LMFDB - Embedded newform 2541.2.a.bk.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:	$1$
Dimension:	$4$
Coefficient field:	4.4.7488.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 4x^{2} + 2x + 1 $ x^4 - 2x^3 - 4x^2 + 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			$0.698857$ 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)

$f(q)$	$=$	$q-2.43091 q^{2} -1.00000 q^{3} +3.90931 q^{4} +3.43091 q^{5} +2.43091 q^{6} -1.00000 q^{7} -4.64136 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.43091 q^{2} -1.00000 q^{3} +3.90931 q^{4} +3.43091 q^{5} +2.43091 q^{6} -1.00000 q^{7} -4.64136 q^{8} +1.00000 q^{9} -8.34022 q^{10} -3.90931 q^{12} +6.11977 q^{13} +2.43091 q^{14} -3.43091 q^{15} +3.46410 q^{16} -3.21046 q^{17} -2.43091 q^{18} -6.34022 q^{19} +13.4125 q^{20} +1.00000 q^{21} -0.210456 q^{23} +4.64136 q^{24} +6.77113 q^{25} -14.8766 q^{26} -1.00000 q^{27} -3.90931 q^{28} -2.74635 q^{29} +8.34022 q^{30} +4.64136 q^{31} +0.861816 q^{32} +7.80432 q^{34} -3.43091 q^{35} +3.90931 q^{36} -9.37341 q^{37} +15.4125 q^{38} -6.11977 q^{39} -15.9241 q^{40} -11.9484 q^{41} -2.43091 q^{42} -7.12976 q^{43} +3.43091 q^{45} +0.511599 q^{46} -5.91520 q^{47} -3.46410 q^{48} +1.00000 q^{49} -16.4600 q^{50} +3.21046 q^{51} +23.9241 q^{52} -6.35452 q^{53} +2.43091 q^{54} +4.64136 q^{56} +6.34022 q^{57} +6.67613 q^{58} -11.8232 q^{59} -13.4125 q^{60} -9.20204 q^{61} -11.2827 q^{62} -1.00000 q^{63} -9.02320 q^{64} +20.9964 q^{65} -3.89042 q^{67} -12.5507 q^{68} +0.210456 q^{69} +8.34022 q^{70} -5.19458 q^{71} -4.64136 q^{72} +13.1747 q^{73} +22.7859 q^{74} -6.77113 q^{75} -24.7859 q^{76} +14.8766 q^{78} +4.33022 q^{79} +11.8850 q^{80} +1.00000 q^{81} +29.0454 q^{82} +0.737935 q^{83} +3.90931 q^{84} -11.0148 q^{85} +17.3318 q^{86} +2.74635 q^{87} -9.34453 q^{89} -8.34022 q^{90} -6.11977 q^{91} -0.822738 q^{92} -4.64136 q^{93} +14.3793 q^{94} -21.7527 q^{95} -0.861816 q^{96} +12.0534 q^{97} -2.43091 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 4 q^{3} + 4 q^{4} + 6 q^{5} + 2 q^{6} - 4 q^{7} + 4 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 - 4 * q^3 + 4 * q^4 + 6 * q^5 + 2 * q^6 - 4 * q^7 + 4 * q^9	$ 4 q - 2 q^{2} - 4 q^{3} + 4 q^{4} + 6 q^{5} + 2 q^{6} - 4 q^{7} + 4 q^{9} - 14 q^{10} - 4 q^{12} + 2 q^{13} + 2 q^{14} - 6 q^{15} - 2 q^{17} - 2 q^{18} - 6 q^{19} + 8 q^{20} + 4 q^{21} + 10 q^{23} - 4 q^{27} - 4 q^{28} - 14 q^{29} + 14 q^{30} - 12 q^{32} - 2 q^{34} - 6 q^{35} + 4 q^{36} - 12 q^{37} + 16 q^{38} - 2 q^{39} - 8 q^{40} - 16 q^{41} - 2 q^{42} - 20 q^{43} + 6 q^{45} - 8 q^{46} + 2 q^{47} + 4 q^{49} - 24 q^{50} + 2 q^{51} + 40 q^{52} - 16 q^{53} + 2 q^{54} + 6 q^{57} - 8 q^{58} + 2 q^{59} - 8 q^{60} - 2 q^{61} - 8 q^{62} - 4 q^{63} - 16 q^{64} + 2 q^{65} - 20 q^{67} - 20 q^{68} - 10 q^{69} + 14 q^{70} - 10 q^{71} + 10 q^{73} + 20 q^{74} - 28 q^{76} - 16 q^{79} + 12 q^{80} + 4 q^{81} + 28 q^{82} - 18 q^{83} + 4 q^{84} + 26 q^{86} + 14 q^{87} - 14 q^{89} - 14 q^{90} - 2 q^{91} - 8 q^{92} + 18 q^{94} - 22 q^{95} + 12 q^{96} + 38 q^{97} - 2 q^{98}+O(q^{100}) $ 4 * q - 2 * q^2 - 4 * q^3 + 4 * q^4 + 6 * q^5 + 2 * q^6 - 4 * q^7 + 4 * q^9 - 14 * q^10 - 4 * q^12 + 2 * q^13 + 2 * q^14 - 6 * q^15 - 2 * q^17 - 2 * q^18 - 6 * q^19 + 8 * q^20 + 4 * q^21 + 10 * q^23 - 4 * q^27 - 4 * q^28 - 14 * q^29 + 14 * q^30 - 12 * q^32 - 2 * q^34 - 6 * q^35 + 4 * q^36 - 12 * q^37 + 16 * q^38 - 2 * q^39 - 8 * q^40 - 16 * q^41 - 2 * q^42 - 20 * q^43 + 6 * q^45 - 8 * q^46 + 2 * q^47 + 4 * q^49 - 24 * q^50 + 2 * q^51 + 40 * q^52 - 16 * q^53 + 2 * q^54 + 6 * q^57 - 8 * q^58 + 2 * q^59 - 8 * q^60 - 2 * q^61 - 8 * q^62 - 4 * q^63 - 16 * q^64 + 2 * q^65 - 20 * q^67 - 20 * q^68 - 10 * q^69 + 14 * q^70 - 10 * q^71 + 10 * q^73 + 20 * q^74 - 28 * q^76 - 16 * q^79 + 12 * q^80 + 4 * q^81 + 28 * q^82 - 18 * q^83 + 4 * q^84 + 26 * q^86 + 14 * q^87 - 14 * q^89 - 14 * q^90 - 2 * q^91 - 8 * q^92 + 18 * q^94 - 22 * q^95 + 12 * q^96 + 38 * 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 $

$2$	−2.43091	−1.71891	−0.859456	−	0.511210i	$-0.829197\pi$
$2$	−2.43091	−1.71891	−0.859456	+	0.511210i	$0.829197\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	3.90931	1.95466
$5$	3.43091	1.53435	0.767174	−	0.641439i	$-0.221662\pi$
$5$	3.43091	1.53435	0.767174	+	0.641439i	$0.221662\pi$
$6$	2.43091	0.992414
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−4.64136	−1.64097
$9$	1.00000	0.333333
$10$	−8.34022	−2.63741
$11$	0	0
$11$	0	0
$12$	−3.90931	−1.12852
$13$	6.11977	1.69732	0.848659	−	0.528940i	$-0.177410\pi$
$13$	6.11977	1.69732	0.848659	+	0.528940i	$0.177410\pi$
$14$	2.43091	0.649687
$15$	−3.43091	−0.885857
$16$	3.46410	0.866025
$17$	−3.21046	−0.778650	−0.389325	−	0.921100i	$-0.627292\pi$
$17$	−3.21046	−0.778650	−0.389325	+	0.921100i	$0.627292\pi$
$18$	−2.43091	−0.572970
$19$	−6.34022	−1.45455	−0.727273	−	0.686348i	$-0.759213\pi$
$19$	−6.34022	−1.45455	−0.727273	+	0.686348i	$0.759213\pi$
$20$	13.4125	2.99912
$21$	1.00000	0.218218
$22$	0	0
$23$	−0.210456	−0.0438831	−0.0219415	−	0.999759i	$-0.506985\pi$
$23$	−0.210456	−0.0438831	−0.0219415	+	0.999759i	$0.506985\pi$
$24$	4.64136	0.947414
$25$	6.77113	1.35423
$26$	−14.8766	−2.91754
$27$	−1.00000	−0.192450
$28$	−3.90931	−0.738791
$29$	−2.74635	−0.509985	−0.254993	−	0.966943i	$-0.582073\pi$
$29$	−2.74635	−0.509985	−0.254993	+	0.966943i	$0.582073\pi$
$30$	8.34022	1.52271
$31$	4.64136	0.833614	0.416807	−	0.908995i	$-0.363149\pi$
$31$	4.64136	0.833614	0.416807	+	0.908995i	$0.363149\pi$
$32$	0.861816	0.152349
$33$	0	0
$34$	7.80432	1.33843
$35$	−3.43091	−0.579929
$36$	3.90931	0.651552
$37$	−9.37341	−1.54098	−0.770490	−	0.637452i	$-0.779988\pi$
$37$	−9.37341	−1.54098	−0.770490	+	0.637452i	$0.779988\pi$
$38$	15.4125	2.50024
$39$	−6.11977	−0.979947
$40$	−15.9241	−2.51782
$41$	−11.9484	−1.86603	−0.933013	−	0.359844i	$-0.882830\pi$
