LMFDB - Embedded newform 2401.4.a.d.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2401,4,Mod(1,2401)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2401, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2401.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 2401 = 7^{4} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2401.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:	$141.663585924$
Analytic rank:	$0$
Dimension:	$39$
Twist minimal:	no (minimal twist has level 49)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	2401.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.58052 q^{2} +3.81461 q^{3} -5.50196 q^{4} +14.4403 q^{5} -6.02907 q^{6} +21.3401 q^{8} -12.4487 q^{9} +O(q^{10})$	\(q-1.58052 q^{2} +3.81461 q^{3} -5.50196 q^{4} +14.4403 q^{5} -6.02907 q^{6} +21.3401 q^{8} -12.4487 q^{9} -22.8232 q^{10} -55.1416 q^{11} -20.9878 q^{12} +9.01710 q^{13} +55.0841 q^{15} +10.2872 q^{16} +86.5568 q^{17} +19.6754 q^{18} -31.5971 q^{19} -79.4499 q^{20} +87.1524 q^{22} +18.3228 q^{23} +81.4043 q^{24} +83.5221 q^{25} -14.2517 q^{26} -150.482 q^{27} -248.405 q^{29} -87.0616 q^{30} +314.177 q^{31} -186.980 q^{32} -210.344 q^{33} -136.805 q^{34} +68.4923 q^{36} +124.099 q^{37} +49.9398 q^{38} +34.3968 q^{39} +308.157 q^{40} +112.098 q^{41} -191.207 q^{43} +303.387 q^{44} -179.763 q^{45} -28.9596 q^{46} -114.181 q^{47} +39.2417 q^{48} -132.008 q^{50} +330.181 q^{51} -49.6117 q^{52} +672.714 q^{53} +237.839 q^{54} -796.261 q^{55} -120.531 q^{57} +392.609 q^{58} +17.8210 q^{59} -303.071 q^{60} -816.008 q^{61} -496.564 q^{62} +213.228 q^{64} +130.210 q^{65} +332.453 q^{66} -308.150 q^{67} -476.232 q^{68} +69.8946 q^{69} +876.294 q^{71} -265.657 q^{72} -102.784 q^{73} -196.140 q^{74} +318.604 q^{75} +173.846 q^{76} -54.3647 q^{78} +258.320 q^{79} +148.550 q^{80} -237.914 q^{81} -177.173 q^{82} +790.340 q^{83} +1249.91 q^{85} +302.206 q^{86} -947.569 q^{87} -1176.73 q^{88} +97.7759 q^{89} +284.119 q^{90} -100.812 q^{92} +1198.47 q^{93} +180.465 q^{94} -456.272 q^{95} -713.257 q^{96} +264.331 q^{97} +686.442 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 39 q + q^{2} + q^{3} + 145 q^{4} + 27 q^{5} + 41 q^{6} - 12 q^{8} + 312 q^{9}+O(q^{10}) $ 39 * q + q^2 + q^3 + 145 * q^4 + 27 * q^5 + 41 * q^6 - 12 * q^8 + 312 * q^9	\( 39 q + q^{2} + q^{3} + 145 q^{4} + 27 q^{5} + 41 q^{6} - 12 q^{8} + 312 q^{9} + 78 q^{10} + q^{11} - 91 q^{12} + 77 q^{13} - 161 q^{15} + 461 q^{16} + 211 q^{17} + 8 q^{18} + 314 q^{19} + 476 q^{20} - 61 q^{22} - 69 q^{23} + 330 q^{24} + 606 q^{25} + 504 q^{26} - 50 q^{27} + 57 q^{29} + 42 q^{30} + 638 q^{31} - 1600 q^{32} + 1574 q^{33} + 1343 q^{34} + 782 q^{36} + 71 q^{37} + 1359 q^{38} - 84 q^{39} - 155 q^{40} + 1393 q^{41} - 125 q^{43} + 52 q^{44} + 1129 q^{45} - 1454 q^{46} + 1483 q^{47} - 974 q^{48} + 3074 q^{50} - 2044 q^{51} + 3899 q^{52} + 2213 q^{53} + 1142 q^{54} + 1604 q^{55} + 98 q^{57} + 2403 q^{58} + 2073 q^{59} - 1519 q^{60} + 2575 q^{61} + 1742 q^{62} + 1358 q^{64} + 1876 q^{65} - 48 q^{66} + 176 q^{67} + 3038 q^{68} - 638 q^{69} - 1259 q^{71} - 3799 q^{72} - 307 q^{73} + 3845 q^{74} + 131 q^{75} + 1974 q^{76} - 6041 q^{78} + 22 q^{79} - 804 q^{80} + 795 q^{81} + 8043 q^{82} + 6349 q^{83} + 3094 q^{85} + 1745 q^{86} + 9508 q^{87} + 1299 q^{88} + 2253 q^{89} + 11156 q^{90} + 1284 q^{92} - 3430 q^{93} + 2738 q^{94} - 3290 q^{95} + 3031 q^{96} - 770 q^{97} + 5384 q^{99}+O(q^{100}) \) 39 * q + q^2 + q^3 + 145 * q^4 + 27 * q^5 + 41 * q^6 - 12 * q^8 + 312 * q^9 + 78 * q^10 + q^11 - 91 * q^12 + 77 * q^13 - 161 * q^15 + 461 * q^16 + 211 * q^17 + 8 * q^18 + 314 * q^19 + 476 * q^20 - 61 * q^22 - 69 * q^23 + 330 * q^24 + 606 * q^25 + 504 * q^26 - 50 * q^27 + 57 * q^29 + 42 * q^30 + 638 * q^31 - 1600 * q^32 + 1574 * q^33 + 1343 * q^34 + 782 * q^36 + 71 * q^37 + 1359 * q^38 - 84 * q^39 - 155 * q^40 + 1393 * q^41 - 125 * q^43 + 52 * q^44 + 1129 * q^45 - 1454 * q^46 + 1483 * q^47 - 974 * q^48 + 3074 * q^50 - 2044 * q^51 + 3899 * q^52 + 2213 * q^53 + 1142 * q^54 + 1604 * q^55 + 98 * q^57 + 2403 * q^58 + 2073 * q^59 - 1519 * q^60 + 2575 * q^61 + 1742 * q^62 + 1358 * q^64 + 1876 * q^65 - 48 * q^66 + 176 * q^67 + 3038 * q^68 - 638 * q^69 - 1259 * q^71 - 3799 * q^72 - 307 * q^73 + 3845 * q^74 + 131 * q^75 + 1974 * q^76 - 6041 * q^78 + 22 * q^79 - 804 * q^80 + 795 * q^81 + 8043 * q^82 + 6349 * q^83 + 3094 * q^85 + 1745 * q^86 + 9508 * q^87 + 1299 * q^88 + 2253 * q^89 + 11156 * q^90 + 1284 * q^92 - 3430 * q^93 + 2738 * q^94 - 3290 * q^95 + 3031 * q^96 - 770 * q^97 + 5384 * 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 $

$2$	−1.58052	−0.558798	−0.279399	−	0.960175i	$-0.590135\pi$
$2$	−1.58052	−0.558798	−0.279399	+	0.960175i	$0.590135\pi$
$3$	3.81461	0.734123	0.367061	−	0.930197i	$-0.380364\pi$
$3$	3.81461	0.734123	0.367061	+	0.930197i	$0.380364\pi$
$4$	−5.50196	−0.687745
$5$	14.4403	1.29158	0.645790	−	0.763515i	$-0.276528\pi$
$5$	14.4403	1.29158	0.645790	+	0.763515i	$0.276528\pi$
$6$	−6.02907	−0.410226
$7$	0	0
$7$	0	0
$8$	21.3401	0.943108
$9$	−12.4487	−0.461064
$10$	−22.8232	−0.721732
$11$	−55.1416	−1.51144	−0.755719	−	0.654896i	$-0.772712\pi$
$11$	−55.1416	−1.51144	−0.755719	+	0.654896i	$0.772712\pi$
$12$	−20.9878	−0.504889
$13$	9.01710	0.192376	0.0961882	−	0.995363i	$-0.469335\pi$
$13$	9.01710	0.192376	0.0961882	+	0.995363i	$0.469335\pi$
$14$	0	0
$15$	55.0841	0.948178
$16$	10.2872	0.160738
$17$	86.5568	1.23489	0.617445	−	0.786614i	$-0.288168\pi$
$17$	86.5568	1.23489	0.617445	+	0.786614i	$0.288168\pi$
$18$	19.6754	0.257641
$19$	−31.5971	−0.381520	−0.190760	−	0.981637i	$-0.561095\pi$
$19$	−31.5971	−0.381520	−0.190760	+	0.981637i	$0.561095\pi$
$20$	−79.4499	−0.888277
$21$	0	0
$22$	87.1524	0.844588
$23$	18.3228	0.166112	0.0830560	−	0.996545i	$-0.473532\pi$
$23$	18.3228	0.166112	0.0830560	+	0.996545i	$0.473532\pi$
$24$	81.4043	0.692357
$25$	83.5221	0.668177
$26$	−14.2517	−0.107500
$27$	−150.482	−1.07260
