LMFDB - Embedded newform 4767.2.a.g.1.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [4767,2,Mod(1,4767)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(4767, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("4767.1"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 4767 = 3 \cdot 7 \cdot 227 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4767.a (trivial)

Newform invariants

comment:select newform

sage:traces = [35,7] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	yes
Analytic conductor:	$38.0646866435$
Analytic rank:	$0$
Dimension:	$35$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	4767.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.838531 q^{2} -1.00000 q^{3} -1.29687 q^{4} +2.50382 q^{5} +0.838531 q^{6} +1.00000 q^{7} +2.76452 q^{8} +1.00000 q^{9} -2.09953 q^{10} +3.24608 q^{11} +1.29687 q^{12} -4.49895 q^{13} -0.838531 q^{14} -2.50382 q^{15} +0.275589 q^{16} +1.27013 q^{17} -0.838531 q^{18} +1.07809 q^{19} -3.24712 q^{20} -1.00000 q^{21} -2.72194 q^{22} +6.45124 q^{23} -2.76452 q^{24} +1.26912 q^{25} +3.77251 q^{26} -1.00000 q^{27} -1.29687 q^{28} +3.44101 q^{29} +2.09953 q^{30} +4.40845 q^{31} -5.76014 q^{32} -3.24608 q^{33} -1.06505 q^{34} +2.50382 q^{35} -1.29687 q^{36} -5.86942 q^{37} -0.904012 q^{38} +4.49895 q^{39} +6.92187 q^{40} +1.72646 q^{41} +0.838531 q^{42} -0.382430 q^{43} -4.20972 q^{44} +2.50382 q^{45} -5.40957 q^{46} +7.24286 q^{47} -0.275589 q^{48} +1.00000 q^{49} -1.06419 q^{50} -1.27013 q^{51} +5.83453 q^{52} +11.6136 q^{53} +0.838531 q^{54} +8.12760 q^{55} +2.76452 q^{56} -1.07809 q^{57} -2.88540 q^{58} +7.27550 q^{59} +3.24712 q^{60} -9.56962 q^{61} -3.69663 q^{62} +1.00000 q^{63} +4.27888 q^{64} -11.2646 q^{65} +2.72194 q^{66} +6.04440 q^{67} -1.64719 q^{68} -6.45124 q^{69} -2.09953 q^{70} +3.52800 q^{71} +2.76452 q^{72} -13.3275 q^{73} +4.92169 q^{74} -1.26912 q^{75} -1.39814 q^{76} +3.24608 q^{77} -3.77251 q^{78} -10.8213 q^{79} +0.690025 q^{80} +1.00000 q^{81} -1.44769 q^{82} +12.5432 q^{83} +1.29687 q^{84} +3.18018 q^{85} +0.320680 q^{86} -3.44101 q^{87} +8.97386 q^{88} -5.44594 q^{89} -2.09953 q^{90} -4.49895 q^{91} -8.36639 q^{92} -4.40845 q^{93} -6.07337 q^{94} +2.69934 q^{95} +5.76014 q^{96} -4.98685 q^{97} -0.838531 q^{98} +3.24608 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 35 q + 7 q^{2} - 35 q^{3} + 45 q^{4} - 4 q^{5} - 7 q^{6} + 35 q^{7} + 21 q^{8} + 35 q^{9} + 11 q^{10} - 3 q^{11} - 45 q^{12} + 19 q^{13} + 7 q^{14} + 4 q^{15} + 65 q^{16} + 20 q^{17} + 7 q^{18} + 9 q^{19}+ \cdots - 3 q^{99}+O(q^{100}) $ 35 * q + 7 * q^2 - 35 * q^3 + 45 * q^4 - 4 * q^5 - 7 * q^6 + 35 * q^7 + 21 * q^8 + 35 * q^9 + 11 * q^10 - 3 * q^11 - 45 * q^12 + 19 * q^13 + 7 * q^14 + 4 * q^15 + 65 * q^16 + 20 * q^17 + 7 * q^18 + 9 * q^19 - 7 * q^20 - 35 * q^21 + 33 * q^22 + 17 * q^23 - 21 * q^24 + 67 * q^25 - 6 * q^26 - 35 * q^27 + 45 * q^28 + 17 * q^29 - 11 * q^30 + 5 * q^31 + 54 * q^32 + 3 * q^33 + 22 * q^34 - 4 * q^35 + 45 * q^36 + 35 * q^37 - 19 * q^38 - 19 * q^39 + 34 * q^40 + 18 * q^41 - 7 * q^42 + 33 * q^43 - 7 * q^44 - 4 * q^45 + 38 * q^46 - 13 * q^47 - 65 * q^48 + 35 * q^49 + 28 * q^50 - 20 * q^51 + 37 * q^52 + 36 * q^53 - 7 * q^54 + 21 * q^55 + 21 * q^56 - 9 * q^57 + 42 * q^58 - 54 * q^59 + 7 * q^60 + 35 * q^61 - 28 * q^62 + 35 * q^63 + 105 * q^64 + 27 * q^65 - 33 * q^66 + 37 * q^67 + 25 * q^68 - 17 * q^69 + 11 * q^70 + 44 * q^71 + 21 * q^72 + 59 * q^73 - 17 * q^74 - 67 * q^75 + 23 * q^76 - 3 * q^77 + 6 * q^78 + 77 * q^79 - 26 * q^80 + 35 * q^81 + 4 * q^82 - 41 * q^83 - 45 * q^84 + 39 * q^85 + 42 * q^86 - 17 * q^87 + 34 * q^88 - 9 * q^89 + 11 * q^90 + 19 * q^91 + 61 * q^92 - 5 * q^93 + 10 * q^94 + 25 * q^95 - 54 * q^96 + 79 * q^97 + 7 * q^98 - 3 * 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 $

$2$	−0.838531	−0.592931	−0.296466	−	0.955044i	$-0.595808\pi$
$2$	−0.838531	−0.592931	−0.296466	+	0.955044i	$0.595808\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.29687	−0.648433
$5$	2.50382	1.11974	0.559871	−	0.828580i	$-0.310851\pi$
$5$	2.50382	1.11974	0.559871	+	0.828580i	$0.310851\pi$
$6$	0.838531	0.342329
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	2.76452	0.977407
$9$	1.00000	0.333333
$10$	−2.09953	−0.663930
$11$	3.24608	0.978729	0.489365	−	0.872079i	$-0.337229\pi$
$11$	3.24608	0.978729	0.489365	+	0.872079i	$0.337229\pi$
$12$	1.29687	0.374373
$13$	−4.49895	−1.24778	−0.623892	−	0.781510i	$-0.714450\pi$
$13$	−4.49895	−1.24778	−0.623892	+	0.781510i	$0.714450\pi$
$14$	−0.838531	−0.224107
$15$	−2.50382	−0.646484
$16$	0.275589	0.0688973
$17$	1.27013	0.308052	0.154026	−	0.988067i	$-0.450776\pi$
$17$	1.27013	0.308052	0.154026	+	0.988067i	$0.450776\pi$
$18$	−0.838531	−0.197644
$19$	1.07809	0.247331	0.123665	−	0.992324i	$-0.460535\pi$
$19$	1.07809	0.247331	0.123665	+	0.992324i	$0.460535\pi$
$20$	−3.24712	−0.726077
$21$	−1.00000	−0.218218
$22$	−2.72194	−0.580319
$23$	6.45124	1.34518	0.672588	−	0.740017i	$-0.265183\pi$
$23$	6.45124	1.34518	0.672588	+	0.740017i	$0.265183\pi$
$24$	−2.76452	−0.564306
$25$	1.26912	0.253823
$26$	3.77251	0.739851
$27$	−1.00000	−0.192450
$28$	−1.29687	−0.245084
$29$	3.44101	0.638980	0.319490	−	0.947590i	$-0.396488\pi$
$29$	3.44101	0.638980	0.319490	+	0.947590i	$0.396488\pi$
$30$	2.09953	0.383320
$31$	4.40845	0.791781	0.395891	−	0.918298i	$-0.370436\pi$
$31$	4.40845	0.791781	0.395891	+	0.918298i	$0.370436\pi$
$32$	−5.76014	−1.01826
$33$	−3.24608	−0.565070
$34$	−1.06505	−0.182654
$35$	2.50382	0.423223
$36$	−1.29687	−0.216144
$37$	−5.86942	−0.964926	−0.482463	−	0.875916i	$-0.660258\pi$
$37$	−5.86942	−0.964926	−0.482463	+	0.875916i	$0.660258\pi$
$38$	−0.904012	−0.146650
$39$	4.49895	0.720409
$40$	6.92187	1.09444
$41$	1.72646	0.269628	0.134814	−	0.990871i	$-0.456956\pi$
$41$	1.72646	0.269628	0.134814	+	0.990871i	$0.456956\pi$
$42$	0.838531	0.129388
$43$	−0.382430	−0.0583201	−0.0291600	−	0.999575i	$-0.509283\pi$
$43$	−0.382430	−0.0583201	−0.0291600	+	0.999575i	$0.509283\pi$
