LMFDB - Embedded newform 3630.2.a.bn.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3630,2,Mod(1,3630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3630, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("3630.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3630 = 2 \cdot 3 \cdot 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3630.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:	$28.9856959337$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{12})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 3 $ x^2 - 3
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.73205$ of defining polynomial
Character	$\chi$	$=$	3630.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} +1.73205 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} +1.73205 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -1.00000 q^{12} -6.46410 q^{13} +1.73205 q^{14} -1.00000 q^{15} +1.00000 q^{16} -4.26795 q^{17} +1.00000 q^{18} -6.46410 q^{19} +1.00000 q^{20} -1.73205 q^{21} +8.19615 q^{23} -1.00000 q^{24} +1.00000 q^{25} -6.46410 q^{26} -1.00000 q^{27} +1.73205 q^{28} -6.46410 q^{29} -1.00000 q^{30} -10.1962 q^{31} +1.00000 q^{32} -4.26795 q^{34} +1.73205 q^{35} +1.00000 q^{36} -7.19615 q^{37} -6.46410 q^{38} +6.46410 q^{39} +1.00000 q^{40} +5.66025 q^{41} -1.73205 q^{42} -4.73205 q^{43} +1.00000 q^{45} +8.19615 q^{46} -6.00000 q^{47} -1.00000 q^{48} -4.00000 q^{49} +1.00000 q^{50} +4.26795 q^{51} -6.46410 q^{52} -2.19615 q^{53} -1.00000 q^{54} +1.73205 q^{56} +6.46410 q^{57} -6.46410 q^{58} +2.19615 q^{59} -1.00000 q^{60} -1.26795 q^{61} -10.1962 q^{62} +1.73205 q^{63} +1.00000 q^{64} -6.46410 q^{65} +14.3923 q^{67} -4.26795 q^{68} -8.19615 q^{69} +1.73205 q^{70} -7.39230 q^{71} +1.00000 q^{72} -1.26795 q^{73} -7.19615 q^{74} -1.00000 q^{75} -6.46410 q^{76} +6.46410 q^{78} +15.4641 q^{79} +1.00000 q^{80} +1.00000 q^{81} +5.66025 q^{82} -5.53590 q^{83} -1.73205 q^{84} -4.26795 q^{85} -4.73205 q^{86} +6.46410 q^{87} +16.3923 q^{89} +1.00000 q^{90} -11.1962 q^{91} +8.19615 q^{92} +10.1962 q^{93} -6.00000 q^{94} -6.46410 q^{95} -1.00000 q^{96} +10.1962 q^{97} -4.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} - 2 q^{6} + 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 - 2 * q^6 + 2 * q^8 + 2 * q^9	$ 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} - 2 q^{6} + 2 q^{8} + 2 q^{9} + 2 q^{10} - 2 q^{12} - 6 q^{13} - 2 q^{15} + 2 q^{16} - 12 q^{17} + 2 q^{18} - 6 q^{19} + 2 q^{20} + 6 q^{23} - 2 q^{24} + 2 q^{25} - 6 q^{26} - 2 q^{27} - 6 q^{29} - 2 q^{30} - 10 q^{31} + 2 q^{32} - 12 q^{34} + 2 q^{36} - 4 q^{37} - 6 q^{38} + 6 q^{39} + 2 q^{40} - 6 q^{41} - 6 q^{43} + 2 q^{45} + 6 q^{46} - 12 q^{47} - 2 q^{48} - 8 q^{49} + 2 q^{50} + 12 q^{51} - 6 q^{52} + 6 q^{53} - 2 q^{54} + 6 q^{57} - 6 q^{58} - 6 q^{59} - 2 q^{60} - 6 q^{61} - 10 q^{62} + 2 q^{64} - 6 q^{65} + 8 q^{67} - 12 q^{68} - 6 q^{69} + 6 q^{71} + 2 q^{72} - 6 q^{73} - 4 q^{74} - 2 q^{75} - 6 q^{76} + 6 q^{78} + 24 q^{79} + 2 q^{80} + 2 q^{81} - 6 q^{82} - 18 q^{83} - 12 q^{85} - 6 q^{86} + 6 q^{87} + 12 q^{89} + 2 q^{90} - 12 q^{91} + 6 q^{92} + 10 q^{93} - 12 q^{94} - 6 q^{95} - 2 q^{96} + 10 q^{97} - 8 q^{98}+O(q^{100}) $ 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 - 2 * q^6 + 2 * q^8 + 2 * q^9 + 2 * q^10 - 2 * q^12 - 6 * q^13 - 2 * q^15 + 2 * q^16 - 12 * q^17 + 2 * q^18 - 6 * q^19 + 2 * q^20 + 6 * q^23 - 2 * q^24 + 2 * q^25 - 6 * q^26 - 2 * q^27 - 6 * q^29 - 2 * q^30 - 10 * q^31 + 2 * q^32 - 12 * q^34 + 2 * q^36 - 4 * q^37 - 6 * q^38 + 6 * q^39 + 2 * q^40 - 6 * q^41 - 6 * q^43 + 2 * q^45 + 6 * q^46 - 12 * q^47 - 2 * q^48 - 8 * q^49 + 2 * q^50 + 12 * q^51 - 6 * q^52 + 6 * q^53 - 2 * q^54 + 6 * q^57 - 6 * q^58 - 6 * q^59 - 2 * q^60 - 6 * q^61 - 10 * q^62 + 2 * q^64 - 6 * q^65 + 8 * q^67 - 12 * q^68 - 6 * q^69 + 6 * q^71 + 2 * q^72 - 6 * q^73 - 4 * q^74 - 2 * q^75 - 6 * q^76 + 6 * q^78 + 24 * q^79 + 2 * q^80 + 2 * q^81 - 6 * q^82 - 18 * q^83 - 12 * q^85 - 6 * q^86 + 6 * q^87 + 12 * q^89 + 2 * q^90 - 12 * q^91 + 6 * q^92 + 10 * q^93 - 12 * q^94 - 6 * q^95 - 2 * q^96 + 10 * q^97 - 8 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−1.00000	−0.408248
$7$	1.73205	0.654654	0.327327	−	0.944911i	$-0.393852\pi$
$7$	1.73205	0.654654	0.327327	+	0.944911i	$0.393852\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	1.00000	0.316228
$11$	0	0
$11$	0	0
$12$	−1.00000	−0.288675
$13$	−6.46410	−1.79282	−0.896410	−	0.443227i	$-0.853834\pi$
$13$	−6.46410	−1.79282	−0.896410	+	0.443227i	$0.853834\pi$
$14$	1.73205	0.462910
$15$	−1.00000	−0.258199
$16$	1.00000	0.250000
$17$	−4.26795	−1.03513	−0.517565	−	0.855644i	$-0.673161\pi$
$17$	−4.26795	−1.03513	−0.517565	+	0.855644i	$0.673161\pi$
$18$	1.00000	0.235702
$19$	−6.46410	−1.48297	−0.741483	−	0.670971i	$-0.765877\pi$
$19$	−6.46410	−1.48297	−0.741483	+	0.670971i	$0.765877\pi$
$20$	1.00000	0.223607
$21$	−1.73205	−0.377964
$22$	0	0
$23$	8.19615	1.70902	0.854508	−	0.519438i	$-0.173859\pi$
$23$	8.19615	1.70902	0.854508	+	0.519438i	$0.173859\pi$
$24$	−1.00000	−0.204124
$25$	1.00000	0.200000
$26$	−6.46410	−1.26771
$27$	−1.00000	−0.192450
$28$	1.73205	0.327327
$29$	−6.46410	−1.20035	−0.600177	−	0.799867i	$-0.704903\pi$
$29$	−6.46410	−1.20035	−0.600177	+	0.799867i	$0.704903\pi$
$30$	−1.00000	−0.182574
$31$	−10.1962	−1.83128	−0.915642	−	0.401996i	$-0.868317\pi$
$31$	−10.1962	−1.83128	−0.915642	+	0.401996i	$0.868317\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	−4.26795	−0.731947
$35$	1.73205	0.292770
$36$	1.00000	0.166667
$37$	−7.19615	−1.18304	−0.591520	−	0.806290i	$-0.701472\pi$
$37$	−7.19615	−1.18304	−0.591520	+	0.806290i	$0.701472\pi$
$38$	−6.46410	−1.04862
$39$	6.46410	1.03508
$40$	1.00000	0.158114
$41$	5.66025	0.883983	0.441992	−	0.897019i	$-0.354272\pi$
$41$	5.66025	0.883983	0.441992	+	0.897019i	$0.354272\pi$
