LMFDB - Embedded newform 507.4.a.l.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,4,Mod(1,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, 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("507.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	507.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:	$29.9139683729$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.1362828.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 23x^{2} + 48 $ x^4 - 23*x^2 + 48
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 39)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-4.54739$ of defining polynomial
Character	$\chi$	$=$	507.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.54739 q^{2} +3.00000 q^{3} +12.6788 q^{4} -12.9118 q^{5} -13.6422 q^{6} -16.7289 q^{7} -21.2762 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-4.54739 q^{2} +3.00000 q^{3} +12.6788 q^{4} -12.9118 q^{5} -13.6422 q^{6} -16.7289 q^{7} -21.2762 q^{8} +9.00000 q^{9} +58.7151 q^{10} -24.9280 q^{11} +38.0363 q^{12} +76.0727 q^{14} -38.7355 q^{15} -4.67878 q^{16} -134.145 q^{17} -40.9265 q^{18} +14.9376 q^{19} -163.706 q^{20} -50.1866 q^{21} +113.358 q^{22} +72.0000 q^{23} -63.8287 q^{24} +41.7151 q^{25} +27.0000 q^{27} -212.101 q^{28} -206.145 q^{29} +176.145 q^{30} +249.142 q^{31} +191.486 q^{32} -74.7841 q^{33} +610.012 q^{34} +216.000 q^{35} +114.109 q^{36} -293.955 q^{37} -67.9273 q^{38} +274.715 q^{40} -250.506 q^{41} +228.218 q^{42} +432.145 q^{43} -316.057 q^{44} -116.206 q^{45} -327.412 q^{46} +159.889 q^{47} -14.0363 q^{48} -63.1454 q^{49} -189.695 q^{50} -402.436 q^{51} -194.581 q^{53} -122.780 q^{54} +321.866 q^{55} +355.927 q^{56} +44.8129 q^{57} +937.424 q^{58} -232.647 q^{59} -491.118 q^{60} -185.006 q^{61} -1132.94 q^{62} -150.560 q^{63} -833.333 q^{64} +340.073 q^{66} +39.4393 q^{67} -1700.80 q^{68} +216.000 q^{69} -982.237 q^{70} -920.460 q^{71} -191.486 q^{72} +549.078 q^{73} +1336.73 q^{74} +125.145 q^{75} +189.391 q^{76} +417.018 q^{77} +933.140 q^{79} +60.4116 q^{80} +81.0000 q^{81} +1139.15 q^{82} +1095.38 q^{83} -636.304 q^{84} +1732.06 q^{85} -1965.13 q^{86} -618.436 q^{87} +530.375 q^{88} +532.114 q^{89} +528.436 q^{90} +912.872 q^{92} +747.425 q^{93} -727.079 q^{94} -192.872 q^{95} +574.459 q^{96} +362.661 q^{97} +287.147 q^{98} -224.352 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 12 q^{3} + 14 q^{4} + 36 q^{9}+O(q^{10}) $ 4 * q + 12 * q^3 + 14 * q^4 + 36 * q^9	$ 4 q + 12 q^{3} + 14 q^{4} + 36 q^{9} + 88 q^{10} + 42 q^{12} + 84 q^{14} + 18 q^{16} - 96 q^{17} + 380 q^{22} + 288 q^{23} + 20 q^{25} + 108 q^{27} - 384 q^{29} + 264 q^{30} + 864 q^{35} + 126 q^{36} - 492 q^{38} + 952 q^{40} + 252 q^{42} + 1288 q^{43} + 54 q^{48} + 188 q^{49} - 288 q^{51} + 984 q^{53} - 328 q^{55} + 1644 q^{56} + 288 q^{61} - 1668 q^{62} - 1314 q^{64} + 1140 q^{66} - 4380 q^{68} + 864 q^{69} + 3144 q^{74} + 60 q^{75} - 1416 q^{77} + 4320 q^{79} + 324 q^{81} + 3088 q^{82} - 1152 q^{87} - 1036 q^{88} + 792 q^{90} + 1008 q^{92} - 1660 q^{94} + 1872 q^{95}+O(q^{100}) $ 4 * q + 12 * q^3 + 14 * q^4 + 36 * q^9 + 88 * q^10 + 42 * q^12 + 84 * q^14 + 18 * q^16 - 96 * q^17 + 380 * q^22 + 288 * q^23 + 20 * q^25 + 108 * q^27 - 384 * q^29 + 264 * q^30 + 864 * q^35 + 126 * q^36 - 492 * q^38 + 952 * q^40 + 252 * q^42 + 1288 * q^43 + 54 * q^48 + 188 * q^49 - 288 * q^51 + 984 * q^53 - 328 * q^55 + 1644 * q^56 + 288 * q^61 - 1668 * q^62 - 1314 * q^64 + 1140 * q^66 - 4380 * q^68 + 864 * q^69 + 3144 * q^74 + 60 * q^75 - 1416 * q^77 + 4320 * q^79 + 324 * q^81 + 3088 * q^82 - 1152 * q^87 - 1036 * q^88 + 792 * q^90 + 1008 * q^92 - 1660 * q^94 + 1872 * q^95

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 $

$2$	−4.54739	−1.60775	−0.803873	−	0.594801i	$-0.797231\pi$
$2$	−4.54739	−1.60775	−0.803873	+	0.594801i	$0.797231\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	12.6788	1.58485
$5$	−12.9118	−1.15487	−0.577434	−	0.816437i	$-0.695946\pi$
$5$	−12.9118	−1.15487	−0.577434	+	0.816437i	$0.695946\pi$
$6$	−13.6422	−0.928233
$7$	−16.7289	−0.903273	−0.451637	−	0.892202i	$-0.649160\pi$
$7$	−16.7289	−0.903273	−0.451637	+	0.892202i	$0.649160\pi$
$8$	−21.2762	−0.940286
$9$	9.00000	0.333333
$10$	58.7151	1.85674
$11$	−24.9280	−0.683280	−0.341640	−	0.939831i	$-0.610982\pi$
$11$	−24.9280	−0.683280	−0.341640	+	0.939831i	$0.610982\pi$
$12$	38.0363	0.915012
$13$	0	0
$13$	0	0
$14$	76.0727	1.45223
$15$	−38.7355	−0.666764
$16$	−4.67878	−0.0731059
$17$	−134.145	−1.91383	−0.956913	−	0.290376i	$-0.906220\pi$
$17$	−134.145	−1.91383	−0.956913	+	0.290376i	$0.906220\pi$
$18$	−40.9265	−0.535915
$19$	14.9376	0.180365	0.0901824	−	0.995925i	$-0.471255\pi$
$19$	14.9376	0.180365	0.0901824	+	0.995925i	$0.471255\pi$
$20$	−163.706	−1.83029
$21$	−50.1866	−0.521505
$22$	113.358	1.09854
$23$	72.0000	0.652741	0.326370	−	0.945242i	$-0.394174\pi$
$23$	72.0000	0.652741	0.326370	+	0.945242i	$0.394174\pi$
$24$	−63.8287	−0.542875
$25$	41.7151	0.333721
$26$	0	0
$27$	27.0000	0.192450
$28$	−212.101	−1.43155
$29$	−206.145	−1.32001	−0.660004	−	0.751262i	$-0.729445\pi$
$29$	−206.145	−1.32001	−0.660004	+	0.751262i	$0.729445\pi$
$30$	176.145	1.07199
$31$	249.142	1.44346	0.721728	−	0.692176i	$-0.243348\pi$
$31$	249.142	1.44346	0.721728	+	0.692176i	$0.243348\pi$
$32$	191.486	1.05782
$33$	−74.7841	−0.394492
$34$	610.012	3.07694
$35$	216.000	1.04316
$36$	114.109	0.528282
$37$	−293.955	−1.30610	−0.653052	−	0.757313i	$-0.726512\pi$
$37$	−293.955	−1.30610	−0.653052	+	0.757313i	$0.726512\pi$
$38$	−67.9273	−0.289981
$39$	0	0
$40$	274.715	1.08591
$41$	−250.506	−0.954208	−0.477104	−	0.878847i	$-0.658314\pi$
$41$	−250.506	−0.954208	−0.477104	+	0.878847i	$0.658314\pi$
$42$	228.218	0.838448
$43$	432.145	1.53259	0.766297	−	0.642486i	$-0.222097\pi$
$43$	432.145	1.53259	0.766297	+	0.642486i	$0.222097\pi$
