Database - lfunc_search

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Table lfunc_search

L-function search data

Column	Type	Example
algebraic	boolean	True
analytic_conductor	double precision	2471.6893441667144
bad_primes	bigint[]	[2, 3, 5, 7, 11, 67]
central_character	text	'1.1'
conductor	numeric	309540
conductor_radical	bigint	154770
degree	smallint	2
dirichlet_coefficients	numeric[]	[1, 0, -1, 0, 1, 0, 1, 0, 1, 0, 1, 0, -5, 0, -1, 0, 4, 0, -5, 0, -1, 0, 0, 0, 1, 0, -1, 0, -10, 0, 1...
euler11	numeric[]	[1, -1, 0]
euler13	numeric[]	[1, 5, 13]
euler17	numeric[]	[1, -4, 17]
euler19	numeric[]	[1, 5, 19]
euler2	numeric[]	[1, 0, 0]
euler23	numeric[]	[1, 0, 23]
euler29	numeric[]	[1, 10, 29]
euler3	numeric[]	[1, 1, 0]
euler31	numeric[]	[1, -1, 31]
euler37	numeric[]	[1, 4, 37]
euler41	numeric[]	[1, 10, 41]
euler43	numeric[]	[1, 6, 43]
euler47	numeric[]	[1, -3, 47]
euler5	numeric[]	[1, -1, 0]
euler53	numeric[]	[1, 7, 53]
euler59	numeric[]	[1, 4, 59]
euler61	numeric[]	[1, 10, 61]
euler67	numeric[]	[1, -1, 0]
euler7	numeric[]	[1, -1, 0]
euler71	numeric[]	[1, 1, 71]
euler73	numeric[]	[1, 8, 73]
euler79	numeric[]	[1, -3, 79]
euler83	numeric[]	[1, 14, 83]
euler89	numeric[]	[1, 6, 89]
euler97	numeric[]	[1, 14, 97]
euler_factors	numeric[]	[[1, 0, 0], [1, 1, 0], [1, -1, 0], [1, -1, 0], [1, -1, 0], [1, 5, 13], [1, -4, 17], [1, 5, 19], [1, ...
index	smallint	38
instance_types	text[]	['ECQ']
instance_urls	text[]	['EllipticCurve/Q/309540/p']
is_instance_Artin	boolean	False
is_instance_BMF	boolean	False
is_instance_CMF	boolean	False
is_instance_DIR	boolean	False
is_instance_ECNF	boolean	False
is_instance_ECQ	boolean	True
is_instance_G2Q	boolean	False
is_instance_HMF	boolean	False
is_instance_MaassGL3	boolean	False
is_instance_MaassGL4	boolean	False
is_instance_MaassGSp4	boolean	False
is_instance_NF	boolean	False
label	text	'2-309540-1.1-c1-0-38'
motivic_weight	smallint	1
mu_imag	numeric[]	[]
mu_real	smallint[]	[]
nu_imag	numeric[]	[0.0]
nu_real_doubled	smallint[]	[1]
order_of_vanishing	smallint	2
prelabel	text	'2-309540-1.1-c1-0'
primitive	boolean	True
rational	boolean	True
root_analytic_conductor	double precision	49.71608737789725
root_angle	double precision	0.0
self_dual	boolean	True
spectral_label	text	'c1-0'
trace_hash	bigint	2117931314497392841
z1	numeric	1.264905326398229

