LMFDB - Embedded newform 5766.2.a.bq.1.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [5766,2,Mod(1,5766)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(5766, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 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("5766.1"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 5766 = 2 \cdot 3 \cdot 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5766.a (trivial)

Newform invariants

comment:select newform

sage:traces = [8,8,8,8,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	yes
Analytic conductor:	$46.0417418055$
Analytic rank:	$1$
Dimension:	$8$
Coefficient field:	$\Q(\zeta_{32})^+$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 8x^{6} + 20x^{4} - 16x^{2} + 2 $ x^8 - 8x^6 + 20x^4 - 16*x^2 + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$1.66294$ of defining polynomial
Character	$\chi$	$=$	5766.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.751274 q^{5} +1.00000 q^{6} +2.15083 q^{7} +1.00000 q^{8} +1.00000 q^{9} -0.751274 q^{10} -5.68697 q^{11} +1.00000 q^{12} +6.01228 q^{13} +2.15083 q^{14} -0.751274 q^{15} +1.00000 q^{16} -6.09775 q^{17} +1.00000 q^{18} -7.42179 q^{19} -0.751274 q^{20} +2.15083 q^{21} -5.68697 q^{22} -7.47004 q^{23} +1.00000 q^{24} -4.43559 q^{25} +6.01228 q^{26} +1.00000 q^{27} +2.15083 q^{28} -4.66311 q^{29} -0.751274 q^{30} +1.00000 q^{32} -5.68697 q^{33} -6.09775 q^{34} -1.61587 q^{35} +1.00000 q^{36} -8.41741 q^{37} -7.42179 q^{38} +6.01228 q^{39} -0.751274 q^{40} +6.22351 q^{41} +2.15083 q^{42} -4.03338 q^{43} -5.68697 q^{44} -0.751274 q^{45} -7.47004 q^{46} -1.65729 q^{47} +1.00000 q^{48} -2.37392 q^{49} -4.43559 q^{50} -6.09775 q^{51} +6.01228 q^{52} +6.18421 q^{53} +1.00000 q^{54} +4.27248 q^{55} +2.15083 q^{56} -7.42179 q^{57} -4.66311 q^{58} -4.00401 q^{59} -0.751274 q^{60} +0.700300 q^{61} +2.15083 q^{63} +1.00000 q^{64} -4.51687 q^{65} -5.68697 q^{66} +0.954994 q^{67} -6.09775 q^{68} -7.47004 q^{69} -1.61587 q^{70} -1.14224 q^{71} +1.00000 q^{72} +12.3662 q^{73} -8.41741 q^{74} -4.43559 q^{75} -7.42179 q^{76} -12.2317 q^{77} +6.01228 q^{78} +0.854729 q^{79} -0.751274 q^{80} +1.00000 q^{81} +6.22351 q^{82} -7.94057 q^{83} +2.15083 q^{84} +4.58108 q^{85} -4.03338 q^{86} -4.66311 q^{87} -5.68697 q^{88} -16.7301 q^{89} -0.751274 q^{90} +12.9314 q^{91} -7.47004 q^{92} -1.65729 q^{94} +5.57580 q^{95} +1.00000 q^{96} +12.0701 q^{97} -2.37392 q^{98} -5.68697 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} + 8 q^{3} + 8 q^{4} - 8 q^{5} + 8 q^{6} + 8 q^{8} + 8 q^{9} - 8 q^{10} - 24 q^{11} + 8 q^{12} - 8 q^{13} - 8 q^{15} + 8 q^{16} - 8 q^{17} + 8 q^{18} - 8 q^{19} - 8 q^{20} - 24 q^{22} - 32 q^{23}+ \cdots - 24 q^{99}+O(q^{100}) $ 8 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 - 8 * q^5 + 8 * q^6 + 8 * q^8 + 8 * q^9 - 8 * q^10 - 24 * q^11 + 8 * q^12 - 8 * q^13 - 8 * q^15 + 8 * q^16 - 8 * q^17 + 8 * q^18 - 8 * q^19 - 8 * q^20 - 24 * q^22 - 32 * q^23 + 8 * q^24 - 8 * q^26 + 8 * q^27 - 16 * q^29 - 8 * q^30 + 8 * q^32 - 24 * q^33 - 8 * q^34 - 16 * q^35 + 8 * q^36 - 8 * q^38 - 8 * q^39 - 8 * q^40 - 16 * q^41 - 32 * q^43 - 24 * q^44 - 8 * q^45 - 32 * q^46 - 24 * q^47 + 8 * q^48 - 8 * q^49 - 8 * q^51 - 8 * q^52 - 16 * q^53 + 8 * q^54 + 24 * q^55 - 8 * q^57 - 16 * q^58 - 16 * q^59 - 8 * q^60 + 8 * q^61 + 8 * q^64 - 24 * q^65 - 24 * q^66 - 8 * q^67 - 8 * q^68 - 32 * q^69 - 16 * q^70 - 8 * q^71 + 8 * q^72 - 8 * q^76 - 16 * q^77 - 8 * q^78 - 24 * q^79 - 8 * q^80 + 8 * q^81 - 16 * q^82 - 40 * q^83 - 8 * q^85 - 32 * q^86 - 16 * q^87 - 24 * q^88 - 16 * q^89 - 8 * q^90 - 32 * q^92 - 24 * q^94 + 8 * q^95 + 8 * q^96 - 8 * q^97 - 8 * q^98 - 24 * q^99

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
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	−0.751274	−0.335980	−0.167990	−	0.985789i	$-0.553728\pi$
$5$	−0.751274	−0.335980	−0.167990	+	0.985789i	$0.553728\pi$
$6$	1.00000	0.408248
$7$	2.15083	0.812938	0.406469	−	0.913665i	$-0.366760\pi$
$7$	2.15083	0.812938	0.406469	+	0.913665i	$0.366760\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−0.751274	−0.237574
$11$	−5.68697	−1.71469	−0.857343	−	0.514745i	$-0.827887\pi$
$11$	−5.68697	−1.71469	−0.857343	+	0.514745i	$0.827887\pi$
$12$	1.00000	0.288675
$13$	6.01228	1.66751	0.833753	−	0.552138i	$-0.186188\pi$
$13$	6.01228	1.66751	0.833753	+	0.552138i	$0.186188\pi$
$14$	2.15083	0.574834
$15$	−0.751274	−0.193978
$16$	1.00000	0.250000
$17$	−6.09775	−1.47892	−0.739460	−	0.673200i	$-0.764919\pi$
$17$	−6.09775	−1.47892	−0.739460	+	0.673200i	$0.764919\pi$
$18$	1.00000	0.235702
$19$	−7.42179	−1.70268	−0.851338	−	0.524618i	$-0.824208\pi$
$19$	−7.42179	−1.70268	−0.851338	+	0.524618i	$0.824208\pi$
$20$	−0.751274	−0.167990
$21$	2.15083	0.469350
$22$	−5.68697	−1.21247
$23$	−7.47004	−1.55761	−0.778806	−	0.627265i	$-0.784174\pi$
$23$	−7.47004	−1.55761	−0.778806	+	0.627265i	$0.784174\pi$
$24$	1.00000	0.204124
$25$	−4.43559	−0.887117
$26$	6.01228	1.17910
$27$	1.00000	0.192450
$28$	2.15083	0.406469
$29$	−4.66311	−0.865917	−0.432959	−	0.901414i	$-0.642530\pi$
$29$	−4.66311	−0.865917	−0.432959	+	0.901414i	$0.642530\pi$
$30$	−0.751274	−0.137163
$31$	0	0
$31$	0	0
$32$	1.00000	0.176777
$33$	−5.68697	−0.989975
$34$	−6.09775	−1.04575
$35$	−1.61587	−0.273131
$36$	1.00000	0.166667
$37$	−8.41741	−1.38381	−0.691907	−	0.721986i	$-0.743229\pi$
$37$	−8.41741	−1.38381	−0.691907	+	0.721986i	$0.743229\pi$
$38$	−7.42179	−1.20397
$39$	6.01228	0.962735
$40$	−0.751274	−0.118787
$41$	6.22351	0.971949	0.485975	−	0.873973i	$-0.338465\pi$
$41$	6.22351	0.971949	0.485975	+	0.873973i	$0.338465\pi$
$42$	2.15083	0.331881
$43$	−4.03338	−0.615084	−0.307542	−	0.951534i	$-0.599506\pi$
$43$	−4.03338	−0.615084	−0.307542	+	0.951534i	$0.599506\pi$
$44$	−5.68697	−0.857343
$45$	−0.751274	−0.111993
$46$	−7.47004	−1.10140
