LMFDB - Embedded newform 5766.2.a.ba.1.3

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			1.3
Root			$-1.95630$ 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)

$f(q)$	$=$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.03615 q^{5} -1.00000 q^{6} +2.20906 q^{7} -1.00000 q^{8} +1.00000 q^{9} -2.03615 q^{10} -3.73968 q^{11} +1.00000 q^{12} +3.23607 q^{13} -2.20906 q^{14} +2.03615 q^{15} +1.00000 q^{16} +2.81795 q^{17} -1.00000 q^{18} +3.23607 q^{19} +2.03615 q^{20} +2.20906 q^{21} +3.73968 q^{22} +6.00000 q^{23} -1.00000 q^{24} -0.854102 q^{25} -3.23607 q^{26} +1.00000 q^{27} +2.20906 q^{28} +1.68408 q^{29} -2.03615 q^{30} -1.00000 q^{32} -3.73968 q^{33} -2.81795 q^{34} +4.49797 q^{35} +1.00000 q^{36} -9.56677 q^{37} -3.23607 q^{38} +3.23607 q^{39} -2.03615 q^{40} +4.84752 q^{41} -2.20906 q^{42} +4.21373 q^{43} -3.73968 q^{44} +2.03615 q^{45} -6.00000 q^{46} +5.44980 q^{47} +1.00000 q^{48} -2.12007 q^{49} +0.854102 q^{50} +2.81795 q^{51} +3.23607 q^{52} +11.3187 q^{53} -1.00000 q^{54} -7.61454 q^{55} -2.20906 q^{56} +3.23607 q^{57} -1.68408 q^{58} +4.79252 q^{59} +2.03615 q^{60} -5.39577 q^{61} +2.20906 q^{63} +1.00000 q^{64} +6.58911 q^{65} +3.73968 q^{66} -6.17100 q^{67} +2.81795 q^{68} +6.00000 q^{69} -4.49797 q^{70} +11.5128 q^{71} -1.00000 q^{72} -9.45426 q^{73} +9.56677 q^{74} -0.854102 q^{75} +3.23607 q^{76} -8.26117 q^{77} -3.23607 q^{78} -17.2461 q^{79} +2.03615 q^{80} +1.00000 q^{81} -4.84752 q^{82} -10.4794 q^{83} +2.20906 q^{84} +5.73777 q^{85} -4.21373 q^{86} +1.68408 q^{87} +3.73968 q^{88} -12.3400 q^{89} -2.03615 q^{90} +7.14866 q^{91} +6.00000 q^{92} -5.44980 q^{94} +6.58911 q^{95} -1.00000 q^{96} +4.67246 q^{97} +2.12007 q^{98} -3.73968 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	2.03615	0.910593	0.455296	−	0.890340i	$-0.349533\pi$
$5$	2.03615	0.910593	0.455296	+	0.890340i	$0.349533\pi$
$6$	−1.00000	−0.408248
$7$	2.20906	0.834945	0.417473	−	0.908690i	$-0.362916\pi$
$7$	2.20906	0.834945	0.417473	+	0.908690i	$0.362916\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−2.03615	−0.643886
$11$	−3.73968	−1.12756	−0.563778	−	0.825926i	$-0.690653\pi$
$11$	−3.73968	−1.12756	−0.563778	+	0.825926i	$0.690653\pi$
$12$	1.00000	0.288675
$13$	3.23607	0.897524	0.448762	−	0.893651i	$-0.351865\pi$
$13$	3.23607	0.897524	0.448762	+	0.893651i	$0.351865\pi$
$14$	−2.20906	−0.590395
$15$	2.03615	0.525731
$16$	1.00000	0.250000
$17$	2.81795	0.683454	0.341727	−	0.939799i	$-0.388988\pi$
$17$	2.81795	0.683454	0.341727	+	0.939799i	$0.388988\pi$
$18$	−1.00000	−0.235702
$19$	3.23607	0.742405	0.371202	−	0.928552i	$-0.378946\pi$
$19$	3.23607	0.742405	0.371202	+	0.928552i	$0.378946\pi$
$20$	2.03615	0.455296
$21$	2.20906	0.482056
$22$	3.73968	0.797303
$23$	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
$25$	−0.854102	−0.170820
$26$	−3.23607	−0.634645
$27$	1.00000	0.192450
$28$	2.20906	0.417473
$29$	1.68408	0.312726	0.156363	−	0.987700i	$-0.450023\pi$
$29$	1.68408	0.312726	0.156363	+	0.987700i	$0.450023\pi$
$30$	−2.03615	−0.371748
$31$	0	0
$31$	0	0
$32$	−1.00000	−0.176777
$33$	−3.73968	−0.650995
$34$	−2.81795	−0.483275
$35$	4.49797	0.760295
$36$	1.00000	0.166667
$37$	−9.56677	−1.57277	−0.786384	−	0.617738i	$-0.788049\pi$
$37$	−9.56677	−1.57277	−0.786384	+	0.617738i	$0.788049\pi$
$38$	−3.23607	−0.524960
$39$	3.23607	0.518186
$40$	−2.03615	−0.321943
$41$	4.84752	0.757056	0.378528	−	0.925590i	$-0.376430\pi$
$41$	4.84752	0.757056	0.378528	+	0.925590i	$0.376430\pi$
$42$	−2.20906	−0.340865
$43$	4.21373	0.642587	0.321294	−	0.946980i	$-0.395882\pi$
$43$	4.21373	0.642587	0.321294	+	0.946980i	$0.395882\pi$
$44$	−3.73968	−0.563778
$45$	2.03615	0.303531
$46$	−6.00000	−0.884652
$47$	5.44980	0.794934	0.397467	−	0.917616i	$-0.369889\pi$
$47$	5.44980	0.794934	0.397467	+	0.917616i	$0.369889\pi$
$48$	1.00000	0.144338
$49$	−2.12007	−0.302867
$50$	0.854102	0.120788
$51$	2.81795	0.394593
$52$	3.23607	0.448762
$53$	11.3187	1.55474	0.777370	−	0.629043i	$-0.216553\pi$
$53$	11.3187	1.55474	0.777370	+	0.629043i	$0.216553\pi$
$54$	−1.00000	−0.136083
$55$	−7.61454	−1.02674
$56$	−2.20906	−0.295198
$57$	3.23607	0.428628
$58$	−1.68408	−0.221130
$59$	4.79252	0.623933	0.311967	−	0.950093i	$-0.399012\pi$
$59$	4.79252	0.623933	0.311967	+	0.950093i	$0.399012\pi$
$60$	2.03615	0.262866
$61$	−5.39577	−0.690858	−0.345429	−	0.938445i	$-0.612267\pi$
$61$	−5.39577	−0.690858	−0.345429	+	0.938445i	$0.612267\pi$
$62$	0	0
$63$	2.20906	0.278315
$64$	1.00000	0.125000
$65$	6.58911	0.817279
$66$	3.73968	0.460323
$67$	−6.17100	−0.753908	−0.376954	−	0.926232i	$-0.623028\pi$
$67$	−6.17100	−0.753908	−0.376954	+	0.926232i	$0.623028\pi$
$68$	2.81795	0.341727
$69$	6.00000	0.722315
$70$	−4.49797	−0.537610
$71$	11.5128	1.36631	0.683156	−	0.730272i	$-0.260607\pi$
$71$	11.5128	1.36631	0.683156	+	0.730272i	$0.260607\pi$
$72$	−1.00000	−0.117851
$73$	−9.45426	−1.10654	−0.553269	−	0.833003i	$-0.686620\pi$
$73$	−9.45426	−1.10654	−0.553269	+	0.833003i	$0.686620\pi$
$74$	9.56677	1.11211
$75$	−0.854102	−0.0986232
$76$	3.23607	0.371202
$77$	−8.26117	−0.941448
$78$	−3.23607	−0.366413
$79$	−17.2461	−1.94033	−0.970166	−	0.242440i	$-0.922052\pi$
$79$	−17.2461	−1.94033	−0.970166	+	0.242440i	$0.922052\pi$
$80$	2.03615	0.227648
$81$	1.00000	0.111111
$82$	−4.84752	−0.535319
$83$	−10.4794	−1.15026	−0.575130	−	0.818062i	$-0.695048\pi$
$83$	−10.4794	−1.15026	−0.575130	+	0.818062i	$0.695048\pi$
$84$	2.20906	0.241028
$85$	5.73777	0.622349
$86$	−4.21373	−0.454378