$41$	−11.9484	−1.86603	−0.933013	+	0.359844i	$0.882830\pi$
$42$	−2.43091	−0.375097
$43$	−7.12976	−1.08728	−0.543639	−	0.839319i	$-0.682954\pi$
$43$	−7.12976	−1.08728	−0.543639	+	0.839319i	$0.682954\pi$
$44$	0	0
$45$	3.43091	0.511450
$46$	0.511599	0.0754311
$47$	−5.91520	−0.862820	−0.431410	−	0.902156i	$-0.641984\pi$
$47$	−5.91520	−0.862820	−0.431410	+	0.902156i	$0.641984\pi$
$48$	−3.46410	−0.500000
$49$	1.00000	0.142857
$50$	−16.4600	−2.32779
$51$	3.21046	0.449554
$52$	23.9241	3.31767
$53$	−6.35452	−0.872861	−0.436431	−	0.899738i	$-0.643758\pi$
$53$	−6.35452	−0.872861	−0.436431	+	0.899738i	$0.643758\pi$
$54$	2.43091	0.330805
$55$	0	0
$56$	4.64136	0.620228
$57$	6.34022	0.839783
$58$	6.67613	0.876619
$59$	−11.8232	−1.53925	−0.769626	−	0.638495i	$-0.779557\pi$
$59$	−11.8232	−1.53925	−0.769626	+	0.638495i	$0.779557\pi$
$60$	−13.4125	−1.73155
$61$	−9.20204	−1.17820	−0.589100	−	0.808060i	$-0.700518\pi$
$61$	−9.20204	−1.17820	−0.589100	+	0.808060i	$0.700518\pi$
$62$	−11.2827	−1.43291
$63$	−1.00000	−0.125988
$64$	−9.02320	−1.12790
$65$	20.9964	2.60428
$66$	0	0
$67$	−3.89042	−0.475291	−0.237645	−	0.971352i	$-0.576376\pi$
$67$	−3.89042	−0.475291	−0.237645	+	0.971352i	$0.576376\pi$
$68$	−12.5507	−1.52199
$69$	0.210456	0.0253359
$70$	8.34022	0.996847
$71$	−5.19458	−0.616483	−0.308241	−	0.951308i	$-0.599740\pi$
$71$	−5.19458	−0.616483	−0.308241	+	0.951308i	$0.599740\pi$
$72$	−4.64136	−0.546990
$73$	13.1747	1.54199	0.770993	−	0.636844i	$-0.219761\pi$
$73$	13.1747	1.54199	0.770993	+	0.636844i	$0.219761\pi$
$74$	22.7859	2.64881
$75$	−6.77113	−0.781863
$76$	−24.7859	−2.84314
$77$	0	0
$78$	14.8766	1.68444
$79$	4.33022	0.487188	0.243594	−	0.969877i	$-0.421674\pi$
$79$	4.33022	0.487188	0.243594	+	0.969877i	$0.421674\pi$
$80$	11.8850	1.32878
$81$	1.00000	0.111111
$82$	29.0454	3.20753
$83$	0.737935	0.0809989	0.0404994	−	0.999180i	$-0.487105\pi$
$83$	0.737935	0.0809989	0.0404994	+	0.999180i	$0.487105\pi$
$84$	3.90931	0.426541
$85$	−11.0148	−1.19472
$86$	17.3318	1.86894
$87$	2.74635	0.294440
$88$	0	0
$89$	−9.34453	−0.990518	−0.495259	−	0.868745i	$-0.664927\pi$
$89$	−9.34453	−0.990518	−0.495259	+	0.868745i	$0.664927\pi$
$90$	−8.34022	−0.879136
$91$	−6.11977	−0.641526
$92$	−0.822738	−0.0857764
$93$	−4.64136	−0.481287
$94$	14.3793	1.48311
$95$	−21.7527	−2.23178
$96$	−0.861816	−0.0879587
$97$	12.0534	1.22384	0.611918	−	0.790921i	$-0.290398\pi$
$97$	12.0534	1.22384	0.611918	+	0.790921i	$0.290398\pi$
$98$	−2.43091	−0.245559
$99$	0	0
$100$	26.4705	2.64705
$101$	1.58798	0.158010	0.0790051	−	0.996874i	$-0.474826\pi$
$101$	1.58798	0.158010	0.0790051	+	0.996874i	$0.474826\pi$
$102$	−7.80432	−0.772743
$103$	9.42249	0.928425	0.464213	−	0.885724i	$-0.346337\pi$
$103$	9.42249	0.928425	0.464213	+	0.885724i	$0.346337\pi$
$104$	−28.4041	−2.78525
$105$	3.43091	0.334822
$106$	15.4473	1.50037
$107$	−7.03319	−0.679925	−0.339962	−	0.940439i	$-0.610414\pi$
$107$	−7.03319	−0.679925	−0.339962	+	0.940439i	$0.610414\pi$
$108$	−3.90931	−0.376174
$109$	2.37040	0.227044	0.113522	−	0.993536i	$-0.463787\pi$
$109$	2.37040	0.227044	0.113522	+	0.993536i	$0.463787\pi$
$110$	0	0
$111$	9.37341	0.889685
$112$	−3.46410	−0.327327
$113$	0.409144	0.0384890	0.0192445	−	0.999815i	$-0.493874\pi$
$113$	0.409144	0.0384890	0.0192445	+	0.999815i	$0.493874\pi$
$114$	−15.4125	−1.44351
$115$	−0.722055	−0.0673320
$116$	−10.7364	−0.996846
$117$	6.11977	0.565773
$118$	28.7411	2.64584
$119$	3.21046	0.294302
$120$	15.9241	1.45366
$121$	0	0
$122$	22.3693	2.02522
$123$	11.9484	1.07735
$124$	18.1445	1.62943
$125$	6.07658	0.543506
$126$	2.43091	0.216562
$127$	19.5307	1.73307	0.866534	−	0.499118i	$-0.166343\pi$
$127$	19.5307	1.73307	0.866534	+	0.499118i	$0.166343\pi$
$128$	20.2109	1.78641
$129$	7.12976	0.627741
$130$	−51.0402	−4.47652
$131$	−19.3750	−1.69280	−0.846400	−	0.532547i	$-0.821235\pi$
$131$	−19.3750	−1.69280	−0.846400	+	0.532547i	$0.821235\pi$
$132$	0	0
$133$	6.34022	0.549767
$134$	9.45726	0.816983
$135$	−3.43091	−0.295286
$136$	14.9009	1.27774
$137$	−6.14277	−0.524812	−0.262406	−	0.964958i	$-0.584516\pi$
$137$	−6.14277	−0.524812	−0.262406	+	0.964958i	$0.584516\pi$
$138$	−0.511599	−0.0435502
$139$	−6.77065	−0.574279	−0.287140	−	0.957889i	$-0.592704\pi$
$139$	−6.77065	−0.574279	−0.287140	+	0.957889i	$0.592704\pi$
$140$	−13.4125	−1.13356
$141$	5.91520	0.498149
$142$	12.6275	1.05968
$143$	0	0
$144$	3.46410	0.288675
$145$	−9.42249	−0.782495
$146$	−32.0265	−2.65054
$147$	−1.00000	−0.0824786
$148$	−36.6436	−3.01209
$149$	17.8204	1.45990	0.729952	−	0.683498i	$-0.239542\pi$
$149$	17.8204	1.45990	0.729952	+	0.683498i	$0.239542\pi$
$150$	16.4600	1.34395
$151$	−0.610705	−0.0496985	−0.0248493	−	0.999691i	$-0.507911\pi$
$151$	−0.610705	−0.0496985	−0.0248493	+	0.999691i	$0.507911\pi$
$152$	29.4273	2.38687
$153$	−3.21046	−0.259550
$154$	0	0
$155$	15.9241	1.27905
$156$	−23.9241	−1.91546
$157$	6.82274	0.544514	0.272257	−	0.962225i	$-0.412230\pi$
$157$	6.82274	0.544514	0.272257	+	0.962225i	$0.412230\pi$
$158$	−10.5264	−0.837434
$159$	6.35452	0.503947
$160$	2.95681	0.233756
$161$	0.210456	0.0165862
$162$	−2.43091	−0.190990
$163$	−12.0738	−0.945697	−0.472848	−	0.881144i	$-0.656774\pi$
$163$	−12.0738	−0.945697	−0.472848	+	0.881144i	$0.656774\pi$
$164$	−46.7100	−3.64744
$165$	0	0
$166$	−1.79385	−0.139230
$167$	2.89932	0.224356	0.112178	−	0.993688i	$-0.464217\pi$
$167$	2.89932	0.224356	0.112178	+	0.993688i	$0.464217\pi$
$168$	−4.64136	−0.358089
$169$	24.4516	1.88089
$170$	26.7759	2.05362
$171$	−6.34022	−0.484849
$172$	−27.8725	−2.12526
$173$	14.5713	1.10784	0.553919	−	0.832570i	$-0.313132\pi$
$173$	14.5713	1.10784	0.553919	+	0.832570i	$0.313132\pi$
$174$	−6.67613	−0.506116
$175$	−6.77113	−0.511849
$176$	0	0
$177$	11.8232	0.888687
$178$	22.7157	1.70261
$179$	18.9082	1.41327	0.706633	−	0.707580i	$-0.250213\pi$
$179$	18.9082	1.41327	0.706633	+	0.707580i	$0.250213\pi$
$180$	13.4125	0.999708
