LMFDB - Embedded newform 787.2.a.b.1.29

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [787,2,Mod(1,787)] 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("787.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(787, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 787 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	787.a (trivial)

Newform invariants

comment:select newform

sage:traces = [37] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	yes
Analytic conductor:	$6.28422663907$
Analytic rank:	$0$
Dimension:	$37$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.29
Character	$\chi$	$=$	787.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.07648 q^{2} +2.52983 q^{3} +2.31176 q^{4} -2.31346 q^{5} +5.25313 q^{6} +3.90087 q^{7} +0.647352 q^{8} +3.40003 q^{9} -4.80384 q^{10} -0.380988 q^{11} +5.84834 q^{12} -1.10393 q^{13} +8.10007 q^{14} -5.85265 q^{15} -3.27930 q^{16} +4.45866 q^{17} +7.06008 q^{18} -4.30960 q^{19} -5.34814 q^{20} +9.86854 q^{21} -0.791112 q^{22} +0.314739 q^{23} +1.63769 q^{24} +0.352078 q^{25} -2.29229 q^{26} +1.01201 q^{27} +9.01786 q^{28} +6.07653 q^{29} -12.1529 q^{30} -6.95047 q^{31} -8.10409 q^{32} -0.963833 q^{33} +9.25830 q^{34} -9.02450 q^{35} +7.86004 q^{36} +4.45206 q^{37} -8.94878 q^{38} -2.79276 q^{39} -1.49762 q^{40} -7.67874 q^{41} +20.4918 q^{42} +2.25227 q^{43} -0.880750 q^{44} -7.86582 q^{45} +0.653548 q^{46} -6.31760 q^{47} -8.29606 q^{48} +8.21681 q^{49} +0.731081 q^{50} +11.2796 q^{51} -2.55202 q^{52} +5.39399 q^{53} +2.10141 q^{54} +0.881398 q^{55} +2.52524 q^{56} -10.9025 q^{57} +12.6178 q^{58} +4.78190 q^{59} -13.5299 q^{60} -7.51715 q^{61} -14.4325 q^{62} +13.2631 q^{63} -10.2694 q^{64} +2.55390 q^{65} -2.00138 q^{66} -3.20121 q^{67} +10.3073 q^{68} +0.796236 q^{69} -18.7392 q^{70} +13.9356 q^{71} +2.20102 q^{72} -0.383692 q^{73} +9.24459 q^{74} +0.890696 q^{75} -9.96273 q^{76} -1.48618 q^{77} -5.79910 q^{78} -11.7189 q^{79} +7.58651 q^{80} -7.63989 q^{81} -15.9447 q^{82} +5.28368 q^{83} +22.8136 q^{84} -10.3149 q^{85} +4.67680 q^{86} +15.3726 q^{87} -0.246633 q^{88} +6.24301 q^{89} -16.3332 q^{90} -4.30630 q^{91} +0.727600 q^{92} -17.5835 q^{93} -13.1183 q^{94} +9.97006 q^{95} -20.5020 q^{96} +2.15977 q^{97} +17.0620 q^{98} -1.29537 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q + 12 q^{2} + 6 q^{3} + 42 q^{4} + 31 q^{5} + 4 q^{6} + 9 q^{7} + 36 q^{8} + 47 q^{9} + 4 q^{10} + 18 q^{11} + 15 q^{12} + 13 q^{13} + 8 q^{14} + 3 q^{15} + 48 q^{16} + 18 q^{17} + 17 q^{18} + 40 q^{20}+ \cdots - 35 q^{99}+O(q^{100}) $ 37 * q + 12 * q^2 + 6 * q^3 + 42 * q^4 + 31 * q^5 + 4 * q^6 + 9 * q^7 + 36 * q^8 + 47 * q^9 + 4 * q^10 + 18 * q^11 + 15 * q^12 + 13 * q^13 + 8 * q^14 + 3 * q^15 + 48 * q^16 + 18 * q^17 + 17 * q^18 + 40 * q^20 - 4 * q^21 - 4 * q^22 + 42 * q^23 - 10 * q^24 + 56 * q^25 - 4 * q^26 + 18 * q^27 + 3 * q^28 + 45 * q^29 - 32 * q^30 - 3 * q^31 + 59 * q^32 + 14 * q^33 - 22 * q^34 + 16 * q^35 + 28 * q^36 + 52 * q^37 - 5 * q^38 - 13 * q^39 - 11 * q^40 + 23 * q^41 - 16 * q^42 + 4 * q^43 + 23 * q^44 + 69 * q^45 - 5 * q^46 + 45 * q^47 - 5 * q^48 + 30 * q^49 + 13 * q^50 - 7 * q^51 + 3 * q^52 + 103 * q^53 - 23 * q^54 - 9 * q^55 + 4 * q^56 + 9 * q^57 + 8 * q^58 + 2 * q^59 - 47 * q^60 - 6 * q^61 + 20 * q^62 + 5 * q^63 + 28 * q^64 + 51 * q^65 - 48 * q^66 + 24 * q^67 - 9 * q^68 - 52 * q^70 + 32 * q^71 + 42 * q^72 + 5 * q^73 + 4 * q^74 - 35 * q^75 - 34 * q^76 + 97 * q^77 - 31 * q^78 - 27 * q^79 + 47 * q^80 + 29 * q^81 - q^82 + 23 * q^83 - 93 * q^84 + 27 * q^85 + 10 * q^86 - 46 * q^87 - 45 * q^88 + 9 * q^89 - 70 * q^90 - 48 * q^91 + 67 * q^92 + 72 * q^93 - 52 * q^94 - 20 * q^95 - 89 * q^96 - 7 * q^97 - 12 * q^98 - 35 * 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 $

$2$	2.07648	1.46829	0.734145	−	0.678992i	$-0.237583\pi$
$2$	2.07648	1.46829	0.734145	+	0.678992i	$0.237583\pi$
$3$	2.52983	1.46060	0.730298	−	0.683128i	$-0.239381\pi$
$3$	2.52983	1.46060	0.730298	+	0.683128i	$0.239381\pi$
$4$	2.31176	1.15588
$5$	−2.31346	−1.03461	−0.517304	−	0.855801i	$-0.673065\pi$
$5$	−2.31346	−1.03461	−0.517304	+	0.855801i	$0.673065\pi$
$6$	5.25313	2.14458
$7$	3.90087	1.47439	0.737196	−	0.675679i	$-0.236150\pi$
$7$	3.90087	1.47439	0.737196	+	0.675679i	$0.236150\pi$
$8$	0.647352	0.228874
$9$	3.40003	1.13334
$10$	−4.80384	−1.51911
$11$	−0.380988	−0.114872	−0.0574361	−	0.998349i	$-0.518293\pi$
$11$	−0.380988	−0.114872	−0.0574361	+	0.998349i	$0.518293\pi$
$12$	5.84834	1.68827
$13$	−1.10393	−0.306176	−0.153088	−	0.988213i	$-0.548922\pi$
$13$	−1.10393	−0.306176	−0.153088	+	0.988213i	$0.548922\pi$
$14$	8.10007	2.16483
$15$	−5.85265	−1.51115
$16$	−3.27930	−0.819825
$17$	4.45866	1.08138	0.540692	−	0.841221i	$-0.318162\pi$
$17$	4.45866	1.08138	0.540692	+	0.841221i	$0.318162\pi$
$18$	7.06008	1.66408
$19$	−4.30960	−0.988689	−0.494345	−	0.869266i	$-0.664592\pi$
$19$	−4.30960	−0.988689	−0.494345	+	0.869266i	$0.664592\pi$
$20$	−5.34814	−1.19588
$21$	9.86854	2.15349
$22$	−0.791112	−0.168666
$23$	0.314739	0.0656276	0.0328138	−	0.999461i	$-0.489553\pi$
$23$	0.314739	0.0656276	0.0328138	+	0.999461i	$0.489553\pi$
$24$	1.63769	0.334292
$25$	0.352078	0.0704155
$26$	−2.29229	−0.449555
$27$	1.01201	0.194761
$28$	9.01786	1.70422
$29$	6.07653	1.12838	0.564192	−	0.825644i	$-0.309188\pi$
$29$	6.07653	1.12838	0.564192	+	0.825644i	$0.309188\pi$
$30$	−12.1529	−2.21880
$31$	−6.95047	−1.24834	−0.624171	−	0.781288i	$-0.714563\pi$
$31$	−6.95047	−1.24834	−0.624171	+	0.781288i	$0.714563\pi$
$32$	−8.10409	−1.43261
$33$	−0.963833	−0.167782
$34$	9.25830	1.58779
$35$	−9.02450	−1.52542
$36$	7.86004	1.31001
$37$	4.45206	0.731913	0.365957	−	0.930632i	$-0.380742\pi$
$37$	4.45206	0.731913	0.365957	+	0.930632i	$0.380742\pi$
$38$	−8.94878	−1.45168
$39$	−2.79276	−0.447199
$40$	−1.49762	−0.236795
$41$	−7.67874	−1.19922	−0.599609	−	0.800293i	$-0.704677\pi$
$41$	−7.67874	−1.19922	−0.599609	+	0.800293i	$0.704677\pi$
$42$	20.4918	3.16195
