LMFDB - Embedded newform 5929.2.a.y.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5929,2,Mod(1,5929)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5929, 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("5929.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5929 = 7^{2} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5929.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:	$47.3433033584$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.568.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 6x - 2 $ x^3 - x^2 - 6*x - 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 847)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.363328$ of defining polynomial
Character	$\chi$	$=$	5929.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.36333 q^{2} -0.363328 q^{3} -0.141336 q^{4} -3.14134 q^{5} -0.495336 q^{6} -2.91934 q^{8} -2.86799 q^{9} +O(q^{10})$	\(q+1.36333 q^{2} -0.363328 q^{3} -0.141336 q^{4} -3.14134 q^{5} -0.495336 q^{6} -2.91934 q^{8} -2.86799 q^{9} -4.28267 q^{10} +0.0513514 q^{12} -4.77801 q^{13} +1.14134 q^{15} -3.69735 q^{16} -4.77801 q^{17} -3.91002 q^{18} -7.00933 q^{19} +0.443984 q^{20} +5.14134 q^{23} +1.06068 q^{24} +4.86799 q^{25} -6.51399 q^{26} +2.13201 q^{27} -7.00933 q^{29} +1.55602 q^{30} +3.63667 q^{31} +0.797984 q^{32} -6.51399 q^{34} +0.405351 q^{36} -9.86799 q^{37} -9.55602 q^{38} +1.73599 q^{39} +9.17064 q^{40} -3.22199 q^{41} -4.28267 q^{43} +9.00933 q^{45} +7.00933 q^{46} +0.778008 q^{47} +1.34335 q^{48} +6.63667 q^{50} +1.73599 q^{51} +0.675305 q^{52} +2.28267 q^{53} +2.90663 q^{54} +2.54669 q^{57} -9.55602 q^{58} +0.363328 q^{59} -0.161312 q^{60} +3.22199 q^{61} +4.95798 q^{62} +8.48262 q^{64} +15.0093 q^{65} -6.59465 q^{67} +0.675305 q^{68} -1.86799 q^{69} -15.1600 q^{71} +8.37266 q^{72} -3.22199 q^{73} -13.4533 q^{74} -1.76868 q^{75} +0.990671 q^{76} +2.36672 q^{78} +3.71733 q^{79} +11.6146 q^{80} +7.82936 q^{81} -4.39263 q^{82} +1.55602 q^{83} +15.0093 q^{85} -5.83869 q^{86} +2.54669 q^{87} +5.58532 q^{89} +12.2827 q^{90} -0.726656 q^{92} -1.32131 q^{93} +1.06068 q^{94} +22.0187 q^{95} -0.289930 q^{96} -6.15066 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 2 q^{2} + q^{3} + 8 q^{4} - q^{5} - 12 q^{6} + 6 q^{8} + 4 q^{9}+O(q^{10}) $ 3 * q + 2 * q^2 + q^3 + 8 * q^4 - q^5 - 12 * q^6 + 6 * q^8 + 4 * q^9	$ 3 q + 2 q^{2} + q^{3} + 8 q^{4} - q^{5} - 12 q^{6} + 6 q^{8} + 4 q^{9} + 4 q^{10} - 2 q^{12} - 8 q^{13} - 5 q^{15} + 10 q^{16} - 8 q^{17} - 18 q^{18} + 14 q^{20} + 7 q^{23} - 20 q^{24} + 2 q^{25} + 12 q^{26} + 19 q^{27} - 8 q^{30} + 13 q^{31} + 34 q^{32} + 12 q^{34} + 18 q^{36} - 17 q^{37} - 16 q^{38} - 20 q^{39} + 36 q^{40} - 16 q^{41} + 4 q^{43} + 6 q^{45} - 4 q^{47} - 36 q^{48} + 22 q^{50} - 20 q^{51} - 10 q^{53} - 8 q^{54} + 16 q^{57} - 16 q^{58} - q^{59} - 30 q^{60} + 16 q^{61} - 4 q^{62} + 34 q^{64} + 24 q^{65} - 3 q^{67} + 7 q^{69} + 5 q^{71} + 2 q^{72} - 16 q^{73} - 32 q^{74} - 20 q^{75} + 24 q^{76} + 28 q^{78} + 28 q^{79} + 56 q^{80} + 15 q^{81} - 28 q^{82} - 8 q^{83} + 24 q^{85} + 12 q^{86} + 16 q^{87} + 21 q^{89} + 20 q^{90} + 2 q^{92} + 17 q^{93} - 20 q^{94} + 24 q^{95} - 20 q^{96} + 11 q^{97}+O(q^{100}) $ 3 * q + 2 * q^2 + q^3 + 8 * q^4 - q^5 - 12 * q^6 + 6 * q^8 + 4 * q^9 + 4 * q^10 - 2 * q^12 - 8 * q^13 - 5 * q^15 + 10 * q^16 - 8 * q^17 - 18 * q^18 + 14 * q^20 + 7 * q^23 - 20 * q^24 + 2 * q^25 + 12 * q^26 + 19 * q^27 - 8 * q^30 + 13 * q^31 + 34 * q^32 + 12 * q^34 + 18 * q^36 - 17 * q^37 - 16 * q^38 - 20 * q^39 + 36 * q^40 - 16 * q^41 + 4 * q^43 + 6 * q^45 - 4 * q^47 - 36 * q^48 + 22 * q^50 - 20 * q^51 - 10 * q^53 - 8 * q^54 + 16 * q^57 - 16 * q^58 - q^59 - 30 * q^60 + 16 * q^61 - 4 * q^62 + 34 * q^64 + 24 * q^65 - 3 * q^67 + 7 * q^69 + 5 * q^71 + 2 * q^72 - 16 * q^73 - 32 * q^74 - 20 * q^75 + 24 * q^76 + 28 * q^78 + 28 * q^79 + 56 * q^80 + 15 * q^81 - 28 * q^82 - 8 * q^83 + 24 * q^85 + 12 * q^86 + 16 * q^87 + 21 * q^89 + 20 * q^90 + 2 * q^92 + 17 * q^93 - 20 * q^94 + 24 * q^95 - 20 * q^96 + 11 * 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 $

$2$	1.36333	0.964019	0.482009	−	0.876166i	$-0.339907\pi$
$2$	1.36333	0.964019	0.482009	+	0.876166i	$0.339907\pi$
$3$	−0.363328	−0.209768	−0.104884	−	0.994484i	$-0.533447\pi$
$3$	−0.363328	−0.209768	−0.104884	+	0.994484i	$0.533447\pi$
$4$	−0.141336	−0.0706681
$5$	−3.14134	−1.40485	−0.702424	−	0.711759i	$-0.747899\pi$
$5$	−3.14134	−1.40485	−0.702424	+	0.711759i	$0.747899\pi$
$6$	−0.495336	−0.202220
$7$	0	0
$7$	0	0
$8$	−2.91934	−1.03214
$9$	−2.86799	−0.955998
$10$	−4.28267	−1.35430
$11$	0	0
$11$	0	0
$12$	0.0513514	0.0148239
$13$	−4.77801	−1.32518	−0.662590	−	0.748982i	$-0.730543\pi$
$13$	−4.77801	−1.32518	−0.662590	+	0.748982i	$0.730543\pi$
$14$	0	0
$15$	1.14134	0.294692
$16$	−3.69735	−0.924338
$17$	−4.77801	−1.15884	−0.579419	−	0.815030i	$-0.696720\pi$
$17$	−4.77801	−1.15884	−0.579419	+	0.815030i	$0.696720\pi$
$18$	−3.91002	−0.921599
$19$	−7.00933	−1.60805	−0.804025	−	0.594595i	$-0.797312\pi$
$19$	−7.00933	−1.60805	−0.804025	+	0.594595i	$0.797312\pi$
$20$	0.443984	0.0992779
$21$	0	0
$22$	0	0
$23$	5.14134	1.07204	0.536021	−	0.844204i	$-0.319927\pi$
$23$	5.14134	1.07204	0.536021	+	0.844204i	$0.319927\pi$
$24$	1.06068	0.216510
$25$	4.86799	0.973599
$26$	−6.51399	−1.27750
$27$	2.13201	0.410305
$28$	0	0
$29$	−7.00933	−1.30160	−0.650800	−	0.759249i	$-0.725566\pi$
$29$	−7.00933	−1.30160	−0.650800	+	0.759249i	$0.725566\pi$
$30$	1.55602	0.284088
$31$	3.63667	0.653166	0.326583	−	0.945169i	$-0.394103\pi$
$31$	3.63667	0.653166	0.326583	+	0.945169i	$0.394103\pi$
$32$	0.797984	0.141065
$33$	0	0
$34$	−6.51399	−1.11714
$35$	0	0
$36$	0.405351	0.0675585
$37$	−9.86799	−1.62229	−0.811144	−	0.584846i	$-0.801155\pi$
