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lfunc_lfunctions • Show schema
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{'Lhash': '1948090572207380577719191699731', 'a10': [-0.2928932188134525, 0.7071067811865476], 'a2': [-0.7071067811865476, -0.7071067811865476], 'a3': [0.0, 0.0], 'a4': [0.0, 1.0], 'a5': [-0.2928932188134525, -0.7071067811865476], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.7071067811865476, -0.7071067811865476], 'a9': [0.7071067811865476, -0.7071067811865476], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.6628846220931641, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.7071067811865476, 0.7071067811865476]]], [7, [[1.0, 0], [0, 0]]], [17, [[1.0, 0], [-0.7071067811865476, 0.7071067811865476]]]], 'bad_primes': [2, 7, 17], 'central_character': '3332.2059', 'coefficient_field': 'CDF', 'conductor': 3332, 'conductor_radical': 238, 'conjugate': '855185611756416307613749170356', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.7071067811865476, 0.7071067811865476]], [[1.0, 0], [0, 0], [-0.7071067811865476, 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'root_number': '-0.73923146412277394210561099758108 + 0.67345144030650048202690003376046*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.3824055255447865', 'prec': 60}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.53677249224403310468810495226', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.31257225325893339478800050740', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.83606717947741136732340941936', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.6628846220931641, 'bad_primes': [2, 7, 17], 'central_character': '68.19', 'conductor': 3332, 'conductor_radical': 238, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3332/1/w/a/2059/1'], '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': '2-3332-68.19-c0-0-2', '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': '2-3332-68.19-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2895288372476066, 'root_angle': 0.3824055255447866, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.53677249224403310468810495226', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1948090572207380577719191699731', 'Lhash_array': ['1948090572207380577719191699731'], 'label': '2-3332-68.19-c0-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3332/1/w/a/2059/1'}