LMFDB - Embedded newform 5586.2.a.bi.1.1

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			1.1
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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.23607 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.23607 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} -3.23607 q^{10} +2.00000 q^{11} -1.00000 q^{12} +3.23607 q^{13} +3.23607 q^{15} +1.00000 q^{16} +6.47214 q^{17} +1.00000 q^{18} +1.00000 q^{19} -3.23607 q^{20} +2.00000 q^{22} -7.70820 q^{23} -1.00000 q^{24} +5.47214 q^{25} +3.23607 q^{26} -1.00000 q^{27} -4.47214 q^{29} +3.23607 q^{30} +0.763932 q^{31} +1.00000 q^{32} -2.00000 q^{33} +6.47214 q^{34} +1.00000 q^{36} +5.23607 q^{37} +1.00000 q^{38} -3.23607 q^{39} -3.23607 q^{40} -2.00000 q^{41} -10.4721 q^{43} +2.00000 q^{44} -3.23607 q^{45} -7.70820 q^{46} -9.70820 q^{47} -1.00000 q^{48} +5.47214 q^{50} -6.47214 q^{51} +3.23607 q^{52} +8.47214 q^{53} -1.00000 q^{54} -6.47214 q^{55} -1.00000 q^{57} -4.47214 q^{58} +3.23607 q^{60} +12.4721 q^{61} +0.763932 q^{62} +1.00000 q^{64} -10.4721 q^{65} -2.00000 q^{66} +6.94427 q^{67} +6.47214 q^{68} +7.70820 q^{69} -2.47214 q^{71} +1.00000 q^{72} -2.94427 q^{73} +5.23607 q^{74} -5.47214 q^{75} +1.00000 q^{76} -3.23607 q^{78} +11.7082 q^{79} -3.23607 q^{80} +1.00000 q^{81} -2.00000 q^{82} -12.9443 q^{83} -20.9443 q^{85} -10.4721 q^{86} +4.47214 q^{87} +2.00000 q^{88} +10.0000 q^{89} -3.23607 q^{90} -7.70820 q^{92} -0.763932 q^{93} -9.70820 q^{94} -3.23607 q^{95} -1.00000 q^{96} +15.4164 q^{97} +2.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} + 2 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} + 2 q^{26} - 2 q^{27} + 2 q^{30} + 6 q^{31} + 2 q^{32} - 4 q^{33} + 4 q^{34} + 2 q^{36} + 6 q^{37} + 2 q^{38} - 2 q^{39} - 2 q^{40} - 4 q^{41} - 12 q^{43} + 4 q^{44} - 2 q^{45} - 2 q^{46} - 6 q^{47} - 2 q^{48} + 2 q^{50} - 4 q^{51} + 2 q^{52} + 8 q^{53} - 2 q^{54} - 4 q^{55} - 2 q^{57} + 2 q^{60} + 16 q^{61} + 6 q^{62} + 2 q^{64} - 12 q^{65} - 4 q^{66} - 4 q^{67} + 4 q^{68} + 2 q^{69} + 4 q^{71} + 2 q^{72} + 12 q^{73} + 6 q^{74} - 2 q^{75} + 2 q^{76} - 2 q^{78} + 10 q^{79} - 2 q^{80} + 2 q^{81} - 4 q^{82} - 8 q^{83} - 24 q^{85} - 12 q^{86} + 4 q^{88} + 20 q^{89} - 2 q^{90} - 2 q^{92} - 6 q^{93} - 6 q^{94} - 2 q^{95} - 2 q^{96} + 4 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 + 2 * 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 + 2 * q^26 - 2 * q^27 + 2 * q^30 + 6 * q^31 + 2 * q^32 - 4 * q^33 + 4 * q^34 + 2 * q^36 + 6 * q^37 + 2 * q^38 - 2 * q^39 - 2 * q^40 - 4 * q^41 - 12 * q^43 + 4 * q^44 - 2 * q^45 - 2 * q^46 - 6 * q^47 - 2 * q^48 + 2 * q^50 - 4 * q^51 + 2 * q^52 + 8 * q^53 - 2 * q^54 - 4 * q^55 - 2 * q^57 + 2 * q^60 + 16 * q^61 + 6 * q^62 + 2 * q^64 - 12 * q^65 - 4 * q^66 - 4 * q^67 + 4 * q^68 + 2 * q^69 + 4 * q^71 + 2 * q^72 + 12 * q^73 + 6 * q^74 - 2 * q^75 + 2 * q^76 - 2 * q^78 + 10 * q^79 - 2 * q^80 + 2 * q^81 - 4 * q^82 - 8 * q^83 - 24 * q^85 - 12 * q^86 + 4 * q^88 + 20 * q^89 - 2 * q^90 - 2 * q^92 - 6 * q^93 - 6 * q^94 - 2 * q^95 - 2 * q^96 + 4 * 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	$-0.757517\pi$
$5$	−3.23607	−1.44721	−0.723607	+	0.690212i	$0.757517\pi$
$6$	−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	$-0.402509\pi$
$11$	2.00000	0.603023	0.301511	+	0.953463i	$0.402509\pi$
$12$	−1.00000	−0.288675
$13$	3.23607	0.897524	0.448762	−	0.893651i	$-0.351865\pi$
$13$	3.23607	0.897524	0.448762	+	0.893651i	$0.351865\pi$
$14$	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	$-0.797104\pi$
$23$	−7.70820	−1.60727	−0.803636	+	0.595121i	$0.797104\pi$
$24$	−1.00000	−0.204124
$25$	5.47214	1.09443
$26$	3.23607	0.634645
$27$	−1.00000	−0.192450
$28$	0	0
$29$	−4.47214	−0.830455	−0.415227	−	0.909718i	$-0.636298\pi$
$29$	−4.47214	−0.830455	−0.415227	+	0.909718i	$0.636298\pi$
$30$	3.23607	0.590822
$31$	0.763932	0.137206	0.0686031	−	0.997644i	$-0.478146\pi$
$31$	0.763932	0.137206	0.0686031	+	0.997644i	$0.478146\pi$
$32$	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
$39$	−3.23607	−0.518186
$40$	−3.23607	−0.511667
$41$	−2.00000	−0.312348	−0.156174	−	0.987730i	$-0.549916\pi$
$41$	−2.00000	−0.312348	−0.156174	+	0.987730i	$0.549916\pi$
$42$	0	0
$43$	−10.4721	−1.59699	−0.798493	−	0.602004i	$-0.794369\pi$
$43$	−10.4721	−1.59699	−0.798493	+	0.602004i	$0.794369\pi$
$44$	2.00000	0.301511
$45$	−3.23607	−0.482405
$46$	−7.70820	−1.13651
$47$	−9.70820	−1.41609	−0.708044	−	0.706169i	$-0.750422\pi$
$47$	−9.70820	−1.41609	−0.708044	+	0.706169i	$0.750422\pi$
$48$	−1.00000	−0.144338
$49$	0	0
$50$	5.47214	0.773877
$51$	−6.47214	−0.906280
$52$	3.23607	0.448762
$53$	8.47214	1.16374	0.581869	−	0.813283i	$-0.302322\pi$
$53$	8.47214	1.16374	0.581869	+	0.813283i	$0.302322\pi$
$54$	−1.00000	−0.136083
$55$	−6.47214	−0.872703
$56$	0	0
$57$	−1.00000	−0.132453
$58$	−4.47214	−0.587220
$59$	0	0		−	1.00000i	$-0.5\pi$
$59$	0	0			1.00000i	$0.5\pi$
$60$	3.23607	0.417775
$61$	12.4721	1.59689	0.798447	−	0.602066i	$-0.205655\pi$
$61$	12.4721	1.59689	0.798447	+	0.602066i	$0.205655\pi$
$62$	0.763932	0.0970195
$63$	0	0
$64$	1.00000	0.125000
$65$	−10.4721	−1.29891
$66$	−2.00000	−0.246183
$67$	6.94427	0.848378	0.424189	−	0.905574i	$-0.360559\pi$
$67$	6.94427	0.848378	0.424189	+	0.905574i	$0.360559\pi$
$68$	6.47214	0.784862
$69$	7.70820	0.927959
$70$	0	0
$71$	−2.47214	−0.293389	−0.146694	−	0.989182i	$-0.546863\pi$
$71$	−2.47214	−0.293389	−0.146694	+	0.989182i	$0.546863\pi$
