LMFDB - Embedded newform 2541.2.a.ba.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2541,2,Mod(1,2541)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2541, 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("2541.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2541 = 3 \cdot 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2541.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:	$20.2899871536$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-0.618034$ of defining polynomial
Character	$\chi$	$=$	2541.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.618034 q^{2} +1.00000 q^{3} -1.61803 q^{4} +0.236068 q^{5} -0.618034 q^{6} -1.00000 q^{7} +2.23607 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.618034 q^{2} +1.00000 q^{3} -1.61803 q^{4} +0.236068 q^{5} -0.618034 q^{6} -1.00000 q^{7} +2.23607 q^{8} +1.00000 q^{9} -0.145898 q^{10} -1.61803 q^{12} +1.76393 q^{13} +0.618034 q^{14} +0.236068 q^{15} +1.85410 q^{16} +4.47214 q^{17} -0.618034 q^{18} +3.00000 q^{19} -0.381966 q^{20} -1.00000 q^{21} -0.472136 q^{23} +2.23607 q^{24} -4.94427 q^{25} -1.09017 q^{26} +1.00000 q^{27} +1.61803 q^{28} -3.00000 q^{29} -0.145898 q^{30} -5.61803 q^{32} -2.76393 q^{34} -0.236068 q^{35} -1.61803 q^{36} -5.47214 q^{37} -1.85410 q^{38} +1.76393 q^{39} +0.527864 q^{40} +10.4721 q^{41} +0.618034 q^{42} -6.94427 q^{43} +0.236068 q^{45} +0.291796 q^{46} -3.00000 q^{47} +1.85410 q^{48} +1.00000 q^{49} +3.05573 q^{50} +4.47214 q^{51} -2.85410 q^{52} -8.94427 q^{53} -0.618034 q^{54} -2.23607 q^{56} +3.00000 q^{57} +1.85410 q^{58} +7.47214 q^{59} -0.381966 q^{60} +12.4721 q^{61} -1.00000 q^{63} -0.236068 q^{64} +0.416408 q^{65} +4.70820 q^{67} -7.23607 q^{68} -0.472136 q^{69} +0.145898 q^{70} +10.4721 q^{71} +2.23607 q^{72} +7.76393 q^{73} +3.38197 q^{74} -4.94427 q^{75} -4.85410 q^{76} -1.09017 q^{78} +13.4164 q^{79} +0.437694 q^{80} +1.00000 q^{81} -6.47214 q^{82} +6.00000 q^{83} +1.61803 q^{84} +1.05573 q^{85} +4.29180 q^{86} -3.00000 q^{87} +4.47214 q^{89} -0.145898 q^{90} -1.76393 q^{91} +0.763932 q^{92} +1.85410 q^{94} +0.708204 q^{95} -5.61803 q^{96} +2.00000 q^{97} -0.618034 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} + 2 q^{3} - q^{4} - 4 q^{5} + q^{6} - 2 q^{7} + 2 q^{9}+O(q^{10}) $ 2 * q + q^2 + 2 * q^3 - q^4 - 4 * q^5 + q^6 - 2 * q^7 + 2 * q^9	$ 2 q + q^{2} + 2 q^{3} - q^{4} - 4 q^{5} + q^{6} - 2 q^{7} + 2 q^{9} - 7 q^{10} - q^{12} + 8 q^{13} - q^{14} - 4 q^{15} - 3 q^{16} + q^{18} + 6 q^{19} - 3 q^{20} - 2 q^{21} + 8 q^{23} + 8 q^{25} + 9 q^{26} + 2 q^{27} + q^{28} - 6 q^{29} - 7 q^{30} - 9 q^{32} - 10 q^{34} + 4 q^{35} - q^{36} - 2 q^{37} + 3 q^{38} + 8 q^{39} + 10 q^{40} + 12 q^{41} - q^{42} + 4 q^{43} - 4 q^{45} + 14 q^{46} - 6 q^{47} - 3 q^{48} + 2 q^{49} + 24 q^{50} + q^{52} + q^{54} + 6 q^{57} - 3 q^{58} + 6 q^{59} - 3 q^{60} + 16 q^{61} - 2 q^{63} + 4 q^{64} - 26 q^{65} - 4 q^{67} - 10 q^{68} + 8 q^{69} + 7 q^{70} + 12 q^{71} + 20 q^{73} + 9 q^{74} + 8 q^{75} - 3 q^{76} + 9 q^{78} + 21 q^{80} + 2 q^{81} - 4 q^{82} + 12 q^{83} + q^{84} + 20 q^{85} + 22 q^{86} - 6 q^{87} - 7 q^{90} - 8 q^{91} + 6 q^{92} - 3 q^{94} - 12 q^{95} - 9 q^{96} + 4 q^{97} + q^{98}+O(q^{100}) $ 2 * q + q^2 + 2 * q^3 - q^4 - 4 * q^5 + q^6 - 2 * q^7 + 2 * q^9 - 7 * q^10 - q^12 + 8 * q^13 - q^14 - 4 * q^15 - 3 * q^16 + q^18 + 6 * q^19 - 3 * q^20 - 2 * q^21 + 8 * q^23 + 8 * q^25 + 9 * q^26 + 2 * q^27 + q^28 - 6 * q^29 - 7 * q^30 - 9 * q^32 - 10 * q^34 + 4 * q^35 - q^36 - 2 * q^37 + 3 * q^38 + 8 * q^39 + 10 * q^40 + 12 * q^41 - q^42 + 4 * q^43 - 4 * q^45 + 14 * q^46 - 6 * q^47 - 3 * q^48 + 2 * q^49 + 24 * q^50 + q^52 + q^54 + 6 * q^57 - 3 * q^58 + 6 * q^59 - 3 * q^60 + 16 * q^61 - 2 * q^63 + 4 * q^64 - 26 * q^65 - 4 * q^67 - 10 * q^68 + 8 * q^69 + 7 * q^70 + 12 * q^71 + 20 * q^73 + 9 * q^74 + 8 * q^75 - 3 * q^76 + 9 * q^78 + 21 * q^80 + 2 * q^81 - 4 * q^82 + 12 * q^83 + q^84 + 20 * q^85 + 22 * q^86 - 6 * q^87 - 7 * q^90 - 8 * q^91 + 6 * q^92 - 3 * q^94 - 12 * q^95 - 9 * q^96 + 4 * q^97 + q^98

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.618034	−0.437016	−0.218508	−	0.975835i	$-0.570119\pi$
$2$	−0.618034	−0.437016	−0.218508	+	0.975835i	$0.570119\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.61803	−0.809017
$5$	0.236068	0.105573	0.0527864	−	0.998606i	$-0.483190\pi$
$5$	0.236068	0.105573	0.0527864	+	0.998606i	$0.483190\pi$
$6$	−0.618034	−0.252311
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	2.23607	0.790569
$9$	1.00000	0.333333
$10$	−0.145898	−0.0461370
$11$	0	0
$11$	0	0
$12$	−1.61803	−0.467086
$13$	1.76393	0.489227	0.244613	−	0.969621i	$-0.421339\pi$
$13$	1.76393	0.489227	0.244613	+	0.969621i	$0.421339\pi$
$14$	0.618034	0.165177
$15$	0.236068	0.0609525
$16$	1.85410	0.463525
$17$	4.47214	1.08465	0.542326	−	0.840168i	$-0.317544\pi$
$17$	4.47214	1.08465	0.542326	+	0.840168i	$0.317544\pi$
$18$	−0.618034	−0.145672
$19$	3.00000	0.688247	0.344124	−	0.938924i	$-0.388176\pi$
$19$	3.00000	0.688247	0.344124	+	0.938924i	$0.388176\pi$
$20$	−0.381966	−0.0854102
$21$	−1.00000	−0.218218
$22$	0	0
$23$	−0.472136	−0.0984472	−0.0492236	−	0.998788i	$-0.515675\pi$
$23$	−0.472136	−0.0984472	−0.0492236	+	0.998788i	$0.515675\pi$
$24$	2.23607	0.456435
$25$	−4.94427	−0.988854
$26$	−1.09017	−0.213800
$27$	1.00000	0.192450
$28$	1.61803	0.305780
$29$	−3.00000	−0.557086	−0.278543	−	0.960424i	$-0.589851\pi$
$29$	−3.00000	−0.557086	−0.278543	+	0.960424i	$0.589851\pi$
$30$	−0.145898	−0.0266372
$31$	0	0		−	1.00000i	$-0.5\pi$
$31$	0	0			1.00000i	$0.5\pi$
$32$	−5.61803	−0.993137
$33$	0	0
$34$	−2.76393	−0.474010
$35$	−0.236068	−0.0399028
$36$	−1.61803	−0.269672
$37$	−5.47214	−0.899614	−0.449807	−	0.893126i	$-0.648507\pi$
$37$	−5.47214	−0.899614	−0.449807	+	0.893126i	$0.648507\pi$
$38$	−1.85410	−0.300775
$39$	1.76393	0.282455
$40$	0.527864	0.0834626