$44$	−316.057	−1.08290
$45$	−116.206	−0.384956
$46$	−327.412	−1.04944
$47$	159.889	0.496217	0.248109	−	0.968732i	$-0.420191\pi$
$47$	159.889	0.496217	0.248109	+	0.968732i	$0.420191\pi$
$48$	−14.0363	−0.0422077
$49$	−63.1454	−0.184097
$50$	−189.695	−0.536539
$51$	−402.436	−1.10495
$52$	0	0
$53$	−194.581	−0.504298	−0.252149	−	0.967688i	$-0.581137\pi$
$53$	−194.581	−0.504298	−0.252149	+	0.967688i	$0.581137\pi$
$54$	−122.780	−0.309411
$55$	321.866	0.789099
$56$	355.927	0.849336
$57$	44.8129	0.104134
$58$	937.424	2.12224
$59$	−232.647	−0.513358	−0.256679	−	0.966497i	$-0.582628\pi$
$59$	−232.647	−0.513358	−0.256679	+	0.966497i	$0.582628\pi$
$60$	−491.118	−1.05672
$61$	−185.006	−0.388321	−0.194160	−	0.980970i	$-0.562198\pi$
$61$	−185.006	−0.388321	−0.194160	+	0.980970i	$0.562198\pi$
$62$	−1132.94	−2.32071
$63$	−150.560	−0.301091
$64$	−833.333	−1.62760
$65$	0	0
$66$	340.073	0.634243
$67$	39.4393	0.0719145	0.0359573	−	0.999353i	$-0.488552\pi$
$67$	39.4393	0.0719145	0.0359573	+	0.999353i	$0.488552\pi$
$68$	−1700.80	−3.03312
$69$	216.000	0.376860
$70$	−982.237	−1.67714
$71$	−920.460	−1.53857	−0.769286	−	0.638905i	$-0.779388\pi$
$71$	−920.460	−1.53857	−0.769286	+	0.638905i	$0.779388\pi$
$72$	−191.486	−0.313429
$73$	549.078	0.880338	0.440169	−	0.897915i	$-0.354918\pi$
$73$	549.078	0.880338	0.440169	+	0.897915i	$0.354918\pi$
$74$	1336.73	2.09988
$75$	125.145	0.192674
$76$	189.391	0.285851
$77$	417.018	0.617189
$78$	0	0
$79$	933.140	1.32894	0.664471	−	0.747314i	$-0.268657\pi$
$79$	933.140	1.32894	0.664471	+	0.747314i	$0.268657\pi$
$80$	60.4116	0.0844277
$81$	81.0000	0.111111
$82$	1139.15	1.53412
$83$	1095.38	1.44860	0.724301	−	0.689484i	$-0.242163\pi$
$83$	1095.38	1.44860	0.724301	+	0.689484i	$0.242163\pi$
$84$	−636.304	−0.826506
$85$	1732.06	2.21022
$86$	−1965.13	−2.46402
$87$	−618.436	−0.762107
$88$	530.375	0.642479
$89$	532.114	0.633753	0.316876	−	0.948467i	$-0.397366\pi$
$89$	532.114	0.633753	0.316876	+	0.948467i	$0.397366\pi$
$90$	528.436	0.618912
$91$	0	0
$92$	912.872	1.03449
$93$	747.425	0.833380
$94$	−727.079	−0.797792
$95$	−192.872	−0.208298
$96$	574.459	0.610734
$97$	362.661	0.379615	0.189808	−	0.981821i	$-0.439214\pi$
$97$	362.661	0.379615	0.189808	+	0.981821i	$0.439214\pi$
$98$	287.147	0.295982
$99$	−224.352	−0.227760
$100$	528.897	0.528897
$101$	1490.58	1.46850	0.734249	−	0.678880i	$-0.237534\pi$
$101$	1490.58	1.46850	0.734249	+	0.678880i	$0.237534\pi$
$102$	1830.03	1.77648
$103$	628.436	0.601181	0.300591	−	0.953753i	$-0.402816\pi$
$103$	628.436	0.601181	0.300591	+	0.953753i	$0.402816\pi$
$104$	0	0
$105$	648.000	0.602270
$106$	884.838	0.810784
$107$	477.454	0.431376	0.215688	−	0.976462i	$-0.430801\pi$
$107$	477.454	0.431376	0.215688	+	0.976462i	$0.430801\pi$
$108$	342.327	0.305004
$109$	378.207	0.332345	0.166173	−	0.986097i	$-0.446859\pi$
$109$	378.207	0.332345	0.166173	+	0.986097i	$0.446859\pi$
$110$	−1463.65	−1.26867
$111$	−881.864	−0.754079
$112$	78.2706	0.0660346
$113$	13.2732	0.0110499	0.00552495	−	0.999985i	$-0.498241\pi$
$113$	13.2732	0.0110499	0.00552495	+	0.999985i	$0.498241\pi$
$114$	−203.782	−0.167420
$115$	−929.651	−0.753830
$116$	−2613.67	−2.09201
$117$	0	0
$118$	1057.94	0.825349
$119$	2244.10	1.72871
$120$	824.145	0.626949
$121$	−709.593	−0.533128
$122$	841.294	0.624321
$123$	−751.519	−0.550912
$124$	3158.81	2.28766
$125$	1075.36	0.769465
$126$	684.654	0.484078
$127$	145.988	0.102003	0.0510015	−	0.998699i	$-0.483759\pi$
$127$	145.988	0.102003	0.0510015	+	0.998699i	$0.483759\pi$
$128$	2257.60	1.55895
$129$	1296.44	0.884844
$130$	0	0
$131$	317.163	0.211532	0.105766	−	0.994391i	$-0.466271\pi$
$131$	317.163	0.211532	0.105766	+	0.994391i	$0.466271\pi$
$132$	−948.171	−0.625210
$133$	−249.890	−0.162919
$134$	−179.346	−0.115620
$135$	−348.619	−0.222255
$136$	2854.11	1.79954
$137$	−443.149	−0.276356	−0.138178	−	0.990407i	$-0.544125\pi$
$137$	−443.149	−0.276356	−0.138178	+	0.990407i	$0.544125\pi$
$138$	−982.237	−0.605895
$139$	785.018	0.479024	0.239512	−	0.970893i	$-0.423013\pi$
$139$	785.018	0.479024	0.239512	+	0.970893i	$0.423013\pi$
$140$	2738.62	1.65325
$141$	479.667	0.286491
$142$	4185.69	2.47363
$143$	0	0
$144$	−42.1090	−0.0243686
$145$	2661.71	1.52444
$146$	−2496.87	−1.41536
$147$	−189.436	−0.106289
$148$	−3726.99	−2.06997
$149$	−135.420	−0.0744566	−0.0372283	−	0.999307i	$-0.511853\pi$
$149$	−135.420	−0.0744566	−0.0372283	+	0.999307i	$0.511853\pi$
$150$	−569.085	−0.309771
$151$	2373.74	1.27929	0.639643	−	0.768672i	$-0.279082\pi$
$151$	2373.74	1.27929	0.639643	+	0.768672i	$0.279082\pi$
$152$	−317.817	−0.169594
$153$	−1207.31	−0.637942
$154$	−1896.34	−0.992283
$155$	−3216.87	−1.66700
$156$	0	0
$157$	−1166.73	−0.593089	−0.296544	−	0.955019i	$-0.595834\pi$
$157$	−1166.73	−0.593089	−0.296544	+	0.955019i	$0.595834\pi$
$158$	−4243.35	−2.13660
$159$	−583.744	−0.291157
$160$	−2472.44	−1.22165
$161$	−1204.48	−0.589603
$162$	−368.339	−0.178638
$163$	2309.19	1.10963	0.554815	−	0.831974i	$-0.312789\pi$
$163$	2309.19	1.10963	0.554815	+	0.831974i	$0.312789\pi$
$164$	−3176.12	−1.51227
$165$	965.599	0.455587
$166$	−4981.14	−2.32898
$167$	600.788	0.278386	0.139193	−	0.990265i	$-0.455549\pi$
$167$	600.788	0.278386	0.139193	+	0.990265i	$0.455549\pi$
$168$	1067.78	0.490364
$169$	0	0
$170$	−7876.36	−3.55347
$171$	134.439	0.0601216
$172$	5479.08	2.42893
$173$	3430.36	1.50755	0.753773	−	0.657135i	$-0.228232\pi$
$173$	3430.36	1.50755	0.753773	+	0.657135i	$0.228232\pi$
$174$	2812.27	1.22527
$175$	−697.846	−0.301441
$176$	116.633	0.0499519
$177$	−697.942	−0.296387
$178$	−2419.73	−1.01891
$179$	978.837	0.408725	0.204362	−	0.978895i	$-0.434488\pi$
$179$	978.837	0.408725	0.204362	+	0.978895i	$0.434488\pi$
$180$	−1473.36	−0.610097
$181$	−3839.09	−1.57656	−0.788279	−	0.615318i	$-0.789028\pi$
$181$	−3839.09	−1.57656	−0.788279	+	0.615318i	$0.789028\pi$
