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lfunc_lfunctions • Show schema
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{'Lhash': '2735712905359598343137968843685', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.7071067811865476, -0.7071067811865476], 'a4': [-0.7071067811865476, 0.7071067811865476], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, -1.8477590650225735], 'a8': [0.0, 0.0], 'a9': [0.0, -1.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.2889586423145084, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-0.7071067811865476, 0.7071067811865476]]], [193, [[1.0, 0], [0.7071067811865476, -0.7071067811865476]]]], 'bad_primes': [3, 193], 'central_character': '579.50', 'coefficient_field': 'CDF', 'conductor': 579, 'conductor_radical': 579, 'conjugate': '1636984486440549940761047852334', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [0.7071067811865476, -0.7071067811865476]], [[1.0, 0], [-0.7071067811865476, 0.7071067811865476]], [[1.0, 0], [0, 0], [-0.3826834323650898, -0.9238795325112867]], [[1.0, 0], [0, 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'9.927058916932733148147056234810808', '10.86254396475716581285268560048987'], 'prelabel': '2-579-579.50-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5375487348273721, 'root_angle': 0.295235527579314, 'root_number': '0.59982834897604011333134789102820 + 0.80012870949908917608635970547616*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.147617763789657', 'prec': 57}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.15809695894677694770600879533', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.26081094306817718324266763834', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.69855014432002677666067823392', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.2889586423145084, 'bad_primes': [3, 193], 'central_character': '579.50', 'conductor': 579, 'conductor_radical': 579, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/579/1/o/a/50/1'], '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': '2-579-579.50-c0-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-579-579.50-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5375487348273721, 'root_angle': 0.147617763789657, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.15809695894677694770600879533', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2735712905359598343137968843685', 'Lhash_array': ['2735712905359598343137968843685'], 'label': '2-579-579.50-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/579/1/o/a/50/1'}