LMFDB - Embedded newform 2541.2.a.br.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2541, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("2541.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$20.2899871536$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 19x^{8} - x^{7} + 124x^{6} + 6x^{5} - 316x^{4} + 17x^{3} + 253x^{2} - 70x - 11 $ x^10 - 19x^8 - x^7 + 124x^6 + 6x^5 - 316x^4 + 17x^3 + 253x^2 - 70*x - 11
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 231)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$-2.39396$ 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)

$f(q)$	$=$	$q+2.39396 q^{2} +1.00000 q^{3} +3.73106 q^{4} -3.93829 q^{5} +2.39396 q^{6} +1.00000 q^{7} +4.14409 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.39396 q^{2} +1.00000 q^{3} +3.73106 q^{4} -3.93829 q^{5} +2.39396 q^{6} +1.00000 q^{7} +4.14409 q^{8} +1.00000 q^{9} -9.42812 q^{10} +3.73106 q^{12} +2.99890 q^{13} +2.39396 q^{14} -3.93829 q^{15} +2.45868 q^{16} +6.60457 q^{17} +2.39396 q^{18} +5.90310 q^{19} -14.6940 q^{20} +1.00000 q^{21} -6.02551 q^{23} +4.14409 q^{24} +10.5101 q^{25} +7.17925 q^{26} +1.00000 q^{27} +3.73106 q^{28} +1.52075 q^{29} -9.42812 q^{30} +8.46902 q^{31} -2.40219 q^{32} +15.8111 q^{34} -3.93829 q^{35} +3.73106 q^{36} -0.607840 q^{37} +14.1318 q^{38} +2.99890 q^{39} -16.3206 q^{40} +1.70333 q^{41} +2.39396 q^{42} +3.23364 q^{43} -3.93829 q^{45} -14.4249 q^{46} -4.80237 q^{47} +2.45868 q^{48} +1.00000 q^{49} +25.1609 q^{50} +6.60457 q^{51} +11.1891 q^{52} -6.12834 q^{53} +2.39396 q^{54} +4.14409 q^{56} +5.90310 q^{57} +3.64062 q^{58} +6.23883 q^{59} -14.6940 q^{60} +2.08899 q^{61} +20.2745 q^{62} +1.00000 q^{63} -10.6681 q^{64} -11.8105 q^{65} -0.599719 q^{67} +24.6420 q^{68} -6.02551 q^{69} -9.42812 q^{70} +1.40968 q^{71} +4.14409 q^{72} -7.08851 q^{73} -1.45515 q^{74} +10.5101 q^{75} +22.0248 q^{76} +7.17925 q^{78} +1.02327 q^{79} -9.68299 q^{80} +1.00000 q^{81} +4.07770 q^{82} -3.08729 q^{83} +3.73106 q^{84} -26.0107 q^{85} +7.74120 q^{86} +1.52075 q^{87} -2.48531 q^{89} -9.42812 q^{90} +2.99890 q^{91} -22.4815 q^{92} +8.46902 q^{93} -11.4967 q^{94} -23.2481 q^{95} -2.40219 q^{96} +2.55296 q^{97} +2.39396 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 10 q^{3} + 18 q^{4} + 5 q^{5} + 10 q^{7} - 3 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q + 10 * q^3 + 18 * q^4 + 5 * q^5 + 10 * q^7 - 3 * q^8 + 10 * q^9	$ 10 q + 10 q^{3} + 18 q^{4} + 5 q^{5} + 10 q^{7} - 3 q^{8} + 10 q^{9} - 6 q^{10} + 18 q^{12} + 6 q^{13} + 5 q^{15} + 38 q^{16} + 8 q^{17} + 7 q^{20} + 10 q^{21} - 3 q^{24} + 31 q^{25} + q^{26} + 10 q^{27} + 18 q^{28} - 14 q^{29} - 6 q^{30} + 26 q^{31} - 41 q^{32} + 21 q^{34} + 5 q^{35} + 18 q^{36} + 24 q^{37} + 8 q^{38} + 6 q^{39} - 5 q^{40} + 19 q^{41} - 6 q^{43} + 5 q^{45} - q^{46} + 15 q^{47} + 38 q^{48} + 10 q^{49} - q^{50} + 8 q^{51} - 25 q^{52} - q^{53} - 3 q^{56} + 11 q^{58} + 23 q^{59} + 7 q^{60} + 11 q^{62} + 10 q^{63} + 53 q^{64} - 29 q^{65} + 38 q^{67} + 87 q^{68} - 6 q^{70} + 26 q^{71} - 3 q^{72} - q^{73} - 39 q^{74} + 31 q^{75} - 2 q^{76} + q^{78} + 5 q^{79} + 6 q^{80} + 10 q^{81} + 5 q^{82} + 6 q^{83} + 18 q^{84} - q^{85} - 41 q^{86} - 14 q^{87} - 9 q^{89} - 6 q^{90} + 6 q^{91} - 48 q^{92} + 26 q^{93} - 42 q^{95} - 41 q^{96} + 24 q^{97}+O(q^{100}) $ 10 * q + 10 * q^3 + 18 * q^4 + 5 * q^5 + 10 * q^7 - 3 * q^8 + 10 * q^9 - 6 * q^10 + 18 * q^12 + 6 * q^13 + 5 * q^15 + 38 * q^16 + 8 * q^17 + 7 * q^20 + 10 * q^21 - 3 * q^24 + 31 * q^25 + q^26 + 10 * q^27 + 18 * q^28 - 14 * q^29 - 6 * q^30 + 26 * q^31 - 41 * q^32 + 21 * q^34 + 5 * q^35 + 18 * q^36 + 24 * q^37 + 8 * q^38 + 6 * q^39 - 5 * q^40 + 19 * q^41 - 6 * q^43 + 5 * q^45 - q^46 + 15 * q^47 + 38 * q^48 + 10 * q^49 - q^50 + 8 * q^51 - 25 * q^52 - q^53 - 3 * q^56 + 11 * q^58 + 23 * q^59 + 7 * q^60 + 11 * q^62 + 10 * q^63 + 53 * q^64 - 29 * q^65 + 38 * q^67 + 87 * q^68 - 6 * q^70 + 26 * q^71 - 3 * q^72 - q^73 - 39 * q^74 + 31 * q^75 - 2 * q^76 + q^78 + 5 * q^79 + 6 * q^80 + 10 * q^81 + 5 * q^82 + 6 * q^83 + 18 * q^84 - q^85 - 41 * q^86 - 14 * q^87 - 9 * q^89 - 6 * q^90 + 6 * q^91 - 48 * q^92 + 26 * q^93 - 42 * q^95 - 41 * q^96 + 24 * q^97

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 $

$2$	2.39396	1.69279	0.846394	−	0.532558i	$-0.178769\pi$
$2$	2.39396	1.69279	0.846394	+	0.532558i	$0.178769\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	3.73106	1.86553
$5$	−3.93829	−1.76126	−0.880629	−	0.473807i	$-0.842879\pi$
$5$	−3.93829	−1.76126	−0.880629	+	0.473807i	$0.842879\pi$
$6$	2.39396	0.977331
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	4.14409	1.46516
$9$	1.00000	0.333333
$10$	−9.42812	−2.98143
$11$	0	0
$11$	0	0
$12$	3.73106	1.07706
$13$	2.99890	0.831744	0.415872	−	0.909423i	$-0.363476\pi$
$13$	2.99890	0.831744	0.415872	+	0.909423i	$0.363476\pi$
$14$	2.39396	0.639813
$15$	−3.93829	−1.01686
$16$	2.45868	0.614669
$17$	6.60457	1.60184	0.800922	−	0.598769i	$-0.204343\pi$
$17$	6.60457	1.60184	0.800922	+	0.598769i	$0.204343\pi$
$18$	2.39396	0.564262
$19$	5.90310	1.35426	0.677132	−	0.735861i	$-0.263222\pi$
$19$	5.90310	1.35426	0.677132	+	0.735861i	$0.263222\pi$
$20$	−14.6940	−3.28568
$21$	1.00000	0.218218
$22$	0	0
$23$	−6.02551	−1.25641	−0.628203	−	0.778049i	$-0.716209\pi$
$23$	−6.02551	−1.25641	−0.628203	+	0.778049i	$0.716209\pi$
$24$	4.14409	0.845908
$25$	10.5101	2.10203
$26$	7.17925	1.40797
$27$	1.00000	0.192450
$28$	3.73106	0.705104
$29$	1.52075	0.282397	0.141198	−	0.989981i	$-0.454904\pi$
$29$	1.52075	0.282397	0.141198	+	0.989981i	$0.454904\pi$
$30$	−9.42812	−1.72133
$31$	8.46902	1.52108	0.760541	−	0.649290i	$-0.224934\pi$
$31$	8.46902	1.52108	0.760541	+	0.649290i	$0.224934\pi$
$32$	−2.40219	−0.424652
$33$	0	0
$34$	15.8111	2.71158
$35$	−3.93829	−0.665693
$36$	3.73106	0.621843
$37$	−0.607840	−0.0999283	−0.0499641	−	0.998751i	$-0.515911\pi$
$37$	−0.607840	−0.0999283	−0.0499641	+	0.998751i	$0.515911\pi$
