$	−14.2282	−0.565073
$635$	15.8543	0.629161
$636$	−0.258313	−0.0102428
$637$	0	0
$638$	19.7871	0.783379
$639$	−13.8610	−0.548333
$640$	2.52852	0.0999486
$641$	−24.6174	−0.972329	−0.486165	−	0.873867i	$-0.661604\pi$
$641$	−24.6174	−0.972329	−0.486165	+	0.873867i	$0.661604\pi$
$642$	−16.5908	−0.654787
$643$	−15.2132	−0.599949	−0.299974	−	0.953947i	$-0.596978\pi$
$643$	−15.2132	−0.599949	−0.299974	+	0.953947i	$0.596978\pi$
$644$	0	0
$645$	−5.05704	−0.199121
$646$	−13.6478	−0.536967
$647$	11.0728	0.435318	0.217659	−	0.976025i	$-0.430158\pi$
$647$	11.0728	0.435318	0.217659	+	0.976025i	$0.430158\pi$
$648$	1.00000	0.0392837
$649$	43.4440	1.70533
$650$	0.548194	0.0215019
$651$	0	0
$652$	12.2544	0.479920
$653$	40.0584	1.56761	0.783803	−	0.621010i	$-0.213277\pi$
$653$	40.0584	1.56761	0.783803	+	0.621010i	$0.213277\pi$
$654$	−14.5656	−0.569560
$655$	−48.2904	−1.88686
$656$	−3.05704	−0.119357
$657$	4.21317	0.164371
$658$	0	0
$659$	−42.3380	−1.64925	−0.824627	−	0.565676i	$-0.808615\pi$
$659$	−42.3380	−1.64925	−0.824627	+	0.565676i	$0.808615\pi$
$660$	−10.8610	−0.422764
$661$	−15.4981	−0.602806	−0.301403	−	0.953497i	$-0.597455\pi$
$661$	−15.4981	−0.602806	−0.301403	+	0.953497i	$0.597455\pi$
$662$	−21.5975	−0.839409
$663$	−2.68465	−0.104263
$664$	−13.6478	−0.529639
$665$	0	0
$666$	9.05704	0.350953
$667$	−4.60658	−0.178368
$668$	4.81975	0.186482
$669$	21.1711	0.818523
$670$	9.46093	0.365508
$671$	13.8018	0.532814
$672$	0	0
$673$	−37.1875	−1.43347	−0.716736	−	0.697345i	$-0.754365\pi$
$673$	−37.1875	−1.43347	−0.716736	+	0.697345i	$0.754365\pi$
$674$	13.2132	0.508952
$675$	−1.39342	−0.0536326
$676$	−12.8452	−0.494047
$677$	−24.7168	−0.949943	−0.474971	−	0.880001i	$-0.657542\pi$
$677$	−24.7168	−0.949943	−0.474971	+	0.880001i	$0.657542\pi$
$678$	9.11932	0.350225
$679$	0	0
$680$	17.2544	0.661677
$681$	2.40948	0.0923316
$682$	−8.59080	−0.328959
$683$	−42.0650	−1.60957	−0.804787	−	0.593564i	$-0.797721\pi$
$683$	−42.0650	−1.60957	−0.804787	+	0.593564i	$0.797721\pi$
$684$	−2.00000	−0.0764719
$685$	−44.3219	−1.69345
$686$	0	0
$687$	−10.6160	−0.405025
$688$	2.00000	0.0762493
$689$	0.101625	0.00387159
$690$	2.52852	0.0962591
$691$	−10.5246	−0.400376	−0.200188	−	0.979758i	$-0.564155\pi$
$691$	−10.5246	−0.400376	−0.200188	+	0.979758i	$0.564155\pi$
$692$	22.9593	0.872782
$693$	0	0
$694$	−19.4189	−0.737131
$695$	32.9751	1.25082
$696$	−4.60658	−0.174612
$697$	−20.8610	−0.790167
$698$	−5.80262	−0.219632
$699$	−13.1816	−0.498574