$181$	15.7713	1.17227	0.586137	−	0.810212i	$-0.300648\pi$
$181$	15.7713	1.17227	0.586137	+	0.810212i	$0.300648\pi$
$182$	14.8766	1.10273
$183$	9.20204	0.680234
$184$	0.976802	0.0720108
$185$	−32.1593	−2.36440
$186$	11.2827	0.827290
$187$	0	0
$188$	−23.1244	−1.68652
$189$	1.00000	0.0727393
$190$	52.8788	3.83623
$191$	−19.5132	−1.41192	−0.705962	−	0.708250i	$-0.749485\pi$
$191$	−19.5132	−1.41192	−0.705962	+	0.708250i	$0.749485\pi$
$192$	9.02320	0.651193
$193$	22.9830	1.65435	0.827177	−	0.561942i	$-0.189945\pi$
$193$	22.9830	1.65435	0.827177	+	0.561942i	$0.189945\pi$
$194$	−29.3007	−2.10366
$195$	−20.9964	−1.50358
$196$	3.90931	0.279237
$197$	−11.3218	−0.806645	−0.403323	−	0.915058i	$-0.632145\pi$
$197$	−11.3218	−0.806645	−0.403323	+	0.915058i	$0.632145\pi$
$198$	0	0
$199$	−6.43837	−0.456404	−0.228202	−	0.973614i	$-0.573285\pi$
$199$	−6.43837	−0.456404	−0.228202	+	0.973614i	$0.573285\pi$
$200$	−31.4273	−2.22224
$201$	3.89042	0.274409
$202$	−3.86024	−0.271605
$203$	2.74635	0.192756
$204$	12.5507	0.878723
$205$	−40.9938	−2.86313
$206$	−22.9052	−1.59588
$207$	−0.210456	−0.0146277
$208$	21.1995	1.46992
$209$	0	0
$210$	−8.34022	−0.575530
$211$	−20.1287	−1.38571	−0.692857	−	0.721075i	$-0.743648\pi$
$211$	−20.1287	−1.38571	−0.692857	+	0.721075i	$0.743648\pi$
$212$	−24.8418	−1.70614
$213$	5.19458	0.355926
$214$	17.0970	1.16873
$215$	−24.4616	−1.66826
$216$	4.64136	0.315805
$217$	−4.64136	−0.315076
$218$	−5.76223	−0.390268
$219$	−13.1747	−0.890266
$220$	0	0
$221$	−19.6472	−1.32162
$222$	−22.7859	−1.52929
$223$	−20.8691	−1.39750	−0.698750	−	0.715366i	$-0.746260\pi$
$223$	−20.8691	−1.39750	−0.698750	+	0.715366i	$0.746260\pi$
$224$	−0.861816	−0.0575825
$225$	6.77113	0.451409
$226$	−0.994591	−0.0661592
$227$	−3.06892	−0.203692	−0.101846	−	0.994800i	$-0.532475\pi$
$227$	−3.06892	−0.203692	−0.101846	+	0.994800i	$0.532475\pi$
$228$	24.7859	1.64149
$229$	−8.35768	−0.552291	−0.276145	−	0.961116i	$-0.589057\pi$
$229$	−8.35768	−0.552291	−0.276145	+	0.961116i	$0.589057\pi$
$230$	1.75525	0.115738
$231$	0	0
$232$	12.7468	0.836870
$233$	5.50270	0.360494	0.180247	−	0.983621i	$-0.442310\pi$
$233$	5.50270	0.360494	0.180247	+	0.983621i	$0.442310\pi$
$234$	−14.8766	−0.972513
$235$	−20.2945	−1.32387
$236$	−46.2206	−3.00871
$237$	−4.33022	−0.281278
$238$	−7.80432	−0.505879
$239$	−2.30368	−0.149013	−0.0745063	−	0.997221i	$-0.523738\pi$
$239$	−2.30368	−0.149013	−0.0745063	+	0.997221i	$0.523738\pi$
$240$	−11.8850	−0.767174
$241$	10.3602	0.667360	0.333680	−	0.942686i	$-0.391710\pi$
$241$	10.3602	0.667360	0.333680	+	0.942686i	$0.391710\pi$
$242$	0	0
$243$	−1.00000	−0.0641500
$244$	−35.9736	−2.30298
$245$	3.43091	0.219193
$246$	−29.0454	−1.85187
$247$	−38.8007	−2.46883
$248$	−21.5423	−1.36793
$249$	−0.737935	−0.0467647
$250$	−14.7716	−0.934238
$251$	11.2627	0.710898	0.355449	−	0.934696i	$-0.384328\pi$
$251$	11.2627	0.710898	0.355449	+	0.934696i	$0.384328\pi$
$252$	−3.90931	−0.246264
$253$	0	0
$254$	−47.4773	−2.97899
$255$	11.0148	0.689772
$256$	−31.0845	−1.94278
$257$	−15.2643	−0.952162	−0.476081	−	0.879402i	$-0.657943\pi$
$257$	−15.2643	−0.952162	−0.476081	+	0.879402i	$0.657943\pi$
$258$	−17.3318	−1.07903
$259$	9.37341	0.582436
$260$	82.0814	5.09047
$261$	−2.74635	−0.169995
$262$	47.0988	2.90977
$263$	8.45315	0.521243	0.260622	−	0.965441i	$-0.416072\pi$
$263$	8.45315	0.521243	0.260622	+	0.965441i	$0.416072\pi$
$264$	0	0
$265$	−21.8018	−1.33927
$266$	−15.4125	−0.945001
$267$	9.34453	0.571876
$268$	−15.2089	−0.929030
$269$	−21.3987	−1.30470	−0.652350	−	0.757918i	$-0.726217\pi$
$269$	−21.3987	−1.30470	−0.652350	+	0.757918i	$0.726217\pi$
$270$	8.34022	0.507570
$271$	−26.2414	−1.59405	−0.797026	−	0.603946i	$-0.793594\pi$
$271$	−26.2414	−1.59405	−0.797026	+	0.603946i	$0.793594\pi$
$272$	−11.1213	−0.674331
$273$	6.11977	0.370385
$274$	14.9325	0.902106
$275$	0	0
$276$	0.822738	0.0495230
$277$	18.5696	1.11574	0.557869	−	0.829929i	$-0.311619\pi$
$277$	18.5696	1.11574	0.557869	+	0.829929i	$0.311619\pi$
$278$	16.4588	0.987135
$279$	4.64136	0.277871
$280$	15.9241	0.951646
$281$	−4.24906	−0.253478	−0.126739	−	0.991936i	$-0.540451\pi$
$281$	−4.24906	−0.253478	−0.126739	+	0.991936i	$0.540451\pi$
$282$	−14.3793	−0.856275
$283$	−20.5277	−1.22024	−0.610122	−	0.792308i	$-0.708879\pi$
$283$	−20.5277	−1.22024	−0.610122	+	0.792308i	$0.708879\pi$
$284$	−20.3072	−1.20501
$285$	21.7527	1.28852
$286$	0	0
$287$	11.9484	0.705291
$288$	0.861816	0.0507830
$289$	−6.69297	−0.393704
$290$	22.9052	1.34504
$291$	−12.0534	−0.706582
$292$	51.5041	3.01405
$293$	21.2022	1.23865	0.619324	−	0.785136i	$-0.287407\pi$
$293$	21.2022	1.23865	0.619324	+	0.785136i	$0.287407\pi$
$294$	2.43091	0.141773
$295$	−40.5644	−2.36175
$296$	43.5054	2.52870
$297$	0	0
$298$	−43.3197	−2.50945
$299$	−1.28794	−0.0744836
$300$	−26.4705	−1.52827
$301$	7.12976	0.410953
$302$	1.48457	0.0854273
$303$	−1.58798	−0.0912272
$304$	−21.9632	−1.25967
$305$	−31.5713	−1.80777
$306$	7.80432	0.446143
$307$	−23.0007	−1.31272	−0.656359	−	0.754449i	$-0.727904\pi$
$307$	−23.0007	−1.31272	−0.656359	+	0.754449i	$0.727904\pi$
$308$	0	0
$309$	−9.42249	−0.536027
$310$	−38.7100	−2.19858
$311$	7.36753	0.417774	0.208887	−	0.977940i	$-0.433016\pi$
$311$	7.36753	0.417774	0.208887	+	0.977940i	$0.433016\pi$
$312$	28.4041	1.60806
$313$	−4.80590	−0.271645	−0.135823	−	0.990733i	$-0.543368\pi$
$313$	−4.80590	−0.271645	−0.135823	+	0.990733i	$0.543368\pi$
$314$	−16.5854	−0.935971
$315$	−3.43091	−0.193310
$316$	16.9282	0.952286
$317$	−1.54178	−0.0865951	−0.0432976	−	0.999062i	$-0.513786\pi$
$317$	−1.54178	−0.0865951	−0.0432976	+	0.999062i	$0.513786\pi$
$318$	−15.4473	−0.866239
$319$	0	0
$320$	−30.9578	−1.73059
$321$	7.03319	0.392555
$322$	−0.511599	−0.0285103
$323$	20.3550	1.13258
$324$	3.90931	0.217184
$325$	41.4377	2.29855
$326$	29.3504	1.62557
$327$	−2.37040	−0.131084
$328$	55.4568	3.06209
$329$	5.91520	0.326115