$37$	−9.86799	−1.62229	−0.811144	+	0.584846i	$0.801155\pi$
$38$	−9.55602	−1.55019
$39$	1.73599	0.277980
$40$	9.17064	1.45001
$41$	−3.22199	−0.503191	−0.251595	−	0.967833i	$-0.580955\pi$
$41$	−3.22199	−0.503191	−0.251595	+	0.967833i	$0.580955\pi$
$42$	0	0
$43$	−4.28267	−0.653101	−0.326551	−	0.945180i	$-0.605886\pi$
$43$	−4.28267	−0.653101	−0.326551	+	0.945180i	$0.605886\pi$
$44$	0	0
$45$	9.00933	1.34303
$46$	7.00933	1.03347
$47$	0.778008	0.113484	0.0567421	−	0.998389i	$-0.481929\pi$
$47$	0.778008	0.113484	0.0567421	+	0.998389i	$0.481929\pi$
$48$	1.34335	0.193896
$49$	0	0
$50$	6.63667	0.938567
$51$	1.73599	0.243087
$52$	0.675305	0.0936480
$53$	2.28267	0.313549	0.156775	−	0.987634i	$-0.449890\pi$
$53$	2.28267	0.313549	0.156775	+	0.987634i	$0.449890\pi$
$54$	2.90663	0.395542
$55$	0	0
$56$	0	0
$57$	2.54669	0.337317
$58$	−9.55602	−1.25477
$59$	0.363328	0.0473013	0.0236507	−	0.999720i	$-0.492471\pi$
$59$	0.363328	0.0473013	0.0236507	+	0.999720i	$0.492471\pi$
$60$	−0.161312	−0.0208253
$61$	3.22199	0.412534	0.206267	−	0.978496i	$-0.433868\pi$
$61$	3.22199	0.412534	0.206267	+	0.978496i	$0.433868\pi$
$62$	4.95798	0.629664
$63$	0	0
$64$	8.48262	1.06033
$65$	15.0093	1.86168
$66$	0	0
$67$	−6.59465	−0.805665	−0.402832	−	0.915274i	$-0.631974\pi$
$67$	−6.59465	−0.805665	−0.402832	+	0.915274i	$0.631974\pi$
$68$	0.675305	0.0818928
$69$	−1.86799	−0.224880
$70$	0	0
$71$	−15.1600	−1.79916	−0.899580	−	0.436756i	$-0.856127\pi$
$71$	−15.1600	−1.79916	−0.899580	+	0.436756i	$0.856127\pi$
$72$	8.37266	0.986727
$73$	−3.22199	−0.377106	−0.188553	−	0.982063i	$-0.560380\pi$
$73$	−3.22199	−0.377106	−0.188553	+	0.982063i	$0.560380\pi$
$74$	−13.4533	−1.56392
$75$	−1.76868	−0.204229
$76$	0.990671	0.113638
$77$	0	0
$78$	2.36672	0.267978
$79$	3.71733	0.418232	0.209116	−	0.977891i	$-0.432941\pi$
$79$	3.71733	0.418232	0.209116	+	0.977891i	$0.432941\pi$
$80$	11.6146	1.29855
$81$	7.82936	0.869929
$82$	−4.39263	−0.485085
$83$	1.55602	0.170795	0.0853975	−	0.996347i	$-0.472784\pi$
$83$	1.55602	0.170795	0.0853975	+	0.996347i	$0.472784\pi$
$84$	0	0
$85$	15.0093	1.62799
$86$	−5.83869	−0.629602
$87$	2.54669	0.273034
$88$	0	0
$89$	5.58532	0.592043	0.296021	−	0.955181i	$-0.404340\pi$
$89$	5.58532	0.592043	0.296021	+	0.955181i	$0.404340\pi$
$90$	12.2827	1.29471
$91$	0	0
$92$	−0.726656	−0.0757592
$93$	−1.32131	−0.137013
$94$	1.06068	0.109401
$95$	22.0187	2.25907
$96$	−0.289930	−0.0295909
$97$	−6.15066	−0.624505	−0.312253	−	0.949999i	$-0.601084\pi$
$97$	−6.15066	−0.624505	−0.312253	+	0.949999i	$0.601084\pi$
$98$	0	0
$99$	0	0
$100$	−0.688023	−0.0688023
$101$	−10.7967	−1.07431	−0.537154	−	0.843484i	$-0.680501\pi$
$101$	−10.7967	−1.07431	−0.537154	+	0.843484i	$0.680501\pi$
$102$	2.36672	0.234340
$103$	13.2406	1.30464	0.652320	−	0.757944i	$-0.273796\pi$
$103$	13.2406	1.30464	0.652320	+	0.757944i	$0.273796\pi$
$104$	13.9486	1.36778
$105$	0	0
$106$	3.11203	0.302267
$107$	−14.0187	−1.35523	−0.677617	−	0.735415i	$-0.736987\pi$
$107$	−14.0187	−1.35523	−0.677617	+	0.735415i	$0.736987\pi$
$108$	−0.301330	−0.0289955
$109$	15.5747	1.49178	0.745892	−	0.666067i	$-0.232024\pi$
$109$	15.5747	1.49178	0.745892	+	0.666067i	$0.232024\pi$
$110$	0	0
$111$	3.58532	0.340304
$112$	0	0
$113$	4.13201	0.388707	0.194353	−	0.980932i	$-0.437739\pi$
$113$	4.13201	0.388707	0.194353	+	0.980932i	$0.437739\pi$
$114$	3.47197	0.325180
$115$	−16.1507	−1.50606
$116$	0.990671	0.0919815
$117$	13.7033	1.26687
$118$	0.495336	0.0455993
$119$	0	0
$120$	−3.33195	−0.304164
$121$	0	0
$122$	4.39263	0.397690
$123$	1.17064	0.105553
$124$	−0.513993	−0.0461579
$125$	0.414680	0.0370901
$126$	0	0
$127$	−22.0187	−1.95384	−0.976920	−	0.213606i	$-0.931479\pi$
$127$	−22.0187	−1.95384	−0.976920	+	0.213606i	$0.931479\pi$
$128$	9.96862	0.881110
$129$	1.55602	0.137000
$130$	20.4626	1.79469
$131$	15.0093	1.31137	0.655686	−	0.755034i	$-0.272380\pi$
$131$	15.0093	1.31137	0.655686	+	0.755034i	$0.272380\pi$
$132$	0	0
$133$	0	0
$134$	−8.99067	−0.776676
$135$	−6.69735	−0.576416
$136$	13.9486	1.19609
$137$	−10.6974	−0.913936	−0.456968	−	0.889483i	$-0.651065\pi$
$137$	−10.6974	−0.913936	−0.456968	+	0.889483i	$0.651065\pi$
$138$	−2.54669	−0.216788
$139$	4.10270	0.347987	0.173993	−	0.984747i	$-0.444333\pi$
$139$	4.10270	0.347987	0.173993	+	0.984747i	$0.444333\pi$
$140$	0	0
$141$	−0.282672	−0.0238053
$142$	−20.6680	−1.73442
$143$	0	0
$144$	10.6040	0.883665
$145$	22.0187	1.82855
$146$	−4.39263	−0.363537
$147$	0	0
$148$	1.39470	0.114644
$149$	−14.0187	−1.14845	−0.574227	−	0.818696i	$-0.694697\pi$
$149$	−14.0187	−1.14845	−0.574227	+	0.818696i	$0.694697\pi$
$150$	−2.41129	−0.196881
$151$	6.82936	0.555765	0.277883	−	0.960615i	$-0.410367\pi$
$151$	6.82936	0.555765	0.277883	+	0.960615i	$0.410367\pi$
$152$	20.4626	1.65974
$153$	13.7033	1.10785
$154$	0	0
$155$	−11.4240	−0.917598
$156$	−0.245357	−0.0196443
$157$	23.4427	1.87093	0.935464	−	0.353421i	$-0.114982\pi$
$157$	23.4427	1.87093	0.935464	+	0.353421i	$0.114982\pi$
$158$	5.06794	0.403183
$159$	−0.829359	−0.0657725
$160$	−2.50674	−0.198175
$161$	0	0
$162$	10.6740	0.838628
$163$	−0.990671	−0.0775954	−0.0387977	−	0.999247i	$-0.512353\pi$
$163$	−0.990671	−0.0775954	−0.0387977	+	0.999247i	$0.512353\pi$
$164$	0.455384	0.0355595
$165$	0	0
$166$	2.12136	0.164649
$167$	0.565344	0.0437477	0.0218738	−	0.999761i	$-0.493037\pi$
$167$	0.565344	0.0437477	0.0218738	+	0.999761i	$0.493037\pi$
$168$	0	0
$169$	9.82936	0.756105
$170$	20.4626	1.56941
$171$	20.1027	1.53729
$172$	0.605296	0.0461534
$173$	−17.2406	−1.31078	−0.655391	−	0.755290i	$-0.727496\pi$
$173$	−17.2406	−1.31078	−0.655391	+	0.755290i	$0.727496\pi$
$174$	3.47197	0.263209
$175$	0	0
$176$	0	0
$177$	−0.132007	−0.00992228
$178$	7.61462	0.570740
$179$	11.3213	0.846194	0.423097	−	0.906084i	$-0.360943\pi$
