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  • lfunc_lfunctions • Show schema
    {'Lhash': '493749516261558856854173527278,567020247777828681750482291613,1124068388502502177796032390936', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': -3, 'a6': 0, 'a7': -3, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 380137.2649529088, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [1]], [3, [1]], [7, [1, 3, 3, 1]]], 'bad_primes': [2, 3, 7], 'central_character': '9072.1', 'coefficient_field': '1.1.1.1', 'conductor': 746636341248, 'conductor_radical': 42, 'degree': 6, 'euler_factors': [[1], [1], [1, 3, 9, 21, 45, 75, 125], [1, 3, 3, 1], [1, -6, 36, -123, 396, -726, 1331], [1, 3, 42, 79, 546, 507, 2197], [1, 0, 18, 9, 306, 0, 4913], [1, 3, 21, 65, 399, 1083, 6859], [1, -6, 54, -177, 1242, -3174, 12167], [1, 15, 135, 807, 3915, 12615, 24389], [1, -3, 15, -133, 465, -2883, 29791], [1, 3, 33, 115, 1221, 4107, 50653], [1, 6, 126, 483, 5166, 10086, 68921], [1, 3, 21, -205, 903, 5547, 79507], [1, -15, 177, 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'5.42840296532811000776675277804723', '5.69499919930806367504630143427081', '5.92276239123946319178184153994249', '6.33761861992199912818364879028831', '6.45721555531639437052036236299809', '6.60350446367447337779851587846506', '6.85506079772465062265222206886788', '7.00006831997122144313325334048566', '7.21959068251372298484695259216237', '7.65114175383913741591578708852408', '7.67837693812765894793196220577345', '7.75241509624435618088966978174746'], 'prelabel': '6-9072e3-1.1-c1e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 8.511185858251809, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e3-0', 'trace_hash': 661798760771655388, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.38949969035053000853888353676', 'prec': 97}, 'z2': {'__RealLiteral__': 0, 'data': '0.44730010594066034148702603379', 'prec': 97}, 'z3': {'__RealLiteral__': 0, 'data': '0.886733606484407846689839335532', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 380137.2649529088, 'bad_primes': [2, 3, 7], 'central_character': '1.1', 'conductor': 746636341248, 'conductor_radical': 42, 'degree': 6, 'dirichlet_coefficients': [1, 0, 0, 0, -3, 0, -3, 0, 0, 0, 6, 0, -3, 0, 0, 0, 0, 0, -3, 0, 0, 0, 6, 0, 0, 0, 0, 0, -15, 0, 3, 0, 0, 0, 9, 0, -3, 0, 0, 0, -6, 0, -3, 0, 0, 0, 15, 0, 6, 0, 0, 0, -18, 0, -18, 0, 0, 0, 3, 0, -6, 0, 0, 0, 9, 0, 6, 0, 0, 0, 15, 0, 9, 0, 0, 0, -18, 0, -3, 0, 0, 0, 18, 0, 0, 0, 0, 0, 6, 0, 9, 0, 0, 0, 9, 0, -15, 0, 0, 0], 'euler11': [1, -6, 36, -123, 396, -726, 1331], 'euler13': [1, 3, 42, 79, 546, 507, 2197], 'euler17': [1, 0, 18, 9, 306, 0, 4913], 'euler19': [1, 3, 21, 65, 399, 1083, 6859], 'euler2': [1, 0, 0, 0, 0, 0, 0], 'euler23': [1, -6, 54, -177, 1242, -3174, 12167], 'euler29': [1, 15, 135, 807, 3915, 12615, 24389], 'euler3': [1, 0, 0, 0, 0, 0, 0], 'euler31': [1, -3, 15, -133, 465, -2883, 29791], 'euler37': [1, 3, 33, 115, 1221, 4107, 50653], 'euler41': [1, 6, 126, 483, 5166, 10086, 68921], 'euler43': [1, 3, 21, -205, 903, 5547, 79507], 'euler47': [1, -15, 177, -1329, 8319, -33135, 103823], 'euler5': [1, 3, 9, 21, 45, 75, 125], 'euler53': [1, 18, 198, 1521, 10494, 50562, 148877], 'euler59': [1, -3, 123, -435, 7257, -10443, 205379], 'euler61': [1, 6, 138, 763, 8418, 22326, 226981], 'euler67': [1, -6, 174, -745, 11658, -26934, 300763], 'euler7': [1, 3, 3, 1, 0, 0, 0], 'euler71': [1, -15, 231, -1833, 16401, -75615, 357911], 'euler73': [1, -9, 207, -1235, 15111, -47961, 389017], 'euler79': [1, 3, 3, -889, 237, 18723, 493039], 'euler83': [1, -18, 324, -3015, 26892, -124002, 571787], 'euler89': [1, -6, 72, 21, 6408, -47526, 704969], 'euler97': [1, 15, 309, 2887, 29973, 141135, 912673], 'euler_factors': [[1, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0], [1, 3, 9, 21, 45, 75, 125], [1, 3, 3, 1, 0, 0, 0], [1, -6, 36, -123, 396, -726, 1331], [1, 3, 42, 79, 546, 507, 2197], [1, 0, 18, 9, 306, 0, 4913], [1, 3, 21, 65, 399, 1083, 6859], [1, -6, 54, -177, 1242, -3174, 12167], [1, 15, 135, 807, 3915, 12615, 24389], [1, -3, 15, -133, 465, -2883, 29791], [1, 3, 33, 115, 1221, 4107, 50653], [1, 6, 126, 483, 5166, 10086, 68921], [1, 3, 21, -205, 903, 5547, 79507], [1, -15, 177, -1329, 8319, -33135, 103823], [1, 18, 198, 1521, 10494, 50562, 148877], [1, -3, 123, -435, 7257, -10443, 205379], [1, 6, 138, 763, 8418, 22326, 226981], [1, -6, 174, -745, 11658, -26934, 300763], [1, -15, 231, -1833, 16401, -75615, 357911], [1, -9, 207, -1235, 15111, -47961, 389017], [1, 3, 3, -889, 237, 18723, 493039], [1, -18, 324, -3015, 26892, -124002, 571787], [1, -6, 72, 21, 6408, -47526, 704969], [1, 15, 309, 2887, 29973, 141135, 912673]], 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/9072/2/a/bt'], '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': '6-9072e3-1.1-c1e3-0-3', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0, 0, 0], 'nu_real_doubled': [1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '6-9072e3-1.1-c1e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 8.511185858251809, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e3-0', 'trace_hash': 661798760771655388, 'z1': {'__RealLiteral__': 0, 'data': '0.38949969035053000853888353676', 'prec': 97}}
  • lfunc_instances • Show schema
    {'Lhash': '493749516261558856854173527278,567020247777828681750482291613,1124068388502502177796032390936', 'Lhash_array': ['493749516261558856854173527278', '567020247777828681750482291613', '1124068388502502177796032390936'], 'factors': ['2-9072-1.1-c1-0-8', '2-9072-1.1-c1-0-14', '2-9072-1.1-c1-0-58'], 'label': '6-9072e3-1.1-c1e3-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9072/2/a/bt'}