$28$	0	0
$29$	−248.405	−1.59061	−0.795304	−	0.606211i	$-0.792689\pi$
$29$	−248.405	−1.59061	−0.795304	+	0.606211i	$0.792689\pi$
$30$	−87.0616	−0.529840
$31$	314.177	1.82026	0.910128	−	0.414327i	$-0.135983\pi$
$31$	314.177	1.82026	0.910128	+	0.414327i	$0.135983\pi$
$32$	−186.980	−1.03293
$33$	−210.344	−1.10958
$34$	−136.805	−0.690054
$35$	0	0
$36$	68.4923	0.317094
$37$	124.099	0.551397	0.275699	−	0.961244i	$-0.411091\pi$
$37$	124.099	0.551397	0.275699	+	0.961244i	$0.411091\pi$
$38$	49.9398	0.213192
$39$	34.3968	0.141228
$40$	308.157	1.21810
$41$	112.098	0.426993	0.213497	−	0.976944i	$-0.431515\pi$
$41$	112.098	0.426993	0.213497	+	0.976944i	$0.431515\pi$
$42$	0	0
$43$	−191.207	−0.678110	−0.339055	−	0.940767i	$-0.610107\pi$
$43$	−191.207	−0.678110	−0.339055	+	0.940767i	$0.610107\pi$
$44$	303.387	1.03948
$45$	−179.763	−0.595500
$46$	−28.9596	−0.0928231
$47$	−114.181	−0.354361	−0.177180	−	0.984178i	$-0.556698\pi$
$47$	−114.181	−0.354361	−0.177180	+	0.984178i	$0.556698\pi$
$48$	39.2417	0.118001
$49$	0	0
$50$	−132.008	−0.373376
$51$	330.181	0.906560
$52$	−49.6117	−0.132306
$53$	672.714	1.74348	0.871739	−	0.489970i	$-0.162992\pi$
$53$	672.714	1.74348	0.871739	+	0.489970i	$0.162992\pi$
$54$	237.839	0.599367
$55$	−796.261	−1.95214
$56$	0	0
$57$	−120.531	−0.280082
$58$	392.609	0.888829
$59$	17.8210	0.0393237	0.0196618	−	0.999807i	$-0.493741\pi$
$59$	17.8210	0.0393237	0.0196618	+	0.999807i	$0.493741\pi$
$60$	−303.071	−0.652104
$61$	−816.008	−1.71277	−0.856387	−	0.516335i	$-0.827296\pi$
$61$	−816.008	−1.71277	−0.856387	+	0.516335i	$0.827296\pi$
$62$	−496.564	−1.01716
$63$	0	0
$64$	213.228	0.416461
$65$	130.210	0.248469
$66$	332.453	0.620032
$67$	−308.150	−0.561888	−0.280944	−	0.959724i	$-0.590647\pi$
$67$	−308.150	−0.561888	−0.280944	+	0.959724i	$0.590647\pi$
$68$	−476.232	−0.849289
$69$	69.8946	0.121947
$70$	0	0
$71$	876.294	1.46475	0.732373	−	0.680904i	$-0.238413\pi$
$71$	876.294	1.46475	0.732373	+	0.680904i	$0.238413\pi$
$72$	−265.657	−0.434833
$73$	−102.784	−0.164794	−0.0823970	−	0.996600i	$-0.526258\pi$
$73$	−102.784	−0.164794	−0.0823970	+	0.996600i	$0.526258\pi$
$74$	−196.140	−0.308120
$75$	318.604	0.490524
$76$	173.846	0.262388
$77$	0	0
$78$	−54.3647	−0.0789179
$79$	258.320	0.367889	0.183944	−	0.982937i	$-0.441113\pi$
$79$	258.320	0.367889	0.183944	+	0.982937i	$0.441113\pi$
$80$	148.550	0.207605
$81$	−237.914	−0.326357
$82$	−177.173	−0.238603
$83$	790.340	1.04519	0.522597	−	0.852580i	$-0.324963\pi$
$83$	790.340	1.04519	0.522597	+	0.852580i	$0.324963\pi$
$84$	0	0
$85$	1249.91	1.59496
$86$	302.206	0.378927
$87$	−947.569	−1.16770
$88$	−1176.73	−1.42545
$89$	97.7759	0.116452	0.0582260	−	0.998303i	$-0.481456\pi$
$89$	97.7759	0.116452	0.0582260	+	0.998303i	$0.481456\pi$
$90$	284.119	0.332764
$91$	0	0
$92$	−100.812	−0.114243
$93$	1198.47	1.33629
$94$	180.465	0.198016
$95$	−456.272	−0.492763
$96$	−713.257	−0.758296
$97$	264.331	0.276688	0.138344	−	0.990384i	$-0.455822\pi$
$97$	264.331	0.276688	0.138344	+	0.990384i	$0.455822\pi$
$98$	0	0
$99$	686.442	0.696869
$100$	−459.535	−0.459535
$101$	554.294	0.546082	0.273041	−	0.962002i	$-0.411970\pi$
$101$	554.294	0.546082	0.273041	+	0.962002i	$0.411970\pi$
$102$	−521.857	−0.506584
$103$	569.083	0.544402	0.272201	−	0.962240i	$-0.412248\pi$
$103$	569.083	0.544402	0.272201	+	0.962240i	$0.412248\pi$
$104$	192.426	0.181432
$105$	0	0
$106$	−1063.24	−0.974252
$107$	406.838	0.367575	0.183787	−	0.982966i	$-0.441164\pi$
$107$	406.838	0.367575	0.183787	+	0.982966i	$0.441164\pi$
$108$	827.944	0.737675
$109$	1900.12	1.66971	0.834856	−	0.550468i	$-0.185551\pi$
$109$	1900.12	1.66971	0.834856	+	0.550468i	$0.185551\pi$
$110$	1258.51	1.09085
$111$	473.389	0.404793
$112$	0	0
$113$	−13.7407	−0.0114391	−0.00571954	−	0.999984i	$-0.501821\pi$
$113$	−13.7407	−0.0114391	−0.00571954	+	0.999984i	$0.501821\pi$
$114$	190.501	0.156509
$115$	264.587	0.214547
$116$	1366.71	1.09393
$117$	−112.251	−0.0886978
$118$	−28.1664	−0.0219740
$119$	0	0
$120$	1175.50	0.894234
$121$	1709.59	1.28444
$122$	1289.72	0.957094
$123$	427.610	0.313465
$124$	−1728.59	−1.25187
$125$	−598.953	−0.428576
$126$	0	0
$127$	2457.73	1.71723	0.858617	−	0.512618i	$-0.171324\pi$
$127$	2457.73	1.71723	0.858617	+	0.512618i	$0.171324\pi$
$128$	1158.83	0.800211
$129$	−729.379	−0.497816
$130$	−205.799	−0.138844
$131$	1439.84	0.960304	0.480152	−	0.877185i	$-0.340582\pi$
$131$	1439.84	0.960304	0.480152	+	0.877185i	$0.340582\pi$
$132$	1157.30	0.763108
$133$	0	0
$134$	487.037	0.313982
$135$	−2173.00	−1.38535
$136$	1847.13	1.16463
$137$	−1021.81	−0.637220	−0.318610	−	0.947886i	$-0.603216\pi$
$137$	−1021.81	−0.637220	−0.318610	+	0.947886i	$0.603216\pi$
$138$	−110.470	−0.0681435
$139$	−2582.61	−1.57593	−0.787966	−	0.615719i	$-0.788866\pi$
$139$	−2582.61	−1.57593	−0.787966	+	0.615719i	$0.788866\pi$
$140$	0	0
$141$	−435.555	−0.260144
$142$	−1385.00	−0.818497
$143$	−497.217	−0.290765
$144$	−128.063	−0.0741103
$145$	−3587.04	−2.05440
$146$	162.452	0.0920865
$147$	0	0
$148$	−682.786	−0.379221
$149$	−2219.87	−1.22053	−0.610265	−	0.792198i	$-0.708937\pi$
$149$	−2219.87	−1.22053	−0.610265	+	0.792198i	$0.708937\pi$
$150$	−503.561	−0.274104
$151$	2270.09	1.22342	0.611712	−	0.791081i	$-0.290481\pi$
$151$	2270.09	1.22342	0.611712	+	0.791081i	$0.290481\pi$
$152$	−674.286	−0.359814
$153$	−1077.52	−0.569363
$154$	0	0
$155$	4536.81	2.35100
$156$	−189.250	−0.0971288
$157$	241.143	0.122581	0.0612907	−	0.998120i	$-0.480478\pi$
$157$	241.143	0.122581	0.0612907	+	0.998120i	$0.480478\pi$
$158$	−408.279	−0.205576
$159$	2566.14	1.27993
$160$	−2700.05	−1.33411
$161$	0	0
$162$	376.028	0.182367
$163$	−499.509	−0.240028	−0.120014	−	0.992772i	$-0.538294\pi$
$163$	−499.509	−0.240028	−0.120014	+	0.992772i	$0.538294\pi$
$164$	−616.757	−0.293662
$165$	−3037.43	−1.43311
$166$	−1249.15	−0.584052
$167$	−1697.59	−0.786606	−0.393303	−	0.919409i	$-0.628668\pi$
$167$	−1697.59	−0.786606	−0.393303	+	0.919409i	$0.628668\pi$
$168$	0	0