$42$	−1.73205	−0.267261
$43$	−4.73205	−0.721631	−0.360815	−	0.932637i	$-0.617502\pi$
$43$	−4.73205	−0.721631	−0.360815	+	0.932637i	$0.617502\pi$
$44$	0	0
$45$	1.00000	0.149071
$46$	8.19615	1.20846
$47$	−6.00000	−0.875190	−0.437595	−	0.899172i	$-0.644170\pi$
$47$	−6.00000	−0.875190	−0.437595	+	0.899172i	$0.644170\pi$
$48$	−1.00000	−0.144338
$49$	−4.00000	−0.571429
$50$	1.00000	0.141421
$51$	4.26795	0.597632
$52$	−6.46410	−0.896410
$53$	−2.19615	−0.301665	−0.150832	−	0.988559i	$-0.548195\pi$
$53$	−2.19615	−0.301665	−0.150832	+	0.988559i	$0.548195\pi$
$54$	−1.00000	−0.136083
$55$	0	0
$56$	1.73205	0.231455
$57$	6.46410	0.856191
$58$	−6.46410	−0.848778
$59$	2.19615	0.285915	0.142957	−	0.989729i	$-0.454339\pi$
$59$	2.19615	0.285915	0.142957	+	0.989729i	$0.454339\pi$
$60$	−1.00000	−0.129099
$61$	−1.26795	−0.162344	−0.0811721	−	0.996700i	$-0.525866\pi$
$61$	−1.26795	−0.162344	−0.0811721	+	0.996700i	$0.525866\pi$
$62$	−10.1962	−1.29491
$63$	1.73205	0.218218
$64$	1.00000	0.125000
$65$	−6.46410	−0.801773
$66$	0	0
$67$	14.3923	1.75830	0.879150	−	0.476545i	$-0.158111\pi$
$67$	14.3923	1.75830	0.879150	+	0.476545i	$0.158111\pi$
$68$	−4.26795	−0.517565
$69$	−8.19615	−0.986701
$70$	1.73205	0.207020
$71$	−7.39230	−0.877305	−0.438653	−	0.898657i	$-0.644544\pi$
$71$	−7.39230	−0.877305	−0.438653	+	0.898657i	$0.644544\pi$
$72$	1.00000	0.117851
$73$	−1.26795	−0.148402	−0.0742011	−	0.997243i	$-0.523641\pi$
$73$	−1.26795	−0.148402	−0.0742011	+	0.997243i	$0.523641\pi$
$74$	−7.19615	−0.836536
$75$	−1.00000	−0.115470
$76$	−6.46410	−0.741483
$77$	0	0
$78$	6.46410	0.731915
$79$	15.4641	1.73985	0.869924	−	0.493186i	$-0.164168\pi$
$79$	15.4641	1.73985	0.869924	+	0.493186i	$0.164168\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	5.66025	0.625070
$83$	−5.53590	−0.607644	−0.303822	−	0.952729i	$-0.598263\pi$
$83$	−5.53590	−0.607644	−0.303822	+	0.952729i	$0.598263\pi$
$84$	−1.73205	−0.188982
$85$	−4.26795	−0.462924
$86$	−4.73205	−0.510270
$87$	6.46410	0.693024
$88$	0	0
$89$	16.3923	1.73758	0.868790	−	0.495180i	$-0.164898\pi$
$89$	16.3923	1.73758	0.868790	+	0.495180i	$0.164898\pi$
$90$	1.00000	0.105409
$91$	−11.1962	−1.17368
$92$	8.19615	0.854508
$93$	10.1962	1.05729
$94$	−6.00000	−0.618853
$95$	−6.46410	−0.663203
$96$	−1.00000	−0.102062
$97$	10.1962	1.03526	0.517631	−	0.855604i	$-0.326814\pi$
$97$	10.1962	1.03526	0.517631	+	0.855604i	$0.326814\pi$
$98$	−4.00000	−0.404061
$99$	0	0
$100$	1.00000	0.100000
$101$	−10.8564	−1.08025	−0.540126	−	0.841584i	$-0.681624\pi$
$101$	−10.8564	−1.08025	−0.540126	+	0.841584i	$0.681624\pi$
$102$	4.26795	0.422590
$103$	−13.0000	−1.28093	−0.640464	−	0.767988i	$-0.721258\pi$
$103$	−13.0000	−1.28093	−0.640464	+	0.767988i	$0.721258\pi$
$104$	−6.46410	−0.633857
$105$	−1.73205	−0.169031
$106$	−2.19615	−0.213309
$107$	−8.53590	−0.825196	−0.412598	−	0.910913i	$-0.635379\pi$
$107$	−8.53590	−0.825196	−0.412598	+	0.910913i	$0.635379\pi$
$108$	−1.00000	−0.0962250
$109$	2.53590	0.242895	0.121448	−	0.992598i	$-0.461246\pi$
$109$	2.53590	0.242895	0.121448	+	0.992598i	$0.461246\pi$
$110$	0	0
$111$	7.19615	0.683029
$112$	1.73205	0.163663
$113$	0	0		−	1.00000i	$-0.5\pi$
$113$	0	0			1.00000i	$0.5\pi$
$114$	6.46410	0.605419
$115$	8.19615	0.764295
$116$	−6.46410	−0.600177
$117$	−6.46410	−0.597606
$118$	2.19615	0.202172
$119$	−7.39230	−0.677651
$120$	−1.00000	−0.0912871
$121$	0	0
$122$	−1.26795	−0.114795
$123$	−5.66025	−0.510368
$124$	−10.1962	−0.915642
$125$	1.00000	0.0894427
$126$	1.73205	0.154303
$127$	4.39230	0.389754	0.194877	−	0.980828i	$-0.437569\pi$
$127$	4.39230	0.389754	0.194877	+	0.980828i	$0.437569\pi$
$128$	1.00000	0.0883883
$129$	4.73205	0.416634
$130$	−6.46410	−0.566939
$131$	5.66025	0.494539	0.247269	−	0.968947i	$-0.420467\pi$
$131$	5.66025	0.494539	0.247269	+	0.968947i	$0.420467\pi$
$132$	0	0
$133$	−11.1962	−0.970830
$134$	14.3923	1.24331
$135$	−1.00000	−0.0860663
$136$	−4.26795	−0.365974
$137$	3.00000	0.256307	0.128154	−	0.991754i	$-0.459095\pi$
$137$	3.00000	0.256307	0.128154	+	0.991754i	$0.459095\pi$
$138$	−8.19615	−0.697703
$139$	12.4641	1.05719	0.528596	−	0.848874i	$-0.322719\pi$
$139$	12.4641	1.05719	0.528596	+	0.848874i	$0.322719\pi$
$140$	1.73205	0.146385
$141$	6.00000	0.505291
$142$	−7.39230	−0.620348
$143$	0	0
$144$	1.00000	0.0833333
$145$	−6.46410	−0.536814
$146$	−1.26795	−0.104936
$147$	4.00000	0.329914
$148$	−7.19615	−0.591520
$149$	9.46410	0.775329	0.387665	−	0.921800i	$-0.373282\pi$
$149$	9.46410	0.775329	0.387665	+	0.921800i	$0.373282\pi$
$150$	−1.00000	−0.0816497
$151$	−4.73205	−0.385089	−0.192544	−	0.981288i	$-0.561674\pi$
$151$	−4.73205	−0.385089	−0.192544	+	0.981288i	$0.561674\pi$
$152$	−6.46410	−0.524308
$153$	−4.26795	−0.345043
$154$	0	0
$155$	−10.1962	−0.818975
$156$	6.46410	0.517542
$157$	4.80385	0.383389	0.191694	−	0.981455i	$-0.438602\pi$
$157$	4.80385	0.383389	0.191694	+	0.981455i	$0.438602\pi$
$158$	15.4641	1.23026
$159$	2.19615	0.174166
$160$	1.00000	0.0790569
$161$	14.1962	1.11881
$162$	1.00000	0.0785674
$163$	−1.80385	−0.141288	−0.0706441	−	0.997502i	$-0.522505\pi$
$163$	−1.80385	−0.141288	−0.0706441	+	0.997502i	$0.522505\pi$
$164$	5.66025	0.441992
$165$	0	0
$166$	−5.53590	−0.429669
$167$	−2.53590	−0.196234	−0.0981169	−	0.995175i	$-0.531282\pi$
$167$	−2.53590	−0.196234	−0.0981169	+	0.995175i	$0.531282\pi$
$168$	−1.73205	−0.133631
$169$	28.7846	2.21420
$170$	−4.26795	−0.327337
$171$	−6.46410	−0.494322
$172$	−4.73205	−0.360815
$173$	−24.5885	−1.86943	−0.934713	−	0.355404i	$-0.884343\pi$
$173$	−24.5885	−1.86943	−0.934713	+	0.355404i	$0.884343\pi$
$174$	6.46410	0.490042
$175$	1.73205	0.130931
$176$	0	0
$177$	−2.19615	−0.165073
$178$	16.3923	1.22866
$179$	−2.19615	−0.164148	−0.0820741	−	0.996626i	$-0.526154\pi$
$179$	−2.19615	−0.164148	−0.0820741	+	0.996626i	$0.526154\pi$
$180$	1.00000	0.0745356
$181$	14.5885	1.08435	0.542176	−	0.840265i	$-0.317601\pi$
