LMFDB - Embedded newform 161.4.a.d.1.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [161,4,Mod(1,161)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(161, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("161.1"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 161 = 7 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	161.a (trivial)

Newform invariants

comment:select newform

sage:traces = [12] 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:	$9.49930751092$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} - 76 x^{10} + 311 x^{9} + 1979 x^{8} - 8466 x^{7} - 19942 x^{6} + 95647 x^{5} + \cdots - 70656 $ x^12 - 4x^11 - 76x^10 + 311x^9 + 1979x^8 - 8466x^7 - 19942x^6 + 95647x^5 + 50294x^4 - 400320x^3 + 178432x^2 + 227072*x - 70656
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$3.76511$ of defining polynomial
Character	$\chi$	$=$	161.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+3.76511 q^{2} +9.31158 q^{3} +6.17602 q^{4} +1.25334 q^{5} +35.0591 q^{6} +7.00000 q^{7} -6.86747 q^{8} +59.7056 q^{9} +4.71897 q^{10} -42.4133 q^{11} +57.5085 q^{12} -78.8059 q^{13} +26.3557 q^{14} +11.6706 q^{15} -75.2649 q^{16} +118.652 q^{17} +224.798 q^{18} +2.87339 q^{19} +7.74068 q^{20} +65.1811 q^{21} -159.691 q^{22} +23.0000 q^{23} -63.9470 q^{24} -123.429 q^{25} -296.713 q^{26} +304.541 q^{27} +43.2322 q^{28} -112.162 q^{29} +43.9411 q^{30} +138.981 q^{31} -228.441 q^{32} -394.935 q^{33} +446.737 q^{34} +8.77340 q^{35} +368.743 q^{36} +389.082 q^{37} +10.8186 q^{38} -733.808 q^{39} -8.60729 q^{40} -286.733 q^{41} +245.414 q^{42} -103.738 q^{43} -261.945 q^{44} +74.8316 q^{45} +86.5974 q^{46} +515.555 q^{47} -700.836 q^{48} +49.0000 q^{49} -464.724 q^{50} +1104.84 q^{51} -486.707 q^{52} +424.566 q^{53} +1146.63 q^{54} -53.1584 q^{55} -48.0723 q^{56} +26.7558 q^{57} -422.302 q^{58} -631.418 q^{59} +72.0780 q^{60} -365.728 q^{61} +523.278 q^{62} +417.939 q^{63} -257.984 q^{64} -98.7709 q^{65} -1486.97 q^{66} -285.493 q^{67} +732.797 q^{68} +214.166 q^{69} +33.0328 q^{70} +531.990 q^{71} -410.026 q^{72} +151.750 q^{73} +1464.93 q^{74} -1149.32 q^{75} +17.7461 q^{76} -296.893 q^{77} -2762.86 q^{78} +115.823 q^{79} -94.3328 q^{80} +1223.70 q^{81} -1079.58 q^{82} -979.050 q^{83} +402.560 q^{84} +148.712 q^{85} -390.584 q^{86} -1044.41 q^{87} +291.272 q^{88} +940.951 q^{89} +281.749 q^{90} -551.641 q^{91} +142.049 q^{92} +1294.13 q^{93} +1941.12 q^{94} +3.60135 q^{95} -2127.14 q^{96} -688.524 q^{97} +184.490 q^{98} -2532.31 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{2} + q^{3} + 72 q^{4} + 16 q^{5} - 15 q^{6} + 84 q^{7} - 21 q^{8} + 203 q^{9} + 106 q^{10} + 50 q^{11} - 139 q^{12} + 21 q^{13} + 28 q^{14} + 192 q^{15} + 516 q^{16} + 26 q^{17} + 251 q^{18}+ \cdots + 2400 q^{99}+O(q^{100}) $ 12 * q + 4 * q^2 + q^3 + 72 * q^4 + 16 * q^5 - 15 * q^6 + 84 * q^7 - 21 * q^8 + 203 * q^9 + 106 * q^10 + 50 * q^11 - 139 * q^12 + 21 * q^13 + 28 * q^14 + 192 * q^15 + 516 * q^16 + 26 * q^17 + 251 * q^18 + 292 * q^19 - 12 * q^20 + 7 * q^21 + 206 * q^22 + 276 * q^23 + 42 * q^24 + 408 * q^25 + 409 * q^26 - 335 * q^27 + 504 * q^28 + 129 * q^29 + 168 * q^30 + 375 * q^31 - 54 * q^32 + 428 * q^33 + 674 * q^34 + 112 * q^35 + 2271 * q^36 + 958 * q^37 - 120 * q^38 + 89 * q^39 + 1424 * q^40 - 347 * q^41 - 105 * q^42 + 392 * q^43 - 1158 * q^44 - 1338 * q^45 + 92 * q^46 + 559 * q^47 - 4767 * q^48 + 588 * q^49 - 888 * q^50 + 204 * q^51 - 1765 * q^52 + 42 * q^53 - 1965 * q^54 + 78 * q^55 - 147 * q^56 + 156 * q^57 - 3695 * q^58 - 620 * q^59 - 1574 * q^60 - 1258 * q^61 + 489 * q^62 + 1421 * q^63 + 4335 * q^64 - 752 * q^65 - 7334 * q^66 + 2024 * q^67 - 5162 * q^68 + 23 * q^69 + 742 * q^70 + 1371 * q^71 - 2483 * q^72 - 1241 * q^73 - 4006 * q^74 + 1357 * q^75 + 4214 * q^76 + 350 * q^77 - 4787 * q^78 + 2660 * q^79 - 5734 * q^80 + 2400 * q^81 - 3551 * q^82 - 1476 * q^83 - 973 * q^84 + 408 * q^85 - 988 * q^86 + 1263 * q^87 + 3324 * q^88 + 1670 * q^89 + 1050 * q^90 + 147 * q^91 + 1656 * q^92 + 135 * q^93 - 3539 * q^94 + 2428 * q^95 - 3973 * q^96 + 1174 * q^97 + 196 * q^98 + 2400 * 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 $

$2$	3.76511	1.33117	0.665583	−	0.746324i	$-0.268183\pi$
$2$	3.76511	1.33117	0.665583	+	0.746324i	$0.268183\pi$
$3$	9.31158	1.79201	0.896007	−	0.444039i	$-0.146455\pi$
$3$	9.31158	1.79201	0.896007	+	0.444039i	$0.146455\pi$
$4$	6.17602	0.772003
$5$	1.25334	0.112102	0.0560512	−	0.998428i	$-0.482149\pi$
$5$	1.25334	0.112102	0.0560512	+	0.998428i	$0.482149\pi$
$6$	35.0591	2.38547
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	−6.86747	−0.303502
$9$	59.7056	2.21132
$10$	4.71897	0.149227
$11$	−42.4133	−1.16255	−0.581277	−	0.813706i	$-0.697447\pi$
$11$	−42.4133	−1.16255	−0.581277	+	0.813706i	$0.697447\pi$
$12$	57.5085	1.38344
$13$	−78.8059	−1.68129	−0.840647	−	0.541583i	$-0.817825\pi$
$13$	−78.8059	−1.68129	−0.840647	+	0.541583i	$0.817825\pi$
$14$	26.3557	0.503133
$15$	11.6706	0.200889
$16$	−75.2649	−1.17601
$17$	118.652	1.69278	0.846392	−	0.532561i	$-0.178770\pi$
$17$	118.652	1.69278	0.846392	+	0.532561i	$0.178770\pi$
$18$	224.798	2.94363
$19$	2.87339	0.0346948	0.0173474	−	0.999850i	$-0.494478\pi$
$19$	2.87339	0.0346948	0.0173474	+	0.999850i	$0.494478\pi$
$20$	7.74068	0.0865434
$21$	65.1811	0.677318
$22$	−159.691	−1.54755
$23$	23.0000	0.208514
$23$	23.0000	0.208514
$24$	−63.9470	−0.543880
$25$	−123.429	−0.987433
$26$	−296.713	−2.23808
$27$	304.541	2.17070
$28$	43.2322	0.291790
$29$	−112.162	−0.718206	−0.359103	−	0.933298i	$-0.616917\pi$
$29$	−112.162	−0.718206	−0.359103	+	0.933298i	$0.616917\pi$
$30$	43.9411	0.267417
$31$	138.981	0.805216	0.402608	−	0.915372i	$-0.368104\pi$
$31$	138.981	0.805216	0.402608	+	0.915372i	$0.368104\pi$
$32$	−228.441	−1.26197
$33$	−394.935	−2.08331
$34$	446.737	2.25338
$35$	8.77340	0.0423707
$36$	368.743	1.70714
$37$	389.082	1.72877	0.864387	−	0.502828i	$-0.167707\pi$
$37$	389.082	1.72877	0.864387	+	0.502828i	$0.167707\pi$
$38$	10.8186	0.0461846
