LMFDB - Embedded newform 4802.2.a.i.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4802,2,Mod(1,4802)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4802, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4802.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4802 = 2 \cdot 7^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4802.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:	$38.3441630506$
Analytic rank:	$1$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} - 14 x^{10} + 22 x^{9} + 68 x^{8} - 70 x^{7} - 153 x^{6} + 77 x^{5} + 157 x^{4} + \cdots + 1 $ x^12 - 2x^11 - 14x^10 + 22x^9 + 68x^8 - 70x^7 - 153x^6 + 77x^5 + 157x^4 - 13x^3 - 56x^2 - 11*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 98)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$-1.15590$ of defining polynomial
Character	$\chi$	$=$	4802.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +0.694675 q^{3} +1.00000 q^{4} +1.84022 q^{5} -0.694675 q^{6} -1.00000 q^{8} -2.51743 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +0.694675 q^{3} +1.00000 q^{4} +1.84022 q^{5} -0.694675 q^{6} -1.00000 q^{8} -2.51743 q^{9} -1.84022 q^{10} +3.99871 q^{11} +0.694675 q^{12} -5.78872 q^{13} +1.27836 q^{15} +1.00000 q^{16} +3.45711 q^{17} +2.51743 q^{18} +3.03954 q^{19} +1.84022 q^{20} -3.99871 q^{22} -8.05684 q^{23} -0.694675 q^{24} -1.61358 q^{25} +5.78872 q^{26} -3.83282 q^{27} -1.76570 q^{29} -1.27836 q^{30} -5.40203 q^{31} -1.00000 q^{32} +2.77780 q^{33} -3.45711 q^{34} -2.51743 q^{36} +6.15572 q^{37} -3.03954 q^{38} -4.02128 q^{39} -1.84022 q^{40} -3.14050 q^{41} +3.89176 q^{43} +3.99871 q^{44} -4.63263 q^{45} +8.05684 q^{46} -7.28372 q^{47} +0.694675 q^{48} +1.61358 q^{50} +2.40157 q^{51} -5.78872 q^{52} -8.94972 q^{53} +3.83282 q^{54} +7.35851 q^{55} +2.11149 q^{57} +1.76570 q^{58} +7.18700 q^{59} +1.27836 q^{60} -3.87049 q^{61} +5.40203 q^{62} +1.00000 q^{64} -10.6525 q^{65} -2.77780 q^{66} +1.85465 q^{67} +3.45711 q^{68} -5.59688 q^{69} -7.24385 q^{71} +2.51743 q^{72} -11.7243 q^{73} -6.15572 q^{74} -1.12091 q^{75} +3.03954 q^{76} +4.02128 q^{78} -4.46206 q^{79} +1.84022 q^{80} +4.88971 q^{81} +3.14050 q^{82} -5.49299 q^{83} +6.36186 q^{85} -3.89176 q^{86} -1.22659 q^{87} -3.99871 q^{88} +11.4326 q^{89} +4.63263 q^{90} -8.05684 q^{92} -3.75265 q^{93} +7.28372 q^{94} +5.59343 q^{95} -0.694675 q^{96} +9.72695 q^{97} -10.0664 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{2} - 7 q^{3} + 12 q^{4} + 7 q^{6} - 12 q^{8} + 5 q^{9}+O(q^{10}) $ 12 * q - 12 * q^2 - 7 * q^3 + 12 * q^4 + 7 * q^6 - 12 * q^8 + 5 * q^9	$ 12 q - 12 q^{2} - 7 q^{3} + 12 q^{4} + 7 q^{6} - 12 q^{8} + 5 q^{9} - 7 q^{12} - 14 q^{13} + 12 q^{16} + 14 q^{17} - 5 q^{18} + 7 q^{23} + 7 q^{24} - 4 q^{25} + 14 q^{26} - 7 q^{27} - 2 q^{29} - 28 q^{31} - 12 q^{32} - 21 q^{33} - 14 q^{34} + 5 q^{36} - 4 q^{37} - 2 q^{39} - 7 q^{41} - 2 q^{43} - 14 q^{45} - 7 q^{46} - 28 q^{47} - 7 q^{48} + 4 q^{50} + 24 q^{51} - 14 q^{52} + 2 q^{53} + 7 q^{54} + 7 q^{55} + 36 q^{57} + 2 q^{58} + 28 q^{59} - 21 q^{61} + 28 q^{62} + 12 q^{64} - 21 q^{65} + 21 q^{66} + 36 q^{67} + 14 q^{68} - 7 q^{69} - 14 q^{71} - 5 q^{72} - 35 q^{73} + 4 q^{74} - 35 q^{75} + 2 q^{78} + 26 q^{79} + 36 q^{81} + 7 q^{82} - 7 q^{85} + 2 q^{86} - 63 q^{87} + 14 q^{90} + 7 q^{92} - 9 q^{93} + 28 q^{94} + 7 q^{95} + 7 q^{96} - 63 q^{97} - 7 q^{99}+O(q^{100}) $ 12 * q - 12 * q^2 - 7 * q^3 + 12 * q^4 + 7 * q^6 - 12 * q^8 + 5 * q^9 - 7 * q^12 - 14 * q^13 + 12 * q^16 + 14 * q^17 - 5 * q^18 + 7 * q^23 + 7 * q^24 - 4 * q^25 + 14 * q^26 - 7 * q^27 - 2 * q^29 - 28 * q^31 - 12 * q^32 - 21 * q^33 - 14 * q^34 + 5 * q^36 - 4 * q^37 - 2 * q^39 - 7 * q^41 - 2 * q^43 - 14 * q^45 - 7 * q^46 - 28 * q^47 - 7 * q^48 + 4 * q^50 + 24 * q^51 - 14 * q^52 + 2 * q^53 + 7 * q^54 + 7 * q^55 + 36 * q^57 + 2 * q^58 + 28 * q^59 - 21 * q^61 + 28 * q^62 + 12 * q^64 - 21 * q^65 + 21 * q^66 + 36 * q^67 + 14 * q^68 - 7 * q^69 - 14 * q^71 - 5 * q^72 - 35 * q^73 + 4 * q^74 - 35 * q^75 + 2 * q^78 + 26 * q^79 + 36 * q^81 + 7 * q^82 - 7 * q^85 + 2 * q^86 - 63 * q^87 + 14 * q^90 + 7 * q^92 - 9 * q^93 + 28 * q^94 + 7 * q^95 + 7 * q^96 - 63 * q^97 - 7 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	0.694675	0.401071	0.200535	−	0.979686i	$-0.435732\pi$
$3$	0.694675	0.401071	0.200535	+	0.979686i	$0.435732\pi$
$4$	1.00000	0.500000
$5$	1.84022	0.822973	0.411486	−	0.911416i	$-0.365010\pi$
$5$	1.84022	0.822973	0.411486	+	0.911416i	$0.365010\pi$
$6$	−0.694675	−0.283600
$7$	0	0
$7$	0	0
$8$	−1.00000	−0.353553
$9$	−2.51743	−0.839142
$10$	−1.84022	−0.581930
$11$	3.99871	1.20566	0.602828	−	0.797872i	$-0.294041\pi$
$11$	3.99871	1.20566	0.602828	+	0.797872i	$0.294041\pi$
$12$	0.694675	0.200535
$13$	−5.78872	−1.60550	−0.802751	−	0.596314i	$-0.796631\pi$
$13$	−5.78872	−1.60550	−0.802751	+	0.596314i	$0.796631\pi$
$14$	0	0
$15$	1.27836	0.330071
$16$	1.00000	0.250000
$17$	3.45711	0.838473	0.419237	−	0.907877i	$-0.362298\pi$
$17$	3.45711	0.838473	0.419237	+	0.907877i	$0.362298\pi$
$18$	2.51743	0.593363
$19$	3.03954	0.697318	0.348659	−	0.937250i	$-0.386637\pi$
$19$	3.03954	0.697318	0.348659	+	0.937250i	$0.386637\pi$
$20$	1.84022	0.411486
$21$	0	0
$22$	−3.99871	−0.852527
$23$	−8.05684	−1.67997	−0.839983	−	0.542612i	$-0.817435\pi$
$23$	−8.05684	−1.67997	−0.839983	+	0.542612i	$0.817435\pi$
$24$	−0.694675	−0.141800
$25$	−1.61358	−0.322715
$26$	5.78872	1.13526
$27$	−3.83282	−0.737626
$28$	0	0
$29$	−1.76570	−0.327883	−0.163941	−	0.986470i	$-0.552421\pi$
$29$	−1.76570	−0.327883	−0.163941	+	0.986470i	$0.552421\pi$
$30$	−1.27836	−0.233395
$31$	−5.40203	−0.970233	−0.485116	−	0.874450i	$-0.661223\pi$
$31$	−5.40203	−0.970233	−0.485116	+	0.874450i	$0.661223\pi$
$32$	−1.00000	−0.176777
$33$	2.77780	0.483553
$34$	−3.45711	−0.592890
$35$	0	0
$36$	−2.51743	−0.419571
$37$	6.15572	1.01199	0.505997	−	0.862535i	$-0.331125\pi$
$37$	6.15572	1.01199	0.505997	+	0.862535i	$0.331125\pi$
