LMFDB - Embedded newform 2541.2.a.n.1.2

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:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 231)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} -1.00000 q^{4} +3.85410 q^{5} +1.00000 q^{6} +1.00000 q^{7} +3.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} -1.00000 q^{4} +3.85410 q^{5} +1.00000 q^{6} +1.00000 q^{7} +3.00000 q^{8} +1.00000 q^{9} -3.85410 q^{10} +1.00000 q^{12} +3.23607 q^{13} -1.00000 q^{14} -3.85410 q^{15} -1.00000 q^{16} +1.14590 q^{17} -1.00000 q^{18} +0.381966 q^{19} -3.85410 q^{20} -1.00000 q^{21} +8.09017 q^{23} -3.00000 q^{24} +9.85410 q^{25} -3.23607 q^{26} -1.00000 q^{27} -1.00000 q^{28} -2.00000 q^{29} +3.85410 q^{30} +8.32624 q^{31} -5.00000 q^{32} -1.14590 q^{34} +3.85410 q^{35} -1.00000 q^{36} -0.909830 q^{37} -0.381966 q^{38} -3.23607 q^{39} +11.5623 q^{40} -4.14590 q^{41} +1.00000 q^{42} +3.23607 q^{43} +3.85410 q^{45} -8.09017 q^{46} +2.00000 q^{47} +1.00000 q^{48} +1.00000 q^{49} -9.85410 q^{50} -1.14590 q^{51} -3.23607 q^{52} -10.1803 q^{53} +1.00000 q^{54} +3.00000 q^{56} -0.381966 q^{57} +2.00000 q^{58} +11.2361 q^{59} +3.85410 q^{60} -8.94427 q^{61} -8.32624 q^{62} +1.00000 q^{63} +7.00000 q^{64} +12.4721 q^{65} +8.00000 q^{67} -1.14590 q^{68} -8.09017 q^{69} -3.85410 q^{70} -8.94427 q^{71} +3.00000 q^{72} -0.763932 q^{73} +0.909830 q^{74} -9.85410 q^{75} -0.381966 q^{76} +3.23607 q^{78} -14.0000 q^{79} -3.85410 q^{80} +1.00000 q^{81} +4.14590 q^{82} -14.9443 q^{83} +1.00000 q^{84} +4.41641 q^{85} -3.23607 q^{86} +2.00000 q^{87} -10.0902 q^{89} -3.85410 q^{90} +3.23607 q^{91} -8.09017 q^{92} -8.32624 q^{93} -2.00000 q^{94} +1.47214 q^{95} +5.00000 q^{96} -12.4721 q^{97} -1.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + q^{5} + 2 q^{6} + 2 q^{7} + 6 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + q^5 + 2 * q^6 + 2 * q^7 + 6 * q^8 + 2 * q^9	$ 2 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + q^{5} + 2 q^{6} + 2 q^{7} + 6 q^{8} + 2 q^{9} - q^{10} + 2 q^{12} + 2 q^{13} - 2 q^{14} - q^{15} - 2 q^{16} + 9 q^{17} - 2 q^{18} + 3 q^{19} - q^{20} - 2 q^{21} + 5 q^{23} - 6 q^{24} + 13 q^{25} - 2 q^{26} - 2 q^{27} - 2 q^{28} - 4 q^{29} + q^{30} + q^{31} - 10 q^{32} - 9 q^{34} + q^{35} - 2 q^{36} - 13 q^{37} - 3 q^{38} - 2 q^{39} + 3 q^{40} - 15 q^{41} + 2 q^{42} + 2 q^{43} + q^{45} - 5 q^{46} + 4 q^{47} + 2 q^{48} + 2 q^{49} - 13 q^{50} - 9 q^{51} - 2 q^{52} + 2 q^{53} + 2 q^{54} + 6 q^{56} - 3 q^{57} + 4 q^{58} + 18 q^{59} + q^{60} - q^{62} + 2 q^{63} + 14 q^{64} + 16 q^{65} + 16 q^{67} - 9 q^{68} - 5 q^{69} - q^{70} + 6 q^{72} - 6 q^{73} + 13 q^{74} - 13 q^{75} - 3 q^{76} + 2 q^{78} - 28 q^{79} - q^{80} + 2 q^{81} + 15 q^{82} - 12 q^{83} + 2 q^{84} - 18 q^{85} - 2 q^{86} + 4 q^{87} - 9 q^{89} - q^{90} + 2 q^{91} - 5 q^{92} - q^{93} - 4 q^{94} - 6 q^{95} + 10 q^{96} - 16 q^{97} - 2 q^{98}+O(q^{100}) $ 2 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + q^5 + 2 * q^6 + 2 * q^7 + 6 * q^8 + 2 * q^9 - q^10 + 2 * q^12 + 2 * q^13 - 2 * q^14 - q^15 - 2 * q^16 + 9 * q^17 - 2 * q^18 + 3 * q^19 - q^20 - 2 * q^21 + 5 * q^23 - 6 * q^24 + 13 * q^25 - 2 * q^26 - 2 * q^27 - 2 * q^28 - 4 * q^29 + q^30 + q^31 - 10 * q^32 - 9 * q^34 + q^35 - 2 * q^36 - 13 * q^37 - 3 * q^38 - 2 * q^39 + 3 * q^40 - 15 * q^41 + 2 * q^42 + 2 * q^43 + q^45 - 5 * q^46 + 4 * q^47 + 2 * q^48 + 2 * q^49 - 13 * q^50 - 9 * q^51 - 2 * q^52 + 2 * q^53 + 2 * q^54 + 6 * q^56 - 3 * q^57 + 4 * q^58 + 18 * q^59 + q^60 - q^62 + 2 * q^63 + 14 * q^64 + 16 * q^65 + 16 * q^67 - 9 * q^68 - 5 * q^69 - q^70 + 6 * q^72 - 6 * q^73 + 13 * q^74 - 13 * q^75 - 3 * q^76 + 2 * q^78 - 28 * q^79 - q^80 + 2 * q^81 + 15 * q^82 - 12 * q^83 + 2 * q^84 - 18 * q^85 - 2 * q^86 + 4 * q^87 - 9 * q^89 - q^90 + 2 * q^91 - 5 * q^92 - q^93 - 4 * q^94 - 6 * q^95 + 10 * q^96 - 16 * q^97 - 2 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107	−0.353553	−	0.935414i	$-0.615027\pi$
$2$	−1.00000	−0.707107	−0.353553	+	0.935414i	$0.615027\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.00000	−0.500000
$5$	3.85410	1.72361	0.861803	−	0.507242i	$-0.169335\pi$
$5$	3.85410	1.72361	0.861803	+	0.507242i	$0.169335\pi$
$6$	1.00000	0.408248
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	3.00000	1.06066
$9$	1.00000	0.333333
$10$	−3.85410	−1.21877
$11$	0	0
$11$	0	0
$12$	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	$0.351865\pi$
$14$	−1.00000	−0.267261
$15$	−3.85410	−0.995125
$16$	−1.00000	−0.250000
$17$	1.14590	0.277921	0.138961	−	0.990298i	$-0.455624\pi$
$17$	1.14590	0.277921	0.138961	+	0.990298i	$0.455624\pi$
$18$	−1.00000	−0.235702
$19$	0.381966	0.0876290	0.0438145	−	0.999040i	$-0.486049\pi$
$19$	0.381966	0.0876290	0.0438145	+	0.999040i	$0.486049\pi$
$20$	−3.85410	−0.861803
$21$	−1.00000	−0.218218
$22$	0	0
$23$	8.09017	1.68692	0.843459	−	0.537194i	$-0.180516\pi$
$23$	8.09017	1.68692	0.843459	+	0.537194i	$0.180516\pi$
$24$	−3.00000	−0.612372
$25$	9.85410	1.97082
$26$	−3.23607	−0.634645
$27$	−1.00000	−0.192450
$28$	−1.00000	−0.188982
$29$	−2.00000	−0.371391	−0.185695	−	0.982607i	$-0.559454\pi$
$29$	−2.00000	−0.371391	−0.185695	+	0.982607i	$0.559454\pi$
$30$	3.85410	0.703660
$31$	8.32624	1.49544	0.747718	−	0.664016i	$-0.231149\pi$
$31$	8.32624	1.49544	0.747718	+	0.664016i	$0.231149\pi$
$32$	−5.00000	−0.883883
$33$	0	0
$34$	−1.14590	−0.196520
$35$	3.85410	0.651462
$36$	−1.00000	−0.166667
$37$	−0.909830	−0.149575	−0.0747876	−	0.997199i	$-0.523828\pi$
$37$	−0.909830	−0.149575	−0.0747876	+	0.997199i	$0.523828\pi$
$38$	−0.381966	−0.0619631
$39$	−3.23607	−0.518186
$40$	11.5623	1.82816
$41$	−4.14590	−0.647480	−0.323740	−	0.946146i	$-0.604940\pi$
$41$	−4.14590	−0.647480	−0.323740	+	0.946146i	$0.604940\pi$
$42$	1.00000	0.154303
$43$	3.23607	0.493496	0.246748	−	0.969080i	$-0.420638\pi$
$43$	3.23607	0.493496	0.246748	+	0.969080i	$0.420638\pi$
$44$	0	0
$45$	3.85410	0.574536
$46$	−8.09017	−1.19283