$39$	−733.808	−3.01291
$40$	−8.60729	−0.0340233
$41$	−286.733	−1.09220	−0.546100	−	0.837720i	$-0.683888\pi$
$41$	−286.733	−1.09220	−0.546100	+	0.837720i	$0.683888\pi$
$42$	245.414	0.901623
$43$	−103.738	−0.367904	−0.183952	−	0.982935i	$-0.558889\pi$
$43$	−103.738	−0.367904	−0.183952	+	0.982935i	$0.558889\pi$
$44$	−261.945	−0.897495
$45$	74.8316	0.247894
$46$	86.5974	0.277567
$47$	515.555	1.60003	0.800016	−	0.599979i	$-0.204824\pi$
$47$	515.555	1.60003	0.800016	+	0.599979i	$0.204824\pi$
$48$	−700.836	−2.10744
$49$	49.0000	0.142857
$50$	−464.724	−1.31444
$51$	1104.84	3.03349
$52$	−486.707	−1.29796
$53$	424.566	1.10035	0.550176	−	0.835049i	$-0.314561\pi$
$53$	424.566	1.10035	0.550176	+	0.835049i	$0.314561\pi$
$54$	1146.63	2.88956
$55$	−53.1584	−0.130325
$56$	−48.0723	−0.114713
$57$	26.7558	0.0621736
$58$	−422.302	−0.956052
$59$	−631.418	−1.39328	−0.696641	−	0.717420i	$-0.745323\pi$
$59$	−631.418	−1.39328	−0.696641	+	0.717420i	$0.745323\pi$
$60$	72.0780	0.155087
$61$	−365.728	−0.767651	−0.383825	−	0.923406i	$-0.625394\pi$
$61$	−365.728	−0.767651	−0.383825	+	0.923406i	$0.625394\pi$
$62$	523.278	1.07188
$63$	417.939	0.835799
$64$	−257.984	−0.503875
$65$	−98.7709	−0.188477
$66$	−1486.97	−2.77324
$67$	−285.493	−0.520574	−0.260287	−	0.965531i	$-0.583817\pi$
$67$	−285.493	−0.520574	−0.260287	+	0.965531i	$0.583817\pi$
$68$	732.797	1.30683
$69$	214.166	0.373661
$70$	33.0328	0.0564025
$71$	531.990	0.889234	0.444617	−	0.895721i	$-0.353340\pi$
$71$	531.990	0.889234	0.444617	+	0.895721i	$0.353340\pi$
$72$	−410.026	−0.671139
$73$	151.750	0.243301	0.121651	−	0.992573i	$-0.461181\pi$
$73$	151.750	0.243301	0.121651	+	0.992573i	$0.461181\pi$
$74$	1464.93	2.30128
$75$	−1149.32	−1.76949
$76$	17.7461	0.0267845
$77$	−296.893	−0.439404
$78$	−2762.86	−4.01068
$79$	115.823	0.164951	0.0824755	−	0.996593i	$-0.473717\pi$
$79$	115.823	0.164951	0.0824755	+	0.996593i	$0.473717\pi$
$80$	−94.3328	−0.131834
$81$	1223.70	1.67861
$82$	−1079.58	−1.45390
$83$	−979.050	−1.29476	−0.647378	−	0.762169i	$-0.724134\pi$
$83$	−979.050	−1.29476	−0.647378	+	0.762169i	$0.724134\pi$
$84$	402.560	0.522891
$85$	148.712	0.189765
$86$	−390.584	−0.489741
$87$	−1044.41	−1.28704
$88$	291.272	0.352837
$89$	940.951	1.12068	0.560341	−	0.828262i	$-0.310670\pi$
$89$	940.951	1.12068	0.560341	+	0.828262i	$0.310670\pi$
$90$	281.749	0.329988
$91$	−551.641	−0.635470
$92$	142.049	0.160974
$93$	1294.13	1.44296
$94$	1941.12	2.12991
$95$	3.60135	0.00388937
$96$	−2127.14	−2.26147
$97$	−688.524	−0.720711	−0.360356	−	0.932815i	$-0.617345\pi$
$97$	−688.524	−0.720711	−0.360356	+	0.932815i	$0.617345\pi$
$98$	184.490	0.190167
$99$	−2532.31	−2.57077
$100$	−762.301	−0.762301
$101$	−1130.94	−1.11418	−0.557091	−	0.830452i	$-0.688082\pi$
$101$	−1130.94	−1.11418	−0.557091	+	0.830452i	$0.688082\pi$
$102$	4159.83	4.03808
$103$	−353.658	−0.338320	−0.169160	−	0.985589i	$-0.554105\pi$
$103$	−353.658	−0.338320	−0.169160	+	0.985589i	$0.554105\pi$
$104$	541.197	0.510276
$105$	81.6943	0.0759290
$106$	1598.54	1.46475
$107$	−117.175	−0.105866	−0.0529332	−	0.998598i	$-0.516857\pi$
$107$	−117.175	−0.105866	−0.0529332	+	0.998598i	$0.516857\pi$
$108$	1880.85	1.67579
$109$	1606.89	1.41204	0.706020	−	0.708192i	$-0.250489\pi$
$109$	1606.89	1.41204	0.706020	+	0.708192i	$0.250489\pi$
$110$	−200.147	−0.173484
$111$	3622.96	3.09799
$112$	−526.854	−0.444492
$113$	1522.58	1.26754	0.633770	−	0.773522i	$-0.281507\pi$
$113$	1522.58	1.26754	0.633770	+	0.773522i	$0.281507\pi$
$114$	100.739	0.0827634
$115$	28.8269	0.0233750
$116$	−692.716	−0.554457
$117$	−4705.15	−3.71788
$118$	−2377.36	−1.85469
$119$	830.564	0.639812
$120$	−80.1475	−0.0609703
$121$	467.887	0.351530
$122$	−1377.01	−1.02187
$123$	−2669.94	−1.95724
$124$	858.349	0.621629
$125$	−311.367	−0.222796
$126$	1573.58	1.11259
$127$	−71.6858	−0.0500873	−0.0250437	−	0.999686i	$-0.507972\pi$
$127$	−71.6858	−0.0500873	−0.0250437	+	0.999686i	$0.507972\pi$
$128$	856.188	0.591227
$129$	−965.963	−0.659289
$130$	−371.883	−0.250894
$131$	−967.035	−0.644964	−0.322482	−	0.946576i	$-0.604517\pi$
$131$	−967.035	−0.644964	−0.322482	+	0.946576i	$0.604517\pi$
$132$	−2439.13	−1.60832
$133$	20.1137	0.0131134
$134$	−1074.91	−0.692971
$135$	381.694	0.243341
$136$	−814.838	−0.513763
$137$	1082.60	0.675127	0.337564	−	0.941303i	$-0.390397\pi$
$137$	1082.60	0.675127	0.337564	+	0.941303i	$0.390397\pi$
$138$	806.359	0.497405
$139$	−255.426	−0.155863	−0.0779314	−	0.996959i	$-0.524832\pi$
$139$	−255.426	−0.155863	−0.0779314	+	0.996959i	$0.524832\pi$
$140$	54.1847	0.0327103
$141$	4800.64	2.86728
$142$	2003.00	1.18372
$143$	3342.42	1.95459
$144$	−4493.74	−2.60054
$145$	−140.578	−0.0805127
$146$	571.355	0.323874
$147$	456.268	0.256002
$148$	2402.98	1.33462
$149$	−2650.45	−1.45727	−0.728635	−	0.684902i	$-0.759845\pi$
$149$	−2650.45	−1.45727	−0.728635	+	0.684902i	$0.759845\pi$
$150$	−4327.31	−2.35549
$151$	2172.54	1.17085	0.585426	−	0.810726i	$-0.300927\pi$
$151$	2172.54	1.17085	0.585426	+	0.810726i	$0.300927\pi$
$152$	−19.7329	−0.0105299
$153$	7084.18	3.74328
$154$	−1117.83	−0.584919
$155$	174.191	0.0902667
$156$	−4532.01	−2.32597
$157$	2023.80	1.02877	0.514384	−	0.857560i	$-0.328021\pi$
$157$	2023.80	1.02877	0.514384	+	0.857560i	$0.328021\pi$
$158$	436.087	0.219577
$159$	3953.38	1.97185
$160$	−286.315	−0.141470
$161$	161.000	0.0788110
$162$	4607.38	2.23450
$163$	1620.72	0.778799	0.389400	−	0.921069i	$-0.372682\pi$
$163$	1620.72	0.778799	0.389400	+	0.921069i	$0.372682\pi$
$164$	−1770.87	−0.843182
$165$	−494.989	−0.233544
$166$	−3686.23	−1.72353
$167$	2640.79	1.22365	0.611827	−	0.790991i	$-0.290435\pi$
$167$	2640.79	1.22365	0.611827	+	0.790991i	$0.290435\pi$
$168$	−447.629	−0.205567
$169$	4013.37	1.82675
$170$	559.915	0.252609
$171$	171.558	0.0767212
$172$	−640.687	−0.284023
$173$	2236.87	0.983040	0.491520	−	0.870866i	$-0.336441\pi$
$173$	2236.87	0.983040	0.491520	+	0.870866i	$0.336441\pi$
$174$	−3932.30	−1.71326
$175$	−864.004	−0.373215
$176$	3192.23	1.36718
$177$	−5879.51	−2.49678
$178$	3542.78	1.49181