$182$	0	0
$183$	−555.018	−0.224197
$184$	−1531.89	−0.613763
$185$	3795.49	1.50838
$186$	−3398.83	−1.33986
$187$	3343.98	1.30768
$188$	2027.20	0.786429
$189$	−451.679	−0.173835
$190$	877.065	0.334890
$191$	−487.709	−0.184761	−0.0923806	−	0.995724i	$-0.529448\pi$
$191$	−487.709	−0.184761	−0.0923806	+	0.995724i	$0.529448\pi$
$192$	−2500.00	−0.939697
$193$	−4245.61	−1.58345	−0.791725	−	0.610878i	$-0.790817\pi$
$193$	−4245.61	−1.58345	−0.791725	+	0.610878i	$0.790817\pi$
$194$	−1649.16	−0.610325
$195$	0	0
$196$	−800.606	−0.291766
$197$	2712.71	0.981079	0.490539	−	0.871419i	$-0.336800\pi$
$197$	2712.71	0.981079	0.490539	+	0.871419i	$0.336800\pi$
$198$	1020.22	0.366180
$199$	3116.90	1.11031	0.555153	−	0.831748i	$-0.312660\pi$
$199$	3116.90	1.11031	0.555153	+	0.831748i	$0.312660\pi$
$200$	−887.541	−0.313793
$201$	118.318	0.0415199
$202$	−6778.26	−2.36097
$203$	3448.58	1.19233
$204$	−5102.40	−1.75117
$205$	3234.49	1.10198
$206$	−2857.75	−0.966546
$207$	648.000	0.217580
$208$	0	0
$209$	−372.366	−0.123240
$210$	−2946.71	−0.968297
$211$	−1051.22	−0.342981	−0.171491	−	0.985186i	$-0.554858\pi$
$211$	−1051.22	−0.342981	−0.171491	+	0.985186i	$0.554858\pi$
$212$	−2467.06	−0.799236
$213$	−2761.38	−0.888294
$214$	−2171.17	−0.693542
$215$	−5579.78	−1.76994
$216$	−574.459	−0.180958
$217$	−4167.85	−1.30384
$218$	−1719.85	−0.534327
$219$	1647.23	0.508264
$220$	4080.87	1.25060
$221$	0	0
$222$	4010.18	1.21237
$223$	−5496.12	−1.65044	−0.825218	−	0.564814i	$-0.808948\pi$
$223$	−5496.12	−1.65044	−0.825218	+	0.564814i	$0.808948\pi$
$224$	−3203.35	−0.955502
$225$	375.436	0.111240
$226$	−60.3585	−0.0177654
$227$	921.570	0.269457	0.134729	−	0.990883i	$-0.456984\pi$
$227$	921.570	0.269457	0.134729	+	0.990883i	$0.456984\pi$
$228$	568.173	0.165036
$229$	−192.941	−0.0556764	−0.0278382	−	0.999612i	$-0.508862\pi$
$229$	−192.941	−0.0556764	−0.0278382	+	0.999612i	$0.508862\pi$
$230$	4227.49	1.21197
$231$	1251.05	0.356334
$232$	4386.00	1.24119
$233$	913.779	0.256926	0.128463	−	0.991714i	$-0.458996\pi$
$233$	913.779	0.256926	0.128463	+	0.991714i	$0.458996\pi$
$234$	0	0
$235$	−2064.46	−0.573066
$236$	−2949.68	−0.813594
$237$	2799.42	0.767265
$238$	−10204.8	−2.77932
$239$	1976.86	0.535032	0.267516	−	0.963553i	$-0.413797\pi$
$239$	1976.86	0.535032	0.267516	+	0.963553i	$0.413797\pi$
$240$	181.235	0.0487444
$241$	−3904.45	−1.04360	−0.521800	−	0.853068i	$-0.674739\pi$
$241$	−3904.45	−1.04360	−0.521800	+	0.853068i	$0.674739\pi$
$242$	3226.80	0.857134
$243$	243.000	0.0641500
$244$	−2345.65	−0.615429
$245$	815.322	0.212608
$246$	3417.45	0.885727
$247$	0	0
$248$	−5300.80	−1.35726
$249$	3286.15	0.836350
$250$	−4890.08	−1.23710
$251$	−942.035	−0.236895	−0.118448	−	0.992960i	$-0.537792\pi$
$251$	−942.035	−0.236895	−0.118448	+	0.992960i	$0.537792\pi$
$252$	−1908.91	−0.477183
$253$	−1794.82	−0.446005
$254$	−663.866	−0.163995
$255$	5196.18	1.27607
$256$	−3599.54	−0.878794
$257$	−812.616	−0.197236	−0.0986179	−	0.995125i	$-0.531442\pi$
$257$	−812.616	−0.197236	−0.0986179	+	0.995125i	$0.531442\pi$
$258$	−5895.40	−1.42260
$259$	4917.52	1.17977
$260$	0	0
$261$	−1855.31	−0.440003
$262$	−1442.26	−0.340089
$263$	−2608.29	−0.611536	−0.305768	−	0.952106i	$-0.598913\pi$
$263$	−2608.29	−0.611536	−0.305768	+	0.952106i	$0.598913\pi$
$264$	1591.13	0.370936
$265$	2512.40	0.582398
$266$	1136.35	0.261932
$267$	1596.34	0.365897
$268$	500.042	0.113974
$269$	−4791.02	−1.08592	−0.542962	−	0.839757i	$-0.682697\pi$
$269$	−4791.02	−1.08592	−0.542962	+	0.839757i	$0.682697\pi$
$270$	1585.31	0.357329
$271$	3663.62	0.821214	0.410607	−	0.911812i	$-0.365317\pi$
$271$	3663.62	0.821214	0.410607	+	0.911812i	$0.365317\pi$
$272$	627.637	0.139912
$273$	0	0
$274$	2015.17	0.444311
$275$	−1039.88	−0.228025
$276$	2738.62	0.597266
$277$	−624.326	−0.135423	−0.0677114	−	0.997705i	$-0.521570\pi$
$277$	−624.326	−0.135423	−0.0677114	+	0.997705i	$0.521570\pi$
$278$	−3569.78	−0.770149
$279$	2242.27	0.481152
$280$	−4595.67	−0.980871
$281$	−5535.12	−1.17508	−0.587540	−	0.809195i	$-0.699904\pi$
$281$	−5535.12	−1.17508	−0.587540	+	0.809195i	$0.699904\pi$
$282$	−2181.24	−0.460605
$283$	175.151	0.0367903	0.0183952	−	0.999831i	$-0.494144\pi$
$283$	175.151	0.0367903	0.0183952	+	0.999831i	$0.494144\pi$
$284$	−11670.3	−2.43840
$285$	−578.616	−0.120261
$286$	0	0
$287$	4190.69	0.861911
$288$	1723.38	0.352607
$289$	13082.0	2.66273
$290$	−12103.8	−2.45091
$291$	1087.98	0.219171
$292$	6961.64	1.39520
$293$	7774.33	1.55011	0.775054	−	0.631895i	$-0.217723\pi$
$293$	7774.33	1.55011	0.775054	+	0.631895i	$0.217723\pi$
$294$	861.440	0.170885
$295$	3003.90	0.592861
$296$	6254.25	1.22811
$297$	−673.057	−0.131497
$298$	615.808	0.119707
$299$	0	0
$300$	1586.69	0.305359
$301$	−7229.30	−1.38435
$302$	−10794.3	−2.05677
$303$	4471.74	0.847838
$304$	−69.8899	−0.0131857
$305$	2388.76	0.448459
$306$	5490.10	1.02565
$307$	−8022.85	−1.49149	−0.745746	−	0.666230i	$-0.767907\pi$
$307$	−8022.85	−1.49149	−0.745746	+	0.666230i	$0.767907\pi$
$308$	5287.27	0.978150
$309$	1885.31	0.347092
$310$	14628.4	2.68012
$311$	−9264.87	−1.68927	−0.844635	−	0.535343i	$-0.820182\pi$
$311$	−9264.87	−1.68927	−0.844635	+	0.535343i	$0.820182\pi$
$312$	0	0
$313$	7423.57	1.34059	0.670296	−	0.742094i	$-0.266167\pi$
$313$	7423.57	1.34059	0.670296	+	0.742094i	$0.266167\pi$
$314$	5305.56	0.953536
$315$	1944.00	0.347721
$316$	11831.1	2.10617
$317$	−2641.04	−0.467935	−0.233968	−	0.972244i	$-0.575171\pi$
$317$	−2641.04	−0.467935	−0.233968	+	0.972244i	$0.575171\pi$
$318$	2654.51	0.468106
$319$	5138.80	0.901936
$320$	10759.8	1.87967
$321$	1432.36	0.249055
$322$	5477.23	0.947932
$323$	−2003.82	−0.345187
$324$	1026.98	0.176094
$325$	0	0
$326$	−10500.8	−1.78400
$327$	1134.62	0.191880
$328$	5329.84	0.897229
$329$	−2674.76	−0.448220
$330$	−4390.96	−0.732467
$331$	−10779.5	−1.79001	−0.895007	−	0.446052i	$-0.852830\pi$
