LMFDB - Embedded newform 5586.2.a.be.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5586,2,Mod(1,5586)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5586, 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("5586.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5586 = 2 \cdot 3 \cdot 7^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5586.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:	$44.6044345691$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 798)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.61803$ of defining polynomial
Character	$\chi$	$=$	5586.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.23607 q^{5} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.23607 q^{5} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} -3.23607 q^{10} -2.00000 q^{11} +1.00000 q^{12} -0.763932 q^{13} +3.23607 q^{15} +1.00000 q^{16} +6.47214 q^{17} -1.00000 q^{18} +1.00000 q^{19} +3.23607 q^{20} +2.00000 q^{22} +7.70820 q^{23} -1.00000 q^{24} +5.47214 q^{25} +0.763932 q^{26} +1.00000 q^{27} -0.472136 q^{29} -3.23607 q^{30} +5.70820 q^{31} -1.00000 q^{32} -2.00000 q^{33} -6.47214 q^{34} +1.00000 q^{36} +5.23607 q^{37} -1.00000 q^{38} -0.763932 q^{39} -3.23607 q^{40} -10.9443 q^{41} +10.4721 q^{43} -2.00000 q^{44} +3.23607 q^{45} -7.70820 q^{46} -7.23607 q^{47} +1.00000 q^{48} -5.47214 q^{50} +6.47214 q^{51} -0.763932 q^{52} -0.472136 q^{53} -1.00000 q^{54} -6.47214 q^{55} +1.00000 q^{57} +0.472136 q^{58} -4.94427 q^{59} +3.23607 q^{60} -3.52786 q^{61} -5.70820 q^{62} +1.00000 q^{64} -2.47214 q^{65} +2.00000 q^{66} -6.94427 q^{67} +6.47214 q^{68} +7.70820 q^{69} +5.52786 q^{71} -1.00000 q^{72} -6.00000 q^{73} -5.23607 q^{74} +5.47214 q^{75} +1.00000 q^{76} +0.763932 q^{78} -10.1803 q^{79} +3.23607 q^{80} +1.00000 q^{81} +10.9443 q^{82} +8.94427 q^{83} +20.9443 q^{85} -10.4721 q^{86} -0.472136 q^{87} +2.00000 q^{88} -14.9443 q^{89} -3.23607 q^{90} +7.70820 q^{92} +5.70820 q^{93} +7.23607 q^{94} +3.23607 q^{95} -1.00000 q^{96} -1.52786 q^{97} -2.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} - 4 q^{11} + 2 q^{12} - 6 q^{13} + 2 q^{15} + 2 q^{16} + 4 q^{17} - 2 q^{18} + 2 q^{19} + 2 q^{20} + 4 q^{22} + 2 q^{23} - 2 q^{24} + 2 q^{25} + 6 q^{26} + 2 q^{27} + 8 q^{29} - 2 q^{30} - 2 q^{31} - 2 q^{32} - 4 q^{33} - 4 q^{34} + 2 q^{36} + 6 q^{37} - 2 q^{38} - 6 q^{39} - 2 q^{40} - 4 q^{41} + 12 q^{43} - 4 q^{44} + 2 q^{45} - 2 q^{46} - 10 q^{47} + 2 q^{48} - 2 q^{50} + 4 q^{51} - 6 q^{52} + 8 q^{53} - 2 q^{54} - 4 q^{55} + 2 q^{57} - 8 q^{58} + 8 q^{59} + 2 q^{60} - 16 q^{61} + 2 q^{62} + 2 q^{64} + 4 q^{65} + 4 q^{66} + 4 q^{67} + 4 q^{68} + 2 q^{69} + 20 q^{71} - 2 q^{72} - 12 q^{73} - 6 q^{74} + 2 q^{75} + 2 q^{76} + 6 q^{78} + 2 q^{79} + 2 q^{80} + 2 q^{81} + 4 q^{82} + 24 q^{85} - 12 q^{86} + 8 q^{87} + 4 q^{88} - 12 q^{89} - 2 q^{90} + 2 q^{92} - 2 q^{93} + 10 q^{94} + 2 q^{95} - 2 q^{96} - 12 q^{97} - 4 q^{99}+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 - 4 * q^11 + 2 * q^12 - 6 * q^13 + 2 * q^15 + 2 * q^16 + 4 * q^17 - 2 * q^18 + 2 * q^19 + 2 * q^20 + 4 * q^22 + 2 * q^23 - 2 * q^24 + 2 * q^25 + 6 * q^26 + 2 * q^27 + 8 * q^29 - 2 * q^30 - 2 * q^31 - 2 * q^32 - 4 * q^33 - 4 * q^34 + 2 * q^36 + 6 * q^37 - 2 * q^38 - 6 * q^39 - 2 * q^40 - 4 * q^41 + 12 * q^43 - 4 * q^44 + 2 * q^45 - 2 * q^46 - 10 * q^47 + 2 * q^48 - 2 * q^50 + 4 * q^51 - 6 * q^52 + 8 * q^53 - 2 * q^54 - 4 * q^55 + 2 * q^57 - 8 * q^58 + 8 * q^59 + 2 * q^60 - 16 * q^61 + 2 * q^62 + 2 * q^64 + 4 * q^65 + 4 * q^66 + 4 * q^67 + 4 * q^68 + 2 * q^69 + 20 * q^71 - 2 * q^72 - 12 * q^73 - 6 * q^74 + 2 * q^75 + 2 * q^76 + 6 * q^78 + 2 * q^79 + 2 * q^80 + 2 * q^81 + 4 * q^82 + 24 * q^85 - 12 * q^86 + 8 * q^87 + 4 * q^88 - 12 * q^89 - 2 * q^90 + 2 * q^92 - 2 * q^93 + 10 * q^94 + 2 * q^95 - 2 * q^96 - 12 * q^97 - 4 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	3.23607	1.44721	0.723607	−	0.690212i	$-0.242483\pi$
$5$	3.23607	1.44721	0.723607	+	0.690212i	$0.242483\pi$
$6$	−1.00000	−0.408248
$7$	0	0
$7$	0	0
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−3.23607	−1.02333
$11$	−2.00000	−0.603023	−0.301511	−	0.953463i	$-0.597491\pi$
$11$	−2.00000	−0.603023	−0.301511	+	0.953463i	$0.597491\pi$
$12$	1.00000	0.288675
$13$	−0.763932	−0.211877	−0.105938	−	0.994373i	$-0.533785\pi$
$13$	−0.763932	−0.211877	−0.105938	+	0.994373i	$0.533785\pi$
$14$	0	0
$15$	3.23607	0.835549
$16$	1.00000	0.250000
$17$	6.47214	1.56972	0.784862	−	0.619671i	$-0.212734\pi$
$17$	6.47214	1.56972	0.784862	+	0.619671i	$0.212734\pi$
$18$	−1.00000	−0.235702
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	3.23607	0.723607
$21$	0	0
$22$	2.00000	0.426401
$23$	7.70820	1.60727	0.803636	−	0.595121i	$-0.202896\pi$
$23$	7.70820	1.60727	0.803636	+	0.595121i	$0.202896\pi$
$24$	−1.00000	−0.204124
$25$	5.47214	1.09443
$26$	0.763932	0.149819
$27$	1.00000	0.192450
$28$	0	0
$29$	−0.472136	−0.0876734	−0.0438367	−	0.999039i	$-0.513958\pi$
$29$	−0.472136	−0.0876734	−0.0438367	+	0.999039i	$0.513958\pi$
$30$	−3.23607	−0.590822
$31$	5.70820	1.02522	0.512612	−	0.858620i	$-0.328678\pi$
$31$	5.70820	1.02522	0.512612	+	0.858620i	$0.328678\pi$
$32$	−1.00000	−0.176777
$33$	−2.00000	−0.348155
$34$	−6.47214	−1.10996
$35$	0	0
$36$	1.00000	0.166667
$37$	5.23607	0.860804	0.430402	−	0.902637i	$-0.358372\pi$
$37$	5.23607	0.860804	0.430402	+	0.902637i	$0.358372\pi$
$38$	−1.00000	−0.162221
$39$	−0.763932	−0.122327
$40$	−3.23607	−0.511667
$41$	−10.9443	−1.70921	−0.854604	−	0.519280i	$-0.826200\pi$
$41$	−10.9443	−1.70921	−0.854604	+	0.519280i	$0.826200\pi$
$42$	0	0
$43$	10.4721	1.59699	0.798493	−	0.602004i	$-0.205631\pi$
$43$	10.4721	1.59699	0.798493	+	0.602004i	$0.205631\pi$
$44$	−2.00000	−0.301511
