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  • lfunc_lfunctions • Show schema
    {'Lhash': '1155986008940675185626611949170,1206985344005457673985811539108,1675018244127285440190113347284', 'a10': 0, 'a2': -2, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': -8, 'a8': 2, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 172768.2590114603, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[3, [1]], [5, [1]], [31, [1, -3, 3, -1]]], 'bad_primes': [3, 5, 31], 'central_character': '6975.1', 'coefficient_field': '1.1.1.1', 'conductor': 339338109375, 'conductor_radical': 465, 'degree': 6, 'euler_factors': [[1, 2, 4, 6, 8, 8, 8], [1], [1], [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], [1, 8, 119, 594, 4403, 10952, 50653], [1, -2, 65, -298, 2665, -3362, 68921], [1, 4, 49, 280, 2107, 7396, 79507], [1, -20, 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'5.99300811871781195143689308922458', '6.28015763317819638869172978197017', '6.53990033046792016285008051359493', '6.60736938090572688280207777531709', '7.10275674714411160090965968611757', '7.18005014779322959888260283557649', '7.41851467524818787739994097884376', '7.54688567788475905713659969811855', '7.59287199289124367728341383388201'], 'prelabel': '6-6975e3-1.1-c1e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.4629521913143115, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'spectral_label': 'c1e3-0', 'trace_hash': 671573142176847062, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.911912169435765673111129315948', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '0.952143551060639675623784722284', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '1.32135640832396013377385105055', 'prec': 100}}
  • lfunc_search • Show schema
    {'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]], '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}}
  • lfunc_instances • Show schema
    {'Lhash': '1155986008940675185626611949170,1206985344005457673985811539108,1675018244127285440190113347284', 'Lhash_array': ['1155986008940675185626611949170', '1206985344005457673985811539108', '1675018244127285440190113347284'], 'factors': ['2-6975-1.1-c1-0-104', '2-6975-1.1-c1-0-113', '2-6975-1.1-c1-0-200'], 'label': '6-6975e3-1.1-c1e3-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6975/2/a/z'}