LMFDB - Embedded newform 1681.2.a.m.1.16

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			1.16
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)

$f(q)$	$=$	$q+1.20692 q^{2} +2.19417 q^{3} -0.543349 q^{4} -2.54506 q^{5} +2.64818 q^{6} +1.13968 q^{7} -3.06961 q^{8} +1.81438 q^{9} +O(q^{10})$	\(q+1.20692 q^{2} +2.19417 q^{3} -0.543349 q^{4} -2.54506 q^{5} +2.64818 q^{6} +1.13968 q^{7} -3.06961 q^{8} +1.81438 q^{9} -3.07168 q^{10} +5.16435 q^{11} -1.19220 q^{12} +2.58408 q^{13} +1.37550 q^{14} -5.58429 q^{15} -2.61807 q^{16} -3.09386 q^{17} +2.18981 q^{18} +8.23902 q^{19} +1.38285 q^{20} +2.50066 q^{21} +6.23295 q^{22} +3.81432 q^{23} -6.73526 q^{24} +1.47733 q^{25} +3.11877 q^{26} -2.60144 q^{27} -0.619245 q^{28} +5.79710 q^{29} -6.73979 q^{30} +4.51957 q^{31} +2.97943 q^{32} +11.3315 q^{33} -3.73403 q^{34} -2.90056 q^{35} -0.985844 q^{36} -0.722027 q^{37} +9.94382 q^{38} +5.66991 q^{39} +7.81235 q^{40} +3.01809 q^{42} +1.84739 q^{43} -2.80604 q^{44} -4.61772 q^{45} +4.60357 q^{46} +3.54323 q^{47} -5.74450 q^{48} -5.70112 q^{49} +1.78301 q^{50} -6.78845 q^{51} -1.40406 q^{52} +5.59631 q^{53} -3.13973 q^{54} -13.1436 q^{55} -3.49839 q^{56} +18.0778 q^{57} +6.99662 q^{58} +0.785599 q^{59} +3.03422 q^{60} -7.05134 q^{61} +5.45476 q^{62} +2.06782 q^{63} +8.83207 q^{64} -6.57664 q^{65} +13.6762 q^{66} -5.34349 q^{67} +1.68104 q^{68} +8.36926 q^{69} -3.50074 q^{70} +4.53100 q^{71} -5.56946 q^{72} -0.149836 q^{73} -0.871428 q^{74} +3.24151 q^{75} -4.47666 q^{76} +5.88573 q^{77} +6.84312 q^{78} -16.1771 q^{79} +6.66316 q^{80} -11.1512 q^{81} +4.27258 q^{83} -1.35873 q^{84} +7.87405 q^{85} +2.22965 q^{86} +12.7198 q^{87} -15.8526 q^{88} +1.70348 q^{89} -5.57321 q^{90} +2.94503 q^{91} -2.07250 q^{92} +9.91672 q^{93} +4.27639 q^{94} -20.9688 q^{95} +6.53737 q^{96} -4.39508 q^{97} -6.88079 q^{98} +9.37012 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.20692	0.853420	0.426710	−	0.904389i	$-0.359673\pi$
$2$	1.20692	0.853420	0.426710	+	0.904389i	$0.359673\pi$
$3$	2.19417	1.26681	0.633403	−	0.773823i	$-0.281658\pi$
$3$	2.19417	1.26681	0.633403	+	0.773823i	$0.281658\pi$
$4$	−0.543349	−0.271674
$5$	−2.54506	−1.13819	−0.569093	−	0.822273i	$-0.692705\pi$
$5$	−2.54506	−1.13819	−0.569093	+	0.822273i	$0.692705\pi$
$6$	2.64818	1.08112
$7$	1.13968	0.430760	0.215380	−	0.976530i	$-0.430901\pi$
$7$	1.13968	0.430760	0.215380	+	0.976530i	$0.430901\pi$
$8$	−3.06961	−1.08527
$9$	1.81438	0.604795
$10$	−3.07168	−0.971350
$11$	5.16435	1.55711	0.778555	−	0.627576i	$-0.215953\pi$
$11$	5.16435	1.55711	0.778555	+	0.627576i	$0.215953\pi$
$12$	−1.19220	−0.344158
$13$	2.58408	0.716695	0.358348	−	0.933588i	$-0.383340\pi$
$13$	2.58408	0.716695	0.358348	+	0.933588i	$0.383340\pi$
$14$	1.37550	0.367619
$15$	−5.58429	−1.44186
$16$	−2.61807	−0.654519
$17$	−3.09386	−0.750370	−0.375185	−	0.926950i	$-0.622421\pi$
$17$	−3.09386	−0.750370	−0.375185	+	0.926950i	$0.622421\pi$
$18$	2.18981	0.516144
$19$	8.23902	1.89016	0.945080	−	0.326839i	$-0.105983\pi$
$19$	8.23902	1.89016	0.945080	+	0.326839i	$0.105983\pi$
$20$	1.38285	0.309216
$21$	2.50066	0.545689
$22$	6.23295	1.32887
$23$	3.81432	0.795340	0.397670	−	0.917529i	$-0.369819\pi$
$23$	3.81432	0.795340	0.397670	+	0.917529i	$0.369819\pi$
$24$	−6.73526	−1.37483
$25$	1.47733	0.295465
$26$	3.11877	0.611642
$27$	−2.60144	−0.500648
$28$	−0.619245	−0.117026
$29$	5.79710	1.07649	0.538247	−	0.842787i	$-0.319087\pi$
$29$	5.79710	1.07649	0.538247	+	0.842787i	$0.319087\pi$
$30$	−6.73979	−1.23051
$31$	4.51957	0.811740	0.405870	−	0.913931i	$-0.366969\pi$
$31$	4.51957	0.811740	0.405870	+	0.913931i	$0.366969\pi$
$32$	2.97943	0.526693
$33$	11.3315	1.97256
$34$	−3.73403	−0.640381
$35$	−2.90056	−0.490284
$36$	−0.985844	−0.164307
$37$	−0.722027	−0.118701	−0.0593503	−	0.998237i	$-0.518903\pi$
$37$	−0.722027	−0.118701	−0.0593503	+	0.998237i	$0.518903\pi$
$38$	9.94382	1.61310
$39$	5.66991	0.907913
$40$	7.81235	1.23524
$41$	0	0
$41$	0	0
$42$	3.01809	0.465702
$43$	1.84739	0.281725	0.140862	−	0.990029i	$-0.455012\pi$
$43$	1.84739	0.281725	0.140862	+	0.990029i	$0.455012\pi$
$44$	−2.80604	−0.423027
$45$	−4.61772	−0.688369
$46$	4.60357	0.678759
$47$	3.54323	0.516834	0.258417	−	0.966033i	$-0.416799\pi$
$47$	3.54323	0.516834	0.258417	+	0.966033i	$0.416799\pi$
$48$	−5.74450	−0.829148
$49$	−5.70112	−0.814446
$50$	1.78301	0.252156
$51$	−6.78845	−0.950573
$52$	−1.40406	−0.194708
$53$	5.59631	0.768713	0.384356	−	0.923185i	$-0.374423\pi$
$53$	5.59631	0.768713	0.384356	+	0.923185i	$0.374423\pi$
$54$	−3.13973	−0.427263
$55$	−13.1436	−1.77228
$56$	−3.49839	−0.467492
$57$	18.0778	2.39446
$58$	6.99662	0.918702
$59$	0.785599	0.102276	0.0511381	−	0.998692i	$-0.483715\pi$
$59$	0.785599	0.102276	0.0511381	+	0.998692i	$0.483715\pi$
$60$	3.03422	0.391716
$61$	−7.05134	−0.902832	−0.451416	−	0.892314i	$-0.649081\pi$
$61$	−7.05134	−0.902832	−0.451416	+	0.892314i	$0.649081\pi$
$62$	5.45476	0.692755
$63$	2.06782	0.260521
$64$	8.83207	1.10401
$65$	−6.57664	−0.815732
$66$	13.6762	1.68342
$67$	−5.34349	−0.652812	−0.326406	−	0.945230i	$-0.605838\pi$
$67$	−5.34349	−0.652812	−0.326406	+	0.945230i	$0.605838\pi$
$68$	1.68104	0.203856
$69$	8.36926	1.00754
$70$	−3.50074	−0.418419
$71$	4.53100	0.537731	0.268865	−	0.963178i	$-0.413351\pi$
$71$	4.53100	0.537731	0.268865	+	0.963178i	$0.413351\pi$
$72$	−5.56946	−0.656367
$73$	−0.149836	−0.0175369	−0.00876846	−	0.999962i	$-0.502791\pi$
$73$	−0.149836	−0.0175369	−0.00876846	+	0.999962i	$0.502791\pi$
$74$	−0.871428	−0.101301
$75$	3.24151	0.374297
$76$	−4.47666	−0.513508
$77$	5.88573	0.670741
