LMFDB - Embedded newform 5766.2.a.ba.1.4

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)

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);

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")

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 = [4,-4,4,4,0] 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:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{15})^+$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 4x^{2} + 4x + 1 $ x^4 - x^3 - 4x^2 + 4x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 186)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$1.82709$ 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)

$f(q)$	$=$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.29456 q^{5} -1.00000 q^{6} +3.95630 q^{7} -1.00000 q^{8} +1.00000 q^{9} -3.29456 q^{10} +4.31592 q^{11} +1.00000 q^{12} -1.23607 q^{13} -3.95630 q^{14} +3.29456 q^{15} +1.00000 q^{16} -5.14866 q^{17} -1.00000 q^{18} -1.23607 q^{19} +3.29456 q^{20} +3.95630 q^{21} -4.31592 q^{22} +6.00000 q^{23} -1.00000 q^{24} +5.85410 q^{25} +1.23607 q^{26} +1.00000 q^{27} +3.95630 q^{28} +1.11442 q^{29} -3.29456 q^{30} -1.00000 q^{32} +4.31592 q^{33} +5.14866 q^{34} +13.0342 q^{35} +1.00000 q^{36} -1.02234 q^{37} +1.23607 q^{38} -1.23607 q^{39} -3.29456 q^{40} -12.4030 q^{41} -3.95630 q^{42} +1.85857 q^{43} +4.31592 q^{44} +3.29456 q^{45} -6.00000 q^{46} -1.37750 q^{47} +1.00000 q^{48} +8.65227 q^{49} -5.85410 q^{50} -5.14866 q^{51} -1.23607 q^{52} -6.85877 q^{53} -1.00000 q^{54} +14.2190 q^{55} -3.95630 q^{56} -1.23607 q^{57} -1.11442 q^{58} +7.99809 q^{59} +3.29456 q^{60} -11.0072 q^{61} +3.95630 q^{63} +1.00000 q^{64} -4.07230 q^{65} -4.31592 q^{66} +7.98489 q^{67} -5.14866 q^{68} +6.00000 q^{69} -13.0342 q^{70} +15.4071 q^{71} -1.00000 q^{72} -14.2071 q^{73} +1.02234 q^{74} +5.85410 q^{75} -1.23607 q^{76} +17.0751 q^{77} +1.23607 q^{78} +13.1401 q^{79} +3.29456 q^{80} +1.00000 q^{81} +12.4030 q^{82} +5.63184 q^{83} +3.95630 q^{84} -16.9625 q^{85} -1.85857 q^{86} +1.11442 q^{87} -4.31592 q^{88} -0.0629548 q^{89} -3.29456 q^{90} -4.89025 q^{91} +6.00000 q^{92} +1.37750 q^{94} -4.07230 q^{95} -1.00000 q^{96} +18.6504 q^{97} -8.65227 q^{98} +4.31592 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} + 4 q^{3} + 4 q^{4} - 4 q^{6} + 7 q^{7} - 4 q^{8} + 4 q^{9} + 9 q^{11} + 4 q^{12} + 4 q^{13} - 7 q^{14} + 4 q^{16} + 6 q^{17} - 4 q^{18} + 4 q^{19} + 7 q^{21} - 9 q^{22} + 24 q^{23} - 4 q^{24}+ \cdots + 9 q^{99}+O(q^{100}) $ 4 * q - 4 * q^2 + 4 * q^3 + 4 * q^4 - 4 * q^6 + 7 * q^7 - 4 * q^8 + 4 * q^9 + 9 * q^11 + 4 * q^12 + 4 * q^13 - 7 * q^14 + 4 * q^16 + 6 * q^17 - 4 * q^18 + 4 * q^19 + 7 * q^21 - 9 * q^22 + 24 * q^23 - 4 * q^24 + 10 * q^25 - 4 * q^26 + 4 * q^27 + 7 * q^28 + 15 * q^29 - 4 * q^32 + 9 * q^33 - 6 * q^34 + 15 * q^35 + 4 * q^36 - 8 * q^37 - 4 * q^38 + 4 * q^39 - 12 * q^41 - 7 * q^42 + 4 * q^43 + 9 * q^44 - 24 * q^46 + 4 * q^48 - 7 * q^49 - 10 * q^50 + 6 * q^51 + 4 * q^52 - 3 * q^53 - 4 * q^54 - 15 * q^55 - 7 * q^56 + 4 * q^57 - 15 * q^58 + 3 * q^59 - 14 * q^61 + 7 * q^63 + 4 * q^64 - 9 * q^66 - 2 * q^67 + 6 * q^68 + 24 * q^69 - 15 * q^70 + 30 * q^71 - 4 * q^72 - 26 * q^73 + 8 * q^74 + 10 * q^75 + 4 * q^76 + 12 * q^77 - 4 * q^78 + 10 * q^79 + 4 * q^81 + 12 * q^82 + 6 * q^83 + 7 * q^84 - 30 * q^85 - 4 * q^86 + 15 * q^87 - 9 * q^88 - 6 * q^89 + 2 * q^91 + 24 * q^92 - 4 * q^96 + 4 * q^97 + 7 * q^98 + 9 * 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
$5$	3.29456	1.47337	0.736685	−	0.676236i	$-0.236390\pi$
$5$	3.29456	1.47337	0.736685	+	0.676236i	$0.236390\pi$
$6$	−1.00000	−0.408248
$7$	3.95630	1.49534	0.747670	−	0.664071i	$-0.231173\pi$
$7$	3.95630	1.49534	0.747670	+	0.664071i	$0.231173\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−3.29456	−1.04183
$11$	4.31592	1.30130	0.650650	−	0.759378i	$-0.274497\pi$
$11$	4.31592	1.30130	0.650650	+	0.759378i	$0.274497\pi$
$12$	1.00000	0.288675
$13$	−1.23607	−0.342824	−0.171412	−	0.985199i	$-0.554833\pi$
$13$	−1.23607	−0.342824	−0.171412	+	0.985199i	$0.554833\pi$
$14$	−3.95630	−1.05736
$15$	3.29456	0.850651
$16$	1.00000	0.250000
$17$	−5.14866	−1.24873	−0.624367	−	0.781132i	$-0.714643\pi$
$17$	−5.14866	−1.24873	−0.624367	+	0.781132i	$0.714643\pi$
$18$	−1.00000	−0.235702
$19$	−1.23607	−0.283573	−0.141787	−	0.989897i	$-0.545285\pi$
$19$	−1.23607	−0.283573	−0.141787	+	0.989897i	$0.545285\pi$
$20$	3.29456	0.736685
$21$	3.95630	0.863334
$22$	−4.31592	−0.920157
$23$	6.00000	1.25109	0.625543	−	0.780189i	$-0.284877\pi$
$23$	6.00000	1.25109	0.625543	+	0.780189i	$0.284877\pi$
$24$	−1.00000	−0.204124
$25$	5.85410	1.17082
$26$	1.23607	0.242413
$27$	1.00000	0.192450
$28$	3.95630	0.747670
$29$	1.11442	0.206943	0.103471	−	0.994632i	$-0.467005\pi$
$29$	1.11442	0.206943	0.103471	+	0.994632i	$0.467005\pi$
$30$	−3.29456	−0.601501
$31$	0	0
$31$	0	0
$32$	−1.00000	−0.176777
$33$	4.31592	0.751305
$34$	5.14866	0.882988
$35$	13.0342	2.20319
$36$	1.00000	0.166667
$37$	−1.02234	−0.168072	−0.0840359	−	0.996463i	$-0.526781\pi$
$37$	−1.02234	−0.168072	−0.0840359	+	0.996463i	$0.526781\pi$
$38$	1.23607	0.200517
$39$	−1.23607	−0.197929
$40$	−3.29456	−0.520915
$41$	−12.4030	−1.93702	−0.968512	−	0.248969i	$-0.919908\pi$
$41$	−12.4030	−1.93702	−0.968512	+	0.248969i	$0.919908\pi$
$42$	−3.95630	−0.610470
$43$	1.85857	0.283429	0.141715	−	0.989908i	$-0.454739\pi$
$43$	1.85857	0.283429	0.141715	+	0.989908i	$0.454739\pi$
$44$	4.31592	0.650650
$45$	3.29456	0.491123
$46$	−6.00000	−0.884652
$47$	−1.37750	−0.200929	−0.100464	−	0.994941i	$-0.532033\pi$
$47$	−1.37750	−0.200929	−0.100464	+	0.994941i	$0.532033\pi$
$48$	1.00000	0.144338
$49$	8.65227	1.23604
$50$	−5.85410	−0.827895
$51$	−5.14866	−0.720956
$52$	−1.23607	−0.171412
$53$	−6.85877	−0.942125	−0.471062	−	0.882100i	$-0.656129\pi$