$38$	−3.03954	−0.493078
$39$	−4.02128	−0.643921
$40$	−1.84022	−0.290965
$41$	−3.14050	−0.490464	−0.245232	−	0.969464i	$-0.578864\pi$
$41$	−3.14050	−0.490464	−0.245232	+	0.969464i	$0.578864\pi$
$42$	0	0
$43$	3.89176	0.593488	0.296744	−	0.954957i	$-0.404099\pi$
$43$	3.89176	0.593488	0.296744	+	0.954957i	$0.404099\pi$
$44$	3.99871	0.602828
$45$	−4.63263	−0.690591
$46$	8.05684	1.18792
$47$	−7.28372	−1.06244	−0.531220	−	0.847234i	$-0.678266\pi$
$47$	−7.28372	−1.06244	−0.531220	+	0.847234i	$0.678266\pi$
$48$	0.694675	0.100268
$49$	0	0
$50$	1.61358	0.228194
$51$	2.40157	0.336287
$52$	−5.78872	−0.802751
$53$	−8.94972	−1.22934	−0.614669	−	0.788785i	$-0.710710\pi$
$53$	−8.94972	−1.22934	−0.614669	+	0.788785i	$0.710710\pi$
$54$	3.83282	0.521581
$55$	7.35851	0.992222
$56$	0	0
$57$	2.11149	0.279674
$58$	1.76570	0.231848
$59$	7.18700	0.935667	0.467834	−	0.883817i	$-0.345035\pi$
$59$	7.18700	0.935667	0.467834	+	0.883817i	$0.345035\pi$
$60$	1.27836	0.165035
$61$	−3.87049	−0.495566	−0.247783	−	0.968816i	$-0.579702\pi$
$61$	−3.87049	−0.495566	−0.247783	+	0.968816i	$0.579702\pi$
$62$	5.40203	0.686058
$63$	0	0
$64$	1.00000	0.125000
$65$	−10.6525	−1.32129
$66$	−2.77780	−0.341924
$67$	1.85465	0.226581	0.113291	−	0.993562i	$-0.463861\pi$
$67$	1.85465	0.226581	0.113291	+	0.993562i	$0.463861\pi$
$68$	3.45711	0.419237
$69$	−5.59688	−0.673786
$70$	0	0
$71$	−7.24385	−0.859687	−0.429844	−	0.902903i	$-0.641431\pi$
$71$	−7.24385	−0.859687	−0.429844	+	0.902903i	$0.641431\pi$
$72$	2.51743	0.296682
$73$	−11.7243	−1.37223	−0.686115	−	0.727493i	$-0.740686\pi$
$73$	−11.7243	−1.37223	−0.686115	+	0.727493i	$0.740686\pi$
$74$	−6.15572	−0.715588
$75$	−1.12091	−0.129432
$76$	3.03954	0.348659
$77$	0	0
$78$	4.02128	0.455321
$79$	−4.46206	−0.502021	−0.251011	−	0.967984i	$-0.580763\pi$
$79$	−4.46206	−0.502021	−0.251011	+	0.967984i	$0.580763\pi$
$80$	1.84022	0.205743
$81$	4.88971	0.543302
$82$	3.14050	0.346810
$83$	−5.49299	−0.602934	−0.301467	−	0.953477i	$-0.597476\pi$
$83$	−5.49299	−0.602934	−0.301467	+	0.953477i	$0.597476\pi$
$84$	0	0
$85$	6.36186	0.690041
$86$	−3.89176	−0.419659
$87$	−1.22659	−0.131504
$88$	−3.99871	−0.426263
$89$	11.4326	1.21185	0.605925	−	0.795522i	$-0.292803\pi$
$89$	11.4326	1.21185	0.605925	+	0.795522i	$0.292803\pi$
$90$	4.63263	0.488322
$91$	0	0
$92$	−8.05684	−0.839983
$93$	−3.75265	−0.389132
$94$	7.28372	0.751258
$95$	5.59343	0.573874
$96$	−0.694675	−0.0709000
$97$	9.72695	0.987622	0.493811	−	0.869569i	$-0.335603\pi$
$97$	9.72695	0.987622	0.493811	+	0.869569i	$0.335603\pi$
$98$	0	0
$99$	−10.0664	−1.01172
$100$	−1.61358	−0.161358
$101$	−7.96670	−0.792717	−0.396358	−	0.918096i	$-0.629726\pi$
$101$	−7.96670	−0.792717	−0.396358	+	0.918096i	$0.629726\pi$
$102$	−2.40157	−0.237791
$103$	17.7422	1.74819	0.874095	−	0.485756i	$-0.161456\pi$
$103$	17.7422	1.74819	0.874095	+	0.485756i	$0.161456\pi$
$104$	5.78872	0.567631
$105$	0	0
$106$	8.94972	0.869273
$107$	3.06659	0.296459	0.148229	−	0.988953i	$-0.452643\pi$
$107$	3.06659	0.296459	0.148229	+	0.988953i	$0.452643\pi$
$108$	−3.83282	−0.368813
$109$	−13.2292	−1.26713	−0.633565	−	0.773690i	$-0.718409\pi$
$109$	−13.2292	−1.26713	−0.633565	+	0.773690i	$0.718409\pi$
$110$	−7.35851	−0.701607
$111$	4.27622	0.405881
$112$	0	0
$113$	−10.3844	−0.976884	−0.488442	−	0.872596i	$-0.662435\pi$
$113$	−10.3844	−0.976884	−0.488442	+	0.872596i	$0.662435\pi$
$114$	−2.11149	−0.197759
$115$	−14.8264	−1.38257
$116$	−1.76570	−0.163941
$117$	14.5727	1.34725
$118$	−7.18700	−0.661617
$119$	0	0
$120$	−1.27836	−0.116698
$121$	4.98965	0.453604
$122$	3.87049	0.350418
$123$	−2.18163	−0.196711
$124$	−5.40203	−0.485116
$125$	−12.1705	−1.08856
$126$	0	0
$127$	−12.4254	−1.10257	−0.551286	−	0.834316i	$-0.685863\pi$
$127$	−12.4254	−1.10257	−0.551286	+	0.834316i	$0.685863\pi$
$128$	−1.00000	−0.0883883
$129$	2.70351	0.238031
$130$	10.6525	0.934290
$131$	−7.38571	−0.645293	−0.322646	−	0.946520i	$-0.604572\pi$
$131$	−7.38571	−0.645293	−0.322646	+	0.946520i	$0.604572\pi$
$132$	2.77780	0.241777
$133$	0	0
$134$	−1.85465	−0.160217
$135$	−7.05324	−0.607047
$136$	−3.45711	−0.296445
$137$	−12.2859	−1.04966	−0.524828	−	0.851208i	$-0.675870\pi$
$137$	−12.2859	−1.04966	−0.524828	+	0.851208i	$0.675870\pi$
$138$	5.59688	0.476438
$139$	−1.18390	−0.100418	−0.0502088	−	0.998739i	$-0.515989\pi$
$139$	−1.18390	−0.100418	−0.0502088	+	0.998739i	$0.515989\pi$
$140$	0	0
$141$	−5.05982	−0.426113
$142$	7.24385	0.607891
$143$	−23.1474	−1.93568
$144$	−2.51743	−0.209786
$145$	−3.24929	−0.269838
$146$	11.7243	0.970314
$147$	0	0
$148$	6.15572	0.505997
$149$	15.9433	1.30613	0.653063	−	0.757304i	$-0.273484\pi$
$149$	15.9433	1.30613	0.653063	+	0.757304i	$0.273484\pi$
$150$	1.12091	0.0915221
$151$	−12.3055	−1.00141	−0.500703	−	0.865619i	$-0.666925\pi$
$151$	−12.3055	−1.00141	−0.500703	+	0.865619i	$0.666925\pi$
$152$	−3.03954	−0.246539
$153$	−8.70303	−0.703598
$154$	0	0
$155$	−9.94094	−0.798475
$156$	−4.02128	−0.321960
$157$	−21.7904	−1.73906	−0.869530	−	0.493880i	$-0.835578\pi$
$157$	−21.7904	−1.73906	−0.869530	+	0.493880i	$0.835578\pi$
$158$	4.46206	0.354983
$159$	−6.21715	−0.493052
$160$	−1.84022	−0.145482
$161$	0	0
$162$	−4.88971	−0.384172
$163$	8.59032	0.672846	0.336423	−	0.941711i	$-0.390783\pi$
$163$	8.59032	0.672846	0.336423	+	0.941711i	$0.390783\pi$
$164$	−3.14050	−0.245232
$165$	5.11178	0.397951
$166$	5.49299	0.426338
$167$	4.00175	0.309665	0.154832	−	0.987941i	$-0.450516\pi$
$167$	4.00175	0.309665	0.154832	+	0.987941i	$0.450516\pi$
$168$	0	0
$169$	20.5093	1.57764
$170$	−6.36186	−0.487932
$171$	−7.65182	−0.585149
$172$	3.89176	0.296744
$173$	−18.4656	−1.40391	−0.701956	−	0.712220i	$-0.747690\pi$
$173$	−18.4656	−1.40391	−0.701956	+	0.712220i	$0.747690\pi$
$174$	1.22659	0.0929875
$175$	0	0
$176$	3.99871	0.301414
$177$	4.99263	0.375269
$178$	−11.4326	−0.856907
$179$	14.2511	1.06518	0.532589	−	0.846374i	$-0.321219\pi$
$179$	14.2511	1.06518	0.532589	+	0.846374i	$0.321219\pi$