$72$	1.00000	0.117851
$73$	−2.94427	−0.344601	−0.172300	−	0.985044i	$-0.555120\pi$
$73$	−2.94427	−0.344601	−0.172300	+	0.985044i	$0.555120\pi$
$74$	5.23607	0.608681
$75$	−5.47214	−0.631868
$76$	1.00000	0.114708
$77$	0	0
$78$	−3.23607	−0.366413
$79$	11.7082	1.31728	0.658638	−	0.752460i	$-0.271133\pi$
$79$	11.7082	1.31728	0.658638	+	0.752460i	$0.271133\pi$
$80$	−3.23607	−0.361803
$81$	1.00000	0.111111
$82$	−2.00000	−0.220863
$83$	−12.9443	−1.42082	−0.710409	−	0.703789i	$-0.751490\pi$
$83$	−12.9443	−1.42082	−0.710409	+	0.703789i	$0.751490\pi$
$84$	0	0
$85$	−20.9443	−2.27173
$86$	−10.4721	−1.12924
$87$	4.47214	0.479463
$88$	2.00000	0.213201
$89$	10.0000	1.06000	0.529999	−	0.847998i	$-0.322192\pi$
$89$	10.0000	1.06000	0.529999	+	0.847998i	$0.322192\pi$
$90$	−3.23607	−0.341112
$91$	0	0
$92$	−7.70820	−0.803636
$93$	−0.763932	−0.0792161
$94$	−9.70820	−1.00132
$95$	−3.23607	−0.332014
$96$	−1.00000	−0.102062
$97$	15.4164	1.56530	0.782650	−	0.622463i	$-0.213868\pi$
$97$	15.4164	1.56530	0.782650	+	0.622463i	$0.213868\pi$
$98$	0	0
$99$	2.00000	0.201008
$100$	5.47214	0.547214
$101$	−8.18034	−0.813974	−0.406987	−	0.913434i	$-0.633421\pi$
$101$	−8.18034	−0.813974	−0.406987	+	0.913434i	$0.633421\pi$
$102$	−6.47214	−0.640837
$103$	−5.70820	−0.562446	−0.281223	−	0.959642i	$-0.590740\pi$
$103$	−5.70820	−0.562446	−0.281223	+	0.959642i	$0.590740\pi$
$104$	3.23607	0.317323
$105$	0	0
$106$	8.47214	0.822887
$107$	16.9443	1.63806	0.819032	−	0.573747i	$-0.194511\pi$
$107$	16.9443	1.63806	0.819032	+	0.573747i	$0.194511\pi$
$108$	−1.00000	−0.0962250
$109$	−6.18034	−0.591969	−0.295985	−	0.955193i	$-0.595648\pi$
$109$	−6.18034	−0.591969	−0.295985	+	0.955193i	$0.595648\pi$
$110$	−6.47214	−0.617094
$111$	−5.23607	−0.496986
$112$	0	0
$113$	17.4164	1.63840	0.819199	−	0.573509i	$-0.194418\pi$
$113$	17.4164	1.63840	0.819199	+	0.573509i	$0.194418\pi$
$114$	−1.00000	−0.0936586
$115$	24.9443	2.32607
$116$	−4.47214	−0.415227
$117$	3.23607	0.299175
$118$	0	0
$119$	0	0
$120$	3.23607	0.295411
$121$	−7.00000	−0.636364
$122$	12.4721	1.12917
$123$	2.00000	0.180334
$124$	0.763932	0.0686031
$125$	−1.52786	−0.136656
$126$	0	0
$127$	14.1803	1.25830	0.629151	−	0.777283i	$-0.283403\pi$
$127$	14.1803	1.25830	0.629151	+	0.777283i	$0.283403\pi$
$128$	1.00000	0.0883883
$129$	10.4721	0.922020
$130$	−10.4721	−0.918467
$131$	16.9443	1.48043	0.740214	−	0.672371i	$-0.234724\pi$
$131$	16.9443	1.48043	0.740214	+	0.672371i	$0.234724\pi$
$132$	−2.00000	−0.174078
$133$	0	0
$134$	6.94427	0.599894
$135$	3.23607	0.278516
$136$	6.47214	0.554981
$137$	12.4721	1.06557	0.532783	−	0.846252i	$-0.321146\pi$
$137$	12.4721	1.06557	0.532783	+	0.846252i	$0.321146\pi$
$138$	7.70820	0.656166
$139$	0	0		−	1.00000i	$-0.5\pi$
$139$	0	0			1.00000i	$0.5\pi$
$140$	0	0
$141$	9.70820	0.817578
$142$	−2.47214	−0.207457
$143$	6.47214	0.541227
$144$	1.00000	0.0833333
$145$	14.4721	1.20185
$146$	−2.94427	−0.243670
$147$	0	0
$148$	5.23607	0.430402
$149$	−11.7082	−0.959173	−0.479587	−	0.877494i	$-0.659213\pi$
$149$	−11.7082	−0.959173	−0.479587	+	0.877494i	$0.659213\pi$
$150$	−5.47214	−0.446798
$151$	−14.1803	−1.15398	−0.576990	−	0.816751i	$-0.695773\pi$
$151$	−14.1803	−1.15398	−0.576990	+	0.816751i	$0.695773\pi$
$152$	1.00000	0.0811107
$153$	6.47214	0.523241
$154$	0	0
$155$	−2.47214	−0.198567
$156$	−3.23607	−0.259093
$157$	16.4721	1.31462	0.657310	−	0.753620i	$-0.271694\pi$
$157$	16.4721	1.31462	0.657310	+	0.753620i	$0.271694\pi$
$158$	11.7082	0.931455
$159$	−8.47214	−0.671884
$160$	−3.23607	−0.255834
$161$	0	0
$162$	1.00000	0.0785674
$163$	−4.94427	−0.387265	−0.193633	−	0.981074i	$-0.562027\pi$
$163$	−4.94427	−0.387265	−0.193633	+	0.981074i	$0.562027\pi$
$164$	−2.00000	−0.156174
$165$	6.47214	0.503855
$166$	−12.9443	−1.00467
$167$	−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
$169$	−2.52786	−0.194451
$170$	−20.9443	−1.60635
$171$	1.00000	0.0764719
$172$	−10.4721	−0.798493
$173$	14.9443	1.13619	0.568096	−	0.822962i	$-0.307680\pi$
$173$	14.9443	1.13619	0.568096	+	0.822962i	$0.307680\pi$
$174$	4.47214	0.339032
$175$	0	0
$176$	2.00000	0.150756
$177$	0	0
$178$	10.0000	0.749532
$179$	14.4721	1.08170	0.540849	−	0.841120i	$-0.318103\pi$
$179$	14.4721	1.08170	0.540849	+	0.841120i	$0.318103\pi$
$180$	−3.23607	−0.241202
$181$	0.763932	0.0567826	0.0283913	−	0.999597i	$-0.490962\pi$
$181$	0.763932	0.0567826	0.0283913	+	0.999597i	$0.490962\pi$
$182$	0	0
$183$	−12.4721	−0.921967
$184$	−7.70820	−0.568256
$185$	−16.9443	−1.24577
$186$	−0.763932	−0.0560142
$187$	12.9443	0.946579
$188$	−9.70820	−0.708044
$189$	0	0
$190$	−3.23607	−0.234769
$191$	18.1803	1.31548	0.657742	−	0.753244i	$-0.271512\pi$
$191$	18.1803	1.31548	0.657742	+	0.753244i	$0.271512\pi$
$192$	−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	$0.401371\pi$
$194$	15.4164	1.10683
$195$	10.4721	0.749925
$196$	0	0
$197$	−3.70820	−0.264199	−0.132099	−	0.991236i	$-0.542172\pi$
$197$	−3.70820	−0.264199	−0.132099	+	0.991236i	$0.542172\pi$
$198$	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
$202$	−8.18034	−0.575567
$203$	0	0
$204$	−6.47214	−0.453140
$205$	6.47214	0.452034
$206$	−5.70820	−0.397709
$207$	−7.70820	−0.535757
$208$	3.23607	0.224381
$209$	2.00000	0.138343
$210$	0	0
$211$	5.41641	0.372881	0.186440	−	0.982466i	$-0.440305\pi$
$211$	5.41641	0.372881	0.186440	+	0.982466i	$0.440305\pi$
$212$	8.47214	0.581869
$213$	2.47214	0.169388
$214$	16.9443	1.15829
$215$	33.8885	2.31118