$87$	1.68408	0.180552
$88$	3.73968	0.398651
$89$	−12.3400	−1.30804	−0.654021	−	0.756476i	$-0.726919\pi$
$89$	−12.3400	−1.30804	−0.654021	+	0.756476i	$0.726919\pi$
$90$	−2.03615	−0.214629
$91$	7.14866	0.749383
$92$	6.00000	0.625543
$93$	0	0
$94$	−5.44980	−0.562103
$95$	6.58911	0.676029
$96$	−1.00000	−0.102062
$97$	4.67246	0.474416	0.237208	−	0.971459i	$-0.423768\pi$
$97$	4.67246	0.474416	0.237208	+	0.971459i	$0.423768\pi$
$98$	2.12007	0.214159
$99$	−3.73968	−0.375852
$100$	−0.854102	−0.0854102
$101$	−5.11718	−0.509179	−0.254589	−	0.967049i	$-0.581940\pi$
$101$	−5.11718	−0.509179	−0.254589	+	0.967049i	$0.581940\pi$
$102$	−2.81795	−0.279019
$103$	−1.60423	−0.158069	−0.0790346	−	0.996872i	$-0.525184\pi$
$103$	−1.60423	−0.158069	−0.0790346	+	0.996872i	$0.525184\pi$
$104$	−3.23607	−0.317323
$105$	4.49797	0.438957
$106$	−11.3187	−1.09937
$107$	12.9217	1.24919	0.624595	−	0.780949i	$-0.285264\pi$
$107$	12.9217	1.24919	0.624595	+	0.780949i	$0.285264\pi$
$108$	1.00000	0.0962250
$109$	13.6837	1.31067	0.655333	−	0.755340i	$-0.272528\pi$
$109$	13.6837	1.31067	0.655333	+	0.755340i	$0.272528\pi$
$110$	7.61454	0.726018
$111$	−9.56677	−0.908038
$112$	2.20906	0.208736
$113$	7.19139	0.676509	0.338254	−	0.941055i	$-0.390164\pi$
$113$	7.19139	0.676509	0.338254	+	0.941055i	$0.390164\pi$
$114$	−3.23607	−0.303086
$115$	12.2169	1.13923
$116$	1.68408	0.156363
$117$	3.23607	0.299175
$118$	−4.79252	−0.441187
$119$	6.22502	0.570647
$120$	−2.03615	−0.185874
$121$	2.98522	0.271383
$122$	5.39577	0.488510
$123$	4.84752	0.437086
$124$	0	0
$125$	−11.9198	−1.06614
$126$	−2.20906	−0.196798
$127$	16.3568	1.45143	0.725715	−	0.687996i	$-0.241509\pi$
$127$	16.3568	1.45143	0.725715	+	0.687996i	$0.241509\pi$
$128$	−1.00000	−0.0883883
$129$	4.21373	0.370998
$130$	−6.58911	−0.577903
$131$	−1.32794	−0.116023	−0.0580115	−	0.998316i	$-0.518476\pi$
$131$	−1.32794	−0.116023	−0.0580115	+	0.998316i	$0.518476\pi$
$132$	−3.73968	−0.325497
$133$	7.14866	0.619867
$134$	6.17100	0.533093
$135$	2.03615	0.175244
$136$	−2.81795	−0.241638
$137$	18.5262	1.58280	0.791398	−	0.611301i	$-0.209353\pi$
$137$	18.5262	1.58280	0.791398	+	0.611301i	$0.209353\pi$
$138$	−6.00000	−0.510754
$139$	−9.27880	−0.787017	−0.393509	−	0.919321i	$-0.628739\pi$
$139$	−9.27880	−0.787017	−0.393509	+	0.919321i	$0.628739\pi$
$140$	4.49797	0.380148
$141$	5.44980	0.458956
$142$	−11.5128	−0.966129
$143$	−12.1019	−1.01201
$144$	1.00000	0.0833333
$145$	3.42903	0.284766
$146$	9.45426	0.782440
$147$	−2.12007	−0.174860
$148$	−9.56677	−0.786384
$149$	16.6145	1.36112	0.680558	−	0.732694i	$-0.261737\pi$
$149$	16.6145	1.36112	0.680558	+	0.732694i	$0.261737\pi$
$150$	0.854102	0.0697371
$151$	14.2091	1.15632	0.578158	−	0.815925i	$-0.303772\pi$
$151$	14.2091	1.15632	0.578158	+	0.815925i	$0.303772\pi$
$152$	−3.23607	−0.262480
$153$	2.81795	0.227818
$154$	8.26117	0.665704
$155$	0	0
$156$	3.23607	0.259093
$157$	11.9698	0.955292	0.477646	−	0.878552i	$-0.341490\pi$
$157$	11.9698	0.955292	0.477646	+	0.878552i	$0.341490\pi$
$158$	17.2461	1.37202
$159$	11.3187	0.897630
$160$	−2.03615	−0.160972
$161$	13.2543	1.04459
$162$	−1.00000	−0.0785674
$163$	17.4549	1.36717	0.683587	−	0.729869i	$-0.260419\pi$
$163$	17.4549	1.36717	0.683587	+	0.729869i	$0.260419\pi$
$164$	4.84752	0.378528
$165$	−7.61454	−0.592791
$166$	10.4794	0.813356
$167$	−3.24500	−0.251106	−0.125553	−	0.992087i	$-0.540070\pi$
$167$	−3.24500	−0.251106	−0.125553	+	0.992087i	$0.540070\pi$
$168$	−2.20906	−0.170432
$169$	−2.52786	−0.194451
$170$	−5.73777	−0.440067
$171$	3.23607	0.247468
$172$	4.21373	0.321294
$173$	−22.8810	−1.73961	−0.869805	−	0.493396i	$-0.835755\pi$
$173$	−22.8810	−1.73961	−0.869805	+	0.493396i	$0.835755\pi$
$174$	−1.68408	−0.127670
$175$	−1.88676	−0.142626
$176$	−3.73968	−0.281889
$177$	4.79252	0.360228
$178$	12.3400	0.924925
$179$	7.67343	0.573539	0.286770	−	0.958000i	$-0.407419\pi$
$179$	7.67343	0.573539	0.286770	+	0.958000i	$0.407419\pi$
$180$	2.03615	0.151765
$181$	1.51893	0.112901	0.0564506	−	0.998405i	$-0.482022\pi$
$181$	1.51893	0.112901	0.0564506	+	0.998405i	$0.482022\pi$
$182$	−7.14866	−0.529894
$183$	−5.39577	−0.398867
$184$	−6.00000	−0.442326
$185$	−19.4794	−1.43215
$186$	0	0
$187$	−10.5383	−0.770633
$188$	5.44980	0.397467
$189$	2.20906	0.160685
$190$	−6.58911	−0.478024
$191$	−19.2303	−1.39146	−0.695728	−	0.718306i	$-0.744918\pi$
$191$	−19.2303	−1.39146	−0.695728	+	0.718306i	$0.744918\pi$
$192$	1.00000	0.0721688
$193$	21.9927	1.58307	0.791534	−	0.611125i	$-0.209283\pi$
$193$	21.9927	1.58307	0.791534	+	0.611125i	$0.209283\pi$
$194$	−4.67246	−0.335463
$195$	6.58911	0.471856
$196$	−2.12007	−0.151433
$197$	−3.81665	−0.271925	−0.135962	−	0.990714i	$-0.543413\pi$
$197$	−3.81665	−0.271925	−0.135962	+	0.990714i	$0.543413\pi$
$198$	3.73968	0.265768
$199$	−23.8400	−1.68997	−0.844985	−	0.534790i	$-0.820391\pi$
$199$	−23.8400	−1.68997	−0.844985	+	0.534790i	$0.820391\pi$
$200$	0.854102	0.0603941
$201$	−6.17100	−0.435269
$202$	5.11718	0.360044
$203$	3.72023	0.261109
$204$	2.81795	0.197296
$205$	9.87027	0.689370
$206$	1.60423	0.111772
$207$	6.00000	0.417029
$208$	3.23607	0.224381
$209$	−12.1019	−0.837103
$210$	−4.49797	−0.310389
$211$	−3.93086	−0.270612	−0.135306	−	0.990804i	$-0.543202\pi$
$211$	−3.93086	−0.270612	−0.135306	+	0.990804i	$0.543202\pi$
$212$	11.3187	0.777370
$213$	11.5128	0.788841
$214$	−12.9217	−0.883311
$215$	8.57977	0.585136
$216$	−1.00000	−0.0680414
$217$	0	0
$218$	−13.6837	−0.926780
$219$	−9.45426	−0.638860