$169$	−2115.69	−0.962991
$170$	−1975.50	−0.891259
$171$	393.344	0.175905
$172$	1052.01	0.466367
$173$	286.778	0.126031	0.0630154	−	0.998013i	$-0.479928\pi$
$173$	286.778	0.126031	0.0630154	+	0.998013i	$0.479928\pi$
$174$	1497.65	0.652509
$175$	0	0
$176$	−567.253	−0.242945
$177$	67.9802	0.0288684
$178$	−154.537	−0.0650731
$179$	1636.21	0.683219	0.341609	−	0.939842i	$-0.389028\pi$
$179$	1636.21	0.683219	0.341609	+	0.939842i	$0.389028\pi$
$180$	989.049	0.409552
$181$	2209.85	0.907497	0.453749	−	0.891130i	$-0.350086\pi$
$181$	2209.85	0.907497	0.453749	+	0.891130i	$0.350086\pi$
$182$	0	0
$183$	−3112.76	−1.25739
$184$	391.012	0.156662
$185$	1792.02	0.712173
$186$	−1894.20	−0.746717
$187$	−4772.88	−1.86646
$188$	628.217	0.243710
$189$	0	0
$190$	721.146	0.275355
$191$	−312.932	−0.118550	−0.0592748	−	0.998242i	$-0.518879\pi$
$191$	−312.932	−0.118550	−0.0592748	+	0.998242i	$0.518879\pi$
$192$	813.382	0.305733
$193$	3712.18	1.38450	0.692250	−	0.721657i	$-0.256619\pi$
$193$	3712.18	1.38450	0.692250	+	0.721657i	$0.256619\pi$
$194$	−417.780	−0.154612
$195$	496.699	0.182407
$196$	0	0
$197$	990.306	0.358154	0.179077	−	0.983835i	$-0.442689\pi$
$197$	990.306	0.358154	0.179077	+	0.983835i	$0.442689\pi$
$198$	−1084.94	−0.389409
$199$	−2160.71	−0.769691	−0.384845	−	0.922981i	$-0.625745\pi$
$199$	−2160.71	−0.769691	−0.384845	+	0.922981i	$0.625745\pi$
$200$	1782.37	0.630163
$201$	−1175.47	−0.412495
$202$	−876.073	−0.305150
$203$	0	0
$204$	−1816.64	−0.623482
$205$	1618.72	0.551496
$206$	−899.447	−0.304211
$207$	−228.096	−0.0765882
$208$	92.7608	0.0309221
$209$	1742.31	0.576643
$210$	0	0
$211$	−4.90696	−0.00160099	−0.000800495	−	1.00000i	$-0.500255\pi$
$211$	−4.90696	−0.00160099	−0.000800495		1.00000i	$0.500255\pi$
$212$	−3701.24	−1.19907
$213$	3342.72	1.07530
$214$	−643.015	−0.205400
$215$	−2761.08	−0.875833
$216$	−3211.29	−1.01158
$217$	0	0
$218$	−3003.18	−0.933032
$219$	−392.081	−0.120979
$220$	4380.99	1.34257
$221$	780.492	0.237564
$222$	−748.200	−0.226198
$223$	−2924.46	−0.878189	−0.439095	−	0.898441i	$-0.644701\pi$
$223$	−2924.46	−0.878189	−0.439095	+	0.898441i	$0.644701\pi$
$224$	0	0
$225$	−1039.74	−0.308072
$226$	21.7175	0.00639214
$227$	4914.50	1.43695	0.718473	−	0.695555i	$-0.244842\pi$
$227$	4914.50	1.43695	0.718473	+	0.695555i	$0.244842\pi$
$228$	663.155	0.192625
$229$	2690.07	0.776266	0.388133	−	0.921603i	$-0.373120\pi$
$229$	2690.07	0.776266	0.388133	+	0.921603i	$0.373120\pi$
$230$	−418.185	−0.119888
$231$	0	0
$232$	−5300.99	−1.50012
$233$	−3315.69	−0.932267	−0.466133	−	0.884714i	$-0.654353\pi$
$233$	−3315.69	−0.932267	−0.466133	+	0.884714i	$0.654353\pi$
$234$	177.415	0.0495641
$235$	−1648.80	−0.457685
$236$	−98.0503	−0.0270446
$237$	985.390	0.270076
$238$	0	0
$239$	3517.53	0.952008	0.476004	−	0.879443i	$-0.342085\pi$
$239$	3517.53	0.952008	0.476004	+	0.879443i	$0.342085\pi$
$240$	566.662	0.152408
$241$	5162.67	1.37990	0.689952	−	0.723855i	$-0.257632\pi$
$241$	5162.67	1.37990	0.689952	+	0.723855i	$0.257632\pi$
$242$	−2702.05	−0.717745
$243$	3155.45	0.833014
$244$	4489.64	1.17795
$245$	0	0
$246$	−675.845	−0.175164
$247$	−284.914	−0.0733954
$248$	6704.58	1.71670
$249$	3014.84	0.767301
$250$	946.657	0.239488
$251$	659.231	0.165778	0.0828891	−	0.996559i	$-0.473585\pi$
$251$	659.231	0.165778	0.0828891	+	0.996559i	$0.473585\pi$
$252$	0	0
$253$	−1010.35	−0.251068
$254$	−3884.50	−0.959587
$255$	4767.91	1.17089
$256$	−3537.37	−0.863617
$257$	−2163.40	−0.525095	−0.262548	−	0.964919i	$-0.584563\pi$
$257$	−2163.40	−0.525095	−0.262548	+	0.964919i	$0.584563\pi$
$258$	1152.80	0.278179
$259$	0	0
$260$	−716.408	−0.170884
$261$	3092.32	0.733372
$262$	−2275.70	−0.536616
$263$	−5187.18	−1.21618	−0.608090	−	0.793868i	$-0.708064\pi$
$263$	−5187.18	−1.21618	−0.608090	+	0.793868i	$0.708064\pi$
$264$	−4488.76	−1.04646
$265$	9714.18	2.25184
$266$	0	0
$267$	372.977	0.0854900
$268$	1695.43	0.386435
$269$	−5425.36	−1.22970	−0.614852	−	0.788643i	$-0.710784\pi$
$269$	−5425.36	−1.22970	−0.614852	+	0.788643i	$0.710784\pi$
$270$	3434.47	0.774130
$271$	−6981.84	−1.56501	−0.782503	−	0.622647i	$-0.786057\pi$
$271$	−6981.84	−1.56501	−0.782503	+	0.622647i	$0.786057\pi$
$272$	890.428	0.198493
$273$	0	0
$274$	1614.99	0.356077
$275$	−4605.54	−1.00991
$276$	−384.557	−0.0838682
$277$	2455.78	0.532685	0.266342	−	0.963878i	$-0.414185\pi$
$277$	2455.78	0.532685	0.266342	+	0.963878i	$0.414185\pi$
$278$	4081.87	0.880627
$279$	−3911.11	−0.839254
$280$	0	0
$281$	5306.98	1.12665	0.563323	−	0.826237i	$-0.309523\pi$
$281$	5306.98	1.12665	0.563323	+	0.826237i	$0.309523\pi$
$282$	688.403	0.145368
$283$	4123.49	0.866135	0.433067	−	0.901362i	$-0.357431\pi$
$283$	4123.49	0.866135	0.433067	+	0.901362i	$0.357431\pi$
$284$	−4821.33	−1.00737
$285$	−1740.50	−0.361748
$286$	785.861	0.162479
$287$	0	0
$288$	2327.66	0.476246
$289$	2579.09	0.524952
$290$	5669.39	1.14799
$291$	1008.32	0.203123
$292$	565.513	0.113336
$293$	−566.073	−0.112868	−0.0564340	−	0.998406i	$-0.517973\pi$
$293$	−566.073	−0.112868	−0.0564340	+	0.998406i	$0.517973\pi$
$294$	0	0
$295$	257.340	0.0507896
$296$	2648.28	0.520027
$297$	8297.80	1.62117
$298$	3508.55	0.682029
$299$	165.219	0.0319560
$300$	−1752.95	−0.337355
$301$	0	0
$302$	−3587.92	−0.683647
$303$	2114.42	0.400892
$304$	−325.046	−0.0613246
$305$	−11783.4	−2.21218
$306$	1703.04	0.318159
$307$	9542.60	1.77402	0.887011	−	0.461747i	$-0.152777\pi$
$307$	9542.60	1.77402	0.887011	+	0.461747i	$0.152777\pi$
$308$	0	0
$309$	2170.83	0.399658
$310$	−7170.52	−1.31374
$311$	7391.98	1.34778	0.673892	−	0.738830i	$-0.264621\pi$
$311$	7391.98	1.34778	0.673892	+	0.738830i	$0.264621\pi$
$312$	734.031	0.133193
$313$	−3662.91	−0.661469	−0.330735	−	0.943724i	$-0.607297\pi$
$313$	−3662.91	−0.661469	−0.330735	+	0.943724i	$0.607297\pi$
$314$	−381.131	−0.0684983
$315$	0	0
$316$	−1421.26	−0.253014
$317$	−9001.41	−1.59486	−0.797428	−	0.603414i	$-0.793807\pi$
$317$	−9001.41	−1.59486	−0.797428	+	0.603414i	$0.793807\pi$