$181$	14.5885	1.08435	0.542176	+	0.840265i	$0.317601\pi$
$182$	−11.1962	−0.829914
$183$	1.26795	0.0937295
$184$	8.19615	0.604228
$185$	−7.19615	−0.529072
$186$	10.1962	0.747618
$187$	0	0
$188$	−6.00000	−0.437595
$189$	−1.73205	−0.125988
$190$	−6.46410	−0.468955
$191$	−15.0000	−1.08536	−0.542681	−	0.839939i	$-0.682591\pi$
$191$	−15.0000	−1.08536	−0.542681	+	0.839939i	$0.682591\pi$
$192$	−1.00000	−0.0721688
$193$	−2.53590	−0.182538	−0.0912690	−	0.995826i	$-0.529092\pi$
$193$	−2.53590	−0.182538	−0.0912690	+	0.995826i	$0.529092\pi$
$194$	10.1962	0.732041
$195$	6.46410	0.462904
$196$	−4.00000	−0.285714
$197$	−23.3205	−1.66152	−0.830759	−	0.556633i	$-0.812093\pi$
$197$	−23.3205	−1.66152	−0.830759	+	0.556633i	$0.812093\pi$
$198$	0	0
$199$	8.39230	0.594915	0.297457	−	0.954735i	$-0.403861\pi$
$199$	8.39230	0.594915	0.297457	+	0.954735i	$0.403861\pi$
$200$	1.00000	0.0707107
$201$	−14.3923	−1.01515
$202$	−10.8564	−0.763854
$203$	−11.1962	−0.785816
$204$	4.26795	0.298816
$205$	5.66025	0.395329
$206$	−13.0000	−0.905753
$207$	8.19615	0.569672
$208$	−6.46410	−0.448205
$209$	0	0
$210$	−1.73205	−0.119523
$211$	−10.8564	−0.747386	−0.373693	−	0.927552i	$-0.621909\pi$
$211$	−10.8564	−0.747386	−0.373693	+	0.927552i	$0.621909\pi$
$212$	−2.19615	−0.150832
$213$	7.39230	0.506512
$214$	−8.53590	−0.583502
$215$	−4.73205	−0.322723
$216$	−1.00000	−0.0680414
$217$	−17.6603	−1.19886
$218$	2.53590	0.171753
$219$	1.26795	0.0856801
$220$	0	0
$221$	27.5885	1.85580
$222$	7.19615	0.482974
$223$	−21.7846	−1.45881	−0.729403	−	0.684085i	$-0.760202\pi$
$223$	−21.7846	−1.45881	−0.729403	+	0.684085i	$0.760202\pi$
$224$	1.73205	0.115728
$225$	1.00000	0.0666667
$226$	0	0
$227$	−27.4641	−1.82286	−0.911428	−	0.411459i	$-0.865019\pi$
$227$	−27.4641	−1.82286	−0.911428	+	0.411459i	$0.865019\pi$
$228$	6.46410	0.428096
$229$	−28.7846	−1.90214	−0.951070	−	0.308975i	$-0.900014\pi$
$229$	−28.7846	−1.90214	−0.951070	+	0.308975i	$0.900014\pi$
$230$	8.19615	0.540438
$231$	0	0
$232$	−6.46410	−0.424389
$233$	1.85641	0.121617	0.0608086	−	0.998149i	$-0.480632\pi$
$233$	1.85641	0.121617	0.0608086	+	0.998149i	$0.480632\pi$
$234$	−6.46410	−0.422572
$235$	−6.00000	−0.391397
$236$	2.19615	0.142957
$237$	−15.4641	−1.00450
$238$	−7.39230	−0.479172
$239$	11.1962	0.724219	0.362109	−	0.932136i	$-0.382057\pi$
$239$	11.1962	0.724219	0.362109	+	0.932136i	$0.382057\pi$
$240$	−1.00000	−0.0645497
$241$	−12.8038	−0.824768	−0.412384	−	0.911010i	$-0.635304\pi$
$241$	−12.8038	−0.824768	−0.412384	+	0.911010i	$0.635304\pi$
$242$	0	0
$243$	−1.00000	−0.0641500
$244$	−1.26795	−0.0811721
$245$	−4.00000	−0.255551
$246$	−5.66025	−0.360885
$247$	41.7846	2.65869
$248$	−10.1962	−0.647456
$249$	5.53590	0.350823
$250$	1.00000	0.0632456
$251$	−16.3923	−1.03467	−0.517337	−	0.855782i	$-0.673076\pi$
$251$	−16.3923	−1.03467	−0.517337	+	0.855782i	$0.673076\pi$
$252$	1.73205	0.109109
$253$	0	0
$254$	4.39230	0.275598
$255$	4.26795	0.267269
$256$	1.00000	0.0625000
$257$	−7.39230	−0.461119	−0.230560	−	0.973058i	$-0.574056\pi$
$257$	−7.39230	−0.461119	−0.230560	+	0.973058i	$0.574056\pi$
$258$	4.73205	0.294605
$259$	−12.4641	−0.774482
$260$	−6.46410	−0.400887
$261$	−6.46410	−0.400118
$262$	5.66025	0.349692
$263$	−15.8038	−0.974507	−0.487253	−	0.873261i	$-0.662001\pi$
$263$	−15.8038	−0.974507	−0.487253	+	0.873261i	$0.662001\pi$
$264$	0	0
$265$	−2.19615	−0.134909
$266$	−11.1962	−0.686480
$267$	−16.3923	−1.00319
$268$	14.3923	0.879150
$269$	12.8038	0.780664	0.390332	−	0.920674i	$-0.372360\pi$
$269$	12.8038	0.780664	0.390332	+	0.920674i	$0.372360\pi$
$270$	−1.00000	−0.0608581
$271$	14.7846	0.898101	0.449051	−	0.893506i	$-0.351762\pi$
$271$	14.7846	0.898101	0.449051	+	0.893506i	$0.351762\pi$
$272$	−4.26795	−0.258782
$273$	11.1962	0.677622
$274$	3.00000	0.181237
$275$	0	0
$276$	−8.19615	−0.493350
$277$	18.9282	1.13729	0.568643	−	0.822585i	$-0.307469\pi$
$277$	18.9282	1.13729	0.568643	+	0.822585i	$0.307469\pi$
$278$	12.4641	0.747547
$279$	−10.1962	−0.610428
$280$	1.73205	0.103510
$281$	2.19615	0.131011	0.0655057	−	0.997852i	$-0.479134\pi$
$281$	2.19615	0.131011	0.0655057	+	0.997852i	$0.479134\pi$
$282$	6.00000	0.357295
$283$	−11.3205	−0.672934	−0.336467	−	0.941695i	$-0.609232\pi$
$283$	−11.3205	−0.672934	−0.336467	+	0.941695i	$0.609232\pi$
$284$	−7.39230	−0.438653
$285$	6.46410	0.382900
$286$	0	0
$287$	9.80385	0.578703
$288$	1.00000	0.0589256
$289$	1.21539	0.0714935
$290$	−6.46410	−0.379585
$291$	−10.1962	−0.597709
$292$	−1.26795	−0.0742011
$293$	−12.0000	−0.701047	−0.350524	−	0.936554i	$-0.613996\pi$
$293$	−12.0000	−0.701047	−0.350524	+	0.936554i	$0.613996\pi$
$294$	4.00000	0.233285
$295$	2.19615	0.127865
$296$	−7.19615	−0.418268
$297$	0	0
$298$	9.46410	0.548241
$299$	−52.9808	−3.06396
$300$	−1.00000	−0.0577350
$301$	−8.19615	−0.472418
$302$	−4.73205	−0.272299
$303$	10.8564	0.623684
$304$	−6.46410	−0.370742
$305$	−1.26795	−0.0726026
$306$	−4.26795	−0.243982
$307$	7.26795	0.414804	0.207402	−	0.978256i	$-0.433499\pi$
$307$	7.26795	0.414804	0.207402	+	0.978256i	$0.433499\pi$
$308$	0	0
$309$	13.0000	0.739544
$310$	−10.1962	−0.579103
$311$	8.78461	0.498130	0.249065	−	0.968487i	$-0.419877\pi$
$311$	8.78461	0.498130	0.249065	+	0.968487i	$0.419877\pi$
$312$	6.46410	0.365958
$313$	−18.9808	−1.07286	−0.536428	−	0.843946i	$-0.680227\pi$
$313$	−18.9808	−1.07286	−0.536428	+	0.843946i	$0.680227\pi$
$314$	4.80385	0.271097
$315$	1.73205	0.0975900
$316$	15.4641	0.869924
$317$	21.8038	1.22463	0.612313	−	0.790615i	$-0.290239\pi$
$317$	21.8038	1.22463	0.612313	+	0.790615i	$0.290239\pi$
$318$	2.19615	0.123154
$319$	0	0
$320$	1.00000	0.0559017
$321$	8.53590	0.476427
$322$	14.1962	0.791121
$323$	27.5885	1.53506
$324$	1.00000	0.0555556
$325$	−6.46410	−0.358564
$326$	−1.80385	−0.0999059
$327$	−2.53590	−0.140236
$328$	5.66025	0.312535
$329$	−10.3923	−0.572946