$78$	6.84312	0.774831
$79$	−16.1771	−1.82006	−0.910032	−	0.414539i	$-0.863943\pi$
$79$	−16.1771	−1.82006	−0.910032	+	0.414539i	$0.863943\pi$
$80$	6.66316	0.744963
$81$	−11.1512	−1.23902
$82$	0	0
$83$	4.27258	0.468977	0.234488	−	0.972119i	$-0.424659\pi$
$83$	4.27258	0.468977	0.234488	+	0.972119i	$0.424659\pi$
$84$	−1.35873	−0.148250
$85$	7.87405	0.854060
$86$	2.22965	0.240430
$87$	12.7198	1.36371
$88$	−15.8526	−1.68989
$89$	1.70348	0.180568	0.0902840	−	0.995916i	$-0.471223\pi$
$89$	1.70348	0.180568	0.0902840	+	0.995916i	$0.471223\pi$
$90$	−5.57321	−0.587468
$91$	2.94503	0.308723
$92$	−2.07250	−0.216073
$93$	9.91672	1.02832
$94$	4.27639	0.441076
$95$	−20.9688	−2.15135
$96$	6.53737	0.667217
$97$	−4.39508	−0.446253	−0.223126	−	0.974790i	$-0.571626\pi$
$97$	−4.39508	−0.446253	−0.223126	+	0.974790i	$0.571626\pi$
$98$	−6.88079	−0.695064
$99$	9.37012	0.941733
$100$	−0.802704	−0.0802704
$101$	3.09598	0.308061	0.154031	−	0.988066i	$-0.450775\pi$
$101$	3.09598	0.308061	0.154031	+	0.988066i	$0.450775\pi$
$102$	−8.19310	−0.811238
$103$	2.94783	0.290459	0.145229	−	0.989398i	$-0.453608\pi$
$103$	2.94783	0.290459	0.145229	+	0.989398i	$0.453608\pi$
$104$	−7.93213	−0.777809
$105$	−6.36433	−0.621095
$106$	6.75429	0.656035
$107$	3.38669	0.327404	0.163702	−	0.986510i	$-0.447656\pi$
$107$	3.38669	0.327404	0.163702	+	0.986510i	$0.447656\pi$
$108$	1.41349	0.136013
$109$	13.6569	1.30809	0.654045	−	0.756455i	$-0.273071\pi$
$109$	13.6569	1.30809	0.654045	+	0.756455i	$0.273071\pi$
$110$	−15.8632	−1.51250
$111$	−1.58425	−0.150370
$112$	−2.98378	−0.281940
$113$	−13.2460	−1.24608	−0.623040	−	0.782190i	$-0.714102\pi$
$113$	−13.2460	−1.24608	−0.623040	+	0.782190i	$0.714102\pi$
$114$	21.8184	2.04348
$115$	−9.70766	−0.905244
$116$	−3.14985	−0.292456
$117$	4.68852	0.433454
$118$	0.948153	0.0872846
$119$	−3.52602	−0.323229
$120$	17.1416	1.56481
$121$	15.6705	1.42459
$122$	−8.51039	−0.770495
$123$	0	0
$124$	−2.45570	−0.220529
$125$	8.96541	0.801891
$126$	2.49569	0.222334
$127$	−13.5114	−1.19894	−0.599472	−	0.800396i	$-0.704623\pi$
$127$	−13.5114	−1.19894	−0.599472	+	0.800396i	$0.704623\pi$
$128$	4.70074	0.415490
$129$	4.05350	0.356890
$130$	−7.93746	−0.696162
$131$	10.2337	0.894122	0.447061	−	0.894503i	$-0.352471\pi$
$131$	10.2337	0.894122	0.447061	+	0.894503i	$0.352471\pi$
$132$	−6.15694	−0.535893
$133$	9.38987	0.814205
$134$	−6.44916	−0.557122
$135$	6.62082	0.569830
$136$	9.49694	0.814356
$137$	−5.73942	−0.490352	−0.245176	−	0.969479i	$-0.578846\pi$
$137$	−5.73942	−0.490352	−0.245176	+	0.969479i	$0.578846\pi$
$138$	10.1010	0.859855
$139$	−16.1261	−1.36780	−0.683899	−	0.729577i	$-0.739717\pi$
$139$	−16.1261	−1.36780	−0.683899	+	0.729577i	$0.739717\pi$
$140$	1.57602	0.133198
$141$	7.77446	0.654728
$142$	5.46855	0.458910
$143$	13.3451	1.11597
$144$	−4.75020	−0.395850
$145$	−14.7540	−1.22525
$146$	−0.180839	−0.0149664
$147$	−12.5092	−1.03174
$148$	0.392313	0.0322479
$149$	5.42979	0.444825	0.222413	−	0.974953i	$-0.428607\pi$
$149$	5.42979	0.444825	0.222413	+	0.974953i	$0.428607\pi$
$150$	3.91223	0.319433
$151$	−3.38766	−0.275684	−0.137842	−	0.990454i	$-0.544017\pi$
$151$	−3.38766	−0.275684	−0.137842	+	0.990454i	$0.544017\pi$
$152$	−25.2906	−2.05134
$153$	−5.61344	−0.453820
$154$	7.10359	0.572424
$155$	−11.5026	−0.923910
$156$	−3.08074	−0.246657
$157$	−10.1157	−0.807322	−0.403661	−	0.914909i	$-0.632262\pi$
$157$	−10.1157	−0.807322	−0.403661	+	0.914909i	$0.632262\pi$
$158$	−19.5244	−1.55328
$159$	12.2793	0.973809
$160$	−7.58281	−0.599474
$161$	4.34711	0.342600
$162$	−13.4585	−1.05740
$163$	−18.7430	−1.46807	−0.734033	−	0.679113i	$-0.762365\pi$
$163$	−18.7430	−1.46807	−0.734033	+	0.679113i	$0.762365\pi$
$164$	0	0
$165$	−28.8393	−2.24513
$166$	5.15665	0.400234
$167$	−3.05792	−0.236629	−0.118315	−	0.992976i	$-0.537749\pi$
$167$	−3.05792	−0.236629	−0.118315	+	0.992976i	$0.537749\pi$
$168$	−7.67606	−0.592221
$169$	−6.32253	−0.486348
$170$	9.50333	0.728872
$171$	14.9487	1.14316
$172$	−1.00378	−0.0765374
$173$	−10.5897	−0.805117	−0.402558	−	0.915394i	$-0.631879\pi$
$173$	−10.5897	−0.805117	−0.402558	+	0.915394i	$0.631879\pi$
$174$	15.3518	1.16382
$175$	1.68369	0.127275
$176$	−13.5207	−1.01916
$177$	1.72374	0.129564
$178$	2.05596	0.154100
$179$	1.90974	0.142740	0.0713702	−	0.997450i	$-0.477263\pi$
$179$	1.90974	0.142740	0.0713702	+	0.997450i	$0.477263\pi$
$180$	2.50903	0.187012
$181$	−5.89430	−0.438120	−0.219060	−	0.975711i	$-0.570299\pi$
$181$	−5.89430	−0.438120	−0.219060	+	0.975711i	$0.570299\pi$
$182$	3.55441	0.263471
$183$	−15.4718	−1.14371
$184$	−11.7085	−0.863160
$185$	1.83760	0.135103
$186$	11.9687	0.877585
$187$	−15.9778	−1.16841
$188$	−1.92521	−0.140410
$189$	−2.96482	−0.215659
$190$	−25.3076	−1.83601
$191$	−3.16214	−0.228805	−0.114402	−	0.993435i	$-0.536495\pi$
$191$	−3.16214	−0.228805	−0.114402	+	0.993435i	$0.536495\pi$
$192$	19.3791	1.39856
$193$	15.7916	1.13671	0.568354	−	0.822784i	$-0.307580\pi$
$193$	15.7916	1.13671	0.568354	+	0.822784i	$0.307580\pi$
$194$	−5.30450	−0.380841
$195$	−14.4303	−1.03337
$196$	3.09770	0.221264
$197$	−4.54521	−0.323833	−0.161916	−	0.986804i	$-0.551767\pi$
$197$	−4.54521	−0.323833	−0.161916	+	0.986804i	$0.551767\pi$
$198$	11.3090	0.803693
$199$	8.98372	0.636839	0.318420	−	0.947950i	$-0.396848\pi$
$199$	8.98372	0.636839	0.318420	+	0.947950i	$0.396848\pi$
$200$	−4.53482	−0.320660
$201$	−11.7245	−0.826985
$202$	3.73659	0.262906
$203$	6.60686	0.463711
$204$	3.68849	0.258246
$205$	0	0
$206$	3.55779	0.247883
$207$	6.92064	0.481017
$208$	−6.76532	−0.469090
$209$	42.5492	2.94319
$210$	−7.68122	−0.530055