$43$	2.25227	0.343469	0.171734	−	0.985143i	$-0.445063\pi$
$43$	2.25227	0.343469	0.171734	+	0.985143i	$0.445063\pi$
$44$	−0.880750	−0.132778
$45$	−7.86582	−1.17257
$46$	0.653548	0.0963605
$47$	−6.31760	−0.921516	−0.460758	−	0.887526i	$-0.652422\pi$
$47$	−6.31760	−0.921516	−0.460758	+	0.887526i	$0.652422\pi$
$48$	−8.29606	−1.19743
$49$	8.21681	1.17383
$50$	0.731081	0.103390
$51$	11.2796	1.57947
$52$	−2.55202	−0.353902
$53$	5.39399	0.740922	0.370461	−	0.928848i	$-0.379200\pi$
$53$	5.39399	0.740922	0.370461	+	0.928848i	$0.379200\pi$
$54$	2.10141	0.285965
$55$	0.881398	0.118848
$56$	2.52524	0.337449
$57$	−10.9025	−1.44408
$58$	12.6178	1.65680
$59$	4.78190	0.622551	0.311275	−	0.950320i	$-0.399244\pi$
$59$	4.78190	0.622551	0.311275	+	0.950320i	$0.399244\pi$
$60$	−13.5299	−1.74670
$61$	−7.51715	−0.962472	−0.481236	−	0.876591i	$-0.659812\pi$
$61$	−7.51715	−0.962472	−0.481236	+	0.876591i	$0.659812\pi$
$62$	−14.4325	−1.83293
$63$	13.2631	1.67099
$64$	−10.2694	−1.28367
$65$	2.55390	0.316772
$66$	−2.00138	−0.246353
$67$	−3.20121	−0.391090	−0.195545	−	0.980695i	$-0.562648\pi$
$67$	−3.20121	−0.391090	−0.195545	+	0.980695i	$0.562648\pi$
$68$	10.3073	1.24995
$69$	0.796236	0.0958555
$70$	−18.7392	−2.23976
$71$	13.9356	1.65385	0.826924	−	0.562314i	$-0.190089\pi$
$71$	13.9356	1.65385	0.826924	+	0.562314i	$0.190089\pi$
$72$	2.20102	0.259392
$73$	−0.383692	−0.0449077	−0.0224539	−	0.999748i	$-0.507148\pi$
$73$	−0.383692	−0.0449077	−0.0224539	+	0.999748i	$0.507148\pi$
$74$	9.24459	1.07466
$75$	0.890696	0.102849
$76$	−9.96273	−1.14280
$77$	−1.48618	−0.169366
$78$	−5.79910	−0.656619
$79$	−11.7189	−1.31847	−0.659237	−	0.751935i	$-0.729121\pi$
$79$	−11.7189	−1.31847	−0.659237	+	0.751935i	$0.729121\pi$
$80$	7.58651	0.848198
$81$	−7.63989	−0.848876
$82$	−15.9447	−1.76080
$83$	5.28368	0.579959	0.289979	−	0.957033i	$-0.406352\pi$
$83$	5.28368	0.579959	0.289979	+	0.957033i	$0.406352\pi$
$84$	22.8136	2.48917
$85$	−10.3149	−1.11881
$86$	4.67680	0.504312
$87$	15.3726	1.64811
$88$	−0.246633	−0.0262912
$89$	6.24301	0.661758	0.330879	−	0.943673i	$-0.392655\pi$
$89$	6.24301	0.661758	0.330879	+	0.943673i	$0.392655\pi$
$90$	−16.3332	−1.72167
$91$	−4.30630	−0.451423
$92$	0.727600	0.0758575
$93$	−17.5835	−1.82332
$94$	−13.1183	−1.35305
$95$	9.97006	1.02291
$96$	−20.5020	−2.09247
$97$	2.15977	0.219291	0.109646	−	0.993971i	$-0.465028\pi$
$97$	2.15977	0.219291	0.109646	+	0.993971i	$0.465028\pi$
$98$	17.0620	1.72352
$99$	−1.29537	−0.130190
$100$	0.813917	0.0813917
$101$	−5.32715	−0.530072	−0.265036	−	0.964239i	$-0.585384\pi$
$101$	−5.32715	−0.530072	−0.265036	+	0.964239i	$0.585384\pi$
$102$	23.4219	2.31911
$103$	7.37491	0.726671	0.363336	−	0.931658i	$-0.381638\pi$
$103$	7.37491	0.726671	0.363336	+	0.931658i	$0.381638\pi$
$104$	−0.714633	−0.0700755
$105$	−22.8304	−2.22802
$106$	11.2005	1.08789
$107$	−13.1643	−1.27264	−0.636322	−	0.771423i	$-0.719545\pi$
$107$	−13.1643	−1.27264	−0.636322	+	0.771423i	$0.719545\pi$
$108$	2.33951	0.225119
$109$	−2.50313	−0.239756	−0.119878	−	0.992789i	$-0.538250\pi$
$109$	−2.50313	−0.239756	−0.119878	+	0.992789i	$0.538250\pi$
$110$	1.83020	0.174503
$111$	11.2629	1.06903
$112$	−12.7921	−1.20874
$113$	−8.23812	−0.774977	−0.387488	−	0.921875i	$-0.626657\pi$
$113$	−8.23812	−0.774977	−0.387488	+	0.921875i	$0.626657\pi$
$114$	−22.6389	−2.12032
$115$	−0.728135	−0.0678989
$116$	14.0475	1.30427
$117$	−3.75340	−0.347002
$118$	9.92951	0.914085
$119$	17.3927	1.59438
$120$	−3.78872	−0.345862
$121$	−10.8548	−0.986804
$122$	−15.6092	−1.41319
$123$	−19.4259	−1.75157
$124$	−16.0678	−1.44293
$125$	10.7528	0.961756
$126$	27.5405	2.45350
$127$	−18.5028	−1.64186	−0.820931	−	0.571027i	$-0.806545\pi$
$127$	−18.5028	−1.64186	−0.820931	+	0.571027i	$0.806545\pi$
$128$	−5.11590	−0.452186
$129$	5.69787	0.501669
$130$	5.30311	0.465114
$131$	4.17157	0.364472	0.182236	−	0.983255i	$-0.441666\pi$
$131$	4.17157	0.364472	0.182236	+	0.983255i	$0.441666\pi$
$132$	−2.22815	−0.193935
$133$	−16.8112	−1.45771
$134$	−6.64724	−0.574234
$135$	−2.34123	−0.201501
$136$	2.88632	0.247500
$137$	4.81002	0.410947	0.205474	−	0.978663i	$-0.434127\pi$
$137$	4.81002	0.410947	0.205474	+	0.978663i	$0.434127\pi$
$138$	1.65336	0.140744
$139$	21.4438	1.81884	0.909418	−	0.415883i	$-0.136527\pi$
$139$	21.4438	1.81884	0.909418	+	0.415883i	$0.136527\pi$
$140$	−20.8624	−1.76320
$141$	−15.9824	−1.34596
$142$	28.9369	2.42833
$143$	0.420585	0.0351711
$144$	−11.1497	−0.929143
$145$	−14.0578	−1.16744
$146$	−0.796727	−0.0659376
$147$	20.7871	1.71449
$148$	10.2921	0.846002
$149$	18.6576	1.52849	0.764246	−	0.644925i	$-0.223112\pi$
$149$	18.6576	1.52849	0.764246	+	0.644925i	$0.223112\pi$
$150$	1.84951	0.151012
$151$	14.3221	1.16551	0.582756	−	0.812647i	$-0.301974\pi$
$151$	14.3221	1.16551	0.582756	+	0.812647i	$0.301974\pi$
$152$	−2.78983	−0.226285
$153$	15.1596	1.22558
$154$	−3.08603	−0.248679
$155$	16.0796	1.29155
$156$	−6.45618	−0.516908
$157$	3.56421	0.284455	0.142227	−	0.989834i	$-0.454574\pi$
$157$	3.56421	0.284455	0.142227	+	0.989834i	$0.454574\pi$
$158$	−24.3339	−1.93590
$159$	13.6459	1.08219
$160$	18.7485	1.48220
$161$	1.22776	0.0967608
$162$	−15.8640	−1.24640
$163$	13.8507	1.08487	0.542434	−	0.840099i	$-0.317503\pi$
$163$	13.8507	1.08487	0.542434	+	0.840099i	$0.317503\pi$
$164$	−17.7514	−1.38615
$165$	2.22979	0.173589
$166$	10.9714	0.851548
$167$	20.7649	1.60684	0.803418	−	0.595415i	$-0.203012\pi$
$167$	20.7649	1.60684	0.803418	+	0.595415i	$0.203012\pi$
$168$	6.38842	0.492877
$169$	−11.7813	−0.906256
$170$	−21.4187	−1.64274
$171$	−14.6528	−1.12052
$172$	5.20671	0.397008
$173$	16.4055	1.24729	0.623643	−	0.781710i	$-0.285652\pi$
$173$	16.4055	1.24729	0.623643	+	0.781710i	$0.285652\pi$
$174$	31.9208	2.41991
$175$	1.37341	0.103820
$176$	1.24937	0.0941750
$177$	12.0974	0.909296
$178$	12.9635	0.971652
$179$	−6.38891	−0.477529	−0.238765	−	0.971077i	$-0.576742\pi$
$179$	−6.38891	−0.477529	−0.238765	+	0.971077i	$0.576742\pi$
