LMFDB - Embedded newform 2541.2.a.u.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:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{17}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 4 $ x^2 - x - 4
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			1.2
Root			$-1.56155$ 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)

$f(q)$	$=$	$q+1.56155 q^{2} +1.00000 q^{3} +0.438447 q^{4} +1.00000 q^{5} +1.56155 q^{6} -1.00000 q^{7} -2.43845 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.56155 q^{2} +1.00000 q^{3} +0.438447 q^{4} +1.00000 q^{5} +1.56155 q^{6} -1.00000 q^{7} -2.43845 q^{8} +1.00000 q^{9} +1.56155 q^{10} +0.438447 q^{12} -5.56155 q^{13} -1.56155 q^{14} +1.00000 q^{15} -4.68466 q^{16} -4.12311 q^{17} +1.56155 q^{18} -6.00000 q^{19} +0.438447 q^{20} -1.00000 q^{21} -4.00000 q^{23} -2.43845 q^{24} -4.00000 q^{25} -8.68466 q^{26} +1.00000 q^{27} -0.438447 q^{28} -6.68466 q^{29} +1.56155 q^{30} +8.24621 q^{31} -2.43845 q^{32} -6.43845 q^{34} -1.00000 q^{35} +0.438447 q^{36} -2.68466 q^{37} -9.36932 q^{38} -5.56155 q^{39} -2.43845 q^{40} +7.56155 q^{41} -1.56155 q^{42} +5.68466 q^{43} +1.00000 q^{45} -6.24621 q^{46} +3.43845 q^{47} -4.68466 q^{48} +1.00000 q^{49} -6.24621 q^{50} -4.12311 q^{51} -2.43845 q^{52} +7.80776 q^{53} +1.56155 q^{54} +2.43845 q^{56} -6.00000 q^{57} -10.4384 q^{58} -12.5616 q^{59} +0.438447 q^{60} +13.3693 q^{61} +12.8769 q^{62} -1.00000 q^{63} +5.56155 q^{64} -5.56155 q^{65} +8.80776 q^{67} -1.80776 q^{68} -4.00000 q^{69} -1.56155 q^{70} +3.12311 q^{71} -2.43845 q^{72} -7.12311 q^{73} -4.19224 q^{74} -4.00000 q^{75} -2.63068 q^{76} -8.68466 q^{78} -3.12311 q^{79} -4.68466 q^{80} +1.00000 q^{81} +11.8078 q^{82} +8.80776 q^{83} -0.438447 q^{84} -4.12311 q^{85} +8.87689 q^{86} -6.68466 q^{87} -11.2462 q^{89} +1.56155 q^{90} +5.56155 q^{91} -1.75379 q^{92} +8.24621 q^{93} +5.36932 q^{94} -6.00000 q^{95} -2.43845 q^{96} +1.31534 q^{97} +1.56155 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} + 2 q^{3} + 5 q^{4} + 2 q^{5} - q^{6} - 2 q^{7} - 9 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q - q^2 + 2 * q^3 + 5 * q^4 + 2 * q^5 - q^6 - 2 * q^7 - 9 * q^8 + 2 * q^9	$ 2 q - q^{2} + 2 q^{3} + 5 q^{4} + 2 q^{5} - q^{6} - 2 q^{7} - 9 q^{8} + 2 q^{9} - q^{10} + 5 q^{12} - 7 q^{13} + q^{14} + 2 q^{15} + 3 q^{16} - q^{18} - 12 q^{19} + 5 q^{20} - 2 q^{21} - 8 q^{23} - 9 q^{24} - 8 q^{25} - 5 q^{26} + 2 q^{27} - 5 q^{28} - q^{29} - q^{30} - 9 q^{32} - 17 q^{34} - 2 q^{35} + 5 q^{36} + 7 q^{37} + 6 q^{38} - 7 q^{39} - 9 q^{40} + 11 q^{41} + q^{42} - q^{43} + 2 q^{45} + 4 q^{46} + 11 q^{47} + 3 q^{48} + 2 q^{49} + 4 q^{50} - 9 q^{52} - 5 q^{53} - q^{54} + 9 q^{56} - 12 q^{57} - 25 q^{58} - 21 q^{59} + 5 q^{60} + 2 q^{61} + 34 q^{62} - 2 q^{63} + 7 q^{64} - 7 q^{65} - 3 q^{67} + 17 q^{68} - 8 q^{69} + q^{70} - 2 q^{71} - 9 q^{72} - 6 q^{73} - 29 q^{74} - 8 q^{75} - 30 q^{76} - 5 q^{78} + 2 q^{79} + 3 q^{80} + 2 q^{81} + 3 q^{82} - 3 q^{83} - 5 q^{84} + 26 q^{86} - q^{87} - 6 q^{89} - q^{90} + 7 q^{91} - 20 q^{92} - 14 q^{94} - 12 q^{95} - 9 q^{96} + 15 q^{97} - q^{98}+O(q^{100}) $ 2 * q - q^2 + 2 * q^3 + 5 * q^4 + 2 * q^5 - q^6 - 2 * q^7 - 9 * q^8 + 2 * q^9 - q^10 + 5 * q^12 - 7 * q^13 + q^14 + 2 * q^15 + 3 * q^16 - q^18 - 12 * q^19 + 5 * q^20 - 2 * q^21 - 8 * q^23 - 9 * q^24 - 8 * q^25 - 5 * q^26 + 2 * q^27 - 5 * q^28 - q^29 - q^30 - 9 * q^32 - 17 * q^34 - 2 * q^35 + 5 * q^36 + 7 * q^37 + 6 * q^38 - 7 * q^39 - 9 * q^40 + 11 * q^41 + q^42 - q^43 + 2 * q^45 + 4 * q^46 + 11 * q^47 + 3 * q^48 + 2 * q^49 + 4 * q^50 - 9 * q^52 - 5 * q^53 - q^54 + 9 * q^56 - 12 * q^57 - 25 * q^58 - 21 * q^59 + 5 * q^60 + 2 * q^61 + 34 * q^62 - 2 * q^63 + 7 * q^64 - 7 * q^65 - 3 * q^67 + 17 * q^68 - 8 * q^69 + q^70 - 2 * q^71 - 9 * q^72 - 6 * q^73 - 29 * q^74 - 8 * q^75 - 30 * q^76 - 5 * q^78 + 2 * q^79 + 3 * q^80 + 2 * q^81 + 3 * q^82 - 3 * q^83 - 5 * q^84 + 26 * q^86 - q^87 - 6 * q^89 - q^90 + 7 * q^91 - 20 * q^92 - 14 * q^94 - 12 * q^95 - 9 * q^96 + 15 * q^97 - q^98

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.56155	1.10418	0.552092	−	0.833783i	$-0.313830\pi$
$2$	1.56155	1.10418	0.552092	+	0.833783i	$0.313830\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	0.438447	0.219224
$5$	1.00000	0.447214	0.223607	−	0.974679i	$-0.428217\pi$
$5$	1.00000	0.447214	0.223607	+	0.974679i	$0.428217\pi$
$6$	1.56155	0.637501
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−2.43845	−0.862121
$9$	1.00000	0.333333
$10$	1.56155	0.493806
$11$	0	0
$11$	0	0
$12$	0.438447	0.126569
$13$	−5.56155	−1.54250	−0.771249	−	0.636534i	$-0.780367\pi$
$13$	−5.56155	−1.54250	−0.771249	+	0.636534i	$0.780367\pi$
$14$	−1.56155	−0.417343
$15$	1.00000	0.258199
$16$	−4.68466	−1.17116
$17$	−4.12311	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$17$	−4.12311	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$18$	1.56155	0.368062
$19$	−6.00000	−1.37649	−0.688247	−	0.725476i	$-0.741620\pi$
$19$	−6.00000	−1.37649	−0.688247	+	0.725476i	$0.741620\pi$
$20$	0.438447	0.0980398
$21$	−1.00000	−0.218218
$22$	0	0
$23$	−4.00000	−0.834058	−0.417029	−	0.908893i	$-0.636929\pi$
$23$	−4.00000	−0.834058	−0.417029	+	0.908893i	$0.636929\pi$
$24$	−2.43845	−0.497746
$25$	−4.00000	−0.800000
$26$	−8.68466	−1.70320
$27$	1.00000	0.192450
$28$	−0.438447	−0.0828587
$29$	−6.68466	−1.24131	−0.620655	−	0.784084i	$-0.713133\pi$
$29$	−6.68466	−1.24131	−0.620655	+	0.784084i	$0.713133\pi$
$30$	1.56155	0.285099
$31$	8.24621	1.48106	0.740532	−	0.672022i	$-0.234574\pi$
$31$	8.24621	1.48106	0.740532	+	0.672022i	$0.234574\pi$
$32$	−2.43845	−0.431061
$33$	0	0
$34$	−6.43845	−1.10418
$35$	−1.00000	−0.169031
$36$	0.438447	0.0730745
$37$	−2.68466	−0.441355	−0.220678	−	0.975347i	$-0.570827\pi$
$37$	−2.68466	−0.441355	−0.220678	+	0.975347i	$0.570827\pi$
$38$	−9.36932	−1.51990
$39$	−5.56155	−0.890561
$40$	−2.43845	−0.385552
