LMFDB - Embedded newform 3630.2.a.bk.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:	$0$
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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} +1.73205 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} +1.73205 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -1.00000 q^{12} -3.00000 q^{13} +1.73205 q^{14} +1.00000 q^{15} +1.00000 q^{16} +1.73205 q^{17} +1.00000 q^{18} +3.00000 q^{19} -1.00000 q^{20} -1.73205 q^{21} +2.19615 q^{23} -1.00000 q^{24} +1.00000 q^{25} -3.00000 q^{26} -1.00000 q^{27} +1.73205 q^{28} -0.464102 q^{29} +1.00000 q^{30} -4.19615 q^{31} +1.00000 q^{32} +1.73205 q^{34} -1.73205 q^{35} +1.00000 q^{36} +9.19615 q^{37} +3.00000 q^{38} +3.00000 q^{39} -1.00000 q^{40} +7.26795 q^{41} -1.73205 q^{42} -8.19615 q^{43} -1.00000 q^{45} +2.19615 q^{46} +6.00000 q^{47} -1.00000 q^{48} -4.00000 q^{49} +1.00000 q^{50} -1.73205 q^{51} -3.00000 q^{52} -8.19615 q^{53} -1.00000 q^{54} +1.73205 q^{56} -3.00000 q^{57} -0.464102 q^{58} +3.80385 q^{59} +1.00000 q^{60} +11.6603 q^{61} -4.19615 q^{62} +1.73205 q^{63} +1.00000 q^{64} +3.00000 q^{65} +14.3923 q^{67} +1.73205 q^{68} -2.19615 q^{69} -1.73205 q^{70} +3.00000 q^{71} +1.00000 q^{72} -4.73205 q^{73} +9.19615 q^{74} -1.00000 q^{75} +3.00000 q^{76} +3.00000 q^{78} -10.3923 q^{79} -1.00000 q^{80} +1.00000 q^{81} +7.26795 q^{82} +6.46410 q^{83} -1.73205 q^{84} -1.73205 q^{85} -8.19615 q^{86} +0.464102 q^{87} +4.39230 q^{89} -1.00000 q^{90} -5.19615 q^{91} +2.19615 q^{92} +4.19615 q^{93} +6.00000 q^{94} -3.00000 q^{95} -1.00000 q^{96} -0.196152 q^{97} -4.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} + 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} + 2 q^{31} + 2 q^{32} + 2 q^{36} + 8 q^{37} + 6 q^{38} + 6 q^{39} - 2 q^{40} + 18 q^{41} - 6 q^{43} - 2 q^{45} - 6 q^{46} + 12 q^{47} - 2 q^{48} - 8 q^{49} + 2 q^{50} - 6 q^{52} - 6 q^{53} - 2 q^{54} - 6 q^{57} + 6 q^{58} + 18 q^{59} + 2 q^{60} + 6 q^{61} + 2 q^{62} + 2 q^{64} + 6 q^{65} + 8 q^{67} + 6 q^{69} + 6 q^{71} + 2 q^{72} - 6 q^{73} + 8 q^{74} - 2 q^{75} + 6 q^{76} + 6 q^{78} - 2 q^{80} + 2 q^{81} + 18 q^{82} + 6 q^{83} - 6 q^{86} - 6 q^{87} - 12 q^{89} - 2 q^{90} - 6 q^{92} - 2 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 + 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 + 2 * q^31 + 2 * q^32 + 2 * q^36 + 8 * q^37 + 6 * q^38 + 6 * q^39 - 2 * q^40 + 18 * q^41 - 6 * q^43 - 2 * q^45 - 6 * q^46 + 12 * q^47 - 2 * q^48 - 8 * q^49 + 2 * q^50 - 6 * q^52 - 6 * q^53 - 2 * q^54 - 6 * q^57 + 6 * q^58 + 18 * q^59 + 2 * q^60 + 6 * q^61 + 2 * q^62 + 2 * q^64 + 6 * q^65 + 8 * q^67 + 6 * q^69 + 6 * q^71 + 2 * q^72 - 6 * q^73 + 8 * q^74 - 2 * q^75 + 6 * q^76 + 6 * q^78 - 2 * q^80 + 2 * q^81 + 18 * q^82 + 6 * q^83 - 6 * q^86 - 6 * q^87 - 12 * q^89 - 2 * q^90 - 6 * q^92 - 2 * 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
$13$	−3.00000	−0.832050	−0.416025	−	0.909353i	$-0.636577\pi$
$13$	−3.00000	−0.832050	−0.416025	+	0.909353i	$0.636577\pi$
$14$	1.73205	0.462910
$15$	1.00000	0.258199
$16$	1.00000	0.250000
$17$	1.73205	0.420084	0.210042	−	0.977692i	$-0.432640\pi$
$17$	1.73205	0.420084	0.210042	+	0.977692i	$0.432640\pi$
$18$	1.00000	0.235702
$19$	3.00000	0.688247	0.344124	−	0.938924i	$-0.388176\pi$
$19$	3.00000	0.688247	0.344124	+	0.938924i	$0.388176\pi$
$20$	−1.00000	−0.223607
$21$	−1.73205	−0.377964
$22$	0	0
$23$	2.19615	0.457929	0.228965	−	0.973435i	$-0.426466\pi$
$23$	2.19615	0.457929	0.228965	+	0.973435i	$0.426466\pi$
$24$	−1.00000	−0.204124
$25$	1.00000	0.200000
$26$	−3.00000	−0.588348
$27$	−1.00000	−0.192450
$28$	1.73205	0.327327
$29$	−0.464102	−0.0861815	−0.0430908	−	0.999071i	$-0.513720\pi$
$29$	−0.464102	−0.0861815	−0.0430908	+	0.999071i	$0.513720\pi$
$30$	1.00000	0.182574
$31$	−4.19615	−0.753651	−0.376826	−	0.926284i	$-0.622984\pi$
$31$	−4.19615	−0.753651	−0.376826	+	0.926284i	$0.622984\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	1.73205	0.297044
$35$	−1.73205	−0.292770
$36$	1.00000	0.166667
$37$	9.19615	1.51184	0.755919	−	0.654665i	$-0.227190\pi$
$37$	9.19615	1.51184	0.755919	+	0.654665i	$0.227190\pi$
$38$	3.00000	0.486664
$39$	3.00000	0.480384
$40$	−1.00000	−0.158114
$41$	7.26795	1.13506	0.567531	−	0.823352i	$-0.307899\pi$
$41$	7.26795	1.13506	0.567531	+	0.823352i	$0.307899\pi$
$42$	−1.73205	−0.267261
$43$	−8.19615	−1.24990	−0.624951	−	0.780664i	$-0.714881\pi$
$43$	−8.19615	−1.24990	−0.624951	+	0.780664i	$0.714881\pi$
$44$	0	0
$45$	−1.00000	−0.149071
$46$	2.19615	0.323805
$47$	6.00000	0.875190	0.437595	−	0.899172i	$-0.355830\pi$
$47$	6.00000	0.875190	0.437595	+	0.899172i	$0.355830\pi$
$48$	−1.00000	−0.144338
$49$	−4.00000	−0.571429
$50$	1.00000	0.141421
$51$	−1.73205	−0.242536
$52$	−3.00000	−0.416025
$53$	−8.19615	−1.12583	−0.562914	−	0.826515i	$-0.690320\pi$
$53$	−8.19615	−1.12583	−0.562914	+	0.826515i	$0.690320\pi$
$54$	−1.00000	−0.136083
$55$	0	0
$56$	1.73205	0.231455
$57$	−3.00000	−0.397360
$58$	−0.464102	−0.0609395
$59$	3.80385	0.495219	0.247609	−	0.968860i	$-0.420355\pi$
$59$	3.80385	0.495219	0.247609	+	0.968860i	$0.420355\pi$
$60$	1.00000	0.129099
$61$	11.6603	1.49294	0.746471	−	0.665418i	$-0.231747\pi$
$61$	11.6603	1.49294	0.746471	+	0.665418i	$0.231747\pi$
$62$	−4.19615	−0.532912
$63$	1.73205	0.218218
$64$	1.00000	0.125000
$65$	3.00000	0.372104
$66$	0	0
$67$	14.3923	1.75830	0.879150	−	0.476545i	$-0.158111\pi$
$67$	14.3923	1.75830	0.879150	+	0.476545i	$0.158111\pi$