$700$	0	0
$701$	−28.1764	−1.06421	−0.532103	−	0.846679i	$-0.678598\pi$
$701$	−28.1764	−1.06421	−0.532103	+	0.846679i	$0.678598\pi$
$702$	−0.393417	−0.0148486
$703$	−18.1141	−0.683186
$704$	4.29540	0.161889
$705$	24.2505	0.913328
$706$	20.9430	0.788199
$707$	0	0
$708$	−10.1141	−0.380111
$709$	−3.86073	−0.144993	−0.0724963	−	0.997369i	$-0.523097\pi$
$709$	−3.86073	−0.144993	−0.0724963	+	0.997369i	$0.523097\pi$
$710$	−35.0478	−1.31532
$711$	3.70460	0.138933
$712$	−8.27021	−0.309939
$713$	2.00000	0.0749006
$714$	0	0
$715$	4.27290	0.159798
$716$	21.8452	0.816394
$717$	−4.25442	−0.158884
$718$	−4.70488	−0.175585
$719$	−30.5180	−1.13813	−0.569064	−	0.822293i	$-0.692694\pi$
$719$	−30.5180	−1.13813	−0.569064	+	0.822293i	$0.692694\pi$
$720$	2.52852	0.0942324
$721$	0	0
$722$	−15.0000	−0.558242
$723$	−15.5338	−0.577707
$724$	−22.0994	−0.821316
$725$	6.41889	0.238392
$726$	−7.45046	−0.276512
$727$	−14.3591	−0.532549	−0.266275	−	0.963897i	$-0.585793\pi$
$727$	−14.3591	−0.532549	−0.266275	+	0.963897i	$0.585793\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	10.6531	0.394288
$731$	13.6478	0.504784
$732$	−3.21317	−0.118762
$733$	−11.9111	−0.439947	−0.219973	−	0.975506i	$-0.570597\pi$
$733$	−11.9111	−0.439947	−0.219973	+	0.975506i	$0.570597\pi$
$734$	−9.43991	−0.348434
$735$	0	0
$736$	−1.00000	−0.0368605
$737$	16.0720	0.592021
$738$	−3.05704	−0.112531
$739$	−41.1238	−1.51276	−0.756381	−	0.654131i	$-0.773034\pi$
$739$	−41.1238	−1.51276	−0.756381	+	0.654131i	$0.773034\pi$
$740$	22.9009	0.841854
$741$	0.786834	0.0289051
$742$	0	0
$743$	10.8610	0.398452	0.199226	−	0.979954i	$-0.436157\pi$
$743$	10.8610	0.398452	0.199226	+	0.979954i	$0.436157\pi$
$744$	2.00000	0.0733236
$745$	−0.157473	−0.00576936
$746$	11.6730	0.427380
$747$	−13.6478	−0.499348
$748$	29.3115	1.07173
$749$	0	0
$750$	9.11932	0.332990
$751$	−52.6733	−1.92208	−0.961038	−	0.276415i	$-0.910853\pi$
$751$	−52.6733	−1.92208	−0.961038	+	0.276415i	$0.910853\pi$
$752$	−9.59080	−0.349740
$753$	21.4266	0.780829
$754$	1.81231	0.0660004
$755$	−5.45181	−0.198412
$756$	0	0
$757$	16.0000	0.581530	0.290765	−	0.956795i	$-0.406090\pi$
$757$	16.0000	0.581530	0.290765	+	0.956795i	$0.406090\pi$
$758$	9.42944	0.342493
$759$	4.29540	0.155913
$760$	−5.05704	−0.183438
$761$	7.37763	0.267439	0.133719	−	0.991019i	$-0.457308\pi$
$761$	7.37763	0.267439	0.133719	+	0.991019i	$0.457308\pi$
$762$	−6.27021	−0.227146
$763$	0	0
$764$	−8.27021	−0.299206
$765$	17.2544	0.623835
$766$	−23.4098	−0.845829