$47$	2.00000	0.291730	0.145865	−	0.989305i	$-0.453403\pi$
$47$	2.00000	0.291730	0.145865	+	0.989305i	$0.453403\pi$
$48$	1.00000	0.144338
$49$	1.00000	0.142857
$50$	−9.85410	−1.39358
$51$	−1.14590	−0.160458
$52$	−3.23607	−0.448762
$53$	−10.1803	−1.39838	−0.699189	−	0.714937i	$-0.746455\pi$
$53$	−10.1803	−1.39838	−0.699189	+	0.714937i	$0.746455\pi$
$54$	1.00000	0.136083
$55$	0	0
$56$	3.00000	0.400892
$57$	−0.381966	−0.0505926
$58$	2.00000	0.262613
$59$	11.2361	1.46281	0.731406	−	0.681943i	$-0.238865\pi$
$59$	11.2361	1.46281	0.731406	+	0.681943i	$0.238865\pi$
$60$	3.85410	0.497562
$61$	−8.94427	−1.14520	−0.572598	−	0.819836i	$-0.694065\pi$
$61$	−8.94427	−1.14520	−0.572598	+	0.819836i	$0.694065\pi$
$62$	−8.32624	−1.05743
$63$	1.00000	0.125988
$64$	7.00000	0.875000
$65$	12.4721	1.54698
$66$	0	0
$67$	8.00000	0.977356	0.488678	−	0.872464i	$-0.337479\pi$
$67$	8.00000	0.977356	0.488678	+	0.872464i	$0.337479\pi$
$68$	−1.14590	−0.138961
$69$	−8.09017	−0.973942
$70$	−3.85410	−0.460653
$71$	−8.94427	−1.06149	−0.530745	−	0.847532i	$-0.678088\pi$
$71$	−8.94427	−1.06149	−0.530745	+	0.847532i	$0.678088\pi$
$72$	3.00000	0.353553
$73$	−0.763932	−0.0894115	−0.0447057	−	0.999000i	$-0.514235\pi$
$73$	−0.763932	−0.0894115	−0.0447057	+	0.999000i	$0.514235\pi$
$74$	0.909830	0.105766
$75$	−9.85410	−1.13785
$76$	−0.381966	−0.0438145
$77$	0	0
$78$	3.23607	0.366413
$79$	−14.0000	−1.57512	−0.787562	−	0.616236i	$-0.788657\pi$
$79$	−14.0000	−1.57512	−0.787562	+	0.616236i	$0.788657\pi$
$80$	−3.85410	−0.430902
$81$	1.00000	0.111111
$82$	4.14590	0.457838
$83$	−14.9443	−1.64035	−0.820173	−	0.572115i	$-0.806123\pi$
$83$	−14.9443	−1.64035	−0.820173	+	0.572115i	$0.806123\pi$
$84$	1.00000	0.109109
$85$	4.41641	0.479027
$86$	−3.23607	−0.348954
$87$	2.00000	0.214423
$88$	0	0
$89$	−10.0902	−1.06956	−0.534778	−	0.844993i	$-0.679605\pi$
$89$	−10.0902	−1.06956	−0.534778	+	0.844993i	$0.679605\pi$
$90$	−3.85410	−0.406258
$91$	3.23607	0.339232
$92$	−8.09017	−0.843459
$93$	−8.32624	−0.863391
$94$	−2.00000	−0.206284
$95$	1.47214	0.151038
$96$	5.00000	0.510310
$97$	−12.4721	−1.26635	−0.633177	−	0.774007i	$-0.718249\pi$
$97$	−12.4721	−1.26635	−0.633177	+	0.774007i	$0.718249\pi$
$98$	−1.00000	−0.101015
$99$	0	0
$100$	−9.85410	−0.985410
$101$	9.09017	0.904506	0.452253	−	0.891890i	$-0.350620\pi$
$101$	9.09017	0.904506	0.452253	+	0.891890i	$0.350620\pi$
$102$	1.14590	0.113461
$103$	5.32624	0.524810	0.262405	−	0.964958i	$-0.415484\pi$
$103$	5.32624	0.524810	0.262405	+	0.964958i	$0.415484\pi$
$104$	9.70820	0.951968
$105$	−3.85410	−0.376122
$106$	10.1803	0.988802
$107$	16.0902	1.55550	0.777748	−	0.628577i	$-0.216362\pi$
$107$	16.0902	1.55550	0.777748	+	0.628577i	$0.216362\pi$
$108$	1.00000	0.0962250
$109$	−9.56231	−0.915903	−0.457951	−	0.888977i	$-0.651417\pi$
$109$	−9.56231	−0.915903	−0.457951	+	0.888977i	$0.651417\pi$
$110$	0	0
$111$	0.909830	0.0863572
$112$	−1.00000	−0.0944911
$113$	5.23607	0.492568	0.246284	−	0.969198i	$-0.420790\pi$
$113$	5.23607	0.492568	0.246284	+	0.969198i	$0.420790\pi$
$114$	0.381966	0.0357744
$115$	31.1803	2.90758
$116$	2.00000	0.185695
$117$	3.23607	0.299175
$118$	−11.2361	−1.03436
$119$	1.14590	0.105044
$120$	−11.5623	−1.05549
$121$	0	0
$122$	8.94427	0.809776
$123$	4.14590	0.373823
$124$	−8.32624	−0.747718
$125$	18.7082	1.67331
$126$	−1.00000	−0.0890871
$127$	1.23607	0.109683	0.0548416	−	0.998495i	$-0.482535\pi$
$127$	1.23607	0.109683	0.0548416	+	0.998495i	$0.482535\pi$
$128$	3.00000	0.265165
$129$	−3.23607	−0.284920
$130$	−12.4721	−1.09388
$131$	15.7082	1.37243	0.686216	−	0.727398i	$-0.259270\pi$
$131$	15.7082	1.37243	0.686216	+	0.727398i	$0.259270\pi$
$132$	0	0
$133$	0.381966	0.0331207
$134$	−8.00000	−0.691095
$135$	−3.85410	−0.331708
$136$	3.43769	0.294780
$137$	11.2361	0.959962	0.479981	−	0.877279i	$-0.340644\pi$
$137$	11.2361	0.959962	0.479981	+	0.877279i	$0.340644\pi$
$138$	8.09017	0.688681
$139$	−19.7984	−1.67928	−0.839638	−	0.543146i	$-0.817233\pi$
$139$	−19.7984	−1.67928	−0.839638	+	0.543146i	$0.817233\pi$
$140$	−3.85410	−0.325731
$141$	−2.00000	−0.168430
$142$	8.94427	0.750587
$143$	0	0
$144$	−1.00000	−0.0833333
$145$	−7.70820	−0.640131
$146$	0.763932	0.0632235
$147$	−1.00000	−0.0824786
$148$	0.909830	0.0747876
$149$	−20.0000	−1.63846	−0.819232	−	0.573462i	$-0.805600\pi$
$149$	−20.0000	−1.63846	−0.819232	+	0.573462i	$0.805600\pi$
$150$	9.85410	0.804584
$151$	−2.00000	−0.162758	−0.0813788	−	0.996683i	$-0.525932\pi$
$151$	−2.00000	−0.162758	−0.0813788	+	0.996683i	$0.525932\pi$
$152$	1.14590	0.0929446
$153$	1.14590	0.0926404
$154$	0	0
$155$	32.0902	2.57754
$156$	3.23607	0.259093
$157$	−3.70820	−0.295947	−0.147973	−	0.988991i	$-0.547275\pi$
$157$	−3.70820	−0.295947	−0.147973	+	0.988991i	$0.547275\pi$
$158$	14.0000	1.11378
$159$	10.1803	0.807353
$160$	−19.2705	−1.52347
$161$	8.09017	0.637595
$162$	−1.00000	−0.0785674
$163$	21.4164	1.67746	0.838731	−	0.544546i	$-0.183298\pi$
$163$	21.4164	1.67746	0.838731	+	0.544546i	$0.183298\pi$
$164$	4.14590	0.323740
$165$	0	0
$166$	14.9443	1.15990
$167$	−14.1803	−1.09731	−0.548654	−	0.836050i	$-0.684859\pi$
$167$	−14.1803	−1.09731	−0.548654	+	0.836050i	$0.684859\pi$
$168$	−3.00000	−0.231455
$169$	−2.52786	−0.194451
$170$	−4.41641	−0.338723
$171$	0.381966	0.0292097
$172$	−3.23607	−0.246748
$173$	13.1459	0.999464	0.499732	−	0.866180i	$-0.333432\pi$
$173$	13.1459	0.999464	0.499732	+	0.866180i	$0.333432\pi$
$174$	−2.00000	−0.151620
$175$	9.85410	0.744900
$176$	0	0
$177$	−11.2361	−0.844555
$178$	10.0902	0.756290
$179$	10.6180	0.793629	0.396815	−	0.917899i	$-0.370116\pi$
$179$	10.6180	0.793629	0.396815	+	0.917899i	$0.370116\pi$
$180$	−3.85410	−0.287268
$181$	−1.05573	−0.0784717	−0.0392358	−	0.999230i	$-0.512492\pi$
$181$	−1.05573	−0.0784717	−0.0392358	+	0.999230i	$0.512492\pi$
$182$	−3.23607	−0.239873
$183$	8.94427	0.661180
$184$	24.2705	1.78925
$185$	−3.50658	−0.257809
$186$	8.32624	0.610509
$187$	0	0
$188$	−2.00000	−0.145865
$189$	−1.00000	−0.0727393