$68$	1.73205	0.210042
$69$	−2.19615	−0.264386
$70$	−1.73205	−0.207020
$71$	3.00000	0.356034	0.178017	−	0.984027i	$-0.443032\pi$
$71$	3.00000	0.356034	0.178017	+	0.984027i	$0.443032\pi$
$72$	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	$0.589314\pi$
$74$	9.19615	1.06903
$75$	−1.00000	−0.115470
$76$	3.00000	0.344124
$77$	0	0
$78$	3.00000	0.339683
$79$	−10.3923	−1.16923	−0.584613	−	0.811312i	$-0.698754\pi$
$79$	−10.3923	−1.16923	−0.584613	+	0.811312i	$0.698754\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	7.26795	0.802611
$83$	6.46410	0.709527	0.354764	−	0.934956i	$-0.384561\pi$
$83$	6.46410	0.709527	0.354764	+	0.934956i	$0.384561\pi$
$84$	−1.73205	−0.188982
$85$	−1.73205	−0.187867
$86$	−8.19615	−0.883814
$87$	0.464102	0.0497569
$88$	0	0
$89$	4.39230	0.465583	0.232792	−	0.972527i	$-0.425214\pi$
$89$	4.39230	0.465583	0.232792	+	0.972527i	$0.425214\pi$
$90$	−1.00000	−0.105409
$91$	−5.19615	−0.544705
$92$	2.19615	0.228965
$93$	4.19615	0.435121
$94$	6.00000	0.618853
$95$	−3.00000	−0.307794
$96$	−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
$101$	15.9282	1.58492	0.792458	−	0.609927i	$-0.208801\pi$
$101$	15.9282	1.58492	0.792458	+	0.609927i	$0.208801\pi$
$102$	−1.73205	−0.171499
$103$	5.00000	0.492665	0.246332	−	0.969185i	$-0.420775\pi$
$103$	5.00000	0.492665	0.246332	+	0.969185i	$0.420775\pi$
$104$	−3.00000	−0.294174
$105$	1.73205	0.169031
$106$	−8.19615	−0.796081
$107$	3.46410	0.334887	0.167444	−	0.985882i	$-0.446449\pi$
$107$	3.46410	0.334887	0.167444	+	0.985882i	$0.446449\pi$
$108$	−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
$111$	−9.19615	−0.872860
$112$	1.73205	0.163663
$113$	0	0		−	1.00000i	$-0.5\pi$
$113$	0	0			1.00000i	$0.5\pi$
$114$	−3.00000	−0.280976
$115$	−2.19615	−0.204792
$116$	−0.464102	−0.0430908
$117$	−3.00000	−0.277350
$118$	3.80385	0.350173
$119$	3.00000	0.275010
$120$	1.00000	0.0912871
$121$	0	0
$122$	11.6603	1.05567
$123$	−7.26795	−0.655329
$124$	−4.19615	−0.376826
$125$	−1.00000	−0.0894427
$126$	1.73205	0.154303
$127$	2.53590	0.225025	0.112512	−	0.993650i	$-0.464110\pi$
$127$	2.53590	0.225025	0.112512	+	0.993650i	$0.464110\pi$
$128$	1.00000	0.0883883
$129$	8.19615	0.721631
$130$	3.00000	0.263117
$131$	7.26795	0.635004	0.317502	−	0.948258i	$-0.397156\pi$
$131$	7.26795	0.635004	0.317502	+	0.948258i	$0.397156\pi$
$132$	0	0
$133$	5.19615	0.450564
$134$	14.3923	1.24331
$135$	1.00000	0.0860663
$136$	1.73205	0.148522
$137$	−13.3923	−1.14418	−0.572091	−	0.820190i	$-0.693868\pi$
$137$	−13.3923	−1.14418	−0.572091	+	0.820190i	$0.693868\pi$
$138$	−2.19615	−0.186949
$139$	16.8564	1.42974	0.714871	−	0.699256i	$-0.246485\pi$
$139$	16.8564	1.42974	0.714871	+	0.699256i	$0.246485\pi$
$140$	−1.73205	−0.146385
$141$	−6.00000	−0.505291
$142$	3.00000	0.251754
$143$	0	0
$144$	1.00000	0.0833333
$145$	0.464102	0.0385415
$146$	−4.73205	−0.391627
$147$	4.00000	0.329914
$148$	9.19615	0.755919
$149$	21.4641	1.75841	0.879204	−	0.476446i	$-0.158075\pi$
$149$	21.4641	1.75841	0.879204	+	0.476446i	$0.158075\pi$
$150$	−1.00000	−0.0816497
$151$	−5.66025	−0.460625	−0.230312	−	0.973117i	$-0.573975\pi$
$151$	−5.66025	−0.460625	−0.230312	+	0.973117i	$0.573975\pi$
$152$	3.00000	0.243332
$153$	1.73205	0.140028
$154$	0	0
$155$	4.19615	0.337043
$156$	3.00000	0.240192
$157$	−11.5885	−0.924860	−0.462430	−	0.886656i	$-0.653022\pi$
$157$	−11.5885	−0.924860	−0.462430	+	0.886656i	$0.653022\pi$
$158$	−10.3923	−0.826767
$159$	8.19615	0.649997
$160$	−1.00000	−0.0790569
$161$	3.80385	0.299785
$162$	1.00000	0.0785674
$163$	−0.196152	−0.0153638	−0.00768192	−	0.999970i	$-0.502445\pi$
$163$	−0.196152	−0.0153638	−0.00768192	+	0.999970i	$0.502445\pi$
$164$	7.26795	0.567531
$165$	0	0
$166$	6.46410	0.501712
$167$	−11.3205	−0.876007	−0.438004	−	0.898973i	$-0.644314\pi$
$167$	−11.3205	−0.876007	−0.438004	+	0.898973i	$0.644314\pi$
$168$	−1.73205	−0.133631
$169$	−4.00000	−0.307692
$170$	−1.73205	−0.132842
$171$	3.00000	0.229416
$172$	−8.19615	−0.624951
$173$	14.1962	1.07931	0.539657	−	0.841885i	$-0.318554\pi$
$173$	14.1962	1.07931	0.539657	+	0.841885i	$0.318554\pi$
$174$	0.464102	0.0351835
$175$	1.73205	0.130931
$176$	0	0
$177$	−3.80385	−0.285915
$178$	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
$181$	8.58846	0.638375	0.319188	−	0.947692i	$-0.396590\pi$
$181$	8.58846	0.638375	0.319188	+	0.947692i	$0.396590\pi$
$182$	−5.19615	−0.385164
$183$	−11.6603	−0.861951
$184$	2.19615	0.161903
$185$	−9.19615	−0.676115
$186$	4.19615	0.307677
$187$	0	0
$188$	6.00000	0.437595
$189$	−1.73205	−0.125988
$190$	−3.00000	−0.217643
$191$	7.39230	0.534888	0.267444	−	0.963573i	$-0.413821\pi$
$191$	7.39230	0.534888	0.267444	+	0.963573i	$0.413821\pi$
$192$	−1.00000	−0.0721688
$193$	2.53590	0.182538	0.0912690	−	0.995826i	$-0.470908\pi$
$193$	2.53590	0.182538	0.0912690	+	0.995826i	$0.470908\pi$
$194$	−0.196152	−0.0140829
$195$	−3.00000	−0.214834
$196$	−4.00000	−0.285714
$197$	9.46410	0.674289	0.337145	−	0.941453i	$-0.390539\pi$
$197$	9.46410	0.674289	0.337145	+	0.941453i	$0.390539\pi$
$198$	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
$201$	−14.3923	−1.01515
$202$	15.9282	1.12070
$203$	−0.803848	−0.0564190
$204$	−1.73205	−0.121268
$205$	−7.26795	−0.507616
$206$	5.00000	0.348367
$207$	2.19615	0.152643
$208$	−3.00000	−0.208013
$209$	0	0
$210$	1.73205	0.119523
$211$	−18.4641	−1.27112	−0.635561	−	0.772051i	$-0.719231\pi$
$211$	−18.4641	−1.27112	−0.635561	+	0.772051i	$0.719231\pi$
$212$	−8.19615	−0.562914