$41$	7.56155	1.18092	0.590458	−	0.807068i	$-0.298947\pi$
$41$	7.56155	1.18092	0.590458	+	0.807068i	$0.298947\pi$
$42$	−1.56155	−0.240953
$43$	5.68466	0.866902	0.433451	−	0.901177i	$-0.357296\pi$
$43$	5.68466	0.866902	0.433451	+	0.901177i	$0.357296\pi$
$44$	0	0
$45$	1.00000	0.149071
$46$	−6.24621	−0.920954
$47$	3.43845	0.501549	0.250775	−	0.968046i	$-0.419315\pi$
$47$	3.43845	0.501549	0.250775	+	0.968046i	$0.419315\pi$
$48$	−4.68466	−0.676172
$49$	1.00000	0.142857
$50$	−6.24621	−0.883348
$51$	−4.12311	−0.577350
$52$	−2.43845	−0.338152
$53$	7.80776	1.07248	0.536239	−	0.844066i	$-0.319844\pi$
$53$	7.80776	1.07248	0.536239	+	0.844066i	$0.319844\pi$
$54$	1.56155	0.212500
$55$	0	0
$56$	2.43845	0.325851
$57$	−6.00000	−0.794719
$58$	−10.4384	−1.37064
$59$	−12.5616	−1.63537	−0.817687	−	0.575662i	$-0.804744\pi$
$59$	−12.5616	−1.63537	−0.817687	+	0.575662i	$0.804744\pi$
$60$	0.438447	0.0566033
$61$	13.3693	1.71177	0.855883	−	0.517170i	$-0.173014\pi$
$61$	13.3693	1.71177	0.855883	+	0.517170i	$0.173014\pi$
$62$	12.8769	1.63537
$63$	−1.00000	−0.125988
$64$	5.56155	0.695194
$65$	−5.56155	−0.689826
$66$	0	0
$67$	8.80776	1.07604	0.538020	−	0.842932i	$-0.319173\pi$
$67$	8.80776	1.07604	0.538020	+	0.842932i	$0.319173\pi$
$68$	−1.80776	−0.219224
$69$	−4.00000	−0.481543
$70$	−1.56155	−0.186641
$71$	3.12311	0.370644	0.185322	−	0.982678i	$-0.440667\pi$
$71$	3.12311	0.370644	0.185322	+	0.982678i	$0.440667\pi$
$72$	−2.43845	−0.287374
$73$	−7.12311	−0.833696	−0.416848	−	0.908976i	$-0.636865\pi$
$73$	−7.12311	−0.833696	−0.416848	+	0.908976i	$0.636865\pi$
$74$	−4.19224	−0.487338
$75$	−4.00000	−0.461880
$76$	−2.63068	−0.301760
$77$	0	0
$78$	−8.68466	−0.983344
$79$	−3.12311	−0.351377	−0.175688	−	0.984446i	$-0.556215\pi$
$79$	−3.12311	−0.351377	−0.175688	+	0.984446i	$0.556215\pi$
$80$	−4.68466	−0.523761
$81$	1.00000	0.111111
$82$	11.8078	1.30395
$83$	8.80776	0.966778	0.483389	−	0.875406i	$-0.339406\pi$
$83$	8.80776	0.966778	0.483389	+	0.875406i	$0.339406\pi$
$84$	−0.438447	−0.0478385
$85$	−4.12311	−0.447214
$86$	8.87689	0.957220
$87$	−6.68466	−0.716671
$88$	0	0
$89$	−11.2462	−1.19210	−0.596048	−	0.802949i	$-0.703263\pi$
$89$	−11.2462	−1.19210	−0.596048	+	0.802949i	$0.703263\pi$
$90$	1.56155	0.164602
$91$	5.56155	0.583009
$92$	−1.75379	−0.182845
$93$	8.24621	0.855092
$94$	5.36932	0.553803
$95$	−6.00000	−0.615587
$96$	−2.43845	−0.248873
$97$	1.31534	0.133553	0.0667764	−	0.997768i	$-0.478729\pi$
$97$	1.31534	0.133553	0.0667764	+	0.997768i	$0.478729\pi$
$98$	1.56155	0.157741
$99$	0	0
$100$	−1.75379	−0.175379
$101$	−4.56155	−0.453891	−0.226946	−	0.973907i	$-0.572874\pi$
$101$	−4.56155	−0.453891	−0.226946	+	0.973907i	$0.572874\pi$
$102$	−6.43845	−0.637501
$103$	−8.00000	−0.788263	−0.394132	−	0.919054i	$-0.628955\pi$
$103$	−8.00000	−0.788263	−0.394132	+	0.919054i	$0.628955\pi$
$104$	13.5616	1.32982
$105$	−1.00000	−0.0975900
$106$	12.1922	1.18421
$107$	3.12311	0.301922	0.150961	−	0.988540i	$-0.451763\pi$
$107$	3.12311	0.301922	0.150961	+	0.988540i	$0.451763\pi$
$108$	0.438447	0.0421896
$109$	−3.87689	−0.371339	−0.185670	−	0.982612i	$-0.559445\pi$
$109$	−3.87689	−0.371339	−0.185670	+	0.982612i	$0.559445\pi$
$110$	0	0
$111$	−2.68466	−0.254817
$112$	4.68466	0.442659
$113$	−8.93087	−0.840146	−0.420073	−	0.907490i	$-0.637995\pi$
$113$	−8.93087	−0.840146	−0.420073	+	0.907490i	$0.637995\pi$
$114$	−9.36932	−0.877517
$115$	−4.00000	−0.373002
$116$	−2.93087	−0.272124
$117$	−5.56155	−0.514166
$118$	−19.6155	−1.80576
$119$	4.12311	0.377964
$120$	−2.43845	−0.222599
$121$	0	0
$122$	20.8769	1.89011
$123$	7.56155	0.681802
$124$	3.61553	0.324684
$125$	−9.00000	−0.804984
$126$	−1.56155	−0.139114
$127$	−21.9309	−1.94605	−0.973025	−	0.230700i	$-0.925899\pi$
$127$	−21.9309	−1.94605	−0.973025	+	0.230700i	$0.925899\pi$
$128$	13.5616	1.19868
$129$	5.68466	0.500506
$130$	−8.68466	−0.761695
$131$	2.56155	0.223804	0.111902	−	0.993719i	$-0.464306\pi$
$131$	2.56155	0.223804	0.111902	+	0.993719i	$0.464306\pi$
$132$	0	0
$133$	6.00000	0.520266
$134$	13.7538	1.18815
$135$	1.00000	0.0860663
$136$	10.0540	0.862121
$137$	−14.0000	−1.19610	−0.598050	−	0.801459i	$-0.704058\pi$
$137$	−14.0000	−1.19610	−0.598050	+	0.801459i	$0.704058\pi$
$138$	−6.24621	−0.531713
$139$	−6.24621	−0.529797	−0.264898	−	0.964276i	$-0.585338\pi$
$139$	−6.24621	−0.529797	−0.264898	+	0.964276i	$0.585338\pi$
$140$	−0.438447	−0.0370556
$141$	3.43845	0.289569
$142$	4.87689	0.409260
$143$	0	0
$144$	−4.68466	−0.390388
$145$	−6.68466	−0.555131
$146$	−11.1231	−0.920555
$147$	1.00000	0.0824786
$148$	−1.17708	−0.0967555
$149$	5.31534	0.435450	0.217725	−	0.976010i	$-0.430136\pi$
$149$	5.31534	0.435450	0.217725	+	0.976010i	$0.430136\pi$
$150$	−6.24621	−0.510001
$151$	−11.4384	−0.930848	−0.465424	−	0.885088i	$-0.654098\pi$
$151$	−11.4384	−0.930848	−0.465424	+	0.885088i	$0.654098\pi$
$152$	14.6307	1.18671
$153$	−4.12311	−0.333333
$154$	0	0
$155$	8.24621	0.662352
$156$	−2.43845	−0.195232
$157$	−5.36932	−0.428518	−0.214259	−	0.976777i	$-0.568734\pi$
$157$	−5.36932	−0.428518	−0.214259	+	0.976777i	$0.568734\pi$
$158$	−4.87689	−0.387985
$159$	7.80776	0.619196
$160$	−2.43845	−0.192776
$161$	4.00000	0.315244
$162$	1.56155	0.122687
$163$	17.3693	1.36047	0.680235	−	0.732994i	$-0.261878\pi$
$163$	17.3693	1.36047	0.680235	+	0.732994i	$0.261878\pi$
$164$	3.31534	0.258885
$165$	0	0
$166$	13.7538	1.06750
$167$	12.8078	0.991095	0.495547	−	0.868581i	$-0.334968\pi$
$167$	12.8078	0.991095	0.495547	+	0.868581i	$0.334968\pi$
$168$	2.43845	0.188130
$169$	17.9309	1.37930
$170$	−6.43845	−0.493806
$171$	−6.00000	−0.458831
$172$	2.49242	0.190045
$173$	−12.5616	−0.955037	−0.477519	−	0.878622i	$-0.658464\pi$
$173$	−12.5616	−0.955037	−0.477519	+	0.878622i	$0.658464\pi$
$174$	−10.4384	−0.791337
$175$	4.00000	0.302372
$176$	0	0
$177$	−12.5616	−0.944184
$178$	−17.5616	−1.31629
$179$	−4.87689	−0.364516	−0.182258	−	0.983251i	$-0.558341\pi$