$180$	−4.63263	−0.345296
$181$	−18.8870	−1.40386	−0.701929	−	0.712247i	$-0.747678\pi$
$181$	−18.8870	−1.40386	−0.701929	+	0.712247i	$0.747678\pi$
$182$	0	0
$183$	−2.68874	−0.198757
$184$	8.05684	0.593958
$185$	11.3279	0.832844
$186$	3.75265	0.275158
$187$	13.8240	1.01091
$188$	−7.28372	−0.531220
$189$	0	0
$190$	−5.59343	−0.405790
$191$	16.6139	1.20214	0.601068	−	0.799198i	$-0.294742\pi$
$191$	16.6139	1.20214	0.601068	+	0.799198i	$0.294742\pi$
$192$	0.694675	0.0501339
$193$	26.7553	1.92589	0.962943	−	0.269704i	$-0.0869257\pi$
$193$	26.7553	1.92589	0.962943	+	0.269704i	$0.0869257\pi$
$194$	−9.72695	−0.698354
$195$	−7.40006	−0.529929
$196$	0	0
$197$	−7.32209	−0.521677	−0.260839	−	0.965382i	$-0.583999\pi$
$197$	−7.32209	−0.521677	−0.260839	+	0.965382i	$0.583999\pi$
$198$	10.0664	0.715391
$199$	−3.80434	−0.269683	−0.134841	−	0.990867i	$-0.543052\pi$
$199$	−3.80434	−0.269683	−0.134841	+	0.990867i	$0.543052\pi$
$200$	1.61358	0.114097
$201$	1.28838	0.0908752
$202$	7.96670	0.560535
$203$	0	0
$204$	2.40157	0.168144
$205$	−5.77922	−0.403638
$206$	−17.7422	−1.23616
$207$	20.2825	1.40973
$208$	−5.78872	−0.401376
$209$	12.1542	0.840725
$210$	0	0
$211$	21.4786	1.47865	0.739325	−	0.673349i	$-0.235145\pi$
$211$	21.4786	1.47865	0.739325	+	0.673349i	$0.235145\pi$
$212$	−8.94972	−0.614669
$213$	−5.03213	−0.344796
$214$	−3.06659	−0.209628
$215$	7.16171	0.488424
$216$	3.83282	0.260790
$217$	0	0
$218$	13.2292	0.895996
$219$	−8.14461	−0.550362
$220$	7.35851	0.496111
$221$	−20.0123	−1.34617
$222$	−4.27622	−0.287001
$223$	5.99781	0.401643	0.200822	−	0.979628i	$-0.435639\pi$
$223$	5.99781	0.401643	0.200822	+	0.979628i	$0.435639\pi$
$224$	0	0
$225$	4.06206	0.270804
$226$	10.3844	0.690761
$227$	−10.5567	−0.700670	−0.350335	−	0.936624i	$-0.613932\pi$
$227$	−10.5567	−0.700670	−0.350335	+	0.936624i	$0.613932\pi$
$228$	2.11149	0.139837
$229$	8.91367	0.589032	0.294516	−	0.955647i	$-0.404842\pi$
$229$	8.91367	0.589032	0.294516	+	0.955647i	$0.404842\pi$
$230$	14.8264	0.977623
$231$	0	0
$232$	1.76570	0.115924
$233$	−1.56972	−0.102836	−0.0514180	−	0.998677i	$-0.516374\pi$
$233$	−1.56972	−0.102836	−0.0514180	+	0.998677i	$0.516374\pi$
$234$	−14.5727	−0.952646
$235$	−13.4037	−0.874359
$236$	7.18700	0.467834
$237$	−3.09968	−0.201346
$238$	0	0
$239$	23.1319	1.49628	0.748139	−	0.663542i	$-0.230947\pi$
$239$	23.1319	1.49628	0.748139	+	0.663542i	$0.230947\pi$
$240$	1.27836	0.0825176
$241$	5.13428	0.330728	0.165364	−	0.986233i	$-0.447120\pi$
$241$	5.13428	0.330728	0.165364	+	0.986233i	$0.447120\pi$
$242$	−4.98965	−0.320747
$243$	14.8952	0.955529
$244$	−3.87049	−0.247783
$245$	0	0
$246$	2.18163	0.139096
$247$	−17.5951	−1.11955
$248$	5.40203	0.343029
$249$	−3.81584	−0.241819
$250$	12.1705	0.769728
$251$	−5.11040	−0.322566	−0.161283	−	0.986908i	$-0.551563\pi$
$251$	−5.11040	−0.322566	−0.161283	+	0.986908i	$0.551563\pi$
$252$	0	0
$253$	−32.2169	−2.02546
$254$	12.4254	0.779637
$255$	4.41943	0.276755
$256$	1.00000	0.0625000
$257$	−15.7557	−0.982815	−0.491408	−	0.870930i	$-0.663517\pi$
$257$	−15.7557	−0.982815	−0.491408	+	0.870930i	$0.663517\pi$
$258$	−2.70351	−0.168313
$259$	0	0
$260$	−10.6525	−0.660643
$261$	4.44502	0.275140
$262$	7.38571	0.456291
$263$	−1.85362	−0.114299	−0.0571494	−	0.998366i	$-0.518201\pi$
$263$	−1.85362	−0.114299	−0.0571494	+	0.998366i	$0.518201\pi$
$264$	−2.77780	−0.170962
$265$	−16.4695	−1.01171
$266$	0	0
$267$	7.94192	0.486037
$268$	1.85465	0.113291
$269$	1.50139	0.0915413	0.0457706	−	0.998952i	$-0.485426\pi$
$269$	1.50139	0.0915413	0.0457706	+	0.998952i	$0.485426\pi$
$270$	7.05324	0.429247
$271$	16.4953	1.00202	0.501010	−	0.865442i	$-0.332962\pi$
$271$	16.4953	1.00202	0.501010	+	0.865442i	$0.332962\pi$
$272$	3.45711	0.209618
$273$	0	0
$274$	12.2859	0.742219
$275$	−6.45222	−0.389084
$276$	−5.59688	−0.336893
$277$	15.5869	0.936529	0.468264	−	0.883588i	$-0.344879\pi$
$277$	15.5869	0.936529	0.468264	+	0.883588i	$0.344879\pi$
$278$	1.18390	0.0710059
$279$	13.5992	0.814163
$280$	0	0
$281$	−0.317665	−0.0189503	−0.00947516	−	0.999955i	$-0.503016\pi$
$281$	−0.317665	−0.0189503	−0.00947516	+	0.999955i	$0.503016\pi$
$282$	5.05982	0.301308
$283$	−21.4000	−1.27210	−0.636048	−	0.771650i	$-0.719432\pi$
$283$	−21.4000	−1.27210	−0.636048	+	0.771650i	$0.719432\pi$
$284$	−7.24385	−0.429844
$285$	3.88562	0.230164
$286$	23.1474	1.36873
$287$	0	0
$288$	2.51743	0.148341
$289$	−5.04837	−0.296963
$290$	3.24929	0.190805
$291$	6.75707	0.396106
$292$	−11.7243	−0.686115
$293$	−9.40795	−0.549618	−0.274809	−	0.961499i	$-0.588615\pi$
$293$	−9.40795	−0.549618	−0.274809	+	0.961499i	$0.588615\pi$
$294$	0	0
$295$	13.2257	0.770029
$296$	−6.15572	−0.357794
$297$	−15.3263	−0.889323
$298$	−15.9433	−0.923570
$299$	46.6388	2.69719
$300$	−1.12091	−0.0647159
$301$	0	0
$302$	12.3055	0.708101
$303$	−5.53427	−0.317936
$304$	3.03954	0.174330
$305$	−7.12258	−0.407837
$306$	8.70303	0.497519
$307$	−26.9426	−1.53769	−0.768847	−	0.639433i	$-0.779169\pi$
$307$	−26.9426	−1.53769	−0.768847	+	0.639433i	$0.779169\pi$
$308$	0	0
$309$	12.3251	0.701148
$310$	9.94094	0.564607
$311$	−11.7111	−0.664077	−0.332039	−	0.943266i	$-0.607736\pi$
$311$	−11.7111	−0.664077	−0.332039	+	0.943266i	$0.607736\pi$
$312$	4.02128	0.227660
$313$	−18.7188	−1.05805	−0.529025	−	0.848606i	$-0.677442\pi$
$313$	−18.7188	−1.05805	−0.529025	+	0.848606i	$0.677442\pi$
$314$	21.7904	1.22970
$315$	0	0
$316$	−4.46206	−0.251011
$317$	20.5279	1.15296	0.576480	−	0.817111i	$-0.304426\pi$
$317$	20.5279	1.15296	0.576480	+	0.817111i	$0.304426\pi$
$318$	6.21715	0.348640
$319$	−7.06052	−0.395313
$320$	1.84022	0.102872
$321$	2.13028	0.118901
$322$	0	0
$323$	10.5080	0.584683
$324$	4.88971	0.271651
$325$	9.34055	0.518121
$326$	−8.59032	−0.475774
$327$	−9.19001	−0.508209
$328$	3.14050	0.173405
$329$	0	0
$330$	−5.11178	−0.281394
$331$	17.3600	0.954193	0.477097	−	0.878851i	$-0.341689\pi$
$331$	17.3600	0.954193	0.477097	+	0.878851i	$0.341689\pi$
$332$	−5.49299	−0.301467