$213$	−3.00000	−0.205557
$214$	3.46410	0.236801
$215$	8.19615	0.558973
$216$	−1.00000	−0.0680414
$217$	−7.26795	−0.493381
$218$	2.53590	0.171753
$219$	4.73205	0.319762
$220$	0	0
$221$	−5.19615	−0.349531
$222$	−9.19615	−0.617205
$223$	−27.7846	−1.86060	−0.930298	−	0.366806i	$-0.880451\pi$
$223$	−27.7846	−1.86060	−0.930298	+	0.366806i	$0.880451\pi$
$224$	1.73205	0.115728
$225$	1.00000	0.0666667
$226$	0	0
$227$	17.3205	1.14960	0.574801	−	0.818293i	$-0.305079\pi$
$227$	17.3205	1.14960	0.574801	+	0.818293i	$0.305079\pi$
$228$	−3.00000	−0.198680
$229$	24.7846	1.63781	0.818907	−	0.573927i	$-0.194581\pi$
$229$	24.7846	1.63781	0.818907	+	0.573927i	$0.194581\pi$
$230$	−2.19615	−0.144810
$231$	0	0
$232$	−0.464102	−0.0304698
$233$	−6.92820	−0.453882	−0.226941	−	0.973909i	$-0.572872\pi$
$233$	−6.92820	−0.453882	−0.226941	+	0.973909i	$0.572872\pi$
$234$	−3.00000	−0.196116
$235$	−6.00000	−0.391397
$236$	3.80385	0.247609
$237$	10.3923	0.675053
$238$	3.00000	0.194461
$239$	18.8038	1.21632	0.608160	−	0.793815i	$-0.291908\pi$
$239$	18.8038	1.21632	0.608160	+	0.793815i	$0.291908\pi$
$240$	1.00000	0.0645497
$241$	−13.0526	−0.840789	−0.420395	−	0.907341i	$-0.638108\pi$
$241$	−13.0526	−0.840789	−0.420395	+	0.907341i	$0.638108\pi$
$242$	0	0
$243$	−1.00000	−0.0641500
$244$	11.6603	0.746471
$245$	4.00000	0.255551
$246$	−7.26795	−0.463388
$247$	−9.00000	−0.572656
$248$	−4.19615	−0.266456
$249$	−6.46410	−0.409646
$250$	−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
$254$	2.53590	0.159116
$255$	1.73205	0.108465
$256$	1.00000	0.0625000
$257$	29.7846	1.85791	0.928956	−	0.370189i	$-0.120707\pi$
$257$	29.7846	1.85791	0.928956	+	0.370189i	$0.120707\pi$
$258$	8.19615	0.510270
$259$	15.9282	0.989730
$260$	3.00000	0.186052
$261$	−0.464102	−0.0287272
$262$	7.26795	0.449015
$263$	2.19615	0.135421	0.0677103	−	0.997705i	$-0.478431\pi$
$263$	2.19615	0.135421	0.0677103	+	0.997705i	$0.478431\pi$
$264$	0	0
$265$	8.19615	0.503486
$266$	5.19615	0.318597
$267$	−4.39230	−0.268805
$268$	14.3923	0.879150
$269$	0.803848	0.0490115	0.0245057	−	0.999700i	$-0.492199\pi$
$269$	0.803848	0.0490115	0.0245057	+	0.999700i	$0.492199\pi$
$270$	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	$0.351762\pi$
$272$	1.73205	0.105021
$273$	5.19615	0.314485
$274$	−13.3923	−0.809059
$275$	0	0
$276$	−2.19615	−0.132193
$277$	0	0		−	1.00000i	$-0.5\pi$
$277$	0	0			1.00000i	$0.5\pi$
$278$	16.8564	1.01098
$279$	−4.19615	−0.251217
$280$	−1.73205	−0.103510
$281$	12.5885	0.750964	0.375482	−	0.926830i	$-0.377477\pi$
$281$	12.5885	0.750964	0.375482	+	0.926830i	$0.377477\pi$
$282$	−6.00000	−0.357295
$283$	28.3923	1.68775	0.843874	−	0.536542i	$-0.180270\pi$
$283$	28.3923	1.68775	0.843874	+	0.536542i	$0.180270\pi$
$284$	3.00000	0.178017
$285$	3.00000	0.177705
$286$	0	0
$287$	12.5885	0.743073
$288$	1.00000	0.0589256
$289$	−14.0000	−0.823529
$290$	0.464102	0.0272530
$291$	0.196152	0.0114987
$292$	−4.73205	−0.276922
$293$	24.0000	1.40209	0.701047	−	0.713115i	$-0.252716\pi$
$293$	24.0000	1.40209	0.701047	+	0.713115i	$0.252716\pi$
$294$	4.00000	0.233285
$295$	−3.80385	−0.221469
$296$	9.19615	0.534516
$297$	0	0
$298$	21.4641	1.24338
$299$	−6.58846	−0.381020
$300$	−1.00000	−0.0577350
$301$	−14.1962	−0.818253
$302$	−5.66025	−0.325711
$303$	−15.9282	−0.915051
$304$	3.00000	0.172062
$305$	−11.6603	−0.667664
$306$	1.73205	0.0990148
$307$	22.7321	1.29739	0.648693	−	0.761050i	$-0.275316\pi$
$307$	22.7321	1.29739	0.648693	+	0.761050i	$0.275316\pi$
$308$	0	0
$309$	−5.00000	−0.284440
$310$	4.19615	0.238325
$311$	0	0		−	1.00000i	$-0.5\pi$
$311$	0	0			1.00000i	$0.5\pi$
$312$	3.00000	0.169842
$313$	−11.8038	−0.667193	−0.333596	−	0.942716i	$-0.608262\pi$
$313$	−11.8038	−0.667193	−0.333596	+	0.942716i	$0.608262\pi$
$314$	−11.5885	−0.653974
$315$	−1.73205	−0.0975900
$316$	−10.3923	−0.584613
$317$	−28.9808	−1.62772	−0.813861	−	0.581060i	$-0.802638\pi$
$317$	−28.9808	−1.62772	−0.813861	+	0.581060i	$0.802638\pi$
$318$	8.19615	0.459617
$319$	0	0
$320$	−1.00000	−0.0559017
$321$	−3.46410	−0.193347
$322$	3.80385	0.211980
$323$	5.19615	0.289122
$324$	1.00000	0.0555556
$325$	−3.00000	−0.166410
$326$	−0.196152	−0.0108639
$327$	−2.53590	−0.140236
$328$	7.26795	0.401305
$329$	10.3923	0.572946
$330$	0	0
$331$	5.58846	0.307169	0.153585	−	0.988135i	$-0.450918\pi$
$331$	5.58846	0.307169	0.153585	+	0.988135i	$0.450918\pi$
$332$	6.46410	0.354764
$333$	9.19615	0.503946
$334$	−11.3205	−0.619431
$335$	−14.3923	−0.786336
$336$	−1.73205	−0.0944911
$337$	−2.87564	−0.156646	−0.0783232	−	0.996928i	$-0.524957\pi$
$337$	−2.87564	−0.156646	−0.0783232	+	0.996928i	$0.524957\pi$
$338$	−4.00000	−0.217571
$339$	0	0
$340$	−1.73205	−0.0939336
$341$	0	0
$342$	3.00000	0.162221
$343$	−19.0526	−1.02874
$344$	−8.19615	−0.441907
$345$	2.19615	0.118237
$346$	14.1962	0.763190
$347$	−33.2487	−1.78488	−0.892442	−	0.451162i	$-0.851010\pi$
$347$	−33.2487	−1.78488	−0.892442	+	0.451162i	$0.851010\pi$
$348$	0.464102	0.0248785
$349$	−14.7846	−0.791402	−0.395701	−	0.918379i	$-0.629498\pi$
$349$	−14.7846	−0.791402	−0.395701	+	0.918379i	$0.629498\pi$
$350$	1.73205	0.0925820
$351$	3.00000	0.160128
$352$	0	0
$353$	−36.0000	−1.91609	−0.958043	−	0.286623i	$-0.907467\pi$
$353$	−36.0000	−1.91609	−0.958043	+	0.286623i	$0.907467\pi$
$354$	−3.80385	−0.202172
$355$	−3.00000	−0.159223
$356$	4.39230	0.232792
$357$	−3.00000	−0.158777
$358$	8.19615	0.433180
$359$	20.5359	1.08384	0.541922	−	0.840429i	$-0.317697\pi$