$330$	0	0
$331$	−9.19615	−0.505466	−0.252733	−	0.967536i	$-0.581329\pi$
$331$	−9.19615	−0.505466	−0.252733	+	0.967536i	$0.581329\pi$
$332$	−5.53590	−0.303822
$333$	−7.19615	−0.394347
$334$	−2.53590	−0.138758
$335$	14.3923	0.786336
$336$	−1.73205	−0.0944911
$337$	31.5167	1.71682	0.858411	−	0.512963i	$-0.171452\pi$
$337$	31.5167	1.71682	0.858411	+	0.512963i	$0.171452\pi$
$338$	28.7846	1.56568
$339$	0	0
$340$	−4.26795	−0.231462
$341$	0	0
$342$	−6.46410	−0.349539
$343$	−19.0526	−1.02874
$344$	−4.73205	−0.255135
$345$	−8.19615	−0.441266
$346$	−24.5885	−1.32188
$347$	20.3205	1.09086	0.545431	−	0.838156i	$-0.316366\pi$
$347$	20.3205	1.09086	0.545431	+	0.838156i	$0.316366\pi$
$348$	6.46410	0.346512
$349$	11.0718	0.592660	0.296330	−	0.955086i	$-0.404237\pi$
$349$	11.0718	0.592660	0.296330	+	0.955086i	$0.404237\pi$
$350$	1.73205	0.0925820
$351$	6.46410	0.345028
$352$	0	0
$353$	20.7846	1.10625	0.553127	−	0.833097i	$-0.313435\pi$
$353$	20.7846	1.10625	0.553127	+	0.833097i	$0.313435\pi$
$354$	−2.19615	−0.116724
$355$	−7.39230	−0.392343
$356$	16.3923	0.868790
$357$	7.39230	0.391242
$358$	−2.19615	−0.116070
$359$	−3.46410	−0.182828	−0.0914141	−	0.995813i	$-0.529139\pi$
$359$	−3.46410	−0.182828	−0.0914141	+	0.995813i	$0.529139\pi$
$360$	1.00000	0.0527046
$361$	22.7846	1.19919
$362$	14.5885	0.766752
$363$	0	0
$364$	−11.1962	−0.586838
$365$	−1.26795	−0.0663675
$366$	1.26795	0.0662768
$367$	6.60770	0.344919	0.172459	−	0.985017i	$-0.444829\pi$
$367$	6.60770	0.344919	0.172459	+	0.985017i	$0.444829\pi$
$368$	8.19615	0.427254
$369$	5.66025	0.294661
$370$	−7.19615	−0.374110
$371$	−3.80385	−0.197486
$372$	10.1962	0.528646
$373$	−0.464102	−0.0240303	−0.0120151	−	0.999928i	$-0.503825\pi$
$373$	−0.464102	−0.0240303	−0.0120151	+	0.999928i	$0.503825\pi$
$374$	0	0
$375$	−1.00000	−0.0516398
$376$	−6.00000	−0.309426
$377$	41.7846	2.15202
$378$	−1.73205	−0.0890871
$379$	4.41154	0.226606	0.113303	−	0.993560i	$-0.463857\pi$
$379$	4.41154	0.226606	0.113303	+	0.993560i	$0.463857\pi$
$380$	−6.46410	−0.331601
$381$	−4.39230	−0.225025
$382$	−15.0000	−0.767467
$383$	−6.00000	−0.306586	−0.153293	−	0.988181i	$-0.548988\pi$
$383$	−6.00000	−0.306586	−0.153293	+	0.988181i	$0.548988\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	−2.53590	−0.129074
$387$	−4.73205	−0.240544
$388$	10.1962	0.517631
$389$	32.7846	1.66225	0.831123	−	0.556089i	$-0.187699\pi$
$389$	32.7846	1.66225	0.831123	+	0.556089i	$0.187699\pi$
$390$	6.46410	0.327323
$391$	−34.9808	−1.76905
$392$	−4.00000	−0.202031
$393$	−5.66025	−0.285522
$394$	−23.3205	−1.17487
$395$	15.4641	0.778083
$396$	0	0
$397$	−15.1962	−0.762673	−0.381337	−	0.924436i	$-0.624536\pi$
$397$	−15.1962	−0.762673	−0.381337	+	0.924436i	$0.624536\pi$
$398$	8.39230	0.420668
$399$	11.1962	0.560509
$400$	1.00000	0.0500000
$401$	5.41154	0.270240	0.135120	−	0.990829i	$-0.456858\pi$
$401$	5.41154	0.270240	0.135120	+	0.990829i	$0.456858\pi$
$402$	−14.3923	−0.717823
$403$	65.9090	3.28316
$404$	−10.8564	−0.540126
$405$	1.00000	0.0496904
$406$	−11.1962	−0.555656
$407$	0	0
$408$	4.26795	0.211295
$409$	31.8564	1.57520	0.787599	−	0.616188i	$-0.211324\pi$
$409$	31.8564	1.57520	0.787599	+	0.616188i	$0.211324\pi$
$410$	5.66025	0.279540
$411$	−3.00000	−0.147979
$412$	−13.0000	−0.640464
$413$	3.80385	0.187175
$414$	8.19615	0.402819
$415$	−5.53590	−0.271747
$416$	−6.46410	−0.316929
$417$	−12.4641	−0.610370
$418$	0	0
$419$	−10.3923	−0.507697	−0.253849	−	0.967244i	$-0.581697\pi$
$419$	−10.3923	−0.507697	−0.253849	+	0.967244i	$0.581697\pi$
$420$	−1.73205	−0.0845154
$421$	24.1962	1.17925	0.589624	−	0.807678i	$-0.299276\pi$
$421$	24.1962	1.17925	0.589624	+	0.807678i	$0.299276\pi$
$422$	−10.8564	−0.528482
$423$	−6.00000	−0.291730
$424$	−2.19615	−0.106655
$425$	−4.26795	−0.207026
$426$	7.39230	0.358158
$427$	−2.19615	−0.106279
$428$	−8.53590	−0.412598
$429$	0	0
$430$	−4.73205	−0.228200
$431$	−24.1244	−1.16203	−0.581015	−	0.813893i	$-0.697344\pi$
$431$	−24.1244	−1.16203	−0.581015	+	0.813893i	$0.697344\pi$
$432$	−1.00000	−0.0481125
$433$	32.0000	1.53782	0.768911	−	0.639356i	$-0.220799\pi$
$433$	32.0000	1.53782	0.768911	+	0.639356i	$0.220799\pi$
$434$	−17.6603	−0.847719
$435$	6.46410	0.309930
$436$	2.53590	0.121448
$437$	−52.9808	−2.53441
$438$	1.26795	0.0605850
$439$	−18.0000	−0.859093	−0.429547	−	0.903045i	$-0.641327\pi$
$439$	−18.0000	−0.859093	−0.429547	+	0.903045i	$0.641327\pi$
$440$	0	0
$441$	−4.00000	−0.190476
$442$	27.5885	1.31225
$443$	15.5885	0.740630	0.370315	−	0.928906i	$-0.379250\pi$
$443$	15.5885	0.740630	0.370315	+	0.928906i	$0.379250\pi$
$444$	7.19615	0.341514
$445$	16.3923	0.777070
$446$	−21.7846	−1.03153
$447$	−9.46410	−0.447637
$448$	1.73205	0.0818317
$449$	1.60770	0.0758718	0.0379359	−	0.999280i	$-0.487922\pi$
$449$	1.60770	0.0758718	0.0379359	+	0.999280i	$0.487922\pi$
$450$	1.00000	0.0471405
$451$	0	0
$452$	0	0
$453$	4.73205	0.222331
$454$	−27.4641	−1.28895
$455$	−11.1962	−0.524884
$456$	6.46410	0.302709
$457$	−9.12436	−0.426819	−0.213410	−	0.976963i	$-0.568457\pi$
$457$	−9.12436	−0.426819	−0.213410	+	0.976963i	$0.568457\pi$
$458$	−28.7846	−1.34502
$459$	4.26795	0.199211
$460$	8.19615	0.382148
$461$	40.8564	1.90287	0.951436	−	0.307846i	$-0.0996081\pi$
$461$	40.8564	1.90287	0.951436	+	0.307846i	$0.0996081\pi$
$462$	0	0
$463$	−14.3923	−0.668867	−0.334434	−	0.942419i	$-0.608545\pi$
$463$	−14.3923	−0.668867	−0.334434	+	0.942419i	$0.608545\pi$
$464$	−6.46410	−0.300088
$465$	10.1962	0.472835
$466$	1.85641	0.0859964
$467$	−2.41154	−0.111593	−0.0557964	−	0.998442i	$-0.517770\pi$
$467$	−2.41154	−0.111593	−0.0557964	+	0.998442i	$0.517770\pi$
$468$	−6.46410	−0.298803
$469$	24.9282	1.15108
$470$	−6.00000	−0.276759
$471$	−4.80385	−0.221350
$472$	2.19615	0.101086
$473$	0	0
$474$	−15.4641	−0.710290
$475$	−6.46410	−0.296593
$476$	−7.39230	−0.338826
$477$	−2.19615	−0.100555
