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lfunc_lfunctions • Show schema
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{'Lhash': '1157998888197006880567375714647', 'a10': [0, 0], 'a2': [0, 2.449489742783178], 'a3': [0, -1.0], 'a4': [-4.0, 0], 'a5': [0, 0], 'a6': [2.449489742783178, 0], 'a7': [0, -1.0], 'a8': [0, -4.898979485566356], 'a9': [-1.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 13.774194348670873, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 1.0]]], [5, [[1.0, 0], [0, 0]]], [23, [[1.0, 0], [0, -1.0]]]], 'bad_primes': [3, 5, 23], 'central_character': '1725.1174', 'coefficient_field': 'CDF', 'conductor': 1725, 'conductor_radical': 345, 'conjugate': '855060923104487516781303403207', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -2.449489742783178], [-2.0, 0]], [[1.0, 0], [0, 1.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 1.0], [-7.0, 0]], [[1.0, 0], [2.449489742783178, 0], [11.0, 0]], [[1.0, 0], [0, -0.4494897427831781], [-13.0, 0]], [[1.0, 0], [0, 0.5505102572168219], [-17.0, 0]], [[1.0, 0], [-0.4494897427831781, 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'3.97675454886921568300778926110507', '4.75796398584492861664010531251019', '5.50965510387386144050262027134820', '6.70185144568402145919445791252721', '8.157936916373713754287337607961149', '8.593999266807196526174576407139923', '9.566154755221709658197628226564286'], 'prelabel': '2-1725-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.711360175012777, 'root_angle': -0.35241638234956674, 'root_number': '0.447213595499957939281834733746255247088123671922305145 - 0.8944271909999158785636694674925104941762473438446102897*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.17620819117478337', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.913500051188016091040801826839', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.38855946280244887698763722718', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.93601270475772718809454508336', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 13.774194348670873, 'bad_primes': [3, 5, 23], 'central_character': '5.4', 'conductor': 1725, 'conductor_radical': 345, 'degree': 2, 'index': 28, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1725/2/b/m/1174/3'], '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': '2-1725-5.4-c1-0-28', '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': '2-1725-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.711360175012777, 'root_angle': -0.17620819117478337, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.913500051188016091040801826839', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1157998888197006880567375714647', 'Lhash_array': ['1157998888197006880567375714647'], 'label': '2-1725-5.4-c1-0-28', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1725/2/b/m/1174/3'}