$220$	−7.61454	−0.513372
$221$	9.11909	0.613416
$222$	9.56677	0.642080
$223$	−22.4221	−1.50150	−0.750748	−	0.660588i	$-0.770307\pi$
$223$	−22.4221	−1.50150	−0.750748	+	0.660588i	$0.770307\pi$
$224$	−2.20906	−0.147599
$225$	−0.854102	−0.0569401
$226$	−7.19139	−0.478364
$227$	−25.0625	−1.66346	−0.831728	−	0.555183i	$-0.812648\pi$
$227$	−25.0625	−1.66346	−0.831728	+	0.555183i	$0.812648\pi$
$228$	3.23607	0.214314
$229$	−15.9553	−1.05436	−0.527179	−	0.849755i	$-0.676750\pi$
$229$	−15.9553	−1.05436	−0.527179	+	0.849755i	$0.676750\pi$
$230$	−12.2169	−0.805558
$231$	−8.26117	−0.543545
$232$	−1.68408	−0.110565
$233$	24.6280	1.61344	0.806718	−	0.590937i	$-0.201242\pi$
$233$	24.6280	1.61344	0.806718	+	0.590937i	$0.201242\pi$
$234$	−3.23607	−0.211548
$235$	11.0966	0.723862
$236$	4.79252	0.311967
$237$	−17.2461	−1.12025
$238$	−6.22502	−0.403508
$239$	4.15655	0.268865	0.134432	−	0.990923i	$-0.457079\pi$
$239$	4.15655	0.268865	0.134432	+	0.990923i	$0.457079\pi$
$240$	2.03615	0.131433
$241$	−3.37283	−0.217263	−0.108632	−	0.994082i	$-0.534647\pi$
$241$	−3.37283	−0.217263	−0.108632	+	0.994082i	$0.534647\pi$
$242$	−2.98522	−0.191897
$243$	1.00000	0.0641500
$244$	−5.39577	−0.345429
$245$	−4.31677	−0.275788
$246$	−4.84752	−0.309067
$247$	10.4721	0.666326
$248$	0	0
$249$	−10.4794	−0.664103
$250$	11.9198	0.753875
$251$	9.47660	0.598158	0.299079	−	0.954228i	$-0.403321\pi$
$251$	9.47660	0.598158	0.299079	+	0.954228i	$0.403321\pi$
$252$	2.20906	0.139158
$253$	−22.4381	−1.41067
$254$	−16.3568	−1.02632
$255$	5.73777	0.359313
$256$	1.00000	0.0625000
$257$	8.63184	0.538439	0.269220	−	0.963079i	$-0.413234\pi$
$257$	8.63184	0.538439	0.269220	+	0.963079i	$0.413234\pi$
$258$	−4.21373	−0.262335
$259$	−21.1335	−1.31317
$260$	6.58911	0.408639
$261$	1.68408	0.104242
$262$	1.32794	0.0820406
$263$	−9.77116	−0.602515	−0.301258	−	0.953543i	$-0.597406\pi$
$263$	−9.77116	−0.602515	−0.301258	+	0.953543i	$0.597406\pi$
$264$	3.73968	0.230161
$265$	23.0465	1.41574
$266$	−7.14866	−0.438312
$267$	−12.3400	−0.755198
$268$	−6.17100	−0.376954
$269$	10.7699	0.656649	0.328325	−	0.944565i	$-0.393516\pi$
$269$	10.7699	0.656649	0.328325	+	0.944565i	$0.393516\pi$
$270$	−2.03615	−0.123916
$271$	−14.1446	−0.859225	−0.429613	−	0.903013i	$-0.641350\pi$
$271$	−14.1446	−0.859225	−0.429613	+	0.903013i	$0.641350\pi$
$272$	2.81795	0.170864
$273$	7.14866	0.432656
$274$	−18.5262	−1.11921
$275$	3.19407	0.192610
$276$	6.00000	0.361158
$277$	19.4755	1.17017	0.585086	−	0.810971i	$-0.301061\pi$
$277$	19.4755	1.17017	0.585086	+	0.810971i	$0.301061\pi$
$278$	9.27880	0.556505
$279$	0	0
$280$	−4.49797	−0.268805
$281$	4.86068	0.289964	0.144982	−	0.989434i	$-0.453688\pi$
$281$	4.86068	0.289964	0.144982	+	0.989434i	$0.453688\pi$
$282$	−5.44980	−0.324531
$283$	5.82713	0.346387	0.173194	−	0.984888i	$-0.444591\pi$
$283$	5.82713	0.346387	0.173194	+	0.984888i	$0.444591\pi$
$284$	11.5128	0.683156
$285$	6.58911	0.390305
$286$	12.1019	0.715598
$287$	10.7085	0.632100
$288$	−1.00000	−0.0589256
$289$	−9.05913	−0.532890
$290$	−3.42903	−0.201360
$291$	4.67246	0.273904
$292$	−9.45426	−0.553269
$293$	6.65613	0.388856	0.194428	−	0.980917i	$-0.437715\pi$
$293$	6.65613	0.388856	0.194428	+	0.980917i	$0.437715\pi$
$294$	2.12007	0.123645
$295$	9.75829	0.568149
$296$	9.56677	0.556057
$297$	−3.73968	−0.216998
$298$	−16.6145	−0.962455
$299$	19.4164	1.12288
$300$	−0.854102	−0.0493116
$301$	9.30836	0.536525
$302$	−14.2091	−0.817639
$303$	−5.11718	−0.293974
$304$	3.23607	0.185601
$305$	−10.9866	−0.629090
$306$	−2.81795	−0.161092
$307$	−25.1002	−1.43254	−0.716271	−	0.697822i	$-0.754152\pi$
$307$	−25.1002	−1.43254	−0.716271	+	0.697822i	$0.754152\pi$
$308$	−8.26117	−0.470724
$309$	−1.60423	−0.0912613
$310$	0	0
$311$	−11.0255	−0.625199	−0.312599	−	0.949885i	$-0.601200\pi$
$311$	−11.0255	−0.625199	−0.312599	+	0.949885i	$0.601200\pi$
$312$	−3.23607	−0.183206
$313$	10.4976	0.593361	0.296681	−	0.954977i	$-0.404120\pi$
$313$	10.4976	0.593361	0.296681	+	0.954977i	$0.404120\pi$
$314$	−11.9698	−0.675493
$315$	4.49797	0.253432
$316$	−17.2461	−0.970166
$317$	−21.4030	−1.20211	−0.601056	−	0.799207i	$-0.705253\pi$
$317$	−21.4030	−1.20211	−0.601056	+	0.799207i	$0.705253\pi$
$318$	−11.3187	−0.634720
$319$	−6.29792	−0.352616
$320$	2.03615	0.113824
$321$	12.9217	0.721220
$322$	−13.2543	−0.738636
$323$	9.11909	0.507400
$324$	1.00000	0.0555556
$325$	−2.76393	−0.153315
$326$	−17.4549	−0.966738
$327$	13.6837	0.756713
$328$	−4.84752	−0.267660
$329$	12.0389	0.663726
$330$	7.61454	0.419167
$331$	−32.7003	−1.79737	−0.898686	−	0.438593i	$-0.855477\pi$
$331$	−32.7003	−1.79737	−0.898686	+	0.438593i	$0.855477\pi$
$332$	−10.4794	−0.575130
$333$	−9.56677	−0.524256
$334$	3.24500	0.177559
$335$	−12.5651	−0.686503
$336$	2.20906	0.120514
$337$	−17.9890	−0.979921	−0.489960	−	0.871745i	$-0.662989\pi$
$337$	−17.9890	−0.979921	−0.489960	+	0.871745i	$0.662989\pi$
$338$	2.52786	0.137498
$339$	7.19139	0.390583
$340$	5.73777	0.311174
$341$	0	0
$342$	−3.23607	−0.174987
$343$	−20.1467	−1.08782
$344$	−4.21373	−0.227189
$345$	12.2169	0.657735
$346$	22.8810	1.23009
$347$	24.7050	1.32623	0.663117	−	0.748516i	$-0.269233\pi$
$347$	24.7050	1.32623	0.663117	+	0.748516i	$0.269233\pi$
$348$	1.68408	0.0902761
$349$	34.5406	1.84892	0.924458	−	0.381283i	$-0.124518\pi$
$349$	34.5406	1.84892	0.924458	+	0.381283i	$0.124518\pi$
$350$	1.88676	0.100852
$351$	3.23607	0.172729
$352$	3.73968	0.199326
$353$	24.5891	1.30875	0.654373	−	0.756172i	$-0.272933\pi$