$211$	−6.45987	−0.444716	−0.222358	−	0.974965i	$-0.571375\pi$
$211$	−6.45987	−0.444716	−0.222358	+	0.974965i	$0.571375\pi$
$212$	−3.04075	−0.208840
$213$	9.94179	0.681200
$214$	4.08746	0.279413
$215$	−4.70173	−0.320655
$216$	7.98542	0.543339
$217$	5.15088	0.349665
$218$	16.4827	1.11635
$219$	−0.328765	−0.0222159
$220$	7.14155	0.481483
$221$	−7.99477	−0.537787
$222$	−1.91206	−0.128329
$223$	−4.09290	−0.274081	−0.137040	−	0.990565i	$-0.543759\pi$
$223$	−4.09290	−0.274081	−0.137040	+	0.990565i	$0.543759\pi$
$224$	3.39560	0.226878
$225$	2.68044	0.178696
$226$	−15.9868	−1.06343
$227$	0.574187	0.0381101	0.0190551	−	0.999818i	$-0.493934\pi$
$227$	0.574187	0.0381101	0.0190551	+	0.999818i	$0.493934\pi$
$228$	−9.82255	−0.650515
$229$	24.0377	1.58846	0.794230	−	0.607618i	$-0.207875\pi$
$229$	24.0377	1.58846	0.794230	+	0.607618i	$0.207875\pi$
$230$	−11.7163	−0.772553
$231$	12.9143	0.849698
$232$	−17.7949	−1.16829
$233$	12.4139	0.813262	0.406631	−	0.913592i	$-0.366703\pi$
$233$	12.4139	0.813262	0.406631	+	0.913592i	$0.366703\pi$
$234$	5.65866	0.369918
$235$	−9.01774	−0.588253
$236$	−0.426854	−0.0277858
$237$	−35.4953	−2.30567
$238$	−4.25561	−0.275850
$239$	−6.78434	−0.438842	−0.219421	−	0.975630i	$-0.570417\pi$
$239$	−6.78434	−0.438842	−0.219421	+	0.975630i	$0.570417\pi$
$240$	14.6201	0.943723
$241$	−19.1787	−1.23541	−0.617705	−	0.786410i	$-0.711937\pi$
$241$	−19.1787	−1.23541	−0.617705	+	0.786410i	$0.711937\pi$
$242$	18.9130	1.21578
$243$	−16.6632	−1.06895
$244$	3.83134	0.245276
$245$	14.5097	0.926990
$246$	0	0
$247$	21.2903	1.35467
$248$	−13.8733	−0.880958
$249$	9.37477	0.594102
$250$	10.8205	0.684350
$251$	−1.88513	−0.118988	−0.0594942	−	0.998229i	$-0.518949\pi$
$251$	−1.88513	−0.118988	−0.0594942	+	0.998229i	$0.518949\pi$
$252$	−1.12355	−0.0707770
$253$	19.6985	1.23843
$254$	−16.3072	−1.02320
$255$	17.2770	1.08193
$256$	−11.9907	−0.749421
$257$	−27.9911	−1.74603	−0.873017	−	0.487690i	$-0.837840\pi$
$257$	−27.9911	−1.74603	−0.873017	+	0.487690i	$0.837840\pi$
$258$	4.89224	0.304577
$259$	−0.822883	−0.0511314
$260$	3.57341	0.221613
$261$	10.5182	0.651058
$262$	12.3512	0.763062
$263$	4.13950	0.255253	0.127626	−	0.991822i	$-0.459264\pi$
$263$	4.13950	0.255253	0.127626	+	0.991822i	$0.459264\pi$
$264$	−34.7832	−2.14076
$265$	−14.2429	−0.874937
$266$	11.3328	0.694859
$267$	3.73772	0.228745
$268$	2.90338	0.177352
$269$	29.7587	1.81442	0.907211	−	0.420675i	$-0.138207\pi$
$269$	29.7587	1.81442	0.907211	+	0.420675i	$0.138207\pi$
$270$	7.99079	0.486304
$271$	−23.1907	−1.40874	−0.704369	−	0.709834i	$-0.748770\pi$
$271$	−23.1907	−1.40874	−0.704369	+	0.709834i	$0.748770\pi$
$272$	8.09994	0.491131
$273$	6.46191	0.391092
$274$	−6.92702	−0.418476
$275$	7.62944	0.460072
$276$	−4.54743	−0.273723
$277$	24.7668	1.48809	0.744047	−	0.668127i	$-0.232904\pi$
$277$	24.7668	1.48809	0.744047	+	0.668127i	$0.232904\pi$
$278$	−19.4629	−1.16731
$279$	8.20025	0.490936
$280$	8.90360	0.532092
$281$	−0.212661	−0.0126863	−0.00634313	−	0.999980i	$-0.502019\pi$
$281$	−0.212661	−0.0126863	−0.00634313	+	0.999980i	$0.502019\pi$
$282$	9.38314	0.558758
$283$	−11.0337	−0.655888	−0.327944	−	0.944697i	$-0.606356\pi$
$283$	−11.0337	−0.655888	−0.327944	+	0.944697i	$0.606356\pi$
$284$	−2.46191	−0.146088
$285$	−46.0091	−2.72534
$286$	16.1064	0.952394
$287$	0	0
$288$	5.40582	0.318541
$289$	−7.42806	−0.436945
$290$	−17.8068	−1.04565
$291$	−9.64355	−0.565315
$292$	0.0814130	0.00476433
$293$	−7.60921	−0.444535	−0.222267	−	0.974986i	$-0.571346\pi$
$293$	−7.60921	−0.444535	−0.222267	+	0.974986i	$0.571346\pi$
$294$	−15.0976	−0.880511
$295$	−1.99939	−0.116409
$296$	2.21635	0.128822
$297$	−13.4348	−0.779564
$298$	6.55331	0.379623
$299$	9.85650	0.570016
$300$	−1.76127	−0.101687
$301$	2.10544	0.121356
$302$	−4.08862	−0.235274
$303$	6.79311	0.390254
$304$	−21.5704	−1.23715
$305$	17.9461	1.02759
$306$	−6.77497	−0.387299
$307$	31.4135	1.79287	0.896433	−	0.443180i	$-0.146150\pi$
$307$	31.4135	1.79287	0.896433	+	0.443180i	$0.146150\pi$
$308$	−3.19800	−0.182223
$309$	6.46805	0.367955
$310$	−13.8827	−0.788483
$311$	−14.7531	−0.836570	−0.418285	−	0.908316i	$-0.637369\pi$
$311$	−14.7531	−0.836570	−0.418285	+	0.908316i	$0.637369\pi$
$312$	−17.4044	−0.985333
$313$	−16.6075	−0.938712	−0.469356	−	0.883009i	$-0.655514\pi$
$313$	−16.6075	−0.938712	−0.469356	+	0.883009i	$0.655514\pi$
$314$	−12.2088	−0.688984
$315$	−5.26274	−0.296522
$316$	8.78979	0.494465
$317$	32.5713	1.82939	0.914693	−	0.404150i	$-0.132433\pi$
$317$	32.5713	1.82939	0.914693	+	0.404150i	$0.132433\pi$
$318$	14.8201	0.831068
$319$	29.9383	1.67622
$320$	−22.4781	−1.25657
$321$	7.43098	0.414757
$322$	5.24661	0.292382
$323$	−25.4903	−1.41832
$324$	6.05897	0.336609
$325$	3.81753	0.211759
$326$	−22.6213	−1.25288
$327$	29.9655	1.65710
$328$	0	0
$329$	4.03816	0.222631
$330$	−34.8066	−1.91604
$331$	1.88295	0.103496	0.0517482	−	0.998660i	$-0.483521\pi$
$331$	1.88295	0.103496	0.0517482	+	0.998660i	$0.483521\pi$
$332$	−2.32150	−0.127409
$333$	−1.31004	−0.0717895
$334$	−3.69066	−0.201944
$335$	13.5995	0.743020
$336$	−6.54692	−0.357163
$337$	−29.3757	−1.60020	−0.800098	−	0.599870i	$-0.795219\pi$
$337$	−29.3757	−1.60020	−0.800098	+	0.599870i	$0.795219\pi$
$338$	−7.63077	−0.415059
$339$	−29.0640	−1.57854
$340$	−4.27835	−0.232026
$341$	23.3407	1.26397
$342$	18.0419	0.975595
$343$	−14.4753	−0.781590
$344$	−5.67078	−0.305748
$345$	−21.3003	−1.14677
$346$	−12.7808	−0.687103
$347$	−28.0219	−1.50430	−0.752148	−	0.658994i	$-0.770982\pi$
$347$	−28.0219	−1.50430	−0.752148	+	0.658994i	$0.770982\pi$
$348$	−6.91130	−0.370485