$179$	−4.87689	−0.364516	−0.182258	+	0.983251i	$0.558341\pi$
$180$	0.438447	0.0326799
$181$	−0.192236	−0.0142888	−0.00714439	−	0.999974i	$-0.502274\pi$
$181$	−0.192236	−0.0142888	−0.00714439	+	0.999974i	$0.502274\pi$
$182$	8.68466	0.643750
$183$	13.3693	0.988288
$184$	9.75379	0.719059
$185$	−2.68466	−0.197380
$186$	12.8769	0.944180
$187$	0	0
$188$	1.50758	0.109951
$189$	−1.00000	−0.0727393
$190$	−9.36932	−0.679722
$191$	−12.2462	−0.886105	−0.443052	−	0.896496i	$-0.646104\pi$
$191$	−12.2462	−0.886105	−0.443052	+	0.896496i	$0.646104\pi$
$192$	5.56155	0.401371
$193$	15.2462	1.09745	0.548723	−	0.836004i	$-0.315114\pi$
$193$	15.2462	1.09745	0.548723	+	0.836004i	$0.315114\pi$
$194$	2.05398	0.147467
$195$	−5.56155	−0.398271
$196$	0.438447	0.0313177
$197$	−27.1771	−1.93629	−0.968143	−	0.250396i	$-0.919439\pi$
$197$	−27.1771	−1.93629	−0.968143	+	0.250396i	$0.919439\pi$
$198$	0	0
$199$	−7.12311	−0.504944	−0.252472	−	0.967604i	$-0.581243\pi$
$199$	−7.12311	−0.504944	−0.252472	+	0.967604i	$0.581243\pi$
$200$	9.75379	0.689697
$201$	8.80776	0.621252
$202$	−7.12311	−0.501180
$203$	6.68466	0.469171
$204$	−1.80776	−0.126569
$205$	7.56155	0.528122
$206$	−12.4924	−0.870388
$207$	−4.00000	−0.278019
$208$	26.0540	1.80652
$209$	0	0
$210$	−1.56155	−0.107757
$211$	−27.0540	−1.86247	−0.931236	−	0.364416i	$-0.881269\pi$
$211$	−27.0540	−1.86247	−0.931236	+	0.364416i	$0.881269\pi$
$212$	3.42329	0.235113
$213$	3.12311	0.213992
$214$	4.87689	0.333378
$215$	5.68466	0.387690
$216$	−2.43845	−0.165915
$217$	−8.24621	−0.559789
$218$	−6.05398	−0.410027
$219$	−7.12311	−0.481335
$220$	0	0
$221$	22.9309	1.54250
$222$	−4.19224	−0.281364
$223$	24.0000	1.60716	0.803579	−	0.595198i	$-0.202926\pi$
$223$	24.0000	1.60716	0.803579	+	0.595198i	$0.202926\pi$
$224$	2.43845	0.162926
$225$	−4.00000	−0.266667
$226$	−13.9460	−0.927676
$227$	−5.68466	−0.377304	−0.188652	−	0.982044i	$-0.560412\pi$
$227$	−5.68466	−0.377304	−0.188652	+	0.982044i	$0.560412\pi$
$228$	−2.63068	−0.174221
$229$	−4.19224	−0.277031	−0.138515	−	0.990360i	$-0.544233\pi$
$229$	−4.19224	−0.277031	−0.138515	+	0.990360i	$0.544233\pi$
$230$	−6.24621	−0.411863
$231$	0	0
$232$	16.3002	1.07016
$233$	27.1771	1.78043	0.890215	−	0.455541i	$-0.150554\pi$
$233$	27.1771	1.78043	0.890215	+	0.455541i	$0.150554\pi$
$234$	−8.68466	−0.567734
$235$	3.43845	0.224300
$236$	−5.50758	−0.358513
$237$	−3.12311	−0.202868
$238$	6.43845	0.417343
$239$	19.3693	1.25290	0.626448	−	0.779463i	$-0.284508\pi$
$239$	19.3693	1.25290	0.626448	+	0.779463i	$0.284508\pi$
$240$	−4.68466	−0.302393
$241$	12.2462	0.788848	0.394424	−	0.918929i	$-0.370944\pi$
$241$	12.2462	0.788848	0.394424	+	0.918929i	$0.370944\pi$
$242$	0	0
$243$	1.00000	0.0641500
$244$	5.86174	0.375259
$245$	1.00000	0.0638877
$246$	11.8078	0.752836
$247$	33.3693	2.12324
$248$	−20.1080	−1.27686
$249$	8.80776	0.558169
$250$	−14.0540	−0.888851
$251$	4.00000	0.252478	0.126239	−	0.992000i	$-0.459709\pi$
$251$	4.00000	0.252478	0.126239	+	0.992000i	$0.459709\pi$
$252$	−0.438447	−0.0276196
$253$	0	0
$254$	−34.2462	−2.14880
$255$	−4.12311	−0.258199
$256$	10.0540	0.628373
$257$	23.0000	1.43470	0.717350	−	0.696713i	$-0.245355\pi$
$257$	23.0000	1.43470	0.717350	+	0.696713i	$0.245355\pi$
$258$	8.87689	0.552651
$259$	2.68466	0.166817
$260$	−2.43845	−0.151226
$261$	−6.68466	−0.413770
$262$	4.00000	0.247121
$263$	−30.7386	−1.89543	−0.947713	−	0.319125i	$-0.896611\pi$
$263$	−30.7386	−1.89543	−0.947713	+	0.319125i	$0.896611\pi$
$264$	0	0
$265$	7.80776	0.479627
$266$	9.36932	0.574470
$267$	−11.2462	−0.688257
$268$	3.86174	0.235893
$269$	−4.43845	−0.270617	−0.135308	−	0.990804i	$-0.543203\pi$
$269$	−4.43845	−0.270617	−0.135308	+	0.990804i	$0.543203\pi$
$270$	1.56155	0.0950331
$271$	0	0		−	1.00000i	$-0.5\pi$
$271$	0	0			1.00000i	$0.5\pi$
$272$	19.3153	1.17116
$273$	5.56155	0.336600
$274$	−21.8617	−1.32072
$275$	0	0
$276$	−1.75379	−0.105566
$277$	13.2462	0.795888	0.397944	−	0.917410i	$-0.369724\pi$
$277$	13.2462	0.795888	0.397944	+	0.917410i	$0.369724\pi$
$278$	−9.75379	−0.584993
$279$	8.24621	0.493688
$280$	2.43845	0.145725
$281$	−20.8769	−1.24541	−0.622706	−	0.782456i	$-0.713967\pi$
$281$	−20.8769	−1.24541	−0.622706	+	0.782456i	$0.713967\pi$
$282$	5.36932	0.319738
$283$	−15.1231	−0.898975	−0.449488	−	0.893287i	$-0.648393\pi$
$283$	−15.1231	−0.898975	−0.449488	+	0.893287i	$0.648393\pi$
$284$	1.36932	0.0812540
$285$	−6.00000	−0.355409
$286$	0	0
$287$	−7.56155	−0.446344
$288$	−2.43845	−0.143687
$289$	0	0
$290$	−10.4384	−0.612967
$291$	1.31534	0.0771067
$292$	−3.12311	−0.182766
$293$	22.3693	1.30683	0.653415	−	0.757000i	$-0.273336\pi$
$293$	22.3693	1.30683	0.653415	+	0.757000i	$0.273336\pi$
$294$	1.56155	0.0910716
$295$	−12.5616	−0.731362
$296$	6.54640	0.380502
$297$	0	0
$298$	8.30019	0.480817
$299$	22.2462	1.28653
$300$	−1.75379	−0.101255
$301$	−5.68466	−0.327658
$302$	−17.8617	−1.02783
$303$	−4.56155	−0.262054
$304$	28.1080	1.61210
$305$	13.3693	0.765525
$306$	−6.43845	−0.368062
$307$	−22.8769	−1.30565	−0.652827	−	0.757507i	$-0.726417\pi$
$307$	−22.8769	−1.30565	−0.652827	+	0.757507i	$0.726417\pi$
$308$	0	0
$309$	−8.00000	−0.455104
$310$	12.8769	0.731358
$311$	4.56155	0.258662	0.129331	−	0.991601i	$-0.458717\pi$
$311$	4.56155	0.258662	0.129331	+	0.991601i	$0.458717\pi$
$312$	13.5616	0.767772
$313$	2.43845	0.137829	0.0689146	−	0.997623i	$-0.478046\pi$
$313$	2.43845	0.137829	0.0689146	+	0.997623i	$0.478046\pi$
$314$	−8.38447	−0.473163
$315$	−1.00000	−0.0563436
$316$	−1.36932	−0.0770301
$317$	−27.1231	−1.52339	−0.761693	−	0.647938i	$-0.775631\pi$
$317$	−27.1231	−1.52339	−0.761693	+	0.647938i	$0.775631\pi$
$318$	12.1922	0.683707
$319$	0	0
$320$	5.56155	0.310900
$321$	3.12311	0.174315
$322$	6.24621	0.348088
$323$	24.7386	1.37649
$324$	0.438447	0.0243582
$325$	22.2462	1.23400
$326$	27.1231	1.50221
$327$	−3.87689	−0.214393
$328$	−18.4384	−1.01809
$329$	−3.43845	−0.189568