$330$	0	0
$331$	−12.8925	−0.708634	−0.354317	−	0.935125i	$-0.615287\pi$
$331$	−12.8925	−0.708634	−0.354317	+	0.935125i	$0.615287\pi$
$332$	2.88482	0.158325
$333$	−9.37341	−0.513660
$334$	−7.04797	−0.385648
$335$	−13.3477	−0.729262
$336$	3.46410	0.188982
$337$	18.6475	1.01580	0.507898	−	0.861417i	$-0.330423\pi$
$337$	18.6475	1.01580	0.507898	+	0.861417i	$0.330423\pi$
$338$	−59.4395	−3.23308
$339$	−0.409144	−0.0222216
$340$	−43.0602	−2.33527
$341$	0	0
$342$	15.4125	0.833412
$343$	−1.00000	−0.0539949
$344$	33.0918	1.78419
$345$	0.722055	0.0388741
$346$	−35.4216	−1.90428
$347$	−12.4700	−0.669424	−0.334712	−	0.942320i	$-0.608639\pi$
$347$	−12.4700	−0.669424	−0.334712	+	0.942320i	$0.608639\pi$
$348$	10.7364	0.575529
$349$	−5.11087	−0.273579	−0.136789	−	0.990600i	$-0.543678\pi$
$349$	−5.11087	−0.273579	−0.136789	+	0.990600i	$0.543678\pi$
$350$	16.4600	0.879823
$351$	−6.11977	−0.326649
$352$	0	0
$353$	26.7386	1.42315	0.711576	−	0.702609i	$-0.247982\pi$
$353$	26.7386	1.42315	0.711576	+	0.702609i	$0.247982\pi$
$354$	−28.7411	−1.52757
$355$	−17.8221	−0.945899
$356$	−36.5307	−1.93612
$357$	−3.21046	−0.169915
$358$	−45.9641	−2.42928
$359$	−0.873109	−0.0460809	−0.0230405	−	0.999735i	$-0.507335\pi$
$359$	−0.873109	−0.0460809	−0.0230405	+	0.999735i	$0.507335\pi$
$360$	−15.9241	−0.839273
$361$	21.1984	1.11571
$362$	−38.3386	−2.01503
$363$	0	0
$364$	−23.9241	−1.25396
$365$	45.2013	2.36594
$366$	−22.3693	−1.16926
$367$	12.4644	0.650635	0.325318	−	0.945605i	$-0.394529\pi$
$367$	12.4644	0.650635	0.325318	+	0.945605i	$0.394529\pi$
$368$	−0.729041	−0.0380039
$369$	−11.9484	−0.622008
$370$	78.1763	4.06419
$371$	6.35452	0.329910
$372$	−18.1445	−0.940751
$373$	2.27617	0.117856	0.0589279	−	0.998262i	$-0.481232\pi$
$373$	2.27617	0.117856	0.0589279	+	0.998262i	$0.481232\pi$
$374$	0	0
$375$	−6.07658	−0.313793
$376$	27.4546	1.41586
$377$	−16.8071	−0.865607
$378$	−2.43091	−0.125032
$379$	20.7575	1.06624	0.533120	−	0.846039i	$-0.321019\pi$
$379$	20.7575	1.06624	0.533120	+	0.846039i	$0.321019\pi$
$380$	−85.0382	−4.36237
$381$	−19.5307	−1.00059
$382$	47.4347	2.42697
$383$	−17.8498	−0.912080	−0.456040	−	0.889959i	$-0.650733\pi$
$383$	−17.8498	−0.912080	−0.456040	+	0.889959i	$0.650733\pi$
$384$	−20.2109	−1.03138
$385$	0	0
$386$	−55.8696	−2.84369
$387$	−7.12976	−0.362426
$388$	47.1204	2.39218
$389$	−8.23954	−0.417761	−0.208881	−	0.977941i	$-0.566982\pi$
$389$	−8.23954	−0.417761	−0.208881	+	0.977941i	$0.566982\pi$
$390$	51.0402	2.58452
$391$	0.675659	0.0341696
$392$	−4.64136	−0.234424
$393$	19.3750	0.977339
$394$	27.5223	1.38655
$395$	14.8566	0.747517
$396$	0	0
$397$	−16.1445	−0.810271	−0.405136	−	0.914257i	$-0.632776\pi$
$397$	−16.1445	−0.810271	−0.405136	+	0.914257i	$0.632776\pi$
$398$	15.6511	0.784518
$399$	−6.34022	−0.317408
$400$	23.4559	1.17279
$401$	27.5236	1.37446	0.687231	−	0.726439i	$-0.258826\pi$
$401$	27.5236	1.37446	0.687231	+	0.726439i	$0.258826\pi$
$402$	−9.45726	−0.471685
$403$	28.4041	1.41491
$404$	6.20792	0.308856
$405$	3.43091	0.170483
$406$	−6.67613	−0.331331
$407$	0	0
$408$	−14.9009	−0.737704
$409$	17.1270	0.846877	0.423439	−	0.905925i	$-0.360823\pi$
$409$	17.1270	0.846877	0.423439	+	0.905925i	$0.360823\pi$
$410$	99.6522	4.92147
$411$	6.14277	0.303001
$412$	36.8355	1.81475
$413$	11.8232	0.581782
$414$	0.511599	0.0251437
$415$	2.53179	0.124281
$416$	5.27411	0.258585
$417$	6.77065	0.331560
$418$	0	0
$419$	14.3995	0.703461	0.351730	−	0.936101i	$-0.385593\pi$
$419$	14.3995	0.703461	0.351730	+	0.936101i	$0.385593\pi$
$420$	13.4125	0.654463
$421$	−11.0695	−0.539496	−0.269748	−	0.962931i	$-0.586940\pi$
$421$	−11.0695	−0.539496	−0.269748	+	0.962931i	$0.586940\pi$
$422$	48.9309	2.38192
$423$	−5.91520	−0.287607
$424$	29.4937	1.43234
$425$	−21.7384	−1.05447
$426$	−12.6275	−0.611806
$427$	9.20204	0.445318
$428$	−27.4950	−1.32902
$429$	0	0
$430$	59.4638	2.86760
$431$	−15.6173	−0.752257	−0.376128	−	0.926568i	$-0.622745\pi$
$431$	−15.6173	−0.752257	−0.376128	+	0.926568i	$0.622745\pi$
$432$	−3.46410	−0.166667
$433$	2.17439	0.104494	0.0522472	−	0.998634i	$-0.483362\pi$
$433$	2.17439	0.104494	0.0522472	+	0.998634i	$0.483362\pi$
$434$	11.2827	0.541588
$435$	9.42249	0.451774
$436$	9.26665	0.443792
$437$	1.33434	0.0638300
$438$	32.0265	1.53029
$439$	9.44726	0.450893	0.225447	−	0.974256i	$-0.427616\pi$
$439$	9.44726	0.450893	0.225447	+	0.974256i	$0.427616\pi$
$440$	0	0
$441$	1.00000	0.0476190
$442$	47.7606	2.27174
$443$	8.08725	0.384237	0.192118	−	0.981372i	$-0.438464\pi$
$443$	8.08725	0.384237	0.192118	+	0.981372i	$0.438464\pi$
$444$	36.6436	1.73903
$445$	−32.0602	−1.51980
$446$	50.7309	2.40218
$447$	−17.8204	−0.842876
$448$	9.02320	0.426306
$449$	−28.5845	−1.34899	−0.674494	−	0.738280i	$-0.735638\pi$
$449$	−28.5845	−1.34899	−0.674494	+	0.738280i	$0.735638\pi$
$450$	−16.4600	−0.775931
$451$	0	0
$452$	1.59947	0.0752328
$453$	0.610705	0.0286934
$454$	7.46027	0.350128
$455$	−20.9964	−0.984325
$456$	−29.4273	−1.37806
$457$	−8.25713	−0.386252	−0.193126	−	0.981174i	$-0.561863\pi$
$457$	−8.25713	−0.386252	−0.193126	+	0.981174i	$0.561863\pi$
$458$	20.3167	0.949339
$459$	3.21046	0.149851
$460$	−2.82274	−0.131611
$461$	13.3346	0.621055	0.310527	−	0.950564i	$-0.399494\pi$
$461$	13.3346	0.621055	0.310527	+	0.950564i	$0.399494\pi$
$462$	0	0
$463$	26.6479	1.23843	0.619217	−	0.785220i	$-0.287450\pi$
$463$	26.6479	1.23843	0.619217	+	0.785220i	$0.287450\pi$
$464$	−9.51365	−0.441660
$465$	−15.9241	−0.738462
$466$	−13.3766	−0.619658
$467$	28.8194	1.33360	0.666801	−	0.745236i	$-0.267663\pi$
$467$	28.8194	1.33360	0.666801	+	0.745236i	$0.267663\pi$
$468$	23.9241	1.10589
$469$	3.89042	0.179643
$470$	49.3340	2.27561
$471$	−6.82274	−0.314375
$472$	54.8758	2.52586
$473$	0	0
$474$	10.5264	0.483493
$475$	−42.9304	−1.96978
$476$	12.5507	0.575259
$477$	−6.35452	−0.290954
$478$	5.60003	0.256139
$479$	−7.03430	−0.321405	−0.160703	−	0.987003i	$-0.551376\pi$