$41$	10.4721	1.63547	0.817736	−	0.575593i	$-0.195229\pi$
$41$	10.4721	1.63547	0.817736	+	0.575593i	$0.195229\pi$
$42$	0.618034	0.0953647
$43$	−6.94427	−1.05899	−0.529496	−	0.848313i	$-0.677619\pi$
$43$	−6.94427	−1.05899	−0.529496	+	0.848313i	$0.677619\pi$
$44$	0	0
$45$	0.236068	0.0351909
$46$	0.291796	0.0430230
$47$	−3.00000	−0.437595	−0.218797	−	0.975770i	$-0.570213\pi$
$47$	−3.00000	−0.437595	−0.218797	+	0.975770i	$0.570213\pi$
$48$	1.85410	0.267617
$49$	1.00000	0.142857
$50$	3.05573	0.432145
$51$	4.47214	0.626224
$52$	−2.85410	−0.395793
$53$	−8.94427	−1.22859	−0.614295	−	0.789076i	$-0.710560\pi$
$53$	−8.94427	−1.22859	−0.614295	+	0.789076i	$0.710560\pi$
$54$	−0.618034	−0.0841038
$55$	0	0
$56$	−2.23607	−0.298807
$57$	3.00000	0.397360
$58$	1.85410	0.243456
$59$	7.47214	0.972789	0.486395	−	0.873739i	$-0.338312\pi$
$59$	7.47214	0.972789	0.486395	+	0.873739i	$0.338312\pi$
$60$	−0.381966	−0.0493116
$61$	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	0
$63$	−1.00000	−0.125988
$64$	−0.236068	−0.0295085
$65$	0.416408	0.0516490
$66$	0	0
$67$	4.70820	0.575199	0.287599	−	0.957751i	$-0.407143\pi$
$67$	4.70820	0.575199	0.287599	+	0.957751i	$0.407143\pi$
$68$	−7.23607	−0.877502
$69$	−0.472136	−0.0568385
$70$	0.145898	0.0174382
$71$	10.4721	1.24281	0.621407	−	0.783488i	$-0.286561\pi$
$71$	10.4721	1.24281	0.621407	+	0.783488i	$0.286561\pi$
$72$	2.23607	0.263523
$73$	7.76393	0.908700	0.454350	−	0.890823i	$-0.349872\pi$
$73$	7.76393	0.908700	0.454350	+	0.890823i	$0.349872\pi$
$74$	3.38197	0.393146
$75$	−4.94427	−0.570915
$76$	−4.85410	−0.556804
$77$	0	0
$78$	−1.09017	−0.123437
$79$	13.4164	1.50946	0.754732	−	0.656033i	$-0.227767\pi$
$79$	13.4164	1.50946	0.754732	+	0.656033i	$0.227767\pi$
$80$	0.437694	0.0489357
$81$	1.00000	0.111111
$82$	−6.47214	−0.714728
$83$	6.00000	0.658586	0.329293	−	0.944228i	$-0.393190\pi$
$83$	6.00000	0.658586	0.329293	+	0.944228i	$0.393190\pi$
$84$	1.61803	0.176542
$85$	1.05573	0.114510
$86$	4.29180	0.462796
$87$	−3.00000	−0.321634
$88$	0	0
$89$	4.47214	0.474045	0.237023	−	0.971504i	$-0.423828\pi$
$89$	4.47214	0.474045	0.237023	+	0.971504i	$0.423828\pi$
$90$	−0.145898	−0.0153790
$91$	−1.76393	−0.184910
$92$	0.763932	0.0796454
$93$	0	0
$94$	1.85410	0.191236
$95$	0.708204	0.0726602
$96$	−5.61803	−0.573388
$97$	2.00000	0.203069	0.101535	−	0.994832i	$-0.467625\pi$
$97$	2.00000	0.203069	0.101535	+	0.994832i	$0.467625\pi$
$98$	−0.618034	−0.0624309
$99$	0	0
$100$	8.00000	0.800000
$101$	0.944272	0.0939586	0.0469793	−	0.998896i	$-0.485041\pi$
$101$	0.944272	0.0939586	0.0469793	+	0.998896i	$0.485041\pi$
$102$	−2.76393	−0.273670
$103$	−2.47214	−0.243587	−0.121793	−	0.992555i	$-0.538865\pi$
$103$	−2.47214	−0.243587	−0.121793	+	0.992555i	$0.538865\pi$
$104$	3.94427	0.386768
$105$	−0.236068	−0.0230379
$106$	5.52786	0.536914
$107$	14.2361	1.37625	0.688126	−	0.725591i	$-0.258433\pi$
$107$	14.2361	1.37625	0.688126	+	0.725591i	$0.258433\pi$
$108$	−1.61803	−0.155695
$109$	0	0		−	1.00000i	$-0.5\pi$
$109$	0	0			1.00000i	$0.5\pi$
$110$	0	0
$111$	−5.47214	−0.519392
$112$	−1.85410	−0.175196
$113$	2.47214	0.232559	0.116279	−	0.993217i	$-0.462903\pi$
$113$	2.47214	0.232559	0.116279	+	0.993217i	$0.462903\pi$
$114$	−1.85410	−0.173653
$115$	−0.111456	−0.0103933
$116$	4.85410	0.450692
$117$	1.76393	0.163076
$118$	−4.61803	−0.425124
$119$	−4.47214	−0.409960
$120$	0.527864	0.0481872
$121$	0	0
$122$	−7.70820	−0.697868
$123$	10.4721	0.944241
$124$	0	0
$125$	−2.34752	−0.209969
$126$	0.618034	0.0550588
$127$	2.00000	0.177471	0.0887357	−	0.996055i	$-0.471717\pi$
$127$	2.00000	0.177471	0.0887357	+	0.996055i	$0.471717\pi$
$128$	11.3820	1.00603
$129$	−6.94427	−0.611409
$130$	−0.257354	−0.0225715
$131$	−6.47214	−0.565473	−0.282737	−	0.959198i	$-0.591242\pi$
$131$	−6.47214	−0.565473	−0.282737	+	0.959198i	$0.591242\pi$
$132$	0	0
$133$	−3.00000	−0.260133
$134$	−2.90983	−0.251371
$135$	0.236068	0.0203175
$136$	10.0000	0.857493
$137$	−14.9443	−1.27678	−0.638388	−	0.769715i	$-0.720398\pi$
$137$	−14.9443	−1.27678	−0.638388	+	0.769715i	$0.720398\pi$
$138$	0.291796	0.0248393
$139$	16.9443	1.43719	0.718597	−	0.695427i	$-0.244785\pi$
$139$	16.9443	1.43719	0.718597	+	0.695427i	$0.244785\pi$
$140$	0.381966	0.0322820
$141$	−3.00000	−0.252646
$142$	−6.47214	−0.543130
$143$	0	0
$144$	1.85410	0.154508
$145$	−0.708204	−0.0588131
$146$	−4.79837	−0.397116
$147$	1.00000	0.0824786
$148$	8.85410	0.727803
$149$	0.0557281	0.00456542	0.00228271	−	0.999997i	$-0.499273\pi$
$149$	0.0557281	0.00456542	0.00228271	+	0.999997i	$0.499273\pi$
$150$	3.05573	0.249499
$151$	−9.41641	−0.766296	−0.383148	−	0.923687i	$-0.625160\pi$
$151$	−9.41641	−0.766296	−0.383148	+	0.923687i	$0.625160\pi$
$152$	6.70820	0.544107
$153$	4.47214	0.361551
$154$	0	0
$155$	0	0
$156$	−2.85410	−0.228511
$157$	13.4164	1.07075	0.535373	−	0.844616i	$-0.320171\pi$
$157$	13.4164	1.07075	0.535373	+	0.844616i	$0.320171\pi$
$158$	−8.29180	−0.659660
$159$	−8.94427	−0.709327
$160$	−1.32624	−0.104848
$161$	0.472136	0.0372095
$162$	−0.618034	−0.0485573
$163$	20.7082	1.62199	0.810996	−	0.585052i	$-0.198926\pi$
$163$	20.7082	1.62199	0.810996	+	0.585052i	$0.198926\pi$
$164$	−16.9443	−1.32313
$165$	0	0
$166$	−3.70820	−0.287812
$167$	1.05573	0.0816947	0.0408473	−	0.999165i	$-0.486994\pi$
$167$	1.05573	0.0816947	0.0408473	+	0.999165i	$0.486994\pi$
$168$	−2.23607	−0.172516
$169$	−9.88854	−0.760657
$170$	−0.652476	−0.0500426
$171$	3.00000	0.229416
$172$	11.2361	0.856742
$173$	16.4721	1.25235	0.626177	−	0.779681i	$-0.284619\pi$
$173$	16.4721	1.25235	0.626177	+	0.779681i	$0.284619\pi$
$174$	1.85410	0.140559
$175$	4.94427	0.373752
$176$	0	0
$177$	7.47214	0.561640
$178$	−2.76393	−0.207165
$179$	−7.52786	−0.562659	−0.281329	−	0.959611i	$-0.590775\pi$
$179$	−7.52786	−0.562659	−0.281329	+	0.959611i	$0.590775\pi$
$180$	−0.381966	−0.0284701
$181$	23.4164	1.74053	0.870264	−	0.492586i	$-0.163948\pi$
