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lfunc_lfunctions • Show schema
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{'Lhash': '3645973990804643062002809606232', 'a10': [-17.11375615602156, -5.025052201094994], 'a2': [1.3097214678905702, -1.5114991487085165], 'a3': [2.5237605984935434, -1.6219224523667928], 'a4': [-0.5692593530931406, -3.9592857675237307], 'a5': [-3.704722927403724, -8.112211651519148], 'a6': [0.8538890296397108, -5.938928651285597], 'a7': [-24.400580906710474, 7.164656997296269], '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], [-106.96498056601688, 26.934976007259248]]]], 'bad_primes': [2, 3, 23], 'central_character': '138.85', 'coefficient_field': 'CDF', 'conductor': 138, 'conductor_radical': 138, 'conjugate': 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0.8797725138549563, 'root_number': '-0.9295131613352138 + 0.3687889408653909*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.439886256927', 'prec': 47}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.87616634279841569828544670432', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.82140875916054913813559793011', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.38277136281290393315648525513', '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': '23.16', 'conductor': 138, 'conductor_radical': 138, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/138/4/e/c/85/2'], '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': '2-138-23.16-c3-0-11', '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': '2-138-23.16-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.8534651882916338, 'root_angle': 0.4398862569274781, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '2.87616634279841569828544670432', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3645973990804643062002809606232', 'Lhash_array': ['3645973990804643062002809606232'], 'label': '2-138-23.16-c3-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/138/4/e/c/85/2'}