$333$	−15.4966	−0.849207
$334$	−4.00175	−0.218966
$335$	3.41297	0.186470
$336$	0	0
$337$	10.1144	0.550965	0.275483	−	0.961306i	$-0.411162\pi$
$337$	10.1144	0.550965	0.275483	+	0.961306i	$0.411162\pi$
$338$	−20.5093	−1.11556
$339$	−7.21380	−0.391800
$340$	6.36186	0.345020
$341$	−21.6011	−1.16977
$342$	7.65182	0.413763
$343$	0	0
$344$	−3.89176	−0.209830
$345$	−10.2995	−0.554507
$346$	18.4656	0.992716
$347$	14.5697	0.782141	0.391071	−	0.920361i	$-0.372105\pi$
$347$	14.5697	0.782141	0.391071	+	0.920361i	$0.372105\pi$
$348$	−1.22659	−0.0657521
$349$	−6.33481	−0.339095	−0.169547	−	0.985522i	$-0.554231\pi$
$349$	−6.33481	−0.339095	−0.169547	+	0.985522i	$0.554231\pi$
$350$	0	0
$351$	22.1871	1.18426
$352$	−3.99871	−0.213132
$353$	34.8408	1.85439	0.927194	−	0.374583i	$-0.122214\pi$
$353$	34.8408	1.85439	0.927194	+	0.374583i	$0.122214\pi$
$354$	−4.99263	−0.265355
$355$	−13.3303	−0.707499
$356$	11.4326	0.605925
$357$	0	0
$358$	−14.2511	−0.753194
$359$	−17.1379	−0.904506	−0.452253	−	0.891890i	$-0.649380\pi$
$359$	−17.1379	−0.904506	−0.452253	+	0.891890i	$0.649380\pi$
$360$	4.63263	0.244161
$361$	−9.76120	−0.513747
$362$	18.8870	0.992678
$363$	3.46618	0.181927
$364$	0	0
$365$	−21.5754	−1.12931
$366$	2.68874	0.140543
$367$	−33.1486	−1.73034	−0.865172	−	0.501475i	$-0.832791\pi$
$367$	−33.1486	−1.73034	−0.865172	+	0.501475i	$0.832791\pi$
$368$	−8.05684	−0.419992
$369$	7.90598	0.411569
$370$	−11.3279	−0.588909
$371$	0	0
$372$	−3.75265	−0.194566
$373$	2.37539	0.122993	0.0614966	−	0.998107i	$-0.480413\pi$
$373$	2.37539	0.122993	0.0614966	+	0.998107i	$0.480413\pi$
$374$	−13.8240	−0.714821
$375$	−8.45452	−0.436589
$376$	7.28372	0.375629
$377$	10.2212	0.526416
$378$	0	0
$379$	−15.6979	−0.806348	−0.403174	−	0.915123i	$-0.632093\pi$
$379$	−15.6979	−0.806348	−0.403174	+	0.915123i	$0.632093\pi$
$380$	5.59343	0.286937
$381$	−8.63159	−0.442210
$382$	−16.6139	−0.850039
$383$	−16.6789	−0.852252	−0.426126	−	0.904664i	$-0.640122\pi$
$383$	−16.6789	−0.852252	−0.426126	+	0.904664i	$0.640122\pi$
$384$	−0.694675	−0.0354500
$385$	0	0
$386$	−26.7553	−1.36181
$387$	−9.79722	−0.498021
$388$	9.72695	0.493811
$389$	−15.4301	−0.782336	−0.391168	−	0.920319i	$-0.627929\pi$
$389$	−15.4301	−0.782336	−0.391168	+	0.920319i	$0.627929\pi$
$390$	7.40006	0.374717
$391$	−27.8534	−1.40861
$392$	0	0
$393$	−5.13067	−0.258808
$394$	7.32209	0.368882
$395$	−8.21119	−0.413150
$396$	−10.0664	−0.505858
$397$	−25.9946	−1.30463	−0.652316	−	0.757947i	$-0.726203\pi$
$397$	−25.9946	−1.30463	−0.652316	+	0.757947i	$0.726203\pi$
$398$	3.80434	0.190694
$399$	0	0
$400$	−1.61358	−0.0806789
$401$	21.1342	1.05539	0.527695	−	0.849434i	$-0.323056\pi$
$401$	21.1342	1.05539	0.527695	+	0.849434i	$0.323056\pi$
$402$	−1.28838	−0.0642585
$403$	31.2708	1.55771
$404$	−7.96670	−0.396358
$405$	8.99817	0.447123
$406$	0	0
$407$	24.6149	1.22012
$408$	−2.40157	−0.118895
$409$	−2.94072	−0.145409	−0.0727047	−	0.997354i	$-0.523163\pi$
$409$	−2.94072	−0.145409	−0.0727047	+	0.997354i	$0.523163\pi$
$410$	5.77922	0.285415
$411$	−8.53471	−0.420986
$412$	17.7422	0.874095
$413$	0	0
$414$	−20.2825	−0.996830
$415$	−10.1083	−0.496198
$416$	5.78872	0.283815
$417$	−0.822429	−0.0402745
$418$	−12.1542	−0.594483
$419$	11.0714	0.540876	0.270438	−	0.962737i	$-0.412832\pi$
$419$	11.0714	0.540876	0.270438	+	0.962737i	$0.412832\pi$
$420$	0	0
$421$	−19.2915	−0.940210	−0.470105	−	0.882610i	$-0.655784\pi$
$421$	−19.2915	−0.940210	−0.470105	+	0.882610i	$0.655784\pi$
$422$	−21.4786	−1.04556
$423$	18.3362	0.891537
$424$	8.94972	0.434637
$425$	−5.57832	−0.270588
$426$	5.03213	0.243807
$427$	0	0
$428$	3.06659	0.148229
$429$	−16.0799	−0.776346
$430$	−7.16171	−0.345368
$431$	−10.3077	−0.496506	−0.248253	−	0.968695i	$-0.579856\pi$
$431$	−10.3077	−0.496506	−0.248253	+	0.968695i	$0.579856\pi$
$432$	−3.83282	−0.184407
$433$	−3.23898	−0.155655	−0.0778277	−	0.996967i	$-0.524798\pi$
$433$	−3.23898	−0.155655	−0.0778277	+	0.996967i	$0.524798\pi$
$434$	0	0
$435$	−2.25720	−0.108224
$436$	−13.2292	−0.633565
$437$	−24.4891	−1.17147
$438$	8.14461	0.389165
$439$	−36.1619	−1.72591	−0.862956	−	0.505279i	$-0.831390\pi$
$439$	−36.1619	−1.72591	−0.862956	+	0.505279i	$0.831390\pi$
$440$	−7.35851	−0.350803
$441$	0	0
$442$	20.0123	0.951886
$443$	−9.80358	−0.465782	−0.232891	−	0.972503i	$-0.574819\pi$
$443$	−9.80358	−0.465782	−0.232891	+	0.972503i	$0.574819\pi$
$444$	4.27622	0.202941
$445$	21.0385	0.997319
$446$	−5.99781	−0.284005
$447$	11.0754	0.523849
$448$	0	0
$449$	7.33099	0.345971	0.172985	−	0.984924i	$-0.444659\pi$
$449$	7.33099	0.345971	0.172985	+	0.984924i	$0.444659\pi$
$450$	−4.06206	−0.191487
$451$	−12.5579	−0.591330
$452$	−10.3844	−0.488442
$453$	−8.54832	−0.401635
$454$	10.5567	0.495449
$455$	0	0
$456$	−2.11149	−0.0988797
$457$	29.3516	1.37301	0.686506	−	0.727124i	$-0.259144\pi$
$457$	29.3516	1.37301	0.686506	+	0.727124i	$0.259144\pi$
$458$	−8.91367	−0.416509
$459$	−13.2505	−0.618480
$460$	−14.8264	−0.691284
$461$	−0.245656	−0.0114413	−0.00572067	−	0.999984i	$-0.501821\pi$
$461$	−0.245656	−0.0114413	−0.00572067	+	0.999984i	$0.501821\pi$
$462$	0	0
$463$	−9.32005	−0.433139	−0.216570	−	0.976267i	$-0.569487\pi$
$463$	−9.32005	−0.433139	−0.216570	+	0.976267i	$0.569487\pi$
$464$	−1.76570	−0.0819706
$465$	−6.90572	−0.320245
$466$	1.56972	0.0727160
$467$	−10.6673	−0.493624	−0.246812	−	0.969063i	$-0.579383\pi$
$467$	−10.6673	−0.493624	−0.246812	+	0.969063i	$0.579383\pi$
$468$	14.5727	0.673623
$469$	0	0
$470$	13.4037	0.618265
$471$	−15.1372	−0.697486
$472$	−7.18700	−0.330808
$473$	15.5620	0.715542
$474$	3.09968	0.142373
$475$	−4.90453	−0.225035
$476$	0	0
$477$	22.5303	1.03159
$478$	−23.1319	−1.05803
$479$	13.0713	0.597245	0.298622	−	0.954371i	$-0.403473\pi$
$479$	13.0713	0.597245	0.298622	+	0.954371i	$0.403473\pi$
$480$	−1.27836	−0.0583488
$481$	−35.6337	−1.62476
$482$	−5.13428	−0.233860
$483$	0	0
$484$	4.98965	0.226802
$485$	17.8998	0.812786
$486$	−14.8952	−0.675661
