LMFDB - Embedded newform 2009.4.a.k.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2009,4,Mod(1,2009)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2009, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("2009.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 2009 = 7^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2009.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$118.534837202$
Analytic rank:	$1$
Dimension:	$36$
Twist minimal:	no (minimal twist has level 287)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	2009.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.67229 q^{2} +4.57802 q^{3} +13.8303 q^{4} -8.79022 q^{5} -21.3898 q^{6} -27.2411 q^{8} -6.04177 q^{9} +O(q^{10})$	\(q-4.67229 q^{2} +4.57802 q^{3} +13.8303 q^{4} -8.79022 q^{5} -21.3898 q^{6} -27.2411 q^{8} -6.04177 q^{9} +41.0705 q^{10} -42.1310 q^{11} +63.3155 q^{12} +83.3095 q^{13} -40.2418 q^{15} +16.6356 q^{16} +119.501 q^{17} +28.2289 q^{18} -85.2375 q^{19} -121.572 q^{20} +196.848 q^{22} +34.2798 q^{23} -124.710 q^{24} -47.7321 q^{25} -389.247 q^{26} -151.266 q^{27} +127.196 q^{29} +188.021 q^{30} -140.862 q^{31} +140.202 q^{32} -192.876 q^{33} -558.343 q^{34} -83.5597 q^{36} -59.2646 q^{37} +398.255 q^{38} +381.392 q^{39} +239.455 q^{40} -41.0000 q^{41} +79.8833 q^{43} -582.686 q^{44} +53.1084 q^{45} -160.165 q^{46} -555.709 q^{47} +76.1579 q^{48} +223.018 q^{50} +547.076 q^{51} +1152.20 q^{52} +355.007 q^{53} +706.758 q^{54} +370.340 q^{55} -390.219 q^{57} -594.300 q^{58} +686.660 q^{59} -556.557 q^{60} +236.667 q^{61} +658.148 q^{62} -788.151 q^{64} -732.309 q^{65} +901.175 q^{66} +772.754 q^{67} +1652.74 q^{68} +156.933 q^{69} +153.968 q^{71} +164.584 q^{72} -1150.97 q^{73} +276.902 q^{74} -218.518 q^{75} -1178.86 q^{76} -1781.98 q^{78} +691.539 q^{79} -146.230 q^{80} -529.369 q^{81} +191.564 q^{82} -926.864 q^{83} -1050.44 q^{85} -373.238 q^{86} +582.308 q^{87} +1147.69 q^{88} +751.374 q^{89} -248.138 q^{90} +474.101 q^{92} -644.868 q^{93} +2596.43 q^{94} +749.256 q^{95} +641.848 q^{96} -432.897 q^{97} +254.545 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 5 q^{2} + 6 q^{3} + 117 q^{4} - 4 q^{5} + 12 q^{6} - 39 q^{8} + 236 q^{9}+O(q^{10}) $ 36 * q - 5 * q^2 + 6 * q^3 + 117 * q^4 - 4 * q^5 + 12 * q^6 - 39 * q^8 + 236 * q^9	\( 36 q - 5 q^{2} + 6 q^{3} + 117 q^{4} - 4 q^{5} + 12 q^{6} - 39 q^{8} + 236 q^{9} + 12 q^{10} - 140 q^{11} - 186 q^{12} + 72 q^{13} - 366 q^{15} - 15 q^{16} + 2 q^{17} - 212 q^{18} - 30 q^{19} + 334 q^{20} - 346 q^{22} - 314 q^{23} - 106 q^{24} + 570 q^{25} - 303 q^{26} + 204 q^{27} - 356 q^{29} - 357 q^{30} + 4 q^{31} - 532 q^{32} + 30 q^{33} + 364 q^{34} + 113 q^{36} - 1398 q^{37} + 264 q^{38} - 1348 q^{39} - 26 q^{40} - 1476 q^{41} - 1072 q^{43} - 1507 q^{44} + 1132 q^{45} - 1356 q^{46} + 622 q^{47} - 1724 q^{48} - 1426 q^{50} - 668 q^{51} + 877 q^{52} - 412 q^{53} + 1814 q^{54} - 1114 q^{55} - 4082 q^{57} - 1309 q^{58} + 620 q^{59} - 3724 q^{60} - 774 q^{61} - 1665 q^{62} - 3285 q^{64} - 1036 q^{65} + 1056 q^{66} - 2972 q^{67} + 1525 q^{68} - 3304 q^{69} - 3540 q^{71} - 821 q^{72} + 60 q^{73} - 2043 q^{74} - 450 q^{75} - 2171 q^{76} - 1136 q^{78} - 5190 q^{79} + 1564 q^{80} + 284 q^{81} + 205 q^{82} - 1656 q^{83} - 5064 q^{85} - 782 q^{86} + 1940 q^{87} - 4232 q^{88} + 1196 q^{89} - 8030 q^{90} - 4618 q^{92} + 698 q^{93} + 35 q^{94} - 1968 q^{95} + 7926 q^{96} - 3862 q^{97} - 5964 q^{99}+O(q^{100}) \) 36 * q - 5 * q^2 + 6 * q^3 + 117 * q^4 - 4 * q^5 + 12 * q^6 - 39 * q^8 + 236 * q^9 + 12 * q^10 - 140 * q^11 - 186 * q^12 + 72 * q^13 - 366 * q^15 - 15 * q^16 + 2 * q^17 - 212 * q^18 - 30 * q^19 + 334 * q^20 - 346 * q^22 - 314 * q^23 - 106 * q^24 + 570 * q^25 - 303 * q^26 + 204 * q^27 - 356 * q^29 - 357 * q^30 + 4 * q^31 - 532 * q^32 + 30 * q^33 + 364 * q^34 + 113 * q^36 - 1398 * q^37 + 264 * q^38 - 1348 * q^39 - 26 * q^40 - 1476 * q^41 - 1072 * q^43 - 1507 * q^44 + 1132 * q^45 - 1356 * q^46 + 622 * q^47 - 1724 * q^48 - 1426 * q^50 - 668 * q^51 + 877 * q^52 - 412 * q^53 + 1814 * q^54 - 1114 * q^55 - 4082 * q^57 - 1309 * q^58 + 620 * q^59 - 3724 * q^60 - 774 * q^61 - 1665 * q^62 - 3285 * q^64 - 1036 * q^65 + 1056 * q^66 - 2972 * q^67 + 1525 * q^68 - 3304 * q^69 - 3540 * q^71 - 821 * q^72 + 60 * q^73 - 2043 * q^74 - 450 * q^75 - 2171 * q^76 - 1136 * q^78 - 5190 * q^79 + 1564 * q^80 + 284 * q^81 + 205 * q^82 - 1656 * q^83 - 5064 * q^85 - 782 * q^86 + 1940 * q^87 - 4232 * q^88 + 1196 * q^89 - 8030 * q^90 - 4618 * q^92 + 698 * q^93 + 35 * q^94 - 1968 * q^95 + 7926 * q^96 - 3862 * q^97 - 5964 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	−4.67229	−1.65191	−0.825953	−	0.563739i	$-0.809362\pi$
$2$	−4.67229	−1.65191	−0.825953	+	0.563739i	$0.809362\pi$
$3$	4.57802	0.881040	0.440520	−	0.897743i	$-0.354794\pi$
$3$	4.57802	0.881040	0.440520	+	0.897743i	$0.354794\pi$
$4$	13.8303	1.72879
$5$	−8.79022	−0.786221	−0.393110	−	0.919491i	$-0.628601\pi$
$5$	−8.79022	−0.786221	−0.393110	+	0.919491i	$0.628601\pi$
$6$	−21.3898	−1.45539
$7$	0	0
$7$	0	0
$8$	−27.2411	−1.20390
$9$	−6.04177	−0.223769
$10$	41.0705	1.29876
$11$	−42.1310	−1.15482	−0.577408	−	0.816456i	$-0.695936\pi$
$11$	−42.1310	−1.15482	−0.577408	+	0.816456i	$0.695936\pi$
$12$	63.3155	1.52313
$13$	83.3095	1.77738	0.888688	−	0.458512i	$-0.151617\pi$
$13$	83.3095	1.77738	0.888688	+	0.458512i	$0.151617\pi$
$14$	0	0
$15$	−40.2418	−0.692692
$16$	16.6356	0.259931
$17$	119.501	1.70489	0.852447	−	0.522814i	$-0.175118\pi$
$17$	119.501	1.70489	0.852447	+	0.522814i	$0.175118\pi$
$18$	28.2289	0.369645
$19$	−85.2375	−1.02920	−0.514601	−	0.857430i	$-0.672060\pi$
$19$	−85.2375	−1.02920	−0.514601	+	0.857430i	$0.672060\pi$
$20$	−121.572	−1.35921
$21$	0	0
$22$	196.848	1.90765
$23$	34.2798	0.310775	0.155388	−	0.987854i	$-0.450337\pi$
$23$	34.2798	0.310775	0.155388	+	0.987854i	$0.450337\pi$
$24$	−124.710	−1.06068
$25$	−47.7321	−0.381857