$47$	−1.65729	−0.241740	−0.120870	−	0.992668i	$-0.538568\pi$
$47$	−1.65729	−0.241740	−0.120870	+	0.992668i	$0.538568\pi$
$48$	1.00000	0.144338
$49$	−2.37392	−0.339132
$50$	−4.43559	−0.627287
$51$	−6.09775	−0.853855
$52$	6.01228	0.833753
$53$	6.18421	0.849467	0.424733	−	0.905318i	$-0.360368\pi$
$53$	6.18421	0.849467	0.424733	+	0.905318i	$0.360368\pi$
$54$	1.00000	0.136083
$55$	4.27248	0.576101
$56$	2.15083	0.287417
$57$	−7.42179	−0.983040
$58$	−4.66311	−0.612296
$59$	−4.00401	−0.521278	−0.260639	−	0.965436i	$-0.583933\pi$
$59$	−4.00401	−0.521278	−0.260639	+	0.965436i	$0.583933\pi$
$60$	−0.751274	−0.0969891
$61$	0.700300	0.0896642	0.0448321	−	0.998995i	$-0.485725\pi$
$61$	0.700300	0.0896642	0.0448321	+	0.998995i	$0.485725\pi$
$62$	0	0
$63$	2.15083	0.270979
$64$	1.00000	0.125000
$65$	−4.51687	−0.560249
$66$	−5.68697	−0.700018
$67$	0.954994	0.116671	0.0583355	−	0.998297i	$-0.481421\pi$
$67$	0.954994	0.116671	0.0583355	+	0.998297i	$0.481421\pi$
$68$	−6.09775	−0.739460
$69$	−7.47004	−0.899287
$70$	−1.61587	−0.193133
$71$	−1.14224	−0.135559	−0.0677793	−	0.997700i	$-0.521591\pi$
$71$	−1.14224	−0.135559	−0.0677793	+	0.997700i	$0.521591\pi$
$72$	1.00000	0.117851
$73$	12.3662	1.44735	0.723675	−	0.690141i	$-0.242452\pi$
$73$	12.3662	1.44735	0.723675	+	0.690141i	$0.242452\pi$
$74$	−8.41741	−0.978505
$75$	−4.43559	−0.512177
$76$	−7.42179	−0.851338
$77$	−12.2317	−1.39393
$78$	6.01228	0.680757
$79$	0.854729	0.0961645	0.0480822	−	0.998843i	$-0.484689\pi$
$79$	0.854729	0.0961645	0.0480822	+	0.998843i	$0.484689\pi$
$80$	−0.751274	−0.0839950
$81$	1.00000	0.111111
$82$	6.22351	0.687272
$83$	−7.94057	−0.871591	−0.435795	−	0.900046i	$-0.643533\pi$
$83$	−7.94057	−0.871591	−0.435795	+	0.900046i	$0.643533\pi$
$84$	2.15083	0.234675
$85$	4.58108	0.496888
$86$	−4.03338	−0.434930
$87$	−4.66311	−0.499937
$88$	−5.68697	−0.606233
$89$	−16.7301	−1.77339	−0.886694	−	0.462357i	$-0.847004\pi$
$89$	−16.7301	−1.77339	−0.886694	+	0.462357i	$0.847004\pi$
$90$	−0.751274	−0.0791913
$91$	12.9314	1.35558
$92$	−7.47004	−0.778806
$93$	0	0
$94$	−1.65729	−0.170936
$95$	5.57580	0.572065
$96$	1.00000	0.102062
$97$	12.0701	1.22554	0.612768	−	0.790263i	$-0.290056\pi$
$97$	12.0701	1.22554	0.612768	+	0.790263i	$0.290056\pi$
$98$	−2.37392	−0.239802
$99$	−5.68697	−0.571562
$100$	−4.43559	−0.443559
$101$	3.34152	0.332494	0.166247	−	0.986084i	$-0.446835\pi$
$101$	3.34152	0.332494	0.166247	+	0.986084i	$0.446835\pi$
$102$	−6.09775	−0.603767
$103$	−7.63419	−0.752219	−0.376109	−	0.926575i	$-0.622738\pi$
$103$	−7.63419	−0.752219	−0.376109	+	0.926575i	$0.622738\pi$
$104$	6.01228	0.589552
$105$	−1.61587	−0.157692
$106$	6.18421	0.600664
$107$	8.91054	0.861414	0.430707	−	0.902492i	$-0.358264\pi$
$107$	8.91054	0.861414	0.430707	+	0.902492i	$0.358264\pi$
$108$	1.00000	0.0962250
$109$	15.2239	1.45818	0.729092	−	0.684416i	$-0.239943\pi$
$109$	15.2239	1.45818	0.729092	+	0.684416i	$0.239943\pi$
$110$	4.27248	0.407365
$111$	−8.41741	−0.798946
$112$	2.15083	0.203235
$113$	4.51057	0.424319	0.212159	−	0.977235i	$-0.431950\pi$
$113$	4.51057	0.424319	0.212159	+	0.977235i	$0.431950\pi$
$114$	−7.42179	−0.695114
$115$	5.61205	0.523326
$116$	−4.66311	−0.432959
$117$	6.01228	0.555835
$118$	−4.00401	−0.368599
$119$	−13.1152	−1.20227
$120$	−0.751274	−0.0685817
$121$	21.3417	1.94015
$122$	0.700300	0.0634022
$123$	6.22351	0.561155
$124$	0	0
$125$	7.08871	0.634034
$126$	2.15083	0.191611
$127$	17.4675	1.54999	0.774996	−	0.631966i	$-0.217752\pi$
$127$	17.4675	1.54999	0.774996	+	0.631966i	$0.217752\pi$
$128$	1.00000	0.0883883
$129$	−4.03338	−0.355119
$130$	−4.51687	−0.396156
$131$	−7.02828	−0.614063	−0.307032	−	0.951699i	$-0.599336\pi$
$131$	−7.02828	−0.614063	−0.307032	+	0.951699i	$0.599336\pi$
$132$	−5.68697	−0.494987
$133$	−15.9630	−1.38417
$134$	0.954994	0.0824989
$135$	−0.751274	−0.0646594
$136$	−6.09775	−0.522877
$137$	14.5750	1.24522	0.622611	−	0.782531i	$-0.286072\pi$
$137$	14.5750	1.24522	0.622611	+	0.782531i	$0.286072\pi$
$138$	−7.47004	−0.635892
$139$	8.84440	0.750172	0.375086	−	0.926990i	$-0.377613\pi$
$139$	8.84440	0.750172	0.375086	+	0.926990i	$0.377613\pi$
$140$	−1.61587	−0.136566
$141$	−1.65729	−0.139569
$142$	−1.14224	−0.0958544
$143$	−34.1917	−2.85925
$144$	1.00000	0.0833333
$145$	3.50327	0.290931
$146$	12.3662	1.02343
$147$	−2.37392	−0.195798
$148$	−8.41741	−0.691907
$149$	−5.30142	−0.434309	−0.217154	−	0.976137i	$-0.569678\pi$
$149$	−5.30142	−0.434309	−0.217154	+	0.976137i	$0.569678\pi$
$150$	−4.43559	−0.362164
$151$	−12.7103	−1.03435	−0.517174	−	0.855881i	$-0.673016\pi$
$151$	−12.7103	−1.03435	−0.517174	+	0.855881i	$0.673016\pi$
$152$	−7.42179	−0.601987
$153$	−6.09775	−0.492974
$154$	−12.2317	−0.985660
$155$	0	0
$156$	6.01228	0.481368
$157$	6.11876	0.488330	0.244165	−	0.969734i	$-0.421486\pi$
$157$	6.11876	0.488330	0.244165	+	0.969734i	$0.421486\pi$
$158$	0.854729	0.0679986
$159$	6.18421	0.490440
$160$	−0.751274	−0.0593935
$161$	−16.0668	−1.26624
$162$	1.00000	0.0785674
$163$	6.58485	0.515765	0.257883	−	0.966176i	$-0.416975\pi$
$163$	6.58485	0.515765	0.257883	+	0.966176i	$0.416975\pi$
$164$	6.22351	0.485975
$165$	4.27248	0.332612
$166$	−7.94057	−0.616308
$167$	0.600030	0.0464318	0.0232159	−	0.999730i	$-0.492609\pi$
$167$	0.600030	0.0464318	0.0232159	+	0.999730i	$0.492609\pi$
$168$	2.15083	0.165940
$169$	23.1475	1.78058
$170$	4.58108	0.351353
$171$	−7.42179	−0.567559
$172$	−4.03338	−0.307542
$173$	−6.62535	−0.503716	−0.251858	−	0.967764i	$-0.581042\pi$
$173$	−6.62535	−0.503716	−0.251858	+	0.967764i	$0.581042\pi$
$174$	−4.66311	−0.353509
$175$	−9.54020	−0.721172
$176$	−5.68697	−0.428672
$177$	−4.00401	−0.300960
$178$	−16.7301	−1.25397
$179$	12.7907	0.956025	0.478013	−	0.878353i	$-0.341357\pi$
$179$	12.7907	0.956025	0.478013	+	0.878353i	$0.341357\pi$
$180$	−0.751274	−0.0559967
$181$	5.50316	0.409046	0.204523	−	0.978862i	$-0.434436\pi$