$45$	3.23607	0.482405
$46$	−7.70820	−1.13651
$47$	−7.23607	−1.05549	−0.527744	−	0.849403i	$-0.676962\pi$
$47$	−7.23607	−1.05549	−0.527744	+	0.849403i	$0.676962\pi$
$48$	1.00000	0.144338
$49$	0	0
$50$	−5.47214	−0.773877
$51$	6.47214	0.906280
$52$	−0.763932	−0.105938
$53$	−0.472136	−0.0648529	−0.0324264	−	0.999474i	$-0.510323\pi$
$53$	−0.472136	−0.0648529	−0.0324264	+	0.999474i	$0.510323\pi$
$54$	−1.00000	−0.136083
$55$	−6.47214	−0.872703
$56$	0	0
$57$	1.00000	0.132453
$58$	0.472136	0.0619945
$59$	−4.94427	−0.643689	−0.321845	−	0.946792i	$-0.604303\pi$
$59$	−4.94427	−0.643689	−0.321845	+	0.946792i	$0.604303\pi$
$60$	3.23607	0.417775
$61$	−3.52786	−0.451697	−0.225848	−	0.974162i	$-0.572515\pi$
$61$	−3.52786	−0.451697	−0.225848	+	0.974162i	$0.572515\pi$
$62$	−5.70820	−0.724943
$63$	0	0
$64$	1.00000	0.125000
$65$	−2.47214	−0.306631
$66$	2.00000	0.246183
$67$	−6.94427	−0.848378	−0.424189	−	0.905574i	$-0.639441\pi$
$67$	−6.94427	−0.848378	−0.424189	+	0.905574i	$0.639441\pi$
$68$	6.47214	0.784862
$69$	7.70820	0.927959
$70$	0	0
$71$	5.52786	0.656037	0.328018	−	0.944671i	$-0.393619\pi$
$71$	5.52786	0.656037	0.328018	+	0.944671i	$0.393619\pi$
$72$	−1.00000	−0.117851
$73$	−6.00000	−0.702247	−0.351123	−	0.936329i	$-0.614200\pi$
$73$	−6.00000	−0.702247	−0.351123	+	0.936329i	$0.614200\pi$
$74$	−5.23607	−0.608681
$75$	5.47214	0.631868
$76$	1.00000	0.114708
$77$	0	0
$78$	0.763932	0.0864983
$79$	−10.1803	−1.14538	−0.572689	−	0.819773i	$-0.694100\pi$
$79$	−10.1803	−1.14538	−0.572689	+	0.819773i	$0.694100\pi$
$80$	3.23607	0.361803
$81$	1.00000	0.111111
$82$	10.9443	1.20859
$83$	8.94427	0.981761	0.490881	−	0.871227i	$-0.336675\pi$
$83$	8.94427	0.981761	0.490881	+	0.871227i	$0.336675\pi$
$84$	0	0
$85$	20.9443	2.27173
$86$	−10.4721	−1.12924
$87$	−0.472136	−0.0506183
$88$	2.00000	0.213201
$89$	−14.9443	−1.58409	−0.792045	−	0.610463i	$-0.790983\pi$
$89$	−14.9443	−1.58409	−0.792045	+	0.610463i	$0.790983\pi$
$90$	−3.23607	−0.341112
$91$	0	0
$92$	7.70820	0.803636
$93$	5.70820	0.591913
$94$	7.23607	0.746343
$95$	3.23607	0.332014
$96$	−1.00000	−0.102062
$97$	−1.52786	−0.155131	−0.0775655	−	0.996987i	$-0.524715\pi$
$97$	−1.52786	−0.155131	−0.0775655	+	0.996987i	$0.524715\pi$
$98$	0	0
$99$	−2.00000	−0.201008
$100$	5.47214	0.547214
$101$	6.29180	0.626057	0.313029	−	0.949744i	$-0.398656\pi$
$101$	6.29180	0.626057	0.313029	+	0.949744i	$0.398656\pi$
$102$	−6.47214	−0.640837
$103$	−18.6525	−1.83788	−0.918942	−	0.394394i	$-0.870955\pi$
$103$	−18.6525	−1.83788	−0.918942	+	0.394394i	$0.870955\pi$
$104$	0.763932	0.0749097
$105$	0	0
$106$	0.472136	0.0458579
$107$	8.94427	0.864675	0.432338	−	0.901712i	$-0.357689\pi$
$107$	8.94427	0.864675	0.432338	+	0.901712i	$0.357689\pi$
$108$	1.00000	0.0962250
$109$	11.7082	1.12144	0.560721	−	0.828005i	$-0.310524\pi$
$109$	11.7082	1.12144	0.560721	+	0.828005i	$0.310524\pi$
$110$	6.47214	0.617094
$111$	5.23607	0.496986
$112$	0	0
$113$	3.52786	0.331874	0.165937	−	0.986136i	$-0.446935\pi$
$113$	3.52786	0.331874	0.165937	+	0.986136i	$0.446935\pi$
$114$	−1.00000	−0.0936586
$115$	24.9443	2.32607
$116$	−0.472136	−0.0438367
$117$	−0.763932	−0.0706255
$118$	4.94427	0.455157
$119$	0	0
$120$	−3.23607	−0.295411
$121$	−7.00000	−0.636364
$122$	3.52786	0.319398
$123$	−10.9443	−0.986812
$124$	5.70820	0.512612
$125$	1.52786	0.136656
$126$	0	0
$127$	8.29180	0.735778	0.367889	−	0.929870i	$-0.380081\pi$
$127$	8.29180	0.735778	0.367889	+	0.929870i	$0.380081\pi$
$128$	−1.00000	−0.0883883
$129$	10.4721	0.922020
$130$	2.47214	0.216821
$131$	20.9443	1.82991	0.914955	−	0.403556i	$-0.132226\pi$
$131$	20.9443	1.82991	0.914955	+	0.403556i	$0.132226\pi$
$132$	−2.00000	−0.174078
$133$	0	0
$134$	6.94427	0.599894
$135$	3.23607	0.278516
$136$	−6.47214	−0.554981
$137$	17.4164	1.48798	0.743992	−	0.668188i	$-0.232930\pi$
$137$	17.4164	1.48798	0.743992	+	0.668188i	$0.232930\pi$
$138$	−7.70820	−0.656166
$139$	16.0000	1.35710	0.678551	−	0.734553i	$-0.262608\pi$
$139$	16.0000	1.35710	0.678551	+	0.734553i	$0.262608\pi$
$140$	0	0
$141$	−7.23607	−0.609387
$142$	−5.52786	−0.463888
$143$	1.52786	0.127766
$144$	1.00000	0.0833333
$145$	−1.52786	−0.126882
$146$	6.00000	0.496564
$147$	0	0
$148$	5.23607	0.430402
$149$	−10.1803	−0.834006	−0.417003	−	0.908905i	$-0.636920\pi$
$149$	−10.1803	−0.834006	−0.417003	+	0.908905i	$0.636920\pi$
$150$	−5.47214	−0.446798
$151$	−0.291796	−0.0237460	−0.0118730	−	0.999930i	$-0.503779\pi$
$151$	−0.291796	−0.0237460	−0.0118730	+	0.999930i	$0.503779\pi$
$152$	−1.00000	−0.0811107
$153$	6.47214	0.523241
$154$	0	0
$155$	18.4721	1.48372
$156$	−0.763932	−0.0611635
$157$	−4.47214	−0.356915	−0.178458	−	0.983948i	$-0.557111\pi$
$157$	−4.47214	−0.356915	−0.178458	+	0.983948i	$0.557111\pi$
$158$	10.1803	0.809904
$159$	−0.472136	−0.0374428
$160$	−3.23607	−0.255834
$161$	0	0
$162$	−1.00000	−0.0785674
$163$	−3.05573	−0.239343	−0.119672	−	0.992814i	$-0.538184\pi$
$163$	−3.05573	−0.239343	−0.119672	+	0.992814i	$0.538184\pi$
$164$	−10.9443	−0.854604
$165$	−6.47214	−0.503855
$166$	−8.94427	−0.694210
$167$	−8.00000	−0.619059	−0.309529	−	0.950890i	$-0.600171\pi$
$167$	−8.00000	−0.619059	−0.309529	+	0.950890i	$0.600171\pi$
$168$	0	0
$169$	−12.4164	−0.955108
$170$	−20.9443	−1.60635
$171$	1.00000	0.0764719
$172$	10.4721	0.798493
$173$	23.8885	1.81621	0.908106	−	0.418740i	$-0.137528\pi$
$173$	23.8885	1.81621	0.908106	+	0.418740i	$0.137528\pi$
$174$	0.472136	0.0357925
$175$	0	0
$176$	−2.00000	−0.150756
$177$	−4.94427	−0.371634
$178$	14.9443	1.12012
$179$	11.4164	0.853302	0.426651	−	0.904416i	$-0.359693\pi$
$179$	11.4164	0.853302	0.426651	+	0.904416i	$0.359693\pi$
$180$	3.23607	0.241202
$181$	4.76393	0.354100	0.177050	−	0.984202i	$-0.443345\pi$
$181$	4.76393	0.354100	0.177050	+	0.984202i	$0.443345\pi$