$181$	23.4164	1.74053	0.870264	+	0.492586i	$0.163948\pi$
$182$	1.09017	0.0808088
$183$	12.4721	0.921967
$184$	−1.05573	−0.0778293
$185$	−1.29180	−0.0949747
$186$	0	0
$187$	0	0
$188$	4.85410	0.354022
$189$	−1.00000	−0.0727393
$190$	−0.437694	−0.0317537
$191$	−14.9443	−1.08133	−0.540665	−	0.841238i	$-0.681827\pi$
$191$	−14.9443	−1.08133	−0.540665	+	0.841238i	$0.681827\pi$
$192$	−0.236068	−0.0170367
$193$	12.0000	0.863779	0.431889	−	0.901927i	$-0.357847\pi$
$193$	12.0000	0.863779	0.431889	+	0.901927i	$0.357847\pi$
$194$	−1.23607	−0.0887445
$195$	0.416408	0.0298196
$196$	−1.61803	−0.115574
$197$	−18.9443	−1.34972	−0.674862	−	0.737944i	$-0.735797\pi$
$197$	−18.9443	−1.34972	−0.674862	+	0.737944i	$0.735797\pi$
$198$	0	0
$199$	−3.52786	−0.250084	−0.125042	−	0.992151i	$-0.539907\pi$
$199$	−3.52786	−0.250084	−0.125042	+	0.992151i	$0.539907\pi$
$200$	−11.0557	−0.781758
$201$	4.70820	0.332091
$202$	−0.583592	−0.0410614
$203$	3.00000	0.210559
$204$	−7.23607	−0.506626
$205$	2.47214	0.172661
$206$	1.52786	0.106451
$207$	−0.472136	−0.0328157
$208$	3.27051	0.226769
$209$	0	0
$210$	0.145898	0.0100679
$211$	25.4164	1.74974	0.874869	−	0.484360i	$-0.160947\pi$
$211$	25.4164	1.74974	0.874869	+	0.484360i	$0.160947\pi$
$212$	14.4721	0.993950
$213$	10.4721	0.717539
$214$	−8.79837	−0.601444
$215$	−1.63932	−0.111801
$216$	2.23607	0.152145
$217$	0	0
$218$	0	0
$219$	7.76393	0.524638
$220$	0	0
$221$	7.88854	0.530641
$222$	3.38197	0.226983
$223$	6.00000	0.401790	0.200895	−	0.979613i	$-0.435615\pi$
$223$	6.00000	0.401790	0.200895	+	0.979613i	$0.435615\pi$
$224$	5.61803	0.375371
$225$	−4.94427	−0.329618
$226$	−1.52786	−0.101632
$227$	−24.4721	−1.62427	−0.812136	−	0.583468i	$-0.801695\pi$
$227$	−24.4721	−1.62427	−0.812136	+	0.583468i	$0.801695\pi$
$228$	−4.85410	−0.321471
$229$	−15.5279	−1.02611	−0.513055	−	0.858356i	$-0.671486\pi$
$229$	−15.5279	−1.02611	−0.513055	+	0.858356i	$0.671486\pi$
$230$	0.0688837	0.00454206
$231$	0	0
$232$	−6.70820	−0.440415
$233$	−15.8885	−1.04089	−0.520447	−	0.853894i	$-0.674235\pi$
$233$	−15.8885	−1.04089	−0.520447	+	0.853894i	$0.674235\pi$
$234$	−1.09017	−0.0712666
$235$	−0.708204	−0.0461981
$236$	−12.0902	−0.787003
$237$	13.4164	0.871489
$238$	2.76393	0.179159
$239$	−0.708204	−0.0458099	−0.0229050	−	0.999738i	$-0.507292\pi$
$239$	−0.708204	−0.0458099	−0.0229050	+	0.999738i	$0.507292\pi$
$240$	0.437694	0.0282530
$241$	−0.708204	−0.0456194	−0.0228097	−	0.999740i	$-0.507261\pi$
$241$	−0.708204	−0.0456194	−0.0228097	+	0.999740i	$0.507261\pi$
$242$	0	0
$243$	1.00000	0.0641500
$244$	−20.1803	−1.29191
$245$	0.236068	0.0150818
$246$	−6.47214	−0.412648
$247$	5.29180	0.336709
$248$	0	0
$249$	6.00000	0.380235
$250$	1.45085	0.0917598
$251$	10.4164	0.657478	0.328739	−	0.944421i	$-0.393376\pi$
$251$	10.4164	0.657478	0.328739	+	0.944421i	$0.393376\pi$
$252$	1.61803	0.101927
$253$	0	0
$254$	−1.23607	−0.0775578
$255$	1.05573	0.0661123
$256$	−6.56231	−0.410144
$257$	31.6525	1.97443	0.987214	−	0.159403i	$-0.0509569\pi$
$257$	31.6525	1.97443	0.987214	+	0.159403i	$0.0509569\pi$
$258$	4.29180	0.267196
$259$	5.47214	0.340022
$260$	−0.673762	−0.0417850
$261$	−3.00000	−0.185695
$262$	4.00000	0.247121
$263$	−4.23607	−0.261207	−0.130604	−	0.991435i	$-0.541692\pi$
$263$	−4.23607	−0.261207	−0.130604	+	0.991435i	$0.541692\pi$
$264$	0	0
$265$	−2.11146	−0.129706
$266$	1.85410	0.113682
$267$	4.47214	0.273690
$268$	−7.61803	−0.465345
$269$	−28.4721	−1.73598	−0.867988	−	0.496584i	$-0.834587\pi$
$269$	−28.4721	−1.73598	−0.867988	+	0.496584i	$0.834587\pi$
$270$	−0.145898	−0.00887907
$271$	5.47214	0.332409	0.166204	−	0.986091i	$-0.446849\pi$
$271$	5.47214	0.332409	0.166204	+	0.986091i	$0.446849\pi$
$272$	8.29180	0.502764
$273$	−1.76393	−0.106758
$274$	9.23607	0.557971
$275$	0	0
$276$	0.763932	0.0459833
$277$	−3.52786	−0.211969	−0.105984	−	0.994368i	$-0.533799\pi$
$277$	−3.52786	−0.211969	−0.105984	+	0.994368i	$0.533799\pi$
$278$	−10.4721	−0.628077
$279$	0	0
$280$	−0.527864	−0.0315459
$281$	−10.4164	−0.621391	−0.310695	−	0.950510i	$-0.600562\pi$
$281$	−10.4164	−0.621391	−0.310695	+	0.950510i	$0.600562\pi$
$282$	1.85410	0.110410
$283$	16.8885	1.00392	0.501960	−	0.864891i	$-0.332613\pi$
$283$	16.8885	1.00392	0.501960	+	0.864891i	$0.332613\pi$
$284$	−16.9443	−1.00546
$285$	0.708204	0.0419504
$286$	0	0
$287$	−10.4721	−0.618151
$288$	−5.61803	−0.331046
$289$	3.00000	0.176471
$290$	0.437694	0.0257023
$291$	2.00000	0.117242
$292$	−12.5623	−0.735153
$293$	−25.8885	−1.51242	−0.756212	−	0.654326i	$-0.772952\pi$
$293$	−25.8885	−1.51242	−0.756212	+	0.654326i	$0.772952\pi$
$294$	−0.618034	−0.0360445
$295$	1.76393	0.102700
$296$	−12.2361	−0.711207
$297$	0	0
$298$	−0.0344419	−0.00199516
$299$	−0.832816	−0.0481630
$300$	8.00000	0.461880
$301$	6.94427	0.400261
$302$	5.81966	0.334884
$303$	0.944272	0.0542470
$304$	5.56231	0.319020
$305$	2.94427	0.168589
$306$	−2.76393	−0.158003
$307$	−0.944272	−0.0538924	−0.0269462	−	0.999637i	$-0.508578\pi$
$307$	−0.944272	−0.0538924	−0.0269462	+	0.999637i	$0.508578\pi$
$308$	0	0
$309$	−2.47214	−0.140635
$310$	0	0
$311$	17.8885	1.01437	0.507183	−	0.861838i	$-0.330687\pi$
$311$	17.8885	1.01437	0.507183	+	0.861838i	$0.330687\pi$
$312$	3.94427	0.223300
$313$	−11.5279	−0.651593	−0.325797	−	0.945440i	$-0.605632\pi$
$313$	−11.5279	−0.651593	−0.325797	+	0.945440i	$0.605632\pi$
$314$	−8.29180	−0.467933
$315$	−0.236068	−0.0133009
$316$	−21.7082	−1.22118
$317$	21.5279	1.20913	0.604563	−	0.796558i	$-0.293348\pi$
$317$	21.5279	1.20913	0.604563	+	0.796558i	$0.293348\pi$
$318$	5.52786	0.309987
$319$	0	0
$320$	−0.0557281	−0.00311529
$321$	14.2361	0.794580
$322$	−0.291796	−0.0162612
$323$	13.4164	0.746509
$324$	−1.61803	−0.0898908
$325$	−8.72136	−0.483774
$326$	−12.7984	−0.708836
$327$	0	0
$328$	23.4164	1.29295
$329$	3.00000	0.165395
$330$	0	0
$331$	24.0000	1.31916	0.659580	−	0.751635i	$-0.270734\pi$