$318$	−4055.84	−0.715221
$319$	13697.4	2.40410
$320$	3079.07	0.537892
$321$	1551.93	0.269845
$322$	0	0
$323$	−2734.95	−0.471135
$324$	1308.99	0.224450
$325$	753.127	0.128541
$326$	789.484	0.134127
$327$	7248.23	1.22577
$328$	2392.18	0.402701
$329$	0	0
$330$	4800.71	0.800820
$331$	3851.39	0.639551	0.319776	−	0.947493i	$-0.396392\pi$
$331$	3851.39	0.639551	0.319776	+	0.947493i	$0.396392\pi$
$332$	−4348.42	−0.718827
$333$	−1544.87	−0.254229
$334$	2683.07	0.439554
$335$	−4449.77	−0.725722
$336$	0	0
$337$	1446.56	0.233826	0.116913	−	0.993142i	$-0.462700\pi$
$337$	1446.56	0.233826	0.116913	+	0.993142i	$0.462700\pi$
$338$	3343.89	0.538118
$339$	−52.4155	−0.00839770
$340$	−6876.93	−1.09692
$341$	−17324.2	−2.75120
$342$	−621.687	−0.0982953
$343$	0	0
$344$	−4080.37	−0.639531
$345$	1009.30	0.157504
$346$	−453.259	−0.0704258
$347$	7164.72	1.10842	0.554211	−	0.832376i	$-0.313020\pi$
$347$	7164.72	1.10842	0.554211	+	0.832376i	$0.313020\pi$
$348$	5213.48	0.803081
$349$	7479.48	1.14718	0.573592	−	0.819141i	$-0.305549\pi$
$349$	7479.48	1.14718	0.573592	+	0.819141i	$0.305549\pi$
$350$	0	0
$351$	−1356.91	−0.206343
$352$	10310.4	1.56121
$353$	5586.17	0.842272	0.421136	−	0.906997i	$-0.361632\pi$
$353$	5586.17	0.842272	0.421136	+	0.906997i	$0.361632\pi$
$354$	−107.444	−0.0161316
$355$	12653.9	1.89183
$356$	−537.959	−0.0800892
$357$	0	0
$358$	−2586.06	−0.381781
$359$	8966.10	1.31814	0.659071	−	0.752081i	$-0.270950\pi$
$359$	8966.10	1.31814	0.659071	+	0.752081i	$0.270950\pi$
$360$	−3836.17	−0.561621
$361$	−5860.62	−0.854443
$362$	−3492.71	−0.507108
$363$	6521.44	0.942939
$364$	0	0
$365$	−1484.23	−0.212844
$366$	4919.77	0.702625
$367$	9315.68	1.32500	0.662499	−	0.749063i	$-0.269496\pi$
$367$	9315.68	1.32500	0.662499	+	0.749063i	$0.269496\pi$
$368$	188.491	0.0267005
$369$	−1395.47	−0.196871
$370$	−2832.33	−0.397961
$371$	0	0
$372$	−6593.91	−0.919027
$373$	3525.24	0.489357	0.244679	−	0.969604i	$-0.421318\pi$
$373$	3525.24	0.489357	0.244679	+	0.969604i	$0.421318\pi$
$374$	7543.63	1.04297
$375$	−2284.78	−0.314628
$376$	−2436.63	−0.334201
$377$	−2239.89	−0.305995
$378$	0	0
$379$	362.942	0.0491902	0.0245951	−	0.999697i	$-0.492170\pi$
$379$	362.942	0.0491902	0.0245951	+	0.999697i	$0.492170\pi$
$380$	2510.39	0.338895
$381$	9375.31	1.26066
$382$	494.595	0.0662453
$383$	11740.5	1.56634	0.783172	−	0.621805i	$-0.213600\pi$
$383$	11740.5	1.56634	0.783172	+	0.621805i	$0.213600\pi$
$384$	4420.49	0.587453
$385$	0	0
$386$	−5867.18	−0.773656
$387$	2380.28	0.312652
$388$	−1454.34	−0.190290
$389$	2578.30	0.336054	0.168027	−	0.985782i	$-0.446260\pi$
$389$	2578.30	0.336054	0.168027	+	0.985782i	$0.446260\pi$
$390$	−785.043	−0.101929
$391$	1585.97	0.205130
$392$	0	0
$393$	5492.45	0.704981
$394$	−1565.20	−0.200136
$395$	3730.21	0.475158
$396$	−3776.78	−0.479268
$397$	12101.3	1.52984	0.764920	−	0.644125i	$-0.222779\pi$
$397$	12101.3	1.52984	0.764920	+	0.644125i	$0.222779\pi$
$398$	3415.04	0.430102
$399$	0	0
$400$	859.209	0.107401
$401$	−14110.0	−1.75715	−0.878576	−	0.477602i	$-0.841506\pi$
$401$	−14110.0	−1.75715	−0.878576	+	0.477602i	$0.841506\pi$
$402$	1857.86	0.230501
$403$	2832.97	0.350174
$404$	−3049.70	−0.375565
$405$	−3435.55	−0.421515
$406$	0	0
$407$	−6843.00	−0.833403
$408$	7046.10	0.854985
$409$	8532.44	1.03154	0.515772	−	0.856726i	$-0.327505\pi$
$409$	8532.44	1.03154	0.515772	+	0.856726i	$0.327505\pi$
$410$	−2558.42	−0.308175
$411$	−3897.81	−0.467797
$412$	−3131.07	−0.374410
$413$	0	0
$414$	360.510	0.0427974
$415$	11412.7	1.34995
$416$	−1686.02	−0.198711
$417$	−9851.67	−1.15693
$418$	−2753.76	−0.322227
$419$	−1470.96	−0.171506	−0.0857530	−	0.996316i	$-0.527330\pi$
$419$	−1470.96	−0.171506	−0.0857530	+	0.996316i	$0.527330\pi$
$420$	0	0
$421$	−6995.13	−0.809790	−0.404895	−	0.914363i	$-0.632692\pi$
$421$	−6995.13	−0.809790	−0.404895	+	0.914363i	$0.632692\pi$
$422$	7.75554	0.000894630 0
$423$	1421.40	0.163383
$424$	14355.8	1.64429
$425$	7229.41	0.825124
$426$	−5283.24	−0.600877
$427$	0	0
$428$	−2238.40	−0.252798
$429$	−1896.69	−0.213457
$430$	4363.94	0.489414
$431$	−509.845	−0.0569800	−0.0284900	−	0.999594i	$-0.509070\pi$
$431$	−509.845	−0.0569800	−0.0284900	+	0.999594i	$0.509070\pi$
$432$	−1548.04	−0.172407
$433$	−3544.94	−0.393438	−0.196719	−	0.980460i	$-0.563029\pi$
$433$	−3544.94	−0.393438	−0.196719	+	0.980460i	$0.563029\pi$
$434$	0	0
$435$	−13683.2	−1.50818
$436$	−10454.4	−1.14834
$437$	−578.949	−0.0633750
$438$	619.692	0.0676028
$439$	−9934.63	−1.08008	−0.540039	−	0.841640i	$-0.681590\pi$
$439$	−9934.63	−1.08008	−0.540039	+	0.841640i	$0.681590\pi$
$440$	−16992.3	−1.84108
$441$	0	0
$442$	−1233.58	−0.132750
$443$	2519.19	0.270181	0.135091	−	0.990833i	$-0.456867\pi$
$443$	2519.19	0.270181	0.135091	+	0.990833i	$0.456867\pi$
$444$	−2604.56	−0.278395
$445$	1411.91	0.150407
$446$	4622.16	0.490730
$447$	−8467.95	−0.896018
$448$	0	0
$449$	7811.30	0.821020	0.410510	−	0.911856i	$-0.365351\pi$
$449$	7811.30	0.821020	0.410510	+	0.911856i	$0.365351\pi$
$450$	1643.33	0.172150
$451$	−6181.25	−0.645374
$452$	75.6008	0.00786717
$453$	8659.50	0.898143
$454$	−7767.46	−0.802962
$455$	0	0
$456$	−2572.14	−0.264148
$457$	−3364.01	−0.344336	−0.172168	−	0.985068i	$-0.555077\pi$
$457$	−3364.01	−0.344336	−0.172168	+	0.985068i	$0.555077\pi$
$458$	−4251.71	−0.433776
$459$	−13025.2	−1.32454
$460$	−1455.75	−0.147553
$461$	−11576.5	−1.16957	−0.584783	−	0.811190i	$-0.698820\pi$
$461$	−11576.5	−1.16957	−0.584783	+	0.811190i	$0.698820\pi$
$462$	0	0
$463$	19340.8	1.94135	0.970675	−	0.240396i	$-0.0772773\pi$
$463$	19340.8	1.94135	0.970675	+	0.240396i	$0.0772773\pi$
$464$	−2555.39	−0.255671
$465$	17306.2	1.72593
$466$	5240.51	0.520949
$467$	8149.45	0.807519	0.403760	−	0.914865i	$-0.367703\pi$
$467$	8149.45	0.807519	0.403760	+	0.914865i	$0.367703\pi$
$468$	617.602	0.0610014
$469$	0	0
$470$	2605.96	0.255753
$471$	919.867	0.0899899
$472$	380.302	0.0370865
$473$	10543.4	1.02492
$474$	−1557.43	−0.150918