$180$	−18.1838	−1.35534
$181$	6.21030	0.461608	0.230804	−	0.973000i	$-0.425864\pi$
$181$	6.21030	0.461608	0.230804	+	0.973000i	$0.425864\pi$
$182$	−8.94193	−0.662820
$183$	−19.0171	−1.40578
$184$	0.203747	0.0150204
$185$	−10.2996	−0.757244
$186$	−36.5117	−2.67717
$187$	−1.69869	−0.124221
$188$	−14.6047	−1.06516
$189$	3.94770	0.287153
$190$	20.7026	1.50192
$191$	13.5193	0.978219	0.489109	−	0.872222i	$-0.337322\pi$
$191$	13.5193	0.978219	0.489109	+	0.872222i	$0.337322\pi$
$192$	−25.9797	−1.87492
$193$	15.5128	1.11664	0.558318	−	0.829627i	$-0.311447\pi$
$193$	15.5128	1.11664	0.558318	+	0.829627i	$0.311447\pi$
$194$	4.48471	0.321983
$195$	6.46092	0.462676
$196$	18.9952	1.35680
$197$	20.2431	1.44226	0.721129	−	0.692801i	$-0.243624\pi$
$197$	20.2431	1.44226	0.721129	+	0.692801i	$0.243624\pi$
$198$	−2.68980	−0.191156
$199$	−17.5392	−1.24332	−0.621660	−	0.783287i	$-0.713541\pi$
$199$	−17.5392	−1.24332	−0.621660	+	0.783287i	$0.713541\pi$
$200$	0.227918	0.0161163
$201$	−8.09851	−0.571225
$202$	−11.0617	−0.778299
$203$	23.7038	1.66368
$204$	26.0758	1.82567
$205$	17.7644	1.24072
$206$	15.3138	1.06696
$207$	1.07012	0.0743786
$208$	3.62012	0.251010
$209$	1.64190	0.113573
$210$	−47.4068	−3.27138
$211$	3.85809	0.265602	0.132801	−	0.991143i	$-0.457603\pi$
$211$	3.85809	0.265602	0.132801	+	0.991143i	$0.457603\pi$
$212$	12.4696	0.856415
$213$	35.2546	2.41560
$214$	−27.3354	−1.86861
$215$	−5.21054	−0.355356
$216$	0.655124	0.0445756
$217$	−27.1129	−1.84054
$218$	−5.19769	−0.352032
$219$	−0.970674	−0.0655921
$220$	2.03758	0.137373
$221$	−4.92206	−0.331094
$222$	23.3872	1.56965
$223$	−9.54769	−0.639361	−0.319680	−	0.947525i	$-0.603575\pi$
$223$	−9.54769	−0.639361	−0.319680	+	0.947525i	$0.603575\pi$
$224$	−31.6130	−2.11223
$225$	1.19707	0.0798049
$226$	−17.1063	−1.13789
$227$	−27.5381	−1.82777	−0.913885	−	0.405972i	$-0.866933\pi$
$227$	−27.5381	−1.82777	−0.913885	+	0.405972i	$0.866933\pi$
$228$	−25.2040	−1.66918
$229$	−12.0707	−0.797652	−0.398826	−	0.917027i	$-0.630582\pi$
$229$	−12.0707	−0.797652	−0.398826	+	0.917027i	$0.630582\pi$
$230$	−1.51196	−0.0996954
$231$	−3.75979	−0.247376
$232$	3.93366	0.258257
$233$	−2.20908	−0.144722	−0.0723609	−	0.997379i	$-0.523053\pi$
$233$	−2.20908	−0.144722	−0.0723609	+	0.997379i	$0.523053\pi$
$234$	−7.79385	−0.509500
$235$	14.6155	0.953409
$236$	11.0546	0.719592
$237$	−29.6467	−1.92576
$238$	36.1155	2.34102
$239$	0.113181	0.00732110	0.00366055	−	0.999993i	$-0.498835\pi$
$239$	0.113181	0.00732110	0.00366055	+	0.999993i	$0.498835\pi$
$240$	19.1926	1.23888
$241$	4.37191	0.281620	0.140810	−	0.990037i	$-0.455029\pi$
$241$	4.37191	0.281620	0.140810	+	0.990037i	$0.455029\pi$
$242$	−22.5398	−1.44892
$243$	−22.3636	−1.43463
$244$	−17.3778	−1.11250
$245$	−19.0092	−1.21445
$246$	−40.3374	−2.57182
$247$	4.75750	0.302713
$248$	−4.49940	−0.285712
$249$	13.3668	0.847086
$250$	22.3279	1.41214
$251$	15.4960	0.978101	0.489050	−	0.872256i	$-0.337343\pi$
$251$	15.4960	0.978101	0.489050	+	0.872256i	$0.337343\pi$
$252$	30.6610	1.93146
$253$	−0.119912	−0.00753879
$254$	−38.4207	−2.41073
$255$	−26.0950	−1.63413
$256$	9.91567	0.619729
$257$	−27.3068	−1.70335	−0.851674	−	0.524072i	$-0.824412\pi$
$257$	−27.3068	−1.70335	−0.851674	+	0.524072i	$0.824412\pi$
$258$	11.8315	0.736596
$259$	17.3669	1.07913
$260$	5.90399	0.366150
$261$	20.6604	1.27885
$262$	8.66218	0.535151
$263$	7.99652	0.493087	0.246543	−	0.969132i	$-0.420705\pi$
$263$	7.99652	0.493087	0.246543	+	0.969132i	$0.420705\pi$
$264$	−0.623940	−0.0384008
$265$	−12.4788	−0.766564
$266$	−34.9080	−2.14035
$267$	15.7937	0.966561
$268$	−7.40041	−0.452052
$269$	−31.0747	−1.89466	−0.947329	−	0.320263i	$-0.896229\pi$
$269$	−31.0747	−1.89466	−0.947329	+	0.320263i	$0.896229\pi$
$270$	−4.86151	−0.295862
$271$	−4.41824	−0.268389	−0.134194	−	0.990955i	$-0.542845\pi$
$271$	−4.41824	−0.268389	−0.134194	+	0.990955i	$0.542845\pi$
$272$	−14.6213	−0.886545
$273$	−10.8942	−0.659347
$274$	9.98788	0.603390
$275$	−0.134137	−0.00808878
$276$	1.84070	0.110797
$277$	21.6684	1.30193	0.650965	−	0.759108i	$-0.274365\pi$
$277$	21.6684	1.30193	0.650965	+	0.759108i	$0.274365\pi$
$278$	44.5275	2.67058
$279$	−23.6318	−1.41480
$280$	−5.84203	−0.349128
$281$	1.54354	0.0920797	0.0460399	−	0.998940i	$-0.485340\pi$
$281$	1.54354	0.0920797	0.0460399	+	0.998940i	$0.485340\pi$
$282$	−33.1872	−1.97627
$283$	−23.9293	−1.42245	−0.711226	−	0.702963i	$-0.751860\pi$
$283$	−23.9293	−1.42245	−0.711226	+	0.702963i	$0.751860\pi$
$284$	32.2156	1.91164
$285$	25.2225	1.49405
$286$	0.873334	0.0516413
$287$	−29.9538	−1.76812
$288$	−27.5541	−1.62364
$289$	2.87965	0.169391
$290$	−29.1907	−1.71414
$291$	5.46384	0.320296
$292$	−0.887001	−0.0519078
$293$	21.9854	1.28440	0.642202	−	0.766536i	$-0.278021\pi$
$293$	21.9854	1.28440	0.642202	+	0.766536i	$0.278021\pi$
$294$	43.1639	2.51737
$295$	−11.0627	−0.644096
$296$	2.88205	0.167516
$297$	−0.385562	−0.0223726
$298$	38.7421	2.24427
$299$	−0.347451	−0.0200936
$300$	2.05907	0.118880
$301$	8.78584	0.506407
$302$	29.7394	1.71131
$303$	−13.4768	−0.774221
$304$	14.1325	0.810552
$305$	17.3906	0.995782
$306$	31.4785	1.79951
$307$	4.69807	0.268133	0.134066	−	0.990972i	$-0.457196\pi$
$307$	4.69807	0.268133	0.134066	+	0.990972i	$0.457196\pi$
$308$	−3.43569	−0.195767
$309$	18.6572	1.06137
$310$	33.3889	1.89636
$311$	18.4888	1.04840	0.524201	−	0.851594i	$-0.324364\pi$
$311$	18.4888	1.04840	0.524201	+	0.851594i	$0.324364\pi$
$312$	−1.80790	−0.102352
$313$	−10.9240	−0.617462	−0.308731	−	0.951149i	$-0.599904\pi$
$313$	−10.9240	−0.617462	−0.308731	+	0.951149i	$0.599904\pi$
$314$	7.40100	0.417663
$315$	−30.6836	−1.72882
$316$	−27.0911	−1.52399
$317$	17.5414	0.985221	0.492610	−	0.870250i	$-0.336043\pi$
$317$	17.5414	0.985221	0.492610	+	0.870250i	$0.336043\pi$
$318$	28.3353	1.58897
$319$	−2.31508	−0.129620
$320$	23.7577	1.32810
$321$	−33.3035	−1.85882
$322$	2.54941	0.142073
$323$	−19.2150	−1.06915
$324$	−17.6616	−0.981197
$325$	−0.388670	−0.0215595