$479$	−7.03430	−0.321405	−0.160703	+	0.987003i	$0.551376\pi$
$480$	−2.95681	−0.134959
$481$	−57.3631	−2.61553
$482$	−25.1847	−1.14713
$483$	−0.210456	−0.00957607
$484$	0	0
$485$	41.3540	1.87779
$486$	2.43091	0.110268
$487$	−15.1823	−0.687977	−0.343988	−	0.938974i	$-0.611778\pi$
$487$	−15.1823	−0.687977	−0.343988	+	0.938974i	$0.611778\pi$
$488$	42.7100	1.93339
$489$	12.0738	0.545998
$490$	−8.34022	−0.376773
$491$	15.6173	0.704801	0.352400	−	0.935849i	$-0.385366\pi$
$491$	15.6173	0.704801	0.352400	+	0.935849i	$0.385366\pi$
$492$	46.7100	2.10585
$493$	8.81705	0.397100
$494$	94.3209	4.24370
$495$	0	0
$496$	16.0782	0.721930
$497$	5.19458	0.233009
$498$	1.79385	0.0803844
$499$	9.99383	0.447385	0.223693	−	0.974660i	$-0.428189\pi$
$499$	9.99383	0.447385	0.223693	+	0.974660i	$0.428189\pi$
$500$	23.7552	1.06237
$501$	−2.89932	−0.129532
$502$	−27.3787	−1.22197
$503$	13.6115	0.606908	0.303454	−	0.952846i	$-0.401860\pi$
$503$	13.6115	0.606908	0.303454	+	0.952846i	$0.401860\pi$
$504$	4.64136	0.206743
$505$	5.44822	0.242443
$506$	0	0
$507$	−24.4516	−1.08593
$508$	76.3516	3.38755
$509$	−20.5379	−0.910325	−0.455162	−	0.890408i	$-0.650419\pi$
$509$	−20.5379	−0.910325	−0.455162	+	0.890408i	$0.650419\pi$
$510$	−26.7759	−1.18566
$511$	−13.1747	−0.582816
$512$	35.1417	1.55306
$513$	6.34022	0.279928
$514$	37.1061	1.63668
$515$	32.3277	1.42453
$516$	27.8725	1.22702
$517$	0	0
$518$	−22.7859	−1.00116
$519$	−14.5713	−0.639611
$520$	−97.4518	−4.27354
$521$	14.7483	0.646133	0.323067	−	0.946376i	$-0.395286\pi$
$521$	14.7483	0.646133	0.323067	+	0.946376i	$0.395286\pi$
$522$	6.67613	0.292206
$523$	22.1029	0.966494	0.483247	−	0.875484i	$-0.339457\pi$
$523$	22.1029	0.966494	0.483247	+	0.875484i	$0.339457\pi$
$524$	−75.7429	−3.30884
$525$	6.77113	0.295516
$526$	−20.5488	−0.895971
$527$	−14.9009	−0.649093
$528$	0	0
$529$	−22.9557	−0.998074
$530$	52.9981	2.30209
$531$	−11.8232	−0.513084
$532$	24.7859	1.07461
$533$	−73.1214	−3.16724
$534$	−22.7157	−0.983004
$535$	−24.1302	−1.04324
$536$	18.0569	0.779938
$537$	−18.9082	−0.815950
$538$	52.0182	2.24266
$539$	0	0
$540$	−13.4125	−0.577182
$541$	−6.86201	−0.295021	−0.147510	−	0.989060i	$-0.547126\pi$
$541$	−6.86201	−0.295021	−0.147510	+	0.989060i	$0.547126\pi$
$542$	63.7904	2.74003
$543$	−15.7713	−0.676812
$544$	−2.76682	−0.118626
$545$	8.13264	0.348364
$546$	−14.8766	−0.636659
$547$	24.7425	1.05791	0.528957	−	0.848649i	$-0.322583\pi$
$547$	24.7425	1.05791	0.528957	+	0.848649i	$0.322583\pi$
$548$	−24.0140	−1.02583
$549$	−9.20204	−0.392733
$550$	0	0
$551$	17.4125	0.741797
$552$	−0.976802	−0.0415755
$553$	−4.33022	−0.184140
$554$	−45.1409	−1.91785
$555$	32.1593	1.36509
$556$	−26.4686	−1.12252
$557$	−4.14961	−0.175825	−0.0879124	−	0.996128i	$-0.528020\pi$
$557$	−4.14961	−0.175825	−0.0879124	+	0.996128i	$0.528020\pi$
$558$	−11.2827	−0.477636
$559$	−43.6325	−1.84546
$560$	−11.8850	−0.502233
$561$	0	0
$562$	10.3291	0.435706
$563$	2.86455	0.120726	0.0603631	−	0.998176i	$-0.480774\pi$
$563$	2.86455	0.120726	0.0603631	+	0.998176i	$0.480774\pi$
$564$	23.1244	0.973711
$565$	1.40373	0.0590556
$566$	49.9009	2.09749
$567$	−1.00000	−0.0419961
$568$	24.1099	1.01163
$569$	10.5736	0.443268	0.221634	−	0.975130i	$-0.428861\pi$
$569$	10.5736	0.443268	0.221634	+	0.975130i	$0.428861\pi$
$570$	−52.8788	−2.21485
$571$	−27.2490	−1.14034	−0.570169	−	0.821528i	$-0.693122\pi$
$571$	−27.2490	−1.14034	−0.570169	+	0.821528i	$0.693122\pi$
$572$	0	0
$573$	19.5132	0.815175
$574$	−29.0454	−1.21233
$575$	−1.42502	−0.0594276
$576$	−9.02320	−0.375967
$577$	−29.8593	−1.24306	−0.621530	−	0.783390i	$-0.713489\pi$
$577$	−29.8593	−1.24306	−0.621530	+	0.783390i	$0.713489\pi$
$578$	16.2700	0.676743
$579$	−22.9830	−0.955142
$580$	−36.8355	−1.52951
$581$	−0.737935	−0.0306147
$582$	29.3007	1.21455
$583$	0	0
$584$	−61.1487	−2.53035
$585$	20.9964	0.868093
$586$	−51.5407	−2.12913
$587$	10.4659	0.431973	0.215986	−	0.976396i	$-0.430703\pi$
$587$	10.4659	0.431973	0.215986	+	0.976396i	$0.430703\pi$
$588$	−3.90931	−0.161217
$589$	−29.4273	−1.21253
$590$	98.6082	4.05964
$591$	11.3218	0.465717
$592$	−32.4705	−1.33453
$593$	−36.5059	−1.49912	−0.749559	−	0.661938i	$-0.769734\pi$
$593$	−36.5059	−1.49912	−0.749559	+	0.661938i	$0.769734\pi$
$594$	0	0
$595$	11.0148	0.451562
$596$	69.6655	2.85361
$597$	6.43837	0.263505
$598$	3.13087	0.128031
$599$	9.49586	0.387990	0.193995	−	0.981002i	$-0.437855\pi$
$599$	9.49586	0.387990	0.193995	+	0.981002i	$0.437855\pi$
$600$	31.4273	1.28301
$601$	7.98125	0.325562	0.162781	−	0.986662i	$-0.447954\pi$
$601$	7.98125	0.325562	0.162781	+	0.986662i	$0.447954\pi$
$602$	−17.3318	−0.706391
$603$	−3.89042	−0.158430
$604$	−2.38744	−0.0971435
$605$	0	0
$606$	3.86024	0.156811
$607$	−32.4406	−1.31672	−0.658362	−	0.752701i	$-0.728750\pi$
$607$	−32.4406	−1.31672	−0.658362	+	0.752701i	$0.728750\pi$
$608$	−5.46410	−0.221599
$609$	−2.74635	−0.111288
$610$	76.7470	3.10740
$611$	−36.1996	−1.46448
$612$	−12.5507	−0.507331
$613$	−33.0240	−1.33382	−0.666912	−	0.745136i	$-0.732384\pi$
$613$	−33.0240	−1.33382	−0.666912	+	0.745136i	$0.732384\pi$
$614$	55.9125	2.25645
$615$	40.9938	1.65303
$616$	0	0
$617$	48.7478	1.96251	0.981256	−	0.192710i	$-0.0617275\pi$
$617$	48.7478	1.96251	0.981256	+	0.192710i	$0.0617275\pi$
$618$	22.9052	0.921382
$619$	−1.29320	−0.0519780	−0.0259890	−	0.999662i	$-0.508273\pi$
$619$	−1.29320	−0.0519780	−0.0259890	+	0.999662i	$0.508273\pi$
$620$	62.2523	2.50011
$621$	0.210456	0.00844530
$622$	−17.9098	−0.718117
$623$	9.34453	0.374381
$624$	−21.1995	−0.848659
$625$	−13.0075	−0.520298
$626$	11.6827	0.466935
$627$	0	0
$628$	26.6722	1.06434
$629$	30.0929	1.19988
$630$	8.34022	0.332282
$631$	−18.7715	−0.747280	−0.373640	−	0.927574i	$-0.621891\pi$
$631$	−18.7715	−0.747280	−0.373640	+	0.927574i	$0.621891\pi$
$632$	−20.0981	−0.799461
$633$	20.1287	0.800043
$634$	3.74793	0.148849