$331$	−10779.5	−1.79001	−0.895007	+	0.446052i	$0.852830\pi$
$332$	13888.1	2.29581
$333$	−2645.59	−0.435368
$334$	−2732.02	−0.447573
$335$	−509.233	−0.0830518
$336$	234.812	0.0381251
$337$	−313.465	−0.0506693	−0.0253346	−	0.999679i	$-0.508065\pi$
$337$	−313.465	−0.0506693	−0.0253346	+	0.999679i	$0.508065\pi$
$338$	0	0
$339$	39.8196	0.00637966
$340$	21960.4	3.50286
$341$	−6210.61	−0.986286
$342$	−611.346	−0.0966602
$343$	6794.35	1.06956
$344$	−9194.43	−1.44108
$345$	−2788.95	−0.435224
$346$	−15599.2	−2.42375
$347$	−2849.23	−0.440792	−0.220396	−	0.975410i	$-0.570735\pi$
$347$	−2849.23	−0.440792	−0.220396	+	0.975410i	$0.570735\pi$
$348$	−7841.01	−1.20782
$349$	−6466.94	−0.991883	−0.495941	−	0.868356i	$-0.665177\pi$
$349$	−6466.94	−0.991883	−0.495941	+	0.868356i	$0.665177\pi$
$350$	3173.38	0.484641
$351$	0	0
$352$	−4773.38	−0.722789
$353$	2773.10	0.418122	0.209061	−	0.977903i	$-0.432959\pi$
$353$	2773.10	0.418122	0.209061	+	0.977903i	$0.432959\pi$
$354$	3173.82	0.476515
$355$	11884.8	1.77685
$356$	6746.56	1.00440
$357$	6732.30	0.998070
$358$	−4451.16	−0.657126
$359$	1467.11	0.215685	0.107843	−	0.994168i	$-0.465606\pi$
$359$	1467.11	0.215685	0.107843	+	0.994168i	$0.465606\pi$
$360$	2472.44	0.361969
$361$	−6635.87	−0.967469
$362$	17457.8	2.53471
$363$	−2128.78	−0.307801
$364$	0	0
$365$	−7089.59	−1.01667
$366$	2523.88	0.360452
$367$	4648.22	0.661130	0.330565	−	0.943783i	$-0.392761\pi$
$367$	4648.22	0.661130	0.330565	+	0.943783i	$0.392761\pi$
$368$	−336.872	−0.0477192
$369$	−2254.56	−0.318069
$370$	−17259.6	−2.42509
$371$	3255.12	0.455519
$372$	9476.44	1.32078
$373$	1763.72	0.244831	0.122416	−	0.992479i	$-0.460936\pi$
$373$	1763.72	0.244831	0.122416	+	0.992479i	$0.460936\pi$
$374$	−15206.4	−2.10242
$375$	3226.08	0.444251
$376$	−3401.84	−0.466586
$377$	0	0
$378$	2053.96	0.279483
$379$	−1930.47	−0.261640	−0.130820	−	0.991406i	$-0.541761\pi$
$379$	−1930.47	−0.261640	−0.130820	+	0.991406i	$0.541761\pi$
$380$	−2445.38	−0.330120
$381$	437.965	0.0588914
$382$	2217.81	0.297049
$383$	8845.93	1.18017	0.590086	−	0.807340i	$-0.299094\pi$
$383$	8845.93	1.18017	0.590086	+	0.807340i	$0.299094\pi$
$384$	6772.81	0.900061
$385$	−5384.46	−0.712772
$386$	19306.5	2.54579
$387$	3889.31	0.510865
$388$	4598.10	0.601632
$389$	−1598.08	−0.208292	−0.104146	−	0.994562i	$-0.533211\pi$
$389$	−1598.08	−0.208292	−0.104146	+	0.994562i	$0.533211\pi$
$390$	0	0
$391$	−9658.47	−1.24923
$392$	1343.50	0.173104
$393$	951.489	0.122128
$394$	−12335.8	−1.57733
$395$	−12048.5	−1.53475
$396$	−2844.51	−0.360965
$397$	−3578.82	−0.452433	−0.226217	−	0.974077i	$-0.572636\pi$
$397$	−3578.82	−0.452433	−0.226217	+	0.974077i	$0.572636\pi$
$398$	−14173.7	−1.78509
$399$	−749.669	−0.0940611
$400$	−195.176	−0.0243970
$401$	3485.99	0.434120	0.217060	−	0.976158i	$-0.430353\pi$
$401$	3485.99	0.434120	0.217060	+	0.976158i	$0.430353\pi$
$402$	−538.038	−0.0667534
$403$	0	0
$404$	18898.8	2.32735
$405$	−1045.86	−0.128319
$406$	−15682.0	−1.91696
$407$	7327.71	0.892435
$408$	8562.33	1.03897
$409$	−14709.1	−1.77828	−0.889139	−	0.457637i	$-0.848696\pi$
$409$	−14709.1	−1.77828	−0.889139	+	0.457637i	$0.848696\pi$
$410$	−14708.5	−1.77171
$411$	−1329.45	−0.159554
$412$	7967.80	0.952780
$413$	3891.92	0.463702
$414$	−2946.71	−0.349814
$415$	−14143.4	−1.67294
$416$	0	0
$417$	2355.05	0.276565
$418$	1693.29	0.198138
$419$	3709.01	0.432451	0.216226	−	0.976343i	$-0.430625\pi$
$419$	3709.01	0.432451	0.216226	+	0.976343i	$0.430625\pi$
$420$	8215.85	0.954506
$421$	−794.029	−0.0919207	−0.0459603	−	0.998943i	$-0.514635\pi$
$421$	−794.029	−0.0919207	−0.0459603	+	0.998943i	$0.514635\pi$
$422$	4780.32	0.551427
$423$	1439.00	0.165406
$424$	4139.96	0.474185
$425$	−5595.89	−0.638684
$426$	12557.1	1.42815
$427$	3094.94	0.350760
$428$	6053.53	0.683664
$429$	0	0
$430$	25373.5	2.84562
$431$	−2891.52	−0.323155	−0.161577	−	0.986860i	$-0.551658\pi$
$431$	−2891.52	−0.323155	−0.161577	+	0.986860i	$0.551658\pi$
$432$	−126.327	−0.0140692
$433$	5560.94	0.617186	0.308593	−	0.951194i	$-0.400142\pi$
$433$	5560.94	0.617186	0.308593	+	0.951194i	$0.400142\pi$
$434$	18952.9	2.09624
$435$	7985.14	0.880133
$436$	4795.20	0.526717
$437$	1075.51	0.117731
$438$	−7490.62	−0.817159
$439$	15127.2	1.64460	0.822302	−	0.569051i	$-0.192689\pi$
$439$	15127.2	1.64460	0.822302	+	0.569051i	$0.192689\pi$
$440$	−6848.11	−0.741979
$441$	−568.308	−0.0613658
$442$	0	0
$443$	2357.89	0.252883	0.126441	−	0.991974i	$-0.459644\pi$
$443$	2357.89	0.252883	0.126441	+	0.991974i	$0.459644\pi$
$444$	−11181.0	−1.19510
$445$	−6870.56	−0.731901
$446$	24993.0	2.65348
$447$	−406.260	−0.0429876
$448$	13940.7	1.47017
$449$	7165.06	0.753096	0.376548	−	0.926397i	$-0.377111\pi$
$449$	7165.06	0.753096	0.376548	+	0.926397i	$0.377111\pi$
$450$	−1707.26	−0.178846
$451$	6244.63	0.651992
$452$	168.288	0.0175124
$453$	7121.22	0.738596
$454$	−4190.74	−0.433219
$455$	0	0
$456$	−953.451	−0.0979154
$457$	−8020.96	−0.821017	−0.410508	−	0.911857i	$-0.634649\pi$
$457$	−8020.96	−0.821017	−0.410508	+	0.911857i	$0.634649\pi$
$458$	877.378	0.0895135
$459$	−3621.92	−0.368316
$460$	−11786.8	−1.19471
$461$	4146.59	0.418928	0.209464	−	0.977816i	$-0.432828\pi$
$461$	4146.59	0.418928	0.209464	+	0.977816i	$0.432828\pi$
$462$	−5689.03	−0.572895
$463$	−7118.21	−0.714495	−0.357248	−	0.934010i	$-0.616285\pi$
$463$	−7118.21	−0.714495	−0.357248	+	0.934010i	$0.616285\pi$
$464$	964.509	0.0965004
$465$	−9650.62	−0.962444
$466$	−4155.31	−0.413071
$467$	−2128.22	−0.210883	−0.105441	−	0.994426i	$-0.533626\pi$
$467$	−2128.22	−0.210883	−0.105441	+	0.994426i	$0.533626\pi$
$468$	0	0
$469$	−659.774	−0.0649585
$470$	9387.91	0.921344
$471$	−3500.18	−0.342420
$472$	4949.86	0.482703
$473$	−10772.5	−1.04719
$474$	−12730.1	−1.23357
$475$	623.125	0.0601915
$476$	28452.4	2.73974
$477$	−1751.23	−0.168099
$478$	−8989.57	−0.860196