$53$	−6.85877	−0.942125	−0.471062	+	0.882100i	$0.656129\pi$
$54$	−1.00000	−0.136083
$55$	14.2190	1.91730
$56$	−3.95630	−0.528682
$57$	−1.23607	−0.163721
$58$	−1.11442	−0.146331
$59$	7.99809	1.04126	0.520631	−	0.853782i	$-0.325697\pi$
$59$	7.99809	1.04126	0.520631	+	0.853782i	$0.325697\pi$
$60$	3.29456	0.425325
$61$	−11.0072	−1.40933	−0.704665	−	0.709540i	$-0.748903\pi$
$61$	−11.0072	−1.40933	−0.704665	+	0.709540i	$0.748903\pi$
$62$	0	0
$63$	3.95630	0.498446
$64$	1.00000	0.125000
$65$	−4.07230	−0.505106
$66$	−4.31592	−0.531253
$67$	7.98489	0.975509	0.487755	−	0.872981i	$-0.337816\pi$
$67$	7.98489	0.975509	0.487755	+	0.872981i	$0.337816\pi$
$68$	−5.14866	−0.624367
$69$	6.00000	0.722315
$70$	−13.0342	−1.55789
$71$	15.4071	1.82848	0.914241	−	0.405170i	$-0.132788\pi$
$71$	15.4071	1.82848	0.914241	+	0.405170i	$0.132788\pi$
$72$	−1.00000	−0.117851
$73$	−14.2071	−1.66282	−0.831410	−	0.555659i	$-0.812466\pi$
$73$	−14.2071	−1.66282	−0.831410	+	0.555659i	$0.812466\pi$
$74$	1.02234	0.118845
$75$	5.85410	0.675973
$76$	−1.23607	−0.141787
$77$	17.0751	1.94588
$78$	1.23607	0.139957
$79$	13.1401	1.47838	0.739190	−	0.673497i	$-0.235209\pi$
$79$	13.1401	1.47838	0.739190	+	0.673497i	$0.235209\pi$
$80$	3.29456	0.368343
$81$	1.00000	0.111111
$82$	12.4030	1.36968
$83$	5.63184	0.618175	0.309087	−	0.951034i	$-0.399976\pi$
$83$	5.63184	0.618175	0.309087	+	0.951034i	$0.399976\pi$
$84$	3.95630	0.431667
$85$	−16.9625	−1.83985
$86$	−1.85857	−0.200415
$87$	1.11442	0.119478
$88$	−4.31592	−0.460079
$89$	−0.0629548	−0.00667319	−0.00333660	−	0.999994i	$-0.501062\pi$
$89$	−0.0629548	−0.00667319	−0.00333660	+	0.999994i	$0.501062\pi$
$90$	−3.29456	−0.347277
$91$	−4.89025	−0.512637
$92$	6.00000	0.625543
$93$	0	0
$94$	1.37750	0.142078
$95$	−4.07230	−0.417809
$96$	−1.00000	−0.102062
$97$	18.6504	1.89366	0.946829	−	0.321738i	$-0.104267\pi$
$97$	18.6504	1.89366	0.946829	+	0.321738i	$0.104267\pi$
$98$	−8.65227	−0.874011
$99$	4.31592	0.433766
$100$	5.85410	0.585410
$101$	12.2825	1.22216	0.611079	−	0.791570i	$-0.290736\pi$
$101$	12.2825	1.22216	0.611079	+	0.791570i	$0.290736\pi$
$102$	5.14866	0.509793
$103$	4.00723	0.394844	0.197422	−	0.980319i	$-0.436743\pi$
$103$	4.00723	0.394844	0.197422	+	0.980319i	$0.436743\pi$
$104$	1.23607	0.121206
$105$	13.0342	1.27201
$106$	6.85877	0.666183
$107$	12.8327	1.24059	0.620294	−	0.784370i	$-0.287013\pi$
$107$	12.8327	1.24059	0.620294	+	0.784370i	$0.287013\pi$
$108$	1.00000	0.0962250
$109$	3.42218	0.327785	0.163893	−	0.986478i	$-0.447595\pi$
$109$	3.42218	0.327785	0.163893	+	0.986478i	$0.447595\pi$
$110$	−14.2190	−1.35573
$111$	−1.02234	−0.0970363
$112$	3.95630	0.373835
$113$	6.95320	0.654102	0.327051	−	0.945007i	$-0.393945\pi$
$113$	6.95320	0.654102	0.327051	+	0.945007i	$0.393945\pi$
$114$	1.23607	0.115768
$115$	19.7673	1.84331
$116$	1.11442	0.103471
$117$	−1.23607	−0.114275
$118$	−7.99809	−0.736284
$119$	−20.3696	−1.86728
$120$	−3.29456	−0.300750
$121$	7.62717	0.693379
$122$	11.0072	0.996547
$123$	−12.4030	−1.11834
$124$	0	0
$125$	2.81389	0.251682
$126$	−3.95630	−0.352455
$127$	−16.5969	−1.47274	−0.736370	−	0.676579i	$-0.763462\pi$
$127$	−16.5969	−1.47274	−0.736370	+	0.676579i	$0.763462\pi$
$128$	−1.00000	−0.0883883
$129$	1.85857	0.163638
$130$	4.07230	0.357164
$131$	−16.0028	−1.39817	−0.699084	−	0.715040i	$-0.746409\pi$
$131$	−16.0028	−1.39817	−0.699084	+	0.715040i	$0.746409\pi$
$132$	4.31592	0.375653
$133$	−4.89025	−0.424038
$134$	−7.98489	−0.689789
$135$	3.29456	0.283550
$136$	5.14866	0.441494
$137$	−2.85686	−0.244078	−0.122039	−	0.992525i	$-0.538943\pi$
$137$	−2.85686	−0.244078	−0.122039	+	0.992525i	$0.538943\pi$
$138$	−6.00000	−0.510754
$139$	−16.6074	−1.40862	−0.704310	−	0.709892i	$-0.748744\pi$
$139$	−16.6074	−1.40862	−0.704310	+	0.709892i	$0.748744\pi$
$140$	13.0342	1.10159
$141$	−1.37750	−0.116006
$142$	−15.4071	−1.29293
$143$	−5.33477	−0.446116
$144$	1.00000	0.0833333
$145$	3.67152	0.304903
$146$	14.2071	1.17579
$147$	8.65227	0.713627
$148$	−1.02234	−0.0840359
$149$	−5.21904	−0.427561	−0.213780	−	0.976882i	$-0.568578\pi$
$149$	−5.21904	−0.427561	−0.213780	+	0.976882i	$0.568578\pi$
$150$	−5.85410	−0.477985
$151$	15.9563	1.29850	0.649252	−	0.760573i	$-0.275082\pi$
$151$	15.9563	1.29850	0.649252	+	0.760573i	$0.275082\pi$
$152$	1.23607	0.100258
$153$	−5.14866	−0.416244
$154$	−17.0751	−1.37595
$155$	0	0
$156$	−1.23607	−0.0989646
$157$	1.86986	0.149231	0.0746156	−	0.997212i	$-0.476227\pi$
$157$	1.86986	0.149231	0.0746156	+	0.997212i	$0.476227\pi$
$158$	−13.1401	−1.04537
$159$	−6.85877	−0.543936
$160$	−3.29456	−0.260458
$161$	23.7378	1.87080
$162$	−1.00000	−0.0785674
$163$	4.49854	0.352353	0.176177	−	0.984359i	$-0.443627\pi$
$163$	4.49854	0.352353	0.176177	+	0.984359i	$0.443627\pi$
$164$	−12.4030	−0.968512
$165$	14.2190	1.10695
$166$	−5.63184	−0.437116
$167$	−21.9332	−1.69724	−0.848622	−	0.529000i	$-0.822567\pi$
$167$	−21.9332	−1.69724	−0.848622	+	0.529000i	$0.822567\pi$
$168$	−3.95630	−0.305235
$169$	−11.4721	−0.882472
$170$	16.9625	1.30097
$171$	−1.23607	−0.0945245
$172$	1.85857	0.141715
$173$	15.4211	1.17244	0.586221	−	0.810151i	$-0.300615\pi$
$173$	15.4211	1.17244	0.586221	+	0.810151i	$0.300615\pi$
$174$	−1.11442	−0.0844840
$175$	23.1606	1.75077
$176$	4.31592	0.325325
$177$	7.99809	0.601173
$178$	0.0629548	0.00471866
$179$	13.6340	1.01905	0.509526	−	0.860455i	$-0.329821\pi$
$179$	13.6340	1.01905	0.509526	+	0.860455i	$0.329821\pi$
$180$	3.29456	0.245562
$181$	−12.6972	−0.943772	−0.471886	−	0.881660i	$-0.656427\pi$
$181$	−12.6972	−0.943772	−0.471886	+	0.881660i	$0.656427\pi$
$182$	4.89025	0.362489
$183$	−11.0072	−0.813678
$184$	−6.00000	−0.442326
$185$	−3.36816	−0.247632
$186$	0	0
$187$	−22.2212	−1.62498
$188$	−1.37750	−0.100464
$189$	3.95630	0.287778
$190$	4.07230	0.295435
$191$	−1.50341	−0.108783	−0.0543914	−	0.998520i	$-0.517322\pi$