$179$	−1714.83	−0.716046	−0.358023	−	0.933713i	$-0.616549\pi$
$179$	−1714.83	−0.716046	−0.358023	+	0.933713i	$0.616549\pi$
$180$	462.162	0.191375
$181$	1705.12	0.700224	0.350112	−	0.936708i	$-0.386144\pi$
$181$	1705.12	0.700224	0.350112	+	0.936708i	$0.386144\pi$
$182$	−2076.99	−0.845916
$183$	−3405.51	−1.37564
$184$	−157.952	−0.0632845
$185$	487.653	0.193800
$186$	4872.54	1.92082
$187$	−5032.42	−1.96795
$188$	3184.08	1.23523
$189$	2131.78	0.820447
$190$	13.5595	0.00517740
$191$	−2397.25	−0.908161	−0.454081	−	0.890961i	$-0.650032\pi$
$191$	−2397.25	−0.908161	−0.454081	+	0.890961i	$0.650032\pi$
$192$	−2402.24	−0.902951
$193$	2846.44	1.06161	0.530807	−	0.847493i	$-0.321889\pi$
$193$	2846.44	1.06161	0.530807	+	0.847493i	$0.321889\pi$
$194$	−2592.36	−0.959386
$195$	−919.713	−0.337754
$196$	302.625	0.110286
$197$	−83.1615	−0.0300762	−0.0150381	−	0.999887i	$-0.504787\pi$
$197$	−83.1615	−0.0300762	−0.0150381	+	0.999887i	$0.504787\pi$
$198$	−9534.41	−3.42213
$199$	−2537.27	−0.903830	−0.451915	−	0.892061i	$-0.649259\pi$
$199$	−2537.27	−0.903830	−0.451915	+	0.892061i	$0.649259\pi$
$200$	847.645	0.299688
$201$	−2658.39	−0.932877
$202$	−4258.09	−1.48316
$203$	−785.135	−0.271457
$204$	6823.50	2.34187
$205$	−359.375	−0.122438
$206$	−1331.56	−0.450360
$207$	1373.23	0.461092
$208$	5931.32	1.97723
$209$	−121.870	−0.0403346
$210$	307.588	0.101074
$211$	−1216.06	−0.396764	−0.198382	−	0.980125i	$-0.563569\pi$
$211$	−1216.06	−0.396764	−0.198382	+	0.980125i	$0.563569\pi$
$212$	2622.13	0.849475
$213$	4953.67	1.59352
$214$	−441.175	−0.140926
$215$	−130.019	−0.0412429
$216$	−2091.42	−0.658811
$217$	972.866	0.304343
$218$	6050.12	1.87966
$219$	1413.03	0.436000
$220$	−328.308	−0.100611
$221$	−9350.48	−2.84607
$222$	13640.8	4.12394
$223$	−2262.87	−0.679521	−0.339760	−	0.940512i	$-0.610346\pi$
$223$	−2262.87	−0.679521	−0.339760	+	0.940512i	$0.610346\pi$
$224$	−1599.08	−0.476979
$225$	−7369.41	−2.18353
$226$	5732.66	1.68730
$227$	2860.43	0.836358	0.418179	−	0.908365i	$-0.362669\pi$
$227$	2860.43	0.836358	0.418179	+	0.908365i	$0.362669\pi$
$228$	165.245	0.0479982
$229$	−2009.94	−0.580001	−0.290001	−	0.957026i	$-0.593656\pi$
$229$	−2009.94	−0.580001	−0.290001	+	0.957026i	$0.593656\pi$
$230$	108.536	0.0311160
$231$	−2764.54	−0.787418
$232$	770.270	0.217977
$233$	−3027.63	−0.851273	−0.425636	−	0.904894i	$-0.639950\pi$
$233$	−3027.63	−0.851273	−0.425636	+	0.904894i	$0.639950\pi$
$234$	−17715.4	−4.94911
$235$	646.168	0.179367
$236$	−3899.66	−1.07562
$237$	1078.50	0.295595
$238$	3127.16	0.851696
$239$	3644.32	0.986325	0.493162	−	0.869937i	$-0.335841\pi$
$239$	3644.32	0.986325	0.493162	+	0.869937i	$0.335841\pi$
$240$	−878.388	−0.236249
$241$	−3661.47	−0.978655	−0.489327	−	0.872100i	$-0.662758\pi$
$241$	−3661.47	−0.978655	−0.489327	+	0.872100i	$0.662758\pi$
$242$	1761.64	0.467945
$243$	3172.03	0.837390
$244$	−2258.75	−0.592629
$245$	61.4138	0.0160146
$246$	−10052.6	−2.60541
$247$	−226.440	−0.0583322
$248$	−954.446	−0.244385
$249$	−9116.51	−2.32022
$250$	−1172.33	−0.296579
$251$	607.560	0.152784	0.0763921	−	0.997078i	$-0.475660\pi$
$251$	607.560	0.152784	0.0763921	+	0.997078i	$0.475660\pi$
$252$	2581.20	0.645240
$253$	−975.506	−0.242409
$254$	−269.905	−0.0666745
$255$	1384.74	0.340062
$256$	5287.51	1.29090
$257$	−7302.77	−1.77251	−0.886254	−	0.463200i	$-0.846701\pi$
$257$	−7302.77	−1.77251	−0.886254	+	0.463200i	$0.846701\pi$
$258$	−3636.95	−0.877623
$259$	2723.57	0.653415
$260$	−610.011	−0.145505
$261$	−6696.70	−1.58818
$262$	−3640.99	−0.858554
$263$	1476.33	0.346138	0.173069	−	0.984910i	$-0.444632\pi$
$263$	1476.33	0.346138	0.173069	+	0.984910i	$0.444632\pi$
$264$	2712.20	0.632290
$265$	532.127	0.123352
$266$	75.7304	0.0174561
$267$	8761.75	2.00828
$268$	−1763.21	−0.401885
$269$	−5589.01	−1.26679	−0.633397	−	0.773827i	$-0.718340\pi$
$269$	−5589.01	−1.26679	−0.633397	+	0.773827i	$0.718340\pi$
$270$	1437.12	0.323927
$271$	795.786	0.178378	0.0891892	−	0.996015i	$-0.471572\pi$
$271$	795.786	0.178378	0.0891892	+	0.996015i	$0.471572\pi$
$272$	−8930.33	−1.99074
$273$	−5136.66	−1.13877
$274$	4076.09	0.898706
$275$	5235.04	1.14794
$276$	1322.70	0.288467
$277$	4429.83	0.960876	0.480438	−	0.877029i	$-0.340478\pi$
$277$	4429.83	0.960876	0.480438	+	0.877029i	$0.340478\pi$
$278$	−961.705	−0.207479
$279$	8297.93	1.78059
$280$	−60.2511	−0.0128596
$281$	−5245.76	−1.11365	−0.556825	−	0.830630i	$-0.687981\pi$
$281$	−5245.76	−1.11365	−0.556825	+	0.830630i	$0.687981\pi$
$282$	18074.9	3.81683
$283$	2121.97	0.445718	0.222859	−	0.974851i	$-0.428461\pi$
$283$	2121.97	0.445718	0.222859	+	0.974851i	$0.428461\pi$
$284$	3285.58	0.686491
$285$	33.5342	0.00696981
$286$	12584.6	2.60189
$287$	−2007.13	−0.412813
$288$	−13639.2	−2.79061
$289$	9165.28	1.86552
$290$	−529.290	−0.107176
$291$	−6411.24	−1.29153
$292$	937.211	0.187829
$293$	−4903.22	−0.977642	−0.488821	−	0.872384i	$-0.662573\pi$
$293$	−4903.22	−0.977642	−0.488821	+	0.872384i	$0.662573\pi$
$294$	1717.90	0.340781
$295$	−791.384	−0.156190
$296$	−2672.00	−0.524686
$297$	−12916.6	−2.52355
$298$	−9979.22	−1.93987
$299$	−1812.54	−0.350574
$300$	−7098.23	−1.36606
$301$	−726.165	−0.139055
$302$	8179.84	1.55860
$303$	−10530.8	−1.99663
$304$	−216.266	−0.0408016
$305$	−458.383	−0.0860555
$306$	26672.7	4.98293
$307$	5260.17	0.977895	0.488947	−	0.872313i	$-0.337381\pi$
$307$	5260.17	0.977895	0.488947	+	0.872313i	$0.337381\pi$
$308$	−1833.62	−0.339221
$309$	−3293.12	−0.606275
$310$	655.847	0.120160
$311$	−4894.95	−0.892498	−0.446249	−	0.894909i	$-0.647240\pi$
$311$	−4894.95	−0.892498	−0.446249	+	0.894909i	$0.647240\pi$
$312$	5039.40	0.914423
$313$	1253.39	0.226344	0.113172	−	0.993575i	$-0.463899\pi$
$313$	1253.39	0.226344	0.113172	+	0.993575i	$0.463899\pi$
$314$	7619.80	1.36946
$315$	523.821	0.0936952
$316$	715.327	0.127343
$317$	−7917.48	−1.40281	−0.701404	−	0.712764i	$-0.747443\pi$
$317$	−7917.48	−1.40281	−0.701404	+	0.712764i	$0.747443\pi$
$318$	14884.9	2.62486
$319$	4757.17	0.834953
$320$	−323.343	−0.0564856
$321$	−1091.08	−0.189714