$179$	11.3213	0.846194	0.423097	+	0.906084i	$0.360943\pi$
$180$	−1.27334	−0.0949094
$181$	−14.8773	−1.10582	−0.552911	−	0.833240i	$-0.686483\pi$
$181$	−14.8773	−1.10582	−0.552911	+	0.833240i	$0.686483\pi$
$182$	0	0
$183$	−1.17064	−0.0865363
$184$	−15.0093	−1.10650
$185$	30.9987	2.27907
$186$	−1.80137	−0.132083
$187$	0	0
$188$	−0.109961	−0.00801970
$189$	0	0
$190$	30.0187	2.17778
$191$	3.84934	0.278528	0.139264	−	0.990255i	$-0.455526\pi$
$191$	3.84934	0.278528	0.139264	+	0.990255i	$0.455526\pi$
$192$	−3.08197	−0.222422
$193$	2.54669	0.183315	0.0916573	−	0.995791i	$-0.470784\pi$
$193$	2.54669	0.183315	0.0916573	+	0.995791i	$0.470784\pi$
$194$	−8.38538	−0.602035
$195$	−5.45331	−0.390520
$196$	0	0
$197$	10.5467	0.751420	0.375710	−	0.926737i	$-0.377399\pi$
$197$	10.5467	0.751420	0.375710	+	0.926737i	$0.377399\pi$
$198$	0	0
$199$	−11.6846	−0.828302	−0.414151	−	0.910208i	$-0.635921\pi$
$199$	−11.6846	−0.828302	−0.414151	+	0.910208i	$0.635921\pi$
$200$	−14.2113	−1.00489
$201$	2.39602	0.169002
$202$	−14.7194	−1.03565
$203$	0	0
$204$	−0.245357	−0.0171785
$205$	10.1214	0.706906
$206$	18.0514	1.25770
$207$	−14.7453	−1.02487
$208$	17.6660	1.22492
$209$	0	0
$210$	0	0
$211$	−11.1120	−0.764984	−0.382492	−	0.923959i	$-0.624934\pi$
$211$	−11.1120	−0.764984	−0.382492	+	0.923959i	$0.624934\pi$
$212$	−0.322624	−0.0221579
$213$	5.50805	0.377406
$214$	−19.1120	−1.30647
$215$	13.4533	0.917508
$216$	−6.22406	−0.423494
$217$	0	0
$218$	21.2334	1.43811
$219$	1.17064	0.0791046
$220$	0	0
$221$	22.8294	1.53567
$222$	4.88797	0.328059
$223$	−28.0407	−1.87774	−0.938872	−	0.344266i	$-0.888128\pi$
$223$	−28.0407	−1.87774	−0.938872	+	0.344266i	$0.888128\pi$
$224$	0	0
$225$	−13.9614	−0.930758
$226$	5.63328	0.374720
$227$	−23.0093	−1.52718	−0.763591	−	0.645700i	$-0.776566\pi$
$227$	−23.0093	−1.52718	−0.763591	+	0.645700i	$0.776566\pi$
$228$	−0.359939	−0.0238375
$229$	−13.4240	−0.887083	−0.443542	−	0.896254i	$-0.646278\pi$
$229$	−13.4240	−0.887083	−0.443542	+	0.896254i	$0.646278\pi$
$230$	−22.0187	−1.45187
$231$	0	0
$232$	20.4626	1.34344
$233$	3.53736	0.231740	0.115870	−	0.993264i	$-0.463034\pi$
$233$	3.53736	0.231740	0.115870	+	0.993264i	$0.463034\pi$
$234$	18.6821	1.22129
$235$	−2.44398	−0.159428
$236$	−0.0513514	−0.00334269
$237$	−1.35061	−0.0877316
$238$	0	0
$239$	−22.0187	−1.42427	−0.712134	−	0.702043i	$-0.752271\pi$
$239$	−22.0187	−1.42427	−0.712134	+	0.702043i	$0.752271\pi$
$240$	−4.21992	−0.272395
$241$	−0.315366	−0.0203145	−0.0101573	−	0.999948i	$-0.503233\pi$
$241$	−0.315366	−0.0203145	−0.0101573	+	0.999948i	$0.503233\pi$
$242$	0	0
$243$	−9.24065	−0.592788
$244$	−0.455384	−0.0291530
$245$	0	0
$246$	1.59597	0.101755
$247$	33.4906	2.13096
$248$	−10.6167	−0.674161
$249$	−0.565344	−0.0358272
$250$	0.565344	0.0357555
$251$	−18.6460	−1.17693	−0.588463	−	0.808524i	$-0.700267\pi$
$251$	−18.6460	−1.17693	−0.588463	+	0.808524i	$0.700267\pi$
$252$	0	0
$253$	0	0
$254$	−30.0187	−1.88354
$255$	−5.45331	−0.341500
$256$	−3.37473	−0.210920
$257$	8.54669	0.533128	0.266564	−	0.963817i	$-0.414112\pi$
$257$	8.54669	0.533128	0.266564	+	0.963817i	$0.414112\pi$
$258$	2.12136	0.132070
$259$	0	0
$260$	−2.12136	−0.131561
$261$	20.1027	1.24433
$262$	20.4626	1.26419
$263$	−16.0000	−0.986602	−0.493301	−	0.869859i	$-0.664210\pi$
$263$	−16.0000	−0.986602	−0.493301	+	0.869859i	$0.664210\pi$
$264$	0	0
$265$	−7.17064	−0.440489
$266$	0	0
$267$	−2.02930	−0.124191
$268$	0.932062	0.0569348
$269$	−7.55602	−0.460698	−0.230349	−	0.973108i	$-0.573987\pi$
$269$	−7.55602	−0.460698	−0.230349	+	0.973108i	$0.573987\pi$
$270$	−9.13069	−0.555676
$271$	14.0187	0.851573	0.425786	−	0.904824i	$-0.359998\pi$
$271$	14.0187	0.851573	0.425786	+	0.904824i	$0.359998\pi$
$272$	17.6660	1.07116
$273$	0	0
$274$	−14.5840	−0.881052
$275$	0	0
$276$	0.264015	0.0158918
$277$	6.01866	0.361626	0.180813	−	0.983517i	$-0.442127\pi$
$277$	6.01866	0.361626	0.180813	+	0.983517i	$0.442127\pi$
$278$	5.59333	0.335466
$279$	−10.4299	−0.624425
$280$	0	0
$281$	20.6680	1.23295	0.616476	−	0.787374i	$-0.288560\pi$
$281$	20.6680	1.23295	0.616476	+	0.787374i	$0.288560\pi$
$282$	−0.385375	−0.0229487
$283$	9.91595	0.589442	0.294721	−	0.955583i	$-0.404773\pi$
$283$	9.91595	0.589442	0.294721	+	0.955583i	$0.404773\pi$
$284$	2.14265	0.127143
$285$	−8.00000	−0.473879
$286$	0	0
$287$	0	0
$288$	−2.28861	−0.134858
$289$	5.82936	0.342903
$290$	30.0187	1.76276
$291$	2.23471	0.131001
$292$	0.455384	0.0266493
$293$	−26.7967	−1.56548	−0.782739	−	0.622350i	$-0.786178\pi$
$293$	−26.7967	−1.56548	−0.782739	+	0.622350i	$0.786178\pi$
$294$	0	0
$295$	−1.14134	−0.0664512
$296$	28.8081	1.67443
$297$	0	0
$298$	−19.1120	−1.10713
$299$	−24.5653	−1.42065
$300$	0.249978	0.0144325
$301$	0	0
$302$	9.31066	0.535768
$303$	3.92273	0.225355
$304$	25.9160	1.48638
$305$	−10.1214	−0.579547
$306$	18.6821	1.06798
$307$	11.8973	0.679015	0.339507	−	0.940603i	$-0.389740\pi$
$307$	11.8973	0.679015	0.339507	+	0.940603i	$0.389740\pi$
$308$	0	0
$309$	−4.81070	−0.273671
$310$	−15.5747	−0.884582
$311$	21.2406	1.20445	0.602223	−	0.798328i	$-0.294282\pi$
$311$	21.2406	1.20445	0.602223	+	0.798328i	$0.294282\pi$
$312$	−5.06794	−0.286915
$313$	12.6974	0.717697	0.358848	−	0.933396i	$-0.383170\pi$
$313$	12.6974	0.717697	0.358848	+	0.933396i	$0.383170\pi$
$314$	31.9600	1.80361
$315$	0	0
$316$	−0.525393	−0.0295556
$317$	−11.8680	−0.666573	−0.333286	−	0.942826i	$-0.608158\pi$
$317$	−11.8680	−0.666573	−0.333286	+	0.942826i	$0.608158\pi$
$318$	−1.13069	−0.0634059
$319$	0	0
$320$	−26.6468	−1.48960
$321$	5.09337	0.284284
$322$	0	0
$323$	33.4906	1.86347
$324$	−1.10657	−0.0614762
$325$	−23.2593	−1.29019
$326$	−1.35061	−0.0748034
$327$	−5.65872	−0.312928
$328$	9.40610	0.519365
$329$	0	0
$330$	0	0
$331$	−11.8867	−0.653349	−0.326675	−	0.945137i	$-0.605928\pi$