$181$	5.50316	0.409046	0.204523	+	0.978862i	$0.434436\pi$
$182$	12.9314	0.958539
$183$	0.700300	0.0517677
$184$	−7.47004	−0.550699
$185$	6.32379	0.464934
$186$	0	0
$187$	34.6777	2.53589
$188$	−1.65729	−0.120870
$189$	2.15083	0.156450
$190$	5.57580	0.404511
$191$	7.76885	0.562134	0.281067	−	0.959688i	$-0.409312\pi$
$191$	7.76885	0.562134	0.281067	+	0.959688i	$0.409312\pi$
$192$	1.00000	0.0721688
$193$	−12.7079	−0.914732	−0.457366	−	0.889279i	$-0.651207\pi$
$193$	−12.7079	−0.914732	−0.457366	+	0.889279i	$0.651207\pi$
$194$	12.0701	0.866585
$195$	−4.51687	−0.323460
$196$	−2.37392	−0.169566
$197$	−7.29092	−0.519456	−0.259728	−	0.965682i	$-0.583633\pi$
$197$	−7.29092	−0.519456	−0.259728	+	0.965682i	$0.583633\pi$
$198$	−5.68697	−0.404156
$199$	−14.3844	−1.01968	−0.509841	−	0.860268i	$-0.670296\pi$
$199$	−14.3844	−1.01968	−0.509841	+	0.860268i	$0.670296\pi$
$200$	−4.43559	−0.313643
$201$	0.954994	0.0673601
$202$	3.34152	0.235109
$203$	−10.0296	−0.703937
$204$	−6.09775	−0.426928
$205$	−4.67557	−0.326556
$206$	−7.63419	−0.531899
$207$	−7.47004	−0.519204
$208$	6.01228	0.416877
$209$	42.2075	2.91956
$210$	−1.61587	−0.111505
$211$	3.00269	0.206713	0.103357	−	0.994644i	$-0.467042\pi$
$211$	3.00269	0.206713	0.103357	+	0.994644i	$0.467042\pi$
$212$	6.18421	0.424733
$213$	−1.14224	−0.0782648
$214$	8.91054	0.609112
$215$	3.03017	0.206656
$216$	1.00000	0.0680414
$217$	0	0
$218$	15.2239	1.03109
$219$	12.3662	0.835628
$220$	4.27248	0.288050
$221$	−36.6614	−2.46611
$222$	−8.41741	−0.564940
$223$	−26.6551	−1.78496	−0.892479	−	0.451088i	$-0.851036\pi$
$223$	−26.6551	−1.78496	−0.892479	+	0.451088i	$0.851036\pi$
$224$	2.15083	0.143709
$225$	−4.43559	−0.295706
$226$	4.51057	0.300039
$227$	9.93774	0.659591	0.329795	−	0.944052i	$-0.393020\pi$
$227$	9.93774	0.659591	0.329795	+	0.944052i	$0.393020\pi$
$228$	−7.42179	−0.491520
$229$	−5.56427	−0.367697	−0.183849	−	0.982955i	$-0.558856\pi$
$229$	−5.56427	−0.367697	−0.183849	+	0.982955i	$0.558856\pi$
$230$	5.61205	0.370048
$231$	−12.2317	−0.804788
$232$	−4.66311	−0.306148
$233$	7.71215	0.505240	0.252620	−	0.967566i	$-0.418708\pi$
$233$	7.71215	0.505240	0.252620	+	0.967566i	$0.418708\pi$
$234$	6.01228	0.393035
$235$	1.24508	0.0812199
$236$	−4.00401	−0.260639
$237$	0.854729	0.0555206
$238$	−13.1152	−0.850134
$239$	−23.3850	−1.51265	−0.756326	−	0.654195i	$-0.773008\pi$
$239$	−23.3850	−1.51265	−0.756326	+	0.654195i	$0.773008\pi$
$240$	−0.751274	−0.0484945
$241$	−19.0910	−1.22976	−0.614880	−	0.788620i	$-0.710796\pi$
$241$	−19.0910	−1.22976	−0.614880	+	0.788620i	$0.710796\pi$
$242$	21.3417	1.37189
$243$	1.00000	0.0641500
$244$	0.700300	0.0448321
$245$	1.78347	0.113941
$246$	6.22351	0.396797
$247$	−44.6219	−2.83922
$248$	0	0
$249$	−7.94057	−0.503213
$250$	7.08871	0.448330
$251$	−0.507765	−0.0320499	−0.0160249	−	0.999872i	$-0.505101\pi$
$251$	−0.507765	−0.0320499	−0.0160249	+	0.999872i	$0.505101\pi$
$252$	2.15083	0.135490
$253$	42.4819	2.67082
$254$	17.4675	1.09601
$255$	4.58108	0.286878
$256$	1.00000	0.0625000
$257$	8.06669	0.503186	0.251593	−	0.967833i	$-0.419046\pi$
$257$	8.06669	0.503186	0.251593	+	0.967833i	$0.419046\pi$
$258$	−4.03338	−0.251107
$259$	−18.1044	−1.12496
$260$	−4.51687	−0.280124
$261$	−4.66311	−0.288639
$262$	−7.02828	−0.434208
$263$	−28.5497	−1.76045	−0.880224	−	0.474558i	$-0.842608\pi$
$263$	−28.5497	−1.76045	−0.880224	+	0.474558i	$0.842608\pi$
$264$	−5.68697	−0.350009
$265$	−4.64604	−0.285404
$266$	−15.9630	−0.978756
$267$	−16.7301	−1.02387
$268$	0.954994	0.0583355
$269$	−5.95702	−0.363206	−0.181603	−	0.983372i	$-0.558129\pi$
$269$	−5.95702	−0.363206	−0.181603	+	0.983372i	$0.558129\pi$
$270$	−0.751274	−0.0457211
$271$	20.8051	1.26382	0.631908	−	0.775043i	$-0.282272\pi$
$271$	20.8051	1.26382	0.631908	+	0.775043i	$0.282272\pi$
$272$	−6.09775	−0.369730
$273$	12.9314	0.782644
$274$	14.5750	0.880505
$275$	25.2251	1.52113
$276$	−7.47004	−0.449644
$277$	7.30945	0.439182	0.219591	−	0.975592i	$-0.429528\pi$
$277$	7.30945	0.439182	0.219591	+	0.975592i	$0.429528\pi$
$278$	8.84440	0.530452
$279$	0	0
$280$	−1.61587	−0.0965664
$281$	−1.45043	−0.0865255	−0.0432627	−	0.999064i	$-0.513775\pi$
$281$	−1.45043	−0.0865255	−0.0432627	+	0.999064i	$0.513775\pi$
$282$	−1.65729	−0.0986900
$283$	−16.1751	−0.961508	−0.480754	−	0.876855i	$-0.659637\pi$
$283$	−16.1751	−0.961508	−0.480754	+	0.876855i	$0.659637\pi$
$284$	−1.14224	−0.0677793
$285$	5.57580	0.330282
$286$	−34.1917	−2.02180
$287$	13.3857	0.790135
$288$	1.00000	0.0589256
$289$	20.1825	1.18721
$290$	3.50327	0.205719
$291$	12.0701	0.707563
$292$	12.3662	0.723675
$293$	13.3584	0.780404	0.390202	−	0.920729i	$-0.372405\pi$
$293$	13.3584	0.780404	0.390202	+	0.920729i	$0.372405\pi$
$294$	−2.37392	−0.138450
$295$	3.00811	0.175139
$296$	−8.41741	−0.489252
$297$	−5.68697	−0.329992
$298$	−5.30142	−0.307103
$299$	−44.9120	−2.59733
$300$	−4.43559	−0.256089
$301$	−8.67512	−0.500025
$302$	−12.7103	−0.731394
$303$	3.34152	0.191966
$304$	−7.42179	−0.425669
$305$	−0.526117	−0.0301254
$306$	−6.09775	−0.348585
$307$	5.52892	0.315552	0.157776	−	0.987475i	$-0.449568\pi$
$307$	5.52892	0.315552	0.157776	+	0.987475i	$0.449568\pi$
$308$	−12.2317	−0.696967
$309$	−7.63419	−0.434294
$310$	0	0
$311$	−23.6415	−1.34059	−0.670294	−	0.742095i	$-0.733832\pi$
$311$	−23.6415	−1.34059	−0.670294	+	0.742095i	$0.733832\pi$
$312$	6.01228	0.340378
$313$	−4.42885	−0.250333	−0.125167	−	0.992136i	$-0.539947\pi$
$313$	−4.42885	−0.250333	−0.125167	+	0.992136i	$0.539947\pi$
$314$	6.11876	0.345302
$315$	−1.61587	−0.0910437
$316$	0.854729	0.0480822
$317$	10.2298	0.574563	0.287281	−	0.957846i	$-0.407249\pi$
$317$	10.2298	0.574563	0.287281	+	0.957846i	$0.407249\pi$
$318$	6.18421	0.346793
$319$	26.5190	1.48478
$320$	−0.751274	−0.0419975
$321$	8.91054	0.497338
$322$	−16.0668	−0.895368
$323$	45.2562	2.51812
$324$	1.00000	0.0555556
$325$	−26.6680	−1.47927
$326$	6.58485	0.364701
