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lfunc_lfunctions • Show schema
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{'Lhash': '1551263549890065323506419335466,1832058691519095514723137241506', 'a10': 0, 'a2': -1, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 2, 'a8': 1, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.4577260512502574, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1, 1]], [3, [1]], [19, [1, -8, 19]]], 'bad_primes': [2, 3, 19], 'central_character': '342.1', 'coefficient_field': '1.1.1.1', 'conductor': 116964, 'conductor_radical': 114, 'degree': 4, 'euler_factors': [[1, 1, 1], [1], [1, 0, -5, 0, 25], [1, -2, 15, -14, 49], [1, -4, 26, -44, 121], [1, -3, -4, -39, 169], [1, -4, -1, -68, 289], [1, -8, 19], [1, -4, -7, -92, 529], [1, 0, -29, 0, 841], [1, 6, 71, 186, 961], [1, 10, 99, 370, 1369], [1, -4, -25, -164, 1681], [1, -9, 38, -387, 1849], [1, -10, 53, -470, 2209], [1, 4, -37, 212, 2809], [1, 14, 137, 826, 3481], [1, 11, 60, 671, 3721], [1, 3, -58, 201, 4489], [1, -14, 125, -994, 5041], [1, -11, 48, -803, 5329], 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['1.22373116820263713944100213477299', '1.44523947780977611155881925702301', '2.89243811900855163697293673280305', '3.48617559706665704132131698909006', '4.10415229931038676578117562284488', '4.87586858957521118499595655105335', '5.37755673532302851801213209369437', '5.84833753542444496259914943910998', '6.66304521052953388567010465269222', '7.05318714727489721208141843971741', '7.70689965926038983256584618083340', '7.88499860384502907608527076965164', '8.639031928671348426855592035890481', '9.034949659383026950616417339882622', '9.418110536988220635410834132229982', '9.629396660823084285906428724081609', '10.58374644622505703347783348293819', '10.73515255721021597639373978246399', '11.25716029823693530957412458319226', '11.54348307164942019598761102173232'], 'prelabel': '4-342e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.6525385771980605, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e2-0', 'trace_hash': 1272098493059421922, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.22373116820263713944100213477', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.44523947780977611155881925702', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.89243811900855163697293673280', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.4577260512502574, 'bad_primes': [2, 3, 19], 'central_character': '1.1', 'conductor': 116964, 'conductor_radical': 114, 'degree': 4, 'dirichlet_coefficients': [1, -1, 0, 0, 0, 0, 2, 1, 0, 0, 4, 0, 3, -2, 0, -1, 4, 0, 8, 0, 0, -4, 4, 0, 5, -3, 0, 0, 0, 0, -6, 0, 0, -4, 0, 0, -10, -8, 0, 0, 4, 0, 9, 0, 0, -4, 10, 0, -11, -5, 0, 0, -4, 0, 0, 2, 0, 0, -14, 0, -11, 6, 0, 1, 0, 0, -3, 0, 0, 0, 14, 0, 11, 10, 0, 0, 8, 0, -1, 0, 0, -4, -16, 0, 0, -9, 0, 4, -14, 0, 6, 0, 0, -10, 0, 0, -2, 11, 0, 0], 'euler11': [1, -4, 26, -44, 121], 'euler13': [1, -3, -4, -39, 169], 'euler17': [1, -4, -1, -68, 289], 'euler19': [1, -8, 19, 0, 0], 'euler2': [1, 1, 1, 0, 0], 'euler23': [1, -4, -7, -92, 529], 'euler29': [1, 0, -29, 0, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 6, 71, 186, 961], 'euler37': [1, 10, 99, 370, 1369], 'euler41': [1, -4, -25, -164, 1681], 'euler43': [1, -9, 38, -387, 1849], 'euler47': [1, -10, 53, -470, 2209], 'euler5': [1, 0, -5, 0, 25], 'euler53': [1, 4, -37, 212, 2809], 'euler59': [1, 14, 137, 826, 3481], 'euler61': [1, 11, 60, 671, 3721], 'euler67': [1, 3, -58, 201, 4489], 'euler7': [1, -2, 15, -14, 49], 'euler71': [1, -14, 125, -994, 5041], 'euler73': [1, -11, 48, -803, 5329], 'euler79': [1, 1, -78, 79, 6241], 'euler83': [1, 16, 230, 1328, 6889], 'euler89': [1, 14, 107, 1246, 7921], 'euler97': [1, 2, -93, 194, 9409], 'euler_factors': [[1, 1, 1, 0, 0], [1, 0, 0, 0, 0], [1, 0, -5, 0, 25], [1, -2, 15, -14, 49], [1, -4, 26, -44, 121], [1, -3, -4, -39, 169], [1, -4, -1, -68, 289], [1, -8, 19, 0, 0], [1, -4, -7, -92, 529], [1, 0, -29, 0, 841], [1, 6, 71, 186, 961], [1, 10, 99, 370, 1369], [1, -4, -25, -164, 1681], [1, -9, 38, -387, 1849], [1, -10, 53, -470, 2209], [1, 4, -37, 212, 2809], [1, 14, 137, 826, 3481], [1, 11, 60, 671, 3721], [1, 3, -58, 201, 4489], [1, -14, 125, -994, 5041], [1, -11, 48, -803, 5329], [1, 1, -78, 79, 6241], [1, 16, 230, 1328, 6889], [1, 14, 107, 1246, 7921], [1, 2, -93, 194, 9409]], 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/342/2/g/c'], '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': '4-342e2-1.1-c1e2-0-13', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'prelabel': '4-342e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.6525385771980605, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1272098493059421922, 'z1': {'__RealLiteral__': 0, 'data': '1.22373116820263713944100213477', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1551263549890065323506419335466,1832058691519095514723137241506', 'Lhash_array': ['1551263549890065323506419335466', '1832058691519095514723137241506'], 'factors': ['2-342-19.11-c1-0-2', '2-342-19.7-c1-0-2'], 'label': '4-342e2-1.1-c1e2-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/342/2/g/c'}