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lfunc_lfunctions • Show schema
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{'Lhash': '3719875175135496289258562535304', 'a10': [-3.91379722779591, -6.778895649064739], 'a2': [1.392728480640038, 0.2455756079379457], 'a3': [2.895930497597251, 0.7833176578414013], 'a4': [1.8793852415718169, 0.6840402866513374], 'a5': [-3.557794143384179, -4.240013952088735], 'a6': [3.8408811719248384, 1.8021187039574504], 'a7': [-10.262544782921823, 3.735260828807449], 'a8': [2.449489742783178, 1.4142135623730951], 'a9': [7.772826893827722, 4.536866989298725], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.4713934275456033, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.392728480640038, -0.2455756079379457]]], [3, [[1.0, 0], [-2.895930497597251, -0.7833176578414013]]]], 'bad_primes': [2, 3], 'central_character': '54.29', 'coefficient_field': 'CDF', 'conductor': 54, 'conductor_radical': 6, 'conjugate': '3883683059142636649343160090813', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.392728480640038, 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'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.93446409796655742873161744395', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.98932022230880128229667946263', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.67814947063367080078474225480', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.4713934275456033, 'bad_primes': [2, 3], 'central_character': '27.2', 'conductor': 54, 'conductor_radical': 6, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/54/3/f/a/29/6'], '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': '2-54-27.2-c2-0-3', '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': '2-54-27.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2130100690207, 'root_angle': -0.031276643929973764, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '2.93446409796655742873161744395', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3719875175135496289258562535304', 'Lhash_array': ['3719875175135496289258562535304'], 'label': '2-54-27.2-c2-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/54/3/f/a/29/6'}