$487$	2.99666	0.135792	0.0678958	−	0.997692i	$-0.478371\pi$
$487$	2.99666	0.135792	0.0678958	+	0.997692i	$0.478371\pi$
$488$	3.87049	0.175209
$489$	5.96748	0.269859
$490$	0	0
$491$	5.19765	0.234567	0.117283	−	0.993098i	$-0.462581\pi$
$491$	5.19765	0.234567	0.117283	+	0.993098i	$0.462581\pi$
$492$	−2.18163	−0.0983554
$493$	−6.10423	−0.274921
$494$	17.5951	0.791639
$495$	−18.5245	−0.832615
$496$	−5.40203	−0.242558
$497$	0	0
$498$	3.81584	0.170992
$499$	−7.40369	−0.331435	−0.165717	−	0.986173i	$-0.552994\pi$
$499$	−7.40369	−0.331435	−0.165717	+	0.986173i	$0.552994\pi$
$500$	−12.1705	−0.544280
$501$	2.77992	0.124197
$502$	5.11040	0.228088
$503$	−9.83604	−0.438567	−0.219284	−	0.975661i	$-0.570372\pi$
$503$	−9.83604	−0.438567	−0.219284	+	0.975661i	$0.570372\pi$
$504$	0	0
$505$	−14.6605	−0.652384
$506$	32.2169	1.43222
$507$	14.2473	0.632745
$508$	−12.4254	−0.551286
$509$	31.6672	1.40362	0.701812	−	0.712362i	$-0.252375\pi$
$509$	31.6672	1.40362	0.701812	+	0.712362i	$0.252375\pi$
$510$	−4.41943	−0.195696
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	−11.6500	−0.514360
$514$	15.7557	0.694955
$515$	32.6496	1.43871
$516$	2.70351	0.119015
$517$	−29.1254	−1.28094
$518$	0	0
$519$	−12.8276	−0.563068
$520$	10.6525	0.467145
$521$	14.6688	0.642652	0.321326	−	0.946969i	$-0.395871\pi$
$521$	14.6688	0.642652	0.321326	+	0.946969i	$0.395871\pi$
$522$	−4.44502	−0.194553
$523$	−16.4098	−0.717550	−0.358775	−	0.933424i	$-0.616805\pi$
$523$	−16.4098	−0.717550	−0.358775	+	0.933424i	$0.616805\pi$
$524$	−7.38571	−0.322646
$525$	0	0
$526$	1.85362	0.0808215
$527$	−18.6754	−0.813514
$528$	2.77780	0.120888
$529$	41.9126	1.82229
$530$	16.4695	0.715388
$531$	−18.0927	−0.785158
$532$	0	0
$533$	18.1795	0.787441
$534$	−7.94192	−0.343680
$535$	5.64321	0.243977
$536$	−1.85465	−0.0801086
$537$	9.89989	0.427212
$538$	−1.50139	−0.0647294
$539$	0	0
$540$	−7.05324	−0.303523
$541$	−9.70295	−0.417163	−0.208581	−	0.978005i	$-0.566885\pi$
$541$	−9.70295	−0.417163	−0.208581	+	0.978005i	$0.566885\pi$
$542$	−16.4953	−0.708534
$543$	−13.1203	−0.563047
$544$	−3.45711	−0.148222
$545$	−24.3447	−1.04281
$546$	0	0
$547$	−22.3950	−0.957539	−0.478770	−	0.877941i	$-0.658917\pi$
$547$	−22.3950	−0.957539	−0.478770	+	0.877941i	$0.658917\pi$
$548$	−12.2859	−0.524828
$549$	9.74368	0.415850
$550$	6.45222	0.275124
$551$	−5.36692	−0.228638
$552$	5.59688	0.238219
$553$	0	0
$554$	−15.5869	−0.662226
$555$	7.86921	0.334029
$556$	−1.18390	−0.0502088
$557$	42.8265	1.81462	0.907309	−	0.420464i	$-0.138133\pi$
$557$	42.8265	1.81462	0.907309	+	0.420464i	$0.138133\pi$
$558$	−13.5992	−0.575700
$559$	−22.5283	−0.952846
$560$	0	0
$561$	9.60317	0.405446
$562$	0.317665	0.0133999
$563$	−11.2575	−0.474446	−0.237223	−	0.971455i	$-0.576237\pi$
$563$	−11.2575	−0.474446	−0.237223	+	0.971455i	$0.576237\pi$
$564$	−5.05982	−0.213057
$565$	−19.1096	−0.803949
$566$	21.4000	0.899507
$567$	0	0
$568$	7.24385	0.303945
$569$	34.0346	1.42680	0.713402	−	0.700755i	$-0.247154\pi$
$569$	34.0346	1.42680	0.713402	+	0.700755i	$0.247154\pi$
$570$	−3.88562	−0.162751
$571$	−10.3773	−0.434276	−0.217138	−	0.976141i	$-0.569672\pi$
$571$	−10.3773	−0.434276	−0.217138	+	0.976141i	$0.569672\pi$
$572$	−23.1474	−0.967841
$573$	11.5412	0.482142
$574$	0	0
$575$	13.0003	0.542151
$576$	−2.51743	−0.104893
$577$	41.6092	1.73221	0.866106	−	0.499860i	$-0.166615\pi$
$577$	41.6092	1.73221	0.866106	+	0.499860i	$0.166615\pi$
$578$	5.04837	0.209985
$579$	18.5862	0.772417
$580$	−3.24929	−0.134919
$581$	0	0
$582$	−6.75707	−0.280090
$583$	−35.7873	−1.48216
$584$	11.7243	0.485157
$585$	26.8170	1.10875
$586$	9.40795	0.388639
$587$	1.39293	0.0574923	0.0287461	−	0.999587i	$-0.490849\pi$
$587$	1.39293	0.0574923	0.0287461	+	0.999587i	$0.490849\pi$
$588$	0	0
$589$	−16.4197	−0.676561
$590$	−13.2257	−0.544493
$591$	−5.08647	−0.209230
$592$	6.15572	0.252998
$593$	−25.9246	−1.06460	−0.532298	−	0.846557i	$-0.678671\pi$
$593$	−25.9246	−1.06460	−0.532298	+	0.846557i	$0.678671\pi$
$594$	15.3263	0.628846
$595$	0	0
$596$	15.9433	0.653063
$597$	−2.64278	−0.108162
$598$	−46.6388	−1.90720
$599$	−37.7050	−1.54058	−0.770291	−	0.637692i	$-0.779889\pi$
$599$	−37.7050	−1.54058	−0.770291	+	0.637692i	$0.779889\pi$
$600$	1.12091	0.0457610
$601$	−8.73462	−0.356293	−0.178146	−	0.984004i	$-0.557010\pi$
$601$	−8.73462	−0.356293	−0.178146	+	0.984004i	$0.557010\pi$
$602$	0	0
$603$	−4.66894	−0.190134
$604$	−12.3055	−0.500703
$605$	9.18206	0.373304
$606$	5.53427	0.224814
$607$	17.5488	0.712284	0.356142	−	0.934432i	$-0.384092\pi$
$607$	17.5488	0.712284	0.356142	+	0.934432i	$0.384092\pi$
$608$	−3.03954	−0.123270
$609$	0	0
$610$	7.12258	0.288385
$611$	42.1634	1.70575
$612$	−8.70303	−0.351799
$613$	2.63172	0.106294	0.0531470	−	0.998587i	$-0.483075\pi$
$613$	2.63172	0.106294	0.0531470	+	0.998587i	$0.483075\pi$
$614$	26.9426	1.08731
$615$	−4.01468	−0.161888
$616$	0	0
$617$	−28.3981	−1.14327	−0.571633	−	0.820510i	$-0.693690\pi$
$617$	−28.3981	−1.14327	−0.571633	+	0.820510i	$0.693690\pi$
$618$	−12.3251	−0.495786
$619$	−25.4591	−1.02329	−0.511644	−	0.859197i	$-0.670963\pi$
$619$	−25.4591	−1.02329	−0.511644	+	0.859197i	$0.670963\pi$
$620$	−9.94094	−0.399238
$621$	30.8804	1.23919
$622$	11.7111	0.469574
$623$	0	0
$624$	−4.02128	−0.160980
$625$	−14.3285	−0.573139
$626$	18.7188	0.748154
$627$	8.44324	0.337190
$628$	−21.7904	−0.869530
$629$	21.2810	0.848529
$630$	0	0
$631$	7.40808	0.294911	0.147455	−	0.989069i	$-0.452892\pi$
$631$	7.40808	0.294911	0.147455	+	0.989069i	$0.452892\pi$
$632$	4.46206	0.177491
$633$	14.9207	0.593043
$634$	−20.5279	−0.815266
$635$	−22.8654	−0.907388
$636$	−6.21715	−0.246526
$637$	0	0
$638$	7.06052	0.279529
$639$	18.2359	0.721400
$640$	−1.84022	−0.0727412
$641$	−13.9557	−0.551217	−0.275608	−	0.961270i	$-0.588879\pi$
$641$	−13.9557	−0.551217	−0.275608	+	0.961270i	$0.588879\pi$
$642$	−2.13028	−0.0840756
$643$	−43.7610	−1.72577	−0.862883	−	0.505404i	$-0.831343\pi$