$331$	24.0000	1.31916	0.659580	+	0.751635i	$0.270734\pi$
$332$	−9.70820	−0.532807
$333$	−5.47214	−0.299871
$334$	−0.652476	−0.0357019
$335$	1.11146	0.0607253
$336$	−1.85410	−0.101150
$337$	−28.8328	−1.57062	−0.785312	−	0.619100i	$-0.787497\pi$
$337$	−28.8328	−1.57062	−0.785312	+	0.619100i	$0.787497\pi$
$338$	6.11146	0.332419
$339$	2.47214	0.134268
$340$	−1.70820	−0.0926404
$341$	0	0
$342$	−1.85410	−0.100258
$343$	−1.00000	−0.0539949
$344$	−15.5279	−0.837206
$345$	−0.111456	−0.00600060
$346$	−10.1803	−0.547298
$347$	−20.9443	−1.12435	−0.562174	−	0.827019i	$-0.690035\pi$
$347$	−20.9443	−1.12435	−0.562174	+	0.827019i	$0.690035\pi$
$348$	4.85410	0.260207
$349$	−9.29180	−0.497378	−0.248689	−	0.968583i	$-0.580000\pi$
$349$	−9.29180	−0.497378	−0.248689	+	0.968583i	$0.580000\pi$
$350$	−3.05573	−0.163336
$351$	1.76393	0.0941517
$352$	0	0
$353$	−16.5967	−0.883356	−0.441678	−	0.897174i	$-0.645617\pi$
$353$	−16.5967	−0.883356	−0.441678	+	0.897174i	$0.645617\pi$
$354$	−4.61803	−0.245446
$355$	2.47214	0.131207
$356$	−7.23607	−0.383511
$357$	−4.47214	−0.236691
$358$	4.65248	0.245891
$359$	−36.9443	−1.94984	−0.974922	−	0.222547i	$-0.928563\pi$
$359$	−36.9443	−1.94984	−0.974922	+	0.222547i	$0.928563\pi$
$360$	0.527864	0.0278209
$361$	−10.0000	−0.526316
$362$	−14.4721	−0.760639
$363$	0	0
$364$	2.85410	0.149596
$365$	1.83282	0.0959340
$366$	−7.70820	−0.402914
$367$	30.8328	1.60946	0.804730	−	0.593641i	$-0.202310\pi$
$367$	30.8328	1.60946	0.804730	+	0.593641i	$0.202310\pi$
$368$	−0.875388	−0.0456328
$369$	10.4721	0.545158
$370$	0.798374	0.0415055
$371$	8.94427	0.464363
$372$	0	0
$373$	29.4164	1.52312	0.761562	−	0.648092i	$-0.224433\pi$
$373$	29.4164	1.52312	0.761562	+	0.648092i	$0.224433\pi$
$374$	0	0
$375$	−2.34752	−0.121226
$376$	−6.70820	−0.345949
$377$	−5.29180	−0.272541
$378$	0.618034	0.0317882
$379$	0.236068	0.0121260	0.00606300	−	0.999982i	$-0.498070\pi$
$379$	0.236068	0.0121260	0.00606300	+	0.999982i	$0.498070\pi$
$380$	−1.14590	−0.0587833
$381$	2.00000	0.102463
$382$	9.23607	0.472558
$383$	−21.8885	−1.11845	−0.559226	−	0.829015i	$-0.688902\pi$
$383$	−21.8885	−1.11845	−0.559226	+	0.829015i	$0.688902\pi$
$384$	11.3820	0.580834
$385$	0	0
$386$	−7.41641	−0.377485
$387$	−6.94427	−0.352997
$388$	−3.23607	−0.164286
$389$	−16.3607	−0.829519	−0.414760	−	0.909931i	$-0.636134\pi$
$389$	−16.3607	−0.829519	−0.414760	+	0.909931i	$0.636134\pi$
$390$	−0.257354	−0.0130316
$391$	−2.11146	−0.106781
$392$	2.23607	0.112938
$393$	−6.47214	−0.326476
$394$	11.7082	0.589851
$395$	3.16718	0.159358
$396$	0	0
$397$	3.52786	0.177058	0.0885292	−	0.996074i	$-0.471783\pi$
$397$	3.52786	0.177058	0.0885292	+	0.996074i	$0.471783\pi$
$398$	2.18034	0.109291
$399$	−3.00000	−0.150188
$400$	−9.16718	−0.458359
$401$	34.3607	1.71589	0.857945	−	0.513741i	$-0.171741\pi$
$401$	34.3607	1.71589	0.857945	+	0.513741i	$0.171741\pi$
$402$	−2.90983	−0.145129
$403$	0	0
$404$	−1.52786	−0.0760141
$405$	0.236068	0.0117303
$406$	−1.85410	−0.0920175
$407$	0	0
$408$	10.0000	0.495074
$409$	29.4164	1.45455	0.727274	−	0.686347i	$-0.240787\pi$
$409$	29.4164	1.45455	0.727274	+	0.686347i	$0.240787\pi$
$410$	−1.52786	−0.0754558
$411$	−14.9443	−0.737147
$412$	4.00000	0.197066
$413$	−7.47214	−0.367680
$414$	0.291796	0.0143410
$415$	1.41641	0.0695287
$416$	−9.90983	−0.485869
$417$	16.9443	0.829765
$418$	0	0
$419$	33.4721	1.63522	0.817610	−	0.575772i	$-0.195298\pi$
$419$	33.4721	1.63522	0.817610	+	0.575772i	$0.195298\pi$
$420$	0.381966	0.0186380
$421$	10.4164	0.507665	0.253832	−	0.967248i	$-0.418309\pi$
$421$	10.4164	0.507665	0.253832	+	0.967248i	$0.418309\pi$
$422$	−15.7082	−0.764663
$423$	−3.00000	−0.145865
$424$	−20.0000	−0.971286
$425$	−22.1115	−1.07256
$426$	−6.47214	−0.313576
$427$	−12.4721	−0.603569
$428$	−23.0344	−1.11341
$429$	0	0
$430$	1.01316	0.0488587
$431$	30.5967	1.47379	0.736897	−	0.676005i	$-0.236290\pi$
$431$	30.5967	1.47379	0.736897	+	0.676005i	$0.236290\pi$
$432$	1.85410	0.0892055
$433$	−17.4164	−0.836979	−0.418490	−	0.908222i	$-0.637440\pi$
$433$	−17.4164	−0.836979	−0.418490	+	0.908222i	$0.637440\pi$
$434$	0	0
$435$	−0.708204	−0.0339558
$436$	0	0
$437$	−1.41641	−0.0677560
$438$	−4.79837	−0.229275
$439$	35.3607	1.68767	0.843837	−	0.536600i	$-0.180292\pi$
$439$	35.3607	1.68767	0.843837	+	0.536600i	$0.180292\pi$
$440$	0	0
$441$	1.00000	0.0476190
$442$	−4.87539	−0.231899
$443$	27.8885	1.32502	0.662512	−	0.749051i	$-0.269490\pi$
$443$	27.8885	1.32502	0.662512	+	0.749051i	$0.269490\pi$
$444$	8.85410	0.420197
$445$	1.05573	0.0500463
$446$	−3.70820	−0.175589
$447$	0.0557281	0.00263585
$448$	0.236068	0.0111532
$449$	19.5279	0.921577	0.460788	−	0.887510i	$-0.347567\pi$
$449$	19.5279	0.921577	0.460788	+	0.887510i	$0.347567\pi$
$450$	3.05573	0.144048
$451$	0	0
$452$	−4.00000	−0.188144
$453$	−9.41641	−0.442421
$454$	15.1246	0.709833
$455$	−0.416408	−0.0195215
$456$	6.70820	0.314140
$457$	26.0000	1.21623	0.608114	−	0.793849i	$-0.291926\pi$
$457$	26.0000	1.21623	0.608114	+	0.793849i	$0.291926\pi$
$458$	9.59675	0.448427
$459$	4.47214	0.208741
$460$	0.180340	0.00840839
$461$	9.05573	0.421767	0.210884	−	0.977511i	$-0.432366\pi$
$461$	9.05573	0.421767	0.210884	+	0.977511i	$0.432366\pi$
$462$	0	0
$463$	8.12461	0.377583	0.188791	−	0.982017i	$-0.439543\pi$
$463$	8.12461	0.377583	0.188791	+	0.982017i	$0.439543\pi$
$464$	−5.56231	−0.258224
$465$	0	0
$466$	9.81966	0.454887
$467$	6.52786	0.302074	0.151037	−	0.988528i	$-0.451739\pi$
$467$	6.52786	0.302074	0.151037	+	0.988528i	$0.451739\pi$
$468$	−2.85410	−0.131931
$469$	−4.70820	−0.217405
$470$	0.437694	0.0201893
$471$	13.4164	0.618195
$472$	16.7082	0.769057
$473$	0	0
$474$	−8.29180	−0.380855
$475$	−14.8328	−0.680576
$476$	7.23607	0.331665
$477$	−8.94427	−0.409530
$478$	0.437694	0.0200197
$479$	−19.5279	−0.892251	−0.446125	−	0.894970i	$-0.647196\pi$
$479$	−19.5279	−0.892251	−0.446125	+	0.894970i	$0.647196\pi$