$475$	−2639.06	−0.254923
$476$	0	0
$477$	−8374.43	−0.803855
$478$	−5559.52	−0.531980
$479$	−9017.39	−0.860157	−0.430078	−	0.902792i	$-0.641514\pi$
$479$	−9017.39	−0.860157	−0.430078	+	0.902792i	$0.641514\pi$
$480$	−10299.6	−0.979400
$481$	1119.01	0.106076
$482$	−8159.70	−0.771088
$483$	0	0
$484$	−9406.12	−0.883369
$485$	3817.01	0.357364
$486$	−4987.26	−0.465487
$487$	12683.5	1.18017	0.590085	−	0.807341i	$-0.299094\pi$
$487$	12683.5	1.18017	0.590085	+	0.807341i	$0.299094\pi$
$488$	−17413.7	−1.61533
$489$	−1905.44	−0.176210
$490$	0	0
$491$	−2782.31	−0.255731	−0.127865	−	0.991792i	$-0.540813\pi$
$491$	−2782.31	−0.255731	−0.127865	+	0.991792i	$0.540813\pi$
$492$	−2352.69	−0.215584
$493$	−21501.1	−1.96422
$494$	450.313	0.0410132
$495$	9912.43	0.900061
$496$	3232.01	0.292584
$497$	0	0
$498$	−4765.02	−0.428766
$499$	−1479.46	−0.132725	−0.0663624	−	0.997796i	$-0.521139\pi$
$499$	−1479.46	−0.132725	−0.0663624	+	0.997796i	$0.521139\pi$
$500$	3295.42	0.294751
$501$	−6475.63	−0.577465
$502$	−1041.93	−0.0926365
$503$	−523.953	−0.0464452	−0.0232226	−	0.999730i	$-0.507393\pi$
$503$	−523.953	−0.0464452	−0.0232226	+	0.999730i	$0.507393\pi$
$504$	0	0
$505$	8004.17	0.705309
$506$	1596.88	0.140296
$507$	−8070.55	−0.706954
$508$	−13522.4	−1.18102
$509$	2333.80	0.203230	0.101615	−	0.994824i	$-0.467599\pi$
$509$	2333.80	0.203230	0.101615	+	0.994824i	$0.467599\pi$
$510$	−7535.77	−0.654294
$511$	0	0
$512$	−3679.74	−0.317623
$513$	4754.78	0.409218
$514$	3419.30	0.293422
$515$	8217.73	0.703139
$516$	4013.01	0.342370
$517$	6296.10	0.535594
$518$	0	0
$519$	1093.95	0.0925222
$520$	2778.69	0.234334
$521$	−3655.45	−0.307386	−0.153693	−	0.988119i	$-0.549117\pi$
$521$	−3655.45	−0.307386	−0.153693	+	0.988119i	$0.549117\pi$
$522$	−4887.48	−0.409807
$523$	13785.6	1.15259	0.576293	−	0.817243i	$-0.304499\pi$
$523$	13785.6	1.15259	0.576293	+	0.817243i	$0.304499\pi$
$524$	−7921.96	−0.660444
$525$	0	0
$526$	8198.44	0.679599
$527$	27194.2	2.24781
$528$	−2163.85	−0.178351
$529$	−11831.3	−0.972407
$530$	−15353.5	−1.25832
$531$	−221.849	−0.0181307
$532$	0	0
$533$	1010.80	0.0821434
$534$	−589.498	−0.0477716
$535$	5874.86	0.474752
$536$	−6575.95	−0.529921
$537$	6241.51	0.501567
$538$	8574.89	0.687156
$539$	0	0
$540$	11955.7	0.952766
$541$	19752.8	1.56976	0.784878	−	0.619650i	$-0.212726\pi$
$541$	19752.8	1.56976	0.784878	+	0.619650i	$0.212726\pi$
$542$	11034.9	0.874522
$543$	8429.73	0.666215
$544$	−16184.4	−1.27555
$545$	27438.3	2.15657
$546$	0	0
$547$	−5603.16	−0.437978	−0.218989	−	0.975727i	$-0.570276\pi$
$547$	−5603.16	−0.437978	−0.218989	+	0.975727i	$0.570276\pi$
$548$	5621.95	0.438244
$549$	10158.3	0.789698
$550$	7279.15	0.564334
$551$	7848.88	0.606848
$552$	1491.56	0.115009
$553$	0	0
$554$	−3881.41	−0.297663
$555$	6835.87	0.522823
$556$	14209.4	1.08384
$557$	21306.8	1.62082	0.810411	−	0.585861i	$-0.199244\pi$
$557$	21306.8	1.62082	0.810411	+	0.585861i	$0.199244\pi$
$558$	6181.58	0.468973
$559$	−1724.13	−0.130452
$560$	0	0
$561$	−18206.7	−1.37021
$562$	−8387.78	−0.629568
$563$	7153.19	0.535472	0.267736	−	0.963492i	$-0.413724\pi$
$563$	7153.19	0.535472	0.267736	+	0.963492i	$0.413724\pi$
$564$	2396.41	0.178913
$565$	−198.420	−0.0147745
$566$	−6517.26	−0.483994
$567$	0	0
$568$	18700.2	1.38141
$569$	−3028.64	−0.223141	−0.111570	−	0.993757i	$-0.535588\pi$
$569$	−3028.64	−0.223141	−0.111570	+	0.993757i	$0.535588\pi$
$570$	2750.89	0.202144
$571$	8039.89	0.589245	0.294622	−	0.955614i	$-0.404806\pi$
$571$	8039.89	0.589245	0.294622	+	0.955614i	$0.404806\pi$
$572$	2735.67	0.199972
$573$	−1193.72	−0.0870300
$574$	0	0
$575$	1530.36	0.110992
$576$	−2654.41	−0.192015
$577$	17091.9	1.23318	0.616591	−	0.787283i	$-0.288513\pi$
$577$	17091.9	1.23318	0.616591	+	0.787283i	$0.288513\pi$
$578$	−4076.30	−0.293342
$579$	14160.5	1.01639
$580$	19735.7	1.41290
$581$	0	0
$582$	−1593.67	−0.113505
$583$	−37094.5	−2.63516
$584$	−2193.42	−0.155419
$585$	−1620.94	−0.114560
$586$	894.689	0.0630704
$587$	6471.23	0.455019	0.227509	−	0.973776i	$-0.426942\pi$
$587$	6471.23	0.455019	0.227509	+	0.973776i	$0.426942\pi$
$588$	0	0
$589$	−9927.10	−0.694464
$590$	−406.731	−0.0283811
$591$	3777.63	0.262929
$592$	1276.63	0.0886303
$593$	21.4337	0.00148428	0.000742138	−	1.00000i	$-0.499764\pi$
$593$	21.4337	0.00148428	0.000742138		1.00000i	$0.499764\pi$
$594$	−13114.8	−0.905906
$595$	0	0
$596$	12213.6	0.839413
$597$	−8242.26	−0.565047
$598$	−261.132	−0.0178570
$599$	−2852.49	−0.194574	−0.0972869	−	0.995256i	$-0.531016\pi$
$599$	−2852.49	−0.194574	−0.0972869	+	0.995256i	$0.531016\pi$
$600$	6799.05	0.462617
$601$	−6077.01	−0.412456	−0.206228	−	0.978504i	$-0.566119\pi$
$601$	−6077.01	−0.412456	−0.206228	+	0.978504i	$0.566119\pi$
$602$	0	0
$603$	3836.07	0.259066
$604$	−12489.9	−0.841403
$605$	24687.0	1.65896
$606$	−3341.88	−0.224017
$607$	−2920.27	−0.195272	−0.0976361	−	0.995222i	$-0.531128\pi$
$607$	−2920.27	−0.195272	−0.0976361	+	0.995222i	$0.531128\pi$
$608$	5908.03	0.394082
$609$	0	0
$610$	18623.9	1.23616
$611$	−1029.58	−0.0681706
$612$	5928.48	0.391576
$613$	12529.6	0.825556	0.412778	−	0.910832i	$-0.364559\pi$
$613$	12529.6	0.825556	0.412778	+	0.910832i	$0.364559\pi$
$614$	−15082.3	−0.991320
$615$	6174.81	0.404865
$616$	0	0
$617$	15986.7	1.04311	0.521557	−	0.853216i	$-0.325351\pi$
$617$	15986.7	1.04311	0.521557	+	0.853216i	$0.325351\pi$
$618$	−3431.04	−0.223328
$619$	−7317.11	−0.475120	−0.237560	−	0.971373i	$-0.576348\pi$
$619$	−7317.11	−0.475120	−0.237560	+	0.971373i	$0.576348\pi$
$620$	−24961.4	−1.61689
$621$	−2757.25	−0.178172
$622$	−11683.2	−0.753139
$623$	0	0
$624$	353.847	0.0227006
$625$	−19089.3	−1.22172
$626$	5789.30	0.369628
$627$	6646.26	0.423327
$628$	−1326.76	−0.0843048
$629$	10741.6	0.680915
$630$	0	0
$631$	19410.9	1.22462	0.612310	−	0.790618i	$-0.290240\pi$
$631$	19410.9	1.22462	0.612310	+	0.790618i	$0.290240\pi$
$632$	5512.57	0.346959
$633$	−18.7181	−0.00117532
$634$	14226.9	0.891203
$635$	35490.4	2.21794
$636$	−14118.8	−0.880263