$349$	20.4395	1.09410	0.547050	−	0.837100i	$-0.315751\pi$
$349$	20.4395	1.09410	0.547050	+	0.837100i	$0.315751\pi$
$350$	2.03207	0.108619
$351$	−6.72234	−0.358812
$352$	15.3868	0.820119
$353$	28.9509	1.54090	0.770450	−	0.637501i	$-0.220032\pi$
$353$	28.9509	1.54090	0.770450	+	0.637501i	$0.220032\pi$
$354$	2.08041	0.110573
$355$	−11.5317	−0.612037
$356$	−0.925581	−0.0490557
$357$	−7.73668	−0.409469
$358$	2.30490	0.121818
$359$	21.7233	1.14651	0.573257	−	0.819376i	$-0.305680\pi$
$359$	21.7233	1.14651	0.573257	+	0.819376i	$0.305680\pi$
$360$	14.1746	0.747067
$361$	48.8814	2.57271
$362$	−7.11393	−0.373900
$363$	34.3838	1.80468
$364$	−1.60018	−0.0838722
$365$	0.381340	0.0199603
$366$	−18.6733	−0.976067
$367$	−17.2489	−0.900384	−0.450192	−	0.892932i	$-0.648645\pi$
$367$	−17.2489	−0.900384	−0.450192	+	0.892932i	$0.648645\pi$
$368$	−9.98616	−0.520565
$369$	0	0
$370$	2.21784	0.115300
$371$	6.37803	0.331131
$372$	−5.38824	−0.279367
$373$	−17.0451	−0.882561	−0.441281	−	0.897369i	$-0.645476\pi$
$373$	−17.0451	−0.882561	−0.441281	+	0.897369i	$0.645476\pi$
$374$	−19.2838	−0.997144
$375$	19.6716	1.01584
$376$	−10.8764	−0.560905
$377$	14.9802	0.771518
$378$	−3.57830	−0.184048
$379$	37.0481	1.90304	0.951518	−	0.307594i	$-0.0995239\pi$
$379$	37.0481	1.90304	0.951518	+	0.307594i	$0.0995239\pi$
$380$	11.3934	0.584467
$381$	−29.6463	−1.51883
$382$	−3.81645	−0.195266
$383$	33.7813	1.72614	0.863072	−	0.505082i	$-0.168538\pi$
$383$	33.7813	1.72614	0.863072	+	0.505082i	$0.168538\pi$
$384$	10.3142	0.526345
$385$	−14.9795	−0.763427
$386$	19.0592	0.970089
$387$	3.35188	0.170386
$388$	2.38806	0.121235
$389$	8.89595	0.451043	0.225521	−	0.974238i	$-0.427591\pi$
$389$	8.89595	0.451043	0.225521	+	0.974238i	$0.427591\pi$
$390$	−17.4162	−0.881901
$391$	−11.8009	−0.596799
$392$	17.5002	0.883896
$393$	22.4545	1.13268
$394$	−5.48570	−0.276365
$395$	41.1716	2.07157
$396$	−5.09124	−0.255845
$397$	−8.38500	−0.420831	−0.210416	−	0.977612i	$-0.567482\pi$
$397$	−8.38500	−0.420831	−0.210416	+	0.977612i	$0.567482\pi$
$398$	10.8426	0.543491
$399$	20.6030	1.03144
$400$	−3.86775	−0.193388
$401$	−24.8940	−1.24315	−0.621573	−	0.783356i	$-0.713506\pi$
$401$	−24.8940	−1.24315	−0.621573	+	0.783356i	$0.713506\pi$
$402$	−14.1506	−0.705766
$403$	11.6789	0.581770
$404$	−1.68220	−0.0836924
$405$	28.3804	1.41023
$406$	7.97394	0.395740
$407$	−3.72880	−0.184830
$408$	20.8379	1.03163
$409$	8.75194	0.432756	0.216378	−	0.976310i	$-0.430576\pi$
$409$	8.75194	0.432756	0.216378	+	0.976310i	$0.430576\pi$
$410$	0	0
$411$	−12.5933	−0.621181
$412$	−1.60170	−0.0789102
$413$	0.895334	0.0440565
$414$	8.35264	0.410510
$415$	−10.8740	−0.533782
$416$	7.69908	0.377478
$417$	−35.3834	−1.73273
$418$	51.3534	2.51178
$419$	24.9286	1.21784	0.608920	−	0.793232i	$-0.291603\pi$
$419$	24.9286	1.21784	0.608920	+	0.793232i	$0.291603\pi$
$420$	3.45805	0.168736
$421$	10.8901	0.530752	0.265376	−	0.964145i	$-0.414504\pi$
$421$	10.8901	0.530752	0.265376	+	0.964145i	$0.414504\pi$
$422$	−7.79653	−0.379529
$423$	6.42879	0.312578
$424$	−17.1785	−0.834263
$425$	−4.57064	−0.221708
$426$	11.9989	0.581350
$427$	−8.03630	−0.388904
$428$	−1.84015	−0.0889472
$429$	29.2814	1.41372
$430$	−5.67460	−0.273653
$431$	−19.4603	−0.937368	−0.468684	−	0.883366i	$-0.655272\pi$
$431$	−19.4603	−0.937368	−0.468684	+	0.883366i	$0.655272\pi$
$432$	6.81077	0.327683
$433$	4.65604	0.223755	0.111878	−	0.993722i	$-0.464314\pi$
$433$	4.65604	0.223755	0.111878	+	0.993722i	$0.464314\pi$
$434$	6.21670	0.298411
$435$	−32.3727	−1.55215
$436$	−7.42044	−0.355375
$437$	31.4262	1.50332
$438$	−0.396792	−0.0189595
$439$	12.4712	0.595219	0.297609	−	0.954688i	$-0.403811\pi$
$439$	12.4712	0.595219	0.297609	+	0.954688i	$0.403811\pi$
$440$	40.3457	1.92341
$441$	−10.3440	−0.492573
$442$	−9.64904	−0.458958
$443$	−13.7859	−0.654989	−0.327495	−	0.944853i	$-0.606204\pi$
$443$	−13.7859	−0.654989	−0.327495	+	0.944853i	$0.606204\pi$
$444$	0.860801	0.0408518
$445$	−4.33545	−0.205520
$446$	−4.93980	−0.233906
$447$	11.9139	0.563507
$448$	10.0658	0.475563
$449$	5.33358	0.251707	0.125854	−	0.992049i	$-0.459833\pi$
$449$	5.33358	0.251707	0.125854	+	0.992049i	$0.459833\pi$
$450$	3.23507	0.152503
$451$	0	0
$452$	7.19720	0.338528
$453$	−7.43309	−0.349237
$454$	0.692996	0.0325239
$455$	−7.49529	−0.351384
$456$	−55.4919	−2.59865
$457$	10.1601	0.475270	0.237635	−	0.971355i	$-0.423628\pi$
$457$	10.1601	0.475270	0.237635	+	0.971355i	$0.423628\pi$
$458$	29.0116	1.35562
$459$	8.04849	0.375671
$460$	5.27464	0.245932
$461$	29.6950	1.38303	0.691517	−	0.722360i	$-0.256943\pi$
$461$	29.6950	1.38303	0.691517	+	0.722360i	$0.256943\pi$
$462$	15.5865	0.725149
$463$	−38.4159	−1.78534	−0.892668	−	0.450714i	$-0.851169\pi$
$463$	−38.4159	−1.78534	−0.892668	+	0.450714i	$0.851169\pi$
$464$	−15.1772	−0.704586
$465$	−25.2386	−1.17041
$466$	14.9826	0.694054
$467$	2.75450	0.127463	0.0637315	−	0.997967i	$-0.479700\pi$
$467$	2.75450	0.127463	0.0637315	+	0.997967i	$0.479700\pi$
$468$	−2.54750	−0.117758
$469$	−6.08989	−0.281205
$470$	−10.8837	−0.502026
$471$	−22.1956	−1.02272
$472$	−2.41148	−0.110998
$473$	9.54059	0.438677
$474$	−42.8399	−1.96770
$475$	12.1717	0.558477
$476$	1.91586	0.0878131
$477$	10.1539	0.464914
$478$	−8.18814	−0.374517
$479$	−36.0315	−1.64632	−0.823161	−	0.567808i	$-0.807792\pi$
$479$	−36.0315	−1.64632	−0.823161	+	0.567808i	$0.807792\pi$
$480$	−16.6380	−0.759417
$481$	−1.86578	−0.0850721
$482$	−23.1471	−1.05432
$483$	9.53831	0.434008
$484$	−8.51456	−0.387025
$485$	11.1857	0.507918
$486$	−20.1111	−0.912260
$487$	−15.3114	−0.693826	−0.346913	−	0.937897i	$-0.612770\pi$