$182$	0	0
$183$	−3.52786	−0.260787
$184$	−7.70820	−0.568256
$185$	16.9443	1.24577
$186$	−5.70820	−0.418546
$187$	−12.9443	−0.946579
$188$	−7.23607	−0.527744
$189$	0	0
$190$	−3.23607	−0.234769
$191$	−26.1803	−1.89434	−0.947171	−	0.320728i	$-0.896073\pi$
$191$	−26.1803	−1.89434	−0.947171	+	0.320728i	$0.896073\pi$
$192$	1.00000	0.0721688
$193$	8.47214	0.609838	0.304919	−	0.952378i	$-0.401371\pi$
$193$	8.47214	0.609838	0.304919	+	0.952378i	$0.401371\pi$
$194$	1.52786	0.109694
$195$	−2.47214	−0.177033
$196$	0	0
$197$	15.7082	1.11916	0.559582	−	0.828775i	$-0.310962\pi$
$197$	15.7082	1.11916	0.559582	+	0.828775i	$0.310962\pi$
$198$	2.00000	0.142134
$199$	14.4721	1.02590	0.512951	−	0.858418i	$-0.328552\pi$
$199$	14.4721	1.02590	0.512951	+	0.858418i	$0.328552\pi$
$200$	−5.47214	−0.386938
$201$	−6.94427	−0.489811
$202$	−6.29180	−0.442689
$203$	0	0
$204$	6.47214	0.453140
$205$	−35.4164	−2.47359
$206$	18.6525	1.29958
$207$	7.70820	0.535757
$208$	−0.763932	−0.0529692
$209$	−2.00000	−0.138343
$210$	0	0
$211$	1.41641	0.0975095	0.0487548	−	0.998811i	$-0.484475\pi$
$211$	1.41641	0.0975095	0.0487548	+	0.998811i	$0.484475\pi$
$212$	−0.472136	−0.0324264
$213$	5.52786	0.378763
$214$	−8.94427	−0.611418
$215$	33.8885	2.31118
$216$	−1.00000	−0.0680414
$217$	0	0
$218$	−11.7082	−0.792980
$219$	−6.00000	−0.405442
$220$	−6.47214	−0.436351
$221$	−4.94427	−0.332588
$222$	−5.23607	−0.351422
$223$	9.70820	0.650109	0.325055	−	0.945695i	$-0.394617\pi$
$223$	9.70820	0.650109	0.325055	+	0.945695i	$0.394617\pi$
$224$	0	0
$225$	5.47214	0.364809
$226$	−3.52786	−0.234670
$227$	24.9443	1.65561	0.827805	−	0.561016i	$-0.189590\pi$
$227$	24.9443	1.65561	0.827805	+	0.561016i	$0.189590\pi$
$228$	1.00000	0.0662266
$229$	−11.8885	−0.785617	−0.392809	−	0.919620i	$-0.628496\pi$
$229$	−11.8885	−0.785617	−0.392809	+	0.919620i	$0.628496\pi$
$230$	−24.9443	−1.64478
$231$	0	0
$232$	0.472136	0.0309972
$233$	6.00000	0.393073	0.196537	−	0.980497i	$-0.437031\pi$
$233$	6.00000	0.393073	0.196537	+	0.980497i	$0.437031\pi$
$234$	0.763932	0.0499398
$235$	−23.4164	−1.52752
$236$	−4.94427	−0.321845
$237$	−10.1803	−0.661284
$238$	0	0
$239$	−8.65248	−0.559682	−0.279841	−	0.960046i	$-0.590282\pi$
$239$	−8.65248	−0.559682	−0.279841	+	0.960046i	$0.590282\pi$
$240$	3.23607	0.208887
$241$	−28.3607	−1.82687	−0.913436	−	0.406982i	$-0.866581\pi$
$241$	−28.3607	−1.82687	−0.913436	+	0.406982i	$0.866581\pi$
$242$	7.00000	0.449977
$243$	1.00000	0.0641500
$244$	−3.52786	−0.225848
$245$	0	0
$246$	10.9443	0.697781
$247$	−0.763932	−0.0486078
$248$	−5.70820	−0.362471
$249$	8.94427	0.566820
$250$	−1.52786	−0.0966306
$251$	0	0		−	1.00000i	$-0.5\pi$
$251$	0	0			1.00000i	$0.5\pi$
$252$	0	0
$253$	−15.4164	−0.969221
$254$	−8.29180	−0.520274
$255$	20.9443	1.31158
$256$	1.00000	0.0625000
$257$	−15.8885	−0.991100	−0.495550	−	0.868579i	$-0.665033\pi$
$257$	−15.8885	−0.991100	−0.495550	+	0.868579i	$0.665033\pi$
$258$	−10.4721	−0.651967
$259$	0	0
$260$	−2.47214	−0.153315
$261$	−0.472136	−0.0292245
$262$	−20.9443	−1.29394
$263$	18.1803	1.12105	0.560524	−	0.828138i	$-0.310600\pi$
$263$	18.1803	1.12105	0.560524	+	0.828138i	$0.310600\pi$
$264$	2.00000	0.123091
$265$	−1.52786	−0.0938559
$266$	0	0
$267$	−14.9443	−0.914575
$268$	−6.94427	−0.424189
$269$	−19.5279	−1.19063	−0.595317	−	0.803491i	$-0.702974\pi$
$269$	−19.5279	−1.19063	−0.595317	+	0.803491i	$0.702974\pi$
$270$	−3.23607	−0.196941
$271$	4.94427	0.300343	0.150172	−	0.988660i	$-0.452017\pi$
$271$	4.94427	0.300343	0.150172	+	0.988660i	$0.452017\pi$
$272$	6.47214	0.392431
$273$	0	0
$274$	−17.4164	−1.05216
$275$	−10.9443	−0.659964
$276$	7.70820	0.463979
$277$	−11.8885	−0.714313	−0.357157	−	0.934044i	$-0.616254\pi$
$277$	−11.8885	−0.714313	−0.357157	+	0.934044i	$0.616254\pi$
$278$	−16.0000	−0.959616
$279$	5.70820	0.341741
$280$	0	0
$281$	21.4164	1.27760	0.638798	−	0.769375i	$-0.279432\pi$
$281$	21.4164	1.27760	0.638798	+	0.769375i	$0.279432\pi$
$282$	7.23607	0.430902
$283$	8.00000	0.475551	0.237775	−	0.971320i	$-0.423582\pi$
$283$	8.00000	0.475551	0.237775	+	0.971320i	$0.423582\pi$
$284$	5.52786	0.328018
$285$	3.23607	0.191688
$286$	−1.52786	−0.0903445
$287$	0	0
$288$	−1.00000	−0.0589256
$289$	24.8885	1.46403
$290$	1.52786	0.0897193
$291$	−1.52786	−0.0895650
$292$	−6.00000	−0.351123
$293$	−0.472136	−0.0275825	−0.0137912	−	0.999905i	$-0.504390\pi$
$293$	−0.472136	−0.0275825	−0.0137912	+	0.999905i	$0.504390\pi$
$294$	0	0
$295$	−16.0000	−0.931556
$296$	−5.23607	−0.304340
$297$	−2.00000	−0.116052
$298$	10.1803	0.589731
$299$	−5.88854	−0.340543
$300$	5.47214	0.315934
$301$	0	0
$302$	0.291796	0.0167910
$303$	6.29180	0.361454
$304$	1.00000	0.0573539
$305$	−11.4164	−0.653702
$306$	−6.47214	−0.369987
$307$	−14.4721	−0.825968	−0.412984	−	0.910738i	$-0.635514\pi$
$307$	−14.4721	−0.825968	−0.412984	+	0.910738i	$0.635514\pi$
$308$	0	0
$309$	−18.6525	−1.06110
$310$	−18.4721	−1.04915
$311$	12.7639	0.723776	0.361888	−	0.932222i	$-0.382132\pi$
$311$	12.7639	0.723776	0.361888	+	0.932222i	$0.382132\pi$
$312$	0.763932	0.0432491
$313$	−30.0000	−1.69570	−0.847850	−	0.530236i	$-0.822103\pi$
$313$	−30.0000	−1.69570	−0.847850	+	0.530236i	$0.822103\pi$
$314$	4.47214	0.252377
$315$	0	0
$316$	−10.1803	−0.572689
$317$	3.52786	0.198145	0.0990723	−	0.995080i	$-0.468412\pi$
$317$	3.52786	0.198145	0.0990723	+	0.995080i	$0.468412\pi$
$318$	0.472136	0.0264761
$319$	0.944272	0.0528691
$320$	3.23607	0.180902
$321$	8.94427	0.499221
$322$	0	0
$323$	6.47214	0.360119
$324$	1.00000	0.0555556
$325$	−4.18034	−0.231884
$326$	3.05573	0.169241
$327$	11.7082	0.647465
$328$	10.9443	0.604296
$329$	0	0
$330$	6.47214	0.356279
$331$	−1.05573	−0.0580281	−0.0290140	−	0.999579i	$-0.509237\pi$
$331$	−1.05573	−0.0580281	−0.0290140	+	0.999579i	$0.509237\pi$