$26$	−389.247	−2.93606
$27$	−151.266	−1.07819
$28$	0	0
$29$	127.196	0.814476	0.407238	−	0.913322i	$-0.366492\pi$
$29$	127.196	0.814476	0.407238	+	0.913322i	$0.366492\pi$
$30$	188.021	1.14426
$31$	−140.862	−0.816114	−0.408057	−	0.912956i	$-0.633794\pi$
$31$	−140.862	−0.816114	−0.408057	+	0.912956i	$0.633794\pi$
$32$	140.202	0.774515
$33$	−192.876	−1.01744
$34$	−558.343	−2.81632
$35$	0	0
$36$	−83.5597	−0.386850
$37$	−59.2646	−0.263326	−0.131663	−	0.991295i	$-0.542032\pi$
$37$	−59.2646	−0.263326	−0.131663	+	0.991295i	$0.542032\pi$
$38$	398.255	1.70014
$39$	381.392	1.56594
$40$	239.455	0.946528
$41$	−41.0000	−0.156174
$41$	−41.0000	−0.156174
$42$	0	0
$43$	79.8833	0.283304	0.141652	−	0.989916i	$-0.454759\pi$
$43$	79.8833	0.283304	0.141652	+	0.989916i	$0.454759\pi$
$44$	−582.686	−1.99644
$45$	53.1084	0.175932
$46$	−160.165	−0.513371
$47$	−555.709	−1.72465	−0.862324	−	0.506357i	$-0.830992\pi$
$47$	−555.709	−1.72465	−0.862324	+	0.506357i	$0.830992\pi$
$48$	76.1579	0.229009
$49$	0	0
$50$	223.018	0.630791
$51$	547.076	1.50208
$52$	1152.20	3.07272
$53$	355.007	0.920076	0.460038	−	0.887899i	$-0.347836\pi$
$53$	355.007	0.920076	0.460038	+	0.887899i	$0.347836\pi$
$54$	706.758	1.78107
$55$	370.340	0.907940
$56$	0	0
$57$	−390.219	−0.906767
$58$	−594.300	−1.34544
$59$	686.660	1.51518	0.757589	−	0.652732i	$-0.226377\pi$
$59$	686.660	1.51518	0.757589	+	0.652732i	$0.226377\pi$
$60$	−556.557	−1.19752
$61$	236.667	0.496756	0.248378	−	0.968663i	$-0.420102\pi$
$61$	236.667	0.496756	0.248378	+	0.968663i	$0.420102\pi$
$62$	658.148	1.34814
$63$	0	0
$64$	−788.151	−1.53936
$65$	−732.309	−1.39741
$66$	901.175	1.68071
$67$	772.754	1.40906	0.704529	−	0.709675i	$-0.251158\pi$
$67$	772.754	1.40906	0.704529	+	0.709675i	$0.251158\pi$
$68$	1652.74	2.94741
$69$	156.933	0.273805
$70$	0	0
$71$	153.968	0.257361	0.128681	−	0.991686i	$-0.458926\pi$
$71$	153.968	0.257361	0.128681	+	0.991686i	$0.458926\pi$
$72$	164.584	0.269395
$73$	−1150.97	−1.84535	−0.922674	−	0.385580i	$-0.874001\pi$
$73$	−1150.97	−1.84535	−0.922674	+	0.385580i	$0.874001\pi$
$74$	276.902	0.434989
$75$	−218.518	−0.336431
$76$	−1178.86	−1.77928
$77$	0	0
$78$	−1781.98	−2.58678
$79$	691.539	0.984864	0.492432	−	0.870351i	$-0.336108\pi$
$79$	691.539	0.984864	0.492432	+	0.870351i	$0.336108\pi$
$80$	−146.230	−0.204363
$81$	−529.369	−0.726158
$82$	191.564	0.257984
$83$	−926.864	−1.22574	−0.612871	−	0.790183i	$-0.709985\pi$
$83$	−926.864	−1.22574	−0.612871	+	0.790183i	$0.709985\pi$
$84$	0	0
$85$	−1050.44	−1.34042
$86$	−373.238	−0.467992
$87$	582.308	0.717585
$88$	1147.69	1.39028
$89$	751.374	0.894893	0.447447	−	0.894311i	$-0.352333\pi$
$89$	751.374	0.894893	0.447447	+	0.894311i	$0.352333\pi$
$90$	−248.138	−0.290623
$91$	0	0
$92$	474.101	0.537266
$93$	−644.868	−0.719029
$94$	2596.43	2.84896
$95$	749.256	0.809180
$96$	641.848	0.682379
$97$	−432.897	−0.453135	−0.226567	−	0.973996i	$-0.572750\pi$
$97$	−432.897	−0.453135	−0.226567	+	0.973996i	$0.572750\pi$
$98$	0	0
$99$	254.545	0.258412
$100$	−660.151	−0.660151
$101$	1204.22	1.18638	0.593189	−	0.805063i	$-0.297869\pi$
$101$	1204.22	1.18638	0.593189	+	0.805063i	$0.297869\pi$
$102$	−2556.10	−2.48129
$103$	298.418	0.285475	0.142738	−	0.989761i	$-0.454409\pi$
$103$	298.418	0.285475	0.142738	+	0.989761i	$0.454409\pi$
$104$	−2269.44	−2.13978
$105$	0	0
$106$	−1658.70	−1.51988
$107$	−171.445	−0.154899	−0.0774496	−	0.996996i	$-0.524678\pi$
$107$	−171.445	−0.154899	−0.0774496	+	0.996996i	$0.524678\pi$
$108$	−2092.06	−1.86397
$109$	−648.154	−0.569559	−0.284780	−	0.958593i	$-0.591920\pi$
$109$	−648.154	−0.569559	−0.284780	+	0.958593i	$0.591920\pi$
$110$	−1730.34	−1.49983
$111$	−271.314	−0.232000
$112$	0	0
$113$	1570.36	1.30732	0.653658	−	0.756790i	$-0.273233\pi$
$113$	1570.36	1.30732	0.653658	+	0.756790i	$0.273233\pi$
$114$	1823.22	1.49789
$115$	−301.327	−0.244338
$116$	1759.17	1.40806
$117$	−503.336	−0.397722
$118$	−3208.28	−2.50293
$119$	0	0
$120$	1096.23	0.833929
$121$	444.019	0.333598
$122$	−1105.78	−0.820594
$123$	−187.699	−0.137595
$124$	−1948.17	−1.41089
$125$	1518.35	1.08644
$126$	0	0
$127$	−1093.83	−0.764268	−0.382134	−	0.924107i	$-0.624811\pi$
$127$	−1093.83	−0.764268	−0.382134	+	0.924107i	$0.624811\pi$
$128$	2560.85	1.76836
$129$	365.707	0.249602
$130$	3421.56	2.30839
$131$	−2661.91	−1.77536	−0.887679	−	0.460462i	$-0.847684\pi$
$131$	−2661.91	−1.77536	−0.887679	+	0.460462i	$0.847684\pi$
$132$	−2667.54	−1.75894
$133$	0	0
$134$	−3610.53	−2.32763
$135$	1329.66	0.847695
$136$	−3255.33	−2.05252
$137$	−533.178	−0.332500	−0.166250	−	0.986084i	$-0.553166\pi$
$137$	−533.178	−0.332500	−0.166250	+	0.986084i	$0.553166\pi$
$138$	−733.239	−0.452300
$139$	−280.727	−0.171302	−0.0856510	−	0.996325i	$-0.527297\pi$
$139$	−280.727	−0.171302	−0.0856510	+	0.996325i	$0.527297\pi$
$140$	0	0
$141$	−2544.04	−1.51948
$142$	−719.385	−0.425137
$143$	−3509.91	−2.05254
$144$	−100.508	−0.0581645
$145$	−1118.08	−0.640358
$146$	5377.66	3.04834
$147$	0	0
$148$	−819.650	−0.455235
$149$	1705.51	0.937721	0.468860	−	0.883272i	$-0.344665\pi$
$149$	1705.51	0.937721	0.468860	+	0.883272i	$0.344665\pi$
$150$	1020.98	0.555752
$151$	−3421.70	−1.84407	−0.922034	−	0.387109i	$-0.873474\pi$
$151$	−3421.70	−1.84407	−0.922034	+	0.387109i	$0.873474\pi$
$152$	2321.96	1.23905
$153$	−721.996	−0.381503
$154$	0	0
$155$	1238.21	0.641646
$156$	5274.78	2.70718
$157$	−1919.08	−0.975536	−0.487768	−	0.872973i	$-0.662189\pi$
$157$	−1919.08	−0.975536	−0.487768	+	0.872973i	$0.662189\pi$
$158$	−3231.08	−1.62690
$159$	1625.23	0.810623
$160$	−1232.41	−0.608940
$161$	0	0
$162$	2473.37	1.19955
$163$	−2508.79	−1.20555	−0.602773	−	0.797913i	$-0.705937\pi$
$163$	−2508.79	−1.20555	−0.602773	+	0.797913i	$0.705937\pi$
$164$	−567.044	−0.269992
$165$	1695.42	0.799931
$166$	4330.58	2.02481
$167$	−773.040	−0.358202	−0.179101	−	0.983831i	$-0.557319\pi$
$167$	−773.040	−0.358202	−0.179101	+	0.983831i	$0.557319\pi$
$168$	0	0