$331$	−11.8867	−0.653349	−0.326675	+	0.945137i	$0.605928\pi$
$332$	−0.219921	−0.0120697
$333$	28.3013	1.55090
$334$	0.770750	0.0421736
$335$	20.7160	1.13184
$336$	0	0
$337$	−0.990671	−0.0539653	−0.0269827	−	0.999636i	$-0.508590\pi$
$337$	−0.990671	−0.0539653	−0.0269827	+	0.999636i	$0.508590\pi$
$338$	13.4006	0.728899
$339$	−1.50127	−0.0815381
$340$	−2.12136	−0.115047
$341$	0	0
$342$	27.4066	1.48198
$343$	0	0
$344$	12.5026	0.674095
$345$	5.86799	0.315922
$346$	−23.5047	−1.26362
$347$	15.1893	0.815404	0.407702	−	0.913115i	$-0.366330\pi$
$347$	15.1893	0.815404	0.407702	+	0.913115i	$0.366330\pi$
$348$	−0.359939	−0.0192947
$349$	−29.7033	−1.58998	−0.794990	−	0.606622i	$-0.792524\pi$
$349$	−29.7033	−1.58998	−0.794990	+	0.606622i	$0.792524\pi$
$350$	0	0
$351$	−10.1867	−0.543728
$352$	0	0
$353$	6.71601	0.357457	0.178729	−	0.983898i	$-0.442802\pi$
$353$	6.71601	0.357457	0.178729	+	0.983898i	$0.442802\pi$
$354$	−0.179969	−0.00956527
$355$	47.6226	2.52755
$356$	−0.789407	−0.0418385
$357$	0	0
$358$	15.4347	0.815747
$359$	−17.7360	−0.936069	−0.468035	−	0.883710i	$-0.655038\pi$
$359$	−17.7360	−0.936069	−0.468035	+	0.883710i	$0.655038\pi$
$360$	−26.3013	−1.38620
$361$	30.1307	1.58583
$362$	−20.2827	−1.06603
$363$	0	0
$364$	0	0
$365$	10.1214	0.529776
$366$	−1.59597	−0.0834226
$367$	8.09931	0.422781	0.211390	−	0.977402i	$-0.432201\pi$
$367$	8.09931	0.422781	0.211390	+	0.977402i	$0.432201\pi$
$368$	−19.0093	−0.990930
$369$	9.24065	0.481049
$370$	42.2614	2.19706
$371$	0	0
$372$	0.186748	0.00968244
$373$	−0.565344	−0.0292724	−0.0146362	−	0.999893i	$-0.504659\pi$
$373$	−0.565344	−0.0292724	−0.0146362	+	0.999893i	$0.504659\pi$
$374$	0	0
$375$	−0.150665	−0.00778030
$376$	−2.27127	−0.117132
$377$	33.4906	1.72486
$378$	0	0
$379$	−22.5360	−1.15760	−0.578799	−	0.815470i	$-0.696479\pi$
$379$	−22.5360	−1.15760	−0.578799	+	0.815470i	$0.696479\pi$
$380$	−3.11203	−0.159644
$381$	8.00000	0.409852
$382$	5.24791	0.268506
$383$	−21.3913	−1.09305	−0.546523	−	0.837444i	$-0.684049\pi$
$383$	−21.3913	−1.09305	−0.546523	+	0.837444i	$0.684049\pi$
$384$	−3.62188	−0.184828
$385$	0	0
$386$	3.47197	0.176719
$387$	12.2827	0.624363
$388$	0.869311	0.0441326
$389$	10.6787	0.541431	0.270716	−	0.962659i	$-0.412740\pi$
$389$	10.6787	0.541431	0.270716	+	0.962659i	$0.412740\pi$
$390$	−7.43466	−0.376468
$391$	−24.5653	−1.24232
$392$	0	0
$393$	−5.45331	−0.275083
$394$	14.3786	0.724383
$395$	−11.6774	−0.587553
$396$	0	0
$397$	23.9160	1.20031	0.600154	−	0.799885i	$-0.295106\pi$
$397$	23.9160	1.20031	0.600154	+	0.799885i	$0.295106\pi$
$398$	−15.9300	−0.798498
$399$	0	0
$400$	−17.9987	−0.899934
$401$	11.6587	0.582209	0.291104	−	0.956691i	$-0.405977\pi$
$401$	11.6587	0.582209	0.291104	+	0.956691i	$0.405977\pi$
$402$	3.26656	0.162921
$403$	−17.3760	−0.865563
$404$	1.52596	0.0759193
$405$	−24.5946	−1.22212
$406$	0	0
$407$	0	0
$408$	−5.06794	−0.250900
$409$	32.8153	1.62261	0.811307	−	0.584621i	$-0.198757\pi$
$409$	32.8153	1.62261	0.811307	+	0.584621i	$0.198757\pi$
$410$	13.7987	0.681471
$411$	3.88665	0.191714
$412$	−1.87138	−0.0921964
$413$	0	0
$414$	−20.1027	−0.987994
$415$	−4.88797	−0.239941
$416$	−3.81277	−0.186937
$417$	−1.49063	−0.0729964
$418$	0	0
$419$	−10.7967	−0.527452	−0.263726	−	0.964598i	$-0.584951\pi$
$419$	−10.7967	−0.527452	−0.263726	+	0.964598i	$0.584951\pi$
$420$	0	0
$421$	−1.15198	−0.0561442	−0.0280721	−	0.999606i	$-0.508937\pi$
$421$	−1.15198	−0.0561442	−0.0280721	+	0.999606i	$0.508937\pi$
$422$	−15.1493	−0.737459
$423$	−2.23132	−0.108491
$424$	−6.66391	−0.323628
$425$	−23.2593	−1.12824
$426$	7.50929	0.363826
$427$	0	0
$428$	1.98134	0.0957718
$429$	0	0
$430$	18.3413	0.884495
$431$	31.9600	1.53946	0.769731	−	0.638369i	$-0.220391\pi$
$431$	31.9600	1.53946	0.769731	+	0.638369i	$0.220391\pi$
$432$	−7.88278	−0.379261
$433$	4.43334	0.213053	0.106526	−	0.994310i	$-0.466027\pi$
$433$	4.43334	0.213053	0.106526	+	0.994310i	$0.466027\pi$
$434$	0	0
$435$	−8.00000	−0.383571
$436$	−2.20126	−0.105421
$437$	−36.0373	−1.72390
$438$	1.59597	0.0762583
$439$	−27.4720	−1.31117	−0.655583	−	0.755123i	$-0.727577\pi$
$439$	−27.4720	−1.31117	−0.655583	+	0.755123i	$0.727577\pi$
$440$	0	0
$441$	0	0
$442$	31.1239	1.48041
$443$	−7.79073	−0.370149	−0.185074	−	0.982725i	$-0.559253\pi$
$443$	−7.79073	−0.370149	−0.185074	+	0.982725i	$0.559253\pi$
$444$	−0.506735	−0.0240486
$445$	−17.5454	−0.831730
$446$	−38.2287	−1.81018
$447$	5.09337	0.240908
$448$	0	0
$449$	20.5106	0.967955	0.483978	−	0.875080i	$-0.339192\pi$
$449$	20.5106	0.967955	0.483978	+	0.875080i	$0.339192\pi$
$450$	−19.0339	−0.897268
$451$	0	0
$452$	−0.584002	−0.0274691
$453$	−2.48130	−0.116582
$454$	−31.3693	−1.47223
$455$	0	0
$456$	−7.43466	−0.348160
$457$	8.56534	0.400670	0.200335	−	0.979727i	$-0.435797\pi$
$457$	8.56534	0.400670	0.200335	+	0.979727i	$0.435797\pi$
$458$	−18.3013	−0.855165
$459$	−10.1867	−0.475477
$460$	2.28267	0.106430
$461$	9.66598	0.450189	0.225095	−	0.974337i	$-0.427731\pi$
$461$	9.66598	0.450189	0.225095	+	0.974337i	$0.427731\pi$
$462$	0	0
$463$	11.4240	0.530919	0.265459	−	0.964122i	$-0.414476\pi$
$463$	11.4240	0.530919	0.265459	+	0.964122i	$0.414476\pi$
$464$	25.9160	1.20312
$465$	4.15066	0.192482
$466$	4.82258	0.223402
$467$	−18.2207	−0.843152	−0.421576	−	0.906793i	$-0.638523\pi$
$467$	−18.2207	−0.843152	−0.421576	+	0.906793i	$0.638523\pi$
$468$	−1.93677	−0.0895272
$469$	0	0
$470$	−3.33195	−0.153692
$471$	−8.51738	−0.392460
$472$	−1.06068	−0.0488218
$473$	0	0
$474$	−1.84132	−0.0845749
$475$	−34.1214	−1.56560
$476$	0	0
$477$	−6.54669	−0.299752
$478$	−30.0187	−1.37302
$479$	3.47197	0.158638	0.0793192	−	0.996849i	$-0.474725\pi$
$479$	3.47197	0.158638	0.0793192	+	0.996849i	$0.474725\pi$
$480$	0.910768	0.0415707