$326$	28.7606	1.59290
$327$	−6.33249	−0.350187
$328$	−4.97085	−0.274469
$329$	−24.6441	−1.35868
$330$	4.63010	0.254878
$331$	31.1256	1.71082	0.855409	−	0.517954i	$-0.173306\pi$
$331$	31.1256	1.71082	0.855409	+	0.517954i	$0.173306\pi$
$332$	12.2146	0.670361
$333$	15.1371	0.829509
$334$	43.1178	2.35930
$335$	7.40586	0.404625
$336$	−32.3619	−1.76548
$337$	6.72792	0.366493	0.183246	−	0.983067i	$-0.441339\pi$
$337$	6.72792	0.366493	0.183246	+	0.983067i	$0.441339\pi$
$338$	−24.4637	−1.33065
$339$	−20.8410	−1.13193
$340$	−23.8456	−1.29321
$341$	2.64804	0.143400
$342$	−30.4261	−1.64526
$343$	4.74660	0.256292
$344$	1.45802	0.0786109
$345$	−1.84206	−0.0991730
$346$	34.0656	1.83138
$347$	0.965147	0.0518118	0.0259059	−	0.999664i	$-0.491753\pi$
$347$	0.965147	0.0518118	0.0259059	+	0.999664i	$0.491753\pi$
$348$	35.5376	1.90502
$349$	36.9488	1.97782	0.988911	−	0.148511i	$-0.0474481\pi$
$349$	36.9488	1.97782	0.988911	+	0.148511i	$0.0474481\pi$
$350$	2.85185	0.152438
$351$	−1.11719	−0.0596310
$352$	3.08756	0.164567
$353$	−11.2463	−0.598581	−0.299290	−	0.954162i	$-0.596750\pi$
$353$	−11.2463	−0.598581	−0.299290	+	0.954162i	$0.596750\pi$
$354$	25.1199	1.33511
$355$	−32.2393	−1.71108
$356$	14.4323	0.764911
$357$	44.0004	2.32875
$358$	−13.2664	−0.701152
$359$	16.9558	0.894893	0.447446	−	0.894311i	$-0.352334\pi$
$359$	16.9558	0.894893	0.447446	+	0.894311i	$0.352334\pi$
$360$	−5.09196	−0.268370
$361$	−0.427380	−0.0224937
$362$	12.8956	0.677775
$363$	−27.4609	−1.44132
$364$	−9.95511	−0.521790
$365$	0.887654	0.0464619
$366$	−39.4885	−2.06410
$367$	−3.48406	−0.181866	−0.0909331	−	0.995857i	$-0.528985\pi$
$367$	−3.48406	−0.181866	−0.0909331	+	0.995857i	$0.528985\pi$
$368$	−1.03212	−0.0538032
$369$	−26.1079	−1.35912
$370$	−21.3869	−1.11185
$371$	21.0413	1.09241
$372$	−40.6487	−2.10754
$373$	−26.1507	−1.35403	−0.677016	−	0.735968i	$-0.736727\pi$
$373$	−26.1507	−1.35403	−0.677016	+	0.735968i	$0.736727\pi$
$374$	−3.52730	−0.182392
$375$	27.2026	1.40474
$376$	−4.08971	−0.210911
$377$	−6.70808	−0.345484
$378$	8.19732	0.421624
$379$	−17.7290	−0.910677	−0.455338	−	0.890319i	$-0.650482\pi$
$379$	−17.7290	−0.910677	−0.455338	+	0.890319i	$0.650482\pi$
$380$	23.0483	1.18235
$381$	−46.8090	−2.39810
$382$	28.0724	1.43631
$383$	0.0510881	0.00261048	0.00130524	−	0.999999i	$-0.499585\pi$
$383$	0.0510881	0.00261048	0.00130524	+	0.999999i	$0.499585\pi$
$384$	−12.9424	−0.660462
$385$	3.43822	0.175228
$386$	32.2120	1.63955
$387$	7.65780	0.389268
$388$	4.99286	0.253474
$389$	22.6121	1.14648	0.573240	−	0.819387i	$-0.305686\pi$
$389$	22.6121	1.14648	0.573240	+	0.819387i	$0.305686\pi$
$390$	13.4160	0.679343
$391$	1.40331	0.0709687
$392$	5.31917	0.268659
$393$	10.5534	0.532347
$394$	42.0342	2.11765
$395$	27.1110	1.36410
$396$	−2.99458	−0.150483
$397$	−37.0191	−1.85794	−0.928969	−	0.370158i	$-0.879303\pi$
$397$	−37.0191	−1.85794	−0.928969	+	0.370158i	$0.879303\pi$
$398$	−36.4197	−1.82556
$399$	−42.5294	−2.12913
$400$	−1.15457	−0.0577284
$401$	−33.6748	−1.68164	−0.840820	−	0.541314i	$-0.817927\pi$
$401$	−33.6748	−1.68164	−0.840820	+	0.541314i	$0.817927\pi$
$402$	−16.8164	−0.838724
$403$	7.67285	0.382212
$404$	−12.3151	−0.612698
$405$	17.6745	0.878255
$406$	49.2203	2.44276
$407$	−1.69618	−0.0840764
$408$	7.30190	0.361498
$409$	8.46710	0.418671	0.209336	−	0.977844i	$-0.432870\pi$
$409$	8.46710	0.418671	0.209336	+	0.977844i	$0.432870\pi$
$410$	36.8874	1.82174
$411$	12.1685	0.600228
$412$	17.0490	0.839943
$413$	18.6536	0.917883
$414$	2.22208	0.109209
$415$	−12.2236	−0.600030
$416$	8.94637	0.438632
$417$	54.2490	2.65659
$418$	3.40937	0.166758
$419$	17.6364	0.861594	0.430797	−	0.902449i	$-0.358233\pi$
$419$	17.6364	0.861594	0.430797	+	0.902449i	$0.358233\pi$
$420$	−52.7783	−2.57532
$421$	23.1751	1.12948	0.564742	−	0.825267i	$-0.308976\pi$
$421$	23.1751	1.12948	0.564742	+	0.825267i	$0.308976\pi$
$422$	8.01124	0.389981
$423$	−21.4800	−1.04439
$424$	3.49181	0.169577
$425$	1.56979	0.0761462
$426$	73.2053	3.54681
$427$	−29.3234	−1.41906
$428$	−30.4327	−1.47102
$429$	1.06401	0.0513707
$430$	−10.8196	−0.521766
$431$	−23.5469	−1.13421	−0.567107	−	0.823644i	$-0.691937\pi$
$431$	−23.5469	−1.13421	−0.567107	+	0.823644i	$0.691937\pi$
$432$	−3.31867	−0.159670
$433$	−13.0763	−0.628406	−0.314203	−	0.949356i	$-0.601737\pi$
$433$	−13.0763	−0.628406	−0.314203	+	0.949356i	$0.601737\pi$
$434$	−56.2993	−2.70245
$435$	−35.5638	−1.70515
$436$	−5.78662	−0.277129
$437$	−1.35640	−0.0648853
$438$	−2.01558	−0.0963082
$439$	−24.1862	−1.15435	−0.577173	−	0.816622i	$-0.695844\pi$
$439$	−24.1862	−1.15435	−0.577173	+	0.816622i	$0.695844\pi$
$440$	0.570575	0.0272011
$441$	27.9374	1.33035
$442$	−10.2205	−0.486142
$443$	−11.6042	−0.551334	−0.275667	−	0.961253i	$-0.588899\pi$
$443$	−11.6042	−0.551334	−0.275667	+	0.961253i	$0.588899\pi$
$444$	26.0371	1.23567
$445$	−14.4429	−0.684660
$446$	−19.8256	−0.938767
$447$	47.2005	2.23251
$448$	−40.0595	−1.89263
$449$	−27.6027	−1.30265	−0.651326	−	0.758798i	$-0.725787\pi$
$449$	−27.6027	−1.30265	−0.651326	+	0.758798i	$0.725787\pi$
$450$	2.48570	0.117177
$451$	2.92550	0.137757
$452$	−19.0445	−0.895778
$453$	36.2323	1.70234
$454$	−57.1823	−2.68370
$455$	9.96243	0.467046
$456$	−7.05778	−0.330511
$457$	30.5773	1.43034	0.715172	−	0.698948i	$-0.246348\pi$
$457$	30.5773	1.43034	0.715172	+	0.698948i	$0.246348\pi$
$458$	−25.0645	−1.17118
$459$	4.51219	0.210611
$460$	−1.68327	−0.0784829
$461$	21.7806	1.01443	0.507213	−	0.861821i	$-0.330676\pi$
$461$	21.7806	1.01443	0.507213	+	0.861821i	$0.330676\pi$
$462$	−7.80712	−0.363220
$463$	36.2620	1.68524	0.842618	−	0.538512i	$-0.181013\pi$
$463$	36.2620	1.68524	0.842618	+	0.538512i	$0.181013\pi$
$464$	−19.9268	−0.925077
$465$	40.6787	1.88643
$466$	−4.58711	−0.212494
$467$	−0.313778	−0.0145199	−0.00725996	−	0.999974i	$-0.502311\pi$
$467$	−0.313778	−0.0145199	−0.00725996	+	0.999974i	$0.502311\pi$
$468$	−8.67695	−0.401092
$469$	−12.4875	−0.576620