$643$	−43.7610	−1.72577	−0.862883	+	0.505404i	$0.831343\pi$
$644$	0	0
$645$	4.97506	0.195893
$646$	−10.5080	−0.413433
$647$	15.2021	0.597655	0.298828	−	0.954307i	$-0.403404\pi$
$647$	15.2021	0.597655	0.298828	+	0.954307i	$0.403404\pi$
$648$	−4.88971	−0.192086
$649$	28.7387	1.12809
$650$	−9.34055	−0.366367
$651$	0	0
$652$	8.59032	0.336423
$653$	−11.4813	−0.449298	−0.224649	−	0.974440i	$-0.572123\pi$
$653$	−11.4813	−0.449298	−0.224649	+	0.974440i	$0.572123\pi$
$654$	9.19001	0.359358
$655$	−13.5914	−0.531058
$656$	−3.14050	−0.122616
$657$	29.5152	1.15150
$658$	0	0
$659$	24.1022	0.938890	0.469445	−	0.882962i	$-0.344454\pi$
$659$	24.1022	0.938890	0.469445	+	0.882962i	$0.344454\pi$
$660$	5.11178	0.198976
$661$	30.6476	1.19205	0.596027	−	0.802965i	$-0.296745\pi$
$661$	30.6476	1.19205	0.596027	+	0.802965i	$0.296745\pi$
$662$	−17.3600	−0.674717
$663$	−13.9020	−0.539910
$664$	5.49299	0.213169
$665$	0	0
$666$	15.4966	0.600480
$667$	14.2260	0.550832
$668$	4.00175	0.154832
$669$	4.16653	0.161087
$670$	−3.41297	−0.131854
$671$	−15.4770	−0.597482
$672$	0	0
$673$	−6.32696	−0.243887	−0.121943	−	0.992537i	$-0.538913\pi$
$673$	−6.32696	−0.243887	−0.121943	+	0.992537i	$0.538913\pi$
$674$	−10.1144	−0.389591
$675$	6.18455	0.238043
$676$	20.5093	0.788820
$677$	10.7588	0.413495	0.206747	−	0.978394i	$-0.433712\pi$
$677$	10.7588	0.413495	0.206747	+	0.978394i	$0.433712\pi$
$678$	7.21380	0.277044
$679$	0	0
$680$	−6.36186	−0.243966
$681$	−7.33345	−0.281019
$682$	21.6011	0.827149
$683$	−42.5809	−1.62931	−0.814656	−	0.579944i	$-0.803074\pi$
$683$	−42.5809	−1.62931	−0.814656	+	0.579944i	$0.803074\pi$
$684$	−7.65182	−0.292575
$685$	−22.6088	−0.863838
$686$	0	0
$687$	6.19211	0.236244
$688$	3.89176	0.148372
$689$	51.8074	1.97371
$690$	10.2995	0.392096
$691$	−18.4600	−0.702251	−0.351125	−	0.936328i	$-0.614201\pi$
$691$	−18.4600	−0.702251	−0.351125	+	0.936328i	$0.614201\pi$
$692$	−18.4656	−0.701956
$693$	0	0
$694$	−14.5697	−0.553057
$695$	−2.17865	−0.0826409
$696$	1.22659	0.0464937
$697$	−10.8571	−0.411241
$698$	6.33481	0.239776
$699$	−1.09045	−0.0412445
$700$	0	0
$701$	8.72517	0.329545	0.164773	−	0.986332i	$-0.447311\pi$
$701$	8.72517	0.329545	0.164773	+	0.986332i	$0.447311\pi$
$702$	−22.1871	−0.837399
$703$	18.7105	0.705682
$704$	3.99871	0.150707
$705$	−9.31119	−0.350680
$706$	−34.8408	−1.31125
$707$	0	0
$708$	4.99263	0.187634
$709$	6.12705	0.230106	0.115053	−	0.993359i	$-0.463296\pi$
$709$	6.12705	0.230106	0.115053	+	0.993359i	$0.463296\pi$
$710$	13.3303	0.500278
$711$	11.2329	0.421267
$712$	−11.4326	−0.428453
$713$	43.5232	1.62996
$714$	0	0
$715$	−42.5964	−1.59301
$716$	14.2511	0.532589
$717$	16.0692	0.600114
$718$	17.1379	0.639582
$719$	−13.8682	−0.517196	−0.258598	−	0.965985i	$-0.583260\pi$
$719$	−13.8682	−0.517196	−0.258598	+	0.965985i	$0.583260\pi$
$720$	−4.63263	−0.172648
$721$	0	0
$722$	9.76120	0.363274
$723$	3.56665	0.132645
$724$	−18.8870	−0.701929
$725$	2.84910	0.105813
$726$	−3.46618	−0.128642
$727$	−48.2208	−1.78841	−0.894206	−	0.447656i	$-0.852259\pi$
$727$	−48.2208	−1.78841	−0.894206	+	0.447656i	$0.852259\pi$
$728$	0	0
$729$	−4.32180	−0.160067
$730$	21.5754	0.798542
$731$	13.4543	0.497624
$732$	−2.68874	−0.0993786
$733$	43.6256	1.61135	0.805674	−	0.592359i	$-0.201803\pi$
$733$	43.6256	1.61135	0.805674	+	0.592359i	$0.201803\pi$
$734$	33.1486	1.22354
$735$	0	0
$736$	8.05684	0.296979
$737$	7.41619	0.273179
$738$	−7.90598	−0.291023
$739$	−32.0109	−1.17754	−0.588770	−	0.808301i	$-0.700388\pi$
$739$	−32.0109	−1.17754	−0.588770	+	0.808301i	$0.700388\pi$
$740$	11.3279	0.416422
$741$	−12.2228	−0.449017
$742$	0	0
$743$	39.7909	1.45979	0.729893	−	0.683561i	$-0.239570\pi$
$743$	39.7909	1.45979	0.729893	+	0.683561i	$0.239570\pi$
$744$	3.75265	0.137579
$745$	29.3392	1.07491
$746$	−2.37539	−0.0869694
$747$	13.8282	0.505947
$748$	13.8240	0.505455
$749$	0	0
$750$	8.45452	0.308715
$751$	−18.8778	−0.688862	−0.344431	−	0.938812i	$-0.611928\pi$
$751$	−18.8778	−0.688862	−0.344431	+	0.938812i	$0.611928\pi$
$752$	−7.28372	−0.265610
$753$	−3.55007	−0.129372
$754$	−10.2212	−0.372233
$755$	−22.6449	−0.824131
$756$	0	0
$757$	11.4828	0.417350	0.208675	−	0.977985i	$-0.433085\pi$
$757$	11.4828	0.417350	0.208675	+	0.977985i	$0.433085\pi$
$758$	15.6979	0.570174
$759$	−22.3803	−0.812353
$760$	−5.59343	−0.202895
$761$	27.2186	0.986675	0.493337	−	0.869838i	$-0.335777\pi$
$761$	27.2186	0.986675	0.493337	+	0.869838i	$0.335777\pi$
$762$	8.63159	0.312690
$763$	0	0
$764$	16.6139	0.601068
$765$	−16.0155	−0.579042
$766$	16.6789	0.602633
$767$	−41.6035	−1.50222
$768$	0.694675	0.0250669
$769$	−34.5238	−1.24496	−0.622480	−	0.782636i	$-0.713875\pi$
$769$	−34.5238	−1.24496	−0.622480	+	0.782636i	$0.713875\pi$
$770$	0	0
$771$	−10.9451	−0.394179
$772$	26.7553	0.962943
$773$	3.42240	0.123095	0.0615475	−	0.998104i	$-0.480396\pi$
$773$	3.42240	0.123095	0.0615475	+	0.998104i	$0.480396\pi$
$774$	9.79722	0.352154
$775$	8.71659	0.313109
$776$	−9.72695	−0.349177
$777$	0	0
$778$	15.4301	0.553195
$779$	−9.54568	−0.342009
$780$	−7.40006	−0.264965
$781$	−28.9660	−1.03649
$782$	27.8534	0.996035
$783$	6.76761	0.241855
$784$	0	0
$785$	−40.0991	−1.43120
$786$	5.13067	0.183005
$787$	−40.7585	−1.45288	−0.726442	−	0.687228i	$-0.758828\pi$
$787$	−40.7585	−1.45288	−0.726442	+	0.687228i	$0.758828\pi$
$788$	−7.32209	−0.260839
$789$	−1.28766	−0.0458419
$790$	8.21119	0.292141
$791$	0	0
$792$	10.0664	0.357696
$793$	22.4052	0.795633
$794$	25.9946	0.922515
$795$	−11.4409	−0.405768
$796$	−3.80434	−0.134841
$797$	−39.4836	−1.39858	−0.699290	−	0.714838i	$-0.746500\pi$
$797$	−39.4836	−1.39858	−0.699290	+	0.714838i	$0.746500\pi$
$798$	0	0
$799$	−25.1806	−0.890827
$800$	1.61358	0.0570486
$801$	−28.7806	−1.01691
$802$	−21.1342	−0.746273
$803$	−46.8822	−1.65444
$804$	1.28838	0.0454376
$805$	0	0
$806$	−31.2708	−1.10147
$807$	1.04298	0.0367145
$808$	7.96670	0.280268
$809$	1.67296	0.0588182	0.0294091	−	0.999567i	$-0.490637\pi$
$809$	1.67296	0.0588182	0.0294091	+	0.999567i	$0.490637\pi$