$332$	8.94427	0.490881
$333$	5.23607	0.286935
$334$	8.00000	0.437741
$335$	−22.4721	−1.22778
$336$	0	0
$337$	18.9443	1.03196	0.515980	−	0.856601i	$-0.327428\pi$
$337$	18.9443	1.03196	0.515980	+	0.856601i	$0.327428\pi$
$338$	12.4164	0.675364
$339$	3.52786	0.191607
$340$	20.9443	1.13586
$341$	−11.4164	−0.618233
$342$	−1.00000	−0.0540738
$343$	0	0
$344$	−10.4721	−0.564620
$345$	24.9443	1.34295
$346$	−23.8885	−1.28426
$347$	10.0000	0.536828	0.268414	−	0.963304i	$-0.413500\pi$
$347$	10.0000	0.536828	0.268414	+	0.963304i	$0.413500\pi$
$348$	−0.472136	−0.0253091
$349$	−22.3607	−1.19694	−0.598470	−	0.801145i	$-0.704224\pi$
$349$	−22.3607	−1.19694	−0.598470	+	0.801145i	$0.704224\pi$
$350$	0	0
$351$	−0.763932	−0.0407757
$352$	2.00000	0.106600
$353$	−8.00000	−0.425797	−0.212899	−	0.977074i	$-0.568290\pi$
$353$	−8.00000	−0.425797	−0.212899	+	0.977074i	$0.568290\pi$
$354$	4.94427	0.262785
$355$	17.8885	0.949425
$356$	−14.9443	−0.792045
$357$	0	0
$358$	−11.4164	−0.603376
$359$	27.7082	1.46238	0.731192	−	0.682172i	$-0.238965\pi$
$359$	27.7082	1.46238	0.731192	+	0.682172i	$0.238965\pi$
$360$	−3.23607	−0.170556
$361$	1.00000	0.0526316
$362$	−4.76393	−0.250387
$363$	−7.00000	−0.367405
$364$	0	0
$365$	−19.4164	−1.01630
$366$	3.52786	0.184404
$367$	36.9443	1.92848	0.964238	−	0.265039i	$-0.0853849\pi$
$367$	36.9443	1.92848	0.964238	+	0.265039i	$0.0853849\pi$
$368$	7.70820	0.401818
$369$	−10.9443	−0.569736
$370$	−16.9443	−0.880891
$371$	0	0
$372$	5.70820	0.295957
$373$	−11.7082	−0.606228	−0.303114	−	0.952954i	$-0.598026\pi$
$373$	−11.7082	−0.606228	−0.303114	+	0.952954i	$0.598026\pi$
$374$	12.9443	0.669332
$375$	1.52786	0.0788986
$376$	7.23607	0.373172
$377$	0.360680	0.0185760
$378$	0	0
$379$	6.94427	0.356703	0.178352	−	0.983967i	$-0.442924\pi$
$379$	6.94427	0.356703	0.178352	+	0.983967i	$0.442924\pi$
$380$	3.23607	0.166007
$381$	8.29180	0.424802
$382$	26.1803	1.33950
$383$	−24.0000	−1.22634	−0.613171	−	0.789950i	$-0.710106\pi$
$383$	−24.0000	−1.22634	−0.613171	+	0.789950i	$0.710106\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	−8.47214	−0.431220
$387$	10.4721	0.532329
$388$	−1.52786	−0.0775655
$389$	−2.76393	−0.140137	−0.0700685	−	0.997542i	$-0.522322\pi$
$389$	−2.76393	−0.140137	−0.0700685	+	0.997542i	$0.522322\pi$
$390$	2.47214	0.125181
$391$	49.8885	2.52297
$392$	0	0
$393$	20.9443	1.05650
$394$	−15.7082	−0.791368
$395$	−32.9443	−1.65761
$396$	−2.00000	−0.100504
$397$	−10.9443	−0.549277	−0.274639	−	0.961548i	$-0.588558\pi$
$397$	−10.9443	−0.549277	−0.274639	+	0.961548i	$0.588558\pi$
$398$	−14.4721	−0.725423
$399$	0	0
$400$	5.47214	0.273607
$401$	−11.5279	−0.575674	−0.287837	−	0.957679i	$-0.592936\pi$
$401$	−11.5279	−0.575674	−0.287837	+	0.957679i	$0.592936\pi$
$402$	6.94427	0.346349
$403$	−4.36068	−0.217221
$404$	6.29180	0.313029
$405$	3.23607	0.160802
$406$	0	0
$407$	−10.4721	−0.519085
$408$	−6.47214	−0.320418
$409$	−14.4721	−0.715601	−0.357801	−	0.933798i	$-0.616473\pi$
$409$	−14.4721	−0.715601	−0.357801	+	0.933798i	$0.616473\pi$
$410$	35.4164	1.74909
$411$	17.4164	0.859088
$412$	−18.6525	−0.918942
$413$	0	0
$414$	−7.70820	−0.378838
$415$	28.9443	1.42082
$416$	0.763932	0.0374548
$417$	16.0000	0.783523
$418$	2.00000	0.0978232
$419$	−24.3607	−1.19010	−0.595049	−	0.803690i	$-0.702867\pi$
$419$	−24.3607	−1.19010	−0.595049	+	0.803690i	$0.702867\pi$
$420$	0	0
$421$	−6.76393	−0.329654	−0.164827	−	0.986323i	$-0.552707\pi$
$421$	−6.76393	−0.329654	−0.164827	+	0.986323i	$0.552707\pi$
$422$	−1.41641	−0.0689497
$423$	−7.23607	−0.351830
$424$	0.472136	0.0229289
$425$	35.4164	1.71795
$426$	−5.52786	−0.267826
$427$	0	0
$428$	8.94427	0.432338
$429$	1.52786	0.0737660
$430$	−33.8885	−1.63425
$431$	−18.4721	−0.889771	−0.444886	−	0.895587i	$-0.646756\pi$
$431$	−18.4721	−0.889771	−0.444886	+	0.895587i	$0.646756\pi$
$432$	1.00000	0.0481125
$433$	22.4721	1.07994	0.539971	−	0.841684i	$-0.318435\pi$
$433$	22.4721	1.07994	0.539971	+	0.841684i	$0.318435\pi$
$434$	0	0
$435$	−1.52786	−0.0732555
$436$	11.7082	0.560721
$437$	7.70820	0.368733
$438$	6.00000	0.286691
$439$	18.6525	0.890234	0.445117	−	0.895472i	$-0.353162\pi$
$439$	18.6525	0.890234	0.445117	+	0.895472i	$0.353162\pi$
$440$	6.47214	0.308547
$441$	0	0
$442$	4.94427	0.235175
$443$	23.8885	1.13498	0.567489	−	0.823381i	$-0.307915\pi$
$443$	23.8885	1.13498	0.567489	+	0.823381i	$0.307915\pi$
$444$	5.23607	0.248493
$445$	−48.3607	−2.29252
$446$	−9.70820	−0.459697
$447$	−10.1803	−0.481514
$448$	0	0
$449$	30.0000	1.41579	0.707894	−	0.706319i	$-0.249646\pi$
$449$	30.0000	1.41579	0.707894	+	0.706319i	$0.249646\pi$
$450$	−5.47214	−0.257959
$451$	21.8885	1.03069
$452$	3.52786	0.165937
$453$	−0.291796	−0.0137098
$454$	−24.9443	−1.17069
$455$	0	0
$456$	−1.00000	−0.0468293
$457$	−26.0000	−1.21623	−0.608114	−	0.793849i	$-0.708074\pi$
$457$	−26.0000	−1.21623	−0.608114	+	0.793849i	$0.708074\pi$
$458$	11.8885	0.555515
$459$	6.47214	0.302093
$460$	24.9443	1.16303
$461$	20.7639	0.967073	0.483536	−	0.875324i	$-0.339352\pi$
$461$	20.7639	0.967073	0.483536	+	0.875324i	$0.339352\pi$
$462$	0	0
$463$	−16.0000	−0.743583	−0.371792	−	0.928316i	$-0.621256\pi$
$463$	−16.0000	−0.743583	−0.371792	+	0.928316i	$0.621256\pi$
$464$	−0.472136	−0.0219184
$465$	18.4721	0.856625
$466$	−6.00000	−0.277945
$467$	5.88854	0.272489	0.136245	−	0.990675i	$-0.456497\pi$
$467$	5.88854	0.272489	0.136245	+	0.990675i	$0.456497\pi$
$468$	−0.763932	−0.0353128
$469$	0	0
$470$	23.4164	1.08012
$471$	−4.47214	−0.206065
$472$	4.94427	0.227579
$473$	−20.9443	−0.963019
$474$	10.1803	0.467598
$475$	5.47214	0.251079
$476$	0	0
$477$	−0.472136	−0.0216176
$478$	8.65248	0.395755
$479$	3.23607	0.147860	0.0739299	−	0.997263i	$-0.476446\pi$