$480$	−1.32624	−0.0605342
$481$	−9.65248	−0.440115
$482$	0.437694	0.0199364
$483$	0.472136	0.0214829
$484$	0	0
$485$	0.472136	0.0214386
$486$	−0.618034	−0.0280346
$487$	−21.8885	−0.991865	−0.495932	−	0.868361i	$-0.665174\pi$
$487$	−21.8885	−0.991865	−0.495932	+	0.868361i	$0.665174\pi$
$488$	27.8885	1.26246
$489$	20.7082	0.936457
$490$	−0.145898	−0.00659100
$491$	−28.5967	−1.29055	−0.645277	−	0.763949i	$-0.723258\pi$
$491$	−28.5967	−1.29055	−0.645277	+	0.763949i	$0.723258\pi$
$492$	−16.9443	−0.763907
$493$	−13.4164	−0.604245
$494$	−3.27051	−0.147147
$495$	0	0
$496$	0	0
$497$	−10.4721	−0.469739
$498$	−3.70820	−0.166169
$499$	−36.7082	−1.64328	−0.821642	−	0.570003i	$-0.806942\pi$
$499$	−36.7082	−1.64328	−0.821642	+	0.570003i	$0.806942\pi$
$500$	3.79837	0.169868
$501$	1.05573	0.0471665
$502$	−6.43769	−0.287328
$503$	7.41641	0.330681	0.165341	−	0.986237i	$-0.447128\pi$
$503$	7.41641	0.330681	0.165341	+	0.986237i	$0.447128\pi$
$504$	−2.23607	−0.0996024
$505$	0.222912	0.00991947
$506$	0	0
$507$	−9.88854	−0.439166
$508$	−3.23607	−0.143577
$509$	−18.3607	−0.813823	−0.406911	−	0.913468i	$-0.633394\pi$
$509$	−18.3607	−0.813823	−0.406911	+	0.913468i	$0.633394\pi$
$510$	−0.652476	−0.0288921
$511$	−7.76393	−0.343456
$512$	−18.7082	−0.826794
$513$	3.00000	0.132453
$514$	−19.5623	−0.862856
$515$	−0.583592	−0.0257161
$516$	11.2361	0.494640
$517$	0	0
$518$	−3.38197	−0.148595
$519$	16.4721	0.723047
$520$	0.931116	0.0408322
$521$	9.76393	0.427766	0.213883	−	0.976859i	$-0.431389\pi$
$521$	9.76393	0.427766	0.213883	+	0.976859i	$0.431389\pi$
$522$	1.85410	0.0811518
$523$	−3.00000	−0.131181	−0.0655904	−	0.997847i	$-0.520893\pi$
$523$	−3.00000	−0.131181	−0.0655904	+	0.997847i	$0.520893\pi$
$524$	10.4721	0.457477
$525$	4.94427	0.215786
$526$	2.61803	0.114152
$527$	0	0
$528$	0	0
$529$	−22.7771	−0.990308
$530$	1.30495	0.0566835
$531$	7.47214	0.324263
$532$	4.85410	0.210452
$533$	18.4721	0.800117
$534$	−2.76393	−0.119607
$535$	3.36068	0.145295
$536$	10.5279	0.454734
$537$	−7.52786	−0.324851
$538$	17.5967	0.758650
$539$	0	0
$540$	−0.381966	−0.0164372
$541$	−11.4164	−0.490830	−0.245415	−	0.969418i	$-0.578924\pi$
$541$	−11.4164	−0.490830	−0.245415	+	0.969418i	$0.578924\pi$
$542$	−3.38197	−0.145268
$543$	23.4164	1.00489
$544$	−25.1246	−1.07721
$545$	0	0
$546$	1.09017	0.0466550
$547$	−16.8328	−0.719719	−0.359860	−	0.933006i	$-0.617175\pi$
$547$	−16.8328	−0.719719	−0.359860	+	0.933006i	$0.617175\pi$
$548$	24.1803	1.03293
$549$	12.4721	0.532298
$550$	0	0
$551$	−9.00000	−0.383413
$552$	−1.05573	−0.0449348
$553$	−13.4164	−0.570524
$554$	2.18034	0.0926338
$555$	−1.29180	−0.0548337
$556$	−27.4164	−1.16271
$557$	−39.0000	−1.65248	−0.826242	−	0.563316i	$-0.809525\pi$
$557$	−39.0000	−1.65248	−0.826242	+	0.563316i	$0.809525\pi$
$558$	0	0
$559$	−12.2492	−0.518087
$560$	−0.437694	−0.0184960
$561$	0	0
$562$	6.43769	0.271558
$563$	6.47214	0.272768	0.136384	−	0.990656i	$-0.456452\pi$
$563$	6.47214	0.272768	0.136384	+	0.990656i	$0.456452\pi$
$564$	4.85410	0.204395
$565$	0.583592	0.0245519
$566$	−10.4377	−0.438729
$567$	−1.00000	−0.0419961
$568$	23.4164	0.982531
$569$	−43.8885	−1.83990	−0.919952	−	0.392032i	$-0.871772\pi$
$569$	−43.8885	−1.83990	−0.919952	+	0.392032i	$0.871772\pi$
$570$	−0.437694	−0.0183330
$571$	5.05573	0.211576	0.105788	−	0.994389i	$-0.466264\pi$
$571$	5.05573	0.211576	0.105788	+	0.994389i	$0.466264\pi$
$572$	0	0
$573$	−14.9443	−0.624306
$574$	6.47214	0.270142
$575$	2.33437	0.0973499
$576$	−0.236068	−0.00983617
$577$	−24.0000	−0.999133	−0.499567	−	0.866276i	$-0.666507\pi$
$577$	−24.0000	−0.999133	−0.499567	+	0.866276i	$0.666507\pi$
$578$	−1.85410	−0.0771205
$579$	12.0000	0.498703
$580$	1.14590	0.0475808
$581$	−6.00000	−0.248922
$582$	−1.23607	−0.0512367
$583$	0	0
$584$	17.3607	0.718390
$585$	0.416408	0.0172163
$586$	16.0000	0.660954
$587$	−45.3607	−1.87224	−0.936118	−	0.351687i	$-0.885608\pi$
$587$	−45.3607	−1.87224	−0.936118	+	0.351687i	$0.885608\pi$
$588$	−1.61803	−0.0667266
$589$	0	0
$590$	−1.09017	−0.0448816
$591$	−18.9443	−0.779263
$592$	−10.1459	−0.416994
$593$	41.7771	1.71558	0.857790	−	0.514001i	$-0.171837\pi$
$593$	41.7771	1.71558	0.857790	+	0.514001i	$0.171837\pi$
$594$	0	0
$595$	−1.05573	−0.0432806
$596$	−0.0901699	−0.00369350
$597$	−3.52786	−0.144386
$598$	0.514708	0.0210480
$599$	−25.4164	−1.03849	−0.519243	−	0.854627i	$-0.673786\pi$
$599$	−25.4164	−1.03849	−0.519243	+	0.854627i	$0.673786\pi$
$600$	−11.0557	−0.451348
$601$	−13.1803	−0.537637	−0.268819	−	0.963191i	$-0.586633\pi$
$601$	−13.1803	−0.537637	−0.268819	+	0.963191i	$0.586633\pi$
$602$	−4.29180	−0.174921
$603$	4.70820	0.191733
$604$	15.2361	0.619947
$605$	0	0
$606$	−0.583592	−0.0237068
$607$	37.2492	1.51190	0.755950	−	0.654630i	$-0.227175\pi$
$607$	37.2492	1.51190	0.755950	+	0.654630i	$0.227175\pi$
$608$	−16.8541	−0.683524
$609$	3.00000	0.121566
$610$	−1.81966	−0.0736759
$611$	−5.29180	−0.214083
$612$	−7.23607	−0.292501
$613$	−26.4721	−1.06920	−0.534600	−	0.845105i	$-0.679538\pi$
$613$	−26.4721	−1.06920	−0.534600	+	0.845105i	$0.679538\pi$
$614$	0.583592	0.0235519
$615$	2.47214	0.0996861
$616$	0	0
$617$	5.88854	0.237064	0.118532	−	0.992950i	$-0.462181\pi$
$617$	5.88854	0.237064	0.118532	+	0.992950i	$0.462181\pi$
$618$	1.52786	0.0614597
$619$	−34.2492	−1.37659	−0.688296	−	0.725430i	$-0.741641\pi$
$619$	−34.2492	−1.37659	−0.688296	+	0.725430i	$0.741641\pi$
$620$	0	0
$621$	−0.472136	−0.0189462
$622$	−11.0557	−0.443294
$623$	−4.47214	−0.179172
$624$	3.27051	0.130925
$625$	24.1672	0.966687
$626$	7.12461	0.284757
$627$	0	0
$628$	−21.7082	−0.866252
$629$	−24.4721	−0.975768
$630$	0.145898	0.00581272
$631$	−12.0000	−0.477712	−0.238856	−	0.971055i	$-0.576772\pi$
$631$	−12.0000	−0.477712	−0.238856	+	0.971055i	$0.576772\pi$
$632$	30.0000	1.19334
$633$	25.4164	1.01021
$634$	−13.3050	−0.528407
$635$	0.472136	0.0187361
$636$	14.4721	0.573858
