LMFDB - Embedded newform 5766.2.a.bl.1.8

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

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

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

Embedding invariants

Embedding label			1.8
Root			$1.96157$ 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)

$f(q)$	$=$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +4.37578 q^{5} +1.00000 q^{6} +0.258666 q^{7} -1.00000 q^{8} +1.00000 q^{9} -4.37578 q^{10} +1.21030 q^{11} -1.00000 q^{12} -4.93957 q^{13} -0.258666 q^{14} -4.37578 q^{15} +1.00000 q^{16} -0.541977 q^{17} -1.00000 q^{18} -2.22835 q^{19} +4.37578 q^{20} -0.258666 q^{21} -1.21030 q^{22} -6.97425 q^{23} +1.00000 q^{24} +14.1475 q^{25} +4.93957 q^{26} -1.00000 q^{27} +0.258666 q^{28} -3.41636 q^{29} +4.37578 q^{30} -1.00000 q^{32} -1.21030 q^{33} +0.541977 q^{34} +1.13187 q^{35} +1.00000 q^{36} -9.23446 q^{37} +2.22835 q^{38} +4.93957 q^{39} -4.37578 q^{40} -5.63202 q^{41} +0.258666 q^{42} +11.8771 q^{43} +1.21030 q^{44} +4.37578 q^{45} +6.97425 q^{46} +8.87634 q^{47} -1.00000 q^{48} -6.93309 q^{49} -14.1475 q^{50} +0.541977 q^{51} -4.93957 q^{52} -1.40786 q^{53} +1.00000 q^{54} +5.29599 q^{55} -0.258666 q^{56} +2.22835 q^{57} +3.41636 q^{58} -7.55810 q^{59} -4.37578 q^{60} +3.10514 q^{61} +0.258666 q^{63} +1.00000 q^{64} -21.6145 q^{65} +1.21030 q^{66} -7.93402 q^{67} -0.541977 q^{68} +6.97425 q^{69} -1.13187 q^{70} -16.2386 q^{71} -1.00000 q^{72} -9.94628 q^{73} +9.23446 q^{74} -14.1475 q^{75} -2.22835 q^{76} +0.313063 q^{77} -4.93957 q^{78} +3.96376 q^{79} +4.37578 q^{80} +1.00000 q^{81} +5.63202 q^{82} +6.64345 q^{83} -0.258666 q^{84} -2.37158 q^{85} -11.8771 q^{86} +3.41636 q^{87} -1.21030 q^{88} -13.5478 q^{89} -4.37578 q^{90} -1.27770 q^{91} -6.97425 q^{92} -8.87634 q^{94} -9.75079 q^{95} +1.00000 q^{96} +6.77418 q^{97} +6.93309 q^{98} +1.21030 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} - 8 q^{3} + 8 q^{4} + 8 q^{5} + 8 q^{6} - 8 q^{8} + 8 q^{9} - 8 q^{10} - 8 q^{11} - 8 q^{12} - 8 q^{13} - 8 q^{15} + 8 q^{16} + 8 q^{17} - 8 q^{18} - 8 q^{19} + 8 q^{20} + 8 q^{22} + 8 q^{24}+ \cdots - 8 q^{99}+O(q^{100}) $ 8 * q - 8 * q^2 - 8 * q^3 + 8 * q^4 + 8 * q^5 + 8 * q^6 - 8 * q^8 + 8 * q^9 - 8 * q^10 - 8 * q^11 - 8 * q^12 - 8 * q^13 - 8 * q^15 + 8 * q^16 + 8 * q^17 - 8 * q^18 - 8 * q^19 + 8 * q^20 + 8 * q^22 + 8 * q^24 + 8 * q^26 - 8 * q^27 - 16 * q^29 + 8 * q^30 - 8 * q^32 + 8 * q^33 - 8 * q^34 + 16 * q^35 + 8 * q^36 + 8 * q^38 + 8 * q^39 - 8 * q^40 + 16 * q^41 - 8 * q^44 + 8 * q^45 + 24 * q^47 - 8 * q^48 - 8 * q^49 - 8 * q^51 - 8 * q^52 - 16 * q^53 + 8 * q^54 - 8 * q^55 + 8 * q^57 + 16 * q^58 + 16 * q^59 - 8 * q^60 - 56 * q^61 + 8 * q^64 - 40 * q^65 - 8 * q^66 - 8 * q^67 + 8 * q^68 - 16 * q^70 + 8 * q^71 - 8 * q^72 - 32 * q^73 - 8 * q^76 - 16 * q^77 - 8 * q^78 + 8 * q^79 + 8 * q^80 + 8 * q^81 - 16 * q^82 + 8 * q^83 - 8 * q^85 + 16 * q^87 + 8 * q^88 - 48 * q^89 - 8 * q^90 - 32 * q^91 - 24 * q^94 - 8 * q^95 + 8 * q^96 - 8 * q^97 + 8 * q^98 - 8 * 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
$5$	4.37578	1.95691	0.978455	−	0.206460i	$-0.0661943\pi$
$5$	4.37578	1.95691	0.978455	+	0.206460i	$0.0661943\pi$
$6$	1.00000	0.408248
$7$	0.258666	0.0977666	0.0488833	−	0.998804i	$-0.484434\pi$
$7$	0.258666	0.0977666	0.0488833	+	0.998804i	$0.484434\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−4.37578	−1.38374
$11$	1.21030	0.364918	0.182459	−	0.983213i	$-0.441594\pi$
$11$	1.21030	0.364918	0.182459	+	0.983213i	$0.441594\pi$
$12$	−1.00000	−0.288675
$13$	−4.93957	−1.36999	−0.684995	−	0.728548i	$-0.740196\pi$
$13$	−4.93957	−1.36999	−0.684995	+	0.728548i	$0.740196\pi$
$14$	−0.258666	−0.0691314
$15$	−4.37578	−1.12982
$16$	1.00000	0.250000
$17$	−0.541977	−0.131449	−0.0657244	−	0.997838i	$-0.520936\pi$
$17$	−0.541977	−0.131449	−0.0657244	+	0.997838i	$0.520936\pi$
$18$	−1.00000	−0.235702
$19$	−2.22835	−0.511219	−0.255609	−	0.966780i	$-0.582276\pi$
$19$	−2.22835	−0.511219	−0.255609	+	0.966780i	$0.582276\pi$
$20$	4.37578	0.978455
$21$	−0.258666	−0.0564456
$22$	−1.21030	−0.258036
$23$	−6.97425	−1.45423	−0.727116	−	0.686514i	$-0.759140\pi$
$23$	−6.97425	−1.45423	−0.727116	+	0.686514i	$0.759140\pi$
$24$	1.00000	0.204124
$25$	14.1475	2.82950
$26$	4.93957	0.968729
$27$	−1.00000	−0.192450
$28$	0.258666	0.0488833
$29$	−3.41636	−0.634402	−0.317201	−	0.948358i	$-0.602743\pi$
$29$	−3.41636	−0.634402	−0.317201	+	0.948358i	$0.602743\pi$
$30$	4.37578	0.798905
$31$	0	0
$31$	0	0
$32$	−1.00000	−0.176777
$33$	−1.21030	−0.210686
$34$	0.541977	0.0929483
$35$	1.13187	0.191320
$36$	1.00000	0.166667
$37$	−9.23446	−1.51814	−0.759068	−	0.651012i	$-0.774345\pi$
$37$	−9.23446	−1.51814	−0.759068	+	0.651012i	$0.774345\pi$
$38$	2.22835	0.361486
$39$	4.93957	0.790964
$40$	−4.37578	−0.691872
$41$	−5.63202	−0.879574	−0.439787	−	0.898102i	$-0.644946\pi$
$41$	−5.63202	−0.879574	−0.439787	+	0.898102i	$0.644946\pi$
$42$	0.258666	0.0399130
$43$	11.8771	1.81124	0.905620	−	0.424090i	$-0.139406\pi$
$43$	11.8771	1.81124	0.905620	+	0.424090i	$0.139406\pi$
$44$	1.21030	0.182459
$45$	4.37578	0.652303
$46$	6.97425	1.02830
$47$	8.87634	1.29475	0.647374	−	0.762173i	$-0.275867\pi$
$47$	8.87634	1.29475	0.647374	+	0.762173i	$0.275867\pi$
$48$	−1.00000	−0.144338
$49$	−6.93309	−0.990442
$50$	−14.1475	−2.00076
$51$	0.541977	0.0758920
$52$	−4.93957	−0.684995
$53$	−1.40786	−0.193384	−0.0966921	−	0.995314i	$-0.530826\pi$
$53$	−1.40786	−0.193384	−0.0966921	+	0.995314i	$0.530826\pi$
$54$	1.00000	0.136083
$55$	5.29599	0.714112
$56$	−0.258666	−0.0345657
$57$	2.22835	0.295152
$58$	3.41636	0.448590
$59$	−7.55810	−0.983980	−0.491990	−	0.870601i	$-0.663730\pi$
$59$	−7.55810	−0.983980	−0.491990	+	0.870601i	$0.663730\pi$
$60$	−4.37578	−0.564911