$487$	−15.3114	−0.693826	−0.346913	+	0.937897i	$0.612770\pi$
$488$	21.6449	0.979818
$489$	−41.1254	−1.85975
$490$	17.5120	0.791112
$491$	−8.39830	−0.379010	−0.189505	−	0.981880i	$-0.560688\pi$
$491$	−8.39830	−0.379010	−0.189505	+	0.981880i	$0.560688\pi$
$492$	0	0
$493$	−17.9354	−0.807769
$494$	25.6956	1.15610
$495$	−23.8475	−1.07187
$496$	−11.8326	−0.531299
$497$	5.16391	0.231633
$498$	11.3146	0.507018
$499$	−7.70449	−0.344900	−0.172450	−	0.985018i	$-0.555168\pi$
$499$	−7.70449	−0.344900	−0.172450	+	0.985018i	$0.555168\pi$
$500$	−4.87134	−0.217853
$501$	−6.70961	−0.299763
$502$	−2.27520	−0.101547
$503$	−18.5834	−0.828593	−0.414297	−	0.910142i	$-0.635972\pi$
$503$	−18.5834	−0.828593	−0.414297	+	0.910142i	$0.635972\pi$
$504$	−6.34742	−0.282737
$505$	−7.87945	−0.350631
$506$	23.7744	1.05690
$507$	−13.8727	−0.616108
$508$	7.34141	0.325722
$509$	−17.6987	−0.784481	−0.392240	−	0.919863i	$-0.628300\pi$
$509$	−17.6987	−0.784481	−0.392240	+	0.919863i	$0.628300\pi$
$510$	20.8519	0.923339
$511$	−0.170765	−0.00755420
$512$	−23.8733	−1.05506
$513$	−21.4333	−0.946304
$514$	−33.7829	−1.49010
$515$	−7.50241	−0.330596
$516$	−2.20246	−0.0969580
$517$	18.2985	0.804767
$518$	−0.993152	−0.0436366
$519$	−23.2355	−1.01993
$520$	20.1877	0.885291
$521$	−25.5766	−1.12053	−0.560265	−	0.828314i	$-0.689301\pi$
$521$	−25.5766	−1.12053	−0.560265	+	0.828314i	$0.689301\pi$
$522$	12.6946	0.555626
$523$	26.4304	1.15572	0.577861	−	0.816135i	$-0.303888\pi$
$523$	26.4304	1.15572	0.577861	+	0.816135i	$0.303888\pi$
$524$	−5.56046	−0.242910
$525$	3.69429	0.161232
$526$	4.99604	0.217838
$527$	−13.9829	−0.609105
$528$	−29.6666	−1.29107
$529$	−8.45100	−0.367435
$530$	−17.1901	−0.746689
$531$	1.42538	0.0618561
$532$	−5.10197	−0.221199
$533$	0	0
$534$	4.51112	0.195215
$535$	−8.61933	−0.372646
$536$	16.4025	0.708478
$537$	4.19029	0.180824
$538$	35.9164	1.54846
$539$	−29.4426	−1.26818
$540$	−3.59742	−0.154808
$541$	18.9652	0.815376	0.407688	−	0.913121i	$-0.366335\pi$
$541$	18.9652	0.815376	0.407688	+	0.913121i	$0.366335\pi$
$542$	−27.9893	−1.20224
$543$	−12.9331	−0.555012
$544$	−9.21791	−0.395215
$545$	−34.7575	−1.48885
$546$	7.79899	0.333766
$547$	−15.6615	−0.669638	−0.334819	−	0.942282i	$-0.608675\pi$
$547$	−15.6615	−0.669638	−0.334819	+	0.942282i	$0.608675\pi$
$548$	3.11851	0.133216
$549$	−12.7938	−0.546028
$550$	9.20811	0.392635
$551$	47.7624	2.03475
$552$	−25.6904	−1.09346
$553$	−18.4367	−0.784010
$554$	29.8915	1.26997
$555$	4.03201	0.171149
$556$	8.76210	0.371596
$557$	−30.7421	−1.30259	−0.651293	−	0.758827i	$-0.725773\pi$
$557$	−30.7421	−1.30259	−0.651293	+	0.758827i	$0.725773\pi$
$558$	9.89703	0.418975
$559$	4.77381	0.201911
$560$	7.59389	0.320900
$561$	−35.0579	−1.48015
$562$	−0.256664	−0.0108267
$563$	−22.2179	−0.936372	−0.468186	−	0.883630i	$-0.655092\pi$
$563$	−22.2179	−0.936372	−0.468186	+	0.883630i	$0.655092\pi$
$564$	−4.22424	−0.177873
$565$	33.7119	1.41827
$566$	−13.3168	−0.559748
$567$	−12.7088	−0.533719
$568$	−13.9084	−0.583585
$569$	4.70549	0.197264	0.0986322	−	0.995124i	$-0.468553\pi$
$569$	4.70549	0.197264	0.0986322	+	0.995124i	$0.468553\pi$
$570$	−55.5292	−2.32586
$571$	13.4260	0.561859	0.280929	−	0.959728i	$-0.409357\pi$
$571$	13.4260	0.561859	0.280929	+	0.959728i	$0.409357\pi$
$572$	−7.25104	−0.303181
$573$	−6.93828	−0.289851
$574$	0	0
$575$	5.63499	0.234995
$576$	16.0248	0.667699
$577$	16.6171	0.691780	0.345890	−	0.938275i	$-0.387577\pi$
$577$	16.6171	0.691780	0.345890	+	0.938275i	$0.387577\pi$
$578$	−8.96506	−0.372897
$579$	34.6496	1.43999
$580$	8.01655	0.332869
$581$	4.86939	0.202016
$582$	−11.6390	−0.482451
$583$	28.9013	1.19697
$584$	0.459937	0.0190323
$585$	−11.9326	−0.493350
$586$	−9.18369	−0.379375
$587$	−26.2360	−1.08287	−0.541437	−	0.840741i	$-0.682120\pi$
$587$	−26.2360	−1.08287	−0.541437	+	0.840741i	$0.682120\pi$
$588$	6.79688	0.280298
$589$	37.2369	1.53432
$590$	−2.41311	−0.0993460
$591$	−9.97297	−0.410233
$592$	1.89032	0.0776917
$593$	2.43376	0.0999427	0.0499714	−	0.998751i	$-0.484087\pi$
$593$	2.43376	0.0999427	0.0499714	+	0.998751i	$0.484087\pi$
$594$	−16.2147	−0.665295
$595$	8.97392	0.367895
$596$	−2.95027	−0.120848
$597$	19.7118	0.806751
$598$	11.8960	0.486463
$599$	−16.7634	−0.684933	−0.342467	−	0.939530i	$-0.611262\pi$
$599$	−16.7634	−0.684933	−0.342467	+	0.939530i	$0.611262\pi$
$600$	−9.95018	−0.406214
$601$	−12.1816	−0.496896	−0.248448	−	0.968645i	$-0.579921\pi$
$601$	−12.1816	−0.496896	−0.248448	+	0.968645i	$0.579921\pi$
$602$	2.54110	0.103567
$603$	−9.69515	−0.394817
$604$	1.84068	0.0748961
$605$	−39.8824	−1.62145
$606$	8.19872	0.333050
$607$	−4.43908	−0.180177	−0.0900883	−	0.995934i	$-0.528715\pi$
$607$	−4.43908	−0.180177	−0.0900883	+	0.995934i	$0.528715\pi$
$608$	24.5475	0.995534
$609$	14.4966	0.587431
$610$	21.6595	0.876966
$611$	9.15600	0.370412
$612$	3.05006	0.123291
$613$	−47.5001	−1.91851	−0.959255	−	0.282541i	$-0.908823\pi$
$613$	−47.5001	−1.91851	−0.959255	+	0.282541i	$0.908823\pi$
$614$	37.9136	1.53007
$615$	0	0
$616$	−18.0669	−0.727936
$617$	−37.4570	−1.50796	−0.753980	−	0.656897i	$-0.771869\pi$
$617$	−37.4570	−1.50796	−0.753980	+	0.656897i	$0.771869\pi$
$618$	7.80641	0.314020
$619$	−15.1762	−0.609981	−0.304991	−	0.952355i	$-0.598653\pi$
$619$	−15.1762	−0.609981	−0.304991	+	0.952355i	$0.598653\pi$
$620$	6.24991	0.251003
$621$	−9.92272	−0.398185
$622$	−17.8058	−0.713946
$623$	1.94142	0.0777815
$624$	−14.8443	−0.594246
$625$	−30.2041	−1.20817
$626$	−20.0439	−0.801116
$627$	93.3602	3.72845
$628$	5.49636	0.219329
$629$	2.23385	0.0890694
$630$	−6.35169	−0.253057