$190$	−1.47214	−0.106800
$191$	15.2705	1.10494	0.552468	−	0.833534i	$-0.313686\pi$
$191$	15.2705	1.10494	0.552468	+	0.833534i	$0.313686\pi$
$192$	−7.00000	−0.505181
$193$	20.6180	1.48412	0.742059	−	0.670334i	$-0.233849\pi$
$193$	20.6180	1.48412	0.742059	+	0.670334i	$0.233849\pi$
$194$	12.4721	0.895447
$195$	−12.4721	−0.893148
$196$	−1.00000	−0.0714286
$197$	4.00000	0.284988	0.142494	−	0.989796i	$-0.454488\pi$
$197$	4.00000	0.284988	0.142494	+	0.989796i	$0.454488\pi$
$198$	0	0
$199$	−0.381966	−0.0270769	−0.0135384	−	0.999908i	$-0.504310\pi$
$199$	−0.381966	−0.0270769	−0.0135384	+	0.999908i	$0.504310\pi$
$200$	29.5623	2.09037
$201$	−8.00000	−0.564276
$202$	−9.09017	−0.639582
$203$	−2.00000	−0.140372
$204$	1.14590	0.0802289
$205$	−15.9787	−1.11600
$206$	−5.32624	−0.371097
$207$	8.09017	0.562306
$208$	−3.23607	−0.224381
$209$	0	0
$210$	3.85410	0.265958
$211$	−2.00000	−0.137686	−0.0688428	−	0.997628i	$-0.521931\pi$
$211$	−2.00000	−0.137686	−0.0688428	+	0.997628i	$0.521931\pi$
$212$	10.1803	0.699189
$213$	8.94427	0.612851
$214$	−16.0902	−1.09990
$215$	12.4721	0.850593
$216$	−3.00000	−0.204124
$217$	8.32624	0.565222
$218$	9.56231	0.647641
$219$	0.763932	0.0516217
$220$	0	0
$221$	3.70820	0.249441
$222$	−0.909830	−0.0610638
$223$	−3.79837	−0.254358	−0.127179	−	0.991880i	$-0.540592\pi$
$223$	−3.79837	−0.254358	−0.127179	+	0.991880i	$0.540592\pi$
$224$	−5.00000	−0.334077
$225$	9.85410	0.656940
$226$	−5.23607	−0.348298
$227$	−5.41641	−0.359500	−0.179750	−	0.983712i	$-0.557529\pi$
$227$	−5.41641	−0.359500	−0.179750	+	0.983712i	$0.557529\pi$
$228$	0.381966	0.0252963
$229$	16.7639	1.10779	0.553896	−	0.832586i	$-0.313141\pi$
$229$	16.7639	1.10779	0.553896	+	0.832586i	$0.313141\pi$
$230$	−31.1803	−2.05597
$231$	0	0
$232$	−6.00000	−0.393919
$233$	7.70820	0.504981	0.252491	−	0.967599i	$-0.418750\pi$
$233$	7.70820	0.504981	0.252491	+	0.967599i	$0.418750\pi$
$234$	−3.23607	−0.211548
$235$	7.70820	0.502828
$236$	−11.2361	−0.731406
$237$	14.0000	0.909398
$238$	−1.14590	−0.0742775
$239$	18.5623	1.20070	0.600348	−	0.799739i	$-0.295029\pi$
$239$	18.5623	1.20070	0.600348	+	0.799739i	$0.295029\pi$
$240$	3.85410	0.248781
$241$	−12.9443	−0.833814	−0.416907	−	0.908949i	$-0.636886\pi$
$241$	−12.9443	−0.833814	−0.416907	+	0.908949i	$0.636886\pi$
$242$	0	0
$243$	−1.00000	−0.0641500
$244$	8.94427	0.572598
$245$	3.85410	0.246230
$246$	−4.14590	−0.264333
$247$	1.23607	0.0786491
$248$	24.9787	1.58615
$249$	14.9443	0.947055
$250$	−18.7082	−1.18321
$251$	1.81966	0.114856	0.0574280	−	0.998350i	$-0.481710\pi$
$251$	1.81966	0.114856	0.0574280	+	0.998350i	$0.481710\pi$
$252$	−1.00000	−0.0629941
$253$	0	0
$254$	−1.23607	−0.0775578
$255$	−4.41641	−0.276566
$256$	−17.0000	−1.06250
$257$	0.381966	0.0238264	0.0119132	−	0.999929i	$-0.496208\pi$
$257$	0.381966	0.0238264	0.0119132	+	0.999929i	$0.496208\pi$
$258$	3.23607	0.201469
$259$	−0.909830	−0.0565341
$260$	−12.4721	−0.773489
$261$	−2.00000	−0.123797
$262$	−15.7082	−0.970456
$263$	22.5623	1.39125	0.695626	−	0.718404i	$-0.255127\pi$
$263$	22.5623	1.39125	0.695626	+	0.718404i	$0.255127\pi$
$264$	0	0
$265$	−39.2361	−2.41025
$266$	−0.381966	−0.0234198
$267$	10.0902	0.617508
$268$	−8.00000	−0.488678
$269$	−7.88854	−0.480973	−0.240487	−	0.970652i	$-0.577307\pi$
$269$	−7.88854	−0.480973	−0.240487	+	0.970652i	$0.577307\pi$
$270$	3.85410	0.234553
$271$	12.9098	0.784216	0.392108	−	0.919919i	$-0.371746\pi$
$271$	12.9098	0.784216	0.392108	+	0.919919i	$0.371746\pi$
$272$	−1.14590	−0.0694803
$273$	−3.23607	−0.195856
$274$	−11.2361	−0.678796
$275$	0	0
$276$	8.09017	0.486971
$277$	−30.5623	−1.83631	−0.918155	−	0.396220i	$-0.870322\pi$
$277$	−30.5623	−1.83631	−0.918155	+	0.396220i	$0.870322\pi$
$278$	19.7984	1.18743
$279$	8.32624	0.498479
$280$	11.5623	0.690980
$281$	18.9443	1.13012	0.565060	−	0.825050i	$-0.308853\pi$
$281$	18.9443	1.13012	0.565060	+	0.825050i	$0.308853\pi$
$282$	2.00000	0.119098
$283$	33.5623	1.99507	0.997536	−	0.0701565i	$-0.0223499\pi$
$283$	33.5623	1.99507	0.997536	+	0.0701565i	$0.0223499\pi$
$284$	8.94427	0.530745
$285$	−1.47214	−0.0872018
$286$	0	0
$287$	−4.14590	−0.244725
$288$	−5.00000	−0.294628
$289$	−15.6869	−0.922760
$290$	7.70820	0.452641
$291$	12.4721	0.731130
$292$	0.763932	0.0447057
$293$	−4.79837	−0.280324	−0.140162	−	0.990129i	$-0.544762\pi$
$293$	−4.79837	−0.280324	−0.140162	+	0.990129i	$0.544762\pi$
$294$	1.00000	0.0583212
$295$	43.3050	2.52131
$296$	−2.72949	−0.158648
$297$	0	0
$298$	20.0000	1.15857
$299$	26.1803	1.51405
$300$	9.85410	0.568927
$301$	3.23607	0.186524
$302$	2.00000	0.115087
$303$	−9.09017	−0.522217
$304$	−0.381966	−0.0219073
$305$	−34.4721	−1.97387
$306$	−1.14590	−0.0655066
$307$	9.27051	0.529096	0.264548	−	0.964373i	$-0.414777\pi$
$307$	9.27051	0.529096	0.264548	+	0.964373i	$0.414777\pi$
$308$	0	0
$309$	−5.32624	−0.302999
$310$	−32.0902	−1.82260
$311$	−5.23607	−0.296910	−0.148455	−	0.988919i	$-0.547430\pi$
$311$	−5.23607	−0.296910	−0.148455	+	0.988919i	$0.547430\pi$
$312$	−9.70820	−0.549619
$313$	−32.1803	−1.81894	−0.909470	−	0.415769i	$-0.863512\pi$
$313$	−32.1803	−1.81894	−0.909470	+	0.415769i	$0.863512\pi$
$314$	3.70820	0.209266
$315$	3.85410	0.217154
$316$	14.0000	0.787562
$317$	21.5967	1.21299	0.606497	−	0.795086i	$-0.292574\pi$
$317$	21.5967	1.21299	0.606497	+	0.795086i	$0.292574\pi$
$318$	−10.1803	−0.570885
$319$	0	0
$320$	26.9787	1.50816
$321$	−16.0902	−0.898066
$322$	−8.09017	−0.450848
$323$	0.437694	0.0243540
$324$	−1.00000	−0.0555556
$325$	31.8885	1.76886
$326$	−21.4164	−1.18615
$327$	9.56231	0.528797
$328$	−12.4377	−0.686757
$329$	2.00000	0.110264
$330$	0	0
$331$	−14.3607	−0.789334	−0.394667	−	0.918824i	$-0.629140\pi$
$331$	−14.3607	−0.789334	−0.394667	+	0.918824i	$0.629140\pi$
$332$	14.9443	0.820173
$333$	−0.909830	−0.0498584
$334$	14.1803	0.775914
$335$	30.8328	1.68458
$336$	1.00000	0.0545545
$337$	−33.8541	−1.84415	−0.922075	−	0.387011i	$-0.873508\pi$
