LMFDB - Embedded newform 3630.2.a.bn.1.1

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			1.1
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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} -1.73205 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} -1.73205 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -1.00000 q^{12} +0.464102 q^{13} -1.73205 q^{14} -1.00000 q^{15} +1.00000 q^{16} -7.73205 q^{17} +1.00000 q^{18} +0.464102 q^{19} +1.00000 q^{20} +1.73205 q^{21} -2.19615 q^{23} -1.00000 q^{24} +1.00000 q^{25} +0.464102 q^{26} -1.00000 q^{27} -1.73205 q^{28} +0.464102 q^{29} -1.00000 q^{30} +0.196152 q^{31} +1.00000 q^{32} -7.73205 q^{34} -1.73205 q^{35} +1.00000 q^{36} +3.19615 q^{37} +0.464102 q^{38} -0.464102 q^{39} +1.00000 q^{40} -11.6603 q^{41} +1.73205 q^{42} -1.26795 q^{43} +1.00000 q^{45} -2.19615 q^{46} -6.00000 q^{47} -1.00000 q^{48} -4.00000 q^{49} +1.00000 q^{50} +7.73205 q^{51} +0.464102 q^{52} +8.19615 q^{53} -1.00000 q^{54} -1.73205 q^{56} -0.464102 q^{57} +0.464102 q^{58} -8.19615 q^{59} -1.00000 q^{60} -4.73205 q^{61} +0.196152 q^{62} -1.73205 q^{63} +1.00000 q^{64} +0.464102 q^{65} -6.39230 q^{67} -7.73205 q^{68} +2.19615 q^{69} -1.73205 q^{70} +13.3923 q^{71} +1.00000 q^{72} -4.73205 q^{73} +3.19615 q^{74} -1.00000 q^{75} +0.464102 q^{76} -0.464102 q^{78} +8.53590 q^{79} +1.00000 q^{80} +1.00000 q^{81} -11.6603 q^{82} -12.4641 q^{83} +1.73205 q^{84} -7.73205 q^{85} -1.26795 q^{86} -0.464102 q^{87} -4.39230 q^{89} +1.00000 q^{90} -0.803848 q^{91} -2.19615 q^{92} -0.196152 q^{93} -6.00000 q^{94} +0.464102 q^{95} -1.00000 q^{96} -0.196152 q^{97} -4.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	$-0.606148\pi$
$7$	−1.73205	−0.654654	−0.327327	+	0.944911i	$0.606148\pi$
$8$	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
$13$	0.464102	0.128719	0.0643593	−	0.997927i	$-0.479500\pi$
$13$	0.464102	0.128719	0.0643593	+	0.997927i	$0.479500\pi$
$14$	−1.73205	−0.462910
$15$	−1.00000	−0.258199
$16$	1.00000	0.250000
$17$	−7.73205	−1.87530	−0.937649	−	0.347584i	$-0.887002\pi$
$17$	−7.73205	−1.87530	−0.937649	+	0.347584i	$0.887002\pi$
$18$	1.00000	0.235702
$19$	0.464102	0.106472	0.0532361	−	0.998582i	$-0.483046\pi$
$19$	0.464102	0.106472	0.0532361	+	0.998582i	$0.483046\pi$
$20$	1.00000	0.223607
$21$	1.73205	0.377964
$22$	0	0
$23$	−2.19615	−0.457929	−0.228965	−	0.973435i	$-0.573534\pi$
$23$	−2.19615	−0.457929	−0.228965	+	0.973435i	$0.573534\pi$
$24$	−1.00000	−0.204124
$25$	1.00000	0.200000
$26$	0.464102	0.0910178
$27$	−1.00000	−0.192450
$28$	−1.73205	−0.327327
$29$	0.464102	0.0861815	0.0430908	−	0.999071i	$-0.486280\pi$
$29$	0.464102	0.0861815	0.0430908	+	0.999071i	$0.486280\pi$
$30$	−1.00000	−0.182574
$31$	0.196152	0.0352300	0.0176150	−	0.999845i	$-0.494393\pi$
$31$	0.196152	0.0352300	0.0176150	+	0.999845i	$0.494393\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	−7.73205	−1.32604
$35$	−1.73205	−0.292770
$36$	1.00000	0.166667
$37$	3.19615	0.525444	0.262722	−	0.964872i	$-0.415380\pi$
$37$	3.19615	0.525444	0.262722	+	0.964872i	$0.415380\pi$
$38$	0.464102	0.0752872
$39$	−0.464102	−0.0743157
$40$	1.00000	0.158114
$41$	−11.6603	−1.82103	−0.910513	−	0.413481i	$-0.864313\pi$
$41$	−11.6603	−1.82103	−0.910513	+	0.413481i	$0.864313\pi$
$42$	1.73205	0.267261
$43$	−1.26795	−0.193360	−0.0966802	−	0.995315i	$-0.530822\pi$
$43$	−1.26795	−0.193360	−0.0966802	+	0.995315i	$0.530822\pi$
$44$	0	0
$45$	1.00000	0.149071
$46$	−2.19615	−0.323805
$47$	−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
$51$	7.73205	1.08270
$52$	0.464102	0.0643593
$53$	8.19615	1.12583	0.562914	−	0.826515i	$-0.309680\pi$
$53$	8.19615	1.12583	0.562914	+	0.826515i	$0.309680\pi$
$54$	−1.00000	−0.136083
$55$	0	0
$56$	−1.73205	−0.231455
$57$	−0.464102	−0.0614718
$58$	0.464102	0.0609395
$59$	−8.19615	−1.06705	−0.533524	−	0.845785i	$-0.679133\pi$
$59$	−8.19615	−1.06705	−0.533524	+	0.845785i	$0.679133\pi$
$60$	−1.00000	−0.129099
$61$	−4.73205	−0.605877	−0.302939	−	0.953010i	$-0.597968\pi$
$61$	−4.73205	−0.605877	−0.302939	+	0.953010i	$0.597968\pi$
$62$	0.196152	0.0249114
$63$	−1.73205	−0.218218
$64$	1.00000	0.125000
$65$	0.464102	0.0575647
$66$	0	0
$67$	−6.39230	−0.780944	−0.390472	−	0.920615i	$-0.627688\pi$
$67$	−6.39230	−0.780944	−0.390472	+	0.920615i	$0.627688\pi$
$68$	−7.73205	−0.937649
$69$	2.19615	0.264386
$70$	−1.73205	−0.207020
$71$	13.3923	1.58937	0.794687	−	0.607019i	$-0.207635\pi$
$71$	13.3923	1.58937	0.794687	+	0.607019i	$0.207635\pi$
$72$	1.00000	0.117851
$73$	−4.73205	−0.553845	−0.276922	−	0.960892i	$-0.589314\pi$
$73$	−4.73205	−0.553845	−0.276922	+	0.960892i	$0.589314\pi$
$74$	3.19615	0.371545
$75$	−1.00000	−0.115470
$76$	0.464102	0.0532361
$77$	0	0
$78$	−0.464102	−0.0525492
$79$	8.53590	0.960364	0.480182	−	0.877169i	$-0.340571\pi$
$79$	8.53590	0.960364	0.480182	+	0.877169i	$0.340571\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	−11.6603	−1.28766
$83$	−12.4641	−1.36811	−0.684056	−	0.729429i	$-0.739786\pi$
$83$	−12.4641	−1.36811	−0.684056	+	0.729429i	$0.739786\pi$
$84$	1.73205	0.188982
$85$	−7.73205	−0.838659
$86$	−1.26795	−0.136726
$87$	−0.464102	−0.0497569
$88$	0	0
$89$	−4.39230	−0.465583	−0.232792	−	0.972527i	$-0.574786\pi$
