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lfunc_lfunctions • Show schema
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{'Lhash': '2413745634098869750065588724227', 'a10': 0, 'a2': 0, 'a3': -1, 'a4': 0, 'a5': 1, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.665638594042921, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [5, [1, -1]]], '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, 1], [1, -1], [1, 0, 7], [1, 4, 11], [1, 2, 13], [1, 2, 17], [1, 8, 19], [1, -4, 23], [1, -6, 29], [1, 0, 31], [1, 2, 37], [1, 6, 41], [1, 4, 43], [1, 12, 47], [1, -6, 53], [1, 12, 59], [1, 14, 61], [1, -12, 67], [1, 0, 71], [1, -2, 73], [1, 8, 79], [1, -4, 83], [1, -2, 89], [1, 14, 97], [1, -14, 101], [1, -8, 103], [1, -12, 107], [1, 14, 109], [1, -6, 113]], 'euler_factors_factorization': [[1], [[[1, 1], 1]], [[[1, -1], 1]], [[[1, 0, 7], 1]], [[[1, 4, 11], 1]], [[[1, 2, 13], 1]], [[[1, 2, 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1.5864887555503007, 3.145774001053156, 4.084975233305791, 4.08801862324001, 3.1668474139730667, 1.6555461676478402, 0.08711007414640642, -1.0020090281441294, -1.267255533466391], 'positive_zeros': ['1.90410956588849953091073290915852', '3.01325599841700254495812174326707', '4.59744237493557402533707286051552', '5.10335741728591181213017059039250', '6.25812475404630879226037514190479', '6.84594392053537268258202260884291', '7.985644465490789105614221217605191', '8.737470649209957690601322363683977', '9.821607031469602717210421551842188'], 'prelabel': '2-960-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.768688966648822, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 1560038282679592288, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.90410956588849953091073290916', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.01325599841700254495812174327', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.59744237493557402533707286052', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.665638594042921, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 960, 'conductor_radical': 30, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, 1, 0, 0, 0, 1, 0, -4, 0, -2, 0, -1, 0, -2, 0, -8, 0, 0, 0, 4, 0, 1, 0, -1, 0, 6, 0, 0, 0, 4, 0, 0, 0, -2, 0, 2, 0, -6, 0, -4, 0, 1, 0, -12, 0, -7, 0, 2, 0, 6, 0, -4, 0, 8, 0, -12, 0, -14, 0, 0, 0, -2, 0, 12, 0, -4, 0, 0, 0, 2, 0, -1, 0, 0, 0, -8, 0, 1, 0, 4, 0, -2, 0, -6, 0, 2, 0, 0, 0, 0, 0, -8, 0, -14, 0, -4, 0], 'euler11': [1, 4, 11], 'euler13': [1, 2, 13], 'euler17': [1, 2, 17], 'euler19': [1, 8, 19], 'euler2': [1, 0, 0], 'euler23': [1, -4, 23], 'euler29': [1, -6, 29], 'euler3': [1, 1, 0], 'euler31': [1, 0, 31], 'euler37': [1, 2, 37], 'euler41': [1, 6, 41], 'euler43': [1, 4, 43], 'euler47': [1, 12, 47], 'euler5': [1, -1, 0], 'euler53': [1, -6, 53], 'euler59': [1, 12, 59], 'euler61': [1, 14, 61], 'euler67': [1, -12, 67], 'euler7': [1, 0, 7], 'euler71': [1, 0, 71], 'euler73': [1, -2, 73], 'euler79': [1, 8, 79], 'euler83': [1, -4, 83], 'euler89': [1, -2, 89], 'euler97': [1, 14, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, -1, 0], [1, 0, 7], [1, 4, 11], [1, 2, 13], [1, 2, 17], [1, 8, 19], [1, -4, 23], [1, -6, 29], [1, 0, 31], [1, 2, 37], [1, 6, 41], [1, 4, 43], [1, 12, 47], [1, -6, 53], [1, 12, 59], [1, 14, 61], [1, -12, 67], [1, 0, 71], [1, -2, 73], [1, 8, 79], [1, -4, 83], [1, -2, 89], [1, 14, 97]], 'index': 12, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/960/f', 'ModularForm/GL2/Q/holomorphic/960/2/a/f/1/1', 'ModularForm/GL2/Q/holomorphic/960/2/a/f'], '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': '2-960-1.1-c1-0-12', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-960-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.768688966648822, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1560038282679592288, 'z1': {'__RealLiteral__': 0, 'data': '1.90410956588849953091073290916', 'prec': 103}}
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lfunc_instances • Show schema
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id: 18645120
{'Lhash': '2413745634098869750065588724227', 'Lhash_array': ['2413745634098869750065588724227'], 'label': '2-960-1.1-c1-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/960/2/a/f'}
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id: 24551199
{'Lhash': '2413745634098869750065588724227', 'Lhash_array': ['2413745634098869750065588724227'], 'label': '2-960-1.1-c1-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/960/2/a/f/1/1'}
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id: 101686
{'Lhash': '1560038282679592288', 'Lhash_array': ['1560038282679592288'], 'label': '2-960-1.1-c1-0-12', 'type': 'ECQ', 'url': 'EllipticCurve/Q/960/f'}