$481$	47.1493	2.14983
$482$	−0.429948	−0.0195836
$483$	0	0
$484$	0	0
$485$	19.3213	0.877335
$486$	−12.5980	−0.571459
$487$	−27.4613	−1.24439	−0.622196	−	0.782862i	$-0.713759\pi$
$487$	−27.4613	−1.24439	−0.622196	+	0.782862i	$0.713759\pi$
$488$	−9.40610	−0.425794
$489$	0.359939	0.0162770
$490$	0	0
$491$	6.26401	0.282691	0.141346	−	0.989960i	$-0.454857\pi$
$491$	6.26401	0.282691	0.141346	+	0.989960i	$0.454857\pi$
$492$	−0.165454	−0.00745923
$493$	33.4906	1.50834
$494$	45.6587	2.05428
$495$	0	0
$496$	−13.4461	−0.603746
$497$	0	0
$498$	−0.770750	−0.0345381
$499$	−20.6680	−0.925229	−0.462614	−	0.886560i	$-0.653089\pi$
$499$	−20.6680	−0.925229	−0.462614	+	0.886560i	$0.653089\pi$
$500$	−0.0586092	−0.00262108
$501$	−0.205406	−0.00917685
$502$	−25.4206	−1.13458
$503$	22.0187	0.981763	0.490882	−	0.871226i	$-0.336675\pi$
$503$	22.0187	0.981763	0.490882	+	0.871226i	$0.336675\pi$
$504$	0	0
$505$	33.9160	1.50924
$506$	0	0
$507$	−3.57128	−0.158606
$508$	3.11203	0.138074
$509$	−21.4240	−0.949602	−0.474801	−	0.880093i	$-0.657480\pi$
$509$	−21.4240	−0.949602	−0.474801	+	0.880093i	$0.657480\pi$
$510$	−7.43466	−0.329212
$511$	0	0
$512$	−24.5381	−1.08444
$513$	−14.9439	−0.659791
$514$	11.6519	0.513945
$515$	−41.5933	−1.83282
$516$	−0.219921	−0.00968149
$517$	0	0
$518$	0	0
$519$	6.26401	0.274960
$520$	−43.8174	−1.92152
$521$	−13.9453	−0.610953	−0.305476	−	0.952200i	$-0.598816\pi$
$521$	−13.9453	−0.610953	−0.305476	+	0.952200i	$0.598816\pi$
$522$	27.4066	1.19955
$523$	−18.4813	−0.808131	−0.404065	−	0.914730i	$-0.632403\pi$
$523$	−18.4813	−0.808131	−0.404065	+	0.914730i	$0.632403\pi$
$524$	−2.12136	−0.0926721
$525$	0	0
$526$	−21.8133	−0.951103
$527$	−17.3760	−0.756912
$528$	0	0
$529$	3.43334	0.149276
$530$	−9.77594	−0.424640
$531$	−1.04202	−0.0452199
$532$	0	0
$533$	15.3947	0.666819
$534$	−2.76661	−0.119723
$535$	44.0373	1.90390
$536$	19.2520	0.831562
$537$	−4.11335	−0.177504
$538$	−10.3013	−0.444122
$539$	0	0
$540$	0.946578	0.0407342
$541$	−37.4533	−1.61024	−0.805122	−	0.593109i	$-0.797900\pi$
$541$	−37.4533	−1.61024	−0.805122	+	0.593109i	$0.797900\pi$
$542$	19.1120	0.820932
$543$	5.40535	0.231966
$544$	−3.81277	−0.163471
$545$	−48.9253	−2.09573
$546$	0	0
$547$	17.1307	0.732455	0.366228	−	0.930525i	$-0.380649\pi$
$547$	17.1307	0.732455	0.366228	+	0.930525i	$0.380649\pi$
$548$	1.51192	0.0645861
$549$	−9.24065	−0.394381
$550$	0	0
$551$	49.1307	2.09304
$552$	5.45331	0.232108
$553$	0	0
$554$	8.20541	0.348614
$555$	−11.2627	−0.478075
$556$	−0.579860	−0.0245915
$557$	−24.5653	−1.04087	−0.520434	−	0.853902i	$-0.674230\pi$
$557$	−24.5653	−1.04087	−0.520434	+	0.853902i	$0.674230\pi$
$558$	−14.2194	−0.601957
$559$	20.4626	0.865478
$560$	0	0
$561$	0	0
$562$	28.1773	1.18859
$563$	−15.0093	−0.632568	−0.316284	−	0.948665i	$-0.602435\pi$
$563$	−15.0093	−0.632568	−0.316284	+	0.948665i	$0.602435\pi$
$564$	0.0399518	0.00168227
$565$	−12.9800	−0.546074
$566$	13.5187	0.568233
$567$	0	0
$568$	44.2572	1.85699
$569$	−12.1027	−0.507372	−0.253686	−	0.967287i	$-0.581643\pi$
$569$	−12.1027	−0.507372	−0.253686	+	0.967287i	$0.581643\pi$
$570$	−10.9066	−0.456828
$571$	−38.9439	−1.62975	−0.814877	−	0.579634i	$-0.803195\pi$
$571$	−38.9439	−1.62975	−0.814877	+	0.579634i	$0.803195\pi$
$572$	0	0
$573$	−1.39857	−0.0584262
$574$	0	0
$575$	25.0280	1.04374
$576$	−24.3281	−1.01367
$577$	−38.1507	−1.58823	−0.794116	−	0.607766i	$-0.792066\pi$
$577$	−38.1507	−1.58823	−0.794116	+	0.607766i	$0.792066\pi$
$578$	7.94733	0.330565
$579$	−0.925283	−0.0384535
$580$	−3.11203	−0.129220
$581$	0	0
$582$	3.04664	0.126287
$583$	0	0
$584$	9.40610	0.389227
$585$	−43.0466	−1.77976
$586$	−36.5327	−1.50915
$587$	34.7967	1.43621	0.718106	−	0.695934i	$-0.245009\pi$
$587$	34.7967	1.43621	0.718106	+	0.695934i	$0.245009\pi$
$588$	0	0
$589$	−25.4906	−1.05032
$590$	−1.55602	−0.0640602
$591$	−3.83191	−0.157624
$592$	36.4854	1.49954
$593$	−18.5913	−0.763452	−0.381726	−	0.924276i	$-0.624670\pi$
$593$	−18.5913	−0.763452	−0.381726	+	0.924276i	$0.624670\pi$
$594$	0	0
$595$	0	0
$596$	1.98134	0.0811590
$597$	4.24536	0.173751
$598$	−33.4906	−1.36953
$599$	24.6680	1.00791	0.503955	−	0.863730i	$-0.331878\pi$
$599$	24.6680	1.00791	0.503955	+	0.863730i	$0.331878\pi$
$600$	5.16338	0.210794
$601$	−30.1286	−1.22897	−0.614486	−	0.788928i	$-0.710637\pi$
$601$	−30.1286	−1.22897	−0.614486	+	0.788928i	$0.710637\pi$
$602$	0	0
$603$	18.9134	0.770213
$604$	−0.965235	−0.0392749
$605$	0	0
$606$	5.34797	0.217247
$607$	−13.6587	−0.554390	−0.277195	−	0.960814i	$-0.589405\pi$
$607$	−13.6587	−0.554390	−0.277195	+	0.960814i	$0.589405\pi$
$608$	−5.59333	−0.226840
$609$	0	0
$610$	−13.7987	−0.558694
$611$	−3.71733	−0.150387
$612$	−1.93677	−0.0782893
$613$	45.0280	1.81866	0.909332	−	0.416072i	$-0.136594\pi$
$613$	45.0280	1.81866	0.909332	+	0.416072i	$0.136594\pi$
$614$	16.2199	0.654583
$615$	−3.67738	−0.148286
$616$	0	0
$617$	−8.26401	−0.332697	−0.166348	−	0.986067i	$-0.553198\pi$
$617$	−8.26401	−0.332697	−0.166348	+	0.986067i	$0.553198\pi$
$618$	−6.55857	−0.263824
$619$	−43.0500	−1.73033	−0.865163	−	0.501490i	$-0.832785\pi$
$619$	−43.0500	−1.73033	−0.865163	+	0.501490i	$0.832785\pi$
$620$	1.61462	0.0648449
$621$	10.9614	0.439864
$622$	28.9580	1.16111
$623$	0	0
$624$	−6.41855	−0.256948
$625$	−25.6426	−1.02570
$626$	17.3107	0.691873
$627$	0	0
$628$	−3.31330	−0.132215
$629$	47.1493	1.87997
$630$	0	0
$631$	1.03863	0.0413473	0.0206737	−	0.999786i	$-0.493419\pi$
$631$	1.03863	0.0413473	0.0206737	+	0.999786i	$0.493419\pi$
$632$	−10.8522	−0.431676
$633$	4.03731	0.160469
$634$	−16.1800	−0.642589
$635$	69.1680	2.74485
$636$	0.117218	0.00464801
$637$	0	0
$638$	0	0
$639$	43.4787	1.71999
$640$	−31.3148	−1.23783
$641$	33.6413	1.32875	0.664376	−	0.747399i	$-0.268698\pi$
