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lfunc_lfunctions • Show schema
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{'Lhash': '794091561871559783210042088873', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0.6388264977574348], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [-9.065369018826724, 0], 'a8': [0, 0], 'a9': [8.59190070576297, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 29.972829079632664, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [-10.09562326238232, 4.367881745657152]]]], 'bad_primes': [2, 5, 11], 'central_character': '1100.549', 'coefficient_field': 'CDF', 'conductor': 1100, 'conductor_radical': 110, 'conjugate': '1257782003788827392853206901185', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, -0.6388264977574348], [-9.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [9.065369018826724, 0], [49.0, 0]], [[1.0, 0], [-10.09562326238232, 4.367881745657152]], [[1.0, 0], [10.430232355821824, 0], [169.0, 0]], [[1.0, 0], [-3.391076794698052, 0], [289.0, 0]], 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['0.62642778832636575409613039264165', '2.07128663505076511358400092055716', '3.27790679451774955311479292833203', '4.21118080200690658368872352348199', '5.22904073202738689602006852647521', '6.45705540458713908095679216338846', '6.97928697589607291009882672603734', '7.61088665156285677940137587944403', '9.120261585564582456800962096975050', '9.415354985761376701508947541729305'], 'prelabel': '2-1100-55.54-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.47474465885238, 'root_angle': -0.13878006309229274, 'root_number': '0.6433112596156415654672085470837068407705893812675088021 - 0.7656047434882679836243504905745700960828760393803712790*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.13878006309229274', 'prec': 67}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.62642778832636575409613039264', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.07128663505076511358400092056', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.27790679451774955311479292833', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 29.972829079632664, 'bad_primes': [2, 5, 11], 'central_character': '55.54', 'conductor': 1100, 'conductor_radical': 110, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1100/3/e/c/549/9'], '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': '2-1100-55.54-c2-0-12', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-1100-55.54-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.47474465885238, 'root_angle': -0.13878006309229274, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.62642778832636575409613039264', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '794091561871559783210042088873', 'Lhash_array': ['794091561871559783210042088873'], 'factors': ['2-1100-55.54-c2-0-12'], 'label': '2-1100-55.54-c2-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1100/3/e/c/549/9'}