$767$	3.97905	0.143675
$768$	−1.00000	−0.0360844
$769$	−26.1462	−0.942857	−0.471428	−	0.881904i	$-0.656261\pi$
$769$	−26.1462	−0.942857	−0.471428	+	0.881904i	$0.656261\pi$
$770$	0	0
$771$	−19.5338	−0.703491
$772$	−6.50750	−0.234210
$773$	22.7588	0.818578	0.409289	−	0.912405i	$-0.365777\pi$
$773$	22.7588	0.818578	0.409289	+	0.912405i	$0.365777\pi$
$774$	2.00000	0.0718885
$775$	−2.78683	−0.100106
$776$	−8.00000	−0.287183
$777$	0	0
$778$	−22.0742	−0.791397
$779$	6.11408	0.219060
$780$	−0.994763	−0.0356182
$781$	−59.5386	−2.13046
$782$	−6.82392	−0.244023
$783$	−4.60658	−0.164626
$784$	0	0
$785$	28.0217	1.00014
$786$	19.0983	0.681214
$787$	−5.59604	−0.199477	−0.0997386	−	0.995014i	$-0.531801\pi$
$787$	−5.59604	−0.199477	−0.0997386	+	0.995014i	$0.531801\pi$
$788$	8.18025	0.291409
$789$	−17.8040	−0.633838
$790$	9.36716	0.333269
$791$	0	0
$792$	4.29540	0.152630
$793$	1.26411	0.0448900
$794$	−16.8281	−0.597207
$795$	−0.653150	−0.0231648
$796$	−14.4095	−0.510731
$797$	52.7993	1.87025	0.935123	−	0.354322i	$-0.115288\pi$
$797$	52.7993	1.87025	0.935123	+	0.354322i	$0.115288\pi$
$798$	0	0
$799$	−65.4469	−2.31534
$800$	1.39342	0.0492647
$801$	−8.27021	−0.292213
$802$	6.23312	0.220099
$803$	18.0972	0.638637
$804$	−3.74169	−0.131959
$805$	0	0
$806$	−0.786834	−0.0277150
$807$	19.6321	0.691081
$808$	5.39342	0.189740
$809$	−5.41754	−0.190471	−0.0952353	−	0.995455i	$-0.530360\pi$
$809$	−5.41754	−0.190471	−0.0952353	+	0.995455i	$0.530360\pi$
$810$	2.52852	0.0888432
$811$	42.4931	1.49213	0.746067	−	0.665871i	$-0.231940\pi$
$811$	42.4931	1.49213	0.746067	+	0.665871i	$0.231940\pi$
$812$	0	0
$813$	−9.37763	−0.328888
$814$	38.9036	1.36357
$815$	30.9856	1.08538
$816$	−6.82392	−0.238885
$817$	−4.00000	−0.139942
$818$	0.369291	0.0129120
$819$	0	0
$820$	−7.72979	−0.269936
$821$	52.0268	1.81575	0.907874	−	0.419242i	$-0.137704\pi$
$821$	52.0268	1.81575	0.907874	+	0.419242i	$0.137704\pi$
$822$	17.5288	0.611387
$823$	40.4031	1.40836	0.704182	−	0.710020i	$-0.251314\pi$
$823$	40.4031	1.40836	0.704182	+	0.710020i	$0.251314\pi$
$824$	−18.1512	−0.632326
$825$	−5.98528	−0.208381
$826$	0	0
$827$	1.31040	0.0455670	0.0227835	−	0.999740i	$-0.492747\pi$
$827$	1.31040	0.0455670	0.0227835	+	0.999740i	$0.492747\pi$
$828$	−1.00000	−0.0347524
$829$	21.4084	0.743545	0.371773	−	0.928324i	$-0.378750\pi$
$829$	21.4084	0.743545	0.371773	+	0.928324i	$0.378750\pi$
$830$	−34.5088	−1.19782
$831$	11.9272	0.413749
$832$	0.393417	0.0136393
$833$	0	0