$470$	30.3487	1.39988
$471$	9.01684	0.415474
$472$	3.09558	0.142485
$473$	−0.858089	−0.0394550
$474$	−61.5606	−2.82757
$475$	−1.51731	−0.0696191
$476$	40.2076	1.84291
$477$	18.3397	0.839718
$478$	0.235019	0.0107495
$479$	6.11467	0.279387	0.139693	−	0.990195i	$-0.455388\pi$
$479$	6.11467	0.279387	0.139693	+	0.990195i	$0.455388\pi$
$480$	47.4304	2.16489
$481$	−4.91477	−0.224094
$482$	9.07817	0.413499
$483$	3.10601	0.141329
$484$	−25.0938	−1.14063
$485$	−4.99653	−0.226881
$486$	−46.4375	−2.10645
$487$	16.0032	0.725172	0.362586	−	0.931950i	$-0.381894\pi$
$487$	16.0032	0.725172	0.362586	+	0.931950i	$0.381894\pi$
$488$	−4.86624	−0.220284
$489$	35.0398	1.58455
$490$	−39.4722	−1.78317
$491$	24.4852	1.10500	0.552500	−	0.833513i	$-0.313674\pi$
$491$	24.4852	1.10500	0.552500	+	0.833513i	$0.313674\pi$
$492$	−44.9079	−2.02460
$493$	27.0932	1.22022
$494$	9.87884	0.444470
$495$	2.99678	0.134695
$496$	22.7927	1.02342
$497$	54.3609	2.43842
$498$	27.7558	1.24377
$499$	−35.7110	−1.59864	−0.799322	−	0.600903i	$-0.794808\pi$
$499$	−35.7110	−1.59864	−0.799322	+	0.600903i	$0.794808\pi$
$500$	24.8578	1.11167
$501$	52.5316	2.34694
$502$	32.1771	1.43614
$503$	−34.5361	−1.53989	−0.769945	−	0.638111i	$-0.779716\pi$
$503$	−34.5361	−1.53989	−0.769945	+	0.638111i	$0.779716\pi$
$504$	8.58589	0.382446
$505$	12.3241	0.548417
$506$	−0.248994	−0.0110691
$507$	−29.8047	−1.32368
$508$	−42.7741	−1.89779
$509$	23.3111	1.03324	0.516622	−	0.856214i	$-0.327189\pi$
$509$	23.3111	1.03324	0.516622	+	0.856214i	$0.327189\pi$
$510$	−54.1856	−2.39938
$511$	−1.49673	−0.0662115
$512$	30.8215	1.36213
$513$	−4.36134	−0.192558
$514$	−56.7018	−2.50101
$515$	−17.0615	−0.751820
$516$	13.1721	0.579868
$517$	2.40693	0.105857
$518$	36.0620	1.58447
$519$	41.5030	1.82178
$520$	1.65327	0.0725008
$521$	−28.3706	−1.24294	−0.621469	−	0.783439i	$-0.713464\pi$
$521$	−28.3706	−1.24294	−0.621469	+	0.783439i	$0.713464\pi$
$522$	42.9008	1.87772
$523$	−25.6360	−1.12099	−0.560493	−	0.828159i	$-0.689388\pi$
$523$	−25.6360	−1.12099	−0.560493	+	0.828159i	$0.689388\pi$
$524$	9.64366	0.421285
$525$	3.47449	0.151639
$526$	16.6046	0.723995
$527$	−30.9898	−1.34994
$528$	3.16070	0.137552
$529$	−22.9009	−0.995693
$530$	−25.9118	−1.12554
$531$	16.2586	0.705564
$532$	−38.8633	−1.68494
$533$	8.47681	0.367171
$534$	32.7953	1.41919
$535$	30.4551	1.31669
$536$	−2.07231	−0.0895102
$537$	−16.1628	−0.697478
$538$	−64.5259	−2.78191
$539$	−3.13050	−0.134840
$540$	−5.41235	−0.232911
$541$	2.52816	0.108694	0.0543471	−	0.998522i	$-0.482692\pi$
$541$	2.52816	0.108694	0.0543471	+	0.998522i	$0.482692\pi$
$542$	−9.17436	−0.394073
$543$	15.7110	0.674224
$544$	−36.1334	−1.54921
$545$	5.79088	0.248054
$546$	−22.6215	−0.968113
$547$	−8.81475	−0.376892	−0.188446	−	0.982084i	$-0.560345\pi$
$547$	−8.81475	−0.376892	−0.188446	+	0.982084i	$0.560345\pi$
$548$	11.1196	0.475005
$549$	−25.5585	−1.09081
$550$	−0.278533	−0.0118767
$551$	−26.1874	−1.11562
$552$	0.515445	0.0219388
$553$	−45.7137	−1.94395
$554$	44.9940	1.91161
$555$	−26.0563	−1.10603
$556$	49.5727	2.10235
$557$	−15.7090	−0.665610	−0.332805	−	0.942996i	$-0.607995\pi$
$557$	−15.7090	−0.665610	−0.332805	+	0.942996i	$0.607995\pi$
$558$	−49.0709	−2.07734
$559$	−2.48636	−0.105162
$560$	29.5940	1.25058
$561$	−4.29740	−0.181437
$562$	3.20512	0.135200
$563$	−7.20511	−0.303659	−0.151830	−	0.988407i	$-0.548517\pi$
$563$	−7.20511	−0.303659	−0.151830	+	0.988407i	$0.548517\pi$
$564$	−36.9475	−1.55577
$565$	19.0585	0.801798
$566$	−49.6887	−2.08857
$567$	−29.8022	−1.25158
$568$	9.02122	0.378522
$569$	8.63700	0.362082	0.181041	−	0.983476i	$-0.442053\pi$
$569$	8.63700	0.362082	0.181041	+	0.983476i	$0.442053\pi$
$570$	52.3740	2.19371
$571$	−24.4187	−1.02189	−0.510946	−	0.859613i	$-0.670705\pi$
$571$	−24.4187	−1.02189	−0.510946	+	0.859613i	$0.670705\pi$
$572$	0.972289	0.0406534
$573$	34.2014	1.42878
$574$	−62.1983	−2.59611
$575$	0.110813	0.00462120
$576$	−34.9161	−1.45484
$577$	−27.9273	−1.16263	−0.581315	−	0.813679i	$-0.697461\pi$
$577$	−27.9273	−1.16263	−0.581315	+	0.813679i	$0.697461\pi$
$578$	5.97952	0.248715
$579$	39.2447	1.63096
$580$	−32.4982	−1.34941
$581$	20.6109	0.855086
$582$	11.3455	0.470288
$583$	−2.05504	−0.0851112
$584$	−0.248384	−0.0102782
$585$	8.68333	0.359012
$586$	45.6523	1.88588
$587$	−9.32538	−0.384899	−0.192450	−	0.981307i	$-0.561643\pi$
$587$	−9.32538	−0.384899	−0.192450	+	0.981307i	$0.561643\pi$
$588$	48.0547	1.98174
$589$	29.9537	1.23422
$590$	−22.9715	−0.945721
$591$	51.2114	2.10656
$592$	−14.5996	−0.600041
$593$	−38.7576	−1.59158	−0.795791	−	0.605571i	$-0.792945\pi$
$593$	−38.7576	−1.59158	−0.795791	+	0.605571i	$0.792945\pi$
$594$	−0.800610	−0.0328494
$595$	−40.2372	−1.64956
$596$	43.1318	1.76675
$597$	−44.3711	−1.81599
$598$	−0.721473	−0.0295032
$599$	20.5011	0.837653	0.418826	−	0.908066i	$-0.362442\pi$
$599$	20.5011	0.837653	0.418826	+	0.908066i	$0.362442\pi$
$600$	0.576594	0.0235393
$601$	44.4309	1.81237	0.906186	−	0.422878i	$-0.138980\pi$
$601$	44.4309	1.81237	0.906186	+	0.422878i	$0.138980\pi$
$602$	18.2436	0.743553
$603$	−10.8842	−0.443239
$604$	33.1091	1.34719
$605$	25.1122	1.02096
$606$	−27.9842	−1.13678
$607$	−31.8059	−1.29096	−0.645481	−	0.763776i	$-0.723343\pi$
$607$	−31.8059	−1.29096	−0.645481	+	0.763776i	$0.723343\pi$
$608$	34.9254	1.41641
$609$	59.9665	2.42996
$610$	36.1111	1.46210
$611$	6.97420	0.282146
$612$	35.0452	1.41662
$613$	38.5995	1.55902	0.779510	−	0.626390i	$-0.215468\pi$
$613$	38.5995	1.55902	0.779510	+	0.626390i	$0.215468\pi$
$614$	9.75542	0.393697
$615$	44.9409	1.81219
$616$	−0.962085	−0.0387635
$617$	−28.9701	−1.16629	−0.583145	−	0.812368i	$-0.698178\pi$
$617$	−28.9701	−1.16629	−0.583145	+	0.812368i	$0.698178\pi$
$618$	38.7413	1.55840
$619$	37.6998	1.51528	0.757641	−	0.652672i	$-0.226352\pi$
$619$	37.6998	1.51528	0.757641	+	0.652672i	$0.226352\pi$
$620$	37.1721	1.49287
$621$	0.318518	0.0127817
$622$	38.3915	1.53936
$623$	24.3532	0.975689
$624$	9.15829	0.366625