$479$	3715.30	0.354397	0.177199	−	0.984175i	$-0.443296\pi$
$479$	3715.30	0.354397	0.177199	+	0.984175i	$0.443296\pi$
$480$	−7417.31	−0.705317
$481$	0	0
$482$	17755.0	1.67784
$483$	−3613.43	−0.340408
$484$	−8996.77	−0.844926
$485$	−4682.62	−0.438405
$486$	−1105.02	−0.103137
$487$	8139.28	0.757343	0.378671	−	0.925531i	$-0.376381\pi$
$487$	8139.28	0.757343	0.378671	+	0.925531i	$0.376381\pi$
$488$	3936.23	0.365133
$489$	6927.57	0.640645
$490$	−3707.59	−0.341820
$491$	18081.7	1.66194	0.830972	−	0.556315i	$-0.187785\pi$
$491$	18081.7	1.66194	0.830972	+	0.556315i	$0.187785\pi$
$492$	−9528.35	−0.873112
$493$	27653.4	2.52626
$494$	0	0
$495$	2896.80	0.263033
$496$	−1165.68	−0.105525
$497$	15398.3	1.38975
$498$	−14943.4	−1.34464
$499$	−11031.5	−0.989659	−0.494829	−	0.868990i	$-0.664769\pi$
$499$	−11031.5	−0.989659	−0.494829	+	0.868990i	$0.664769\pi$
$500$	13634.2	1.21948
$501$	1802.37	0.160726
$502$	4283.80	0.380868
$503$	8016.14	0.710581	0.355290	−	0.934756i	$-0.384382\pi$
$503$	8016.14	0.710581	0.355290	+	0.934756i	$0.384382\pi$
$504$	3203.35	0.283112
$505$	−19246.1	−1.69592
$506$	8161.74	0.717063
$507$	0	0
$508$	1850.95	0.161659
$509$	−20173.9	−1.75676	−0.878382	−	0.477959i	$-0.841377\pi$
$509$	−20173.9	−1.75676	−0.878382	+	0.477959i	$0.841377\pi$
$510$	−23629.1	−2.05159
$511$	−9185.44	−0.795186
$512$	−1692.30	−0.146074
$513$	403.316	0.0347112
$514$	3695.29	0.317105
$515$	−8114.25	−0.694285
$516$	16437.2	1.40234
$517$	−3985.72	−0.339056
$518$	−22361.9	−1.89677
$519$	10291.1	0.870382
$520$	0	0
$521$	9746.95	0.819619	0.409810	−	0.912171i	$-0.365595\pi$
$521$	9746.95	0.819619	0.409810	+	0.912171i	$0.365595\pi$
$522$	8436.81	0.707413
$523$	−18929.3	−1.58264	−0.791320	−	0.611402i	$-0.790606\pi$
$523$	−18929.3	−1.58264	−0.791320	+	0.611402i	$0.790606\pi$
$524$	4021.24	0.335245
$525$	−2093.54	−0.174037
$526$	11860.9	0.983195
$527$	−33421.2	−2.76252
$528$	349.898	0.0288397
$529$	−6983.00	−0.573929
$530$	−11424.9	−0.936349
$531$	−2093.83	−0.171119
$532$	−3168.30	−0.258201
$533$	0	0
$534$	−7259.20	−0.588270
$535$	−6164.80	−0.498182
$536$	−839.120	−0.0676203
$537$	2936.51	0.235977
$538$	21786.6	1.74589
$539$	1574.09	0.125790
$540$	−4420.07	−0.352240
$541$	11366.8	0.903321	0.451661	−	0.892190i	$-0.350832\pi$
$541$	11366.8	0.903321	0.451661	+	0.892190i	$0.350832\pi$
$542$	−16659.9	−1.32030
$543$	−11517.3	−0.910227
$544$	−25687.0	−2.02449
$545$	−4883.34	−0.383815
$546$	0	0
$547$	17495.4	1.36755	0.683775	−	0.729693i	$-0.260337\pi$
$547$	17495.4	1.36755	0.683775	+	0.729693i	$0.260337\pi$
$548$	−5618.59	−0.437983
$549$	−1665.05	−0.129440
$550$	4728.72	0.366606
$551$	−3079.33	−0.238083
$552$	−4595.67	−0.354356
$553$	−15610.4	−1.20040
$554$	2839.05	0.217725
$555$	11386.5	0.870862
$556$	9953.06	0.759180
$557$	11873.1	0.903192	0.451596	−	0.892223i	$-0.350855\pi$
$557$	11873.1	0.903192	0.451596	+	0.892223i	$0.350855\pi$
$558$	−10196.5	−0.773571
$559$	0	0
$560$	−1010.62	−0.0762613
$561$	10031.9	0.754989
$562$	25170.4	1.88923
$563$	−2829.31	−0.211796	−0.105898	−	0.994377i	$-0.533772\pi$
$563$	−2829.31	−0.211796	−0.105898	+	0.994377i	$0.533772\pi$
$564$	6081.60	0.454045
$565$	−171.381	−0.0127612
$566$	−796.481	−0.0591495
$567$	−1355.04	−0.100364
$568$	19583.9	1.44670
$569$	16136.8	1.18891	0.594453	−	0.804130i	$-0.297368\pi$
$569$	16136.8	1.18891	0.594453	+	0.804130i	$0.297368\pi$
$570$	2631.20	0.193349
$571$	−17840.5	−1.30754	−0.653769	−	0.756695i	$-0.726813\pi$
$571$	−17840.5	−1.30754	−0.653769	+	0.756695i	$0.726813\pi$
$572$	0	0
$573$	−1463.13	−0.106672
$574$	−19056.7	−1.38573
$575$	3003.49	0.217833
$576$	−7500.00	−0.542534
$577$	−8516.17	−0.614442	−0.307221	−	0.951638i	$-0.599399\pi$
$577$	−8516.17	−0.614442	−0.307221	+	0.951638i	$0.599399\pi$
$578$	−59488.9	−4.28099
$579$	−12736.8	−0.914205
$580$	33747.3	2.41600
$581$	−18324.5	−1.30848
$582$	−4947.49	−0.352371
$583$	4850.53	0.344577
$584$	−11682.3	−0.827770
$585$	0	0
$586$	−35352.9	−2.49218
$587$	20688.3	1.45468	0.727340	−	0.686277i	$-0.240756\pi$
$587$	20688.3	1.45468	0.727340	+	0.686277i	$0.240756\pi$
$588$	−2401.82	−0.168451
$589$	3721.59	0.260349
$590$	−13659.9	−0.953169
$591$	8138.13	0.566426
$592$	1375.35	0.0954839
$593$	−11435.9	−0.791933	−0.395966	−	0.918265i	$-0.629590\pi$
$593$	−11435.9	−0.791933	−0.395966	+	0.918265i	$0.629590\pi$
$594$	3060.65	0.211414
$595$	−28975.4	−1.99643
$596$	−1716.96	−0.118002
$597$	9350.69	0.641035
$598$	0	0
$599$	1260.80	0.0860016	0.0430008	−	0.999075i	$-0.486308\pi$
$599$	1260.80	0.0860016	0.0430008	+	0.999075i	$0.486308\pi$
$600$	−2662.62	−0.181169
$601$	6261.10	0.424951	0.212476	−	0.977166i	$-0.431847\pi$
$601$	6261.10	0.424951	0.212476	+	0.977166i	$0.431847\pi$
$602$	32874.5	2.22569
$603$	354.954	0.0239715
$604$	30096.1	2.02747
$605$	9162.14	0.615692
$606$	−20334.8	−1.36311
$607$	3230.33	0.216005	0.108003	−	0.994151i	$-0.465555\pi$
$607$	3230.33	0.216005	0.108003	+	0.994151i	$0.465555\pi$
$608$	2860.35	0.190794
$609$	10345.7	0.688391
$610$	−10862.6	−0.721009
$611$	0	0
$612$	−15307.2	−1.01104
$613$	−14868.5	−0.979660	−0.489830	−	0.871818i	$-0.662941\pi$
$613$	−14868.5	−0.979660	−0.489830	+	0.871818i	$0.662941\pi$
$614$	36483.0	2.39794
$615$	9703.48	0.636231
$616$	−8872.57	−0.580334
$617$	19952.8	1.30190	0.650949	−	0.759121i	$-0.274371\pi$
$617$	19952.8	1.30190	0.650949	+	0.759121i	$0.274371\pi$
$618$	−8573.24	−0.558036
$619$	−8316.48	−0.540012	−0.270006	−	0.962859i	$-0.587026\pi$
$619$	−8316.48	−0.540012	−0.270006	+	0.962859i	$0.587026\pi$
$620$	−40786.0	−2.64194
$621$	1944.00	0.125620
$622$	42131.0	2.71592
$623$	−8901.66	−0.572452
$624$	0	0
$625$	−19099.2	−1.22235
$626$	−33757.9	−2.15533
$627$	−1117.10	−0.0711525
$628$	−14792.7	−0.939955
$629$	39432.6	2.49965
$630$	−8840.13	−0.559046
$631$	12605.9	0.795299	0.397649	−	0.917537i	$-0.369826\pi$
