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lfunc_lfunctions • Show schema
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{'Lhash': '186061517792375854462414979388', 'a10': [0, 0], 'a2': [0, 0], 'a3': [33.0681115275729, 33.0681115275729], 'a4': [0, 0], 'a5': [-341.57073600175295, -341.57073600175295], 'a6': [0, 0], 'a7': [-1351.2420822377471, 0], 'a8': [0, 0], 'a9': [0, 2187.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 78.21669313173645, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '4.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-33.0681115275729, -33.0681115275729]]]], 'bad_primes': [2, 3], 'central_character': '192.79', 'coefficient_field': 'CDF', 'conductor': 192, 'conductor_radical': 6, 'conjugate': '1540790001645066098014975793496', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-33.0681115275729, -33.0681115275729]], [[1.0, 0], [341.57073600175295, 341.57073600175295], [0, 390625.0]], [[1.0, 0], [1351.2420822377471, 0], [5764801.0, 0]], [[1.0, 0], [7124.360467019804, -7124.360467019804], [0, -214358881.0]], [[1.0, 0], 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-0.4051730428408281, 'root_number': '-0.8276912161993261691786940629883952927133804571008758829 - 0.5611837939806176416987046688428923639824385734655347594*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.4051730428408281', 'prec': 64}, 'spectral_label': 'c8-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.14677665735248901061630841373', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.59624196471688017886032098758', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.11172739572510215766815527203', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 78.21669313173645, 'bad_primes': [2, 3], 'central_character': '16.11', 'conductor': 192, 'conductor_radical': 6, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/192/9/l/a/79/20'], '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': '2-192-16.11-c8-0-5', 'motivic_weight': 8, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [8], 'order_of_vanishing': 0, 'prelabel': '2-192-16.11-c8-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.844020190599773, 'root_angle': -0.4051730428408281, 'self_dual': False, 'spectral_label': 'c8-0', 'z1': {'__RealLiteral__': 0, 'data': '0.14677665735248901061630841373', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '186061517792375854462414979388', 'Lhash_array': ['186061517792375854462414979388'], 'factors': ['2-192-16.11-c8-0-5'], 'label': '2-192-16.11-c8-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/192/9/l/a/79/20'}