LMFDB - Embedded newform 1681.2.a.m.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1681,2,Mod(1,1681)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1681, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1681.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1681 = 41^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1681.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:	$13.4228525798$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	no (minimal twist has level 41)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	1681.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.888284 q^{2} -1.39100 q^{3} -1.21095 q^{4} +1.07324 q^{5} +1.23560 q^{6} -3.99983 q^{7} +2.85224 q^{8} -1.06513 q^{9} +O(q^{10})$	\(q-0.888284 q^{2} -1.39100 q^{3} -1.21095 q^{4} +1.07324 q^{5} +1.23560 q^{6} -3.99983 q^{7} +2.85224 q^{8} -1.06513 q^{9} -0.953338 q^{10} -2.51378 q^{11} +1.68443 q^{12} -4.30504 q^{13} +3.55299 q^{14} -1.49287 q^{15} -0.111696 q^{16} -4.78272 q^{17} +0.946136 q^{18} -0.979059 q^{19} -1.29964 q^{20} +5.56375 q^{21} +2.23295 q^{22} -2.20548 q^{23} -3.96745 q^{24} -3.84817 q^{25} +3.82410 q^{26} +5.65458 q^{27} +4.84360 q^{28} +2.05607 q^{29} +1.32609 q^{30} +6.55728 q^{31} -5.60526 q^{32} +3.49666 q^{33} +4.24842 q^{34} -4.29276 q^{35} +1.28982 q^{36} -10.8406 q^{37} +0.869683 q^{38} +5.98830 q^{39} +3.06112 q^{40} -4.94220 q^{42} -2.01642 q^{43} +3.04407 q^{44} -1.14313 q^{45} +1.95909 q^{46} -9.95352 q^{47} +0.155368 q^{48} +8.99865 q^{49} +3.41827 q^{50} +6.65275 q^{51} +5.21319 q^{52} -7.76440 q^{53} -5.02287 q^{54} -2.69788 q^{55} -11.4085 q^{56} +1.36187 q^{57} -1.82637 q^{58} -9.60480 q^{59} +1.80779 q^{60} +0.448149 q^{61} -5.82473 q^{62} +4.26033 q^{63} +5.20245 q^{64} -4.62032 q^{65} -3.10603 q^{66} +3.50681 q^{67} +5.79164 q^{68} +3.06781 q^{69} +3.81319 q^{70} +14.0886 q^{71} -3.03800 q^{72} +8.75882 q^{73} +9.62952 q^{74} +5.35279 q^{75} +1.18559 q^{76} +10.0547 q^{77} -5.31931 q^{78} +2.73261 q^{79} -0.119876 q^{80} -4.67012 q^{81} -2.79623 q^{83} -6.73743 q^{84} -5.13299 q^{85} +1.79115 q^{86} -2.85998 q^{87} -7.16990 q^{88} -11.1072 q^{89} +1.01543 q^{90} +17.2194 q^{91} +2.67073 q^{92} -9.12116 q^{93} +8.84156 q^{94} -1.05076 q^{95} +7.79690 q^{96} +3.76003 q^{97} -7.99336 q^{98} +2.67750 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 8 q^{2} + 20 q^{4} + 12 q^{5} + 24 q^{8} + 24 q^{9}+O(q^{10}) $ 24 * q + 8 * q^2 + 20 * q^4 + 12 * q^5 + 24 * q^8 + 24 * q^9	$ 24 q + 8 q^{2} + 20 q^{4} + 12 q^{5} + 24 q^{8} + 24 q^{9} - 4 q^{10} + 20 q^{16} + 20 q^{18} + 40 q^{20} + 56 q^{21} + 48 q^{23} + 8 q^{25} + 32 q^{31} + 36 q^{32} + 24 q^{33} + 108 q^{36} + 60 q^{39} + 44 q^{40} - 40 q^{42} + 36 q^{43} - 36 q^{45} + 36 q^{46} + 32 q^{49} - 60 q^{50} + 36 q^{51} - 60 q^{57} + 116 q^{59} + 40 q^{61} + 48 q^{62} + 60 q^{64} + 16 q^{66} + 4 q^{72} + 16 q^{73} + 24 q^{74} - 16 q^{77} - 60 q^{78} + 84 q^{80} - 28 q^{81} + 80 q^{83} - 24 q^{84} - 24 q^{86} + 76 q^{87} + 56 q^{90} + 40 q^{91} - 40 q^{92} + 36 q^{98}+O(q^{100}) $ 24 * q + 8 * q^2 + 20 * q^4 + 12 * q^5 + 24 * q^8 + 24 * q^9 - 4 * q^10 + 20 * q^16 + 20 * q^18 + 40 * q^20 + 56 * q^21 + 48 * q^23 + 8 * q^25 + 32 * q^31 + 36 * q^32 + 24 * q^33 + 108 * q^36 + 60 * q^39 + 44 * q^40 - 40 * q^42 + 36 * q^43 - 36 * q^45 + 36 * q^46 + 32 * q^49 - 60 * q^50 + 36 * q^51 - 60 * q^57 + 116 * q^59 + 40 * q^61 + 48 * q^62 + 60 * q^64 + 16 * q^66 + 4 * q^72 + 16 * q^73 + 24 * q^74 - 16 * q^77 - 60 * q^78 + 84 * q^80 - 28 * q^81 + 80 * q^83 - 24 * q^84 - 24 * q^86 + 76 * q^87 + 56 * q^90 + 40 * q^91 - 40 * q^92 + 36 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.888284	−0.628112	−0.314056	−	0.949404i	$-0.601688\pi$
$2$	−0.888284	−0.628112	−0.314056	+	0.949404i	$0.601688\pi$
$3$	−1.39100	−0.803093	−0.401546	−	0.915839i	$-0.631527\pi$
$3$	−1.39100	−0.803093	−0.401546	+	0.915839i	$0.631527\pi$
$4$	−1.21095	−0.605475
$5$	1.07324	0.479966	0.239983	−	0.970777i	$-0.422858\pi$
$5$	1.07324	0.479966	0.239983	+	0.970777i	$0.422858\pi$
$6$	1.23560	0.504432
$7$	−3.99983	−1.51179	−0.755897	−	0.654690i	$-0.772799\pi$
$7$	−3.99983	−1.51179	−0.755897	+	0.654690i	$0.772799\pi$
$8$	2.85224	1.00842
$9$	−1.06513	−0.355042
$10$	−0.953338	−0.301472
$11$	−2.51378	−0.757934	−0.378967	−	0.925410i	$-0.623721\pi$
$11$	−2.51378	−0.757934	−0.378967	+	0.925410i	$0.623721\pi$
$12$	1.68443	0.486253
$13$	−4.30504	−1.19400	−0.597002	−	0.802240i	$-0.703641\pi$
$13$	−4.30504	−1.19400	−0.597002	+	0.802240i	$0.703641\pi$
$14$	3.55299	0.949576
$15$	−1.49287	−0.385457
$16$	−0.111696	−0.0279239
$17$	−4.78272	−1.15998	−0.579990	−	0.814623i	$-0.696944\pi$
$17$	−4.78272	−1.15998	−0.579990	+	0.814623i	$0.696944\pi$
$18$	0.946136	0.223006
$19$	−0.979059	−0.224612	−0.112306	−	0.993674i	$-0.535824\pi$
$19$	−0.979059	−0.224612	−0.112306	+	0.993674i	$0.535824\pi$
$20$	−1.29964	−0.290607
$21$	5.56375	1.21411
$22$	2.23295	0.476067
$23$	−2.20548	−0.459874	−0.229937	−	0.973206i	$-0.573852\pi$
$23$	−2.20548	−0.459874	−0.229937	+	0.973206i	$0.573852\pi$
$24$	−3.96745	−0.809853
$25$	−3.84817	−0.769633
$26$	3.82410	0.749968
$27$	5.65458	1.08822
$28$	4.84360	0.915354
$29$	2.05607	0.381802	0.190901	−	0.981609i	$-0.438859\pi$
$29$	2.05607	0.381802	0.190901	+	0.981609i	$0.438859\pi$
$30$	1.32609	0.242110
$31$	6.55728	1.17772	0.588862	−	0.808234i	$-0.299576\pi$
$31$	6.55728	1.17772	0.588862	+	0.808234i	$0.299576\pi$
$32$	−5.60526	−0.990879
$33$	3.49666	0.608691
$34$	4.24842	0.728597
$35$	−4.29276	−0.725609
$36$	1.28982	0.214969
$37$	−10.8406	−1.78218	−0.891090	−	0.453826i	$-0.850059\pi$
$37$	−10.8406	−1.78218	−0.891090	+	0.453826i	$0.850059\pi$
$38$	0.869683	0.141081
$39$	5.98830	0.958895
$40$	3.06112	0.484006
$41$	0	0
$41$	0	0
$42$	−4.94220	−0.762597
$43$	−2.01642	−0.307501	−0.153750	−	0.988110i	$-0.549135\pi$
$43$	−2.01642	−0.307501	−0.153750	+	0.988110i	$0.549135\pi$
$44$	3.04407	0.458910
$45$	−1.14313	−0.170408
$46$	1.95909	0.288852
