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lfunc_lfunctions • Show schema
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{'Lhash': '1413672514954298671372217772681', 'a10': 0, 'a2': 0, 'a3': -1, 'a4': -1, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.33088010337568063, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [1, 1]], [13, [1, -1]], [17, [1, 1]]], 'bad_primes': [3, 13, 17], 'central_character': '663.662', 'coefficient_field': '1.1.1.1', 'conductor': 663, 'conductor_radical': 663, 'degree': 2, 'euler_factors': [[1, 0, 1], [1, 1], [1, 0, -1], [1, 0, 1], [1, 0, -1], [1, -1], [1, 1], [1, 0, -1], [1, -2, 1], [1, -2, 1], [1, 0, 1], [1, 0, 1], [1, 0, -1], [1, 2, 1], [1, 0, 1], [1, 0, -1], [1, 0, 1], [1, 0, -1], [1, 0, -1], [1, 0, -1], [1, 0, 1], [1, 0, -1], [1, 0, 1], [1, 0, 1], [1, 0, 1], [1, 0, -1], [1, -2, 1], [1, 2, 1], [1, 0, 1], [1, -2, 1]], 'euler_factors_factorization': [[[[1, 0, 1], 1]], [[[1, 1], 1]], [[[1, -1], 1], [[1, 1], 1]], [[[1, 0, 1], 1]], [[[1, -1], 1], [[1, 1], 1]], [[[1, -1], 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-2.613004063026634, -2.372254523516054, -1.9838162373128025, -1.474059355511881, -0.8761624507295969, -0.22804451017212482, 0.42999633266573717, 1.0577867587079635, 1.6177642045852867, 2.0772844541619313, 2.410601554060407, 2.6003917378476222, 2.6387227609063726, 2.5274065638384955], 'positive_zeros': ['1.11519097983291239832997370224514', '3.28988102135128638814816860891293', '4.60021500321488830639239683246279', '5.04125243326520469064759691898440', '6.28380074178497794556108203765746', '6.95696202508489808699934997289025', '8.363591650842082987448856734974955', '8.952391434061781417043692343644262', '9.992514726477694523288268333026138', '10.76442110915722872977724570456755'], 'prelabel': '2-663-663.662-c0-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.5752217862491655, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c0-0', 'trace_hash': 301953723367175189, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.11519097983291239832997370225', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.28988102135128638814816860891', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.60021500321488830639239683246', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.33088010337568063, 'bad_primes': [3, 13, 17], 'central_character': '663.662', 'conductor': 663, 'conductor_radical': 663, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, -1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, -1, 0, 0, 0, 0, 0, 2, 0, 1, 0, -1, 0, 2, 0, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, -2, 0, 0, 0, 0, -1, -1, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -1], 'euler11': [1, 0, -1], 'euler13': [1, -1, 0], 'euler17': [1, 1, 0], 'euler19': [1, 0, -1], 'euler2': [1, 0, 1], 'euler23': [1, -2, 1], 'euler29': [1, -2, 1], 'euler3': [1, 1, 0], 'euler31': [1, 0, 1], 'euler37': [1, 0, 1], 'euler41': [1, 0, -1], 'euler43': [1, 2, 1], 'euler47': [1, 0, 1], 'euler5': [1, 0, -1], 'euler53': [1, 0, -1], 'euler59': [1, 0, 1], 'euler61': [1, 0, -1], 'euler67': [1, 0, -1], 'euler7': [1, 0, 1], 'euler71': [1, 0, -1], 'euler73': [1, 0, 1], 'euler79': [1, 0, -1], 'euler83': [1, 0, 1], 'euler89': [1, 0, 1], 'euler97': [1, 0, 1], 'euler_factors': [[1, 0, 1], [1, 1, 0], [1, 0, -1], [1, 0, 1], [1, 0, -1], [1, -1, 0], [1, 1, 0], [1, 0, -1], [1, -2, 1], [1, -2, 1], [1, 0, 1], [1, 0, 1], [1, 0, -1], [1, 2, 1], [1, 0, 1], [1, 0, -1], [1, 0, 1], [1, 0, -1], [1, 0, -1], [1, 0, -1], [1, 0, 1], [1, 0, -1], [1, 0, 1], [1, 0, 1], [1, 0, 1]], 'index': 1, 'instance_types': ['CMF', 'CMF', 'Artin', 'Artin'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/663/1/g/a/662/1', 'ModularForm/GL2/Q/holomorphic/663/1/g/a', 'ArtinRepresentation/2.663.4t3.a.a', 'ArtinRepresentation/2.663.4t3.a'], 'is_instance_Artin': True, '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': '2-663-663.662-c0-0-1', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-663-663.662-c0-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.5752217862491655, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c0-0', 'trace_hash': 301953723367175189, 'z1': {'__RealLiteral__': 0, 'data': '1.11519097983291239832997370225', 'prec': 103}}
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lfunc_instances • Show schema
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id: 24603490
{'Lhash': '1413672514954298671372217772681', 'Lhash_array': ['1413672514954298671372217772681'], 'label': '2-663-663.662-c0-0-1', 'type': 'Artin', 'url': 'ArtinRepresentation/2.663.4t3.a'}
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id: 24597097
{'Lhash': '1413672514954298671372217772681', 'Lhash_array': ['1413672514954298671372217772681'], 'label': '2-663-663.662-c0-0-1', 'type': 'Artin', 'url': 'ArtinRepresentation/2.663.4t3.a.a'}
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id: 19808154
{'Lhash': '1413672514954298671372217772681', 'Lhash_array': ['1413672514954298671372217772681'], 'label': '2-663-663.662-c0-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/663/1/g/a'}
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id: 24546034
{'Lhash': '1413672514954298671372217772681', 'Lhash_array': ['1413672514954298671372217772681'], 'label': '2-663-663.662-c0-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/663/1/g/a/662/1'}