$61$	3.10514	0.397572	0.198786	−	0.980043i	$-0.436300\pi$
$61$	3.10514	0.397572	0.198786	+	0.980043i	$0.436300\pi$
$62$	0	0
$63$	0.258666	0.0325889
$64$	1.00000	0.125000
$65$	−21.6145	−2.68095
$66$	1.21030	0.148977
$67$	−7.93402	−0.969294	−0.484647	−	0.874710i	$-0.661052\pi$
$67$	−7.93402	−0.969294	−0.484647	+	0.874710i	$0.661052\pi$
$68$	−0.541977	−0.0657244
$69$	6.97425	0.839602
$70$	−1.13187	−0.135284
$71$	−16.2386	−1.92717	−0.963585	−	0.267403i	$-0.913835\pi$
$71$	−16.2386	−1.92717	−0.963585	+	0.267403i	$0.913835\pi$
$72$	−1.00000	−0.117851
$73$	−9.94628	−1.16412	−0.582062	−	0.813144i	$-0.697754\pi$
$73$	−9.94628	−1.16412	−0.582062	+	0.813144i	$0.697754\pi$
$74$	9.23446	1.07348
$75$	−14.1475	−1.63361
$76$	−2.22835	−0.255609
$77$	0.313063	0.0356768
$78$	−4.93957	−0.559296
$79$	3.96376	0.445957	0.222979	−	0.974823i	$-0.428422\pi$
$79$	3.96376	0.445957	0.222979	+	0.974823i	$0.428422\pi$
$80$	4.37578	0.489228
$81$	1.00000	0.111111
$82$	5.63202	0.621953
$83$	6.64345	0.729213	0.364607	−	0.931162i	$-0.381203\pi$
$83$	6.64345	0.729213	0.364607	+	0.931162i	$0.381203\pi$
$84$	−0.258666	−0.0282228
$85$	−2.37158	−0.257233
$86$	−11.8771	−1.28074
$87$	3.41636	0.366272
$88$	−1.21030	−0.129018
$89$	−13.5478	−1.43607	−0.718033	−	0.696009i	$-0.754957\pi$
$89$	−13.5478	−1.43607	−0.718033	+	0.696009i	$0.754957\pi$
$90$	−4.37578	−0.461248
$91$	−1.27770	−0.133939
$92$	−6.97425	−0.727116
$93$	0	0
$94$	−8.87634	−0.915524
$95$	−9.75079	−1.00041
$96$	1.00000	0.102062
$97$	6.77418	0.687813	0.343907	−	0.939004i	$-0.388250\pi$
$97$	6.77418	0.687813	0.343907	+	0.939004i	$0.388250\pi$
$98$	6.93309	0.700348
$99$	1.21030	0.121639
$100$	14.1475	1.41475
$101$	−13.3009	−1.32349	−0.661743	−	0.749731i	$-0.730183\pi$
$101$	−13.3009	−1.32349	−0.661743	+	0.749731i	$0.730183\pi$
$102$	−0.541977	−0.0536637
$103$	6.23054	0.613913	0.306957	−	0.951724i	$-0.400689\pi$
$103$	6.23054	0.613913	0.306957	+	0.951724i	$0.400689\pi$
$104$	4.93957	0.484364
$105$	−1.13187	−0.110459
$106$	1.40786	0.136743
$107$	11.2449	1.08708	0.543541	−	0.839383i	$-0.317083\pi$
$107$	11.2449	1.08708	0.543541	+	0.839383i	$0.317083\pi$
$108$	−1.00000	−0.0962250
$109$	−12.3292	−1.18092	−0.590461	−	0.807066i	$-0.701054\pi$
$109$	−12.3292	−1.18092	−0.590461	+	0.807066i	$0.701054\pi$
$110$	−5.29599	−0.504953
$111$	9.23446	0.876496
$112$	0.258666	0.0244416
$113$	−10.5583	−0.993239	−0.496620	−	0.867968i	$-0.665426\pi$
$113$	−10.5583	−0.993239	−0.496620	+	0.867968i	$0.665426\pi$
$114$	−2.22835	−0.208704
$115$	−30.5178	−2.84580
$116$	−3.41636	−0.317201
$117$	−4.93957	−0.456663
$118$	7.55810	0.695779
$119$	−0.140191	−0.0128513
$120$	4.37578	0.399453
$121$	−9.53518	−0.866835
$122$	−3.10514	−0.281126
$123$	5.63202	0.507822
$124$	0	0
$125$	40.0274	3.58016
$126$	−0.258666	−0.0230438
$127$	−4.31499	−0.382893	−0.191447	−	0.981503i	$-0.561318\pi$
$127$	−4.31499	−0.382893	−0.191447	+	0.981503i	$0.561318\pi$
$128$	−1.00000	−0.0883883
$129$	−11.8771	−1.04572
$130$	21.6145	1.89572
$131$	3.11621	0.272264	0.136132	−	0.990691i	$-0.456533\pi$
$131$	3.11621	0.272264	0.136132	+	0.990691i	$0.456533\pi$
$132$	−1.21030	−0.105343
$133$	−0.576399	−0.0499801
$134$	7.93402	0.685395
$135$	−4.37578	−0.376608
$136$	0.541977	0.0464742
$137$	3.19152	0.272670	0.136335	−	0.990663i	$-0.456468\pi$
$137$	3.19152	0.272670	0.136335	+	0.990663i	$0.456468\pi$
$138$	−6.97425	−0.593688
$139$	−21.7020	−1.84074	−0.920368	−	0.391054i	$-0.872111\pi$
$139$	−21.7020	−1.84074	−0.920368	+	0.391054i	$0.872111\pi$
$140$	1.13187	0.0956602
$141$	−8.87634	−0.747523
$142$	16.2386	1.36271
$143$	−5.97834	−0.499934
$144$	1.00000	0.0833333
$145$	−14.9493	−1.24147
$146$	9.94628	0.823160
$147$	6.93309	0.571832
$148$	−9.23446	−0.759068
$149$	−5.90850	−0.484043	−0.242022	−	0.970271i	$-0.577811\pi$
$149$	−5.90850	−0.484043	−0.242022	+	0.970271i	$0.577811\pi$
$150$	14.1475	1.15514
$151$	13.9599	1.13604	0.568019	−	0.823015i	$-0.307710\pi$
$151$	13.9599	1.13604	0.568019	+	0.823015i	$0.307710\pi$
$152$	2.22835	0.180743
$153$	−0.541977	−0.0438163
$154$	−0.313063	−0.0252273
$155$	0	0
$156$	4.93957	0.395482
$157$	−5.27600	−0.421071	−0.210535	−	0.977586i	$-0.567521\pi$
$157$	−5.27600	−0.421071	−0.210535	+	0.977586i	$0.567521\pi$
$158$	−3.96376	−0.315339
$159$	1.40786	0.111650
$160$	−4.37578	−0.345936
$161$	−1.80400	−0.142175
$162$	−1.00000	−0.0785674
$163$	8.82811	0.691471	0.345736	−	0.938332i	$-0.387629\pi$
$163$	8.82811	0.691471	0.345736	+	0.938332i	$0.387629\pi$
$164$	−5.63202	−0.439787
$165$	−5.29599	−0.412293
$166$	−6.64345	−0.515632
$167$	7.28761	0.563933	0.281966	−	0.959424i	$-0.409013\pi$
$167$	7.28761	0.563933	0.281966	+	0.959424i	$0.409013\pi$
$168$	0.258666	0.0199565
$169$	11.3993	0.876871
$170$	2.37158	0.181892
$171$	−2.22835	−0.170406
$172$	11.8771	0.905620
$173$	8.02040	0.609780	0.304890	−	0.952388i	$-0.401380\pi$
$173$	8.02040	0.609780	0.304890	+	0.952388i	$0.401380\pi$
$174$	−3.41636	−0.258994
$175$	3.65947	0.276630
$176$	1.21030	0.0912295
$177$	7.55810	0.568101
$178$	13.5478	1.01545
$179$	20.5972	1.53951	0.769755	−	0.638340i	$-0.220379\pi$
$179$	20.5972	1.53951	0.769755	+	0.638340i	$0.220379\pi$
$180$	4.37578	0.326152
$181$	−7.13983	−0.530699	−0.265350	−	0.964152i	$-0.585487\pi$
$181$	−7.13983	−0.530699	−0.265350	+	0.964152i	$0.585487\pi$
$182$	1.27770	0.0947093
$183$	−3.10514	−0.229538
$184$	6.97425	0.514149
$185$	−40.4080	−2.97085
$186$	0	0
$187$	−0.655953	−0.0479680
$188$	8.87634	0.647374
$189$	−0.258666	−0.0188152
$190$	9.75079	0.707396
$191$	−13.4609	−0.973999	−0.487000	−	0.873402i	$-0.661909\pi$
$191$	−13.4609	−0.973999	−0.487000	+	0.873402i	$0.661909\pi$
$192$	−1.00000	−0.0721688
$193$	−11.2960	−0.813107	−0.406553	−	0.913627i	$-0.633270\pi$
$193$	−11.2960	−0.813107	−0.406553	+	0.913627i	$0.633270\pi$