$38$	14.1318	2.29248
$39$	2.99890	0.480208
$40$	−16.3206	−2.58052
$41$	1.70333	0.266015	0.133007	−	0.991115i	$-0.457537\pi$
$41$	1.70333	0.266015	0.133007	+	0.991115i	$0.457537\pi$
$42$	2.39396	0.369396
$43$	3.23364	0.493125	0.246562	−	0.969127i	$-0.420699\pi$
$43$	3.23364	0.493125	0.246562	+	0.969127i	$0.420699\pi$
$44$	0	0
$45$	−3.93829	−0.587086
$46$	−14.4249	−2.12683
$47$	−4.80237	−0.700498	−0.350249	−	0.936657i	$-0.613903\pi$
$47$	−4.80237	−0.700498	−0.350249	+	0.936657i	$0.613903\pi$
$48$	2.45868	0.354879
$49$	1.00000	0.142857
$50$	25.1609	3.55829
$51$	6.60457	0.924825
$52$	11.1891	1.55164
$53$	−6.12834	−0.841793	−0.420896	−	0.907109i	$-0.638284\pi$
$53$	−6.12834	−0.841793	−0.420896	+	0.907109i	$0.638284\pi$
$54$	2.39396	0.325777
$55$	0	0
$56$	4.14409	0.553777
$57$	5.90310	0.781885
$58$	3.64062	0.478037
$59$	6.23883	0.812227	0.406113	−	0.913823i	$-0.366884\pi$
$59$	6.23883	0.812227	0.406113	+	0.913823i	$0.366884\pi$
$60$	−14.6940	−1.89699
$61$	2.08899	0.267467	0.133734	−	0.991017i	$-0.457303\pi$
$61$	2.08899	0.267467	0.133734	+	0.991017i	$0.457303\pi$
$62$	20.2745	2.57487
$63$	1.00000	0.125988
$64$	−10.6681	−1.33351
$65$	−11.8105	−1.46492
$66$	0	0
$67$	−0.599719	−0.0732673	−0.0366337	−	0.999329i	$-0.511663\pi$
$67$	−0.599719	−0.0732673	−0.0366337	+	0.999329i	$0.511663\pi$
$68$	24.6420	2.98829
$69$	−6.02551	−0.725386
$70$	−9.42812	−1.12688
$71$	1.40968	0.167298	0.0836489	−	0.996495i	$-0.473343\pi$
$71$	1.40968	0.167298	0.0836489	+	0.996495i	$0.473343\pi$
$72$	4.14409	0.488385
$73$	−7.08851	−0.829648	−0.414824	−	0.909902i	$-0.636157\pi$
$73$	−7.08851	−0.829648	−0.414824	+	0.909902i	$0.636157\pi$
$74$	−1.45515	−0.169157
$75$	10.5101	1.21361
$76$	22.0248	2.52642
$77$	0	0
$78$	7.17925	0.812890
$79$	1.02327	0.115126	0.0575632	−	0.998342i	$-0.481667\pi$
$79$	1.02327	0.115126	0.0575632	+	0.998342i	$0.481667\pi$
$80$	−9.68299	−1.08259
$81$	1.00000	0.111111
$82$	4.07770	0.450307
$83$	−3.08729	−0.338874	−0.169437	−	0.985541i	$-0.554195\pi$
$83$	−3.08729	−0.338874	−0.169437	+	0.985541i	$0.554195\pi$
$84$	3.73106	0.407092
$85$	−26.0107	−2.82126
$86$	7.74120	0.834755
$87$	1.52075	0.163042
$88$	0	0
$89$	−2.48531	−0.263442	−0.131721	−	0.991287i	$-0.542050\pi$
$89$	−2.48531	−0.263442	−0.131721	+	0.991287i	$0.542050\pi$
$90$	−9.42812	−0.993811
$91$	2.99890	0.314370
$92$	−22.4815	−2.34386
$93$	8.46902	0.878197
$94$	−11.4967	−1.18579
$95$	−23.2481	−2.38521
$96$	−2.40219	−0.245173
$97$	2.55296	0.259214	0.129607	−	0.991565i	$-0.458628\pi$
$97$	2.55296	0.259214	0.129607	+	0.991565i	$0.458628\pi$
$98$	2.39396	0.241827
$99$	0	0
$100$	39.2139	3.92139
$101$	15.1573	1.50821	0.754106	−	0.656753i	$-0.228071\pi$
$101$	15.1573	1.50821	0.754106	+	0.656753i	$0.228071\pi$
$102$	15.8111	1.56553
$103$	−13.8364	−1.36334	−0.681670	−	0.731660i	$-0.738746\pi$
$103$	−13.8364	−1.36334	−0.681670	+	0.731660i	$0.738746\pi$
$104$	12.4277	1.21864
$105$	−3.93829	−0.384338
$106$	−14.6710	−1.42498
$107$	−0.445651	−0.0430827	−0.0215413	−	0.999768i	$-0.506857\pi$
$107$	−0.445651	−0.0430827	−0.0215413	+	0.999768i	$0.506857\pi$
$108$	3.73106	0.359021
$109$	−11.0988	−1.06307	−0.531536	−	0.847036i	$-0.678385\pi$
$109$	−11.0988	−1.06307	−0.531536	+	0.847036i	$0.678385\pi$
$110$	0	0
$111$	−0.607840	−0.0576936
$112$	2.45868	0.232323
$113$	−8.08938	−0.760985	−0.380492	−	0.924784i	$-0.624245\pi$
$113$	−8.08938	−0.760985	−0.380492	+	0.924784i	$0.624245\pi$
$114$	14.1318	1.32357
$115$	23.7302	2.21285
$116$	5.67401	0.526819
$117$	2.99890	0.277248
$118$	14.9355	1.37493
$119$	6.60457	0.605440
$120$	−16.3206	−1.48986
$121$	0	0
$122$	5.00096	0.452765
$123$	1.70333	0.153584
$124$	31.5984	2.83762
$125$	−21.7005	−1.94095
$126$	2.39396	0.213271
$127$	−0.179659	−0.0159422	−0.00797109	−	0.999968i	$-0.502537\pi$
$127$	−0.179659	−0.0159422	−0.00797109	+	0.999968i	$0.502537\pi$
$128$	−20.7347	−1.83271
$129$	3.23364	0.284706
$130$	−28.2740	−2.47979
$131$	−9.38232	−0.819737	−0.409868	−	0.912145i	$-0.634425\pi$
$131$	−9.38232	−0.819737	−0.409868	+	0.912145i	$0.634425\pi$
$132$	0	0
$133$	5.90310	0.511864
$134$	−1.43570	−0.124026
$135$	−3.93829	−0.338954
$136$	27.3699	2.34695
$137$	0.893617	0.0763468	0.0381734	−	0.999271i	$-0.487846\pi$
$137$	0.893617	0.0763468	0.0381734	+	0.999271i	$0.487846\pi$
$138$	−14.4249	−1.22792
$139$	−2.12281	−0.180054	−0.0900271	−	0.995939i	$-0.528695\pi$
$139$	−2.12281	−0.180054	−0.0900271	+	0.995939i	$0.528695\pi$
$140$	−14.6940	−1.24187
$141$	−4.80237	−0.404433
$142$	3.37471	0.283199
$143$	0	0
$144$	2.45868	0.204890
$145$	−5.98916	−0.497373
$146$	−16.9696	−1.40442
$147$	1.00000	0.0824786
$148$	−2.26789	−0.186419
$149$	−14.3220	−1.17331	−0.586653	−	0.809838i	$-0.699555\pi$
$149$	−14.3220	−1.17331	−0.586653	+	0.809838i	$0.699555\pi$
$150$	25.1609	2.05438
$151$	13.7837	1.12170	0.560850	−	0.827918i	$-0.310475\pi$
$151$	13.7837	1.12170	0.560850	+	0.827918i	$0.310475\pi$
$152$	24.4630	1.98421
$153$	6.60457	0.533948
$154$	0	0
$155$	−33.3535	−2.67902
$156$	11.1891	0.895842
$157$	−11.4608	−0.914668	−0.457334	−	0.889295i	$-0.651196\pi$
$157$	−11.4608	−0.914668	−0.457334	+	0.889295i	$0.651196\pi$
$158$	2.44966	0.194884
$159$	−6.12834	−0.486009
$160$	9.46054	0.747922
$161$	−6.02551	−0.474877
$162$	2.39396	0.188087
$163$	4.94262	0.387136	0.193568	−	0.981087i	$-0.437994\pi$
$163$	4.94262	0.387136	0.193568	+	0.981087i	$0.437994\pi$
$164$	6.35521	0.496258
$165$	0	0
$166$	−7.39086	−0.573642
$167$	−8.53421	−0.660397	−0.330198	−	0.943912i	$-0.607116\pi$
$167$	−8.53421	−0.660397	−0.330198	+	0.943912i	$0.607116\pi$
$168$	4.14409	0.319723
$169$	−4.00662	−0.308201
$170$	−62.2687	−4.77579
$171$	5.90310	0.451422
$172$	12.0649	0.919939
$173$	−13.0876	−0.995031	−0.497515	−	0.867455i	$-0.665754\pi$
$173$	−13.0876	−0.995031	−0.497515	+	0.867455i	$0.665754\pi$
$174$	3.64062	0.275995
$175$	10.5101	0.794492
$176$	0	0
$177$	6.23883	0.468939
$178$	−5.94973	−0.445951
