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lfunc_lfunctions • Show schema
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{'Lhash': '862242241594555039902316971123,4877048843679233746516225040815', 'a10': 0, 'a2': 0, 'a3': -8, 'a4': -16, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 37, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.7910544435304887, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [1, 8, 27]], [11, [1, 0, 1331]]], 'bad_primes': [3, 11], 'central_character': '33.1', 'coefficient_field': '1.1.1.1', 'conductor': 1089, 'conductor_radical': 33, 'degree': 4, 'euler_factors': [[1, 0, 16, 0, 64], [1, 8, 27], [1, 0, -74, 0, 15625], [1, 0, -686, 0, 117649], [1, 0, 1331], [1, 0, -4394, 0, 4826809], [1, 0, 9826, 0, 24137569], [1, 0, -13718, 0, 47045881], [1, 0, 12670, 0, 148035889], [1, 0, 48778, 0, 594823321], [1, 680, 175182, 20257880, 887503681], [1, -868, 289662, -43966804, 2565726409], [1, 0, 137842, 0, 4750104241], [1, 0, -159014, 0, 6321363049], [1, 0, 206350, 0, 10779215329], [1, 0, -246890, 0, 22164361129], [1, 0, -107642, 0, 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{'algebraic': True, 'analytic_conductor': 3.7910544435304887, 'bad_primes': [3, 11], 'central_character': '1.1', 'conductor': 1089, 'conductor_radical': 33, 'degree': 4, 'dirichlet_coefficients': [1, 0, -8, -16, 0, 0, 0, 0, 37, 0, 0, 128, 0, 0, 0, 192, 0, 0, 0, 0, 0, 0, 0, 0, 74, 0, -80, 0, 0, 0, -680, 0, 0, 0, 0, -592, 868, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1536, 686, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2048, 0, 0, 832, 0, 0, 0, 0, 0, 0, 0, -592, 0, 0, 0, 0, 0, -359, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5440, 0, 0, 0, -68, 0, 0, -1184], 'euler11': [1, 0, 1331, 0, 0], 'euler13': [1, 0, -4394, 0, 4826809], 'euler17': [1, 0, 9826, 0, 24137569], 'euler19': [1, 0, -13718, 0, 47045881], 'euler2': [1, 0, 16, 0, 64], 'euler23': [1, 0, 12670, 0, 148035889], 'euler29': [1, 0, 48778, 0, 594823321], 'euler3': [1, 8, 27, 0, 0], 'euler31': [1, 680, 175182, 20257880, 887503681], 'euler37': [1, -868, 289662, -43966804, 2565726409], 'euler41': [1, 0, 137842, 0, 4750104241], 'euler43': [1, 0, -159014, 0, 6321363049], 'euler47': [1, 0, 206350, 0, 10779215329], 'euler5': [1, 0, -74, 0, 15625], 'euler53': [1, 0, -246890, 0, 22164361129], 'euler59': [1, 0, -107642, 0, 42180533641], 'euler61': [1, 0, -453962, 0, 51520374361], 'euler67': [1, -832, 774582, -250234816, 90458382169], 'euler7': [1, 0, -686, 0, 117649], 'euler71': [1, 0, 341278, 0, 128100283921], 'euler73': [1, 0, -778034, 0, 151334226289], 'euler79': [1, 0, -986078, 0, 243087455521], 'euler83': [1, 0, 1143574, 0, 326940373369], 'euler89': [1, 0, -1392338, 0, 496981290961], 'euler97': [1, 68, 1826502, 62061764, 832972004929], 'euler_factors': [[1, 0, 16, 0, 64], [1, 8, 27, 0, 0], [1, 0, -74, 0, 15625], [1, 0, -686, 0, 117649], [1, 0, 1331, 0, 0], [1, 0, -4394, 0, 4826809], [1, 0, 9826, 0, 24137569], [1, 0, -13718, 0, 47045881], [1, 0, 12670, 0, 148035889], [1, 0, 48778, 0, 594823321], [1, 680, 175182, 20257880, 887503681], [1, -868, 289662, -43966804, 2565726409], [1, 0, 137842, 0, 4750104241], [1, 0, -159014, 0, 6321363049], [1, 0, 206350, 0, 10779215329], [1, 0, -246890, 0, 22164361129], [1, 0, -107642, 0, 42180533641], [1, 0, -453962, 0, 51520374361], [1, -832, 774582, -250234816, 90458382169], [1, 0, 341278, 0, 128100283921], [1, 0, -778034, 0, 151334226289], [1, 0, -986078, 0, 243087455521], [1, 0, 1143574, 0, 326940373369], [1, 0, -1392338, 0, 496981290961], [1, 68, 1826502, 62061764, 832972004929]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/33/4/d/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': '4-33e2-1.1-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': '4-33e2-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.395372004230213, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3e2-0', 'trace_hash': 1784193026071476463, 'z1': {'__RealLiteral__': 0, 'data': '0.68018919522407504636672132604', 'prec': 103}}
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{'Lhash': '862242241594555039902316971123,4877048843679233746516225040815', 'Lhash_array': ['862242241594555039902316971123', '4877048843679233746516225040815'], 'label': '4-33e2-1.1-c3e2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/33/4/d/a'}