$631$	−5.91607	−0.235515	−0.117758	−	0.993042i	$-0.537571\pi$
$631$	−5.91607	−0.235515	−0.117758	+	0.993042i	$0.537571\pi$
$632$	49.6574	1.97526
$633$	−14.1741	−0.563368
$634$	39.3109	1.56123
$635$	34.3873	1.36462
$636$	−6.67192	−0.264559
$637$	−14.7322	−0.583709
$638$	36.1330	1.43052
$639$	8.22098	0.325217
$640$	−11.9637	−0.472905
$641$	−34.9031	−1.37859	−0.689295	−	0.724481i	$-0.742080\pi$
$641$	−34.9031	−1.37859	−0.689295	+	0.724481i	$0.742080\pi$
$642$	8.96858	0.353962
$643$	32.3091	1.27415	0.637074	−	0.770803i	$-0.280145\pi$
$643$	32.3091	1.27415	0.637074	+	0.770803i	$0.280145\pi$
$644$	−2.36200	−0.0930757
$645$	−10.3164	−0.406207
$646$	−30.7647	−1.21042
$647$	−0.686839	−0.0270024	−0.0135012	−	0.999909i	$-0.504298\pi$
$647$	−0.686839	−0.0270024	−0.0135012	+	0.999909i	$0.504298\pi$
$648$	34.2298	1.34467
$649$	4.05711	0.159255
$650$	4.60745	0.180719
$651$	11.3019	0.442957
$652$	10.1840	0.398836
$653$	47.6682	1.86540	0.932701	−	0.360651i	$-0.117446\pi$
$653$	47.6682	1.86540	0.932701	+	0.360651i	$0.117446\pi$
$654$	36.1659	1.41420
$655$	−26.0454	−1.01768
$656$	0	0
$657$	−0.271859	−0.0106062
$658$	4.87373	0.189998
$659$	−44.4524	−1.73162	−0.865811	−	0.500372i	$-0.833197\pi$
$659$	−44.4524	−1.73162	−0.865811	+	0.500372i	$0.833197\pi$
$660$	15.6698	0.609945
$661$	24.0143	0.934049	0.467025	−	0.884244i	$-0.345326\pi$
$661$	24.0143	0.934049	0.467025	+	0.884244i	$0.345326\pi$
$662$	2.27257	0.0883258
$663$	−17.5419	−0.681271
$664$	−13.1152	−0.508967
$665$	−23.8978	−0.926716
$666$	−1.58111	−0.0612666
$667$	22.1120	0.856179
$668$	1.66152	0.0642861
$669$	−8.98052	−0.347207
$670$	16.4135	0.634109
$671$	−36.4156	−1.40581
$672$	7.45053	0.287410
$673$	15.3647	0.592267	0.296134	−	0.955147i	$-0.404303\pi$
$673$	15.3647	0.592267	0.296134	+	0.955147i	$0.404303\pi$
$674$	−35.4540	−1.36564
$675$	−3.84318	−0.147924
$676$	3.43534	0.132128
$677$	−32.2857	−1.24084	−0.620419	−	0.784270i	$-0.713038\pi$
$677$	−32.2857	−1.24084	−0.620419	+	0.784270i	$0.713038\pi$
$678$	−35.0779	−1.34716
$679$	−5.00900	−0.192228
$680$	−24.1703	−0.926888
$681$	1.25986	0.0482781
$682$	28.1703	1.07870
$683$	16.7987	0.642786	0.321393	−	0.946946i	$-0.395849\pi$
$683$	16.7987	0.642786	0.321393	+	0.946946i	$0.395849\pi$
$684$	−8.12238	−0.310567
$685$	14.6072	0.558112
$686$	−17.4705	−0.667025
$687$	52.7429	2.01227
$688$	−4.83661	−0.184394
$689$	14.4613	0.550933
$690$	−25.7077	−0.978674
$691$	−25.9498	−0.987177	−0.493589	−	0.869695i	$-0.664315\pi$
$691$	−25.9498	−0.987177	−0.493589	+	0.869695i	$0.664315\pi$
$692$	5.75387	0.218729
$693$	10.6790	0.405661
$694$	−33.8202	−1.28380
$695$	41.0419	1.55681
$696$	−39.0450	−1.48000
$697$	0	0
$698$	24.6688	0.933727
$699$	27.2382	1.03024
$700$	−0.914828	−0.0345773
$701$	27.2911	1.03077	0.515385	−	0.856959i	$-0.327649\pi$
$701$	27.2911	1.03077	0.515385	+	0.856959i	$0.327649\pi$
$702$	−8.11331	−0.306217
$703$	−5.94880	−0.224363
$704$	45.6119	1.71906
$705$	−19.7865	−0.745201
$706$	34.9413	1.31503
$707$	3.52844	0.132700
$708$	−0.936590	−0.0351992
$709$	45.4162	1.70564	0.852821	−	0.522204i	$-0.174890\pi$
$709$	45.4162	1.70564	0.852821	+	0.522204i	$0.174890\pi$
$710$	−13.9178	−0.522325
$711$	−29.3514	−1.10077
$712$	−5.22901	−0.195966
$713$	17.2391	0.645609
$714$	−9.33754	−0.349449
$715$	−33.9641	−1.27018
$716$	−1.03765	−0.0387789
$717$	−14.8860	−0.555928
$718$	26.2183	0.978458
$719$	27.7828	1.03612	0.518061	−	0.855343i	$-0.326654\pi$
$719$	27.7828	1.03612	0.518061	+	0.855343i	$0.326654\pi$
$720$	12.0895	0.450550
$721$	3.35960	0.125118
$722$	58.9959	2.19560
$723$	−42.0814	−1.56502
$724$	3.20266	0.119026
$725$	8.56421	0.318067
$726$	41.4984	1.54015
$727$	−17.6427	−0.654332	−0.327166	−	0.944967i	$-0.606094\pi$
$727$	−17.6427	−0.654332	−0.327166	+	0.944967i	$0.606094\pi$
$728$	−9.04012	−0.335049
$729$	−3.10848	−0.115129
$730$	0.460247	0.0170345
$731$	−5.71557	−0.211398
$732$	8.40661	0.310717
$733$	−9.42091	−0.347969	−0.173985	−	0.984748i	$-0.555664\pi$
$733$	−9.42091	−0.347969	−0.173985	+	0.984748i	$0.555664\pi$
$734$	−20.8180	−0.768406
$735$	31.8367	1.17432
$736$	11.3645	0.418900
$737$	−27.5957	−1.01650
$738$	0	0
$739$	0.347492	0.0127827	0.00639135	−	0.999980i	$-0.497966\pi$
$739$	0.347492	0.0127827	0.00639135	+	0.999980i	$0.497966\pi$
$740$	−0.998459	−0.0367041
$741$	46.7145	1.71610
$742$	7.69775	0.282593
$743$	−7.21001	−0.264510	−0.132255	−	0.991216i	$-0.542222\pi$
$743$	−7.21001	−0.264510	−0.132255	+	0.991216i	$0.542222\pi$
$744$	−30.4405	−1.11600
$745$	−13.8191	−0.506294
$746$	−20.5720	−0.753195
$747$	7.75210	0.283635
$748$	8.68149	0.317427
$749$	3.85975	0.141032
$750$	23.7421	0.866938
$751$	19.5054	0.711762	0.355881	−	0.934531i	$-0.384181\pi$
$751$	19.5054	0.711762	0.355881	+	0.934531i	$0.384181\pi$
$752$	−9.27645	−0.338277
$753$	−4.13630	−0.150735
$754$	18.0798	0.658429
$755$	8.62179	0.313779
$756$	1.61093	0.0585890
$757$	−17.5957	−0.639527	−0.319763	−	0.947497i	$-0.603603\pi$
$757$	−17.5957	−0.639527	−0.319763	+	0.947497i	$0.603603\pi$
$758$	44.7141	1.62409
$759$	43.2218	1.56885
$760$	64.3661	2.33480
$761$	−25.4358	−0.922047	−0.461024	−	0.887388i	$-0.652518\pi$
$761$	−25.4358	−0.922047	−0.461024	+	0.887388i	$0.652518\pi$
$762$	−35.7807	−1.29620
$763$	15.5645	0.563473
$764$	1.71815	0.0621603
$765$	14.2865	0.516531
$766$	40.7712	1.47313
$767$	2.03005	0.0733009
$768$	−26.3097	−0.949371
$769$	−13.4103	−0.483587	−0.241793	−	0.970328i	$-0.577736\pi$
$769$	−13.4103	−0.483587	−0.241793	+	0.970328i	$0.577736\pi$
$770$	−18.0791	−0.651524
$771$	−61.4171	−2.21188
$772$	−8.58037	−0.308814
$773$	38.0118	1.36719	0.683595	−	0.729862i	$-0.260416\pi$