$169$	4743.47	2.15907
$170$	4907.95	2.21425
$171$	514.985	0.230303
$172$	1104.81	0.489774
$173$	4313.11	1.89549	0.947745	−	0.319029i	$-0.103357\pi$
$173$	4313.11	1.89549	0.947745	+	0.319029i	$0.103357\pi$
$174$	−2720.71	−1.18538
$175$	0	0
$176$	−700.873	−0.300172
$177$	3143.54	1.33493
$178$	−3510.64	−1.47828
$179$	−1298.92	−0.542378	−0.271189	−	0.962526i	$-0.587417\pi$
$179$	−1298.92	−0.542378	−0.271189	+	0.962526i	$0.587417\pi$
$180$	734.508	0.304150
$181$	378.170	0.155299	0.0776496	−	0.996981i	$-0.475258\pi$
$181$	378.170	0.155299	0.0776496	+	0.996981i	$0.475258\pi$
$182$	0	0
$183$	1083.47	0.437662
$184$	−933.817	−0.374141
$185$	520.949	0.207032
$186$	3013.01	1.18777
$187$	−5034.68	−1.96884
$188$	−7685.64	−2.98156
$189$	0	0
$190$	−3500.75	−1.33669
$191$	−3361.69	−1.27353	−0.636763	−	0.771060i	$-0.719727\pi$
$191$	−3361.69	−1.27353	−0.636763	+	0.771060i	$0.719727\pi$
$192$	−3608.17	−1.35623
$193$	−1961.54	−0.731580	−0.365790	−	0.930697i	$-0.619201\pi$
$193$	−1961.54	−0.731580	−0.365790	+	0.930697i	$0.619201\pi$
$194$	2022.62	0.748536
$195$	−3352.52	−1.23117
$196$	0	0
$197$	2074.99	0.750443	0.375221	−	0.926935i	$-0.377567\pi$
$197$	2074.99	0.750443	0.375221	+	0.926935i	$0.377567\pi$
$198$	−1189.31	−0.426872
$199$	4333.80	1.54379	0.771896	−	0.635748i	$-0.219308\pi$
$199$	4333.80	1.54379	0.771896	+	0.635748i	$0.219308\pi$
$200$	1300.27	0.459716
$201$	3537.68	1.24144
$202$	−5626.46	−1.95978
$203$	0	0
$204$	7566.25	2.59678
$205$	360.399	0.122787
$206$	−1394.30	−0.471578
$207$	−207.110	−0.0695418
$208$	1385.90	0.461995
$209$	3591.14	1.18854
$210$	0	0
$211$	−383.533	−0.125135	−0.0625675	−	0.998041i	$-0.519929\pi$
$211$	−383.533	−0.125135	−0.0625675	+	0.998041i	$0.519929\pi$
$212$	4909.87	1.59062
$213$	704.869	0.226746
$214$	801.041	0.255879
$215$	−702.191	−0.222740
$216$	4120.64	1.29803
$217$	0	0
$218$	3028.37	0.940858
$219$	−5269.14	−1.62583
$220$	5121.93	1.56964
$221$	9955.55	3.03024
$222$	1267.66	0.383243
$223$	2641.01	0.793073	0.396537	−	0.918019i	$-0.370212\pi$
$223$	2641.01	0.793073	0.396537	+	0.918019i	$0.370212\pi$
$224$	0	0
$225$	288.386	0.0854477
$226$	−7337.17	−2.15956
$227$	−4559.88	−1.33326	−0.666629	−	0.745390i	$-0.732264\pi$
$227$	−4559.88	−1.33326	−0.666629	+	0.745390i	$0.732264\pi$
$228$	−5396.86	−1.56761
$229$	453.898	0.130980	0.0654901	−	0.997853i	$-0.479139\pi$
$229$	453.898	0.130980	0.0654901	+	0.997853i	$0.479139\pi$
$230$	1407.89	0.403623
$231$	0	0
$232$	−3464.97	−0.980544
$233$	−1372.10	−0.385791	−0.192896	−	0.981219i	$-0.561788\pi$
$233$	−1372.10	−0.385791	−0.192896	+	0.981219i	$0.561788\pi$
$234$	2351.74	0.656999
$235$	4884.80	1.35595
$236$	9496.74	2.61943
$237$	3165.88	0.867704
$238$	0	0
$239$	5552.54	1.50278	0.751389	−	0.659859i	$-0.229384\pi$
$239$	5552.54	1.50278	0.751389	+	0.659859i	$0.229384\pi$
$240$	−669.445	−0.180052
$241$	1840.90	0.492046	0.246023	−	0.969264i	$-0.420876\pi$
$241$	1840.90	0.492046	0.246023	+	0.969264i	$0.420876\pi$
$242$	−2074.59	−0.551073
$243$	1660.71	0.438415
$244$	3273.19	0.858788
$245$	0	0
$246$	876.984	0.227294
$247$	−7101.09	−1.82928
$248$	3837.23	0.982517
$249$	−4243.20	−1.07993
$250$	−7094.19	−1.79470
$251$	−5253.89	−1.32121	−0.660603	−	0.750735i	$-0.729699\pi$
$251$	−5253.89	−1.32121	−0.660603	+	0.750735i	$0.729699\pi$
$252$	0	0
$253$	−1444.24	−0.358888
$254$	5110.71	1.26250
$255$	−4808.92	−1.18097
$256$	−5659.86	−1.38180
$257$	3017.69	0.732444	0.366222	−	0.930528i	$-0.380651\pi$
$257$	3017.69	0.732444	0.366222	+	0.930528i	$0.380651\pi$
$258$	−1708.69	−0.412320
$259$	0	0
$260$	−10128.1	−2.41583
$261$	−768.491	−0.182254
$262$	12437.2	2.93273
$263$	5033.85	1.18023	0.590115	−	0.807319i	$-0.299082\pi$
$263$	5033.85	1.18023	0.590115	+	0.807319i	$0.299082\pi$
$264$	5254.16	1.22489
$265$	−3120.59	−0.723383
$266$	0	0
$267$	3439.80	0.788437
$268$	10687.4	2.43597
$269$	−4352.24	−0.986471	−0.493235	−	0.869896i	$-0.664186\pi$
$269$	−4352.24	−0.986471	−0.493235	+	0.869896i	$0.664186\pi$
$270$	−6212.56	−1.40031
$271$	−3291.73	−0.737854	−0.368927	−	0.929458i	$-0.620275\pi$
$271$	−3291.73	−0.737854	−0.368927	+	0.929458i	$0.620275\pi$
$272$	1987.96	0.443154
$273$	0	0
$274$	2491.16	0.549258
$275$	2011.00	0.440974
$276$	2170.44	0.473352
$277$	−7901.49	−1.71392	−0.856958	−	0.515387i	$-0.827648\pi$
$277$	−7901.49	−1.71392	−0.856958	+	0.515387i	$0.827648\pi$
$278$	1311.64	0.282975
$279$	851.055	0.182621
$280$	0	0
$281$	−5269.92	−1.11878	−0.559390	−	0.828905i	$-0.688964\pi$
$281$	−5269.92	−1.11878	−0.559390	+	0.828905i	$0.688964\pi$
$282$	11886.5	2.51004
$283$	−2980.39	−0.626029	−0.313014	−	0.949748i	$-0.601339\pi$
$283$	−2980.39	−0.626029	−0.313014	+	0.949748i	$0.601339\pi$
$284$	2129.43	0.444925
$285$	3430.11	0.712919
$286$	16399.3	3.39061
$287$	0	0
$288$	−847.069	−0.173313
$289$	9367.43	1.90666
$290$	5224.02	1.05781
$291$	−1981.81	−0.399230
$292$	−15918.3	−3.19022
$293$	1480.79	0.295252	0.147626	−	0.989043i	$-0.452837\pi$
$293$	1480.79	0.295252	0.147626	+	0.989043i	$0.452837\pi$
$294$	0	0
$295$	−6035.89	−1.19126
$296$	1614.43	0.317017
$297$	6372.97	1.24511
$298$	−7968.62	−1.54903
$299$	2855.83	0.552364
$300$	−3022.18	−0.581619
$301$	0	0
$302$	15987.2	3.04623
$303$	5512.93	1.04525
$304$	−1417.97	−0.267521
$305$	−2080.35	−0.390560
$306$	3373.38	0.630206
$307$	−5858.84	−1.08919	−0.544596	−	0.838699i	$-0.683317\pi$
$307$	−5858.84	−1.08919	−0.544596	+	0.838699i	$0.683317\pi$
$308$	0	0
$309$	1366.16	0.251515
$310$	−5785.27	−1.05994
$311$	5308.21	0.967848	0.483924	−	0.875110i	$-0.339211\pi$
$311$	5308.21	0.967848	0.483924	+	0.875110i	$0.339211\pi$
$312$	−10389.5	−1.88523
$313$	2974.07	0.537074	0.268537	−	0.963269i	$-0.413460\pi$
$313$	2974.07	0.537074	0.268537	+	0.963269i	$0.413460\pi$
$314$	8966.50	1.61149
$315$	0	0
$316$	9564.22	1.70263
$317$	−887.400	−0.157228	−0.0786141	−	0.996905i	$-0.525049\pi$
$317$	−887.400	−0.157228	−0.0786141	+	0.996905i	$0.525049\pi$
$318$	−7593.55	−1.33907
