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lfunc_lfunctions • Show schema
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{'Lhash': '576493055633070696032812534412,1890902847341349922940523876174', 'a10': 0, 'a2': 0, 'a3': -6, 'a4': 16, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 27, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 894.84550381549, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [1, 6, 9]], [13, [1]]], 'bad_primes': [3, 13], 'central_character': '507.1', 'coefficient_field': '1.1.1.1', 'conductor': 257049, 'conductor_radical': 39, 'degree': 4, 'euler_factors': [[1, 0, -16, 0, 64], [1, 6, 9], [1, 0, -223, 0, 15625], [1, 0, -578, 0, 117649], [1, 0, 38, 0, 1771561], [1], [1, 234, 23515, 1149642, 24137569], [1, 0, -13130, 0, 47045881], [1, -36, 24658, -438012, 148035889], [1, 198, 58579, 4829022, 594823321], [1, 0, -21950, 0, 887503681], [1, 0, -88631, 0, 2565726409], [1, 0, -136519, 0, 4750104241], [1, 164, 165738, 13039148, 6321363049], [1, 0, -202354, 0, 10779215329], [1, 522, 365875, 77713794, 22164361129], [1, 0, 213050, 0, 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{'algebraic': True, 'analytic_conductor': 894.84550381549, 'bad_primes': [3, 13], 'central_character': '1.1', 'conductor': 257049, 'conductor_radical': 39, 'degree': 4, 'dirichlet_coefficients': [1, 0, -6, 16, 0, 0, 0, 0, 27, 0, 0, -96, 0, 0, 0, 192, -234, 0, 0, 0, 0, 0, 36, 0, 223, 0, -108, 0, -198, 0, 0, 0, 0, 0, 0, 432, 0, 0, 0, 0, 0, 0, -164, 0, 0, 0, 0, -1152, 578, 0, 1404, 0, -522, 0, 0, 0, 0, 0, 0, 0, -1438, 0, 0, 2048, 0, 0, 0, -3744, -216, 0, 0, 0, 0, 0, -1338, 0, 0, 0, -880, 0, 405, 0, 0, 0, 0, 0, 1188, 0, 0, 0, 0, 576, 0, 0, 0, 0, 0, 0, 0, 3568], 'euler11': [1, 0, 38, 0, 1771561], 'euler13': [1, 0, 0, 0, 0], 'euler17': [1, 234, 23515, 1149642, 24137569], 'euler19': [1, 0, -13130, 0, 47045881], 'euler2': [1, 0, -16, 0, 64], 'euler23': [1, -36, 24658, -438012, 148035889], 'euler29': [1, 198, 58579, 4829022, 594823321], 'euler3': [1, 6, 9, 0, 0], 'euler31': [1, 0, -21950, 0, 887503681], 'euler37': [1, 0, -88631, 0, 2565726409], 'euler41': [1, 0, -136519, 0, 4750104241], 'euler43': [1, 164, 165738, 13039148, 6321363049], 'euler47': [1, 0, -202354, 0, 10779215329], 'euler5': [1, 0, -223, 0, 15625], 'euler53': [1, 522, 365875, 77713794, 22164361129], 'euler59': [1, 0, 213050, 0, 42180533641], 'euler61': [1, 1438, 970923, 326398678, 51520374361], 'euler67': [1, 0, -107018, 0, 90458382169], 'euler7': [1, 0, -578, 0, 117649], 'euler71': [1, 0, -497122, 0, 128100283921], 'euler73': [1, 0, -309959, 0, 151334226289], 'euler79': [1, 880, 1179678, 433874320, 243087455521], 'euler83': [1, 0, 284726, 0, 326940373369], 'euler89': [1, 0, 892190, 0, 496981290961], 'euler97': [1, 0, -486674, 0, 832972004929], 'euler_factors': [[1, 0, -16, 0, 64], [1, 6, 9, 0, 0], [1, 0, -223, 0, 15625], [1, 0, -578, 0, 117649], [1, 0, 38, 0, 1771561], [1, 0, 0, 0, 0], [1, 234, 23515, 1149642, 24137569], [1, 0, -13130, 0, 47045881], [1, -36, 24658, -438012, 148035889], [1, 198, 58579, 4829022, 594823321], [1, 0, -21950, 0, 887503681], [1, 0, -88631, 0, 2565726409], [1, 0, -136519, 0, 4750104241], [1, 164, 165738, 13039148, 6321363049], [1, 0, -202354, 0, 10779215329], [1, 522, 365875, 77713794, 22164361129], [1, 0, 213050, 0, 42180533641], [1, 1438, 970923, 326398678, 51520374361], [1, 0, -107018, 0, 90458382169], [1, 0, -497122, 0, 128100283921], [1, 0, -309959, 0, 151334226289], [1, 880, 1179678, 433874320, 243087455521], [1, 0, 284726, 0, 326940373369], [1, 0, 892190, 0, 496981290961], [1, 0, -486674, 0, 832972004929]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/507/4/b/a'], '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': '4-507e2-1.1-c3e2-0-0', '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': 0, 'prelabel': '4-507e2-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.469366359361064, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3e2-0', 'trace_hash': 2204613261696199118, 'z1': {'__RealLiteral__': 0, 'data': '0.45477283372033126823421343651', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '576493055633070696032812534412,1890902847341349922940523876174', 'Lhash_array': ['576493055633070696032812534412', '1890902847341349922940523876174'], 'label': '4-507e2-1.1-c3e2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/507/4/b/a'}