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lfunc_lfunctions • Show schema
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{'Lhash': '276851805513141189194360412342', 'a10': [0.3192499738373463, 0.9703814800454786], 'a2': [0.39564392373896, -0.22842512587392833], 'a3': [-0.8660254037844386, 0.5], 'a4': [-0.89564392373896, 1.5513007814062236], 'a5': [-0.45685025174785665, 2.1889010593167337], 'a6': [-0.22842512587392833, 0.39564392373896], 'a7': [-1.5, -0.8660254037844386], 'a8': [0.0, 1.7320508075688772], 'a9': [-1.0, 1.7320508075688772], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.747358970798196, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0.45685025174785665, -2.1889010593167337]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [5, 13], 'central_character': '845.484', 'coefficient_field': 'CDF', 'conductor': 845, 'conductor_radical': 65, 'conjugate': '3163241504712737762263095490081', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.39564392373896, 0.22842512587392833], [1.0, -1.7320508075688772]], [[1.0, 0], [0.8660254037844386, 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'prelabel': '2-845-65.29-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.5975678953201964, 'root_angle': 0.8339543639689928, 'root_number': '-0.8669992675447014 + 0.4983094119891288*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.416977181984', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.21839756590916806526859545790', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.40143656070778313428923789867', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.38285625969659846949786558759', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.747358970798196, 'bad_primes': [5, 13], 'central_character': '65.29', 'conductor': 845, 'conductor_radical': 65, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/845/2/n/c/484/3'], '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': '2-845-65.29-c1-0-4', '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': '2-845-65.29-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.5975678953201964, 'root_angle': 0.4169771819844964, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.21839756590916806526859545790', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '276851805513141189194360412342', 'Lhash_array': ['276851805513141189194360412342'], 'label': '2-845-65.29-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/845/2/n/c/484/3'}