LMFDB - Embedded newform 3362.2.a.bd.1.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [3362,2,Mod(1,3362)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3362, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("3362.1"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 3362 = 2 \cdot 41^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3362.a (trivial)

Newform invariants

comment:select newform

sage:traces = [16,-16,0,16,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	yes
Analytic conductor:	$26.8457051596$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 32x^{14} + 414x^{12} - 2768x^{10} + 10091x^{8} - 19280x^{6} + 16790x^{4} - 5200x^{2} + 25 $ x^16 - 32x^14 + 414x^12 - 2768x^10 + 10091x^8 - 19280x^6 + 16790x^4 - 5200*x^2 + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 82)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Root			$2.25481$ of defining polynomial
Character	$\chi$	$=$	3362.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000 q^{2} +2.25481 q^{3} +1.00000 q^{4} +1.32349 q^{5} -2.25481 q^{6} +2.61440 q^{7} -1.00000 q^{8} +2.08415 q^{9} -1.32349 q^{10} -1.04263 q^{11} +2.25481 q^{12} +5.77131 q^{13} -2.61440 q^{14} +2.98422 q^{15} +1.00000 q^{16} -1.87038 q^{17} -2.08415 q^{18} +5.95574 q^{19} +1.32349 q^{20} +5.89496 q^{21} +1.04263 q^{22} +7.11545 q^{23} -2.25481 q^{24} -3.24837 q^{25} -5.77131 q^{26} -2.06506 q^{27} +2.61440 q^{28} +8.11168 q^{29} -2.98422 q^{30} -5.59227 q^{31} -1.00000 q^{32} -2.35093 q^{33} +1.87038 q^{34} +3.46013 q^{35} +2.08415 q^{36} -4.56589 q^{37} -5.95574 q^{38} +13.0132 q^{39} -1.32349 q^{40} -5.89496 q^{42} +1.31029 q^{43} -1.04263 q^{44} +2.75836 q^{45} -7.11545 q^{46} -9.94576 q^{47} +2.25481 q^{48} -0.164930 q^{49} +3.24837 q^{50} -4.21735 q^{51} +5.77131 q^{52} -4.20980 q^{53} +2.06506 q^{54} -1.37992 q^{55} -2.61440 q^{56} +13.4290 q^{57} -8.11168 q^{58} -0.321282 q^{59} +2.98422 q^{60} -7.68988 q^{61} +5.59227 q^{62} +5.44879 q^{63} +1.00000 q^{64} +7.63829 q^{65} +2.35093 q^{66} +10.6318 q^{67} -1.87038 q^{68} +16.0440 q^{69} -3.46013 q^{70} -14.9240 q^{71} -2.08415 q^{72} +15.9512 q^{73} +4.56589 q^{74} -7.32444 q^{75} +5.95574 q^{76} -2.72585 q^{77} -13.0132 q^{78} +5.27618 q^{79} +1.32349 q^{80} -10.9088 q^{81} -7.50785 q^{83} +5.89496 q^{84} -2.47544 q^{85} -1.31029 q^{86} +18.2903 q^{87} +1.04263 q^{88} +2.34721 q^{89} -2.75836 q^{90} +15.0885 q^{91} +7.11545 q^{92} -12.6095 q^{93} +9.94576 q^{94} +7.88238 q^{95} -2.25481 q^{96} -4.97951 q^{97} +0.164930 q^{98} -2.17300 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{2} + 16 q^{4} - 16 q^{8} + 16 q^{9} + 16 q^{16} - 16 q^{18} - 16 q^{21} + 4 q^{23} + 4 q^{25} + 60 q^{31} - 16 q^{32} - 16 q^{33} + 16 q^{36} + 44 q^{37} - 12 q^{39} + 16 q^{42} + 40 q^{43}+ \cdots + 24 q^{98}+O(q^{100}) $ 16 * q - 16 * q^2 + 16 * q^4 - 16 * q^8 + 16 * q^9 + 16 * q^16 - 16 * q^18 - 16 * q^21 + 4 * q^23 + 4 * q^25 + 60 * q^31 - 16 * q^32 - 16 * q^33 + 16 * q^36 + 44 * q^37 - 12 * q^39 + 16 * q^42 + 40 * q^43 + 52 * q^45 - 4 * q^46 - 24 * q^49 - 4 * q^50 + 44 * q^51 + 60 * q^57 - 12 * q^59 - 24 * q^61 - 60 * q^62 + 16 * q^64 + 16 * q^66 - 16 * q^72 + 44 * q^73 - 44 * q^74 + 16 * q^77 + 12 * q^78 - 40 * q^81 + 24 * q^83 - 16 * q^84 - 40 * q^86 + 96 * q^87 - 52 * q^90 + 88 * q^91 + 4 * q^92 + 24 * q^98

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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	2.25481	1.30181	0.650906	−	0.759158i	$-0.274389\pi$
$3$	2.25481	1.30181	0.650906	+	0.759158i	$0.274389\pi$
$4$	1.00000	0.500000
$5$	1.32349	0.591884	0.295942	−	0.955206i	$-0.404366\pi$
$5$	1.32349	0.591884	0.295942	+	0.955206i	$0.404366\pi$
$6$	−2.25481	−0.920521
$7$	2.61440	0.988149	0.494075	−	0.869420i	$-0.335507\pi$
$7$	2.61440	0.988149	0.494075	+	0.869420i	$0.335507\pi$
$8$	−1.00000	−0.353553
$9$	2.08415	0.694717
$10$	−1.32349	−0.418525
$11$	−1.04263	−0.314365	−0.157183	−	0.987570i	$-0.550241\pi$
$11$	−1.04263	−0.314365	−0.157183	+	0.987570i	$0.550241\pi$
$12$	2.25481	0.650906
$13$	5.77131	1.60067	0.800337	−	0.599550i	$-0.204654\pi$
$13$	5.77131	1.60067	0.800337	+	0.599550i	$0.204654\pi$
$14$	−2.61440	−0.698727
$15$	2.98422	0.770522
$16$	1.00000	0.250000
$17$	−1.87038	−0.453635	−0.226817	−	0.973937i	$-0.572832\pi$
$17$	−1.87038	−0.453635	−0.226817	+	0.973937i	$0.572832\pi$
$18$	−2.08415	−0.491239
$19$	5.95574	1.36634	0.683170	−	0.730259i	$-0.260601\pi$
$19$	5.95574	1.36634	0.683170	+	0.730259i	$0.260601\pi$
$20$	1.32349	0.295942
$21$	5.89496	1.28639
$22$	1.04263	0.222290
$23$	7.11545	1.48367	0.741837	−	0.670580i	$-0.233955\pi$
$23$	7.11545	1.48367	0.741837	+	0.670580i	$0.233955\pi$
$24$	−2.25481	−0.460260
$25$	−3.24837	−0.649673
$26$	−5.77131	−1.13185
$27$	−2.06506	−0.397422
$28$	2.61440	0.494075
$29$	8.11168	1.50630	0.753151	−	0.657848i	$-0.228533\pi$
$29$	8.11168	1.50630	0.753151	+	0.657848i	$0.228533\pi$
$30$	−2.98422	−0.544841
$31$	−5.59227	−1.00440	−0.502201	−	0.864751i	$-0.667476\pi$
$31$	−5.59227	−1.00440	−0.502201	+	0.864751i	$0.667476\pi$
$32$	−1.00000	−0.176777
$33$	−2.35093	−0.409245
$34$	1.87038	0.320768
$35$	3.46013	0.584870
$36$	2.08415	0.347358
$37$	−4.56589	−0.750628	−0.375314	−	0.926898i	$-0.622465\pi$
$37$	−4.56589	−0.750628	−0.375314	+	0.926898i	$0.622465\pi$
$38$	−5.95574	−0.966149
$39$	13.0132	2.08378
$40$	−1.32349	−0.209263
$41$	0	0
$41$	0	0
$42$	−5.89496	−0.909612
$43$	1.31029	0.199817	0.0999084	−	0.994997i	$-0.468145\pi$
$43$	1.31029	0.199817	0.0999084	+	0.994997i	$0.468145\pi$
$44$	−1.04263	−0.157183
$45$	2.75836	0.411192
$46$	−7.11545	−1.04912
$47$	−9.94576	−1.45074	−0.725369	−	0.688360i	$-0.758331\pi$
$47$	−9.94576	−1.45074	−0.725369	+	0.688360i	$0.758331\pi$
$48$	2.25481	0.325453
$49$	−0.164930	−0.0235615
$50$	3.24837	0.459388
$51$	−4.21735	−0.590547
$52$	5.77131	0.800337