$631$	12605.9	0.795299	0.397649	+	0.917537i	$0.369826\pi$
$632$	−19853.7	−1.24959
$633$	−3153.66	−0.198020
$634$	12009.8	0.752321
$635$	−1884.98	−0.117800
$636$	−7401.17	−0.461439
$637$	0	0
$638$	−23368.1	−1.45008
$639$	−8284.14	−0.512857
$640$	−29149.8	−1.80038
$641$	−9224.04	−0.568374	−0.284187	−	0.958769i	$-0.591724\pi$
$641$	−9224.04	−0.568374	−0.284187	+	0.958769i	$0.591724\pi$
$642$	−6513.51	−0.400417
$643$	−4439.16	−0.272260	−0.136130	−	0.990691i	$-0.543467\pi$
$643$	−4439.16	−0.272260	−0.136130	+	0.990691i	$0.543467\pi$
$644$	−15271.3	−0.934431
$645$	−16739.4	−1.02188
$646$	9112.13	0.554972
$647$	−9601.15	−0.583401	−0.291700	−	0.956510i	$-0.594221\pi$
$647$	−9601.15	−0.583401	−0.291700	+	0.956510i	$0.594221\pi$
$648$	−1723.38	−0.104476
$649$	5799.44	0.350767
$650$	0	0
$651$	−12503.6	−0.752770
$652$	29277.7	1.75859
$653$	27112.8	1.62482	0.812410	−	0.583087i	$-0.198155\pi$
$653$	27112.8	1.62482	0.812410	+	0.583087i	$0.198155\pi$
$654$	−5159.56	−0.308494
$655$	−4095.15	−0.244291
$656$	1172.06	0.0697583
$657$	4941.70	0.293446
$658$	12163.2	0.720624
$659$	5587.26	0.330271	0.165136	−	0.986271i	$-0.447194\pi$
$659$	5587.26	0.330271	0.165136	+	0.986271i	$0.447194\pi$
$660$	12242.6	0.722035
$661$	3060.13	0.180069	0.0900343	−	0.995939i	$-0.471302\pi$
$661$	3060.13	0.180069	0.0900343	+	0.995939i	$0.471302\pi$
$662$	49018.6	2.87789
$663$	0	0
$664$	−23305.6	−1.36210
$665$	3226.53	0.188150
$666$	12030.5	0.699961
$667$	−14842.5	−0.861623
$668$	7617.26	0.441199
$669$	−16488.4	−0.952880
$670$	2315.68	0.133526
$671$	4611.83	0.265332
$672$	−9610.04	−0.551660
$673$	4121.55	0.236069	0.118034	−	0.993010i	$-0.462341\pi$
$673$	4121.55	0.236069	0.118034	+	0.993010i	$0.462341\pi$
$674$	1425.45	0.0814633
$675$	1126.31	0.0642246
$676$	0	0
$677$	22889.5	1.29943	0.649715	−	0.760178i	$-0.274888\pi$
$677$	22889.5	1.29943	0.649715	+	0.760178i	$0.274888\pi$
$678$	−181.075	−0.0102569
$679$	−6066.91	−0.342896
$680$	−36851.8	−2.07824
$681$	2764.71	0.155571
$682$	28242.1	1.58570
$683$	19297.9	1.08113	0.540566	−	0.841301i	$-0.318210\pi$
$683$	19297.9	1.08113	0.540566	+	0.841301i	$0.318210\pi$
$684$	1704.52	0.0952835
$685$	5721.87	0.319155
$686$	−30896.6	−1.71959
$687$	−578.823	−0.0321448
$688$	−2021.91	−0.112042
$689$	0	0
$690$	12682.5	0.699729
$691$	30317.8	1.66910	0.834548	−	0.550935i	$-0.185729\pi$
$691$	30317.8	1.66910	0.834548	+	0.550935i	$0.185729\pi$
$692$	43492.8	2.38923
$693$	3753.16	0.205730
$694$	12956.6	0.708682
$695$	−10136.0	−0.553210
$696$	13158.0	0.716599
$697$	33604.3	1.82619
$698$	29407.7	1.59470
$699$	2741.34	0.148336
$700$	−8847.84	−0.477738
$701$	9606.16	0.517574	0.258787	−	0.965934i	$-0.416677\pi$
$701$	9606.16	0.517574	0.258787	+	0.965934i	$0.416677\pi$
$702$	0	0
$703$	−4390.99	−0.235575
$704$	20773.4	1.11211
$705$	−6193.38	−0.330860
$706$	−12610.4	−0.672235
$707$	−24935.7	−1.32646
$708$	−8849.05	−0.469729
$709$	23398.8	1.23944	0.619718	−	0.784825i	$-0.287247\pi$
$709$	23398.8	1.23944	0.619718	+	0.784825i	$0.287247\pi$
$710$	−54044.9	−2.85672
$711$	8398.26	0.442981
$712$	−11321.4	−0.595909
$713$	17938.2	0.942203
$714$	−30614.4	−1.60464
$715$	0	0
$716$	12410.5	0.647766
$717$	5930.59	0.308901
$718$	−6671.51	−0.346767
$719$	−23588.7	−1.22352	−0.611758	−	0.791045i	$-0.709537\pi$
$719$	−23588.7	−1.22352	−0.611758	+	0.791045i	$0.709537\pi$
$720$	543.704	0.0281426
$721$	−10513.0	−0.543031
$722$	30175.9	1.55544
$723$	−11713.3	−0.602522
$724$	−48674.9	−2.49861
$725$	−8599.38	−0.440514
$726$	9680.40	0.494867
$727$	15733.5	0.802644	0.401322	−	0.915937i	$-0.368551\pi$
$727$	15733.5	0.802644	0.401322	+	0.915937i	$0.368551\pi$
$728$	0	0
$729$	729.000	0.0370370
$730$	32239.2	1.63455
$731$	−57970.3	−2.93312
$732$	−7036.94	−0.355318
$733$	17297.1	0.871598	0.435799	−	0.900044i	$-0.356466\pi$
$733$	17297.1	0.871598	0.435799	+	0.900044i	$0.356466\pi$
$734$	−21137.3	−1.06293
$735$	2445.96	0.122749
$736$	13787.0	0.690484
$737$	−983.144	−0.0491378
$738$	10252.4	0.511375
$739$	−38749.2	−1.92884	−0.964419	−	0.264377i	$-0.914834\pi$
$739$	−38749.2	−1.92884	−0.964419	+	0.264377i	$0.914834\pi$
$740$	48122.2	2.39055
$741$	0	0
$742$	−14802.3	−0.732359
$743$	3139.76	0.155029	0.0775144	−	0.996991i	$-0.475302\pi$
$743$	3139.76	0.155029	0.0775144	+	0.996991i	$0.475302\pi$
$744$	−15902.4	−0.783616
$745$	1748.52	0.0859876
$746$	−8020.33	−0.393626
$747$	9858.45	0.482867
$748$	42397.6	2.07247
$749$	−7987.25	−0.389650
$750$	−14670.2	−0.714242
$751$	40628.6	1.97411	0.987055	−	0.160380i	$-0.0512721\pi$
$751$	40628.6	1.97411	0.987055	+	0.160380i	$0.0512721\pi$
$752$	−748.086	−0.0362764
$753$	−2826.11	−0.136772
$754$	0	0
$755$	−30649.3	−1.47741
$756$	−5726.74	−0.275502
$757$	24004.9	1.15254	0.576271	−	0.817259i	$-0.304507\pi$
$757$	24004.9	1.15254	0.576271	+	0.817259i	$0.304507\pi$
$758$	8778.62	0.420651
$759$	−5384.46	−0.257501
$760$	4103.60	0.195859
$761$	−29540.1	−1.40713	−0.703566	−	0.710630i	$-0.748410\pi$
$761$	−29540.1	−1.40713	−0.703566	+	0.710630i	$0.748410\pi$
$762$	−1991.60	−0.0946824
$763$	−6326.97	−0.300199
$764$	−6183.56	−0.292818
$765$	15588.5	0.736739
$766$	−40225.9	−1.89742
$767$	0	0
$768$	−10798.6	−0.507372
$769$	−7585.63	−0.355715	−0.177857	−	0.984056i	$-0.556917\pi$
$769$	−7585.63	−0.355715	−0.177857	+	0.984056i	$0.556917\pi$
$770$	24485.2	1.14596
$771$	−2437.85	−0.113874
$772$	−53829.2	−2.50953
$773$	−3284.29	−0.152817	−0.0764086	−	0.997077i	$-0.524345\pi$
$773$	−3284.29	−0.152817	−0.0764086	+	0.997077i	$0.524345\pi$
$774$	−17686.2	−0.821341
$775$	10393.0	0.481712
$776$	−7716.07	−0.356947
$777$	14752.6	0.681140
$778$	7267.08	0.334881
$779$	−3741.98	−0.172106
$780$	0	0
$781$	22945.3	1.05128
$782$	43920.8	2.00845
$783$	−5565.92	−0.254036
$784$	295.443	0.0134586
$785$	15064.6	0.684939
$786$	−4326.79	−0.196351
$787$	41624.1	1.88531	0.942654	−	0.333772i	$-0.108321\pi$