$179$	25.8622	1.93303	0.966514	−	0.256612i	$-0.0826063\pi$
$179$	25.8622	1.93303	0.966514	+	0.256612i	$0.0826063\pi$
$180$	−14.6940	−1.09523
$181$	21.4202	1.59215	0.796077	−	0.605195i	$-0.206905\pi$
$181$	21.4202	1.59215	0.796077	+	0.605195i	$0.206905\pi$
$182$	7.17925	0.532161
$183$	2.08899	0.154422
$184$	−24.9703	−1.84083
$185$	2.39385	0.175999
$186$	20.2745	1.48660
$187$	0	0
$188$	−17.9179	−1.30680
$189$	1.00000	0.0727393
$190$	−55.6552	−4.03765
$191$	−3.73988	−0.270608	−0.135304	−	0.990804i	$-0.543201\pi$
$191$	−3.73988	−0.270608	−0.135304	+	0.990804i	$0.543201\pi$
$192$	−10.6681	−0.769905
$193$	−6.07932	−0.437599	−0.218799	−	0.975770i	$-0.570214\pi$
$193$	−6.07932	−0.437599	−0.218799	+	0.975770i	$0.570214\pi$
$194$	6.11169	0.438794
$195$	−11.8105	−0.845770
$196$	3.73106	0.266504
$197$	−21.5458	−1.53508	−0.767538	−	0.641003i	$-0.778518\pi$
$197$	−21.5458	−1.53508	−0.767538	+	0.641003i	$0.778518\pi$
$198$	0	0
$199$	−14.8965	−1.05598	−0.527992	−	0.849249i	$-0.677055\pi$
$199$	−14.8965	−1.05598	−0.527992	+	0.849249i	$0.677055\pi$
$200$	43.5549	3.07980
$201$	−0.599719	−0.0423009
$202$	36.2861	2.55308
$203$	1.52075	0.106736
$204$	24.6420	1.72529
$205$	−6.70819	−0.468521
$206$	−33.1238	−2.30784
$207$	−6.02551	−0.418802
$208$	7.37332	0.511248
$209$	0	0
$210$	−9.42812	−0.650602
$211$	−16.9594	−1.16753	−0.583766	−	0.811922i	$-0.698421\pi$
$211$	−16.9594	−1.16753	−0.583766	+	0.811922i	$0.698421\pi$
$212$	−22.8652	−1.57039
$213$	1.40968	0.0965894
$214$	−1.06687	−0.0729298
$215$	−12.7350	−0.868520
$216$	4.14409	0.281969
$217$	8.46902	0.574915
$218$	−26.5701	−1.79955
$219$	−7.08851	−0.478997
$220$	0	0
$221$	19.8064	1.33232
$222$	−1.45515	−0.0976630
$223$	−13.8125	−0.924954	−0.462477	−	0.886631i	$-0.653039\pi$
$223$	−13.8125	−0.924954	−0.462477	+	0.886631i	$0.653039\pi$
$224$	−2.40219	−0.160503
$225$	10.5101	0.700676
$226$	−19.3657	−1.28819
$227$	7.25345	0.481428	0.240714	−	0.970596i	$-0.422618\pi$
$227$	7.25345	0.481428	0.240714	+	0.970596i	$0.422618\pi$
$228$	22.0248	1.45863
$229$	−0.327136	−0.0216178	−0.0108089	−	0.999942i	$-0.503441\pi$
$229$	−0.327136	−0.0216178	−0.0108089	+	0.999942i	$0.503441\pi$
$230$	56.8093	3.74589
$231$	0	0
$232$	6.30213	0.413755
$233$	−16.2452	−1.06426	−0.532128	−	0.846664i	$-0.678607\pi$
$233$	−16.2452	−1.06426	−0.532128	+	0.846664i	$0.678607\pi$
$234$	7.17925	0.469322
$235$	18.9131	1.23376
$236$	23.2774	1.51523
$237$	1.02327	0.0664683
$238$	15.8111	1.02488
$239$	29.0009	1.87591	0.937955	−	0.346756i	$-0.112717\pi$
$239$	29.0009	1.87591	0.937955	+	0.346756i	$0.112717\pi$
$240$	−9.68299	−0.625034
$241$	29.3358	1.88968	0.944841	−	0.327530i	$-0.106216\pi$
$241$	29.3358	1.88968	0.944841	+	0.327530i	$0.106216\pi$
$242$	0	0
$243$	1.00000	0.0641500
$244$	7.79413	0.498968
$245$	−3.93829	−0.251608
$246$	4.07770	0.259985
$247$	17.7028	1.12640
$248$	35.0964	2.22862
$249$	−3.08729	−0.195649
$250$	−51.9502	−3.28562
$251$	12.8316	0.809925	0.404963	−	0.914333i	$-0.367285\pi$
$251$	12.8316	0.809925	0.404963	+	0.914333i	$0.367285\pi$
$252$	3.73106	0.235035
$253$	0	0
$254$	−0.430097	−0.0269867
$255$	−26.0107	−1.62885
$256$	−28.3018	−1.76887
$257$	19.5210	1.21769	0.608844	−	0.793290i	$-0.291633\pi$
$257$	19.5210	1.21769	0.608844	+	0.793290i	$0.291633\pi$
$258$	7.74120	0.481946
$259$	−0.607840	−0.0377693
$260$	−44.0658	−2.73284
$261$	1.52075	0.0941322
$262$	−22.4609	−1.38764
$263$	−23.9606	−1.47747	−0.738736	−	0.673995i	$-0.764577\pi$
$263$	−23.9606	−1.47747	−0.738736	+	0.673995i	$0.764577\pi$
$264$	0	0
$265$	24.1352	1.48261
$266$	14.1318	0.866477
$267$	−2.48531	−0.152098
$268$	−2.23759	−0.136682
$269$	11.3260	0.690558	0.345279	−	0.938500i	$-0.387784\pi$
$269$	11.3260	0.690558	0.345279	+	0.938500i	$0.387784\pi$
$270$	−9.42812	−0.573777
$271$	−6.12278	−0.371932	−0.185966	−	0.982556i	$-0.559541\pi$
$271$	−6.12278	−0.371932	−0.185966	+	0.982556i	$0.559541\pi$
$272$	16.2385	0.984604
$273$	2.99890	0.181502
$274$	2.13929	0.129239
$275$	0	0
$276$	−22.4815	−1.35323
$277$	−0.600165	−0.0360604	−0.0180302	−	0.999837i	$-0.505740\pi$
$277$	−0.600165	−0.0360604	−0.0180302	+	0.999837i	$0.505740\pi$
$278$	−5.08192	−0.304793
$279$	8.46902	0.507027
$280$	−16.3206	−0.975344
$281$	−23.8022	−1.41992	−0.709960	−	0.704242i	$-0.751287\pi$
$281$	−23.8022	−1.41992	−0.709960	+	0.704242i	$0.751287\pi$
$282$	−11.4967	−0.684618
$283$	17.3400	1.03076	0.515379	−	0.856962i	$-0.327651\pi$
$283$	17.3400	1.03076	0.515379	+	0.856962i	$0.327651\pi$
$284$	5.25958	0.312099
$285$	−23.2481	−1.37710
$286$	0	0
$287$	1.70333	0.100544
$288$	−2.40219	−0.141551
$289$	26.6204	1.56590
$290$	−14.3378	−0.841947
$291$	2.55296	0.149657
$292$	−26.4477	−1.54773
$293$	14.9122	0.871179	0.435589	−	0.900145i	$-0.356540\pi$
$293$	14.9122	0.871179	0.435589	+	0.900145i	$0.356540\pi$
$294$	2.39396	0.139619
$295$	−24.5703	−1.43054
$296$	−2.51894	−0.146411
$297$	0	0
$298$	−34.2864	−1.98616
$299$	−18.0699	−1.04501
$300$	39.2139	2.26402
$301$	3.23364	0.186384
$302$	32.9976	1.89880
$303$	15.1573	0.870766
$304$	14.5138	0.832425
$305$	−8.22704	−0.471079
$306$	15.8111	0.903860
$307$	−29.0453	−1.65771	−0.828853	−	0.559467i	$-0.811006\pi$
$307$	−29.0453	−1.65771	−0.828853	+	0.559467i	$0.811006\pi$
$308$	0	0
$309$	−13.8364	−0.787124
$310$	−79.8470	−4.53500
$311$	−20.3651	−1.15480	−0.577399	−	0.816462i	$-0.695932\pi$
$311$	−20.3651	−1.15480	−0.577399	+	0.816462i	$0.695932\pi$
$312$	12.4277	0.703580
$313$	−29.4807	−1.66635	−0.833174	−	0.553010i	$-0.813479\pi$
$313$	−29.4807	−1.66635	−0.833174	+	0.553010i	$0.813479\pi$
$314$	−27.4366	−1.54834
$315$	−3.93829	−0.221898
$316$	3.81786	0.214772
$317$	7.62530	0.428280	0.214140	−	0.976803i	$-0.431305\pi$
$317$	7.62530	0.428280	0.214140	+	0.976803i	$0.431305\pi$
$318$	−14.6710	−0.822710
$319$	0	0
$320$	42.0142	2.34866
$321$	−0.445651	−0.0248738
$322$	−14.4249	−0.803865
$323$	38.9875	2.16932
$324$	3.73106	0.207281
$325$	31.5188	1.74835
$326$	11.8324	0.655338
$327$	−11.0988	−0.613764