$637$	0	0
$638$	−21649.1	−1.34341
$639$	−10908.7	−0.675341
$640$	16733.8	1.03354
$641$	9515.17	0.586313	0.293156	−	0.956064i	$-0.405294\pi$
$641$	9515.17	0.586313	0.293156	+	0.956064i	$0.405294\pi$
$642$	−2452.85	−0.150789
$643$	−23936.7	−1.46807	−0.734036	−	0.679110i	$-0.762366\pi$
$643$	−23936.7	−1.46807	−0.734036	+	0.679110i	$0.762366\pi$
$644$	0	0
$645$	−10532.5	−0.642969
$646$	4322.64	0.263269
$647$	24129.2	1.46618	0.733090	−	0.680132i	$-0.238077\pi$
$647$	24129.2	1.46618	0.733090	+	0.680132i	$0.238077\pi$
$648$	−5077.11	−0.307790
$649$	−982.678	−0.0594352
$650$	−1190.33	−0.0718287
$651$	0	0
$652$	2748.28	0.165078
$653$	−3682.09	−0.220661	−0.110330	−	0.993895i	$-0.535191\pi$
$653$	−3682.09	−0.220661	−0.110330	+	0.993895i	$0.535191\pi$
$654$	−11456.0	−0.684960
$655$	20791.8	1.24031
$656$	1153.17	0.0686339
$657$	1279.53	0.0759805
$658$	0	0
$659$	−6202.85	−0.366660	−0.183330	−	0.983051i	$-0.558688\pi$
$659$	−6202.85	−0.366660	−0.183330	+	0.983051i	$0.558688\pi$
$660$	16711.8	0.985615
$661$	−21930.1	−1.29044	−0.645221	−	0.763996i	$-0.723235\pi$
$661$	−21930.1	−1.29044	−0.645221	+	0.763996i	$0.723235\pi$
$662$	−6087.20	−0.357380
$663$	2977.27	0.174401
$664$	16865.9	0.985731
$665$	0	0
$666$	2441.70	0.142063
$667$	−4551.48	−0.264219
$668$	9340.05	0.540984
$669$	−11155.7	−0.644699
$670$	7032.95	0.405532
$671$	44996.0	2.58875
$672$	0	0
$673$	−6260.49	−0.358580	−0.179290	−	0.983796i	$-0.557380\pi$
$673$	−6260.49	−0.358580	−0.179290	+	0.983796i	$0.557380\pi$
$674$	−2286.32	−0.130661
$675$	−12568.5	−0.716686
$676$	11640.4	0.662292
$677$	−20425.0	−1.15952	−0.579760	−	0.814787i	$-0.696854\pi$
$677$	−20425.0	−1.15952	−0.579760	+	0.814787i	$0.696854\pi$
$678$	82.8437	0.00469262
$679$	0	0
$680$	26673.1	1.50422
$681$	18746.9	1.05489
$682$	27381.3	1.53737
$683$	−13180.1	−0.738393	−0.369197	−	0.929351i	$-0.620367\pi$
$683$	−13180.1	−0.738393	−0.369197	+	0.929351i	$0.620367\pi$
$684$	−2164.16	−0.120978
$685$	−14755.2	−0.823019
$686$	0	0
$687$	10261.6	0.569874
$688$	−1966.98	−0.108998
$689$	6065.93	0.335404
$690$	−1595.22	−0.0880128
$691$	9750.91	0.536819	0.268410	−	0.963305i	$-0.413502\pi$
$691$	9750.91	0.536819	0.268410	+	0.963305i	$0.413502\pi$
$692$	−1577.84	−0.0866771
$693$	0	0
$694$	−11324.0	−0.619384
$695$	−37293.7	−2.03544
$696$	−20221.2	−1.10127
$697$	9702.83	0.527289
$698$	−11821.5	−0.641044
$699$	−12648.1	−0.684398
$700$	0	0
$701$	21494.3	1.15810	0.579049	−	0.815292i	$-0.303424\pi$
$701$	21494.3	1.15810	0.579049	+	0.815292i	$0.303424\pi$
$702$	2144.62	0.115304
$703$	−3921.16	−0.210369
$704$	−11757.7	−0.629454
$705$	−6289.54	−0.335997
$706$	−8829.06	−0.470660
$707$	0	0
$708$	−374.024	−0.0198541
$709$	−35430.8	−1.87677	−0.938385	−	0.345591i	$-0.887678\pi$
$709$	−35430.8	−1.87677	−0.938385	+	0.345591i	$0.887678\pi$
$710$	−19999.8	−1.05715
$711$	−3215.75	−0.169620
$712$	2086.55	0.109827
$713$	5756.62	0.302366
$714$	0	0
$715$	−7179.96	−0.375546
$716$	−9002.37	−0.469880
$717$	13418.0	0.698891
$718$	−14171.1	−0.736575
$719$	189.810	0.00984524	0.00492262	−	0.999988i	$-0.498433\pi$
$719$	189.810	0.00984524	0.00492262	+	0.999988i	$0.498433\pi$
$720$	−1849.26	−0.0957193
$721$	0	0
$722$	9262.83	0.477461
$723$	19693.6	1.01302
$724$	−12158.5	−0.624127
$725$	−20747.3	−1.06281
$726$	−10307.3	−0.526913
$727$	14299.5	0.729490	0.364745	−	0.931107i	$-0.381156\pi$
$727$	14299.5	0.729490	0.364745	+	0.931107i	$0.381156\pi$
$728$	0	0
$729$	18460.5	0.937891
$730$	2345.86	0.118937
$731$	−16550.2	−0.837391
$732$	17126.3	0.864761
$733$	31458.9	1.58521	0.792606	−	0.609734i	$-0.208724\pi$
$733$	31458.9	1.58521	0.792606	+	0.609734i	$0.208724\pi$
$734$	−14723.6	−0.740406
$735$	0	0
$736$	−3426.01	−0.171582
$737$	16991.9	0.849258
$738$	2205.57	0.110011
$739$	28862.9	1.43672	0.718362	−	0.695670i	$-0.244892\pi$
$739$	28862.9	1.43672	0.718362	+	0.695670i	$0.244892\pi$
$740$	−9859.63	−0.489793
$741$	−1086.84	−0.0538812
$742$	0	0
$743$	5568.01	0.274926	0.137463	−	0.990507i	$-0.456105\pi$
$743$	5568.01	0.274926	0.137463	+	0.990507i	$0.456105\pi$
$744$	25575.4	1.26027
$745$	−32055.6	−1.57641
$746$	−5571.72	−0.273452
$747$	−9838.72	−0.481901
$748$	26260.2	1.28365
$749$	0	0
$750$	3611.13	0.175813
$751$	−4252.62	−0.206632	−0.103316	−	0.994649i	$-0.532945\pi$
$751$	−4252.62	−0.206632	−0.103316	+	0.994649i	$0.532945\pi$
$752$	−1174.60	−0.0569591
$753$	2514.71	0.121701
$754$	3540.19	0.170990
$755$	32780.7	1.58015
$756$	0	0
$757$	−7252.08	−0.348192	−0.174096	−	0.984729i	$-0.555700\pi$
$757$	−7252.08	−0.348192	−0.174096	+	0.984729i	$0.555700\pi$
$758$	−573.637	−0.0274874
$759$	−3854.10	−0.184315
$760$	−9736.88	−0.464729
$761$	5472.42	0.260677	0.130338	−	0.991470i	$-0.458394\pi$
$761$	5472.42	0.260677	0.130338	+	0.991470i	$0.458394\pi$
$762$	−14817.9	−0.704455
$763$	0	0
$764$	1721.74	0.0815319
$765$	−15559.7	−0.735377
$766$	−18556.0	−0.875270
$767$	160.694	0.00756494
$768$	−13493.7	−0.634001
$769$	−9056.52	−0.424690	−0.212345	−	0.977195i	$-0.568110\pi$
$769$	−9056.52	−0.424690	−0.212345	+	0.977195i	$0.568110\pi$
$770$	0	0
$771$	−8252.55	−0.385484
$772$	−20424.3	−0.952183
$773$	−10981.6	−0.510970	−0.255485	−	0.966813i	$-0.582235\pi$
$773$	−10981.6	−0.510970	−0.255485	+	0.966813i	$0.582235\pi$
$774$	−3762.07	−0.174709
$775$	26240.8	1.21625
$776$	5640.84	0.260946
$777$	0	0
$778$	−4075.05	−0.187786
$779$	−3541.96	−0.162906
$780$	−2732.82	−0.125449
$781$	−48320.2	−2.21387
$782$	−2506.65	−0.114626
$783$	37380.4	1.70609
$784$	0	0
$785$	3482.17	0.158324
$786$	−8680.92	−0.393942
$787$	−33905.2	−1.53569	−0.767845	−	0.640636i	$-0.778671\pi$
$787$	−33905.2	−1.53569	−0.767845	+	0.640636i	$0.778671\pi$
$788$	−5448.62	−0.246319
$789$	−19787.1	−0.892826
$790$	−5895.67	−0.265517
$791$	0	0
$792$	14648.7	0.657223
$793$	−7358.03	−0.329497
$794$	−19126.3	−0.854871
$795$	37055.9	1.65313
$796$	11888.1	0.529351
$797$	−37396.5	−1.66205	−0.831024	−	0.556236i	$-0.812245\pi$
$797$	−37396.5	−1.66205	−0.831024	+	0.556236i	$0.812245\pi$