$194$	−6.77418	−0.486358
$195$	21.6145	1.54785
$196$	−6.93309	−0.495221
$197$	−9.94310	−0.708417	−0.354208	−	0.935167i	$-0.615250\pi$
$197$	−9.94310	−0.708417	−0.354208	+	0.935167i	$0.615250\pi$
$198$	−1.21030	−0.0860120
$199$	11.4488	0.811585	0.405793	−	0.913965i	$-0.366996\pi$
$199$	11.4488	0.811585	0.405793	+	0.913965i	$0.366996\pi$
$200$	−14.1475	−1.00038
$201$	7.93402	0.559622
$202$	13.3009	0.935845
$203$	−0.883696	−0.0620233
$204$	0.541977	0.0379460
$205$	−24.6445	−1.72125
$206$	−6.23054	−0.434102
$207$	−6.97425	−0.484744
$208$	−4.93957	−0.342497
$209$	−2.69697	−0.186553
$210$	1.13187	0.0781062
$211$	8.64021	0.594817	0.297408	−	0.954750i	$-0.403878\pi$
$211$	8.64021	0.594817	0.297408	+	0.954750i	$0.403878\pi$
$212$	−1.40786	−0.0966921
$213$	16.2386	1.11265
$214$	−11.2449	−0.768683
$215$	51.9716	3.54443
$216$	1.00000	0.0680414
$217$	0	0
$218$	12.3292	0.835039
$219$	9.94628	0.672108
$220$	5.29599	0.357056
$221$	2.67713	0.180083
$222$	−9.23446	−0.619776
$223$	−10.2037	−0.683291	−0.341645	−	0.939829i	$-0.610984\pi$
$223$	−10.2037	−0.683291	−0.341645	+	0.939829i	$0.610984\pi$
$224$	−0.258666	−0.0172829
$225$	14.1475	0.943166
$226$	10.5583	0.702326
$227$	20.2391	1.34332	0.671659	−	0.740860i	$-0.265582\pi$
$227$	20.2391	1.34332	0.671659	+	0.740860i	$0.265582\pi$
$228$	2.22835	0.147576
$229$	−8.76358	−0.579114	−0.289557	−	0.957161i	$-0.593508\pi$
$229$	−8.76358	−0.579114	−0.289557	+	0.957161i	$0.593508\pi$
$230$	30.5178	2.01229
$231$	−0.313063	−0.0205980
$232$	3.41636	0.224295
$233$	28.4266	1.86229	0.931144	−	0.364651i	$-0.118812\pi$
$233$	28.4266	1.86229	0.931144	+	0.364651i	$0.118812\pi$
$234$	4.93957	0.322910
$235$	38.8409	2.53370
$236$	−7.55810	−0.491990
$237$	−3.96376	−0.257474
$238$	0.140191	0.00908724
$239$	−6.02792	−0.389914	−0.194957	−	0.980812i	$-0.562457\pi$
$239$	−6.02792	−0.389914	−0.194957	+	0.980812i	$0.562457\pi$
$240$	−4.37578	−0.282456
$241$	12.6739	0.816397	0.408198	−	0.912893i	$-0.366157\pi$
$241$	12.6739	0.816397	0.408198	+	0.912893i	$0.366157\pi$
$242$	9.53518	0.612945
$243$	−1.00000	−0.0641500
$244$	3.10514	0.198786
$245$	−30.3377	−1.93821
$246$	−5.63202	−0.359085
$247$	11.0071	0.700365
$248$	0	0
$249$	−6.64345	−0.421011
$250$	−40.0274	−2.53156
$251$	−21.3335	−1.34656	−0.673278	−	0.739390i	$-0.735114\pi$
$251$	−21.3335	−1.34656	−0.673278	+	0.739390i	$0.735114\pi$
$252$	0.258666	0.0162944
$253$	−8.44091	−0.530676
$254$	4.31499	0.270746
$255$	2.37158	0.148514
$256$	1.00000	0.0625000
$257$	18.7501	1.16960	0.584799	−	0.811178i	$-0.301174\pi$
$257$	18.7501	1.16960	0.584799	+	0.811178i	$0.301174\pi$
$258$	11.8771	0.739436
$259$	−2.38864	−0.148423
$260$	−21.6145	−1.34047
$261$	−3.41636	−0.211467
$262$	−3.11621	−0.192520
$263$	10.1879	0.628214	0.314107	−	0.949388i	$-0.398295\pi$
$263$	10.1879	0.628214	0.314107	+	0.949388i	$0.398295\pi$
$264$	1.21030	0.0744886
$265$	−6.16048	−0.378435
$266$	0.576399	0.0353413
$267$	13.5478	0.829113
$268$	−7.93402	−0.484647
$269$	−14.0860	−0.858840	−0.429420	−	0.903105i	$-0.641282\pi$
$269$	−14.0860	−0.858840	−0.429420	+	0.903105i	$0.641282\pi$
$270$	4.37578	0.266302
$271$	6.79515	0.412776	0.206388	−	0.978470i	$-0.433829\pi$
$271$	6.79515	0.412776	0.206388	+	0.978470i	$0.433829\pi$
$272$	−0.541977	−0.0328622
$273$	1.27770	0.0773298
$274$	−3.19152	−0.192807
$275$	17.1226	1.03253
$276$	6.97425	0.419801
$277$	29.7523	1.78764	0.893820	−	0.448425i	$-0.148015\pi$
$277$	29.7523	1.78764	0.893820	+	0.448425i	$0.148015\pi$
$278$	21.7020	1.30160
$279$	0	0
$280$	−1.13187	−0.0676420
$281$	16.0309	0.956321	0.478161	−	0.878272i	$-0.341304\pi$
$281$	16.0309	0.956321	0.478161	+	0.878272i	$0.341304\pi$
$282$	8.87634	0.528578
$283$	−20.0057	−1.18922	−0.594608	−	0.804016i	$-0.702693\pi$
$283$	−20.0057	−1.18922	−0.594608	+	0.804016i	$0.702693\pi$
$284$	−16.2386	−0.963585
$285$	9.75079	0.577587
$286$	5.97834	0.353507
$287$	−1.45681	−0.0859930
$288$	−1.00000	−0.0589256
$289$	−16.7063	−0.982721
$290$	14.9493	0.877851
$291$	−6.77418	−0.397109
$292$	−9.94628	−0.582062
$293$	−2.09882	−0.122614	−0.0613072	−	0.998119i	$-0.519527\pi$
$293$	−2.09882	−0.122614	−0.0613072	+	0.998119i	$0.519527\pi$
$294$	−6.93309	−0.404346
$295$	−33.0726	−1.92556
$296$	9.23446	0.536742
$297$	−1.21030	−0.0702285
$298$	5.90850	0.342270
$299$	34.4498	1.99228
$300$	−14.1475	−0.816806
$301$	3.07220	0.177079
$302$	−13.9599	−0.803300
$303$	13.3009	0.764114
$304$	−2.22835	−0.127805
$305$	13.5874	0.778013
$306$	0.541977	0.0309828
$307$	−16.7444	−0.955653	−0.477827	−	0.878454i	$-0.658575\pi$
$307$	−16.7444	−0.955653	−0.477827	+	0.878454i	$0.658575\pi$
$308$	0.313063	0.0178384
$309$	−6.23054	−0.354443
$310$	0	0
$311$	12.1126	0.686843	0.343422	−	0.939181i	$-0.388414\pi$
$311$	12.1126	0.686843	0.343422	+	0.939181i	$0.388414\pi$
$312$	−4.93957	−0.279648
$313$	16.7775	0.948319	0.474160	−	0.880439i	$-0.342752\pi$
$313$	16.7775	0.948319	0.474160	+	0.880439i	$0.342752\pi$
$314$	5.27600	0.297742
$315$	1.13187	0.0637735
$316$	3.96376	0.222979
$317$	5.52147	0.310117	0.155058	−	0.987905i	$-0.450443\pi$
$317$	5.52147	0.310117	0.155058	+	0.987905i	$0.450443\pi$
$318$	−1.40786	−0.0789488
$319$	−4.13481	−0.231505
$320$	4.37578	0.244614
$321$	−11.2449	−0.627627
$322$	1.80400	0.100533
$323$	1.20772	0.0671991
$324$	1.00000	0.0555556
$325$	−69.8825	−3.87638
$326$	−8.82811	−0.488944
$327$	12.3292	0.681806
$328$	5.63202	0.310976
$329$	2.29601	0.126583
$330$	5.29599	0.291535
$331$	−4.56512	−0.250922	−0.125461	−	0.992099i	$-0.540041\pi$
$331$	−4.56512	−0.250922	−0.125461	+	0.992099i	$0.540041\pi$
$332$	6.64345	0.364607
$333$	−9.23446	−0.506045
$334$	−7.28761	−0.398761
$335$	−34.7175	−1.89682
$336$	−0.258666	−0.0141114
$337$	4.53915	0.247263	0.123632	−	0.992328i	$-0.460546\pi$