$328$	7.05873	0.389753
$329$	−4.80237	−0.264763
$330$	0	0
$331$	20.6731	1.13630	0.568148	−	0.822926i	$-0.307660\pi$
$331$	20.6731	1.13630	0.568148	+	0.822926i	$0.307660\pi$
$332$	−11.5189	−0.632180
$333$	−0.607840	−0.0333094
$334$	−20.4306	−1.11791
$335$	2.36187	0.129043
$336$	2.45868	0.134132
$337$	5.46255	0.297564	0.148782	−	0.988870i	$-0.452465\pi$
$337$	5.46255	0.297564	0.148782	+	0.988870i	$0.452465\pi$
$338$	−9.59169	−0.521719
$339$	−8.08938	−0.439355
$340$	−97.0475	−5.26314
$341$	0	0
$342$	14.1318	0.764161
$343$	1.00000	0.0539949
$344$	13.4005	0.722505
$345$	23.7302	1.27759
$346$	−31.3312	−1.68438
$347$	−9.58110	−0.514341	−0.257170	−	0.966366i	$-0.582790\pi$
$347$	−9.58110	−0.514341	−0.257170	+	0.966366i	$0.582790\pi$
$348$	5.67401	0.304159
$349$	−9.36045	−0.501054	−0.250527	−	0.968110i	$-0.580604\pi$
$349$	−9.36045	−0.501054	−0.250527	+	0.968110i	$0.580604\pi$
$350$	25.1609	1.34491
$351$	2.99890	0.160069
$352$	0	0
$353$	−27.6629	−1.47235	−0.736173	−	0.676794i	$-0.763369\pi$
$353$	−27.6629	−1.47235	−0.736173	+	0.676794i	$0.763369\pi$
$354$	14.9355	0.793815
$355$	−5.55171	−0.294654
$356$	−9.27282	−0.491459
$357$	6.60457	0.349551
$358$	61.9131	3.27221
$359$	2.60258	0.137359	0.0686796	−	0.997639i	$-0.478121\pi$
$359$	2.60258	0.137359	0.0686796	+	0.997639i	$0.478121\pi$
$360$	−16.3206	−0.860172
$361$	15.8466	0.834033
$362$	51.2793	2.69518
$363$	0	0
$364$	11.1891	0.586466
$365$	27.9166	1.46122
$366$	5.00096	0.261404
$367$	−10.3394	−0.539710	−0.269855	−	0.962901i	$-0.586976\pi$
$367$	−10.3394	−0.539710	−0.269855	+	0.962901i	$0.586976\pi$
$368$	−14.8148	−0.772274
$369$	1.70333	0.0886716
$370$	5.73079	0.297930
$371$	−6.12834	−0.318168
$372$	31.5984	1.63830
$373$	5.15587	0.266961	0.133480	−	0.991051i	$-0.457385\pi$
$373$	5.15587	0.266961	0.133480	+	0.991051i	$0.457385\pi$
$374$	0	0
$375$	−21.7005	−1.12061
$376$	−19.9015	−1.02634
$377$	4.56058	0.234882
$378$	2.39396	0.123132
$379$	−35.4223	−1.81952	−0.909761	−	0.415133i	$-0.863735\pi$
$379$	−35.4223	−1.81952	−0.909761	+	0.415133i	$0.863735\pi$
$380$	−86.7401	−4.44968
$381$	−0.179659	−0.00920422
$382$	−8.95313	−0.458082
$383$	−31.4076	−1.60486	−0.802428	−	0.596750i	$-0.796459\pi$
$383$	−31.4076	−1.60486	−0.802428	+	0.596750i	$0.796459\pi$
$384$	−20.7347	−1.05811
$385$	0	0
$386$	−14.5537	−0.740762
$387$	3.23364	0.164375
$388$	9.52524	0.483571
$389$	20.0789	1.01804	0.509020	−	0.860755i	$-0.330008\pi$
$389$	20.0789	1.01804	0.509020	+	0.860755i	$0.330008\pi$
$390$	−28.2740	−1.43171
$391$	−39.7959	−2.01257
$392$	4.14409	0.209308
$393$	−9.38232	−0.473275
$394$	−51.5799	−2.59856
$395$	−4.02992	−0.202767
$396$	0	0
$397$	3.63351	0.182361	0.0911804	−	0.995834i	$-0.470936\pi$
$397$	3.63351	0.182361	0.0911804	+	0.995834i	$0.470936\pi$
$398$	−35.6616	−1.78756
$399$	5.90310	0.295525
$400$	25.8410	1.29205
$401$	37.6309	1.87920	0.939598	−	0.342279i	$-0.111199\pi$
$401$	37.6309	1.87920	0.939598	+	0.342279i	$0.111199\pi$
$402$	−1.43570	−0.0716064
$403$	25.3977	1.26515
$404$	56.5529	2.81361
$405$	−3.93829	−0.195695
$406$	3.64062	0.180681
$407$	0	0
$408$	27.3699	1.35501
$409$	−16.1059	−0.796386	−0.398193	−	0.917302i	$-0.630363\pi$
$409$	−16.1059	−0.796386	−0.398193	+	0.917302i	$0.630363\pi$
$410$	−16.0592	−0.793106
$411$	0.893617	0.0440789
$412$	−51.6243	−2.54335
$413$	6.23883	0.306993
$414$	−14.4249	−0.708943
$415$	12.1587	0.596845
$416$	−7.20393	−0.353202
$417$	−2.12281	−0.103954
$418$	0	0
$419$	−17.7128	−0.865325	−0.432662	−	0.901556i	$-0.642426\pi$
$419$	−17.7128	−0.865325	−0.432662	+	0.901556i	$0.642426\pi$
$420$	−14.6940	−0.716993
$421$	30.2721	1.47537	0.737686	−	0.675144i	$-0.235919\pi$
$421$	30.2721	1.47537	0.737686	+	0.675144i	$0.235919\pi$
$422$	−40.6001	−1.97638
$423$	−4.80237	−0.233499
$424$	−25.3964	−1.23336
$425$	69.4149	3.36712
$426$	3.37471	0.163505
$427$	2.08899	0.101093
$428$	−1.66275	−0.0803720
$429$	0	0
$430$	−30.4871	−1.47022
$431$	−19.1918	−0.924438	−0.462219	−	0.886766i	$-0.652947\pi$
$431$	−19.1918	−0.924438	−0.462219	+	0.886766i	$0.652947\pi$
$432$	2.45868	0.118293
$433$	21.7538	1.04542	0.522711	−	0.852510i	$-0.324921\pi$
$433$	21.7538	1.04542	0.522711	+	0.852510i	$0.324921\pi$
$434$	20.2745	0.973208
$435$	−5.98916	−0.287158
$436$	−41.4102	−1.98319
$437$	−35.5692	−1.70151
$438$	−16.9696	−0.810841
$439$	−2.70519	−0.129112	−0.0645558	−	0.997914i	$-0.520563\pi$
$439$	−2.70519	−0.129112	−0.0645558	+	0.997914i	$0.520563\pi$
$440$	0	0
$441$	1.00000	0.0476190
$442$	47.4159	2.25534
$443$	38.2274	1.81624	0.908118	−	0.418713i	$-0.137519\pi$
$443$	38.2274	1.81624	0.908118	+	0.418713i	$0.137519\pi$
$444$	−2.26789	−0.107629
$445$	9.78786	0.463989
$446$	−33.0666	−1.56575
$447$	−14.3220	−0.677409
$448$	−10.6681	−0.504021
$449$	22.7112	1.07181	0.535904	−	0.844279i	$-0.319971\pi$
$449$	22.7112	1.07181	0.535904	+	0.844279i	$0.319971\pi$
$450$	25.1609	1.18610
$451$	0	0
$452$	−30.1819	−1.41964
$453$	13.7837	0.647614
$454$	17.3645	0.814956
$455$	−11.8105	−0.553686
$456$	24.4630	1.14558
$457$	1.57183	0.0735271	0.0367636	−	0.999324i	$-0.488295\pi$
$457$	1.57183	0.0735271	0.0367636	+	0.999324i	$0.488295\pi$
$458$	−0.783152	−0.0365943
$459$	6.60457	0.308275
$460$	88.5388	4.12814
$461$	28.1276	1.31003	0.655017	−	0.755614i	$-0.272661\pi$
$461$	28.1276	1.31003	0.655017	+	0.755614i	$0.272661\pi$
$462$	0	0
$463$	−4.69202	−0.218057	−0.109028	−	0.994039i	$-0.534774\pi$
$463$	−4.69202	−0.218057	−0.109028	+	0.994039i	$0.534774\pi$
$464$	3.73904	0.173580
$465$	−33.3535	−1.54673
$466$	−38.8903	−1.80156
$467$	−17.6135	−0.815054	−0.407527	−	0.913193i	$-0.633609\pi$
$467$	−17.6135	−0.815054	−0.407527	+	0.913193i	$0.633609\pi$
$468$	11.1891	0.517214
$469$	−0.599719	−0.0276924
$470$	45.2773	2.08849
$471$	−11.4608	−0.528084
$472$	25.8543	1.19004
$473$	0	0
$474$	2.44966	0.112517
$475$	62.0424	2.84670
$476$	24.6420	1.12947
$477$	−6.12834	−0.280598
$478$	69.4270	3.17552
$479$	10.7070	0.489215	0.244608	−	0.969622i	$-0.421341\pi$