$89$	−4.39230	−0.465583	−0.232792	+	0.972527i	$0.574786\pi$
$90$	1.00000	0.105409
$91$	−0.803848	−0.0842661
$92$	−2.19615	−0.228965
$93$	−0.196152	−0.0203401
$94$	−6.00000	−0.618853
$95$	0.464102	0.0476158
$96$	−1.00000	−0.102062
$97$	−0.196152	−0.0199163	−0.00995813	−	0.999950i	$-0.503170\pi$
$97$	−0.196152	−0.0199163	−0.00995813	+	0.999950i	$0.503170\pi$
$98$	−4.00000	−0.404061
$99$	0	0
$100$	1.00000	0.100000
$101$	16.8564	1.67728	0.838638	−	0.544690i	$-0.183353\pi$
$101$	16.8564	1.67728	0.838638	+	0.544690i	$0.183353\pi$
$102$	7.73205	0.765587
$103$	−13.0000	−1.28093	−0.640464	−	0.767988i	$-0.721258\pi$
$103$	−13.0000	−1.28093	−0.640464	+	0.767988i	$0.721258\pi$
$104$	0.464102	0.0455089
$105$	1.73205	0.169031
$106$	8.19615	0.796081
$107$	−15.4641	−1.49497	−0.747486	−	0.664278i	$-0.768739\pi$
$107$	−15.4641	−1.49497	−0.747486	+	0.664278i	$0.768739\pi$
$108$	−1.00000	−0.0962250
$109$	9.46410	0.906497	0.453248	−	0.891384i	$-0.350265\pi$
$109$	9.46410	0.906497	0.453248	+	0.891384i	$0.350265\pi$
$110$	0	0
$111$	−3.19615	−0.303365
$112$	−1.73205	−0.163663
$113$	0	0		−	1.00000i	$-0.5\pi$
$113$	0	0			1.00000i	$0.5\pi$
$114$	−0.464102	−0.0434671
$115$	−2.19615	−0.204792
$116$	0.464102	0.0430908
$117$	0.464102	0.0429062
$118$	−8.19615	−0.754517
$119$	13.3923	1.22767
$120$	−1.00000	−0.0912871
$121$	0	0
$122$	−4.73205	−0.428420
$123$	11.6603	1.05137
$124$	0.196152	0.0176150
$125$	1.00000	0.0894427
$126$	−1.73205	−0.154303
$127$	−16.3923	−1.45458	−0.727291	−	0.686329i	$-0.759221\pi$
$127$	−16.3923	−1.45458	−0.727291	+	0.686329i	$0.759221\pi$
$128$	1.00000	0.0883883
$129$	1.26795	0.111637
$130$	0.464102	0.0407044
$131$	−11.6603	−1.01876	−0.509381	−	0.860541i	$-0.670125\pi$
$131$	−11.6603	−1.01876	−0.509381	+	0.860541i	$0.670125\pi$
$132$	0	0
$133$	−0.803848	−0.0697024
$134$	−6.39230	−0.552211
$135$	−1.00000	−0.0860663
$136$	−7.73205	−0.663018
$137$	3.00000	0.256307	0.128154	−	0.991754i	$-0.459095\pi$
$137$	3.00000	0.256307	0.128154	+	0.991754i	$0.459095\pi$
$138$	2.19615	0.186949
$139$	5.53590	0.469549	0.234774	−	0.972050i	$-0.424565\pi$
$139$	5.53590	0.469549	0.234774	+	0.972050i	$0.424565\pi$
$140$	−1.73205	−0.146385
$141$	6.00000	0.505291
$142$	13.3923	1.12386
$143$	0	0
$144$	1.00000	0.0833333
$145$	0.464102	0.0385415
$146$	−4.73205	−0.391627
$147$	4.00000	0.329914
$148$	3.19615	0.262722
$149$	2.53590	0.207749	0.103874	−	0.994590i	$-0.466876\pi$
$149$	2.53590	0.207749	0.103874	+	0.994590i	$0.466876\pi$
$150$	−1.00000	−0.0816497
$151$	−1.26795	−0.103184	−0.0515921	−	0.998668i	$-0.516430\pi$
$151$	−1.26795	−0.103184	−0.0515921	+	0.998668i	$0.516430\pi$
$152$	0.464102	0.0376436
$153$	−7.73205	−0.625099
$154$	0	0
$155$	0.196152	0.0157553
$156$	−0.464102	−0.0371579
$157$	15.1962	1.21278	0.606392	−	0.795165i	$-0.292616\pi$
$157$	15.1962	1.21278	0.606392	+	0.795165i	$0.292616\pi$
$158$	8.53590	0.679080
$159$	−8.19615	−0.649997
$160$	1.00000	0.0790569
$161$	3.80385	0.299785
$162$	1.00000	0.0785674
$163$	−12.1962	−0.955276	−0.477638	−	0.878557i	$-0.658507\pi$
$163$	−12.1962	−0.955276	−0.477638	+	0.878557i	$0.658507\pi$
$164$	−11.6603	−0.910513
$165$	0	0
$166$	−12.4641	−0.967402
$167$	−9.46410	−0.732354	−0.366177	−	0.930545i	$-0.619334\pi$
$167$	−9.46410	−0.732354	−0.366177	+	0.930545i	$0.619334\pi$
$168$	1.73205	0.133631
$169$	−12.7846	−0.983432
$170$	−7.73205	−0.593021
$171$	0.464102	0.0354907
$172$	−1.26795	−0.0966802
$173$	6.58846	0.500911	0.250456	−	0.968128i	$-0.419420\pi$
$173$	6.58846	0.500911	0.250456	+	0.968128i	$0.419420\pi$
$174$	−0.464102	−0.0351835
$175$	−1.73205	−0.130931
$176$	0	0
$177$	8.19615	0.616061
$178$	−4.39230	−0.329217
$179$	8.19615	0.612609	0.306305	−	0.951934i	$-0.400907\pi$
$179$	8.19615	0.612609	0.306305	+	0.951934i	$0.400907\pi$
$180$	1.00000	0.0745356
$181$	−16.5885	−1.23301	−0.616505	−	0.787351i	$-0.711452\pi$
$181$	−16.5885	−1.23301	−0.616505	+	0.787351i	$0.711452\pi$
$182$	−0.803848	−0.0595851
$183$	4.73205	0.349803
$184$	−2.19615	−0.161903
$185$	3.19615	0.234986
$186$	−0.196152	−0.0143826
$187$	0	0
$188$	−6.00000	−0.437595
$189$	1.73205	0.125988
$190$	0.464102	0.0336695
$191$	−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
$193$	−9.46410	−0.681241	−0.340620	−	0.940201i	$-0.610637\pi$
$193$	−9.46410	−0.681241	−0.340620	+	0.940201i	$0.610637\pi$
$194$	−0.196152	−0.0140829
$195$	−0.464102	−0.0332350
$196$	−4.00000	−0.285714
$197$	11.3205	0.806553	0.403276	−	0.915078i	$-0.367871\pi$
$197$	11.3205	0.806553	0.403276	+	0.915078i	$0.367871\pi$
$198$	0	0
$199$	−12.3923	−0.878467	−0.439234	−	0.898373i	$-0.644750\pi$
$199$	−12.3923	−0.878467	−0.439234	+	0.898373i	$0.644750\pi$
$200$	1.00000	0.0707107
$201$	6.39230	0.450878
$202$	16.8564	1.18601
$203$	−0.803848	−0.0564190
$204$	7.73205	0.541352
$205$	−11.6603	−0.814387
$206$	−13.0000	−0.905753
$207$	−2.19615	−0.152643
$208$	0.464102	0.0321797
$209$	0	0
$210$	1.73205	0.119523
$211$	16.8564	1.16044	0.580221	−	0.814459i	$-0.302966\pi$
$211$	16.8564	1.16044	0.580221	+	0.814459i	$0.302966\pi$
$212$	8.19615	0.562914
$213$	−13.3923	−0.917626
$214$	−15.4641	−1.05710
$215$	−1.26795	−0.0864734
$216$	−1.00000	−0.0680414
$217$	−0.339746	−0.0230635
