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lfunc_lfunctions • Show schema
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{'Lhash': '2187880282951156966859997502216', 'a10': 0, 'a2': 0, 'a3': 3, 'a4': 0, 'a5': 5, 'a6': 0, 'a7': 4, 'a8': 0, 'a9': 9, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 56.64183360551102, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -3]], [5, [1, -5]]], 'bad_primes': [2, 3, 5], 'central_character': '960.1', 'coefficient_field': '1.1.1.1', 'conductor': 960, 'conductor_radical': 30, 'degree': 2, 'euler_factors': [[1], [1, -3], [1, -5], [1, -4, 343], [1, 48, 1331], [1, 2, 2197], [1, 114, 4913], [1, -140, 6859], [1, 72, 12167], [1, 210, 24389], [1, 272, 29791], [1, -334, 50653], [1, 198, 68921], [1, 268, 79507], [1, 216, 103823], [1, -78, 148877], [1, -240, 205379], [1, 302, 226981], [1, -596, 300763], [1, -768, 357911], [1, 478, 389017], [1, -640, 493039], [1, 348, 571787], [1, -210, 704969], [1, 1534, 912673], [1, 1722, 1030301], [1, 1052, 1092727], [1, 564, 1225043], [1, -610, 1295029], [1, -1302, 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{'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'trace_hash': 2041801563707407533, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.72593322052405312703399137589', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.59957517821615905574863321613', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.68335909929705216953658165337', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 56.64183360551102, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 960, 'conductor_radical': 30, 'degree': 2, 'dirichlet_coefficients': [1, 0, 3, 0, 5, 0, 4, 0, 9, 0, -48, 0, -2, 0, 15, 0, -114, 0, 140, 0, 12, 0, -72, 0, 25, 0, 27, 0, -210, 0, -272, 0, -144, 0, 20, 0, 334, 0, -6, 0, -198, 0, -268, 0, 45, 0, -216, 0, -327, 0, -342, 0, 78, 0, -240, 0, 420, 0, 240, 0, -302, 0, 36, 0, -10, 0, 596, 0, -216, 0, 768, 0, -478, 0, 75, 0, -192, 0, 640, 0, 81, 0, -348, 0, -570, 0, -630, 0, 210, 0, -8, 0, -816, 0, 700, 0, -1534, 0, -432, 0], 'euler11': [1, 48, 1331], 'euler13': [1, 2, 2197], 'euler17': [1, 114, 4913], 'euler19': [1, -140, 6859], 'euler2': [1, 0, 0], 'euler23': [1, 72, 12167], 'euler29': [1, 210, 24389], 'euler3': [1, -3, 0], 'euler31': [1, 272, 29791], 'euler37': [1, -334, 50653], 'euler41': [1, 198, 68921], 'euler43': [1, 268, 79507], 'euler47': [1, 216, 103823], 'euler5': [1, -5, 0], 'euler53': [1, -78, 148877], 'euler59': [1, -240, 205379], 'euler61': [1, 302, 226981], 'euler67': [1, -596, 300763], 'euler7': [1, -4, 343], 'euler71': [1, -768, 357911], 'euler73': [1, 478, 389017], 'euler79': [1, -640, 493039], 'euler83': [1, 348, 571787], 'euler89': [1, -210, 704969], 'euler97': [1, 1534, 912673], 'euler_factors': [[1, 0, 0], [1, -3, 0], [1, -5, 0], [1, -4, 343], [1, 48, 1331], [1, 2, 2197], [1, 114, 4913], [1, -140, 6859], [1, 72, 12167], [1, 210, 24389], [1, 272, 29791], [1, -334, 50653], [1, 198, 68921], [1, 268, 79507], [1, 216, 103823], [1, -78, 148877], [1, -240, 205379], [1, 302, 226981], [1, -596, 300763], [1, -768, 357911], [1, 478, 389017], [1, -640, 493039], [1, 348, 571787], [1, -210, 704969], [1, 1534, 912673]], 'index': 45, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/960/4/a/bg/1/1', 'ModularForm/GL2/Q/holomorphic/960/4/a/bg'], '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': '2-960-1.1-c3-0-45', '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': '2-960-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 7.526076906696543, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 2041801563707407533, 'z1': {'__RealLiteral__': 0, 'data': '1.72593322052405312703399137589', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20433743
{'Lhash': '2187880282951156966859997502216', 'Lhash_array': ['2187880282951156966859997502216'], 'factors': ['2-960-1.1-c3-0-45'], 'label': '2-960-1.1-c3-0-45', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/960/4/a/bg'}
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id: 24578109
{'Lhash': '2187880282951156966859997502216', 'Lhash_array': ['2187880282951156966859997502216'], 'factors': ['2-960-1.1-c3-0-45'], 'label': '2-960-1.1-c3-0-45', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/960/4/a/bg/1/1'}