$479$	10.7070	0.489215	0.244608	+	0.969622i	$0.421341\pi$
$480$	9.46054	0.431813
$481$	−1.82285	−0.0831148
$482$	70.2287	3.19883
$483$	−6.02551	−0.274170
$484$	0	0
$485$	−10.0543	−0.456542
$486$	2.39396	0.108592
$487$	38.7602	1.75639	0.878197	−	0.478299i	$-0.158746\pi$
$487$	38.7602	1.75639	0.878197	+	0.478299i	$0.158746\pi$
$488$	8.65695	0.391882
$489$	4.94262	0.223513
$490$	−9.42812	−0.425919
$491$	6.00061	0.270804	0.135402	−	0.990791i	$-0.456767\pi$
$491$	6.00061	0.270804	0.135402	+	0.990791i	$0.456767\pi$
$492$	6.35521	0.286515
$493$	10.0439	0.452355
$494$	42.3798	1.90676
$495$	0	0
$496$	20.8226	0.934962
$497$	1.40968	0.0632326
$498$	−7.39086	−0.331193
$499$	−28.9776	−1.29722	−0.648608	−	0.761123i	$-0.724648\pi$
$499$	−28.9776	−1.29722	−0.648608	+	0.761123i	$0.724648\pi$
$500$	−80.9659	−3.62091
$501$	−8.53421	−0.381280
$502$	30.7184	1.37103
$503$	12.8657	0.573653	0.286827	−	0.957982i	$-0.407400\pi$
$503$	12.8657	0.573653	0.286827	+	0.957982i	$0.407400\pi$
$504$	4.14409	0.184592
$505$	−59.6940	−2.65635
$506$	0	0
$507$	−4.00662	−0.177940
$508$	−0.670319	−0.0297406
$509$	19.7361	0.874788	0.437394	−	0.899270i	$-0.355902\pi$
$509$	19.7361	0.874788	0.437394	+	0.899270i	$0.355902\pi$
$510$	−62.2687	−2.75730
$511$	−7.08851	−0.313577
$512$	−26.2842	−1.16161
$513$	5.90310	0.260628
$514$	46.7326	2.06129
$515$	54.4917	2.40119
$516$	12.0649	0.531127
$517$	0	0
$518$	−1.45515	−0.0639355
$519$	−13.0876	−0.574481
$520$	−48.9439	−2.14633
$521$	−23.3926	−1.02485	−0.512423	−	0.858733i	$-0.671252\pi$
$521$	−23.3926	−1.02485	−0.512423	+	0.858733i	$0.671252\pi$
$522$	3.64062	0.159346
$523$	10.7796	0.471361	0.235680	−	0.971831i	$-0.424268\pi$
$523$	10.7796	0.471361	0.235680	+	0.971831i	$0.424268\pi$
$524$	−35.0060	−1.52924
$525$	10.5101	0.458700
$526$	−57.3607	−2.50105
$527$	55.9343	2.43653
$528$	0	0
$529$	13.3068	0.578556
$530$	57.7788	2.50975
$531$	6.23883	0.270742
$532$	22.0248	0.954897
$533$	5.10810	0.221256
$534$	−5.94973	−0.257470
$535$	1.75510	0.0758797
$536$	−2.48529	−0.107348
$537$	25.8622	1.11603
$538$	27.1140	1.16897
$539$	0	0
$540$	−14.6940	−0.632329
$541$	6.42155	0.276084	0.138042	−	0.990426i	$-0.455919\pi$
$541$	6.42155	0.276084	0.138042	+	0.990426i	$0.455919\pi$
$542$	−14.6577	−0.629602
$543$	21.4202	0.919231
$544$	−15.8655	−0.680226
$545$	43.7103	1.87234
$546$	7.17925	0.307243
$547$	28.0529	1.19946	0.599728	−	0.800204i	$-0.295276\pi$
$547$	28.0529	1.19946	0.599728	+	0.800204i	$0.295276\pi$
$548$	3.33414	0.142427
$549$	2.08899	0.0891558
$550$	0	0
$551$	8.97715	0.382440
$552$	−24.9703	−1.06280
$553$	1.02327	0.0435137
$554$	−1.43677	−0.0610427
$555$	2.39385	0.101613
$556$	−7.92031	−0.335896
$557$	−23.1102	−0.979211	−0.489606	−	0.871944i	$-0.662859\pi$
$557$	−23.1102	−0.979211	−0.489606	+	0.871944i	$0.662859\pi$
$558$	20.2745	0.858289
$559$	9.69734	0.410154
$560$	−9.68299	−0.409181
$561$	0	0
$562$	−56.9815	−2.40362
$563$	28.8436	1.21561	0.607806	−	0.794086i	$-0.292050\pi$
$563$	28.8436	1.21561	0.607806	+	0.794086i	$0.292050\pi$
$564$	−17.9179	−0.754481
$565$	31.8583	1.34029
$566$	41.5114	1.74485
$567$	1.00000	0.0419961
$568$	5.84182	0.245117
$569$	17.7760	0.745208	0.372604	−	0.927991i	$-0.378465\pi$
$569$	17.7760	0.745208	0.372604	+	0.927991i	$0.378465\pi$
$570$	−55.6552	−2.33114
$571$	−17.8981	−0.749012	−0.374506	−	0.927225i	$-0.622188\pi$
$571$	−17.8981	−0.749012	−0.374506	+	0.927225i	$0.622188\pi$
$572$	0	0
$573$	−3.73988	−0.156236
$574$	4.07770	0.170200
$575$	−63.3289	−2.64100
$576$	−10.6681	−0.444505
$577$	21.0769	0.877441	0.438721	−	0.898624i	$-0.355432\pi$
$577$	21.0769	0.877441	0.438721	+	0.898624i	$0.355432\pi$
$578$	63.7281	2.65074
$579$	−6.07932	−0.252648
$580$	−22.3459	−0.927864
$581$	−3.08729	−0.128083
$582$	6.11169	0.253338
$583$	0	0
$584$	−29.3754	−1.21556
$585$	−11.8105	−0.488305
$586$	35.6992	1.47472
$587$	17.3136	0.714609	0.357305	−	0.933988i	$-0.383696\pi$
$587$	17.3136	0.714609	0.357305	+	0.933988i	$0.383696\pi$
$588$	3.73106	0.153866
$589$	49.9935	2.05995
$590$	−58.8205	−2.42160
$591$	−21.5458	−0.886277
$592$	−1.49448	−0.0614228
$593$	26.3881	1.08363	0.541814	−	0.840498i	$-0.317738\pi$
$593$	26.3881	1.08363	0.541814	+	0.840498i	$0.317738\pi$
$594$	0	0
$595$	−26.0107	−1.06634
$596$	−53.4363	−2.18884
$597$	−14.8965	−0.609673
$598$	−43.2586	−1.76898
$599$	−28.2593	−1.15465	−0.577323	−	0.816516i	$-0.695903\pi$
$599$	−28.2593	−1.15465	−0.577323	+	0.816516i	$0.695903\pi$
$600$	43.5549	1.77812
$601$	0.440908	0.0179850	0.00899251	−	0.999960i	$-0.497138\pi$
$601$	0.440908	0.0179850	0.00899251	+	0.999960i	$0.497138\pi$
$602$	7.74120	0.315508
$603$	−0.599719	−0.0244224
$604$	51.4277	2.09256
$605$	0	0
$606$	36.2861	1.47402
$607$	−0.559085	−0.0226925	−0.0113463	−	0.999936i	$-0.503612\pi$
$607$	−0.559085	−0.0226925	−0.0113463	+	0.999936i	$0.503612\pi$
$608$	−14.1804	−0.575091
$609$	1.52075	0.0616240
$610$	−19.6952	−0.797436
$611$	−14.4018	−0.582635
$612$	24.6420	0.996095
$613$	−30.3820	−1.22712	−0.613559	−	0.789649i	$-0.710263\pi$
$613$	−30.3820	−1.22712	−0.613559	+	0.789649i	$0.710263\pi$
$614$	−69.5335	−2.80614
$615$	−6.70819	−0.270500
$616$	0	0
$617$	2.35080	0.0946395	0.0473198	−	0.998880i	$-0.484932\pi$
$617$	2.35080	0.0946395	0.0473198	+	0.998880i	$0.484932\pi$
$618$	−33.1238	−1.33243
$619$	6.11038	0.245597	0.122798	−	0.992432i	$-0.460813\pi$
$619$	6.11038	0.245597	0.122798	+	0.992432i	$0.460813\pi$
$620$	−124.444	−4.99778
$621$	−6.02551	−0.241795
$622$	−48.7532	−1.95483
$623$	−2.48531	−0.0995717
$624$	7.37332	0.295169
$625$	32.9123	1.31649
$626$	−70.5757	−2.82077
$627$	0	0
$628$	−42.7608	−1.70634
$629$	−4.01452	−0.160069
$630$	−9.42812	−0.375625
$631$	−28.8822	−1.14978	−0.574891	−	0.818230i	$-0.694955\pi$
$631$	−28.8822	−1.14978	−0.574891	+	0.818230i	$0.694955\pi$
$632$	4.24050	0.168678
$633$	−16.9594	−0.674075
$634$	18.2547	0.724987
$635$	0.707550	0.0280783
$636$	−22.8652	−0.906664
$637$	2.99890	0.118821