$44$	−4.20972	−0.634640
$45$	2.50382	0.373248
$46$	−5.40957	−0.797597
$47$	7.24286	1.05648	0.528240	−	0.849095i	$-0.322852\pi$
$47$	7.24286	1.05648	0.528240	+	0.849095i	$0.322852\pi$
$48$	−0.275589	−0.0397778
$49$	1.00000	0.142857
$50$	−1.06419	−0.150500
$51$	−1.27013	−0.177854
$52$	5.83453	0.809104
$53$	11.6136	1.59525	0.797625	−	0.603153i	$-0.206089\pi$
$53$	11.6136	1.59525	0.797625	+	0.603153i	$0.206089\pi$
$54$	0.838531	0.114110
$55$	8.12760	1.09592
$56$	2.76452	0.369425
$57$	−1.07809	−0.142796
$58$	−2.88540	−0.378871
$59$	7.27550	0.947189	0.473594	−	0.880743i	$-0.342956\pi$
$59$	7.27550	0.947189	0.473594	+	0.880743i	$0.342956\pi$
$60$	3.24712	0.419201
$61$	−9.56962	−1.22526	−0.612632	−	0.790368i	$-0.709889\pi$
$61$	−9.56962	−1.22526	−0.612632	+	0.790368i	$0.709889\pi$
$62$	−3.69663	−0.469472
$63$	1.00000	0.125988
$64$	4.27888	0.534860
$65$	−11.2646	−1.39720
$66$	2.72194	0.335047
$67$	6.04440	0.738441	0.369221	−	0.929342i	$-0.379625\pi$
$67$	6.04440	0.738441	0.369221	+	0.929342i	$0.379625\pi$
$68$	−1.64719	−0.199751
$69$	−6.45124	−0.776638
$70$	−2.09953	−0.250942
$71$	3.52800	0.418697	0.209348	−	0.977841i	$-0.432866\pi$
$71$	3.52800	0.418697	0.209348	+	0.977841i	$0.432866\pi$
$72$	2.76452	0.325802
$73$	−13.3275	−1.55987	−0.779933	−	0.625863i	$-0.784747\pi$
$73$	−13.3275	−1.55987	−0.779933	+	0.625863i	$0.784747\pi$
$74$	4.92169	0.572135
$75$	−1.26912	−0.146545
$76$	−1.39814	−0.160377
$77$	3.24608	0.369925
$78$	−3.77251	−0.427153
$79$	−10.8213	−1.21749	−0.608744	−	0.793367i	$-0.708326\pi$
$79$	−10.8213	−1.21749	−0.608744	+	0.793367i	$0.708326\pi$
$80$	0.690025	0.0771472
$81$	1.00000	0.111111
$82$	−1.44769	−0.159871
$83$	12.5432	1.37679	0.688395	−	0.725336i	$-0.258315\pi$
$83$	12.5432	1.37679	0.688395	+	0.725336i	$0.258315\pi$
$84$	1.29687	0.141500
$85$	3.18018	0.344939
$86$	0.320680	0.0345798
$87$	−3.44101	−0.368915
$88$	8.97386	0.956617
$89$	−5.44594	−0.577269	−0.288634	−	0.957439i	$-0.593201\pi$
$89$	−5.44594	−0.577269	−0.288634	+	0.957439i	$0.593201\pi$
$90$	−2.09953	−0.221310
$91$	−4.49895	−0.471618
$92$	−8.36639	−0.872256
$93$	−4.40845	−0.457135
$94$	−6.07337	−0.626420
$95$	2.69934	0.276947
$96$	5.76014	0.587892
$97$	−4.98685	−0.506338	−0.253169	−	0.967422i	$-0.581473\pi$
$97$	−4.98685	−0.506338	−0.253169	+	0.967422i	$0.581473\pi$
$98$	−0.838531	−0.0847045
$99$	3.24608	0.326243
$100$	−1.64587	−0.164587
$101$	0.473401	0.0471052	0.0235526	−	0.999723i	$-0.492502\pi$
$101$	0.473401	0.0471052	0.0235526	+	0.999723i	$0.492502\pi$
$102$	1.06505	0.105455
$103$	−6.55626	−0.646008	−0.323004	−	0.946398i	$-0.604693\pi$
$103$	−6.55626	−0.646008	−0.323004	+	0.946398i	$0.604693\pi$
$104$	−12.4375	−1.21959
$105$	−2.50382	−0.244348
$106$	−9.73837	−0.945874
$107$	6.01726	0.581711	0.290855	−	0.956767i	$-0.406060\pi$
$107$	6.01726	0.581711	0.290855	+	0.956767i	$0.406060\pi$
$108$	1.29687	0.124791
$109$	15.0384	1.44042	0.720209	−	0.693757i	$-0.244046\pi$
$109$	15.0384	1.44042	0.720209	+	0.693757i	$0.244046\pi$
$110$	−6.81524	−0.649808
$111$	5.86942	0.557100
$112$	0.275589	0.0260407
$113$	2.34409	0.220514	0.110257	−	0.993903i	$-0.464833\pi$
$113$	2.34409	0.220514	0.110257	+	0.993903i	$0.464833\pi$
$114$	0.904012	0.0846684
$115$	16.1527	1.50625
$116$	−4.46253	−0.414336
$117$	−4.49895	−0.415928
$118$	−6.10073	−0.561618
$119$	1.27013	0.116433
$120$	−6.92187	−0.631878
$121$	−0.462979	−0.0420890
$122$	8.02442	0.726497
$123$	−1.72646	−0.155670
$124$	−5.71717	−0.513417
$125$	−9.34146	−0.835526
$126$	−0.838531	−0.0747023
$127$	2.83049	0.251166	0.125583	−	0.992083i	$-0.459920\pi$
$127$	2.83049	0.251166	0.125583	+	0.992083i	$0.459920\pi$
$128$	7.93230	0.701123
$129$	0.382430	0.0336711
$130$	9.44569	0.828442
$131$	−0.0553473	−0.00483571	−0.00241786	−	0.999997i	$-0.500770\pi$
$131$	−0.0553473	−0.00483571	−0.00241786	+	0.999997i	$0.500770\pi$
$132$	4.20972	0.366410
$133$	1.07809	0.0934822
$134$	−5.06842	−0.437845
$135$	−2.50382	−0.215495
$136$	3.51131	0.301093
$137$	8.25886	0.705602	0.352801	−	0.935698i	$-0.385229\pi$
$137$	8.25886	0.705602	0.352801	+	0.935698i	$0.385229\pi$
$138$	5.40957	0.460493
$139$	−20.4447	−1.73409	−0.867047	−	0.498226i	$-0.833985\pi$
$139$	−20.4447	−1.73409	−0.867047	+	0.498226i	$0.833985\pi$
$140$	−3.24712	−0.274431
$141$	−7.24286	−0.609959
$142$	−2.95834	−0.248258
$143$	−14.6039	−1.22124
$144$	0.275589	0.0229658
$145$	8.61568	0.715493
$146$	11.1755	0.924893
$147$	−1.00000	−0.0824786
$148$	7.61184	0.625689
$149$	−7.42854	−0.608569	−0.304285	−	0.952581i	$-0.598417\pi$
$149$	−7.42854	−0.608569	−0.304285	+	0.952581i	$0.598417\pi$
$150$	1.06419	0.0868911
$151$	−5.15346	−0.419383	−0.209691	−	0.977768i	$-0.567246\pi$
$151$	−5.15346	−0.419383	−0.209691	+	0.977768i	$0.567246\pi$
$152$	2.98040	0.241743
$153$	1.27013	0.102684
$154$	−2.72194	−0.219340
$155$	11.0380	0.886591
$156$	−5.83453	−0.467136
$157$	−6.59247	−0.526136	−0.263068	−	0.964777i	$-0.584734\pi$
$157$	−6.59247	−0.526136	−0.263068	+	0.964777i	$0.584734\pi$
$158$	9.07398	0.721887
$159$	−11.6136	−0.921018
$160$	−14.4224	−1.14019
$161$	6.45124	0.508429
$162$	−0.838531	−0.0658813
$163$	9.99286	0.782701	0.391351	−	0.920242i	$-0.372008\pi$
$163$	9.99286	0.782701	0.391351	+	0.920242i	$0.372008\pi$
$164$	−2.23899	−0.174836
$165$	−8.12760	−0.632732
$166$	−10.5178	−0.816342
$167$	−14.1546	−1.09531	−0.547657	−	0.836703i	$-0.684480\pi$
$167$	−14.1546	−1.09531	−0.547657	+	0.836703i	$0.684480\pi$
$168$	−2.76452	−0.213288
$169$	7.24056	0.556966
$170$	−2.66668	−0.204525
$171$	1.07809	0.0824435
$172$	0.495961	0.0378166
$173$	3.39858	0.258390	0.129195	−	0.991619i	$-0.458761\pi$
$173$	3.39858	0.258390	0.129195	+	0.991619i	$0.458761\pi$
$174$	2.88540	0.218741
$175$	1.26912	0.0959362
$176$	0.894583	0.0674318
$177$	−7.27550	−0.546860
$178$	4.56659	0.342281
$179$	−22.8363	−1.70687	−0.853434	−	0.521201i	$-0.825484\pi$
$179$	−22.8363	−1.70687	−0.853434	+	0.521201i	$0.825484\pi$
$180$	−3.24712	−0.242026