$216$	−1.00000	−0.0680414
$217$	0	0
$218$	−6.18034	−0.418585
$219$	2.94427	0.198955
$220$	−6.47214	−0.436351
$221$	20.9443	1.40886
$222$	−5.23607	−0.351422
$223$	−11.2361	−0.752423	−0.376211	−	0.926534i	$-0.622773\pi$
$223$	−11.2361	−0.752423	−0.376211	+	0.926534i	$0.622773\pi$
$224$	0	0
$225$	5.47214	0.364809
$226$	17.4164	1.15852
$227$	0.944272	0.0626735	0.0313368	−	0.999509i	$-0.490024\pi$
$227$	0.944272	0.0626735	0.0313368	+	0.999509i	$0.490024\pi$
$228$	−1.00000	−0.0662266
$229$	1.05573	0.0697645	0.0348822	−	0.999391i	$-0.488894\pi$
$229$	1.05573	0.0697645	0.0348822	+	0.999391i	$0.488894\pi$
$230$	24.9443	1.64478
$231$	0	0
$232$	−4.47214	−0.293610
$233$	−26.0000	−1.70332	−0.851658	−	0.524097i	$-0.824403\pi$
$233$	−26.0000	−1.70332	−0.851658	+	0.524097i	$0.824403\pi$
$234$	3.23607	0.211548
$235$	31.4164	2.04938
$236$	0	0
$237$	−11.7082	−0.760530
$238$	0	0
$239$	22.7639	1.47248	0.736238	−	0.676723i	$-0.236600\pi$
$239$	22.7639	1.47248	0.736238	+	0.676723i	$0.236600\pi$
$240$	3.23607	0.208887
$241$	22.4721	1.44756	0.723779	−	0.690032i	$-0.242404\pi$
$241$	22.4721	1.44756	0.723779	+	0.690032i	$0.242404\pi$
$242$	−7.00000	−0.449977
$243$	−1.00000	−0.0641500
$244$	12.4721	0.798447
$245$	0	0
$246$	2.00000	0.127515
$247$	3.23607	0.205906
$248$	0.763932	0.0485097
$249$	12.9443	0.820310
$250$	−1.52786	−0.0966306
$251$	−12.0000	−0.757433	−0.378717	−	0.925513i	$-0.623635\pi$
$251$	−12.0000	−0.757433	−0.378717	+	0.925513i	$0.623635\pi$
$252$	0	0
$253$	−15.4164	−0.969221
$254$	14.1803	0.889754
$255$	20.9443	1.31158
$256$	1.00000	0.0625000
$257$	−24.8328	−1.54903	−0.774514	−	0.632556i	$-0.782006\pi$
$257$	−24.8328	−1.54903	−0.774514	+	0.632556i	$0.782006\pi$
$258$	10.4721	0.651967
$259$	0	0
$260$	−10.4721	−0.649454
$261$	−4.47214	−0.276818
$262$	16.9443	1.04682
$263$	−2.18034	−0.134446	−0.0672228	−	0.997738i	$-0.521414\pi$
$263$	−2.18034	−0.134446	−0.0672228	+	0.997738i	$0.521414\pi$
$264$	−2.00000	−0.123091
$265$	−27.4164	−1.68418
$266$	0	0
$267$	−10.0000	−0.611990
$268$	6.94427	0.424189
$269$	−4.47214	−0.272671	−0.136335	−	0.990663i	$-0.543533\pi$
$269$	−4.47214	−0.272671	−0.136335	+	0.990663i	$0.543533\pi$
$270$	3.23607	0.196941
$271$	25.8885	1.57262	0.786309	−	0.617834i	$-0.211990\pi$
$271$	25.8885	1.57262	0.786309	+	0.617834i	$0.211990\pi$
$272$	6.47214	0.392431
$273$	0	0
$274$	12.4721	0.753469
$275$	10.9443	0.659964
$276$	7.70820	0.463979
$277$	26.9443	1.61892	0.809462	−	0.587172i	$-0.199759\pi$
$277$	26.9443	1.61892	0.809462	+	0.587172i	$0.199759\pi$
$278$	0	0
$279$	0.763932	0.0457354
$280$	0	0
$281$	7.52786	0.449075	0.224537	−	0.974465i	$-0.427913\pi$
$281$	7.52786	0.449075	0.224537	+	0.974465i	$0.427913\pi$
$282$	9.70820	0.578115
$283$	16.0000	0.951101	0.475551	−	0.879688i	$-0.342249\pi$
$283$	16.0000	0.951101	0.475551	+	0.879688i	$0.342249\pi$
$284$	−2.47214	−0.146694
$285$	3.23607	0.191688
$286$	6.47214	0.382705
$287$	0	0
$288$	1.00000	0.0589256
$289$	24.8885	1.46403
$290$	14.4721	0.849833
$291$	−15.4164	−0.903726
$292$	−2.94427	−0.172300
$293$	−17.4164	−1.01748	−0.508739	−	0.860921i	$-0.669888\pi$
$293$	−17.4164	−1.01748	−0.508739	+	0.860921i	$0.669888\pi$
$294$	0	0
$295$	0	0
$296$	5.23607	0.304340
$297$	−2.00000	−0.116052
$298$	−11.7082	−0.678238
$299$	−24.9443	−1.44256
$300$	−5.47214	−0.315934
$301$	0	0
$302$	−14.1803	−0.815987
$303$	8.18034	0.469948
$304$	1.00000	0.0573539
$305$	−40.3607	−2.31105
$306$	6.47214	0.369987
$307$	−4.58359	−0.261599	−0.130800	−	0.991409i	$-0.541754\pi$
$307$	−4.58359	−0.261599	−0.130800	+	0.991409i	$0.541754\pi$
$308$	0	0
$309$	5.70820	0.324728
$310$	−2.47214	−0.140408
$311$	4.18034	0.237045	0.118523	−	0.992951i	$-0.462184\pi$
$311$	4.18034	0.237045	0.118523	+	0.992951i	$0.462184\pi$
$312$	−3.23607	−0.183206
$313$	−2.94427	−0.166420	−0.0832100	−	0.996532i	$-0.526517\pi$
$313$	−2.94427	−0.166420	−0.0832100	+	0.996532i	$0.526517\pi$
$314$	16.4721	0.929576
$315$	0	0
$316$	11.7082	0.658638
$317$	−34.3607	−1.92989	−0.964944	−	0.262456i	$-0.915468\pi$
$317$	−34.3607	−1.92989	−0.964944	+	0.262456i	$0.915468\pi$
$318$	−8.47214	−0.475094
$319$	−8.94427	−0.500783
$320$	−3.23607	−0.180902
$321$	−16.9443	−0.945737
$322$	0	0
$323$	6.47214	0.360119
$324$	1.00000	0.0555556
$325$	17.7082	0.982274
$326$	−4.94427	−0.273838
$327$	6.18034	0.341774
$328$	−2.00000	−0.110432
$329$	0	0
$330$	6.47214	0.356279
$331$	−6.94427	−0.381692	−0.190846	−	0.981620i	$-0.561123\pi$
$331$	−6.94427	−0.381692	−0.190846	+	0.981620i	$0.561123\pi$
$332$	−12.9443	−0.710409
$333$	5.23607	0.286935
$334$	−8.00000	−0.437741
$335$	−22.4721	−1.22778
$336$	0	0
$337$	9.05573	0.493297	0.246648	−	0.969105i	$-0.420671\pi$
$337$	9.05573	0.493297	0.246648	+	0.969105i	$0.420671\pi$
$338$	−2.52786	−0.137498
$339$	−17.4164	−0.945929
$340$	−20.9443	−1.13586
$341$	1.52786	0.0827385
$342$	1.00000	0.0540738
$343$	0	0
$344$	−10.4721	−0.564620
$345$	−24.9443	−1.34295
$346$	14.9443	0.803409
$347$	−2.00000	−0.107366	−0.0536828	−	0.998558i	$-0.517096\pi$
$347$	−2.00000	−0.107366	−0.0536828	+	0.998558i	$0.517096\pi$
$348$	4.47214	0.239732
$349$	13.4164	0.718164	0.359082	−	0.933306i	$-0.383090\pi$
$349$	13.4164	0.718164	0.359082	+	0.933306i	$0.383090\pi$
$350$	0	0
$351$	−3.23607	−0.172729
$352$	2.00000	0.106600
$353$	4.94427	0.263157	0.131579	−	0.991306i	$-0.457995\pi$
$353$	4.94427	0.263157	0.131579	+	0.991306i	$0.457995\pi$
$354$	0	0
$355$	8.00000	0.424596
$356$	10.0000	0.529999
$357$	0	0
