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lfunc_lfunctions • Show schema
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{'Lhash': '1387056848977619900846245657604,2877306697633358977209880892160', 'a10': 0, 'a2': 0, 'a3': -2, 'a4': 3, 'a5': 2, 'a6': 0, 'a7': -2, 'a8': 0, 'a9': 3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.1789764244793455, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1, 2, 1]], [5, [1, -2, 1]], [19, [1, 2, 1]]], 'bad_primes': [3, 5, 19], 'central_character': '285.1', 'coefficient_field': '1.1.1.1', 'conductor': 81225, 'conductor_radical': 285, 'degree': 4, 'euler_factors': [[1, 0, -3, 0, 4], [1, 2, 1], [1, -2, 1], [1, 2, 8, 14, 49], [1, -6, 24, -66, 121], [1, 6, 28, 78, 169], [1, 8, 50, 136, 289], [1, 2, 1], [1, -8, 34, -184, 529], [1, -2, -4, -58, 841], [1, -12, 98, -372, 961], [1, -2, 68, -74, 1369], [1, 14, 124, 574, 1681], [1, -6, 88, -258, 1849], [1, -8, 82, -376, 2209], [1, -12, 114, -636, 2809], [1, -12, 126, -708, 3481], [1, 12, 130, 732, 3721], [1, -8, 38, -536, 4489], [1, -4, 118, -284, 5041], [1, -20, 246, 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False, 'rational': True, 'root_analytic_conductor': 1.5085544264647837, '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': 470291384588819443, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.09419492147748949812882672059', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.26979476609353166891886826979', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.54350021810836172772364651152', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.1789764244793455, 'bad_primes': [3, 5, 19], 'central_character': '1.1', 'conductor': 81225, 'conductor_radical': 285, 'degree': 4, 'dirichlet_coefficients': [1, 0, -2, 3, 2, 0, -2, 0, 3, 0, 6, -6, -6, 0, -4, 5, -8, 0, -2, 6, 4, 0, 8, 0, 3, 0, -4, -6, 2, 0, 12, 0, -12, 0, -4, 9, 2, 0, 12, 0, -14, 0, 6, 18, 6, 0, 8, -10, -4, 0, 16, -18, 12, 0, 12, 0, 4, 0, 12, -12, -12, 0, -6, 3, -12, 0, 8, -24, -16, 0, 4, 0, 20, 0, -6, -6, -12, 0, -8, 10, 5, 0, 12, 12, -16, 0, -4, 0, -18, 0, 12, 24, -24, 0, -4, 0, 10, 0, 18, 9], 'euler11': [1, -6, 24, -66, 121], 'euler13': [1, 6, 28, 78, 169], 'euler17': [1, 8, 50, 136, 289], 'euler19': [1, 2, 1, 0, 0], 'euler2': [1, 0, -3, 0, 4], 'euler23': [1, -8, 34, -184, 529], 'euler29': [1, -2, -4, -58, 841], 'euler3': [1, 2, 1, 0, 0], 'euler31': [1, -12, 98, -372, 961], 'euler37': [1, -2, 68, -74, 1369], 'euler41': [1, 14, 124, 574, 1681], 'euler43': [1, -6, 88, -258, 1849], 'euler47': [1, -8, 82, -376, 2209], 'euler5': [1, -2, 1, 0, 0], 'euler53': [1, -12, 114, -636, 2809], 'euler59': [1, -12, 126, -708, 3481], 'euler61': [1, 12, 130, 732, 3721], 'euler67': [1, -8, 38, -536, 4489], 'euler7': [1, 2, 8, 14, 49], 'euler71': [1, -4, 118, -284, 5041], 'euler73': [1, -20, 246, -1460, 5329], 'euler79': [1, 8, 62, 632, 6241], 'euler83': [1, -12, 202, -996, 6889], 'euler89': [1, 18, 196, 1602, 7921], 'euler97': [1, -10, 156, -970, 9409], 'euler_factors': [[1, 0, -3, 0, 4], [1, 2, 1, 0, 0], [1, -2, 1, 0, 0], [1, 2, 8, 14, 49], [1, -6, 24, -66, 121], [1, 6, 28, 78, 169], [1, 8, 50, 136, 289], [1, 2, 1, 0, 0], [1, -8, 34, -184, 529], [1, -2, -4, -58, 841], [1, -12, 98, -372, 961], [1, -2, 68, -74, 1369], [1, 14, 124, 574, 1681], [1, -6, 88, -258, 1849], [1, -8, 82, -376, 2209], [1, -12, 114, -636, 2809], [1, -12, 126, -708, 3481], [1, 12, 130, 732, 3721], [1, -8, 38, -536, 4489], [1, -4, 118, -284, 5041], [1, -20, 246, -1460, 5329], [1, 8, 62, 632, 6241], [1, -12, 202, -996, 6889], [1, 18, 196, 1602, 7921], [1, -10, 156, -970, 9409]], 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/285/2/a/d'], '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': '4-285e2-1.1-c1e2-0-3', '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': '4-285e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.5085544264647837, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 470291384588819443, 'z1': {'__RealLiteral__': 0, 'data': '1.09419492147748949812882672059', 'prec': 103}}
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{'Lhash': '1387056848977619900846245657604,2877306697633358977209880892160', 'Lhash_array': ['1387056848977619900846245657604', '2877306697633358977209880892160'], 'factors': ['2-285-1.1-c1-0-1', '2-285-1.1-c1-0-7'], 'label': '4-285e2-1.1-c1e2-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/285/2/a/d'}