$191$	−1.50341	−0.108783	−0.0543914	+	0.998520i	$0.517322\pi$
$192$	1.00000	0.0721688
$193$	−26.8943	−1.93589	−0.967946	−	0.251160i	$-0.919188\pi$
$193$	−26.8943	−1.93589	−0.967946	+	0.251160i	$0.919188\pi$
$194$	−18.6504	−1.33902
$195$	−4.07230	−0.291623
$196$	8.65227	0.618019
$197$	5.82453	0.414981	0.207490	−	0.978237i	$-0.433470\pi$
$197$	5.82453	0.414981	0.207490	+	0.978237i	$0.433470\pi$
$198$	−4.31592	−0.306719
$199$	−4.06447	−0.288122	−0.144061	−	0.989569i	$-0.546016\pi$
$199$	−4.06447	−0.288122	−0.144061	+	0.989569i	$0.546016\pi$
$200$	−5.85410	−0.413948
$201$	7.98489	0.563210
$202$	−12.2825	−0.864196
$203$	4.40898	0.309450
$204$	−5.14866	−0.360478
$205$	−40.8624	−2.85395
$206$	−4.00723	−0.279197
$207$	6.00000	0.417029
$208$	−1.23607	−0.0857059
$209$	−5.33477	−0.369014
$210$	−13.0342	−0.899448
$211$	−11.3197	−0.779277	−0.389639	−	0.920968i	$-0.627400\pi$
$211$	−11.3197	−0.779277	−0.389639	+	0.920968i	$0.627400\pi$
$212$	−6.85877	−0.471062
$213$	15.4071	1.05567
$214$	−12.8327	−0.877228
$215$	6.12316	0.417596
$216$	−1.00000	−0.0680414
$217$	0	0
$218$	−3.42218	−0.231779
$219$	−14.2071	−0.960030
$220$	14.2190	0.958648
$221$	6.36409	0.428095
$222$	1.02234	0.0686150
$223$	−2.43038	−0.162751	−0.0813753	−	0.996684i	$-0.525931\pi$
$223$	−2.43038	−0.162751	−0.0813753	+	0.996684i	$0.525931\pi$
$224$	−3.95630	−0.264341
$225$	5.85410	0.390273
$226$	−6.95320	−0.462520
$227$	−0.717714	−0.0476363	−0.0238182	−	0.999716i	$-0.507582\pi$
$227$	−0.717714	−0.0476363	−0.0238182	+	0.999716i	$0.507582\pi$
$228$	−1.23607	−0.0818606
$229$	−20.1893	−1.33414	−0.667072	−	0.744993i	$-0.732453\pi$
$229$	−20.1893	−1.33414	−0.667072	+	0.744993i	$0.732453\pi$
$230$	−19.7673	−1.30342
$231$	17.0751	1.12346
$232$	−1.11442	−0.0731653
$233$	−3.52209	−0.230740	−0.115370	−	0.993323i	$-0.536805\pi$
$233$	−3.52209	−0.230740	−0.115370	+	0.993323i	$0.536805\pi$
$234$	1.23607	0.0808043
$235$	−4.53825	−0.296043
$236$	7.99809	0.520631
$237$	13.1401	0.853543
$238$	20.3696	1.32037
$239$	4.33452	0.280377	0.140189	−	0.990125i	$-0.455229\pi$
$239$	4.33452	0.280377	0.140189	+	0.990125i	$0.455229\pi$
$240$	3.29456	0.212663
$241$	1.86889	0.120386	0.0601928	−	0.998187i	$-0.480828\pi$
$241$	1.86889	0.120386	0.0601928	+	0.998187i	$0.480828\pi$
$242$	−7.62717	−0.490293
$243$	1.00000	0.0641500
$244$	−11.0072	−0.704665
$245$	28.5054	1.82114
$246$	12.4030	0.790786
$247$	1.52786	0.0972157
$248$	0	0
$249$	5.63184	0.356903
$250$	−2.81389	−0.177966
$251$	12.1125	0.764535	0.382267	−	0.924052i	$-0.375143\pi$
$251$	12.1125	0.764535	0.382267	+	0.924052i	$0.375143\pi$
$252$	3.95630	0.249223
$253$	25.8955	1.62804
$254$	16.5969	1.04138
$255$	−16.9625	−1.06224
$256$	1.00000	0.0625000
$257$	9.77116	0.609508	0.304754	−	0.952431i	$-0.401426\pi$
$257$	9.77116	0.609508	0.304754	+	0.952431i	$0.401426\pi$
$258$	−1.85857	−0.115709
$259$	−4.04468	−0.251324
$260$	−4.07230	−0.252553
$261$	1.11442	0.0689809
$262$	16.0028	0.988654
$263$	−7.07636	−0.436347	−0.218174	−	0.975910i	$-0.570010\pi$
$263$	−7.07636	−0.436347	−0.218174	+	0.975910i	$0.570010\pi$
$264$	−4.31592	−0.265627
$265$	−22.5966	−1.38810
$266$	4.89025	0.299840
$267$	−0.0629548	−0.00385277
$268$	7.98489	0.487755
$269$	6.40049	0.390245	0.195122	−	0.980779i	$-0.437490\pi$
$269$	6.40049	0.390245	0.195122	+	0.980779i	$0.437490\pi$
$270$	−3.29456	−0.200500
$271$	11.5011	0.698644	0.349322	−	0.937003i	$-0.386412\pi$
$271$	11.5011	0.698644	0.349322	+	0.937003i	$0.386412\pi$
$272$	−5.14866	−0.312183
$273$	−4.89025	−0.295971
$274$	2.85686	0.172589
$275$	25.2658	1.52359
$276$	6.00000	0.361158
$277$	−25.9251	−1.55769	−0.778844	−	0.627218i	$-0.784194\pi$
$277$	−25.9251	−1.55769	−0.778844	+	0.627218i	$0.784194\pi$
$278$	16.6074	0.996045
$279$	0	0
$280$	−13.0342	−0.778945
$281$	8.69480	0.518688	0.259344	−	0.965785i	$-0.416494\pi$
$281$	8.69480	0.518688	0.259344	+	0.965785i	$0.416494\pi$
$282$	1.37750	0.0820289
$283$	−25.3411	−1.50637	−0.753186	−	0.657808i	$-0.771484\pi$
$283$	−25.3411	−1.50637	−0.753186	+	0.657808i	$0.771484\pi$
$284$	15.4071	0.914241
$285$	−4.07230	−0.241222
$286$	5.33477	0.315452
$287$	−49.0699	−2.89651
$288$	−1.00000	−0.0589256
$289$	9.50868	0.559334
$290$	−3.67152	−0.215599
$291$	18.6504	1.09330
$292$	−14.2071	−0.831410
$293$	−10.3562	−0.605016	−0.302508	−	0.953147i	$-0.597824\pi$
$293$	−10.3562	−0.605016	−0.302508	+	0.953147i	$0.597824\pi$
$294$	−8.65227	−0.504611
$295$	26.3502	1.53417
$296$	1.02234	0.0594223
$297$	4.31592	0.250435
$298$	5.21904	0.302331
$299$	−7.41641	−0.428902
$300$	5.85410	0.337987
$301$	7.35304	0.423822
$302$	−15.9563	−0.918182
$303$	12.2825	0.705613
$304$	−1.23607	−0.0708934
$305$	−36.2639	−2.07647
$306$	5.14866	0.294329
$307$	11.9942	0.684547	0.342273	−	0.939600i	$-0.388803\pi$
$307$	11.9942	0.684547	0.342273	+	0.939600i	$0.388803\pi$
$308$	17.0751	0.972942
$309$	4.00723	0.227963
$310$	0	0
$311$	−18.8141	−1.06685	−0.533426	−	0.845847i	$-0.679096\pi$
$311$	−18.8141	−1.06685	−0.533426	+	0.845847i	$0.679096\pi$
$312$	1.23607	0.0699786
$313$	9.34200	0.528041	0.264020	−	0.964517i	$-0.414951\pi$
$313$	9.34200	0.528041	0.264020	+	0.964517i	$0.414951\pi$
$314$	−1.86986	−0.105522
$315$	13.0342	0.734396
$316$	13.1401	0.739190
$317$	−19.8475	−1.11475	−0.557374	−	0.830262i	$-0.688191\pi$
$317$	−19.8475	−1.11475	−0.557374	+	0.830262i	$0.688191\pi$
$318$	6.85877	0.384621
$319$	4.80975	0.269294
$320$	3.29456	0.184171
$321$	12.8327	0.716254
$322$	−23.7378	−1.32285
$323$	6.36409	0.354108
$324$	1.00000	0.0555556
$325$	−7.23607	−0.401385
$326$	−4.49854	−0.249151
$327$	3.42218	0.189247
$328$	12.4030	0.684841
$329$	−5.44980	−0.300457
$330$	−14.2190	−0.782733
$331$	−7.06702	−0.388439	−0.194219	−	0.980958i	$-0.562217\pi$
$331$	−7.06702	−0.388439	−0.194219	+	0.980958i	$0.562217\pi$
$332$	5.63184	0.309087
$333$	−1.02234	−0.0560239