$625$	−26.6364	−1.06546
$626$	−22.6835	−0.906614
$627$	4.15373	0.165884
$628$	8.23958	0.328795
$629$	19.8502	0.791479
$630$	−63.7137	−2.53841
$631$	22.6688	0.902430	0.451215	−	0.892415i	$-0.350991\pi$
$631$	22.6688	0.902430	0.451215	+	0.892415i	$0.350991\pi$
$632$	−7.58623	−0.301764
$633$	9.76031	0.387937
$634$	36.4242	1.44659
$635$	42.8055	1.69869
$636$	31.5459	1.25088
$637$	−9.07080	−0.359398
$638$	−4.80722	−0.190320
$639$	47.3813	1.87438
$640$	11.8354	0.467836
$641$	7.69219	0.303823	0.151912	−	0.988394i	$-0.451457\pi$
$641$	7.69219	0.303823	0.151912	+	0.988394i	$0.451457\pi$
$642$	−69.1540	−2.72929
$643$	24.6245	0.971097	0.485548	−	0.874210i	$-0.338620\pi$
$643$	24.6245	0.971097	0.485548	+	0.874210i	$0.338620\pi$
$644$	2.83827	0.111844
$645$	−13.1818	−0.519032
$646$	−39.8995	−1.56983
$647$	−45.2604	−1.77937	−0.889684	−	0.456576i	$-0.849076\pi$
$647$	−45.2604	−1.77937	−0.889684	+	0.456576i	$0.849076\pi$
$648$	−4.94570	−0.194285
$649$	−1.82185	−0.0715137
$650$	−0.807064	−0.0316556
$651$	−68.5910	−2.68829
$652$	32.0193	1.25397
$653$	24.0108	0.939613	0.469807	−	0.882769i	$-0.344324\pi$
$653$	24.0108	0.939613	0.469807	+	0.882769i	$0.344324\pi$
$654$	−13.1493	−0.514177
$655$	−9.65075	−0.377086
$656$	25.1809	0.983148
$657$	−1.30456	−0.0508958
$658$	−51.1730	−1.99493
$659$	−3.21060	−0.125067	−0.0625336	−	0.998043i	$-0.519918\pi$
$659$	−3.21060	−0.125067	−0.0625336	+	0.998043i	$0.519918\pi$
$660$	5.15472	0.200647
$661$	−38.0377	−1.47949	−0.739747	−	0.672885i	$-0.765055\pi$
$661$	−38.0377	−1.47949	−0.739747	+	0.672885i	$0.765055\pi$
$662$	64.6316	2.51198
$663$	−12.4520	−0.483594
$664$	3.42040	0.132737
$665$	38.8919	1.50816
$666$	31.4319	1.21796
$667$	1.91252	0.0740532
$668$	48.0034	1.85731
$669$	−24.1540	−0.933848
$670$	15.3781	0.594107
$671$	2.86394	0.110561
$672$	−79.9755	−3.08512
$673$	32.4431	1.25059	0.625294	−	0.780389i	$-0.284979\pi$
$673$	32.4431	1.25059	0.625294	+	0.780389i	$0.284979\pi$
$674$	13.9704	0.538118
$675$	0.356304	0.0137142
$676$	−27.2356	−1.04752
$677$	−28.8453	−1.10861	−0.554307	−	0.832312i	$-0.687017\pi$
$677$	−28.8453	−1.10861	−0.554307	+	0.832312i	$0.687017\pi$
$678$	−43.2759	−1.66200
$679$	8.42498	0.323321
$680$	−6.67738	−0.256066
$681$	−69.6668	−2.66964
$682$	5.49860	0.210552
$683$	−19.6204	−0.750754	−0.375377	−	0.926872i	$-0.622487\pi$
$683$	−19.6204	−0.750754	−0.375377	+	0.926872i	$0.622487\pi$
$684$	−33.8736	−1.29519
$685$	−11.1278	−0.425170
$686$	9.85621	0.376312
$687$	−30.5367	−1.16505
$688$	−7.38588	−0.281584
$689$	−5.95460	−0.226852
$690$	−3.82499	−0.145615
$691$	−27.1603	−1.03323	−0.516614	−	0.856218i	$-0.672808\pi$
$691$	−27.1603	−1.03323	−0.516614	+	0.856218i	$0.672808\pi$
$692$	37.9254	1.44171
$693$	−5.05307	−0.191950
$694$	2.00411	0.0760748
$695$	−49.6092	−1.88178
$696$	9.95148	0.377210
$697$	−34.2369	−1.29681
$698$	76.7232	2.90402
$699$	−5.58860	−0.211380
$700$	3.17499	0.120003
$701$	0.984355	0.0371786	0.0185893	−	0.999827i	$-0.494083\pi$
$701$	0.984355	0.0371786	0.0185893	+	0.999827i	$0.494083\pi$
$702$	−2.31981	−0.0875556
$703$	−19.1866	−0.723635
$704$	3.91250	0.147458
$705$	36.9747	1.39255
$706$	−23.3527	−0.878890
$707$	−20.7805	−0.781533
$708$	27.9662	1.05103
$709$	6.83688	0.256764	0.128382	−	0.991725i	$-0.459022\pi$
$709$	6.83688	0.256764	0.128382	+	0.991725i	$0.459022\pi$
$710$	−66.9442	−2.51237
$711$	−39.8444	−1.49428
$712$	4.04143	0.151459
$713$	−2.18759	−0.0819257
$714$	91.3659	3.41928
$715$	−0.973004	−0.0363883
$716$	−14.7696	−0.551965
$717$	0.286330	0.0106932
$718$	35.2083	1.31396
$719$	22.3360	0.832994	0.416497	−	0.909137i	$-0.363258\pi$
$719$	22.3360	0.832994	0.416497	+	0.909137i	$0.363258\pi$
$720$	25.7944	0.961299
$721$	28.7686	1.07140
$722$	−0.887446	−0.0330273
$723$	11.0602	0.411333
$724$	14.3567	0.533563
$725$	2.13941	0.0794557
$726$	−57.0219	−2.11628
$727$	−31.9716	−1.18576	−0.592881	−	0.805290i	$-0.702010\pi$
$727$	−31.9716	−1.18576	−0.592881	+	0.805290i	$0.702010\pi$
$728$	−2.78769	−0.103319
$729$	−33.6564	−1.24654
$730$	1.84319	0.0682196
$731$	10.0421	0.371422
$732$	−43.9628	−1.62491
$733$	−23.0428	−0.851105	−0.425553	−	0.904934i	$-0.639920\pi$
$733$	−23.0428	−0.851105	−0.425553	+	0.904934i	$0.639920\pi$
$734$	−7.23456	−0.267033
$735$	−48.0900	−1.77383
$736$	−2.55067	−0.0940191
$737$	1.21962	0.0449253
$738$	−54.2125	−1.99559
$739$	36.5318	1.34384	0.671921	−	0.740622i	$-0.265469\pi$
$739$	36.5318	1.34384	0.671921	+	0.740622i	$0.265469\pi$
$740$	−23.8102	−0.875282
$741$	12.0357	0.442141
$742$	43.6917	1.60397
$743$	−0.139955	−0.00513444	−0.00256722	−	0.999997i	$-0.500817\pi$
$743$	−0.139955	−0.00513444	−0.00256722	+	0.999997i	$0.500817\pi$
$744$	−11.3827	−0.417311
$745$	−43.1636	−1.58139
$746$	−54.3013	−1.98811
$747$	17.9647	0.657292
$748$	−3.92697	−0.143584
$749$	−51.3524	−1.87638
$750$	56.4856	2.06256
$751$	−1.12934	−0.0412100	−0.0206050	−	0.999788i	$-0.506559\pi$
$751$	−1.12934	−0.0412100	−0.0206050	+	0.999788i	$0.506559\pi$
$752$	20.7173	0.755482
$753$	39.2023	1.42861
$754$	−13.9292	−0.507271
$755$	−33.1334	−1.20585
$756$	9.12613	0.331914
$757$	−26.7815	−0.973392	−0.486696	−	0.873572i	$-0.661798\pi$
$757$	−26.7815	−0.973392	−0.486696	+	0.873572i	$0.661798\pi$
$758$	−36.8138	−1.33714
$759$	−0.303356	−0.0110111
$760$	6.45414	0.234116
$761$	−1.80740	−0.0655181	−0.0327591	−	0.999463i	$-0.510429\pi$
$761$	−1.80740	−0.0655181	−0.0327591	+	0.999463i	$0.510429\pi$
$762$	−97.1978	−3.52111
$763$	−9.76439	−0.353495
$764$	31.2532	1.13070
$765$	−35.0710	−1.26799
$766$	0.106083	0.00383294
$767$	−5.27890	−0.190610
$768$	25.0849	0.905175
$769$	−17.9685	−0.647960	−0.323980	−	0.946064i	$-0.605021\pi$
$769$	−17.9685	−0.647960	−0.323980	+	0.946064i	$0.605021\pi$
$770$	7.13939	0.257286
$771$	−69.0814	−2.48791
$772$	35.8618	1.29070
$773$	−6.07971	−0.218672	−0.109336	−	0.994005i	$-0.534872\pi$
$773$	−6.07971	−0.218672	−0.109336	+	0.994005i	$0.534872\pi$
$774$	15.9012	0.571558
$775$	−2.44711	−0.0879026