$337$	−33.8541	−1.84415	−0.922075	+	0.387011i	$0.873508\pi$
$338$	2.52786	0.137498
$339$	−5.23607	−0.284384
$340$	−4.41641	−0.239513
$341$	0	0
$342$	−0.381966	−0.0206544
$343$	1.00000	0.0539949
$344$	9.70820	0.523431
$345$	−31.1803	−1.67869
$346$	−13.1459	−0.706728
$347$	−14.6180	−0.784737	−0.392369	−	0.919808i	$-0.628344\pi$
$347$	−14.6180	−0.784737	−0.392369	+	0.919808i	$0.628344\pi$
$348$	−2.00000	−0.107211
$349$	27.2361	1.45791	0.728957	−	0.684560i	$-0.240006\pi$
$349$	27.2361	1.45791	0.728957	+	0.684560i	$0.240006\pi$
$350$	−9.85410	−0.526724
$351$	−3.23607	−0.172729
$352$	0	0
$353$	3.52786	0.187769	0.0938846	−	0.995583i	$-0.470072\pi$
$353$	3.52786	0.187769	0.0938846	+	0.995583i	$0.470072\pi$
$354$	11.2361	0.597190
$355$	−34.4721	−1.82959
$356$	10.0902	0.534778
$357$	−1.14590	−0.0606474
$358$	−10.6180	−0.561181
$359$	−22.0344	−1.16293	−0.581467	−	0.813570i	$-0.697521\pi$
$359$	−22.0344	−1.16293	−0.581467	+	0.813570i	$0.697521\pi$
$360$	11.5623	0.609387
$361$	−18.8541	−0.992321
$362$	1.05573	0.0554878
$363$	0	0
$364$	−3.23607	−0.169616
$365$	−2.94427	−0.154110
$366$	−8.94427	−0.467525
$367$	−17.2705	−0.901513	−0.450757	−	0.892647i	$-0.648846\pi$
$367$	−17.2705	−0.901513	−0.450757	+	0.892647i	$0.648846\pi$
$368$	−8.09017	−0.421729
$369$	−4.14590	−0.215827
$370$	3.50658	0.182298
$371$	−10.1803	−0.528537
$372$	8.32624	0.431695
$373$	−7.67376	−0.397332	−0.198666	−	0.980067i	$-0.563661\pi$
$373$	−7.67376	−0.397332	−0.198666	+	0.980067i	$0.563661\pi$
$374$	0	0
$375$	−18.7082	−0.966087
$376$	6.00000	0.309426
$377$	−6.47214	−0.333332
$378$	1.00000	0.0514344
$379$	−6.47214	−0.332451	−0.166226	−	0.986088i	$-0.553158\pi$
$379$	−6.47214	−0.332451	−0.166226	+	0.986088i	$0.553158\pi$
$380$	−1.47214	−0.0755190
$381$	−1.23607	−0.0633257
$382$	−15.2705	−0.781307
$383$	−30.9443	−1.58118	−0.790589	−	0.612347i	$-0.790226\pi$
$383$	−30.9443	−1.58118	−0.790589	+	0.612347i	$0.790226\pi$
$384$	−3.00000	−0.153093
$385$	0	0
$386$	−20.6180	−1.04943
$387$	3.23607	0.164499
$388$	12.4721	0.633177
$389$	−0.180340	−0.00914360	−0.00457180	−	0.999990i	$-0.501455\pi$
$389$	−0.180340	−0.00914360	−0.00457180	+	0.999990i	$0.501455\pi$
$390$	12.4721	0.631551
$391$	9.27051	0.468830
$392$	3.00000	0.151523
$393$	−15.7082	−0.792374
$394$	−4.00000	−0.201517
$395$	−53.9574	−2.71489
$396$	0	0
$397$	−16.6525	−0.835764	−0.417882	−	0.908501i	$-0.637227\pi$
$397$	−16.6525	−0.835764	−0.417882	+	0.908501i	$0.637227\pi$
$398$	0.381966	0.0191462
$399$	−0.381966	−0.0191222
$400$	−9.85410	−0.492705
$401$	9.52786	0.475799	0.237899	−	0.971290i	$-0.423541\pi$
$401$	9.52786	0.475799	0.237899	+	0.971290i	$0.423541\pi$
$402$	8.00000	0.399004
$403$	26.9443	1.34219
$404$	−9.09017	−0.452253
$405$	3.85410	0.191512
$406$	2.00000	0.0992583
$407$	0	0
$408$	−3.43769	−0.170191
$409$	33.2361	1.64342	0.821709	−	0.569907i	$-0.193021\pi$
$409$	33.2361	1.64342	0.821709	+	0.569907i	$0.193021\pi$
$410$	15.9787	0.789132
$411$	−11.2361	−0.554234
$412$	−5.32624	−0.262405
$413$	11.2361	0.552891
$414$	−8.09017	−0.397610
$415$	−57.5967	−2.82731
$416$	−16.1803	−0.793306
$417$	19.7984	0.969531
$418$	0	0
$419$	19.2361	0.939743	0.469872	−	0.882735i	$-0.344300\pi$
$419$	19.2361	0.939743	0.469872	+	0.882735i	$0.344300\pi$
$420$	3.85410	0.188061
$421$	11.3262	0.552007	0.276004	−	0.961157i	$-0.410990\pi$
$421$	11.3262	0.552007	0.276004	+	0.961157i	$0.410990\pi$
$422$	2.00000	0.0973585
$423$	2.00000	0.0972433
$424$	−30.5410	−1.48320
$425$	11.2918	0.547733
$426$	−8.94427	−0.433351
$427$	−8.94427	−0.432844
$428$	−16.0902	−0.777748
$429$	0	0
$430$	−12.4721	−0.601460
$431$	9.09017	0.437858	0.218929	−	0.975741i	$-0.429744\pi$
$431$	9.09017	0.437858	0.218929	+	0.975741i	$0.429744\pi$
$432$	1.00000	0.0481125
$433$	−12.7639	−0.613395	−0.306698	−	0.951807i	$-0.599224\pi$
$433$	−12.7639	−0.613395	−0.306698	+	0.951807i	$0.599224\pi$
$434$	−8.32624	−0.399672
$435$	7.70820	0.369580
$436$	9.56231	0.457951
$437$	3.09017	0.147823
$438$	−0.763932	−0.0365021
$439$	2.79837	0.133559	0.0667795	−	0.997768i	$-0.478728\pi$
$439$	2.79837	0.133559	0.0667795	+	0.997768i	$0.478728\pi$
$440$	0	0
$441$	1.00000	0.0476190
$442$	−3.70820	−0.176381
$443$	16.0902	0.764467	0.382234	−	0.924066i	$-0.375155\pi$
$443$	16.0902	0.764467	0.382234	+	0.924066i	$0.375155\pi$
$444$	−0.909830	−0.0431786
$445$	−38.8885	−1.84349
$446$	3.79837	0.179858
$447$	20.0000	0.945968
$448$	7.00000	0.330719
$449$	6.11146	0.288417	0.144209	−	0.989547i	$-0.453936\pi$
$449$	6.11146	0.288417	0.144209	+	0.989547i	$0.453936\pi$
$450$	−9.85410	−0.464527
$451$	0	0
$452$	−5.23607	−0.246284
$453$	2.00000	0.0939682
$454$	5.41641	0.254205
$455$	12.4721	0.584703
$456$	−1.14590	−0.0536616
$457$	3.52786	0.165027	0.0825133	−	0.996590i	$-0.473705\pi$
$457$	3.52786	0.165027	0.0825133	+	0.996590i	$0.473705\pi$
$458$	−16.7639	−0.783327
$459$	−1.14590	−0.0534859
$460$	−31.1803	−1.45379
$461$	38.3607	1.78663	0.893317	−	0.449426i	$-0.148372\pi$
$461$	38.3607	1.78663	0.893317	+	0.449426i	$0.148372\pi$
$462$	0	0
$463$	−15.4164	−0.716461	−0.358231	−	0.933633i	$-0.616620\pi$
$463$	−15.4164	−0.716461	−0.358231	+	0.933633i	$0.616620\pi$
$464$	2.00000	0.0928477
$465$	−32.0902	−1.48815
$466$	−7.70820	−0.357076
$467$	14.7639	0.683193	0.341597	−	0.939847i	$-0.389032\pi$
$467$	14.7639	0.683193	0.341597	+	0.939847i	$0.389032\pi$
$468$	−3.23607	−0.149587
$469$	8.00000	0.369406
$470$	−7.70820	−0.355553
$471$	3.70820	0.170865
$472$	33.7082	1.55155
$473$	0	0
$474$	−14.0000	−0.643041
$475$	3.76393	0.172701
$476$	−1.14590	−0.0525222
$477$	−10.1803	−0.466126
$478$	−18.5623	−0.849020
$479$	−28.9443	−1.32250	−0.661249	−	0.750167i	$-0.729973\pi$
$479$	−28.9443	−1.32250	−0.661249	+	0.750167i	$0.729973\pi$
$480$	19.2705	0.879574
$481$	−2.94427	−0.134247
$482$	12.9443	0.589595
$483$	−8.09017	−0.368115
$484$	0	0
$485$	−48.0689	−2.18270
$486$	1.00000	0.0453609
$487$	−34.7639	−1.57530	−0.787652	−	0.616120i	$-0.788704\pi$
$487$	−34.7639	−1.57530	−0.787652	+	0.616120i	$0.788704\pi$