$47$	−9.95352	−1.45187	−0.725935	−	0.687763i	$-0.758593\pi$
$47$	−9.95352	−1.45187	−0.725935	+	0.687763i	$0.758593\pi$
$48$	0.155368	0.0224255
$49$	8.99865	1.28552
$50$	3.41827	0.483416
$51$	6.65275	0.931572
$52$	5.21319	0.722940
$53$	−7.76440	−1.06652	−0.533261	−	0.845951i	$-0.679034\pi$
$53$	−7.76440	−1.06652	−0.533261	+	0.845951i	$0.679034\pi$
$54$	−5.02287	−0.683527
$55$	−2.69788	−0.363782
$56$	−11.4085	−1.52452
$57$	1.36187	0.180384
$58$	−1.82637	−0.239814
$59$	−9.60480	−1.25044	−0.625219	−	0.780449i	$-0.714990\pi$
$59$	−9.60480	−1.25044	−0.625219	+	0.780449i	$0.714990\pi$
$60$	1.80779	0.233385
$61$	0.448149	0.0573797	0.0286898	−	0.999588i	$-0.490866\pi$
$61$	0.448149	0.0573797	0.0286898	+	0.999588i	$0.490866\pi$
$62$	−5.82473	−0.739742
$63$	4.26033	0.536751
$64$	5.20245	0.650307
$65$	−4.62032	−0.573080
$66$	−3.10603	−0.382326
$67$	3.50681	0.428425	0.214212	−	0.976787i	$-0.431282\pi$
$67$	3.50681	0.428425	0.214212	+	0.976787i	$0.431282\pi$
$68$	5.79164	0.702340
$69$	3.06781	0.369321
$70$	3.81319	0.455764
$71$	14.0886	1.67201	0.836006	−	0.548720i	$-0.184885\pi$
$71$	14.0886	1.67201	0.836006	+	0.548720i	$0.184885\pi$
$72$	−3.03800	−0.358031
$73$	8.75882	1.02514	0.512571	−	0.858645i	$-0.328693\pi$
$73$	8.75882	1.02514	0.512571	+	0.858645i	$0.328693\pi$
$74$	9.62952	1.11941
$75$	5.35279	0.618087
$76$	1.18559	0.135997
$77$	10.0547	1.14584
$78$	−5.31931	−0.602293
$79$	2.73261	0.307442	0.153721	−	0.988114i	$-0.450874\pi$
$79$	2.73261	0.307442	0.153721	+	0.988114i	$0.450874\pi$
$80$	−0.119876	−0.0134025
$81$	−4.67012	−0.518903
$82$	0	0
$83$	−2.79623	−0.306926	−0.153463	−	0.988154i	$-0.549043\pi$
$83$	−2.79623	−0.306926	−0.153463	+	0.988154i	$0.549043\pi$
$84$	−6.73743	−0.735114
$85$	−5.13299	−0.556751
$86$	1.79115	0.193145
$87$	−2.85998	−0.306622
$88$	−7.16990	−0.764314
$89$	−11.1072	−1.17736	−0.588678	−	0.808368i	$-0.700351\pi$
$89$	−11.1072	−1.17736	−0.588678	+	0.808368i	$0.700351\pi$
$90$	1.01543	0.107035
$91$	17.2194	1.80509
$92$	2.67073	0.278442
$93$	−9.12116	−0.945821
$94$	8.84156	0.911937
$95$	−1.05076	−0.107806
$96$	7.79690	0.795767
$97$	3.76003	0.381773	0.190887	−	0.981612i	$-0.438864\pi$
$97$	3.76003	0.381773	0.190887	+	0.981612i	$0.438864\pi$
$98$	−7.99336	−0.807451
$99$	2.67750	0.269099
$100$	4.65994	0.465994
$101$	1.82787	0.181880	0.0909400	−	0.995856i	$-0.471013\pi$
$101$	1.82787	0.181880	0.0909400	+	0.995856i	$0.471013\pi$
$102$	−5.90954	−0.585131
$103$	11.1213	1.09581	0.547907	−	0.836540i	$-0.315425\pi$
$103$	11.1213	1.09581	0.547907	+	0.836540i	$0.315425\pi$
$104$	−12.2790	−1.20405
$105$	5.97122	0.582731
$106$	6.89699	0.669895
$107$	12.9270	1.24970	0.624852	−	0.780744i	$-0.285159\pi$
$107$	12.9270	1.24970	0.624852	+	0.780744i	$0.285159\pi$
$108$	−6.84742	−0.658893
$109$	6.67066	0.638933	0.319466	−	0.947598i	$-0.396496\pi$
$109$	6.67066	0.638933	0.319466	+	0.947598i	$0.396496\pi$
$110$	2.39648	0.228496
$111$	15.0792	1.43126
$112$	0.446764	0.0422152
$113$	13.0730	1.22981	0.614903	−	0.788603i	$-0.289195\pi$
$113$	13.0730	1.22981	0.614903	+	0.788603i	$0.289195\pi$
$114$	−1.20973	−0.113301
$115$	−2.36700	−0.220724
$116$	−2.48979	−0.231172
$117$	4.58541	0.423922
$118$	8.53179	0.785415
$119$	19.1301	1.75365
$120$	−4.25801	−0.388702
$121$	−4.68090	−0.425536
$122$	−0.398084	−0.0360408
$123$	0	0
$124$	−7.94055	−0.713082
$125$	−9.49617	−0.849363
$126$	−3.78438	−0.337140
$127$	−9.20929	−0.817193	−0.408596	−	0.912715i	$-0.633982\pi$
$127$	−9.20929	−0.817193	−0.408596	+	0.912715i	$0.633982\pi$
$128$	6.58926	0.582414
$129$	2.80483	0.246952
$130$	4.10416	0.359959
$131$	−0.188953	−0.0165089	−0.00825443	−	0.999966i	$-0.502627\pi$
$131$	−0.188953	−0.0165089	−0.00825443	+	0.999966i	$0.502627\pi$
$132$	−4.23429	−0.368547
$133$	3.91607	0.339567
$134$	−3.11504	−0.269099
$135$	6.06870	0.522310
$136$	−13.6415	−1.16975
$137$	−6.42839	−0.549215	−0.274607	−	0.961556i	$-0.588548\pi$
$137$	−6.42839	−0.549215	−0.274607	+	0.961556i	$0.588548\pi$
$138$	−2.72509	−0.231975
$139$	−7.20171	−0.610841	−0.305421	−	0.952218i	$-0.598797\pi$
$139$	−7.20171	−0.610841	−0.305421	+	0.952218i	$0.598797\pi$
$140$	5.19832	0.439339
$141$	13.8453	1.16599
$142$	−12.5147	−1.05021
$143$	10.8219	0.904976
$144$	0.118970	0.00991418
$145$	2.20664	0.183252
$146$	−7.78032	−0.643904
$147$	−12.5171	−1.03239
$148$	13.1274	1.07907
$149$	4.86268	0.398367	0.199183	−	0.979962i	$-0.436171\pi$
$149$	4.86268	0.398367	0.199183	+	0.979962i	$0.436171\pi$
$150$	−4.75480	−0.388228
$151$	−9.51749	−0.774523	−0.387261	−	0.921970i	$-0.626579\pi$
$151$	−9.51749	−0.774523	−0.387261	+	0.921970i	$0.626579\pi$
$152$	−2.79251	−0.226502
$153$	5.09421	0.411842
$154$	−8.93144	−0.719716
$155$	7.03751	0.565266
$156$	−7.25154	−0.580588
$157$	7.86599	0.627775	0.313887	−	0.949460i	$-0.398369\pi$
$157$	7.86599	0.627775	0.313887	+	0.949460i	$0.398369\pi$
$158$	−2.42733	−0.193108
$159$	10.8003	0.856516
$160$	−6.01576	−0.475588
$161$	8.82154	0.695235
$162$	4.14840	0.325929
$163$	14.6310	1.14599	0.572994	−	0.819560i	$-0.305782\pi$
$163$	14.6310	1.14599	0.572994	+	0.819560i	$0.305782\pi$
$164$	0	0
$165$	3.75274	0.292151
$166$	2.48385	0.192784
$167$	0.189670	0.0146771	0.00733856	−	0.999973i	$-0.497664\pi$
$167$	0.189670	0.0146771	0.00733856	+	0.999973i	$0.497664\pi$
$168$	15.8691	1.22433
$169$	5.53337	0.425644
$170$	4.55955	0.349702
$171$	1.04282	0.0797466
$172$	2.44178	0.186184
$173$	−5.31858	−0.404364	−0.202182	−	0.979348i	$-0.564803\pi$
$173$	−5.31858	−0.404364	−0.202182	+	0.979348i	$0.564803\pi$
$174$	2.54048	0.192593
$175$	15.3920	1.16353
$176$	0.280779	0.0211645
$177$	13.3602	1.00422
$178$	9.86631	0.739511
$179$	16.6600	1.24523	0.622614	−	0.782529i	$-0.286071\pi$
$179$	16.6600	1.24523	0.622614	+	0.782529i	$0.286071\pi$
$180$	1.38428	0.103178
$181$	10.5478	0.784012	0.392006	−	0.919963i	$-0.371781\pi$
$181$	10.5478	0.784012	0.392006	+	0.919963i	$0.371781\pi$
$182$	−15.2958	−1.13380
$183$	−0.623375	−0.0460812
$184$	−6.29055	−0.463745