$53$	−4.20980	−0.578260	−0.289130	−	0.957290i	$-0.593366\pi$
$53$	−4.20980	−0.578260	−0.289130	+	0.957290i	$0.593366\pi$
$54$	2.06506	0.281020
$55$	−1.37992	−0.186068
$56$	−2.61440	−0.349363
$57$	13.4290	1.77872
$58$	−8.11168	−1.06512
$59$	−0.321282	−0.0418274	−0.0209137	−	0.999781i	$-0.506658\pi$
$59$	−0.321282	−0.0418274	−0.0209137	+	0.999781i	$0.506658\pi$
$60$	2.98422	0.385261
$61$	−7.68988	−0.984588	−0.492294	−	0.870429i	$-0.663841\pi$
$61$	−7.68988	−0.984588	−0.492294	+	0.870429i	$0.663841\pi$
$62$	5.59227	0.710219
$63$	5.44879	0.686483
$64$	1.00000	0.125000
$65$	7.63829	0.947413
$66$	2.35093	0.289380
$67$	10.6318	1.29888	0.649440	−	0.760413i	$-0.275003\pi$
$67$	10.6318	1.29888	0.649440	+	0.760413i	$0.275003\pi$
$68$	−1.87038	−0.226817
$69$	16.0440	1.93147
$70$	−3.46013	−0.413565
$71$	−14.9240	−1.77115	−0.885577	−	0.464493i	$-0.846237\pi$
$71$	−14.9240	−1.77115	−0.885577	+	0.464493i	$0.846237\pi$
$72$	−2.08415	−0.245619
$73$	15.9512	1.86695	0.933473	−	0.358648i	$-0.116762\pi$
$73$	15.9512	1.86695	0.933473	+	0.358648i	$0.116762\pi$
$74$	4.56589	0.530774
$75$	−7.32444	−0.845753
$76$	5.95574	0.683170
$77$	−2.72585	−0.310640
$78$	−13.0132	−1.47345
$79$	5.27618	0.593617	0.296808	−	0.954937i	$-0.404078\pi$
$79$	5.27618	0.593617	0.296808	+	0.954937i	$0.404078\pi$
$80$	1.32349	0.147971
$81$	−10.9088	−1.21209
$82$	0	0
$83$	−7.50785	−0.824094	−0.412047	−	0.911163i	$-0.635186\pi$
$83$	−7.50785	−0.824094	−0.412047	+	0.911163i	$0.635186\pi$
$84$	5.89496	0.643193
$85$	−2.47544	−0.268499
$86$	−1.31029	−0.141292
$87$	18.2903	1.96092
$88$	1.04263	0.111145
$89$	2.34721	0.248804	0.124402	−	0.992232i	$-0.460299\pi$
$89$	2.34721	0.248804	0.124402	+	0.992232i	$0.460299\pi$
$90$	−2.75836	−0.290756
$91$	15.0885	1.58170
$92$	7.11545	0.741837
$93$	−12.6095	−1.30754
$94$	9.94576	1.02583
$95$	7.88238	0.808715
$96$	−2.25481	−0.230130
$97$	−4.97951	−0.505593	−0.252797	−	0.967519i	$-0.581350\pi$
$97$	−4.97951	−0.505593	−0.252797	+	0.967519i	$0.581350\pi$
$98$	0.164930	0.0166605
$99$	−2.17300	−0.218395
$100$	−3.24837	−0.324837
$101$	2.72439	0.271087	0.135543	−	0.990771i	$-0.456722\pi$
$101$	2.72439	0.271087	0.135543	+	0.990771i	$0.456722\pi$
$102$	4.21735	0.417580
$103$	−4.28424	−0.422138	−0.211069	−	0.977471i	$-0.567695\pi$
$103$	−4.28424	−0.422138	−0.211069	+	0.977471i	$0.567695\pi$
$104$	−5.77131	−0.565924
$105$	7.80193	0.761391
$106$	4.20980	0.408892
$107$	0.419287	0.0405340	0.0202670	−	0.999795i	$-0.493548\pi$
$107$	0.419287	0.0405340	0.0202670	+	0.999795i	$0.493548\pi$
$108$	−2.06506	−0.198711
$109$	9.63246	0.922622	0.461311	−	0.887238i	$-0.347379\pi$
$109$	9.63246	0.922622	0.461311	+	0.887238i	$0.347379\pi$
$110$	1.37992	0.131570
$111$	−10.2952	−0.977176
$112$	2.61440	0.247037
$113$	−3.61822	−0.340374	−0.170187	−	0.985412i	$-0.554437\pi$
$113$	−3.61822	−0.340374	−0.170187	+	0.985412i	$0.554437\pi$
$114$	−13.4290	−1.25775
$115$	9.41725	0.878163
$116$	8.11168	0.753151
$117$	12.0283	1.11201
$118$	0.321282	0.0295764
$119$	−4.88992	−0.448259
$120$	−2.98422	−0.272421
$121$	−9.91292	−0.901174
$122$	7.68988	0.696209
$123$	0	0
$124$	−5.59227	−0.502201
$125$	−10.9167	−0.976415
$126$	−5.44879	−0.485417
$127$	1.94379	0.172483	0.0862416	−	0.996274i	$-0.472514\pi$
$127$	1.94379	0.172483	0.0862416	+	0.996274i	$0.472514\pi$
$128$	−1.00000	−0.0883883
$129$	2.95444	0.260124
$130$	−7.63829	−0.669922
$131$	7.46070	0.651844	0.325922	−	0.945397i	$-0.394325\pi$
$131$	7.46070	0.651844	0.325922	+	0.945397i	$0.394325\pi$
$132$	−2.35093	−0.204622
$133$	15.5707	1.35015
$134$	−10.6318	−0.918447
$135$	−2.73310	−0.235228
$136$	1.87038	0.160384
$137$	11.6687	0.996922	0.498461	−	0.866912i	$-0.333899\pi$
$137$	11.6687	0.996922	0.498461	+	0.866912i	$0.333899\pi$
$138$	−16.0440	−1.36575
$139$	4.41416	0.374404	0.187202	−	0.982321i	$-0.440058\pi$
$139$	4.41416	0.374404	0.187202	+	0.982321i	$0.440058\pi$
$140$	3.46013	0.292435
$141$	−22.4257	−1.88859
$142$	14.9240	1.25239
$143$	−6.01735	−0.503196
$144$	2.08415	0.173679
$145$	10.7358	0.891556
$146$	−15.9512	−1.32013
$147$	−0.371886	−0.0306726
$148$	−4.56589	−0.375314
$149$	−7.65260	−0.626926	−0.313463	−	0.949600i	$-0.601489\pi$
$149$	−7.65260	−0.626926	−0.313463	+	0.949600i	$0.601489\pi$
$150$	7.32444	0.598038
$151$	14.8640	1.20961	0.604806	−	0.796373i	$-0.293251\pi$
$151$	14.8640	1.20961	0.604806	+	0.796373i	$0.293251\pi$
$152$	−5.95574	−0.483074
$153$	−3.89816	−0.315147
$154$	2.72585	0.219655
$155$	−7.40133	−0.594489
$156$	13.0132	1.04189
$157$	14.2965	1.14099	0.570494	−	0.821302i	$-0.306752\pi$
$157$	14.2965	1.14099	0.570494	+	0.821302i	$0.306752\pi$
$158$	−5.27618	−0.419750
$159$	−9.49228	−0.752787
$160$	−1.32349	−0.104631
$161$	18.6026	1.46609
$162$	10.9088	0.857074
$163$	12.5915	0.986243	0.493121	−	0.869961i	$-0.335856\pi$
$163$	12.5915	0.986243	0.493121	+	0.869961i	$0.335856\pi$
$164$	0	0
$165$	−3.11144	−0.242225
$166$	7.50785	0.582722
$167$	−14.4030	−1.11454	−0.557268	−	0.830333i	$-0.688151\pi$
$167$	−14.4030	−1.11454	−0.557268	+	0.830333i	$0.688151\pi$
$168$	−5.89496	−0.454806
$169$	20.3080	1.56216
$170$	2.47544	0.189857
$171$	12.4127	0.949220
$172$	1.31029	0.0999084
$173$	7.22825	0.549554	0.274777	−	0.961508i	$-0.411396\pi$
$173$	7.22825	0.549554	0.274777	+	0.961508i	$0.411396\pi$
$174$	−18.2903	−1.38658
$175$	−8.49252	−0.641974
$176$	−1.04263	−0.0785913
$177$	−0.724429	−0.0544514
$178$	−2.34721	−0.175931
$179$	1.33467	0.0997577	0.0498789	−	0.998755i	$-0.484116\pi$
$179$	1.33467	0.0997577	0.0498789	+	0.998755i	$0.484116\pi$
$180$	2.75836	0.205596
$181$	−18.9481	−1.40840	−0.704200	−	0.710002i	$-0.748694\pi$
$181$	−18.9481	−1.40840	−0.704200	+	0.710002i	$0.748694\pi$
$182$	−15.0885	−1.11843
$183$	−17.3392	−1.28175
$184$	−7.11545	−0.524558
$185$	−6.04292	−0.444284
$186$	12.6095	0.924572
$187$	1.95012	0.142607
$188$	−9.94576	−0.725369
$189$	−5.39890	−0.392712