$359$	20.5359	1.08384	0.541922	+	0.840429i	$0.317697\pi$
$360$	−1.00000	−0.0527046
$361$	−10.0000	−0.526316
$362$	8.58846	0.451399
$363$	0	0
$364$	−5.19615	−0.272352
$365$	4.73205	0.247687
$366$	−11.6603	−0.609491
$367$	30.1769	1.57522	0.787611	−	0.616173i	$-0.211318\pi$
$367$	30.1769	1.57522	0.787611	+	0.616173i	$0.211318\pi$
$368$	2.19615	0.114482
$369$	7.26795	0.378354
$370$	−9.19615	−0.478085
$371$	−14.1962	−0.737028
$372$	4.19615	0.217560
$373$	−14.0718	−0.728610	−0.364305	−	0.931280i	$-0.618693\pi$
$373$	−14.0718	−0.728610	−0.364305	+	0.931280i	$0.618693\pi$
$374$	0	0
$375$	1.00000	0.0516398
$376$	6.00000	0.309426
$377$	1.39230	0.0717073
$378$	−1.73205	−0.0890871
$379$	15.9808	0.820877	0.410438	−	0.911888i	$-0.365376\pi$
$379$	15.9808	0.820877	0.410438	+	0.911888i	$0.365376\pi$
$380$	−3.00000	−0.153897
$381$	−2.53590	−0.129918
$382$	7.39230	0.378223
$383$	−26.7846	−1.36863	−0.684315	−	0.729187i	$-0.739899\pi$
$383$	−26.7846	−1.36863	−0.684315	+	0.729187i	$0.739899\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	2.53590	0.129074
$387$	−8.19615	−0.416634
$388$	−0.196152	−0.00995813
$389$	−32.7846	−1.66225	−0.831123	−	0.556089i	$-0.812301\pi$
$389$	−32.7846	−1.66225	−0.831123	+	0.556089i	$0.812301\pi$
$390$	−3.00000	−0.151911
$391$	3.80385	0.192369
$392$	−4.00000	−0.202031
$393$	−7.26795	−0.366620
$394$	9.46410	0.476795
$395$	10.3923	0.522894
$396$	0	0
$397$	−7.58846	−0.380854	−0.190427	−	0.981701i	$-0.560987\pi$
$397$	−7.58846	−0.380854	−0.190427	+	0.981701i	$0.560987\pi$
$398$	−12.3923	−0.621170
$399$	−5.19615	−0.260133
$400$	1.00000	0.0500000
$401$	−8.19615	−0.409296	−0.204648	−	0.978836i	$-0.565605\pi$
$401$	−8.19615	−0.409296	−0.204648	+	0.978836i	$0.565605\pi$
$402$	−14.3923	−0.717823
$403$	12.5885	0.627076
$404$	15.9282	0.792458
$405$	−1.00000	−0.0496904
$406$	−0.803848	−0.0398943
$407$	0	0
$408$	−1.73205	−0.0857493
$409$	−0.928203	−0.0458967	−0.0229483	−	0.999737i	$-0.507305\pi$
$409$	−0.928203	−0.0458967	−0.0229483	+	0.999737i	$0.507305\pi$
$410$	−7.26795	−0.358938
$411$	13.3923	0.660594
$412$	5.00000	0.246332
$413$	6.58846	0.324197
$414$	2.19615	0.107935
$415$	−6.46410	−0.317310
$416$	−3.00000	−0.147087
$417$	−16.8564	−0.825462
$418$	0	0
$419$	1.60770	0.0785410	0.0392705	−	0.999229i	$-0.487497\pi$
$419$	1.60770	0.0785410	0.0392705	+	0.999229i	$0.487497\pi$
$420$	1.73205	0.0845154
$421$	−29.8038	−1.45255	−0.726275	−	0.687404i	$-0.758750\pi$
$421$	−29.8038	−1.45255	−0.726275	+	0.687404i	$0.758750\pi$
$422$	−18.4641	−0.898818
$423$	6.00000	0.291730
$424$	−8.19615	−0.398040
$425$	1.73205	0.0840168
$426$	−3.00000	−0.145350
$427$	20.1962	0.977360
$428$	3.46410	0.167444
$429$	0	0
$430$	8.19615	0.395254
$431$	37.0526	1.78476	0.892379	−	0.451286i	$-0.149034\pi$
$431$	37.0526	1.78476	0.892379	+	0.451286i	$0.149034\pi$
$432$	−1.00000	−0.0481125
$433$	−36.7846	−1.76776	−0.883878	−	0.467718i	$-0.845076\pi$
$433$	−36.7846	−1.76776	−0.883878	+	0.467718i	$0.845076\pi$
$434$	−7.26795	−0.348873
$435$	−0.464102	−0.0222520
$436$	2.53590	0.121448
$437$	6.58846	0.315169
$438$	4.73205	0.226106
$439$	26.7846	1.27836	0.639180	−	0.769057i	$-0.279274\pi$
$439$	26.7846	1.27836	0.639180	+	0.769057i	$0.279274\pi$
$440$	0	0
$441$	−4.00000	−0.190476
$442$	−5.19615	−0.247156
$443$	25.9808	1.23438	0.617192	−	0.786813i	$-0.288270\pi$
$443$	25.9808	1.23438	0.617192	+	0.786813i	$0.288270\pi$
$444$	−9.19615	−0.436430
$445$	−4.39230	−0.208215
$446$	−27.7846	−1.31564
$447$	−21.4641	−1.01522
$448$	1.73205	0.0818317
$449$	−34.3923	−1.62307	−0.811537	−	0.584302i	$-0.801369\pi$
$449$	−34.3923	−1.62307	−0.811537	+	0.584302i	$0.801369\pi$
$450$	1.00000	0.0471405
$451$	0	0
$452$	0	0
$453$	5.66025	0.265942
$454$	17.3205	0.812892
$455$	5.19615	0.243599
$456$	−3.00000	−0.140488
$457$	−22.7321	−1.06336	−0.531680	−	0.846945i	$-0.678439\pi$
$457$	−22.7321	−1.06336	−0.531680	+	0.846945i	$0.678439\pi$
$458$	24.7846	1.15811
$459$	−1.73205	−0.0808452
$460$	−2.19615	−0.102396
$461$	−21.9282	−1.02130	−0.510649	−	0.859789i	$-0.670595\pi$
$461$	−21.9282	−1.02130	−0.510649	+	0.859789i	$0.670595\pi$
$462$	0	0
$463$	−14.3923	−0.668867	−0.334434	−	0.942419i	$-0.608545\pi$
$463$	−14.3923	−0.668867	−0.334434	+	0.942419i	$0.608545\pi$
$464$	−0.464102	−0.0215454
$465$	−4.19615	−0.194592
$466$	−6.92820	−0.320943
$467$	−42.3731	−1.96079	−0.980396	−	0.197038i	$-0.936868\pi$
$467$	−42.3731	−1.96079	−0.980396	+	0.197038i	$0.936868\pi$
$468$	−3.00000	−0.138675
$469$	24.9282	1.15108
$470$	−6.00000	−0.276759
$471$	11.5885	0.533968
$472$	3.80385	0.175086
$473$	0	0
$474$	10.3923	0.477334
$475$	3.00000	0.137649
$476$	3.00000	0.137505
$477$	−8.19615	−0.375276
$478$	18.8038	0.860068
$479$	−4.26795	−0.195008	−0.0975038	−	0.995235i	$-0.531086\pi$
$479$	−4.26795	−0.195008	−0.0975038	+	0.995235i	$0.531086\pi$
$480$	1.00000	0.0456435
$481$	−27.5885	−1.25793
$482$	−13.0526	−0.594528
$483$	−3.80385	−0.173081
$484$	0	0
$485$	0.196152	0.00890682
$486$	−1.00000	−0.0453609
$487$	−11.0000	−0.498458	−0.249229	−	0.968445i	$-0.580177\pi$
$487$	−11.0000	−0.498458	−0.249229	+	0.968445i	$0.580177\pi$
$488$	11.6603	0.527835
$489$	0.196152	0.00887032
$490$	4.00000	0.180702
$491$	8.87564	0.400552	0.200276	−	0.979739i	$-0.435816\pi$
$491$	8.87564	0.400552	0.200276	+	0.979739i	$0.435816\pi$
$492$	−7.26795	−0.327664
$493$	−0.803848	−0.0362035
$494$	−9.00000	−0.404929
$495$	0	0
$496$	−4.19615	−0.188413
$497$	5.19615	0.233079
$498$	−6.46410	−0.289663