$218$	9.46410	0.640990
$219$	4.73205	0.319762
$220$	0	0
$221$	−3.58846	−0.241386
$222$	−3.19615	−0.214512
$223$	19.7846	1.32488	0.662438	−	0.749117i	$-0.269522\pi$
$223$	19.7846	1.32488	0.662438	+	0.749117i	$0.269522\pi$
$224$	−1.73205	−0.115728
$225$	1.00000	0.0666667
$226$	0	0
$227$	−20.5359	−1.36302	−0.681508	−	0.731811i	$-0.738675\pi$
$227$	−20.5359	−1.36302	−0.681508	+	0.731811i	$0.738675\pi$
$228$	−0.464102	−0.0307359
$229$	12.7846	0.844831	0.422415	−	0.906402i	$-0.361182\pi$
$229$	12.7846	0.844831	0.422415	+	0.906402i	$0.361182\pi$
$230$	−2.19615	−0.144810
$231$	0	0
$232$	0.464102	0.0304698
$233$	−25.8564	−1.69391	−0.846955	−	0.531665i	$-0.821567\pi$
$233$	−25.8564	−1.69391	−0.846955	+	0.531665i	$0.821567\pi$
$234$	0.464102	0.0303393
$235$	−6.00000	−0.391397
$236$	−8.19615	−0.533524
$237$	−8.53590	−0.554466
$238$	13.3923	0.868094
$239$	0.803848	0.0519966	0.0259983	−	0.999662i	$-0.491724\pi$
$239$	0.803848	0.0519966	0.0259983	+	0.999662i	$0.491724\pi$
$240$	−1.00000	−0.0645497
$241$	−23.1962	−1.49420	−0.747098	−	0.664714i	$-0.768553\pi$
$241$	−23.1962	−1.49420	−0.747098	+	0.664714i	$0.768553\pi$
$242$	0	0
$243$	−1.00000	−0.0641500
$244$	−4.73205	−0.302939
$245$	−4.00000	−0.255551
$246$	11.6603	0.743431
$247$	0.215390	0.0137050
$248$	0.196152	0.0124557
$249$	12.4641	0.789880
$250$	1.00000	0.0632456
$251$	4.39230	0.277240	0.138620	−	0.990346i	$-0.455733\pi$
$251$	4.39230	0.277240	0.138620	+	0.990346i	$0.455733\pi$
$252$	−1.73205	−0.109109
$253$	0	0
$254$	−16.3923	−1.02854
$255$	7.73205	0.484200
$256$	1.00000	0.0625000
$257$	13.3923	0.835389	0.417695	−	0.908588i	$-0.362838\pi$
$257$	13.3923	0.835389	0.417695	+	0.908588i	$0.362838\pi$
$258$	1.26795	0.0789391
$259$	−5.53590	−0.343984
$260$	0.464102	0.0287824
$261$	0.464102	0.0287272
$262$	−11.6603	−0.720373
$263$	−26.1962	−1.61532	−0.807662	−	0.589646i	$-0.799267\pi$
$263$	−26.1962	−1.61532	−0.807662	+	0.589646i	$0.799267\pi$
$264$	0	0
$265$	8.19615	0.503486
$266$	−0.803848	−0.0492871
$267$	4.39230	0.268805
$268$	−6.39230	−0.390472
$269$	23.1962	1.41429	0.707147	−	0.707066i	$-0.249982\pi$
$269$	23.1962	1.41429	0.707147	+	0.707066i	$0.249982\pi$
$270$	−1.00000	−0.0608581
$271$	−26.7846	−1.62705	−0.813525	−	0.581531i	$-0.802454\pi$
$271$	−26.7846	−1.62705	−0.813525	+	0.581531i	$0.802454\pi$
$272$	−7.73205	−0.468824
$273$	0.803848	0.0486511
$274$	3.00000	0.181237
$275$	0	0
$276$	2.19615	0.132193
$277$	5.07180	0.304735	0.152367	−	0.988324i	$-0.451310\pi$
$277$	5.07180	0.304735	0.152367	+	0.988324i	$0.451310\pi$
$278$	5.53590	0.332021
$279$	0.196152	0.0117433
$280$	−1.73205	−0.103510
$281$	−8.19615	−0.488941	−0.244471	−	0.969657i	$-0.578614\pi$
$281$	−8.19615	−0.488941	−0.244471	+	0.969657i	$0.578614\pi$
$282$	6.00000	0.357295
$283$	23.3205	1.38626	0.693130	−	0.720812i	$-0.256231\pi$
$283$	23.3205	1.38626	0.693130	+	0.720812i	$0.256231\pi$
$284$	13.3923	0.794687
$285$	−0.464102	−0.0274910
$286$	0	0
$287$	20.1962	1.19214
$288$	1.00000	0.0589256
$289$	42.7846	2.51674
$290$	0.464102	0.0272530
$291$	0.196152	0.0114987
$292$	−4.73205	−0.276922
$293$	−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
$295$	−8.19615	−0.477198
$296$	3.19615	0.185773
$297$	0	0
$298$	2.53590	0.146901
$299$	−1.01924	−0.0589440
$300$	−1.00000	−0.0577350
$301$	2.19615	0.126584
$302$	−1.26795	−0.0729623
$303$	−16.8564	−0.968375
$304$	0.464102	0.0266181
$305$	−4.73205	−0.270956
$306$	−7.73205	−0.442012
$307$	10.7321	0.612510	0.306255	−	0.951949i	$-0.400924\pi$
$307$	10.7321	0.612510	0.306255	+	0.951949i	$0.400924\pi$
$308$	0	0
$309$	13.0000	0.739544
$310$	0.196152	0.0111407
$311$	−32.7846	−1.85904	−0.929522	−	0.368766i	$-0.879780\pi$
$311$	−32.7846	−1.85904	−0.929522	+	0.368766i	$0.879780\pi$
$312$	−0.464102	−0.0262746
$313$	32.9808	1.86418	0.932091	−	0.362223i	$-0.117982\pi$
$313$	32.9808	1.86418	0.932091	+	0.362223i	$0.117982\pi$
$314$	15.1962	0.857568
$315$	−1.73205	−0.0975900
$316$	8.53590	0.480182
$317$	32.1962	1.80832	0.904158	−	0.427198i	$-0.140499\pi$
$317$	32.1962	1.80832	0.904158	+	0.427198i	$0.140499\pi$
$318$	−8.19615	−0.459617
$319$	0	0
$320$	1.00000	0.0559017
$321$	15.4641	0.863122
$322$	3.80385	0.211980
$323$	−3.58846	−0.199667
$324$	1.00000	0.0555556
$325$	0.464102	0.0257437
$326$	−12.1962	−0.675482
$327$	−9.46410	−0.523366
$328$	−11.6603	−0.643830
$329$	10.3923	0.572946
$330$	0	0
$331$	1.19615	0.0657465	0.0328732	−	0.999460i	$-0.489534\pi$
$331$	1.19615	0.0657465	0.0328732	+	0.999460i	$0.489534\pi$
$332$	−12.4641	−0.684056
$333$	3.19615	0.175148
$334$	−9.46410	−0.517853
$335$	−6.39230	−0.349249
$336$	1.73205	0.0944911
$337$	−13.5167	−0.736299	−0.368150	−	0.929767i	$-0.620009\pi$
$337$	−13.5167	−0.736299	−0.368150	+	0.929767i	$0.620009\pi$
$338$	−12.7846	−0.695391
$339$	0	0
$340$	−7.73205	−0.419329
$341$	0	0
$342$	0.464102	0.0250957
$343$	19.0526	1.02874
$344$	−1.26795	−0.0683632
$345$	2.19615	0.118237
$346$	6.58846	0.354198
$347$	−14.3205	−0.768765	−0.384383	−	0.923174i	$-0.625586\pi$
$347$	−14.3205	−0.768765	−0.384383	+	0.923174i	$0.625586\pi$
$348$	−0.464102	−0.0248785
$349$	24.9282	1.33438	0.667188	−	0.744889i	$-0.267498\pi$
$349$	24.9282	1.33438	0.667188	+	0.744889i	$0.267498\pi$