$185$	−11.6345	−0.855385
$186$	8.10219	0.594081
$187$	12.0227	0.879188
$188$	12.0532	0.879072
$189$	−22.6174	−1.64517
$190$	0.933375	0.0677141
$191$	−15.7538	−1.13990	−0.569951	−	0.821679i	$-0.693038\pi$
$191$	−15.7538	−1.13990	−0.569951	+	0.821679i	$0.693038\pi$
$192$	−7.23660	−0.522256
$193$	−23.3738	−1.68248	−0.841241	−	0.540660i	$-0.818175\pi$
$193$	−23.3738	−1.68248	−0.841241	+	0.540660i	$0.818175\pi$
$194$	−3.33997	−0.239796
$195$	6.42686	0.460237
$196$	−10.8969	−0.778352
$197$	11.8424	0.843737	0.421868	−	0.906657i	$-0.361374\pi$
$197$	11.8424	0.843737	0.421868	+	0.906657i	$0.361374\pi$
$198$	−2.37838	−0.169024
$199$	8.47167	0.600541	0.300270	−	0.953854i	$-0.402923\pi$
$199$	8.47167	0.600541	0.300270	+	0.953854i	$0.402923\pi$
$200$	−10.9759	−0.776112
$201$	−4.87796	−0.344065
$202$	−1.62367	−0.114241
$203$	−8.22392	−0.577206
$204$	−8.05616	−0.564044
$205$	0	0
$206$	−9.87887	−0.688293
$207$	2.34911	0.163275
$208$	0.480855	0.0333413
$209$	2.46114	0.170241
$210$	−5.30414	−0.366020
$211$	9.60891	0.661505	0.330752	−	0.943718i	$-0.392698\pi$
$211$	9.60891	0.661505	0.330752	+	0.943718i	$0.392698\pi$
$212$	9.40231	0.645753
$213$	−19.5972	−1.34278
$214$	−11.4829	−0.784953
$215$	−2.16409	−0.147590
$216$	16.1282	1.09739
$217$	−26.2280	−1.78047
$218$	−5.92544	−0.401321
$219$	−12.1835	−0.823284
$220$	3.26700	0.220261
$221$	20.5898	1.38502
$222$	−13.3946	−0.898989
$223$	5.34590	0.357988	0.178994	−	0.983850i	$-0.442716\pi$
$223$	5.34590	0.357988	0.178994	+	0.983850i	$0.442716\pi$
$224$	22.4201	1.49800
$225$	4.09878	0.273252
$226$	−11.6125	−0.772455
$227$	6.93997	0.460622	0.230311	−	0.973117i	$-0.426026\pi$
$227$	6.93997	0.460622	0.230311	+	0.973117i	$0.426026\pi$
$228$	−1.64916	−0.109218
$229$	−17.8589	−1.18015	−0.590075	−	0.807349i	$-0.700902\pi$
$229$	−17.8589	−1.18015	−0.590075	+	0.807349i	$0.700902\pi$
$230$	2.10257	0.138639
$231$	−13.9861	−0.920216
$232$	5.86439	0.385016
$233$	−4.35926	−0.285585	−0.142792	−	0.989753i	$-0.545608\pi$
$233$	−4.35926	−0.285585	−0.142792	+	0.989753i	$0.545608\pi$
$234$	−4.07315	−0.266270
$235$	−10.6825	−0.696848
$236$	11.6309	0.757110
$237$	−3.80105	−0.246905
$238$	−16.9930	−1.10149
$239$	11.1184	0.719189	0.359594	−	0.933109i	$-0.382915\pi$
$239$	11.1184	0.719189	0.359594	+	0.933109i	$0.382915\pi$
$240$	0.166747	0.0107635
$241$	−19.4104	−1.25034	−0.625168	−	0.780490i	$-0.714970\pi$
$241$	−19.4104	−1.25034	−0.625168	+	0.780490i	$0.714970\pi$
$242$	4.15797	0.267284
$243$	−10.4676	−0.671498
$244$	−0.542687	−0.0347420
$245$	9.65767	0.617006
$246$	0	0
$247$	4.21489	0.268187
$248$	18.7029	1.18764
$249$	3.88955	0.246490
$250$	8.43529	0.533495
$251$	−2.32743	−0.146906	−0.0734532	−	0.997299i	$-0.523402\pi$
$251$	−2.32743	−0.146906	−0.0734532	+	0.997299i	$0.523402\pi$
$252$	−5.15905	−0.324990
$253$	5.54409	0.348554
$254$	8.18047	0.513288
$255$	7.13997	0.447122
$256$	−16.2580	−1.01613
$257$	−19.5191	−1.21757	−0.608784	−	0.793336i	$-0.708342\pi$
$257$	−19.5191	−1.21757	−0.608784	+	0.793336i	$0.708342\pi$
$258$	−2.49149	−0.155113
$259$	43.3605	2.69429
$260$	5.59498	0.346986
$261$	−2.18997	−0.135556
$262$	0.167844	0.0103694
$263$	−3.27200	−0.201760	−0.100880	−	0.994899i	$-0.532166\pi$
$263$	−3.27200	−0.201760	−0.100880	+	0.994899i	$0.532166\pi$
$264$	9.97331	0.613815
$265$	−8.33303	−0.511894
$266$	−3.47859	−0.213286
$267$	15.4500	0.945526
$268$	−4.24657	−0.259401
$269$	−11.1444	−0.679484	−0.339742	−	0.940519i	$-0.610340\pi$
$269$	−11.1444	−0.679484	−0.339742	+	0.940519i	$0.610340\pi$
$270$	−5.39073	−0.328069
$271$	−6.39394	−0.388404	−0.194202	−	0.980962i	$-0.562212\pi$
$271$	−6.39394	−0.388404	−0.194202	+	0.980962i	$0.562212\pi$
$272$	0.534210	0.0323912
$273$	−23.9522	−1.44965
$274$	5.71024	0.344968
$275$	9.67345	0.583331
$276$	−3.71497	−0.223615
$277$	−25.1941	−1.51377	−0.756885	−	0.653548i	$-0.773280\pi$
$277$	−25.1941	−1.51377	−0.756885	+	0.653548i	$0.773280\pi$
$278$	6.39717	0.383677
$279$	−6.98434	−0.418142
$280$	−12.2440	−0.731717
$281$	−3.39760	−0.202684	−0.101342	−	0.994852i	$-0.532314\pi$
$281$	−3.39760	−0.202684	−0.101342	+	0.994852i	$0.532314\pi$
$282$	−12.2986	−0.732370
$283$	7.53451	0.447880	0.223940	−	0.974603i	$-0.428108\pi$
$283$	7.53451	0.447880	0.223940	+	0.974603i	$0.428108\pi$
$284$	−17.0606	−1.01236
$285$	1.46161	0.0865781
$286$	−9.61295	−0.568426
$287$	0	0
$288$	5.97031	0.351804
$289$	5.87443	0.345554
$290$	−1.96013	−0.115103
$291$	−5.23019	−0.306599
$292$	−10.6065	−0.620699
$293$	5.97515	0.349072	0.174536	−	0.984651i	$-0.444157\pi$
$293$	5.97515	0.349072	0.174536	+	0.984651i	$0.444157\pi$
$294$	11.1187	0.648458
$295$	−10.3082	−0.600167
$296$	−30.9199	−1.79718
$297$	−14.2144	−0.824802
$298$	−4.31945	−0.250219
$299$	9.49467	0.549091
$300$	−6.48196	−0.374236
$301$	8.06533	0.464878
$302$	8.45424	0.486487
$303$	−2.54256	−0.146067
$304$	0.109357	0.00627204
$305$	0.480970	0.0275403
$306$	−4.52510	−0.258683
$307$	−0.736335	−0.0420249	−0.0210124	−	0.999779i	$-0.506689\pi$
$307$	−0.736335	−0.0420249	−0.0210124	+	0.999779i	$0.506689\pi$
$308$	−12.1758	−0.693778
$309$	−15.4697	−0.880039
$310$	−6.25131	−0.355051
$311$	28.8605	1.63653	0.818263	−	0.574844i	$-0.194937\pi$
$311$	28.8605	1.63653	0.818263	+	0.574844i	$0.194937\pi$
$312$	17.0800	0.966967
$313$	16.4147	0.927812	0.463906	−	0.885884i	$-0.346447\pi$
$313$	16.4147	0.927812	0.463906	+	0.885884i	$0.346447\pi$
$314$	−6.98724	−0.394313
$315$	4.57234	0.257622
$316$	−3.30905	−0.186149
$317$	−33.7701	−1.89672	−0.948358	−	0.317201i	$-0.897257\pi$
$317$	−33.7701	−1.89672	−0.948358	+	0.317201i	$0.897257\pi$
$318$	−9.59370	−0.537988
$319$	−5.16850	−0.289380
$320$	5.58346	0.312125
$321$	−17.9815	−1.00363
$322$	−7.83604	−0.436685
$323$	4.68257	0.260545
$324$	5.65529	0.314183
$325$	16.5665	0.918945
$326$	−12.9965	−0.719808
$327$	−9.27886	−0.513122
$328$	0	0
$329$	39.8124	2.19493
$330$	−3.33350	−0.183503
$331$	−12.0508	−0.662371	−0.331186	−	0.943566i	$-0.607449\pi$
$331$	−12.0508	−0.662371	−0.331186	+	0.943566i	$0.607449\pi$