$478$	11.1962	0.512100
$479$	15.3397	0.700891	0.350445	−	0.936583i	$-0.386030\pi$
$479$	15.3397	0.700891	0.350445	+	0.936583i	$0.386030\pi$
$480$	−1.00000	−0.0456435
$481$	46.5167	2.12098
$482$	−12.8038	−0.583199
$483$	−14.1962	−0.645947
$484$	0	0
$485$	10.1962	0.462983
$486$	−1.00000	−0.0453609
$487$	3.78461	0.171497	0.0857485	−	0.996317i	$-0.472672\pi$
$487$	3.78461	0.171497	0.0857485	+	0.996317i	$0.472672\pi$
$488$	−1.26795	−0.0573974
$489$	1.80385	0.0815728
$490$	−4.00000	−0.180702
$491$	−28.7321	−1.29666	−0.648330	−	0.761360i	$-0.724532\pi$
$491$	−28.7321	−1.29666	−0.648330	+	0.761360i	$0.724532\pi$
$492$	−5.66025	−0.255184
$493$	27.5885	1.24252
$494$	41.7846	1.87998
$495$	0	0
$496$	−10.1962	−0.457821
$497$	−12.8038	−0.574331
$498$	5.53590	0.248070
$499$	−13.1962	−0.590741	−0.295370	−	0.955383i	$-0.595443\pi$
$499$	−13.1962	−0.590741	−0.295370	+	0.955383i	$0.595443\pi$
$500$	1.00000	0.0447214
$501$	2.53590	0.113296
$502$	−16.3923	−0.731624
$503$	28.0526	1.25080	0.625401	−	0.780304i	$-0.284935\pi$
$503$	28.0526	1.25080	0.625401	+	0.780304i	$0.284935\pi$
$504$	1.73205	0.0771517
$505$	−10.8564	−0.483104
$506$	0	0
$507$	−28.7846	−1.27837
$508$	4.39230	0.194877
$509$	26.7846	1.18721	0.593603	−	0.804758i	$-0.297705\pi$
$509$	26.7846	1.18721	0.593603	+	0.804758i	$0.297705\pi$
$510$	4.26795	0.188988
$511$	−2.19615	−0.0971521
$512$	1.00000	0.0441942
$513$	6.46410	0.285397
$514$	−7.39230	−0.326061
$515$	−13.0000	−0.572848
$516$	4.73205	0.208317
$517$	0	0
$518$	−12.4641	−0.547641
$519$	24.5885	1.07931
$520$	−6.46410	−0.283470
$521$	3.80385	0.166650	0.0833248	−	0.996522i	$-0.473446\pi$
$521$	3.80385	0.166650	0.0833248	+	0.996522i	$0.473446\pi$
$522$	−6.46410	−0.282926
$523$	27.1244	1.18607	0.593033	−	0.805178i	$-0.297931\pi$
$523$	27.1244	1.18607	0.593033	+	0.805178i	$0.297931\pi$
$524$	5.66025	0.247269
$525$	−1.73205	−0.0755929
$526$	−15.8038	−0.689081
$527$	43.5167	1.89562
$528$	0	0
$529$	44.1769	1.92074
$530$	−2.19615	−0.0953948
$531$	2.19615	0.0953049
$532$	−11.1962	−0.485415
$533$	−36.5885	−1.58482
$534$	−16.3923	−0.709364
$535$	−8.53590	−0.369039
$536$	14.3923	0.621653
$537$	2.19615	0.0947710
$538$	12.8038	0.552013
$539$	0	0
$540$	−1.00000	−0.0430331
$541$	−7.26795	−0.312474	−0.156237	−	0.987720i	$-0.549936\pi$
$541$	−7.26795	−0.312474	−0.156237	+	0.987720i	$0.549936\pi$
$542$	14.7846	0.635053
$543$	−14.5885	−0.626051
$544$	−4.26795	−0.182987
$545$	2.53590	0.108626
$546$	11.1962	0.479151
$547$	−26.7846	−1.14523	−0.572614	−	0.819825i	$-0.694070\pi$
$547$	−26.7846	−1.14523	−0.572614	+	0.819825i	$0.694070\pi$
$548$	3.00000	0.128154
$549$	−1.26795	−0.0541148
$550$	0	0
$551$	41.7846	1.78008
$552$	−8.19615	−0.348851
$553$	26.7846	1.13900
$554$	18.9282	0.804182
$555$	7.19615	0.305460
$556$	12.4641	0.528596
$557$	−32.5359	−1.37859	−0.689295	−	0.724481i	$-0.742080\pi$
$557$	−32.5359	−1.37859	−0.689295	+	0.724481i	$0.742080\pi$
$558$	−10.1962	−0.431638
$559$	30.5885	1.29375
$560$	1.73205	0.0731925
$561$	0	0
$562$	2.19615	0.0926391
$563$	−14.3205	−0.603537	−0.301769	−	0.953381i	$-0.597577\pi$
$563$	−14.3205	−0.603537	−0.301769	+	0.953381i	$0.597577\pi$
$564$	6.00000	0.252646
$565$	0	0
$566$	−11.3205	−0.475836
$567$	1.73205	0.0727393
$568$	−7.39230	−0.310174
$569$	20.1962	0.846667	0.423333	−	0.905974i	$-0.360860\pi$
$569$	20.1962	0.846667	0.423333	+	0.905974i	$0.360860\pi$
$570$	6.46410	0.270751
$571$	3.46410	0.144968	0.0724841	−	0.997370i	$-0.476907\pi$
$571$	3.46410	0.144968	0.0724841	+	0.997370i	$0.476907\pi$
$572$	0	0
$573$	15.0000	0.626634
$574$	9.80385	0.409205
$575$	8.19615	0.341803
$576$	1.00000	0.0416667
$577$	−9.60770	−0.399974	−0.199987	−	0.979799i	$-0.564090\pi$
$577$	−9.60770	−0.399974	−0.199987	+	0.979799i	$0.564090\pi$
$578$	1.21539	0.0505536
$579$	2.53590	0.105388
$580$	−6.46410	−0.268407
$581$	−9.58846	−0.397796
$582$	−10.1962	−0.422644
$583$	0	0
$584$	−1.26795	−0.0524681
$585$	−6.46410	−0.267258
$586$	−12.0000	−0.495715
$587$	−21.5885	−0.891051	−0.445525	−	0.895269i	$-0.646983\pi$
$587$	−21.5885	−0.891051	−0.445525	+	0.895269i	$0.646983\pi$
$588$	4.00000	0.164957
$589$	65.9090	2.71573
$590$	2.19615	0.0904142
$591$	23.3205	0.959278
$592$	−7.19615	−0.295760
$593$	6.00000	0.246390	0.123195	−	0.992382i	$-0.460686\pi$
$593$	6.00000	0.246390	0.123195	+	0.992382i	$0.460686\pi$
$594$	0	0
$595$	−7.39230	−0.303055
$596$	9.46410	0.387665
$597$	−8.39230	−0.343474
$598$	−52.9808	−2.16654
$599$	−31.1769	−1.27385	−0.636927	−	0.770924i	$-0.719795\pi$
$599$	−31.1769	−1.27385	−0.636927	+	0.770924i	$0.719795\pi$
$600$	−1.00000	−0.0408248
$601$	−26.7846	−1.09257	−0.546284	−	0.837600i	$-0.683958\pi$
$601$	−26.7846	−1.09257	−0.546284	+	0.837600i	$0.683958\pi$
$602$	−8.19615	−0.334050
$603$	14.3923	0.586100
$604$	−4.73205	−0.192544
$605$	0	0
$606$	10.8564	0.441011
$607$	−11.4449	−0.464533	−0.232266	−	0.972652i	$-0.574614\pi$
$607$	−11.4449	−0.464533	−0.232266	+	0.972652i	$0.574614\pi$
$608$	−6.46410	−0.262154
$609$	11.1962	0.453691
$610$	−1.26795	−0.0513378
$611$	38.7846	1.56906
$612$	−4.26795	−0.172522
$613$	3.67949	0.148613	0.0743066	−	0.997235i	$-0.476326\pi$
$613$	3.67949	0.148613	0.0743066	+	0.997235i	$0.476326\pi$
$614$	7.26795	0.293311
$615$	−5.66025	−0.228243
$616$	0	0
$617$	−44.5692	−1.79429	−0.897145	−	0.441737i	$-0.854362\pi$
$617$	−44.5692	−1.79429	−0.897145	+	0.441737i	$0.854362\pi$
$618$	13.0000	0.522937
$619$	19.1962	0.771559	0.385779	−	0.922591i	$-0.373933\pi$
$619$	19.1962	0.771559	0.385779	+	0.922591i	$0.373933\pi$
$620$	−10.1962	−0.409487
$621$	−8.19615	−0.328900
$622$	8.78461	0.352231
$623$	28.3923	1.13751
$624$	6.46410	0.258771
$625$	1.00000	0.0400000
$626$	−18.9808	−0.758624
$627$	0	0
$628$	4.80385	0.191694
$629$	30.7128	1.22460
$630$	1.73205	0.0690066
$631$	20.9808	0.835231	0.417615	−	0.908624i	$-0.362866\pi$
$631$	20.9808	0.835231	0.417615	+	0.908624i	$0.362866\pi$