$773$	38.0118	1.36719	0.683595	+	0.729862i	$0.260416\pi$
$774$	4.04545	0.145411
$775$	6.67689	0.239841
$776$	13.4912	0.484305
$777$	−1.80555	−0.0647736
$778$	10.7367	0.384929
$779$	0	0
$780$	7.84067	0.280741
$781$	23.3997	0.837307
$782$	−14.2428	−0.509320
$783$	−15.0808	−0.538945
$784$	14.9260	0.533070
$785$	25.7451	0.918882
$786$	27.1007	0.966650
$787$	−49.1693	−1.75269	−0.876347	−	0.481680i	$-0.840027\pi$
$787$	−49.1693	−1.75269	−0.876347	+	0.481680i	$0.840027\pi$
$788$	2.46963	0.0879771
$789$	9.08277	0.323355
$790$	49.6908	1.76792
$791$	−15.0963	−0.536761
$792$	−28.7626	−1.02204
$793$	−18.2212	−0.647055
$794$	−10.1200	−0.359146
$795$	−31.2515	−1.10838
$796$	−4.88129	−0.173013
$797$	5.37939	0.190548	0.0952739	−	0.995451i	$-0.469627\pi$
$797$	5.37939	0.190548	0.0952739	+	0.995451i	$0.469627\pi$
$798$	24.8661	0.880251
$799$	−10.9623	−0.387817
$800$	4.40159	0.155620
$801$	3.09076	0.109207
$802$	−30.0450	−1.06093
$803$	−0.773804	−0.0273069
$804$	6.37051	0.224671
$805$	−11.0637	−0.389943
$806$	14.0955	0.496494
$807$	65.2958	2.29852
$808$	−9.50346	−0.334330
$809$	−31.3391	−1.10182	−0.550911	−	0.834564i	$-0.685720\pi$
$809$	−31.3391	−1.10182	−0.550911	+	0.834564i	$0.685720\pi$
$810$	34.2528	1.20352
$811$	−18.8699	−0.662610	−0.331305	−	0.943524i	$-0.607489\pi$
$811$	−18.8699	−0.662610	−0.331305	+	0.943524i	$0.607489\pi$
$812$	−3.58983	−0.125978
$813$	−50.8845	−1.78460
$814$	−4.50036	−0.157738
$815$	47.7021	1.67093
$816$	17.7727	0.622168
$817$	15.2207	0.532505
$818$	10.5629	0.369322
$819$	5.34342	0.186714
$820$	0	0
$821$	1.59911	0.0558094	0.0279047	−	0.999611i	$-0.491117\pi$
$821$	1.59911	0.0558094	0.0279047	+	0.999611i	$0.491117\pi$
$822$	−15.1991	−0.530128
$823$	25.9916	0.906012	0.453006	−	0.891508i	$-0.350352\pi$
$823$	25.9916	0.906012	0.453006	+	0.891508i	$0.350352\pi$
$824$	−9.04871	−0.315227
$825$	16.7403	0.582822
$826$	1.08059	0.0375987
$827$	−8.50051	−0.295592	−0.147796	−	0.989018i	$-0.547218\pi$
$827$	−8.50051	−0.295592	−0.147796	+	0.989018i	$0.547218\pi$
$828$	−3.76032	−0.130680
$829$	0.285264	0.00990764	0.00495382	−	0.999988i	$-0.498423\pi$
$829$	0.285264	0.00990764	0.00495382	+	0.999988i	$0.498423\pi$
$830$	−13.1240	−0.455540
$831$	54.3426	1.88512
$832$	22.8228	0.791238
$833$	17.6384	0.611136
$834$	−42.7049	−1.47875
$835$	7.78260	0.269328
$836$	−23.1190	−0.799589
$837$	−11.7574	−0.406396
$838$	30.0867	1.03933
$839$	−11.6914	−0.403632	−0.201816	−	0.979423i	$-0.564684\pi$
$839$	−11.6914	−0.403632	−0.201816	+	0.979423i	$0.564684\pi$
$840$	19.5360	0.674057
$841$	4.60636	0.158840
$842$	13.1435	0.452954
$843$	−0.466614	−0.0160710
$844$	3.50996	0.120818
$845$	16.0912	0.553554
$846$	7.75902	0.266761
$847$	17.8594	0.613658
$848$	−14.6516	−0.503137
$849$	−24.2099	−0.830882
$850$	−5.51638	−0.189210
$851$	−2.75404	−0.0944073
$852$	−5.40186	−0.185065
$853$	24.3584	0.834017	0.417009	−	0.908903i	$-0.363079\pi$
$853$	24.3584	0.834017	0.417009	+	0.908903i	$0.363079\pi$
$854$	−9.69915	−0.331898
$855$	−38.0455	−1.30113
$856$	−10.3958	−0.355322
$857$	5.10571	0.174408	0.0872039	−	0.996190i	$-0.472207\pi$
$857$	5.10571	0.174408	0.0872039	+	0.996190i	$0.472207\pi$
$858$	35.3403	1.20650
$859$	−0.404507	−0.0138016	−0.00690081	−	0.999976i	$-0.502197\pi$
$859$	−0.404507	−0.0138016	−0.00690081	+	0.999976i	$0.502197\pi$
$860$	2.55468	0.0871137
$861$	0	0
$862$	−23.4869	−0.799969
$863$	37.9612	1.29222	0.646108	−	0.763246i	$-0.276396\pi$
$863$	37.9612	1.29222	0.646108	+	0.763246i	$0.276396\pi$
$864$	−7.75080	−0.263688
$865$	26.9513	0.916372
$866$	5.61946	0.190957
$867$	−16.2984	−0.553524
$868$	−2.79873	−0.0949950
$869$	−83.5441	−2.83404
$870$	−39.0712	−1.32464
$871$	−13.8080	−0.467867
$872$	−41.9213	−1.41963
$873$	−7.97436	−0.269891
$874$	37.9289	1.28296
$875$	10.2177	0.345422
$876$	0.178634	0.00603548
$877$	36.9079	1.24629	0.623146	−	0.782106i	$-0.285854\pi$
$877$	36.9079	1.24629	0.623146	+	0.782106i	$0.285854\pi$
$878$	15.0517	0.507972
$879$	−16.6959	−0.563139
$880$	34.4109	1.15999
$881$	11.1665	0.376211	0.188105	−	0.982149i	$-0.439765\pi$
$881$	11.1665	0.376211	0.188105	+	0.982149i	$0.439765\pi$
$882$	−12.4844	−0.420371
$883$	23.4595	0.789477	0.394738	−	0.918794i	$-0.370835\pi$
$883$	23.4595	0.789477	0.394738	+	0.918794i	$0.370835\pi$
$884$	4.34395	0.146103
$885$	−4.38701	−0.147468
$886$	−16.6385	−0.558981
$887$	27.8642	0.935590	0.467795	−	0.883837i	$-0.345049\pi$
$887$	27.8642	0.935590	0.467795	+	0.883837i	$0.345049\pi$
$888$	4.86304	0.163193
$889$	−15.3987	−0.516457
$890$	−5.23253	−0.175395
$891$	−57.5885	−1.92929
$892$	2.22387	0.0744607
$893$	29.1928	0.976899
$894$	14.3791	0.480908
$895$	−4.86039	−0.162465
$896$	5.35735	0.178977
$897$	21.6268	0.722099
$898$	6.43720	0.214812
$899$	26.2004	0.873833
$900$	−1.45641	−0.0485471
$901$	−17.3142	−0.576819
$902$	0	0
$903$	4.61970	0.153734
$904$	40.6601	1.35234
$905$	15.0013	0.498661
$906$	−8.97114	−0.298046
$907$	−37.9086	−1.25873	−0.629367	−	0.777108i	$-0.716686\pi$
$907$	−37.9086	−1.25873	−0.629367	+	0.777108i	$0.716686\pi$
$908$	−0.311984	−0.0103535
$909$	5.61730	0.186314
$910$	−9.04620	−0.299879
$911$	23.3777	0.774537	0.387269	−	0.921967i	$-0.373419\pi$
$911$	23.3777	0.774537	0.387269	+	0.921967i	$0.373419\pi$
$912$	−47.3291	−1.56722
$913$	22.0651	0.730248
$914$	12.2624	0.405605
$915$	39.3768	1.30176
$916$	−13.0609	−0.431544
$917$	11.6632	0.385152
$918$	9.71386	0.320605
$919$	19.6766	0.649072	0.324536	−	0.945873i	$-0.394792\pi$
$919$	19.6766	0.649072	0.324536	+	0.945873i	$0.394792\pi$
$920$	29.7988	0.982436
$921$	68.9267	2.27121