$787$	41624.1	1.88531	0.942654	+	0.333772i	$0.108321\pi$
$788$	34393.8	1.55486
$789$	−7824.87	−0.353071
$790$	54789.4	2.46749
$791$	−222.046	−0.00998108
$792$	4773.38	0.214160
$793$	0	0
$794$	16274.3	0.727398
$795$	7537.20	0.336248
$796$	39518.4	1.75967
$797$	−30333.3	−1.34813	−0.674066	−	0.738671i	$-0.735454\pi$
$797$	−30333.3	−1.34813	−0.674066	+	0.738671i	$0.735454\pi$
$798$	3409.04	0.151226
$799$	−21448.4	−0.949674
$800$	7987.87	0.353017
$801$	4789.03	0.211251
$802$	−15852.2	−0.697954
$803$	−13687.4	−0.601518
$804$	1500.13	0.0658027
$805$	15552.0	0.680914
$806$	0	0
$807$	−14373.1	−0.626958
$808$	−31714.0	−1.38081
$809$	−24853.9	−1.08012	−0.540060	−	0.841627i	$-0.681598\pi$
$809$	−24853.9	−1.08012	−0.540060	+	0.841627i	$0.681598\pi$
$810$	4755.92	0.206304
$811$	17383.5	0.752674	0.376337	−	0.926483i	$-0.377184\pi$
$811$	17383.5	0.752674	0.376337	+	0.926483i	$0.377184\pi$
$812$	43723.7	1.88966
$813$	10990.9	0.474128
$814$	−33322.0	−1.43481
$815$	−29815.8	−1.28148
$816$	1882.91	0.0807782
$817$	6455.23	0.276426
$818$	66887.8	2.85902
$819$	0	0
$820$	41009.4	1.74648
$821$	31169.4	1.32499	0.662496	−	0.749065i	$-0.269497\pi$
$821$	31169.4	1.32499	0.662496	+	0.749065i	$0.269497\pi$
$822$	6045.52	0.256523
$823$	5512.79	0.233492	0.116746	−	0.993162i	$-0.462754\pi$
$823$	5512.79	0.233492	0.116746	+	0.993162i	$0.462754\pi$
$824$	−13370.8	−0.565282
$825$	−3119.63	−0.131650
$826$	−17698.1	−0.745516
$827$	13335.8	0.560738	0.280369	−	0.959892i	$-0.409543\pi$
$827$	13335.8	0.560738	0.280369	+	0.959892i	$0.409543\pi$
$828$	8215.85	0.344832
$829$	−28338.5	−1.18726	−0.593628	−	0.804739i	$-0.702305\pi$
$829$	−28338.5	−1.18726	−0.593628	+	0.804739i	$0.702305\pi$
$830$	64315.5	2.68967
$831$	−1872.98	−0.0781864
$832$	0	0
$833$	8470.66	0.352330
$834$	−10709.3	−0.444646
$835$	−7757.27	−0.321499
$836$	−4721.15	−0.195316
$837$	6726.82	0.277793
$838$	−16866.3	−0.695272
$839$	27149.5	1.11717	0.558585	−	0.829447i	$-0.311344\pi$
$839$	27149.5	1.11717	0.558585	+	0.829447i	$0.311344\pi$
$840$	−13787.0	−0.566306
$841$	18106.9	0.742421
$842$	3610.76	0.147785
$843$	−16605.4	−0.678433
$844$	−13328.2	−0.543573
$845$	0	0
$846$	−6543.71	−0.265931
$847$	11870.7	0.481560
$848$	910.404	0.0368672
$849$	525.454	0.0212409
$850$	25446.7	1.02684
$851$	−21164.7	−0.852547
$852$	−35010.9	−1.40781
$853$	−7978.22	−0.320245	−0.160123	−	0.987097i	$-0.551189\pi$
$853$	−7978.22	−0.320245	−0.160123	+	0.987097i	$0.551189\pi$
$854$	−14073.9	−0.563933
$855$	−1735.85	−0.0694325
$856$	−10158.4	−0.405616
$857$	−13614.4	−0.542657	−0.271329	−	0.962487i	$-0.587463\pi$
$857$	−13614.4	−0.542657	−0.271329	+	0.962487i	$0.587463\pi$
$858$	0	0
$859$	−35007.7	−1.39051	−0.695255	−	0.718763i	$-0.744709\pi$
$859$	−35007.7	−1.39051	−0.695255	+	0.718763i	$0.744709\pi$
$860$	−70744.8	−2.80509
$861$	12572.1	0.497624
$862$	13148.9	0.519551
$863$	24461.5	0.964867	0.482434	−	0.875933i	$-0.339753\pi$
$863$	24461.5	0.964867	0.482434	+	0.875933i	$0.339753\pi$
$864$	5170.13	0.203578
$865$	−44292.2	−1.74102
$866$	−25287.8	−0.992278
$867$	39245.9	1.53733
$868$	−52843.3	−2.06638
$869$	−23261.3	−0.908040
$870$	−36311.5	−1.41503
$871$	0	0
$872$	−8046.82	−0.312500
$873$	3263.95	0.126538
$874$	−4890.77	−0.189282
$875$	−17989.5	−0.695037
$876$	20884.9	0.805520
$877$	43121.6	1.66034	0.830168	−	0.557514i	$-0.188245\pi$
$877$	43121.6	1.66034	0.830168	+	0.557514i	$0.188245\pi$
$878$	−68789.3	−2.64411
$879$	23323.0	0.894955
$880$	−1505.94	−0.0576878
$881$	−40824.5	−1.56120	−0.780598	−	0.625034i	$-0.785085\pi$
$881$	−40824.5	−1.56120	−0.780598	+	0.625034i	$0.785085\pi$
$882$	2584.32	0.0986605
$883$	8262.14	0.314885	0.157442	−	0.987528i	$-0.449675\pi$
$883$	8262.14	0.314885	0.157442	+	0.987528i	$0.449675\pi$
$884$	0	0
$885$	9011.70	0.342288
$886$	−10722.3	−0.406571
$887$	−40858.6	−1.54667	−0.773336	−	0.633997i	$-0.781413\pi$
$887$	−40858.6	−1.54667	−0.773336	+	0.633997i	$0.781413\pi$
$888$	18762.8	0.709050
$889$	−2442.22	−0.0921365
$890$	31243.2	1.17671
$891$	−2019.17	−0.0759201
$892$	−69684.1	−2.61569
$893$	2388.37	0.0895001
$894$	1847.42	0.0691131
$895$	−12638.6	−0.472023
$896$	−37767.1	−1.40816
$897$	0	0
$898$	−32582.3	−1.21079
$899$	−51359.4	−1.90537
$900$	4760.07	0.176299
$901$	26102.2	0.965139
$902$	−28396.8	−1.04824
$903$	−21687.9	−0.799256
$904$	−282.404	−0.0103901
$905$	49569.6	1.82072
$906$	−32383.0	−1.18747
$907$	−32729.3	−1.19819	−0.599095	−	0.800678i	$-0.704473\pi$
$907$	−32729.3	−1.19819	−0.599095	+	0.800678i	$0.704473\pi$
$908$	11684.4	0.427048
$909$	13415.2	0.489500
$910$	0	0
$911$	11065.9	0.402447	0.201223	−	0.979545i	$-0.435508\pi$
$911$	11065.9	0.402447	0.201223	+	0.979545i	$0.435508\pi$
$912$	−209.670	−0.00761279
$913$	−27305.7	−0.989801
$914$	36474.5	1.31999
$915$	7166.29	0.258918
$916$	−2446.26	−0.0882386
$917$	−5305.77	−0.191071
$918$	16470.3	0.592158
$919$	50682.2	1.81921	0.909604	−	0.415477i	$-0.136385\pi$
$919$	50682.2	1.81921	0.909604	+	0.415477i	$0.136385\pi$
$920$	19779.5	0.708816
$921$	−24068.5	−0.861114
$922$	−18856.2	−0.673531
$923$	0	0
$924$	15861.8	0.564735
$925$	−12262.3	−0.435874
$926$	32369.3	1.14873
$927$	5655.92	0.200394
$928$	−39474.0	−1.39633
$929$	−41045.5	−1.44958	−0.724790	−	0.688970i	$-0.758063\pi$
$929$	−41045.5	−1.44958	−0.724790	+	0.688970i	$0.758063\pi$
$930$	43885.1	1.54737
$931$	−943.243	−0.0332047
$932$	11585.6	0.407188
$933$	−27794.6	−0.975300
$934$	9677.86	0.339046
$935$	−43176.9	−1.51020
$936$	0	0
$937$	−788.985	−0.0275080	−0.0137540	−	0.999905i	$-0.504378\pi$
$937$	−788.985	−0.0275080	−0.0137540	+	0.999905i	$0.504378\pi$
$938$	3000.25	0.104437
$939$	22270.7	0.773991
$940$	−26174.8	−0.908222
$941$	25676.2	0.889499	0.444750	−	0.895655i	$-0.353293\pi$
$941$	25676.2	0.889499	0.444750	+	0.895655i	$0.353293\pi$
$942$	15916.7	0.550524
$943$	−18036.5	−0.622851
$944$	1088.51	0.0375295
$945$	5832.00	0.200757