$834$	−13.0413	−0.451582
$835$	12.1868	0.421743
$836$	−8.59080	−0.297119
$837$	2.00000	0.0691301
$838$	30.4837	1.05304
$839$	−43.5238	−1.50261	−0.751305	−	0.659955i	$-0.770575\pi$
$839$	−43.5238	−1.50261	−0.751305	+	0.659955i	$0.770575\pi$
$840$	0	0
$841$	−7.77939	−0.268255
$842$	34.2954	1.18190
$843$	10.6783	0.367779
$844$	15.1974	0.523115
$845$	−32.4794	−1.11733
$846$	−9.59080	−0.329738
$847$	0	0
$848$	0.258313	0.00887051
$849$	11.2334	0.385529
$850$	9.50857	0.326141
$851$	−9.05704	−0.310471
$852$	13.8610	0.474870
$853$	41.2137	1.41113	0.705566	−	0.708645i	$-0.250693\pi$
$853$	41.2137	1.41113	0.705566	+	0.708645i	$0.250693\pi$
$854$	0	0
$855$	−5.05704	−0.172947
$856$	16.5908	0.567062
$857$	27.4917	0.939099	0.469550	−	0.882906i	$-0.344416\pi$
$857$	27.4917	0.939099	0.469550	+	0.882906i	$0.344416\pi$
$858$	−1.68988	−0.0576916
$859$	3.04126	0.103766	0.0518832	−	0.998653i	$-0.483478\pi$
$859$	3.04126	0.103766	0.0518832	+	0.998653i	$0.483478\pi$
$860$	5.05704	0.172444
$861$	0	0
$862$	32.1966	1.09662
$863$	9.70488	0.330358	0.165179	−	0.986264i	$-0.447180\pi$
$863$	9.70488	0.330358	0.165179	+	0.986264i	$0.447180\pi$
$864$	−1.00000	−0.0340207
$865$	58.0531	1.97386
$866$	−22.5592	−0.766594
$867$	−29.5659	−1.00411
$868$	0	0
$869$	15.9127	0.539803
$870$	−11.6478	−0.394899
$871$	1.47204	0.0498783
$872$	14.5656	0.493254
$873$	−8.00000	−0.270759
$874$	2.00000	0.0676510
$875$	0	0
$876$	−4.21317	−0.142350
$877$	2.97587	0.100488	0.0502441	−	0.998737i	$-0.484000\pi$
$877$	2.97587	0.100488	0.0502441	+	0.998737i	$0.484000\pi$
$878$	5.94962	0.200790
$879$	−22.1764	−0.747990
$880$	10.8610	0.366124
$881$	−26.9064	−0.906501	−0.453250	−	0.891383i	$-0.649736\pi$
$881$	−26.9064	−0.906501	−0.453250	+	0.891383i	$0.649736\pi$
$882$	0	0
$883$	19.9159	0.670224	0.335112	−	0.942178i	$-0.391226\pi$
$883$	19.9159	0.670224	0.335112	+	0.942178i	$0.391226\pi$
$884$	2.68465	0.0902944
$885$	−25.5737	−0.859649
$886$	15.2439	0.512130
$887$	17.2079	0.577783	0.288892	−	0.957362i	$-0.406713\pi$
$887$	17.2079	0.577783	0.288892	+	0.957362i	$0.406713\pi$
$888$	−9.05704	−0.303934
$889$	0	0
$890$	−20.9114	−0.700951
$891$	4.29540	0.143901
$892$	−21.1711	−0.708862
$893$	19.1816	0.641888
$894$	0.0622786	0.00208291
$895$	55.2361	1.84634
$896$	0	0
$897$	0.393417	0.0131358
$898$	−22.5488	−0.752462
$899$	−9.21317	−0.307276
$900$	1.39342	0.0464472
$901$	1.76271	0.0587243
$902$	−13.1312	−0.437222
$903$	0	0
$904$	−9.11932	−0.303304
$905$	−55.8787	−1.85747