$798$	0	0
$799$	−9883.11	−0.437596
$800$	−15617.0	−0.690179
$801$	−1217.18	−0.0536918
$802$	22301.1	0.981893
$803$	5667.67	0.249076
$804$	6467.40	0.283691
$805$	0	0
$806$	−4477.56	−0.195677
$807$	−20695.7	−0.902753
$808$	11828.7	0.515015
$809$	−35306.4	−1.53437	−0.767187	−	0.641424i	$-0.778344\pi$
$809$	−35306.4	−1.53437	−0.767187	+	0.641424i	$0.778344\pi$
$810$	5429.95	0.235542
$811$	−23080.1	−0.999324	−0.499662	−	0.866220i	$-0.666542\pi$
$811$	−23080.1	−0.999324	−0.499662	+	0.866220i	$0.666542\pi$
$812$	0	0
$813$	−26633.0	−1.14891
$814$	10815.5	0.465704
$815$	−7213.06	−0.310015
$816$	3396.64	0.145718
$817$	6041.58	0.258712
$818$	−13485.7	−0.576425
$819$	0	0
$820$	−8906.15	−0.379288
$821$	−14226.2	−0.604748	−0.302374	−	0.953189i	$-0.597779\pi$
$821$	−14226.2	−0.604748	−0.302374	+	0.953189i	$0.597779\pi$
$822$	6160.56	0.261404
$823$	11931.6	0.505358	0.252679	−	0.967550i	$-0.418688\pi$
$823$	11931.6	0.505358	0.252679	+	0.967550i	$0.418688\pi$
$824$	12144.3	0.513430
$825$	−17568.4	−0.741396
$826$	0	0
$827$	−16078.2	−0.676050	−0.338025	−	0.941137i	$-0.609759\pi$
$827$	−16078.2	−0.676050	−0.338025	+	0.941137i	$0.609759\pi$
$828$	1254.97	0.0526732
$829$	−33417.5	−1.40004	−0.700022	−	0.714121i	$-0.746826\pi$
$829$	−33417.5	−1.40004	−0.700022	+	0.714121i	$0.746826\pi$
$830$	−18038.1	−0.754350
$831$	9367.86	0.391056
$832$	1922.70	0.0801172
$833$	0	0
$834$	15570.8	0.646489
$835$	−24513.6	−1.01596
$836$	−9586.14	−0.396583
$837$	−47277.9	−1.95241
$838$	2324.88	0.0958372
$839$	3301.41	0.135849	0.0679246	−	0.997690i	$-0.478362\pi$
$839$	3301.41	0.135849	0.0679246	+	0.997690i	$0.478362\pi$
$840$	0	0
$841$	37316.0	1.53003
$842$	11055.9	0.452509
$843$	20244.1	0.827097
$844$	26.9979	0.00110107
$845$	−30551.2	−1.24378
$846$	−2246.55	−0.0912980
$847$	0	0
$848$	6920.35	0.280243
$849$	15729.5	0.635849
$850$	−11426.2	−0.461078
$851$	2273.84	0.0915937
$852$	−18391.5	−0.739534
$853$	−24780.7	−0.994696	−0.497348	−	0.867551i	$-0.665693\pi$
$853$	−24780.7	−0.994696	−0.497348	+	0.867551i	$0.665693\pi$
$854$	0	0
$855$	5680.00	0.227195
$856$	8681.96	0.346663
$857$	−14120.8	−0.562845	−0.281422	−	0.959584i	$-0.590806\pi$
$857$	−14120.8	−0.562845	−0.281422	+	0.959584i	$0.590806\pi$
$858$	2997.76	0.119279
$859$	−7454.92	−0.296110	−0.148055	−	0.988979i	$-0.547301\pi$
$859$	−7454.92	−0.296110	−0.148055	+	0.988979i	$0.547301\pi$
$860$	15191.3	0.602349
$861$	0	0
$862$	805.821	0.0318403
$863$	−8314.15	−0.327945	−0.163973	−	0.986465i	$-0.552431\pi$
$863$	−8314.15	−0.327945	−0.163973	+	0.986465i	$0.552431\pi$
$864$	28137.1	1.10792
$865$	4141.16	0.162779
$866$	5602.84	0.219853
$867$	9838.22	0.385379
$868$	0	0
$869$	−14244.2	−0.556041
$870$	21626.5	0.842767
$871$	−2778.62	−0.108094
$872$	40548.8	1.57472
$873$	−3290.58	−0.127571
$874$	915.040	0.0354138
$875$	0	0
$876$	2157.21	0.0832027
$877$	40724.7	1.56804	0.784022	−	0.620733i	$-0.213165\pi$
$877$	40724.7	1.56804	0.784022	+	0.620733i	$0.213165\pi$
$878$	15701.9	0.603545
$879$	−2159.35	−0.0828590
$880$	−8191.30	−0.313783
$881$	38718.7	1.48067	0.740333	−	0.672240i	$-0.234668\pi$
$881$	38718.7	1.48067	0.740333	+	0.672240i	$0.234668\pi$
$882$	0	0
$883$	31082.3	1.18460	0.592300	−	0.805718i	$-0.298220\pi$
$883$	31082.3	1.18460	0.592300	+	0.805718i	$0.298220\pi$
$884$	−4294.23	−0.163383
$885$	981.654	0.0372858
$886$	−3981.62	−0.150977
$887$	−9484.75	−0.359038	−0.179519	−	0.983755i	$-0.557454\pi$
$887$	−9484.75	−0.359038	−0.179519	+	0.983755i	$0.557454\pi$
$888$	10102.2	0.381764
$889$	0	0
$890$	−2231.55	−0.0840471
$891$	13119.0	0.493268
$892$	16090.2	0.603970
$893$	3607.78	0.135196
$894$	13383.8	0.500693
$895$	23627.4	0.882431
$896$	0	0
$897$	630.246	0.0234597
$898$	−12345.9	−0.458785
$899$	−78043.2	−2.89531
$900$	5720.62	0.211875
$901$	58228.0	2.15300
$902$	9769.58	0.360634
$903$	0	0
$904$	−293.228	−0.0107883
$905$	31910.9	1.17210
$906$	−13686.5	−0.501881
$907$	−4966.32	−0.181812	−0.0909062	−	0.995859i	$-0.528976\pi$
$907$	−4966.32	−0.181812	−0.0909062	+	0.995859i	$0.528976\pi$
$908$	−27039.3	−0.988251
$909$	−6900.25	−0.251779
$910$	0	0
$911$	−7487.17	−0.272295	−0.136148	−	0.990689i	$-0.543472\pi$
$911$	−7487.17	−0.272295	−0.136148	+	0.990689i	$0.543472\pi$
$912$	−1239.93	−0.0450198
$913$	−43580.6	−1.57975
$914$	5316.88	0.192415
$915$	−44949.1	−1.62401
$916$	−14800.7	−0.533873
$917$	0	0
$918$	20586.6	0.740152
$919$	−23157.1	−0.831211	−0.415605	−	0.909545i	$-0.636430\pi$
$919$	−23157.1	−0.831211	−0.415605	+	0.909545i	$0.636430\pi$
$920$	5646.32	0.202341
$921$	36401.3	1.30235
$922$	18296.8	0.653551
$923$	7901.63	0.281782
$924$	0	0
$925$	10365.0	0.368431
$926$	−30568.6	−1.08482
$927$	−7084.36	−0.251004
$928$	46446.7	1.64298
$929$	−40012.3	−1.41309	−0.706546	−	0.707668i	$-0.749747\pi$
$929$	−40012.3	−1.41309	−0.706546	+	0.707668i	$0.749747\pi$
$930$	−27352.8	−0.964444
$931$	0	0
$932$	18242.8	0.641162
$933$	28197.5	0.989438
$934$	−12880.4	−0.451240
$935$	−68921.8	−2.41068
$936$	−2395.46	−0.0836516
$937$	−19420.9	−0.677112	−0.338556	−	0.940946i	$-0.609938\pi$
$937$	−19420.9	−0.677112	−0.338556	+	0.940946i	$0.609938\pi$
$938$	0	0
$939$	−13972.6	−0.485600
$940$	9071.64	0.314770
$941$	−15910.0	−0.551170	−0.275585	−	0.961277i	$-0.588872\pi$
$941$	−15910.0	−0.551170	−0.275585	+	0.961277i	$0.588872\pi$
$942$	−1453.87	−0.0502862
$943$	2053.95	0.0709287
$944$	183.328	0.00632079
$945$	0	0
$946$	−16664.1	−0.572724
$947$	43869.2	1.50534	0.752669	−	0.658399i	$-0.228766\pi$
$947$	43869.2	1.50534	0.752669	+	0.658399i	$0.228766\pi$
$948$	−5421.57	−0.185743
$949$	−926.814	−0.0317025
$950$	4171.08	0.142450
$951$	−34336.9	−1.17082
$952$	0	0
$953$	−1754.15	−0.0596247	−0.0298124	−	0.999556i	$-0.509491\pi$
$953$	−1754.15	−0.0596247	−0.0298124	+	0.999556i	$0.509491\pi$
$954$	13235.9	0.449192
$955$	−4518.83	−0.153116
$956$	−19353.3	−0.654739
$957$	52250.4	1.76491
$958$	14252.2	0.480654
$959$	0	0
$960$	11745.5	0.394879
$961$	68916.5	2.31333