$190$	−7.88238	−0.571848
$191$	−22.9998	−1.66421	−0.832104	−	0.554620i	$-0.812864\pi$
$191$	−22.9998	−1.66421	−0.832104	+	0.554620i	$0.812864\pi$
$192$	2.25481	0.162727
$193$	−24.2497	−1.74553	−0.872764	−	0.488142i	$-0.837675\pi$
$193$	−24.2497	−1.74553	−0.872764	+	0.488142i	$0.837675\pi$
$194$	4.97951	0.357508
$195$	17.2229	1.23335
$196$	−0.164930	−0.0117807
$197$	−1.56898	−0.111785	−0.0558925	−	0.998437i	$-0.517800\pi$
$197$	−1.56898	−0.111785	−0.0558925	+	0.998437i	$0.517800\pi$
$198$	2.17300	0.154428
$199$	−11.0614	−0.784120	−0.392060	−	0.919940i	$-0.628237\pi$
$199$	−11.0614	−0.784120	−0.392060	+	0.919940i	$0.628237\pi$
$200$	3.24837	0.229694
$201$	23.9726	1.69090
$202$	−2.72439	−0.191687
$203$	21.2072	1.48845
$204$	−4.21735	−0.295274
$205$	0	0
$206$	4.28424	0.298497
$207$	14.8297	1.03073
$208$	5.77131	0.400169
$209$	−6.20964	−0.429530
$210$	−7.80193	−0.538384
$211$	0.341606	0.0235171	0.0117586	−	0.999931i	$-0.496257\pi$
$211$	0.341606	0.0235171	0.0117586	+	0.999931i	$0.496257\pi$
$212$	−4.20980	−0.289130
$213$	−33.6507	−2.30571
$214$	−0.419287	−0.0286619
$215$	1.73415	0.118268
$216$	2.06506	0.140510
$217$	−14.6204	−0.992499
$218$	−9.63246	−0.652393
$219$	35.9668	2.43041
$220$	−1.37992	−0.0930339
$221$	−10.7946	−0.726121
$222$	10.2952	0.690968
$223$	13.5821	0.909525	0.454762	−	0.890613i	$-0.349724\pi$
$223$	13.5821	0.909525	0.454762	+	0.890613i	$0.349724\pi$
$224$	−2.61440	−0.174682
$225$	−6.77008	−0.451339
$226$	3.61822	0.240681
$227$	−21.4958	−1.42673	−0.713365	−	0.700793i	$-0.752830\pi$
$227$	−21.4958	−1.42673	−0.713365	+	0.700793i	$0.752830\pi$
$228$	13.4290	0.889360
$229$	17.8482	1.17944	0.589720	−	0.807608i	$-0.299238\pi$
$229$	17.8482	1.17944	0.589720	+	0.807608i	$0.299238\pi$
$230$	−9.41725	−0.620955
$231$	−6.14627	−0.404395
$232$	−8.11168	−0.532558
$233$	2.00703	0.131485	0.0657426	−	0.997837i	$-0.479058\pi$
$233$	2.00703	0.131485	0.0657426	+	0.997837i	$0.479058\pi$
$234$	−12.0283	−0.786313
$235$	−13.1631	−0.858668
$236$	−0.321282	−0.0209137
$237$	11.8968	0.772778
$238$	4.88992	0.316967
$239$	10.7741	0.696919	0.348460	−	0.937324i	$-0.386705\pi$
$239$	10.7741	0.696919	0.348460	+	0.937324i	$0.386705\pi$
$240$	2.98422	0.192631
$241$	13.7854	0.887997	0.443998	−	0.896028i	$-0.353560\pi$
$241$	13.7854	0.887997	0.443998	+	0.896028i	$0.353560\pi$
$242$	9.91292	0.637227
$243$	−18.4020	−1.18049
$244$	−7.68988	−0.492294
$245$	−0.218284	−0.0139457
$246$	0	0
$247$	34.3724	2.18707
$248$	5.59227	0.355110
$249$	−16.9287	−1.07282
$250$	10.9167	0.690430
$251$	23.8814	1.50738	0.753692	−	0.657228i	$-0.228271\pi$
$251$	23.8814	1.50738	0.753692	+	0.657228i	$0.228271\pi$
$252$	5.44879	0.343242
$253$	−7.41879	−0.466415
$254$	−1.94379	−0.121964
$255$	−5.58163	−0.349535
$256$	1.00000	0.0625000
$257$	−5.94710	−0.370970	−0.185485	−	0.982647i	$-0.559386\pi$
$257$	−5.94710	−0.370970	−0.185485	+	0.982647i	$0.559386\pi$
$258$	−2.95444	−0.183935
$259$	−11.9370	−0.741732
$260$	7.63829	0.473707
$261$	16.9060	1.04645
$262$	−7.46070	−0.460923
$263$	−16.6758	−1.02827	−0.514137	−	0.857708i	$-0.671888\pi$
$263$	−16.6758	−1.02827	−0.514137	+	0.857708i	$0.671888\pi$
$264$	2.35093	0.144690
$265$	−5.57164	−0.342263
$266$	−15.5707	−0.954699
$267$	5.29250	0.323896
$268$	10.6318	0.649440
$269$	1.30452	0.0795382	0.0397691	−	0.999209i	$-0.487338\pi$
$269$	1.30452	0.0795382	0.0397691	+	0.999209i	$0.487338\pi$
$270$	2.73310	0.166331
$271$	11.1831	0.679323	0.339662	−	0.940548i	$-0.389687\pi$
$271$	11.1831	0.679323	0.339662	+	0.940548i	$0.389687\pi$
$272$	−1.87038	−0.113409
$273$	34.0216	2.05908
$274$	−11.6687	−0.704930
$275$	3.38685	0.204235
$276$	16.0440	0.965733
$277$	3.56676	0.214306	0.107153	−	0.994243i	$-0.465827\pi$
$277$	3.56676	0.214306	0.107153	+	0.994243i	$0.465827\pi$
$278$	−4.41416	−0.264744
$279$	−11.6551	−0.697774
$280$	−3.46013	−0.206783
$281$	−16.9431	−1.01074	−0.505372	−	0.862902i	$-0.668645\pi$
$281$	−16.9431	−1.01074	−0.505372	+	0.862902i	$0.668645\pi$
$282$	22.4257	1.33543
$283$	12.3166	0.732146	0.366073	−	0.930586i	$-0.380702\pi$
$283$	12.3166	0.732146	0.366073	+	0.930586i	$0.380702\pi$
$284$	−14.9240	−0.885577
$285$	17.7732	1.05280
$286$	6.01735	0.355814
$287$	0	0
$288$	−2.08415	−0.122810
$289$	−13.5017	−0.794216
$290$	−10.7358	−0.630425
$291$	−11.2278	−0.658188
$292$	15.9512	0.933473
$293$	13.1018	0.765416	0.382708	−	0.923869i	$-0.374992\pi$
$293$	13.1018	0.765416	0.382708	+	0.923869i	$0.374992\pi$
$294$	0.371886	0.0216888
$295$	−0.425215	−0.0247570
$296$	4.56589	0.265387
$297$	2.15310	0.124936
$298$	7.65260	0.443303
$299$	41.0655	2.37488
$300$	−7.32444	−0.422877
$301$	3.42561	0.197449
$302$	−14.8640	−0.855325
$303$	6.14296	0.352904
$304$	5.95574	0.341585
$305$	−10.1775	−0.582762
$306$	3.89816	0.222843
$307$	−20.3617	−1.16210	−0.581052	−	0.813867i	$-0.697359\pi$
$307$	−20.3617	−1.16210	−0.581052	+	0.813867i	$0.697359\pi$
$308$	−2.72585	−0.155320
$309$	−9.66012	−0.549545
$310$	7.40133	0.420367
$311$	−12.1514	−0.689040	−0.344520	−	0.938779i	$-0.611958\pi$
$311$	−12.1514	−0.689040	−0.344520	+	0.938779i	$0.611958\pi$
$312$	−13.0132	−0.736727
$313$	−2.48863	−0.140666	−0.0703329	−	0.997524i	$-0.522406\pi$
$313$	−2.48863	−0.140666	−0.0703329	+	0.997524i	$0.522406\pi$
$314$	−14.2965	−0.806801
$315$	7.21144	0.406319
$316$	5.27618	0.296808
$317$	−14.8586	−0.834543	−0.417271	−	0.908782i	$-0.637013\pi$
$317$	−14.8586	−0.834543	−0.417271	+	0.908782i	$0.637013\pi$
$318$	9.49228	0.532301
$319$	−8.45750	−0.473529
$320$	1.32349	0.0739855
$321$	0.945411	0.0527677
$322$	−18.6026	−1.03668
$323$	−11.1395	−0.619819
$324$	−10.9088	−0.606043
$325$	−18.7473	−1.03992
$326$	−12.5915	−0.697379
$327$	21.7193	1.20108
$328$	0	0
$329$	−26.0021	−1.43354
$330$	3.11144	0.171279
$331$	26.5369	1.45860	0.729300	−	0.684195i	$-0.239846\pi$
$331$	26.5369	1.45860	0.729300	+	0.684195i	$0.239846\pi$