$632$	15.4641	0.615129
$633$	10.8564	0.431503
$634$	21.8038	0.865941
$635$	4.39230	0.174303
$636$	2.19615	0.0870831
$637$	25.8564	1.02447
$638$	0	0
$639$	−7.39230	−0.292435
$640$	1.00000	0.0395285
$641$	6.00000	0.236986	0.118493	−	0.992955i	$-0.462194\pi$
$641$	6.00000	0.236986	0.118493	+	0.992955i	$0.462194\pi$
$642$	8.53590	0.336885
$643$	−4.00000	−0.157745	−0.0788723	−	0.996885i	$-0.525132\pi$
$643$	−4.00000	−0.157745	−0.0788723	+	0.996885i	$0.525132\pi$
$644$	14.1962	0.559407
$645$	4.73205	0.186324
$646$	27.5885	1.08545
$647$	19.6077	0.770858	0.385429	−	0.922737i	$-0.374053\pi$
$647$	19.6077	0.770858	0.385429	+	0.922737i	$0.374053\pi$
$648$	1.00000	0.0392837
$649$	0	0
$650$	−6.46410	−0.253543
$651$	17.6603	0.692160
$652$	−1.80385	−0.0706441
$653$	−44.1962	−1.72953	−0.864765	−	0.502178i	$-0.832532\pi$
$653$	−44.1962	−1.72953	−0.864765	+	0.502178i	$0.832532\pi$
$654$	−2.53590	−0.0991615
$655$	5.66025	0.221164
$656$	5.66025	0.220996
$657$	−1.26795	−0.0494674
$658$	−10.3923	−0.405134
$659$	−43.1769	−1.68193	−0.840967	−	0.541087i	$-0.818013\pi$
$659$	−43.1769	−1.68193	−0.840967	+	0.541087i	$0.818013\pi$
$660$	0	0
$661$	−41.3731	−1.60923	−0.804613	−	0.593800i	$-0.797627\pi$
$661$	−41.3731	−1.60923	−0.804613	+	0.593800i	$0.797627\pi$
$662$	−9.19615	−0.357419
$663$	−27.5885	−1.07145
$664$	−5.53590	−0.214835
$665$	−11.1962	−0.434168
$666$	−7.19615	−0.278845
$667$	−52.9808	−2.05142
$668$	−2.53590	−0.0981169
$669$	21.7846	0.842242
$670$	14.3923	0.556023
$671$	0	0
$672$	−1.73205	−0.0668153
$673$	−5.07180	−0.195503	−0.0977517	−	0.995211i	$-0.531165\pi$
$673$	−5.07180	−0.195503	−0.0977517	+	0.995211i	$0.531165\pi$
$674$	31.5167	1.21398
$675$	−1.00000	−0.0384900
$676$	28.7846	1.10710
$677$	10.9808	0.422025	0.211012	−	0.977483i	$-0.432324\pi$
$677$	10.9808	0.422025	0.211012	+	0.977483i	$0.432324\pi$
$678$	0	0
$679$	17.6603	0.677738
$680$	−4.26795	−0.163668
$681$	27.4641	1.05243
$682$	0	0
$683$	−24.8038	−0.949093	−0.474546	−	0.880230i	$-0.657388\pi$
$683$	−24.8038	−0.949093	−0.474546	+	0.880230i	$0.657388\pi$
$684$	−6.46410	−0.247161
$685$	3.00000	0.114624
$686$	−19.0526	−0.727430
$687$	28.7846	1.09820
$688$	−4.73205	−0.180408
$689$	14.1962	0.540830
$690$	−8.19615	−0.312022
$691$	−0.411543	−0.0156558	−0.00782791	−	0.999969i	$-0.502492\pi$
$691$	−0.411543	−0.0156558	−0.00782791	+	0.999969i	$0.502492\pi$
$692$	−24.5885	−0.934713
$693$	0	0
$694$	20.3205	0.771356
$695$	12.4641	0.472790
$696$	6.46410	0.245021
$697$	−24.1577	−0.915037
$698$	11.0718	0.419074
$699$	−1.85641	−0.0702157
$700$	1.73205	0.0654654
$701$	−24.7128	−0.933390	−0.466695	−	0.884418i	$-0.654555\pi$
$701$	−24.7128	−0.933390	−0.466695	+	0.884418i	$0.654555\pi$
$702$	6.46410	0.243972
$703$	46.5167	1.75441
$704$	0	0
$705$	6.00000	0.225973
$706$	20.7846	0.782239
$707$	−18.8038	−0.707191
$708$	−2.19615	−0.0825365
$709$	−8.58846	−0.322546	−0.161273	−	0.986910i	$-0.551560\pi$
$709$	−8.58846	−0.322546	−0.161273	+	0.986910i	$0.551560\pi$
$710$	−7.39230	−0.277428
$711$	15.4641	0.579949
$712$	16.3923	0.614328
$713$	−83.5692	−3.12969
$714$	7.39230	0.276650
$715$	0	0
$716$	−2.19615	−0.0820741
$717$	−11.1962	−0.418128
$718$	−3.46410	−0.129279
$719$	43.1769	1.61023	0.805114	−	0.593121i	$-0.202104\pi$
$719$	43.1769	1.61023	0.805114	+	0.593121i	$0.202104\pi$
$720$	1.00000	0.0372678
$721$	−22.5167	−0.838564
$722$	22.7846	0.847955
$723$	12.8038	0.476180
$724$	14.5885	0.542176
$725$	−6.46410	−0.240071
$726$	0	0
$727$	−36.1769	−1.34173	−0.670864	−	0.741581i	$-0.734076\pi$
$727$	−36.1769	−1.34173	−0.670864	+	0.741581i	$0.734076\pi$
$728$	−11.1962	−0.414957
$729$	1.00000	0.0370370
$730$	−1.26795	−0.0469289
$731$	20.1962	0.746982
$732$	1.26795	0.0468648
$733$	30.9282	1.14236	0.571180	−	0.820825i	$-0.306486\pi$
$733$	30.9282	1.14236	0.571180	+	0.820825i	$0.306486\pi$
$734$	6.60770	0.243894
$735$	4.00000	0.147542
$736$	8.19615	0.302114
$737$	0	0
$738$	5.66025	0.208357
$739$	−0.464102	−0.0170723	−0.00853613	−	0.999964i	$-0.502717\pi$
$739$	−0.464102	−0.0170723	−0.00853613	+	0.999964i	$0.502717\pi$
$740$	−7.19615	−0.264536
$741$	−41.7846	−1.53500
$742$	−3.80385	−0.139644
$743$	−27.3731	−1.00422	−0.502110	−	0.864804i	$-0.667443\pi$
$743$	−27.3731	−1.00422	−0.502110	+	0.864804i	$0.667443\pi$
$744$	10.1962	0.373809
$745$	9.46410	0.346738
$746$	−0.464102	−0.0169920
$747$	−5.53590	−0.202548
$748$	0	0
$749$	−14.7846	−0.540218
$750$	−1.00000	−0.0365148
$751$	−38.5885	−1.40811	−0.704056	−	0.710144i	$-0.748630\pi$
$751$	−38.5885	−1.40811	−0.704056	+	0.710144i	$0.748630\pi$
$752$	−6.00000	−0.218797
$753$	16.3923	0.597369
$754$	41.7846	1.52171
$755$	−4.73205	−0.172217
$756$	−1.73205	−0.0629941
$757$	35.1769	1.27853	0.639263	−	0.768988i	$-0.279239\pi$
$757$	35.1769	1.27853	0.639263	+	0.768988i	$0.279239\pi$
$758$	4.41154	0.160234
$759$	0	0
$760$	−6.46410	−0.234478
$761$	−9.46410	−0.343073	−0.171537	−	0.985178i	$-0.554873\pi$
$761$	−9.46410	−0.343073	−0.171537	+	0.985178i	$0.554873\pi$
$762$	−4.39230	−0.159116
$763$	4.39230	0.159012
$764$	−15.0000	−0.542681
$765$	−4.26795	−0.154308
$766$	−6.00000	−0.216789
$767$	−14.1962	−0.512593
$768$	−1.00000	−0.0360844
$769$	−1.98076	−0.0714281	−0.0357141	−	0.999362i	$-0.511371\pi$
$769$	−1.98076	−0.0714281	−0.0357141	+	0.999362i	$0.511371\pi$
$770$	0	0
$771$	7.39230	0.266227
$772$	−2.53590	−0.0912690
$773$	−17.4115	−0.626250	−0.313125	−	0.949712i	$-0.601376\pi$
$773$	−17.4115	−0.626250	−0.313125	+	0.949712i	$0.601376\pi$
$774$	−4.73205	−0.170090
$775$	−10.1962	−0.366257
$776$	10.1962	0.366021
$777$	12.4641	0.447147
$778$	32.7846	1.17539
$779$	−36.5885	−1.31092
$780$	6.46410	0.231452
$781$	0	0
$782$	−34.9808	−1.25091
$783$	6.46410	0.231008
$784$	−4.00000	−0.142857
$785$	4.80385	0.171457
$786$	−5.66025	−0.201895
$787$	−35.9090	−1.28002	−0.640008	−	0.768368i	$-0.721069\pi$