$488$	−26.8328	−1.21466
$489$	−21.4164	−0.968483
$490$	−3.85410	−0.174111
$491$	15.3262	0.691663	0.345832	−	0.938297i	$-0.387597\pi$
$491$	15.3262	0.691663	0.345832	+	0.938297i	$0.387597\pi$
$492$	−4.14590	−0.186912
$493$	−2.29180	−0.103217
$494$	−1.23607	−0.0556133
$495$	0	0
$496$	−8.32624	−0.373859
$497$	−8.94427	−0.401205
$498$	−14.9443	−0.669669
$499$	3.81966	0.170991	0.0854957	−	0.996339i	$-0.472753\pi$
$499$	3.81966	0.170991	0.0854957	+	0.996339i	$0.472753\pi$
$500$	−18.7082	−0.836656
$501$	14.1803	0.633531
$502$	−1.81966	−0.0812154
$503$	−27.4164	−1.22244	−0.611219	−	0.791462i	$-0.709320\pi$
$503$	−27.4164	−1.22244	−0.611219	+	0.791462i	$0.709320\pi$
$504$	3.00000	0.133631
$505$	35.0344	1.55901
$506$	0	0
$507$	2.52786	0.112266
$508$	−1.23607	−0.0548416
$509$	−17.0902	−0.757508	−0.378754	−	0.925497i	$-0.623647\pi$
$509$	−17.0902	−0.757508	−0.378754	+	0.925497i	$0.623647\pi$
$510$	4.41641	0.195562
$511$	−0.763932	−0.0337944
$512$	11.0000	0.486136
$513$	−0.381966	−0.0168642
$514$	−0.381966	−0.0168478
$515$	20.5279	0.904566
$516$	3.23607	0.142460
$517$	0	0
$518$	0.909830	0.0399756
$519$	−13.1459	−0.577041
$520$	37.4164	1.64082
$521$	−9.38197	−0.411031	−0.205516	−	0.978654i	$-0.565887\pi$
$521$	−9.38197	−0.411031	−0.205516	+	0.978654i	$0.565887\pi$
$522$	2.00000	0.0875376
$523$	14.0902	0.616120	0.308060	−	0.951367i	$-0.400320\pi$
$523$	14.0902	0.616120	0.308060	+	0.951367i	$0.400320\pi$
$524$	−15.7082	−0.686216
$525$	−9.85410	−0.430068
$526$	−22.5623	−0.983763
$527$	9.54102	0.415613
$528$	0	0
$529$	42.4508	1.84569
$530$	39.2361	1.70431
$531$	11.2361	0.487604
$532$	−0.381966	−0.0165603
$533$	−13.4164	−0.581129
$534$	−10.0902	−0.436644
$535$	62.0132	2.68106
$536$	24.0000	1.03664
$537$	−10.6180	−0.458202
$538$	7.88854	0.340099
$539$	0	0
$540$	3.85410	0.165854
$541$	10.1459	0.436206	0.218103	−	0.975926i	$-0.430013\pi$
$541$	10.1459	0.436206	0.218103	+	0.975926i	$0.430013\pi$
$542$	−12.9098	−0.554525
$543$	1.05573	0.0453056
$544$	−5.72949	−0.245650
$545$	−36.8541	−1.57866
$546$	3.23607	0.138491
$547$	−27.5279	−1.17701	−0.588503	−	0.808495i	$-0.700283\pi$
$547$	−27.5279	−1.17701	−0.588503	+	0.808495i	$0.700283\pi$
$548$	−11.2361	−0.479981
$549$	−8.94427	−0.381732
$550$	0	0
$551$	−0.763932	−0.0325446
$552$	−24.2705	−1.03302
$553$	−14.0000	−0.595341
$554$	30.5623	1.29847
$555$	3.50658	0.148846
$556$	19.7984	0.839638
$557$	5.41641	0.229501	0.114750	−	0.993394i	$-0.463393\pi$
$557$	5.41641	0.229501	0.114750	+	0.993394i	$0.463393\pi$
$558$	−8.32624	−0.352478
$559$	10.4721	0.442924
$560$	−3.85410	−0.162866
$561$	0	0
$562$	−18.9443	−0.799116
$563$	−4.36068	−0.183781	−0.0918904	−	0.995769i	$-0.529291\pi$
$563$	−4.36068	−0.183781	−0.0918904	+	0.995769i	$0.529291\pi$
$564$	2.00000	0.0842152
$565$	20.1803	0.848993
$566$	−33.5623	−1.41073
$567$	1.00000	0.0419961
$568$	−26.8328	−1.12588
$569$	4.18034	0.175249	0.0876245	−	0.996154i	$-0.472072\pi$
$569$	4.18034	0.175249	0.0876245	+	0.996154i	$0.472072\pi$
$570$	1.47214	0.0616610
$571$	−38.5410	−1.61289	−0.806446	−	0.591308i	$-0.798612\pi$
$571$	−38.5410	−1.61289	−0.806446	+	0.591308i	$0.798612\pi$
$572$	0	0
$573$	−15.2705	−0.637935
$574$	4.14590	0.173046
$575$	79.7214	3.32461
$576$	7.00000	0.291667
$577$	16.6525	0.693252	0.346626	−	0.938003i	$-0.387327\pi$
$577$	16.6525	0.693252	0.346626	+	0.938003i	$0.387327\pi$
$578$	15.6869	0.652490
$579$	−20.6180	−0.856856
$580$	7.70820	0.320066
$581$	−14.9443	−0.619993
$582$	−12.4721	−0.516987
$583$	0	0
$584$	−2.29180	−0.0948352
$585$	12.4721	0.515659
$586$	4.79837	0.198219
$587$	−31.8885	−1.31618	−0.658091	−	0.752939i	$-0.728636\pi$
$587$	−31.8885	−1.31618	−0.658091	+	0.752939i	$0.728636\pi$
$588$	1.00000	0.0412393
$589$	3.18034	0.131044
$590$	−43.3050	−1.78284
$591$	−4.00000	−0.164538
$592$	0.909830	0.0373938
$593$	23.5623	0.967588	0.483794	−	0.875182i	$-0.339258\pi$
$593$	23.5623	0.967588	0.483794	+	0.875182i	$0.339258\pi$
$594$	0	0
$595$	4.41641	0.181055
$596$	20.0000	0.819232
$597$	0.381966	0.0156328
$598$	−26.1803	−1.07059
$599$	18.5623	0.758435	0.379218	−	0.925308i	$-0.376193\pi$
$599$	18.5623	0.758435	0.379218	+	0.925308i	$0.376193\pi$
$600$	−29.5623	−1.20688
$601$	6.00000	0.244745	0.122373	−	0.992484i	$-0.460950\pi$
$601$	6.00000	0.244745	0.122373	+	0.992484i	$0.460950\pi$
$602$	−3.23607	−0.131892
$603$	8.00000	0.325785
$604$	2.00000	0.0813788
$605$	0	0
$606$	9.09017	0.369263
$607$	5.32624	0.216185	0.108093	−	0.994141i	$-0.465526\pi$
$607$	5.32624	0.216185	0.108093	+	0.994141i	$0.465526\pi$
$608$	−1.90983	−0.0774538
$609$	2.00000	0.0810441
$610$	34.4721	1.39574
$611$	6.47214	0.261835
$612$	−1.14590	−0.0463202
$613$	0.854102	0.0344969	0.0172484	−	0.999851i	$-0.494509\pi$
$613$	0.854102	0.0344969	0.0172484	+	0.999851i	$0.494509\pi$
$614$	−9.27051	−0.374127
$615$	15.9787	0.644324
$616$	0	0
$617$	13.3475	0.537351	0.268676	−	0.963231i	$-0.413414\pi$
$617$	13.3475	0.537351	0.268676	+	0.963231i	$0.413414\pi$
$618$	5.32624	0.214253
$619$	26.5066	1.06539	0.532695	−	0.846308i	$-0.321179\pi$
$619$	26.5066	1.06539	0.532695	+	0.846308i	$0.321179\pi$
$620$	−32.0902	−1.28877
$621$	−8.09017	−0.324647
$622$	5.23607	0.209947
$623$	−10.0902	−0.404254
$624$	3.23607	0.129546
$625$	22.8328	0.913313
$626$	32.1803	1.28619
$627$	0	0
$628$	3.70820	0.147973
$629$	−1.04257	−0.0415701
$630$	−3.85410	−0.153551
$631$	−5.88854	−0.234419	−0.117210	−	0.993107i	$-0.537395\pi$
$631$	−5.88854	−0.234419	−0.117210	+	0.993107i	$0.537395\pi$
$632$	−42.0000	−1.67067
$633$	2.00000	0.0794929
$634$	−21.5967	−0.857716
$635$	4.76393	0.189051
$636$	−10.1803	−0.403677
$637$	3.23607	0.128218
$638$	0	0
$639$	−8.94427	−0.353830
$640$	11.5623	0.457040
$641$	−22.6525	−0.894719	−0.447360	−	0.894354i	$-0.647636\pi$
$641$	−22.6525	−0.894719	−0.447360	+	0.894354i	$0.647636\pi$
$642$	16.0902	0.635028
$643$	−16.9230	−0.667377	−0.333689	−	0.942683i	$-0.608293\pi$
$643$	−16.9230	−0.667377	−0.333689	+	0.942683i	$0.608293\pi$