$479$	3.23607	0.147860	0.0739299	+	0.997263i	$0.476446\pi$
$480$	−3.23607	−0.147706
$481$	−4.00000	−0.182384
$482$	28.3607	1.29179
$483$	0	0
$484$	−7.00000	−0.318182
$485$	−4.94427	−0.224508
$486$	−1.00000	−0.0453609
$487$	14.7639	0.669018	0.334509	−	0.942393i	$-0.391430\pi$
$487$	14.7639	0.669018	0.334509	+	0.942393i	$0.391430\pi$
$488$	3.52786	0.159699
$489$	−3.05573	−0.138185
$490$	0	0
$491$	32.4721	1.46545	0.732723	−	0.680526i	$-0.238249\pi$
$491$	32.4721	1.46545	0.732723	+	0.680526i	$0.238249\pi$
$492$	−10.9443	−0.493406
$493$	−3.05573	−0.137623
$494$	0.763932	0.0343709
$495$	−6.47214	−0.290901
$496$	5.70820	0.256306
$497$	0	0
$498$	−8.94427	−0.400802
$499$	−36.3607	−1.62773	−0.813864	−	0.581056i	$-0.802640\pi$
$499$	−36.3607	−1.62773	−0.813864	+	0.581056i	$0.802640\pi$
$500$	1.52786	0.0683282
$501$	−8.00000	−0.357414
$502$	0	0
$503$	−29.1246	−1.29860	−0.649301	−	0.760531i	$-0.724939\pi$
$503$	−29.1246	−1.29860	−0.649301	+	0.760531i	$0.724939\pi$
$504$	0	0
$505$	20.3607	0.906038
$506$	15.4164	0.685343
$507$	−12.4164	−0.551432
$508$	8.29180	0.367889
$509$	15.5279	0.688260	0.344130	−	0.938922i	$-0.388174\pi$
$509$	15.5279	0.688260	0.344130	+	0.938922i	$0.388174\pi$
$510$	−20.9443	−0.927428
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	1.00000	0.0441511
$514$	15.8885	0.700814
$515$	−60.3607	−2.65981
$516$	10.4721	0.461010
$517$	14.4721	0.636484
$518$	0	0
$519$	23.8885	1.04859
$520$	2.47214	0.108410
$521$	−24.8328	−1.08795	−0.543973	−	0.839103i	$-0.683080\pi$
$521$	−24.8328	−1.08795	−0.543973	+	0.839103i	$0.683080\pi$
$522$	0.472136	0.0206648
$523$	−6.47214	−0.283007	−0.141503	−	0.989938i	$-0.545194\pi$
$523$	−6.47214	−0.283007	−0.141503	+	0.989938i	$0.545194\pi$
$524$	20.9443	0.914955
$525$	0	0
$526$	−18.1803	−0.792700
$527$	36.9443	1.60932
$528$	−2.00000	−0.0870388
$529$	36.4164	1.58332
$530$	1.52786	0.0663662
$531$	−4.94427	−0.214563
$532$	0	0
$533$	8.36068	0.362141
$534$	14.9443	0.646702
$535$	28.9443	1.25137
$536$	6.94427	0.299947
$537$	11.4164	0.492654
$538$	19.5279	0.841906
$539$	0	0
$540$	3.23607	0.139258
$541$	−28.8328	−1.23962	−0.619810	−	0.784752i	$-0.712790\pi$
$541$	−28.8328	−1.23962	−0.619810	+	0.784752i	$0.712790\pi$
$542$	−4.94427	−0.212375
$543$	4.76393	0.204440
$544$	−6.47214	−0.277491
$545$	37.8885	1.62297
$546$	0	0
$547$	−18.0000	−0.769624	−0.384812	−	0.922995i	$-0.625734\pi$
$547$	−18.0000	−0.769624	−0.384812	+	0.922995i	$0.625734\pi$
$548$	17.4164	0.743992
$549$	−3.52786	−0.150566
$550$	10.9443	0.466665
$551$	−0.472136	−0.0201137
$552$	−7.70820	−0.328083
$553$	0	0
$554$	11.8885	0.505096
$555$	16.9443	0.719244
$556$	16.0000	0.678551
$557$	30.5410	1.29406	0.647032	−	0.762463i	$-0.276010\pi$
$557$	30.5410	1.29406	0.647032	+	0.762463i	$0.276010\pi$
$558$	−5.70820	−0.241648
$559$	−8.00000	−0.338364
$560$	0	0
$561$	−12.9443	−0.546508
$562$	−21.4164	−0.903397
$563$	−25.8885	−1.09107	−0.545536	−	0.838087i	$-0.683674\pi$
$563$	−25.8885	−1.09107	−0.545536	+	0.838087i	$0.683674\pi$
$564$	−7.23607	−0.304693
$565$	11.4164	0.480292
$566$	−8.00000	−0.336265
$567$	0	0
$568$	−5.52786	−0.231944
$569$	30.9443	1.29725	0.648626	−	0.761108i	$-0.275344\pi$
$569$	30.9443	1.29725	0.648626	+	0.761108i	$0.275344\pi$
$570$	−3.23607	−0.135544
$571$	−17.5279	−0.733518	−0.366759	−	0.930316i	$-0.619533\pi$
$571$	−17.5279	−0.733518	−0.366759	+	0.930316i	$0.619533\pi$
$572$	1.52786	0.0638832
$573$	−26.1803	−1.09370
$574$	0	0
$575$	42.1803	1.75904
$576$	1.00000	0.0416667
$577$	−18.0000	−0.749350	−0.374675	−	0.927156i	$-0.622246\pi$
$577$	−18.0000	−0.749350	−0.374675	+	0.927156i	$0.622246\pi$
$578$	−24.8885	−1.03523
$579$	8.47214	0.352090
$580$	−1.52786	−0.0634411
$581$	0	0
$582$	1.52786	0.0633320
$583$	0.944272	0.0391077
$584$	6.00000	0.248282
$585$	−2.47214	−0.102210
$586$	0.472136	0.0195038
$587$	7.41641	0.306108	0.153054	−	0.988218i	$-0.451089\pi$
$587$	7.41641	0.306108	0.153054	+	0.988218i	$0.451089\pi$
$588$	0	0
$589$	5.70820	0.235202
$590$	16.0000	0.658710
$591$	15.7082	0.646149
$592$	5.23607	0.215201
$593$	4.00000	0.164260	0.0821302	−	0.996622i	$-0.473828\pi$
$593$	4.00000	0.164260	0.0821302	+	0.996622i	$0.473828\pi$
$594$	2.00000	0.0820610
$595$	0	0
$596$	−10.1803	−0.417003
$597$	14.4721	0.592305
$598$	5.88854	0.240800
$599$	−12.3607	−0.505044	−0.252522	−	0.967591i	$-0.581260\pi$
$599$	−12.3607	−0.505044	−0.252522	+	0.967591i	$0.581260\pi$
$600$	−5.47214	−0.223399
$601$	−4.94427	−0.201681	−0.100841	−	0.994903i	$-0.532153\pi$
$601$	−4.94427	−0.201681	−0.100841	+	0.994903i	$0.532153\pi$
$602$	0	0
$603$	−6.94427	−0.282793
$604$	−0.291796	−0.0118730
$605$	−22.6525	−0.920954
$606$	−6.29180	−0.255587
$607$	−24.5410	−0.996089	−0.498045	−	0.867151i	$-0.665948\pi$
$607$	−24.5410	−0.996089	−0.498045	+	0.867151i	$0.665948\pi$
$608$	−1.00000	−0.0405554
$609$	0	0
$610$	11.4164	0.462237
$611$	5.52786	0.223633
$612$	6.47214	0.261621
$613$	30.3607	1.22626	0.613128	−	0.789983i	$-0.289911\pi$
$613$	30.3607	1.22626	0.613128	+	0.789983i	$0.289911\pi$
$614$	14.4721	0.584048
$615$	−35.4164	−1.42813
$616$	0	0
$617$	9.05573	0.364570	0.182285	−	0.983246i	$-0.441651\pi$
$617$	9.05573	0.364570	0.182285	+	0.983246i	$0.441651\pi$
$618$	18.6525	0.750313
$619$	−26.8328	−1.07850	−0.539251	−	0.842145i	$-0.681293\pi$
$619$	−26.8328	−1.07850	−0.539251	+	0.842145i	$0.681293\pi$
$620$	18.4721	0.741859
$621$	7.70820	0.309320
$622$	−12.7639	−0.511787
$623$	0	0
$624$	−0.763932	−0.0305818
$625$	−22.4164	−0.896656
$626$	30.0000	1.19904
$627$	−2.00000	−0.0798723
$628$	−4.47214	−0.178458
$629$	33.8885	1.35122
$630$	0	0
$631$	−12.3607	−0.492071	−0.246035	−	0.969261i	$-0.579128\pi$
$631$	−12.3607	−0.492071	−0.246035	+	0.969261i	$0.579128\pi$
$632$	10.1803	0.404952
$633$	1.41641	0.0562972
$634$	−3.52786	−0.140109