$922$	35.8394	1.18031
$923$	11.7085	0.385389
$924$	−7.01696	−0.230841
$925$	−1.06667	−0.0350719
$926$	−46.3648	−1.52364
$927$	5.34851	0.175668
$928$	17.2720	0.566982
$929$	7.16054	0.234930	0.117465	−	0.993077i	$-0.462523\pi$
$929$	7.16054	0.234930	0.117465	+	0.993077i	$0.462523\pi$
$930$	−30.4610	−0.998854
$931$	−46.9716	−1.53943
$932$	−6.74508	−0.220942
$933$	−32.3708	−1.05977
$934$	3.32445	0.108779
$935$	40.6643	1.32987
$936$	−14.3919	−0.470415
$937$	43.7552	1.42942	0.714709	−	0.699422i	$-0.246559\pi$
$937$	43.7552	1.42942	0.714709	+	0.699422i	$0.246559\pi$
$938$	−7.35000	−0.239986
$939$	−36.4397	−1.18917
$940$	4.89978	0.159813
$941$	26.2103	0.854432	0.427216	−	0.904150i	$-0.359494\pi$
$941$	26.2103	0.854432	0.427216	+	0.904150i	$0.359494\pi$
$942$	−26.7883	−0.872809
$943$	0	0
$944$	−2.05676	−0.0669417
$945$	7.54564	0.245460
$946$	11.5147	0.374375
$947$	33.0086	1.07264	0.536318	−	0.844016i	$-0.319815\pi$
$947$	33.0086	1.07264	0.536318	+	0.844016i	$0.319815\pi$
$948$	19.2863	0.626390
$949$	−0.387187	−0.0125686
$950$	14.6903	0.476615
$951$	71.4669	2.31747
$952$	10.8235	0.350792
$953$	2.66009	0.0861686	0.0430843	−	0.999071i	$-0.486282\pi$
$953$	2.66009	0.0861686	0.0430843	+	0.999071i	$0.486282\pi$
$954$	12.2549	0.396767
$955$	8.04784	0.260422
$956$	3.68626	0.119222
$957$	65.6896	2.12344
$958$	−43.4871	−1.40500
$959$	−6.54113	−0.211224
$960$	−49.3209	−1.59182
$961$	−10.5734	−0.341079
$962$	−2.25184	−0.0726022
$963$	6.14476	0.198012
$964$	10.4207	0.335629
$965$	−40.1907	−1.29378
$966$	11.5120	0.370391
$967$	−13.0065	−0.418260	−0.209130	−	0.977888i	$-0.567063\pi$
$967$	−13.0065	−0.418260	−0.209130	+	0.977888i	$0.567063\pi$
$968$	−48.1025	−1.54607
$969$	−55.9301	−1.79673
$970$	13.5003	0.433467
$971$	7.26331	0.233091	0.116545	−	0.993185i	$-0.462818\pi$
$971$	7.26331	0.233091	0.116545	+	0.993185i	$0.462818\pi$
$972$	9.05394	0.290405
$973$	−18.3787	−0.589193
$974$	−18.4796	−0.592125
$975$	8.37632	0.268257
$976$	18.4609	0.590920
$977$	29.9985	0.959737	0.479868	−	0.877340i	$-0.340684\pi$
$977$	29.9985	0.959737	0.479868	+	0.877340i	$0.340684\pi$
$978$	−49.6350	−1.58715
$979$	8.79735	0.281164
$980$	−7.88382	−0.251839
$981$	24.7788	0.791127
$982$	−10.1361	−0.323455
$983$	47.8093	1.52488	0.762439	−	0.647060i	$-0.224002\pi$
$983$	47.8093	1.52488	0.762439	+	0.647060i	$0.224002\pi$
$984$	0	0
$985$	11.5678	0.368582
$986$	−21.6465	−0.689366
$987$	8.86042	0.282030
$988$	−11.5680	−0.368029
$989$	7.04654	0.224067
$990$	−28.7820	−0.914752
$991$	42.4706	1.34912	0.674561	−	0.738219i	$-0.264333\pi$
$991$	42.4706	1.34912	0.674561	+	0.738219i	$0.264333\pi$
$992$	13.4657	0.427537
$993$	4.13151	0.131110
$994$	6.23241	0.197680
$995$	−22.8641	−0.724841
$996$	−5.09377	−0.161402
$997$	−42.3597	−1.34154	−0.670772	−	0.741664i	$-0.734037\pi$
$997$	−42.3597	−1.34154	−0.670772	+	0.741664i	$0.734037\pi$
$998$	−9.29868	−0.294345
$999$	1.87831	0.0594272

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1681.2.a.m.1.16		24
41.26	odd	40		41.2.g.a.20.3	✓	24
41.30	odd	40		41.2.g.a.39.3	yes	24
41.40	even	2	inner	1681.2.a.m.1.15		24
123.26	even	40		369.2.u.a.307.1		24
123.71	even	40		369.2.u.a.244.1		24
164.67	even	40		656.2.bs.d.225.2		24
164.71	even	40		656.2.bs.d.449.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
41.2.g.a.20.3	✓	24	41.26	odd	40
41.2.g.a.39.3	yes	24	41.30	odd	40
369.2.u.a.244.1		24	123.71	even	40
369.2.u.a.307.1		24	123.26	even	40
656.2.bs.d.225.2		24	164.67	even	40
656.2.bs.d.449.2		24	164.71	even	40
1681.2.a.m.1.15		24	41.40	even	2	inner
1681.2.a.m.1.16		24	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+1.20692 q^{2} +2.19417 q^{3} -0.543349 q^{4} -2.54506 q^{5} +2.64818 q^{6} +1.13968 q^{7} -3.06961 q^{8} +1.81438 q^{9} +O(q^{10})\)	\(q+1.20692 q^{2} +2.19417 q^{3} -0.543349 q^{4} -2.54506 q^{5} +2.64818 q^{6} +1.13968 q^{7} -3.06961 q^{8} +1.81438 q^{9} -3.07168 q^{10} +5.16435 q^{11} -1.19220 q^{12} +2.58408 q^{13} +1.37550 q^{14} -5.58429 q^{15} -2.61807 q^{16} -3.09386 q^{17} +2.18981 q^{18} +8.23902 q^{19} +1.38285 q^{20} +2.50066 q^{21} +6.23295 q^{22} +3.81432 q^{23} -6.73526 q^{24} +1.47733 q^{25} +3.11877 q^{26} -2.60144 q^{27} -0.619245 q^{28} +5.79710 q^{29} -6.73979 q^{30} +4.51957 q^{31} +2.97943 q^{32} +11.3315 q^{33} -3.73403 q^{34} -2.90056 q^{35} -0.985844 q^{36} -0.722027 q^{37} +9.94382 q^{38} +5.66991 q^{39} +7.81235 q^{40} +3.01809 q^{42} +1.84739 q^{43} -2.80604 q^{44} -4.61772 q^{45} +4.60357 q^{46} +3.54323 q^{47} -5.74450 q^{48} -5.70112 q^{49} +1.78301 q^{50} -6.78845 q^{51} -1.40406 q^{52} +5.59631 q^{53} -3.13973 q^{54} -13.1436 q^{55} -3.49839 q^{56} +18.0778 q^{57} +6.99662 q^{58} +0.785599 q^{59} +3.03422 q^{60} -7.05134 q^{61} +5.45476 q^{62} +2.06782 q^{63} +8.83207 q^{64} -6.57664 q^{65} +13.6762 q^{66} -5.34349 q^{67} +1.68104 q^{68} +8.36926 q^{69} -3.50074 q^{70} +4.53100 q^{71} -5.56946 q^{72} -0.149836 q^{73} -0.871428 q^{74} +3.24151 q^{75} -4.47666 q^{76} +5.88573 q^{77} +6.84312 q^{78} -16.1771 q^{79} +6.66316 q^{80} -11.1512 q^{81} +4.27258 q^{83} -1.35873 q^{84} +7.87405 q^{85} +2.22965 q^{86} +12.7198 q^{87} -15.8526 q^{88} +1.70348 q^{89} -5.57321 q^{90} +2.94503 q^{91} -2.07250 q^{92} +9.91672 q^{93} +4.27639 q^{94} -20.9688 q^{95} +6.53737 q^{96} -4.39508 q^{97} -6.88079 q^{98} +9.37012 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{2} + 20 q^{4} + 12 q^{5} + 24 q^{8} + 24 q^{9}+O(q^{10}) \) 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

Fields

Representations

Groups

Database

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