$322$	606.182	0.104911
$323$	340.934	0.0587308
$324$	7557.63	1.29589
$325$	9726.95	1.66017
$326$	6102.17	1.03671
$327$	14962.7	2.53040
$328$	1969.13	0.331485
$329$	3608.89	0.604755
$330$	−1863.69	−0.310886
$331$	−9641.15	−1.60098	−0.800492	−	0.599343i	$-0.795428\pi$
$331$	−9641.15	−1.60098	−0.800492	+	0.599343i	$0.795428\pi$
$332$	−6046.64	−0.999555
$333$	23230.3	3.82287
$334$	9942.85	1.62889
$335$	−357.820	−0.0583576
$336$	−4905.85	−0.796536
$337$	8702.27	1.40666	0.703328	−	0.710866i	$-0.251697\pi$
$337$	8702.27	1.40666	0.703328	+	0.710866i	$0.251697\pi$
$338$	15110.8	2.43171
$339$	14177.6	2.27145
$340$	918.446	0.146499
$341$	−5894.63	−0.936107
$342$	645.932	0.102129
$343$	343.000	0.0539949
$344$	712.416	0.111660
$345$	268.424	0.0418883
$346$	8422.05	1.30859
$347$	−4064.10	−0.628738	−0.314369	−	0.949301i	$-0.601793\pi$
$347$	−4064.10	−0.628738	−0.314369	+	0.949301i	$0.601793\pi$
$348$	−6450.28	−0.993596
$349$	−7527.05	−1.15448	−0.577240	−	0.816574i	$-0.695870\pi$
$349$	−7527.05	−1.15448	−0.577240	+	0.816574i	$0.695870\pi$
$350$	−3253.07	−0.496811
$351$	−23999.6	−3.64958
$352$	9688.92	1.46711
$353$	−3814.92	−0.575206	−0.287603	−	0.957750i	$-0.592858\pi$
$353$	−3814.92	−0.575206	−0.287603	+	0.957750i	$0.592858\pi$
$354$	−22137.0	−3.32363
$355$	666.766	0.0996853
$356$	5811.34	0.865169
$357$	7733.86	1.14655
$358$	−6456.51	−0.953176
$359$	−3620.75	−0.532301	−0.266150	−	0.963932i	$-0.585752\pi$
$359$	−3620.75	−0.532301	−0.266150	+	0.963932i	$0.585752\pi$
$360$	−513.903	−0.0752364
$361$	−6850.74	−0.998796
$362$	6419.96	0.932114
$363$	4356.77	0.629948
$364$	−3406.95	−0.490584
$365$	190.195	0.0272747
$366$	−12822.1	−1.83121
$367$	4800.81	0.682834	0.341417	−	0.939912i	$-0.389093\pi$
$367$	4800.81	0.682834	0.341417	+	0.939912i	$0.389093\pi$
$368$	−1731.09	−0.245216
$369$	−17119.6	−2.41520
$370$	1836.06	0.257980
$371$	2971.96	0.415894
$372$	7992.59	1.11397
$373$	−795.372	−0.110410	−0.0552048	−	0.998475i	$-0.517581\pi$
$373$	−795.372	−0.110410	−0.0552048	+	0.998475i	$0.517581\pi$
$374$	−18947.6	−2.61967
$375$	−2899.32	−0.399254
$376$	−3540.56	−0.485613
$377$	8839.04	1.20752
$378$	8026.39	1.09215
$379$	3398.29	0.460577	0.230288	−	0.973122i	$-0.426033\pi$
$379$	3398.29	0.460577	0.230288	+	0.973122i	$0.426033\pi$
$380$	22.2420	0.00300261
$381$	−667.508	−0.0897572
$382$	−9025.89	−1.20891
$383$	10443.2	1.39327	0.696633	−	0.717428i	$-0.254681\pi$
$383$	10443.2	1.39327	0.696633	+	0.717428i	$0.254681\pi$
$384$	7972.47	1.05949
$385$	−372.109	−0.0492582
$386$	10717.2	1.41318
$387$	−6193.73	−0.813552
$388$	−4252.34	−0.556391
$389$	−7512.80	−0.979213	−0.489607	−	0.871943i	$-0.662860\pi$
$389$	−7512.80	−0.979213	−0.489607	+	0.871943i	$0.662860\pi$
$390$	−3462.82	−0.449607
$391$	2728.99	0.352970
$392$	−336.506	−0.0433574
$393$	−9004.63	−1.15578
$394$	−313.112	−0.0400364
$395$	145.166	0.0184914
$396$	−15639.6	−1.98465
$397$	1340.17	0.169424	0.0847118	−	0.996405i	$-0.473003\pi$
$397$	1340.17	0.169424	0.0847118	+	0.996405i	$0.473003\pi$
$398$	−9553.09	−1.20315
$399$	187.291	0.0234994
$400$	9289.88	1.16124
$401$	−7535.94	−0.938472	−0.469236	−	0.883073i	$-0.655471\pi$
$401$	−7535.94	−0.938472	−0.469236	+	0.883073i	$0.655471\pi$
$402$	−10009.1	−1.24181
$403$	−10952.5	−1.35381
$404$	−6984.68	−0.860151
$405$	1533.72	0.188176
$406$	−2956.12	−0.361354
$407$	−16502.2	−2.00979
$408$	−7587.43	−0.920671
$409$	−6704.20	−0.810516	−0.405258	−	0.914202i	$-0.632818\pi$
$409$	−6704.20	−0.810516	−0.405258	+	0.914202i	$0.632818\pi$
$410$	−1353.09	−0.162986
$411$	10080.7	1.20984
$412$	−2184.20	−0.261184
$413$	−4419.93	−0.526611
$414$	5170.35	0.613789
$415$	−1227.09	−0.145145
$416$	18002.5	2.12174
$417$	−2378.42	−0.279308
$418$	−458.854	−0.0536920
$419$	8519.69	0.993352	0.496676	−	0.867936i	$-0.334554\pi$
$419$	8519.69	0.993352	0.496676	+	0.867936i	$0.334554\pi$
$420$	504.546	0.0586174
$421$	−10566.8	−1.22326	−0.611631	−	0.791144i	$-0.709486\pi$
$421$	−10566.8	−1.22326	−0.611631	+	0.791144i	$0.709486\pi$
$422$	−4578.60	−0.528159
$423$	30781.5	3.53818
$424$	−2915.69	−0.333959
$425$	−14645.1	−1.67151
$426$	18651.1	2.12124
$427$	−2560.10	−0.290145
$428$	−723.674	−0.0817292
$429$	31123.2	3.50266
$430$	−489.536	−0.0549012
$431$	4540.75	0.507471	0.253736	−	0.967274i	$-0.418341\pi$
$431$	4540.75	0.507471	0.253736	+	0.967274i	$0.418341\pi$
$432$	−22921.2	−2.55277
$433$	−378.177	−0.0419724	−0.0209862	−	0.999780i	$-0.506681\pi$
$433$	−378.177	−0.0419724	−0.0209862	+	0.999780i	$0.506681\pi$
$434$	3662.94	0.405131
$435$	−1309.00	−0.144280
$436$	9924.20	1.09010
$437$	66.0880	0.00723437
$438$	5320.22	0.580388
$439$	−11835.7	−1.28676	−0.643382	−	0.765545i	$-0.722469\pi$
$439$	−11835.7	−1.28676	−0.643382	+	0.765545i	$0.722469\pi$
$440$	365.064	0.0395539
$441$	2925.57	0.315902
$442$	−35205.5	−3.78859
$443$	−5709.62	−0.612352	−0.306176	−	0.951975i	$-0.599050\pi$
$443$	−5709.62	−0.612352	−0.306176	+	0.951975i	$0.599050\pi$
$444$	22375.5	2.39166
$445$	1179.34	0.125631
$446$	−8519.95	−0.904555
$447$	−24679.9	−2.61145
$448$	−1805.89	−0.190447
$449$	−8495.56	−0.892940	−0.446470	−	0.894799i	$-0.647319\pi$
$449$	−8495.56	−0.892940	−0.446470	+	0.894799i	$0.647319\pi$
$450$	−27746.6	−2.90664
$451$	12161.3	1.26974
$452$	9403.47	0.978544
$453$	20229.8	2.09819
$454$	10769.8	1.11333
$455$	−691.396	−0.0712377
$456$	−183.745	−0.0188698
$457$	12451.1	1.27448	0.637239	−	0.770667i	$-0.280077\pi$
$457$	12451.1	1.27448	0.637239	+	0.770667i	$0.280077\pi$
$458$	−7567.62	−0.772078
$459$	36134.3	3.67452
$460$	178.036	0.0180455
$461$	7838.56	0.791927	0.395963	−	0.918266i	$-0.370411\pi$
$461$	7838.56	0.791927	0.395963	+	0.918266i	$0.370411\pi$
$462$	−10408.8	−1.04818
$463$	13312.0	1.33620	0.668102	−	0.744070i	$-0.267107\pi$
$463$	13312.0	1.33620	0.668102	+	0.744070i	$0.267107\pi$
$464$	8441.88	0.844621
$465$	1621.99	0.161759
$466$	−11399.3	−1.13319
$467$	−15246.3	−1.51074	−0.755370	−	0.655298i	$-0.772543\pi$
$467$	−15246.3	−1.51074	−0.755370	+	0.655298i	$0.772543\pi$
$468$	−29059.1	−2.87021