$358$	14.4721	0.764876
$359$	−11.7082	−0.617935	−0.308968	−	0.951073i	$-0.599983\pi$
$359$	−11.7082	−0.617935	−0.308968	+	0.951073i	$0.599983\pi$
$360$	−3.23607	−0.170556
$361$	1.00000	0.0526316
$362$	0.763932	0.0401514
$363$	7.00000	0.367405
$364$	0	0
$365$	9.52786	0.498711
$366$	−12.4721	−0.651929
$367$	−25.8885	−1.35137	−0.675685	−	0.737190i	$-0.736152\pi$
$367$	−25.8885	−1.35137	−0.675685	+	0.737190i	$0.736152\pi$
$368$	−7.70820	−0.401818
$369$	−2.00000	−0.104116
$370$	−16.9443	−0.880891
$371$	0	0
$372$	−0.763932	−0.0396080
$373$	12.2918	0.636445	0.318223	−	0.948016i	$-0.396914\pi$
$373$	12.2918	0.636445	0.318223	+	0.948016i	$0.396914\pi$
$374$	12.9443	0.669332
$375$	1.52786	0.0788986
$376$	−9.70820	−0.500662
$377$	−14.4721	−0.745353
$378$	0	0
$379$	1.05573	0.0542291	0.0271146	−	0.999632i	$-0.491368\pi$
$379$	1.05573	0.0542291	0.0271146	+	0.999632i	$0.491368\pi$
$380$	−3.23607	−0.166007
$381$	−14.1803	−0.726481
$382$	18.1803	0.930187
$383$	−12.9443	−0.661421	−0.330711	−	0.943732i	$-0.607288\pi$
$383$	−12.9443	−0.661421	−0.330711	+	0.943732i	$0.607288\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	8.47214	0.431220
$387$	−10.4721	−0.532329
$388$	15.4164	0.782650
$389$	22.7639	1.15418	0.577089	−	0.816682i	$-0.304189\pi$
$389$	22.7639	1.15418	0.577089	+	0.816682i	$0.304189\pi$
$390$	10.4721	0.530277
$391$	−49.8885	−2.52297
$392$	0	0
$393$	−16.9443	−0.854725
$394$	−3.70820	−0.186817
$395$	−37.8885	−1.90638
$396$	2.00000	0.100504
$397$	2.00000	0.100377	0.0501886	−	0.998740i	$-0.484018\pi$
$397$	2.00000	0.100377	0.0501886	+	0.998740i	$0.484018\pi$
$398$	14.4721	0.725423
$399$	0	0
$400$	5.47214	0.273607
$401$	−23.5279	−1.17493	−0.587463	−	0.809251i	$-0.699873\pi$
$401$	−23.5279	−1.17493	−0.587463	+	0.809251i	$0.699873\pi$
$402$	−6.94427	−0.346349
$403$	2.47214	0.123146
$404$	−8.18034	−0.406987
$405$	−3.23607	−0.160802
$406$	0	0
$407$	10.4721	0.519085
$408$	−6.47214	−0.320418
$409$	34.4721	1.70454	0.852269	−	0.523104i	$-0.175226\pi$
$409$	34.4721	1.70454	0.852269	+	0.523104i	$0.175226\pi$
$410$	6.47214	0.319636
$411$	−12.4721	−0.615205
$412$	−5.70820	−0.281223
$413$	0	0
$414$	−7.70820	−0.378838
$415$	41.8885	2.05623
$416$	3.23607	0.158661
$417$	0	0
$418$	2.00000	0.0978232
$419$	−5.52786	−0.270054	−0.135027	−	0.990842i	$-0.543112\pi$
$419$	−5.52786	−0.270054	−0.135027	+	0.990842i	$0.543112\pi$
$420$	0	0
$421$	9.23607	0.450138	0.225069	−	0.974343i	$-0.427739\pi$
$421$	9.23607	0.450138	0.225069	+	0.974343i	$0.427739\pi$
$422$	5.41641	0.263667
$423$	−9.70820	−0.472029
$424$	8.47214	0.411443
$425$	35.4164	1.71795
$426$	2.47214	0.119775
$427$	0	0
$428$	16.9443	0.819032
$429$	−6.47214	−0.312478
$430$	33.8885	1.63425
$431$	15.4164	0.742582	0.371291	−	0.928517i	$-0.378915\pi$
$431$	15.4164	0.742582	0.371291	+	0.928517i	$0.378915\pi$
$432$	−1.00000	−0.0481125
$433$	−0.583592	−0.0280456	−0.0140228	−	0.999902i	$-0.504464\pi$
$433$	−0.583592	−0.0280456	−0.0140228	+	0.999902i	$0.504464\pi$
$434$	0	0
$435$	−14.4721	−0.693886
$436$	−6.18034	−0.295985
$437$	−7.70820	−0.368733
$438$	2.94427	0.140683
$439$	−36.1803	−1.72679	−0.863397	−	0.504526i	$-0.831667\pi$
$439$	−36.1803	−1.72679	−0.863397	+	0.504526i	$0.831667\pi$
$440$	−6.47214	−0.308547
$441$	0	0
$442$	20.9443	0.996217
$443$	11.8885	0.564842	0.282421	−	0.959291i	$-0.408863\pi$
$443$	11.8885	0.564842	0.282421	+	0.959291i	$0.408863\pi$
$444$	−5.23607	−0.248493
$445$	−32.3607	−1.53404
$446$	−11.2361	−0.532043
$447$	11.7082	0.553779
$448$	0	0
$449$	27.8885	1.31614	0.658071	−	0.752956i	$-0.271373\pi$
$449$	27.8885	1.31614	0.658071	+	0.752956i	$0.271373\pi$
$450$	5.47214	0.257959
$451$	−4.00000	−0.188353
$452$	17.4164	0.819199
$453$	14.1803	0.666250
$454$	0.944272	0.0443169
$455$	0	0
$456$	−1.00000	−0.0468293
$457$	−19.8885	−0.930347	−0.465173	−	0.885220i	$-0.654008\pi$
$457$	−19.8885	−0.930347	−0.465173	+	0.885220i	$0.654008\pi$
$458$	1.05573	0.0493309
$459$	−6.47214	−0.302093
$460$	24.9443	1.16303
$461$	−22.6525	−1.05503	−0.527515	−	0.849545i	$-0.676876\pi$
$461$	−22.6525	−1.05503	−0.527515	+	0.849545i	$0.676876\pi$
$462$	0	0
$463$	12.9443	0.601571	0.300786	−	0.953692i	$-0.402751\pi$
$463$	12.9443	0.601571	0.300786	+	0.953692i	$0.402751\pi$
$464$	−4.47214	−0.207614
$465$	2.47214	0.114643
$466$	−26.0000	−1.20443
$467$	9.88854	0.457587	0.228794	−	0.973475i	$-0.426522\pi$
$467$	9.88854	0.457587	0.228794	+	0.973475i	$0.426522\pi$
$468$	3.23607	0.149587
$469$	0	0
$470$	31.4164	1.44913
$471$	−16.4721	−0.758996
$472$	0	0
$473$	−20.9443	−0.963019
$474$	−11.7082	−0.537776
$475$	5.47214	0.251079
$476$	0	0
$477$	8.47214	0.387912
$478$	22.7639	1.04120
$479$	−36.1803	−1.65312	−0.826561	−	0.562847i	$-0.809706\pi$
$479$	−36.1803	−1.65312	−0.826561	+	0.562847i	$0.809706\pi$
$480$	3.23607	0.147706
$481$	16.9443	0.772592
$482$	22.4721	1.02358
$483$	0	0
$484$	−7.00000	−0.318182
$485$	−49.8885	−2.26532
$486$	−1.00000	−0.0453609
$487$	10.7639	0.487760	0.243880	−	0.969805i	$-0.421580\pi$
$487$	10.7639	0.487760	0.243880	+	0.969805i	$0.421580\pi$
$488$	12.4721	0.564587
$489$	4.94427	0.223588
$490$	0	0
$491$	7.52786	0.339728	0.169864	−	0.985468i	$-0.445667\pi$
$491$	7.52786	0.339728	0.169864	+	0.985468i	$0.445667\pi$
$492$	2.00000	0.0901670
$493$	−28.9443	−1.30358
$494$	3.23607	0.145598
$495$	−6.47214	−0.290901
$496$	0.763932	0.0343016
$497$	0	0
$498$	12.9443	0.580047
$499$	−41.3050	−1.84906	−0.924532	−	0.381105i	$-0.875544\pi$