$334$	21.9332	1.20013
$335$	26.3067	1.43729
$336$	3.95630	0.215834
$337$	4.13354	0.225169	0.112584	−	0.993642i	$-0.464087\pi$
$337$	4.13354	0.225169	0.112584	+	0.993642i	$0.464087\pi$
$338$	11.4721	0.624002
$339$	6.95320	0.377646
$340$	−16.9625	−0.919923
$341$	0	0
$342$	1.23607	0.0668389
$343$	6.53687	0.352958
$344$	−1.85857	−0.100207
$345$	19.7673	1.06424
$346$	−15.4211	−0.829042
$347$	−5.03071	−0.270062	−0.135031	−	0.990841i	$-0.543113\pi$
$347$	−5.03071	−0.270062	−0.135031	+	0.990841i	$0.543113\pi$
$348$	1.11442	0.0597392
$349$	−1.17627	−0.0629644	−0.0314822	−	0.999504i	$-0.510023\pi$
$349$	−1.17627	−0.0629644	−0.0314822	+	0.999504i	$0.510023\pi$
$350$	−23.1606	−1.23798
$351$	−1.23607	−0.0659764
$352$	−4.31592	−0.230039
$353$	13.9277	0.741297	0.370648	−	0.928773i	$-0.379135\pi$
$353$	13.9277	0.741297	0.370648	+	0.928773i	$0.379135\pi$
$354$	−7.99809	−0.425094
$355$	50.7595	2.69403
$356$	−0.0629548	−0.00333660
$357$	−20.3696	−1.07807
$358$	−13.6340	−0.720579
$359$	14.6707	0.774293	0.387146	−	0.922018i	$-0.373461\pi$
$359$	14.6707	0.774293	0.387146	+	0.922018i	$0.373461\pi$
$360$	−3.29456	−0.173638
$361$	−17.4721	−0.919586
$362$	12.6972	0.667348
$363$	7.62717	0.400323
$364$	−4.89025	−0.256319
$365$	−46.8062	−2.44995
$366$	11.0072	0.575357
$367$	−8.42981	−0.440032	−0.220016	−	0.975496i	$-0.570611\pi$
$367$	−8.42981	−0.440032	−0.220016	+	0.975496i	$0.570611\pi$
$368$	6.00000	0.312772
$369$	−12.4030	−0.645674
$370$	3.36816	0.175102
$371$	−27.1353	−1.40880
$372$	0	0
$373$	−13.4530	−0.696568	−0.348284	−	0.937389i	$-0.613235\pi$
$373$	−13.4530	−0.696568	−0.348284	+	0.937389i	$0.613235\pi$
$374$	22.2212	1.14903
$375$	2.81389	0.145309
$376$	1.37750	0.0710391
$377$	−1.37750	−0.0709448
$378$	−3.95630	−0.203490
$379$	27.2392	1.39919	0.699593	−	0.714542i	$-0.253365\pi$
$379$	27.2392	1.39919	0.699593	+	0.714542i	$0.253365\pi$
$380$	−4.07230	−0.208904
$381$	−16.5969	−0.850287
$382$	1.50341	0.0769211
$383$	5.14866	0.263084	0.131542	−	0.991311i	$-0.458007\pi$
$383$	5.14866	0.263084	0.131542	+	0.991311i	$0.458007\pi$
$384$	−1.00000	−0.0510310
$385$	56.2547	2.86701
$386$	26.8943	1.36888
$387$	1.85857	0.0944763
$388$	18.6504	0.946829
$389$	−19.8971	−1.00882	−0.504411	−	0.863464i	$-0.668290\pi$
$389$	−19.8971	−1.00882	−0.504411	+	0.863464i	$0.668290\pi$
$390$	4.07230	0.206209
$391$	−30.8920	−1.56227
$392$	−8.65227	−0.437006
$393$	−16.0028	−0.807232
$394$	−5.82453	−0.293436
$395$	43.2909	2.17820
$396$	4.31592	0.216883
$397$	−18.4625	−0.926608	−0.463304	−	0.886199i	$-0.653336\pi$
$397$	−18.4625	−0.926608	−0.463304	+	0.886199i	$0.653336\pi$
$398$	4.06447	0.203733
$399$	−4.89025	−0.244819
$400$	5.85410	0.292705
$401$	26.1916	1.30795	0.653974	−	0.756517i	$-0.273101\pi$
$401$	26.1916	1.30795	0.653974	+	0.756517i	$0.273101\pi$
$402$	−7.98489	−0.398250
$403$	0	0
$404$	12.2825	0.611079
$405$	3.29456	0.163708
$406$	−4.40898	−0.218814
$407$	−4.41234	−0.218712
$408$	5.14866	0.254897
$409$	−10.7892	−0.533493	−0.266747	−	0.963767i	$-0.585949\pi$
$409$	−10.7892	−0.533493	−0.266747	+	0.963767i	$0.585949\pi$
$410$	40.8624	2.01805
$411$	−2.85686	−0.140919
$412$	4.00723	0.197422
$413$	31.6428	1.55704
$414$	−6.00000	−0.294884
$415$	18.5544	0.910801
$416$	1.23607	0.0606032
$417$	−16.6074	−0.813267
$418$	5.33477	0.260932
$419$	−26.3857	−1.28903	−0.644513	−	0.764593i	$-0.722940\pi$
$419$	−26.3857	−1.28903	−0.644513	+	0.764593i	$0.722940\pi$
$420$	13.0342	0.636006
$421$	−5.86173	−0.285683	−0.142842	−	0.989746i	$-0.545624\pi$
$421$	−5.86173	−0.285683	−0.142842	+	0.989746i	$0.545624\pi$
$422$	11.3197	0.551032
$423$	−1.37750	−0.0669763
$424$	6.85877	0.333091
$425$	−30.1408	−1.46204
$426$	−15.4071	−0.746475
$427$	−43.5478	−2.10743
$428$	12.8327	0.620294
$429$	−5.33477	−0.257565
$430$	−6.12316	−0.295285
$431$	6.78839	0.326985	0.163493	−	0.986545i	$-0.447724\pi$
$431$	6.78839	0.326985	0.163493	+	0.986545i	$0.447724\pi$
$432$	1.00000	0.0481125
$433$	−18.5244	−0.890228	−0.445114	−	0.895474i	$-0.646837\pi$
$433$	−18.5244	−0.890228	−0.445114	+	0.895474i	$0.646837\pi$
$434$	0	0
$435$	3.67152	0.176036
$436$	3.42218	0.163893
$437$	−7.41641	−0.354775
$438$	14.2071	0.678844
$439$	31.2074	1.48945	0.744723	−	0.667374i	$-0.232582\pi$
$439$	31.2074	1.48945	0.744723	+	0.667374i	$0.232582\pi$
$440$	−14.2190	−0.677866
$441$	8.65227	0.412013
$442$	−6.36409	−0.302709
$443$	23.4192	1.11268	0.556339	−	0.830955i	$-0.312206\pi$
$443$	23.4192	1.11268	0.556339	+	0.830955i	$0.312206\pi$
$444$	−1.02234	−0.0485181
$445$	−0.207408	−0.00983208
$446$	2.43038	0.115082
$447$	−5.21904	−0.246852
$448$	3.95630	0.186917
$449$	−5.59700	−0.264139	−0.132069	−	0.991240i	$-0.542162\pi$
$449$	−5.59700	−0.264139	−0.132069	+	0.991240i	$0.542162\pi$
$450$	−5.85410	−0.275965
$451$	−53.5304	−2.52065
$452$	6.95320	0.327051
$453$	15.9563	0.749692
$454$	0.717714	0.0336840
$455$	−16.1112	−0.755305
$456$	1.23607	0.0578842
$457$	−30.2879	−1.41681	−0.708404	−	0.705808i	$-0.750584\pi$
$457$	−30.2879	−1.41681	−0.708404	+	0.705808i	$0.750584\pi$
$458$	20.1893	0.943383
$459$	−5.14866	−0.240319
$460$	19.7673	0.921657
$461$	17.1561	0.799039	0.399519	−	0.916725i	$-0.369177\pi$
$461$	17.1561	0.799039	0.399519	+	0.916725i	$0.369177\pi$
$462$	−17.0751	−0.794404
$463$	7.55377	0.351054	0.175527	−	0.984475i	$-0.443837\pi$
$463$	7.55377	0.351054	0.175527	+	0.984475i	$0.443837\pi$
$464$	1.11442	0.0517357
$465$	0	0
$466$	3.52209	0.163158
$467$	0.890953	0.0412284	0.0206142	−	0.999788i	$-0.493438\pi$
$467$	0.890953	0.0412284	0.0206142	+	0.999788i	$0.493438\pi$
$468$	−1.23607	−0.0571373
$469$	31.5906	1.45872
$470$	4.53825	0.209334
$471$	1.86986	0.0861587
$472$	−7.99809	−0.368142
$473$	8.02143	0.368826
$474$	−13.1401	−0.603546
$475$	−7.23607	−0.332014
$476$	−20.3696	−0.933640
$477$	−6.85877	−0.314042
$478$	−4.33452	−0.198257