$350$	−1.73205	−0.0925820
$351$	−0.464102	−0.0247719
$352$	0	0
$353$	−20.7846	−1.10625	−0.553127	−	0.833097i	$-0.686565\pi$
$353$	−20.7846	−1.10625	−0.553127	+	0.833097i	$0.686565\pi$
$354$	8.19615	0.435621
$355$	13.3923	0.710790
$356$	−4.39230	−0.232792
$357$	−13.3923	−0.708796
$358$	8.19615	0.433180
$359$	3.46410	0.182828	0.0914141	−	0.995813i	$-0.470861\pi$
$359$	3.46410	0.182828	0.0914141	+	0.995813i	$0.470861\pi$
$360$	1.00000	0.0527046
$361$	−18.7846	−0.988664
$362$	−16.5885	−0.871870
$363$	0	0
$364$	−0.803848	−0.0421331
$365$	−4.73205	−0.247687
$366$	4.73205	0.247348
$367$	27.3923	1.42987	0.714933	−	0.699193i	$-0.246457\pi$
$367$	27.3923	1.42987	0.714933	+	0.699193i	$0.246457\pi$
$368$	−2.19615	−0.114482
$369$	−11.6603	−0.607009
$370$	3.19615	0.166160
$371$	−14.1962	−0.737028
$372$	−0.196152	−0.0101700
$373$	6.46410	0.334698	0.167349	−	0.985898i	$-0.446479\pi$
$373$	6.46410	0.334698	0.167349	+	0.985898i	$0.446479\pi$
$374$	0	0
$375$	−1.00000	−0.0516398
$376$	−6.00000	−0.309426
$377$	0.215390	0.0110932
$378$	1.73205	0.0890871
$379$	35.5885	1.82806	0.914028	−	0.405651i	$-0.132955\pi$
$379$	35.5885	1.82806	0.914028	+	0.405651i	$0.132955\pi$
$380$	0.464102	0.0238079
$381$	16.3923	0.839803
$382$	−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
$386$	−9.46410	−0.481710
$387$	−1.26795	−0.0644535
$388$	−0.196152	−0.00995813
$389$	−8.78461	−0.445397	−0.222699	−	0.974887i	$-0.571487\pi$
$389$	−8.78461	−0.445397	−0.222699	+	0.974887i	$0.571487\pi$
$390$	−0.464102	−0.0235007
$391$	16.9808	0.858754
$392$	−4.00000	−0.202031
$393$	11.6603	0.588182
$394$	11.3205	0.570319
$395$	8.53590	0.429488
$396$	0	0
$397$	−4.80385	−0.241098	−0.120549	−	0.992707i	$-0.538466\pi$
$397$	−4.80385	−0.241098	−0.120549	+	0.992707i	$0.538466\pi$
$398$	−12.3923	−0.621170
$399$	0.803848	0.0402427
$400$	1.00000	0.0500000
$401$	36.5885	1.82714	0.913570	−	0.406681i	$-0.133314\pi$
$401$	36.5885	1.82714	0.913570	+	0.406681i	$0.133314\pi$
$402$	6.39230	0.318819
$403$	0.0910347	0.00453476
$404$	16.8564	0.838638
$405$	1.00000	0.0496904
$406$	−0.803848	−0.0398943
$407$	0	0
$408$	7.73205	0.382794
$409$	4.14359	0.204888	0.102444	−	0.994739i	$-0.467334\pi$
$409$	4.14359	0.204888	0.102444	+	0.994739i	$0.467334\pi$
$410$	−11.6603	−0.575859
$411$	−3.00000	−0.147979
$412$	−13.0000	−0.640464
$413$	14.1962	0.698547
$414$	−2.19615	−0.107935
$415$	−12.4641	−0.611839
$416$	0.464102	0.0227545
$417$	−5.53590	−0.271094
$418$	0	0
$419$	10.3923	0.507697	0.253849	−	0.967244i	$-0.418303\pi$
$419$	10.3923	0.507697	0.253849	+	0.967244i	$0.418303\pi$
$420$	1.73205	0.0845154
$421$	13.8038	0.672758	0.336379	−	0.941727i	$-0.390798\pi$
$421$	13.8038	0.672758	0.336379	+	0.941727i	$0.390798\pi$
$422$	16.8564	0.820557
$423$	−6.00000	−0.291730
$424$	8.19615	0.398040
$425$	−7.73205	−0.375060
$426$	−13.3923	−0.648859
$427$	8.19615	0.396640
$428$	−15.4641	−0.747486
$429$	0	0
$430$	−1.26795	−0.0611459
$431$	0.124356	0.00599000	0.00299500	−	0.999996i	$-0.499047\pi$
$431$	0.124356	0.00599000	0.00299500	+	0.999996i	$0.499047\pi$
$432$	−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	$0.220799\pi$
$434$	−0.339746	−0.0163083
$435$	−0.464102	−0.0222520
$436$	9.46410	0.453248
$437$	−1.01924	−0.0487568
$438$	4.73205	0.226106
$439$	−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
$442$	−3.58846	−0.170686
$443$	−15.5885	−0.740630	−0.370315	−	0.928906i	$-0.620750\pi$
$443$	−15.5885	−0.740630	−0.370315	+	0.928906i	$0.620750\pi$
$444$	−3.19615	−0.151683
$445$	−4.39230	−0.208215
$446$	19.7846	0.936828
$447$	−2.53590	−0.119944
$448$	−1.73205	−0.0818317
$449$	22.3923	1.05676	0.528379	−	0.849009i	$-0.322800\pi$
$449$	22.3923	1.05676	0.528379	+	0.849009i	$0.322800\pi$
$450$	1.00000	0.0471405
$451$	0	0
$452$	0	0
$453$	1.26795	0.0595734
$454$	−20.5359	−0.963797
$455$	−0.803848	−0.0376850
$456$	−0.464102	−0.0217335
$457$	15.1244	0.707488	0.353744	−	0.935342i	$-0.384908\pi$
$457$	15.1244	0.707488	0.353744	+	0.935342i	$0.384908\pi$
$458$	12.7846	0.597386
$459$	7.73205	0.360901
$460$	−2.19615	−0.102396
$461$	13.1436	0.612158	0.306079	−	0.952006i	$-0.400983\pi$
$461$	13.1436	0.612158	0.306079	+	0.952006i	$0.400983\pi$
$462$	0	0
$463$	6.39230	0.297076	0.148538	−	0.988907i	$-0.452543\pi$
$463$	6.39230	0.297076	0.148538	+	0.988907i	$0.452543\pi$
$464$	0.464102	0.0215454
$465$	−0.196152	−0.00909635
$466$	−25.8564	−1.19777
$467$	−33.5885	−1.55429	−0.777144	−	0.629323i	$-0.783332\pi$
$467$	−33.5885	−1.55429	−0.777144	+	0.629323i	$0.783332\pi$
$468$	0.464102	0.0214531
$469$	11.0718	0.511248
$470$	−6.00000	−0.276759
$471$	−15.1962	−0.700202
$472$	−8.19615	−0.377258
$473$	0	0
$474$	−8.53590	−0.392067
$475$	0.464102	0.0212944
$476$	13.3923	0.613835
$477$	8.19615	0.375276
$478$	0.803848	0.0367671
$479$	32.6603	1.49229	0.746143	−	0.665786i	$-0.231904\pi$
$479$	32.6603	1.49229	0.746143	+	0.665786i	$0.231904\pi$
$480$	−1.00000	−0.0456435
$481$	1.48334	0.0676345
$482$	−23.1962	−1.05656
$483$	−3.80385	−0.173081
$484$	0	0
$485$	−0.196152	−0.00890682
$486$	−1.00000	−0.0453609
$487$	−37.7846	−1.71218	−0.856092	−	0.516823i	$-0.827114\pi$
$487$	−37.7846	−1.71218	−0.856092	+	0.516823i	$0.827114\pi$
$488$	−4.73205	−0.214210