$327$	15.2239	0.841883
$328$	6.22351	0.343636
$329$	−3.56455	−0.196520
$330$	4.27248	0.235192
$331$	16.0944	0.884628	0.442314	−	0.896860i	$-0.354158\pi$
$331$	16.0944	0.884628	0.442314	+	0.896860i	$0.354158\pi$
$332$	−7.94057	−0.435795
$333$	−8.41741	−0.461271
$334$	0.600030	0.0328322
$335$	−0.717462	−0.0391992
$336$	2.15083	0.117338
$337$	−24.4117	−1.32979	−0.664895	−	0.746937i	$-0.731524\pi$
$337$	−24.4117	−1.32979	−0.664895	+	0.746937i	$0.731524\pi$
$338$	23.1475	1.25906
$339$	4.51057	0.244981
$340$	4.58108	0.248444
$341$	0	0
$342$	−7.42179	−0.401325
$343$	−20.1617	−1.08863
$344$	−4.03338	−0.217465
$345$	5.61205	0.302143
$346$	−6.62535	−0.356181
$347$	−12.3738	−0.664260	−0.332130	−	0.943234i	$-0.607767\pi$
$347$	−12.3738	−0.664260	−0.332130	+	0.943234i	$0.607767\pi$
$348$	−4.66311	−0.249969
$349$	−14.9115	−0.798192	−0.399096	−	0.916909i	$-0.630676\pi$
$349$	−14.9115	−0.798192	−0.399096	+	0.916909i	$0.630676\pi$
$350$	−9.54020	−0.509945
$351$	6.01228	0.320912
$352$	−5.68697	−0.303117
$353$	−21.4153	−1.13982	−0.569911	−	0.821706i	$-0.693022\pi$
$353$	−21.4153	−1.13982	−0.569911	+	0.821706i	$0.693022\pi$
$354$	−4.00401	−0.212811
$355$	0.858133	0.0455450
$356$	−16.7301	−0.886694
$357$	−13.1152	−0.694132
$358$	12.7907	0.676012
$359$	−7.54031	−0.397962	−0.198981	−	0.980003i	$-0.563763\pi$
$359$	−7.54031	−0.397962	−0.198981	+	0.980003i	$0.563763\pi$
$360$	−0.751274	−0.0395956
$361$	36.0830	1.89910
$362$	5.50316	0.289240
$363$	21.3417	1.12015
$364$	12.9314	0.677790
$365$	−9.29038	−0.486281
$366$	0.700300	0.0366053
$367$	−24.9142	−1.30051	−0.650256	−	0.759715i	$-0.725339\pi$
$367$	−24.9142	−1.30051	−0.650256	+	0.759715i	$0.725339\pi$
$368$	−7.47004	−0.389403
$369$	6.22351	0.323983
$370$	6.32379	0.328758
$371$	13.3012	0.690564
$372$	0	0
$373$	−7.90324	−0.409214	−0.204607	−	0.978844i	$-0.565592\pi$
$373$	−7.90324	−0.409214	−0.204607	+	0.978844i	$0.565592\pi$
$374$	34.6777	1.79314
$375$	7.08871	0.366060
$376$	−1.65729	−0.0854681
$377$	−28.0359	−1.44392
$378$	2.15083	0.110627
$379$	−7.71253	−0.396166	−0.198083	−	0.980185i	$-0.563472\pi$
$379$	−7.71253	−0.396166	−0.198083	+	0.980185i	$0.563472\pi$
$380$	5.57580	0.286033
$381$	17.4675	0.894888
$382$	7.76885	0.397489
$383$	1.71607	0.0876870	0.0438435	−	0.999038i	$-0.486040\pi$
$383$	1.71607	0.0876870	0.0438435	+	0.999038i	$0.486040\pi$
$384$	1.00000	0.0510310
$385$	9.18938	0.468334
$386$	−12.7079	−0.646813
$387$	−4.03338	−0.205028
$388$	12.0701	0.612768
$389$	10.9949	0.557463	0.278732	−	0.960369i	$-0.410086\pi$
$389$	10.9949	0.557463	0.278732	+	0.960369i	$0.410086\pi$
$390$	−4.51687	−0.228721
$391$	45.5504	2.30358
$392$	−2.37392	−0.119901
$393$	−7.02828	−0.354530
$394$	−7.29092	−0.367311
$395$	−0.642136	−0.0323094
$396$	−5.68697	−0.285781
$397$	−15.9396	−0.799985	−0.399992	−	0.916518i	$-0.630987\pi$
$397$	−15.9396	−0.799985	−0.399992	+	0.916518i	$0.630987\pi$
$398$	−14.3844	−0.721025
$399$	−15.9630	−0.799151
$400$	−4.43559	−0.221779
$401$	7.77012	0.388021	0.194011	−	0.980999i	$-0.437850\pi$
$401$	7.77012	0.388021	0.194011	+	0.980999i	$0.437850\pi$
$402$	0.954994	0.0476308
$403$	0	0
$404$	3.34152	0.166247
$405$	−0.751274	−0.0373311
$406$	−10.0296	−0.497759
$407$	47.8696	2.37281
$408$	−6.09775	−0.301883
$409$	−17.2489	−0.852904	−0.426452	−	0.904510i	$-0.640237\pi$
$409$	−17.2489	−0.852904	−0.426452	+	0.904510i	$0.640237\pi$
$410$	−4.67557	−0.230910
$411$	14.5750	0.718929
$412$	−7.63419	−0.376109
$413$	−8.61195	−0.423767
$414$	−7.47004	−0.367133
$415$	5.96555	0.292837
$416$	6.01228	0.294776
$417$	8.84440	0.433112
$418$	42.2075	2.06444
$419$	21.2911	1.04014	0.520070	−	0.854124i	$-0.325906\pi$
$419$	21.2911	1.04014	0.520070	+	0.854124i	$0.325906\pi$
$420$	−1.61587	−0.0788461
$421$	−24.7251	−1.20503	−0.602515	−	0.798108i	$-0.705834\pi$
$421$	−24.7251	−1.20503	−0.602515	+	0.798108i	$0.705834\pi$
$422$	3.00269	0.146169
$423$	−1.65729	−0.0805801
$424$	6.18421	0.300332
$425$	27.0471	1.31198
$426$	−1.14224	−0.0553415
$427$	1.50623	0.0728915
$428$	8.91054	0.430707
$429$	−34.1917	−1.65079
$430$	3.03017	0.146128
$431$	2.93778	0.141508	0.0707539	−	0.997494i	$-0.477460\pi$
$431$	2.93778	0.141508	0.0707539	+	0.997494i	$0.477460\pi$
$432$	1.00000	0.0481125
$433$	5.35403	0.257298	0.128649	−	0.991690i	$-0.458936\pi$
$433$	5.35403	0.257298	0.128649	+	0.991690i	$0.458936\pi$
$434$	0	0
$435$	3.50327	0.167969
$436$	15.2239	0.729092
$437$	55.4411	2.65211
$438$	12.3662	0.590878
$439$	13.7938	0.658342	0.329171	−	0.944270i	$-0.393231\pi$
$439$	13.7938	0.658342	0.329171	+	0.944270i	$0.393231\pi$
$440$	4.27248	0.203682
$441$	−2.37392	−0.113044
$442$	−36.6614	−1.74380
$443$	23.7488	1.12834	0.564169	−	0.825659i	$-0.309196\pi$
$443$	23.7488	1.12834	0.564169	+	0.825659i	$0.309196\pi$
$444$	−8.41741	−0.399473
$445$	12.5689	0.595823
$446$	−26.6551	−1.26216
$447$	−5.30142	−0.250748
$448$	2.15083	0.101617
$449$	11.3692	0.536546	0.268273	−	0.963343i	$-0.413547\pi$
$449$	11.3692	0.536546	0.268273	+	0.963343i	$0.413547\pi$
$450$	−4.43559	−0.209096
$451$	−35.3929	−1.66659
$452$	4.51057	0.212159
$453$	−12.7103	−0.597181
$454$	9.93774	0.466401
$455$	−9.71503	−0.455448
$456$	−7.42179	−0.347557
$457$	38.4430	1.79829	0.899144	−	0.437652i	$-0.144190\pi$
$457$	38.4430	1.79829	0.899144	+	0.437652i	$0.144190\pi$
$458$	−5.56427	−0.260001
$459$	−6.09775	−0.284618
$460$	5.61205	0.261663
$461$	7.95968	0.370719	0.185360	−	0.982671i	$-0.440655\pi$
$461$	7.95968	0.370719	0.185360	+	0.982671i	$0.440655\pi$
$462$	−12.2317	−0.569071
$463$	25.2360	1.17281	0.586407	−	0.810016i	$-0.300542\pi$
$463$	25.2360	1.17281	0.586407	+	0.810016i	$0.300542\pi$
$464$	−4.66311	−0.216479
$465$	0	0
$466$	7.71215	0.357258
$467$	−22.8647	−1.05805	−0.529026	−	0.848606i	$-0.677442\pi$
$467$	−22.8647	−1.05805	−0.529026	+	0.848606i	$0.677442\pi$
$468$	6.01228	0.277918
$469$	2.05403	0.0948463