$479$	−29.0644	−1.32799	−0.663993	−	0.747738i	$-0.731140\pi$
$479$	−29.0644	−1.32799	−0.663993	+	0.747738i	$0.731140\pi$
$480$	−3.29456	−0.150375
$481$	1.26368	0.0576190
$482$	−1.86889	−0.0851254
$483$	23.7378	1.08011
$484$	7.62717	0.346690
$485$	61.4447	2.79006
$486$	−1.00000	−0.0453609
$487$	−18.2901	−0.828803	−0.414402	−	0.910094i	$-0.636009\pi$
$487$	−18.2901	−0.828803	−0.414402	+	0.910094i	$0.636009\pi$
$488$	11.0072	0.498274
$489$	4.49854	0.203431
$490$	−28.5054	−1.28774
$491$	29.1074	1.31360	0.656799	−	0.754066i	$-0.271910\pi$
$491$	29.1074	1.31360	0.656799	+	0.754066i	$0.271910\pi$
$492$	−12.4030	−0.559170
$493$	−5.73777	−0.258416
$494$	−1.52786	−0.0687419
$495$	14.2190	0.639098
$496$	0	0
$497$	60.9549	2.73420
$498$	−5.63184	−0.252369
$499$	−14.3902	−0.644196	−0.322098	−	0.946706i	$-0.604388\pi$
$499$	−14.3902	−0.644196	−0.322098	+	0.946706i	$0.604388\pi$
$500$	2.81389	0.125841
$501$	−21.9332	−0.979904
$502$	−12.1125	−0.540608
$503$	−18.6412	−0.831169	−0.415585	−	0.909555i	$-0.636423\pi$
$503$	−18.6412	−0.831169	−0.415585	+	0.909555i	$0.636423\pi$
$504$	−3.95630	−0.176227
$505$	40.4655	1.80069
$506$	−25.8955	−1.15120
$507$	−11.4721	−0.509495
$508$	−16.5969	−0.736370
$509$	−25.1112	−1.11303	−0.556517	−	0.830836i	$-0.687863\pi$
$509$	−25.1112	−1.11303	−0.556517	+	0.830836i	$0.687863\pi$
$510$	16.9625	0.751114
$511$	−56.2077	−2.48648
$512$	−1.00000	−0.0441942
$513$	−1.23607	−0.0545737
$514$	−9.77116	−0.430987
$515$	13.2020	0.581751
$516$	1.85857	0.0818189
$517$	−5.94518	−0.261469
$518$	4.04468	0.177713
$519$	15.4211	0.676910
$520$	4.07230	0.178582
$521$	14.8569	0.650891	0.325445	−	0.945561i	$-0.394486\pi$
$521$	14.8569	0.650891	0.325445	+	0.945561i	$0.394486\pi$
$522$	−1.11442	−0.0487769
$523$	−0.170999	−0.00747726	−0.00373863	−	0.999993i	$-0.501190\pi$
$523$	−0.170999	−0.00747726	−0.00373863	+	0.999993i	$0.501190\pi$
$524$	−16.0028	−0.699084
$525$	23.1606	1.01081
$526$	7.07636	0.308544
$527$	0	0
$528$	4.31592	0.187826
$529$	13.0000	0.565217
$530$	22.5966	0.981534
$531$	7.99809	0.347088
$532$	−4.89025	−0.212019
$533$	15.3310	0.664057
$534$	0.0629548	0.00272432
$535$	42.2782	1.82785
$536$	−7.98489	−0.344895
$537$	13.6340	0.588350
$538$	−6.40049	−0.275945
$539$	37.3425	1.60846
$540$	3.29456	0.141775
$541$	−4.19479	−0.180348	−0.0901741	−	0.995926i	$-0.528742\pi$
$541$	−4.19479	−0.180348	−0.0901741	+	0.995926i	$0.528742\pi$
$542$	−11.5011	−0.494016
$543$	−12.6972	−0.544887
$544$	5.14866	0.220747
$545$	11.2746	0.482949
$546$	4.89025	0.209283
$547$	17.0827	0.730403	0.365201	−	0.930929i	$-0.381000\pi$
$547$	17.0827	0.730403	0.365201	+	0.930929i	$0.381000\pi$
$548$	−2.85686	−0.122039
$549$	−11.0072	−0.469777
$550$	−25.2658	−1.07734
$551$	−1.37750	−0.0586835
$552$	−6.00000	−0.255377
$553$	51.9862	2.21068
$554$	25.9251	1.10145
$555$	−3.36816	−0.142970
$556$	−16.6074	−0.704310
$557$	9.28660	0.393486	0.196743	−	0.980455i	$-0.436964\pi$
$557$	9.28660	0.393486	0.196743	+	0.980455i	$0.436964\pi$
$558$	0	0
$559$	−2.29732	−0.0971661
$560$	13.0342	0.550797
$561$	−22.2212	−0.938180
$562$	−8.69480	−0.366768
$563$	16.1662	0.681324	0.340662	−	0.940186i	$-0.389349\pi$
$563$	16.1662	0.681324	0.340662	+	0.940186i	$0.389349\pi$
$564$	−1.37750	−0.0580032
$565$	22.9077	0.963735
$566$	25.3411	1.06517
$567$	3.95630	0.166149
$568$	−15.4071	−0.646466
$569$	13.1701	0.552119	0.276059	−	0.961141i	$-0.410971\pi$
$569$	13.1701	0.552119	0.276059	+	0.961141i	$0.410971\pi$
$570$	4.07230	0.170570
$571$	8.35093	0.349476	0.174738	−	0.984615i	$-0.444092\pi$
$571$	8.35093	0.349476	0.174738	+	0.984615i	$0.444092\pi$
$572$	−5.33477	−0.223058
$573$	−1.50341	−0.0628058
$574$	49.0699	2.04814
$575$	35.1246	1.46480
$576$	1.00000	0.0416667
$577$	3.31780	0.138122	0.0690610	−	0.997612i	$-0.478000\pi$
$577$	3.31780	0.138122	0.0690610	+	0.997612i	$0.478000\pi$
$578$	−9.50868	−0.395509
$579$	−26.8943	−1.11769
$580$	3.67152	0.152452
$581$	22.2812	0.924381
$582$	−18.6504	−0.773082
$583$	−29.6019	−1.22599
$584$	14.2071	0.587896
$585$	−4.07230	−0.168369
$586$	10.3562	0.427811
$587$	−7.18343	−0.296492	−0.148246	−	0.988951i	$-0.547363\pi$
$587$	−7.18343	−0.296492	−0.148246	+	0.988951i	$0.547363\pi$
$588$	8.65227	0.356814
$589$	0	0
$590$	−26.3502	−1.08482
$591$	5.82453	0.239589
$592$	−1.02234	−0.0420179
$593$	34.1999	1.40442	0.702211	−	0.711969i	$-0.252196\pi$
$593$	34.1999	1.40442	0.702211	+	0.711969i	$0.252196\pi$
$594$	−4.31592	−0.177084
$595$	−67.1088	−2.75119
$596$	−5.21904	−0.213780
$597$	−4.06447	−0.166348
$598$	7.41641	0.303279
$599$	12.1150	0.495006	0.247503	−	0.968887i	$-0.420390\pi$
$599$	12.1150	0.495006	0.247503	+	0.968887i	$0.420390\pi$
$600$	−5.85410	−0.238993
$601$	8.56522	0.349383	0.174691	−	0.984623i	$-0.444107\pi$
$601$	8.56522	0.349383	0.174691	+	0.984623i	$0.444107\pi$
$602$	−7.35304	−0.299688
$603$	7.98489	0.325170
$604$	15.9563	0.649252
$605$	25.1281	1.02160
$606$	−12.2825	−0.498944
$607$	1.12696	0.0457421	0.0228710	−	0.999738i	$-0.492719\pi$
$607$	1.12696	0.0457421	0.0228710	+	0.999738i	$0.492719\pi$
$608$	1.23607	0.0501292
$609$	4.40898	0.178661
$610$	36.2639	1.46828
$611$	1.70268	0.0688832
$612$	−5.14866	−0.208122
$613$	31.8458	1.28624	0.643120	−	0.765765i	$-0.277640\pi$
$613$	31.8458	1.28624	0.643120	+	0.765765i	$0.277640\pi$
$614$	−11.9942	−0.484048
$615$	−40.8624	−1.64773
$616$	−17.0751	−0.687974
$617$	−42.5745	−1.71399	−0.856993	−	0.515328i	$-0.827670\pi$
$617$	−42.5745	−1.71399	−0.856993	+	0.515328i	$0.827670\pi$
$618$	−4.00723	−0.161194
$619$	−22.6218	−0.909249	−0.454624	−	0.890683i	$-0.650226\pi$
$619$	−22.6218	−0.909249	−0.454624	+	0.890683i	$0.650226\pi$
$620$	0	0
$621$	6.00000	0.240772
$622$	18.8141	0.754378
$623$	−0.249068	−0.00997869
$624$	−1.23607	−0.0494823
$625$	−20.0000	−0.800000
$626$	−9.34200	−0.373381
$627$	−5.33477	−0.213050
$628$	1.86986	0.0746156