$644$	−8.09017	−0.318797
$645$	−12.4721	−0.491090
$646$	−0.437694	−0.0172208
$647$	14.3607	0.564577	0.282288	−	0.959330i	$-0.408907\pi$
$647$	14.3607	0.564577	0.282288	+	0.959330i	$0.408907\pi$
$648$	3.00000	0.117851
$649$	0	0
$650$	−31.8885	−1.25077
$651$	−8.32624	−0.326331
$652$	−21.4164	−0.838731
$653$	9.88854	0.386969	0.193484	−	0.981103i	$-0.438021\pi$
$653$	9.88854	0.386969	0.193484	+	0.981103i	$0.438021\pi$
$654$	−9.56231	−0.373916
$655$	60.5410	2.36553
$656$	4.14590	0.161870
$657$	−0.763932	−0.0298038
$658$	−2.00000	−0.0779681
$659$	−5.96556	−0.232385	−0.116193	−	0.993227i	$-0.537069\pi$
$659$	−5.96556	−0.232385	−0.116193	+	0.993227i	$0.537069\pi$
$660$	0	0
$661$	21.7082	0.844351	0.422176	−	0.906514i	$-0.361267\pi$
$661$	21.7082	0.844351	0.422176	+	0.906514i	$0.361267\pi$
$662$	14.3607	0.558144
$663$	−3.70820	−0.144015
$664$	−44.8328	−1.73985
$665$	1.47214	0.0570870
$666$	0.909830	0.0352552
$667$	−16.1803	−0.626505
$668$	14.1803	0.548654
$669$	3.79837	0.146854
$670$	−30.8328	−1.19118
$671$	0	0
$672$	5.00000	0.192879
$673$	0.111456	0.00429632	0.00214816	−	0.999998i	$-0.499316\pi$
$673$	0.111456	0.00429632	0.00214816	+	0.999998i	$0.499316\pi$
$674$	33.8541	1.30401
$675$	−9.85410	−0.379285
$676$	2.52786	0.0972255
$677$	−11.8885	−0.456914	−0.228457	−	0.973554i	$-0.573368\pi$
$677$	−11.8885	−0.456914	−0.228457	+	0.973554i	$0.573368\pi$
$678$	5.23607	0.201090
$679$	−12.4721	−0.478637
$680$	13.2492	0.508085
$681$	5.41641	0.207557
$682$	0	0
$683$	−23.9230	−0.915388	−0.457694	−	0.889110i	$-0.651324\pi$
$683$	−23.9230	−0.915388	−0.457694	+	0.889110i	$0.651324\pi$
$684$	−0.381966	−0.0146048
$685$	43.3050	1.65460
$686$	−1.00000	−0.0381802
$687$	−16.7639	−0.639584
$688$	−3.23607	−0.123374
$689$	−32.9443	−1.25508
$690$	31.1803	1.18702
$691$	−24.9230	−0.948115	−0.474058	−	0.880494i	$-0.657211\pi$
$691$	−24.9230	−0.948115	−0.474058	+	0.880494i	$0.657211\pi$
$692$	−13.1459	−0.499732
$693$	0	0
$694$	14.6180	0.554893
$695$	−76.3050	−2.89441
$696$	6.00000	0.227429
$697$	−4.75078	−0.179948
$698$	−27.2361	−1.03090
$699$	−7.70820	−0.291551
$700$	−9.85410	−0.372450
$701$	−34.0689	−1.28676	−0.643382	−	0.765545i	$-0.722469\pi$
$701$	−34.0689	−1.28676	−0.643382	+	0.765545i	$0.722469\pi$
$702$	3.23607	0.122138
$703$	−0.347524	−0.0131071
$704$	0	0
$705$	−7.70820	−0.290308
$706$	−3.52786	−0.132773
$707$	9.09017	0.341871
$708$	11.2361	0.422277
$709$	40.6869	1.52803	0.764015	−	0.645199i	$-0.223226\pi$
$709$	40.6869	1.52803	0.764015	+	0.645199i	$0.223226\pi$
$710$	34.4721	1.29372
$711$	−14.0000	−0.525041
$712$	−30.2705	−1.13444
$713$	67.3607	2.52268
$714$	1.14590	0.0428842
$715$	0	0
$716$	−10.6180	−0.396815
$717$	−18.5623	−0.693222
$718$	22.0344	0.822318
$719$	45.1246	1.68286	0.841432	−	0.540363i	$-0.181713\pi$
$719$	45.1246	1.68286	0.841432	+	0.540363i	$0.181713\pi$
$720$	−3.85410	−0.143634
$721$	5.32624	0.198359
$722$	18.8541	0.701677
$723$	12.9443	0.481403
$724$	1.05573	0.0392358
$725$	−19.7082	−0.731944
$726$	0	0
$727$	−16.7426	−0.620950	−0.310475	−	0.950581i	$-0.600488\pi$
$727$	−16.7426	−0.620950	−0.310475	+	0.950581i	$0.600488\pi$
$728$	9.70820	0.359810
$729$	1.00000	0.0370370
$730$	2.94427	0.108972
$731$	3.70820	0.137153
$732$	−8.94427	−0.330590
$733$	−9.12461	−0.337025	−0.168513	−	0.985699i	$-0.553896\pi$
$733$	−9.12461	−0.337025	−0.168513	+	0.985699i	$0.553896\pi$
$734$	17.2705	0.637466
$735$	−3.85410	−0.142161
$736$	−40.4508	−1.49104
$737$	0	0
$738$	4.14590	0.152613
$739$	−27.0132	−0.993695	−0.496847	−	0.867838i	$-0.665509\pi$
$739$	−27.0132	−0.993695	−0.496847	+	0.867838i	$0.665509\pi$
$740$	3.50658	0.128904
$741$	−1.23607	−0.0454081
$742$	10.1803	0.373732
$743$	1.67376	0.0614044	0.0307022	−	0.999529i	$-0.490226\pi$
$743$	1.67376	0.0614044	0.0307022	+	0.999529i	$0.490226\pi$
$744$	−24.9787	−0.915764
$745$	−77.0820	−2.82407
$746$	7.67376	0.280956
$747$	−14.9443	−0.546782
$748$	0	0
$749$	16.0902	0.587922
$750$	18.7082	0.683127
$751$	−1.52786	−0.0557526	−0.0278763	−	0.999611i	$-0.508874\pi$
$751$	−1.52786	−0.0557526	−0.0278763	+	0.999611i	$0.508874\pi$
$752$	−2.00000	−0.0729325
$753$	−1.81966	−0.0663121
$754$	6.47214	0.235701
$755$	−7.70820	−0.280530
$756$	1.00000	0.0363696
$757$	−15.3262	−0.557042	−0.278521	−	0.960430i	$-0.589844\pi$
$757$	−15.3262	−0.557042	−0.278521	+	0.960430i	$0.589844\pi$
$758$	6.47214	0.235079
$759$	0	0
$760$	4.41641	0.160200
$761$	−25.7771	−0.934419	−0.467209	−	0.884147i	$-0.654741\pi$
$761$	−25.7771	−0.934419	−0.467209	+	0.884147i	$0.654741\pi$
$762$	1.23607	0.0447780
$763$	−9.56231	−0.346179
$764$	−15.2705	−0.552468
$765$	4.41641	0.159676
$766$	30.9443	1.11806
$767$	36.3607	1.31291
$768$	17.0000	0.613435
$769$	41.4164	1.49351	0.746757	−	0.665097i	$-0.231610\pi$
$769$	41.4164	1.49351	0.746757	+	0.665097i	$0.231610\pi$
$770$	0	0
$771$	−0.381966	−0.0137562
$772$	−20.6180	−0.742059
$773$	−21.0557	−0.757322	−0.378661	−	0.925535i	$-0.623615\pi$
$773$	−21.0557	−0.757322	−0.378661	+	0.925535i	$0.623615\pi$
$774$	−3.23607	−0.116318
$775$	82.0476	2.94724
$776$	−37.4164	−1.34317
$777$	0.909830	0.0326400
$778$	0.180340	0.00646550
$779$	−1.58359	−0.0567381
$780$	12.4721	0.446574
$781$	0	0
$782$	−9.27051	−0.331513
$783$	2.00000	0.0714742
$784$	−1.00000	−0.0357143
$785$	−14.2918	−0.510096
$786$	15.7082	0.560293
$787$	−21.2705	−0.758212	−0.379106	−	0.925353i	$-0.623768\pi$
$787$	−21.2705	−0.758212	−0.379106	+	0.925353i	$0.623768\pi$
$788$	−4.00000	−0.142494
$789$	−22.5623	−0.803239
$790$	53.9574	1.91972
$791$	5.23607	0.186173
$792$	0	0
$793$	−28.9443	−1.02784
$794$	16.6525	0.590974
$795$	39.2361	1.39156
$796$	0.381966	0.0135384
$797$	−23.2705	−0.824284	−0.412142	−	0.911120i	$-0.635219\pi$
$797$	−23.2705	−0.824284	−0.412142	+	0.911120i	$0.635219\pi$
$798$	0.381966	0.0135215
$799$	2.29180	0.0810779
$800$	−49.2705	−1.74198
$801$	−10.0902	−0.356519
$802$	−9.52786	−0.336441
$803$	0	0
$804$	8.00000	0.282138
$805$	31.1803	1.09896