$319$	−5358.91	−0.940569
$320$	6928.02	1.21027
$321$	−784.878	−0.136472
$322$	0	0
$323$	−10185.9	−1.75468
$324$	−7321.36	−1.25538
$325$	−3976.54	−0.678703
$326$	11721.8	1.99145
$327$	−2967.26	−0.501804
$328$	1116.88	0.188017
$329$	0	0
$330$	−7921.52	−1.32141
$331$	−3674.23	−0.610133	−0.305066	−	0.952331i	$-0.598679\pi$
$331$	−3674.23	−0.610133	−0.305066	+	0.952331i	$0.598679\pi$
$332$	−12818.8	−2.11905
$333$	358.063	0.0589241
$334$	3611.87	0.591715
$335$	−6792.67	−1.10783
$336$	0	0
$337$	−3812.84	−0.616316	−0.308158	−	0.951335i	$-0.599713\pi$
$337$	−3812.84	−0.616316	−0.308158	+	0.951335i	$0.599713\pi$
$338$	−22162.9	−3.56658
$339$	7189.12	1.15180
$340$	−14527.9	−2.31731
$341$	5934.65	0.942461
$342$	−2406.16	−0.380440
$343$	0	0
$344$	−2176.11	−0.341069
$345$	−1379.48	−0.215271
$346$	−20152.1	−3.13117
$347$	−12635.9	−1.95484	−0.977418	−	0.211316i	$-0.932225\pi$
$347$	−12635.9	−1.95484	−0.977418	+	0.211316i	$0.932225\pi$
$348$	8053.51	1.24056
$349$	−6725.07	−1.03147	−0.515737	−	0.856747i	$-0.672482\pi$
$349$	−6725.07	−1.03147	−0.515737	+	0.856747i	$0.672482\pi$
$350$	0	0
$351$	−12601.9	−1.91635
$352$	−5906.86	−0.894422
$353$	2076.20	0.313046	0.156523	−	0.987674i	$-0.449972\pi$
$353$	2076.20	0.313046	0.156523	+	0.987674i	$0.449972\pi$
$354$	−14687.5	−2.20518
$355$	−1353.41	−0.202343
$356$	10391.8	1.54708
$357$	0	0
$358$	6068.93	0.895958
$359$	−1959.02	−0.288004	−0.144002	−	0.989577i	$-0.545997\pi$
$359$	−1959.02	−0.288004	−0.144002	+	0.989577i	$0.545997\pi$
$360$	−1446.73	−0.211804
$361$	406.432	0.0592553
$362$	−1766.92	−0.256540
$363$	2032.73	0.293913
$364$	0	0
$365$	10117.2	1.45085
$366$	−5062.27	−0.722976
$367$	−1289.63	−0.183429	−0.0917143	−	0.995785i	$-0.529235\pi$
$367$	−1289.63	−0.183429	−0.0917143	+	0.995785i	$0.529235\pi$
$368$	570.264	0.0807800
$369$	247.712	0.0349469
$370$	−2434.03	−0.341997
$371$	0	0
$372$	−8918.75	−1.24305
$373$	−2762.27	−0.383445	−0.191722	−	0.981449i	$-0.561407\pi$
$373$	−2762.27	−0.383445	−0.191722	+	0.981449i	$0.561407\pi$
$374$	23523.5	3.25233
$375$	6951.04	0.957201
$376$	15138.1	2.07630
$377$	10596.7	1.44763
$378$	0	0
$379$	−5567.32	−0.754549	−0.377275	−	0.926101i	$-0.623139\pi$
$379$	−5567.32	−0.754549	−0.377275	+	0.926101i	$0.623139\pi$
$380$	10362.5	1.39890
$381$	−5007.59	−0.673350
$382$	15706.8	2.10374
$383$	−6255.76	−0.834606	−0.417303	−	0.908767i	$-0.637025\pi$
$383$	−6255.76	−0.834606	−0.417303	+	0.908767i	$0.637025\pi$
$384$	11723.6	1.55799
$385$	0	0
$386$	9164.91	1.20850
$387$	−482.636	−0.0633948
$388$	−5987.12	−0.783376
$389$	−5651.60	−0.736626	−0.368313	−	0.929702i	$-0.620064\pi$
$389$	−5651.60	−0.736626	−0.368313	+	0.929702i	$0.620064\pi$
$390$	15664.0	2.03378
$391$	4096.46	0.529838
$392$	0	0
$393$	−12186.3	−1.56416
$394$	−9694.99	−1.23966
$395$	−6078.78	−0.774321
$396$	3520.45	0.446741
$397$	−6939.97	−0.877348	−0.438674	−	0.898646i	$-0.644552\pi$
$397$	−6939.97	−0.877348	−0.438674	+	0.898646i	$0.644552\pi$
$398$	−20248.8	−2.55020
$399$	0	0
$400$	−794.051	−0.0992563
$401$	6266.85	0.780428	0.390214	−	0.920724i	$-0.372401\pi$
$401$	6266.85	0.780428	0.390214	+	0.920724i	$0.372401\pi$
$402$	−16529.1	−2.05074
$403$	−11735.1	−1.45054
$404$	16654.7	2.05100
$405$	4653.27	0.570921
$406$	0	0
$407$	2496.88	0.304092
$408$	−14902.9	−1.80835
$409$	−7891.58	−0.954067	−0.477034	−	0.878885i	$-0.658288\pi$
$409$	−7891.58	−0.954067	−0.477034	+	0.878885i	$0.658288\pi$
$410$	−1683.89	−0.202833
$411$	−2440.90	−0.292945
$412$	4127.22	0.493528
$413$	0	0
$414$	967.680	0.114877
$415$	8147.34	0.963704
$416$	11680.2	1.37661
$417$	−1285.17	−0.150924
$418$	−16778.9	−1.96335
$419$	−3864.91	−0.450628	−0.225314	−	0.974286i	$-0.572341\pi$
$419$	−3864.91	−0.450628	−0.225314	+	0.974286i	$0.572341\pi$
$420$	0	0
$421$	−10936.4	−1.26605	−0.633025	−	0.774131i	$-0.718187\pi$
$421$	−10936.4	−1.26605	−0.633025	+	0.774131i	$0.718187\pi$
$422$	1791.98	0.206711
$423$	3357.46	0.385923
$424$	−9670.78	−1.10768
$425$	−5704.02	−0.651025
$426$	−3293.36	−0.374562
$427$	0	0
$428$	−2371.14	−0.267788
$429$	−16068.4	−1.80837
$430$	3280.85	0.367945
$431$	2796.73	0.312561	0.156281	−	0.987713i	$-0.450050\pi$
$431$	2796.73	0.312561	0.156281	+	0.987713i	$0.450050\pi$
$432$	−2516.39	−0.280255
$433$	−7251.19	−0.804780	−0.402390	−	0.915468i	$-0.631820\pi$
$433$	−7251.19	−0.804780	−0.402390	+	0.915468i	$0.631820\pi$
$434$	0	0
$435$	−5118.61	−0.564181
$436$	−8964.20	−0.984649
$437$	−2921.92	−0.319850
$438$	24619.0	2.68571
$439$	6759.54	0.734886	0.367443	−	0.930046i	$-0.380233\pi$
$439$	6759.54	0.734886	0.367443	+	0.930046i	$0.380233\pi$
$440$	−10088.5	−1.09307
$441$	0	0
$442$	−46515.3	−5.00567
$443$	−17031.6	−1.82663	−0.913313	−	0.407258i	$-0.866485\pi$
$443$	−17031.6	−1.82663	−0.913313	+	0.407258i	$0.866485\pi$
$444$	−3752.37	−0.401080
$445$	−6604.74	−0.703584
$446$	−12339.6	−1.31008
$447$	7807.83	0.826169
$448$	0	0
$449$	−13802.5	−1.45074	−0.725369	−	0.688360i	$-0.758331\pi$
$449$	−13802.5	−1.45074	−0.725369	+	0.688360i	$0.758331\pi$
$450$	−1347.42	−0.141152
$451$	1727.37	0.180352
$452$	21718.6	2.26008
$453$	−15664.6	−1.62470
$454$	21305.1	2.20242
$455$	0	0
$456$	10630.0	1.09165
$457$	10648.4	1.08996	0.544981	−	0.838449i	$-0.316537\pi$
$457$	10648.4	1.08996	0.544981	+	0.838449i	$0.316537\pi$
$458$	−2120.75	−0.216367
$459$	−18076.4	−1.83820
$460$	−4167.45	−0.422409
$461$	−115.842	−0.0117034	−0.00585172	−	0.999983i	$-0.501863\pi$
$461$	−115.842	−0.0117034	−0.00585172	+	0.999983i	$0.501863\pi$
$462$	0	0
$463$	2528.09	0.253759	0.126879	−	0.991918i	$-0.459504\pi$
$463$	2528.09	0.253759	0.126879	+	0.991918i	$0.459504\pi$
$464$	2115.99	0.211707
$465$	5668.53	0.565316
$466$	6410.87	0.637291
$467$	−10124.2	−1.00320	−0.501599	−	0.865100i	$-0.667255\pi$
$467$	−10124.2	−1.00320	−0.501599	+	0.865100i	$0.667255\pi$
$468$	−6961.31	−0.687579
$469$	0	0
$470$	−22823.2	−2.23991
$471$	−8785.58	−0.859486
$472$	−18705.3	−1.82412
$473$	−3365.56	−0.327164
