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lfunc_lfunctions • Show schema
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{'Lhash': '1799658715937120976378195322251', 'a10': [0.0, 0.0], 'a2': [-2.0440631301456316, 0.0], 'a3': [0.0, 0.0], 'a4': [2.178194080020756, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [1.4336646297832873, 0.0], 'a8': [-0.36423994898064826, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 34.13604686409738, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [3, 5, 19], 'central_character': '4275.1', 'coefficient_field': 'CDF', 'conductor': 4275, 'conductor_radical': 285, 'degree': 2, 'euler_factors': [[[1.0, 0], [2.0440631301456316, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.4336646297832873, 0], [7.0, 0]], [[1.0, 0], [-5.703044038840832, 0], [11.0, 0]], [[1.0, 0], [2.0, 0], [13.0, 0]], [[1.0, 0], [-3.359646362329966, 0], [17.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [9.062690401170798, 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'6.80183653880787300928661532995841', '7.51102022955150097959169858525343', '8.178782901628190495745151371575138'], 'prelabel': '2-4275-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.842606170545588, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.41968040374304099845440305878', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.82800062146487716894009639816', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.27112213102617056044905691920', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 34.13604686409738, 'bad_primes': [3, 5, 19], 'central_character': '1.1', 'conductor': 4275, 'conductor_radical': 285, 'degree': 2, 'index': 118, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4275/2/a/bq/1/2'], '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': '2-4275-1.1-c1-0-118', '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': '2-4275-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.842606170545588, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.41968040374304099845440305878', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1799658715937120976378195322251', 'Lhash_array': ['1799658715937120976378195322251'], 'factors': ['2-4275-1.1-c1-0-118'], 'label': '2-4275-1.1-c1-0-118', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4275/2/a/bq/1/2'}