{'algebraic': True, 'analytic_conductor': 172768.2590114603, 'bad_primes': [3, 5, 31], 'central_character': '1.1', 'conductor': 339338109375, 'conductor_radical': 465, 'degree': 6, 'dirichlet_coefficients': [1, -2, 0, 0, 0, 0, -8, 2, 0, 0, 3, 0, -4, 16, 0, 0, -7, 0, 9, 0, 0, -6, -9, 0, 0, 8, 0, 0, 9, 0, 3, 0, 0, 14, 0, 0, -8, -18, 0, 0, 2, 0, -4, 0, 0, 18, 20, 0, 27, 0, 0, 0, 25, 0, 0, -16, 0, -18, 2, 0, 2, -6, 0, -4, 0, 0, -15, 0, 0, 0, -12, 0, -2, 16, 0, 0, -24, 0, 12, 0, 0, -4, -13, 0, 0, 8, 0, 6, -15, 0, 32, 0, 0, -40, 0, 0, -7, -54, 0, 0], 'euler11': [1, -3, 32, -65, 352, -363, 1331], 'euler13': [1, 4, 23, 114, 299, 676, 2197], 'euler17': [1, 7, 44, 179, 748, 2023, 4913], 'euler19': [1, -9, 84, -369, 1596, -3249, 6859], 'euler2': [1, 2, 4, 6, 8, 8, 8], 'euler23': [1, 9, 92, 431, 2116, 4761, 12167], 'euler29': [1, -9, 80, -509, 2320, -7569, 24389], 'euler3': [1, 0, 0, 0, 0, 0, 0], 'euler31': [1, -3, 3, -1, 0, 0, 0], 'euler37': [1, 8, 119, 594, 4403, 10952, 50653], 'euler41': [1, -2, 65, -298, 2665, -3362, 68921], 'euler43': [1, 4, 49, 280, 2107, 7396, 79507], 'euler47': [1, -20, 261, -2088, 12267, -44180, 103823], 'euler5': [1, 0, 0, 0, 0, 0, 0], 'euler53': [1, -25, 288, -2301, 15264, -70225, 148877], 'euler59': [1, -2, 103, -162, 6077, -6962, 205379], 'euler61': [1, -2, 131, -204, 7991, -7442, 226981], 'euler67': [1, 15, 236, 2011, 15812, 67335, 300763], 'euler7': [1, 8, 37, 116, 259, 392, 343], 'euler71': [1, 12, 101, 520, 7171, 60492, 357911], 'euler73': [1, 2, 71, 588, 5183, 10658, 389017], 'euler79': [1, -12, 165, -1982, 13035, -74892, 493039], 'euler83': [1, 13, 192, 1287, 15936, 89557, 571787], 'euler89': [1, 15, 338, 2773, 30082, 118815, 704969], 'euler97': [1, 7, 262, 1255, 25414, 65863, 912673], 'euler_factors': [[1, 2, 4, 6, 8, 8, 8], [1, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0], [1, 8, 37, 116, 259, 392, 343], [1, -3, 32, -65, 352, -363, 1331], [1, 4, 23, 114, 299, 676, 2197], [1, 7, 44, 179, 748, 2023, 4913], [1, -9, 84, -369, 1596, -3249, 6859], [1, 9, 92, 431, 2116, 4761, 12167], [1, -9, 80, -509, 2320, -7569, 24389], [1, -3, 3, -1, 0, 0, 0], [1, 8, 119, 594, 4403, 10952, 50653], [1, -2, 65, -298, 2665, -3362, 68921], [1, 4, 49, 280, 2107, 7396, 79507], [1, -20, 261, -2088, 12267, -44180, 103823], [1, -25, 288, -2301, 15264, -70225, 148877], [1, -2, 103, -162, 6077, -6962, 205379], [1, -2, 131, -204, 7991, -7442, 226981], [1, 15, 236, 2011, 15812, 67335, 300763], [1, 12, 101, 520, 7171, 60492, 357911], [1, 2, 71, 588, 5183, 10658, 389017], [1, -12, 165, -1982, 13035, -74892, 493039], [1, 13, 192, 1287, 15936, 89557, 571787], [1, 15, 338, 2773, 30082, 118815, 704969], [1, 7, 262, 1255, 25414, 65863, 912673]], 'id': 21512000, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/6975/2/a/z'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '6-6975e3-1.1-c1e3-0-5', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0, 0, 0], 'nu_real_doubled': [1, 1, 1], 'order_of_vanishing': 3, 'prelabel': '6-6975e3-1.1-c1e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.4629521913143115, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e3-0', 'trace_hash': 671573142176847062, 'z1': {'__RealLiteral__': 0, 'data': '0.911912169435765673111129315948', 'prec': 100}}