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lfunc_lfunctions • Show schema
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{'Lhash': '1934200848035273040029967325524', 'a10': 2, 'a2': 1, 'a3': -1, 'a4': 1, 'a5': 2, 'a6': -1, 'a7': -3, 'a8': 1, 'a9': -2, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 36.715214849384736, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [11, [1]], [19, [1, 1]]], 'bad_primes': [2, 11, 19], 'central_character': '4598.1', 'coefficient_field': '1.1.1.1', 'conductor': 4598, 'conductor_radical': 418, 'degree': 2, 'euler_factors': [[1, -1], [1, 1, 3], [1, -2, 5], [1, 3, 7], [1], [1, -2, 13], [1, -2, 17], [1, 1], [1, 1, 23], [1, 5, 29], [1, 8, 31], [1, -3, 37], [1, -6, 41], [1, 2, 43], [1, 3, 47], [1, -1, 53], [1, 3, 59], [1, -6, 61], [1, 12, 67], [1, 14, 71], [1, 6, 73], [1, -4, 79], [1, -2, 83], [1, 4, 89], [1, 4, 97], [1, 18, 101], [1, 12, 103], [1, 7, 107], [1, -1, 109], [1, -6, 113]], 'euler_factors_factorization': [[[[1, -1], 1]], [[[1, 1, 3], 1]], [[[1, -2, 5], 1]], [[[1, 3, 7], 1]], [1], [[[1, -2, 13], 1]], [[[1, -2, 17], 1]], [[[1, 1], 1]], [[[1, 1, 23], 1]], [[[1, 5, 29], 1]], [[[1, 8, 31], 1]], [[[1, -3, 37], 1]], [[[1, -6, 41], 1]], [[[1, 2, 43], 1]], [[[1, 3, 47], 1]], [[[1, -1, 53], 1]], [[[1, 3, 59], 1]], [[[1, -6, 61], 1]], [[[1, 12, 67], 1]], [[[1, 14, 71], 1]], [[[1, 6, 73], 1]], [[[1, -4, 79], 1]], [[[1, -2, 83], 1]], [[[1, 4, 89], 1]], [[[1, 4, 97], 1]], [[[1, 18, 101], 1]], [[[1, 12, 103], 1]], [[[1, 7, 107], 1]], [[[1, -1, 109], 1]], [[[1, -6, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 133, 'label': '2-4598-1.1-c1-0-133', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/4598/2/a/l', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [-1.615310020366691e-60, 0.2236522506362219, 0.44658646221263265, 0.6680397546760429, 0.8871622463411398, 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2.2271045610540035, 2.386977486423729, 2.4572156362553534, 2.4346119782283746, 2.3206746950204162, 2.1215124126681446, 1.847479741321794, 1.5126024034045624, 1.133812889635277], 'positive_zeros': ['1.52581543186035418373331338990846', '2.59902861333584776243201559533447', '3.35469611081304078184838017363849', '4.16020356360102787822054571441384', '5.30812815840586472937784833665623', '5.84051037869200021796884427587301', '6.15364013153051301443253467181001', '6.93584518468912270900995746602761', '7.78151218288077478977168753185005'], 'prelabel': '2-4598-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.059308116392889, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 334441150733301365, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.52581543186035418373331338991', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.59902861333584776243201559533', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.35469611081304078184838017364', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 36.715214849384736, 'bad_primes': [2, 11, 19], 'central_character': '1.1', 'conductor': 4598, 'conductor_radical': 418, 'degree': 2, 'dirichlet_coefficients': [1, 1, -1, 1, 2, -1, -3, 1, -2, 2, 0, -1, 2, -3, -2, 1, 2, -2, -1, 2, 3, 0, -1, -1, -1, 2, 5, -3, -5, -2, -8, 1, 0, 2, -6, -2, 3, -1, -2, 2, 6, 3, -2, 0, -4, -1, -3, -1, 2, -1, -2, 2, 1, 5, 0, -3, 1, -5, -3, -2, 6, -8, 6, 1, 4, 0, -12, 2, 1, -6, -14, -2, -6, 3, 1, -1, 0, -2, 4, 2, 1, 6, 2, 3, 4, -2, 5, 0, -4, -4, -6, -1, 8, -3, -2, -1, -4, 2, 0, -1], 'euler11': [1, 0, 0], 'euler13': [1, -2, 13], 'euler17': [1, -2, 17], 'euler19': [1, 1, 0], 'euler2': [1, -1, 0], 'euler23': [1, 1, 23], 'euler29': [1, 5, 29], 'euler3': [1, 1, 3], 'euler31': [1, 8, 31], 'euler37': [1, -3, 37], 'euler41': [1, -6, 41], 'euler43': [1, 2, 43], 'euler47': [1, 3, 47], 'euler5': [1, -2, 5], 'euler53': [1, -1, 53], 'euler59': [1, 3, 59], 'euler61': [1, -6, 61], 'euler67': [1, 12, 67], 'euler7': [1, 3, 7], 'euler71': [1, 14, 71], 'euler73': [1, 6, 73], 'euler79': [1, -4, 79], 'euler83': [1, -2, 83], 'euler89': [1, 4, 89], 'euler97': [1, 4, 97], 'euler_factors': [[1, -1, 0], [1, 1, 3], [1, -2, 5], [1, 3, 7], [1, 0, 0], [1, -2, 13], [1, -2, 17], [1, 1, 0], [1, 1, 23], [1, 5, 29], [1, 8, 31], [1, -3, 37], [1, -6, 41], [1, 2, 43], [1, 3, 47], [1, -1, 53], [1, 3, 59], [1, -6, 61], [1, 12, 67], [1, 14, 71], [1, 6, 73], [1, -4, 79], [1, -2, 83], [1, 4, 89], [1, 4, 97]], 'index': 133, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/4598/l', 'ModularForm/GL2/Q/holomorphic/4598/2/a/l/1/1', 'ModularForm/GL2/Q/holomorphic/4598/2/a/l'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-4598-1.1-c1-0-133', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-4598-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.059308116392889, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 334441150733301365, 'z1': {'__RealLiteral__': 0, 'data': '1.52581543186035418373331338991', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20335610
{'Lhash': '1934200848035273040029967325524', 'Lhash_array': ['1934200848035273040029967325524'], 'label': '2-4598-1.1-c1-0-133', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4598/2/a/l'}
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id: 24566638
{'Lhash': '1934200848035273040029967325524', 'Lhash_array': ['1934200848035273040029967325524'], 'label': '2-4598-1.1-c1-0-133', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4598/2/a/l/1/1'}
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id: 91224
{'Lhash': '334441150733301365', 'Lhash_array': ['334441150733301365'], 'label': '2-4598-1.1-c1-0-133', 'type': 'ECQ', 'url': 'EllipticCurve/Q/4598/l'}