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lfunc_lfunctions • Show schema
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{'Lhash': '812858808235113269986306055939', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': -2, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 43.11921709149143, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1]]], 'bad_primes': [2, 3, 5], 'central_character': '5400.1', 'coefficient_field': '1.1.1.1', 'conductor': 5400, 'conductor_radical': 30, 'degree': 2, 'euler_factors': [[1], [1], [1], [1, 2, 7], [1, 1, 11], [1, 1, 13], [1, 1, 17], [1, -4, 19], [1, -1, 23], [1, -5, 29], [1, -1, 31], [1, 6, 37], [1, 0, 41], [1, 7, 43], [1, -7, 47], [1, 12, 53], [1, -4, 59], [1, -10, 61], [1, -4, 67], [1, 12, 71], [1, 6, 73], [1, -15, 79], [1, -2, 83], [1, -12, 89], [1, 10, 97], [1, -15, 101], [1, -14, 103], [1, -18, 107], [1, 4, 109], [1, -3, 113]], 'euler_factors_factorization': [[1], [1], [1], [[[1, 2, 7], 1]], [[[1, 1, 11], 1]], [[[1, 1, 13], 1]], [[[1, 1, 17], 1]], [[[1, -4, 19], 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2.3277303976371946, 2.281053946652108, 2.1179112168745577, 1.849242960486418, 1.4929553237810238, 1.0727443888775945, 0.6165379855934738, 0.15465375681960883, -0.28220817174071455, -0.6650076798542184, -0.9683085277921167, -1.1719950068241916], 'positive_zeros': ['0.64123253528122429969177517196626', '1.92970764474191076466338159375347', '2.97046151281418265357600520915614', '3.50478602576255188217533958541291', '4.61211048766057560995193968159616', '5.22644316417081378559806102543578', '6.09788577130007395789882661902152', '6.76495726913731380199515593188016', '7.38748725149846239732154601566998', '8.184622414576606606317287853769884'], 'prelabel': '2-5400-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.566522450391183, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'trace_hash': 2001004235704244373, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.64123253528122429969177517197', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.92970764474191076466338159375', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.97046151281418265357600520916', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 43.11921709149143, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 5400, 'conductor_radical': 30, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, -2, 0, 0, 0, -1, 0, -1, 0, 0, 0, -1, 0, 4, 0, 0, 0, 1, 0, 0, 0, 0, 0, 5, 0, 1, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, -7, 0, 0, 0, 7, 0, -3, 0, 0, 0, -12, 0, 0, 0, 0, 0, 4, 0, 10, 0, 0, 0, 0, 0, 4, 0, 0, 0, -12, 0, -6, 0, 0, 0, 2, 0, 15, 0, 0, 0, 2, 0, 0, 0, 0, 0, 12, 0, 2, 0, 0, 0, 0, 0, -10, 0, 0, 0], 'euler11': [1, 1, 11], 'euler13': [1, 1, 13], 'euler17': [1, 1, 17], 'euler19': [1, -4, 19], 'euler2': [1, 0, 0], 'euler23': [1, -1, 23], 'euler29': [1, -5, 29], 'euler3': [1, 0, 0], 'euler31': [1, -1, 31], 'euler37': [1, 6, 37], 'euler41': [1, 0, 41], 'euler43': [1, 7, 43], 'euler47': [1, -7, 47], 'euler5': [1, 0, 0], 'euler53': [1, 12, 53], 'euler59': [1, -4, 59], 'euler61': [1, -10, 61], 'euler67': [1, -4, 67], 'euler7': [1, 2, 7], 'euler71': [1, 12, 71], 'euler73': [1, 6, 73], 'euler79': [1, -15, 79], 'euler83': [1, -2, 83], 'euler89': [1, -12, 89], 'euler97': [1, 10, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, 0, 0], [1, 2, 7], [1, 1, 11], [1, 1, 13], [1, 1, 17], [1, -4, 19], [1, -1, 23], [1, -5, 29], [1, -1, 31], [1, 6, 37], [1, 0, 41], [1, 7, 43], [1, -7, 47], [1, 12, 53], [1, -4, 59], [1, -10, 61], [1, -4, 67], [1, 12, 71], [1, 6, 73], [1, -15, 79], [1, -2, 83], [1, -12, 89], [1, 10, 97]], 'index': 10, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/5400/m', 'ModularForm/GL2/Q/holomorphic/5400/2/a/m/1/1', 'ModularForm/GL2/Q/holomorphic/5400/2/a/m'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-5400-1.1-c1-0-10', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-5400-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.566522450391183, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 2001004235704244373, 'z1': {'__RealLiteral__': 0, 'data': '0.64123253528122429969177517197', 'prec': 103}}
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lfunc_instances • Show schema
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id: 21465991
{'Lhash': '812858808235113269986306055939', 'Lhash_array': ['812858808235113269986306055939'], 'factors': ['2-5400-1.1-c1-0-10'], 'label': '2-5400-1.1-c1-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5400/2/a/m'}
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id: 24570162
{'Lhash': '812858808235113269986306055939', 'Lhash_array': ['812858808235113269986306055939'], 'factors': ['2-5400-1.1-c1-0-10'], 'label': '2-5400-1.1-c1-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5400/2/a/m/1/1'}
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id: 89585
{'Lhash': '2001004235704244373', 'Lhash_array': ['2001004235704244373'], 'factors': ['2-5400-1.1-c1-0-10'], 'label': '2-5400-1.1-c1-0-10', 'type': 'ECQ', 'url': 'EllipticCurve/Q/5400/m'}