$638$	0	0
$639$	1.40968	0.0557659
$640$	81.6592	3.22787
$641$	−39.8256	−1.57302	−0.786508	−	0.617579i	$-0.788113\pi$
$641$	−39.8256	−1.57302	−0.786508	+	0.617579i	$0.788113\pi$
$642$	−1.06687	−0.0421060
$643$	5.85723	0.230987	0.115493	−	0.993308i	$-0.463155\pi$
$643$	5.85723	0.230987	0.115493	+	0.993308i	$0.463155\pi$
$644$	−22.4815	−0.885896
$645$	−12.7350	−0.501440
$646$	93.3345	3.67220
$647$	22.5855	0.887926	0.443963	−	0.896045i	$-0.353572\pi$
$647$	22.5855	0.887926	0.443963	+	0.896045i	$0.353572\pi$
$648$	4.14409	0.162795
$649$	0	0
$650$	75.4549	2.95958
$651$	8.46902	0.331927
$652$	18.4412	0.722213
$653$	−40.8369	−1.59807	−0.799035	−	0.601284i	$-0.794656\pi$
$653$	−40.8369	−1.59807	−0.799035	+	0.601284i	$0.794656\pi$
$654$	−26.5701	−1.03897
$655$	36.9503	1.44377
$656$	4.18793	0.163511
$657$	−7.08851	−0.276549
$658$	−11.4967	−0.448188
$659$	−32.5869	−1.26941	−0.634703	−	0.772756i	$-0.718878\pi$
$659$	−32.5869	−1.26941	−0.634703	+	0.772756i	$0.718878\pi$
$660$	0	0
$661$	43.6393	1.69737	0.848686	−	0.528898i	$-0.177395\pi$
$661$	43.6393	1.69737	0.848686	+	0.528898i	$0.177395\pi$
$662$	49.4906	1.92351
$663$	19.8064	0.769218
$664$	−12.7940	−0.496504
$665$	−23.2481	−0.901524
$666$	−1.45515	−0.0563858
$667$	−9.16331	−0.354805
$668$	−31.8416	−1.23199
$669$	−13.8125	−0.534023
$670$	5.65422	0.218442
$671$	0	0
$672$	−2.40219	−0.0926667
$673$	23.8718	0.920190	0.460095	−	0.887870i	$-0.347815\pi$
$673$	23.8718	0.920190	0.460095	+	0.887870i	$0.347815\pi$
$674$	13.0771	0.503712
$675$	10.5101	0.404535
$676$	−14.9489	−0.574958
$677$	4.26651	0.163975	0.0819877	−	0.996633i	$-0.473873\pi$
$677$	4.26651	0.163975	0.0819877	+	0.996633i	$0.473873\pi$
$678$	−19.3657	−0.743734
$679$	2.55296	0.0979736
$680$	−107.791	−4.13359
$681$	7.25345	0.277953
$682$	0	0
$683$	5.88217	0.225075	0.112537	−	0.993647i	$-0.464102\pi$
$683$	5.88217	0.225075	0.112537	+	0.993647i	$0.464102\pi$
$684$	22.0248	0.842140
$685$	−3.51932	−0.134466
$686$	2.39396	0.0914019
$687$	−0.327136	−0.0124810
$688$	7.95047	0.303109
$689$	−18.3783	−0.700156
$690$	56.8093	2.16269
$691$	−0.237559	−0.00903716	−0.00451858	−	0.999990i	$-0.501438\pi$
$691$	−0.237559	−0.00903716	−0.00451858	+	0.999990i	$0.501438\pi$
$692$	−48.8305	−1.85626
$693$	0	0
$694$	−22.9368	−0.870669
$695$	8.36023	0.317122
$696$	6.30213	0.238882
$697$	11.2497	0.426114
$698$	−22.4086	−0.848177
$699$	−16.2452	−0.614448
$700$	39.2139	1.48215
$701$	10.6036	0.400494	0.200247	−	0.979745i	$-0.435826\pi$
$701$	10.6036	0.400494	0.200247	+	0.979745i	$0.435826\pi$
$702$	7.17925	0.270963
$703$	−3.58814	−0.135329
$704$	0	0
$705$	18.9131	0.712310
$706$	−66.2239	−2.49237
$707$	15.1573	0.570050
$708$	23.2774	0.874820
$709$	−48.3236	−1.81483	−0.907415	−	0.420235i	$-0.861947\pi$
$709$	−48.3236	−1.81483	−0.907415	+	0.420235i	$0.861947\pi$
$710$	−13.2906	−0.498787
$711$	1.02327	0.0383755
$712$	−10.2993	−0.385984
$713$	−51.0302	−1.91110
$714$	15.8111	0.591715
$715$	0	0
$716$	96.4932	3.60612
$717$	29.0009	1.08306
$718$	6.23049	0.232520
$719$	−36.2637	−1.35241	−0.676203	−	0.736715i	$-0.736376\pi$
$719$	−36.2637	−1.35241	−0.676203	+	0.736715i	$0.736376\pi$
$720$	−9.68299	−0.360864
$721$	−13.8364	−0.515294
$722$	37.9362	1.41184
$723$	29.3358	1.09101
$724$	79.9202	2.97021
$725$	15.9833	0.593605
$726$	0	0
$727$	1.15184	0.0427195	0.0213597	−	0.999772i	$-0.493200\pi$
$727$	1.15184	0.0427195	0.0213597	+	0.999772i	$0.493200\pi$
$728$	12.4277	0.460601
$729$	1.00000	0.0370370
$730$	66.8314	2.47354
$731$	21.3568	0.789909
$732$	7.79413	0.288079
$733$	27.1042	1.00111	0.500557	−	0.865703i	$-0.333128\pi$
$733$	27.1042	1.00111	0.500557	+	0.865703i	$0.333128\pi$
$734$	−24.7520	−0.913614
$735$	−3.93829	−0.145266
$736$	14.4745	0.533535
$737$	0	0
$738$	4.07770	0.150102
$739$	23.8018	0.875563	0.437782	−	0.899081i	$-0.355764\pi$
$739$	23.8018	0.875563	0.437782	+	0.899081i	$0.355764\pi$
$740$	8.93160	0.328332
$741$	17.7028	0.650328
$742$	−14.6710	−0.538590
$743$	−15.0656	−0.552704	−0.276352	−	0.961056i	$-0.589126\pi$
$743$	−15.0656	−0.552704	−0.276352	+	0.961056i	$0.589126\pi$
$744$	35.0964	1.28670
$745$	56.4043	2.06650
$746$	12.3430	0.451908
$747$	−3.08729	−0.112958
$748$	0	0
$749$	−0.445651	−0.0162837
$750$	−51.9502	−1.89695
$751$	10.6107	0.387191	0.193596	−	0.981081i	$-0.437985\pi$
$751$	10.6107	0.387191	0.193596	+	0.981081i	$0.437985\pi$
$752$	−11.8075	−0.430575
$753$	12.8316	0.467611
$754$	10.9179	0.397605
$755$	−54.2841	−1.97560
$756$	3.73106	0.135697
$757$	−35.0862	−1.27523	−0.637615	−	0.770355i	$-0.720079\pi$
$757$	−35.0862	−1.27523	−0.637615	+	0.770355i	$0.720079\pi$
$758$	−84.7997	−3.08006
$759$	0	0
$760$	−96.3423	−3.49470
$761$	−37.2895	−1.35174	−0.675872	−	0.737019i	$-0.736233\pi$
$761$	−37.2895	−1.35174	−0.675872	+	0.737019i	$0.736233\pi$
$762$	−0.430097	−0.0155808
$763$	−11.0988	−0.401803
$764$	−13.9537	−0.504827
$765$	−26.0107	−0.940420
$766$	−75.1887	−2.71668
$767$	18.7096	0.675565
$768$	−28.3018	−1.02125
$769$	−21.8827	−0.789110	−0.394555	−	0.918872i	$-0.629101\pi$
$769$	−21.8827	−0.789110	−0.394555	+	0.918872i	$0.629101\pi$
$770$	0	0
$771$	19.5210	0.703033
$772$	−22.6823	−0.816353
$773$	−34.4742	−1.23995	−0.619975	−	0.784622i	$-0.712857\pi$
$773$	−34.4742	−1.23995	−0.619975	+	0.784622i	$0.712857\pi$
$774$	7.74120	0.278252
$775$	89.0106	3.19735
$776$	10.5797	0.379789
$777$	−0.607840	−0.0218061
$778$	48.0681	1.72332
$779$	10.0549	0.360254
$780$	−44.0658	−1.57781
$781$	0	0
$782$	−95.2699	−3.40685
$783$	1.52075	0.0543472
$784$	2.45868	0.0878099
$785$	45.1358	1.61097
$786$	−22.4609	−0.801154
$787$	−11.6668	−0.415878	−0.207939	−	0.978142i	$-0.566676\pi$
$787$	−11.6668	−0.415878	−0.207939	+	0.978142i	$0.566676\pi$
$788$	−80.3887	−2.86373
$789$	−23.9606	−0.853019
$790$	−9.64747	−0.343242
$791$	−8.08938	−0.287625
$792$	0	0
$793$	6.26466	0.222464
$794$	8.69849	0.308698
$795$	24.1352	0.855987
$796$	−55.5797	−1.96997
$797$	−35.1322	−1.24445	−0.622223	−	0.782840i	$-0.713770\pi$