$499$	−41.3050	−1.84906	−0.924532	+	0.381105i	$0.875544\pi$
$500$	−1.52786	−0.0683282
$501$	8.00000	0.357414
$502$	−12.0000	−0.535586
$503$	12.1803	0.543095	0.271547	−	0.962425i	$-0.412465\pi$
$503$	12.1803	0.543095	0.271547	+	0.962425i	$0.412465\pi$
$504$	0	0
$505$	26.4721	1.17799
$506$	−15.4164	−0.685343
$507$	2.52786	0.112266
$508$	14.1803	0.629151
$509$	13.4164	0.594672	0.297336	−	0.954773i	$-0.403902\pi$
$509$	13.4164	0.594672	0.297336	+	0.954773i	$0.403902\pi$
$510$	20.9443	0.927428
$511$	0	0
$512$	1.00000	0.0441942
$513$	−1.00000	−0.0441511
$514$	−24.8328	−1.09533
$515$	18.4721	0.813980
$516$	10.4721	0.461010
$517$	−19.4164	−0.853933
$518$	0	0
$519$	−14.9443	−0.655981
$520$	−10.4721	−0.459234
$521$	18.0000	0.788594	0.394297	−	0.918983i	$-0.370988\pi$
$521$	18.0000	0.788594	0.394297	+	0.918983i	$0.370988\pi$
$522$	−4.47214	−0.195740
$523$	37.3050	1.63123	0.815616	−	0.578594i	$-0.196398\pi$
$523$	37.3050	1.63123	0.815616	+	0.578594i	$0.196398\pi$
$524$	16.9443	0.740214
$525$	0	0
$526$	−2.18034	−0.0950673
$527$	4.94427	0.215376
$528$	−2.00000	−0.0870388
$529$	36.4164	1.58332
$530$	−27.4164	−1.19089
$531$	0	0
$532$	0	0
$533$	−6.47214	−0.280339
$534$	−10.0000	−0.432742
$535$	−54.8328	−2.37063
$536$	6.94427	0.299947
$537$	−14.4721	−0.624519
$538$	−4.47214	−0.192807
$539$	0	0
$540$	3.23607	0.139258
$541$	19.8885	0.855075	0.427538	−	0.903998i	$-0.359381\pi$
$541$	19.8885	0.855075	0.427538	+	0.903998i	$0.359381\pi$
$542$	25.8885	1.11201
$543$	−0.763932	−0.0327835
$544$	6.47214	0.277491
$545$	20.0000	0.856706
$546$	0	0
$547$	35.8885	1.53448	0.767242	−	0.641358i	$-0.221629\pi$
$547$	35.8885	1.53448	0.767242	+	0.641358i	$0.221629\pi$
$548$	12.4721	0.532783
$549$	12.4721	0.532298
$550$	10.9443	0.466665
$551$	−4.47214	−0.190519
$552$	7.70820	0.328083
$553$	0	0
$554$	26.9443	1.14475
$555$	16.9443	0.719244
$556$	0	0
$557$	3.12461	0.132394	0.0661970	−	0.997807i	$-0.478913\pi$
$557$	3.12461	0.132394	0.0661970	+	0.997807i	$0.478913\pi$
$558$	0.763932	0.0323398
$559$	−33.8885	−1.43333
$560$	0	0
$561$	−12.9443	−0.546508
$562$	7.52786	0.317544
$563$	22.8328	0.962288	0.481144	−	0.876641i	$-0.340221\pi$
$563$	22.8328	0.962288	0.481144	+	0.876641i	$0.340221\pi$
$564$	9.70820	0.408789
$565$	−56.3607	−2.37111
$566$	16.0000	0.672530
$567$	0	0
$568$	−2.47214	−0.103729
$569$	−38.9443	−1.63263	−0.816314	−	0.577608i	$-0.803986\pi$
$569$	−38.9443	−1.63263	−0.816314	+	0.577608i	$0.803986\pi$
$570$	3.23607	0.135544
$571$	−4.58359	−0.191817	−0.0959087	−	0.995390i	$-0.530576\pi$
$571$	−4.58359	−0.191817	−0.0959087	+	0.995390i	$0.530576\pi$
$572$	6.47214	0.270614
$573$	−18.1803	−0.759495
$574$	0	0
$575$	−42.1803	−1.75904
$576$	1.00000	0.0416667
$577$	−35.8885	−1.49406	−0.747030	−	0.664791i	$-0.768521\pi$
$577$	−35.8885	−1.49406	−0.747030	+	0.664791i	$0.768521\pi$
$578$	24.8885	1.03523
$579$	−8.47214	−0.352090
$580$	14.4721	0.600923
$581$	0	0
$582$	−15.4164	−0.639031
$583$	16.9443	0.701760
$584$	−2.94427	−0.121835
$585$	−10.4721	−0.432970
$586$	−17.4164	−0.719465
$587$	24.3607	1.00547	0.502736	−	0.864440i	$-0.332327\pi$
$587$	24.3607	1.00547	0.502736	+	0.864440i	$0.332327\pi$
$588$	0	0
$589$	0.763932	0.0314773
$590$	0	0
$591$	3.70820	0.152535
$592$	5.23607	0.215201
$593$	−10.8328	−0.444850	−0.222425	−	0.974950i	$-0.571397\pi$
$593$	−10.8328	−0.444850	−0.222425	+	0.974950i	$0.571397\pi$
$594$	−2.00000	−0.0820610
$595$	0	0
$596$	−11.7082	−0.479587
$597$	−14.4721	−0.592305
$598$	−24.9443	−1.02005
$599$	−23.4164	−0.956768	−0.478384	−	0.878151i	$-0.658777\pi$
$599$	−23.4164	−0.956768	−0.478384	+	0.878151i	$0.658777\pi$
$600$	−5.47214	−0.223399
$601$	23.7771	0.969888	0.484944	−	0.874545i	$-0.338840\pi$
$601$	23.7771	0.969888	0.484944	+	0.874545i	$0.338840\pi$
$602$	0	0
$603$	6.94427	0.282793
$604$	−14.1803	−0.576990
$605$	22.6525	0.920954
$606$	8.18034	0.332304
$607$	8.18034	0.332030	0.166015	−	0.986123i	$-0.446910\pi$
$607$	8.18034	0.332030	0.166015	+	0.986123i	$0.446910\pi$
$608$	1.00000	0.0405554
$609$	0	0
$610$	−40.3607	−1.63416
$611$	−31.4164	−1.27097
$612$	6.47214	0.261621
$613$	17.4164	0.703442	0.351721	−	0.936105i	$-0.385597\pi$
$613$	17.4164	0.703442	0.351721	+	0.936105i	$0.385597\pi$
$614$	−4.58359	−0.184979
$615$	−6.47214	−0.260982
$616$	0	0
$617$	26.9443	1.08474	0.542368	−	0.840141i	$-0.317528\pi$
$617$	26.9443	1.08474	0.542368	+	0.840141i	$0.317528\pi$
$618$	5.70820	0.229618
$619$	26.8328	1.07850	0.539251	−	0.842145i	$-0.318707\pi$
$619$	26.8328	1.07850	0.539251	+	0.842145i	$0.318707\pi$
$620$	−2.47214	−0.0992834
$621$	7.70820	0.309320
$622$	4.18034	0.167616
$623$	0	0
$624$	−3.23607	−0.129546
$625$	−22.4164	−0.896656
$626$	−2.94427	−0.117677
$627$	−2.00000	−0.0798723
$628$	16.4721	0.657310
$629$	33.8885	1.35122
$630$	0	0
$631$	−20.3607	−0.810546	−0.405273	−	0.914196i	$-0.632824\pi$
$631$	−20.3607	−0.810546	−0.405273	+	0.914196i	$0.632824\pi$
$632$	11.7082	0.465727
$633$	−5.41641	−0.215283
$634$	−34.3607	−1.36464
$635$	−45.8885	−1.82103
$636$	−8.47214	−0.335942
$637$	0	0
$638$	−8.94427	−0.354107
$639$	−2.47214	−0.0977962
$640$	−3.23607	−0.127917
$641$	−44.8328	−1.77079	−0.885395	−	0.464840i	$-0.846112\pi$
$641$	−44.8328	−1.77079	−0.885395	+	0.464840i	$0.846112\pi$
$642$	−16.9443	−0.668737
$643$	4.94427	0.194983	0.0974915	−	0.995236i	$-0.468918\pi$
$643$	4.94427	0.194983	0.0974915	+	0.995236i	$0.468918\pi$
$644$	0	0
$645$	−33.8885	−1.33436
$646$	6.47214	0.254643
$647$	13.7082	0.538925	0.269463	−	0.963011i	$-0.413154\pi$