$469$	−1998.45	−0.196759
$470$	2432.89	0.238768
$471$	18844.7	1.84357
$472$	4336.25	0.422864
$473$	4399.86	0.427708
$474$	4060.66	0.393486
$475$	−354.660	−0.0342588
$476$	5129.58	0.493937
$477$	25349.0	2.43323
$478$	13721.3	1.31296
$479$	7348.08	0.700924	0.350462	−	0.936577i	$-0.386025\pi$
$479$	7348.08	0.700924	0.350462	+	0.936577i	$0.386025\pi$
$480$	−2666.04	−0.253516
$481$	−30661.9	−2.90658
$482$	−13785.8	−1.30275
$483$	1499.16	0.141231
$484$	2889.68	0.271382
$485$	−862.956	−0.0807935
$486$	11943.0	1.11471
$487$	9433.69	0.877785	0.438893	−	0.898539i	$-0.355371\pi$
$487$	9433.69	0.877785	0.438893	+	0.898539i	$0.355371\pi$
$488$	2511.63	0.232984
$489$	15091.4	1.39562
$490$	231.230	0.0213181
$491$	972.045	0.0893437	0.0446719	−	0.999002i	$-0.485776\pi$
$491$	972.045	0.0893437	0.0446719	+	0.999002i	$0.485776\pi$
$492$	−16489.6	−1.51099
$493$	−13308.3	−1.21577
$494$	−852.572	−0.0776498
$495$	−3173.85	−0.288190
$496$	−10460.4	−0.946946
$497$	3723.93	0.336099
$498$	−34324.6	−3.08860
$499$	6691.66	0.600320	0.300160	−	0.953889i	$-0.402960\pi$
$499$	6691.66	0.600320	0.300160	+	0.953889i	$0.402960\pi$
$500$	−1923.01	−0.171999
$501$	24589.9	2.19281
$502$	2287.53	0.203381
$503$	−18003.2	−1.59587	−0.797934	−	0.602745i	$-0.794074\pi$
$503$	−18003.2	−1.59587	−0.797934	+	0.602745i	$0.794074\pi$
$504$	−2870.18	−0.253667
$505$	−1417.45	−0.124902
$506$	−3672.88	−0.322687
$507$	37370.9	3.27357
$508$	−442.733	−0.0386675
$509$	−15154.2	−1.31964	−0.659822	−	0.751422i	$-0.729368\pi$
$509$	−15154.2	−1.31964	−0.659822	+	0.751422i	$0.729368\pi$
$510$	5213.70	0.452679
$511$	1062.25	0.0919592
$512$	13058.5	1.12717
$513$	875.065	0.0753120
$514$	−27495.7	−2.35950
$515$	−443.255	−0.0379265
$516$	−5965.81	−0.508973
$517$	−21866.4	−1.86012
$518$	10254.5	0.869804
$519$	20828.8	1.76162
$520$	678.306	0.0572032
$521$	−3265.62	−0.274606	−0.137303	−	0.990529i	$-0.543843\pi$
$521$	−3265.62	−0.274606	−0.137303	+	0.990529i	$0.543843\pi$
$522$	−25213.8	−2.11413
$523$	14860.0	1.24242	0.621208	−	0.783646i	$-0.286642\pi$
$523$	14860.0	1.24242	0.621208	+	0.783646i	$0.286642\pi$
$524$	−5972.43	−0.497914
$525$	−8045.24	−0.668806
$526$	5558.53	0.460767
$527$	16490.3	1.36306
$528$	29724.7	2.45001
$529$	529.000	0.0434783
$530$	2003.52	0.164202
$531$	−37699.2	−3.08099
$532$	124.223	0.0101236
$533$	22596.3	1.83631
$534$	32988.9	2.67335
$535$	−146.860	−0.0118679
$536$	1960.61	0.157995
$537$	−15967.8	−1.28316
$538$	−21043.2	−1.68631
$539$	−2078.25	−0.166079
$540$	2357.35	0.187860
$541$	19982.0	1.58797	0.793986	−	0.607935i	$-0.208002\pi$
$541$	19982.0	1.58797	0.793986	+	0.607935i	$0.208002\pi$
$542$	2996.22	0.237451
$543$	15877.4	1.25481
$544$	−27104.9	−2.13624
$545$	2013.99	0.158293
$546$	−19340.1	−1.51589
$547$	−13306.5	−1.04012	−0.520059	−	0.854130i	$-0.674090\pi$
$547$	−13306.5	−1.04012	−0.520059	+	0.854130i	$0.674090\pi$
$548$	6686.14	0.521200
$549$	−21836.0	−1.69752
$550$	19710.5	1.52810
$551$	−322.286	−0.0249180
$552$	−1470.78	−0.113407
$553$	810.763	0.0623456
$554$	16678.8	1.27908
$555$	4540.82	0.347292
$556$	−1577.51	−0.120326
$557$	−20718.0	−1.57603	−0.788016	−	0.615654i	$-0.788892\pi$
$557$	−20718.0	−1.57603	−0.788016	+	0.615654i	$0.788892\pi$
$558$	31242.6	2.37026
$559$	8175.15	0.618555
$560$	−660.330	−0.0498286
$561$	−46859.8	−3.52660
$562$	−19750.8	−1.48245
$563$	−13095.9	−0.980328	−0.490164	−	0.871630i	$-0.663063\pi$
$563$	−13095.9	−0.980328	−0.490164	+	0.871630i	$0.663063\pi$
$564$	29648.8	2.21355
$565$	1908.31	0.142094
$566$	7989.45	0.593324
$567$	8565.93	0.634454
$568$	−3653.42	−0.269884
$569$	−1067.59	−0.0786566	−0.0393283	−	0.999226i	$-0.512522\pi$
$569$	−1067.59	−0.0786566	−0.0393283	+	0.999226i	$0.512522\pi$
$570$	126.260	0.00927798
$571$	1164.39	0.0853383	0.0426691	−	0.999089i	$-0.486414\pi$
$571$	1164.39	0.0853383	0.0426691	+	0.999089i	$0.486414\pi$
$572$	20642.9	1.50895
$573$	−22322.2	−1.62744
$574$	−7557.07	−0.549522
$575$	−2838.87	−0.205894
$576$	−15403.1	−1.11423
$577$	9173.42	0.661862	0.330931	−	0.943655i	$-0.392637\pi$
$577$	9173.42	0.661862	0.330931	+	0.943655i	$0.392637\pi$
$578$	34508.3	2.48331
$579$	26504.9	1.90243
$580$	−868.211	−0.0621560
$581$	−6853.35	−0.489372
$582$	−24139.0	−1.71923
$583$	−18007.3	−1.27922
$584$	−1042.14	−0.0738424
$585$	−5897.17	−0.416783
$586$	−18461.1	−1.30140
$587$	20093.3	1.41284	0.706422	−	0.707790i	$-0.250308\pi$
$587$	20093.3	1.41284	0.706422	+	0.707790i	$0.250308\pi$
$588$	2817.92	0.197634
$589$	399.347	0.0279368
$590$	−2979.65	−0.207915
$591$	−774.365	−0.0538970
$592$	−29284.2	−2.03306
$593$	4833.05	0.334687	0.167344	−	0.985899i	$-0.446481\pi$
$593$	4833.05	0.334687	0.167344	+	0.985899i	$0.446481\pi$
$594$	−48632.2	−3.35927
$595$	1040.98	0.0717245
$596$	−16369.2	−1.12502
$597$	−23626.0	−1.61968
$598$	−6824.39	−0.466672
$599$	18617.2	1.26991	0.634956	−	0.772548i	$-0.281018\pi$
$599$	18617.2	1.26991	0.634956	+	0.772548i	$0.281018\pi$
$600$	7892.92	0.537045
$601$	−19183.1	−1.30199	−0.650994	−	0.759083i	$-0.725648\pi$
$601$	−19183.1	−1.30199	−0.650994	+	0.759083i	$0.725648\pi$
$602$	−2734.09	−0.185105
$603$	−17045.5	−1.15115
$604$	13417.7	0.903902
$605$	586.423	0.0394074
$606$	−39649.6	−2.65784
$607$	−148.347	−0.00991961	−0.00495980	−	0.999988i	$-0.501579\pi$
$607$	−148.347	−0.00991961	−0.00495980	+	0.999988i	$0.501579\pi$
$608$	−656.400	−0.0437838
$609$	−7310.85	−0.486454
$610$	−1725.86	−0.114554
$611$	−40628.8	−2.69012
$612$	43752.1	2.88982
$613$	5019.62	0.330735	0.165367	−	0.986232i	$-0.447119\pi$
$613$	5019.62	0.330735	0.165367	+	0.986232i	$0.447119\pi$
$614$	19805.1	1.30174
$615$	−3346.35	−0.219411
$616$	2038.90	0.133360
$617$	24911.0	1.62541	0.812707	−	0.582673i	$-0.197993\pi$
$617$	24911.0	1.62541	0.812707	+	0.582673i	$0.197993\pi$
$618$	−12398.9	−0.807052
$619$	26324.7	1.70933	0.854667	−	0.519177i	$-0.173761\pi$
$619$	26324.7	1.70933	0.854667	+	0.519177i	$0.173761\pi$
$620$	1075.81	0.0696861
$621$	7004.43	0.452622
$622$	−18430.0	−1.18806
$623$	6586.66	0.423578
$624$	55230.0	3.54322