$776$	1.39813	0.0501900
$777$	43.9353	1.57617
$778$	46.9536	1.68337
$779$	33.0923	1.18565
$780$	14.9361	0.534797
$781$	−5.30928	−0.189981
$782$	2.91395	0.104203
$783$	6.14949	0.219765
$784$	−26.9454	−0.962334
$785$	−8.24564	−0.294300
$786$	21.9138	0.781640
$787$	1.00000	0.0356462
$787$	1.00000	0.0356462
$788$	46.7970	1.66707
$789$	20.2298	0.720201
$790$	56.2955	2.00290
$791$	−32.1358	−1.14262
$792$	−0.838560	−0.0297969
$793$	8.29842	0.294686
$794$	−76.8694	−2.72799
$795$	−31.5691	−1.11964
$796$	−40.5463	−1.43713
$797$	17.3934	0.616105	0.308053	−	0.951369i	$-0.400323\pi$
$797$	17.3934	0.616105	0.308053	+	0.951369i	$0.400323\pi$
$798$	−88.3113	−3.12619
$799$	−28.1680	−0.996513
$800$	−2.85327	−0.100878
$801$	21.2264	0.749998
$802$	−69.9250	−2.46914
$803$	0.146182	0.00515864
$804$	−18.7218	−0.660266
$805$	−2.84036	−0.100110
$806$	15.9325	0.561198
$807$	−78.6136	−2.76733
$808$	−3.44855	−0.121319
$809$	−4.45670	−0.156689	−0.0783446	−	0.996926i	$-0.524963\pi$
$809$	−4.45670	−0.156689	−0.0783446	+	0.996926i	$0.524963\pi$
$810$	36.7008	1.28953
$811$	1.07311	0.0376818	0.0188409	−	0.999822i	$-0.494002\pi$
$811$	1.07311	0.0376818	0.0188409	+	0.999822i	$0.494002\pi$
$812$	54.7973	1.92301
$813$	−11.1774	−0.392008
$814$	−3.52207	−0.123449
$815$	−32.0429	−1.12241
$816$	−36.9893	−1.29488
$817$	−9.70640	−0.339584
$818$	17.5817	0.614731
$819$	−14.6415	−0.511617
$820$	41.0670	1.43412
$821$	14.0245	0.489457	0.244729	−	0.969592i	$-0.421301\pi$
$821$	14.0245	0.489457	0.244729	+	0.969592i	$0.421301\pi$
$822$	25.2676	0.881310
$823$	−0.184859	−0.00644380	−0.00322190	−	0.999995i	$-0.501026\pi$
$823$	−0.184859	−0.00644380	−0.00322190	+	0.999995i	$0.501026\pi$
$824$	4.77416	0.166316
$825$	−0.339344	−0.0118144
$826$	38.7337	1.34772
$827$	−53.7047	−1.86750	−0.933748	−	0.357930i	$-0.883483\pi$
$827$	−53.7047	−1.86750	−0.933748	+	0.357930i	$0.883483\pi$
$828$	2.47386	0.0859726
$829$	−11.8428	−0.411317	−0.205659	−	0.978624i	$-0.565934\pi$
$829$	−11.8428	−0.411317	−0.205659	+	0.978624i	$0.565934\pi$
$830$	−25.3819	−0.881019
$831$	54.8174	1.90159
$832$	11.3367	0.393029
$833$	36.6359	1.26936
$834$	112.647	3.90064
$835$	−48.0387	−1.66245
$836$	3.79568	0.131276
$837$	−7.03392	−0.243128
$838$	36.6215	1.26507
$839$	−21.7516	−0.750948	−0.375474	−	0.926833i	$-0.622520\pi$
$839$	−21.7516	−0.750948	−0.375474	+	0.926833i	$0.622520\pi$
$840$	−14.7793	−0.509935
$841$	7.92425	0.273250
$842$	48.1225	1.65841
$843$	3.90488	0.134491
$844$	8.91896	0.307003
$845$	27.2556	0.937621
$846$	−44.6028	−1.53347
$847$	−42.3434	−1.45494
$848$	−17.6885	−0.607426
$849$	−60.5371	−2.07763
$850$	3.25964	0.111805
$851$	1.40124	0.0480338
$852$	81.5000	2.79214
$853$	−44.3857	−1.51974	−0.759868	−	0.650077i	$-0.774737\pi$
$853$	−44.3857	−1.51974	−0.759868	+	0.650077i	$0.774737\pi$
$854$	−60.8894	−2.08359
$855$	33.8985	1.15930
$856$	−8.52197	−0.291275
$857$	−22.2173	−0.758930	−0.379465	−	0.925206i	$-0.623892\pi$
$857$	−22.2173	−0.758930	−0.379465	+	0.925206i	$0.623892\pi$
$858$	2.20939	0.0754272
$859$	34.6252	1.18140	0.590698	−	0.806893i	$-0.298852\pi$
$859$	34.6252	1.18140	0.590698	+	0.806893i	$0.298852\pi$
$860$	−12.0455	−0.410748
$861$	−75.7779	−2.58250
$862$	−48.8946	−1.66536
$863$	29.0002	0.987178	0.493589	−	0.869695i	$-0.335685\pi$
$863$	29.0002	0.987178	0.493589	+	0.869695i	$0.335685\pi$
$864$	−8.20139	−0.279017
$865$	−37.9533	−1.29045
$866$	−27.1526	−0.922682
$867$	7.28501	0.247412
$868$	−62.6784	−2.12744
$869$	4.46474	0.151456
$870$	−73.8474	−2.50366
$871$	3.53392	0.119742
$872$	−1.62041	−0.0548739
$873$	7.34328	0.248532
$874$	−2.81653	−0.0952705
$875$	41.9452	1.41801
$876$	−2.24396	−0.0758164
$877$	10.3515	0.349545	0.174773	−	0.984609i	$-0.444081\pi$
$877$	10.3515	0.349545	0.174773	+	0.984609i	$0.444081\pi$
$878$	−50.2221	−1.69491
$879$	55.6194	1.87600
$880$	−2.89037	−0.0974343
$881$	25.0203	0.842955	0.421477	−	0.906839i	$-0.361512\pi$
$881$	25.0203	0.842955	0.421477	+	0.906839i	$0.361512\pi$
$882$	58.0113	1.95334
$883$	36.5474	1.22992	0.614959	−	0.788559i	$-0.289172\pi$
$883$	36.5474	1.22992	0.614959	+	0.788559i	$0.289172\pi$
$884$	−11.3786	−0.382704
$885$	−27.9868	−0.940765
$886$	−24.0959	−0.809519
$887$	18.5505	0.622863	0.311432	−	0.950269i	$-0.399191\pi$
$887$	18.5505	0.622863	0.311432	+	0.950269i	$0.399191\pi$
$888$	7.29109	0.244673
$889$	−72.1772	−2.42075
$890$	−29.9904	−1.00528
$891$	2.91070	0.0975122
$892$	−22.0719	−0.739022
$893$	27.2263	0.911093
$894$	98.0108	3.27797
$895$	14.7805	0.494056
$896$	−19.9565	−0.666699
$897$	−0.878990	−0.0293486
$898$	−57.3164	−1.91267
$899$	−42.2348	−1.40861
$900$	2.76734	0.0922447
$901$	24.0500	0.801221
$902$	6.07474	0.202267
$903$	22.2267	0.739657
$904$	−5.33296	−0.177372
$905$	−14.3673	−0.477584
$906$	75.2356	2.49954
$907$	−31.3800	−1.04196	−0.520978	−	0.853570i	$-0.674433\pi$
$907$	−31.3800	−1.04196	−0.520978	+	0.853570i	$0.674433\pi$
$908$	−63.6614	−2.11268
$909$	−18.1125	−0.600753
$910$	20.6868	0.685759
$911$	10.5046	0.348032	0.174016	−	0.984743i	$-0.444326\pi$
$911$	10.5046	0.348032	0.174016	+	0.984743i	$0.444326\pi$
$912$	35.7527	1.18389
$913$	−2.01302	−0.0666211
$914$	63.4930	2.10016
$915$	43.9952	1.45444
$916$	−27.9044	−0.921988
$917$	16.2728	0.537374
$918$	9.36945	0.309238
$919$	−60.1165	−1.98306	−0.991530	−	0.129879i	$-0.958541\pi$
$919$	−60.1165	−1.98306	−0.991530	+	0.129879i	$0.958541\pi$
$920$	−0.471360	−0.0155403
$921$	11.8853	0.391634
$922$	45.2270	1.48947
$923$	−15.3839	−0.506368
$924$	−8.69172	−0.285936
$925$	1.56747	0.0515381
$926$	75.2971	2.47442
$927$	25.0749	0.823568
$928$	−49.2448	−1.61654
$929$	55.9915	1.83702	0.918510	−	0.395397i	$-0.129393\pi$
$929$	55.9915	1.83702	0.918510	+	0.395397i	$0.129393\pi$
$930$	84.4683	2.76982
$931$	−35.4111	−1.16055
$932$	−5.10686	−0.167281
$933$	46.7734	1.53129
$934$	−0.651553	−0.0213195
$935$	3.92985	0.128520
$936$	−2.42977	−0.0794196
$937$	−38.4536	−1.25623	−0.628113	−	0.778122i	$-0.716172\pi$