$332$	3.38610	0.185836
$333$	11.5466	0.632750
$334$	−0.168481	−0.00921887
$335$	3.76363	0.205629
$336$	−0.621448	−0.0339027
$337$	3.80509	0.207276	0.103638	−	0.994615i	$-0.466952\pi$
$337$	3.80509	0.207276	0.103638	+	0.994615i	$0.466952\pi$
$338$	−4.91521	−0.267352
$339$	−18.1845	−0.987647
$340$	6.21580	0.337099
$341$	−16.4836	−0.892636
$342$	−0.926323	−0.0500898
$343$	−7.99427	−0.431650
$344$	−5.75130	−0.310090
$345$	3.29249	0.177262
$346$	4.72441	0.253986
$347$	16.1504	0.866998	0.433499	−	0.901154i	$-0.357279\pi$
$347$	16.1504	0.866998	0.433499	+	0.901154i	$0.357279\pi$
$348$	3.46330	0.185652
$349$	−0.916485	−0.0490583	−0.0245292	−	0.999699i	$-0.507809\pi$
$349$	−0.916485	−0.0490583	−0.0245292	+	0.999699i	$0.507809\pi$
$350$	−13.6725	−0.730825
$351$	−24.3432	−1.29934
$352$	14.0904	0.751021
$353$	−4.30763	−0.229272	−0.114636	−	0.993408i	$-0.536570\pi$
$353$	−4.30763	−0.229272	−0.114636	+	0.993408i	$0.536570\pi$
$354$	−11.8677	−0.630761
$355$	15.1204	0.802508
$356$	13.4502	0.712860
$357$	−26.6099	−1.40834
$358$	−14.7988	−0.782142
$359$	−25.9883	−1.37161	−0.685806	−	0.727785i	$-0.740550\pi$
$359$	−25.9883	−1.37161	−0.685806	+	0.727785i	$0.740550\pi$
$360$	−3.26048	−0.171843
$361$	−18.0414	−0.949550
$362$	−9.36945	−0.492447
$363$	6.51112	0.341745
$364$	−20.8519	−1.09294
$365$	9.40028	0.492033
$366$	0.553734	0.0289441
$367$	−13.7804	−0.719330	−0.359665	−	0.933082i	$-0.617109\pi$
$367$	−13.7804	−0.719330	−0.359665	+	0.933082i	$0.617109\pi$
$368$	0.246343	0.0128415
$369$	0	0
$370$	10.3347	0.537278
$371$	31.0563	1.61236
$372$	11.0453	0.572671
$373$	−34.6509	−1.79415	−0.897077	−	0.441875i	$-0.854313\pi$
$373$	−34.6509	−1.79415	−0.897077	+	0.441875i	$0.854313\pi$
$374$	−10.6796	−0.552229
$375$	13.2091	0.682117
$376$	−28.3898	−1.46409
$377$	−8.85145	−0.455873
$378$	20.0907	1.03335
$379$	−9.52332	−0.489180	−0.244590	−	0.969627i	$-0.578653\pi$
$379$	−9.52332	−0.489180	−0.244590	+	0.969627i	$0.578653\pi$
$380$	1.27242	0.0652738
$381$	12.8101	0.656281
$382$	13.9938	0.715986
$383$	−23.7102	−1.21153	−0.605767	−	0.795642i	$-0.707134\pi$
$383$	−23.7102	−1.21153	−0.605767	+	0.795642i	$0.707134\pi$
$384$	−9.16564	−0.467732
$385$	10.7911	0.549964
$386$	20.7626	1.05679
$387$	2.14774	0.109176
$388$	−4.55321	−0.231154
$389$	10.9748	0.556444	0.278222	−	0.960517i	$-0.410255\pi$
$389$	10.9748	0.556444	0.278222	+	0.960517i	$0.410255\pi$
$390$	−5.70887	−0.289080
$391$	10.5482	0.533445
$392$	25.6663	1.29634
$393$	0.262832	0.0132581
$394$	−10.5194	−0.529961
$395$	2.93273	0.147562
$396$	−3.24232	−0.162933
$397$	−25.6661	−1.28814	−0.644072	−	0.764965i	$-0.722756\pi$
$397$	−25.6661	−1.28814	−0.644072	+	0.764965i	$0.722756\pi$
$398$	−7.52525	−0.377207
$399$	−5.44725	−0.272703
$400$	0.429824	0.0214912
$401$	26.7180	1.33423	0.667117	−	0.744953i	$-0.267528\pi$
$401$	26.7180	1.33423	0.667117	+	0.744953i	$0.267528\pi$
$402$	4.33301	0.216111
$403$	−28.2294	−1.40621
$404$	−2.21346	−0.110124
$405$	−5.01214	−0.249055
$406$	7.30518	0.362550
$407$	27.2509	1.35077
$408$	18.9752	0.939414
$409$	−35.3318	−1.74704	−0.873522	−	0.486785i	$-0.838169\pi$
$409$	−35.3318	−1.74704	−0.873522	+	0.486785i	$0.838169\pi$
$410$	0	0
$411$	8.94188	0.441070
$412$	−13.4673	−0.663488
$413$	38.4176	1.89041
$414$	−2.08668	−0.102555
$415$	−3.00102	−0.147314
$416$	24.1309	1.18311
$417$	10.0176	0.490562
$418$	−2.18619	−0.106930
$419$	−28.5341	−1.39398	−0.696991	−	0.717080i	$-0.745478\pi$
$419$	−28.5341	−1.39398	−0.696991	+	0.717080i	$0.745478\pi$
$420$	−7.23085	−0.352830
$421$	10.2514	0.499624	0.249812	−	0.968294i	$-0.419631\pi$
$421$	10.2514	0.499624	0.249812	+	0.968294i	$0.419631\pi$
$422$	−8.53544	−0.415499
$423$	10.6018	0.515475
$424$	−22.1459	−1.07550
$425$	18.4047	0.892759
$426$	17.4079	0.843417
$427$	−1.79252	−0.0867462
$428$	−15.6540	−0.756665
$429$	−15.0533	−0.726779
$430$	1.92233	0.0927029
$431$	20.7643	1.00018	0.500090	−	0.865974i	$-0.333300\pi$
$431$	20.7643	1.00018	0.500090	+	0.865974i	$0.333300\pi$
$432$	−0.631592	−0.0303875
$433$	−16.4531	−0.790683	−0.395342	−	0.918534i	$-0.629374\pi$
$433$	−16.4531	−0.790683	−0.395342	+	0.918534i	$0.629374\pi$
$434$	23.2980	1.11834
$435$	−3.06943	−0.147168
$436$	−8.07784	−0.386858
$437$	2.15929	0.103293
$438$	10.8224	0.517115
$439$	22.9952	1.09750	0.548751	−	0.835986i	$-0.315103\pi$
$439$	22.9952	1.09750	0.548751	+	0.835986i	$0.315103\pi$
$440$	−7.69499	−0.366844
$441$	−9.58471	−0.456415
$442$	−18.2896	−0.869948
$443$	0.348758	0.0165700	0.00828499	−	0.999966i	$-0.497363\pi$
$443$	0.348758	0.0165700	0.00828499	+	0.999966i	$0.497363\pi$
$444$	−18.2602	−0.866590
$445$	−11.9206	−0.565090
$446$	−4.74868	−0.224856
$447$	−6.76398	−0.319925
$448$	−20.8089	−0.983130
$449$	29.3605	1.38561	0.692804	−	0.721126i	$-0.256375\pi$
$449$	29.3605	1.38561	0.692804	+	0.721126i	$0.256375\pi$
$450$	−3.64089	−0.171633
$451$	0	0
$452$	−15.8308	−0.744617
$453$	13.2388	0.622013
$454$	−6.16466	−0.289322
$455$	18.4805	0.866380
$456$	3.88437	0.181902
$457$	8.54996	0.399950	0.199975	−	0.979801i	$-0.435914\pi$
$457$	8.54996	0.399950	0.199975	+	0.979801i	$0.435914\pi$
$458$	15.8638	0.741266
$459$	−27.0443	−1.26232
$460$	2.86632	0.133643
$461$	35.0214	1.63111	0.815555	−	0.578680i	$-0.196432\pi$
$461$	35.0214	1.63111	0.815555	+	0.578680i	$0.196432\pi$
$462$	12.4236	0.577998
$463$	4.62254	0.214828	0.107414	−	0.994214i	$-0.465743\pi$
$463$	4.62254	0.214828	0.107414	+	0.994214i	$0.465743\pi$
$464$	−0.229654	−0.0106614
$465$	−9.78916	−0.453961
$466$	3.87226	0.179379
$467$	−27.6694	−1.28039	−0.640193	−	0.768214i	$-0.721146\pi$
$467$	−27.6694	−1.28039	−0.640193	+	0.768214i	$0.721146\pi$
$468$	−5.55271	−0.256674
$469$	−14.0266	−0.647690
$470$	9.48907	0.437698
$471$	−10.9416	−0.504161
$472$	−27.3952	−1.26096
$473$	5.06884	0.233065
$474$	3.37641	0.155084
$475$	3.76758	0.172869
$476$	−23.1656	−1.06179
$477$	8.27007	0.378660
$478$	−9.87629	−0.451731
$479$	5.11147	0.233549	0.116774	−	0.993158i	$-0.462745\pi$