$499$	−15.9808	−0.715397	−0.357699	−	0.933837i	$-0.616438\pi$
$499$	−15.9808	−0.715397	−0.357699	+	0.933837i	$0.616438\pi$
$500$	−1.00000	−0.0447214
$501$	11.3205	0.505763
$502$	−16.3923	−0.731624
$503$	1.26795	0.0565351	0.0282675	−	0.999600i	$-0.491001\pi$
$503$	1.26795	0.0565351	0.0282675	+	0.999600i	$0.491001\pi$
$504$	1.73205	0.0771517
$505$	−15.9282	−0.708796
$506$	0	0
$507$	4.00000	0.177646
$508$	2.53590	0.112512
$509$	38.7846	1.71910	0.859549	−	0.511054i	$-0.170745\pi$
$509$	38.7846	1.71910	0.859549	+	0.511054i	$0.170745\pi$
$510$	1.73205	0.0766965
$511$	−8.19615	−0.362576
$512$	1.00000	0.0441942
$513$	−3.00000	−0.132453
$514$	29.7846	1.31374
$515$	−5.00000	−0.220326
$516$	8.19615	0.360815
$517$	0	0
$518$	15.9282	0.699845
$519$	−14.1962	−0.623142
$520$	3.00000	0.131559
$521$	−21.8038	−0.955244	−0.477622	−	0.878565i	$-0.658501\pi$
$521$	−21.8038	−0.955244	−0.477622	+	0.878565i	$0.658501\pi$
$522$	−0.464102	−0.0203132
$523$	−9.12436	−0.398980	−0.199490	−	0.979900i	$-0.563929\pi$
$523$	−9.12436	−0.398980	−0.199490	+	0.979900i	$0.563929\pi$
$524$	7.26795	0.317502
$525$	−1.73205	−0.0755929
$526$	2.19615	0.0957568
$527$	−7.26795	−0.316597
$528$	0	0
$529$	−18.1769	−0.790301
$530$	8.19615	0.356018
$531$	3.80385	0.165073
$532$	5.19615	0.225282
$533$	−21.8038	−0.944429
$534$	−4.39230	−0.190074
$535$	−3.46410	−0.149766
$536$	14.3923	0.621653
$537$	−8.19615	−0.353690
$538$	0.803848	0.0346563
$539$	0	0
$540$	1.00000	0.0430331
$541$	−11.4115	−0.490621	−0.245310	−	0.969445i	$-0.578890\pi$
$541$	−11.4115	−0.490621	−0.245310	+	0.969445i	$0.578890\pi$
$542$	14.7846	0.635053
$543$	−8.58846	−0.368566
$544$	1.73205	0.0742611
$545$	−2.53590	−0.108626
$546$	5.19615	0.222375
$547$	−42.0000	−1.79579	−0.897895	−	0.440209i	$-0.854904\pi$
$547$	−42.0000	−1.79579	−0.897895	+	0.440209i	$0.854904\pi$
$548$	−13.3923	−0.572091
$549$	11.6603	0.497648
$550$	0	0
$551$	−1.39230	−0.0593142
$552$	−2.19615	−0.0934745
$553$	−18.0000	−0.765438
$554$	0	0
$555$	9.19615	0.390355
$556$	16.8564	0.714871
$557$	−41.3205	−1.75081	−0.875403	−	0.483394i	$-0.839404\pi$
$557$	−41.3205	−1.75081	−0.875403	+	0.483394i	$0.839404\pi$
$558$	−4.19615	−0.177637
$559$	24.5885	1.03998
$560$	−1.73205	−0.0731925
$561$	0	0
$562$	12.5885	0.531012
$563$	−2.32051	−0.0977978	−0.0488989	−	0.998804i	$-0.515571\pi$
$563$	−2.32051	−0.0977978	−0.0488989	+	0.998804i	$0.515571\pi$
$564$	−6.00000	−0.252646
$565$	0	0
$566$	28.3923	1.19342
$567$	1.73205	0.0727393
$568$	3.00000	0.125877
$569$	9.80385	0.410999	0.205499	−	0.978657i	$-0.434118\pi$
$569$	9.80385	0.410999	0.205499	+	0.978657i	$0.434118\pi$
$570$	3.00000	0.125656
$571$	−32.5359	−1.36158	−0.680792	−	0.732476i	$-0.738364\pi$
$571$	−32.5359	−1.36158	−0.680792	+	0.732476i	$0.738364\pi$
$572$	0	0
$573$	−7.39230	−0.308818
$574$	12.5885	0.525432
$575$	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	$0.718022\pi$
$578$	−14.0000	−0.582323
$579$	−2.53590	−0.105388
$580$	0.464102	0.0192708
$581$	11.1962	0.464495
$582$	0.196152	0.00813078
$583$	0	0
$584$	−4.73205	−0.195814
$585$	3.00000	0.124035
$586$	24.0000	0.991431
$587$	24.8038	1.02376	0.511882	−	0.859056i	$-0.328948\pi$
$587$	24.8038	1.02376	0.511882	+	0.859056i	$0.328948\pi$
$588$	4.00000	0.164957
$589$	−12.5885	−0.518698
$590$	−3.80385	−0.156602
$591$	−9.46410	−0.389301
$592$	9.19615	0.377960
$593$	−35.5692	−1.46065	−0.730326	−	0.683098i	$-0.760632\pi$
$593$	−35.5692	−1.46065	−0.730326	+	0.683098i	$0.760632\pi$
$594$	0	0
$595$	−3.00000	−0.122988
$596$	21.4641	0.879204
$597$	12.3923	0.507183
$598$	−6.58846	−0.269422
$599$	34.3923	1.40523	0.702616	−	0.711569i	$-0.252015\pi$
$599$	34.3923	1.40523	0.702616	+	0.711569i	$0.252015\pi$
$600$	−1.00000	−0.0408248
$601$	0.928203	0.0378622	0.0189311	−	0.999821i	$-0.493974\pi$
$601$	0.928203	0.0378622	0.0189311	+	0.999821i	$0.493974\pi$
$602$	−14.1962	−0.578592
$603$	14.3923	0.586100
$604$	−5.66025	−0.230312
$605$	0	0
$606$	−15.9282	−0.647039
$607$	−23.4449	−0.951598	−0.475799	−	0.879554i	$-0.657841\pi$
$607$	−23.4449	−0.951598	−0.475799	+	0.879554i	$0.657841\pi$
$608$	3.00000	0.121666
$609$	0.803848	0.0325735
$610$	−11.6603	−0.472110
$611$	−18.0000	−0.728202
$612$	1.73205	0.0700140
$613$	7.14359	0.288527	0.144264	−	0.989539i	$-0.453919\pi$
$613$	7.14359	0.288527	0.144264	+	0.989539i	$0.453919\pi$
$614$	22.7321	0.917391
$615$	7.26795	0.293072
$616$	0	0
$617$	22.1769	0.892809	0.446404	−	0.894831i	$-0.352704\pi$
$617$	22.1769	0.892809	0.446404	+	0.894831i	$0.352704\pi$
$618$	−5.00000	−0.201129
$619$	37.1962	1.49504	0.747520	−	0.664240i	$-0.231245\pi$
$619$	37.1962	1.49504	0.747520	+	0.664240i	$0.231245\pi$
$620$	4.19615	0.168522
$621$	−2.19615	−0.0881286
$622$	0	0
$623$	7.60770	0.304796
$624$	3.00000	0.120096
$625$	1.00000	0.0400000
$626$	−11.8038	−0.471777
$627$	0	0
$628$	−11.5885	−0.462430
$629$	15.9282	0.635099
$630$	−1.73205	−0.0690066
$631$	−47.3731	−1.88589	−0.942946	−	0.332946i	$-0.891957\pi$
$631$	−47.3731	−1.88589	−0.942946	+	0.332946i	$0.891957\pi$
$632$	−10.3923	−0.413384
$633$	18.4641	0.733882
$634$	−28.9808	−1.15097
$635$	−2.53590	−0.100634
$636$	8.19615	0.324999
$637$	12.0000	0.475457
$638$	0	0
$639$	3.00000	0.118678
$640$	−1.00000	−0.0395285
$641$	2.78461	0.109985	0.0549927	−	0.998487i	$-0.482486\pi$
$641$	2.78461	0.109985	0.0549927	+	0.998487i	$0.482486\pi$
$642$	−3.46410	−0.136717
$643$	16.7846	0.661920	0.330960	−	0.943645i	$-0.392627\pi$
$643$	16.7846	0.661920	0.330960	+	0.943645i	$0.392627\pi$
$644$	3.80385	0.149893