$906$	2.15612	0.0716324
$907$	−15.9377	−0.529203	−0.264602	−	0.964358i	$-0.585240\pi$
$907$	−15.9377	−0.529203	−0.264602	+	0.964358i	$0.585240\pi$
$908$	−2.40948	−0.0799615
$909$	5.39342	0.178888
$910$	0	0
$911$	−30.6965	−1.01702	−0.508511	−	0.861056i	$-0.669804\pi$
$911$	−30.6965	−1.01702	−0.508511	+	0.861056i	$0.669804\pi$
$912$	2.00000	0.0662266
$913$	−58.6229	−1.94014
$914$	2.11408	0.0699276
$915$	−8.12456	−0.268590
$916$	10.6160	0.350762
$917$	0	0
$918$	−6.82392	−0.225223
$919$	2.66780	0.0880025	0.0440012	−	0.999031i	$-0.485989\pi$
$919$	2.66780	0.0880025	0.0440012	+	0.999031i	$0.485989\pi$
$920$	−2.52852	−0.0833629
$921$	8.01578	0.264129
$922$	6.00000	0.197599
$923$	−5.45315	−0.179493
$924$	0	0
$925$	12.6202	0.414951
$926$	−2.42633	−0.0797342
$927$	−18.1512	−0.596163
$928$	4.60658	0.151218
$929$	46.9540	1.54051	0.770255	−	0.637736i	$-0.220129\pi$
$929$	46.9540	1.54051	0.770255	+	0.637736i	$0.220129\pi$
$930$	5.05704	0.165827
$931$	0	0
$932$	13.1816	0.431778
$933$	−21.5908	−0.706851
$934$	−19.7871	−0.647454
$935$	74.1146	2.42381
$936$	0.393417	0.0128592
$937$	11.9895	0.391681	0.195840	−	0.980636i	$-0.437257\pi$
$937$	11.9895	0.391681	0.195840	+	0.980636i	$0.437257\pi$
$938$	0	0
$939$	−13.1816	−0.430165
$940$	−24.2505	−0.790965
$941$	34.8931	1.13748	0.568742	−	0.822516i	$-0.307430\pi$
$941$	34.8931	1.13748	0.568742	+	0.822516i	$0.307430\pi$
$942$	−11.0822	−0.361079
$943$	3.05704	0.0995510
$944$	10.1141	0.329185
$945$	0	0
$946$	8.59080	0.279311
$947$	−17.5142	−0.569134	−0.284567	−	0.958656i	$-0.591850\pi$
$947$	−17.5142	−0.569134	−0.284567	+	0.958656i	$0.591850\pi$
$948$	−3.70460	−0.120320
$949$	1.65753	0.0538057
$950$	−2.78683	−0.0904168
$951$	14.2282	0.461380
$952$	0	0
$953$	−13.3209	−0.431505	−0.215753	−	0.976448i	$-0.569221\pi$
$953$	−13.3209	−0.431505	−0.215753	+	0.976448i	$0.569221\pi$
$954$	0.258313	0.00836320
$955$	−20.9114	−0.676677
$956$	4.25442	0.137598
$957$	−19.7871	−0.639627
$958$	22.1246	0.714812
$959$	0	0
$960$	−2.52852	−0.0816077
$961$	−27.0000	−0.870968
$962$	3.56319	0.114882
$963$	16.5908	0.534631
$964$	15.5338	0.500309
$965$	−16.4543	−0.529684
$966$	0	0
$967$	−61.9397	−1.99185	−0.995923	−	0.0902039i	$-0.971248\pi$
$967$	−61.9397	−1.99185	−0.995923	+	0.0902039i	$0.971248\pi$
$968$	7.45046	0.239467
$969$	13.6478	0.438432
$970$	−20.2282	−0.649487
$971$	7.14593	0.229324	0.114662	−	0.993405i	$-0.463422\pi$
$971$	7.14593	0.229324	0.114662	+	0.993405i	$0.463422\pi$
$972$	−1.00000	−0.0320750