$330$	0	0
$331$	−17.6847	−0.972037	−0.486018	−	0.873949i	$-0.661551\pi$
$331$	−17.6847	−0.972037	−0.486018	+	0.873949i	$0.661551\pi$
$332$	3.86174	0.211940
$333$	−2.68466	−0.147118
$334$	20.0000	1.09435
$335$	8.80776	0.481220
$336$	4.68466	0.255569
$337$	−27.1771	−1.48043	−0.740215	−	0.672370i	$-0.765276\pi$
$337$	−27.1771	−1.48043	−0.740215	+	0.672370i	$0.765276\pi$
$338$	28.0000	1.52300
$339$	−8.93087	−0.485058
$340$	−1.80776	−0.0980398
$341$	0	0
$342$	−9.36932	−0.506635
$343$	−1.00000	−0.0539949
$344$	−13.8617	−0.747375
$345$	−4.00000	−0.215353
$346$	−19.6155	−1.05454
$347$	14.0000	0.751559	0.375780	−	0.926709i	$-0.377375\pi$
$347$	14.0000	0.751559	0.375780	+	0.926709i	$0.377375\pi$
$348$	−2.93087	−0.157111
$349$	8.05398	0.431119	0.215560	−	0.976491i	$-0.430842\pi$
$349$	8.05398	0.431119	0.215560	+	0.976491i	$0.430842\pi$
$350$	6.24621	0.333874
$351$	−5.56155	−0.296854
$352$	0	0
$353$	23.1771	1.23359	0.616796	−	0.787123i	$-0.288430\pi$
$353$	23.1771	1.23359	0.616796	+	0.787123i	$0.288430\pi$
$354$	−19.6155	−1.04255
$355$	3.12311	0.165757
$356$	−4.93087	−0.261336
$357$	4.12311	0.218218
$358$	−7.61553	−0.402493
$359$	−28.0000	−1.47778	−0.738892	−	0.673824i	$-0.764651\pi$
$359$	−28.0000	−1.47778	−0.738892	+	0.673824i	$0.764651\pi$
$360$	−2.43845	−0.128517
$361$	17.0000	0.894737
$362$	−0.300187	−0.0157775
$363$	0	0
$364$	2.43845	0.127809
$365$	−7.12311	−0.372840
$366$	20.8769	1.09125
$367$	14.4924	0.756498	0.378249	−	0.925704i	$-0.376526\pi$
$367$	14.4924	0.756498	0.378249	+	0.925704i	$0.376526\pi$
$368$	18.7386	0.976819
$369$	7.56155	0.393639
$370$	−4.19224	−0.217944
$371$	−7.80776	−0.405359
$372$	3.61553	0.187456
$373$	−6.80776	−0.352493	−0.176246	−	0.984346i	$-0.556396\pi$
$373$	−6.80776	−0.352493	−0.176246	+	0.984346i	$0.556396\pi$
$374$	0	0
$375$	−9.00000	−0.464758
$376$	−8.38447	−0.432396
$377$	37.1771	1.91472
$378$	−1.56155	−0.0803176
$379$	−14.5616	−0.747977	−0.373988	−	0.927433i	$-0.622010\pi$
$379$	−14.5616	−0.747977	−0.373988	+	0.927433i	$0.622010\pi$
$380$	−2.63068	−0.134951
$381$	−21.9309	−1.12355
$382$	−19.1231	−0.978423
$383$	17.4384	0.891063	0.445532	−	0.895266i	$-0.353015\pi$
$383$	17.4384	0.891063	0.445532	+	0.895266i	$0.353015\pi$
$384$	13.5616	0.692060
$385$	0	0
$386$	23.8078	1.21178
$387$	5.68466	0.288967
$388$	0.576708	0.0292779
$389$	17.5616	0.890406	0.445203	−	0.895430i	$-0.353132\pi$
$389$	17.5616	0.890406	0.445203	+	0.895430i	$0.353132\pi$
$390$	−8.68466	−0.439765
$391$	16.4924	0.834058
$392$	−2.43845	−0.123160
$393$	2.56155	0.129213
$394$	−42.4384	−2.13802
$395$	−3.12311	−0.157140
$396$	0	0
$397$	−13.3153	−0.668278	−0.334139	−	0.942524i	$-0.608445\pi$
$397$	−13.3153	−0.668278	−0.334139	+	0.942524i	$0.608445\pi$
$398$	−11.1231	−0.557551
$399$	6.00000	0.300376
$400$	18.7386	0.936932
$401$	−15.3153	−0.764812	−0.382406	−	0.923994i	$-0.624904\pi$
$401$	−15.3153	−0.764812	−0.382406	+	0.923994i	$0.624904\pi$
$402$	13.7538	0.685977
$403$	−45.8617	−2.28454
$404$	−2.00000	−0.0995037
$405$	1.00000	0.0496904
$406$	10.4384	0.518051
$407$	0	0
$408$	10.0540	0.497746
$409$	−34.3002	−1.69604	−0.848018	−	0.529968i	$-0.822204\pi$
$409$	−34.3002	−1.69604	−0.848018	+	0.529968i	$0.822204\pi$
$410$	11.8078	0.583144
$411$	−14.0000	−0.690569
$412$	−3.50758	−0.172806
$413$	12.5616	0.618114
$414$	−6.24621	−0.306985
$415$	8.80776	0.432356
$416$	13.5616	0.664910
$417$	−6.24621	−0.305878
$418$	0	0
$419$	−21.3002	−1.04058	−0.520291	−	0.853989i	$-0.674177\pi$
$419$	−21.3002	−1.04058	−0.520291	+	0.853989i	$0.674177\pi$
$420$	−0.438447	−0.0213940
$421$	−7.00000	−0.341159	−0.170580	−	0.985344i	$-0.554564\pi$
$421$	−7.00000	−0.341159	−0.170580	+	0.985344i	$0.554564\pi$
$422$	−42.2462	−2.05651
$423$	3.43845	0.167183
$424$	−19.0388	−0.924607
$425$	16.4924	0.800000
$426$	4.87689	0.236286
$427$	−13.3693	−0.646987
$428$	1.36932	0.0661884
$429$	0	0
$430$	8.87689	0.428082
$431$	−10.6307	−0.512062	−0.256031	−	0.966669i	$-0.582415\pi$
$431$	−10.6307	−0.512062	−0.256031	+	0.966669i	$0.582415\pi$
$432$	−4.68466	−0.225391
$433$	−12.9309	−0.621418	−0.310709	−	0.950505i	$-0.600566\pi$
$433$	−12.9309	−0.621418	−0.310709	+	0.950505i	$0.600566\pi$
$434$	−12.8769	−0.618111
$435$	−6.68466	−0.320505
$436$	−1.69981	−0.0814063
$437$	24.0000	1.14808
$438$	−11.1231	−0.531483
$439$	1.12311	0.0536029	0.0268015	−	0.999641i	$-0.491468\pi$
$439$	1.12311	0.0536029	0.0268015	+	0.999641i	$0.491468\pi$
$440$	0	0
$441$	1.00000	0.0476190
$442$	35.8078	1.70320
$443$	−8.49242	−0.403487	−0.201744	−	0.979438i	$-0.564661\pi$
$443$	−8.49242	−0.403487	−0.201744	+	0.979438i	$0.564661\pi$
$444$	−1.17708	−0.0558618
$445$	−11.2462	−0.533122
$446$	37.4773	1.77460
$447$	5.31534	0.251407
$448$	−5.56155	−0.262759
$449$	28.0540	1.32395	0.661974	−	0.749526i	$-0.269719\pi$
$449$	28.0540	1.32395	0.661974	+	0.749526i	$0.269719\pi$
$450$	−6.24621	−0.294449
$451$	0	0
$452$	−3.91571	−0.184180
$453$	−11.4384	−0.537425
$454$	−8.87689	−0.416613
$455$	5.56155	0.260730
$456$	14.6307	0.685145
$457$	10.6155	0.496573	0.248287	−	0.968687i	$-0.420132\pi$
$457$	10.6155	0.496573	0.248287	+	0.968687i	$0.420132\pi$
$458$	−6.54640	−0.305893
$459$	−4.12311	−0.192450
$460$	−1.75379	−0.0817708
$461$	10.3693	0.482947	0.241474	−	0.970407i	$-0.422369\pi$
$461$	10.3693	0.482947	0.241474	+	0.970407i	$0.422369\pi$
$462$	0	0
$463$	0.876894	0.0407527	0.0203764	−	0.999792i	$-0.493514\pi$
$463$	0.876894	0.0407527	0.0203764	+	0.999792i	$0.493514\pi$
$464$	31.3153	1.45378
$465$	8.24621	0.382409
$466$	42.4384	1.96592
$467$	−21.7538	−1.00665	−0.503323	−	0.864099i	$-0.667889\pi$
$467$	−21.7538	−1.00665	−0.503323	+	0.864099i	$0.667889\pi$
$468$	−2.43845	−0.112717
$469$	−8.80776	−0.406705
$470$	5.36932	0.247668
$471$	−5.36932	−0.247405
$472$	30.6307	1.40989
$473$	0	0
$474$	−4.87689	−0.224003
$475$	24.0000	1.10120
$476$	1.80776	0.0828587
$477$	7.80776	0.357493
$478$	30.2462	1.38343