$645$	−8.19615	−0.322723
$646$	5.19615	0.204440
$647$	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
$650$	−3.00000	−0.117670
$651$	7.26795	0.284853
$652$	−0.196152	−0.00768192
$653$	−2.19615	−0.0859421	−0.0429710	−	0.999076i	$-0.513682\pi$
$653$	−2.19615	−0.0859421	−0.0429710	+	0.999076i	$0.513682\pi$
$654$	−2.53590	−0.0991615
$655$	−7.26795	−0.283982
$656$	7.26795	0.283766
$657$	−4.73205	−0.184615
$658$	10.3923	0.405134
$659$	−22.3923	−0.872280	−0.436140	−	0.899879i	$-0.643655\pi$
$659$	−22.3923	−0.872280	−0.436140	+	0.899879i	$0.643655\pi$
$660$	0	0
$661$	38.9808	1.51618	0.758088	−	0.652152i	$-0.226134\pi$
$661$	38.9808	1.51618	0.758088	+	0.652152i	$0.226134\pi$
$662$	5.58846	0.217202
$663$	5.19615	0.201802
$664$	6.46410	0.250856
$665$	−5.19615	−0.201498
$666$	9.19615	0.356344
$667$	−1.01924	−0.0394650
$668$	−11.3205	−0.438004
$669$	27.7846	1.07422
$670$	−14.3923	−0.556023
$671$	0	0
$672$	−1.73205	−0.0668153
$673$	41.5692	1.60238	0.801188	−	0.598413i	$-0.204202\pi$
$673$	41.5692	1.60238	0.801188	+	0.598413i	$0.204202\pi$
$674$	−2.87564	−0.110766
$675$	−1.00000	−0.0384900
$676$	−4.00000	−0.153846
$677$	−27.8038	−1.06859	−0.534294	−	0.845299i	$-0.679423\pi$
$677$	−27.8038	−1.06859	−0.534294	+	0.845299i	$0.679423\pi$
$678$	0	0
$679$	−0.339746	−0.0130383
$680$	−1.73205	−0.0664211
$681$	−17.3205	−0.663723
$682$	0	0
$683$	−19.9808	−0.764543	−0.382271	−	0.924050i	$-0.624858\pi$
$683$	−19.9808	−0.764543	−0.382271	+	0.924050i	$0.624858\pi$
$684$	3.00000	0.114708
$685$	13.3923	0.511694
$686$	−19.0526	−0.727430
$687$	−24.7846	−0.945592
$688$	−8.19615	−0.312475
$689$	24.5885	0.936746
$690$	2.19615	0.0836061
$691$	5.58846	0.212595	0.106297	−	0.994334i	$-0.466100\pi$
$691$	5.58846	0.212595	0.106297	+	0.994334i	$0.466100\pi$
$692$	14.1962	0.539657
$693$	0	0
$694$	−33.2487	−1.26210
$695$	−16.8564	−0.639400
$696$	0.464102	0.0175917
$697$	12.5885	0.476822
$698$	−14.7846	−0.559606
$699$	6.92820	0.262049
$700$	1.73205	0.0654654
$701$	−30.7128	−1.16001	−0.580003	−	0.814614i	$-0.696949\pi$
$701$	−30.7128	−1.16001	−0.580003	+	0.814614i	$0.696949\pi$
$702$	3.00000	0.113228
$703$	27.5885	1.04052
$704$	0	0
$705$	6.00000	0.225973
$706$	−36.0000	−1.35488
$707$	27.5885	1.03757
$708$	−3.80385	−0.142957
$709$	42.1962	1.58471	0.792355	−	0.610060i	$-0.208855\pi$
$709$	42.1962	1.58471	0.792355	+	0.610060i	$0.208855\pi$
$710$	−3.00000	−0.112588
$711$	−10.3923	−0.389742
$712$	4.39230	0.164609
$713$	−9.21539	−0.345119
$714$	−3.00000	−0.112272
$715$	0	0
$716$	8.19615	0.306305
$717$	−18.8038	−0.702243
$718$	20.5359	0.766393
$719$	1.60770	0.0599569	0.0299785	−	0.999551i	$-0.490456\pi$
$719$	1.60770	0.0599569	0.0299785	+	0.999551i	$0.490456\pi$
$720$	−1.00000	−0.0372678
$721$	8.66025	0.322525
$722$	−10.0000	−0.372161
$723$	13.0526	0.485430
$724$	8.58846	0.319188
$725$	−0.464102	−0.0172363
$726$	0	0
$727$	−33.3923	−1.23845	−0.619226	−	0.785213i	$-0.712554\pi$
$727$	−33.3923	−1.23845	−0.619226	+	0.785213i	$0.712554\pi$
$728$	−5.19615	−0.192582
$729$	1.00000	0.0370370
$730$	4.73205	0.175141
$731$	−14.1962	−0.525064
$732$	−11.6603	−0.430975
$733$	−1.85641	−0.0685679	−0.0342840	−	0.999412i	$-0.510915\pi$
$733$	−1.85641	−0.0685679	−0.0342840	+	0.999412i	$0.510915\pi$
$734$	30.1769	1.11385
$735$	−4.00000	−0.147542
$736$	2.19615	0.0809513
$737$	0	0
$738$	7.26795	0.267537
$739$	−23.7846	−0.874931	−0.437466	−	0.899235i	$-0.644124\pi$
$739$	−23.7846	−0.874931	−0.437466	+	0.899235i	$0.644124\pi$
$740$	−9.19615	−0.338057
$741$	9.00000	0.330623
$742$	−14.1962	−0.521157
$743$	16.9808	0.622964	0.311482	−	0.950252i	$-0.399175\pi$
$743$	16.9808	0.622964	0.311482	+	0.950252i	$0.399175\pi$
$744$	4.19615	0.153838
$745$	−21.4641	−0.786384
$746$	−14.0718	−0.515205
$747$	6.46410	0.236509
$748$	0	0
$749$	6.00000	0.219235
$750$	1.00000	0.0365148
$751$	32.9808	1.20349	0.601743	−	0.798690i	$-0.294473\pi$
$751$	32.9808	1.20349	0.601743	+	0.798690i	$0.294473\pi$
$752$	6.00000	0.218797
$753$	16.3923	0.597369
$754$	1.39230	0.0507048
$755$	5.66025	0.205998
$756$	−1.73205	−0.0629941
$757$	−21.6077	−0.785345	−0.392673	−	0.919678i	$-0.628449\pi$
$757$	−21.6077	−0.785345	−0.392673	+	0.919678i	$0.628449\pi$
$758$	15.9808	0.580447
$759$	0	0
$760$	−3.00000	−0.108821
$761$	35.3205	1.28037	0.640184	−	0.768222i	$-0.278858\pi$
$761$	35.3205	1.28037	0.640184	+	0.768222i	$0.278858\pi$
$762$	−2.53590	−0.0918659
$763$	4.39230	0.159012
$764$	7.39230	0.267444
$765$	−1.73205	−0.0626224
$766$	−26.7846	−0.967767
$767$	−11.4115	−0.412047
$768$	−1.00000	−0.0360844
$769$	20.9090	0.753997	0.376998	−	0.926214i	$-0.376956\pi$
$769$	20.9090	0.753997	0.376998	+	0.926214i	$0.376956\pi$
$770$	0	0
$771$	−29.7846	−1.07267
$772$	2.53590	0.0912690
$773$	0.588457	0.0211653	0.0105827	−	0.999944i	$-0.496631\pi$
$773$	0.588457	0.0211653	0.0105827	+	0.999944i	$0.496631\pi$
$774$	−8.19615	−0.294605
$775$	−4.19615	−0.150730
$776$	−0.196152	−0.00704146
$777$	−15.9282	−0.571421
$778$	−32.7846	−1.17539
$779$	21.8038	0.781204
$780$	−3.00000	−0.107417
$781$	0	0
$782$	3.80385	0.136025
$783$	0.464102	0.0165856
$784$	−4.00000	−0.142857
$785$	11.5885	0.413610
$786$	−7.26795	−0.259239
$787$	−2.87564	−0.102506	−0.0512528	−	0.998686i	$-0.516321\pi$
$787$	−2.87564	−0.102506	−0.0512528	+	0.998686i	$0.516321\pi$
$788$	9.46410	0.337145
$789$	−2.19615	−0.0781851
$790$	10.3923	0.369742
$791$	0	0
$792$	0	0
$793$	−34.9808	−1.24220
$794$	−7.58846	−0.269304
$795$	−8.19615	−0.290688