$629$	5.26368	0.209877
$630$	−13.0342	−0.519296
$631$	11.4923	0.457501	0.228750	−	0.973485i	$-0.426536\pi$
$631$	11.4923	0.457501	0.228750	+	0.973485i	$0.426536\pi$
$632$	−13.1401	−0.522686
$633$	−11.3197	−0.449916
$634$	19.8475	0.788246
$635$	−54.6796	−2.16989
$636$	−6.85877	−0.271968
$637$	−10.6948	−0.423743
$638$	−4.80975	−0.190420
$639$	15.4071	0.609494
$640$	−3.29456	−0.130229
$641$	21.4202	0.846048	0.423024	−	0.906118i	$-0.360969\pi$
$641$	21.4202	0.846048	0.423024	+	0.906118i	$0.360969\pi$
$642$	−12.8327	−0.506468
$643$	14.0691	0.554833	0.277416	−	0.960750i	$-0.410522\pi$
$643$	14.0691	0.554833	0.277416	+	0.960750i	$0.410522\pi$
$644$	23.7378	0.935399
$645$	6.12316	0.241099
$646$	−6.36409	−0.250392
$647$	11.2587	0.442623	0.221312	−	0.975203i	$-0.428966\pi$
$647$	11.2587	0.442623	0.221312	+	0.975203i	$0.428966\pi$
$648$	−1.00000	−0.0392837
$649$	34.5191	1.35499
$650$	7.23607	0.283822
$651$	0	0
$652$	4.49854	0.176177
$653$	−38.7882	−1.51790	−0.758949	−	0.651150i	$-0.774287\pi$
$653$	−38.7882	−1.51790	−0.758949	+	0.651150i	$0.774287\pi$
$654$	−3.42218	−0.133818
$655$	−52.7220	−2.06002
$656$	−12.4030	−0.484256
$657$	−14.2071	−0.554274
$658$	5.44980	0.212455
$659$	15.9953	0.623090	0.311545	−	0.950231i	$-0.399154\pi$
$659$	15.9953	0.623090	0.311545	+	0.950231i	$0.399154\pi$
$660$	14.2190	0.553476
$661$	5.30284	0.206257	0.103128	−	0.994668i	$-0.467115\pi$
$661$	5.30284	0.206257	0.103128	+	0.994668i	$0.467115\pi$
$662$	7.06702	0.274668
$663$	6.36409	0.247161
$664$	−5.63184	−0.218558
$665$	−16.1112	−0.624766
$666$	1.02234	0.0396149
$667$	6.68652	0.258903
$668$	−21.9332	−0.848622
$669$	−2.43038	−0.0939641
$670$	−26.3067	−1.01631
$671$	−47.5063	−1.83396
$672$	−3.95630	−0.152617
$673$	−16.1964	−0.624327	−0.312163	−	0.950028i	$-0.601054\pi$
$673$	−16.1964	−0.624327	−0.312163	+	0.950028i	$0.601054\pi$
$674$	−4.13354	−0.159218
$675$	5.85410	0.225324
$676$	−11.4721	−0.441236
$677$	−0.408443	−0.0156977	−0.00784886	−	0.999969i	$-0.502498\pi$
$677$	−0.408443	−0.0156977	−0.00784886	+	0.999969i	$0.502498\pi$
$678$	−6.95320	−0.267036
$679$	73.7863	2.83166
$680$	16.9625	0.650484
$681$	−0.717714	−0.0275028
$682$	0	0
$683$	−6.73225	−0.257602	−0.128801	−	0.991670i	$-0.541113\pi$
$683$	−6.73225	−0.257602	−0.128801	+	0.991670i	$0.541113\pi$
$684$	−1.23607	−0.0472622
$685$	−9.41209	−0.359618
$686$	−6.53687	−0.249579
$687$	−20.1893	−0.770269
$688$	1.85857	0.0708573
$689$	8.47791	0.322983
$690$	−19.7673	−0.752530
$691$	3.84150	0.146138	0.0730688	−	0.997327i	$-0.476721\pi$
$691$	3.84150	0.146138	0.0730688	+	0.997327i	$0.476721\pi$
$692$	15.4211	0.586221
$693$	17.0751	0.648628
$694$	5.03071	0.190963
$695$	−54.7140	−2.07542
$696$	−1.11442	−0.0422420
$697$	63.8588	2.41882
$698$	1.17627	0.0445226
$699$	−3.52209	−0.133218
$700$	23.1606	0.875387
$701$	−3.18611	−0.120338	−0.0601689	−	0.998188i	$-0.519164\pi$
$701$	−3.18611	−0.120338	−0.0601689	+	0.998188i	$0.519164\pi$
$702$	1.23607	0.0466524
$703$	1.26368	0.0476607
$704$	4.31592	0.162662
$705$	−4.53825	−0.170920
$706$	−13.9277	−0.524176
$707$	48.5933	1.82754
$708$	7.99809	0.300587
$709$	−34.9373	−1.31210	−0.656049	−	0.754718i	$-0.727773\pi$
$709$	−34.9373	−1.31210	−0.656049	+	0.754718i	$0.727773\pi$
$710$	−50.7595	−1.90497
$711$	13.1401	0.492793
$712$	0.0629548	0.00235933
$713$	0	0
$714$	20.3696	0.762314
$715$	−17.5757	−0.657294
$716$	13.6340	0.509526
$717$	4.33452	0.161876
$718$	−14.6707	−0.547508
$719$	31.1021	1.15991	0.579956	−	0.814647i	$-0.303070\pi$
$719$	31.1021	1.15991	0.579956	+	0.814647i	$0.303070\pi$
$720$	3.29456	0.122781
$721$	15.8538	0.590425
$722$	17.4721	0.650246
$723$	1.86889	0.0695046
$724$	−12.6972	−0.471886
$725$	6.52393	0.242293
$726$	−7.62717	−0.283071
$727$	−50.4824	−1.87229	−0.936145	−	0.351614i	$-0.885633\pi$
$727$	−50.4824	−1.87229	−0.936145	+	0.351614i	$0.885633\pi$
$728$	4.89025	0.181245
$729$	1.00000	0.0370370
$730$	46.8062	1.73238
$731$	−9.56913	−0.353927
$732$	−11.0072	−0.406839
$733$	33.1088	1.22290	0.611451	−	0.791282i	$-0.290586\pi$
$733$	33.1088	1.22290	0.611451	+	0.791282i	$0.290586\pi$
$734$	8.42981	0.311150
$735$	28.5054	1.05144
$736$	−6.00000	−0.221163
$737$	34.4621	1.26943
$738$	12.4030	0.456561
$739$	34.8417	1.28167	0.640837	−	0.767677i	$-0.278587\pi$
$739$	34.8417	1.28167	0.640837	+	0.767677i	$0.278587\pi$
$740$	−3.36816	−0.123816
$741$	1.52786	0.0561275
$742$	27.1353	0.996169
$743$	3.17391	0.116440	0.0582198	−	0.998304i	$-0.481458\pi$
$743$	3.17391	0.116440	0.0582198	+	0.998304i	$0.481458\pi$
$744$	0	0
$745$	−17.1944	−0.629955
$746$	13.4530	0.492548
$747$	5.63184	0.206058
$748$	−22.2212	−0.812488
$749$	50.7701	1.85510
$750$	−2.81389	−0.102749
$751$	−15.3198	−0.559028	−0.279514	−	0.960142i	$-0.590173\pi$
$751$	−15.3198	−0.559028	−0.279514	+	0.960142i	$0.590173\pi$
$752$	−1.37750	−0.0502322
$753$	12.1125	0.441404
$754$	1.37750	0.0501656
$755$	52.5689	1.91318
$756$	3.95630	0.143889
$757$	45.9062	1.66849	0.834244	−	0.551396i	$-0.185905\pi$
$757$	45.9062	1.66849	0.834244	+	0.551396i	$0.185905\pi$
$758$	−27.2392	−0.989373
$759$	25.8955	0.939948
$760$	4.07230	0.147718
$761$	27.7258	1.00506	0.502530	−	0.864560i	$-0.332403\pi$
$761$	27.7258	1.00506	0.502530	+	0.864560i	$0.332403\pi$
$762$	16.5969	0.601244
$763$	13.5392	0.490150
$764$	−1.50341	−0.0543914
$765$	−16.9625	−0.613282
$766$	−5.14866	−0.186029
$767$	−9.88618	−0.356969
$768$	1.00000	0.0360844
$769$	−34.4040	−1.24064	−0.620321	−	0.784348i	$-0.712998\pi$
$769$	−34.4040	−1.24064	−0.620321	+	0.784348i	$0.712998\pi$
$770$	−56.2547	−2.02728
$771$	9.77116	0.351900
$772$	−26.8943	−0.967946
$773$	−8.93046	−0.321206	−0.160603	−	0.987019i	$-0.551344\pi$
$773$	−8.93046	−0.321206	−0.160603	+	0.987019i	$0.551344\pi$
$774$	−1.85857	−0.0668049
$775$	0	0
$776$	−18.6504	−0.669509
$777$	−4.04468	−0.145102