$181$	20.6192	1.53261	0.766307	−	0.642475i	$-0.222092\pi$
$181$	20.6192	1.53261	0.766307	+	0.642475i	$0.222092\pi$
$182$	3.77251	0.279637
$183$	9.56962	0.707406
$184$	17.8346	1.31479
$185$	−14.6960	−1.08047
$186$	3.69663	0.271050
$187$	4.12295	0.301500
$188$	−9.39302	−0.685056
$189$	−1.00000	−0.0727393
$190$	−2.26348	−0.164210
$191$	−26.8271	−1.94114	−0.970571	−	0.240815i	$-0.922585\pi$
$191$	−26.8271	−1.94114	−0.970571	+	0.240815i	$0.922585\pi$
$192$	−4.27888	−0.308802
$193$	3.30869	0.238164	0.119082	−	0.992884i	$-0.462005\pi$
$193$	3.30869	0.238164	0.119082	+	0.992884i	$0.462005\pi$
$194$	4.18163	0.300224
$195$	11.2646	0.806672
$196$	−1.29687	−0.0926332
$197$	14.7641	1.05190	0.525948	−	0.850517i	$-0.323711\pi$
$197$	14.7641	1.05190	0.525948	+	0.850517i	$0.323711\pi$
$198$	−2.72194	−0.193440
$199$	−5.90846	−0.418839	−0.209420	−	0.977826i	$-0.567157\pi$
$199$	−5.90846	−0.418839	−0.209420	+	0.977826i	$0.567157\pi$
$200$	3.50850	0.248089
$201$	−6.04440	−0.426339
$202$	−0.396962	−0.0279302
$203$	3.44101	0.241512
$204$	1.64719	0.115326
$205$	4.32275	0.301914
$206$	5.49763	0.383038
$207$	6.45124	0.448392
$208$	−1.23986	−0.0859689
$209$	3.49956	0.242070
$210$	2.09953	0.144881
$211$	7.99730	0.550557	0.275279	−	0.961365i	$-0.411230\pi$
$211$	7.99730	0.550557	0.275279	+	0.961365i	$0.411230\pi$
$212$	−15.0613	−1.03441
$213$	−3.52800	−0.241735
$214$	−5.04566	−0.344914
$215$	−0.957537	−0.0653035
$216$	−2.76452	−0.188102
$217$	4.40845	0.299265
$218$	−12.6102	−0.854069
$219$	13.3275	0.900589
$220$	−10.5404	−0.710633
$221$	−5.71426	−0.384383
$222$	−4.92169	−0.330322
$223$	−13.7164	−0.918515	−0.459258	−	0.888303i	$-0.651885\pi$
$223$	−13.7164	−0.918515	−0.459258	+	0.888303i	$0.651885\pi$
$224$	−5.76014	−0.384866
$225$	1.26912	0.0846078
$226$	−1.96560	−0.130750
$227$	−1.00000	−0.0663723
$227$	−1.00000	−0.0663723
$228$	1.39814	0.0925938
$229$	14.9093	0.985237	0.492618	−	0.870245i	$-0.336040\pi$
$229$	14.9093	0.985237	0.492618	+	0.870245i	$0.336040\pi$
$230$	−13.5446	−0.893104
$231$	−3.24608	−0.213576
$232$	9.51277	0.624544
$233$	7.72947	0.506374	0.253187	−	0.967417i	$-0.418521\pi$
$233$	7.72947	0.506374	0.253187	+	0.967417i	$0.418521\pi$
$234$	3.77251	0.246617
$235$	18.1348	1.18299
$236$	−9.43534	−0.614188
$237$	10.8213	0.702917
$238$	−1.06505	−0.0690367
$239$	19.8732	1.28549	0.642745	−	0.766080i	$-0.277795\pi$
$239$	19.8732	1.28549	0.642745	+	0.766080i	$0.277795\pi$
$240$	−0.690025	−0.0445409
$241$	19.0302	1.22584	0.612921	−	0.790144i	$-0.289994\pi$
$241$	19.0302	1.22584	0.612921	+	0.790144i	$0.289994\pi$
$242$	0.388223	0.0249559
$243$	−1.00000	−0.0641500
$244$	12.4105	0.794501
$245$	2.50382	0.159963
$246$	1.44769	0.0923015
$247$	−4.85027	−0.308615
$248$	12.1873	0.773893
$249$	−12.5432	−0.794890
$250$	7.83311	0.495409
$251$	−20.7963	−1.31265	−0.656326	−	0.754478i	$-0.727890\pi$
$251$	−20.7963	−1.31265	−0.656326	+	0.754478i	$0.727890\pi$
$252$	−1.29687	−0.0816948
$253$	20.9412	1.31656
$254$	−2.37346	−0.148924
$255$	−3.18018	−0.199151
$256$	−15.2092	−0.950578
$257$	27.6502	1.72477	0.862386	−	0.506251i	$-0.168969\pi$
$257$	27.6502	1.72477	0.862386	+	0.506251i	$0.168969\pi$
$258$	−0.320680	−0.0199647
$259$	−5.86942	−0.364708
$260$	14.6086	0.905988
$261$	3.44101	0.212993
$262$	0.0464104	0.00286725
$263$	17.1208	1.05571	0.527856	−	0.849334i	$-0.322996\pi$
$263$	17.1208	1.05571	0.527856	+	0.849334i	$0.322996\pi$
$264$	−8.97386	−0.552303
$265$	29.0784	1.78627
$266$	−0.904012	−0.0554285
$267$	5.44594	0.333286
$268$	−7.83877	−0.478829
$269$	6.09874	0.371847	0.185923	−	0.982564i	$-0.440472\pi$
$269$	6.09874	0.371847	0.185923	+	0.982564i	$0.440472\pi$
$270$	2.09953	0.127773
$271$	16.0857	0.977134	0.488567	−	0.872526i	$-0.337520\pi$
$271$	16.0857	0.977134	0.488567	+	0.872526i	$0.337520\pi$
$272$	0.350034	0.0212240
$273$	4.49895	0.272289
$274$	−6.92531	−0.418373
$275$	4.11965	0.248424
$276$	8.36639	0.503597
$277$	15.5248	0.932797	0.466399	−	0.884575i	$-0.345551\pi$
$277$	15.5248	0.932797	0.466399	+	0.884575i	$0.345551\pi$
$278$	17.1435	1.02820
$279$	4.40845	0.263927
$280$	6.92187	0.413661
$281$	26.9330	1.60669	0.803344	−	0.595515i	$-0.203052\pi$
$281$	26.9330	1.60669	0.803344	+	0.595515i	$0.203052\pi$
$282$	6.07337	0.361664
$283$	−27.7956	−1.65228	−0.826139	−	0.563466i	$-0.809468\pi$
$283$	−27.7956	−1.65228	−0.826139	+	0.563466i	$0.809468\pi$
$284$	−4.57534	−0.271497
$285$	−2.69934	−0.159895
$286$	12.2459	0.724113
$287$	1.72646	0.101910
$288$	−5.76014	−0.339420
$289$	−15.3868	−0.905104
$290$	−7.22452	−0.424238
$291$	4.98685	0.292334
$292$	17.2840	1.01147
$293$	33.0167	1.92886	0.964429	−	0.264342i	$-0.0851547\pi$
$293$	33.0167	1.92886	0.964429	+	0.264342i	$0.0851547\pi$
$294$	0.838531	0.0489041
$295$	18.2165	1.06061
$296$	−16.2261	−0.943126
$297$	−3.24608	−0.188357
$298$	6.22906	0.360840
$299$	−29.0238	−1.67849
$300$	1.64587	0.0950245
$301$	−0.382430	−0.0220429
$302$	4.32134	0.248665
$303$	−0.473401	−0.0271962
$304$	0.297110	0.0170404
$305$	−23.9606	−1.37198
$306$	−1.06505	−0.0608846
$307$	19.2005	1.09583	0.547915	−	0.836534i	$-0.315422\pi$
$307$	19.2005	1.09583	0.547915	+	0.836534i	$0.315422\pi$
$308$	−4.20972	−0.239871
$309$	6.55626	0.372973
$310$	−9.25569	−0.525688
$311$	31.9360	1.81093	0.905463	−	0.424425i	$-0.139524\pi$
$311$	31.9360	1.81093	0.905463	+	0.424425i	$0.139524\pi$
$312$	12.4375	0.704133
$313$	7.55326	0.426935	0.213468	−	0.976950i	$-0.431524\pi$
$313$	7.55326	0.426935	0.213468	+	0.976950i	$0.431524\pi$
$314$	5.52799	0.311963
$315$	2.50382	0.141074
$316$	14.0337	0.789459
$317$	−16.1376	−0.906378	−0.453189	−	0.891415i	$-0.649714\pi$
$317$	−16.1376	−0.906378	−0.453189	+	0.891415i	$0.649714\pi$
$318$	9.73837	0.546101
$319$	11.1698	0.625389
$320$	10.7135	0.598906
$321$	−6.01726	−0.335851
$322$	−5.40957	−0.301463
$323$	1.36932	0.0761908
$324$	−1.29687	−0.0720481
$325$	−5.70969	−0.316717
$326$	−8.37933	−0.464088
$327$	−15.0384	−0.831626
$328$	4.77285	0.263537
$329$	7.24286	0.399312
$330$	6.81524	0.375167