$796$	−12.3923	−0.439234
$797$	11.4115	0.404218	0.202109	−	0.979363i	$-0.435221\pi$
$797$	11.4115	0.404218	0.202109	+	0.979363i	$0.435221\pi$
$798$	−5.19615	−0.183942
$799$	10.3923	0.367653
$800$	1.00000	0.0353553
$801$	4.39230	0.155194
$802$	−8.19615	−0.289416
$803$	0	0
$804$	−14.3923	−0.507577
$805$	−3.80385	−0.134068
$806$	12.5885	0.443409
$807$	−0.803848	−0.0282968
$808$	15.9282	0.560352
$809$	4.05256	0.142480	0.0712402	−	0.997459i	$-0.477304\pi$
$809$	4.05256	0.142480	0.0712402	+	0.997459i	$0.477304\pi$
$810$	−1.00000	−0.0351364
$811$	30.4641	1.06974	0.534870	−	0.844935i	$-0.320361\pi$
$811$	30.4641	1.06974	0.534870	+	0.844935i	$0.320361\pi$
$812$	−0.803848	−0.0282095
$813$	−14.7846	−0.518519
$814$	0	0
$815$	0.196152	0.00687092
$816$	−1.73205	−0.0606339
$817$	−24.5885	−0.860241
$818$	−0.928203	−0.0324539
$819$	−5.19615	−0.181568
$820$	−7.26795	−0.253808
$821$	16.3923	0.572095	0.286048	−	0.958215i	$-0.407658\pi$
$821$	16.3923	0.572095	0.286048	+	0.958215i	$0.407658\pi$
$822$	13.3923	0.467110
$823$	25.7846	0.898795	0.449397	−	0.893332i	$-0.351639\pi$
$823$	25.7846	0.898795	0.449397	+	0.893332i	$0.351639\pi$
$824$	5.00000	0.174183
$825$	0	0
$826$	6.58846	0.229242
$827$	17.7846	0.618431	0.309216	−	0.950992i	$-0.399933\pi$
$827$	17.7846	0.618431	0.309216	+	0.950992i	$0.399933\pi$
$828$	2.19615	0.0763216
$829$	−16.5885	−0.576141	−0.288070	−	0.957609i	$-0.593014\pi$
$829$	−16.5885	−0.576141	−0.288070	+	0.957609i	$0.593014\pi$
$830$	−6.46410	−0.224372
$831$	0	0
$832$	−3.00000	−0.104006
$833$	−6.92820	−0.240048
$834$	−16.8564	−0.583690
$835$	11.3205	0.391762
$836$	0	0
$837$	4.19615	0.145040
$838$	1.60770	0.0555369
$839$	47.7846	1.64971	0.824854	−	0.565346i	$-0.191257\pi$
$839$	47.7846	1.64971	0.824854	+	0.565346i	$0.191257\pi$
$840$	1.73205	0.0597614
$841$	−28.7846	−0.992573
$842$	−29.8038	−1.02711
$843$	−12.5885	−0.433569
$844$	−18.4641	−0.635561
$845$	4.00000	0.137604
$846$	6.00000	0.206284
$847$	0	0
$848$	−8.19615	−0.281457
$849$	−28.3923	−0.974421
$850$	1.73205	0.0594089
$851$	20.1962	0.692315
$852$	−3.00000	−0.102778
$853$	−29.1051	−0.996540	−0.498270	−	0.867022i	$-0.666031\pi$
$853$	−29.1051	−0.996540	−0.498270	+	0.867022i	$0.666031\pi$
$854$	20.1962	0.691098
$855$	−3.00000	−0.102598
$856$	3.46410	0.118401
$857$	−43.9808	−1.50235	−0.751177	−	0.660101i	$-0.770514\pi$
$857$	−43.9808	−1.50235	−0.751177	+	0.660101i	$0.770514\pi$
$858$	0	0
$859$	−35.1769	−1.20022	−0.600110	−	0.799917i	$-0.704877\pi$
$859$	−35.1769	−1.20022	−0.600110	+	0.799917i	$0.704877\pi$
$860$	8.19615	0.279486
$861$	−12.5885	−0.429013
$862$	37.0526	1.26202
$863$	−1.60770	−0.0547266	−0.0273633	−	0.999626i	$-0.508711\pi$
$863$	−1.60770	−0.0547266	−0.0273633	+	0.999626i	$0.508711\pi$
$864$	−1.00000	−0.0340207
$865$	−14.1962	−0.482684
$866$	−36.7846	−1.24999
$867$	14.0000	0.475465
$868$	−7.26795	−0.246690
$869$	0	0
$870$	−0.464102	−0.0157345
$871$	−43.1769	−1.46299
$872$	2.53590	0.0858764
$873$	−0.196152	−0.00663875
$874$	6.58846	0.222858
$875$	−1.73205	−0.0585540
$876$	4.73205	0.159881
$877$	−40.8564	−1.37962	−0.689811	−	0.723989i	$-0.742307\pi$
$877$	−40.8564	−1.37962	−0.689811	+	0.723989i	$0.742307\pi$
$878$	26.7846	0.903937
$879$	−24.0000	−0.809500
$880$	0	0
$881$	−4.98076	−0.167806	−0.0839031	−	0.996474i	$-0.526739\pi$
$881$	−4.98076	−0.167806	−0.0839031	+	0.996474i	$0.526739\pi$
$882$	−4.00000	−0.134687
$883$	−5.80385	−0.195315	−0.0976575	−	0.995220i	$-0.531135\pi$
$883$	−5.80385	−0.195315	−0.0976575	+	0.995220i	$0.531135\pi$
$884$	−5.19615	−0.174766
$885$	3.80385	0.127865
$886$	25.9808	0.872841
$887$	−30.9282	−1.03847	−0.519234	−	0.854632i	$-0.673783\pi$
$887$	−30.9282	−1.03847	−0.519234	+	0.854632i	$0.673783\pi$
$888$	−9.19615	−0.308603
$889$	4.39230	0.147313
$890$	−4.39230	−0.147230
$891$	0	0
$892$	−27.7846	−0.930298
$893$	18.0000	0.602347
$894$	−21.4641	−0.717867
$895$	−8.19615	−0.273967
$896$	1.73205	0.0578638
$897$	6.58846	0.219982
$898$	−34.3923	−1.14769
$899$	1.94744	0.0649508
$900$	1.00000	0.0333333
$901$	−14.1962	−0.472942
$902$	0	0
$903$	14.1962	0.472418
$904$	0	0
$905$	−8.58846	−0.285490
$906$	5.66025	0.188049
$907$	−51.5692	−1.71233	−0.856164	−	0.516704i	$-0.827159\pi$
$907$	−51.5692	−1.71233	−0.856164	+	0.516704i	$0.827159\pi$
$908$	17.3205	0.574801
$909$	15.9282	0.528305
$910$	5.19615	0.172251
$911$	33.0000	1.09334	0.546669	−	0.837349i	$-0.315895\pi$
$911$	33.0000	1.09334	0.546669	+	0.837349i	$0.315895\pi$
$912$	−3.00000	−0.0993399
$913$	0	0
$914$	−22.7321	−0.751909
$915$	11.6603	0.385476
$916$	24.7846	0.818907
$917$	12.5885	0.415707
$918$	−1.73205	−0.0571662
$919$	−20.1962	−0.666210	−0.333105	−	0.942890i	$-0.608096\pi$
$919$	−20.1962	−0.666210	−0.333105	+	0.942890i	$0.608096\pi$
$920$	−2.19615	−0.0724050
$921$	−22.7321	−0.749047
$922$	−21.9282	−0.722167
$923$	−9.00000	−0.296239
$924$	0	0
$925$	9.19615	0.302368
$926$	−14.3923	−0.472960
$927$	5.00000	0.164222
$928$	−0.464102	−0.0152349
$929$	22.9808	0.753974	0.376987	−	0.926218i	$-0.376960\pi$
$929$	22.9808	0.753974	0.376987	+	0.926218i	$0.376960\pi$
$930$	−4.19615	−0.137597
$931$	−12.0000	−0.393284
$932$	−6.92820	−0.226941
$933$	0	0
$934$	−42.3731	−1.38649
$935$	0	0
$936$	−3.00000	−0.0980581
$937$	31.8564	1.04070	0.520352	−	0.853952i	$-0.325801\pi$
$937$	31.8564	1.04070	0.520352	+	0.853952i	$0.325801\pi$
$938$	24.9282	0.813935
$939$	11.8038	0.385204
$940$	−6.00000	−0.195698
$941$	12.4641	0.406318	0.203159	−	0.979146i	$-0.434879\pi$