$637$	1.76393	0.0698895
$638$	0	0
$639$	10.4721	0.414271
$640$	2.68692	0.106210
$641$	14.8328	0.585861	0.292930	−	0.956134i	$-0.405370\pi$
$641$	14.8328	0.585861	0.292930	+	0.956134i	$0.405370\pi$
$642$	−8.79837	−0.347244
$643$	25.4164	1.00233	0.501163	−	0.865353i	$-0.332906\pi$
$643$	25.4164	1.00233	0.501163	+	0.865353i	$0.332906\pi$
$644$	−0.763932	−0.0301031
$645$	−1.63932	−0.0645482
$646$	−8.29180	−0.326236
$647$	−30.8885	−1.21435	−0.607177	−	0.794567i	$-0.707698\pi$
$647$	−30.8885	−1.21435	−0.607177	+	0.794567i	$0.707698\pi$
$648$	2.23607	0.0878410
$649$	0	0
$650$	5.39010	0.211417
$651$	0	0
$652$	−33.5066	−1.31222
$653$	−27.0557	−1.05877	−0.529386	−	0.848381i	$-0.677578\pi$
$653$	−27.0557	−1.05877	−0.529386	+	0.848381i	$0.677578\pi$
$654$	0	0
$655$	−1.52786	−0.0596986
$656$	19.4164	0.758083
$657$	7.76393	0.302900
$658$	−1.85410	−0.0722804
$659$	30.2361	1.17783	0.588915	−	0.808195i	$-0.299555\pi$
$659$	30.2361	1.17783	0.588915	+	0.808195i	$0.299555\pi$
$660$	0	0
$661$	−22.8328	−0.888094	−0.444047	−	0.896004i	$-0.646458\pi$
$661$	−22.8328	−0.888094	−0.444047	+	0.896004i	$0.646458\pi$
$662$	−14.8328	−0.576494
$663$	7.88854	0.306366
$664$	13.4164	0.520658
$665$	−0.708204	−0.0274630
$666$	3.38197	0.131049
$667$	1.41641	0.0548435
$668$	−1.70820	−0.0660924
$669$	6.00000	0.231973
$670$	−0.686918	−0.0265379
$671$	0	0
$672$	5.61803	0.216720
$673$	−29.3050	−1.12962	−0.564811	−	0.825220i	$-0.691051\pi$
$673$	−29.3050	−1.12962	−0.564811	+	0.825220i	$0.691051\pi$
$674$	17.8197	0.686388
$675$	−4.94427	−0.190305
$676$	16.0000	0.615385
$677$	−16.3607	−0.628792	−0.314396	−	0.949292i	$-0.601802\pi$
$677$	−16.3607	−0.628792	−0.314396	+	0.949292i	$0.601802\pi$
$678$	−1.52786	−0.0586773
$679$	−2.00000	−0.0767530
$680$	2.36068	0.0905279
$681$	−24.4721	−0.937774
$682$	0	0
$683$	−18.4721	−0.706817	−0.353408	−	0.935469i	$-0.614977\pi$
$683$	−18.4721	−0.706817	−0.353408	+	0.935469i	$0.614977\pi$
$684$	−4.85410	−0.185601
$685$	−3.52786	−0.134793
$686$	0.618034	0.0235966
$687$	−15.5279	−0.592425
$688$	−12.8754	−0.490870
$689$	−15.7771	−0.601059
$690$	0.0688837	0.00262236
$691$	−32.0000	−1.21734	−0.608669	−	0.793424i	$-0.708296\pi$
$691$	−32.0000	−1.21734	−0.608669	+	0.793424i	$0.708296\pi$
$692$	−26.6525	−1.01318
$693$	0	0
$694$	12.9443	0.491358
$695$	4.00000	0.151729
$696$	−6.70820	−0.254274
$697$	46.8328	1.77392
$698$	5.74265	0.217362
$699$	−15.8885	−0.600960
$700$	−8.00000	−0.302372
$701$	−10.9443	−0.413359	−0.206680	−	0.978409i	$-0.566266\pi$
$701$	−10.9443	−0.413359	−0.206680	+	0.978409i	$0.566266\pi$
$702$	−1.09017	−0.0411458
$703$	−16.4164	−0.619157
$704$	0	0
$705$	−0.708204	−0.0266725
$706$	10.2574	0.386041
$707$	−0.944272	−0.0355130
$708$	−12.0902	−0.454376
$709$	38.4164	1.44276	0.721379	−	0.692540i	$-0.243508\pi$
$709$	38.4164	1.44276	0.721379	+	0.692540i	$0.243508\pi$
$710$	−1.52786	−0.0573397
$711$	13.4164	0.503155
$712$	10.0000	0.374766
$713$	0	0
$714$	2.76393	0.103438
$715$	0	0
$716$	12.1803	0.455201
$717$	−0.708204	−0.0264484
$718$	22.8328	0.852113
$719$	46.7771	1.74449	0.872246	−	0.489068i	$-0.162663\pi$
$719$	46.7771	1.74449	0.872246	+	0.489068i	$0.162663\pi$
$720$	0.437694	0.0163119
$721$	2.47214	0.0920672
$722$	6.18034	0.230008
$723$	−0.708204	−0.0263384
$724$	−37.8885	−1.40812
$725$	14.8328	0.550877
$726$	0	0
$727$	−8.83282	−0.327591	−0.163796	−	0.986494i	$-0.552374\pi$
$727$	−8.83282	−0.327591	−0.163796	+	0.986494i	$0.552374\pi$
$728$	−3.94427	−0.146184
$729$	1.00000	0.0370370
$730$	−1.13274	−0.0419247
$731$	−31.0557	−1.14864
$732$	−20.1803	−0.745887
$733$	15.5279	0.573535	0.286767	−	0.958000i	$-0.407419\pi$
$733$	15.5279	0.573535	0.286767	+	0.958000i	$0.407419\pi$
$734$	−19.0557	−0.703360
$735$	0.236068	0.00870750
$736$	2.65248	0.0977716
$737$	0	0
$738$	−6.47214	−0.238243
$739$	−11.3050	−0.415859	−0.207930	−	0.978144i	$-0.566673\pi$
$739$	−11.3050	−0.415859	−0.207930	+	0.978144i	$0.566673\pi$
$740$	2.09017	0.0768362
$741$	5.29180	0.194399
$742$	−5.52786	−0.202934
$743$	−20.2361	−0.742389	−0.371195	−	0.928555i	$-0.621052\pi$
$743$	−20.2361	−0.742389	−0.371195	+	0.928555i	$0.621052\pi$
$744$	0	0
$745$	0.0131556	0.000481985 0
$746$	−18.1803	−0.665630
$747$	6.00000	0.219529
$748$	0	0
$749$	−14.2361	−0.520175
$750$	1.45085	0.0529775
$751$	−13.7639	−0.502253	−0.251127	−	0.967954i	$-0.580801\pi$
$751$	−13.7639	−0.502253	−0.251127	+	0.967954i	$0.580801\pi$
$752$	−5.56231	−0.202836
$753$	10.4164	0.379595
$754$	3.27051	0.119105
$755$	−2.22291	−0.0809001
$756$	1.61803	0.0588473
$757$	−2.41641	−0.0878258	−0.0439129	−	0.999035i	$-0.513982\pi$
$757$	−2.41641	−0.0878258	−0.0439129	+	0.999035i	$0.513982\pi$
$758$	−0.145898	−0.00529926
$759$	0	0
$760$	1.58359	0.0574429
$761$	−38.3607	−1.39057	−0.695287	−	0.718732i	$-0.744723\pi$
$761$	−38.3607	−1.39057	−0.695287	+	0.718732i	$0.744723\pi$
$762$	−1.23607	−0.0447780
$763$	0	0
$764$	24.1803	0.874814
$765$	1.05573	0.0381699
$766$	13.5279	0.488782
$767$	13.1803	0.475914
$768$	−6.56231	−0.236797
$769$	26.1246	0.942078	0.471039	−	0.882112i	$-0.343879\pi$
$769$	26.1246	0.942078	0.471039	+	0.882112i	$0.343879\pi$
$770$	0	0
$771$	31.6525	1.13994
$772$	−19.4164	−0.698812
$773$	−24.7082	−0.888692	−0.444346	−	0.895855i	$-0.646564\pi$
$773$	−24.7082	−0.888692	−0.444346	+	0.895855i	$0.646564\pi$
$774$	4.29180	0.154265
$775$	0	0
$776$	4.47214	0.160540
$777$	5.47214	0.196312
$778$	10.1115	0.362513
$779$	31.4164	1.12561
$780$	−0.673762	−0.0241246
$781$	0	0
$782$	1.30495	0.0466650
$783$	−3.00000	−0.107211
$784$	1.85410	0.0662179
$785$	3.16718	0.113042
$786$	4.00000	0.142675
$787$	−27.0000	−0.962446	−0.481223	−	0.876598i	$-0.659807\pi$
$787$	−27.0000	−0.962446	−0.481223	+	0.876598i	$0.659807\pi$
$788$	30.6525	1.09195
$789$	−4.23607	−0.150808
$790$	−1.95743	−0.0696421
$791$	−2.47214	−0.0878990
$792$	0	0
$793$	22.0000	0.781243
$794$	−2.18034	−0.0773774