$337$	4.53915	0.247263	0.123632	+	0.992328i	$0.460546\pi$
$338$	−11.3993	−0.620042
$339$	10.5583	0.573447
$340$	−2.37158	−0.128617
$341$	0	0
$342$	2.22835	0.120495
$343$	−3.60402	−0.194599
$344$	−11.8771	−0.640370
$345$	30.5178	1.64302
$346$	−8.02040	−0.431179
$347$	8.07440	0.433457	0.216728	−	0.976232i	$-0.430461\pi$
$347$	8.07440	0.433457	0.216728	+	0.976232i	$0.430461\pi$
$348$	3.41636	0.183136
$349$	−34.4190	−1.84241	−0.921204	−	0.389081i	$-0.872793\pi$
$349$	−34.4190	−1.84241	−0.921204	+	0.389081i	$0.872793\pi$
$350$	−3.65947	−0.195607
$351$	4.93957	0.263655
$352$	−1.21030	−0.0645090
$353$	14.0492	0.747763	0.373882	−	0.927476i	$-0.378027\pi$
$353$	14.0492	0.747763	0.373882	+	0.927476i	$0.378027\pi$
$354$	−7.55810	−0.401708
$355$	−71.0567	−3.77130
$356$	−13.5478	−0.718033
$357$	0.140191	0.00741970
$358$	−20.5972	−1.08860
$359$	−7.81882	−0.412662	−0.206331	−	0.978482i	$-0.566152\pi$
$359$	−7.81882	−0.412662	−0.206331	+	0.978482i	$0.566152\pi$
$360$	−4.37578	−0.230624
$361$	−14.0344	−0.738655
$362$	7.13983	0.375261
$363$	9.53518	0.500467
$364$	−1.27770	−0.0669696
$365$	−43.5228	−2.27809
$366$	3.10514	0.162308
$367$	6.51066	0.339854	0.169927	−	0.985457i	$-0.445647\pi$
$367$	6.51066	0.339854	0.169927	+	0.985457i	$0.445647\pi$
$368$	−6.97425	−0.363558
$369$	−5.63202	−0.293191
$370$	40.4080	2.10071
$371$	−0.364165	−0.0189065
$372$	0	0
$373$	14.2068	0.735603	0.367801	−	0.929904i	$-0.380111\pi$
$373$	14.2068	0.735603	0.367801	+	0.929904i	$0.380111\pi$
$374$	0.655953	0.0339185
$375$	−40.0274	−2.06701
$376$	−8.87634	−0.457762
$377$	16.8753	0.869124
$378$	0.258666	0.0133043
$379$	−26.7742	−1.37530	−0.687648	−	0.726044i	$-0.741357\pi$
$379$	−26.7742	−1.37530	−0.687648	+	0.726044i	$0.741357\pi$
$380$	−9.75079	−0.500205
$381$	4.31499	0.221064
$382$	13.4609	0.688722
$383$	−7.95941	−0.406707	−0.203354	−	0.979105i	$-0.565184\pi$
$383$	−7.95941	−0.406707	−0.203354	+	0.979105i	$0.565184\pi$
$384$	1.00000	0.0510310
$385$	1.36989	0.0698163
$386$	11.2960	0.574953
$387$	11.8771	0.603747
$388$	6.77418	0.343907
$389$	6.71406	0.340416	0.170208	−	0.985408i	$-0.445556\pi$
$389$	6.71406	0.340416	0.170208	+	0.985408i	$0.445556\pi$
$390$	−21.6145	−1.09449
$391$	3.77989	0.191157
$392$	6.93309	0.350174
$393$	−3.11621	−0.157192
$394$	9.94310	0.500926
$395$	17.3445	0.872698
$396$	1.21030	0.0608197
$397$	−13.2791	−0.666459	−0.333229	−	0.942846i	$-0.608138\pi$
$397$	−13.2791	−0.666459	−0.333229	+	0.942846i	$0.608138\pi$
$398$	−11.4488	−0.573877
$399$	0.576399	0.0288560
$400$	14.1475	0.707374
$401$	−29.1276	−1.45456	−0.727281	−	0.686340i	$-0.759216\pi$
$401$	−29.1276	−1.45456	−0.727281	+	0.686340i	$0.759216\pi$
$402$	−7.93402	−0.395713
$403$	0	0
$404$	−13.3009	−0.661743
$405$	4.37578	0.217434
$406$	0.883696	0.0438571
$407$	−11.1764	−0.553995
$408$	−0.541977	−0.0268319
$409$	−1.70322	−0.0842188	−0.0421094	−	0.999113i	$-0.513408\pi$
$409$	−1.70322	−0.0842188	−0.0421094	+	0.999113i	$0.513408\pi$
$410$	24.6445	1.21711
$411$	−3.19152	−0.157426
$412$	6.23054	0.306957
$413$	−1.95502	−0.0962004
$414$	6.97425	0.342766
$415$	29.0703	1.42700
$416$	4.93957	0.242182
$417$	21.7020	1.06275
$418$	2.69697	0.131913
$419$	11.2484	0.549521	0.274761	−	0.961513i	$-0.411401\pi$
$419$	11.2484	0.549521	0.274761	+	0.961513i	$0.411401\pi$
$420$	−1.13187	−0.0552294
$421$	−3.69820	−0.180239	−0.0901197	−	0.995931i	$-0.528725\pi$
$421$	−3.69820	−0.180239	−0.0901197	+	0.995931i	$0.528725\pi$
$422$	−8.64021	−0.420599
$423$	8.87634	0.431582
$424$	1.40786	0.0683716
$425$	−7.66762	−0.371934
$426$	−16.2386	−0.786764
$427$	0.803194	0.0388693
$428$	11.2449	0.543541
$429$	5.97834	0.288637
$430$	−51.9716	−2.50629
$431$	−6.68202	−0.321862	−0.160931	−	0.986966i	$-0.551450\pi$
$431$	−6.68202	−0.321862	−0.160931	+	0.986966i	$0.551450\pi$
$432$	−1.00000	−0.0481125
$433$	7.36940	0.354151	0.177075	−	0.984197i	$-0.443336\pi$
$433$	7.36940	0.354151	0.177075	+	0.984197i	$0.443336\pi$
$434$	0	0
$435$	14.9493	0.716762
$436$	−12.3292	−0.590461
$437$	15.5411	0.743431
$438$	−9.94628	−0.475252
$439$	−8.67078	−0.413834	−0.206917	−	0.978359i	$-0.566343\pi$
$439$	−8.67078	−0.413834	−0.206917	+	0.978359i	$0.566343\pi$
$440$	−5.29599	−0.252477
$441$	−6.93309	−0.330147
$442$	−2.67713	−0.127338
$443$	6.83273	0.324633	0.162316	−	0.986739i	$-0.448104\pi$
$443$	6.83273	0.324633	0.162316	+	0.986739i	$0.448104\pi$
$444$	9.23446	0.438248
$445$	−59.2823	−2.81025
$446$	10.2037	0.483160
$447$	5.90850	0.279463
$448$	0.258666	0.0122208
$449$	7.22758	0.341090	0.170545	−	0.985350i	$-0.445447\pi$
$449$	7.22758	0.341090	0.170545	+	0.985350i	$0.445447\pi$
$450$	−14.1475	−0.666919
$451$	−6.81642	−0.320973
$452$	−10.5583	−0.496620
$453$	−13.9599	−0.655892
$454$	−20.2391	−0.949870
$455$	−5.59093	−0.262107
$456$	−2.22835	−0.104352
$457$	2.39566	0.112064	0.0560322	−	0.998429i	$-0.482155\pi$
$457$	2.39566	0.112064	0.0560322	+	0.998429i	$0.482155\pi$
$458$	8.76358	0.409495
$459$	0.541977	0.0252973
$460$	−30.5178	−1.42290
$461$	4.86262	0.226475	0.113237	−	0.993568i	$-0.463878\pi$
$461$	4.86262	0.226475	0.113237	+	0.993568i	$0.463878\pi$
$462$	0.313063	0.0145650
$463$	−38.6724	−1.79726	−0.898630	−	0.438708i	$-0.855436\pi$
$463$	−38.6724	−1.79726	−0.898630	+	0.438708i	$0.855436\pi$
$464$	−3.41636	−0.158601
$465$	0	0
$466$	−28.4266	−1.31684
$467$	40.4656	1.87253	0.936263	−	0.351299i	$-0.114260\pi$
$467$	40.4656	1.87253	0.936263	+	0.351299i	$0.114260\pi$
$468$	−4.93957	−0.228332
$469$	−2.05226	−0.0947646
$470$	−38.8409	−1.79160
$471$	5.27600	0.243105
$472$	7.55810	0.347890
$473$	14.3748	0.660954
$474$	3.96376	0.182061
$475$	−31.5256	−1.44649
$476$	−0.140191	−0.00642565
$477$	−1.40786	−0.0644614
$478$	6.02792	0.275711
$479$	−28.2118	−1.28903	−0.644515	−	0.764592i	$-0.722941\pi$
$479$	−28.2118	−1.28903	−0.644515	+	0.764592i	$0.722941\pi$
