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lfunc_lfunctions • Show schema
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{'Lhash': '1109302219135811340877038269628', 'a10': [0, 0], 'a2': [-0.8660254037844386, 0.5], 'a3': [-0.8660254037844386, 0.5], 'a4': [0.5, -0.8660254037844386], 'a5': [0, 0], 'a6': [0.5, -0.8660254037844386], 'a7': [2.7386127875258306, 1.5811388300841898], 'a8': [0, 1.0], 'a9': [0.5, -0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 15.570828394149682, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.8660254037844386, -0.5]]], [3, [[1.0, 0], [0.8660254037844386, -0.5]]], [5, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [-3.6046381913102694, -0.08113883008418966]]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '1950.1849', 'coefficient_field': 'CDF', 'conductor': 1950, 'conductor_radical': 390, 'conjugate': '1141058247497075999424098071259', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.8660254037844386, -0.5]], [[1.0, 0], [0.8660254037844386, -0.5]], [[1.0, 0], [0, 0]], [[1.0, 0], 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'8.112906983158558170463670606093060', '9.110837430765287683019890195552255'], 'prelabel': '2-1950-65.29-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.9459888993951417, 'root_angle': -0.22579409572965523, 'root_number': '0.7587834065458439926553119077175259345053545397259914517 - 0.6513430294020842869549690499608447310683044396518821592*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.11289704786482761', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.875085152751153338471966518835', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.78262166114189413941131189005', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.96089064787993921546580617378', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 15.570828394149682, 'bad_primes': [2, 3, 5, 13], 'central_character': '65.29', 'conductor': 1950, 'conductor_radical': 390, 'degree': 2, 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1950/2/z/o/1849/2'], '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': '2-1950-65.29-c1-0-13', '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': '2-1950-65.29-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.9459888993951417, 'root_angle': -0.11289704786482761, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.875085152751153338471966518835', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1109302219135811340877038269628', 'Lhash_array': ['1109302219135811340877038269628'], 'label': '2-1950-65.29-c1-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1950/2/z/o/1849/2'}