$635$	67.0080	2.65913
$636$	24.8418	0.985042
$637$	6.11977	0.242474
$638$	0	0
$639$	−5.19458	−0.205494
$640$	69.3418	2.74098
$641$	−17.9563	−0.709232	−0.354616	−	0.935012i	$-0.615388\pi$
$641$	−17.9563	−0.709232	−0.354616	+	0.935012i	$0.615388\pi$
$642$	−17.0970	−0.674767
$643$	23.2796	0.918057	0.459028	−	0.888422i	$-0.348198\pi$
$643$	23.2796	0.918057	0.459028	+	0.888422i	$0.348198\pi$
$644$	0.822738	0.0324204
$645$	24.4616	0.963173
$646$	−49.4811	−1.94681
$647$	−42.2211	−1.65988	−0.829942	−	0.557850i	$-0.811626\pi$
$647$	−42.2211	−1.65988	−0.829942	+	0.557850i	$0.811626\pi$
$648$	−4.64136	−0.182330
$649$	0	0
$650$	−100.731	−3.95101
$651$	4.64136	0.181909
$652$	−47.2005	−1.84851
$653$	−1.27048	−0.0497179	−0.0248590	−	0.999691i	$-0.507914\pi$
$653$	−1.27048	−0.0497179	−0.0248590	+	0.999691i	$0.507914\pi$
$654$	5.76223	0.225321
$655$	−66.4738	−2.59735
$656$	−41.3904	−1.61603
$657$	13.1747	0.513995
$658$	−14.3793	−0.560563
$659$	−35.1838	−1.37056	−0.685282	−	0.728278i	$-0.740321\pi$
$659$	−35.1838	−1.37056	−0.685282	+	0.728278i	$0.740321\pi$
$660$	0	0
$661$	2.90089	0.112832	0.0564158	−	0.998407i	$-0.482033\pi$
$661$	2.90089	0.112832	0.0564158	+	0.998407i	$0.482033\pi$
$662$	31.3404	1.21808
$663$	19.6472	0.763036
$664$	−3.42502	−0.132917
$665$	21.7527	0.843534
$666$	22.7859	0.882936
$667$	0.577986	0.0223797
$668$	11.3343	0.438539
$669$	20.8691	0.806847
$670$	32.4470	1.25354
$671$	0	0
$672$	0.861816	0.0332453
$673$	−37.1846	−1.43336	−0.716680	−	0.697402i	$-0.754339\pi$
$673$	−37.1846	−1.43336	−0.716680	+	0.697402i	$0.754339\pi$
$674$	−45.3304	−1.74606
$675$	−6.77113	−0.260621
$676$	95.5888	3.67649
$677$	−26.7675	−1.02876	−0.514379	−	0.857563i	$-0.671978\pi$
$677$	−26.7675	−1.02876	−0.514379	+	0.857563i	$0.671978\pi$
$678$	0.994591	0.0381970
$679$	−12.0534	−0.462566
$680$	51.1236	1.96050
$681$	3.06892	0.117601
$682$	0	0
$683$	40.9076	1.56529	0.782643	−	0.622471i	$-0.213871\pi$
$683$	40.9076	1.56529	0.782643	+	0.622471i	$0.213871\pi$
$684$	−24.7859	−0.947713
$685$	−21.0753	−0.805245
$686$	2.43091	0.0928125
$687$	8.35768	0.318865
$688$	−24.6982	−0.941611
$689$	−38.8882	−1.48152
$690$	−1.75525	−0.0668212
$691$	41.0267	1.56073	0.780365	−	0.625324i	$-0.215033\pi$
$691$	41.0267	1.56073	0.780365	+	0.625324i	$0.215033\pi$
$692$	56.9639	2.16544
$693$	0	0
$694$	30.3134	1.15068
$695$	−23.2295	−0.881145
$696$	−12.7468	−0.483167
$697$	38.3598	1.45298
$698$	12.4241	0.470258
$699$	−5.50270	−0.208131
$700$	−26.4705	−1.00049
$701$	−18.6482	−0.704333	−0.352167	−	0.935937i	$-0.614555\pi$
$701$	−18.6482	−0.704333	−0.352167	+	0.935937i	$0.614555\pi$
$702$	14.8766	0.561481
$703$	59.4295	2.24143
$704$	0	0
$705$	20.2945	0.764335
$706$	−64.9991	−2.44627
$707$	−1.58798	−0.0597222
$708$	46.2206	1.73708
$709$	−35.4041	−1.32963	−0.664814	−	0.747009i	$-0.731489\pi$
$709$	−35.4041	−1.32963	−0.664814	+	0.747009i	$0.731489\pi$
$710$	43.3239	1.62592
$711$	4.33022	0.162396
$712$	43.3714	1.62541
$713$	−0.976802	−0.0365815
$714$	7.80432	0.292069
$715$	0	0
$716$	73.9181	2.76245
$717$	2.30368	0.0860324
$718$	2.12245	0.0792090
$719$	22.9482	0.855823	0.427912	−	0.903821i	$-0.359249\pi$
$719$	22.9482	0.855823	0.427912	+	0.903821i	$0.359249\pi$
$720$	11.8850	0.442928
$721$	−9.42249	−0.350912
$722$	−51.5314	−1.91780
$723$	−10.3602	−0.385300
$724$	61.6550	2.29139
$725$	−18.5959	−0.690635
$726$	0	0
$727$	4.75027	0.176178	0.0880889	−	0.996113i	$-0.471924\pi$
$727$	4.75027	0.176178	0.0880889	+	0.996113i	$0.471924\pi$
$728$	28.4041	1.05272
$729$	1.00000	0.0370370
$730$	−109.880	−4.06685
$731$	22.8898	0.846610
$732$	35.9736	1.32962
$733$	26.7529	0.988141	0.494071	−	0.869422i	$-0.335508\pi$
$733$	26.7529	0.988141	0.494071	+	0.869422i	$0.335508\pi$
$734$	−30.2998	−1.11838
$735$	−3.43091	−0.126551
$736$	−0.181374	−0.00668554
$737$	0	0
$738$	29.0454	1.06918
$739$	4.44616	0.163555	0.0817773	−	0.996651i	$-0.473940\pi$
$739$	4.44616	0.163555	0.0817773	+	0.996651i	$0.473940\pi$
$740$	−125.721	−4.62159
$741$	38.8007	1.42538
$742$	−15.4473	−0.567087
$743$	−8.17268	−0.299826	−0.149913	−	0.988699i	$-0.547899\pi$
$743$	−8.17268	−0.299826	−0.149913	+	0.988699i	$0.547899\pi$
$744$	21.5423	0.789777
$745$	61.1401	2.24000
$746$	−5.53317	−0.202584
$747$	0.737935	0.0269996
$748$	0	0
$749$	7.03319	0.256987
$750$	14.7716	0.539383
$751$	−23.9396	−0.873568	−0.436784	−	0.899566i	$-0.643883\pi$
$751$	−23.9396	−0.873568	−0.436784	+	0.899566i	$0.643883\pi$
$752$	−20.4908	−0.747224
$753$	−11.2627	−0.410437
$754$	40.8564	1.48790
$755$	−2.09527	−0.0762548
$756$	3.90931	0.142180
$757$	19.9431	0.724845	0.362423	−	0.932014i	$-0.381950\pi$
$757$	19.9431	0.724845	0.362423	+	0.932014i	$0.381950\pi$
$758$	−50.4596	−1.83277
$759$	0	0
$760$	100.962	3.66229
$761$	−10.2909	−0.373044	−0.186522	−	0.982451i	$-0.559722\pi$
$761$	−10.2909	−0.373044	−0.186522	+	0.982451i	$0.559722\pi$
$762$	47.4773	1.71992
$763$	−2.37040	−0.0858144
$764$	−76.2831	−2.75983
$765$	−11.0148	−0.398240
$766$	43.3911	1.56778
$767$	−72.3553	−2.61260
$768$	31.0845	1.12167
$769$	39.4073	1.42106	0.710531	−	0.703665i	$-0.248455\pi$
$769$	39.4073	1.42106	0.710531	+	0.703665i	$0.248455\pi$
$770$	0	0
$771$	15.2643	0.549731
$772$	89.8478	3.23369
$773$	22.7516	0.818317	0.409158	−	0.912463i	$-0.365822\pi$
$773$	22.7516	0.818317	0.409158	+	0.912463i	$0.365822\pi$
$774$	17.3318	0.622979
$775$	31.4273	1.12890
$776$	−55.9441	−2.00828
$777$	−9.37341	−0.336269
$778$	20.0296	0.718094
$779$	75.7554	2.71422
$780$	−82.0814	−2.93898
$781$	0	0
$782$	−1.64247	−0.0587344
$783$	2.74635	0.0981467
$784$	3.46410	0.123718
$785$	23.4082	0.835474
$786$	−47.0988	−1.67996
$787$	36.2328	1.29156	0.645780	−	0.763524i	$-0.276533\pi$
$787$	36.2328	1.29156	0.645780	+	0.763524i	$0.276533\pi$
$788$	−44.2605	−1.57671
$789$	−8.45315	−0.300940
$790$	−36.1150	−1.28492
$791$	−0.409144	−0.0145475
$792$	0	0
$793$	−56.3143	−1.99978
$794$	39.2459	1.39278
