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lfunc_lfunctions • Show schema
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{'Lhash': '1853845175926732969563056484670', 'a10': [0, 0], 'a2': [0, 0], 'a3': [1.5811388300841898, 0.7071067811865476], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [0, -4.242640687119285], 'a8': [0, 0], 'a9': [2.0, 2.23606797749979], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.58204824255365, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-1.5811388300841898, -0.7071067811865476]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 5], 'central_character': '1200.1151', 'coefficient_field': 'CDF', 'conductor': 1200, 'conductor_radical': 30, 'conjugate': '1299350030431462921360348032312', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.5811388300841898, -0.7071067811865476]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 4.242640687119285], [-7.0, 0]], [[1.0, 0], [0, 0], [11.0, 0]], [[1.0, 0], [0, 0], [13.0, 0]], [[1.0, 0], [0, 0], [-17.0, 0]], [[1.0, 0], [0, 0], [-19.0, 0]], 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'9.073521363571290174084166347156788', '9.301250554805345830268443050308872'], 'prelabel': '2-1200-12.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.095488368990207, 'root_angle': 0.133860236400615, 'root_number': '0.91287092917527685576161630466800355658790782499663875705 + 0.40824829046386301636621401245098189866099124677611168807*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0669301182003075', 'prec': 60}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.46242598362116845334824100896', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.64654296774814580417924265032', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.24408181734925928681211336652', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.58204824255365, 'bad_primes': [2, 3, 5], 'central_character': '12.11', 'conductor': 1200, 'conductor_radical': 30, 'degree': 2, 'index': 29, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1200/2/h/l/1151/4'], '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': '2-1200-12.11-c1-0-29', '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': '2-1200-12.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.095488368990207, 'root_angle': 0.0669301182003075, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.46242598362116845334824100896', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1853845175926732969563056484670', 'Lhash_array': ['1853845175926732969563056484670'], 'label': '2-1200-12.11-c1-0-29', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1200/2/h/l/1151/4'}