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lfunc_lfunctions • Show schema
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{'Lhash': '5519091402655710849614402582338,8137874377805647654232490244804', 'a10': 0, 'a2': -2, 'a3': 0, 'a4': -4, 'a5': 0, 'a6': 0, 'a7': -16, 'a8': 24, 'a9': 26, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.22279842459683313, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 2, 8]]], 'bad_primes': [2], 'central_character': '8.1', 'coefficient_field': '1.1.1.1', 'conductor': 64, 'conductor_radical': 2, 'degree': 4, 'euler_factors': [[1, 2, 8], [1, 0, -26, 0, 729], [1, 0, -138, 0, 15625], [1, 16, 750, 5488, 117649], [1, 0, -2410, 0, 1771561], [1, 0, -1594, 0, 4826809], [1, 28, 10022, 137564, 24137569], [1, 0, -12346, 0, 47045881], [1, 304, 47438, 3698768, 148035889], [1, 0, -23578, 0, 594823321], [1, -448, 109758, -13346368, 887503681], [1, 0, -42058, 0, 2565726409], [1, 140, 142742, 9648940, 4750104241], [1, 0, 33878, 0, 6321363049], [1, -672, 320542, -69769056, 10779215329], [1, 0, -296746, 0, 22164361129], [1, 0, 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{'algebraic': True, 'analytic_conductor': 0.22279842459683313, 'bad_primes': [2], 'central_character': '1.1', 'conductor': 64, 'conductor_radical': 2, 'degree': 4, 'dirichlet_coefficients': [1, -2, 0, -4, 0, 0, -16, 24, 26, 0, 0, 0, 0, 32, 0, -16, -28, -52, 0, 0, 0, 0, -304, 0, 138, 0, 0, 64, 0, 0, 448, -160, 0, 56, 0, -104, 0, 0, 0, 0, -140, 0, 0, 0, 0, 608, 672, 0, -494, -276, 0, 0, 0, 0, 0, -384, 0, 0, 0, 0, 0, -896, -416, 448, 0, 0, 0, 112, 0, 0, -144, 624, -588, 0, 0, 0, 0, 0, -928, 0, -53, 280, 0, 0, 0, 0, 0, 0, 532, 0, 0, 1216, 0, -1344, 0, 0, 1988, 988, 0, -552], 'euler11': [1, 0, -2410, 0, 1771561], 'euler13': [1, 0, -1594, 0, 4826809], 'euler17': [1, 28, 10022, 137564, 24137569], 'euler19': [1, 0, -12346, 0, 47045881], 'euler2': [1, 2, 8, 0, 0], 'euler23': [1, 304, 47438, 3698768, 148035889], 'euler29': [1, 0, -23578, 0, 594823321], 'euler3': [1, 0, -26, 0, 729], 'euler31': [1, -448, 109758, -13346368, 887503681], 'euler37': [1, 0, -42058, 0, 2565726409], 'euler41': [1, 140, 142742, 9648940, 4750104241], 'euler43': [1, 0, 33878, 0, 6321363049], 'euler47': [1, -672, 320542, -69769056, 10779215329], 'euler5': [1, 0, -138, 0, 15625], 'euler53': [1, 0, -296746, 0, 22164361129], 'euler59': [1, 0, -125130, 0, 42180533641], 'euler61': [1, 0, -444890, 0, 51520374361], 'euler67': [1, 0, -571034, 0, 90458382169], 'euler7': [1, 16, 750, 5488, 117649], 'euler71': [1, 144, 721006, 51539184, 128100283921], 'euler73': [1, 588, 864470, 228741996, 151334226289], 'euler79': [1, 928, 1201374, 457540192, 243087455521], 'euler83': [1, 0, -846522, 0, 326940373369], 'euler89': [1, -532, 1480694, -375043508, 496981290961], 'euler97': [1, -1988, 2813382, -1814393924, 832972004929], 'euler_factors': [[1, 2, 8, 0, 0], [1, 0, -26, 0, 729], [1, 0, -138, 0, 15625], [1, 16, 750, 5488, 117649], [1, 0, -2410, 0, 1771561], [1, 0, -1594, 0, 4826809], [1, 28, 10022, 137564, 24137569], [1, 0, -12346, 0, 47045881], [1, 304, 47438, 3698768, 148035889], [1, 0, -23578, 0, 594823321], [1, -448, 109758, -13346368, 887503681], [1, 0, -42058, 0, 2565726409], [1, 140, 142742, 9648940, 4750104241], [1, 0, 33878, 0, 6321363049], [1, -672, 320542, -69769056, 10779215329], [1, 0, -296746, 0, 22164361129], [1, 0, -125130, 0, 42180533641], [1, 0, -444890, 0, 51520374361], [1, 0, -571034, 0, 90458382169], [1, 144, 721006, 51539184, 128100283921], [1, 588, 864470, 228741996, 151334226289], [1, 928, 1201374, 457540192, 243087455521], [1, 0, -846522, 0, 326940373369], [1, -532, 1480694, -375043508, 496981290961], [1, -1988, 2813382, -1814393924, 832972004929]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8/4/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': '4-2e6-1.1-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': '4-2e6-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.6870336818860667, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3e2-0', 'trace_hash': 1437430701473977649, 'z1': {'__RealLiteral__': 0, 'data': '4.35379543989648781937842455545', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '5519091402655710849614402582338,8137874377805647654232490244804', 'Lhash_array': ['5519091402655710849614402582338', '8137874377805647654232490244804'], 'label': '4-2e6-1.1-c3e2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8/4/b/a'}