$480$	4.37578	0.199726
$481$	45.6142	2.07983
$482$	−12.6739	−0.577280
$483$	1.80400	0.0820850
$484$	−9.53518	−0.433417
$485$	29.6423	1.34599
$486$	1.00000	0.0453609
$487$	−24.0583	−1.09018	−0.545092	−	0.838376i	$-0.683505\pi$
$487$	−24.0583	−1.09018	−0.545092	+	0.838376i	$0.683505\pi$
$488$	−3.10514	−0.140563
$489$	−8.82811	−0.399221
$490$	30.3377	1.37052
$491$	25.8649	1.16727	0.583634	−	0.812017i	$-0.301630\pi$
$491$	25.8649	1.16727	0.583634	+	0.812017i	$0.301630\pi$
$492$	5.63202	0.253911
$493$	1.85159	0.0833914
$494$	−11.0071	−0.495233
$495$	5.29599	0.238037
$496$	0	0
$497$	−4.20038	−0.188413
$498$	6.64345	0.297700
$499$	−8.44013	−0.377832	−0.188916	−	0.981993i	$-0.560497\pi$
$499$	−8.44013	−0.377832	−0.188916	+	0.981993i	$0.560497\pi$
$500$	40.0274	1.79008
$501$	−7.28761	−0.325587
$502$	21.3335	0.952159
$503$	19.2560	0.858583	0.429291	−	0.903166i	$-0.358763\pi$
$503$	19.2560	0.858583	0.429291	+	0.903166i	$0.358763\pi$
$504$	−0.258666	−0.0115219
$505$	−58.2017	−2.58994
$506$	8.44091	0.375244
$507$	−11.3993	−0.506262
$508$	−4.31499	−0.191447
$509$	−15.4601	−0.685258	−0.342629	−	0.939471i	$-0.611317\pi$
$509$	−15.4601	−0.685258	−0.342629	+	0.939471i	$0.611317\pi$
$510$	−2.37158	−0.105015
$511$	−2.57277	−0.113812
$512$	−1.00000	−0.0441942
$513$	2.22835	0.0983841
$514$	−18.7501	−0.827030
$515$	27.2635	1.20137
$516$	−11.8771	−0.522860
$517$	10.7430	0.472477
$518$	2.38864	0.104951
$519$	−8.02040	−0.352056
$520$	21.6145	0.947858
$521$	23.2076	1.01674	0.508371	−	0.861138i	$-0.330248\pi$
$521$	23.2076	1.01674	0.508371	+	0.861138i	$0.330248\pi$
$522$	3.41636	0.149530
$523$	−5.65617	−0.247327	−0.123664	−	0.992324i	$-0.539464\pi$
$523$	−5.65617	−0.247327	−0.123664	+	0.992324i	$0.539464\pi$
$524$	3.11621	0.136132
$525$	−3.65947	−0.159713
$526$	−10.1879	−0.444215
$527$	0	0
$528$	−1.21030	−0.0526714
$529$	25.6402	1.11479
$530$	6.16048	0.267594
$531$	−7.55810	−0.327993
$532$	−0.576399	−0.0249901
$533$	27.8198	1.20501
$534$	−13.5478	−0.586272
$535$	49.2051	2.12732
$536$	7.93402	0.342697
$537$	−20.5972	−0.888836
$538$	14.0860	0.607292
$539$	−8.39109	−0.361430
$540$	−4.37578	−0.188304
$541$	13.9142	0.598219	0.299109	−	0.954219i	$-0.403310\pi$
$541$	13.9142	0.598219	0.299109	+	0.954219i	$0.403310\pi$
$542$	−6.79515	−0.291877
$543$	7.13983	0.306399
$544$	0.541977	0.0232371
$545$	−53.9499	−2.31096
$546$	−1.27770	−0.0546804
$547$	14.3350	0.612918	0.306459	−	0.951884i	$-0.400856\pi$
$547$	14.3350	0.612918	0.306459	+	0.951884i	$0.400856\pi$
$548$	3.19152	0.136335
$549$	3.10514	0.132524
$550$	−17.1226	−0.730112
$551$	7.61285	0.324318
$552$	−6.97425	−0.296844
$553$	1.02529	0.0435997
$554$	−29.7523	−1.26405
$555$	40.4080	1.71522
$556$	−21.7020	−0.920368
$557$	−24.1589	−1.02364	−0.511822	−	0.859091i	$-0.671029\pi$
$557$	−24.1589	−1.02364	−0.511822	+	0.859091i	$0.671029\pi$
$558$	0	0
$559$	−58.6677	−2.48138
$560$	1.13187	0.0478301
$561$	0.655953	0.0276944
$562$	−16.0309	−0.676221
$563$	−8.70162	−0.366730	−0.183365	−	0.983045i	$-0.558699\pi$
$563$	−8.70162	−0.366730	−0.183365	+	0.983045i	$0.558699\pi$
$564$	−8.87634	−0.373761
$565$	−46.2007	−1.94368
$566$	20.0057	0.840902
$567$	0.258666	0.0108630
$568$	16.2386	0.681357
$569$	−2.18128	−0.0914439	−0.0457219	−	0.998954i	$-0.514559\pi$
$569$	−2.18128	−0.0914439	−0.0457219	+	0.998954i	$0.514559\pi$
$570$	−9.75079	−0.408415
$571$	15.6185	0.653613	0.326806	−	0.945091i	$-0.394027\pi$
$571$	15.6185	0.653613	0.326806	+	0.945091i	$0.394027\pi$
$572$	−5.97834	−0.249967
$573$	13.4609	0.562339
$574$	1.45681	0.0608062
$575$	−98.6682	−4.11475
$576$	1.00000	0.0416667
$577$	−33.1763	−1.38115	−0.690573	−	0.723263i	$-0.742642\pi$
$577$	−33.1763	−1.38115	−0.690573	+	0.723263i	$0.742642\pi$
$578$	16.7063	0.694889
$579$	11.2960	0.469448
$580$	−14.9493	−0.620734
$581$	1.71843	0.0712927
$582$	6.77418	0.280799
$583$	−1.70393	−0.0705694
$584$	9.94628	0.411580
$585$	−21.6145	−0.893649
$586$	2.09882	0.0867015
$587$	−16.7603	−0.691771	−0.345886	−	0.938277i	$-0.612421\pi$
$587$	−16.7603	−0.691771	−0.345886	+	0.938277i	$0.612421\pi$
$588$	6.93309	0.285916
$589$	0	0
$590$	33.0726	1.36158
$591$	9.94310	0.409005
$592$	−9.23446	−0.379534
$593$	14.6352	0.600997	0.300499	−	0.953782i	$-0.402847\pi$
$593$	14.6352	0.600997	0.300499	+	0.953782i	$0.402847\pi$
$594$	1.21030	0.0496591
$595$	−0.613446	−0.0251488
$596$	−5.90850	−0.242022
$597$	−11.4488	−0.468569
$598$	−34.4498	−1.40876
$599$	−26.9900	−1.10278	−0.551391	−	0.834247i	$-0.685903\pi$
$599$	−26.9900	−1.10278	−0.551391	+	0.834247i	$0.685903\pi$
$600$	14.1475	0.577569
$601$	28.5835	1.16595	0.582973	−	0.812492i	$-0.301889\pi$
$601$	28.5835	1.16595	0.582973	+	0.812492i	$0.301889\pi$
$602$	−3.07220	−0.125214
$603$	−7.93402	−0.323098
$604$	13.9599	0.568019
$605$	−41.7239	−1.69632
$606$	−13.3009	−0.540311
$607$	0.594883	0.0241456	0.0120728	−	0.999927i	$-0.496157\pi$
$607$	0.594883	0.0241456	0.0120728	+	0.999927i	$0.496157\pi$
$608$	2.22835	0.0903716
$609$	0.883696	0.0358092
$610$	−13.5874	−0.550138
$611$	−43.8453	−1.77379
$612$	−0.541977	−0.0219081
$613$	−8.50798	−0.343634	−0.171817	−	0.985129i	$-0.554964\pi$
$613$	−8.50798	−0.343634	−0.171817	+	0.985129i	$0.554964\pi$
$614$	16.7444	0.675749
$615$	24.6445	0.993763
$616$	−0.313063	−0.0126136
$617$	−8.64747	−0.348134	−0.174067	−	0.984734i	$-0.555691\pi$
$617$	−8.64747	−0.348134	−0.174067	+	0.984734i	$0.555691\pi$
$618$	6.23054	0.250629
$619$	−11.2620	−0.452658	−0.226329	−	0.974051i	$-0.572672\pi$
$619$	−11.2620	−0.452658	−0.226329	+	0.974051i	$0.572672\pi$
$620$	0	0
$621$	6.97425	0.279867
$622$	−12.1126	−0.485671
$623$	−3.50436	−0.140399
$624$	4.93957	0.197741
$625$	104.414	4.17656
$626$	−16.7775	−0.670563
$627$	2.69697	0.107706
$628$	−5.27600	−0.210535