$331$	12.0473	0.662180	0.331090	−	0.943599i	$-0.392584\pi$
$331$	12.0473	0.662180	0.331090	+	0.943599i	$0.392584\pi$
$332$	−16.2668	−0.892756
$333$	−5.86942	−0.321642
$334$	11.8691	0.649446
$335$	15.1341	0.826864
$336$	−0.275589	−0.0150346
$337$	23.7765	1.29519	0.647593	−	0.761986i	$-0.275776\pi$
$337$	23.7765	1.29519	0.647593	+	0.761986i	$0.275776\pi$
$338$	−6.07144	−0.330243
$339$	−2.34409	−0.127314
$340$	−4.12427	−0.223670
$341$	14.3102	0.774940
$342$	−0.904012	−0.0488833
$343$	1.00000	0.0539949
$344$	−1.05724	−0.0570025
$345$	−16.1527	−0.869635
$346$	−2.84982	−0.153207
$347$	−7.42452	−0.398569	−0.199285	−	0.979942i	$-0.563862\pi$
$347$	−7.42452	−0.398569	−0.199285	+	0.979942i	$0.563862\pi$
$348$	4.46253	0.239217
$349$	3.83777	0.205431	0.102715	−	0.994711i	$-0.467247\pi$
$349$	3.83777	0.205431	0.102715	+	0.994711i	$0.467247\pi$
$350$	−1.06419	−0.0568836
$351$	4.49895	0.240136
$352$	−18.6979	−0.996599
$353$	−10.6396	−0.566288	−0.283144	−	0.959077i	$-0.591378\pi$
$353$	−10.6396	−0.566288	−0.283144	+	0.959077i	$0.591378\pi$
$354$	6.10073	0.324250
$355$	8.83348	0.468833
$356$	7.06265	0.374320
$357$	−1.27013	−0.0672225
$358$	19.1490	1.01206
$359$	−0.228010	−0.0120339	−0.00601696	−	0.999982i	$-0.501915\pi$
$359$	−0.228010	−0.0120339	−0.00601696	+	0.999982i	$0.501915\pi$
$360$	6.92187	0.364815
$361$	−17.8377	−0.938828
$362$	−17.2898	−0.908734
$363$	0.462979	0.0243001
$364$	5.83453	0.305813
$365$	−33.3697	−1.74665
$366$	−8.02442	−0.419443
$367$	−5.69691	−0.297376	−0.148688	−	0.988884i	$-0.547505\pi$
$367$	−5.69691	−0.297376	−0.148688	+	0.988884i	$0.547505\pi$
$368$	1.77789	0.0926790
$369$	1.72646	0.0898761
$370$	12.3230	0.640644
$371$	11.6136	0.602948
$372$	5.71717	0.296421
$373$	15.2891	0.791642	0.395821	−	0.918328i	$-0.370460\pi$
$373$	15.2891	0.791642	0.395821	+	0.918328i	$0.370460\pi$
$374$	−3.45722	−0.178769
$375$	9.34146	0.482391
$376$	20.0231	1.03261
$377$	−15.4810	−0.797310
$378$	0.838531	0.0431294
$379$	−25.4296	−1.30623	−0.653116	−	0.757258i	$-0.726539\pi$
$379$	−25.4296	−1.30623	−0.653116	+	0.757258i	$0.726539\pi$
$380$	−3.50068	−0.179581
$381$	−2.83049	−0.145011
$382$	22.4954	1.15096
$383$	23.2298	1.18699	0.593493	−	0.804839i	$-0.297748\pi$
$383$	23.2298	1.18699	0.593493	+	0.804839i	$0.297748\pi$
$384$	−7.93230	−0.404794
$385$	8.12760	0.414221
$386$	−2.77444	−0.141215
$387$	−0.382430	−0.0194400
$388$	6.46727	0.328326
$389$	−0.726311	−0.0368254	−0.0184127	−	0.999830i	$-0.505861\pi$
$389$	−0.726311	−0.0368254	−0.0184127	+	0.999830i	$0.505861\pi$
$390$	−9.44569	−0.478301
$391$	8.19393	0.414385
$392$	2.76452	0.139630
$393$	0.0553473	0.00279190
$394$	−12.3801	−0.623702
$395$	−27.0945	−1.36327
$396$	−4.20972	−0.211547
$397$	25.8604	1.29790	0.648948	−	0.760833i	$-0.275209\pi$
$397$	25.8604	1.29790	0.648948	+	0.760833i	$0.275209\pi$
$398$	4.95443	0.248343
$399$	−1.07809	−0.0539720
$400$	0.349755	0.0174877
$401$	5.49207	0.274261	0.137131	−	0.990553i	$-0.456212\pi$
$401$	5.49207	0.274261	0.137131	+	0.990553i	$0.456212\pi$
$402$	5.06842	0.252790
$403$	−19.8334	−0.987973
$404$	−0.613938	−0.0305445
$405$	2.50382	0.124416
$406$	−2.88540	−0.143200
$407$	−19.0526	−0.944401
$408$	−3.51131	−0.173836
$409$	26.0734	1.28925	0.644624	−	0.764500i	$-0.277014\pi$
$409$	26.0734	1.28925	0.644624	+	0.764500i	$0.277014\pi$
$410$	−3.62476	−0.179014
$411$	−8.25886	−0.407379
$412$	8.50259	0.418892
$413$	7.27550	0.358004
$414$	−5.40957	−0.265866
$415$	31.4058	1.54165
$416$	25.9146	1.27057
$417$	20.4447	1.00118
$418$	−2.93449	−0.143531
$419$	−27.6585	−1.35121	−0.675604	−	0.737265i	$-0.736117\pi$
$419$	−27.6585	−1.35121	−0.675604	+	0.737265i	$0.736117\pi$
$420$	3.24712	0.158443
$421$	−25.7456	−1.25476	−0.627382	−	0.778712i	$-0.715873\pi$
$421$	−25.7456	−1.25476	−0.627382	+	0.778712i	$0.715873\pi$
$422$	−6.70599	−0.326443
$423$	7.24286	0.352160
$424$	32.1061	1.55921
$425$	1.61195	0.0781908
$426$	2.95834	0.143332
$427$	−9.56962	−0.463106
$428$	−7.80358	−0.377200
$429$	14.6039	0.705085
$430$	0.802925	0.0387205
$431$	25.7361	1.23967	0.619833	−	0.784734i	$-0.287200\pi$
$431$	25.7361	1.23967	0.619833	+	0.784734i	$0.287200\pi$
$432$	−0.275589	−0.0132593
$433$	27.6109	1.32689	0.663447	−	0.748223i	$-0.269093\pi$
$433$	27.6109	1.32689	0.663447	+	0.748223i	$0.269093\pi$
$434$	−3.69663	−0.177444
$435$	−8.61568	−0.413090
$436$	−19.5028	−0.934014
$437$	6.95501	0.332703
$438$	−11.1755	−0.533987
$439$	3.13406	0.149580	0.0747902	−	0.997199i	$-0.476171\pi$
$439$	3.13406	0.149580	0.0747902	+	0.997199i	$0.476171\pi$
$440$	22.4689	1.07116
$441$	1.00000	0.0476190
$442$	4.79159	0.227913
$443$	−4.06227	−0.193004	−0.0965022	−	0.995333i	$-0.530765\pi$
$443$	−4.06227	−0.193004	−0.0965022	+	0.995333i	$0.530765\pi$
$444$	−7.61184	−0.361242
$445$	−13.6357	−0.646392
$446$	11.5016	0.544617
$447$	7.42854	0.351358
$448$	4.27888	0.202158
$449$	23.2762	1.09847	0.549235	−	0.835668i	$-0.314919\pi$
$449$	23.2762	1.09847	0.549235	+	0.835668i	$0.314919\pi$
$450$	−1.06419	−0.0501666
$451$	5.60423	0.263893
$452$	−3.03997	−0.142988
$453$	5.15346	0.242131
$454$	0.838531	0.0393542
$455$	−11.2646	−0.528091
$456$	−2.98040	−0.139570
$457$	−5.06757	−0.237051	−0.118526	−	0.992951i	$-0.537817\pi$
$457$	−5.06757	−0.237051	−0.118526	+	0.992951i	$0.537817\pi$
$458$	−12.5019	−0.584178
$459$	−1.27013	−0.0592847
$460$	−20.9479	−0.976702
$461$	−1.78034	−0.0829186	−0.0414593	−	0.999140i	$-0.513201\pi$
$461$	−1.78034	−0.0829186	−0.0414593	+	0.999140i	$0.513201\pi$
$462$	2.72194	0.126636
$463$	31.2690	1.45319	0.726596	−	0.687065i	$-0.241101\pi$
$463$	31.2690	1.45319	0.726596	+	0.687065i	$0.241101\pi$
$464$	0.948306	0.0440240
$465$	−11.0380	−0.511874
$466$	−6.48140	−0.300245
$467$	−2.11201	−0.0977321	−0.0488660	−	0.998805i	$-0.515561\pi$
$467$	−2.11201	−0.0977321	−0.0488660	+	0.998805i	$0.515561\pi$
$468$	5.83453	0.269701
$469$	6.04440	0.279105
$470$	−15.2066	−0.701429
$471$	6.59247	0.303765
$472$	20.1133	0.925789
$473$	−1.24140	−0.0570796
$474$	−9.07398	−0.416782