$778$	19.8971	0.713345
$779$	15.3310	0.549288
$780$	−4.07230	−0.145812
$781$	66.4957	2.37940
$782$	30.8920	1.10469
$783$	1.11442	0.0398261
$784$	8.65227	0.309010
$785$	6.16037	0.219873
$786$	16.0028	0.570800
$787$	−44.6002	−1.58982	−0.794912	−	0.606725i	$-0.792483\pi$
$787$	−44.6002	−1.58982	−0.794912	+	0.606725i	$0.792483\pi$
$788$	5.82453	0.207490
$789$	−7.07636	−0.251925
$790$	−43.2909	−1.54022
$791$	27.5089	0.978105
$792$	−4.31592	−0.153360
$793$	13.6057	0.483152
$794$	18.4625	0.655211
$795$	−22.5966	−0.801419
$796$	−4.06447	−0.144061
$797$	10.3874	0.367942	0.183971	−	0.982932i	$-0.441105\pi$
$797$	10.3874	0.367942	0.183971	+	0.982932i	$0.441105\pi$
$798$	4.89025	0.173113
$799$	7.09228	0.250907
$800$	−5.85410	−0.206974
$801$	−0.0629548	−0.00222440
$802$	−26.1916	−0.924859
$803$	−61.3169	−2.16383
$804$	7.98489	0.281605
$805$	78.2054	2.75638
$806$	0	0
$807$	6.40049	0.225308
$808$	−12.2825	−0.432098
$809$	−4.40561	−0.154893	−0.0774466	−	0.996997i	$-0.524677\pi$
$809$	−4.40561	−0.154893	−0.0774466	+	0.996997i	$0.524677\pi$
$810$	−3.29456	−0.115759
$811$	−23.5051	−0.825376	−0.412688	−	0.910872i	$-0.635410\pi$
$811$	−23.5051	−0.825376	−0.412688	+	0.910872i	$0.635410\pi$
$812$	4.40898	0.154725
$813$	11.5011	0.403362
$814$	4.41234	0.154652
$815$	14.8207	0.519147
$816$	−5.14866	−0.180239
$817$	−2.29732	−0.0803729
$818$	10.7892	0.377237
$819$	−4.89025	−0.170879
$820$	−40.8624	−1.42698
$821$	37.7359	1.31699	0.658495	−	0.752585i	$-0.271193\pi$
$821$	37.7359	1.31699	0.658495	+	0.752585i	$0.271193\pi$
$822$	2.85686	0.0996445
$823$	34.3828	1.19851	0.599255	−	0.800558i	$-0.295464\pi$
$823$	34.3828	1.19851	0.599255	+	0.800558i	$0.295464\pi$
$824$	−4.00723	−0.139598
$825$	25.2658	0.879644
$826$	−31.6428	−1.10099
$827$	29.3712	1.02134	0.510668	−	0.859778i	$-0.329398\pi$
$827$	29.3712	1.02134	0.510668	+	0.859778i	$0.329398\pi$
$828$	6.00000	0.208514
$829$	−38.3902	−1.33335	−0.666674	−	0.745349i	$-0.732283\pi$
$829$	−38.3902	−1.33335	−0.666674	+	0.745349i	$0.732283\pi$
$830$	−18.5544	−0.644033
$831$	−25.9251	−0.899331
$832$	−1.23607	−0.0428529
$833$	−44.5476	−1.54348
$834$	16.6074	0.575067
$835$	−72.2602	−2.50067
$836$	−5.33477	−0.184507
$837$	0	0
$838$	26.3857	0.911479
$839$	27.6547	0.954747	0.477374	−	0.878700i	$-0.341589\pi$
$839$	27.6547	0.954747	0.477374	+	0.878700i	$0.341589\pi$
$840$	−13.0342	−0.449724
$841$	−27.7581	−0.957175
$842$	5.86173	0.202008
$843$	8.69480	0.299465
$844$	−11.3197	−0.389639
$845$	−37.7956	−1.30021
$846$	1.37750	0.0473594
$847$	30.1753	1.03684
$848$	−6.85877	−0.235531
$849$	−25.3411	−0.869704
$850$	30.1408	1.03382
$851$	−6.13404	−0.210272
$852$	15.4071	0.527837
$853$	−13.4460	−0.460381	−0.230191	−	0.973146i	$-0.573935\pi$
$853$	−13.4460	−0.460381	−0.230191	+	0.973146i	$0.573935\pi$
$854$	43.5478	1.49018
$855$	−4.07230	−0.139270
$856$	−12.8327	−0.438614
$857$	−18.9143	−0.646100	−0.323050	−	0.946382i	$-0.604708\pi$
$857$	−18.9143	−0.646100	−0.323050	+	0.946382i	$0.604708\pi$
$858$	5.33477	0.182126
$859$	−52.8713	−1.80395	−0.901973	−	0.431792i	$-0.857881\pi$
$859$	−52.8713	−1.80395	−0.901973	+	0.431792i	$0.857881\pi$
$860$	6.12316	0.208798
$861$	−49.0699	−1.67230
$862$	−6.78839	−0.231213
$863$	21.7499	0.740374	0.370187	−	0.928957i	$-0.379294\pi$
$863$	21.7499	0.740374	0.370187	+	0.928957i	$0.379294\pi$
$864$	−1.00000	−0.0340207
$865$	50.8056	1.72744
$866$	18.5244	0.629486
$867$	9.50868	0.322932
$868$	0	0
$869$	56.7117	1.92381
$870$	−3.67152	−0.124476
$871$	−9.86986	−0.334428
$872$	−3.42218	−0.115890
$873$	18.6504	0.631219
$874$	7.41641	0.250864
$875$	11.1326	0.376349
$876$	−14.2071	−0.480015
$877$	4.12973	0.139451	0.0697255	−	0.997566i	$-0.477788\pi$
$877$	4.12973	0.139451	0.0697255	+	0.997566i	$0.477788\pi$
$878$	−31.2074	−1.05320
$879$	−10.3562	−0.349306
$880$	14.2190	0.479324
$881$	−55.1981	−1.85967	−0.929836	−	0.367975i	$-0.880051\pi$
$881$	−55.1981	−1.85967	−0.929836	+	0.367975i	$0.880051\pi$
$882$	−8.65227	−0.291337
$883$	−3.27693	−0.110277	−0.0551387	−	0.998479i	$-0.517560\pi$
$883$	−3.27693	−0.110277	−0.0551387	+	0.998479i	$0.517560\pi$
$884$	6.36409	0.214048
$885$	26.3502	0.885751
$886$	−23.4192	−0.786782
$887$	−50.5317	−1.69669	−0.848344	−	0.529446i	$-0.822400\pi$
$887$	−50.5317	−1.69669	−0.848344	+	0.529446i	$0.822400\pi$
$888$	1.02234	0.0343075
$889$	−65.6624	−2.20225
$890$	0.207408	0.00695233
$891$	4.31592	0.144589
$892$	−2.43038	−0.0813753
$893$	1.70268	0.0569781
$894$	5.21904	0.174551
$895$	44.9180	1.50144
$896$	−3.95630	−0.132171
$897$	−7.41641	−0.247627
$898$	5.59700	0.186774
$899$	0	0
$900$	5.85410	0.195137
$901$	35.3135	1.17646
$902$	53.5304	1.78237
$903$	7.35304	0.244694
$904$	−6.95320	−0.231260
$905$	−41.8315	−1.39053
$906$	−15.9563	−0.530112
$907$	7.12038	0.236428	0.118214	−	0.992988i	$-0.462283\pi$
$907$	7.12038	0.236428	0.118214	+	0.992988i	$0.462283\pi$
$908$	−0.717714	−0.0238182
$909$	12.2825	0.407386
$910$	16.1112	0.534081
$911$	23.8419	0.789918	0.394959	−	0.918699i	$-0.370759\pi$
$911$	23.8419	0.789918	0.394959	+	0.918699i	$0.370759\pi$
$912$	−1.23607	−0.0409303
$913$	24.3066	0.804430
$914$	30.2879	1.00183
$915$	−36.2639	−1.19885
$916$	−20.1893	−0.667072
$917$	−63.3116	−2.09073
$918$	5.14866	0.169931
$919$	5.04509	0.166422	0.0832111	−	0.996532i	$-0.473482\pi$
$919$	5.04509	0.166422	0.0832111	+	0.996532i	$0.473482\pi$
$920$	−19.7673	−0.651710
$921$	11.9942	0.395223
$922$	−17.1561	−0.565006
$923$	−19.0442	−0.626847
$924$	17.0751	0.561728
$925$	−5.98489	−0.196782
$926$	−7.55377	−0.248232
$927$	4.00723	0.131615
$928$	−1.11442	−0.0365826
$929$	28.3444	0.929948	0.464974	−	0.885324i	$-0.346064\pi$
$929$	28.3444	0.929948	0.464974	+	0.885324i	$0.346064\pi$
$930$	0	0
$931$	−10.6948	−0.350508
$932$	−3.52209	−0.115370
$933$	−18.8141	−0.615947
$934$	−0.890953	−0.0291529
$935$	−73.2090	−2.39419