$470$	1.24508	0.0574311
$471$	6.11876	0.281938
$472$	−4.00401	−0.184300
$473$	22.9377	1.05468
$474$	0.854729	0.0392590
$475$	32.9200	1.51047
$476$	−13.1152	−0.601136
$477$	6.18421	0.283156
$478$	−23.3850	−1.06961
$479$	−5.23181	−0.239047	−0.119524	−	0.992831i	$-0.538137\pi$
$479$	−5.23181	−0.239047	−0.119524	+	0.992831i	$0.538137\pi$
$480$	−0.751274	−0.0342908
$481$	−50.6078	−2.30752
$482$	−19.0910	−0.869572
$483$	−16.0668	−0.731065
$484$	21.3417	0.970075
$485$	−9.06798	−0.411756
$486$	1.00000	0.0453609
$487$	−10.0505	−0.455434	−0.227717	−	0.973727i	$-0.573126\pi$
$487$	−10.0505	−0.455434	−0.227717	+	0.973727i	$0.573126\pi$
$488$	0.700300	0.0317011
$489$	6.58485	0.297777
$490$	1.78347	0.0805688
$491$	−1.93361	−0.0872626	−0.0436313	−	0.999048i	$-0.513893\pi$
$491$	−1.93361	−0.0872626	−0.0436313	+	0.999048i	$0.513893\pi$
$492$	6.22351	0.280578
$493$	28.4344	1.28062
$494$	−44.6219	−2.00763
$495$	4.27248	0.192034
$496$	0	0
$497$	−2.45676	−0.110201
$498$	−7.94057	−0.355825
$499$	−25.8445	−1.15696	−0.578479	−	0.815698i	$-0.696353\pi$
$499$	−25.8445	−1.15696	−0.578479	+	0.815698i	$0.696353\pi$
$500$	7.08871	0.317017
$501$	0.600030	0.0268074
$502$	−0.507765	−0.0226627
$503$	−14.8350	−0.661462	−0.330731	−	0.943725i	$-0.607295\pi$
$503$	−14.8350	−0.661462	−0.330731	+	0.943725i	$0.607295\pi$
$504$	2.15083	0.0958057
$505$	−2.51040	−0.111711
$506$	42.4819	1.88855
$507$	23.1475	1.02802
$508$	17.4675	0.774996
$509$	−14.3163	−0.634559	−0.317280	−	0.948332i	$-0.602769\pi$
$509$	−14.3163	−0.634559	−0.317280	+	0.948332i	$0.602769\pi$
$510$	4.58108	0.202854
$511$	26.5975	1.17661
$512$	1.00000	0.0441942
$513$	−7.42179	−0.327680
$514$	8.06669	0.355806
$515$	5.73537	0.252730
$516$	−4.03338	−0.177560
$517$	9.42495	0.414509
$518$	−18.1044	−0.795464
$519$	−6.62535	−0.290821
$520$	−4.51687	−0.198078
$521$	14.0969	0.617595	0.308797	−	0.951128i	$-0.400074\pi$
$521$	14.0969	0.617595	0.308797	+	0.951128i	$0.400074\pi$
$522$	−4.66311	−0.204099
$523$	−21.6079	−0.944849	−0.472424	−	0.881371i	$-0.656621\pi$
$523$	−21.6079	−0.944849	−0.472424	+	0.881371i	$0.656621\pi$
$524$	−7.02828	−0.307032
$525$	−9.54020	−0.416369
$526$	−28.5497	−1.24482
$527$	0	0
$528$	−5.68697	−0.247494
$529$	32.8015	1.42615
$530$	−4.64604	−0.201811
$531$	−4.00401	−0.173759
$532$	−15.9630	−0.692085
$533$	37.4175	1.62073
$534$	−16.7301	−0.723983
$535$	−6.69426	−0.289418
$536$	0.954994	0.0412494
$537$	12.7907	0.551962
$538$	−5.95702	−0.256826
$539$	13.5004	0.581504
$540$	−0.751274	−0.0323297
$541$	−29.0379	−1.24844	−0.624219	−	0.781250i	$-0.714583\pi$
$541$	−29.0379	−1.24844	−0.624219	+	0.781250i	$0.714583\pi$
$542$	20.8051	0.893654
$543$	5.50316	0.236163
$544$	−6.09775	−0.261439
$545$	−11.4373	−0.489921
$546$	12.9314	0.553413
$547$	−18.1224	−0.774860	−0.387430	−	0.921899i	$-0.626637\pi$
$547$	−18.1224	−0.774860	−0.387430	+	0.921899i	$0.626637\pi$
$548$	14.5750	0.622611
$549$	0.700300	0.0298881
$550$	25.2251	1.07560
$551$	34.6086	1.47438
$552$	−7.47004	−0.317946
$553$	1.83838	0.0781758
$554$	7.30945	0.310549
$555$	6.32379	0.268430
$556$	8.84440	0.375086
$557$	−17.8513	−0.756385	−0.378193	−	0.925727i	$-0.623454\pi$
$557$	−17.8513	−0.756385	−0.378193	+	0.925727i	$0.623454\pi$
$558$	0	0
$559$	−24.2498	−1.02566
$560$	−1.61587	−0.0682828
$561$	34.6777	1.46409
$562$	−1.45043	−0.0611828
$563$	−27.9746	−1.17899	−0.589494	−	0.807773i	$-0.700673\pi$
$563$	−27.9746	−1.17899	−0.589494	+	0.807773i	$0.700673\pi$
$564$	−1.65729	−0.0697844
$565$	−3.38868	−0.142563
$566$	−16.1751	−0.679889
$567$	2.15083	0.0903265
$568$	−1.14224	−0.0479272
$569$	−43.7405	−1.83370	−0.916849	−	0.399235i	$-0.869276\pi$
$569$	−43.7405	−1.83370	−0.916849	+	0.399235i	$0.869276\pi$
$570$	5.57580	0.233545
$571$	−0.970320	−0.0406066	−0.0203033	−	0.999794i	$-0.506463\pi$
$571$	−0.970320	−0.0406066	−0.0203033	+	0.999794i	$0.506463\pi$
$572$	−34.1917	−1.42963
$573$	7.76885	0.324548
$574$	13.3857	0.558710
$575$	33.1340	1.38178
$576$	1.00000	0.0416667
$577$	−22.4113	−0.932995	−0.466497	−	0.884523i	$-0.654484\pi$
$577$	−22.4113	−0.932995	−0.466497	+	0.884523i	$0.654484\pi$
$578$	20.1825	0.839482
$579$	−12.7079	−0.528121
$580$	3.50327	0.145465
$581$	−17.0788	−0.708549
$582$	12.0701	0.500323
$583$	−35.1694	−1.45657
$584$	12.3662	0.511715
$585$	−4.51687	−0.186750
$586$	13.3584	0.551829
$587$	27.9297	1.15278	0.576392	−	0.817174i	$-0.304460\pi$
$587$	27.9297	1.15278	0.576392	+	0.817174i	$0.304460\pi$
$588$	−2.37392	−0.0978989
$589$	0	0
$590$	3.00811	0.123842
$591$	−7.29092	−0.299908
$592$	−8.41741	−0.345954
$593$	−37.8271	−1.55337	−0.776687	−	0.629886i	$-0.783101\pi$
$593$	−37.8271	−1.55337	−0.776687	+	0.629886i	$0.783101\pi$
$594$	−5.68697	−0.233339
$595$	9.85314	0.403939
$596$	−5.30142	−0.217154
$597$	−14.3844	−0.588714
$598$	−44.9120	−1.83659
$599$	−1.90972	−0.0780290	−0.0390145	−	0.999239i	$-0.512422\pi$
$599$	−1.90972	−0.0780290	−0.0390145	+	0.999239i	$0.512422\pi$
$600$	−4.43559	−0.181082
$601$	33.8567	1.38104	0.690522	−	0.723311i	$-0.257381\pi$
$601$	33.8567	1.38104	0.690522	+	0.723311i	$0.257381\pi$
$602$	−8.67512	−0.353571
$603$	0.954994	0.0388903
$604$	−12.7103	−0.517174
$605$	−16.0334	−0.651852
$606$	3.34152	0.135740
$607$	30.4002	1.23391	0.616953	−	0.787000i	$-0.288367\pi$
$607$	30.4002	1.23391	0.616953	+	0.787000i	$0.288367\pi$
$608$	−7.42179	−0.300993
$609$	−10.0296	−0.406418
$610$	−0.526117	−0.0213019
$611$	−9.96407	−0.403103
$612$	−6.09775	−0.246487
$613$	37.9600	1.53319	0.766595	−	0.642131i	$-0.221950\pi$
$613$	37.9600	1.53319	0.766595	+	0.642131i	$0.221950\pi$
$614$	5.52892	0.223129
$615$	−4.67557	−0.188537
$616$	−12.2317	−0.492830
$617$	−34.5175	−1.38962	−0.694812	−	0.719191i	$-0.744512\pi$
$617$	−34.5175	−1.38962	−0.694812	+	0.719191i	$0.744512\pi$
$618$	−7.63419	−0.307092
$619$	4.30055	0.172854	0.0864268	−	0.996258i	$-0.472455\pi$
