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lfunc_lfunctions • Show schema
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{'Lhash': '1445593511236673447306199683700,2340558283830275079927099465981', 'a10': 0, 'a2': 4, 'a3': 0, 'a4': 12, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 32, 'a9': -4, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 20896.05536941392, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -4, 4]], [5, [1]], [7, [1]]], 'bad_primes': [2, 5, 7], 'central_character': '2450.1', 'coefficient_field': '1.1.1.1', 'conductor': 6002500, 'conductor_radical': 70, 'degree': 4, 'euler_factors': [[1, -4, 4], [1, 0, 4, 0, 729], [1], [1], [1, 28, 2858, 37268, 1771561], [1, 0, 1802, 0, 4826809], [1, 0, 9824, 0, 24137569], [1, 0, 13716, 0, 47045881], [1, 280, 43934, 3406760, 148035889], [1, 572, 130574, 13950508, 594823321], [1, 0, 50870, 0, 887503681], [1, -76, 102750, -3849628, 2565726409], [1, 0, 122000, 0, 4750104241], [1, -68, 160170, -5406476, 6321363049], [1, 0, -66154, 0, 10779215329], [1, -148, 303230, -22033796, 22164361129], [1, 0, 222260, 0, 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'7.65920894953528450080644322598328', '7.960028318862136626563638551732366', '7.972573588764912874047333041867701'], 'prelabel': '4-2450e2-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 12.023089433006168, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c3e2-0', 'trace_hash': 1609963721587411932, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.14037220585578311664133561774', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.84637492650488867793094513198', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.28411736587091172824019237619', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 20896.05536941392, 'bad_primes': [2, 5, 7], 'central_character': '1.1', 'conductor': 6002500, 'conductor_radical': 70, 'degree': 4, 'dirichlet_coefficients': [1, 4, 0, 12, 0, 0, 0, 32, -4, 0, -28, 0, 0, 0, 0, 80, 0, -16, 0, 0, 0, -112, -280, 0, 0, 0, 0, 0, -572, 0, 0, 192, 0, 0, 0, -48, 76, 0, 0, 0, 0, 0, 68, -336, 0, -1120, 0, 0, 0, 0, 0, 0, 148, 0, 0, 0, 0, -2288, 0, 0, 0, 0, 0, 448, 0, 0, -1368, 0, 0, 0, 1176, -128, 0, 304, 0, 0, 0, 0, 2440, 0, -713, 0, 0, 0, 0, 272, 0, -896, 0, 0, 0, -3360, 0, 0, 0, 0, 0, 0, 112, 0], 'euler11': [1, 28, 2858, 37268, 1771561], 'euler13': [1, 0, 1802, 0, 4826809], 'euler17': [1, 0, 9824, 0, 24137569], 'euler19': [1, 0, 13716, 0, 47045881], 'euler2': [1, -4, 4, 0, 0], 'euler23': [1, 280, 43934, 3406760, 148035889], 'euler29': [1, 572, 130574, 13950508, 594823321], 'euler3': [1, 0, 4, 0, 729], 'euler31': [1, 0, 50870, 0, 887503681], 'euler37': [1, -76, 102750, -3849628, 2565726409], 'euler41': [1, 0, 122000, 0, 4750104241], 'euler43': [1, -68, 160170, -5406476, 6321363049], 'euler47': [1, 0, -66154, 0, 10779215329], 'euler5': [1, 0, 0, 0, 0], 'euler53': [1, -148, 303230, -22033796, 22164361129], 'euler59': [1, 0, 222260, 0, 42180533641], 'euler61': [1, 0, 453762, 0, 51520374361], 'euler67': [1, 1368, 1069382, 411443784, 90458382169], 'euler7': [1, 0, 0, 0, 0], 'euler71': [1, -1176, 1061566, -420903336, 128100283921], 'euler73': [1, 0, 705072, 0, 151334226289], 'euler79': [1, -2440, 2474478, -1203015160, 243087455521], 'euler83': [1, 0, 964772, 0, 326940373369], 'euler89': [1, 0, 1028000, 0, 496981290961], 'euler97': [1, 0, -375456, 0, 832972004929], 'euler_factors': [[1, -4, 4, 0, 0], [1, 0, 4, 0, 729], [1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, 28, 2858, 37268, 1771561], [1, 0, 1802, 0, 4826809], [1, 0, 9824, 0, 24137569], [1, 0, 13716, 0, 47045881], [1, 280, 43934, 3406760, 148035889], [1, 572, 130574, 13950508, 594823321], [1, 0, 50870, 0, 887503681], [1, -76, 102750, -3849628, 2565726409], [1, 0, 122000, 0, 4750104241], [1, -68, 160170, -5406476, 6321363049], [1, 0, -66154, 0, 10779215329], [1, -148, 303230, -22033796, 22164361129], [1, 0, 222260, 0, 42180533641], [1, 0, 453762, 0, 51520374361], [1, 1368, 1069382, 411443784, 90458382169], [1, -1176, 1061566, -420903336, 128100283921], [1, 0, 705072, 0, 151334226289], [1, -2440, 2474478, -1203015160, 243087455521], [1, 0, 964772, 0, 326940373369], [1, 0, 1028000, 0, 496981290961], [1, 0, -375456, 0, 832972004929]], 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2450/4/a/bx'], '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': '4-2450e2-1.1-c3e2-0-5', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3, 3], 'order_of_vanishing': 2, 'prelabel': '4-2450e2-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 12.023089433006168, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3e2-0', 'trace_hash': 1609963721587411932, 'z1': {'__RealLiteral__': 0, 'data': '1.14037220585578311664133561774', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1445593511236673447306199683700,2340558283830275079927099465981', 'Lhash_array': ['1445593511236673447306199683700', '2340558283830275079927099465981'], 'label': '4-2450e2-1.1-c3e2-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2450/4/a/bx'}