$353$	24.5891	1.30875	0.654373	+	0.756172i	$0.272933\pi$
$354$	−4.79252	−0.254720
$355$	23.4417	1.24415
$356$	−12.3400	−0.654021
$357$	6.22502	0.329463
$358$	−7.67343	−0.405553
$359$	−21.4460	−1.13188	−0.565938	−	0.824448i	$-0.691486\pi$
$359$	−21.4460	−1.13188	−0.565938	+	0.824448i	$0.691486\pi$
$360$	−2.03615	−0.107314
$361$	−8.52786	−0.448835
$362$	−1.51893	−0.0798333
$363$	2.98522	0.156683
$364$	7.14866	0.374692
$365$	−19.2503	−1.00761
$366$	5.39577	0.282042
$367$	−8.78708	−0.458682	−0.229341	−	0.973346i	$-0.573657\pi$
$367$	−8.78708	−0.458682	−0.229341	+	0.973346i	$0.573657\pi$
$368$	6.00000	0.312772
$369$	4.84752	0.252352
$370$	19.4794	1.01268
$371$	25.0036	1.29812
$372$	0	0
$373$	23.0034	1.19107	0.595536	−	0.803329i	$-0.296940\pi$
$373$	23.0034	1.19107	0.595536	+	0.803329i	$0.296940\pi$
$374$	10.5383	0.544920
$375$	−11.9198	−0.615537
$376$	−5.44980	−0.281052
$377$	5.44980	0.280679
$378$	−2.20906	−0.113622
$379$	3.79943	0.195164	0.0975819	−	0.995227i	$-0.468889\pi$
$379$	3.79943	0.195164	0.0975819	+	0.995227i	$0.468889\pi$
$380$	6.58911	0.338014
$381$	16.3568	0.837983
$382$	19.2303	0.983907
$383$	−2.81795	−0.143991	−0.0719954	−	0.997405i	$-0.522937\pi$
$383$	−2.81795	−0.143991	−0.0719954	+	0.997405i	$0.522937\pi$
$384$	−1.00000	−0.0510310
$385$	−16.8210	−0.857276
$386$	−21.9927	−1.11940
$387$	4.21373	0.214196
$388$	4.67246	0.237208
$389$	−6.53956	−0.331569	−0.165784	−	0.986162i	$-0.553016\pi$
$389$	−6.53956	−0.331569	−0.165784	+	0.986162i	$0.553016\pi$
$390$	−6.58911	−0.333653
$391$	16.9077	0.855060
$392$	2.12007	0.107080
$393$	−1.32794	−0.0669859
$394$	3.81665	0.192280
$395$	−35.1155	−1.76685
$396$	−3.73968	−0.187926
$397$	33.9872	1.70577	0.852886	−	0.522098i	$-0.174850\pi$
$397$	33.9872	1.70577	0.852886	+	0.522098i	$0.174850\pi$
$398$	23.8400	1.19499
$399$	7.14866	0.357881
$400$	−0.854102	−0.0427051
$401$	11.5757	0.578063	0.289032	−	0.957320i	$-0.406667\pi$
$401$	11.5757	0.578063	0.289032	+	0.957320i	$0.406667\pi$
$402$	6.17100	0.307781
$403$	0	0
$404$	−5.11718	−0.254589
$405$	2.03615	0.101177
$406$	−3.72023	−0.184632
$407$	35.7767	1.77338
$408$	−2.81795	−0.139510
$409$	11.4016	0.563774	0.281887	−	0.959448i	$-0.409040\pi$
$409$	11.4016	0.563774	0.281887	+	0.959448i	$0.409040\pi$
$410$	−9.87027	−0.487458
$411$	18.5262	0.913828
$412$	−1.60423	−0.0790346
$413$	10.5870	0.520950
$414$	−6.00000	−0.294884
$415$	−21.3375	−1.04742
$416$	−3.23607	−0.158661
$417$	−9.27880	−0.454385
$418$	12.1019	0.591921
$419$	−29.2886	−1.43084	−0.715420	−	0.698694i	$-0.753765\pi$
$419$	−29.2886	−1.43084	−0.715420	+	0.698694i	$0.753765\pi$
$420$	4.49797	0.219478
$421$	10.7508	0.523961	0.261980	−	0.965073i	$-0.415624\pi$
$421$	10.7508	0.523961	0.261980	+	0.965073i	$0.415624\pi$
$422$	3.93086	0.191351
$423$	5.44980	0.264978
$424$	−11.3187	−0.549684
$425$	−2.40682	−0.116748
$426$	−11.5128	−0.557795
$427$	−11.9196	−0.576828
$428$	12.9217	0.624595
$429$	−12.1019	−0.584283
$430$	−8.57977	−0.413753
$431$	2.47791	0.119357	0.0596783	−	0.998218i	$-0.480993\pi$
$431$	2.47791	0.119357	0.0596783	+	0.998218i	$0.480993\pi$
$432$	1.00000	0.0481125
$433$	−16.7647	−0.805662	−0.402831	−	0.915274i	$-0.631974\pi$
$433$	−16.7647	−0.805662	−0.402831	+	0.915274i	$0.631974\pi$
$434$	0	0
$435$	3.42903	0.164410
$436$	13.6837	0.655333
$437$	19.4164	0.928813
$438$	9.45426	0.451742
$439$	5.92185	0.282635	0.141317	−	0.989964i	$-0.454866\pi$
$439$	5.92185	0.282635	0.141317	+	0.989964i	$0.454866\pi$
$440$	7.61454	0.363009
$441$	−2.12007	−0.100956
$442$	−9.11909	−0.433751
$443$	−18.0885	−0.859409	−0.429704	−	0.902970i	$-0.641382\pi$
$443$	−18.0885	−0.859409	−0.429704	+	0.902970i	$0.641382\pi$
$444$	−9.56677	−0.454019
$445$	−25.1262	−1.19109
$446$	22.4221	1.06172
$447$	16.6145	0.785841
$448$	2.20906	0.104368
$449$	−22.8475	−1.07824	−0.539121	−	0.842229i	$-0.681243\pi$
$449$	−22.8475	−1.07824	−0.539121	+	0.842229i	$0.681243\pi$
$450$	0.854102	0.0402628
$451$	−18.1282	−0.853623
$452$	7.19139	0.338254
$453$	14.2091	0.667600
$454$	25.0625	1.17624
$455$	14.5557	0.682383
$456$	−3.23607	−0.151543
$457$	40.3888	1.88931	0.944654	−	0.328069i	$-0.106398\pi$
$457$	40.3888	1.88931	0.944654	+	0.328069i	$0.106398\pi$
$458$	15.9553	0.745543
$459$	2.81795	0.131531
$460$	12.2169	0.569615
$461$	−16.9546	−0.789654	−0.394827	−	0.918755i	$-0.629195\pi$
$461$	−16.9546	−0.789654	−0.394827	+	0.918755i	$0.629195\pi$
$462$	8.26117	0.384344
$463$	−34.9904	−1.62614	−0.813071	−	0.582164i	$-0.802206\pi$
$463$	−34.9904	−1.62614	−0.813071	+	0.582164i	$0.802206\pi$
$464$	1.68408	0.0781814
$465$	0	0
$466$	−24.6280	−1.14087
$467$	41.7085	1.93004	0.965020	−	0.262176i	$-0.0844401\pi$
$467$	41.7085	1.93004	0.965020	+	0.262176i	$0.0844401\pi$
$468$	3.23607	0.149587
$469$	−13.6321	−0.629471
$470$	−11.0966	−0.511847
$471$	11.9698	0.551538
$472$	−4.79252	−0.220594
$473$	−15.7580	−0.724554
$474$	17.2461	0.792138
$475$	−2.76393	−0.126818
$476$	6.22502	0.285323
$477$	11.3187	0.518247
$478$	−4.15655	−0.190116
$479$	1.36434	0.0623382	0.0311691	−	0.999514i	$-0.490077\pi$
$479$	1.36434	0.0623382	0.0311691	+	0.999514i	$0.490077\pi$
$480$	−2.03615	−0.0929370
$481$	−30.9587	−1.41160
$482$	3.37283	0.153628
$483$	13.2543	0.603093
$484$	2.98522	0.135692
$485$	9.51381	0.432000
$486$	−1.00000	−0.0453609
$487$	−7.96832	−0.361079	−0.180539	−	0.983568i	$-0.557784\pi$
$487$	−7.96832	−0.361079	−0.180539	+	0.983568i	$0.557784\pi$
$488$	5.39577	0.244255
$489$	17.4549	0.789338
$490$	4.31677	0.195012
$491$	−7.97068	−0.359712	−0.179856	−	0.983693i	$-0.557563\pi$