$647$	13.7082	0.538925	0.269463	+	0.963011i	$0.413154\pi$
$648$	1.00000	0.0392837
$649$	0	0
$650$	17.7082	0.694573
$651$	0	0
$652$	−4.94427	−0.193633
$653$	−18.7639	−0.734289	−0.367145	−	0.930164i	$-0.619665\pi$
$653$	−18.7639	−0.734289	−0.367145	+	0.930164i	$0.619665\pi$
$654$	6.18034	0.241670
$655$	−54.8328	−2.14250
$656$	−2.00000	−0.0780869
$657$	−2.94427	−0.114867
$658$	0	0
$659$	50.2492	1.95743	0.978716	−	0.205220i	$-0.0657909\pi$
$659$	50.2492	1.95743	0.978716	+	0.205220i	$0.0657909\pi$
$660$	6.47214	0.251928
$661$	−2.65248	−0.103169	−0.0515847	−	0.998669i	$-0.516427\pi$
$661$	−2.65248	−0.103169	−0.0515847	+	0.998669i	$0.516427\pi$
$662$	−6.94427	−0.269897
$663$	−20.9443	−0.813408
$664$	−12.9443	−0.502335
$665$	0	0
$666$	5.23607	0.202894
$667$	34.4721	1.33477
$668$	−8.00000	−0.309529
$669$	11.2361	0.434411
$670$	−22.4721	−0.868174
$671$	24.9443	0.962963
$672$	0	0
$673$	6.36068	0.245186	0.122593	−	0.992457i	$-0.460879\pi$
$673$	6.36068	0.245186	0.122593	+	0.992457i	$0.460879\pi$
$674$	9.05573	0.348814
$675$	−5.47214	−0.210623
$676$	−2.52786	−0.0972255
$677$	−14.5836	−0.560493	−0.280246	−	0.959928i	$-0.590416\pi$
$677$	−14.5836	−0.560493	−0.280246	+	0.959928i	$0.590416\pi$
$678$	−17.4164	−0.668873
$679$	0	0
$680$	−20.9443	−0.803176
$681$	−0.944272	−0.0361846
$682$	1.52786	0.0585049
$683$	−21.5279	−0.823741	−0.411870	−	0.911242i	$-0.635124\pi$
$683$	−21.5279	−0.823741	−0.411870	+	0.911242i	$0.635124\pi$
$684$	1.00000	0.0382360
$685$	−40.3607	−1.54210
$686$	0	0
$687$	−1.05573	−0.0402785
$688$	−10.4721	−0.399246
$689$	27.4164	1.04448
$690$	−24.9443	−0.949612
$691$	28.0000	1.06517	0.532585	−	0.846376i	$-0.321221\pi$
$691$	28.0000	1.06517	0.532585	+	0.846376i	$0.321221\pi$
$692$	14.9443	0.568096
$693$	0	0
$694$	−2.00000	−0.0759190
$695$	0	0
$696$	4.47214	0.169516
$697$	−12.9443	−0.490299
$698$	13.4164	0.507819
$699$	26.0000	0.983410
$700$	0	0
$701$	−7.34752	−0.277512	−0.138756	−	0.990327i	$-0.544310\pi$
$701$	−7.34752	−0.277512	−0.138756	+	0.990327i	$0.544310\pi$
$702$	−3.23607	−0.122138
$703$	5.23607	0.197482
$704$	2.00000	0.0753778
$705$	−31.4164	−1.18321
$706$	4.94427	0.186080
$707$	0	0
$708$	0	0
$709$	24.4721	0.919070	0.459535	−	0.888160i	$-0.348016\pi$
$709$	24.4721	0.919070	0.459535	+	0.888160i	$0.348016\pi$
$710$	8.00000	0.300235
$711$	11.7082	0.439092
$712$	10.0000	0.374766
$713$	−5.88854	−0.220528
$714$	0	0
$715$	−20.9443	−0.783271
$716$	14.4721	0.540849
$717$	−22.7639	−0.850135
$718$	−11.7082	−0.436946
$719$	−21.7082	−0.809579	−0.404790	−	0.914410i	$-0.632655\pi$
$719$	−21.7082	−0.809579	−0.404790	+	0.914410i	$0.632655\pi$
$720$	−3.23607	−0.120601
$721$	0	0
$722$	1.00000	0.0372161
$723$	−22.4721	−0.835748
$724$	0.763932	0.0283913
$725$	−24.4721	−0.908872
$726$	7.00000	0.259794
$727$	−29.3050	−1.08686	−0.543430	−	0.839454i	$-0.682875\pi$
$727$	−29.3050	−1.08686	−0.543430	+	0.839454i	$0.682875\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	9.52786	0.352642
$731$	−67.7771	−2.50683
$732$	−12.4721	−0.460983
$733$	−17.4164	−0.643290	−0.321645	−	0.946860i	$-0.604236\pi$
$733$	−17.4164	−0.643290	−0.321645	+	0.946860i	$0.604236\pi$
$734$	−25.8885	−0.955564
$735$	0	0
$736$	−7.70820	−0.284128
$737$	13.8885	0.511591
$738$	−2.00000	−0.0736210
$739$	44.7214	1.64510	0.822551	−	0.568691i	$-0.192550\pi$
$739$	44.7214	1.64510	0.822551	+	0.568691i	$0.192550\pi$
$740$	−16.9443	−0.622884
$741$	−3.23607	−0.118880
$742$	0	0
$743$	−27.0557	−0.992578	−0.496289	−	0.868157i	$-0.665304\pi$
$743$	−27.0557	−0.992578	−0.496289	+	0.868157i	$0.665304\pi$
$744$	−0.763932	−0.0280071
$745$	37.8885	1.38813
$746$	12.2918	0.450035
$747$	−12.9443	−0.473606
$748$	12.9443	0.473289
$749$	0	0
$750$	1.52786	0.0557897
$751$	−16.2918	−0.594496	−0.297248	−	0.954800i	$-0.596069\pi$
$751$	−16.2918	−0.594496	−0.297248	+	0.954800i	$0.596069\pi$
$752$	−9.70820	−0.354022
$753$	12.0000	0.437304
$754$	−14.4721	−0.527044
$755$	45.8885	1.67006
$756$	0	0
$757$	5.63932	0.204965	0.102482	−	0.994735i	$-0.467322\pi$
$757$	5.63932	0.204965	0.102482	+	0.994735i	$0.467322\pi$
$758$	1.05573	0.0383458
$759$	15.4164	0.559580
$760$	−3.23607	−0.117385
$761$	24.5836	0.891155	0.445577	−	0.895243i	$-0.352998\pi$
$761$	24.5836	0.891155	0.445577	+	0.895243i	$0.352998\pi$
$762$	−14.1803	−0.513700
$763$	0	0
$764$	18.1803	0.657742
$765$	−20.9443	−0.757242
$766$	−12.9443	−0.467696
$767$	0	0
$768$	−1.00000	−0.0360844
$769$	38.9443	1.40437	0.702183	−	0.711996i	$-0.252209\pi$
$769$	38.9443	1.40437	0.702183	+	0.711996i	$0.252209\pi$
$770$	0	0
$771$	24.8328	0.894332
$772$	8.47214	0.304919
$773$	47.3050	1.70144	0.850720	−	0.525618i	$-0.176166\pi$
$773$	47.3050	1.70144	0.850720	+	0.525618i	$0.176166\pi$
$774$	−10.4721	−0.376413
$775$	4.18034	0.150162
$776$	15.4164	0.553417
$777$	0	0
$778$	22.7639	0.816127
$779$	−2.00000	−0.0716574
$780$	10.4721	0.374963
$781$	−4.94427	−0.176920
$782$	−49.8885	−1.78401
$783$	4.47214	0.159821
$784$	0	0
$785$	−53.3050	−1.90254
$786$	−16.9443	−0.604382
$787$	38.8328	1.38424	0.692120	−	0.721782i	$-0.256677\pi$
$787$	38.8328	1.38424	0.692120	+	0.721782i	$0.256677\pi$
$788$	−3.70820	−0.132099
$789$	2.18034	0.0776222
$790$	−37.8885	−1.34801
$791$	0	0
$792$	2.00000	0.0710669
$793$	40.3607	1.43325
$794$	2.00000	0.0709773
$795$	27.4164	0.972360
$796$	14.4721	0.512951
$797$	37.7771	1.33813	0.669067	−	0.743202i	$-0.266694\pi$
$797$	37.7771	1.33813	0.669067	+	0.743202i	$0.266694\pi$
$798$	0	0
$799$	−62.8328	−2.22287