$641$	33.6413	1.32875	0.664376	+	0.747399i	$0.268698\pi$
$642$	6.94394	0.274055
$643$	21.0314	0.829396	0.414698	−	0.909959i	$-0.363887\pi$
$643$	21.0314	0.829396	0.414698	+	0.909959i	$0.363887\pi$
$644$	0	0
$645$	−4.88797	−0.192464
$646$	45.6587	1.79642
$647$	−25.2300	−0.991894	−0.495947	−	0.868353i	$-0.665179\pi$
$647$	−25.2300	−0.991894	−0.495947	+	0.868353i	$0.665179\pi$
$648$	−22.8566	−0.897892
$649$	0	0
$650$	−31.7101	−1.24377
$651$	0	0
$652$	0.140018	0.00548351
$653$	20.6387	0.807656	0.403828	−	0.914835i	$-0.367679\pi$
$653$	20.6387	0.807656	0.403828	+	0.914835i	$0.367679\pi$
$654$	−7.71469	−0.301668
$655$	−47.1493	−1.84228
$656$	11.9128	0.465118
$657$	9.24065	0.360512
$658$	0	0
$659$	18.5067	0.720920	0.360460	−	0.932775i	$-0.382620\pi$
$659$	18.5067	0.720920	0.360460	+	0.932775i	$0.382620\pi$
$660$	0	0
$661$	−16.8001	−0.653446	−0.326723	−	0.945120i	$-0.605944\pi$
$661$	−16.8001	−0.653446	−0.326723	+	0.945120i	$0.605944\pi$
$662$	−16.2054	−0.629841
$663$	−8.29455	−0.322134
$664$	−4.54255	−0.176285
$665$	0	0
$666$	38.5840	1.49510
$667$	−36.0373	−1.39537
$668$	−0.0799036	−0.00309156
$669$	10.1880	0.393890
$670$	28.2427	1.09111
$671$	0	0
$672$	0	0
$673$	−17.5560	−0.676735	−0.338367	−	0.941014i	$-0.609875\pi$
$673$	−17.5560	−0.676735	−0.338367	+	0.941014i	$0.609875\pi$
$674$	−1.35061	−0.0520236
$675$	10.3786	0.399472
$676$	−1.38924	−0.0534324
$677$	−3.64732	−0.140178	−0.0700889	−	0.997541i	$-0.522328\pi$
$677$	−3.64732	−0.140178	−0.0700889	+	0.997541i	$0.522328\pi$
$678$	−2.04673	−0.0786042
$679$	0	0
$680$	−43.8174	−1.68032
$681$	8.35994	0.320354
$682$	0	0
$683$	27.4720	1.05119	0.525593	−	0.850736i	$-0.323844\pi$
$683$	27.4720	1.05119	0.525593	+	0.850736i	$0.323844\pi$
$684$	−2.84124	−0.108637
$685$	33.6040	1.28394
$686$	0	0
$687$	4.87732	0.186081
$688$	15.8345	0.603686
$689$	−10.9066	−0.415509
$690$	8.00000	0.304555
$691$	5.95666	0.226602	0.113301	−	0.993561i	$-0.463858\pi$
$691$	5.95666	0.226602	0.113301	+	0.993561i	$0.463858\pi$
$692$	2.43673	0.0926304
$693$	0	0
$694$	20.7080	0.786065
$695$	−12.8880	−0.488869
$696$	−7.43466	−0.281810
$697$	15.3947	0.583116
$698$	−40.4953	−1.53277
$699$	−1.28522	−0.0486116
$700$	0	0
$701$	−7.36927	−0.278333	−0.139167	−	0.990269i	$-0.544442\pi$
$701$	−7.36927	−0.278333	−0.139167	+	0.990269i	$0.544442\pi$
$702$	−13.8879	−0.524164
$703$	69.1680	2.60872
$704$	0	0
$705$	0.887968	0.0334428
$706$	9.15613	0.344595
$707$	0	0
$708$	0.0186574	0.000701189 0
$709$	−34.7160	−1.30379	−0.651894	−	0.758310i	$-0.726025\pi$
$709$	−34.7160	−1.30379	−0.651894	+	0.758310i	$0.726025\pi$
$710$	64.9253	2.43660
$711$	−10.6613	−0.399829
$712$	−16.3055	−0.611073
$713$	18.6974	0.700221
$714$	0	0
$715$	0	0
$716$	−1.60011	−0.0597989
$717$	8.00000	0.298765
$718$	−24.1800	−0.902388
$719$	4.06200	0.151487	0.0757435	−	0.997127i	$-0.475867\pi$
$719$	4.06200	0.151487	0.0757435	+	0.997127i	$0.475867\pi$
$720$	−33.3107	−1.24141
$721$	0	0
$722$	41.0780	1.52877
$723$	0.114581	0.00426133
$724$	2.10270	0.0781463
$725$	−34.1214	−1.26724
$726$	0	0
$727$	30.5433	1.13279	0.566394	−	0.824135i	$-0.308338\pi$
$727$	30.5433	1.13279	0.566394	+	0.824135i	$0.308338\pi$
$728$	0	0
$729$	−20.1307	−0.745581
$730$	13.7987	0.510714
$731$	20.4626	0.756838
$732$	0.165454	0.00611535
$733$	−30.8340	−1.13888	−0.569440	−	0.822033i	$-0.692840\pi$
$733$	−30.8340	−1.13888	−0.569440	+	0.822033i	$0.692840\pi$
$734$	11.0420	0.407568
$735$	0	0
$736$	4.10270	0.151228
$737$	0	0
$738$	12.5980	0.463740
$739$	−22.2241	−0.817525	−0.408763	−	0.912641i	$-0.634040\pi$
$739$	−22.2241	−0.817525	−0.408763	+	0.912641i	$0.634040\pi$
$740$	−4.38123	−0.161057
$741$	−12.1681	−0.447006
$742$	0	0
$743$	31.1493	1.14276	0.571379	−	0.820686i	$-0.306409\pi$
$743$	31.1493	1.14276	0.571379	+	0.820686i	$0.306409\pi$
$744$	3.85735	0.141417
$745$	44.0373	1.61340
$746$	−0.770750	−0.0282192
$747$	−4.46264	−0.163280
$748$	0	0
$749$	0	0
$750$	−0.205406	−0.00750035
$751$	11.9894	0.437498	0.218749	−	0.975781i	$-0.429802\pi$
$751$	11.9894	0.437498	0.218749	+	0.975781i	$0.429802\pi$
$752$	−2.87657	−0.104898
$753$	6.77462	0.246881
$754$	45.6587	1.66279
$755$	−21.4533	−0.780766
$756$	0	0
$757$	−11.4533	−0.416278	−0.208139	−	0.978099i	$-0.566741\pi$
$757$	−11.4533	−0.416278	−0.208139	+	0.978099i	$0.566741\pi$
$758$	−30.7240	−1.11595
$759$	0	0
$760$	−64.2800	−2.33168
$761$	7.89004	0.286014	0.143007	−	0.989722i	$-0.454323\pi$
$761$	7.89004	0.286014	0.143007	+	0.989722i	$0.454323\pi$
$762$	10.9066	0.395105
$763$	0	0
$764$	−0.544050	−0.0196830
$765$	−43.0466	−1.55635
$766$	−29.1634	−1.05372
$767$	−1.73599	−0.0626828
$768$	1.22613	0.0442443
$769$	−48.8153	−1.76033	−0.880163	−	0.474672i	$-0.842567\pi$
$769$	−48.8153	−1.76033	−0.880163	+	0.474672i	$0.842567\pi$
$770$	0	0
$771$	−3.10525	−0.111833
$772$	−0.359939	−0.0129545
$773$	3.19608	0.114955	0.0574774	−	0.998347i	$-0.481694\pi$
$773$	3.19608	0.114955	0.0574774	+	0.998347i	$0.481694\pi$
$774$	16.7453	0.601898
$775$	17.7033	0.635921
$776$	17.9559	0.644579
$777$	0	0
$778$	14.5586	0.521950
$779$	22.5840	0.809156
$780$	0.770750	0.0275973
$781$	0	0
$782$	−33.4906	−1.19762
$783$	−14.9439	−0.534053
$784$	0	0
$785$	−73.6413	−2.62837
$786$	−7.43466	−0.265185
$787$	−42.4813	−1.51429	−0.757147	−	0.653244i	$-0.773408\pi$
$787$	−42.4813	−1.51429	−0.757147	+	0.653244i	$0.773408\pi$
$788$	−1.49063	−0.0531014
$789$	5.81325	0.206957
$790$	−15.9201	−0.566412
$791$	0	0
$792$	0	0
$793$	−15.3947	−0.546682
$794$	32.6053	1.15712
$795$	2.60530	0.0924003
$796$	1.65146	0.0585345
$797$	28.8587	1.02223	0.511113	−	0.859513i	$-0.329233\pi$
$797$	28.8587	1.02223	0.511113	+	0.859513i	$0.329233\pi$
$798$	0	0
$799$	−3.71733	−0.131510
$800$	3.88458	0.137341
$801$	−16.0187	−0.565991
$802$	15.8947	0.561260
$803$	0	0
$804$	−0.338644	−0.0119431