$479$	5.11147	0.233549	0.116774	+	0.993158i	$0.462745\pi$
$480$	8.36791	0.381941
$481$	46.6691	2.12793
$482$	17.2420	0.785351
$483$	−12.2707	−0.558338
$484$	5.66834	0.257652
$485$	4.03540	0.183238
$486$	9.29822	0.421776
$487$	−22.3766	−1.01398	−0.506991	−	0.861952i	$-0.669242\pi$
$487$	−22.3766	−1.01398	−0.506991	+	0.861952i	$0.669242\pi$
$488$	1.27823	0.0578627
$489$	−20.3517	−0.920334
$490$	−8.57876	−0.387549
$491$	40.1125	1.81025	0.905125	−	0.425146i	$-0.139777\pi$
$491$	40.1125	1.81025	0.905125	+	0.425146i	$0.139777\pi$
$492$	0	0
$493$	−9.83359	−0.442883
$494$	−3.74402	−0.168451
$495$	2.87359	0.129158
$496$	−0.732421	−0.0328867
$497$	−56.3521	−2.52774
$498$	−3.45503	−0.154823
$499$	31.7119	1.41962	0.709810	−	0.704393i	$-0.248781\pi$
$499$	31.7119	1.41962	0.709810	+	0.704393i	$0.248781\pi$
$500$	11.4994	0.514268
$501$	−0.263831	−0.0117871
$502$	2.06742	0.0922736
$503$	3.53811	0.157757	0.0788784	−	0.996884i	$-0.474866\pi$
$503$	3.53811	0.157757	0.0788784	+	0.996884i	$0.474866\pi$
$504$	12.1515	0.541269
$505$	1.96174	0.0872962
$506$	−4.92473	−0.218931
$507$	−7.69691	−0.341832
$508$	11.1520	0.494790
$509$	−4.94012	−0.218967	−0.109484	−	0.993989i	$-0.534920\pi$
$509$	−4.94012	−0.218967	−0.109484	+	0.993989i	$0.534920\pi$
$510$	−6.34232	−0.280843
$511$	−35.0338	−1.54980
$512$	1.26325	0.0558282
$513$	−5.53617	−0.244428
$514$	17.3385	0.764769
$515$	11.9358	0.525953
$516$	−3.39651	−0.149523
$517$	25.0210	1.10042
$518$	−38.5165	−1.69232
$519$	7.39813	0.324742
$520$	−13.1783	−0.577905
$521$	−1.17922	−0.0516627	−0.0258313	−	0.999666i	$-0.508223\pi$
$521$	−1.17922	−0.0516627	−0.0258313	+	0.999666i	$0.508223\pi$
$522$	1.94532	0.0851442
$523$	−0.0293832	−0.00128484	−0.000642420	−	1.00000i	$-0.500204\pi$
$523$	−0.0293832	−0.00128484	−0.000642420		1.00000i	$0.500204\pi$
$524$	0.228812	0.00999571
$525$	−21.4102	−0.934420
$526$	2.90647	0.126728
$527$	−31.3617	−1.36614
$528$	−0.390562	−0.0169970
$529$	−18.1359	−0.788516
$530$	7.40210	0.321527
$531$	10.2303	0.443959
$532$	−4.74217	−0.205599
$533$	0	0
$534$	−13.7240	−0.593896
$535$	13.8737	0.599814
$536$	10.0022	0.432031
$537$	−23.1740	−1.00003
$538$	9.89937	0.426792
$539$	−22.6207	−0.974340
$540$	−7.34889	−0.316246
$541$	−35.7382	−1.53650	−0.768252	−	0.640148i	$-0.778873\pi$
$541$	−35.7382	−1.53650	−0.768252	+	0.640148i	$0.778873\pi$
$542$	5.67963	0.243961
$543$	−14.6720	−0.629634
$544$	26.8084	1.14940
$545$	7.15918	0.306666
$546$	21.2764	0.910544
$547$	−6.84844	−0.292818	−0.146409	−	0.989224i	$-0.546772\pi$
$547$	−6.84844	−0.292818	−0.146409	+	0.989224i	$0.546772\pi$
$548$	7.78447	0.332536
$549$	−0.477336	−0.0203722
$550$	−8.59277	−0.366397
$551$	−2.01301	−0.0857571
$552$	8.75014	0.372430
$553$	−10.9300	−0.464790
$554$	22.3796	0.950817
$555$	16.1836	0.686954
$556$	8.72092	0.369849
$557$	24.1663	1.02396	0.511980	−	0.858998i	$-0.328912\pi$
$557$	24.1663	1.02396	0.511980	+	0.858998i	$0.328912\pi$
$558$	6.20408	0.262640
$559$	8.68076	0.367157
$560$	0.479483	0.0202619
$561$	−16.7236	−0.706070
$562$	3.01803	0.127308
$563$	−7.39150	−0.311515	−0.155757	−	0.987795i	$-0.549782\pi$
$563$	−7.39150	−0.311515	−0.155757	+	0.987795i	$0.549782\pi$
$564$	−16.7660	−0.705976
$565$	14.0304	0.590264
$566$	−6.69279	−0.281319
$567$	18.6797	0.784474
$568$	40.1841	1.68609
$569$	3.82572	0.160383	0.0801913	−	0.996779i	$-0.474447\pi$
$569$	3.82572	0.160383	0.0801913	+	0.996779i	$0.474447\pi$
$570$	−1.29832	−0.0543807
$571$	11.0407	0.462038	0.231019	−	0.972949i	$-0.425794\pi$
$571$	11.0407	0.462038	0.231019	+	0.972949i	$0.425794\pi$
$572$	−13.1048	−0.547941
$573$	21.9134	0.915446
$574$	0	0
$575$	8.48705	0.353934
$576$	−5.54127	−0.230886
$577$	−10.2261	−0.425719	−0.212859	−	0.977083i	$-0.568278\pi$
$577$	−10.2261	−0.425719	−0.212859	+	0.977083i	$0.568278\pi$
$578$	−5.21816	−0.217047
$579$	32.5129	1.35119
$580$	−2.67214	−0.110954
$581$	11.1845	0.464009
$582$	4.64590	0.192579
$583$	19.5180	0.808353
$584$	24.9822	1.03377
$585$	4.92123	0.203468
$586$	−5.30764	−0.219256
$587$	−11.7684	−0.485734	−0.242867	−	0.970060i	$-0.578088\pi$
$587$	−11.7684	−0.485734	−0.242867	+	0.970060i	$0.578088\pi$
$588$	15.1576	0.625089
$589$	−6.41997	−0.264530
$590$	9.15662	0.376972
$591$	−16.4728	−0.677599
$592$	1.21085	0.0497655
$593$	27.3144	1.12167	0.560834	−	0.827928i	$-0.310481\pi$
$593$	27.3144	1.12167	0.560834	+	0.827928i	$0.310481\pi$
$594$	12.6264	0.518068
$595$	20.5311	0.841692
$596$	−5.88847	−0.241201
$597$	−11.7841	−0.482290
$598$	−8.43397	−0.344891
$599$	10.0921	0.412350	0.206175	−	0.978515i	$-0.433898\pi$
$599$	10.0921	0.412350	0.206175	+	0.978515i	$0.433898\pi$
$600$	15.2674	0.623290
$601$	13.9743	0.570024	0.285012	−	0.958524i	$-0.408002\pi$
$601$	13.9743	0.570024	0.285012	+	0.958524i	$0.408002\pi$
$602$	−7.16431	−0.291995
$603$	−3.73519	−0.152109
$604$	11.5252	0.468954
$605$	−5.02371	−0.204243
$606$	2.25852	0.0917461
$607$	6.26272	0.254196	0.127098	−	0.991890i	$-0.459434\pi$
$607$	6.26272	0.254196	0.127098	+	0.991890i	$0.459434\pi$
$608$	5.48788	0.222563
$609$	11.4394	0.463550
$610$	−0.427238	−0.0172984
$611$	42.8503	1.73354
$612$	−6.16883	−0.249360
$613$	−23.5577	−0.951487	−0.475744	−	0.879584i	$-0.657821\pi$
$613$	−23.5577	−0.951487	−0.475744	+	0.879584i	$0.657821\pi$
$614$	0.654075	0.0263963
$615$	0	0
$616$	28.6784	1.15549
$617$	−33.3329	−1.34193	−0.670966	−	0.741488i	$-0.734121\pi$
$617$	−33.3329	−1.34193	−0.670966	+	0.741488i	$0.734121\pi$
$618$	13.7415	0.552763
$619$	43.0834	1.73167	0.865834	−	0.500332i	$-0.166789\pi$
$619$	43.0834	1.73167	0.865834	+	0.500332i	$0.166789\pi$
$620$	−8.52208	−0.342255
$621$	−12.4711	−0.500446
$622$	−25.6363	−1.02792
$623$	44.4267	1.77992
$624$	−0.668867	−0.0267761
$625$	9.04921	0.361968
$626$	−14.5809	−0.582770
$627$	−3.42344	−0.136719
$628$	−9.52533	−0.380102
$629$	51.8475	2.06729
$630$	−4.06153	−0.161815
$631$	−7.27473	−0.289602	−0.144801	−	0.989461i	$-0.546254\pi$
$631$	−7.27473	−0.289602	−0.144801	+	0.989461i	$0.546254\pi$
$632$	7.79405	0.310031