$629$	5.00487	0.199557
$630$	−1.13187	−0.0450947
$631$	−8.50675	−0.338648	−0.169324	−	0.985560i	$-0.554158\pi$
$631$	−8.50675	−0.338648	−0.169324	+	0.985560i	$0.554158\pi$
$632$	−3.96376	−0.157670
$633$	−8.64021	−0.343417
$634$	−5.52147	−0.219286
$635$	−18.8815	−0.749288
$636$	1.40786	0.0558252
$637$	34.2465	1.35689
$638$	4.13481	0.163699
$639$	−16.2386	−0.642390
$640$	−4.37578	−0.172968
$641$	−6.47546	−0.255765	−0.127883	−	0.991789i	$-0.540818\pi$
$641$	−6.47546	−0.255765	−0.127883	+	0.991789i	$0.540818\pi$
$642$	11.2449	0.443799
$643$	−45.6762	−1.80129	−0.900646	−	0.434553i	$-0.856906\pi$
$643$	−45.6762	−1.80129	−0.900646	+	0.434553i	$0.856906\pi$
$644$	−1.80400	−0.0710877
$645$	−51.9716	−2.04638
$646$	−1.20772	−0.0475169
$647$	18.5488	0.729227	0.364613	−	0.931159i	$-0.381201\pi$
$647$	18.5488	0.729227	0.364613	+	0.931159i	$0.381201\pi$
$648$	−1.00000	−0.0392837
$649$	−9.14754	−0.359072
$650$	69.8825	2.74102
$651$	0	0
$652$	8.82811	0.345736
$653$	−11.7721	−0.460676	−0.230338	−	0.973111i	$-0.573983\pi$
$653$	−11.7721	−0.460676	−0.230338	+	0.973111i	$0.573983\pi$
$654$	−12.3292	−0.482110
$655$	13.6359	0.532797
$656$	−5.63202	−0.219894
$657$	−9.94628	−0.388041
$658$	−2.29601	−0.0895077
$659$	5.36549	0.209010	0.104505	−	0.994524i	$-0.466674\pi$
$659$	5.36549	0.209010	0.104505	+	0.994524i	$0.466674\pi$
$660$	−5.29599	−0.206146
$661$	23.9847	0.932895	0.466447	−	0.884549i	$-0.345534\pi$
$661$	23.9847	0.932895	0.466447	+	0.884549i	$0.345534\pi$
$662$	4.56512	0.177428
$663$	−2.67713	−0.103971
$664$	−6.64345	−0.257816
$665$	−2.52220	−0.0978066
$666$	9.23446	0.357828
$667$	23.8266	0.922568
$668$	7.28761	0.281966
$669$	10.2037	0.394498
$670$	34.7175	1.34126
$671$	3.75814	0.145081
$672$	0.258666	0.00997826
$673$	−45.4554	−1.75218	−0.876088	−	0.482151i	$-0.839856\pi$
$673$	−45.4554	−1.75218	−0.876088	+	0.482151i	$0.839856\pi$
$674$	−4.53915	−0.174842
$675$	−14.1475	−0.544537
$676$	11.3993	0.438436
$677$	−38.9486	−1.49692	−0.748458	−	0.663182i	$-0.769206\pi$
$677$	−38.9486	−1.49692	−0.748458	+	0.663182i	$0.769206\pi$
$678$	−10.5583	−0.405488
$679$	1.75225	0.0672452
$680$	2.37158	0.0909458
$681$	−20.2391	−0.775565
$682$	0	0
$683$	−23.7142	−0.907397	−0.453699	−	0.891155i	$-0.649896\pi$
$683$	−23.7142	−0.907397	−0.453699	+	0.891155i	$0.649896\pi$
$684$	−2.22835	−0.0852032
$685$	13.9654	0.533591
$686$	3.60402	0.137602
$687$	8.76358	0.334352
$688$	11.8771	0.452810
$689$	6.95421	0.264934
$690$	−30.5178	−1.16179
$691$	15.1535	0.576468	0.288234	−	0.957560i	$-0.406932\pi$
$691$	15.1535	0.576468	0.288234	+	0.957560i	$0.406932\pi$
$692$	8.02040	0.304890
$693$	0.313063	0.0118923
$694$	−8.07440	−0.306500
$695$	−94.9631	−3.60215
$696$	−3.41636	−0.129497
$697$	3.05243	0.115619
$698$	34.4190	1.30278
$699$	−28.4266	−1.07519
$700$	3.65947	0.138315
$701$	24.7191	0.933629	0.466815	−	0.884355i	$-0.345402\pi$
$701$	24.7191	0.933629	0.466815	+	0.884355i	$0.345402\pi$
$702$	−4.93957	−0.186432
$703$	20.5776	0.776099
$704$	1.21030	0.0456148
$705$	−38.8409	−1.46283
$706$	−14.0492	−0.528748
$707$	−3.44048	−0.129393
$708$	7.55810	0.284051
$709$	−24.1011	−0.905134	−0.452567	−	0.891730i	$-0.649492\pi$
$709$	−24.1011	−0.905134	−0.452567	+	0.891730i	$0.649492\pi$
$710$	71.0567	2.66671
$711$	3.96376	0.148652
$712$	13.5478	0.507726
$713$	0	0
$714$	−0.140191	−0.00524652
$715$	−26.1599	−0.978326
$716$	20.5972	0.769755
$717$	6.02792	0.225117
$718$	7.81882	0.291796
$719$	−24.2546	−0.904542	−0.452271	−	0.891881i	$-0.649386\pi$
$719$	−24.2546	−0.904542	−0.452271	+	0.891881i	$0.649386\pi$
$720$	4.37578	0.163076
$721$	1.61163	0.0600202
$722$	14.0344	0.522308
$723$	−12.6739	−0.471347
$724$	−7.13983	−0.265350
$725$	−48.3329	−1.79504
$726$	−9.53518	−0.353884
$727$	−22.9799	−0.852277	−0.426138	−	0.904658i	$-0.640126\pi$
$727$	−22.9799	−0.852277	−0.426138	+	0.904658i	$0.640126\pi$
$728$	1.27770	0.0473547
$729$	1.00000	0.0370370
$730$	43.5228	1.61085
$731$	−6.43712	−0.238085
$732$	−3.10514	−0.114769
$733$	−22.2689	−0.822521	−0.411260	−	0.911518i	$-0.634911\pi$
$733$	−22.2689	−0.822521	−0.411260	+	0.911518i	$0.634911\pi$
$734$	−6.51066	−0.240313
$735$	30.3377	1.11902
$736$	6.97425	0.257074
$737$	−9.60251	−0.353713
$738$	5.63202	0.207318
$739$	−5.02347	−0.184792	−0.0923958	−	0.995722i	$-0.529452\pi$
$739$	−5.02347	−0.184792	−0.0923958	+	0.995722i	$0.529452\pi$
$740$	−40.4080	−1.48543
$741$	−11.0071	−0.404356
$742$	0.364165	0.0133689
$743$	34.3780	1.26121	0.630603	−	0.776106i	$-0.282808\pi$
$743$	34.3780	1.26121	0.630603	+	0.776106i	$0.282808\pi$
$744$	0	0
$745$	−25.8543	−0.947229
$746$	−14.2068	−0.520150
$747$	6.64345	0.243071
$748$	−0.655953	−0.0239840
$749$	2.90866	0.106280
$750$	40.0274	1.46159
$751$	−1.52046	−0.0554824	−0.0277412	−	0.999615i	$-0.508831\pi$
$751$	−1.52046	−0.0554824	−0.0277412	+	0.999615i	$0.508831\pi$
$752$	8.87634	0.323687
$753$	21.3335	0.777434
$754$	−16.8753	−0.614564
$755$	61.0854	2.22312
$756$	−0.258666	−0.00940759
$757$	34.8458	1.26649	0.633246	−	0.773951i	$-0.281722\pi$
$757$	34.8458	1.26649	0.633246	+	0.773951i	$0.281722\pi$
$758$	26.7742	0.972482
$759$	8.44091	0.306386
$760$	9.75079	0.353698
$761$	−16.9849	−0.615701	−0.307850	−	0.951435i	$-0.599610\pi$
$761$	−16.9849	−0.615701	−0.307850	+	0.951435i	$0.599610\pi$
$762$	−4.31499	−0.156316
$763$	−3.18914	−0.115455
$764$	−13.4609	−0.487000
$765$	−2.37158	−0.0857445
$766$	7.95941	0.287585
$767$	37.3337	1.34804
$768$	−1.00000	−0.0360844
$769$	32.9565	1.18844	0.594221	−	0.804302i	$-0.297461\pi$
$769$	32.9565	1.18844	0.594221	+	0.804302i	$0.297461\pi$
$770$	−1.36989	−0.0493676
$771$	−18.7501	−0.675267
$772$	−11.2960	−0.406553
$773$	−22.2756	−0.801198	−0.400599	−	0.916253i	$-0.631198\pi$
$773$	−22.2756	−0.801198	−0.400599	+	0.916253i	$0.631198\pi$