$479$	29.6847	1.35633	0.678163	−	0.734911i	$-0.262776\pi$
$479$	29.6847	1.35633	0.678163	+	0.734911i	$0.262776\pi$
$480$	−2.43845	−0.111299
$481$	14.9309	0.680789
$482$	19.1231	0.871034
$483$	4.00000	0.182006
$484$	0	0
$485$	1.31534	0.0597266
$486$	1.56155	0.0708335
$487$	19.4384	0.880840	0.440420	−	0.897792i	$-0.354830\pi$
$487$	19.4384	0.880840	0.440420	+	0.897792i	$0.354830\pi$
$488$	−32.6004	−1.47575
$489$	17.3693	0.785468
$490$	1.56155	0.0705438
$491$	−20.0000	−0.902587	−0.451294	−	0.892375i	$-0.649037\pi$
$491$	−20.0000	−0.902587	−0.451294	+	0.892375i	$0.649037\pi$
$492$	3.31534	0.149467
$493$	27.5616	1.24131
$494$	52.1080	2.34445
$495$	0	0
$496$	−38.6307	−1.73457
$497$	−3.12311	−0.140090
$498$	13.7538	0.616322
$499$	−39.5464	−1.77034	−0.885170	−	0.465268i	$-0.845958\pi$
$499$	−39.5464	−1.77034	−0.885170	+	0.465268i	$0.845958\pi$
$500$	−3.94602	−0.176472
$501$	12.8078	0.572209
$502$	6.24621	0.278782
$503$	19.6847	0.877696	0.438848	−	0.898561i	$-0.355387\pi$
$503$	19.6847	0.877696	0.438848	+	0.898561i	$0.355387\pi$
$504$	2.43845	0.108617
$505$	−4.56155	−0.202986
$506$	0	0
$507$	17.9309	0.796338
$508$	−9.61553	−0.426620
$509$	25.6847	1.13845	0.569226	−	0.822181i	$-0.307243\pi$
$509$	25.6847	1.13845	0.569226	+	0.822181i	$0.307243\pi$
$510$	−6.43845	−0.285099
$511$	7.12311	0.315108
$512$	−11.4233	−0.504843
$513$	−6.00000	−0.264906
$514$	35.9157	1.58417
$515$	−8.00000	−0.352522
$516$	2.49242	0.109723
$517$	0	0
$518$	4.19224	0.184196
$519$	−12.5616	−0.551391
$520$	13.5616	0.594713
$521$	43.9309	1.92465	0.962323	−	0.271908i	$-0.0876547\pi$
$521$	43.9309	1.92465	0.962323	+	0.271908i	$0.0876547\pi$
$522$	−10.4384	−0.456878
$523$	25.1231	1.09856	0.549278	−	0.835639i	$-0.314903\pi$
$523$	25.1231	1.09856	0.549278	+	0.835639i	$0.314903\pi$
$524$	1.12311	0.0490631
$525$	4.00000	0.174574
$526$	−48.0000	−2.09290
$527$	−34.0000	−1.48106
$528$	0	0
$529$	−7.00000	−0.304348
$530$	12.1922	0.529597
$531$	−12.5616	−0.545125
$532$	2.63068	0.114055
$533$	−42.0540	−1.82156
$534$	−17.5616	−0.759963
$535$	3.12311	0.135024
$536$	−21.4773	−0.927677
$537$	−4.87689	−0.210454
$538$	−6.93087	−0.298811
$539$	0	0
$540$	0.438447	0.0188678
$541$	−11.9309	−0.512948	−0.256474	−	0.966551i	$-0.582561\pi$
$541$	−11.9309	−0.512948	−0.256474	+	0.966551i	$0.582561\pi$
$542$	0	0
$543$	−0.192236	−0.00824963
$544$	10.0540	0.431061
$545$	−3.87689	−0.166068
$546$	8.68466	0.371669
$547$	21.3693	0.913686	0.456843	−	0.889547i	$-0.348980\pi$
$547$	21.3693	0.913686	0.456843	+	0.889547i	$0.348980\pi$
$548$	−6.13826	−0.262213
$549$	13.3693	0.570589
$550$	0	0
$551$	40.1080	1.70866
$552$	9.75379	0.415149
$553$	3.12311	0.132808
$554$	20.6847	0.878807
$555$	−2.68466	−0.113957
$556$	−2.73863	−0.116144
$557$	42.4924	1.80046	0.900231	−	0.435413i	$-0.143398\pi$
$557$	42.4924	1.80046	0.900231	+	0.435413i	$0.143398\pi$
$558$	12.8769	0.545122
$559$	−31.6155	−1.33719
$560$	4.68466	0.197963
$561$	0	0
$562$	−32.6004	−1.37516
$563$	−6.80776	−0.286913	−0.143457	−	0.989657i	$-0.545822\pi$
$563$	−6.80776	−0.286913	−0.143457	+	0.989657i	$0.545822\pi$
$564$	1.50758	0.0634805
$565$	−8.93087	−0.375725
$566$	−23.6155	−0.992635
$567$	−1.00000	−0.0419961
$568$	−7.61553	−0.319540
$569$	6.00000	0.251533	0.125767	−	0.992060i	$-0.459861\pi$
$569$	6.00000	0.251533	0.125767	+	0.992060i	$0.459861\pi$
$570$	−9.36932	−0.392437
$571$	10.2462	0.428791	0.214395	−	0.976747i	$-0.431222\pi$
$571$	10.2462	0.428791	0.214395	+	0.976747i	$0.431222\pi$
$572$	0	0
$573$	−12.2462	−0.511593
$574$	−11.8078	−0.492847
$575$	16.0000	0.667246
$576$	5.56155	0.231731
$577$	−27.8078	−1.15765	−0.578826	−	0.815451i	$-0.696489\pi$
$577$	−27.8078	−1.15765	−0.578826	+	0.815451i	$0.696489\pi$
$578$	0	0
$579$	15.2462	0.633611
$580$	−2.93087	−0.121698
$581$	−8.80776	−0.365408
$582$	2.05398	0.0851400
$583$	0	0
$584$	17.3693	0.718747
$585$	−5.56155	−0.229942
$586$	34.9309	1.44298
$587$	−3.43845	−0.141920	−0.0709600	−	0.997479i	$-0.522606\pi$
$587$	−3.43845	−0.141920	−0.0709600	+	0.997479i	$0.522606\pi$
$588$	0.438447	0.0180813
$589$	−49.4773	−2.03868
$590$	−19.6155	−0.807559
$591$	−27.1771	−1.11792
$592$	12.5767	0.516900
$593$	44.3693	1.82203	0.911015	−	0.412374i	$-0.135300\pi$
$593$	44.3693	1.82203	0.911015	+	0.412374i	$0.135300\pi$
$594$	0	0
$595$	4.12311	0.169031
$596$	2.33050	0.0954609
$597$	−7.12311	−0.291529
$598$	34.7386	1.42057
$599$	−41.2311	−1.68466	−0.842328	−	0.538966i	$-0.818815\pi$
$599$	−41.2311	−1.68466	−0.842328	+	0.538966i	$0.818815\pi$
$600$	9.75379	0.398197
$601$	−4.68466	−0.191091	−0.0955456	−	0.995425i	$-0.530460\pi$
$601$	−4.68466	−0.191091	−0.0955456	+	0.995425i	$0.530460\pi$
$602$	−8.87689	−0.361795
$603$	8.80776	0.358680
$604$	−5.01515	−0.204064
$605$	0	0
$606$	−7.12311	−0.289356
$607$	14.2462	0.578236	0.289118	−	0.957293i	$-0.406638\pi$
$607$	14.2462	0.578236	0.289118	+	0.957293i	$0.406638\pi$
$608$	14.6307	0.593353
$609$	6.68466	0.270876
$610$	20.8769	0.845281
$611$	−19.1231	−0.773638
$612$	−1.80776	−0.0730745
$613$	27.4924	1.11041	0.555204	−	0.831714i	$-0.312640\pi$
$613$	27.4924	1.11041	0.555204	+	0.831714i	$0.312640\pi$
$614$	−35.7235	−1.44168
$615$	7.56155	0.304911
$616$	0	0
$617$	−47.1771	−1.89928	−0.949639	−	0.313346i	$-0.898550\pi$
$617$	−47.1771	−1.89928	−0.949639	+	0.313346i	$0.898550\pi$
$618$	−12.4924	−0.502519
$619$	−46.4924	−1.86869	−0.934344	−	0.356372i	$-0.884014\pi$
$619$	−46.4924	−1.86869	−0.934344	+	0.356372i	$0.884014\pi$
$620$	3.61553	0.145203
$621$	−4.00000	−0.160514
$622$	7.12311	0.285611
$623$	11.2462	0.450570
$624$	26.0540	1.04299
$625$	11.0000	0.440000
$626$	3.80776	0.152189
$627$	0	0
$628$	−2.35416	−0.0939413
$629$	11.0691	0.441355
$630$	−1.56155	−0.0622138
$631$	−47.9309	−1.90810	−0.954049	−	0.299651i	$-0.903130\pi$
$631$	−47.9309	−1.90810	−0.954049	+	0.299651i	$0.903130\pi$
$632$	7.61553	0.302929
$633$	−27.0540	−1.07530
$634$	−42.3542	−1.68210