$635$	26.8328	1.06483
$636$	−0.472136	−0.0187214
$637$	0	0
$638$	−0.944272	−0.0373841
$639$	5.52786	0.218679
$640$	−3.23607	−0.127917
$641$	−46.9443	−1.85419	−0.927094	−	0.374830i	$-0.877701\pi$
$641$	−46.9443	−1.85419	−0.927094	+	0.374830i	$0.877701\pi$
$642$	−8.94427	−0.353002
$643$	−40.7214	−1.60589	−0.802947	−	0.596051i	$-0.796736\pi$
$643$	−40.7214	−1.60589	−0.802947	+	0.596051i	$0.796736\pi$
$644$	0	0
$645$	33.8885	1.33436
$646$	−6.47214	−0.254643
$647$	45.1246	1.77403	0.887016	−	0.461739i	$-0.152774\pi$
$647$	45.1246	1.77403	0.887016	+	0.461739i	$0.152774\pi$
$648$	−1.00000	−0.0392837
$649$	9.88854	0.388159
$650$	4.18034	0.163966
$651$	0	0
$652$	−3.05573	−0.119672
$653$	−43.1246	−1.68760	−0.843798	−	0.536661i	$-0.819686\pi$
$653$	−43.1246	−1.68760	−0.843798	+	0.536661i	$0.819686\pi$
$654$	−11.7082	−0.457827
$655$	67.7771	2.64827
$656$	−10.9443	−0.427302
$657$	−6.00000	−0.234082
$658$	0	0
$659$	33.5279	1.30606	0.653030	−	0.757332i	$-0.273498\pi$
$659$	33.5279	1.30606	0.653030	+	0.757332i	$0.273498\pi$
$660$	−6.47214	−0.251928
$661$	39.0132	1.51744	0.758718	−	0.651419i	$-0.225826\pi$
$661$	39.0132	1.51744	0.758718	+	0.651419i	$0.225826\pi$
$662$	1.05573	0.0410320
$663$	−4.94427	−0.192020
$664$	−8.94427	−0.347105
$665$	0	0
$666$	−5.23607	−0.202894
$667$	−3.63932	−0.140915
$668$	−8.00000	−0.309529
$669$	9.70820	0.375341
$670$	22.4721	0.868174
$671$	7.05573	0.272383
$672$	0	0
$673$	−27.5279	−1.06112	−0.530561	−	0.847647i	$-0.678019\pi$
$673$	−27.5279	−1.06112	−0.530561	+	0.847647i	$0.678019\pi$
$674$	−18.9443	−0.729706
$675$	5.47214	0.210623
$676$	−12.4164	−0.477554
$677$	1.63932	0.0630042	0.0315021	−	0.999504i	$-0.489971\pi$
$677$	1.63932	0.0630042	0.0315021	+	0.999504i	$0.489971\pi$
$678$	−3.52786	−0.135487
$679$	0	0
$680$	−20.9443	−0.803176
$681$	24.9443	0.955867
$682$	11.4164	0.437157
$683$	−4.36068	−0.166857	−0.0834284	−	0.996514i	$-0.526587\pi$
$683$	−4.36068	−0.166857	−0.0834284	+	0.996514i	$0.526587\pi$
$684$	1.00000	0.0382360
$685$	56.3607	2.15343
$686$	0	0
$687$	−11.8885	−0.453576
$688$	10.4721	0.399246
$689$	0.360680	0.0137408
$690$	−24.9443	−0.949612
$691$	−21.8885	−0.832679	−0.416340	−	0.909209i	$-0.636687\pi$
$691$	−21.8885	−0.832679	−0.416340	+	0.909209i	$0.636687\pi$
$692$	23.8885	0.908106
$693$	0	0
$694$	−10.0000	−0.379595
$695$	51.7771	1.96402
$696$	0.472136	0.0178963
$697$	−70.8328	−2.68298
$698$	22.3607	0.846364
$699$	6.00000	0.226941
$700$	0	0
$701$	−34.7639	−1.31302	−0.656508	−	0.754319i	$-0.727967\pi$
$701$	−34.7639	−1.31302	−0.656508	+	0.754319i	$0.727967\pi$
$702$	0.763932	0.0288328
$703$	5.23607	0.197482
$704$	−2.00000	−0.0753778
$705$	−23.4164	−0.881913
$706$	8.00000	0.301084
$707$	0	0
$708$	−4.94427	−0.185817
$709$	37.4164	1.40520	0.702601	−	0.711584i	$-0.252022\pi$
$709$	37.4164	1.40520	0.702601	+	0.711584i	$0.252022\pi$
$710$	−17.8885	−0.671345
$711$	−10.1803	−0.381793
$712$	14.9443	0.560060
$713$	44.0000	1.64781
$714$	0	0
$715$	4.94427	0.184905
$716$	11.4164	0.426651
$717$	−8.65248	−0.323133
$718$	−27.7082	−1.03406
$719$	48.5410	1.81027	0.905137	−	0.425119i	$-0.139768\pi$
$719$	48.5410	1.81027	0.905137	+	0.425119i	$0.139768\pi$
$720$	3.23607	0.120601
$721$	0	0
$722$	−1.00000	−0.0372161
$723$	−28.3607	−1.05475
$724$	4.76393	0.177050
$725$	−2.58359	−0.0959522
$726$	7.00000	0.259794
$727$	1.52786	0.0566653	0.0283327	−	0.999599i	$-0.490980\pi$
$727$	1.52786	0.0566653	0.0283327	+	0.999599i	$0.490980\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	19.4164	0.718633
$731$	67.7771	2.50683
$732$	−3.52786	−0.130394
$733$	−43.3050	−1.59950	−0.799752	−	0.600330i	$-0.795036\pi$
$733$	−43.3050	−1.59950	−0.799752	+	0.600330i	$0.795036\pi$
$734$	−36.9443	−1.36364
$735$	0	0
$736$	−7.70820	−0.284128
$737$	13.8885	0.511591
$738$	10.9443	0.402864
$739$	15.0557	0.553834	0.276917	−	0.960894i	$-0.410687\pi$
$739$	15.0557	0.553834	0.276917	+	0.960894i	$0.410687\pi$
$740$	16.9443	0.622884
$741$	−0.763932	−0.0280637
$742$	0	0
$743$	−52.9443	−1.94234	−0.971168	−	0.238394i	$-0.923379\pi$
$743$	−52.9443	−1.94234	−0.971168	+	0.238394i	$0.923379\pi$
$744$	−5.70820	−0.209273
$745$	−32.9443	−1.20698
$746$	11.7082	0.428668
$747$	8.94427	0.327254
$748$	−12.9443	−0.473289
$749$	0	0
$750$	−1.52786	−0.0557897
$751$	31.4853	1.14891	0.574457	−	0.818535i	$-0.305213\pi$
$751$	31.4853	1.14891	0.574457	+	0.818535i	$0.305213\pi$
$752$	−7.23607	−0.263872
$753$	0	0
$754$	−0.360680	−0.0131352
$755$	−0.944272	−0.0343656
$756$	0	0
$757$	−23.3050	−0.847033	−0.423516	−	0.905888i	$-0.639204\pi$
$757$	−23.3050	−0.847033	−0.423516	+	0.905888i	$0.639204\pi$
$758$	−6.94427	−0.252227
$759$	−15.4164	−0.559580
$760$	−3.23607	−0.117385
$761$	28.3607	1.02807	0.514037	−	0.857768i	$-0.328149\pi$
$761$	28.3607	1.02807	0.514037	+	0.857768i	$0.328149\pi$
$762$	−8.29180	−0.300380
$763$	0	0
$764$	−26.1803	−0.947171
$765$	20.9443	0.757242
$766$	24.0000	0.867155
$767$	3.77709	0.136383
$768$	1.00000	0.0360844
$769$	11.8885	0.428712	0.214356	−	0.976756i	$-0.431235\pi$
$769$	11.8885	0.428712	0.214356	+	0.976756i	$0.431235\pi$
$770$	0	0
$771$	−15.8885	−0.572212
$772$	8.47214	0.304919
$773$	−40.4721	−1.45568	−0.727841	−	0.685746i	$-0.759476\pi$
$773$	−40.4721	−1.45568	−0.727841	+	0.685746i	$0.759476\pi$
$774$	−10.4721	−0.376413
$775$	31.2361	1.12203
$776$	1.52786	0.0548471
$777$	0	0
$778$	2.76393	0.0990918
$779$	−10.9443	−0.392119
$780$	−2.47214	−0.0885167
$781$	−11.0557	−0.395605
$782$	−49.8885	−1.78401
$783$	−0.472136	−0.0168728
$784$	0	0
$785$	−14.4721	−0.516533
$786$	−20.9443	−0.747057
$787$	−14.8328	−0.528733	−0.264366	−	0.964422i	$-0.585163\pi$
$787$	−14.8328	−0.528733	−0.264366	+	0.964422i	$0.585163\pi$
$788$	15.7082	0.559582
$789$	18.1803	0.647237