$800$	5.47214	0.193469
$801$	10.0000	0.353333
$802$	−23.5279	−0.830798
$803$	−5.88854	−0.207802
$804$	−6.94427	−0.244906
$805$	0	0
$806$	2.47214	0.0870773
$807$	4.47214	0.157427
$808$	−8.18034	−0.287783
$809$	13.4164	0.471696	0.235848	−	0.971790i	$-0.424213\pi$
$809$	13.4164	0.471696	0.235848	+	0.971790i	$0.424213\pi$
$810$	−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
$813$	−25.8885	−0.907951
$814$	10.4721	0.367048
$815$	16.0000	0.560456
$816$	−6.47214	−0.226570
$817$	−10.4721	−0.366374
$818$	34.4721	1.20529
$819$	0	0
$820$	6.47214	0.226017
$821$	−34.1803	−1.19290	−0.596451	−	0.802649i	$-0.703423\pi$
$821$	−34.1803	−1.19290	−0.596451	+	0.802649i	$0.703423\pi$
$822$	−12.4721	−0.435016
$823$	−44.9443	−1.56666	−0.783329	−	0.621607i	$-0.786480\pi$
$823$	−44.9443	−1.56666	−0.783329	+	0.621607i	$0.786480\pi$
$824$	−5.70820	−0.198855
$825$	−10.9443	−0.381031
$826$	0	0
$827$	−6.47214	−0.225058	−0.112529	−	0.993648i	$-0.535895\pi$
$827$	−6.47214	−0.225058	−0.112529	+	0.993648i	$0.535895\pi$
$828$	−7.70820	−0.267879
$829$	−16.1803	−0.561966	−0.280983	−	0.959713i	$-0.590661\pi$
$829$	−16.1803	−0.561966	−0.280983	+	0.959713i	$0.590661\pi$
$830$	41.8885	1.45397
$831$	−26.9443	−0.934686
$832$	3.23607	0.112190
$833$	0	0
$834$	0	0
$835$	25.8885	0.895910
$836$	2.00000	0.0691714
$837$	−0.763932	−0.0264054
$838$	−5.52786	−0.190957
$839$	−46.8328	−1.61685	−0.808424	−	0.588600i	$-0.799679\pi$
$839$	−46.8328	−1.61685	−0.808424	+	0.588600i	$0.799679\pi$
$840$	0	0
$841$	−9.00000	−0.310345
$842$	9.23607	0.318296
$843$	−7.52786	−0.259273
$844$	5.41641	0.186440
$845$	8.18034	0.281412
$846$	−9.70820	−0.333775
$847$	0	0
$848$	8.47214	0.290934
$849$	−16.0000	−0.549119
$850$	35.4164	1.21477
$851$	−40.3607	−1.38355
$852$	2.47214	0.0846940
$853$	9.41641	0.322412	0.161206	−	0.986921i	$-0.448462\pi$
$853$	9.41641	0.322412	0.161206	+	0.986921i	$0.448462\pi$
$854$	0	0
$855$	−3.23607	−0.110671
$856$	16.9443	0.579143
$857$	−44.8328	−1.53146	−0.765730	−	0.643162i	$-0.777622\pi$
$857$	−44.8328	−1.53146	−0.765730	+	0.643162i	$0.777622\pi$
$858$	−6.47214	−0.220955
$859$	2.11146	0.0720420	0.0360210	−	0.999351i	$-0.488532\pi$
$859$	2.11146	0.0720420	0.0360210	+	0.999351i	$0.488532\pi$
$860$	33.8885	1.15559
$861$	0	0
$862$	15.4164	0.525085
$863$	−4.94427	−0.168305	−0.0841525	−	0.996453i	$-0.526818\pi$
$863$	−4.94427	−0.168305	−0.0841525	+	0.996453i	$0.526818\pi$
$864$	−1.00000	−0.0340207
$865$	−48.3607	−1.64431
$866$	−0.583592	−0.0198313
$867$	−24.8885	−0.845259
$868$	0	0
$869$	23.4164	0.794347
$870$	−14.4721	−0.490651
$871$	22.4721	0.761439
$872$	−6.18034	−0.209293
$873$	15.4164	0.521766
$874$	−7.70820	−0.260734
$875$	0	0
$876$	2.94427	0.0994777
$877$	16.2918	0.550135	0.275067	−	0.961425i	$-0.411300\pi$
$877$	16.2918	0.550135	0.275067	+	0.961425i	$0.411300\pi$
$878$	−36.1803	−1.22103
$879$	17.4164	0.587441
$880$	−6.47214	−0.218176
$881$	48.0000	1.61716	0.808581	−	0.588386i	$-0.200236\pi$
$881$	48.0000	1.61716	0.808581	+	0.588386i	$0.200236\pi$
$882$	0	0
$883$	−50.4721	−1.69852	−0.849261	−	0.527973i	$-0.822952\pi$
$883$	−50.4721	−1.69852	−0.849261	+	0.527973i	$0.822952\pi$
$884$	20.9443	0.704432
$885$	0	0
$886$	11.8885	0.399403
$887$	6.47214	0.217313	0.108657	−	0.994079i	$-0.465345\pi$
$887$	6.47214	0.217313	0.108657	+	0.994079i	$0.465345\pi$
$888$	−5.23607	−0.175711
$889$	0	0
$890$	−32.3607	−1.08473
$891$	2.00000	0.0670025
$892$	−11.2361	−0.376211
$893$	−9.70820	−0.324873
$894$	11.7082	0.391581
$895$	−46.8328	−1.56545
$896$	0	0
$897$	24.9443	0.832865
$898$	27.8885	0.930653
$899$	−3.41641	−0.113944
$900$	5.47214	0.182405
$901$	54.8328	1.82675
$902$	−4.00000	−0.133185
$903$	0	0
$904$	17.4164	0.579261
$905$	−2.47214	−0.0821766
$906$	14.1803	0.471110
$907$	−2.00000	−0.0664089	−0.0332045	−	0.999449i	$-0.510571\pi$
$907$	−2.00000	−0.0664089	−0.0332045	+	0.999449i	$0.510571\pi$
$908$	0.944272	0.0313368
$909$	−8.18034	−0.271325
$910$	0	0
$911$	−2.47214	−0.0819055	−0.0409528	−	0.999161i	$-0.513039\pi$
$911$	−2.47214	−0.0819055	−0.0409528	+	0.999161i	$0.513039\pi$
$912$	−1.00000	−0.0331133
$913$	−25.8885	−0.856786
$914$	−19.8885	−0.657855
$915$	40.3607	1.33428
$916$	1.05573	0.0348822
$917$	0	0
$918$	−6.47214	−0.213612
$919$	−17.8885	−0.590089	−0.295044	−	0.955484i	$-0.595334\pi$
$919$	−17.8885	−0.590089	−0.295044	+	0.955484i	$0.595334\pi$
$920$	24.9443	0.822388
$921$	4.58359	0.151034
$922$	−22.6525	−0.746020
$923$	−8.00000	−0.263323
$924$	0	0
$925$	28.6525	0.942088
$926$	12.9443	0.425375
$927$	−5.70820	−0.187482
$928$	−4.47214	−0.146805
$929$	−7.63932	−0.250638	−0.125319	−	0.992117i	$-0.539995\pi$
$929$	−7.63932	−0.250638	−0.125319	+	0.992117i	$0.539995\pi$
$930$	2.47214	0.0810645
$931$	0	0
$932$	−26.0000	−0.851658
$933$	−4.18034	−0.136858
$934$	9.88854	0.323563
$935$	−41.8885	−1.36990
$936$	3.23607	0.105774
$937$	28.8328	0.941927	0.470964	−	0.882153i	$-0.343906\pi$
$937$	28.8328	0.941927	0.470964	+	0.882153i	$0.343906\pi$
$938$	0	0
$939$	2.94427	0.0960827
$940$	31.4164	1.02469
$941$	−36.4721	−1.18896	−0.594479	−	0.804111i	$-0.702642\pi$
$941$	−36.4721	−1.18896	−0.594479	+	0.804111i	$0.702642\pi$
$942$	−16.4721	−0.536691
$943$	15.4164	0.502027
$944$	0	0
$945$	0	0
$946$	−20.9443	−0.680957
$947$	52.4721	1.70512	0.852558	−	0.522633i	$-0.175050\pi$
$947$	52.4721	1.70512	0.852558	+	0.522633i	$0.175050\pi$
$948$	−11.7082	−0.380265
$949$	−9.52786	−0.309288
$950$	5.47214	0.177540
$951$	34.3607	1.11422