$635$	−21.9309	−0.870300
$636$	3.42329	0.135742
$637$	−5.56155	−0.220357
$638$	0	0
$639$	3.12311	0.123548
$640$	13.5616	0.536067
$641$	−14.6847	−0.580009	−0.290005	−	0.957025i	$-0.593657\pi$
$641$	−14.6847	−0.580009	−0.290005	+	0.957025i	$0.593657\pi$
$642$	4.87689	0.192476
$643$	−10.7386	−0.423490	−0.211745	−	0.977325i	$-0.567915\pi$
$643$	−10.7386	−0.423490	−0.211745	+	0.977325i	$0.567915\pi$
$644$	1.75379	0.0691090
$645$	5.68466	0.223833
$646$	38.6307	1.51990
$647$	13.9309	0.547679	0.273840	−	0.961775i	$-0.411706\pi$
$647$	13.9309	0.547679	0.273840	+	0.961775i	$0.411706\pi$
$648$	−2.43845	−0.0957913
$649$	0	0
$650$	34.7386	1.36256
$651$	−8.24621	−0.323195
$652$	7.61553	0.298247
$653$	8.24621	0.322699	0.161350	−	0.986897i	$-0.448415\pi$
$653$	8.24621	0.322699	0.161350	+	0.986897i	$0.448415\pi$
$654$	−6.05398	−0.236729
$655$	2.56155	0.100088
$656$	−35.4233	−1.38305
$657$	−7.12311	−0.277899
$658$	−5.36932	−0.209318
$659$	10.0000	0.389545	0.194772	−	0.980848i	$-0.437603\pi$
$659$	10.0000	0.389545	0.194772	+	0.980848i	$0.437603\pi$
$660$	0	0
$661$	−31.4233	−1.22222	−0.611112	−	0.791544i	$-0.709278\pi$
$661$	−31.4233	−1.22222	−0.611112	+	0.791544i	$0.709278\pi$
$662$	−27.6155	−1.07331
$663$	22.9309	0.890561
$664$	−21.4773	−0.833480
$665$	6.00000	0.232670
$666$	−4.19224	−0.162446
$667$	26.7386	1.03532
$668$	5.61553	0.217271
$669$	24.0000	0.927894
$670$	13.7538	0.531355
$671$	0	0
$672$	2.43845	0.0940651
$673$	−27.9309	−1.07666	−0.538328	−	0.842735i	$-0.680944\pi$
$673$	−27.9309	−1.07666	−0.538328	+	0.842735i	$0.680944\pi$
$674$	−42.4384	−1.63467
$675$	−4.00000	−0.153960
$676$	7.86174	0.302375
$677$	22.8617	0.878648	0.439324	−	0.898329i	$-0.355218\pi$
$677$	22.8617	0.878648	0.439324	+	0.898329i	$0.355218\pi$
$678$	−13.9460	−0.535594
$679$	−1.31534	−0.0504782
$680$	10.0540	0.385552
$681$	−5.68466	−0.217837
$682$	0	0
$683$	13.6155	0.520984	0.260492	−	0.965476i	$-0.416115\pi$
$683$	13.6155	0.520984	0.260492	+	0.965476i	$0.416115\pi$
$684$	−2.63068	−0.100587
$685$	−14.0000	−0.534913
$686$	−1.56155	−0.0596204
$687$	−4.19224	−0.159944
$688$	−26.6307	−1.01529
$689$	−43.4233	−1.65430
$690$	−6.24621	−0.237789
$691$	36.1080	1.37361	0.686806	−	0.726841i	$-0.259012\pi$
$691$	36.1080	1.37361	0.686806	+	0.726841i	$0.259012\pi$
$692$	−5.50758	−0.209367
$693$	0	0
$694$	21.8617	0.829860
$695$	−6.24621	−0.236932
$696$	16.3002	0.617857
$697$	−31.1771	−1.18092
$698$	12.5767	0.476035
$699$	27.1771	1.02793
$700$	1.75379	0.0662870
$701$	−7.17708	−0.271075	−0.135537	−	0.990772i	$-0.543276\pi$
$701$	−7.17708	−0.271075	−0.135537	+	0.990772i	$0.543276\pi$
$702$	−8.68466	−0.327781
$703$	16.1080	0.607523
$704$	0	0
$705$	3.43845	0.129499
$706$	36.1922	1.36211
$707$	4.56155	0.171555
$708$	−5.50758	−0.206987
$709$	−35.9309	−1.34941	−0.674706	−	0.738087i	$-0.735730\pi$
$709$	−35.9309	−1.34941	−0.674706	+	0.738087i	$0.735730\pi$
$710$	4.87689	0.183027
$711$	−3.12311	−0.117126
$712$	27.4233	1.02773
$713$	−32.9848	−1.23529
$714$	6.43845	0.240953
$715$	0	0
$716$	−2.13826	−0.0799106
$717$	19.3693	0.723360
$718$	−43.7235	−1.63175
$719$	−21.8617	−0.815305	−0.407653	−	0.913137i	$-0.633653\pi$
$719$	−21.8617	−0.815305	−0.407653	+	0.913137i	$0.633653\pi$
$720$	−4.68466	−0.174587
$721$	8.00000	0.297936
$722$	26.5464	0.987955
$723$	12.2462	0.455441
$724$	−0.0842853	−0.00313244
$725$	26.7386	0.993048
$726$	0	0
$727$	−49.2311	−1.82588	−0.912939	−	0.408095i	$-0.866193\pi$
$727$	−49.2311	−1.82588	−0.912939	+	0.408095i	$0.866193\pi$
$728$	−13.5616	−0.502625
$729$	1.00000	0.0370370
$730$	−11.1231	−0.411685
$731$	−23.4384	−0.866902
$732$	5.86174	0.216656
$733$	34.4384	1.27201	0.636007	−	0.771684i	$-0.280585\pi$
$733$	34.4384	1.27201	0.636007	+	0.771684i	$0.280585\pi$
$734$	22.6307	0.835314
$735$	1.00000	0.0368856
$736$	9.75379	0.359529
$737$	0	0
$738$	11.8078	0.434650
$739$	−8.38447	−0.308428	−0.154214	−	0.988037i	$-0.549284\pi$
$739$	−8.38447	−0.308428	−0.154214	+	0.988037i	$0.549284\pi$
$740$	−1.17708	−0.0432704
$741$	33.3693	1.22585
$742$	−12.1922	−0.447591
$743$	32.8769	1.20614	0.603068	−	0.797690i	$-0.293945\pi$
$743$	32.8769	1.20614	0.603068	+	0.797690i	$0.293945\pi$
$744$	−20.1080	−0.737193
$745$	5.31534	0.194739
$746$	−10.6307	−0.389217
$747$	8.80776	0.322259
$748$	0	0
$749$	−3.12311	−0.114116
$750$	−14.0540	−0.513179
$751$	12.5616	0.458378	0.229189	−	0.973382i	$-0.426393\pi$
$751$	12.5616	0.458378	0.229189	+	0.973382i	$0.426393\pi$
$752$	−16.1080	−0.587397
$753$	4.00000	0.145768
$754$	58.0540	2.11420
$755$	−11.4384	−0.416288
$756$	−0.438447	−0.0159462
$757$	−0.615528	−0.0223718	−0.0111859	−	0.999937i	$-0.503561\pi$
$757$	−0.615528	−0.0223718	−0.0111859	+	0.999937i	$0.503561\pi$
$758$	−22.7386	−0.825904
$759$	0	0
$760$	14.6307	0.530711
$761$	13.9848	0.506950	0.253475	−	0.967342i	$-0.418426\pi$
$761$	13.9848	0.506950	0.253475	+	0.967342i	$0.418426\pi$
$762$	−34.2462	−1.24061
$763$	3.87689	0.140353
$764$	−5.36932	−0.194255
$765$	−4.12311	−0.149071
$766$	27.2311	0.983898
$767$	69.8617	2.52256
$768$	10.0540	0.362792
$769$	20.3002	0.732043	0.366022	−	0.930606i	$-0.380720\pi$
$769$	20.3002	0.732043	0.366022	+	0.930606i	$0.380720\pi$
$770$	0	0
$771$	23.0000	0.828325
$772$	6.68466	0.240586
$773$	29.5464	1.06271	0.531355	−	0.847149i	$-0.321683\pi$
$773$	29.5464	1.06271	0.531355	+	0.847149i	$0.321683\pi$
$774$	8.87689	0.319073
$775$	−32.9848	−1.18485
$776$	−3.20739	−0.115139
$777$	2.68466	0.0963116
$778$	27.4233	0.983173
$779$	−45.3693	−1.62552
$780$	−2.43845	−0.0873104
$781$	0	0
$782$	25.7538	0.920954
$783$	−6.68466	−0.238890
$784$	−4.68466	−0.167309
$785$	−5.36932	−0.191639
$786$	4.00000	0.142675
$787$	−37.1231	−1.32330	−0.661648	−	0.749815i	$-0.730143\pi$
$787$	−37.1231	−1.32330	−0.661648	+	0.749815i	$0.730143\pi$
$788$	−11.9157	−0.424480
$789$	−30.7386	−1.09432
$790$	−4.87689	−0.173512
$791$	8.93087	0.317545
$792$	0	0
$793$	−74.3542	−2.64039