$805$	0	0
$806$	−23.6893	−0.834418
$807$	2.74531	0.0966396
$808$	31.5192	1.10884
$809$	29.4533	1.03552	0.517762	−	0.855525i	$-0.326765\pi$
$809$	29.4533	1.03552	0.517762	+	0.855525i	$0.326765\pi$
$810$	−33.5306	−1.17814
$811$	−2.48130	−0.0871302	−0.0435651	−	0.999051i	$-0.513872\pi$
$811$	−2.48130	−0.0871302	−0.0435651	+	0.999051i	$0.513872\pi$
$812$	0	0
$813$	−5.09337	−0.178632
$814$	0	0
$815$	3.11203	0.109010
$816$	−6.41855	−0.224694
$817$	30.0187	1.05022
$818$	44.7381	1.56423
$819$	0	0
$820$	−1.43051	−0.0499557
$821$	14.0187	0.489255	0.244627	−	0.969617i	$-0.421334\pi$
$821$	14.0187	0.489255	0.244627	+	0.969617i	$0.421334\pi$
$822$	5.29878	0.184816
$823$	−42.7933	−1.49168	−0.745840	−	0.666125i	$-0.767952\pi$
$823$	−42.7933	−1.49168	−0.745840	+	0.666125i	$0.767952\pi$
$824$	−38.6540	−1.34658
$825$	0	0
$826$	0	0
$827$	−9.17064	−0.318894	−0.159447	−	0.987206i	$-0.550971\pi$
$827$	−9.17064	−0.318894	−0.159447	+	0.987206i	$0.550971\pi$
$828$	2.08405	0.0724256
$829$	−29.1973	−1.01406	−0.507032	−	0.861927i	$-0.669257\pi$
$829$	−29.1973	−1.01406	−0.507032	+	0.861927i	$0.669257\pi$
$830$	−6.66391	−0.231308
$831$	−2.18675	−0.0758575
$832$	−40.5300	−1.40513
$833$	0	0
$834$	−2.03221	−0.0703698
$835$	−1.77594	−0.0614588
$836$	0	0
$837$	7.75341	0.267997
$838$	−14.7194	−0.508473
$839$	−19.7326	−0.681245	−0.340622	−	0.940200i	$-0.610638\pi$
$839$	−19.7326	−0.681245	−0.340622	+	0.940200i	$0.610638\pi$
$840$	0	0
$841$	20.1307	0.694162
$842$	−1.57053	−0.0541241
$843$	−7.50929	−0.258634
$844$	1.57053	0.0540599
$845$	−30.8773	−1.06221
$846$	−3.04202	−0.104587
$847$	0	0
$848$	−8.43984	−0.289825
$849$	−3.60275	−0.123646
$850$	−31.7101	−1.08765
$851$	−50.7347	−1.73916
$852$	−0.778487	−0.0266705
$853$	28.3527	0.970777	0.485389	−	0.874298i	$-0.338678\pi$
$853$	28.3527	0.970777	0.485389	+	0.874298i	$0.338678\pi$
$854$	0	0
$855$	−63.1493	−2.15966
$856$	40.9253	1.39880
$857$	−13.2033	−0.451017	−0.225509	−	0.974241i	$-0.572404\pi$
$857$	−13.2033	−0.451017	−0.225509	+	0.974241i	$0.572404\pi$
$858$	0	0
$859$	20.8260	0.710573	0.355286	−	0.934757i	$-0.384383\pi$
$859$	20.8260	0.710573	0.355286	+	0.934757i	$0.384383\pi$
$860$	−1.90144	−0.0648385
$861$	0	0
$862$	43.5720	1.48407
$863$	34.9439	1.18951	0.594753	−	0.803909i	$-0.297250\pi$
$863$	34.9439	1.18951	0.594753	+	0.803909i	$0.297250\pi$
$864$	1.70131	0.0578797
$865$	54.1587	1.84145
$866$	6.04409	0.205387
$867$	−2.11797	−0.0719301
$868$	0	0
$869$	0	0
$870$	−10.9066	−0.369769
$871$	31.5093	1.06765
$872$	−45.4678	−1.53973
$873$	17.6401	0.597026
$874$	−49.1307	−1.66187
$875$	0	0
$876$	−0.165454	−0.00559017
$877$	−26.4813	−0.894210	−0.447105	−	0.894481i	$-0.647545\pi$
$877$	−26.4813	−0.894210	−0.447105	+	0.894481i	$0.647545\pi$
$878$	−37.4533	−1.26399
$879$	9.73599	0.328387
$880$	0	0
$881$	−17.2627	−0.581595	−0.290798	−	0.956785i	$-0.593921\pi$
$881$	−17.2627	−0.581595	−0.290798	+	0.956785i	$0.593921\pi$
$882$	0	0
$883$	−44.6027	−1.50100	−0.750499	−	0.660871i	$-0.770187\pi$
$883$	−44.6027	−1.50100	−0.750499	+	0.660871i	$0.770187\pi$
$884$	−3.22661	−0.108523
$885$	0.414680	0.0139393
$886$	−10.6213	−0.356830
$887$	−30.7894	−1.03381	−0.516904	−	0.856044i	$-0.672915\pi$
$887$	−30.7894	−1.03381	−0.516904	+	0.856044i	$0.672915\pi$
$888$	−10.4668	−0.351242
$889$	0	0
$890$	−23.9201	−0.801803
$891$	0	0
$892$	3.96316	0.132697
$893$	−5.45331	−0.182488
$894$	6.94394	0.232240
$895$	−35.5640	−1.18877
$896$	0	0
$897$	8.92528	0.298007
$898$	27.9627	0.933127
$899$	−25.4906	−0.850160
$900$	1.97325	0.0657748
$901$	−10.9066	−0.363352
$902$	0	0
$903$	0	0
$904$	−12.0628	−0.401201
$905$	46.7347	1.55351
$906$	−3.38283	−0.112387
$907$	23.7801	0.789605	0.394802	−	0.918766i	$-0.370813\pi$
$907$	23.7801	0.789605	0.394802	+	0.918766i	$0.370813\pi$
$908$	3.25205	0.107923
$909$	30.9648	1.02704
$910$	0	0
$911$	49.0280	1.62437	0.812185	−	0.583400i	$-0.198278\pi$
$911$	49.0280	1.62437	0.812185	+	0.583400i	$0.198278\pi$
$912$	−9.41600	−0.311795
$913$	0	0
$914$	11.6774	0.386253
$915$	3.67738	0.121570
$916$	1.89730	0.0626885
$917$	0	0
$918$	−13.8879	−0.458368
$919$	−40.0000	−1.31948	−0.659739	−	0.751495i	$-0.729333\pi$
$919$	−40.0000	−1.31948	−0.659739	+	0.751495i	$0.729333\pi$
$920$	47.1493	1.55447
$921$	−4.32262	−0.142435
$922$	13.1779	0.433991
$923$	72.4346	2.38421
$924$	0	0
$925$	−48.0373	−1.57946
$926$	15.5747	0.511816
$927$	−37.9741	−1.24723
$928$	−5.59333	−0.183610
$929$	56.5840	1.85646	0.928230	−	0.372006i	$-0.121330\pi$
$929$	56.5840	1.85646	0.928230	+	0.372006i	$0.121330\pi$
$930$	5.65872	0.185557
$931$	0	0
$932$	−0.499956	−0.0163766
$933$	−7.71733	−0.252654
$934$	−24.8408	−0.812814
$935$	0	0
$936$	−40.0046	−1.30759
$937$	−16.8153	−0.549333	−0.274666	−	0.961540i	$-0.588567\pi$
$937$	−16.8153	−0.549333	−0.274666	+	0.961540i	$0.588567\pi$
$938$	0	0
$939$	−4.61331	−0.150550
$940$	0.345423	0.0112665
$941$	7.25931	0.236647	0.118323	−	0.992975i	$-0.462248\pi$
$941$	7.25931	0.236647	0.118323	+	0.992975i	$0.462248\pi$
$942$	−11.6120	−0.378339
$943$	−16.5653	−0.539442
$944$	−1.34335	−0.0437224
$945$	0	0
$946$	0	0
$947$	−25.6040	−0.832017	−0.416009	−	0.909361i	$-0.636571\pi$
$947$	−25.6040	−0.832017	−0.416009	+	0.909361i	$0.636571\pi$
$948$	0.190890	0.00619982
$949$	15.3947	0.499733
$950$	−46.5186	−1.50926
$951$	4.31198	0.139825
$952$	0	0
$953$	−7.14935	−0.231590	−0.115795	−	0.993273i	$-0.536942\pi$
$953$	−7.14935	−0.231590	−0.115795	+	0.993273i	$0.536942\pi$
$954$	−8.92528	−0.288967
$955$	−12.0921	−0.391290
$956$	3.11203	0.100650
$957$	0	0
$958$	4.73344	0.152930
$959$	0	0
$960$	9.68152	0.312470
$961$	−17.7746	−0.573375
$962$	64.2800	2.07247
$963$	40.2054	1.29560
$964$	0.0445726	0.00143559
$965$	−8.00000	−0.257529
$966$	0	0
$967$	−15.9600	−0.513241	−0.256620	−	0.966512i	$-0.582609\pi$