$491$	−7.97068	−0.359712	−0.179856	+	0.983693i	$0.557563\pi$
$492$	4.84752	0.218543
$493$	4.74566	0.213734
$494$	−10.4721	−0.471164
$495$	−7.61454	−0.342248
$496$	0	0
$497$	25.4323	1.14080
$498$	10.4794	0.469591
$499$	27.3981	1.22651	0.613254	−	0.789885i	$-0.289860\pi$
$499$	27.3981	1.22651	0.613254	+	0.789885i	$0.289860\pi$
$500$	−11.9198	−0.533070
$501$	−3.24500	−0.144976
$502$	−9.47660	−0.422961
$503$	20.4085	0.909971	0.454985	−	0.890499i	$-0.349644\pi$
$503$	20.4085	0.909971	0.454985	+	0.890499i	$0.349644\pi$
$504$	−2.20906	−0.0983992
$505$	−10.4193	−0.463654
$506$	22.4381	0.997495
$507$	−2.52786	−0.112266
$508$	16.3568	0.725715
$509$	5.55573	0.246253	0.123127	−	0.992391i	$-0.460708\pi$
$509$	5.55573	0.246253	0.123127	+	0.992391i	$0.460708\pi$
$510$	−5.73777	−0.254073
$511$	−20.8850	−0.923898
$512$	−1.00000	−0.0441942
$513$	3.23607	0.142876
$514$	−8.63184	−0.380734
$515$	−3.26644	−0.143937
$516$	4.21373	0.185499
$517$	−20.3805	−0.896333
$518$	21.1335	0.928555
$519$	−22.8810	−1.00436
$520$	−6.58911	−0.288952
$521$	−6.52616	−0.285916	−0.142958	−	0.989729i	$-0.545661\pi$
$521$	−6.52616	−0.285916	−0.142958	+	0.989729i	$0.545661\pi$
$522$	−1.68408	−0.0737102
$523$	−0.748818	−0.0327435	−0.0163718	−	0.999866i	$-0.505212\pi$
$523$	−0.748818	−0.0327435	−0.0163718	+	0.999866i	$0.505212\pi$
$524$	−1.32794	−0.0580115
$525$	−1.88676	−0.0823450
$526$	9.77116	0.426043
$527$	0	0
$528$	−3.73968	−0.162749
$529$	13.0000	0.565217
$530$	−23.0465	−1.00108
$531$	4.79252	0.207978
$532$	7.14866	0.309934
$533$	15.6869	0.679475
$534$	12.3400	0.534006
$535$	26.3105	1.13750
$536$	6.17100	0.266547
$537$	7.67343	0.331133
$538$	−10.7699	−0.464321
$539$	7.92838	0.341499
$540$	2.03615	0.0876219
$541$	29.3888	1.26352	0.631761	−	0.775163i	$-0.282332\pi$
$541$	29.3888	1.26352	0.631761	+	0.775163i	$0.282332\pi$
$542$	14.1446	0.607564
$543$	1.51893	0.0651836
$544$	−2.81795	−0.120819
$545$	27.8621	1.19348
$546$	−7.14866	−0.305934
$547$	−18.1578	−0.776373	−0.388187	−	0.921581i	$-0.626898\pi$
$547$	−18.1578	−0.776373	−0.388187	+	0.921581i	$0.626898\pi$
$548$	18.5262	0.791398
$549$	−5.39577	−0.230286
$550$	−3.19407	−0.136196
$551$	5.44980	0.232169
$552$	−6.00000	−0.255377
$553$	−38.0975	−1.62007
$554$	−19.4755	−0.827437
$555$	−19.4794	−0.826853
$556$	−9.27880	−0.393509
$557$	5.24309	0.222157	0.111078	−	0.993812i	$-0.464570\pi$
$557$	5.24309	0.222157	0.111078	+	0.993812i	$0.464570\pi$
$558$	0	0
$559$	13.6359	0.576737
$560$	4.49797	0.190074
$561$	−10.5383	−0.444925
$562$	−4.86068	−0.205036
$563$	−5.00874	−0.211093	−0.105547	−	0.994414i	$-0.533659\pi$
$563$	−5.00874	−0.211093	−0.105547	+	0.994414i	$0.533659\pi$
$564$	5.44980	0.229478
$565$	14.6427	0.616024
$566$	−5.82713	−0.244933
$567$	2.20906	0.0927717
$568$	−11.5128	−0.483064
$569$	−18.5760	−0.778744	−0.389372	−	0.921081i	$-0.627308\pi$
$569$	−18.5760	−0.778744	−0.389372	+	0.921081i	$0.627308\pi$
$570$	−6.58911	−0.275988
$571$	27.6333	1.15642	0.578209	−	0.815889i	$-0.303752\pi$
$571$	27.6333	1.15642	0.578209	+	0.815889i	$0.303752\pi$
$572$	−12.1019	−0.506004
$573$	−19.2303	−0.803357
$574$	−10.7085	−0.446962
$575$	−5.12461	−0.213711
$576$	1.00000	0.0416667
$577$	42.9277	1.78710	0.893552	−	0.448961i	$-0.148206\pi$
$577$	42.9277	1.78710	0.893552	+	0.448961i	$0.148206\pi$
$578$	9.05913	0.376810
$579$	21.9927	0.913985
$580$	3.42903	0.142383
$581$	−23.1495	−0.960403
$582$	−4.67246	−0.193680
$583$	−42.3283	−1.75306
$584$	9.45426	0.391220
$585$	6.58911	0.272426
$586$	−6.65613	−0.274962
$587$	17.1627	0.708379	0.354190	−	0.935174i	$-0.384757\pi$
$587$	17.1627	0.708379	0.354190	+	0.935174i	$0.384757\pi$
$588$	−2.12007	−0.0874301
$589$	0	0
$590$	−9.75829	−0.401742
$591$	−3.81665	−0.156996
$592$	−9.56677	−0.393192
$593$	12.3319	0.506411	0.253205	−	0.967413i	$-0.418515\pi$
$593$	12.3319	0.506411	0.253205	+	0.967413i	$0.418515\pi$
$594$	3.73968	0.153441
$595$	12.6751	0.519627
$596$	16.6145	0.680558
$597$	−23.8400	−0.975705
$598$	−19.4164	−0.793996
$599$	−12.1408	−0.496058	−0.248029	−	0.968753i	$-0.579783\pi$
$599$	−12.1408	−0.496058	−0.248029	+	0.968753i	$0.579783\pi$
$600$	0.854102	0.0348686
$601$	−37.4721	−1.52852	−0.764260	−	0.644908i	$-0.776896\pi$
$601$	−37.4721	−1.52852	−0.764260	+	0.644908i	$0.776896\pi$
$602$	−9.30836	−0.379381
$603$	−6.17100	−0.251303
$604$	14.2091	0.578158
$605$	6.07834	0.247120
$606$	5.11718	0.207871
$607$	−12.7319	−0.516770	−0.258385	−	0.966042i	$-0.583190\pi$
$607$	−12.7319	−0.516770	−0.258385	+	0.966042i	$0.583190\pi$
$608$	−3.23607	−0.131240
$609$	3.72023	0.150751
$610$	10.9866	0.444834
$611$	17.6359	0.713472
$612$	2.81795	0.113909
$613$	9.66311	0.390290	0.195145	−	0.980774i	$-0.437482\pi$
$613$	9.66311	0.390290	0.195145	+	0.980774i	$0.437482\pi$
$614$	25.1002	1.01296
$615$	9.87027	0.398008
$616$	8.26117	0.332852
$617$	49.1279	1.97781	0.988907	−	0.148539i	$-0.0474571\pi$
$617$	49.1279	1.97781	0.988907	+	0.148539i	$0.0474571\pi$
$618$	1.60423	0.0645315
$619$	−4.07034	−0.163601	−0.0818004	−	0.996649i	$-0.526067\pi$
$619$	−4.07034	−0.163601	−0.0818004	+	0.996649i	$0.526067\pi$
$620$	0	0
$621$	6.00000	0.240772
$622$	11.0255	0.442082
$623$	−27.2599	−1.09214
$624$	3.23607	0.129546
$625$	−20.0000	−0.800000
$626$	−10.4976	−0.419570
$627$	−12.1019	−0.483302
$628$	11.9698	0.477646
$629$	−26.9587	−1.07491
$630$	−4.49797	−0.179203
$631$	45.4017	1.80741	0.903707	−	0.428151i	$-0.140835\pi$
$631$	45.4017	1.80741	0.903707	+	0.428151i	$0.140835\pi$
$632$	17.2461	0.686011