$474$	−14791.9	−1.43337
$475$	4068.56	0.393007
$476$	0	0
$477$	−2144.87	−0.205884
$478$	−25943.1	−2.48245
$479$	−9296.88	−0.886817	−0.443409	−	0.896320i	$-0.646231\pi$
$479$	−9296.88	−0.886817	−0.443409	+	0.896320i	$0.646231\pi$
$480$	−5641.98	−0.536500
$481$	−4937.31	−0.468029
$482$	−8601.24	−0.812813
$483$	0	0
$484$	6140.94	0.576722
$485$	3805.26	0.356264
$486$	−7759.34	−0.724220
$487$	8041.25	0.748221	0.374111	−	0.927384i	$-0.377948\pi$
$487$	8041.25	0.748221	0.374111	+	0.927384i	$0.377948\pi$
$488$	−6447.06	−0.598043
$489$	−11485.3	−1.06213
$490$	0	0
$491$	−5080.22	−0.466940	−0.233470	−	0.972364i	$-0.575008\pi$
$491$	−5080.22	−0.466940	−0.233470	+	0.972364i	$0.575008\pi$
$492$	−2595.94	−0.237874
$493$	15200.1	1.38859
$494$	33178.4	3.02180
$495$	−2237.51	−0.203169
$496$	−2343.32	−0.212133
$497$	0	0
$498$	19825.5	1.78394
$499$	8831.95	0.792330	0.396165	−	0.918179i	$-0.370341\pi$
$499$	8831.95	0.792330	0.396165	+	0.918179i	$0.370341\pi$
$500$	20999.3	1.87824
$501$	−3538.99	−0.315590
$502$	24547.7	2.18251
$503$	−4336.89	−0.384438	−0.192219	−	0.981352i	$-0.561568\pi$
$503$	−4336.89	−0.384438	−0.192219	+	0.981352i	$0.561568\pi$
$504$	0	0
$505$	−10585.3	−0.932755
$506$	6747.92	0.592849
$507$	21715.7	1.90222
$508$	−15128.1	−1.32126
$509$	−3231.76	−0.281425	−0.140712	−	0.990051i	$-0.544939\pi$
$509$	−3231.76	−0.281425	−0.140712	+	0.990051i	$0.544939\pi$
$510$	22468.7	1.95084
$511$	0	0
$512$	5957.71	0.514250
$513$	12893.5	1.10967
$514$	−14099.5	−1.20993
$515$	−2623.16	−0.224447
$516$	5057.85	0.431511
$517$	23412.5	1.99165
$518$	0	0
$519$	19745.5	1.67000
$520$	19948.9	1.68234
$521$	−1796.22	−0.151044	−0.0755218	−	0.997144i	$-0.524062\pi$
$521$	−1796.22	−0.151044	−0.0755218	+	0.997144i	$0.524062\pi$
$522$	3590.62	0.301067
$523$	10359.5	0.866133	0.433066	−	0.901362i	$-0.357432\pi$
$523$	10359.5	0.866133	0.433066	+	0.901362i	$0.357432\pi$
$524$	−36815.1	−3.06923
$525$	0	0
$526$	−23519.6	−1.94963
$527$	−16833.1	−1.39139
$528$	−3208.61	−0.264464
$529$	−10991.9	−0.903419
$530$	14580.3	1.19496
$531$	−4148.64	−0.339050
$532$	0	0
$533$	−3415.69	−0.277580
$534$	−16071.8	−1.30242
$535$	1507.04	0.121785
$536$	−21050.6	−1.69636
$537$	−5946.47	−0.477857
$538$	20334.9	1.62956
$539$	0	0
$540$	18389.6	1.46549
$541$	−8456.25	−0.672020	−0.336010	−	0.941858i	$-0.609078\pi$
$541$	−8456.25	−0.672020	−0.336010	+	0.941858i	$0.609078\pi$
$542$	15379.9	1.21887
$543$	1731.27	0.136825
$544$	16754.3	1.32047
$545$	5697.42	0.447799
$546$	0	0
$547$	4114.92	0.321648	0.160824	−	0.986983i	$-0.448585\pi$
$547$	4114.92	0.321648	0.160824	+	0.986983i	$0.448585\pi$
$548$	−7374.03	−0.574823
$549$	−1429.89	−0.111159
$550$	−9395.98	−0.728447
$551$	−10841.9	−0.838259
$552$	−4275.03	−0.329633
$553$	0	0
$554$	36918.1	2.83123
$555$	2384.91	0.182403
$556$	−3882.55	−0.296146
$557$	6472.32	0.492354	0.246177	−	0.969225i	$-0.420826\pi$
$557$	6472.32	0.492354	0.246177	+	0.969225i	$0.420826\pi$
$558$	−3976.38	−0.301673
$559$	6655.04	0.503539
$560$	0	0
$561$	−23048.9	−1.73462
$562$	24622.6	1.84812
$563$	−22085.2	−1.65325	−0.826627	−	0.562750i	$-0.809743\pi$
$563$	−22085.2	−1.65325	−0.826627	+	0.562750i	$0.809743\pi$
$564$	−35185.0	−2.62687
$565$	−13803.8	−1.02784
$566$	13925.3	1.03414
$567$	0	0
$568$	−4194.26	−0.309837
$569$	20469.4	1.50812	0.754060	−	0.656806i	$-0.228093\pi$
$569$	20469.4	1.50812	0.754060	+	0.656806i	$0.228093\pi$
$570$	−16026.5	−1.17768
$571$	−14696.7	−1.07712	−0.538561	−	0.842586i	$-0.681032\pi$
$571$	−14696.7	−1.07712	−0.538561	+	0.842586i	$0.681032\pi$
$572$	−48543.3	−3.54842
$573$	−15389.9	−1.12203
$574$	0	0
$575$	−1636.25	−0.118672
$576$	4761.82	0.344460
$577$	726.893	0.0524453	0.0262227	−	0.999656i	$-0.491652\pi$
$577$	726.893	0.0524453	0.0262227	+	0.999656i	$0.491652\pi$
$578$	−43767.4	−3.14963
$579$	−8979.98	−0.644551
$580$	−15463.5	−1.10705
$581$	0	0
$582$	9259.60	0.659490
$583$	−14956.8	−1.06252
$584$	31353.6	2.22161
$585$	4424.44	0.312697
$586$	−6918.70	−0.487729
$587$	−11919.0	−0.838074	−0.419037	−	0.907969i	$-0.637632\pi$
$587$	−11919.0	−0.838074	−0.419037	+	0.907969i	$0.637632\pi$
$588$	0	0
$589$	12006.7	0.839946
$590$	28201.5	1.96786
$591$	9499.36	0.661170
$592$	−985.901	−0.0684464
$593$	−27506.9	−1.90485	−0.952424	−	0.304777i	$-0.901418\pi$
$593$	−27506.9	−1.90485	−0.952424	+	0.304777i	$0.901418\pi$
$594$	−29776.4	−2.05680
$595$	0	0
$596$	23587.7	1.62112
$597$	19840.2	1.36014
$598$	−13343.3	−0.912454
$599$	949.174	0.0647449	0.0323724	−	0.999476i	$-0.489694\pi$
$599$	949.174	0.0647449	0.0323724	+	0.999476i	$0.489694\pi$
$600$	5952.67	0.405028
$601$	19058.3	1.29351	0.646757	−	0.762696i	$-0.276125\pi$
$601$	19058.3	1.29351	0.646757	+	0.762696i	$0.276125\pi$
$602$	0	0
$603$	−4668.80	−0.315304
$604$	−47323.3	−3.18801
$605$	−3903.02	−0.262282
$606$	−25758.0	−1.72665
$607$	−15048.0	−1.00623	−0.503113	−	0.864221i	$-0.667812\pi$
$607$	−15048.0	−1.00623	−0.503113	+	0.864221i	$0.667812\pi$
$608$	−11950.5	−0.797132
$609$	0	0
$610$	9720.03	0.645168
$611$	−46295.8	−3.06535
$612$	−9985.44	−0.659539
$613$	5161.19	0.340063	0.170031	−	0.985439i	$-0.445613\pi$
$613$	5161.19	0.340063	0.170031	+	0.985439i	$0.445613\pi$
$614$	27374.2	1.79924
$615$	1649.91	0.108180
$616$	0	0
$617$	16078.6	1.04911	0.524553	−	0.851378i	$-0.324232\pi$
$617$	16078.6	1.04911	0.524553	+	0.851378i	$0.324232\pi$
$618$	−6383.11	−0.415479
$619$	4486.17	0.291300	0.145650	−	0.989336i	$-0.453473\pi$
$619$	4486.17	0.291300	0.145650	+	0.989336i	$0.453473\pi$
$620$	17124.8	1.10927
$621$	−5185.35	−0.335074
$622$	−24801.5	−1.59879
$623$	0	0
$624$	6344.68	0.407036
$625$	−7380.14	−0.472329
$626$	−13895.7	−0.887196
$627$	16440.3	1.04715
$628$	−26541.5	−1.68650
$629$	−7082.17	−0.448942
$630$	0	0
$631$	−22643.1	−1.42854	−0.714268	−	0.699873i	$-0.753240\pi$
$631$	−22643.1	−1.42854	−0.714268	+	0.699873i	$0.753240\pi$
$632$	−18838.3	−1.18567
$633$	−1755.82	−0.110249
$634$	4146.19	0.259726