$489$	12.1962	0.551529
$490$	−4.00000	−0.180702
$491$	−25.2679	−1.14033	−0.570163	−	0.821531i	$-0.693120\pi$
$491$	−25.2679	−1.14033	−0.570163	+	0.821531i	$0.693120\pi$
$492$	11.6603	0.525685
$493$	−3.58846	−0.161616
$494$	0.215390	0.00969087
$495$	0	0
$496$	0.196152	0.00880750
$497$	−23.1962	−1.04049
$498$	12.4641	0.558530
$499$	−2.80385	−0.125517	−0.0627587	−	0.998029i	$-0.519990\pi$
$499$	−2.80385	−0.125517	−0.0627587	+	0.998029i	$0.519990\pi$
$500$	1.00000	0.0447214
$501$	9.46410	0.422825
$502$	4.39230	0.196038
$503$	−10.0526	−0.448221	−0.224111	−	0.974564i	$-0.571948\pi$
$503$	−10.0526	−0.448221	−0.224111	+	0.974564i	$0.571948\pi$
$504$	−1.73205	−0.0771517
$505$	16.8564	0.750100
$506$	0	0
$507$	12.7846	0.567784
$508$	−16.3923	−0.727291
$509$	−14.7846	−0.655316	−0.327658	−	0.944796i	$-0.606259\pi$
$509$	−14.7846	−0.655316	−0.327658	+	0.944796i	$0.606259\pi$
$510$	7.73205	0.342381
$511$	8.19615	0.362576
$512$	1.00000	0.0441942
$513$	−0.464102	−0.0204906
$514$	13.3923	0.590709
$515$	−13.0000	−0.572848
$516$	1.26795	0.0558184
$517$	0	0
$518$	−5.53590	−0.243233
$519$	−6.58846	−0.289201
$520$	0.464102	0.0203522
$521$	14.1962	0.621945	0.310972	−	0.950419i	$-0.399345\pi$
$521$	14.1962	0.621945	0.310972	+	0.950419i	$0.399345\pi$
$522$	0.464102	0.0203132
$523$	2.87564	0.125743	0.0628716	−	0.998022i	$-0.479974\pi$
$523$	2.87564	0.125743	0.0628716	+	0.998022i	$0.479974\pi$
$524$	−11.6603	−0.509381
$525$	1.73205	0.0755929
$526$	−26.1962	−1.14221
$527$	−1.51666	−0.0660668
$528$	0	0
$529$	−18.1769	−0.790301
$530$	8.19615	0.356018
$531$	−8.19615	−0.355683
$532$	−0.803848	−0.0348512
$533$	−5.41154	−0.234400
$534$	4.39230	0.190074
$535$	−15.4641	−0.668571
$536$	−6.39230	−0.276106
$537$	−8.19615	−0.353690
$538$	23.1962	1.00006
$539$	0	0
$540$	−1.00000	−0.0430331
$541$	−10.7321	−0.461407	−0.230703	−	0.973024i	$-0.574103\pi$
$541$	−10.7321	−0.461407	−0.230703	+	0.973024i	$0.574103\pi$
$542$	−26.7846	−1.15050
$543$	16.5885	0.711879
$544$	−7.73205	−0.331509
$545$	9.46410	0.405398
$546$	0.803848	0.0344015
$547$	14.7846	0.632144	0.316072	−	0.948735i	$-0.397636\pi$
$547$	14.7846	0.632144	0.316072	+	0.948735i	$0.397636\pi$
$548$	3.00000	0.128154
$549$	−4.73205	−0.201959
$550$	0	0
$551$	0.215390	0.00917594
$552$	2.19615	0.0934745
$553$	−14.7846	−0.628706
$554$	5.07180	0.215480
$555$	−3.19615	−0.135669
$556$	5.53590	0.234774
$557$	−39.4641	−1.67215	−0.836074	−	0.548617i	$-0.815155\pi$
$557$	−39.4641	−1.67215	−0.836074	+	0.548617i	$0.815155\pi$
$558$	0.196152	0.00830379
$559$	−0.588457	−0.0248891
$560$	−1.73205	−0.0731925
$561$	0	0
$562$	−8.19615	−0.345734
$563$	20.3205	0.856407	0.428204	−	0.903682i	$-0.359147\pi$
$563$	20.3205	0.856407	0.428204	+	0.903682i	$0.359147\pi$
$564$	6.00000	0.252646
$565$	0	0
$566$	23.3205	0.980234
$567$	−1.73205	−0.0727393
$568$	13.3923	0.561929
$569$	9.80385	0.410999	0.205499	−	0.978657i	$-0.434118\pi$
$569$	9.80385	0.410999	0.205499	+	0.978657i	$0.434118\pi$
$570$	−0.464102	−0.0194391
$571$	−3.46410	−0.144968	−0.0724841	−	0.997370i	$-0.523093\pi$
$571$	−3.46410	−0.144968	−0.0724841	+	0.997370i	$0.523093\pi$
$572$	0	0
$573$	15.0000	0.626634
$574$	20.1962	0.842971
$575$	−2.19615	−0.0915859
$576$	1.00000	0.0416667
$577$	−30.3923	−1.26525	−0.632624	−	0.774459i	$-0.718022\pi$
$577$	−30.3923	−1.26525	−0.632624	+	0.774459i	$0.718022\pi$
$578$	42.7846	1.77961
$579$	9.46410	0.393315
$580$	0.464102	0.0192708
$581$	21.5885	0.895640
$582$	0.196152	0.00813078
$583$	0	0
$584$	−4.73205	−0.195814
$585$	0.464102	0.0191882
$586$	−12.0000	−0.495715
$587$	9.58846	0.395758	0.197879	−	0.980226i	$-0.436595\pi$
$587$	9.58846	0.395758	0.197879	+	0.980226i	$0.436595\pi$
$588$	4.00000	0.164957
$589$	0.0910347	0.00375102
$590$	−8.19615	−0.337430
$591$	−11.3205	−0.465663
$592$	3.19615	0.131361
$593$	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
$595$	13.3923	0.549031
$596$	2.53590	0.103874
$597$	12.3923	0.507183
$598$	−1.01924	−0.0416797
$599$	31.1769	1.27385	0.636927	−	0.770924i	$-0.280205\pi$
$599$	31.1769	1.27385	0.636927	+	0.770924i	$0.280205\pi$
$600$	−1.00000	−0.0408248
$601$	14.7846	0.603077	0.301538	−	0.953454i	$-0.402500\pi$
$601$	14.7846	0.603077	0.301538	+	0.953454i	$0.402500\pi$
$602$	2.19615	0.0895085
$603$	−6.39230	−0.260315
$604$	−1.26795	−0.0515921
$605$	0	0
$606$	−16.8564	−0.684745
$607$	47.4449	1.92573	0.962864	−	0.269988i	$-0.0870196\pi$
$607$	47.4449	1.92573	0.962864	+	0.269988i	$0.0870196\pi$
$608$	0.464102	0.0188218
$609$	0.803848	0.0325735
$610$	−4.73205	−0.191595
$611$	−2.78461	−0.112653
$612$	−7.73205	−0.312550
$613$	38.3205	1.54775	0.773875	−	0.633338i	$-0.218316\pi$
$613$	38.3205	1.54775	0.773875	+	0.633338i	$0.218316\pi$
$614$	10.7321	0.433110
$615$	11.6603	0.470187
$616$	0	0
$617$	38.5692	1.55274	0.776369	−	0.630278i	$-0.217059\pi$
$617$	38.5692	1.55274	0.776369	+	0.630278i	$0.217059\pi$
$618$	13.0000	0.522937
$619$	8.80385	0.353857	0.176928	−	0.984224i	$-0.443384\pi$
$619$	8.80385	0.353857	0.176928	+	0.984224i	$0.443384\pi$
$620$	0.196152	0.00787767
$621$	2.19615	0.0881286
$622$	−32.7846	−1.31454
$623$	7.60770	0.304796
$624$	−0.464102	−0.0185789
$625$	1.00000	0.0400000
$626$	32.9808	1.31818
$627$	0	0