$795$	21.8018	0.773230
$796$	−25.1696	−0.892113
$797$	21.3161	0.755054	0.377527	−	0.925999i	$-0.376775\pi$
$797$	21.3161	0.755054	0.377527	+	0.925999i	$0.376775\pi$
$798$	15.4125	0.545596
$799$	18.9905	0.671835
$800$	5.83546	0.206315
$801$	−9.34453	−0.330173
$802$	−66.9072	−2.36258
$803$	0	0
$804$	15.2089	0.536376
$805$	0.722055	0.0254491
$806$	−69.0477	−2.43210
$807$	21.3987	0.753269
$808$	−7.37040	−0.259290
$809$	37.6282	1.32294	0.661469	−	0.749973i	$-0.269933\pi$
$809$	37.6282	1.32294	0.661469	+	0.749973i	$0.269933\pi$
$810$	−8.34022	−0.293045
$811$	3.04195	0.106817	0.0534087	−	0.998573i	$-0.482991\pi$
$811$	3.04195	0.106817	0.0534087	+	0.998573i	$0.482991\pi$
$812$	10.7364	0.376772
$813$	26.2414	0.920326
$814$	0	0
$815$	−41.4243	−1.45103
$816$	11.1213	0.389325
$817$	45.2043	1.58150
$818$	−41.6342	−1.45571
$819$	−6.11977	−0.213842
$820$	−160.258	−5.59644
$821$	−37.2094	−1.29862	−0.649309	−	0.760525i	$-0.724942\pi$
$821$	−37.2094	−1.29862	−0.649309	+	0.760525i	$0.724942\pi$
$822$	−14.9325	−0.520831
$823$	−36.4957	−1.27216	−0.636080	−	0.771623i	$-0.719445\pi$
$823$	−36.4957	−1.27216	−0.636080	+	0.771623i	$0.719445\pi$
$824$	−43.7332	−1.52352
$825$	0	0
$826$	−28.7411	−1.00003
$827$	−52.8436	−1.83755	−0.918776	−	0.394779i	$-0.870821\pi$
$827$	−52.8436	−1.83755	−0.918776	+	0.394779i	$0.870821\pi$
$828$	−0.822738	−0.0285921
$829$	−43.4225	−1.50813	−0.754063	−	0.656802i	$-0.771909\pi$
$829$	−43.4225	−1.50813	−0.754063	+	0.656802i	$0.771909\pi$
$830$	−6.15454	−0.213627
$831$	−18.5696	−0.644171
$832$	−55.2199	−1.91441
$833$	−3.21046	−0.111236
$834$	−16.4588	−0.569923
$835$	9.94729	0.344240
$836$	0	0
$837$	−4.64136	−0.160429
$838$	−35.0038	−1.20919
$839$	27.6102	0.953211	0.476605	−	0.879117i	$-0.341867\pi$
$839$	27.6102	0.953211	0.476605	+	0.879117i	$0.341867\pi$
$840$	−15.9241	−0.549433
$841$	−21.4575	−0.739915
$842$	26.9090	0.927347
$843$	4.24906	0.146345
$844$	−78.6892	−2.70860
$845$	83.8911	2.88594
$846$	14.3793	0.494370
$847$	0	0
$848$	−22.0127	−0.755920
$849$	20.5277	0.704508
$850$	52.8441	1.81254
$851$	1.97269	0.0676229
$852$	20.3072	0.695714
$853$	−22.4005	−0.766980	−0.383490	−	0.923545i	$-0.625278\pi$
$853$	−22.4005	−0.766980	−0.383490	+	0.923545i	$0.625278\pi$
$854$	−22.3693	−0.765462
$855$	−21.7527	−0.743927
$856$	32.6436	1.11574
$857$	8.30018	0.283529	0.141764	−	0.989900i	$-0.454722\pi$
$857$	8.30018	0.283529	0.141764	+	0.989900i	$0.454722\pi$
$858$	0	0
$859$	5.09088	0.173699	0.0868493	−	0.996221i	$-0.472320\pi$
$859$	5.09088	0.173699	0.0868493	+	0.996221i	$0.472320\pi$
$860$	−95.6279	−3.26088
$861$	−11.9484	−0.407200
$862$	37.9641	1.29306
$863$	44.7322	1.52270	0.761352	−	0.648339i	$-0.224536\pi$
$863$	44.7322	1.52270	0.761352	+	0.648339i	$0.224536\pi$
$864$	−0.861816	−0.0293196
$865$	49.9929	1.69981
$866$	−5.28574	−0.179617
$867$	6.69297	0.227305
$868$	−18.1445	−0.615866
$869$	0	0
$870$	−22.9052	−0.776559
$871$	−23.8085	−0.806720
$872$	−11.0019	−0.372572
$873$	12.0534	0.407945
$874$	−3.24365	−0.109718
$875$	−6.07658	−0.205426
$876$	−51.5041	−1.74016
$877$	8.54938	0.288692	0.144346	−	0.989527i	$-0.453892\pi$
$877$	8.54938	0.288692	0.144346	+	0.989527i	$0.453892\pi$
$878$	−22.9654	−0.775046
$879$	−21.2022	−0.715134
$880$	0	0
$881$	38.1169	1.28419	0.642095	−	0.766625i	$-0.278065\pi$
$881$	38.1169	1.28419	0.642095	+	0.766625i	$0.278065\pi$
$882$	−2.43091	−0.0818529
$883$	2.36088	0.0794500	0.0397250	−	0.999211i	$-0.487352\pi$
$883$	2.36088	0.0794500	0.0397250	+	0.999211i	$0.487352\pi$
$884$	−76.8072	−2.58331
$885$	40.5644	1.36356
$886$	−19.6593	−0.660469
$887$	−11.5996	−0.389477	−0.194738	−	0.980855i	$-0.562386\pi$
$887$	−11.5996	−0.389477	−0.194738	+	0.980855i	$0.562386\pi$
$888$	−43.5054	−1.45995
$889$	−19.5307	−0.655038
$890$	77.9354	2.61240
$891$	0	0
$892$	−81.5840	−2.73163
$893$	37.5037	1.25501
$894$	43.3197	1.44883
$895$	64.8723	2.16844
$896$	−20.2109	−0.675200
$897$	1.28794	0.0430031
$898$	69.4864	2.31879
$899$	−12.7468	−0.425131
$900$	26.4705	0.882349
$901$	20.4009	0.679653
$902$	0	0
$903$	−7.12976	−0.237264
$904$	−1.89899	−0.0631593
$905$	54.1100	1.79868
$906$	−1.48457	−0.0493215
$907$	−5.25241	−0.174403	−0.0872017	−	0.996191i	$-0.527792\pi$
$907$	−5.25241	−0.174403	−0.0872017	+	0.996191i	$0.527792\pi$
$908$	−11.9974	−0.398147
$909$	1.58798	0.0526701
$910$	51.0402	1.69197
$911$	14.4254	0.477934	0.238967	−	0.971028i	$-0.423191\pi$
$911$	14.4254	0.477934	0.238967	+	0.971028i	$0.423191\pi$
$912$	21.9632	0.727273
$913$	0	0
$914$	20.0723	0.663933
$915$	31.5713	1.04372
$916$	−32.6728	−1.07954
$917$	19.3750	0.639819
$918$	−7.80432	−0.257581
$919$	0.440140	0.0145189	0.00725945	−	0.999974i	$-0.497689\pi$
$919$	0.440140	0.0145189	0.00725945	+	0.999974i	$0.497689\pi$
$920$	3.35132	0.110490
$921$	23.0007	0.757898
$922$	−32.4152	−1.06754
$923$	−31.7896	−1.04637
$924$	0	0
$925$	−63.4686	−2.08683
$926$	−64.7786	−2.12876
$927$	9.42249	0.309475
$928$	−2.36685	−0.0776957
$929$	−44.8443	−1.47130	−0.735648	−	0.677364i	$-0.763122\pi$
$929$	−44.8443	−1.47130	−0.735648	+	0.677364i	$0.763122\pi$
$930$	38.7100	1.26935
$931$	−6.34022	−0.207792
$932$	21.5118	0.704642
$933$	−7.36753	−0.241202
$934$	−70.0573	−2.29234
$935$	0	0
$936$	−28.4041	−0.928416
$937$	25.6547	0.838103	0.419051	−	0.907963i	$-0.362363\pi$
$937$	25.6547	0.838103	0.419051	+	0.907963i	$0.362363\pi$
$938$	−9.45726	−0.308790
$939$	4.80590	0.156835
$940$	−79.3375	−2.58771
$941$	−47.6122	−1.55211	−0.776056	−	0.630663i	$-0.782783\pi$
$941$	−47.6122	−1.55211	−0.776056	+	0.630663i	$0.782783\pi$
$942$	16.5854	0.540383
$943$	2.51461	0.0818869
$944$	−40.9568	−1.33303
$945$	3.43091	0.111607
$946$	0	0
$947$	−43.8549	−1.42509	−0.712546	−	0.701625i	$-0.752458\pi$
$947$	−43.8549	−1.42509	−0.712546	+	0.701625i	$0.752458\pi$
$948$	−16.9282	−0.549802
$949$	80.6263	2.61724
$950$	104.360	3.38588
$951$	1.54178	0.0499957
$952$	−14.9009	−0.482941