$946$	48986.9	1.68362
$947$	679.352	0.0233115	0.0116557	−	0.999932i	$-0.496290\pi$
$947$	679.352	0.0233115	0.0116557	+	0.999932i	$0.496290\pi$
$948$	35493.2	1.21600
$949$	0	0
$950$	−2833.60	−0.0967726
$951$	−7923.12	−0.270163
$952$	−47746.0	−1.62548
$953$	−20238.4	−0.687917	−0.343958	−	0.938985i	$-0.611768\pi$
$953$	−20238.4	−0.687917	−0.343958	+	0.938985i	$0.611768\pi$
$954$	7963.54	0.270261
$955$	6297.21	0.213375
$956$	25064.2	0.847944
$957$	15416.4	0.520733
$958$	−16894.9	−0.569781
$959$	7413.38	0.249625
$960$	32279.5	1.08523
$961$	32280.6	1.08357
$962$	0	0
$963$	4297.08	0.143792
$964$	−49503.6	−1.65395
$965$	54818.6	1.82868
$966$	16431.7	0.547289
$967$	6161.63	0.204906	0.102453	−	0.994738i	$-0.467331\pi$
$967$	6161.63	0.204906	0.102453	+	0.994738i	$0.467331\pi$
$968$	15097.5	0.501293
$969$	−6011.45	−0.199294
$970$	21293.7	0.704845
$971$	−48569.5	−1.60522	−0.802610	−	0.596504i	$-0.796556\pi$
$971$	−48569.5	−1.60522	−0.802610	+	0.596504i	$0.796556\pi$
$972$	3080.94	0.101668
$973$	−13132.4	−0.432689
$974$	−37012.5	−1.21761
$975$	0	0
$976$	865.602	0.0283886
$977$	44595.8	1.46033	0.730167	−	0.683269i	$-0.239442\pi$
$977$	44595.8	1.46033	0.730167	+	0.683269i	$0.239442\pi$
$978$	−31502.4	−1.03000
$979$	−13264.6	−0.433031
$980$	10337.3	0.336951
$981$	3403.86	0.110782
$982$	−82224.4	−2.67198
$983$	29599.0	0.960389	0.480195	−	0.877162i	$-0.340566\pi$
$983$	29599.0	0.960389	0.480195	+	0.877162i	$0.340566\pi$
$984$	15989.5	0.518015
$985$	−35026.0	−1.13302
$986$	−125751.	−4.06159
$987$	−8024.29	−0.258780
$988$	0	0
$989$	31114.5	1.00039
$990$	−13172.9	−0.422890
$991$	5718.45	0.183302	0.0916511	−	0.995791i	$-0.470786\pi$
$991$	5718.45	0.183302	0.0916511	+	0.995791i	$0.470786\pi$
$992$	47707.2	1.52692
$993$	−32338.5	−1.03347
$994$	−70021.9	−2.23437
$995$	−40244.8	−1.28226
$996$	41664.4	1.32549
$997$	−1491.44	−0.0473766	−0.0236883	−	0.999719i	$-0.507541\pi$
$997$	−1491.44	−0.0473766	−0.0236883	+	0.999719i	$0.507541\pi$
$998$	50164.8	1.59112
$999$	−7936.77	−0.251360

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.4.a.l.1.1		4
3.2	odd	2		1521.4.a.w.1.4		4
13.5	odd	4		39.4.b.b.25.4	yes	4
13.8	odd	4		39.4.b.b.25.1	✓	4
13.12	even	2	inner	507.4.a.l.1.4		4
39.5	even	4		117.4.b.e.64.1		4
39.8	even	4		117.4.b.e.64.4		4
39.38	odd	2		1521.4.a.w.1.1		4
52.31	even	4		624.4.c.c.337.4		4
52.47	even	4		624.4.c.c.337.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.4.b.b.25.1	✓	4	13.8	odd	4
39.4.b.b.25.4	yes	4	13.5	odd	4
117.4.b.e.64.1		4	39.5	even	4
117.4.b.e.64.4		4	39.8	even	4
507.4.a.l.1.1		4	1.1	even	1	trivial
507.4.a.l.1.4		4	13.12	even	2	inner
624.4.c.c.337.1		4	52.47	even	4
624.4.c.c.337.4		4	52.31	even	4
1521.4.a.w.1.1		4	39.38	odd	2
1521.4.a.w.1.4		4	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	507.a (trivial)

\(f(q)\)	\(=\)	\(q-4.54739 q^{2} +3.00000 q^{3} +12.6788 q^{4} -12.9118 q^{5} -13.6422 q^{6} -16.7289 q^{7} -21.2762 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-4.54739 q^{2} +3.00000 q^{3} +12.6788 q^{4} -12.9118 q^{5} -13.6422 q^{6} -16.7289 q^{7} -21.2762 q^{8} +9.00000 q^{9} +58.7151 q^{10} -24.9280 q^{11} +38.0363 q^{12} +76.0727 q^{14} -38.7355 q^{15} -4.67878 q^{16} -134.145 q^{17} -40.9265 q^{18} +14.9376 q^{19} -163.706 q^{20} -50.1866 q^{21} +113.358 q^{22} +72.0000 q^{23} -63.8287 q^{24} +41.7151 q^{25} +27.0000 q^{27} -212.101 q^{28} -206.145 q^{29} +176.145 q^{30} +249.142 q^{31} +191.486 q^{32} -74.7841 q^{33} +610.012 q^{34} +216.000 q^{35} +114.109 q^{36} -293.955 q^{37} -67.9273 q^{38} +274.715 q^{40} -250.506 q^{41} +228.218 q^{42} +432.145 q^{43} -316.057 q^{44} -116.206 q^{45} -327.412 q^{46} +159.889 q^{47} -14.0363 q^{48} -63.1454 q^{49} -189.695 q^{50} -402.436 q^{51} -194.581 q^{53} -122.780 q^{54} +321.866 q^{55} +355.927 q^{56} +44.8129 q^{57} +937.424 q^{58} -232.647 q^{59} -491.118 q^{60} -185.006 q^{61} -1132.94 q^{62} -150.560 q^{63} -833.333 q^{64} +340.073 q^{66} +39.4393 q^{67} -1700.80 q^{68} +216.000 q^{69} -982.237 q^{70} -920.460 q^{71} -191.486 q^{72} +549.078 q^{73} +1336.73 q^{74} +125.145 q^{75} +189.391 q^{76} +417.018 q^{77} +933.140 q^{79} +60.4116 q^{80} +81.0000 q^{81} +1139.15 q^{82} +1095.38 q^{83} -636.304 q^{84} +1732.06 q^{85} -1965.13 q^{86} -618.436 q^{87} +530.375 q^{88} +532.114 q^{89} +528.436 q^{90} +912.872 q^{92} +747.425 q^{93} -727.079 q^{94} -192.872 q^{95} +574.459 q^{96} +362.661 q^{97} +287.147 q^{98} -224.352 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 12 q^{3} + 14 q^{4} + 36 q^{9}+O(q^{10}) \) 4 * q + 12 * q^3 + 14 * q^4 + 36 * q^9	\( 4 q + 12 q^{3} + 14 q^{4} + 36 q^{9} + 88 q^{10} + 42 q^{12} + 84 q^{14} + 18 q^{16} - 96 q^{17} + 380 q^{22} + 288 q^{23} + 20 q^{25} + 108 q^{27} - 384 q^{29} + 264 q^{30} + 864 q^{35} + 126 q^{36} - 492 q^{38} + 952 q^{40} + 252 q^{42} + 1288 q^{43} + 54 q^{48} + 188 q^{49} - 288 q^{51} + 984 q^{53} - 328 q^{55} + 1644 q^{56} + 288 q^{61} - 1668 q^{62} - 1314 q^{64} + 1140 q^{66} - 4380 q^{68} + 864 q^{69} + 3144 q^{74} + 60 q^{75} - 1416 q^{77} + 4320 q^{79} + 324 q^{81} + 3088 q^{82} - 1152 q^{87} - 1036 q^{88} + 792 q^{90} + 1008 q^{92} - 1660 q^{94} + 1872 q^{95}+O(q^{100}) \) 4 * q + 12 * q^3 + 14 * q^4 + 36 * q^9 + 88 * q^10 + 42 * q^12 + 84 * q^14 + 18 * q^16 - 96 * q^17 + 380 * q^22 + 288 * q^23 + 20 * q^25 + 108 * q^27 - 384 * q^29 + 264 * q^30 + 864 * q^35 + 126 * q^36 - 492 * q^38 + 952 * q^40 + 252 * q^42 + 1288 * q^43 + 54 * q^48 + 188 * q^49 - 288 * q^51 + 984 * q^53 - 328 * q^55 + 1644 * q^56 + 288 * q^61 - 1668 * q^62 - 1314 * q^64 + 1140 * q^66 - 4380 * q^68 + 864 * q^69 + 3144 * q^74 + 60 * q^75 - 1416 * q^77 + 4320 * q^79 + 324 * q^81 + 3088 * q^82 - 1152 * q^87 - 1036 * q^88 + 792 * q^90 + 1008 * q^92 - 1660 * q^94 + 1872 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more