$810$	−8.99817	−0.316163
$811$	−23.5089	−0.825509	−0.412754	−	0.910842i	$-0.635433\pi$
$811$	−23.5089	−0.825509	−0.412754	+	0.910842i	$0.635433\pi$
$812$	0	0
$813$	11.4589	0.401881
$814$	−24.6149	−0.862752
$815$	15.8081	0.553734
$816$	2.40157	0.0840718
$817$	11.8292	0.413850
$818$	2.94072	0.102820
$819$	0	0
$820$	−5.77922	−0.201819
$821$	23.5901	0.823301	0.411651	−	0.911342i	$-0.364952\pi$
$821$	23.5901	0.823301	0.411651	+	0.911342i	$0.364952\pi$
$822$	8.53471	0.297682
$823$	34.8200	1.21375	0.606875	−	0.794797i	$-0.292423\pi$
$823$	34.8200	1.21375	0.606875	+	0.794797i	$0.292423\pi$
$824$	−17.7422	−0.618078
$825$	−4.48220	−0.156050
$826$	0	0
$827$	−33.0243	−1.14837	−0.574183	−	0.818727i	$-0.694680\pi$
$827$	−33.0243	−1.14837	−0.574183	+	0.818727i	$0.694680\pi$
$828$	20.2825	0.704865
$829$	7.60529	0.264143	0.132071	−	0.991240i	$-0.457837\pi$
$829$	7.60529	0.264143	0.132071	+	0.991240i	$0.457837\pi$
$830$	10.1083	0.350865
$831$	10.8279	0.375614
$832$	−5.78872	−0.200688
$833$	0	0
$834$	0.822429	0.0284784
$835$	7.36411	0.254846
$836$	12.1542	0.420363
$837$	20.7050	0.715669
$838$	−11.0714	−0.382457
$839$	30.2367	1.04389	0.521943	−	0.852980i	$-0.325207\pi$
$839$	30.2367	1.04389	0.521943	+	0.852980i	$0.325207\pi$
$840$	0	0
$841$	−25.8823	−0.892493
$842$	19.2915	0.664829
$843$	−0.220674	−0.00760042
$844$	21.4786	0.739325
$845$	37.7417	1.29835
$846$	−18.3362	−0.630412
$847$	0	0
$848$	−8.94972	−0.307335
$849$	−14.8660	−0.510200
$850$	5.57832	0.191335
$851$	−49.5956	−1.70012
$852$	−5.03213	−0.172398
$853$	51.5689	1.76568	0.882842	−	0.469669i	$-0.155627\pi$
$853$	51.5689	1.76568	0.882842	+	0.469669i	$0.155627\pi$
$854$	0	0
$855$	−14.0811	−0.481562
$856$	−3.06659	−0.104814
$857$	18.4677	0.630844	0.315422	−	0.948951i	$-0.397854\pi$
$857$	18.4677	0.630844	0.315422	+	0.948951i	$0.397854\pi$
$858$	16.0799	0.548960
$859$	14.8999	0.508379	0.254189	−	0.967154i	$-0.418191\pi$
$859$	14.8999	0.508379	0.254189	+	0.967154i	$0.418191\pi$
$860$	7.16171	0.244212
$861$	0	0
$862$	10.3077	0.351082
$863$	4.21019	0.143317	0.0716583	−	0.997429i	$-0.477171\pi$
$863$	4.21019	0.143317	0.0716583	+	0.997429i	$0.477171\pi$
$864$	3.83282	0.130395
$865$	−33.9808	−1.15538
$866$	3.23898	0.110065
$867$	−3.50698	−0.119103
$868$	0	0
$869$	−17.8425	−0.605264
$870$	2.25720	0.0765262
$871$	−10.7360	−0.363777
$872$	13.2292	0.447998
$873$	−24.4869	−0.828755
$874$	24.4891	0.828355
$875$	0	0
$876$	−8.14461	−0.275181
$877$	24.7551	0.835921	0.417960	−	0.908465i	$-0.362745\pi$
$877$	24.7551	0.835921	0.417960	+	0.908465i	$0.362745\pi$
$878$	36.1619	1.22040
$879$	−6.53547	−0.220436
$880$	7.35851	0.248055
$881$	−7.51988	−0.253351	−0.126676	−	0.991944i	$-0.540431\pi$
$881$	−7.51988	−0.253351	−0.126676	+	0.991944i	$0.540431\pi$
$882$	0	0
$883$	−27.5069	−0.925681	−0.462840	−	0.886442i	$-0.653170\pi$
$883$	−27.5069	−0.925681	−0.462840	+	0.886442i	$0.653170\pi$
$884$	−20.0123	−0.673085
$885$	9.18755	0.308836
$886$	9.80358	0.329358
$887$	−15.0043	−0.503795	−0.251897	−	0.967754i	$-0.581055\pi$
$887$	−15.0043	−0.503795	−0.251897	+	0.967754i	$0.581055\pi$
$888$	−4.27622	−0.143501
$889$	0	0
$890$	−21.0385	−0.705211
$891$	19.5525	0.655034
$892$	5.99781	0.200822
$893$	−22.1391	−0.740858
$894$	−11.0754	−0.370417
$895$	26.2252	0.876612
$896$	0	0
$897$	32.3988	1.08176
$898$	−7.33099	−0.244638
$899$	9.53837	0.318122
$900$	4.06206	0.135402
$901$	−30.9402	−1.03077
$902$	12.5579	0.418134
$903$	0	0
$904$	10.3844	0.345381
$905$	−34.7563	−1.15534
$906$	8.54832	0.283999
$907$	−5.26169	−0.174711	−0.0873557	−	0.996177i	$-0.527842\pi$
$907$	−5.26169	−0.174711	−0.0873557	+	0.996177i	$0.527842\pi$
$908$	−10.5567	−0.350335
$909$	20.0556	0.665202
$910$	0	0
$911$	50.2006	1.66322	0.831611	−	0.555359i	$-0.187419\pi$
$911$	50.2006	1.66322	0.831611	+	0.555359i	$0.187419\pi$
$912$	2.11149	0.0699185
$913$	−21.9648	−0.726930
$914$	−29.3516	−0.970866
$915$	−4.94788	−0.163572
$916$	8.91367	0.294516
$917$	0	0
$918$	13.2505	0.437331
$919$	16.9846	0.560271	0.280136	−	0.959960i	$-0.409621\pi$
$919$	16.9846	0.560271	0.280136	+	0.959960i	$0.409621\pi$
$920$	14.8264	0.488811
$921$	−18.7163	−0.616724
$922$	0.245656	0.00809026
$923$	41.9327	1.38023
$924$	0	0
$925$	−9.93273	−0.326586
$926$	9.32005	0.306276
$927$	−44.6646	−1.46698
$928$	1.76570	0.0579620
$929$	56.4393	1.85171	0.925856	−	0.377876i	$-0.123346\pi$
$929$	56.4393	1.85171	0.925856	+	0.377876i	$0.123346\pi$
$930$	6.90572	0.226448
$931$	0	0
$932$	−1.56972	−0.0514180
$933$	−8.13543	−0.266342
$934$	10.6673	0.349045
$935$	25.4392	0.831951
$936$	−14.5727	−0.476323
$937$	6.21293	0.202968	0.101484	−	0.994837i	$-0.467641\pi$
$937$	6.21293	0.202968	0.101484	+	0.994837i	$0.467641\pi$
$938$	0	0
$939$	−13.0035	−0.424353
$940$	−13.4037	−0.437179
$941$	52.1366	1.69960	0.849802	−	0.527103i	$-0.176722\pi$
$941$	52.1366	1.69960	0.849802	+	0.527103i	$0.176722\pi$
$942$	15.1372	0.493197
$943$	25.3025	0.823963
$944$	7.18700	0.233917
$945$	0	0
$946$	−15.5620	−0.505964
$947$	45.9597	1.49349	0.746745	−	0.665110i	$-0.231615\pi$
$947$	45.9597	1.49349	0.746745	+	0.665110i	$0.231615\pi$
$948$	−3.09968	−0.100673
$949$	67.8690	2.20312
$950$	4.90453	0.159124
$951$	14.2602	0.462419
$952$	0	0
$953$	−23.1620	−0.750289	−0.375145	−	0.926966i	$-0.622407\pi$
$953$	−23.1620	−0.750289	−0.375145	+	0.926966i	$0.622407\pi$
$954$	−22.5303	−0.729444
$955$	30.5732	0.989326
$956$	23.1319	0.748139
$957$	−4.90477	−0.158549
$958$	−13.0713	−0.422316
$959$	0	0
$960$	1.27836	0.0412588
$961$	−1.81811	−0.0586486
$962$	35.6337	1.14888
$963$	−7.71992	−0.248771
$964$	5.13428	0.165364
$965$	49.2357	1.58495
$966$	0	0
$967$	10.1039	0.324920	0.162460	−	0.986715i	$-0.448057\pi$
$967$	10.1039	0.324920	0.162460	+	0.986715i	$0.448057\pi$
$968$	−4.98965	−0.160373
$969$	7.29967	0.234499
$970$	−17.8998	−0.574727
$971$	29.1011	0.933898	0.466949	−	0.884284i	$-0.345353\pi$
$971$	29.1011	0.933898	0.466949	+	0.884284i	$0.345353\pi$