$941$	12.4641	0.406318	0.203159	+	0.979146i	$0.434879\pi$
$942$	11.5885	0.377572
$943$	15.9615	0.519779
$944$	3.80385	0.123805
$945$	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	$0.266574\pi$
$948$	10.3923	0.337526
$949$	14.1962	0.460827
$950$	3.00000	0.0973329
$951$	28.9808	0.939766
$952$	3.00000	0.0972306
$953$	−12.9282	−0.418786	−0.209393	−	0.977832i	$-0.567149\pi$
$953$	−12.9282	−0.418786	−0.209393	+	0.977832i	$0.567149\pi$
$954$	−8.19615	−0.265360
$955$	−7.39230	−0.239209
$956$	18.8038	0.608160
$957$	0	0
$958$	−4.26795	−0.137891
$959$	−23.1962	−0.749043
$960$	1.00000	0.0322749
$961$	−13.3923	−0.432010
$962$	−27.5885	−0.889488
$963$	3.46410	0.111629
$964$	−13.0526	−0.420395
$965$	−2.53590	−0.0816335
$966$	−3.80385	−0.122387
$967$	20.5359	0.660390	0.330195	−	0.943913i	$-0.392885\pi$
$967$	20.5359	0.660390	0.330195	+	0.943913i	$0.392885\pi$
$968$	0	0
$969$	−5.19615	−0.166924
$970$	0.196152	0.00629807
$971$	7.60770	0.244143	0.122071	−	0.992521i	$-0.461046\pi$
$971$	7.60770	0.244143	0.122071	+	0.992521i	$0.461046\pi$
$972$	−1.00000	−0.0320750
$973$	29.1962	0.935986
$974$	−11.0000	−0.352463
$975$	3.00000	0.0960769
$976$	11.6603	0.373236
$977$	6.00000	0.191957	0.0959785	−	0.995383i	$-0.469402\pi$
$977$	6.00000	0.191957	0.0959785	+	0.995383i	$0.469402\pi$
$978$	0.196152	0.00627226
$979$	0	0
$980$	4.00000	0.127775
$981$	2.53590	0.0809650
$982$	8.87564	0.283233
$983$	7.01924	0.223879	0.111939	−	0.993715i	$-0.464294\pi$
$983$	7.01924	0.223879	0.111939	+	0.993715i	$0.464294\pi$
$984$	−7.26795	−0.231694
$985$	−9.46410	−0.301551
$986$	−0.803848	−0.0255997
$987$	−10.3923	−0.330791
$988$	−9.00000	−0.286328
$989$	−18.0000	−0.572367
$990$	0	0
$991$	−38.0000	−1.20711	−0.603555	−	0.797321i	$-0.706250\pi$
$991$	−38.0000	−1.20711	−0.603555	+	0.797321i	$0.706250\pi$
$992$	−4.19615	−0.133228
$993$	−5.58846	−0.177344
$994$	5.19615	0.164812
$995$	12.3923	0.392862
$996$	−6.46410	−0.204823
$997$	−47.1051	−1.49183	−0.745917	−	0.666039i	$-0.767988\pi$
$997$	−47.1051	−1.49183	−0.745917	+	0.666039i	$0.767988\pi$
$998$	−15.9808	−0.505862
$999$	−9.19615	−0.290953

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3630.2.a.ba.1.1	✓	2	11.10	odd	2
3630.2.a.bk.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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} +1.73205 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} +1.73205 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -1.00000 q^{12} -3.00000 q^{13} +1.73205 q^{14} +1.00000 q^{15} +1.00000 q^{16} +1.73205 q^{17} +1.00000 q^{18} +3.00000 q^{19} -1.00000 q^{20} -1.73205 q^{21} +2.19615 q^{23} -1.00000 q^{24} +1.00000 q^{25} -3.00000 q^{26} -1.00000 q^{27} +1.73205 q^{28} -0.464102 q^{29} +1.00000 q^{30} -4.19615 q^{31} +1.00000 q^{32} +1.73205 q^{34} -1.73205 q^{35} +1.00000 q^{36} +9.19615 q^{37} +3.00000 q^{38} +3.00000 q^{39} -1.00000 q^{40} +7.26795 q^{41} -1.73205 q^{42} -8.19615 q^{43} -1.00000 q^{45} +2.19615 q^{46} +6.00000 q^{47} -1.00000 q^{48} -4.00000 q^{49} +1.00000 q^{50} -1.73205 q^{51} -3.00000 q^{52} -8.19615 q^{53} -1.00000 q^{54} +1.73205 q^{56} -3.00000 q^{57} -0.464102 q^{58} +3.80385 q^{59} +1.00000 q^{60} +11.6603 q^{61} -4.19615 q^{62} +1.73205 q^{63} +1.00000 q^{64} +3.00000 q^{65} +14.3923 q^{67} +1.73205 q^{68} -2.19615 q^{69} -1.73205 q^{70} +3.00000 q^{71} +1.00000 q^{72} -4.73205 q^{73} +9.19615 q^{74} -1.00000 q^{75} +3.00000 q^{76} +3.00000 q^{78} -10.3923 q^{79} -1.00000 q^{80} +1.00000 q^{81} +7.26795 q^{82} +6.46410 q^{83} -1.73205 q^{84} -1.73205 q^{85} -8.19615 q^{86} +0.464102 q^{87} +4.39230 q^{89} -1.00000 q^{90} -5.19615 q^{91} +2.19615 q^{92} +4.19615 q^{93} +6.00000 q^{94} -3.00000 q^{95} -1.00000 q^{96} -0.196152 q^{97} -4.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{5} - 2 q^{6} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 2 * q^5 - 2 * q^6 + 2 * q^8 + 2 * q^9	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{5} - 2 q^{6} + 2 q^{8} + 2 q^{9} - 2 q^{10} - 2 q^{12} - 6 q^{13} + 2 q^{15} + 2 q^{16} + 2 q^{18} + 6 q^{19} - 2 q^{20} - 6 q^{23} - 2 q^{24} + 2 q^{25} - 6 q^{26} - 2 q^{27} + 6 q^{29} + 2 q^{30} + 2 q^{31} + 2 q^{32} + 2 q^{36} + 8 q^{37} + 6 q^{38} + 6 q^{39} - 2 q^{40} + 18 q^{41} - 6 q^{43} - 2 q^{45} - 6 q^{46} + 12 q^{47} - 2 q^{48} - 8 q^{49} + 2 q^{50} - 6 q^{52} - 6 q^{53} - 2 q^{54} - 6 q^{57} + 6 q^{58} + 18 q^{59} + 2 q^{60} + 6 q^{61} + 2 q^{62} + 2 q^{64} + 6 q^{65} + 8 q^{67} + 6 q^{69} + 6 q^{71} + 2 q^{72} - 6 q^{73} + 8 q^{74} - 2 q^{75} + 6 q^{76} + 6 q^{78} - 2 q^{80} + 2 q^{81} + 18 q^{82} + 6 q^{83} - 6 q^{86} - 6 q^{87} - 12 q^{89} - 2 q^{90} - 6 q^{92} - 2 q^{93} + 12 q^{94} - 6 q^{95} - 2 q^{96} + 10 q^{97} - 8 q^{98}+O(q^{100}) \) 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 + 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 + 2 * q^31 + 2 * q^32 + 2 * q^36 + 8 * q^37 + 6 * q^38 + 6 * q^39 - 2 * q^40 + 18 * q^41 - 6 * q^43 - 2 * q^45 - 6 * q^46 + 12 * q^47 - 2 * q^48 - 8 * q^49 + 2 * q^50 - 6 * q^52 - 6 * q^53 - 2 * q^54 - 6 * q^57 + 6 * q^58 + 18 * q^59 + 2 * q^60 + 6 * q^61 + 2 * q^62 + 2 * q^64 + 6 * q^65 + 8 * q^67 + 6 * q^69 + 6 * q^71 + 2 * q^72 - 6 * q^73 + 8 * q^74 - 2 * q^75 + 6 * q^76 + 6 * q^78 - 2 * q^80 + 2 * q^81 + 18 * q^82 + 6 * q^83 - 6 * q^86 - 6 * q^87 - 12 * q^89 - 2 * q^90 - 6 * q^92 - 2 * q^93 + 12 * q^94 - 6 * q^95 - 2 * q^96 + 10 * q^97 - 8 * q^98

Introduction

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