$633$	−13.3660	−0.531249
$634$	29.9974	1.19135
$635$	−9.88374	−0.392224
$636$	−13.0786	−0.518599
$637$	−38.7396	−1.53492
$638$	4.59110	0.181763
$639$	−15.0062	−0.593635
$640$	7.07182	0.279538
$641$	−30.8003	−1.21654	−0.608270	−	0.793730i	$-0.708136\pi$
$641$	−30.8003	−1.21654	−0.608270	+	0.793730i	$0.708136\pi$
$642$	15.9726	0.630390
$643$	15.1965	0.599292	0.299646	−	0.954050i	$-0.403131\pi$
$643$	15.1965	0.599292	0.299646	+	0.954050i	$0.403131\pi$
$644$	−10.6825	−0.420948
$645$	3.01025	0.118528
$646$	−4.15945	−0.163651
$647$	−5.82135	−0.228861	−0.114430	−	0.993431i	$-0.536504\pi$
$647$	−5.82135	−0.228861	−0.114430	+	0.993431i	$0.536504\pi$
$648$	−13.3203	−0.523271
$649$	24.1444	0.947749
$650$	−14.7158	−0.577200
$651$	36.4831	1.42989
$652$	−17.7174	−0.693867
$653$	11.2690	0.440989	0.220495	−	0.975388i	$-0.429233\pi$
$653$	11.2690	0.440989	0.220495	+	0.975388i	$0.429233\pi$
$654$	8.24227	0.322298
$655$	−0.202791	−0.00792368
$656$	0	0
$657$	−9.32926	−0.363969
$658$	−35.3647	−1.37866
$659$	−26.5809	−1.03544	−0.517722	−	0.855549i	$-0.673220\pi$
$659$	−26.5809	−1.03544	−0.517722	+	0.855549i	$0.673220\pi$
$660$	−4.54439	−0.176890
$661$	3.01229	0.117165	0.0585823	−	0.998283i	$-0.481342\pi$
$661$	3.01229	0.117165	0.0585823	+	0.998283i	$0.481342\pi$
$662$	10.7045	0.416043
$663$	−28.6404	−1.11230
$664$	−7.97552	−0.309510
$665$	4.20287	0.162980
$666$	−10.2567	−0.397438
$667$	−4.53461	−0.175581
$668$	−0.229681	−0.00888663
$669$	−7.43613	−0.287497
$670$	−3.34317	−0.129158
$671$	−1.12655	−0.0434900
$672$	−31.1863	−1.20304
$673$	5.92009	0.228203	0.114101	−	0.993469i	$-0.463601\pi$
$673$	5.92009	0.228203	0.114101	+	0.993469i	$0.463601\pi$
$674$	−3.38000	−0.130193
$675$	−21.7598	−0.837534
$676$	−6.70064	−0.257717
$677$	−10.3925	−0.399415	−0.199708	−	0.979856i	$-0.563999\pi$
$677$	−10.3925	−0.399415	−0.199708	+	0.979856i	$0.563999\pi$
$678$	16.1530	0.620353
$679$	−15.0395	−0.577162
$680$	−14.6405	−0.561437
$681$	−9.65348	−0.369922
$682$	14.6421	0.560675
$683$	−36.1128	−1.38182	−0.690909	−	0.722942i	$-0.742789\pi$
$683$	−36.1128	−1.38182	−0.690909	+	0.722942i	$0.742789\pi$
$684$	−1.26281	−0.0482846
$685$	−6.89918	−0.263604
$686$	7.10119	0.271125
$687$	24.8417	0.947769
$688$	0.225225	0.00858663
$689$	33.4260	1.27343
$690$	−2.92466	−0.111340
$691$	4.15561	0.158087	0.0790434	−	0.996871i	$-0.474813\pi$
$691$	4.15561	0.158087	0.0790434	+	0.996871i	$0.474813\pi$
$692$	6.44054	0.244833
$693$	−10.7095	−0.406822
$694$	−14.3461	−0.544572
$695$	−7.72913	−0.293183
$696$	−8.15735	−0.309203
$697$	0	0
$698$	0.814099	0.0308141
$699$	6.06372	0.229351
$700$	−18.6390	−0.704487
$701$	9.20925	0.347828	0.173914	−	0.984761i	$-0.444358\pi$
$701$	9.20925	0.347828	0.173914	+	0.984761i	$0.444358\pi$
$702$	21.6237	0.816133
$703$	10.6136	0.400298
$704$	−13.0778	−0.492889
$705$	14.8593	0.559633
$706$	3.82640	0.144008
$707$	−7.31118	−0.274965
$708$	−16.1786	−0.608029
$709$	32.5524	1.22253	0.611266	−	0.791425i	$-0.290661\pi$
$709$	32.5524	1.22253	0.611266	+	0.791425i	$0.290661\pi$
$710$	−13.4312	−0.504065
$711$	−2.91057	−0.109155
$712$	−31.6802	−1.18727
$713$	−14.4620	−0.541604
$714$	23.6371	0.884598
$715$	11.6145	0.434357
$716$	−20.1745	−0.753955
$717$	−15.4656	−0.577575
$718$	23.0850	0.861525
$719$	−10.1718	−0.379345	−0.189673	−	0.981847i	$-0.560743\pi$
$719$	−10.1718	−0.379345	−0.189673	+	0.981847i	$0.560743\pi$
$720$	0.127683	0.00475846
$721$	−44.4833	−1.65664
$722$	16.0259	0.596423
$723$	26.9999	1.00414
$724$	−12.7729	−0.474700
$725$	−7.91208	−0.293847
$726$	−5.78372	−0.214654
$727$	−45.9083	−1.70265	−0.851323	−	0.524642i	$-0.824199\pi$
$727$	−45.9083	−1.70265	−0.851323	+	0.524642i	$0.824199\pi$
$728$	49.1139	1.82028
$729$	28.5708	1.05818
$730$	−8.35012	−0.309052
$731$	9.64397	0.356695
$732$	0.754876	0.0279010
$733$	37.7759	1.39529	0.697643	−	0.716445i	$-0.254232\pi$
$733$	37.7759	1.39529	0.697643	+	0.716445i	$0.254232\pi$
$734$	12.2409	0.451820
$735$	−13.4338	−0.495513
$736$	12.3623	0.455680
$737$	−8.81535	−0.324718
$738$	0	0
$739$	−37.9331	−1.39539	−0.697697	−	0.716393i	$-0.745792\pi$
$739$	−37.9331	−1.39539	−0.697697	+	0.716393i	$0.745792\pi$
$740$	14.0888	0.517915
$741$	−5.86290	−0.215379
$742$	−27.5868	−1.01274
$743$	19.7752	0.725480	0.362740	−	0.931890i	$-0.381841\pi$
$743$	19.7752	0.725480	0.362740	+	0.931890i	$0.381841\pi$
$744$	−26.0157	−0.953783
$745$	5.21880	0.191202
$746$	30.7798	1.12693
$747$	2.97834	0.108972
$748$	−14.5589	−0.532327
$749$	−51.7059	−1.88929
$750$	−11.7335	−0.428446
$751$	−15.8402	−0.578016	−0.289008	−	0.957327i	$-0.593325\pi$
$751$	−15.8402	−0.578016	−0.289008	+	0.957327i	$0.593325\pi$
$752$	1.11177	0.0405419
$753$	3.23745	0.117979
$754$	7.86260	0.286339
$755$	−10.2145	−0.371744
$756$	27.3885	0.996111
$757$	−22.9561	−0.834355	−0.417178	−	0.908825i	$-0.636981\pi$
$757$	−22.9561	−0.834355	−0.417178	+	0.908825i	$0.636981\pi$
$758$	8.45942	0.307260
$759$	−7.71182	−0.279921
$760$	−2.99702	−0.108713
$761$	45.1563	1.63692	0.818458	−	0.574567i	$-0.194830\pi$
$761$	45.1563	1.63692	0.818458	+	0.574567i	$0.194830\pi$
$762$	−11.3790	−0.412218
$763$	−26.6815	−0.965935
$764$	19.0770	0.690182
$765$	5.46728	0.197670
$766$	21.0614	0.760979
$767$	41.3490	1.49303
$768$	22.6149	0.816044
$769$	22.4279	0.808770	0.404385	−	0.914589i	$-0.367486\pi$
$769$	22.4279	0.808770	0.404385	+	0.914589i	$0.367486\pi$
$770$	−9.58553	−0.345439
$771$	27.1510	0.977820
$772$	28.3045	1.01870
$773$	10.8157	0.389014	0.194507	−	0.980901i	$-0.437689\pi$
$773$	10.8157	0.389014	0.194507	+	0.980901i	$0.437689\pi$
$774$	−1.90781	−0.0685746
$775$	−25.2335	−0.906415
$776$	10.7245	0.384987
$777$	−60.3143	−2.16376
$778$	−9.74874	−0.349509
$779$	0	0
$780$	−7.78261	−0.278662
$781$	−35.4157	−1.26727
$782$	−9.36979	−0.335063
$783$	11.6262	0.415486
$784$	−1.00511	−0.0358968
$785$	8.44206	0.301310
$786$	−0.233470	−0.00832760
$787$	29.1744	1.03996	0.519978	−	0.854179i	$-0.325940\pi$
$787$	29.1744	1.03996	0.519978	+	0.854179i	$0.325940\pi$