$972$	14.8952	0.477764
$973$	0	0
$974$	−2.99666	−0.0960191
$975$	6.48865	0.207803
$976$	−3.87049	−0.123892
$977$	−31.2515	−0.999824	−0.499912	−	0.866076i	$-0.666634\pi$
$977$	−31.2515	−0.999824	−0.499912	+	0.866076i	$0.666634\pi$
$978$	−5.96748	−0.190819
$979$	45.7154	1.46107
$980$	0	0
$981$	33.3036	1.06330
$982$	−5.19765	−0.165864
$983$	29.6045	0.944237	0.472118	−	0.881535i	$-0.343490\pi$
$983$	29.6045	0.944237	0.472118	+	0.881535i	$0.343490\pi$
$984$	2.18163	0.0695478
$985$	−13.4743	−0.429326
$986$	6.10423	0.194398
$987$	0	0
$988$	−17.5951	−0.559773
$989$	−31.3553	−0.997040
$990$	18.5245	0.588748
$991$	39.5433	1.25614	0.628068	−	0.778159i	$-0.283846\pi$
$991$	39.5433	1.25614	0.628068	+	0.778159i	$0.283846\pi$
$992$	5.40203	0.171515
$993$	12.0596	0.382699
$994$	0	0
$995$	−7.00084	−0.221941
$996$	−3.81584	−0.120910
$997$	49.8164	1.57770	0.788850	−	0.614586i	$-0.210677\pi$
$997$	49.8164	1.57770	0.788850	+	0.614586i	$0.210677\pi$
$998$	7.40369	0.234360
$999$	−23.5938	−0.746473

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4802.2.a.i.1.10		12
7.6	odd	2		4802.2.a.k.1.3		12
49.4	even	21		98.2.g.a.65.2	✓	24
49.12	odd	42		686.2.g.b.557.1		24
49.17	odd	42		686.2.g.c.79.1		24
49.20	odd	14		686.2.e.e.393.4		24
49.22	even	7		686.2.e.f.295.1		24
49.23	even	21		686.2.g.a.165.2		24
49.26	odd	42		686.2.g.c.165.1		24
49.27	odd	14		686.2.e.e.295.4		24
49.29	even	7		686.2.e.f.393.1		24
49.32	even	21		686.2.g.a.79.2		24
49.37	even	21		98.2.g.a.95.2	yes	24
49.45	odd	42		686.2.g.b.569.1		24
147.53	odd	42		882.2.z.d.163.1		24
147.86	odd	42		882.2.z.d.487.1		24
196.135	odd	42		784.2.bg.a.193.1		24
196.151	odd	42		784.2.bg.a.65.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
98.2.g.a.65.2	✓	24	49.4	even	21
98.2.g.a.95.2	yes	24	49.37	even	21
686.2.e.e.295.4		24	49.27	odd	14
686.2.e.e.393.4		24	49.20	odd	14
686.2.e.f.295.1		24	49.22	even	7
686.2.e.f.393.1		24	49.29	even	7
686.2.g.a.79.2		24	49.32	even	21
686.2.g.a.165.2		24	49.23	even	21
686.2.g.b.557.1		24	49.12	odd	42
686.2.g.b.569.1		24	49.45	odd	42
686.2.g.c.79.1		24	49.17	odd	42
686.2.g.c.165.1		24	49.26	odd	42
784.2.bg.a.65.1		24	196.151	odd	42
784.2.bg.a.193.1		24	196.135	odd	42
882.2.z.d.163.1		24	147.53	odd	42
882.2.z.d.487.1		24	147.86	odd	42
4802.2.a.i.1.10		12	1.1	even	1	trivial
4802.2.a.k.1.3		12	7.6	odd	2

Overview	Random
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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:	\( N \)	\(=\)	\( 4802 = 2 \cdot 7^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4802.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.694675 q^{3} +1.00000 q^{4} +1.84022 q^{5} -0.694675 q^{6} -1.00000 q^{8} -2.51743 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +0.694675 q^{3} +1.00000 q^{4} +1.84022 q^{5} -0.694675 q^{6} -1.00000 q^{8} -2.51743 q^{9} -1.84022 q^{10} +3.99871 q^{11} +0.694675 q^{12} -5.78872 q^{13} +1.27836 q^{15} +1.00000 q^{16} +3.45711 q^{17} +2.51743 q^{18} +3.03954 q^{19} +1.84022 q^{20} -3.99871 q^{22} -8.05684 q^{23} -0.694675 q^{24} -1.61358 q^{25} +5.78872 q^{26} -3.83282 q^{27} -1.76570 q^{29} -1.27836 q^{30} -5.40203 q^{31} -1.00000 q^{32} +2.77780 q^{33} -3.45711 q^{34} -2.51743 q^{36} +6.15572 q^{37} -3.03954 q^{38} -4.02128 q^{39} -1.84022 q^{40} -3.14050 q^{41} +3.89176 q^{43} +3.99871 q^{44} -4.63263 q^{45} +8.05684 q^{46} -7.28372 q^{47} +0.694675 q^{48} +1.61358 q^{50} +2.40157 q^{51} -5.78872 q^{52} -8.94972 q^{53} +3.83282 q^{54} +7.35851 q^{55} +2.11149 q^{57} +1.76570 q^{58} +7.18700 q^{59} +1.27836 q^{60} -3.87049 q^{61} +5.40203 q^{62} +1.00000 q^{64} -10.6525 q^{65} -2.77780 q^{66} +1.85465 q^{67} +3.45711 q^{68} -5.59688 q^{69} -7.24385 q^{71} +2.51743 q^{72} -11.7243 q^{73} -6.15572 q^{74} -1.12091 q^{75} +3.03954 q^{76} +4.02128 q^{78} -4.46206 q^{79} +1.84022 q^{80} +4.88971 q^{81} +3.14050 q^{82} -5.49299 q^{83} +6.36186 q^{85} -3.89176 q^{86} -1.22659 q^{87} -3.99871 q^{88} +11.4326 q^{89} +4.63263 q^{90} -8.05684 q^{92} -3.75265 q^{93} +7.28372 q^{94} +5.59343 q^{95} -0.694675 q^{96} +9.72695 q^{97} -10.0664 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{2} - 7 q^{3} + 12 q^{4} + 7 q^{6} - 12 q^{8} + 5 q^{9}+O(q^{10}) \) 12 * q - 12 * q^2 - 7 * q^3 + 12 * q^4 + 7 * q^6 - 12 * q^8 + 5 * q^9	\( 12 q - 12 q^{2} - 7 q^{3} + 12 q^{4} + 7 q^{6} - 12 q^{8} + 5 q^{9} - 7 q^{12} - 14 q^{13} + 12 q^{16} + 14 q^{17} - 5 q^{18} + 7 q^{23} + 7 q^{24} - 4 q^{25} + 14 q^{26} - 7 q^{27} - 2 q^{29} - 28 q^{31} - 12 q^{32} - 21 q^{33} - 14 q^{34} + 5 q^{36} - 4 q^{37} - 2 q^{39} - 7 q^{41} - 2 q^{43} - 14 q^{45} - 7 q^{46} - 28 q^{47} - 7 q^{48} + 4 q^{50} + 24 q^{51} - 14 q^{52} + 2 q^{53} + 7 q^{54} + 7 q^{55} + 36 q^{57} + 2 q^{58} + 28 q^{59} - 21 q^{61} + 28 q^{62} + 12 q^{64} - 21 q^{65} + 21 q^{66} + 36 q^{67} + 14 q^{68} - 7 q^{69} - 14 q^{71} - 5 q^{72} - 35 q^{73} + 4 q^{74} - 35 q^{75} + 2 q^{78} + 26 q^{79} + 36 q^{81} + 7 q^{82} - 7 q^{85} + 2 q^{86} - 63 q^{87} + 14 q^{90} + 7 q^{92} - 9 q^{93} + 28 q^{94} + 7 q^{95} + 7 q^{96} - 63 q^{97} - 7 q^{99}+O(q^{100}) \) 12 * q - 12 * q^2 - 7 * q^3 + 12 * q^4 + 7 * q^6 - 12 * q^8 + 5 * q^9 - 7 * q^12 - 14 * q^13 + 12 * q^16 + 14 * q^17 - 5 * q^18 + 7 * q^23 + 7 * q^24 - 4 * q^25 + 14 * q^26 - 7 * q^27 - 2 * q^29 - 28 * q^31 - 12 * q^32 - 21 * q^33 - 14 * q^34 + 5 * q^36 - 4 * q^37 - 2 * q^39 - 7 * q^41 - 2 * q^43 - 14 * q^45 - 7 * q^46 - 28 * q^47 - 7 * q^48 + 4 * q^50 + 24 * q^51 - 14 * q^52 + 2 * q^53 + 7 * q^54 + 7 * q^55 + 36 * q^57 + 2 * q^58 + 28 * q^59 - 21 * q^61 + 28 * q^62 + 12 * q^64 - 21 * q^65 + 21 * q^66 + 36 * q^67 + 14 * q^68 - 7 * q^69 - 14 * q^71 - 5 * q^72 - 35 * q^73 + 4 * q^74 - 35 * q^75 + 2 * q^78 + 26 * q^79 + 36 * q^81 + 7 * q^82 - 7 * q^85 + 2 * q^86 - 63 * q^87 + 14 * q^90 + 7 * q^92 - 9 * q^93 + 28 * q^94 + 7 * q^95 + 7 * q^96 - 63 * q^97 - 7 * q^99

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