$953$	−30.5035	−0.988106	−0.494053	−	0.869432i	$-0.664485\pi$
$953$	−30.5035	−0.988106	−0.494053	+	0.869432i	$0.664485\pi$
$954$	15.4473	0.500124
$955$	−66.9479	−2.16638
$956$	−9.00580	−0.291268
$957$	0	0
$958$	17.0997	0.552467
$959$	6.14277	0.198360
$960$	30.9578	0.999157
$961$	−9.45774	−0.305088
$962$	139.444	4.49587
$963$	−7.03319	−0.226642
$964$	40.5013	1.30446
$965$	78.8526	2.53836
$966$	0.511599	0.0164604
$967$	−14.1404	−0.454726	−0.227363	−	0.973810i	$-0.573010\pi$
$967$	−14.1404	−0.454726	−0.227363	+	0.973810i	$0.573010\pi$
$968$	0	0
$969$	−20.3550	−0.653897
$970$	−100.528	−3.22776
$971$	18.1712	0.583141	0.291571	−	0.956549i	$-0.405822\pi$
$971$	18.1712	0.583141	0.291571	+	0.956549i	$0.405822\pi$
$972$	−3.90931	−0.125391
$973$	6.77065	0.217057
$974$	36.9068	1.18257
$975$	−41.4377	−1.32707
$976$	−31.8768	−1.02035
$977$	47.4599	1.51838	0.759188	−	0.650871i	$-0.225596\pi$
$977$	47.4599	1.51838	0.759188	+	0.650871i	$0.225596\pi$
$978$	−29.3504	−0.938523
$979$	0	0
$980$	13.4125	0.428446
$981$	2.37040	0.0756812
$982$	−37.9643	−1.21149
$983$	53.8977	1.71907	0.859535	−	0.511076i	$-0.170753\pi$
$983$	53.8977	1.71907	0.859535	+	0.511076i	$0.170753\pi$
$984$	−55.4568	−1.76790
$985$	−38.8441	−1.23767
$986$	−21.4334	−0.682580
$987$	−5.91520	−0.188283
$988$	−151.684	−4.82571
$989$	1.50050	0.0477132
$990$	0	0
$991$	−5.06529	−0.160904	−0.0804521	−	0.996758i	$-0.525636\pi$
$991$	−5.06529	−0.160904	−0.0804521	+	0.996758i	$0.525636\pi$
$992$	4.00000	0.127000
$993$	12.8925	0.409130
$994$	−12.6275	−0.400521
$995$	−22.0894	−0.700283
$996$	−2.88482	−0.0914090
$997$	−14.8081	−0.468979	−0.234489	−	0.972119i	$-0.575342\pi$
$997$	−14.8081	−0.468979	−0.234489	+	0.972119i	$0.575342\pi$
$998$	−24.2941	−0.769015
$999$	9.37341	0.296562

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2541.2.a.bk.1.1	✓	4
3.2	odd	2		7623.2.a.cm.1.4		4
11.10	odd	2		2541.2.a.bo.1.4	yes	4
33.32	even	2		7623.2.a.cf.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2541.2.a.bk.1.1	✓	4	1.1	even	1	trivial
2541.2.a.bo.1.4	yes	4	11.10	odd	2
7623.2.a.cf.1.1		4	33.32	even	2
7623.2.a.cm.1.4		4	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)

\(f(q)\)	\(=\)	\(q-2.43091 q^{2} -1.00000 q^{3} +3.90931 q^{4} +3.43091 q^{5} +2.43091 q^{6} -1.00000 q^{7} -4.64136 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.43091 q^{2} -1.00000 q^{3} +3.90931 q^{4} +3.43091 q^{5} +2.43091 q^{6} -1.00000 q^{7} -4.64136 q^{8} +1.00000 q^{9} -8.34022 q^{10} -3.90931 q^{12} +6.11977 q^{13} +2.43091 q^{14} -3.43091 q^{15} +3.46410 q^{16} -3.21046 q^{17} -2.43091 q^{18} -6.34022 q^{19} +13.4125 q^{20} +1.00000 q^{21} -0.210456 q^{23} +4.64136 q^{24} +6.77113 q^{25} -14.8766 q^{26} -1.00000 q^{27} -3.90931 q^{28} -2.74635 q^{29} +8.34022 q^{30} +4.64136 q^{31} +0.861816 q^{32} +7.80432 q^{34} -3.43091 q^{35} +3.90931 q^{36} -9.37341 q^{37} +15.4125 q^{38} -6.11977 q^{39} -15.9241 q^{40} -11.9484 q^{41} -2.43091 q^{42} -7.12976 q^{43} +3.43091 q^{45} +0.511599 q^{46} -5.91520 q^{47} -3.46410 q^{48} +1.00000 q^{49} -16.4600 q^{50} +3.21046 q^{51} +23.9241 q^{52} -6.35452 q^{53} +2.43091 q^{54} +4.64136 q^{56} +6.34022 q^{57} +6.67613 q^{58} -11.8232 q^{59} -13.4125 q^{60} -9.20204 q^{61} -11.2827 q^{62} -1.00000 q^{63} -9.02320 q^{64} +20.9964 q^{65} -3.89042 q^{67} -12.5507 q^{68} +0.210456 q^{69} +8.34022 q^{70} -5.19458 q^{71} -4.64136 q^{72} +13.1747 q^{73} +22.7859 q^{74} -6.77113 q^{75} -24.7859 q^{76} +14.8766 q^{78} +4.33022 q^{79} +11.8850 q^{80} +1.00000 q^{81} +29.0454 q^{82} +0.737935 q^{83} +3.90931 q^{84} -11.0148 q^{85} +17.3318 q^{86} +2.74635 q^{87} -9.34453 q^{89} -8.34022 q^{90} -6.11977 q^{91} -0.822738 q^{92} -4.64136 q^{93} +14.3793 q^{94} -21.7527 q^{95} -0.861816 q^{96} +12.0534 q^{97} -2.43091 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 4 q^{3} + 4 q^{4} + 6 q^{5} + 2 q^{6} - 4 q^{7} + 4 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 - 4 * q^3 + 4 * q^4 + 6 * q^5 + 2 * q^6 - 4 * q^7 + 4 * q^9	\( 4 q - 2 q^{2} - 4 q^{3} + 4 q^{4} + 6 q^{5} + 2 q^{6} - 4 q^{7} + 4 q^{9} - 14 q^{10} - 4 q^{12} + 2 q^{13} + 2 q^{14} - 6 q^{15} - 2 q^{17} - 2 q^{18} - 6 q^{19} + 8 q^{20} + 4 q^{21} + 10 q^{23} - 4 q^{27} - 4 q^{28} - 14 q^{29} + 14 q^{30} - 12 q^{32} - 2 q^{34} - 6 q^{35} + 4 q^{36} - 12 q^{37} + 16 q^{38} - 2 q^{39} - 8 q^{40} - 16 q^{41} - 2 q^{42} - 20 q^{43} + 6 q^{45} - 8 q^{46} + 2 q^{47} + 4 q^{49} - 24 q^{50} + 2 q^{51} + 40 q^{52} - 16 q^{53} + 2 q^{54} + 6 q^{57} - 8 q^{58} + 2 q^{59} - 8 q^{60} - 2 q^{61} - 8 q^{62} - 4 q^{63} - 16 q^{64} + 2 q^{65} - 20 q^{67} - 20 q^{68} - 10 q^{69} + 14 q^{70} - 10 q^{71} + 10 q^{73} + 20 q^{74} - 28 q^{76} - 16 q^{79} + 12 q^{80} + 4 q^{81} + 28 q^{82} - 18 q^{83} + 4 q^{84} + 26 q^{86} + 14 q^{87} - 14 q^{89} - 14 q^{90} - 2 q^{91} - 8 q^{92} + 18 q^{94} - 22 q^{95} + 12 q^{96} + 38 q^{97} - 2 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 - 4 * q^3 + 4 * q^4 + 6 * q^5 + 2 * q^6 - 4 * q^7 + 4 * q^9 - 14 * q^10 - 4 * q^12 + 2 * q^13 + 2 * q^14 - 6 * q^15 - 2 * q^17 - 2 * q^18 - 6 * q^19 + 8 * q^20 + 4 * q^21 + 10 * q^23 - 4 * q^27 - 4 * q^28 - 14 * q^29 + 14 * q^30 - 12 * q^32 - 2 * q^34 - 6 * q^35 + 4 * q^36 - 12 * q^37 + 16 * q^38 - 2 * q^39 - 8 * q^40 - 16 * q^41 - 2 * q^42 - 20 * q^43 + 6 * q^45 - 8 * q^46 + 2 * q^47 + 4 * q^49 - 24 * q^50 + 2 * q^51 + 40 * q^52 - 16 * q^53 + 2 * q^54 + 6 * q^57 - 8 * q^58 + 2 * q^59 - 8 * q^60 - 2 * q^61 - 8 * q^62 - 4 * q^63 - 16 * q^64 + 2 * q^65 - 20 * q^67 - 20 * q^68 - 10 * q^69 + 14 * q^70 - 10 * q^71 + 10 * q^73 + 20 * q^74 - 28 * q^76 - 16 * q^79 + 12 * q^80 + 4 * q^81 + 28 * q^82 - 18 * q^83 + 4 * q^84 + 26 * q^86 + 14 * q^87 - 14 * q^89 - 14 * q^90 - 2 * q^91 - 8 * q^92 + 18 * q^94 - 22 * q^95 + 12 * q^96 + 38 * q^97 - 2 * q^98

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