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lfunc_lfunctions • Show schema
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{'Lhash': '2352147923955520570634490852798', 'a10': [2.0, 0.0], 'a2': [0.0, 2.0], 'a3': [0.0, 0.0], 'a4': [-2.0, 0.0], 'a5': [0.0, -1.0], 'a6': [0.0, 0.0], 'a7': [0.0, -3.605551275463989], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.671248518244905, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 1.0]]], [13, [[1.0, 0], [0, 3.605551275463989]]]], 'bad_primes': [3, 5, 13], 'central_character': '585.181', 'coefficient_field': 'CDF', 'conductor': 585, 'conductor_radical': 195, 'conjugate': '888723039543818984953356148273', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -2.0], [-2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 1.0]], [[1.0, 0], [0, 3.605551275463989], [-7.0, 0]], [[1.0, 0], [0, 3.0], [-11.0, 0]], [[1.0, 0], [0, 3.605551275463989]], [[1.0, 0], [3.605551275463989, 0], [17.0, 0]], [[1.0, 0], [0, 7.211102550927978], [-19.0, 0]], [[1.0, 0], 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'10.76244194943917901207514640954199'], 'prelabel': '2-585-13.12-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.161307131863703, 'root_angle': 1.853068186906925e-61, 'root_number': '1.0 + 5.8215854025877535e-61*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0000000000000000000000000000000000000000000000000000000000000926534093453', 'prec': 250}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.85551754050527559636569970945', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.50548538284112622547594275756', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.76840870973028695816046339357', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.671248518244905, 'bad_primes': [3, 5, 13], 'central_character': '13.12', 'conductor': 585, 'conductor_radical': 195, 'degree': 2, 'index': 16, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/585/2/b/f/181/3'], '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': '2-585-13.12-c1-0-16', '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': '2-585-13.12-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.161307131863703, 'root_angle': 9.265340934534626e-62, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.85551754050527559636569970945', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2352147923955520570634490852798', 'Lhash_array': ['2352147923955520570634490852798'], 'label': '2-585-13.12-c1-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/585/2/b/f/181/3'}