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lfunc_lfunctions • Show schema
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{'Lhash': '2715801517999249225179216658776', 'a10': -10, 'a2': -2, 'a3': 2, 'a4': 4, 'a5': 5, 'a6': -4, 'a7': -12, 'a8': -8, 'a9': -23, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 11.210362901090722, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 2]], [5, [1, -5]], [19, [1, 19]]], 'bad_primes': [2, 5, 19], 'central_character': '190.1', 'coefficient_field': '1.1.1.1', 'conductor': 190, 'conductor_radical': 190, 'degree': 2, 'euler_factors': [[1, 2], [1, -2, 27], [1, -5], [1, 12, 343], [1, 20, 1331], [1, 4, 2197], [1, 34, 4913], [1, 19], [1, -40, 12167], [1, 150, 24389], [1, 200, 29791], [1, 156, 50653], [1, 218, 68921], [1, -248, 79507], [1, 180, 103823], [1, -72, 148877], [1, 48, 205379], [1, 134, 226981], [1, -334, 300763], [1, 520, 357911], [1, -438, 389017], [1, -980, 493039], [1, 156, 571787], [1, -670, 704969], [1, -1124, 912673], [1, 1454, 1030301], [1, -1370, 1092727], [1, -338, 1225043], [1, -102, 1295029], 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{'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'trace_hash': 1952882770947534929, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.14238964388948572972835276313', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.36109750994214809893125246849', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.36523194234257699335348370860', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 11.210362901090722, 'bad_primes': [2, 5, 19], 'central_character': '1.1', 'conductor': 190, 'conductor_radical': 190, 'degree': 2, 'dirichlet_coefficients': [1, -2, 2, 4, 5, -4, -12, -8, -23, -10, -20, 8, -4, 24, 10, 16, -34, 46, -19, 20, -24, 40, 40, -16, 25, 8, -100, -48, -150, -20, -200, -32, -40, 68, -60, -92, -156, 38, -8, -40, -218, 48, 248, -80, -115, -80, -180, 32, -199, -50, -68, -16, 72, 200, -100, 96, -38, 300, -48, 40, -134, 400, 276, 64, -20, 80, 334, -136, 80, 120, -520, 184, 438, 312, 50, -76, 240, 16, 980, 80, 421, 436, -156, -96, -170, -496, -300, 160, 670, 230, 48, 160, -400, 360, -95, -64, 1124, 398, 460, 100], 'euler11': [1, 20, 1331], 'euler13': [1, 4, 2197], 'euler17': [1, 34, 4913], 'euler19': [1, 19, 0], 'euler2': [1, 2, 0], 'euler23': [1, -40, 12167], 'euler29': [1, 150, 24389], 'euler3': [1, -2, 27], 'euler31': [1, 200, 29791], 'euler37': [1, 156, 50653], 'euler41': [1, 218, 68921], 'euler43': [1, -248, 79507], 'euler47': [1, 180, 103823], 'euler5': [1, -5, 0], 'euler53': [1, -72, 148877], 'euler59': [1, 48, 205379], 'euler61': [1, 134, 226981], 'euler67': [1, -334, 300763], 'euler7': [1, 12, 343], 'euler71': [1, 520, 357911], 'euler73': [1, -438, 389017], 'euler79': [1, -980, 493039], 'euler83': [1, 156, 571787], 'euler89': [1, -670, 704969], 'euler97': [1, -1124, 912673], 'euler_factors': [[1, 2, 0], [1, -2, 27], [1, -5, 0], [1, 12, 343], [1, 20, 1331], [1, 4, 2197], [1, 34, 4913], [1, 19, 0], [1, -40, 12167], [1, 150, 24389], [1, 200, 29791], [1, 156, 50653], [1, 218, 68921], [1, -248, 79507], [1, 180, 103823], [1, -72, 148877], [1, 48, 205379], [1, 134, 226981], [1, -334, 300763], [1, 520, 357911], [1, -438, 389017], [1, -980, 493039], [1, 156, 571787], [1, -670, 704969], [1, -1124, 912673]], 'index': 13, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/190/4/a/b/1/1', 'ModularForm/GL2/Q/holomorphic/190/4/a/b'], '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': '2-190-1.1-c3-0-13', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'prelabel': '2-190-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.348188002650198, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 1952882770947534929, 'z1': {'__RealLiteral__': 0, 'data': '2.14238964388948572972835276313', 'prec': 103}}
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lfunc_instances • Show schema
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id: 14250480
{'Lhash': '2715801517999249225179216658776', 'Lhash_array': ['2715801517999249225179216658776'], 'label': '2-190-1.1-c3-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/190/4/a/b'}
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id: 24552975
{'Lhash': '2715801517999249225179216658776', 'Lhash_array': ['2715801517999249225179216658776'], 'label': '2-190-1.1-c3-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/190/4/a/b/1/1'}