$967$	−15.9600	−0.513241	−0.256620	+	0.966512i	$0.582609\pi$
$968$	0	0
$969$	−12.1681	−0.390895
$970$	26.3413	0.845768
$971$	30.4779	0.978083	0.489041	−	0.872261i	$-0.337347\pi$
$971$	30.4779	0.978083	0.489041	+	0.872261i	$0.337347\pi$
$972$	1.30604	0.0418912
$973$	0	0
$974$	−37.4388	−1.19962
$975$	8.45076	0.270641
$976$	−11.9128	−0.381321
$977$	4.13201	0.132195	0.0660973	−	0.997813i	$-0.478945\pi$
$977$	4.13201	0.132195	0.0660973	+	0.997813i	$0.478945\pi$
$978$	0.490715	0.0156913
$979$	0	0
$980$	0	0
$981$	−44.6680	−1.42614
$982$	8.53991	0.272519
$983$	25.0246	0.798161	0.399080	−	0.916916i	$-0.369329\pi$
$983$	25.0246	0.798161	0.399080	+	0.916916i	$0.369329\pi$
$984$	−3.41750	−0.108946
$985$	−33.1307	−1.05563
$986$	45.6587	1.45407
$987$	0	0
$988$	−4.73344	−0.150591
$989$	−22.0187	−0.700153
$990$	0	0
$991$	−27.5747	−0.875938	−0.437969	−	0.898990i	$-0.644302\pi$
$991$	−27.5747	−0.875938	−0.437969	+	0.898990i	$0.644302\pi$
$992$	2.90201	0.0921388
$993$	4.31876	0.137052
$994$	0	0
$995$	36.7054	1.16364
$996$	0.0799036	0.00253184
$997$	23.6846	0.750100	0.375050	−	0.927005i	$-0.377626\pi$
$997$	23.6846	0.750100	0.375050	+	0.927005i	$0.377626\pi$
$998$	−28.1773	−0.891938
$999$	−21.0386	−0.665633

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5929.2.a.y.1.2		3
7.6	odd	2		847.2.a.j.1.2	yes	3
11.10	odd	2		5929.2.a.t.1.2		3
21.20	even	2		7623.2.a.bz.1.2		3
77.6	even	10		847.2.f.u.729.2		12
77.13	even	10		847.2.f.u.323.2		12
77.20	odd	10		847.2.f.t.323.2		12
77.27	odd	10		847.2.f.t.729.2		12
77.41	even	10		847.2.f.u.372.2		12
77.48	odd	10		847.2.f.t.148.2		12
77.62	even	10		847.2.f.u.148.2		12
77.69	odd	10		847.2.f.t.372.2		12
77.76	even	2		847.2.a.i.1.2	✓	3
231.230	odd	2		7623.2.a.ce.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
847.2.a.i.1.2	✓	3	77.76	even	2
847.2.a.j.1.2	yes	3	7.6	odd	2
847.2.f.t.148.2		12	77.48	odd	10
847.2.f.t.323.2		12	77.20	odd	10
847.2.f.t.372.2		12	77.69	odd	10
847.2.f.t.729.2		12	77.27	odd	10
847.2.f.u.148.2		12	77.62	even	10
847.2.f.u.323.2		12	77.13	even	10
847.2.f.u.372.2		12	77.41	even	10
847.2.f.u.729.2		12	77.6	even	10
5929.2.a.t.1.2		3	11.10	odd	2
5929.2.a.y.1.2		3	1.1	even	1	trivial
7623.2.a.bz.1.2		3	21.20	even	2
7623.2.a.ce.1.2		3	231.230	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:	\( N \)	\(=\)	\( 5929 = 7^{2} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5929.a (trivial)

\(f(q)\)	\(=\)	\(q+1.36333 q^{2} -0.363328 q^{3} -0.141336 q^{4} -3.14134 q^{5} -0.495336 q^{6} -2.91934 q^{8} -2.86799 q^{9} +O(q^{10})\)	\(q+1.36333 q^{2} -0.363328 q^{3} -0.141336 q^{4} -3.14134 q^{5} -0.495336 q^{6} -2.91934 q^{8} -2.86799 q^{9} -4.28267 q^{10} +0.0513514 q^{12} -4.77801 q^{13} +1.14134 q^{15} -3.69735 q^{16} -4.77801 q^{17} -3.91002 q^{18} -7.00933 q^{19} +0.443984 q^{20} +5.14134 q^{23} +1.06068 q^{24} +4.86799 q^{25} -6.51399 q^{26} +2.13201 q^{27} -7.00933 q^{29} +1.55602 q^{30} +3.63667 q^{31} +0.797984 q^{32} -6.51399 q^{34} +0.405351 q^{36} -9.86799 q^{37} -9.55602 q^{38} +1.73599 q^{39} +9.17064 q^{40} -3.22199 q^{41} -4.28267 q^{43} +9.00933 q^{45} +7.00933 q^{46} +0.778008 q^{47} +1.34335 q^{48} +6.63667 q^{50} +1.73599 q^{51} +0.675305 q^{52} +2.28267 q^{53} +2.90663 q^{54} +2.54669 q^{57} -9.55602 q^{58} +0.363328 q^{59} -0.161312 q^{60} +3.22199 q^{61} +4.95798 q^{62} +8.48262 q^{64} +15.0093 q^{65} -6.59465 q^{67} +0.675305 q^{68} -1.86799 q^{69} -15.1600 q^{71} +8.37266 q^{72} -3.22199 q^{73} -13.4533 q^{74} -1.76868 q^{75} +0.990671 q^{76} +2.36672 q^{78} +3.71733 q^{79} +11.6146 q^{80} +7.82936 q^{81} -4.39263 q^{82} +1.55602 q^{83} +15.0093 q^{85} -5.83869 q^{86} +2.54669 q^{87} +5.58532 q^{89} +12.2827 q^{90} -0.726656 q^{92} -1.32131 q^{93} +1.06068 q^{94} +22.0187 q^{95} -0.289930 q^{96} -6.15066 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 2 q^{2} + q^{3} + 8 q^{4} - q^{5} - 12 q^{6} + 6 q^{8} + 4 q^{9}+O(q^{10}) \) 3 * q + 2 * q^2 + q^3 + 8 * q^4 - q^5 - 12 * q^6 + 6 * q^8 + 4 * q^9	\( 3 q + 2 q^{2} + q^{3} + 8 q^{4} - q^{5} - 12 q^{6} + 6 q^{8} + 4 q^{9} + 4 q^{10} - 2 q^{12} - 8 q^{13} - 5 q^{15} + 10 q^{16} - 8 q^{17} - 18 q^{18} + 14 q^{20} + 7 q^{23} - 20 q^{24} + 2 q^{25} + 12 q^{26} + 19 q^{27} - 8 q^{30} + 13 q^{31} + 34 q^{32} + 12 q^{34} + 18 q^{36} - 17 q^{37} - 16 q^{38} - 20 q^{39} + 36 q^{40} - 16 q^{41} + 4 q^{43} + 6 q^{45} - 4 q^{47} - 36 q^{48} + 22 q^{50} - 20 q^{51} - 10 q^{53} - 8 q^{54} + 16 q^{57} - 16 q^{58} - q^{59} - 30 q^{60} + 16 q^{61} - 4 q^{62} + 34 q^{64} + 24 q^{65} - 3 q^{67} + 7 q^{69} + 5 q^{71} + 2 q^{72} - 16 q^{73} - 32 q^{74} - 20 q^{75} + 24 q^{76} + 28 q^{78} + 28 q^{79} + 56 q^{80} + 15 q^{81} - 28 q^{82} - 8 q^{83} + 24 q^{85} + 12 q^{86} + 16 q^{87} + 21 q^{89} + 20 q^{90} + 2 q^{92} + 17 q^{93} - 20 q^{94} + 24 q^{95} - 20 q^{96} + 11 q^{97}+O(q^{100}) \) 3 * q + 2 * q^2 + q^3 + 8 * q^4 - q^5 - 12 * q^6 + 6 * q^8 + 4 * q^9 + 4 * q^10 - 2 * q^12 - 8 * q^13 - 5 * q^15 + 10 * q^16 - 8 * q^17 - 18 * q^18 + 14 * q^20 + 7 * q^23 - 20 * q^24 + 2 * q^25 + 12 * q^26 + 19 * q^27 - 8 * q^30 + 13 * q^31 + 34 * q^32 + 12 * q^34 + 18 * q^36 - 17 * q^37 - 16 * q^38 - 20 * q^39 + 36 * q^40 - 16 * q^41 + 4 * q^43 + 6 * q^45 - 4 * q^47 - 36 * q^48 + 22 * q^50 - 20 * q^51 - 10 * q^53 - 8 * q^54 + 16 * q^57 - 16 * q^58 - q^59 - 30 * q^60 + 16 * q^61 - 4 * q^62 + 34 * q^64 + 24 * q^65 - 3 * q^67 + 7 * q^69 + 5 * q^71 + 2 * q^72 - 16 * q^73 - 32 * q^74 - 20 * q^75 + 24 * q^76 + 28 * q^78 + 28 * q^79 + 56 * q^80 + 15 * q^81 - 28 * q^82 - 8 * q^83 + 24 * q^85 + 12 * q^86 + 16 * q^87 + 21 * q^89 + 20 * q^90 + 2 * q^92 + 17 * q^93 - 20 * q^94 + 24 * q^95 - 20 * q^96 + 11 * q^97

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