$332$	−7.50785	−0.412047
$333$	−9.51600	−0.521473
$334$	14.4030	0.788096
$335$	14.0711	0.768787
$336$	5.89496	0.321596
$337$	−32.9779	−1.79642	−0.898211	−	0.439564i	$-0.855133\pi$
$337$	−32.9779	−1.79642	−0.898211	+	0.439564i	$0.855133\pi$
$338$	−20.3080	−1.10461
$339$	−8.15839	−0.443103
$340$	−2.47544	−0.134250
$341$	5.83068	0.315749
$342$	−12.4127	−0.671200
$343$	−18.7320	−1.01143
$344$	−1.31029	−0.0706459
$345$	21.2341	1.14320
$346$	−7.22825	−0.388593
$347$	−4.62777	−0.248432	−0.124216	−	0.992255i	$-0.539642\pi$
$347$	−4.62777	−0.248432	−0.124216	+	0.992255i	$0.539642\pi$
$348$	18.2903	0.980462
$349$	33.1782	1.77599	0.887994	−	0.459855i	$-0.152099\pi$
$349$	33.1782	1.77599	0.887994	+	0.459855i	$0.152099\pi$
$350$	8.49252	0.453944
$351$	−11.9181	−0.636143
$352$	1.04263	0.0555724
$353$	6.84489	0.364317	0.182158	−	0.983269i	$-0.441692\pi$
$353$	6.84489	0.364317	0.182158	+	0.983269i	$0.441692\pi$
$354$	0.724429	0.0385030
$355$	−19.7518	−1.04832
$356$	2.34721	0.124402
$357$	−11.0258	−0.583549
$358$	−1.33467	−0.0705393
$359$	1.56372	0.0825300	0.0412650	−	0.999148i	$-0.486861\pi$
$359$	1.56372	0.0825300	0.0412650	+	0.999148i	$0.486861\pi$
$360$	−2.75836	−0.145378
$361$	16.4709	0.866887
$362$	18.9481	0.995889
$363$	−22.3517	−1.17316
$364$	15.0885	0.790852
$365$	21.1113	1.10502
$366$	17.3392	0.906333
$367$	−13.2834	−0.693385	−0.346693	−	0.937979i	$-0.612695\pi$
$367$	−13.2834	−0.693385	−0.346693	+	0.937979i	$0.612695\pi$
$368$	7.11545	0.370918
$369$	0	0
$370$	6.04292	0.314156
$371$	−11.0061	−0.571408
$372$	−12.6095	−0.653771
$373$	5.42217	0.280749	0.140375	−	0.990098i	$-0.455169\pi$
$373$	5.42217	0.280749	0.140375	+	0.990098i	$0.455169\pi$
$374$	−1.95012	−0.100838
$375$	−24.6149	−1.27111
$376$	9.94576	0.512913
$377$	46.8151	2.41110
$378$	5.39890	0.277689
$379$	20.3906	1.04739	0.523697	−	0.851904i	$-0.324552\pi$
$379$	20.3906	1.04739	0.523697	+	0.851904i	$0.324552\pi$
$380$	7.88238	0.404358
$381$	4.38286	0.224541
$382$	22.9998	1.17677
$383$	−17.0495	−0.871189	−0.435595	−	0.900143i	$-0.643462\pi$
$383$	−17.0495	−0.871189	−0.435595	+	0.900143i	$0.643462\pi$
$384$	−2.25481	−0.115065
$385$	−3.60765	−0.183863
$386$	24.2497	1.23427
$387$	2.73083	0.138816
$388$	−4.97951	−0.252797
$389$	25.4416	1.28994	0.644970	−	0.764208i	$-0.276870\pi$
$389$	25.4416	1.28994	0.644970	+	0.764208i	$0.276870\pi$
$390$	−17.2229	−0.872113
$391$	−13.3086	−0.673046
$392$	0.164930	0.00833024
$393$	16.8224	0.848579
$394$	1.56898	0.0790439
$395$	6.98299	0.351352
$396$	−2.17300	−0.109197
$397$	−31.0990	−1.56081	−0.780407	−	0.625272i	$-0.784988\pi$
$397$	−31.0990	−1.56081	−0.780407	+	0.625272i	$0.784988\pi$
$398$	11.0614	0.554457
$399$	35.1088	1.75764
$400$	−3.24837	−0.162418
$401$	0.789586	0.0394301	0.0197150	−	0.999806i	$-0.493724\pi$
$401$	0.789586	0.0394301	0.0197150	+	0.999806i	$0.493724\pi$
$402$	−23.9726	−1.19565
$403$	−32.2747	−1.60772
$404$	2.72439	0.135543
$405$	−14.4377	−0.717414
$406$	−21.2072	−1.05249
$407$	4.76054	0.235971
$408$	4.21735	0.208790
$409$	−17.8143	−0.880860	−0.440430	−	0.897787i	$-0.645174\pi$
$409$	−17.8143	−0.880860	−0.440430	+	0.897787i	$0.645174\pi$
$410$	0	0
$411$	26.3106	1.29781
$412$	−4.28424	−0.211069
$413$	−0.839959	−0.0413317
$414$	−14.8297	−0.728838
$415$	−9.93659	−0.487768
$416$	−5.77131	−0.282962
$417$	9.95308	0.487404
$418$	6.20964	0.303724
$419$	2.74105	0.133909	0.0669545	−	0.997756i	$-0.478672\pi$
$419$	2.74105	0.133909	0.0669545	+	0.997756i	$0.478672\pi$
$420$	7.80193	0.380695
$421$	20.8336	1.01537	0.507683	−	0.861544i	$-0.330502\pi$
$421$	20.8336	1.01537	0.507683	+	0.861544i	$0.330502\pi$
$422$	−0.341606	−0.0166291
$423$	−20.7284	−1.00785
$424$	4.20980	0.204446
$425$	6.07569	0.294714
$426$	33.6507	1.63038
$427$	−20.1044	−0.972919
$428$	0.419287	0.0202670
$429$	−13.5680	−0.655067
$430$	−1.73415	−0.0836283
$431$	−29.0034	−1.39705	−0.698523	−	0.715588i	$-0.746159\pi$
$431$	−29.0034	−1.39705	−0.698523	+	0.715588i	$0.746159\pi$
$432$	−2.06506	−0.0993555
$433$	36.6852	1.76298	0.881488	−	0.472206i	$-0.156542\pi$
$433$	36.6852	1.76298	0.881488	+	0.472206i	$0.156542\pi$
$434$	14.6204	0.701802
$435$	24.2070	1.16064
$436$	9.63246	0.461311
$437$	42.3778	2.02720
$438$	−35.9668	−1.71856
$439$	−8.20145	−0.391434	−0.195717	−	0.980660i	$-0.562703\pi$
$439$	−8.20145	−0.391434	−0.195717	+	0.980660i	$0.562703\pi$
$440$	1.37992	0.0657849
$441$	−0.343740	−0.0163686
$442$	10.7946	0.513445
$443$	16.9777	0.806634	0.403317	−	0.915060i	$-0.367857\pi$
$443$	16.9777	0.806634	0.403317	+	0.915060i	$0.367857\pi$
$444$	−10.2952	−0.488588
$445$	3.10651	0.147263
$446$	−13.5821	−0.643131
$447$	−17.2551	−0.816140
$448$	2.61440	0.123519
$449$	−24.3424	−1.14879	−0.574394	−	0.818579i	$-0.694762\pi$
$449$	−24.3424	−1.14879	−0.574394	+	0.818579i	$0.694762\pi$
$450$	6.77008	0.319145
$451$	0	0
$452$	−3.61822	−0.170187
$453$	33.5153	1.57469
$454$	21.4958	1.00885
$455$	19.9695	0.936185
$456$	−13.4290	−0.628873
$457$	−2.84453	−0.133062	−0.0665308	−	0.997784i	$-0.521193\pi$
$457$	−2.84453	−0.133062	−0.0665308	+	0.997784i	$0.521193\pi$
$458$	−17.8482	−0.833990
$459$	3.86246	0.180284
$460$	9.41725	0.439081
$461$	28.7349	1.33832	0.669158	−	0.743120i	$-0.266655\pi$
$461$	28.7349	1.33832	0.669158	+	0.743120i	$0.266655\pi$
$462$	6.14627	0.285950
$463$	−12.5975	−0.585457	−0.292729	−	0.956196i	$-0.594563\pi$
$463$	−12.5975	−0.585457	−0.292729	+	0.956196i	$0.594563\pi$
$464$	8.11168	0.376575
$465$	−16.6886	−0.773914
$466$	−2.00703	−0.0929741
$467$	7.17150	0.331858	0.165929	−	0.986138i	$-0.446938\pi$
$467$	7.17150	0.331858	0.165929	+	0.986138i	$0.446938\pi$
$468$	12.0283	0.556007
$469$	27.7957	1.28349
$470$	13.1631	0.607170
$471$	32.2359	1.48535
$472$	0.321282	0.0147882
$473$	−1.36615	−0.0628154
$474$	−11.8968	−0.546436
$475$	−19.3464	−0.887675
$476$	−4.88992	−0.224129
$477$	−8.77385	−0.401727
$478$	−10.7741	−0.492796