$795$	−2.11146	−0.0748856
$796$	5.70820	0.202322
$797$	−37.1803	−1.31700	−0.658498	−	0.752583i	$-0.728808\pi$
$797$	−37.1803	−1.31700	−0.658498	+	0.752583i	$0.728808\pi$
$798$	1.85410	0.0656345
$799$	−13.4164	−0.474638
$800$	27.7771	0.982068
$801$	4.47214	0.158015
$802$	−21.2361	−0.749872
$803$	0	0
$804$	−7.61803	−0.268667
$805$	0.111456	0.00392831
$806$	0	0
$807$	−28.4721	−1.00227
$808$	2.11146	0.0742808
$809$	13.3607	0.469736	0.234868	−	0.972027i	$-0.424534\pi$
$809$	13.3607	0.469736	0.234868	+	0.972027i	$0.424534\pi$
$810$	−0.145898	−0.00512633
$811$	2.16718	0.0761001	0.0380501	−	0.999276i	$-0.487885\pi$
$811$	2.16718	0.0761001	0.0380501	+	0.999276i	$0.487885\pi$
$812$	−4.85410	−0.170346
$813$	5.47214	0.191916
$814$	0	0
$815$	4.88854	0.171238
$816$	8.29180	0.290271
$817$	−20.8328	−0.728848
$818$	−18.1803	−0.635661
$819$	−1.76393	−0.0616368
$820$	−4.00000	−0.139686
$821$	−0.0557281	−0.00194492	−0.000972462	−	1.00000i	$-0.500310\pi$
$821$	−0.0557281	−0.00194492	−0.000972462		1.00000i	$0.500310\pi$
$822$	9.23607	0.322145
$823$	7.18034	0.250291	0.125145	−	0.992138i	$-0.460060\pi$
$823$	7.18034	0.250291	0.125145	+	0.992138i	$0.460060\pi$
$824$	−5.52786	−0.192572
$825$	0	0
$826$	4.61803	0.160682
$827$	20.1246	0.699801	0.349901	−	0.936787i	$-0.386215\pi$
$827$	20.1246	0.699801	0.349901	+	0.936787i	$0.386215\pi$
$828$	0.763932	0.0265485
$829$	14.8328	0.515165	0.257582	−	0.966256i	$-0.417074\pi$
$829$	14.8328	0.515165	0.257582	+	0.966256i	$0.417074\pi$
$830$	−0.875388	−0.0303852
$831$	−3.52786	−0.122380
$832$	−0.416408	−0.0144363
$833$	4.47214	0.154950
$834$	−10.4721	−0.362620
$835$	0.249224	0.00862474
$836$	0	0
$837$	0	0
$838$	−20.6869	−0.714618
$839$	−23.9443	−0.826648	−0.413324	−	0.910584i	$-0.635632\pi$
$839$	−23.9443	−0.826648	−0.413324	+	0.910584i	$0.635632\pi$
$840$	−0.527864	−0.0182130
$841$	−20.0000	−0.689655
$842$	−6.43769	−0.221858
$843$	−10.4164	−0.358760
$844$	−41.1246	−1.41557
$845$	−2.33437	−0.0803047
$846$	1.85410	0.0637453
$847$	0	0
$848$	−16.5836	−0.569483
$849$	16.8885	0.579613
$850$	13.6656	0.468727
$851$	2.58359	0.0885644
$852$	−16.9443	−0.580501
$853$	49.4164	1.69199	0.845993	−	0.533194i	$-0.179009\pi$
$853$	49.4164	1.69199	0.845993	+	0.533194i	$0.179009\pi$
$854$	7.70820	0.263769
$855$	0.708204	0.0242201
$856$	31.8328	1.08802
$857$	−19.5279	−0.667059	−0.333530	−	0.942740i	$-0.608240\pi$
$857$	−19.5279	−0.667059	−0.333530	+	0.942740i	$0.608240\pi$
$858$	0	0
$859$	−33.7771	−1.15246	−0.576230	−	0.817288i	$-0.695477\pi$
$859$	−33.7771	−1.15246	−0.576230	+	0.817288i	$0.695477\pi$
$860$	2.65248	0.0904487
$861$	−10.4721	−0.356889
$862$	−18.9098	−0.644071
$863$	52.3607	1.78238	0.891189	−	0.453632i	$-0.149872\pi$
$863$	52.3607	1.78238	0.891189	+	0.453632i	$0.149872\pi$
$864$	−5.61803	−0.191129
$865$	3.88854	0.132214
$866$	10.7639	0.365773
$867$	3.00000	0.101885
$868$	0	0
$869$	0	0
$870$	0.437694	0.0148392
$871$	8.30495	0.281403
$872$	0	0
$873$	2.00000	0.0676897
$874$	0.875388	0.0296104
$875$	2.34752	0.0793608
$876$	−12.5623	−0.424441
$877$	50.8328	1.71650	0.858251	−	0.513230i	$-0.171551\pi$
$877$	50.8328	1.71650	0.858251	+	0.513230i	$0.171551\pi$
$878$	−21.8541	−0.737540
$879$	−25.8885	−0.873199
$880$	0	0
$881$	58.4853	1.97042	0.985210	−	0.171353i	$-0.0548137\pi$
$881$	58.4853	1.97042	0.985210	+	0.171353i	$0.0548137\pi$
$882$	−0.618034	−0.0208103
$883$	27.2918	0.918442	0.459221	−	0.888322i	$-0.348129\pi$
$883$	27.2918	0.918442	0.459221	+	0.888322i	$0.348129\pi$
$884$	−12.7639	−0.429297
$885$	1.76393	0.0592939
$886$	−17.2361	−0.579057
$887$	−19.4164	−0.651939	−0.325970	−	0.945380i	$-0.605691\pi$
$887$	−19.4164	−0.651939	−0.325970	+	0.945380i	$0.605691\pi$
$888$	−12.2361	−0.410616
$889$	−2.00000	−0.0670778
$890$	−0.652476	−0.0218710
$891$	0	0
$892$	−9.70820	−0.325055
$893$	−9.00000	−0.301174
$894$	−0.0344419	−0.00115191
$895$	−1.77709	−0.0594015
$896$	−11.3820	−0.380245
$897$	−0.832816	−0.0278069
$898$	−12.0689	−0.402744
$899$	0	0
$900$	8.00000	0.266667
$901$	−40.0000	−1.33259
$902$	0	0
$903$	6.94427	0.231091
$904$	5.52786	0.183854
$905$	5.52786	0.183752
$906$	5.81966	0.193345
$907$	−12.0000	−0.398453	−0.199227	−	0.979953i	$-0.563843\pi$
$907$	−12.0000	−0.398453	−0.199227	+	0.979953i	$0.563843\pi$
$908$	39.5967	1.31406
$909$	0.944272	0.0313195
$910$	0.257354	0.00853121
$911$	41.3050	1.36849	0.684247	−	0.729250i	$-0.260131\pi$
$911$	41.3050	1.36849	0.684247	+	0.729250i	$0.260131\pi$
$912$	5.56231	0.184186
$913$	0	0
$914$	−16.0689	−0.531511
$915$	2.94427	0.0973346
$916$	25.1246	0.830141
$917$	6.47214	0.213729
$918$	−2.76393	−0.0912234
$919$	−40.9443	−1.35063	−0.675313	−	0.737531i	$-0.735992\pi$
$919$	−40.9443	−1.35063	−0.675313	+	0.737531i	$0.735992\pi$
$920$	−0.249224	−0.00821666
$921$	−0.944272	−0.0311148
$922$	−5.59675	−0.184319
$923$	18.4721	0.608018
$924$	0	0
$925$	27.0557	0.889587
$926$	−5.02129	−0.165010
$927$	−2.47214	−0.0811956
$928$	16.8541	0.553263
$929$	29.0689	0.953719	0.476860	−	0.878979i	$-0.341775\pi$
$929$	29.0689	0.953719	0.476860	+	0.878979i	$0.341775\pi$
$930$	0	0
$931$	3.00000	0.0983210
$932$	25.7082	0.842100
$933$	17.8885	0.585645
$934$	−4.03444	−0.132011
$935$	0	0
$936$	3.94427	0.128923
$937$	−2.58359	−0.0844023	−0.0422011	−	0.999109i	$-0.513437\pi$
$937$	−2.58359	−0.0844023	−0.0422011	+	0.999109i	$0.513437\pi$
$938$	2.90983	0.0950093
$939$	−11.5279	−0.376198
$940$	1.14590	0.0373751
$941$	22.3607	0.728937	0.364469	−	0.931216i	$-0.381251\pi$
$941$	22.3607	0.728937	0.364469	+	0.931216i	$0.381251\pi$
$942$	−8.29180	−0.270161
$943$	−4.94427	−0.161008
$944$	13.8541	0.450913
$945$	−0.236068	−0.00767929
$946$	0	0
$947$	−36.0000	−1.16984	−0.584921	−	0.811090i	$-0.698875\pi$
$947$	−36.0000	−1.16984	−0.584921	+	0.811090i	$0.698875\pi$
$948$	−21.7082	−0.705050
$949$	13.6950	0.444560
$950$	9.16718	0.297423
$951$	21.5279	0.698089
$952$	−10.0000	−0.324102