$628$	15.1962	0.606392
$629$	−24.7128	−0.985364
$630$	−1.73205	−0.0690066
$631$	−30.9808	−1.23332	−0.616662	−	0.787228i	$-0.711516\pi$
$631$	−30.9808	−1.23332	−0.616662	+	0.787228i	$0.711516\pi$
$632$	8.53590	0.339540
$633$	−16.8564	−0.669982
$634$	32.1962	1.27867
$635$	−16.3923	−0.650509
$636$	−8.19615	−0.324999
$637$	−1.85641	−0.0735535
$638$	0	0
$639$	13.3923	0.529791
$640$	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	$0.462194\pi$
$642$	15.4641	0.610319
$643$	−4.00000	−0.157745	−0.0788723	−	0.996885i	$-0.525132\pi$
$643$	−4.00000	−0.157745	−0.0788723	+	0.996885i	$0.525132\pi$
$644$	3.80385	0.149893
$645$	1.26795	0.0499255
$646$	−3.58846	−0.141186
$647$	40.3923	1.58799	0.793993	−	0.607927i	$-0.207999\pi$
$647$	40.3923	1.58799	0.793993	+	0.607927i	$0.207999\pi$
$648$	1.00000	0.0392837
$649$	0	0
$650$	0.464102	0.0182036
$651$	0.339746	0.0133157
$652$	−12.1962	−0.477638
$653$	−33.8038	−1.32285	−0.661423	−	0.750013i	$-0.730047\pi$
$653$	−33.8038	−1.32285	−0.661423	+	0.750013i	$0.730047\pi$
$654$	−9.46410	−0.370076
$655$	−11.6603	−0.455604
$656$	−11.6603	−0.455256
$657$	−4.73205	−0.184615
$658$	10.3923	0.405134
$659$	19.1769	0.747027	0.373513	−	0.927625i	$-0.378153\pi$
$659$	19.1769	0.747027	0.373513	+	0.927625i	$0.378153\pi$
$660$	0	0
$661$	31.3731	1.22027	0.610135	−	0.792297i	$-0.291115\pi$
$661$	31.3731	1.22027	0.610135	+	0.792297i	$0.291115\pi$
$662$	1.19615	0.0464898
$663$	3.58846	0.139364
$664$	−12.4641	−0.483701
$665$	−0.803848	−0.0311719
$666$	3.19615	0.123848
$667$	−1.01924	−0.0394650
$668$	−9.46410	−0.366177
$669$	−19.7846	−0.764917
$670$	−6.39230	−0.246956
$671$	0	0
$672$	1.73205	0.0668153
$673$	−18.9282	−0.729629	−0.364814	−	0.931080i	$-0.618868\pi$
$673$	−18.9282	−0.729629	−0.364814	+	0.931080i	$0.618868\pi$
$674$	−13.5167	−0.520642
$675$	−1.00000	−0.0384900
$676$	−12.7846	−0.491716
$677$	−40.9808	−1.57502	−0.787509	−	0.616303i	$-0.788630\pi$
$677$	−40.9808	−1.57502	−0.787509	+	0.616303i	$0.788630\pi$
$678$	0	0
$679$	0.339746	0.0130383
$680$	−7.73205	−0.296511
$681$	20.5359	0.786937
$682$	0	0
$683$	−35.1962	−1.34674	−0.673372	−	0.739304i	$-0.735155\pi$
$683$	−35.1962	−1.34674	−0.673372	+	0.739304i	$0.735155\pi$
$684$	0.464102	0.0177454
$685$	3.00000	0.114624
$686$	19.0526	0.727430
$687$	−12.7846	−0.487763
$688$	−1.26795	−0.0483401
$689$	3.80385	0.144915
$690$	2.19615	0.0836061
$691$	−31.5885	−1.20168	−0.600841	−	0.799369i	$-0.705167\pi$
$691$	−31.5885	−1.20168	−0.600841	+	0.799369i	$0.705167\pi$
$692$	6.58846	0.250456
$693$	0	0
$694$	−14.3205	−0.543599
$695$	5.53590	0.209989
$696$	−0.464102	−0.0175917
$697$	90.1577	3.41497
$698$	24.9282	0.943546
$699$	25.8564	0.977979
$700$	−1.73205	−0.0654654
$701$	30.7128	1.16001	0.580003	−	0.814614i	$-0.303051\pi$
$701$	30.7128	1.16001	0.580003	+	0.814614i	$0.303051\pi$
$702$	−0.464102	−0.0175164
$703$	1.48334	0.0559452
$704$	0	0
$705$	6.00000	0.225973
$706$	−20.7846	−0.782239
$707$	−29.1962	−1.09803
$708$	8.19615	0.308030
$709$	22.5885	0.848327	0.424164	−	0.905586i	$-0.360568\pi$
$709$	22.5885	0.848327	0.424164	+	0.905586i	$0.360568\pi$
$710$	13.3923	0.502604
$711$	8.53590	0.320121
$712$	−4.39230	−0.164609
$713$	−0.430781	−0.0161329
$714$	−13.3923	−0.501194
$715$	0	0
$716$	8.19615	0.306305
$717$	−0.803848	−0.0300202
$718$	3.46410	0.129279
$719$	−19.1769	−0.715178	−0.357589	−	0.933879i	$-0.616401\pi$
$719$	−19.1769	−0.715178	−0.357589	+	0.933879i	$0.616401\pi$
$720$	1.00000	0.0372678
$721$	22.5167	0.838564
$722$	−18.7846	−0.699091
$723$	23.1962	0.862674
$724$	−16.5885	−0.616505
$725$	0.464102	0.0172363
$726$	0	0
$727$	26.1769	0.970848	0.485424	−	0.874279i	$-0.338665\pi$
$727$	26.1769	0.970848	0.485424	+	0.874279i	$0.338665\pi$
$728$	−0.803848	−0.0297926
$729$	1.00000	0.0370370
$730$	−4.73205	−0.175141
$731$	9.80385	0.362608
$732$	4.73205	0.174902
$733$	17.0718	0.630561	0.315281	−	0.948998i	$-0.397901\pi$
$733$	17.0718	0.630561	0.315281	+	0.948998i	$0.397901\pi$
$734$	27.3923	1.01107
$735$	4.00000	0.147542
$736$	−2.19615	−0.0809513
$737$	0	0
$738$	−11.6603	−0.429220
$739$	6.46410	0.237786	0.118893	−	0.992907i	$-0.462065\pi$
$739$	6.46410	0.237786	0.118893	+	0.992907i	$0.462065\pi$
$740$	3.19615	0.117493
$741$	−0.215390	−0.00791256
$742$	−14.1962	−0.521157
$743$	45.3731	1.66458	0.832288	−	0.554343i	$-0.187030\pi$
$743$	45.3731	1.66458	0.832288	+	0.554343i	$0.187030\pi$
$744$	−0.196152	−0.00719130
$745$	2.53590	0.0929081
$746$	6.46410	0.236668
$747$	−12.4641	−0.456038
$748$	0	0
$749$	26.7846	0.978688
$750$	−1.00000	−0.0365148
$751$	−7.41154	−0.270451	−0.135226	−	0.990815i	$-0.543176\pi$
$751$	−7.41154	−0.270451	−0.135226	+	0.990815i	$0.543176\pi$
$752$	−6.00000	−0.218797
$753$	−4.39230	−0.160064
$754$	0.215390	0.00784405
$755$	−1.26795	−0.0461454
$756$	1.73205	0.0629941
$757$	−27.1769	−0.987762	−0.493881	−	0.869530i	$-0.664422\pi$
$757$	−27.1769	−0.987762	−0.493881	+	0.869530i	$0.664422\pi$
$758$	35.5885	1.29263
$759$	0	0
$760$	0.464102	0.0168347
$761$	−2.53590	−0.0919262	−0.0459631	−	0.998943i	$-0.514636\pi$
$761$	−2.53590	−0.0919262	−0.0459631	+	0.998943i	$0.514636\pi$
$762$	16.3923	0.593831
$763$	−16.3923	−0.593441
$764$	−15.0000	−0.542681
$765$	−7.73205	−0.279553
$766$	−6.00000	−0.216789