$936$	1.23607	0.0404021
$937$	7.00292	0.228775	0.114388	−	0.993436i	$-0.463509\pi$
$937$	7.00292	0.228775	0.114388	+	0.993436i	$0.463509\pi$
$938$	−31.5906	−1.03147
$939$	9.34200	0.304865
$940$	−4.53825	−0.148021
$941$	−34.8873	−1.13729	−0.568646	−	0.822582i	$-0.692533\pi$
$941$	−34.8873	−1.13729	−0.568646	+	0.822582i	$0.692533\pi$
$942$	−1.86986	−0.0609234
$943$	−74.4180	−2.42338
$944$	7.99809	0.260316
$945$	13.0342	0.424004
$946$	−8.02143	−0.260799
$947$	5.78326	0.187931	0.0939653	−	0.995575i	$-0.470046\pi$
$947$	5.78326	0.187931	0.0939653	+	0.995575i	$0.470046\pi$
$948$	13.1401	0.426771
$949$	17.5610	0.570054
$950$	7.23607	0.234769
$951$	−19.8475	−0.643600
$952$	20.3696	0.660183
$953$	34.4512	1.11599	0.557993	−	0.829846i	$-0.311572\pi$
$953$	34.4512	1.11599	0.557993	+	0.829846i	$0.311572\pi$
$954$	6.85877	0.222061
$955$	−4.95307	−0.160277
$956$	4.33452	0.140189
$957$	4.80975	0.155477
$958$	29.0644	0.939028
$959$	−11.3026	−0.364980
$960$	3.29456	0.106331
$961$	0	0
$962$	−1.26368	−0.0407428
$963$	12.8327	0.413529
$964$	1.86889	0.0601928
$965$	−88.6047	−2.85228
$966$	−23.7378	−0.763750
$967$	13.5465	0.435628	0.217814	−	0.975990i	$-0.430107\pi$
$967$	13.5465	0.435628	0.217814	+	0.975990i	$0.430107\pi$
$968$	−7.62717	−0.245147
$969$	6.36409	0.204444
$970$	−61.4447	−1.97287
$971$	44.6519	1.43295	0.716473	−	0.697615i	$-0.245755\pi$
$971$	44.6519	1.43295	0.716473	+	0.697615i	$0.245755\pi$
$972$	1.00000	0.0320750
$973$	−65.7037	−2.10636
$974$	18.2901	0.586052
$975$	−7.23607	−0.231740
$976$	−11.0072	−0.352333
$977$	−39.7779	−1.27261	−0.636304	−	0.771439i	$-0.719537\pi$
$977$	−39.7779	−1.27261	−0.636304	+	0.771439i	$0.719537\pi$
$978$	−4.49854	−0.143848
$979$	−0.271708	−0.00868382
$980$	28.5054	0.910572
$981$	3.42218	0.109262
$982$	−29.1074	−0.928854
$983$	43.7565	1.39561	0.697807	−	0.716286i	$-0.254159\pi$
$983$	43.7565	1.39561	0.697807	+	0.716286i	$0.254159\pi$
$984$	12.4030	0.395393
$985$	19.1893	0.611421
$986$	5.73777	0.182728
$987$	−5.44980	−0.173469
$988$	1.52786	0.0486078
$989$	11.1514	0.354594
$990$	−14.2190	−0.451911
$991$	−42.9432	−1.36414	−0.682068	−	0.731289i	$-0.738919\pi$
$991$	−42.9432	−1.36414	−0.682068	+	0.731289i	$0.738919\pi$
$992$	0	0
$993$	−7.06702	−0.224265
$994$	−60.9549	−1.93337
$995$	−13.3906	−0.424511
$996$	5.63184	0.178452
$997$	43.0271	1.36268	0.681341	−	0.731966i	$-0.261397\pi$
$997$	43.0271	1.36268	0.681341	+	0.731966i	$0.261397\pi$
$998$	14.3902	0.455515
$999$	−1.02234	−0.0323454

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5766.2.a.ba.1.4		4
31.7	even	15		186.2.m.d.49.1	yes	8
31.9	even	15		186.2.m.d.19.1	✓	8
31.30	odd	2		5766.2.a.x.1.4		4
93.38	odd	30		558.2.ba.b.235.1		8
93.71	odd	30		558.2.ba.b.19.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
186.2.m.d.19.1	✓	8	31.9	even	15
186.2.m.d.49.1	yes	8	31.7	even	15
558.2.ba.b.19.1		8	93.71	odd	30
558.2.ba.b.235.1		8	93.38	odd	30
5766.2.a.x.1.4		4	31.30	odd	2
5766.2.a.ba.1.4		4	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.29456 q^{5} -1.00000 q^{6} +3.95630 q^{7} -1.00000 q^{8} +1.00000 q^{9} -3.29456 q^{10} +4.31592 q^{11} +1.00000 q^{12} -1.23607 q^{13} -3.95630 q^{14} +3.29456 q^{15} +1.00000 q^{16} -5.14866 q^{17} -1.00000 q^{18} -1.23607 q^{19} +3.29456 q^{20} +3.95630 q^{21} -4.31592 q^{22} +6.00000 q^{23} -1.00000 q^{24} +5.85410 q^{25} +1.23607 q^{26} +1.00000 q^{27} +3.95630 q^{28} +1.11442 q^{29} -3.29456 q^{30} -1.00000 q^{32} +4.31592 q^{33} +5.14866 q^{34} +13.0342 q^{35} +1.00000 q^{36} -1.02234 q^{37} +1.23607 q^{38} -1.23607 q^{39} -3.29456 q^{40} -12.4030 q^{41} -3.95630 q^{42} +1.85857 q^{43} +4.31592 q^{44} +3.29456 q^{45} -6.00000 q^{46} -1.37750 q^{47} +1.00000 q^{48} +8.65227 q^{49} -5.85410 q^{50} -5.14866 q^{51} -1.23607 q^{52} -6.85877 q^{53} -1.00000 q^{54} +14.2190 q^{55} -3.95630 q^{56} -1.23607 q^{57} -1.11442 q^{58} +7.99809 q^{59} +3.29456 q^{60} -11.0072 q^{61} +3.95630 q^{63} +1.00000 q^{64} -4.07230 q^{65} -4.31592 q^{66} +7.98489 q^{67} -5.14866 q^{68} +6.00000 q^{69} -13.0342 q^{70} +15.4071 q^{71} -1.00000 q^{72} -14.2071 q^{73} +1.02234 q^{74} +5.85410 q^{75} -1.23607 q^{76} +17.0751 q^{77} +1.23607 q^{78} +13.1401 q^{79} +3.29456 q^{80} +1.00000 q^{81} +12.4030 q^{82} +5.63184 q^{83} +3.95630 q^{84} -16.9625 q^{85} -1.85857 q^{86} +1.11442 q^{87} -4.31592 q^{88} -0.0629548 q^{89} -3.29456 q^{90} -4.89025 q^{91} +6.00000 q^{92} +1.37750 q^{94} -4.07230 q^{95} -1.00000 q^{96} +18.6504 q^{97} -8.65227 q^{98} +4.31592 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + 4 q^{3} + 4 q^{4} - 4 q^{6} + 7 q^{7} - 4 q^{8} + 4 q^{9} + 9 q^{11} + 4 q^{12} + 4 q^{13} - 7 q^{14} + 4 q^{16} + 6 q^{17} - 4 q^{18} + 4 q^{19} + 7 q^{21} - 9 q^{22} + 24 q^{23} - 4 q^{24}+ \cdots + 9 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 + 4 * q^3 + 4 * q^4 - 4 * q^6 + 7 * q^7 - 4 * q^8 + 4 * q^9 + 9 * q^11 + 4 * q^12 + 4 * q^13 - 7 * q^14 + 4 * q^16 + 6 * q^17 - 4 * q^18 + 4 * q^19 + 7 * q^21 - 9 * q^22 + 24 * q^23 - 4 * q^24 + 10 * q^25 - 4 * q^26 + 4 * q^27 + 7 * q^28 + 15 * q^29 - 4 * q^32 + 9 * q^33 - 6 * q^34 + 15 * q^35 + 4 * q^36 - 8 * q^37 - 4 * q^38 + 4 * q^39 - 12 * q^41 - 7 * q^42 + 4 * q^43 + 9 * q^44 - 24 * q^46 + 4 * q^48 - 7 * q^49 - 10 * q^50 + 6 * q^51 + 4 * q^52 - 3 * q^53 - 4 * q^54 - 15 * q^55 - 7 * q^56 + 4 * q^57 - 15 * q^58 + 3 * q^59 - 14 * q^61 + 7 * q^63 + 4 * q^64 - 9 * q^66 - 2 * q^67 + 6 * q^68 + 24 * q^69 - 15 * q^70 + 30 * q^71 - 4 * q^72 - 26 * q^73 + 8 * q^74 + 10 * q^75 + 4 * q^76 + 12 * q^77 - 4 * q^78 + 10 * q^79 + 4 * q^81 + 12 * q^82 + 6 * q^83 + 7 * q^84 - 30 * q^85 - 4 * q^86 + 15 * q^87 - 9 * q^88 - 6 * q^89 + 2 * q^91 + 24 * q^92 - 4 * q^96 + 4 * q^97 + 7 * q^98 + 9 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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