$479$	21.3585	0.975893	0.487946	−	0.872874i	$-0.337746\pi$
$479$	21.3585	0.975893	0.487946	+	0.872874i	$0.337746\pi$
$480$	−2.98422	−0.136210
$481$	−26.3512	−1.20151
$482$	−13.7854	−0.627908
$483$	41.9453	1.90858
$484$	−9.91292	−0.450587
$485$	−6.59035	−0.299252
$486$	18.4020	0.834730
$487$	−6.19153	−0.280565	−0.140282	−	0.990112i	$-0.544801\pi$
$487$	−6.19153	−0.280565	−0.140282	+	0.990112i	$0.544801\pi$
$488$	7.68988	0.348104
$489$	28.3914	1.28390
$490$	0.218284	0.00986107
$491$	−13.8868	−0.626705	−0.313352	−	0.949637i	$-0.601452\pi$
$491$	−13.8868	−0.626705	−0.313352	+	0.949637i	$0.601452\pi$
$492$	0	0
$493$	−15.1720	−0.683311
$494$	−34.3724	−1.54649
$495$	−2.87595	−0.129264
$496$	−5.59227	−0.251100
$497$	−39.0173	−1.75016
$498$	16.9287	0.758595
$499$	19.4064	0.868748	0.434374	−	0.900733i	$-0.356970\pi$
$499$	19.4064	0.868748	0.434374	+	0.900733i	$0.356970\pi$
$500$	−10.9167	−0.488208
$501$	−32.4759	−1.45092
$502$	−23.8814	−1.06588
$503$	−18.0178	−0.803376	−0.401688	−	0.915777i	$-0.631576\pi$
$503$	−18.0178	−0.803376	−0.401688	+	0.915777i	$0.631576\pi$
$504$	−5.44879	−0.242709
$505$	3.60571	0.160452
$506$	7.41879	0.329806
$507$	45.7907	2.03364
$508$	1.94379	0.0862416
$509$	−5.96342	−0.264324	−0.132162	−	0.991228i	$-0.542192\pi$
$509$	−5.96342	−0.264324	−0.132162	+	0.991228i	$0.542192\pi$
$510$	5.58163	0.247159
$511$	41.7027	1.84482
$512$	−1.00000	−0.0441942
$513$	−12.2990	−0.543014
$514$	5.94710	0.262315
$515$	−5.67016	−0.249857
$516$	2.95444	0.130062
$517$	10.3698	0.456061
$518$	11.9370	0.524484
$519$	16.2983	0.715416
$520$	−7.63829	−0.334961
$521$	43.8157	1.91960	0.959801	−	0.280681i	$-0.0905602\pi$
$521$	43.8157	1.91960	0.959801	+	0.280681i	$0.0905602\pi$
$522$	−16.9060	−0.739954
$523$	−6.57592	−0.287545	−0.143772	−	0.989611i	$-0.545923\pi$
$523$	−6.57592	−0.287545	−0.143772	+	0.989611i	$0.545923\pi$
$524$	7.46070	0.325922
$525$	−19.1490	−0.835730
$526$	16.6758	0.727100
$527$	10.4597	0.455631
$528$	−2.35093	−0.102311
$529$	27.6296	1.20129
$530$	5.57164	0.242017
$531$	−0.669600	−0.0290582
$532$	15.5707	0.675074
$533$	0	0
$534$	−5.29250	−0.229029
$535$	0.554923	0.0239914
$536$	−10.6318	−0.459224
$537$	3.00942	0.129866
$538$	−1.30452	−0.0562420
$539$	0.171962	0.00740691
$540$	−2.73310	−0.117614
$541$	−0.231158	−0.00993827	−0.00496913	−	0.999988i	$-0.501582\pi$
$541$	−0.231158	−0.00993827	−0.00496913	+	0.999988i	$0.501582\pi$
$542$	−11.1831	−0.480354
$543$	−42.7243	−1.83347
$544$	1.87038	0.0801920
$545$	12.7485	0.546085
$546$	−34.0216	−1.45599
$547$	−20.2020	−0.863775	−0.431887	−	0.901928i	$-0.642152\pi$
$547$	−20.2020	−0.863775	−0.431887	+	0.901928i	$0.642152\pi$
$548$	11.6687	0.498461
$549$	−16.0269	−0.684009
$550$	−3.38685	−0.144416
$551$	48.3111	2.05812
$552$	−16.0440	−0.682876
$553$	13.7940	0.586582
$554$	−3.56676	−0.151537
$555$	−13.6256	−0.578375
$556$	4.41416	0.187202
$557$	25.3586	1.07448	0.537239	−	0.843430i	$-0.319467\pi$
$557$	25.3586	1.07448	0.537239	+	0.843430i	$0.319467\pi$
$558$	11.6551	0.493401
$559$	7.56207	0.319842
$560$	3.46013	0.146217
$561$	4.39714	0.185648
$562$	16.9431	0.714704
$563$	44.5781	1.87874	0.939371	−	0.342901i	$-0.111410\pi$
$563$	44.5781	1.87874	0.939371	+	0.342901i	$0.111410\pi$
$564$	−22.4257	−0.944294
$565$	−4.78869	−0.201462
$566$	−12.3166	−0.517705
$567$	−28.5198	−1.19772
$568$	14.9240	0.626197
$569$	−4.12870	−0.173084	−0.0865422	−	0.996248i	$-0.527582\pi$
$569$	−4.12870	−0.173084	−0.0865422	+	0.996248i	$0.527582\pi$
$570$	−17.7732	−0.744439
$571$	4.62908	0.193721	0.0968605	−	0.995298i	$-0.469120\pi$
$571$	4.62908	0.193721	0.0968605	+	0.995298i	$0.469120\pi$
$572$	−6.01735	−0.251598
$573$	−51.8601	−2.16649
$574$	0	0
$575$	−23.1136	−0.963903
$576$	2.08415	0.0868396
$577$	26.1354	1.08803	0.544015	−	0.839075i	$-0.316903\pi$
$577$	26.1354	1.08803	0.544015	+	0.839075i	$0.316903\pi$
$578$	13.5017	0.561595
$579$	−54.6783	−2.27235
$580$	10.7358	0.445778
$581$	−19.6285	−0.814327
$582$	11.2278	0.465409
$583$	4.38927	0.181785
$584$	−15.9512	−0.660065
$585$	15.9193	0.658184
$586$	−13.1018	−0.541231
$587$	−22.5143	−0.929266	−0.464633	−	0.885503i	$-0.653814\pi$
$587$	−22.5143	−0.929266	−0.464633	+	0.885503i	$0.653814\pi$
$588$	−0.371886	−0.0153363
$589$	−33.3061	−1.37236
$590$	0.425215	0.0175058
$591$	−3.53774	−0.145523
$592$	−4.56589	−0.187657
$593$	−22.0956	−0.907359	−0.453680	−	0.891165i	$-0.649889\pi$
$593$	−22.0956	−0.907359	−0.453680	+	0.891165i	$0.649889\pi$
$594$	−2.15310	−0.0883428
$595$	−6.47178	−0.265317
$596$	−7.65260	−0.313463
$597$	−24.9413	−1.02078
$598$	−41.0655	−1.67929
$599$	15.6707	0.640287	0.320143	−	0.947369i	$-0.396269\pi$
$599$	15.6707	0.640287	0.320143	+	0.947369i	$0.396269\pi$
$600$	7.32444	0.299019
$601$	−25.0870	−1.02332	−0.511661	−	0.859188i	$-0.670969\pi$
$601$	−25.0870	−1.02332	−0.511661	+	0.859188i	$0.670969\pi$
$602$	−3.42561	−0.139617
$603$	22.1583	0.902354
$604$	14.8640	0.604806
$605$	−13.1197	−0.533391
$606$	−6.14296	−0.249541
$607$	−10.6948	−0.434089	−0.217045	−	0.976162i	$-0.569642\pi$
$607$	−10.6948	−0.434089	−0.217045	+	0.976162i	$0.569642\pi$
$608$	−5.95574	−0.241537
$609$	47.8180	1.93768
$610$	10.1775	0.412075
$611$	−57.4001	−2.32216
$612$	−3.89816	−0.157574
$613$	−6.97398	−0.281676	−0.140838	−	0.990033i	$-0.544980\pi$
$613$	−6.97398	−0.281676	−0.140838	+	0.990033i	$0.544980\pi$
$614$	20.3617	0.821731
$615$	0	0
$616$	2.72585	0.109828
$617$	−43.9215	−1.76821	−0.884107	−	0.467284i	$-0.845233\pi$
$617$	−43.9215	−1.76821	−0.884107	+	0.467284i	$0.845233\pi$
$618$	9.66012	0.388587
$619$	42.0760	1.69118	0.845589	−	0.533834i	$-0.179249\pi$
$619$	42.0760	1.69118	0.845589	+	0.533834i	$0.179249\pi$
$620$	−7.40133	−0.297245
$621$	−14.6939	−0.589645
$622$	12.1514	0.487225
$623$	6.13654	0.245855
$624$	13.0132	0.520944
$625$	1.79372	0.0717490
$626$	2.48863	0.0994657
$627$	−14.0015	−0.559168