$790$	32.9443	1.17210
$791$	0	0
$792$	2.00000	0.0710669
$793$	2.69505	0.0957040
$794$	10.9443	0.388398
$795$	−1.52786	−0.0541878
$796$	14.4721	0.512951
$797$	6.00000	0.212531	0.106265	−	0.994338i	$-0.466111\pi$
$797$	6.00000	0.212531	0.106265	+	0.994338i	$0.466111\pi$
$798$	0	0
$799$	−46.8328	−1.65683
$800$	−5.47214	−0.193469
$801$	−14.9443	−0.528030
$802$	11.5279	0.407063
$803$	12.0000	0.423471
$804$	−6.94427	−0.244906
$805$	0	0
$806$	4.36068	0.153598
$807$	−19.5279	−0.687413
$808$	−6.29180	−0.221345
$809$	6.58359	0.231467	0.115733	−	0.993280i	$-0.463078\pi$
$809$	6.58359	0.231467	0.115733	+	0.993280i	$0.463078\pi$
$810$	−3.23607	−0.113704
$811$	4.58359	0.160952	0.0804758	−	0.996757i	$-0.474356\pi$
$811$	4.58359	0.160952	0.0804758	+	0.996757i	$0.474356\pi$
$812$	0	0
$813$	4.94427	0.173403
$814$	10.4721	0.367048
$815$	−9.88854	−0.346381
$816$	6.47214	0.226570
$817$	10.4721	0.366374
$818$	14.4721	0.506006
$819$	0	0
$820$	−35.4164	−1.23679
$821$	−35.7082	−1.24622	−0.623112	−	0.782132i	$-0.714132\pi$
$821$	−35.7082	−1.24622	−0.623112	+	0.782132i	$0.714132\pi$
$822$	−17.4164	−0.607467
$823$	−19.7771	−0.689386	−0.344693	−	0.938715i	$-0.612017\pi$
$823$	−19.7771	−0.689386	−0.344693	+	0.938715i	$0.612017\pi$
$824$	18.6525	0.649790
$825$	−10.9443	−0.381031
$826$	0	0
$827$	6.47214	0.225058	0.112529	−	0.993648i	$-0.464105\pi$
$827$	6.47214	0.225058	0.112529	+	0.993648i	$0.464105\pi$
$828$	7.70820	0.267879
$829$	−36.1803	−1.25660	−0.628298	−	0.777973i	$-0.716248\pi$
$829$	−36.1803	−1.25660	−0.628298	+	0.777973i	$0.716248\pi$
$830$	−28.9443	−1.00467
$831$	−11.8885	−0.412409
$832$	−0.763932	−0.0264846
$833$	0	0
$834$	−16.0000	−0.554035
$835$	−25.8885	−0.895910
$836$	−2.00000	−0.0691714
$837$	5.70820	0.197304
$838$	24.3607	0.841526
$839$	−6.11146	−0.210991	−0.105495	−	0.994420i	$-0.533643\pi$
$839$	−6.11146	−0.210991	−0.105495	+	0.994420i	$0.533643\pi$
$840$	0	0
$841$	−28.7771	−0.992313
$842$	6.76393	0.233100
$843$	21.4164	0.737620
$844$	1.41641	0.0487548
$845$	−40.1803	−1.38225
$846$	7.23607	0.248781
$847$	0	0
$848$	−0.472136	−0.0162132
$849$	8.00000	0.274559
$850$	−35.4164	−1.21477
$851$	40.3607	1.38355
$852$	5.52786	0.189382
$853$	10.5836	0.362375	0.181188	−	0.983449i	$-0.442006\pi$
$853$	10.5836	0.362375	0.181188	+	0.983449i	$0.442006\pi$
$854$	0	0
$855$	3.23607	0.110671
$856$	−8.94427	−0.305709
$857$	23.8885	0.816017	0.408009	−	0.912978i	$-0.366223\pi$
$857$	23.8885	0.816017	0.408009	+	0.912978i	$0.366223\pi$
$858$	−1.52786	−0.0521604
$859$	−18.1115	−0.617955	−0.308977	−	0.951069i	$-0.599987\pi$
$859$	−18.1115	−0.617955	−0.308977	+	0.951069i	$0.599987\pi$
$860$	33.8885	1.15559
$861$	0	0
$862$	18.4721	0.629163
$863$	27.0557	0.920988	0.460494	−	0.887663i	$-0.347672\pi$
$863$	27.0557	0.920988	0.460494	+	0.887663i	$0.347672\pi$
$864$	−1.00000	−0.0340207
$865$	77.3050	2.62845
$866$	−22.4721	−0.763634
$867$	24.8885	0.845259
$868$	0	0
$869$	20.3607	0.690689
$870$	1.52786	0.0517994
$871$	5.30495	0.179751
$872$	−11.7082	−0.396490
$873$	−1.52786	−0.0517104
$874$	−7.70820	−0.260734
$875$	0	0
$876$	−6.00000	−0.202721
$877$	−15.7082	−0.530428	−0.265214	−	0.964190i	$-0.585443\pi$
$877$	−15.7082	−0.530428	−0.265214	+	0.964190i	$0.585443\pi$
$878$	−18.6525	−0.629491
$879$	−0.472136	−0.0159248
$880$	−6.47214	−0.218176
$881$	19.0557	0.642004	0.321002	−	0.947079i	$-0.395980\pi$
$881$	19.0557	0.642004	0.321002	+	0.947079i	$0.395980\pi$
$882$	0	0
$883$	44.3607	1.49286	0.746428	−	0.665466i	$-0.231767\pi$
$883$	44.3607	1.49286	0.746428	+	0.665466i	$0.231767\pi$
$884$	−4.94427	−0.166294
$885$	−16.0000	−0.537834
$886$	−23.8885	−0.802551
$887$	−55.1935	−1.85322	−0.926608	−	0.376028i	$-0.877289\pi$
$887$	−55.1935	−1.85322	−0.926608	+	0.376028i	$0.877289\pi$
$888$	−5.23607	−0.175711
$889$	0	0
$890$	48.3607	1.62105
$891$	−2.00000	−0.0670025
$892$	9.70820	0.325055
$893$	−7.23607	−0.242146
$894$	10.1803	0.340481
$895$	36.9443	1.23491
$896$	0	0
$897$	−5.88854	−0.196613
$898$	−30.0000	−1.00111
$899$	−2.69505	−0.0898849
$900$	5.47214	0.182405
$901$	−3.05573	−0.101801
$902$	−21.8885	−0.728809
$903$	0	0
$904$	−3.52786	−0.117335
$905$	15.4164	0.512459
$906$	0.291796	0.00969428
$907$	34.0000	1.12895	0.564476	−	0.825450i	$-0.309078\pi$
$907$	34.0000	1.12895	0.564476	+	0.825450i	$0.309078\pi$
$908$	24.9443	0.827805
$909$	6.29180	0.208686
$910$	0	0
$911$	−13.5279	−0.448198	−0.224099	−	0.974566i	$-0.571944\pi$
$911$	−13.5279	−0.448198	−0.224099	+	0.974566i	$0.571944\pi$
$912$	1.00000	0.0331133
$913$	−17.8885	−0.592024
$914$	26.0000	0.860004
$915$	−11.4164	−0.377415
$916$	−11.8885	−0.392809
$917$	0	0
$918$	−6.47214	−0.213612
$919$	−30.8328	−1.01708	−0.508540	−	0.861038i	$-0.669815\pi$
$919$	−30.8328	−1.01708	−0.508540	+	0.861038i	$0.669815\pi$
$920$	−24.9443	−0.822388
$921$	−14.4721	−0.476873
$922$	−20.7639	−0.683824
$923$	−4.22291	−0.138999
$924$	0	0
$925$	28.6525	0.942088
$926$	16.0000	0.525793
$927$	−18.6525	−0.612628
$928$	0.472136	0.0154986
$929$	12.5836	0.412854	0.206427	−	0.978462i	$-0.433816\pi$
$929$	12.5836	0.412854	0.206427	+	0.978462i	$0.433816\pi$
$930$	−18.4721	−0.605725
$931$	0	0
$932$	6.00000	0.196537
$933$	12.7639	0.417872
$934$	−5.88854	−0.192679
$935$	−41.8885	−1.36990
$936$	0.763932	0.0249699
$937$	−37.7771	−1.23412	−0.617062	−	0.786915i	$-0.711677\pi$
$937$	−37.7771	−1.23412	−0.617062	+	0.786915i	$0.711677\pi$
$938$	0	0
$939$	−30.0000	−0.979013
$940$	−23.4164	−0.763759
$941$	7.52786	0.245401	0.122701	−	0.992444i	$-0.460844\pi$
$941$	7.52786	0.245401	0.122701	+	0.992444i	$0.460844\pi$
$942$	4.47214	0.145710
$943$	−84.3607	−2.74716
$944$	−4.94427	−0.160922
$945$	0	0
$946$	20.9443	0.680957
$947$	−48.2492	−1.56789	−0.783945	−	0.620831i	$-0.786795\pi$
$947$	−48.2492	−1.56789	−0.783945	+	0.620831i	$0.786795\pi$