$475$	1.36822	0.0627783
$476$	−1.64719	−0.0754988
$477$	11.6136	0.531750
$478$	−16.6643	−0.762207
$479$	−10.4476	−0.477362	−0.238681	−	0.971098i	$-0.576715\pi$
$479$	−10.4476	−0.477362	−0.238681	+	0.971098i	$0.576715\pi$
$480$	14.4224	0.658287
$481$	26.4062	1.20402
$482$	−15.9574	−0.726840
$483$	−6.45124	−0.293542
$484$	0.600422	0.0272919
$485$	−12.4862	−0.566968
$486$	0.838531	0.0380366
$487$	−32.9514	−1.49317	−0.746585	−	0.665290i	$-0.768308\pi$
$487$	−32.9514	−1.49317	−0.746585	+	0.665290i	$0.768308\pi$
$488$	−26.4554	−1.19758
$489$	−9.99286	−0.451893
$490$	−2.09953	−0.0948472
$491$	32.1505	1.45093	0.725466	−	0.688258i	$-0.241624\pi$
$491$	32.1505	1.45093	0.725466	+	0.688258i	$0.241624\pi$
$492$	2.23899	0.100941
$493$	4.37054	0.196839
$494$	4.06710	0.182988
$495$	8.12760	0.365308
$496$	1.21492	0.0545516
$497$	3.52800	0.158253
$498$	10.5178	0.471315
$499$	−29.6690	−1.32817	−0.664084	−	0.747658i	$-0.731178\pi$
$499$	−29.6690	−1.32817	−0.664084	+	0.747658i	$0.731178\pi$
$500$	12.1146	0.541782
$501$	14.1546	0.632380
$502$	17.4384	0.778312
$503$	35.9066	1.60099	0.800497	−	0.599337i	$-0.204569\pi$
$503$	35.9066	1.60099	0.800497	+	0.599337i	$0.204569\pi$
$504$	2.76452	0.123142
$505$	1.18531	0.0527457
$506$	−17.5599	−0.780632
$507$	−7.24056	−0.321565
$508$	−3.67077	−0.162864
$509$	−44.9314	−1.99155	−0.995775	−	0.0918254i	$-0.970730\pi$
$509$	−44.9314	−1.99155	−0.995775	+	0.0918254i	$0.970730\pi$
$510$	2.66668	0.118083
$511$	−13.3275	−0.589574
$512$	−3.11118	−0.137496
$513$	−1.07809	−0.0475988
$514$	−23.1856	−1.02267
$515$	−16.4157	−0.723362
$516$	−0.495961	−0.0218334
$517$	23.5109	1.03401
$518$	4.92169	0.216247
$519$	−3.39858	−0.149181
$520$	−31.1412	−1.36563
$521$	−5.76642	−0.252631	−0.126316	−	0.991990i	$-0.540315\pi$
$521$	−5.76642	−0.252631	−0.126316	+	0.991990i	$0.540315\pi$
$522$	−2.88540	−0.126290
$523$	−16.4520	−0.719397	−0.359698	−	0.933069i	$-0.617120\pi$
$523$	−16.4520	−0.719397	−0.359698	+	0.933069i	$0.617120\pi$
$524$	0.0717779	0.00313563
$525$	−1.26912	−0.0553888
$526$	−14.3563	−0.625965
$527$	5.59932	0.243910
$528$	−0.894583	−0.0389317
$529$	18.6185	0.809500
$530$	−24.3831	−1.05914
$531$	7.27550	0.315730
$532$	−1.39814	−0.0606169
$533$	−7.76727	−0.336438
$534$	−4.56659	−0.197616
$535$	15.0661	0.651366
$536$	16.7099	0.721758
$537$	22.8363	0.985460
$538$	−5.11398	−0.220479
$539$	3.24608	0.139818
$540$	3.24712	0.139734
$541$	11.5347	0.495914	0.247957	−	0.968771i	$-0.420241\pi$
$541$	11.5347	0.495914	0.247957	+	0.968771i	$0.420241\pi$
$542$	−13.4883	−0.579373
$543$	−20.6192	−0.884855
$544$	−7.31614	−0.313677
$545$	37.6535	1.61290
$546$	−3.77251	−0.161449
$547$	26.4267	1.12992	0.564961	−	0.825117i	$-0.308891\pi$
$547$	26.4267	1.12992	0.564961	+	0.825117i	$0.308891\pi$
$548$	−10.7106	−0.457535
$549$	−9.56962	−0.408421
$550$	−3.45446	−0.147299
$551$	3.70972	0.158039
$552$	−17.8346	−0.759092
$553$	−10.8213	−0.460167
$554$	−13.0181	−0.553085
$555$	14.6960	0.623809
$556$	26.5140	1.12444
$557$	−29.6431	−1.25602	−0.628009	−	0.778206i	$-0.716130\pi$
$557$	−29.6431	−1.25602	−0.628009	+	0.778206i	$0.716130\pi$
$558$	−3.69663	−0.156491
$559$	1.72054	0.0727709
$560$	0.690025	0.0291589
$561$	−4.12295	−0.174071
$562$	−22.5842	−0.952656
$563$	1.82456	0.0768961	0.0384480	−	0.999261i	$-0.487759\pi$
$563$	1.82456	0.0768961	0.0384480	+	0.999261i	$0.487759\pi$
$564$	9.39302	0.395517
$565$	5.86919	0.246919
$566$	23.3075	0.979687
$567$	1.00000	0.0419961
$568$	9.75325	0.409237
$569$	−26.2758	−1.10154	−0.550769	−	0.834658i	$-0.685665\pi$
$569$	−26.2758	−1.10154	−0.550769	+	0.834658i	$0.685665\pi$
$570$	2.26348	0.0948069
$571$	15.0746	0.630854	0.315427	−	0.948950i	$-0.397852\pi$
$571$	15.0746	0.630854	0.315427	+	0.948950i	$0.397852\pi$
$572$	18.9393	0.791894
$573$	26.8271	1.12072
$574$	−1.44769	−0.0604255
$575$	8.18738	0.341437
$576$	4.27888	0.178287
$577$	−0.0530706	−0.00220936	−0.00110468	−	0.999999i	$-0.500352\pi$
$577$	−0.0530706	−0.00220936	−0.00110468	+	0.999999i	$0.500352\pi$
$578$	12.9023	0.536664
$579$	−3.30869	−0.137504
$580$	−11.1734	−0.463949
$581$	12.5432	0.520378
$582$	−4.18163	−0.173334
$583$	37.6986	1.56132
$584$	−36.8442	−1.52462
$585$	−11.2646	−0.465732
$586$	−27.6856	−1.14368
$587$	−32.4035	−1.33744	−0.668719	−	0.743515i	$-0.733157\pi$
$587$	−32.4035	−1.33744	−0.668719	+	0.743515i	$0.733157\pi$
$588$	1.29687	0.0534818
$589$	4.75270	0.195832
$590$	−15.2751	−0.628867
$591$	−14.7641	−0.607312
$592$	−1.61755	−0.0664807
$593$	−20.9758	−0.861372	−0.430686	−	0.902502i	$-0.641728\pi$
$593$	−20.9758	−0.861372	−0.430686	+	0.902502i	$0.641728\pi$
$594$	2.72194	0.111682
$595$	3.18018	0.130375
$596$	9.63381	0.394616
$597$	5.90846	0.241817
$598$	24.3374	0.995230
$599$	21.2539	0.868409	0.434205	−	0.900814i	$-0.357030\pi$
$599$	21.2539	0.868409	0.434205	+	0.900814i	$0.357030\pi$
$600$	−3.50850	−0.143234
$601$	22.8237	0.930999	0.465499	−	0.885048i	$-0.345875\pi$
$601$	22.8237	0.930999	0.465499	+	0.885048i	$0.345875\pi$
$602$	0.320680	0.0130699
$603$	6.04440	0.246147
$604$	6.68334	0.271941
$605$	−1.15922	−0.0471289
$606$	0.396962	0.0161255
$607$	−33.3136	−1.35216	−0.676079	−	0.736829i	$-0.736322\pi$
$607$	−33.3136	−1.35216	−0.676079	+	0.736829i	$0.736322\pi$
$608$	−6.20994	−0.251846
$609$	−3.44101	−0.139437
$610$	20.0917	0.813490
$611$	−32.5853	−1.31826
$612$	−1.64719	−0.0665837
$613$	25.9004	1.04611	0.523053	−	0.852300i	$-0.324793\pi$
$613$	25.9004	1.04611	0.523053	+	0.852300i	$0.324793\pi$
$614$	−16.1002	−0.649752
$615$	−4.32275	−0.174310
$616$	8.97386	0.361567
$617$	36.5533	1.47158	0.735791	−	0.677209i	$-0.236811\pi$
$617$	36.5533	1.47158	0.735791	+	0.677209i	$0.236811\pi$
$618$	−5.49763	−0.221147
$619$	10.3253	0.415009	0.207504	−	0.978234i	$-0.433466\pi$
$619$	10.3253	0.415009	0.207504	+	0.978234i	$0.433466\pi$
$620$	−14.3148	−0.574895
$621$	−6.45124	−0.258879
$622$	−26.7794	−1.07375
$623$	−5.44594	−0.218187
$624$	1.23986	0.0496342
$625$	−29.7349	−1.18940
$626$	−6.33364	−0.253143