$633$	−3.93086	−0.156238
$634$	21.4030	0.850022
$635$	33.3048	1.32166
$636$	11.3187	0.448815
$637$	−6.86068	−0.271830
$638$	6.29792	0.249337
$639$	11.5128	0.455437
$640$	−2.03615	−0.0804858
$641$	0.998546	0.0394402	0.0197201	−	0.999806i	$-0.493722\pi$
$641$	0.998546	0.0394402	0.0197201	+	0.999806i	$0.493722\pi$
$642$	−12.9217	−0.509980
$643$	22.3754	0.882399	0.441200	−	0.897409i	$-0.354553\pi$
$643$	22.3754	0.882399	0.441200	+	0.897409i	$0.354553\pi$
$644$	13.2543	0.522294
$645$	8.57977	0.337828
$646$	−9.11909	−0.358786
$647$	22.2760	0.875761	0.437880	−	0.899033i	$-0.355729\pi$
$647$	22.2760	0.875761	0.437880	+	0.899033i	$0.355729\pi$
$648$	−1.00000	−0.0392837
$649$	−17.9225	−0.703520
$650$	2.76393	0.108410
$651$	0	0
$652$	17.4549	0.683587
$653$	4.48863	0.175654	0.0878269	−	0.996136i	$-0.472008\pi$
$653$	4.48863	0.175654	0.0878269	+	0.996136i	$0.472008\pi$
$654$	−13.6837	−0.535077
$655$	−2.70389	−0.105650
$656$	4.84752	0.189264
$657$	−9.45426	−0.368846
$658$	−12.0389	−0.469326
$659$	27.4646	1.06987	0.534934	−	0.844894i	$-0.320336\pi$
$659$	27.4646	1.06987	0.534934	+	0.844894i	$0.320336\pi$
$660$	−7.61454	−0.296396
$661$	19.5189	0.759198	0.379599	−	0.925151i	$-0.376062\pi$
$661$	19.5189	0.759198	0.379599	+	0.925151i	$0.376062\pi$
$662$	32.7003	1.27093
$663$	9.11909	0.354156
$664$	10.4794	0.406678
$665$	14.5557	0.564447
$666$	9.56677	0.370705
$667$	10.1045	0.391247
$668$	−3.24500	−0.125553
$669$	−22.4221	−0.866889
$670$	12.5651	0.485431
$671$	20.1785	0.778981
$672$	−2.20906	−0.0852162
$673$	−23.3333	−0.899431	−0.449716	−	0.893172i	$-0.648475\pi$
$673$	−23.3333	−0.899431	−0.449716	+	0.893172i	$0.648475\pi$
$674$	17.9890	0.692909
$675$	−0.854102	−0.0328744
$676$	−2.52786	−0.0972255
$677$	−7.56291	−0.290666	−0.145333	−	0.989383i	$-0.546425\pi$
$677$	−7.56291	−0.290666	−0.145333	+	0.989383i	$0.546425\pi$
$678$	−7.19139	−0.276184
$679$	10.3217	0.396111
$680$	−5.73777	−0.220033
$681$	−25.0625	−0.960397
$682$	0	0
$683$	−25.5985	−0.979498	−0.489749	−	0.871864i	$-0.662912\pi$
$683$	−25.5985	−0.979498	−0.489749	+	0.871864i	$0.662912\pi$
$684$	3.23607	0.123734
$685$	37.7220	1.44128
$686$	20.1467	0.769206
$687$	−15.9553	−0.608733
$688$	4.21373	0.160647
$689$	36.6280	1.39542
$690$	−12.2169	−0.465089
$691$	−38.6425	−1.47003	−0.735015	−	0.678051i	$-0.762825\pi$
$691$	−38.6425	−1.47003	−0.735015	+	0.678051i	$0.762825\pi$
$692$	−22.8810	−0.869805
$693$	−8.26117	−0.313816
$694$	−24.7050	−0.937788
$695$	−18.8930	−0.716652
$696$	−1.68408	−0.0638349
$697$	13.6601	0.517413
$698$	−34.5406	−1.30738
$699$	24.6280	0.931517
$700$	−1.88676	−0.0713128
$701$	−17.9198	−0.676822	−0.338411	−	0.940998i	$-0.609889\pi$
$701$	−17.9198	−0.676822	−0.338411	+	0.940998i	$0.609889\pi$
$702$	−3.23607	−0.122138
$703$	−30.9587	−1.16763
$704$	−3.73968	−0.140945
$705$	11.0966	0.417922
$706$	−24.5891	−0.925423
$707$	−11.3041	−0.425136
$708$	4.79252	0.180114
$709$	−29.6053	−1.11185	−0.555925	−	0.831233i	$-0.687636\pi$
$709$	−29.6053	−1.11185	−0.555925	+	0.831233i	$0.687636\pi$
$710$	−23.4417	−0.879750
$711$	−17.2461	−0.646778
$712$	12.3400	0.462463
$713$	0	0
$714$	−6.22502	−0.232966
$715$	−24.6412	−0.921528
$716$	7.67343	0.286770
$717$	4.15655	0.155229
$718$	21.4460	0.800357
$719$	30.3188	1.13070	0.565349	−	0.824852i	$-0.308741\pi$
$719$	30.3188	1.13070	0.565349	+	0.824852i	$0.308741\pi$
$720$	2.03615	0.0758827
$721$	−3.54383	−0.131979
$722$	8.52786	0.317374
$723$	−3.37283	−0.125437
$724$	1.51893	0.0564506
$725$	−1.43838	−0.0534199
$726$	−2.98522	−0.110792
$727$	−11.2147	−0.415931	−0.207966	−	0.978136i	$-0.566684\pi$
$727$	−11.2147	−0.415931	−0.207966	+	0.978136i	$0.566684\pi$
$728$	−7.14866	−0.264947
$729$	1.00000	0.0370370
$730$	19.2503	0.712485
$731$	11.8741	0.439179
$732$	−5.39577	−0.199434
$733$	−46.6751	−1.72398	−0.861991	−	0.506923i	$-0.830783\pi$
$733$	−46.6751	−1.72398	−0.861991	+	0.506923i	$0.830783\pi$
$734$	8.78708	0.324337
$735$	−4.31677	−0.159226
$736$	−6.00000	−0.221163
$737$	23.0776	0.850073
$738$	−4.84752	−0.178440
$739$	−0.697157	−0.0256453	−0.0128227	−	0.999918i	$-0.504082\pi$
$739$	−0.697157	−0.0256453	−0.0128227	+	0.999918i	$0.504082\pi$
$740$	−19.4794	−0.716076
$741$	10.4721	0.384704
$742$	−25.0036	−0.917911
$743$	−22.1610	−0.813008	−0.406504	−	0.913649i	$-0.633252\pi$
$743$	−22.1610	−0.813008	−0.406504	+	0.913649i	$0.633252\pi$
$744$	0	0
$745$	33.8297	1.23942
$746$	−23.0034	−0.842215
$747$	−10.4794	−0.383420
$748$	−10.5383	−0.385317
$749$	28.5448	1.04301
$750$	11.9198	0.435250
$751$	40.0793	1.46251	0.731257	−	0.682102i	$-0.238934\pi$
$751$	40.0793	1.46251	0.731257	+	0.682102i	$0.238934\pi$
$752$	5.44980	0.198734
$753$	9.47660	0.345347
$754$	−5.44980	−0.198470
$755$	28.9317	1.05293
$756$	2.20906	0.0803426
$757$	−20.0615	−0.729147	−0.364574	−	0.931175i	$-0.618785\pi$
$757$	−20.0615	−0.729147	−0.364574	+	0.931175i	$0.618785\pi$
$758$	−3.79943	−0.138002
$759$	−22.4381	−0.814451
$760$	−6.58911	−0.239012
$761$	−15.8812	−0.575691	−0.287846	−	0.957677i	$-0.592939\pi$
$761$	−15.8812	−0.575691	−0.287846	+	0.957677i	$0.592939\pi$
$762$	−16.3568	−0.592544
$763$	30.2282	1.09433
$764$	−19.2303	−0.695728
$765$	5.73777	0.207450
$766$	2.81795	0.101817
$767$	15.5089	0.559995
$768$	1.00000	0.0360844
$769$	−15.5129	−0.559410	−0.279705	−	0.960086i	$-0.590237\pi$
$769$	−15.5129	−0.559410	−0.279705	+	0.960086i	$0.590237\pi$
$770$	16.8210	0.606185
$771$	8.63184	0.310868
$772$	21.9927	0.791534
$773$	−4.91706	−0.176854	−0.0884271	−	0.996083i	$-0.528184\pi$