$788$	−14.3406	−0.510862
$789$	4.55135	0.162032
$790$	−2.60510	−0.0926853
$791$	−52.2898	−1.85921
$792$	7.63686	0.271364
$793$	−1.92930	−0.0685115
$794$	22.7988	0.809099
$795$	11.5912	0.411098
$796$	−10.2588	−0.363613
$797$	21.7440	0.770213	0.385106	−	0.922872i	$-0.374165\pi$
$797$	21.7440	0.770213	0.385106	+	0.922872i	$0.374165\pi$
$798$	4.83870	0.171288
$799$	47.6049	1.68414
$800$	21.5700	0.762613
$801$	11.8305	0.418011
$802$	−23.7332	−0.838048
$803$	−22.0178	−0.776990
$804$	5.90697	0.208323
$805$	9.46759	0.333689
$806$	25.0757	0.883254
$807$	15.5018	0.545689
$808$	5.21353	0.183411
$809$	47.3059	1.66319	0.831594	−	0.555384i	$-0.187429\pi$
$809$	47.3059	1.66319	0.831594	+	0.555384i	$0.187429\pi$
$810$	4.45221	0.156435
$811$	−53.0392	−1.86246	−0.931228	−	0.364436i	$-0.881262\pi$
$811$	−53.0392	−1.86246	−0.931228	+	0.364436i	$0.881262\pi$
$812$	9.95876	0.349484
$813$	8.89395	0.311924
$814$	−24.2065	−0.848438
$815$	15.7025	0.550034
$816$	−0.743084	−0.0260131
$817$	1.97419	0.0690683
$818$	31.3847	1.09734
$819$	−18.3409	−0.640882
$820$	0	0
$821$	−38.9809	−1.36044	−0.680222	−	0.733006i	$-0.738117\pi$
$821$	−38.9809	−1.36044	−0.680222	+	0.733006i	$0.738117\pi$
$822$	−7.94293	−0.277041
$823$	1.44873	0.0504997	0.0252499	−	0.999681i	$-0.491962\pi$
$823$	1.44873	0.0504997	0.0252499	+	0.999681i	$0.491962\pi$
$824$	31.7206	1.10504
$825$	−13.4557	−0.468469
$826$	−34.1257	−1.18739
$827$	−43.1009	−1.49876	−0.749382	−	0.662138i	$-0.769649\pi$
$827$	−43.1009	−1.49876	−0.749382	+	0.662138i	$0.769649\pi$
$828$	−2.84466	−0.0988589
$829$	−12.8894	−0.447667	−0.223834	−	0.974627i	$-0.571857\pi$
$829$	−12.8894	−0.447667	−0.223834	+	0.974627i	$0.571857\pi$
$830$	2.66575	0.0925297
$831$	35.0450	1.21570
$832$	−22.3968	−0.776468
$833$	−43.0380	−1.49118
$834$	−8.89844	−0.308128
$835$	0.203561	0.00704451
$836$	−2.98032	−0.103077
$837$	37.0787	1.28163
$838$	25.3464	0.875577
$839$	41.7230	1.44044	0.720218	−	0.693747i	$-0.244042\pi$
$839$	41.7230	1.44044	0.720218	+	0.693747i	$0.244042\pi$
$840$	17.0313	0.587637
$841$	−24.7726	−0.854227
$842$	−9.10619	−0.313820
$843$	4.72605	0.162774
$844$	−11.6359	−0.400525
$845$	5.93861	0.204294
$846$	−9.41738	−0.323776
$847$	18.7228	0.643323
$848$	0.867250	0.0297815
$849$	−10.4805	−0.359689
$850$	−16.3486	−0.560753
$851$	23.9087	0.819579
$852$	23.7313	0.813021
$853$	33.9805	1.16347	0.581735	−	0.813379i	$-0.302374\pi$
$853$	33.9805	1.16347	0.581735	+	0.813379i	$0.302374\pi$
$854$	1.59227	0.0544863
$855$	1.11919	0.0382756
$856$	36.8710	1.26022
$857$	−16.5145	−0.564123	−0.282062	−	0.959396i	$-0.591018\pi$
$857$	−16.5145	−0.564123	−0.282062	+	0.959396i	$0.591018\pi$
$858$	13.3716	0.456499
$859$	40.8503	1.39380	0.696898	−	0.717171i	$-0.254563\pi$
$859$	40.8503	1.39380	0.696898	+	0.717171i	$0.254563\pi$
$860$	2.62061	0.0893620
$861$	0	0
$862$	−18.4446	−0.628224
$863$	32.9999	1.12333	0.561665	−	0.827365i	$-0.310161\pi$
$863$	32.9999	1.12333	0.561665	+	0.827365i	$0.310161\pi$
$864$	−31.6954	−1.07830
$865$	−5.70809	−0.194081
$866$	14.6150	0.496637
$867$	−8.17131	−0.277512
$868$	31.7609	1.07803
$869$	−6.86918	−0.233021
$870$	2.72653	0.0924380
$871$	−15.0969	−0.511540
$872$	19.0263	0.644312
$873$	−4.00491	−0.135546
$874$	−1.91807	−0.0648796
$875$	37.9831	1.28406
$876$	14.7536	0.498478
$877$	11.1414	0.376219	0.188110	−	0.982148i	$-0.439764\pi$
$877$	11.1414	0.376219	0.188110	+	0.982148i	$0.439764\pi$
$878$	−20.4263	−0.689354
$879$	−8.31142	−0.280337
$880$	0.301342	0.0101582
$881$	−24.6693	−0.831132	−0.415566	−	0.909563i	$-0.636416\pi$
$881$	−24.6693	−0.831132	−0.415566	+	0.909563i	$0.636416\pi$
$882$	8.51395	0.286679
$883$	21.7460	0.731810	0.365905	−	0.930652i	$-0.380760\pi$
$883$	21.7460	0.731810	0.365905	+	0.930652i	$0.380760\pi$
$884$	−24.9333	−0.838596
$885$	14.3387	0.481990
$886$	−0.309796	−0.0104078
$887$	45.9328	1.54227	0.771136	−	0.636670i	$-0.219689\pi$
$887$	45.9328	1.54227	0.771136	+	0.636670i	$0.219689\pi$
$888$	43.0095	1.44330
$889$	36.8356	1.23543
$890$	10.5889	0.354940
$891$	11.7397	0.393294
$892$	−6.47362	−0.216753
$893$	9.74509	0.326107
$894$	6.00834	0.200949
$895$	17.8801	0.597666
$896$	−26.3559	−0.880489
$897$	−13.2071	−0.440971
$898$	−26.0805	−0.870317
$899$	13.4822	0.449657
$900$	−4.96343	−0.165448
$901$	37.1350	1.23714
$902$	0	0
$903$	−11.2189	−0.373340
$904$	37.2873	1.24016
$905$	11.3203	0.376299
$906$	−11.7598	−0.390694
$907$	49.3098	1.63731	0.818653	−	0.574288i	$-0.194721\pi$
$907$	49.3098	1.63731	0.818653	+	0.574288i	$0.194721\pi$
$908$	−8.40396	−0.278895
$909$	−1.94692	−0.0645751
$910$	−16.4159	−0.544183
$911$	8.88306	0.294309	0.147154	−	0.989114i	$-0.452989\pi$
$911$	8.88306	0.294309	0.147154	+	0.989114i	$0.452989\pi$
$912$	−0.152115	−0.00503703
$913$	7.02912	0.232630
$914$	−7.59480	−0.251214
$915$	−0.669028	−0.0221174
$916$	21.6263	0.714552
$917$	0.755778	0.0249580
$918$	24.0230	0.792878
$919$	−12.2532	−0.404196	−0.202098	−	0.979365i	$-0.564776\pi$
$919$	−12.2532	−0.404196	−0.202098	+	0.979365i	$0.564776\pi$
$920$	−6.75124	−0.222582
$921$	1.02424	0.0337499
$922$	−31.1090	−1.02452
$923$	−60.6521	−1.99639
$924$	16.9364	0.557168
$925$	41.7164	1.37163
$926$	−4.10613	−0.134936
$927$	−11.8456	−0.389060
$928$	−11.5248	−0.378319
$929$	−28.3240	−0.929279	−0.464639	−	0.885500i	$-0.653816\pi$
$929$	−28.3240	−0.929279	−0.464639	+	0.885500i	$0.653816\pi$
$930$	8.69555	0.285138
$931$	−8.81021	−0.288743
$932$	5.27885	0.172915
$933$	−40.1448	−1.31428
$934$	24.5783	0.804226
$935$	12.9032	0.421980
$936$	13.0787	0.427490
$937$	42.8770	1.40073	0.700365	−	0.713785i	$-0.253021\pi$
$937$	42.8770	1.40073	0.700365	+	0.713785i	$0.253021\pi$
$938$	12.4596	0.406822
$939$	−22.8328	−0.745119
$940$	12.9359	0.421924
$941$	42.3449	1.38041	0.690203	−	0.723616i	$-0.257521\pi$
$941$	42.3449	1.38041	0.690203	+	0.723616i	$0.257521\pi$
$942$	9.71923	0.316670
$943$	0	0
$944$	1.07281	0.0349172
$945$	−24.2738	−0.789626
$946$	−4.50257	−0.146391
$947$	4.24592	0.137974	0.0689869	−	0.997618i	$-0.478023\pi$