$797$	−35.1322	−1.24445	−0.622223	+	0.782840i	$0.713770\pi$
$798$	14.1318	0.500261
$799$	−31.7176	−1.12209
$800$	−25.2474	−0.892630
$801$	−2.48531	−0.0878140
$802$	90.0869	3.18108
$803$	0	0
$804$	−2.23759	−0.0789136
$805$	23.7302	0.836380
$806$	60.8012	2.14163
$807$	11.3260	0.398694
$808$	62.8133	2.20977
$809$	14.5235	0.510620	0.255310	−	0.966859i	$-0.417822\pi$
$809$	14.5235	0.510620	0.255310	+	0.966859i	$0.417822\pi$
$810$	−9.42812	−0.331270
$811$	−1.76417	−0.0619483	−0.0309741	−	0.999520i	$-0.509861\pi$
$811$	−1.76417	−0.0619483	−0.0309741	+	0.999520i	$0.509861\pi$
$812$	5.67401	0.199119
$813$	−6.12278	−0.214735
$814$	0	0
$815$	−19.4655	−0.681846
$816$	16.2385	0.568461
$817$	19.0885	0.667821
$818$	−38.5570	−1.34811
$819$	2.99890	0.104790
$820$	−25.0287	−0.874039
$821$	9.76074	0.340652	0.170326	−	0.985388i	$-0.445518\pi$
$821$	9.76074	0.340652	0.170326	+	0.985388i	$0.445518\pi$
$822$	2.13929	0.0746162
$823$	−45.6322	−1.59064	−0.795319	−	0.606191i	$-0.792697\pi$
$823$	−45.6322	−1.59064	−0.795319	+	0.606191i	$0.792697\pi$
$824$	−57.3392	−1.99750
$825$	0	0
$826$	14.9355	0.519674
$827$	−20.7517	−0.721608	−0.360804	−	0.932642i	$-0.617498\pi$
$827$	−20.7517	−0.721608	−0.360804	+	0.932642i	$0.617498\pi$
$828$	−22.4815	−0.781287
$829$	16.3868	0.569137	0.284568	−	0.958656i	$-0.408150\pi$
$829$	16.3868	0.569137	0.284568	+	0.958656i	$0.408150\pi$
$830$	29.1074	1.01033
$831$	−0.600165	−0.0208195
$832$	−31.9926	−1.10914
$833$	6.60457	0.228835
$834$	−5.08192	−0.175973
$835$	33.6102	1.16313
$836$	0	0
$837$	8.46902	0.292732
$838$	−42.4037	−1.46481
$839$	35.0935	1.21156	0.605782	−	0.795631i	$-0.292860\pi$
$839$	35.0935	1.21156	0.605782	+	0.795631i	$0.292860\pi$
$840$	−16.3206	−0.563115
$841$	−26.6873	−0.920252
$842$	72.4703	2.49749
$843$	−23.8022	−0.819791
$844$	−63.2764	−2.17806
$845$	15.7792	0.542822
$846$	−11.4967	−0.395265
$847$	0	0
$848$	−15.0676	−0.517424
$849$	17.3400	0.595108
$850$	166.177	5.69982
$851$	3.66255	0.125550
$852$	5.25958	0.180190
$853$	11.3030	0.387007	0.193504	−	0.981100i	$-0.438015\pi$
$853$	11.3030	0.387007	0.193504	+	0.981100i	$0.438015\pi$
$854$	5.00096	0.171129
$855$	−23.2481	−0.795069
$856$	−1.84682	−0.0631229
$857$	−13.8531	−0.473214	−0.236607	−	0.971605i	$-0.576035\pi$
$857$	−13.8531	−0.473214	−0.236607	+	0.971605i	$0.576035\pi$
$858$	0	0
$859$	−5.23831	−0.178729	−0.0893645	−	0.995999i	$-0.528484\pi$
$859$	−5.23831	−0.178729	−0.0893645	+	0.995999i	$0.528484\pi$
$860$	−47.5150	−1.62025
$861$	1.70333	0.0580492
$862$	−45.9445	−1.56488
$863$	−41.1289	−1.40004	−0.700022	−	0.714121i	$-0.746826\pi$
$863$	−41.1289	−1.40004	−0.700022	+	0.714121i	$0.746826\pi$
$864$	−2.40219	−0.0817243
$865$	51.5427	1.75250
$866$	52.0779	1.76968
$867$	26.6204	0.904075
$868$	31.5984	1.07252
$869$	0	0
$870$	−14.3378	−0.486098
$871$	−1.79849	−0.0609397
$872$	−45.9944	−1.55757
$873$	2.55296	0.0864046
$874$	−85.1514	−2.88029
$875$	−21.7005	−0.733612
$876$	−26.4477	−0.893584
$877$	5.41488	0.182848	0.0914238	−	0.995812i	$-0.470858\pi$
$877$	5.41488	0.182848	0.0914238	+	0.995812i	$0.470858\pi$
$878$	−6.47612	−0.218558
$879$	14.9122	0.502975
$880$	0	0
$881$	11.0961	0.373837	0.186918	−	0.982375i	$-0.440150\pi$
$881$	11.0961	0.373837	0.186918	+	0.982375i	$0.440150\pi$
$882$	2.39396	0.0806089
$883$	−51.4596	−1.73175	−0.865877	−	0.500256i	$-0.833239\pi$
$883$	−51.4596	−1.73175	−0.865877	+	0.500256i	$0.833239\pi$
$884$	73.8989	2.48549
$885$	−24.5703	−0.825923
$886$	91.5149	3.07450
$887$	19.9938	0.671325	0.335662	−	0.941982i	$-0.391040\pi$
$887$	19.9938	0.671325	0.335662	+	0.941982i	$0.391040\pi$
$888$	−2.51894	−0.0845302
$889$	−0.179659	−0.00602558
$890$	23.4318	0.785435
$891$	0	0
$892$	−51.5353	−1.72553
$893$	−28.3489	−0.948659
$894$	−34.2864	−1.14671
$895$	−101.853	−3.40456
$896$	−20.7347	−0.692697
$897$	−18.0699	−0.603336
$898$	54.3697	1.81434
$899$	12.8793	0.429548
$900$	39.2139	1.30713
$901$	−40.4751	−1.34842
$902$	0	0
$903$	3.23364	0.107609
$904$	−33.5231	−1.11496
$905$	−84.3591	−2.80419
$906$	32.9976	1.09627
$907$	−5.23855	−0.173943	−0.0869716	−	0.996211i	$-0.527719\pi$
$907$	−5.23855	−0.173943	−0.0869716	+	0.996211i	$0.527719\pi$
$908$	27.0630	0.898119
$909$	15.1573	0.502737
$910$	−28.2740	−0.937273
$911$	−11.0131	−0.364882	−0.182441	−	0.983217i	$-0.558400\pi$
$911$	−11.0131	−0.364882	−0.182441	+	0.983217i	$0.558400\pi$
$912$	14.5138	0.480601
$913$	0	0
$914$	3.76290	0.124466
$915$	−8.22704	−0.271978
$916$	−1.22056	−0.0403286
$917$	−9.38232	−0.309831
$918$	15.8111	0.521844
$919$	28.8457	0.951533	0.475767	−	0.879572i	$-0.342171\pi$
$919$	28.8457	0.951533	0.475767	+	0.879572i	$0.342171\pi$
$920$	98.3401	3.24218
$921$	−29.0453	−0.957077
$922$	67.3365	2.21761
$923$	4.22747	0.139149
$924$	0	0
$925$	−6.38848	−0.210052
$926$	−11.2325	−0.369123
$927$	−13.8364	−0.454446
$928$	−3.65314	−0.119920
$929$	16.2208	0.532186	0.266093	−	0.963947i	$-0.414267\pi$
$929$	16.2208	0.532186	0.266093	+	0.963947i	$0.414267\pi$
$930$	−79.8470	−2.61829
$931$	5.90310	0.193466
$932$	−60.6116	−1.98540
$933$	−20.3651	−0.666723
$934$	−42.1660	−1.37971
$935$	0	0
$936$	12.4277	0.406212
$937$	27.4672	0.897315	0.448657	−	0.893704i	$-0.351902\pi$
$937$	27.4672	0.897315	0.448657	+	0.893704i	$0.351902\pi$
$938$	−1.43570	−0.0468774
$939$	−29.4807	−0.962067
$940$	70.5660	2.30161
$941$	−48.7222	−1.58830	−0.794150	−	0.607722i	$-0.792084\pi$
$941$	−48.7222	−1.58830	−0.794150	+	0.607722i	$0.792084\pi$
$942$	−27.4366	−0.893934
$943$	−10.2634	−0.334223
$944$	15.3393	0.499251
$945$	−3.93829	−0.128113
$946$	0	0
$947$	21.1998	0.688902	0.344451	−	0.938804i	$-0.388065\pi$
$947$	21.1998	0.688902	0.344451	+	0.938804i	$0.388065\pi$
$948$	3.81786	0.123998
$949$	−21.2577	−0.690055
$950$	148.527	4.81886
$951$	7.62530	0.247267
$952$	27.3699	0.887064
$953$	−34.1228	−1.10535	−0.552673	−	0.833398i	$-0.686392\pi$
$953$	−34.1228	−1.10535	−0.552673	+	0.833398i	$0.686392\pi$