$625$	15038.4	0.962457
$626$	4719.13	0.301301
$627$	−1134.80	−0.0722802
$628$	12499.0	0.794211
$629$	46165.3	2.92644
$630$	1972.24	0.124724
$631$	4312.09	0.272047	0.136023	−	0.990706i	$-0.456568\pi$
$631$	4312.09	0.272047	0.136023	+	0.990706i	$0.456568\pi$
$632$	−795.412	−0.0500630
$633$	−11323.5	−0.711007
$634$	−29810.1	−1.86737
$635$	−89.8470	−0.00561491
$636$	24416.2	1.52227
$637$	−3861.49	−0.240185
$638$	17911.2	1.11146
$639$	31762.8	1.96638
$640$	1073.10	0.0662780
$641$	−7151.59	−0.440672	−0.220336	−	0.975424i	$-0.570715\pi$
$641$	−7151.59	−0.440672	−0.220336	+	0.975424i	$0.570715\pi$
$642$	−4108.04	−0.252541
$643$	31125.0	1.90895	0.954473	−	0.298298i	$-0.0964190\pi$
$643$	31125.0	1.90895	0.954473	+	0.298298i	$0.0964190\pi$
$644$	994.340	0.0608424
$645$	−1210.68	−0.0739079
$646$	1283.65	0.0781805
$647$	−26953.4	−1.63779	−0.818893	−	0.573947i	$-0.805412\pi$
$647$	−26953.4	−1.63779	−0.818893	+	0.573947i	$0.805412\pi$
$648$	−8403.75	−0.509461
$649$	26780.5	1.61977
$650$	36623.0	2.20996
$651$	9058.92	0.545387
$652$	10009.6	0.601235
$653$	20397.4	1.22238	0.611188	−	0.791485i	$-0.290692\pi$
$653$	20397.4	1.22238	0.611188	+	0.791485i	$0.290692\pi$
$654$	56336.2	3.36838
$655$	−1212.03	−0.0723020
$656$	21581.0	1.28444
$657$	9060.32	0.538016
$658$	13587.8	0.805029
$659$	−16996.5	−1.00469	−0.502343	−	0.864668i	$-0.667529\pi$
$659$	−16996.5	−1.00469	−0.502343	+	0.864668i	$0.667529\pi$
$660$	−3057.06	−0.180297
$661$	9516.13	0.559962	0.279981	−	0.960006i	$-0.409672\pi$
$661$	9516.13	0.559962	0.279981	+	0.960006i	$0.409672\pi$
$662$	−36300.0	−2.13118
$663$	−87067.7	−5.10020
$664$	6723.59	0.392961
$665$	25.2094	0.00147004
$666$	87464.7	5.08887
$667$	−2579.73	−0.149756
$668$	16309.6	0.944665
$669$	−21070.9	−1.21771
$670$	−1347.23	−0.0776837
$671$	15511.7	0.892435
$672$	−14890.0	−0.854754
$673$	−19493.6	−1.11653	−0.558263	−	0.829664i	$-0.688532\pi$
$673$	−19493.6	−1.11653	−0.558263	+	0.829664i	$0.688532\pi$
$674$	32765.0	1.87249
$675$	−37589.2	−2.14342
$676$	24786.7	1.41026
$677$	9604.20	0.545228	0.272614	−	0.962123i	$-0.412112\pi$
$677$	9604.20	0.545228	0.272614	+	0.962123i	$0.412112\pi$
$678$	53380.1	3.02368
$679$	−4819.66	−0.272403
$680$	−1021.27	−0.0575941
$681$	26635.1	1.49877
$682$	−22193.9	−1.24611
$683$	17113.2	0.958737	0.479369	−	0.877614i	$-0.340866\pi$
$683$	17113.2	0.958737	0.479369	+	0.877614i	$0.340866\pi$
$684$	1059.54	0.0592290
$685$	1356.86	0.0756834
$686$	1291.43	0.0718762
$687$	−18715.7	−1.03937
$688$	7807.82	0.432660
$689$	−33458.3	−1.85002
$690$	1010.64	0.0557603
$691$	−7396.94	−0.407226	−0.203613	−	0.979051i	$-0.565268\pi$
$691$	−7396.94	−0.407226	−0.203613	+	0.979051i	$0.565268\pi$
$692$	13815.0	0.758910
$693$	−17726.2	−0.971661
$694$	−15301.8	−0.836955
$695$	−320.136	−0.0174726
$696$	7172.43	0.390618
$697$	−34021.5	−1.84886
$698$	−28340.1	−1.53681
$699$	−28192.0	−1.52549
$700$	−5336.11	−0.288123
$701$	7089.35	0.381970	0.190985	−	0.981593i	$-0.438832\pi$
$701$	7089.35	0.381970	0.190985	+	0.981593i	$0.438832\pi$
$702$	−90361.1	−4.85820
$703$	1117.98	0.0599795
$704$	10941.9	0.585782
$705$	6016.85	0.321429
$706$	−14363.6	−0.765694
$707$	−7916.55	−0.421121
$708$	−36312.0	−1.92752
$709$	32194.9	1.70536	0.852682	−	0.522430i	$-0.174974\pi$
$709$	32194.9	1.70536	0.852682	+	0.522430i	$0.174974\pi$
$710$	2510.45	0.132698
$711$	6915.29	0.364759
$712$	−6461.95	−0.340129
$713$	3196.56	0.167899
$714$	29118.8	1.52625
$715$	4189.20	0.219115
$716$	−10590.8	−0.552789
$717$	33934.4	1.76751
$718$	−13632.5	−0.708580
$719$	12572.2	0.652107	0.326053	−	0.945351i	$-0.394281\pi$
$719$	12572.2	0.652107	0.326053	+	0.945351i	$0.394281\pi$
$720$	−5632.19	−0.291527
$721$	−2475.61	−0.127873
$722$	−25793.8	−1.32956
$723$	−34094.0	−1.75376
$724$	10530.9	0.540575
$725$	13844.1	0.709181
$726$	16403.7	0.838565
$727$	−26522.4	−1.35304	−0.676521	−	0.736424i	$-0.736513\pi$
$727$	−26522.4	−1.35304	−0.676521	+	0.736424i	$0.736513\pi$
$728$	3788.38	0.192866
$729$	−3503.40	−0.177991
$730$	716.104	0.0363071
$731$	−12308.7	−0.622782
$732$	−21032.5	−1.06200
$733$	11845.3	0.596886	0.298443	−	0.954427i	$-0.403533\pi$
$733$	11845.3	0.596886	0.298443	+	0.954427i	$0.403533\pi$
$734$	18075.6	0.908966
$735$	571.860	0.0286985
$736$	−5254.14	−0.263139
$737$	12108.7	0.605195
$738$	−64457.0	−3.21503
$739$	−581.255	−0.0289335	−0.0144667	−	0.999895i	$-0.504605\pi$
$739$	−581.255	−0.0289335	−0.0144667	+	0.999895i	$0.504605\pi$
$740$	3011.75	0.149614
$741$	−2108.52	−0.104532
$742$	11189.8	0.553624
$743$	34358.5	1.69649	0.848246	−	0.529603i	$-0.177659\pi$
$743$	34358.5	1.69649	0.848246	+	0.529603i	$0.177659\pi$
$744$	−8887.41	−0.437941
$745$	−3321.92	−0.163364
$746$	−2994.66	−0.146974
$747$	−58454.8	−2.86312
$748$	−31080.3	−1.51926
$749$	−820.223	−0.0400137
$750$	−10916.2	−0.531473
$751$	31565.6	1.53375	0.766875	−	0.641797i	$-0.221811\pi$
$751$	31565.6	1.53375	0.766875	+	0.641797i	$0.221811\pi$
$752$	−38803.2	−1.88166
$753$	5657.34	0.273792
$754$	33279.9	1.60741
$755$	2722.94	0.131255
$756$	13165.9	0.633387
$757$	7911.75	0.379864	0.189932	−	0.981797i	$-0.439173\pi$
$757$	7911.75	0.379864	0.189932	+	0.981797i	$0.439173\pi$
$758$	12794.9	0.613104
$759$	−9083.50	−0.434401
$760$	−24.7321	−0.00118043
$761$	18428.9	0.877852	0.438926	−	0.898523i	$-0.355359\pi$
$761$	18428.9	0.877852	0.438926	+	0.898523i	$0.355359\pi$
$762$	−2513.24	−0.119482
$763$	11248.2	0.533701
$764$	−14805.5	−0.701103
$765$	8878.91	0.419631
$766$	39319.6	1.85467
$767$	49759.5	2.34252
$768$	49235.1	2.31331
$769$	−19689.0	−0.923281	−0.461640	−	0.887067i	$-0.652739\pi$
$769$	−19689.0	−0.923281	−0.461640	+	0.887067i	$0.652739\pi$
$770$	−1401.03	−0.0655709
$771$	−68000.4	−3.17636
$772$	17579.7	0.819569
$773$	−22405.8	−1.04254	−0.521269	−	0.853392i	$-0.674541\pi$
$773$	−22405.8	−1.04254	−0.521269	+	0.853392i	$0.674541\pi$
$774$	−23320.0	−1.08297
$775$	−17154.3	−0.795097
$776$	4728.41	0.218737
$777$	25360.8	1.17093
$778$	−28286.5	−1.30350
$779$	−823.897	−0.0378937
$780$	−5680.17	−0.260747
$781$	−22563.5	−1.03378
