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lfunc_lfunctions • Show schema
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{'Lhash': '914647092477033124240716849896', 'a10': [-26.130853920978847, 45.25996663629577], 'a2': [1.4675757755177479, 2.5419158071540364], 'a3': [-1.5, 2.598076211353316], 'a4': [-0.3075573137730382, 0.5327048936943053], 'a5': [8.902727326553244, 15.419976055522058], 'a6': [-8.805454653106487, 0], 'a7': [-15.308714336822876, 10.423208016419597], 'a8': [21.67575775517748, 0], 'a9': [-4.5, -7.794228634059948], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 16.107521431567196, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.5, -2.598076211353316]]], [7, [[1.0, 0], [15.308714336822876, -10.423208016419597]]], [13, [[1.0, 0], [13.0, 0]]]], 'bad_primes': [3, 7, 13], 'central_character': '273.235', 'coefficient_field': 'CDF', 'conductor': 273, 'conductor_radical': 273, 'conjugate': '2882346158673615411528337395857', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.4675757755177479, -2.5419158071540364], [-4.0, 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'1.91810956550769787853106213461647', '3.36682692387648757585059143915761', '4.71709379236326167605465277692980', '5.64355671804193258020397831410404', '6.95261003585125827271803816398115', '8.086927558608298618545712339483713', '9.336536916795995306769037764430013', '10.13893426751230252834947542432046', '11.21769284079867348385533446518544'], 'prelabel': '2-273-7.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.013417674696616, 'root_angle': 0.49828180581623743, 'root_number': '-0.9999417266464035336715453022281264921051232740852081825912 + 0.01079552274830604384634125175272220258402083988243735732*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.49828180581623743', 'prec': 64}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.72152933332919884732644667902', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.91810956550769787853106213462', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.36682692387648757585059143916', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 16.107521431567196, 'bad_primes': [3, 7, 13], 'central_character': '7.4', 'conductor': 273, 'conductor_radical': 273, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/273/4/i/b/235/3'], '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': '2-273-7.4-c3-0-11', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-273-7.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.013417674696616, 'root_angle': 0.49828180581623743, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.72152933332919884732644667902', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '914647092477033124240716849896', 'Lhash_array': ['914647092477033124240716849896'], 'factors': ['2-273-7.4-c3-0-11'], 'label': '2-273-7.4-c3-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/273/4/i/b/235/3'}