$628$	14.2965	0.570494
$629$	8.53996	0.340511
$630$	−7.21144	−0.287311
$631$	−16.8291	−0.669956	−0.334978	−	0.942226i	$-0.608729\pi$
$631$	−16.8291	−0.669956	−0.334978	+	0.942226i	$0.608729\pi$
$632$	−5.27618	−0.209875
$633$	0.770256	0.0306149
$634$	14.8586	0.590111
$635$	2.57259	0.102090
$636$	−9.49228	−0.376393
$637$	−0.951865	−0.0377143
$638$	8.45750	0.334836
$639$	−31.1039	−1.23045
$640$	−1.32349	−0.0523156
$641$	−27.0061	−1.06668	−0.533339	−	0.845902i	$-0.679063\pi$
$641$	−27.0061	−1.06668	−0.533339	+	0.845902i	$0.679063\pi$
$642$	−0.945411	−0.0373124
$643$	−24.1050	−0.950608	−0.475304	−	0.879822i	$-0.657662\pi$
$643$	−24.1050	−0.950608	−0.475304	+	0.879822i	$0.657662\pi$
$644$	18.6026	0.733045
$645$	3.91018	0.153963
$646$	11.1395	0.438279
$647$	−12.8206	−0.504028	−0.252014	−	0.967724i	$-0.581093\pi$
$647$	−12.8206	−0.504028	−0.252014	+	0.967724i	$0.581093\pi$
$648$	10.9088	0.428537
$649$	0.334979	0.0131491
$650$	18.7473	0.735331
$651$	−32.9662	−1.29205
$652$	12.5915	0.493121
$653$	−7.28736	−0.285176	−0.142588	−	0.989782i	$-0.545542\pi$
$653$	−7.28736	−0.285176	−0.142588	+	0.989782i	$0.545542\pi$
$654$	−21.7193	−0.849293
$655$	9.87418	0.385816
$656$	0	0
$657$	33.2447	1.29700
$658$	26.0021	1.01367
$659$	−0.244872	−0.00953886	−0.00476943	−	0.999989i	$-0.501518\pi$
$659$	−0.244872	−0.00953886	−0.00476943	+	0.999989i	$0.501518\pi$
$660$	−3.11144	−0.121113
$661$	−17.6654	−0.687104	−0.343552	−	0.939134i	$-0.611630\pi$
$661$	−17.6654	−0.687104	−0.343552	+	0.939134i	$0.611630\pi$
$662$	−26.5369	−1.03139
$663$	−24.3397	−0.945274
$664$	7.50785	0.291361
$665$	20.6077	0.799131
$666$	9.51600	0.368737
$667$	57.7183	2.23486
$668$	−14.4030	−0.557268
$669$	30.6250	1.18403
$670$	−14.0711	−0.543614
$671$	8.01771	0.309520
$672$	−5.89496	−0.227403
$673$	30.0025	1.15651	0.578256	−	0.815856i	$-0.303734\pi$
$673$	30.0025	1.15651	0.578256	+	0.815856i	$0.303734\pi$
$674$	32.9779	1.27026
$675$	6.70809	0.258194
$676$	20.3080	0.781079
$677$	31.5711	1.21338	0.606689	−	0.794940i	$-0.292497\pi$
$677$	31.5711	1.21338	0.606689	+	0.794940i	$0.292497\pi$
$678$	8.15839	0.313321
$679$	−13.0184	−0.499601
$680$	2.47544	0.0949287
$681$	−48.4690	−1.85733
$682$	−5.83068	−0.223268
$683$	10.9891	0.420487	0.210243	−	0.977649i	$-0.432574\pi$
$683$	10.9891	0.420487	0.210243	+	0.977649i	$0.432574\pi$
$684$	12.4127	0.474610
$685$	15.4434	0.590062
$686$	18.7320	0.715190
$687$	40.2442	1.53541
$688$	1.31029	0.0499542
$689$	−24.2961	−0.925607
$690$	−21.2341	−0.808367
$691$	−22.2567	−0.846686	−0.423343	−	0.905969i	$-0.639143\pi$
$691$	−22.2567	−0.846686	−0.423343	+	0.905969i	$0.639143\pi$
$692$	7.22825	0.274777
$693$	−5.68108	−0.215807
$694$	4.62777	0.175668
$695$	5.84211	0.221604
$696$	−18.2903	−0.693291
$697$	0	0
$698$	−33.1782	−1.25581
$699$	4.52547	0.171169
$700$	−8.49252	−0.320987
$701$	−26.5566	−1.00303	−0.501515	−	0.865149i	$-0.667224\pi$
$701$	−26.5566	−1.00303	−0.501515	+	0.865149i	$0.667224\pi$
$702$	11.9181	0.449821
$703$	−27.1933	−1.02561
$704$	−1.04263	−0.0392957
$705$	−29.6803	−1.11783
$706$	−6.84489	−0.257611
$707$	7.12263	0.267874
$708$	−0.724429	−0.0272257
$709$	−19.4703	−0.731221	−0.365611	−	0.930768i	$-0.619140\pi$
$709$	−19.4703	−0.731221	−0.365611	+	0.930768i	$0.619140\pi$
$710$	19.7518	0.741272
$711$	10.9964	0.412395
$712$	−2.34721	−0.0879654
$713$	−39.7915	−1.49020
$714$	11.0258	0.412631
$715$	−7.96392	−0.297834
$716$	1.33467	0.0498789
$717$	24.2935	0.907258
$718$	−1.56372	−0.0583575
$719$	−13.9734	−0.521120	−0.260560	−	0.965458i	$-0.583907\pi$
$719$	−13.9734	−0.521120	−0.260560	+	0.965458i	$0.583907\pi$
$720$	2.75836	0.102798
$721$	−11.2007	−0.417136
$722$	−16.4709	−0.612982
$723$	31.0834	1.15601
$724$	−18.9481	−0.704200
$725$	−26.3497	−0.978604
$726$	22.3517	0.829550
$727$	15.6555	0.580632	0.290316	−	0.956931i	$-0.406240\pi$
$727$	15.6555	0.580632	0.290316	+	0.956931i	$0.406240\pi$
$728$	−15.0885	−0.559217
$729$	−8.76654	−0.324687
$730$	−21.1113	−0.781364
$731$	−2.45074	−0.0906438
$732$	−17.3392	−0.640874
$733$	−43.6573	−1.61252	−0.806260	−	0.591561i	$-0.798512\pi$
$733$	−43.6573	−1.61252	−0.806260	+	0.591561i	$0.798512\pi$
$734$	13.2834	0.490297
$735$	−0.492188	−0.0181546
$736$	−7.11545	−0.262279
$737$	−11.0850	−0.408323
$738$	0	0
$739$	−21.2137	−0.780359	−0.390179	−	0.920739i	$-0.627587\pi$
$739$	−21.2137	−0.780359	−0.390179	+	0.920739i	$0.627587\pi$
$740$	−6.04292	−0.222142
$741$	77.5032	2.84715
$742$	11.0061	0.404046
$743$	41.9673	1.53963	0.769815	−	0.638268i	$-0.220349\pi$
$743$	41.9673	1.53963	0.769815	+	0.638268i	$0.220349\pi$
$744$	12.6095	0.462286
$745$	−10.1282	−0.371067
$746$	−5.42217	−0.198520
$747$	−15.6475	−0.572512
$748$	1.95012	0.0713035
$749$	1.09618	0.0400536
$750$	24.6149	0.898810
$751$	35.9896	1.31328	0.656639	−	0.754205i	$-0.271978\pi$
$751$	35.9896	1.31328	0.656639	+	0.754205i	$0.271978\pi$
$752$	−9.94576	−0.362684
$753$	53.8480	1.96233
$754$	−46.8151	−1.70490
$755$	19.6723	0.715950
$756$	−5.39890	−0.196356
$757$	−10.5859	−0.384753	−0.192376	−	0.981321i	$-0.561619\pi$
$757$	−10.5859	−0.384753	−0.192376	+	0.981321i	$0.561619\pi$
$758$	−20.3906	−0.740620
$759$	−16.7279	−0.607186
$760$	−7.88238	−0.285924
$761$	−30.9205	−1.12087	−0.560434	−	0.828199i	$-0.689366\pi$
$761$	−30.9205	−1.12087	−0.560434	+	0.828199i	$0.689366\pi$
$762$	−4.38286	−0.158774
$763$	25.1831	0.911688
$764$	−22.9998	−0.832104
$765$	−5.15918	−0.186531
$766$	17.0495	0.616024
$767$	−1.85422	−0.0669520
$768$	2.25481	0.0813633
$769$	−15.6032	−0.562667	−0.281334	−	0.959610i	$-0.590777\pi$
$769$	−15.6032	−0.562667	−0.281334	+	0.959610i	$0.590777\pi$
$770$	3.60765	0.130011
$771$	−13.4095	−0.482933
$772$	−24.2497	−0.872764
$773$	−11.2557	−0.404839	−0.202420	−	0.979299i	$-0.564880\pi$
$773$	−11.2557	−0.404839	−0.202420	+	0.979299i	$0.564880\pi$
$774$	−2.73083	−0.0981577
$775$	18.1658	0.652533