$787$	−35.9090	−1.28002	−0.640008	+	0.768368i	$0.721069\pi$
$788$	−23.3205	−0.830759
$789$	15.8038	0.562632
$790$	15.4641	0.550188
$791$	0	0
$792$	0	0
$793$	8.19615	0.291054
$794$	−15.1962	−0.539291
$795$	2.19615	0.0778895
$796$	8.39230	0.297457
$797$	55.7654	1.97531	0.987655	−	0.156642i	$-0.0500670\pi$
$797$	55.7654	1.97531	0.987655	+	0.156642i	$0.0500670\pi$
$798$	11.1962	0.396339
$799$	25.6077	0.905935
$800$	1.00000	0.0353553
$801$	16.3923	0.579194
$802$	5.41154	0.191088
$803$	0	0
$804$	−14.3923	−0.507577
$805$	14.1962	0.500349
$806$	65.9090	2.32154
$807$	−12.8038	−0.450717
$808$	−10.8564	−0.381927
$809$	38.4449	1.35165	0.675825	−	0.737062i	$-0.263788\pi$
$809$	38.4449	1.35165	0.675825	+	0.737062i	$0.263788\pi$
$810$	1.00000	0.0351364
$811$	14.0718	0.494128	0.247064	−	0.968999i	$-0.420534\pi$
$811$	14.0718	0.494128	0.247064	+	0.968999i	$0.420534\pi$
$812$	−11.1962	−0.392908
$813$	−14.7846	−0.518519
$814$	0	0
$815$	−1.80385	−0.0631860
$816$	4.26795	0.149408
$817$	30.5885	1.07015
$818$	31.8564	1.11383
$819$	−11.1962	−0.391225
$820$	5.66025	0.197665
$821$	−4.39230	−0.153292	−0.0766462	−	0.997058i	$-0.524421\pi$
$821$	−4.39230	−0.153292	−0.0766462	+	0.997058i	$0.524421\pi$
$822$	−3.00000	−0.104637
$823$	23.0000	0.801730	0.400865	−	0.916137i	$-0.368710\pi$
$823$	23.0000	0.801730	0.400865	+	0.916137i	$0.368710\pi$
$824$	−13.0000	−0.452876
$825$	0	0
$826$	3.80385	0.132353
$827$	17.7846	0.618431	0.309216	−	0.950992i	$-0.399933\pi$
$827$	17.7846	0.618431	0.309216	+	0.950992i	$0.399933\pi$
$828$	8.19615	0.284836
$829$	13.4115	0.465802	0.232901	−	0.972500i	$-0.425178\pi$
$829$	13.4115	0.465802	0.232901	+	0.972500i	$0.425178\pi$
$830$	−5.53590	−0.192154
$831$	−18.9282	−0.656612
$832$	−6.46410	−0.224102
$833$	17.0718	0.591503
$834$	−12.4641	−0.431597
$835$	−2.53590	−0.0877584
$836$	0	0
$837$	10.1962	0.352431
$838$	−10.3923	−0.358996
$839$	13.3923	0.462354	0.231177	−	0.972912i	$-0.425742\pi$
$839$	13.3923	0.462354	0.231177	+	0.972912i	$0.425742\pi$
$840$	−1.73205	−0.0597614
$841$	12.7846	0.440849
$842$	24.1962	0.833854
$843$	−2.19615	−0.0756395
$844$	−10.8564	−0.373693
$845$	28.7846	0.990221
$846$	−6.00000	−0.206284
$847$	0	0
$848$	−2.19615	−0.0754162
$849$	11.3205	0.388519
$850$	−4.26795	−0.146389
$851$	−58.9808	−2.02183
$852$	7.39230	0.253256
$853$	27.9282	0.956243	0.478122	−	0.878294i	$-0.341318\pi$
$853$	27.9282	0.956243	0.478122	+	0.878294i	$0.341318\pi$
$854$	−2.19615	−0.0751508
$855$	−6.46410	−0.221068
$856$	−8.53590	−0.291751
$857$	−25.9808	−0.887486	−0.443743	−	0.896154i	$-0.646350\pi$
$857$	−25.9808	−0.887486	−0.443743	+	0.896154i	$0.646350\pi$
$858$	0	0
$859$	51.1769	1.74613	0.873067	−	0.487600i	$-0.162128\pi$
$859$	51.1769	1.74613	0.873067	+	0.487600i	$0.162128\pi$
$860$	−4.73205	−0.161362
$861$	−9.80385	−0.334114
$862$	−24.1244	−0.821679
$863$	−55.1769	−1.87824	−0.939122	−	0.343584i	$-0.888359\pi$
$863$	−55.1769	−1.87824	−0.939122	+	0.343584i	$0.888359\pi$
$864$	−1.00000	−0.0340207
$865$	−24.5885	−0.836033
$866$	32.0000	1.08740
$867$	−1.21539	−0.0412768
$868$	−17.6603	−0.599428
$869$	0	0
$870$	6.46410	0.219154
$871$	−93.0333	−3.15231
$872$	2.53590	0.0858764
$873$	10.1962	0.345087
$874$	−52.9808	−1.79210
$875$	1.73205	0.0585540
$876$	1.26795	0.0428400
$877$	−16.6077	−0.560802	−0.280401	−	0.959883i	$-0.590467\pi$
$877$	−16.6077	−0.560802	−0.280401	+	0.959883i	$0.590467\pi$
$878$	−18.0000	−0.607471
$879$	12.0000	0.404750
$880$	0	0
$881$	−18.5885	−0.626261	−0.313131	−	0.949710i	$-0.601378\pi$
$881$	−18.5885	−0.626261	−0.313131	+	0.949710i	$0.601378\pi$
$882$	−4.00000	−0.134687
$883$	40.5885	1.36591	0.682955	−	0.730460i	$-0.260694\pi$
$883$	40.5885	1.36591	0.682955	+	0.730460i	$0.260694\pi$
$884$	27.5885	0.927900
$885$	−2.19615	−0.0738229
$886$	15.5885	0.523704
$887$	−6.92820	−0.232626	−0.116313	−	0.993213i	$-0.537108\pi$
$887$	−6.92820	−0.232626	−0.116313	+	0.993213i	$0.537108\pi$
$888$	7.19615	0.241487
$889$	7.60770	0.255154
$890$	16.3923	0.549471
$891$	0	0
$892$	−21.7846	−0.729403
$893$	38.7846	1.29788
$894$	−9.46410	−0.316527
$895$	−2.19615	−0.0734093
$896$	1.73205	0.0578638
$897$	52.9808	1.76898
$898$	1.60770	0.0536495
$899$	65.9090	2.19819
$900$	1.00000	0.0333333
$901$	9.37307	0.312262
$902$	0	0
$903$	8.19615	0.272751
$904$	0	0
$905$	14.5885	0.484937
$906$	4.73205	0.157212
$907$	2.00000	0.0664089	0.0332045	−	0.999449i	$-0.489429\pi$
$907$	2.00000	0.0664089	0.0332045	+	0.999449i	$0.489429\pi$
$908$	−27.4641	−0.911428
$909$	−10.8564	−0.360084
$910$	−11.1962	−0.371149
$911$	19.3923	0.642496	0.321248	−	0.946995i	$-0.395898\pi$
$911$	19.3923	0.642496	0.321248	+	0.946995i	$0.395898\pi$
$912$	6.46410	0.214048
$913$	0	0
$914$	−9.12436	−0.301807
$915$	1.26795	0.0419171
$916$	−28.7846	−0.951070
$917$	9.80385	0.323752
$918$	4.26795	0.140863
$919$	−55.7654	−1.83953	−0.919765	−	0.392470i	$-0.871621\pi$
$919$	−55.7654	−1.83953	−0.919765	+	0.392470i	$0.871621\pi$
$920$	8.19615	0.270219
$921$	−7.26795	−0.239487
$922$	40.8564	1.34553
$923$	47.7846	1.57285
$924$	0	0
$925$	−7.19615	−0.236608
$926$	−14.3923	−0.472960
$927$	−13.0000	−0.426976
$928$	−6.46410	−0.212195
$929$	−4.98076	−0.163414	−0.0817068	−	0.996656i	$-0.526037\pi$
$929$	−4.98076	−0.163414	−0.0817068	+	0.996656i	$0.526037\pi$
$930$	10.1962	0.334345
$931$	25.8564	0.847409
$932$	1.85641	0.0608086
$933$	−8.78461	−0.287595
$934$	−2.41154	−0.0789081
$935$	0	0
$936$	−6.46410	−0.211286
$937$	52.6410	1.71971	0.859854	−	0.510541i	$-0.170555\pi$
$937$	52.6410	1.71971	0.859854	+	0.510541i	$0.170555\pi$
$938$	24.9282	0.813935
$939$	18.9808	0.619414
$940$	−6.00000	−0.195698
$941$	60.0333	1.95703	0.978515	−	0.206175i	$-0.0661016\pi$
$941$	60.0333	1.95703	0.978515	+	0.206175i	$0.0661016\pi$
$942$	−4.80385	−0.156518
$943$	46.3923	1.51074
$944$	2.19615	0.0714787
$945$	−1.73205	−0.0563436
$946$	0	0