$773$	−4.91706	−0.176854	−0.0884271	+	0.996083i	$0.528184\pi$
$774$	−4.21373	−0.151459
$775$	0	0
$776$	−4.67246	−0.167731
$777$	−21.1335	−0.758162
$778$	6.53956	0.234454
$779$	15.6869	0.562042
$780$	6.58911	0.235928
$781$	−43.0540	−1.54059
$782$	−16.9077	−0.604619
$783$	1.68408	0.0601841
$784$	−2.12007	−0.0757167
$785$	24.3722	0.869882
$786$	1.32794	0.0473662
$787$	16.6159	0.592294	0.296147	−	0.955142i	$-0.404298\pi$
$787$	16.6159	0.592294	0.296147	+	0.955142i	$0.404298\pi$
$788$	−3.81665	−0.135962
$789$	−9.77116	−0.347862
$790$	35.1155	1.24935
$791$	15.8862	0.564848
$792$	3.73968	0.132884
$793$	−17.4611	−0.620061
$794$	−33.9872	−1.20616
$795$	23.0465	0.817375
$796$	−23.8400	−0.844985
$797$	−44.2038	−1.56578	−0.782890	−	0.622161i	$-0.786255\pi$
$797$	−44.2038	−1.56578	−0.782890	+	0.622161i	$0.786255\pi$
$798$	−7.14866	−0.253060
$799$	15.3573	0.543301
$800$	0.854102	0.0301971
$801$	−12.3400	−0.436014
$802$	−11.5757	−0.408752
$803$	35.3559	1.24768
$804$	−6.17100	−0.217634
$805$	26.9878	0.951195
$806$	0	0
$807$	10.7699	0.379117
$808$	5.11718	0.180022
$809$	−43.2171	−1.51943	−0.759717	−	0.650254i	$-0.774662\pi$
$809$	−43.2171	−1.51943	−0.759717	+	0.650254i	$0.774662\pi$
$810$	−2.03615	−0.0715429
$811$	−5.47123	−0.192121	−0.0960604	−	0.995376i	$-0.530624\pi$
$811$	−5.47123	−0.192121	−0.0960604	+	0.995376i	$0.530624\pi$
$812$	3.72023	0.130554
$813$	−14.1446	−0.496074
$814$	−35.7767	−1.25397
$815$	35.5408	1.24494
$816$	2.81795	0.0986481
$817$	13.6359	0.477060
$818$	−11.4016	−0.398648
$819$	7.14866	0.249794
$820$	9.87027	0.344685
$821$	24.0469	0.839241	0.419621	−	0.907700i	$-0.362163\pi$
$821$	24.0469	0.839241	0.419621	+	0.907700i	$0.362163\pi$
$822$	−18.5262	−0.646174
$823$	18.7385	0.653183	0.326592	−	0.945166i	$-0.394100\pi$
$823$	18.7385	0.653183	0.326592	+	0.945166i	$0.394100\pi$
$824$	1.60423	0.0558859
$825$	3.19407	0.111203
$826$	−10.5870	−0.368367
$827$	37.7526	1.31279	0.656394	−	0.754419i	$-0.272081\pi$
$827$	37.7526	1.31279	0.656394	+	0.754419i	$0.272081\pi$
$828$	6.00000	0.208514
$829$	3.39813	0.118022	0.0590110	−	0.998257i	$-0.481205\pi$
$829$	3.39813	0.118022	0.0590110	+	0.998257i	$0.481205\pi$
$830$	21.3375	0.740637
$831$	19.4755	0.675599
$832$	3.23607	0.112190
$833$	−5.97425	−0.206996
$834$	9.27880	0.321298
$835$	−6.60730	−0.228655
$836$	−12.1019	−0.418552
$837$	0	0
$838$	29.2886	1.01176
$839$	−54.9417	−1.89680	−0.948400	−	0.317077i	$-0.897299\pi$
$839$	−54.9417	−1.89680	−0.948400	+	0.317077i	$0.897299\pi$
$840$	−4.49797	−0.155195
$841$	−26.1639	−0.902203
$842$	−10.7508	−0.370496
$843$	4.86068	0.167411
$844$	−3.93086	−0.135306
$845$	−5.14710	−0.177066
$846$	−5.44980	−0.187368
$847$	6.59451	0.226590
$848$	11.3187	0.388685
$849$	5.82713	0.199987
$850$	2.40682	0.0825533
$851$	−57.4006	−1.96767
$852$	11.5128	0.394420
$853$	10.4539	0.357933	0.178967	−	0.983855i	$-0.442725\pi$
$853$	10.4539	0.357933	0.178967	+	0.983855i	$0.442725\pi$
$854$	11.9196	0.407879
$855$	6.58911	0.225343
$856$	−12.9217	−0.441656
$857$	−39.1580	−1.33761	−0.668806	−	0.743437i	$-0.733194\pi$
$857$	−39.1580	−1.33761	−0.668806	+	0.743437i	$0.733194\pi$
$858$	12.1019	0.413151
$859$	−20.2654	−0.691446	−0.345723	−	0.938337i	$-0.612366\pi$
$859$	−20.2654	−0.691446	−0.345723	+	0.938337i	$0.612366\pi$
$860$	8.57977	0.292568
$861$	10.7085	0.364943
$862$	−2.47791	−0.0843979
$863$	10.4255	0.354888	0.177444	−	0.984131i	$-0.443217\pi$
$863$	10.4255	0.354888	0.177444	+	0.984131i	$0.443217\pi$
$864$	−1.00000	−0.0340207
$865$	−46.5891	−1.58408
$866$	16.7647	0.569689
$867$	−9.05913	−0.307664
$868$	0	0
$869$	64.4947	2.18783
$870$	−3.42903	−0.116255
$871$	−19.9698	−0.676650
$872$	−13.6837	−0.463390
$873$	4.67246	0.158139
$874$	−19.4164	−0.656770
$875$	−26.3316	−0.890169
$876$	−9.45426	−0.319430
$877$	35.0950	1.18508	0.592538	−	0.805543i	$-0.298126\pi$
$877$	35.0950	1.18508	0.592538	+	0.805543i	$0.298126\pi$
$878$	−5.92185	−0.199853
$879$	6.65613	0.224506
$880$	−7.61454	−0.256686
$881$	45.3634	1.52833	0.764166	−	0.645019i	$-0.223151\pi$
$881$	45.3634	1.52833	0.764166	+	0.645019i	$0.223151\pi$
$882$	2.12007	0.0713864
$883$	−9.48252	−0.319112	−0.159556	−	0.987189i	$-0.551006\pi$
$883$	−9.48252	−0.319112	−0.159556	+	0.987189i	$0.551006\pi$
$884$	9.11909	0.306708
$885$	9.75829	0.328021
$886$	18.0885	0.607694
$887$	−6.38814	−0.214493	−0.107246	−	0.994232i	$-0.534203\pi$
$887$	−6.38814	−0.214493	−0.107246	+	0.994232i	$0.534203\pi$
$888$	9.56677	0.321040
$889$	36.1331	1.21186
$890$	25.1262	0.842231
$891$	−3.73968	−0.125284
$892$	−22.4221	−0.750748
$893$	17.6359	0.590163
$894$	−16.6145	−0.555673
$895$	15.6242	0.522261
$896$	−2.20906	−0.0737994
$897$	19.4164	0.648295
$898$	22.8475	0.762432
$899$	0	0
$900$	−0.854102	−0.0284701
$901$	31.8955	1.06259
$902$	18.1282	0.603603
$903$	9.30836	0.309763
$904$	−7.19139	−0.239182
$905$	3.09277	0.102807
$906$	−14.2091	−0.472064
$907$	1.52525	0.0506451	0.0253226	−	0.999679i	$-0.491939\pi$
$907$	1.52525	0.0506451	0.0253226	+	0.999679i	$0.491939\pi$
$908$	−25.0625	−0.831728
$909$	−5.11718	−0.169726
$910$	−14.5557	−0.482518
$911$	−59.7073	−1.97819	−0.989095	−	0.147276i	$-0.952949\pi$
$911$	−59.7073	−1.97819	−0.989095	+	0.147276i	$0.952949\pi$
$912$	3.23607	0.107157
$913$	39.1895	1.29698
$914$	−40.3888	−1.33594
$915$	−10.9866	−0.363206
$916$	−15.9553	−0.527179
$917$	−2.93350	−0.0968728
$918$	−2.81795	−0.0930063
$919$	−18.9313	−0.624485	−0.312243	−	0.950002i	$-0.601080\pi$
$919$	−18.9313	−0.624485	−0.312243	+	0.950002i	$0.601080\pi$