$937$	−38.4536	−1.25623	−0.628113	+	0.778122i	$0.716172\pi$
$938$	−25.9300	−0.846645
$939$	−27.6359	−0.901863
$940$	33.7874	1.10202
$941$	32.6005	1.06275	0.531373	−	0.847138i	$-0.321676\pi$
$941$	32.6005	1.06275	0.531373	+	0.847138i	$0.321676\pi$
$942$	18.7233	0.610037
$943$	−2.41680	−0.0787018
$944$	−15.6813	−0.510382
$945$	−9.13284	−0.297091
$946$	−1.78180	−0.0579314
$947$	−1.28168	−0.0416491	−0.0208246	−	0.999783i	$-0.506629\pi$
$947$	−1.28168	−0.0416491	−0.0208246	+	0.999783i	$0.506629\pi$
$948$	−68.5359	−2.22594
$949$	0.423570	0.0137497
$950$	−3.15066	−0.102221
$951$	44.3766	1.43901
$952$	11.2592	0.364912
$953$	18.5934	0.602299	0.301149	−	0.953577i	$-0.402630\pi$
$953$	18.5934	0.602299	0.301149	+	0.953577i	$0.402630\pi$
$954$	38.0820	1.23295
$955$	−31.2762	−1.01207
$956$	0.261648	0.00846229
$957$	−5.85676	−0.189322
$958$	12.6970	0.410221
$959$	18.7633	0.605897
$960$	60.1029	1.93981
$961$	17.3091	0.558357
$962$	−10.2054	−0.329035
$963$	−44.7591	−1.44234
$964$	10.1068	0.325518
$965$	−35.8882	−1.15528
$966$	6.44957	0.207511
$967$	−33.4828	−1.07674	−0.538368	−	0.842710i	$-0.680959\pi$
$967$	−33.4828	−1.07674	−0.538368	+	0.842710i	$0.680959\pi$
$968$	−7.02691	−0.225853
$969$	−48.6107	−1.56160
$970$	−10.3752	−0.333127
$971$	−52.0820	−1.67139	−0.835695	−	0.549194i	$-0.814935\pi$
$971$	−52.0820	−1.67139	−0.835695	+	0.549194i	$0.814935\pi$
$972$	−51.6992	−1.65825
$973$	83.6494	2.68168
$974$	33.2302	1.06476
$975$	−0.983268	−0.0314898
$976$	24.6510	0.789058
$977$	42.2873	1.35289	0.676445	−	0.736493i	$-0.263520\pi$
$977$	42.2873	1.35289	0.676445	+	0.736493i	$0.263520\pi$
$978$	72.7593	2.32659
$979$	−2.37851	−0.0760175
$980$	−43.9447	−1.40376
$981$	−8.51071	−0.271726
$982$	50.8429	1.62246
$983$	−20.3961	−0.650535	−0.325268	−	0.945622i	$-0.605454\pi$
$983$	−20.3961	−0.650535	−0.325268	+	0.945622i	$0.605454\pi$
$984$	−12.5754	−0.400889
$985$	−46.8314	−1.49217
$986$	56.2584	1.79163
$987$	−62.3454	−1.98448
$988$	10.9982	0.349899
$989$	0.708879	0.0225410
$990$	6.22274	0.197772
$991$	−15.0800	−0.479031	−0.239516	−	0.970892i	$-0.576989\pi$
$991$	−15.0800	−0.479031	−0.239516	+	0.970892i	$0.576989\pi$
$992$	56.3273	1.78839
$993$	78.7424	2.49881
$994$	112.879	3.58031
$995$	40.5761	1.28635
$996$	30.9007	0.979128
$997$	−1.31697	−0.0417090	−0.0208545	−	0.999783i	$-0.506639\pi$
$997$	−1.31697	−0.0417090	−0.0208545	+	0.999783i	$0.506639\pi$
$998$	−74.1531	−2.34727
$999$	4.50551	0.142548

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	787.2.a.b.1.29	✓	37
3.2	odd	2		7083.2.a.g.1.9		37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
787.2.a.b.1.29	✓	37	1.1	even	1	trivial
7083.2.a.g.1.9		37	3.2	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:	\( N \)	\(=\)	\( 787 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	787.a (trivial)

\(f(q)\)	\(=\)	\(q+2.07648 q^{2} +2.52983 q^{3} +2.31176 q^{4} -2.31346 q^{5} +5.25313 q^{6} +3.90087 q^{7} +0.647352 q^{8} +3.40003 q^{9} -4.80384 q^{10} -0.380988 q^{11} +5.84834 q^{12} -1.10393 q^{13} +8.10007 q^{14} -5.85265 q^{15} -3.27930 q^{16} +4.45866 q^{17} +7.06008 q^{18} -4.30960 q^{19} -5.34814 q^{20} +9.86854 q^{21} -0.791112 q^{22} +0.314739 q^{23} +1.63769 q^{24} +0.352078 q^{25} -2.29229 q^{26} +1.01201 q^{27} +9.01786 q^{28} +6.07653 q^{29} -12.1529 q^{30} -6.95047 q^{31} -8.10409 q^{32} -0.963833 q^{33} +9.25830 q^{34} -9.02450 q^{35} +7.86004 q^{36} +4.45206 q^{37} -8.94878 q^{38} -2.79276 q^{39} -1.49762 q^{40} -7.67874 q^{41} +20.4918 q^{42} +2.25227 q^{43} -0.880750 q^{44} -7.86582 q^{45} +0.653548 q^{46} -6.31760 q^{47} -8.29606 q^{48} +8.21681 q^{49} +0.731081 q^{50} +11.2796 q^{51} -2.55202 q^{52} +5.39399 q^{53} +2.10141 q^{54} +0.881398 q^{55} +2.52524 q^{56} -10.9025 q^{57} +12.6178 q^{58} +4.78190 q^{59} -13.5299 q^{60} -7.51715 q^{61} -14.4325 q^{62} +13.2631 q^{63} -10.2694 q^{64} +2.55390 q^{65} -2.00138 q^{66} -3.20121 q^{67} +10.3073 q^{68} +0.796236 q^{69} -18.7392 q^{70} +13.9356 q^{71} +2.20102 q^{72} -0.383692 q^{73} +9.24459 q^{74} +0.890696 q^{75} -9.96273 q^{76} -1.48618 q^{77} -5.79910 q^{78} -11.7189 q^{79} +7.58651 q^{80} -7.63989 q^{81} -15.9447 q^{82} +5.28368 q^{83} +22.8136 q^{84} -10.3149 q^{85} +4.67680 q^{86} +15.3726 q^{87} -0.246633 q^{88} +6.24301 q^{89} -16.3332 q^{90} -4.30630 q^{91} +0.727600 q^{92} -17.5835 q^{93} -13.1183 q^{94} +9.97006 q^{95} -20.5020 q^{96} +2.15977 q^{97} +17.0620 q^{98} -1.29537 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q + 12 q^{2} + 6 q^{3} + 42 q^{4} + 31 q^{5} + 4 q^{6} + 9 q^{7} + 36 q^{8} + 47 q^{9} + 4 q^{10} + 18 q^{11} + 15 q^{12} + 13 q^{13} + 8 q^{14} + 3 q^{15} + 48 q^{16} + 18 q^{17} + 17 q^{18} + 40 q^{20}+ \cdots - 35 q^{99}+O(q^{100}) \) 37 * q + 12 * q^2 + 6 * q^3 + 42 * q^4 + 31 * q^5 + 4 * q^6 + 9 * q^7 + 36 * q^8 + 47 * q^9 + 4 * q^10 + 18 * q^11 + 15 * q^12 + 13 * q^13 + 8 * q^14 + 3 * q^15 + 48 * q^16 + 18 * q^17 + 17 * q^18 + 40 * q^20 - 4 * q^21 - 4 * q^22 + 42 * q^23 - 10 * q^24 + 56 * q^25 - 4 * q^26 + 18 * q^27 + 3 * q^28 + 45 * q^29 - 32 * q^30 - 3 * q^31 + 59 * q^32 + 14 * q^33 - 22 * q^34 + 16 * q^35 + 28 * q^36 + 52 * q^37 - 5 * q^38 - 13 * q^39 - 11 * q^40 + 23 * q^41 - 16 * q^42 + 4 * q^43 + 23 * q^44 + 69 * q^45 - 5 * q^46 + 45 * q^47 - 5 * q^48 + 30 * q^49 + 13 * q^50 - 7 * q^51 + 3 * q^52 + 103 * q^53 - 23 * q^54 - 9 * q^55 + 4 * q^56 + 9 * q^57 + 8 * q^58 + 2 * q^59 - 47 * q^60 - 6 * q^61 + 20 * q^62 + 5 * q^63 + 28 * q^64 + 51 * q^65 - 48 * q^66 + 24 * q^67 - 9 * q^68 - 52 * q^70 + 32 * q^71 + 42 * q^72 + 5 * q^73 + 4 * q^74 - 35 * q^75 - 34 * q^76 + 97 * q^77 - 31 * q^78 - 27 * q^79 + 47 * q^80 + 29 * q^81 - q^82 + 23 * q^83 - 93 * q^84 + 27 * q^85 + 10 * q^86 - 46 * q^87 - 45 * q^88 + 9 * q^89 - 70 * q^90 - 48 * q^91 + 67 * q^92 + 72 * q^93 - 52 * q^94 - 20 * q^95 - 89 * q^96 - 7 * q^97 - 12 * q^98 - 35 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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