$973$	0	0
$974$	8.54876	0.273920
$975$	−0.548194	−0.0175563
$976$	3.21317	0.102851
$977$	−24.3325	−0.778465	−0.389233	−	0.921140i	$-0.627260\pi$
$977$	−24.3325	−0.778465	−0.389233	+	0.921140i	$0.627260\pi$
$978$	−12.2544	−0.391853
$979$	−35.5238	−1.13535
$980$	0	0
$981$	14.5656	0.465044
$982$	22.4360	0.715962
$983$	−36.1561	−1.15320	−0.576601	−	0.817026i	$-0.695621\pi$
$983$	−36.1561	−1.15320	−0.576601	+	0.817026i	$0.695621\pi$
$984$	3.05704	0.0974549
$985$	20.6839	0.659045
$986$	31.4350	1.00109
$987$	0	0
$988$	−0.786834	−0.0250325
$989$	−2.00000	−0.0635963
$990$	10.8610	0.345185
$991$	−3.77240	−0.119834	−0.0599171	−	0.998203i	$-0.519084\pi$
$991$	−3.77240	−0.119834	−0.0599171	+	0.998203i	$0.519084\pi$
$992$	−2.00000	−0.0635001
$993$	21.5975	0.685375
$994$	0	0
$995$	−36.4347	−1.15506
$996$	13.6478	0.432448
$997$	−33.2641	−1.05349	−0.526743	−	0.850025i	$-0.676587\pi$
$997$	−33.2641	−1.05349	−0.526743	+	0.850025i	$0.676587\pi$
$998$	−36.4931	−1.15517
$999$	−9.05704	−0.286552

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6762.2.a.cl.1.3		4
7.2	even	3		966.2.i.m.277.2	✓	8
7.4	even	3		966.2.i.m.415.2	yes	8
7.6	odd	2		6762.2.a.cr.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.i.m.277.2	✓	8	7.2	even	3
966.2.i.m.415.2	yes	8	7.4	even	3
6762.2.a.cl.1.3		4	1.1	even	1	trivial
6762.2.a.cr.1.2		4	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:	\( N \)	\(=\)	\( 6762 = 2 \cdot 3 \cdot 7^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6762.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.52852 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.52852 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +2.52852 q^{10} +4.29540 q^{11} -1.00000 q^{12} +0.393417 q^{13} -2.52852 q^{15} +1.00000 q^{16} +6.82392 q^{17} +1.00000 q^{18} -2.00000 q^{19} +2.52852 q^{20} +4.29540 q^{22} -1.00000 q^{23} -1.00000 q^{24} +1.39342 q^{25} +0.393417 q^{26} -1.00000 q^{27} +4.60658 q^{29} -2.52852 q^{30} -2.00000 q^{31} +1.00000 q^{32} -4.29540 q^{33} +6.82392 q^{34} +1.00000 q^{36} +9.05704 q^{37} -2.00000 q^{38} -0.393417 q^{39} +2.52852 q^{40} -3.05704 q^{41} +2.00000 q^{43} +4.29540 q^{44} +2.52852 q^{45} -1.00000 q^{46} -9.59080 q^{47} -1.00000 q^{48} +1.39342 q^{50} -6.82392 q^{51} +0.393417 q^{52} +0.258313 q^{53} -1.00000 q^{54} +10.8610 q^{55} +2.00000 q^{57} +4.60658 q^{58} +10.1141 q^{59} -2.52852 q^{60} +3.21317 q^{61} -2.00000 q^{62} +1.00000 q^{64} +0.994763 q^{65} -4.29540 q^{66} +3.74169 