$767$	−3.80385	−0.137349
$768$	−1.00000	−0.0360844
$769$	49.9808	1.80235	0.901176	−	0.433453i	$-0.142705\pi$
$769$	49.9808	1.80235	0.901176	+	0.433453i	$0.142705\pi$
$770$	0	0
$771$	−13.3923	−0.482312
$772$	−9.46410	−0.340620
$773$	−48.5885	−1.74761	−0.873803	−	0.486281i	$-0.838353\pi$
$773$	−48.5885	−1.74761	−0.873803	+	0.486281i	$0.838353\pi$
$774$	−1.26795	−0.0455755
$775$	0.196152	0.00704600
$776$	−0.196152	−0.00704146
$777$	5.53590	0.198599
$778$	−8.78461	−0.314944
$779$	−5.41154	−0.193889
$780$	−0.464102	−0.0166175
$781$	0	0
$782$	16.9808	0.607231
$783$	−0.464102	−0.0165856
$784$	−4.00000	−0.142857
$785$	15.1962	0.542374
$786$	11.6603	0.415907
$787$	29.9090	1.06614	0.533070	−	0.846071i	$-0.321038\pi$
$787$	29.9090	1.06614	0.533070	+	0.846071i	$0.321038\pi$
$788$	11.3205	0.403276
$789$	26.1962	0.932608
$790$	8.53590	0.303694
$791$	0	0
$792$	0	0
$793$	−2.19615	−0.0779877
$794$	−4.80385	−0.170482
$795$	−8.19615	−0.290688
$796$	−12.3923	−0.439234
$797$	−37.7654	−1.33772	−0.668859	−	0.743389i	$-0.733217\pi$
$797$	−37.7654	−1.33772	−0.668859	+	0.743389i	$0.733217\pi$
$798$	0.803848	0.0284559
$799$	46.3923	1.64124
$800$	1.00000	0.0353553
$801$	−4.39230	−0.155194
$802$	36.5885	1.29198
$803$	0	0
$804$	6.39230	0.225439
$805$	3.80385	0.134068
$806$	0.0910347	0.00320656
$807$	−23.1962	−0.816543
$808$	16.8564	0.593006
$809$	−20.4449	−0.718803	−0.359402	−	0.933183i	$-0.617019\pi$
$809$	−20.4449	−0.718803	−0.359402	+	0.933183i	$0.617019\pi$
$810$	1.00000	0.0351364
$811$	27.9282	0.980692	0.490346	−	0.871528i	$-0.336870\pi$
$811$	27.9282	0.980692	0.490346	+	0.871528i	$0.336870\pi$
$812$	−0.803848	−0.0282095
$813$	26.7846	0.939377
$814$	0	0
$815$	−12.1962	−0.427213
$816$	7.73205	0.270676
$817$	−0.588457	−0.0205875
$818$	4.14359	0.144877
$819$	−0.803848	−0.0280887
$820$	−11.6603	−0.407194
$821$	16.3923	0.572095	0.286048	−	0.958215i	$-0.407658\pi$
$821$	16.3923	0.572095	0.286048	+	0.958215i	$0.407658\pi$
$822$	−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
$826$	14.1962	0.493947
$827$	−23.7846	−0.827072	−0.413536	−	0.910488i	$-0.635706\pi$
$827$	−23.7846	−0.827072	−0.413536	+	0.910488i	$0.635706\pi$
$828$	−2.19615	−0.0763216
$829$	44.5885	1.54862	0.774311	−	0.632806i	$-0.218097\pi$
$829$	44.5885	1.54862	0.774311	+	0.632806i	$0.218097\pi$
$830$	−12.4641	−0.432635
$831$	−5.07180	−0.175939
$832$	0.464102	0.0160898
$833$	30.9282	1.07160
$834$	−5.53590	−0.191692
$835$	−9.46410	−0.327519
$836$	0	0
$837$	−0.196152	−0.00678002
$838$	10.3923	0.358996
$839$	−7.39230	−0.255211	−0.127605	−	0.991825i	$-0.540729\pi$
$839$	−7.39230	−0.255211	−0.127605	+	0.991825i	$0.540729\pi$
$840$	1.73205	0.0597614
$841$	−28.7846	−0.992573
$842$	13.8038	0.475712
$843$	8.19615	0.282290
$844$	16.8564	0.580221
$845$	−12.7846	−0.439804
$846$	−6.00000	−0.206284
$847$	0	0
$848$	8.19615	0.281457
$849$	−23.3205	−0.800358
$850$	−7.73205	−0.265207
$851$	−7.01924	−0.240616
$852$	−13.3923	−0.458813
$853$	14.0718	0.481809	0.240905	−	0.970549i	$-0.422556\pi$
$853$	14.0718	0.481809	0.240905	+	0.970549i	$0.422556\pi$
$854$	8.19615	0.280467
$855$	0.464102	0.0158719
$856$	−15.4641	−0.528552
$857$	25.9808	0.887486	0.443743	−	0.896154i	$-0.353650\pi$
$857$	25.9808	0.887486	0.443743	+	0.896154i	$0.353650\pi$
$858$	0	0
$859$	−11.1769	−0.381351	−0.190676	−	0.981653i	$-0.561068\pi$
$859$	−11.1769	−0.381351	−0.190676	+	0.981653i	$0.561068\pi$
$860$	−1.26795	−0.0432367
$861$	−20.1962	−0.688283
$862$	0.124356	0.00423557
$863$	7.17691	0.244305	0.122153	−	0.992511i	$-0.461020\pi$
$863$	7.17691	0.244305	0.122153	+	0.992511i	$0.461020\pi$
$864$	−1.00000	−0.0340207
$865$	6.58846	0.224014
$866$	32.0000	1.08740
$867$	−42.7846	−1.45304
$868$	−0.339746	−0.0115317
$869$	0	0
$870$	−0.464102	−0.0157345
$871$	−2.96668	−0.100522
$872$	9.46410	0.320495
$873$	−0.196152	−0.00663875
$874$	−1.01924	−0.0344762
$875$	−1.73205	−0.0585540
$876$	4.73205	0.159881
$877$	−37.3923	−1.26265	−0.631324	−	0.775519i	$-0.717488\pi$
$877$	−37.3923	−1.26265	−0.631324	+	0.775519i	$0.717488\pi$
$878$	−18.0000	−0.607471
$879$	12.0000	0.404750
$880$	0	0
$881$	12.5885	0.424116	0.212058	−	0.977257i	$-0.431983\pi$
$881$	12.5885	0.424116	0.212058	+	0.977257i	$0.431983\pi$
$882$	−4.00000	−0.134687
$883$	9.41154	0.316724	0.158362	−	0.987381i	$-0.449379\pi$
$883$	9.41154	0.316724	0.158362	+	0.987381i	$0.449379\pi$
$884$	−3.58846	−0.120693
$885$	8.19615	0.275511
$886$	−15.5885	−0.523704
$887$	6.92820	0.232626	0.116313	−	0.993213i	$-0.462892\pi$
$887$	6.92820	0.232626	0.116313	+	0.993213i	$0.462892\pi$
$888$	−3.19615	−0.107256
$889$	28.3923	0.952247
$890$	−4.39230	−0.147230
$891$	0	0
$892$	19.7846	0.662438
$893$	−2.78461	−0.0931834
$894$	−2.53590	−0.0848131
$895$	8.19615	0.273967
$896$	−1.73205	−0.0578638
$897$	1.01924	0.0340314
$898$	22.3923	0.747241
$899$	0.0910347	0.00303618
$900$	1.00000	0.0333333
$901$	−63.3731	−2.11126
$902$	0	0
$903$	−2.19615	−0.0730834
$904$	0	0
$905$	−16.5885	−0.551419
$906$	1.26795	0.0421248
$907$	2.00000	0.0664089	0.0332045	−	0.999449i	$-0.489429\pi$
$907$	2.00000	0.0664089	0.0332045	+	0.999449i	$0.489429\pi$
$908$	−20.5359	−0.681508
$909$	16.8564	0.559092
$910$	−0.803848	−0.0266473