$806$	−26.9443	−0.949071
$807$	7.88854	0.277690
$808$	27.2705	0.959373
$809$	2.65248	0.0932561	0.0466280	−	0.998912i	$-0.485152\pi$
$809$	2.65248	0.0932561	0.0466280	+	0.998912i	$0.485152\pi$
$810$	−3.85410	−0.135419
$811$	28.3607	0.995878	0.497939	−	0.867212i	$-0.334090\pi$
$811$	28.3607	0.995878	0.497939	+	0.867212i	$0.334090\pi$
$812$	2.00000	0.0701862
$813$	−12.9098	−0.452768
$814$	0	0
$815$	82.5410	2.89129
$816$	1.14590	0.0401145
$817$	1.23607	0.0432445
$818$	−33.2361	−1.16207
$819$	3.23607	0.113077
$820$	15.9787	0.558001
$821$	−14.3607	−0.501191	−0.250596	−	0.968092i	$-0.580626\pi$
$821$	−14.3607	−0.501191	−0.250596	+	0.968092i	$0.580626\pi$
$822$	11.2361	0.391903
$823$	15.5279	0.541267	0.270634	−	0.962682i	$-0.412767\pi$
$823$	15.5279	0.541267	0.270634	+	0.962682i	$0.412767\pi$
$824$	15.9787	0.556645
$825$	0	0
$826$	−11.2361	−0.390953
$827$	11.3262	0.393852	0.196926	−	0.980418i	$-0.436904\pi$
$827$	11.3262	0.393852	0.196926	+	0.980418i	$0.436904\pi$
$828$	−8.09017	−0.281153
$829$	11.0557	0.383981	0.191991	−	0.981397i	$-0.438506\pi$
$829$	11.0557	0.383981	0.191991	+	0.981397i	$0.438506\pi$
$830$	57.5967	1.99921
$831$	30.5623	1.06019
$832$	22.6525	0.785333
$833$	1.14590	0.0397030
$834$	−19.7984	−0.685562
$835$	−54.6525	−1.89133
$836$	0	0
$837$	−8.32624	−0.287797
$838$	−19.2361	−0.664499
$839$	6.58359	0.227291	0.113645	−	0.993521i	$-0.463747\pi$
$839$	6.58359	0.227291	0.113645	+	0.993521i	$0.463747\pi$
$840$	−11.5623	−0.398937
$841$	−25.0000	−0.862069
$842$	−11.3262	−0.390328
$843$	−18.9443	−0.652475
$844$	2.00000	0.0688428
$845$	−9.74265	−0.335157
$846$	−2.00000	−0.0687614
$847$	0	0
$848$	10.1803	0.349594
$849$	−33.5623	−1.15186
$850$	−11.2918	−0.387305
$851$	−7.36068	−0.252321
$852$	−8.94427	−0.306426
$853$	−2.29180	−0.0784696	−0.0392348	−	0.999230i	$-0.512492\pi$
$853$	−2.29180	−0.0784696	−0.0392348	+	0.999230i	$0.512492\pi$
$854$	8.94427	0.306067
$855$	1.47214	0.0503460
$856$	48.2705	1.64985
$857$	−1.05573	−0.0360630	−0.0180315	−	0.999837i	$-0.505740\pi$
$857$	−1.05573	−0.0360630	−0.0180315	+	0.999837i	$0.505740\pi$
$858$	0	0
$859$	29.8885	1.01978	0.509892	−	0.860238i	$-0.329685\pi$
$859$	29.8885	1.01978	0.509892	+	0.860238i	$0.329685\pi$
$860$	−12.4721	−0.425296
$861$	4.14590	0.141292
$862$	−9.09017	−0.309612
$863$	−22.6869	−0.772272	−0.386136	−	0.922442i	$-0.626190\pi$
$863$	−22.6869	−0.772272	−0.386136	+	0.922442i	$0.626190\pi$
$864$	5.00000	0.170103
$865$	50.6656	1.72268
$866$	12.7639	0.433736
$867$	15.6869	0.532756
$868$	−8.32624	−0.282611
$869$	0	0
$870$	−7.70820	−0.261333
$871$	25.8885	0.877200
$872$	−28.6869	−0.971462
$873$	−12.4721	−0.422118
$874$	−3.09017	−0.104527
$875$	18.7082	0.632453
$876$	−0.763932	−0.0258109
$877$	−1.63932	−0.0553559	−0.0276780	−	0.999617i	$-0.508811\pi$
$877$	−1.63932	−0.0553559	−0.0276780	+	0.999617i	$0.508811\pi$
$878$	−2.79837	−0.0944405
$879$	4.79837	0.161845
$880$	0	0
$881$	22.4508	0.756388	0.378194	−	0.925726i	$-0.376545\pi$
$881$	22.4508	0.756388	0.378194	+	0.925726i	$0.376545\pi$
$882$	−1.00000	−0.0336718
$883$	−5.70820	−0.192096	−0.0960482	−	0.995377i	$-0.530620\pi$
$883$	−5.70820	−0.192096	−0.0960482	+	0.995377i	$0.530620\pi$
$884$	−3.70820	−0.124720
$885$	−43.3050	−1.45568
$886$	−16.0902	−0.540560
$887$	20.5410	0.689700	0.344850	−	0.938658i	$-0.387930\pi$
$887$	20.5410	0.689700	0.344850	+	0.938658i	$0.387930\pi$
$888$	2.72949	0.0915957
$889$	1.23607	0.0414564
$890$	38.8885	1.30355
$891$	0	0
$892$	3.79837	0.127179
$893$	0.763932	0.0255640
$894$	−20.0000	−0.668900
$895$	40.9230	1.36790
$896$	3.00000	0.100223
$897$	−26.1803	−0.874136
$898$	−6.11146	−0.203942
$899$	−16.6525	−0.555391
$900$	−9.85410	−0.328470
$901$	−11.6656	−0.388639
$902$	0	0
$903$	−3.23607	−0.107690
$904$	15.7082	0.522447
$905$	−4.06888	−0.135254
$906$	−2.00000	−0.0664455
$907$	−42.7639	−1.41995	−0.709977	−	0.704225i	$-0.751294\pi$
$907$	−42.7639	−1.41995	−0.709977	+	0.704225i	$0.751294\pi$
$908$	5.41641	0.179750
$909$	9.09017	0.301502
$910$	−12.4721	−0.413447
$911$	−28.9443	−0.958967	−0.479483	−	0.877551i	$-0.659176\pi$
$911$	−28.9443	−0.958967	−0.479483	+	0.877551i	$0.659176\pi$
$912$	0.381966	0.0126482
$913$	0	0
$914$	−3.52786	−0.116691
$915$	34.4721	1.13961
$916$	−16.7639	−0.553896
$917$	15.7082	0.518731
$918$	1.14590	0.0378203
$919$	−19.4164	−0.640488	−0.320244	−	0.947335i	$-0.603765\pi$
$919$	−19.4164	−0.640488	−0.320244	+	0.947335i	$0.603765\pi$
$920$	93.5410	3.08396
$921$	−9.27051	−0.305474
$922$	−38.3607	−1.26334
$923$	−28.9443	−0.952712
$924$	0	0
$925$	−8.96556	−0.294786
$926$	15.4164	0.506615
$927$	5.32624	0.174937
$928$	10.0000	0.328266
$929$	−4.20163	−0.137851	−0.0689254	−	0.997622i	$-0.521957\pi$
$929$	−4.20163	−0.137851	−0.0689254	+	0.997622i	$0.521957\pi$
$930$	32.0902	1.05228
$931$	0.381966	0.0125184
$932$	−7.70820	−0.252491
$933$	5.23607	0.171421
$934$	−14.7639	−0.483091
$935$	0	0
$936$	9.70820	0.317323
$937$	−1.70820	−0.0558046	−0.0279023	−	0.999611i	$-0.508883\pi$
$937$	−1.70820	−0.0558046	−0.0279023	+	0.999611i	$0.508883\pi$
$938$	−8.00000	−0.261209
$939$	32.1803	1.05017
$940$	−7.70820	−0.251414
$941$	−5.14590	−0.167751	−0.0838757	−	0.996476i	$-0.526730\pi$
$941$	−5.14590	−0.167751	−0.0838757	+	0.996476i	$0.526730\pi$
$942$	−3.70820	−0.120820
$943$	−33.5410	−1.09225
$944$	−11.2361	−0.365703
$945$	−3.85410	−0.125374
$946$	0	0
$947$	−43.5623	−1.41558	−0.707792	−	0.706421i	$-0.750309\pi$
$947$	−43.5623	−1.41558	−0.707792	+	0.706421i	$0.750309\pi$
$948$	−14.0000	−0.454699
$949$	−2.47214	−0.0802489
$950$	−3.76393	−0.122118
$951$	−21.5967	−0.700323
$952$	3.43769	0.111416
$953$	−48.8328	−1.58185	−0.790925	−	0.611913i	$-0.790400\pi$
$953$	−48.8328	−1.58185	−0.790925	+	0.611913i	$0.790400\pi$
$954$	10.1803	0.329601
$955$	58.8541	1.90447
$956$	−18.5623	−0.600348
$957$	0	0
$958$	28.9443	0.935147
$959$	11.2361	0.362832
$960$	−26.9787	−0.870734
$961$	38.3262	1.23633
$962$	2.94427	0.0949271
$963$	16.0902	0.518498