$782$	10275.0	0.469861
$783$	−34157.9	−1.55901
$784$	−3687.98	−0.168002
$785$	2536.51	0.115327
$786$	−33903.4	−1.53854
$787$	−36959.8	−1.67405	−0.837023	−	0.547168i	$-0.815706\pi$
$787$	−36959.8	−1.67405	−0.837023	+	0.547168i	$0.815706\pi$
$788$	−513.607	−0.0232189
$789$	13746.9	0.620284
$790$	546.567	0.0246151
$791$	10658.0	0.479085
$792$	17390.6	0.780235
$793$	28821.5	1.29065
$794$	5045.88	0.225531
$795$	4954.95	0.221049
$796$	−15670.2	−0.697760
$797$	18571.4	0.825385	0.412692	−	0.910870i	$-0.364588\pi$
$797$	18571.4	0.825385	0.412692	+	0.910870i	$0.364588\pi$
$798$	705.170	0.0312816
$799$	61171.6	2.70851
$800$	28196.2	1.24611
$801$	56180.0	2.47818
$802$	−28373.6	−1.24926
$803$	−6436.22	−0.282851
$804$	−16418.3	−0.720183
$805$	201.788	0.00883491
$806$	−41237.4	−1.80214
$807$	−52042.5	−2.27011
$808$	7766.66	0.338156
$809$	−30541.9	−1.32731	−0.663656	−	0.748038i	$-0.730996\pi$
$809$	−30541.9	−1.32731	−0.663656	+	0.748038i	$0.730996\pi$
$810$	5774.63	0.250493
$811$	11493.8	0.497661	0.248830	−	0.968547i	$-0.419954\pi$
$811$	11493.8	0.497661	0.248830	+	0.968547i	$0.419954\pi$
$812$	−4849.01	−0.209565
$813$	7410.03	0.319657
$814$	−62132.6	−2.67537
$815$	2031.31	0.0873053
$816$	−83155.5	−3.56743
$817$	−298.079	−0.0127644
$818$	−25242.0	−1.07893
$819$	−32936.1	−1.40523
$820$	−2219.51	−0.0945227
$821$	7959.92	0.338372	0.169186	−	0.985584i	$-0.445886\pi$
$821$	7959.92	0.338372	0.169186	+	0.985584i	$0.445886\pi$
$822$	37954.8	1.61050
$823$	21475.9	0.909603	0.454802	−	0.890593i	$-0.349710\pi$
$823$	21475.9	0.909603	0.454802	+	0.890593i	$0.349710\pi$
$824$	2428.74	0.102681
$825$	48746.5	2.05713
$826$	−16641.5	−0.701007
$827$	−18521.4	−0.778783	−0.389392	−	0.921072i	$-0.627315\pi$
$827$	−18521.4	−0.778783	−0.389392	+	0.921072i	$0.627315\pi$
$828$	8481.09	0.355964
$829$	−3374.12	−0.141361	−0.0706803	−	0.997499i	$-0.522517\pi$
$829$	−3374.12	−0.141361	−0.0706803	+	0.997499i	$0.522517\pi$
$830$	−4620.11	−0.193212
$831$	41248.7	1.72190
$832$	20330.7	0.847162
$833$	5813.95	0.241826
$834$	−8954.99	−0.371806
$835$	3309.81	0.137175
$836$	−752.672	−0.0311384
$837$	42325.3	1.74788
$838$	32077.6	1.32232
$839$	−4028.81	−0.165780	−0.0828902	−	0.996559i	$-0.526415\pi$
$839$	−4028.81	−0.165780	−0.0828902	+	0.996559i	$0.526415\pi$
$840$	−561.033	−0.0230446
$841$	−11808.7	−0.484179
$842$	−39785.0	−1.62836
$843$	−48846.3	−1.99568
$844$	−7510.43	−0.306303
$845$	5030.14	0.204783
$846$	115896.	4.70990
$847$	3275.21	0.132866
$848$	−31954.9	−1.29403
$849$	19758.9	0.798733
$850$	−55140.4	−2.22506
$851$	8948.88	0.360474
$852$	30594.0	1.23020
$853$	19547.1	0.784621	0.392310	−	0.919833i	$-0.371676\pi$
$853$	19547.1	0.784621	0.392310	+	0.919833i	$0.371676\pi$
$854$	−9639.04	−0.386231
$855$	215.021	0.00860064
$856$	804.693	0.0321307
$857$	−15870.4	−0.632581	−0.316291	−	0.948662i	$-0.602437\pi$
$857$	−15870.4	−0.632581	−0.316291	+	0.948662i	$0.602437\pi$
$858$	117182.	4.66263
$859$	35606.1	1.41428	0.707139	−	0.707075i	$-0.249986\pi$
$859$	35606.1	1.41428	0.707139	+	0.707075i	$0.249986\pi$
$860$	−803.001	−0.0318397
$861$	−18689.6	−0.739767
$862$	17096.4	0.675528
$863$	−30593.4	−1.20673	−0.603366	−	0.797464i	$-0.706174\pi$
$863$	−30593.4	−1.20673	−0.603366	+	0.797464i	$0.706174\pi$
$864$	−69569.5	−2.73935
$865$	2803.57	0.110201
$866$	−1423.88	−0.0558722
$867$	85343.3	3.34303
$868$	6008.44	0.234954
$869$	−4912.45	−0.191764
$870$	−4928.53	−0.192061
$871$	22498.5	0.875239
$872$	−11035.3	−0.428557
$873$	−41108.7	−1.59372
$874$	248.828	0.00963015
$875$	−2179.57	−0.0842090
$876$	8726.92	0.336593
$877$	18579.7	0.715385	0.357692	−	0.933839i	$-0.383564\pi$
$877$	18579.7	0.715385	0.357692	+	0.933839i	$0.383564\pi$
$878$	−44562.8	−1.71290
$879$	−45656.7	−1.75195
$880$	4000.96	0.153264
$881$	−2860.60	−0.109394	−0.0546971	−	0.998503i	$-0.517419\pi$
$881$	−2860.60	−0.109394	−0.0546971	+	0.998503i	$0.517419\pi$
$882$	11015.1	0.420519
$883$	1117.59	0.0425933	0.0212967	−	0.999773i	$-0.493221\pi$
$883$	1117.59	0.0425933	0.0212967	+	0.999773i	$0.493221\pi$
$884$	−57748.8	−2.19717
$885$	−7369.04	−0.279896
$886$	−21497.3	−0.815142
$887$	11829.3	0.447789	0.223895	−	0.974613i	$-0.428123\pi$
$887$	11829.3	0.447789	0.223895	+	0.974613i	$0.428123\pi$
$888$	−24880.6	−0.940245
$889$	−501.801	−0.0189312
$890$	4440.32	0.167236
$891$	−51901.3	−1.95147
$892$	−13975.6	−0.524592
$893$	1481.39	0.0555128
$894$	−92922.3	−3.47627
$895$	−2149.27	−0.0802705
$896$	5993.32	0.223463
$897$	−16877.6	−0.628234
$898$	−31986.7	−1.18865
$899$	−15588.4	−0.578311
$900$	−45513.6	−1.68569
$901$	50375.6	1.86266
$902$	45788.6	1.69024
$903$	−6761.74	−0.249188
$904$	−10456.2	−0.384701
$905$	2137.10	0.0784968
$906$	76167.3	2.79303
$907$	32567.9	1.19228	0.596140	−	0.802880i	$-0.296700\pi$
$907$	32567.9	1.19228	0.596140	+	0.802880i	$0.296700\pi$
$908$	17666.1	0.645671
$909$	−67523.1	−2.46381
$910$	−2603.18	−0.0948292
$911$	3223.08	0.117218	0.0586090	−	0.998281i	$-0.481333\pi$
$911$	3223.08	0.117218	0.0586090	+	0.998281i	$0.481333\pi$
$912$	−2013.78	−0.0731171
$913$	41524.7	1.50522
$914$	46879.6	1.69654
$915$	−4268.27	−0.154213
$916$	−12413.4	−0.447763
$917$	−6769.25	−0.243773
$918$	136050.	4.89140
$919$	−40432.2	−1.45129	−0.725646	−	0.688069i	$-0.758459\pi$
$919$	−40432.2	−1.45129	−0.725646	+	0.688069i	$0.758459\pi$
$920$	−197.968	−0.00709435
$921$	48980.5	1.75240
$922$	29513.0	1.05419
$923$	−41924.0	−1.49506
$924$	−17073.9	−0.607889
$925$	−48024.0	−1.70705
$926$	50121.2	1.77871
$927$	−21115.4	−0.748133
$928$	25622.4	0.906354
$929$	−46858.0	−1.65486	−0.827429	−	0.561571i	$-0.810197\pi$
$929$	−46858.0	−1.65486	−0.827429	+	0.561571i	$0.810197\pi$
$930$	6106.97	0.215328
$931$	140.796	0.00495640
$932$	−18698.7	−0.657185
$933$	−45579.7	−1.59937
$934$	−57404.0	−2.01105
$935$	−6307.35	−0.220612
$936$	32312.5	1.12838
$937$	−6908.84	−0.240877	−0.120439	−	0.992721i	$-0.538430\pi$
$937$	−6908.84	−0.240877	−0.120439	+	0.992721i	$0.538430\pi$
$938$	−7524.37	−0.261918
$939$	11671.0	0.405612
$940$	3990.75	0.138472
