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lfunc_lfunctions • Show schema
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{'Lhash': '2223053832966303474754293976439', 'a10': [-2.724744871391589, 1.5731321849709863], 'a2': [0.5, -0.8660254037844386], 'a3': [0, 0], 'a4': [-0.5, -0.8660254037844386], 'a5': [-2.724744871391589, -1.5731321849709863], 'a6': [0, 0], 'a7': [1.0, 0], 'a8': [-1.0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 19.116186243894532, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.5, 0.8660254037844386]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-1.0, 0]]], [19, [[1.0, 0], [0.5, 4.330127018922194]]]], 'bad_primes': [2, 3, 7, 19], 'central_character': '2394.1205', 'coefficient_field': 'CDF', 'conductor': 2394, 'conductor_radical': 798, 'conjugate': '295976517589466927178287612303', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.724744871391589, 1.5731321849709863], [2.5, 4.330127018922194]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, 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'9.136632540966265284243489163265021'], 'prelabel': '2-2394-57.8-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.372206107206582, 'root_angle': -0.3818332820387902, 'root_number': '-0.73680528833379265455453429862434444742387256289083352540 - 0.6761049970850360975358055330818255086069471609085331100*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.3818332820387902', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.75368025902883813475066299922', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.20245457035456001731236666262', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.89305218970925027697875112736', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 19.116186243894532, 'bad_primes': [2, 3, 7, 19], 'central_character': '57.8', 'conductor': 2394, 'conductor_radical': 798, 'degree': 2, 'index': 38, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2394/2/cq/b/1205/1'], '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': '2-2394-57.8-c1-0-38', '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': '2-2394-57.8-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.372206107206582, 'root_angle': -0.3818332820387902, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.75368025902883813475066299922', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2223053832966303474754293976439', 'Lhash_array': ['2223053832966303474754293976439'], 'factors': ['2-2394-57.8-c1-0-38'], 'label': '2-2394-57.8-c1-0-38', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2394/2/cq/b/1205/1'}