$964$	12.9443	0.416907
$965$	79.4640	2.55804
$966$	8.09017	0.260297
$967$	−13.3050	−0.427858	−0.213929	−	0.976849i	$-0.568626\pi$
$967$	−13.3050	−0.427858	−0.213929	+	0.976849i	$0.568626\pi$
$968$	0	0
$969$	−0.437694	−0.0140608
$970$	48.0689	1.54340
$971$	−16.0689	−0.515675	−0.257838	−	0.966188i	$-0.583010\pi$
$971$	−16.0689	−0.515675	−0.257838	+	0.966188i	$0.583010\pi$
$972$	1.00000	0.0320750
$973$	−19.7984	−0.634707
$974$	34.7639	1.11391
$975$	−31.8885	−1.02125
$976$	8.94427	0.286299
$977$	−53.4164	−1.70894	−0.854471	−	0.519499i	$-0.826119\pi$
$977$	−53.4164	−1.70894	−0.854471	+	0.519499i	$0.826119\pi$
$978$	21.4164	0.684821
$979$	0	0
$980$	−3.85410	−0.123115
$981$	−9.56231	−0.305301
$982$	−15.3262	−0.489080
$983$	39.5279	1.26074	0.630372	−	0.776294i	$-0.282903\pi$
$983$	39.5279	1.26074	0.630372	+	0.776294i	$0.282903\pi$
$984$	12.4377	0.396499
$985$	15.4164	0.491208
$986$	2.29180	0.0729857
$987$	−2.00000	−0.0636607
$988$	−1.23607	−0.0393246
$989$	26.1803	0.832486
$990$	0	0
$991$	−12.6525	−0.401919	−0.200960	−	0.979600i	$-0.564406\pi$
$991$	−12.6525	−0.401919	−0.200960	+	0.979600i	$0.564406\pi$
$992$	−41.6312	−1.32179
$993$	14.3607	0.455722
$994$	8.94427	0.283695
$995$	−1.47214	−0.0466698
$996$	−14.9443	−0.473527
$997$	14.5410	0.460519	0.230259	−	0.973129i	$-0.426043\pi$
$997$	14.5410	0.460519	0.230259	+	0.973129i	$0.426043\pi$
$998$	−3.81966	−0.120909
$999$	0.909830	0.0287857

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2541.2.a.n.1.2		2
3.2	odd	2		7623.2.a.bu.1.1		2
11.3	even	5		231.2.j.c.64.1	✓	4
11.4	even	5		231.2.j.c.148.1	yes	4
11.10	odd	2		2541.2.a.bd.1.2		2
33.14	odd	10		693.2.m.c.64.1		4
33.26	odd	10		693.2.m.c.379.1		4
33.32	even	2		7623.2.a.w.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.j.c.64.1	✓	4	11.3	even	5
231.2.j.c.148.1	yes	4	11.4	even	5
693.2.m.c.64.1		4	33.14	odd	10
693.2.m.c.379.1		4	33.26	odd	10
2541.2.a.n.1.2		2	1.1	even	1	trivial
2541.2.a.bd.1.2		2	11.10	odd	2
7623.2.a.w.1.1		2	33.32	even	2
7623.2.a.bu.1.1		2	3.2	odd	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:	\( N \)	\(=\)	\( 2541 = 3 \cdot 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2541.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} -1.00000 q^{4} +3.85410 q^{5} +1.00000 q^{6} +1.00000 q^{7} +3.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} -1.00000 q^{4} +3.85410 q^{5} +1.00000 q^{6} +1.00000 q^{7} +3.00000 q^{8} +1.00000 q^{9} -3.85410 q^{10} +1.00000 q^{12} +3.23607 q^{13} -1.00000 q^{14} -3.85410 q^{15} -1.00000 q^{16} +1.14590 q^{17} -1.00000 q^{18} +0.381966 q^{19} -3.85410 q^{20} -1.00000 q^{21} +8.09017 q^{23} -3.00000 q^{24} +9.85410 q^{25} -3.23607 q^{26} -1.00000 q^{27} -1.00000 q^{28} -2.00000 q^{29} +3.85410 q^{30} +8.32624 q^{31} -5.00000 q^{32} -1.14590 q^{34} +3.85410 q^{35} -1.00000 q^{36} -0.909830 q^{37} -0.381966 q^{38} -3.23607 q^{39} +11.5623 q^{40} -4.14590 q^{41} +1.00000 q^{42} +3.23607 q^{43} +3.85410 q^{45} -8.09017 q^{46} +2.00000 q^{47} +1.00000 q^{48} +1.00000 q^{49} -9.85410 q^{50} -1.14590 q^{51} -3.23607 q^{52} -10.1803 q^{53} +1.00000 q^{54} +3.00000 q^{56} -0.381966 q^{57} +2.00000 q^{58} +11.2361 q^{59} +3.85410 q^{60} -8.94427 q^{61} -8.32624 q^{62} +1.00000 q^{63} +7.00000 q^{64} +12.4721 q^{65} +8.00000 q^{67} -1.14590 q^{68} -8.09017 q^{69} -3.85410 q^{70} -8.94427 q^{71} +3.00000 q^{72} -0.763932 q^{73} +0.909830 q^{74} -9.85410 q^{75} -0.381966 q^{76} +3.23607 q^{78} -14.0000 q^{79} -3.85410 q^{80} +1.00000 q^{81} +4.14590 q^{82} -14.9443 q^{83} +1.00000 q^{84} +4.41641 q^{85} -3.23607 q^{86} +2.00000 q^{87} -10.0902 q^{89} -3.85410 q^{90} +3.23607 q^{91} -8.09017 q^{92} -8.32624 q^{93} -2.00000 q^{94} +1.47214 q^{95} +5.00000 q^{96} -12.4721 q^{97} -1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + q^{5} + 2 q^{6} + 2 q^{7} + 6 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + q^5 + 2 * q^6 + 2 * q^7 + 6 * q^8 + 2 * q^9	\( 2 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + q^{5} + 2 q^{6} + 2 q^{7} + 6 q^{8} + 2 q^{9} - q^{10} + 2 q^{12} + 2 q^{13} - 2 q^{14} - q^{15} - 2 q^{16} + 9 q^{17} - 2 q^{18} + 3 q^{19} - q^{20} - 2 q^{21} + 5 q^{23} - 6 q^{24} + 13 q^{25} - 2 q^{26} - 2 q^{27} - 2 q^{28} - 4 q^{29} + q^{30} + q^{31} - 10 q^{32} - 9 q^{34} + q^{35} - 2 q^{36} - 13 q^{37} - 3 q^{38} - 2 q^{39} + 3 q^{40} - 15 q^{41} + 2 q^{42} + 2 q^{43} + q^{45} - 5 q^{46} + 4 q^{47} + 2 q^{48} + 2 q^{49} - 13 q^{50} - 9 q^{51} - 2 q^{52} + 2 q^{53} + 2 q^{54} + 6 q^{56} - 3 q^{57} + 4 q^{58} + 18 q^{59} + q^{60} - q^{62} + 2 q^{63} + 14 q^{64} + 16 q^{65} + 16 q^{67} - 9 q^{68} - 5 q^{69} - q^{70} + 6 q^{72} - 6 q^{73} + 13 q^{74} - 13 q^{75} - 3 q^{76} + 2 q^{78} - 28 q^{79} - q^{80} + 2 q^{81} + 15 q^{82} - 12 q^{83} + 2 q^{84} - 18 q^{85} - 2 q^{86} + 4 q^{87} - 9 q^{89} - q^{90} + 2 q^{91} - 5 q^{92} - q^{93} - 4 q^{94} - 6 q^{95} + 10 q^{96} - 16 q^{97} - 2 q^{98}+O(q^{100}) \) 2 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + q^5 + 2 * q^6 + 2 * q^7 + 6 * q^8 + 2 * q^9 - q^10 + 2 * q^12 + 2 * q^13 - 2 * q^14 - q^15 - 2 * q^16 + 9 * q^17 - 2 * q^18 + 3 * q^19 - q^20 - 2 * q^21 + 5 * q^23 - 6 * q^24 + 13 * q^25 - 2 * q^26 - 2 * q^27 - 2 * q^28 - 4 * q^29 + q^30 + q^31 - 10 * q^32 - 9 * q^34 + q^35 - 2 * q^36 - 13 * q^37 - 3 * q^38 - 2 * q^39 + 3 * q^40 - 15 * q^41 + 2 * q^42 + 2 * q^43 + q^45 - 5 * q^46 + 4 * q^47 + 2 * q^48 + 2 * q^49 - 13 * q^50 - 9 * q^51 - 2 * q^52 + 2 * q^53 + 2 * q^54 + 6 * q^56 - 3 * q^57 + 4 * q^58 + 18 * q^59 + q^60 - q^62 + 2 * q^63 + 14 * q^64 + 16 * q^65 + 16 * q^67 - 9 * q^68 - 5 * q^69 - q^70 + 6 * q^72 - 6 * q^73 + 13 * q^74 - 13 * q^75 - 3 * q^76 + 2 * q^78 - 28 * q^79 - q^80 + 2 * q^81 + 15 * q^82 - 12 * q^83 + 2 * q^84 - 18 * q^85 - 2 * q^86 + 4 * q^87 - 9 * q^89 - q^90 + 2 * q^91 - 5 * q^92 - q^93 - 4 * q^94 - 6 * q^95 + 10 * q^96 - 16 * q^97 - 2 * q^98

Introduction

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