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lfunc_lfunctions • Show schema
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{'Lhash': '1468985535089618166390101262580', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-1.4142135623730951, -1.0], 'a4': [0.0, 0.0], 'a5': [2.8284271247461903, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 2.8284271247461903], 'a8': [0.0, 0.0], 'a9': [1.0, 2.8284271247461903], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.0662554376171682, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [1.4142135623730951, 1.0]]]], 'bad_primes': [2, 3], 'central_character': '384.191', 'coefficient_field': 'CDF', 'conductor': 384, 'conductor_radical': 6, 'conjugate': '1961380788611449570497718821298', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.4142135623730951, 1.0]], [[1.0, 0], [-2.8284271247461903, 0], [5.0, 0]], [[1.0, 0], [0, -2.8284271247461903], [-7.0, 0]], [[1.0, 0], [0, -2.0], [-11.0, 0]], [[1.0, 0], [0, 4.0], [-13.0, 0]], [[1.0, 0], [0, -5.656854249492381], [-17.0, 0]], [[1.0, 0], 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'11.12000131174485754522757097780838'], 'prelabel': '2-384-24.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7510726534376488, 'root_angle': -0.05408672398469636, 'root_number': '0.9855985596534887 - 0.16910197872576274*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0270433619923', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.15882525896736858807680651954', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.17345858220063849604074900420', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.62376623683424415542603396228', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.0662554376171682, 'bad_primes': [2, 3], 'central_character': '24.11', 'conductor': 384, 'conductor_radical': 6, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/384/2/f/b/191/1'], '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': '2-384-24.11-c1-0-5', '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': '2-384-24.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7510726534376488, 'root_angle': -0.02704336199234818, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.15882525896736858807680651954', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1468985535089618166390101262580', 'Lhash_array': ['1468985535089618166390101262580'], 'label': '2-384-24.11-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/384/2/f/b/191/1'}