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lfunc_lfunctions • Show schema
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{'Lhash': '1176122307195315355755090082240', 'a10': [-23.001615417173845, 6.753883666861823], 'a2': [1.3097214678905702, 1.5114991487085165], 'a3': [2.5237605984935434, 1.6219224523667928], 'a4': [-0.5692593530931406, 3.9592857675237307], 'a5': [-4.979305023774324, 10.903157138025842], 'a6': [0.8538890296397108, 5.938928651285597], 'a7': [10.566613069225815, 3.1026375377534867], 'a8': [-6.73002826264945, 4.32512653964478], 'a9': [3.738735117016978, 8.186687958190666], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.142263580792209, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.3097214678905702, -1.5114991487085165]]], [3, [[1.0, 0], [-2.5237605984935434, -1.6219224523667928]]], [23, [[1.0, 0], [-81.26292189662226, -74.58778401872165]]]], 'bad_primes': [2, 3, 23], 'central_character': '138.13', 'coefficient_field': 'CDF', 'conductor': 138, 'conductor_radical': 138, 'conjugate': 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'root_analytic_conductor': 2.8534651882916338, 'root_angle': -0.7219190024240338, 'root_number': '-0.6420575895099253 - 0.7666564104947563*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.360959501212', 'prec': 50}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.927796907904721397799601605091', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.61363645676384229926876805114', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.34415748876267142979654255619', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.142263580792209, 'bad_primes': [2, 3, 23], 'central_character': '23.13', 'conductor': 138, 'conductor_radical': 138, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/138/4/e/c/13/1'], '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': '2-138-23.13-c3-0-5', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-138-23.13-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.8534651882916338, 'root_angle': -0.3609595012120169, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.927796907904721397799601605091', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1176122307195315355755090082240', 'Lhash_array': ['1176122307195315355755090082240'], 'label': '2-138-23.13-c3-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/138/4/e/c/13/1'}