$635$	9615.03	0.600883
$636$	22477.5	1.40140
$637$	0	0
$638$	25038.4	1.55373
$639$	−930.240	−0.0575895
$640$	−22510.5	−1.39032
$641$	2410.02	0.148503	0.0742514	−	0.997240i	$-0.476343\pi$
$641$	2410.02	0.148503	0.0742514	+	0.997240i	$0.476343\pi$
$642$	3667.18	0.225439
$643$	21231.9	1.30218	0.651092	−	0.758999i	$-0.274311\pi$
$643$	21231.9	1.30218	0.651092	+	0.758999i	$0.274311\pi$
$644$	0	0
$645$	−3214.64	−0.196243
$646$	47591.7	2.89856
$647$	16581.8	1.00757	0.503786	−	0.863828i	$-0.331940\pi$
$647$	16581.8	1.00757	0.503786	+	0.863828i	$0.331940\pi$
$648$	14420.6	0.874219
$649$	−28929.7	−1.74975
$650$	18579.6	1.12115
$651$	0	0
$652$	−34697.5	−2.08414
$653$	−253.184	−0.0151729	−0.00758643	−	0.999971i	$-0.502415\pi$
$653$	−253.184	−0.0151729	−0.00758643	+	0.999971i	$0.502415\pi$
$654$	13863.9	0.828933
$655$	23398.8	1.39582
$656$	−682.058	−0.0405944
$657$	6953.87	0.412932
$658$	0	0
$659$	−13070.4	−0.772613	−0.386307	−	0.922370i	$-0.626249\pi$
$659$	−13070.4	−0.772613	−0.386307	+	0.922370i	$0.626249\pi$
$660$	23448.3	1.38291
$661$	−979.244	−0.0576221	−0.0288110	−	0.999585i	$-0.509172\pi$
$661$	−979.244	−0.0576221	−0.0288110	+	0.999585i	$0.509172\pi$
$662$	17167.1	1.00788
$663$	45576.7	2.66976
$664$	25248.8	1.47567
$665$	0	0
$666$	−1672.98	−0.0973371
$667$	4360.27	0.253119
$668$	−10691.4	−0.619256
$669$	12090.6	0.698729
$670$	31737.4	1.83003
$671$	−9971.02	−0.573661
$672$	0	0
$673$	−12752.1	−0.730397	−0.365198	−	0.930930i	$-0.618999\pi$
$673$	−12752.1	−0.730397	−0.365198	+	0.930930i	$0.618999\pi$
$674$	17814.7	1.01810
$675$	7220.23	0.411714
$676$	65603.8	3.73258
$677$	19852.6	1.12703	0.563515	−	0.826106i	$-0.309449\pi$
$677$	19852.6	1.12703	0.563515	+	0.826106i	$0.309449\pi$
$678$	−33589.7	−1.90266
$679$	0	0
$680$	28615.0	1.61373
$681$	−20875.2	−1.17465
$682$	−27728.4	−1.55686
$683$	−109.524	−0.00613589	−0.00306794	−	0.999995i	$-0.500977\pi$
$683$	−109.524	−0.00613589	−0.00306794	+	0.999995i	$0.500977\pi$
$684$	7122.42	0.398147
$685$	4686.75	0.261418
$686$	0	0
$687$	2077.95	0.115399
$688$	1328.90	0.0736395
$689$	29575.5	1.63532
$690$	6445.33	0.355608
$691$	11393.2	0.627234	0.313617	−	0.949550i	$-0.398459\pi$
$691$	11393.2	0.627234	0.313617	+	0.949550i	$0.398459\pi$
$692$	59651.8	3.27691
$693$	0	0
$694$	59038.4	3.22920
$695$	2467.65	0.134681
$696$	−15862.7	−0.863899
$697$	−4899.53	−0.266260
$698$	31421.5	1.70390
$699$	−6281.51	−0.339898
$700$	0	0
$701$	−10516.7	−0.566634	−0.283317	−	0.959026i	$-0.591435\pi$
$701$	−10516.7	−0.566634	−0.283317	+	0.959026i	$0.591435\pi$
$702$	58879.7	3.16563
$703$	5051.57	0.271015
$704$	33205.6	1.77767
$705$	22362.7	1.19465
$706$	−9700.63	−0.517122
$707$	0	0
$708$	43476.2	2.30782
$709$	−6906.15	−0.365819	−0.182910	−	0.983130i	$-0.558552\pi$
$709$	−6906.15	−0.365819	−0.182910	+	0.983130i	$0.558552\pi$
$710$	6323.55	0.334251
$711$	−4178.12	−0.220382
$712$	−20468.2	−1.07736
$713$	−4828.71	−0.253628
$714$	0	0
$715$	30852.9	1.61375
$716$	−17964.5	−0.937660
$717$	25419.6	1.32401
$718$	9153.14	0.475755
$719$	6819.71	0.353731	0.176865	−	0.984235i	$-0.443404\pi$
$719$	6819.71	0.353731	0.176865	+	0.984235i	$0.443404\pi$
$720$	883.489	0.0457301
$721$	0	0
$722$	−1898.97	−0.0978842
$723$	8427.68	0.433512
$724$	5230.22	0.268480
$725$	−6071.35	−0.311013
$726$	−9497.50	−0.485517
$727$	−8740.29	−0.445886	−0.222943	−	0.974831i	$-0.571566\pi$
$727$	−8740.29	−0.445886	−0.222943	+	0.974831i	$0.571566\pi$
$728$	0	0
$729$	21895.7	1.11242
$730$	−47270.8	−2.39667
$731$	9546.11	0.483004
$732$	14984.7	0.756626
$733$	9568.62	0.482162	0.241081	−	0.970505i	$-0.422498\pi$
$733$	9568.62	0.482162	0.241081	+	0.970505i	$0.422498\pi$
$734$	6025.55	0.303007
$735$	0	0
$736$	4806.10	0.240700
$737$	−32556.9	−1.62720
$738$	−1157.39	−0.0577289
$739$	−2498.07	−0.124348	−0.0621738	−	0.998065i	$-0.519803\pi$
$739$	−2498.07	−0.124348	−0.0621738	+	0.998065i	$0.519803\pi$
$740$	7204.90	0.357915
$741$	−32508.9	−1.61167
$742$	0	0
$743$	12492.2	0.616817	0.308408	−	0.951254i	$-0.400204\pi$
$743$	12492.2	0.616817	0.308408	+	0.951254i	$0.400204\pi$
$744$	17566.9	0.865637
$745$	−14991.8	−0.737256
$746$	12906.1	0.633415
$747$	5599.90	0.274283
$748$	−69631.4	−3.40371
$749$	0	0
$750$	−32477.3	−1.58121
$751$	−22541.4	−1.09527	−0.547634	−	0.836718i	$-0.684471\pi$
$751$	−22541.4	−1.09527	−0.547634	+	0.836718i	$0.684471\pi$
$752$	−9244.53	−0.448289
$753$	−24052.4	−1.16404
$754$	−49510.8	−2.39135
$755$	30077.5	1.44984
$756$	0	0
$757$	−10189.6	−0.489228	−0.244614	−	0.969621i	$-0.578661\pi$
$757$	−10189.6	−0.489228	−0.244614	+	0.969621i	$0.578661\pi$
$758$	26012.2	1.24644
$759$	−6611.75	−0.316194
$760$	−20410.5	−0.974168
$761$	−33068.7	−1.57522	−0.787609	−	0.616176i	$-0.788681\pi$
$761$	−33068.7	−1.57522	−0.787609	+	0.616176i	$0.788681\pi$
$762$	23396.9	1.11231
$763$	0	0
$764$	−46493.3	−2.20166
$765$	6346.50	0.299945
$766$	29228.7	1.37869
$767$	57205.3	2.69304
$768$	−25910.9	−1.21742
$769$	−14017.9	−0.657345	−0.328673	−	0.944444i	$-0.606601\pi$
$769$	−14017.9	−0.657345	−0.328673	+	0.944444i	$0.606601\pi$
$770$	0	0
$771$	13815.0	0.645312
$772$	−27128.8	−1.26475
$773$	−39494.0	−1.83765	−0.918823	−	0.394670i	$-0.870859\pi$
$773$	−39494.0	−1.83765	−0.918823	+	0.394670i	$0.870859\pi$
$774$	2255.02	0.104722
$775$	6723.63	0.311639
$776$	11792.6	0.545527
$777$	0	0
$778$	26405.9	1.21684
$779$	3494.74	0.160734
$780$	−46366.5	−2.12844
$781$	−6486.83	−0.297205
$782$	−19139.9	−0.875243
$783$	−19240.5	−0.878159
$784$	0	0
$785$	16869.1	0.766987
$786$	56937.8	2.58385
$787$	19488.5	0.882706	0.441353	−	0.897333i	$-0.354499\pi$
$787$	19488.5	0.882706	0.441353	+	0.897333i	$0.354499\pi$
$788$	28697.9	1.29736
$789$	23045.1	1.03983
$790$	28401.9	1.27910
$791$	0	0
$792$	−6934.09	−0.311101
$793$	19716.6	0.882923
$794$	32425.6	1.44930
$795$	−14286.1	−0.637329
$796$	59937.9	2.66890
$797$	−15683.6	−0.697040	−0.348520	−	0.937301i	$-0.613316\pi$
