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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': -3, 'A5': 0, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': -3, 'Lhash': '91216303966333709,467045135390574132', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [-1.5, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [-1.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.7358896048808887, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1, 0, 3]], [5, [1, 0, -1]], [11, [1, 0, -1]]], 'bad_primes': [3, 5, 11], 'central_character': '27225.1', 'coefficient_field': '1.1.1.1', 'conductor': 27225, 'conductor_radical': 165, 'degree': 4, 'euler_factors': [[1, 0, 3, 0, 4], [1, 0, 3], [1, 0, -1], [1, 0, 14, 0, 49], [1, 0, -1], [1, -4, 30, -52, 169], [1, 0, -2, 0, 289], [1, 8, 54, 152, 361], [1, 0, 30, 0, 529], [1, 0, 22, 0, 841], [1, 16, 126, 496, 961], [1, 4, 78, 148, 1369], [1, 0, 78, 0, 1681], [1, -8, 102, -344, 1849], [1, 0, -50, 0, 2209], [1, 0, 102, 0, 2809], [1, 0, 102, 0, 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-9.236253940355752, -8.984118655595244, -8.077423307295785], 'positive_zeros': ['1.86919846930486895513918273600269', '3.25423179226253980082861279896285', '3.79000489498233733500749844862208', '4.52659700416500112028212971426474', '5.09766059609940450216711100862429', '5.89992194836808220350577312386668', '6.16821463973303244938343944630412', '7.06776652987294055072227501878037', '7.963920428420679646091651044326135', '8.248642768475844318802620430882067', '8.877176431244694382657420951838394', '9.301659499748329006626376523885700', '9.365267708430525132762162914792497', '10.63828874077951155959665793654031'], 'prelabel': '4-165e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.1478378079463696, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 558261439356907841, 'z1': {'__RealLiteral__': 0, 'data': '1.86919846930486895513918273600269', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '3.25423179226253980082861279896285', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '3.79000489498233733500749844862208', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.7358896048808887, 'bad_primes': [3, 5, 11], 'central_character': '1.1', 'conductor': 27225, 'conductor_radical': 165, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, -3, 0, 0, 0, 0, -3, 0, 0, 0, 4, 0, 0, 5, 0, 0, -8, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 9, -4, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, -14, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, -20, 0, 0, -3, 0, 0, -32, 0, 0, 0, 0, 0, 28, 0, 0, 24, 0, 0, 16, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 20, 0, 0, -3], 'euler11': [1, 0, -1, 0, 0], 'euler13': [1, -4, 30, -52, 169], 'euler17': [1, 0, -2, 0, 289], 'euler19': [1, 8, 54, 152, 361], 'euler2': [1, 0, 3, 0, 4], 'euler23': [1, 0, 30, 0, 529], 'euler29': [1, 0, 22, 0, 841], 'euler3': [1, 0, 3, 0, 0], 'euler31': [1, 16, 126, 496, 961], 'euler37': [1, 4, 78, 148, 1369], 'euler41': [1, 0, 78, 0, 1681], 'euler43': [1, -8, 102, -344, 1849], 'euler47': [1, 0, -50, 0, 2209], 'euler5': [1, 0, -1, 0, 0], 'euler53': [1, 0, 102, 0, 2809], 'euler59': [1, 0, 102, 0, 3481], 'euler61': [1, 20, 222, 1220, 3721], 'euler67': [1, 32, 390, 2144, 4489], 'euler7': [1, 0, 14, 0, 49], 'euler71': [1, 0, 78, 0, 5041], 'euler73': [1, -28, 342, -2044, 5329], 'euler79': [1, -16, 222, -1264, 6241], 'euler83': [1, 0, 150, 0, 6889], 'euler89': [1, 0, 78, 0, 7921], 'euler97': [1, -20, 294, -1940, 9409], 'euler_factors': [[1, 0, 3, 0, 4], [1, 0, 3, 0, 0], [1, 0, -1, 0, 0], [1, 0, 14, 0, 49], [1, 0, -1, 0, 0], [1, -4, 30, -52, 169], [1, 0, -2, 0, 289], [1, 8, 54, 152, 361], [1, 0, 30, 0, 529], [1, 0, 22, 0, 841], [1, 16, 126, 496, 961], [1, 4, 78, 148, 1369], [1, 0, 78, 0, 1681], [1, -8, 102, -344, 1849], [1, 0, -50, 0, 2209], [1, 0, 102, 0, 2809], [1, 0, 102, 0, 3481], [1, 20, 222, 1220, 3721], [1, 32, 390, 2144, 4489], [1, 0, 78, 0, 5041], [1, -28, 342, -2044, 5329], [1, -16, 222, -1264, 6241], [1, 0, 150, 0, 6889], [1, 0, 78, 0, 7921], [1, -20, 294, -1940, 9409]], 'index': 11, 'instance_types': ['BMF', 'ECNF'], 'instance_urls': ['ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/3025.1/a', 'EllipticCurve/2.0.3.1/3025.1/a'], 'is_instance_Artin': False, 'is_instance_BMF': True, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': True, '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': '4-165e2-1.1-c1e2-0-11', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 1, 'prelabel': '4-165e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.1478378079463696, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 558261439356907841, 'z1': {'__RealLiteral__': 0, 'data': '1.86919846930486895513918273600269', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9752668
{'Lhash': '91216303966333709,467045135390574132', 'Lhash_array': ['91216303966333709', '467045135390574132'], 'factors': ['2-495-1.1-c1-0-12', '2-55-1.1-c1-0-1'], 'label': '4-165e2-1.1-c1e2-0-11', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.3.1/3025.1/a'}
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id: 9751734
{'Lhash': '91216303966333709,467045135390574132', 'Lhash_array': ['91216303966333709', '467045135390574132'], 'factors': ['2-495-1.1-c1-0-12', '2-55-1.1-c1-0-1'], 'label': '4-165e2-1.1-c1e2-0-11', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/3025.1/a'}