$948$	−10.1803	−0.330642
$949$	4.58359	0.148790
$950$	−5.47214	−0.177540
$951$	3.52786	0.114399
$952$	0	0
$953$	45.4164	1.47118	0.735591	−	0.677426i	$-0.236905\pi$
$953$	45.4164	1.47118	0.735591	+	0.677426i	$0.236905\pi$
$954$	0.472136	0.0152860
$955$	−84.7214	−2.74152
$956$	−8.65248	−0.279841
$957$	0.944272	0.0305240
$958$	−3.23607	−0.104553
$959$	0	0
$960$	3.23607	0.104444
$961$	1.58359	0.0510836
$962$	4.00000	0.128965
$963$	8.94427	0.288225
$964$	−28.3607	−0.913436
$965$	27.4164	0.882565
$966$	0	0
$967$	7.41641	0.238496	0.119248	−	0.992865i	$-0.461952\pi$
$967$	7.41641	0.238496	0.119248	+	0.992865i	$0.461952\pi$
$968$	7.00000	0.224989
$969$	6.47214	0.207915
$970$	4.94427	0.158751
$971$	−44.7214	−1.43518	−0.717588	−	0.696467i	$-0.754754\pi$
$971$	−44.7214	−1.43518	−0.717588	+	0.696467i	$0.754754\pi$
$972$	1.00000	0.0320750
$973$	0	0
$974$	−14.7639	−0.473067
$975$	−4.18034	−0.133878
$976$	−3.52786	−0.112924
$977$	−21.4164	−0.685172	−0.342586	−	0.939487i	$-0.611303\pi$
$977$	−21.4164	−0.685172	−0.342586	+	0.939487i	$0.611303\pi$
$978$	3.05573	0.0977114
$979$	29.8885	0.955242
$980$	0	0
$981$	11.7082	0.373814
$982$	−32.4721	−1.03623
$983$	45.3050	1.44500	0.722502	−	0.691369i	$-0.242992\pi$
$983$	45.3050	1.44500	0.722502	+	0.691369i	$0.242992\pi$
$984$	10.9443	0.348891
$985$	50.8328	1.61967
$986$	3.05573	0.0973142
$987$	0	0
$988$	−0.763932	−0.0243039
$989$	80.7214	2.56679
$990$	6.47214	0.205698
$991$	36.2918	1.15285	0.576423	−	0.817151i	$-0.304448\pi$
$991$	36.2918	1.15285	0.576423	+	0.817151i	$0.304448\pi$
$992$	−5.70820	−0.181236
$993$	−1.05573	−0.0335025
$994$	0	0
$995$	46.8328	1.48470
$996$	8.94427	0.283410
$997$	−39.5279	−1.25186	−0.625930	−	0.779879i	$-0.715280\pi$
$997$	−39.5279	−1.25186	−0.625930	+	0.779879i	$0.715280\pi$
$998$	36.3607	1.15098
$999$	5.23607	0.165662

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5586.2.a.be.1.2		2
7.6	odd	2		798.2.a.j.1.1	✓	2
21.20	even	2		2394.2.a.z.1.2		2
28.27	even	2		6384.2.a.bn.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.a.j.1.1	✓	2	7.6	odd	2
2394.2.a.z.1.2		2	21.20	even	2
5586.2.a.be.1.2		2	1.1	even	1	trivial
6384.2.a.bn.1.1		2	28.27	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 5586 = 2 \cdot 3 \cdot 7^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5586.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.23607 q^{5} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.23607 q^{5} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} -3.23607 q^{10} -2.00000 q^{11} +1.00000 q^{12} -0.763932 q^{13} +3.23607 q^{15} +1.00000 q^{16} +6.47214 q^{17} -1.00000 q^{18} +1.00000 q^{19} +3.23607 q^{20} +2.00000 q^{22} +7.70820 q^{23} -1.00000 q^{24} +5.47214 q^{25} +0.763932 q^{26} +1.00000 q^{27} -0.472136 q^{29} -3.23607 q^{30} +5.70820 q^{31} -1.00000 q^{32} -2.00000 q^{33} -6.47214 q^{34} +1.00000 q^{36} +5.23607 q^{37} -1.00000 q^{38} -0.763932 q^{39} -3.23607 q^{40} -10.9443 q^{41} +10.4721 q^{43} -2.00000 q^{44} +3.23607 q^{45} -7.70820 q^{46} -7.23607 q^{47} +1.00000 q^{48} -5.47214 q^{50} +6.47214 q^{51} -0.763932 q^{52} -0.472136 q^{53} -1.00000 q^{54} -6.47214 q^{55} +1.00000 q^{57} +0.472136 q^{58} -4.94427 q^{59} +3.23607 q^{60} -3.52786 q^{61} -5.70820 q^{62} +1.00000 q^{64} -2.47214 q^{65} +2.00000 q^{66} -6.94427 q^{67} +6.47214 q^{68} +7.70820 q^{69} +5.52786 q^{71} -1.00000 q^{72} -6.00000 q^{73} -5.23607 q^{74} +5.47214 q^{75} +1.00000 q^{76} +0.763932 q^{78} -10.1803 q^{79} +3.23607 q^{80} +1.00000 q^{81} +10.9443 q^{82} +8.94427 q^{83} +20.9443 q^{85} -10.4721 q^{86} -0.472136 q^{87} +2.00000 q^{88} -14.9443 q^{89} -3.23607 q^{90} +7.70820 q^{92} +5.70820 q^{93} +7.23607 q^{94} +3.23607 q^{95} -1.00000 q^{96} -1.52786 q^{97} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^8 + 2 * q^9	\( 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{8} + 2 q^{9} - 2 q^{10} - 4 q^{11} + 2 q^{12} - 6 q^{13} + 2 q^{15} + 2 q^{16} + 4 q^{17} - 2 q^{18} + 2 q^{19} + 2 q^{20} + 4 q^{22} + 2 q^{23} - 2 q^{24} + 2 q^{25} + 6 q^{26} + 2 q^{27} + 8 q^{29} - 2 q^{30} - 2 q^{31} - 2 q^{32} - 4 q^{33} - 4 q^{34} + 2 q^{36} + 6 q^{37} - 2 q^{38} - 6 q^{39} - 2 q^{40} - 4 q^{41} + 12 q^{43} - 4 q^{44} + 2 q^{45} - 2 q^{46} - 10 q^{47} + 2 q^{48} - 2 q^{50} + 4 q^{51} - 6 q^{52} + 8 q^{53} - 2 q^{54} - 4 q^{55} + 2 q^{57} - 8 q^{58} + 8 q^{59} + 2 q^{60} - 16 q^{61} + 2 q^{62} + 2 q^{64} + 4 q^{65} + 4 q^{66} + 4 q^{67} + 4 q^{68} + 2 q^{69} + 20 q^{71} - 2 q^{72} - 12 q^{73} - 6 q^{74} + 2 q^{75} + 2 q^{76} + 6 q^{78} + 2 q^{79} + 2 q^{80} + 2 q^{81} + 4 q^{82} + 24 q^{85} - 12 q^{86} + 8 q^{87} + 4 q^{88} - 12 q^{89} - 2 q^{90} + 2 q^{92} - 2 q^{93} + 10 q^{94} + 2 q^{95} - 2 q^{96} - 12 q^{97} - 4 q^{99}+O(q^{100}) \) 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 - 4 * q^11 + 2 * q^12 - 6 * q^13 + 2 * q^15 + 2 * q^16 + 4 * q^17 - 2 * q^18 + 2 * q^19 + 2 * q^20 + 4 * q^22 + 2 * q^23 - 2 * q^24 + 2 * q^25 + 6 * q^26 + 2 * q^27 + 8 * q^29 - 2 * q^30 - 2 * q^31 - 2 * q^32 - 4 * q^33 - 4 * q^34 + 2 * q^36 + 6 * q^37 - 2 * q^38 - 6 * q^39 - 2 * q^40 - 4 * q^41 + 12 * q^43 - 4 * q^44 + 2 * q^45 - 2 * q^46 - 10 * q^47 + 2 * q^48 - 2 * q^50 + 4 * q^51 - 6 * q^52 + 8 * q^53 - 2 * q^54 - 4 * q^55 + 2 * q^57 - 8 * q^58 + 8 * q^59 + 2 * q^60 - 16 * q^61 + 2 * q^62 + 2 * q^64 + 4 * q^65 + 4 * q^66 + 4 * q^67 + 4 * q^68 + 2 * q^69 + 20 * q^71 - 2 * q^72 - 12 * q^73 - 6 * q^74 + 2 * q^75 + 2 * q^76 + 6 * q^78 + 2 * q^79 + 2 * q^80 + 2 * q^81 + 4 * q^82 + 24 * q^85 - 12 * q^86 + 8 * q^87 + 4 * q^88 - 12 * q^89 - 2 * q^90 + 2 * q^92 - 2 * q^93 + 10 * q^94 + 2 * q^95 - 2 * q^96 - 12 * q^97 - 4 * q^99

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