$797$	−15683.6	−0.697040	−0.348520	+	0.937301i	$0.613316\pi$
$798$	0	0
$799$	−66407.6	−2.94034
$800$	−6692.15	−0.295754
$801$	−4539.63	−0.200249
$802$	−29280.6	−1.28919
$803$	48491.3	2.13104
$804$	48927.3	2.14619
$805$	0	0
$806$	54830.0	2.39616
$807$	−19924.6	−0.869120
$808$	−32804.2	−1.42828
$809$	27845.5	1.21013	0.605065	−	0.796176i	$-0.293147\pi$
$809$	27845.5	1.21013	0.605065	+	0.796176i	$0.293147\pi$
$810$	−21741.5	−0.943107
$811$	−20777.0	−0.899605	−0.449802	−	0.893128i	$-0.648506\pi$
$811$	−20777.0	−0.899605	−0.449802	+	0.893128i	$0.648506\pi$
$812$	0	0
$813$	−15069.6	−0.650079
$814$	−11666.1	−0.502332
$815$	22052.8	0.947825
$816$	9100.93	0.390437
$817$	−6809.05	−0.291577
$818$	36871.8	1.57603
$819$	0	0
$820$	4984.44	0.212273
$821$	33249.5	1.41342	0.706708	−	0.707506i	$-0.250180\pi$
$821$	33249.5	1.41342	0.706708	+	0.707506i	$0.250180\pi$
$822$	11404.6	0.483918
$823$	−14421.7	−0.610825	−0.305413	−	0.952220i	$-0.598794\pi$
$823$	−14421.7	−0.610825	−0.305413	+	0.952220i	$0.598794\pi$
$824$	−8129.22	−0.343683
$825$	9206.39	0.388516
$826$	0	0
$827$	25779.1	1.08395	0.541975	−	0.840395i	$-0.317677\pi$
$827$	25779.1	1.08395	0.541975	+	0.840395i	$0.317677\pi$
$828$	−2864.41	−0.120223
$829$	−8440.89	−0.353636	−0.176818	−	0.984244i	$-0.556580\pi$
$829$	−8440.89	−0.353636	−0.176818	+	0.984244i	$0.556580\pi$
$830$	−38066.8	−1.59195
$831$	−36173.2	−1.51003
$832$	−65660.4	−2.73602
$833$	0	0
$834$	6004.71	0.249312
$835$	6795.19	0.281626
$836$	49666.7	2.05473
$837$	21307.6	0.879926
$838$	18058.0	0.744396
$839$	23882.2	0.982723	0.491362	−	0.870956i	$-0.336499\pi$
$839$	23882.2	0.982723	0.491362	+	0.870956i	$0.336499\pi$
$840$	0	0
$841$	−8210.05	−0.336629
$842$	51098.0	2.09140
$843$	−24125.8	−0.985689
$844$	−5304.39	−0.216333
$845$	−41696.2	−1.69750
$846$	−15687.1	−0.637508
$847$	0	0
$848$	5905.75	0.239156
$849$	−13644.3	−0.551556
$850$	26650.9	1.07543
$851$	−2031.58	−0.0818350
$852$	9748.58	0.391996
$853$	21167.4	0.849658	0.424829	−	0.905274i	$-0.360334\pi$
$853$	21167.4	0.849658	0.424829	+	0.905274i	$0.360334\pi$
$854$	0	0
$855$	−4526.83	−0.181069
$856$	4670.34	0.186483
$857$	1745.05	0.0695563	0.0347781	−	0.999395i	$-0.488928\pi$
$857$	1745.05	0.0695563	0.0347781	+	0.999395i	$0.488928\pi$
$858$	75076.4	2.98726
$859$	17565.4	0.697700	0.348850	−	0.937179i	$-0.386572\pi$
$859$	17565.4	0.697700	0.348850	+	0.937179i	$0.386572\pi$
$860$	−9711.55	−0.385071
$861$	0	0
$862$	−13067.2	−0.516321
$863$	5881.37	0.231986	0.115993	−	0.993250i	$-0.462995\pi$
$863$	5881.37	0.231986	0.115993	+	0.993250i	$0.462995\pi$
$864$	−21207.8	−0.835074
$865$	−37913.2	−1.49027
$866$	33879.7	1.32942
$867$	42884.3	1.67985
$868$	0	0
$869$	−29135.2	−1.13734
$870$	23915.7	0.931973
$871$	64377.7	2.50443
$872$	17656.4	0.685690
$873$	2615.46	0.101398
$874$	13652.1	0.528362
$875$	0	0
$876$	−72874.0	−2.81071
$877$	−18859.4	−0.726152	−0.363076	−	0.931759i	$-0.618274\pi$
$877$	−18859.4	−0.726152	−0.363076	+	0.931759i	$0.618274\pi$
$878$	−31582.6	−1.21396
$879$	6779.10	0.260129
$880$	6160.82	0.236002
$881$	−33493.6	−1.28085	−0.640424	−	0.768021i	$-0.721241\pi$
$881$	−33493.6	−1.28085	−0.640424	+	0.768021i	$0.721241\pi$
$882$	0	0
$883$	−22692.0	−0.864833	−0.432416	−	0.901674i	$-0.642339\pi$
$883$	−22692.0	−0.864833	−0.432416	+	0.901674i	$0.642339\pi$
$884$	137689.	5.23865
$885$	−27632.4	−1.04955
$886$	79576.6	3.01741
$887$	21455.6	0.812187	0.406093	−	0.913832i	$-0.366891\pi$
$887$	21455.6	0.812187	0.406093	+	0.913832i	$0.366891\pi$
$888$	7390.90	0.279304
$889$	0	0
$890$	30859.3	1.16225
$891$	22302.8	0.838579
$892$	36526.1	1.37106
$893$	47367.2	1.77501
$894$	−36480.5	−1.36475
$895$	11417.8	0.426429
$896$	0	0
$897$	13074.0	0.486655
$898$	64489.5	2.39648
$899$	−17917.1	−0.664705
$900$	3988.48	0.147721
$901$	42423.6	1.56863
$902$	−8070.78	−0.297924
$903$	0	0
$904$	−42778.2	−1.57387
$905$	−3324.20	−0.122100
$906$	73189.7	2.68385
$907$	37640.8	1.37800	0.688998	−	0.724763i	$-0.258051\pi$
$907$	37640.8	1.37800	0.688998	+	0.724763i	$0.258051\pi$
$908$	−63064.6	−2.30493
$909$	−7275.60	−0.265475
$910$	0	0
$911$	31246.2	1.13637	0.568185	−	0.822901i	$-0.307646\pi$
$911$	31246.2	1.13637	0.568185	+	0.822901i	$0.307646\pi$
$912$	−6491.51	−0.235697
$913$	39049.7	1.41551
$914$	−49752.6	−1.80051
$915$	−9523.90	−0.344099
$916$	6277.57	0.226437
$917$	0	0
$918$	84458.1	3.03653
$919$	−37653.3	−1.35154	−0.675772	−	0.737111i	$-0.736190\pi$
$919$	−37653.3	−1.35154	−0.675772	+	0.737111i	$0.736190\pi$
$920$	8208.46	0.294157
$921$	−26821.9	−0.959621
$922$	541.247	0.0193330
$923$	12827.0	0.457428
$924$	0	0
$925$	2828.83	0.100553
$926$	−11812.0	−0.419185
$927$	−1802.97	−0.0638806
$928$	17833.2	0.630824
$929$	−16083.8	−0.568020	−0.284010	−	0.958821i	$-0.591665\pi$
$929$	−16083.8	−0.568020	−0.284010	+	0.958821i	$0.591665\pi$
$930$	−26485.0	−0.933848
$931$	0	0
$932$	−18976.6	−0.666953
$933$	24301.1	0.852713
$934$	47303.4	1.65719
$935$	44256.0	1.54794
$936$	13711.4	0.478816
$937$	21508.6	0.749898	0.374949	−	0.927045i	$-0.377660\pi$
$937$	21508.6	0.749898	0.374949	+	0.927045i	$0.377660\pi$
$938$	0	0
$939$	13615.3	0.473184
$940$	67558.4	2.34416
$941$	−16725.0	−0.579406	−0.289703	−	0.957117i	$-0.593557\pi$
$941$	−16725.0	−0.579406	−0.289703	+	0.957117i	$0.593557\pi$
$942$	41048.8	1.41979
$943$	−1405.47	−0.0485349
$944$	11423.0	0.393841
$945$	0	0
$946$	15724.9	0.540444
$947$	−45072.4	−1.54663	−0.773313	−	0.634025i	$-0.781402\pi$
$947$	−45072.4	−1.54663	−0.773313	+	0.634025i	$0.781402\pi$
$948$	43785.2	1.50008
$949$	−95886.5	−3.27988
$950$	−19009.5	−0.649211
$951$	−4062.53	−0.138524
$952$	0	0
$953$	2861.43	0.0972623	0.0486311	−	0.998817i	$-0.484514\pi$
$953$	2861.43	0.0972623	0.0486311	+	0.998817i	$0.484514\pi$
$954$	10021.5	0.340102
$955$	29550.0	1.00127
$956$	76793.5	2.59799
$957$	−24533.2	−0.828679
$958$	43437.8	1.46494
$959$	0	0
$960$	31716.6	1.06630
$961$	−9948.92	−0.333957
$962$	23068.6	0.773139
$963$	1035.83	0.0346616