$776$	4.97951	0.178754
$777$	−26.9157	−0.965596
$778$	−25.4416	−0.912126
$779$	0	0
$780$	17.2229	0.616677
$781$	15.5602	0.556789
$782$	13.3086	0.475915
$783$	−16.7512	−0.598637
$784$	−0.164930	−0.00589037
$785$	18.9214	0.675333
$786$	−16.8224	−0.600036
$787$	−13.7773	−0.491108	−0.245554	−	0.969383i	$-0.578970\pi$
$787$	−13.7773	−0.491108	−0.245554	+	0.969383i	$0.578970\pi$
$788$	−1.56898	−0.0558925
$789$	−37.6007	−1.33862
$790$	−6.98299	−0.248444
$791$	−9.45947	−0.336340
$792$	2.17300	0.0772142
$793$	−44.3807	−1.57600
$794$	31.0990	1.10366
$795$	−12.5630	−0.445562
$796$	−11.0614	−0.392060
$797$	−6.22248	−0.220412	−0.110206	−	0.993909i	$-0.535151\pi$
$797$	−6.22248	−0.220412	−0.110206	+	0.993909i	$0.535151\pi$
$798$	−35.1088	−1.24284
$799$	18.6024	0.658105
$800$	3.24837	0.114847
$801$	4.89194	0.172848
$802$	−0.789586	−0.0278813
$803$	−16.6312	−0.586903
$804$	23.9726	0.845450
$805$	24.6204	0.867756
$806$	32.2747	1.13683
$807$	2.94145	0.103544
$808$	−2.72439	−0.0958436
$809$	−34.6072	−1.21673	−0.608363	−	0.793659i	$-0.708173\pi$
$809$	−34.6072	−1.21673	−0.608363	+	0.793659i	$0.708173\pi$
$810$	14.4377	0.507288
$811$	−7.63635	−0.268148	−0.134074	−	0.990971i	$-0.542806\pi$
$811$	−7.63635	−0.268148	−0.134074	+	0.990971i	$0.542806\pi$
$812$	21.2072	0.744225
$813$	25.2156	0.884351
$814$	−4.76054	−0.166857
$815$	16.6648	0.583741
$816$	−4.21735	−0.147637
$817$	7.80373	0.273018
$818$	17.8143	0.622862
$819$	31.4467	1.09884
$820$	0	0
$821$	32.1343	1.12149	0.560747	−	0.827987i	$-0.310514\pi$
$821$	32.1343	1.12149	0.560747	+	0.827987i	$0.310514\pi$
$822$	−26.3106	−0.917687
$823$	12.1086	0.422079	0.211040	−	0.977478i	$-0.432315\pi$
$823$	12.1086	0.422079	0.211040	+	0.977478i	$0.432315\pi$
$824$	4.28424	0.149248
$825$	7.63669	0.265875
$826$	0.839959	0.0292259
$827$	−37.7363	−1.31222	−0.656110	−	0.754665i	$-0.727799\pi$
$827$	−37.7363	−1.31222	−0.656110	+	0.754665i	$0.727799\pi$
$828$	14.8297	0.515366
$829$	−10.1597	−0.352862	−0.176431	−	0.984313i	$-0.556455\pi$
$829$	−10.1597	−0.352862	−0.176431	+	0.984313i	$0.556455\pi$
$830$	9.93659	0.344904
$831$	8.04236	0.278986
$832$	5.77131	0.200084
$833$	0.308483	0.0106883
$834$	−9.95308	−0.344647
$835$	−19.0622	−0.659676
$836$	−6.20964	−0.214765
$837$	11.5484	0.399171
$838$	−2.74105	−0.0946879
$839$	−9.41493	−0.325039	−0.162520	−	0.986705i	$-0.551962\pi$
$839$	−9.41493	−0.325039	−0.162520	+	0.986705i	$0.551962\pi$
$840$	−7.80193	−0.269192
$841$	36.7994	1.26895
$842$	−20.8336	−0.717973
$843$	−38.2035	−1.31580
$844$	0.341606	0.0117586
$845$	26.8776	0.924616
$846$	20.7284	0.712659
$847$	−25.9163	−0.890495
$848$	−4.20980	−0.144565
$849$	27.7715	0.953117
$850$	−6.07569	−0.208395
$851$	−32.4884	−1.11369
$852$	−33.6507	−1.15286
$853$	−16.4360	−0.562758	−0.281379	−	0.959597i	$-0.590792\pi$
$853$	−16.4360	−0.562758	−0.281379	+	0.959597i	$0.590792\pi$
$854$	20.1044	0.687958
$855$	16.4281	0.561828
$856$	−0.419287	−0.0143309
$857$	8.21370	0.280575	0.140287	−	0.990111i	$-0.455197\pi$
$857$	8.21370	0.280575	0.140287	+	0.990111i	$0.455197\pi$
$858$	13.5680	0.463203
$859$	−47.3003	−1.61386	−0.806932	−	0.590644i	$-0.798874\pi$
$859$	−47.3003	−1.61386	−0.806932	+	0.590644i	$0.798874\pi$
$860$	1.73415	0.0591342
$861$	0	0
$862$	29.0034	0.987860
$863$	11.5370	0.392724	0.196362	−	0.980532i	$-0.437087\pi$
$863$	11.5370	0.392724	0.196362	+	0.980532i	$0.437087\pi$
$864$	2.06506	0.0702549
$865$	9.56654	0.325272
$866$	−36.6852	−1.24661
$867$	−30.4436	−1.03392
$868$	−14.6204	−0.496249
$869$	−5.50111	−0.186612
$870$	−24.2070	−0.820696
$871$	61.3594	2.07908
$872$	−9.63246	−0.326196
$873$	−10.3781	−0.351244
$874$	−42.3778	−1.43345
$875$	−28.5405	−0.964844
$876$	35.9668	1.21521
$877$	−9.61096	−0.324539	−0.162270	−	0.986746i	$-0.551881\pi$
$877$	−9.61096	−0.324539	−0.162270	+	0.986746i	$0.551881\pi$
$878$	8.20145	0.276786
$879$	29.5420	0.996428
$880$	−1.37992	−0.0465169
$881$	−52.7508	−1.77722	−0.888610	−	0.458663i	$-0.848328\pi$
$881$	−52.7508	−1.77722	−0.888610	+	0.458663i	$0.848328\pi$
$882$	0.343740	0.0115743
$883$	41.9580	1.41200	0.705999	−	0.708213i	$-0.250498\pi$
$883$	41.9580	1.41200	0.705999	+	0.708213i	$0.250498\pi$
$884$	−10.7946	−0.363061
$885$	−0.958776	−0.0322289
$886$	−16.9777	−0.570377
$887$	27.1633	0.912055	0.456027	−	0.889966i	$-0.349272\pi$
$887$	27.1633	0.912055	0.456027	+	0.889966i	$0.349272\pi$
$888$	10.2952	0.345484
$889$	5.08183	0.170439
$890$	−3.10651	−0.104131
$891$	11.3738	0.381038
$892$	13.5821	0.454762
$893$	−59.2344	−1.98220
$894$	17.2551	0.577098
$895$	1.76642	0.0590450
$896$	−2.61440	−0.0873409
$897$	92.5947	3.09165
$898$	24.3424	0.812316
$899$	−45.3627	−1.51293
$900$	−6.77008	−0.225669
$901$	7.87394	0.262319
$902$	0	0
$903$	7.72408	0.257041
$904$	3.61822	0.120340
$905$	−25.0777	−0.833609
$906$	−33.5153	−1.11347
$907$	−24.7408	−0.821504	−0.410752	−	0.911747i	$-0.634734\pi$
$907$	−24.7408	−0.821504	−0.410752	+	0.911747i	$0.634734\pi$
$908$	−21.4958	−0.713365
$909$	5.67803	0.188328
$910$	−19.9695	−0.661983
$911$	−3.90997	−0.129543	−0.0647716	−	0.997900i	$-0.520632\pi$
$911$	−3.90997	−0.129543	−0.0647716	+	0.997900i	$0.520632\pi$
$912$	13.4290	0.444680
$913$	7.82792	0.259066
$914$	2.84453	0.0940888
$915$	−22.9483	−0.758647
$916$	17.8482	0.589720
$917$	19.5052	0.644119
$918$	−3.86246	−0.127480
$919$	−8.48206	−0.279797	−0.139899	−	0.990166i	$-0.544678\pi$
$919$	−8.48206	−0.279797	−0.139899	+	0.990166i	$0.544678\pi$
$920$	−9.41725	−0.310477
$921$	−45.9117	−1.51284
$922$	−28.7349	−0.946333
$923$	−86.1311	−2.83504
$924$	−6.14627	−0.202197
$925$	14.8317	0.487663
$926$	12.5975	0.413981
$927$	−8.92899	−0.293267
$928$	−8.11168	−0.266279
$929$	−24.4828	−0.803255	−0.401627	−	0.915803i	$-0.631555\pi$
$929$	−24.4828	−0.803255	−0.401627	+	0.915803i	$0.631555\pi$
$930$	16.6886	0.547240
$931$	−0.982283	−0.0321930
$932$	2.00703	0.0657426