$794$	−20.7926	−0.737902
$795$	7.80776	0.276913
$796$	−3.12311	−0.110696
$797$	39.3002	1.39208	0.696042	−	0.718001i	$-0.254943\pi$
$797$	39.3002	1.39208	0.696042	+	0.718001i	$0.254943\pi$
$798$	9.36932	0.331670
$799$	−14.1771	−0.501549
$800$	9.75379	0.344849
$801$	−11.2462	−0.397365
$802$	−23.9157	−0.844493
$803$	0	0
$804$	3.86174	0.136193
$805$	4.00000	0.140981
$806$	−71.6155	−2.52255
$807$	−4.43845	−0.156241
$808$	11.1231	0.391309
$809$	−45.8617	−1.61241	−0.806206	−	0.591634i	$-0.798483\pi$
$809$	−45.8617	−1.61241	−0.806206	+	0.591634i	$0.798483\pi$
$810$	1.56155	0.0548674
$811$	−22.0000	−0.772524	−0.386262	−	0.922389i	$-0.626234\pi$
$811$	−22.0000	−0.772524	−0.386262	+	0.922389i	$0.626234\pi$
$812$	2.93087	0.102853
$813$	0	0
$814$	0	0
$815$	17.3693	0.608421
$816$	19.3153	0.676172
$817$	−34.1080	−1.19329
$818$	−53.5616	−1.87274
$819$	5.56155	0.194336
$820$	3.31534	0.115777
$821$	1.50758	0.0526148	0.0263074	−	0.999654i	$-0.491625\pi$
$821$	1.50758	0.0526148	0.0263074	+	0.999654i	$0.491625\pi$
$822$	−21.8617	−0.762516
$823$	−38.2462	−1.33318	−0.666590	−	0.745425i	$-0.732247\pi$
$823$	−38.2462	−1.33318	−0.666590	+	0.745425i	$0.732247\pi$
$824$	19.5076	0.679579
$825$	0	0
$826$	19.6155	0.682512
$827$	39.1231	1.36044	0.680222	−	0.733006i	$-0.261883\pi$
$827$	39.1231	1.36044	0.680222	+	0.733006i	$0.261883\pi$
$828$	−1.75379	−0.0609484
$829$	47.8078	1.66043	0.830216	−	0.557442i	$-0.188217\pi$
$829$	47.8078	1.66043	0.830216	+	0.557442i	$0.188217\pi$
$830$	13.7538	0.477401
$831$	13.2462	0.459506
$832$	−30.9309	−1.07233
$833$	−4.12311	−0.142857
$834$	−9.75379	−0.337746
$835$	12.8078	0.443231
$836$	0	0
$837$	8.24621	0.285031
$838$	−33.2614	−1.14899
$839$	57.0540	1.96972	0.984861	−	0.173346i	$-0.0554579\pi$
$839$	57.0540	1.96972	0.984861	+	0.173346i	$0.0554579\pi$
$840$	2.43845	0.0841344
$841$	15.6847	0.540850
$842$	−10.9309	−0.376703
$843$	−20.8769	−0.719038
$844$	−11.8617	−0.408298
$845$	17.9309	0.616841
$846$	5.36932	0.184601
$847$	0	0
$848$	−36.5767	−1.25605
$849$	−15.1231	−0.519024
$850$	25.7538	0.883348
$851$	10.7386	0.368116
$852$	1.36932	0.0469120
$853$	−52.7926	−1.80758	−0.903792	−	0.427971i	$-0.859228\pi$
$853$	−52.7926	−1.80758	−0.903792	+	0.427971i	$0.859228\pi$
$854$	−20.8769	−0.714393
$855$	−6.00000	−0.205196
$856$	−7.61553	−0.260293
$857$	9.19224	0.314001	0.157000	−	0.987599i	$-0.449818\pi$
$857$	9.19224	0.314001	0.157000	+	0.987599i	$0.449818\pi$
$858$	0	0
$859$	16.6307	0.567432	0.283716	−	0.958908i	$-0.408433\pi$
$859$	16.6307	0.567432	0.283716	+	0.958908i	$0.408433\pi$
$860$	2.49242	0.0849909
$861$	−7.56155	−0.257697
$862$	−16.6004	−0.565411
$863$	36.2462	1.23384	0.616918	−	0.787028i	$-0.288381\pi$
$863$	36.2462	1.23384	0.616918	+	0.787028i	$0.288381\pi$
$864$	−2.43845	−0.0829577
$865$	−12.5616	−0.427106
$866$	−20.1922	−0.686160
$867$	0	0
$868$	−3.61553	−0.122719
$869$	0	0
$870$	−10.4384	−0.353897
$871$	−48.9848	−1.65979
$872$	9.45360	0.320139
$873$	1.31534	0.0445176
$874$	37.4773	1.26769
$875$	9.00000	0.304256
$876$	−3.12311	−0.105520
$877$	53.4233	1.80398	0.901988	−	0.431761i	$-0.142107\pi$
$877$	53.4233	1.80398	0.901988	+	0.431761i	$0.142107\pi$
$878$	1.75379	0.0591875
$879$	22.3693	0.754498
$880$	0	0
$881$	−19.0691	−0.642455	−0.321228	−	0.947002i	$-0.604095\pi$
$881$	−19.0691	−0.642455	−0.321228	+	0.947002i	$0.604095\pi$
$882$	1.56155	0.0525802
$883$	−2.17708	−0.0732646	−0.0366323	−	0.999329i	$-0.511663\pi$
$883$	−2.17708	−0.0732646	−0.0366323	+	0.999329i	$0.511663\pi$
$884$	10.0540	0.338152
$885$	−12.5616	−0.422252
$886$	−13.2614	−0.445524
$887$	−7.19224	−0.241492	−0.120746	−	0.992683i	$-0.538529\pi$
$887$	−7.19224	−0.241492	−0.120746	+	0.992683i	$0.538529\pi$
$888$	6.54640	0.219683
$889$	21.9309	0.735538
$890$	−17.5616	−0.588665
$891$	0	0
$892$	10.5227	0.352327
$893$	−20.6307	−0.690379
$894$	8.30019	0.277600
$895$	−4.87689	−0.163017
$896$	−13.5616	−0.453060
$897$	22.2462	0.742779
$898$	43.8078	1.46188
$899$	−55.1231	−1.83846
$900$	−1.75379	−0.0584596
$901$	−32.1922	−1.07248
$902$	0	0
$903$	−5.68466	−0.189174
$904$	21.7775	0.724307
$905$	−0.192236	−0.00639014
$906$	−17.8617	−0.593417
$907$	18.6307	0.618622	0.309311	−	0.950961i	$-0.399902\pi$
$907$	18.6307	0.618622	0.309311	+	0.950961i	$0.399902\pi$
$908$	−2.49242	−0.0827139
$909$	−4.56155	−0.151297
$910$	8.68466	0.287894
$911$	−19.3693	−0.641734	−0.320867	−	0.947124i	$-0.603974\pi$
$911$	−19.3693	−0.641734	−0.320867	+	0.947124i	$0.603974\pi$
$912$	28.1080	0.930747
$913$	0	0
$914$	16.5767	0.548309
$915$	13.3693	0.441976
$916$	−1.83807	−0.0607317
$917$	−2.56155	−0.0845899
$918$	−6.43845	−0.212500
$919$	−11.6155	−0.383161	−0.191580	−	0.981477i	$-0.561361\pi$
$919$	−11.6155	−0.383161	−0.191580	+	0.981477i	$0.561361\pi$
$920$	9.75379	0.321573
$921$	−22.8769	−0.753819
$922$	16.1922	0.533263
$923$	−17.3693	−0.571718
$924$	0	0
$925$	10.7386	0.353084
$926$	1.36932	0.0449985
$927$	−8.00000	−0.262754
$928$	16.3002	0.535080
$929$	2.50758	0.0822709	0.0411355	−	0.999154i	$-0.486902\pi$
$929$	2.50758	0.0822709	0.0411355	+	0.999154i	$0.486902\pi$
$930$	12.8769	0.422250
$931$	−6.00000	−0.196642
$932$	11.9157	0.390312
$933$	4.56155	0.149339
$934$	−33.9697	−1.11152
$935$	0	0
$936$	13.5616	0.443273
$937$	4.93087	0.161084	0.0805422	−	0.996751i	$-0.474335\pi$
$937$	4.93087	0.161084	0.0805422	+	0.996751i	$0.474335\pi$
$938$	−13.7538	−0.449077
$939$	2.43845	0.0795757
$940$	1.50758	0.0491718
$941$	28.4384	0.927067	0.463533	−	0.886079i	$-0.346581\pi$
$941$	28.4384	0.927067	0.463533	+	0.886079i	$0.346581\pi$
$942$	−8.38447	−0.273181
$943$	−30.2462	−0.984952
$944$	58.8466	1.91529
$945$	−1.00000	−0.0325300
$946$	0	0
$947$	2.00000	0.0649913	0.0324956	−	0.999472i	$-0.489654\pi$
$947$	2.00000	0.0649913	0.0324956	+	0.999472i	$0.489654\pi$
$948$	−1.36932	−0.0444733
$949$	39.6155	1.28597
$950$	37.4773	1.21592
$951$	−27.1231	−0.879527
$952$	−10.0540	−0.325851
