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lfunc_lfunctions • Show schema
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{'Lhash': '3645845177562555347899945125880', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [2.0, -2.23606797749979], 'a4': [0.0, 0.0], 'a5': [0.0, -2.23606797749979], 'a6': [0.0, 0.0], 'a7': [2.0, 0.0], 'a8': [0.0, 0.0], 'a9': [-1.0, -8.94427190999916], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.6348815861617816, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-2.0, 2.23606797749979]]], [5, [[1.0, 0], [0, 2.23606797749979]]]], 'bad_primes': [2, 3, 5], 'central_character': '60.41', 'coefficient_field': 'CDF', 'conductor': 60, 'conductor_radical': 30, 'conjugate': '2398692587305671440663522007012', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-2.0, 2.23606797749979]], [[1.0, 0], [0, 2.23606797749979]], [[1.0, 0], [-2.0, 0], [49.0, 0]], [[1.0, 0], [0, -13.416407864998739], [-121.0, 0]], [[1.0, 0], [-8.0, 0], [169.0, 0]], [[1.0, 0], [0, -13.416407864998739], [-289.0, 0]], 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'11.16421606278365258658772828018077', '12.98218510276332119757938288328484', '14.15359525255581184575442336731963', '14.79968700639781218625433619832732'], 'prelabel': '2-60-3.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2786248809411545, 'root_angle': 0.23227952719876999, 'root_number': '0.7453559924999299 + 0.6666666666666666*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.116139763599', 'prec': 47}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.87606472706765793080168502350', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.47219991278825650452245220563', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.29280108209387160444954218493', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.6348815861617816, 'bad_primes': [2, 3, 5], 'central_character': '3.2', 'conductor': 60, 'conductor_radical': 30, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/60/3/g/a/41/1'], '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': '2-60-3.2-c2-0-1', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-60-3.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2786248809411545, 'root_angle': 0.11613976359938499, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '2.87606472706765793080168502350', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3645845177562555347899945125880', 'Lhash_array': ['3645845177562555347899945125880'], 'label': '2-60-3.2-c2-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/60/3/g/a/41/1'}