$627$	−3.49956	−0.139759
$628$	8.54954	0.341164
$629$	−7.45493	−0.297248
$630$	−2.09953	−0.0836474
$631$	−10.2516	−0.408110	−0.204055	−	0.978959i	$-0.565412\pi$
$631$	−10.2516	−0.408110	−0.204055	+	0.978959i	$0.565412\pi$
$632$	−29.9157	−1.18998
$633$	−7.99730	−0.317864
$634$	13.5319	0.537420
$635$	7.08705	0.281241
$636$	15.0613	0.597218
$637$	−4.49895	−0.178255
$638$	−9.36623	−0.370813
$639$	3.52800	0.139566
$640$	19.8611	0.785078
$641$	−19.3301	−0.763492	−0.381746	−	0.924267i	$-0.624677\pi$
$641$	−19.3301	−0.763492	−0.381746	+	0.924267i	$0.624677\pi$
$642$	5.04566	0.199136
$643$	−37.3089	−1.47132	−0.735660	−	0.677351i	$-0.763128\pi$
$643$	−37.3089	−1.47132	−0.735660	+	0.677351i	$0.763128\pi$
$644$	−8.36639	−0.329682
$645$	0.957537	0.0377030
$646$	−1.14821	−0.0451759
$647$	18.8313	0.740334	0.370167	−	0.928965i	$-0.379301\pi$
$647$	18.8313	0.740334	0.370167	+	0.928965i	$0.379301\pi$
$648$	2.76452	0.108601
$649$	23.6168	0.927041
$650$	4.78776	0.187791
$651$	−4.40845	−0.172781
$652$	−12.9594	−0.507529
$653$	29.2543	1.14481	0.572404	−	0.819972i	$-0.306011\pi$
$653$	29.2543	1.14481	0.572404	+	0.819972i	$0.306011\pi$
$654$	12.6102	0.493097
$655$	−0.138580	−0.00541475
$656$	0.475794	0.0185766
$657$	−13.3275	−0.519955
$658$	−6.07337	−0.236765
$659$	14.3624	0.559481	0.279740	−	0.960076i	$-0.409752\pi$
$659$	14.3624	0.559481	0.279740	+	0.960076i	$0.409752\pi$
$660$	10.5404	0.410284
$661$	−11.5933	−0.450929	−0.225464	−	0.974251i	$-0.572390\pi$
$661$	−11.5933	−0.450929	−0.225464	+	0.974251i	$0.572390\pi$
$662$	−10.1020	−0.392627
$663$	5.71426	0.221924
$664$	34.6759	1.34568
$665$	2.69934	0.104676
$666$	4.92169	0.190712
$667$	22.1988	0.859541
$668$	18.3566	0.710237
$669$	13.7164	0.530305
$670$	−12.6904	−0.490274
$671$	−31.0637	−1.19920
$672$	5.76014	0.222202
$673$	−43.6572	−1.68286	−0.841431	−	0.540365i	$-0.818286\pi$
$673$	−43.6572	−1.68286	−0.841431	+	0.540365i	$0.818286\pi$
$674$	−19.9373	−0.767957
$675$	−1.26912	−0.0488483
$676$	−9.39003	−0.361155
$677$	−27.2502	−1.04731	−0.523656	−	0.851930i	$-0.675432\pi$
$677$	−27.2502	−1.04731	−0.523656	+	0.851930i	$0.675432\pi$
$678$	1.96560	0.0754883
$679$	−4.98685	−0.191378
$680$	8.79169	0.337146
$681$	1.00000	0.0383201
$682$	−11.9995	−0.459486
$683$	5.54103	0.212022	0.106011	−	0.994365i	$-0.466192\pi$
$683$	5.54103	0.212022	0.106011	+	0.994365i	$0.466192\pi$
$684$	−1.39814	−0.0534591
$685$	20.6787	0.790093
$686$	−0.838531	−0.0320153
$687$	−14.9093	−0.568827
$688$	−0.105394	−0.00401809
$689$	−52.2490	−1.99053
$690$	13.5446	0.515634
$691$	41.1679	1.56610	0.783051	−	0.621958i	$-0.213663\pi$
$691$	41.1679	1.56610	0.783051	+	0.621958i	$0.213663\pi$
$692$	−4.40751	−0.167548
$693$	3.24608	0.123308
$694$	6.22570	0.236324
$695$	−51.1898	−1.94174
$696$	−9.51277	−0.360581
$697$	2.19284	0.0830596
$698$	−3.21809	−0.121806
$699$	−7.72947	−0.292355
$700$	−1.64587	−0.0622081
$701$	−4.00556	−0.151288	−0.0756440	−	0.997135i	$-0.524101\pi$
$701$	−4.00556	−0.151288	−0.0756440	+	0.997135i	$0.524101\pi$
$702$	−3.77251	−0.142384
$703$	−6.32775	−0.238656
$704$	13.8896	0.523483
$705$	−18.1348	−0.682997
$706$	8.92163	0.335770
$707$	0.473401	0.0178041
$708$	9.43534	0.354602
$709$	−31.1569	−1.17012	−0.585062	−	0.810989i	$-0.698930\pi$
$709$	−31.1569	−1.17012	−0.585062	+	0.810989i	$0.698930\pi$
$710$	−7.40715	−0.277986
$711$	−10.8213	−0.405829
$712$	−15.0554	−0.564227
$713$	28.4400	1.06509
$714$	1.06505	0.0398583
$715$	−36.5657	−1.36748
$716$	29.6156	1.10679
$717$	−19.8732	−0.742178
$718$	0.191194	0.00713528
$719$	−31.9709	−1.19231	−0.596157	−	0.802868i	$-0.703306\pi$
$719$	−31.9709	−1.19231	−0.596157	+	0.802868i	$0.703306\pi$
$720$	0.690025	0.0257157
$721$	−6.55626	−0.244168
$722$	14.9575	0.556660
$723$	−19.0302	−0.707740
$724$	−26.7403	−0.993796
$725$	4.36705	0.162188
$726$	−0.388223	−0.0144083
$727$	−34.7208	−1.28772	−0.643862	−	0.765141i	$-0.722669\pi$
$727$	−34.7208	−1.28772	−0.643862	+	0.765141i	$0.722669\pi$
$728$	−12.4375	−0.460963
$729$	1.00000	0.0370370
$730$	27.9815	1.03564
$731$	−0.485737	−0.0179656
$732$	−12.4105	−0.458705
$733$	−24.6689	−0.911166	−0.455583	−	0.890193i	$-0.650569\pi$
$733$	−24.6689	−0.911166	−0.455583	+	0.890193i	$0.650569\pi$
$734$	4.77704	0.176324
$735$	−2.50382	−0.0923548
$736$	−37.1600	−1.36974
$737$	19.6206	0.722734
$738$	−1.44769	−0.0532903
$739$	44.9930	1.65510	0.827548	−	0.561396i	$-0.189735\pi$
$739$	44.9930	1.65510	0.827548	+	0.561396i	$0.189735\pi$
$740$	19.0587	0.700611
$741$	4.85027	0.178179
$742$	−9.73837	−0.357507
$743$	51.5279	1.89037	0.945187	−	0.326530i	$-0.105879\pi$
$743$	51.5279	1.89037	0.945187	+	0.326530i	$0.105879\pi$
$744$	−12.1873	−0.446807
$745$	−18.5997	−0.681441
$746$	−12.8204	−0.469389
$747$	12.5432	0.458930
$748$	−5.34691	−0.195502
$749$	6.01726	0.219866
$750$	−7.83311	−0.286025
$751$	−5.00188	−0.182521	−0.0912606	−	0.995827i	$-0.529090\pi$
$751$	−5.00188	−0.182521	−0.0912606	+	0.995827i	$0.529090\pi$
$752$	1.99605	0.0727886
$753$	20.7963	0.757860
$754$	12.9813	0.472750
$755$	−12.9033	−0.469601
$756$	1.29687	0.0471665
$757$	−25.7247	−0.934979	−0.467489	−	0.883999i	$-0.654841\pi$
$757$	−25.7247	−0.934979	−0.467489	+	0.883999i	$0.654841\pi$
$758$	21.3235	0.774506
$759$	−20.9412	−0.760118
$760$	7.46240	0.270690
$761$	7.10941	0.257716	0.128858	−	0.991663i	$-0.458869\pi$
$761$	7.10941	0.257716	0.128858	+	0.991663i	$0.458869\pi$
$762$	2.37346	0.0859813
$763$	15.0384	0.544427
$764$	34.7911	1.25870
$765$	3.18018	0.114980
$766$	−19.4789	−0.703801
$767$	−32.7321	−1.18189
$768$	15.2092	0.548816
$769$	0.319272	0.0115132	0.00575661	−	0.999983i	$-0.498168\pi$
$769$	0.319272	0.0115132	0.00575661	+	0.999983i	$0.498168\pi$
$770$	−6.81524	−0.245604
$771$	−27.6502	−0.995798
$772$	−4.29092	−0.154434
$773$	5.34474	0.192237	0.0961185	−	0.995370i	$-0.469357\pi$
$773$	5.34474	0.192237	0.0961185	+	0.995370i	$0.469357\pi$
$774$	0.320680	0.0115266
$775$	5.59484	0.200973
$776$	−13.7863	−0.494898
$777$	5.86942	0.210564
$778$	0.609035	0.0218350
