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lfunc_lfunctions • Show schema
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{'Lhash': '5709092708804284635613657015083', 'a10': [1.0, -2.0], 'a2': [-0.7071067811865476, -0.7071067811865476], 'a3': [-0.2928932188134525, -1.7071067811865475], 'a4': [0.0, 1.0], 'a5': [0.7071067811865476, 2.1213203435596424], 'a6': [-1.0, 1.4142135623730951], 'a7': [-1.0, 1.0], 'a8': [0.7071067811865476, -0.7071067811865476], 'a9': [-2.8284271247461903, 1.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.23955120606384128, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.7071067811865476, 0.7071067811865476]]], [3, [[1.0, 0], [0.2928932188134525, 1.7071067811865475]]], [5, [[1.0, 0], [-0.7071067811865476, -2.1213203435596424]]]], 'bad_primes': [2, 3, 5], 'central_character': '30.23', 'coefficient_field': 'CDF', 'conductor': 30, 'conductor_radical': 30, 'conjugate': '3408082167835782798416530038007', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.7071067811865476, 0.7071067811865476]], [[1.0, 0], 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-0.39396894302460334], 'positive_zeros': ['4.50368004225802633236355559239112', '6.10595906160915434301636909296688', '8.279743490344514498393476746398930', '9.526070664807416336095550719717382', '10.45471285693397489650266968308568', '12.23668530395967147757095350018454', '13.85289691093411225209009374022262', '15.19197698537520675261550340977011', '16.32141304116390009919213512708611', '16.90375285714291204555643085105499'], 'prelabel': '2-30-15.8-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.4894396858284392, 'root_angle': 0.2697050848405203, 'root_number': '0.6620065617666444 + 0.7494980401428052*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.13485254242', 'prec': 44}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '4.50368004225802633236355559239', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '6.10595906160915434301636909297', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '8.279743490344514498393476746399', 'prec': 107}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.23955120606384128, 'bad_primes': [2, 3, 5], 'central_character': '15.8', 'conductor': 30, 'conductor_radical': 30, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/30/2/e/a/23/1'], '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': '2-30-15.8-c1-0-1', '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': '2-30-15.8-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.4894396858284392, 'root_angle': 0.13485254242026015, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '4.50368004225802633236355559239', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '5709092708804284635613657015083', 'Lhash_array': ['5709092708804284635613657015083'], 'label': '2-30-15.8-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/30/2/e/a/23/1'}