$962$	−1768.62	−0.0592750
$963$	−5064.61	−0.169475
$964$	−28404.8	−0.949022
$965$	53605.0	1.78819
$966$	0	0
$967$	−17600.1	−0.585295	−0.292648	−	0.956220i	$-0.594536\pi$
$967$	−17600.1	−0.585295	−0.292648	+	0.956220i	$0.594536\pi$
$968$	36482.9	1.21137
$969$	−10432.8	−0.345871
$970$	−6032.86	−0.199694
$971$	−29049.1	−0.960073	−0.480037	−	0.877248i	$-0.659377\pi$
$971$	−29049.1	−0.960073	−0.480037	+	0.877248i	$0.659377\pi$
$972$	−17361.2	−0.572901
$973$	0	0
$974$	−20046.5	−0.659477
$975$	2872.89	0.0943652
$976$	−8394.45	−0.275307
$977$	48712.4	1.59514	0.797568	−	0.603229i	$-0.206119\pi$
$977$	48712.4	1.59514	0.797568	+	0.603229i	$0.206119\pi$
$978$	3011.58	0.0984659
$979$	−5391.52	−0.176010
$980$	0	0
$981$	−23654.1	−0.769844
$982$	4397.49	0.142902
$983$	30781.8	0.998768	0.499384	−	0.866381i	$-0.333560\pi$
$983$	30781.8	0.998768	0.499384	+	0.866381i	$0.333560\pi$
$984$	9125.23	0.295632
$985$	14300.3	0.462584
$986$	33983.0	1.09760
$987$	0	0
$988$	1567.59	0.0504773
$989$	−3503.45	−0.112642
$990$	−15666.8	−0.502953
$991$	8740.91	0.280186	0.140093	−	0.990138i	$-0.455260\pi$
$991$	8740.91	0.280186	0.140093	+	0.990138i	$0.455260\pi$
$992$	−58744.9	−1.88019
$993$	14691.6	0.469509
$994$	0	0
$995$	−31201.2	−0.994116
$996$	−16587.5	−0.527707
$997$	42406.4	1.34707	0.673533	−	0.739157i	$-0.264776\pi$
$997$	42406.4	1.34707	0.673533	+	0.739157i	$0.264776\pi$
$998$	2338.32	0.0741664
$999$	−18674.6	−0.591429

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2401.4.a.d.1.16		39
7.6	odd	2		2401.4.a.c.1.16		39
49.15	even	7		49.4.e.a.29.8	yes	78
49.36	even	7		49.4.e.a.22.8	✓	78

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.4.e.a.22.8	✓	78	49.36	even	7
49.4.e.a.29.8	yes	78	49.15	even	7
2401.4.a.c.1.16		39	7.6	odd	2
2401.4.a.d.1.16		39	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:	\( N \)	\(=\)	\( 2401 = 7^{4} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2401.a (trivial)

\(f(q)\)	\(=\)	\(q-1.58052 q^{2} +3.81461 q^{3} -5.50196 q^{4} +14.4403 q^{5} -6.02907 q^{6} +21.3401 q^{8} -12.4487 q^{9} +O(q^{10})\)	\(q-1.58052 q^{2} +3.81461 q^{3} -5.50196 q^{4} +14.4403 q^{5} -6.02907 q^{6} +21.3401 q^{8} -12.4487 q^{9} -22.8232 q^{10} -55.1416 q^{11} -20.9878 q^{12} +9.01710 q^{13} +55.0841 q^{15} +10.2872 q^{16} +86.5568 q^{17} +19.6754 q^{18} -31.5971 q^{19} -79.4499 q^{20} +87.1524 q^{22} +18.3228 q^{23} +81.4043 q^{24} +83.5221 q^{25} -14.2517 q^{26} -150.482 q^{27} -248.405 q^{29} -87.0616 q^{30} +314.177 q^{31} -186.980 q^{32} -210.344 q^{33} -136.805 q^{34} +68.4923 q^{36} +124.099 q^{37} +49.9398 q^{38} +34.3968 q^{39} +308.157 q^{40} +112.098 q^{41} -191.207 q^{43} +303.387 q^{44} -179.763 q^{45} -28.9596 q^{46} -114.181 q^{47} +39.2417 q^{48} -132.008 q^{50} +330.181 q^{51} -49.6117 q^{52} +672.714 q^{53} +237.839 q^{54} -796.261 q^{55} -120.531 q^{57} +392.609 q^{58} +17.8210 q^{59} -303.071 q^{60} -816.008 q^{61} -496.564 q^{62} +213.228 q^{64} +130.210 q^{65} +332.453 q^{66} -308.150 q^{67} -476.232 q^{68} +69.8946 q^{69} +876.294 q^{71} -265.657 q^{72} -102.784 q^{73} -196.140 q^{74} +318.604 q^{75} +173.846 q^{76} -54.3647 q^{78} +258.320 q^{79} +148.550 q^{80} -237.914 q^{81} -177.173 q^{82} +790.340 q^{83} +1249.91 q^{85} +302.206 q^{86} -947.569 q^{87} -1176.73 q^{88} +97.7759 q^{89} +284.119 q^{90} -100.812 q^{92} +1198.47 q^{93} +180.465 q^{94} -456.272 q^{95} -713.257 q^{96} +264.331 q^{97} +686.442 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q + q^{2} + q^{3} + 145 q^{4} + 27 q^{5} + 41 q^{6} - 12 q^{8} + 312 q^{9}+O(q^{10}) \) 39 * q + q^2 + q^3 + 145 * q^4 + 27 * q^5 + 41 * q^6 - 12 * q^8 + 312 * q^9	\( 39 q + q^{2} + q^{3} + 145 q^{4} + 27 q^{5} + 41 q^{6} - 12 q^{8} + 312 q^{9} + 78 q^{10} + q^{11} - 91 q^{12} + 77 q^{13} - 161 q^{15} + 461 q^{16} + 211 q^{17} + 8 q^{18} + 314 q^{19} + 476 q^{20} - 61 q^{22} - 69 q^{23} + 330 q^{24} + 606 q^{25} + 504 q^{26} - 50 q^{27} + 57 q^{29} + 42 q^{30} + 638 q^{31} - 1600 q^{32} + 1574 q^{33} + 1343 q^{34} + 782 q^{36} + 71 q^{37} + 1359 q^{38} - 84 q^{39} - 155 q^{40} + 1393 q^{41} - 125 q^{43} + 52 q^{44} + 1129 q^{45} - 1454 q^{46} + 1483 q^{47} - 974 q^{48} + 3074 q^{50} - 2044 q^{51} + 3899 q^{52} + 2213 q^{53} + 1142 q^{54} + 1604 q^{55} + 98 q^{57} + 2403 q^{58} + 2073 q^{59} - 1519 q^{60} + 2575 q^{61} + 1742 q^{62} + 1358 q^{64} + 1876 q^{65} - 48 q^{66} + 176 q^{67} + 3038 q^{68} - 638 q^{69} - 1259 q^{71} - 3799 q^{72} - 307 q^{73} + 3845 q^{74} + 131 q^{75} + 1974 q^{76} - 6041 q^{78} + 22 q^{79} - 804 q^{80} + 795 q^{81} + 8043 q^{82} + 6349 q^{83} + 3094 q^{85} + 1745 q^{86} + 9508 q^{87} + 1299 q^{88} + 2253 q^{89} + 11156 q^{90} + 1284 q^{92} - 3430 q^{93} + 2738 q^{94} - 3290 q^{95} + 3031 q^{96} - 770 q^{97} + 5384 q^{99}+O(q^{100}) \) 39 * q + q^2 + q^3 + 145 * q^4 + 27 * q^5 + 41 * q^6 - 12 * q^8 + 312 * q^9 + 78 * q^10 + q^11 - 91 * q^12 + 77 * q^13 - 161 * q^15 + 461 * q^16 + 211 * q^17 + 8 * q^18 + 314 * q^19 + 476 * q^20 - 61 * q^22 - 69 * q^23 + 330 * q^24 + 606 * q^25 + 504 * q^26 - 50 * q^27 + 57 * q^29 + 42 * q^30 + 638 * q^31 - 1600 * q^32 + 1574 * q^33 + 1343 * q^34 + 782 * q^36 + 71 * q^37 + 1359 * q^38 - 84 * q^39 - 155 * q^40 + 1393 * q^41 - 125 * q^43 + 52 * q^44 + 1129 * q^45 - 1454 * q^46 + 1483 * q^47 - 974 * q^48 + 3074 * q^50 - 2044 * q^51 + 3899 * q^52 + 2213 * q^53 + 1142 * q^54 + 1604 * q^55 + 98 * q^57 + 2403 * q^58 + 2073 * q^59 - 1519 * q^60 + 2575 * q^61 + 1742 * q^62 + 1358 * q^64 + 1876 * q^65 - 48 * q^66 + 176 * q^67 + 3038 * q^68 - 638 * q^69 - 1259 * q^71 - 3799 * q^72 - 307 * q^73 + 3845 * q^74 + 131 * q^75 + 1974 * q^76 - 6041 * q^78 + 22 * q^79 - 804 * q^80 + 795 * q^81 + 8043 * q^82 + 6349 * q^83 + 3094 * q^85 + 1745 * q^86 + 9508 * q^87 + 1299 * q^88 + 2253 * q^89 + 11156 * q^90 + 1284 * q^92 - 3430 * q^93 + 2738 * q^94 - 3290 * q^95 + 3031 * q^96 - 770 * q^97 + 5384 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more