$774$	−11.8771	−0.426913
$775$	0	0
$776$	−6.77418	−0.243179
$777$	2.38864	0.0856920
$778$	−6.71406	−0.240711
$779$	12.5501	0.449655
$780$	21.6145	0.773923
$781$	−19.6535	−0.703259
$782$	−3.77989	−0.135169
$783$	3.41636	0.122091
$784$	−6.93309	−0.247610
$785$	−23.0866	−0.823998
$786$	3.11621	0.111151
$787$	22.5624	0.804264	0.402132	−	0.915582i	$-0.368269\pi$
$787$	22.5624	0.804264	0.402132	+	0.915582i	$0.368269\pi$
$788$	−9.94310	−0.354208
$789$	−10.1879	−0.362700
$790$	−17.3445	−0.617091
$791$	−2.73107	−0.0971056
$792$	−1.21030	−0.0430060
$793$	−15.3380	−0.544670
$794$	13.2791	0.471257
$795$	6.16048	0.218490
$796$	11.4488	0.405793
$797$	31.5174	1.11640	0.558201	−	0.829706i	$-0.311492\pi$
$797$	31.5174	1.11640	0.558201	+	0.829706i	$0.311492\pi$
$798$	−0.576399	−0.0204043
$799$	−4.81077	−0.170193
$800$	−14.1475	−0.500189
$801$	−13.5478	−0.478689
$802$	29.1276	1.02853
$803$	−12.0379	−0.424810
$804$	7.93402	0.279811
$805$	−7.89393	−0.278224
$806$	0	0
$807$	14.0860	0.495852
$808$	13.3009	0.467923
$809$	13.3728	0.470164	0.235082	−	0.971976i	$-0.424464\pi$
$809$	13.3728	0.470164	0.235082	+	0.971976i	$0.424464\pi$
$810$	−4.37578	−0.153749
$811$	−15.3421	−0.538734	−0.269367	−	0.963038i	$-0.586814\pi$
$811$	−15.3421	−0.538734	−0.269367	+	0.963038i	$0.586814\pi$
$812$	−0.883696	−0.0310117
$813$	−6.79515	−0.238316
$814$	11.1764	0.391734
$815$	38.6299	1.35315
$816$	0.541977	0.0189730
$817$	−26.4663	−0.925940
$818$	1.70322	0.0595517
$819$	−1.27770	−0.0446464
$820$	−24.6445	−0.860624
$821$	19.5364	0.681824	0.340912	−	0.940095i	$-0.389264\pi$
$821$	19.5364	0.681824	0.340912	+	0.940095i	$0.389264\pi$
$822$	3.19152	0.111317
$823$	33.5864	1.17075	0.585375	−	0.810763i	$-0.300947\pi$
$823$	33.5864	1.17075	0.585375	+	0.810763i	$0.300947\pi$
$824$	−6.23054	−0.217051
$825$	−17.1226	−0.596134
$826$	1.95502	0.0680240
$827$	−48.4432	−1.68453	−0.842267	−	0.539061i	$-0.818779\pi$
$827$	−48.4432	−1.68453	−0.842267	+	0.539061i	$0.818779\pi$
$828$	−6.97425	−0.242372
$829$	35.4361	1.23075	0.615374	−	0.788236i	$-0.289005\pi$
$829$	35.4361	1.23075	0.615374	+	0.788236i	$0.289005\pi$
$830$	−29.0703	−1.00904
$831$	−29.7523	−1.03209
$832$	−4.93957	−0.171249
$833$	3.75758	0.130192
$834$	−21.7020	−0.751477
$835$	31.8890	1.10357
$836$	−2.69697	−0.0932765
$837$	0	0
$838$	−11.2484	−0.388570
$839$	40.0762	1.38358	0.691792	−	0.722097i	$-0.256822\pi$
$839$	40.0762	1.38358	0.691792	+	0.722097i	$0.256822\pi$
$840$	1.13187	0.0390531
$841$	−17.3285	−0.597534
$842$	3.69820	0.127448
$843$	−16.0309	−0.552132
$844$	8.64021	0.297408
$845$	49.8810	1.71596
$846$	−8.87634	−0.305175
$847$	−2.46643	−0.0847475
$848$	−1.40786	−0.0483460
$849$	20.0057	0.686594
$850$	7.66762	0.262997
$851$	64.4034	2.20772
$852$	16.2386	0.556326
$853$	−0.628280	−0.0215119	−0.0107559	−	0.999942i	$-0.503424\pi$
$853$	−0.628280	−0.0215119	−0.0107559	+	0.999942i	$0.503424\pi$
$854$	−0.803194	−0.0274847
$855$	−9.75079	−0.333470
$856$	−11.2449	−0.384342
$857$	−0.474902	−0.0162223	−0.00811116	−	0.999967i	$-0.502582\pi$
$857$	−0.474902	−0.0162223	−0.00811116	+	0.999967i	$0.502582\pi$
$858$	−5.97834	−0.204097
$859$	43.8168	1.49501	0.747504	−	0.664257i	$-0.231252\pi$
$859$	43.8168	1.49501	0.747504	+	0.664257i	$0.231252\pi$
$860$	51.9716	1.77222
$861$	1.45681	0.0496481
$862$	6.68202	0.227591
$863$	8.03984	0.273679	0.136840	−	0.990593i	$-0.456306\pi$
$863$	8.03984	0.273679	0.136840	+	0.990593i	$0.456306\pi$
$864$	1.00000	0.0340207
$865$	35.0955	1.19328
$866$	−7.36940	−0.250422
$867$	16.7063	0.567374
$868$	0	0
$869$	4.79732	0.162738
$870$	−14.9493	−0.506827
$871$	39.1906	1.32792
$872$	12.3292	0.417519
$873$	6.77418	0.229271
$874$	−15.5411	−0.525685
$875$	10.3537	0.350020
$876$	9.94628	0.336054
$877$	−19.1409	−0.646343	−0.323171	−	0.946340i	$-0.604749\pi$
$877$	−19.1409	−0.646343	−0.323171	+	0.946340i	$0.604749\pi$
$878$	8.67078	0.292625
$879$	2.09882	0.0707915
$880$	5.29599	0.178528
$881$	11.5400	0.388794	0.194397	−	0.980923i	$-0.437725\pi$
$881$	11.5400	0.388794	0.194397	+	0.980923i	$0.437725\pi$
$882$	6.93309	0.233449
$883$	45.9535	1.54646	0.773230	−	0.634126i	$-0.218640\pi$
$883$	45.9535	1.54646	0.773230	+	0.634126i	$0.218640\pi$
$884$	2.67713	0.0900417
$885$	33.0726	1.11172
$886$	−6.83273	−0.229550
$887$	37.4044	1.25592	0.627958	−	0.778247i	$-0.283891\pi$
$887$	37.4044	1.25592	0.627958	+	0.778247i	$0.283891\pi$
$888$	−9.23446	−0.309888
$889$	−1.11614	−0.0374342
$890$	59.2823	1.98715
$891$	1.21030	0.0405464
$892$	−10.2037	−0.341645
$893$	−19.7796	−0.661899
$894$	−5.90850	−0.197610
$895$	90.1290	3.01268
$896$	−0.258666	−0.00864143
$897$	−34.4498	−1.15025
$898$	−7.22758	−0.241187
$899$	0	0
$900$	14.1475	0.471583
$901$	0.763027	0.0254201
$902$	6.81642	0.226962
$903$	−3.07220	−0.102236
$904$	10.5583	0.351163
$905$	−31.2424	−1.03853
$906$	13.9599	0.463786
$907$	−35.7629	−1.18749	−0.593744	−	0.804654i	$-0.702351\pi$
$907$	−35.7629	−1.18749	−0.593744	+	0.804654i	$0.702351\pi$
$908$	20.2391	0.671659
$909$	−13.3009	−0.441162
$910$	5.59093	0.185338
$911$	18.2085	0.603274	0.301637	−	0.953423i	$-0.402467\pi$
$911$	18.2085	0.603274	0.301637	+	0.953423i	$0.402467\pi$
$912$	2.22835	0.0737881
$913$	8.04054	0.266103
$914$	−2.39566	−0.0792414
$915$	−13.5874	−0.449186
$916$	−8.76358	−0.289557
$917$	0.806057	0.0266183
$918$	−0.541977	−0.0178879
$919$	−49.5236	−1.63363	−0.816817	−	0.576897i	$-0.804264\pi$
$919$	−49.5236	−1.63363	−0.816817	+	0.576897i	$0.804264\pi$
$920$	30.5178	1.00614
$921$	16.7444	0.551747
$922$	−4.86262	−0.160142
$923$	80.2118	2.64020
$924$	−0.313063	−0.0102990
$925$	−130.644	−4.29556
$926$	38.6724	1.27085
$927$	6.23054	0.204638
$928$	3.41636	0.112148
$929$	40.6031	1.33214	0.666072	−	0.745887i	$-0.267974\pi$
$929$	40.6031	1.33214	0.666072	+	0.745887i	$0.267974\pi$