$964$	25460.3	0.850645
$965$	17242.4	0.575184
$966$	0	0
$967$	−1341.05	−0.0445971	−0.0222985	−	0.999751i	$-0.507098\pi$
$967$	−1341.05	−0.0445971	−0.0222985	+	0.999751i	$0.507098\pi$
$968$	−12095.6	−0.401618
$969$	−46631.4	−1.54594
$970$	−17779.3	−0.588514
$971$	13674.4	0.451939	0.225969	−	0.974134i	$-0.427445\pi$
$971$	13674.4	0.451939	0.225969	+	0.974134i	$0.427445\pi$
$972$	22968.2	0.757928
$973$	0	0
$974$	−37571.1	−1.23599
$975$	−18204.7	−0.597965
$976$	3937.09	0.129122
$977$	−8477.45	−0.277603	−0.138801	−	0.990320i	$-0.544325\pi$
$977$	−8477.45	−0.277603	−0.138801	+	0.990320i	$0.544325\pi$
$978$	53662.7	1.75454
$979$	−31656.1	−1.03344
$980$	0	0
$981$	3916.00	0.127450
$982$	23736.3	0.771340
$983$	16136.5	0.523577	0.261788	−	0.965125i	$-0.415688\pi$
$983$	16136.5	0.523577	0.261788	+	0.965125i	$0.415688\pi$
$984$	5113.11	0.165650
$985$	−18239.7	−0.590014
$986$	−71019.2	−2.29383
$987$	0	0
$988$	−98210.5	−3.16244
$989$	2738.38	0.0880439
$990$	10454.3	0.335616
$991$	−33090.4	−1.06070	−0.530348	−	0.847780i	$-0.677939\pi$
$991$	−33090.4	−1.06070	−0.530348	+	0.847780i	$0.677939\pi$
$992$	−19749.2	−0.632093
$993$	−16820.7	−0.537551
$994$	0	0
$995$	−38095.0	−1.21376
$996$	−58684.9	−1.86697
$997$	−39943.4	−1.26883	−0.634413	−	0.772994i	$-0.718758\pi$
$997$	−39943.4	−1.26883	−0.634413	+	0.772994i	$0.718758\pi$
$998$	−41265.5	−1.30885
$999$	8964.71	0.283915

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2009.4.a.k.1.4		36
7.3	odd	6		287.4.e.a.247.33	yes	72
7.5	odd	6		287.4.e.a.165.33	✓	72
7.6	odd	2		2009.4.a.j.1.4		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.4.e.a.165.33	✓	72	7.5	odd	6
287.4.e.a.247.33	yes	72	7.3	odd	6
2009.4.a.j.1.4		36	7.6	odd	2
2009.4.a.k.1.4		36	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2009 = 7^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2009.a (trivial)

\(f(q)\)	\(=\)	\(q-4.67229 q^{2} +4.57802 q^{3} +13.8303 q^{4} -8.79022 q^{5} -21.3898 q^{6} -27.2411 q^{8} -6.04177 q^{9} +O(q^{10})\)	\(q-4.67229 q^{2} +4.57802 q^{3} +13.8303 q^{4} -8.79022 q^{5} -21.3898 q^{6} -27.2411 q^{8} -6.04177 q^{9} +41.0705 q^{10} -42.1310 q^{11} +63.3155 q^{12} +83.3095 q^{13} -40.2418 q^{15} +16.6356 q^{16} +119.501 q^{17} +28.2289 q^{18} -85.2375 q^{19} -121.572 q^{20} +196.848 q^{22} +34.2798 q^{23} -124.710 q^{24} -47.7321 q^{25} -389.247 q^{26} -151.266 q^{27} +127.196 q^{29} +188.021 q^{30} -140.862 q^{31} +140.202 q^{32} -192.876 q^{33} -558.343 q^{34} -83.5597 q^{36} -59.2646 q^{37} +398.255 q^{38} +381.392 q^{39} +239.455 q^{40} -41.0000 q^{41} +79.8833 q^{43} -582.686 q^{44} +53.1084 q^{45} -160.165 q^{46} -555.709 q^{47} +76.1579 q^{48} +223.018 q^{50} +547.076 q^{51} +1152.20 q^{52} +355.007 q^{53} +706.758 q^{54} +370.340 q^{55} -390.219 q^{57} -594.300 q^{58} +686.660 q^{59} -556.557 q^{60} +236.667 q^{61} +658.148 q^{62} -788.151 q^{64} -732.309 q^{65} +901.175 q^{66} +772.754 q^{67} +1652.74 q^{68} +156.933 q^{69} +153.968 q^{71} +164.584 q^{72} -1150.97 q^{73} +276.902 q^{74} -218.518 q^{75} -1178.86 q^{76} -1781.98 q^{78} +691.539 q^{79} -146.230 q^{80} -529.369 q^{81} +191.564 q^{82} -926.864 q^{83} -1050.44 q^{85} -373.238 q^{86} +582.308 q^{87} +1147.69 q^{88} +751.374 q^{89} -248.138 q^{90} +474.101 q^{92} -644.868 q^{93} +2596.43 q^{94} +749.256 q^{95} +641.848 q^{96} -432.897 q^{97} +254.545 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 5 q^{2} + 6 q^{3} + 117 q^{4} - 4 q^{5} + 12 q^{6} - 39 q^{8} + 236 q^{9}+O(q^{10}) \) 36 * q - 5 * q^2 + 6 * q^3 + 117 * q^4 - 4 * q^5 + 12 * q^6 - 39 * q^8 + 236 * q^9	\( 36 q - 5 q^{2} + 6 q^{3} + 117 q^{4} - 4 q^{5} + 12 q^{6} - 39 q^{8} + 236 q^{9} + 12 q^{10} - 140 q^{11} - 186 q^{12} + 72 q^{13} - 366 q^{15} - 15 q^{16} + 2 q^{17} - 212 q^{18} - 30 q^{19} + 334 q^{20} - 346 q^{22} - 314 q^{23} - 106 q^{24} + 570 q^{25} - 303 q^{26} + 204 q^{27} - 356 q^{29} - 357 q^{30} + 4 q^{31} - 532 q^{32} + 30 q^{33} + 364 q^{34} + 113 q^{36} - 1398 q^{37} + 264 q^{38} - 1348 q^{39} - 26 q^{40} - 1476 q^{41} - 1072 q^{43} - 1507 q^{44} + 1132 q^{45} - 1356 q^{46} + 622 q^{47} - 1724 q^{48} - 1426 q^{50} - 668 q^{51} + 877 q^{52} - 412 q^{53} + 1814 q^{54} - 1114 q^{55} - 4082 q^{57} - 1309 q^{58} + 620 q^{59} - 3724 q^{60} - 774 q^{61} - 1665 q^{62} - 3285 q^{64} - 1036 q^{65} + 1056 q^{66} - 2972 q^{67} + 1525 q^{68} - 3304 q^{69} - 3540 q^{71} - 821 q^{72} + 60 q^{73} - 2043 q^{74} - 450 q^{75} - 2171 q^{76} - 1136 q^{78} - 5190 q^{79} + 1564 q^{80} + 284 q^{81} + 205 q^{82} - 1656 q^{83} - 5064 q^{85} - 782 q^{86} + 1940 q^{87} - 4232 q^{88} + 1196 q^{89} - 8030 q^{90} - 4618 q^{92} + 698 q^{93} + 35 q^{94} - 1968 q^{95} + 7926 q^{96} - 3862 q^{97} - 5964 q^{99}+O(q^{100}) \) 36 * q - 5 * q^2 + 6 * q^3 + 117 * q^4 - 4 * q^5 + 12 * q^6 - 39 * q^8 + 236 * q^9 + 12 * q^10 - 140 * q^11 - 186 * q^12 + 72 * q^13 - 366 * q^15 - 15 * q^16 + 2 * q^17 - 212 * q^18 - 30 * q^19 + 334 * q^20 - 346 * q^22 - 314 * q^23 - 106 * q^24 + 570 * q^25 - 303 * q^26 + 204 * q^27 - 356 * q^29 - 357 * q^30 + 4 * q^31 - 532 * q^32 + 30 * q^33 + 364 * q^34 + 113 * q^36 - 1398 * q^37 + 264 * q^38 - 1348 * q^39 - 26 * q^40 - 1476 * q^41 - 1072 * q^43 - 1507 * q^44 + 1132 * q^45 - 1356 * q^46 + 622 * q^47 - 1724 * q^48 - 1426 * q^50 - 668 * q^51 + 877 * q^52 - 412 * q^53 + 1814 * q^54 - 1114 * q^55 - 4082 * q^57 - 1309 * q^58 + 620 * q^59 - 3724 * q^60 - 774 * q^61 - 1665 * q^62 - 3285 * q^64 - 1036 * q^65 + 1056 * q^66 - 2972 * q^67 + 1525 * q^68 - 3304 * q^69 - 3540 * q^71 - 821 * q^72 + 60 * q^73 - 2043 * q^74 - 450 * q^75 - 2171 * q^76 - 1136 * q^78 - 5190 * q^79 + 1564 * q^80 + 284 * q^81 + 205 * q^82 - 1656 * q^83 - 5064 * q^85 - 782 * q^86 + 1940 * q^87 - 4232 * q^88 + 1196 * q^89 - 8030 * q^90 - 4618 * q^92 + 698 * q^93 + 35 * q^94 - 1968 * q^95 + 7926 * q^96 - 3862 * q^97 - 5964 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more