$779$	1.86128	0.0666873
$780$	−14.6086	−0.523073
$781$	11.4522	0.409791
$782$	−6.87087	−0.245702
$783$	−3.44101	−0.122972
$784$	0.275589	0.00984246
$785$	−16.5064	−0.589137
$786$	−0.0464104	−0.00165540
$787$	10.2156	0.364149	0.182074	−	0.983285i	$-0.441719\pi$
$787$	10.2156	0.364149	0.182074	+	0.983285i	$0.441719\pi$
$788$	−19.1470	−0.682084
$789$	−17.1208	−0.609516
$790$	22.7196	0.808327
$791$	2.34409	0.0833464
$792$	8.97386	0.318872
$793$	43.0532	1.52887
$794$	−21.6847	−0.769563
$795$	−29.0784	−1.03130
$796$	7.66247	0.271589
$797$	−21.1132	−0.747867	−0.373933	−	0.927456i	$-0.621991\pi$
$797$	−21.1132	−0.747867	−0.373933	+	0.927456i	$0.621991\pi$
$798$	0.904012	0.0320017
$799$	9.19940	0.325451
$800$	−7.31029	−0.258458
$801$	−5.44594	−0.192423
$802$	−4.60528	−0.162618
$803$	−43.2621	−1.52669
$804$	7.83877	0.276452
$805$	16.1527	0.569310
$806$	16.6309	0.585800
$807$	−6.09874	−0.214686
$808$	1.30873	0.0460410
$809$	16.4336	0.577775	0.288888	−	0.957363i	$-0.406715\pi$
$809$	16.4336	0.577775	0.288888	+	0.957363i	$0.406715\pi$
$810$	−2.09953	−0.0737700
$811$	33.7609	1.18551	0.592753	−	0.805385i	$-0.298041\pi$
$811$	33.7609	1.18551	0.592753	+	0.805385i	$0.298041\pi$
$812$	−4.46253	−0.156604
$813$	−16.0857	−0.564149
$814$	15.9762	0.559965
$815$	25.0203	0.876424
$816$	−0.350034	−0.0122537
$817$	−0.412294	−0.0144243
$818$	−21.8634	−0.764435
$819$	−4.49895	−0.157206
$820$	−5.60603	−0.195771
$821$	17.6987	0.617690	0.308845	−	0.951112i	$-0.400058\pi$
$821$	17.6987	0.617690	0.308845	+	0.951112i	$0.400058\pi$
$822$	6.92531	0.241548
$823$	−13.9331	−0.485679	−0.242839	−	0.970067i	$-0.578079\pi$
$823$	−13.9331	−0.485679	−0.242839	+	0.970067i	$0.578079\pi$
$824$	−18.1249	−0.631413
$825$	−4.11965	−0.143428
$826$	−6.10073	−0.212272
$827$	21.3924	0.743885	0.371942	−	0.928256i	$-0.378692\pi$
$827$	21.3924	0.743885	0.371942	+	0.928256i	$0.378692\pi$
$828$	−8.36639	−0.290752
$829$	8.79504	0.305464	0.152732	−	0.988268i	$-0.451193\pi$
$829$	8.79504	0.305464	0.152732	+	0.988268i	$0.451193\pi$
$830$	−26.3348	−0.914093
$831$	−15.5248	−0.538551
$832$	−19.2505	−0.667390
$833$	1.27013	0.0440075
$834$	−17.1435	−0.593631
$835$	−35.4405	−1.22647
$836$	−4.53846	−0.156966
$837$	−4.40845	−0.152378
$838$	23.1925	0.801173
$839$	−14.1418	−0.488230	−0.244115	−	0.969746i	$-0.578497\pi$
$839$	−14.1418	−0.488230	−0.244115	+	0.969746i	$0.578497\pi$
$840$	−6.92187	−0.238827
$841$	−17.1594	−0.591704
$842$	21.5885	0.743988
$843$	−26.9330	−0.927622
$844$	−10.3714	−0.356999
$845$	18.1291	0.623659
$846$	−6.07337	−0.208807
$847$	−0.462979	−0.0159082
$848$	3.20058	0.109908
$849$	27.7956	0.953943
$850$	−1.35167	−0.0463618
$851$	−37.8650	−1.29800
$852$	4.57534	0.156749
$853$	34.1272	1.16849	0.584246	−	0.811577i	$-0.301390\pi$
$853$	34.1272	1.16849	0.584246	+	0.811577i	$0.301390\pi$
$854$	8.02442	0.274590
$855$	2.69934	0.0923155
$856$	16.6349	0.568568
$857$	30.6559	1.04719	0.523593	−	0.851968i	$-0.324591\pi$
$857$	30.6559	1.04719	0.523593	+	0.851968i	$0.324591\pi$
$858$	−12.2459	−0.418067
$859$	42.9934	1.46692	0.733459	−	0.679734i	$-0.237905\pi$
$859$	42.9934	1.46692	0.733459	+	0.679734i	$0.237905\pi$
$860$	1.24180	0.0423449
$861$	−1.72646	−0.0588377
$862$	−21.5806	−0.735037
$863$	4.11633	0.140122	0.0700608	−	0.997543i	$-0.477681\pi$
$863$	4.11633	0.140122	0.0700608	+	0.997543i	$0.477681\pi$
$864$	5.76014	0.195964
$865$	8.50945	0.289330
$866$	−23.1526	−0.786757
$867$	15.3868	0.522562
$868$	−5.71717	−0.194053
$869$	−35.1267	−1.19159
$870$	7.22452	0.244934
$871$	−27.1935	−0.921416
$872$	41.5741	1.40788
$873$	−4.98685	−0.168779
$874$	−5.83200	−0.197270
$875$	−9.34146	−0.315799
$876$	−17.2840	−0.583971
$877$	1.31427	0.0443799	0.0221899	−	0.999754i	$-0.492936\pi$
$877$	1.31427	0.0443799	0.0221899	+	0.999754i	$0.492936\pi$
$878$	−2.62801	−0.0886909
$879$	−33.0167	−1.11363
$880$	2.23988	0.0755062
$881$	26.8956	0.906137	0.453068	−	0.891476i	$-0.350329\pi$
$881$	26.8956	0.906137	0.453068	+	0.891476i	$0.350329\pi$
$882$	−0.838531	−0.0282348
$883$	−59.0137	−1.98597	−0.992985	−	0.118239i	$-0.962275\pi$
$883$	−59.0137	−1.98597	−0.992985	+	0.118239i	$0.962275\pi$
$884$	7.41063	0.249246
$885$	−18.2165	−0.612342
$886$	3.40634	0.114438
$887$	1.05992	0.0355886	0.0177943	−	0.999842i	$-0.494336\pi$
$887$	1.05992	0.0355886	0.0177943	+	0.999842i	$0.494336\pi$
$888$	16.2261	0.544514
$889$	2.83049	0.0949317
$890$	11.4339	0.383266
$891$	3.24608	0.108748
$892$	17.7883	0.595595
$893$	7.80845	0.261300
$894$	−6.22906	−0.208331
$895$	−57.1781	−1.91125
$896$	7.93230	0.265000
$897$	29.0238	0.969077
$898$	−19.5178	−0.651317
$899$	15.1695	0.505933
$900$	−1.64587	−0.0548624
$901$	14.7508	0.491421
$902$	−4.69932	−0.156470
$903$	0.382430	0.0127265
$904$	6.48031	0.215532
$905$	51.6268	1.71613
$906$	−4.32134	−0.143567
$907$	7.97735	0.264884	0.132442	−	0.991191i	$-0.457718\pi$
$907$	7.97735	0.264884	0.132442	+	0.991191i	$0.457718\pi$
$908$	1.29687	0.0430380
$909$	0.473401	0.0157017
$910$	9.44569	0.313122
$911$	26.5751	0.880472	0.440236	−	0.897882i	$-0.354895\pi$
$911$	26.5751	0.880472	0.440236	+	0.897882i	$0.354895\pi$
$912$	−0.297110	−0.00983828
$913$	40.7161	1.34751
$914$	4.24932	0.140555
$915$	23.9606	0.792113
$916$	−19.3354	−0.638859
$917$	−0.0553473	−0.00182773
$918$	1.06505	0.0351517
$919$	−9.54484	−0.314855	−0.157428	−	0.987531i	$-0.550320\pi$
$919$	−9.54484	−0.314855	−0.157428	+	0.987531i	$0.550320\pi$
$920$	44.6547	1.47222
$921$	−19.2005	−0.632678
$922$	1.49287	0.0491651
$923$	−15.8723	−0.522443
$924$	4.20972	0.138490
$925$	−7.44897	−0.244921
$926$	−26.2200	−0.861643
$927$	−6.55626	−0.215336
$928$	−19.8207	−0.650647
$929$	−19.3866	−0.636054	−0.318027	−	0.948082i	$-0.603020\pi$
$929$	−19.3866	−0.636054	−0.318027	+	0.948082i	$0.603020\pi$
$930$	9.25569	0.303506
$931$	1.07809	0.0353329
$932$	−10.0241	−0.328349
$933$	−31.9360	−1.04554
$934$	1.77099	0.0579484
$935$	10.3231	0.337602
$936$	−12.4375	−0.406531
$937$	33.7796	1.10353	0.551765	−	0.834000i	$-0.313955\pi$