$947$	30.8038	1.00099	0.500495	−	0.865739i	$-0.333151\pi$
$947$	30.8038	1.00099	0.500495	+	0.865739i	$0.333151\pi$
$948$	−15.4641	−0.502251
$949$	8.19615	0.266058
$950$	−6.46410	−0.209723
$951$	−21.8038	−0.707038
$952$	−7.39230	−0.239586
$953$	−45.7128	−1.48078	−0.740392	−	0.672176i	$-0.765360\pi$
$953$	−45.7128	−1.48078	−0.740392	+	0.672176i	$0.765360\pi$
$954$	−2.19615	−0.0711031
$955$	−15.0000	−0.485389
$956$	11.1962	0.362109
$957$	0	0
$958$	15.3397	0.495605
$959$	5.19615	0.167793
$960$	−1.00000	−0.0322749
$961$	72.9615	2.35360
$962$	46.5167	1.49976
$963$	−8.53590	−0.275065
$964$	−12.8038	−0.412384
$965$	−2.53590	−0.0816335
$966$	−14.1962	−0.456754
$967$	48.2487	1.55157	0.775787	−	0.630995i	$-0.217353\pi$
$967$	48.2487	1.55157	0.775787	+	0.630995i	$0.217353\pi$
$968$	0	0
$969$	−27.5885	−0.886269
$970$	10.1962	0.327379
$971$	−31.6077	−1.01434	−0.507170	−	0.861846i	$-0.669308\pi$
$971$	−31.6077	−1.01434	−0.507170	+	0.861846i	$0.669308\pi$
$972$	−1.00000	−0.0320750
$973$	21.5885	0.692094
$974$	3.78461	0.121267
$975$	6.46410	0.207017
$976$	−1.26795	−0.0405861
$977$	47.5692	1.52187	0.760937	−	0.648826i	$-0.224740\pi$
$977$	47.5692	1.52187	0.760937	+	0.648826i	$0.224740\pi$
$978$	1.80385	0.0576807
$979$	0	0
$980$	−4.00000	−0.127775
$981$	2.53590	0.0809650
$982$	−28.7321	−0.916877
$983$	−38.1962	−1.21827	−0.609134	−	0.793067i	$-0.708483\pi$
$983$	−38.1962	−1.21827	−0.609134	+	0.793067i	$0.708483\pi$
$984$	−5.66025	−0.180442
$985$	−23.3205	−0.743053
$986$	27.5885	0.878595
$987$	10.3923	0.330791
$988$	41.7846	1.32935
$989$	−38.7846	−1.23328
$990$	0	0
$991$	−43.5692	−1.38402	−0.692011	−	0.721887i	$-0.743275\pi$
$991$	−43.5692	−1.38402	−0.692011	+	0.721887i	$0.743275\pi$
$992$	−10.1962	−0.323728
$993$	9.19615	0.291831
$994$	−12.8038	−0.406113
$995$	8.39230	0.266054
$996$	5.53590	0.175412
$997$	−2.07180	−0.0656145	−0.0328072	−	0.999462i	$-0.510445\pi$
$997$	−2.07180	−0.0656145	−0.0328072	+	0.999462i	$0.510445\pi$
$998$	−13.1962	−0.417717
$999$	7.19615	0.227676

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3630.2.a.bn.1.2	yes	2
11.10	odd	2		3630.2.a.bd.1.1	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3630.2.a.bd.1.1	✓	2	11.10	odd	2
3630.2.a.bn.1.2	yes	2	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 3630 = 2 \cdot 3 \cdot 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3630.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} +1.73205 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} +1.73205 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -1.00000 q^{12} -6.46410 q^{13} +1.73205 q^{14} -1.00000 q^{15} +1.00000 q^{16} -4.26795 q^{17} +1.00000 q^{18} -6.46410 q^{19} +1.00000 q^{20} -1.73205 q^{21} +8.19615 q^{23} -1.00000 q^{24} +1.00000 q^{25} -6.46410 q^{26} -1.00000 q^{27} +1.73205 q^{28} -6.46410 q^{29} -1.00000 q^{30} -10.1962 q^{31} +1.00000 q^{32} -4.26795 q^{34} +1.73205 q^{35} +1.00000 q^{36} -7.19615 q^{37} -6.46410 q^{38} +6.46410 q^{39} +1.00000 q^{40} +5.66025 q^{41} -1.73205 q^{42} -4.73205 q^{43} +1.00000 q^{45} +8.19615 q^{46} -6.00000 q^{47} -1.00000 q^{48} -4.00000 q^{49} +1.00000 q^{50} +4.26795 q^{51} -6.46410 q^{52} -2.19615 q^{53} -1.00000 q^{54} +1.73205 q^{56} +6.46410 q^{57} -6.46410 q^{58} +2.19615 q^{59} -1.00000 q^{60} -1.26795 q^{61} -10.1962 q^{62} +1.73205 q^{63} +1.00000 q^{64} -6.46410 q^{65} +14.3923 q^{67} -4.26795 q^{68} -8.19615 q^{69} +1.73205 q^{70} -7.39230 q^{71} +1.00000 q^{72} -1.26795 q^{73} -7.19615 q^{74} -1.00000 q^{75} -6.46410 q^{76} +6.46410 q^{78} +15.4641 q^{79} +1.00000 q^{80} +1.00000 q^{81} +5.66025 q^{82} -5.53590 q^{83} -1.73205 q^{84} -4.26795 q^{85} -4.73205 q^{86} +6.46410 q^{87} +16.3923 q^{89} +1.00000 q^{90} -11.1962 q^{91} +8.19615 q^{92} +10.1962 q^{93} -6.00000 q^{94} -6.46410 q^{95} -1.00000 q^{96} +10.1962 q^{97} -4.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} - 2 q^{6} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 - 2 * q^6 + 2 * q^8 + 2 * q^9	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} - 2 q^{6} + 2 q^{8} + 2 q^{9} + 2 q^{10} - 2 q^{12} - 6 q^{13} - 2 q^{15} + 2 q^{16} - 12 q^{17} + 2 q^{18} - 6 q^{19} + 2 q^{20} + 6 q^{23} - 2 q^{24} + 2 q^{25} - 6 q^{26} - 2 q^{27} - 6 q^{29} - 2 q^{30} - 10 q^{31} + 2 q^{32} - 12 q^{34} + 2 q^{36} - 4 q^{37} - 6 q^{38} + 6 q^{39} + 2 q^{40} - 6 q^{41} - 6 q^{43} + 2 q^{45} + 6 q^{46} - 12 q^{47} - 2 q^{48} - 8 q^{49} + 2 q^{50} + 12 q^{51} - 6 q^{52} + 6 q^{53} - 2 q^{54} + 6 q^{57} - 6 q^{58} - 6 q^{59} - 2 q^{60} - 6 q^{61} - 10 q^{62} + 2 q^{64} - 6 q^{65} + 8 q^{67} - 12 q^{68} - 6 q^{69} + 6 q^{71} + 2 q^{72} - 6 q^{73} - 4 q^{74} - 2 q^{75} - 6 q^{76} + 6 q^{78} + 24 q^{79} + 2 q^{80} + 2 q^{81} - 6 q^{82} - 18 q^{83} - 12 q^{85} - 6 q^{86} + 6 q^{87} + 12 q^{89} + 2 q^{90} - 12 q^{91} + 6 q^{92} + 10 q^{93} - 12 q^{94} - 6 q^{95} - 2 q^{96} + 10 q^{97} - 8 q^{98}+O(q^{100}) \) 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 - 2 * q^6 + 2 * q^8 + 2 * q^9 + 2 * q^10 - 2 * q^12 - 6 * q^13 - 2 * q^15 + 2 * q^16 - 12 * q^17 + 2 * q^18 - 6 * q^19 + 2 * q^20 + 6 * q^23 - 2 * q^24 + 2 * q^25 - 6 * q^26 - 2 * q^27 - 6 * q^29 - 2 * q^30 - 10 * q^31 + 2 * q^32 - 12 * q^34 + 2 * q^36 - 4 * q^37 - 6 * q^38 + 6 * q^39 + 2 * q^40 - 6 * q^41 - 6 * q^43 + 2 * q^45 + 6 * q^46 - 12 * q^47 - 2 * q^48 - 8 * q^49 + 2 * q^50 + 12 * q^51 - 6 * q^52 + 6 * q^53 - 2 * q^54 + 6 * q^57 - 6 * q^58 - 6 * q^59 - 2 * q^60 - 6 * q^61 - 10 * q^62 + 2 * q^64 - 6 * q^65 + 8 * q^67 - 12 * q^68 - 6 * q^69 + 6 * q^71 + 2 * q^72 - 6 * q^73 - 4 * q^74 - 2 * q^75 - 6 * q^76 + 6 * q^78 + 24 * q^79 + 2 * q^80 + 2 * q^81 - 6 * q^82 - 18 * q^83 - 12 * q^85 - 6 * q^86 + 6 * q^87 + 12 * q^89 + 2 * q^90 - 12 * q^91 + 6 * q^92 + 10 * q^93 - 12 * q^94 - 6 * q^95 - 2 * q^96 + 10 * q^97 - 8 * q^98

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