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lfunc_lfunctions • Show schema
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{'Lhash': '4392377382796989760487596145255', 'a10': [-2.8142942750155777, 1.6248335572590664], 'a2': [0.0, -2.593539933613937], 'a3': [0.0, 0.0], 'a4': [-4.7264493872501845, 0.0], 'a5': [-0.6264925926916274, -1.085117001107453], 'a6': [0.0, 0.0], 'a7': [-1.8973507910503662, -1.8439251545820805], 'a8': [0.0, 7.071155362810602], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.5091725982022, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [1.8973507910503662, 1.8439251545820805]]]], 'bad_primes': [3, 7], 'central_character': '189.152', 'coefficient_field': 'CDF', 'conductor': 189, 'conductor_radical': 21, 'conjugate': '930525637906615834728813218241', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 2.593539933613937], [-2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.6264925926916274, 1.085117001107453], [-2.5, 4.330127018922194]], [[1.0, 0], [1.8973507910503662, 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'13.30821700522437731150432931346227'], 'prelabel': '2-189-63.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2284838615961546, 'root_angle': -0.8210800213370208, 'root_number': '-0.8461411153163848 - 0.5329589224050427*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.410540010669', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.46497479826553202915558422995', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.95897476055166927272855153680', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.19584429311653994373531911368', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.5091725982022, 'bad_primes': [3, 7], 'central_character': '63.5', 'conductor': 189, 'conductor_radical': 21, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/189/2/i/b/152/1'], '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': '2-189-63.5-c1-0-5', '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': '2-189-63.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2284838615961546, 'root_angle': -0.4105400106685104, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '3.46497479826553202915558422995', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '4392377382796989760487596145255', 'Lhash_array': ['4392377382796989760487596145255'], 'label': '2-189-63.5-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/189/2/i/b/152/1'}