$619$	4.30055	0.172854	0.0864268	+	0.996258i	$0.472455\pi$
$620$	0	0
$621$	−7.47004	−0.299762
$622$	−23.6415	−0.947939
$623$	−35.9837	−1.44165
$624$	6.01228	0.240684
$625$	16.8524	0.674095
$626$	−4.42885	−0.177012
$627$	42.2075	1.68561
$628$	6.11876	0.244165
$629$	51.3273	2.04655
$630$	−1.61587	−0.0643776
$631$	35.2840	1.40463	0.702317	−	0.711864i	$-0.252149\pi$
$631$	35.2840	1.40463	0.702317	+	0.711864i	$0.252149\pi$
$632$	0.854729	0.0339993
$633$	3.00269	0.119346
$634$	10.2298	0.406277
$635$	−13.1229	−0.520766
$636$	6.18421	0.245220
$637$	−14.2727	−0.565504
$638$	26.5190	1.04990
$639$	−1.14224	−0.0451862
$640$	−0.751274	−0.0296967
$641$	−45.7834	−1.80833	−0.904167	−	0.427179i	$-0.859507\pi$
$641$	−45.7834	−1.80833	−0.904167	+	0.427179i	$0.859507\pi$
$642$	8.91054	0.351671
$643$	18.2754	0.720711	0.360356	−	0.932815i	$-0.382655\pi$
$643$	18.2754	0.720711	0.360356	+	0.932815i	$0.382655\pi$
$644$	−16.0668	−0.633121
$645$	3.03017	0.119313
$646$	45.2562	1.78058
$647$	−32.7165	−1.28622	−0.643109	−	0.765774i	$-0.722356\pi$
$647$	−32.7165	−1.28622	−0.643109	+	0.765774i	$0.722356\pi$
$648$	1.00000	0.0392837
$649$	22.7707	0.893828
$650$	−26.6680	−1.04600
$651$	0	0
$652$	6.58485	0.257883
$653$	−13.5375	−0.529763	−0.264882	−	0.964281i	$-0.585333\pi$
$653$	−13.5375	−0.529763	−0.264882	+	0.964281i	$0.585333\pi$
$654$	15.2239	0.595301
$655$	5.28016	0.206313
$656$	6.22351	0.242987
$657$	12.3662	0.482450
$658$	−3.56455	−0.138961
$659$	−5.43174	−0.211591	−0.105795	−	0.994388i	$-0.533739\pi$
$659$	−5.43174	−0.211591	−0.105795	+	0.994388i	$0.533739\pi$
$660$	4.27248	0.166306
$661$	−45.6612	−1.77601	−0.888007	−	0.459829i	$-0.847911\pi$
$661$	−45.6612	−1.77601	−0.888007	+	0.459829i	$0.847911\pi$
$662$	16.0944	0.625527
$663$	−36.6614	−1.42381
$664$	−7.94057	−0.308154
$665$	11.9926	0.465054
$666$	−8.41741	−0.326168
$667$	34.8336	1.34876
$668$	0.600030	0.0232159
$669$	−26.6551	−1.03055
$670$	−0.717462	−0.0277180
$671$	−3.98259	−0.153746
$672$	2.15083	0.0829702
$673$	−37.7992	−1.45705	−0.728526	−	0.685018i	$-0.759794\pi$
$673$	−37.7992	−1.45705	−0.728526	+	0.685018i	$0.759794\pi$
$674$	−24.4117	−0.940304
$675$	−4.43559	−0.170726
$676$	23.1475	0.890288
$677$	33.6195	1.29210	0.646051	−	0.763294i	$-0.276419\pi$
$677$	33.6195	1.29210	0.646051	+	0.763294i	$0.276419\pi$
$678$	4.51057	0.173227
$679$	25.9608	0.996285
$680$	4.58108	0.175676
$681$	9.93774	0.380815
$682$	0	0
$683$	3.30089	0.126305	0.0631526	−	0.998004i	$-0.479885\pi$
$683$	3.30089	0.126305	0.0631526	+	0.998004i	$0.479885\pi$
$684$	−7.42179	−0.283779
$685$	−10.9498	−0.418370
$686$	−20.1617	−0.769778
$687$	−5.56427	−0.212290
$688$	−4.03338	−0.153771
$689$	37.1812	1.41649
$690$	5.61205	0.213647
$691$	−12.7597	−0.485403	−0.242701	−	0.970101i	$-0.578034\pi$
$691$	−12.7597	−0.485403	−0.242701	+	0.970101i	$0.578034\pi$
$692$	−6.62535	−0.251858
$693$	−12.2317	−0.464645
$694$	−12.3738	−0.469703
$695$	−6.64457	−0.252043
$696$	−4.66311	−0.176755
$697$	−37.9494	−1.43744
$698$	−14.9115	−0.564407
$699$	7.71215	0.291700
$700$	−9.54020	−0.360586
$701$	−24.2415	−0.915590	−0.457795	−	0.889058i	$-0.651361\pi$
$701$	−24.2415	−0.915590	−0.457795	+	0.889058i	$0.651361\pi$
$702$	6.01228	0.226919
$703$	62.4723	2.35619
$704$	−5.68697	−0.214336
$705$	1.24508	0.0468923
$706$	−21.4153	−0.805976
$707$	7.18706	0.270297
$708$	−4.00401	−0.150480
$709$	46.3882	1.74215	0.871073	−	0.491153i	$-0.163425\pi$
$709$	46.3882	1.74215	0.871073	+	0.491153i	$0.163425\pi$
$710$	0.858133	0.0322052
$711$	0.854729	0.0320548
$712$	−16.7301	−0.626987
$713$	0	0
$714$	−13.1152	−0.490825
$715$	25.6873	0.960651
$716$	12.7907	0.478013
$717$	−23.3850	−0.873330
$718$	−7.54031	−0.281402
$719$	20.8442	0.777359	0.388680	−	0.921373i	$-0.372931\pi$
$719$	20.8442	0.777359	0.388680	+	0.921373i	$0.372931\pi$
$720$	−0.751274	−0.0279983
$721$	−16.4199	−0.611507
$722$	36.0830	1.34287
$723$	−19.0910	−0.710003
$724$	5.50316	0.204523
$725$	20.6836	0.768170
$726$	21.3417	0.792063
$727$	19.3813	0.718812	0.359406	−	0.933181i	$-0.382979\pi$
$727$	19.3813	0.718812	0.359406	+	0.933181i	$0.382979\pi$
$728$	12.9314	0.479270
$729$	1.00000	0.0370370
$730$	−9.29038	−0.343852
$731$	24.5945	0.909661
$732$	0.700300	0.0258838
$733$	−31.9590	−1.18043	−0.590217	−	0.807245i	$-0.700958\pi$
$733$	−31.9590	−1.18043	−0.590217	+	0.807245i	$0.700958\pi$
$734$	−24.9142	−0.919601
$735$	1.78347	0.0657841
$736$	−7.47004	−0.275349
$737$	−5.43102	−0.200054
$738$	6.22351	0.229091
$739$	51.0194	1.87678	0.938389	−	0.345581i	$-0.112318\pi$
$739$	51.0194	1.87678	0.938389	+	0.345581i	$0.112318\pi$
$740$	6.32379	0.232467
$741$	−44.6219	−1.63923
$742$	13.3012	0.488302
$743$	−0.344545	−0.0126401	−0.00632006	−	0.999980i	$-0.502012\pi$
$743$	−0.344545	−0.0126401	−0.00632006	+	0.999980i	$0.502012\pi$
$744$	0	0
$745$	3.98282	0.145919
$746$	−7.90324	−0.289358
$747$	−7.94057	−0.290530
$748$	34.6777	1.26794
$749$	19.1651	0.700277
$750$	7.08871	0.258843
$751$	11.9122	0.434682	0.217341	−	0.976096i	$-0.430262\pi$
$751$	11.9122	0.434682	0.217341	+	0.976096i	$0.430262\pi$
$752$	−1.65729	−0.0604350
$753$	−0.507765	−0.0185040
$754$	−28.0359	−1.02101
$755$	9.54890	0.347520
$756$	2.15083	0.0782250
$757$	3.87670	0.140901	0.0704506	−	0.997515i	$-0.477556\pi$
$757$	3.87670	0.140901	0.0704506	+	0.997515i	$0.477556\pi$
$758$	−7.71253	−0.280132
$759$	42.4819	1.54200
$760$	5.57580	0.202256
$761$	−1.65209	−0.0598881	−0.0299441	−	0.999552i	$-0.509533\pi$
$761$	−1.65209	−0.0598881	−0.0299441	+	0.999552i	$0.509533\pi$
$762$	17.4675	0.632782
$763$	32.7440	1.18541
$764$	7.76885	0.281067
$765$	4.58108	0.165629
$766$	1.71607	0.0620040
$767$	−24.0732	−0.869234
$768$	1.00000	0.0360844
$769$	20.1841	0.727856	0.363928	−	0.931427i	$-0.381435\pi$
$769$	20.1841	0.727856	0.363928	+	0.931427i	$0.381435\pi$
$770$	9.18938	0.331162
$771$	8.06669	0.290515
$772$	−12.7079	−0.457366