$920$	−12.2169	−0.402779
$921$	−25.1002	−0.827078
$922$	16.9546	0.558370
$923$	37.2560	1.22630
$924$	−8.26117	−0.271773
$925$	8.17100	0.268661
$926$	34.9904	1.14986
$927$	−1.60423	−0.0526897
$928$	−1.68408	−0.0552826
$929$	19.1180	0.627242	0.313621	−	0.949548i	$-0.398458\pi$
$929$	19.1180	0.627242	0.313621	+	0.949548i	$0.398458\pi$
$930$	0	0
$931$	−6.86068	−0.224850
$932$	24.6280	0.806718
$933$	−11.0255	−0.360959
$934$	−41.7085	−1.36474
$935$	−21.4574	−0.701733
$936$	−3.23607	−0.105774
$937$	−55.6822	−1.81906	−0.909529	−	0.415641i	$-0.863557\pi$
$937$	−55.6822	−1.81906	−0.909529	+	0.415641i	$0.863557\pi$
$938$	13.6321	0.445103
$939$	10.4976	0.342577
$940$	11.0966	0.361931
$941$	1.44315	0.0470452	0.0235226	−	0.999723i	$-0.492512\pi$
$941$	1.44315	0.0470452	0.0235226	+	0.999723i	$0.492512\pi$
$942$	−11.9698	−0.389996
$943$	29.0851	0.947142
$944$	4.79252	0.155983
$945$	4.49797	0.146319
$946$	15.7580	0.512337
$947$	−32.9694	−1.07136	−0.535680	−	0.844421i	$-0.679945\pi$
$947$	−32.9694	−1.07136	−0.535680	+	0.844421i	$0.679945\pi$
$948$	−17.2461	−0.560126
$949$	−30.5946	−0.993144
$950$	2.76393	0.0896738
$951$	−21.4030	−0.694040
$952$	−6.22502	−0.201754
$953$	−25.7433	−0.833907	−0.416954	−	0.908928i	$-0.636902\pi$
$953$	−25.7433	−0.833907	−0.416954	+	0.908928i	$0.636902\pi$
$954$	−11.3187	−0.366456
$955$	−39.1557	−1.26705
$956$	4.15655	0.134432
$957$	−6.29792	−0.203583
$958$	−1.36434	−0.0440798
$959$	40.9253	1.32155
$960$	2.03615	0.0657164
$961$	0	0
$962$	30.9587	0.998149
$963$	12.9217	0.416397
$964$	−3.37283	−0.108632
$965$	44.7804	1.44153
$966$	−13.2543	−0.426451
$967$	−23.3862	−0.752049	−0.376024	−	0.926610i	$-0.622709\pi$
$967$	−23.3862	−0.752049	−0.376024	+	0.926610i	$0.622709\pi$
$968$	−2.98522	−0.0959485
$969$	9.11909	0.292947
$970$	−9.51381	−0.305470
$971$	15.4458	0.495679	0.247840	−	0.968801i	$-0.420279\pi$
$971$	15.4458	0.495679	0.247840	+	0.968801i	$0.420279\pi$
$972$	1.00000	0.0320750
$973$	−20.4974	−0.657116
$974$	7.96832	0.255321
$975$	−2.76393	−0.0885167
$976$	−5.39577	−0.172714
$977$	40.3620	1.29129	0.645647	−	0.763636i	$-0.276588\pi$
$977$	40.3620	1.29129	0.645647	+	0.763636i	$0.276588\pi$
$978$	−17.4549	−0.558146
$979$	46.1478	1.47489
$980$	−4.31677	−0.137894
$981$	13.6837	0.436888
$982$	7.97068	0.254355
$983$	−12.6040	−0.402004	−0.201002	−	0.979591i	$-0.564420\pi$
$983$	−12.6040	−0.402004	−0.201002	+	0.979591i	$0.564420\pi$
$984$	−4.84752	−0.154533
$985$	−7.77126	−0.247613
$986$	−4.74566	−0.151133
$987$	12.0389	0.383203
$988$	10.4721	0.333163
$989$	25.2824	0.803932
$990$	7.61454	0.242006
$991$	−3.96872	−0.126070	−0.0630352	−	0.998011i	$-0.520078\pi$
$991$	−3.96872	−0.126070	−0.0630352	+	0.998011i	$0.520078\pi$
$992$	0	0
$993$	−32.7003	−1.03771
$994$	−25.4323	−0.806664
$995$	−48.5417	−1.53888
$996$	−10.4794	−0.332051
$997$	−58.1122	−1.84043	−0.920217	−	0.391409i	$-0.871988\pi$
$997$	−58.1122	−1.84043	−0.920217	+	0.391409i	$0.871988\pi$
$998$	−27.3981	−0.867273
$999$	−9.56677	−0.302679

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5766.2.a.ba.1.3		4
31.10	even	15		186.2.m.d.7.1	✓	8
31.28	even	15		186.2.m.d.133.1	yes	8
31.30	odd	2		5766.2.a.x.1.3		4
93.41	odd	30		558.2.ba.b.379.1		8
93.59	odd	30		558.2.ba.b.505.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
186.2.m.d.7.1	✓	8	31.10	even	15
186.2.m.d.133.1	yes	8	31.28	even	15
558.2.ba.b.379.1		8	93.41	odd	30
558.2.ba.b.505.1		8	93.59	odd	30
5766.2.a.x.1.3		4	31.30	odd	2
5766.2.a.ba.1.3		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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.03615 q^{5} -1.00000 q^{6} +2.20906 q^{7} -1.00000 q^{8} +1.00000 q^{9} -2.03615 q^{10} -3.73968 q^{11} +1.00000 q^{12} +3.23607 q^{13} -2.20906 q^{14} +2.03615 q^{15} +1.00000 q^{16} +2.81795 q^{17} -1.00000 q^{18} +3.23607 q^{19} +2.03615 q^{20} +2.20906 q^{21} +3.73968 q^{22} +6.00000 q^{23} -1.00000 q^{24} -0.854102 q^{25} -3.23607 q^{26} +1.00000 q^{27} +2.20906 q^{28} +1.68408 q^{29} -2.03615 q^{30} -1.00000 q^{32} -3.73968 q^{33} -2.81795 q^{34} +4.49797 q^{35} +1.00000 q^{36} -9.56677 q^{37} -3.23607 q^{38} +3.23607 q^{39} -2.03615 q^{40} +4.84752 q^{41} -2.20906 q^{42} +4.21373 q^{43} -3.73968 q^{44} +2.03615 q^{45} -6.00000 q^{46} +5.44980 q^{47} +1.00000 q^{48} -2.12007 q^{49} +0.854102 q^{50} +2.81795 q^{51} +3.23607 q^{52} +11.3187 q^{53} -1.00000 q^{54} -7.61454 q^{55} -2.20906 q^{56} +3.23607 q^{57} -1.68408 q^{58} +4.79252 q^{59} +2.03615 q^{60} -5.39577 q^{61} +2.20906 q^{63} +1.00000 q^{64} +6.58911 q^{65} +3.73968 q^{66} -6.17100 q^{67} +2.81795 q^{68} +6.00000 q^{69} -4.49797 q^{70} +11.5128 q^{71} -1.00000 q^{72} -9.45426 q^{73} +9.56677 q^{74} -0.854102 q^{75} +3.23607 q^{76} -8.26117 q^{77} -3.23607 q^{78} -17.2461 q^{79} +2.03615 q^{80} +1.00000 q^{81} -4.84752 q^{82} -10.4794 q^{83} +2.20906 q^{84} +5.73777 q^{85} -4.21373 q^{86} +1.68408 q^{87} +3.73968 q^{88} -12.3400 q^{89} -2.03615 q^{90} +7.14866 q^{91} +6.00000 q^{92} -5.44980 q^{94} +6.58911 q^{95} -1.00000 q^{96} +4.67246 q^{97} +2.12007 q^{98} -3.73968 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + 4 q^{3} + 4 q^{4} - 4 q^{6} + 7 q^{7} - 4 q^{8} + 4 q^{9} + 9 q^{11} + 4 q^{12} + 4 q^{13} - 7 q^{14} + 4 q^{16} + 6 q^{17} - 4 q^{18} + 4 q^{19} + 7 q^{21} - 9 q^{22} + 24 q^{23} - 4 q^{24}+ \cdots + 9 q^{99}+O(q^{100}) \) 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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