q^{67} +6.82392 q^{68} +1.00000 q^{69} -13.8610 q^{71} +1.00000 q^{72} +4.21317 q^{73} +9.05704 q^{74} -1.39342 q^{75} -2.00000 q^{76} -0.393417 q^{78} +3.70460 q^{79} +2.52852 q^{80} +1.00000 q^{81} -3.05704 q^{82} -13.6478 q^{83} +17.2544 q^{85} +2.00000 q^{86} -4.60658 q^{87} +4.29540 q^{88} -8.27021 q^{89} +2.52852 q^{90} -1.00000 q^{92} +2.00000 q^{93} -9.59080 q^{94} -5.05704 q^{95} -1.00000 q^{96} -8.00000 q^{97} +4.29540 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} + 2 q^{5} - 4 q^{6} + 4 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 + 2 * q^5 - 4 * q^6 + 4 * q^8 + 4 * q^9	\( 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} + 2 q^{5} - 4 q^{6} + 4 q^{8} + 4 q^{9} + 2 q^{10} - 4 q^{12} + 6 q^{13} - 2 q^{15} + 4 q^{16} + 2 q^{17} + 4 q^{18} - 8 q^{19} + 2 q^{20} - 4 q^{23} - 4 q^{24} + 10 q^{25} + 6 q^{26} - 4 q^{27} + 14 q^{29} - 2 q^{30} - 8 q^{31} + 4 q^{32} + 2 q^{34} + 4 q^{36} + 20 q^{37} - 8 q^{38} - 6 q^{39} + 2 q^{40} + 4 q^{41} + 8 q^{43} + 2 q^{45} - 4 q^{46} - 4 q^{47} - 4 q^{48} + 10 q^{50} - 2 q^{51} + 6 q^{52} + 18 q^{53} - 4 q^{54} - 16 q^{55} + 8 q^{57} + 14 q^{58} + 8 q^{59} - 2 q^{60} + 4 q^{61} - 8 q^{62} + 4 q^{64} + 14 q^{65} - 2 q^{67} + 2 q^{68} + 4 q^{69} + 4 q^{71} + 4 q^{72} + 8 q^{73} + 20 q^{74} - 10 q^{75} - 8 q^{76} - 6 q^{78} + 32 q^{79} + 2 q^{80} + 4 q^{81} + 4 q^{82} - 4 q^{83} + 14 q^{85} + 8 q^{86} - 14 q^{87} - 8 q^{89} + 2 q^{90} - 4 q^{92} + 8 q^{93} - 4 q^{94} - 4 q^{95} - 4 q^{96} - 32 q^{97}+O(q^{100}) \) 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 + 2 * q^5 - 4 * q^6 + 4 * q^8 + 4 * q^9 + 2 * q^10 - 4 * q^12 + 6 * q^13 - 2 * q^15 + 4 * q^16 + 2 * q^17 + 4 * q^18 - 8 * q^19 + 2 * q^20 - 4 * q^23 - 4 * q^24 + 10 * q^25 + 6 * q^26 - 4 * q^27 + 14 * q^29 - 2 * q^30 - 8 * q^31 + 4 * q^32 + 2 * q^34 + 4 * q^36 + 20 * q^37 - 8 * q^38 - 6 * q^39 + 2 * q^40 + 4 * q^41 + 8 * q^43 + 2 * q^45 - 4 * q^46 - 4 * q^47 - 4 * q^48 + 10 * q^50 - 2 * q^51 + 6 * q^52 + 18 * q^53 - 4 * q^54 - 16 * q^55 + 8 * q^57 + 14 * q^58 + 8 * q^59 - 2 * q^60 + 4 * q^61 - 8 * q^62 + 4 * q^64 + 14 * q^65 - 2 * q^67 + 2 * q^68 + 4 * q^69 + 4 * q^71 + 4 * q^72 + 8 * q^73 + 20 * q^74 - 10 * q^75 - 8 * q^76 - 6 * q^78 + 32 * q^79 + 2 * q^80 + 4 * q^81 + 4 * q^82 - 4 * q^83 + 14 * q^85 + 8 * q^86 - 14 * q^87 - 8 * q^89 + 2 * q^90 - 4 * q^92 + 8 * q^93 - 4 * q^94 - 4 * q^95 - 4 * q^96 - 32 * q^97

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