$941$	−11721.1	−0.406055	−0.203028	−	0.979173i	$-0.565078\pi$
$941$	−11721.1	−0.406055	−0.203028	+	0.979173i	$0.565078\pi$
$942$	70952.4	2.45409
$943$	−6594.86	−0.227739
$944$	47523.7	1.63852
$945$	2671.86	0.0919741
$946$	16565.9	0.569350
$947$	53708.5	1.84297	0.921485	−	0.388414i	$-0.126977\pi$
$947$	53708.5	1.84297	0.921485	+	0.388414i	$0.126977\pi$
$948$	6660.83	0.228200
$949$	−11958.8	−0.409061
$950$	−1335.33	−0.0456042
$951$	−73724.3	−2.51385
$952$	−5703.87	−0.194184
$953$	40584.2	1.37949	0.689743	−	0.724054i	$-0.257723\pi$
$953$	40584.2	1.37949	0.689743	+	0.724054i	$0.257723\pi$
$954$	95441.6	3.23903
$955$	−3004.58	−0.101807
$956$	22507.4	0.761445
$957$	44296.7	1.49625
$958$	27666.3	0.933046
$959$	7578.17	0.255174
$960$	−3010.83	−0.101223
$961$	−10475.3	−0.351627
$962$	−115445.	−3.86914
$963$	−6995.98	−0.234104
$964$	−22613.3	−0.755524
$965$	3567.57	0.119010
$966$	5644.51	0.188001
$967$	12480.6	0.415045	0.207523	−	0.978230i	$-0.433460\pi$
$967$	12480.6	0.415045	0.207523	+	0.978230i	$0.433460\pi$
$968$	−3213.20	−0.106690
$969$	3174.63	0.105246
$970$	−3249.12	−0.107550
$971$	−1341.50	−0.0443366	−0.0221683	−	0.999754i	$-0.507057\pi$
$971$	−1341.50	−0.0443366	−0.0221683	+	0.999754i	$0.507057\pi$
$972$	19590.5	0.646468
$973$	−1787.98	−0.0589106
$974$	35518.9	1.16848
$975$	90573.3	2.97504
$976$	27526.5	0.902768
$977$	−21010.5	−0.688009	−0.344005	−	0.938968i	$-0.611784\pi$
$977$	−21010.5	−0.688009	−0.344005	+	0.938968i	$0.611784\pi$
$978$	56820.8	1.85780
$979$	−39908.8	−1.30285
$980$	379.293	0.0123633
$981$	95940.4	3.12247
$982$	3659.85	0.118931
$983$	28808.0	0.934722	0.467361	−	0.884067i	$-0.345205\pi$
$983$	28808.0	0.934722	0.467361	+	0.884067i	$0.345205\pi$
$984$	18335.7	0.594026
$985$	−104.230	−0.00337162
$986$	−50107.0	−1.61839
$987$	33604.5	1.08373
$988$	−1398.50	−0.0450326
$989$	−2385.97	−0.0767133
$990$	−11949.9	−0.383629
$991$	14431.5	0.462595	0.231298	−	0.972883i	$-0.425703\pi$
$991$	14431.5	0.462595	0.231298	+	0.972883i	$0.425703\pi$
$992$	−31748.9	−1.01616
$993$	−89774.4	−2.86899
$994$	14021.0	0.447403
$995$	−3180.07	−0.101322
$996$	−56303.8	−1.79122
$997$	−7627.63	−0.242296	−0.121148	−	0.992634i	$-0.538658\pi$
$997$	−7627.63	−0.242296	−0.121148	+	0.992634i	$0.538658\pi$
$998$	25194.8	0.799125
$999$	118491.	3.75265

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	161.4.a.d.1.9	✓	12
3.2	odd	2		1449.4.a.o.1.4		12
7.6	odd	2		1127.4.a.h.1.9		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
161.4.a.d.1.9	✓	12	1.1	even	1	trivial
1127.4.a.h.1.9		12	7.6	odd	2
1449.4.a.o.1.4		12	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:	\( N \)	\(=\)	\( 161 = 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	161.a (trivial)

\(f(q)\)	\(=\)	\(q+3.76511 q^{2} +9.31158 q^{3} +6.17602 q^{4} +1.25334 q^{5} +35.0591 q^{6} +7.00000 q^{7} -6.86747 q^{8} +59.7056 q^{9} +4.71897 q^{10} -42.4133 q^{11} +57.5085 q^{12} -78.8059 q^{13} +26.3557 q^{14} +11.6706 q^{15} -75.2649 q^{16} +118.652 q^{17} +224.798 q^{18} +2.87339 q^{19} +7.74068 q^{20} +65.1811 q^{21} -159.691 q^{22} +23.0000 q^{23} -63.9470 q^{24} -123.429 q^{25} -296.713 q^{26} +304.541 q^{27} +43.2322 q^{28} -112.162 q^{29} +43.9411 q^{30} +138.981 q^{31} -228.441 q^{32} -394.935 q^{33} +446.737 q^{34} +8.77340 q^{35} +368.743 q^{36} +389.082 q^{37} +10.8186 q^{38} -733.808 q^{39} -8.60729 q^{40} -286.733 q^{41} +245.414 q^{42} -103.738 q^{43} -261.945 q^{44} +74.8316 q^{45} +86.5974 q^{46} +515.555 q^{47} -700.836 q^{48} +49.0000 q^{49} -464.724 q^{50} +1104.84 q^{51} -486.707 q^{52} +424.566 q^{53} +1146.63 q^{54} -53.1584 q^{55} -48.0723 q^{56} +26.7558 q^{57} -422.302 q^{58} -631.418 q^{59} +72.0780 q^{60} -365.728 q^{61} +523.278 q^{62} +417.939 q^{63} -257.984 q^{64} -98.7709 q^{65} -1486.97 q^{66} -285.493 q^{67} +732.797 q^{68} +214.166 q^{69} +33.0328 q^{70} +531.990 q^{71} -410.026 q^{72} +151.750 q^{73} +1464.93 q^{74} -1149.32 q^{75} +17.7461 q^{76} -296.893 q^{77} -2762.86 q^{78} +115.823 q^{79} -94.3328 q^{80} +1223.70 q^{81} -1079.58 q^{82} -979.050 q^{83} +402.560 q^{84} +148.712 q^{85} -390.584 q^{86} -1044.41 q^{87} +291.272 q^{88} +940.951 q^{89} +281.749 q^{90} -551.641 q^{91} +142.049 q^{92} +1294.13 q^{93} +1941.12 q^{94} +3.60135 q^{95} -2127.14 q^{96} -688.524 q^{97} +184.490 q^{98} -2532.31 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{2} + q^{3} + 72 q^{4} + 16 q^{5} - 15 q^{6} + 84 q^{7} - 21 q^{8} + 203 q^{9} + 106 q^{10} + 50 q^{11} - 139 q^{12} + 21 q^{13} + 28 q^{14} + 192 q^{15} + 516 q^{16} + 26 q^{17} + 251 q^{18}+ \cdots + 2400 q^{99}+O(q^{100}) \) 12 * q + 4 * q^2 + q^3 + 72 * q^4 + 16 * q^5 - 15 * q^6 + 84 * q^7 - 21 * q^8 + 203 * q^9 + 106 * q^10 + 50 * q^11 - 139 * q^12 + 21 * q^13 + 28 * q^14 + 192 * q^15 + 516 * q^16 + 26 * q^17 + 251 * q^18 + 292 * q^19 - 12 * q^20 + 7 * q^21 + 206 * q^22 + 276 * q^23 + 42 * q^24 + 408 * q^25 + 409 * q^26 - 335 * q^27 + 504 * q^28 + 129 * q^29 + 168 * q^30 + 375 * q^31 - 54 * q^32 + 428 * q^33 + 674 * q^34 + 112 * q^35 + 2271 * q^36 + 958 * q^37 - 120 * q^38 + 89 * q^39 + 1424 * q^40 - 347 * q^41 - 105 * q^42 + 392 * q^43 - 1158 * q^44 - 1338 * q^45 + 92 * q^46 + 559 * q^47 - 4767 * q^48 + 588 * q^49 - 888 * q^50 + 204 * q^51 - 1765 * q^52 + 42 * q^53 - 1965 * q^54 + 78 * q^55 - 147 * q^56 + 156 * q^57 - 3695 * q^58 - 620 * q^59 - 1574 * q^60 - 1258 * q^61 + 489 * q^62 + 1421 * q^63 + 4335 * q^64 - 752 * q^65 - 7334 * q^66 + 2024 * q^67 - 5162 * q^68 + 23 * q^69 + 742 * q^70 + 1371 * q^71 - 2483 * q^72 - 1241 * q^73 - 4006 * q^74 + 1357 * q^75 + 4214 * q^76 + 350 * q^77 - 4787 * q^78 + 2660 * q^79 - 5734 * q^80 + 2400 * q^81 - 3551 * q^82 - 1476 * q^83 - 973 * q^84 + 408 * q^85 - 988 * q^86 + 1263 * q^87 + 3324 * q^88 + 1670 * q^89 + 1050 * q^90 + 147 * q^91 + 1656 * q^92 + 135 * q^93 - 3539 * q^94 + 2428 * q^95 - 3973 * q^96 + 1174 * q^97 + 196 * q^98 + 2400 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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