$953$	33.3607	1.08066	0.540329	−	0.841454i	$-0.318300\pi$
$953$	33.3607	1.08066	0.540329	+	0.841454i	$0.318300\pi$
$954$	5.52786	0.178971
$955$	−3.52786	−0.114159
$956$	1.14590	0.0370610
$957$	0	0
$958$	12.0689	0.389928
$959$	14.9443	0.482576
$960$	−0.0557281	−0.00179862
$961$	−31.0000	−1.00000
$962$	5.96556	0.192337
$963$	14.2361	0.458751
$964$	1.14590	0.0369069
$965$	2.83282	0.0911916
$966$	−0.291796	−0.00938838
$967$	−38.4721	−1.23718	−0.618590	−	0.785714i	$-0.712296\pi$
$967$	−38.4721	−1.23718	−0.618590	+	0.785714i	$0.712296\pi$
$968$	0	0
$969$	13.4164	0.430997
$970$	−0.291796	−0.00936901
$971$	−14.5279	−0.466221	−0.233111	−	0.972450i	$-0.574890\pi$
$971$	−14.5279	−0.466221	−0.233111	+	0.972450i	$0.574890\pi$
$972$	−1.61803	−0.0518985
$973$	−16.9443	−0.543208
$974$	13.5279	0.433461
$975$	−8.72136	−0.279307
$976$	23.1246	0.740201
$977$	−13.7771	−0.440768	−0.220384	−	0.975413i	$-0.570731\pi$
$977$	−13.7771	−0.440768	−0.220384	+	0.975413i	$0.570731\pi$
$978$	−12.7984	−0.409247
$979$	0	0
$980$	−0.381966	−0.0122015
$981$	0	0
$982$	17.6738	0.563992
$983$	6.11146	0.194925	0.0974626	−	0.995239i	$-0.468927\pi$
$983$	6.11146	0.194925	0.0974626	+	0.995239i	$0.468927\pi$
$984$	23.4164	0.746488
$985$	−4.47214	−0.142494
$986$	8.29180	0.264065
$987$	3.00000	0.0954911
$988$	−8.56231	−0.272403
$989$	3.27864	0.104255
$990$	0	0
$991$	−49.7639	−1.58080	−0.790402	−	0.612589i	$-0.790128\pi$
$991$	−49.7639	−1.58080	−0.790402	+	0.612589i	$0.790128\pi$
$992$	0	0
$993$	24.0000	0.761617
$994$	6.47214	0.205284
$995$	−0.832816	−0.0264020
$996$	−9.70820	−0.307616
$997$	−37.4164	−1.18499	−0.592495	−	0.805574i	$-0.701857\pi$
$997$	−37.4164	−1.18499	−0.592495	+	0.805574i	$0.701857\pi$
$998$	22.6869	0.718142
$999$	−5.47214	−0.173131

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2541.2.a.ba.1.1	yes	2
3.2	odd	2		7623.2.a.bb.1.2		2
11.10	odd	2		2541.2.a.r.1.2	✓	2
33.32	even	2		7623.2.a.bq.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2541.2.a.r.1.2	✓	2	11.10	odd	2
2541.2.a.ba.1.1	yes	2	1.1	even	1	trivial
7623.2.a.bb.1.2		2	3.2	odd	2
7623.2.a.bq.1.1		2	33.32	even	2

Overview	Random
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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:	\( N \)	\(=\)	\( 2541 = 3 \cdot 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2541.a (trivial)

\(f(q)\)	\(=\)	\(q-0.618034 q^{2} +1.00000 q^{3} -1.61803 q^{4} +0.236068 q^{5} -0.618034 q^{6} -1.00000 q^{7} +2.23607 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.618034 q^{2} +1.00000 q^{3} -1.61803 q^{4} +0.236068 q^{5} -0.618034 q^{6} -1.00000 q^{7} +2.23607 q^{8} +1.00000 q^{9} -0.145898 q^{10} -1.61803 q^{12} +1.76393 q^{13} +0.618034 q^{14} +0.236068 q^{15} +1.85410 q^{16} +4.47214 q^{17} -0.618034 q^{18} +3.00000 q^{19} -0.381966 q^{20} -1.00000 q^{21} -0.472136 q^{23} +2.23607 q^{24} -4.94427 q^{25} -1.09017 q^{26} +1.00000 q^{27} +1.61803 q^{28} -3.00000 q^{29} -0.145898 q^{30} -5.61803 q^{32} -2.76393 q^{34} -0.236068 q^{35} -1.61803 q^{36} -5.47214 q^{37} -1.85410 q^{38} +1.76393 q^{39} +0.527864 q^{40} +10.4721 q^{41} +0.618034 q^{42} -6.94427 q^{43} +0.236068 q^{45} +0.291796 q^{46} -3.00000 q^{47} +1.85410 q^{48} +1.00000 q^{49} +3.05573 q^{50} +4.47214 q^{51} -2.85410 q^{52} -8.94427 q^{53} -0.618034 q^{54} -2.23607 q^{56} +3.00000 q^{57} +1.85410 q^{58} +7.47214 q^{59} -0.381966 q^{60} +12.4721 q^{61} -1.00000 q^{63} -0.236068 q^{64} +0.416408 q^{65} +4.70820 q^{67} -7.23607 q^{68} -0.472136 q^{69} +0.145898 q^{70} +10.4721 q^{71} +2.23607 q^{72} +7.76393 q^{73} +3.38197 q^{74} -4.94427 q^{75} -4.85410 q^{76} -1.09017 q^{78} +13.4164 q^{79} +0.437694 q^{80} +1.00000 q^{81} -6.47214 q^{82} +6.00000 q^{83} +1.61803 q^{84} +1.05573 q^{85} +4.29180 q^{86} -3.00000 q^{87} +4.47214 q^{89} -0.145898 q^{90} -1.76393 q^{91} +0.763932 q^{92} +1.85410 q^{94} +0.708204 q^{95} -5.61803 q^{96} +2.00000 q^{97} -0.618034 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} + 2 q^{3} - q^{4} - 4 q^{5} + q^{6} - 2 q^{7} + 2 q^{9}+O(q^{10}) \) 2 * q + q^2 + 2 * q^3 - q^4 - 4 * q^5 + q^6 - 2 * q^7 + 2 * q^9	\( 2 q + q^{2} + 2 q^{3} - q^{4} - 4 q^{5} + q^{6} - 2 q^{7} + 2 q^{9} - 7 q^{10} - q^{12} + 8 q^{13} - q^{14} - 4 q^{15} - 3 q^{16} + q^{18} + 6 q^{19} - 3 q^{20} - 2 q^{21} + 8 q^{23} + 8 q^{25} + 9 q^{26} + 2 q^{27} + q^{28} - 6 q^{29} - 7 q^{30} - 9 q^{32} - 10 q^{34} + 4 q^{35} - q^{36} - 2 q^{37} + 3 q^{38} + 8 q^{39} + 10 q^{40} + 12 q^{41} - q^{42} + 4 q^{43} - 4 q^{45} + 14 q^{46} - 6 q^{47} - 3 q^{48} + 2 q^{49} + 24 q^{50} + q^{52} + q^{54} + 6 q^{57} - 3 q^{58} + 6 q^{59} - 3 q^{60} + 16 q^{61} - 2 q^{63} + 4 q^{64} - 26 q^{65} - 4 q^{67} - 10 q^{68} + 8 q^{69} + 7 q^{70} + 12 q^{71} + 20 q^{73} + 9 q^{74} + 8 q^{75} - 3 q^{76} + 9 q^{78} + 21 q^{80} + 2 q^{81} - 4 q^{82} + 12 q^{83} + q^{84} + 20 q^{85} + 22 q^{86} - 6 q^{87} - 7 q^{90} - 8 q^{91} + 6 q^{92} - 3 q^{94} - 12 q^{95} - 9 q^{96} + 4 q^{97} + q^{98}+O(q^{100}) \) 2 * q + q^2 + 2 * q^3 - q^4 - 4 * q^5 + q^6 - 2 * q^7 + 2 * q^9 - 7 * q^10 - q^12 + 8 * q^13 - q^14 - 4 * q^15 - 3 * q^16 + q^18 + 6 * q^19 - 3 * q^20 - 2 * q^21 + 8 * q^23 + 8 * q^25 + 9 * q^26 + 2 * q^27 + q^28 - 6 * q^29 - 7 * q^30 - 9 * q^32 - 10 * q^34 + 4 * q^35 - q^36 - 2 * q^37 + 3 * q^38 + 8 * q^39 + 10 * q^40 + 12 * q^41 - q^42 + 4 * q^43 - 4 * q^45 + 14 * q^46 - 6 * q^47 - 3 * q^48 + 2 * q^49 + 24 * q^50 + q^52 + q^54 + 6 * q^57 - 3 * q^58 + 6 * q^59 - 3 * q^60 + 16 * q^61 - 2 * q^63 + 4 * q^64 - 26 * q^65 - 4 * q^67 - 10 * q^68 + 8 * q^69 + 7 * q^70 + 12 * q^71 + 20 * q^73 + 9 * q^74 + 8 * q^75 - 3 * q^76 + 9 * q^78 + 21 * q^80 + 2 * q^81 - 4 * q^82 + 12 * q^83 + q^84 + 20 * q^85 + 22 * q^86 - 6 * q^87 - 7 * q^90 - 8 * q^91 + 6 * q^92 - 3 * q^94 - 12 * q^95 - 9 * q^96 + 4 * q^97 + q^98

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