$933$	−27.3989	−0.897001
$934$	−7.17150	−0.234659
$935$	2.58097	0.0844068
$936$	−12.0283	−0.393157
$937$	5.39742	0.176326	0.0881630	−	0.996106i	$-0.471900\pi$
$937$	5.39742	0.176326	0.0881630	+	0.996106i	$0.471900\pi$
$938$	−27.7957	−0.907563
$939$	−5.61138	−0.183121
$940$	−13.1631	−0.429334
$941$	21.2325	0.692161	0.346080	−	0.938205i	$-0.387512\pi$
$941$	21.2325	0.692161	0.346080	+	0.938205i	$0.387512\pi$
$942$	−32.2359	−1.05030
$943$	0	0
$944$	−0.321282	−0.0104568
$945$	−7.14540	−0.232440
$946$	1.36615	0.0444172
$947$	−26.5281	−0.862049	−0.431024	−	0.902340i	$-0.641848\pi$
$947$	−26.5281	−0.862049	−0.431024	+	0.902340i	$0.641848\pi$
$948$	11.8968	0.386389
$949$	92.0593	2.98837
$950$	19.3464	0.627681
$951$	−33.5033	−1.08642
$952$	4.88992	0.158483
$953$	−50.1602	−1.62485	−0.812424	−	0.583067i	$-0.801853\pi$
$953$	−50.1602	−1.62485	−0.812424	+	0.583067i	$0.801853\pi$
$954$	8.77385	0.284064
$955$	−30.4401	−0.985018
$956$	10.7741	0.348460
$957$	−19.0700	−0.616446
$958$	−21.3585	−0.690060
$959$	30.5065	0.985107
$960$	2.98422	0.0963153
$961$	0.273506	0.00882277
$962$	26.3512	0.849596
$963$	0.873857	0.0281596
$964$	13.7854	0.443998
$965$	−32.0942	−1.03315
$966$	−41.9453	−1.34957
$967$	−29.4017	−0.945495	−0.472747	−	0.881198i	$-0.656738\pi$
$967$	−29.4017	−0.945495	−0.472747	+	0.881198i	$0.656738\pi$
$968$	9.91292	0.318613
$969$	−25.1175	−0.806889
$970$	6.59035	0.211603
$971$	−30.0159	−0.963255	−0.481628	−	0.876376i	$-0.659954\pi$
$971$	−30.0159	−0.963255	−0.481628	+	0.876376i	$0.659954\pi$
$972$	−18.4020	−0.590243
$973$	11.5404	0.369967
$974$	6.19153	0.198389
$975$	−42.2716	−1.35378
$976$	−7.68988	−0.246147
$977$	−58.1476	−1.86031	−0.930154	−	0.367169i	$-0.880327\pi$
$977$	−58.1476	−1.86031	−0.930154	+	0.367169i	$0.880327\pi$
$978$	−28.3914	−0.907857
$979$	−2.44727	−0.0782152
$980$	−0.218284	−0.00697283
$981$	20.0755	0.640961
$982$	13.8868	0.443147
$983$	−8.93048	−0.284838	−0.142419	−	0.989806i	$-0.545488\pi$
$983$	−8.93048	−0.284838	−0.142419	+	0.989806i	$0.545488\pi$
$984$	0	0
$985$	−2.07653	−0.0661637
$986$	15.1720	0.483174
$987$	−58.6298	−1.86621
$988$	34.3724	1.09353
$989$	9.32328	0.296463
$990$	2.87595	0.0914037
$991$	−8.48064	−0.269397	−0.134698	−	0.990887i	$-0.543007\pi$
$991$	−8.48064	−0.269397	−0.134698	+	0.990887i	$0.543007\pi$
$992$	5.59227	0.177555
$993$	59.8355	1.89882
$994$	39.0173	1.23755
$995$	−14.6397	−0.464108
$996$	−16.9287	−0.536408
$997$	−31.2870	−0.990868	−0.495434	−	0.868646i	$-0.664991\pi$
$997$	−31.2870	−0.990868	−0.495434	+	0.868646i	$0.664991\pi$
$998$	−19.4064	−0.614298
$999$	9.42886	0.298316

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3362.2.a.bd.1.13		16
41.34	odd	40		82.2.g.b.49.2	✓	16
41.35	odd	40		82.2.g.b.77.2	yes	16
41.40	even	2	inner	3362.2.a.bd.1.4		16
123.35	even	40		738.2.u.b.487.2		16
123.116	even	40		738.2.u.b.541.2		16
164.35	even	40		656.2.bs.b.241.1		16
164.75	even	40		656.2.bs.b.49.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
82.2.g.b.49.2	✓	16	41.34	odd	40
82.2.g.b.77.2	yes	16	41.35	odd	40
656.2.bs.b.49.1		16	164.75	even	40
656.2.bs.b.241.1		16	164.35	even	40
738.2.u.b.487.2		16	123.35	even	40
738.2.u.b.541.2		16	123.116	even	40
3362.2.a.bd.1.4		16	41.40	even	2	inner
3362.2.a.bd.1.13		16	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 3362 = 2 \cdot 41^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3362.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.25481 q^{3} +1.00000 q^{4} +1.32349 q^{5} -2.25481 q^{6} +2.61440 q^{7} -1.00000 q^{8} +2.08415 q^{9} -1.32349 q^{10} -1.04263 q^{11} +2.25481 q^{12} +5.77131 q^{13} -2.61440 q^{14} +2.98422 q^{15} +1.00000 q^{16} -1.87038 q^{17} -2.08415 q^{18} +5.95574 q^{19} +1.32349 q^{20} +5.89496 q^{21} +1.04263 q^{22} +7.11545 q^{23} -2.25481 q^{24} -3.24837 q^{25} -5.77131 q^{26} -2.06506 q^{27} +2.61440 q^{28} +8.11168 q^{29} -2.98422 q^{30} -5.59227 q^{31} -1.00000 q^{32} -2.35093 q^{33} +1.87038 q^{34} +3.46013 q^{35} +2.08415 q^{36} -4.56589 q^{37} -5.95574 q^{38} +13.0132 q^{39} -1.32349 q^{40} -5.89496 q^{42} +1.31029 q^{43} -1.04263 q^{44} +2.75836 q^{45} -7.11545 q^{46} -9.94576 q^{47} +2.25481 q^{48} -0.164930 q^{49} +3.24837 q^{50} -4.21735 q^{51} +5.77131 q^{52} -4.20980 q^{53} +2.06506 q^{54} -1.37992 q^{55} -2.61440 q^{56} +13.4290 q^{57} -8.11168 q^{58} -0.321282 q^{59} +2.98422 q^{60} -7.68988 q^{61} +5.59227 q^{62} +5.44879 q^{63} +1.00000 q^{64} +7.63829 q^{65} +2.35093 q^{66} +10.6318 q^{67} -1.87038 q^{68} +16.0440 q^{69} -3.46013 q^{70} -14.9240 q^{71} -2.08415 q^{72} +15.9512 q^{73} +4.56589 q^{74} -7.32444 q^{75} +5.95574 q^{76} -2.72585 q^{77} -13.0132 q^{78} +5.27618 q^{79} +1.32349 q^{80} -10.9088 q^{81} -7.50785 q^{83} +5.89496 q^{84} -2.47544 q^{85} -1.31029 q^{86} +18.2903 q^{87} +1.04263 q^{88} +2.34721 q^{89} -2.75836 q^{90} +15.0885 q^{91} +7.11545 q^{92} -12.6095 q^{93} +9.94576 q^{94} +7.88238 q^{95} -2.25481 q^{96} -4.97951 q^{97} +0.164930 q^{98} -2.17300 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{2} + 16 q^{4} - 16 q^{8} + 16 q^{9} + 16 q^{16} - 16 q^{18} - 16 q^{21} + 4 q^{23} + 4 q^{25} + 60 q^{31} - 16 q^{32} - 16 q^{33} + 16 q^{36} + 44 q^{37} - 12 q^{39} + 16 q^{42} + 40 q^{43}+ \cdots + 24 q^{98}+O(q^{100}) \) 16 * q - 16 * q^2 + 16 * q^4 - 16 * q^8 + 16 * q^9 + 16 * q^16 - 16 * q^18 - 16 * q^21 + 4 * q^23 + 4 * q^25 + 60 * q^31 - 16 * q^32 - 16 * q^33 + 16 * q^36 + 44 * q^37 - 12 * q^39 + 16 * q^42 + 40 * q^43 + 52 * q^45 - 4 * q^46 - 24 * q^49 - 4 * q^50 + 44 * q^51 + 60 * q^57 - 12 * q^59 - 24 * q^61 - 60 * q^62 + 16 * q^64 + 16 * q^66 - 16 * q^72 + 44 * q^73 - 44 * q^74 + 16 * q^77 + 12 * q^78 - 40 * q^81 + 24 * q^83 - 16 * q^84 - 40 * q^86 + 96 * q^87 - 52 * q^90 + 88 * q^91 + 4 * q^92 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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