$911$	−1.39230	−0.0461291	−0.0230646	−	0.999734i	$-0.507342\pi$
$911$	−1.39230	−0.0461291	−0.0230646	+	0.999734i	$0.507342\pi$
$912$	−0.464102	−0.0153679
$913$	0	0
$914$	15.1244	0.500269
$915$	4.73205	0.156437
$916$	12.7846	0.422415
$917$	20.1962	0.666936
$918$	7.73205	0.255196
$919$	37.7654	1.24576	0.622882	−	0.782316i	$-0.285962\pi$
$919$	37.7654	1.24576	0.622882	+	0.782316i	$0.285962\pi$
$920$	−2.19615	−0.0724050
$921$	−10.7321	−0.353633
$922$	13.1436	0.432861
$923$	6.21539	0.204582
$924$	0	0
$925$	3.19615	0.105089
$926$	6.39230	0.210064
$927$	−13.0000	−0.426976
$928$	0.464102	0.0152349
$929$	46.9808	1.54139	0.770694	−	0.637205i	$-0.219910\pi$
$929$	46.9808	1.54139	0.770694	+	0.637205i	$0.219910\pi$
$930$	−0.196152	−0.00643209
$931$	−1.85641	−0.0608413
$932$	−25.8564	−0.846955
$933$	32.7846	1.07332
$934$	−33.5885	−1.09905
$935$	0	0
$936$	0.464102	0.0151696
$937$	−16.6410	−0.543638	−0.271819	−	0.962348i	$-0.587625\pi$
$937$	−16.6410	−0.543638	−0.271819	+	0.962348i	$0.587625\pi$
$938$	11.0718	0.361507
$939$	−32.9808	−1.07629
$940$	−6.00000	−0.195698
$941$	−30.0333	−0.979058	−0.489529	−	0.871987i	$-0.662831\pi$
$941$	−30.0333	−0.979058	−0.489529	+	0.871987i	$0.662831\pi$
$942$	−15.1962	−0.495117
$943$	25.6077	0.833901
$944$	−8.19615	−0.266762
$945$	1.73205	0.0563436
$946$	0	0
$947$	41.1962	1.33870	0.669348	−	0.742949i	$-0.266574\pi$
$947$	41.1962	1.33870	0.669348	+	0.742949i	$0.266574\pi$
$948$	−8.53590	−0.277233
$949$	−2.19615	−0.0712901
$950$	0.464102	0.0150574
$951$	−32.1962	−1.04403
$952$	13.3923	0.434047
$953$	9.71281	0.314629	0.157314	−	0.987549i	$-0.449716\pi$
$953$	9.71281	0.314629	0.157314	+	0.987549i	$0.449716\pi$
$954$	8.19615	0.265360
$955$	−15.0000	−0.485389
$956$	0.803848	0.0259983
$957$	0	0
$958$	32.6603	1.05520
$959$	−5.19615	−0.167793
$960$	−1.00000	−0.0322749
$961$	−30.9615	−0.998759
$962$	1.48334	0.0478248
$963$	−15.4641	−0.498324
$964$	−23.1962	−0.747098
$965$	−9.46410	−0.304660
$966$	−3.80385	−0.122387
$967$	−0.248711	−0.00799802	−0.00399901	−	0.999992i	$-0.501273\pi$
$967$	−0.248711	−0.00799802	−0.00399901	+	0.999992i	$0.501273\pi$
$968$	0	0
$969$	3.58846	0.115278
$970$	−0.196152	−0.00629807
$971$	−52.3923	−1.68135	−0.840675	−	0.541541i	$-0.817841\pi$
$971$	−52.3923	−1.68135	−0.840675	+	0.541541i	$0.817841\pi$
$972$	−1.00000	−0.0320750
$973$	−9.58846	−0.307392
$974$	−37.7846	−1.21070
$975$	−0.464102	−0.0148631
$976$	−4.73205	−0.151469
$977$	−35.5692	−1.13796	−0.568980	−	0.822351i	$-0.692662\pi$
$977$	−35.5692	−1.13796	−0.568980	+	0.822351i	$0.692662\pi$
$978$	12.1962	0.389990
$979$	0	0
$980$	−4.00000	−0.127775
$981$	9.46410	0.302166
$982$	−25.2679	−0.806333
$983$	−27.8038	−0.886805	−0.443403	−	0.896323i	$-0.646229\pi$
$983$	−27.8038	−0.886805	−0.443403	+	0.896323i	$0.646229\pi$
$984$	11.6603	0.371715
$985$	11.3205	0.360701
$986$	−3.58846	−0.114280
$987$	−10.3923	−0.330791
$988$	0.215390	0.00685248
$989$	2.78461	0.0885454
$990$	0	0
$991$	39.5692	1.25696	0.628479	−	0.777827i	$-0.283678\pi$
$991$	39.5692	1.25696	0.628479	+	0.777827i	$0.283678\pi$
$992$	0.196152	0.00622785
$993$	−1.19615	−0.0379587
$994$	−23.1962	−0.735737
$995$	−12.3923	−0.392862
$996$	12.4641	0.394940
$997$	−15.9282	−0.504451	−0.252226	−	0.967668i	$-0.581163\pi$
$997$	−15.9282	−0.504451	−0.252226	+	0.967668i	$0.581163\pi$
$998$	−2.80385	−0.0887542
$999$	−3.19615	−0.101122

Twists

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

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

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} -1.73205 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} -1.73205 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -1.00000 q^{12} +0.464102 q^{13} -1.73205 q^{14} -1.00000 q^{15} +1.00000 q^{16} -7.73205 q^{17} +1.00000 q^{18} +0.464102 q^{19} +1.00000 q^{20} +1.73205 q^{21} -2.19615 q^{23} -1.00000 q^{24} +1.00000 q^{25} +0.464102 q^{26} -1.00000 q^{27} -1.73205 q^{28} +0.464102 q^{29} -1.00000 q^{30} +0.196152 q^{31} +1.00000 q^{32} -7.73205 q^{34} -1.73205 q^{35} +1.00000 q^{36} +3.19615 q^{37} +0.464102 q^{38} -0.464102 q^{39} +1.00000 q^{40} -11.6603 q^{41} +1.73205 q^{42} -1.26795 q^{43} +1.00000 q^{45} -2.19615 q^{46} -6.00000 q^{47} -1.00000 q^{48} -4.00000 q^{49} +1.00000 q^{50} +7.73205 q^{51} +0.464102 q^{52} +8.19615 q^{53} -1.00000 q^{54} -1.73205 q^{56} -0.464102 q^{57} +0.464102 q^{58} -8.19615 q^{59} -1.00000 q^{60} -4.73205 q^{61} +0.196152 q^{62} -1.73205 q^{63} +1.00000 q^{64} +0.464102 q^{65} -6.39230 q^{67} -7.73205 q^{68} +2.19615 q^{69} -1.73205 q^{70} +13.3923 q^{71} +1.00000 q^{72} -4.73205 q^{73} +3.19615 q^{74} -1.00000 q^{75} +0.464102 q^{76} -0.464102 q^{78} +8.53590 q^{79} +1.00000 q^{80} +1.00000 q^{81} -11.6603 q^{82} -12.4641 q^{83} +1.73205 q^{84} -7.73205 q^{85} -1.26795 q^{86} -0.464102 q^{87} -4.39230 q^{89} +1.00000 q^{90} -0.803848 q^{91} -2.19615 q^{92} -0.196152 q^{93} -6.00000 q^{94} +0.464102 q^{95} -1.00000 q^{96} -0.196152 q^{97} -4.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} - 2 q^{6} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 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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