$954$	−14.6710	−0.474992
$955$	14.7287	0.476610
$956$	108.204	3.49957
$957$	0	0
$958$	25.6322	0.828138
$959$	0.893617	0.0288564
$960$	42.0142	1.35600
$961$	40.7243	1.31369
$962$	−4.36383	−0.140696
$963$	−0.445651	−0.0143609
$964$	109.453	3.52526
$965$	23.9421	0.770724
$966$	−14.4249	−0.464112
$967$	18.8881	0.607400	0.303700	−	0.952768i	$-0.401778\pi$
$967$	18.8881	0.607400	0.303700	+	0.952768i	$0.401778\pi$
$968$	0	0
$969$	38.9875	1.25246
$970$	−24.0696	−0.772829
$971$	12.4847	0.400652	0.200326	−	0.979729i	$-0.435800\pi$
$971$	12.4847	0.400652	0.200326	+	0.979729i	$0.435800\pi$
$972$	3.73106	0.119674
$973$	−2.12281	−0.0680541
$974$	92.7906	2.97320
$975$	31.5188	1.00941
$976$	5.13614	0.164404
$977$	−13.8747	−0.443890	−0.221945	−	0.975059i	$-0.571241\pi$
$977$	−13.8747	−0.443890	−0.221945	+	0.975059i	$0.571241\pi$
$978$	11.8324	0.378360
$979$	0	0
$980$	−14.6940	−0.469382
$981$	−11.0988	−0.354357
$982$	14.3652	0.458413
$983$	43.8326	1.39804	0.699021	−	0.715101i	$-0.253619\pi$
$983$	43.8326	1.39804	0.699021	+	0.715101i	$0.253619\pi$
$984$	7.05873	0.225024
$985$	84.8537	2.70366
$986$	24.0448	0.765741
$987$	−4.80237	−0.152861
$988$	66.0502	2.10134
$989$	−19.4843	−0.619565
$990$	0	0
$991$	42.8926	1.36253	0.681264	−	0.732037i	$-0.261430\pi$
$991$	42.8926	1.36253	0.681264	+	0.732037i	$0.261430\pi$
$992$	−20.3442	−0.645930
$993$	20.6731	0.656041
$994$	3.37471	0.107039
$995$	58.6667	1.85986
$996$	−11.5189	−0.364989
$997$	28.2985	0.896224	0.448112	−	0.893977i	$-0.352097\pi$
$997$	28.2985	0.896224	0.448112	+	0.893977i	$0.352097\pi$
$998$	−69.3713	−2.19591
$999$	−0.607840	−0.0192312

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2541.2.a.br.1.9		10
3.2	odd	2		7623.2.a.cy.1.2		10
11.7	odd	10		231.2.j.g.148.1	yes	20
11.8	odd	10		231.2.j.g.64.1	✓	20
11.10	odd	2		2541.2.a.bq.1.2		10
33.8	even	10		693.2.m.j.64.5		20
33.29	even	10		693.2.m.j.379.5		20
33.32	even	2		7623.2.a.cx.1.9		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.j.g.64.1	✓	20	11.8	odd	10
231.2.j.g.148.1	yes	20	11.7	odd	10
693.2.m.j.64.5		20	33.8	even	10
693.2.m.j.379.5		20	33.29	even	10
2541.2.a.bq.1.2		10	11.10	odd	2
2541.2.a.br.1.9		10	1.1	even	1	trivial
7623.2.a.cx.1.9		10	33.32	even	2
7623.2.a.cy.1.2		10	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)

\(f(q)\)	\(=\)	\(q+2.39396 q^{2} +1.00000 q^{3} +3.73106 q^{4} -3.93829 q^{5} +2.39396 q^{6} +1.00000 q^{7} +4.14409 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.39396 q^{2} +1.00000 q^{3} +3.73106 q^{4} -3.93829 q^{5} +2.39396 q^{6} +1.00000 q^{7} +4.14409 q^{8} +1.00000 q^{9} -9.42812 q^{10} +3.73106 q^{12} +2.99890 q^{13} +2.39396 q^{14} -3.93829 q^{15} +2.45868 q^{16} +6.60457 q^{17} +2.39396 q^{18} +5.90310 q^{19} -14.6940 q^{20} +1.00000 q^{21} -6.02551 q^{23} +4.14409 q^{24} +10.5101 q^{25} +7.17925 q^{26} +1.00000 q^{27} +3.73106 q^{28} +1.52075 q^{29} -9.42812 q^{30} +8.46902 q^{31} -2.40219 q^{32} +15.8111 q^{34} -3.93829 q^{35} +3.73106 q^{36} -0.607840 q^{37} +14.1318 q^{38} +2.99890 q^{39} -16.3206 q^{40} +1.70333 q^{41} +2.39396 q^{42} +3.23364 q^{43} -3.93829 q^{45} -14.4249 q^{46} -4.80237 q^{47} +2.45868 q^{48} +1.00000 q^{49} +25.1609 q^{50} +6.60457 q^{51} +11.1891 q^{52} -6.12834 q^{53} +2.39396 q^{54} +4.14409 q^{56} +5.90310 q^{57} +3.64062 q^{58} +6.23883 q^{59} -14.6940 q^{60} +2.08899 q^{61} +20.2745 q^{62} +1.00000 q^{63} -10.6681 q^{64} -11.8105 q^{65} -0.599719 q^{67} +24.6420 q^{68} -6.02551 q^{69} -9.42812 q^{70} +1.40968 q^{71} +4.14409 q^{72} -7.08851 q^{73} -1.45515 q^{74} +10.5101 q^{75} +22.0248 q^{76} +7.17925 q^{78} +1.02327 q^{79} -9.68299 q^{80} +1.00000 q^{81} +4.07770 q^{82} -3.08729 q^{83} +3.73106 q^{84} -26.0107 q^{85} +7.74120 q^{86} +1.52075 q^{87} -2.48531 q^{89} -9.42812 q^{90} +2.99890 q^{91} -22.4815 q^{92} +8.46902 q^{93} -11.4967 q^{94} -23.2481 q^{95} -2.40219 q^{96} +2.55296 q^{97} +2.39396 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 10 q^{3} + 18 q^{4} + 5 q^{5} + 10 q^{7} - 3 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q + 10 * q^3 + 18 * q^4 + 5 * q^5 + 10 * q^7 - 3 * q^8 + 10 * q^9	\( 10 q + 10 q^{3} + 18 q^{4} + 5 q^{5} + 10 q^{7} - 3 q^{8} + 10 q^{9} - 6 q^{10} + 18 q^{12} + 6 q^{13} + 5 q^{15} + 38 q^{16} + 8 q^{17} + 7 q^{20} + 10 q^{21} - 3 q^{24} + 31 q^{25} + q^{26} + 10 q^{27} + 18 q^{28} - 14 q^{29} - 6 q^{30} + 26 q^{31} - 41 q^{32} + 21 q^{34} + 5 q^{35} + 18 q^{36} + 24 q^{37} + 8 q^{38} + 6 q^{39} - 5 q^{40} + 19 q^{41} - 6 q^{43} + 5 q^{45} - q^{46} + 15 q^{47} + 38 q^{48} + 10 q^{49} - q^{50} + 8 q^{51} - 25 q^{52} - q^{53} - 3 q^{56} + 11 q^{58} + 23 q^{59} + 7 q^{60} + 11 q^{62} + 10 q^{63} + 53 q^{64} - 29 q^{65} + 38 q^{67} + 87 q^{68} - 6 q^{70} + 26 q^{71} - 3 q^{72} - q^{73} - 39 q^{74} + 31 q^{75} - 2 q^{76} + q^{78} + 5 q^{79} + 6 q^{80} + 10 q^{81} + 5 q^{82} + 6 q^{83} + 18 q^{84} - q^{85} - 41 q^{86} - 14 q^{87} - 9 q^{89} - 6 q^{90} + 6 q^{91} - 48 q^{92} + 26 q^{93} - 42 q^{95} - 41 q^{96} + 24 q^{97}+O(q^{100}) \) 10 * q + 10 * q^3 + 18 * q^4 + 5 * q^5 + 10 * q^7 - 3 * q^8 + 10 * q^9 - 6 * q^10 + 18 * q^12 + 6 * q^13 + 5 * q^15 + 38 * q^16 + 8 * q^17 + 7 * q^20 + 10 * q^21 - 3 * q^24 + 31 * q^25 + q^26 + 10 * q^27 + 18 * q^28 - 14 * q^29 - 6 * q^30 + 26 * q^31 - 41 * q^32 + 21 * q^34 + 5 * q^35 + 18 * q^36 + 24 * q^37 + 8 * q^38 + 6 * q^39 - 5 * q^40 + 19 * q^41 - 6 * q^43 + 5 * q^45 - q^46 + 15 * q^47 + 38 * q^48 + 10 * q^49 - q^50 + 8 * q^51 - 25 * q^52 - q^53 - 3 * q^56 + 11 * q^58 + 23 * q^59 + 7 * q^60 + 11 * q^62 + 10 * q^63 + 53 * q^64 - 29 * q^65 + 38 * q^67 + 87 * q^68 - 6 * q^70 + 26 * q^71 - 3 * q^72 - q^73 - 39 * q^74 + 31 * q^75 - 2 * q^76 + q^78 + 5 * q^79 + 6 * q^80 + 10 * q^81 + 5 * q^82 + 6 * q^83 + 18 * q^84 - q^85 - 41 * q^86 - 14 * q^87 - 9 * q^89 - 6 * q^90 + 6 * q^91 - 48 * q^92 + 26 * q^93 - 42 * q^95 - 41 * q^96 + 24 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more