$773$	18.7958	0.676038	0.338019	−	0.941139i	$-0.390243\pi$
$773$	18.7958	0.676038	0.338019	+	0.941139i	$0.390243\pi$
$774$	−4.03338	−0.144977
$775$	0	0
$776$	12.0701	0.433292
$777$	−18.1044	−0.649493
$778$	10.9949	0.394186
$779$	−46.1896	−1.65491
$780$	−4.51687	−0.161730
$781$	6.49587	0.232440
$782$	45.5504	1.62888
$783$	−4.66311	−0.166646
$784$	−2.37392	−0.0847829
$785$	−4.59687	−0.164069
$786$	−7.02828	−0.250690
$787$	−33.9613	−1.21059	−0.605295	−	0.796001i	$-0.706945\pi$
$787$	−33.9613	−1.21059	−0.605295	+	0.796001i	$0.706945\pi$
$788$	−7.29092	−0.259728
$789$	−28.5497	−1.01640
$790$	−0.642136	−0.0228462
$791$	9.70148	0.344945
$792$	−5.68697	−0.202078
$793$	4.21040	0.149516
$794$	−15.9396	−0.565675
$795$	−4.64604	−0.164778
$796$	−14.3844	−0.509841
$797$	29.9531	1.06099	0.530497	−	0.847687i	$-0.322005\pi$
$797$	29.9531	1.06099	0.530497	+	0.847687i	$0.322005\pi$
$798$	−15.9630	−0.565085
$799$	10.1057	0.357515
$800$	−4.43559	−0.156822
$801$	−16.7301	−0.591129
$802$	7.77012	0.274372
$803$	−70.3260	−2.48175
$804$	0.954994	0.0336800
$805$	12.0706	0.425432
$806$	0	0
$807$	−5.95702	−0.209697
$808$	3.34152	0.117554
$809$	30.5439	1.07387	0.536933	−	0.843625i	$-0.319583\pi$
$809$	30.5439	1.07387	0.536933	+	0.843625i	$0.319583\pi$
$810$	−0.751274	−0.0263971
$811$	17.1184	0.601108	0.300554	−	0.953765i	$-0.402829\pi$
$811$	17.1184	0.601108	0.300554	+	0.953765i	$0.402829\pi$
$812$	−10.0296	−0.351969
$813$	20.8051	0.729665
$814$	47.8696	1.67783
$815$	−4.94703	−0.173287
$816$	−6.09775	−0.213464
$817$	29.9349	1.04729
$818$	−17.2489	−0.603094
$819$	12.9314	0.451860
$820$	−4.67557	−0.163278
$821$	8.21225	0.286610	0.143305	−	0.989679i	$-0.454227\pi$
$821$	8.21225	0.286610	0.143305	+	0.989679i	$0.454227\pi$
$822$	14.5750	0.508360
$823$	4.18314	0.145815	0.0729075	−	0.997339i	$-0.476772\pi$
$823$	4.18314	0.145815	0.0729075	+	0.997339i	$0.476772\pi$
$824$	−7.63419	−0.265949
$825$	25.2251	0.878224
$826$	−8.61195	−0.299648
$827$	41.0330	1.42686	0.713429	−	0.700727i	$-0.247141\pi$
$827$	41.0330	1.42686	0.713429	+	0.700727i	$0.247141\pi$
$828$	−7.47004	−0.259602
$829$	4.22708	0.146813	0.0734064	−	0.997302i	$-0.476613\pi$
$829$	4.22708	0.146813	0.0734064	+	0.997302i	$0.476613\pi$
$830$	5.96555	0.207067
$831$	7.30945	0.253562
$832$	6.01228	0.208438
$833$	14.4756	0.501549
$834$	8.84440	0.306257
$835$	−0.450788	−0.0156001
$836$	42.2075	1.45978
$837$	0	0
$838$	21.2911	0.735490
$839$	29.2909	1.01124	0.505618	−	0.862758i	$-0.331265\pi$
$839$	29.2909	1.01124	0.505618	+	0.862758i	$0.331265\pi$
$840$	−1.61587	−0.0557526
$841$	−7.25544	−0.250188
$842$	−24.7251	−0.852084
$843$	−1.45043	−0.0499555
$844$	3.00269	0.103357
$845$	−17.3901	−0.598238
$846$	−1.65729	−0.0569787
$847$	45.9023	1.57722
$848$	6.18421	0.212367
$849$	−16.1751	−0.555127
$850$	27.0471	0.927707
$851$	62.8784	2.15545
$852$	−1.14224	−0.0391324
$853$	−32.6951	−1.11946	−0.559730	−	0.828675i	$-0.689095\pi$
$853$	−32.6951	−1.11946	−0.559730	+	0.828675i	$0.689095\pi$
$854$	1.50623	0.0515420
$855$	5.57580	0.190688
$856$	8.91054	0.304556
$857$	−5.07748	−0.173444	−0.0867218	−	0.996233i	$-0.527639\pi$
$857$	−5.07748	−0.173444	−0.0867218	+	0.996233i	$0.527639\pi$
$858$	−34.1917	−1.16728
$859$	2.28083	0.0778211	0.0389105	−	0.999243i	$-0.487611\pi$
$859$	2.28083	0.0778211	0.0389105	+	0.999243i	$0.487611\pi$
$860$	3.03017	0.103328
$861$	13.3857	0.456185
$862$	2.93778	0.100061
$863$	−31.4897	−1.07192	−0.535961	−	0.844243i	$-0.680051\pi$
$863$	−31.4897	−1.07192	−0.535961	+	0.844243i	$0.680051\pi$
$864$	1.00000	0.0340207
$865$	4.97746	0.169239
$866$	5.35403	0.181937
$867$	20.1825	0.685434
$868$	0	0
$869$	−4.86082	−0.164892
$870$	3.50327	0.118772
$871$	5.74169	0.194550
$872$	15.2239	0.515546
$873$	12.0701	0.408512
$874$	55.4411	1.87532
$875$	15.2466	0.515430
$876$	12.3662	0.417814
$877$	−22.8243	−0.770722	−0.385361	−	0.922766i	$-0.625923\pi$
$877$	−22.8243	−0.770722	−0.385361	+	0.922766i	$0.625923\pi$
$878$	13.7938	0.465518
$879$	13.3584	0.450567
$880$	4.27248	0.144025
$881$	31.3885	1.05751	0.528753	−	0.848776i	$-0.322660\pi$
$881$	31.3885	1.05751	0.528753	+	0.848776i	$0.322660\pi$
$882$	−2.37392	−0.0799341
$883$	34.3653	1.15648	0.578242	−	0.815865i	$-0.303739\pi$
$883$	34.3653	1.15648	0.578242	+	0.815865i	$0.303739\pi$
$884$	−36.6614	−1.23305
$885$	3.00811	0.101117
$886$	23.7488	0.797856
$887$	33.8322	1.13597	0.567986	−	0.823038i	$-0.307723\pi$
$887$	33.8322	1.13597	0.567986	+	0.823038i	$0.307723\pi$
$888$	−8.41741	−0.282470
$889$	37.5697	1.26005
$890$	12.5689	0.421310
$891$	−5.68697	−0.190521
$892$	−26.6551	−0.892479
$893$	12.3000	0.411605
$894$	−5.30142	−0.177306
$895$	−9.60936	−0.321206
$896$	2.15083	0.0718543
$897$	−44.9120	−1.49957
$898$	11.3692	0.379395
$899$	0	0
$900$	−4.43559	−0.147853
$901$	−37.7098	−1.25629
$902$	−35.3929	−1.17846
$903$	−8.67512	−0.288690
$904$	4.51057	0.150019
$905$	−4.13438	−0.137431
$906$	−12.7103	−0.422270
$907$	−34.8732	−1.15795	−0.578973	−	0.815347i	$-0.696546\pi$
$907$	−34.8732	−1.15795	−0.578973	+	0.815347i	$0.696546\pi$
$908$	9.93774	0.329795
$909$	3.34152	0.110831
$910$	−9.71503	−0.322050
$911$	56.4474	1.87019	0.935093	−	0.354401i	$-0.115315\pi$
$911$	56.4474	1.87019	0.935093	+	0.354401i	$0.115315\pi$
$912$	−7.42179	−0.245760
$913$	45.1578	1.49450
$914$	38.4430	1.27158
$915$	−0.526117	−0.0173929
$916$	−5.56427	−0.183849
$917$	−15.1166	−0.499195
$918$	−6.09775	−0.201256
$919$	14.8650	0.490351	0.245176	−	0.969479i	$-0.421154\pi$
$919$	14.8650	0.490351	0.245176	+	0.969479i	$0.421154\pi$
$920$	5.61205	0.185024
$921$	5.52892	0.182184
$922$	7.95968	0.262138
$923$	−6.86745	−0.226045
$924$	−12.2317	−0.402394
$925$	37.3362	1.22761
$926$	25.2360	0.829305
$927$	−7.63419	−0.250740
$928$	−4.66311	−0.153074
$929$	48.8104	1.60142	0.800708	−	0.599055i	$-0.204457\pi$
$929$	48.8104	1.60142	0.800708	+	0.599055i	$0.204457\pi$
$930$	0	0
$931$	17.6187	0.577431