$952$	0	0
$953$	−58.3607	−1.89049	−0.945244	−	0.326365i	$-0.894176\pi$
$953$	−58.3607	−1.89049	−0.945244	+	0.326365i	$0.894176\pi$
$954$	8.47214	0.274296
$955$	−58.8328	−1.90379
$956$	22.7639	0.736238
$957$	8.94427	0.289127
$958$	−36.1803	−1.16893
$959$	0	0
$960$	3.23607	0.104444
$961$	−30.4164	−0.981174
$962$	16.9443	0.546305
$963$	16.9443	0.546022
$964$	22.4721	0.723779
$965$	−27.4164	−0.882565
$966$	0	0
$967$	−55.4164	−1.78207	−0.891036	−	0.453933i	$-0.850021\pi$
$967$	−55.4164	−1.78207	−0.891036	+	0.453933i	$0.850021\pi$
$968$	−7.00000	−0.224989
$969$	−6.47214	−0.207915
$970$	−49.8885	−1.60182
$971$	34.8328	1.11784	0.558919	−	0.829222i	$-0.311216\pi$
$971$	34.8328	1.11784	0.558919	+	0.829222i	$0.311216\pi$
$972$	−1.00000	−0.0320750
$973$	0	0
$974$	10.7639	0.344899
$975$	−17.7082	−0.567116
$976$	12.4721	0.399223
$977$	28.2492	0.903773	0.451886	−	0.892076i	$-0.350751\pi$
$977$	28.2492	0.903773	0.451886	+	0.892076i	$0.350751\pi$
$978$	4.94427	0.158100
$979$	20.0000	0.639203
$980$	0	0
$981$	−6.18034	−0.197323
$982$	7.52786	0.240224
$983$	−38.4721	−1.22707	−0.613535	−	0.789667i	$-0.710253\pi$
$983$	−38.4721	−1.22707	−0.613535	+	0.789667i	$0.710253\pi$
$984$	2.00000	0.0637577
$985$	12.0000	0.382352
$986$	−28.9443	−0.921773
$987$	0	0
$988$	3.23607	0.102953
$989$	80.7214	2.56679
$990$	−6.47214	−0.205698
$991$	18.1803	0.577518	0.288759	−	0.957402i	$-0.406757\pi$
$991$	18.1803	0.577518	0.288759	+	0.957402i	$0.406757\pi$
$992$	0.763932	0.0242549
$993$	6.94427	0.220370
$994$	0	0
$995$	−46.8328	−1.48470
$996$	12.9443	0.410155
$997$	−48.2492	−1.52807	−0.764034	−	0.645176i	$-0.776784\pi$
$997$	−48.2492	−1.52807	−0.764034	+	0.645176i	$0.776784\pi$
$998$	−41.3050	−1.30749
$999$	−5.23607	−0.165662

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5586.2.a.bi.1.1		2
7.6	odd	2		798.2.a.m.1.2	✓	2
21.20	even	2		2394.2.a.p.1.1		2
28.27	even	2		6384.2.a.bl.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.a.m.1.2	✓	2	7.6	odd	2
2394.2.a.p.1.1		2	21.20	even	2
5586.2.a.bi.1.1		2	1.1	even	1	trivial
6384.2.a.bl.1.2		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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.23607 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.23607 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} -3.23607 q^{10} +2.00000 q^{11} -1.00000 q^{12} +3.23607 q^{13} +3.23607 q^{15} +1.00000 q^{16} +6.47214 q^{17} +1.00000 q^{18} +1.00000 q^{19} -3.23607 q^{20} +2.00000 q^{22} -7.70820 q^{23} -1.00000 q^{24} +5.47214 q^{25} +3.23607 q^{26} -1.00000 q^{27} -4.47214 q^{29} +3.23607 q^{30} +0.763932 q^{31} +1.00000 q^{32} -2.00000 q^{33} +6.47214 q^{34} +1.00000 q^{36} +5.23607 q^{37} +1.00000 q^{38} -3.23607 q^{39} -3.23607 q^{40} -2.00000 q^{41} -10.4721 q^{43} +2.00000 q^{44} -3.23607 q^{45} -7.70820 q^{46} -9.70820 q^{47} -1.00000 q^{48} +5.47214 q^{50} -6.47214 q^{51} +3.23607 q^{52} +8.47214 q^{53} -1.00000 q^{54} -6.47214 q^{55} -1.00000 q^{57} -4.47214 q^{58} +3.23607 q^{60} +12.4721 q^{61} +0.763932 q^{62} +1.00000 q^{64} -10.4721 q^{65} -2.00000 q^{66} +6.94427 q^{67} +6.47214 q^{68} +7.70820 q^{69} -2.47214 q^{71} +1.00000 q^{72} -2.94427 q^{73} +5.23607 q^{74} -5.47214 q^{75} +1.00000 q^{76} -3.23607 q^{78} +11.7082 q^{79} -3.23607 q^{80} +1.00000 q^{81} -2.00000 q^{82} -12.9443 q^{83} -20.9443 q^{85} -10.4721 q^{86} +4.47214 q^{87} +2.00000 q^{88} +10.0000 q^{89} -3.23607 q^{90} -7.70820 q^{92} -0.763932 q^{93} -9.70820 q^{94} -3.23607 q^{95} -1.00000 q^{96} +15.4164 q^{97} +2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{5} - 2 q^{6} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 2 * q^5 - 2 * q^6 + 2 * q^8 + 2 * q^9	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{5} - 2 q^{6} + 2 q^{8} + 2 q^{9} - 2 q^{10} + 4 q^{11} - 2 q^{12} + 2 q^{13} + 2 q^{15} + 2 q^{16} + 4 q^{17} + 2 q^{18} + 2 q^{19} - 2 q^{20} + 4 q^{22} - 2 q^{23} - 2 q^{24} + 2 q^{25} + 2 q^{26} - 2 q^{27} + 2 q^{30} + 6 q^{31} + 2 q^{32} - 4 q^{33} + 4 q^{34} + 2 q^{36} + 6 q^{37} + 2 q^{38} - 2 q^{39} - 2 q^{40} - 4 q^{41} - 12 q^{43} + 4 q^{44} - 2 q^{45} - 2 q^{46} - 6 q^{47} - 2 q^{48} + 2 q^{50} - 4 q^{51} + 2 q^{52} + 8 q^{53} - 2 q^{54} - 4 q^{55} - 2 q^{57} + 2 q^{60} + 16 q^{61} + 6 q^{62} + 2 q^{64} - 12 q^{65} - 4 q^{66} - 4 q^{67} + 4 q^{68} + 2 q^{69} + 4 q^{71} + 2 q^{72} + 12 q^{73} + 6 q^{74} - 2 q^{75} + 2 q^{76} - 2 q^{78} + 10 q^{79} - 2 q^{80} + 2 q^{81} - 4 q^{82} - 8 q^{83} - 24 q^{85} - 12 q^{86} + 4 q^{88} + 20 q^{89} - 2 q^{90} - 2 q^{92} - 6 q^{93} - 6 q^{94} - 2 q^{95} - 2 q^{96} + 4 q^{97} + 4 q^{99}+O(q^{100}) \) 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 + 2 * 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 + 2 * q^26 - 2 * q^27 + 2 * q^30 + 6 * q^31 + 2 * q^32 - 4 * q^33 + 4 * q^34 + 2 * q^36 + 6 * q^37 + 2 * q^38 - 2 * q^39 - 2 * q^40 - 4 * q^41 - 12 * q^43 + 4 * q^44 - 2 * q^45 - 2 * q^46 - 6 * q^47 - 2 * q^48 + 2 * q^50 - 4 * q^51 + 2 * q^52 + 8 * q^53 - 2 * q^54 - 4 * q^55 - 2 * q^57 + 2 * q^60 + 16 * q^61 + 6 * q^62 + 2 * q^64 - 12 * q^65 - 4 * q^66 - 4 * q^67 + 4 * q^68 + 2 * q^69 + 4 * q^71 + 2 * q^72 + 12 * q^73 + 6 * q^74 - 2 * q^75 + 2 * q^76 - 2 * q^78 + 10 * q^79 - 2 * q^80 + 2 * q^81 - 4 * q^82 - 8 * q^83 - 24 * q^85 - 12 * q^86 + 4 * q^88 + 20 * q^89 - 2 * q^90 - 2 * q^92 - 6 * q^93 - 6 * q^94 - 2 * q^95 - 2 * q^96 + 4 * q^97 + 4 * q^99

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