$947$	4.24592	0.137974	0.0689869	+	0.997618i	$0.478023\pi$
$948$	4.60289	0.149495
$949$	−37.7071	−1.22402
$950$	−3.34668	−0.108581
$951$	46.9741	1.52324
$952$	54.5635	1.76841
$953$	36.4894	1.18201	0.591004	−	0.806668i	$-0.298732\pi$
$953$	36.4894	1.18201	0.591004	+	0.806668i	$0.298732\pi$
$954$	−7.34617	−0.237841
$955$	−16.9075	−0.547113
$956$	−13.4638	−0.435451
$957$	7.18937	0.232399
$958$	−4.54044	−0.146695
$959$	25.7125	0.830300
$960$	−7.76657	−0.250665
$961$	11.9980	0.387032
$962$	−41.4555	−1.33658
$963$	−13.7689	−0.443698
$964$	23.5051	0.757048
$965$	−25.0856	−0.807534
$966$	10.8999	0.350699
$967$	−39.9583	−1.28497	−0.642486	−	0.766297i	$-0.722097\pi$
$967$	−39.9583	−1.28497	−0.642486	+	0.766297i	$0.722097\pi$
$968$	−13.3510	−0.429119
$969$	−6.51344	−0.209242
$970$	−3.58458	−0.115094
$971$	−24.9173	−0.799633	−0.399816	−	0.916595i	$-0.630926\pi$
$971$	−24.9173	−0.799633	−0.399816	+	0.916595i	$0.630926\pi$
$972$	12.6758	0.406575
$973$	28.8056	0.923466
$974$	19.8768	0.636894
$975$	−23.0440	−0.737998
$976$	−0.0500564	−0.00160227
$977$	9.54904	0.305501	0.152750	−	0.988265i	$-0.451187\pi$
$977$	9.54904	0.305501	0.152750	+	0.988265i	$0.451187\pi$
$978$	18.0781	0.578073
$979$	27.9210	0.892358
$980$	−11.6950	−0.373582
$981$	−7.10510	−0.226848
$982$	−35.6313	−1.13704
$983$	21.0349	0.670908	0.335454	−	0.942057i	$-0.391110\pi$
$983$	21.0349	0.670908	0.335454	+	0.942057i	$0.391110\pi$
$984$	0	0
$985$	12.7097	0.404965
$986$	8.73502	0.278180
$987$	−55.3789	−1.76273
$988$	−5.10403	−0.162381
$989$	4.44717	0.141412
$990$	−2.55256	−0.0811257
$991$	8.43266	0.267872	0.133936	−	0.990990i	$-0.457238\pi$
$991$	8.43266	0.267872	0.133936	+	0.990990i	$0.457238\pi$
$992$	−36.7553	−1.16698
$993$	16.7626	0.531945
$994$	50.0567	1.58770
$995$	9.09209	0.288239
$996$	−4.71005	−0.149244
$997$	−12.1051	−0.383372	−0.191686	−	0.981456i	$-0.561396\pi$
$997$	−12.1051	−0.383372	−0.191686	+	0.981456i	$0.561396\pi$
$998$	−28.1692	−0.891681
$999$	−61.2989	−1.93941

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1681.2.a.m.1.7		24
41.22	odd	40		41.2.g.a.33.2	yes	24
41.28	odd	40		41.2.g.a.5.2	✓	24
41.40	even	2	inner	1681.2.a.m.1.8		24
123.104	even	40		369.2.u.a.361.2		24
123.110	even	40		369.2.u.a.46.2		24
164.63	even	40		656.2.bs.d.33.2		24
164.151	even	40		656.2.bs.d.497.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
41.2.g.a.5.2	✓	24	41.28	odd	40
41.2.g.a.33.2	yes	24	41.22	odd	40
369.2.u.a.46.2		24	123.110	even	40
369.2.u.a.361.2		24	123.104	even	40
656.2.bs.d.33.2		24	164.63	even	40
656.2.bs.d.497.2		24	164.151	even	40
1681.2.a.m.1.7		24	1.1	even	1	trivial
1681.2.a.m.1.8		24	41.40	even	2	inner

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:	\( N \)	\(=\)	\( 1681 = 41^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1681.a (trivial)

\(f(q)\)	\(=\)	\(q-0.888284 q^{2} -1.39100 q^{3} -1.21095 q^{4} +1.07324 q^{5} +1.23560 q^{6} -3.99983 q^{7} +2.85224 q^{8} -1.06513 q^{9} +O(q^{10})\)	\(q-0.888284 q^{2} -1.39100 q^{3} -1.21095 q^{4} +1.07324 q^{5} +1.23560 q^{6} -3.99983 q^{7} +2.85224 q^{8} -1.06513 q^{9} -0.953338 q^{10} -2.51378 q^{11} +1.68443 q^{12} -4.30504 q^{13} +3.55299 q^{14} -1.49287 q^{15} -0.111696 q^{16} -4.78272 q^{17} +0.946136 q^{18} -0.979059 q^{19} -1.29964 q^{20} +5.56375 q^{21} +2.23295 q^{22} -2.20548 q^{23} -3.96745 q^{24} -3.84817 q^{25} +3.82410 q^{26} +5.65458 q^{27} +4.84360 q^{28} +2.05607 q^{29} +1.32609 q^{30} +6.55728 q^{31} -5.60526 q^{32} +3.49666 q^{33} +4.24842 q^{34} -4.29276 q^{35} +1.28982 q^{36} -10.8406 q^{37} +0.869683 q^{38} +5.98830 q^{39} +3.06112 q^{40} -4.94220 q^{42} -2.01642 q^{43} +3.04407 q^{44} -1.14313 q^{45} +1.95909 q^{46} -9.95352 q^{47} +0.155368 q^{48} +8.99865 q^{49} +3.41827 q^{50} +6.65275 q^{51} +5.21319 q^{52} -7.76440 q^{53} -5.02287 q^{54} -2.69788 q^{55} -11.4085 q^{56} +1.36187 q^{57} -1.82637 q^{58} -9.60480 q^{59} +1.80779 q^{60} +0.448149 q^{61} -5.82473 q^{62} +4.26033 q^{63} +5.20245 q^{64} -4.62032 q^{65} -3.10603 q^{66} +3.50681 q^{67} +5.79164 q^{68} +3.06781 q^{69} +3.81319 q^{70} +14.0886 q^{71} -3.03800 q^{72} +8.75882 q^{73} +9.62952 q^{74} +5.35279 q^{75} +1.18559 q^{76} +10.0547 q^{77} -5.31931 q^{78} +2.73261 q^{79} -0.119876 q^{80} -4.67012 q^{81} -2.79623 q^{83} -6.73743 q^{84} -5.13299 q^{85} +1.79115 q^{86} -2.85998 q^{87} -7.16990 q^{88} -11.1072 q^{89} +1.01543 q^{90} +17.2194 q^{91} +2.67073 q^{92} -9.12116 q^{93} +8.84156 q^{94} -1.05076 q^{95} +7.79690 q^{96} +3.76003 q^{97} -7.99336 q^{98} +2.67750 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{2} + 20 q^{4} + 12 q^{5} + 24 q^{8} + 24 q^{9}+O(q^{10}) \) 24 * q + 8 * q^2 + 20 * q^4 + 12 * q^5 + 24 * q^8 + 24 * q^9	\( 24 q + 8 q^{2} + 20 q^{4} + 12 q^{5} + 24 q^{8} + 24 q^{9} - 4 q^{10} + 20 q^{16} + 20 q^{18} + 40 q^{20} + 56 q^{21} + 48 q^{23} + 8 q^{25} + 32 q^{31} + 36 q^{32} + 24 q^{33} + 108 q^{36} + 60 q^{39} + 44 q^{40} - 40 q^{42} + 36 q^{43} - 36 q^{45} + 36 q^{46} + 32 q^{49} - 60 q^{50} + 36 q^{51} - 60 q^{57} + 116 q^{59} + 40 q^{61} + 48 q^{62} + 60 q^{64} + 16 q^{66} + 4 q^{72} + 16 q^{73} + 24 q^{74} - 16 q^{77} - 60 q^{78} + 84 q^{80} - 28 q^{81} + 80 q^{83} - 24 q^{84} - 24 q^{86} + 76 q^{87} + 56 q^{90} + 40 q^{91} - 40 q^{92} + 36 q^{98}+O(q^{100}) \) 24 * q + 8 * q^2 + 20 * q^4 + 12 * q^5 + 24 * q^8 + 24 * q^9 - 4 * q^10 + 20 * q^16 + 20 * q^18 + 40 * q^20 + 56 * q^21 + 48 * q^23 + 8 * q^25 + 32 * q^31 + 36 * q^32 + 24 * q^33 + 108 * q^36 + 60 * q^39 + 44 * q^40 - 40 * q^42 + 36 * q^43 - 36 * q^45 + 36 * q^46 + 32 * q^49 - 60 * q^50 + 36 * q^51 - 60 * q^57 + 116 * q^59 + 40 * q^61 + 48 * q^62 + 60 * q^64 + 16 * q^66 + 4 * q^72 + 16 * q^73 + 24 * q^74 - 16 * q^77 - 60 * q^78 + 84 * q^80 - 28 * q^81 + 80 * q^83 - 24 * q^84 - 24 * q^86 + 76 * q^87 + 56 * q^90 + 40 * q^91 - 40 * q^92 + 36 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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