$953$	43.6695	1.41459	0.707297	−	0.706917i	$-0.249914\pi$
$953$	43.6695	1.41459	0.707297	+	0.706917i	$0.249914\pi$
$954$	12.1922	0.394738
$955$	−12.2462	−0.396278
$956$	8.49242	0.274665
$957$	0	0
$958$	46.3542	1.49763
$959$	14.0000	0.452084
$960$	5.56155	0.179498
$961$	37.0000	1.19355
$962$	23.3153	0.751717
$963$	3.12311	0.100641
$964$	5.36932	0.172934
$965$	15.2462	0.490793
$966$	6.24621	0.200969
$967$	−19.3002	−0.620652	−0.310326	−	0.950630i	$-0.600438\pi$
$967$	−19.3002	−0.620652	−0.310326	+	0.950630i	$0.600438\pi$
$968$	0	0
$969$	24.7386	0.794719
$970$	2.05398	0.0659492
$971$	16.3153	0.523584	0.261792	−	0.965124i	$-0.415687\pi$
$971$	16.3153	0.523584	0.261792	+	0.965124i	$0.415687\pi$
$972$	0.438447	0.0140632
$973$	6.24621	0.200244
$974$	30.3542	0.972610
$975$	22.2462	0.712449
$976$	−62.6307	−2.00476
$977$	57.6695	1.84501	0.922505	−	0.385984i	$-0.126138\pi$
$977$	57.6695	1.84501	0.922505	+	0.385984i	$0.126138\pi$
$978$	27.1231	0.867301
$979$	0	0
$980$	0.438447	0.0140057
$981$	−3.87689	−0.123780
$982$	−31.2311	−0.996623
$983$	−6.63068	−0.211486	−0.105743	−	0.994393i	$-0.533722\pi$
$983$	−6.63068	−0.211486	−0.105743	+	0.994393i	$0.533722\pi$
$984$	−18.4384	−0.587796
$985$	−27.1771	−0.865934
$986$	43.0388	1.37064
$987$	−3.43845	−0.109447
$988$	14.6307	0.465464
$989$	−22.7386	−0.723046
$990$	0	0
$991$	61.8617	1.96510	0.982551	−	0.185991i	$-0.0595495\pi$
$991$	61.8617	1.96510	0.982551	+	0.185991i	$0.0595495\pi$
$992$	−20.1080	−0.638428
$993$	−17.6847	−0.561206
$994$	−4.87689	−0.154686
$995$	−7.12311	−0.225818
$996$	3.86174	0.122364
$997$	41.0388	1.29971	0.649856	−	0.760057i	$-0.274829\pi$
$997$	41.0388	1.29971	0.649856	+	0.760057i	$0.274829\pi$
$998$	−61.7538	−1.95478
$999$	−2.68466	−0.0849388

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2541.2.a.u.1.2	✓	2
3.2	odd	2		7623.2.a.bt.1.1		2
11.10	odd	2		2541.2.a.bc.1.1	yes	2
33.32	even	2		7623.2.a.be.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2541.2.a.u.1.2	✓	2	1.1	even	1	trivial
2541.2.a.bc.1.1	yes	2	11.10	odd	2
7623.2.a.be.1.2		2	33.32	even	2
7623.2.a.bt.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)

\(f(q)\)	\(=\)	\(q+1.56155 q^{2} +1.00000 q^{3} +0.438447 q^{4} +1.00000 q^{5} +1.56155 q^{6} -1.00000 q^{7} -2.43845 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.56155 q^{2} +1.00000 q^{3} +0.438447 q^{4} +1.00000 q^{5} +1.56155 q^{6} -1.00000 q^{7} -2.43845 q^{8} +1.00000 q^{9} +1.56155 q^{10} +0.438447 q^{12} -5.56155 q^{13} -1.56155 q^{14} +1.00000 q^{15} -4.68466 q^{16} -4.12311 q^{17} +1.56155 q^{18} -6.00000 q^{19} +0.438447 q^{20} -1.00000 q^{21} -4.00000 q^{23} -2.43845 q^{24} -4.00000 q^{25} -8.68466 q^{26} +1.00000 q^{27} -0.438447 q^{28} -6.68466 q^{29} +1.56155 q^{30} +8.24621 q^{31} -2.43845 q^{32} -6.43845 q^{34} -1.00000 q^{35} +0.438447 q^{36} -2.68466 q^{37} -9.36932 q^{38} -5.56155 q^{39} -2.43845 q^{40} +7.56155 q^{41} -1.56155 q^{42} +5.68466 q^{43} +1.00000 q^{45} -6.24621 q^{46} +3.43845 q^{47} -4.68466 q^{48} +1.00000 q^{49} -6.24621 q^{50} -4.12311 q^{51} -2.43845 q^{52} +7.80776 q^{53} +1.56155 q^{54} +2.43845 q^{56} -6.00000 q^{57} -10.4384 q^{58} -12.5616 q^{59} +0.438447 q^{60} +13.3693 q^{61} +12.8769 q^{62} -1.00000 q^{63} +5.56155 q^{64} -5.56155 q^{65} +8.80776 q^{67} -1.80776 q^{68} -4.00000 q^{69} -1.56155 q^{70} +3.12311 q^{71} -2.43845 q^{72} -7.12311 q^{73} -4.19224 q^{74} -4.00000 q^{75} -2.63068 q^{76} -8.68466 q^{78} -3.12311 q^{79} -4.68466 q^{80} +1.00000 q^{81} +11.8078 q^{82} +8.80776 q^{83} -0.438447 q^{84} -4.12311 q^{85} +8.87689 q^{86} -6.68466 q^{87} -11.2462 q^{89} +1.56155 q^{90} +5.56155 q^{91} -1.75379 q^{92} +8.24621 q^{93} +5.36932 q^{94} -6.00000 q^{95} -2.43845 q^{96} +1.31534 q^{97} +1.56155 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} + 2 q^{3} + 5 q^{4} + 2 q^{5} - q^{6} - 2 q^{7} - 9 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - q^2 + 2 * q^3 + 5 * q^4 + 2 * q^5 - q^6 - 2 * q^7 - 9 * q^8 + 2 * q^9	\( 2 q - q^{2} + 2 q^{3} + 5 q^{4} + 2 q^{5} - q^{6} - 2 q^{7} - 9 q^{8} + 2 q^{9} - q^{10} + 5 q^{12} - 7 q^{13} + q^{14} + 2 q^{15} + 3 q^{16} - q^{18} - 12 q^{19} + 5 q^{20} - 2 q^{21} - 8 q^{23} - 9 q^{24} - 8 q^{25} - 5 q^{26} + 2 q^{27} - 5 q^{28} - q^{29} - q^{30} - 9 q^{32} - 17 q^{34} - 2 q^{35} + 5 q^{36} + 7 q^{37} + 6 q^{38} - 7 q^{39} - 9 q^{40} + 11 q^{41} + q^{42} - q^{43} + 2 q^{45} + 4 q^{46} + 11 q^{47} + 3 q^{48} + 2 q^{49} + 4 q^{50} - 9 q^{52} - 5 q^{53} - q^{54} + 9 q^{56} - 12 q^{57} - 25 q^{58} - 21 q^{59} + 5 q^{60} + 2 q^{61} + 34 q^{62} - 2 q^{63} + 7 q^{64} - 7 q^{65} - 3 q^{67} + 17 q^{68} - 8 q^{69} + q^{70} - 2 q^{71} - 9 q^{72} - 6 q^{73} - 29 q^{74} - 8 q^{75} - 30 q^{76} - 5 q^{78} + 2 q^{79} + 3 q^{80} + 2 q^{81} + 3 q^{82} - 3 q^{83} - 5 q^{84} + 26 q^{86} - q^{87} - 6 q^{89} - q^{90} + 7 q^{91} - 20 q^{92} - 14 q^{94} - 12 q^{95} - 9 q^{96} + 15 q^{97} - q^{98}+O(q^{100}) \) 2 * q - q^2 + 2 * q^3 + 5 * q^4 + 2 * q^5 - q^6 - 2 * q^7 - 9 * q^8 + 2 * q^9 - q^10 + 5 * q^12 - 7 * q^13 + q^14 + 2 * q^15 + 3 * q^16 - q^18 - 12 * q^19 + 5 * q^20 - 2 * q^21 - 8 * q^23 - 9 * q^24 - 8 * q^25 - 5 * q^26 + 2 * q^27 - 5 * q^28 - q^29 - q^30 - 9 * q^32 - 17 * q^34 - 2 * q^35 + 5 * q^36 + 7 * q^37 + 6 * q^38 - 7 * q^39 - 9 * q^40 + 11 * q^41 + q^42 - q^43 + 2 * q^45 + 4 * q^46 + 11 * q^47 + 3 * q^48 + 2 * q^49 + 4 * q^50 - 9 * q^52 - 5 * q^53 - q^54 + 9 * q^56 - 12 * q^57 - 25 * q^58 - 21 * q^59 + 5 * q^60 + 2 * q^61 + 34 * q^62 - 2 * q^63 + 7 * q^64 - 7 * q^65 - 3 * q^67 + 17 * q^68 - 8 * q^69 + q^70 - 2 * q^71 - 9 * q^72 - 6 * q^73 - 29 * q^74 - 8 * q^75 - 30 * q^76 - 5 * q^78 + 2 * q^79 + 3 * q^80 + 2 * q^81 + 3 * q^82 - 3 * q^83 - 5 * q^84 + 26 * q^86 - q^87 - 6 * q^89 - q^90 + 7 * q^91 - 20 * q^92 - 14 * q^94 - 12 * q^95 - 9 * q^96 + 15 * q^97 - q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more