$937$	33.7796	1.10353	0.551765	+	0.834000i	$0.313955\pi$
$938$	−5.06842	−0.165490
$939$	−7.55326	−0.246491
$940$	−23.5184	−0.767087
$941$	−42.0505	−1.37081	−0.685403	−	0.728164i	$-0.740374\pi$
$941$	−42.0505	−1.37081	−0.685403	+	0.728164i	$0.740374\pi$
$942$	−5.52799	−0.180112
$943$	11.1378	0.362698
$944$	2.00505	0.0652587
$945$	−2.50382	−0.0814493
$946$	1.04095	0.0338443
$947$	12.9333	0.420276	0.210138	−	0.977672i	$-0.432609\pi$
$947$	12.9333	0.420276	0.210138	+	0.977672i	$0.432609\pi$
$948$	−14.0337	−0.455794
$949$	59.9598	1.94638
$950$	−1.14730	−0.0372232
$951$	16.1376	0.523297
$952$	3.51131	0.113802
$953$	24.7227	0.800845	0.400423	−	0.916331i	$-0.368863\pi$
$953$	24.7227	0.800845	0.400423	+	0.916331i	$0.368863\pi$
$954$	−9.73837	−0.315291
$955$	−67.1703	−2.17358
$956$	−25.7729	−0.833554
$957$	−11.1698	−0.361068
$958$	8.76063	0.283043
$959$	8.25886	0.266692
$960$	−10.7135	−0.345778
$961$	−11.5655	−0.373082
$962$	−22.1424	−0.713901
$963$	6.01726	0.193904
$964$	−24.6796	−0.794876
$965$	8.28436	0.266683
$966$	5.40957	0.174050
$967$	−47.2747	−1.52025	−0.760126	−	0.649776i	$-0.774863\pi$
$967$	−47.2747	−1.52025	−0.760126	+	0.649776i	$0.774863\pi$
$968$	−1.27992	−0.0411381
$969$	−1.36932	−0.0439888
$970$	10.4701	0.336173
$971$	12.6570	0.406184	0.203092	−	0.979160i	$-0.434901\pi$
$971$	12.6570	0.406184	0.203092	+	0.979160i	$0.434901\pi$
$972$	1.29687	0.0415970
$973$	−20.4447	−0.655426
$974$	27.6308	0.885347
$975$	5.70969	0.182857
$976$	−2.63728	−0.0844173
$977$	24.0096	0.768134	0.384067	−	0.923305i	$-0.374523\pi$
$977$	24.0096	0.768134	0.384067	+	0.923305i	$0.374523\pi$
$978$	8.37933	0.267941
$979$	−17.6780	−0.564990
$980$	−3.24712	−0.103725
$981$	15.0384	0.480140
$982$	−26.9592	−0.860303
$983$	−37.5203	−1.19671	−0.598356	−	0.801230i	$-0.704179\pi$
$983$	−37.5203	−1.19671	−0.598356	+	0.801230i	$0.704179\pi$
$984$	−4.77285	−0.152153
$985$	36.9666	1.17785
$986$	−3.66484	−0.116712
$987$	−7.24286	−0.230543
$988$	6.29015	0.200116
$989$	−2.46715	−0.0784508
$990$	−6.81524	−0.216603
$991$	28.7670	0.913815	0.456908	−	0.889514i	$-0.348957\pi$
$991$	28.7670	0.913815	0.456908	+	0.889514i	$0.348957\pi$
$992$	−25.3933	−0.806238
$993$	−12.0473	−0.382310
$994$	−2.95834	−0.0938329
$995$	−14.7937	−0.468992
$996$	16.2668	0.515433
$997$	−37.4511	−1.18609	−0.593044	−	0.805170i	$-0.702074\pi$
$997$	−37.4511	−1.18609	−0.593044	+	0.805170i	$0.702074\pi$
$998$	24.8784	0.787512
$999$	5.86942	0.185700

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4767.2.a.g.1.13	✓	35

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4767.2.a.g.1.13	✓	35	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:	\( N \)	\(=\)	\( 4767 = 3 \cdot 7 \cdot 227 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4767.a (trivial)

\(f(q)\)	\(=\)	\(q-0.838531 q^{2} -1.00000 q^{3} -1.29687 q^{4} +2.50382 q^{5} +0.838531 q^{6} +1.00000 q^{7} +2.76452 q^{8} +1.00000 q^{9} -2.09953 q^{10} +3.24608 q^{11} +1.29687 q^{12} -4.49895 q^{13} -0.838531 q^{14} -2.50382 q^{15} +0.275589 q^{16} +1.27013 q^{17} -0.838531 q^{18} +1.07809 q^{19} -3.24712 q^{20} -1.00000 q^{21} -2.72194 q^{22} +6.45124 q^{23} -2.76452 q^{24} +1.26912 q^{25} +3.77251 q^{26} -1.00000 q^{27} -1.29687 q^{28} +3.44101 q^{29} +2.09953 q^{30} +4.40845 q^{31} -5.76014 q^{32} -3.24608 q^{33} -1.06505 q^{34} +2.50382 q^{35} -1.29687 q^{36} -5.86942 q^{37} -0.904012 q^{38} +4.49895 q^{39} +6.92187 q^{40} +1.72646 q^{41} +0.838531 q^{42} -0.382430 q^{43} -4.20972 q^{44} +2.50382 q^{45} -5.40957 q^{46} +7.24286 q^{47} -0.275589 q^{48} +1.00000 q^{49} -1.06419 q^{50} -1.27013 q^{51} +5.83453 q^{52} +11.6136 q^{53} +0.838531 q^{54} +8.12760 q^{55} +2.76452 q^{56} -1.07809 q^{57} -2.88540 q^{58} +7.27550 q^{59} +3.24712 q^{60} -9.56962 q^{61} -3.69663 q^{62} +1.00000 q^{63} +4.27888 q^{64} -11.2646 q^{65} +2.72194 q^{66} +6.04440 q^{67} -1.64719 q^{68} -6.45124 q^{69} -2.09953 q^{70} +3.52800 q^{71} +2.76452 q^{72} -13.3275 q^{73} +4.92169 q^{74} -1.26912 q^{75} -1.39814 q^{76} +3.24608 q^{77} -3.77251 q^{78} -10.8213 q^{79} +0.690025 q^{80} +1.00000 q^{81} -1.44769 q^{82} +12.5432 q^{83} +1.29687 q^{84} +3.18018 q^{85} +0.320680 q^{86} -3.44101 q^{87} +8.97386 q^{88} -5.44594 q^{89} -2.09953 q^{90} -4.49895 q^{91} -8.36639 q^{92} -4.40845 q^{93} -6.07337 q^{94} +2.69934 q^{95} +5.76014 q^{96} -4.98685 q^{97} -0.838531 q^{98} +3.24608 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 35 q + 7 q^{2} - 35 q^{3} + 45 q^{4} - 4 q^{5} - 7 q^{6} + 35 q^{7} + 21 q^{8} + 35 q^{9} + 11 q^{10} - 3 q^{11} - 45 q^{12} + 19 q^{13} + 7 q^{14} + 4 q^{15} + 65 q^{16} + 20 q^{17} + 7 q^{18} + 9 q^{19}+ \cdots - 3 q^{99}+O(q^{100}) \) 35 * q + 7 * q^2 - 35 * q^3 + 45 * q^4 - 4 * q^5 - 7 * q^6 + 35 * q^7 + 21 * q^8 + 35 * q^9 + 11 * q^10 - 3 * q^11 - 45 * q^12 + 19 * q^13 + 7 * q^14 + 4 * q^15 + 65 * q^16 + 20 * q^17 + 7 * q^18 + 9 * q^19 - 7 * q^20 - 35 * q^21 + 33 * q^22 + 17 * q^23 - 21 * q^24 + 67 * q^25 - 6 * q^26 - 35 * q^27 + 45 * q^28 + 17 * q^29 - 11 * q^30 + 5 * q^31 + 54 * q^32 + 3 * q^33 + 22 * q^34 - 4 * q^35 + 45 * q^36 + 35 * q^37 - 19 * q^38 - 19 * q^39 + 34 * q^40 + 18 * q^41 - 7 * q^42 + 33 * q^43 - 7 * q^44 - 4 * q^45 + 38 * q^46 - 13 * q^47 - 65 * q^48 + 35 * q^49 + 28 * q^50 - 20 * q^51 + 37 * q^52 + 36 * q^53 - 7 * q^54 + 21 * q^55 + 21 * q^56 - 9 * q^57 + 42 * q^58 - 54 * q^59 + 7 * q^60 + 35 * q^61 - 28 * q^62 + 35 * q^63 + 105 * q^64 + 27 * q^65 - 33 * q^66 + 37 * q^67 + 25 * q^68 - 17 * q^69 + 11 * q^70 + 44 * q^71 + 21 * q^72 + 59 * q^73 - 17 * q^74 - 67 * q^75 + 23 * q^76 - 3 * q^77 + 6 * q^78 + 77 * q^79 - 26 * q^80 + 35 * q^81 + 4 * q^82 - 41 * q^83 - 45 * q^84 + 39 * q^85 + 42 * q^86 - 17 * q^87 + 34 * q^88 - 9 * q^89 + 11 * q^90 + 19 * q^91 + 61 * q^92 - 5 * q^93 + 10 * q^94 + 25 * q^95 - 54 * q^96 + 79 * q^97 + 7 * q^98 - 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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