$930$	0	0
$931$	15.4494	0.506333
$932$	28.4266	0.931144
$933$	−12.1126	−0.396549
$934$	−40.4656	−1.32408
$935$	−2.87031	−0.0938691
$936$	4.93957	0.161455
$937$	−36.2959	−1.18574	−0.592868	−	0.805299i	$-0.702005\pi$
$937$	−36.2959	−1.18574	−0.592868	+	0.805299i	$0.702005\pi$
$938$	2.05226	0.0670087
$939$	−16.7775	−0.547512
$940$	38.8409	1.26685
$941$	−10.6162	−0.346078	−0.173039	−	0.984915i	$-0.555359\pi$
$941$	−10.6162	−0.346078	−0.173039	+	0.984915i	$0.555359\pi$
$942$	−5.27600	−0.171901
$943$	39.2792	1.27911
$944$	−7.55810	−0.245995
$945$	−1.13187	−0.0368196
$946$	−14.3748	−0.467365
$947$	44.4937	1.44585	0.722926	−	0.690926i	$-0.242797\pi$
$947$	44.4937	1.44585	0.722926	+	0.690926i	$0.242797\pi$
$948$	−3.96376	−0.128737
$949$	49.1303	1.59484
$950$	31.5256	1.02282
$951$	−5.52147	−0.179046
$952$	0.140191	0.00454362
$953$	−22.0111	−0.713008	−0.356504	−	0.934294i	$-0.616031\pi$
$953$	−22.0111	−0.713008	−0.356504	+	0.934294i	$0.616031\pi$
$954$	1.40786	0.0455811
$955$	−58.9022	−1.90603
$956$	−6.02792	−0.194957
$957$	4.13481	0.133659
$958$	28.2118	0.911482
$959$	0.825539	0.0266580
$960$	−4.37578	−0.141228
$961$	0	0
$962$	−45.6142	−1.47066
$963$	11.2449	0.362361
$964$	12.6739	0.408198
$965$	−49.4290	−1.59118
$966$	−1.80400	−0.0580428
$967$	−27.9802	−0.899782	−0.449891	−	0.893083i	$-0.648537\pi$
$967$	−27.9802	−0.899782	−0.449891	+	0.893083i	$0.648537\pi$
$968$	9.53518	0.306472
$969$	−1.20772	−0.0387974
$970$	−29.6423	−0.951758
$971$	27.3040	0.876226	0.438113	−	0.898920i	$-0.355647\pi$
$971$	27.3040	0.876226	0.438113	+	0.898920i	$0.355647\pi$
$972$	−1.00000	−0.0320750
$973$	−5.61356	−0.179962
$974$	24.0583	0.770877
$975$	69.8825	2.23803
$976$	3.10514	0.0993930
$977$	−16.1251	−0.515886	−0.257943	−	0.966160i	$-0.583045\pi$
$977$	−16.1251	−0.515886	−0.257943	+	0.966160i	$0.583045\pi$
$978$	8.82811	0.282292
$979$	−16.3969	−0.524047
$980$	−30.3377	−0.969103
$981$	−12.3292	−0.393641
$982$	−25.8649	−0.825383
$983$	−12.6626	−0.403874	−0.201937	−	0.979398i	$-0.564724\pi$
$983$	−12.6626	−0.403874	−0.201937	+	0.979398i	$0.564724\pi$
$984$	−5.63202	−0.179542
$985$	−43.5089	−1.38631
$986$	−1.85159	−0.0589666
$987$	−2.29601	−0.0730827
$988$	11.0071	0.350182
$989$	−82.8339	−2.63396
$990$	−5.29599	−0.168318
$991$	−5.20999	−0.165501	−0.0827504	−	0.996570i	$-0.526370\pi$
$991$	−5.20999	−0.165501	−0.0827504	+	0.996570i	$0.526370\pi$
$992$	0	0
$993$	4.56512	0.144870
$994$	4.20038	0.133228
$995$	50.0976	1.58820
$996$	−6.64345	−0.210506
$997$	−36.6500	−1.16072	−0.580358	−	0.814361i	$-0.697088\pi$
$997$	−36.6500	−1.16072	−0.580358	+	0.814361i	$0.697088\pi$
$998$	8.44013	0.267168
$999$	9.23446	0.292165

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5766.2.a.bl.1.8	✓	8
31.30	odd	2		5766.2.a.bn.1.8	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5766.2.a.bl.1.8	✓	8	1.1	even	1	trivial
5766.2.a.bn.1.8	yes	8	31.30	odd	2

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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +4.37578 q^{5} +1.00000 q^{6} +0.258666 q^{7} -1.00000 q^{8} +1.00000 q^{9} -4.37578 q^{10} +1.21030 q^{11} -1.00000 q^{12} -4.93957 q^{13} -0.258666 q^{14} -4.37578 q^{15} +1.00000 q^{16} -0.541977 q^{17} -1.00000 q^{18} -2.22835 q^{19} +4.37578 q^{20} -0.258666 q^{21} -1.21030 q^{22} -6.97425 q^{23} +1.00000 q^{24} +14.1475 q^{25} +4.93957 q^{26} -1.00000 q^{27} +0.258666 q^{28} -3.41636 q^{29} +4.37578 q^{30} -1.00000 q^{32} -1.21030 q^{33} +0.541977 q^{34} +1.13187 q^{35} +1.00000 q^{36} -9.23446 q^{37} +2.22835 q^{38} +4.93957 q^{39} -4.37578 q^{40} -5.63202 q^{41} +0.258666 q^{42} +11.8771 q^{43} +1.21030 q^{44} +4.37578 q^{45} +6.97425 q^{46} +8.87634 q^{47} -1.00000 q^{48} -6.93309 q^{49} -14.1475 q^{50} +0.541977 q^{51} -4.93957 q^{52} -1.40786 q^{53} +1.00000 q^{54} +5.29599 q^{55} -0.258666 q^{56} +2.22835 q^{57} +3.41636 q^{58} -7.55810 q^{59} -4.37578 q^{60} +3.10514 q^{61} +0.258666 q^{63} +1.00000 q^{64} -21.6145 q^{65} +1.21030 q^{66} -7.93402 q^{67} -0.541977 q^{68} +6.97425 q^{69} -1.13187 q^{70} -16.2386 q^{71} -1.00000 q^{72} -9.94628 q^{73} +9.23446 q^{74} -14.1475 q^{75} -2.22835 q^{76} +0.313063 q^{77} -4.93957 q^{78} +3.96376 q^{79} +4.37578 q^{80} +1.00000 q^{81} +5.63202 q^{82} +6.64345 q^{83} -0.258666 q^{84} -2.37158 q^{85} -11.8771 q^{86} +3.41636 q^{87} -1.21030 q^{88} -13.5478 q^{89} -4.37578 q^{90} -1.27770 q^{91} -6.97425 q^{92} -8.87634 q^{94} -9.75079 q^{95} +1.00000 q^{96} +6.77418 q^{97} +6.93309 q^{98} +1.21030 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} - 8 q^{3} + 8 q^{4} + 8 q^{5} + 8 q^{6} - 8 q^{8} + 8 q^{9} - 8 q^{10} - 8 q^{11} - 8 q^{12} - 8 q^{13} - 8 q^{15} + 8 q^{16} + 8 q^{17} - 8 q^{18} - 8 q^{19} + 8 q^{20} + 8 q^{22} + 8 q^{24}+ \cdots - 8 q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 - 8 * q^3 + 8 * q^4 + 8 * q^5 + 8 * q^6 - 8 * q^8 + 8 * q^9 - 8 * q^10 - 8 * q^11 - 8 * q^12 - 8 * q^13 - 8 * q^15 + 8 * q^16 + 8 * q^17 - 8 * q^18 - 8 * q^19 + 8 * q^20 + 8 * q^22 + 8 * q^24 + 8 * q^26 - 8 * q^27 - 16 * q^29 + 8 * q^30 - 8 * q^32 + 8 * q^33 - 8 * q^34 + 16 * q^35 + 8 * q^36 + 8 * q^38 + 8 * q^39 - 8 * q^40 + 16 * q^41 - 8 * q^44 + 8 * q^45 + 24 * q^47 - 8 * q^48 - 8 * q^49 - 8 * q^51 - 8 * q^52 - 16 * q^53 + 8 * q^54 - 8 * q^55 + 8 * q^57 + 16 * q^58 + 16 * q^59 - 8 * q^60 - 56 * q^61 + 8 * q^64 - 40 * q^65 - 8 * q^66 - 8 * q^67 + 8 * q^68 - 16 * q^70 + 8 * q^71 - 8 * q^72 - 32 * q^73 - 8 * q^76 - 16 * q^77 - 8 * q^78 + 8 * q^79 + 8 * q^80 + 8 * q^81 - 16 * q^82 + 8 * q^83 - 8 * q^85 + 16 * q^87 + 8 * q^88 - 48 * q^89 - 8 * q^90 - 32 * q^91 - 24 * q^94 - 8 * q^95 + 8 * q^96 - 8 * q^97 + 8 * q^98 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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