$932$	7.71215	0.252620
$933$	−23.6415	−0.773989
$934$	−22.8647	−0.748155
$935$	−26.0525	−0.852007
$936$	6.01228	0.196517
$937$	−41.4262	−1.35334	−0.676668	−	0.736288i	$-0.736577\pi$
$937$	−41.4262	−1.35334	−0.676668	+	0.736288i	$0.736577\pi$
$938$	2.05403	0.0670665
$939$	−4.42885	−0.144530
$940$	1.24508	0.0406099
$941$	−23.8602	−0.777819	−0.388909	−	0.921276i	$-0.627148\pi$
$941$	−23.8602	−0.777819	−0.388909	+	0.921276i	$0.627148\pi$
$942$	6.11876	0.199360
$943$	−46.4899	−1.51392
$944$	−4.00401	−0.130319
$945$	−1.61587	−0.0525641
$946$	22.9377	0.745769
$947$	−54.8222	−1.78148	−0.890741	−	0.454511i	$-0.849814\pi$
$947$	−54.8222	−1.78148	−0.890741	+	0.454511i	$0.849814\pi$
$948$	0.854729	0.0277603
$949$	74.3488	2.41346
$950$	32.9200	1.06807
$951$	10.2298	0.331724
$952$	−13.1152	−0.425067
$953$	−19.1031	−0.618810	−0.309405	−	0.950930i	$-0.600130\pi$
$953$	−19.1031	−0.618810	−0.309405	+	0.950930i	$0.600130\pi$
$954$	6.18421	0.200221
$955$	−5.83654	−0.188866
$956$	−23.3850	−0.756326
$957$	26.5190	0.857236
$958$	−5.23181	−0.169032
$959$	31.3483	1.01229
$960$	−0.751274	−0.0242473
$961$	0	0
$962$	−50.6078	−1.63166
$963$	8.91054	0.287138
$964$	−19.0910	−0.614880
$965$	9.54709	0.307332
$966$	−16.0668	−0.516941
$967$	−30.4676	−0.979772	−0.489886	−	0.871787i	$-0.662962\pi$
$967$	−30.4676	−0.979772	−0.489886	+	0.871787i	$0.662962\pi$
$968$	21.3417	0.685947
$969$	45.2562	1.45384
$970$	−9.06798	−0.291155
$971$	3.69377	0.118539	0.0592694	−	0.998242i	$-0.481123\pi$
$971$	3.69377	0.118539	0.0592694	+	0.998242i	$0.481123\pi$
$972$	1.00000	0.0320750
$973$	19.0228	0.609844
$974$	−10.0505	−0.322040
$975$	−26.6680	−0.854059
$976$	0.700300	0.0224161
$977$	−3.45852	−0.110648	−0.0553239	−	0.998468i	$-0.517619\pi$
$977$	−3.45852	−0.110648	−0.0553239	+	0.998468i	$0.517619\pi$
$978$	6.58485	0.210560
$979$	95.1436	3.04080
$980$	1.78347	0.0569707
$981$	15.2239	0.486061
$982$	−1.93361	−0.0617040
$983$	22.6215	0.721513	0.360757	−	0.932660i	$-0.382518\pi$
$983$	22.6215	0.721513	0.360757	+	0.932660i	$0.382518\pi$
$984$	6.22351	0.198398
$985$	5.47748	0.174527
$986$	28.4344	0.905537
$987$	−3.56455	−0.113461
$988$	−44.6219	−1.41961
$989$	30.1295	0.958062
$990$	4.27248	0.135788
$991$	−4.09327	−0.130027	−0.0650136	−	0.997884i	$-0.520709\pi$
$991$	−4.09327	−0.130027	−0.0650136	+	0.997884i	$0.520709\pi$
$992$	0	0
$993$	16.0944	0.510740
$994$	−2.45676	−0.0779237
$995$	10.8066	0.342593
$996$	−7.94057	−0.251607
$997$	−21.6220	−0.684777	−0.342388	−	0.939559i	$-0.611236\pi$
$997$	−21.6220	−0.684777	−0.342388	+	0.939559i	$0.611236\pi$
$998$	−25.8445	−0.818092
$999$	−8.41741	−0.266315

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5766.2.a.bq.1.5	yes	8
31.30	odd	2		5766.2.a.bo.1.5	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5766.2.a.bo.1.5	✓	8	31.30	odd	2
5766.2.a.bq.1.5	yes	8	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:	\( N \)	\(=\)	\( 5766 = 2 \cdot 3 \cdot 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5766.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.751274 q^{5} +1.00000 q^{6} +2.15083 q^{7} +1.00000 q^{8} +1.00000 q^{9} -0.751274 q^{10} -5.68697 q^{11} +1.00000 q^{12} +6.01228 q^{13} +2.15083 q^{14} -0.751274 q^{15} +1.00000 q^{16} -6.09775 q^{17} +1.00000 q^{18} -7.42179 q^{19} -0.751274 q^{20} +2.15083 q^{21} -5.68697 q^{22} -7.47004 q^{23} +1.00000 q^{24} -4.43559 q^{25} +6.01228 q^{26} +1.00000 q^{27} +2.15083 q^{28} -4.66311 q^{29} -0.751274 q^{30} +1.00000 q^{32} -5.68697 q^{33} -6.09775 q^{34} -1.61587 q^{35} +1.00000 q^{36} -8.41741 q^{37} -7.42179 q^{38} +6.01228 q^{39} -0.751274 q^{40} +6.22351 q^{41} +2.15083 q^{42} -4.03338 q^{43} -5.68697 q^{44} -0.751274 q^{45} -7.47004 q^{46} -1.65729 q^{47} +1.00000 q^{48} -2.37392 q^{49} -4.43559 q^{50} -6.09775 q^{51} +6.01228 q^{52} +6.18421 q^{53} +1.00000 q^{54} +4.27248 q^{55} +2.15083 q^{56} -7.42179 q^{57} -4.66311 q^{58} -4.00401 q^{59} -0.751274 q^{60} +0.700300 q^{61} +2.15083 q^{63} +1.00000 q^{64} -4.51687 q^{65} -5.68697 q^{66} +0.954994 q^{67} -6.09775 q^{68} -7.47004 q^{69} -1.61587 q^{70} -1.14224 q^{71} +1.00000 q^{72} +12.3662 q^{73} -8.41741 q^{74} -4.43559 q^{75} -7.42179 q^{76} -12.2317 q^{77} +6.01228 q^{78} +0.854729 q^{79} -0.751274 q^{80} +1.00000 q^{81} +6.22351 q^{82} -7.94057 q^{83} +2.15083 q^{84} +4.58108 q^{85} -4.03338 q^{86} -4.66311 q^{87} -5.68697 q^{88} -16.7301 q^{89} -0.751274 q^{90} +12.9314 q^{91} -7.47004 q^{92} -1.65729 q^{94} +5.57580 q^{95} +1.00000 q^{96} +12.0701 q^{97} -2.37392 q^{98} -5.68697 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} + 8 q^{3} + 8 q^{4} - 8 q^{5} + 8 q^{6} + 8 q^{8} + 8 q^{9} - 8 q^{10} - 24 q^{11} + 8 q^{12} - 8 q^{13} - 8 q^{15} + 8 q^{16} - 8 q^{17} + 8 q^{18} - 8 q^{19} - 8 q^{20} - 24 q^{22} - 32 q^{23}+ \cdots - 24 q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 - 8 * q^5 + 8 * q^6 + 8 * q^8 + 8 * q^9 - 8 * q^10 - 24 * q^11 + 8 * q^12 - 8 * q^13 - 8 * q^15 + 8 * q^16 - 8 * q^17 + 8 * q^18 - 8 * q^19 - 8 * q^20 - 24 * q^22 - 32 * q^23 + 8 * q^24 - 8 * q^26 + 8 * q^27 - 16 * q^29 - 8 * q^30 + 8 * q^32 - 24 * q^33 - 8 * q^34 - 16 * q^35 + 8 * q^36 - 8 * q^38 - 8 * q^39 - 8 * q^40 - 16 * q^41 - 32 * q^43 - 24 * q^44 - 8 * q^45 - 32 * q^46 - 24 * q^47 + 8 * q^48 - 8 * q^49 - 8 * q^51 - 8 * q^52 - 16 * q^53 + 8 * q^54 + 24 * q^55 - 8 * q^57 - 16 * q^58 - 16 * q^59 - 8 * q^60 + 8 * q^61 + 8 * q^64 - 24 * q^65 - 24 * q^66 - 8 * q^67 - 8 * q^68 - 32 * q^69 - 16 * q^70 - 8 * q^71 + 8 * q^72 - 8 * q^76 - 16 * q^77 - 8 * q^78 - 24 * q^79 - 8 * q^80 + 8 * q^81 - 16 * q^82 - 40 * q^83 - 8 * q^85 - 32 * q^86 - 16 * q^87 - 24 * q^88 - 16 * q^89 - 8 * q^90 - 32 * q^92 - 24 * q^94 + 8 * q^95 + 8 * q^96 - 8 * q^97 - 8 * q^98 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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